LMFDB - Embedded newform 525.2.q.g.299.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [525,2,Mod(299,525)]

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, 3, 5]))

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

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

chi := DirichletCharacter("525.299");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 525 = 3 \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	525.q (of order $6$, degree $2$, not 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:	$40$
Relative dimension:	$20$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			299.8
Character	$\chi$	$=$	525.299
Dual form			525.2.q.g.374.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.450666 + 0.780577i) q^{2} +(1.60886 + 0.641538i) q^{3} +(0.593800 + 1.02849i) q^{4} +(-1.22583 + 0.966719i) q^{6} +(2.64365 + 0.105498i) q^{7} -2.87309 q^{8} +(2.17686 + 2.06429i) q^{9} +O(q^{10})$	\(q+(-0.450666 + 0.780577i) q^{2} +(1.60886 + 0.641538i) q^{3} +(0.593800 + 1.02849i) q^{4} +(-1.22583 + 0.966719i) q^{6} +(2.64365 + 0.105498i) q^{7} -2.87309 q^{8} +(2.17686 + 2.06429i) q^{9} +(-5.46176 + 3.15335i) q^{11} +(0.295524 + 2.03564i) q^{12} -3.77183 q^{13} +(-1.27375 + 2.01603i) q^{14} +(0.107205 - 0.185685i) q^{16} +(3.27294 - 1.88963i) q^{17} +(-2.59237 + 0.768900i) q^{18} +(4.57893 + 2.64365i) q^{19} +(4.18558 + 1.86573i) q^{21} -5.68443i q^{22} +(3.38933 - 5.87050i) q^{23} +(-4.62239 - 1.84320i) q^{24} +(1.69984 - 2.94420i) q^{26} +(2.17794 + 4.71769i) q^{27} +(1.46129 + 2.78161i) q^{28} +3.06327i q^{29} +(0.349819 - 0.201968i) q^{31} +(-2.77646 - 4.80897i) q^{32} +(-10.8102 + 1.56937i) q^{33} +3.40637i q^{34} +(-0.830485 + 3.46465i) q^{36} +(-1.15705 - 0.668021i) q^{37} +(-4.12714 + 2.38281i) q^{38} +(-6.06834 - 2.41977i) q^{39} +6.53749 q^{41} +(-3.34265 + 2.42634i) q^{42} -4.84564i q^{43} +(-6.48638 - 3.74491i) q^{44} +(3.05492 + 5.29127i) q^{46} +(1.68073 + 0.970371i) q^{47} +(0.291602 - 0.229964i) q^{48} +(6.97774 + 0.557800i) q^{49} +(6.47796 - 0.940437i) q^{51} +(-2.23971 - 3.87929i) q^{52} +(0.720381 + 1.24774i) q^{53} +(-4.66404 - 0.426055i) q^{54} +(-7.59543 - 0.303106i) q^{56} +(5.67086 + 7.19082i) q^{57} +(-2.39112 - 1.38051i) q^{58} +(-1.60223 - 2.77514i) q^{59} +(-11.3644 - 6.56124i) q^{61} +0.364081i q^{62} +(5.53707 + 5.68691i) q^{63} +5.43385 q^{64} +(3.64678 - 9.14545i) q^{66} +(2.68611 - 1.55082i) q^{67} +(3.88694 + 2.24412i) q^{68} +(9.21911 - 7.27042i) q^{69} +2.21562i q^{71} +(-6.25430 - 5.93088i) q^{72} +(-1.25932 - 2.18121i) q^{73} +(1.04288 - 0.602109i) q^{74} +6.27919i q^{76} +(-14.7716 + 7.76013i) q^{77} +(4.62362 - 3.64630i) q^{78} +(3.05960 - 5.29938i) q^{79} +(0.477421 + 8.98733i) q^{81} +(-2.94623 + 5.10301i) q^{82} +8.53654i q^{83} +(0.566504 + 5.41270i) q^{84} +(3.78240 + 2.18377i) q^{86} +(-1.96520 + 4.92836i) q^{87} +(15.6921 - 9.05984i) q^{88} +(-0.590783 + 1.02327i) q^{89} +(-9.97138 - 0.397921i) q^{91} +8.05034 q^{92} +(0.692381 - 0.100516i) q^{93} +(-1.51490 + 0.874627i) q^{94} +(-1.38180 - 9.51816i) q^{96} +9.10556 q^{97} +(-3.58004 + 5.19528i) q^{98} +(-18.3989 - 4.41026i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q - 28 q^{4} + 14 q^{9}+O(q^{10}) $ 40 * q - 28 * q^4 + 14 * q^9	$ 40 q - 28 q^{4} + 14 q^{9} - 36 q^{16} - 18 q^{21} - 36 q^{24} + 84 q^{31} - 72 q^{36} - 16 q^{46} + 8 q^{49} + 42 q^{51} + 150 q^{54} - 180 q^{61} + 240 q^{64} + 12 q^{66} - 92 q^{79} + 58 q^{81} - 150 q^{84} - 60 q^{91} - 12 q^{94} + 270 q^{96} - 188 q^{99}+O(q^{100}) $ 40 * q - 28 * q^4 + 14 * q^9 - 36 * q^16 - 18 * q^21 - 36 * q^24 + 84 * q^31 - 72 * q^36 - 16 * q^46 + 8 * q^49 + 42 * q^51 + 150 * q^54 - 180 * q^61 + 240 * q^64 + 12 * q^66 - 92 * q^79 + 58 * q^81 - 150 * q^84 - 60 * q^91 - 12 * q^94 + 270 * q^96 - 188 * 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 $

$2$	−0.450666	+	0.780577i	−0.318669	+	0.551951i	−0.980211	−	0.197957i	$-0.936569\pi$
$2$	−0.450666	+	0.780577i	−0.318669	+	0.551951i	0.661541	+	0.749909i	$0.269903\pi$
$3$	1.60886	+	0.641538i	0.928875	+	0.370392i
$3$	1.60886	+	0.641538i	0.928875	+	0.370392i
$4$	0.593800	+	1.02849i	0.296900	+	0.514245i
$5$		0			0
$5$		0			0
$6$	−1.22583	+	0.966719i	−0.500443	+	0.394662i
$7$	2.64365	+	0.105498i	0.999205	+	0.0398746i
$7$	2.64365	+	0.105498i	0.999205	+	0.0398746i
$8$	−2.87309			−1.01579
$9$	2.17686	+	2.06429i	0.725619	+	0.688096i
$10$		0			0
$11$	−5.46176	+	3.15335i	−1.64678	+	0.950770i	−0.668442	+	0.743765i	$0.733038\pi$
$11$	−5.46176	+	3.15335i	−1.64678	+	0.950770i	−0.978340	+	0.207005i	$0.933628\pi$
$12$	0.295524	+	2.03564i	0.0853104	+	0.587639i
$13$	−3.77183			−1.04612			−0.523059	−	0.852297i	$-0.675209\pi$
$13$	−3.77183			−1.04612			−0.523059	+	0.852297i	$0.675209\pi$
$14$	−1.27375	+	2.01603i	−0.340425	+	0.538806i
$15$		0			0
$16$	0.107205	−	0.185685i	0.0268013	−	0.0464212i
$17$	3.27294	−	1.88963i	0.793804	−	0.458303i	−0.0474963	−	0.998871i	$-0.515124\pi$
$17$	3.27294	−	1.88963i	0.793804	−	0.458303i	0.841300	+	0.540569i	$0.181791\pi$
$18$	−2.59237	+	0.768900i	−0.611028	+	0.181231i
$19$	4.57893	+	2.64365i	1.05048	+	0.606494i	0.922783	−	0.385319i	$-0.125909\pi$
$19$	4.57893	+	2.64365i	1.05048	+	0.606494i	0.127695	+	0.991813i	$0.459242\pi$
$20$		0			0
$21$	4.18558	+	1.86573i	0.913367	+	0.407136i
$22$		−	5.68443i		−	1.21192i
$23$	3.38933	−	5.87050i	0.706725	−	1.22408i	−0.259340	−	0.965786i	$-0.583505\pi$
$23$	3.38933	−	5.87050i	0.706725	−	1.22408i	0.966065	−	0.258298i	$-0.0831615\pi$
$24$	−4.62239	−	1.84320i	−0.943542	−	0.376241i
$25$		0			0
$26$	1.69984	−	2.94420i	0.333365	−	0.577406i
$27$	2.17794	+	4.71769i	0.419144	+	0.907920i
$28$	1.46129	+	2.78161i	0.276158	+	0.525675i
$29$			3.06327i			0.568834i	0.958701	+	0.284417i	$0.0918000\pi$
$29$			3.06327i			0.568834i	−0.958701	+	0.284417i	$0.908200\pi$
$30$		0			0
$31$	0.349819	−	0.201968i	0.0628294	−	0.0362746i	−0.468256	−	0.883593i	$-0.655118\pi$
$31$	0.349819	−	0.201968i	0.0628294	−	0.0362746i	0.531086	+	0.847318i	$0.321784\pi$
$32$	−2.77646	−	4.80897i	−0.490813	−	0.850114i
$33$	−10.8102	+	1.56937i	−1.88181	+	0.273192i
$34$			3.40637i			0.584188i
$35$		0			0
$36$	−0.830485	+	3.46465i	−0.138414	+	0.577442i
$37$	−1.15705	−	0.668021i	−0.190217	−	0.109822i	0.401867	−	0.915698i	$-0.368361\pi$
$37$	−1.15705	−	0.668021i	−0.190217	−	0.109822i	−0.592084	+	0.805876i	$0.701695\pi$
$38$	−4.12714	+	2.38281i	−0.669511	+	0.386542i
$39$	−6.06834	−	2.41977i	−0.971713	−	0.387474i
$40$		0			0
$41$	6.53749			1.02098			0.510492	−	0.859882i	$-0.329463\pi$
$41$	6.53749			1.02098			0.510492	+	0.859882i	$0.329463\pi$
$42$	−3.34265	+	2.42634i	−0.515782	+	0.374393i
$43$		−	4.84564i		−	0.738954i	−0.929240	−	0.369477i	$-0.879537\pi$
$43$		−	4.84564i		−	0.738954i	0.929240	−	0.369477i	$-0.120463\pi$
$44$	−6.48638	−	3.74491i	−0.977858	−	0.564567i
$45$		0			0
$46$	3.05492	+	5.29127i	0.450423	+	0.780156i
$47$	1.68073	+	0.970371i	0.245160	+	0.141543i	0.617546	−	0.786535i	$-0.288127\pi$
$47$	1.68073	+	0.970371i	0.245160	+	0.141543i	−0.372386	+	0.928078i	$0.621460\pi$
$48$	0.291602	−	0.229964i	0.0420891	−	0.0331925i
$49$	6.97774	+	0.557800i	0.996820	+	0.0796858i
$50$		0			0
$51$	6.47796	−	0.940437i	0.907096	−	0.131688i
$52$	−2.23971	−	3.87929i	−0.310592	−	0.537961i
$53$	0.720381	+	1.24774i	0.0989519	+	0.171390i	0.911251	−	0.411851i	$-0.135118\pi$
$53$	0.720381	+	1.24774i	0.0989519	+	0.171390i	−0.812299	+	0.583241i	$0.801784\pi$
$54$	−4.66404	−	0.426055i	−0.634696	−	0.0579787i
$55$		0			0
$56$	−7.59543	−	0.303106i	−1.01498	−	0.0405042i
$57$	5.67086	+	7.19082i	0.751123	+	0.952447i
$58$	−2.39112	−	1.38051i	−0.313969	−	0.181270i
$59$	−1.60223	−	2.77514i	−0.208592	−	0.361293i	0.742679	−	0.669648i	$-0.233555\pi$
$59$	−1.60223	−	2.77514i	−0.208592	−	0.361293i	−0.951271	+	0.308355i	$0.900222\pi$
$60$		0			0
$61$	−11.3644	−	6.56124i	−1.45506	−	0.840080i	−0.456300	−	0.889826i	$-0.650825\pi$
$61$	−11.3644	−	6.56124i	−1.45506	−	0.840080i	−0.998762	+	0.0497461i	$0.984159\pi$
$62$			0.364081i			0.0462384i
$63$	5.53707	+	5.68691i	0.697605	+	0.716483i
$64$	5.43385			0.679231
$65$		0			0
$66$	3.64678	−	9.14545i	0.448887	−	1.12573i
$67$	2.68611	−	1.55082i	0.328160	−	0.189463i	−0.326864	−	0.945071i	$-0.605992\pi$
$67$	2.68611	−	1.55082i	0.328160	−	0.189463i	0.655024	+	0.755608i	$0.272659\pi$
$68$	3.88694	+	2.24412i	0.471360	+	0.272140i
$69$	9.21911	−	7.27042i	1.10985	−	0.875256i
$70$		0			0
$71$			2.21562i			0.262946i	0.991320	+	0.131473i	$0.0419707\pi$
$71$			2.21562i			0.262946i	−0.991320	+	0.131473i	$0.958029\pi$
$72$	−6.25430	−	5.93088i	−0.737077	−	0.698961i
$73$	−1.25932	−	2.18121i	−0.147393	−	0.255292i	0.782870	−	0.622185i	$-0.213755\pi$
$73$	−1.25932	−	2.18121i	−0.147393	−	0.255292i	−0.930263	+	0.366893i	$0.880421\pi$
$74$	1.04288	−	0.602109i	0.121233	−	0.0699938i
$75$		0			0
$76$			6.27919i			0.720272i
$77$	−14.7716	+	7.76013i	−1.68338	+	0.884349i
$78$	4.62362	−	3.64630i	0.523522	−	0.412862i
$79$	3.05960	−	5.29938i	0.344232	−	0.596227i	−0.640982	−	0.767556i	$-0.721473\pi$
$79$	3.05960	−	5.29938i	0.344232	−	0.596227i	0.985214	+	0.171329i	$0.0548061\pi$
$80$		0			0
$81$	0.477421	+	8.98733i	0.0530468	+	0.998592i
$82$	−2.94623	+	5.10301i	−0.325356	+	0.563534i
$83$			8.53654i			0.937007i	0.883462	+	0.468503i	$0.155207\pi$
$83$			8.53654i			0.937007i	−0.883462	+	0.468503i	$0.844793\pi$
$84$	0.566504	+	5.41270i	0.0618107	+	0.590574i
$85$		0			0
$86$	3.78240	+	2.18377i	0.407867	+	0.235482i
$87$	−1.96520	+	4.92836i	−0.210692	+	0.528376i
$88$	15.6921	−	9.05984i	1.67278	−	0.965782i
$89$	−0.590783	+	1.02327i	−0.0626229	+	0.108466i	−0.895637	−	0.444786i	$-0.853280\pi$
$89$	−0.590783	+	1.02327i	−0.0626229	+	0.108466i	0.833014	+	0.553252i	$0.186613\pi$
$90$		0			0
$91$	−9.97138	−	0.397921i	−1.04529	−	0.0417135i
$92$	8.05034			0.839306
$93$	0.692381	−	0.100516i	0.0717965	−	0.0104230i
$94$	−1.51490	+	0.874627i	−0.156250	+	0.0902109i
$95$		0			0
$96$	−1.38180	−	9.51816i	−0.141029	−	0.971443i
$97$	9.10556			0.924530			0.462265	−	0.886742i	$-0.347037\pi$
$97$	9.10556			0.924530			0.462265	+	0.886742i	$0.347037\pi$
$98$	−3.58004	+	5.19528i	−0.361639	+	0.524803i
$99$	−18.3989	−	4.41026i	−1.84916	−	0.443247i
$100$		0			0
$101$	−1.15241	−	1.99604i	−0.114669	−	0.198613i	0.802978	−	0.596008i	$-0.203247\pi$
$101$	−1.15241	−	1.99604i	−0.114669	−	0.198613i	−0.917647	+	0.397395i	$0.869914\pi$
$102$	−2.18532	+	5.48037i	−0.216379	+	0.542638i
$103$	3.89335	−	6.74347i	0.383623	−	0.664454i	−0.607954	−	0.793972i	$-0.708010\pi$
$103$	3.89335	−	6.74347i	0.383623	−	0.664454i	0.991577	+	0.129518i	$0.0413429\pi$
$104$	10.8368			1.06264
$105$		0			0
$106$	−1.29861			−0.126132
$107$	2.72952	−	4.72768i	0.263873	−	0.457042i	−0.703395	−	0.710800i	$-0.748333\pi$
$107$	2.72952	−	4.72768i	0.263873	−	0.457042i	0.967268	+	0.253758i	$0.0816666\pi$
$108$	−3.55884	+	5.04135i	−0.342450	+	0.485104i
$109$	−3.29331	−	5.70418i	−0.315442	−	0.546362i	0.664089	−	0.747653i	$-0.268819\pi$
$109$	−3.29331	−	5.70418i	−0.315442	−	0.546362i	−0.979531	+	0.201292i	$0.935486\pi$
$110$		0			0
$111$	−1.43296	−	1.81704i	−0.136011	−	0.172466i
$112$	0.303002	−	0.479575i	0.0286310	−	0.0453156i
$113$	−0.214344			−0.0201638			−0.0100819	−	0.999949i	$-0.503209\pi$
$113$	−0.214344			−0.0201638			−0.0100819	+	0.999949i	$0.503209\pi$
$114$	−8.16865	+	1.18588i	−0.765064	+	0.111068i
$115$		0			0
$116$	−3.15054	+	1.81897i	−0.292520	+	0.168887i
$117$	−8.21074	−	7.78615i	−0.759083	−	0.719829i
$118$	2.88828			0.265888
$119$	8.85184	−	4.65023i	0.811447	−	0.426286i
$120$		0			0
$121$	14.3872	−	24.9193i	1.30793	−	2.26539i
$122$	10.2431	−	5.91386i	0.927367	−	0.535415i
$123$	10.5179	+	4.19405i	0.948367	+	0.378165i
$124$	0.415445	+	0.239857i	0.0373081	+	0.0215398i
$125$		0			0
$126$	−6.93444	+	1.75921i	−0.617769	+	0.156723i
$127$		−	1.05320i		−	0.0934560i	−0.998908	−	0.0467280i	$-0.985121\pi$
$127$		−	1.05320i		−	0.0934560i	0.998908	−	0.0467280i	$-0.0148794\pi$
$128$	3.10407	−	5.37640i	0.274363	−	0.475211i
$129$	3.10867	−	7.79596i	0.273703	−	0.686396i
$130$		0			0
$131$	5.22860	−	9.05621i	0.456825	−	0.791245i	−0.541966	−	0.840401i	$-0.682320\pi$
$131$	5.22860	−	9.05621i	0.456825	−	0.791245i	0.998791	+	0.0491560i	$0.0156531\pi$
$132$	−8.03317	−	10.1863i	−0.699197	−	0.886603i
$133$	11.8262	+	7.47194i	1.02546	+	0.647899i
$134$			2.79562i			0.241505i
$135$		0			0
$136$	−9.40343	+	5.42907i	−0.806338	+	0.465539i
$137$	3.64697	+	6.31673i	0.311581	+	0.539675i	0.978705	−	0.205272i	$-0.0658080\pi$
$137$	3.64697	+	6.31673i	0.311581	+	0.539675i	−0.667124	+	0.744947i	$0.732475\pi$
$138$	1.52038	+	10.4728i	0.129423	+	0.891501i
$139$			10.8548i			0.920693i	0.887739	+	0.460347i	$0.152275\pi$
$139$			10.8548i			0.920693i	−0.887739	+	0.460347i	$0.847725\pi$
$140$		0			0
$141$	2.08153	+	2.63944i	0.175297	+	0.222281i
$142$	−1.72946	−	0.998507i	−0.145133	−	0.0837928i
$143$	20.6008	−	11.8939i	1.72273	−	0.994617i
$144$	0.616677	−	0.182907i	0.0513898	−	0.0152422i
$145$		0			0
$146$	2.27014			0.187878
$147$	10.8684	+	5.37391i	0.896407	+	0.443232i
$148$		−	1.58668i		−	0.130425i
$149$	2.54658	+	1.47027i	0.208624	+	0.120449i	0.600672	−	0.799496i	$-0.294900\pi$
$149$	2.54658	+	1.47027i	0.208624	+	0.120449i	−0.392048	+	0.919945i	$0.628233\pi$
$150$		0			0
$151$	−2.49298	−	4.31797i	−0.202876	−	0.351391i	0.746578	−	0.665298i	$-0.231695\pi$
$151$	−2.49298	−	4.31797i	−0.202876	−	0.351391i	−0.949454	+	0.313907i	$0.898362\pi$
$152$	−13.1557	−	7.59543i	−1.06707	−	0.616071i
$153$	11.0255	+	2.64283i	0.891356	+	0.213660i
$154$	0.599698	−	15.0276i	0.0483250	−	1.21096i
$155$		0			0
$156$	−1.11467	−	7.67810i	−0.0892447	−	0.614740i
$157$	−3.54960	−	6.14808i	−0.283289	−	0.490671i	0.688904	−	0.724853i	$-0.258092\pi$
$157$	−3.54960	−	6.14808i	−0.283289	−	0.490671i	−0.972193	+	0.234182i	$0.924759\pi$
$158$	2.75772	+	4.77650i	0.219392	+	0.379998i
$159$	0.358521	+	2.46958i	0.0284326	+	0.195851i
$160$		0			0
$161$	9.57953	−	15.1620i	0.754973	−	1.19493i
$162$	−7.23046	−	3.67762i	−0.568079	−	0.288941i
$163$	−15.3156	−	8.84246i	−1.19961	−	0.692595i	−0.239141	−	0.970985i	$-0.576866\pi$
$163$	−15.3156	−	8.84246i	−1.19961	−	0.692595i	−0.960468	+	0.278390i	$0.910199\pi$
$164$	3.88196	+	6.72375i	0.303130	+	0.525036i
$165$		0			0
$166$	−6.66343	−	3.84713i	−0.517182	−	0.298595i
$167$			10.9235i			0.845287i	0.906296	+	0.422643i	$0.138898\pi$
$167$			10.9235i			0.845287i	−0.906296	+	0.422643i	$0.861102\pi$
$168$	−12.0255	−	5.36041i	−0.927790	−	0.413565i
$169$	1.22669			0.0943611
$170$		0			0
$171$	4.51043	+	15.2071i	0.344921	+	1.16291i
$172$	4.98370	−	2.87734i	0.380004	−	0.219395i
$173$	−20.0145	−	11.5554i	−1.52167	−	0.878539i	−0.999672	−	0.0255936i	$-0.991852\pi$
$173$	−20.0145	−	11.5554i	−1.52167	−	0.878539i	−0.522001	−	0.852945i	$-0.674814\pi$
$174$	−2.96132	−	3.75504i	−0.224497	−	0.284669i
$175$		0			0
$176$			1.35222i			0.101927i
$177$	−0.797402	−	5.49270i	−0.0599364	−	0.412857i
$178$	−0.532492	−	0.922304i	−0.0399120	−	0.0691296i
$179$	15.2776	−	8.82051i	1.14190	−	0.659276i	0.194999	−	0.980803i	$-0.437530\pi$
$179$	15.2776	−	8.82051i	1.14190	−	0.659276i	0.946900	+	0.321527i	$0.104196\pi$
$180$		0			0
$181$			14.8545i			1.10413i	0.833802	+	0.552064i	$0.186160\pi$
$181$			14.8545i			1.10413i	−0.833802	+	0.552064i	$0.813840\pi$
$182$	4.80438	−	7.60411i	0.356124	−	0.563654i
$183$	−14.0744	−	17.8468i	−1.04041	−	1.31927i
$184$	−9.73785	+	16.8665i	−0.717884	+	1.24341i
$185$		0			0
$186$	−0.233572	+	0.585756i	−0.0171263	+	0.0429497i
$187$	−11.9173	+	20.6414i	−0.871481	+	1.50945i
$188$			2.30482i			0.168097i
$189$	5.25999	+	12.7017i	0.382608	+	0.923911i
$190$		0			0
$191$	16.1877	+	9.34599i	1.17130	+	0.676252i	0.953987	−	0.299850i	$-0.0969365\pi$
$191$	16.1877	+	9.34599i	1.17130	+	0.676252i	0.217316	+	0.976101i	$0.430270\pi$
$192$	8.74230	+	3.48602i	0.630921	+	0.251582i
$193$	−2.24781	+	1.29778i	−0.161801	+	0.0934160i	−0.578714	−	0.815530i	$-0.696445\pi$
$193$	−2.24781	+	1.29778i	−0.161801	+	0.0934160i	0.416913	+	0.908946i	$0.363112\pi$
$194$	−4.10357	+	7.10759i	−0.294619	+	0.510295i
$195$		0			0
$196$	3.56969	+	7.50776i	0.254978	+	0.536269i
$197$	−7.83600			−0.558292			−0.279146	−	0.960249i	$-0.590051\pi$
$197$	−7.83600			−0.558292			−0.279146	+	0.960249i	$0.590051\pi$
$198$	11.7343	−	12.3742i	0.833921	−	0.879396i
$199$	−3.06915	+	1.77198i	−0.217566	+	0.125612i	−0.604823	−	0.796360i	$-0.706756\pi$
$199$	−3.06915	+	1.77198i	−0.217566	+	0.125612i	0.387256	+	0.921972i	$0.373423\pi$
$200$		0			0
$201$	5.31648	−	0.771819i	0.374996	−	0.0544399i
$202$	2.07741			0.146166
$203$	−0.323169	+	8.09819i	−0.0226820	+	0.568382i
$204$	4.81384	+	6.10410i	0.337036	+	0.427372i
$205$		0			0
$206$	3.50920	+	6.07811i	0.244498	+	0.423482i
$207$	19.4965	−	5.78268i	1.35510	−	0.401924i
$208$	−0.404359	+	0.700371i	−0.0280373	+	0.0485620i
$209$	−33.3453			−2.30655
$210$		0			0
$211$	23.9742			1.65045			0.825225	−	0.564804i	$-0.191048\pi$
$211$	23.9742			1.65045			0.825225	+	0.564804i	$0.191048\pi$
$212$	−0.855523	+	1.48181i	−0.0587576	+	0.101771i
$213$	−1.42141	+	3.56463i	−0.0973931	+	0.244244i
$214$	2.46021	+	4.26121i	0.168177	+	0.291290i
$215$		0			0
$216$	−6.25741	−	13.5543i	−0.425763	−	0.922256i
$217$	0.946107	−	0.497028i	0.0642259	−	0.0337404i
$218$	5.93674			0.402087
$219$	−0.626744	−	4.31717i	−0.0423515	−	0.291727i
$220$		0			0
$221$	−12.3450	+	7.12736i	−0.830412	+	0.479438i
$222$	2.06413	−	0.299660i	0.138535	−	0.0201118i
$223$	−16.9380			−1.13425			−0.567125	−	0.823632i	$-0.691944\pi$
$223$	−16.9380			−1.13425			−0.567125	+	0.823632i	$0.691944\pi$
$224$	−6.83264	−	13.0061i	−0.456525	−	0.869009i
$225$		0			0
$226$	0.0965976	−	0.167312i	0.00642557	−	0.0111294i
$227$	−18.9635	+	10.9486i	−1.25865	+	0.726685i	−0.972813	−	0.231592i	$-0.925606\pi$
$227$	−18.9635	+	10.9486i	−1.25865	+	0.726685i	−0.285842	+	0.958277i	$0.592273\pi$
$228$	−4.02834	+	10.1023i	−0.266783	+	0.669043i
$229$	0.218276	+	0.126022i	0.0144241	+	0.00832775i	0.507195	−	0.861831i	$-0.330682\pi$
$229$	0.218276	+	0.126022i	0.0144241	+	0.00832775i	−0.492771	+	0.870159i	$0.664016\pi$
$230$		0			0
$231$	−28.7439	+	3.00840i	−1.89121	+	0.197938i
$232$		−	8.80103i		−	0.577816i
$233$	−7.47118	+	12.9405i	−0.489453	+	0.847758i	−0.999926	−	0.0121359i	$-0.996137\pi$
$233$	−7.47118	+	12.9405i	−0.489453	+	0.847758i	0.510473	+	0.859894i	$0.329470\pi$
$234$	9.77799	−	2.90016i	0.639207	−	0.189589i
$235$		0			0
$236$	1.90281	−	3.29576i	0.123862	−	0.214535i
$237$	8.32221	−	6.56311i	0.540586	−	0.426320i
$238$	−0.359366	+	9.00525i	−0.0232943	+	0.583723i
$239$		−	19.5021i		−	1.26149i	−0.775991	−	0.630744i	$-0.782750\pi$
$239$		−	19.5021i		−	1.26149i	0.775991	−	0.630744i	$-0.217250\pi$
$240$		0			0
$241$	8.54154	−	4.93146i	0.550209	−	0.317663i	−0.198997	−	0.980000i	$-0.563768\pi$
$241$	8.54154	−	4.93146i	0.550209	−	0.317663i	0.749206	+	0.662337i	$0.230435\pi$
$242$	12.9676	+	22.4606i	0.833592	+	1.44382i
$243$	−4.99761	+	14.7656i	−0.320597	+	0.947216i
$244$		−	15.5842i		−	0.997678i
$245$		0			0
$246$	−8.01384	+	6.31992i	−0.510944	+	0.402943i
$247$	−17.2709	−	9.97138i	−1.09892	−	0.634464i
$248$	−1.00506	+	0.580273i	−0.0638215	+	0.0368474i
$249$	−5.47651	+	13.7341i	−0.347060	+	0.870363i
$250$		0			0
$251$	−26.5460			−1.67557			−0.837784	−	0.546002i	$-0.816149\pi$
$251$	−26.5460			−1.67557			−0.837784	+	0.546002i	$0.816149\pi$
$252$	−2.56103	+	9.07170i	−0.161329	+	0.571464i
$253$			42.7510i			2.68773i
$254$	0.822100	+	0.474640i	0.0515832	+	0.0297815i
$255$		0			0
$256$	8.23165	+	14.2576i	0.514478	+	0.891102i
$257$	13.2758	+	7.66481i	0.828124	+	0.478117i	0.853210	−	0.521568i	$-0.174653\pi$
$257$	13.2758	+	7.66481i	0.828124	+	0.478117i	−0.0250861	+	0.999685i	$0.507986\pi$
$258$	4.68438	+	5.93993i	0.291637	+	0.369804i
$259$	−2.98835	−	1.88808i	−0.185687	−	0.117319i
$260$		0			0
$261$	−6.32347	+	6.66829i	−0.391413	+	0.412757i
$262$	4.71271	+	8.16266i	0.291152	+	0.504291i
$263$	−10.9949	−	19.0437i	−0.677972	−	1.17428i	−0.975591	−	0.219598i	$-0.929526\pi$
$263$	−10.9949	−	19.0437i	−0.677972	−	1.17428i	0.297618	−	0.954685i	$-0.403808\pi$
$264$	31.0586	−	4.50893i	1.91153	−	0.277505i
$265$		0			0
$266$	−11.1621	+	5.86389i	−0.684391	+	0.359538i
$267$	−1.60695	+	1.26728i	−0.0983438	+	0.0775564i
$268$	3.19002	+	1.84176i	0.194861	+	0.112503i
$269$	14.9395	+	25.8760i	0.910878	+	1.57769i	0.812826	+	0.582506i	$0.197928\pi$
$269$	14.9395	+	25.8760i	0.910878	+	1.57769i	0.0980517	+	0.995181i	$0.468739\pi$
$270$		0			0
$271$	−10.7412	−	6.20142i	−0.652480	−	0.376710i	0.136926	−	0.990581i	$-0.456278\pi$
$271$	−10.7412	−	6.20142i	−0.652480	−	0.376710i	−0.789406	+	0.613872i	$0.789611\pi$
$272$		−	0.810312i		−	0.0491324i
$273$	−15.7873	−	7.03722i	−0.955489	−	0.425912i
$274$	−6.57426			−0.397166
$275$		0			0
$276$	12.9519	+	5.16460i	0.779611	+	0.310872i
$277$	6.98725	−	4.03409i	0.419823	−	0.242385i	−0.275178	−	0.961393i	$-0.588737\pi$
$277$	6.98725	−	4.03409i	0.419823	−	0.242385i	0.695002	+	0.719008i	$0.255404\pi$
$278$	−8.47302	−	4.89190i	−0.508178	−	0.293397i
$279$	1.17843	+	0.282472i	0.0705507	+	0.0169112i
$280$		0			0
$281$			17.6732i			1.05430i	0.849773	+	0.527149i	$0.176739\pi$
$281$			17.6732i			1.05430i	−0.849773	+	0.527149i	$0.823261\pi$
$282$	−2.99837	+	0.435287i	−0.178550	+	0.0259210i
$283$	−11.8369	−	20.5021i	−0.703629	−	1.21872i	−0.967184	−	0.254077i	$-0.918228\pi$
$283$	−11.8369	−	20.5021i	−0.703629	−	1.21872i	0.263555	−	0.964644i	$-0.415105\pi$
$284$	−2.27875	+	1.31564i	−0.135219	+	0.0780686i
$285$		0			0
$286$			21.4407i			1.26781i
$287$	17.2828	+	0.689694i	1.02017	+	0.0407113i
$288$	3.88315	−	16.1999i	0.228817	−	0.954586i
$289$	−1.35859	+	2.35315i	−0.0799172	+	0.138421i
$290$		0			0
$291$	14.6496	+	5.84156i	0.858773	+	0.342439i
$292$	1.49557	−	2.59041i	0.0875217	−	0.151592i
$293$		−	2.70804i		−	0.158205i	−0.996866	−	0.0791026i	$-0.974795\pi$
$293$		−	2.70804i		−	0.158205i	0.996866	−	0.0791026i	$-0.0252055\pi$
$294$	−9.09275	+	6.06175i	−0.530300	+	0.353528i
$295$		0			0
$296$	3.32430	+	1.91928i	0.193221	+	0.111556i
$297$	−26.7719	−	18.8991i	−1.55346	−	1.09664i
$298$	−2.29532	+	1.32520i	−0.132964	+	0.0767670i
$299$	−12.7840	+	22.1425i	−0.739317	+	1.28053i
$300$		0			0
$301$	0.511207	−	12.8102i	0.0294655	−	0.738366i
$302$	4.49401			0.258601
$303$	−0.573536	−	3.95066i	−0.0329488	−	0.226959i
$304$	0.981769	−	0.566825i	0.0563083	−	0.0325096i
$305$		0			0
$306$	−7.03174	+	7.41519i	−0.401978	+	0.423898i
$307$	−5.49592			−0.313669			−0.156834	−	0.987625i	$-0.550129\pi$
$307$	−5.49592			−0.313669			−0.156834	+	0.987625i	$0.550129\pi$
$308$	−16.7526	−	10.5845i	−0.954569	−	0.603109i
$309$	10.5900	−	8.35157i	0.602446	−	0.475104i
$310$		0			0
$311$	−10.9235	−	18.9201i	−0.619416	−	1.07286i	−0.989593	−	0.143898i	$-0.954036\pi$
$311$	−10.9235	−	18.9201i	−0.619416	−	1.07286i	0.370177	−	0.928961i	$-0.379297\pi$
$312$	17.4349	+	6.95222i	0.987056	+	0.393592i
$313$	−12.2955	+	21.2964i	−0.694983	+	1.20375i	0.275203	+	0.961386i	$0.411255\pi$
$313$	−12.2955	+	21.2964i	−0.694983	+	1.20375i	−0.970186	+	0.242360i	$0.922079\pi$
$314$	6.39874			0.361102
$315$		0			0
$316$	7.26715			0.408809
$317$	11.9775	−	20.7457i	0.672726	−	1.16520i	−0.304402	−	0.952544i	$-0.598457\pi$
$317$	11.9775	−	20.7457i	0.672726	−	1.16520i	0.977128	−	0.212652i	$-0.0682101\pi$
$318$	−2.08927	−	0.833105i	−0.117161	−	0.0467182i
$319$	−9.65954	−	16.7308i	−0.540830	−	0.936746i
$320$		0			0
$321$	7.42441	−	5.85507i	0.414390	−	0.326798i
$322$	7.51791	+	14.3105i	0.418956	+	0.797496i
$323$	19.9821			1.11183
$324$	−8.95989	+	5.82769i	−0.497772	+	0.323761i
$325$		0			0
$326$	13.8044	−	7.97000i	0.764557	−	0.441417i
$327$	−1.63903	−	11.2900i	−0.0906383	−	0.624339i
$328$	−18.7828			−1.03711
$329$	4.34089	+	2.74263i	0.239321	+	0.151206i
$330$		0			0
$331$	−13.5511	+	23.4712i	−0.744837	+	1.29009i	0.205434	+	0.978671i	$0.434139\pi$
$331$	−13.5511	+	23.4712i	−0.744837	+	1.29009i	−0.950271	+	0.311424i	$0.899194\pi$
$332$	−8.77975	+	5.06899i	−0.481852	+	0.278197i
$333$	−1.13974	−	3.84267i	−0.0624572	−	0.210577i
$334$	−8.52664	−	4.92286i	−0.466557	−	0.269367i
$335$		0			0
$336$	0.795153	−	0.577181i	0.0433791	−	0.0314878i
$337$			3.19846i			0.174231i	0.996198	+	0.0871155i	$0.0277649\pi$
$337$			3.19846i			0.174231i	−0.996198	+	0.0871155i	$0.972235\pi$
$338$	−0.552830	+	0.957529i	−0.0300700	+	0.0520827i
$339$	−0.344849	−	0.137510i	−0.0187296	−	0.00746850i
$340$		0			0
$341$	−1.27375	+	2.20620i	−0.0689776	+	0.119473i
$342$	−13.9030	−	3.33258i	−0.751788	−	0.180205i
$343$	18.3878	+	2.21077i	0.992850	+	0.119370i
$344$			13.9220i			0.750622i
$345$		0			0
$346$	18.0397	−	10.4152i	0.969821	−	0.559926i
$347$	−16.3140	−	28.2567i	−0.875783	−	1.51690i	−0.855927	−	0.517097i	$-0.827012\pi$
$347$	−16.3140	−	28.2567i	−0.875783	−	1.51690i	−0.0198563	−	0.999803i	$-0.506321\pi$
$348$	−6.23571	+	0.905269i	−0.334269	+	0.0485275i
$349$			32.4849i			1.73888i	0.494041	+	0.869439i	$0.335519\pi$
$349$			32.4849i			1.73888i	−0.494041	+	0.869439i	$0.664481\pi$
$350$		0			0
$351$	−8.21481	−	17.7943i	−0.438474	−	0.949790i
$352$	30.3287	+	17.5103i	1.61653	+	0.933301i
$353$	−5.77784	+	3.33584i	−0.307523	+	0.177549i	−0.645818	−	0.763492i	$-0.723483\pi$
$353$	−5.77784	+	3.33584i	−0.307523	+	0.177549i	0.338294	+	0.941040i	$0.390150\pi$
$354$	4.64684	+	1.85294i	0.246977	+	0.0984828i
$355$		0			0
$356$	−1.40323			−0.0743709
$357$	17.2247	−	1.80277i	0.911626	−	0.0954127i
$358$			15.9004i			0.840364i
$359$	−14.0322	−	8.10148i	−0.740590	−	0.427580i	0.0816940	−	0.996657i	$-0.473967\pi$
$359$	−14.0322	−	8.10148i	−0.740590	−	0.427580i	−0.822284	+	0.569078i	$0.807300\pi$
$360$		0			0
$361$	4.47774	+	7.75567i	0.235671	+	0.408193i
$362$	−11.5951	−	6.69443i	−0.609425	−	0.351852i
$363$	39.1337	−	30.8618i	2.05398	−	1.61982i
$364$	−5.51175	−	10.4918i	−0.288894	−	0.549918i
$365$		0			0
$366$	20.2737	−	2.94323i	1.05972	−	0.153845i
$367$	8.60716	+	14.9080i	0.449290	+	0.778193i	0.998340	−	0.0575965i	$-0.0183437\pi$
$367$	8.60716	+	14.9080i	0.449290	+	0.778193i	−0.549050	+	0.835789i	$0.685010\pi$
$368$	−0.726708	−	1.25869i	−0.0378823	−	0.0656140i
$369$	14.2312	+	13.4953i	0.740846	+	0.702535i
$370$		0			0
$371$	1.77280	+	3.37457i	0.0920391	+	0.175199i
$372$	0.514515	+	0.652421i	0.0266764	+	0.0338264i
$373$	−10.6793	−	6.16568i	−0.552952	−	0.319247i	0.197360	−	0.980331i	$-0.436763\pi$
$373$	−10.6793	−	6.16568i	−0.552952	−	0.319247i	−0.750312	+	0.661084i	$0.770097\pi$
$374$	−10.7415	−	18.6048i	−0.555428	−	0.962030i
$375$		0			0
$376$	−4.82889	−	2.78796i	−0.249031	−	0.143778i
$377$		−	11.5541i		−	0.595067i
$378$	−12.2851	−	1.61839i	−0.631879	−	0.0832408i
$379$	3.57576			0.183675			0.0918373	−	0.995774i	$-0.470726\pi$
$379$	3.57576			0.183675			0.0918373	+	0.995774i	$0.470726\pi$
$380$		0			0
$381$	0.675665	−	1.69444i	0.0346154	−	0.0868090i
$382$	−14.5905	+	8.42384i	−0.746516	+	0.431001i
$383$	20.0319	+	11.5654i	1.02358	+	0.590965i	0.915139	−	0.403138i	$-0.132081\pi$
$383$	20.0319	+	11.5654i	1.02358	+	0.590965i	0.108442	+	0.994103i	$0.465414\pi$
$384$	8.44317	−	6.65850i	0.430864	−	0.339790i
$385$		0			0
$386$		−	2.33946i		−	0.119075i
$387$	10.0028	−	10.5483i	0.508471	−	0.536199i
$388$	5.40688	+	9.36499i	0.274493	+	0.475435i
$389$	14.7169	−	8.49679i	0.746175	−	0.430804i	−0.0781352	−	0.996943i	$-0.524897\pi$
$389$	14.7169	−	8.49679i	0.746175	−	0.430804i	0.824310	+	0.566138i	$0.191563\pi$
$390$		0			0
$391$		−	25.6184i		−	1.29558i
$392$	−20.0477	−	1.60261i	−1.01256	−	0.0809440i
$393$	14.2220	−	11.2158i	0.717405	−	0.565763i
$394$	3.53142	−	6.11660i	0.177910	−	0.308150i
$395$		0			0
$396$	−6.38934	−	21.5419i	−0.321076	−	1.08252i
$397$	−10.8448	+	18.7837i	−0.544283	+	0.942726i	0.454368	+	0.890814i	$0.349865\pi$
$397$	−10.8448	+	18.7837i	−0.544283	+	0.942726i	−0.998652	+	0.0519125i	$0.983468\pi$
$398$		−	3.19428i		−	0.160115i
$399$	14.2331	+	19.6082i	0.712548	+	0.981640i
$400$		0			0
$401$	0.425230	+	0.245507i	0.0212350	+	0.0122600i	0.510580	−	0.859830i	$-0.329431\pi$
$401$	0.425230	+	0.245507i	0.0212350	+	0.0122600i	−0.489345	+	0.872090i	$0.662764\pi$
$402$	−1.79349	+	4.49776i	−0.0894514	+	0.224328i
$403$	−1.31946	+	0.761790i	−0.0657270	+	0.0379475i
$404$	1.36860	−	2.37049i	0.0680906	−	0.117936i
$405$		0			0
$406$	−6.17562	−	3.90184i	−0.306491	−	0.193645i
$407$	8.42601			0.417662
$408$	−18.6118	+	2.70196i	−0.921419	+	0.133767i
$409$	−24.2867	+	14.0219i	−1.20090	+	0.693339i	−0.960755	−	0.277399i	$-0.910528\pi$
$409$	−24.2867	+	14.0219i	−1.20090	+	0.693339i	−0.240143	+	0.970738i	$0.577194\pi$
$410$		0			0
$411$	1.81503	+	12.5024i	0.0895290	+	0.616698i
$412$	9.24747			0.455590
$413$	−3.94295	−	7.50553i	−0.194020	−	0.369323i
$414$	−4.27260	+	17.8246i	−0.209987	+	0.876031i
$415$		0			0
$416$	10.4723	+	18.1386i	0.513448	+	0.889319i
$417$	−6.96378	+	17.4639i	−0.341018	+	0.855210i
$418$	15.0276	−	26.0286i	0.735025	−	1.27310i
$419$	−3.44153			−0.168130			−0.0840649	−	0.996460i	$-0.526790\pi$
$419$	−3.44153			−0.168130			−0.0840649	+	0.996460i	$0.526790\pi$
$420$		0			0
$421$	18.7964			0.916078			0.458039	−	0.888932i	$-0.348552\pi$
$421$	18.7964			0.916078			0.458039	+	0.888932i	$0.348552\pi$
$422$	−10.8044	+	18.7137i	−0.525948	+	0.910968i
$423$	1.65559	+	5.58188i	0.0804975	+	0.271400i
$424$	−2.06972	−	3.58485i	−0.100514	−	0.174096i
$425$		0			0
$426$	−2.14188	−	2.71597i	−0.103775	−	0.131589i
$427$	−29.3512	−	18.5445i	−1.42041	−	0.897432i
$428$	6.48316			0.313375
$429$	40.7742	−	5.91938i	1.96860	−	0.285791i
$430$		0			0
$431$	5.95390	−	3.43749i	0.286789	−	0.165578i	−0.349704	−	0.936860i	$-0.613718\pi$
$431$	5.95390	−	3.43749i	0.286789	−	0.165578i	0.636493	+	0.771282i	$0.280384\pi$
$432$	1.10949	+	0.101350i	0.0533803	+	0.00487622i
$433$	15.2776			0.734193			0.367096	−	0.930183i	$-0.380352\pi$
$433$	15.2776			0.734193			0.367096	+	0.930183i	$0.380352\pi$
$434$	−0.0384100	+	0.962503i	−0.00184374	+	0.0462016i
$435$		0			0
$436$	3.91113	−	6.77428i	0.187309	−	0.324429i
$437$	31.0391	−	17.9204i	1.48480	−	0.857249i
$438$	3.65234	+	1.45638i	0.174515	+	0.0695886i
$439$	−33.3367	−	19.2469i	−1.59107	−	0.918606i	−0.993124	−	0.117071i	$-0.962650\pi$
$439$	−33.3367	−	19.2469i	−1.59107	−	0.918606i	−0.597948	−	0.801535i	$-0.704017\pi$
$440$		0			0
$441$	14.0381	+	15.6183i	0.668480	+	0.743730i
$442$		−	12.8483i		−	0.611129i
$443$	−1.92829	+	3.33990i	−0.0916158	+	0.158683i	−0.908191	−	0.418556i	$-0.862536\pi$
$443$	−1.92829	+	3.33990i	−0.0916158	+	0.158683i	0.816575	+	0.577239i	$0.195870\pi$
$444$	1.01792	−	2.55275i	0.0483082	−	0.121148i
$445$		0			0
$446$	7.63337	−	13.2214i	0.361450	−	0.626050i
$447$	3.15386	+	3.99919i	0.149172	+	0.189155i
$448$	14.3652	+	0.573262i	0.678691	+	0.0270841i
$449$		−	2.52159i		−	0.119001i	−0.998228	−	0.0595005i	$-0.981049\pi$
$449$		−	2.52159i		−	0.119001i	0.998228	−	0.0595005i	$-0.0189508\pi$
$450$		0			0
$451$	−35.7062	+	20.6150i	−1.68134	+	0.970721i
$452$	−0.127277	−	0.220451i	−0.00598662	−	0.0103691i
$453$	−1.24071	−	8.54635i	−0.0582938	−	0.401542i
$454$		−	19.7367i		−	0.926288i
$455$		0			0
$456$	−16.2929	−	20.6598i	−0.762984	−	0.967486i
$457$	−8.05795	−	4.65226i	−0.376935	−	0.217623i	0.299549	−	0.954081i	$-0.403164\pi$
$457$	−8.05795	−	4.65226i	−0.376935	−	0.217623i	−0.676484	+	0.736457i	$0.736497\pi$
$458$	−0.196739	+	0.113588i	−0.00919303	+	0.00530760i
$459$	16.0429	+	11.3252i	0.748820	+	0.528615i
$460$		0			0
$461$	−11.3898			−0.530477			−0.265238	−	0.964183i	$-0.585451\pi$
$461$	−11.3898			−0.530477			−0.265238	+	0.964183i	$0.585451\pi$
$462$	10.6056	−	23.7926i	0.493418	−	1.10693i
$463$		−	0.322319i		−	0.0149795i	−0.999972	−	0.00748973i	$-0.997616\pi$
$463$		−	0.322319i		−	0.0149795i	0.999972	−	0.00748973i	$-0.00238408\pi$
$464$	0.568801	+	0.328398i	0.0264059	+	0.0152455i
$465$		0			0
$466$	−6.73402	−	11.6637i	−0.311947	−	0.540309i
$467$	−20.1915	−	11.6576i	−0.934353	−	0.539449i	−0.0461675	−	0.998934i	$-0.514701\pi$
$467$	−20.1915	−	11.6576i	−0.934353	−	0.539449i	−0.888186	+	0.459485i	$0.848034\pi$
$468$	3.13245	−	13.0681i	0.144798	−	0.604072i
$469$	7.26473	−	3.81645i	0.335454	−	0.176227i
$470$		0			0
$471$	−1.76657	−	12.1686i	−0.0813995	−	0.560700i
$472$	4.60334	+	7.97323i	0.211886	+	0.366997i
$473$	15.2800	+	26.4657i	0.702575	+	1.21690i
$474$	1.37247	+	9.45390i	0.0630396	+	0.434232i
$475$		0			0
$476$	10.0389	+	6.34274i	0.460134	+	0.290719i
$477$	−1.00752	+	4.20322i	−0.0461312	+	0.192452i
$478$	15.2229	+	8.78895i	0.696280	+	0.401997i
$479$	0.316556	+	0.548292i	0.0144638	+	0.0250521i	0.873167	−	0.487422i	$-0.162063\pi$
$479$	0.316556	+	0.548292i	0.0144638	+	0.0250521i	−0.858703	+	0.512474i	$0.828729\pi$
$480$		0			0
$481$	4.36418	+	2.51966i	0.198990	+	0.114887i
$482$			8.88978i			0.404918i
$483$	25.1391	−	18.2478i	1.14387	−	0.830305i
$484$	34.1724			1.55329
$485$		0			0
$486$	−9.27346	−	10.5554i	−0.420653	−	0.478802i
$487$	−18.7500	+	10.8253i	−0.849642	+	0.490541i	−0.860530	−	0.509400i	$-0.829868\pi$
$487$	−18.7500	+	10.8253i	−0.849642	+	0.490541i	0.0108880	+	0.999941i	$0.496534\pi$
$488$	32.6509	+	18.8510i	1.47804	+	0.853345i
$489$	−18.9679	−	24.0518i	−0.857756	−	1.08766i
$490$		0			0
$491$		−	36.1608i		−	1.63191i	−0.578112	−	0.815957i	$-0.696211\pi$
$491$		−	36.1608i		−	1.63191i	0.578112	−	0.815957i	$-0.303789\pi$
$492$	1.93198	+	13.3080i	0.0871006	+	0.599970i
$493$	5.78844	+	10.0259i	0.260698	+	0.451543i
$494$	15.5669	−	8.98754i	0.700387	−	0.404368i
$495$		0			0
$496$		−	0.0866082i		−	0.00388882i
$497$	−0.233744	+	5.85732i	−0.0104849	+	0.262737i
$498$	−8.25244	−	10.4643i	−0.369801	−	0.468918i
$499$	−4.50676	+	7.80593i	−0.201750	+	0.349442i	−0.949092	−	0.314998i	$-0.897996\pi$
$499$	−4.50676	+	7.80593i	−0.201750	+	0.349442i	0.747342	+	0.664439i	$0.231330\pi$
$500$		0			0
$501$	−7.00785	+	17.5744i	−0.313088	+	0.785166i
$502$	11.9634	−	20.7212i	0.533952	−	0.924832i
$503$			18.9044i			0.842907i	0.906850	+	0.421453i	$0.138480\pi$
$503$			18.9044i			0.842907i	−0.906850	+	0.421453i	$0.861520\pi$
$504$	−15.9085	−	16.3390i	−0.708620	−	0.727796i
$505$		0			0
$506$	−33.3704	−	19.2664i	−1.48350	−	0.856497i
$507$	1.97358	+	0.786971i	0.0876497	+	0.0349506i
$508$	1.08320	−	0.625387i	0.0480593	−	0.0277471i
$509$	19.6636	−	34.0584i	0.871574	−	1.50961i	0.0112055	−	0.999937i	$-0.496433\pi$
$509$	19.6636	−	34.0584i	0.871574	−	1.50961i	0.860368	−	0.509673i	$-0.170234\pi$
$510$		0			0
$511$	−3.09909	−	5.89921i	−0.137096	−	0.260966i
$512$	−2.42264			−0.107067
$513$	−2.49927	+	27.3597i	−0.110346	+	1.20796i
$514$	−11.9659	+	6.90854i	−0.527795	+	0.304723i
$515$		0			0
$516$	9.86400	−	1.43200i	0.434238	−	0.0630405i
$517$	−12.2397			−0.538300
$518$	2.82054	−	1.48174i	0.123927	−	0.0651040i
$519$	−24.7873	−	31.4310i	−1.08804	−	1.37967i
$520$		0			0
$521$	8.61869	+	14.9280i	0.377592	+	0.654008i	0.990711	−	0.135982i	$-0.0434190\pi$
$521$	8.61869	+	14.9280i	0.377592	+	0.654008i	−0.613120	+	0.789990i	$0.710086\pi$
$522$	−2.35534	−	7.94113i	−0.103091	−	0.347574i
$523$	18.8880	−	32.7149i	0.825914	−	1.43052i	−0.0753051	−	0.997161i	$-0.523993\pi$
$523$	18.8880	−	32.7149i	0.825914	−	1.43052i	0.901219	−	0.433364i	$-0.142674\pi$
$524$	12.4190			0.542525
$525$		0			0
$526$	19.8201			0.864196
$527$	0.763291	−	1.32206i	0.0332495	−	0.0575898i
$528$	−0.867500	+	2.17553i	−0.0377531	+	0.0946778i
$529$	−11.4752	−	19.8756i	−0.498920	−	0.864156i
$530$		0			0
$531$	2.24087	−	9.34855i	0.0972455	−	0.405693i
$532$	−0.662443	+	16.6000i	−0.0287206	+	0.719699i
$533$	−24.6583			−1.06807
$534$	−0.265012	−	1.82547i	−0.0114682	−	0.0789959i
$535$		0			0
$536$	−7.71742	+	4.45565i	−0.333342	+	0.192455i
$537$	30.2382	−	4.38982i	1.30487	−	0.189435i
$538$	−26.9309			−1.16108
$539$	−39.8697	+	18.9567i	−1.71731	+	0.816521i
$540$		0			0
$541$	−9.89533	+	17.1392i	−0.425433	+	0.736872i	−0.996461	−	0.0840587i	$-0.973212\pi$
$541$	−9.89533	+	17.1392i	−0.425433	+	0.736872i	0.571027	+	0.820931i	$0.306545\pi$
$542$	9.68138	−	5.58955i	0.415851	−	0.240092i
$543$	−9.52974	+	23.8988i	−0.408960	+	1.02560i
$544$	−18.1744	−	10.4930i	−0.779219	−	0.449882i
$545$		0			0
$546$	12.6079	−	9.15175i	0.539568	−	0.391659i
$547$			8.91454i			0.381158i	0.981672	+	0.190579i	$0.0610365\pi$
$547$			8.91454i			0.381158i	−0.981672	+	0.190579i	$0.938963\pi$
$548$	−4.33113	+	7.50174i	−0.185017	+	0.320459i
$549$	−11.1944	−	37.7423i	−0.477765	−	1.61080i
$550$		0			0
$551$	−8.09819	+	14.0265i	−0.344995	+	0.597548i
$552$	−26.4873	+	20.8886i	−1.12737	+	0.889076i
$553$	8.64757	−	13.6869i	0.367732	−	0.582026i
$554$			7.27212i			0.308963i
$555$		0			0
$556$	−11.1641	+	6.44558i	−0.473462	+	0.273354i
$557$	−10.4847	−	18.1599i	−0.444249	−	0.769462i	0.553751	−	0.832683i	$-0.313196\pi$
$557$	−10.4847	−	18.1599i	−0.444249	−	0.769462i	−0.998000	+	0.0632208i	$0.979863\pi$
$558$	−0.751569	+	0.792554i	−0.0318165	+	0.0335515i
$559$			18.2769i			0.773032i
$560$		0			0
$561$	−32.4155	+	25.5637i	−1.36859	+	1.07930i
$562$	−13.7953	−	7.96474i	−0.581921	−	0.335972i
$563$	−15.6638	+	9.04347i	−0.660148	+	0.381137i	−0.792333	−	0.610088i	$-0.791134\pi$
$563$	−15.6638	+	9.04347i	−0.660148	+	0.381137i	0.132185	+	0.991225i	$0.457801\pi$
$564$	−1.47863	+	3.70814i	−0.0622616	+	0.156141i
$565$		0			0
$566$	21.3379			0.896900
$567$	0.313985	+	23.8097i	0.0131861	+	0.999913i
$568$		−	6.36568i		−	0.267098i
$569$	22.0888	+	12.7530i	0.926010	+	0.534632i	0.885547	−	0.464549i	$-0.153784\pi$
$569$	22.0888	+	12.7530i	0.926010	+	0.534632i	0.0404626	+	0.999181i	$0.487117\pi$
$570$		0			0
$571$	−19.8853	−	34.4424i	−0.832175	−	1.44137i	−0.896310	−	0.443428i	$-0.853762\pi$
$571$	−19.8853	−	34.4424i	−0.832175	−	1.44137i	0.0641352	−	0.997941i	$-0.479571\pi$
$572$	24.4655	+	14.1252i	1.02295	+	0.590603i
$573$	20.0480	+	25.4214i	0.837516	+	1.06199i
$574$	−8.32714	+	13.1797i	−0.347568	+	0.550112i
$575$		0			0
$576$	11.8287	+	11.2170i	0.492863	+	0.467377i
$577$	0.997811	+	1.72826i	0.0415394	+	0.0719484i	0.886048	−	0.463594i	$-0.153440\pi$
$577$	0.997811	+	1.72826i	0.0415394	+	0.0719484i	−0.844508	+	0.535543i	$0.820107\pi$
$578$	−1.22454	−	2.12097i	−0.0509343	−	0.0882208i
$579$	−4.44899	+	0.645881i	−0.184894	+	0.0268419i
$580$		0			0
$581$	−0.900590	+	22.5676i	−0.0373628	+	0.936262i
$582$	−11.1619	+	8.80252i	−0.462674	+	0.364876i
$583$	−7.86909	−	4.54322i	−0.325904	−	0.188161i
$584$	3.61815	+	6.26682i	0.149720	+	0.259323i
$585$		0			0
$586$	2.11383	+	1.22042i	0.0873216	+	0.0504152i
$587$			27.4257i			1.13198i	0.824413	+	0.565989i	$0.191506\pi$
$587$			27.4257i			1.13198i	−0.824413	+	0.565989i	$0.808494\pi$
$588$	0.926607	+	14.3690i	0.0382126	+	0.592569i
$589$	2.13573			0.0880013
$590$		0			0
$591$	−12.6070	−	5.02709i	−0.518583	−	0.206787i
$592$	−0.248083	+	0.143231i	−0.0101961	+	0.00588674i
$593$	1.05094	+	0.606763i	0.0431571	+	0.0249168i	0.521423	−	0.853298i	$-0.325401\pi$
$593$	1.05094	+	0.606763i	0.0431571	+	0.0249168i	−0.478266	+	0.878215i	$0.658735\pi$
$594$	26.8174	−	12.3803i	1.10033	−	0.507971i
$595$		0			0
$596$			3.49218i			0.143045i
$597$	−6.07463	+	0.881883i	−0.248618	+	0.0360930i
$598$	−11.5226	−	19.9578i	−0.471195	−	0.816134i
$599$	−32.9617	+	19.0304i	−1.34678	+	0.777563i	−0.987792	−	0.155780i	$-0.950211\pi$
$599$	−32.9617	+	19.0304i	−1.34678	+	0.777563i	−0.358986	+	0.933343i	$0.616878\pi$
$600$		0			0
$601$			8.32414i			0.339549i	0.985483	+	0.169774i	$0.0543039\pi$
$601$			8.32414i			0.339549i	−0.985483	+	0.169774i	$0.945696\pi$
$602$	9.76894	+	6.17215i	0.398152	+	0.251558i
$603$	9.04862	+	2.16898i	0.368488	+	0.0883275i
$604$	2.96066	−	5.12802i	0.120468	−	0.208656i
$605$		0			0
$606$	3.34227	+	1.33274i	0.135770	+	0.0541388i
$607$	15.1263	−	26.1996i	0.613959	−	1.06341i	−0.376607	−	0.926373i	$-0.622909\pi$
$607$	15.1263	−	26.1996i	0.613959	−	1.06341i	0.990566	−	0.137036i	$-0.0437575\pi$
$608$		−	29.3599i		−	1.19070i
$609$	−5.71523	+	12.8215i	−0.231593	+	0.519555i
$610$		0			0
$611$	−6.33943	−	3.66007i	−0.256466	−	0.148071i
$612$	3.82879	+	12.9089i	0.154770	+	0.521811i
$613$	−2.45694	+	1.41851i	−0.0992349	+	0.0572933i	−0.548796	−	0.835956i	$-0.684914\pi$
$613$	−2.45694	+	1.41851i	−0.0992349	+	0.0572933i	0.449561	+	0.893249i	$0.351580\pi$
$614$	2.47683	−	4.28999i	0.0999566	−	0.173130i
$615$		0			0
$616$	42.4402	−	22.2955i	1.70996	−	0.898313i
$617$	−23.3983			−0.941979			−0.470990	−	0.882139i	$-0.656103\pi$
$617$	−23.3983			−0.941979			−0.470990	+	0.882139i	$0.656103\pi$
$618$	1.74647	+	12.0301i	0.0702533	+	0.483922i
$619$	34.7980	−	20.0907i	1.39865	−	0.807511i	0.404400	−	0.914582i	$-0.367481\pi$
$619$	34.7980	−	20.0907i	1.39865	−	0.807511i	0.994251	+	0.107071i	$0.0341472\pi$
$620$		0			0
$621$	35.0769	+	3.20424i	1.40759	+	0.128582i
$622$	19.6914			0.789555
$623$	−1.66978	+	2.64283i	−0.0668981	+	0.105883i
$624$	−1.09987	+	0.867386i	−0.0440301	+	0.0347232i
$625$		0			0
$626$	−11.0823	−	19.1952i	−0.442939	−	0.767194i
$627$	−53.6480	−	21.3923i	−2.14249	−	0.854326i
$628$	4.21550	−	7.30146i	0.168217	−	0.291360i
$629$	−5.04925			−0.201327
$630$		0			0
$631$	−22.9329			−0.912945			−0.456473	−	0.889737i	$-0.650887\pi$
$631$	−22.9329			−0.912945			−0.456473	+	0.889737i	$0.650887\pi$
$632$	−8.79049	+	15.2256i	−0.349667	+	0.605641i
$633$	38.5711	+	15.3803i	1.53306	+	0.611314i
$634$	10.7958	+	18.6988i	0.428754	+	0.742624i
$635$		0			0
$636$	−2.32705	+	1.83517i	−0.0922737	+	0.0727694i
$637$	−26.3188	−	2.10393i	−1.04279	−	0.0833607i
$638$	17.4129			0.689384
$639$	−4.57369	+	4.82310i	−0.180932	+	0.190799i
$640$		0			0
$641$	1.70493	−	0.984339i	0.0673405	−	0.0388791i	−0.465952	−	0.884810i	$-0.654288\pi$
$641$	1.70493	−	0.984339i	0.0673405	−	0.0388791i	0.533292	+	0.845931i	$0.320955\pi$
$642$	1.22441	+	8.43401i	0.0483234	+	0.332864i
$643$	−18.9036			−0.745483			−0.372742	−	0.927935i	$-0.621582\pi$
$643$	−18.9036			−0.745483			−0.372742	+	0.927935i	$0.621582\pi$
$644$	21.2823	+	0.849297i	0.838638	+	0.0334670i
$645$		0			0
$646$	−9.00525	+	15.5975i	−0.354307	+	0.613677i
$647$	−5.77380	+	3.33350i	−0.226991	+	0.131054i	−0.609183	−	0.793029i	$-0.708503\pi$
$647$	−5.77380	+	3.33350i	−0.226991	+	0.131054i	0.382192	+	0.924083i	$0.375169\pi$
$648$	−1.37167	−	25.8214i	−0.0538844	−	1.01436i
$649$	17.5020	+	10.1048i	0.687012	+	0.396647i
$650$		0			0
$651$	1.84101	−	0.192684i	0.0721551	−	0.00755190i
$652$		−	21.0026i		−	0.822525i
$653$	16.9206	−	29.3074i	0.662156	−	1.14689i	−0.317892	−	0.948127i	$-0.602975\pi$
$653$	16.9206	−	29.3074i	0.662156	−	1.14689i	0.980048	−	0.198761i	$-0.0636917\pi$
$654$	9.55138	+	3.80864i	0.373488	+	0.148930i
$655$		0			0
$656$	0.700852	−	1.21391i	0.0273637	−	0.0473953i
$657$	1.76129	−	7.34780i	0.0687143	−	0.286665i
$658$	−4.09713	+	2.15239i	−0.159723	+	0.0839088i
$659$		−	22.0797i		−	0.860101i	−0.902805	−	0.430051i	$-0.858496\pi$
$659$		−	22.0797i		−	0.860101i	0.902805	−	0.430051i	$-0.141504\pi$
$660$		0			0
$661$	27.1770	−	15.6907i	1.05706	−	0.610296i	0.132445	−	0.991190i	$-0.457717\pi$
$661$	27.1770	−	15.6907i	1.05706	−	0.610296i	0.924619	+	0.380894i	$0.124384\pi$
$662$	−12.2141	−	21.1554i	−0.474713	−	0.822227i
$663$	−24.4338	+	3.54717i	−0.948929	+	0.137761i
$664$		−	24.5262i		−	0.951802i
$665$		0			0
$666$	3.51314	+	0.842108i	0.136131	+	0.0326310i
$667$	17.9829	+	10.3824i	0.696301	+	0.402009i
$668$	−11.2347	+	6.48638i	−0.434685	+	0.250965i
$669$	−27.2508	−	10.8663i	−1.05358	−	0.420117i
$670$		0			0
$671$	82.7594			3.19489
$672$	−2.64883	−	25.3084i	−0.102181	−	0.976294i
$673$			40.5686i			1.56380i	0.623401	+	0.781902i	$0.285751\pi$
$673$			40.5686i			1.56380i	−0.623401	+	0.781902i	$0.714249\pi$
$674$	−2.49664	−	1.44144i	−0.0961671	−	0.0555221i
$675$		0			0
$676$	0.728410	+	1.26164i	0.0280158	+	0.0485248i
$677$	34.4733	+	19.9031i	1.32491	+	0.764940i	0.984508	−	0.175338i	$-0.0561019\pi$
$677$	34.4733	+	19.9031i	1.32491	+	0.764940i	0.340407	+	0.940278i	$0.389435\pi$
$678$	0.262749	−	0.207210i	0.0100908	−	0.00795786i
$679$	24.0719	+	0.960621i	0.923794	+	0.0368653i
$680$		0			0
$681$	−37.5336	+	5.44894i	−1.43829	+	0.208804i
$682$	−1.14808	−	1.98852i	−0.0439621	−	0.0761445i
$683$	−11.4962	−	19.9121i	−0.439892	−	0.761915i	0.557789	−	0.829983i	$-0.311650\pi$
$683$	−11.4962	−	19.9121i	−0.439892	−	0.761915i	−0.997681	+	0.0680680i	$0.978317\pi$
$684$	−12.9621	+	13.6689i	−0.495617	+	0.522643i
$685$		0			0
$686$	−10.0125	+	13.3568i	−0.382277	+	0.509965i
$687$	0.270328	+	0.342784i	0.0103137	+	0.0130780i
$688$	−0.899762	−	0.519478i	−0.0343031	−	0.0198049i
$689$	−2.71715	−	4.70625i	−0.103515	−	0.179294i
$690$		0			0
$691$	20.7325	+	11.9699i	0.788702	+	0.455358i	0.839506	−	0.543351i	$-0.182845\pi$
$691$	20.7325	+	11.9699i	0.788702	+	0.455358i	−0.0508031	+	0.998709i	$0.516178\pi$
$692$		−	27.4463i		−	1.04335i
$693$	−48.1749	−	13.6002i	−1.83001	−	0.516629i
$694$	29.4087			1.11634
$695$		0			0
$696$	5.64620	−	14.1596i	0.214019	−	0.536719i
$697$	21.3968	−	12.3534i	0.810461	−	0.467920i
$698$	−25.3570	−	14.6399i	−0.959776	−	0.554127i
$699$	−20.3219	+	16.0263i	−0.768644	+	0.606172i
$700$		0			0
$701$		−	7.70996i		−	0.291201i	−0.989343	−	0.145601i	$-0.953489\pi$
$701$		−	7.70996i		−	0.291201i	0.989343	−	0.145601i	$-0.0465115\pi$
$702$	17.5920	+	1.60700i	0.663966	+	0.0606525i
$703$	−3.53202	−	6.11765i	−0.133213	−	0.230731i
$704$	−29.6784	+	17.1348i	−1.11855	+	0.645793i
$705$		0			0
$706$		−	6.01340i		−	0.226317i
$707$	−2.83599	−	5.39839i	−0.106658	−	0.203027i
$708$	5.17570	−	4.08169i	0.194515	−	0.153399i
$709$	−1.62353	+	2.81203i	−0.0609729	+	0.105608i	−0.894901	−	0.446266i	$-0.852754\pi$
$709$	−1.62353	+	2.81203i	−0.0609729	+	0.105608i	0.833928	+	0.551874i	$0.186087\pi$
$710$		0			0
$711$	17.5998	−	5.22010i	0.660042	−	0.195769i
$712$	1.69737	−	2.93993i	0.0636117	−	0.110179i
$713$		−	2.73815i		−	0.102545i
$714$	−6.35538	+	14.2576i	−0.237844	+	0.533578i
$715$		0			0
$716$	18.1436	+	10.4752i	0.678060	+	0.391478i
$717$	12.5114	−	31.3762i	0.467245	−	1.17176i
$718$	12.6477	−	7.30213i	0.472006	−	0.272513i
$719$	17.8697	−	30.9513i	0.666429	−	1.15429i	−0.312467	−	0.949929i	$-0.601155\pi$
$719$	17.8697	−	30.9513i	0.666429	−	1.15429i	0.978896	−	0.204360i	$-0.0655114\pi$
$720$		0			0
$721$	11.0041	−	17.4166i	0.409813	−	0.648629i
$722$	−8.07187			−0.300404
$723$	16.9059	−	2.45431i	0.628736	−	0.0912766i
$724$	−15.2777	+	8.82061i	−0.567793	+	0.327815i
$725$		0			0
$726$	6.45378	+	44.4552i	0.239522	+	1.64989i
$727$	33.2693			1.23389			0.616945	−	0.787006i	$-0.288370\pi$
$727$	33.2693			1.23389			0.616945	+	0.787006i	$0.288370\pi$
$728$	28.6487	+	1.14326i	1.06179	+	0.0423722i
$729$	−17.5132	+	20.5497i	−0.648636	+	0.761099i
$730$		0			0
$731$	−9.15648	−	15.8595i	−0.338665	−	0.586584i
$732$	9.99788	−	25.0728i	0.369532	−	0.926719i
$733$	8.40163	−	14.5521i	0.310321	−	0.537492i	−0.668111	−	0.744062i	$-0.732897\pi$
$733$	8.40163	−	14.5521i	0.310321	−	0.537492i	0.978432	+	0.206570i	$0.0662300\pi$
$734$	−15.5158			−0.572700
$735$		0			0
$736$	−37.6414			−1.38748
$737$	−9.78057	+	16.9404i	−0.360272	+	0.624009i
$738$	−16.9476	+	5.02667i	−0.623850	+	0.185034i
$739$	18.4120	+	31.8906i	0.677297	+	1.17311i	0.975792	+	0.218702i	$0.0701823\pi$
$739$	18.4120	+	31.8906i	0.677297	+	1.17311i	−0.298494	+	0.954411i	$0.596484\pi$
$740$		0			0
$741$	−21.3895	−	27.1225i	−0.785763	−	0.996371i
$742$	−3.43305	−	0.137001i	−0.126031	−	0.00502945i
$743$	−45.3970			−1.66545			−0.832727	−	0.553684i	$-0.813221\pi$
$743$	−45.3970			−1.66545			−0.832727	+	0.553684i	$0.813221\pi$
$744$	−1.98927	+	0.288792i	−0.0729302	+	0.0105876i
$745$		0			0
$746$	9.62558	−	5.55733i	0.352417	−	0.203468i
$747$	−17.6219	+	18.5828i	−0.644751	+	0.679910i
$748$	−28.3060			−1.03497
$749$	7.71466	−	12.2103i	0.281888	−	0.446156i
$750$		0			0
$751$	−9.49215	+	16.4409i	−0.346374	+	0.599937i	−0.985602	−	0.169080i	$-0.945920\pi$
$751$	−9.49215	+	16.4409i	−0.346374	+	0.599937i	0.639229	+	0.769017i	$0.279254\pi$
$752$	0.360366	−	0.208057i	0.0131412	−	0.00758707i
$753$	−42.7088	−	17.0303i	−1.55639	−	0.620617i
$754$	9.01888	+	5.20705i	0.328448	+	0.189630i
$755$		0			0
$756$	−9.94017	+	12.9521i	−0.361521	+	0.471063i
$757$			24.7352i			0.899017i	0.893276	+	0.449508i	$0.148401\pi$
$757$			24.7352i			0.899017i	−0.893276	+	0.449508i	$0.851599\pi$
$758$	−1.61148	+	2.79116i	−0.0585315	+	0.101379i
$759$	−27.4264	+	68.7803i	−0.995514	+	2.49657i
$760$		0			0
$761$	−23.8401	+	41.2923i	−0.864204	+	1.49685i	0.00363106	+	0.999993i	$0.498844\pi$
$761$	−23.8401	+	41.2923i	−0.864204	+	1.49685i	−0.867835	+	0.496852i	$0.834489\pi$
$762$	1.01814	+	1.29104i	0.0368835	+	0.0467693i
$763$	−8.10457	−	15.4273i	−0.293405	−	0.558505i
$764$			22.1986i			0.803116i
$765$		0			0
$766$	−18.0554	+	10.4243i	−0.652368	+	0.376645i
$767$	6.04333	+	10.4674i	0.218212	+	0.377954i
$768$	4.09675	+	28.2194i	0.147829	+	1.01828i
$769$			48.8811i			1.76270i	0.472467	+	0.881349i	$0.343364\pi$
$769$			48.8811i			1.76270i	−0.472467	+	0.881349i	$0.656636\pi$
$770$		0			0
$771$	16.4417	+	20.8485i	0.592133	+	0.750842i
$772$	−2.66950	−	1.54124i	−0.0960775	−	0.0554704i
$773$	−9.55974	+	5.51932i	−0.343840	+	0.198516i	−0.661969	−	0.749531i	$-0.730279\pi$
$773$	−9.55974	+	5.51932i	−0.343840	+	0.198516i	0.318129	+	0.948047i	$0.396946\pi$
$774$	3.72581	+	12.5617i	0.133922	+	0.451522i
$775$		0			0
$776$	−26.1611			−0.939128
$777$	−3.59656	−	4.95479i	−0.129026	−	0.177752i
$778$			15.3169i			0.549136i
$779$	29.9347	+	17.2828i	1.07252	+	0.619221i
$780$		0			0
$781$	−6.98662	−	12.1012i	−0.250001	−	0.433015i
$782$	19.9971	+	11.5453i	0.715095	+	0.412860i
$783$	−14.4515	+	6.67161i	−0.516456	+	0.238424i
$784$	0.851624	−	1.23586i	0.0304152	−	0.0441379i
$785$		0			0
$786$	2.34544	+	16.1560i	0.0836590	+	0.576264i
$787$	−8.48325	−	14.6934i	−0.302395	−	0.523764i	0.674283	−	0.738473i	$-0.264453\pi$
$787$	−8.48325	−	14.6934i	−0.302395	−	0.523764i	−0.976678	+	0.214709i	$0.931120\pi$
$788$	−4.65301	−	8.05925i	−0.165757	−	0.287099i
$789$	−5.47196	−	37.6922i	−0.194807	−	1.34188i
$790$		0			0
$791$	−0.566649	−	0.0226129i	−0.0201477	−	0.000804022i
$792$	52.8616	+	12.6711i	1.87836	+	0.450246i
$793$	42.8645	+	24.7479i	1.52216	+	0.878822i
$794$	−9.77475	−	16.9304i	−0.346893	−	0.600836i
$795$		0			0
$796$	−3.64492	−	2.10440i	−0.129191	−	0.0745884i
$797$			11.9116i			0.421930i	0.977494	+	0.210965i	$0.0676605\pi$
$797$			11.9116i			0.421930i	−0.977494	+	0.210965i	$0.932339\pi$
$798$	−21.7201	+	2.27328i	−0.768885	+	0.0804731i
$799$	7.33457			0.259478
$800$		0			0
$801$	−3.39837	+	1.00796i	−0.120075	+	0.0356145i
$802$	−0.383274	+	0.221283i	−0.0135339	+	0.00781378i
$803$	13.7562	+	7.94217i	0.485447	+	0.280273i
$804$	3.95073	+	5.00965i	0.139332	+	0.176677i
$805$		0			0
$806$		−	1.37325i		−	0.0483708i
$807$	7.43514	+	51.2151i	0.261729	+	1.80286i
$808$	3.31098	+	5.73479i	0.116480	+	0.201749i
$809$	−8.58544	+	4.95680i	−0.301848	+	0.174272i	−0.643273	−	0.765637i	$-0.722424\pi$
$809$	−8.58544	+	4.95680i	−0.301848	+	0.174272i	0.341425	+	0.939909i	$0.389091\pi$
$810$		0			0
$811$			40.3504i			1.41689i	0.705765	+	0.708446i	$0.250604\pi$
$811$			40.3504i			1.41689i	−0.705765	+	0.708446i	$0.749396\pi$
$812$	−8.52082	+	4.47633i	−0.299022	+	0.157088i
$813$	−13.3026	−	16.8681i	−0.466543	−	0.591590i
$814$	−3.79732	+	6.57715i	−0.133096	+	0.230529i
$815$		0			0
$816$	0.519846	−	1.30368i	0.0181982	−	0.0456379i
$817$	12.8102	−	22.1879i	0.448171	−	0.776255i
$818$		−	25.2768i		−	0.883783i
$819$	−20.8849	−	21.4500i	−0.729776	−	0.749525i
$820$		0			0
$821$	−21.2757	−	12.2835i	−0.742527	−	0.428698i	0.0804605	−	0.996758i	$-0.474361\pi$
$821$	−21.2757	−	12.2835i	−0.742527	−	0.428698i	−0.822987	+	0.568060i	$0.807694\pi$
$822$	−10.5771	−	4.21764i	−0.368917	−	0.147107i
$823$	−28.9152	+	16.6942i	−1.00792	+	0.581924i	−0.910583	−	0.413327i	$-0.864367\pi$
$823$	−28.9152	+	16.6942i	−1.00792	+	0.581924i	−0.0973396	+	0.995251i	$0.531033\pi$
$824$	−11.1859	+	19.3746i	−0.389680	+	0.674946i
$825$		0			0
$826$	7.63560	+	0.304709i	0.265677	+	0.0106022i
$827$	35.0677			1.21942			0.609712	−	0.792623i	$-0.291285\pi$
$827$	35.0677			1.21942			0.609712	+	0.792623i	$0.291285\pi$
$828$	17.5244	+	16.6182i	0.609017	+	0.577523i
$829$	20.7299	−	11.9684i	0.719979	−	0.415680i	−0.0947660	−	0.995500i	$-0.530210\pi$
$829$	20.7299	−	11.9684i	0.719979	−	0.415680i	0.814745	+	0.579820i	$0.196877\pi$
$830$		0			0
$831$	13.8295	−	2.00770i	0.479741	−	0.0696463i
$832$	−20.4956			−0.710555
$833$	23.8917	−	11.3597i	0.827800	−	0.393590i
$834$	−10.4936	−	13.3061i	−0.363362	−	0.460754i
$835$		0			0
$836$	−19.8004	−	34.2954i	−0.684813	−	1.18613i
$837$	1.71471	+	1.21046i	0.0592690	+	0.0418398i
$838$	1.55098	−	2.68638i	0.0535778	−	0.0927994i
$839$	44.6267			1.54068			0.770342	−	0.637631i	$-0.220086\pi$
$839$	44.6267			1.54068			0.770342	+	0.637631i	$0.220086\pi$
$840$		0			0
$841$	19.6164			0.676428
$842$	−8.47088	+	14.6720i	−0.291926	+	0.505631i
$843$	−11.3381	+	28.4338i	−0.390503	+	0.979311i
$844$	14.2358	+	24.6572i	0.490018	+	0.848736i
$845$		0			0
$846$	−5.10320	−	1.22325i	−0.175452	−	0.0420562i
$847$	40.6636	−	64.3601i	1.39722	−	2.21144i
$848$	0.308914			0.0106081
$849$	−5.89101	−	40.5787i	−0.202179	−	1.39266i
$850$		0			0
$851$	−7.84323	+	4.52829i	−0.268863	+	0.155228i
$852$	−4.51022	+	0.654770i	−0.154517	+	0.0224320i
$853$	−1.24909			−0.0427680			−0.0213840	−	0.999771i	$-0.506807\pi$
$853$	−1.24909			−0.0427680			−0.0213840	+	0.999771i	$0.506807\pi$
$854$	27.7030	−	14.5535i	0.947979	−	0.498011i
$855$		0			0
$856$	−7.84216	+	13.5830i	−0.268040	+	0.464258i
$857$	−7.97918	+	4.60678i	−0.272564	+	0.157365i	−0.630052	−	0.776553i	$-0.716966\pi$
$857$	−7.97918	+	4.60678i	−0.272564	+	0.157365i	0.357488	+	0.933918i	$0.383633\pi$
$858$	−13.7550	+	34.4951i	−0.469589	+	1.17764i
$859$	−0.860775	−	0.496969i	−0.0293693	−	0.0169564i	0.485243	−	0.874379i	$-0.338731\pi$
$859$	−0.860775	−	0.496969i	−0.0293693	−	0.0169564i	−0.514613	+	0.857423i	$0.672064\pi$
$860$		0			0
$861$	27.3632	+	12.1972i	0.932534	+	0.415680i
$862$			6.19664i			0.211058i
$863$	−2.04843	+	3.54799i	−0.0697295	+	0.120775i	−0.898782	−	0.438395i	$-0.855547\pi$
$863$	−2.04843	+	3.54799i	−0.0697295	+	0.120775i	0.829053	+	0.559170i	$0.188880\pi$
$864$	16.6403	−	23.5721i	0.566113	−	0.801940i
$865$		0			0
$866$	−6.88508	+	11.9253i	−0.233965	+	0.405239i
$867$	−3.69542	+	2.91430i	−0.125503	+	0.0989749i
$868$	1.07299	+	0.677927i	0.0364195	+	0.0230104i
$869$			38.5919i			1.30914i
$870$		0			0
$871$	−10.1315	+	5.84944i	−0.343294	+	0.198201i
$872$	9.46197	+	16.3886i	0.320423	+	0.554989i
$873$	19.8215	+	18.7965i	0.670857	+	0.636166i
$874$			32.3045i			1.09272i
$875$		0			0
$876$	4.06801	−	3.20813i	0.137445	−	0.108393i
$877$	8.72731	+	5.03871i	0.294700	+	0.170145i	0.640060	−	0.768325i	$-0.278910\pi$
$877$	8.72731	+	5.03871i	0.294700	+	0.170145i	−0.345359	+	0.938471i	$0.612243\pi$
$878$	30.0474	−	17.3479i	1.01405	−	0.585463i
$879$	1.73731	−	4.35685i	0.0585980	−	0.146953i
$880$		0			0
$881$	−30.3645			−1.02301			−0.511503	−	0.859281i	$-0.670911\pi$
$881$	−30.3645			−1.02301			−0.511503	+	0.859281i	$0.670911\pi$
$882$	−18.5178	+	3.91916i	−0.623527	+	0.131965i
$883$			16.1748i			0.544326i	0.962251	+	0.272163i	$0.0877390\pi$
$883$			16.1748i			0.544326i	−0.962251	+	0.272163i	$0.912261\pi$
$884$	−14.6609	−	8.46445i	−0.493098	−	0.284690i
$885$		0			0
$886$	−1.73803	−	3.01036i	−0.0583903	−	0.101135i
$887$	−3.97469	−	2.29479i	−0.133457	−	0.0770514i	0.431785	−	0.901977i	$-0.357884\pi$
$887$	−3.97469	−	2.29479i	−0.133457	−	0.0770514i	−0.565242	+	0.824925i	$0.691217\pi$
$888$	4.11703	+	5.22052i	0.138159	+	0.175189i
$889$	0.111110	−	2.78428i	0.00372652	−	0.0933816i
$890$		0			0
$891$	−30.9477	−	47.5811i	−1.03679	−	1.59403i
$892$	−10.0577	−	17.4205i	−0.336758	−	0.583283i
$893$	5.13064	+	8.88652i	0.171690	+	0.297376i
$894$	−4.54301	+	0.659531i	−0.151941	+	0.0220580i
$895$		0			0
$896$	8.77326	−	13.8858i	0.293094	−	0.463893i
$897$	−34.7729	+	27.4228i	−1.16103	+	0.915620i
$898$	1.96829	+	1.13639i	0.0656827	+	0.0379220i
$899$	0.618683	+	1.07159i	0.0206342	+	0.0357395i
$900$		0			0
$901$	4.71552	+	2.72251i	0.157097	+	0.0906998i
$902$		−	37.1619i		−	1.23736i
$903$	9.04067	−	20.2818i	0.300855	−	0.674936i
$904$	0.615829			0.0204822
$905$		0			0
$906$	7.23023	+	2.88308i	0.240208	+	0.0957839i
$907$	−27.1205	+	15.6580i	−0.900521	+	0.519916i	−0.877369	−	0.479816i	$-0.840703\pi$
$907$	−27.1205	+	15.6580i	−0.900521	+	0.519916i	−0.0231520	+	0.999732i	$0.507370\pi$
$908$	−22.5211	−	13.0026i	−0.747389	−	0.431505i
$909$	1.61176	−	6.72400i	0.0534586	−	0.223021i
$910$		0			0
$911$			2.78118i			0.0921447i	0.998938	+	0.0460724i	$0.0146705\pi$
$911$			2.78118i			0.0921447i	−0.998938	+	0.0460724i	$0.985330\pi$
$912$	1.94317	−	0.282099i	0.0643447	−	0.00934124i
$913$	−26.9187	−	46.6245i	−0.890878	−	1.54305i
$914$	7.26289	−	4.19323i	0.240235	−	0.138700i
$915$		0			0
$916$			0.299327i			0.00989003i
$917$	14.7780	−	23.3898i	0.488012	−	0.772400i
$918$	−16.0702	+	7.41887i	−0.530396	+	0.244859i
$919$	29.0225	−	50.2685i	0.957365	−	1.65821i	0.228506	−	0.973543i	$-0.426616\pi$
$919$	29.0225	−	50.2685i	0.957365	−	1.65821i	0.728860	−	0.684663i	$-0.240051\pi$
$920$		0			0
$921$	−8.84217	−	3.52584i	−0.291359	−	0.116180i
$922$	5.13301	−	8.89063i	0.169047	−	0.292797i
$923$		−	8.35695i		−	0.275072i
$924$	−20.1622	−	27.7765i	−0.663288	−	0.913778i
$925$		0			0
$926$	0.251595	+	0.145259i	0.00826793	+	0.00477349i
$927$	22.3957	−	6.64259i	0.735573	−	0.218171i
$928$	14.7312	−	8.50504i	0.483574	−	0.279191i
$929$	−20.7329	+	35.9104i	−0.680224	+	1.17818i	0.294689	+	0.955593i	$0.404784\pi$
$929$	−20.7329	+	35.9104i	−0.680224	+	1.17818i	−0.974912	+	0.222589i	$0.928549\pi$
$930$		0			0
$931$	30.4760	+	21.0008i	0.998809	+	0.688274i
$932$	−17.7455			−0.581274
$933$	−5.43645	−	37.4476i	−0.177981	−	1.22598i
$934$	18.1993	−	10.5074i	0.595499	−	0.343812i
$935$		0			0
$936$	23.5902	+	22.3703i	0.771069	+	0.731195i
$937$	15.3201			0.500486			0.250243	−	0.968183i	$-0.419489\pi$
$937$	15.3201			0.500486			0.250243	+	0.968183i	$0.419489\pi$
$938$	−0.294933	+	7.39063i	−0.00962990	+	0.241312i
$939$	−33.4442	+	26.3749i	−1.09141	+	0.860714i
$940$		0			0
$941$	25.5592	+	44.2698i	0.833206	+	1.44316i	0.895483	+	0.445096i	$0.146830\pi$
$941$	25.5592	+	44.2698i	0.833206	+	1.44316i	−0.0622769	+	0.998059i	$0.519836\pi$
$942$	10.2947	+	4.10503i	0.335419	+	0.133749i
$943$	22.1577	−	38.3783i	0.721555	−	1.24977i
$944$	−0.687068			−0.0223622
$945$		0			0
$946$	−27.5447			−0.895556
$947$	4.01829	−	6.95988i	0.130577	−	0.226166i	−0.793322	−	0.608802i	$-0.791650\pi$
$947$	4.01829	−	6.95988i	0.130577	−	0.226166i	0.923899	+	0.382636i	$0.124984\pi$
$948$	11.6918	+	4.66215i	0.379733	+	0.151420i
$949$	4.74996	+	8.22716i	0.154190	+	0.267065i
$950$		0			0
$951$	32.5794	−	25.6929i	1.05646	−	0.833149i
$952$	−25.4321	+	13.3605i	−0.824260	+	0.433017i
$953$	−43.7448			−1.41703			−0.708516	−	0.705695i	$-0.750635\pi$
$953$	−43.7448			−1.41703			−0.708516	+	0.705695i	$0.750635\pi$
$954$	−2.82688	−	2.68070i	−0.0915236	−	0.0867908i
$955$		0			0
$956$	20.0578	−	11.5804i	0.648714	−	0.374535i
$957$	−4.80739	−	33.1145i	−0.155401	−	1.07044i
$958$	−0.570645			−0.0184367
$959$	8.97489	+	17.0840i	0.289814	+	0.551670i
$960$		0			0
$961$	−15.4184	+	26.7055i	−0.497368	+	0.861467i
$962$	−3.93358	+	2.27105i	−0.126824	+	0.0732217i
$963$	15.7011	−	4.65695i	0.505960	−	0.150068i
$964$	10.1439	+	5.85660i	0.326714	+	0.188628i
$965$		0			0
$966$	2.91449	+	27.8467i	0.0937723	+	0.895952i
$967$		−	28.3067i		−	0.910281i	−0.890420	−	0.455140i	$-0.849589\pi$
$967$		−	28.3067i		−	0.910281i	0.890420	−	0.455140i	$-0.150411\pi$
$968$	−41.3357	+	71.5954i	−1.32858	+	2.30116i
$969$	32.1483	+	12.8193i	1.03275	+	0.411814i
$970$		0			0
$971$	−16.4304	+	28.4583i	−0.527277	+	0.913270i	0.472218	+	0.881482i	$0.343454\pi$
$971$	−16.4304	+	28.4583i	−0.527277	+	0.913270i	−0.999495	+	0.0317882i	$0.989880\pi$
$972$	−18.1539	+	3.62783i	−0.582287	+	0.116363i
$973$	−1.14516	+	28.6963i	−0.0367123	+	0.919961i
$974$		−	19.5144i		−	0.625282i
$975$		0			0
$976$	−2.43664	+	1.40680i	−0.0779950	+	0.0450304i
$977$	25.5291	+	44.2178i	0.816750	+	1.41465i	0.908065	+	0.418830i	$0.137560\pi$
$977$	25.5291	+	44.2178i	0.816750	+	1.41465i	−0.0913150	+	0.995822i	$0.529107\pi$
$978$	27.3225	−	3.96653i	0.873676	−	0.126836i
$979$		−	7.45178i		−	0.238160i
$980$		0			0
$981$	4.60601	−	19.2155i	0.147059	−	0.613505i
$982$	28.2263	+	16.2965i	0.900737	+	0.520041i
$983$	26.1076	−	15.0732i	0.832704	−	0.480762i	−0.0220736	−	0.999756i	$-0.507027\pi$
$983$	26.1076	−	15.0732i	0.832704	−	0.480762i	0.854778	+	0.518994i	$0.173693\pi$
$984$	−30.2189	−	12.0499i	−0.963342	−	0.384136i
$985$		0			0
$986$	−10.4346			−0.332306
$987$	5.22438	+	7.19736i	0.166294	+	0.229094i
$988$		−	23.6840i		−	0.753489i
$989$	−28.4463	−	16.4235i	−0.904541	−	0.522237i
$990$		0			0
$991$	−25.9382	−	44.9263i	−0.823955	−	1.42713i	−0.902715	−	0.430238i	$-0.858430\pi$
$991$	−25.9382	−	44.9263i	−0.823955	−	1.42713i	0.0787606	−	0.996894i	$-0.474904\pi$
$992$	−1.94252	−	1.12151i	−0.0616751	−	0.0356081i
$993$	−36.8595	+	29.0683i	−1.16970	+	0.922456i
$994$	−4.46675	−	2.82215i	−0.141677	−	0.0895133i
$995$		0			0
$996$	−17.3773	+	2.52275i	−0.550622	+	0.0799365i
$997$	25.3390	+	43.8884i	0.802494	+	1.38996i	0.917970	+	0.396649i	$0.129827\pi$
$997$	25.3390	+	43.8884i	0.802494	+	1.38996i	−0.115477	+	0.993310i	$0.536840\pi$
$998$	−4.06209	−	7.03574i	−0.128583	−	0.222713i
$999$	0.631539	−	6.91349i	0.0199810	−	0.218733i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	525.2.q.g.299.8		40
3.2	odd	2	inner	525.2.q.g.299.14		40
5.2	odd	4		525.2.t.i.26.4	yes	20
5.3	odd	4		525.2.t.h.26.7	yes	20
5.4	even	2	inner	525.2.q.g.299.13		40
7.3	odd	6	inner	525.2.q.g.374.7		40
15.2	even	4		525.2.t.i.26.7	yes	20
15.8	even	4		525.2.t.h.26.4	✓	20
15.14	odd	2	inner	525.2.q.g.299.7		40
21.17	even	6	inner	525.2.q.g.374.13		40
35.3	even	12		525.2.t.h.101.4	yes	20
35.17	even	12		525.2.t.i.101.7	yes	20
35.24	odd	6	inner	525.2.q.g.374.14		40
105.17	odd	12		525.2.t.i.101.4	yes	20
105.38	odd	12		525.2.t.h.101.7	yes	20
105.59	even	6	inner	525.2.q.g.374.8		40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
525.2.q.g.299.7		40	15.14	odd	2	inner
525.2.q.g.299.8		40	1.1	even	1	trivial
525.2.q.g.299.13		40	5.4	even	2	inner
525.2.q.g.299.14		40	3.2	odd	2	inner
525.2.q.g.374.7		40	7.3	odd	6	inner
525.2.q.g.374.8		40	105.59	even	6	inner
525.2.q.g.374.13		40	21.17	even	6	inner
525.2.q.g.374.14		40	35.24	odd	6	inner
525.2.t.h.26.4	✓	20	15.8	even	4
525.2.t.h.26.7	yes	20	5.3	odd	4
525.2.t.h.101.4	yes	20	35.3	even	12
525.2.t.h.101.7	yes	20	105.38	odd	12
525.2.t.i.26.4	yes	20	5.2	odd	4
525.2.t.i.26.7	yes	20	15.2	even	4
525.2.t.i.101.4	yes	20	105.17	odd	12
525.2.t.i.101.7	yes	20	35.17	even	12

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 525 = 3 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	525.q (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.450666 + 0.780577i) q^{2} +(1.60886 + 0.641538i) q^{3} +(0.593800 + 1.02849i) q^{4} +(-1.22583 + 0.966719i) q^{6} +(2.64365 + 0.105498i) q^{7} -2.87309 q^{8} +(2.17686 + 2.06429i) q^{9} +O(q^{10})\)	\(q+(-0.450666 + 0.780577i) q^{2} +(1.60886 + 0.641538i) q^{3} +(0.593800 + 1.02849i) q^{4} +(-1.22583 + 0.966719i) q^{6} +(2.64365 + 0.105498i) q^{7} -2.87309 q^{8} +(2.17686 + 2.06429i) q^{9} +(-5.46176 + 3.15335i) q^{11} +(0.295524 + 2.03564i) q^{12} -3.77183 q^{13} +(-1.27375 + 2.01603i) q^{14} +(0.107205 - 0.185685i) q^{16} +(3.27294 - 1.88963i) q^{17} +(-2.59237 + 0.768900i) q^{18} +(4.57893 + 2.64365i) q^{19} +(4.18558 + 1.86573i) q^{21} -5.68443i q^{22} +(3.38933 - 5.87050i) q^{23} +(-4.62239 - 1.84320i) q^{24} +(1.69984 - 2.94420i) q^{26} +(2.17794 + 4.71769i) q^{27} +(1.46129 + 2.78161i) q^{28} +3.06327i q^{29} +(0.349819 - 0.201968i) q^{31} +(-2.77646 - 4.80897i) q^{32} +(-10.8102 + 1.56937i) q^{33} +3.40637i q^{34} +(-0.830485 + 3.46465i) q^{36} +(-1.15705 - 0.668021i) q^{37} +(-4.12714 + 2.38281i) q^{38} +(-6.06834 - 2.41977i) q^{39} +6.53749 q^{41} +(-3.34265 + 2.42634i) q^{42} -4.84564i q^{43} +(-6.48638 - 3.74491i) q^{44} +(3.05492 + 5.29127i) q^{46} +(1.68073 + 0.970371i) q^{47} +(0.291602 - 0.229964i) q^{48} +(6.97774 + 0.557800i) q^{49} +(6.47796 - 0.940437i) q^{51} +(-2.23971 - 3.87929i) q^{52} +(0.720381 + 1.24774i) q^{53} +(-4.66404 - 0.426055i) q^{54} +(-7.59543 - 0.303106i) q^{56} +(5.67086 + 7.19082i) q^{57} +(-2.39112 - 1.38051i) q^{58} +(-1.60223 - 2.77514i) q^{59} +(-11.3644 - 6.56124i) q^{61} +0.364081i q^{62} +(5.53707 + 5.68691i) q^{63} +5.43385 q^{64} +(3.64678 - 9.14545i) q^{66} +(2.68611 - 1.55082i) q^{67} +(3.88694 + 2.24412i) q^{68} +(9.21911 - 7.27042i) q^{69} +2.21562i q^{71} +(-6.25430 - 5.93088i) q^{72} +(-1.25932 - 2.18121i) q^{73} +(1.04288 - 0.602109i) q^{74} +6.27919i q^{76} +(-14.7716 + 7.76013i) q^{77} +(4.62362 - 3.64630i) q^{78} +(3.05960 - 5.29938i) q^{79} +(0.477421 + 8.98733i) q^{81} +(-2.94623 + 5.10301i) q^{82} +8.53654i q^{83} +(0.566504 + 5.41270i) q^{84} +(3.78240 + 2.18377i) q^{86} +(-1.96520 + 4.92836i) q^{87} +(15.6921 - 9.05984i) q^{88} +(-0.590783 + 1.02327i) q^{89} +(-9.97138 - 0.397921i) q^{91} +8.05034 q^{92} +(0.692381 - 0.100516i) q^{93} +(-1.51490 + 0.874627i) q^{94} +(-1.38180 - 9.51816i) q^{96} +9.10556 q^{97} +(-3.58004 + 5.19528i) q^{98} +(-18.3989 - 4.41026i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q - 28 q^{4} + 14 q^{9}+O(q^{10}) \) 40 * q - 28 * q^4 + 14 * q^9	\( 40 q - 28 q^{4} + 14 q^{9} - 36 q^{16} - 18 q^{21} - 36 q^{24} + 84 q^{31} - 72 q^{36} - 16 q^{46} + 8 q^{49} + 42 q^{51} + 150 q^{54} - 180 q^{61} + 240 q^{64} + 12 q^{66} - 92 q^{79} + 58 q^{81} - 150 q^{84} - 60 q^{91} - 12 q^{94} + 270 q^{96} - 188 q^{99}+O(q^{100}) \) 40 * q - 28 * q^4 + 14 * q^9 - 36 * q^16 - 18 * q^21 - 36 * q^24 + 84 * q^31 - 72 * q^36 - 16 * q^46 + 8 * q^49 + 42 * q^51 + 150 * q^54 - 180 * q^61 + 240 * q^64 + 12 * q^66 - 92 * q^79 + 58 * q^81 - 150 * q^84 - 60 * q^91 - 12 * q^94 + 270 * q^96 - 188 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more