LMFDB - Embedded newform 1148.2.ba.a.701.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1148,2,Mod(113,1148)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1148, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 0, 7]))

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

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

chi := DirichletCharacter("1148.113");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1148 = 2^{2} \cdot 7 \cdot 41 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1148.ba (of order $10$, degree $4$, 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:	$9.16682615204$
Analytic rank:	$0$
Dimension:	$80$
Relative dimension:	$20$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			701.16
Character	$\chi$	$=$	1148.701
Dual form			1148.2.ba.a.113.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.92602i q^{3} +(-0.139283 + 0.428669i) q^{5} +(0.587785 - 0.809017i) q^{7} -0.709536 q^{9} +O(q^{10})$	\(q+1.92602i q^{3} +(-0.139283 + 0.428669i) q^{5} +(0.587785 - 0.809017i) q^{7} -0.709536 q^{9} +(-2.10233 + 0.683089i) q^{11} +(-0.972224 - 1.33815i) q^{13} +(-0.825623 - 0.268261i) q^{15} +(-2.14323 + 0.696377i) q^{17} +(-5.11495 + 7.04013i) q^{19} +(1.55818 + 1.13208i) q^{21} +(-3.19690 + 2.32268i) q^{23} +(3.88073 + 2.81951i) q^{25} +4.41147i q^{27} +(0.718030 + 0.233302i) q^{29} +(-1.81584 - 5.58857i) q^{31} +(-1.31564 - 4.04912i) q^{33} +(0.264932 + 0.364648i) q^{35} +(-2.05784 + 6.33339i) q^{37} +(2.57730 - 1.87252i) q^{39} +(-1.14365 + 6.30016i) q^{41} +(0.280406 - 0.203727i) q^{43} +(0.0988263 - 0.304156i) q^{45} +(-5.20384 - 7.16247i) q^{47} +(-0.309017 - 0.951057i) q^{49} +(-1.34123 - 4.12789i) q^{51} +(1.15547 + 0.375434i) q^{53} -0.996346i q^{55} +(-13.5594 - 9.85147i) q^{57} +(-2.93755 + 2.13426i) q^{59} +(-7.32118 - 5.31915i) q^{61} +(-0.417055 + 0.574027i) q^{63} +(0.709038 - 0.230381i) q^{65} +(11.0803 + 3.60019i) q^{67} +(-4.47353 - 6.15728i) q^{69} +(-1.00436 + 0.326337i) q^{71} +9.55551 q^{73} +(-5.43043 + 7.47434i) q^{75} +(-0.683089 + 2.10233i) q^{77} +6.59667i q^{79} -10.6252 q^{81} -17.0599 q^{83} -1.01573i q^{85} +(-0.449343 + 1.38294i) q^{87} +(0.654613 - 0.900998i) q^{89} -1.65405 q^{91} +(10.7637 - 3.49733i) q^{93} +(-2.30546 - 3.17319i) q^{95} +(14.0674 + 4.57079i) q^{97} +(1.49168 - 0.484676i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 80 q - 4 q^{5} - 60 q^{9}+O(q^{10}) $ 80 * q - 4 * q^5 - 60 * q^9	$ 80 q - 4 q^{5} - 60 q^{9} + 10 q^{11} + 20 q^{15} - 10 q^{17} - 30 q^{19} - 4 q^{21} - 20 q^{25} + 2 q^{31} + 10 q^{33} + 10 q^{37} + 36 q^{39} - 14 q^{41} + 30 q^{43} + 44 q^{45} - 60 q^{47} + 20 q^{49} - 32 q^{51} + 16 q^{57} - 60 q^{59} + 44 q^{61} - 10 q^{65} - 10 q^{67} - 40 q^{71} - 88 q^{73} - 70 q^{75} - 8 q^{77} - 40 q^{81} + 28 q^{83} - 24 q^{87} + 24 q^{91} - 100 q^{93} + 120 q^{97} - 100 q^{99}+O(q^{100}) $ 80 * q - 4 * q^5 - 60 * q^9 + 10 * q^11 + 20 * q^15 - 10 * q^17 - 30 * q^19 - 4 * q^21 - 20 * q^25 + 2 * q^31 + 10 * q^33 + 10 * q^37 + 36 * q^39 - 14 * q^41 + 30 * q^43 + 44 * q^45 - 60 * q^47 + 20 * q^49 - 32 * q^51 + 16 * q^57 - 60 * q^59 + 44 * q^61 - 10 * q^65 - 10 * q^67 - 40 * q^71 - 88 * q^73 - 70 * q^75 - 8 * q^77 - 40 * q^81 + 28 * q^83 - 24 * q^87 + 24 * q^91 - 100 * q^93 + 120 * q^97 - 100 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1148\mathbb{Z}\right)^\times$.

$n$	$493$	$575$	$785$
$\chi(n)$	$1$	$1$	$e\left(\frac{3}{10}\right)$

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
$3$			1.92602i			1.11199i	0.831187	+	0.555993i	$0.187662\pi$
$3$			1.92602i			1.11199i	−0.831187	+	0.555993i	$0.812338\pi$
$4$		0			0
$5$	−0.139283	+	0.428669i	−0.0622892	+	0.191707i	−0.977358	−	0.211590i	$-0.932136\pi$
$5$	−0.139283	+	0.428669i	−0.0622892	+	0.191707i	0.915069	+	0.403297i	$0.132136\pi$
$6$		0			0
$7$	0.587785	−	0.809017i	0.222162	−	0.305780i
$7$	0.587785	−	0.809017i	0.222162	−	0.305780i
$8$		0			0
$9$	−0.709536			−0.236512
$10$		0			0
$11$	−2.10233	+	0.683089i	−0.633877	+	0.205959i	−0.608292	−	0.793714i	$-0.708145\pi$
$11$	−2.10233	+	0.683089i	−0.633877	+	0.205959i	−0.0255851	+	0.999673i	$0.508145\pi$
$12$		0			0
$13$	−0.972224	−	1.33815i	−0.269647	−	0.371137i	0.652624	−	0.757682i	$-0.273668\pi$
$13$	−0.972224	−	1.33815i	−0.269647	−	0.371137i	−0.922270	+	0.386546i	$0.873668\pi$
$14$		0			0
$15$	−0.825623	−	0.268261i	−0.213175	−	0.0692647i
$16$		0			0
$17$	−2.14323	+	0.696377i	−0.519809	+	0.168896i	−0.557159	−	0.830406i	$-0.688108\pi$
$17$	−2.14323	+	0.696377i	−0.519809	+	0.168896i	0.0373496	+	0.999302i	$0.488108\pi$
$18$		0			0
$19$	−5.11495	+	7.04013i	−1.17345	+	1.61512i	−0.538156	+	0.842845i	$0.680879\pi$
$19$	−5.11495	+	7.04013i	−1.17345	+	1.61512i	−0.635294	+	0.772270i	$0.719121\pi$
$20$		0			0
$21$	1.55818	+	1.13208i	0.340023	+	0.247041i
$22$		0			0
$23$	−3.19690	+	2.32268i	−0.666600	+	0.484313i	−0.868885	−	0.495014i	$-0.835163\pi$
$23$	−3.19690	+	2.32268i	−0.666600	+	0.484313i	0.202286	+	0.979327i	$0.435163\pi$
$24$		0			0
$25$	3.88073	+	2.81951i	0.776146	+	0.563903i
$26$		0			0
$27$			4.41147i			0.848988i
$28$		0			0
$29$	0.718030	+	0.233302i	0.133335	+	0.0433231i	0.374924	−	0.927055i	$-0.377669\pi$
$29$	0.718030	+	0.233302i	0.133335	+	0.0433231i	−0.241589	+	0.970379i	$0.577669\pi$
$30$		0			0
$31$	−1.81584	−	5.58857i	−0.326134	−	1.00374i	−0.970926	−	0.239379i	$-0.923056\pi$
$31$	−1.81584	−	5.58857i	−0.326134	−	1.00374i	0.644792	−	0.764358i	$-0.276944\pi$
$32$		0			0
$33$	−1.31564	−	4.04912i	−0.229023	−	0.704862i
$34$		0			0
$35$	0.264932	+	0.364648i	0.0447817	+	0.0616367i
$36$		0			0
$37$	−2.05784	+	6.33339i	−0.338308	+	1.04120i	0.626762	+	0.779211i	$0.284380\pi$
$37$	−2.05784	+	6.33339i	−0.338308	+	1.04120i	−0.965070	+	0.261993i	$0.915620\pi$
$38$		0			0
$39$	2.57730	−	1.87252i	0.412699	−	0.299843i
$40$		0			0
$41$	−1.14365	+	6.30016i	−0.178608	+	0.983920i
$41$	−1.14365	+	6.30016i	−0.178608	+	0.983920i
$42$		0			0
$43$	0.280406	−	0.203727i	0.0427616	−	0.0310681i	−0.566199	−	0.824268i	$-0.691587\pi$
$43$	0.280406	−	0.203727i	0.0427616	−	0.0310681i	0.608961	+	0.793200i	$0.291587\pi$
$44$		0			0
$45$	0.0988263	−	0.304156i	0.0147322	−	0.0453409i
$46$		0			0
$47$	−5.20384	−	7.16247i	−0.759058	−	1.04475i	−0.997292	−	0.0735459i	$-0.976568\pi$
$47$	−5.20384	−	7.16247i	−0.759058	−	1.04475i	0.238234	−	0.971208i	$-0.423432\pi$
$48$		0			0
$49$	−0.309017	−	0.951057i	−0.0441453	−	0.135865i
$50$		0			0
$51$	−1.34123	−	4.12789i	−0.187810	−	0.578020i
$52$		0			0
$53$	1.15547	+	0.375434i	0.158715	+	0.0515698i	0.387297	−	0.921955i	$-0.373409\pi$
$53$	1.15547	+	0.375434i	0.158715	+	0.0515698i	−0.228582	+	0.973525i	$0.573409\pi$
$54$		0			0
$55$		−	0.996346i		−	0.134347i
$56$		0			0
$57$	−13.5594	−	9.85147i	−1.79599	−	1.30486i
$58$		0			0
$59$	−2.93755	+	2.13426i	−0.382437	+	0.277857i	−0.762349	−	0.647166i	$-0.775954\pi$
$59$	−2.93755	+	2.13426i	−0.382437	+	0.277857i	0.379912	+	0.925022i	$0.375954\pi$
$60$		0			0
$61$	−7.32118	−	5.31915i	−0.937381	−	0.681047i	0.0104081	−	0.999946i	$-0.496687\pi$
$61$	−7.32118	−	5.31915i	−0.937381	−	0.681047i	−0.947789	+	0.318899i	$0.896687\pi$
$62$		0			0
$63$	−0.417055	+	0.574027i	−0.0525440	+	0.0723206i
$64$		0			0
$65$	0.709038	−	0.230381i	0.0879454	−	0.0285752i
$66$		0			0
$67$	11.0803	+	3.60019i	1.35367	+	0.439834i	0.893925	−	0.448217i	$-0.147941\pi$
$67$	11.0803	+	3.60019i	1.35367	+	0.439834i	0.459745	+	0.888051i	$0.347941\pi$
$68$		0			0
$69$	−4.47353	−	6.15728i	−0.538549	−	0.741249i
$70$		0			0
$71$	−1.00436	+	0.326337i	−0.119196	+	0.0387291i	−0.368008	−	0.929823i	$-0.619960\pi$
$71$	−1.00436	+	0.326337i	−0.119196	+	0.0387291i	0.248812	+	0.968552i	$0.419960\pi$
$72$		0			0
$73$	9.55551			1.11839			0.559194	−	0.829037i	$-0.311111\pi$
$73$	9.55551			1.11839			0.559194	+	0.829037i	$0.311111\pi$
$74$		0			0
$75$	−5.43043	+	7.47434i	−0.627052	+	0.863063i
$76$		0			0
$77$	−0.683089	+	2.10233i	−0.0778452	+	0.239583i
$78$		0			0
$79$			6.59667i			0.742183i	0.928596	+	0.371092i	$0.121016\pi$
$79$			6.59667i			0.742183i	−0.928596	+	0.371092i	$0.878984\pi$
$80$		0			0
$81$	−10.6252			−1.18057
$82$		0			0
$83$	−17.0599			−1.87256			−0.936282	−	0.351249i	$-0.885757\pi$
$83$	−17.0599			−1.87256			−0.936282	+	0.351249i	$0.885757\pi$
$84$		0			0
$85$		−	1.01573i		−	0.110171i
$86$		0			0
$87$	−0.449343	+	1.38294i	−0.0481747	+	0.148266i
$88$		0			0
$89$	0.654613	−	0.900998i	0.0693888	−	0.0955056i	−0.772912	−	0.634513i	$-0.781201\pi$
$89$	0.654613	−	0.900998i	0.0693888	−	0.0955056i	0.842301	+	0.539008i	$0.181201\pi$
$90$		0			0
$91$	−1.65405			−0.173391
$92$		0			0
$93$	10.7637	−	3.49733i	1.11614	−	0.362656i
$94$		0			0
$95$	−2.30546	−	3.17319i	−0.236535	−	0.325562i
$96$		0			0
$97$	14.0674	+	4.57079i	1.42833	+	0.464093i	0.918240	−	0.396026i	$-0.129611\pi$
$97$	14.0674	+	4.57079i	1.42833	+	0.464093i	0.510093	+	0.860119i	$0.329611\pi$
$98$		0			0
$99$	1.49168	−	0.484676i	0.149920	−	0.0487118i
$100$		0			0
$101$	8.75730	−	12.0534i	0.871384	−	1.19936i	−0.107350	−	0.994221i	$-0.534236\pi$
$101$	8.75730	−	12.0534i	0.871384	−	1.19936i	0.978734	−	0.205136i	$-0.0657635\pi$
$102$		0			0
$103$	−8.73706	−	6.34785i	−0.860888	−	0.625472i	0.0672382	−	0.997737i	$-0.478581\pi$
$103$	−8.73706	−	6.34785i	−0.860888	−	0.625472i	−0.928126	+	0.372265i	$0.878581\pi$
$104$		0			0
$105$	−0.702317	+	0.510263i	−0.0685391	+	0.0497966i
$106$		0			0
$107$	7.71510	+	5.60535i	0.745847	+	0.541890i	0.894537	−	0.446994i	$-0.147506\pi$
$107$	7.71510	+	5.60535i	0.745847	+	0.541890i	−0.148690	+	0.988884i	$0.547506\pi$
$108$		0			0
$109$		−	5.26522i		−	0.504316i	−0.967686	−	0.252158i	$-0.918860\pi$
$109$		−	5.26522i		−	0.504316i	0.967686	−	0.252158i	$-0.0811403\pi$
$110$		0			0
$111$	−12.1982	−	3.96344i	−1.15780	−	0.376193i
$112$		0			0
$113$	−4.54679	−	13.9936i	−0.427726	−	1.31641i	−0.900360	−	0.435147i	$-0.856697\pi$
$113$	−4.54679	−	13.9936i	−0.427726	−	1.31641i	0.472633	−	0.881259i	$-0.343303\pi$
$114$		0			0
$115$	−0.550389	−	1.69392i	−0.0513240	−	0.157959i
$116$		0			0
$117$	0.689829	+	0.949468i	0.0637747	+	0.0877783i
$118$		0			0
$119$	−0.696377	+	2.14323i	−0.0638368	+	0.196469i
$120$		0			0
$121$	−4.94600	+	3.59348i	−0.449636	+	0.326680i
$122$		0			0
$123$	−12.1342	−	2.20269i	−1.09411	−	0.198610i
$124$		0			0
$125$	−3.57239	+	2.59550i	−0.319525	+	0.232148i
$126$		0			0
$127$	0.115096	−	0.354230i	0.0102131	−	0.0314328i	−0.945820	−	0.324691i	$-0.894740\pi$
$127$	0.115096	−	0.354230i	0.0102131	−	0.0314328i	0.956033	+	0.293258i	$0.0947396\pi$
$128$		0			0
$129$	0.392382	+	0.540067i	0.0345473	+	0.0475502i
$130$		0			0
$131$	6.21892	+	19.1399i	0.543350	+	1.67226i	0.724881	+	0.688874i	$0.241895\pi$
$131$	6.21892	+	19.1399i	0.543350	+	1.67226i	−0.181531	+	0.983385i	$0.558105\pi$
$132$		0			0
$133$	2.68909	+	8.27616i	0.233174	+	0.717634i
$134$		0			0
$135$	−1.89106	−	0.614442i	−0.162756	−	0.0528828i
$136$		0			0
$137$		−	10.3062i		−	0.880514i	−0.897872	−	0.440257i	$-0.854887\pi$
$137$		−	10.3062i		−	0.880514i	0.897872	−	0.440257i	$-0.145113\pi$
$138$		0			0
$139$	2.15444	+	1.56529i	0.182737	+	0.132766i	0.675393	−	0.737458i	$-0.263974\pi$
$139$	2.15444	+	1.56529i	0.182737	+	0.132766i	−0.492656	+	0.870224i	$0.663974\pi$
$140$		0			0
$141$	13.7950	−	10.0227i	1.16175	−	0.844062i
$142$		0			0
$143$	2.95801	+	2.14912i	0.247362	+	0.179719i
$144$		0			0
$145$	−0.200019	+	0.275302i	−0.0166106	+	0.0228626i
$146$		0			0
$147$	1.83175	−	0.595172i	0.151080	−	0.0490889i
$148$		0			0
$149$	9.36952	+	3.04434i	0.767581	+	0.249402i	0.666529	−	0.745479i	$-0.267779\pi$
$149$	9.36952	+	3.04434i	0.767581	+	0.249402i	0.101052	+	0.994881i	$0.467779\pi$
$150$		0			0
$151$	12.4149	+	17.0876i	1.01031	+	1.39057i	0.918781	+	0.394769i	$0.129175\pi$
$151$	12.4149	+	17.0876i	1.01031	+	1.39057i	0.0915286	+	0.995802i	$0.470825\pi$
$152$		0			0
$153$	1.52070	−	0.494105i	0.122941	−	0.0399460i
$154$		0			0
$155$	2.64856			0.212738
$156$		0			0
$157$	−2.86206	+	3.93928i	−0.228417	+	0.314389i	−0.907807	−	0.419388i	$-0.862245\pi$
$157$	−2.86206	+	3.93928i	−0.228417	+	0.314389i	0.679390	+	0.733778i	$0.262245\pi$
$158$		0			0
$159$	−0.723091	+	2.22545i	−0.0573449	+	0.176489i
$160$		0			0
$161$			3.95159i			0.311429i
$162$		0			0
$163$	3.29317			0.257941			0.128971	−	0.991648i	$-0.458833\pi$
$163$	3.29317			0.257941			0.128971	+	0.991648i	$0.458833\pi$
$164$		0			0
$165$	1.91898			0.149392
$166$		0			0
$167$			18.8829i			1.46120i	0.682804	+	0.730602i	$0.260760\pi$
$167$			18.8829i			1.46120i	−0.682804	+	0.730602i	$0.739240\pi$
$168$		0			0
$169$	3.17179	−	9.76177i	0.243984	−	0.750905i
$170$		0			0
$171$	3.62924	−	4.99523i	0.277535	−	0.381994i
$172$		0			0
$173$	−20.7077			−1.57438			−0.787188	−	0.616714i	$-0.788464\pi$
$173$	−20.7077			−1.57438			−0.787188	+	0.616714i	$0.788464\pi$
$174$		0			0
$175$	4.56207	−	1.48231i	0.344860	−	0.112052i
$176$		0			0
$177$	−4.11061	−	5.65777i	−0.308973	−	0.425264i
$178$		0			0
$179$	8.31791	+	2.70265i	0.621710	+	0.202006i	0.602899	−	0.797817i	$-0.294012\pi$
$179$	8.31791	+	2.70265i	0.621710	+	0.202006i	0.0188107	+	0.999823i	$0.494012\pi$
$180$		0			0
$181$	15.2537	−	4.95623i	1.13380	−	0.368394i	0.318781	−	0.947828i	$-0.396727\pi$
$181$	15.2537	−	4.95623i	1.13380	−	0.368394i	0.815019	+	0.579435i	$0.196727\pi$
$182$		0			0
$183$	10.2448	−	14.1007i	0.757314	−	1.04235i
$184$		0			0
$185$	−2.42831	−	1.76427i	−0.178533	−	0.129712i
$186$		0			0
$187$	4.03009	−	2.92803i	0.294709	−	0.214119i
$188$		0			0
$189$	3.56895	+	2.59300i	0.259603	+	0.188613i
$190$		0			0
$191$		−	7.15899i		−	0.518006i	−0.965876	−	0.259003i	$-0.916606\pi$
$191$		−	7.15899i		−	0.518006i	0.965876	−	0.259003i	$-0.0833940\pi$
$192$		0			0
$193$	23.9479	+	7.78113i	1.72380	+	0.560098i	0.992532	−	0.121987i	$-0.0389265\pi$
$193$	23.9479	+	7.78113i	1.72380	+	0.560098i	0.731273	+	0.682085i	$0.238926\pi$
$194$		0			0
$195$	0.443717	+	1.36562i	0.0317752	+	0.0977940i
$196$		0			0
$197$	7.66918	+	23.6033i	0.546407	+	1.68167i	0.717622	+	0.696433i	$0.245231\pi$
$197$	7.66918	+	23.6033i	0.546407	+	1.68167i	−0.171215	+	0.985234i	$0.554769\pi$
$198$		0			0
$199$	6.41021	+	8.82289i	0.454408	+	0.625438i	0.973337	−	0.229379i	$-0.0736694\pi$
$199$	6.41021	+	8.82289i	0.454408	+	0.625438i	−0.518930	+	0.854817i	$0.673669\pi$
$200$		0			0
$201$	−6.93403	+	21.3408i	−0.489089	+	1.50526i
$202$		0			0
$203$	0.610792	−	0.443767i	0.0428692	−	0.0311463i
$204$		0			0
$205$	−2.54139	−	1.36775i	−0.177499	−	0.0955280i
$206$		0			0
$207$	2.26832	−	1.64803i	0.157659	−	0.114546i
$208$		0			0
$209$	5.94429	−	18.2946i	0.411175	−	1.26547i
$210$		0			0
$211$	−6.54725	−	9.01151i	−0.450731	−	0.620378i	0.521823	−	0.853054i	$-0.325252\pi$
$211$	−6.54725	−	9.01151i	−0.450731	−	0.620378i	−0.972554	+	0.232675i	$0.925252\pi$
$212$		0			0
$213$	−0.628530	−	1.93442i	−0.0430662	−	0.132544i
$214$		0			0
$215$	0.0482756	+	0.148577i	0.00329237	+	0.0101329i
$216$		0			0
$217$	−5.58857	−	1.81584i	−0.379377	−	0.123267i
$218$		0			0
$219$			18.4041i			1.24363i
$220$		0			0
$221$	3.01556	+	2.19093i	0.202848	+	0.147378i
$222$		0			0
$223$	−2.86057	+	2.07833i	−0.191558	+	0.139175i	−0.679431	−	0.733740i	$-0.737773\pi$
$223$	−2.86057	+	2.07833i	−0.191558	+	0.139175i	0.487872	+	0.872915i	$0.337773\pi$
$224$		0			0
$225$	−2.75352	−	2.00055i	−0.183568	−	0.133370i
$226$		0			0
$227$	−12.6120	+	17.3590i	−0.837091	+	1.15216i	0.149470	+	0.988766i	$0.452243\pi$
$227$	−12.6120	+	17.3590i	−0.837091	+	1.15216i	−0.986561	+	0.163391i	$0.947757\pi$
$228$		0			0
$229$	−0.122283	+	0.0397321i	−0.00808067	+	0.00262557i	−0.313055	−	0.949735i	$-0.601352\pi$
$229$	−0.122283	+	0.0397321i	−0.00808067	+	0.00262557i	0.304974	+	0.952361i	$0.401352\pi$
$230$		0			0
$231$	−4.04912	−	1.31564i	−0.266413	−	0.0865627i
$232$		0			0
$233$	3.12780	+	4.30505i	0.204909	+	0.282033i	0.899087	−	0.437771i	$-0.144232\pi$
$233$	3.12780	+	4.30505i	0.204909	+	0.282033i	−0.694178	+	0.719804i	$0.744232\pi$
$234$		0			0
$235$	3.79513	−	1.23311i	0.247567	−	0.0804395i
$236$		0			0
$237$	−12.7053			−0.825297
$238$		0			0
$239$	11.0216	−	15.1699i	0.712925	−	0.981257i	−0.286804	−	0.957989i	$-0.592593\pi$
$239$	11.0216	−	15.1699i	0.712925	−	0.981257i	0.999729	−	0.0232681i	$-0.00740713\pi$
$240$		0			0
$241$	3.26751	−	10.0564i	0.210479	−	0.647787i	−0.788965	−	0.614438i	$-0.789383\pi$
$241$	3.26751	−	10.0564i	0.210479	−	0.647787i	0.999444	−	0.0333489i	$-0.0106173\pi$
$242$		0			0
$243$		−	7.22983i		−	0.463794i
$244$		0			0
$245$	0.450729			0.0287960
$246$		0			0
$247$	14.3936			0.915845
$248$		0			0
$249$		−	32.8576i		−	2.08226i
$250$		0			0
$251$	−4.36736	+	13.4413i	−0.275665	+	0.848410i	0.713377	+	0.700780i	$0.247165\pi$
$251$	−4.36736	+	13.4413i	−0.275665	+	0.848410i	−0.989043	+	0.147630i	$0.952835\pi$
$252$		0			0
$253$	5.13434	−	7.06682i	0.322793	−	0.444287i
$254$		0			0
$255$	1.95631			0.122509
$256$		0			0
$257$	−11.4037	+	3.70529i	−0.711344	+	0.231130i	−0.642266	−	0.766482i	$-0.722006\pi$
$257$	−11.4037	+	3.70529i	−0.711344	+	0.231130i	−0.0690779	+	0.997611i	$0.522006\pi$
$258$		0			0
$259$	3.91425	+	5.38751i	0.243220	+	0.334763i
$260$		0			0
$261$	−0.509468	−	0.165536i	−0.0315353	−	0.0102464i
$262$		0			0
$263$	19.9964	−	6.49722i	1.23303	−	0.400636i	0.381219	−	0.924485i	$-0.375504\pi$
$263$	19.9964	−	6.49722i	1.23303	−	0.400636i	0.851811	+	0.523849i	$0.175504\pi$
$264$		0			0
$265$	−0.321873	+	0.443021i	−0.0197725	+	0.0272146i
$266$		0			0
$267$	1.73534	+	1.26080i	0.106201	+	0.0771594i
$268$		0			0
$269$	16.6790	−	12.1180i	1.01694	−	0.738848i	0.0512846	−	0.998684i	$-0.483668\pi$
$269$	16.6790	−	12.1180i	1.01694	−	0.738848i	0.965653	+	0.259836i	$0.0836684\pi$
$270$		0			0
$271$	1.66117	+	1.20691i	0.100909	+	0.0733146i	0.637096	−	0.770785i	$-0.280136\pi$
$271$	1.66117	+	1.20691i	0.100909	+	0.0733146i	−0.536187	+	0.844099i	$0.680136\pi$
$272$		0			0
$273$		−	3.18572i		−	0.192809i
$274$		0			0
$275$	−10.0846	−	3.27667i	−0.608121	−	0.197591i
$276$		0			0
$277$	−2.96520	−	9.12593i	−0.178161	−	0.548324i	0.821602	−	0.570061i	$-0.193080\pi$
$277$	−2.96520	−	9.12593i	−0.178161	−	0.548324i	−0.999764	+	0.0217368i	$0.993080\pi$
$278$		0			0
$279$	1.28840	+	3.96529i	0.0771346	+	0.237396i
$280$		0			0
$281$	−7.07083	−	9.73217i	−0.421810	−	0.580572i	0.544239	−	0.838930i	$-0.316819\pi$
$281$	−7.07083	−	9.73217i	−0.421810	−	0.580572i	−0.966049	+	0.258358i	$0.916819\pi$
$282$		0			0
$283$	7.99148	−	24.5952i	0.475044	−	1.46204i	−0.370854	−	0.928691i	$-0.620935\pi$
$283$	7.99148	−	24.5952i	0.475044	−	1.46204i	0.845898	−	0.533344i	$-0.179065\pi$
$284$		0			0
$285$	6.11161	−	4.44035i	0.362021	−	0.263023i
$286$		0			0
$287$	4.42472	+	4.62838i	0.261183	+	0.273204i
$288$		0			0
$289$	−9.64480	+	7.00736i	−0.567341	+	0.412198i
$290$		0			0
$291$	−8.80341	+	27.0941i	−0.516065	+	1.58829i
$292$		0			0
$293$	14.0447	+	19.3309i	0.820500	+	1.12932i	0.989618	+	0.143725i	$0.0459082\pi$
$293$	14.0447	+	19.3309i	0.820500	+	1.12932i	−0.169118	+	0.985596i	$0.554092\pi$
$294$		0			0
$295$	−0.505738	−	1.55650i	−0.0294452	−	0.0906231i
$296$		0			0
$297$	−3.01342	−	9.27437i	−0.174857	−	0.538153i
$298$		0			0
$299$	6.21621	+	2.01977i	0.359493	+	0.116806i
$300$		0			0
$301$		−	0.346601i		−	0.0199778i
$302$		0			0
$303$	23.2150	+	16.8667i	1.33367	+	0.968966i
$304$		0			0
$305$	3.29987	−	2.39749i	0.188950	−	0.137280i
$306$		0			0
$307$	21.0299	+	15.2791i	1.20024	+	0.872026i	0.994308	−	0.106541i	$-0.0339774\pi$
$307$	21.0299	+	15.2791i	1.20024	+	0.872026i	0.205932	+	0.978566i	$0.433977\pi$
$308$		0			0
$309$	12.2261	−	16.8277i	0.695516	−	0.957295i
$310$		0			0
$311$	−18.8804	+	6.13462i	−1.07061	+	0.347862i	−0.790725	−	0.612171i	$-0.790296\pi$
$311$	−18.8804	+	6.13462i	−1.07061	+	0.347862i	−0.279885	+	0.960033i	$0.590296\pi$
$312$		0			0
$313$	−5.77610	−	1.87677i	−0.326484	−	0.106081i	0.141189	−	0.989983i	$-0.454908\pi$
$313$	−5.77610	−	1.87677i	−0.326484	−	0.106081i	−0.467673	+	0.883901i	$0.654908\pi$
$314$		0			0
$315$	−0.187979	−	0.258731i	−0.0105914	−	0.0145778i
$316$		0			0
$317$	−8.94765	+	2.90727i	−0.502550	+	0.163288i	−0.549312	−	0.835618i	$-0.685110\pi$
$317$	−8.94765	+	2.90727i	−0.502550	+	0.163288i	0.0467613	+	0.998906i	$0.485110\pi$
$318$		0			0
$319$	−1.66890			−0.0934406
$320$		0			0
$321$	−10.7960	+	14.8594i	−0.602573	+	0.829371i
$322$		0			0
$323$	6.05992	−	18.6505i	0.337183	−	1.03774i
$324$		0			0
$325$		−	7.93420i		−	0.440110i
$326$		0			0
$327$	10.1409			0.560792
$328$		0			0
$329$	−8.85330			−0.488098
$330$		0			0
$331$		−	0.605520i		−	0.0332824i	−0.999862	−	0.0166412i	$-0.994703\pi$
$331$		−	0.605520i		−	0.0332824i	0.999862	−	0.0166412i	$-0.00529730\pi$
$332$		0			0
$333$	1.46012	−	4.49377i	0.0800138	−	0.246257i
$334$		0			0
$335$	−3.08658	+	4.24832i	−0.168638	+	0.232110i
$336$		0			0
$337$	9.68438			0.527542			0.263771	−	0.964585i	$-0.415034\pi$
$337$	9.68438			0.527542			0.263771	+	0.964585i	$0.415034\pi$
$338$		0			0
$339$	26.9519	−	8.75719i	1.46382	−	0.475625i
$340$		0			0
$341$	7.63498	+	10.5086i	0.413457	+	0.569075i
$342$		0			0
$343$	−0.951057	−	0.309017i	−0.0513522	−	0.0166853i
$344$		0			0
$345$	3.26252	−	1.06006i	0.175648	−	0.0570715i
$346$		0			0
$347$	−14.9107	+	20.5228i	−0.800446	+	1.10172i	0.192282	+	0.981340i	$0.438411\pi$
$347$	−14.9107	+	20.5228i	−0.800446	+	1.10172i	−0.992728	+	0.120380i	$0.961589\pi$
$348$		0			0
$349$	−6.92358	−	5.03027i	−0.370611	−	0.269264i	0.386853	−	0.922141i	$-0.373562\pi$
$349$	−6.92358	−	5.03027i	−0.370611	−	0.269264i	−0.757464	+	0.652877i	$0.773562\pi$
$350$		0			0
$351$	5.90322	−	4.28894i	0.315090	−	0.228927i
$352$		0			0
$353$	17.1474	+	12.4583i	0.912665	+	0.663090i	0.941687	−	0.336489i	$-0.109239\pi$
$353$	17.1474	+	12.4583i	0.912665	+	0.663090i	−0.0290225	+	0.999579i	$0.509239\pi$
$354$		0			0
$355$		−	0.475992i		−	0.0252630i
$356$		0			0
$357$	−4.12789	−	1.34123i	−0.218471	−	0.0709856i
$358$		0			0
$359$	−11.2362	−	34.5813i	−0.593022	−	1.82513i	−0.564336	−	0.825545i	$-0.690868\pi$
$359$	−11.2362	−	34.5813i	−0.593022	−	1.82513i	−0.0286860	−	0.999588i	$-0.509132\pi$
$360$		0			0
$361$	−17.5293	−	53.9497i	−0.922596	−	2.83946i
$362$		0			0
$363$	−6.92110	−	9.52608i	−0.363264	−	0.499989i
$364$		0			0
$365$	−1.33092	+	4.09615i	−0.0696635	+	0.214402i
$366$		0			0
$367$	12.5308	−	9.10414i	0.654101	−	0.475232i	−0.210564	−	0.977580i	$-0.567530\pi$
$367$	12.5308	−	9.10414i	0.654101	−	0.475232i	0.864666	+	0.502347i	$0.167530\pi$
$368$		0			0
$369$	0.811461	−	4.47020i	0.0422430	−	0.232709i
$370$		0			0
$371$	0.982898	−	0.714117i	0.0510295	−	0.0370751i
$372$		0			0
$373$	−4.24556	+	13.0665i	−0.219827	+	0.676558i	0.778949	+	0.627088i	$0.215753\pi$
$373$	−4.24556	+	13.0665i	−0.219827	+	0.676558i	−0.998776	+	0.0494701i	$0.984247\pi$
$374$		0			0
$375$	−4.99897	−	6.88049i	−0.258146	−	0.355307i
$376$		0			0
$377$	−0.385892	−	1.18765i	−0.0198745	−	0.0611673i
$378$		0			0
$379$	−2.10986	−	6.49347i	−0.108376	−	0.333547i	0.882132	−	0.471002i	$-0.156108\pi$
$379$	−2.10986	−	6.49347i	−0.108376	−	0.333547i	−0.990508	+	0.137455i	$0.956108\pi$
$380$		0			0
$381$	0.682252	+	0.221677i	0.0349528	+	0.0113569i
$382$		0			0
$383$		−	6.69312i		−	0.342002i	−0.985271	−	0.171001i	$-0.945300\pi$
$383$		−	6.69312i		−	0.342002i	0.985271	−	0.171001i	$-0.0547002\pi$
$384$		0			0
$385$	−0.806061	−	0.585638i	−0.0410807	−	0.0298469i
$386$		0			0
$387$	−0.198958	+	0.144552i	−0.0101136	+	0.00734798i
$388$		0			0
$389$	−0.403781	−	0.293364i	−0.0204725	−	0.0148742i	0.577502	−	0.816389i	$-0.304028\pi$
$389$	−0.403781	−	0.293364i	−0.0204725	−	0.0148742i	−0.597974	+	0.801515i	$0.704028\pi$
$390$		0			0
$391$	5.23422	−	7.20429i	0.264706	−	0.364337i
$392$		0			0
$393$	−36.8637	+	11.9777i	−1.85953	+	0.604197i
$394$		0			0
$395$	−2.82779	−	0.918803i	−0.142281	−	0.0462300i
$396$		0			0
$397$	20.3359	+	27.9900i	1.02063	+	1.40478i	0.911761	+	0.410720i	$0.134723\pi$
$397$	20.3359	+	27.9900i	1.02063	+	1.40478i	0.108869	+	0.994056i	$0.465277\pi$
$398$		0			0
$399$	−15.9400	+	5.17923i	−0.797999	+	0.259286i
$400$		0			0
$401$	−20.3228			−1.01487			−0.507437	−	0.861689i	$-0.669407\pi$
$401$	−20.3228			−1.01487			−0.507437	+	0.861689i	$0.669407\pi$
$402$		0			0
$403$	−5.71296	+	7.86321i	−0.284583	+	0.391694i
$404$		0			0
$405$	1.47990	−	4.55468i	0.0735371	−	0.226324i
$406$		0			0
$407$		−	14.7206i		−	0.729672i
$408$		0			0
$409$	−1.61976			−0.0800918			−0.0400459	−	0.999198i	$-0.512750\pi$
$409$	−1.61976			−0.0800918			−0.0400459	+	0.999198i	$0.512750\pi$
$410$		0			0
$411$	19.8498			0.979119
$412$		0			0
$413$			3.63101i			0.178671i
$414$		0			0
$415$	2.37615	−	7.31304i	0.116641	−	0.358983i
$416$		0			0
$417$	−3.01478	+	4.14949i	−0.147634	+	0.203201i
$418$		0			0
$419$	−24.1276			−1.17871			−0.589354	−	0.807875i	$-0.700618\pi$
$419$	−24.1276			−1.17871			−0.589354	+	0.807875i	$0.700618\pi$
$420$		0			0
$421$	17.5365	−	5.69795i	0.854676	−	0.277701i	0.151273	−	0.988492i	$-0.451663\pi$
$421$	17.5365	−	5.69795i	0.854676	−	0.277701i	0.703403	+	0.710791i	$0.251663\pi$
$422$		0			0
$423$	3.69231	+	5.08203i	0.179526	+	0.247097i
$424$		0			0
$425$	−10.2807	−	3.34041i	−0.498689	−	0.162034i
$426$		0			0
$427$	−8.60656	+	2.79644i	−0.416501	+	0.135329i
$428$		0			0
$429$	−4.13924	+	5.69718i	−0.199845	+	0.275062i
$430$		0			0
$431$	3.52675	+	2.56233i	0.169878	+	0.123423i	0.669476	−	0.742834i	$-0.266519\pi$
$431$	3.52675	+	2.56233i	0.169878	+	0.123423i	−0.499598	+	0.866257i	$0.666519\pi$
$432$		0			0
$433$	4.66687	−	3.39068i	0.224275	−	0.162946i	−0.469974	−	0.882680i	$-0.655737\pi$
$433$	4.66687	−	3.39068i	0.224275	−	0.162946i	0.694249	+	0.719735i	$0.255737\pi$
$434$		0			0
$435$	−0.530236	−	0.385239i	−0.0254229	−	0.0184708i
$436$		0			0
$437$		−	34.3870i		−	1.64495i
$438$		0			0
$439$	28.7707	+	9.34816i	1.37315	+	0.446163i	0.900411	−	0.435040i	$-0.143266\pi$
$439$	28.7707	+	9.34816i	1.37315	+	0.446163i	0.472738	+	0.881203i	$0.343266\pi$
$440$		0			0
$441$	0.219259	+	0.674809i	0.0104409	+	0.0321338i
$442$		0			0
$443$	4.33994	+	13.3570i	0.206197	+	0.634609i	0.999662	+	0.0259932i	$0.00827483\pi$
$443$	4.33994	+	13.3570i	0.206197	+	0.634609i	−0.793465	+	0.608616i	$0.791725\pi$
$444$		0			0
$445$	0.295053	+	0.406106i	0.0139869	+	0.0192513i
$446$		0			0
$447$	−5.86345	+	18.0458i	−0.277332	+	0.853539i
$448$		0			0
$449$	−3.25616	+	2.36574i	−0.153668	+	0.111646i	−0.661962	−	0.749537i	$-0.730276\pi$
$449$	−3.25616	+	2.36574i	−0.153668	+	0.111646i	0.508295	+	0.861183i	$0.330276\pi$
$450$		0			0
$451$	−1.89924	−	14.0262i	−0.0894317	−	0.660470i
$452$		0			0
$453$	−32.9110	+	23.9113i	−1.54630	+	1.12345i
$454$		0			0
$455$	0.230381	−	0.709038i	0.0108004	−	0.0332402i
$456$		0			0
$457$	8.77548	+	12.0784i	0.410500	+	0.565004i	0.963340	−	0.268283i	$-0.0864561\pi$
$457$	8.77548	+	12.0784i	0.410500	+	0.565004i	−0.552841	+	0.833287i	$0.686456\pi$
$458$		0			0
$459$	−3.07205	−	9.45478i	−0.143391	−	0.441311i
$460$		0			0
$461$	−1.42179	−	4.37582i	−0.0662194	−	0.203802i	0.912472	−	0.409139i	$-0.134171\pi$
$461$	−1.42179	−	4.37582i	−0.0662194	−	0.203802i	−0.978691	+	0.205337i	$0.934171\pi$
$462$		0			0
$463$	8.03576	+	2.61098i	0.373453	+	0.121342i	0.489729	−	0.871875i	$-0.337096\pi$
$463$	8.03576	+	2.61098i	0.373453	+	0.121342i	−0.116276	+	0.993217i	$0.537096\pi$
$464$		0			0
$465$			5.10117i			0.236561i
$466$		0			0
$467$	6.01936	+	4.37332i	0.278543	+	0.202373i	0.718282	−	0.695753i	$-0.244929\pi$
$467$	6.01936	+	4.37332i	0.278543	+	0.202373i	−0.439739	+	0.898126i	$0.644929\pi$
$468$		0			0
$469$	9.42543	−	6.84798i	0.435226	−	0.316210i
$470$		0			0
$471$	−7.58712	−	5.51237i	−0.349596	−	0.253997i
$472$		0			0
$473$	−0.450343	+	0.619844i	−0.0207068	+	0.0285005i
$474$		0			0
$475$	−39.6995	+	12.8991i	−1.82154	+	0.591853i
$476$		0			0
$477$	−0.819845	−	0.266384i	−0.0375381	−	0.0121969i
$478$		0			0
$479$	−4.77228	−	6.56847i	−0.218051	−	0.300121i	0.685953	−	0.727646i	$-0.259386\pi$
$479$	−4.77228	−	6.56847i	−0.218051	−	0.300121i	−0.904004	+	0.427525i	$0.859386\pi$
$480$		0			0
$481$	10.4757	−	3.40377i	0.477652	−	0.155199i
$482$		0			0
$483$	−7.61082			−0.346304
$484$		0			0
$485$	−3.91871	+	5.39364i	−0.177940	+	0.244913i
$486$		0			0
$487$	−6.04231	+	18.5963i	−0.273803	+	0.842679i	0.715731	+	0.698377i	$0.246094\pi$
$487$	−6.04231	+	18.5963i	−0.273803	+	0.842679i	−0.989534	+	0.144303i	$0.953906\pi$
$488$		0			0
$489$			6.34270i			0.286827i
$490$		0			0
$491$	16.2184			0.731926			0.365963	−	0.930629i	$-0.380740\pi$
$491$	16.2184			0.731926			0.365963	+	0.930629i	$0.380740\pi$
$492$		0			0
$493$	−1.70137			−0.0766257
$494$		0			0
$495$			0.706944i			0.0317748i
$496$		0			0
$497$	−0.326337	+	1.00436i	−0.0146382	+	0.0450518i
$498$		0			0
$499$	−20.4446	+	28.1396i	−0.915226	+	1.25970i	0.0501240	+	0.998743i	$0.484038\pi$
$499$	−20.4446	+	28.1396i	−0.915226	+	1.25970i	−0.965350	+	0.260958i	$0.915962\pi$
$500$		0			0
$501$	−36.3688			−1.62484
$502$		0			0
$503$	3.86840	−	1.25692i	0.172483	−	0.0560433i	−0.221502	−	0.975160i	$-0.571096\pi$
$503$	3.86840	−	1.25692i	0.172483	−	0.0560433i	0.393986	+	0.919117i	$0.371096\pi$
$504$		0			0
$505$	3.94717	+	5.43281i	0.175647	+	0.241757i
$506$		0			0
$507$	18.8013	+	6.10892i	0.834996	+	0.271307i
$508$		0			0
$509$	12.9517	−	4.20828i	0.574076	−	0.186529i	−0.00756907	−	0.999971i	$-0.502409\pi$
$509$	12.9517	−	4.20828i	0.574076	−	0.186529i	0.581645	+	0.813443i	$0.302409\pi$
$510$		0			0
$511$	5.61659	−	7.73057i	0.248463	−	0.341980i
$512$		0			0
$513$	−31.0573	−	22.5644i	−1.37121	−	0.996245i
$514$		0			0
$515$	3.93805	−	2.86116i	0.173531	−	0.126078i
$516$		0			0
$517$	15.8328	+	11.5032i	0.696326	+	0.505910i
$518$		0			0
$519$		−	39.8833i		−	1.75068i
$520$		0			0
$521$	−37.9858	−	12.3423i	−1.66419	−	0.540728i	−0.682446	−	0.730936i	$-0.739084\pi$
$521$	−37.9858	−	12.3423i	−1.66419	−	0.540728i	−0.981744	+	0.190208i	$0.939084\pi$
$522$		0			0
$523$	−1.48048	−	4.55646i	−0.0647371	−	0.199240i	0.913456	−	0.406937i	$-0.133403\pi$
$523$	−1.48048	−	4.55646i	−0.0647371	−	0.199240i	−0.978193	+	0.207697i	$0.933403\pi$
$524$		0			0
$525$	2.85494	+	8.78662i	0.124600	+	0.383479i
$526$		0			0
$527$	7.78350	+	10.7131i	0.339055	+	0.466669i
$528$		0			0
$529$	−2.28208	+	7.02353i	−0.0992210	+	0.305371i
$530$		0			0
$531$	2.08430	−	1.51433i	0.0904509	−	0.0657165i
$532$		0			0
$533$	9.54246	−	4.59480i	0.413330	−	0.199023i
$534$		0			0
$535$	−3.47742	+	2.52649i	−0.150342	+	0.109230i
$536$		0			0
$537$	−5.20535	+	16.0204i	−0.224628	+	0.691333i
$538$		0			0
$539$	1.29931	+	1.78835i	0.0559653	+	0.0770297i
$540$		0			0
$541$	−4.33937	−	13.3552i	−0.186564	−	0.574185i	0.813408	−	0.581694i	$-0.197610\pi$
$541$	−4.33937	−	13.3552i	−0.186564	−	0.574185i	−0.999972	+	0.00750878i	$0.997610\pi$
$542$		0			0
$543$	9.54578	+	29.3789i	0.409649	+	1.26077i
$544$		0			0
$545$	2.25703	+	0.733355i	0.0966807	+	0.0314135i
$546$		0			0
$547$		−	29.2085i		−	1.24886i	−0.781079	−	0.624432i	$-0.785330\pi$
$547$		−	29.2085i		−	1.24886i	0.781079	−	0.624432i	$-0.214670\pi$
$548$		0			0
$549$	5.19464	+	3.77413i	0.221702	+	0.161076i
$550$		0			0
$551$	−5.31516	+	3.86169i	−0.226433	+	0.164514i
$552$		0			0
$553$	5.33682	+	3.87742i	0.226944	+	0.164885i
$554$		0			0
$555$	3.39801	−	4.67696i	0.144237	−	0.198526i
$556$		0			0
$557$	−18.1699	+	5.90377i	−0.769885	+	0.250151i	−0.667516	−	0.744596i	$-0.732642\pi$
$557$	−18.1699	+	5.90377i	−0.769885	+	0.250151i	−0.102369	+	0.994746i	$0.532642\pi$
$558$		0			0
$559$	−0.545236	−	0.177158i	−0.0230610	−	0.00749297i
$560$		0			0
$561$	5.63943	+	7.76201i	0.238097	+	0.327712i
$562$		0			0
$563$	−29.4374	+	9.56479i	−1.24064	+	0.403108i	−0.854557	−	0.519357i	$-0.826171\pi$
$563$	−29.4374	+	9.56479i	−1.24064	+	0.403108i	−0.386081	+	0.922465i	$0.626171\pi$
$564$		0			0
$565$	6.63191			0.279006
$566$		0			0
$567$	−6.24532	+	8.59594i	−0.262279	+	0.360996i
$568$		0			0
$569$	−1.23356	+	3.79651i	−0.0517136	+	0.159158i	−0.973578	−	0.228354i	$-0.926666\pi$
$569$	−1.23356	+	3.79651i	−0.0517136	+	0.159158i	0.921865	+	0.387512i	$0.126666\pi$
$570$		0			0
$571$		−	32.2310i		−	1.34882i	−0.738355	−	0.674412i	$-0.764397\pi$
$571$		−	32.2310i		−	1.34882i	0.738355	−	0.674412i	$-0.235603\pi$
$572$		0			0
$573$	13.7883			0.576016
$574$		0			0
$575$	−18.9551			−0.790484
$576$		0			0
$577$			40.0742i			1.66831i	0.551530	+	0.834155i	$0.314044\pi$
$577$			40.0742i			1.66831i	−0.551530	+	0.834155i	$0.685956\pi$
$578$		0			0
$579$	−14.9866	+	46.1240i	−0.622821	+	1.91685i
$580$		0			0
$581$	−10.0275	+	13.8017i	−0.416013	+	0.572592i
$582$		0			0
$583$	−2.68563			−0.111227
$584$		0			0
$585$	−0.503089	+	0.163463i	−0.0208002	+	0.00675838i
$586$		0			0
$587$	5.69573	+	7.83950i	0.235088	+	0.323571i	0.910219	−	0.414127i	$-0.135913\pi$
$587$	5.69573	+	7.83950i	0.235088	+	0.323571i	−0.675131	+	0.737698i	$0.735913\pi$
$588$		0			0
$589$	48.6322	+	15.8015i	2.00385	+	0.651091i
$590$		0			0
$591$	−45.4604	+	14.7710i	−1.86999	+	0.607596i
$592$		0			0
$593$	−11.7409	+	16.1600i	−0.482142	+	0.663611i	−0.978915	−	0.204270i	$-0.934518\pi$
$593$	−11.7409	+	16.1600i	−0.482142	+	0.663611i	0.496773	+	0.867880i	$0.334518\pi$
$594$		0			0
$595$	−0.821742	−	0.597030i	−0.0336881	−	0.0244759i
$596$		0			0
$597$	−16.9930	+	12.3462i	−0.695478	+	0.505295i
$598$		0			0
$599$	−25.1345	−	18.2613i	−1.02697	−	0.746135i	−0.0592674	−	0.998242i	$-0.518876\pi$
$599$	−25.1345	−	18.2613i	−1.02697	−	0.746135i	−0.967699	+	0.252107i	$0.918876\pi$
$600$		0			0
$601$		−	1.38917i		−	0.0566655i	−0.999599	−	0.0283327i	$-0.990980\pi$
$601$		−	1.38917i		−	0.0566655i	0.999599	−	0.0283327i	$-0.00901980\pi$
$602$		0			0
$603$	−7.86185	−	2.55447i	−0.320159	−	0.104026i
$604$		0			0
$605$	−0.851519	−	2.62071i	−0.0346192	−	0.106547i
$606$		0			0
$607$	9.24189	+	28.4436i	0.375117	+	1.15449i	0.943400	+	0.331657i	$0.107608\pi$
$607$	9.24189	+	28.4436i	0.375117	+	1.15449i	−0.568283	+	0.822833i	$0.692392\pi$
$608$		0			0
$609$	0.854702	+	1.17640i	0.0346343	+	0.0476700i
$610$		0			0
$611$	−4.52518	+	13.9271i	−0.183069	+	0.563428i
$612$		0			0
$613$	−5.70143	+	4.14233i	−0.230278	+	0.167307i	−0.696941	−	0.717128i	$-0.745456\pi$
$613$	−5.70143	+	4.14233i	−0.230278	+	0.167307i	0.466663	+	0.884435i	$0.345456\pi$
$614$		0			0
$615$	2.63431	−	4.89476i	0.106226	−	0.197376i
$616$		0			0
$617$	3.80328	−	2.76324i	0.153114	−	0.111244i	−0.508590	−	0.861009i	$-0.669833\pi$
$617$	3.80328	−	2.76324i	0.153114	−	0.111244i	0.661705	+	0.749765i	$0.269833\pi$
$618$		0			0
$619$	11.8899	−	36.5934i	0.477896	−	1.47081i	−0.364116	−	0.931354i	$-0.618629\pi$
$619$	11.8899	−	36.5934i	0.477896	−	1.47081i	0.842012	−	0.539459i	$-0.181371\pi$
$620$		0			0
$621$	−10.2464	−	14.1030i	−0.411176	−	0.565935i
$622$		0			0
$623$	−0.344150	−	1.05919i	−0.0137881	−	0.0424354i
$624$		0			0
$625$	6.79650	+	20.9175i	0.271860	+	0.836698i
$626$		0			0
$627$	35.2358	+	11.4488i	1.40718	+	0.457221i
$628$		0			0
$629$		−	15.0069i		−	0.598366i
$630$		0			0
$631$	1.02881	+	0.747472i	0.0409562	+	0.0297564i	0.608075	−	0.793880i	$-0.291942\pi$
$631$	1.02881	+	0.747472i	0.0409562	+	0.0297564i	−0.567119	+	0.823636i	$0.691942\pi$
$632$		0			0
$633$	17.3563	−	12.6101i	0.689852	−	0.501207i
$634$		0			0
$635$	0.135816	+	0.0986763i	0.00538971	+	0.00391585i
$636$		0			0
$637$	−0.972224	+	1.33815i	−0.0385209	+	0.0530195i
$638$		0			0
$639$	0.712632	−	0.231548i	0.0281913	−	0.00915990i
$640$		0			0
$641$	−2.23897	−	0.727487i	−0.0884342	−	0.0287340i	0.264466	−	0.964395i	$-0.414804\pi$
$641$	−2.23897	−	0.727487i	−0.0884342	−	0.0287340i	−0.352900	+	0.935661i	$0.614804\pi$
$642$		0			0
$643$	3.06309	+	4.21599i	0.120797	+	0.166262i	0.865133	−	0.501543i	$-0.167234\pi$
$643$	3.06309	+	4.21599i	0.120797	+	0.166262i	−0.744336	+	0.667805i	$0.767234\pi$
$644$		0			0
$645$	−0.286162	+	0.0929796i	−0.0112676	+	0.00366107i
$646$		0			0
$647$	−29.1066			−1.14430			−0.572149	−	0.820150i	$-0.693890\pi$
$647$	−29.1066			−1.14430			−0.572149	+	0.820150i	$0.693890\pi$
$648$		0			0
$649$	4.71782	−	6.49352i	0.185191	−	0.254893i
$650$		0			0
$651$	3.49733	−	10.7637i	0.137071	−	0.421862i
$652$		0			0
$653$		−	25.9950i		−	1.01726i	−0.860984	−	0.508631i	$-0.830152\pi$
$653$		−	25.9950i		−	1.01726i	0.860984	−	0.508631i	$-0.169848\pi$
$654$		0			0
$655$	−9.07086			−0.354428
$656$		0			0
$657$	−6.77998			−0.264512
$658$		0			0
$659$			49.8227i			1.94082i	0.241470	+	0.970408i	$0.422370\pi$
$659$			49.8227i			1.94082i	−0.241470	+	0.970408i	$0.577630\pi$
$660$		0			0
$661$	−5.90574	+	18.1760i	−0.229707	+	0.706965i	0.768073	+	0.640362i	$0.221216\pi$
$661$	−5.90574	+	18.1760i	−0.229707	+	0.706965i	−0.997780	+	0.0666022i	$0.978784\pi$
$662$		0			0
$663$	−4.21977	+	5.80801i	−0.163882	+	0.225564i
$664$		0			0
$665$	−3.92228			−0.152099
$666$		0			0
$667$	−2.83736	+	0.921913i	−0.109863	+	0.0356966i
$668$		0			0
$669$	−4.00289	−	5.50951i	−0.154761	−	0.213010i
$670$		0			0
$671$	19.0250	+	6.18159i	0.734451	+	0.238638i
$672$		0			0
$673$	25.2612	−	8.20785i	0.973746	−	0.316389i	0.221419	−	0.975179i	$-0.428931\pi$
$673$	25.2612	−	8.20785i	0.973746	−	0.316389i	0.752327	+	0.658790i	$0.228931\pi$
$674$		0			0
$675$	−12.4382	+	17.1197i	−0.478746	+	0.658938i
$676$		0			0
$677$	7.30645	+	5.30845i	0.280810	+	0.204020i	0.719270	−	0.694730i	$-0.244476\pi$
$677$	7.30645	+	5.30845i	0.280810	+	0.204020i	−0.438461	+	0.898750i	$0.644476\pi$
$678$		0			0
$679$	11.9665	−	8.69416i	0.459232	−	0.333651i
$680$		0			0
$681$	−33.4337	−	24.2910i	−1.28118	−	0.930833i
$682$		0			0
$683$		−	12.7724i		−	0.488721i	−0.969684	−	0.244361i	$-0.921422\pi$
$683$		−	12.7724i		−	0.488721i	0.969684	−	0.244361i	$-0.0785780\pi$
$684$		0			0
$685$	4.41793	+	1.43547i	0.168800	+	0.0548465i
$686$		0			0
$687$	−0.0765246	−	0.235519i	−0.00291960	−	0.00898559i
$688$		0			0
$689$	−0.620985	−	1.91119i	−0.0236576	−	0.0728107i
$690$		0			0
$691$	−19.6788	−	27.0856i	−0.748618	−	1.03038i	−0.998076	−	0.0619989i	$-0.980252\pi$
$691$	−19.6788	−	27.0856i	−0.748618	−	1.03038i	0.249458	−	0.968386i	$-0.419748\pi$
$692$		0			0
$693$	0.484676	−	1.49168i	0.0184113	−	0.0566643i
$694$		0			0
$695$	−0.971069	+	0.705523i	−0.0368347	+	0.0267620i
$696$		0			0
$697$	−1.93619	−	14.2991i	−0.0733383	−	0.541617i
$698$		0			0
$699$	−8.29159	+	6.02419i	−0.313617	+	0.227856i
$700$		0			0
$701$	−6.97042	+	21.4527i	−0.263269	+	0.810259i	0.728818	+	0.684707i	$0.240070\pi$
$701$	−6.97042	+	21.4527i	−0.263269	+	0.810259i	−0.992087	+	0.125551i	$0.959930\pi$
$702$		0			0
$703$	−34.0621	−	46.8825i	−1.28468	−	1.76821i
$704$		0			0
$705$	2.37500	+	7.30949i	0.0894476	+	0.275291i
$706$		0			0
$707$	−4.60398	−	14.1696i	−0.173151	−	0.532903i
$708$		0			0
$709$	39.6349	+	12.8781i	1.48852	+	0.483649i	0.936645	−	0.350279i	$-0.113913\pi$
$709$	39.6349	+	12.8781i	1.48852	+	0.483649i	0.551873	+	0.833928i	$0.313913\pi$
$710$		0			0
$711$		−	4.68058i		−	0.175535i
$712$		0			0
$713$	18.7855	+	13.6485i	0.703524	+	0.511140i
$714$		0			0
$715$	−1.33326	+	0.968672i	−0.0498612	+	0.0362263i
$716$		0			0
$717$	29.2174	+	21.2277i	1.09114	+	0.792763i
$718$		0			0
$719$	−25.8899	+	35.6344i	−0.965530	+	1.32894i	−0.0212573	+	0.999774i	$0.506767\pi$
$719$	−25.8899	+	35.6344i	−0.965530	+	1.32894i	−0.944273	+	0.329164i	$0.893233\pi$
$720$		0			0
$721$	−10.2710	+	3.33726i	−0.382513	+	0.124286i
$722$		0			0
$723$	19.3687	+	6.29327i	0.720330	+	0.234049i
$724$		0			0
$725$	2.12868	+	2.92988i	0.0790572	+	0.108813i
$726$		0			0
$727$	−31.3662	+	10.1915i	−1.16331	+	0.377982i	−0.826142	−	0.563462i	$-0.809469\pi$
$727$	−31.3662	+	10.1915i	−1.16331	+	0.377982i	−0.337168	+	0.941445i	$0.609469\pi$
$728$		0			0
$729$	−17.9507			−0.664842
$730$		0			0
$731$	−0.459104	+	0.631902i	−0.0169806	+	0.0233717i
$732$		0			0
$733$	11.1282	−	34.2489i	0.411028	−	1.26501i	−0.504728	−	0.863278i	$-0.668407\pi$
$733$	11.1282	−	34.2489i	0.411028	−	1.26501i	0.915756	−	0.401735i	$-0.131593\pi$
$734$		0			0
$735$			0.868111i			0.0320208i
$736$		0			0
$737$	−25.7536			−0.948647
$738$		0			0
$739$	26.9701			0.992110			0.496055	−	0.868291i	$-0.334781\pi$
$739$	26.9701			0.992110			0.496055	+	0.868291i	$0.334781\pi$
$740$		0			0
$741$			27.7224i			1.01841i
$742$		0			0
$743$	6.66286	−	20.5062i	0.244437	−	0.752299i	−0.751292	−	0.659970i	$-0.770569\pi$
$743$	6.66286	−	20.5062i	0.244437	−	0.752299i	0.995729	−	0.0923289i	$-0.0294311\pi$
$744$		0			0
$745$	−2.61003	+	3.59240i	−0.0956241	+	0.131615i
$746$		0			0
$747$	12.1046			0.442884
$748$		0			0
$749$	9.06965	−	2.94691i	0.331398	−	0.107678i
$750$		0			0
$751$	−26.0233	−	35.8180i	−0.949603	−	1.30702i	−0.951704	−	0.307018i	$-0.900669\pi$
$751$	−26.0233	−	35.8180i	−0.949603	−	1.30702i	0.00210110	−	0.999998i	$-0.499331\pi$
$752$		0			0
$753$	−25.8882	−	8.41160i	−0.943420	−	0.306536i
$754$		0			0
$755$	−9.05411	+	2.94186i	−0.329513	+	0.107065i
$756$		0			0
$757$	−4.15546	+	5.71950i	−0.151033	+	0.207879i	−0.877829	−	0.478975i	$-0.841009\pi$
$757$	−4.15546	+	5.71950i	−0.151033	+	0.207879i	0.726796	+	0.686853i	$0.241009\pi$
$758$		0			0
$759$	13.6108	+	9.88882i	0.494041	+	0.358942i
$760$		0			0
$761$	25.6482	−	18.6345i	0.929747	−	0.675501i	−0.0161835	−	0.999869i	$-0.505152\pi$
$761$	25.6482	−	18.6345i	0.929747	−	0.675501i	0.945931	+	0.324368i	$0.105152\pi$
$762$		0			0
$763$	−4.25965	−	3.09482i	−0.154210	−	0.112040i
$764$		0			0
$765$			0.720696i			0.0260568i
$766$		0			0
$767$	5.71192	+	1.85592i	0.206245	+	0.0670132i
$768$		0			0
$769$	−2.92490	−	9.00191i	−0.105474	−	0.324617i	0.884367	−	0.466792i	$-0.154590\pi$
$769$	−2.92490	−	9.00191i	−0.105474	−	0.324617i	−0.989842	+	0.142175i	$0.954590\pi$
$770$		0			0
$771$	−7.13645	−	21.9637i	−0.257013	−	0.791005i
$772$		0			0
$773$	−1.83069	−	2.51973i	−0.0658453	−	0.0906282i	0.774824	−	0.632177i	$-0.217838\pi$
$773$	−1.83069	−	2.51973i	−0.0658453	−	0.0906282i	−0.840670	+	0.541548i	$0.817838\pi$
$774$		0			0
$775$	8.71028	−	26.8075i	0.312883	−	0.962954i
$776$		0			0
$777$	−10.3764	+	7.53891i	−0.372252	+	0.270457i
$778$		0			0
$779$	−38.5042	−	40.2765i	−1.37956	−	1.44305i
$780$		0			0
$781$	1.88859	−	1.37214i	0.0675789	−	0.0490989i
$782$		0			0
$783$	−1.02920	+	3.16757i	−0.0367808	+	0.113200i
$784$		0			0
$785$	−1.29001	−	1.77555i	−0.0460425	−	0.0633721i
$786$		0			0
$787$	−4.96058	−	15.2671i	−0.176826	−	0.544213i	0.822887	−	0.568206i	$-0.192362\pi$
$787$	−4.96058	−	15.2671i	−0.176826	−	0.544213i	−0.999712	+	0.0239924i	$0.992362\pi$
$788$		0			0
$789$	12.5138	+	38.5134i	0.445501	+	1.37111i
$790$		0			0
$791$	−13.9936	−	4.54679i	−0.497555	−	0.161665i
$792$		0			0
$793$			14.9682i			0.531538i
$794$		0			0
$795$	−0.853265	−	0.619933i	−0.0302622	−	0.0219868i
$796$		0			0
$797$	36.3590	−	26.4164i	1.28790	−	0.935716i	0.288141	−	0.957588i	$-0.406963\pi$
$797$	36.3590	−	26.4164i	1.28790	−	0.935716i	0.999761	+	0.0218721i	$0.00696267\pi$
$798$		0			0
$799$	16.1408	+	11.7270i	0.571020	+	0.414871i
$800$		0			0
$801$	−0.464472	+	0.639291i	−0.0164113	+	0.0225882i
$802$		0			0
$803$	−20.0889	+	6.52726i	−0.708920	+	0.230342i
$804$		0			0
$805$	−1.69392	−	0.550389i	−0.0597029	−	0.0193986i
$806$		0			0
$807$	23.3395	+	32.1240i	0.821589	+	1.13082i
$808$		0			0
$809$	−24.2048	+	7.86461i	−0.850995	+	0.276505i	−0.701863	−	0.712312i	$-0.747648\pi$
$809$	−24.2048	+	7.86461i	−0.850995	+	0.276505i	−0.149132	+	0.988817i	$0.547648\pi$
$810$		0			0
$811$	−40.3213			−1.41587			−0.707937	−	0.706276i	$-0.750374\pi$
$811$	−40.3213			−1.41587			−0.707937	+	0.706276i	$0.750374\pi$
$812$		0			0
$813$	−2.32453	+	3.19944i	−0.0815248	+	0.112209i
$814$		0			0
$815$	−0.458683	+	1.41168i	−0.0160670	+	0.0494490i
$816$		0			0
$817$			3.01615i			0.105522i
$818$		0			0
$819$	1.17361			0.0410091
$820$		0			0
$821$	1.43762			0.0501732			0.0250866	−	0.999685i	$-0.492014\pi$
$821$	1.43762			0.0501732			0.0250866	+	0.999685i	$0.492014\pi$
$822$		0			0
$823$		−	18.8641i		−	0.657561i	−0.944406	−	0.328780i	$-0.893362\pi$
$823$		−	18.8641i		−	0.657561i	0.944406	−	0.328780i	$-0.106638\pi$
$824$		0			0
$825$	6.31092	−	19.4230i	0.219718	−	0.676222i
$826$		0			0
$827$	8.40166	−	11.5639i	0.292154	−	0.402116i	−0.637558	−	0.770402i	$-0.720055\pi$
$827$	8.40166	−	11.5639i	0.292154	−	0.402116i	0.929712	+	0.368286i	$0.120055\pi$
$828$		0			0
$829$	−31.9993			−1.11138			−0.555690	−	0.831390i	$-0.687546\pi$
$829$	−31.9993			−1.11138			−0.555690	+	0.831390i	$0.687546\pi$
$830$		0			0
$831$	17.5767	−	5.71101i	0.609729	−	0.198113i
$832$		0			0
$833$	1.32459	+	1.82314i	0.0458942	+	0.0631680i
$834$		0			0
$835$	−8.09451	−	2.63007i	−0.280122	−	0.0910172i
$836$		0			0
$837$	24.6538	−	8.01051i	0.852160	−	0.276884i
$838$		0			0
$839$	27.9502	−	38.4701i	0.964947	−	1.32814i	0.0203888	−	0.999792i	$-0.493510\pi$
$839$	27.9502	−	38.4701i	0.964947	−	1.32814i	0.944558	−	0.328344i	$-0.106490\pi$
$840$		0			0
$841$	−23.0004	−	16.7107i	−0.793116	−	0.576232i
$842$		0			0
$843$	18.7443	−	13.6185i	0.645588	−	0.469047i
$844$		0			0
$845$	3.74279	+	2.71930i	0.128756	+	0.0935466i
$846$		0			0
$847$			6.11359i			0.210066i
$848$		0			0
$849$	47.3708	+	15.3917i	1.62576	+	0.528242i
$850$		0			0
$851$	−8.13175	−	25.0269i	−0.278753	−	0.857913i
$852$		0			0
$853$	17.7655	+	54.6766i	0.608279	+	1.87209i	0.472450	+	0.881358i	$0.343370\pi$
$853$	17.7655	+	54.6766i	0.608279	+	1.87209i	0.135829	+	0.990732i	$0.456630\pi$
$854$		0			0
$855$	1.63581	+	2.25149i	0.0559434	+	0.0769995i
$856$		0			0
$857$	−6.59547	+	20.2988i	−0.225297	+	0.693393i	0.772964	+	0.634449i	$0.218773\pi$
$857$	−6.59547	+	20.2988i	−0.225297	+	0.693393i	−0.998261	+	0.0589433i	$0.981227\pi$
$858$		0			0
$859$	26.0483	−	18.9252i	0.888756	−	0.645719i	−0.0467972	−	0.998904i	$-0.514901\pi$
$859$	26.0483	−	18.9252i	0.888756	−	0.645719i	0.935553	+	0.353185i	$0.114901\pi$
$860$		0			0
$861$	−8.91432	+	8.52208i	−0.303799	+	0.290432i
$862$		0			0
$863$	2.09696	−	1.52353i	0.0713812	−	0.0518615i	−0.551522	−	0.834160i	$-0.685953\pi$
$863$	2.09696	−	1.52353i	0.0713812	−	0.0518615i	0.622904	+	0.782299i	$0.285953\pi$
$864$		0			0
$865$	2.88423	−	8.87673i	0.0980666	−	0.301818i
$866$		0			0
$867$	−13.4963	−	18.5760i	−0.458358	−	0.630875i
$868$		0			0
$869$	−4.50611	−	13.8684i	−0.152859	−	0.470452i
$870$		0			0
$871$	−5.95489	−	18.3273i	−0.201774	−	0.620996i
$872$		0			0
$873$	−9.98137	−	3.24314i	−0.337818	−	0.109764i
$874$		0			0
$875$			4.41572i			0.149279i
$876$		0			0
$877$	−18.5505	−	13.4778i	−0.626407	−	0.455112i	0.228746	−	0.973486i	$-0.426537\pi$
$877$	−18.5505	−	13.4778i	−0.626407	−	0.455112i	−0.855154	+	0.518374i	$0.826537\pi$
$878$		0			0
$879$	−37.2315	+	27.0503i	−1.25579	+	0.912384i
$880$		0			0
$881$	−33.9397	−	24.6586i	−1.14346	−	0.830770i	−0.155860	−	0.987779i	$-0.549815\pi$
$881$	−33.9397	−	24.6586i	−1.14346	−	0.830770i	−0.987597	+	0.157009i	$0.949815\pi$
$882$		0			0
$883$	4.60226	−	6.33447i	0.154878	−	0.213172i	−0.724526	−	0.689248i	$-0.757941\pi$
$883$	4.60226	−	6.33447i	0.154878	−	0.213172i	0.879404	+	0.476076i	$0.157941\pi$
$884$		0			0
$885$	2.99785	−	0.974060i	0.100772	−	0.0327427i
$886$		0			0
$887$	46.5927	+	15.1389i	1.56443	+	0.508314i	0.957987	−	0.286812i	$-0.0925954\pi$
$887$	46.5927	+	15.1389i	1.56443	+	0.508314i	0.606444	+	0.795126i	$0.292595\pi$
$888$		0			0
$889$	−0.218926	−	0.301326i	−0.00734254	−	0.0101061i
$890$		0			0
$891$	22.3376	−	7.25793i	0.748338	−	0.243150i
$892$		0			0
$893$	77.0421			2.57811
$894$		0			0
$895$	−2.31709	+	3.18920i	−0.0774517	+	0.106603i
$896$		0			0
$897$	−3.89011	+	11.9725i	−0.129887	+	0.399751i
$898$		0			0
$899$		−	4.43640i		−	0.147962i
$900$		0			0
$901$	−2.73787			−0.0912117
$902$		0			0
$903$	0.667559			0.0222150
$904$		0			0
$905$			7.22911i			0.240304i
$906$		0			0
$907$	3.94204	−	12.1323i	0.130893	−	0.402848i	−0.864035	−	0.503431i	$-0.832071\pi$
$907$	3.94204	−	12.1323i	0.130893	−	0.402848i	0.994929	+	0.100583i	$0.0320708\pi$
$908$		0			0
$909$	−6.21362	+	8.55232i	−0.206093	+	0.283662i
$910$		0			0
$911$	−30.8696			−1.02276			−0.511378	−	0.859356i	$-0.670865\pi$
$911$	−30.8696			−1.02276			−0.511378	+	0.859356i	$0.670865\pi$
$912$		0			0
$913$	35.8655	−	11.6534i	1.18697	−	0.385672i
$914$		0			0
$915$	4.61761	+	6.35560i	0.152654	+	0.210110i
$916$		0			0
$917$	19.1399	+	6.21892i	0.632055	+	0.205367i
$918$		0			0
$919$	22.1316	−	7.19100i	0.730054	−	0.237209i	0.0796774	−	0.996821i	$-0.474611\pi$
$919$	22.1316	−	7.19100i	0.730054	−	0.237209i	0.650377	+	0.759612i	$0.274611\pi$
$920$		0			0
$921$	−29.4278	+	40.5039i	−0.969680	+	1.33465i
$922$		0			0
$923$	1.41315	+	1.02672i	0.0465145	+	0.0337948i
$924$		0			0
$925$	−25.8430	+	18.7761i	−0.849713	+	0.617353i
$926$		0			0
$927$	6.19926	+	4.50403i	0.203611	+	0.147932i
$928$		0			0
$929$		−	10.5977i		−	0.347699i	−0.984772	−	0.173849i	$-0.944379\pi$
$929$		−	10.5977i		−	0.347699i	0.984772	−	0.173849i	$-0.0556206\pi$
$930$		0			0
$931$	8.27616	+	2.68909i	0.271240	+	0.0881313i
$932$		0			0
$933$	−11.8154	−	36.3640i	−0.386818	−	1.19050i
$934$		0			0
$935$	0.693833	+	2.13540i	0.0226908	+	0.0698350i
$936$		0			0
$937$	−4.83099	−	6.64929i	−0.157822	−	0.217223i	0.722782	−	0.691076i	$-0.242863\pi$
$937$	−4.83099	−	6.64929i	−0.157822	−	0.217223i	−0.880604	+	0.473853i	$0.842863\pi$
$938$		0			0
$939$	3.61468	−	11.1249i	0.117961	−	0.363046i
$940$		0			0
$941$	10.7429	−	7.80517i	0.350208	−	0.254441i	−0.398748	−	0.917060i	$-0.630555\pi$
$941$	10.7429	−	7.80517i	0.350208	−	0.254441i	0.748956	+	0.662619i	$0.230555\pi$
$942$		0			0
$943$	−10.9772	−	22.7973i	−0.357465	−	0.742383i
$944$		0			0
$945$	−1.60863	+	1.16874i	−0.0523288	+	0.0380191i
$946$		0			0
$947$	16.8748	−	51.9353i	0.548358	−	1.68767i	−0.164512	−	0.986375i	$-0.552605\pi$
$947$	16.8748	−	51.9353i	0.548358	−	1.68767i	0.712870	−	0.701296i	$-0.247395\pi$
$948$		0			0
$949$	−9.29010	−	12.7867i	−0.301569	−	0.415075i
$950$		0			0
$951$	−5.59944	−	17.2333i	−0.181574	−	0.558829i
$952$		0			0
$953$	−1.95656	−	6.02167i	−0.0633791	−	0.195061i	0.914353	−	0.404918i	$-0.132700\pi$
$953$	−1.95656	−	6.02167i	−0.0633791	−	0.195061i	−0.977732	+	0.209857i	$0.932700\pi$
$954$		0			0
$955$	3.06884	+	0.997126i	0.0993052	+	0.0322662i
$956$		0			0
$957$		−	3.21433i		−	0.103905i
$958$		0			0
$959$	−8.33785	−	6.05780i	−0.269243	−	0.195617i
$960$		0			0
$961$	−2.85534	+	2.07452i	−0.0921076	+	0.0669201i
$962$		0			0
$963$	−5.47415	−	3.97720i	−0.176402	−	0.128163i
$964$		0			0
$965$	−6.67106	+	9.18192i	−0.214749	+	0.295577i
$966$		0			0
$967$	15.2761	−	4.96350i	0.491245	−	0.159615i	−0.0529108	−	0.998599i	$-0.516850\pi$
$967$	15.2761	−	4.96350i	0.491245	−	0.159615i	0.544156	+	0.838984i	$0.316850\pi$
$968$		0			0
$969$	35.9212	+	11.6715i	1.15396	+	0.374943i
$970$		0			0
$971$	−7.97667	−	10.9789i	−0.255984	−	0.352331i	0.661612	−	0.749846i	$-0.269873\pi$
$971$	−7.97667	−	10.9789i	−0.255984	−	0.352331i	−0.917596	+	0.397515i	$0.869873\pi$
$972$		0			0
$973$	2.53270	−	0.822923i	0.0811945	−	0.0263817i
$974$		0			0
$975$	15.2814			0.489396
$976$		0			0
$977$	−2.47572	+	3.40754i	−0.0792054	+	0.109017i	−0.846781	−	0.531941i	$-0.821463\pi$
$977$	−2.47572	+	3.40754i	−0.0792054	+	0.109017i	0.767576	+	0.640958i	$0.221463\pi$
$978$		0			0
$979$	−0.760752	+	2.34135i	−0.0243137	+	0.0748300i
$980$		0			0
$981$			3.73586i			0.119277i
$982$		0			0
$983$	51.1471			1.63134			0.815670	−	0.578518i	$-0.196369\pi$
$983$	51.1471			1.63134			0.815670	+	0.578518i	$0.196369\pi$
$984$		0			0
$985$	−11.1862			−0.356422
$986$		0			0
$987$		−	17.0516i		−	0.542758i
$988$		0			0
$989$	−0.423237	+	1.30259i	−0.0134582	+	0.0414200i
$990$		0			0
$991$	−14.6732	+	20.1959i	−0.466109	+	0.641544i	−0.975762	−	0.218836i	$-0.929774\pi$
$991$	−14.6732	+	20.1959i	−0.466109	+	0.641544i	0.509653	+	0.860380i	$0.329774\pi$
$992$		0			0
$993$	1.16624			0.0370095
$994$		0			0
$995$	−4.67493	+	1.51898i	−0.148205	+	0.0481548i
$996$		0			0
$997$	17.6854	+	24.3419i	0.560102	+	0.770915i	0.991340	−	0.131324i	$-0.0419228\pi$
$997$	17.6854	+	24.3419i	0.560102	+	0.770915i	−0.431237	+	0.902239i	$0.641923\pi$
$998$		0			0
$999$	−27.9396	−	9.07812i	−0.883969	−	0.287219i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1148.2.ba.a.701.16	yes	80
41.31	even	10	inner	1148.2.ba.a.113.5	✓	80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1148.2.ba.a.113.5	✓	80	41.31	even	10	inner
1148.2.ba.a.701.16	yes	80	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 1148 = 2^{2} \cdot 7 \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1148.ba (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+1.92602i q^{3} +(-0.139283 + 0.428669i) q^{5} +(0.587785 - 0.809017i) q^{7} -0.709536 q^{9} +O(q^{10})\)	\(q+1.92602i q^{3} +(-0.139283 + 0.428669i) q^{5} +(0.587785 - 0.809017i) q^{7} -0.709536 q^{9} +(-2.10233 + 0.683089i) q^{11} +(-0.972224 - 1.33815i) q^{13} +(-0.825623 - 0.268261i) q^{15} +(-2.14323 + 0.696377i) q^{17} +(-5.11495 + 7.04013i) q^{19} +(1.55818 + 1.13208i) q^{21} +(-3.19690 + 2.32268i) q^{23} +(3.88073 + 2.81951i) q^{25} +4.41147i q^{27} +(0.718030 + 0.233302i) q^{29} +(-1.81584 - 5.58857i) q^{31} +(-1.31564 - 4.04912i) q^{33} +(0.264932 + 0.364648i) q^{35} +(-2.05784 + 6.33339i) q^{37} +(2.57730 - 1.87252i) q^{39} +(-1.14365 + 6.30016i) q^{41} +(0.280406 - 0.203727i) q^{43} +(0.0988263 - 0.304156i) q^{45} +(-5.20384 - 7.16247i) q^{47} +(-0.309017 - 0.951057i) q^{49} +(-1.34123 - 4.12789i) q^{51} +(1.15547 + 0.375434i) q^{53} -0.996346i q^{55} +(-13.5594 - 9.85147i) q^{57} +(-2.93755 + 2.13426i) q^{59} +(-7.32118 - 5.31915i) q^{61} +(-0.417055 + 0.574027i) q^{63} +(0.709038 - 0.230381i) q^{65} +(11.0803 + 3.60019i) q^{67} +(-4.47353 - 6.15728i) q^{69} +(-1.00436 + 0.326337i) q^{71} +9.55551 q^{73} +(-5.43043 + 7.47434i) q^{75} +(-0.683089 + 2.10233i) q^{77} +6.59667i q^{79} -10.6252 q^{81} -17.0599 q^{83} -1.01573i q^{85} +(-0.449343 + 1.38294i) q^{87} +(0.654613 - 0.900998i) q^{89} -1.65405 q^{91} +(10.7637 - 3.49733i) q^{93} +(-2.30546 - 3.17319i) q^{95} +(14.0674 + 4.57079i) q^{97} +(1.49168 - 0.484676i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q - 4 q^{5} - 60 q^{9}+O(q^{10}) \) 80 * q - 4 * q^5 - 60 * q^9	\( 80 q - 4 q^{5} - 60 q^{9} + 10 q^{11} + 20 q^{15} - 10 q^{17} - 30 q^{19} - 4 q^{21} - 20 q^{25} + 2 q^{31} + 10 q^{33} + 10 q^{37} + 36 q^{39} - 14 q^{41} + 30 q^{43} + 44 q^{45} - 60 q^{47} + 20 q^{49} - 32 q^{51} + 16 q^{57} - 60 q^{59} + 44 q^{61} - 10 q^{65} - 10 q^{67} - 40 q^{71} - 88 q^{73} - 70 q^{75} - 8 q^{77} - 40 q^{81} + 28 q^{83} - 24 q^{87} + 24 q^{91} - 100 q^{93} + 120 q^{97} - 100 q^{99}+O(q^{100}) \) 80 * q - 4 * q^5 - 60 * q^9 + 10 * q^11 + 20 * q^15 - 10 * q^17 - 30 * q^19 - 4 * q^21 - 20 * q^25 + 2 * q^31 + 10 * q^33 + 10 * q^37 + 36 * q^39 - 14 * q^41 + 30 * q^43 + 44 * q^45 - 60 * q^47 + 20 * q^49 - 32 * q^51 + 16 * q^57 - 60 * q^59 + 44 * q^61 - 10 * q^65 - 10 * q^67 - 40 * q^71 - 88 * q^73 - 70 * q^75 - 8 * q^77 - 40 * q^81 + 28 * q^83 - 24 * q^87 + 24 * q^91 - 100 * q^93 + 120 * q^97 - 100 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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