LMFDB - Embedded newform 1400.2.bh.b.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:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{6})$
Coefficient field:	$\Q(\zeta_{12})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{2} + 1 $ x^4 - x^2 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 280)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			849.1
Root			$-0.866025 + 0.500000i$ of defining polynomial
Character	$\chi$	$=$	1400.849
Dual form			1400.2.bh.b.249.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.866025 + 0.500000i) q^{3} +(0.866025 - 2.50000i) q^{7} +(-1.00000 + 1.73205i) q^{9} +O(q^{10})$	$q+(-0.866025 + 0.500000i) q^{3} +(0.866025 - 2.50000i) q^{7} +(-1.00000 + 1.73205i) q^{9} +(-1.00000 - 1.73205i) q^{11} +(3.46410 - 2.00000i) q^{17} +(-1.00000 + 1.73205i) q^{19} +(0.500000 + 2.59808i) q^{21} +(0.866025 + 0.500000i) q^{23} -5.00000i q^{27} -9.00000 q^{29} +(-2.00000 - 3.46410i) q^{31} +(1.73205 + 1.00000i) q^{33} +(-3.46410 - 2.00000i) q^{37} +1.00000 q^{41} -9.00000i q^{43} +(-5.50000 - 4.33013i) q^{49} +(-2.00000 + 3.46410i) q^{51} +(8.66025 - 5.00000i) q^{53} -2.00000i q^{57} +(-5.00000 - 8.66025i) q^{59} +(-4.50000 + 7.79423i) q^{61} +(3.46410 + 4.00000i) q^{63} +(4.33013 - 2.50000i) q^{67} -1.00000 q^{69} +14.0000 q^{71} +(-10.3923 + 6.00000i) q^{73} +(-5.19615 + 1.00000i) q^{77} +(7.00000 - 12.1244i) q^{79} +(-0.500000 - 0.866025i) q^{81} -11.0000i q^{83} +(7.79423 - 4.50000i) q^{87} +(-7.50000 + 12.9904i) q^{89} +(3.46410 + 2.00000i) q^{93} -18.0000i q^{97} +4.00000 q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 4 q^{9}+O(q^{10}) $ 4 * q - 4 * q^9	$ 4 q - 4 q^{9} - 4 q^{11} - 4 q^{19} + 2 q^{21} - 36 q^{29} - 8 q^{31} + 4 q^{41} - 22 q^{49} - 8 q^{51} - 20 q^{59} - 18 q^{61} - 4 q^{69} + 56 q^{71} + 28 q^{79} - 2 q^{81} - 30 q^{89} + 16 q^{99}+O(q^{100}) $ 4 * q - 4 * q^9 - 4 * q^11 - 4 * q^19 + 2 * q^21 - 36 * q^29 - 8 * q^31 + 4 * q^41 - 22 * q^49 - 8 * q^51 - 20 * q^59 - 18 * q^61 - 4 * q^69 + 56 * q^71 + 28 * q^79 - 2 * q^81 - 30 * q^89 + 16 * 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
$3$	−0.866025	+	0.500000i	−0.500000	+	0.288675i	−0.728714	−	0.684819i	$-0.759881\pi$
$3$	−0.866025	+	0.500000i	−0.500000	+	0.288675i	0.228714	+	0.973494i	$0.426548\pi$
$4$		0			0
$5$		0			0
$5$		0			0
$6$		0			0
$7$	0.866025	−	2.50000i	0.327327	−	0.944911i
$7$	0.866025	−	2.50000i	0.327327	−	0.944911i
$8$		0			0
$9$	−1.00000	+	1.73205i	−0.333333	+	0.577350i
$10$		0			0
$11$	−1.00000	−	1.73205i	−0.301511	−	0.522233i	0.674967	−	0.737848i	$-0.264158\pi$
$11$	−1.00000	−	1.73205i	−0.301511	−	0.522233i	−0.976478	+	0.215615i	$0.930824\pi$
$12$		0			0
$13$		0			0		1.00000			$0$
$13$		0			0		−1.00000			$\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	3.46410	−	2.00000i	0.840168	−	0.485071i	−0.0171533	−	0.999853i	$-0.505460\pi$
$17$	3.46410	−	2.00000i	0.840168	−	0.485071i	0.857321	+	0.514782i	$0.172127\pi$
$18$		0			0
$19$	−1.00000	+	1.73205i	−0.229416	+	0.397360i	−0.957635	−	0.287984i	$-0.907015\pi$
$19$	−1.00000	+	1.73205i	−0.229416	+	0.397360i	0.728219	+	0.685344i	$0.240348\pi$
$20$		0			0
$21$	0.500000	+	2.59808i	0.109109	+	0.566947i
$22$		0			0
$23$	0.866025	+	0.500000i	0.180579	+	0.104257i	0.587565	−	0.809177i	$-0.300087\pi$
$23$	0.866025	+	0.500000i	0.180579	+	0.104257i	−0.406986	+	0.913434i	$0.633420\pi$
$24$		0			0
$25$		0			0
$26$		0			0
$27$		−	5.00000i		−	0.962250i
$28$		0			0
$29$	−9.00000			−1.67126			−0.835629	−	0.549294i	$-0.814897\pi$
$29$	−9.00000			−1.67126			−0.835629	+	0.549294i	$0.814897\pi$
$30$		0			0
$31$	−2.00000	−	3.46410i	−0.359211	−	0.622171i	0.628619	−	0.777714i	$-0.283621\pi$
$31$	−2.00000	−	3.46410i	−0.359211	−	0.622171i	−0.987829	+	0.155543i	$0.950287\pi$
$32$		0			0
$33$	1.73205	+	1.00000i	0.301511	+	0.174078i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	−3.46410	−	2.00000i	−0.569495	−	0.328798i	0.187453	−	0.982274i	$-0.439977\pi$
$37$	−3.46410	−	2.00000i	−0.569495	−	0.328798i	−0.756948	+	0.653476i	$0.773310\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	1.00000			0.156174			0.0780869	−	0.996947i	$-0.475119\pi$
$41$	1.00000			0.156174			0.0780869	+	0.996947i	$0.475119\pi$
$42$		0			0
$43$		−	9.00000i		−	1.37249i	−0.727372	−	0.686244i	$-0.759258\pi$
$43$		−	9.00000i		−	1.37249i	0.727372	−	0.686244i	$-0.240742\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$47$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$48$		0			0
$49$	−5.50000	−	4.33013i	−0.785714	−	0.618590i
$50$		0			0
$51$	−2.00000	+	3.46410i	−0.280056	+	0.485071i
$52$		0			0
$53$	8.66025	−	5.00000i	1.18958	−	0.686803i	0.231367	−	0.972867i	$-0.425680\pi$
$53$	8.66025	−	5.00000i	1.18958	−	0.686803i	0.958211	+	0.286064i	$0.0923469\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$		−	2.00000i		−	0.264906i
$58$		0			0
$59$	−5.00000	−	8.66025i	−0.650945	−	1.12747i	−0.982894	−	0.184172i	$-0.941040\pi$
$59$	−5.00000	−	8.66025i	−0.650945	−	1.12747i	0.331949	−	0.943297i	$-0.392294\pi$
$60$		0			0
$61$	−4.50000	+	7.79423i	−0.576166	+	0.997949i	0.419748	+	0.907641i	$0.362118\pi$
$61$	−4.50000	+	7.79423i	−0.576166	+	0.997949i	−0.995914	+	0.0903080i	$0.971215\pi$
$62$		0			0
$63$	3.46410	+	4.00000i	0.436436	+	0.503953i
$64$		0			0
$65$		0			0
$66$		0			0
$67$	4.33013	−	2.50000i	0.529009	−	0.305424i	−0.211604	−	0.977356i	$-0.567869\pi$
$67$	4.33013	−	2.50000i	0.529009	−	0.305424i	0.740613	+	0.671932i	$0.234535\pi$
$68$		0			0
$69$	−1.00000			−0.120386
$70$		0			0
$71$	14.0000			1.66149			0.830747	−	0.556650i	$-0.187914\pi$
$71$	14.0000			1.66149			0.830747	+	0.556650i	$0.187914\pi$
$72$		0			0
$73$	−10.3923	+	6.00000i	−1.21633	+	0.702247i	−0.964130	−	0.265429i	$-0.914486\pi$
$73$	−10.3923	+	6.00000i	−1.21633	+	0.702247i	−0.252197	+	0.967676i	$0.581153\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−5.19615	+	1.00000i	−0.592157	+	0.113961i
$78$		0			0
$79$	7.00000	−	12.1244i	0.787562	−	1.36410i	−0.139895	−	0.990166i	$-0.544677\pi$
$79$	7.00000	−	12.1244i	0.787562	−	1.36410i	0.927457	−	0.373930i	$-0.121990\pi$
$80$		0			0
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$		0			0
$83$		−	11.0000i		−	1.20741i	−0.797209	−	0.603703i	$-0.793691\pi$
$83$		−	11.0000i		−	1.20741i	0.797209	−	0.603703i	$-0.206309\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$	7.79423	−	4.50000i	0.835629	−	0.482451i
$88$		0			0
$89$	−7.50000	+	12.9904i	−0.794998	+	1.37698i	0.127842	+	0.991795i	$0.459195\pi$
$89$	−7.50000	+	12.9904i	−0.794998	+	1.37698i	−0.922840	+	0.385183i	$0.874138\pi$
$90$		0			0
$91$		0			0
$92$		0			0
$93$	3.46410	+	2.00000i	0.359211	+	0.207390i
$94$		0			0
$95$		0			0
$96$		0			0
$97$		−	18.0000i		−	1.82762i	−0.406138	−	0.913812i	$-0.633125\pi$
$97$		−	18.0000i		−	1.82762i	0.406138	−	0.913812i	$-0.366875\pi$
$98$		0			0
$99$	4.00000			0.402015
$100$		0			0
$101$	−1.50000	−	2.59808i	−0.149256	−	0.258518i	0.781697	−	0.623658i	$-0.214354\pi$
$101$	−1.50000	−	2.59808i	−0.149256	−	0.258518i	−0.930953	+	0.365140i	$0.881021\pi$
$102$		0			0
$103$	−11.2583	−	6.50000i	−1.10932	−	0.640464i	−0.170664	−	0.985329i	$-0.554591\pi$
$103$	−11.2583	−	6.50000i	−1.10932	−	0.640464i	−0.938652	+	0.344865i	$0.887925\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−7.79423	−	4.50000i	−0.753497	−	0.435031i	0.0734594	−	0.997298i	$-0.476596\pi$
$107$	−7.79423	−	4.50000i	−0.753497	−	0.435031i	−0.826956	+	0.562267i	$0.809929\pi$
$108$		0			0
$109$	−0.500000	−	0.866025i	−0.0478913	−	0.0829502i	0.841086	−	0.540901i	$-0.181917\pi$
$109$	−0.500000	−	0.866025i	−0.0478913	−	0.0829502i	−0.888977	+	0.457951i	$0.848583\pi$
$110$		0			0
$111$	4.00000			0.379663
$112$		0			0
$113$		−	2.00000i		−	0.188144i	−0.995565	−	0.0940721i	$-0.970012\pi$
$113$		−	2.00000i		−	0.188144i	0.995565	−	0.0940721i	$-0.0299884\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$		0			0
$118$		0			0
$119$	−2.00000	−	10.3923i	−0.183340	−	0.952661i
$120$		0			0
$121$	3.50000	−	6.06218i	0.318182	−	0.551107i
$122$		0			0
$123$	−0.866025	+	0.500000i	−0.0780869	+	0.0450835i
$124$		0			0
$125$		0			0
$126$		0			0
$127$			8.00000i			0.709885i	0.934888	+	0.354943i	$0.115500\pi$
$127$			8.00000i			0.709885i	−0.934888	+	0.354943i	$0.884500\pi$
$128$		0			0
$129$	4.50000	+	7.79423i	0.396203	+	0.686244i
$130$		0			0
$131$	4.00000	−	6.92820i	0.349482	−	0.605320i	−0.636676	−	0.771132i	$-0.719691\pi$
$131$	4.00000	−	6.92820i	0.349482	−	0.605320i	0.986157	+	0.165812i	$0.0530244\pi$
$132$		0			0
$133$	3.46410	+	4.00000i	0.300376	+	0.346844i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	10.3923	−	6.00000i	0.887875	−	0.512615i	0.0146279	−	0.999893i	$-0.495344\pi$
$137$	10.3923	−	6.00000i	0.887875	−	0.512615i	0.873247	+	0.487278i	$0.162010\pi$
$138$		0			0
$139$	2.00000			0.169638			0.0848189	−	0.996396i	$-0.472969\pi$
$139$	2.00000			0.169638			0.0848189	+	0.996396i	$0.472969\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$		0			0
$144$		0			0
$145$		0			0
$146$		0			0
$147$	6.92820	+	1.00000i	0.571429	+	0.0824786i
$148$		0			0
$149$	−2.50000	+	4.33013i	−0.204808	+	0.354738i	−0.950072	−	0.312032i	$-0.898990\pi$
$149$	−2.50000	+	4.33013i	−0.204808	+	0.354738i	0.745264	+	0.666770i	$0.232324\pi$
$150$		0			0
$151$	−4.00000	−	6.92820i	−0.325515	−	0.563809i	0.656101	−	0.754673i	$-0.272204\pi$
$151$	−4.00000	−	6.92820i	−0.325515	−	0.563809i	−0.981617	+	0.190864i	$0.938871\pi$
$152$		0			0
$153$			8.00000i			0.646762i
$154$		0			0
$155$		0			0
$156$		0			0
$157$	1.73205	−	1.00000i	0.138233	−	0.0798087i	−0.429289	−	0.903167i	$-0.641236\pi$
$157$	1.73205	−	1.00000i	0.138233	−	0.0798087i	0.567521	+	0.823359i	$0.307902\pi$
$158$		0			0
$159$	−5.00000	+	8.66025i	−0.396526	+	0.686803i
$160$		0			0
$161$	2.00000	−	1.73205i	0.157622	−	0.136505i
$162$		0			0
$163$	−17.3205	−	10.0000i	−1.35665	−	0.783260i	−0.367477	−	0.930033i	$-0.619778\pi$
$163$	−17.3205	−	10.0000i	−1.35665	−	0.783260i	−0.989170	+	0.146772i	$0.953112\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$			17.0000i			1.31550i	0.753237	+	0.657750i	$0.228492\pi$
$167$			17.0000i			1.31550i	−0.753237	+	0.657750i	$0.771508\pi$
$168$		0			0
$169$	13.0000			1.00000
$170$		0			0
$171$	−2.00000	−	3.46410i	−0.152944	−	0.264906i
$172$		0			0
$173$	13.8564	+	8.00000i	1.05348	+	0.608229i	0.923622	−	0.383304i	$-0.125214\pi$
$173$	13.8564	+	8.00000i	1.05348	+	0.608229i	0.129861	+	0.991532i	$0.458547\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	8.66025	+	5.00000i	0.650945	+	0.375823i
$178$		0			0
$179$	6.00000	+	10.3923i	0.448461	+	0.776757i	0.998286	−	0.0585225i	$-0.0186389\pi$
$179$	6.00000	+	10.3923i	0.448461	+	0.776757i	−0.549825	+	0.835280i	$0.685306\pi$
$180$		0			0
$181$	−25.0000			−1.85824			−0.929118	−	0.369784i	$-0.879432\pi$
$181$	−25.0000			−1.85824			−0.929118	+	0.369784i	$0.879432\pi$
$182$		0			0
$183$		−	9.00000i		−	0.665299i
$184$		0			0
$185$		0			0
$186$		0			0
$187$	−6.92820	−	4.00000i	−0.506640	−	0.292509i
$188$		0			0
$189$	−12.5000	−	4.33013i	−0.909241	−	0.314970i
$190$		0			0
$191$	−9.00000	+	15.5885i	−0.651217	+	1.12794i	0.331611	+	0.943416i	$0.392408\pi$
$191$	−9.00000	+	15.5885i	−0.651217	+	1.12794i	−0.982828	+	0.184525i	$0.940925\pi$
$192$		0			0
$193$	12.1244	−	7.00000i	0.872730	−	0.503871i	0.00447566	−	0.999990i	$-0.498575\pi$
$193$	12.1244	−	7.00000i	0.872730	−	0.503871i	0.868255	+	0.496119i	$0.165242\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$			18.0000i			1.28245i	0.767354	+	0.641223i	$0.221573\pi$
$197$			18.0000i			1.28245i	−0.767354	+	0.641223i	$0.778427\pi$
$198$		0			0
$199$	−2.00000	−	3.46410i	−0.141776	−	0.245564i	0.786389	−	0.617731i	$-0.211948\pi$
$199$	−2.00000	−	3.46410i	−0.141776	−	0.245564i	−0.928166	+	0.372168i	$0.878615\pi$
$200$		0			0
$201$	−2.50000	+	4.33013i	−0.176336	+	0.305424i
$202$		0			0
$203$	−7.79423	+	22.5000i	−0.547048	+	1.57919i
$204$		0			0
$205$		0			0
$206$		0			0
$207$	−1.73205	+	1.00000i	−0.120386	+	0.0695048i
$208$		0			0
$209$	4.00000			0.276686
$210$		0			0
$211$	2.00000			0.137686			0.0688428	−	0.997628i	$-0.478069\pi$
$211$	2.00000			0.137686			0.0688428	+	0.997628i	$0.478069\pi$
$212$		0			0
$213$	−12.1244	+	7.00000i	−0.830747	+	0.479632i
$214$		0			0
$215$		0			0
$216$		0			0
$217$	−10.3923	+	2.00000i	−0.705476	+	0.135769i
$218$		0			0
$219$	6.00000	−	10.3923i	0.405442	−	0.702247i
$220$		0			0
$221$		0			0
$222$		0			0
$223$			4.00000i			0.267860i	0.990991	+	0.133930i	$0.0427597\pi$
$223$			4.00000i			0.267860i	−0.990991	+	0.133930i	$0.957240\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−17.3205	+	10.0000i	−1.14960	+	0.663723i	−0.948790	−	0.315906i	$-0.897691\pi$
$227$	−17.3205	+	10.0000i	−1.14960	+	0.663723i	−0.200812	+	0.979630i	$0.564358\pi$
$228$		0			0
$229$	−5.00000	+	8.66025i	−0.330409	+	0.572286i	−0.982592	−	0.185776i	$-0.940520\pi$
$229$	−5.00000	+	8.66025i	−0.330409	+	0.572286i	0.652183	+	0.758062i	$0.273853\pi$
$230$		0			0
$231$	4.00000	−	3.46410i	0.263181	−	0.227921i
$232$		0			0
$233$	6.92820	+	4.00000i	0.453882	+	0.262049i	0.709468	−	0.704737i	$-0.248935\pi$
$233$	6.92820	+	4.00000i	0.453882	+	0.262049i	−0.255586	+	0.966786i	$0.582269\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$			14.0000i			0.909398i
$238$		0			0
$239$	24.0000			1.55243			0.776215	−	0.630468i	$-0.217137\pi$
$239$	24.0000			1.55243			0.776215	+	0.630468i	$0.217137\pi$
$240$		0			0
$241$	11.0000	+	19.0526i	0.708572	+	1.22728i	0.965387	+	0.260822i	$0.0839937\pi$
$241$	11.0000	+	19.0526i	0.708572	+	1.22728i	−0.256814	+	0.966461i	$0.582673\pi$
$242$		0			0
$243$	13.8564	+	8.00000i	0.888889	+	0.513200i
$244$		0			0
$245$		0			0
$246$		0			0
$247$		0			0
$248$		0			0
$249$	5.50000	+	9.52628i	0.348548	+	0.603703i
$250$		0			0
$251$	8.00000			0.504956			0.252478	−	0.967603i	$-0.418755\pi$
$251$	8.00000			0.504956			0.252478	+	0.967603i	$0.418755\pi$
$252$		0			0
$253$		−	2.00000i		−	0.125739i
$254$		0			0
$255$		0			0
$256$		0			0
$257$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$257$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$258$		0			0
$259$	−8.00000	+	6.92820i	−0.497096	+	0.430498i
$260$		0			0
$261$	9.00000	−	15.5885i	0.557086	−	0.964901i
$262$		0			0
$263$	0.866025	−	0.500000i	0.0534014	−	0.0308313i	−0.473062	−	0.881029i	$-0.656851\pi$
$263$	0.866025	−	0.500000i	0.0534014	−	0.0308313i	0.526463	+	0.850198i	$0.323518\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$		−	15.0000i		−	0.917985i
$268$		0			0
$269$	−10.5000	−	18.1865i	−0.640196	−	1.10885i	−0.985389	−	0.170321i	$-0.945520\pi$
$269$	−10.5000	−	18.1865i	−0.640196	−	1.10885i	0.345192	−	0.938532i	$-0.387814\pi$
$270$		0			0
$271$	−11.0000	+	19.0526i	−0.668202	+	1.15736i	0.310204	+	0.950670i	$0.399603\pi$
$271$	−11.0000	+	19.0526i	−0.668202	+	1.15736i	−0.978406	+	0.206691i	$0.933731\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$		0			0
$276$		0			0
$277$	−24.2487	+	14.0000i	−1.45696	+	0.841178i	−0.998861	−	0.0477206i	$-0.984804\pi$
$277$	−24.2487	+	14.0000i	−1.45696	+	0.841178i	−0.458103	+	0.888899i	$0.651471\pi$
$278$		0			0
$279$	8.00000			0.478947
$280$		0			0
$281$	18.0000			1.07379			0.536895	−	0.843649i	$-0.319597\pi$
$281$	18.0000			1.07379			0.536895	+	0.843649i	$0.319597\pi$
$282$		0			0
$283$	3.46410	−	2.00000i	0.205919	−	0.118888i	−0.393494	−	0.919327i	$-0.628734\pi$
$283$	3.46410	−	2.00000i	0.205919	−	0.118888i	0.599414	+	0.800439i	$0.295400\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	0.866025	−	2.50000i	0.0511199	−	0.147570i
$288$		0			0
$289$	−0.500000	+	0.866025i	−0.0294118	+	0.0509427i
$290$		0			0
$291$	9.00000	+	15.5885i	0.527589	+	0.913812i
$292$		0			0
$293$		−	12.0000i		−	0.701047i	−0.936554	−	0.350524i	$-0.886004\pi$
$293$		−	12.0000i		−	0.701047i	0.936554	−	0.350524i	$-0.113996\pi$
$294$		0			0
$295$		0			0
$296$		0			0
$297$	−8.66025	+	5.00000i	−0.502519	+	0.290129i
$298$		0			0
$299$		0			0
$300$		0			0
$301$	−22.5000	−	7.79423i	−1.29688	−	0.449252i
$302$		0			0
$303$	2.59808	+	1.50000i	0.149256	+	0.0861727i
$304$		0			0
$305$		0			0
$306$		0			0
$307$			21.0000i			1.19853i	0.800549	+	0.599267i	$0.204541\pi$
$307$			21.0000i			1.19853i	−0.800549	+	0.599267i	$0.795459\pi$
$308$		0			0
$309$	13.0000			0.739544
$310$		0			0
$311$	−13.0000	−	22.5167i	−0.737162	−	1.27680i	−0.953768	−	0.300544i	$-0.902832\pi$
$311$	−13.0000	−	22.5167i	−0.737162	−	1.27680i	0.216606	−	0.976259i	$-0.430501\pi$
$312$		0			0
$313$	13.8564	+	8.00000i	0.783210	+	0.452187i	0.837567	−	0.546335i	$-0.183977\pi$
$313$	13.8564	+	8.00000i	0.783210	+	0.452187i	−0.0543564	+	0.998522i	$0.517311\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	13.8564	+	8.00000i	0.778253	+	0.449325i	0.835811	−	0.549017i	$-0.184998\pi$
$317$	13.8564	+	8.00000i	0.778253	+	0.449325i	−0.0575576	+	0.998342i	$0.518331\pi$
$318$		0			0
$319$	9.00000	+	15.5885i	0.503903	+	0.872786i
$320$		0			0
$321$	9.00000			0.502331
$322$		0			0
$323$			8.00000i			0.445132i
$324$		0			0
$325$		0			0
$326$		0			0
$327$	0.866025	+	0.500000i	0.0478913	+	0.0276501i
$328$		0			0
$329$		0			0
$330$		0			0
$331$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$331$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$332$		0			0
$333$	6.92820	−	4.00000i	0.379663	−	0.219199i
$334$		0			0
$335$		0			0
$336$		0			0
$337$		−	2.00000i		−	0.108947i	−0.998515	−	0.0544735i	$-0.982652\pi$
$337$		−	2.00000i		−	0.108947i	0.998515	−	0.0544735i	$-0.0173480\pi$
$338$		0			0
$339$	1.00000	+	1.73205i	0.0543125	+	0.0940721i
$340$		0			0
$341$	−4.00000	+	6.92820i	−0.216612	+	0.375183i
$342$		0			0
$343$	−15.5885	+	10.0000i	−0.841698	+	0.539949i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−6.06218	+	3.50000i	−0.325435	+	0.187890i	−0.653812	−	0.756657i	$-0.726831\pi$
$347$	−6.06218	+	3.50000i	−0.325435	+	0.187890i	0.328378	+	0.944547i	$0.393498\pi$
$348$		0			0
$349$	19.0000			1.01705			0.508523	−	0.861048i	$-0.330192\pi$
$349$	19.0000			1.01705			0.508523	+	0.861048i	$0.330192\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	−12.1244	+	7.00000i	−0.645314	+	0.372572i	−0.786659	−	0.617388i	$-0.788191\pi$
$353$	−12.1244	+	7.00000i	−0.645314	+	0.372572i	0.141344	+	0.989960i	$0.454858\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$	6.92820	+	8.00000i	0.366679	+	0.423405i
$358$		0			0
$359$	6.00000	−	10.3923i	0.316668	−	0.548485i	−0.663123	−	0.748511i	$-0.730769\pi$
$359$	6.00000	−	10.3923i	0.316668	−	0.548485i	0.979791	+	0.200026i	$0.0641026\pi$
$360$		0			0
$361$	7.50000	+	12.9904i	0.394737	+	0.683704i
$362$		0			0
$363$			7.00000i			0.367405i
$364$		0			0
$365$		0			0
$366$		0			0
$367$	6.06218	−	3.50000i	0.316443	−	0.182699i	−0.333363	−	0.942799i	$-0.608183\pi$
$367$	6.06218	−	3.50000i	0.316443	−	0.182699i	0.649806	+	0.760100i	$0.274850\pi$
$368$		0			0
$369$	−1.00000	+	1.73205i	−0.0520579	+	0.0901670i
$370$		0			0
$371$	−5.00000	−	25.9808i	−0.259587	−	1.34885i
$372$		0			0
$373$	−24.2487	−	14.0000i	−1.25555	−	0.724893i	−0.283344	−	0.959018i	$-0.591444\pi$
$373$	−24.2487	−	14.0000i	−1.25555	−	0.724893i	−0.972206	+	0.234126i	$0.924777\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$		0			0
$378$		0			0
$379$	30.0000			1.54100			0.770498	−	0.637442i	$-0.220007\pi$
$379$	30.0000			1.54100			0.770498	+	0.637442i	$0.220007\pi$
$380$		0			0
$381$	−4.00000	−	6.92820i	−0.204926	−	0.354943i
$382$		0			0
$383$	18.1865	+	10.5000i	0.929288	+	0.536525i	0.886586	−	0.462563i	$-0.153070\pi$
$383$	18.1865	+	10.5000i	0.929288	+	0.536525i	0.0427020	+	0.999088i	$0.486403\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	15.5885	+	9.00000i	0.792406	+	0.457496i
$388$		0			0
$389$	13.0000	+	22.5167i	0.659126	+	1.14164i	0.980842	+	0.194804i	$0.0624070\pi$
$389$	13.0000	+	22.5167i	0.659126	+	1.14164i	−0.321716	+	0.946836i	$0.604260\pi$
$390$		0			0
$391$	4.00000			0.202289
$392$		0			0
$393$			8.00000i			0.403547i
$394$		0			0
$395$		0			0
$396$		0			0
$397$	−5.19615	−	3.00000i	−0.260787	−	0.150566i	0.363906	−	0.931436i	$-0.381443\pi$
$397$	−5.19615	−	3.00000i	−0.260787	−	0.150566i	−0.624694	+	0.780870i	$0.714776\pi$
$398$		0			0
$399$	−5.00000	−	1.73205i	−0.250313	−	0.0867110i
$400$		0			0
$401$	8.50000	−	14.7224i	0.424470	−	0.735203i	−0.571901	−	0.820323i	$-0.693794\pi$
$401$	8.50000	−	14.7224i	0.424470	−	0.735203i	0.996371	+	0.0851195i	$0.0271272\pi$
$402$		0			0
$403$		0			0
$404$		0			0
$405$		0			0
$406$		0			0
$407$			8.00000i			0.396545i
$408$		0			0
$409$	−10.5000	−	18.1865i	−0.519192	−	0.899266i	−0.999751	−	0.0223042i	$-0.992900\pi$
$409$	−10.5000	−	18.1865i	−0.519192	−	0.899266i	0.480560	−	0.876962i	$-0.340434\pi$
$410$		0			0
$411$	−6.00000	+	10.3923i	−0.295958	+	0.512615i
$412$		0			0
$413$	−25.9808	+	5.00000i	−1.27843	+	0.246034i
$414$		0			0
$415$		0			0
$416$		0			0
$417$	−1.73205	+	1.00000i	−0.0848189	+	0.0489702i
$418$		0			0
$419$	−16.0000			−0.781651			−0.390826	−	0.920465i	$-0.627810\pi$
$419$	−16.0000			−0.781651			−0.390826	+	0.920465i	$0.627810\pi$
$420$		0			0
$421$	−27.0000			−1.31590			−0.657950	−	0.753062i	$-0.728576\pi$
$421$	−27.0000			−1.31590			−0.657950	+	0.753062i	$0.728576\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$		0			0
$426$		0			0
$427$	15.5885	+	18.0000i	0.754378	+	0.871081i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	−7.00000	−	12.1244i	−0.337178	−	0.584010i	0.646723	−	0.762725i	$-0.276139\pi$
$431$	−7.00000	−	12.1244i	−0.337178	−	0.584010i	−0.983901	+	0.178716i	$0.942806\pi$
$432$		0			0
$433$		−	30.0000i		−	1.44171i	−0.693087	−	0.720854i	$-0.743750\pi$
$433$		−	30.0000i		−	1.44171i	0.693087	−	0.720854i	$-0.256250\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−1.73205	+	1.00000i	−0.0828552	+	0.0478365i
$438$		0			0
$439$	−14.0000	+	24.2487i	−0.668184	+	1.15733i	0.310228	+	0.950662i	$0.399595\pi$
$439$	−14.0000	+	24.2487i	−0.668184	+	1.15733i	−0.978412	+	0.206666i	$0.933739\pi$
$440$		0			0
$441$	13.0000	−	5.19615i	0.619048	−	0.247436i
$442$		0			0
$443$	−9.52628	−	5.50000i	−0.452607	−	0.261313i	0.256323	−	0.966591i	$-0.417489\pi$
$443$	−9.52628	−	5.50000i	−0.452607	−	0.261313i	−0.708931	+	0.705278i	$0.750822\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$		−	5.00000i		−	0.236492i
$448$		0			0
$449$	41.0000			1.93491			0.967455	−	0.253044i	$-0.0814317\pi$
$449$	41.0000			1.93491			0.967455	+	0.253044i	$0.0814317\pi$
$450$		0			0
$451$	−1.00000	−	1.73205i	−0.0470882	−	0.0815591i
$452$		0			0
$453$	6.92820	+	4.00000i	0.325515	+	0.187936i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	−6.92820	−	4.00000i	−0.324088	−	0.187112i	0.329125	−	0.944286i	$-0.393246\pi$
$457$	−6.92820	−	4.00000i	−0.324088	−	0.187112i	−0.653213	+	0.757174i	$0.726579\pi$
$458$		0			0
$459$	−10.0000	−	17.3205i	−0.466760	−	0.808452i
$460$		0			0
$461$	2.00000			0.0931493			0.0465746	−	0.998915i	$-0.485169\pi$
$461$	2.00000			0.0931493			0.0465746	+	0.998915i	$0.485169\pi$
$462$		0			0
$463$		−	39.0000i		−	1.81248i	−0.422760	−	0.906242i	$-0.638939\pi$
$463$		−	39.0000i		−	1.81248i	0.422760	−	0.906242i	$-0.361061\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	6.06218	+	3.50000i	0.280524	+	0.161961i	0.633661	−	0.773611i	$-0.281552\pi$
$467$	6.06218	+	3.50000i	0.280524	+	0.161961i	−0.353137	+	0.935572i	$0.614885\pi$
$468$		0			0
$469$	−2.50000	−	12.9904i	−0.115439	−	0.599840i
$470$		0			0
$471$	−1.00000	+	1.73205i	−0.0460776	+	0.0798087i
$472$		0			0
$473$	−15.5885	+	9.00000i	−0.716758	+	0.413820i
$474$		0			0
$475$		0			0
$476$		0			0
$477$			20.0000i			0.915737i
$478$		0			0
$479$	−8.00000	−	13.8564i	−0.365529	−	0.633115i	0.623332	−	0.781958i	$-0.285779\pi$
$479$	−8.00000	−	13.8564i	−0.365529	−	0.633115i	−0.988861	+	0.148842i	$0.952445\pi$
$480$		0			0
$481$		0			0
$482$		0			0
$483$	−0.866025	+	2.50000i	−0.0394055	+	0.113754i
$484$		0			0
$485$		0			0
$486$		0			0
$487$	−6.92820	+	4.00000i	−0.313947	+	0.181257i	−0.648691	−	0.761052i	$-0.724683\pi$
$487$	−6.92820	+	4.00000i	−0.313947	+	0.181257i	0.334744	+	0.942309i	$0.391350\pi$
$488$		0			0
$489$	20.0000			0.904431
$490$		0			0
$491$	−20.0000			−0.902587			−0.451294	−	0.892375i	$-0.649037\pi$
$491$	−20.0000			−0.902587			−0.451294	+	0.892375i	$0.649037\pi$
$492$		0			0
$493$	−31.1769	+	18.0000i	−1.40414	+	0.810679i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	12.1244	−	35.0000i	0.543852	−	1.56996i
$498$		0			0
$499$	−19.0000	+	32.9090i	−0.850557	+	1.47321i	0.0301498	+	0.999545i	$0.490402\pi$
$499$	−19.0000	+	32.9090i	−0.850557	+	1.47321i	−0.880707	+	0.473662i	$0.842932\pi$
$500$		0			0
$501$	−8.50000	−	14.7224i	−0.379752	−	0.657750i
$502$		0			0
$503$			23.0000i			1.02552i	0.858532	+	0.512760i	$0.171377\pi$
$503$			23.0000i			1.02552i	−0.858532	+	0.512760i	$0.828623\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	−11.2583	+	6.50000i	−0.500000	+	0.288675i
$508$		0			0
$509$	−7.50000	+	12.9904i	−0.332432	+	0.575789i	−0.982988	−	0.183669i	$-0.941202\pi$
$509$	−7.50000	+	12.9904i	−0.332432	+	0.575789i	0.650556	+	0.759458i	$0.274536\pi$
$510$		0			0
$511$	6.00000	+	31.1769i	0.265424	+	1.37919i
$512$		0			0
$513$	8.66025	+	5.00000i	0.382360	+	0.220755i
$514$		0			0
$515$		0			0
$516$		0			0
$517$		0			0
$518$		0			0
$519$	−16.0000			−0.702322
$520$		0			0
$521$	21.0000	+	36.3731i	0.920027	+	1.59353i	0.799370	+	0.600839i	$0.205167\pi$
$521$	21.0000	+	36.3731i	0.920027	+	1.59353i	0.120656	+	0.992694i	$0.461500\pi$
$522$		0			0
$523$	24.2487	+	14.0000i	1.06032	+	0.612177i	0.925521	−	0.378695i	$-0.123627\pi$
$523$	24.2487	+	14.0000i	1.06032	+	0.612177i	0.134801	+	0.990873i	$0.456961\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−13.8564	−	8.00000i	−0.603595	−	0.348485i
$528$		0			0
$529$	−11.0000	−	19.0526i	−0.478261	−	0.828372i
$530$		0			0
$531$	20.0000			0.867926
$532$		0			0
$533$		0			0
$534$		0			0
$535$		0			0
$536$		0			0
$537$	−10.3923	−	6.00000i	−0.448461	−	0.258919i
$538$		0			0
$539$	−2.00000	+	13.8564i	−0.0861461	+	0.596838i
$540$		0			0
$541$	6.50000	−	11.2583i	0.279457	−	0.484033i	−0.691793	−	0.722096i	$-0.743179\pi$
$541$	6.50000	−	11.2583i	0.279457	−	0.484033i	0.971250	+	0.238062i	$0.0765123\pi$
$542$		0			0
$543$	21.6506	−	12.5000i	0.929118	−	0.536426i
$544$		0			0
$545$		0			0
$546$		0			0
$547$		−	35.0000i		−	1.49649i	−0.663421	−	0.748246i	$-0.730896\pi$
$547$		−	35.0000i		−	1.49649i	0.663421	−	0.748246i	$-0.269104\pi$
$548$		0			0
$549$	−9.00000	−	15.5885i	−0.384111	−	0.665299i
$550$		0			0
$551$	9.00000	−	15.5885i	0.383413	−	0.664091i
$552$		0			0
$553$	−24.2487	−	28.0000i	−1.03116	−	1.19068i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	25.9808	−	15.0000i	1.10084	−	0.635570i	0.164399	−	0.986394i	$-0.447432\pi$
$557$	25.9808	−	15.0000i	1.10084	−	0.635570i	0.936442	+	0.350824i	$0.114098\pi$
$558$		0			0
$559$		0			0
$560$		0			0
$561$	8.00000			0.337760
$562$		0			0
$563$	38.9711	−	22.5000i	1.64244	−	0.948262i	0.662474	−	0.749085i	$-0.269506\pi$
$563$	38.9711	−	22.5000i	1.64244	−	0.948262i	0.979963	−	0.199177i	$-0.0638270\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$	−2.59808	+	0.500000i	−0.109109	+	0.0209980i
$568$		0			0
$569$	23.0000	−	39.8372i	0.964210	−	1.67006i	0.252488	−	0.967600i	$-0.418751\pi$
$569$	23.0000	−	39.8372i	0.964210	−	1.67006i	0.711722	−	0.702461i	$-0.247915\pi$
$570$		0			0
$571$	13.0000	+	22.5167i	0.544033	+	0.942293i	0.998667	+	0.0516146i	$0.0164367\pi$
$571$	13.0000	+	22.5167i	0.544033	+	0.942293i	−0.454634	+	0.890678i	$0.650230\pi$
$572$		0			0
$573$		−	18.0000i		−	0.751961i
$574$		0			0
$575$		0			0
$576$		0			0
$577$	1.73205	−	1.00000i	0.0721062	−	0.0416305i	−0.463513	−	0.886090i	$-0.653411\pi$
$577$	1.73205	−	1.00000i	0.0721062	−	0.0416305i	0.535620	+	0.844459i	$0.320078\pi$
$578$		0			0
$579$	−7.00000	+	12.1244i	−0.290910	+	0.503871i
$580$		0			0
$581$	−27.5000	−	9.52628i	−1.14089	−	0.395217i
$582$		0			0
$583$	−17.3205	−	10.0000i	−0.717342	−	0.414158i
$584$		0			0
$585$		0			0
$586$		0			0
$587$		−	12.0000i		−	0.495293i	−0.968850	−	0.247647i	$-0.920343\pi$
$587$		−	12.0000i		−	0.495293i	0.968850	−	0.247647i	$-0.0796572\pi$
$588$		0			0
$589$	8.00000			0.329634
$590$		0			0
$591$	−9.00000	−	15.5885i	−0.370211	−	0.641223i
$592$		0			0
$593$	15.5885	+	9.00000i	0.640141	+	0.369586i	0.784669	−	0.619915i	$-0.212833\pi$
$593$	15.5885	+	9.00000i	0.640141	+	0.369586i	−0.144528	+	0.989501i	$0.546166\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	3.46410	+	2.00000i	0.141776	+	0.0818546i
$598$		0			0
$599$	2.00000	+	3.46410i	0.0817178	+	0.141539i	0.903988	−	0.427558i	$-0.140626\pi$
$599$	2.00000	+	3.46410i	0.0817178	+	0.141539i	−0.822270	+	0.569097i	$0.807293\pi$
$600$		0			0
$601$	10.0000			0.407909			0.203954	−	0.978980i	$-0.434621\pi$
$601$	10.0000			0.407909			0.203954	+	0.978980i	$0.434621\pi$
$602$		0			0
$603$			10.0000i			0.407231i
$604$		0			0
$605$		0			0
$606$		0			0
$607$	−23.3827	−	13.5000i	−0.949074	−	0.547948i	−0.0562808	−	0.998415i	$-0.517924\pi$
$607$	−23.3827	−	13.5000i	−0.949074	−	0.547948i	−0.892793	+	0.450467i	$0.851258\pi$
$608$		0			0
$609$	−4.50000	−	23.3827i	−0.182349	−	0.947514i
$610$		0			0
$611$		0			0
$612$		0			0
$613$	17.3205	−	10.0000i	0.699569	−	0.403896i	−0.107618	−	0.994192i	$-0.534322\pi$
$613$	17.3205	−	10.0000i	0.699569	−	0.403896i	0.807187	+	0.590296i	$0.200989\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$		−	12.0000i		−	0.483102i	−0.970388	−	0.241551i	$-0.922344\pi$
$617$		−	12.0000i		−	0.483102i	0.970388	−	0.241551i	$-0.0776561\pi$
$618$		0			0
$619$	−17.0000	−	29.4449i	−0.683288	−	1.18349i	−0.973972	−	0.226670i	$-0.927216\pi$
$619$	−17.0000	−	29.4449i	−0.683288	−	1.18349i	0.290684	−	0.956819i	$-0.406117\pi$
$620$		0			0
$621$	2.50000	−	4.33013i	0.100322	−	0.173762i
$622$		0			0
$623$	25.9808	+	30.0000i	1.04090	+	1.20192i
$624$		0			0
$625$		0			0
$626$		0			0
$627$	−3.46410	+	2.00000i	−0.138343	+	0.0798723i
$628$		0			0
$629$	−16.0000			−0.637962
$630$		0			0
$631$	−2.00000			−0.0796187			−0.0398094	−	0.999207i	$-0.512675\pi$
$631$	−2.00000			−0.0796187			−0.0398094	+	0.999207i	$0.512675\pi$
$632$		0			0
$633$	−1.73205	+	1.00000i	−0.0688428	+	0.0397464i
$634$		0			0
$635$		0			0
$636$		0			0
$637$		0			0
$638$		0			0
$639$	−14.0000	+	24.2487i	−0.553831	+	0.959264i
$640$		0			0
$641$	9.50000	+	16.4545i	0.375227	+	0.649913i	0.990361	−	0.138510i	$-0.0442313\pi$
$641$	9.50000	+	16.4545i	0.375227	+	0.649913i	−0.615134	+	0.788423i	$0.710898\pi$
$642$		0			0
$643$			4.00000i			0.157745i	0.996885	+	0.0788723i	$0.0251319\pi$
$643$			4.00000i			0.157745i	−0.996885	+	0.0788723i	$0.974868\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	19.9186	−	11.5000i	0.783080	−	0.452112i	−0.0544405	−	0.998517i	$-0.517338\pi$
$647$	19.9186	−	11.5000i	0.783080	−	0.452112i	0.837521	+	0.546405i	$0.184004\pi$
$648$		0			0
$649$	−10.0000	+	17.3205i	−0.392534	+	0.679889i
$650$		0			0
$651$	8.00000	−	6.92820i	0.313545	−	0.271538i
$652$		0			0
$653$	31.1769	+	18.0000i	1.22005	+	0.704394i	0.964928	−	0.262515i	$-0.0845520\pi$
$653$	31.1769	+	18.0000i	1.22005	+	0.704394i	0.255119	+	0.966910i	$0.417885\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$		−	24.0000i		−	0.936329i
$658$		0			0
$659$	−2.00000			−0.0779089			−0.0389545	−	0.999241i	$-0.512403\pi$
$659$	−2.00000			−0.0779089			−0.0389545	+	0.999241i	$0.512403\pi$
$660$		0			0
$661$	1.50000	+	2.59808i	0.0583432	+	0.101053i	0.893722	−	0.448622i	$-0.148085\pi$
$661$	1.50000	+	2.59808i	0.0583432	+	0.101053i	−0.835379	+	0.549675i	$0.814752\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$		0			0
$666$		0			0
$667$	−7.79423	−	4.50000i	−0.301794	−	0.174241i
$668$		0			0
$669$	−2.00000	−	3.46410i	−0.0773245	−	0.133930i
$670$		0			0
$671$	18.0000			0.694882
$672$		0			0
$673$		−	24.0000i		−	0.925132i	−0.886585	−	0.462566i	$-0.846929\pi$
$673$		−	24.0000i		−	0.925132i	0.886585	−	0.462566i	$-0.153071\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	20.7846	+	12.0000i	0.798817	+	0.461197i	0.843057	−	0.537823i	$-0.180753\pi$
$677$	20.7846	+	12.0000i	0.798817	+	0.461197i	−0.0442400	+	0.999021i	$0.514087\pi$
$678$		0			0
$679$	−45.0000	−	15.5885i	−1.72694	−	0.598230i
$680$		0			0
$681$	10.0000	−	17.3205i	0.383201	−	0.663723i
$682$		0			0
$683$	−7.79423	+	4.50000i	−0.298238	+	0.172188i	−0.641651	−	0.766997i	$-0.721750\pi$
$683$	−7.79423	+	4.50000i	−0.298238	+	0.172188i	0.343413	+	0.939184i	$0.388417\pi$
$684$		0			0
$685$		0			0
$686$		0			0
$687$		−	10.0000i		−	0.381524i
$688$		0			0
$689$		0			0
$690$		0			0
$691$	−25.0000	+	43.3013i	−0.951045	+	1.64726i	−0.207875	+	0.978155i	$0.566655\pi$
$691$	−25.0000	+	43.3013i	−0.951045	+	1.64726i	−0.743170	+	0.669102i	$0.766679\pi$
$692$		0			0
$693$	3.46410	−	10.0000i	0.131590	−	0.379869i
$694$		0			0
$695$		0			0
$696$		0			0
$697$	3.46410	−	2.00000i	0.131212	−	0.0757554i
$698$		0			0
$699$	−8.00000			−0.302588
$700$		0			0
$701$	9.00000			0.339925			0.169963	−	0.985451i	$-0.445635\pi$
$701$	9.00000			0.339925			0.169963	+	0.985451i	$0.445635\pi$
$702$		0			0
$703$	6.92820	−	4.00000i	0.261302	−	0.150863i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−7.79423	+	1.50000i	−0.293132	+	0.0564133i
$708$		0			0
$709$	10.5000	−	18.1865i	0.394336	−	0.683010i	−0.598680	−	0.800988i	$-0.704308\pi$
$709$	10.5000	−	18.1865i	0.394336	−	0.683010i	0.993016	+	0.117978i	$0.0376414\pi$
$710$		0			0
$711$	14.0000	+	24.2487i	0.525041	+	0.909398i
$712$		0			0
$713$		−	4.00000i		−	0.149801i
$714$		0			0
$715$		0			0
$716$		0			0
$717$	−20.7846	+	12.0000i	−0.776215	+	0.448148i
$718$		0			0
$719$	−21.0000	+	36.3731i	−0.783168	+	1.35649i	0.146920	+	0.989148i	$0.453064\pi$
$719$	−21.0000	+	36.3731i	−0.783168	+	1.35649i	−0.930087	+	0.367338i	$0.880269\pi$
$720$		0			0
$721$	−26.0000	+	22.5167i	−0.968291	+	0.838564i
$722$		0			0
$723$	−19.0526	−	11.0000i	−0.708572	−	0.409094i
$724$		0			0
$725$		0			0
$726$		0			0
$727$		−	31.0000i		−	1.14973i	−0.818250	−	0.574863i	$-0.805055\pi$
$727$		−	31.0000i		−	1.14973i	0.818250	−	0.574863i	$-0.194945\pi$
$728$		0			0
$729$	−13.0000			−0.481481
$730$		0			0
$731$	−18.0000	−	31.1769i	−0.665754	−	1.15312i
$732$		0			0
$733$	−22.5167	−	13.0000i	−0.831672	−	0.480166i	0.0227529	−	0.999741i	$-0.492757\pi$
$733$	−22.5167	−	13.0000i	−0.831672	−	0.480166i	−0.854425	+	0.519575i	$0.826090\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−8.66025	−	5.00000i	−0.319005	−	0.184177i
$738$		0			0
$739$	5.00000	+	8.66025i	0.183928	+	0.318573i	0.943215	−	0.332184i	$-0.107785\pi$
$739$	5.00000	+	8.66025i	0.183928	+	0.318573i	−0.759287	+	0.650756i	$0.774452\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$		−	27.0000i		−	0.990534i	−0.868741	−	0.495267i	$-0.835070\pi$
$743$		−	27.0000i		−	0.990534i	0.868741	−	0.495267i	$-0.164930\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	19.0526	+	11.0000i	0.697097	+	0.402469i
$748$		0			0
$749$	−18.0000	+	15.5885i	−0.657706	+	0.569590i
$750$		0			0
$751$	−6.00000	+	10.3923i	−0.218943	+	0.379221i	−0.954485	−	0.298259i	$-0.903594\pi$
$751$	−6.00000	+	10.3923i	−0.218943	+	0.379221i	0.735542	+	0.677479i	$0.236928\pi$
$752$		0			0
$753$	−6.92820	+	4.00000i	−0.252478	+	0.145768i
$754$		0			0
$755$		0			0
$756$		0			0
$757$		−	24.0000i		−	0.872295i	−0.899875	−	0.436147i	$-0.856343\pi$
$757$		−	24.0000i		−	0.872295i	0.899875	−	0.436147i	$-0.143657\pi$
$758$		0			0
$759$	1.00000	+	1.73205i	0.0362977	+	0.0628695i
$760$		0			0
$761$	3.00000	−	5.19615i	0.108750	−	0.188360i	−0.806514	−	0.591215i	$-0.798649\pi$
$761$	3.00000	−	5.19615i	0.108750	−	0.188360i	0.915264	+	0.402854i	$0.131982\pi$
$762$		0			0
$763$	−2.59808	+	0.500000i	−0.0940567	+	0.0181012i
$764$		0			0
$765$		0			0
$766$		0			0
$767$		0			0
$768$		0			0
$769$	−34.0000			−1.22607			−0.613036	−	0.790055i	$-0.710052\pi$
$769$	−34.0000			−1.22607			−0.613036	+	0.790055i	$0.710052\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$773$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$	3.46410	−	10.0000i	0.124274	−	0.358748i
$778$		0			0
$779$	−1.00000	+	1.73205i	−0.0358287	+	0.0620572i
$780$		0			0
$781$	−14.0000	−	24.2487i	−0.500959	−	0.867687i
$782$		0			0
$783$			45.0000i			1.60817i
$784$		0			0
$785$		0			0
$786$		0			0
$787$	38.9711	−	22.5000i	1.38917	−	0.802038i	0.395949	−	0.918272i	$-0.370416\pi$
$787$	38.9711	−	22.5000i	1.38917	−	0.802038i	0.993222	+	0.116234i	$0.0370822\pi$
$788$		0			0
$789$	−0.500000	+	0.866025i	−0.0178005	+	0.0308313i
$790$		0			0
$791$	−5.00000	−	1.73205i	−0.177780	−	0.0615846i
$792$		0			0
$793$		0			0
$794$		0			0
$795$		0			0
$796$		0			0
$797$			8.00000i			0.283375i	0.989911	+	0.141687i	$0.0452527\pi$
$797$			8.00000i			0.283375i	−0.989911	+	0.141687i	$0.954747\pi$
$798$		0			0
$799$		0			0
$800$		0			0
$801$	−15.0000	−	25.9808i	−0.529999	−	0.917985i
$802$		0			0
$803$	20.7846	+	12.0000i	0.733473	+	0.423471i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	18.1865	+	10.5000i	0.640196	+	0.369618i
$808$		0			0
$809$	6.50000	+	11.2583i	0.228528	+	0.395822i	0.957372	−	0.288858i	$-0.0932755\pi$
$809$	6.50000	+	11.2583i	0.228528	+	0.395822i	−0.728844	+	0.684680i	$0.759942\pi$
$810$		0			0
$811$	−44.0000			−1.54505			−0.772524	−	0.634985i	$-0.781006\pi$
$811$	−44.0000			−1.54505			−0.772524	+	0.634985i	$0.781006\pi$
$812$		0			0
$813$		−	22.0000i		−	0.771574i
$814$		0			0
$815$		0			0
$816$		0			0
$817$	15.5885	+	9.00000i	0.545371	+	0.314870i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−15.0000	+	25.9808i	−0.523504	+	0.906735i	0.476122	+	0.879379i	$0.342042\pi$
$821$	−15.0000	+	25.9808i	−0.523504	+	0.906735i	−0.999626	+	0.0273557i	$0.991291\pi$
$822$		0			0
$823$	−42.4352	+	24.5000i	−1.47920	+	0.854016i	−0.999723	−	0.0235383i	$-0.992507\pi$
$823$	−42.4352	+	24.5000i	−1.47920	+	0.854016i	−0.479477	+	0.877555i	$0.659174\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$		−	17.0000i		−	0.591148i	−0.955320	−	0.295574i	$-0.904489\pi$
$827$		−	17.0000i		−	0.591148i	0.955320	−	0.295574i	$-0.0955109\pi$
$828$		0			0
$829$	1.00000	+	1.73205i	0.0347314	+	0.0601566i	0.882869	−	0.469620i	$-0.155609\pi$
$829$	1.00000	+	1.73205i	0.0347314	+	0.0601566i	−0.848137	+	0.529777i	$0.822276\pi$
$830$		0			0
$831$	14.0000	−	24.2487i	0.485655	−	0.841178i
$832$		0			0
$833$	−27.7128	−	4.00000i	−0.960192	−	0.138592i
$834$		0			0
$835$		0			0
$836$		0			0
$837$	−17.3205	+	10.0000i	−0.598684	+	0.345651i
$838$		0			0
$839$	−10.0000			−0.345238			−0.172619	−	0.984989i	$-0.555223\pi$
$839$	−10.0000			−0.345238			−0.172619	+	0.984989i	$0.555223\pi$
$840$		0			0
$841$	52.0000			1.79310
$842$		0			0
$843$	−15.5885	+	9.00000i	−0.536895	+	0.309976i
$844$		0			0
$845$		0			0
$846$		0			0
$847$	−12.1244	−	14.0000i	−0.416598	−	0.481046i
$848$		0			0
$849$	−2.00000	+	3.46410i	−0.0686398	+	0.118888i
$850$		0			0
$851$	−2.00000	−	3.46410i	−0.0685591	−	0.118748i
$852$		0			0
$853$		−	38.0000i		−	1.30110i	−0.759465	−	0.650548i	$-0.774539\pi$
$853$		−	38.0000i		−	1.30110i	0.759465	−	0.650548i	$-0.225461\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	25.9808	−	15.0000i	0.887486	−	0.512390i	0.0143666	−	0.999897i	$-0.495427\pi$
$857$	25.9808	−	15.0000i	0.887486	−	0.512390i	0.873119	+	0.487507i	$0.162093\pi$
$858$		0			0
$859$	20.0000	−	34.6410i	0.682391	−	1.18194i	−0.291858	−	0.956462i	$-0.594273\pi$
$859$	20.0000	−	34.6410i	0.682391	−	1.18194i	0.974249	−	0.225475i	$-0.0723932\pi$
$860$		0			0
$861$	0.500000	+	2.59808i	0.0170400	+	0.0885422i
$862$		0			0
$863$	−0.866025	−	0.500000i	−0.0294798	−	0.0170202i	0.485188	−	0.874410i	$-0.338751\pi$
$863$	−0.866025	−	0.500000i	−0.0294798	−	0.0170202i	−0.514667	+	0.857390i	$0.672085\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$		−	1.00000i		−	0.0339618i
$868$		0			0
$869$	−28.0000			−0.949835
$870$		0			0
$871$		0			0
$872$		0			0
$873$	31.1769	+	18.0000i	1.05518	+	0.609208i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	−5.19615	−	3.00000i	−0.175462	−	0.101303i	0.409697	−	0.912222i	$-0.365634\pi$
$877$	−5.19615	−	3.00000i	−0.175462	−	0.101303i	−0.585159	+	0.810919i	$0.698968\pi$
$878$		0			0
$879$	6.00000	+	10.3923i	0.202375	+	0.350524i
$880$		0			0
$881$	17.0000			0.572745			0.286372	−	0.958118i	$-0.407551\pi$
$881$	17.0000			0.572745			0.286372	+	0.958118i	$0.407551\pi$
$882$		0			0
$883$		−	20.0000i		−	0.673054i	−0.941674	−	0.336527i	$-0.890748\pi$
$883$		−	20.0000i		−	0.673054i	0.941674	−	0.336527i	$-0.109252\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−12.9904	−	7.50000i	−0.436174	−	0.251825i	0.265799	−	0.964028i	$-0.414364\pi$
$887$	−12.9904	−	7.50000i	−0.436174	−	0.251825i	−0.701974	+	0.712203i	$0.747698\pi$
$888$		0			0
$889$	20.0000	+	6.92820i	0.670778	+	0.232364i
$890$		0			0
$891$	−1.00000	+	1.73205i	−0.0335013	+	0.0580259i
$892$		0			0
$893$		0			0
$894$		0			0
$895$		0			0
$896$		0			0
$897$		0			0
$898$		0			0
$899$	18.0000	+	31.1769i	0.600334	+	1.03981i
$900$		0			0
$901$	20.0000	−	34.6410i	0.666297	−	1.15406i
$902$		0			0
$903$	23.3827	−	4.50000i	0.778127	−	0.149751i
$904$		0			0
$905$		0			0
$906$		0			0
$907$	6.06218	−	3.50000i	0.201291	−	0.116216i	−0.395966	−	0.918265i	$-0.629590\pi$
$907$	6.06218	−	3.50000i	0.201291	−	0.116216i	0.597258	+	0.802049i	$0.296257\pi$
$908$		0			0
$909$	6.00000			0.199007
$910$		0			0
$911$	−6.00000			−0.198789			−0.0993944	−	0.995048i	$-0.531691\pi$
$911$	−6.00000			−0.198789			−0.0993944	+	0.995048i	$0.531691\pi$
$912$		0			0
$913$	−19.0526	+	11.0000i	−0.630548	+	0.364047i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	−13.8564	−	16.0000i	−0.457579	−	0.528367i
$918$		0			0
$919$	21.0000	−	36.3731i	0.692726	−	1.19984i	−0.278215	−	0.960519i	$-0.589743\pi$
$919$	21.0000	−	36.3731i	0.692726	−	1.19984i	0.970941	−	0.239318i	$-0.0769238\pi$
$920$		0			0
$921$	−10.5000	−	18.1865i	−0.345987	−	0.599267i
$922$		0			0
$923$		0			0
$924$		0			0
$925$		0			0
$926$		0			0
$927$	22.5167	−	13.0000i	0.739544	−	0.426976i
$928$		0			0
$929$	−6.50000	+	11.2583i	−0.213258	+	0.369374i	−0.952732	−	0.303811i	$-0.901741\pi$
$929$	−6.50000	+	11.2583i	−0.213258	+	0.369374i	0.739474	+	0.673185i	$0.235074\pi$
$930$		0			0
$931$	13.0000	−	5.19615i	0.426058	−	0.170297i
$932$		0			0
$933$	22.5167	+	13.0000i	0.737162	+	0.425601i
$934$		0			0
$935$		0			0
$936$		0			0
$937$			4.00000i			0.130674i	0.997863	+	0.0653372i	$0.0208123\pi$
$937$			4.00000i			0.130674i	−0.997863	+	0.0653372i	$0.979188\pi$
$938$		0			0
$939$	−16.0000			−0.522140
$940$		0			0
$941$	15.0000	+	25.9808i	0.488986	+	0.846949i	0.999920	−	0.0126715i	$-0.00403357\pi$
$941$	15.0000	+	25.9808i	0.488986	+	0.846949i	−0.510934	+	0.859620i	$0.670700\pi$
$942$		0			0
$943$	0.866025	+	0.500000i	0.0282017	+	0.0162822i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−4.33013	−	2.50000i	−0.140710	−	0.0812391i	0.427992	−	0.903782i	$-0.359221\pi$
$947$	−4.33013	−	2.50000i	−0.140710	−	0.0812391i	−0.568702	+	0.822543i	$0.692554\pi$
$948$		0			0
$949$		0			0
$950$		0			0
$951$	−16.0000			−0.518836
$952$		0			0
$953$		−	28.0000i		−	0.907009i	−0.891254	−	0.453504i	$-0.850174\pi$
$953$		−	28.0000i		−	0.907009i	0.891254	−	0.453504i	$-0.149826\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$	−15.5885	−	9.00000i	−0.503903	−	0.290929i
$958$		0			0
$959$	−6.00000	−	31.1769i	−0.193750	−	1.00676i
$960$		0			0
$961$	7.50000	−	12.9904i	0.241935	−	0.419045i
$962$		0			0
$963$	15.5885	−	9.00000i	0.502331	−	0.290021i
$964$		0			0
$965$		0			0
$966$		0			0
$967$			55.0000i			1.76868i	0.466843	+	0.884340i	$0.345391\pi$
$967$			55.0000i			1.76868i	−0.466843	+	0.884340i	$0.654609\pi$
$968$		0			0
$969$	−4.00000	−	6.92820i	−0.128499	−	0.222566i
$970$		0			0
$971$	4.00000	−	6.92820i	0.128366	−	0.222337i	−0.794678	−	0.607032i	$-0.792360\pi$
$971$	4.00000	−	6.92820i	0.128366	−	0.222337i	0.923044	+	0.384695i	$0.125693\pi$
$972$		0			0
$973$	1.73205	−	5.00000i	0.0555270	−	0.160293i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	36.3731	−	21.0000i	1.16368	−	0.671850i	0.211495	−	0.977379i	$-0.432167\pi$
$977$	36.3731	−	21.0000i	1.16368	−	0.671850i	0.952183	+	0.305530i	$0.0988335\pi$
$978$		0			0
$979$	30.0000			0.958804
$980$		0			0
$981$	2.00000			0.0638551
$982$		0			0
$983$	−2.59808	+	1.50000i	−0.0828658	+	0.0478426i	−0.540860	−	0.841112i	$-0.681901\pi$
$983$	−2.59808	+	1.50000i	−0.0828658	+	0.0478426i	0.457995	+	0.888955i	$0.348568\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$		0			0
$988$		0			0
$989$	4.50000	−	7.79423i	0.143092	−	0.247842i
$990$		0			0
$991$	20.0000	+	34.6410i	0.635321	+	1.10041i	0.986447	+	0.164080i	$0.0524655\pi$
$991$	20.0000	+	34.6410i	0.635321	+	1.10041i	−0.351126	+	0.936328i	$0.614201\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$		0			0
$996$		0			0
$997$	8.66025	−	5.00000i	0.274273	−	0.158352i	−0.356555	−	0.934274i	$-0.616049\pi$
$997$	8.66025	−	5.00000i	0.274273	−	0.158352i	0.630828	+	0.775923i	$0.282715\pi$
$998$		0			0
$999$	−10.0000	+	17.3205i	−0.316386	+	0.547997i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1400.2.bh.b.849.1		4
5.2	odd	4		1400.2.q.e.401.1		2
5.3	odd	4		280.2.q.a.121.1	yes	2
5.4	even	2	inner	1400.2.bh.b.849.2		4
7.4	even	3	inner	1400.2.bh.b.249.2		4
15.8	even	4		2520.2.bi.a.1801.1		2
20.3	even	4		560.2.q.h.401.1		2
35.2	odd	12		9800.2.a.r.1.1		1
35.3	even	12		1960.2.q.k.361.1		2
35.4	even	6	inner	1400.2.bh.b.249.1		4
35.12	even	12		9800.2.a.bc.1.1		1
35.13	even	4		1960.2.q.k.961.1		2
35.18	odd	12		280.2.q.a.81.1	✓	2
35.23	odd	12		1960.2.a.i.1.1		1
35.32	odd	12		1400.2.q.e.1201.1		2
35.33	even	12		1960.2.a.e.1.1		1
105.53	even	12		2520.2.bi.a.361.1		2
140.23	even	12		3920.2.a.m.1.1		1
140.103	odd	12		3920.2.a.y.1.1		1
140.123	even	12		560.2.q.h.81.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
280.2.q.a.81.1	✓	2	35.18	odd	12
280.2.q.a.121.1	yes	2	5.3	odd	4
560.2.q.h.81.1		2	140.123	even	12
560.2.q.h.401.1		2	20.3	even	4
1400.2.q.e.401.1		2	5.2	odd	4
1400.2.q.e.1201.1		2	35.32	odd	12
1400.2.bh.b.249.1		4	35.4	even	6	inner
1400.2.bh.b.249.2		4	7.4	even	3	inner
1400.2.bh.b.849.1		4	1.1	even	1	trivial
1400.2.bh.b.849.2		4	5.4	even	2	inner
1960.2.a.e.1.1		1	35.33	even	12
1960.2.a.i.1.1		1	35.23	odd	12
1960.2.q.k.361.1		2	35.3	even	12
1960.2.q.k.961.1		2	35.13	even	4
2520.2.bi.a.361.1		2	105.53	even	12
2520.2.bi.a.1801.1		2	15.8	even	4
3920.2.a.m.1.1		1	140.23	even	12
3920.2.a.y.1.1		1	140.103	odd	12
9800.2.a.r.1.1		1	35.2	odd	12
9800.2.a.bc.1.1		1	35.12	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)

\(f(q)\)	\(=\)	\(q+(-0.866025 + 0.500000i) q^{3} +(0.866025 - 2.50000i) q^{7} +(-1.00000 + 1.73205i) q^{9} +O(q^{10})\)	\(q+(-0.866025 + 0.500000i) q^{3} +(0.866025 - 2.50000i) q^{7} +(-1.00000 + 1.73205i) q^{9} +(-1.00000 - 1.73205i) q^{11} +(3.46410 - 2.00000i) q^{17} +(-1.00000 + 1.73205i) q^{19} +(0.500000 + 2.59808i) q^{21} +(0.866025 + 0.500000i) q^{23} -5.00000i q^{27} -9.00000 q^{29} +(-2.00000 - 3.46410i) q^{31} +(1.73205 + 1.00000i) q^{33} +(-3.46410 - 2.00000i) q^{37} +1.00000 q^{41} -9.00000i q^{43} +(-5.50000 - 4.33013i) q^{49} +(-2.00000 + 3.46410i) q^{51} +(8.66025 - 5.00000i) q^{53} -2.00000i q^{57} +(-5.00000 - 8.66025i) q^{59} +(-4.50000 + 7.79423i) q^{61} +(3.46410 + 4.00000i) q^{63} +(4.33013 - 2.50000i) q^{67} -1.00000 q^{69} +14.0000 q^{71} +(-10.3923 + 6.00000i) q^{73} +(-5.19615 + 1.00000i) q^{77} +(7.00000 - 12.1244i) q^{79} +(-0.500000 - 0.866025i) q^{81} -11.0000i q^{83} +(7.79423 - 4.50000i) q^{87} +(-7.50000 + 12.9904i) q^{89} +(3.46410 + 2.00000i) q^{93} -18.0000i q^{97} +4.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 4 q^{9}+O(q^{10}) \) 4 * q - 4 * q^9	\( 4 q - 4 q^{9} - 4 q^{11} - 4 q^{19} + 2 q^{21} - 36 q^{29} - 8 q^{31} + 4 q^{41} - 22 q^{49} - 8 q^{51} - 20 q^{59} - 18 q^{61} - 4 q^{69} + 56 q^{71} + 28 q^{79} - 2 q^{81} - 30 q^{89} + 16 q^{99}+O(q^{100}) \) 4 * q - 4 * q^9 - 4 * q^11 - 4 * q^19 + 2 * q^21 - 36 * q^29 - 8 * q^31 + 4 * q^41 - 22 * q^49 - 8 * q^51 - 20 * q^59 - 18 * q^61 - 4 * q^69 + 56 * q^71 + 28 * q^79 - 2 * q^81 - 30 * q^89 + 16 * q^99

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