LMFDB - Embedded newform 1148.2.ba.a.113.5

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			113.5
Character	$\chi$	$=$	1148.113
Dual form			1148.2.ba.a.701.16

$q$-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 $\left(\mathbb{Z}/1148\mathbb{Z}\right)^\times$.

$n$	$493$	$575$	$785$
$\chi(n)$	$1$	$1$	$e\left(\frac{7}{10}\right)$

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	$-0.812338\pi$
$3$		−	1.92602i		−	1.11199i	0.831187	−	0.555993i	$-0.187662\pi$
$4$		0			0
$5$	−0.139283	−	0.428669i	−0.0622892	−	0.191707i	0.915069	−	0.403297i	$-0.132136\pi$
$5$	−0.139283	−	0.428669i	−0.0622892	−	0.191707i	−0.977358	+	0.211590i	$0.932136\pi$
$6$		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	−0.0255851	−	0.999673i	$-0.508145\pi$
$11$	−2.10233	−	0.683089i	−0.633877	−	0.205959i	−0.608292	+	0.793714i	$0.708145\pi$
$12$		0			0
$13$	−0.972224	+	1.33815i	−0.269647	+	0.371137i	−0.922270	−	0.386546i	$-0.873668\pi$
$13$	−0.972224	+	1.33815i	−0.269647	+	0.371137i	0.652624	+	0.757682i	$0.273668\pi$
$14$		0			0
$15$	−0.825623	+	0.268261i	−0.213175	+	0.0692647i
$16$		0			0
$17$	−2.14323	−	0.696377i	−0.519809	−	0.168896i	0.0373496	−	0.999302i	$-0.488108\pi$
$17$	−2.14323	−	0.696377i	−0.519809	−	0.168896i	−0.557159	+	0.830406i	$0.688108\pi$
$18$		0			0
$19$	−5.11495	−	7.04013i	−1.17345	−	1.61512i	−0.635294	−	0.772270i	$-0.719121\pi$
$19$	−5.11495	−	7.04013i	−1.17345	−	1.61512i	−0.538156	−	0.842845i	$-0.680879\pi$
$20$		0			0
$21$	1.55818	−	1.13208i	0.340023	−	0.247041i
$22$		0			0
$23$	−3.19690	−	2.32268i	−0.666600	−	0.484313i	0.202286	−	0.979327i	$-0.435163\pi$
$23$	−3.19690	−	2.32268i	−0.666600	−	0.484313i	−0.868885	+	0.495014i	$0.835163\pi$
$24$		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	−0.241589	−	0.970379i	$-0.577669\pi$
$29$	0.718030	−	0.233302i	0.133335	−	0.0433231i	0.374924	+	0.927055i	$0.377669\pi$
$30$		0			0
$31$	−1.81584	+	5.58857i	−0.326134	+	1.00374i	0.644792	+	0.764358i	$0.276944\pi$
$31$	−1.81584	+	5.58857i	−0.326134	+	1.00374i	−0.970926	+	0.239379i	$0.923056\pi$
$32$		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	−0.965070	−	0.261993i	$-0.915620\pi$
$37$	−2.05784	−	6.33339i	−0.338308	−	1.04120i	0.626762	−	0.779211i	$-0.284380\pi$
$38$		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	0.608961	−	0.793200i	$-0.291587\pi$
$43$	0.280406	+	0.203727i	0.0427616	+	0.0310681i	−0.566199	+	0.824268i	$0.691587\pi$
$44$		0			0
$45$	0.0988263	+	0.304156i	0.0147322	+	0.0453409i
$46$		0			0
$47$	−5.20384	+	7.16247i	−0.759058	+	1.04475i	0.238234	+	0.971208i	$0.423432\pi$
$47$	−5.20384	+	7.16247i	−0.759058	+	1.04475i	−0.997292	+	0.0735459i	$0.976568\pi$
$48$		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	−0.228582	−	0.973525i	$-0.573409\pi$
$53$	1.15547	−	0.375434i	0.158715	−	0.0515698i	0.387297	+	0.921955i	$0.373409\pi$
$54$		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	0.379912	−	0.925022i	$-0.375954\pi$
$59$	−2.93755	−	2.13426i	−0.382437	−	0.277857i	−0.762349	+	0.647166i	$0.775954\pi$
$60$		0			0
$61$	−7.32118	+	5.31915i	−0.937381	+	0.681047i	−0.947789	−	0.318899i	$-0.896687\pi$
$61$	−7.32118	+	5.31915i	−0.937381	+	0.681047i	0.0104081	+	0.999946i	$0.496687\pi$
$62$		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	0.459745	−	0.888051i	$-0.347941\pi$
$67$	11.0803	−	3.60019i	1.35367	−	0.439834i	0.893925	+	0.448217i	$0.147941\pi$
$68$		0			0
$69$	−4.47353	+	6.15728i	−0.538549	+	0.741249i
$70$		0			0
$71$	−1.00436	−	0.326337i	−0.119196	−	0.0387291i	0.248812	−	0.968552i	$-0.419960\pi$
$71$	−1.00436	−	0.326337i	−0.119196	−	0.0387291i	−0.368008	+	0.929823i	$0.619960\pi$
$72$		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	$-0.878984\pi$
$79$		−	6.59667i		−	0.742183i	0.928596	−	0.371092i	$-0.121016\pi$
$80$		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	0.842301	−	0.539008i	$-0.181201\pi$
$89$	0.654613	+	0.900998i	0.0693888	+	0.0955056i	−0.772912	+	0.634513i	$0.781201\pi$
$90$		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	0.510093	−	0.860119i	$-0.329611\pi$
$97$	14.0674	−	4.57079i	1.42833	−	0.464093i	0.918240	+	0.396026i	$0.129611\pi$
$98$		0			0
$99$	1.49168	+	0.484676i	0.149920	+	0.0487118i
$100$		0			0
$101$	8.75730	+	12.0534i	0.871384	+	1.19936i	0.978734	+	0.205136i	$0.0657635\pi$
$101$	8.75730	+	12.0534i	0.871384	+	1.19936i	−0.107350	+	0.994221i	$0.534236\pi$
$102$		0			0
$103$	−8.73706	+	6.34785i	−0.860888	+	0.625472i	−0.928126	−	0.372265i	$-0.878581\pi$
$103$	−8.73706	+	6.34785i	−0.860888	+	0.625472i	0.0672382	+	0.997737i	$0.478581\pi$
$104$		0			0
$105$	−0.702317	−	0.510263i	−0.0685391	−	0.0497966i
$106$		0			0
$107$	7.71510	−	5.60535i	0.745847	−	0.541890i	−0.148690	−	0.988884i	$-0.547506\pi$
$107$	7.71510	−	5.60535i	0.745847	−	0.541890i	0.894537	+	0.446994i	$0.147506\pi$
$108$		0			0
$109$			5.26522i			0.504316i	0.967686	+	0.252158i	$0.0811403\pi$
$109$			5.26522i			0.504316i	−0.967686	+	0.252158i	$0.918860\pi$
$110$		0			0
$111$	−12.1982	+	3.96344i	−1.15780	+	0.376193i
$112$		0			0
$113$	−4.54679	+	13.9936i	−0.427726	+	1.31641i	0.472633	+	0.881259i	$0.343303\pi$
$113$	−4.54679	+	13.9936i	−0.427726	+	1.31641i	−0.900360	+	0.435147i	$0.856697\pi$
$114$		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	0.956033	−	0.293258i	$-0.0947396\pi$
$127$	0.115096	+	0.354230i	0.0102131	+	0.0314328i	−0.945820	+	0.324691i	$0.894740\pi$
$128$		0			0
$129$	0.392382	−	0.540067i	0.0345473	−	0.0475502i
$130$		0			0
$131$	6.21892	−	19.1399i	0.543350	−	1.67226i	−0.181531	−	0.983385i	$-0.558105\pi$
$131$	6.21892	−	19.1399i	0.543350	−	1.67226i	0.724881	−	0.688874i	$-0.241895\pi$
$132$		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	$0.145113\pi$
$137$			10.3062i			0.880514i	−0.897872	+	0.440257i	$0.854887\pi$
$138$		0			0
$139$	2.15444	−	1.56529i	0.182737	−	0.132766i	−0.492656	−	0.870224i	$-0.663974\pi$
$139$	2.15444	−	1.56529i	0.182737	−	0.132766i	0.675393	+	0.737458i	$0.263974\pi$
$140$		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	0.101052	−	0.994881i	$-0.467779\pi$
$149$	9.36952	−	3.04434i	0.767581	−	0.249402i	0.666529	+	0.745479i	$0.267779\pi$
$150$		0			0
$151$	12.4149	−	17.0876i	1.01031	−	1.39057i	0.0915286	−	0.995802i	$-0.470825\pi$
$151$	12.4149	−	17.0876i	1.01031	−	1.39057i	0.918781	−	0.394769i	$-0.129175\pi$
$152$		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	0.679390	−	0.733778i	$-0.262245\pi$
$157$	−2.86206	−	3.93928i	−0.228417	−	0.314389i	−0.907807	+	0.419388i	$0.862245\pi$
$158$		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	$-0.739240\pi$
$167$		−	18.8829i		−	1.46120i	0.682804	−	0.730602i	$-0.260760\pi$
$168$		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	0.0188107	−	0.999823i	$-0.494012\pi$
$179$	8.31791	−	2.70265i	0.621710	−	0.202006i	0.602899	+	0.797817i	$0.294012\pi$
$180$		0			0
$181$	15.2537	+	4.95623i	1.13380	+	0.368394i	0.815019	−	0.579435i	$-0.196727\pi$
$181$	15.2537	+	4.95623i	1.13380	+	0.368394i	0.318781	+	0.947828i	$0.396727\pi$
$182$		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	$0.0833940\pi$
$191$			7.15899i			0.518006i	−0.965876	+	0.259003i	$0.916606\pi$
$192$		0			0
$193$	23.9479	−	7.78113i	1.72380	−	0.560098i	0.731273	−	0.682085i	$-0.238926\pi$
$193$	23.9479	−	7.78113i	1.72380	−	0.560098i	0.992532	+	0.121987i	$0.0389265\pi$
$194$		0			0
$195$	0.443717	−	1.36562i	0.0317752	−	0.0977940i
$196$		0			0
$197$	7.66918	−	23.6033i	0.546407	−	1.68167i	−0.171215	−	0.985234i	$-0.554769\pi$
$197$	7.66918	−	23.6033i	0.546407	−	1.68167i	0.717622	−	0.696433i	$-0.245231\pi$
$198$		0			0
$199$	6.41021	−	8.82289i	0.454408	−	0.625438i	−0.518930	−	0.854817i	$-0.673669\pi$
$199$	6.41021	−	8.82289i	0.454408	−	0.625438i	0.973337	+	0.229379i	$0.0736694\pi$
$200$		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	−0.972554	−	0.232675i	$-0.925252\pi$
$211$	−6.54725	+	9.01151i	−0.450731	+	0.620378i	0.521823	+	0.853054i	$0.325252\pi$
$212$		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	0.487872	−	0.872915i	$-0.337773\pi$
$223$	−2.86057	−	2.07833i	−0.191558	−	0.139175i	−0.679431	+	0.733740i	$0.737773\pi$
$224$		0			0
$225$	−2.75352	+	2.00055i	−0.183568	+	0.133370i
$226$		0			0
$227$	−12.6120	−	17.3590i	−0.837091	−	1.15216i	−0.986561	−	0.163391i	$-0.947757\pi$
$227$	−12.6120	−	17.3590i	−0.837091	−	1.15216i	0.149470	−	0.988766i	$-0.452243\pi$
$228$		0			0
$229$	−0.122283	−	0.0397321i	−0.00808067	−	0.00262557i	0.304974	−	0.952361i	$-0.401352\pi$
$229$	−0.122283	−	0.0397321i	−0.00808067	−	0.00262557i	−0.313055	+	0.949735i	$0.601352\pi$
$230$		0			0
$231$	−4.04912	+	1.31564i	−0.266413	+	0.0865627i
$232$		0			0
$233$	3.12780	−	4.30505i	0.204909	−	0.282033i	−0.694178	−	0.719804i	$-0.744232\pi$
$233$	3.12780	−	4.30505i	0.204909	−	0.282033i	0.899087	+	0.437771i	$0.144232\pi$
$234$		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	0.999729	+	0.0232681i	$0.00740713\pi$
$239$	11.0216	+	15.1699i	0.712925	+	0.981257i	−0.286804	+	0.957989i	$0.592593\pi$
$240$		0			0
$241$	3.26751	+	10.0564i	0.210479	+	0.647787i	0.999444	+	0.0333489i	$0.0106173\pi$
$241$	3.26751	+	10.0564i	0.210479	+	0.647787i	−0.788965	+	0.614438i	$0.789383\pi$
$242$		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	−0.989043	−	0.147630i	$-0.952835\pi$
$251$	−4.36736	−	13.4413i	−0.275665	−	0.848410i	0.713377	−	0.700780i	$-0.247165\pi$
$252$		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	−0.0690779	−	0.997611i	$-0.522006\pi$
$257$	−11.4037	−	3.70529i	−0.711344	−	0.231130i	−0.642266	+	0.766482i	$0.722006\pi$
$258$		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	0.851811	−	0.523849i	$-0.175504\pi$
$263$	19.9964	+	6.49722i	1.23303	+	0.400636i	0.381219	+	0.924485i	$0.375504\pi$
$264$		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	0.965653	−	0.259836i	$-0.0836684\pi$
$269$	16.6790	+	12.1180i	1.01694	+	0.738848i	0.0512846	+	0.998684i	$0.483668\pi$
$270$		0			0
$271$	1.66117	−	1.20691i	0.100909	−	0.0733146i	−0.536187	−	0.844099i	$-0.680136\pi$
$271$	1.66117	−	1.20691i	0.100909	−	0.0733146i	0.637096	+	0.770785i	$0.280136\pi$
$272$		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	−0.999764	−	0.0217368i	$-0.993080\pi$
$277$	−2.96520	+	9.12593i	−0.178161	+	0.548324i	0.821602	+	0.570061i	$0.193080\pi$
$278$		0			0
$279$	1.28840	−	3.96529i	0.0771346	−	0.237396i
$280$		0			0
$281$	−7.07083	+	9.73217i	−0.421810	+	0.580572i	−0.966049	−	0.258358i	$-0.916819\pi$
$281$	−7.07083	+	9.73217i	−0.421810	+	0.580572i	0.544239	+	0.838930i	$0.316819\pi$
$282$		0			0
$283$	7.99148	+	24.5952i	0.475044	+	1.46204i	0.845898	+	0.533344i	$0.179065\pi$
$283$	7.99148	+	24.5952i	0.475044	+	1.46204i	−0.370854	+	0.928691i	$0.620935\pi$
$284$		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	−0.169118	−	0.985596i	$-0.554092\pi$
$293$	14.0447	−	19.3309i	0.820500	−	1.12932i	0.989618	−	0.143725i	$-0.0459082\pi$
$294$		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	0.205932	−	0.978566i	$-0.433977\pi$
$307$	21.0299	−	15.2791i	1.20024	−	0.872026i	0.994308	+	0.106541i	$0.0339774\pi$
$308$		0			0
$309$	12.2261	+	16.8277i	0.695516	+	0.957295i
$310$		0			0
$311$	−18.8804	−	6.13462i	−1.07061	−	0.347862i	−0.279885	−	0.960033i	$-0.590296\pi$
$311$	−18.8804	−	6.13462i	−1.07061	−	0.347862i	−0.790725	+	0.612171i	$0.790296\pi$
$312$		0			0
$313$	−5.77610	+	1.87677i	−0.326484	+	0.106081i	−0.467673	−	0.883901i	$-0.654908\pi$
$313$	−5.77610	+	1.87677i	−0.326484	+	0.106081i	0.141189	+	0.989983i	$0.454908\pi$
$314$		0			0
$315$	−0.187979	+	0.258731i	−0.0105914	+	0.0145778i
$316$		0			0
$317$	−8.94765	−	2.90727i	−0.502550	−	0.163288i	0.0467613	−	0.998906i	$-0.485110\pi$
$317$	−8.94765	−	2.90727i	−0.502550	−	0.163288i	−0.549312	+	0.835618i	$0.685110\pi$
$318$		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	$0.00529730\pi$
$331$			0.605520i			0.0332824i	−0.999862	+	0.0166412i	$0.994703\pi$
$332$		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	−0.992728	−	0.120380i	$-0.961589\pi$
$347$	−14.9107	−	20.5228i	−0.800446	−	1.10172i	0.192282	−	0.981340i	$-0.438411\pi$
$348$		0			0
$349$	−6.92358	+	5.03027i	−0.370611	+	0.269264i	−0.757464	−	0.652877i	$-0.773562\pi$
$349$	−6.92358	+	5.03027i	−0.370611	+	0.269264i	0.386853	+	0.922141i	$0.373562\pi$
$350$		0			0
$351$	5.90322	+	4.28894i	0.315090	+	0.228927i
$352$		0			0
$353$	17.1474	−	12.4583i	0.912665	−	0.663090i	−0.0290225	−	0.999579i	$-0.509239\pi$
$353$	17.1474	−	12.4583i	0.912665	−	0.663090i	0.941687	+	0.336489i	$0.109239\pi$
$354$		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	−0.0286860	+	0.999588i	$0.509132\pi$
$359$	−11.2362	+	34.5813i	−0.593022	+	1.82513i	−0.564336	+	0.825545i	$0.690868\pi$
$360$		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	0.864666	−	0.502347i	$-0.167530\pi$
$367$	12.5308	+	9.10414i	0.654101	+	0.475232i	−0.210564	+	0.977580i	$0.567530\pi$
$368$		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	−0.998776	−	0.0494701i	$-0.984247\pi$
$373$	−4.24556	−	13.0665i	−0.219827	−	0.676558i	0.778949	−	0.627088i	$-0.215753\pi$
$374$		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	−0.990508	−	0.137455i	$-0.956108\pi$
$379$	−2.10986	+	6.49347i	−0.108376	+	0.333547i	0.882132	+	0.471002i	$0.156108\pi$
$380$		0			0
$381$	0.682252	−	0.221677i	0.0349528	−	0.0113569i
$382$		0			0
$383$			6.69312i			0.342002i	0.985271	+	0.171001i	$0.0547002\pi$
$383$			6.69312i			0.342002i	−0.985271	+	0.171001i	$0.945300\pi$
$384$		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	−0.597974	−	0.801515i	$-0.704028\pi$
$389$	−0.403781	+	0.293364i	−0.0204725	+	0.0148742i	0.577502	+	0.816389i	$0.304028\pi$
$390$		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	0.108869	−	0.994056i	$-0.465277\pi$
$397$	20.3359	−	27.9900i	1.02063	−	1.40478i	0.911761	−	0.410720i	$-0.134723\pi$
$398$		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	0.703403	−	0.710791i	$-0.251663\pi$
$421$	17.5365	+	5.69795i	0.854676	+	0.277701i	0.151273	+	0.988492i	$0.451663\pi$
$422$		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	−0.499598	−	0.866257i	$-0.666519\pi$
$431$	3.52675	−	2.56233i	0.169878	−	0.123423i	0.669476	+	0.742834i	$0.266519\pi$
$432$		0			0
$433$	4.66687	+	3.39068i	0.224275	+	0.162946i	0.694249	−	0.719735i	$-0.255737\pi$
$433$	4.66687	+	3.39068i	0.224275	+	0.162946i	−0.469974	+	0.882680i	$0.655737\pi$
$434$		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	0.472738	−	0.881203i	$-0.343266\pi$
$439$	28.7707	−	9.34816i	1.37315	−	0.446163i	0.900411	+	0.435040i	$0.143266\pi$
$440$		0			0
$441$	0.219259	−	0.674809i	0.0104409	−	0.0321338i
$442$		0			0
$443$	4.33994	−	13.3570i	0.206197	−	0.634609i	−0.793465	−	0.608616i	$-0.791725\pi$
$443$	4.33994	−	13.3570i	0.206197	−	0.634609i	0.999662	−	0.0259932i	$-0.00827483\pi$
$444$		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	0.508295	−	0.861183i	$-0.330276\pi$
$449$	−3.25616	−	2.36574i	−0.153668	−	0.111646i	−0.661962	+	0.749537i	$0.730276\pi$
$450$		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	−0.552841	−	0.833287i	$-0.686456\pi$
$457$	8.77548	−	12.0784i	0.410500	−	0.565004i	0.963340	+	0.268283i	$0.0864561\pi$
$458$		0			0
$459$	−3.07205	+	9.45478i	−0.143391	+	0.441311i
$460$		0			0
$461$	−1.42179	+	4.37582i	−0.0662194	+	0.203802i	−0.978691	−	0.205337i	$-0.934171\pi$
$461$	−1.42179	+	4.37582i	−0.0662194	+	0.203802i	0.912472	+	0.409139i	$0.134171\pi$
$462$		0			0
$463$	8.03576	−	2.61098i	0.373453	−	0.121342i	−0.116276	−	0.993217i	$-0.537096\pi$
$463$	8.03576	−	2.61098i	0.373453	−	0.121342i	0.489729	+	0.871875i	$0.337096\pi$
$464$		0			0
$465$		−	5.10117i		−	0.236561i
$466$		0			0
$467$	6.01936	−	4.37332i	0.278543	−	0.202373i	−0.439739	−	0.898126i	$-0.644929\pi$
$467$	6.01936	−	4.37332i	0.278543	−	0.202373i	0.718282	+	0.695753i	$0.244929\pi$
$468$		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	−0.904004	−	0.427525i	$-0.859386\pi$
$479$	−4.77228	+	6.56847i	−0.218051	+	0.300121i	0.685953	+	0.727646i	$0.259386\pi$
$480$		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	−0.989534	−	0.144303i	$-0.953906\pi$
$487$	−6.04231	−	18.5963i	−0.273803	−	0.842679i	0.715731	−	0.698377i	$-0.246094\pi$
$488$		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	−0.965350	−	0.260958i	$-0.915962\pi$
$499$	−20.4446	−	28.1396i	−0.915226	−	1.25970i	0.0501240	−	0.998743i	$-0.484038\pi$
$500$		0			0
$501$	−36.3688			−1.62484
$502$		0			0
$503$	3.86840	+	1.25692i	0.172483	+	0.0560433i	0.393986	−	0.919117i	$-0.371096\pi$
$503$	3.86840	+	1.25692i	0.172483	+	0.0560433i	−0.221502	+	0.975160i	$0.571096\pi$
$504$		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	0.581645	−	0.813443i	$-0.302409\pi$
$509$	12.9517	+	4.20828i	0.574076	+	0.186529i	−0.00756907	+	0.999971i	$0.502409\pi$
$510$		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	−0.981744	−	0.190208i	$-0.939084\pi$
$521$	−37.9858	+	12.3423i	−1.66419	+	0.540728i	−0.682446	+	0.730936i	$0.739084\pi$
$522$		0			0
$523$	−1.48048	+	4.55646i	−0.0647371	+	0.199240i	−0.978193	−	0.207697i	$-0.933403\pi$
$523$	−1.48048	+	4.55646i	−0.0647371	+	0.199240i	0.913456	+	0.406937i	$0.133403\pi$
$524$		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	−0.999972	−	0.00750878i	$-0.997610\pi$
$541$	−4.33937	+	13.3552i	−0.186564	+	0.574185i	0.813408	+	0.581694i	$0.197610\pi$
$542$		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	$0.214670\pi$
$547$			29.2085i			1.24886i	−0.781079	+	0.624432i	$0.785330\pi$
$548$		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	−0.102369	−	0.994746i	$-0.532642\pi$
$557$	−18.1699	−	5.90377i	−0.769885	−	0.250151i	−0.667516	+	0.744596i	$0.732642\pi$
$558$		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	−0.386081	−	0.922465i	$-0.626171\pi$
$563$	−29.4374	−	9.56479i	−1.24064	−	0.403108i	−0.854557	+	0.519357i	$0.826171\pi$
$564$		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	0.921865	−	0.387512i	$-0.126666\pi$
$569$	−1.23356	−	3.79651i	−0.0517136	−	0.159158i	−0.973578	+	0.228354i	$0.926666\pi$
$570$		0			0
$571$			32.2310i			1.34882i	0.738355	+	0.674412i	$0.235603\pi$
$571$			32.2310i			1.34882i	−0.738355	+	0.674412i	$0.764397\pi$
$572$		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	$-0.685956\pi$
$577$		−	40.0742i		−	1.66831i	0.551530	−	0.834155i	$-0.314044\pi$
$578$		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	−0.675131	−	0.737698i	$-0.735913\pi$
$587$	5.69573	−	7.83950i	0.235088	−	0.323571i	0.910219	+	0.414127i	$0.135913\pi$
$588$		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	0.496773	−	0.867880i	$-0.334518\pi$
$593$	−11.7409	−	16.1600i	−0.482142	−	0.663611i	−0.978915	+	0.204270i	$0.934518\pi$
$594$		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	−0.967699	−	0.252107i	$-0.918876\pi$
$599$	−25.1345	+	18.2613i	−1.02697	+	0.746135i	−0.0592674	+	0.998242i	$0.518876\pi$
$600$		0			0
$601$			1.38917i			0.0566655i	0.999599	+	0.0283327i	$0.00901980\pi$
$601$			1.38917i			0.0566655i	−0.999599	+	0.0283327i	$0.990980\pi$
$602$		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	−0.568283	−	0.822833i	$-0.692392\pi$
$607$	9.24189	−	28.4436i	0.375117	−	1.15449i	0.943400	−	0.331657i	$-0.107608\pi$
$608$		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	0.466663	−	0.884435i	$-0.345456\pi$
$613$	−5.70143	−	4.14233i	−0.230278	−	0.167307i	−0.696941	+	0.717128i	$0.745456\pi$
$614$		0			0
$615$	2.63431	+	4.89476i	0.106226	+	0.197376i
$616$		0			0
$617$	3.80328	+	2.76324i	0.153114	+	0.111244i	0.661705	−	0.749765i	$-0.269833\pi$
$617$	3.80328	+	2.76324i	0.153114	+	0.111244i	−0.508590	+	0.861009i	$0.669833\pi$
$618$		0			0
$619$	11.8899	+	36.5934i	0.477896	+	1.47081i	0.842012	+	0.539459i	$0.181371\pi$
$619$	11.8899	+	36.5934i	0.477896	+	1.47081i	−0.364116	+	0.931354i	$0.618629\pi$
$620$		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	−0.567119	−	0.823636i	$-0.691942\pi$
$631$	1.02881	−	0.747472i	0.0409562	−	0.0297564i	0.608075	+	0.793880i	$0.291942\pi$
$632$		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	−0.352900	−	0.935661i	$-0.614804\pi$
$641$	−2.23897	+	0.727487i	−0.0884342	+	0.0287340i	0.264466	+	0.964395i	$0.414804\pi$
$642$		0			0
$643$	3.06309	−	4.21599i	0.120797	−	0.166262i	−0.744336	−	0.667805i	$-0.767234\pi$
$643$	3.06309	−	4.21599i	0.120797	−	0.166262i	0.865133	+	0.501543i	$0.167234\pi$
$644$		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	$0.169848\pi$
$653$			25.9950i			1.01726i	−0.860984	+	0.508631i	$0.830152\pi$
$654$		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	$-0.577630\pi$
$659$		−	49.8227i		−	1.94082i	0.241470	−	0.970408i	$-0.422370\pi$
$660$		0			0
$661$	−5.90574	−	18.1760i	−0.229707	−	0.706965i	−0.997780	−	0.0666022i	$-0.978784\pi$
$661$	−5.90574	−	18.1760i	−0.229707	−	0.706965i	0.768073	−	0.640362i	$-0.221216\pi$
$662$		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	0.752327	−	0.658790i	$-0.228931\pi$
$673$	25.2612	+	8.20785i	0.973746	+	0.316389i	0.221419	+	0.975179i	$0.428931\pi$
$674$		0			0
$675$	−12.4382	−	17.1197i	−0.478746	−	0.658938i
$676$		0			0
$677$	7.30645	−	5.30845i	0.280810	−	0.204020i	−0.438461	−	0.898750i	$-0.644476\pi$
$677$	7.30645	−	5.30845i	0.280810	−	0.204020i	0.719270	+	0.694730i	$0.244476\pi$
$678$		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	$0.0785780\pi$
$683$			12.7724i			0.488721i	−0.969684	+	0.244361i	$0.921422\pi$
$684$		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	0.249458	+	0.968386i	$0.419748\pi$
$691$	−19.6788	+	27.0856i	−0.748618	+	1.03038i	−0.998076	+	0.0619989i	$0.980252\pi$
$692$		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	−0.992087	−	0.125551i	$-0.959930\pi$
$701$	−6.97042	−	21.4527i	−0.263269	−	0.810259i	0.728818	−	0.684707i	$-0.240070\pi$
$702$		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	0.551873	−	0.833928i	$-0.313913\pi$
$709$	39.6349	−	12.8781i	1.48852	−	0.483649i	0.936645	+	0.350279i	$0.113913\pi$
$710$		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	−0.944273	−	0.329164i	$-0.893233\pi$
$719$	−25.8899	−	35.6344i	−0.965530	−	1.32894i	−0.0212573	−	0.999774i	$-0.506767\pi$
$720$		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	−0.337168	−	0.941445i	$-0.609469\pi$
$727$	−31.3662	−	10.1915i	−1.16331	−	0.377982i	−0.826142	+	0.563462i	$0.809469\pi$
$728$		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	0.915756	+	0.401735i	$0.131593\pi$
$733$	11.1282	+	34.2489i	0.411028	+	1.26501i	−0.504728	+	0.863278i	$0.668407\pi$
$734$		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	0.995729	+	0.0923289i	$0.0294311\pi$
$743$	6.66286	+	20.5062i	0.244437	+	0.752299i	−0.751292	+	0.659970i	$0.770569\pi$
$744$		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	0.00210110	+	0.999998i	$0.499331\pi$
$751$	−26.0233	+	35.8180i	−0.949603	+	1.30702i	−0.951704	+	0.307018i	$0.900669\pi$
$752$		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	0.726796	−	0.686853i	$-0.241009\pi$
$757$	−4.15546	−	5.71950i	−0.151033	−	0.207879i	−0.877829	+	0.478975i	$0.841009\pi$
$758$		0			0
$759$	13.6108	−	9.88882i	0.494041	−	0.358942i
$760$		0			0
$761$	25.6482	+	18.6345i	0.929747	+	0.675501i	0.945931	−	0.324368i	$-0.105152\pi$
$761$	25.6482	+	18.6345i	0.929747	+	0.675501i	−0.0161835	+	0.999869i	$0.505152\pi$
$762$		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	−0.989842	−	0.142175i	$-0.954590\pi$
$769$	−2.92490	+	9.00191i	−0.105474	+	0.324617i	0.884367	+	0.466792i	$0.154590\pi$
$770$		0			0
$771$	−7.13645	+	21.9637i	−0.257013	+	0.791005i
$772$		0			0
$773$	−1.83069	+	2.51973i	−0.0658453	+	0.0906282i	−0.840670	−	0.541548i	$-0.817838\pi$
$773$	−1.83069	+	2.51973i	−0.0658453	+	0.0906282i	0.774824	+	0.632177i	$0.217838\pi$
$774$		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	−0.999712	−	0.0239924i	$-0.992362\pi$
$787$	−4.96058	+	15.2671i	−0.176826	+	0.544213i	0.822887	+	0.568206i	$0.192362\pi$
$788$		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	0.999761	−	0.0218721i	$-0.00696267\pi$
$797$	36.3590	+	26.4164i	1.28790	+	0.935716i	0.288141	+	0.957588i	$0.406963\pi$
$798$		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	−0.149132	−	0.988817i	$-0.547648\pi$
$809$	−24.2048	−	7.86461i	−0.850995	−	0.276505i	−0.701863	+	0.712312i	$0.747648\pi$
$810$		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	$0.106638\pi$
$823$			18.8641i			0.657561i	−0.944406	+	0.328780i	$0.893362\pi$
$824$		0			0
$825$	6.31092	+	19.4230i	0.219718	+	0.676222i
$826$		0			0
$827$	8.40166	+	11.5639i	0.292154	+	0.402116i	0.929712	−	0.368286i	$-0.120055\pi$
$827$	8.40166	+	11.5639i	0.292154	+	0.402116i	−0.637558	+	0.770402i	$0.720055\pi$
$828$		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	0.944558	+	0.328344i	$0.106490\pi$
$839$	27.9502	+	38.4701i	0.964947	+	1.32814i	0.0203888	+	0.999792i	$0.493510\pi$
$840$		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	0.135829	−	0.990732i	$-0.456630\pi$
$853$	17.7655	−	54.6766i	0.608279	−	1.87209i	0.472450	−	0.881358i	$-0.343370\pi$
$854$		0			0
$855$	1.63581	−	2.25149i	0.0559434	−	0.0769995i
$856$		0			0
$857$	−6.59547	−	20.2988i	−0.225297	−	0.693393i	−0.998261	−	0.0589433i	$-0.981227\pi$
$857$	−6.59547	−	20.2988i	−0.225297	−	0.693393i	0.772964	−	0.634449i	$-0.218773\pi$
$858$		0			0
$859$	26.0483	+	18.9252i	0.888756	+	0.645719i	0.935553	−	0.353185i	$-0.114901\pi$
$859$	26.0483	+	18.9252i	0.888756	+	0.645719i	−0.0467972	+	0.998904i	$0.514901\pi$
$860$		0			0
$861$	−8.91432	−	8.52208i	−0.303799	−	0.290432i
$862$		0			0
$863$	2.09696	+	1.52353i	0.0713812	+	0.0518615i	0.622904	−	0.782299i	$-0.285953\pi$
$863$	2.09696	+	1.52353i	0.0713812	+	0.0518615i	−0.551522	+	0.834160i	$0.685953\pi$
$864$		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	−0.855154	−	0.518374i	$-0.826537\pi$
$877$	−18.5505	+	13.4778i	−0.626407	+	0.455112i	0.228746	+	0.973486i	$0.426537\pi$
$878$		0			0
$879$	−37.2315	−	27.0503i	−1.25579	−	0.912384i
$880$		0			0
$881$	−33.9397	+	24.6586i	−1.14346	+	0.830770i	−0.987597	−	0.157009i	$-0.949815\pi$
$881$	−33.9397	+	24.6586i	−1.14346	+	0.830770i	−0.155860	+	0.987779i	$0.549815\pi$
$882$		0			0
$883$	4.60226	+	6.33447i	0.154878	+	0.213172i	0.879404	−	0.476076i	$-0.157941\pi$
$883$	4.60226	+	6.33447i	0.154878	+	0.213172i	−0.724526	+	0.689248i	$0.757941\pi$
$884$		0			0
$885$	2.99785	+	0.974060i	0.100772	+	0.0327427i
$886$		0			0
$887$	46.5927	−	15.1389i	1.56443	−	0.508314i	0.606444	−	0.795126i	$-0.292595\pi$
$887$	46.5927	−	15.1389i	1.56443	−	0.508314i	0.957987	+	0.286812i	$0.0925954\pi$
$888$		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	0.994929	−	0.100583i	$-0.0320708\pi$
$907$	3.94204	+	12.1323i	0.130893	+	0.402848i	−0.864035	+	0.503431i	$0.832071\pi$
$908$		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	0.650377	−	0.759612i	$-0.274611\pi$
$919$	22.1316	+	7.19100i	0.730054	+	0.237209i	0.0796774	+	0.996821i	$0.474611\pi$
$920$		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	$0.0556206\pi$
$929$			10.5977i			0.347699i	−0.984772	+	0.173849i	$0.944379\pi$
$930$		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	−0.880604	−	0.473853i	$-0.842863\pi$
$937$	−4.83099	+	6.64929i	−0.157822	+	0.217223i	0.722782	+	0.691076i	$0.242863\pi$
$938$		0			0
$939$	3.61468	+	11.1249i	0.117961	+	0.363046i
$940$		0			0
$941$	10.7429	+	7.80517i	0.350208	+	0.254441i	0.748956	−	0.662619i	$-0.230555\pi$
$941$	10.7429	+	7.80517i	0.350208	+	0.254441i	−0.398748	+	0.917060i	$0.630555\pi$
$942$		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	0.712870	+	0.701296i	$0.247395\pi$
$947$	16.8748	+	51.9353i	0.548358	+	1.68767i	−0.164512	+	0.986375i	$0.552605\pi$
$948$		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	−0.977732	−	0.209857i	$-0.932700\pi$
$953$	−1.95656	+	6.02167i	−0.0633791	+	0.195061i	0.914353	+	0.404918i	$0.132700\pi$
$954$		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	0.544156	−	0.838984i	$-0.316850\pi$
$967$	15.2761	+	4.96350i	0.491245	+	0.159615i	−0.0529108	+	0.998599i	$0.516850\pi$
$968$		0			0
$969$	35.9212	−	11.6715i	1.15396	−	0.374943i
$970$		0			0
$971$	−7.97667	+	10.9789i	−0.255984	+	0.352331i	−0.917596	−	0.397515i	$-0.869873\pi$
$971$	−7.97667	+	10.9789i	−0.255984	+	0.352331i	0.661612	+	0.749846i	$0.269873\pi$
$972$		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	0.767576	−	0.640958i	$-0.221463\pi$
$977$	−2.47572	−	3.40754i	−0.0792054	−	0.109017i	−0.846781	+	0.531941i	$0.821463\pi$
$978$		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	0.509653	−	0.860380i	$-0.329774\pi$
$991$	−14.6732	−	20.1959i	−0.466109	−	0.641544i	−0.975762	+	0.218836i	$0.929774\pi$
$992$		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	−0.431237	−	0.902239i	$-0.641923\pi$
$997$	17.6854	−	24.3419i	0.560102	−	0.770915i	0.991340	+	0.131324i	$0.0419228\pi$
$998$		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.113.5	✓	80
41.4	even	10	inner	1148.2.ba.a.701.16	yes	80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1148.2.ba.a.113.5	✓	80	1.1	even	1	trivial
1148.2.ba.a.701.16	yes	80	41.4	even	10	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:	\( N \)	\(=\)	\( 1148 = 2^{2} \cdot 7 \cdot 41 \)
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

Related objects

Downloads

Learn more