LMFDB - Embedded newform 1400.2.q.j.401.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1400,2,Mod(401,1400)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1400, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 0, 2]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("1400.401");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1400 = 2^{3} \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1400.q (of order $3$, degree $2$, 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:	$11.1790562830$
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:	$\Z[a_1, \ldots, a_{9}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 280)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			401.3
Root			$-0.391571i$ of defining polynomial
Character	$\chi$	$=$	1400.401
Dual form			1400.2.q.j.1201.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.29211 + 2.23800i) q^{3} +(0.292113 + 2.62958i) q^{7} +(-1.83911 + 3.18543i) q^{9} +O(q^{10})$	$q+(1.29211 + 2.23800i) q^{3} +(0.292113 + 2.62958i) q^{7} +(-1.83911 + 3.18543i) q^{9} +(-0.839111 - 1.45338i) q^{11} +4.84667 q^{13} +(1.00000 + 1.73205i) q^{17} +(-3.42334 + 5.92939i) q^{19} +(-5.50756 + 4.05146i) q^{21} +(-1.13122 + 1.95934i) q^{23} -1.75268 q^{27} +3.32178 q^{29} +(-4.58423 - 7.94011i) q^{31} +(2.16845 - 3.75587i) q^{33} +(-1.42334 + 2.46529i) q^{37} +(6.26245 + 10.8469i) q^{39} +9.52489 q^{41} -6.58423 q^{43} +(-6.10156 + 10.5682i) q^{47} +(-6.82934 + 1.53627i) q^{49} +(-2.58423 + 4.47601i) q^{51} +(3.74511 + 6.48673i) q^{53} -17.6933 q^{57} +(-4.00000 - 6.92820i) q^{59} +(3.24511 - 5.62070i) q^{61} +(-8.91357 - 3.90558i) q^{63} +(-2.87634 - 4.98196i) q^{67} -5.84667 q^{69} +(-5.84667 - 10.1267i) q^{73} +(3.57666 - 2.63106i) q^{77} +(-2.84667 + 4.93058i) q^{79} +(3.25268 + 5.63380i) q^{81} +12.5842 q^{83} +(4.29211 + 7.43416i) q^{87} +(2.92334 - 5.06337i) q^{89} +(1.41577 + 12.7447i) q^{91} +(11.8467 - 20.5190i) q^{93} +2.00000 q^{97} +6.17287 q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 6 q^{7} - 9 q^{9}+O(q^{10}) $ 6 * q - 6 * q^7 - 9 * q^9	$ 6 q - 6 q^{7} - 9 q^{9} - 3 q^{11} - 6 q^{13} + 6 q^{17} - 3 q^{19} + 3 q^{23} + 36 q^{27} + 24 q^{29} - 12 q^{31} - 18 q^{33} + 9 q^{37} + 18 q^{39} + 18 q^{41} - 24 q^{43} - 15 q^{47} - 12 q^{49} + 9 q^{53} - 36 q^{57} - 24 q^{59} + 6 q^{61} - 9 q^{63} + 6 q^{67} + 39 q^{77} + 18 q^{79} - 27 q^{81} + 60 q^{83} + 18 q^{87} + 24 q^{91} + 36 q^{93} + 12 q^{97} + 126 q^{99}+O(q^{100}) $ 6 * q - 6 * q^7 - 9 * q^9 - 3 * q^11 - 6 * q^13 + 6 * q^17 - 3 * q^19 + 3 * q^23 + 36 * q^27 + 24 * q^29 - 12 * q^31 - 18 * q^33 + 9 * q^37 + 18 * q^39 + 18 * q^41 - 24 * q^43 - 15 * q^47 - 12 * q^49 + 9 * q^53 - 36 * q^57 - 24 * q^59 + 6 * q^61 - 9 * q^63 + 6 * q^67 + 39 * q^77 + 18 * q^79 - 27 * q^81 + 60 * q^83 + 18 * q^87 + 24 * q^91 + 36 * q^93 + 12 * q^97 + 126 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1400\mathbb{Z}\right)^\times$.

$n$	$351$	$701$	$801$	$1177$
$\chi(n)$	$1$	$1$	$e\left(\frac{1}{3}\right)$	$1$

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			0
$5$		0			0
$6$		0			0
$7$	0.292113	+	2.62958i	0.110408	+	0.993886i
$7$	0.292113	+	2.62958i	0.110408	+	0.993886i
$8$		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
$15$		0			0
$16$		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	$0.454192\pi$
$19$	−3.42334	+	5.92939i	−0.785367	+	1.36030i	−0.928779	+	0.370633i	$0.879141\pi$
$20$		0			0
$21$	−5.50756	+	4.05146i	−1.20185	+	0.884101i
$22$		0			0
$23$	−1.13122	+	1.95934i	−0.235876	+	0.408550i	−0.959527	−	0.281617i	$-0.909129\pi$
$23$	−1.13122	+	1.95934i	−0.235876	+	0.408550i	0.723651	+	0.690166i	$0.242463\pi$
$24$		0			0
$25$		0			0
$26$		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	$-0.858768\pi$
$31$	−4.58423	−	7.94011i	−0.823351	−	1.42609i	0.0798217	−	0.996809i	$-0.474565\pi$
$32$		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	$-0.908513\pi$
$37$	−1.42334	+	2.46529i	−0.233995	+	0.405291i	0.724985	+	0.688765i	$0.241847\pi$
$38$		0			0
$39$	6.26245	+	10.8469i	1.00279	+	1.73689i
$40$		0			0
$41$	9.52489			1.48754			0.743769	−	0.668437i	$-0.233036\pi$
$41$	9.52489			1.48754			0.743769	+	0.668437i	$0.233036\pi$
$42$		0			0
$43$	−6.58423			−1.00408			−0.502042	−	0.864843i	$-0.667418\pi$
$43$	−6.58423			−1.00408			−0.502042	+	0.864843i	$0.667418\pi$
$44$		0			0
$45$		0			0
$46$		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
$49$	−6.82934	+	1.53627i	−0.975620	+	0.219466i
$50$		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	$0.00533020\pi$
$53$	3.74511	+	6.48673i	0.514431	+	0.891021i	−0.485429	+	0.874276i	$0.661336\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$	−17.6933			−2.34354
$58$		0			0
$59$	−4.00000	−	6.92820i	−0.520756	−	0.901975i	−0.999709	−	0.0241347i	$-0.992317\pi$
$59$	−4.00000	−	6.92820i	−0.520756	−	0.901975i	0.478953	−	0.877841i	$-0.341016\pi$
$60$		0			0
$61$	3.24511	−	5.62070i	0.415494	−	0.719657i	−0.579986	−	0.814627i	$-0.696942\pi$
$61$	3.24511	−	5.62070i	0.415494	−	0.719657i	0.995480	+	0.0949692i	$0.0302753\pi$
$62$		0			0
$63$	−8.91357	−	3.90558i	−1.12300	−	0.492056i
$64$		0			0
$65$		0			0
$66$		0			0
$67$	−2.87634	−	4.98196i	−0.351401	−	0.608644i	0.635094	−	0.772434i	$-0.280961\pi$
$67$	−2.87634	−	4.98196i	−0.351401	−	0.608644i	−0.986495	+	0.163791i	$0.947628\pi$
$68$		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
$75$		0			0
$76$		0			0
$77$	3.57666	−	2.63106i	0.407599	−	0.299837i
$78$		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
$85$		0			0
$86$		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	$-0.733047\pi$
$89$	2.92334	−	5.06337i	0.309873	−	0.536716i	0.978334	+	0.207031i	$0.0663801\pi$
$90$		0			0
$91$	1.41577	+	12.7447i	0.148414	+	1.33601i
$92$		0			0
$93$	11.8467	−	20.5190i	1.22844	−	2.12773i
$94$		0			0
$95$		0			0
$96$		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	$0.154648\pi$
$101$	8.50756	+	14.7355i	0.846534	+	1.46624i	−0.0377483	+	0.999287i	$0.512019\pi$
$102$		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	−0.905271	−	0.424834i	$-0.860333\pi$
$107$	−0.876338	+	1.51786i	−0.0847188	+	0.146737i	0.820553	+	0.571571i	$0.193666\pi$
$108$		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	$-0.661620\pi$
$113$	−10.3369			−0.972414			−0.486207	+	0.873844i	$0.661620\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$	−8.91357	+	15.4387i	−0.824059	+	1.42731i
$118$		0			0
$119$	−4.26245	+	3.13553i	−0.390738	+	0.287434i
$120$		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
$125$		0			0
$126$		0			0
$127$	19.1836			1.70227			0.851133	−	0.524949i	$-0.175916\pi$
$127$	19.1836			1.70227			0.851133	+	0.524949i	$0.175916\pi$
$128$		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	$-0.549171\pi$
$131$	8.91357	−	15.4387i	0.778782	−	1.34889i	0.932644	−	0.360797i	$-0.117495\pi$
$132$		0			0
$133$	−16.5918	−	7.26987i	−1.43869	−	0.630378i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	2.00000	+	3.46410i	0.170872	+	0.295958i	0.938725	−	0.344668i	$-0.112008\pi$
$137$	2.00000	+	3.46410i	0.170872	+	0.295958i	−0.767853	+	0.640626i	$0.778675\pi$
$138$		0			0
$139$	−5.16845			−0.438382			−0.219191	−	0.975682i	$-0.570342\pi$
$139$	−5.16845			−0.438382			−0.219191	+	0.975682i	$0.570342\pi$
$140$		0			0
$141$	−31.5356			−2.65578
$142$		0			0
$143$	−4.06689	−	7.04407i	−0.340091	−	0.589054i
$144$		0			0
$145$		0			0
$146$		0			0
$147$	−12.2624	−	13.2991i	−1.01139	−	1.09689i
$148$		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
$155$		0			0
$156$		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
$161$	−5.48267	−	2.40229i	−0.432095	−	0.189327i
$162$		0			0
$163$	1.84667	−	3.19853i	0.144643	−	0.250528i	−0.784597	−	0.620006i	$-0.787130\pi$
$163$	1.84667	−	3.19853i	0.144643	−	0.250528i	0.929240	+	0.369478i	$0.120463\pi$
$164$		0			0
$165$		0			0
$166$		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	$-0.572002\pi$
$181$	−6.03466			−0.448553			−0.224276	+	0.974526i	$0.572002\pi$
$182$		0			0
$183$	16.7722			1.23984
$184$		0			0
$185$		0			0
$186$		0			0
$187$	1.67822	−	2.90676i	0.122724	−	0.212564i
$188$		0			0
$189$	−0.511979	−	4.60880i	−0.0372410	−	0.335241i
$190$		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	0.999297	−	0.0374948i	$-0.0119378\pi$
$193$	6.49023	+	11.2414i	0.467177	+	0.809174i	−0.532120	+	0.846669i	$0.678604\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	4.84667			0.345311			0.172656	−	0.984982i	$-0.444765\pi$
$197$	4.84667			0.345311			0.172656	+	0.984982i	$0.444765\pi$
$198$		0			0
$199$	7.69334	+	13.3253i	0.545367	+	0.944603i	0.998584	+	0.0532026i	$0.0169429\pi$
$199$	7.69334	+	13.3253i	0.545367	+	0.944603i	−0.453217	+	0.891400i	$0.649724\pi$
$200$		0			0
$201$	7.43311	−	12.8745i	0.524291	−	0.908098i
$202$		0			0
$203$	0.970334	+	8.73487i	0.0681041	+	0.613068i
$204$		0			0
$205$		0			0
$206$		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
$215$		0			0
$216$		0			0
$217$	19.5400	−	14.3740i	1.32646	−	0.975769i
$218$		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
$225$		0			0
$226$		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	−0.928361	−	0.371680i	$-0.878782\pi$
$229$	−2.15333	+	3.72967i	−0.142296	+	0.246464i	0.786065	+	0.618144i	$0.212115\pi$
$230$		0			0
$231$	10.5098	+	4.60497i	0.691492	+	0.302985i
$232$		0			0
$233$	9.00000	−	15.5885i	0.589610	−	1.02123i	−0.404674	−	0.914461i	$-0.632615\pi$
$233$	9.00000	−	15.5885i	0.589610	−	1.02123i	0.994283	−	0.106773i	$-0.0340517\pi$
$234$		0			0
$235$		0			0
$236$		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	$-0.168749\pi$
$241$	−0.101557	−	0.175902i	−0.00654187	−	0.0113309i	−0.869278	+	0.494324i	$0.835416\pi$
$242$		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	$-0.449208\pi$
$251$	5.03466			0.317785			0.158893	+	0.987296i	$0.449208\pi$
$252$		0			0
$253$	3.79689			0.238708
$254$		0			0
$255$		0			0
$256$		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
$259$	−6.89844	−	3.02263i	−0.428648	−	0.187817i
$260$		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	$0.148335\pi$
$263$	13.5546	+	23.4772i	0.835810	+	1.44767i	−0.0575594	+	0.998342i	$0.518332\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$	15.1091			0.924663
$268$		0			0
$269$	−3.24511	−	5.62070i	−0.197858	−	0.342700i	0.749976	−	0.661466i	$-0.230065\pi$
$269$	−3.24511	−	5.62070i	−0.197858	−	0.342700i	−0.947834	+	0.318765i	$0.896732\pi$
$270$		0			0
$271$	11.6933	−	20.2535i	0.710320	−	1.23031i	−0.254417	−	0.967095i	$-0.581884\pi$
$271$	11.6933	−	20.2535i	0.710320	−	1.23031i	0.964737	−	0.263216i	$-0.0847831\pi$
$272$		0			0
$273$	−26.6933	+	19.6361i	−1.61555	+	1.18843i
$274$		0			0
$275$		0			0
$276$		0			0
$277$	1.83155	+	3.17234i	0.110047	+	0.190607i	0.915789	−	0.401660i	$-0.131566\pi$
$277$	1.83155	+	3.17234i	0.110047	+	0.190607i	−0.805742	+	0.592267i	$0.798233\pi$
$278$		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
$285$		0			0
$286$		0			0
$287$	2.78234	+	25.0464i	0.164236	+	1.47844i
$288$		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
$295$		0			0
$296$		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
$301$	−1.92334	−	17.3137i	−0.110859	−	0.997946i
$302$		0			0
$303$	−21.9855	+	38.0799i	−1.26303	+	2.18763i
$304$		0			0
$305$		0			0
$306$		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	$-0.115336\pi$
$311$	2.83155	+	4.90439i	0.160562	+	0.278102i	−0.774508	+	0.632564i	$0.782003\pi$
$312$		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	$-0.653656\pi$
$317$	9.52489	−	16.4976i	0.534971	−	0.926597i	0.999165	−	0.0408636i	$-0.0130109\pi$
$318$		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
$325$		0			0
$326$		0			0
$327$	25.2479	−	43.7307i	1.39621	−	2.41831i
$328$		0			0
$329$	−29.5722	−	12.9574i	−1.63037	−	0.714365i
$330$		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
$335$		0			0
$336$		0			0
$337$	16.4062			0.893704			0.446852	−	0.894608i	$-0.352545\pi$
$337$	16.4062			0.893704			0.446852	+	0.894608i	$0.352545\pi$
$338$		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
$343$	−6.03466	−	17.5095i	−0.325841	−	0.945425i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	2.29211	+	3.97006i	0.123047	+	0.213124i	0.920968	−	0.389639i	$-0.127400\pi$
$347$	2.29211	+	3.97006i	0.123047	+	0.213124i	−0.797921	+	0.602762i	$0.794067\pi$
$348$		0			0
$349$	12.3716			0.662235			0.331117	−	0.943590i	$-0.392574\pi$
$349$	12.3716			0.662235			0.331117	+	0.943590i	$0.392574\pi$
$350$		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
$357$	−12.5249	−	5.48792i	−0.662888	−	0.290451i
$358$		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
$365$		0			0
$366$		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
$371$	−15.9634	+	11.7429i	−0.828776	+	0.609662i
$372$		0			0
$373$	−8.20311	+	14.2082i	−0.424741	+	0.735673i	−0.996396	−	0.0848208i	$-0.972968\pi$
$373$	−8.20311	+	14.2082i	−0.424741	+	0.735673i	0.571655	+	0.820494i	$0.306302\pi$
$374$		0			0
$375$		0			0
$376$		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
$395$		0			0
$396$		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
$399$	−5.16845	−	46.5260i	−0.258746	−	2.32921i
$400$		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
$405$		0			0
$406$		0			0
$407$	4.77735			0.236804
$408$		0			0
$409$	−14.0325	−	24.3049i	−0.693860	−	1.20180i	−0.970563	−	0.240846i	$-0.922575\pi$
$409$	−14.0325	−	24.3049i	−0.693860	−	1.20180i	0.276703	−	0.960955i	$-0.410758\pi$
$410$		0			0
$411$	−5.16845	+	8.95202i	−0.254941	+	0.441571i
$412$		0			0
$413$	17.0498	−	12.5421i	0.838965	−	0.617157i
$414$		0			0
$415$		0			0
$416$		0			0
$417$	−6.67822	−	11.5670i	−0.327034	−	0.566439i
$418$		0			0
$419$	−18.8769			−0.922198			−0.461099	−	0.887349i	$-0.652545\pi$
$419$	−18.8769			−0.922198			−0.461099	+	0.887349i	$0.652545\pi$
$420$		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
$425$		0			0
$426$		0			0
$427$	15.7280	+	6.89140i	0.761132	+	0.333498i
$428$		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
$435$		0			0
$436$		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	$-0.787068\pi$
$439$	3.03466	−	5.25619i	0.144837	−	0.250864i	0.929312	+	0.369296i	$0.120401\pi$
$440$		0			0
$441$	7.66624	−	24.5798i	0.365059	−	1.17047i
$442$		0			0
$443$	5.80188	−	10.0492i	0.275656	−	0.477450i	−0.694645	−	0.719353i	$-0.744438\pi$
$443$	5.80188	−	10.0492i	0.275656	−	0.477450i	0.970300	+	0.241903i	$0.0777717\pi$
$444$		0			0
$445$		0			0
$446$		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	$-0.928893\pi$
$457$	−6.32178	+	10.9496i	−0.295720	+	0.512203i	0.679432	+	0.733739i	$0.262226\pi$
$458$		0			0
$459$	−1.75268	−	3.03572i	−0.0818079	−	0.141695i
$460$		0			0
$461$	20.7129			0.964695			0.482348	−	0.875980i	$-0.339784\pi$
$461$	20.7129			0.964695			0.482348	+	0.875980i	$0.339784\pi$
$462$		0			0
$463$	16.3811			0.761295			0.380647	−	0.924720i	$-0.375701\pi$
$463$	16.3811			0.761295			0.380647	+	0.924720i	$0.375701\pi$
$464$		0			0
$465$		0			0
$466$		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
$469$	12.2602	−	9.01884i	0.566125	−	0.416452i
$470$		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
$475$		0			0
$476$		0			0
$477$	−27.5507			−1.26146
$478$		0			0
$479$	0.890881	+	1.54305i	0.0407054	+	0.0705038i	0.885660	−	0.464334i	$-0.153706\pi$
$479$	0.890881	+	1.54305i	0.0407054	+	0.0705038i	−0.844955	+	0.534838i	$0.820373\pi$
$480$		0			0
$481$	−6.89844	+	11.9485i	−0.314542	+	0.544803i
$482$		0			0
$483$	−1.70789	−	15.3743i	−0.0777116	−	0.699553i
$484$		0			0
$485$		0			0
$486$		0			0
$487$	−5.50977	−	9.54320i	−0.249672	−	0.432444i	0.713763	−	0.700387i	$-0.246989\pi$
$487$	−5.50977	−	9.54320i	−0.249672	−	0.432444i	−0.963435	+	0.267943i	$0.913656\pi$
$488$		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
$495$		0			0
$496$		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
$505$		0			0
$506$		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	$-0.931223\pi$
$509$	−6.82934	+	11.8288i	−0.302705	+	0.524301i	0.674043	+	0.738693i	$0.264556\pi$
$510$		0			0
$511$	24.9211	−	18.3324i	1.10245	−	0.810978i
$512$		0			0
$513$	6.00000	−	10.3923i	0.264906	−	0.458831i
$514$		0			0
$515$		0			0
$516$		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	$0.208118\pi$
$521$	21.0820	+	36.5151i	0.923620	+	1.59976i	0.129854	+	0.991533i	$0.458549\pi$
$522$		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			0
$536$		0			0
$537$	−15.5249	+	26.8899i	−0.669949	+	1.16038i
$538$		0			0
$539$	7.96335	+	8.63654i	0.343006	+	0.372002i
$540$		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
$545$		0			0
$546$		0			0
$547$	3.03979			0.129972			0.0649861	−	0.997886i	$-0.479300\pi$
$547$	3.03979			0.129972			0.0649861	+	0.997886i	$0.479300\pi$
$548$		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
$553$	−13.7969	−	6.04526i	−0.586703	−	0.257070i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	9.08202	+	15.7305i	0.384817	+	0.666523i	0.991744	−	0.128235i	$-0.0409311\pi$
$557$	9.08202	+	15.7305i	0.384817	+	0.666523i	−0.606926	+	0.794758i	$0.707598\pi$
$558$		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
$565$		0			0
$566$		0			0
$567$	−13.8644	+	10.1989i	−0.582248	+	0.428312i
$568$		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
$575$		0			0
$576$		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
$581$	3.67601	+	33.0912i	0.152507	+	1.37285i
$582$		0			0
$583$	6.28513	−	10.8862i	0.260304	−	0.450859i
$584$		0			0
$585$		0			0
$586$		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	$-0.573940\pi$
$601$	−11.2871			−0.460411			−0.230206	+	0.973142i	$0.573940\pi$
$602$		0			0
$603$	21.1596			0.861686
$604$		0			0
$605$		0			0
$606$		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
$609$	−18.2949	+	13.4580i	−0.741347	+	0.545348i
$610$		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	$-0.314387\pi$
$613$	−11.0820	−	19.1946i	−0.447598	−	0.775263i	−0.998229	+	0.0594857i	$0.981054\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	14.9805			0.603091			0.301545	−	0.953452i	$-0.402498\pi$
$617$	14.9805			0.603091			0.301545	+	0.953452i	$0.402498\pi$
$618$		0			0
$619$	−11.8196	−	20.4721i	−0.475069	−	0.822843i	0.524524	−	0.851396i	$-0.324243\pi$
$619$	−11.8196	−	20.4721i	−0.475069	−	0.822843i	−0.999592	+	0.0285529i	$0.990910\pi$
$620$		0			0
$621$	1.98267	−	3.43408i	0.0795617	−	0.137805i
$622$		0			0
$623$	14.1685	+	6.20806i	0.567647	+	0.248721i
$624$		0			0
$625$		0			0
$626$		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
$635$		0			0
$636$		0			0
$637$	−33.0996	+	7.44577i	−1.31145	+	0.295012i
$638$		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
$645$		0			0
$646$		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
$651$	57.4169	+	25.1579i	2.25035	+	0.986014i
$652$		0			0
$653$	0.408213	−	0.707046i	0.0159746	−	0.0276688i	−0.857928	−	0.513771i	$-0.828248\pi$
$653$	0.408213	−	0.707046i	0.0159746	−	0.0276688i	0.873902	+	0.486102i	$0.161582\pi$
$654$		0			0
$655$		0			0
$656$		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	$-0.998308\pi$
$661$	−12.9731	−	22.4701i	−0.504596	−	0.873986i	0.495390	−	0.868671i	$-0.335025\pi$
$662$		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	$-0.639851\pi$
$673$	−22.0693			−0.850710			−0.425355	+	0.905027i	$0.639851\pi$
$674$		0			0
$675$		0			0
$676$		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
$679$	0.584225	+	5.25915i	0.0224205	+	0.201828i
$680$		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	$-0.0467554\pi$
$683$	9.61389	+	16.6517i	0.367865	+	0.637161i	−0.621366	+	0.783520i	$0.713422\pi$
$684$		0			0
$685$		0			0
$686$		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	$-0.920504\pi$
$691$	−7.10912	+	12.3134i	−0.270444	+	0.468422i	0.698532	+	0.715579i	$0.253837\pi$
$692$		0			0
$693$	1.80317	+	16.2320i	0.0684969	+	0.616604i
$694$		0			0
$695$		0			0
$696$		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
$705$		0			0
$706$		0			0
$707$	−36.2630	+	26.6757i	−1.36381	+	1.00324i
$708$		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
$715$		0			0
$716$		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	$-0.764509\pi$
$719$	5.75268	−	9.96393i	0.214539	−	0.371592i	0.953130	+	0.302562i	$0.0978419\pi$
$720$		0			0
$721$	17.2278	+	7.54854i	0.641596	+	0.281122i
$722$		0			0
$723$	0.262447	−	0.454571i	0.00976049	−	0.0169057i
$724$		0			0
$725$		0			0
$726$		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	$-0.205633\pi$
$743$	43.5305			1.59698			0.798489	+	0.602009i	$0.205633\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	−23.1438	+	40.0862i	−0.846787	+	1.46668i
$748$		0			0
$749$	−4.24732	−	1.86101i	−0.155194	−	0.0679999i
$750$		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
$755$		0			0
$756$		0			0
$757$	−24.3369			−0.884540			−0.442270	−	0.896882i	$-0.645827\pi$
$757$	−24.3369			−0.884540			−0.442270	+	0.896882i	$0.645827\pi$
$758$		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	$-0.662541\pi$
$761$	14.1016	−	24.4246i	0.511181	−	0.885392i	0.999916	−	0.0129592i	$-0.00412517\pi$
$762$		0			0
$763$	41.6441	−	30.6342i	1.50762	−	1.10903i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−19.3867	−	33.5787i	−0.700013	−	1.21246i
$768$		0			0
$769$	−41.8965			−1.51082			−0.755412	−	0.655250i	$-0.772563\pi$
$769$	−41.8965			−1.51082			−0.755412	+	0.655250i	$0.772563\pi$
$770$		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
$775$		0			0
$776$		0			0
$777$	−2.14891	−	19.3443i	−0.0770917	−	0.693974i
$778$		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
$785$		0			0
$786$		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
$791$	−3.01954	−	27.1817i	−0.107363	−	0.966469i
$792$		0			0
$793$	15.7280	−	27.2417i	0.558518	−	0.967381i
$794$		0			0
$795$		0			0
$796$		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	$-0.498589\pi$
$811$	0.252452			0.00886479			0.00443239	+	0.999990i	$0.498589\pi$
$812$		0			0
$813$	60.4365			2.11960
$814$		0			0
$815$		0			0
$816$		0			0
$817$	22.5400	−	39.0405i	0.788575	−	1.36585i
$818$		0			0
$819$	−43.2011	−	18.9290i	−1.50957	−	0.661434i
$820$		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	0.893327	−	0.449408i	$-0.148365\pi$
$823$	1.64856	+	2.85538i	0.0574650	+	0.0995323i	−0.835862	+	0.548940i	$0.815032\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−9.41577			−0.327419			−0.163709	−	0.986509i	$-0.552346\pi$
$827$	−9.41577			−0.327419			−0.163709	+	0.986509i	$0.552346\pi$
$828$		0			0
$829$	2.35644	+	4.08148i	0.0818426	+	0.141756i	0.904041	−	0.427445i	$-0.140586\pi$
$829$	2.35644	+	4.08148i	0.0818426	+	0.141756i	−0.822199	+	0.569200i	$0.807253\pi$
$830$		0			0
$831$	−4.73314	+	8.19803i	−0.164191	+	0.284387i
$832$		0			0
$833$	−9.49023	−	10.2925i	−0.328817	−	0.356614i
$834$		0			0
$835$		0			0
$836$		0			0
$837$	8.03466	+	13.9164i	0.277719	+	0.481023i
$838$		0			0
$839$	22.1880			0.766015			0.383007	−	0.923745i	$-0.374888\pi$
$839$	22.1880			0.766015			0.383007	+	0.923745i	$0.374888\pi$
$840$		0			0
$841$	−17.9658			−0.619510
$842$		0			0
$843$	17.9558	+	31.1003i	0.618430	+	1.07115i
$844$		0			0
$845$		0			0
$846$		0			0
$847$	19.8315	+	8.68941i	0.681420	+	0.298572i
$848$		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
$855$		0			0
$856$		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	−0.926161	−	0.377128i	$-0.876912\pi$
$859$	−4.00000	+	6.92820i	−0.136478	+	0.236387i	0.789683	+	0.613515i	$0.210245\pi$
$860$		0			0
$861$	−52.4589	+	38.5897i	−1.78780	+	1.31513i
$862$		0			0
$863$	9.11168	−	15.7819i	0.310165	−	0.537222i	−0.668233	−	0.743952i	$-0.732949\pi$
$863$	9.11168	−	15.7819i	0.310165	−	0.537222i	0.978398	+	0.206730i	$0.0662823\pi$
$864$		0			0
$865$		0			0
$866$		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	$0.495578\pi$
$877$	−25.4385	+	44.0607i	−0.858996	+	1.48782i	−0.872888	+	0.487921i	$0.837756\pi$
$878$		0			0
$879$	−24.3520	−	42.1789i	−0.821373	−	1.42266i
$880$		0			0
$881$	−19.1187			−0.644124			−0.322062	−	0.946719i	$-0.604376\pi$
$881$	−19.1187			−0.644124			−0.322062	+	0.946719i	$0.604376\pi$
$882$		0			0
$883$	−39.3174			−1.32313			−0.661567	−	0.749886i	$-0.730108\pi$
$883$	−39.3174			−1.32313			−0.661567	+	0.749886i	$0.730108\pi$
$884$		0			0
$885$		0			0
$886$		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
$889$	5.60377	+	50.4447i	0.187944	+	1.69186i
$890$		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
$895$		0			0
$896$		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
$903$	36.2630	−	26.6757i	1.20676	−	0.887712i
$904$		0			0
$905$		0			0
$906$		0			0
$907$	16.4012	+	28.4078i	0.544594	+	0.943264i	0.998632	+	0.0522823i	$0.0166496\pi$
$907$	16.4012	+	28.4078i	0.544594	+	0.943264i	−0.454038	+	0.890982i	$0.650017\pi$
$908$		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
$915$		0			0
$916$		0			0
$917$	43.2011	+	18.9290i	1.42663	+	0.625092i
$918$		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
$925$		0			0
$926$		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	$-0.606460\pi$
$929$	19.9309	−	34.5213i	0.653912	−	1.13261i	0.982165	−	0.188018i	$-0.0602065\pi$
$930$		0			0
$931$	14.2700	−	45.7530i	0.467681	−	1.49949i
$932$		0			0
$933$	−7.31736	+	12.6740i	−0.239560	+	0.414929i
$934$		0			0
$935$		0			0
$936$		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	$-0.981847\pi$
$941$	−16.8271	−	29.1454i	−0.548549	−	0.950114i	0.449825	−	0.893116i	$-0.351486\pi$
$942$		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	$-0.803079\pi$
$947$	2.92055	−	5.05854i	0.0949050	−	0.164380i	0.909569	+	0.415553i	$0.136412\pi$
$948$		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	$-0.673796\pi$
$953$	−32.0605			−1.03854			−0.519271	+	0.854610i	$0.673796\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$	7.20311	−	12.4762i	0.232844	−	0.403297i
$958$		0			0
$959$	−8.52489	+	6.27106i	−0.275283	+	0.202503i
$960$		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
$965$		0			0
$966$		0			0
$967$	−24.0896			−0.774669			−0.387334	−	0.921939i	$-0.626604\pi$
$967$	−24.0896			−0.774669			−0.387334	+	0.921939i	$0.626604\pi$
$968$		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	$-0.929112\pi$
$971$	−9.23534	+	15.9961i	−0.296376	+	0.513339i	0.678928	+	0.734205i	$0.262445\pi$
$972$		0			0
$973$	−1.50977	−	13.5908i	−0.0484010	−	0.435702i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	12.1685	+	21.0764i	0.389303	+	0.674293i	0.992356	−	0.123408i	$-0.0393825\pi$
$977$	12.1685	+	21.0764i	0.389303	+	0.674293i	−0.603053	+	0.797701i	$0.706049\pi$
$978$		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
$985$		0			0
$986$		0			0
$987$	−9.21195	−	82.9253i	−0.293220	−	2.63954i
$988$		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
$995$		0			0
$996$		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	1400.2.q.j.401.3		6
5.2	odd	4		1400.2.bh.i.849.5		12
5.3	odd	4		1400.2.bh.i.849.2		12
5.4	even	2		280.2.q.e.121.1	yes	6
7.2	even	3		9800.2.a.ce.1.1		3
7.4	even	3	inner	1400.2.q.j.1201.3		6
7.5	odd	6		9800.2.a.cf.1.3		3
15.14	odd	2		2520.2.bi.q.1801.1		6
20.19	odd	2		560.2.q.l.401.3		6
35.4	even	6		280.2.q.e.81.1	✓	6
35.9	even	6		1960.2.a.w.1.3		3
35.18	odd	12		1400.2.bh.i.249.5		12
35.19	odd	6		1960.2.a.v.1.1		3
35.24	odd	6		1960.2.q.w.361.3		6
35.32	odd	12		1400.2.bh.i.249.2		12
35.34	odd	2		1960.2.q.w.961.3		6
105.74	odd	6		2520.2.bi.q.361.1		6
140.19	even	6		3920.2.a.cb.1.3		3
140.39	odd	6		560.2.q.l.81.3		6
140.79	odd	6		3920.2.a.cc.1.1		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
280.2.q.e.81.1	✓	6	35.4	even	6
280.2.q.e.121.1	yes	6	5.4	even	2
560.2.q.l.81.3		6	140.39	odd	6
560.2.q.l.401.3		6	20.19	odd	2
1400.2.q.j.401.3		6	1.1	even	1	trivial
1400.2.q.j.1201.3		6	7.4	even	3	inner
1400.2.bh.i.249.2		12	35.32	odd	12
1400.2.bh.i.249.5		12	35.18	odd	12
1400.2.bh.i.849.2		12	5.3	odd	4
1400.2.bh.i.849.5		12	5.2	odd	4
1960.2.a.v.1.1		3	35.19	odd	6
1960.2.a.w.1.3		3	35.9	even	6
1960.2.q.w.361.3		6	35.24	odd	6
1960.2.q.w.961.3		6	35.34	odd	2
2520.2.bi.q.361.1		6	105.74	odd	6
2520.2.bi.q.1801.1		6	15.14	odd	2
3920.2.a.cb.1.3		3	140.19	even	6
3920.2.a.cc.1.1		3	140.79	odd	6
9800.2.a.ce.1.1		3	7.2	even	3
9800.2.a.cf.1.3		3	7.5	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1400 = 2^{3} \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1400.q (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.29211 + 2.23800i) q^{3} +(0.292113 + 2.62958i) q^{7} +(-1.83911 + 3.18543i) q^{9} +O(q^{10})\)	\(q+(1.29211 + 2.23800i) q^{3} +(0.292113 + 2.62958i) q^{7} +(-1.83911 + 3.18543i) q^{9} +(-0.839111 - 1.45338i) q^{11} +4.84667 q^{13} +(1.00000 + 1.73205i) q^{17} +(-3.42334 + 5.92939i) q^{19} +(-5.50756 + 4.05146i) q^{21} +(-1.13122 + 1.95934i) q^{23} -1.75268 q^{27} +3.32178 q^{29} +(-4.58423 - 7.94011i) q^{31} +(2.16845 - 3.75587i) q^{33} +(-1.42334 + 2.46529i) q^{37} +(6.26245 + 10.8469i) q^{39} +9.52489 q^{41} -6.58423 q^{43} +(-6.10156 + 10.5682i) q^{47} +(-6.82934 + 1.53627i) q^{49} +(-2.58423 + 4.47601i) q^{51} +(3.74511 + 6.48673i) q^{53} -17.6933 q^{57} +(-4.00000 - 6.92820i) q^{59} +(3.24511 - 5.62070i) q^{61} +(-8.91357 - 3.90558i) q^{63} +(-2.87634 - 4.98196i) q^{67} -5.84667 q^{69} +(-5.84667 - 10.1267i) q^{73} +(3.57666 - 2.63106i) q^{77} +(-2.84667 + 4.93058i) q^{79} +(3.25268 + 5.63380i) q^{81} +12.5842 q^{83} +(4.29211 + 7.43416i) q^{87} +(2.92334 - 5.06337i) q^{89} +(1.41577 + 12.7447i) q^{91} +(11.8467 - 20.5190i) q^{93} +2.00000 q^{97} +6.17287 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 6 q^{7} - 9 q^{9}+O(q^{10}) \) 6 * q - 6 * q^7 - 9 * q^9	\( 6 q - 6 q^{7} - 9 q^{9} - 3 q^{11} - 6 q^{13} + 6 q^{17} - 3 q^{19} + 3 q^{23} + 36 q^{27} + 24 q^{29} - 12 q^{31} - 18 q^{33} + 9 q^{37} + 18 q^{39} + 18 q^{41} - 24 q^{43} - 15 q^{47} - 12 q^{49} + 9 q^{53} - 36 q^{57} - 24 q^{59} + 6 q^{61} - 9 q^{63} + 6 q^{67} + 39 q^{77} + 18 q^{79} - 27 q^{81} + 60 q^{83} + 18 q^{87} + 24 q^{91} + 36 q^{93} + 12 q^{97} + 126 q^{99}+O(q^{100}) \) 6 * q - 6 * q^7 - 9 * q^9 - 3 * q^11 - 6 * q^13 + 6 * q^17 - 3 * q^19 + 3 * q^23 + 36 * q^27 + 24 * q^29 - 12 * q^31 - 18 * q^33 + 9 * q^37 + 18 * q^39 + 18 * q^41 - 24 * q^43 - 15 * q^47 - 12 * q^49 + 9 * q^53 - 36 * q^57 - 24 * q^59 + 6 * q^61 - 9 * q^63 + 6 * q^67 + 39 * q^77 + 18 * q^79 - 27 * q^81 + 60 * q^83 + 18 * q^87 + 24 * q^91 + 36 * q^93 + 12 * q^97 + 126 * q^99

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