LMFDB - Embedded newform 1248.2.bb.f.655.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1248,2,Mod(463,1248)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1248, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 2, 0, 1]))

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

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

chi := DirichletCharacter("1248.463");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1248 = 2^{5} \cdot 3 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1248.bb (of order $4$, 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:	$9.96533017226$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(i)$
Twist minimal:	no (minimal twist has level 312)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			655.6
Character	$\chi$	$=$	1248.655
Dual form			1248.2.bb.f.463.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{3} +(-0.220561 - 0.220561i) q^{5} +(0.834354 - 0.834354i) q^{7} +1.00000 q^{9} +O(q^{10})$	\(q+1.00000 q^{3} +(-0.220561 - 0.220561i) q^{5} +(0.834354 - 0.834354i) q^{7} +1.00000 q^{9} +(-4.19582 - 4.19582i) q^{11} +(1.68204 + 3.18916i) q^{13} +(-0.220561 - 0.220561i) q^{15} -5.40681i q^{17} +(-1.07948 + 1.07948i) q^{19} +(0.834354 - 0.834354i) q^{21} +8.62668 q^{23} -4.90271i q^{25} +1.00000 q^{27} -7.07841i q^{29} +(-0.834354 - 0.834354i) q^{31} +(-4.19582 - 4.19582i) q^{33} -0.368051 q^{35} +(-3.93764 + 3.93764i) q^{37} +(1.68204 + 3.18916i) q^{39} +(7.68210 - 7.68210i) q^{41} -4.27983i q^{43} +(-0.220561 - 0.220561i) q^{45} +(-6.33808 + 6.33808i) q^{47} +5.60771i q^{49} -5.40681i q^{51} -0.517929i q^{53} +1.85087i q^{55} +(-1.07948 + 1.07948i) q^{57} +(3.64977 + 3.64977i) q^{59} -8.80884i q^{61} +(0.834354 - 0.834354i) q^{63} +(0.332412 - 1.07440i) q^{65} +(-3.20036 + 3.20036i) q^{67} +8.62668 q^{69} +(9.26104 + 9.26104i) q^{71} +(-1.70500 - 1.70500i) q^{73} -4.90271i q^{75} -7.00160 q^{77} -10.7776i q^{79} +1.00000 q^{81} +(5.49082 - 5.49082i) q^{83} +(-1.19253 + 1.19253i) q^{85} -7.07841i q^{87} +(-2.33241 - 2.33241i) q^{89} +(4.06431 + 1.25747i) q^{91} +(-0.834354 - 0.834354i) q^{93} +0.476180 q^{95} +(-1.70181 + 1.70181i) q^{97} +(-4.19582 - 4.19582i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 24 q^{3} + 24 q^{9}+O(q^{10}) $ 24 * q + 24 * q^3 + 24 * q^9	$ 24 q + 24 q^{3} + 24 q^{9} - 8 q^{11} - 20 q^{19} + 24 q^{27} - 8 q^{33} - 16 q^{35} - 12 q^{41} - 20 q^{57} + 16 q^{59} - 76 q^{65} - 28 q^{67} - 8 q^{73} + 24 q^{81} + 72 q^{83} + 28 q^{89} + 4 q^{91} + 24 q^{97} - 8 q^{99}+O(q^{100}) $ 24 * q + 24 * q^3 + 24 * q^9 - 8 * q^11 - 20 * q^19 + 24 * q^27 - 8 * q^33 - 16 * q^35 - 12 * q^41 - 20 * q^57 + 16 * q^59 - 76 * q^65 - 28 * q^67 - 8 * q^73 + 24 * q^81 + 72 * q^83 + 28 * q^89 + 4 * q^91 + 24 * q^97 - 8 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1248\mathbb{Z}\right)^\times$.

$n$	$703$	$769$	$833$	$1093$
$\chi(n)$	$-1$	$e\left(\frac{3}{4}\right)$	$1$	$-1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$		0			0
$2$		0			0
$3$	1.00000			0.577350
$3$	1.00000			0.577350
$4$		0			0
$5$	−0.220561	−	0.220561i	−0.0986377	−	0.0986377i	0.656066	−	0.754704i	$-0.272219\pi$
$5$	−0.220561	−	0.220561i	−0.0986377	−	0.0986377i	−0.754704	+	0.656066i	$0.772219\pi$
$6$		0			0
$7$	0.834354	−	0.834354i	0.315356	−	0.315356i	−0.531624	−	0.846980i	$-0.678418\pi$
$7$	0.834354	−	0.834354i	0.315356	−	0.315356i	0.846980	+	0.531624i	$0.178418\pi$
$8$		0			0
$9$	1.00000			0.333333
$10$		0			0
$11$	−4.19582	−	4.19582i	−1.26509	−	1.26509i	−0.948595	−	0.316492i	$-0.897495\pi$
$11$	−4.19582	−	4.19582i	−1.26509	−	1.26509i	−0.316492	−	0.948595i	$-0.602505\pi$
$12$		0			0
$13$	1.68204	+	3.18916i	0.466514	+	0.884514i
$13$	1.68204	+	3.18916i	0.466514	+	0.884514i
$14$		0			0
$15$	−0.220561	−	0.220561i	−0.0569485	−	0.0569485i
$16$		0			0
$17$		−	5.40681i		−	1.31134i	−0.755046	−	0.655672i	$-0.772386\pi$
$17$		−	5.40681i		−	1.31134i	0.755046	−	0.655672i	$-0.227614\pi$
$18$		0			0
$19$	−1.07948	+	1.07948i	−0.247649	+	0.247649i	−0.820005	−	0.572356i	$-0.806029\pi$
$19$	−1.07948	+	1.07948i	−0.247649	+	0.247649i	0.572356	+	0.820005i	$0.306029\pi$
$20$		0			0
$21$	0.834354	−	0.834354i	0.182071	−	0.182071i
$22$		0			0
$23$	8.62668			1.79879			0.899393	−	0.437140i	$-0.144009\pi$
$23$	8.62668			1.79879			0.899393	+	0.437140i	$0.144009\pi$
$24$		0			0
$25$		−	4.90271i		−	0.980541i
$26$		0			0
$27$	1.00000			0.192450
$28$		0			0
$29$		−	7.07841i		−	1.31443i	−0.753704	−	0.657214i	$-0.771735\pi$
$29$		−	7.07841i		−	1.31443i	0.753704	−	0.657214i	$-0.228265\pi$
$30$		0			0
$31$	−0.834354	−	0.834354i	−0.149854	−	0.149854i	0.628199	−	0.778053i	$-0.283793\pi$
$31$	−0.834354	−	0.834354i	−0.149854	−	0.149854i	−0.778053	+	0.628199i	$0.783793\pi$
$32$		0			0
$33$	−4.19582	−	4.19582i	−0.730398	−	0.730398i
$34$		0			0
$35$	−0.368051			−0.0622121
$36$		0			0
$37$	−3.93764	+	3.93764i	−0.647343	+	0.647343i	−0.952350	−	0.305007i	$-0.901341\pi$
$37$	−3.93764	+	3.93764i	−0.647343	+	0.647343i	0.305007	+	0.952350i	$0.401341\pi$
$38$		0			0
$39$	1.68204	+	3.18916i	0.269342	+	0.510674i
$40$		0			0
$41$	7.68210	−	7.68210i	1.19974	−	1.19974i	0.225499	−	0.974243i	$-0.427599\pi$
$41$	7.68210	−	7.68210i	1.19974	−	1.19974i	0.974243	−	0.225499i	$-0.0724013\pi$
$42$		0			0
$43$		−	4.27983i		−	0.652668i	−0.945255	−	0.326334i	$-0.894187\pi$
$43$		−	4.27983i		−	0.652668i	0.945255	−	0.326334i	$-0.105813\pi$
$44$		0			0
$45$	−0.220561	−	0.220561i	−0.0328792	−	0.0328792i
$46$		0			0
$47$	−6.33808	+	6.33808i	−0.924505	+	0.924505i	−0.997344	−	0.0728391i	$-0.976794\pi$
$47$	−6.33808	+	6.33808i	−0.924505	+	0.924505i	0.0728391	+	0.997344i	$0.476794\pi$
$48$		0			0
$49$			5.60771i			0.801101i
$50$		0			0
$51$		−	5.40681i		−	0.757104i
$52$		0			0
$53$		−	0.517929i		−	0.0711431i	−0.999367	−	0.0355715i	$-0.988675\pi$
$53$		−	0.517929i		−	0.0711431i	0.999367	−	0.0355715i	$-0.0113252\pi$
$54$		0			0
$55$			1.85087i			0.249571i
$56$		0			0
$57$	−1.07948	+	1.07948i	−0.142980	+	0.142980i
$58$		0			0
$59$	3.64977	+	3.64977i	0.475160	+	0.475160i	0.903580	−	0.428420i	$-0.140930\pi$
$59$	3.64977	+	3.64977i	0.475160	+	0.475160i	−0.428420	+	0.903580i	$0.640930\pi$
$60$		0			0
$61$		−	8.80884i		−	1.12786i	−0.825824	−	0.563928i	$-0.809290\pi$
$61$		−	8.80884i		−	1.12786i	0.825824	−	0.563928i	$-0.190710\pi$
$62$		0			0
$63$	0.834354	−	0.834354i	0.105119	−	0.105119i
$64$		0			0
$65$	0.332412	−	1.07440i	0.0412306	−	0.133262i
$66$		0			0
$67$	−3.20036	+	3.20036i	−0.390986	+	0.390986i	−0.875039	−	0.484053i	$-0.839164\pi$
$67$	−3.20036	+	3.20036i	−0.390986	+	0.390986i	0.484053	+	0.875039i	$0.339164\pi$
$68$		0			0
$69$	8.62668			1.03853
$70$		0			0
$71$	9.26104	+	9.26104i	1.09908	+	1.09908i	0.994518	+	0.104565i	$0.0333451\pi$
$71$	9.26104	+	9.26104i	1.09908	+	1.09908i	0.104565	+	0.994518i	$0.466655\pi$
$72$		0			0
$73$	−1.70500	−	1.70500i	−0.199555	−	0.199555i	0.600254	−	0.799809i	$-0.295066\pi$
$73$	−1.70500	−	1.70500i	−0.199555	−	0.199555i	−0.799809	+	0.600254i	$0.795066\pi$
$74$		0			0
$75$		−	4.90271i		−	0.566116i
$76$		0			0
$77$	−7.00160			−0.797906
$78$		0			0
$79$		−	10.7776i		−	1.21258i	−0.795244	−	0.606290i	$-0.792657\pi$
$79$		−	10.7776i		−	1.21258i	0.795244	−	0.606290i	$-0.207343\pi$
$80$		0			0
$81$	1.00000			0.111111
$82$		0			0
$83$	5.49082	−	5.49082i	0.602696	−	0.602696i	−0.338331	−	0.941027i	$-0.609862\pi$
$83$	5.49082	−	5.49082i	0.602696	−	0.602696i	0.941027	+	0.338331i	$0.109862\pi$
$84$		0			0
$85$	−1.19253	+	1.19253i	−0.129348	+	0.129348i
$86$		0			0
$87$		−	7.07841i		−	0.758885i
$88$		0			0
$89$	−2.33241	−	2.33241i	−0.247235	−	0.247235i	0.572600	−	0.819835i	$-0.305935\pi$
$89$	−2.33241	−	2.33241i	−0.247235	−	0.247235i	−0.819835	+	0.572600i	$0.805935\pi$
$90$		0			0
$91$	4.06431	+	1.25747i	0.426055	+	0.131819i
$92$		0			0
$93$	−0.834354	−	0.834354i	−0.0865185	−	0.0865185i
$94$		0			0
$95$	0.476180			0.0488550
$96$		0			0
$97$	−1.70181	+	1.70181i	−0.172792	+	0.172792i	−0.788205	−	0.615413i	$-0.788989\pi$
$97$	−1.70181	+	1.70181i	−0.172792	+	0.172792i	0.615413	+	0.788205i	$0.288989\pi$
$98$		0			0
$99$	−4.19582	−	4.19582i	−0.421696	−	0.421696i
$100$		0			0
$101$	13.1978			1.31323			0.656613	−	0.754227i	$-0.271988\pi$
$101$	13.1978			1.31323			0.656613	+	0.754227i	$0.271988\pi$
$102$		0			0
$103$	−5.35347			−0.527493			−0.263747	−	0.964592i	$-0.584958\pi$
$103$	−5.35347			−0.527493			−0.263747	+	0.964592i	$0.584958\pi$
$104$		0			0
$105$	−0.368051			−0.0359181
$106$		0			0
$107$	−8.34149			−0.806402			−0.403201	−	0.915111i	$-0.632102\pi$
$107$	−8.34149			−0.806402			−0.403201	+	0.915111i	$0.632102\pi$
$108$		0			0
$109$	10.0825	+	10.0825i	0.965726	+	0.965726i	0.999432	−	0.0337056i	$-0.0107308\pi$
$109$	10.0825	+	10.0825i	0.965726	+	0.965726i	−0.0337056	+	0.999432i	$0.510731\pi$
$110$		0			0
$111$	−3.93764	+	3.93764i	−0.373744	+	0.373744i
$112$		0			0
$113$	−5.95740			−0.560425			−0.280212	−	0.959938i	$-0.590405\pi$
$113$	−5.95740			−0.560425			−0.280212	+	0.959938i	$0.590405\pi$
$114$		0			0
$115$	−1.90271	−	1.90271i	−0.177428	−	0.177428i
$116$		0			0
$117$	1.68204	+	3.18916i	0.155505	+	0.294838i
$118$		0			0
$119$	−4.51119	−	4.51119i	−0.413540	−	0.413540i
$120$		0			0
$121$			24.2098i			2.20089i
$122$		0			0
$123$	7.68210	−	7.68210i	0.692672	−	0.692672i
$124$		0			0
$125$	−2.18415	+	2.18415i	−0.195356	+	0.195356i
$126$		0			0
$127$	−4.01202			−0.356009			−0.178004	−	0.984030i	$-0.556964\pi$
$127$	−4.01202			−0.356009			−0.178004	+	0.984030i	$0.556964\pi$
$128$		0			0
$129$		−	4.27983i		−	0.376818i
$130$		0			0
$131$	−1.93969			−0.169471			−0.0847357	−	0.996403i	$-0.527005\pi$
$131$	−1.93969			−0.169471			−0.0847357	+	0.996403i	$0.527005\pi$
$132$		0			0
$133$			1.80133i			0.156195i
$134$		0			0
$135$	−0.220561	−	0.220561i	−0.0189828	−	0.0189828i
$136$		0			0
$137$	−6.89207	−	6.89207i	−0.588830	−	0.588830i	0.348485	−	0.937314i	$-0.386696\pi$
$137$	−6.89207	−	6.89207i	−0.588830	−	0.588830i	−0.937314	+	0.348485i	$0.886696\pi$
$138$		0			0
$139$	14.6624			1.24365			0.621824	−	0.783157i	$-0.286392\pi$
$139$	14.6624			1.24365			0.621824	+	0.783157i	$0.286392\pi$
$140$		0			0
$141$	−6.33808	+	6.33808i	−0.533763	+	0.533763i
$142$		0			0
$143$	6.32361	−	20.4387i	0.528807	−	1.70917i
$144$		0			0
$145$	−1.56122	+	1.56122i	−0.129652	+	0.129652i
$146$		0			0
$147$			5.60771i			0.462516i
$148$		0			0
$149$	0.971968	+	0.971968i	0.0796267	+	0.0796267i	0.745798	−	0.666172i	$-0.232068\pi$
$149$	0.971968	+	0.971968i	0.0796267	+	0.0796267i	−0.666172	+	0.745798i	$0.732068\pi$
$150$		0			0
$151$	−8.49241	+	8.49241i	−0.691103	+	0.691103i	−0.962475	−	0.271372i	$-0.912523\pi$
$151$	−8.49241	+	8.49241i	−0.691103	+	0.691103i	0.271372	+	0.962475i	$0.412523\pi$
$152$		0			0
$153$		−	5.40681i		−	0.437114i
$154$		0			0
$155$			0.368051i			0.0295626i
$156$		0			0
$157$		−	4.57470i		−	0.365101i	−0.983197	−	0.182550i	$-0.941565\pi$
$157$		−	4.57470i		−	0.365101i	0.983197	−	0.182550i	$-0.0584352\pi$
$158$		0			0
$159$		−	0.517929i		−	0.0410745i
$160$		0			0
$161$	7.19771	−	7.19771i	0.567259	−	0.567259i
$162$		0			0
$163$	12.5646	+	12.5646i	0.984132	+	0.984132i	0.999876	−	0.0157440i	$-0.00501167\pi$
$163$	12.5646	+	12.5646i	0.984132	+	0.984132i	−0.0157440	+	0.999876i	$0.505012\pi$
$164$		0			0
$165$			1.85087i			0.144090i
$166$		0			0
$167$	−0.619886	+	0.619886i	−0.0479682	+	0.0479682i	−0.730684	−	0.682716i	$-0.760799\pi$
$167$	−0.619886	+	0.619886i	−0.0479682	+	0.0479682i	0.682716	+	0.730684i	$0.260799\pi$
$168$		0			0
$169$	−7.34149	+	10.7286i	−0.564730	+	0.825276i
$170$		0			0
$171$	−1.07948	+	1.07948i	−0.0825496	+	0.0825496i
$172$		0			0
$173$	−24.0873			−1.83132			−0.915661	−	0.401952i	$-0.868332\pi$
$173$	−24.0873			−1.83132			−0.915661	+	0.401952i	$0.868332\pi$
$174$		0			0
$175$	−4.09059	−	4.09059i	−0.309220	−	0.309220i
$176$		0			0
$177$	3.64977	+	3.64977i	0.274333	+	0.274333i
$178$		0			0
$179$		−	7.74133i		−	0.578614i	−0.957236	−	0.289307i	$-0.906575\pi$
$179$		−	7.74133i		−	0.578614i	0.957236	−	0.289307i	$-0.0934248\pi$
$180$		0			0
$181$	−1.87145			−0.139104			−0.0695518	−	0.997578i	$-0.522157\pi$
$181$	−1.87145			−0.139104			−0.0695518	+	0.997578i	$0.522157\pi$
$182$		0			0
$183$		−	8.80884i		−	0.651168i
$184$		0			0
$185$	1.73698			0.127705
$186$		0			0
$187$	−22.6860	+	22.6860i	−1.65896	+	1.65896i
$188$		0			0
$189$	0.834354	−	0.834354i	0.0606903	−	0.0606903i
$190$		0			0
$191$			8.54621i			0.618382i	0.951000	+	0.309191i	$0.100058\pi$
$191$			8.54621i			0.618382i	−0.951000	+	0.309191i	$0.899942\pi$
$192$		0			0
$193$	10.4304	+	10.4304i	0.750796	+	0.750796i	0.974628	−	0.223832i	$-0.0718566\pi$
$193$	10.4304	+	10.4304i	0.750796	+	0.750796i	−0.223832	+	0.974628i	$0.571857\pi$
$194$		0			0
$195$	0.332412	−	1.07440i	0.0238045	−	0.0769390i
$196$		0			0
$197$	17.3971	+	17.3971i	1.23949	+	1.23949i	0.960208	+	0.279284i	$0.0900972\pi$
$197$	17.3971	+	17.3971i	1.23949	+	1.23949i	0.279284	+	0.960208i	$0.409903\pi$
$198$		0			0
$199$	−3.64770			−0.258579			−0.129289	−	0.991607i	$-0.541270\pi$
$199$	−3.64770			−0.258579			−0.129289	+	0.991607i	$0.541270\pi$
$200$		0			0
$201$	−3.20036	+	3.20036i	−0.225736	+	0.225736i
$202$		0			0
$203$	−5.90590	−	5.90590i	−0.414513	−	0.414513i
$204$		0			0
$205$	−3.38874			−0.236680
$206$		0			0
$207$	8.62668			0.599596
$208$		0			0
$209$	9.05857			0.626594
$210$		0			0
$211$	−0.114235			−0.00786425			−0.00393213	−	0.999992i	$-0.501252\pi$
$211$	−0.114235			−0.00786425			−0.00393213	+	0.999992i	$0.501252\pi$
$212$		0			0
$213$	9.26104	+	9.26104i	0.634556	+	0.634556i
$214$		0			0
$215$	−0.943962	+	0.943962i	−0.0643777	+	0.0643777i
$216$		0			0
$217$	−1.39229			−0.0945151
$218$		0			0
$219$	−1.70500	−	1.70500i	−0.115213	−	0.115213i
$220$		0			0
$221$	17.2432	−	9.09446i	1.15990	−	0.611760i
$222$		0			0
$223$	13.3225	+	13.3225i	0.892138	+	0.892138i	0.994724	−	0.102586i	$-0.0327118\pi$
$223$	13.3225	+	13.3225i	0.892138	+	0.892138i	−0.102586	+	0.994724i	$0.532712\pi$
$224$		0			0
$225$		−	4.90271i		−	0.326847i
$226$		0			0
$227$	4.69172	−	4.69172i	0.311400	−	0.311400i	−0.534052	−	0.845452i	$-0.679331\pi$
$227$	4.69172	−	4.69172i	0.311400	−	0.311400i	0.845452	+	0.534052i	$0.179331\pi$
$228$		0			0
$229$	−7.56068	+	7.56068i	−0.499624	+	0.499624i	−0.911321	−	0.411697i	$-0.864936\pi$
$229$	−7.56068	+	7.56068i	−0.499624	+	0.499624i	0.411697	+	0.911321i	$0.364936\pi$
$230$		0			0
$231$	−7.00160			−0.460671
$232$		0			0
$233$			5.14059i			0.336771i	0.985721	+	0.168386i	$0.0538554\pi$
$233$			5.14059i			0.336771i	−0.985721	+	0.168386i	$0.946145\pi$
$234$		0			0
$235$	2.79586			0.182382
$236$		0			0
$237$		−	10.7776i		−	0.700083i
$238$		0			0
$239$	−5.22603	−	5.22603i	−0.338044	−	0.338044i	0.517587	−	0.855631i	$-0.326830\pi$
$239$	−5.22603	−	5.22603i	−0.338044	−	0.338044i	−0.855631	+	0.517587i	$0.826830\pi$
$240$		0			0
$241$	−8.31859	−	8.31859i	−0.535847	−	0.535847i	0.386459	−	0.922306i	$-0.373698\pi$
$241$	−8.31859	−	8.31859i	−0.535847	−	0.535847i	−0.922306	+	0.386459i	$0.873698\pi$
$242$		0			0
$243$	1.00000			0.0641500
$244$		0			0
$245$	1.23684	−	1.23684i	0.0790188	−	0.0790188i
$246$		0			0
$247$	−5.25834	−	1.62690i	−0.334580	−	0.103517i
$248$		0			0
$249$	5.49082	−	5.49082i	0.347967	−	0.347967i
$250$		0			0
$251$		−	15.2053i		−	0.959747i	−0.877338	−	0.479873i	$-0.840683\pi$
$251$		−	15.2053i		−	0.959747i	0.877338	−	0.479873i	$-0.159317\pi$
$252$		0			0
$253$	−36.1960	−	36.1960i	−2.27562	−	2.27562i
$254$		0			0
$255$	−1.19253	+	1.19253i	−0.0746791	+	0.0746791i
$256$		0			0
$257$			26.5978i			1.65912i	0.558416	+	0.829561i	$0.311409\pi$
$257$			26.5978i			1.65912i	−0.558416	+	0.829561i	$0.688591\pi$
$258$		0			0
$259$			6.57077i			0.408288i
$260$		0			0
$261$		−	7.07841i		−	0.438142i
$262$		0			0
$263$			15.1896i			0.936634i	0.883561	+	0.468317i	$0.155139\pi$
$263$			15.1896i			0.936634i	−0.883561	+	0.468317i	$0.844861\pi$
$264$		0			0
$265$	−0.114235	+	0.114235i	−0.00701739	+	0.00701739i
$266$		0			0
$267$	−2.33241	−	2.33241i	−0.142741	−	0.142741i
$268$		0			0
$269$		−	0.531993i		−	0.0324362i	−0.999868	−	0.0162181i	$-0.994837\pi$
$269$		−	0.531993i		−	0.0324362i	0.999868	−	0.0162181i	$-0.00516261\pi$
$270$		0			0
$271$	5.60569	−	5.60569i	0.340521	−	0.340521i	−0.516042	−	0.856563i	$-0.672595\pi$
$271$	5.60569	−	5.60569i	0.340521	−	0.340521i	0.856563	+	0.516042i	$0.172595\pi$
$272$		0			0
$273$	4.06431	+	1.25747i	0.245983	+	0.0761057i
$274$		0			0
$275$	−20.5709	+	20.5709i	−1.24047	+	1.24047i
$276$		0			0
$277$	2.37287			0.142572			0.0712861	−	0.997456i	$-0.477290\pi$
$277$	2.37287			0.142572			0.0712861	+	0.997456i	$0.477290\pi$
$278$		0			0
$279$	−0.834354	−	0.834354i	−0.0499515	−	0.0499515i
$280$		0			0
$281$	−2.55059	−	2.55059i	−0.152155	−	0.152155i	0.626925	−	0.779080i	$-0.284313\pi$
$281$	−2.55059	−	2.55059i	−0.152155	−	0.152155i	−0.779080	+	0.626925i	$0.784313\pi$
$282$		0			0
$283$			12.1486i			0.722157i	0.932535	+	0.361078i	$0.117591\pi$
$283$			12.1486i			0.722157i	−0.932535	+	0.361078i	$0.882409\pi$
$284$		0			0
$285$	0.476180			0.0282064
$286$		0			0
$287$		−	12.8192i		−	0.756693i
$288$		0			0
$289$	−12.2336			−0.719621
$290$		0			0
$291$	−1.70181	+	1.70181i	−0.0997617	+	0.0997617i
$292$		0			0
$293$	−6.58440	+	6.58440i	−0.384665	+	0.384665i	−0.872780	−	0.488115i	$-0.837685\pi$
$293$	−6.58440	+	6.58440i	−0.384665	+	0.384665i	0.488115	+	0.872780i	$0.337685\pi$
$294$		0			0
$295$		−	1.60999i		−	0.0937373i
$296$		0			0
$297$	−4.19582	−	4.19582i	−0.243466	−	0.243466i
$298$		0			0
$299$	14.5104	+	27.5119i	0.839159	+	1.59105i
$300$		0			0
$301$	−3.57090	−	3.57090i	−0.205823	−	0.205823i
$302$		0			0
$303$	13.1978			0.758192
$304$		0			0
$305$	−1.94288	+	1.94288i	−0.111249	+	0.111249i
$306$		0			0
$307$	11.1310	+	11.1310i	0.635278	+	0.635278i	0.949387	−	0.314109i	$-0.101706\pi$
$307$	11.1310	+	11.1310i	0.635278	+	0.635278i	−0.314109	+	0.949387i	$0.601706\pi$
$308$		0			0
$309$	−5.35347			−0.304548
$310$		0			0
$311$	2.10922			0.119603			0.0598014	−	0.998210i	$-0.480953\pi$
$311$	2.10922			0.119603			0.0598014	+	0.998210i	$0.480953\pi$
$312$		0			0
$313$	23.5722			1.33238			0.666189	−	0.745783i	$-0.267924\pi$
$313$	23.5722			1.33238			0.666189	+	0.745783i	$0.267924\pi$
$314$		0			0
$315$	−0.368051			−0.0207374
$316$		0			0
$317$	−17.8629	−	17.8629i	−1.00328	−	1.00328i	−0.999995	−	0.00328531i	$-0.998954\pi$
$317$	−17.8629	−	17.8629i	−1.00328	−	1.00328i	−0.00328531	−	0.999995i	$-0.501046\pi$
$318$		0			0
$319$	−29.6997	+	29.6997i	−1.66286	+	1.66286i
$320$		0			0
$321$	−8.34149			−0.465576
$322$		0			0
$323$	5.83652	+	5.83652i	0.324752	+	0.324752i
$324$		0			0
$325$	15.6355	−	8.24654i	0.867302	−	0.457436i
$326$		0			0
$327$	10.0825	+	10.0825i	0.557562	+	0.557562i
$328$		0			0
$329$			10.5764i			0.583097i
$330$		0			0
$331$	−6.91280	+	6.91280i	−0.379962	+	0.379962i	−0.871088	−	0.491127i	$-0.836585\pi$
$331$	−6.91280	+	6.91280i	−0.379962	+	0.379962i	0.491127	+	0.871088i	$0.336585\pi$
$332$		0			0
$333$	−3.93764	+	3.93764i	−0.215781	+	0.215781i
$334$		0			0
$335$	1.41175			0.0771319
$336$		0			0
$337$			11.9944i			0.653375i	0.945132	+	0.326688i	$0.105933\pi$
$337$			11.9944i			0.653375i	−0.945132	+	0.326688i	$0.894067\pi$
$338$		0			0
$339$	−5.95740			−0.323561
$340$		0			0
$341$			7.00160i			0.379158i
$342$		0			0
$343$	10.5193	+	10.5193i	0.567988	+	0.567988i
$344$		0			0
$345$	−1.90271	−	1.90271i	−0.102438	−	0.102438i
$346$		0			0
$347$	21.3429			1.14575			0.572874	−	0.819643i	$-0.305828\pi$
$347$	21.3429			1.14575			0.572874	+	0.819643i	$0.305828\pi$
$348$		0			0
$349$	−2.87324	+	2.87324i	−0.153801	+	0.153801i	−0.779813	−	0.626012i	$-0.784686\pi$
$349$	−2.87324	+	2.87324i	−0.153801	+	0.153801i	0.626012	+	0.779813i	$0.284686\pi$
$350$		0			0
$351$	1.68204	+	3.18916i	0.0897806	+	0.170225i
$352$		0			0
$353$	−10.3324	+	10.3324i	−0.549939	+	0.549939i	−0.926423	−	0.376484i	$-0.877133\pi$
$353$	−10.3324	+	10.3324i	−0.549939	+	0.549939i	0.376484	+	0.926423i	$0.377133\pi$
$354$		0			0
$355$		−	4.08524i		−	0.216822i
$356$		0			0
$357$	−4.51119	−	4.51119i	−0.238758	−	0.238758i
$358$		0			0
$359$	−15.7969	+	15.7969i	−0.833726	+	0.833726i	−0.988024	−	0.154298i	$-0.950688\pi$
$359$	−15.7969	+	15.7969i	−0.833726	+	0.833726i	0.154298	+	0.988024i	$0.450688\pi$
$360$		0			0
$361$			16.6695i			0.877340i
$362$		0			0
$363$			24.2098i			1.27068i
$364$		0			0
$365$			0.752112i			0.0393673i
$366$		0			0
$367$			22.9385i			1.19738i	0.800981	+	0.598690i	$0.204312\pi$
$367$			22.9385i			1.19738i	−0.800981	+	0.598690i	$0.795688\pi$
$368$		0			0
$369$	7.68210	−	7.68210i	0.399914	−	0.399914i
$370$		0			0
$371$	−0.432137	−	0.432137i	−0.0224354	−	0.0224354i
$372$		0			0
$373$			31.2421i			1.61765i	0.588047	+	0.808827i	$0.299897\pi$
$373$			31.2421i			1.61765i	−0.588047	+	0.808827i	$0.700103\pi$
$374$		0			0
$375$	−2.18415	+	2.18415i	−0.112789	+	0.112789i
$376$		0			0
$377$	22.5742	−	11.9062i	1.16263	−	0.613198i
$378$		0			0
$379$	−10.1831	+	10.1831i	−0.523070	+	0.523070i	−0.918497	−	0.395427i	$-0.870596\pi$
$379$	−10.1831	+	10.1831i	−0.523070	+	0.523070i	0.395427	+	0.918497i	$0.370596\pi$
$380$		0			0
$381$	−4.01202			−0.205542
$382$		0			0
$383$	−22.9472	−	22.9472i	−1.17255	−	1.17255i	−0.981601	−	0.190945i	$-0.938845\pi$
$383$	−22.9472	−	22.9472i	−1.17255	−	1.17255i	−0.190945	−	0.981601i	$-0.561155\pi$
$384$		0			0
$385$	1.54428	+	1.54428i	0.0787037	+	0.0787037i
$386$		0			0
$387$		−	4.27983i		−	0.217556i
$388$		0			0
$389$	3.30485			0.167563			0.0837813	−	0.996484i	$-0.473300\pi$
$389$	3.30485			0.167563			0.0837813	+	0.996484i	$0.473300\pi$
$390$		0			0
$391$		−	46.6428i		−	2.35883i
$392$		0			0
$393$	−1.93969			−0.0978444
$394$		0			0
$395$	−2.37712	+	2.37712i	−0.119606	+	0.119606i
$396$		0			0
$397$	3.86083	−	3.86083i	0.193769	−	0.193769i	−0.603553	−	0.797323i	$-0.706249\pi$
$397$	3.86083	−	3.86083i	0.193769	−	0.193769i	0.797323	+	0.603553i	$0.206249\pi$
$398$		0			0
$399$			1.80133i			0.0901793i
$400$		0			0
$401$	2.18232	+	2.18232i	0.108980	+	0.108980i	0.759494	−	0.650514i	$-0.225447\pi$
$401$	2.18232	+	2.18232i	0.108980	+	0.108980i	−0.650514	+	0.759494i	$0.725447\pi$
$402$		0			0
$403$	1.25747	−	4.06431i	0.0626392	−	0.202458i
$404$		0			0
$405$	−0.220561	−	0.220561i	−0.0109597	−	0.0109597i
$406$		0			0
$407$	33.0432			1.63789
$408$		0			0
$409$	11.5798	−	11.5798i	0.572584	−	0.572584i	−0.360266	−	0.932850i	$-0.617314\pi$
$409$	11.5798	−	11.5798i	0.572584	−	0.572584i	0.932850	+	0.360266i	$0.117314\pi$
$410$		0			0
$411$	−6.89207	−	6.89207i	−0.339961	−	0.339961i
$412$		0			0
$413$	6.09040			0.299689
$414$		0			0
$415$	−2.42212			−0.118897
$416$		0			0
$417$	14.6624			0.718021
$418$		0			0
$419$	12.6793			0.619426			0.309713	−	0.950830i	$-0.399767\pi$
$419$	12.6793			0.619426			0.309713	+	0.950830i	$0.399767\pi$
$420$		0			0
$421$	1.01585	+	1.01585i	0.0495097	+	0.0495097i	0.731428	−	0.681919i	$-0.238854\pi$
$421$	1.01585	+	1.01585i	0.0495097	+	0.0495097i	−0.681919	+	0.731428i	$0.738854\pi$
$422$		0			0
$423$	−6.33808	+	6.33808i	−0.308168	+	0.308168i
$424$		0			0
$425$	−26.5080			−1.28583
$426$		0			0
$427$	−7.34969	−	7.34969i	−0.355676	−	0.355676i
$428$		0			0
$429$	6.32361	−	20.4387i	0.305307	−	0.986788i
$430$		0			0
$431$	−10.4063	−	10.4063i	−0.501255	−	0.501255i	0.410573	−	0.911828i	$-0.365329\pi$
$431$	−10.4063	−	10.4063i	−0.501255	−	0.501255i	−0.911828	+	0.410573i	$0.865329\pi$
$432$		0			0
$433$		−	10.0791i		−	0.484373i	−0.970230	−	0.242186i	$-0.922135\pi$
$433$		−	10.0791i		−	0.484373i	0.970230	−	0.242186i	$-0.0778646\pi$
$434$		0			0
$435$	−1.56122	+	1.56122i	−0.0748547	+	0.0748547i
$436$		0			0
$437$	−9.31229	+	9.31229i	−0.445467	+	0.445467i
$438$		0			0
$439$	36.1431			1.72501			0.862507	−	0.506045i	$-0.168893\pi$
$439$	36.1431			1.72501			0.862507	+	0.506045i	$0.168893\pi$
$440$		0			0
$441$			5.60771i			0.267034i
$442$		0			0
$443$	−13.7451			−0.653049			−0.326525	−	0.945189i	$-0.605878\pi$
$443$	−13.7451			−0.653049			−0.326525	+	0.945189i	$0.605878\pi$
$444$		0			0
$445$			1.02888i			0.0487734i
$446$		0			0
$447$	0.971968	+	0.971968i	0.0459725	+	0.0459725i
$448$		0			0
$449$	−16.4989	−	16.4989i	−0.778632	−	0.778632i	0.200967	−	0.979598i	$-0.435592\pi$
$449$	−16.4989	−	16.4989i	−0.778632	−	0.778632i	−0.979598	+	0.200967i	$0.935592\pi$
$450$		0			0
$451$	−64.4654			−3.03556
$452$		0			0
$453$	−8.49241	+	8.49241i	−0.399008	+	0.399008i
$454$		0			0
$455$	−0.619077	−	1.17378i	−0.0290228	−	0.0550274i
$456$		0			0
$457$	8.32291	−	8.32291i	0.389329	−	0.389329i	−0.485119	−	0.874448i	$-0.661224\pi$
$457$	8.32291	−	8.32291i	0.389329	−	0.389329i	0.874448	+	0.485119i	$0.161224\pi$
$458$		0			0
$459$		−	5.40681i		−	0.252368i
$460$		0			0
$461$	−1.06284	−	1.06284i	−0.0495014	−	0.0495014i	0.681923	−	0.731424i	$-0.261144\pi$
$461$	−1.06284	−	1.06284i	−0.0495014	−	0.0495014i	−0.731424	+	0.681923i	$0.761144\pi$
$462$		0			0
$463$	21.2018	−	21.2018i	0.985332	−	0.985332i	−0.0145623	−	0.999894i	$-0.504636\pi$
$463$	21.2018	−	21.2018i	0.985332	−	0.985332i	0.999894	+	0.0145623i	$0.00463550\pi$
$464$		0			0
$465$			0.368051i			0.0170680i
$466$		0			0
$467$		−	39.5564i		−	1.83045i	−0.402942	−	0.915226i	$-0.632012\pi$
$467$		−	39.5564i		−	1.83045i	0.402942	−	0.915226i	$-0.367988\pi$
$468$		0			0
$469$			5.34046i			0.246600i
$470$		0			0
$471$		−	4.57470i		−	0.210791i
$472$		0			0
$473$	−17.9574	+	17.9574i	−0.825682	+	0.825682i
$474$		0			0
$475$	5.29235	+	5.29235i	0.242830	+	0.242830i
$476$		0			0
$477$		−	0.517929i		−	0.0237144i
$478$		0			0
$479$	−16.4037	+	16.4037i	−0.749502	+	0.749502i	−0.974386	−	0.224883i	$-0.927800\pi$
$479$	−16.4037	+	16.4037i	−0.749502	+	0.749502i	0.224883	+	0.974386i	$0.427800\pi$
$480$		0			0
$481$	−19.1810	−	5.93449i	−0.874579	−	0.270590i
$482$		0			0
$483$	7.19771	−	7.19771i	0.327507	−	0.327507i
$484$		0			0
$485$	0.750703			0.0340877
$486$		0			0
$487$	−17.5252	−	17.5252i	−0.794140	−	0.794140i	0.188024	−	0.982164i	$-0.439792\pi$
$487$	−17.5252	−	17.5252i	−0.794140	−	0.794140i	−0.982164	+	0.188024i	$0.939792\pi$
$488$		0			0
$489$	12.5646	+	12.5646i	0.568189	+	0.568189i
$490$		0			0
$491$		−	6.62564i		−	0.299011i	−0.988761	−	0.149506i	$-0.952232\pi$
$491$		−	6.62564i		−	0.299011i	0.988761	−	0.149506i	$-0.0477682\pi$
$492$		0			0
$493$	−38.2716			−1.72367
$494$		0			0
$495$			1.85087i			0.0831902i
$496$		0			0
$497$	15.4540			0.693206
$498$		0			0
$499$	16.3729	−	16.3729i	0.732954	−	0.732954i	−0.238250	−	0.971204i	$-0.576574\pi$
$499$	16.3729	−	16.3729i	0.732954	−	0.732954i	0.971204	+	0.238250i	$0.0765738\pi$
$500$		0			0
$501$	−0.619886	+	0.619886i	−0.0276945	+	0.0276945i
$502$		0			0
$503$			4.36527i			0.194638i	0.995253	+	0.0973189i	$0.0310267\pi$
$503$			4.36527i			0.194638i	−0.995253	+	0.0973189i	$0.968973\pi$
$504$		0			0
$505$	−2.91091	−	2.91091i	−0.129534	−	0.129534i
$506$		0			0
$507$	−7.34149	+	10.7286i	−0.326047	+	0.476473i
$508$		0			0
$509$	11.4086	+	11.4086i	0.505677	+	0.505677i	0.913196	−	0.407520i	$-0.133606\pi$
$509$	11.4086	+	11.4086i	0.505677	+	0.505677i	−0.407520	+	0.913196i	$0.633606\pi$
$510$		0			0
$511$	−2.84515			−0.125862
$512$		0			0
$513$	−1.07948	+	1.07948i	−0.0476600	+	0.0476600i
$514$		0			0
$515$	1.18077	+	1.18077i	0.0520307	+	0.0520307i
$516$		0			0
$517$	53.1869			2.33916
$518$		0			0
$519$	−24.0873			−1.05731
$520$		0			0
$521$	4.24982			0.186188			0.0930939	−	0.995657i	$-0.470324\pi$
$521$	4.24982			0.186188			0.0930939	+	0.995657i	$0.470324\pi$
$522$		0			0
$523$	30.3472			1.32699			0.663495	−	0.748181i	$-0.269072\pi$
$523$	30.3472			1.32699			0.663495	+	0.748181i	$0.269072\pi$
$524$		0			0
$525$	−4.09059	−	4.09059i	−0.178528	−	0.178528i
$526$		0			0
$527$	−4.51119	+	4.51119i	−0.196511	+	0.196511i
$528$		0			0
$529$	51.4196			2.23563
$530$		0			0
$531$	3.64977	+	3.64977i	0.158387	+	0.158387i
$532$		0			0
$533$	37.4210	+	11.5779i	1.62089	+	0.501493i
$534$		0			0
$535$	1.83980	+	1.83980i	0.0795417	+	0.0795417i
$536$		0			0
$537$		−	7.74133i		−	0.334063i
$538$		0			0
$539$	23.5289	−	23.5289i	1.01346	−	1.01346i
$540$		0			0
$541$	−5.50895	+	5.50895i	−0.236848	+	0.236848i	−0.815544	−	0.578695i	$-0.803562\pi$
$541$	−5.50895	+	5.50895i	−0.236848	+	0.236848i	0.578695	+	0.815544i	$0.303562\pi$
$542$		0			0
$543$	−1.87145			−0.0803115
$544$		0			0
$545$		−	4.44760i		−	0.190514i
$546$		0			0
$547$	29.4202			1.25792			0.628958	−	0.777439i	$-0.283482\pi$
$547$	29.4202			1.25792			0.628958	+	0.777439i	$0.283482\pi$
$548$		0			0
$549$		−	8.80884i		−	0.375952i
$550$		0			0
$551$	7.64097	+	7.64097i	0.325516	+	0.325516i
$552$		0			0
$553$	−8.99238	−	8.99238i	−0.382395	−	0.382395i
$554$		0			0
$555$	1.73698			0.0737305
$556$		0			0
$557$	0.751379	−	0.751379i	0.0318369	−	0.0318369i	−0.691009	−	0.722846i	$-0.742834\pi$
$557$	0.751379	−	0.751379i	0.0318369	−	0.0318369i	0.722846	+	0.691009i	$0.242834\pi$
$558$		0			0
$559$	13.6491	−	7.19884i	0.577294	−	0.304479i
$560$		0			0
$561$	−22.6860	+	22.6860i	−0.957803	+	0.957803i
$562$		0			0
$563$			28.4216i			1.19783i	0.800813	+	0.598914i	$0.204401\pi$
$563$			28.4216i			1.19783i	−0.800813	+	0.598914i	$0.795599\pi$
$564$		0			0
$565$	1.31397	+	1.31397i	0.0552790	+	0.0552790i
$566$		0			0
$567$	0.834354	−	0.834354i	0.0350396	−	0.0350396i
$568$		0			0
$569$		−	6.96879i		−	0.292147i	−0.989274	−	0.146073i	$-0.953336\pi$
$569$		−	6.96879i		−	0.292147i	0.989274	−	0.146073i	$-0.0466636\pi$
$570$		0			0
$571$		−	38.0937i		−	1.59417i	−0.603866	−	0.797086i	$-0.706374\pi$
$571$		−	38.0937i		−	1.59417i	0.603866	−	0.797086i	$-0.293626\pi$
$572$		0			0
$573$			8.54621i			0.357023i
$574$		0			0
$575$		−	42.2941i		−	1.76378i
$576$		0			0
$577$	19.0751	−	19.0751i	0.794106	−	0.794106i	−0.188053	−	0.982159i	$-0.560218\pi$
$577$	19.0751	−	19.0751i	0.794106	−	0.794106i	0.982159	+	0.188053i	$0.0602176\pi$
$578$		0			0
$579$	10.4304	+	10.4304i	0.433472	+	0.433472i
$580$		0			0
$581$		−	9.16258i		−	0.380128i
$582$		0			0
$583$	−2.17314	+	2.17314i	−0.0900022	+	0.0900022i
$584$		0			0
$585$	0.332412	−	1.07440i	0.0137435	−	0.0444208i
$586$		0			0
$587$	11.3273	−	11.3273i	0.467529	−	0.467529i	−0.433584	−	0.901113i	$-0.642751\pi$
$587$	11.3273	−	11.3273i	0.467529	−	0.467529i	0.901113	+	0.433584i	$0.142751\pi$
$588$		0			0
$589$	1.80133			0.0742225
$590$		0			0
$591$	17.3971	+	17.3971i	0.715621	+	0.715621i
$592$		0			0
$593$	−29.6899	−	29.6899i	−1.21922	−	1.21922i	−0.967907	−	0.251310i	$-0.919139\pi$
$593$	−29.6899	−	29.6899i	−1.21922	−	1.21922i	−0.251310	−	0.967907i	$-0.580861\pi$
$594$		0			0
$595$			1.98998i			0.0815814i
$596$		0			0
$597$	−3.64770			−0.149291
$598$		0			0
$599$		−	20.7462i		−	0.847666i	−0.905740	−	0.423833i	$-0.860684\pi$
$599$		−	20.7462i		−	0.847666i	0.905740	−	0.423833i	$-0.139316\pi$
$600$		0			0
$601$	−26.2716			−1.07164			−0.535819	−	0.844333i	$-0.679997\pi$
$601$	−26.2716			−1.07164			−0.535819	+	0.844333i	$0.679997\pi$
$602$		0			0
$603$	−3.20036	+	3.20036i	−0.130329	+	0.130329i
$604$		0			0
$605$	5.33973	−	5.33973i	0.217091	−	0.217091i
$606$		0			0
$607$			6.01885i			0.244297i	0.992512	+	0.122149i	$0.0389785\pi$
$607$			6.01885i			0.244297i	−0.992512	+	0.122149i	$0.961022\pi$
$608$		0			0
$609$	−5.90590	−	5.90590i	−0.239319	−	0.239319i
$610$		0			0
$611$	−30.8741	−	9.55226i	−1.24903	−	0.386443i
$612$		0			0
$613$	25.1655	+	25.1655i	1.01642	+	1.01642i	0.999863	+	0.0165605i	$0.00527161\pi$
$613$	25.1655	+	25.1655i	1.01642	+	1.01642i	0.0165605	+	0.999863i	$0.494728\pi$
$614$		0			0
$615$	−3.38874			−0.136647
$616$		0			0
$617$	−1.39230	+	1.39230i	−0.0560518	+	0.0560518i	−0.734577	−	0.678525i	$-0.762619\pi$
$617$	−1.39230	+	1.39230i	−0.0560518	+	0.0560518i	0.678525	+	0.734577i	$0.262619\pi$
$618$		0			0
$619$	−25.8695	−	25.8695i	−1.03978	−	1.03978i	−0.999175	−	0.0406091i	$-0.987070\pi$
$619$	−25.8695	−	25.8695i	−1.03978	−	1.03978i	−0.0406091	−	0.999175i	$-0.512930\pi$
$620$		0			0
$621$	8.62668			0.346177
$622$		0			0
$623$	−3.89212			−0.155934
$624$		0			0
$625$	−23.5501			−0.942002
$626$		0			0
$627$	9.05857			0.361764
$628$		0			0
$629$	21.2900	+	21.2900i	0.848889	+	0.848889i
$630$		0			0
$631$	−4.75571	+	4.75571i	−0.189322	+	0.189322i	−0.795403	−	0.606081i	$-0.792741\pi$
$631$	−4.75571	+	4.75571i	−0.189322	+	0.189322i	0.606081	+	0.795403i	$0.292741\pi$
$632$		0			0
$633$	−0.114235			−0.00454043
$634$		0			0
$635$	0.884893	+	0.884893i	0.0351159	+	0.0351159i
$636$		0			0
$637$	−17.8839	+	9.43238i	−0.708585	+	0.373725i
$638$		0			0
$639$	9.26104	+	9.26104i	0.366361	+	0.366361i
$640$		0			0
$641$			31.9180i			1.26068i	0.776317	+	0.630342i	$0.217085\pi$
$641$			31.9180i			1.26068i	−0.776317	+	0.630342i	$0.782915\pi$
$642$		0			0
$643$	26.6316	−	26.6316i	1.05025	−	1.05025i	0.0515808	−	0.998669i	$-0.483574\pi$
$643$	26.6316	−	26.6316i	1.05025	−	1.05025i	0.998669	−	0.0515808i	$-0.0164260\pi$
$644$		0			0
$645$	−0.943962	+	0.943962i	−0.0371685	+	0.0371685i
$646$		0			0
$647$	13.5346			0.532100			0.266050	−	0.963959i	$-0.414281\pi$
$647$	13.5346			0.532100			0.266050	+	0.963959i	$0.414281\pi$
$648$		0			0
$649$		−	30.6275i		−	1.20224i
$650$		0			0
$651$	−1.39229			−0.0545683
$652$		0			0
$653$		−	17.7853i		−	0.695995i	−0.937496	−	0.347997i	$-0.886862\pi$
$653$		−	17.7853i		−	0.695995i	0.937496	−	0.347997i	$-0.113138\pi$
$654$		0			0
$655$	0.427819	+	0.427819i	0.0167163	+	0.0167163i
$656$		0			0
$657$	−1.70500	−	1.70500i	−0.0665184	−	0.0665184i
$658$		0			0
$659$	15.9755			0.622316			0.311158	−	0.950358i	$-0.399283\pi$
$659$	15.9755			0.622316			0.311158	+	0.950358i	$0.399283\pi$
$660$		0			0
$661$	23.6975	−	23.6975i	0.921725	−	0.921725i	−0.0754259	−	0.997151i	$-0.524032\pi$
$661$	23.6975	−	23.6975i	0.921725	−	0.921725i	0.997151	+	0.0754259i	$0.0240316\pi$
$662$		0			0
$663$	17.2432	−	9.09446i	0.669669	−	0.353200i
$664$		0			0
$665$	0.397303	−	0.397303i	0.0154067	−	0.0154067i
$666$		0			0
$667$		−	61.0631i		−	2.36437i
$668$		0			0
$669$	13.3225	+	13.3225i	0.515076	+	0.515076i
$670$		0			0
$671$	−36.9603	+	36.9603i	−1.42684	+	1.42684i
$672$		0			0
$673$		−	26.0065i		−	1.00248i	−0.865310	−	0.501238i	$-0.832878\pi$
$673$		−	26.0065i		−	1.00248i	0.865310	−	0.501238i	$-0.167122\pi$
$674$		0			0
$675$		−	4.90271i		−	0.188705i
$676$		0			0
$677$		−	24.0614i		−	0.924756i	−0.886683	−	0.462378i	$-0.846996\pi$
$677$		−	24.0614i		−	0.924756i	0.886683	−	0.462378i	$-0.153004\pi$
$678$		0			0
$679$			2.83982i			0.108982i
$680$		0			0
$681$	4.69172	−	4.69172i	0.179787	−	0.179787i
$682$		0			0
$683$	−13.4750	−	13.4750i	−0.515606	−	0.515606i	0.400633	−	0.916239i	$-0.368790\pi$
$683$	−13.4750	−	13.4750i	−0.515606	−	0.515606i	−0.916239	+	0.400633i	$0.868790\pi$
$684$		0			0
$685$			3.04024i			0.116162i
$686$		0			0
$687$	−7.56068	+	7.56068i	−0.288458	+	0.288458i
$688$		0			0
$689$	1.65176	−	0.871178i	0.0629270	−	0.0331892i
$690$		0			0
$691$	0.330206	−	0.330206i	0.0125616	−	0.0125616i	−0.700798	−	0.713360i	$-0.747173\pi$
$691$	0.330206	−	0.330206i	0.0125616	−	0.0125616i	0.713360	+	0.700798i	$0.247173\pi$
$692$		0			0
$693$	−7.00160			−0.265969
$694$		0			0
$695$	−3.23395	−	3.23395i	−0.122671	−	0.122671i
$696$		0			0
$697$	−41.5356	−	41.5356i	−1.57327	−	1.57327i
$698$		0			0
$699$			5.14059i			0.194435i
$700$		0			0
$701$	−42.8348			−1.61785			−0.808924	−	0.587913i	$-0.799950\pi$
$701$	−42.8348			−1.61785			−0.808924	+	0.587913i	$0.799950\pi$
$702$		0			0
$703$		−	8.50116i		−	0.320627i
$704$		0			0
$705$	2.79586			0.105298
$706$		0			0
$707$	11.0116	−	11.0116i	0.414134	−	0.414134i
$708$		0			0
$709$	29.6260	−	29.6260i	1.11263	−	1.11263i	0.119834	−	0.992794i	$-0.461764\pi$
$709$	29.6260	−	29.6260i	1.11263	−	1.11263i	0.992794	−	0.119834i	$-0.0382361\pi$
$710$		0			0
$711$		−	10.7776i		−	0.404193i
$712$		0			0
$713$	−7.19771	−	7.19771i	−0.269556	−	0.269556i
$714$		0			0
$715$	−5.90271	+	3.11323i	−0.220749	+	0.116428i
$716$		0			0
$717$	−5.22603	−	5.22603i	−0.195170	−	0.195170i
$718$		0			0
$719$	48.0116			1.79053			0.895265	−	0.445535i	$-0.146986\pi$
$719$	48.0116			1.79053			0.895265	+	0.445535i	$0.146986\pi$
$720$		0			0
$721$	−4.46669	+	4.46669i	−0.166348	+	0.166348i
$722$		0			0
$723$	−8.31859	−	8.31859i	−0.309372	−	0.309372i
$724$		0			0
$725$	−34.7033			−1.28885
$726$		0			0
$727$	−42.2954			−1.56865			−0.784325	−	0.620350i	$-0.786990\pi$
$727$	−42.2954			−1.56865			−0.784325	+	0.620350i	$0.786990\pi$
$728$		0			0
$729$	1.00000			0.0370370
$730$		0			0
$731$	−23.1402			−0.855872
$732$		0			0
$733$	16.2927	+	16.2927i	0.601785	+	0.601785i	0.940786	−	0.339001i	$-0.110089\pi$
$733$	16.2927	+	16.2927i	0.601785	+	0.601785i	−0.339001	+	0.940786i	$0.610089\pi$
$734$		0			0
$735$	1.23684	−	1.23684i	0.0456215	−	0.0456215i
$736$		0			0
$737$	26.8562			0.989262
$738$		0			0
$739$	−7.34780	−	7.34780i	−0.270293	−	0.270293i	0.558925	−	0.829218i	$-0.311214\pi$
$739$	−7.34780	−	7.34780i	−0.270293	−	0.270293i	−0.829218	+	0.558925i	$0.811214\pi$
$740$		0			0
$741$	−5.25834	−	1.62690i	−0.193170	−	0.0597657i
$742$		0			0
$743$	26.6519	+	26.6519i	0.977764	+	0.977764i	0.999758	−	0.0219938i	$-0.00700142\pi$
$743$	26.6519	+	26.6519i	0.977764	+	0.977764i	−0.0219938	+	0.999758i	$0.507001\pi$
$744$		0			0
$745$		−	0.428756i		−	0.0157084i
$746$		0			0
$747$	5.49082	−	5.49082i	0.200899	−	0.200899i
$748$		0			0
$749$	−6.95976	+	6.95976i	−0.254304	+	0.254304i
$750$		0			0
$751$	42.4302			1.54830			0.774149	−	0.633003i	$-0.218178\pi$
$751$	42.4302			1.54830			0.774149	+	0.633003i	$0.218178\pi$
$752$		0			0
$753$		−	15.2053i		−	0.554110i
$754$		0			0
$755$	3.74618			0.136338
$756$		0			0
$757$			22.1367i			0.804573i	0.915514	+	0.402287i	$0.131784\pi$
$757$			22.1367i			0.804573i	−0.915514	+	0.402287i	$0.868216\pi$
$758$		0			0
$759$	−36.1960	−	36.1960i	−1.31383	−	1.31383i
$760$		0			0
$761$	23.0586	+	23.0586i	0.835872	+	0.835872i	0.988313	−	0.152440i	$-0.0487131\pi$
$761$	23.0586	+	23.0586i	0.835872	+	0.835872i	−0.152440	+	0.988313i	$0.548713\pi$
$762$		0			0
$763$	16.8247			0.609096
$764$		0			0
$765$	−1.19253	+	1.19253i	−0.0431160	+	0.0431160i
$766$		0			0
$767$	−5.50065	+	17.7788i	−0.198617	+	0.641954i
$768$		0			0
$769$	6.73359	−	6.73359i	0.242820	−	0.242820i	−0.575196	−	0.818016i	$-0.695074\pi$
$769$	6.73359	−	6.73359i	0.242820	−	0.242820i	0.818016	+	0.575196i	$0.195074\pi$
$770$		0			0
$771$			26.5978i			0.957895i
$772$		0			0
$773$	−2.09870	−	2.09870i	−0.0754849	−	0.0754849i	0.668356	−	0.743841i	$-0.266998\pi$
$773$	−2.09870	−	2.09870i	−0.0754849	−	0.0754849i	−0.743841	+	0.668356i	$0.766998\pi$
$774$		0			0
$775$	−4.09059	+	4.09059i	−0.146938	+	0.146938i
$776$		0			0
$777$			6.57077i			0.235725i
$778$		0			0
$779$			16.5853i			0.594229i
$780$		0			0
$781$		−	77.7153i		−	2.78087i
$782$		0			0
$783$		−	7.07841i		−	0.252962i
$784$		0			0
$785$	−1.00900	+	1.00900i	−0.0360127	+	0.0360127i
$786$		0			0
$787$	−14.9629	−	14.9629i	−0.533371	−	0.533371i	0.388203	−	0.921574i	$-0.373096\pi$
$787$	−14.9629	−	14.9629i	−0.533371	−	0.533371i	−0.921574	+	0.388203i	$0.873096\pi$
$788$		0			0
$789$			15.1896i			0.540766i
$790$		0			0
$791$	−4.97058	+	4.97058i	−0.176733	+	0.176733i
$792$		0			0
$793$	28.0928	−	14.8168i	0.997604	−	0.526160i
$794$		0			0
$795$	−0.114235	+	0.114235i	−0.00405149	+	0.00405149i
$796$		0			0
$797$	44.6730			1.58240			0.791199	−	0.611559i	$-0.209457\pi$
$797$	44.6730			1.58240			0.791199	+	0.611559i	$0.209457\pi$
$798$		0			0
$799$	34.2688	+	34.2688i	1.21234	+	1.21234i
$800$		0			0
$801$	−2.33241	−	2.33241i	−0.0824117	−	0.0824117i
$802$		0			0
$803$			14.3077i			0.504909i
$804$		0			0
$805$	−3.17506			−0.111906
$806$		0			0
$807$		−	0.531993i		−	0.0187270i
$808$		0			0
$809$	37.1270			1.30532			0.652658	−	0.757653i	$-0.273654\pi$
$809$	37.1270			1.30532			0.652658	+	0.757653i	$0.273654\pi$
$810$		0			0
$811$	−11.4240	+	11.4240i	−0.401150	+	0.401150i	−0.878638	−	0.477488i	$-0.841547\pi$
$811$	−11.4240	+	11.4240i	−0.401150	+	0.401150i	0.477488	+	0.878638i	$0.341547\pi$
$812$		0			0
$813$	5.60569	−	5.60569i	0.196600	−	0.196600i
$814$		0			0
$815$		−	5.54249i		−	0.194145i
$816$		0			0
$817$	4.61997	+	4.61997i	0.161632	+	0.161632i
$818$		0			0
$819$	4.06431	+	1.25747i	0.142018	+	0.0439397i
$820$		0			0
$821$	7.65039	+	7.65039i	0.267001	+	0.267001i	0.827890	−	0.560890i	$-0.189541\pi$
$821$	7.65039	+	7.65039i	0.267001	+	0.267001i	−0.560890	+	0.827890i	$0.689541\pi$
$822$		0			0
$823$	−7.76748			−0.270757			−0.135379	−	0.990794i	$-0.543225\pi$
$823$	−7.76748			−0.270757			−0.135379	+	0.990794i	$0.543225\pi$
$824$		0			0
$825$	−20.5709	+	20.5709i	−0.716186	+	0.716186i
$826$		0			0
$827$	22.9537	+	22.9537i	0.798177	+	0.798177i	0.982808	−	0.184631i	$-0.0591090\pi$
$827$	22.9537	+	22.9537i	0.798177	+	0.798177i	−0.184631	+	0.982808i	$0.559109\pi$
$828$		0			0
$829$	−3.99393			−0.138715			−0.0693574	−	0.997592i	$-0.522095\pi$
$829$	−3.99393			−0.138715			−0.0693574	+	0.997592i	$0.522095\pi$
$830$		0			0
$831$	2.37287			0.0823141
$832$		0			0
$833$	30.3198			1.05052
$834$		0			0
$835$	0.273445			0.00946295
$836$		0			0
$837$	−0.834354	−	0.834354i	−0.0288395	−	0.0288395i
$838$		0			0
$839$	−8.50102	+	8.50102i	−0.293488	+	0.293488i	−0.838456	−	0.544969i	$-0.816542\pi$
$839$	−8.50102	+	8.50102i	−0.293488	+	0.293488i	0.544969	+	0.838456i	$0.316542\pi$
$840$		0			0
$841$	−21.1038			−0.727719
$842$		0			0
$843$	−2.55059	−	2.55059i	−0.0878468	−	0.0878468i
$844$		0			0
$845$	3.98555	−	0.747061i	0.137107	−	0.0256997i
$846$		0			0
$847$	20.1995	+	20.1995i	0.694064	+	0.694064i
$848$		0			0
$849$			12.1486i			0.416937i
$850$		0			0
$851$	−33.9687	+	33.9687i	−1.16443	+	1.16443i
$852$		0			0
$853$	−37.7172	+	37.7172i	−1.29141	+	1.29141i	−0.357497	+	0.933914i	$0.616370\pi$
$853$	−37.7172	+	37.7172i	−1.29141	+	1.29141i	−0.933914	+	0.357497i	$0.883630\pi$
$854$		0			0
$855$	0.476180			0.0162850
$856$		0			0
$857$			41.7335i			1.42559i	0.701373	+	0.712794i	$0.252571\pi$
$857$			41.7335i			1.42559i	−0.701373	+	0.712794i	$0.747429\pi$
$858$		0			0
$859$	11.0618			0.377422			0.188711	−	0.982033i	$-0.439569\pi$
$859$	11.0618			0.377422			0.188711	+	0.982033i	$0.439569\pi$
$860$		0			0
$861$		−	12.8192i		−	0.436877i
$862$		0			0
$863$	−1.63275	−	1.63275i	−0.0555794	−	0.0555794i	0.678771	−	0.734350i	$-0.262513\pi$
$863$	−1.63275	−	1.63275i	−0.0555794	−	0.0555794i	−0.734350	+	0.678771i	$0.762513\pi$
$864$		0			0
$865$	5.31271	+	5.31271i	0.180637	+	0.180637i
$866$		0			0
$867$	−12.2336			−0.415473
$868$		0			0
$869$	−45.2211	+	45.2211i	−1.53402	+	1.53402i
$870$		0			0
$871$	−15.5896	−	4.82332i	−0.528232	−	0.163432i
$872$		0			0
$873$	−1.70181	+	1.70181i	−0.0575974	+	0.0575974i
$874$		0			0
$875$			3.64471i			0.123214i
$876$		0			0
$877$	−6.65378	−	6.65378i	−0.224682	−	0.224682i	0.585785	−	0.810467i	$-0.300786\pi$
$877$	−6.65378	−	6.65378i	−0.224682	−	0.224682i	−0.810467	+	0.585785i	$0.800786\pi$
$878$		0			0
$879$	−6.58440	+	6.58440i	−0.222086	+	0.222086i
$880$		0			0
$881$		−	38.0472i		−	1.28184i	−0.767607	−	0.640921i	$-0.778553\pi$
$881$		−	38.0472i		−	1.28184i	0.767607	−	0.640921i	$-0.221447\pi$
$882$		0			0
$883$		−	15.0006i		−	0.504812i	−0.967621	−	0.252406i	$-0.918778\pi$
$883$		−	15.0006i		−	0.504812i	0.967621	−	0.252406i	$-0.0812218\pi$
$884$		0			0
$885$		−	1.60999i		−	0.0541193i
$886$		0			0
$887$		−	7.50537i		−	0.252006i	−0.992030	−	0.126003i	$-0.959785\pi$
$887$		−	7.50537i		−	0.252006i	0.992030	−	0.126003i	$-0.0402148\pi$
$888$		0			0
$889$	−3.34744	+	3.34744i	−0.112270	+	0.112270i
$890$		0			0
$891$	−4.19582	−	4.19582i	−0.140565	−	0.140565i
$892$		0			0
$893$		−	13.6836i		−	0.457905i
$894$		0			0
$895$	−1.70743	+	1.70743i	−0.0570732	+	0.0570732i
$896$		0			0
$897$	14.5104	+	27.5119i	0.484489	+	0.918594i
$898$		0			0
$899$	−5.90590	+	5.90590i	−0.196973	+	0.196973i
$900$		0			0
$901$	−2.80034			−0.0932930
$902$		0			0
$903$	−3.57090	−	3.57090i	−0.118832	−	0.118832i
$904$		0			0
$905$	0.412768	+	0.412768i	0.0137209	+	0.0137209i
$906$		0			0
$907$			46.8891i			1.55693i	0.627690	+	0.778463i	$0.284001\pi$
$907$			46.8891i			1.55693i	−0.627690	+	0.778463i	$0.715999\pi$
$908$		0			0
$909$	13.1978			0.437742
$910$		0			0
$911$		−	46.9106i		−	1.55422i	−0.629366	−	0.777109i	$-0.716685\pi$
$911$		−	46.9106i		−	1.55422i	0.629366	−	0.777109i	$-0.283315\pi$
$912$		0			0
$913$	−46.0770			−1.52492
$914$		0			0
$915$	−1.94288	+	1.94288i	−0.0642297	+	0.0642297i
$916$		0			0
$917$	−1.61839	+	1.61839i	−0.0534439	+	0.0534439i
$918$		0			0
$919$			31.5754i			1.04158i	0.853686	+	0.520788i	$0.174362\pi$
$919$			31.5754i			1.04158i	−0.853686	+	0.520788i	$0.825638\pi$
$920$		0			0
$921$	11.1310	+	11.1310i	0.366778	+	0.366778i
$922$		0			0
$923$	−13.9575	+	45.1124i	−0.459417	+	1.48489i
$924$		0			0
$925$	19.3051	+	19.3051i	0.634747	+	0.634747i
$926$		0			0
$927$	−5.35347			−0.175831
$928$		0			0
$929$	8.53608	−	8.53608i	0.280060	−	0.280060i	−0.553073	−	0.833133i	$-0.686545\pi$
$929$	8.53608	−	8.53608i	0.280060	−	0.280060i	0.833133	+	0.553073i	$0.186545\pi$
$930$		0			0
$931$	−6.05338	−	6.05338i	−0.198392	−	0.198392i
$932$		0			0
$933$	2.10922			0.0690527
$934$		0			0
$935$	10.0073			0.327273
$936$		0			0
$937$	33.0280			1.07898			0.539490	−	0.841992i	$-0.318617\pi$
$937$	33.0280			1.07898			0.539490	+	0.841992i	$0.318617\pi$
$938$		0			0
$939$	23.5722			0.769249
$940$		0			0
$941$	−27.1309	−	27.1309i	−0.884443	−	0.884443i	0.109539	−	0.993982i	$-0.465062\pi$
$941$	−27.1309	−	27.1309i	−0.884443	−	0.884443i	−0.993982	+	0.109539i	$0.965062\pi$
$942$		0			0
$943$	66.2710	−	66.2710i	2.15808	−	2.15808i
$944$		0			0
$945$	−0.368051			−0.0119727
$946$		0			0
$947$	−2.01437	−	2.01437i	−0.0654582	−	0.0654582i	0.673620	−	0.739078i	$-0.264739\pi$
$947$	−2.01437	−	2.01437i	−0.0654582	−	0.0654582i	−0.739078	+	0.673620i	$0.764739\pi$
$948$		0			0
$949$	2.56964	−	8.30539i	0.0834141	−	0.269605i
$950$		0			0
$951$	−17.8629	−	17.8629i	−0.579244	−	0.579244i
$952$		0			0
$953$		−	27.6272i		−	0.894934i	−0.894300	−	0.447467i	$-0.852326\pi$
$953$		−	27.6272i		−	0.894934i	0.894300	−	0.447467i	$-0.147674\pi$
$954$		0			0
$955$	1.88496	−	1.88496i	0.0609958	−	0.0609958i
$956$		0			0
$957$	−29.6997	+	29.6997i	−0.960055	+	0.960055i
$958$		0			0
$959$	−11.5009			−0.371382
$960$		0			0
$961$		−	29.6077i		−	0.955087i
$962$		0			0
$963$	−8.34149			−0.268801
$964$		0			0
$965$		−	4.60107i		−	0.148114i
$966$		0			0
$967$	−16.1148	−	16.1148i	−0.518217	−	0.518217i	0.398815	−	0.917032i	$-0.369422\pi$
$967$	−16.1148	−	16.1148i	−0.518217	−	0.518217i	−0.917032	+	0.398815i	$0.869422\pi$
$968$		0			0
$969$	5.83652	+	5.83652i	0.187496	+	0.187496i
$970$		0			0
$971$	−34.6254			−1.11118			−0.555591	−	0.831456i	$-0.687508\pi$
$971$	−34.6254			−1.11118			−0.555591	+	0.831456i	$0.687508\pi$
$972$		0			0
$973$	12.2336	−	12.2336i	0.392192	−	0.392192i
$974$		0			0
$975$	15.6355	−	8.24654i	0.500737	−	0.264101i
$976$		0			0
$977$	−20.9243	+	20.9243i	−0.669427	+	0.669427i	−0.957583	−	0.288156i	$-0.906958\pi$
$977$	−20.9243	+	20.9243i	−0.669427	+	0.669427i	0.288156	+	0.957583i	$0.406958\pi$
$978$		0			0
$979$			19.5728i			0.625548i
$980$		0			0
$981$	10.0825	+	10.0825i	0.321909	+	0.321909i
$982$		0			0
$983$	1.84906	−	1.84906i	0.0589759	−	0.0589759i	−0.677004	−	0.735980i	$-0.736722\pi$
$983$	1.84906	−	1.84906i	0.0589759	−	0.0589759i	0.735980	+	0.677004i	$0.236722\pi$
$984$		0			0
$985$		−	7.67424i		−	0.244521i
$986$		0			0
$987$			10.5764i			0.336651i
$988$		0			0
$989$		−	36.9207i		−	1.17401i
$990$		0			0
$991$			48.1666i			1.53006i	0.643994	+	0.765031i	$0.277276\pi$
$991$			48.1666i			1.53006i	−0.643994	+	0.765031i	$0.722724\pi$
$992$		0			0
$993$	−6.91280	+	6.91280i	−0.219371	+	0.219371i
$994$		0			0
$995$	0.804540	+	0.804540i	0.0255056	+	0.0255056i
$996$		0			0
$997$		−	21.8116i		−	0.690779i	−0.938459	−	0.345389i	$-0.887747\pi$
$997$		−	21.8116i		−	0.690779i	0.938459	−	0.345389i	$-0.112253\pi$
$998$		0			0
$999$	−3.93764	+	3.93764i	−0.124581	+	0.124581i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1248.2.bb.f.655.6		24
4.3	odd	2		312.2.t.e.187.11	yes	24
8.3	odd	2	inner	1248.2.bb.f.655.7		24
8.5	even	2		312.2.t.e.187.4	✓	24
12.11	even	2		936.2.w.j.811.2		24
13.8	odd	4	inner	1248.2.bb.f.463.7		24
24.5	odd	2		936.2.w.j.811.9		24
52.47	even	4		312.2.t.e.307.4	yes	24
104.21	odd	4		312.2.t.e.307.11	yes	24
104.99	even	4	inner	1248.2.bb.f.463.6		24
156.47	odd	4		936.2.w.j.307.9		24
312.125	even	4		936.2.w.j.307.2		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
312.2.t.e.187.4	✓	24	8.5	even	2
312.2.t.e.187.11	yes	24	4.3	odd	2
312.2.t.e.307.4	yes	24	52.47	even	4
312.2.t.e.307.11	yes	24	104.21	odd	4
936.2.w.j.307.2		24	312.125	even	4
936.2.w.j.307.9		24	156.47	odd	4
936.2.w.j.811.2		24	12.11	even	2
936.2.w.j.811.9		24	24.5	odd	2
1248.2.bb.f.463.6		24	104.99	even	4	inner
1248.2.bb.f.463.7		24	13.8	odd	4	inner
1248.2.bb.f.655.6		24	1.1	even	1	trivial
1248.2.bb.f.655.7		24	8.3	odd	2	inner

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:	\( N \)	\(=\)	\( 1248 = 2^{5} \cdot 3 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1248.bb (of order \(4\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+1.00000 q^{3} +(-0.220561 - 0.220561i) q^{5} +(0.834354 - 0.834354i) q^{7} +1.00000 q^{9} +O(q^{10})\)	\(q+1.00000 q^{3} +(-0.220561 - 0.220561i) q^{5} +(0.834354 - 0.834354i) q^{7} +1.00000 q^{9} +(-4.19582 - 4.19582i) q^{11} +(1.68204 + 3.18916i) q^{13} +(-0.220561 - 0.220561i) q^{15} -5.40681i q^{17} +(-1.07948 + 1.07948i) q^{19} +(0.834354 - 0.834354i) q^{21} +8.62668 q^{23} -4.90271i q^{25} +1.00000 q^{27} -7.07841i q^{29} +(-0.834354 - 0.834354i) q^{31} +(-4.19582 - 4.19582i) q^{33} -0.368051 q^{35} +(-3.93764 + 3.93764i) q^{37} +(1.68204 + 3.18916i) q^{39} +(7.68210 - 7.68210i) q^{41} -4.27983i q^{43} +(-0.220561 - 0.220561i) q^{45} +(-6.33808 + 6.33808i) q^{47} +5.60771i q^{49} -5.40681i q^{51} -0.517929i q^{53} +1.85087i q^{55} +(-1.07948 + 1.07948i) q^{57} +(3.64977 + 3.64977i) q^{59} -8.80884i q^{61} +(0.834354 - 0.834354i) q^{63} +(0.332412 - 1.07440i) q^{65} +(-3.20036 + 3.20036i) q^{67} +8.62668 q^{69} +(9.26104 + 9.26104i) q^{71} +(-1.70500 - 1.70500i) q^{73} -4.90271i q^{75} -7.00160 q^{77} -10.7776i q^{79} +1.00000 q^{81} +(5.49082 - 5.49082i) q^{83} +(-1.19253 + 1.19253i) q^{85} -7.07841i q^{87} +(-2.33241 - 2.33241i) q^{89} +(4.06431 + 1.25747i) q^{91} +(-0.834354 - 0.834354i) q^{93} +0.476180 q^{95} +(-1.70181 + 1.70181i) q^{97} +(-4.19582 - 4.19582i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 24 q^{3} + 24 q^{9}+O(q^{10}) \) 24 * q + 24 * q^3 + 24 * q^9	\( 24 q + 24 q^{3} + 24 q^{9} - 8 q^{11} - 20 q^{19} + 24 q^{27} - 8 q^{33} - 16 q^{35} - 12 q^{41} - 20 q^{57} + 16 q^{59} - 76 q^{65} - 28 q^{67} - 8 q^{73} + 24 q^{81} + 72 q^{83} + 28 q^{89} + 4 q^{91} + 24 q^{97} - 8 q^{99}+O(q^{100}) \) 24 * q + 24 * q^3 + 24 * q^9 - 8 * q^11 - 20 * q^19 + 24 * q^27 - 8 * q^33 - 16 * q^35 - 12 * q^41 - 20 * q^57 + 16 * q^59 - 76 * q^65 - 28 * q^67 - 8 * q^73 + 24 * q^81 + 72 * q^83 + 28 * q^89 + 4 * q^91 + 24 * q^97 - 8 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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