LMFDB - Embedded newform 525.2.t.j.101.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [525,2,Mod(26,525)]

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

lf = mfeigenbasis(mf)

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")

//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);

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: f = N[0] # Warning: the index may be different

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			101.3
Character	$\chi$	$=$	525.101
Dual form			525.2.t.j.26.3

$q$-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} +(-1.20362 - 1.24551i) q^{3} +(0.147140 - 0.254854i) q^{4} +(2.52214 + 0.722254i) q^{6} +(-2.64468 + 0.0753638i) q^{7} -2.58363i q^{8} +(-0.102593 + 2.99825i) q^{9} +(-1.86048 - 1.07415i) q^{11} +(-0.494525 + 0.123483i) q^{12} +3.48097i q^{13} +(3.41210 - 2.10179i) q^{14} +(2.25098 + 3.89881i) q^{16} +(1.78859 - 3.09793i) q^{17} +(-2.13613 - 4.01067i) q^{18} +(1.05858 - 0.611171i) q^{19} +(3.27706 + 3.20326i) q^{21} +3.25401 q^{22} +(-1.31176 + 0.757344i) q^{23} +(-3.21794 + 3.10972i) 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} +(0.901451 + 3.61012i) q^{33} +5.41832i q^{34} +(0.749020 + 0.467309i) q^{36} +(3.90175 + 6.75803i) q^{37} +(-0.925734 + 1.60342i) q^{38} +(4.33559 - 4.18977i) q^{39} +11.8685 q^{41} +(-6.72468 - 1.72005i) 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} +(-6.01129 + 1.50103i) q^{51} +(0.887140 + 0.512191i) q^{52} +(9.72202 + 5.61301i) q^{53} +(-2.42425 + 7.48790i) 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} +(0.0453652 - 7.93712i) q^{63} -6.50196 q^{64} +(-3.91659 - 4.05290i) q^{66} +(5.15882 - 8.93534i) q^{67} +(-0.526347 - 0.911660i) q^{68} +(2.52214 + 0.722254i) q^{69} -10.3968i q^{71} +(7.74637 + 0.265062i) 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} +(-8.97895 - 0.615196i) q^{81} +(-15.5686 + 8.98853i) q^{82} -9.10486 q^{83} +(1.29855 - 0.363843i) q^{84} +(-3.92601 + 2.26668i) q^{86} +(-7.41882 + 7.16930i) q^{87} +(-2.77521 + 4.80681i) q^{88} +(0.889962 + 1.54146i) q^{89} +(-0.262339 - 9.20605i) q^{91} +0.445743i q^{92} +(-1.33292 - 5.33806i) q^{93} +(-8.00392 - 4.62107i) q^{94} +(0.693113 + 2.77577i) 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	−0.886037	−	0.463615i	$-0.846552\pi$
$2$	−1.31176	+	0.757344i	−0.927553	+	0.535523i	−0.0415164	+	0.999138i	$0.513219\pi$
$3$	−1.20362	−	1.24551i	−0.694911	−	0.719096i
$3$	−1.20362	−	1.24551i	−0.694911	−	0.719096i
$4$	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
$9$	−0.102593	+	2.99825i	−0.0341975	+	0.999415i
$10$		0			0
$11$	−1.86048	−	1.07415i	−0.560957	−	0.323869i	0.192573	−	0.981283i	$-0.438317\pi$
$11$	−1.86048	−	1.07415i	−0.560957	−	0.323869i	−0.753529	+	0.657414i	$0.771650\pi$
$12$	−0.494525	+	0.123483i	−0.142757	+	0.0356466i
$13$			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	−0.563399	−	0.826185i	$-0.690507\pi$
$17$	1.78859	−	3.09793i	0.433797	−	0.751359i	0.997197	+	0.0748259i	$0.0238401\pi$
$18$	−2.13613	−	4.01067i	−0.503490	−	0.945324i
$19$	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
$21$	3.27706	+	3.20326i	0.715112	+	0.699010i
$22$	3.25401			0.693757
$23$	−1.31176	+	0.757344i	−0.273521	+	0.157917i	−0.630486	−	0.776200i	$-0.717145\pi$
$23$	−1.31176	+	0.757344i	−0.273521	+	0.157917i	0.356966	+	0.934117i	$0.383811\pi$
$24$	−3.21794	+	3.10972i	−0.656860	+	0.634768i
$25$		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	$-0.813467\pi$
$29$		−	5.95645i		−	1.10608i	0.833153	−	0.553042i	$-0.186533\pi$
$30$		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
$33$	0.901451	+	3.61012i	0.156923	+	0.628442i
$34$			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
$39$	4.33559	−	4.18977i	0.694249	−	0.670900i
$40$		0			0
$41$	11.8685			1.85355			0.926773	−	0.375622i	$-0.122571\pi$
$41$	11.8685			1.85355			0.926773	+	0.375622i	$0.122571\pi$
$42$	−6.72468	−	1.72005i	−1.03764	−	0.265409i
$43$	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	0.998053	−	0.0623727i	$-0.0198667\pi$
$47$	3.05084	+	5.28420i	0.445010	+	0.770780i	−0.553043	+	0.833153i	$0.686533\pi$
$48$	2.14668	−	7.49631i	0.309847	−	1.08200i
$49$	6.98864	−	0.398626i	0.998377	−	0.0569466i
$50$		0			0
$51$	−6.01129	+	1.50103i	−0.841749	+	0.210186i
$52$	0.887140	+	0.512191i	0.123024	+	0.0710281i
$53$	9.72202	+	5.61301i	1.33542	+	0.771006i	0.986125	−	0.166006i	$-0.0530871\pi$
$53$	9.72202	+	5.61301i	1.33542	+	0.771006i	0.349297	+	0.937012i	$0.386420\pi$
$54$	−2.42425	+	7.48790i	−0.329898	+	1.01897i
$55$		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	−0.927954	−	0.372696i	$-0.878433\pi$
$59$	−1.08467	+	1.87871i	−0.141213	+	0.244587i	0.786741	+	0.617283i	$0.211767\pi$
$60$		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
$63$	0.0453652	−	7.93712i	0.00571548	−	0.999984i
$64$	−6.50196			−0.812745
$65$		0			0
$66$	−3.91659	−	4.05290i	−0.482099	−	0.498877i
$67$	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	$-0.788374\pi$
$71$		−	10.3968i		−	1.23387i	0.787013	−	0.616936i	$-0.211626\pi$
$72$	7.74637	+	0.265062i	0.912918	+	0.0312378i
$73$	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
$81$	−8.97895	−	0.615196i	−0.997661	−	0.0683551i
$82$	−15.5686	+	8.98853i	−1.71926	+	0.992617i
$83$	−9.10486			−0.999388			−0.499694	−	0.866202i	$-0.666554\pi$
$83$	−9.10486			−0.999388			−0.499694	+	0.866202i	$0.666554\pi$
$84$	1.29855	−	0.363843i	0.141684	−	0.0396985i
$85$		0			0
$86$	−3.92601	+	2.26668i	−0.423353	+	0.244423i
$87$	−7.41882	+	7.16930i	−0.795380	+	0.768630i
$88$	−2.77521	+	4.80681i	−0.295839	+	0.512407i
$89$	0.889962	+	1.54146i	0.0943358	+	0.163394i	0.909331	−	0.416073i	$-0.136594\pi$
$89$	0.889962	+	1.54146i	0.0943358	+	0.163394i	−0.814995	+	0.579467i	$0.803261\pi$
$90$		0			0
$91$	−0.262339	−	9.20605i	−0.0275006	−	0.965056i
$92$			0.445743i			0.0464719i
$93$	−1.33292	−	5.33806i	−0.138217	−	0.553531i
$94$	−8.00392	−	4.62107i	−0.825541	−	0.476626i
$95$		0			0
$96$	0.693113	+	2.77577i	0.0707406	+	0.283301i
$97$			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	$0.399377\pi$
$101$	−6.71005	+	11.6221i	−0.667675	+	1.15645i	−0.978553	+	0.205997i	$0.933956\pi$
$102$	6.74857	−	6.52160i	0.668208	−	0.645735i
$103$	−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	−0.328408	−	0.944536i	$-0.606512\pi$
$107$	3.36576	−	1.94323i	0.325381	−	0.187859i	0.653788	+	0.756677i	$0.273179\pi$
$108$	−0.319499	−	1.49537i	−0.0307438	−	0.143893i
$109$	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	$-0.854848\pi$
$113$		−	9.36235i		−	0.880736i	0.897817	−	0.440368i	$-0.145152\pi$
$114$	3.11131	−	0.776896i	0.291401	−	0.0727630i
$115$		0			0
$116$	−1.51803	−	0.876432i	−0.140945	−	0.0813747i
$117$	−10.4368	−	0.357122i	−0.964883	−	0.0330159i
$118$		−	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
$123$	−14.2852	−	14.7823i	−1.28805	−	1.33288i
$124$	0.809559	−	0.467399i	0.0727006	−	0.0419737i
$125$		0			0
$126$	5.95163	+	10.4459i	0.530213	+	0.930599i
$127$	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
$129$	−3.60236	−	3.72774i	−0.317170	−	0.328209i
$130$		0			0
$131$	4.72508	+	8.18408i	0.412832	+	0.715047i	0.995198	−	0.0978802i	$-0.0312062\pi$
$131$	4.72508	+	8.18408i	0.412832	+	0.715047i	−0.582366	+	0.812927i	$0.697873\pi$
$132$	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	0.0486038	−	0.998818i	$-0.484523\pi$
$137$	−9.27125	−	5.35276i	−0.792096	−	0.457317i	−0.840700	+	0.541501i	$0.817856\pi$
$138$	−3.85543	+	0.962706i	−0.328196	+	0.0819510i
$139$		−	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
$144$	−11.9205	+	6.34900i	−0.993377	+	0.529083i
$145$		0			0
$146$	−10.3841			−0.859390
$147$	−8.90817	−	8.22463i	−0.734733	−	0.678356i
$148$	2.29642			0.188764
$149$	−2.20294	+	1.27187i	−0.180472	+	0.104196i	−0.587514	−	0.809214i	$-0.699893\pi$
$149$	−2.20294	+	1.27187i	−0.180472	+	0.104196i	0.407042	+	0.913409i	$0.366560\pi$
$150$		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
$156$	−0.429842	−	1.72143i	−0.0344149	−	0.137824i
$157$	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
$159$	−4.71056	−	18.8648i	−0.373572	−	1.49608i
$160$		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	$-0.681803\pi$
$167$	−13.9722			−1.08120			−0.540602	+	0.841279i	$0.681803\pi$
$168$	8.27606	−	8.46671i	0.638512	−	0.653221i
$169$	0.882841			0.0679109
$170$		0			0
$171$	1.72384	+	3.23658i	0.131825	+	0.247508i
$172$	0.440382	−	0.762763i	0.0335788	−	0.0581602i
$173$	−5.00133	−	8.66256i	−0.380244	−	0.658602i	0.610853	−	0.791744i	$-0.290827\pi$
$173$	−5.00133	−	8.66256i	−0.380244	−	0.658602i	−0.991097	+	0.133142i	$0.957493\pi$
$174$	4.30206	−	15.0230i	0.326139	−	1.13889i
$175$		0			0
$176$		−	9.67157i		−	0.729022i
$177$	3.64549	−	0.910283i	0.274012	−	0.0684211i
$178$	−2.33483	−	1.34801i	−0.175003	−	0.101038i
$179$	14.0378	+	8.10475i	1.04924	+	0.605777i	0.922436	−	0.386151i	$-0.126196\pi$
$179$	14.0378	+	8.10475i	1.04924	+	0.605777i	0.126801	+	0.991928i	$0.459529\pi$
$180$		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
$186$	5.79122	+	5.99277i	0.424633	+	0.439411i
$187$	−6.65529	+	3.84243i	−0.486683	+	0.280987i
$188$	1.79560			0.130958
$189$	−9.94037	+	9.49679i	−0.723056	+	0.690790i
$190$		0			0
$191$	−11.0018	+	6.35188i	−0.796061	+	0.459606i	−0.842092	−	0.539334i	$-0.818676\pi$
$191$	−11.0018	+	6.35188i	−0.796061	+	0.459606i	0.0460309	+	0.998940i	$0.485343\pi$
$192$	7.82590	+	8.09826i	0.564785	+	0.584441i
$193$	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	$-0.974634\pi$
$197$		−	2.23465i		−	0.159212i	0.996826	−	0.0796062i	$-0.0253663\pi$
$198$	−0.333837	+	9.75631i	−0.0237248	+	0.693351i
$199$	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
$201$	−17.3383	+	4.32940i	−1.22295	+	0.305372i
$202$		−	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
$207$	−2.13613	−	4.01067i	−0.148471	−	0.278761i
$208$	−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
$213$	−12.9493	+	12.5138i	−0.887272	+	0.857431i
$214$	−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
$219$	−2.87667	−	11.5205i	−0.194388	−	0.778481i
$220$		0			0
$221$	10.7838	+	6.22604i	0.725398	+	0.418808i
$222$	4.95975	+	19.8627i	0.332877	+	1.33310i
$223$			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	−0.620630	−	0.784104i	$-0.713123\pi$
$227$	5.55561	−	9.62260i	0.368739	−	0.638675i	0.989369	+	0.145429i	$0.0464563\pi$
$228$	−0.448024	+	0.432956i	−0.0296711	+	0.0286732i
$229$	−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
$231$	−2.65612	−	9.47967i	−0.174760	−	0.623717i
$232$	−15.3893			−1.01036
$233$	−17.8650	+	10.3144i	−1.17037	+	0.675716i	−0.953768	−	0.300543i	$-0.902832\pi$
$233$	−17.8650	+	10.3144i	−1.17037	+	0.675716i	−0.216606	+	0.976259i	$0.569499\pi$
$234$	13.9610	−	7.43579i	0.912661	−	0.486093i
$235$		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	$-0.970375\pi$
$239$		−	2.87353i		−	0.185873i	0.995672	−	0.0929365i	$-0.0296254\pi$
$240$		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
$243$	10.0410	+	11.9238i	0.644132	+	0.764915i
$244$			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
$249$	10.9588	+	11.3402i	0.694486	+	0.718656i
$250$		0			0
$251$	−0.161120			−0.0101698			−0.00508489	−	0.999987i	$-0.501619\pi$
$251$	−0.161120			−0.0101698			−0.00508489	+	0.999987i	$0.501619\pi$
$252$	−2.01613	−	1.17943i	−0.127005	−	0.0742972i
$253$	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	0.994836	−	0.101493i	$-0.0323620\pi$
$257$	6.56514	+	11.3712i	0.409522	+	0.709314i	−0.585314	+	0.810807i	$0.699029\pi$
$258$	7.54861	+	2.16166i	0.469956	+	0.134579i
$259$	−10.8282	−	17.5788i	−0.672830	−	1.09229i
$260$		0			0
$261$	17.8589	+	0.611087i	1.10544	+	0.0378254i
$262$	−12.3963	−	7.15703i	−0.765848	−	0.442163i
$263$	15.3551	+	8.86526i	0.946835	+	0.546655i	0.892096	−	0.451846i	$-0.149234\pi$
$263$	15.3551	+	8.86526i	0.946835	+	0.546655i	0.0547384	+	0.998501i	$0.482568\pi$
$264$	9.32723	−	2.32902i	0.574051	−	0.143341i
$265$		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	−0.791020	−	0.611790i	$-0.790450\pi$
$269$	2.20294	−	3.81561i	0.134316	−	0.232642i	0.925336	+	0.379148i	$0.123783\pi$
$270$		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
$273$	−11.1505	+	11.4073i	−0.674857	+	0.690403i
$274$	16.2155			0.979615
$275$		0			0
$276$	0.555178	−	0.536506i	0.0334178	−	0.0322938i
$277$	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	$0.218394\pi$
$281$			21.2397i			1.26706i	−0.773719	+	0.633528i	$0.781606\pi$
$282$	3.87810	+	15.5310i	0.230938	+	0.924856i
$283$	−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
$291$	1.65134	−	1.59581i	0.0968035	−	0.0935477i
$292$	1.74717	−	1.00873i	0.102245	−	0.0590315i
$293$	−3.71937			−0.217288			−0.108644	−	0.994081i	$-0.534651\pi$
$293$	−3.71937			−0.217288			−0.108644	+	0.994081i	$0.534651\pi$
$294$	17.9142	+	4.04218i	1.04478	+	0.235745i
$295$		0			0
$296$	17.4603	−	10.0807i	1.01486	−	0.585928i
$297$	−10.9165	+	2.33240i	−0.633440	+	0.135340i
$298$	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
$303$	22.5519	−	5.63123i	1.29557	−	0.323505i
$304$	4.76568	+	2.75147i	0.273331	+	0.157808i
$305$		0			0
$306$	−16.2454	−	0.555880i	−0.928690	−	0.0317775i
$307$			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	$-0.653096\pi$
$311$	9.46050	−	16.3861i	0.536456	−	0.929168i	0.999091	−	0.0426199i	$-0.0135704\pi$
$312$	−10.8248	−	11.2016i	−0.612835	−	0.634164i
$313$	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	−0.725439	−	0.688286i	$-0.758363\pi$
$317$	−8.76134	+	5.05836i	−0.492086	+	0.284106i	0.233353	+	0.972392i	$0.425030\pi$
$318$	20.4663	+	21.1786i	1.14769	+	1.18763i
$319$	−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
$324$	−1.47795	+	2.19780i	−0.0821083	+	0.122100i
$325$		0			0
$326$	−5.33977	−	3.08292i	−0.295743	−	0.170747i
$327$	−8.75127	+	2.18520i	−0.483946	+	0.120842i
$328$		−	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
$333$	−20.6625	+	11.0051i	−1.13230	+	0.603075i
$334$	18.3282	−	10.5818i	1.00287	−	0.579009i
$335$		0			0
$336$	−5.11234	+	19.9871i	−0.278901	+	1.09039i
$337$	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
$339$	−11.6609	+	11.2687i	−0.633333	+	0.612033i
$340$		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	0.821901	−	0.569631i	$-0.192914\pi$
$347$	13.7760	+	7.95360i	0.739536	+	0.426971i	−0.0823644	+	0.996602i	$0.526247\pi$
$348$	0.735522	+	2.94561i	0.0394281	+	0.157901i
$349$		−	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	$-0.596836\pi$
$353$	12.7100	−	22.0143i	0.676484	−	1.17170i	0.976033	−	0.217624i	$-0.0698305\pi$
$354$	−4.09261	+	3.95496i	−0.217520	+	0.210204i
$355$		0			0
$356$	0.523797			0.0277612
$357$	15.7848	−	4.42276i	0.835421	−	0.234078i
$358$	−24.5523			−1.29763
$359$	20.9396	−	12.0895i	1.10515	−	0.638057i	0.167579	−	0.985859i	$-0.446405\pi$
$359$	20.9396	−	12.0895i	1.10515	−	0.638057i	0.937568	+	0.347801i	$0.113072\pi$
$360$		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
$366$	−8.65099	+	2.16016i	−0.452194	+	0.112913i
$367$	−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
$369$	−1.21762	+	35.5846i	−0.0633867	+	1.85246i
$370$		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
$378$	5.84703	−	19.9858i	0.300739	−	1.02796i
$379$	−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
$381$	−11.5280	−	11.9292i	−0.590598	−	0.611153i
$382$	9.62112	−	16.6643i	0.492259	−	0.852618i
$383$	−5.28833	−	9.15965i	−0.270221	−	0.468036i	0.698697	−	0.715417i	$-0.253763\pi$
$383$	−5.28833	−	9.15965i	−0.270221	−	0.468036i	−0.968918	+	0.247381i	$0.920430\pi$
$384$	−21.8997	−	6.27133i	−1.11757	−	0.320032i
$385$		0			0
$386$			31.5351i			1.60509i
$387$	−0.307054	+	8.97356i	−0.0156084	+	0.456152i
$388$	0.337895	+	0.195084i	0.0171540	+	0.00990388i
$389$	14.6659	+	8.46736i	0.743590	+	0.429312i	0.823373	−	0.567500i	$-0.192089\pi$
$389$	14.6659	+	8.46736i	0.743590	+	0.429312i	−0.0797828	+	0.996812i	$0.525423\pi$
$390$		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
$396$	−0.891580	−	1.67398i	−0.0448036	−	0.0841207i
$397$	−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
$399$	5.42677	+	1.38807i	0.271678	+	0.0694903i
$400$		0			0
$401$	24.2302	−	13.9893i	1.21000	−	0.698593i	0.247240	−	0.968954i	$-0.420476\pi$
$401$	24.2302	−	13.9893i	1.21000	−	0.698593i	0.962759	+	0.270361i	$0.0871430\pi$
$402$	19.4649	−	18.8102i	0.970819	−	0.938168i
$403$	−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
$408$	3.87810	+	15.5310i	0.191995	+	0.768898i
$409$	−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
$411$	4.49215	+	17.9901i	0.221582	+	0.887388i
$412$			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
$417$	−5.12074	+	4.94852i	−0.250764	+	0.242330i
$418$	3.44462	−	1.98876i	0.168482	−	0.0972732i
$419$	−8.39649			−0.410195			−0.205098	−	0.978742i	$-0.565751\pi$
$419$	−8.39649			−0.410195			−0.205098	+	0.978742i	$0.565751\pi$
$420$		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
$423$	−16.1563	+	8.60503i	−0.785548	+	0.418391i
$424$	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
$429$	−12.5667	+	3.13793i	−0.606727	+	0.151500i
$430$		0			0
$431$	10.6154	+	6.12880i	0.511326	+	0.295214i	0.733378	−	0.679821i	$-0.237942\pi$
$431$	10.6154	+	6.12880i	0.511326	+	0.295214i	−0.222053	+	0.975035i	$0.571276\pi$
$432$	22.2555	+	7.20535i	1.07077	+	0.346668i
$433$			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
$438$	12.4985	+	12.9334i	0.597200	+	0.617984i
$439$	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
$441$	0.478196	+	20.9946i	0.0227712	+	0.999741i
$442$	−18.8610			−0.897127
$443$	0.218429	−	0.126110i	0.0103779	−	0.00599167i	−0.494802	−	0.869006i	$-0.664759\pi$
$443$	0.218429	−	0.126110i	0.0103779	−	0.00599167i	0.505180	+	0.863014i	$0.331426\pi$
$444$	−2.76402	−	2.86021i	−0.131174	−	0.135740i
$445$		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	$-0.761436\pi$
$449$		−	28.8710i		−	1.36250i	0.732049	−	0.681252i	$-0.238564\pi$
$450$		0			0
$451$	−22.0811	−	12.7485i	−1.03976	−	0.600305i
$452$	−2.38603	−	1.37758i	−0.112230	−	0.0647958i
$453$	−9.44267	+	2.35785i	−0.443655	+	0.110781i
$454$			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
$459$	−3.88373	−	18.1773i	−0.181277	−	0.848445i
$460$		0			0
$461$	−39.8709			−1.85697			−0.928486	−	0.371367i	$-0.878889\pi$
$461$	−39.8709			−1.85697			−0.928486	+	0.371367i	$0.878889\pi$
$462$	10.6636	+	10.4234i	0.496114	+	0.484943i
$463$	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	0.910338	−	0.413865i	$-0.135821\pi$
$467$	2.09082	+	3.62140i	0.0967515	+	0.167579i	−0.813587	+	0.581444i	$0.802488\pi$
$468$	−1.62669	+	2.60732i	−0.0751937	+	0.120523i
$469$	−12.9700	+	24.0199i	−0.598900	+	1.10914i
$470$		0			0
$471$	−5.84262	−	23.3984i	−0.269214	−	1.07814i
$472$	4.85390	+	2.80240i	0.223419	+	0.128991i
$473$	−5.56831	−	3.21487i	−0.256031	−	0.147820i
$474$	−1.19670	−	4.79252i	−0.0549661	−	0.220128i
$475$		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	$0.386986\pi$
$479$	−13.9676	+	24.1926i	−0.638196	+	1.10539i	−0.985828	+	0.167757i	$0.946348\pi$
$480$		0			0
$481$	−23.5245	+	13.5819i	−1.07262	+	0.619280i
$482$	−39.4912			−1.79878
$483$	−6.72468	−	1.72005i	−0.305984	−	0.0782650i
$484$	−1.87892			−0.0854055
$485$		0			0
$486$	−22.2018	−	8.03669i	−1.00710	−	0.364552i
$487$	−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	$0.0425448\pi$
$491$			5.90572i			0.266522i	−0.991081	+	0.133261i	$0.957455\pi$
$492$	−5.86926	+	1.46556i	−0.264607	+	0.0660725i
$493$	−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
$501$	16.8173	+	17.4025i	0.751340	+	0.777489i
$502$	0.211350	−	0.122023i	0.00943301	−	0.00544615i
$503$	32.0398			1.42858			0.714291	−	0.699849i	$-0.246749\pi$
$503$	32.0398			1.42858			0.714291	+	0.699849i	$0.246749\pi$
$504$	−20.5066	−	0.117207i	−0.913437	−	0.00522082i
$505$		0			0
$506$	−4.26847	+	2.46440i	−0.189757	+	0.109556i
$507$	−1.06261	−	1.09959i	−0.0471920	−	0.0488344i
$508$	1.40928	−	2.44094i	0.0625265	−	0.108299i
$509$	9.57465	+	16.5838i	0.424389	+	0.735063i	0.996363	−	0.0852085i	$-0.0271556\pi$
$509$	9.57465	+	16.5838i	0.424389	+	0.735063i	−0.571974	+	0.820272i	$0.693822\pi$
$510$		0			0
$511$	−15.9600	−	8.61794i	−0.706031	−	0.381235i
$512$			15.8265i			0.699439i
$513$	1.95635	−	6.04268i	0.0863749	−	0.266791i
$514$	−17.2238	−	9.94415i	−0.759708	−	0.438617i
$515$		0			0
$516$	−1.48008	+	0.369578i	−0.0651570	+	0.0162698i
$517$		−	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	−0.905408	−	0.424543i	$-0.860435\pi$
$521$	−1.94104	+	3.36199i	−0.0850387	+	0.147291i	0.820369	+	0.571834i	$0.193768\pi$
$522$	−23.8893	+	12.7237i	−1.04561	+	0.556902i
$523$	−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
$528$	−12.0460	+	11.6409i	−0.524236	+	0.506605i
$529$	−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
$534$	1.13128	+	4.53055i	0.0489555	+	0.196056i
$535$		0			0
$536$	−23.0856	−	13.3285i	−0.997148	−	0.575704i
$537$	−6.80168	−	27.2393i	−0.293514	−	1.17546i
$538$			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
$543$	24.1782	−	23.3650i	1.03759	−	1.00269i
$544$	−5.11716	+	2.95439i	−0.219396	+	0.126669i
$545$		0			0
$546$	5.98744	−	23.4084i	0.256239	−	1.00179i
$547$	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
$549$	−4.79313	−	8.99932i	−0.204566	−	0.384082i
$550$		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	0.662494	−	0.749068i	$-0.269498\pi$
$557$	8.14298	+	4.70135i	0.345029	+	0.199203i	−0.317465	+	0.948270i	$0.602831\pi$
$558$	0.493624	−	14.4260i	0.0208968	−	0.610703i
$559$			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	−0.995051	−	0.0993632i	$-0.968319\pi$
$563$	−9.76331	+	16.9106i	−0.411475	+	0.712695i	0.583577	+	0.812058i	$0.301653\pi$
$564$	−2.16122	−	2.23644i	−0.0910040	−	0.0941712i
$565$		0			0
$566$	9.92744			0.417281
$567$	23.7928	+	0.950307i	0.999203	+	0.0399091i
$568$	−26.8615			−1.12708
$569$	−11.1702	+	6.44911i	−0.468279	+	0.270361i	−0.715519	−	0.698593i	$-0.753810\pi$
$569$	−11.1702	+	6.44911i	−0.468279	+	0.270361i	0.247240	+	0.968954i	$0.420476\pi$
$570$		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
$576$	0.667053	−	19.4945i	0.0277939	−	0.812270i
$577$	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
$579$	−34.9863	+	8.73611i	−1.45398	+	0.363060i
$580$		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	$-0.348573\pi$
$587$	22.1920			0.915961			0.457981	+	0.888962i	$0.348573\pi$
$588$	−3.40683	+	1.06011i	−0.140495	+	0.0437182i
$589$	3.88284			0.159990
$590$		0			0
$591$	−2.78328	+	2.68967i	−0.114489	+	0.110638i
$592$	−17.5655	+	30.4244i	−0.721938	+	1.25043i
$593$	3.15687	+	5.46787i	0.129637	+	0.224538i	0.923536	−	0.383512i	$-0.125285\pi$
$593$	3.15687	+	5.46787i	0.129637	+	0.224538i	−0.793899	+	0.608050i	$0.791952\pi$
$594$	12.5534	−	11.3271i	0.515072	−	0.464757i
$595$		0			0
$596$			0.748572i			0.0306627i
$597$	−10.4575	−	41.8803i	−0.427999	−	1.71405i
$598$	6.91636	+	3.99316i	0.282831	+	0.163293i
$599$	−17.8962	−	10.3324i	−0.731219	−	0.422170i	0.0876487	−	0.996151i	$-0.472065\pi$
$599$	−17.8962	−	10.3324i	−0.731219	−	0.422170i	−0.818868	+	0.573982i	$0.805398\pi$
$600$		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
$606$	−25.3178	+	24.4663i	−1.02847	+	0.993877i
$607$	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
$609$	19.0801	−	19.5196i	0.773163	−	0.790974i
$610$		0			0
$611$	−18.3942	+	10.6199i	−0.744148	+	0.429634i
$612$	2.78738	−	1.48459i	0.112673	−	0.0600110i
$613$	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	$-0.792815\pi$
$617$		−	30.1002i		−	1.21179i	0.795545	−	0.605895i	$-0.207185\pi$
$618$	−14.7296	+	3.67800i	−0.592511	+	0.147951i
$619$	−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
$621$	−2.42425	+	7.48790i	−0.0972817	+	0.300479i
$622$			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
$627$	3.16066	+	3.27066i	0.126225	+	0.130618i
$628$	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
$633$	7.96219	+	8.23930i	0.316469	+	0.327483i
$634$	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
$639$	31.1721	+	1.06663i	1.23315	+	0.0421954i
$640$		0			0
$641$	1.13893	+	0.657564i	0.0449852	+	0.0259722i	0.522324	−	0.852747i	$-0.325065\pi$
$641$	1.13893	+	0.657564i	0.0449852	+	0.0259722i	−0.477339	+	0.878719i	$0.658399\pi$
$642$	9.89243	−	2.47015i	0.390423	−	0.0974891i
$643$			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	−0.798261	−	0.602311i	$-0.794247\pi$
$647$	3.11558	−	5.39634i	0.122486	−	0.212152i	0.920747	+	0.390159i	$0.127580\pi$
$648$	−1.58944	+	23.1983i	−0.0624391	+	0.911316i
$649$	4.03604	−	2.33021i	0.158428	−	0.0914687i
$650$		0			0
$651$	3.92744	+	14.0170i	0.153928	+	0.549369i
$652$	1.19793			0.0469144
$653$	−16.3348	+	9.43091i	−0.639230	+	0.369060i	−0.784318	−	0.620359i	$-0.786987\pi$
$653$	−16.3348	+	9.43091i	−0.639230	+	0.369060i	0.145088	+	0.989419i	$0.453654\pi$
$654$	9.82460	−	9.49418i	0.384172	−	0.371252i
$655$		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	$0.300850\pi$
$659$			41.6170i			1.62117i	−0.585622	+	0.810584i	$0.699150\pi$
$660$		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
$663$	−5.22503	−	20.9251i	−0.202923	−	0.812665i
$664$			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
$669$	5.36848	−	5.18793i	0.207558	−	0.200577i
$670$		0			0
$671$	7.30148			0.281871
$672$	−2.04225	−	7.28879i	−0.0787816	−	0.281171i
$673$	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	0.769773	−	0.638317i	$-0.220369\pi$
$677$	−4.36895	−	7.56724i	−0.167912	−	0.290832i	−0.937686	+	0.347485i	$0.887036\pi$
$678$	6.76199	−	23.6132i	0.259693	−	0.906858i
$679$	−0.0999201	−	3.50641i	−0.00383458	−	0.134564i
$680$		0			0
$681$	−18.6719	+	4.66239i	−0.715509	+	0.178663i
$682$	8.95171	+	5.16827i	0.342779	+	0.197903i
$683$	−18.9393	−	10.9346i	−0.724691	−	0.418401i	0.0917858	−	0.995779i	$-0.470743\pi$
$683$	−18.9393	−	10.9346i	−0.724691	−	0.418401i	−0.816477	+	0.577378i	$0.804076\pi$
$684$	1.07850	+	0.0369037i	0.0412376	+	0.00141105i
$685$		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
$693$	−8.61007	+	14.7182i	−0.327069	+	0.559097i
$694$	−24.0944			−0.914612
$695$		0			0
$696$	18.5229	+	19.1675i	0.702107	+	0.726542i
$697$	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	$-0.766104\pi$
$701$		−	35.5019i		−	1.34089i	0.741960	−	0.670444i	$-0.233896\pi$
$702$	−26.0652	−	8.43873i	−0.983766	−	0.318499i
$703$	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
$711$	4.98549	−	2.65532i	0.186970	−	0.0995824i
$712$	3.98257	−	2.29934i	0.149253	−	0.0861712i
$713$	−4.81149			−0.180192
$714$	−17.3563	+	17.7561i	−0.649543	+	0.664506i
$715$		0			0
$716$	4.13106	−	2.38507i	0.154385	−	0.0891342i
$717$	−3.57901	+	3.45864i	−0.133660	+	0.129165i
$718$	−18.3118	+	31.7169i	−0.683389	+	1.18366i
$719$	−15.2703	−	26.4489i	−0.569484	−	0.986376i	−0.996617	−	0.0821868i	$-0.973810\pi$
$719$	−15.2703	−	26.4489i	−0.569484	−	0.986376i	0.427133	−	0.904189i	$-0.359524\pi$
$720$		0			0
$721$	13.0359	−	8.02984i	0.485481	−	0.299047i
$722$		−	26.5159i		−	0.986821i
$723$	−10.9402	−	43.8131i	−0.406869	−	1.62943i
$724$	4.94730	+	2.85632i	0.183865	+	0.106154i
$725$		0			0
$726$	−4.05805	−	16.2516i	−0.150608	−	0.603155i
$727$			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
$732$	1.24573	−	1.20383i	0.0460436	−	0.0444950i
$733$	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
$738$	−25.3526	−	47.6006i	−0.933242	−	1.75220i
$739$	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	$-0.736312\pi$
$743$		−	40.1701i		−	1.47370i	0.676056	−	0.736850i	$-0.263688\pi$
$744$	−13.7916	+	3.44377i	−0.505624	+	0.126255i
$745$		0			0
$746$	20.4158	+	11.7870i	0.747474	+	0.431554i
$747$	0.934092	−	27.2986i	0.0341766	−	0.998804i
$748$			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
$753$	0.193927	+	0.200676i	0.00706709	+	0.00731305i
$754$	−27.1983	+	15.7029i	−0.990503	+	0.571867i
$755$		0			0
$756$	0.957668	+	3.93071i	0.0348301	+	0.142958i
$757$	−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
$759$	−3.91659	−	4.05290i	−0.142163	−	0.147111i
$760$		0			0
$761$	−9.91711	−	17.1769i	−0.359495	−	0.622663i	0.628382	−	0.777905i	$-0.283718\pi$
$761$	−9.91711	−	17.1769i	−0.359495	−	0.622663i	−0.987876	+	0.155242i	$0.950384\pi$
$762$	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
$768$	11.6242	−	2.90258i	0.419454	−	0.104738i
$769$		−	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	−0.708015	−	0.706197i	$-0.750409\pi$
$773$	7.16138	−	12.4039i	0.257577	−	0.446136i	0.965592	+	0.260061i	$0.0837426\pi$
$774$	−6.39330	−	12.0037i	−0.229802	−	0.431464i
$775$		0			0
$776$	3.42548			0.122967
$777$	−8.86150	+	34.6448i	−0.317904	+	1.24287i
$778$	−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
$786$	6.00634	+	24.0541i	0.214239	+	0.857982i
$787$	−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
$789$	−7.43992	−	29.7953i	−0.264868	−	1.06074i
$790$		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	$-0.731106\pi$
$797$	−37.4862			−1.32783			−0.663914	+	0.747809i	$0.731106\pi$
$798$	−8.16985	+	2.28912i	−0.289210	+	0.0810340i
$799$	21.8268			0.772177
$800$		0			0
$801$	−4.71298	+	2.51018i	−0.166525	+	0.0886929i
$802$	−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
$807$	−7.40389	+	1.84876i	−0.260629	+	0.0650794i
$808$	30.0274	+	17.3363i	1.05636	+	0.609889i
$809$	−22.1518	−	12.7893i	−0.778814	−	0.449649i	0.0571956	−	0.998363i	$-0.481784\pi$
$809$	−22.1518	−	12.7893i	−0.778814	−	0.449649i	−0.836010	+	0.548714i	$0.815117\pi$
$810$		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
$816$	−19.3835	−	20.0581i	−0.678559	−	0.702175i
$817$	3.16826	−	1.82920i	0.110844	−	0.0639955i
$818$	3.96956			0.138792
$819$	27.6289	+	0.157915i	0.965432	+	0.00551800i
$820$		0			0
$821$	0.00729231	−	0.00421022i	0.000254504	−	0.000146938i	−0.499873	−	0.866099i	$-0.666620\pi$
$821$	0.00729231	−	0.00421022i	0.000254504	−	0.000146938i	0.500127	+	0.865952i	$0.333287\pi$
$822$	−19.5173	−	20.1966i	−0.680745	−	0.704437i
$823$	−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	$0.232097\pi$
$827$			38.3189i			1.33248i	−0.745738	+	0.666239i	$0.767903\pi$
$828$	−1.33645	−	0.0457300i	−0.0464447	−	0.00158923i
$829$	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
$831$	−21.5632	+	5.38436i	−0.748020	+	0.186781i
$832$		−	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
$837$	16.1416	−	3.44877i	0.557934	−	0.119207i
$838$	11.0142	−	6.35903i	0.380478	−	0.219669i
$839$	20.6544			0.713069			0.356535	−	0.934282i	$-0.383958\pi$
$839$	20.6544			0.713069			0.356535	+	0.934282i	$0.383958\pi$
$840$		0			0
$841$	−6.47924			−0.223422
$842$	10.2967	−	5.94479i	0.354847	−	0.204871i
$843$	26.4543	−	25.5646i	0.911135	−	0.880492i
$844$	−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
$849$	2.75018	+	11.0139i	0.0943859	+	0.377996i
$850$		0			0
$851$	−10.2363	−	5.90993i	−0.350896	−	0.202590i
$852$	1.28383	+	5.14147i	0.0439833	+	0.176144i
$853$		−	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	−0.685708	−	0.727877i	$-0.740507\pi$
$857$	8.41661	−	14.5780i	0.287506	−	0.497975i	0.973214	+	0.229902i	$0.0738406\pi$
$858$	14.1080	−	13.6335i	0.481640	−	0.465441i
$859$	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
$861$	38.8937	+	38.0179i	1.32549	+	1.29565i
$862$	−18.5665			−0.632376
$863$	−32.8880	+	18.9879i	−1.11952	+	0.646356i	−0.941279	−	0.337630i	$-0.890375\pi$
$863$	−32.8880	+	18.9879i	−1.11952	+	0.646356i	−0.178243	+	0.983986i	$0.557041\pi$
$864$	−8.39355	+	1.79335i	−0.285554	+	0.0610110i
$865$		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
$873$	−3.97518	−	0.136021i	−0.134540	−	0.00460362i
$874$		−	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
$879$	4.47672	+	4.63252i	0.150996	+	0.156251i
$880$		0			0
$881$	23.6698			0.797455			0.398728	−	0.917069i	$-0.369452\pi$
$881$	23.6698			0.797455			0.398728	+	0.917069i	$0.369452\pi$
$882$	−16.5274	−	27.1776i	−0.556506	−	0.915118i
$883$	−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	$0.177670\pi$
$887$	26.2917	+	45.5385i	0.882789	+	1.52903i	0.0345613	+	0.999403i	$0.488997\pi$
$888$	−33.5712	−	9.61362i	−1.12657	−	0.322612i
$889$	−25.3301	+	0.721818i	−0.849546	+	0.0242090i
$890$		0			0
$891$	16.0444	+	10.7893i	0.537507	+	0.361455i
$892$	1.09849	+	0.634214i	0.0367802	+	0.0212350i
$893$	6.45910	+	3.72917i	0.216146	+	0.124792i
$894$	−6.47474	+	1.61675i	−0.216548	+	0.0540722i
$895$		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
$903$	9.80803	+	9.58717i	0.326391	+	0.319041i
$904$	−24.1889			−0.804510
$905$		0			0
$906$	10.6008	−	10.2443i	0.352188	−	0.340343i
$907$	−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	$-0.913974\pi$
$911$		−	16.1165i		−	0.533963i	0.963702	−	0.266981i	$-0.0860262\pi$
$912$	−2.30909	−	9.24743i	−0.0764617	−	0.306213i
$913$	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
$921$	13.9624	−	13.4928i	0.460077	−	0.444604i
$922$	52.3010	−	30.1960i	1.72244	−	0.994452i
$923$	36.1909			1.19124
$924$	−2.80676	−	0.717917i	−0.0923355	−	0.0236177i
$925$		0			0
$926$	−39.1451	+	22.6004i	−1.28639	+	0.742696i
$927$	−8.16102	−	15.3227i	−0.268043	−	0.503263i
$928$	−4.91942	+	8.52069i	−0.161488	+	0.279705i
$929$	18.2593	+	31.6261i	0.599069	+	1.03762i	0.992959	+	0.118461i	$0.0377960\pi$
$929$	18.2593	+	31.6261i	0.599069	+	1.03762i	−0.393889	+	0.919158i	$0.628871\pi$
$930$		0			0
$931$	7.15440	−	4.69323i	0.234476	−	0.153814i
$932$			6.07063i			0.198850i
$933$	−31.7959	+	7.93946i	−1.04095	+	0.259926i
$934$	−5.48530	−	3.16694i	−0.179484	−	0.103625i
$935$		0			0
$936$	−0.922672	+	26.9649i	−0.0301585	+	0.881375i
$937$			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	−0.987791	−	0.155782i	$-0.950210\pi$
$941$	−11.0121	+	19.0735i	−0.358985	+	0.621780i	0.628807	+	0.777562i	$0.283544\pi$
$942$	25.3848	+	26.2682i	0.827081	+	0.855866i
$943$	−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	−0.992888	−	0.119053i	$-0.962014\pi$
$947$	−42.6589	+	24.6291i	−1.38623	+	0.800339i	−0.393341	+	0.919393i	$0.628681\pi$
$948$	0.666906	+	0.690116i	0.0216601	+	0.0224139i
$949$	−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	$0.0531101\pi$
$953$			10.2538i			0.332154i	−0.986113	+	0.166077i	$0.946890\pi$
$954$	1.74448	−	50.9819i	0.0564795	−	1.65060i
$955$		0			0
$956$	−0.732331	−	0.422811i	−0.0236853	−	0.0136747i
$957$	21.5035	−	5.36945i	0.695109	−	0.173570i
$958$		−	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
$963$	5.48096	+	10.2907i	0.176622	+	0.331615i
$964$	6.64460	−	3.83626i	0.214008	−	0.123558i
$965$		0			0
$966$	10.1238	−	2.83661i	0.325729	−	0.0912663i
$967$	−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
$969$	−5.44605	+	5.26288i	−0.174952	+	0.169068i
$970$		0			0
$971$	−12.6443	−	21.9006i	−0.405775	−	0.702822i	0.588637	−	0.808398i	$-0.299665\pi$
$971$	−12.6443	−	21.9006i	−0.405775	−	0.702822i	−0.994411	+	0.105575i	$0.966332\pi$
$972$	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	0.127318	−	0.991862i	$-0.459363\pi$
$977$	−20.8797	−	12.0549i	−0.668000	−	0.385670i	−0.795318	+	0.606192i	$0.792696\pi$
$978$	2.58725	+	10.3614i	0.0827313	+	0.331321i
$979$		−	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	$0.444863\pi$
$983$	−24.0441	+	41.6456i	−0.766888	+	1.32829i	−0.939243	+	0.343254i	$0.888471\pi$
$984$	−38.1921	+	36.9076i	−1.21752	+	1.17657i
$985$		0			0
$986$	32.2739			1.02781
$987$	−6.92894	+	27.0893i	−0.220550	+	0.862261i
$988$	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
$996$	4.50258	−	1.12430i	0.142670	−	0.0356248i
$997$	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
$999$	38.5768	+	12.4894i	1.22052	+	0.395148i

Twists

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

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

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} +(-1.20362 - 1.24551i) q^{3} +(0.147140 - 0.254854i) q^{4} +(2.52214 + 0.722254i) q^{6} +(-2.64468 + 0.0753638i) q^{7} -2.58363i q^{8} +(-0.102593 + 2.99825i) q^{9} +(-1.86048 - 1.07415i) q^{11} +(-0.494525 + 0.123483i) q^{12} +3.48097i q^{13} +(3.41210 - 2.10179i) q^{14} +(2.25098 + 3.89881i) q^{16} +(1.78859 - 3.09793i) q^{17} +(-2.13613 - 4.01067i) q^{18} +(1.05858 - 0.611171i) q^{19} +(3.27706 + 3.20326i) q^{21} +3.25401 q^{22} +(-1.31176 + 0.757344i) q^{23} +(-3.21794 + 3.10972i) 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} +(0.901451 + 3.61012i) q^{33} +5.41832i q^{34} +(0.749020 + 0.467309i) q^{36} +(3.90175 + 6.75803i) q^{37} +(-0.925734 + 1.60342i) q^{38} +(4.33559 - 4.18977i) q^{39} +11.8685 q^{41} +(-6.72468 - 1.72005i) 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} +(-6.01129 + 1.50103i) q^{51} +(0.887140 + 0.512191i) q^{52} +(9.72202 + 5.61301i) q^{53} +(-2.42425 + 7.48790i) 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} +(0.0453652 - 7.93712i) q^{63} -6.50196 q^{64} +(-3.91659 - 4.05290i) q^{66} +(5.15882 - 8.93534i) q^{67} +(-0.526347 - 0.911660i) q^{68} +(2.52214 + 0.722254i) q^{69} -10.3968i q^{71} +(7.74637 + 0.265062i) 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} +(-8.97895 - 0.615196i) q^{81} +(-15.5686 + 8.98853i) q^{82} -9.10486 q^{83} +(1.29855 - 0.363843i) q^{84} +(-3.92601 + 2.26668i) q^{86} +(-7.41882 + 7.16930i) q^{87} +(-2.77521 + 4.80681i) q^{88} +(0.889962 + 1.54146i) q^{89} +(-0.262339 - 9.20605i) q^{91} +0.445743i q^{92} +(-1.33292 - 5.33806i) q^{93} +(-8.00392 - 4.62107i) q^{94} +(0.693113 + 2.77577i) 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

Properties

Related objects

Downloads

Learn more