LMFDB - Embedded newform 1400.2.bh.h.849.2

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:	$\Q(\zeta_{36})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - x^{6} + 1 $ x^12 - x^6 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			849.2
Root			$-0.984808 + 0.173648i$ of defining polynomial
Character	$\chi$	$=$	1400.849
Dual form			1400.2.bh.h.249.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.16679 + 0.673648i) q^{3} +(-0.0412527 + 2.64543i) q^{7} +(-0.592396 + 1.02606i) q^{9} +O(q^{10})$	\(q+(-1.16679 + 0.673648i) q^{3} +(-0.0412527 + 2.64543i) q^{7} +(-0.592396 + 1.02606i) q^{9} +(-0.705737 - 1.22237i) q^{11} +6.47565i q^{13} +(2.24843 - 1.29813i) q^{17} +(0.581252 - 1.00676i) q^{19} +(-1.73396 - 3.11446i) q^{21} +(-1.36310 - 0.786989i) q^{23} -5.63816i q^{27} -6.22668 q^{29} +(-2.49273 - 4.31753i) q^{31} +(1.64690 + 0.950837i) q^{33} +(7.34013 + 4.23783i) q^{37} +(-4.36231 - 7.55574i) q^{39} +3.57398 q^{41} +7.24897i q^{43} +(-9.47740 - 5.47178i) q^{47} +(-6.99660 - 0.218262i) q^{49} +(-1.74897 + 3.02931i) q^{51} +(-11.0731 + 6.39306i) q^{53} +1.56624i q^{57} +(-1.02094 - 1.76833i) q^{59} +(0.307934 - 0.533356i) q^{61} +(-2.68993 - 1.60947i) q^{63} +(5.26871 - 3.04189i) q^{67} +2.12061 q^{69} -8.27631 q^{71} +(-3.04628 + 1.75877i) q^{73} +(3.26281 - 1.81655i) q^{77} +(0.439693 - 0.761570i) q^{79} +(2.02094 + 3.50038i) q^{81} +3.90167i q^{83} +(7.26525 - 4.19459i) q^{87} +(2.98158 - 5.16425i) q^{89} +(-17.1309 - 0.267138i) q^{91} +(5.81699 + 3.35844i) q^{93} +3.23442i q^{97} +1.67230 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q+O(q^{10}) $ 12 * q	$ 12 q + 12 q^{11} + 12 q^{19} - 30 q^{21} - 48 q^{29} + 6 q^{31} + 12 q^{39} + 12 q^{41} + 30 q^{51} - 6 q^{59} - 18 q^{61} + 48 q^{69} + 36 q^{71} - 6 q^{79} + 18 q^{81} + 12 q^{89} - 102 q^{91} + 36 q^{99}+O(q^{100}) $ 12 * q + 12 * q^11 + 12 * q^19 - 30 * q^21 - 48 * q^29 + 6 * q^31 + 12 * q^39 + 12 * q^41 + 30 * q^51 - 6 * q^59 - 18 * q^61 + 48 * q^69 + 36 * q^71 - 6 * q^79 + 18 * q^81 + 12 * q^89 - 102 * q^91 + 36 * 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
$3$	−1.16679	+	0.673648i	−0.673648	+	0.388931i	−0.797458	−	0.603375i	$-0.793822\pi$
$3$	−1.16679	+	0.673648i	−0.673648	+	0.388931i	0.123809	+	0.992306i	$0.460489\pi$
$4$		0			0
$5$		0			0
$5$		0			0
$6$		0			0
$7$	−0.0412527	+	2.64543i	−0.0155920	+	0.999878i
$7$	−0.0412527	+	2.64543i	−0.0155920	+	0.999878i
$8$		0			0
$9$	−0.592396	+	1.02606i	−0.197465	+	0.342020i
$10$		0			0
$11$	−0.705737	−	1.22237i	−0.212788	−	0.368559i	0.739798	−	0.672829i	$-0.234921\pi$
$11$	−0.705737	−	1.22237i	−0.212788	−	0.368559i	−0.952586	+	0.304270i	$0.901588\pi$
$12$		0			0
$13$			6.47565i			1.79602i	0.439972	+	0.898011i	$0.354988\pi$
$13$			6.47565i			1.79602i	−0.439972	+	0.898011i	$0.645012\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	2.24843	−	1.29813i	0.545325	−	0.314844i	−0.201909	−	0.979404i	$-0.564715\pi$
$17$	2.24843	−	1.29813i	0.545325	−	0.314844i	0.747234	+	0.664561i	$0.231381\pi$
$18$		0			0
$19$	0.581252	−	1.00676i	0.133348	−	0.230966i	−0.791617	−	0.611018i	$-0.790760\pi$
$19$	0.581252	−	1.00676i	0.133348	−	0.230966i	0.924965	+	0.380052i	$0.124094\pi$
$20$		0			0
$21$	−1.73396	−	3.11446i	−0.378380	−	0.679631i
$22$		0			0
$23$	−1.36310	−	0.786989i	−0.284227	−	0.164099i	0.351108	−	0.936335i	$-0.385805\pi$
$23$	−1.36310	−	0.786989i	−0.284227	−	0.164099i	−0.635335	+	0.772236i	$0.719138\pi$
$24$		0			0
$25$		0			0
$26$		0			0
$27$		−	5.63816i		−	1.08506i
$28$		0			0
$29$	−6.22668			−1.15627			−0.578133	−	0.815943i	$-0.696218\pi$
$29$	−6.22668			−1.15627			−0.578133	+	0.815943i	$0.696218\pi$
$30$		0			0
$31$	−2.49273	−	4.31753i	−0.447707	−	0.775451i	0.550530	−	0.834816i	$-0.314426\pi$
$31$	−2.49273	−	4.31753i	−0.447707	−	0.775451i	−0.998236	+	0.0593647i	$0.981093\pi$
$32$		0			0
$33$	1.64690	+	0.950837i	0.286688	+	0.165519i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	7.34013	+	4.23783i	1.20671	+	0.696694i	0.962039	−	0.272912i	$-0.0879868\pi$
$37$	7.34013	+	4.23783i	1.20671	+	0.696694i	0.244671	+	0.969606i	$0.421320\pi$
$38$		0			0
$39$	−4.36231	−	7.55574i	−0.698529	−	1.20989i
$40$		0			0
$41$	3.57398			0.558162			0.279081	−	0.960268i	$-0.409970\pi$
$41$	3.57398			0.558162			0.279081	+	0.960268i	$0.409970\pi$
$42$		0			0
$43$			7.24897i			1.10546i	0.833361	+	0.552729i	$0.186413\pi$
$43$			7.24897i			1.10546i	−0.833361	+	0.552729i	$0.813587\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−9.47740	−	5.47178i	−1.38242	−	0.798141i	−0.389976	−	0.920825i	$-0.627517\pi$
$47$	−9.47740	−	5.47178i	−1.38242	−	0.798141i	−0.992446	+	0.122684i	$0.960850\pi$
$48$		0			0
$49$	−6.99660	−	0.218262i	−0.999514	−	0.0311803i
$50$		0			0
$51$	−1.74897	+	3.02931i	−0.244905	+	0.424188i
$52$		0			0
$53$	−11.0731	+	6.39306i	−1.52101	+	0.878154i	−0.521314	+	0.853365i	$0.674558\pi$
$53$	−11.0731	+	6.39306i	−1.52101	+	0.878154i	−0.999693	+	0.0247889i	$0.992109\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$			1.56624i			0.207453i
$58$		0			0
$59$	−1.02094	−	1.76833i	−0.132916	−	0.230217i	0.791884	−	0.610672i	$-0.209101\pi$
$59$	−1.02094	−	1.76833i	−0.132916	−	0.230217i	−0.924799	+	0.380455i	$0.875767\pi$
$60$		0			0
$61$	0.307934	−	0.533356i	0.0394268	−	0.0682893i	−0.845639	−	0.533756i	$-0.820780\pi$
$61$	0.307934	−	0.533356i	0.0394268	−	0.0682893i	0.885065	+	0.465467i	$0.154113\pi$
$62$		0			0
$63$	−2.68993	−	1.60947i	−0.338900	−	0.202774i
$64$		0			0
$65$		0			0
$66$		0			0
$67$	5.26871	−	3.04189i	0.643675	−	0.371626i	−0.142354	−	0.989816i	$-0.545467\pi$
$67$	5.26871	−	3.04189i	0.643675	−	0.371626i	0.786029	+	0.618190i	$0.212134\pi$
$68$		0			0
$69$	2.12061			0.255292
$70$		0			0
$71$	−8.27631			−0.982217			−0.491109	−	0.871098i	$-0.663408\pi$
$71$	−8.27631			−0.982217			−0.491109	+	0.871098i	$0.663408\pi$
$72$		0			0
$73$	−3.04628	+	1.75877i	−0.356540	+	0.205849i	−0.667562	−	0.744554i	$-0.732662\pi$
$73$	−3.04628	+	1.75877i	−0.356540	+	0.205849i	0.311022	+	0.950403i	$0.399329\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	3.26281	−	1.81655i	0.371832	−	0.207015i
$78$		0			0
$79$	0.439693	−	0.761570i	0.0494693	−	0.0856833i	−0.840230	−	0.542229i	$-0.817580\pi$
$79$	0.439693	−	0.761570i	0.0494693	−	0.0856833i	0.889700	+	0.456546i	$0.150914\pi$
$80$		0			0
$81$	2.02094	+	3.50038i	0.224549	+	0.388931i
$82$		0			0
$83$			3.90167i			0.428264i	0.976805	+	0.214132i	$0.0686923\pi$
$83$			3.90167i			0.428264i	−0.976805	+	0.214132i	$0.931308\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$	7.26525	−	4.19459i	0.778916	−	0.449708i
$88$		0			0
$89$	2.98158	−	5.16425i	0.316047	−	0.547410i	−0.663612	−	0.748077i	$-0.730978\pi$
$89$	2.98158	−	5.16425i	0.316047	−	0.547410i	0.979660	+	0.200667i	$0.0643109\pi$
$90$		0			0
$91$	−17.1309	−	0.267138i	−1.79580	−	0.0280037i
$92$		0			0
$93$	5.81699	+	3.35844i	0.603194	+	0.348254i
$94$		0			0
$95$		0			0
$96$		0			0
$97$			3.23442i			0.328406i	0.986427	+	0.164203i	$0.0525052\pi$
$97$			3.23442i			0.328406i	−0.986427	+	0.164203i	$0.947495\pi$
$98$		0			0
$99$	1.67230			0.168073
$100$		0			0
$101$	−7.26604	−	12.5852i	−0.722998	−	1.25227i	−0.959793	−	0.280710i	$-0.909430\pi$
$101$	−7.26604	−	12.5852i	−0.722998	−	1.25227i	0.236794	−	0.971560i	$-0.423903\pi$
$102$		0			0
$103$	−13.8335	−	7.98680i	−1.36306	−	0.786962i	−0.373029	−	0.927820i	$-0.621681\pi$
$103$	−13.8335	−	7.98680i	−1.36306	−	0.786962i	−0.990030	+	0.140857i	$0.955014\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−15.4418	−	8.91534i	−1.49282	−	0.861879i	−0.492852	−	0.870113i	$-0.664046\pi$
$107$	−15.4418	−	8.91534i	−1.49282	−	0.861879i	−0.999966	+	0.00823431i	$0.997379\pi$
$108$		0			0
$109$	6.11721	+	10.5953i	0.585923	+	1.01485i	0.994760	+	0.102240i	$0.0326011\pi$
$109$	6.11721	+	10.5953i	0.585923	+	1.01485i	−0.408837	+	0.912607i	$0.634066\pi$
$110$		0			0
$111$	−11.4192			−1.08386
$112$		0			0
$113$			4.29086i			0.403650i	0.979422	+	0.201825i	$0.0646872\pi$
$113$			4.29086i			0.403650i	−0.979422	+	0.201825i	$0.935313\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$	−6.64441	−	3.83615i	−0.614276	−	0.354652i
$118$		0			0
$119$	3.34137	+	6.00162i	0.306303	+	0.550168i
$120$		0			0
$121$	4.50387	−	7.80093i	0.409443	−	0.709176i
$122$		0			0
$123$	−4.17009	+	2.40760i	−0.376005	+	0.217086i
$124$		0			0
$125$		0			0
$126$		0			0
$127$			9.89899i			0.878393i	0.898391	+	0.439196i	$0.144737\pi$
$127$			9.89899i			0.878393i	−0.898391	+	0.439196i	$0.855263\pi$
$128$		0			0
$129$	−4.88326	−	8.45805i	−0.429947	−	0.744690i
$130$		0			0
$131$	−7.98293	+	13.8268i	−0.697471	+	1.20806i	0.271869	+	0.962334i	$0.412358\pi$
$131$	−7.98293	+	13.8268i	−0.697471	+	1.20806i	−0.969340	+	0.245722i	$0.920975\pi$
$132$		0			0
$133$	2.63933	+	1.57919i	0.228859	+	0.136933i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	11.0175	−	6.36097i	0.941290	−	0.543454i	0.0509256	−	0.998702i	$-0.483783\pi$
$137$	11.0175	−	6.36097i	0.941290	−	0.543454i	0.890364	+	0.455248i	$0.150450\pi$
$138$		0			0
$139$	−7.65270			−0.649094			−0.324547	−	0.945870i	$-0.605212\pi$
$139$	−7.65270			−0.649094			−0.324547	+	0.945870i	$0.605212\pi$
$140$		0			0
$141$	14.7442			1.24169
$142$		0			0
$143$	7.91566	−	4.57011i	0.661941	−	0.382172i
$144$		0			0
$145$		0			0
$146$		0			0
$147$	8.31061	−	4.45858i	0.685448	−	0.367737i
$148$		0			0
$149$	1.64543	−	2.84997i	0.134799	−	0.233478i	−0.790722	−	0.612176i	$-0.790295\pi$
$149$	1.64543	−	2.84997i	0.134799	−	0.233478i	0.925521	+	0.378697i	$0.123628\pi$
$150$		0			0
$151$	9.36231	+	16.2160i	0.761894	+	1.31964i	0.941873	+	0.335969i	$0.109064\pi$
$151$	9.36231	+	16.2160i	0.761894	+	1.31964i	−0.179979	+	0.983670i	$0.557603\pi$
$152$		0			0
$153$			3.07604i			0.248683i
$154$		0			0
$155$		0			0
$156$		0			0
$157$	−16.2011	+	9.35369i	−1.29299	+	0.746506i	−0.979182	−	0.202982i	$-0.934937\pi$
$157$	−16.2011	+	9.35369i	−1.29299	+	0.746506i	−0.313804	+	0.949488i	$0.601603\pi$
$158$		0			0
$159$	8.61334	−	14.9187i	0.683082	−	1.18313i
$160$		0			0
$161$	2.13816	−	3.57353i	0.168510	−	0.281634i
$162$		0			0
$163$	−1.62760	−	0.939693i	−0.127483	−	0.0736024i	0.434902	−	0.900478i	$-0.356783\pi$
$163$	−1.62760	−	0.939693i	−0.127483	−	0.0736024i	−0.562385	+	0.826875i	$0.690116\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$		−	1.25402i		−	0.0970392i	−0.998822	−	0.0485196i	$-0.984550\pi$
$167$		−	1.25402i		−	0.0970392i	0.998822	−	0.0485196i	$-0.0154503\pi$
$168$		0			0
$169$	−28.9341			−2.22570
$170$		0			0
$171$	0.688663	+	1.19280i	0.0526634	+	0.0912156i
$172$		0			0
$173$	1.17350	+	0.677519i	0.0892193	+	0.0515108i	0.543946	−	0.839120i	$-0.316930\pi$
$173$	1.17350	+	0.677519i	0.0892193	+	0.0515108i	−0.454727	+	0.890631i	$0.650263\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	2.38246	+	1.37551i	0.179077	+	0.103390i
$178$		0			0
$179$	5.70233	+	9.87673i	0.426212	+	0.738222i	0.996533	−	0.0832008i	$-0.0265143\pi$
$179$	5.70233	+	9.87673i	0.426212	+	0.738222i	−0.570320	+	0.821422i	$0.693181\pi$
$180$		0			0
$181$	9.40373			0.698974			0.349487	−	0.936941i	$-0.386356\pi$
$181$	9.40373			0.698974			0.349487	+	0.936941i	$0.386356\pi$
$182$		0			0
$183$			0.829755i			0.0613373i
$184$		0			0
$185$		0			0
$186$		0			0
$187$	−3.17360	−	1.83228i	−0.232077	−	0.133990i
$188$		0			0
$189$	14.9153	+	0.232589i	1.08493	+	0.0169184i
$190$		0			0
$191$	12.3871	−	21.4551i	0.896301	−	1.55244i	0.0641148	−	0.997943i	$-0.479578\pi$
$191$	12.3871	−	21.4551i	0.896301	−	1.55244i	0.832186	−	0.554496i	$-0.187089\pi$
$192$		0			0
$193$	9.50779	−	5.48932i	0.684385	−	0.395130i	−0.117120	−	0.993118i	$-0.537366\pi$
$193$	9.50779	−	5.48932i	0.684385	−	0.395130i	0.801505	+	0.597988i	$0.204033\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$			24.1019i			1.71719i	0.512652	+	0.858596i	$0.328663\pi$
$197$			24.1019i			1.71719i	−0.512652	+	0.858596i	$0.671337\pi$
$198$		0			0
$199$	4.89780	+	8.48324i	0.347196	+	0.601361i	0.985750	−	0.168216i	$-0.0538005\pi$
$199$	4.89780	+	8.48324i	0.347196	+	0.601361i	−0.638554	+	0.769577i	$0.720467\pi$
$200$		0			0
$201$	−4.09833	+	7.09851i	−0.289074	+	0.500690i
$202$		0			0
$203$	0.256867	−	16.4722i	0.0180285	−	1.15613i
$204$		0			0
$205$		0			0
$206$		0			0
$207$	1.61500	−	0.932419i	0.112250	−	0.0648076i
$208$		0			0
$209$	−1.64084			−0.113500
$210$		0			0
$211$	6.68954			0.460527			0.230263	−	0.973128i	$-0.426041\pi$
$211$	6.68954			0.460527			0.230263	+	0.973128i	$0.426041\pi$
$212$		0			0
$213$	9.65674	−	5.57532i	0.661669	−	0.382015i
$214$		0			0
$215$		0			0
$216$		0			0
$217$	11.5245	−	6.41622i	0.782337	−	0.435562i
$218$		0			0
$219$	2.36959	−	4.10424i	0.160122	−	0.277339i
$220$		0			0
$221$	8.40626	+	14.5601i	0.565466	+	0.979416i
$222$		0			0
$223$		−	25.4911i		−	1.70701i	−0.521083	−	0.853506i	$-0.674472\pi$
$223$		−	25.4911i		−	1.70701i	0.521083	−	0.853506i	$-0.325528\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	9.82034	−	5.66978i	0.651799	−	0.376316i	−0.137346	−	0.990523i	$-0.543857\pi$
$227$	9.82034	−	5.66978i	0.651799	−	0.376316i	0.789145	+	0.614207i	$0.210524\pi$
$228$		0			0
$229$	−2.82160	+	4.88716i	−0.186457	+	0.322953i	−0.944066	−	0.329755i	$-0.893034\pi$
$229$	−2.82160	+	4.88716i	−0.186457	+	0.322953i	0.757610	+	0.652708i	$0.226367\pi$
$230$		0			0
$231$	−2.58331	+	4.31753i	−0.169969	+	0.284072i
$232$		0			0
$233$	8.97210	+	5.18004i	0.587782	+	0.339356i	0.764220	−	0.644956i	$-0.223124\pi$
$233$	8.97210	+	5.18004i	0.587782	+	0.339356i	−0.176438	+	0.984312i	$0.556458\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$			1.18479i			0.0769605i
$238$		0			0
$239$	12.2422			0.791880			0.395940	−	0.918276i	$-0.370419\pi$
$239$	12.2422			0.791880			0.395940	+	0.918276i	$0.370419\pi$
$240$		0			0
$241$	−8.92989	−	15.4670i	−0.575225	−	0.996319i	−0.996017	−	0.0891618i	$-0.971581\pi$
$241$	−8.92989	−	15.4670i	−0.575225	−	0.996319i	0.420792	−	0.907157i	$-0.361752\pi$
$242$		0			0
$243$	9.93231	+	5.73442i	0.637158	+	0.367863i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	6.51941	+	3.76399i	0.414820	+	0.239497i
$248$		0			0
$249$	−2.62836	−	4.55245i	−0.166565	−	0.288500i
$250$		0			0
$251$	16.7888			1.05970			0.529850	−	0.848091i	$-0.322248\pi$
$251$	16.7888			1.05970			0.529850	+	0.848091i	$0.322248\pi$
$252$		0			0
$253$			2.22163i			0.139673i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−15.8699	−	9.16250i	−0.989939	−	0.571541i	−0.0846826	−	0.996408i	$-0.526988\pi$
$257$	−15.8699	−	9.16250i	−0.989939	−	0.571541i	−0.905256	+	0.424867i	$0.860321\pi$
$258$		0			0
$259$	−11.5137	+	19.2430i	−0.715425	+	1.19570i
$260$		0			0
$261$	3.68866	−	6.38895i	0.228323	−	0.395466i
$262$		0			0
$263$	−11.7089	+	6.76011i	−0.721999	+	0.416847i	−0.815488	−	0.578774i	$-0.803531\pi$
$263$	−11.7089	+	6.76011i	−0.721999	+	0.416847i	0.0934888	+	0.995620i	$0.470198\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$			8.03415i			0.491682i
$268$		0			0
$269$	13.8824	+	24.0450i	0.846424	+	1.46605i	0.884379	+	0.466769i	$0.154582\pi$
$269$	13.8824	+	24.0450i	0.846424	+	1.46605i	−0.0379556	+	0.999279i	$0.512085\pi$
$270$		0			0
$271$	−7.93969	+	13.7520i	−0.482302	+	0.835372i	−0.999794	−	0.0203167i	$-0.993533\pi$
$271$	−7.93969	+	13.7520i	−0.482302	+	0.835372i	0.517492	+	0.855688i	$0.326866\pi$
$272$		0			0
$273$	20.1681	−	11.2285i	1.22063	−	0.679579i
$274$		0			0
$275$		0			0
$276$		0			0
$277$	−14.4690	+	8.35369i	−0.869359	+	0.501925i	−0.867135	−	0.498073i	$-0.834041\pi$
$277$	−14.4690	+	8.35369i	−0.869359	+	0.501925i	−0.00222396	+	0.999998i	$0.500708\pi$
$278$		0			0
$279$	5.90673			0.353626
$280$		0			0
$281$	32.0155			1.90988			0.954942	−	0.296793i	$-0.0959172\pi$
$281$	32.0155			1.90988			0.954942	+	0.296793i	$0.0959172\pi$
$282$		0			0
$283$	9.27287	−	5.35369i	0.551215	−	0.318244i	−0.198397	−	0.980122i	$-0.563574\pi$
$283$	9.27287	−	5.35369i	0.551215	−	0.318244i	0.749612	+	0.661878i	$0.230240\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	−0.147436	+	9.45471i	−0.00870288	+	0.558094i
$288$		0			0
$289$	−5.12970	+	8.88490i	−0.301747	+	0.522641i
$290$		0			0
$291$	−2.17886	−	3.77390i	−0.127727	−	0.221230i
$292$		0			0
$293$			8.20439i			0.479306i	0.970859	+	0.239653i	$0.0770336\pi$
$293$			8.20439i			0.479306i	−0.970859	+	0.239653i	$0.922966\pi$
$294$		0			0
$295$		0			0
$296$		0			0
$297$	−6.89193	+	3.97906i	−0.399910	+	0.230888i
$298$		0			0
$299$	5.09627	−	8.82699i	0.294725	−	0.510478i
$300$		0			0
$301$	−19.1766	−	0.299039i	−1.10532	−	0.0172363i
$302$		0			0
$303$	16.9559	+	9.78952i	0.974093	+	0.562393i
$304$		0			0
$305$		0			0
$306$		0			0
$307$			26.3678i			1.50489i	0.658654	+	0.752446i	$0.271126\pi$
$307$			26.3678i			1.50489i	−0.658654	+	0.752446i	$0.728874\pi$
$308$		0			0
$309$	21.5212			1.22430
$310$		0			0
$311$	7.33275	+	12.7007i	0.415802	+	0.720190i	0.995512	−	0.0946325i	$-0.0301676\pi$
$311$	7.33275	+	12.7007i	0.415802	+	0.720190i	−0.579710	+	0.814823i	$0.696834\pi$
$312$		0			0
$313$	−26.4313	−	15.2601i	−1.49399	−	0.862553i	−0.494009	−	0.869457i	$-0.664469\pi$
$313$	−26.4313	−	15.2601i	−1.49399	−	0.862553i	−0.999976	+	0.00690417i	$0.997802\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	14.6113	+	8.43582i	0.820651	+	0.473803i	0.850641	−	0.525747i	$-0.176214\pi$
$317$	14.6113	+	8.43582i	0.820651	+	0.473803i	−0.0299900	+	0.999550i	$0.509548\pi$
$318$		0			0
$319$	4.39440	+	7.61132i	0.246039	+	0.426152i
$320$		0			0
$321$	24.0232			1.34085
$322$		0			0
$323$		−	3.01817i		−	0.167935i
$324$		0			0
$325$		0			0
$326$		0			0
$327$	−14.2750	−	8.24170i	−0.789411	−	0.455767i
$328$		0			0
$329$	14.8662	−	24.8461i	0.819599	−	1.36981i
$330$		0			0
$331$	−7.18779	+	12.4496i	−0.395076	+	0.684292i	−0.993111	−	0.117178i	$-0.962615\pi$
$331$	−7.18779	+	12.4496i	−0.395076	+	0.684292i	0.598035	+	0.801470i	$0.295949\pi$
$332$		0			0
$333$	−8.69653	+	5.02094i	−0.476567	+	0.275146i
$334$		0			0
$335$		0			0
$336$		0			0
$337$			18.2909i			0.996367i	0.867072	+	0.498183i	$0.165999\pi$
$337$			18.2909i			0.996367i	−0.867072	+	0.498183i	$0.834001\pi$
$338$		0			0
$339$	−2.89053	−	5.00654i	−0.156992	−	0.271918i
$340$		0			0
$341$	−3.51842	+	6.09408i	−0.190533	+	0.330013i
$342$		0			0
$343$	0.866025	−	18.5000i	0.0467610	−	0.998906i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−26.8795	+	15.5189i	−1.44297	+	0.833097i	−0.998047	−	0.0624727i	$-0.980101\pi$
$347$	−26.8795	+	15.5189i	−1.44297	+	0.833097i	−0.444920	+	0.895570i	$0.646768\pi$
$348$		0			0
$349$	21.3286			1.14170			0.570848	−	0.821056i	$-0.306615\pi$
$349$	21.3286			1.14170			0.570848	+	0.821056i	$0.306615\pi$
$350$		0			0
$351$	36.5107			1.94880
$352$		0			0
$353$	29.9916	−	17.3157i	1.59629	−	0.921620i	0.604100	−	0.796908i	$-0.293533\pi$
$353$	29.9916	−	17.3157i	1.59629	−	0.921620i	0.992193	−	0.124712i	$-0.0398007\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$	−7.94166	−	4.75174i	−0.420317	−	0.251489i
$358$		0			0
$359$	−11.3576	+	19.6719i	−0.599429	+	1.03824i	0.393476	+	0.919335i	$0.371272\pi$
$359$	−11.3576	+	19.6719i	−0.599429	+	1.03824i	−0.992905	+	0.118907i	$0.962061\pi$
$360$		0			0
$361$	8.82429	+	15.2841i	0.464436	+	0.804428i
$362$		0			0
$363$			12.1361i			0.636980i
$364$		0			0
$365$		0			0
$366$		0			0
$367$	26.5913	−	15.3525i	1.38806	−	0.801395i	0.394960	−	0.918698i	$-0.370758\pi$
$367$	26.5913	−	15.3525i	1.38806	−	0.801395i	0.993096	+	0.117304i	$0.0374251\pi$
$368$		0			0
$369$	−2.11721	+	3.66712i	−0.110218	+	0.190903i
$370$		0			0
$371$	−16.4556	−	29.5568i	−0.854331	−	1.53451i
$372$		0			0
$373$	−15.0433	−	8.68526i	−0.778913	−	0.449706i	0.0571319	−	0.998367i	$-0.481804\pi$
$373$	−15.0433	−	8.68526i	−0.778913	−	0.449706i	−0.836045	+	0.548661i	$0.815138\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$		−	40.3218i		−	2.07668i
$378$		0			0
$379$	−2.78880			−0.143251			−0.0716255	−	0.997432i	$-0.522819\pi$
$379$	−2.78880			−0.143251			−0.0716255	+	0.997432i	$0.522819\pi$
$380$		0			0
$381$	−6.66843	−	11.5501i	−0.341634	−	0.591728i
$382$		0			0
$383$	−4.39160	−	2.53549i	−0.224400	−	0.129558i	0.383586	−	0.923505i	$-0.374689\pi$
$383$	−4.39160	−	2.53549i	−0.224400	−	0.129558i	−0.607986	+	0.793948i	$0.708022\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	−7.43788	−	4.29426i	−0.378089	−	0.218290i
$388$		0			0
$389$	−4.29948	−	7.44691i	−0.217992	−	0.377574i	0.736202	−	0.676762i	$-0.236617\pi$
$389$	−4.29948	−	7.44691i	−0.217992	−	0.377574i	−0.954194	+	0.299189i	$0.903284\pi$
$390$		0			0
$391$	−4.08647			−0.206661
$392$		0			0
$393$		−	21.5107i		−	1.08507i
$394$		0			0
$395$		0			0
$396$		0			0
$397$	−2.22913	−	1.28699i	−0.111877	−	0.0645921i	0.443017	−	0.896513i	$-0.353908\pi$
$397$	−2.22913	−	1.28699i	−0.111877	−	0.0645921i	−0.554894	+	0.831921i	$0.687241\pi$
$398$		0			0
$399$	−4.14337	−	0.0646115i	−0.207428	−	0.00323462i
$400$		0			0
$401$	−14.7310	+	25.5149i	−0.735632	+	1.27415i	0.218814	+	0.975767i	$0.429781\pi$
$401$	−14.7310	+	25.5149i	−0.735632	+	1.27415i	−0.954446	+	0.298385i	$0.903552\pi$
$402$		0			0
$403$	27.9588	−	16.1420i	1.39273	−	0.804092i
$404$		0			0
$405$		0			0
$406$		0			0
$407$		−	11.9632i		−	0.592992i
$408$		0			0
$409$	2.92602	+	5.06802i	0.144682	+	0.250597i	0.929254	−	0.369440i	$-0.120451\pi$
$409$	2.92602	+	5.06802i	0.144682	+	0.250597i	−0.784572	+	0.620038i	$0.787117\pi$
$410$		0			0
$411$	−8.57011	+	14.8439i	−0.422732	+	0.732194i
$412$		0			0
$413$	4.72010	−	2.62789i	0.232261	−	0.129310i
$414$		0			0
$415$		0			0
$416$		0			0
$417$	8.92912	−	5.15523i	0.437261	−	0.252453i
$418$		0			0
$419$	1.03952			0.0507841			0.0253921	−	0.999678i	$-0.491917\pi$
$419$	1.03952			0.0507841			0.0253921	+	0.999678i	$0.491917\pi$
$420$		0			0
$421$	−32.1566			−1.56722			−0.783609	−	0.621254i	$-0.786623\pi$
$421$	−32.1566			−1.56722			−0.783609	+	0.621254i	$0.786623\pi$
$422$		0			0
$423$	11.2288	−	6.48293i	0.545961	−	0.315211i
$424$		0			0
$425$		0			0
$426$		0			0
$427$	1.39825	+	0.836619i	0.0676663	+	0.0404868i
$428$		0			0
$429$	−6.15729	+	10.6647i	−0.297277	+	0.514898i
$430$		0			0
$431$	−0.230085	−	0.398519i	−0.0110828	−	0.0191960i	0.860431	−	0.509567i	$-0.170195\pi$
$431$	−0.230085	−	0.398519i	−0.0110828	−	0.0191960i	−0.871514	+	0.490371i	$0.836861\pi$
$432$		0			0
$433$		−	24.6509i		−	1.18465i	−0.805699	−	0.592325i	$-0.798210\pi$
$433$		−	24.6509i		−	1.18465i	0.805699	−	0.592325i	$-0.201790\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−1.58461	+	0.914878i	−0.0758024	+	0.0437645i
$438$		0			0
$439$	14.9572	−	25.9067i	0.713870	−	1.23646i	−0.249524	−	0.968369i	$-0.580274\pi$
$439$	14.9572	−	25.9067i	0.713870	−	1.23646i	0.963394	−	0.268090i	$-0.0863925\pi$
$440$		0			0
$441$	4.36871	−	7.04963i	0.208034	−	0.335697i
$442$		0			0
$443$	−10.9005	−	6.29339i	−0.517897	−	0.299008i	0.218177	−	0.975909i	$-0.429989\pi$
$443$	−10.9005	−	6.29339i	−0.517897	−	0.299008i	−0.736074	+	0.676901i	$0.763322\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$			4.43376i			0.209710i
$448$		0			0
$449$	−24.4783			−1.15520			−0.577602	−	0.816318i	$-0.696011\pi$
$449$	−24.4783			−1.15520			−0.577602	+	0.816318i	$0.696011\pi$
$450$		0			0
$451$	−2.52229	−	4.36873i	−0.118770	−	0.205716i
$452$		0			0
$453$	−21.8478	−	12.6138i	−1.02650	−	0.592648i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	35.0403	+	20.2306i	1.63912	+	0.946345i	0.981138	+	0.193310i	$0.0619224\pi$
$457$	35.0403	+	20.2306i	1.63912	+	0.946345i	0.657980	+	0.753035i	$0.271411\pi$
$458$		0			0
$459$	−7.31908	−	12.6770i	−0.341625	−	0.591712i
$460$		0			0
$461$	−5.22668			−0.243431			−0.121715	−	0.992565i	$-0.538840\pi$
$461$	−5.22668			−0.243431			−0.121715	+	0.992565i	$0.538840\pi$
$462$		0			0
$463$			40.0547i			1.86150i	0.365658	+	0.930749i	$0.380844\pi$
$463$			40.0547i			1.86150i	−0.365658	+	0.930749i	$0.619156\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−17.8199	−	10.2883i	−0.824607	−	0.476087i	0.0273953	−	0.999625i	$-0.491279\pi$
$467$	−17.8199	−	10.2883i	−0.824607	−	0.476087i	−0.852003	+	0.523537i	$0.824612\pi$
$468$		0			0
$469$	7.82976	+	14.0635i	0.361545	+	0.649391i
$470$		0			0
$471$	12.6022	−	21.8276i	0.580679	−	1.00576i
$472$		0			0
$473$	8.86094	−	5.11587i	0.407427	−	0.235228i
$474$		0			0
$475$		0			0
$476$		0			0
$477$		−	15.1489i		−	0.693620i
$478$		0			0
$479$	11.3020	+	19.5756i	0.516402	+	0.894434i	0.999819	+	0.0190438i	$0.00606219\pi$
$479$	11.3020	+	19.5756i	0.516402	+	0.894434i	−0.483417	+	0.875390i	$0.660604\pi$
$480$		0			0
$481$	−27.4427	+	47.5321i	−1.25128	+	2.16728i
$482$		0			0
$483$	−0.0874810	+	5.60994i	−0.00398052	+	0.255261i
$484$		0			0
$485$		0			0
$486$		0			0
$487$	−22.4403	+	12.9559i	−1.01687	+	0.587087i	−0.913194	−	0.407524i	$-0.866392\pi$
$487$	−22.4403	+	12.9559i	−1.01687	+	0.587087i	−0.103671	+	0.994612i	$0.533059\pi$
$488$		0			0
$489$	2.53209			0.114505
$490$		0			0
$491$	39.7297			1.79298			0.896488	−	0.443069i	$-0.146110\pi$
$491$	39.7297			1.79298			0.896488	+	0.443069i	$0.146110\pi$
$492$		0			0
$493$	−14.0003	+	8.08306i	−0.630541	+	0.364043i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	0.341420	−	21.8944i	0.0153148	−	0.982098i
$498$		0			0
$499$	10.0963	−	17.4872i	0.451971	−	0.782837i	−0.546537	−	0.837435i	$-0.684054\pi$
$499$	10.0963	−	17.4872i	0.451971	−	0.782837i	0.998508	+	0.0545980i	$0.0173877\pi$
$500$		0			0
$501$	0.844770	+	1.46318i	0.0377415	+	0.0653703i
$502$		0			0
$503$			7.29086i			0.325083i	0.986702	+	0.162542i	$0.0519692\pi$
$503$			7.29086i			0.325083i	−0.986702	+	0.162542i	$0.948031\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	33.7601	−	19.4914i	1.49934	−	0.865643i
$508$		0			0
$509$	3.27126	−	5.66599i	0.144996	−	0.251140i	−0.784375	−	0.620286i	$-0.787016\pi$
$509$	3.27126	−	5.66599i	0.144996	−	0.251140i	0.929371	+	0.369146i	$0.120350\pi$
$510$		0			0
$511$	−4.52704	−	8.13127i	−0.200264	−	0.359706i
$512$		0			0
$513$	−5.67626	−	3.27719i	−0.250613	−	0.144691i
$514$		0			0
$515$		0			0
$516$		0			0
$517$			15.4466i			0.679339i
$518$		0			0
$519$	−1.82564			−0.0801366
$520$		0			0
$521$	−5.87939	−	10.1834i	−0.257581	−	0.446143i	0.708013	−	0.706200i	$-0.249592\pi$
$521$	−5.87939	−	10.1834i	−0.257581	−	0.446143i	−0.965593	+	0.260057i	$0.916259\pi$
$522$		0			0
$523$	0.852618	+	0.492259i	0.0372824	+	0.0215250i	0.518525	−	0.855062i	$-0.326481\pi$
$523$	0.852618	+	0.492259i	0.0372824	+	0.0215250i	−0.481243	+	0.876587i	$0.659815\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−11.2095	−	6.47178i	−0.488292	−	0.281915i
$528$		0			0
$529$	−10.2613	−	17.7731i	−0.446143	−	0.772743i
$530$		0			0
$531$	2.41921			0.104985
$532$		0			0
$533$			23.1438i			1.00247i
$534$		0			0
$535$		0			0
$536$		0			0
$537$	−13.3069	−	7.68273i	−0.574234	−	0.331534i
$538$		0			0
$539$	4.67096	+	8.70648i	0.201192	+	0.375015i
$540$		0			0
$541$	−8.10488	+	14.0381i	−0.348456	+	0.603544i	−0.985975	−	0.166891i	$-0.946627\pi$
$541$	−8.10488	+	14.0381i	−0.348456	+	0.603544i	0.637519	+	0.770434i	$0.279961\pi$
$542$		0			0
$543$	−10.9722	+	6.33481i	−0.470863	+	0.271853i
$544$		0			0
$545$		0			0
$546$		0			0
$547$			29.3337i			1.25422i	0.778932	+	0.627109i	$0.215762\pi$
$547$			29.3337i			1.25422i	−0.778932	+	0.627109i	$0.784238\pi$
$548$		0			0
$549$	0.364837	+	0.631917i	0.0155709	+	0.0269696i
$550$		0			0
$551$	−3.61927	+	6.26876i	−0.154186	+	0.267058i
$552$		0			0
$553$	1.99654	+	1.19459i	0.0849016	+	0.0507992i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−11.2990	+	6.52347i	−0.478753	+	0.276408i	−0.719897	−	0.694081i	$-0.755811\pi$
$557$	−11.2990	+	6.52347i	−0.478753	+	0.276408i	0.241144	+	0.970489i	$0.422478\pi$
$558$		0			0
$559$	−46.9418			−1.98543
$560$		0			0
$561$	4.93725			0.208451
$562$		0			0
$563$	−23.3323	+	13.4709i	−0.983339	+	0.567731i	−0.903276	−	0.429059i	$-0.858845\pi$
$563$	−23.3323	+	13.4709i	−0.983339	+	0.567731i	−0.0800623	+	0.996790i	$0.525512\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$	−9.34337	+	5.20187i	−0.392385	+	0.218458i
$568$		0			0
$569$	6.61633	−	11.4598i	0.277371	−	0.480421i	−0.693359	−	0.720592i	$-0.743870\pi$
$569$	6.61633	−	11.4598i	0.277371	−	0.480421i	0.970731	+	0.240171i	$0.0772035\pi$
$570$		0			0
$571$	3.16385	+	5.47995i	0.132403	+	0.229329i	0.924602	−	0.380934i	$-0.124397\pi$
$571$	3.16385	+	5.47995i	0.132403	+	0.229329i	−0.792199	+	0.610262i	$0.791064\pi$
$572$		0			0
$573$			33.3783i			1.39440i
$574$		0			0
$575$		0			0
$576$		0			0
$577$	−5.36208	+	3.09580i	−0.223226	+	0.128880i	−0.607443	−	0.794363i	$-0.707805\pi$
$577$	−5.36208	+	3.09580i	−0.223226	+	0.128880i	0.384217	+	0.923243i	$0.374471\pi$
$578$		0			0
$579$	−7.39574	+	12.8098i	−0.307357	+	0.532357i
$580$		0			0
$581$	−10.3216	−	0.160954i	−0.428212	−	0.00667752i
$582$		0			0
$583$	15.6294	+	9.02363i	0.647303	+	0.373721i
$584$		0			0
$585$		0			0
$586$		0			0
$587$			26.6186i			1.09867i	0.835604	+	0.549333i	$0.185118\pi$
$587$			26.6186i			1.09867i	−0.835604	+	0.549333i	$0.814882\pi$
$588$		0			0
$589$	−5.79561			−0.238804
$590$		0			0
$591$	−16.2362	−	28.1220i	−0.667869	−	1.15678i
$592$		0			0
$593$	−11.7317	−	6.77332i	−0.481764	−	0.278147i	0.239387	−	0.970924i	$-0.423054\pi$
$593$	−11.7317	−	6.77332i	−0.481764	−	0.278147i	−0.721152	+	0.692777i	$0.756387\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	−11.4294	−	6.59879i	−0.467776	−	0.270071i
$598$		0			0
$599$	−14.8007	−	25.6355i	−0.604739	−	1.04744i	−0.992093	−	0.125507i	$-0.959944\pi$
$599$	−14.8007	−	25.6355i	−0.604739	−	1.04744i	0.387354	−	0.921931i	$-0.373389\pi$
$600$		0			0
$601$	−20.9050			−0.852732			−0.426366	−	0.904551i	$-0.640206\pi$
$601$	−20.9050			−0.852732			−0.426366	+	0.904551i	$0.640206\pi$
$602$		0			0
$603$			7.20801i			0.293533i
$604$		0			0
$605$		0			0
$606$		0			0
$607$	32.2192	+	18.6018i	1.30774	+	0.755023i	0.981718	−	0.190340i	$-0.0609589\pi$
$607$	32.2192	+	18.6018i	1.30774	+	0.755023i	0.326020	+	0.945363i	$0.394292\pi$
$608$		0			0
$609$	10.7968	+	19.3927i	0.437508	+	0.785833i
$610$		0			0
$611$	35.4334	−	61.3724i	1.43348	−	2.48286i
$612$		0			0
$613$	−22.6152	+	13.0569i	−0.913420	+	0.527363i	−0.881530	−	0.472128i	$-0.843486\pi$
$613$	−22.6152	+	13.0569i	−0.913420	+	0.527363i	−0.0318902	+	0.999491i	$0.510153\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$		−	25.4698i		−	1.02537i	−0.858575	−	0.512687i	$-0.828650\pi$
$617$		−	25.4698i		−	1.02537i	0.858575	−	0.512687i	$-0.171350\pi$
$618$		0			0
$619$	7.51455	+	13.0156i	0.302035	+	0.523140i	0.976597	−	0.215078i	$-0.0690007\pi$
$619$	7.51455	+	13.0156i	0.302035	+	0.523140i	−0.674562	+	0.738219i	$0.735667\pi$
$620$		0			0
$621$	−4.43717	+	7.68540i	−0.178057	+	0.308404i
$622$		0			0
$623$	13.5387	+	8.10060i	0.542415	+	0.324544i
$624$		0			0
$625$		0			0
$626$		0			0
$627$	1.91453	−	1.10535i	0.0764588	−	0.0441435i
$628$		0			0
$629$	22.0051			0.877399
$630$		0			0
$631$	0.605762			0.0241150			0.0120575	−	0.999927i	$-0.496162\pi$
$631$	0.605762			0.0241150			0.0120575	+	0.999927i	$0.496162\pi$
$632$		0			0
$633$	−7.80531	+	4.50640i	−0.310233	+	0.179113i
$634$		0			0
$635$		0			0
$636$		0			0
$637$	1.41339	−	45.3075i	0.0560005	−	1.79515i
$638$		0			0
$639$	4.90286	−	8.49200i	0.193954	−	0.335938i
$640$		0			0
$641$	−11.3772	−	19.7058i	−0.449371	−	0.778333i	0.548974	−	0.835839i	$-0.315019\pi$
$641$	−11.3772	−	19.7058i	−0.449371	−	0.778333i	−0.998345	+	0.0575060i	$0.981685\pi$
$642$		0			0
$643$		−	1.85204i		−	0.0730375i	−0.999333	−	0.0365187i	$-0.988373\pi$
$643$		−	1.85204i		−	0.0730375i	0.999333	−	0.0365187i	$-0.0116269\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	5.79098	−	3.34343i	0.227667	−	0.131444i	−0.381828	−	0.924233i	$-0.624705\pi$
$647$	5.79098	−	3.34343i	0.227667	−	0.131444i	0.609495	+	0.792790i	$0.291372\pi$
$648$		0			0
$649$	−1.44104	+	2.49595i	−0.0565656	+	0.0979746i
$650$		0			0
$651$	−9.12449	+	15.2499i	−0.357617	+	0.597690i
$652$		0			0
$653$	9.55461	+	5.51636i	0.373901	+	0.215872i	0.675161	−	0.737670i	$-0.264074\pi$
$653$	9.55461	+	5.51636i	0.373901	+	0.215872i	−0.301260	+	0.953542i	$0.597407\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$		−	4.16756i		−	0.162592i
$658$		0			0
$659$	13.5202			0.526673			0.263337	−	0.964704i	$-0.415177\pi$
$659$	13.5202			0.526673			0.263337	+	0.964704i	$0.415177\pi$
$660$		0			0
$661$	−21.0692	−	36.4930i	−0.819498	−	1.41941i	−0.906053	−	0.423165i	$-0.860919\pi$
$661$	−21.0692	−	36.4930i	−0.819498	−	1.41941i	0.0865545	−	0.996247i	$-0.472414\pi$
$662$		0			0
$663$	−19.6167	−	11.3257i	−0.761851	−	0.439855i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	8.48762	+	4.90033i	0.328642	+	0.189742i
$668$		0			0
$669$	17.1721	+	29.7429i	0.663910	+	1.14993i
$670$		0			0
$671$	−0.869280			−0.0335582
$672$		0			0
$673$			18.8494i			0.726589i	0.931674	+	0.363295i	$0.118348\pi$
$673$			18.8494i			0.726589i	−0.931674	+	0.363295i	$0.881652\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	21.6298	+	12.4880i	0.831301	+	0.479952i	0.854298	−	0.519784i	$-0.173987\pi$
$677$	21.6298	+	12.4880i	0.831301	+	0.479952i	−0.0229968	+	0.999736i	$0.507321\pi$
$678$		0			0
$679$	−8.55644	−	0.133429i	−0.328366	−	0.00512052i
$680$		0			0
$681$	−7.63887	+	13.2309i	−0.292722	+	0.507010i
$682$		0			0
$683$	−14.8321	+	8.56330i	−0.567533	+	0.327666i	−0.756164	−	0.654383i	$-0.772929\pi$
$683$	−14.8321	+	8.56330i	−0.567533	+	0.327666i	0.188630	+	0.982048i	$0.439595\pi$
$684$		0			0
$685$		0			0
$686$		0			0
$687$		−	7.60307i		−	0.290075i
$688$		0			0
$689$	−41.3992	−	71.7055i	−1.57718	−	2.73176i
$690$		0			0
$691$	6.80500	−	11.7866i	0.258874	−	0.448383i	−0.707066	−	0.707147i	$-0.749982\pi$
$691$	6.80500	−	11.7866i	0.258874	−	0.448383i	0.965941	+	0.258764i	$0.0833151\pi$
$692$		0			0
$693$	−0.0689870	+	4.42396i	−0.00262060	+	0.168052i
$694$		0			0
$695$		0			0
$696$		0			0
$697$	8.03585	−	4.63950i	0.304380	−	0.175734i
$698$		0			0
$699$	−13.9581			−0.527944
$700$		0			0
$701$	3.86247			0.145884			0.0729418	−	0.997336i	$-0.476761\pi$
$701$	3.86247			0.145884			0.0729418	+	0.997336i	$0.476761\pi$
$702$		0			0
$703$	8.53293	−	4.92649i	0.321826	−	0.185806i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	33.5929	−	18.7026i	1.26339	−	0.703385i
$708$		0			0
$709$	−10.8935	+	18.8681i	−0.409115	+	0.708608i	−0.994791	−	0.101938i	$-0.967496\pi$
$709$	−10.8935	+	18.8681i	−0.409115	+	0.708608i	0.585676	+	0.810545i	$0.300829\pi$
$710$		0			0
$711$	0.520945	+	0.902302i	0.0195369	+	0.0338390i
$712$		0			0
$713$			7.84699i			0.293872i
$714$		0			0
$715$		0			0
$716$		0			0
$717$	−14.2841	+	8.24691i	−0.533448	+	0.307987i
$718$		0			0
$719$	−25.3926	+	43.9814i	−0.946986	+	1.64023i	−0.195260	+	0.980751i	$0.562555\pi$
$719$	−25.3926	+	43.9814i	−0.946986	+	1.64023i	−0.751725	+	0.659476i	$0.770778\pi$
$720$		0			0
$721$	21.6992	−	36.2662i	0.808120	−	1.35062i
$722$		0			0
$723$	20.8387	+	12.0312i	0.774998	+	0.447446i
$724$		0			0
$725$		0			0
$726$		0			0
$727$			38.1607i			1.41530i	0.706561	+	0.707652i	$0.250245\pi$
$727$			38.1607i			1.41530i	−0.706561	+	0.707652i	$0.749755\pi$
$728$		0			0
$729$	−27.5776			−1.02139
$730$		0			0
$731$	9.41013	+	16.2988i	0.348046	+	0.602834i
$732$		0			0
$733$	−13.3318	−	7.69712i	−0.492421	−	0.284300i	0.233157	−	0.972439i	$-0.425094\pi$
$733$	−13.3318	−	7.69712i	−0.492421	−	0.284300i	−0.725578	+	0.688140i	$0.758428\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−7.43664	−	4.29355i	−0.273932	−	0.158155i
$738$		0			0
$739$	−22.0749	−	38.2349i	−0.812039	−	1.40649i	−0.911435	−	0.411444i	$-0.865024\pi$
$739$	−22.0749	−	38.2349i	−0.812039	−	1.40649i	0.0993961	−	0.995048i	$-0.468309\pi$
$740$		0			0
$741$	−10.1424			−0.372591
$742$		0			0
$743$			53.0378i			1.94577i	0.231296	+	0.972884i	$0.425704\pi$
$743$			53.0378i			1.94577i	−0.231296	+	0.972884i	$0.574296\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	−4.00335	−	2.31134i	−0.146475	−	0.0845674i
$748$		0			0
$749$	24.2219	−	40.4825i	0.885050	−	1.47920i
$750$		0			0
$751$	−4.85844	+	8.41507i	−0.177287	+	0.307070i	−0.940950	−	0.338545i	$-0.890065\pi$
$751$	−4.85844	+	8.41507i	−0.177287	+	0.307070i	0.763663	+	0.645615i	$0.223399\pi$
$752$		0			0
$753$	−19.5891	+	11.3097i	−0.713865	+	0.412150i
$754$		0			0
$755$		0			0
$756$		0			0
$757$			22.2030i			0.806980i	0.914984	+	0.403490i	$0.132203\pi$
$757$			22.2030i			0.806980i	−0.914984	+	0.403490i	$0.867797\pi$
$758$		0			0
$759$	−1.49660	−	2.59218i	−0.0543230	−	0.0940902i
$760$		0			0
$761$	−18.5273	+	32.0903i	−0.671616	+	1.16327i	0.305830	+	0.952086i	$0.401066\pi$
$761$	−18.5273	+	32.0903i	−0.671616	+	1.16327i	−0.977446	+	0.211186i	$0.932267\pi$
$762$		0			0
$763$	−28.2815	+	15.7456i	−1.02386	+	0.570028i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	11.4511	−	6.61128i	0.413474	−	0.238720i
$768$		0			0
$769$	−41.7948			−1.50716			−0.753579	−	0.657357i	$-0.771674\pi$
$769$	−41.7948			−1.50716			−0.753579	+	0.657357i	$0.771674\pi$
$770$		0			0
$771$	24.6892			0.889160
$772$		0			0
$773$	27.1396	−	15.6691i	0.976144	−	0.563577i	0.0750402	−	0.997181i	$-0.476091\pi$
$773$	27.1396	−	15.6691i	0.976144	−	0.563577i	0.901104	+	0.433603i	$0.142758\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$	0.471073	−	30.2087i	0.0168997	−	1.08373i
$778$		0			0
$779$	2.07738	−	3.59813i	0.0744299	−	0.128916i
$780$		0			0
$781$	5.84090	+	10.1167i	0.209004	+	0.362005i
$782$		0			0
$783$			35.1070i			1.25462i
$784$		0			0
$785$		0			0
$786$		0			0
$787$	21.4531	−	12.3859i	0.764720	−	0.441511i	−0.0662679	−	0.997802i	$-0.521109\pi$
$787$	21.4531	−	12.3859i	0.764720	−	0.441511i	0.830988	+	0.556291i	$0.187776\pi$
$788$		0			0
$789$	9.10788	−	15.7753i	0.324249	−	0.561616i
$790$		0			0
$791$	−11.3512	−	0.177009i	−0.403601	−	0.00629373i
$792$		0			0
$793$	3.45383	+	1.99407i	0.122649	+	0.0708115i
$794$		0			0
$795$		0			0
$796$		0			0
$797$			5.07697i			0.179836i	0.995949	+	0.0899178i	$0.0286604\pi$
$797$			5.07697i			0.179836i	−0.995949	+	0.0899178i	$0.971340\pi$
$798$		0			0
$799$	−28.4124			−1.00516
$800$		0			0
$801$	3.53256	+	6.11857i	0.124817	+	0.216189i
$802$		0			0
$803$	4.29975	+	2.48246i	0.151735	+	0.0876041i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	−32.3957	−	18.7037i	−1.14038	−	0.658401i
$808$		0			0
$809$	1.47519	+	2.55510i	0.0518647	+	0.0898324i	0.890792	−	0.454411i	$-0.150150\pi$
$809$	1.47519	+	2.55510i	0.0518647	+	0.0898324i	−0.838927	+	0.544243i	$0.816817\pi$
$810$		0			0
$811$	−13.1753			−0.462647			−0.231324	−	0.972877i	$-0.574306\pi$
$811$	−13.1753			−0.462647			−0.231324	+	0.972877i	$0.574306\pi$
$812$		0			0
$813$		−	21.3942i		−	0.750329i
$814$		0			0
$815$		0			0
$816$		0			0
$817$	7.29796	+	4.21348i	0.255323	+	0.147411i
$818$		0			0
$819$	10.4224	−	17.4191i	0.364187	−	0.608672i
$820$		0			0
$821$	11.8032	−	20.4437i	0.411934	−	0.713491i	−0.583167	−	0.812352i	$-0.698187\pi$
$821$	11.8032	−	20.4437i	0.411934	−	0.713491i	0.995101	+	0.0988615i	$0.0315201\pi$
$822$		0			0
$823$	−4.88511	+	2.82042i	−0.170284	+	0.0983137i	−0.582720	−	0.812673i	$-0.698012\pi$
$823$	−4.88511	+	2.82042i	−0.170284	+	0.0983137i	0.412436	+	0.910987i	$0.364678\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$		−	19.2368i		−	0.668929i	−0.942408	−	0.334464i	$-0.891445\pi$
$827$		−	19.2368i		−	0.668929i	0.942408	−	0.334464i	$-0.108555\pi$
$828$		0			0
$829$	13.6762	+	23.6878i	0.474993	+	0.822712i	0.999590	−	0.0286386i	$-0.00911719\pi$
$829$	13.6762	+	23.6878i	0.474993	+	0.822712i	−0.524597	+	0.851351i	$0.675784\pi$
$830$		0			0
$831$	11.2549	−	19.4941i	0.390428	−	0.676241i
$832$		0			0
$833$	−16.0147	+	8.59177i	−0.554877	+	0.297687i
$834$		0			0
$835$		0			0
$836$		0			0
$837$	−24.3429	+	14.0544i	−0.841414	+	0.485790i
$838$		0			0
$839$	−16.5425			−0.571111			−0.285556	−	0.958362i	$-0.592178\pi$
$839$	−16.5425			−0.571111			−0.285556	+	0.958362i	$0.592178\pi$
$840$		0			0
$841$	9.77156			0.336950
$842$		0			0
$843$	−37.3554	+	21.5672i	−1.28659	+	0.742813i
$844$		0			0
$845$		0			0
$846$		0			0
$847$	20.4510	+	12.2365i	0.702705	+	0.420450i
$848$		0			0
$849$	−7.21301	+	12.4933i	−0.247550	+	0.428769i
$850$		0			0
$851$	−6.67024	−	11.5532i	−0.228653	−	0.396039i
$852$		0			0
$853$			0.633103i			0.0216770i	0.999941	+	0.0108385i	$0.00345008\pi$
$853$			0.633103i			0.0216770i	−0.999941	+	0.0108385i	$0.996550\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	5.33099	−	3.07785i	0.182103	−	0.105137i	−0.406177	−	0.913794i	$-0.633138\pi$
$857$	5.33099	−	3.07785i	0.182103	−	0.105137i	0.588280	+	0.808657i	$0.299805\pi$
$858$		0			0
$859$	−12.7554	+	22.0929i	−0.435208	+	0.753802i	−0.997313	−	0.0732643i	$-0.976658\pi$
$859$	−12.7554	+	22.0929i	−0.435208	+	0.753802i	0.562105	+	0.827066i	$0.309992\pi$
$860$		0			0
$861$	−6.19712	−	11.1310i	−0.211197	−	0.379344i
$862$		0			0
$863$	11.0391	+	6.37346i	0.375777	+	0.216955i	0.675979	−	0.736921i	$-0.263721\pi$
$863$	11.0391	+	6.37346i	0.375777	+	0.216955i	−0.300202	+	0.953876i	$0.597054\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$		−	13.8225i		−	0.469435i
$868$		0			0
$869$	−1.24123			−0.0421058
$870$		0			0
$871$	19.6982	+	34.1183i	0.667449	+	1.15605i
$872$		0			0
$873$	−3.31871	−	1.91606i	−0.112321	−	0.0648488i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	36.8769	+	21.2909i	1.24524	+	0.718941i	0.970157	−	0.242478i	$-0.0779604\pi$
$877$	36.8769	+	21.2909i	1.24524	+	0.718941i	0.275086	+	0.961420i	$0.411294\pi$
$878$		0			0
$879$	−5.52687	−	9.57283i	−0.186417	−	0.322883i
$880$		0			0
$881$	−23.0033			−0.775001			−0.387500	−	0.921870i	$-0.626661\pi$
$881$	−23.0033			−0.775001			−0.387500	+	0.921870i	$0.626661\pi$
$882$		0			0
$883$		−	1.92303i		−	0.0647151i	−0.999476	−	0.0323575i	$-0.989698\pi$
$883$		−	1.92303i		−	0.0647151i	0.999476	−	0.0323575i	$-0.0103015\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−17.9725	−	10.3764i	−0.603459	−	0.348407i	0.166942	−	0.985967i	$-0.446611\pi$
$887$	−17.9725	−	10.3764i	−0.603459	−	0.348407i	−0.770401	+	0.637560i	$0.779944\pi$
$888$		0			0
$889$	−26.1871	−	0.408360i	−0.878286	−	0.0136959i
$890$		0			0
$891$	2.85251	−	4.94069i	0.0955627	−	0.165519i
$892$		0			0
$893$	−11.0175	+	6.36097i	−0.368687	+	0.212862i
$894$		0			0
$895$		0			0
$896$		0			0
$897$			13.7324i			0.458510i
$898$		0			0
$899$	15.5214	+	26.8839i	0.517668	+	0.896627i
$900$		0			0
$901$	−16.5981	+	28.7487i	−0.552962	+	0.957759i
$902$		0			0
$903$	22.5766	−	12.5694i	0.751303	−	0.418283i
$904$		0			0
$905$		0			0
$906$		0			0
$907$	−3.25876	+	1.88144i	−0.108205	+	0.0624723i	−0.553126	−	0.833098i	$-0.686565\pi$
$907$	−3.25876	+	1.88144i	−0.108205	+	0.0624723i	0.444921	+	0.895570i	$0.353232\pi$
$908$		0			0
$909$	17.2175			0.571069
$910$		0			0
$911$	−19.0618			−0.631546			−0.315773	−	0.948835i	$-0.602264\pi$
$911$	−19.0618			−0.631546			−0.315773	+	0.948835i	$0.602264\pi$
$912$		0			0
$913$	4.76930	−	2.75356i	0.157841	−	0.0911294i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	−36.2486	−	21.6887i	−1.19703	−	0.716223i
$918$		0			0
$919$	9.61334	−	16.6508i	0.317115	−	0.549259i	−0.662770	−	0.748823i	$-0.730619\pi$
$919$	9.61334	−	16.6508i	0.317115	−	0.549259i	0.979885	+	0.199564i	$0.0639526\pi$
$920$		0			0
$921$	−17.7626	−	30.7658i	−0.585299	−	1.01377i
$922$		0			0
$923$		−	53.5945i		−	1.76408i
$924$		0			0
$925$		0			0
$926$		0			0
$927$	16.3899	−	9.46270i	0.538314	−	0.310796i
$928$		0			0
$929$	26.1621	−	45.3141i	0.858350	−	1.48671i	−0.0151511	−	0.999885i	$-0.504823\pi$
$929$	26.1621	−	45.3141i	0.858350	−	1.48671i	0.873502	−	0.486821i	$-0.161844\pi$
$930$		0			0
$931$	−4.28652	+	6.91701i	−0.140485	+	0.226696i
$932$		0			0
$933$	−17.1116	−	9.87939i	−0.560209	−	0.323437i
$934$		0			0
$935$		0			0
$936$		0			0
$937$		−	36.0145i		−	1.17654i	−0.808663	−	0.588272i	$-0.799808\pi$
$937$		−	36.0145i		−	1.17654i	0.808663	−	0.588272i	$-0.200192\pi$
$938$		0			0
$939$	41.1198			1.34189
$940$		0			0
$941$	−15.4108	−	26.6922i	−0.502376	−	0.870141i	−0.999996	−	0.00274619i	$-0.999126\pi$
$941$	−15.4108	−	26.6922i	−0.502376	−	0.870141i	0.497620	−	0.867395i	$-0.334207\pi$
$942$		0			0
$943$	−4.87171	−	2.81268i	−0.158645	−	0.0915935i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	6.03341	+	3.48339i	0.196060	+	0.113195i	0.594816	−	0.803862i	$-0.297225\pi$
$947$	6.03341	+	3.48339i	0.196060	+	0.113195i	−0.398757	+	0.917057i	$0.630558\pi$
$948$		0			0
$949$	−11.3892	−	19.7266i	−0.369709	−	0.640354i
$950$		0			0
$951$	−22.7311			−0.737107
$952$		0			0
$953$			6.84491i			0.221728i	0.993836	+	0.110864i	$0.0353619\pi$
$953$			6.84491i			0.221728i	−0.993836	+	0.110864i	$0.964638\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$	−10.2547	−	5.92056i	−0.331488	−	0.191384i
$958$		0			0
$959$	16.3730	+	29.4085i	0.528711	+	0.949649i
$960$		0			0
$961$	3.07263	−	5.32196i	0.0991172	−	0.171676i
$962$		0			0
$963$	18.2954	−	10.5628i	0.589560	−	0.340383i
$964$		0			0
$965$		0			0
$966$		0			0
$967$		−	19.2909i		−	0.620352i	−0.950679	−	0.310176i	$-0.899612\pi$
$967$		−	19.2909i		−	0.620352i	0.950679	−	0.310176i	$-0.100388\pi$
$968$		0			0
$969$	2.03318	+	3.52158i	0.0653153	+	0.113129i
$970$		0			0
$971$	−21.3726	+	37.0184i	−0.685879	+	1.18798i	0.287281	+	0.957846i	$0.407249\pi$
$971$	−21.3726	+	37.0184i	−0.685879	+	1.18798i	−0.973160	+	0.230130i	$0.926085\pi$
$972$		0			0
$973$	0.315695	−	20.2447i	0.0101207	−	0.649015i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	10.8382	−	6.25743i	0.346744	−	0.200193i	−0.316506	−	0.948590i	$-0.602510\pi$
$977$	10.8382	−	6.25743i	0.346744	−	0.200193i	0.663250	+	0.748398i	$0.269176\pi$
$978$		0			0
$979$	−8.41685			−0.269004
$980$		0			0
$981$	−14.4953			−0.462798
$982$		0			0
$983$	−25.2334	+	14.5685i	−0.804821	+	0.464663i	−0.845154	−	0.534523i	$-0.820491\pi$
$983$	−25.2334	+	14.5685i	−0.804821	+	0.464663i	0.0403333	+	0.999186i	$0.487158\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$	−0.608239	+	39.0048i	−0.0193604	+	1.24154i
$988$		0			0
$989$	5.70486	−	9.88111i	0.181404	−	0.314201i
$990$		0			0
$991$	−30.0107	−	51.9801i	−0.953322	−	1.65120i	−0.738161	−	0.674624i	$-0.764306\pi$
$991$	−30.0107	−	51.9801i	−0.953322	−	1.65120i	−0.215161	−	0.976579i	$-0.569028\pi$
$992$		0			0
$993$		−	19.3682i		−	0.614630i
$994$		0			0
$995$		0			0
$996$		0			0
$997$	−30.8296	+	17.7995i	−0.976383	+	0.563715i	−0.901176	−	0.433453i	$-0.857295\pi$
$997$	−30.8296	+	17.7995i	−0.976383	+	0.563715i	−0.0752070	+	0.997168i	$0.523962\pi$
$998$		0			0
$999$	23.8935	−	41.3848i	0.755958	−	1.30936i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1400.2.bh.h.849.2		12
5.2	odd	4		1400.2.q.k.401.2	yes	6
5.3	odd	4		1400.2.q.i.401.2	✓	6
5.4	even	2	inner	1400.2.bh.h.849.5		12
7.4	even	3	inner	1400.2.bh.h.249.5		12
35.2	odd	12		9800.2.a.cc.1.2		3
35.4	even	6	inner	1400.2.bh.h.249.2		12
35.12	even	12		9800.2.a.ch.1.2		3
35.18	odd	12		1400.2.q.i.1201.2	yes	6
35.23	odd	12		9800.2.a.ci.1.2		3
35.32	odd	12		1400.2.q.k.1201.2	yes	6
35.33	even	12		9800.2.a.cb.1.2		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1400.2.q.i.401.2	✓	6	5.3	odd	4
1400.2.q.i.1201.2	yes	6	35.18	odd	12
1400.2.q.k.401.2	yes	6	5.2	odd	4
1400.2.q.k.1201.2	yes	6	35.32	odd	12
1400.2.bh.h.249.2		12	35.4	even	6	inner
1400.2.bh.h.249.5		12	7.4	even	3	inner
1400.2.bh.h.849.2		12	1.1	even	1	trivial
1400.2.bh.h.849.5		12	5.4	even	2	inner
9800.2.a.cb.1.2		3	35.33	even	12
9800.2.a.cc.1.2		3	35.2	odd	12
9800.2.a.ch.1.2		3	35.12	even	12
9800.2.a.ci.1.2		3	35.23	odd	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)

\(f(q)\)	\(=\)	\(q+(-1.16679 + 0.673648i) q^{3} +(-0.0412527 + 2.64543i) q^{7} +(-0.592396 + 1.02606i) q^{9} +O(q^{10})\)	\(q+(-1.16679 + 0.673648i) q^{3} +(-0.0412527 + 2.64543i) q^{7} +(-0.592396 + 1.02606i) q^{9} +(-0.705737 - 1.22237i) q^{11} +6.47565i q^{13} +(2.24843 - 1.29813i) q^{17} +(0.581252 - 1.00676i) q^{19} +(-1.73396 - 3.11446i) q^{21} +(-1.36310 - 0.786989i) q^{23} -5.63816i q^{27} -6.22668 q^{29} +(-2.49273 - 4.31753i) q^{31} +(1.64690 + 0.950837i) q^{33} +(7.34013 + 4.23783i) q^{37} +(-4.36231 - 7.55574i) q^{39} +3.57398 q^{41} +7.24897i q^{43} +(-9.47740 - 5.47178i) q^{47} +(-6.99660 - 0.218262i) q^{49} +(-1.74897 + 3.02931i) q^{51} +(-11.0731 + 6.39306i) q^{53} +1.56624i q^{57} +(-1.02094 - 1.76833i) q^{59} +(0.307934 - 0.533356i) q^{61} +(-2.68993 - 1.60947i) q^{63} +(5.26871 - 3.04189i) q^{67} +2.12061 q^{69} -8.27631 q^{71} +(-3.04628 + 1.75877i) q^{73} +(3.26281 - 1.81655i) q^{77} +(0.439693 - 0.761570i) q^{79} +(2.02094 + 3.50038i) q^{81} +3.90167i q^{83} +(7.26525 - 4.19459i) q^{87} +(2.98158 - 5.16425i) q^{89} +(-17.1309 - 0.267138i) q^{91} +(5.81699 + 3.35844i) q^{93} +3.23442i q^{97} +1.67230 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q+O(q^{10}) \) 12 * q	\( 12 q + 12 q^{11} + 12 q^{19} - 30 q^{21} - 48 q^{29} + 6 q^{31} + 12 q^{39} + 12 q^{41} + 30 q^{51} - 6 q^{59} - 18 q^{61} + 48 q^{69} + 36 q^{71} - 6 q^{79} + 18 q^{81} + 12 q^{89} - 102 q^{91} + 36 q^{99}+O(q^{100}) \) 12 * q + 12 * q^11 + 12 * q^19 - 30 * q^21 - 48 * q^29 + 6 * q^31 + 12 * q^39 + 12 * q^41 + 30 * q^51 - 6 * q^59 - 18 * q^61 + 48 * q^69 + 36 * q^71 - 6 * q^79 + 18 * q^81 + 12 * q^89 - 102 * q^91 + 36 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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