LMFDB - Embedded newform 1400.2.bh.i.249.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1400,2,Mod(249,1400)]

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, 3, 4]))

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

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

chi := DirichletCharacter("1400.249");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1400 = 2^{3} \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1400.bh (of order $6$, 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:	$11.1790562830$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{6})$
Coefficient field:	12.0.32905425960566784.37
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} + 36x^{10} + 432x^{8} + 2040x^{6} + 3780x^{4} + 2592x^{2} + 576 $ x^12 + 36x^10 + 432x^8 + 2040x^6 + 3780x^4 + 2592*x^2 + 576
Coefficient ring:	$\Z[a_1, \ldots, a_{9}]$
Coefficient ring index:	$ 2^{6} $
Twist minimal:	no (minimal twist has level 280)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			249.5
Root			$-4.06501i$ of defining polynomial
Character	$\chi$	$=$	1400.249
Dual form			1400.2.bh.i.849.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.23800 + 1.29211i) q^{3} +(-2.62958 - 0.292113i) q^{7} +(1.83911 + 3.18543i) q^{9} +O(q^{10})$	$q+(2.23800 + 1.29211i) q^{3} +(-2.62958 - 0.292113i) q^{7} +(1.83911 + 3.18543i) q^{9} +(-0.839111 + 1.45338i) q^{11} +4.84667i q^{13} +(-1.73205 - 1.00000i) q^{17} +(3.42334 + 5.92939i) q^{19} +(-5.50756 - 4.05146i) q^{21} +(1.95934 - 1.13122i) q^{23} +1.75268i q^{27} -3.32178 q^{29} +(-4.58423 + 7.94011i) q^{31} +(-3.75587 + 2.16845i) q^{33} +(-2.46529 + 1.42334i) q^{37} +(-6.26245 + 10.8469i) q^{39} +9.52489 q^{41} -6.58423i q^{43} +(-10.5682 + 6.10156i) q^{47} +(6.82934 + 1.53627i) q^{49} +(-2.58423 - 4.47601i) q^{51} +(6.48673 + 3.74511i) q^{53} +17.6933i q^{57} +(4.00000 - 6.92820i) q^{59} +(3.24511 + 5.62070i) q^{61} +(-3.90558 - 8.91357i) q^{63} +(4.98196 + 2.87634i) q^{67} +5.84667 q^{69} +(-10.1267 - 5.84667i) q^{73} +(2.63106 - 3.57666i) q^{77} +(2.84667 + 4.93058i) q^{79} +(3.25268 - 5.63380i) q^{81} +12.5842i q^{83} +(-7.43416 - 4.29211i) q^{87} +(-2.92334 - 5.06337i) q^{89} +(1.41577 - 12.7447i) q^{91} +(-20.5190 + 11.8467i) q^{93} -2.00000i q^{97} -6.17287 q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 18 q^{9}+O(q^{10}) $ 12 * q + 18 * q^9	$ 12 q + 18 q^{9} - 6 q^{11} + 6 q^{19} - 48 q^{29} - 24 q^{31} - 36 q^{39} + 36 q^{41} + 24 q^{49} + 48 q^{59} + 12 q^{61} - 36 q^{79} - 54 q^{81} + 48 q^{91} - 252 q^{99}+O(q^{100}) $ 12 * q + 18 * q^9 - 6 * q^11 + 6 * q^19 - 48 * q^29 - 24 * q^31 - 36 * q^39 + 36 * q^41 + 24 * q^49 + 48 * q^59 + 12 * q^61 - 36 * q^79 - 54 * q^81 + 48 * q^91 - 252 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$351$	$701$	$801$	$1177$
$\chi(n)$	$1$	$1$	$e\left(\frac{2}{3}\right)$	$-1$

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
$3$	2.23800	+	1.29211i	1.29211	+	0.746002i	0.979028	−	0.203724i	$-0.0653044\pi$
$3$	2.23800	+	1.29211i	1.29211	+	0.746002i	0.313084	+	0.949725i	$0.398638\pi$
$4$		0			0
$5$		0			0
$5$		0			0
$6$		0			0
$7$	−2.62958	−	0.292113i	−0.993886	−	0.110408i
$7$	−2.62958	−	0.292113i	−0.993886	−	0.110408i
$8$		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
$13$			4.84667i			1.34422i	0.740449	+	0.672112i	$0.234613\pi$
$13$			4.84667i			1.34422i	−0.740449	+	0.672112i	$0.765387\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−1.73205	−	1.00000i	−0.420084	−	0.242536i	0.275029	−	0.961436i	$-0.411312\pi$
$17$	−1.73205	−	1.00000i	−0.420084	−	0.242536i	−0.695113	+	0.718900i	$0.744646\pi$
$18$		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
$21$	−5.50756	−	4.05146i	−1.20185	−	0.884101i
$22$		0			0
$23$	1.95934	−	1.13122i	0.408550	−	0.235876i	−0.281617	−	0.959527i	$-0.590871\pi$
$23$	1.95934	−	1.13122i	0.408550	−	0.235876i	0.690166	+	0.723651i	$0.257537\pi$
$24$		0			0
$25$		0			0
$26$		0			0
$27$			1.75268i			0.337303i
$28$		0			0
$29$	−3.32178			−0.616839			−0.308419	−	0.951250i	$-0.599800\pi$
$29$	−3.32178			−0.616839			−0.308419	+	0.951250i	$0.599800\pi$
$30$		0			0
$31$	−4.58423	+	7.94011i	−0.823351	+	1.42609i	0.0798217	+	0.996809i	$0.474565\pi$
$31$	−4.58423	+	7.94011i	−0.823351	+	1.42609i	−0.903173	+	0.429277i	$0.858768\pi$
$32$		0			0
$33$	−3.75587	+	2.16845i	−0.653813	+	0.377479i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	−2.46529	+	1.42334i	−0.405291	+	0.233995i	−0.688765	−	0.724985i	$-0.741847\pi$
$37$	−2.46529	+	1.42334i	−0.405291	+	0.233995i	0.283473	+	0.958980i	$0.408513\pi$
$38$		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
$43$		−	6.58423i		−	1.00408i	−0.864843	−	0.502042i	$-0.832582\pi$
$43$		−	6.58423i		−	1.00408i	0.864843	−	0.502042i	$-0.167418\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−10.5682	+	6.10156i	−1.54153	+	0.890004i	−0.542789	+	0.839869i	$0.682632\pi$
$47$	−10.5682	+	6.10156i	−1.54153	+	0.890004i	−0.998742	+	0.0501344i	$0.984035\pi$
$48$		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
$53$	6.48673	+	3.74511i	0.891021	+	0.514431i	0.874276	−	0.485429i	$-0.161336\pi$
$53$	6.48673	+	3.74511i	0.891021	+	0.514431i	0.0167445	+	0.999860i	$0.494670\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$			17.6933i			2.34354i
$58$		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	0.995480	−	0.0949692i	$-0.0302753\pi$
$61$	3.24511	+	5.62070i	0.415494	+	0.719657i	−0.579986	+	0.814627i	$0.696942\pi$
$62$		0			0
$63$	−3.90558	−	8.91357i	−0.492056	−	1.12300i
$64$		0			0
$65$		0			0
$66$		0			0
$67$	4.98196	+	2.87634i	0.608644	+	0.351401i	0.772434	−	0.635094i	$-0.219039\pi$
$67$	4.98196	+	2.87634i	0.608644	+	0.351401i	−0.163791	+	0.986495i	$0.552372\pi$
$68$		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
$73$	−10.1267	−	5.84667i	−1.18524	−	0.684301i	−0.228022	−	0.973656i	$-0.573226\pi$
$73$	−10.1267	−	5.84667i	−1.18524	−	0.684301i	−0.957222	+	0.289355i	$0.906559\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	2.63106	−	3.57666i	0.299837	−	0.407599i
$78$		0			0
$79$	2.84667	+	4.93058i	0.320276	+	0.554734i	0.980545	−	0.196295i	$-0.0628911\pi$
$79$	2.84667	+	4.93058i	0.320276	+	0.554734i	−0.660269	+	0.751029i	$0.729558\pi$
$80$		0			0
$81$	3.25268	−	5.63380i	0.361408	−	0.625978i
$82$		0			0
$83$			12.5842i			1.38130i	0.723190	+	0.690649i	$0.242675\pi$
$83$			12.5842i			1.38130i	−0.723190	+	0.690649i	$0.757325\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$	−7.43416	−	4.29211i	−0.797025	−	0.460163i
$88$		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
$91$	1.41577	−	12.7447i	0.148414	−	1.33601i
$92$		0			0
$93$	−20.5190	+	11.8467i	−2.12773	+	1.22844i
$94$		0			0
$95$		0			0
$96$		0			0
$97$		−	2.00000i		−	0.203069i	−0.994832	−	0.101535i	$-0.967625\pi$
$97$		−	2.00000i		−	0.203069i	0.994832	−	0.101535i	$-0.0323753\pi$
$98$		0			0
$99$	−6.17287			−0.620397
$100$		0			0
$101$	8.50756	−	14.7355i	0.846534	−	1.46624i	−0.0377483	−	0.999287i	$-0.512019\pi$
$101$	8.50756	−	14.7355i	0.846534	−	1.46624i	0.884282	−	0.466953i	$-0.154648\pi$
$102$		0			0
$103$	−6.15668	+	3.55456i	−0.606635	+	0.350241i	−0.771648	−	0.636050i	$-0.780567\pi$
$103$	−6.15668	+	3.55456i	−0.606635	+	0.350241i	0.165012	+	0.986292i	$0.447234\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−1.51786	+	0.876338i	−0.146737	+	0.0847188i	−0.571571	−	0.820553i	$-0.693666\pi$
$107$	−1.51786	+	0.876338i	−0.146737	+	0.0847188i	0.424834	+	0.905271i	$0.360333\pi$
$108$		0			0
$109$	9.77001	−	16.9222i	0.935797	−	1.62085i	0.162591	−	0.986694i	$-0.448015\pi$
$109$	9.77001	−	16.9222i	0.935797	−	1.62085i	0.773206	−	0.634154i	$-0.218652\pi$
$110$		0			0
$111$	−7.35644			−0.698243
$112$		0			0
$113$		−	10.3369i		−	0.972414i	−0.873844	−	0.486207i	$-0.838380\pi$
$113$		−	10.3369i		−	0.972414i	0.873844	−	0.486207i	$-0.161620\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$	−15.4387	+	8.91357i	−1.42731	+	0.824059i
$118$		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
$123$	21.3168	+	12.3072i	1.92207	+	1.10971i
$124$		0			0
$125$		0			0
$126$		0			0
$127$		−	19.1836i		−	1.70227i	−0.524949	−	0.851133i	$-0.675916\pi$
$127$		−	19.1836i		−	1.70227i	0.524949	−	0.851133i	$-0.324084\pi$
$128$		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	$0.117495\pi$
$131$	8.91357	+	15.4387i	0.778782	+	1.34889i	−0.153862	+	0.988092i	$0.549171\pi$
$132$		0			0
$133$	−7.26987	−	16.5918i	−0.630378	−	1.43869i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−3.46410	−	2.00000i	−0.295958	−	0.170872i	0.344668	−	0.938725i	$-0.387992\pi$
$137$	−3.46410	−	2.00000i	−0.295958	−	0.170872i	−0.640626	+	0.767853i	$0.721325\pi$
$138$		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
$143$	−7.04407	−	4.06689i	−0.589054	−	0.340091i
$144$		0			0
$145$		0			0
$146$		0			0
$147$	13.2991	+	12.2624i	1.09689	+	1.01139i
$148$		0			0
$149$	0.398443	+	0.690123i	0.0326417	+	0.0565371i	0.881885	−	0.471465i	$-0.156275\pi$
$149$	0.398443	+	0.690123i	0.0326417	+	0.0565371i	−0.849243	+	0.528002i	$0.822941\pi$
$150$		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
$153$		−	7.35644i		−	0.594733i
$154$		0			0
$155$		0			0
$156$		0			0
$157$	−7.10411	−	4.10156i	−0.566969	−	0.327340i	0.188969	−	0.981983i	$-0.439486\pi$
$157$	−7.10411	−	4.10156i	−0.566969	−	0.327340i	−0.755938	+	0.654643i	$0.772819\pi$
$158$		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
$163$	−3.19853	+	1.84667i	−0.250528	+	0.144643i	−0.620006	−	0.784597i	$-0.712870\pi$
$163$	−3.19853	+	1.84667i	−0.250528	+	0.144643i	0.369478	+	0.929240i	$0.379537\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$		−	0.262447i		−	0.0203087i	−0.999948	−	0.0101544i	$-0.996768\pi$
$167$		−	0.262447i		−	0.0203087i	0.999948	−	0.0101544i	$-0.00323229\pi$
$168$		0			0
$169$	−10.4902			−0.806941
$170$		0			0
$171$	−12.5918	+	21.8096i	−0.962918	+	1.66782i
$172$		0			0
$173$	16.3217	−	9.42334i	1.24092	−	0.716443i	0.271635	−	0.962400i	$-0.412436\pi$
$173$	16.3217	−	9.42334i	1.24092	−	0.716443i	0.969281	+	0.245957i	$0.0791023\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	17.9040	−	10.3369i	1.34575	−	0.776969i
$178$		0			0
$179$	−6.00756	+	10.4054i	−0.449026	+	0.777736i	−0.998323	−	0.0578912i	$-0.981562\pi$
$179$	−6.00756	+	10.4054i	−0.449026	+	0.777736i	0.549297	+	0.835627i	$0.314896\pi$
$180$		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
$183$			16.7722i			1.23984i
$184$		0			0
$185$		0			0
$186$		0			0
$187$	2.90676	−	1.67822i	0.212564	−	0.122724i
$188$		0			0
$189$	0.511979	−	4.60880i	0.0372410	−	0.335241i
$190$		0			0
$191$	−1.41577	−	2.45219i	−0.102442	−	0.177434i	0.810248	−	0.586087i	$-0.199332\pi$
$191$	−1.41577	−	2.45219i	−0.102442	−	0.177434i	−0.912690	+	0.408652i	$0.865999\pi$
$192$		0			0
$193$	11.2414	+	6.49023i	0.809174	+	0.467177i	0.846669	−	0.532120i	$-0.178604\pi$
$193$	11.2414	+	6.49023i	0.809174	+	0.467177i	−0.0374948	+	0.999297i	$0.511938\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$		−	4.84667i		−	0.345311i	−0.984982	−	0.172656i	$-0.944765\pi$
$197$		−	4.84667i		−	0.345311i	0.984982	−	0.172656i	$-0.0552347\pi$
$198$		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
$203$	8.73487	+	0.970334i	0.613068	+	0.0681041i
$204$		0			0
$205$		0			0
$206$		0			0
$207$	7.20687	+	4.16089i	0.500912	+	0.289202i
$208$		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
$217$	14.3740	−	19.5400i	0.975769	−	1.32646i
$218$		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
$223$			12.9805i			0.869236i	0.900615	+	0.434618i	$0.143117\pi$
$223$			12.9805i			0.869236i	−0.900615	+	0.434618i	$0.856883\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	19.0788	+	11.0151i	1.26630	+	0.731099i	0.974286	−	0.225314i	$-0.0723409\pi$
$227$	19.0788	+	11.0151i	1.26630	+	0.731099i	0.292015	+	0.956414i	$0.405674\pi$
$228$		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
$231$	10.5098	−	4.60497i	0.691492	−	0.302985i
$232$		0			0
$233$	−15.5885	+	9.00000i	−1.02123	+	0.589610i	−0.914461	−	0.404674i	$-0.867385\pi$
$233$	−15.5885	+	9.00000i	−1.02123	+	0.589610i	−0.106773	+	0.994283i	$0.534052\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$			14.7129i			0.955705i
$238$		0			0
$239$	−10.8618			−0.702591			−0.351296	−	0.936265i	$-0.614259\pi$
$239$	−10.8618			−0.702591			−0.351296	+	0.936265i	$0.614259\pi$
$240$		0			0
$241$	−0.101557	+	0.175902i	−0.00654187	+	0.0113309i	−0.869278	−	0.494324i	$-0.835416\pi$
$241$	−0.101557	+	0.175902i	−0.00654187	+	0.0113309i	0.862736	+	0.505655i	$0.168749\pi$
$242$		0			0
$243$	19.1126	−	11.0347i	1.22607	−	0.707874i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	−28.7378	+	16.5918i	−1.82854	+	1.05571i
$248$		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
$253$			3.79689i			0.238708i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	20.2535	−	11.6933i	1.26338	−	0.729411i	0.289650	−	0.957133i	$-0.406461\pi$
$257$	20.2535	−	11.6933i	1.26338	−	0.729411i	0.973726	+	0.227722i	$0.0731277\pi$
$258$		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
$263$	23.4772	+	13.5546i	1.44767	+	0.835810i	0.998342	−	0.0575594i	$-0.0183318\pi$
$263$	23.4772	+	13.5546i	1.44767	+	0.835810i	0.449323	+	0.893369i	$0.351665\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$		−	15.1091i		−	0.924663i
$268$		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	$0.0847831\pi$
$271$	11.6933	+	20.2535i	0.710320	+	1.23031i	−0.254417	+	0.967095i	$0.581884\pi$
$272$		0			0
$273$	19.6361	−	26.6933i	1.18843	−	1.61555i
$274$		0			0
$275$		0			0
$276$		0			0
$277$	−3.17234	−	1.83155i	−0.190607	−	0.110047i	0.401660	−	0.915789i	$-0.368434\pi$
$277$	−3.17234	−	1.83155i	−0.190607	−	0.110047i	−0.592267	+	0.805742i	$0.701767\pi$
$278$		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
$283$	−17.6123	−	10.1685i	−1.04694	−	0.604452i	−0.125150	−	0.992138i	$-0.539941\pi$
$283$	−17.6123	−	10.1685i	−1.04694	−	0.604452i	−0.921791	+	0.387686i	$0.873274\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	−25.0464	−	2.78234i	−1.47844	−	0.164236i
$288$		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
$293$		−	18.8467i		−	1.10103i	−0.834824	−	0.550517i	$-0.814431\pi$
$293$		−	18.8467i		−	1.10103i	0.834824	−	0.550517i	$-0.185569\pi$
$294$		0			0
$295$		0			0
$296$		0			0
$297$	−2.54731	−	1.47069i	−0.147810	−	0.0853380i
$298$		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
$303$	38.0799	−	21.9855i	2.18763	−	1.26303i
$304$		0			0
$305$		0			0
$306$		0			0
$307$		−	2.39623i		−	0.136760i	−0.997659	−	0.0683802i	$-0.978217\pi$
$307$		−	2.39623i		−	0.136760i	0.997659	−	0.0683802i	$-0.0217831\pi$
$308$		0			0
$309$	−18.3716			−1.04512
$310$		0			0
$311$	2.83155	−	4.90439i	0.160562	−	0.278102i	−0.774508	−	0.632564i	$-0.782003\pi$
$311$	2.83155	−	4.90439i	0.160562	−	0.278102i	0.935071	+	0.354462i	$0.115336\pi$
$312$		0			0
$313$	−25.7414	+	14.8618i	−1.45499	+	0.840038i	−0.998758	−	0.0498231i	$-0.984134\pi$
$313$	−25.7414	+	14.8618i	−1.45499	+	0.840038i	−0.456231	+	0.889861i	$0.650801\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	16.4976	−	9.52489i	0.926597	−	0.534971i	0.0408636	−	0.999165i	$-0.486989\pi$
$317$	16.4976	−	9.52489i	0.926597	−	0.534971i	0.885734	+	0.464193i	$0.153656\pi$
$318$		0			0
$319$	2.78734	−	4.82781i	0.156061	−	0.270306i
$320$		0			0
$321$	−4.52931			−0.252801
$322$		0			0
$323$		−	13.6933i		−	0.761918i
$324$		0			0
$325$		0			0
$326$		0			0
$327$	43.7307	−	25.2479i	2.41831	−	1.39621i
$328$		0			0
$329$	29.5722	−	12.9574i	1.63037	−	0.714365i
$330$		0			0
$331$	−1.16089	−	2.01072i	−0.0638083	−	0.110519i	0.832356	−	0.554241i	$-0.186991\pi$
$331$	−1.16089	−	2.01072i	−0.0638083	−	0.110519i	−0.896165	+	0.443722i	$0.853658\pi$
$332$		0			0
$333$	−9.06788	−	5.23534i	−0.496917	−	0.286895i
$334$		0			0
$335$		0			0
$336$		0			0
$337$		−	16.4062i		−	0.893704i	−0.894608	−	0.446852i	$-0.852545\pi$
$337$		−	16.4062i		−	0.893704i	0.894608	−	0.446852i	$-0.147455\pi$
$338$		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
$343$	−17.5095	−	6.03466i	−0.945425	−	0.325841i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−3.97006	−	2.29211i	−0.213124	−	0.123047i	0.389639	−	0.920968i	$-0.372600\pi$
$347$	−3.97006	−	2.29211i	−0.213124	−	0.123047i	−0.602762	+	0.797921i	$0.705933\pi$
$348$		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
$353$	16.7894	+	9.69334i	0.893608	+	0.515925i	0.875121	−	0.483904i	$-0.160782\pi$
$353$	16.7894	+	9.69334i	0.893608	+	0.515925i	0.0184869	+	0.999829i	$0.494115\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$	5.48792	+	12.5249i	0.290451	+	0.662888i
$358$		0			0
$359$	−4.90600	−	8.49745i	−0.258929	−	0.448478i	0.707026	−	0.707187i	$-0.250036\pi$
$359$	−4.90600	−	8.49745i	−0.258929	−	0.448478i	−0.965955	+	0.258709i	$0.916703\pi$
$360$		0			0
$361$	−13.9385	+	24.1421i	−0.733603	+	1.27064i
$362$		0			0
$363$			21.1482i			1.10999i
$364$		0			0
$365$		0			0
$366$		0			0
$367$	11.0141	+	6.35901i	0.574933	+	0.331937i	0.759117	−	0.650954i	$-0.225631\pi$
$367$	11.0141	+	6.35901i	0.574933	+	0.331937i	−0.184184	+	0.982892i	$0.558964\pi$
$368$		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
$373$	14.2082	−	8.20311i	0.735673	−	0.424741i	−0.0848208	−	0.996396i	$-0.527032\pi$
$373$	14.2082	−	8.20311i	0.735673	−	0.424741i	0.820494	+	0.571655i	$0.193698\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$		−	16.0996i		−	0.829170i
$378$		0			0
$379$	−14.4707			−0.743309			−0.371655	−	0.928371i	$-0.621209\pi$
$379$	−14.4707			−0.743309			−0.371655	+	0.928371i	$0.621209\pi$
$380$		0			0
$381$	24.7873	−	42.9329i	1.26989	−	2.19952i
$382$		0			0
$383$	3.07401	−	1.77478i	0.157075	−	0.0906871i	−0.419402	−	0.907800i	$-0.637760\pi$
$383$	3.07401	−	1.77478i	0.157075	−	0.0906871i	0.576477	+	0.817113i	$0.304427\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	20.9736	−	12.1091i	1.06615	−	0.615541i
$388$		0			0
$389$	4.49023	−	7.77731i	0.227664	−	0.394325i	−0.729452	−	0.684032i	$-0.760225\pi$
$389$	4.49023	−	7.77731i	0.227664	−	0.394325i	0.957115	+	0.289707i	$0.0935580\pi$
$390$		0			0
$391$	−4.52489			−0.228834
$392$		0			0
$393$			46.0693i			2.32389i
$394$		0			0
$395$		0			0
$396$		0			0
$397$	−24.3349	+	14.0498i	−1.22134	+	0.705139i	−0.965203	−	0.261503i	$-0.915782\pi$
$397$	−24.3349	+	14.0498i	−1.22134	+	0.705139i	−0.256133	+	0.966642i	$0.582449\pi$
$398$		0			0
$399$	5.16845	−	46.5260i	0.258746	−	2.32921i
$400$		0			0
$401$	13.3467	+	23.1171i	0.666501	+	1.15441i	0.978876	+	0.204455i	$0.0655421\pi$
$401$	13.3467	+	23.1171i	0.666501	+	1.15441i	−0.312375	+	0.949959i	$0.601125\pi$
$402$		0			0
$403$	−38.4831	−	22.2182i	−1.91698	−	1.10677i
$404$		0			0
$405$		0			0
$406$		0			0
$407$		−	4.77735i		−	0.236804i
$408$		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
$413$	−12.5421	+	17.0498i	−0.617157	+	0.838965i
$414$		0			0
$415$		0			0
$416$		0			0
$417$	11.5670	+	6.67822i	0.566439	+	0.327034i
$418$		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
$423$	−38.8722	−	22.4429i	−1.89003	−	1.09121i
$424$		0			0
$425$		0			0
$426$		0			0
$427$	−6.89140	−	15.7280i	−0.333498	−	0.761132i
$428$		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
$433$			2.33690i			0.112304i	0.998422	+	0.0561522i	$0.0178832\pi$
$433$			2.33690i			0.112304i	−0.998422	+	0.0561522i	$0.982117\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	13.4149	+	7.74511i	0.641723	+	0.370499i
$438$		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
$441$	7.66624	+	24.5798i	0.365059	+	1.17047i
$442$		0			0
$443$	−10.0492	+	5.80188i	−0.477450	+	0.275656i	−0.719353	−	0.694645i	$-0.755562\pi$
$443$	−10.0492	+	5.80188i	−0.477450	+	0.275656i	0.241903	+	0.970300i	$0.422228\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$			2.05933i			0.0974031i
$448$		0			0
$449$	−4.13821			−0.195294			−0.0976470	−	0.995221i	$-0.531132\pi$
$449$	−4.13821			−0.195294			−0.0976470	+	0.995221i	$0.531132\pi$
$450$		0			0
$451$	−7.99244	+	13.8433i	−0.376349	+	0.651856i
$452$		0			0
$453$	36.9828	−	21.3520i	1.73760	−	1.00321i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	−10.9496	+	6.32178i	−0.512203	+	0.295720i	−0.733739	−	0.679432i	$-0.762226\pi$
$457$	−10.9496	+	6.32178i	−0.512203	+	0.295720i	0.221536	+	0.975152i	$0.428893\pi$
$458$		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
$463$			16.3811i			0.761295i	0.924720	+	0.380647i	$0.124299\pi$
$463$			16.3811i			0.761295i	−0.924720	+	0.380647i	$0.875701\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−1.49167	+	0.861215i	−0.0690262	+	0.0398523i	−0.534116	−	0.845411i	$-0.679355\pi$
$467$	−1.49167	+	0.861215i	−0.0690262	+	0.0398523i	0.465090	+	0.885264i	$0.346022\pi$
$468$		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
$473$	9.56940	+	5.52489i	0.440001	+	0.254035i
$474$		0			0
$475$		0			0
$476$		0			0
$477$			27.5507i			1.26146i
$478$		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
$483$	−15.3743	−	1.70789i	−0.699553	−	0.0777116i
$484$		0			0
$485$		0			0
$486$		0			0
$487$	9.54320	+	5.50977i	0.432444	+	0.249672i	0.700387	−	0.713763i	$-0.253011\pi$
$487$	9.54320	+	5.50977i	0.432444	+	0.249672i	−0.267943	+	0.963435i	$0.586344\pi$
$488$		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
$493$	5.75349	+	3.32178i	0.259124	+	0.149605i
$494$		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	$-0.220395\pi$
$499$	−3.75268	−	6.49983i	−0.167993	−	0.290972i	−0.937714	+	0.347408i	$0.887062\pi$
$500$		0			0
$501$	0.339111	−	0.587357i	0.0151503	−	0.0262412i
$502$		0			0
$503$		−	20.5842i		−	0.917805i	−0.888487	−	0.458903i	$-0.848243\pi$
$503$		−	20.5842i		−	0.917805i	0.888487	−	0.458903i	$-0.151757\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	−23.4772	−	13.5546i	−1.04266	−	0.601979i
$508$		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
$511$	24.9211	+	18.3324i	1.10245	+	0.810978i
$512$		0			0
$513$	−10.3923	+	6.00000i	−0.458831	+	0.264906i
$514$		0			0
$515$		0			0
$516$		0			0
$517$		−	20.4795i		−	0.900688i
$518$		0			0
$519$	48.7040			2.13787
$520$		0			0
$521$	21.0820	−	36.5151i	0.923620	−	1.59976i	0.129854	−	0.991533i	$-0.458549\pi$
$521$	21.0820	−	36.5151i	0.923620	−	1.59976i	0.793766	−	0.608224i	$-0.208118\pi$
$522$		0			0
$523$	26.5381	−	15.3218i	1.16043	−	0.669975i	0.209023	−	0.977911i	$-0.432972\pi$
$523$	26.5381	−	15.3218i	1.16043	−	0.669975i	0.951407	+	0.307936i	$0.0996383\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	15.8802	−	9.16845i	0.691753	−	0.399384i
$528$		0			0
$529$	−8.94067	+	15.4857i	−0.388725	+	0.673291i
$530$		0			0
$531$	29.4258			1.27697
$532$		0			0
$533$			46.1640i			1.99959i
$534$		0			0
$535$		0			0
$536$		0			0
$537$	−26.8899	+	15.5249i	−1.16038	+	0.669949i
$538$		0			0
$539$	−7.96335	+	8.63654i	−0.343006	+	0.372002i
$540$		0			0
$541$	16.8445	+	29.1755i	0.724200	+	1.25435i	0.959302	+	0.282381i	$0.0911241\pi$
$541$	16.8445	+	29.1755i	0.724200	+	1.25435i	−0.235102	+	0.971971i	$0.575543\pi$
$542$		0			0
$543$	−13.5056	−	7.79747i	−0.579581	−	0.334621i
$544$		0			0
$545$		0			0
$546$		0			0
$547$		−	3.03979i		−	0.129972i	−0.997886	−	0.0649861i	$-0.979300\pi$
$547$		−	3.03979i		−	0.129972i	0.997886	−	0.0649861i	$-0.0207003\pi$
$548$		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
$553$	−6.04526	−	13.7969i	−0.257070	−	0.586703i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−15.7305	−	9.08202i	−0.666523	−	0.384817i	0.128235	−	0.991744i	$-0.459069\pi$
$557$	−15.7305	−	9.08202i	−0.666523	−	0.384817i	−0.794758	+	0.606926i	$0.792402\pi$
$558$		0			0
$559$	31.9116			1.34972
$560$		0			0
$561$	8.67380			0.366208
$562$		0			0
$563$	−32.0347	−	18.4952i	−1.35010	−	0.779481i	−0.361837	−	0.932241i	$-0.617850\pi$
$563$	−32.0347	−	18.4952i	−1.35010	−	0.779481i	−0.988263	+	0.152760i	$0.951184\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$	−10.1989	+	13.8644i	−0.428312	+	0.582248i
$568$		0			0
$569$	16.3047	+	28.2405i	0.683527	+	1.18390i	0.973897	+	0.226990i	$0.0728884\pi$
$569$	16.3047	+	28.2405i	0.683527	+	1.18390i	−0.290370	+	0.956915i	$0.593778\pi$
$570$		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
$573$		−	7.31736i		−	0.305687i
$574$		0			0
$575$		0			0
$576$		0			0
$577$	32.9352	+	19.0151i	1.37111	+	0.791610i	0.991068	−	0.133360i	$-0.0425766\pi$
$577$	32.9352	+	19.0151i	1.37111	+	0.791610i	0.380041	+	0.924970i	$0.375910\pi$
$578$		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
$583$	−10.8862	+	6.28513i	−0.450859	+	0.260304i
$584$		0			0
$585$		0			0
$586$		0			0
$587$			34.0302i			1.40458i	0.711892	+	0.702289i	$0.247839\pi$
$587$			34.0302i			1.40458i	−0.711892	+	0.702289i	$0.752161\pi$
$588$		0			0
$589$	−62.7734			−2.58653
$590$		0			0
$591$	6.26245	−	10.8469i	0.257603	−	0.446181i
$592$		0			0
$593$	29.2055	−	16.8618i	1.19933	−	0.692431i	0.238921	−	0.971039i	$-0.423206\pi$
$593$	29.2055	−	16.8618i	1.19933	−	0.692431i	0.960405	+	0.278608i	$0.0898731\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	−34.4355	+	19.8813i	−1.40935	+	0.813689i
$598$		0			0
$599$	3.15333	−	5.46172i	0.128841	−	0.223160i	−0.794387	−	0.607413i	$-0.792207\pi$
$599$	3.15333	−	5.46172i	0.128841	−	0.223160i	0.923228	+	0.384253i	$0.125541\pi$
$600$		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
$603$			21.1596i			0.861686i
$604$		0			0
$605$		0			0
$606$		0			0
$607$	−13.3897	+	7.73057i	−0.543473	+	0.313774i	−0.746485	−	0.665402i	$-0.768260\pi$
$607$	−13.3897	+	7.73057i	−0.543473	+	0.313774i	0.203012	+	0.979176i	$0.434927\pi$
$608$		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
$613$	−19.1946	−	11.0820i	−0.775263	−	0.447598i	0.0594857	−	0.998229i	$-0.481054\pi$
$613$	−19.1946	−	11.0820i	−0.775263	−	0.447598i	−0.834749	+	0.550631i	$0.814387\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$		−	14.9805i		−	0.603091i	−0.953452	−	0.301545i	$-0.902498\pi$
$617$		−	14.9805i		−	0.603091i	0.953452	−	0.301545i	$-0.0975024\pi$
$618$		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
$623$	6.20806	+	14.1685i	0.248721	+	0.567647i
$624$		0			0
$625$		0			0
$626$		0			0
$627$	−25.7152	−	14.8467i	−1.02697	−	0.592919i
$628$		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
$633$	20.5529	+	11.8662i	0.816904	+	0.471640i
$634$		0			0
$635$		0			0
$636$		0			0
$637$	−7.44577	+	33.0996i	−0.295012	+	1.31145i
$638$		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
$643$		−	7.04979i		−	0.278016i	−0.990291	−	0.139008i	$-0.955609\pi$
$643$		−	7.04979i		−	0.278016i	0.990291	−	0.139008i	$-0.0443914\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	21.2009	+	12.2403i	0.833493	+	0.481217i	0.855047	−	0.518550i	$-0.173528\pi$
$647$	21.2009	+	12.2403i	0.833493	+	0.481217i	−0.0215540	+	0.999768i	$0.506861\pi$
$648$		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
$653$	−0.707046	+	0.408213i	−0.0276688	+	0.0159746i	−0.513771	−	0.857928i	$-0.671752\pi$
$653$	−0.707046	+	0.408213i	−0.0276688	+	0.0159746i	0.486102	+	0.873902i	$0.338418\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$		−	43.0107i		−	1.67801i
$658$		0			0
$659$	−21.2871			−0.829228			−0.414614	−	0.909997i	$-0.636083\pi$
$659$	−21.2871			−0.829228			−0.414614	+	0.909997i	$0.636083\pi$
$660$		0			0
$661$	−12.9731	+	22.4701i	−0.504596	+	0.873986i	0.495390	+	0.868671i	$0.335025\pi$
$661$	−12.9731	+	22.4701i	−0.504596	+	0.873986i	−0.999986	+	0.00531513i	$0.998308\pi$
$662$		0			0
$663$	21.6938	−	12.5249i	0.842515	−	0.486427i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	−6.50848	+	3.75767i	−0.252009	+	0.145498i
$668$		0			0
$669$	−16.7722	+	29.0503i	−0.648451	+	1.12315i
$670$		0			0
$671$	−10.8920			−0.420483
$672$		0			0
$673$		−	22.0693i		−	0.850710i	−0.905027	−	0.425355i	$-0.860149\pi$
$673$		−	22.0693i		−	0.850710i	0.905027	−	0.425355i	$-0.139851\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	4.75468	−	2.74511i	0.182737	−	0.105503i	−0.405841	−	0.913944i	$-0.633021\pi$
$677$	4.75468	−	2.74511i	0.182737	−	0.105503i	0.588578	+	0.808440i	$0.299688\pi$
$678$		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
$683$	16.6517	+	9.61389i	0.637161	+	0.367865i	0.783520	−	0.621366i	$-0.213422\pi$
$683$	16.6517	+	9.61389i	0.637161	+	0.367865i	−0.146359	+	0.989232i	$0.546755\pi$
$684$		0			0
$685$		0			0
$686$		0			0
$687$			11.1294i			0.424612i
$688$		0			0
$689$	−18.1513	+	31.4390i	−0.691511	+	1.19773i
$690$		0			0
$691$	−7.10912	−	12.3134i	−0.270444	−	0.468422i	0.698532	−	0.715579i	$-0.253837\pi$
$691$	−7.10912	−	12.3134i	−0.270444	−	0.468422i	−0.968975	+	0.247157i	$0.920504\pi$
$692$		0			0
$693$	16.2320	+	1.80317i	0.616604	+	0.0684969i
$694$		0			0
$695$		0			0
$696$		0			0
$697$	−16.4976	−	9.52489i	−0.624891	−	0.360781i
$698$		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
$703$	−16.8790	−	9.74511i	−0.636605	−	0.367544i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−26.6757	+	36.2630i	−1.00324	+	1.36381i
$708$		0			0
$709$	8.52268	+	14.7617i	0.320076	+	0.554388i	0.980503	−	0.196502i	$-0.0629582\pi$
$709$	8.52268	+	14.7617i	0.320076	+	0.554388i	−0.660427	+	0.750890i	$0.729625\pi$
$710$		0			0
$711$	−10.4707	+	18.1358i	−0.392682	+	0.680144i
$712$		0			0
$713$			20.7431i			0.776836i
$714$		0			0
$715$		0			0
$716$		0			0
$717$	−24.3088	−	14.0347i	−0.907827	−	0.524134i
$718$		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
$721$	17.2278	−	7.54854i	0.641596	−	0.281122i
$722$		0			0
$723$	−0.454571	+	0.262447i	−0.0169057	+	0.00976049i
$724$		0			0
$725$		0			0
$726$		0			0
$727$			16.4114i			0.608664i	0.952566	+	0.304332i	$0.0984331\pi$
$727$			16.4114i			0.608664i	−0.952566	+	0.304332i	$0.901567\pi$
$728$		0			0
$729$	37.5161			1.38948
$730$		0			0
$731$	−6.58423	+	11.4042i	−0.243526	+	0.421800i
$732$		0			0
$733$	7.89317	−	4.55712i	0.291541	−	0.168321i	−0.347096	−	0.937830i	$-0.612832\pi$
$733$	7.89317	−	4.55712i	0.291541	−	0.168321i	0.638637	+	0.769509i	$0.279499\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−8.36084	+	4.82713i	−0.307975	+	0.177810i
$738$		0			0
$739$	−17.4978	+	30.3071i	−0.643667	+	1.11486i	0.340941	+	0.940085i	$0.389254\pi$
$739$	−17.4978	+	30.3071i	−0.643667	+	1.11486i	−0.984608	+	0.174779i	$0.944079\pi$
$740$		0			0
$741$	−85.7538			−3.15025
$742$		0			0
$743$			43.5305i			1.59698i	0.602009	+	0.798489i	$0.294367\pi$
$743$			43.5305i			1.59698i	−0.602009	+	0.798489i	$0.705633\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	−40.0862	+	23.1438i	−1.46668	+	0.846787i
$748$		0			0
$749$	4.24732	−	1.86101i	0.155194	−	0.0679999i
$750$		0			0
$751$	−3.15333	−	5.46172i	−0.115067	−	0.199301i	0.802740	−	0.596329i	$-0.203375\pi$
$751$	−3.15333	−	5.46172i	−0.115067	−	0.199301i	−0.917806	+	0.397028i	$0.870041\pi$
$752$		0			0
$753$	11.2676	+	6.50535i	0.410614	+	0.237068i
$754$		0			0
$755$		0			0
$756$		0			0
$757$			24.3369i			0.884540i	0.896882	+	0.442270i	$0.145827\pi$
$757$			24.3369i			0.884540i	−0.896882	+	0.442270i	$0.854173\pi$
$758$		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	$0.00412517\pi$
$761$	14.1016	+	24.4246i	0.511181	+	0.885392i	−0.488735	+	0.872432i	$0.662541\pi$
$762$		0			0
$763$	−30.6342	+	41.6441i	−1.10903	+	1.50762i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	33.5787	+	19.3867i	1.21246	+	0.700013i
$768$		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
$773$	34.5175	+	19.9287i	1.24151	+	0.716785i	0.969401	−	0.245482i	$-0.0789462\pi$
$773$	34.5175	+	19.9287i	1.24151	+	0.716785i	0.272107	+	0.962267i	$0.412280\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$	19.3443	+	2.14891i	0.693974	+	0.0770917i
$778$		0			0
$779$	32.6069	+	56.4768i	1.16826	+	2.02349i
$780$		0			0
$781$		0			0
$782$		0			0
$783$		−	5.82200i		−	0.208061i
$784$		0			0
$785$		0			0
$786$		0			0
$787$	−30.5944	−	17.6637i	−1.09057	−	0.629642i	−0.156843	−	0.987623i	$-0.550132\pi$
$787$	−30.5944	−	17.6637i	−1.09057	−	0.629642i	−0.933729	+	0.357981i	$0.883465\pi$
$788$		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
$793$	−27.2417	+	15.7280i	−0.967381	+	0.558518i
$794$		0			0
$795$		0			0
$796$		0			0
$797$			29.6933i			1.05179i	0.850549	+	0.525896i	$0.176270\pi$
$797$			29.6933i			1.05179i	−0.850549	+	0.525896i	$0.823730\pi$
$798$		0			0
$799$	24.4062			0.863430
$800$		0			0
$801$	10.7527	−	18.6242i	0.379927	−	0.658053i
$802$		0			0
$803$	16.9949	−	9.81201i	0.599737	−	0.346258i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	14.5252	−	8.38611i	0.511310	−	0.295205i
$808$		0			0
$809$	−9.82178	+	17.0118i	−0.345315	+	0.598104i	−0.985411	−	0.170191i	$-0.945561\pi$
$809$	−9.82178	+	17.0118i	−0.345315	+	0.598104i	0.640096	+	0.768295i	$0.278895\pi$
$810$		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
$813$			60.4365i			2.11960i
$814$		0			0
$815$		0			0
$816$		0			0
$817$	39.0405	−	22.5400i	1.36585	−	0.788575i
$818$		0			0
$819$	43.2011	−	18.9290i	1.50957	−	0.661434i
$820$		0			0
$821$	−22.3867	−	38.7749i	−0.781301	−	1.35325i	−0.931184	−	0.364549i	$-0.881223\pi$
$821$	−22.3867	−	38.7749i	−0.781301	−	1.35325i	0.149883	−	0.988704i	$-0.452110\pi$
$822$		0			0
$823$	2.85538	+	1.64856i	0.0995323	+	0.0574650i	0.548940	−	0.835862i	$-0.315032\pi$
$823$	2.85538	+	1.64856i	0.0995323	+	0.0574650i	−0.449408	+	0.893327i	$0.648365\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$			9.41577i			0.327419i	0.986509	+	0.163709i	$0.0523459\pi$
$827$			9.41577i			0.327419i	−0.986509	+	0.163709i	$0.947654\pi$
$828$		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
$833$	−10.2925	−	9.49023i	−0.356614	−	0.328817i
$834$		0			0
$835$		0			0
$836$		0			0
$837$	−13.9164	−	8.03466i	−0.481023	−	0.277719i
$838$		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
$843$	31.1003	+	17.9558i	1.07115	+	0.618430i
$844$		0			0
$845$		0			0
$846$		0			0
$847$	−8.68941	−	19.8315i	−0.298572	−	0.681420i
$848$		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
$853$		−	39.9267i		−	1.36706i	−0.729920	−	0.683532i	$-0.760443\pi$
$853$		−	39.9267i		−	1.36706i	0.729920	−	0.683532i	$-0.239557\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	1.40644	+	0.812009i	0.0480431	+	0.0277377i	0.523829	−	0.851823i	$-0.324503\pi$
$857$	1.40644	+	0.812009i	0.0480431	+	0.0277377i	−0.475786	+	0.879561i	$0.657836\pi$
$858$		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
$861$	−52.4589	−	38.5897i	−1.78780	−	1.31513i
$862$		0			0
$863$	−15.7819	+	9.11168i	−0.537222	+	0.310165i	−0.743952	−	0.668233i	$-0.767051\pi$
$863$	−15.7819	+	9.11168i	−0.537222	+	0.310165i	0.206730	+	0.978398i	$0.433718\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$		−	33.5949i		−	1.14094i
$868$		0			0
$869$	−9.55469			−0.324121
$870$		0			0
$871$	−13.9407	+	24.1459i	−0.472362	+	0.818154i
$872$		0			0
$873$	6.37087	−	3.67822i	0.215621	−	0.124489i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	−44.0607	+	25.4385i	−1.48782	+	0.858996i	−0.999903	−	0.0138922i	$-0.995578\pi$
$877$	−44.0607	+	25.4385i	−1.48782	+	0.858996i	−0.487921	+	0.872888i	$0.662244\pi$
$878$		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
$883$		−	39.3174i		−	1.32313i	−0.749886	−	0.661567i	$-0.769892\pi$
$883$		−	39.3174i		−	1.32313i	0.749886	−	0.661567i	$-0.230108\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	23.4171	−	13.5199i	0.786271	−	0.453954i	−0.0523772	−	0.998627i	$-0.516680\pi$
$887$	23.4171	−	13.5199i	0.786271	−	0.453954i	0.838648	+	0.544674i	$0.183346\pi$
$888$		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
$893$	−72.3570	−	41.7754i	−2.42134	−	1.39796i
$894$		0			0
$895$		0			0
$896$		0			0
$897$			28.3369i			0.946142i
$898$		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
$903$	−26.6757	+	36.2630i	−0.887712	+	1.20676i
$904$		0			0
$905$		0			0
$906$		0			0
$907$	−28.4078	−	16.4012i	−0.943264	−	0.544594i	−0.0522823	−	0.998632i	$-0.516650\pi$
$907$	−28.4078	−	16.4012i	−0.943264	−	0.544594i	−0.890982	+	0.454038i	$0.849983\pi$
$908$		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
$913$	−18.2897	−	10.5596i	−0.605300	−	0.349470i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	−18.9290	−	43.2011i	−0.625092	−	1.42663i
$918$		0			0
$919$	−23.8965	−	41.3899i	−0.788271	−	1.36533i	−0.927025	−	0.374999i	$-0.877643\pi$
$919$	−23.8965	−	41.3899i	−0.788271	−	1.36533i	0.138754	−	0.990327i	$-0.455690\pi$
$920$		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
$927$	−22.6456	−	13.0745i	−0.743780	−	0.429421i
$928$		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
$931$	14.2700	+	45.7530i	0.467681	+	1.49949i
$932$		0			0
$933$	12.6740	−	7.31736i	0.414929	−	0.239560i
$934$		0			0
$935$		0			0
$936$		0			0
$937$			0.406229i			0.0132709i	0.999978	+	0.00663546i	$0.00211215\pi$
$937$			0.406229i			0.0132709i	−0.999978	+	0.00663546i	$0.997888\pi$
$938$		0			0
$939$	−76.8125			−2.50668
$940$		0			0
$941$	−16.8271	+	29.1454i	−0.548549	+	0.950114i	0.449825	+	0.893116i	$0.351486\pi$
$941$	−16.8271	+	29.1454i	−0.548549	+	0.950114i	−0.998374	+	0.0569979i	$0.981847\pi$
$942$		0			0
$943$	18.6625	−	10.7748i	0.607734	−	0.350875i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	5.05854	−	2.92055i	0.164380	−	0.0949050i	−0.415553	−	0.909569i	$-0.636412\pi$
$947$	5.05854	−	2.92055i	0.164380	−	0.0949050i	0.579933	+	0.814664i	$0.303079\pi$
$948$		0			0
$949$	28.3369	−	49.0810i	0.919855	−	1.59324i
$950$		0			0
$951$	49.2289			1.59636
$952$		0			0
$953$		−	32.0605i		−	1.03854i	−0.854610	−	0.519271i	$-0.826204\pi$
$953$		−	32.0605i		−	1.03854i	0.854610	−	0.519271i	$-0.173796\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$	12.4762	−	7.20311i	0.403297	−	0.232844i
$958$		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
$963$	−5.58303	−	3.22337i	−0.179911	−	0.103872i
$964$		0			0
$965$		0			0
$966$		0			0
$967$			24.0896i			0.774669i	0.921939	+	0.387334i	$0.126604\pi$
$967$			24.0896i			0.774669i	−0.921939	+	0.387334i	$0.873396\pi$
$968$		0			0
$969$	17.6933	−	30.6458i	0.568392	−	0.984484i
$970$		0			0
$971$	−9.23534	−	15.9961i	−0.296376	−	0.513339i	0.678928	−	0.734205i	$-0.262445\pi$
$971$	−9.23534	−	15.9961i	−0.296376	−	0.513339i	−0.975304	+	0.220866i	$0.929112\pi$
$972$		0			0
$973$	−13.5908	−	1.50977i	−0.435702	−	0.0484010i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−21.0764	−	12.1685i	−0.674293	−	0.389303i	0.123408	−	0.992356i	$-0.460618\pi$
$977$	−21.0764	−	12.1685i	−0.674293	−	0.389303i	−0.797701	+	0.603053i	$0.793951\pi$
$978$		0			0
$979$	9.81201			0.313593
$980$		0			0
$981$	71.8725			2.29471
$982$		0			0
$983$	7.50729	+	4.33434i	0.239445	+	0.138244i	0.614922	−	0.788588i	$-0.289188\pi$
$983$	7.50729	+	4.33434i	0.239445	+	0.138244i	−0.375476	+	0.926832i	$0.622521\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$	82.9253	+	9.21195i	2.63954	+	0.293220i
$988$		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
$993$		−	6.00000i		−	0.190404i
$994$		0			0
$995$		0			0
$996$		0			0
$997$	30.4140	+	17.5596i	0.963222	+	0.556117i	0.897163	−	0.441699i	$-0.145624\pi$
$997$	30.4140	+	17.5596i	0.963222	+	0.556117i	0.0660591	+	0.997816i	$0.478957\pi$
$998$		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.bh.i.249.5		12
5.2	odd	4		1400.2.q.j.1201.3		6
5.3	odd	4		280.2.q.e.81.1	✓	6
5.4	even	2	inner	1400.2.bh.i.249.2		12
7.2	even	3	inner	1400.2.bh.i.849.2		12
15.8	even	4		2520.2.bi.q.361.1		6
20.3	even	4		560.2.q.l.81.3		6
35.2	odd	12		1400.2.q.j.401.3		6
35.3	even	12		1960.2.a.v.1.1		3
35.9	even	6	inner	1400.2.bh.i.849.5		12
35.13	even	4		1960.2.q.w.361.3		6
35.17	even	12		9800.2.a.cf.1.3		3
35.18	odd	12		1960.2.a.w.1.3		3
35.23	odd	12		280.2.q.e.121.1	yes	6
35.32	odd	12		9800.2.a.ce.1.1		3
35.33	even	12		1960.2.q.w.961.3		6
105.23	even	12		2520.2.bi.q.1801.1		6
140.3	odd	12		3920.2.a.cb.1.3		3
140.23	even	12		560.2.q.l.401.3		6
140.123	even	12		3920.2.a.cc.1.1		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
280.2.q.e.81.1	✓	6	5.3	odd	4
280.2.q.e.121.1	yes	6	35.23	odd	12
560.2.q.l.81.3		6	20.3	even	4
560.2.q.l.401.3		6	140.23	even	12
1400.2.q.j.401.3		6	35.2	odd	12
1400.2.q.j.1201.3		6	5.2	odd	4
1400.2.bh.i.249.2		12	5.4	even	2	inner
1400.2.bh.i.249.5		12	1.1	even	1	trivial
1400.2.bh.i.849.2		12	7.2	even	3	inner
1400.2.bh.i.849.5		12	35.9	even	6	inner
1960.2.a.v.1.1		3	35.3	even	12
1960.2.a.w.1.3		3	35.18	odd	12
1960.2.q.w.361.3		6	35.13	even	4
1960.2.q.w.961.3		6	35.33	even	12
2520.2.bi.q.361.1		6	15.8	even	4
2520.2.bi.q.1801.1		6	105.23	even	12
3920.2.a.cb.1.3		3	140.3	odd	12
3920.2.a.cc.1.1		3	140.123	even	12
9800.2.a.ce.1.1		3	35.32	odd	12
9800.2.a.cf.1.3		3	35.17	even	12

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.bh (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(2.23800 + 1.29211i) q^{3} +(-2.62958 - 0.292113i) q^{7} +(1.83911 + 3.18543i) q^{9} +O(q^{10})\)	\(q+(2.23800 + 1.29211i) q^{3} +(-2.62958 - 0.292113i) q^{7} +(1.83911 + 3.18543i) q^{9} +(-0.839111 + 1.45338i) q^{11} +4.84667i q^{13} +(-1.73205 - 1.00000i) q^{17} +(3.42334 + 5.92939i) q^{19} +(-5.50756 - 4.05146i) q^{21} +(1.95934 - 1.13122i) q^{23} +1.75268i q^{27} -3.32178 q^{29} +(-4.58423 + 7.94011i) q^{31} +(-3.75587 + 2.16845i) q^{33} +(-2.46529 + 1.42334i) q^{37} +(-6.26245 + 10.8469i) q^{39} +9.52489 q^{41} -6.58423i q^{43} +(-10.5682 + 6.10156i) q^{47} +(6.82934 + 1.53627i) q^{49} +(-2.58423 - 4.47601i) q^{51} +(6.48673 + 3.74511i) q^{53} +17.6933i q^{57} +(4.00000 - 6.92820i) q^{59} +(3.24511 + 5.62070i) q^{61} +(-3.90558 - 8.91357i) q^{63} +(4.98196 + 2.87634i) q^{67} +5.84667 q^{69} +(-10.1267 - 5.84667i) q^{73} +(2.63106 - 3.57666i) q^{77} +(2.84667 + 4.93058i) q^{79} +(3.25268 - 5.63380i) q^{81} +12.5842i q^{83} +(-7.43416 - 4.29211i) q^{87} +(-2.92334 - 5.06337i) q^{89} +(1.41577 - 12.7447i) q^{91} +(-20.5190 + 11.8467i) q^{93} -2.00000i q^{97} -6.17287 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 18 q^{9}+O(q^{10}) \) 12 * q + 18 * q^9	\( 12 q + 18 q^{9} - 6 q^{11} + 6 q^{19} - 48 q^{29} - 24 q^{31} - 36 q^{39} + 36 q^{41} + 24 q^{49} + 48 q^{59} + 12 q^{61} - 36 q^{79} - 54 q^{81} + 48 q^{91} - 252 q^{99}+O(q^{100}) \) 12 * q + 18 * q^9 - 6 * q^11 + 6 * q^19 - 48 * q^29 - 24 * q^31 - 36 * q^39 + 36 * q^41 + 24 * q^49 + 48 * q^59 + 12 * q^61 - 36 * q^79 - 54 * q^81 + 48 * q^91 - 252 * q^99

Introduction

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