LMFDB - Embedded newform 1400.2.bh.j.849.8

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:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 15x^{14} + 170x^{12} - 789x^{10} + 2754x^{8} - 960x^{6} + 269x^{4} - 18x^{2} + 1 $ x^16 - 15x^14 + 170x^12 - 789x^10 + 2754x^8 - 960x^6 + 269x^4 - 18*x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 3^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			849.8
Root			$2.00531 - 1.15777i$ of defining polynomial
Character	$\chi$	$=$	1400.849
Dual form			1400.2.bh.j.249.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.87134 - 1.65777i) q^{3} +(2.49733 + 0.873699i) q^{7} +(3.99638 - 6.92193i) q^{9} +O(q^{10})$	\(q+(2.87134 - 1.65777i) q^{3} +(2.49733 + 0.873699i) q^{7} +(3.99638 - 6.92193i) q^{9} +(2.12268 + 3.67659i) q^{11} -5.10909i q^{13} +(-0.765278 + 0.441833i) q^{17} +(-3.27048 + 5.66463i) q^{19} +(8.61906 - 1.63130i) q^{21} +(4.62065 + 2.66773i) q^{23} -16.5536i q^{27} -4.54096 q^{29} +(-0.338612 - 0.586493i) q^{31} +(12.1898 + 7.03781i) q^{33} +(-1.31807 - 0.760988i) q^{37} +(-8.46968 - 14.6699i) q^{39} -5.92666 q^{41} +5.49796i q^{43} +(-6.29546 - 3.63469i) q^{47} +(5.47330 + 4.36383i) q^{49} +(-1.46491 + 2.53730i) q^{51} +(-2.22407 + 1.28407i) q^{53} +21.6868i q^{57} +(-3.97330 - 6.88196i) q^{59} +(4.50997 - 7.81149i) q^{61} +(16.0280 - 13.7947i) q^{63} +(2.63614 - 1.52198i) q^{67} +17.6899 q^{69} +5.39840 q^{71} +(-3.34256 + 1.92983i) q^{73} +(2.08879 + 11.0362i) q^{77} +(0.352201 - 0.610030i) q^{79} +(-15.4529 - 26.7653i) q^{81} +10.8135i q^{83} +(-13.0386 + 7.52784i) q^{87} +(-4.20282 + 7.27950i) q^{89} +(4.46381 - 12.7591i) q^{91} +(-1.94454 - 1.12268i) q^{93} +0.614293i q^{97} +33.9321 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 10 q^{9}+O(q^{10}) $ 16 * q + 10 * q^9	$ 16 q + 10 q^{9} - 20 q^{19} + 50 q^{21} - 8 q^{29} + 28 q^{31} - 20 q^{39} - 16 q^{41} + 26 q^{49} - 10 q^{51} - 2 q^{59} + 50 q^{61} + 64 q^{69} - 80 q^{71} + 4 q^{79} - 48 q^{81} - 38 q^{89} + 34 q^{91} + 204 q^{99}+O(q^{100}) $ 16 * q + 10 * q^9 - 20 * q^19 + 50 * q^21 - 8 * q^29 + 28 * q^31 - 20 * q^39 - 16 * q^41 + 26 * q^49 - 10 * q^51 - 2 * q^59 + 50 * q^61 + 64 * q^69 - 80 * q^71 + 4 * q^79 - 48 * q^81 - 38 * q^89 + 34 * q^91 + 204 * 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
$3$	2.87134	−	1.65777i	1.65777	−	0.957112i	0.684024	−	0.729460i	$-0.260228\pi$
$3$	2.87134	−	1.65777i	1.65777	−	0.957112i	0.973743	−	0.227652i	$-0.0731049\pi$
$4$		0			0
$5$		0			0
$5$		0			0
$6$		0			0
$7$	2.49733	+	0.873699i	0.943901	+	0.330227i
$7$	2.49733	+	0.873699i	0.943901	+	0.330227i
$8$		0			0
$9$	3.99638	−	6.92193i	1.33213	−	2.30731i
$10$		0			0
$11$	2.12268	+	3.67659i	0.640012	+	1.10853i	0.985430	+	0.170084i	$0.0544039\pi$
$11$	2.12268	+	3.67659i	0.640012	+	1.10853i	−0.345418	+	0.938449i	$0.612263\pi$
$12$		0			0
$13$		−	5.10909i		−	1.41701i	−0.705708	−	0.708503i	$-0.749371\pi$
$13$		−	5.10909i		−	1.41701i	0.705708	−	0.708503i	$-0.250629\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−0.765278	+	0.441833i	−0.185607	+	0.107160i	−0.589924	−	0.807458i	$-0.700842\pi$
$17$	−0.765278	+	0.441833i	−0.185607	+	0.107160i	0.404317	+	0.914619i	$0.367509\pi$
$18$		0			0
$19$	−3.27048	+	5.66463i	−0.750299	+	1.29956i	0.197379	+	0.980327i	$0.436757\pi$
$19$	−3.27048	+	5.66463i	−0.750299	+	1.29956i	−0.947678	+	0.319229i	$0.896576\pi$
$20$		0			0
$21$	8.61906	−	1.63130i	1.88083	−	0.355980i
$22$		0			0
$23$	4.62065	+	2.66773i	0.963472	+	0.556261i	0.897240	−	0.441543i	$-0.145569\pi$
$23$	4.62065	+	2.66773i	0.963472	+	0.556261i	0.0662322	+	0.997804i	$0.478902\pi$
$24$		0			0
$25$		0			0
$26$		0			0
$27$		−	16.5536i		−	3.18575i
$28$		0			0
$29$	−4.54096			−0.843234			−0.421617	−	0.906774i	$-0.638537\pi$
$29$	−4.54096			−0.843234			−0.421617	+	0.906774i	$0.638537\pi$
$30$		0			0
$31$	−0.338612	−	0.586493i	−0.0608165	−	0.105337i	0.834014	−	0.551743i	$-0.186037\pi$
$31$	−0.338612	−	0.586493i	−0.0608165	−	0.105337i	−0.894831	+	0.446406i	$0.852704\pi$
$32$		0			0
$33$	12.1898	+	7.03781i	2.12198	+	1.22513i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	−1.31807	−	0.760988i	−0.216689	−	0.125106i	0.387727	−	0.921774i	$-0.373260\pi$
$37$	−1.31807	−	0.760988i	−0.216689	−	0.125106i	−0.604416	+	0.796669i	$0.706594\pi$
$38$		0			0
$39$	−8.46968	−	14.6699i	−1.35623	−	2.34907i
$40$		0			0
$41$	−5.92666			−0.925589			−0.462795	−	0.886466i	$-0.653153\pi$
$41$	−5.92666			−0.925589			−0.462795	+	0.886466i	$0.653153\pi$
$42$		0			0
$43$			5.49796i			0.838431i	0.907887	+	0.419215i	$0.137695\pi$
$43$			5.49796i			0.838431i	−0.907887	+	0.419215i	$0.862305\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−6.29546	−	3.63469i	−0.918288	−	0.530174i	−0.0351992	−	0.999380i	$-0.511207\pi$
$47$	−6.29546	−	3.63469i	−0.918288	−	0.530174i	−0.883088	+	0.469207i	$0.844540\pi$
$48$		0			0
$49$	5.47330	+	4.36383i	0.781900	+	0.623404i
$50$		0			0
$51$	−1.46491	+	2.53730i	−0.205129	+	0.355293i
$52$		0			0
$53$	−2.22407	+	1.28407i	−0.305499	+	0.176380i	−0.644911	−	0.764258i	$-0.723105\pi$
$53$	−2.22407	+	1.28407i	−0.305499	+	0.176380i	0.339411	+	0.940638i	$0.389772\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$			21.6868i			2.87248i
$58$		0			0
$59$	−3.97330	−	6.88196i	−0.517279	−	0.895954i	−0.999799	−	0.0200689i	$-0.993611\pi$
$59$	−3.97330	−	6.88196i	−0.517279	−	0.895954i	0.482519	−	0.875885i	$-0.339722\pi$
$60$		0			0
$61$	4.50997	−	7.81149i	0.577442	−	1.00016i	−0.418329	−	0.908295i	$-0.637384\pi$
$61$	4.50997	−	7.81149i	0.577442	−	1.00016i	0.995772	−	0.0918637i	$-0.0292824\pi$
$62$		0			0
$63$	16.0280	−	13.7947i	2.01933	−	1.73797i
$64$		0			0
$65$		0			0
$66$		0			0
$67$	2.63614	−	1.52198i	0.322056	−	0.185939i	−0.330253	−	0.943892i	$-0.607134\pi$
$67$	2.63614	−	1.52198i	0.322056	−	0.185939i	0.652308	+	0.757954i	$0.273801\pi$
$68$		0			0
$69$	17.6899			2.12962
$70$		0			0
$71$	5.39840			0.640672			0.320336	−	0.947304i	$-0.396204\pi$
$71$	5.39840			0.640672			0.320336	+	0.947304i	$0.396204\pi$
$72$		0			0
$73$	−3.34256	+	1.92983i	−0.391216	+	0.225869i	−0.682687	−	0.730711i	$-0.739189\pi$
$73$	−3.34256	+	1.92983i	−0.391216	+	0.225869i	0.291471	+	0.956580i	$0.405855\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	2.08879	+	11.0362i	0.238040	+	1.25770i
$78$		0			0
$79$	0.352201	−	0.610030i	0.0396257	−	0.0686337i	−0.845532	−	0.533924i	$-0.820717\pi$
$79$	0.352201	−	0.610030i	0.0396257	−	0.0686337i	0.885158	+	0.465290i	$0.154050\pi$
$80$		0			0
$81$	−15.4529	−	26.7653i	−1.71699	−	2.97392i
$82$		0			0
$83$			10.8135i			1.18693i	0.804858	+	0.593467i	$0.202241\pi$
$83$			10.8135i			1.18693i	−0.804858	+	0.593467i	$0.797759\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$	−13.0386	+	7.52784i	−1.39789	+	0.807070i
$88$		0			0
$89$	−4.20282	+	7.27950i	−0.445498	+	0.771625i	−0.998087	−	0.0618287i	$-0.980307\pi$
$89$	−4.20282	+	7.27950i	−0.445498	+	0.771625i	0.552589	+	0.833454i	$0.313640\pi$
$90$		0			0
$91$	4.46381	−	12.7591i	0.467934	−	1.33751i
$92$		0			0
$93$	−1.94454	−	1.12268i	−0.201639	−	0.116416i
$94$		0			0
$95$		0			0
$96$		0			0
$97$			0.614293i			0.0623720i	0.999514	+	0.0311860i	$0.00992842\pi$
$97$			0.614293i			0.0623720i	−0.999514	+	0.0311860i	$0.990072\pi$
$98$		0			0
$99$	33.9321			3.41031
$100$		0			0
$101$	−2.82550	−	4.89391i	−0.281148	−	0.486962i	0.690520	−	0.723313i	$-0.257382\pi$
$101$	−2.82550	−	4.89391i	−0.281148	−	0.486962i	−0.971668	+	0.236351i	$0.924048\pi$
$102$		0			0
$103$	−2.02802	−	1.17088i	−0.199827	−	0.115370i	0.396748	−	0.917928i	$-0.370139\pi$
$103$	−2.02802	−	1.17088i	−0.199827	−	0.115370i	−0.596575	+	0.802558i	$0.703472\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−0.859752	−	0.496378i	−0.0831154	−	0.0479867i	0.457866	−	0.889021i	$-0.348614\pi$
$107$	−0.859752	−	0.496378i	−0.0831154	−	0.0479867i	−0.540982	+	0.841034i	$0.681947\pi$
$108$		0			0
$109$	−9.06928	−	15.7084i	−0.868679	−	1.50460i	−0.863347	−	0.504611i	$-0.831636\pi$
$109$	−9.06928	−	15.7084i	−0.868679	−	1.50460i	−0.00533214	−	0.999986i	$-0.501697\pi$
$110$		0			0
$111$	−5.04616			−0.478960
$112$		0			0
$113$			6.22638i			0.585728i	0.956154	+	0.292864i	$0.0946084\pi$
$113$			6.22638i			0.585728i	−0.956154	+	0.292864i	$0.905392\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$	−35.3648	−	20.4179i	−3.26947	−	1.88763i
$118$		0			0
$119$	−2.29718	+	0.434780i	−0.210582	+	0.0398562i
$120$		0			0
$121$	−3.51153	+	6.08215i	−0.319230	+	0.552923i
$122$		0			0
$123$	−17.0174	+	9.82502i	−1.53441	+	0.885892i
$124$		0			0
$125$		0			0
$126$		0			0
$127$		−	1.62382i		−	0.144091i	−0.997401	−	0.0720454i	$-0.977047\pi$
$127$		−	1.62382i		−	0.144091i	0.997401	−	0.0720454i	$-0.0229527\pi$
$128$		0			0
$129$	9.11433	+	15.7865i	0.802472	+	1.38992i
$130$		0			0
$131$	−3.14103	+	5.44043i	−0.274433	+	0.475332i	−0.969992	−	0.243137i	$-0.921824\pi$
$131$	−3.14103	+	5.44043i	−0.274433	+	0.475332i	0.695559	+	0.718469i	$0.255157\pi$
$132$		0			0
$133$	−13.1166	+	11.2890i	−1.13736	+	0.978884i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	15.5124	−	8.95609i	1.32531	−	0.765170i	0.340743	−	0.940157i	$-0.389321\pi$
$137$	15.5124	−	8.95609i	1.32531	−	0.765170i	0.984571	+	0.174986i	$0.0559881\pi$
$138$		0			0
$139$	−23.0023			−1.95103			−0.975514	−	0.219936i	$-0.929415\pi$
$139$	−23.0023			−1.95103			−0.975514	+	0.219936i	$0.929415\pi$
$140$		0			0
$141$	−24.1018			−2.02974
$142$		0			0
$143$	18.7840	−	10.8450i	1.57080	−	0.906901i
$144$		0			0
$145$		0			0
$146$		0			0
$147$	22.9499	+	3.45656i	1.89287	+	0.285093i
$148$		0			0
$149$	−5.20030	+	9.00719i	−0.426025	+	0.737898i	−0.996516	−	0.0834067i	$-0.973420\pi$
$149$	−5.20030	+	9.00719i	−0.426025	+	0.737898i	0.570490	+	0.821304i	$0.306753\pi$
$150$		0			0
$151$	−10.5860	−	18.3355i	−0.861477	−	1.49212i	−0.870503	−	0.492163i	$-0.836206\pi$
$151$	−10.5860	−	18.3355i	−0.861477	−	1.49212i	0.00902561	−	0.999959i	$-0.497127\pi$
$152$		0			0
$153$			7.06293i			0.571004i
$154$		0			0
$155$		0			0
$156$		0			0
$157$	6.77296	−	3.91037i	0.540541	−	0.312081i	−0.204757	−	0.978813i	$-0.565641\pi$
$157$	6.77296	−	3.91037i	0.540541	−	0.312081i	0.745298	+	0.666731i	$0.232307\pi$
$158$		0			0
$159$	−4.25737	+	7.37397i	−0.337631	+	0.584794i
$160$		0			0
$161$	9.20848	+	10.6993i	0.725730	+	0.843220i
$162$		0			0
$163$	19.2960	+	11.1406i	1.51138	+	0.872596i	0.999912	+	0.0132936i	$0.00423160\pi$
$163$	19.2960	+	11.1406i	1.51138	+	0.872596i	0.511468	+	0.859302i	$0.329102\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$			23.8180i			1.84309i	0.388270	+	0.921546i	$0.373073\pi$
$167$			23.8180i			1.84309i	−0.388270	+	0.921546i	$0.626927\pi$
$168$		0			0
$169$	−13.1028			−1.00791
$170$		0			0
$171$	26.1401	+	45.2760i	1.99899	+	3.46235i
$172$		0			0
$173$	−6.31546	−	3.64624i	−0.480156	−	0.277218i	0.240326	−	0.970692i	$-0.422746\pi$
$173$	−6.31546	−	3.64624i	−0.480156	−	0.277218i	−0.720481	+	0.693474i	$0.756079\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	−22.8173	−	13.1736i	−1.71506	−	0.990189i
$178$		0			0
$179$	8.92258	+	15.4544i	0.666905	+	1.15511i	0.978765	+	0.204985i	$0.0657147\pi$
$179$	8.92258	+	15.4544i	0.666905	+	1.15511i	−0.311860	+	0.950128i	$0.600952\pi$
$180$		0			0
$181$	−9.62478			−0.715404			−0.357702	−	0.933836i	$-0.616440\pi$
$181$	−9.62478			−0.715404			−0.357702	+	0.933836i	$0.616440\pi$
$182$		0			0
$183$		−	29.9059i		−	2.21071i
$184$		0			0
$185$		0			0
$186$		0			0
$187$	−3.24888	−	1.87574i	−0.237581	−	0.137168i
$188$		0			0
$189$	14.4629	−	41.3399i	1.05202	−	3.00703i
$190$		0			0
$191$	8.71818	−	15.1003i	0.630825	−	1.09262i	−0.356558	−	0.934273i	$-0.616050\pi$
$191$	8.71818	−	15.1003i	0.630825	−	1.09262i	0.987383	−	0.158348i	$-0.0506169\pi$
$192$		0			0
$193$	−2.26213	+	1.30604i	−0.162832	+	0.0940110i	−0.579201	−	0.815184i	$-0.696636\pi$
$193$	−2.26213	+	1.30604i	−0.162832	+	0.0940110i	0.416370	+	0.909195i	$0.363302\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$			18.4853i			1.31703i	0.752569	+	0.658513i	$0.228814\pi$
$197$			18.4853i			1.31703i	−0.752569	+	0.658513i	$0.771186\pi$
$198$		0			0
$199$	−10.7637	−	18.6433i	−0.763019	−	1.32159i	−0.941287	−	0.337606i	$-0.890383\pi$
$199$	−10.7637	−	18.6433i	−0.763019	−	1.32159i	0.178268	−	0.983982i	$-0.442951\pi$
$200$		0			0
$201$	5.04616	−	8.74020i	0.355929	−	0.616486i
$202$		0			0
$203$	−11.3403	−	3.96743i	−0.795930	−	0.278459i
$204$		0			0
$205$		0			0
$206$		0			0
$207$	36.9317	−	21.3225i	2.56693	−	1.48202i
$208$		0			0
$209$	−27.7687			−1.92080
$210$		0			0
$211$	18.3200			1.26120			0.630601	−	0.776107i	$-0.282808\pi$
$211$	18.3200			1.26120			0.630601	+	0.776107i	$0.282808\pi$
$212$		0			0
$213$	15.5006	−	8.94928i	1.06208	−	0.613195i
$214$		0			0
$215$		0			0
$216$		0			0
$217$	−0.333207	−	1.76051i	−0.0226195	−	0.119511i
$218$		0			0
$219$	−6.39840	+	11.0824i	−0.432364	+	0.748876i
$220$		0			0
$221$	2.25737	+	3.90987i	0.151847	+	0.263006i
$222$		0			0
$223$		−	2.61429i		−	0.175066i	−0.996162	−	0.0875330i	$-0.972102\pi$
$223$		−	2.61429i		−	0.175066i	0.996162	−	0.0875330i	$-0.0278983\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−5.21695	+	3.01201i	−0.346261	+	0.199914i	−0.663037	−	0.748586i	$-0.730733\pi$
$227$	−5.21695	+	3.01201i	−0.346261	+	0.199914i	0.316776	+	0.948500i	$0.397400\pi$
$228$		0			0
$229$	−7.52150	+	13.0276i	−0.497035	+	0.860889i	−0.999994	−	0.00342076i	$-0.998911\pi$
$229$	−7.52150	+	13.0276i	−0.497035	+	0.860889i	0.502960	+	0.864310i	$0.332244\pi$
$230$		0			0
$231$	24.2931	+	28.2260i	1.59837	+	1.85713i
$232$		0			0
$233$	−1.47332	−	0.850620i	−0.0965202	−	0.0557260i	0.450963	−	0.892543i	$-0.351081\pi$
$233$	−1.47332	−	0.850620i	−0.0965202	−	0.0557260i	−0.547483	+	0.836817i	$0.684414\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$		−	2.33547i		−	0.151705i
$238$		0			0
$239$	25.8208			1.67021			0.835105	−	0.550091i	$-0.185407\pi$
$239$	25.8208			1.67021			0.835105	+	0.550091i	$0.185407\pi$
$240$		0			0
$241$	5.54254	+	9.59996i	0.357026	+	0.618387i	0.987463	−	0.157853i	$-0.0504574\pi$
$241$	5.54254	+	9.59996i	0.357026	+	0.618387i	−0.630436	+	0.776241i	$0.717124\pi$
$242$		0			0
$243$	−45.7335	−	26.4043i	−2.93381	−	1.69383i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	28.9411	+	16.7092i	1.84148	+	1.06318i
$248$		0			0
$249$	17.9262	+	31.0492i	1.13603	+	1.96766i
$250$		0			0
$251$	6.96558			0.439663			0.219832	−	0.975538i	$-0.429449\pi$
$251$	6.96558			0.439663			0.219832	+	0.975538i	$0.429449\pi$
$252$		0			0
$253$			22.6510i			1.42405i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	2.62359	+	1.51473i	0.163655	+	0.0944864i	0.579591	−	0.814908i	$-0.303212\pi$
$257$	2.62359	+	1.51473i	0.163655	+	0.0944864i	−0.415935	+	0.909394i	$0.636546\pi$
$258$		0			0
$259$	−2.62678	−	3.05203i	−0.163220	−	0.189644i
$260$		0			0
$261$	−18.1474	+	31.4322i	−1.12329	+	1.94560i
$262$		0			0
$263$	6.35461	−	3.66884i	0.391842	−	0.226230i	−0.291116	−	0.956688i	$-0.594027\pi$
$263$	6.35461	−	3.66884i	0.391842	−	0.226230i	0.682958	+	0.730458i	$0.260693\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$			27.8692i			1.70557i
$268$		0			0
$269$	7.70711	+	13.3491i	0.469911	+	0.813909i	0.999408	−	0.0344024i	$-0.0109528\pi$
$269$	7.70711	+	13.3491i	0.469911	+	0.813909i	−0.529497	+	0.848312i	$0.677619\pi$
$270$		0			0
$271$	−3.30467	+	5.72385i	−0.200744	+	0.347699i	−0.948768	−	0.315972i	$-0.897669\pi$
$271$	−3.30467	+	5.72385i	−0.200744	+	0.347699i	0.748024	+	0.663671i	$0.231003\pi$
$272$		0			0
$273$	−8.33447	−	44.0355i	−0.504425	−	2.66515i
$274$		0			0
$275$		0			0
$276$		0			0
$277$	9.31660	−	5.37894i	0.559780	−	0.323189i	−0.193277	−	0.981144i	$-0.561912\pi$
$277$	9.31660	−	5.37894i	0.559780	−	0.323189i	0.753057	+	0.657955i	$0.228578\pi$
$278$		0			0
$279$	−5.41289			−0.324061
$280$		0			0
$281$	25.3033			1.50947			0.754735	−	0.656030i	$-0.227765\pi$
$281$	25.3033			1.50947			0.754735	+	0.656030i	$0.227765\pi$
$282$		0			0
$283$	−5.49493	+	3.17250i	−0.326640	+	0.188585i	−0.654348	−	0.756193i	$-0.727057\pi$
$283$	−5.49493	+	3.17250i	−0.326640	+	0.188585i	0.327709	+	0.944779i	$0.393724\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	−14.8008	−	5.17812i	−0.873665	−	0.305655i
$288$		0			0
$289$	−8.10957	+	14.0462i	−0.477033	+	0.826246i
$290$		0			0
$291$	1.01835	+	1.76384i	0.0596969	+	0.103398i
$292$		0			0
$293$			20.3589i			1.18938i	0.803954	+	0.594691i	$0.202726\pi$
$293$			20.3589i			1.18938i	−0.803954	+	0.594691i	$0.797274\pi$
$294$		0			0
$295$		0			0
$296$		0			0
$297$	60.8609	−	35.1381i	3.53151	−	2.03892i
$298$		0			0
$299$	13.6297	−	23.6073i	0.788225	−	1.36525i
$300$		0			0
$301$	−4.80356	+	13.7302i	−0.276873	+	0.791396i
$302$		0			0
$303$	−16.2259	−	9.36804i	−0.932154	−	0.538180i
$304$		0			0
$305$		0			0
$306$		0			0
$307$		−	29.5695i		−	1.68762i	−0.536643	−	0.843809i	$-0.680308\pi$
$307$		−	29.5695i		−	1.68762i	0.536643	−	0.843809i	$-0.319692\pi$
$308$		0			0
$309$	−7.76417			−0.441688
$310$		0			0
$311$	6.24153	+	10.8106i	0.353925	+	0.613016i	0.986933	−	0.161129i	$-0.0515136\pi$
$311$	6.24153	+	10.8106i	0.353925	+	0.613016i	−0.633009	+	0.774145i	$0.718180\pi$
$312$		0			0
$313$	−0.912273	−	0.526701i	−0.0515647	−	0.0297709i	0.473996	−	0.880527i	$-0.342811\pi$
$313$	−0.912273	−	0.526701i	−0.0515647	−	0.0297709i	−0.525561	+	0.850756i	$0.676144\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−2.26840	−	1.30966i	−0.127406	−	0.0735581i	0.434942	−	0.900458i	$-0.356769\pi$
$317$	−2.26840	−	1.30966i	−0.127406	−	0.0735581i	−0.562349	+	0.826900i	$0.690102\pi$
$318$		0			0
$319$	−9.63899	−	16.6952i	−0.539680	−	0.934753i
$320$		0			0
$321$	−3.29152			−0.183715
$322$		0			0
$323$		−	5.78002i		−	0.321609i
$324$		0			0
$325$		0			0
$326$		0			0
$327$	−52.0819	−	30.0695i	−2.88013	−	1.66285i
$328$		0			0
$329$	−12.5462	−	14.5773i	−0.691695	−	0.803675i
$330$		0			0
$331$	−9.63693	+	16.6917i	−0.529694	+	0.917457i	0.469706	+	0.882823i	$0.344360\pi$
$331$	−9.63693	+	16.6917i	−0.529694	+	0.917457i	−0.999400	+	0.0346338i	$0.988974\pi$
$332$		0			0
$333$	−10.5350	+	6.08239i	−0.577315	+	0.333313i
$334$		0			0
$335$		0			0
$336$		0			0
$337$		−	10.2979i		−	0.560961i	−0.959860	−	0.280481i	$-0.909506\pi$
$337$		−	10.2979i		−	0.560961i	0.959860	−	0.280481i	$-0.0904939\pi$
$338$		0			0
$339$	10.3219	+	17.8780i	0.560607	+	0.971001i
$340$		0			0
$341$	1.43753	−	2.48987i	0.0778465	−	0.134834i
$342$		0			0
$343$	9.85595	+	15.6799i	0.532171	+	0.846637i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−17.5848	+	10.1526i	−0.943999	+	0.545018i	−0.891212	−	0.453588i	$-0.850144\pi$
$347$	−17.5848	+	10.1526i	−0.943999	+	0.545018i	−0.0527875	+	0.998606i	$0.516811\pi$
$348$		0			0
$349$	2.62249			0.140379			0.0701893	−	0.997534i	$-0.477640\pi$
$349$	2.62249			0.140379			0.0701893	+	0.997534i	$0.477640\pi$
$350$		0			0
$351$	−84.5741			−4.51423
$352$		0			0
$353$	7.55629	−	4.36263i	0.402181	−	0.232199i	−0.285244	−	0.958455i	$-0.592075\pi$
$353$	7.55629	−	4.36263i	0.402181	−	0.232199i	0.687425	+	0.726256i	$0.258741\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$	−5.87521	+	5.05659i	−0.310949	+	0.267623i
$358$		0			0
$359$	−6.02470	+	10.4351i	−0.317971	+	0.550743i	−0.980065	−	0.198679i	$-0.936335\pi$
$359$	−6.02470	+	10.4351i	−0.317971	+	0.550743i	0.662093	+	0.749421i	$0.269668\pi$
$360$		0			0
$361$	−11.8921	−	20.5976i	−0.625898	−	1.08409i
$362$		0			0
$363$			23.2852i			1.22216i
$364$		0			0
$365$		0			0
$366$		0			0
$367$	−3.01833	+	1.74263i	−0.157556	+	0.0909648i	−0.576705	−	0.816953i	$-0.695662\pi$
$367$	−3.01833	+	1.74263i	−0.157556	+	0.0909648i	0.419149	+	0.907917i	$0.362328\pi$
$368$		0			0
$369$	−23.6852	+	41.0240i	−1.23300	+	2.13562i
$370$		0			0
$371$	−6.67612	+	1.26357i	−0.346607	+	0.0656012i
$372$		0			0
$373$	−32.5362	−	18.7848i	−1.68466	−	0.972639i	−0.958490	−	0.285125i	$-0.907965\pi$
$373$	−32.5362	−	18.7848i	−1.68466	−	0.972639i	−0.726171	−	0.687515i	$-0.758702\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$			23.2002i			1.19487i
$378$		0			0
$379$	2.48935			0.127869			0.0639347	−	0.997954i	$-0.479635\pi$
$379$	2.48935			0.127869			0.0639347	+	0.997954i	$0.479635\pi$
$380$		0			0
$381$	−2.69192	−	4.66254i	−0.137911	−	0.238869i
$382$		0			0
$383$	18.5981	+	10.7376i	0.950320	+	0.548668i	0.893180	−	0.449699i	$-0.148469\pi$
$383$	18.5981	+	10.7376i	0.950320	+	0.548668i	0.0571398	+	0.998366i	$0.481802\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	38.0565	+	21.9719i	1.93452	+	1.11690i
$388$		0			0
$389$	5.67880	+	9.83598i	0.287927	+	0.498704i	0.973315	−	0.229474i	$-0.0737007\pi$
$389$	5.67880	+	9.83598i	0.287927	+	0.498704i	−0.685388	+	0.728178i	$0.740367\pi$
$390$		0			0
$391$	−4.71477			−0.238436
$392$		0			0
$393$			20.8284i			1.05065i
$394$		0			0
$395$		0			0
$396$		0			0
$397$	21.5675	+	12.4520i	1.08244	+	0.624948i	0.931554	−	0.363603i	$-0.118453\pi$
$397$	21.5675	+	12.4520i	1.08244	+	0.624948i	0.150888	+	0.988551i	$0.451787\pi$
$398$		0			0
$399$	−18.9477	+	54.1589i	−0.948572	+	2.71134i
$400$		0			0
$401$	−4.68494	+	8.11456i	−0.233955	+	0.405222i	−0.958968	−	0.283513i	$-0.908500\pi$
$401$	−4.68494	+	8.11456i	−0.233955	+	0.405222i	0.725014	+	0.688735i	$0.241833\pi$
$402$		0			0
$403$	−2.99645	+	1.73000i	−0.149264	+	0.0861774i
$404$		0			0
$405$		0			0
$406$		0			0
$407$		−	6.46133i		−	0.320276i
$408$		0			0
$409$	−6.50724	−	11.2709i	−0.321762	−	0.557309i	0.659089	−	0.752065i	$-0.270942\pi$
$409$	−6.50724	−	11.2709i	−0.321762	−	0.557309i	−0.980852	+	0.194756i	$0.937609\pi$
$410$		0			0
$411$	29.6942	−	51.4319i	1.46471	−	2.53695i
$412$		0			0
$413$	−3.90987	−	20.6580i	−0.192392	−	1.01651i
$414$		0			0
$415$		0			0
$416$		0			0
$417$	−66.0473	+	38.1324i	−3.23435	+	1.86735i
$418$		0			0
$419$	−9.76954			−0.477273			−0.238637	−	0.971109i	$-0.576700\pi$
$419$	−9.76954			−0.477273			−0.238637	+	0.971109i	$0.576700\pi$
$420$		0			0
$421$	−21.5881			−1.05214			−0.526069	−	0.850442i	$-0.676335\pi$
$421$	−21.5881			−1.05214			−0.526069	+	0.850442i	$0.676335\pi$
$422$		0			0
$423$	−50.3181	+	29.0512i	−2.44655	+	1.41252i
$424$		0			0
$425$		0			0
$426$		0			0
$427$	18.0878	−	15.5675i	0.875328	−	0.753364i
$428$		0			0
$429$	35.9568	−	62.2790i	1.73601	−	3.00686i
$430$		0			0
$431$	−8.99844	−	15.5857i	−0.433439	−	0.750739i	0.563727	−	0.825961i	$-0.309367\pi$
$431$	−8.99844	−	15.5857i	−0.433439	−	0.750739i	−0.997167	+	0.0752218i	$0.976034\pi$
$432$		0			0
$433$		−	24.2236i		−	1.16411i	−0.813148	−	0.582057i	$-0.802248\pi$
$433$		−	24.2236i		−	1.16411i	0.813148	−	0.582057i	$-0.197752\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−30.2235	+	17.4495i	−1.44578	+	0.834724i
$438$		0			0
$439$	−0.507449	+	0.878928i	−0.0242192	+	0.0419490i	−0.877881	−	0.478879i	$-0.841043\pi$
$439$	−0.507449	+	0.878928i	−0.0242192	+	0.0419490i	0.853662	+	0.520828i	$0.174377\pi$
$440$		0			0
$441$	52.0795	−	20.4463i	2.47998	−	0.973633i
$442$		0			0
$443$	−12.1326	−	7.00476i	−0.576438	−	0.332806i	0.183279	−	0.983061i	$-0.441329\pi$
$443$	−12.1326	−	7.00476i	−0.576438	−	0.332806i	−0.759716	+	0.650255i	$0.774662\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$			34.4835i			1.63102i
$448$		0			0
$449$	9.76134			0.460666			0.230333	−	0.973112i	$-0.426018\pi$
$449$	9.76134			0.460666			0.230333	+	0.973112i	$0.426018\pi$
$450$		0			0
$451$	−12.5804	−	21.7899i	−0.592388	−	1.02605i
$452$		0			0
$453$	−60.7920	−	35.0983i	−2.85626	−	1.64906i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	22.2826	+	12.8649i	1.04234	+	0.601794i	0.920495	−	0.390755i	$-0.127786\pi$
$457$	22.2826	+	12.8649i	1.04234	+	0.601794i	0.121844	+	0.992549i	$0.461119\pi$
$458$		0			0
$459$	7.31395	+	12.6681i	0.341386	+	0.591298i
$460$		0			0
$461$	25.3115			1.17888			0.589438	−	0.807814i	$-0.299349\pi$
$461$	25.3115			1.17888			0.589438	+	0.807814i	$0.299349\pi$
$462$		0			0
$463$			35.8484i			1.66602i	0.553261	+	0.833008i	$0.313383\pi$
$463$			35.8484i			1.66602i	−0.553261	+	0.833008i	$0.686617\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−3.16733	−	1.82866i	−0.146567	−	0.0846204i	0.424923	−	0.905229i	$-0.360301\pi$
$467$	−3.16733	−	1.82866i	−0.146567	−	0.0846204i	−0.571490	+	0.820609i	$0.693634\pi$
$468$		0			0
$469$	7.91305	−	1.49768i	0.365391	−	0.0691564i
$470$		0			0
$471$	12.9650	−	22.4560i	0.597393	−	1.03472i
$472$		0			0
$473$	−20.2137	+	11.6704i	−0.929428	+	0.536606i
$474$		0			0
$475$		0			0
$476$		0			0
$477$			20.5265i			0.939842i
$478$		0			0
$479$	0.935505	+	1.62034i	0.0427443	+	0.0740353i	0.886606	−	0.462525i	$-0.153057\pi$
$479$	0.935505	+	1.62034i	0.0427443	+	0.0740353i	−0.843862	+	0.536561i	$0.819723\pi$
$480$		0			0
$481$	−3.88795	+	6.73413i	−0.177275	+	0.307050i
$482$		0			0
$483$	44.1775	+	15.4557i	2.01015	+	0.703257i
$484$		0			0
$485$		0			0
$486$		0			0
$487$	−8.12552	+	4.69127i	−0.368203	+	0.212582i	−0.672673	−	0.739940i	$-0.734854\pi$
$487$	−8.12552	+	4.69127i	−0.368203	+	0.212582i	0.304470	+	0.952522i	$0.401521\pi$
$488$		0			0
$489$	73.8738			3.34069
$490$		0			0
$491$	−38.6545			−1.74445			−0.872227	−	0.489100i	$-0.837325\pi$
$491$	−38.6545			−1.74445			−0.872227	+	0.489100i	$0.837325\pi$
$492$		0			0
$493$	3.47509	−	2.00635i	0.156510	−	0.0903613i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	13.4816	+	4.71658i	0.604731	+	0.211567i
$498$		0			0
$499$	2.05298	−	3.55587i	0.0919040	−	0.159182i	−0.816408	−	0.577475i	$-0.804038\pi$
$499$	2.05298	−	3.55587i	0.0919040	−	0.159182i	0.908312	+	0.418293i	$0.137371\pi$
$500$		0			0
$501$	39.4847	+	68.3894i	1.76404	+	3.05541i
$502$		0			0
$503$		−	26.6922i		−	1.19015i	−0.803672	−	0.595073i	$-0.797123\pi$
$503$		−	26.6922i		−	1.19015i	0.803672	−	0.595073i	$-0.202877\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	−37.6225	+	21.7214i	−1.67088	+	0.964680i
$508$		0			0
$509$	−6.40469	+	11.0932i	−0.283883	+	0.491699i	−0.972338	−	0.233580i	$-0.924956\pi$
$509$	−6.40469	+	11.0932i	−0.283883	+	0.491699i	0.688455	+	0.725279i	$0.258289\pi$
$510$		0			0
$511$	−10.0335	+	1.89902i	−0.443858	+	0.0840077i
$512$		0			0
$513$	93.7704	+	54.1383i	4.14006	+	2.39027i
$514$		0			0
$515$		0			0
$516$		0			0
$517$		−	30.8611i		−	1.35727i
$518$		0			0
$519$	−24.1784			−1.06131
$520$		0			0
$521$	−11.9106	−	20.6297i	−0.521811	−	0.903803i	−0.999678	−	0.0253710i	$-0.991923\pi$
$521$	−11.9106	−	20.6297i	−0.521811	−	0.903803i	0.477867	−	0.878432i	$-0.341410\pi$
$522$		0			0
$523$	11.0580	+	6.38433i	0.483532	+	0.279167i	0.721887	−	0.692011i	$-0.243275\pi$
$523$	11.0580	+	6.38433i	0.483532	+	0.279167i	−0.238355	+	0.971178i	$0.576608\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	0.518264	+	0.299220i	0.0225759	+	0.0130342i
$528$		0			0
$529$	2.73360	+	4.73474i	0.118852	+	0.205858i
$530$		0			0
$531$	−63.5152			−2.75633
$532$		0			0
$533$			30.2799i			1.31157i
$534$		0			0
$535$		0			0
$536$		0			0
$537$	51.2395	+	29.5831i	2.21115	+	1.27661i
$538$		0			0
$539$	−4.42594	+	29.3861i	−0.190639	+	1.26575i
$540$		0			0
$541$	8.84180	−	15.3144i	0.380138	−	0.658419i	−0.610943	−	0.791674i	$-0.709210\pi$
$541$	8.84180	−	15.3144i	0.380138	−	0.658419i	0.991082	+	0.133255i	$0.0425430\pi$
$542$		0			0
$543$	−27.6360	+	15.9556i	−1.18597	+	0.684722i
$544$		0			0
$545$		0			0
$546$		0			0
$547$		−	24.0580i		−	1.02864i	−0.857597	−	0.514322i	$-0.828044\pi$
$547$		−	24.0580i		−	1.02864i	0.857597	−	0.514322i	$-0.171956\pi$
$548$		0			0
$549$	−36.0471	−	62.4354i	−1.53845	−	2.66468i
$550$		0			0
$551$	14.8511	−	25.7229i	0.632678	−	1.09583i
$552$		0			0
$553$	1.41254	−	1.21573i	0.0600675	−	0.0516980i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−4.21103	+	2.43124i	−0.178427	+	0.103015i	−0.586553	−	0.809911i	$-0.699516\pi$
$557$	−4.21103	+	2.43124i	−0.178427	+	0.103015i	0.408126	+	0.912925i	$0.366182\pi$
$558$		0			0
$559$	28.0896			1.18806
$560$		0			0
$561$	−12.4382			−0.525139
$562$		0			0
$563$	9.59960	−	5.54233i	0.404575	−	0.233581i	−0.283881	−	0.958859i	$-0.591622\pi$
$563$	9.59960	−	5.54233i	0.404575	−	0.233581i	0.688456	+	0.725278i	$0.258289\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$	−15.2063	−	80.3429i	−0.638603	−	3.37409i
$568$		0			0
$569$	−8.47854	+	14.6853i	−0.355439	+	0.615638i	−0.987193	−	0.159531i	$-0.949002\pi$
$569$	−8.47854	+	14.6853i	−0.355439	+	0.615638i	0.631754	+	0.775169i	$0.282335\pi$
$570$		0			0
$571$	−10.1725	−	17.6193i	−0.425706	−	0.737344i	0.570780	−	0.821103i	$-0.306641\pi$
$571$	−10.1725	−	17.6193i	−0.425706	−	0.737344i	−0.996486	+	0.0837588i	$0.973307\pi$
$572$		0			0
$573$		−	57.8108i		−	2.41508i
$574$		0			0
$575$		0			0
$576$		0			0
$577$	36.1689	−	20.8821i	1.50573	−	0.869335i	0.505754	−	0.862678i	$-0.331214\pi$
$577$	36.1689	−	20.8821i	1.50573	−	0.869335i	0.999978	−	0.00665740i	$-0.00211913\pi$
$578$		0			0
$579$	−4.33023	+	7.50017i	−0.179958	+	0.311696i
$580$		0			0
$581$	−9.44774	+	27.0048i	−0.391958	+	1.12035i
$582$		0			0
$583$	−9.44197	−	5.45132i	−0.391046	−	0.225771i
$584$		0			0
$585$		0			0
$586$		0			0
$587$		−	38.6858i		−	1.59674i	−0.602170	−	0.798368i	$-0.705697\pi$
$587$		−	38.6858i		−	1.59674i	0.602170	−	0.798368i	$-0.294303\pi$
$588$		0			0
$589$	4.42969			0.182522
$590$		0			0
$591$	30.6444	+	53.0776i	1.26054	+	2.18332i
$592$		0			0
$593$	16.1049	+	9.29817i	0.661349	+	0.381830i	0.792791	−	0.609494i	$-0.208627\pi$
$593$	16.1049	+	9.29817i	0.661349	+	0.381830i	−0.131442	+	0.991324i	$0.541961\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	−61.8125	−	35.6874i	−2.52982	−	1.46059i
$598$		0			0
$599$	−11.0269	−	19.0991i	−0.450547	−	0.780369i	0.547873	−	0.836561i	$-0.315438\pi$
$599$	−11.0269	−	19.0991i	−0.450547	−	0.780369i	−0.998420	+	0.0561917i	$0.982104\pi$
$600$		0			0
$601$	−20.6533			−0.842465			−0.421233	−	0.906953i	$-0.638402\pi$
$601$	−20.6533			−0.842465			−0.421233	+	0.906953i	$0.638402\pi$
$602$		0			0
$603$		−	24.3296i		−	0.990776i
$604$		0			0
$605$		0			0
$606$		0			0
$607$	20.9329	+	12.0856i	0.849638	+	0.490539i	0.860529	−	0.509402i	$-0.170133\pi$
$607$	20.9329	+	12.0856i	0.849638	+	0.490539i	−0.0108905	+	0.999941i	$0.503467\pi$
$608$		0			0
$609$	−39.1388	+	7.40768i	−1.58598	+	0.300174i
$610$		0			0
$611$	−18.5699	+	32.1641i	−0.751259	+	1.30122i
$612$		0			0
$613$	39.7302	−	22.9383i	1.60469	−	0.926467i	0.614156	−	0.789184i	$-0.289496\pi$
$613$	39.7302	−	22.9383i	1.60469	−	0.926467i	0.990532	−	0.137283i	$-0.0438369\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$		−	25.8072i		−	1.03896i	−0.854483	−	0.519479i	$-0.826126\pi$
$617$		−	25.8072i		−	1.03896i	0.854483	−	0.519479i	$-0.173874\pi$
$618$		0			0
$619$	−21.5216	−	37.2764i	−0.865024	−	1.49827i	−0.867023	−	0.498268i	$-0.833970\pi$
$619$	−21.5216	−	37.2764i	−0.865024	−	1.49827i	0.00199877	−	0.999998i	$-0.499364\pi$
$620$		0			0
$621$	44.1607	−	76.4886i	1.77211	−	3.06938i
$622$		0			0
$623$	−16.8559	+	14.5073i	−0.675318	+	0.581223i
$624$		0			0
$625$		0			0
$626$		0			0
$627$	−79.7332	+	46.0340i	−3.18424	+	1.83842i
$628$		0			0
$629$	1.34492			0.0536254
$630$		0			0
$631$	20.8872			0.831508			0.415754	−	0.909477i	$-0.363518\pi$
$631$	20.8872			0.831508			0.415754	+	0.909477i	$0.363518\pi$
$632$		0			0
$633$	52.6029	−	30.3703i	2.09078	−	1.20711i
$634$		0			0
$635$		0			0
$636$		0			0
$637$	22.2952	−	27.9636i	0.883368	−	1.10796i
$638$		0			0
$639$	21.5740	−	37.3673i	0.853456	−	1.47823i
$640$		0			0
$641$	15.9466	+	27.6203i	0.629853	+	1.09094i	0.987581	+	0.157112i	$0.0502184\pi$
$641$	15.9466	+	27.6203i	0.629853	+	1.09094i	−0.357727	+	0.933826i	$0.616448\pi$
$642$		0			0
$643$		−	0.850088i		−	0.0335242i	−0.999860	−	0.0167621i	$-0.994664\pi$
$643$		−	0.850088i		−	0.0335242i	0.999860	−	0.0167621i	$-0.00533579\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	29.7557	−	17.1795i	1.16982	−	0.675395i	0.216181	−	0.976353i	$-0.430640\pi$
$647$	29.7557	−	17.1795i	1.16982	−	0.675395i	0.953637	+	0.300959i	$0.0973066\pi$
$648$		0			0
$649$	16.8681	−	29.2164i	0.662130	−	1.14684i
$650$		0			0
$651$	−3.87526	−	4.50264i	−0.151884	−	0.176472i
$652$		0			0
$653$	−19.0945	−	11.0242i	−0.747226	−	0.431411i	0.0774647	−	0.996995i	$-0.475317\pi$
$653$	−19.0945	−	11.0242i	−0.747226	−	0.431411i	−0.824691	+	0.565584i	$0.808651\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$			30.8492i			1.20354i
$658$		0			0
$659$	16.9046			0.658508			0.329254	−	0.944241i	$-0.393203\pi$
$659$	16.9046			0.658508			0.329254	+	0.944241i	$0.393203\pi$
$660$		0			0
$661$	−7.44864	−	12.9014i	−0.289718	−	0.501807i	0.684024	−	0.729460i	$-0.260228\pi$
$661$	−7.44864	−	12.9014i	−0.289718	−	0.501807i	−0.973742	+	0.227652i	$0.926895\pi$
$662$		0			0
$663$	12.9633	+	7.48437i	0.503453	+	0.290669i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	−20.9822	−	12.1141i	−0.812433	−	0.469058i
$668$		0			0
$669$	−4.33389	−	7.50651i	−0.167558	−	0.290218i
$670$		0			0
$671$	38.2928			1.47828
$672$		0			0
$673$			26.1490i			1.00797i	0.863713	+	0.503984i	$0.168133\pi$
$673$			26.1490i			1.00797i	−0.863713	+	0.503984i	$0.831867\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−28.0943	−	16.2202i	−1.07975	−	0.623394i	−0.148922	−	0.988849i	$-0.547580\pi$
$677$	−28.0943	−	16.2202i	−1.07975	−	0.623394i	−0.930829	+	0.365455i	$0.880914\pi$
$678$		0			0
$679$	−0.536707	+	1.53409i	−0.0205969	+	0.0588730i
$680$		0			0
$681$	−9.98641	+	17.2970i	−0.382680	+	0.662821i
$682$		0			0
$683$	38.3251	−	22.1270i	1.46647	−	0.846667i	0.467174	−	0.884166i	$-0.345272\pi$
$683$	38.3251	−	22.1270i	1.46647	−	0.846667i	0.999297	+	0.0374987i	$0.0119390\pi$
$684$		0			0
$685$		0			0
$686$		0			0
$687$			49.8755i			1.90287i
$688$		0			0
$689$	6.56041	+	11.3630i	0.249932	+	0.432895i
$690$		0			0
$691$	19.1793	−	33.2196i	0.729616	−	1.26373i	−0.227430	−	0.973794i	$-0.573032\pi$
$691$	19.1793	−	33.2196i	0.729616	−	1.26373i	0.957046	−	0.289937i	$-0.0936344\pi$
$692$		0			0
$693$	84.7396	+	29.6465i	3.21899	+	1.12618i
$694$		0			0
$695$		0			0
$696$		0			0
$697$	4.53554	−	2.61860i	0.171796	−	0.0991864i
$698$		0			0
$699$	−5.64052			−0.213344
$700$		0			0
$701$	13.0696			0.493633			0.246817	−	0.969062i	$-0.420615\pi$
$701$	13.0696			0.493633			0.246817	+	0.969062i	$0.420615\pi$
$702$		0			0
$703$	8.62143	−	4.97759i	0.325164	−	0.187733i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−2.78040	−	14.6903i	−0.104568	−	0.552487i
$708$		0			0
$709$	−4.97959	+	8.62490i	−0.187012	+	0.323915i	−0.944253	−	0.329221i	$-0.893214\pi$
$709$	−4.97959	+	8.62490i	−0.187012	+	0.323915i	0.757240	+	0.653136i	$0.226547\pi$
$710$		0			0
$711$	−2.81506	−	4.87582i	−0.105573	−	0.182858i
$712$		0			0
$713$		−	3.61331i		−	0.135319i
$714$		0			0
$715$		0			0
$716$		0			0
$717$	74.1402	−	42.8049i	2.76882	−	1.59858i
$718$		0			0
$719$	23.7298	−	41.1012i	0.884971	−	1.53281i	0.0392240	−	0.999230i	$-0.487511\pi$
$719$	23.7298	−	41.1012i	0.884971	−	1.53281i	0.845747	−	0.533584i	$-0.179155\pi$
$720$		0			0
$721$	−4.04164	−	4.69595i	−0.150518	−	0.174886i
$722$		0			0
$723$	31.8290	+	18.3765i	1.18373	+	0.683428i
$724$		0			0
$725$		0			0
$726$		0			0
$727$			3.84829i			0.142725i	0.997450	+	0.0713626i	$0.0227348\pi$
$727$			3.84829i			0.142725i	−0.997450	+	0.0713626i	$0.977265\pi$
$728$		0			0
$729$	−82.3708			−3.05077
$730$		0			0
$731$	−2.42918	−	4.20747i	−0.0898465	−	0.155619i
$732$		0			0
$733$	−2.82391	−	1.63038i	−0.104303	−	0.0602196i	0.446941	−	0.894563i	$-0.352513\pi$
$733$	−2.82391	−	1.63038i	−0.104303	−	0.0602196i	−0.551244	+	0.834344i	$0.685847\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	11.1914	+	6.46133i	0.412239	+	0.238006i
$738$		0			0
$739$	−9.50067	−	16.4556i	−0.349488	−	0.605330i	0.636671	−	0.771136i	$-0.280311\pi$
$739$	−9.50067	−	16.4556i	−0.349488	−	0.605330i	−0.986159	+	0.165805i	$0.946978\pi$
$740$		0			0
$741$	110.800			4.07032
$742$		0			0
$743$		−	4.02310i		−	0.147593i	−0.997273	−	0.0737965i	$-0.976488\pi$
$743$		−	4.02310i		−	0.147593i	0.997273	−	0.0737965i	$-0.0235115\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	74.8502	+	43.2148i	2.73863	+	1.58115i
$748$		0			0
$749$	−1.71340	−	1.99078i	−0.0626062	−	0.0727417i
$750$		0			0
$751$	0.345395	−	0.598242i	0.0126037	−	0.0218302i	−0.859655	−	0.510875i	$-0.829321\pi$
$751$	0.345395	−	0.598242i	0.0126037	−	0.0218302i	0.872258	+	0.489045i	$0.162655\pi$
$752$		0			0
$753$	20.0005	−	11.5473i	0.728859	−	0.420807i
$754$		0			0
$755$		0			0
$756$		0			0
$757$		−	23.5723i		−	0.856751i	−0.903601	−	0.428375i	$-0.859086\pi$
$757$		−	23.5723i		−	0.856751i	0.903601	−	0.428375i	$-0.140914\pi$
$758$		0			0
$759$	37.5500	+	65.0385i	1.36298	+	2.36075i
$760$		0			0
$761$	−2.86169	+	4.95659i	−0.103736	+	0.179676i	−0.913221	−	0.407464i	$-0.866413\pi$
$761$	−2.86169	+	4.95659i	−0.103736	+	0.179676i	0.809485	+	0.587141i	$0.199746\pi$
$762$		0			0
$763$	−8.92450	−	47.1530i	−0.323089	−	1.70705i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−35.1605	+	20.2999i	−1.26957	+	0.732988i
$768$		0			0
$769$	34.8252			1.25583			0.627915	−	0.778282i	$-0.283909\pi$
$769$	34.8252			1.25583			0.627915	+	0.778282i	$0.283909\pi$
$770$		0			0
$771$	10.0443			0.361736
$772$		0			0
$773$	−5.63093	+	3.25102i	−0.202531	+	0.116931i	−0.597835	−	0.801619i	$-0.703972\pi$
$773$	−5.63093	+	3.25102i	−0.202531	+	0.116931i	0.395305	+	0.918550i	$0.370639\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$	−12.6019	−	4.40883i	−0.452091	−	0.158166i
$778$		0			0
$779$	19.3830	−	33.5724i	0.694469	−	1.20286i
$780$		0			0
$781$	11.4591	+	19.8477i	0.410038	+	0.710206i
$782$		0			0
$783$			75.1694i			2.68633i
$784$		0			0
$785$		0			0
$786$		0			0
$787$	−22.2834	+	12.8653i	−0.794317	+	0.458599i	−0.841480	−	0.540288i	$-0.818315\pi$
$787$	−22.2834	+	12.8653i	−0.794317	+	0.458599i	0.0471634	+	0.998887i	$0.484982\pi$
$788$		0			0
$789$	12.1642	−	21.0689i	0.433055	−	0.750074i
$790$		0			0
$791$	−5.43998	+	15.5493i	−0.193423	+	0.552870i
$792$		0			0
$793$	−39.9096	−	23.0418i	−1.41723	−	0.818239i
$794$		0			0
$795$		0			0
$796$		0			0
$797$			44.8212i			1.58765i	0.608147	+	0.793825i	$0.291913\pi$
$797$			44.8212i			1.58765i	−0.608147	+	0.793825i	$0.708087\pi$
$798$		0			0
$799$	6.42370			0.227254
$800$		0			0
$801$	33.5921	+	58.1833i	1.18692	+	2.05580i
$802$		0			0
$803$	−14.1903	−	8.19280i	−0.500766	−	0.289118i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	44.2594	+	25.5532i	1.55800	+	0.899514i
$808$		0			0
$809$	12.6919	+	21.9831i	0.446225	+	0.772884i	0.998137	−	0.0610184i	$-0.0194348\pi$
$809$	12.6919	+	21.9831i	0.446225	+	0.772884i	−0.551912	+	0.833902i	$0.686102\pi$
$810$		0			0
$811$	−6.86499			−0.241062			−0.120531	−	0.992710i	$-0.538460\pi$
$811$	−6.86499			−0.241062			−0.120531	+	0.992710i	$0.538460\pi$
$812$		0			0
$813$			21.9135i			0.768539i
$814$		0			0
$815$		0			0
$816$		0			0
$817$	−31.1439	−	17.9810i	−1.08959	−	0.629074i
$818$		0			0
$819$	−70.4784	−	81.8883i	−2.46271	−	2.86141i
$820$		0			0
$821$	−15.6253	+	27.0639i	−0.545328	+	0.944536i	0.453258	+	0.891379i	$0.350262\pi$
$821$	−15.6253	+	27.0639i	−0.545328	+	0.944536i	−0.998586	+	0.0531570i	$0.983072\pi$
$822$		0			0
$823$	−10.7965	+	6.23335i	−0.376342	+	0.217281i	−0.676225	−	0.736695i	$-0.736385\pi$
$823$	−10.7965	+	6.23335i	−0.376342	+	0.217281i	0.299884	+	0.953976i	$0.403052\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$		−	20.0893i		−	0.698572i	−0.937016	−	0.349286i	$-0.886424\pi$
$827$		−	20.0893i		−	0.698572i	0.937016	−	0.349286i	$-0.113576\pi$
$828$		0			0
$829$	−24.1383	−	41.8088i	−0.838359	−	1.45208i	−0.891266	−	0.453482i	$-0.850182\pi$
$829$	−24.1383	−	41.8088i	−0.838359	−	1.45208i	0.0529061	−	0.998599i	$-0.483152\pi$
$830$		0			0
$831$	17.8341	−	30.8895i	0.618656	−	1.07154i
$832$		0			0
$833$	−6.11668	−	0.921255i	−0.211930	−	0.0319196i
$834$		0			0
$835$		0			0
$836$		0			0
$837$	−9.70860	+	5.60526i	−0.335578	+	0.193746i
$838$		0			0
$839$	56.1020			1.93686			0.968429	−	0.249291i	$-0.0801975\pi$
$839$	56.1020			1.93686			0.968429	+	0.249291i	$0.0801975\pi$
$840$		0			0
$841$	−8.37972			−0.288956
$842$		0			0
$843$	72.6544	−	41.9470i	2.50235	−	1.44473i
$844$		0			0
$845$		0			0
$846$		0			0
$847$	−14.0834	+	12.1211i	−0.483912	+	0.416486i
$848$		0			0
$849$	−10.5185	+	18.2186i	−0.360995	+	0.625261i
$850$		0			0
$851$	−4.06022	−	7.03251i	−0.139183	−	0.241072i
$852$		0			0
$853$			16.4092i			0.561840i	0.959731	+	0.280920i	$0.0906395\pi$
$853$			16.4092i			0.561840i	−0.959731	+	0.280920i	$0.909360\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−3.87379	+	2.23653i	−0.132326	+	0.0763985i	−0.564702	−	0.825295i	$-0.691009\pi$
$857$	−3.87379	+	2.23653i	−0.132326	+	0.0763985i	0.432376	+	0.901694i	$0.357675\pi$
$858$		0			0
$859$	−7.25579	+	12.5674i	−0.247564	+	0.428794i	−0.962849	−	0.270039i	$-0.912963\pi$
$859$	−7.25579	+	12.5674i	−0.247564	+	0.428794i	0.715285	+	0.698833i	$0.246297\pi$
$860$		0			0
$861$	−51.0823	+	9.66818i	−1.74088	+	0.329491i
$862$		0			0
$863$	−12.6317	−	7.29293i	−0.429989	−	0.248254i	0.269353	−	0.963042i	$-0.413190\pi$
$863$	−12.6317	−	7.29293i	−0.429989	−	0.248254i	−0.699342	+	0.714787i	$0.746524\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$			53.7751i			1.82630i
$868$		0			0
$869$	2.99044			0.101444
$870$		0			0
$871$	−7.77591	−	13.4683i	−0.263477	−	0.456355i
$872$		0			0
$873$	4.25209	+	2.45495i	0.143911	+	0.0830873i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	−32.6133	−	18.8293i	−1.10127	−	0.635821i	−0.164718	−	0.986341i	$-0.552672\pi$
$877$	−32.6133	−	18.8293i	−1.10127	−	0.635821i	−0.936555	+	0.350520i	$0.886005\pi$
$878$		0			0
$879$	33.7504	+	58.4574i	1.13837	+	1.97172i
$880$		0			0
$881$	−44.4007			−1.49590			−0.747949	−	0.663757i	$-0.768961\pi$
$881$	−44.4007			−1.49590			−0.747949	+	0.663757i	$0.768961\pi$
$882$		0			0
$883$			51.7213i			1.74056i	0.492558	+	0.870279i	$0.336062\pi$
$883$			51.7213i			1.74056i	−0.492558	+	0.870279i	$0.663938\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−0.423886	−	0.244731i	−0.0142327	−	0.00821725i	0.492867	−	0.870105i	$-0.335949\pi$
$887$	−0.423886	−	0.244731i	−0.0142327	−	0.00821725i	−0.507099	+	0.861888i	$0.669282\pi$
$888$		0			0
$889$	1.41873	−	4.05522i	0.0475827	−	0.136008i
$890$		0			0
$891$	65.6033	−	113.628i	2.19779	−	3.80669i
$892$		0			0
$893$	41.1783	−	23.7743i	1.37798	−	0.795578i
$894$		0			0
$895$		0			0
$896$		0			0
$897$		−	90.3794i		−	3.01768i
$898$		0			0
$899$	1.53762	+	2.66324i	0.0512826	+	0.0888240i
$900$		0			0
$901$	1.13469	−	1.96534i	0.0378019	−	0.0654748i
$902$		0			0
$903$	8.96884	+	47.3872i	0.298464	+	1.57695i
$904$		0			0
$905$		0			0
$906$		0			0
$907$	37.6323	−	21.7270i	1.24956	−	0.721435i	0.278539	−	0.960425i	$-0.410150\pi$
$907$	37.6323	−	21.7270i	1.24956	−	0.721435i	0.971022	+	0.238990i	$0.0768164\pi$
$908$		0			0
$909$	−45.1671			−1.49810
$910$		0			0
$911$	−4.77049			−0.158054			−0.0790268	−	0.996872i	$-0.525181\pi$
$911$	−4.77049			−0.158054			−0.0790268	+	0.996872i	$0.525181\pi$
$912$		0			0
$913$	−39.7568	+	22.9536i	−1.31576	+	0.759652i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	−12.5975	+	10.8422i	−0.416006	+	0.358042i
$918$		0			0
$919$	−20.6175	+	35.7106i	−0.680109	+	1.17798i	0.294838	+	0.955547i	$0.404734\pi$
$919$	−20.6175	+	35.7106i	−0.680109	+	1.17798i	−0.974947	+	0.222436i	$0.928599\pi$
$920$		0			0
$921$	−49.0193	−	84.9039i	−1.61524	−	2.79768i
$922$		0			0
$923$		−	27.5809i		−	0.907836i
$924$		0			0
$925$		0			0
$926$		0			0
$927$	−16.2095	+	9.35855i	−0.532389	+	0.307375i
$928$		0			0
$929$	15.9461	−	27.6195i	0.523175	−	0.906166i	−0.476461	−	0.879196i	$-0.658081\pi$
$929$	15.9461	−	27.6195i	0.523175	−	0.906166i	0.999636	−	0.0269705i	$-0.00858602\pi$
$930$		0			0
$931$	−42.6198	+	16.7324i	−1.39681	+	0.548383i
$932$		0			0
$933$	35.8431	+	20.6940i	1.17345	+	0.677491i
$934$		0			0
$935$		0			0
$936$		0			0
$937$			23.2518i			0.759602i	0.925068	+	0.379801i	$0.124008\pi$
$937$			23.2518i			0.759602i	−0.925068	+	0.379801i	$0.875992\pi$
$938$		0			0
$939$	−3.49259			−0.113976
$940$		0			0
$941$	−13.3260	−	23.0812i	−0.434414	−	0.752427i	0.562834	−	0.826570i	$-0.309711\pi$
$941$	−13.3260	−	23.0812i	−0.434414	−	0.752427i	−0.997248	+	0.0741432i	$0.976378\pi$
$942$		0			0
$943$	−27.3850	−	15.8108i	−0.891780	−	0.514869i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−4.51554	−	2.60705i	−0.146735	−	0.0847177i	0.424835	−	0.905271i	$-0.360332\pi$
$947$	−4.51554	−	2.60705i	−0.146735	−	0.0847177i	−0.571570	+	0.820553i	$0.693666\pi$
$948$		0			0
$949$	9.85965	+	17.0774i	0.320058	+	0.554356i
$950$		0			0
$951$	−8.68447			−0.281613
$952$		0			0
$953$		−	37.8674i		−	1.22664i	−0.789833	−	0.613322i	$-0.789833\pi$
$953$		−	37.8674i		−	1.22664i	0.789833	−	0.613322i	$-0.210167\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$	−55.3536	−	31.9584i	−1.78933	−	1.03307i
$958$		0			0
$959$	46.5645	−	8.81312i	1.50365	−	0.284591i
$960$		0			0
$961$	15.2707	−	26.4496i	0.492603	−	0.853213i
$962$		0			0
$963$	−6.87179	+	3.96743i	−0.221440	+	0.127849i
$964$		0			0
$965$		0			0
$966$		0			0
$967$		−	17.7266i		−	0.570049i	−0.958520	−	0.285024i	$-0.907998\pi$
$967$		−	17.7266i		−	0.570049i	0.958520	−	0.285024i	$-0.0920017\pi$
$968$		0			0
$969$	−9.58193	−	16.5964i	−0.307816	−	0.533153i
$970$		0			0
$971$	−5.38205	+	9.32198i	−0.172718	+	0.299157i	−0.939369	−	0.342907i	$-0.888588\pi$
$971$	−5.38205	+	9.32198i	−0.172718	+	0.299157i	0.766651	+	0.642064i	$0.221922\pi$
$972$		0			0
$973$	−57.4443	−	20.0971i	−1.84158	−	0.644283i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−34.2753	+	19.7888i	−1.09656	+	0.633101i	−0.935316	−	0.353813i	$-0.884885\pi$
$977$	−34.2753	+	19.7888i	−1.09656	+	0.633101i	−0.161247	+	0.986914i	$0.551551\pi$
$978$		0			0
$979$	−35.6850			−1.14050
$980$		0			0
$981$	−144.977			−4.62876
$982$		0			0
$983$	26.8261	−	15.4880i	0.855618	−	0.493991i	−0.00692422	−	0.999976i	$-0.502204\pi$
$983$	26.8261	−	15.4880i	0.855618	−	0.493991i	0.862543	+	0.505985i	$0.168871\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$	−60.1902	−	21.0578i	−1.91588	−	0.670276i
$988$		0			0
$989$	−14.6671	+	25.4041i	−0.466386	+	0.807805i
$990$		0			0
$991$	16.5946	+	28.7427i	0.527145	+	0.913042i	0.999500	+	0.0316332i	$0.0100708\pi$
$991$	16.5946	+	28.7427i	0.527145	+	0.913042i	−0.472355	+	0.881409i	$0.656596\pi$
$992$		0			0
$993$			63.9031i			2.02790i
$994$		0			0
$995$		0			0
$996$		0			0
$997$	−7.65077	+	4.41717i	−0.242302	+	0.139893i	−0.616234	−	0.787563i	$-0.711343\pi$
$997$	−7.65077	+	4.41717i	−0.242302	+	0.139893i	0.373932	+	0.927456i	$0.378009\pi$
$998$		0			0
$999$	−12.5971	+	21.8189i	−0.398555	+	0.690318i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1400.2.bh.j.849.8		16
5.2	odd	4		1400.2.q.l.401.1	✓	8
5.3	odd	4		1400.2.q.m.401.4	yes	8
5.4	even	2	inner	1400.2.bh.j.849.1		16
7.4	even	3	inner	1400.2.bh.j.249.1		16
35.2	odd	12		9800.2.a.ct.1.4		4
35.4	even	6	inner	1400.2.bh.j.249.8		16
35.12	even	12		9800.2.a.ck.1.1		4
35.18	odd	12		1400.2.q.m.1201.4	yes	8
35.23	odd	12		9800.2.a.cj.1.1		4
35.32	odd	12		1400.2.q.l.1201.1	yes	8
35.33	even	12		9800.2.a.cu.1.4		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1400.2.q.l.401.1	✓	8	5.2	odd	4
1400.2.q.l.1201.1	yes	8	35.32	odd	12
1400.2.q.m.401.4	yes	8	5.3	odd	4
1400.2.q.m.1201.4	yes	8	35.18	odd	12
1400.2.bh.j.249.1		16	7.4	even	3	inner
1400.2.bh.j.249.8		16	35.4	even	6	inner
1400.2.bh.j.849.1		16	5.4	even	2	inner
1400.2.bh.j.849.8		16	1.1	even	1	trivial
9800.2.a.cj.1.1		4	35.23	odd	12
9800.2.a.ck.1.1		4	35.12	even	12
9800.2.a.ct.1.4		4	35.2	odd	12
9800.2.a.cu.1.4		4	35.33	even	12

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1400 = 2^{3} \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1400.bh (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(2.87134 - 1.65777i) q^{3} +(2.49733 + 0.873699i) q^{7} +(3.99638 - 6.92193i) q^{9} +O(q^{10})\)	\(q+(2.87134 - 1.65777i) q^{3} +(2.49733 + 0.873699i) q^{7} +(3.99638 - 6.92193i) q^{9} +(2.12268 + 3.67659i) q^{11} -5.10909i q^{13} +(-0.765278 + 0.441833i) q^{17} +(-3.27048 + 5.66463i) q^{19} +(8.61906 - 1.63130i) q^{21} +(4.62065 + 2.66773i) q^{23} -16.5536i q^{27} -4.54096 q^{29} +(-0.338612 - 0.586493i) q^{31} +(12.1898 + 7.03781i) q^{33} +(-1.31807 - 0.760988i) q^{37} +(-8.46968 - 14.6699i) q^{39} -5.92666 q^{41} +5.49796i q^{43} +(-6.29546 - 3.63469i) q^{47} +(5.47330 + 4.36383i) q^{49} +(-1.46491 + 2.53730i) q^{51} +(-2.22407 + 1.28407i) q^{53} +21.6868i q^{57} +(-3.97330 - 6.88196i) q^{59} +(4.50997 - 7.81149i) q^{61} +(16.0280 - 13.7947i) q^{63} +(2.63614 - 1.52198i) q^{67} +17.6899 q^{69} +5.39840 q^{71} +(-3.34256 + 1.92983i) q^{73} +(2.08879 + 11.0362i) q^{77} +(0.352201 - 0.610030i) q^{79} +(-15.4529 - 26.7653i) q^{81} +10.8135i q^{83} +(-13.0386 + 7.52784i) q^{87} +(-4.20282 + 7.27950i) q^{89} +(4.46381 - 12.7591i) q^{91} +(-1.94454 - 1.12268i) q^{93} +0.614293i q^{97} +33.9321 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 10 q^{9}+O(q^{10}) \) 16 * q + 10 * q^9	\( 16 q + 10 q^{9} - 20 q^{19} + 50 q^{21} - 8 q^{29} + 28 q^{31} - 20 q^{39} - 16 q^{41} + 26 q^{49} - 10 q^{51} - 2 q^{59} + 50 q^{61} + 64 q^{69} - 80 q^{71} + 4 q^{79} - 48 q^{81} - 38 q^{89} + 34 q^{91} + 204 q^{99}+O(q^{100}) \) 16 * q + 10 * q^9 - 20 * q^19 + 50 * q^21 - 8 * q^29 + 28 * q^31 - 20 * q^39 - 16 * q^41 + 26 * q^49 - 10 * q^51 - 2 * q^59 + 50 * q^61 + 64 * q^69 - 80 * q^71 + 4 * q^79 - 48 * q^81 - 38 * q^89 + 34 * q^91 + 204 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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