LMFDB - Embedded newform 525.2.t.j.26.4

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			26.4
Character	$\chi$	$=$	525.26
Dual form			525.2.t.j.101.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.31176 - 0.757344i) q^{2} +(1.68045 - 0.419611i) q^{3} +(0.147140 + 0.254854i) q^{4} +(-2.52214 - 0.722254i) q^{6} +(2.64468 + 0.0753638i) q^{7} +2.58363i q^{8} +(2.64785 - 1.41027i) q^{9} +O(q^{10})$	\(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}+O(q^{10}) $ 24 * q + 12 * q^4 + 6 * q^9	$ 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}+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

Display 100 coefficients 10 coefficients

Character values

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

$n$	$127$	$176$	$451$
$\chi(n)$	$1$	$-1$	$e\left(\frac{5}{6}\right)$

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	$-0.513219\pi$
$2$	−1.31176	−	0.757344i	−0.927553	−	0.535523i	−0.886037	+	0.463615i	$0.846552\pi$
$3$	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	−0.192573	−	0.981283i	$-0.561683\pi$
$11$	1.86048	−	1.07415i	0.560957	−	0.323869i	0.753529	+	0.657414i	$0.228350\pi$
$12$	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	$-0.0238401\pi$
$17$	1.78859	+	3.09793i	0.433797	+	0.751359i	−0.563399	+	0.826185i	$0.690507\pi$
$18$	−4.54141	−	0.155396i	−1.07042	−	0.0366272i
$19$	1.05858	+	0.611171i	0.242855	+	0.140212i	0.616488	−	0.787364i	$-0.288555\pi$
$19$	1.05858	+	0.611171i	0.242855	+	0.140212i	−0.373633	+	0.927576i	$0.621888\pi$
$20$		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	$-0.383811\pi$
$23$	−1.31176	−	0.757344i	−0.273521	−	0.157917i	−0.630486	+	0.776200i	$0.717145\pi$
$24$	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	$-0.813467\pi$
$29$		−	5.95645i		−	1.10608i	0.833153	−	0.553042i	$-0.186533\pi$
$30$		0			0
$31$	2.75098	−	1.58828i	0.494091	−	0.285263i	−0.232179	−	0.972673i	$-0.574586\pi$
$31$	2.75098	−	1.58828i	0.494091	−	0.285263i	0.726270	+	0.687410i	$0.241252\pi$
$32$	−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	0.343667	+	0.939092i	$0.388331\pi$
$37$	−3.90175	+	6.75803i	−0.641444	+	1.11101i	−0.985111	+	0.171921i	$0.945002\pi$
$38$	−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	$-0.573287\pi$
$43$	−2.99294			−0.456419			−0.228209	+	0.973612i	$0.573287\pi$
$44$	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	$-0.686533\pi$
$47$	3.05084	−	5.28420i	0.445010	−	0.770780i	0.998053	+	0.0623727i	$0.0198667\pi$
$48$	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	$-0.386420\pi$
$53$	9.72202	−	5.61301i	1.33542	−	0.771006i	0.986125	+	0.166006i	$0.0530871\pi$
$54$	−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	0.927954	−	0.372696i	$-0.121567\pi$
$59$	1.08467	+	1.87871i	0.141213	+	0.244587i	−0.786741	+	0.617283i	$0.788233\pi$
$60$		0			0
$61$	−2.94338	−	1.69936i	−0.376861	−	0.217581i	0.299591	−	0.954068i	$-0.403150\pi$
$61$	−2.94338	−	1.69936i	−0.376861	−	0.217581i	−0.676452	+	0.736487i	$0.736483\pi$
$62$	−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	−0.987500	−	0.157617i	$-0.949619\pi$
$67$	−5.15882	−	8.93534i	−0.630250	−	1.09163i	0.357250	−	0.934009i	$-0.383714\pi$
$68$	−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	$-0.211626\pi$
$72$	3.64363	+	6.84108i	0.429406	+	0.806229i
$73$	−5.93710	+	3.42779i	−0.694885	+	0.401192i	−0.805439	−	0.592678i	$-0.798071\pi$
$73$	−5.93710	+	3.42779i	−0.694885	+	0.401192i	0.110555	+	0.993870i	$0.464737\pi$
$74$	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	−0.914113	−	0.405460i	$-0.867111\pi$
$79$	−0.941421	+	1.63059i	−0.105918	+	0.183456i	0.808195	+	0.588915i	$0.200445\pi$
$80$		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	$-0.666554\pi$
$83$	−9.10486			−0.999388			−0.499694	+	0.866202i	$0.666554\pi$
$84$	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	−0.909331	−	0.416073i	$-0.863406\pi$
$89$	−0.889962	+	1.54146i	−0.0943358	+	0.163394i	0.814995	+	0.579467i	$0.196739\pi$
$90$		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	0.978553	+	0.205997i	$0.0660438\pi$
$101$	6.71005	+	11.6221i	0.667675	+	1.15645i	−0.310878	+	0.950450i	$0.600623\pi$
$102$	−2.27359	−	9.10523i	−0.225119	−	0.901553i
$103$	5.01154	+	2.89342i	0.493802	+	0.285097i	0.726150	−	0.687536i	$-0.241308\pi$
$103$	5.01154	+	2.89342i	0.493802	+	0.285097i	−0.232348	+	0.972633i	$0.574641\pi$
$104$	−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	$-0.273179\pi$
$107$	3.36576	+	1.94323i	0.325381	+	0.187859i	−0.328408	+	0.944536i	$0.606512\pi$
$108$	1.45478	+	0.470993i	0.139986	+	0.0453214i
$109$	2.60384	+	4.50998i	0.249403	+	0.431978i	0.963360	−	0.268211i	$-0.0864324\pi$
$109$	2.60384	+	4.50998i	0.249403	+	0.431978i	−0.713958	+	0.700189i	$0.753099\pi$
$110$		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	$-0.639707\pi$
$127$	−9.57778			−0.849891			−0.424945	+	0.905219i	$0.639707\pi$
$128$	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	−0.995198	−	0.0978802i	$-0.968794\pi$
$131$	−4.72508	+	8.18408i	−0.412832	+	0.715047i	0.582366	+	0.812927i	$0.302127\pi$
$132$	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	$-0.817856\pi$
$137$	−9.27125	+	5.35276i	−0.792096	+	0.457317i	0.0486038	+	0.998818i	$0.484523\pi$
$138$	2.76144	+	2.85755i	0.235070	+	0.243251i
$139$			4.11136i			0.348721i	0.984682	+	0.174360i	$0.0557858\pi$
$139$			4.11136i			0.348721i	−0.984682	+	0.174360i	$0.944214\pi$
$140$		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	0.587514	−	0.809214i	$-0.300107\pi$
$149$	2.20294	+	1.27187i	0.180472	+	0.104196i	−0.407042	+	0.913409i	$0.633440\pi$
$150$		0			0
$151$	2.80956	+	4.86630i	0.228639	+	0.396014i	0.957405	−	0.288749i	$-0.0932392\pi$
$151$	2.80956	+	4.86630i	0.228639	+	0.396014i	−0.728766	+	0.684763i	$0.759906\pi$
$152$	−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	$-0.854187\pi$
$157$	−12.0584	+	6.96194i	−0.962368	+	0.555623i	−0.0654670	+	0.997855i	$0.520854\pi$
$158$	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	$-0.884296\pi$
$163$	−2.03535	+	3.52533i	−0.159421	+	0.276125i	0.775239	+	0.631668i	$0.217629\pi$
$164$	−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	$0.681803\pi$
$168$	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	$-0.957493\pi$
$173$	−5.00133	+	8.66256i	−0.380244	+	0.658602i	0.610853	+	0.791744i	$0.290827\pi$
$174$	−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	−0.922436	−	0.386151i	$-0.873804\pi$
$179$	−14.0378	+	8.10475i	−1.04924	+	0.605777i	−0.126801	+	0.991928i	$0.540471\pi$
$180$		0			0
$181$		−	19.4123i		−	1.44290i	−0.692465	−	0.721451i	$-0.743475\pi$
$181$		−	19.4123i		−	1.44290i	0.692465	−	0.721451i	$-0.256525\pi$
$182$	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	0.842092	−	0.539334i	$-0.181324\pi$
$191$	11.0018	+	6.35188i	0.796061	+	0.459606i	−0.0460309	+	0.998940i	$0.514657\pi$
$192$	−10.9262	+	2.72830i	−0.788534	+	0.196898i
$193$	−10.4098	−	18.0302i	−0.749311	−	1.29785i	−0.948153	−	0.317813i	$-0.897051\pi$
$193$	−10.4098	−	18.0302i	−0.749311	−	1.29785i	0.198842	−	0.980032i	$-0.436282\pi$
$194$	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	0.530622	−	0.847608i	$-0.321958\pi$
$199$	21.5831	−	12.4610i	1.52998	−	0.883337i	0.999362	−	0.0357284i	$-0.0113751\pi$
$200$		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	$-0.0464563\pi$
$227$	5.55561	+	9.62260i	0.368739	+	0.638675i	−0.620630	+	0.784104i	$0.713123\pi$
$228$	0.150939	+	0.604478i	0.00999617	+	0.0400326i
$229$	−8.63774	−	4.98700i	−0.570798	−	0.329550i	0.186670	−	0.982423i	$-0.440230\pi$
$229$	−8.63774	−	4.98700i	−0.570798	−	0.329550i	−0.757468	+	0.652872i	$0.773564\pi$
$230$		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	$-0.569499\pi$
$233$	−17.8650	−	10.3144i	−1.17037	−	0.675716i	−0.953768	+	0.300543i	$0.902832\pi$
$234$	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	$-0.970375\pi$
$239$		−	2.87353i		−	0.185873i	0.995672	−	0.0929365i	$-0.0296254\pi$
$240$		0			0
$241$	22.5792	−	13.0361i	1.45445	−	0.839728i	0.455722	−	0.890122i	$-0.349381\pi$
$241$	22.5792	−	13.0361i	1.45445	−	0.839728i	0.998729	+	0.0503940i	$0.0160477\pi$
$242$	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	$-0.699029\pi$
$257$	6.56514	−	11.3712i	0.409522	−	0.709314i	0.994836	+	0.101493i	$0.0323620\pi$
$258$	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	$-0.482568\pi$
$263$	15.3551	−	8.86526i	0.946835	−	0.546655i	0.892096	+	0.451846i	$0.149234\pi$
$264$	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	0.791020	−	0.611790i	$-0.209550\pi$
$269$	−2.20294	−	3.81561i	−0.134316	−	0.232642i	−0.925336	+	0.379148i	$0.876217\pi$
$270$		0			0
$271$	20.4287	+	11.7945i	1.24095	+	0.716465i	0.969288	−	0.245927i	$-0.0790923\pi$
$271$	20.4287	+	11.7945i	1.24095	+	0.716465i	0.271665	+	0.962392i	$0.412426\pi$
$272$	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	$-0.292636\pi$
$277$	−6.41589	−	11.1127i	−0.385494	−	0.667695i	−0.991838	+	0.127508i	$0.959302\pi$
$278$	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	$0.781606\pi$
$282$	−11.5112	+	11.1240i	−0.685480	+	0.662426i
$283$	5.67603	−	3.27706i	0.337405	−	0.194801i	−0.321719	−	0.946835i	$-0.604261\pi$
$283$	5.67603	−	3.27706i	0.337405	−	0.194801i	0.659124	+	0.752034i	$0.270927\pi$
$284$	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	$-0.534651\pi$
$293$	−3.71937			−0.217288			−0.108644	+	0.994081i	$0.534651\pi$
$294$	−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	−0.999091	−	0.0426199i	$-0.986430\pi$
$311$	−9.46050	−	16.3861i	−0.536456	−	0.929168i	0.462636	−	0.886548i	$-0.346904\pi$
$312$	−15.1133	+	3.77380i	−0.855620	+	0.213649i
$313$	−14.1859	−	8.19024i	−0.801835	−	0.462940i	0.0422775	−	0.999106i	$-0.486539\pi$
$313$	−14.1859	−	8.19024i	−0.801835	−	0.462940i	−0.844112	+	0.536166i	$0.819872\pi$
$314$	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	$-0.425030\pi$
$317$	−8.76134	−	5.05836i	−0.492086	−	0.284106i	−0.725439	+	0.688286i	$0.758363\pi$
$318$	−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	0.469660	+	0.882847i	$0.344376\pi$
$331$	−9.63774	+	16.6931i	−0.529738	+	0.917533i	−0.999398	+	0.0346861i	$0.988957\pi$
$332$	−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	$-0.722653\pi$
$337$	−23.6381			−1.28765			−0.643824	+	0.765174i	$0.722653\pi$
$338$	−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	$-0.526247\pi$
$347$	13.7760	−	7.95360i	0.739536	−	0.426971i	0.821901	+	0.569631i	$0.192914\pi$
$348$	2.18321	−	2.10979i	0.117032	−	0.113096i
$349$			0.0192397i			0.00102988i	1.00000		0.000514938i	$0.000163910\pi$
$349$			0.0192397i			0.00102988i	−1.00000		0.000514938i	$0.999836\pi$
$350$		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	0.976033	+	0.217624i	$0.0698305\pi$
$353$	12.7100	+	22.0143i	0.676484	+	1.17170i	−0.299549	+	0.954081i	$0.596836\pi$
$354$	−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	−0.167579	−	0.985859i	$-0.553595\pi$
$359$	−20.9396	−	12.0895i	−1.10515	−	0.638057i	−0.937568	+	0.347801i	$0.886928\pi$
$360$		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	$-0.590569\pi$
$367$	7.85721	−	4.53636i	0.410143	−	0.236796i	0.690851	+	0.722997i	$0.257236\pi$
$368$	−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	$-0.701326\pi$
$373$	7.78183	−	13.4785i	0.402928	−	0.697891i	0.994078	+	0.108670i	$0.0346592\pi$
$374$	−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	$-0.920430\pi$
$383$	−5.28833	+	9.15965i	−0.270221	+	0.468036i	0.698697	+	0.715417i	$0.253763\pi$
$384$	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	−0.823373	−	0.567500i	$-0.807911\pi$
$389$	−14.6659	+	8.46736i	−0.743590	+	0.429312i	0.0797828	+	0.996812i	$0.474577\pi$
$390$		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	$-0.330076\pi$
$397$	0.353188	+	0.203913i	0.0177260	+	0.0102341i	−0.491111	+	0.871097i	$0.663409\pi$
$398$	−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	−0.247240	−	0.968954i	$-0.579524\pi$
$401$	−24.2302	−	13.9893i	−1.21000	−	0.698593i	−0.962759	+	0.270361i	$0.912857\pi$
$402$	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	−0.555062	−	0.831809i	$-0.687305\pi$
$409$	−2.26960	+	1.31036i	−0.112225	+	0.0647929i	0.442837	+	0.896602i	$0.353972\pi$
$410$		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	−0.733378	−	0.679821i	$-0.762058\pi$
$431$	−10.6154	+	6.12880i	−0.511326	+	0.295214i	0.222053	+	0.975035i	$0.428724\pi$
$432$	−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	0.803700	−	0.595035i	$-0.202862\pi$
$439$	14.4620	+	8.34964i	0.690234	+	0.398507i	−0.113466	+	0.993542i	$0.536195\pi$
$440$		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	$-0.331426\pi$
$443$	0.218429	+	0.126110i	0.0103779	+	0.00599167i	−0.494802	+	0.869006i	$0.664759\pi$
$444$	−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	$-0.761436\pi$
$449$		−	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
$453$	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	−0.434171	−	0.900830i	$-0.642959\pi$
$457$	12.0368	−	20.8483i	0.563056	−	0.975242i	0.997228	−	0.0744117i	$-0.0237079\pi$
$458$	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	$-0.743901\pi$
$463$	−29.8417			−1.38686			−0.693430	+	0.720524i	$0.743901\pi$
$464$	−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	$-0.802488\pi$
$467$	2.09082	−	3.62140i	0.0967515	−	0.167579i	0.910338	+	0.413865i	$0.135821\pi$
$468$	−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	0.985828	+	0.167757i	$0.0536525\pi$
$479$	13.9676	+	24.1926i	0.638196	+	1.10539i	−0.347632	+	0.937631i	$0.613014\pi$
$480$		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	0.886637	+	0.462466i	$0.153035\pi$
$487$	18.6216	+	32.2536i	0.843826	+	1.46155i	−0.0428116	+	0.999083i	$0.513632\pi$
$488$	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	$0.957455\pi$
$492$	−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	−0.995886	−	0.0906204i	$-0.971115\pi$
$499$	−9.37010	+	16.2295i	−0.419463	+	0.726532i	0.576422	+	0.817152i	$0.304448\pi$
$500$		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	$-0.246749\pi$
$503$	32.0398			1.42858			0.714291	+	0.699849i	$0.246749\pi$
$504$	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	−0.996363	−	0.0852085i	$-0.972844\pi$
$509$	−9.57465	+	16.5838i	−0.424389	+	0.735063i	0.571974	+	0.820272i	$0.306178\pi$
$510$		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	0.905408	−	0.424543i	$-0.139565\pi$
$521$	1.94104	+	3.36199i	0.0850387	+	0.147291i	−0.820369	+	0.571834i	$0.806232\pi$
$522$	−0.925607	+	27.0506i	−0.0405127	+	1.18397i
$523$	1.83929	+	1.06192i	0.0804266	+	0.0464343i	0.539674	−	0.841874i	$-0.318548\pi$
$523$	1.83929	+	1.06192i	0.0804266	+	0.0464343i	−0.459247	+	0.888308i	$0.651881\pi$
$524$	−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	−0.655441	−	0.755246i	$-0.727517\pi$
$541$	7.59052	−	13.1472i	0.326342	−	0.565241i	0.981783	+	0.190005i	$0.0608506\pi$
$542$	−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	$-0.580852\pi$
$547$	−11.7540			−0.502566			−0.251283	+	0.967914i	$0.580852\pi$
$548$	−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	$-0.602831\pi$
$557$	8.14298	−	4.70135i	0.345029	−	0.199203i	0.662494	+	0.749068i	$0.269498\pi$
$558$	−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	$-0.301653\pi$
$563$	−9.76331	−	16.9106i	−0.411475	−	0.712695i	−0.995051	+	0.0993632i	$0.968319\pi$
$564$	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	0.715519	−	0.698593i	$-0.246190\pi$
$569$	11.1702	+	6.44911i	0.468279	+	0.270361i	−0.247240	+	0.968954i	$0.579524\pi$
$570$		0			0
$571$	20.8321	+	36.0823i	0.871796	+	1.51000i	0.860137	+	0.510063i	$0.170378\pi$
$571$	20.8321	+	36.0823i	0.871796	+	1.51000i	0.0116595	+	0.999932i	$0.496289\pi$
$572$	−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	$-0.716495\pi$
$577$	−6.48634	+	3.74489i	−0.270030	+	0.155902i	0.358871	+	0.933387i	$0.383162\pi$
$578$	−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	$-0.348573\pi$
$587$	22.1920			0.915961			0.457981	+	0.888962i	$0.348573\pi$
$588$	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	$-0.791952\pi$
$593$	3.15687	−	5.46787i	0.129637	−	0.224538i	0.923536	+	0.383512i	$0.125285\pi$
$594$	−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	−0.0876487	−	0.996151i	$-0.527935\pi$
$599$	17.8962	−	10.3324i	0.731219	−	0.422170i	0.818868	+	0.573982i	$0.194602\pi$
$600$		0			0
$601$		−	12.5956i		−	0.513785i	−0.966440	−	0.256892i	$-0.917301\pi$
$601$		−	12.5956i		−	0.513785i	0.966440	−	0.256892i	$-0.0826986\pi$
$602$	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	−1.00000		0.000139312i	$-0.999956\pi$
$607$	−36.9590	−	21.3383i	−1.50012	−	0.866095i	−0.500121	−	0.865956i	$-0.666711\pi$
$608$	−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	$-0.200949\pi$
$613$	−2.66142	−	4.60972i	−0.107494	−	0.186185i	−0.914754	+	0.404011i	$0.867616\pi$
$614$	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	−0.704950	−	0.709257i	$-0.749031\pi$
$619$	−11.0265	+	6.36613i	−0.443191	+	0.255876i	0.261759	+	0.965133i	$0.415697\pi$
$620$		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	−0.522324	−	0.852747i	$-0.674935\pi$
$641$	−1.13893	+	0.657564i	−0.0449852	+	0.0259722i	0.477339	+	0.878719i	$0.341601\pi$
$642$	−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	$-0.127580\pi$
$647$	3.11558	+	5.39634i	0.122486	+	0.212152i	−0.798261	+	0.602311i	$0.794247\pi$
$648$	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	$-0.453654\pi$
$653$	−16.3348	−	9.43091i	−0.639230	−	0.369060i	−0.784318	+	0.620359i	$0.786987\pi$
$654$	−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	$0.300850\pi$
$659$			41.6170i			1.62117i	−0.585622	+	0.810584i	$0.699150\pi$
$660$		0			0
$661$	3.27232	−	1.88927i	0.127278	−	0.0734842i	−0.435009	−	0.900426i	$-0.643255\pi$
$661$	3.27232	−	1.88927i	0.127278	−	0.0734842i	0.562287	+	0.826942i	$0.309921\pi$
$662$	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	$-0.705805\pi$
$673$	−31.2573			−1.20488			−0.602441	+	0.798163i	$0.705805\pi$
$674$	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	$-0.887036\pi$
$677$	−4.36895	+	7.56724i	−0.167912	+	0.290832i	0.769773	+	0.638317i	$0.220369\pi$
$678$	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	$-0.804076\pi$
$683$	−18.9393	+	10.9346i	−0.724691	+	0.418401i	0.0917858	+	0.995779i	$0.470743\pi$
$684$	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	0.822959	−	0.568101i	$-0.192322\pi$
$691$	19.5167	+	11.2680i	0.742449	+	0.428653i	−0.0805102	+	0.996754i	$0.525655\pi$
$692$	−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	$-0.766104\pi$
$701$		−	35.5019i		−	1.34089i	0.741960	−	0.670444i	$-0.233896\pi$
$702$	−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	−0.825303	−	0.564690i	$-0.808996\pi$
$709$	2.03390	−	3.52282i	0.0763847	−	0.132302i	0.901688	+	0.432388i	$0.142329\pi$
$710$		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	−0.427133	−	0.904189i	$-0.640476\pi$
$719$	15.2703	−	26.4489i	0.569484	−	0.986376i	0.996617	−	0.0821868i	$-0.0261904\pi$
$720$		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	$-0.434311\pi$
$733$	−14.6277	−	8.44533i	−0.540288	−	0.311935i	−0.745196	+	0.666846i	$0.767644\pi$
$734$	−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	0.999948	+	0.0102170i	$0.00325222\pi$
$739$	13.8321	+	23.9579i	0.508822	+	0.881306i	−0.491126	+	0.871089i	$0.663414\pi$
$740$		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	0.0856082	−	0.996329i	$-0.472717\pi$
$751$	24.8188	−	42.9874i	0.905650	−	1.56863i	0.820042	−	0.572303i	$-0.193950\pi$
$752$	−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	$-0.166011\pi$
$757$	47.7116			1.73411			0.867054	+	0.498214i	$0.166011\pi$
$758$	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	−0.628382	−	0.777905i	$-0.716282\pi$
$761$	9.91711	−	17.1769i	0.359495	−	0.622663i	0.987876	+	0.155242i	$0.0496157\pi$
$762$	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	$0.0614100\pi$
$769$			10.6337i			0.383461i	−0.981448	+	0.191731i	$0.938590\pi$
$770$		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	$-0.0837426\pi$
$773$	7.16138	+	12.4039i	0.257577	+	0.446136i	−0.708015	+	0.706197i	$0.750409\pi$
$774$	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	$-0.437951\pi$
$787$	31.9859	−	18.4671i	1.14017	−	0.658280i	0.946474	+	0.322781i	$0.104618\pi$
$788$	−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	$-0.731106\pi$
$797$	−37.4862			−1.32783			−0.663914	+	0.747809i	$0.731106\pi$
$798$	−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	−0.0571956	−	0.998363i	$-0.518216\pi$
$809$	22.1518	−	12.7893i	0.778814	−	0.449649i	0.836010	+	0.548714i	$0.184883\pi$
$810$		0			0
$811$			7.28791i			0.255913i	0.991780	+	0.127957i	$0.0408418\pi$
$811$			7.28791i			0.255913i	−0.991780	+	0.127957i	$0.959158\pi$
$812$	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	0.499873	−	0.866099i	$-0.333380\pi$
$821$	−0.00729231	−	0.00421022i	−0.000254504	−	0.000146938i	−0.500127	+	0.865952i	$0.666713\pi$
$822$	27.2494	−	6.80421i	0.950433	−	0.237324i
$823$	15.6119	+	27.0406i	0.544198	+	0.942578i	0.998657	+	0.0518103i	$0.0164991\pi$
$823$	15.6119	+	27.0406i	0.544198	+	0.942578i	−0.454459	+	0.890767i	$0.650168\pi$
$824$	−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	−0.465907	−	0.884834i	$-0.654272\pi$
$829$	1.94142	−	1.12088i	0.0674283	−	0.0389298i	0.533335	+	0.845904i	$0.320938\pi$
$830$		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	$-0.0738406\pi$
$857$	8.41661	+	14.5780i	0.287506	+	0.497975i	−0.685708	+	0.727877i	$0.740507\pi$
$858$	−4.75298	−	19.0347i	−0.162264	−	0.649833i
$859$	30.4698	+	17.5918i	1.03962	+	0.600223i	0.919725	−	0.392563i	$-0.128412\pi$
$859$	30.4698	+	17.5918i	1.03962	+	0.600223i	0.119893	+	0.992787i	$0.461745\pi$
$860$		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	$-0.557041\pi$
$863$	−32.8880	−	18.9879i	−1.11952	−	0.646356i	−0.941279	+	0.337630i	$0.890375\pi$
$864$	−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	$-0.771410\pi$
$877$	5.72481	−	9.91566i	0.193313	−	0.334828i	0.946346	+	0.323155i	$0.104743\pi$
$878$	−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	$-0.408577\pi$
$883$	16.8355			0.566560			0.283280	+	0.959037i	$0.408577\pi$
$884$	−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	0.0345613	−	0.999403i	$-0.488997\pi$
$887$	26.2917	−	45.5385i	0.882789	−	1.52903i	0.848227	−	0.529632i	$-0.177670\pi$
$888$	−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	0.887415	+	0.460971i	$0.152499\pi$
$907$	25.3858	+	43.9694i	0.842920	+	1.45998i	−0.0444946	+	0.999010i	$0.514168\pi$
$908$	−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	$-0.0860262\pi$
$912$	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	−0.326245	−	0.945285i	$-0.605783\pi$
$919$	19.8721	−	34.4194i	0.655519	−	1.13539i	0.981763	−	0.190106i	$-0.0608833\pi$
$920$		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	0.393889	+	0.919158i	$0.371129\pi$
$929$	−18.2593	+	31.6261i	−0.599069	+	1.03762i	−0.992959	+	0.118461i	$0.962204\pi$
$930$		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	0.987791	−	0.155782i	$-0.0497897\pi$
$941$	11.0121	+	19.0735i	0.358985	+	0.621780i	−0.628807	+	0.777562i	$0.716456\pi$
$942$	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	$-0.628681\pi$
$947$	−42.6589	−	24.6291i	−1.38623	−	0.800339i	−0.992888	+	0.119053i	$0.962014\pi$
$948$	−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	$-0.476300\pi$
$967$	4.62632			0.148772			0.0743862	+	0.997230i	$0.476300\pi$
$968$	−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	−0.588637	−	0.808398i	$-0.700335\pi$
$971$	12.6443	−	21.9006i	0.405775	−	0.702822i	0.994411	+	0.105575i	$0.0336684\pi$
$972$	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	$-0.792696\pi$
$977$	−20.8797	+	12.0549i	−0.668000	+	0.385670i	0.127318	+	0.991862i	$0.459363\pi$
$978$	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	−0.939243	−	0.343254i	$-0.888471\pi$
$983$	−24.0441	−	41.6456i	−0.766888	−	1.32829i	0.172354	−	0.985035i	$-0.444863\pi$
$984$	−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	0.527483	−	0.849565i	$-0.323136\pi$
$991$	−14.8587	−	25.7361i	−0.472003	−	0.817534i	−0.999487	+	0.0320314i	$0.989802\pi$
$992$	−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	$-0.805888\pi$
$997$	−23.1647	+	13.3742i	−0.733634	+	0.423564i	0.0861161	+	0.996285i	$0.472554\pi$
$998$	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.26.4		24
3.2	odd	2	inner	525.2.t.j.26.10		24
5.2	odd	4		105.2.p.a.89.9	yes	24
5.3	odd	4		105.2.p.a.89.4	yes	24
5.4	even	2	inner	525.2.t.j.26.9		24
7.3	odd	6	inner	525.2.t.j.101.10		24
15.2	even	4		105.2.p.a.89.3	yes	24
15.8	even	4		105.2.p.a.89.10	yes	24
15.14	odd	2	inner	525.2.t.j.26.3		24
21.17	even	6	inner	525.2.t.j.101.4		24
35.2	odd	12		735.2.g.b.734.8		24
35.3	even	12		105.2.p.a.59.3	✓	24
35.12	even	12		735.2.g.b.734.5		24
35.13	even	4		735.2.p.f.509.3		24
35.17	even	12		105.2.p.a.59.10	yes	24
35.18	odd	12		735.2.p.f.374.4		24
35.23	odd	12		735.2.g.b.734.17		24
35.24	odd	6	inner	525.2.t.j.101.3		24
35.27	even	4		735.2.p.f.509.10		24
35.32	odd	12		735.2.p.f.374.9		24
35.33	even	12		735.2.g.b.734.20		24
105.2	even	12		735.2.g.b.734.19		24
105.17	odd	12		105.2.p.a.59.4	yes	24
105.23	even	12		735.2.g.b.734.6		24
105.32	even	12		735.2.p.f.374.3		24
105.38	odd	12		105.2.p.a.59.9	yes	24
105.47	odd	12		735.2.g.b.734.18		24
105.53	even	12		735.2.p.f.374.10		24
105.59	even	6	inner	525.2.t.j.101.9		24
105.62	odd	4		735.2.p.f.509.4		24
105.68	odd	12		735.2.g.b.734.7		24
105.83	odd	4		735.2.p.f.509.9		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
105.2.p.a.59.3	✓	24	35.3	even	12
105.2.p.a.59.4	yes	24	105.17	odd	12
105.2.p.a.59.9	yes	24	105.38	odd	12
105.2.p.a.59.10	yes	24	35.17	even	12
105.2.p.a.89.3	yes	24	15.2	even	4
105.2.p.a.89.4	yes	24	5.3	odd	4
105.2.p.a.89.9	yes	24	5.2	odd	4
105.2.p.a.89.10	yes	24	15.8	even	4
525.2.t.j.26.3		24	15.14	odd	2	inner
525.2.t.j.26.4		24	1.1	even	1	trivial
525.2.t.j.26.9		24	5.4	even	2	inner
525.2.t.j.26.10		24	3.2	odd	2	inner
525.2.t.j.101.3		24	35.24	odd	6	inner
525.2.t.j.101.4		24	21.17	even	6	inner
525.2.t.j.101.9		24	105.59	even	6	inner
525.2.t.j.101.10		24	7.3	odd	6	inner
735.2.g.b.734.5		24	35.12	even	12
735.2.g.b.734.6		24	105.23	even	12
735.2.g.b.734.7		24	105.68	odd	12
735.2.g.b.734.8		24	35.2	odd	12
735.2.g.b.734.17		24	35.23	odd	12
735.2.g.b.734.18		24	105.47	odd	12
735.2.g.b.734.19		24	105.2	even	12
735.2.g.b.734.20		24	35.33	even	12
735.2.p.f.374.3		24	105.32	even	12
735.2.p.f.374.4		24	35.18	odd	12
735.2.p.f.374.9		24	35.32	odd	12
735.2.p.f.374.10		24	105.53	even	12
735.2.p.f.509.3		24	35.13	even	4
735.2.p.f.509.4		24	105.62	odd	4
735.2.p.f.509.9		24	105.83	odd	4
735.2.p.f.509.10		24	35.27	even	4

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)

\(f(q)\)	\(=\)	\(q+(-1.31176 - 0.757344i) q^{2} +(1.68045 - 0.419611i) q^{3} +(0.147140 + 0.254854i) q^{4} +(-2.52214 - 0.722254i) q^{6} +(2.64468 + 0.0753638i) q^{7} +2.58363i q^{8} +(2.64785 - 1.41027i) q^{9} +O(q^{10})\)	\(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})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 12 q^{4} + 6 q^{9}+O(q^{10}) \) 24 * q + 12 * q^4 + 6 * q^9	\( 24 q + 12 q^{4} + 6 q^{9} - 12 q^{16} - 6 q^{21} - 18 q^{24} + 84 q^{36} + 12 q^{39} + 36 q^{46} + 12 q^{49} - 12 q^{51} + 36 q^{54} + 36 q^{61} - 24 q^{64} - 72 q^{66} - 48 q^{79} - 6 q^{81} - 48 q^{84} - 96 q^{91} + 72 q^{94} - 90 q^{96} + 48 q^{99}+O(q^{100}) \) 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

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