LMFDB - Embedded newform 525.2.t.j.101.9

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [525,2,Mod(26,525)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("525.26"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(525, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([3, 0, 5])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 525 = 3 \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	525.t (of order $6$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [24,0,0,12,0,0,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$4.19214610612$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 105)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			101.9
Character	$\chi$	$=$	525.101
Dual form			525.2.t.j.26.9

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.31176 - 0.757344i) q^{2} +(-1.68045 - 0.419611i) q^{3} +(0.147140 - 0.254854i) q^{4} +(-2.52214 + 0.722254i) q^{6} +(-2.64468 + 0.0753638i) q^{7} +2.58363i q^{8} +(2.64785 + 1.41027i) q^{9} +(1.86048 + 1.07415i) q^{11} +(-0.354202 + 0.366529i) q^{12} +3.48097i q^{13} +(-3.41210 + 2.10179i) q^{14} +(2.25098 + 3.89881i) q^{16} +(-1.78859 + 3.09793i) q^{17} +(4.54141 - 0.155396i) q^{18} +(1.05858 - 0.611171i) q^{19} +(4.47588 + 0.983091i) q^{21} +3.25401 q^{22} +(1.31176 - 0.757344i) q^{23} +(1.08412 - 4.34168i) q^{24} +(2.63629 + 4.56619i) q^{26} +(-3.85783 - 3.48097i) q^{27} +(-0.369932 + 0.685096i) q^{28} +5.95645i q^{29} +(2.75098 + 1.58828i) q^{31} +(1.43050 + 0.825899i) q^{32} +(-2.67573 - 2.58574i) q^{33} +5.41832i q^{34} +(0.749020 - 0.467309i) q^{36} +(3.90175 + 6.75803i) q^{37} +(0.925734 - 1.60342i) q^{38} +(1.46065 - 5.84961i) q^{39} -11.8685 q^{41} +(6.61582 - 2.10021i) q^{42} +2.99294 q^{43} +(0.547504 - 0.316101i) q^{44} +(1.14714 - 1.98691i) q^{46} +(-3.05084 - 5.28420i) q^{47} +(-2.14668 - 7.49631i) q^{48} +(6.98864 - 0.398626i) q^{49} +(4.30557 - 4.45542i) q^{51} +(0.887140 + 0.512191i) q^{52} +(-9.72202 - 5.61301i) q^{53} +(-7.69683 - 1.64449i) q^{54} +(-0.194713 - 6.83288i) q^{56} +(-2.03535 + 0.582853i) q^{57} +(4.51108 + 7.81342i) q^{58} +(1.08467 - 1.87871i) q^{59} +(-2.94338 + 1.69936i) q^{61} +4.81149 q^{62} +(-7.10900 - 3.53017i) q^{63} -6.50196 q^{64} +(-5.46821 - 1.36542i) q^{66} +(5.15882 - 8.93534i) q^{67} +(0.526347 + 0.911660i) q^{68} +(-2.52214 + 0.722254i) q^{69} +10.3968i q^{71} +(-3.64363 + 6.84108i) q^{72} +(5.93710 + 3.42779i) q^{73} +(10.2363 + 5.90993i) q^{74} -0.359711i q^{76} +(-5.00133 - 2.70057i) q^{77} +(-2.51414 - 8.77950i) q^{78} +(-0.941421 - 1.63059i) q^{79} +(5.02225 + 7.46840i) q^{81} +(-15.5686 + 8.98853i) q^{82} +9.10486 q^{83} +(0.909127 - 0.996046i) q^{84} +(3.92601 - 2.26668i) q^{86} +(2.49939 - 10.0095i) q^{87} +(-2.77521 + 4.80681i) q^{88} +(-0.889962 - 1.54146i) q^{89} +(-0.262339 - 9.20605i) q^{91} -0.445743i q^{92} +(-3.95644 - 3.82337i) q^{93} +(-8.00392 - 4.62107i) q^{94} +(-2.05733 - 1.98814i) q^{96} +1.32584i q^{97} +(8.86551 - 5.81571i) q^{98} +(3.41144 + 5.46799i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 12 q^{4} + 6 q^{9} - 12 q^{16} - 6 q^{21} - 18 q^{24} + 84 q^{36} + 12 q^{39} + 36 q^{46} + 12 q^{49} - 12 q^{51} + 36 q^{54} + 36 q^{61} - 24 q^{64} - 72 q^{66} - 48 q^{79} - 6 q^{81} - 48 q^{84}+ \cdots + 48 q^{99}+O(q^{100}) $ 24 * q + 12 * q^4 + 6 * q^9 - 12 * q^16 - 6 * q^21 - 18 * q^24 + 84 * q^36 + 12 * q^39 + 36 * q^46 + 12 * q^49 - 12 * q^51 + 36 * q^54 + 36 * q^61 - 24 * q^64 - 72 * q^66 - 48 * q^79 - 6 * q^81 - 48 * q^84 - 96 * q^91 + 72 * q^94 - 90 * q^96 + 48 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/525\mathbb{Z}\right)^\times$.

$n$	$127$	$176$	$451$
$\chi(n)$	$1$	$-1$	$e\left(\frac{1}{6}\right)$

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 $

$2$	1.31176	−	0.757344i	0.927553	−	0.535523i	0.0415164	−	0.999138i	$-0.486781\pi$
$2$	1.31176	−	0.757344i	0.927553	−	0.535523i	0.886037	+	0.463615i	$0.153448\pi$
$3$	−1.68045	−	0.419611i	−0.970211	−	0.242263i
$3$	−1.68045	−	0.419611i	−0.970211	−	0.242263i
$4$	0.147140	−	0.254854i	0.0735701	−	0.127427i
$5$		0			0
$5$		0			0
$6$	−2.52214	+	0.722254i	−1.02966	+	0.294859i
$7$	−2.64468	+	0.0753638i	−0.999594	+	0.0284849i
$7$	−2.64468	+	0.0753638i	−0.999594	+	0.0284849i
$8$			2.58363i			0.913452i
$9$	2.64785	+	1.41027i	0.882618	+	0.470092i
$10$		0			0
$11$	1.86048	+	1.07415i	0.560957	+	0.323869i	0.753529	−	0.657414i	$-0.228350\pi$
$11$	1.86048	+	1.07415i	0.560957	+	0.323869i	−0.192573	+	0.981283i	$0.561683\pi$
$12$	−0.354202	+	0.366529i	−0.102249	+	0.105808i
$13$			3.48097i			0.965448i	0.875773	+	0.482724i	$0.160353\pi$
$13$			3.48097i			0.965448i	−0.875773	+	0.482724i	$0.839647\pi$
$14$	−3.41210	+	2.10179i	−0.911923	+	0.561727i
$15$		0			0
$16$	2.25098	+	3.89881i	0.562745	+	0.974703i
$17$	−1.78859	+	3.09793i	−0.433797	+	0.751359i	−0.997197	−	0.0748259i	$-0.976160\pi$
$17$	−1.78859	+	3.09793i	−0.433797	+	0.751359i	0.563399	+	0.826185i	$0.309493\pi$
$18$	4.54141	−	0.155396i	1.07042	−	0.0366272i
$19$	1.05858	−	0.611171i	0.242855	−	0.140212i	−0.373633	−	0.927576i	$-0.621888\pi$
$19$	1.05858	−	0.611171i	0.242855	−	0.140212i	0.616488	+	0.787364i	$0.288555\pi$
$20$		0			0
$21$	4.47588	+	0.983091i	0.976718	+	0.214528i
$22$	3.25401			0.693757
$23$	1.31176	−	0.757344i	0.273521	−	0.157917i	−0.356966	−	0.934117i	$-0.616189\pi$
$23$	1.31176	−	0.757344i	0.273521	−	0.157917i	0.630486	+	0.776200i	$0.282855\pi$
$24$	1.08412	−	4.34168i	0.221295	−	0.886241i
$25$		0			0
$26$	2.63629	+	4.56619i	0.517020	+	0.895504i
$27$	−3.85783	−	3.48097i	−0.742439	−	0.669913i
$28$	−0.369932	+	0.685096i	−0.0699105	+	0.129471i
$29$			5.95645i			1.10608i	0.833153	+	0.553042i	$0.186533\pi$
$29$			5.95645i			1.10608i	−0.833153	+	0.553042i	$0.813467\pi$
$30$		0			0
$31$	2.75098	+	1.58828i	0.494091	+	0.285263i	0.726270	−	0.687410i	$-0.241252\pi$
$31$	2.75098	+	1.58828i	0.494091	+	0.285263i	−0.232179	+	0.972673i	$0.574586\pi$
$32$	1.43050	+	0.825899i	0.252879	+	0.146000i
$33$	−2.67573	−	2.58574i	−0.465785	−	0.450120i
$34$			5.41832i			0.929234i
$35$		0			0
$36$	0.749020	−	0.467309i	0.124837	−	0.0778848i
$37$	3.90175	+	6.75803i	0.641444	+	1.11101i	0.985111	+	0.171921i	$0.0549975\pi$
$37$	3.90175	+	6.75803i	0.641444	+	1.11101i	−0.343667	+	0.939092i	$0.611669\pi$
$38$	0.925734	−	1.60342i	0.150174	−	0.260109i
$39$	1.46065	−	5.84961i	0.233892	−	0.936688i
$40$		0			0
$41$	−11.8685			−1.85355			−0.926773	−	0.375622i	$-0.877429\pi$
$41$	−11.8685			−1.85355			−0.926773	+	0.375622i	$0.877429\pi$
$42$	6.61582	−	2.10021i	1.02084	−	0.324069i
$43$	2.99294			0.456419			0.228209	−	0.973612i	$-0.426713\pi$
$43$	2.99294			0.456419			0.228209	+	0.973612i	$0.426713\pi$
$44$	0.547504	−	0.316101i	0.0825393	−	0.0476541i
$45$		0			0
$46$	1.14714	−	1.98691i	0.169137	−	0.292953i
$47$	−3.05084	−	5.28420i	−0.445010	−	0.770780i	0.553043	−	0.833153i	$-0.313467\pi$
$47$	−3.05084	−	5.28420i	−0.445010	−	0.770780i	−0.998053	+	0.0623727i	$0.980133\pi$
$48$	−2.14668	−	7.49631i	−0.309847	−	1.08200i
$49$	6.98864	−	0.398626i	0.998377	−	0.0569466i
$50$		0			0
$51$	4.30557	−	4.45542i	0.602901	−	0.623883i
$52$	0.887140	+	0.512191i	0.123024	+	0.0710281i
$53$	−9.72202	−	5.61301i	−1.33542	−	0.771006i	−0.349297	−	0.937012i	$-0.613580\pi$
$53$	−9.72202	−	5.61301i	−1.33542	−	0.771006i	−0.986125	+	0.166006i	$0.946913\pi$
$54$	−7.69683	−	1.64449i	−1.04741	−	0.223787i
$55$		0			0
$56$	−0.194713	−	6.83288i	−0.0260196	−	0.913082i
$57$	−2.03535	+	0.582853i	−0.269589	+	0.0772008i
$58$	4.51108	+	7.81342i	0.592334	+	1.02595i
$59$	1.08467	−	1.87871i	0.141213	−	0.244587i	−0.786741	−	0.617283i	$-0.788233\pi$
$59$	1.08467	−	1.87871i	0.141213	−	0.244587i	0.927954	+	0.372696i	$0.121567\pi$
$60$		0			0
$61$	−2.94338	+	1.69936i	−0.376861	+	0.217581i	−0.676452	−	0.736487i	$-0.736483\pi$
$61$	−2.94338	+	1.69936i	−0.376861	+	0.217581i	0.299591	+	0.954068i	$0.403150\pi$
$62$	4.81149			0.611060
$63$	−7.10900	−	3.53017i	−0.895650	−	0.444760i
$64$	−6.50196			−0.812745
$65$		0			0
$66$	−5.46821	−	1.36542i	−0.673090	−	0.168071i
$67$	5.15882	−	8.93534i	0.630250	−	1.09163i	−0.357250	−	0.934009i	$-0.616286\pi$
$67$	5.15882	−	8.93534i	0.630250	−	1.09163i	0.987500	−	0.157617i	$-0.0503811\pi$
$68$	0.526347	+	0.911660i	0.0638290	+	0.110555i
$69$	−2.52214	+	0.722254i	−0.303630	+	0.0869491i
$70$		0			0
$71$			10.3968i			1.23387i	0.787013	+	0.616936i	$0.211626\pi$
$71$			10.3968i			1.23387i	−0.787013	+	0.616936i	$0.788374\pi$
$72$	−3.64363	+	6.84108i	−0.429406	+	0.806229i
$73$	5.93710	+	3.42779i	0.694885	+	0.401192i	0.805439	−	0.592678i	$-0.201929\pi$
$73$	5.93710	+	3.42779i	0.694885	+	0.401192i	−0.110555	+	0.993870i	$0.535263\pi$
$74$	10.2363	+	5.90993i	1.18995	+	0.687016i
$75$		0			0
$76$		−	0.359711i		−	0.0412617i
$77$	−5.00133	−	2.70057i	−0.569955	−	0.307758i
$78$	−2.51414	−	8.77950i	−0.284671	−	0.994082i
$79$	−0.941421	−	1.63059i	−0.105918	−	0.183456i	0.808195	−	0.588915i	$-0.200445\pi$
$79$	−0.941421	−	1.63059i	−0.105918	−	0.183456i	−0.914113	+	0.405460i	$0.867111\pi$
$80$		0			0
$81$	5.02225	+	7.46840i	0.558028	+	0.829822i
$82$	−15.5686	+	8.98853i	−1.71926	+	0.992617i
$83$	9.10486			0.999388			0.499694	−	0.866202i	$-0.333446\pi$
$83$	9.10486			0.999388			0.499694	+	0.866202i	$0.333446\pi$
$84$	0.909127	−	0.996046i	0.0991939	−	0.108678i
$85$		0			0
$86$	3.92601	−	2.26668i	0.423353	−	0.244423i
$87$	2.49939	−	10.0095i	0.267963	−	1.07313i
$88$	−2.77521	+	4.80681i	−0.295839	+	0.512407i
$89$	−0.889962	−	1.54146i	−0.0943358	−	0.163394i	0.814995	−	0.579467i	$-0.196739\pi$
$89$	−0.889962	−	1.54146i	−0.0943358	−	0.163394i	−0.909331	+	0.416073i	$0.863406\pi$
$90$		0			0
$91$	−0.262339	−	9.20605i	−0.0275006	−	0.965056i
$92$		−	0.445743i		−	0.0464719i
$93$	−3.95644	−	3.82337i	−0.410263	−	0.396465i
$94$	−8.00392	−	4.62107i	−0.825541	−	0.476626i
$95$		0			0
$96$	−2.05733	−	1.98814i	−0.209976	−	0.202914i
$97$			1.32584i			0.134618i	0.997732	+	0.0673092i	$0.0214414\pi$
$97$			1.32584i			0.134618i	−0.997732	+	0.0673092i	$0.978559\pi$
$98$	8.86551	−	5.81571i	0.895552	−	0.587475i
$99$	3.41144	+	5.46799i	0.342863	+	0.549553i
$100$		0			0
$101$	6.71005	−	11.6221i	0.667675	−	1.15645i	−0.310878	−	0.950450i	$-0.600623\pi$
$101$	6.71005	−	11.6221i	0.667675	−	1.15645i	0.978553	−	0.205997i	$-0.0660438\pi$
$102$	2.27359	−	9.10523i	0.225119	−	0.901553i
$103$	−5.01154	+	2.89342i	−0.493802	+	0.285097i	−0.726150	−	0.687536i	$-0.758692\pi$
$103$	−5.01154	+	2.89342i	−0.493802	+	0.285097i	0.232348	+	0.972633i	$0.425359\pi$
$104$	−8.99355			−0.881890
$105$		0			0
$106$	−17.0039			−1.65157
$107$	−3.36576	+	1.94323i	−0.325381	+	0.187859i	−0.653788	−	0.756677i	$-0.726821\pi$
$107$	−3.36576	+	1.94323i	−0.325381	+	0.187859i	0.328408	+	0.944536i	$0.393488\pi$
$108$	−1.45478	+	0.470993i	−0.139986	+	0.0453214i
$109$	2.60384	−	4.50998i	0.249403	−	0.431978i	−0.713958	−	0.700189i	$-0.753099\pi$
$109$	2.60384	−	4.50998i	0.249403	−	0.431978i	0.963360	+	0.268211i	$0.0864324\pi$
$110$		0			0
$111$	−3.72097	−	12.9938i	−0.353179	−	1.23331i
$112$	−6.24695	−	10.1415i	−0.590281	−	0.958278i
$113$			9.36235i			0.880736i	0.897817	+	0.440368i	$0.145152\pi$
$113$			9.36235i			0.880736i	−0.897817	+	0.440368i	$0.854848\pi$
$114$	−2.22847	+	2.30602i	−0.208715	+	0.215979i
$115$		0			0
$116$	1.51803	+	0.876432i	0.140945	+	0.0813747i
$117$	−4.90913	+	9.21710i	−0.453849	+	0.852121i
$118$		−	3.28589i		−	0.302490i
$119$	4.49678	−	8.32783i	0.412219	−	0.763411i
$120$		0			0
$121$	−3.19240	−	5.52940i	−0.290218	−	0.502673i
$122$	−2.57400	+	4.45830i	−0.233039	+	0.403636i
$123$	19.9444	+	4.98015i	1.79833	+	0.449045i
$124$	0.809559	−	0.467399i	0.0727006	−	0.0419737i
$125$		0			0
$126$	−11.9988	+	0.753230i	−1.06894	+	0.0671030i
$127$	9.57778			0.849891			0.424945	−	0.905219i	$-0.360293\pi$
$127$	9.57778			0.849891			0.424945	+	0.905219i	$0.360293\pi$
$128$	−11.3900	+	6.57602i	−1.00674	+	0.581243i
$129$	−5.02950	−	1.25587i	−0.442823	−	0.110573i
$130$		0			0
$131$	−4.72508	−	8.18408i	−0.412832	−	0.715047i	0.582366	−	0.812927i	$-0.302127\pi$
$131$	−4.72508	−	8.18408i	−0.412832	−	0.715047i	−0.995198	+	0.0978802i	$0.968794\pi$
$132$	−1.05269	+	0.301455i	−0.0916253	+	0.0262383i
$133$	−2.75354	+	1.69613i	−0.238762	+	0.147073i
$134$		−	15.6280i		−	1.35005i
$135$		0			0
$136$	−8.00392	−	4.62107i	−0.686330	−	0.396253i
$137$	9.27125	+	5.35276i	0.792096	+	0.457317i	0.840700	−	0.541501i	$-0.182144\pi$
$137$	9.27125	+	5.35276i	0.792096	+	0.457317i	−0.0486038	+	0.998818i	$0.515477\pi$
$138$	−2.76144	+	2.85755i	−0.235070	+	0.243251i
$139$		−	4.11136i		−	0.348721i	−0.984682	−	0.174360i	$-0.944214\pi$
$139$		−	4.11136i		−	0.348721i	0.984682	−	0.174360i	$-0.0557858\pi$
$140$		0			0
$141$	2.90948	+	10.1600i	0.245022	+	0.855629i
$142$	7.87395	+	13.6381i	0.660767	+	1.14448i
$143$	−3.73909	+	6.47629i	−0.312678	+	0.541575i
$144$	0.461868	+	13.4980i	0.0384890	+	1.12483i
$145$		0			0
$146$	10.3841			0.859390
$147$	−11.9114	−	2.26264i	−0.982432	−	0.186619i
$148$	2.29642			0.188764
$149$	2.20294	−	1.27187i	0.180472	−	0.104196i	−0.407042	−	0.913409i	$-0.633440\pi$
$149$	2.20294	−	1.27187i	0.180472	−	0.104196i	0.587514	+	0.809214i	$0.300107\pi$
$150$		0			0
$151$	2.80956	−	4.86630i	0.228639	−	0.396014i	−0.728766	−	0.684763i	$-0.759906\pi$
$151$	2.80956	−	4.86630i	0.228639	−	0.396014i	0.957405	+	0.288749i	$0.0932392\pi$
$152$	1.57904	+	2.73498i	0.128077	+	0.221836i
$153$	−9.10486	+	5.68046i	−0.736084	+	0.459238i
$154$	−8.60580	+	0.245234i	−0.693475	+	0.0197616i
$155$		0			0
$156$	−1.27588	−	1.23297i	−0.102152	−	0.0987164i
$157$	12.0584	+	6.96194i	0.962368	+	0.555623i	0.896901	−	0.442231i	$-0.145813\pi$
$157$	12.0584	+	6.96194i	0.962368	+	0.555623i	0.0654670	+	0.997855i	$0.479146\pi$
$158$	−2.46983	−	1.42596i	−0.196489	−	0.113443i
$159$	13.9821	+	13.5119i	1.10885	+	1.07156i
$160$		0			0
$161$	−3.41210	+	2.10179i	−0.268911	+	0.165644i
$162$	12.2441	+	5.99317i	0.961990	+	0.470868i
$163$	2.03535	+	3.52533i	0.159421	+	0.276125i	0.934660	−	0.355543i	$-0.115704\pi$
$163$	2.03535	+	3.52533i	0.159421	+	0.276125i	−0.775239	+	0.631668i	$0.782371\pi$
$164$	−1.74633	+	3.02473i	−0.136366	+	0.236192i
$165$		0			0
$166$	11.9434	−	6.89551i	0.926986	−	0.535196i
$167$	13.9722			1.08120			0.540602	−	0.841279i	$-0.318197\pi$
$167$	13.9722			1.08120			0.540602	+	0.841279i	$0.318197\pi$
$168$	−2.53995	+	11.5640i	−0.195961	+	0.892185i
$169$	0.882841			0.0679109
$170$		0			0
$171$	3.66488	−	0.125403i	0.280261	−	0.00958983i
$172$	0.440382	−	0.762763i	0.0335788	−	0.0581602i
$173$	5.00133	+	8.66256i	0.380244	+	0.658602i	0.991097	−	0.133142i	$-0.0425066\pi$
$173$	5.00133	+	8.66256i	0.380244	+	0.658602i	−0.610853	+	0.791744i	$0.709173\pi$
$174$	−4.30206	−	15.0230i	−0.326139	−	1.13889i
$175$		0			0
$176$			9.67157i			0.729022i
$177$	−2.61107	+	2.70195i	−0.196260	+	0.203091i
$178$	−2.33483	−	1.34801i	−0.175003	−	0.101038i
$179$	−14.0378	−	8.10475i	−1.04924	−	0.605777i	−0.126801	−	0.991928i	$-0.540471\pi$
$179$	−14.0378	−	8.10475i	−1.04924	−	0.605777i	−0.922436	+	0.386151i	$0.873804\pi$
$180$		0			0
$181$			19.4123i			1.44290i	0.692465	+	0.721451i	$0.256525\pi$
$181$			19.4123i			1.44290i	−0.692465	+	0.721451i	$0.743475\pi$
$182$	−7.31627	−	11.8774i	−0.542318	−	0.880414i
$183$	5.65929	−	1.62062i	0.418347	−	0.119800i
$184$	1.95670	+	3.38910i	0.144250	+	0.249848i
$185$		0			0
$186$	−8.08550	−	2.01896i	−0.592857	−	0.148037i
$187$	−6.65529	+	3.84243i	−0.486683	+	0.280987i
$188$	−1.79560			−0.130958
$189$	10.4651	+	8.91531i	0.761221	+	0.648493i
$190$		0			0
$191$	11.0018	−	6.35188i	0.796061	−	0.459606i	−0.0460309	−	0.998940i	$-0.514657\pi$
$191$	11.0018	−	6.35188i	0.796061	−	0.459606i	0.842092	+	0.539334i	$0.181324\pi$
$192$	10.9262	+	2.72830i	0.788534	+	0.196898i
$193$	10.4098	−	18.0302i	0.749311	−	1.29785i	−0.198842	−	0.980032i	$-0.563718\pi$
$193$	10.4098	−	18.0302i	0.749311	−	1.29785i	0.948153	−	0.317813i	$-0.102949\pi$
$194$	1.00411	+	1.73918i	0.0720912	+	0.124866i
$195$		0			0
$196$	0.926718	−	1.83974i	0.0661942	−	0.131410i
$197$			2.23465i			0.159212i	0.996826	+	0.0796062i	$0.0253663\pi$
$197$			2.23465i			0.159212i	−0.996826	+	0.0796062i	$0.974634\pi$
$198$	8.61613	+	4.58904i	0.612322	+	0.326129i
$199$	21.5831	+	12.4610i	1.52998	+	0.883337i	0.999362	+	0.0357284i	$0.0113751\pi$
$199$	21.5831	+	12.4610i	1.52998	+	0.883337i	0.530622	+	0.847608i	$0.321958\pi$
$200$		0			0
$201$	−12.4185	+	12.8507i	−0.875936	+	0.906421i
$202$		−	20.3273i		−	1.43022i
$203$	−0.448901	−	15.7529i	−0.0315066	−	1.10564i
$204$	−0.501960	−	1.75286i	−0.0351442	−	0.122725i
$205$		0			0
$206$	−4.38262	+	7.59093i	−0.305352	+	0.528885i
$207$	4.54141	−	0.155396i	0.315650	−	0.0108008i
$208$	−13.5716	+	7.83560i	−0.941025	+	0.543301i
$209$	2.62596			0.181641
$210$		0			0
$211$	−6.61520			−0.455409			−0.227705	−	0.973730i	$-0.573122\pi$
$211$	−6.61520			−0.455409			−0.227705	+	0.973730i	$0.573122\pi$
$212$	−2.86100	+	1.65180i	−0.196494	+	0.113446i
$213$	4.36261	−	17.4713i	0.298921	−	1.19712i
$214$	−2.94338	+	5.09808i	−0.201205	+	0.348498i
$215$		0			0
$216$	8.99355	−	9.96721i	0.611934	−	0.678183i
$217$	−7.39515	−	3.99316i	−0.502016	−	0.271073i
$218$		−	7.88801i		−	0.534243i
$219$	−8.53868	−	8.25151i	−0.576991	−	0.557585i
$220$		0			0
$221$	−10.7838	−	6.22604i	−0.725398	−	0.418808i
$222$	−14.7218	−	14.2266i	−0.988060	−	0.954830i
$223$			4.31027i			0.288637i	0.989531	+	0.144318i	$0.0460990\pi$
$223$			4.31027i			0.288637i	−0.989531	+	0.144318i	$0.953901\pi$
$224$	−3.84545	−	2.07643i	−0.256935	−	0.138737i
$225$		0			0
$226$	7.09052	+	12.2811i	0.471654	+	0.816929i
$227$	−5.55561	+	9.62260i	−0.368739	+	0.638675i	−0.989369	−	0.145429i	$-0.953544\pi$
$227$	−5.55561	+	9.62260i	−0.368739	+	0.638675i	0.620630	+	0.784104i	$0.286877\pi$
$228$	−0.150939	+	0.604478i	−0.00999617	+	0.0400326i
$229$	−8.63774	+	4.98700i	−0.570798	+	0.329550i	−0.757468	−	0.652872i	$-0.773564\pi$
$229$	−8.63774	+	4.98700i	−0.570798	+	0.329550i	0.186670	+	0.982423i	$0.440230\pi$
$230$		0			0
$231$	7.27132	+	6.63680i	0.478418	+	0.436669i
$232$	−15.3893			−1.01036
$233$	17.8650	−	10.3144i	1.17037	−	0.675716i	0.216606	−	0.976259i	$-0.430501\pi$
$233$	17.8650	−	10.3144i	1.17037	−	0.675716i	0.953768	+	0.300543i	$0.0971678\pi$
$234$	0.540929	+	15.8085i	0.0353616	+	1.03343i
$235$		0			0
$236$	−0.319198	−	0.552868i	−0.0207780	−	0.0359886i
$237$	0.897801	+	3.13516i	0.0583184	+	0.203650i
$238$	−0.408345	−	14.3297i	−0.0264691	−	0.928857i
$239$			2.87353i			0.185873i	0.995672	+	0.0929365i	$0.0296254\pi$
$239$			2.87353i			0.185873i	−0.995672	+	0.0929365i	$0.970375\pi$
$240$		0			0
$241$	22.5792	+	13.0361i	1.45445	+	0.839728i	0.998729	−	0.0503940i	$-0.0160477\pi$
$241$	22.5792	+	13.0361i	1.45445	+	0.839728i	0.455722	+	0.890122i	$0.349381\pi$
$242$	−8.37532	−	4.83549i	−0.538386	−	0.310837i
$243$	−5.30584	−	14.6577i	−0.340370	−	0.940292i
$244$			1.00018i			0.0640298i
$245$		0			0
$246$	29.9340	−	8.57206i	1.90852	−	0.546534i
$247$	2.12747	+	3.68488i	0.135368	+	0.234464i
$248$	−4.10353	+	7.10752i	−0.260574	+	0.451328i
$249$	−15.3003	−	3.82050i	−0.969617	−	0.242114i
$250$		0			0
$251$	0.161120			0.0101698			0.00508489	−	0.999987i	$-0.498381\pi$
$251$	0.161120			0.0101698			0.00508489	+	0.999987i	$0.498381\pi$
$252$	−1.94570	+	1.29233i	−0.122567	+	0.0814091i
$253$	3.25401			0.204578
$254$	12.5637	−	7.25368i	0.788319	−	0.455136i
$255$		0			0
$256$	−3.45866	+	5.99057i	−0.216166	+	0.374411i
$257$	−6.56514	−	11.3712i	−0.409522	−	0.709314i	0.585314	−	0.810807i	$-0.300971\pi$
$257$	−6.56514	−	11.3712i	−0.409522	−	0.709314i	−0.994836	+	0.101493i	$0.967638\pi$
$258$	−7.54861	+	2.16166i	−0.469956	+	0.134579i
$259$	−10.8282	−	17.5788i	−0.672830	−	1.09229i
$260$		0			0
$261$	−8.40022	+	15.7718i	−0.519961	+	0.976249i
$262$	−12.3963	−	7.15703i	−0.765848	−	0.442163i
$263$	−15.3551	−	8.86526i	−0.946835	−	0.546655i	−0.0547384	−	0.998501i	$-0.517432\pi$
$263$	−15.3551	−	8.86526i	−0.946835	−	0.546655i	−0.892096	+	0.451846i	$0.850766\pi$
$264$	6.68061	−	6.91311i	0.411163	−	0.425473i
$265$		0			0
$266$	−2.32743	+	4.31029i	−0.142704	+	0.264281i
$267$	0.848727	+	2.96379i	0.0519412	+	0.181381i
$268$	−1.51814	−	2.62950i	−0.0927352	−	0.160622i
$269$	−2.20294	+	3.81561i	−0.134316	+	0.232642i	−0.925336	−	0.379148i	$-0.876217\pi$
$269$	−2.20294	+	3.81561i	−0.134316	+	0.232642i	0.791020	+	0.611790i	$0.209550\pi$
$270$		0			0
$271$	20.4287	−	11.7945i	1.24095	−	0.716465i	0.271665	−	0.962392i	$-0.412426\pi$
$271$	20.4287	−	11.7945i	1.24095	−	0.716465i	0.969288	+	0.245927i	$0.0790923\pi$
$272$	−16.1043			−0.976469
$273$	−3.42211	+	15.5804i	−0.207116	+	0.942970i
$274$	16.2155			0.979615
$275$		0			0
$276$	−0.187039	+	0.749051i	−0.0112584	+	0.0450876i
$277$	6.41589	−	11.1127i	0.385494	−	0.667695i	−0.606344	−	0.795203i	$-0.707364\pi$
$277$	6.41589	−	11.1127i	0.385494	−	0.667695i	0.991838	+	0.127508i	$0.0406978\pi$
$278$	−3.11371	−	5.39311i	−0.186748	−	0.323457i
$279$	5.04428	+	8.08517i	0.301993	+	0.484046i
$280$		0			0
$281$		−	21.2397i		−	1.26706i	−0.773719	−	0.633528i	$-0.781606\pi$
$281$		−	21.2397i		−	1.26706i	0.773719	−	0.633528i	$-0.218394\pi$
$282$	11.5112	+	11.1240i	0.685480	+	0.662426i
$283$	−5.67603	−	3.27706i	−0.337405	−	0.194801i	0.321719	−	0.946835i	$-0.395739\pi$
$283$	−5.67603	−	3.27706i	−0.337405	−	0.194801i	−0.659124	+	0.752034i	$0.729073\pi$
$284$	2.64967	+	1.52979i	0.157229	+	0.0907761i
$285$		0			0
$286$			11.3271i			0.669786i
$287$	31.3883	−	0.894454i	1.85279	−	0.0527980i
$288$	2.62301	+	4.20426i	0.154562	+	0.247738i
$289$	2.10188	+	3.64056i	0.123640	+	0.214151i
$290$		0			0
$291$	0.556336	−	2.22801i	0.0326130	−	0.130608i
$292$	1.74717	−	1.00873i	0.102245	−	0.0590315i
$293$	3.71937			0.217288			0.108644	−	0.994081i	$-0.465349\pi$
$293$	3.71937			0.217288			0.108644	+	0.994081i	$0.465349\pi$
$294$	−17.3384	+	6.05296i	−1.01120	+	0.353016i
$295$		0			0
$296$	−17.4603	+	10.0807i	−1.01486	+	0.585928i
$297$	−3.43834	−	10.6202i	−0.199513	−	0.616245i
$298$	1.92648	−	3.33677i	0.111598	−	0.193294i
$299$	2.63629	+	4.56619i	0.152461	+	0.264070i
$300$		0			0
$301$	−7.91536	+	0.225559i	−0.456234	+	0.0130010i
$302$		−	8.51121i		−	0.489765i
$303$	−16.1527	+	16.7149i	−0.927949	+	0.960245i
$304$	4.76568	+	2.75147i	0.273331	+	0.157808i
$305$		0			0
$306$	−7.64132	+	14.3469i	−0.436825	+	0.820158i
$307$			11.2102i			0.639800i	0.947451	+	0.319900i	$0.103649\pi$
$307$			11.2102i			0.639800i	−0.947451	+	0.319900i	$0.896351\pi$
$308$	−1.42415	+	0.877248i	−0.0811484	+	0.0499859i
$309$	9.63578	−	2.75935i	0.548160	−	0.156974i
$310$		0			0
$311$	−9.46050	+	16.3861i	−0.536456	+	0.929168i	0.462636	+	0.886548i	$0.346904\pi$
$311$	−9.46050	+	16.3861i	−0.536456	+	0.929168i	−0.999091	+	0.0426199i	$0.986430\pi$
$312$	15.1133	+	3.77380i	0.855620	+	0.213649i
$313$	14.1859	−	8.19024i	0.801835	−	0.462940i	−0.0422775	−	0.999106i	$-0.513461\pi$
$313$	14.1859	−	8.19024i	0.801835	−	0.462940i	0.844112	+	0.536166i	$0.180128\pi$
$314$	21.0903			1.19020
$315$		0			0
$316$	−0.554083			−0.0311696
$317$	8.76134	−	5.05836i	0.492086	−	0.284106i	−0.233353	−	0.972392i	$-0.574970\pi$
$317$	8.76134	−	5.05836i	0.492086	−	0.284106i	0.725439	+	0.688286i	$0.241637\pi$
$318$	28.5743	+	7.13503i	1.60237	+	0.400113i
$319$	−6.39812	+	11.0819i	−0.358226	+	0.620466i
$320$		0			0
$321$	6.47141	−	1.85319i	0.361199	−	0.103435i
$322$	−2.88408	+	5.34118i	−0.160723	+	0.297652i
$323$			4.37254i			0.243295i
$324$	2.64233	−	0.181040i	0.146796	−	0.0100578i
$325$		0			0
$326$	5.33977	+	3.08292i	0.295743	+	0.170747i
$327$	−6.26807	+	6.48622i	−0.346625	+	0.358689i
$328$		−	30.6638i		−	1.69313i
$329$	8.46672	+	13.7451i	0.466785	+	0.757791i
$330$		0			0
$331$	−9.63774	−	16.6931i	−0.529738	−	0.917533i	−0.999398	−	0.0346861i	$-0.988957\pi$
$331$	−9.63774	−	16.6931i	−0.529738	−	0.917533i	0.469660	−	0.882847i	$-0.344376\pi$
$332$	1.33969	−	2.32041i	0.0735251	−	0.127349i
$333$	0.800582	+	23.3968i	0.0438716	+	1.28214i
$334$	18.3282	−	10.5818i	1.00287	−	0.579009i
$335$		0			0
$336$	6.24224	+	19.6635i	0.340542	+	1.07273i
$337$	23.6381			1.28765			0.643824	−	0.765174i	$-0.277347\pi$
$337$	23.6381			1.28765			0.643824	+	0.765174i	$0.277347\pi$
$338$	1.15807	−	0.668614i	0.0629909	−	0.0363678i
$339$	3.92855	−	15.7330i	0.213369	−	0.854499i
$340$		0			0
$341$	3.41210	+	5.90993i	0.184776	+	0.320041i
$342$	4.71247	−	2.94008i	0.254821	−	0.158981i
$343$	−18.4527	+	1.58093i	−0.996350	+	0.0853621i
$344$			7.73266i			0.416917i
$345$		0			0
$346$	13.1211	+	7.57546i	0.705394	+	0.407259i
$347$	−13.7760	−	7.95360i	−0.739536	−	0.426971i	0.0823644	−	0.996602i	$-0.473753\pi$
$347$	−13.7760	−	7.95360i	−0.739536	−	0.426971i	−0.821901	+	0.569631i	$0.807086\pi$
$348$	−2.18321	−	2.10979i	−0.117032	−	0.113096i
$349$		−	0.0192397i		−	0.00102988i	−1.00000		0.000514938i	$-0.999836\pi$
$349$		−	0.0192397i		−	0.00102988i	1.00000		0.000514938i	$-0.000163910\pi$
$350$		0			0
$351$	12.1172	−	13.4290i	0.646766	−	0.716786i
$352$	1.77428	+	3.07314i	0.0945695	+	0.163799i
$353$	−12.7100	+	22.0143i	−0.676484	+	1.17170i	0.299549	+	0.954081i	$0.403164\pi$
$353$	−12.7100	+	22.0143i	−0.676484	+	1.17170i	−0.976033	+	0.217624i	$0.930170\pi$
$354$	−1.37880	+	5.52178i	−0.0732821	+	0.293479i
$355$		0			0
$356$	−0.523797			−0.0277612
$357$	−11.0511	+	12.1076i	−0.584885	+	0.640804i
$358$	−24.5523			−1.29763
$359$	−20.9396	+	12.0895i	−1.10515	+	0.638057i	−0.937568	−	0.347801i	$-0.886928\pi$
$359$	−20.9396	+	12.0895i	−1.10515	+	0.638057i	−0.167579	+	0.985859i	$0.553595\pi$
$360$		0			0
$361$	−8.75294	+	15.1605i	−0.460681	+	0.797923i
$362$	14.7018	+	25.4642i	0.772708	+	1.33837i
$363$	3.04448	+	10.6315i	0.159794	+	0.558007i
$364$	−2.38480	−	1.28772i	−0.124998	−	0.0674949i
$365$		0			0
$366$	6.19625	−	6.41189i	0.323883	−	0.335155i
$367$	−7.85721	−	4.53636i	−0.410143	−	0.236796i	0.280708	−	0.959793i	$-0.409431\pi$
$367$	−7.85721	−	4.53636i	−0.410143	−	0.236796i	−0.690851	+	0.722997i	$0.742764\pi$
$368$	5.90548	+	3.40953i	0.307845	+	0.177734i
$369$	−31.4260	−	16.7378i	−1.63597	−	0.871336i
$370$		0			0
$371$	26.1346	+	14.1119i	1.35684	+	0.732654i
$372$	−1.55655	+	0.445743i	−0.0807035	+	0.0231107i
$373$	−7.78183	−	13.4785i	−0.402928	−	0.697891i	0.591150	−	0.806562i	$-0.298674\pi$
$373$	−7.78183	−	13.4785i	−0.402928	−	0.697891i	−0.994078	+	0.108670i	$0.965341\pi$
$374$	−5.82009	+	10.0807i	−0.300950	+	0.521260i
$375$		0			0
$376$	13.6524	−	7.88224i	0.704071	−	0.406496i
$377$	−20.7342			−1.06787
$378$	20.4796	+	3.76908i	1.05336	+	0.193861i
$379$	−34.0984			−1.75152			−0.875758	−	0.482751i	$-0.839638\pi$
$379$	−34.0984			−1.75152			−0.875758	+	0.482751i	$0.839638\pi$
$380$		0			0
$381$	−16.0950	−	4.01894i	−0.824573	−	0.205897i
$382$	9.62112	−	16.6643i	0.492259	−	0.852618i
$383$	5.28833	+	9.15965i	0.270221	+	0.468036i	0.968918	−	0.247381i	$-0.0795699\pi$
$383$	5.28833	+	9.15965i	0.270221	+	0.468036i	−0.698697	+	0.715417i	$0.746237\pi$
$384$	21.8997	−	6.27133i	1.11757	−	0.320032i
$385$		0			0
$386$		−	31.5351i		−	1.60509i
$387$	7.92486	+	4.22087i	0.402843	+	0.214559i
$388$	0.337895	+	0.195084i	0.0171540	+	0.00990388i
$389$	−14.6659	−	8.46736i	−0.743590	−	0.429312i	0.0797828	−	0.996812i	$-0.474577\pi$
$389$	−14.6659	−	8.46736i	−0.743590	−	0.429312i	−0.823373	+	0.567500i	$0.807911\pi$
$390$		0			0
$391$			5.41832i			0.274016i
$392$	1.02990	+	18.0561i	0.0520180	+	0.911970i
$393$	4.50615	+	15.7357i	0.227305	+	0.793760i
$394$	1.69240	+	2.93132i	0.0852619	+	0.147678i
$395$		0			0
$396$	1.89550	−	0.0648594i	0.0952524	−	0.00325931i
$397$	−0.353188	+	0.203913i	−0.0177260	+	0.0102341i	−0.508837	−	0.860863i	$-0.669924\pi$
$397$	−0.353188	+	0.203913i	−0.0177260	+	0.0102341i	0.491111	+	0.871097i	$0.336591\pi$
$398$	37.7491			1.89219
$399$	5.33892	−	1.69485i	0.267280	−	0.0848487i
$400$		0			0
$401$	−24.2302	+	13.9893i	−1.21000	+	0.698593i	−0.962759	−	0.270361i	$-0.912857\pi$
$401$	−24.2302	+	13.9893i	−1.21000	+	0.698593i	−0.247240	+	0.968954i	$0.579524\pi$
$402$	−6.55769	+	26.2622i	−0.327068	+	1.30984i
$403$	−5.52875	+	9.57608i	−0.275407	+	0.477019i
$404$	−1.97464	−	3.42017i	−0.0982418	−	0.170160i
$405$		0			0
$406$	−12.5192	−	20.3240i	−0.621317	−	1.00866i
$407$			16.7643i			0.830974i
$408$	11.5112	+	11.1240i	0.569888	+	0.550721i
$409$	−2.26960	−	1.31036i	−0.112225	−	0.0647929i	0.442837	−	0.896602i	$-0.353972\pi$
$409$	−2.26960	−	1.31036i	−0.112225	−	0.0647929i	−0.555062	+	0.831809i	$0.687305\pi$
$410$		0			0
$411$	−13.3338	−	12.8854i	−0.657709	−	0.635589i
$412$			1.70295i			0.0838984i
$413$	−2.72703	+	5.05033i	−0.134188	+	0.248511i
$414$	5.83954	−	3.64325i	0.286998	−	0.179056i
$415$		0			0
$416$	−2.87493	+	4.97953i	−0.140955	+	0.244141i
$417$	−1.72517	+	6.90895i	−0.0844820	+	0.338333i
$418$	3.44462	−	1.98876i	0.168482	−	0.0972732i
$419$	8.39649			0.410195			0.205098	−	0.978742i	$-0.434249\pi$
$419$	8.39649			0.410195			0.205098	+	0.978742i	$0.434249\pi$
$420$		0			0
$421$	−7.84952			−0.382562			−0.191281	−	0.981535i	$-0.561264\pi$
$421$	−7.84952			−0.382562			−0.191281	+	0.981535i	$0.561264\pi$
$422$	−8.67754	+	5.00998i	−0.422416	+	0.243882i
$423$	−0.625987	−	18.2943i	−0.0304365	−	0.889500i
$424$	14.5020	−	25.1181i	0.704277	−	1.21984i
$425$		0			0
$426$	−7.50912	−	26.2222i	−0.363818	−	1.27047i
$427$	7.65622	−	4.71609i	0.370511	−	0.228227i
$428$			1.14371i			0.0552831i
$429$	9.00089	−	9.31415i	0.434567	−	0.449691i
$430$		0			0
$431$	−10.6154	−	6.12880i	−0.511326	−	0.295214i	0.222053	−	0.975035i	$-0.428724\pi$
$431$	−10.6154	−	6.12880i	−0.511326	−	0.295214i	−0.733378	+	0.679821i	$0.762058\pi$
$432$	4.88776	−	22.8765i	0.235162	−	1.10065i
$433$			5.13957i			0.246992i	0.992345	+	0.123496i	$0.0394106\pi$
$433$			5.13957i			0.246992i	−0.992345	+	0.123496i	$0.960589\pi$
$434$	−12.7249	+	0.362613i	−0.610813	+	0.0174060i
$435$		0			0
$436$	−0.766259	−	1.32720i	−0.0366971	−	0.0635613i
$437$	0.925734	−	1.60342i	0.0442838	−	0.0767019i
$438$	−17.4499	−	4.35726i	−0.833790	−	0.208198i
$439$	14.4620	−	8.34964i	0.690234	−	0.398507i	−0.113466	−	0.993542i	$-0.536195\pi$
$439$	14.4620	−	8.34964i	0.690234	−	0.398507i	0.803700	+	0.595035i	$0.202862\pi$
$440$		0			0
$441$	19.0671	+	8.80040i	0.907955	+	0.419067i
$442$	−18.8610			−0.897127
$443$	−0.218429	+	0.126110i	−0.0103779	+	0.00599167i	−0.505180	−	0.863014i	$-0.668574\pi$
$443$	−0.218429	+	0.126110i	−0.0103779	+	0.00599167i	0.494802	+	0.869006i	$0.335241\pi$
$444$	−3.85902	−	0.963602i	−0.183141	−	0.0457305i
$445$		0			0
$446$	3.26436	+	5.65403i	0.154572	+	0.267726i
$447$	−4.23563	+	1.21294i	−0.200339	+	0.0573700i
$448$	17.1956	−	0.490013i	0.812415	−	0.0231509i
$449$			28.8710i			1.36250i	0.732049	+	0.681252i	$0.238564\pi$
$449$			28.8710i			1.36250i	−0.732049	+	0.681252i	$0.761436\pi$
$450$		0			0
$451$	−22.0811	−	12.7485i	−1.03976	−	0.600305i
$452$	2.38603	+	1.37758i	0.112230	+	0.0647958i
$453$	−6.76329	+	6.99867i	−0.317767	+	0.328826i
$454$			16.8300i			0.789873i
$455$		0			0
$456$	−1.50588	−	5.25859i	−0.0705193	−	0.246256i
$457$	−12.0368	−	20.8483i	−0.563056	−	0.975242i	−0.997228	−	0.0744117i	$-0.976292\pi$
$457$	−12.0368	−	20.8483i	−0.563056	−	0.975242i	0.434171	−	0.900830i	$-0.357041\pi$
$458$	−7.55375	+	13.0835i	−0.352964	+	0.611351i
$459$	17.6839	−	5.72525i	0.825413	−	0.267232i
$460$		0			0
$461$	39.8709			1.85697			0.928486	−	0.371367i	$-0.121111\pi$
$461$	39.8709			1.85697			0.928486	+	0.371367i	$0.121111\pi$
$462$	14.5646	+	3.19898i	0.677604	+	0.148830i
$463$	29.8417			1.38686			0.693430	−	0.720524i	$-0.256099\pi$
$463$	29.8417			1.38686			0.693430	+	0.720524i	$0.256099\pi$
$464$	−23.2231	+	13.4078i	−1.07810	+	0.622443i
$465$		0			0
$466$	15.6230	−	27.0599i	0.723723	−	1.25353i
$467$	−2.09082	−	3.62140i	−0.0967515	−	0.167579i	0.813587	−	0.581444i	$-0.197512\pi$
$467$	−2.09082	−	3.62140i	−0.0967515	−	0.167579i	−0.910338	+	0.413865i	$0.864179\pi$
$468$	1.62669	+	2.60732i	0.0751937	+	0.120523i
$469$	−12.9700	+	24.0199i	−0.598900	+	1.10914i
$470$		0			0
$471$	−17.3423	−	16.7591i	−0.799093	−	0.772218i
$472$	4.85390	+	2.80240i	0.223419	+	0.128991i
$473$	5.56831	+	3.21487i	0.256031	+	0.147820i
$474$	3.55209	+	3.43263i	0.163153	+	0.157666i
$475$		0			0
$476$	−1.46073	−	2.37138i	−0.0669522	−	0.108692i
$477$	−17.8266	−	28.5731i	−0.816223	−	1.30827i
$478$	2.17625	+	3.76937i	0.0995393	+	0.172407i
$479$	13.9676	−	24.1926i	0.638196	−	1.10539i	−0.347632	−	0.937631i	$-0.613014\pi$
$479$	13.9676	−	24.1926i	0.638196	−	1.10539i	0.985828	−	0.167757i	$-0.0536525\pi$
$480$		0			0
$481$	−23.5245	+	13.5819i	−1.07262	+	0.619280i
$482$	39.4912			1.79878
$483$	6.61582	−	2.10021i	0.301030	−	0.0955627i
$484$	−1.87892			−0.0854055
$485$		0			0
$486$	−18.0609	−	15.2090i	−0.819259	−	0.689895i
$487$	−18.6216	+	32.2536i	−0.843826	+	1.46155i	0.0428116	+	0.999083i	$0.486368\pi$
$487$	−18.6216	+	32.2536i	−0.843826	+	1.46155i	−0.886637	+	0.462466i	$0.846965\pi$
$488$	−4.39053	−	7.60462i	−0.198750	−	0.344245i
$489$	−1.94104	−	6.77821i	−0.0877770	−	0.306521i
$490$		0			0
$491$		−	5.90572i		−	0.266522i	−0.991081	−	0.133261i	$-0.957455\pi$
$491$		−	5.90572i		−	0.266522i	0.991081	−	0.133261i	$-0.0425448\pi$
$492$	4.20384	−	4.35015i	0.189524	−	0.196120i
$493$	−18.4527	−	10.6536i	−0.831066	−	0.479816i
$494$	5.58145	+	3.22245i	0.251121	+	0.144985i
$495$		0			0
$496$			14.3007i			0.642122i
$497$	−0.783542	−	27.4962i	−0.0351467	−	1.23337i
$498$	−22.9637	+	6.57602i	−1.02903	+	0.294678i
$499$	−9.37010	−	16.2295i	−0.419463	−	0.726532i	0.576422	−	0.817152i	$-0.304448\pi$
$499$	−9.37010	−	16.2295i	−0.419463	−	0.726532i	−0.995886	+	0.0906204i	$0.971115\pi$
$500$		0			0
$501$	−23.4797	−	5.86290i	−1.04899	−	0.261935i
$502$	0.211350	−	0.122023i	0.00943301	−	0.00544615i
$503$	−32.0398			−1.42858			−0.714291	−	0.699849i	$-0.753251\pi$
$503$	−32.0398			−1.42858			−0.714291	+	0.699849i	$0.753251\pi$
$504$	9.12067	−	18.3671i	0.406267	−	0.818134i
$505$		0			0
$506$	4.26847	−	2.46440i	0.189757	−	0.109556i
$507$	−1.48357	−	0.370450i	−0.0658878	−	0.0164523i
$508$	1.40928	−	2.44094i	0.0625265	−	0.108299i
$509$	−9.57465	−	16.5838i	−0.424389	−	0.735063i	0.571974	−	0.820272i	$-0.306178\pi$
$509$	−9.57465	−	16.5838i	−0.424389	−	0.735063i	−0.996363	+	0.0852085i	$0.972844\pi$
$510$		0			0
$511$	−15.9600	−	8.61794i	−0.706031	−	0.381235i
$512$		−	15.8265i		−	0.699439i
$513$	−6.21129	−	1.32709i	−0.274235	−	0.0585925i
$514$	−17.2238	−	9.94415i	−0.759708	−	0.438617i
$515$		0			0
$516$	−1.06011	+	1.09700i	−0.0466685	+	0.0482927i
$517$		−	13.1082i		−	0.576499i
$518$	−27.5171	−	14.8584i	−1.20903	−	0.652842i
$519$	−4.76960	−	16.6557i	−0.209362	−	0.731102i
$520$		0			0
$521$	1.94104	−	3.36199i	0.0850387	−	0.147291i	−0.820369	−	0.571834i	$-0.806232\pi$
$521$	1.94104	−	3.36199i	0.0850387	−	0.147291i	0.905408	+	0.424543i	$0.139565\pi$
$522$	0.925607	+	27.0506i	0.0405127	+	1.18397i
$523$	−1.83929	+	1.06192i	−0.0804266	+	0.0464343i	−0.539674	−	0.841874i	$-0.681452\pi$
$523$	−1.83929	+	1.06192i	−0.0804266	+	0.0464343i	0.459247	+	0.888308i	$0.348119\pi$
$524$	−2.78100			−0.121488
$525$		0			0
$526$	−26.8562			−1.17099
$527$	−9.84076	+	5.68157i	−0.428670	+	0.247493i
$528$	4.05830	−	16.2526i	0.176615	−	0.707305i
$529$	−10.3529	+	17.9317i	−0.450124	+	0.779638i
$530$		0			0
$531$	5.52156	−	3.44486i	0.239615	−	0.149494i
$532$	0.0271092	+	0.951321i	0.00117533	+	0.0412450i
$533$		−	41.3138i		−	1.78950i
$534$	3.35793	+	3.24500i	0.145312	+	0.140425i
$535$		0			0
$536$	23.0856	+	13.3285i	0.997148	+	0.575704i
$537$	20.1891	+	19.5101i	0.871224	+	0.841922i
$538$			6.67354i			0.287717i
$539$	13.4304	+	6.76522i	0.578490	+	0.291398i
$540$		0			0
$541$	7.59052	+	13.1472i	0.326342	+	0.565241i	0.981783	−	0.190005i	$-0.0608506\pi$
$541$	7.59052	+	13.1472i	0.326342	+	0.565241i	−0.655441	+	0.755246i	$0.727517\pi$
$542$	17.8650	−	30.9431i	0.767367	−	1.32912i
$543$	8.14561	−	32.6214i	0.349561	−	1.39992i
$544$	−5.11716	+	2.95439i	−0.219396	+	0.126669i
$545$		0			0
$546$	7.31076	+	23.0295i	0.312871	+	0.985570i
$547$	11.7540			0.502566			0.251283	−	0.967914i	$-0.419148\pi$
$547$	11.7540			0.502566			0.251283	+	0.967914i	$0.419148\pi$
$548$	2.72835	−	1.57521i	0.116549	−	0.0672897i
$549$	−10.1902	+	0.348684i	−0.434907	+	0.0148815i
$550$		0			0
$551$	3.64041	+	6.30537i	0.155087	+	0.268618i
$552$	−1.86604	−	6.51629i	−0.0794239	−	0.277352i
$553$	2.61264	+	4.24143i	0.111101	+	0.180364i
$554$		−	19.4362i		−	0.825763i
$555$		0			0
$556$	−1.04780	−	0.604946i	−0.0444365	−	0.0256554i
$557$	−8.14298	−	4.70135i	−0.345029	−	0.199203i	0.317465	−	0.948270i	$-0.397169\pi$
$557$	−8.14298	−	4.70135i	−0.345029	−	0.199203i	−0.662494	+	0.749068i	$0.730502\pi$
$558$	12.7401	+	6.78553i	0.539333	+	0.287254i
$559$			10.4183i			0.440649i
$560$		0			0
$561$	12.7962	−	3.66440i	0.540258	−	0.154711i
$562$	−16.0858	−	27.8614i	−0.678538	−	1.17526i
$563$	9.76331	−	16.9106i	0.411475	−	0.712695i	−0.583577	−	0.812058i	$-0.698347\pi$
$563$	9.76331	−	16.9106i	0.411475	−	0.712695i	0.995051	+	0.0993632i	$0.0316806\pi$
$564$	3.01743	+	0.753455i	0.127057	+	0.0317262i
$565$		0			0
$566$	−9.92744			−0.417281
$567$	−13.8451	−	19.3730i	−0.581439	−	0.813590i
$568$	−26.8615			−1.12708
$569$	11.1702	−	6.44911i	0.468279	−	0.270361i	−0.247240	−	0.968954i	$-0.579524\pi$
$569$	11.1702	−	6.44911i	0.468279	−	0.270361i	0.715519	+	0.698593i	$0.246190\pi$
$570$		0			0
$571$	20.8321	−	36.0823i	0.871796	−	1.51000i	0.0116595	−	0.999932i	$-0.496289\pi$
$571$	20.8321	−	36.0823i	0.871796	−	1.51000i	0.860137	−	0.510063i	$-0.170378\pi$
$572$	1.10034	+	1.90584i	0.0460075	+	0.0796874i
$573$	−21.1533	+	6.05758i	−0.883692	+	0.253059i
$574$	40.4965	−	24.9451i	1.69029	−	1.04119i
$575$		0			0
$576$	−17.2162	−	9.16955i	−0.717343	−	0.382065i
$577$	6.48634	+	3.74489i	0.270030	+	0.155902i	0.628901	−	0.777485i	$-0.283505\pi$
$577$	6.48634	+	3.74489i	0.270030	+	0.155902i	−0.358871	+	0.933387i	$0.616838\pi$
$578$	5.51432	+	3.18369i	0.229365	+	0.132424i
$579$	−25.0588	+	25.9309i	−1.04141	+	1.07765i
$580$		0			0
$581$	−24.0794	+	0.686177i	−0.998983	+	0.0284674i
$582$	−0.957590	−	3.34395i	−0.0396934	−	0.138611i
$583$	−12.0584	−	20.8858i	−0.499409	−	0.865003i
$584$	−8.85614	+	15.3393i	−0.366470	+	0.634744i
$585$		0			0
$586$	4.87892	−	2.81685i	0.201546	−	0.116363i
$587$	−22.1920			−0.915961			−0.457981	−	0.888962i	$-0.651427\pi$
$587$	−22.1920			−0.915961			−0.457981	+	0.888962i	$0.651427\pi$
$588$	−2.32928	+	2.70274i	−0.0960580	+	0.111459i
$589$	3.88284			0.159990
$590$		0			0
$591$	0.937685	−	3.75523i	0.0385712	−	0.154470i
$592$	−17.5655	+	30.4244i	−0.721938	+	1.25043i
$593$	−3.15687	−	5.46787i	−0.129637	−	0.224538i	0.793899	−	0.608050i	$-0.208048\pi$
$593$	−3.15687	−	5.46787i	−0.129637	−	0.224538i	−0.923536	+	0.383512i	$0.874715\pi$
$594$	−12.5534	−	11.3271i	−0.515072	−	0.464757i
$595$		0			0
$596$		−	0.748572i		−	0.0306627i
$597$	−31.0406	−	29.9966i	−1.27041	−	1.22768i
$598$	6.91636	+	3.99316i	0.282831	+	0.163293i
$599$	17.8962	+	10.3324i	0.731219	+	0.422170i	0.818868	−	0.573982i	$-0.194602\pi$
$599$	17.8962	+	10.3324i	0.731219	+	0.422170i	−0.0876487	+	0.996151i	$0.527935\pi$
$600$		0			0
$601$			12.5956i			0.513785i	0.966440	+	0.256892i	$0.0826986\pi$
$601$			12.5956i			0.513785i	−0.966440	+	0.256892i	$0.917301\pi$
$602$	−10.2122	+	6.29053i	−0.416219	+	0.256383i
$603$	26.2611	−	16.3841i	1.06943	−	0.667213i
$604$	−0.826798	−	1.43206i	−0.0336419	−	0.0582695i
$605$		0			0
$606$	−8.52955	+	34.1590i	−0.346489	+	1.38762i
$607$	36.9590	−	21.3383i	1.50012	−	0.866095i	0.500121	−	0.865956i	$-0.333289\pi$
$607$	36.9590	−	21.3383i	1.50012	−	0.866095i	1.00000		0.000139312i	$-4.43443e-5\pi$
$608$	2.01906			0.0818838
$609$	−5.85573	+	26.6604i	−0.237286	+	1.08033i
$610$		0			0
$611$	18.3942	−	10.6199i	0.744148	−	0.429634i
$612$	0.107999	+	3.15624i	0.00436559	+	0.127583i
$613$	2.66142	−	4.60972i	0.107494	−	0.186185i	−0.807261	−	0.590195i	$-0.799051\pi$
$613$	2.66142	−	4.60972i	0.107494	−	0.186185i	0.914754	+	0.404011i	$0.132384\pi$
$614$	8.48998	+	14.7051i	0.342628	+	0.593448i
$615$		0			0
$616$	6.97728	−	12.9216i	0.281123	−	0.520626i
$617$			30.1002i			1.21179i	0.795545	+	0.605895i	$0.207185\pi$
$617$			30.1002i			1.21179i	−0.795545	+	0.605895i	$0.792815\pi$
$618$	10.5500	−	10.9172i	0.424385	−	0.439154i
$619$	−11.0265	−	6.36613i	−0.443191	−	0.255876i	0.261759	−	0.965133i	$-0.415697\pi$
$619$	−11.0265	−	6.36613i	−0.443191	−	0.255876i	−0.704950	+	0.709257i	$0.749031\pi$
$620$		0			0
$621$	−7.69683	−	1.64449i	−0.308863	−	0.0659911i
$622$			28.6594i			1.14914i
$623$	2.46983	+	4.00959i	0.0989518	+	0.160641i
$624$	26.0944	−	7.47254i	1.04461	−	0.299141i
$625$		0			0
$626$	12.4057	−	21.4872i	0.495830	−	0.858802i
$627$	−4.41281	−	1.10188i	−0.176230	−	0.0440049i
$628$	3.54856	−	2.04876i	0.141603	−	0.0817545i
$629$	−27.9145			−1.11303
$630$		0			0
$631$	−17.4114			−0.693138			−0.346569	−	0.938024i	$-0.612653\pi$
$631$	−17.4114			−0.693138			−0.346569	+	0.938024i	$0.612653\pi$
$632$	4.21284	−	2.43229i	0.167578	−	0.0967511i
$633$	11.1165	+	2.77581i	0.441843	+	0.110329i
$634$	7.66184	−	13.2707i	0.304291	−	0.527047i
$635$		0			0
$636$	5.50089	−	1.57526i	0.218125	−	0.0624633i
$637$	1.38761	+	24.3273i	0.0549789	+	0.963881i
$638$			19.3823i			0.767353i
$639$	−14.6623	+	27.5292i	−0.580033	+	1.08904i
$640$		0			0
$641$	−1.13893	−	0.657564i	−0.0449852	−	0.0259722i	0.477339	−	0.878719i	$-0.341601\pi$
$641$	−1.13893	−	0.657564i	−0.0449852	−	0.0259722i	−0.522324	+	0.852747i	$0.674935\pi$
$642$	7.08543	−	7.33202i	0.279640	−	0.289372i
$643$			39.2223i			1.54678i	0.633932	+	0.773389i	$0.281440\pi$
$643$			39.2223i			1.54678i	−0.633932	+	0.773389i	$0.718560\pi$
$644$	0.0335929	+	1.17885i	0.00132375	+	0.0464531i
$645$		0			0
$646$	3.31152	+	5.73572i	0.130290	+	0.225669i
$647$	−3.11558	+	5.39634i	−0.122486	+	0.212152i	−0.920747	−	0.390159i	$-0.872420\pi$
$647$	−3.11558	+	5.39634i	−0.122486	+	0.212152i	0.798261	+	0.602311i	$0.205753\pi$
$648$	−19.2956	+	12.9757i	−0.758003	+	0.509732i
$649$	4.03604	−	2.33021i	0.158428	−	0.0914687i
$650$		0			0
$651$	10.7516	+	9.81341i	0.421390	+	0.384618i
$652$	1.19793			0.0469144
$653$	16.3348	−	9.43091i	0.639230	−	0.369060i	−0.145088	−	0.989419i	$-0.546346\pi$
$653$	16.3348	−	9.43091i	0.639230	−	0.369060i	0.784318	+	0.620359i	$0.213013\pi$
$654$	−3.30990	+	13.2554i	−0.129427	+	0.518329i
$655$		0			0
$656$	−26.7157	−	46.2730i	−1.04307	−	1.80666i
$657$	10.8864	+	17.4492i	0.424721	+	0.680759i
$658$	21.5160	+	11.6180i	0.838783	+	0.452918i
$659$		−	41.6170i		−	1.62117i	−0.585622	−	0.810584i	$-0.699150\pi$
$659$		−	41.6170i		−	1.62117i	0.585622	−	0.810584i	$-0.300850\pi$
$660$		0			0
$661$	3.27232	+	1.88927i	0.127278	+	0.0734842i	0.562287	−	0.826942i	$-0.309921\pi$
$661$	3.27232	+	1.88927i	0.127278	+	0.0734842i	−0.435009	+	0.900426i	$0.643255\pi$
$662$	−25.2848	−	14.5982i	−0.982721	−	0.567374i
$663$	15.5092	+	14.9876i	0.602327	+	0.582069i
$664$			23.5236i			0.912894i
$665$		0			0
$666$	18.7696	+	30.0846i	0.727307	+	1.16576i
$667$	4.51108	+	7.81342i	0.174670	+	0.302537i
$668$	2.05588	−	3.56088i	0.0795442	−	0.137775i
$669$	1.80864	−	7.24321i	0.0699259	−	0.280039i
$670$		0			0
$671$	−7.30148			−0.281871
$672$	5.59081	+	5.10294i	0.215670	+	0.196850i
$673$	31.2573			1.20488			0.602441	−	0.798163i	$-0.294195\pi$
$673$	31.2573			1.20488			0.602441	+	0.798163i	$0.294195\pi$
$674$	31.0075	−	17.9022i	1.19436	−	0.689565i
$675$		0			0
$676$	0.129901	−	0.224996i	0.00499621	−	0.00865369i
$677$	4.36895	+	7.56724i	0.167912	+	0.290832i	0.937686	−	0.347485i	$-0.112964\pi$
$677$	4.36895	+	7.56724i	0.167912	+	0.290832i	−0.769773	+	0.638317i	$0.779631\pi$
$678$	−6.76199	−	23.6132i	−0.259693	−	0.906858i
$679$	−0.0999201	−	3.50641i	−0.00383458	−	0.134564i
$680$		0			0
$681$	13.3737	−	13.8391i	0.512481	−	0.530317i
$682$	8.95171	+	5.16827i	0.342779	+	0.197903i
$683$	18.9393	+	10.9346i	0.724691	+	0.418401i	0.816477	−	0.577378i	$-0.195924\pi$
$683$	18.9393	+	10.9346i	0.724691	+	0.418401i	−0.0917858	+	0.995779i	$0.529257\pi$
$684$	0.507292	−	0.952463i	0.0193968	−	0.0364183i
$685$		0			0
$686$	−23.0081	+	16.0488i	−0.878454	+	0.612746i
$687$	16.6079	−	4.75594i	0.633632	−	0.181450i
$688$	6.73705	+	11.6689i	0.256847	+	0.444873i
$689$	19.5387	−	33.8421i	0.744366	−	1.28928i
$690$		0			0
$691$	19.5167	−	11.2680i	0.742449	−	0.428653i	−0.0805102	−	0.996754i	$-0.525655\pi$
$691$	19.5167	−	11.2680i	0.742449	−	0.428653i	0.822959	+	0.568101i	$0.192322\pi$
$692$	2.94359			0.111898
$693$	−9.43425	−	14.2040i	−0.358377	−	0.539564i
$694$	−24.0944			−0.914612
$695$		0			0
$696$	25.8610	+	6.45751i	0.980257	+	0.244771i
$697$	21.2279	−	36.7678i	0.804063	−	1.39268i
$698$	−0.0145711	−	0.0252378i	−0.000551523	−	0.000955266i
$699$	−34.3493	+	9.83646i	−1.29921	+	0.372049i
$700$		0			0
$701$			35.5019i			1.34089i	0.741960	+	0.670444i	$0.233896\pi$
$701$			35.5019i			1.34089i	−0.741960	+	0.670444i	$0.766104\pi$
$702$	5.72442	−	26.7924i	0.216054	−	1.01122i
$703$	8.26062	+	4.76927i	0.311555	+	0.179877i
$704$	−12.0968	−	6.98408i	−0.455915	−	0.263223i
$705$		0			0
$706$			38.5033i			1.44909i
$707$	−16.8700	+	31.2425i	−0.634463	+	1.17500i
$708$	0.304409	+	1.06301i	0.0114404	+	0.0399503i
$709$	2.03390	+	3.52282i	0.0763847	+	0.132302i	0.901688	−	0.432388i	$-0.142329\pi$
$709$	2.03390	+	3.52282i	0.0763847	+	0.132302i	−0.825303	+	0.564690i	$0.808996\pi$
$710$		0			0
$711$	−0.193166	−	5.64522i	−0.00724428	−	0.211712i
$712$	3.98257	−	2.29934i	0.149253	−	0.0861712i
$713$	4.81149			0.180192
$714$	−5.32670	+	24.2518i	−0.199347	+	0.907599i
$715$		0			0
$716$	−4.13106	+	2.38507i	−0.154385	+	0.0891342i
$717$	1.20576	−	4.82883i	0.0450301	−	0.180336i
$718$	−18.3118	+	31.7169i	−0.683389	+	1.18366i
$719$	15.2703	+	26.4489i	0.569484	+	0.986376i	0.996617	+	0.0821868i	$0.0261904\pi$
$719$	15.2703	+	26.4489i	0.569484	+	0.986376i	−0.427133	+	0.904189i	$0.640476\pi$
$720$		0			0
$721$	13.0359	−	8.02984i	0.485481	−	0.299047i
$722$			26.5159i			0.986821i
$723$	−32.4732	−	31.3810i	−1.20769	−	1.16707i
$724$	4.94730	+	2.85632i	0.183865	+	0.106154i
$725$		0			0
$726$	12.0453	+	11.6402i	0.447043	+	0.432008i
$727$			23.4181i			0.868528i	0.900786	+	0.434264i	$0.142992\pi$
$727$			23.4181i			0.868528i	−0.900786	+	0.434264i	$0.857008\pi$
$728$	23.7850	−	0.677789i	0.881533	−	0.0251205i
$729$	2.76568	+	26.8580i	0.102433	+	0.994740i
$730$		0			0
$731$	−5.35315	+	9.27192i	−0.197993	+	0.342934i
$732$	0.419686	−	1.68075i	0.0155120	−	0.0621224i
$733$	14.6277	−	8.44533i	0.540288	−	0.311935i	−0.204908	−	0.978781i	$-0.565689\pi$
$733$	14.6277	−	8.44533i	0.540288	−	0.311935i	0.745196	+	0.666846i	$0.232356\pi$
$734$	−13.7423			−0.507239
$735$		0			0
$736$	2.50196			0.0922235
$737$	19.1958	−	11.0827i	0.707087	−	0.408237i
$738$	−53.8996	+	1.84431i	−1.98407	+	0.0678901i
$739$	13.8321	−	23.9579i	0.508822	−	0.881306i	−0.491126	−	0.871089i	$-0.663414\pi$
$739$	13.8321	−	23.9579i	0.508822	−	0.881306i	0.999948	−	0.0102170i	$-0.00325222\pi$
$740$		0			0
$741$	−2.02890	−	7.08499i	−0.0745333	−	0.260274i
$742$	44.9699	−	1.28148i	1.65090	−	0.0470446i
$743$			40.1701i			1.47370i	0.676056	+	0.736850i	$0.263688\pi$
$743$			40.1701i			1.47370i	−0.676056	+	0.736850i	$0.736312\pi$
$744$	9.87819	−	10.2220i	0.362152	−	0.374756i
$745$		0			0
$746$	−20.4158	−	11.7870i	−0.747474	−	0.431554i
$747$	24.1083	+	12.8404i	0.882078	+	0.469804i
$748$			2.26151i			0.0826888i
$749$	8.75491	−	5.39286i	0.319898	−	0.197051i
$750$		0			0
$751$	24.8188	+	42.9874i	0.905650	+	1.56863i	0.820042	+	0.572303i	$0.193950\pi$
$751$	24.8188	+	42.9874i	0.905650	+	1.56863i	0.0856082	+	0.996329i	$0.472717\pi$
$752$	13.7347	−	23.7893i	0.500854	−	0.867505i
$753$	−0.270754	−	0.0676076i	−0.00986683	−	0.00246376i
$754$	−27.1983	+	15.7029i	−0.990503	+	0.571867i
$755$		0			0
$756$	3.81193	−	1.35526i	0.138639	−	0.0492905i
$757$	−47.7116			−1.73411			−0.867054	−	0.498214i	$-0.833989\pi$
$757$	−47.7116			−1.73411			−0.867054	+	0.498214i	$0.833989\pi$
$758$	−44.7288	+	25.8242i	−1.62462	+	0.937977i
$759$	−5.46821	−	1.36542i	−0.198483	−	0.0495615i
$760$		0			0
$761$	9.91711	+	17.1769i	0.359495	+	0.622663i	0.987876	−	0.155242i	$-0.0496157\pi$
$761$	9.91711	+	17.1769i	0.359495	+	0.622663i	−0.628382	+	0.777905i	$0.716282\pi$
$762$	−24.1565	+	6.91759i	−0.875098	+	0.250598i
$763$	−6.54643	+	12.1237i	−0.236997	+	0.438907i
$764$		−	3.73847i		−	0.135253i
$765$		0			0
$766$	13.8740	+	8.01017i	0.501289	+	0.289419i
$767$	6.53974	+	3.77572i	0.236136	+	0.136333i
$768$	8.32583	−	8.61559i	0.300433	−	0.310888i
$769$		−	10.6337i		−	0.383461i	−0.981448	−	0.191731i	$-0.938590\pi$
$769$		−	10.6337i		−	0.383461i	0.981448	−	0.191731i	$-0.0614100\pi$
$770$		0			0
$771$	6.26096	+	21.8635i	0.225483	+	0.787396i
$772$	−3.06339	−	5.30595i	−0.110254	−	0.190965i
$773$	−7.16138	+	12.4039i	−0.257577	+	0.446136i	−0.965592	−	0.260061i	$-0.916257\pi$
$773$	−7.16138	+	12.4039i	−0.257577	+	0.446136i	0.708015	+	0.706197i	$0.249591\pi$
$774$	13.5922	−	0.465090i	0.488560	−	0.0167173i
$775$		0			0
$776$	−3.42548			−0.122967
$777$	10.8200	+	34.0839i	0.388166	+	1.22275i
$778$	−25.6508			−0.919626
$779$	−12.5637	+	7.25368i	−0.450142	+	0.259890i
$780$		0			0
$781$	−11.1677	+	19.3431i	−0.399613	+	0.692149i
$782$	4.10353	+	7.10752i	0.146742	+	0.254165i
$783$	20.7342	−	22.9789i	0.740980	−	0.821200i
$784$	17.2855	+	26.3501i	0.617338	+	0.941075i
$785$		0			0
$786$	17.8283	+	17.2287i	0.635914	+	0.614527i
$787$	−31.9859	−	18.4671i	−1.14017	−	0.658280i	−0.193700	−	0.981061i	$-0.562049\pi$
$787$	−31.9859	−	18.4671i	−1.14017	−	0.658280i	−0.946474	+	0.322781i	$0.895382\pi$
$788$	0.569511	+	0.328807i	0.0202880	+	0.0117133i
$789$	22.0835	+	21.3408i	0.786195	+	0.759753i
$790$		0			0
$791$	−0.705583	−	24.7604i	−0.0250876	−	0.880378i
$792$	−14.1273	+	8.81391i	−0.501991	+	0.313189i
$793$	−5.91543	−	10.2458i	−0.210063	−	0.363840i
$794$	−0.308865	+	0.534970i	−0.0109612	+	0.0189854i
$795$		0			0
$796$	6.35148	−	3.66703i	0.225122	−	0.129974i
$797$	37.4862			1.32783			0.663914	−	0.747809i	$-0.268894\pi$
$797$	37.4862			1.32783			0.663914	+	0.747809i	$0.268894\pi$
$798$	5.71978	−	6.26663i	0.202478	−	0.221836i
$799$	21.8268			0.772177
$800$		0			0
$801$	−0.182607	−	5.33665i	−0.00645210	−	0.188561i
$802$	−21.1895	+	36.7012i	−0.748226	+	1.29597i
$803$	7.36392	+	12.7547i	0.259867	+	0.450103i
$804$	1.44780	+	5.05578i	0.0510599	+	0.178303i
$805$		0			0
$806$			16.7487i			0.589947i
$807$	5.30301	−	5.48757i	0.186675	−	0.193172i
$808$	30.0274	+	17.3363i	1.05636	+	0.609889i
$809$	22.1518	+	12.7893i	0.778814	+	0.449649i	0.836010	−	0.548714i	$-0.184883\pi$
$809$	22.1518	+	12.7893i	0.778814	+	0.449649i	−0.0571956	+	0.998363i	$0.518216\pi$
$810$		0			0
$811$		−	7.28791i		−	0.255913i	−0.991780	−	0.127957i	$-0.959158\pi$
$811$		−	7.28791i		−	0.255913i	0.991780	−	0.127957i	$-0.0408418\pi$
$812$	−4.08074	−	2.20348i	−0.143206	−	0.0773269i
$813$	−39.2786	+	11.2480i	−1.37756	+	0.394485i
$814$	12.6963	+	21.9907i	0.445006	+	0.770773i
$815$		0			0
$816$	27.0626	+	6.75756i	0.947380	+	0.236562i
$817$	3.16826	−	1.82920i	0.110844	−	0.0639955i
$818$	−3.96956			−0.138792
$819$	12.2884	−	24.7462i	0.429392	−	0.864703i
$820$		0			0
$821$	−0.00729231	+	0.00421022i	−0.000254504	+	0.000146938i	−0.500127	−	0.865952i	$-0.666713\pi$
$821$	−0.00729231	+	0.00421022i	−0.000254504	+	0.000146938i	0.499873	+	0.866099i	$0.333380\pi$
$822$	−27.2494	−	6.80421i	−0.950433	−	0.237324i
$823$	−15.6119	+	27.0406i	−0.544198	+	0.942578i	0.454459	+	0.890767i	$0.349832\pi$
$823$	−15.6119	+	27.0406i	−0.544198	+	0.942578i	−0.998657	+	0.0518103i	$0.983501\pi$
$824$	−7.47553	−	12.9480i	−0.260422	−	0.451065i
$825$		0			0
$826$	0.247637	+	8.69011i	0.00861639	+	0.302368i
$827$		−	38.3189i		−	1.33248i	−0.745738	−	0.666239i	$-0.767903\pi$
$827$		−	38.3189i		−	1.33248i	0.745738	−	0.666239i	$-0.232097\pi$
$828$	0.628620	−	1.18026i	0.0218461	−	0.0410169i
$829$	1.94142	+	1.12088i	0.0674283	+	0.0389298i	0.533335	−	0.845904i	$-0.320938\pi$
$829$	1.94142	+	1.12088i	0.0674283	+	0.0389298i	−0.465907	+	0.884834i	$0.654272\pi$
$830$		0			0
$831$	−15.4446	+	15.9821i	−0.535768	+	0.554414i
$832$		−	22.6331i		−	0.784663i
$833$	−11.2649	+	22.3633i	−0.390306	+	0.774843i
$834$	2.96944	+	10.3694i	0.102823	+	0.359064i
$835$		0			0
$836$	0.386384	−	0.669237i	0.0133634	−	0.0231460i
$837$	−5.08406	−	15.7034i	−0.175731	−	0.542789i
$838$	11.0142	−	6.35903i	0.380478	−	0.219669i
$839$	−20.6544			−0.713069			−0.356535	−	0.934282i	$-0.616042\pi$
$839$	−20.6544			−0.713069			−0.356535	+	0.934282i	$0.616042\pi$
$840$		0			0
$841$	−6.47924			−0.223422
$842$	−10.2967	+	5.94479i	−0.354847	+	0.204871i
$843$	−8.91243	+	35.6924i	−0.306961	+	1.22931i
$844$	−0.973362	+	1.68591i	−0.0335045	+	0.0580315i
$845$		0			0
$846$	−14.6762	−	23.5236i	−0.504579	−	0.808759i
$847$	8.85959	+	14.3829i	0.304419	+	0.494202i
$848$		−	50.5391i		−	1.73552i
$849$	8.16322	+	7.88867i	0.280161	+	0.270738i
$850$		0			0
$851$	10.2363	+	5.90993i	0.350896	+	0.202590i
$852$	−3.81073	−	3.68257i	−0.130553	−	0.126163i
$853$		−	7.06831i		−	0.242014i	−0.992652	−	0.121007i	$-0.961388\pi$
$853$		−	7.06831i		−	0.242014i	0.992652	−	0.121007i	$-0.0386124\pi$
$854$	6.47141	−	11.9848i	0.221447	−	0.410110i
$855$		0			0
$856$	−5.02058	−	8.69590i	−0.171600	−	0.297220i
$857$	−8.41661	+	14.5780i	−0.287506	+	0.497975i	−0.973214	−	0.229902i	$-0.926159\pi$
$857$	−8.41661	+	14.5780i	−0.287506	+	0.497975i	0.685708	+	0.727877i	$0.259493\pi$
$858$	4.75298	−	19.0347i	0.162264	−	0.649833i
$859$	30.4698	−	17.5918i	1.03962	−	0.600223i	0.119893	−	0.992787i	$-0.461745\pi$
$859$	30.4698	−	17.5918i	1.03962	−	0.600223i	0.919725	+	0.392563i	$0.128412\pi$
$860$		0			0
$861$	−53.1220	−	11.6678i	−1.81039	−	0.397638i
$862$	−18.5665			−0.632376
$863$	32.8880	−	18.9879i	1.11952	−	0.646356i	0.178243	−	0.983986i	$-0.442959\pi$
$863$	32.8880	−	18.9879i	1.11952	−	0.646356i	0.941279	+	0.337630i	$0.109625\pi$
$864$	−2.64369	−	8.16571i	−0.0899402	−	0.277803i
$865$		0			0
$866$	3.89242	+	6.74187i	0.132270	+	0.229098i
$867$	−2.00449	−	6.99977i	−0.0680761	−	0.237725i
$868$	−2.10580	+	1.29713i	−0.0714755	+	0.0440275i
$869$		−	4.04491i		−	0.137214i
$870$		0			0
$871$	31.1037	+	17.9577i	1.05391	+	0.608474i
$872$	11.6521	+	6.72737i	0.394591	+	0.227817i
$873$	−1.86979	+	3.51062i	−0.0632829	+	0.118817i
$874$		−	2.80440i		−	0.0948601i
$875$		0			0
$876$	−3.35932	+	0.961992i	−0.113501	+	0.0325027i
$877$	−5.72481	−	9.91566i	−0.193313	−	0.334828i	0.753033	−	0.657983i	$-0.228590\pi$
$877$	−5.72481	−	9.91566i	−0.193313	−	0.334828i	−0.946346	+	0.323155i	$0.895257\pi$
$878$	12.6471	−	21.9054i	0.426819	−	0.739272i
$879$	−6.25024	−	1.56069i	−0.210815	−	0.0526408i
$880$		0			0
$881$	−23.6698			−0.797455			−0.398728	−	0.917069i	$-0.630548\pi$
$881$	−23.6698			−0.797455			−0.398728	+	0.917069i	$0.630548\pi$
$882$	31.6763	−	2.89633i	1.06660	−	0.0975245i
$883$	−16.8355			−0.566560			−0.283280	−	0.959037i	$-0.591423\pi$
$883$	−16.8355			−0.566560			−0.283280	+	0.959037i	$0.591423\pi$
$884$	−3.17346	+	1.83220i	−0.106735	+	0.0616236i
$885$		0			0
$886$	−0.191017	+	0.330852i	−0.00641735	+	0.0111152i
$887$	−26.2917	−	45.5385i	−0.882789	−	1.52903i	−0.848227	−	0.529632i	$-0.822330\pi$
$887$	−26.2917	−	45.5385i	−0.882789	−	1.52903i	−0.0345613	−	0.999403i	$-0.511003\pi$
$888$	33.5712	−	9.61362i	1.12657	−	0.322612i
$889$	−25.3301	+	0.721818i	−0.849546	+	0.0242090i
$890$		0			0
$891$	1.32163	+	19.2895i	0.0442761	+	0.646222i
$892$	1.09849	+	0.634214i	0.0367802	+	0.0212350i
$893$	−6.45910	−	3.72917i	−0.216146	−	0.124792i
$894$	−4.63752	+	4.79891i	−0.155102	+	0.160500i
$895$		0			0
$896$	29.6273	−	18.2498i	0.989778	−	0.609685i
$897$	−2.51414	−	8.77950i	−0.0839448	−	0.293139i
$898$	21.8652	+	37.8717i	0.729653	+	1.26380i
$899$	−9.46050	+	16.3861i	−0.315525	+	0.546506i
$900$		0			0
$901$	34.7774	−	20.0788i	1.15860	−	0.668921i
$902$	−38.6201			−1.28591
$903$	13.3960	+	2.94233i	0.445792	+	0.0979146i
$904$	−24.1889			−0.804510
$905$		0			0
$906$	−3.57140	+	14.3027i	−0.118652	+	0.475176i
$907$	−25.3858	+	43.9694i	−0.842920	+	1.45998i	0.0444946	+	0.999010i	$0.485832\pi$
$907$	−25.3858	+	43.9694i	−0.842920	+	1.45998i	−0.887415	+	0.460971i	$0.847501\pi$
$908$	1.63491	+	2.83174i	0.0542563	+	0.0939747i
$909$	34.1577	−	21.3107i	1.13294	−	0.706832i
$910$		0			0
$911$			16.1165i			0.533963i	0.963702	+	0.266981i	$0.0860262\pi$
$911$			16.1165i			0.533963i	−0.963702	+	0.266981i	$0.913974\pi$
$912$	−6.85396	−	6.62345i	−0.226957	−	0.219324i
$913$	16.9394	+	9.77999i	0.560614	+	0.323671i
$914$	−31.5787	−	18.2319i	−1.04453	−	0.603059i
$915$		0			0
$916$			2.93515i			0.0969802i
$917$	13.1131	+	21.2882i	0.433033	+	0.702997i
$918$	18.8610	−	20.9029i	0.622506	−	0.689900i
$919$	19.8721	+	34.4194i	0.655519	+	1.13539i	0.981763	+	0.190106i	$0.0608833\pi$
$919$	19.8721	+	34.4194i	0.655519	+	1.13539i	−0.326245	+	0.945285i	$0.605783\pi$
$920$		0			0
$921$	4.70392	−	18.8382i	0.155000	−	0.620740i
$922$	52.3010	−	30.1960i	1.72244	−	0.994452i
$923$	−36.1909			−1.19124
$924$	2.76132	−	0.876587i	0.0908407	−	0.0288376i
$925$		0			0
$926$	39.1451	−	22.6004i	1.28639	−	0.742696i
$927$	−17.3503	+	0.593686i	−0.569860	+	0.0194992i
$928$	−4.91942	+	8.52069i	−0.161488	+	0.279705i
$929$	−18.2593	−	31.6261i	−0.599069	−	1.03762i	−0.992959	−	0.118461i	$-0.962204\pi$
$929$	−18.2593	−	31.6261i	−0.599069	−	1.03762i	0.393889	−	0.919158i	$-0.371129\pi$
$930$		0			0
$931$	7.15440	−	4.69323i	0.234476	−	0.153814i
$932$		−	6.07063i		−	0.198850i
$933$	22.7737	−	23.5663i	0.745578	−	0.771526i
$934$	−5.48530	−	3.16694i	−0.179484	−	0.103625i
$935$		0			0
$936$	−23.8136	−	12.6834i	−0.778372	−	0.414569i
$937$			7.60980i			0.248601i	0.992245	+	0.124301i	$0.0396687\pi$
$937$			7.60980i			0.248601i	−0.992245	+	0.124301i	$0.960331\pi$
$938$	1.17779	+	41.3311i	0.0384561	+	1.34951i
$939$	−27.2755	+	7.81075i	−0.890102	+	0.254894i
$940$		0			0
$941$	11.0121	−	19.0735i	0.358985	−	0.621780i	−0.628807	−	0.777562i	$-0.716456\pi$
$941$	11.0121	−	19.0735i	0.358985	−	0.621780i	0.987791	+	0.155782i	$0.0497897\pi$
$942$	−35.4414	−	8.84974i	−1.15474	−	0.288340i
$943$	−15.5686	+	8.98853i	−0.506983	+	0.292707i
$944$	9.76632			0.317867
$945$		0			0
$946$	9.73904			0.316644
$947$	42.6589	−	24.6291i	1.38623	−	0.800339i	0.393341	−	0.919393i	$-0.371319\pi$
$947$	42.6589	−	24.6291i	1.38623	−	0.800339i	0.992888	+	0.119053i	$0.0379860\pi$
$948$	0.931111	+	0.232499i	0.0302411	+	0.00755123i
$949$	−11.9320	+	20.6669i	−0.387330	+	0.670875i
$950$		0			0
$951$	−16.8456	+	4.82399i	−0.546255	+	0.156429i
$952$	21.5160	+	11.6180i	0.697339	+	0.376542i
$953$		−	10.2538i		−	0.332154i	−0.986113	−	0.166077i	$-0.946890\pi$
$953$		−	10.2538i		−	0.332154i	0.986113	−	0.166077i	$-0.0531101\pi$
$954$	−45.0239	−	23.9802i	−1.45770	−	0.776388i
$955$		0			0
$956$	0.732331	+	0.422811i	0.0236853	+	0.0136747i
$957$	15.4018	−	15.9379i	0.497870	−	0.515198i
$958$		−	42.3131i		−	1.36708i
$959$	−24.9229	−	13.4576i	−0.804801	−	0.434569i
$960$		0			0
$961$	−10.4547	−	18.1081i	−0.337250	−	0.584134i
$962$	−20.5723	+	35.6323i	−0.663278	+	1.14883i
$963$	−11.6525	+	0.398721i	−0.375498	+	0.0128486i
$964$	6.64460	−	3.83626i	0.214008	−	0.123558i
$965$		0			0
$966$	7.08777	−	7.76541i	0.228045	−	0.249848i
$967$	−4.62632			−0.148772			−0.0743862	−	0.997230i	$-0.523700\pi$
$967$	−4.62632			−0.148772			−0.0743862	+	0.997230i	$0.523700\pi$
$968$	14.2859	−	8.24799i	0.459168	−	0.265101i
$969$	1.83477	−	7.34786i	0.0589412	−	0.236047i
$970$		0			0
$971$	12.6443	+	21.9006i	0.405775	+	0.702822i	0.994411	−	0.105575i	$-0.0336684\pi$
$971$	12.6443	+	21.9006i	0.405775	+	0.702822i	−0.588637	+	0.808398i	$0.700335\pi$
$972$	−4.51628	−	0.804521i	−0.144860	−	0.0258050i
$973$	0.309848	+	10.8732i	0.00993326	+	0.348579i
$974$			56.4119i			1.80755i
$975$		0			0
$976$	−13.2510	−	7.65046i	−0.424154	−	0.244885i
$977$	20.8797	+	12.0549i	0.668000	+	0.385670i	0.795318	−	0.606192i	$-0.207304\pi$
$977$	20.8797	+	12.0549i	0.668000	+	0.385670i	−0.127318	+	0.991862i	$0.540637\pi$
$978$	−7.67961	−	7.42133i	−0.245567	−	0.237308i
$979$		−	3.82381i		−	0.122210i
$980$		0			0
$981$	13.2549	−	8.26964i	0.423196	−	0.264029i
$982$	−4.47267	−	7.74688i	−0.142728	−	0.247213i
$983$	24.0441	−	41.6456i	0.766888	−	1.32829i	−0.172354	−	0.985035i	$-0.555137\pi$
$983$	24.0441	−	41.6456i	0.766888	−	1.32829i	0.939243	−	0.343254i	$-0.111529\pi$
$984$	−12.8669	+	51.5291i	−0.410181	+	1.64269i
$985$		0			0
$986$	−32.2739			−1.02781
$987$	−8.46033	−	26.6507i	−0.269295	−	0.848302i
$988$	1.25214			0.0398360
$989$	3.92601	−	2.26668i	0.124840	−	0.0720764i
$990$		0			0
$991$	−14.8587	+	25.7361i	−0.472003	+	0.817534i	−0.999487	−	0.0320314i	$-0.989802\pi$
$991$	−14.8587	+	25.7361i	−0.472003	+	0.817534i	0.527483	+	0.849565i	$0.323136\pi$
$992$	2.62352	+	4.54406i	0.0832967	+	0.144274i
$993$	9.19119	+	32.0960i	0.291674	+	1.01854i
$994$	−21.8519	−	35.4749i	−0.693099	−	1.12520i
$995$		0			0
$996$	−3.22496	+	3.33720i	−0.102187	+	0.105743i
$997$	23.1647	+	13.3742i	0.733634	+	0.423564i	0.819750	−	0.572721i	$-0.194112\pi$
$997$	23.1647	+	13.3742i	0.733634	+	0.423564i	−0.0861161	+	0.996285i	$0.527446\pi$
$998$	−24.5826	−	14.1928i	−0.778149	−	0.449265i
$999$	8.47222	−	39.6532i	0.268049	−	1.25457i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	525.2.t.j.101.9		24
3.2	odd	2	inner	525.2.t.j.101.3		24
5.2	odd	4		105.2.p.a.59.9	yes	24
5.3	odd	4		105.2.p.a.59.4	yes	24
5.4	even	2	inner	525.2.t.j.101.4		24
7.5	odd	6	inner	525.2.t.j.26.3		24
15.2	even	4		105.2.p.a.59.3	✓	24
15.8	even	4		105.2.p.a.59.10	yes	24
15.14	odd	2	inner	525.2.t.j.101.10		24
21.5	even	6	inner	525.2.t.j.26.9		24
35.2	odd	12		735.2.p.f.509.9		24
35.3	even	12		735.2.g.b.734.19		24
35.12	even	12		105.2.p.a.89.10	yes	24
35.13	even	4		735.2.p.f.374.3		24
35.17	even	12		735.2.g.b.734.6		24
35.18	odd	12		735.2.g.b.734.18		24
35.19	odd	6	inner	525.2.t.j.26.10		24
35.23	odd	12		735.2.p.f.509.4		24
35.27	even	4		735.2.p.f.374.10		24
35.32	odd	12		735.2.g.b.734.7		24
35.33	even	12		105.2.p.a.89.3	yes	24
105.2	even	12		735.2.p.f.509.3		24
105.17	odd	12		735.2.g.b.734.17		24
105.23	even	12		735.2.p.f.509.10		24
105.32	even	12		735.2.g.b.734.20		24
105.38	odd	12		735.2.g.b.734.8		24
105.47	odd	12		105.2.p.a.89.4	yes	24
105.53	even	12		735.2.g.b.734.5		24
105.62	odd	4		735.2.p.f.374.4		24
105.68	odd	12		105.2.p.a.89.9	yes	24
105.83	odd	4		735.2.p.f.374.9		24
105.89	even	6	inner	525.2.t.j.26.4		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
105.2.p.a.59.3	✓	24	15.2	even	4
105.2.p.a.59.4	yes	24	5.3	odd	4
105.2.p.a.59.9	yes	24	5.2	odd	4
105.2.p.a.59.10	yes	24	15.8	even	4
105.2.p.a.89.3	yes	24	35.33	even	12
105.2.p.a.89.4	yes	24	105.47	odd	12
105.2.p.a.89.9	yes	24	105.68	odd	12
105.2.p.a.89.10	yes	24	35.12	even	12
525.2.t.j.26.3		24	7.5	odd	6	inner
525.2.t.j.26.4		24	105.89	even	6	inner
525.2.t.j.26.9		24	21.5	even	6	inner
525.2.t.j.26.10		24	35.19	odd	6	inner
525.2.t.j.101.3		24	3.2	odd	2	inner
525.2.t.j.101.4		24	5.4	even	2	inner
525.2.t.j.101.9		24	1.1	even	1	trivial
525.2.t.j.101.10		24	15.14	odd	2	inner
735.2.g.b.734.5		24	105.53	even	12
735.2.g.b.734.6		24	35.17	even	12
735.2.g.b.734.7		24	35.32	odd	12
735.2.g.b.734.8		24	105.38	odd	12
735.2.g.b.734.17		24	105.17	odd	12
735.2.g.b.734.18		24	35.18	odd	12
735.2.g.b.734.19		24	35.3	even	12
735.2.g.b.734.20		24	105.32	even	12
735.2.p.f.374.3		24	35.13	even	4
735.2.p.f.374.4		24	105.62	odd	4
735.2.p.f.374.9		24	105.83	odd	4
735.2.p.f.374.10		24	35.27	even	4
735.2.p.f.509.3		24	105.2	even	12
735.2.p.f.509.4		24	35.23	odd	12
735.2.p.f.509.9		24	35.2	odd	12
735.2.p.f.509.10		24	105.23	even	12

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 525 = 3 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	525.t (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.31176 - 0.757344i) q^{2} +(-1.68045 - 0.419611i) q^{3} +(0.147140 - 0.254854i) q^{4} +(-2.52214 + 0.722254i) q^{6} +(-2.64468 + 0.0753638i) q^{7} +2.58363i q^{8} +(2.64785 + 1.41027i) q^{9} +(1.86048 + 1.07415i) q^{11} +(-0.354202 + 0.366529i) q^{12} +3.48097i q^{13} +(-3.41210 + 2.10179i) q^{14} +(2.25098 + 3.89881i) q^{16} +(-1.78859 + 3.09793i) q^{17} +(4.54141 - 0.155396i) q^{18} +(1.05858 - 0.611171i) q^{19} +(4.47588 + 0.983091i) q^{21} +3.25401 q^{22} +(1.31176 - 0.757344i) q^{23} +(1.08412 - 4.34168i) q^{24} +(2.63629 + 4.56619i) q^{26} +(-3.85783 - 3.48097i) q^{27} +(-0.369932 + 0.685096i) q^{28} +5.95645i q^{29} +(2.75098 + 1.58828i) q^{31} +(1.43050 + 0.825899i) q^{32} +(-2.67573 - 2.58574i) q^{33} +5.41832i q^{34} +(0.749020 - 0.467309i) q^{36} +(3.90175 + 6.75803i) q^{37} +(0.925734 - 1.60342i) q^{38} +(1.46065 - 5.84961i) q^{39} -11.8685 q^{41} +(6.61582 - 2.10021i) q^{42} +2.99294 q^{43} +(0.547504 - 0.316101i) q^{44} +(1.14714 - 1.98691i) q^{46} +(-3.05084 - 5.28420i) q^{47} +(-2.14668 - 7.49631i) q^{48} +(6.98864 - 0.398626i) q^{49} +(4.30557 - 4.45542i) q^{51} +(0.887140 + 0.512191i) q^{52} +(-9.72202 - 5.61301i) q^{53} +(-7.69683 - 1.64449i) q^{54} +(-0.194713 - 6.83288i) q^{56} +(-2.03535 + 0.582853i) q^{57} +(4.51108 + 7.81342i) q^{58} +(1.08467 - 1.87871i) q^{59} +(-2.94338 + 1.69936i) q^{61} +4.81149 q^{62} +(-7.10900 - 3.53017i) q^{63} -6.50196 q^{64} +(-5.46821 - 1.36542i) q^{66} +(5.15882 - 8.93534i) q^{67} +(0.526347 + 0.911660i) q^{68} +(-2.52214 + 0.722254i) q^{69} +10.3968i q^{71} +(-3.64363 + 6.84108i) q^{72} +(5.93710 + 3.42779i) q^{73} +(10.2363 + 5.90993i) q^{74} -0.359711i q^{76} +(-5.00133 - 2.70057i) q^{77} +(-2.51414 - 8.77950i) q^{78} +(-0.941421 - 1.63059i) q^{79} +(5.02225 + 7.46840i) q^{81} +(-15.5686 + 8.98853i) q^{82} +9.10486 q^{83} +(0.909127 - 0.996046i) q^{84} +(3.92601 - 2.26668i) q^{86} +(2.49939 - 10.0095i) q^{87} +(-2.77521 + 4.80681i) q^{88} +(-0.889962 - 1.54146i) q^{89} +(-0.262339 - 9.20605i) q^{91} -0.445743i q^{92} +(-3.95644 - 3.82337i) q^{93} +(-8.00392 - 4.62107i) q^{94} +(-2.05733 - 1.98814i) q^{96} +1.32584i q^{97} +(8.86551 - 5.81571i) q^{98} +(3.41144 + 5.46799i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 12 q^{4} + 6 q^{9} - 12 q^{16} - 6 q^{21} - 18 q^{24} + 84 q^{36} + 12 q^{39} + 36 q^{46} + 12 q^{49} - 12 q^{51} + 36 q^{54} + 36 q^{61} - 24 q^{64} - 72 q^{66} - 48 q^{79} - 6 q^{81} - 48 q^{84}+ \cdots + 48 q^{99}+O(q^{100}) \) 24 * q + 12 * q^4 + 6 * q^9 - 12 * q^16 - 6 * q^21 - 18 * q^24 + 84 * q^36 + 12 * q^39 + 36 * q^46 + 12 * q^49 - 12 * q^51 + 36 * q^54 + 36 * q^61 - 24 * q^64 - 72 * q^66 - 48 * q^79 - 6 * q^81 - 48 * q^84 - 96 * q^91 + 72 * q^94 - 90 * q^96 + 48 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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