LMFDB - Embedded newform 756.2.l.b.289.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [756,2,Mod(289,756)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(756, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 4, 2]))

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

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

chi := DirichletCharacter("756.289");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 756 = 2^{2} \cdot 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	756.l (of order $3$, 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:	$6.03669039281$
Analytic rank:	$0$
Dimension:	$14$
Relative dimension:	$7$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{14} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{14} - 5x^{12} - 3x^{11} + 7x^{10} + 30x^{9} - 117x^{7} + 270x^{5} + 189x^{4} - 243x^{3} - 1215x^{2} + 2187 $ x^14 - 5x^12 - 3x^11 + 7x^10 + 30x^9 - 117x^7 + 270x^5 + 189x^4 - 243x^3 - 1215*x^2 + 2187
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 3^{7} $
Twist minimal:	no (minimal twist has level 252)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			289.4
Root			$1.64515 - 0.541745i$ of defining polynomial
Character	$\chi$	$=$	756.289
Dual form			756.2.l.b.361.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.763837 q^{5} +(-1.05641 - 2.42569i) q^{7} +O(q^{10})$	$q+0.763837 q^{5} +(-1.05641 - 2.42569i) q^{7} -6.03389 q^{11} +(-1.26032 - 2.18294i) q^{13} +(-1.94444 - 3.36787i) q^{17} +(-2.13503 + 3.69798i) q^{19} +1.46425 q^{23} -4.41655 q^{25} +(3.00732 - 5.20884i) q^{29} +(-3.28482 + 5.68948i) q^{31} +(-0.806926 - 1.85283i) q^{35} +(4.82492 - 8.35700i) q^{37} +(2.24844 + 3.89442i) q^{41} +(-2.13503 + 3.69798i) q^{43} +(-3.38924 - 5.87034i) q^{47} +(-4.76799 + 5.12507i) q^{49} +(0.265581 + 0.460000i) q^{53} -4.60891 q^{55} +(5.59926 - 9.69821i) q^{59} +(-4.19144 - 7.25979i) q^{61} +(-0.962681 - 1.66741i) q^{65} +(0.961979 - 1.66620i) q^{67} -9.90353 q^{71} +(-2.13099 - 3.69098i) q^{73} +(6.37428 + 14.6364i) q^{77} +(3.70372 + 6.41503i) q^{79} +(8.05178 - 13.9461i) q^{83} +(-1.48523 - 2.57250i) q^{85} +(-1.76310 + 3.05377i) q^{89} +(-3.96373 + 5.36325i) q^{91} +(-1.63081 + 2.82465i) q^{95} +(2.33513 - 4.04456i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 14 q - 4 q^{5} - 3 q^{7}+O(q^{10}) $ 14 * q - 4 * q^5 - 3 * q^7	$ 14 q - 4 q^{5} - 3 q^{7} + 4 q^{11} + 2 q^{13} - 2 q^{17} + 7 q^{19} + 22 q^{23} + 18 q^{25} - q^{29} - q^{31} + 19 q^{35} + 10 q^{37} + 33 q^{41} + 7 q^{43} + 3 q^{47} - 13 q^{49} + 15 q^{53} - 28 q^{55} + 14 q^{59} - 10 q^{61} - 15 q^{65} + 6 q^{67} - 2 q^{71} + 21 q^{73} - 19 q^{77} - 10 q^{79} + 25 q^{83} + 8 q^{85} + 6 q^{89} + 2 q^{91} + 28 q^{95} - 18 q^{97}+O(q^{100}) $ 14 * q - 4 * q^5 - 3 * q^7 + 4 * q^11 + 2 * q^13 - 2 * q^17 + 7 * q^19 + 22 * q^23 + 18 * q^25 - q^29 - q^31 + 19 * q^35 + 10 * q^37 + 33 * q^41 + 7 * q^43 + 3 * q^47 - 13 * q^49 + 15 * q^53 - 28 * q^55 + 14 * q^59 - 10 * q^61 - 15 * q^65 + 6 * q^67 - 2 * q^71 + 21 * q^73 - 19 * q^77 - 10 * q^79 + 25 * q^83 + 8 * q^85 + 6 * q^89 + 2 * q^91 + 28 * q^95 - 18 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/756\mathbb{Z}\right)^\times$.

$n$	$29$	$325$	$379$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{3}\right)$	$1$

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			0
$3$		0			0
$4$		0			0
$5$	0.763837			0.341598			0.170799	−	0.985306i	$-0.445365\pi$
$5$	0.763837			0.341598			0.170799	+	0.985306i	$0.445365\pi$
$6$		0			0
$7$	−1.05641	−	2.42569i	−0.399286	−	0.916826i
$7$	−1.05641	−	2.42569i	−0.399286	−	0.916826i
$8$		0			0
$9$		0			0
$10$		0			0
$11$	−6.03389			−1.81929			−0.909644	−	0.415389i	$-0.863645\pi$
$11$	−6.03389			−1.81929			−0.909644	+	0.415389i	$0.863645\pi$
$12$		0			0
$13$	−1.26032	−	2.18294i	−0.349551	−	0.605440i	0.636619	−	0.771179i	$-0.280332\pi$
$13$	−1.26032	−	2.18294i	−0.349551	−	0.605440i	−0.986170	+	0.165739i	$0.946999\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−1.94444	−	3.36787i	−0.471596	−	0.816828i	0.527876	−	0.849322i	$-0.322989\pi$
$17$	−1.94444	−	3.36787i	−0.471596	−	0.816828i	−0.999472	+	0.0324932i	$0.989655\pi$
$18$		0			0
$19$	−2.13503	+	3.69798i	−0.489809	+	0.848375i	−0.999931	−	0.0117275i	$-0.996267\pi$
$19$	−2.13503	+	3.69798i	−0.489809	+	0.848375i	0.510122	+	0.860102i	$0.329600\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	1.46425			0.305317			0.152658	−	0.988279i	$-0.451217\pi$
$23$	1.46425			0.305317			0.152658	+	0.988279i	$0.451217\pi$
$24$		0			0
$25$	−4.41655			−0.883311
$26$		0			0
$27$		0			0
$28$		0			0
$29$	3.00732	−	5.20884i	0.558446	−	0.967257i	−0.439180	−	0.898399i	$-0.644731\pi$
$29$	3.00732	−	5.20884i	0.558446	−	0.967257i	0.997626	−	0.0688580i	$-0.0219355\pi$
$30$		0			0
$31$	−3.28482	+	5.68948i	−0.589972	+	1.02186i	0.404264	+	0.914642i	$0.367528\pi$
$31$	−3.28482	+	5.68948i	−0.589972	+	1.02186i	−0.994235	+	0.107219i	$0.965806\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	−0.806926	−	1.85283i	−0.136395	−	0.313186i
$36$		0			0
$37$	4.82492	−	8.35700i	0.793211	−	1.37388i	−0.130758	−	0.991414i	$-0.541741\pi$
$37$	4.82492	−	8.35700i	0.793211	−	1.37388i	0.923969	−	0.382468i	$-0.124926\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	2.24844	+	3.89442i	0.351148	+	0.608206i	0.986451	−	0.164057i	$-0.0524581\pi$
$41$	2.24844	+	3.89442i	0.351148	+	0.608206i	−0.635303	+	0.772263i	$0.719125\pi$
$42$		0			0
$43$	−2.13503	+	3.69798i	−0.325589	+	0.563937i	−0.981631	−	0.190787i	$-0.938896\pi$
$43$	−2.13503	+	3.69798i	−0.325589	+	0.563937i	0.656042	+	0.754724i	$0.272229\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−3.38924	−	5.87034i	−0.494372	−	0.856277i	0.505607	−	0.862764i	$-0.331269\pi$
$47$	−3.38924	−	5.87034i	−0.494372	−	0.856277i	−0.999979	+	0.00648676i	$0.997935\pi$
$48$		0			0
$49$	−4.76799	+	5.12507i	−0.681141	+	0.732152i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	0.265581	+	0.460000i	0.0364804	+	0.0631859i	0.883689	−	0.468074i	$-0.155052\pi$
$53$	0.265581	+	0.460000i	0.0364804	+	0.0631859i	−0.847209	+	0.531260i	$0.821719\pi$
$54$		0			0
$55$	−4.60891			−0.621465
$56$		0			0
$57$		0			0
$58$		0			0
$59$	5.59926	−	9.69821i	0.728962	−	1.26260i	−0.228360	−	0.973577i	$-0.573336\pi$
$59$	5.59926	−	9.69821i	0.728962	−	1.26260i	0.957322	−	0.289023i	$-0.0933303\pi$
$60$		0			0
$61$	−4.19144	−	7.25979i	−0.536659	−	0.929521i	−0.999081	−	0.0428608i	$-0.986353\pi$
$61$	−4.19144	−	7.25979i	−0.536659	−	0.929521i	0.462422	−	0.886660i	$-0.346981\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	−0.962681	−	1.66741i	−0.119406	−	0.206817i
$66$		0			0
$67$	0.961979	−	1.66620i	0.117524	−	0.203558i	−0.801262	−	0.598314i	$-0.795838\pi$
$67$	0.961979	−	1.66620i	0.117524	−	0.203558i	0.918786	+	0.394756i	$0.129171\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	−9.90353			−1.17533			−0.587666	−	0.809103i	$-0.699953\pi$
$71$	−9.90353			−1.17533			−0.587666	+	0.809103i	$0.699953\pi$
$72$		0			0
$73$	−2.13099	−	3.69098i	−0.249413	−	0.431997i	0.713950	−	0.700197i	$-0.246904\pi$
$73$	−2.13099	−	3.69098i	−0.249413	−	0.431997i	−0.963363	+	0.268200i	$0.913571\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	6.37428	+	14.6364i	0.726416	+	1.66797i
$78$		0			0
$79$	3.70372	+	6.41503i	0.416701	+	0.721748i	0.995605	−	0.0936479i	$-0.0298528\pi$
$79$	3.70372	+	6.41503i	0.416701	+	0.721748i	−0.578904	+	0.815396i	$0.696519\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	8.05178	−	13.9461i	0.883798	−	1.53078i	0.0367125	−	0.999326i	$-0.488311\pi$
$83$	8.05178	−	13.9461i	0.883798	−	1.53078i	0.847085	−	0.531457i	$-0.178355\pi$
$84$		0			0
$85$	−1.48523	−	2.57250i	−0.161096	−	0.279027i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	−1.76310	+	3.05377i	−0.186888	+	0.323699i	−0.944211	−	0.329341i	$-0.893173\pi$
$89$	−1.76310	+	3.05377i	−0.186888	+	0.323699i	0.757323	+	0.653040i	$0.226507\pi$
$90$		0			0
$91$	−3.96373	+	5.36325i	−0.415512	+	0.562221i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	−1.63081	+	2.82465i	−0.167318	+	0.289803i
$96$		0			0
$97$	2.33513	−	4.04456i	0.237096	−	0.410662i	−0.722784	−	0.691074i	$-0.757138\pi$
$97$	2.33513	−	4.04456i	0.237096	−	0.410662i	0.959880	+	0.280412i	$0.0904710\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	4.71965			0.469623			0.234811	−	0.972041i	$-0.424553\pi$
$101$	4.71965			0.469623			0.234811	+	0.972041i	$0.424553\pi$
$102$		0			0
$103$	3.16531			0.311888			0.155944	−	0.987766i	$-0.450158\pi$
$103$	3.16531			0.311888			0.155944	+	0.987766i	$0.450158\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−7.65537	+	13.2595i	−0.740073	+	1.28184i	0.212389	+	0.977185i	$0.431876\pi$
$107$	−7.65537	+	13.2595i	−0.740073	+	1.28184i	−0.952462	+	0.304659i	$0.901458\pi$
$108$		0			0
$109$	7.65371	+	13.2566i	0.733092	+	1.26975i	0.955555	+	0.294812i	$0.0952569\pi$
$109$	7.65371	+	13.2566i	0.733092	+	1.26975i	−0.222463	+	0.974941i	$0.571410\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	1.56114	+	2.70397i	0.146860	+	0.254368i	0.930065	−	0.367395i	$-0.119750\pi$
$113$	1.56114	+	2.70397i	0.146860	+	0.254368i	−0.783206	+	0.621763i	$0.786417\pi$
$114$		0			0
$115$	1.11845			0.104296
$116$		0			0
$117$		0			0
$118$		0			0
$119$	−6.11529	+	8.27448i	−0.560588	+	0.758520i
$120$		0			0
$121$	25.4079			2.30981
$122$		0			0
$123$		0			0
$124$		0			0
$125$	−7.19271			−0.643335
$126$		0			0
$127$	1.27814			0.113416			0.0567082	−	0.998391i	$-0.481940\pi$
$127$	1.27814			0.113416			0.0567082	+	0.998391i	$0.481940\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	−7.77465			−0.679274			−0.339637	−	0.940557i	$-0.610304\pi$
$131$	−7.77465			−0.679274			−0.339637	+	0.940557i	$0.610304\pi$
$132$		0			0
$133$	11.2256	+	1.27234i	0.973386	+	0.110326i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−2.82307			−0.241191			−0.120596	−	0.992702i	$-0.538480\pi$
$137$	−2.82307			−0.241191			−0.120596	+	0.992702i	$0.538480\pi$
$138$		0			0
$139$	−11.2206	−	19.4346i	−0.951718	−	1.64842i	−0.741705	−	0.670726i	$-0.765983\pi$
$139$	−11.2206	−	19.4346i	−0.951718	−	1.64842i	−0.210013	−	0.977699i	$-0.567351\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	7.60466	+	13.1717i	0.635933	+	1.10147i
$144$		0			0
$145$	2.29710	−	3.97870i	0.190764	−	0.330413i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	20.1703			1.65241			0.826206	−	0.563369i	$-0.190495\pi$
$149$	20.1703			1.65241			0.826206	+	0.563369i	$0.190495\pi$
$150$		0			0
$151$	8.29450			0.674997			0.337498	−	0.941326i	$-0.390419\pi$
$151$	8.29450			0.674997			0.337498	+	0.941326i	$0.390419\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	−2.50907	+	4.34583i	−0.201533	+	0.349066i
$156$		0			0
$157$	3.33332	−	5.77348i	0.266028	−	0.460774i	−0.701804	−	0.712370i	$-0.747622\pi$
$157$	3.33332	−	5.77348i	0.266028	−	0.460774i	0.967832	+	0.251596i	$0.0809553\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	−1.54685	−	3.55182i	−0.121909	−	0.279922i
$162$		0			0
$163$	3.69751	−	6.40428i	0.289611	−	0.501622i	−0.684106	−	0.729383i	$-0.739807\pi$
$163$	3.69751	−	6.40428i	0.289611	−	0.501622i	0.973717	+	0.227761i	$0.0731406\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	0.475526	+	0.823635i	0.0367973	+	0.0637348i	0.883838	−	0.467794i	$-0.154951\pi$
$167$	0.475526	+	0.823635i	0.0367973	+	0.0637348i	−0.847040	+	0.531529i	$0.821618\pi$
$168$		0			0
$169$	3.32317	−	5.75590i	0.255629	−	0.442762i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	2.33554	+	4.04527i	0.177568	+	0.307557i	0.941047	−	0.338276i	$-0.109844\pi$
$173$	2.33554	+	4.04527i	0.177568	+	0.307557i	−0.763479	+	0.645833i	$0.776510\pi$
$174$		0			0
$175$	4.66570	+	10.7132i	0.352694	+	0.809843i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	7.49486	+	12.9815i	0.560192	+	0.970281i	0.997479	+	0.0709591i	$0.0226060\pi$
$179$	7.49486	+	12.9815i	0.560192	+	0.970281i	−0.437287	+	0.899322i	$0.644061\pi$
$180$		0			0
$181$	−13.6525			−1.01478			−0.507391	−	0.861716i	$-0.669390\pi$
$181$	−13.6525			−1.01478			−0.507391	+	0.861716i	$0.669390\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	3.68545	−	6.38338i	0.270959	−	0.469316i
$186$		0			0
$187$	11.7325	+	20.3214i	0.857969	+	1.48605i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	6.14528	+	10.6439i	0.444657	+	0.770168i	0.998028	−	0.0627667i	$-0.0199924\pi$
$191$	6.14528	+	10.6439i	0.444657	+	0.770168i	−0.553372	+	0.832934i	$0.686659\pi$
$192$		0			0
$193$	−3.58578	+	6.21075i	−0.258110	+	0.447060i	−0.965736	−	0.259528i	$-0.916433\pi$
$193$	−3.58578	+	6.21075i	−0.258110	+	0.447060i	0.707626	+	0.706588i	$0.249766\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	13.0286			0.928247			0.464124	−	0.885770i	$-0.346369\pi$
$197$	13.0286			0.928247			0.464124	+	0.885770i	$0.346369\pi$
$198$		0			0
$199$	−2.48087	−	4.29699i	−0.175864	−	0.304606i	0.764596	−	0.644510i	$-0.222939\pi$
$199$	−2.48087	−	4.29699i	−0.175864	−	0.304606i	−0.940460	+	0.339904i	$0.889605\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	−15.8120	−	1.79217i	−1.10979	−	0.125786i
$204$		0			0
$205$	1.71744	+	2.97470i	0.119951	+	0.207762i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	12.8825	−	22.3132i	0.891104	−	1.54344i
$210$		0			0
$211$	2.07384	+	3.59199i	0.142769	+	0.247283i	0.928538	−	0.371237i	$-0.121066\pi$
$211$	2.07384	+	3.59199i	0.142769	+	0.247283i	−0.785769	+	0.618519i	$0.787733\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	−1.63081	+	2.82465i	−0.111221	+	0.192640i
$216$		0			0
$217$	17.2711	+	1.95754i	1.17244	+	0.132887i
$218$		0			0
$219$		0			0
$220$		0			0
$221$	−4.90125	+	8.48921i	−0.329694	+	0.571046i
$222$		0			0
$223$	−4.63830	+	8.03378i	−0.310604	+	0.537982i	−0.978493	−	0.206279i	$-0.933865\pi$
$223$	−4.63830	+	8.03378i	−0.310604	+	0.537982i	0.667889	+	0.744261i	$0.267198\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	21.3602			1.41773			0.708863	−	0.705346i	$-0.249208\pi$
$227$	21.3602			1.41773			0.708863	+	0.705346i	$0.249208\pi$
$228$		0			0
$229$	−20.0071			−1.32210			−0.661052	−	0.750340i	$-0.729890\pi$
$229$	−20.0071			−1.32210			−0.661052	+	0.750340i	$0.729890\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−7.63657	+	13.2269i	−0.500288	+	0.866525i	0.499712	+	0.866192i	$0.333439\pi$
$233$	−7.63657	+	13.2269i	−0.500288	+	0.866525i	−1.00000		0.000332882i	$0.999894\pi$
$234$		0			0
$235$	−2.58883	−	4.48398i	−0.168876	−	0.292503i
$236$		0			0
$237$		0			0
$238$		0			0
$239$	−9.03828	−	15.6548i	−0.584638	−	1.01262i	−0.994920	−	0.100664i	$-0.967903\pi$
$239$	−9.03828	−	15.6548i	−0.584638	−	1.01262i	0.410283	−	0.911958i	$-0.365430\pi$
$240$		0			0
$241$	4.31045			0.277660			0.138830	−	0.990316i	$-0.455666\pi$
$241$	4.31045			0.277660			0.138830	+	0.990316i	$0.455666\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	−3.64196	+	3.91471i	−0.232677	+	0.250102i
$246$		0			0
$247$	10.7633			0.684853
$248$		0			0
$249$		0			0
$250$		0			0
$251$	−16.3348			−1.03104			−0.515521	−	0.856877i	$-0.672401\pi$
$251$	−16.3348			−1.03104			−0.515521	+	0.856877i	$0.672401\pi$
$252$		0			0
$253$	−8.83512			−0.555459
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−1.29540			−0.0808046			−0.0404023	−	0.999183i	$-0.512864\pi$
$257$	−1.29540			−0.0808046			−0.0404023	+	0.999183i	$0.512864\pi$
$258$		0			0
$259$	−25.3686	−	2.87534i	−1.57633	−	0.178665i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	−28.2728			−1.74337			−0.871687	−	0.490062i	$-0.836974\pi$
$263$	−28.2728			−1.74337			−0.871687	+	0.490062i	$0.836974\pi$
$264$		0			0
$265$	0.202861	+	0.351365i	0.0124616	+	0.0215842i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	−7.10969	−	12.3143i	−0.433485	−	0.750818i	0.563685	−	0.825990i	$-0.309383\pi$
$269$	−7.10969	−	12.3143i	−0.433485	−	0.750818i	−0.997171	+	0.0751711i	$0.976050\pi$
$270$		0			0
$271$	−7.18914	+	12.4520i	−0.436709	+	0.756403i	−0.997433	−	0.0716001i	$-0.977189\pi$
$271$	−7.18914	+	12.4520i	−0.436709	+	0.756403i	0.560724	+	0.828003i	$0.310523\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	26.6490			1.60700
$276$		0			0
$277$	−15.4361			−0.927468			−0.463734	−	0.885974i	$-0.653491\pi$
$277$	−15.4361			−0.927468			−0.463734	+	0.885974i	$0.653491\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	9.39609	−	16.2745i	0.560524	−	0.970856i	−0.436927	−	0.899497i	$-0.643933\pi$
$281$	9.39609	−	16.2745i	0.560524	−	0.970856i	0.997451	−	0.0713587i	$-0.0227335\pi$
$282$		0			0
$283$	16.2864	−	28.2089i	0.968128	−	1.67685i	0.267163	−	0.963651i	$-0.413914\pi$
$283$	16.2864	−	28.2089i	0.968128	−	1.67685i	0.700965	−	0.713196i	$-0.252753\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	7.07139	−	9.56815i	0.417411	−	0.564790i
$288$		0			0
$289$	0.938304	−	1.62519i	0.0551944	−	0.0955994i
$290$		0			0
$291$		0			0
$292$		0			0
$293$	1.69821	+	2.94138i	0.0992103	+	0.171837i	0.911358	−	0.411615i	$-0.135035\pi$
$293$	1.69821	+	2.94138i	0.0992103	+	0.171837i	−0.812148	+	0.583452i	$0.801702\pi$
$294$		0			0
$295$	4.27692	−	7.40785i	0.249012	−	0.431302i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	−1.84543	−	3.19637i	−0.106724	−	0.184851i
$300$		0			0
$301$	11.2256	+	1.27234i	0.647035	+	0.0733364i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	−3.20158	−	5.54529i	−0.183322	−	0.317523i
$306$		0			0
$307$	3.69564			0.210921			0.105461	−	0.994423i	$-0.466368\pi$
$307$	3.69564			0.210921			0.105461	+	0.994423i	$0.466368\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	−8.58119	+	14.8631i	−0.486594	+	0.842806i	−0.999881	−	0.0154108i	$-0.995094\pi$
$311$	−8.58119	+	14.8631i	−0.486594	+	0.842806i	0.513287	+	0.858217i	$0.328428\pi$
$312$		0			0
$313$	−2.64824	−	4.58688i	−0.149687	−	0.259266i	0.781425	−	0.624000i	$-0.214493\pi$
$313$	−2.64824	−	4.58688i	−0.149687	−	0.259266i	−0.931112	+	0.364734i	$0.881160\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	14.0890	+	24.4028i	0.791315	+	1.37060i	0.925153	+	0.379594i	$0.123936\pi$
$317$	14.0890	+	24.4028i	0.791315	+	1.37060i	−0.133838	+	0.991003i	$0.542730\pi$
$318$		0			0
$319$	−18.1459	+	31.4296i	−1.01597	+	1.75972i
$320$		0			0
$321$		0			0
$322$		0			0
$323$	16.6057			0.923968
$324$		0			0
$325$	5.56628	+	9.64109i	0.308762	+	0.534791i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	−10.6592	+	14.4228i	−0.587662	+	0.795153i
$330$		0			0
$331$	−14.5860	−	25.2637i	−0.801720	−	1.38862i	−0.918483	−	0.395461i	$-0.870585\pi$
$331$	−14.5860	−	25.2637i	−0.801720	−	1.38862i	0.116762	−	0.993160i	$-0.462748\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	0.734794	−	1.27270i	0.0401461	−	0.0695351i
$336$		0			0
$337$	−0.447174	−	0.774528i	−0.0243591	−	0.0421912i	0.853589	−	0.520947i	$-0.174421\pi$
$337$	−0.447174	−	0.774528i	−0.0243591	−	0.0421912i	−0.877948	+	0.478756i	$0.841088\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	19.8203	−	34.3297i	1.07333	−	1.85906i
$342$		0			0
$343$	17.4688	+	6.15150i	0.943227	+	0.332150i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	9.98982	−	17.3029i	0.536282	−	0.928867i	−0.462818	−	0.886453i	$-0.653162\pi$
$347$	9.98982	−	17.3029i	0.536282	−	0.928867i	0.999100	−	0.0424143i	$-0.0135049\pi$
$348$		0			0
$349$	2.58530	−	4.47788i	0.138388	−	0.239695i	−0.788499	−	0.615037i	$-0.789141\pi$
$349$	2.58530	−	4.47788i	0.138388	−	0.239695i	0.926887	+	0.375341i	$0.122475\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	−33.1222			−1.76292			−0.881459	−	0.472261i	$-0.843438\pi$
$353$	−33.1222			−1.76292			−0.881459	+	0.472261i	$0.843438\pi$
$354$		0			0
$355$	−7.56468			−0.401491
$356$		0			0
$357$		0			0
$358$		0			0
$359$	17.2965	−	29.9584i	0.912874	−	1.58114i	0.102889	−	0.994693i	$-0.467191\pi$
$359$	17.2965	−	29.9584i	0.912874	−	1.58114i	0.809985	−	0.586451i	$-0.199475\pi$
$360$		0			0
$361$	0.383301	+	0.663897i	0.0201737	+	0.0349420i
$362$		0			0
$363$		0			0
$364$		0			0
$365$	−1.62773	−	2.81931i	−0.0851992	−	0.147569i
$366$		0			0
$367$	−3.29611			−0.172055			−0.0860277	−	0.996293i	$-0.527417\pi$
$367$	−3.29611			−0.172055			−0.0860277	+	0.996293i	$0.527417\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	0.835256	−	1.13017i	0.0433644	−	0.0586754i
$372$		0			0
$373$	−23.6754			−1.22587			−0.612933	−	0.790135i	$-0.710010\pi$
$373$	−23.6754			−1.22587			−0.612933	+	0.790135i	$0.710010\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	−15.1608			−0.780821
$378$		0			0
$379$	−25.4415			−1.30684			−0.653421	−	0.756995i	$-0.726667\pi$
$379$	−25.4415			−1.30684			−0.653421	+	0.756995i	$0.726667\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	−23.7278			−1.21244			−0.606218	−	0.795299i	$-0.707314\pi$
$383$	−23.7278			−1.21244			−0.606218	+	0.795299i	$0.707314\pi$
$384$		0			0
$385$	4.86891	+	11.1798i	0.248142	+	0.569776i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	−19.5275			−0.990082			−0.495041	−	0.868870i	$-0.664847\pi$
$389$	−19.5275			−0.990082			−0.495041	+	0.868870i	$0.664847\pi$
$390$		0			0
$391$	−2.84714	−	4.93139i	−0.143986	−	0.249391i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	2.82904	+	4.90004i	0.142344	+	0.246548i
$396$		0			0
$397$	14.4468	−	25.0226i	0.725064	−	1.25585i	−0.233884	−	0.972265i	$-0.575144\pi$
$397$	14.4468	−	25.0226i	0.725064	−	1.25585i	0.958948	−	0.283583i	$-0.0915231\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	−5.50584			−0.274949			−0.137474	−	0.990505i	$-0.543898\pi$
$401$	−5.50584			−0.274949			−0.137474	+	0.990505i	$0.543898\pi$
$402$		0			0
$403$	16.5598			0.824900
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−29.1130	+	50.4253i	−1.44308	+	2.49949i
$408$		0			0
$409$	0.511954	−	0.886731i	0.0253145	−	0.0438460i	−0.853091	−	0.521763i	$-0.825275\pi$
$409$	0.511954	−	0.886731i	0.0253145	−	0.0438460i	0.878405	+	0.477917i	$0.158608\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	−29.4400	−	3.33680i	−1.44865	−	0.164193i
$414$		0			0
$415$	6.15025	−	10.6525i	0.301904	−	0.522912i
$416$		0			0
$417$		0			0
$418$		0			0
$419$	−16.9398	−	29.3405i	−0.827562	−	1.43338i	−0.899946	−	0.436002i	$-0.856394\pi$
$419$	−16.9398	−	29.3405i	−0.827562	−	1.43338i	0.0723837	−	0.997377i	$-0.476939\pi$
$420$		0			0
$421$	0.563823	−	0.976570i	0.0274790	−	0.0475951i	−0.851959	−	0.523609i	$-0.824585\pi$
$421$	0.563823	−	0.976570i	0.0274790	−	0.0475951i	0.879438	+	0.476014i	$0.157919\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	8.58772	+	14.8744i	0.416566	+	0.721513i
$426$		0			0
$427$	−13.1821	+	17.8365i	−0.637929	+	0.863168i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	1.44172	+	2.49713i	0.0694450	+	0.120282i	0.898657	−	0.438652i	$-0.144544\pi$
$431$	1.44172	+	2.49713i	0.0694450	+	0.120282i	−0.829212	+	0.558934i	$0.811210\pi$
$432$		0			0
$433$	−14.3808			−0.691097			−0.345548	−	0.938401i	$-0.612307\pi$
$433$	−14.3808			−0.691097			−0.345548	+	0.938401i	$0.612307\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−3.12621	+	5.41476i	−0.149547	+	0.259023i
$438$		0			0
$439$	−10.4958	−	18.1792i	−0.500936	−	0.867646i	−0.999999	−	0.00108089i	$-0.999656\pi$
$439$	−10.4958	−	18.1792i	−0.500936	−	0.867646i	0.499064	−	0.866565i	$-0.333677\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	−10.0293	−	17.3713i	−0.476507	−	0.825335i	0.523130	−	0.852253i	$-0.324764\pi$
$443$	−10.0293	−	17.3713i	−0.476507	−	0.825335i	−0.999638	+	0.0269179i	$0.991431\pi$
$444$		0			0
$445$	−1.34672	+	2.33258i	−0.0638405	+	0.110575i
$446$		0			0
$447$		0			0
$448$		0			0
$449$	11.4192			0.538903			0.269452	−	0.963014i	$-0.413158\pi$
$449$	11.4192			0.538903			0.269452	+	0.963014i	$0.413158\pi$
$450$		0			0
$451$	−13.5669	−	23.4985i	−0.638839	−	1.10650i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	−3.02765	+	4.09664i	−0.141938	+	0.192054i
$456$		0			0
$457$	9.10294	+	15.7667i	0.425817	+	0.737537i	0.996496	−	0.0836359i	$-0.0266533\pi$
$457$	9.10294	+	15.7667i	0.425817	+	0.737537i	−0.570679	+	0.821173i	$0.693320\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	18.6430	−	32.2906i	0.868289	−	1.50392i	0.00454533	−	0.999990i	$-0.498553\pi$
$461$	18.6430	−	32.2906i	0.868289	−	1.50392i	0.863744	−	0.503931i	$-0.168113\pi$
$462$		0			0
$463$	−0.530345	−	0.918584i	−0.0246472	−	0.0426902i	0.853439	−	0.521193i	$-0.174513\pi$
$463$	−0.530345	−	0.918584i	−0.0246472	−	0.0426902i	−0.878086	+	0.478503i	$0.841180\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	14.0374	−	24.3134i	0.649571	−	1.12509i	−0.333654	−	0.942696i	$-0.608282\pi$
$467$	14.0374	−	24.3134i	0.649571	−	1.12509i	0.983225	−	0.182395i	$-0.0583850\pi$
$468$		0			0
$469$	−5.05793	−	0.573277i	−0.233553	−	0.0264715i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	12.8825	−	22.3132i	0.592340	−	1.02596i
$474$		0			0
$475$	9.42947	−	16.3323i	0.432654	−	0.749378i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	−7.23410			−0.330535			−0.165267	−	0.986249i	$-0.552849\pi$
$479$	−7.23410			−0.330535			−0.165267	+	0.986249i	$0.552849\pi$
$480$		0			0
$481$	−24.3238			−1.10907
$482$		0			0
$483$		0			0
$484$		0			0
$485$	1.78365	−	3.08938i	0.0809916	−	0.140282i
$486$		0			0
$487$	16.9145	+	29.2968i	0.766470	+	1.32756i	0.939466	+	0.342642i	$0.111322\pi$
$487$	16.9145	+	29.2968i	0.766470	+	1.32756i	−0.172996	+	0.984922i	$0.555345\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	0.300406	+	0.520319i	0.0135572	+	0.0234817i	0.872724	−	0.488213i	$-0.162351\pi$
$491$	0.300406	+	0.520319i	0.0135572	+	0.0234817i	−0.859167	+	0.511695i	$0.829018\pi$
$492$		0			0
$493$	−23.3902			−1.05344
$494$		0			0
$495$		0			0
$496$		0			0
$497$	10.4622	+	24.0229i	0.469294	+	1.07758i
$498$		0			0
$499$	5.64134			0.252541			0.126271	−	0.991996i	$-0.459699\pi$
$499$	5.64134			0.252541			0.126271	+	0.991996i	$0.459699\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	31.0034			1.38237			0.691186	−	0.722677i	$-0.257089\pi$
$503$	31.0034			1.38237			0.691186	+	0.722677i	$0.257089\pi$
$504$		0			0
$505$	3.60504			0.160422
$506$		0			0
$507$		0			0
$508$		0			0
$509$	−34.6959			−1.53787			−0.768935	−	0.639327i	$-0.779213\pi$
$509$	−34.6959			−1.53787			−0.768935	+	0.639327i	$0.779213\pi$
$510$		0			0
$511$	−6.70199	+	9.06833i	−0.296479	+	0.401159i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	2.41778			0.106540
$516$		0			0
$517$	20.4503	+	35.4210i	0.899405	+	1.55781i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	12.5083	+	21.6650i	0.547998	+	0.949161i	0.998412	+	0.0563408i	$0.0179433\pi$
$521$	12.5083	+	21.6650i	0.547998	+	0.949161i	−0.450413	+	0.892820i	$0.648723\pi$
$522$		0			0
$523$	−1.59320	+	2.75950i	−0.0696656	+	0.120664i	−0.898754	−	0.438453i	$-0.855527\pi$
$523$	−1.59320	+	2.75950i	−0.0696656	+	0.120664i	0.829088	+	0.559117i	$0.188860\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	25.5486			1.11291
$528$		0			0
$529$	−20.8560			−0.906782
$530$		0			0
$531$		0			0
$532$		0			0
$533$	5.66753	−	9.81645i	0.245488	−	0.425198i
$534$		0			0
$535$	−5.84745	+	10.1281i	−0.252808	+	0.437875i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	28.7695	−	30.9241i	1.23919	−	1.33200i
$540$		0			0
$541$	−6.80693	+	11.7900i	−0.292653	+	0.506890i	−0.974436	−	0.224664i	$-0.927871\pi$
$541$	−6.80693	+	11.7900i	−0.292653	+	0.506890i	0.681783	+	0.731554i	$0.261205\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	5.84618	+	10.1259i	0.250423	+	0.433745i
$546$		0			0
$547$	−5.91254	+	10.2408i	−0.252802	+	0.437866i	−0.964296	−	0.264826i	$-0.914685\pi$
$547$	−5.91254	+	10.2408i	−0.252802	+	0.437866i	0.711494	+	0.702692i	$0.248019\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	12.8414	+	22.2420i	0.547064	+	0.947543i
$552$		0			0
$553$	11.6483	−	15.7610i	0.495334	−	0.670226i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	9.32911	+	16.1585i	0.395287	+	0.684657i	0.993138	−	0.116950i	$-0.0373119\pi$
$557$	9.32911	+	16.1585i	0.395287	+	0.684657i	−0.597851	+	0.801607i	$0.703979\pi$
$558$		0			0
$559$	10.7633			0.455239
$560$		0			0
$561$		0			0
$562$		0			0
$563$	11.3196	−	19.6060i	0.477062	−	0.826296i	−0.522592	−	0.852583i	$-0.675035\pi$
$563$	11.3196	−	19.6060i	0.477062	−	0.826296i	0.999654	+	0.0262866i	$0.00836825\pi$
$564$		0			0
$565$	1.19246	+	2.06539i	0.0501670	+	0.0868917i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	5.45277	+	9.44447i	0.228592	+	0.395933i	0.957391	−	0.288795i	$-0.0932545\pi$
$569$	5.45277	+	9.44447i	0.228592	+	0.395933i	−0.728799	+	0.684728i	$0.759921\pi$
$570$		0			0
$571$	13.8055	−	23.9119i	0.577743	−	1.00068i	−0.417994	−	0.908450i	$-0.637267\pi$
$571$	13.8055	−	23.9119i	0.577743	−	1.00068i	0.995738	−	0.0922313i	$-0.0293999\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	−6.46693			−0.269690
$576$		0			0
$577$	−10.2592	−	17.7695i	−0.427096	−	0.739753i	0.569517	−	0.821979i	$-0.307130\pi$
$577$	−10.2592	−	17.7695i	−0.427096	−	0.739753i	−0.996614	+	0.0822267i	$0.973797\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	−42.3350	−	4.79834i	−1.75635	−	0.199069i
$582$		0			0
$583$	−1.60249	−	2.77559i	−0.0663683	−	0.114953i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−7.59632	+	13.1572i	−0.313534	+	0.543056i	−0.979125	−	0.203260i	$-0.934846\pi$
$587$	−7.59632	+	13.1572i	−0.313534	+	0.543056i	0.665591	+	0.746317i	$0.268180\pi$
$588$		0			0
$589$	−14.0264	−	24.2944i	−0.577947	−	1.00103i
$590$		0			0
$591$		0			0
$592$		0			0
$593$	−3.39373	+	5.87812i	−0.139364	+	0.241385i	−0.927256	−	0.374428i	$-0.877839\pi$
$593$	−3.39373	+	5.87812i	−0.139364	+	0.241385i	0.787892	+	0.615813i	$0.211172\pi$
$594$		0			0
$595$	−4.67108	+	6.32035i	−0.191496	+	0.259109i
$596$		0			0
$597$		0			0
$598$		0			0
$599$	6.32519	−	10.9555i	0.258440	−	0.447632i	−0.707384	−	0.706829i	$-0.750125\pi$
$599$	6.32519	−	10.9555i	0.258440	−	0.447632i	0.965824	+	0.259198i	$0.0834582\pi$
$600$		0			0
$601$	−11.3699	+	19.6932i	−0.463787	+	0.803303i	−0.999146	−	0.0413219i	$-0.986843\pi$
$601$	−11.3699	+	19.6932i	−0.463787	+	0.803303i	0.535359	+	0.844625i	$0.320176\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	19.4075			0.789026
$606$		0			0
$607$	41.9226			1.70159			0.850794	−	0.525500i	$-0.176122\pi$
$607$	41.9226			1.70159			0.850794	+	0.525500i	$0.176122\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	−8.54308	+	14.7971i	−0.345616	+	0.598625i
$612$		0			0
$613$	−13.7038	−	23.7356i	−0.553490	−	0.958673i	−0.998019	−	0.0629086i	$-0.979962\pi$
$613$	−13.7038	−	23.7356i	−0.553490	−	0.958673i	0.444529	−	0.895764i	$-0.353371\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−5.75420	−	9.96656i	−0.231655	−	0.401239i	0.726640	−	0.687018i	$-0.241081\pi$
$617$	−5.75420	−	9.96656i	−0.231655	−	0.401239i	−0.958295	+	0.285780i	$0.907747\pi$
$618$		0			0
$619$	37.7559			1.51754			0.758770	−	0.651359i	$-0.225801\pi$
$619$	37.7559			1.51754			0.758770	+	0.651359i	$0.225801\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	9.27007	+	1.05069i	0.371398	+	0.0420951i
$624$		0			0
$625$	16.5887			0.663549
$626$		0			0
$627$		0			0
$628$		0			0
$629$	−37.5270			−1.49630
$630$		0			0
$631$	45.4466			1.80920			0.904600	−	0.426262i	$-0.140170\pi$
$631$	45.4466			1.80920			0.904600	+	0.426262i	$0.140170\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	0.976288			0.0387428
$636$		0			0
$637$	17.1969	+	3.94901i	0.681367	+	0.156466i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	0.299606			0.0118337			0.00591687	−	0.999982i	$-0.498117\pi$
$641$	0.299606			0.0118337			0.00591687	+	0.999982i	$0.498117\pi$
$642$		0			0
$643$	−3.61580	−	6.26275i	−0.142593	−	0.246979i	0.785879	−	0.618380i	$-0.212211\pi$
$643$	−3.61580	−	6.26275i	−0.142593	−	0.246979i	−0.928472	+	0.371401i	$0.878877\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	4.78298	+	8.28437i	0.188039	+	0.325692i	0.944596	−	0.328235i	$-0.106454\pi$
$647$	4.78298	+	8.28437i	0.188039	+	0.325692i	−0.756558	+	0.653927i	$0.773120\pi$
$648$		0			0
$649$	−33.7854	+	58.5180i	−1.32619	+	2.29703i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	−39.0070			−1.52646			−0.763232	−	0.646125i	$-0.776388\pi$
$653$	−39.0070			−1.52646			−0.763232	+	0.646125i	$0.776388\pi$
$654$		0			0
$655$	−5.93856			−0.232039
$656$		0			0
$657$		0			0
$658$		0			0
$659$	0.251281	−	0.435231i	0.00978851	−	0.0169542i	−0.861090	−	0.508453i	$-0.830218\pi$
$659$	0.251281	−	0.435231i	0.00978851	−	0.0169542i	0.870878	+	0.491499i	$0.163551\pi$
$660$		0			0
$661$	1.09910	−	1.90370i	0.0427501	−	0.0740453i	−0.843859	−	0.536566i	$-0.819721\pi$
$661$	1.09910	−	1.90370i	0.0427501	−	0.0740453i	0.886609	+	0.462520i	$0.153055\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	8.57455	+	0.971859i	0.332507	+	0.0376871i
$666$		0			0
$667$	4.40347	−	7.62703i	0.170503	−	0.295320i
$668$		0			0
$669$		0			0
$670$		0			0
$671$	25.2907	+	43.8048i	0.976337	+	1.69107i
$672$		0			0
$673$	7.50630	−	13.0013i	0.289346	−	0.501163i	−0.684307	−	0.729194i	$-0.739895\pi$
$673$	7.50630	−	13.0013i	0.289346	−	0.501163i	0.973654	+	0.228031i	$0.0732287\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	14.8304	+	25.6869i	0.569977	+	0.987229i	0.996568	+	0.0827841i	$0.0263812\pi$
$677$	14.8304	+	25.6869i	0.569977	+	0.987229i	−0.426591	+	0.904445i	$0.640285\pi$
$678$		0			0
$679$	−12.2777	−	1.39158i	−0.471175	−	0.0534041i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	12.7295	+	22.0482i	0.487083	+	0.843652i	0.999890	−	0.0148520i	$-0.00472773\pi$
$683$	12.7295	+	22.0482i	0.487083	+	0.843652i	−0.512807	+	0.858504i	$0.671394\pi$
$684$		0			0
$685$	−2.15636			−0.0823904
$686$		0			0
$687$		0			0
$688$		0			0
$689$	0.669436	−	1.15950i	0.0255035	−	0.0441733i
$690$		0			0
$691$	5.95499	+	10.3143i	0.226538	+	0.392376i	0.956780	−	0.290813i	$-0.0939258\pi$
$691$	5.95499	+	10.3143i	0.226538	+	0.392376i	−0.730241	+	0.683189i	$0.760592\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	−8.57070	−	14.8449i	−0.325105	−	0.563099i
$696$		0			0
$697$	8.74393	−	15.1449i	0.331200	−	0.573655i
$698$		0			0
$699$		0			0
$700$		0			0
$701$	3.84543			0.145240			0.0726199	−	0.997360i	$-0.476864\pi$
$701$	3.84543			0.145240			0.0726199	+	0.997360i	$0.476864\pi$
$702$		0			0
$703$	20.6027	+	35.6849i	0.777044	+	1.34588i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−4.98589	−	11.4484i	−0.187514	−	0.430562i
$708$		0			0
$709$	13.3533	+	23.1286i	0.501494	+	0.868614i	0.999999	+	0.00172652i	$0.000549569\pi$
$709$	13.3533	+	23.1286i	0.501494	+	0.868614i	−0.498504	+	0.866887i	$0.666117\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	−4.80979	+	8.33081i	−0.180128	+	0.311991i
$714$		0			0
$715$	5.80872	+	10.0610i	0.217234	+	0.376260i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	−13.3611	+	23.1420i	−0.498284	+	0.863052i	−0.999998	−	0.00198088i	$-0.999369\pi$
$719$	−13.3611	+	23.1420i	−0.498284	+	0.863052i	0.501715	+	0.865033i	$0.332703\pi$
$720$		0			0
$721$	−3.34388	−	7.67808i	−0.124532	−	0.285947i
$722$		0			0
$723$		0			0
$724$		0			0
$725$	−13.2820	+	23.0051i	−0.493281	+	0.854388i
$726$		0			0
$727$	−1.13012	+	1.95743i	−0.0419139	+	0.0725970i	−0.886221	−	0.463262i	$-0.846679\pi$
$727$	−1.13012	+	1.95743i	−0.0419139	+	0.0725970i	0.844307	+	0.535859i	$0.180012\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	16.6057			0.614186
$732$		0			0
$733$	36.7404			1.35704			0.678519	−	0.734583i	$-0.262622\pi$
$733$	36.7404			1.35704			0.678519	+	0.734583i	$0.262622\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−5.80448	+	10.0536i	−0.213811	+	0.370331i
$738$		0			0
$739$	−17.0909	−	29.6022i	−0.628697	−	1.08894i	−0.987813	−	0.155643i	$-0.950255\pi$
$739$	−17.0909	−	29.6022i	−0.628697	−	1.08894i	0.359116	−	0.933293i	$-0.383078\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	4.56487	+	7.90658i	0.167469	+	0.290064i	0.937529	−	0.347907i	$-0.113107\pi$
$743$	4.56487	+	7.90658i	0.167469	+	0.290064i	−0.770061	+	0.637971i	$0.779774\pi$
$744$		0			0
$745$	15.4068			0.564461
$746$		0			0
$747$		0			0
$748$		0			0
$749$	40.2507	+	4.56211i	1.47073	+	0.166696i
$750$		0			0
$751$	−38.1295			−1.39137			−0.695683	−	0.718349i	$-0.744898\pi$
$751$	−38.1295			−1.39137			−0.695683	+	0.718349i	$0.744898\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	6.33564			0.230578
$756$		0			0
$757$	18.6952			0.679488			0.339744	−	0.940518i	$-0.389660\pi$
$757$	18.6952			0.679488			0.339744	+	0.940518i	$0.389660\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	16.1572			0.585697			0.292849	−	0.956159i	$-0.405397\pi$
$761$	16.1572			0.585697			0.292849	+	0.956159i	$0.405397\pi$
$762$		0			0
$763$	24.0710	−	32.5700i	0.871429	−	1.17911i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−28.2275			−1.01924
$768$		0			0
$769$	−16.9628	−	29.3804i	−0.611694	−	1.05949i	−0.990955	−	0.134195i	$-0.957155\pi$
$769$	−16.9628	−	29.3804i	−0.611694	−	1.05949i	0.379261	−	0.925290i	$-0.376178\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	−19.8452	−	34.3728i	−0.713781	−	1.23630i	−0.963428	−	0.267968i	$-0.913648\pi$
$773$	−19.8452	−	34.3728i	−0.713781	−	1.23630i	0.249647	−	0.968337i	$-0.419685\pi$
$774$		0			0
$775$	14.5076	−	25.1279i	0.521128	−	0.902621i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	−19.2020			−0.687982
$780$		0			0
$781$	59.7568			2.13827
$782$		0			0
$783$		0			0
$784$		0			0
$785$	2.54611	−	4.41000i	0.0908746	−	0.157400i
$786$		0			0
$787$	0.158840	−	0.275119i	0.00566204	−	0.00980695i	−0.863180	−	0.504895i	$-0.831531\pi$
$787$	0.158840	−	0.275119i	0.00566204	−	0.00980695i	0.868843	+	0.495089i	$0.164864\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	4.90980	−	6.64335i	0.174573	−	0.236211i
$792$		0			0
$793$	−10.5651	+	18.2994i	−0.375179	+	0.649829i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	21.0702	+	36.4946i	0.746344	+	1.29271i	0.949564	+	0.313572i	$0.101526\pi$
$797$	21.0702	+	36.4946i	0.746344	+	1.29271i	−0.203221	+	0.979133i	$0.565141\pi$
$798$		0			0
$799$	−13.1804	+	22.8290i	−0.466288	+	0.807634i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	12.8582	+	22.2710i	0.453755	+	0.785926i
$804$		0			0
$805$	−1.18154	−	2.71301i	−0.0416438	−	0.0956210i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	6.40052	+	11.0860i	0.225030	+	0.389764i	0.956329	−	0.292294i	$-0.0944185\pi$
$809$	6.40052	+	11.0860i	0.225030	+	0.389764i	−0.731298	+	0.682058i	$0.761085\pi$
$810$		0			0
$811$	27.1410			0.953051			0.476526	−	0.879161i	$-0.341896\pi$
$811$	27.1410			0.953051			0.476526	+	0.879161i	$0.341896\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	2.82429	−	4.89182i	0.0989307	−	0.171353i
$816$		0			0
$817$	−9.11670	−	15.7906i	−0.318953	−	0.552443i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−5.95924	−	10.3217i	−0.207979	−	0.360230i	0.743099	−	0.669182i	$-0.233355\pi$
$821$	−5.95924	−	10.3217i	−0.207979	−	0.360230i	−0.951078	+	0.308952i	$0.900022\pi$
$822$		0			0
$823$	9.26505	−	16.0475i	0.322959	−	0.559382i	−0.658138	−	0.752897i	$-0.728656\pi$
$823$	9.26505	−	16.0475i	0.322959	−	0.559382i	0.981097	+	0.193515i	$0.0619890\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−9.64616			−0.335430			−0.167715	−	0.985836i	$-0.553639\pi$
$827$	−9.64616			−0.335430			−0.167715	+	0.985836i	$0.553639\pi$
$828$		0			0
$829$	10.2155	+	17.6938i	0.354800	+	0.614531i	0.987084	−	0.160206i	$-0.0512158\pi$
$829$	10.2155	+	17.6938i	0.354800	+	0.614531i	−0.632284	+	0.774737i	$0.717882\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	26.5316	+	6.09258i	0.919266	+	0.211095i
$834$		0			0
$835$	0.363224	+	0.629122i	0.0125699	+	0.0217717i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	7.18866	−	12.4511i	0.248180	−	0.429861i	−0.714841	−	0.699287i	$-0.753501\pi$
$839$	7.18866	−	12.4511i	0.248180	−	0.429861i	0.963021	+	0.269427i	$0.0868342\pi$
$840$		0			0
$841$	−3.58799	−	6.21459i	−0.123724	−	0.214296i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	2.53836	−	4.39657i	0.0873222	−	0.151247i
$846$		0			0
$847$	−26.8412	−	61.6318i	−0.922274	−	2.11769i
$848$		0			0
$849$		0			0
$850$		0			0
$851$	7.06487	−	12.2367i	0.242181	−	0.419469i
$852$		0			0
$853$	−2.05636	+	3.56173i	−0.0704085	+	0.121951i	−0.899080	−	0.437784i	$-0.855764\pi$
$853$	−2.05636	+	3.56173i	−0.0704085	+	0.121951i	0.828672	+	0.559735i	$0.189097\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−51.1084			−1.74583			−0.872915	−	0.487873i	$-0.837773\pi$
$857$	−51.1084			−1.74583			−0.872915	+	0.487873i	$0.837773\pi$
$858$		0			0
$859$	15.3165			0.522592			0.261296	−	0.965259i	$-0.415850\pi$
$859$	15.3165			0.522592			0.261296	+	0.965259i	$0.415850\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	−12.4865	+	21.6272i	−0.425045	+	0.736199i	−0.996425	−	0.0844866i	$-0.973075\pi$
$863$	−12.4865	+	21.6272i	−0.425045	+	0.736199i	0.571380	+	0.820686i	$0.306408\pi$
$864$		0			0
$865$	1.78397	+	3.08993i	0.0606568	+	0.105061i
$866$		0			0
$867$		0			0
$868$		0			0
$869$	−22.3479	−	38.7076i	−0.758099	−	1.31307i
$870$		0			0
$871$	−4.84962			−0.164323
$872$		0			0
$873$		0			0
$874$		0			0
$875$	7.59846	+	17.4473i	0.256875	+	0.589827i
$876$		0			0
$877$	36.3918			1.22886			0.614432	−	0.788970i	$-0.289385\pi$
$877$	36.3918			1.22886			0.614432	+	0.788970i	$0.289385\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	−56.1807			−1.89277			−0.946387	−	0.323035i	$-0.895297\pi$
$881$	−56.1807			−1.89277			−0.946387	+	0.323035i	$0.895297\pi$
$882$		0			0
$883$	−22.7585			−0.765884			−0.382942	−	0.923772i	$-0.625089\pi$
$883$	−22.7585			−0.765884			−0.382942	+	0.923772i	$0.625089\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	10.0314			0.336820			0.168410	−	0.985717i	$-0.446137\pi$
$887$	10.0314			0.336820			0.168410	+	0.985717i	$0.446137\pi$
$888$		0			0
$889$	−1.35024	−	3.10037i	−0.0452856	−	0.103983i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	28.9445			0.968592
$894$		0			0
$895$	5.72485	+	9.91573i	0.191361	+	0.331446i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	19.7571	+	34.2202i	0.658935	+	1.14131i
$900$		0			0
$901$	1.03281	−	1.78888i	0.0344080	−	0.0595964i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	−10.4283			−0.346647
$906$		0			0
$907$	−20.5712			−0.683054			−0.341527	−	0.939872i	$-0.610944\pi$
$907$	−20.5712			−0.683054			−0.341527	+	0.939872i	$0.610944\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	1.19047	−	2.06196i	0.0394421	−	0.0683157i	−0.845630	−	0.533769i	$-0.820775\pi$
$911$	1.19047	−	2.06196i	0.0394421	−	0.0683157i	0.885073	+	0.465453i	$0.154109\pi$
$912$		0			0
$913$	−48.5836	+	84.1493i	−1.60788	+	2.78493i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	8.21323	+	18.8589i	0.271225	+	0.622777i
$918$		0			0
$919$	−11.8130	+	20.4608i	−0.389676	+	0.674939i	−0.992406	−	0.123007i	$-0.960746\pi$
$919$	−11.8130	+	20.4608i	−0.389676	+	0.674939i	0.602730	+	0.797945i	$0.294080\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	12.4816	+	21.6188i	0.410838	+	0.711593i
$924$		0			0
$925$	−21.3095	+	36.9091i	−0.700652	+	1.21356i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	−29.6884	−	51.4219i	−0.974046	−	1.68710i	−0.683047	−	0.730374i	$-0.739346\pi$
$929$	−29.6884	−	51.4219i	−0.974046	−	1.68710i	−0.290999	−	0.956723i	$-0.593988\pi$
$930$		0			0
$931$	−8.77259	−	28.5741i	−0.287510	−	0.936478i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	8.96175	+	15.5222i	0.293081	+	0.507630i
$936$		0			0
$937$	16.1455			0.527451			0.263725	−	0.964598i	$-0.415049\pi$
$937$	16.1455			0.527451			0.263725	+	0.964598i	$0.415049\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	9.88063	−	17.1137i	0.322099	−	0.557892i	−0.658822	−	0.752299i	$-0.728945\pi$
$941$	9.88063	−	17.1137i	0.322099	−	0.557892i	0.980921	+	0.194407i	$0.0622782\pi$
$942$		0			0
$943$	3.29228	+	5.70239i	0.107211	+	0.185695i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−24.4618	−	42.3691i	−0.794902	−	1.37681i	−0.922902	−	0.385036i	$-0.874189\pi$
$947$	−24.4618	−	42.3691i	−0.794902	−	1.37681i	0.128000	−	0.991774i	$-0.459144\pi$
$948$		0			0
$949$	−5.37147	+	9.30366i	−0.174365	+	0.302010i
$950$		0			0
$951$		0			0
$952$		0			0
$953$	48.6464			1.57581			0.787905	−	0.615797i	$-0.211166\pi$
$953$	48.6464			1.57581			0.787905	+	0.615797i	$0.211166\pi$
$954$		0			0
$955$	4.69399	+	8.13022i	0.151894	+	0.263088i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	2.98232	+	6.84790i	0.0963043	+	0.221130i
$960$		0			0
$961$	−6.08013	−	10.5311i	−0.196133	−	0.339713i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	−2.73895	+	4.74400i	−0.0881699	+	0.152715i
$966$		0			0
$967$	22.1435	+	38.3537i	0.712087	+	1.23337i	0.964072	+	0.265639i	$0.0855831\pi$
$967$	22.1435	+	38.3537i	0.712087	+	1.23337i	−0.251986	+	0.967731i	$0.581084\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	18.6355	−	32.2776i	0.598040	−	1.03584i	−0.395070	−	0.918651i	$-0.629280\pi$
$971$	18.6355	−	32.2776i	0.598040	−	1.03584i	0.993110	−	0.117185i	$-0.0373871\pi$
$972$		0			0
$973$	−35.2889	+	47.7487i	−1.13131	+	1.53075i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	30.9312	−	53.5744i	0.989577	−	1.71400i	0.370078	−	0.929001i	$-0.379331\pi$
$977$	30.9312	−	53.5744i	0.989577	−	1.71400i	0.619499	−	0.784997i	$-0.287336\pi$
$978$		0			0
$979$	10.6383	−	18.4261i	0.340003	−	0.588902i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	10.9765			0.350096			0.175048	−	0.984560i	$-0.443992\pi$
$983$	10.9765			0.350096			0.175048	+	0.984560i	$0.443992\pi$
$984$		0			0
$985$	9.95170			0.317088
$986$		0			0
$987$		0			0
$988$		0			0
$989$	−3.12621	+	5.41476i	−0.0994077	+	0.172179i
$990$		0			0
$991$	−5.43169	−	9.40796i	−0.172543	−	0.298854i	0.766765	−	0.641928i	$-0.221865\pi$
$991$	−5.43169	−	9.40796i	−0.172543	−	0.298854i	−0.939308	+	0.343074i	$0.888532\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	−1.89498	−	3.28220i	−0.0600749	−	0.104053i
$996$		0			0
$997$	−40.9291			−1.29624			−0.648119	−	0.761539i	$-0.724444\pi$
$997$	−40.9291			−1.29624			−0.648119	+	0.761539i	$0.724444\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	756.2.l.b.289.4		14
3.2	odd	2		252.2.l.b.205.6	yes	14
4.3	odd	2		3024.2.t.j.289.4		14
7.2	even	3		5292.2.j.h.3529.4		14
7.3	odd	6		5292.2.i.i.2125.4		14
7.4	even	3		756.2.i.b.613.4		14
7.5	odd	6		5292.2.j.g.3529.4		14
7.6	odd	2		5292.2.l.i.3313.4		14
9.2	odd	6		2268.2.k.e.1297.4		14
9.4	even	3		756.2.i.b.37.4		14
9.5	odd	6		252.2.i.b.121.1	yes	14
9.7	even	3		2268.2.k.f.1297.4		14
12.11	even	2		1008.2.t.j.961.2		14
21.2	odd	6		1764.2.j.g.1177.4		14
21.5	even	6		1764.2.j.h.1177.4		14
21.11	odd	6		252.2.i.b.25.1	✓	14
21.17	even	6		1764.2.i.i.1537.7		14
21.20	even	2		1764.2.l.i.961.2		14
28.11	odd	6		3024.2.q.j.2881.4		14
36.23	even	6		1008.2.q.j.625.7		14
36.31	odd	6		3024.2.q.j.2305.4		14
63.4	even	3	inner	756.2.l.b.361.4		14
63.5	even	6		1764.2.j.h.589.4		14
63.11	odd	6		2268.2.k.e.1621.4		14
63.13	odd	6		5292.2.i.i.1549.4		14
63.23	odd	6		1764.2.j.g.589.4		14
63.25	even	3		2268.2.k.f.1621.4		14
63.31	odd	6		5292.2.l.i.361.4		14
63.32	odd	6		252.2.l.b.193.6	yes	14
63.40	odd	6		5292.2.j.g.1765.4		14
63.41	even	6		1764.2.i.i.373.7		14
63.58	even	3		5292.2.j.h.1765.4		14
63.59	even	6		1764.2.l.i.949.2		14
84.11	even	6		1008.2.q.j.529.7		14
252.67	odd	6		3024.2.t.j.1873.4		14
252.95	even	6		1008.2.t.j.193.2		14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
252.2.i.b.25.1	✓	14	21.11	odd	6
252.2.i.b.121.1	yes	14	9.5	odd	6
252.2.l.b.193.6	yes	14	63.32	odd	6
252.2.l.b.205.6	yes	14	3.2	odd	2
756.2.i.b.37.4		14	9.4	even	3
756.2.i.b.613.4		14	7.4	even	3
756.2.l.b.289.4		14	1.1	even	1	trivial
756.2.l.b.361.4		14	63.4	even	3	inner
1008.2.q.j.529.7		14	84.11	even	6
1008.2.q.j.625.7		14	36.23	even	6
1008.2.t.j.193.2		14	252.95	even	6
1008.2.t.j.961.2		14	12.11	even	2
1764.2.i.i.373.7		14	63.41	even	6
1764.2.i.i.1537.7		14	21.17	even	6
1764.2.j.g.589.4		14	63.23	odd	6
1764.2.j.g.1177.4		14	21.2	odd	6
1764.2.j.h.589.4		14	63.5	even	6
1764.2.j.h.1177.4		14	21.5	even	6
1764.2.l.i.949.2		14	63.59	even	6
1764.2.l.i.961.2		14	21.20	even	2
2268.2.k.e.1297.4		14	9.2	odd	6
2268.2.k.e.1621.4		14	63.11	odd	6
2268.2.k.f.1297.4		14	9.7	even	3
2268.2.k.f.1621.4		14	63.25	even	3
3024.2.q.j.2305.4		14	36.31	odd	6
3024.2.q.j.2881.4		14	28.11	odd	6
3024.2.t.j.289.4		14	4.3	odd	2
3024.2.t.j.1873.4		14	252.67	odd	6
5292.2.i.i.1549.4		14	63.13	odd	6
5292.2.i.i.2125.4		14	7.3	odd	6
5292.2.j.g.1765.4		14	63.40	odd	6
5292.2.j.g.3529.4		14	7.5	odd	6
5292.2.j.h.1765.4		14	63.58	even	3
5292.2.j.h.3529.4		14	7.2	even	3
5292.2.l.i.361.4		14	63.31	odd	6
5292.2.l.i.3313.4		14	7.6	odd	2

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:	\( N \)	\(=\)	\( 756 = 2^{2} \cdot 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	756.l (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+0.763837 q^{5} +(-1.05641 - 2.42569i) q^{7} +O(q^{10})\)	\(q+0.763837 q^{5} +(-1.05641 - 2.42569i) q^{7} -6.03389 q^{11} +(-1.26032 - 2.18294i) q^{13} +(-1.94444 - 3.36787i) q^{17} +(-2.13503 + 3.69798i) q^{19} +1.46425 q^{23} -4.41655 q^{25} +(3.00732 - 5.20884i) q^{29} +(-3.28482 + 5.68948i) q^{31} +(-0.806926 - 1.85283i) q^{35} +(4.82492 - 8.35700i) q^{37} +(2.24844 + 3.89442i) q^{41} +(-2.13503 + 3.69798i) q^{43} +(-3.38924 - 5.87034i) q^{47} +(-4.76799 + 5.12507i) q^{49} +(0.265581 + 0.460000i) q^{53} -4.60891 q^{55} +(5.59926 - 9.69821i) q^{59} +(-4.19144 - 7.25979i) q^{61} +(-0.962681 - 1.66741i) q^{65} +(0.961979 - 1.66620i) q^{67} -9.90353 q^{71} +(-2.13099 - 3.69098i) q^{73} +(6.37428 + 14.6364i) q^{77} +(3.70372 + 6.41503i) q^{79} +(8.05178 - 13.9461i) q^{83} +(-1.48523 - 2.57250i) q^{85} +(-1.76310 + 3.05377i) q^{89} +(-3.96373 + 5.36325i) q^{91} +(-1.63081 + 2.82465i) q^{95} +(2.33513 - 4.04456i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q - 4 q^{5} - 3 q^{7}+O(q^{10}) \) 14 * q - 4 * q^5 - 3 * q^7	\( 14 q - 4 q^{5} - 3 q^{7} + 4 q^{11} + 2 q^{13} - 2 q^{17} + 7 q^{19} + 22 q^{23} + 18 q^{25} - q^{29} - q^{31} + 19 q^{35} + 10 q^{37} + 33 q^{41} + 7 q^{43} + 3 q^{47} - 13 q^{49} + 15 q^{53} - 28 q^{55} + 14 q^{59} - 10 q^{61} - 15 q^{65} + 6 q^{67} - 2 q^{71} + 21 q^{73} - 19 q^{77} - 10 q^{79} + 25 q^{83} + 8 q^{85} + 6 q^{89} + 2 q^{91} + 28 q^{95} - 18 q^{97}+O(q^{100}) \) 14 * q - 4 * q^5 - 3 * q^7 + 4 * q^11 + 2 * q^13 - 2 * q^17 + 7 * q^19 + 22 * q^23 + 18 * q^25 - q^29 - q^31 + 19 * q^35 + 10 * q^37 + 33 * q^41 + 7 * q^43 + 3 * q^47 - 13 * q^49 + 15 * q^53 - 28 * q^55 + 14 * q^59 - 10 * q^61 - 15 * q^65 + 6 * q^67 - 2 * q^71 + 21 * q^73 - 19 * q^77 - 10 * q^79 + 25 * q^83 + 8 * q^85 + 6 * q^89 + 2 * q^91 + 28 * q^95 - 18 * q^97

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