LMFDB - Embedded newform 1400.2.bh.h.849.1

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			849.1
Root			$0.642788 + 0.766044i$ of defining polynomial
Character	$\chi$	$=$	1400.849
Dual form			1400.2.bh.h.249.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.19285 + 1.26604i) q^{3} +(2.31164 - 1.28699i) q^{7} +(1.70574 - 2.95442i) q^{9} +O(q^{10})$	$q+(-2.19285 + 1.26604i) q^{3} +(2.31164 - 1.28699i) q^{7} +(1.70574 - 2.95442i) q^{9} +(2.11334 + 3.66041i) q^{11} -5.98545i q^{13} +(-6.61484 + 3.81908i) q^{17} +(3.47178 - 6.01330i) q^{19} +(-3.43969 + 5.74881i) q^{21} +(-1.48686 - 0.858441i) q^{23} +1.04189i q^{27} -5.18479 q^{29} +(0.254900 + 0.441500i) q^{31} +(-9.26849 - 5.35117i) q^{33} +(-3.45150 - 1.99273i) q^{37} +(7.57785 + 13.1252i) q^{39} +3.71688 q^{41} -4.17024i q^{43} +(-1.64019 - 0.946967i) q^{47} +(3.68732 - 5.95010i) q^{49} +(9.67024 - 16.7494i) q^{51} +(-5.53553 + 3.19594i) q^{53} +17.5817i q^{57} +(-2.79813 - 4.84651i) q^{59} +(2.15657 - 3.73530i) q^{61} +(0.140732 - 9.02481i) q^{63} +(11.4251 - 6.59627i) q^{67} +4.34730 q^{69} +5.08378 q^{71} +(4.66717 - 2.69459i) q^{73} +(9.59619 + 5.74170i) q^{77} +(-0.673648 + 1.16679i) q^{79} +(3.79813 + 6.57856i) q^{81} -8.70233i q^{83} +(11.3695 - 6.56418i) q^{87} +(5.42262 - 9.39225i) q^{89} +(-7.70321 - 13.8362i) q^{91} +(-1.11792 - 0.645430i) q^{93} -13.6800i q^{97} +14.4192 q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	−2.19285	+	1.26604i	−1.26604	+	0.730951i	−0.974237	−	0.225526i	$-0.927590\pi$
$3$	−2.19285	+	1.26604i	−1.26604	+	0.730951i	−0.291807	+	0.956477i	$0.594257\pi$
$4$		0			0
$5$		0			0
$5$		0			0
$6$		0			0
$7$	2.31164	−	1.28699i	0.873716	−	0.486436i
$7$	2.31164	−	1.28699i	0.873716	−	0.486436i
$8$		0			0
$9$	1.70574	−	2.95442i	0.568579	−	0.984808i
$10$		0			0
$11$	2.11334	+	3.66041i	0.637196	+	1.10366i	0.986045	+	0.166477i	$0.0532393\pi$
$11$	2.11334	+	3.66041i	0.637196	+	1.10366i	−0.348849	+	0.937179i	$0.613427\pi$
$12$		0			0
$13$		−	5.98545i		−	1.66007i	−0.557714	−	0.830033i	$-0.688322\pi$
$13$		−	5.98545i		−	1.66007i	0.557714	−	0.830033i	$-0.311678\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−6.61484	+	3.81908i	−1.60433	+	0.926262i	−0.613727	+	0.789518i	$0.710331\pi$
$17$	−6.61484	+	3.81908i	−1.60433	+	0.926262i	−0.990606	+	0.136744i	$0.956336\pi$
$18$		0			0
$19$	3.47178	−	6.01330i	0.796481	−	1.37955i	−0.125413	−	0.992105i	$-0.540026\pi$
$19$	3.47178	−	6.01330i	0.796481	−	1.37955i	0.921894	−	0.387441i	$-0.126641\pi$
$20$		0			0
$21$	−3.43969	+	5.74881i	−0.750602	+	1.25449i
$22$		0			0
$23$	−1.48686	−	0.858441i	−0.310032	−	0.178997i	0.336909	−	0.941537i	$-0.390619\pi$
$23$	−1.48686	−	0.858441i	−0.310032	−	0.178997i	−0.646941	+	0.762540i	$0.723952\pi$
$24$		0			0
$25$		0			0
$26$		0			0
$27$			1.04189i			0.200512i
$28$		0			0
$29$	−5.18479			−0.962792			−0.481396	−	0.876503i	$-0.659870\pi$
$29$	−5.18479			−0.962792			−0.481396	+	0.876503i	$0.659870\pi$
$30$		0			0
$31$	0.254900	+	0.441500i	0.0457814	+	0.0792957i	0.888008	−	0.459828i	$-0.152089\pi$
$31$	0.254900	+	0.441500i	0.0457814	+	0.0792957i	−0.842227	+	0.539124i	$0.818756\pi$
$32$		0			0
$33$	−9.26849	−	5.35117i	−1.61344	−	0.931519i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	−3.45150	−	1.99273i	−0.567424	−	0.327602i	0.188696	−	0.982036i	$-0.439574\pi$
$37$	−3.45150	−	1.99273i	−0.567424	−	0.327602i	−0.756120	+	0.654433i	$0.772907\pi$
$38$		0			0
$39$	7.57785	+	13.1252i	1.21343	+	2.10172i
$40$		0			0
$41$	3.71688			0.580479			0.290240	−	0.956954i	$-0.406265\pi$
$41$	3.71688			0.580479			0.290240	+	0.956954i	$0.406265\pi$
$42$		0			0
$43$		−	4.17024i		−	0.635956i	−0.948098	−	0.317978i	$-0.896996\pi$
$43$		−	4.17024i		−	0.635956i	0.948098	−	0.317978i	$-0.103004\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−1.64019	−	0.946967i	−0.239247	−	0.138129i	0.375584	−	0.926789i	$-0.377442\pi$
$47$	−1.64019	−	0.946967i	−0.239247	−	0.138129i	−0.614831	+	0.788659i	$0.710776\pi$
$48$		0			0
$49$	3.68732	−	5.95010i	0.526760	−	0.850014i
$50$		0			0
$51$	9.67024	−	16.7494i	1.35411	−	2.34538i
$52$		0			0
$53$	−5.53553	+	3.19594i	−0.760363	+	0.438996i	−0.829426	−	0.558617i	$-0.811332\pi$
$53$	−5.53553	+	3.19594i	−0.760363	+	0.438996i	0.0690632	+	0.997612i	$0.477999\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$			17.5817i			2.32876i
$58$		0			0
$59$	−2.79813	−	4.84651i	−0.364286	−	0.630962i	0.624375	−	0.781124i	$-0.285354\pi$
$59$	−2.79813	−	4.84651i	−0.364286	−	0.630962i	−0.988661	+	0.150163i	$0.952020\pi$
$60$		0			0
$61$	2.15657	−	3.73530i	0.276121	−	0.478256i	−0.694296	−	0.719689i	$-0.744284\pi$
$61$	2.15657	−	3.73530i	0.276121	−	0.478256i	0.970417	+	0.241434i	$0.0776176\pi$
$62$		0			0
$63$	0.140732	−	9.02481i	0.0177306	−	1.13702i
$64$		0			0
$65$		0			0
$66$		0			0
$67$	11.4251	−	6.59627i	1.39579	−	0.805862i	0.401846	−	0.915707i	$-0.368369\pi$
$67$	11.4251	−	6.59627i	1.39579	−	0.805862i	0.993949	+	0.109845i	$0.0350355\pi$
$68$		0			0
$69$	4.34730			0.523353
$70$		0			0
$71$	5.08378			0.603333			0.301667	−	0.953413i	$-0.402457\pi$
$71$	5.08378			0.603333			0.301667	+	0.953413i	$0.402457\pi$
$72$		0			0
$73$	4.66717	−	2.69459i	0.546251	−	0.315378i	−0.201357	−	0.979518i	$-0.564535\pi$
$73$	4.66717	−	2.69459i	0.546251	−	0.315378i	0.747609	+	0.664140i	$0.231202\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	9.59619	+	5.74170i	1.09359	+	0.654327i
$78$		0			0
$79$	−0.673648	+	1.16679i	−0.0757913	+	0.131274i	−0.901430	−	0.432925i	$-0.857482\pi$
$79$	−0.673648	+	1.16679i	−0.0757913	+	0.131274i	0.825639	+	0.564199i	$0.190815\pi$
$80$		0			0
$81$	3.79813	+	6.57856i	0.422015	+	0.730951i
$82$		0			0
$83$		−	8.70233i		−	0.955205i	−0.878576	−	0.477603i	$-0.841506\pi$
$83$		−	8.70233i		−	0.955205i	0.878576	−	0.477603i	$-0.158494\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$	11.3695	−	6.56418i	1.21894	−	0.703754i
$88$		0			0
$89$	5.42262	−	9.39225i	0.574796	−	0.995577i	−0.421267	−	0.906937i	$-0.638415\pi$
$89$	5.42262	−	9.39225i	0.574796	−	0.995577i	0.996064	−	0.0886401i	$-0.0282521\pi$
$90$		0			0
$91$	−7.70321	−	13.8362i	−0.807516	−	1.45043i
$92$		0			0
$93$	−1.11792	−	0.645430i	−0.115923	−	0.0669279i
$94$		0			0
$95$		0			0
$96$		0			0
$97$		−	13.6800i		−	1.38900i	−0.719494	−	0.694499i	$-0.755626\pi$
$97$		−	13.6800i		−	1.38900i	0.719494	−	0.694499i	$-0.244374\pi$
$98$		0			0
$99$	14.4192			1.44919
$100$		0			0
$101$	−5.56031	−	9.63073i	−0.553271	−	0.958294i	−0.998036	−	0.0626464i	$-0.980046\pi$
$101$	−5.56031	−	9.63073i	−0.553271	−	0.958294i	0.444765	−	0.895648i	$-0.353287\pi$
$102$		0			0
$103$	16.7368	+	9.66297i	1.64912	+	0.952121i	0.977422	+	0.211297i	$0.0677688\pi$
$103$	16.7368	+	9.66297i	1.64912	+	0.952121i	0.671700	+	0.740823i	$0.265565\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	8.06980	+	4.65910i	0.780137	+	0.450412i	0.836479	−	0.547999i	$-0.184610\pi$
$107$	8.06980	+	4.65910i	0.780137	+	0.450412i	−0.0563419	+	0.998412i	$0.517944\pi$
$108$		0			0
$109$	−2.34002	−	4.05304i	−0.224133	−	0.388211i	0.731926	−	0.681385i	$-0.238622\pi$
$109$	−2.34002	−	4.05304i	−0.224133	−	0.388211i	−0.956059	+	0.293174i	$0.905288\pi$
$110$		0			0
$111$	10.0915			0.957845
$112$		0			0
$113$		−	3.57398i		−	0.336212i	−0.985769	−	0.168106i	$-0.946235\pi$
$113$		−	3.57398i		−	0.336212i	0.985769	−	0.168106i	$-0.0537650\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$	−17.6836	−	10.2096i	−1.63485	−	0.943879i
$118$		0			0
$119$	−10.3760	+	17.3415i	−0.951165	+	1.58970i
$120$		0			0
$121$	−3.43242	+	5.94512i	−0.312038	+	0.540466i
$122$		0			0
$123$	−8.15058	+	4.70574i	−0.734913	+	0.424302i
$124$		0			0
$125$		0			0
$126$		0			0
$127$			21.6040i			1.91705i	0.285016	+	0.958523i	$0.408001\pi$
$127$			21.6040i			1.91705i	−0.285016	+	0.958523i	$0.591999\pi$
$128$		0			0
$129$	5.27972	+	9.14473i	0.464853	+	0.805149i
$130$		0			0
$131$	1.73055	−	2.99740i	0.151199	−	0.261884i	−0.780469	−	0.625194i	$-0.785020\pi$
$131$	1.73055	−	2.99740i	0.151199	−	0.261884i	0.931669	+	0.363309i	$0.118353\pi$
$132$		0			0
$133$	0.286441	−	18.3687i	0.0248375	−	1.59277i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	11.3888	−	6.57532i	0.973010	−	0.561768i	0.0728576	−	0.997342i	$-0.476788\pi$
$137$	11.3888	−	6.57532i	0.973010	−	0.561768i	0.900153	+	0.435575i	$0.143455\pi$
$138$		0			0
$139$	−6.46791			−0.548601			−0.274301	−	0.961644i	$-0.588446\pi$
$139$	−6.46791			−0.548601			−0.274301	+	0.961644i	$0.588446\pi$
$140$		0			0
$141$	4.79561			0.403863
$142$		0			0
$143$	21.9092	−	12.6493i	1.83214	−	1.05779i
$144$		0			0
$145$		0			0
$146$		0			0
$147$	−0.552659	+	17.7160i	−0.0455826	+	1.46119i
$148$		0			0
$149$	−2.28699	+	3.96118i	−0.187357	+	0.324513i	−0.944368	−	0.328890i	$-0.893326\pi$
$149$	−2.28699	+	3.96118i	−0.187357	+	0.324513i	0.757011	+	0.653402i	$0.226659\pi$
$150$		0			0
$151$	−2.57785	−	4.46496i	−0.209782	−	0.363354i	0.741864	−	0.670551i	$-0.233942\pi$
$151$	−2.57785	−	4.46496i	−0.209782	−	0.363354i	−0.951646	+	0.307197i	$0.900609\pi$
$152$		0			0
$153$			26.0574i			2.10661i
$154$		0			0
$155$		0			0
$156$		0			0
$157$	−11.8133	+	6.82042i	−0.942805	+	0.544329i	−0.890839	−	0.454320i	$-0.849882\pi$
$157$	−11.8133	+	6.82042i	−0.942805	+	0.544329i	−0.0519668	+	0.998649i	$0.516549\pi$
$158$		0			0
$159$	8.09240	−	14.0164i	0.641769	−	1.11158i
$160$		0			0
$161$	−4.54189	−	0.0708260i	−0.357951	−	0.00558187i
$162$		0			0
$163$	0.300767	+	0.173648i	0.0235579	+	0.0136012i	0.511733	−	0.859145i	$-0.329004\pi$
$163$	0.300767	+	0.173648i	0.0235579	+	0.0136012i	−0.488175	+	0.872746i	$0.662337\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$			1.72874i			0.133774i	0.997761	+	0.0668870i	$0.0213067\pi$
$167$			1.72874i			0.133774i	−0.997761	+	0.0668870i	$0.978693\pi$
$168$		0			0
$169$	−22.8256			−1.75582
$170$		0			0
$171$	−11.8439	−	20.5142i	−0.905725	−	1.56876i
$172$		0			0
$173$	−11.5465	−	6.66637i	−0.877864	−	0.506835i	−0.00791050	−	0.999969i	$-0.502518\pi$
$173$	−11.5465	−	6.66637i	−0.877864	−	0.506835i	−0.869954	+	0.493134i	$0.835851\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	12.2718	+	7.08512i	0.922404	+	0.532550i
$178$		0			0
$179$	−7.80066	−	13.5111i	−0.583049	−	1.00987i	−0.995116	−	0.0987163i	$-0.968526\pi$
$179$	−7.80066	−	13.5111i	−0.583049	−	1.00987i	0.412067	−	0.911154i	$-0.364807\pi$
$180$		0			0
$181$	19.6382			1.45969			0.729846	−	0.683611i	$-0.239592\pi$
$181$	19.6382			1.45969			0.729846	+	0.683611i	$0.239592\pi$
$182$		0			0
$183$			10.9213i			0.807324i
$184$		0			0
$185$		0			0
$186$		0			0
$187$	−27.9588	−	16.1420i	−2.04455	−	1.18042i
$188$		0			0
$189$	1.34090	+	2.40847i	0.0975361	+	0.175190i
$190$		0			0
$191$	−5.71213	+	9.89371i	−0.413315	+	0.715883i	−0.995250	−	0.0973522i	$-0.968963\pi$
$191$	−5.71213	+	9.89371i	−0.413315	+	0.715883i	0.581935	+	0.813236i	$0.302296\pi$
$192$		0			0
$193$	−13.7563	+	7.94222i	−0.990202	+	0.571693i	−0.905335	−	0.424699i	$-0.860380\pi$
$193$	−13.7563	+	7.94222i	−0.990202	+	0.571693i	−0.0848674	+	0.996392i	$0.527047\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$		−	24.8435i		−	1.77002i	−0.465567	−	0.885012i	$-0.654150\pi$
$197$		−	24.8435i		−	1.77002i	0.465567	−	0.885012i	$-0.345850\pi$
$198$		0			0
$199$	0.230085	+	0.398519i	0.0163103	+	0.0282503i	0.874065	−	0.485808i	$-0.161475\pi$
$199$	0.230085	+	0.398519i	0.0163103	+	0.0282503i	−0.857755	+	0.514059i	$0.828141\pi$
$200$		0			0
$201$	−16.7023	+	28.9293i	−1.17809	+	2.04051i
$202$		0			0
$203$	−11.9854	+	6.67277i	−0.841207	+	0.468337i
$204$		0			0
$205$		0			0
$206$		0			0
$207$	−5.07239	+	2.92855i	−0.352556	+	0.203548i
$208$		0			0
$209$	29.3482			2.03006
$210$		0			0
$211$	0.622674			0.0428667			0.0214333	−	0.999770i	$-0.493177\pi$
$211$	0.622674			0.0428667			0.0214333	+	0.999770i	$0.493177\pi$
$212$		0			0
$213$	−11.1480	+	6.43629i	−0.763847	+	0.441007i
$214$		0			0
$215$		0			0
$216$		0			0
$217$	1.15744	+	0.692533i	0.0785723	+	0.0470122i
$218$		0			0
$219$	−6.82295	+	11.8177i	−0.461052	+	0.798566i
$220$		0			0
$221$	22.8589	+	39.5928i	1.53766	+	2.66330i
$222$		0			0
$223$			18.7151i			1.25326i	0.779318	+	0.626629i	$0.215566\pi$
$223$			18.7151i			1.25326i	−0.779318	+	0.626629i	$0.784434\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	24.5925	−	14.1985i	1.63226	−	0.942385i	0.648864	−	0.760904i	$-0.275244\pi$
$227$	24.5925	−	14.1985i	1.63226	−	0.942385i	0.983394	−	0.181481i	$-0.0580891\pi$
$228$		0			0
$229$	−3.69981	+	6.40825i	−0.244490	+	0.423469i	−0.961988	−	0.273091i	$-0.911954\pi$
$229$	−3.69981	+	6.40825i	−0.244490	+	0.423469i	0.717498	+	0.696561i	$0.245287\pi$
$230$		0			0
$231$	−28.3123	−	0.441500i	−1.86281	−	0.0290486i
$232$		0			0
$233$	3.55829	+	2.05438i	0.233111	+	0.134587i	0.612006	−	0.790853i	$-0.290363\pi$
$233$	3.55829	+	2.05438i	0.233111	+	0.134587i	−0.378895	+	0.925440i	$0.623696\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$		−	3.41147i		−	0.221599i
$238$		0			0
$239$	−20.5449			−1.32894			−0.664469	−	0.747316i	$-0.731342\pi$
$239$	−20.5449			−1.32894			−0.664469	+	0.747316i	$0.731342\pi$
$240$		0			0
$241$	−0.850700	−	1.47346i	−0.0547984	−	0.0949136i	0.837325	−	0.546706i	$-0.184118\pi$
$241$	−0.850700	−	1.47346i	−0.0547984	−	0.0949136i	−0.892123	+	0.451792i	$0.850785\pi$
$242$		0			0
$243$	−19.3644	−	11.1800i	−1.24223	−	0.717200i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	−35.9923	−	20.7802i	−2.29014	−	1.32221i
$248$		0			0
$249$	11.0175	+	19.0829i	0.698208	+	1.20933i
$250$		0			0
$251$	−13.9145			−0.878273			−0.439137	−	0.898420i	$-0.644716\pi$
$251$	−13.9145			−0.878273			−0.439137	+	0.898420i	$0.644716\pi$
$252$		0			0
$253$		−	7.25671i		−	0.456226i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−25.8830	−	14.9436i	−1.61454	−	0.932154i	−0.988300	−	0.152522i	$-0.951261\pi$
$257$	−25.8830	−	14.9436i	−1.61454	−	0.932154i	−0.626238	−	0.779632i	$-0.715406\pi$
$258$		0			0
$259$	−10.5432	−	0.164411i	−0.655125	−	0.0102160i
$260$		0			0
$261$	−8.84389	+	15.3181i	−0.547423	+	0.948165i
$262$		0			0
$263$	17.0568	−	9.84776i	1.05177	−	0.607239i	0.128625	−	0.991693i	$-0.458944\pi$
$263$	17.0568	−	9.84776i	1.05177	−	0.607239i	0.923144	+	0.384454i	$0.125610\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$			27.4611i			1.68059i
$268$		0			0
$269$	−2.74628	−	4.75670i	−0.167444	−	0.290021i	0.770077	−	0.637951i	$-0.220218\pi$
$269$	−2.74628	−	4.75670i	−0.167444	−	0.290021i	−0.937520	+	0.347930i	$0.886885\pi$
$270$		0			0
$271$	−6.82635	+	11.8236i	−0.414671	+	0.718232i	−0.995394	−	0.0958697i	$-0.969437\pi$
$271$	−6.82635	+	11.8236i	−0.414671	+	0.718232i	0.580723	+	0.814102i	$0.302770\pi$
$272$		0			0
$273$	34.4092	+	20.5881i	2.08254	+	1.24605i
$274$		0			0
$275$		0			0
$276$		0			0
$277$	−10.0813	+	5.82042i	−0.605725	+	0.349715i	−0.771290	−	0.636483i	$-0.780388\pi$
$277$	−10.0813	+	5.82042i	−0.605725	+	0.349715i	0.165566	+	0.986199i	$0.447055\pi$
$278$		0			0
$279$	1.73917			0.104121
$280$		0			0
$281$	0.270325			0.0161263			0.00806313	−	0.999967i	$-0.497433\pi$
$281$	0.270325			0.0161263			0.00806313	+	0.999967i	$0.497433\pi$
$282$		0			0
$283$	4.88511	−	2.82042i	0.290390	−	0.167657i	−0.347728	−	0.937596i	$-0.613047\pi$
$283$	4.88511	−	2.82042i	0.290390	−	0.167657i	0.638118	+	0.769939i	$0.279713\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	8.59208	−	4.78359i	0.507174	−	0.282366i
$288$		0			0
$289$	20.6707	−	35.8027i	1.21592	−	2.10604i
$290$		0			0
$291$	17.3195	+	29.9983i	1.01529	+	1.75853i
$292$		0			0
$293$			17.5398i			1.02469i	0.858780	+	0.512344i	$0.171223\pi$
$293$			17.5398i			1.02469i	−0.858780	+	0.512344i	$0.828777\pi$
$294$		0			0
$295$		0			0
$296$		0			0
$297$	−3.81374	+	2.20187i	−0.221296	+	0.127765i
$298$		0			0
$299$	−5.13816	+	8.89955i	−0.297147	+	0.514674i
$300$		0			0
$301$	−5.36706	−	9.64009i	−0.309352	−	0.555645i
$302$		0			0
$303$	24.3859	+	14.0792i	1.40093	+	0.808828i
$304$		0			0
$305$		0			0
$306$		0			0
$307$			4.24392i			0.242213i	0.992640	+	0.121107i	$0.0386443\pi$
$307$			4.24392i			0.242213i	−0.992640	+	0.121107i	$0.961356\pi$
$308$		0			0
$309$	−48.9350			−2.78381
$310$		0			0
$311$	3.02229	+	5.23476i	0.171378	+	0.296836i	0.938902	−	0.344185i	$-0.111845\pi$
$311$	3.02229	+	5.23476i	0.171378	+	0.296836i	−0.767524	+	0.641021i	$0.778511\pi$
$312$		0			0
$313$	2.33439	+	1.34776i	0.131948	+	0.0761801i	0.564521	−	0.825419i	$-0.309061\pi$
$313$	2.33439	+	1.34776i	0.131948	+	0.0761801i	−0.432573	+	0.901599i	$0.642394\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	26.4290	+	15.2588i	1.48440	+	0.857018i	0.999843	−	0.0177423i	$-0.00564785\pi$
$317$	26.4290	+	15.2588i	1.48440	+	0.857018i	0.484556	+	0.874760i	$0.338981\pi$
$318$		0			0
$319$	−10.9572	−	18.9785i	−0.613487	−	1.06259i
$320$		0			0
$321$	−23.5945			−1.31692
$322$		0			0
$323$			53.0360i			2.95100i
$324$		0			0
$325$		0			0
$326$		0			0
$327$	10.2627	+	5.92514i	0.567526	+	0.327661i
$328$		0			0
$329$	−5.01027	−	0.0781298i	−0.276225	−	0.00430744i
$330$		0			0
$331$	11.8105	−	20.4563i	0.649162	−	1.12438i	−0.334162	−	0.942516i	$-0.608453\pi$
$331$	11.8105	−	20.4563i	0.649162	−	1.12438i	0.983323	−	0.181865i	$-0.0582134\pi$
$332$		0			0
$333$	−11.7747	+	6.79813i	−0.645250	+	0.372535i
$334$		0			0
$335$		0			0
$336$		0			0
$337$			10.4260i			0.567942i	0.958833	+	0.283971i	$0.0916519\pi$
$337$			10.4260i			0.567942i	−0.958833	+	0.283971i	$0.908348\pi$
$338$		0			0
$339$	4.52481	+	7.83721i	0.245754	+	0.425659i
$340$		0			0
$341$	−1.07738	+	1.86608i	−0.0583435	+	0.101054i
$342$		0			0
$343$	0.866025	−	18.5000i	0.0467610	−	0.998906i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	9.59964	−	5.54236i	0.515336	−	0.297529i	−0.219688	−	0.975570i	$-0.570504\pi$
$347$	9.59964	−	5.54236i	0.515336	−	0.297529i	0.735024	+	0.678041i	$0.237171\pi$
$348$		0			0
$349$	−28.6587			−1.53406			−0.767032	−	0.641609i	$-0.778267\pi$
$349$	−28.6587			−1.53406			−0.767032	+	0.641609i	$0.778267\pi$
$350$		0			0
$351$	6.23618			0.332863
$352$		0			0
$353$	5.70146	−	3.29174i	0.303458	−	0.175201i	−0.340537	−	0.940231i	$-0.610609\pi$
$353$	5.70146	−	3.29174i	0.303458	−	0.175201i	0.643995	+	0.765030i	$0.277276\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$	0.797847	−	51.1639i	0.0422265	−	2.70788i
$358$		0			0
$359$	−0.888003	+	1.53807i	−0.0468670	+	0.0811761i	−0.888507	−	0.458863i	$-0.848257\pi$
$359$	−0.888003	+	1.53807i	−0.0468670	+	0.0811761i	0.841640	+	0.540039i	$0.181590\pi$
$360$		0			0
$361$	−14.6065	−	25.2993i	−0.768765	−	1.33154i
$362$		0			0
$363$		−	17.3824i		−	0.912338i
$364$		0			0
$365$		0			0
$366$		0			0
$367$	−6.15484	+	3.55350i	−0.321280	+	0.185491i	−0.651963	−	0.758251i	$-0.726054\pi$
$367$	−6.15484	+	3.55350i	−0.321280	+	0.185491i	0.330683	+	0.943742i	$0.392721\pi$
$368$		0			0
$369$	6.34002	−	10.9812i	0.330048	−	0.571661i
$370$		0			0
$371$	−8.68298	+	14.5120i	−0.450798	+	0.753426i
$372$		0			0
$373$	25.1688	+	14.5312i	1.30319	+	0.752398i	0.980950	−	0.194260i	$-0.0622306\pi$
$373$	25.1688	+	14.5312i	1.30319	+	0.752398i	0.322241	+	0.946658i	$0.395564\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$			31.0333i			1.59830i
$378$		0			0
$379$	27.9145			1.43387			0.716935	−	0.697140i	$-0.245544\pi$
$379$	27.9145			1.43387			0.716935	+	0.697140i	$0.245544\pi$
$380$		0			0
$381$	−27.3516	−	47.3744i	−1.40127	−	2.42707i
$382$		0			0
$383$	−16.9878	−	9.80793i	−0.868038	−	0.501162i	−0.00134227	−	0.999999i	$-0.500427\pi$
$383$	−16.9878	−	9.80793i	−0.868038	−	0.501162i	−0.866696	+	0.498837i	$0.833761\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	−12.3207	−	7.11334i	−0.626295	−	0.361591i
$388$		0			0
$389$	12.9722	+	22.4686i	0.657719	+	1.13920i	0.981205	+	0.192970i	$0.0618119\pi$
$389$	12.9722	+	22.4686i	0.657719	+	1.13920i	−0.323486	+	0.946233i	$0.604855\pi$
$390$		0			0
$391$	13.1138			0.663194
$392$		0			0
$393$			8.76382i			0.442076i
$394$		0			0
$395$		0			0
$396$		0			0
$397$	−2.35289	−	1.35844i	−0.118088	−	0.0681782i	0.439793	−	0.898099i	$-0.355052\pi$
$397$	−2.35289	−	1.35844i	−0.118088	−	0.0681782i	−0.557881	+	0.829921i	$0.688385\pi$
$398$		0			0
$399$	22.6275	+	40.6425i	1.13279	+	2.03467i
$400$		0			0
$401$	12.8674	−	22.2869i	0.642565	−	1.11296i	−0.342293	−	0.939593i	$-0.611203\pi$
$401$	12.8674	−	22.2869i	0.642565	−	1.11296i	0.984858	−	0.173363i	$-0.0554633\pi$
$402$		0			0
$403$	2.64258	−	1.52569i	0.131636	−	0.0760001i
$404$		0			0
$405$		0			0
$406$		0			0
$407$		−	16.8452i		−	0.834987i
$408$		0			0
$409$	2.78312	+	4.82050i	0.137616	+	0.238359i	0.926594	−	0.376064i	$-0.122723\pi$
$409$	2.78312	+	4.82050i	0.137616	+	0.238359i	−0.788978	+	0.614422i	$0.789389\pi$
$410$		0			0
$411$	−16.6493	+	28.8374i	−0.821249	+	1.42245i
$412$		0			0
$413$	−12.7057	−	7.60220i	−0.625205	−	0.374080i
$414$		0			0
$415$		0			0
$416$		0			0
$417$	14.1832	−	8.18866i	0.694553	−	0.401001i
$418$		0			0
$419$	−28.1516			−1.37529			−0.687647	−	0.726045i	$-0.741356\pi$
$419$	−28.1516			−1.37529			−0.687647	+	0.726045i	$0.741356\pi$
$420$		0			0
$421$	20.6705			1.00742			0.503710	−	0.863873i	$-0.331968\pi$
$421$	20.6705			1.00742			0.503710	+	0.863873i	$0.331968\pi$
$422$		0			0
$423$	−5.59548	+	3.23055i	−0.272062	+	0.157075i
$424$		0			0
$425$		0			0
$426$		0			0
$427$	0.177929	−	11.4101i	0.00861058	−	0.552175i
$428$		0			0
$429$	−32.0292	+	55.4761i	−1.54638	+	2.67841i
$430$		0			0
$431$	−9.87211	−	17.0990i	−0.475523	−	0.823630i	0.524084	−	0.851667i	$-0.324408\pi$
$431$	−9.87211	−	17.0990i	−0.475523	−	0.823630i	−0.999607	+	0.0280368i	$0.991074\pi$
$432$		0			0
$433$		−	10.5348i		−	0.506269i	−0.967431	−	0.253135i	$-0.918538\pi$
$433$		−	10.5348i		−	0.506269i	0.967431	−	0.253135i	$-0.0814615\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−10.3241	+	5.96064i	−0.493870	+	0.285136i
$438$		0			0
$439$	4.93717	−	8.55142i	0.235638	−	0.408137i	−0.723820	−	0.689989i	$-0.757615\pi$
$439$	4.93717	−	8.55142i	0.235638	−	0.408137i	0.959458	+	0.281852i	$0.0909487\pi$
$440$		0			0
$441$	−11.2895	−	21.0432i	−0.537596	−	1.00206i
$442$		0			0
$443$	−4.58435	−	2.64677i	−0.217809	−	0.125752i	0.387126	−	0.922027i	$-0.373468\pi$
$443$	−4.58435	−	2.64677i	−0.217809	−	0.125752i	−0.604935	+	0.796275i	$0.706801\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$		−	11.5817i		−	0.547796i
$448$		0			0
$449$	12.2918			0.580086			0.290043	−	0.957014i	$-0.406330\pi$
$449$	12.2918			0.580086			0.290043	+	0.957014i	$0.406330\pi$
$450$		0			0
$451$	7.85504	+	13.6053i	0.369879	+	0.640650i
$452$		0			0
$453$	11.3057	+	6.52734i	0.531187	+	0.306681i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	19.4897	+	11.2524i	0.911689	+	0.526364i	0.880974	−	0.473164i	$-0.156888\pi$
$457$	19.4897	+	11.2524i	0.911689	+	0.526364i	0.0307147	+	0.999528i	$0.490222\pi$
$458$		0			0
$459$	−3.97906	−	6.89193i	−0.185726	−	0.321688i
$460$		0			0
$461$	−4.18479			−0.194905			−0.0974526	−	0.995240i	$-0.531069\pi$
$461$	−4.18479			−0.194905			−0.0974526	+	0.995240i	$0.531069\pi$
$462$		0			0
$463$			36.1729i			1.68110i	0.541735	+	0.840549i	$0.317768\pi$
$463$			36.1729i			1.68110i	−0.541735	+	0.840549i	$0.682232\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	3.10856	+	1.79473i	0.143847	+	0.0830502i	0.570196	−	0.821509i	$-0.306867\pi$
$467$	3.10856	+	1.79473i	0.143847	+	0.0830502i	−0.426349	+	0.904559i	$0.640200\pi$
$468$		0			0
$469$	17.9213	−	29.9521i	0.827528	−	1.38306i
$470$		0			0
$471$	17.2699	−	29.9124i	0.795756	−	1.37829i
$472$		0			0
$473$	15.2648	−	8.81315i	0.701877	−	0.405229i
$474$		0			0
$475$		0			0
$476$		0			0
$477$			21.8057i			0.998415i
$478$		0			0
$479$	−1.75150	−	3.03368i	−0.0800279	−	0.138612i	0.823234	−	0.567703i	$-0.192168\pi$
$479$	−1.75150	−	3.03368i	−0.0800279	−	0.138612i	−0.903262	+	0.429090i	$0.858834\pi$
$480$		0			0
$481$	−11.9274	+	20.6588i	−0.543841	+	0.941960i
$482$		0			0
$483$	10.0494	−	5.59492i	0.457262	−	0.254578i
$484$		0			0
$485$		0			0
$486$		0			0
$487$	−26.1372	+	15.0903i	−1.18439	+	0.683808i	−0.957026	−	0.290001i	$-0.906344\pi$
$487$	−26.1372	+	15.0903i	−1.18439	+	0.683808i	−0.227365	+	0.973810i	$0.573011\pi$
$488$		0			0
$489$	−0.879385			−0.0397672
$490$		0			0
$491$	24.2858			1.09600			0.548002	−	0.836477i	$-0.315389\pi$
$491$	24.2858			1.09600			0.548002	+	0.836477i	$0.315389\pi$
$492$		0			0
$493$	34.2966	−	19.8011i	1.54464	−	0.891798i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	11.7518	−	6.54277i	0.527142	−	0.293483i
$498$		0			0
$499$	−0.138156	+	0.239293i	−0.00618470	+	0.0107122i	−0.869101	−	0.494634i	$-0.835302\pi$
$499$	−0.138156	+	0.239293i	−0.00618470	+	0.0107122i	0.862916	+	0.505347i	$0.168635\pi$
$500$		0			0
$501$	−2.18866	−	3.79088i	−0.0977822	−	0.169364i
$502$		0			0
$503$		−	0.573978i		−	0.0255924i	−0.999918	−	0.0127962i	$-0.995927\pi$
$503$		−	0.573978i		−	0.0255924i	0.999918	−	0.0127962i	$-0.00407327\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	50.0533	−	28.8983i	2.22294	−	1.28342i
$508$		0			0
$509$	−18.5253	+	32.0867i	−0.821119	+	1.42222i	0.0837312	+	0.996488i	$0.473316\pi$
$509$	−18.5253	+	32.0867i	−0.821119	+	1.42222i	−0.904850	+	0.425731i	$0.860017\pi$
$510$		0			0
$511$	7.32089	−	12.2355i	0.323857	−	0.541267i
$512$		0			0
$513$	6.26519	+	3.61721i	0.276615	+	0.159704i
$514$		0			0
$515$		0			0
$516$		0			0
$517$		−	8.00505i		−	0.352062i
$518$		0			0
$519$	33.7597			1.48189
$520$		0			0
$521$	−3.65270	−	6.32667i	−0.160028	−	0.277176i	0.774851	−	0.632144i	$-0.217825\pi$
$521$	−3.65270	−	6.32667i	−0.160028	−	0.277176i	−0.934878	+	0.354968i	$0.884492\pi$
$522$		0			0
$523$	28.3447	+	16.3648i	1.23943	+	0.715584i	0.968977	−	0.247149i	$-0.0794938\pi$
$523$	28.3447	+	16.3648i	1.23943	+	0.715584i	0.270451	+	0.962734i	$0.412827\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−3.37225	−	1.94697i	−0.146897	−	0.0848112i
$528$		0			0
$529$	−10.0262	−	17.3658i	−0.435920	−	0.755036i
$530$		0			0
$531$	−19.0915			−0.828501
$532$		0			0
$533$		−	22.2472i		−	0.963634i
$534$		0			0
$535$		0			0
$536$		0			0
$537$	34.2114	+	19.7520i	1.47633	+	0.852360i
$538$		0			0
$539$	29.5724	+	0.922524i	1.27377	+	0.0397359i
$540$		0			0
$541$	11.5364	−	19.9817i	0.495990	−	0.859079i	−0.504000	−	0.863704i	$-0.668139\pi$
$541$	11.5364	−	19.9817i	0.495990	−	0.859079i	0.999989	+	0.00462452i	$0.00147204\pi$
$542$		0			0
$543$	−43.0636	+	24.8628i	−1.84804	+	1.06696i
$544$		0			0
$545$		0			0
$546$		0			0
$547$		−	12.2172i		−	0.522369i	−0.965289	−	0.261185i	$-0.915887\pi$
$547$		−	12.2172i		−	0.522369i	0.965289	−	0.261185i	$-0.0841131\pi$
$548$		0			0
$549$	−7.35710	−	12.7429i	−0.313993	−	0.543852i
$550$		0			0
$551$	−18.0005	+	31.1777i	−0.766846	+	1.32822i
$552$		0			0
$553$	−0.0555796	+	3.56418i	−0.00236348	+	0.151564i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−21.6833	+	12.5189i	−0.918753	+	0.530442i	−0.883237	−	0.468927i	$-0.844641\pi$
$557$	−21.6833	+	12.5189i	−0.918753	+	0.530442i	−0.0355159	+	0.999369i	$0.511307\pi$
$558$		0			0
$559$	−24.9608			−1.05573
$560$		0			0
$561$	81.7461			3.45132
$562$		0			0
$563$	−4.29618	+	2.48040i	−0.181062	+	0.104536i	−0.587792	−	0.809012i	$-0.700003\pi$
$563$	−4.29618	+	2.48040i	−0.181062	+	0.104536i	0.406729	+	0.913549i	$0.366669\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$	17.2464	+	10.3191i	0.724282	+	0.433361i
$568$		0			0
$569$	−8.30659	+	14.3874i	−0.348230	+	0.603153i	−0.985935	−	0.167128i	$-0.946551\pi$
$569$	−8.30659	+	14.3874i	−0.348230	+	0.603153i	0.637705	+	0.770281i	$0.279884\pi$
$570$		0			0
$571$	−3.20961	−	5.55920i	−0.134318	−	0.232645i	0.791019	−	0.611792i	$-0.209551\pi$
$571$	−3.20961	−	5.55920i	−0.134318	−	0.232645i	−0.925337	+	0.379146i	$0.876218\pi$
$572$		0			0
$573$		−	28.9273i		−	1.20845i
$574$		0			0
$575$		0			0
$576$		0			0
$577$	−19.8867	+	11.4816i	−0.827893	+	0.477984i	−0.853131	−	0.521697i	$-0.825299\pi$
$577$	−19.8867	+	11.4816i	−0.827893	+	0.477984i	0.0252374	+	0.999681i	$0.491966\pi$
$578$		0			0
$579$	20.1104	−	34.8322i	0.835760	−	1.44758i
$580$		0			0
$581$	−11.1998	−	20.1166i	−0.464646	−	0.834578i
$582$		0			0
$583$	−23.3969	−	13.5082i	−0.969001	−	0.559453i
$584$		0			0
$585$		0			0
$586$		0			0
$587$			6.00681i			0.247927i	0.992287	+	0.123964i	$0.0395606\pi$
$587$			6.00681i			0.247927i	−0.992287	+	0.123964i	$0.960439\pi$
$588$		0			0
$589$	3.53983			0.145856
$590$		0			0
$591$	31.4530	+	54.4781i	1.29380	+	2.24093i
$592$		0			0
$593$	−13.5363	−	7.81521i	−0.555871	−	0.320932i	0.195616	−	0.980681i	$-0.437329\pi$
$593$	−13.5363	−	7.81521i	−0.555871	−	0.320932i	−0.751486	+	0.659749i	$0.770663\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	−1.00909	−	0.582596i	−0.0412991	−	0.0238441i
$598$		0			0
$599$	−13.9017	−	24.0784i	−0.568007	−	0.983817i	−0.996763	−	0.0803966i	$-0.974381\pi$
$599$	−13.9017	−	24.0784i	−0.568007	−	0.983817i	0.428756	−	0.903420i	$-0.358952\pi$
$600$		0			0
$601$	−3.80604			−0.155251			−0.0776257	−	0.996983i	$-0.524734\pi$
$601$	−3.80604			−0.155251			−0.0776257	+	0.996983i	$0.524734\pi$
$602$		0			0
$603$		−	45.0060i		−	1.83279i
$604$		0			0
$605$		0			0
$606$		0			0
$607$	−3.14608	−	1.81639i	−0.127695	−	0.0737250i	0.434792	−	0.900531i	$-0.356822\pi$
$607$	−3.14608	−	1.81639i	−0.127695	−	0.0737250i	−0.562487	+	0.826806i	$0.690155\pi$
$608$		0			0
$609$	17.8341	−	29.8064i	0.722674	−	1.20782i
$610$		0			0
$611$	−5.66802	+	9.81730i	−0.229304	+	0.397166i
$612$		0			0
$613$	−6.03850	+	3.48633i	−0.243893	+	0.140812i	−0.616965	−	0.786991i	$-0.711638\pi$
$613$	−6.03850	+	3.48633i	−0.243893	+	0.140812i	0.373072	+	0.927802i	$0.378304\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$			45.5996i			1.83577i	0.396847	+	0.917885i	$0.370104\pi$
$617$			45.5996i			1.83577i	−0.396847	+	0.917885i	$0.629896\pi$
$618$		0			0
$619$	13.0098	+	22.5336i	0.522908	+	0.905703i	0.999645	+	0.0266571i	$0.00848621\pi$
$619$	13.0098	+	22.5336i	0.522908	+	0.905703i	−0.476737	+	0.879046i	$0.658180\pi$
$620$		0			0
$621$	0.894400	−	1.54915i	0.0358910	−	0.0621651i
$622$		0			0
$623$	0.447395	−	28.6903i	0.0179245	−	1.14945i
$624$		0			0
$625$		0			0
$626$		0			0
$627$	−64.3564	+	37.1562i	−2.57015	+	1.48387i
$628$		0			0
$629$	30.4415			1.21378
$630$		0			0
$631$	−12.5699			−0.500398			−0.250199	−	0.968194i	$-0.580496\pi$
$631$	−12.5699			−0.500398			−0.250199	+	0.968194i	$0.580496\pi$
$632$		0			0
$633$	−1.36543	+	0.788333i	−0.0542711	+	0.0313334i
$634$		0			0
$635$		0			0
$636$		0			0
$637$	−35.6140	−	22.0703i	−1.41108	−	0.874456i
$638$		0			0
$639$	8.67159	−	15.0196i	0.343043	−	0.594167i
$640$		0			0
$641$	−14.8393	−	25.7024i	−0.586117	−	1.01519i	−0.994735	−	0.102479i	$-0.967322\pi$
$641$	−14.8393	−	25.7024i	−0.586117	−	1.01519i	0.408618	−	0.912706i	$-0.366011\pi$
$642$		0			0
$643$		−	1.56624i		−	0.0617664i	−0.999523	−	0.0308832i	$-0.990168\pi$
$643$		−	1.56624i		−	0.0617664i	0.999523	−	0.0308832i	$-0.00983199\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	21.5892	−	12.4645i	0.848757	−	0.490030i	−0.0114739	−	0.999934i	$-0.503652\pi$
$647$	21.5892	−	12.4645i	0.848757	−	0.490030i	0.860231	+	0.509904i	$0.170319\pi$
$648$		0			0
$649$	11.8268	−	20.4847i	0.464243	−	0.804093i
$650$		0			0
$651$	−3.41488	−	0.0532514i	−0.133840	−	0.00208709i
$652$		0			0
$653$	−34.2307	−	19.7631i	−1.33955	−	0.773390i	−0.352810	−	0.935695i	$-0.614774\pi$
$653$	−34.2307	−	19.7631i	−1.33955	−	0.773390i	−0.986741	+	0.162305i	$0.948107\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$		−	18.3851i		−	0.717270i
$658$		0			0
$659$	−19.6955			−0.767229			−0.383614	−	0.923493i	$-0.625321\pi$
$659$	−19.6955			−0.767229			−0.383614	+	0.923493i	$0.625321\pi$
$660$		0			0
$661$	−22.6827	−	39.2876i	−0.882256	−	1.52811i	−0.848827	−	0.528671i	$-0.822690\pi$
$661$	−22.6827	−	39.2876i	−0.882256	−	1.52811i	−0.0334294	−	0.999441i	$-0.510643\pi$
$662$		0			0
$663$	−100.252	−	57.8808i	−3.89348	−	2.24790i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	7.70908	+	4.45084i	0.298497	+	0.172337i
$668$		0			0
$669$	−23.6942	−	41.0395i	−0.916070	−	1.58668i
$670$		0			0
$671$	18.2303			0.703773
$672$		0			0
$673$			42.8726i			1.65262i	0.563218	+	0.826308i	$0.309563\pi$
$673$			42.8726i			1.65262i	−0.563218	+	0.826308i	$0.690437\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	19.4179	+	11.2110i	0.746292	+	0.430872i	0.824353	−	0.566077i	$-0.191539\pi$
$677$	19.4179	+	11.2110i	0.746292	+	0.430872i	−0.0780606	+	0.996949i	$0.524873\pi$
$678$		0			0
$679$	−17.6061	−	31.6233i	−0.675659	−	1.21359i
$680$		0			0
$681$	−35.9518	+	62.2703i	−1.37767	+	2.38620i
$682$		0			0
$683$	8.18452	−	4.72534i	0.313172	−	0.180810i	−0.335173	−	0.942157i	$-0.608795\pi$
$683$	8.18452	−	4.72534i	0.313172	−	0.180810i	0.648345	+	0.761347i	$0.275461\pi$
$684$		0			0
$685$		0			0
$686$		0			0
$687$		−	18.7365i		−	0.714841i
$688$		0			0
$689$	19.1291	+	33.1326i	0.728762	+	1.26225i
$690$		0			0
$691$	−20.6505	+	35.7677i	−0.785581	+	1.36067i	0.143070	+	0.989713i	$0.454303\pi$
$691$	−20.6505	+	35.7677i	−0.785581	+	1.36067i	−0.928651	+	0.370954i	$0.879031\pi$
$692$		0			0
$693$	33.3320	−	18.5574i	1.26618	−	0.704936i
$694$		0			0
$695$		0			0
$696$		0			0
$697$	−24.5866	+	14.1951i	−0.931283	+	0.537676i
$698$		0			0
$699$	−10.4037			−0.393505
$700$		0			0
$701$	−36.6049			−1.38255			−0.691275	−	0.722592i	$-0.742951\pi$
$701$	−36.6049			−1.38255			−0.691275	+	0.722592i	$0.742951\pi$
$702$		0			0
$703$	−23.9657	+	13.8366i	−0.903885	+	0.521858i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−25.2481	−	15.1067i	−0.949551	−	0.568146i
$708$		0			0
$709$	10.9238	−	18.9206i	0.410252	−	0.710577i	−0.584665	−	0.811275i	$-0.698774\pi$
$709$	10.9238	−	18.9206i	0.410252	−	0.710577i	0.994917	+	0.100698i	$0.0321074\pi$
$710$		0			0
$711$	2.29813	+	3.98048i	0.0861867	+	0.149280i
$712$		0			0
$713$		−	0.875266i		−	0.0327790i
$714$		0			0
$715$		0			0
$716$		0			0
$717$	45.0519	−	26.0107i	1.68249	−	0.971389i
$718$		0			0
$719$	2.89037	−	5.00626i	0.107793	−	0.186702i	−0.807083	−	0.590438i	$-0.798955\pi$
$719$	2.89037	−	5.00626i	0.107793	−	0.186702i	0.914876	+	0.403736i	$0.132288\pi$
$720$		0			0
$721$	51.1254	+	0.797247i	1.90401	+	0.0296910i
$722$		0			0
$723$	3.73092	+	2.15405i	0.138754	+	0.0801099i
$724$		0			0
$725$		0			0
$726$		0			0
$727$			31.0104i			1.15011i	0.818114	+	0.575057i	$0.195020\pi$
$727$			31.0104i			1.15011i	−0.818114	+	0.575057i	$0.804980\pi$
$728$		0			0
$729$	33.8289			1.25292
$730$		0			0
$731$	15.9265	+	27.5855i	0.589062	+	1.02029i
$732$		0			0
$733$	−24.7422	−	14.2849i	−0.913875	−	0.527626i	−0.0321990	−	0.999481i	$-0.510251\pi$
$733$	−24.7422	−	14.2849i	−0.913875	−	0.527626i	−0.881676	+	0.471856i	$0.843584\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	48.2901	+	27.8803i	1.77879	+	1.02698i
$738$		0			0
$739$	15.0226	+	26.0199i	0.552615	+	0.957157i	0.998085	+	0.0618603i	$0.0197033\pi$
$739$	15.0226	+	26.0199i	0.552615	+	0.957157i	−0.445470	+	0.895297i	$0.646963\pi$
$740$		0			0
$741$	105.235			3.86589
$742$		0			0
$743$			10.9153i			0.400443i	0.979751	+	0.200222i	$0.0641662\pi$
$743$			10.9153i			0.400443i	−0.979751	+	0.200222i	$0.935834\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	−25.7104	−	14.8439i	−0.940693	−	0.543110i
$748$		0			0
$749$	24.6506	+	0.384401i	0.900715	+	0.0140457i
$750$		0			0
$751$	−0.854570	+	1.48016i	−0.0311837	+	0.0540118i	−0.881196	−	0.472751i	$-0.843261\pi$
$751$	−0.854570	+	1.48016i	−0.0311837	+	0.0540118i	0.850012	+	0.526763i	$0.176594\pi$
$752$		0			0
$753$	30.5124	−	17.6163i	1.11193	−	0.641975i
$754$		0			0
$755$		0			0
$756$		0			0
$757$		−	38.4475i		−	1.39740i	−0.715416	−	0.698699i	$-0.753763\pi$
$757$		−	38.4475i		−	1.39740i	0.715416	−	0.698699i	$-0.246237\pi$
$758$		0			0
$759$	9.18732	+	15.9129i	0.333479	+	0.577602i
$760$		0			0
$761$	−16.5865	+	28.7286i	−0.601259	+	1.04141i	0.391372	+	0.920233i	$0.372001\pi$
$761$	−16.5865	+	28.7286i	−0.601259	+	1.04141i	−0.992631	+	0.121178i	$0.961333\pi$
$762$		0			0
$763$	−10.6255	−	6.35756i	−0.384669	−	0.230159i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−29.0085	+	16.7481i	−1.04744	+	0.604739i
$768$		0			0
$769$	17.7124			0.638727			0.319363	−	0.947632i	$-0.396531\pi$
$769$	17.7124			0.638727			0.319363	+	0.947632i	$0.396531\pi$
$770$		0			0
$771$	75.6769			2.72544
$772$		0			0
$773$	−18.6978	+	10.7952i	−0.672514	+	0.388276i	−0.797029	−	0.603942i	$-0.793596\pi$
$773$	−18.6978	+	10.7952i	−0.672514	+	0.388276i	0.124514	+	0.992218i	$0.460263\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$	23.3279	−	12.9877i	0.836884	−	0.465930i
$778$		0			0
$779$	12.9042	−	22.3507i	0.462341	−	0.800798i
$780$		0			0
$781$	10.7438	+	18.6087i	0.384442	+	0.665873i
$782$		0			0
$783$		−	5.40198i		−	0.193051i
$784$		0			0
$785$		0			0
$786$		0			0
$787$	−38.2542	+	22.0861i	−1.36361	+	0.787283i	−0.990103	−	0.140343i	$-0.955180\pi$
$787$	−38.2542	+	22.0861i	−1.36361	+	0.787283i	−0.373511	+	0.927626i	$0.621846\pi$
$788$		0			0
$789$	−24.9354	+	43.1894i	−0.887724	+	1.53758i
$790$		0			0
$791$	−4.59967	−	8.26173i	−0.163545	−	0.293753i
$792$		0			0
$793$	−22.3574	−	12.9081i	−0.793936	−	0.458379i
$794$		0			0
$795$		0			0
$796$		0			0
$797$		−	9.18210i		−	0.325247i	−0.986688	−	0.162623i	$-0.948004\pi$
$797$		−	9.18210i		−	0.325247i	0.986688	−	0.162623i	$-0.0519956\pi$
$798$		0			0
$799$	14.4662			0.511776
$800$		0			0
$801$	−18.4991	−	32.0414i	−0.653634	−	1.13213i
$802$		0			0
$803$	19.7266	+	11.3892i	0.696138	+	0.401916i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	12.0444	+	6.95383i	0.423982	+	0.244786i
$808$		0			0
$809$	7.63429	+	13.2230i	0.268407	+	0.464895i	0.968451	−	0.249205i	$-0.0801694\pi$
$809$	7.63429	+	13.2230i	0.268407	+	0.464895i	−0.700043	+	0.714100i	$0.746836\pi$
$810$		0			0
$811$	−11.5202			−0.404530			−0.202265	−	0.979331i	$-0.564830\pi$
$811$	−11.5202			−0.404530			−0.202265	+	0.979331i	$0.564830\pi$
$812$		0			0
$813$		−	34.5699i		−	1.21242i
$814$		0			0
$815$		0			0
$816$		0			0
$817$	−25.0769	−	14.4782i	−0.877331	−	0.506527i
$818$		0			0
$819$	−54.0176	−	0.842347i	−1.88753	−	0.0294340i
$820$		0			0
$821$	15.1224	−	26.1928i	0.527776	−	0.914135i	−0.471699	−	0.881759i	$-0.656359\pi$
$821$	15.1224	−	26.1928i	0.527776	−	0.914135i	0.999476	−	0.0323760i	$-0.0103074\pi$
$822$		0			0
$823$	21.9522	−	12.6741i	0.765206	−	0.441792i	−0.0659558	−	0.997823i	$-0.521010\pi$
$823$	21.9522	−	12.6741i	0.765206	−	0.441792i	0.831162	+	0.556031i	$0.187676\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$		−	35.0678i		−	1.21943i	−0.792622	−	0.609713i	$-0.791285\pi$
$827$		−	35.0678i		−	1.21943i	0.792622	−	0.609713i	$-0.208715\pi$
$828$		0			0
$829$	18.4868	+	32.0201i	0.642073	+	1.11210i	0.984969	+	0.172730i	$0.0552587\pi$
$829$	18.4868	+	32.0201i	0.642073	+	1.11210i	−0.342896	+	0.939373i	$0.611408\pi$
$830$		0			0
$831$	14.7378	−	25.5267i	0.511250	−	0.885510i
$832$		0			0
$833$	−1.66712	+	53.4411i	−0.0577623	+	1.85162i
$834$		0			0
$835$		0			0
$836$		0			0
$837$	−0.459994	+	0.265578i	−0.0158997	+	0.00917971i
$838$		0			0
$839$	27.0506			0.933889			0.466945	−	0.884287i	$-0.345355\pi$
$839$	27.0506			0.933889			0.466945	+	0.884287i	$0.345355\pi$
$840$		0			0
$841$	−2.11793			−0.0730319
$842$		0			0
$843$	−0.592784	+	0.342244i	−0.0204166	+	0.0117875i
$844$		0			0
$845$		0			0
$846$		0			0
$847$	−0.283193	+	18.1604i	−0.00973062	+	0.624000i
$848$		0			0
$849$	−7.14156	+	12.3695i	−0.245098	+	0.424522i
$850$		0			0
$851$	3.42127	+	5.92582i	0.117280	+	0.203135i
$852$		0			0
$853$		−	14.4834i		−	0.495902i	−0.968773	−	0.247951i	$-0.920243\pi$
$853$		−	14.4834i		−	0.495902i	0.968773	−	0.247951i	$-0.0797572\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−8.16755	+	4.71554i	−0.278998	+	0.161080i	−0.632970	−	0.774176i	$-0.718164\pi$
$857$	−8.16755	+	4.71554i	−0.278998	+	0.161080i	0.353972	+	0.935256i	$0.384831\pi$
$858$		0			0
$859$	2.38191	−	4.12559i	0.0812698	−	0.140763i	−0.822526	−	0.568728i	$-0.807436\pi$
$859$	2.38191	−	4.12559i	0.0812698	−	0.140763i	0.903796	+	0.427964i	$0.140769\pi$
$860$		0			0
$861$	−12.7849	+	21.3677i	−0.435709	+	0.728208i
$862$		0			0
$863$	−18.6288	−	10.7554i	−0.634133	−	0.366117i	0.148218	−	0.988955i	$-0.452646\pi$
$863$	−18.6288	−	10.7554i	−0.634133	−	0.366117i	−0.782351	+	0.622838i	$0.785980\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$			104.680i			3.55512i
$868$		0			0
$869$	−5.69459			−0.193176
$870$		0			0
$871$	−39.4816	−	68.3842i	−1.33778	−	2.31711i
$872$		0			0
$873$	−40.4166	−	23.3346i	−1.36790	−	0.789755i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	23.2546	+	13.4260i	0.785250	+	0.453365i	0.838288	−	0.545228i	$-0.183557\pi$
$877$	23.2546	+	13.4260i	0.785250	+	0.453365i	−0.0530374	+	0.998593i	$0.516890\pi$
$878$		0			0
$879$	−22.2062	−	38.4623i	−0.748997	−	1.29730i
$880$		0			0
$881$	−18.5084			−0.623563			−0.311781	−	0.950154i	$-0.600926\pi$
$881$	−18.5084			−0.623563			−0.311781	+	0.950154i	$0.600926\pi$
$882$		0			0
$883$		−	16.1821i		−	0.544571i	−0.962216	−	0.272286i	$-0.912220\pi$
$883$		−	16.1821i		−	0.544571i	0.962216	−	0.272286i	$-0.0877795\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	36.6404	+	21.1544i	1.23026	+	0.710294i	0.967085	−	0.254453i	$-0.0818955\pi$
$887$	36.6404	+	21.1544i	1.23026	+	0.710294i	0.263180	+	0.964747i	$0.415229\pi$
$888$		0			0
$889$	27.8041	+	49.9406i	0.932520	+	1.67495i
$890$		0			0
$891$	−16.0535	+	27.8055i	−0.537812	+	0.931519i
$892$		0			0
$893$	−11.3888	+	6.57532i	−0.381111	+	0.220035i
$894$		0			0
$895$		0			0
$896$		0			0
$897$		−	26.0205i		−	0.868800i
$898$		0			0
$899$	−1.32160	−	2.28909i	−0.0440780	−	0.0763453i
$900$		0			0
$901$	24.4111	−	42.2812i	0.813250	−	1.40859i
$902$		0			0
$903$	23.9740	+	14.3444i	0.797803	+	0.477350i
$904$		0			0
$905$		0			0
$906$		0			0
$907$	−38.9594	+	22.4932i	−1.29362	+	0.746874i	−0.979295	−	0.202440i	$-0.935113\pi$
$907$	−38.9594	+	22.4932i	−1.29362	+	0.746874i	−0.314329	+	0.949314i	$0.601780\pi$
$908$		0			0
$909$	−37.9377			−1.25831
$910$		0			0
$911$	20.5066			0.679414			0.339707	−	0.940531i	$-0.389672\pi$
$911$	20.5066			0.679414			0.339707	+	0.940531i	$0.389672\pi$
$912$		0			0
$913$	31.8541	−	18.3910i	1.05422	−	0.608653i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	0.142780	−	9.15611i	0.00471500	−	0.302361i
$918$		0			0
$919$	9.09240	−	15.7485i	0.299930	−	0.519495i	−0.676189	−	0.736728i	$-0.736370\pi$
$919$	9.09240	−	15.7485i	0.299930	−	0.519495i	0.976120	+	0.217233i	$0.0697032\pi$
$920$		0			0
$921$	−5.37299	−	9.30629i	−0.177046	−	0.306653i
$922$		0			0
$923$		−	30.4287i		−	1.00157i
$924$		0			0
$925$		0			0
$926$		0			0
$927$	57.0970	−	32.9650i	1.87531	−	1.08271i
$928$		0			0
$929$	6.85726	−	11.8771i	0.224979	−	0.389676i	−0.731334	−	0.682020i	$-0.761102\pi$
$929$	6.85726	−	11.8771i	0.224979	−	0.389676i	0.956313	+	0.292344i	$0.0944352\pi$
$930$		0			0
$931$	−22.9782	−	42.8304i	−0.753079	−	1.40371i
$932$		0			0
$933$	−13.2549	−	7.65270i	−0.433945	−	0.250538i
$934$		0			0
$935$		0			0
$936$		0			0
$937$		−	41.5098i		−	1.35607i	−0.735031	−	0.678033i	$-0.762833\pi$
$937$		−	41.5098i		−	1.35607i	0.735031	−	0.678033i	$-0.237167\pi$
$938$		0			0
$939$	−6.82531			−0.222736
$940$		0			0
$941$	25.2203	+	43.6829i	0.822160	+	1.42402i	0.904071	+	0.427383i	$0.140564\pi$
$941$	25.2203	+	43.6829i	0.822160	+	1.42402i	−0.0819112	+	0.996640i	$0.526102\pi$
$942$		0			0
$943$	−5.52649	−	3.19072i	−0.179967	−	0.103904i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−43.0420	−	24.8503i	−1.39868	−	0.807526i	−0.404422	−	0.914573i	$-0.632527\pi$
$947$	−43.0420	−	24.8503i	−1.39868	−	0.807526i	−0.994254	+	0.107047i	$0.965861\pi$
$948$		0			0
$949$	−16.1284	−	27.9351i	−0.523549	−	0.906813i
$950$		0			0
$951$	−77.2731			−2.50575
$952$		0			0
$953$			42.2458i			1.36848i	0.729259	+	0.684238i	$0.239865\pi$
$953$			42.2458i			1.36848i	−0.729259	+	0.684238i	$0.760135\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$	48.0552	+	27.7447i	1.55340	+	0.896858i
$958$		0			0
$959$	17.8644	−	29.8570i	0.576871	−	0.964133i
$960$		0			0
$961$	15.3701	−	26.6217i	0.495808	−	0.858765i
$962$		0			0
$963$	27.5299	−	15.8944i	0.887139	−	0.512190i
$964$		0			0
$965$		0			0
$966$		0			0
$967$		−	11.4260i		−	0.367436i	−0.982979	−	0.183718i	$-0.941187\pi$
$967$		−	11.4260i		−	0.367436i	0.982979	−	0.183718i	$-0.0588133\pi$
$968$		0			0
$969$	−67.1460	−	116.300i	−2.15704	−	3.73610i
$970$		0			0
$971$	2.22193	−	3.84850i	0.0713053	−	0.123504i	−0.828168	−	0.560479i	$-0.810617\pi$
$971$	2.22193	−	3.84850i	0.0713053	−	0.123504i	0.899474	+	0.436975i	$0.143950\pi$
$972$		0			0
$973$	−14.9515	+	8.32413i	−0.479322	+	0.266859i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	24.1770	−	13.9586i	0.773490	−	0.446574i	−0.0606284	−	0.998160i	$-0.519310\pi$
$977$	24.1770	−	13.9586i	0.773490	−	0.446574i	0.834118	+	0.551586i	$0.185977\pi$
$978$		0			0
$979$	45.8394			1.46503
$980$		0			0
$981$	−15.9659			−0.509750
$982$		0			0
$983$	32.5815	−	18.8109i	1.03919	−	0.599975i	0.119585	−	0.992824i	$-0.461844\pi$
$983$	32.5815	−	18.8109i	1.03919	−	0.599975i	0.919603	+	0.392849i	$0.128510\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$	11.0857	−	6.17189i	0.352862	−	0.196454i
$988$		0			0
$989$	−3.57991	+	6.20058i	−0.113834	+	0.197167i
$990$		0			0
$991$	0.263823	+	0.456955i	0.00838061	+	0.0145156i	0.870185	−	0.492725i	$-0.163999\pi$
$991$	0.263823	+	0.456955i	0.00838061	+	0.0145156i	−0.861805	+	0.507240i	$0.830666\pi$
$992$		0			0
$993$			59.8103i			1.89802i
$994$		0			0
$995$		0			0
$996$		0			0
$997$	−0.914093	+	0.527752i	−0.0289496	+	0.0167141i	−0.514405	−	0.857547i	$-0.671987\pi$
$997$	−0.914093	+	0.527752i	−0.0289496	+	0.0167141i	0.485455	+	0.874261i	$0.338654\pi$
$998$		0			0
$999$	2.07620	−	3.59608i	0.0656880	−	0.113775i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1400.2.bh.h.849.1		12
5.2	odd	4		1400.2.q.k.401.3	yes	6
5.3	odd	4		1400.2.q.i.401.1	✓	6
5.4	even	2	inner	1400.2.bh.h.849.6		12
7.4	even	3	inner	1400.2.bh.h.249.6		12
35.2	odd	12		9800.2.a.cc.1.1		3
35.4	even	6	inner	1400.2.bh.h.249.1		12
35.12	even	12		9800.2.a.ch.1.3		3
35.18	odd	12		1400.2.q.i.1201.1	yes	6
35.23	odd	12		9800.2.a.ci.1.3		3
35.32	odd	12		1400.2.q.k.1201.3	yes	6
35.33	even	12		9800.2.a.cb.1.1		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1400.2.q.i.401.1	✓	6	5.3	odd	4
1400.2.q.i.1201.1	yes	6	35.18	odd	12
1400.2.q.k.401.3	yes	6	5.2	odd	4
1400.2.q.k.1201.3	yes	6	35.32	odd	12
1400.2.bh.h.249.1		12	35.4	even	6	inner
1400.2.bh.h.249.6		12	7.4	even	3	inner
1400.2.bh.h.849.1		12	1.1	even	1	trivial
1400.2.bh.h.849.6		12	5.4	even	2	inner
9800.2.a.cb.1.1		3	35.33	even	12
9800.2.a.cc.1.1		3	35.2	odd	12
9800.2.a.ch.1.3		3	35.12	even	12
9800.2.a.ci.1.3		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)

\(f(q)\)	\(=\)	\(q+(-2.19285 + 1.26604i) q^{3} +(2.31164 - 1.28699i) q^{7} +(1.70574 - 2.95442i) q^{9} +O(q^{10})\)	\(q+(-2.19285 + 1.26604i) q^{3} +(2.31164 - 1.28699i) q^{7} +(1.70574 - 2.95442i) q^{9} +(2.11334 + 3.66041i) q^{11} -5.98545i q^{13} +(-6.61484 + 3.81908i) q^{17} +(3.47178 - 6.01330i) q^{19} +(-3.43969 + 5.74881i) q^{21} +(-1.48686 - 0.858441i) q^{23} +1.04189i q^{27} -5.18479 q^{29} +(0.254900 + 0.441500i) q^{31} +(-9.26849 - 5.35117i) q^{33} +(-3.45150 - 1.99273i) q^{37} +(7.57785 + 13.1252i) q^{39} +3.71688 q^{41} -4.17024i q^{43} +(-1.64019 - 0.946967i) q^{47} +(3.68732 - 5.95010i) q^{49} +(9.67024 - 16.7494i) q^{51} +(-5.53553 + 3.19594i) q^{53} +17.5817i q^{57} +(-2.79813 - 4.84651i) q^{59} +(2.15657 - 3.73530i) q^{61} +(0.140732 - 9.02481i) q^{63} +(11.4251 - 6.59627i) q^{67} +4.34730 q^{69} +5.08378 q^{71} +(4.66717 - 2.69459i) q^{73} +(9.59619 + 5.74170i) q^{77} +(-0.673648 + 1.16679i) q^{79} +(3.79813 + 6.57856i) q^{81} -8.70233i q^{83} +(11.3695 - 6.56418i) q^{87} +(5.42262 - 9.39225i) q^{89} +(-7.70321 - 13.8362i) q^{91} +(-1.11792 - 0.645430i) q^{93} -13.6800i q^{97} +14.4192 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q+O(q^{10}) \) 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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