LMFDB - Embedded newform 1040.2.bp.a.287.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1040,2,Mod(287,1040)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1040, base_ring=CyclotomicField(4))

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

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

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

chi := DirichletCharacter("1040.287");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1040 = 2^{4} \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1040.bp (of order $4$, degree $2$, 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:	$8.30444181021$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			287.6
Character	$\chi$	$=$	1040.287
Dual form			1040.2.bp.a.703.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.343801 - 0.343801i) q^{3} +(0.441404 - 2.19207i) q^{5} +(3.35962 - 3.35962i) q^{7} -2.76360i q^{9} +O(q^{10})$	\(q+(-0.343801 - 0.343801i) q^{3} +(0.441404 - 2.19207i) q^{5} +(3.35962 - 3.35962i) q^{7} -2.76360i q^{9} +0.364979i q^{11} +(0.707107 - 0.707107i) q^{13} +(-0.905390 + 0.601880i) q^{15} +(-1.37490 - 1.37490i) q^{17} -2.47969 q^{19} -2.31008 q^{21} +(3.63121 + 3.63121i) q^{23} +(-4.61033 - 1.93517i) q^{25} +(-1.98153 + 1.98153i) q^{27} +0.280570i q^{29} +9.30889i q^{31} +(0.125480 - 0.125480i) q^{33} +(-5.88156 - 8.84745i) q^{35} +(-5.28228 - 5.28228i) q^{37} -0.486208 q^{39} +2.51379 q^{41} +(7.71393 + 7.71393i) q^{43} +(-6.05800 - 1.21986i) q^{45} +(1.27037 - 1.27037i) q^{47} -15.5740i q^{49} +0.945386i q^{51} +(-8.30910 + 8.30910i) q^{53} +(0.800059 + 0.161103i) q^{55} +(0.852519 + 0.852519i) q^{57} -10.1713 q^{59} +7.78207 q^{61} +(-9.28464 - 9.28464i) q^{63} +(-1.23791 - 1.86215i) q^{65} +(6.01075 - 6.01075i) q^{67} -2.49683i q^{69} -15.2512i q^{71} +(5.72201 - 5.72201i) q^{73} +(0.919719 + 2.25035i) q^{75} +(1.22619 + 1.22619i) q^{77} +10.9646 q^{79} -6.92830 q^{81} +(6.23409 + 6.23409i) q^{83} +(-3.62077 + 2.40699i) q^{85} +(0.0964601 - 0.0964601i) q^{87} -9.52909i q^{89} -4.75121i q^{91} +(3.20041 - 3.20041i) q^{93} +(-1.09454 + 5.43564i) q^{95} +(6.96779 + 6.96779i) q^{97} +1.00866 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 8 q^{5}+O(q^{10}) $ 24 * q - 8 * q^5	$ 24 q - 8 q^{5} + 16 q^{17} + 16 q^{21} - 16 q^{25} - 24 q^{33} - 24 q^{37} + 16 q^{41} + 48 q^{45} + 8 q^{53} + 8 q^{57} + 16 q^{61} + 8 q^{73} + 24 q^{77} + 40 q^{81} + 16 q^{85} + 56 q^{93} + 32 q^{97}+O(q^{100}) $ 24 * q - 8 * q^5 + 16 * q^17 + 16 * q^21 - 16 * q^25 - 24 * q^33 - 24 * q^37 + 16 * q^41 + 48 * q^45 + 8 * q^53 + 8 * q^57 + 16 * q^61 + 8 * q^73 + 24 * q^77 + 40 * q^81 + 16 * q^85 + 56 * q^93 + 32 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1040\mathbb{Z}\right)^\times$.

$n$	$261$	$417$	$561$	$911$
$\chi(n)$	$1$	$e\left(\frac{1}{4}\right)$	$1$	$-1$

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
$3$	−0.343801	−	0.343801i	−0.198494	−	0.198494i	0.600860	−	0.799354i	$-0.294825\pi$
$3$	−0.343801	−	0.343801i	−0.198494	−	0.198494i	−0.799354	+	0.600860i	$0.794825\pi$
$4$		0			0
$5$	0.441404	−	2.19207i	0.197402	−	0.980323i
$5$	0.441404	−	2.19207i	0.197402	−	0.980323i
$6$		0			0
$7$	3.35962	−	3.35962i	1.26982	−	1.26982i	0.323632	−	0.946183i	$-0.395096\pi$
$7$	3.35962	−	3.35962i	1.26982	−	1.26982i	0.946183	−	0.323632i	$-0.104904\pi$
$8$		0			0
$9$		−	2.76360i		−	0.921201i
$10$		0			0
$11$			0.364979i			0.110045i	0.998485	+	0.0550227i	$0.0175231\pi$
$11$			0.364979i			0.110045i	−0.998485	+	0.0550227i	$0.982477\pi$
$12$		0			0
$13$	0.707107	−	0.707107i	0.196116	−	0.196116i
$13$	0.707107	−	0.707107i	0.196116	−	0.196116i
$14$		0			0
$15$	−0.905390	+	0.601880i	−0.233771	+	0.155405i
$16$		0			0
$17$	−1.37490	−	1.37490i	−0.333463	−	0.333463i	0.520437	−	0.853900i	$-0.325769\pi$
$17$	−1.37490	−	1.37490i	−0.333463	−	0.333463i	−0.853900	+	0.520437i	$0.825769\pi$
$18$		0			0
$19$	−2.47969			−0.568879			−0.284440	−	0.958694i	$-0.591808\pi$
$19$	−2.47969			−0.568879			−0.284440	+	0.958694i	$0.591808\pi$
$20$		0			0
$21$	−2.31008			−0.504100
$22$		0			0
$23$	3.63121	+	3.63121i	0.757159	+	0.757159i	0.975804	−	0.218645i	$-0.0701637\pi$
$23$	3.63121	+	3.63121i	0.757159	+	0.757159i	−0.218645	+	0.975804i	$0.570164\pi$
$24$		0			0
$25$	−4.61033	−	1.93517i	−0.922065	−	0.387035i
$26$		0			0
$27$	−1.98153	+	1.98153i	−0.381346	+	0.381346i
$28$		0			0
$29$			0.280570i			0.0521005i	0.999661	+	0.0260502i	$0.00829299\pi$
$29$			0.280570i			0.0521005i	−0.999661	+	0.0260502i	$0.991707\pi$
$30$		0			0
$31$			9.30889i			1.67193i	0.548786	+	0.835963i	$0.315090\pi$
$31$			9.30889i			1.67193i	−0.548786	+	0.835963i	$0.684910\pi$
$32$		0			0
$33$	0.125480	−	0.125480i	0.0218433	−	0.0218433i
$34$		0			0
$35$	−5.88156	−	8.84745i	−0.994165	−	1.49549i
$36$		0			0
$37$	−5.28228	−	5.28228i	−0.868402	−	0.868402i	0.123894	−	0.992295i	$-0.460462\pi$
$37$	−5.28228	−	5.28228i	−0.868402	−	0.868402i	−0.992295	+	0.123894i	$0.960462\pi$
$38$		0			0
$39$	−0.486208			−0.0778556
$40$		0			0
$41$	2.51379			0.392588			0.196294	−	0.980545i	$-0.437109\pi$
$41$	2.51379			0.392588			0.196294	+	0.980545i	$0.437109\pi$
$42$		0			0
$43$	7.71393	+	7.71393i	1.17636	+	1.17636i	0.980664	+	0.195700i	$0.0626979\pi$
$43$	7.71393	+	7.71393i	1.17636	+	1.17636i	0.195700	+	0.980664i	$0.437302\pi$
$44$		0			0
$45$	−6.05800	−	1.21986i	−0.903074	−	0.181847i
$46$		0			0
$47$	1.27037	−	1.27037i	0.185302	−	0.185302i	−0.608359	−	0.793662i	$-0.708172\pi$
$47$	1.27037	−	1.27037i	0.185302	−	0.185302i	0.793662	+	0.608359i	$0.208172\pi$
$48$		0			0
$49$		−	15.5740i		−	2.22486i
$50$		0			0
$51$			0.945386i			0.132381i
$52$		0			0
$53$	−8.30910	+	8.30910i	−1.14134	+	1.14134i	−0.153138	+	0.988205i	$0.548938\pi$
$53$	−8.30910	+	8.30910i	−1.14134	+	1.14134i	−0.988205	+	0.153138i	$0.951062\pi$
$54$		0			0
$55$	0.800059	+	0.161103i	0.107880	+	0.0217231i
$56$		0			0
$57$	0.852519	+	0.852519i	0.112919	+	0.112919i
$58$		0			0
$59$	−10.1713			−1.32419			−0.662097	−	0.749418i	$-0.730333\pi$
$59$	−10.1713			−1.32419			−0.662097	+	0.749418i	$0.730333\pi$
$60$		0			0
$61$	7.78207			0.996392			0.498196	−	0.867065i	$-0.333996\pi$
$61$	7.78207			0.996392			0.498196	+	0.867065i	$0.333996\pi$
$62$		0			0
$63$	−9.28464	−	9.28464i	−1.16975	−	1.16975i
$64$		0			0
$65$	−1.23791	−	1.86215i	−0.153543	−	0.230971i
$66$		0			0
$67$	6.01075	−	6.01075i	0.734329	−	0.734329i	−0.237145	−	0.971474i	$-0.576212\pi$
$67$	6.01075	−	6.01075i	0.734329	−	0.734329i	0.971474	+	0.237145i	$0.0762116\pi$
$68$		0			0
$69$		−	2.49683i		−	0.300583i
$70$		0			0
$71$		−	15.2512i		−	1.80999i	−0.425425	−	0.904994i	$-0.639875\pi$
$71$		−	15.2512i		−	1.80999i	0.425425	−	0.904994i	$-0.360125\pi$
$72$		0			0
$73$	5.72201	−	5.72201i	0.669711	−	0.669711i	−0.287938	−	0.957649i	$-0.592970\pi$
$73$	5.72201	−	5.72201i	0.669711	−	0.669711i	0.957649	+	0.287938i	$0.0929698\pi$
$74$		0			0
$75$	0.919719	+	2.25035i	0.106200	+	0.259848i
$76$		0			0
$77$	1.22619	+	1.22619i	0.139737	+	0.139737i
$78$		0			0
$79$	10.9646			1.23361			0.616805	−	0.787116i	$-0.288427\pi$
$79$	10.9646			1.23361			0.616805	+	0.787116i	$0.288427\pi$
$80$		0			0
$81$	−6.92830			−0.769811
$82$		0			0
$83$	6.23409	+	6.23409i	0.684280	+	0.684280i	0.960962	−	0.276681i	$-0.0892346\pi$
$83$	6.23409	+	6.23409i	0.684280	+	0.684280i	−0.276681	+	0.960962i	$0.589235\pi$
$84$		0			0
$85$	−3.62077	+	2.40699i	−0.392728	+	0.261075i
$86$		0			0
$87$	0.0964601	−	0.0964601i	0.0103416	−	0.0103416i
$88$		0			0
$89$		−	9.52909i		−	1.01008i	−0.863095	−	0.505041i	$-0.831477\pi$
$89$		−	9.52909i		−	1.01008i	0.863095	−	0.505041i	$-0.168523\pi$
$90$		0			0
$91$		−	4.75121i		−	0.498063i
$92$		0			0
$93$	3.20041	−	3.20041i	0.331867	−	0.331867i
$94$		0			0
$95$	−1.09454	+	5.43564i	−0.112298	+	0.557685i
$96$		0			0
$97$	6.96779	+	6.96779i	0.707472	+	0.707472i	0.966003	−	0.258531i	$-0.0832384\pi$
$97$	6.96779	+	6.96779i	0.707472	+	0.707472i	−0.258531	+	0.966003i	$0.583238\pi$
$98$		0			0
$99$	1.00866			0.101374
$100$		0			0
$101$	−4.68475			−0.466150			−0.233075	−	0.972459i	$-0.574879\pi$
$101$	−4.68475			−0.466150			−0.233075	+	0.972459i	$0.574879\pi$
$102$		0			0
$103$	−6.19273	−	6.19273i	−0.610188	−	0.610188i	0.332807	−	0.942995i	$-0.392004\pi$
$103$	−6.19273	−	6.19273i	−0.610188	−	0.610188i	−0.942995	+	0.332807i	$0.892004\pi$
$104$		0			0
$105$	−1.01968	+	5.06385i	−0.0995103	+	0.494181i
$106$		0			0
$107$	−9.34202	+	9.34202i	−0.903127	+	0.903127i	−0.995705	−	0.0925785i	$-0.970489\pi$
$107$	−9.34202	+	9.34202i	−0.903127	+	0.903127i	0.0925785	+	0.995705i	$0.470489\pi$
$108$		0			0
$109$		−	8.93645i		−	0.855956i	−0.903789	−	0.427978i	$-0.859226\pi$
$109$		−	8.93645i		−	0.855956i	0.903789	−	0.427978i	$-0.140774\pi$
$110$		0			0
$111$			3.63211i			0.344744i
$112$		0			0
$113$	4.90412	−	4.90412i	0.461341	−	0.461341i	−0.437754	−	0.899095i	$-0.644226\pi$
$113$	4.90412	−	4.90412i	0.461341	−	0.461341i	0.899095	+	0.437754i	$0.144226\pi$
$114$		0			0
$115$	9.56269	−	6.35703i	0.891725	−	0.592796i
$116$		0			0
$117$	−1.95416	−	1.95416i	−0.180662	−	0.180662i
$118$		0			0
$119$	−9.23829			−0.846873
$120$		0			0
$121$	10.8668			0.987890
$122$		0			0
$123$	−0.864242	−	0.864242i	−0.0779261	−	0.0779261i
$124$		0			0
$125$	−6.27705	+	9.25195i	−0.561436	+	0.827520i
$126$		0			0
$127$	−8.78281	+	8.78281i	−0.779348	+	0.779348i	−0.979720	−	0.200372i	$-0.935785\pi$
$127$	−8.78281	+	8.78281i	−0.779348	+	0.779348i	0.200372	+	0.979720i	$0.435785\pi$
$128$		0			0
$129$		−	5.30412i		−	0.467001i
$130$		0			0
$131$			6.61304i			0.577784i	0.957362	+	0.288892i	$0.0932869\pi$
$131$			6.61304i			0.577784i	−0.957362	+	0.288892i	$0.906713\pi$
$132$		0			0
$133$	−8.33079	+	8.33079i	−0.722371	+	0.722371i
$134$		0			0
$135$	3.46900	+	5.21831i	0.298564	+	0.449121i
$136$		0			0
$137$	11.4355	+	11.4355i	0.977003	+	0.977003i	0.999741	−	0.0227385i	$-0.00723850\pi$
$137$	11.4355	+	11.4355i	0.977003	+	0.977003i	−0.0227385	+	0.999741i	$0.507239\pi$
$138$		0			0
$139$	4.66599			0.395764			0.197882	−	0.980226i	$-0.436594\pi$
$139$	4.66599			0.395764			0.197882	+	0.980226i	$0.436594\pi$
$140$		0			0
$141$	−0.873508			−0.0735627
$142$		0			0
$143$	0.258079	+	0.258079i	0.0215817	+	0.0215817i
$144$		0			0
$145$	0.615028	+	0.123845i	0.0510753	+	0.0102847i
$146$		0			0
$147$	−5.35437	+	5.35437i	−0.441621	+	0.441621i
$148$		0			0
$149$		−	0.441443i		−	0.0361644i	−0.999837	−	0.0180822i	$-0.994244\pi$
$149$		−	0.441443i		−	0.0361644i	0.999837	−	0.0180822i	$-0.00575606\pi$
$150$		0			0
$151$		−	0.00912877i		−	0.000742889i	−1.00000		0.000371445i	$-0.999882\pi$
$151$		−	0.00912877i		−	0.000742889i	1.00000		0.000371445i	$-0.000118234\pi$
$152$		0			0
$153$	−3.79969	+	3.79969i	−0.307186	+	0.307186i
$154$		0			0
$155$	20.4057	+	4.10898i	1.63903	+	0.330041i
$156$		0			0
$157$	3.81597	+	3.81597i	0.304547	+	0.304547i	0.842790	−	0.538243i	$-0.180912\pi$
$157$	3.81597	+	3.81597i	0.304547	+	0.304547i	−0.538243	+	0.842790i	$0.680912\pi$
$158$		0			0
$159$	5.71335			0.453099
$160$		0			0
$161$	24.3989			1.92291
$162$		0			0
$163$	−7.92178	−	7.92178i	−0.620482	−	0.620482i	0.325173	−	0.945655i	$-0.394578\pi$
$163$	−7.92178	−	7.92178i	−0.620482	−	0.620482i	−0.945655	+	0.325173i	$0.894578\pi$
$164$		0			0
$165$	−0.219674	−	0.330448i	−0.0171016	−	0.0257254i
$166$		0			0
$167$	−5.34860	+	5.34860i	−0.413887	+	0.413887i	−0.883090	−	0.469203i	$-0.844541\pi$
$167$	−5.34860	+	5.34860i	−0.413887	+	0.413887i	0.469203	+	0.883090i	$0.344541\pi$
$168$		0			0
$169$		−	1.00000i		−	0.0769231i
$170$		0			0
$171$			6.85287i			0.524052i
$172$		0			0
$173$	−11.6854	+	11.6854i	−0.888423	+	0.888423i	−0.994372	−	0.105948i	$-0.966212\pi$
$173$	−11.6854	+	11.6854i	−0.888423	+	0.888423i	0.105948	+	0.994372i	$0.466212\pi$
$174$		0			0
$175$	−21.9904	+	8.98748i	−1.66232	+	0.679389i
$176$		0			0
$177$	3.49691	+	3.49691i	0.262844	+	0.262844i
$178$		0			0
$179$	13.4231			1.00329			0.501646	−	0.865073i	$-0.332728\pi$
$179$	13.4231			1.00329			0.501646	+	0.865073i	$0.332728\pi$
$180$		0			0
$181$	−6.34361			−0.471517			−0.235759	−	0.971812i	$-0.575757\pi$
$181$	−6.34361			−0.471517			−0.235759	+	0.971812i	$0.575757\pi$
$182$		0			0
$183$	−2.67548	−	2.67548i	−0.197777	−	0.197777i
$184$		0			0
$185$	−13.9107	+	9.24750i	−1.02274	+	0.679890i
$186$		0			0
$187$	0.501811	−	0.501811i	0.0366960	−	0.0366960i
$188$		0			0
$189$			13.3144i			0.968478i
$190$		0			0
$191$		−	15.1408i		−	1.09555i	−0.836625	−	0.547776i	$-0.815475\pi$
$191$		−	15.1408i		−	1.09555i	0.836625	−	0.547776i	$-0.184525\pi$
$192$		0			0
$193$	4.53425	−	4.53425i	0.326383	−	0.326383i	−0.524827	−	0.851209i	$-0.675870\pi$
$193$	4.53425	−	4.53425i	0.326383	−	0.326383i	0.851209	+	0.524827i	$0.175870\pi$
$194$		0			0
$195$	−0.214614	+	1.06580i	−0.0153688	+	0.0763236i
$196$		0			0
$197$	14.6435	+	14.6435i	1.04331	+	1.04331i	0.999019	+	0.0442894i	$0.0141024\pi$
$197$	14.6435	+	14.6435i	1.04331	+	1.04331i	0.0442894	+	0.999019i	$0.485898\pi$
$198$		0			0
$199$	14.3902			1.02009			0.510047	−	0.860147i	$-0.329628\pi$
$199$	14.3902			1.02009			0.510047	+	0.860147i	$0.329628\pi$
$200$		0			0
$201$	−4.13300			−0.291519
$202$		0			0
$203$	0.942606	+	0.942606i	0.0661580	+	0.0661580i
$204$		0			0
$205$	1.10960	−	5.51039i	0.0774975	−	0.384862i
$206$		0			0
$207$	10.0352	−	10.0352i	0.697496	−	0.697496i
$208$		0			0
$209$		−	0.905033i		−	0.0626025i
$210$		0			0
$211$		−	16.8120i		−	1.15739i	−0.815544	−	0.578695i	$-0.803562\pi$
$211$		−	16.8120i		−	1.15739i	0.815544	−	0.578695i	$-0.196438\pi$
$212$		0			0
$213$	−5.24339	+	5.24339i	−0.359271	+	0.359271i
$214$		0			0
$215$	20.3144	−	13.5045i	1.38543	−	0.921000i
$216$		0			0
$217$	31.2743	+	31.2743i	2.12304	+	2.12304i
$218$		0			0
$219$	−3.93447			−0.265867
$220$		0			0
$221$	−1.94441			−0.130795
$222$		0			0
$223$	−0.199092	−	0.199092i	−0.0133322	−	0.0133322i	0.700409	−	0.713741i	$-0.253001\pi$
$223$	−0.199092	−	0.199092i	−0.0133322	−	0.0133322i	−0.713741	+	0.700409i	$0.753001\pi$
$224$		0			0
$225$	−5.34805	+	12.7411i	−0.356537	+	0.849407i
$226$		0			0
$227$	−1.71829	+	1.71829i	−0.114047	+	0.114047i	−0.761827	−	0.647780i	$-0.775698\pi$
$227$	−1.71829	+	1.71829i	−0.114047	+	0.114047i	0.647780	+	0.761827i	$0.275698\pi$
$228$		0			0
$229$		−	12.3048i		−	0.813122i	−0.913624	−	0.406561i	$-0.866728\pi$
$229$		−	12.3048i		−	0.813122i	0.913624	−	0.406561i	$-0.133272\pi$
$230$		0			0
$231$		−	0.843130i		−	0.0554739i
$232$		0			0
$233$	−12.1046	+	12.1046i	−0.792999	+	0.792999i	−0.981981	−	0.188982i	$-0.939481\pi$
$233$	−12.1046	+	12.1046i	−0.792999	+	0.792999i	0.188982	+	0.981981i	$0.439481\pi$
$234$		0			0
$235$	−2.22399	−	3.34548i	−0.145077	−	0.218235i
$236$		0			0
$237$	−3.76963	−	3.76963i	−0.244864	−	0.244864i
$238$		0			0
$239$	−17.3246			−1.12063			−0.560317	−	0.828278i	$-0.689321\pi$
$239$	−17.3246			−1.12063			−0.560317	+	0.828278i	$0.689321\pi$
$240$		0			0
$241$	15.8282			1.01958			0.509791	−	0.860298i	$-0.329723\pi$
$241$	15.8282			1.01958			0.509791	+	0.860298i	$0.329723\pi$
$242$		0			0
$243$	8.32655	+	8.32655i	0.534149	+	0.534149i
$244$		0			0
$245$	−34.1393	−	6.87444i	−2.18108	−	0.439192i
$246$		0			0
$247$	−1.75340	+	1.75340i	−0.111566	+	0.111566i
$248$		0			0
$249$		−	4.28657i		−	0.271651i
$250$		0			0
$251$		−	26.3136i		−	1.66090i	−0.557091	−	0.830451i	$-0.688083\pi$
$251$		−	26.3136i		−	1.66090i	0.557091	−	0.830451i	$-0.311917\pi$
$252$		0			0
$253$	−1.32532	+	1.32532i	−0.0833218	+	0.0833218i
$254$		0			0
$255$	2.07235	+	0.417297i	0.129776	+	0.0261322i
$256$		0			0
$257$	−4.21135	−	4.21135i	−0.262697	−	0.262697i	0.563452	−	0.826149i	$-0.309473\pi$
$257$	−4.21135	−	4.21135i	−0.262697	−	0.262697i	−0.826149	+	0.563452i	$0.809473\pi$
$258$		0			0
$259$	−35.4929			−2.20542
$260$		0			0
$261$	0.775383			0.0479950
$262$		0			0
$263$	7.15389	+	7.15389i	0.441128	+	0.441128i	0.892391	−	0.451263i	$-0.149026\pi$
$263$	7.15389	+	7.15389i	0.441128	+	0.441128i	−0.451263	+	0.892391i	$0.649026\pi$
$264$		0			0
$265$	14.5464	+	21.8818i	0.893581	+	1.34419i
$266$		0			0
$267$	−3.27611	+	3.27611i	−0.200495	+	0.200495i
$268$		0			0
$269$			17.9880i			1.09675i	0.836234	+	0.548373i	$0.184753\pi$
$269$			17.9880i			1.09675i	−0.836234	+	0.548373i	$0.815247\pi$
$270$		0			0
$271$			27.4229i			1.66582i	0.553407	+	0.832911i	$0.313327\pi$
$271$			27.4229i			1.66582i	−0.553407	+	0.832911i	$0.686673\pi$
$272$		0			0
$273$	−1.63347	+	1.63347i	−0.0988622	+	0.0988622i
$274$		0			0
$275$	0.706298	−	1.68267i	0.0425914	−	0.101469i
$276$		0			0
$277$	−2.28134	−	2.28134i	−0.137072	−	0.137072i	0.635241	−	0.772314i	$-0.280901\pi$
$277$	−2.28134	−	2.28134i	−0.137072	−	0.137072i	−0.772314	+	0.635241i	$0.780901\pi$
$278$		0			0
$279$	25.7261			1.54018
$280$		0			0
$281$	20.9300			1.24858			0.624289	−	0.781193i	$-0.285389\pi$
$281$	20.9300			1.24858			0.624289	+	0.781193i	$0.285389\pi$
$282$		0			0
$283$	−4.37857	−	4.37857i	−0.260279	−	0.260279i	0.564888	−	0.825167i	$-0.308919\pi$
$283$	−4.37857	−	4.37857i	−0.260279	−	0.260279i	−0.825167	+	0.564888i	$0.808919\pi$
$284$		0			0
$285$	2.24508	−	1.49247i	0.132987	−	0.0884065i
$286$		0			0
$287$	8.44536	−	8.44536i	0.498514	−	0.498514i
$288$		0			0
$289$		−	13.2193i		−	0.777605i
$290$		0			0
$291$		−	4.79107i		−	0.280857i
$292$		0			0
$293$	−8.23512	+	8.23512i	−0.481101	+	0.481101i	−0.905483	−	0.424382i	$-0.860491\pi$
$293$	−8.23512	+	8.23512i	−0.481101	+	0.481101i	0.424382	+	0.905483i	$0.360491\pi$
$294$		0			0
$295$	−4.48967	+	22.2963i	−0.261398	+	1.29814i
$296$		0			0
$297$	−0.723218	−	0.723218i	−0.0419653	−	0.0419653i
$298$		0			0
$299$	5.13531			0.296982
$300$		0			0
$301$	51.8317			2.98753
$302$		0			0
$303$	1.61062	+	1.61062i	0.0925277	+	0.0925277i
$304$		0			0
$305$	3.43503	−	17.0588i	0.196689	−	0.976785i
$306$		0			0
$307$	9.63727	−	9.63727i	0.550028	−	0.550028i	−0.376421	−	0.926449i	$-0.622845\pi$
$307$	9.63727	−	9.63727i	0.550028	−	0.550028i	0.926449	+	0.376421i	$0.122845\pi$
$308$		0			0
$309$			4.25813i			0.242237i
$310$		0			0
$311$			27.9603i			1.58548i	0.609558	+	0.792741i	$0.291347\pi$
$311$			27.9603i			1.58548i	−0.609558	+	0.792741i	$0.708653\pi$
$312$		0			0
$313$	9.23182	−	9.23182i	0.521813	−	0.521813i	−0.396306	−	0.918119i	$-0.629708\pi$
$313$	9.23182	−	9.23182i	0.521813	−	0.521813i	0.918119	+	0.396306i	$0.129708\pi$
$314$		0			0
$315$	−24.4508	+	16.2543i	−1.37765	+	0.915825i
$316$		0			0
$317$	4.75774	+	4.75774i	0.267221	+	0.267221i	0.827979	−	0.560758i	$-0.189490\pi$
$317$	4.75774	+	4.75774i	0.267221	+	0.267221i	−0.560758	+	0.827979i	$0.689490\pi$
$318$		0			0
$319$	−0.102402			−0.00573341
$320$		0			0
$321$	6.42359			0.358530
$322$		0			0
$323$	3.40933	+	3.40933i	0.189700	+	0.189700i
$324$		0			0
$325$	−4.62837	+	1.89162i	−0.256736	+	0.104928i
$326$		0			0
$327$	−3.07236	+	3.07236i	−0.169902	+	0.169902i
$328$		0			0
$329$		−	8.53590i		−	0.470600i
$330$		0			0
$331$			3.91850i			0.215380i	0.994185	+	0.107690i	$0.0343454\pi$
$331$			3.91850i			0.215380i	−0.994185	+	0.107690i	$0.965655\pi$
$332$		0			0
$333$	−14.5981	+	14.5981i	−0.799972	+	0.799972i
$334$		0			0
$335$	−10.5228	−	15.8291i	−0.574922	−	0.864838i
$336$		0			0
$337$	−3.01276	−	3.01276i	−0.164115	−	0.164115i	0.620272	−	0.784387i	$-0.287022\pi$
$337$	−3.01276	−	3.01276i	−0.164115	−	0.164115i	−0.784387	+	0.620272i	$0.787022\pi$
$338$		0			0
$339$	−3.37208			−0.183146
$340$		0			0
$341$	−3.39755			−0.183988
$342$		0			0
$343$	−28.8055	−	28.8055i	−1.55535	−	1.55535i
$344$		0			0
$345$	−5.47321	−	1.10211i	−0.294668	−	0.0593356i
$346$		0			0
$347$	−11.5948	+	11.5948i	−0.622443	+	0.622443i	−0.946156	−	0.323712i	$-0.895069\pi$
$347$	−11.5948	+	11.5948i	−0.622443	+	0.622443i	0.323712	+	0.946156i	$0.395069\pi$
$348$		0			0
$349$			9.23209i			0.494182i	0.968992	+	0.247091i	$0.0794747\pi$
$349$			9.23209i			0.494182i	−0.968992	+	0.247091i	$0.920525\pi$
$350$		0			0
$351$			2.80231i			0.149576i
$352$		0			0
$353$	8.82510	−	8.82510i	0.469713	−	0.469713i	−0.432109	−	0.901822i	$-0.642230\pi$
$353$	8.82510	−	8.82510i	0.469713	−	0.469713i	0.901822	+	0.432109i	$0.142230\pi$
$354$		0			0
$355$	−33.4317	−	6.73195i	−1.77437	−	0.357295i
$356$		0			0
$357$	3.17613	+	3.17613i	0.168099	+	0.168099i
$358$		0			0
$359$	−1.96294			−0.103600			−0.0518000	−	0.998657i	$-0.516496\pi$
$359$	−1.96294			−0.103600			−0.0518000	+	0.998657i	$0.516496\pi$
$360$		0			0
$361$	−12.8512			−0.676377
$362$		0			0
$363$	−3.73601	−	3.73601i	−0.196090	−	0.196090i
$364$		0			0
$365$	−10.0173	−	15.0688i	−0.524330	−	0.788735i
$366$		0			0
$367$	11.4909	−	11.4909i	0.599821	−	0.599821i	−0.340444	−	0.940265i	$-0.610577\pi$
$367$	11.4909	−	11.4909i	0.599821	−	0.599821i	0.940265	+	0.340444i	$0.110577\pi$
$368$		0			0
$369$		−	6.94711i		−	0.361652i
$370$		0			0
$371$			55.8308i			2.89859i
$372$		0			0
$373$	20.6309	−	20.6309i	1.06823	−	1.06823i	0.0707319	−	0.997495i	$-0.477467\pi$
$373$	20.6309	−	20.6309i	1.06823	−	1.06823i	0.997495	−	0.0707319i	$-0.0225335\pi$
$374$		0			0
$375$	5.33889	−	1.02277i	0.275699	−	0.0528159i
$376$		0			0
$377$	0.198393	+	0.198393i	0.0102177	+	0.0102177i
$378$		0			0
$379$	23.5922			1.21185			0.605926	−	0.795521i	$-0.292803\pi$
$379$	23.5922			1.21185			0.605926	+	0.795521i	$0.292803\pi$
$380$		0			0
$381$	6.03908			0.309391
$382$		0			0
$383$	25.6147	+	25.6147i	1.30885	+	1.30885i	0.922246	+	0.386605i	$0.126352\pi$
$383$	25.6147	+	25.6147i	1.30885	+	1.30885i	0.386605	+	0.922246i	$0.373648\pi$
$384$		0			0
$385$	3.22913	−	2.14665i	0.164572	−	0.109403i
$386$		0			0
$387$	21.3182	−	21.3182i	1.08367	−	1.08367i
$388$		0			0
$389$		−	24.9387i		−	1.26444i	−0.774788	−	0.632222i	$-0.782143\pi$
$389$		−	24.9387i		−	1.26444i	0.774788	−	0.632222i	$-0.217857\pi$
$390$		0			0
$391$		−	9.98513i		−	0.504970i
$392$		0			0
$393$	2.27357	−	2.27357i	0.114686	−	0.114686i
$394$		0			0
$395$	4.83980	−	24.0351i	0.243517	−	1.20934i
$396$		0			0
$397$	5.83353	+	5.83353i	0.292777	+	0.292777i	0.838176	−	0.545400i	$-0.183622\pi$
$397$	5.83353	+	5.83353i	0.292777	+	0.292777i	−0.545400	+	0.838176i	$0.683622\pi$
$398$		0			0
$399$	5.72827			0.286772
$400$		0			0
$401$	−30.9919			−1.54766			−0.773832	−	0.633391i	$-0.781662\pi$
$401$	−30.9919			−1.54766			−0.773832	+	0.633391i	$0.781662\pi$
$402$		0			0
$403$	6.58238	+	6.58238i	0.327892	+	0.327892i
$404$		0			0
$405$	−3.05818	+	15.1873i	−0.151962	+	0.754663i
$406$		0			0
$407$	1.92792	−	1.92792i	0.0955635	−	0.0955635i
$408$		0			0
$409$		−	11.4517i		−	0.566249i	−0.959083	−	0.283125i	$-0.908629\pi$
$409$		−	11.4517i		−	0.566249i	0.959083	−	0.283125i	$-0.0913710\pi$
$410$		0			0
$411$		−	7.86309i		−	0.387858i
$412$		0			0
$413$	−34.1718	+	34.1718i	−1.68148	+	1.68148i
$414$		0			0
$415$	16.4173	−	10.9138i	0.805894	−	0.535737i
$416$		0			0
$417$	−1.60417	−	1.60417i	−0.0785567	−	0.0785567i
$418$		0			0
$419$	−17.6899			−0.864210			−0.432105	−	0.901823i	$-0.642229\pi$
$419$	−17.6899			−0.864210			−0.432105	+	0.901823i	$0.642229\pi$
$420$		0			0
$421$	15.6445			0.762468			0.381234	−	0.924478i	$-0.375499\pi$
$421$	15.6445			0.762468			0.381234	+	0.924478i	$0.375499\pi$
$422$		0			0
$423$	−3.51079	−	3.51079i	−0.170701	−	0.170701i
$424$		0			0
$425$	3.67807	+	8.99943i	0.178413	+	0.436537i
$426$		0			0
$427$	26.1448	−	26.1448i	1.26523	−	1.26523i
$428$		0			0
$429$		−	0.177456i		−	0.00856764i
$430$		0			0
$431$		−	6.83579i		−	0.329269i	−0.986355	−	0.164634i	$-0.947356\pi$
$431$		−	6.83579i		−	0.329269i	0.986355	−	0.164634i	$-0.0526444\pi$
$432$		0			0
$433$	−1.41319	+	1.41319i	−0.0679137	+	0.0679137i	−0.740248	−	0.672334i	$-0.765292\pi$
$433$	−1.41319	+	1.41319i	−0.0679137	+	0.0679137i	0.672334	+	0.740248i	$0.265292\pi$
$434$		0			0
$435$	−0.168869	−	0.254025i	−0.00809666	−	0.0121796i
$436$		0			0
$437$	−9.00426	−	9.00426i	−0.430732	−	0.430732i
$438$		0			0
$439$	−35.5326			−1.69588			−0.847939	−	0.530094i	$-0.822157\pi$
$439$	−35.5326			−1.69588			−0.847939	+	0.530094i	$0.822157\pi$
$440$		0			0
$441$	−43.0404			−2.04954
$442$		0			0
$443$	−6.68722	−	6.68722i	−0.317719	−	0.317719i	0.530171	−	0.847891i	$-0.322128\pi$
$443$	−6.68722	−	6.68722i	−0.317719	−	0.317719i	−0.847891	+	0.530171i	$0.822128\pi$
$444$		0			0
$445$	−20.8884	−	4.20618i	−0.990206	−	0.199392i
$446$		0			0
$447$	−0.151769	+	0.151769i	−0.00717841	+	0.00717841i
$448$		0			0
$449$		−	13.9645i		−	0.659026i	−0.944151	−	0.329513i	$-0.893115\pi$
$449$		−	13.9645i		−	0.659026i	0.944151	−	0.329513i	$-0.106885\pi$
$450$		0			0
$451$			0.917479i			0.0432024i
$452$		0			0
$453$	−0.00313848	+	0.00313848i	−0.000147459	+	0.000147459i
$454$		0			0
$455$	−10.4150	−	2.09720i	−0.488262	−	0.0983184i
$456$		0			0
$457$	0.768261	+	0.768261i	0.0359378	+	0.0359378i	0.724847	−	0.688910i	$-0.241910\pi$
$457$	0.768261	+	0.768261i	0.0359378	+	0.0359378i	−0.688910	+	0.724847i	$0.741910\pi$
$458$		0			0
$459$	5.44883			0.254330
$460$		0			0
$461$	−9.84087			−0.458335			−0.229168	−	0.973387i	$-0.573600\pi$
$461$	−9.84087			−0.458335			−0.229168	+	0.973387i	$0.573600\pi$
$462$		0			0
$463$	4.39586	+	4.39586i	0.204293	+	0.204293i	0.801837	−	0.597543i	$-0.203856\pi$
$463$	4.39586	+	4.39586i	0.204293	+	0.204293i	−0.597543	+	0.801837i	$0.703856\pi$
$464$		0			0
$465$	−5.60284	−	8.42818i	−0.259825	−	0.390848i
$466$		0			0
$467$	18.6641	−	18.6641i	0.863673	−	0.863673i	−0.128090	−	0.991763i	$-0.540884\pi$
$467$	18.6641	−	18.6641i	0.863673	−	0.863673i	0.991763	+	0.128090i	$0.0408845\pi$
$468$		0			0
$469$		−	40.3876i		−	1.86493i
$470$		0			0
$471$		−	2.62387i		−	0.120901i
$472$		0			0
$473$	−2.81542	+	2.81542i	−0.129453	+	0.129453i
$474$		0			0
$475$	11.4322	+	4.79863i	0.524544	+	0.220176i
$476$		0			0
$477$	22.9630	+	22.9630i	1.05141	+	1.05141i
$478$		0			0
$479$	−22.3835			−1.02273			−0.511365	−	0.859364i	$-0.670860\pi$
$479$	−22.3835			−1.02273			−0.511365	+	0.859364i	$0.670860\pi$
$480$		0			0
$481$	−7.47027			−0.340615
$482$		0			0
$483$	−8.38838	−	8.38838i	−0.381684	−	0.381684i
$484$		0			0
$485$	18.3495	−	12.1983i	0.833207	−	0.553894i
$486$		0			0
$487$	−28.9966	+	28.9966i	−1.31396	+	1.31396i	−0.395494	+	0.918469i	$0.629427\pi$
$487$	−28.9966	+	28.9966i	−1.31396	+	1.31396i	−0.918469	+	0.395494i	$0.870573\pi$
$488$		0			0
$489$			5.44703i			0.246323i
$490$		0			0
$491$		−	18.6642i		−	0.842303i	−0.906990	−	0.421151i	$-0.861626\pi$
$491$		−	18.6642i		−	0.842303i	0.906990	−	0.421151i	$-0.138374\pi$
$492$		0			0
$493$	0.385756	−	0.385756i	0.0173736	−	0.0173736i
$494$		0			0
$495$	0.445225	−	2.21104i	0.0200114	−	0.0993790i
$496$		0			0
$497$	−51.2383	−	51.2383i	−2.29835	−	2.29835i
$498$		0			0
$499$	22.7559			1.01870			0.509348	−	0.860561i	$-0.329887\pi$
$499$	22.7559			1.01870			0.509348	+	0.860561i	$0.329887\pi$
$500$		0			0
$501$	3.67771			0.164308
$502$		0			0
$503$	19.2882	+	19.2882i	0.860018	+	0.860018i	0.991340	−	0.131321i	$-0.0419220\pi$
$503$	19.2882	+	19.2882i	0.860018	+	0.860018i	−0.131321	+	0.991340i	$0.541922\pi$
$504$		0			0
$505$	−2.06787	+	10.2693i	−0.0920188	+	0.456977i
$506$		0			0
$507$	−0.343801	+	0.343801i	−0.0152687	+	0.0152687i
$508$		0			0
$509$			30.7202i			1.36165i	0.732447	+	0.680824i	$0.238378\pi$
$509$			30.7202i			1.36165i	−0.732447	+	0.680824i	$0.761622\pi$
$510$		0			0
$511$		−	38.4475i		−	1.70082i
$512$		0			0
$513$	4.91358	−	4.91358i	0.216940	−	0.216940i
$514$		0			0
$515$	−16.3084	+	10.8414i	−0.718633	+	0.477729i
$516$		0			0
$517$	0.463658	+	0.463658i	0.0203917	+	0.0203917i
$518$		0			0
$519$	8.03489			0.352693
$520$		0			0
$521$	−10.7012			−0.468828			−0.234414	−	0.972137i	$-0.575317\pi$
$521$	−10.7012			−0.468828			−0.234414	+	0.972137i	$0.575317\pi$
$522$		0			0
$523$	15.4359	+	15.4359i	0.674966	+	0.674966i	0.958857	−	0.283891i	$-0.0916252\pi$
$523$	15.4359	+	15.4359i	0.674966	+	0.674966i	−0.283891	+	0.958857i	$0.591625\pi$
$524$		0			0
$525$	10.6502	+	4.47040i	0.464813	+	0.195104i
$526$		0			0
$527$	12.7988	−	12.7988i	0.557526	−	0.557526i
$528$		0			0
$529$			3.37136i			0.146581i
$530$		0			0
$531$			28.1095i			1.21985i
$532$		0			0
$533$	1.77752	−	1.77752i	0.0769928	−	0.0769928i
$534$		0			0
$535$	16.3547	+	24.6019i	0.707077	+	1.06363i
$536$		0			0
$537$	−4.61489	−	4.61489i	−0.199147	−	0.199147i
$538$		0			0
$539$	5.68419			0.244836
$540$		0			0
$541$	4.73363			0.203515			0.101757	−	0.994809i	$-0.467553\pi$
$541$	4.73363			0.203515			0.101757	+	0.994809i	$0.467553\pi$
$542$		0			0
$543$	2.18094	+	2.18094i	0.0935931	+	0.0935931i
$544$		0			0
$545$	−19.5893	−	3.94458i	−0.839113	−	0.168967i
$546$		0			0
$547$	−16.1424	+	16.1424i	−0.690200	+	0.690200i	−0.962276	−	0.272076i	$-0.912290\pi$
$547$	−16.1424	+	16.1424i	−0.690200	+	0.690200i	0.272076	+	0.962276i	$0.412290\pi$
$548$		0			0
$549$		−	21.5065i		−	0.917877i
$550$		0			0
$551$		−	0.695725i		−	0.0296389i
$552$		0			0
$553$	36.8367	−	36.8367i	1.56646	−	1.56646i
$554$		0			0
$555$	7.96183	+	1.60323i	0.337961	+	0.0680532i
$556$		0			0
$557$	−30.2176	−	30.2176i	−1.28036	−	1.28036i	−0.940462	−	0.339899i	$-0.889607\pi$
$557$	−30.2176	−	30.2176i	−1.28036	−	1.28036i	−0.339899	−	0.940462i	$-0.610393\pi$
$558$		0			0
$559$	10.9092			0.461408
$560$		0			0
$561$	−0.345046			−0.0145679
$562$		0			0
$563$	3.07538	+	3.07538i	0.129612	+	0.129612i	0.768937	−	0.639325i	$-0.220786\pi$
$563$	3.07538	+	3.07538i	0.129612	+	0.129612i	−0.639325	+	0.768937i	$0.720786\pi$
$564$		0			0
$565$	−8.58547	−	12.9149i	−0.361193	−	0.543332i
$566$		0			0
$567$	−23.2764	+	23.2764i	−0.977518	+	0.977518i
$568$		0			0
$569$		−	35.0160i		−	1.46795i	−0.679178	−	0.733974i	$-0.737663\pi$
$569$		−	35.0160i		−	1.46795i	0.679178	−	0.733974i	$-0.262337\pi$
$570$		0			0
$571$			44.5201i			1.86311i	0.363602	+	0.931554i	$0.381547\pi$
$571$			44.5201i			1.86311i	−0.363602	+	0.931554i	$0.618453\pi$
$572$		0			0
$573$	−5.20543	+	5.20543i	−0.217460	+	0.217460i
$574$		0			0
$575$	−9.71403	−	23.7681i	−0.405103	−	0.991197i
$576$		0			0
$577$	27.1142	+	27.1142i	1.12878	+	1.12878i	0.990376	+	0.138404i	$0.0441973\pi$
$577$	27.1142	+	27.1142i	1.12878	+	1.12878i	0.138404	+	0.990376i	$0.455803\pi$
$578$		0			0
$579$	−3.11776			−0.129570
$580$		0			0
$581$	41.8883			1.73782
$582$		0			0
$583$	−3.03265	−	3.03265i	−0.125599	−	0.125599i
$584$		0			0
$585$	−5.14623	+	3.42108i	−0.212770	+	0.141444i
$586$		0			0
$587$	−16.3746	+	16.3746i	−0.675852	+	0.675852i	−0.959059	−	0.283207i	$-0.908602\pi$
$587$	−16.3746	+	16.3746i	−0.675852	+	0.675852i	0.283207	+	0.959059i	$0.408602\pi$
$588$		0			0
$589$		−	23.0831i		−	0.951124i
$590$		0			0
$591$		−	10.0689i		−	0.414180i
$592$		0			0
$593$	27.3588	−	27.3588i	1.12349	−	1.12349i	0.132279	−	0.991213i	$-0.457771\pi$
$593$	27.3588	−	27.3588i	1.12349	−	1.12349i	0.991213	−	0.132279i	$-0.0422294\pi$
$594$		0			0
$595$	−4.07782	+	20.2510i	−0.167174	+	0.830209i
$596$		0			0
$597$	−4.94736	−	4.94736i	−0.202482	−	0.202482i
$598$		0			0
$599$	2.97215			0.121439			0.0607195	−	0.998155i	$-0.480661\pi$
$599$	2.97215			0.121439			0.0607195	+	0.998155i	$0.480661\pi$
$600$		0			0
$601$	−18.7149			−0.763397			−0.381698	−	0.924287i	$-0.624661\pi$
$601$	−18.7149			−0.763397			−0.381698	+	0.924287i	$0.624661\pi$
$602$		0			0
$603$	−16.6113	−	16.6113i	−0.676465	−	0.676465i
$604$		0			0
$605$	4.79664	−	23.8207i	0.195011	−	0.968451i
$606$		0			0
$607$	−3.05201	+	3.05201i	−0.123877	+	0.123877i	−0.766328	−	0.642450i	$-0.777918\pi$
$607$	−3.05201	+	3.05201i	−0.123877	+	0.123877i	0.642450	+	0.766328i	$0.277918\pi$
$608$		0			0
$609$		−	0.648138i		−	0.0262639i
$610$		0			0
$611$		−	1.79657i		−	0.0726816i
$612$		0			0
$613$	16.2086	−	16.2086i	0.654659	−	0.654659i	−0.299452	−	0.954111i	$-0.596804\pi$
$613$	16.2086	−	16.2086i	0.654659	−	0.654659i	0.954111	+	0.299452i	$0.0968038\pi$
$614$		0			0
$615$	−2.27596	+	1.51300i	−0.0917755	+	0.0610100i
$616$		0			0
$617$	28.0158	+	28.0158i	1.12788	+	1.12788i	0.990522	+	0.137353i	$0.0438595\pi$
$617$	28.0158	+	28.0158i	1.12788	+	1.12788i	0.137353	+	0.990522i	$0.456140\pi$
$618$		0			0
$619$	24.3338			0.978058			0.489029	−	0.872268i	$-0.337351\pi$
$619$	24.3338			0.978058			0.489029	+	0.872268i	$0.337351\pi$
$620$		0			0
$621$	−14.3907			−0.577480
$622$		0			0
$623$	−32.0141	−	32.0141i	−1.28262	−	1.28262i
$624$		0			0
$625$	17.5102	+	17.8436i	0.700408	+	0.713743i
$626$		0			0
$627$	−0.311151	+	0.311151i	−0.0124262	+	0.0124262i
$628$		0			0
$629$			14.5253i			0.579160i
$630$		0			0
$631$		−	7.48044i		−	0.297791i	−0.988853	−	0.148896i	$-0.952428\pi$
$631$		−	7.48044i		−	0.297791i	0.988853	−	0.148896i	$-0.0475719\pi$
$632$		0			0
$633$	−5.78000	+	5.78000i	−0.229734	+	0.229734i
$634$		0			0
$635$	15.3758	+	23.1293i	0.610168	+	0.917858i
$636$		0			0
$637$	−11.0125	−	11.0125i	−0.436331	−	0.436331i
$638$		0			0
$639$	−42.1483			−1.66736
$640$		0			0
$641$	−28.2134			−1.11436			−0.557182	−	0.830391i	$-0.688117\pi$
$641$	−28.2134			−1.11436			−0.557182	+	0.830391i	$0.688117\pi$
$642$		0			0
$643$	3.40758	+	3.40758i	0.134382	+	0.134382i	0.771098	−	0.636716i	$-0.219708\pi$
$643$	3.40758	+	3.40758i	0.134382	+	0.134382i	−0.636716	+	0.771098i	$0.719708\pi$
$644$		0			0
$645$	−11.6270	−	2.34126i	−0.457812	−	0.0921869i
$646$		0			0
$647$	−2.26568	+	2.26568i	−0.0890729	+	0.0890729i	−0.750239	−	0.661166i	$-0.770062\pi$
$647$	−2.26568	+	2.26568i	−0.0890729	+	0.0890729i	0.661166	+	0.750239i	$0.270062\pi$
$648$		0			0
$649$		−	3.71232i		−	0.145721i
$650$		0			0
$651$		−	21.5043i		−	0.842819i
$652$		0			0
$653$	15.2039	−	15.2039i	0.594976	−	0.594976i	−0.343996	−	0.938971i	$-0.611781\pi$
$653$	15.2039	−	15.2039i	0.594976	−	0.594976i	0.938971	+	0.343996i	$0.111781\pi$
$654$		0			0
$655$	14.4962	+	2.91902i	0.566415	+	0.114056i
$656$		0			0
$657$	−15.8134	−	15.8134i	−0.616938	−	0.616938i
$658$		0			0
$659$	29.2781			1.14051			0.570256	−	0.821467i	$-0.306844\pi$
$659$	29.2781			1.14051			0.570256	+	0.821467i	$0.306844\pi$
$660$		0			0
$661$	−11.7884			−0.458514			−0.229257	−	0.973366i	$-0.573630\pi$
$661$	−11.7884			−0.458514			−0.229257	+	0.973366i	$0.573630\pi$
$662$		0			0
$663$	0.668489	+	0.668489i	0.0259620	+	0.0259620i
$664$		0			0
$665$	14.5844	+	21.9389i	0.565560	+	0.850754i
$666$		0			0
$667$	−1.01881	+	1.01881i	−0.0394484	+	0.0394484i
$668$		0			0
$669$			0.136896i			0.00529271i
$670$		0			0
$671$			2.84029i			0.109648i
$672$		0			0
$673$	−8.01952	+	8.01952i	−0.309130	+	0.309130i	−0.844572	−	0.535442i	$-0.820145\pi$
$673$	−8.01952	+	8.01952i	−0.309130	+	0.309130i	0.535442	+	0.844572i	$0.320145\pi$
$674$		0			0
$675$	12.9701	−	5.30090i	0.499220	−	0.204032i
$676$		0			0
$677$	−23.6368	−	23.6368i	−0.908438	−	0.908438i	0.0877085	−	0.996146i	$-0.472046\pi$
$677$	−23.6368	−	23.6368i	−0.908438	−	0.908438i	−0.996146	+	0.0877085i	$0.972046\pi$
$678$		0			0
$679$	46.8182			1.79672
$680$		0			0
$681$	1.18150			0.0452753
$682$		0			0
$683$	−30.4768	−	30.4768i	−1.16616	−	1.16616i	−0.983102	−	0.183061i	$-0.941399\pi$
$683$	−30.4768	−	30.4768i	−1.16616	−	1.16616i	−0.183061	−	0.983102i	$-0.558601\pi$
$684$		0			0
$685$	30.1151	−	20.0198i	1.15064	−	0.764916i
$686$		0			0
$687$	−4.23039	+	4.23039i	−0.161400	+	0.161400i
$688$		0			0
$689$			11.7508i			0.447672i
$690$		0			0
$691$		−	27.6705i		−	1.05264i	−0.850288	−	0.526318i	$-0.823572\pi$
$691$		−	27.6705i		−	1.05264i	0.850288	−	0.526318i	$-0.176428\pi$
$692$		0			0
$693$	3.38870	−	3.38870i	0.128726	−	0.128726i
$694$		0			0
$695$	2.05959	−	10.2282i	0.0781246	−	0.387977i
$696$		0			0
$697$	−3.45621	−	3.45621i	−0.130913	−	0.130913i
$698$		0			0
$699$	8.32315			0.314810
$700$		0			0
$701$	13.0590			0.493231			0.246615	−	0.969113i	$-0.420682\pi$
$701$	13.0590			0.493231			0.246615	+	0.969113i	$0.420682\pi$
$702$		0			0
$703$	13.0984	+	13.0984i	0.494016	+	0.494016i
$704$		0			0
$705$	−0.385570	+	1.91479i	−0.0145214	+	0.0721152i
$706$		0			0
$707$	−15.7389	+	15.7389i	−0.591924	+	0.591924i
$708$		0			0
$709$		−	6.57956i		−	0.247101i	−0.992338	−	0.123550i	$-0.960572\pi$
$709$		−	6.57956i		−	0.247101i	0.992338	−	0.123550i	$-0.0394280\pi$
$710$		0			0
$711$		−	30.3017i		−	1.13640i
$712$		0			0
$713$	−33.8025	+	33.8025i	−1.26591	+	1.26591i
$714$		0			0
$715$	0.679644	−	0.451810i	0.0254172	−	0.0168967i
$716$		0			0
$717$	5.95621	+	5.95621i	0.222439	+	0.222439i
$718$		0			0
$719$	−15.5493			−0.579890			−0.289945	−	0.957043i	$-0.593637\pi$
$719$	−15.5493			−0.579890			−0.289945	+	0.957043i	$0.593637\pi$
$720$		0			0
$721$	−41.6104			−1.54965
$722$		0			0
$723$	−5.44174	−	5.44174i	−0.202380	−	0.202380i
$724$		0			0
$725$	0.542951	−	1.29352i	0.0201647	−	0.0480400i
$726$		0			0
$727$	−10.3026	+	10.3026i	−0.382104	+	0.382104i	−0.871860	−	0.489756i	$-0.837086\pi$
$727$	−10.3026	+	10.3026i	−0.382104	+	0.382104i	0.489756	+	0.871860i	$0.337086\pi$
$728$		0			0
$729$			15.0595i			0.557761i
$730$		0			0
$731$		−	21.2118i		−	0.784548i
$732$		0			0
$733$	11.8901	−	11.8901i	0.439171	−	0.439171i	−0.452562	−	0.891733i	$-0.649490\pi$
$733$	11.8901	−	11.8901i	0.439171	−	0.439171i	0.891733	+	0.452562i	$0.149490\pi$
$734$		0			0
$735$	9.37370	+	14.1006i	0.345754	+	0.520108i
$736$		0			0
$737$	2.19380	+	2.19380i	0.0808095	+	0.0808095i
$738$		0			0
$739$	−15.6423			−0.575411			−0.287705	−	0.957719i	$-0.592892\pi$
$739$	−15.6423			−0.575411			−0.287705	+	0.957719i	$0.592892\pi$
$740$		0			0
$741$	1.20564			0.0442904
$742$		0			0
$743$	18.2962	+	18.2962i	0.671223	+	0.671223i	0.957998	−	0.286775i	$-0.0925831\pi$
$743$	18.2962	+	18.2962i	0.671223	+	0.671223i	−0.286775	+	0.957998i	$0.592583\pi$
$744$		0			0
$745$	−0.967673	−	0.194855i	−0.0354528	−	0.00713892i
$746$		0			0
$747$	17.2285	−	17.2285i	0.630359	−	0.630359i
$748$		0			0
$749$			62.7712i			2.29361i
$750$		0			0
$751$			21.3020i			0.777320i	0.921381	+	0.388660i	$0.127062\pi$
$751$			21.3020i			0.777320i	−0.921381	+	0.388660i	$0.872938\pi$
$752$		0			0
$753$	−9.04666	+	9.04666i	−0.329678	+	0.329678i
$754$		0			0
$755$	−0.0200109	−	0.00402948i	−0.000728271	−	0.000146648i
$756$		0			0
$757$	−22.9031	−	22.9031i	−0.832427	−	0.832427i	0.155422	−	0.987848i	$-0.450326\pi$
$757$	−22.9031	−	22.9031i	−0.832427	−	0.832427i	−0.987848	+	0.155422i	$0.950326\pi$
$758$		0			0
$759$	0.911289			0.0330777
$760$		0			0
$761$	17.5919			0.637706			0.318853	−	0.947804i	$-0.396702\pi$
$761$	17.5919			0.637706			0.318853	+	0.947804i	$0.396702\pi$
$762$		0			0
$763$	−30.0230	−	30.0230i	−1.08691	−	1.08691i
$764$		0			0
$765$	6.65197	+	10.0064i	0.240503	+	0.361781i
$766$		0			0
$767$	−7.19222	+	7.19222i	−0.259696	+	0.259696i
$768$		0			0
$769$			43.6643i			1.57457i	0.616587	+	0.787287i	$0.288515\pi$
$769$			43.6643i			1.57457i	−0.616587	+	0.787287i	$0.711485\pi$
$770$		0			0
$771$			2.89573i			0.104287i
$772$		0			0
$773$	−21.3751	+	21.3751i	−0.768809	+	0.768809i	−0.977897	−	0.209088i	$-0.932951\pi$
$773$	−21.3751	+	21.3751i	−0.768809	+	0.768809i	0.209088	+	0.977897i	$0.432951\pi$
$774$		0			0
$775$	18.0143	−	42.9170i	0.647094	−	1.54162i
$776$		0			0
$777$	12.2025	+	12.2025i	0.437762	+	0.437762i
$778$		0			0
$779$	−6.23340			−0.223335
$780$		0			0
$781$	5.56638			0.199181
$782$		0			0
$783$	−0.555958	−	0.555958i	−0.0198683	−	0.0198683i
$784$		0			0
$785$	10.0492	−	6.68048i	0.358673	−	0.238437i
$786$		0			0
$787$	1.04024	−	1.04024i	0.0370804	−	0.0370804i	−0.688323	−	0.725404i	$-0.741653\pi$
$787$	1.04024	−	1.04024i	0.0370804	−	0.0370804i	0.725404	+	0.688323i	$0.241653\pi$
$788$		0			0
$789$		−	4.91903i		−	0.175122i
$790$		0			0
$791$		−	32.9519i		−	1.17164i
$792$		0			0
$793$	5.50275	−	5.50275i	0.195408	−	0.195408i
$794$		0			0
$795$	2.52190	−	12.5241i	0.0894425	−	0.444183i
$796$		0			0
$797$	−2.43161	−	2.43161i	−0.0861321	−	0.0861321i	0.662728	−	0.748860i	$-0.269399\pi$
$797$	−2.43161	−	2.43161i	−0.0861321	−	0.0861321i	−0.748860	+	0.662728i	$0.769399\pi$
$798$		0			0
$799$	−3.49327			−0.123583
$800$		0			0
$801$	−26.3346			−0.930488
$802$		0			0
$803$	2.08841	+	2.08841i	0.0736985	+	0.0736985i
$804$		0			0
$805$	10.7698	−	53.4841i	0.379585	−	1.88507i
$806$		0			0
$807$	6.18428	−	6.18428i	0.217697	−	0.217697i
$808$		0			0
$809$			24.3433i			0.855866i	0.903810	+	0.427933i	$0.140758\pi$
$809$			24.3433i			0.855866i	−0.903810	+	0.427933i	$0.859242\pi$
$810$		0			0
$811$			33.2796i			1.16860i	0.811537	+	0.584302i	$0.198632\pi$
$811$			33.2796i			1.16860i	−0.811537	+	0.584302i	$0.801368\pi$
$812$		0			0
$813$	9.42802	−	9.42802i	0.330655	−	0.330655i
$814$		0			0
$815$	−20.8618	+	13.8684i	−0.730757	+	0.485788i
$816$		0			0
$817$	−19.1281	−	19.1281i	−0.669209	−	0.669209i
$818$		0			0
$819$	−13.1305			−0.458815
$820$		0			0
$821$	46.4989			1.62282			0.811411	−	0.584476i	$-0.198700\pi$
$821$	46.4989			1.62282			0.811411	+	0.584476i	$0.198700\pi$
$822$		0			0
$823$	23.6833	+	23.6833i	0.825547	+	0.825547i	0.986897	−	0.161350i	$-0.0515849\pi$
$823$	23.6833	+	23.6833i	0.825547	+	0.825547i	−0.161350	+	0.986897i	$0.551585\pi$
$824$		0			0
$825$	−0.821330	+	0.335678i	−0.0285950	+	0.0116868i
$826$		0			0
$827$	−10.5912	+	10.5912i	−0.368294	+	0.368294i	−0.866855	−	0.498561i	$-0.833862\pi$
$827$	−10.5912	+	10.5912i	−0.368294	+	0.368294i	0.498561	+	0.866855i	$0.333862\pi$
$828$		0			0
$829$			25.8318i			0.897177i	0.893739	+	0.448588i	$0.148073\pi$
$829$			25.8318i			0.897177i	−0.893739	+	0.448588i	$0.851927\pi$
$830$		0			0
$831$			1.56865i			0.0544159i
$832$		0			0
$833$	−21.4128	+	21.4128i	−0.741909	+	0.741909i
$834$		0			0
$835$	9.36361	+	14.0854i	0.324041	+	0.487445i
$836$		0			0
$837$	−18.4459	−	18.4459i	−0.637582	−	0.637582i
$838$		0			0
$839$	−21.6802			−0.748483			−0.374242	−	0.927331i	$-0.622097\pi$
$839$	−21.6802			−0.748483			−0.374242	+	0.927331i	$0.622097\pi$
$840$		0			0
$841$	28.9213			0.997286
$842$		0			0
$843$	−7.19575	−	7.19575i	−0.247835	−	0.247835i
$844$		0			0
$845$	−2.19207	−	0.441404i	−0.0754094	−	0.0151848i
$846$		0			0
$847$	36.5082	−	36.5082i	1.25444	−	1.25444i
$848$		0			0
$849$			3.01071i			0.103327i
$850$		0			0
$851$		−	38.3621i		−	1.31504i
$852$		0			0
$853$	−5.93379	+	5.93379i	−0.203169	+	0.203169i	−0.801356	−	0.598187i	$-0.795888\pi$
$853$	−5.93379	+	5.93379i	−0.203169	+	0.203169i	0.598187	+	0.801356i	$0.295888\pi$
$854$		0			0
$855$	15.0219	+	3.02488i	0.513740	+	0.103449i
$856$		0			0
$857$	15.4318	+	15.4318i	0.527140	+	0.527140i	0.919718	−	0.392579i	$-0.128417\pi$
$857$	15.4318	+	15.4318i	0.527140	+	0.527140i	−0.392579	+	0.919718i	$0.628417\pi$
$858$		0			0
$859$	−27.2415			−0.929469			−0.464734	−	0.885450i	$-0.653850\pi$
$859$	−27.2415			−0.929469			−0.464734	+	0.885450i	$0.653850\pi$
$860$		0			0
$861$	−5.80704			−0.197904
$862$		0			0
$863$	36.7672	+	36.7672i	1.25157	+	1.25157i	0.955016	+	0.296554i	$0.0958375\pi$
$863$	36.7672	+	36.7672i	1.25157	+	1.25157i	0.296554	+	0.955016i	$0.404162\pi$
$864$		0			0
$865$	20.4572	+	30.7731i	0.695565	+	1.04632i
$866$		0			0
$867$	−4.54480	+	4.54480i	−0.154350	+	0.154350i
$868$		0			0
$869$			4.00183i			0.135753i
$870$		0			0
$871$		−	8.50048i		−	0.288028i
$872$		0			0
$873$	19.2562	−	19.2562i	0.651723	−	0.651723i
$874$		0			0
$875$	9.99453	+	52.1715i	0.337877	+	1.76372i
$876$		0			0
$877$	26.3747	+	26.3747i	0.890612	+	0.890612i	0.994581	−	0.103969i	$-0.0331542\pi$
$877$	26.3747	+	26.3747i	0.890612	+	0.890612i	−0.103969	+	0.994581i	$0.533154\pi$
$878$		0			0
$879$	5.66248			0.190991
$880$		0			0
$881$	−45.1451			−1.52098			−0.760489	−	0.649351i	$-0.775040\pi$
$881$	−45.1451			−1.52098			−0.760489	+	0.649351i	$0.775040\pi$
$882$		0			0
$883$	7.07335	+	7.07335i	0.238037	+	0.238037i	0.816037	−	0.578000i	$-0.196167\pi$
$883$	7.07335	+	7.07335i	0.238037	+	0.238037i	−0.578000	+	0.816037i	$0.696167\pi$
$884$		0			0
$885$	9.20903	−	6.12192i	0.309558	−	0.205786i
$886$		0			0
$887$	−34.1608	+	34.1608i	−1.14701	+	1.14701i	−0.159869	+	0.987138i	$0.551107\pi$
$887$	−34.1608	+	34.1608i	−1.14701	+	1.14701i	−0.987138	+	0.159869i	$0.948893\pi$
$888$		0			0
$889$			59.0137i			1.97926i
$890$		0			0
$891$		−	2.52868i		−	0.0847141i
$892$		0			0
$893$	−3.15012	+	3.15012i	−0.105415	+	0.105415i
$894$		0			0
$895$	5.92502	−	29.4244i	0.198052	−	0.983550i
$896$		0			0
$897$	−1.76552	−	1.76552i	−0.0589491	−	0.0589491i
$898$		0			0
$899$	−2.61179			−0.0871082
$900$		0			0
$901$	22.8484			0.761191
$902$		0			0
$903$	−17.8198	−	17.8198i	−0.593006	−	0.593006i
$904$		0			0
$905$	−2.80010	+	13.9056i	−0.0930783	+	0.462239i
$906$		0			0
$907$	−20.6153	+	20.6153i	−0.684520	+	0.684520i	−0.961015	−	0.276495i	$-0.910827\pi$
$907$	−20.6153	+	20.6153i	−0.684520	+	0.684520i	0.276495	+	0.961015i	$0.410827\pi$
$908$		0			0
$909$			12.9468i			0.429417i
$910$		0			0
$911$			53.6136i			1.77630i	0.459555	+	0.888149i	$0.348009\pi$
$911$			53.6136i			1.77630i	−0.459555	+	0.888149i	$0.651991\pi$
$912$		0			0
$913$	−2.27531	+	2.27531i	−0.0753018	+	0.0753018i
$914$		0			0
$915$	−7.04581	+	4.68387i	−0.232927	+	0.154844i
$916$		0			0
$917$	22.2173	+	22.2173i	0.733679	+	0.733679i
$918$		0			0
$919$	−47.3047			−1.56044			−0.780219	−	0.625507i	$-0.784892\pi$
$919$	−47.3047			−1.56044			−0.780219	+	0.625507i	$0.784892\pi$
$920$		0			0
$921$	−6.62661			−0.218354
$922$		0			0
$923$	−10.7842	−	10.7842i	−0.354968	−	0.354968i
$924$		0			0
$925$	14.1309	+	34.5752i	0.464621	+	1.13682i
$926$		0			0
$927$	−17.1142	+	17.1142i	−0.562106	+	0.562106i
$928$		0			0
$929$		−	2.43565i		−	0.0799112i	−0.999201	−	0.0399556i	$-0.987278\pi$
$929$		−	2.43565i		−	0.0799112i	0.999201	−	0.0399556i	$-0.0127217\pi$
$930$		0			0
$931$			38.6187i			1.26568i
$932$		0			0
$933$	9.61278	−	9.61278i	0.314708	−	0.314708i
$934$		0			0
$935$	−0.878502	−	1.32150i	−0.0287301	−	0.0432178i
$936$		0			0
$937$	−1.76513	−	1.76513i	−0.0576641	−	0.0576641i	0.677687	−	0.735351i	$-0.262983\pi$
$937$	−1.76513	−	1.76513i	−0.0576641	−	0.0576641i	−0.735351	+	0.677687i	$0.762983\pi$
$938$		0			0
$939$	−6.34782			−0.207153
$940$		0			0
$941$	58.6875			1.91316			0.956578	−	0.291476i	$-0.0941463\pi$
$941$	58.6875			1.91316			0.956578	+	0.291476i	$0.0941463\pi$
$942$		0			0
$943$	9.12809	+	9.12809i	0.297251	+	0.297251i
$944$		0			0
$945$	29.1860	+	5.87701i	0.949421	+	0.191179i
$946$		0			0
$947$	7.14068	−	7.14068i	0.232041	−	0.232041i	−0.581503	−	0.813544i	$-0.697535\pi$
$947$	7.14068	−	7.14068i	0.232041	−	0.232041i	0.813544	+	0.581503i	$0.197535\pi$
$948$		0			0
$949$		−	8.09215i		−	0.262682i
$950$		0			0
$951$		−	3.27143i		−	0.106083i
$952$		0			0
$953$	2.13961	−	2.13961i	0.0693087	−	0.0693087i	−0.671603	−	0.740911i	$-0.734394\pi$
$953$	2.13961	−	2.13961i	0.0693087	−	0.0693087i	0.740911	+	0.671603i	$0.234394\pi$
$954$		0			0
$955$	−33.1897	−	6.68322i	−1.07399	−	0.216264i
$956$		0			0
$957$	0.0352059	+	0.0352059i	0.00113805	+	0.00113805i
$958$		0			0
$959$	76.8379			2.48123
$960$		0			0
$961$	−55.6555			−1.79534
$962$		0			0
$963$	25.8176	+	25.8176i	0.831961	+	0.831961i
$964$		0			0
$965$	−7.93796	−	11.9408i	−0.255532	−	0.384389i
$966$		0			0
$967$	21.5496	−	21.5496i	0.692988	−	0.692988i	−0.269900	−	0.962888i	$-0.586991\pi$
$967$	21.5496	−	21.5496i	0.692988	−	0.692988i	0.962888	+	0.269900i	$0.0869908\pi$
$968$		0			0
$969$		−	2.34426i		−	0.0753085i
$970$		0			0
$971$			7.61461i			0.244364i	0.992508	+	0.122182i	$0.0389892\pi$
$971$			7.61461i			0.244364i	−0.992508	+	0.122182i	$0.961011\pi$
$972$		0			0
$973$	15.6759	−	15.6759i	0.502548	−	0.502548i
$974$		0			0
$975$	2.24158	+	0.940897i	0.0717879	+	0.0301328i
$976$		0			0
$977$	−6.46323	−	6.46323i	−0.206777	−	0.206777i	0.596119	−	0.802896i	$-0.296709\pi$
$977$	−6.46323	−	6.46323i	−0.206777	−	0.206777i	−0.802896	+	0.596119i	$0.796709\pi$
$978$		0			0
$979$	3.47792			0.111155
$980$		0			0
$981$	−24.6968			−0.788508
$982$		0			0
$983$	−13.0357	−	13.0357i	−0.415775	−	0.415775i	0.467970	−	0.883745i	$-0.344986\pi$
$983$	−13.0357	−	13.0357i	−0.415775	−	0.415775i	−0.883745	+	0.467970i	$0.844986\pi$
$984$		0			0
$985$	38.5633	−	25.6359i	1.22873	−	0.816828i
$986$		0			0
$987$	−2.93465	+	2.93465i	−0.0934110	+	0.0934110i
$988$		0			0
$989$			56.0218i			1.78139i
$990$		0			0
$991$			4.26249i			0.135402i	0.997706	+	0.0677012i	$0.0215665\pi$
$991$			4.26249i			0.135402i	−0.997706	+	0.0677012i	$0.978434\pi$
$992$		0			0
$993$	1.34718	−	1.34718i	0.0427515	−	0.0427515i
$994$		0			0
$995$	6.35189	−	31.5443i	0.201368	−	1.00002i
$996$		0			0
$997$	22.1816	+	22.1816i	0.702499	+	0.702499i	0.964946	−	0.262447i	$-0.0845296\pi$
$997$	22.1816	+	22.1816i	0.702499	+	0.702499i	−0.262447	+	0.964946i	$0.584530\pi$
$998$		0			0
$999$	20.9340			0.662323

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1040.2.bp.a.287.6	✓	24
4.3	odd	2	inner	1040.2.bp.a.287.7	yes	24
5.3	odd	4	inner	1040.2.bp.a.703.7	yes	24
20.3	even	4	inner	1040.2.bp.a.703.6	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1040.2.bp.a.287.6	✓	24	1.1	even	1	trivial
1040.2.bp.a.287.7	yes	24	4.3	odd	2	inner
1040.2.bp.a.703.6	yes	24	20.3	even	4	inner
1040.2.bp.a.703.7	yes	24	5.3	odd	4	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:	\( N \)	\(=\)	\( 1040 = 2^{4} \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1040.bp (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.343801 - 0.343801i) q^{3} +(0.441404 - 2.19207i) q^{5} +(3.35962 - 3.35962i) q^{7} -2.76360i q^{9} +O(q^{10})\)	\(q+(-0.343801 - 0.343801i) q^{3} +(0.441404 - 2.19207i) q^{5} +(3.35962 - 3.35962i) q^{7} -2.76360i q^{9} +0.364979i q^{11} +(0.707107 - 0.707107i) q^{13} +(-0.905390 + 0.601880i) q^{15} +(-1.37490 - 1.37490i) q^{17} -2.47969 q^{19} -2.31008 q^{21} +(3.63121 + 3.63121i) q^{23} +(-4.61033 - 1.93517i) q^{25} +(-1.98153 + 1.98153i) q^{27} +0.280570i q^{29} +9.30889i q^{31} +(0.125480 - 0.125480i) q^{33} +(-5.88156 - 8.84745i) q^{35} +(-5.28228 - 5.28228i) q^{37} -0.486208 q^{39} +2.51379 q^{41} +(7.71393 + 7.71393i) q^{43} +(-6.05800 - 1.21986i) q^{45} +(1.27037 - 1.27037i) q^{47} -15.5740i q^{49} +0.945386i q^{51} +(-8.30910 + 8.30910i) q^{53} +(0.800059 + 0.161103i) q^{55} +(0.852519 + 0.852519i) q^{57} -10.1713 q^{59} +7.78207 q^{61} +(-9.28464 - 9.28464i) q^{63} +(-1.23791 - 1.86215i) q^{65} +(6.01075 - 6.01075i) q^{67} -2.49683i q^{69} -15.2512i q^{71} +(5.72201 - 5.72201i) q^{73} +(0.919719 + 2.25035i) q^{75} +(1.22619 + 1.22619i) q^{77} +10.9646 q^{79} -6.92830 q^{81} +(6.23409 + 6.23409i) q^{83} +(-3.62077 + 2.40699i) q^{85} +(0.0964601 - 0.0964601i) q^{87} -9.52909i q^{89} -4.75121i q^{91} +(3.20041 - 3.20041i) q^{93} +(-1.09454 + 5.43564i) q^{95} +(6.96779 + 6.96779i) q^{97} +1.00866 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 8 q^{5}+O(q^{10}) \) 24 * q - 8 * q^5	\( 24 q - 8 q^{5} + 16 q^{17} + 16 q^{21} - 16 q^{25} - 24 q^{33} - 24 q^{37} + 16 q^{41} + 48 q^{45} + 8 q^{53} + 8 q^{57} + 16 q^{61} + 8 q^{73} + 24 q^{77} + 40 q^{81} + 16 q^{85} + 56 q^{93} + 32 q^{97}+O(q^{100}) \) 24 * q - 8 * q^5 + 16 * q^17 + 16 * q^21 - 16 * q^25 - 24 * q^33 - 24 * q^37 + 16 * q^41 + 48 * q^45 + 8 * q^53 + 8 * q^57 + 16 * q^61 + 8 * q^73 + 24 * q^77 + 40 * q^81 + 16 * q^85 + 56 * q^93 + 32 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

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Database

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