LMFDB - Embedded newform 980.2.c.e.979.41

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [980,2,Mod(979,980)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(980, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 1, 1]))

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

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

chi := DirichletCharacter("980.979");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 980 = 2^{2} \cdot 5 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	980.c (of order $2$, degree $1$, 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:	$7.82533939809$
Analytic rank:	$0$
Dimension:	$48$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			979.41
Character	$\chi$	$=$	980.979
Dual form			980.2.c.e.979.44

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.36075 - 0.385185i) q^{2} -0.423388i q^{3} +(1.70326 - 1.04828i) q^{4} +(-1.74517 + 1.39799i) q^{5} +(-0.163083 - 0.576124i) q^{6} +(1.91393 - 2.08252i) q^{8} +2.82074 q^{9} +(-1.83626 + 2.57452i) q^{10} +4.89551i q^{11} +(-0.443829 - 0.721142i) q^{12} -2.54664 q^{13} +(0.591890 + 0.738886i) q^{15} +(1.80222 - 3.57099i) q^{16} +5.11429 q^{17} +(3.83832 - 1.08651i) q^{18} +6.26601 q^{19} +(-1.50701 + 4.21057i) q^{20} +(1.88568 + 6.66155i) q^{22} +4.63109 q^{23} +(-0.881712 - 0.810335i) q^{24} +(1.09127 - 4.87946i) q^{25} +(-3.46533 + 0.980929i) q^{26} -2.46443i q^{27} -1.88958 q^{29} +(1.09002 + 0.777450i) q^{30} -1.47756 q^{31} +(1.07687 - 5.55341i) q^{32} +2.07270 q^{33} +(6.95926 - 1.96995i) q^{34} +(4.80447 - 2.95693i) q^{36} -2.35920i q^{37} +(8.52645 - 2.41357i) q^{38} +1.07822i q^{39} +(-0.428815 + 6.31000i) q^{40} -7.05393i q^{41} -10.7790 q^{43} +(5.13187 + 8.33835i) q^{44} +(-4.92269 + 3.94336i) q^{45} +(6.30175 - 1.78383i) q^{46} +12.2145i q^{47} +(-1.51192 - 0.763038i) q^{48} +(-0.394553 - 7.06005i) q^{50} -2.16533i q^{51} +(-4.33760 + 2.66959i) q^{52} -2.23621i q^{53} +(-0.949263 - 3.35347i) q^{54} +(-6.84386 - 8.54352i) q^{55} -2.65295i q^{57} +(-2.57124 + 0.727837i) q^{58} -5.69000 q^{59} +(1.78271 + 0.638052i) q^{60} +3.87005i q^{61} +(-2.01059 + 0.569136i) q^{62} +(-0.673743 - 7.97158i) q^{64} +(4.44433 - 3.56017i) q^{65} +(2.82042 - 0.798374i) q^{66} +0.889310 q^{67} +(8.71100 - 5.36121i) q^{68} -1.96075i q^{69} +14.3310i q^{71} +(5.39870 - 5.87424i) q^{72} +7.87187 q^{73} +(-0.908729 - 3.21027i) q^{74} +(-2.06590 - 0.462031i) q^{75} +(10.6727 - 6.56853i) q^{76} +(0.415314 + 1.46718i) q^{78} +4.63973i q^{79} +(1.84701 + 8.75149i) q^{80} +7.41882 q^{81} +(-2.71707 - 9.59861i) q^{82} -4.32876i q^{83} +(-8.92534 + 7.14971i) q^{85} +(-14.6675 + 4.15191i) q^{86} +0.800024i q^{87} +(10.1950 + 9.36967i) q^{88} -2.18254i q^{89} +(-5.17961 + 7.26206i) q^{90} +(7.88798 - 4.85468i) q^{92} +0.625583i q^{93} +(4.70485 + 16.6208i) q^{94} +(-10.9353 + 8.75979i) q^{95} +(-2.35125 - 0.455934i) q^{96} -3.42330 q^{97} +13.8090i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 16 q^{4} - 64 q^{9} + 16 q^{16} - 16 q^{25} - 48 q^{29} - 8 q^{30} + 176 q^{36} - 48 q^{44} - 32 q^{46} + 32 q^{50} + 24 q^{60} - 80 q^{64} - 16 q^{65} - 112 q^{74} - 48 q^{81} - 64 q^{85} - 112 q^{86}+O(q^{100}) $ 48 * q + 16 * q^4 - 64 * q^9 + 16 * q^16 - 16 * q^25 - 48 * q^29 - 8 * q^30 + 176 * q^36 - 48 * q^44 - 32 * q^46 + 32 * q^50 + 24 * q^60 - 80 * q^64 - 16 * q^65 - 112 * q^74 - 48 * q^81 - 64 * q^85 - 112 * q^86

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/980\mathbb{Z}\right)^\times$.

$n$	$101$	$197$	$491$
$\chi(n)$	$-1$	$-1$	$-1$

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 $

$2$	1.36075	−	0.385185i	0.962193	−	0.272367i
$2$	1.36075	−	0.385185i	0.962193	−	0.272367i
$3$		−	0.423388i		−	0.244443i	−0.992503	−	0.122222i	$-0.960998\pi$
$3$		−	0.423388i		−	0.244443i	0.992503	−	0.122222i	$-0.0390019\pi$
$4$	1.70326	−	1.04828i	0.851632	−	0.524140i
$5$	−1.74517	+	1.39799i	−0.780466	+	0.625198i
$5$	−1.74517	+	1.39799i	−0.780466	+	0.625198i
$6$	−0.163083	−	0.576124i	−0.0665783	−	0.235202i
$7$		0			0
$7$		0			0
$8$	1.91393	−	2.08252i	0.676676	−	0.736280i
$9$	2.82074			0.940248
$10$	−1.83626	+	2.57452i	−0.580676	+	0.814135i
$11$			4.89551i			1.47605i	0.674772	+	0.738026i	$0.264242\pi$
$11$			4.89551i			1.47605i	−0.674772	+	0.738026i	$0.735758\pi$
$12$	−0.443829	−	0.721142i	−0.128122	−	0.208176i
$13$	−2.54664			−0.706311			−0.353156	−	0.935565i	$-0.614891\pi$
$13$	−2.54664			−0.706311			−0.353156	+	0.935565i	$0.614891\pi$
$14$		0			0
$15$	0.591890	+	0.738886i	0.152825	+	0.190780i
$16$	1.80222	−	3.57099i	0.450555	−	0.892749i
$17$	5.11429			1.24040			0.620199	−	0.784444i	$-0.287052\pi$
$17$	5.11429			1.24040			0.620199	+	0.784444i	$0.287052\pi$
$18$	3.83832	−	1.08651i	0.904700	−	0.256093i
$19$	6.26601			1.43752			0.718760	−	0.695258i	$-0.244710\pi$
$19$	6.26601			1.43752			0.718760	+	0.695258i	$0.244710\pi$
$20$	−1.50701	+	4.21057i	−0.336979	+	0.941512i
$21$		0			0
$22$	1.88568	+	6.66155i	0.402028	+	1.42025i
$23$	4.63109			0.965650			0.482825	−	0.875717i	$-0.339611\pi$
$23$	4.63109			0.965650			0.482825	+	0.875717i	$0.339611\pi$
$24$	−0.881712	−	0.810335i	−0.179979	−	0.165409i
$25$	1.09127	−	4.87946i	0.218254	−	0.975892i
$26$	−3.46533	+	0.980929i	−0.679608	+	0.192376i
$27$		−	2.46443i		−	0.474280i
$28$		0			0
$29$	−1.88958			−0.350886			−0.175443	−	0.984490i	$-0.556136\pi$
$29$	−1.88958			−0.350886			−0.175443	+	0.984490i	$0.556136\pi$
$30$	1.09002	+	0.777450i	0.199010	+	0.141942i
$31$	−1.47756			−0.265378			−0.132689	−	0.991158i	$-0.542361\pi$
$31$	−1.47756			−0.265378			−0.132689	+	0.991158i	$0.542361\pi$
$32$	1.07687	−	5.55341i	0.190366	−	0.981713i
$33$	2.07270			0.360811
$34$	6.95926	−	1.96995i	1.19350	−	0.337844i
$35$		0			0
$36$	4.80447	−	2.95693i	0.800745	−	0.492821i
$37$		−	2.35920i		−	0.387850i	−0.981016	−	0.193925i	$-0.937878\pi$
$37$		−	2.35920i		−	0.387850i	0.981016	−	0.193925i	$-0.0621218\pi$
$38$	8.52645	−	2.41357i	1.38317	−	0.391533i
$39$			1.07822i			0.172653i
$40$	−0.428815	+	6.31000i	−0.0678016	+	0.997699i
$41$		−	7.05393i		−	1.10164i	−0.834624	−	0.550819i	$-0.814315\pi$
$41$		−	7.05393i		−	1.10164i	0.834624	−	0.550819i	$-0.185685\pi$
$42$		0			0
$43$	−10.7790			−1.64378			−0.821890	−	0.569646i	$-0.807080\pi$
$43$	−10.7790			−1.64378			−0.821890	+	0.569646i	$0.807080\pi$
$44$	5.13187	+	8.33835i	0.773658	+	1.25705i
$45$	−4.92269	+	3.94336i	−0.733831	+	0.587841i
$46$	6.30175	−	1.78383i	0.929142	−	0.263011i
$47$			12.2145i			1.78167i	0.454329	+	0.890834i	$0.349879\pi$
$47$			12.2145i			1.78167i	−0.454329	+	0.890834i	$0.650121\pi$
$48$	−1.51192	−	0.763038i	−0.218226	−	0.110135i
$49$		0			0
$50$	−0.394553	−	7.06005i	−0.0557982	−	0.998442i
$51$		−	2.16533i		−	0.303207i
$52$	−4.33760	+	2.66959i	−0.601517	+	0.370206i
$53$		−	2.23621i		−	0.307167i	−0.988136	−	0.153583i	$-0.950919\pi$
$53$		−	2.23621i		−	0.307167i	0.988136	−	0.153583i	$-0.0490813\pi$
$54$	−0.949263	−	3.35347i	−0.129178	−	0.456349i
$55$	−6.84386	−	8.54352i	−0.922825	−	1.15201i
$56$		0			0
$57$		−	2.65295i		−	0.351392i
$58$	−2.57124	+	0.727837i	−0.337620	+	0.0955697i
$59$	−5.69000			−0.740774			−0.370387	−	0.928877i	$-0.620775\pi$
$59$	−5.69000			−0.740774			−0.370387	+	0.928877i	$0.620775\pi$
$60$	1.78271	+	0.638052i	0.230146	+	0.0823721i
$61$			3.87005i			0.495509i	0.968823	+	0.247754i	$0.0796926\pi$
$61$			3.87005i			0.495509i	−0.968823	+	0.247754i	$0.920307\pi$
$62$	−2.01059	+	0.569136i	−0.255345	+	0.0722803i
$63$		0			0
$64$	−0.673743	−	7.97158i	−0.0842179	−	0.996447i
$65$	4.44433	−	3.56017i	0.551252	−	0.441585i
$66$	2.82042	−	0.798374i	0.347170	−	0.0982731i
$67$	0.889310			0.108646			0.0543232	−	0.998523i	$-0.482700\pi$
$67$	0.889310			0.108646			0.0543232	+	0.998523i	$0.482700\pi$
$68$	8.71100	−	5.36121i	1.05636	−	0.650142i
$69$		−	1.96075i		−	0.236046i
$70$		0			0
$71$			14.3310i			1.70078i	0.526152	+	0.850391i	$0.323634\pi$
$71$			14.3310i			1.70078i	−0.526152	+	0.850391i	$0.676366\pi$
$72$	5.39870	−	5.87424i	0.636243	−	0.692286i
$73$	7.87187			0.921333			0.460667	−	0.887573i	$-0.347610\pi$
$73$	7.87187			0.921333			0.460667	+	0.887573i	$0.347610\pi$
$74$	−0.908729	−	3.21027i	−0.105638	−	0.373187i
$75$	−2.06590	−	0.462031i	−0.238550	−	0.0533507i
$76$	10.6727	−	6.56853i	1.22424	−	0.753462i
$77$		0			0
$78$	0.415314	+	1.46718i	0.0470250	+	0.166126i
$79$			4.63973i			0.522010i	0.965337	+	0.261005i	$0.0840540\pi$
$79$			4.63973i			0.522010i	−0.965337	+	0.261005i	$0.915946\pi$
$80$	1.84701	+	8.75149i	0.206502	+	0.978446i
$81$	7.41882			0.824313
$82$	−2.71707	−	9.59861i	−0.300050	−	1.05999i
$83$		−	4.32876i		−	0.475143i	−0.971370	−	0.237571i	$-0.923649\pi$
$83$		−	4.32876i		−	0.475143i	0.971370	−	0.237571i	$-0.0763514\pi$
$84$		0			0
$85$	−8.92534	+	7.14971i	−0.968089	+	0.775495i
$86$	−14.6675	+	4.15191i	−1.58163	+	0.447712i
$87$			0.800024i			0.0857716i
$88$	10.1950	+	9.36967i	1.08679	+	0.998810i
$89$		−	2.18254i		−	0.231349i	−0.993287	−	0.115674i	$-0.963097\pi$
$89$		−	2.18254i		−	0.231349i	0.993287	−	0.115674i	$-0.0369029\pi$
$90$	−5.17961	+	7.26206i	−0.545979	+	0.765488i
$91$		0			0
$92$	7.88798	−	4.85468i	0.822378	−	0.506135i
$93$			0.625583i			0.0648699i
$94$	4.70485	+	16.6208i	0.485268	+	1.71431i
$95$	−10.9353	+	8.75979i	−1.12194	+	0.898735i
$96$	−2.35125	−	0.455934i	−0.239973	−	0.0465336i
$97$	−3.42330			−0.347584			−0.173792	−	0.984782i	$-0.555602\pi$
$97$	−3.42330			−0.347584			−0.173792	+	0.984782i	$0.555602\pi$
$98$		0			0
$99$			13.8090i			1.38785i
$100$	−3.25631	−	9.45497i	−0.325631	−	0.945497i
$101$		−	7.30698i		−	0.727072i	−0.931580	−	0.363536i	$-0.881569\pi$
$101$		−	7.30698i		−	0.727072i	0.931580	−	0.363536i	$-0.118431\pi$
$102$	−0.834054	−	2.94647i	−0.0825836	−	0.291744i
$103$		−	6.75072i		−	0.665168i	−0.943074	−	0.332584i	$-0.892079\pi$
$103$		−	6.75072i		−	0.665168i	0.943074	−	0.332584i	$-0.107921\pi$
$104$	−4.87409	+	5.30342i	−0.477944	+	0.520043i
$105$		0			0
$106$	−0.861354	−	3.04291i	−0.0836621	−	0.295554i
$107$	−9.82994			−0.950296			−0.475148	−	0.879906i	$-0.657605\pi$
$107$	−9.82994			−0.950296			−0.475148	+	0.879906i	$0.657605\pi$
$108$	−2.58341	−	4.19758i	−0.248589	−	0.403912i
$109$	−9.41221			−0.901526			−0.450763	−	0.892644i	$-0.648848\pi$
$109$	−9.41221			−0.901526			−0.450763	+	0.892644i	$0.648848\pi$
$110$	−12.6036	−	8.98942i	−1.20171	−	0.857108i
$111$	−0.998857			−0.0948073
$112$		0			0
$113$		−	15.9261i		−	1.49820i	−0.662455	−	0.749102i	$-0.730485\pi$
$113$		−	15.9261i		−	1.49820i	0.662455	−	0.749102i	$-0.269515\pi$
$114$	−1.02188	−	3.61000i	−0.0957077	−	0.338107i
$115$	−8.08207	+	6.47420i	−0.753657	+	0.603722i
$116$	−3.21845	+	1.98080i	−0.298826	+	0.183913i
$117$	−7.18342			−0.664107
$118$	−7.74264	+	2.19170i	−0.712768	+	0.201763i
$119$		0			0
$120$	2.67158	+	0.181555i	0.243881	+	0.0165736i
$121$	−12.9660			−1.17873
$122$	1.49069	+	5.26615i	0.134960	+	0.476775i
$123$	−2.98655			−0.269288
$124$	−2.51668	+	1.54890i	−0.226005	+	0.139095i
$125$	4.91696	+	10.0411i	0.439786	+	0.898103i
$126$		0			0
$127$	−12.2192			−1.08428			−0.542138	−	0.840290i	$-0.682385\pi$
$127$	−12.2192			−1.08428			−0.542138	+	0.840290i	$0.682385\pi$
$128$	−3.98733	−	10.5878i	−0.352433	−	0.935837i
$129$			4.56369i			0.401811i
$130$	4.67629	−	6.55638i	0.410138	−	0.575033i
$131$	9.85060			0.860651			0.430325	−	0.902674i	$-0.358399\pi$
$131$	9.85060			0.860651			0.430325	+	0.902674i	$0.358399\pi$
$132$	3.53036	−	2.17277i	0.307278	−	0.189115i
$133$		0			0
$134$	1.21013	−	0.342549i	0.104539	−	0.0295917i
$135$	3.44524	+	4.30087i	0.296519	+	0.370160i
$136$	9.78840	−	10.6506i	0.839348	−	0.913281i
$137$		−	4.69484i		−	0.401107i	−0.979683	−	0.200554i	$-0.935726\pi$
$137$		−	4.69484i		−	0.401107i	0.979683	−	0.200554i	$-0.0642741\pi$
$138$	−0.755252	−	2.66808i	−0.0642913	−	0.227122i
$139$	−13.8745			−1.17682			−0.588409	−	0.808564i	$-0.700245\pi$
$139$	−13.8745			−1.17682			−0.588409	+	0.808564i	$0.700245\pi$
$140$		0			0
$141$	5.17147			0.435516
$142$	5.52011	+	19.5009i	0.463237	+	1.63648i
$143$		−	12.4671i		−	1.04255i
$144$	5.08360	−	10.0729i	0.423633	−	0.839405i
$145$	3.29764	−	2.64160i	0.273854	−	0.219373i
$146$	10.7116	−	3.03213i	0.886501	−	0.250941i
$147$		0			0
$148$	−2.47310	−	4.01834i	−0.203288	−	0.330306i
$149$	−5.46359			−0.447595			−0.223797	−	0.974636i	$-0.571845\pi$
$149$	−5.46359			−0.447595			−0.223797	+	0.974636i	$0.571845\pi$
$150$	−2.98914	+	0.167049i	−0.244062	+	0.0136395i
$151$			1.49611i			0.121751i	0.998145	+	0.0608757i	$0.0193893\pi$
$151$			1.49611i			0.121751i	−0.998145	+	0.0608757i	$0.980611\pi$
$152$	11.9927	−	13.0491i	0.972736	−	1.05842i
$153$	14.4261			1.16628
$154$		0			0
$155$	2.57861	−	2.06561i	0.207119	−	0.165914i
$156$	1.13027	+	1.83649i	0.0904943	+	0.147037i
$157$	−22.9035			−1.82790			−0.913948	−	0.405831i	$-0.866982\pi$
$157$	−22.9035			−1.82790			−0.913948	+	0.405831i	$0.866982\pi$
$158$	1.78716	+	6.31350i	0.142179	+	0.502275i
$159$	−0.946783			−0.0750848
$160$	5.88426	+	11.1971i	0.465192	+	0.885210i
$161$		0			0
$162$	10.0951	−	2.85762i	0.793148	−	0.224516i
$163$	1.93051			0.151209			0.0756047	−	0.997138i	$-0.475911\pi$
$163$	1.93051			0.151209			0.0756047	+	0.997138i	$0.475911\pi$
$164$	−7.39449	−	12.0147i	−0.577413	−	0.938191i
$165$	−3.61723	+	2.89761i	−0.281601	+	0.225578i
$166$	−1.66737	−	5.89034i	−0.129413	−	0.457179i
$167$			16.9677i			1.31300i	0.754327	+	0.656499i	$0.227963\pi$
$167$			16.9677i			1.31300i	−0.754327	+	0.656499i	$0.772037\pi$
$168$		0			0
$169$	−6.51462			−0.501124
$170$	−9.39116	+	13.1669i	−0.720269	+	1.00985i
$171$	17.6748			1.35163
$172$	−18.3595	+	11.2994i	−1.39990	+	0.861570i
$173$	10.0363			0.763047			0.381524	−	0.924359i	$-0.375399\pi$
$173$	10.0363			0.763047			0.381524	+	0.924359i	$0.375399\pi$
$174$	0.308158	+	1.08863i	0.0233614	+	0.0825289i
$175$		0			0
$176$	17.4818	+	8.82279i	1.31774	+	0.665043i
$177$			2.40908i			0.181077i
$178$	−0.840682	−	2.96988i	−0.0630118	−	0.222602i
$179$			3.55282i			0.265550i	0.991146	+	0.132775i	$0.0423888\pi$
$179$			3.55282i			0.265550i	−0.991146	+	0.132775i	$0.957611\pi$
$180$	−4.25090	+	11.8769i	−0.316843	+	0.885255i
$181$		−	22.2716i		−	1.65543i	−0.561148	−	0.827716i	$-0.689640\pi$
$181$		−	22.2716i		−	1.65543i	0.561148	−	0.827716i	$-0.310360\pi$
$182$		0			0
$183$	1.63853			0.121124
$184$	8.86359	−	9.64432i	0.653432	−	0.710989i
$185$	3.29813	+	4.11722i	0.242483	+	0.302704i
$186$	0.240965	+	0.851260i	0.0176684	+	0.0624174i
$187$			25.0371i			1.83089i
$188$	12.8042	+	20.8045i	0.933843	+	1.51733i
$189$		0			0
$190$	−11.5060	+	16.1320i	−0.834733	+	1.17034i
$191$		−	17.8460i		−	1.29129i	−0.763636	−	0.645647i	$-0.776588\pi$
$191$		−	17.8460i		−	1.29129i	0.763636	−	0.645647i	$-0.223412\pi$
$192$	−3.37507	+	0.285255i	−0.243575	+	0.0205865i
$193$			18.2331i			1.31245i	0.754567	+	0.656223i	$0.227847\pi$
$193$			18.2331i			1.31245i	−0.754567	+	0.656223i	$0.772153\pi$
$194$	−4.65825	+	1.31861i	−0.334443	+	0.0946703i
$195$	−1.50733	−	1.88168i	−0.107942	−	0.134750i
$196$		0			0
$197$			11.3569i			0.809148i	0.914505	+	0.404574i	$0.132580\pi$
$197$			11.3569i			0.809148i	−0.914505	+	0.404574i	$0.867420\pi$
$198$	5.31902	+	18.7905i	0.378006	+	1.33538i
$199$	9.02829			0.639998			0.319999	−	0.947418i	$-0.396317\pi$
$199$	9.02829			0.639998			0.319999	+	0.947418i	$0.396317\pi$
$200$	−8.07294	−	11.6115i	−0.570843	−	0.821059i
$201$		−	0.376523i		−	0.0265579i
$202$	−2.81454	−	9.94295i	−0.198030	−	0.699584i
$203$		0			0
$204$	−2.26987	−	3.68813i	−0.158923	−	0.258221i
$205$	9.86129	+	12.3103i	0.688743	+	0.859792i
$206$	−2.60028	−	9.18602i	−0.181170	−	0.640021i
$207$	13.0631			0.907950
$208$	−4.58961	+	9.09404i	−0.318232	+	0.630558i
$209$			30.6753i			2.12186i
$210$		0			0
$211$		−	4.40164i		−	0.303021i	−0.988456	−	0.151511i	$-0.951586\pi$
$211$		−	4.40164i		−	0.303021i	0.988456	−	0.151511i	$-0.0484138\pi$
$212$	−2.34417	−	3.80885i	−0.160998	−	0.261593i
$213$	6.06759			0.415744
$214$	−13.3761	+	3.78635i	−0.914369	+	0.258829i
$215$	18.8112	−	15.0689i	1.28291	−	1.02769i
$216$	−5.13222	−	4.71675i	−0.349203	−	0.320934i
$217$		0			0
$218$	−12.8076	+	3.62544i	−0.867442	+	0.245546i
$219$		−	3.33286i		−	0.225214i
$220$	−20.6129	−	7.37761i	−1.38972	−	0.497398i
$221$	−13.0243			−0.876107
$222$	−1.35919	+	0.384745i	−0.0912230	+	0.0258224i
$223$		−	14.1103i		−	0.944899i	−0.881358	−	0.472449i	$-0.843370\pi$
$223$		−	14.1103i		−	0.944899i	0.881358	−	0.472449i	$-0.156630\pi$
$224$		0			0
$225$	3.07819	−	13.7637i	0.205213	−	0.917580i
$226$	−6.13451	−	21.6714i	−0.408062	−	1.44156i
$227$		−	10.9976i		−	0.729936i	−0.931020	−	0.364968i	$-0.881080\pi$
$227$		−	10.9976i		−	0.729936i	0.931020	−	0.364968i	$-0.118920\pi$
$228$	−2.78104	−	4.51868i	−0.184179	−	0.299257i
$229$			8.10937i			0.535883i	0.963435	+	0.267941i	$0.0863433\pi$
$229$			8.10937i			0.535883i	−0.963435	+	0.267941i	$0.913657\pi$
$230$	−8.50388	+	11.9228i	−0.560729	+	0.786169i
$231$		0			0
$232$	−3.61652	+	3.93507i	−0.237436	+	0.258350i
$233$			15.8742i			1.03995i	0.854180	+	0.519977i	$0.174059\pi$
$233$			15.8742i			1.03995i	−0.854180	+	0.519977i	$0.825941\pi$
$234$	−9.77482	+	2.76695i	−0.639000	+	0.180881i
$235$	−17.0757	−	21.3164i	−1.11390	−	1.39053i
$236$	−9.69157	+	5.96471i	−0.630867	+	0.388269i
$237$	1.96441			0.127602
$238$		0			0
$239$		−	24.4934i		−	1.58435i	−0.610295	−	0.792174i	$-0.708949\pi$
$239$		−	24.4934i		−	1.58435i	0.610295	−	0.792174i	$-0.291051\pi$
$240$	3.70528	−	0.782002i	0.239175	−	0.0504780i
$241$		−	19.1862i		−	1.23589i	−0.786222	−	0.617945i	$-0.787966\pi$
$241$		−	19.1862i		−	1.23589i	0.786222	−	0.617945i	$-0.212034\pi$
$242$	−17.6435	+	4.99433i	−1.13417	+	0.321048i
$243$		−	10.5343i		−	0.675778i
$244$	4.05689	+	6.59171i	0.259716	+	0.421991i
$245$		0			0
$246$	−4.06394	+	1.15038i	−0.259107	+	0.0733452i
$247$	−15.9573			−1.01534
$248$	−2.82795	+	3.07705i	−0.179575	+	0.195393i
$249$	−1.83274			−0.116145
$250$	10.5584	+	11.7694i	0.667773	+	0.744365i
$251$	21.1323			1.33386			0.666929	−	0.745121i	$-0.267608\pi$
$251$	21.1323			1.33386			0.666929	+	0.745121i	$0.267608\pi$
$252$		0			0
$253$			22.6716i			1.42535i
$254$	−16.6272	+	4.70664i	−1.04328	+	0.295321i
$255$	3.02710	+	3.77888i	0.189564	+	0.236643i
$256$	−9.50401	−	12.8714i	−0.594000	−	0.804465i
$257$	−25.6520			−1.60013			−0.800064	−	0.599915i	$-0.795201\pi$
$257$	−25.6520			−1.60013			−0.800064	+	0.599915i	$0.795201\pi$
$258$	1.75787	+	6.21003i	0.109440	+	0.386620i
$259$		0			0
$260$	3.83783	−	10.7228i	0.238012	−	0.665001i
$261$	−5.33001			−0.329919
$262$	13.4042	−	3.79431i	0.828113	−	0.234413i
$263$	−10.0198			−0.617845			−0.308922	−	0.951087i	$-0.599968\pi$
$263$	−10.0198			−0.617845			−0.308922	+	0.951087i	$0.599968\pi$
$264$	3.96701	−	4.31643i	0.244152	−	0.265658i
$265$	3.12619	+	3.90257i	0.192040	+	0.239733i
$266$		0			0
$267$	−0.924061			−0.0565516
$268$	1.51473	−	0.932245i	0.0925269	−	0.0569459i
$269$		−	13.6945i		−	0.834966i	−0.908685	−	0.417483i	$-0.862912\pi$
$269$		−	13.6945i		−	0.834966i	0.908685	−	0.417483i	$-0.137088\pi$
$270$	6.34473	+	4.52533i	0.386128	+	0.275403i
$271$	−15.3609			−0.933107			−0.466554	−	0.884493i	$-0.654505\pi$
$271$	−15.3609			−0.933107			−0.466554	+	0.884493i	$0.654505\pi$
$272$	9.21708	−	18.2631i	0.558868	−	1.10736i
$273$		0			0
$274$	−1.80838	−	6.38849i	−0.109249	−	0.385943i
$275$	23.8875	+	5.34233i	1.44047	+	0.322155i
$276$	−2.05541	−	3.33967i	−0.123721	−	0.201025i
$277$			17.8089i			1.07004i	0.844841	+	0.535018i	$0.179695\pi$
$277$			17.8089i			1.07004i	−0.844841	+	0.535018i	$0.820305\pi$
$278$	−18.8796	+	5.34424i	−1.13233	+	0.320526i
$279$	−4.16783			−0.249521
$280$		0			0
$281$	29.6169			1.76680			0.883398	−	0.468624i	$-0.155250\pi$
$281$	29.6169			1.76680			0.883398	+	0.468624i	$0.155250\pi$
$282$	7.03706	−	1.99198i	0.419051	−	0.118620i
$283$		−	3.57827i		−	0.212706i	−0.994328	−	0.106353i	$-0.966083\pi$
$283$		−	3.57827i		−	0.212706i	0.994328	−	0.106353i	$-0.0339174\pi$
$284$	15.0229	+	24.4095i	0.891447	+	1.44844i
$285$	3.70879	+	4.62987i	0.219690	+	0.274250i
$286$	−4.80215	−	16.9646i	−0.283957	−	1.00314i
$287$		0			0
$288$	3.03757	−	15.6647i	0.178991	−	0.923053i
$289$	9.15600			0.538588
$290$	3.46975	−	4.86476i	0.203751	−	0.285668i
$291$			1.44938i			0.0849644i
$292$	13.4079	−	8.25192i	0.784637	−	0.482907i
$293$	−17.7739			−1.03836			−0.519180	−	0.854665i	$-0.673763\pi$
$293$	−17.7739			−1.03836			−0.519180	+	0.854665i	$0.673763\pi$
$294$		0			0
$295$	9.93004	−	7.95453i	0.578149	−	0.463131i
$296$	−4.91307	−	4.51534i	−0.285566	−	0.262449i
$297$	12.0647			0.700063
$298$	−7.43456	+	2.10449i	−0.430673	+	0.121910i
$299$	−11.7937			−0.682049
$300$	−4.00312	+	1.37868i	−0.231120	+	0.0795984i
$301$		0			0
$302$	0.576278	+	2.03582i	0.0331611	+	0.117148i
$303$	−3.09369			−0.177728
$304$	11.2927	−	22.3759i	0.647682	−	1.28334i
$305$	−5.41027	−	6.75391i	−0.309791	−	0.386728i
$306$	19.6303	−	5.55672i	1.12219	−	0.317657i
$307$			32.8923i			1.87726i	0.344923	+	0.938631i	$0.387905\pi$
$307$			32.8923i			1.87726i	−0.344923	+	0.938631i	$0.612095\pi$
$308$		0			0
$309$	−2.85818			−0.162596
$310$	2.71319	−	3.80402i	0.154099	−	0.216054i
$311$	−19.8748			−1.12700			−0.563499	−	0.826117i	$-0.690545\pi$
$311$	−19.8748			−1.12700			−0.563499	+	0.826117i	$0.690545\pi$
$312$	2.24540	+	2.06363i	0.127121	+	0.116830i
$313$	−6.37144			−0.360135			−0.180068	−	0.983654i	$-0.557632\pi$
$313$	−6.37144			−0.360135			−0.180068	+	0.983654i	$0.557632\pi$
$314$	−31.1658	+	8.82208i	−1.75879	+	0.497859i
$315$		0			0
$316$	4.86373	+	7.90269i	0.273606	+	0.444561i
$317$		−	17.0023i		−	0.954942i	−0.878648	−	0.477471i	$-0.841554\pi$
$317$		−	17.0023i		−	0.954942i	0.878648	−	0.477471i	$-0.158446\pi$
$318$	−1.28833	+	0.364687i	−0.0722461	+	0.0204506i
$319$		−	9.25045i		−	0.517926i
$320$	12.3200	+	12.9699i	0.688706	+	0.725040i
$321$			4.16188i			0.232293i
$322$		0			0
$323$	32.0462			1.78310
$324$	12.6362	−	7.77699i	0.702011	−	0.432055i
$325$	−2.77908	+	12.4262i	−0.154155	+	0.689283i
$326$	2.62694	−	0.743605i	0.145493	−	0.0411845i
$327$			3.98502i			0.220372i
$328$	−14.6899	−	13.5007i	−0.811115	−	0.745453i
$329$		0			0
$330$	−3.80601	+	5.33621i	−0.209514	+	0.293749i
$331$			14.6613i			0.805857i	0.915231	+	0.402929i	$0.132008\pi$
$331$			14.6613i			0.805857i	−0.915231	+	0.402929i	$0.867992\pi$
$332$	−4.53775	−	7.37302i	−0.249041	−	0.404647i
$333$		−	6.65469i		−	0.364675i
$334$	6.53570	+	23.0887i	0.357618	+	1.26336i
$335$	−1.55200	+	1.24324i	−0.0847949	+	0.0679256i
$336$		0			0
$337$		−	15.2435i		−	0.830368i	−0.909738	−	0.415184i	$-0.863717\pi$
$337$		−	15.2435i		−	0.830368i	0.909738	−	0.415184i	$-0.136283\pi$
$338$	−8.86475	+	2.50934i	−0.482179	+	0.136490i
$339$	−6.74293			−0.366226
$340$	−7.70731	+	21.5341i	−0.417988	+	1.16785i
$341$		−	7.23343i		−	0.391712i
$342$	24.0509	−	6.80807i	1.30052	−	0.368138i
$343$		0			0
$344$	−20.6302	+	22.4474i	−1.11231	+	1.21028i
$345$	2.74110	+	3.42185i	0.147576	+	0.184226i
$346$	13.6569	−	3.86584i	0.734199	−	0.207829i
$347$	33.4194			1.79405			0.897024	−	0.441983i	$-0.145725\pi$
$347$	33.4194			1.79405			0.897024	+	0.441983i	$0.145725\pi$
$348$	0.838649	+	1.36265i	0.0449563	+	0.0730459i
$349$		−	16.1586i		−	0.864951i	−0.901646	−	0.432476i	$-0.857640\pi$
$349$		−	16.1586i		−	0.864951i	0.901646	−	0.432476i	$-0.142360\pi$
$350$		0			0
$351$			6.27603i			0.334990i
$352$	27.1868	+	5.27183i	1.44906	+	0.280990i
$353$	−22.6854			−1.20742			−0.603711	−	0.797203i	$-0.706312\pi$
$353$	−22.6854			−1.20742			−0.603711	+	0.797203i	$0.706312\pi$
$354$	0.927941	+	3.27814i	0.0493195	+	0.174231i
$355$	−20.0346	−	25.0102i	−1.06333	−	1.32740i
$356$	−2.28791	−	3.71744i	−0.121259	−	0.197024i
$357$		0			0
$358$	1.36850	+	4.83449i	0.0723272	+	0.255511i
$359$		−	16.7678i		−	0.884971i	−0.896776	−	0.442486i	$-0.854097\pi$
$359$		−	16.7678i		−	0.884971i	0.896776	−	0.442486i	$-0.145903\pi$
$360$	−1.20958	+	17.7989i	−0.0637503	+	0.938084i
$361$	20.2628			1.06647
$362$	−8.57867	−	30.3059i	−0.450885	−	1.59285i
$363$			5.48966i			0.288133i
$364$		0			0
$365$	−13.7378	+	11.0048i	−0.719069	+	0.576016i
$366$	2.22963	−	0.631138i	0.116544	−	0.0329901i
$367$			15.6432i			0.816567i	0.912855	+	0.408284i	$0.133873\pi$
$367$			15.6432i			0.816567i	−0.912855	+	0.408284i	$0.866127\pi$
$368$	8.34625	−	16.5376i	0.435078	−	0.862082i
$369$		−	19.8973i		−	1.03581i
$370$	6.07381	+	4.33210i	0.315762	+	0.225215i
$371$		0			0
$372$	0.655785	+	1.06553i	0.0340009	+	0.0552453i
$373$		−	17.1045i		−	0.885637i	−0.896611	−	0.442819i	$-0.853979\pi$
$373$		−	17.1045i		−	0.885637i	0.896611	−	0.442819i	$-0.146021\pi$
$374$	9.64392	+	34.0691i	0.498675	+	1.76167i
$375$	4.25128	−	2.08178i	0.219535	−	0.107503i
$376$	25.4369	+	23.3777i	1.31181	+	1.20561i
$377$	4.81207			0.247834
$378$		0			0
$379$		−	10.3762i		−	0.532990i	−0.963836	−	0.266495i	$-0.914134\pi$
$379$		−	10.3762i		−	0.532990i	0.963836	−	0.266495i	$-0.0858655\pi$
$380$	−9.44296	+	26.3835i	−0.484414	+	1.35344i
$381$			5.17345i			0.265044i
$382$	−6.87403	−	24.2839i	−0.351706	−	1.24247i
$383$		−	9.23779i		−	0.472029i	−0.971750	−	0.236015i	$-0.924159\pi$
$383$		−	9.23779i		−	0.472029i	0.971750	−	0.236015i	$-0.0758413\pi$
$384$	−4.48274	+	1.68819i	−0.228759	+	0.0861500i
$385$		0			0
$386$	7.02311	+	24.8106i	0.357467	+	1.26283i
$387$	−30.4047			−1.54556
$388$	−5.83079	+	3.58858i	−0.296013	+	0.182182i
$389$	17.0843			0.866208			0.433104	−	0.901344i	$-0.357418\pi$
$389$	17.0843			0.866208			0.433104	+	0.901344i	$0.357418\pi$
$390$	−2.77589	−	1.97989i	−0.140563	−	0.100255i
$391$	23.6848			1.19779
$392$		0			0
$393$		−	4.17063i		−	0.210380i
$394$	4.37452	+	15.4539i	0.220385	+	0.778557i
$395$	−6.48628	−	8.09714i	−0.326360	−	0.407411i
$396$	14.4757	+	23.5203i	0.727430	+	1.18194i
$397$	33.5365			1.68315			0.841573	−	0.540143i	$-0.181630\pi$
$397$	33.5365			1.68315			0.841573	+	0.540143i	$0.181630\pi$
$398$	12.2852	−	3.47756i	0.615802	−	0.174315i
$399$		0			0
$400$	−15.4578	−	12.6908i	−0.772891	−	0.634539i
$401$	−12.8286			−0.640627			−0.320314	−	0.947312i	$-0.603788\pi$
$401$	−12.8286			−0.640627			−0.320314	+	0.947312i	$0.603788\pi$
$402$	−0.145031	−	0.512353i	−0.00723350	−	0.0255538i
$403$	3.76282			0.187440
$404$	−7.65976	−	12.4457i	−0.381087	−	0.619198i
$405$	−12.9471	+	10.3714i	−0.643348	+	0.515359i
$406$		0			0
$407$	11.5495			0.572487
$408$	−4.50934	−	4.14429i	−0.223245	−	0.205173i
$409$			21.5972i			1.06791i	0.845511	+	0.533957i	$0.179296\pi$
$409$			21.5972i			1.06791i	−0.845511	+	0.533957i	$0.820704\pi$
$410$	18.1605	+	12.9528i	0.896883	+	0.639695i
$411$	−1.98774			−0.0980480
$412$	−7.07664	−	11.4983i	−0.348641	−	0.566479i
$413$		0			0
$414$	17.7756	−	5.03172i	0.873623	−	0.247296i
$415$	6.05154	+	7.55444i	0.297058	+	0.370833i
$416$	−2.74240	+	14.1425i	−0.134457	+	0.693395i
$417$			5.87429i			0.287665i
$418$	11.8157	+	41.7413i	0.577924	+	2.04164i
$419$	18.7281			0.914929			0.457464	−	0.889228i	$-0.348758\pi$
$419$	18.7281			0.914929			0.457464	+	0.889228i	$0.348758\pi$
$420$		0			0
$421$	−18.9665			−0.924371			−0.462186	−	0.886783i	$-0.652935\pi$
$421$	−18.9665			−0.924371			−0.462186	+	0.886783i	$0.652935\pi$
$422$	−1.69545	−	5.98951i	−0.0825330	−	0.291565i
$423$			34.4540i			1.67521i
$424$	−4.65694	−	4.27994i	−0.226161	−	0.207852i
$425$	5.58108	−	24.9550i	0.270722	−	1.21049i
$426$	8.25645	−	2.33715i	0.400026	−	0.113235i
$427$		0			0
$428$	−16.7430	+	10.3045i	−0.809303	+	0.498088i
$429$	−5.27843			−0.254845
$430$	19.7930	−	27.7507i	0.954503	−	1.33826i
$431$		−	27.0242i		−	1.30171i	−0.759203	−	0.650854i	$-0.774411\pi$
$431$		−	27.0242i		−	1.30171i	0.759203	−	0.650854i	$-0.225589\pi$
$432$	−8.80048	−	4.44145i	−0.423413	−	0.213689i
$433$	15.0015			0.720928			0.360464	−	0.932773i	$-0.382618\pi$
$433$	15.0015			0.720928			0.360464	+	0.932773i	$0.382618\pi$
$434$		0			0
$435$	−1.11842	−	1.39618i	−0.0536243	−	0.0669418i
$436$	−16.0315	+	9.86662i	−0.767769	+	0.472526i
$437$	29.0185			1.38814
$438$	−1.28377	−	4.53517i	−0.0613408	−	0.216699i
$439$	−18.4380			−0.879997			−0.439998	−	0.897999i	$-0.645021\pi$
$439$	−18.4380			−0.879997			−0.439998	+	0.897999i	$0.645021\pi$
$440$	−30.8907	−	2.09927i	−1.47266	−	0.100079i
$441$		0			0
$442$	−17.7227	+	5.01676i	−0.842985	+	0.238623i
$443$	20.8595			0.991067			0.495533	−	0.868589i	$-0.334973\pi$
$443$	20.8595			0.991067			0.495533	+	0.868589i	$0.334973\pi$
$444$	−1.70132	+	1.04708i	−0.0807410	+	0.0496923i
$445$	3.05116	+	3.80891i	0.144639	+	0.180560i
$446$	−5.43510	−	19.2006i	−0.257359	−	0.909175i
$447$			2.31322i			0.109411i
$448$		0			0
$449$	14.6483			0.691298			0.345649	−	0.938364i	$-0.387659\pi$
$449$	14.6483			0.691298			0.345649	+	0.938364i	$0.387659\pi$
$450$	−1.11293	−	19.9146i	−0.0524641	−	0.938783i
$451$	34.5326			1.62608
$452$	−16.6950	−	27.1264i	−0.785268	−	1.27592i
$453$	0.633433			0.0297613
$454$	−4.23611	−	14.9649i	−0.198811	−	0.702339i
$455$		0			0
$456$	−5.52481	−	5.07756i	−0.258723	−	0.237779i
$457$		−	1.19001i		−	0.0556663i	−0.999613	−	0.0278331i	$-0.991139\pi$
$457$		−	1.19001i		−	0.0556663i	0.999613	−	0.0278331i	$-0.00886070\pi$
$458$	3.12361	+	11.0348i	0.145957	+	0.515623i
$459$		−	12.6038i		−	0.588297i
$460$	−6.97912	+	19.4995i	−0.325403	+	0.909171i
$461$		−	14.5645i		−	0.678336i	−0.940726	−	0.339168i	$-0.889854\pi$
$461$		−	14.5645i		−	0.678336i	0.940726	−	0.339168i	$-0.110146\pi$
$462$		0			0
$463$	4.69391			0.218145			0.109072	−	0.994034i	$-0.465212\pi$
$463$	4.69391			0.218145			0.109072	+	0.994034i	$0.465212\pi$
$464$	−3.40543	+	6.74767i	−0.158093	+	0.313253i
$465$	−0.874556	−	1.09175i	−0.0405565	−	0.0506287i
$466$	6.11451	+	21.6008i	0.283249	+	1.00064i
$467$			25.2818i			1.16990i	0.811068	+	0.584952i	$0.198887\pi$
$467$			25.2818i			1.16990i	−0.811068	+	0.584952i	$0.801113\pi$
$468$	−12.2353	+	7.53023i	−0.565575	+	0.348085i
$469$		0			0
$470$	−31.4465	−	22.4290i	−1.45052	−	1.03457i
$471$			9.69706i			0.446817i
$472$	−10.8903	+	11.8495i	−0.501265	+	0.545418i
$473$		−	52.7686i		−	2.42631i
$474$	2.67306	−	0.756661i	0.122778	−	0.0347546i
$475$	6.83791	−	30.5747i	0.313745	−	1.40286i
$476$		0			0
$477$		−	6.30776i		−	0.288813i
$478$	−9.43451	−	33.3294i	−0.431525	−	1.52445i
$479$	−4.10286			−0.187464			−0.0937322	−	0.995597i	$-0.529880\pi$
$479$	−4.10286			−0.187464			−0.0937322	+	0.995597i	$0.529880\pi$
$480$	4.74073	−	2.49133i	0.216384	−	0.113713i
$481$			6.00804i			0.273943i
$482$	−7.39023	−	26.1075i	−0.336616	−	1.18916i
$483$		0			0
$484$	−22.0846	+	13.5920i	−1.00385	+	0.617820i
$485$	5.97426	−	4.78573i	0.271277	−	0.217309i
$486$	−4.05767	−	14.3346i	−0.184060	−	0.650229i
$487$	33.8115			1.53215			0.766073	−	0.642754i	$-0.222208\pi$
$487$	33.8115			1.53215			0.766073	+	0.642754i	$0.222208\pi$
$488$	8.05943	+	7.40700i	0.364833	+	0.335299i
$489$		−	0.817356i		−	0.0369621i
$490$		0			0
$491$		−	25.9116i		−	1.16937i	−0.811259	−	0.584686i	$-0.801218\pi$
$491$		−	25.9116i		−	1.16937i	0.811259	−	0.584686i	$-0.198782\pi$
$492$	−5.08688	+	3.13074i	−0.229334	+	0.141145i
$493$	−9.66385			−0.435238
$494$	−21.7138	+	6.14651i	−0.976950	+	0.276544i
$495$	−19.3048	−	24.0991i	−0.867684	−	1.08317i
$496$	−2.66289	+	5.27637i	−0.119567	+	0.236916i
$497$		0			0
$498$	−2.49390	+	0.705946i	−0.111754	+	0.0316342i
$499$			24.3024i			1.08792i	0.839110	+	0.543962i	$0.183077\pi$
$499$			24.3024i			1.08792i	−0.839110	+	0.543962i	$0.816923\pi$
$500$	18.9008	+	11.9483i	0.845267	+	0.534344i
$501$	7.18391			0.320953
$502$	28.7557	−	8.13985i	1.28343	−	0.363299i
$503$			11.5222i			0.513750i	0.966445	+	0.256875i	$0.0826928\pi$
$503$			11.5222i			0.513750i	−0.966445	+	0.256875i	$0.917307\pi$
$504$		0			0
$505$	10.2151	+	12.7520i	0.454564	+	0.567455i
$506$	8.73276	+	30.8503i	0.388218	+	1.37146i
$507$			2.75821i			0.122496i
$508$	−20.8125	+	12.8091i	−0.923404	+	0.568312i
$509$			27.1315i			1.20258i	0.799031	+	0.601290i	$0.205347\pi$
$509$			27.1315i			1.20258i	−0.799031	+	0.601290i	$0.794653\pi$
$510$	5.57469	+	3.97611i	0.246851	+	0.176065i
$511$		0			0
$512$	−17.8904	−	13.8540i	−0.790653	−	0.612264i
$513$		−	15.4422i		−	0.681788i
$514$	−34.9059	+	9.88077i	−1.53963	+	0.435822i
$515$	9.43741	+	11.7812i	0.415862	+	0.519141i
$516$	4.78403	+	7.77318i	0.210605	+	0.342195i
$517$	−59.7962			−2.62983
$518$		0			0
$519$		−	4.24926i		−	0.186522i
$520$	1.09204	−	16.0693i	0.0478891	−	0.704686i
$521$			17.2809i			0.757090i	0.925583	+	0.378545i	$0.123576\pi$
$521$			17.2809i			0.757090i	−0.925583	+	0.378545i	$0.876424\pi$
$522$	−7.25279	+	2.05304i	−0.317446	+	0.0898592i
$523$		−	19.0461i		−	0.832828i	−0.909175	−	0.416414i	$-0.863287\pi$
$523$		−	19.0461i		−	0.832828i	0.909175	−	0.416414i	$-0.136713\pi$
$524$	16.7782	−	10.3262i	0.732958	−	0.451101i
$525$		0			0
$526$	−13.6344	+	3.85946i	−0.594486	+	0.168281i
$527$	−7.55669			−0.329175
$528$	3.73546	−	7.40160i	0.162565	−	0.322114i
$529$	−1.55298			−0.0675209
$530$	5.75716	+	4.10625i	0.250075	+	0.178364i
$531$	−16.0500			−0.696511
$532$		0			0
$533$			17.9638i			0.778100i
$534$	−1.25741	+	0.355935i	−0.0544136	+	0.0154028i
$535$	17.1550	−	13.7421i	0.741674	−	0.594123i
$536$	1.70208	−	1.85200i	0.0735185	−	0.0799943i
$537$	1.50422			0.0649120
$538$	−5.27490	−	18.6347i	−0.227417	−	0.803399i
$539$		0			0
$540$	10.3767	+	3.71394i	0.446541	+	0.159822i
$541$	18.3881			0.790564			0.395282	−	0.918560i	$-0.370647\pi$
$541$	18.3881			0.790564			0.395282	+	0.918560i	$0.370647\pi$
$542$	−20.9023	+	5.91679i	−0.897830	+	0.254148i
$543$	−9.42951			−0.404659
$544$	5.50743	−	28.4018i	0.236129	−	1.21772i
$545$	16.4259	−	13.1581i	0.703610	−	0.563632i
$546$		0			0
$547$	−18.9519			−0.810323			−0.405161	−	0.914245i	$-0.632785\pi$
$547$	−18.9519			−0.810323			−0.405161	+	0.914245i	$0.632785\pi$
$548$	−4.92151	−	7.99656i	−0.210236	−	0.341596i
$549$			10.9164i			0.465901i
$550$	34.5626	−	1.93154i	1.47375	−	0.0823611i
$551$	−11.8401			−0.504405
$552$	−4.08329	−	3.75274i	−0.173796	−	0.159727i
$553$		0			0
$554$	6.85974	+	24.2335i	0.291443	+	1.02958i
$555$	1.74318	−	1.39639i	0.0739939	−	0.0592734i
$556$	−23.6319	+	14.5443i	−1.00222	+	0.616817i
$557$			25.5109i			1.08093i	0.841365	+	0.540467i	$0.181752\pi$
$557$			25.5109i			1.08093i	−0.841365	+	0.540467i	$0.818248\pi$
$558$	−5.67136	+	1.60539i	−0.240088	+	0.0679614i
$559$	27.4502			1.16102
$560$		0			0
$561$	10.6004			0.447549
$562$	40.3011	−	11.4080i	1.70000	−	0.481217i
$563$			31.4612i			1.32593i	0.748650	+	0.662965i	$0.230702\pi$
$563$			31.4612i			1.32593i	−0.748650	+	0.662965i	$0.769298\pi$
$564$	8.80838	−	5.42115i	0.370900	−	0.228272i
$565$	22.2645	+	27.7939i	0.936675	+	1.16930i
$566$	−1.37830	−	4.86912i	−0.0579342	−	0.204665i
$567$		0			0
$568$	29.8446	+	27.4286i	1.25225	+	1.15088i
$569$	16.4346			0.688972			0.344486	−	0.938791i	$-0.388053\pi$
$569$	16.4346			0.688972			0.344486	+	0.938791i	$0.388053\pi$
$570$	6.83008	+	4.87150i	0.286081	+	0.204045i
$571$			15.0067i			0.628011i	0.949421	+	0.314005i	$0.101671\pi$
$571$			15.0067i			0.628011i	−0.949421	+	0.314005i	$0.898329\pi$
$572$	−13.0690	−	21.2348i	−0.546443	−	0.887871i
$573$	−7.55580			−0.315648
$574$		0			0
$575$	5.05378	−	22.5972i	0.210757	−	0.942370i
$576$	−1.90046	−	22.4858i	−0.0791857	−	0.936907i
$577$	2.49932			0.104048			0.0520240	−	0.998646i	$-0.483433\pi$
$577$	2.49932			0.104048			0.0520240	+	0.998646i	$0.483433\pi$
$578$	12.4590	−	3.52676i	0.518226	−	0.146694i
$579$	7.71967			0.320818
$580$	2.84762	−	7.95620i	0.118241	−	0.330363i
$581$		0			0
$582$	0.558282	+	1.97225i	0.0231415	+	0.0817522i
$583$	10.9474			0.453394
$584$	15.0662	−	16.3933i	0.623444	−	0.678360i
$585$	12.5363	−	10.0423i	0.518313	−	0.415199i
$586$	−24.1857	+	6.84624i	−0.999104	+	0.282815i
$587$			22.1562i			0.914482i	0.889343	+	0.457241i	$0.151162\pi$
$587$			22.1562i			0.914482i	−0.889343	+	0.457241i	$0.848838\pi$
$588$		0			0
$589$	−9.25842			−0.381487
$590$	10.4483	−	14.6490i	0.430150	−	0.603090i
$591$	4.80839			0.197791
$592$	−8.42469	−	4.25180i	−0.346253	−	0.174748i
$593$	−28.6502			−1.17652			−0.588262	−	0.808670i	$-0.700188\pi$
$593$	−28.6502			−1.17652			−0.588262	+	0.808670i	$0.700188\pi$
$594$	16.4169	−	4.64713i	0.673596	−	0.190674i
$595$		0			0
$596$	−9.30594	+	5.72737i	−0.381186	+	0.234602i
$597$		−	3.82247i		−	0.156443i
$598$	−16.0483	+	4.54277i	−0.656263	+	0.185768i
$599$			16.4006i			0.670110i	0.942199	+	0.335055i	$0.108755\pi$
$599$			16.4006i			0.670110i	−0.942199	+	0.335055i	$0.891245\pi$
$600$	−4.91618	+	3.41798i	−0.200702	+	0.139539i
$601$			22.1672i			0.904220i	0.891962	+	0.452110i	$0.149329\pi$
$601$			22.1672i			0.904220i	−0.891962	+	0.452110i	$0.850671\pi$
$602$		0			0
$603$	2.50851			0.102155
$604$	1.56834	+	2.54826i	0.0638147	+	0.103687i
$605$	22.6280	−	18.1263i	0.919959	−	0.736940i
$606$	−4.20973	+	1.19164i	−0.171008	+	0.0484072i
$607$			28.7504i			1.16694i	0.812133	+	0.583472i	$0.198306\pi$
$607$			28.7504i			1.16694i	−0.812133	+	0.583472i	$0.801694\pi$
$608$	6.74768	−	34.7977i	0.273654	−	1.41123i
$609$		0			0
$610$	−9.96351	−	7.10640i	−0.403411	−	0.287730i
$611$		−	31.1059i		−	1.25841i
$612$	24.5715	−	15.1226i	0.993243	−	0.611295i
$613$			12.1472i			0.490620i	0.969445	+	0.245310i	$0.0788898\pi$
$613$			12.1472i			0.490620i	−0.969445	+	0.245310i	$0.921110\pi$
$614$	12.6696	+	44.7581i	0.511305	+	1.80629i
$615$	5.21205	−	4.17515i	0.210170	−	0.168358i
$616$		0			0
$617$		−	15.9265i		−	0.641175i	−0.947219	−	0.320588i	$-0.896120\pi$
$617$		−	15.9265i		−	0.641175i	0.947219	−	0.320588i	$-0.103880\pi$
$618$	−3.88925	+	1.10093i	−0.156449	+	0.0442858i
$619$	3.88335			0.156085			0.0780424	−	0.996950i	$-0.475133\pi$
$619$	3.88335			0.156085			0.0780424	+	0.996950i	$0.475133\pi$
$620$	2.22671	−	6.22139i	0.0894268	−	0.249857i
$621$		−	11.4130i		−	0.457989i
$622$	−27.0446	+	7.65549i	−1.08439	+	0.306957i
$623$		0			0
$624$	3.85031	+	1.94319i	0.154136	+	0.0777897i
$625$	−22.6183	−	10.6496i	−0.904730	−	0.425985i
$626$	−8.66992	+	2.45419i	−0.346520	+	0.0980890i
$627$	12.9876			0.518673
$628$	−39.0107	+	24.0092i	−1.55670	+	0.958073i
$629$		−	12.0656i		−	0.481089i
$630$		0			0
$631$		−	12.2743i		−	0.488633i	−0.969696	−	0.244316i	$-0.921436\pi$
$631$		−	12.2743i		−	0.488633i	0.969696	−	0.244316i	$-0.0785636\pi$
$632$	9.66231	+	8.88012i	0.384346	+	0.353232i
$633$	−1.86360			−0.0740715
$634$	−6.54902	−	23.1358i	−0.260095	−	0.918838i
$635$	21.3246	−	17.0822i	0.846240	−	0.677887i
$636$	−1.61262	+	0.992493i	−0.0639446	+	0.0393549i
$637$		0			0
$638$	−3.56314	−	12.5875i	−0.141066	−	0.498345i
$639$			40.4242i			1.59916i
$640$	21.7602	+	12.9033i	0.860146	+	0.510048i
$641$	14.8270			0.585631			0.292816	−	0.956169i	$-0.405408\pi$
$641$	14.8270			0.585631			0.292816	+	0.956169i	$0.405408\pi$
$642$	1.60309	+	5.66326i	0.0632691	+	0.223511i
$643$		−	11.8058i		−	0.465577i	−0.972527	−	0.232789i	$-0.925215\pi$
$643$		−	11.8058i		−	0.465577i	0.972527	−	0.232789i	$-0.0747850\pi$
$644$		0			0
$645$	−6.37998	−	7.96444i	−0.251211	−	0.313600i
$646$	43.6068	−	12.3437i	1.71569	−	0.485657i
$647$		−	34.6071i		−	1.36054i	−0.732960	−	0.680272i	$-0.761862\pi$
$647$		−	34.6071i		−	1.36054i	0.732960	−	0.680272i	$-0.238138\pi$
$648$	14.1991	−	15.4498i	0.557793	−	0.606926i
$649$		−	27.8554i		−	1.09342i
$650$	1.00478	+	17.9794i	0.0394109	+	0.705211i
$651$		0			0
$652$	3.28817	−	2.02372i	0.128775	−	0.0792549i
$653$			28.1875i			1.10306i	0.834155	+	0.551531i	$0.185956\pi$
$653$			28.1875i			1.10306i	−0.834155	+	0.551531i	$0.814044\pi$
$654$	1.53497	+	5.42260i	0.0600221	+	0.212040i
$655$	−17.1910	+	13.7710i	−0.671709	+	0.538077i
$656$	−25.1895	−	12.7127i	−0.983487	−	0.496349i
$657$	22.2045			0.866281
$658$		0			0
$659$		−	9.79123i		−	0.381412i	−0.981647	−	0.190706i	$-0.938922\pi$
$659$		−	9.79123i		−	0.381412i	0.981647	−	0.190706i	$-0.0610777\pi$
$660$	−3.12359	+	8.72726i	−0.121586	+	0.339708i
$661$		−	0.817006i		−	0.0317779i	−0.999874	−	0.0158889i	$-0.994942\pi$
$661$		−	0.817006i		−	0.0317779i	0.999874	−	0.0158889i	$-0.00505782\pi$
$662$	5.64731	+	19.9503i	0.219489	+	0.775391i
$663$			5.51432i			0.214158i
$664$	−9.01470	−	8.28494i	−0.349838	−	0.321518i
$665$		0			0
$666$	−2.56329	−	9.05536i	−0.0993255	−	0.350888i
$667$	−8.75081			−0.338833
$668$	17.7869	+	28.9004i	0.688194	+	1.11819i
$669$	−5.97415			−0.230974
$670$	−1.63300	+	2.28955i	−0.0630884	+	0.0884529i
$671$	−18.9459			−0.731397
$672$		0			0
$673$			9.43129i			0.363550i	0.983340	+	0.181775i	$0.0581842\pi$
$673$			9.43129i			0.363550i	−0.983340	+	0.181775i	$0.941816\pi$
$674$	−5.87158	−	20.7426i	−0.226165	−	0.798974i
$675$	−12.0251	−	2.68936i	−0.462846	−	0.103514i
$676$	−11.0961	+	6.82914i	−0.426774	+	0.262659i
$677$	−2.47400			−0.0950837			−0.0475418	−	0.998869i	$-0.515139\pi$
$677$	−2.47400			−0.0950837			−0.0475418	+	0.998869i	$0.515139\pi$
$678$	−9.17542	+	2.59728i	−0.352380	+	0.0997479i
$679$		0			0
$680$	−2.19309	+	32.2712i	−0.0841010	+	1.23754i
$681$	−4.65625			−0.178428
$682$	−2.78621	−	9.84287i	−0.106690	−	0.376903i
$683$	−18.7560			−0.717679			−0.358840	−	0.933399i	$-0.616827\pi$
$683$	−18.7560			−0.717679			−0.358840	+	0.933399i	$0.616827\pi$
$684$	30.1048	−	18.5281i	1.15109	−	0.708440i
$685$	6.56332	+	8.19332i	0.250772	+	0.313051i
$686$		0			0
$687$	3.43341			0.130993
$688$	−19.4261	+	38.4917i	−0.740613	+	1.46748i
$689$			5.69482i			0.216955i
$690$	5.04799	+	3.60044i	0.192174	+	0.137066i
$691$	−4.22127			−0.160585			−0.0802923	−	0.996771i	$-0.525585\pi$
$691$	−4.22127			−0.160585			−0.0802923	+	0.996771i	$0.525585\pi$
$692$	17.0945	−	10.5209i	0.649836	−	0.399943i
$693$		0			0
$694$	45.4753	−	12.8727i	1.72622	−	0.488640i
$695$	24.2134	−	19.3963i	0.918466	−	0.735744i
$696$	1.66606	+	1.53119i	0.0631520	+	0.0580396i
$697$		−	36.0759i		−	1.36647i
$698$	−6.22406	−	21.9878i	−0.235584	−	0.832250i
$699$	6.72095			0.254210
$700$		0			0
$701$	−12.2843			−0.463971			−0.231985	−	0.972719i	$-0.574522\pi$
$701$	−12.2843			−0.463971			−0.231985	+	0.972719i	$0.574522\pi$
$702$	2.41743	+	8.54008i	0.0912401	+	0.322325i
$703$		−	14.7828i		−	0.557542i
$704$	39.0250	−	3.29832i	1.47081	−	0.124310i
$705$	−9.02512	+	7.22964i	−0.339906	+	0.272284i
$706$	−30.8691	+	8.73809i	−1.16177	+	0.328862i
$707$		0			0
$708$	2.52539	+	4.10329i	0.0949098	+	0.154211i
$709$	2.93616			0.110270			0.0551348	−	0.998479i	$-0.482441\pi$
$709$	2.93616			0.110270			0.0551348	+	0.998479i	$0.482441\pi$
$710$	−36.8956	−	26.3155i	−1.38467	−	0.987602i
$711$			13.0875i			0.490819i
$712$	−4.54517	−	4.17723i	−0.170337	−	0.156548i
$713$	−6.84273			−0.256262
$714$		0			0
$715$	17.4288	+	21.7573i	0.651802	+	0.813677i
$716$	3.72435	+	6.05140i	0.139186	+	0.226151i
$717$	−10.3702			−0.387283
$718$	−6.45872	−	22.8168i	−0.241037	−	0.851514i
$719$	47.5276			1.77248			0.886240	−	0.463226i	$-0.153308\pi$
$719$	47.5276			1.77248			0.886240	+	0.463226i	$0.153308\pi$
$720$	5.20994	+	24.6857i	0.194163	+	0.919982i
$721$		0			0
$722$	27.5726	−	7.80495i	1.02615	−	0.290470i
$723$	−8.12319			−0.302105
$724$	−23.3468	−	37.9343i	−0.867677	−	1.40982i
$725$	−2.06204	+	9.22011i	−0.0765823	+	0.342426i
$726$	2.11454	+	7.47004i	0.0784779	+	0.277239i
$727$			8.28795i			0.307383i	0.988119	+	0.153692i	$0.0491162\pi$
$727$			8.28795i			0.307383i	−0.988119	+	0.153692i	$0.950884\pi$
$728$		0			0
$729$	17.7963			0.659124
$730$	−14.4548	+	20.2663i	−0.534996	+	0.750089i
$731$	−55.1269			−2.03894
$732$	2.79085	−	1.71764i	0.103153	−	0.0634858i
$733$	41.9860			1.55079			0.775395	−	0.631477i	$-0.217551\pi$
$733$	41.9860			1.55079			0.775395	+	0.631477i	$0.217551\pi$
$734$	6.02552	+	21.2864i	0.222406	+	0.785696i
$735$		0			0
$736$	4.98709	−	25.7184i	0.183826	−	0.947991i
$737$			4.35363i			0.160368i
$738$	−7.66416	−	27.0752i	−0.282121	−	0.996653i
$739$		−	25.9230i		−	0.953593i	−0.879014	−	0.476796i	$-0.841798\pi$
$739$		−	25.9230i		−	0.953593i	0.879014	−	0.476796i	$-0.158202\pi$
$740$	9.93358	+	3.55535i	0.365166	+	0.130697i
$741$			6.75612i			0.248192i
$742$		0			0
$743$	11.2976			0.414470			0.207235	−	0.978291i	$-0.433554\pi$
$743$	11.2976			0.414470			0.207235	+	0.978291i	$0.433554\pi$
$744$	1.30279	+	1.19732i	0.0477624	+	0.0438959i
$745$	9.53492	−	7.63802i	0.349332	−	0.279835i
$746$	−6.58840	−	23.2749i	−0.241219	−	0.852155i
$747$		−	12.2103i		−	0.446752i
$748$	26.2459	+	42.6448i	0.959644	+	1.55925i
$749$		0			0
$750$	4.98304	−	4.47031i	0.181955	−	0.163233i
$751$			5.61823i			0.205012i	0.994732	+	0.102506i	$0.0326861\pi$
$751$			5.61823i			0.205012i	−0.994732	+	0.102506i	$0.967314\pi$
$752$	43.6179	+	22.0132i	1.59058	+	0.802739i
$753$		−	8.94716i		−	0.326053i
$754$	6.54802	−	1.85354i	0.238465	−	0.0675020i
$755$	−2.09153	−	2.61097i	−0.0761187	−	0.0950228i
$756$		0			0
$757$			27.0456i			0.982990i	0.870880	+	0.491495i	$0.163549\pi$
$757$			27.0456i			0.982990i	−0.870880	+	0.491495i	$0.836451\pi$
$758$	−3.99676	−	14.1194i	−0.145169	−	0.512839i
$759$	9.59887			0.348417
$760$	−2.68696	+	39.5385i	−0.0974662	+	1.43421i
$761$			25.8142i			0.935765i	0.883791	+	0.467883i	$0.154983\pi$
$761$			25.8142i			0.935765i	−0.883791	+	0.467883i	$0.845017\pi$
$762$	1.99274	+	7.03975i	0.0721892	+	0.255023i
$763$		0			0
$764$	−18.7076	−	30.3965i	−0.676818	−	1.09971i
$765$	−25.1761	+	20.1675i	−0.910243	+	0.729157i
$766$	−3.55826	−	12.5703i	−0.128565	−	0.454183i
$767$	14.4904			0.523217
$768$	−5.44961	+	4.02388i	−0.196646	+	0.145199i
$769$		−	5.58909i		−	0.201548i	−0.994909	−	0.100774i	$-0.967868\pi$
$769$		−	5.58909i		−	0.201548i	0.994909	−	0.100774i	$-0.0321319\pi$
$770$		0			0
$771$			10.8608i			0.391140i
$772$	19.1134	+	31.0557i	0.687905	+	1.11772i
$773$	−8.77216			−0.315513			−0.157756	−	0.987478i	$-0.550426\pi$
$773$	−8.77216			−0.315513			−0.157756	+	0.987478i	$0.550426\pi$
$774$	−41.3732	+	11.7115i	−1.48713	+	0.420960i
$775$	−1.61242	+	7.20971i	−0.0579199	+	0.258980i
$776$	−6.55196	+	7.12908i	−0.235202	+	0.255919i
$777$		0			0
$778$	23.2474	−	6.58062i	0.833459	−	0.235927i
$779$		−	44.2000i		−	1.58363i
$780$	−4.53991	−	1.62489i	−0.162555	−	0.0581804i
$781$	−70.1578			−2.51044
$782$	32.2290	−	9.12303i	1.15251	−	0.326239i
$783$			4.65674i			0.166418i
$784$		0			0
$785$	39.9706	−	32.0187i	1.42661	−	1.14280i
$786$	−1.60646	−	5.67517i	−0.0573007	−	0.202426i
$787$			9.89262i			0.352634i	0.984333	+	0.176317i	$0.0564183\pi$
$787$			9.89262i			0.352634i	−0.984333	+	0.176317i	$0.943582\pi$
$788$	11.9052	+	19.3439i	0.424107	+	0.689096i
$789$			4.24225i			0.151028i
$790$	−11.9451	−	8.51974i	−0.424987	−	0.303119i
$791$		0			0
$792$	28.7574	+	26.4294i	1.02185	+	0.939129i
$793$		−	9.85562i		−	0.349983i
$794$	45.6346	−	12.9178i	1.61951	−	0.458434i
$795$	1.65230	−	1.32359i	0.0586011	−	0.0469429i
$796$	15.3776	−	9.46417i	0.545043	−	0.335449i
$797$	31.5699			1.11826			0.559132	−	0.829079i	$-0.311135\pi$
$797$	31.5699			1.11826			0.559132	+	0.829079i	$0.311135\pi$
$798$		0			0
$799$			62.4685i			2.20998i
$800$	−25.9225	−	11.3148i	−0.916498	−	0.400039i
$801$		−	6.15638i		−	0.217525i
$802$	−17.4564	+	4.94137i	−0.616407	+	0.174486i
$803$			38.5368i			1.35994i
$804$	−0.394702	−	0.641319i	−0.0139200	−	0.0226176i
$805$		0			0
$806$	5.12025	−	1.44938i	0.180353	−	0.0510524i
$807$	−5.79807			−0.204102
$808$	−15.2169	−	13.9851i	−0.535329	−	0.491992i
$809$	30.7765			1.08204			0.541021	−	0.841009i	$-0.318038\pi$
$809$	30.7765			1.08204			0.541021	+	0.841009i	$0.318038\pi$
$810$	−13.6229	+	19.0999i	−0.478658	+	0.671102i
$811$	−19.0962			−0.670557			−0.335278	−	0.942119i	$-0.608830\pi$
$811$	−19.0962			−0.670557			−0.335278	+	0.942119i	$0.608830\pi$
$812$		0			0
$813$			6.50362i			0.228092i
$814$	15.7159	−	4.44869i	0.550843	−	0.155927i
$815$	−3.36908	+	2.69883i	−0.118014	+	0.0945358i
$816$	−7.73238	−	3.90240i	−0.270688	−	0.136611i
$817$	−67.5412			−2.36297
$818$	8.31894	+	29.3884i	0.290865	+	1.02754i
$819$		0			0
$820$	29.7011	+	10.6304i	1.03721	+	0.371229i
$821$	48.1711			1.68118			0.840591	−	0.541671i	$-0.182208\pi$
$821$	48.1711			1.68118			0.840591	+	0.541671i	$0.182208\pi$
$822$	−2.70481	+	0.765648i	−0.0943411	+	0.0267051i
$823$	−9.53508			−0.332372			−0.166186	−	0.986094i	$-0.553145\pi$
$823$	−9.53508			−0.332372			−0.166186	+	0.986094i	$0.553145\pi$
$824$	−14.0585	−	12.9204i	−0.489751	−	0.450104i
$825$	2.26188	−	10.1137i	0.0787485	−	0.352113i
$826$		0			0
$827$	−0.650873			−0.0226331			−0.0113165	−	0.999936i	$-0.503602\pi$
$827$	−0.650873			−0.0226331			−0.0113165	+	0.999936i	$0.503602\pi$
$828$	22.2499	−	13.6938i	0.773239	−	0.475893i
$829$		−	46.7979i		−	1.62536i	−0.582711	−	0.812679i	$-0.698008\pi$
$829$		−	46.7979i		−	1.62536i	0.582711	−	0.812679i	$-0.301992\pi$
$830$	11.1445	+	7.94871i	0.386830	+	0.275904i
$831$	7.54009			0.261563
$832$	1.71578	+	20.3008i	0.0594841	+	0.703802i
$833$		0			0
$834$	2.26269	+	7.99342i	0.0783505	+	0.276789i
$835$	−23.7206	−	29.6116i	−0.820884	−	1.02475i
$836$	32.1563	+	52.2482i	1.11215	+	1.80704i
$837$			3.64136i			0.125864i
$838$	25.4842	−	7.21380i	0.880339	−	0.249197i
$839$	−50.2124			−1.73353			−0.866763	−	0.498720i	$-0.833803\pi$
$839$	−50.2124			−1.73353			−0.866763	+	0.498720i	$0.833803\pi$
$840$		0			0
$841$	−25.4295			−0.876879
$842$	−25.8086	+	7.30562i	−0.889424	+	0.251768i
$843$		−	12.5394i		−	0.431881i
$844$	−4.61415	−	7.49715i	−0.158825	−	0.258063i
$845$	11.3691	−	9.10734i	0.391111	−	0.313302i
$846$	13.2712	+	46.8831i	0.456272	+	1.61187i
$847$		0			0
$848$	−7.98548	−	4.03014i	−0.274223	−	0.138395i
$849$	−1.51500			−0.0519946
$850$	−2.01786	−	36.1072i	−0.0692120	−	1.23847i
$851$		−	10.9257i		−	0.374527i
$852$	10.3347	−	6.36053i	0.354061	−	0.217908i
$853$	12.0132			0.411323			0.205661	−	0.978623i	$-0.434065\pi$
$853$	12.0132			0.411323			0.205661	+	0.978623i	$0.434065\pi$
$854$		0			0
$855$	−30.8456	+	24.7091i	−1.05490	+	0.845034i
$856$	−18.8138	+	20.4710i	−0.643043	+	0.699684i
$857$	−27.0264			−0.923205			−0.461603	−	0.887087i	$-0.652725\pi$
$857$	−27.0264			−0.923205			−0.461603	+	0.887087i	$0.652725\pi$
$858$	−7.18260	+	2.03317i	−0.245210	+	0.0694114i
$859$	−20.5765			−0.702060			−0.351030	−	0.936364i	$-0.614168\pi$
$859$	−20.5765			−0.702060			−0.351030	+	0.936364i	$0.614168\pi$
$860$	16.2441	−	45.3857i	0.553919	−	1.54764i
$861$		0			0
$862$	−10.4093	−	36.7731i	−0.354543	−	1.25250i
$863$	9.46391			0.322155			0.161078	−	0.986942i	$-0.448503\pi$
$863$	9.46391			0.322155			0.161078	+	0.986942i	$0.448503\pi$
$864$	−13.6860	−	2.65387i	−0.465607	−	0.0902867i
$865$	−17.5151	+	14.0306i	−0.595532	+	0.477056i
$866$	20.4133	−	5.77837i	0.693672	−	0.196357i
$867$		−	3.87654i		−	0.131654i
$868$		0			0
$869$	−22.7139			−0.770515
$870$	−2.05968	−	1.46905i	−0.0698297	−	0.0498055i
$871$	−2.26475			−0.0767382
$872$	−18.0143	+	19.6011i	−0.610041	+	0.663776i
$873$	−9.65625			−0.326815
$874$	39.4868	−	11.1775i	1.33566	−	0.378084i
$875$		0			0
$876$	−3.49377	−	5.67674i	−0.118043	−	0.191799i
$877$			20.2436i			0.683578i	0.939777	+	0.341789i	$0.111033\pi$
$877$			20.2436i			0.683578i	−0.939777	+	0.341789i	$0.888967\pi$
$878$	−25.0894	+	7.10204i	−0.846727	+	0.239682i
$879$			7.52525i			0.253820i
$880$	−42.8430	+	9.04207i	−1.44424	+	0.304808i
$881$			58.2514i			1.96254i	0.192638	+	0.981270i	$0.438296\pi$
$881$			58.2514i			1.96254i	−0.192638	+	0.981270i	$0.561704\pi$
$882$		0			0
$883$	−39.7551			−1.33786			−0.668932	−	0.743323i	$-0.733248\pi$
$883$	−39.7551			−1.33786			−0.668932	+	0.743323i	$0.733248\pi$
$884$	−22.1838	+	13.6531i	−0.746121	+	0.459203i
$885$	−3.36785	−	4.20426i	−0.113209	−	0.141325i
$886$	28.3846	−	8.03479i	0.953598	−	0.269934i
$887$			45.2774i			1.52027i	0.649767	+	0.760134i	$0.274867\pi$
$887$			45.2774i			1.52027i	−0.649767	+	0.760134i	$0.725133\pi$
$888$	−1.91174	+	2.08014i	−0.0641539	+	0.0698048i
$889$		0			0
$890$	5.61899	+	4.00770i	0.188349	+	0.134339i
$891$			36.3189i			1.21673i
$892$	−14.7916	−	24.0336i	−0.495259	−	0.804706i
$893$			76.5361i			2.56118i
$894$	0.891018	+	3.14770i	0.0298001	+	0.105275i
$895$	−4.96680	−	6.20030i	−0.166022	−	0.207253i
$896$		0			0
$897$			4.99333i			0.166722i
$898$	19.9327	−	5.64233i	0.665162	−	0.188287i
$899$	2.79197			0.0931174
$900$	−9.18523	−	26.6700i	−0.306174	−	0.889001i
$901$		−	11.4366i		−	0.381009i
$902$	46.9901	−	13.3015i	1.56460	−	0.442890i
$903$		0			0
$904$	−33.1664	−	30.4815i	−1.10310	−	1.01380i
$905$	31.1353	+	38.8678i	1.03497	+	1.29201i
$906$	0.861942	−	0.243989i	0.0286361	−	0.00810600i
$907$	−50.5578			−1.67875			−0.839373	−	0.543556i	$-0.817078\pi$
$907$	−50.5578			−1.67875			−0.839373	+	0.543556i	$0.817078\pi$
$908$	−11.5286	−	18.7318i	−0.382588	−	0.621637i
$909$		−	20.6111i		−	0.683627i
$910$		0			0
$911$		−	0.524910i		−	0.0173910i	−0.999962	−	0.00869552i	$-0.997232\pi$
$911$		−	0.524910i		−	0.0173910i	0.999962	−	0.00869552i	$-0.00276790\pi$
$912$	−9.47368	−	4.78120i	−0.313705	−	0.158321i
$913$	21.1915			0.701336
$914$	−0.458374	−	1.61930i	−0.0151617	−	0.0535617i
$915$	−2.85952	+	2.29064i	−0.0945329	+	0.0757263i
$916$	8.50089	+	13.8124i	0.280877	+	0.456375i
$917$		0			0
$918$	−4.85481	−	17.1506i	−0.160233	−	0.566055i
$919$		−	21.5126i		−	0.709634i	−0.934936	−	0.354817i	$-0.884543\pi$
$919$		−	21.5126i		−	0.709634i	0.934936	−	0.354817i	$-0.115457\pi$
$920$	−1.98588	+	29.2222i	−0.0654726	+	0.963427i
$921$	13.9262			0.458884
$922$	−5.61003	−	19.8186i	−0.184757	−	0.652691i
$923$		−	36.4960i		−	1.20128i
$924$		0			0
$925$	−11.5116	−	2.57453i	−0.378500	−	0.0846499i
$926$	6.38723	−	1.80803i	0.209897	−	0.0594155i
$927$		−	19.0421i		−	0.625423i
$928$	−2.03483	+	10.4936i	−0.0667966	+	0.344469i
$929$			15.6019i			0.511882i	0.966692	+	0.255941i	$0.0823853\pi$
$929$			15.6019i			0.511882i	−0.966692	+	0.255941i	$0.917615\pi$
$930$	−1.61058	−	1.14873i	−0.0528129	−	0.0376684i
$931$		0			0
$932$	16.6406	+	27.0380i	0.545081	+	0.885658i
$933$			8.41476i			0.275487i
$934$	9.73820	+	34.4022i	0.318644	+	1.12567i
$935$	−35.0015	−	43.6941i	−1.14467	−	1.42895i
$936$	−13.7486	+	14.9596i	−0.449386	+	0.488969i
$937$	7.15521			0.233751			0.116875	−	0.993147i	$-0.462712\pi$
$937$	7.15521			0.233751			0.116875	+	0.993147i	$0.462712\pi$
$938$		0			0
$939$			2.69759i			0.0880326i
$940$	−51.4300	−	18.4074i	−1.67746	−	0.600384i
$941$			7.12846i			0.232381i	0.993227	+	0.116191i	$0.0370683\pi$
$941$			7.12846i			0.232381i	−0.993227	+	0.116191i	$0.962932\pi$
$942$	3.73516	+	13.1952i	0.121698	+	0.429924i
$943$		−	32.6674i		−	1.06380i
$944$	−10.2546	+	20.3189i	−0.333760	+	0.661325i
$945$		0			0
$946$	−20.3257	−	71.8048i	−0.660846	−	2.33457i
$947$	23.1014			0.750696			0.375348	−	0.926884i	$-0.377523\pi$
$947$	23.1014			0.750696			0.375348	+	0.926884i	$0.377523\pi$
$948$	3.34590	−	2.05925i	0.108670	−	0.0668812i
$949$	−20.0468			−0.650748
$950$	−2.47227	−	44.2383i	−0.0802110	−	1.43528i
$951$	−7.19855			−0.233429
$952$		0			0
$953$		−	36.2840i		−	1.17535i	−0.809096	−	0.587677i	$-0.800043\pi$
$953$		−	36.2840i		−	1.17535i	0.809096	−	0.587677i	$-0.199957\pi$
$954$	−2.42966	−	8.58327i	−0.0786631	−	0.277894i
$955$	24.9485	+	31.1445i	0.807315	+	1.00781i
$956$	−25.6760	−	41.7188i	−0.830420	−	1.34928i
$957$	−3.91653			−0.126603
$958$	−5.58295	+	1.58036i	−0.180377	+	0.0510592i
$959$		0			0
$960$	5.49131	−	5.21612i	0.177231	−	0.168350i
$961$	−28.8168			−0.929574
$962$	2.31421	+	8.17542i	0.0746130	+	0.263586i
$963$	−27.7277			−0.893513
$964$	−20.1125	−	32.6791i	−0.647779	−	1.05252i
$965$	−25.4896	−	31.8199i	−0.820539	−	1.02432i
$966$		0			0
$967$	−41.0345			−1.31958			−0.659790	−	0.751450i	$-0.729355\pi$
$967$	−41.0345			−1.31958			−0.659790	+	0.751450i	$0.729355\pi$
$968$	−24.8161	+	27.0020i	−0.797619	+	0.867876i
$969$		−	13.5680i		−	0.435866i
$970$	6.28606	−	8.81336i	0.201833	−	0.282980i
$971$	44.2483			1.41999			0.709997	−	0.704204i	$-0.248696\pi$
$971$	44.2483			1.41999			0.709997	+	0.704204i	$0.248696\pi$
$972$	−11.0429	−	17.9428i	−0.354202	−	0.575514i
$973$		0			0
$974$	46.0089	−	13.0237i	1.47422	−	0.417306i
$975$	5.26112	+	1.17663i	0.168491	+	0.0376822i
$976$	13.8199	+	6.97467i	0.442365	+	0.223254i
$977$			11.5368i			0.369095i	0.982824	+	0.184547i	$0.0590819\pi$
$977$			11.5368i			0.369095i	−0.982824	+	0.184547i	$0.940918\pi$
$978$	−0.314833	−	1.11221i	−0.0100673	−	0.0355647i
$979$	10.6846			0.341483
$980$		0			0
$981$	−26.5494			−0.847658
$982$	−9.98076	−	35.2591i	−0.318499	−	1.12516i
$983$		−	15.7501i		−	0.502349i	−0.967942	−	0.251174i	$-0.919183\pi$
$983$		−	15.7501i		−	0.502349i	0.967942	−	0.251174i	$-0.0808167\pi$
$984$	−5.71605	+	6.21954i	−0.182221	+	0.198272i
$985$	−15.8768	−	19.8198i	−0.505878	−	0.631512i
$986$	−13.1501	+	3.72237i	−0.418783	+	0.118545i
$987$		0			0
$988$	−27.1795	+	16.7277i	−0.864694	+	0.532178i
$989$	−49.9185			−1.58732
$990$	−35.5515	−	25.3568i	−1.12990	−	0.805893i
$991$			2.71611i			0.0862801i	0.999069	+	0.0431401i	$0.0137362\pi$
$991$			2.71611i			0.0862801i	−0.999069	+	0.0431401i	$0.986264\pi$
$992$	−1.59114	+	8.20551i	−0.0505189	+	0.260525i
$993$	6.20742			0.196986
$994$		0			0
$995$	−15.7559	+	12.6214i	−0.499497	+	0.400126i
$996$	−3.12165	+	1.92123i	−0.0989132	+	0.0608764i
$997$	−8.96159			−0.283817			−0.141908	−	0.989880i	$-0.545324\pi$
$997$	−8.96159			−0.283817			−0.141908	+	0.989880i	$0.545324\pi$
$998$	9.36093	+	33.0694i	0.296315	+	1.04679i
$999$	−5.81409			−0.183950

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	980.2.c.e.979.41	yes	48
4.3	odd	2	inner	980.2.c.e.979.6	yes	48
5.4	even	2	inner	980.2.c.e.979.8	yes	48
7.2	even	3		980.2.s.g.619.12		96
7.3	odd	6		980.2.s.g.19.20		96
7.4	even	3		980.2.s.g.19.19		96
7.5	odd	6		980.2.s.g.619.11		96
7.6	odd	2	inner	980.2.c.e.979.42	yes	48
20.19	odd	2	inner	980.2.c.e.979.43	yes	48
28.3	even	6		980.2.s.g.19.37		96
28.11	odd	6		980.2.s.g.19.38		96
28.19	even	6		980.2.s.g.619.30		96
28.23	odd	6		980.2.s.g.619.29		96
28.27	even	2	inner	980.2.c.e.979.5	✓	48
35.4	even	6		980.2.s.g.19.30		96
35.9	even	6		980.2.s.g.619.37		96
35.19	odd	6		980.2.s.g.619.38		96
35.24	odd	6		980.2.s.g.19.29		96
35.34	odd	2	inner	980.2.c.e.979.7	yes	48
140.19	even	6		980.2.s.g.619.19		96
140.39	odd	6		980.2.s.g.19.11		96
140.59	even	6		980.2.s.g.19.12		96
140.79	odd	6		980.2.s.g.619.20		96
140.139	even	2	inner	980.2.c.e.979.44	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
980.2.c.e.979.5	✓	48	28.27	even	2	inner
980.2.c.e.979.6	yes	48	4.3	odd	2	inner
980.2.c.e.979.7	yes	48	35.34	odd	2	inner
980.2.c.e.979.8	yes	48	5.4	even	2	inner
980.2.c.e.979.41	yes	48	1.1	even	1	trivial
980.2.c.e.979.42	yes	48	7.6	odd	2	inner
980.2.c.e.979.43	yes	48	20.19	odd	2	inner
980.2.c.e.979.44	yes	48	140.139	even	2	inner
980.2.s.g.19.11		96	140.39	odd	6
980.2.s.g.19.12		96	140.59	even	6
980.2.s.g.19.19		96	7.4	even	3
980.2.s.g.19.20		96	7.3	odd	6
980.2.s.g.19.29		96	35.24	odd	6
980.2.s.g.19.30		96	35.4	even	6
980.2.s.g.19.37		96	28.3	even	6
980.2.s.g.19.38		96	28.11	odd	6
980.2.s.g.619.11		96	7.5	odd	6
980.2.s.g.619.12		96	7.2	even	3
980.2.s.g.619.19		96	140.19	even	6
980.2.s.g.619.20		96	140.79	odd	6
980.2.s.g.619.29		96	28.23	odd	6
980.2.s.g.619.30		96	28.19	even	6
980.2.s.g.619.37		96	35.9	even	6
980.2.s.g.619.38		96	35.19	odd	6

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:	\( N \)	\(=\)	\( 980 = 2^{2} \cdot 5 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	980.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(1.36075 - 0.385185i) q^{2} -0.423388i q^{3} +(1.70326 - 1.04828i) q^{4} +(-1.74517 + 1.39799i) q^{5} +(-0.163083 - 0.576124i) q^{6} +(1.91393 - 2.08252i) q^{8} +2.82074 q^{9} +(-1.83626 + 2.57452i) q^{10} +4.89551i q^{11} +(-0.443829 - 0.721142i) q^{12} -2.54664 q^{13} +(0.591890 + 0.738886i) q^{15} +(1.80222 - 3.57099i) q^{16} +5.11429 q^{17} +(3.83832 - 1.08651i) q^{18} +6.26601 q^{19} +(-1.50701 + 4.21057i) q^{20} +(1.88568 + 6.66155i) q^{22} +4.63109 q^{23} +(-0.881712 - 0.810335i) q^{24} +(1.09127 - 4.87946i) q^{25} +(-3.46533 + 0.980929i) q^{26} -2.46443i q^{27} -1.88958 q^{29} +(1.09002 + 0.777450i) q^{30} -1.47756 q^{31} +(1.07687 - 5.55341i) q^{32} +2.07270 q^{33} +(6.95926 - 1.96995i) q^{34} +(4.80447 - 2.95693i) q^{36} -2.35920i q^{37} +(8.52645 - 2.41357i) q^{38} +1.07822i q^{39} +(-0.428815 + 6.31000i) q^{40} -7.05393i q^{41} -10.7790 q^{43} +(5.13187 + 8.33835i) q^{44} +(-4.92269 + 3.94336i) q^{45} +(6.30175 - 1.78383i) q^{46} +12.2145i q^{47} +(-1.51192 - 0.763038i) q^{48} +(-0.394553 - 7.06005i) q^{50} -2.16533i q^{51} +(-4.33760 + 2.66959i) q^{52} -2.23621i q^{53} +(-0.949263 - 3.35347i) q^{54} +(-6.84386 - 8.54352i) q^{55} -2.65295i q^{57} +(-2.57124 + 0.727837i) q^{58} -5.69000 q^{59} +(1.78271 + 0.638052i) q^{60} +3.87005i q^{61} +(-2.01059 + 0.569136i) q^{62} +(-0.673743 - 7.97158i) q^{64} +(4.44433 - 3.56017i) q^{65} +(2.82042 - 0.798374i) q^{66} +0.889310 q^{67} +(8.71100 - 5.36121i) q^{68} -1.96075i q^{69} +14.3310i q^{71} +(5.39870 - 5.87424i) q^{72} +7.87187 q^{73} +(-0.908729 - 3.21027i) q^{74} +(-2.06590 - 0.462031i) q^{75} +(10.6727 - 6.56853i) q^{76} +(0.415314 + 1.46718i) q^{78} +4.63973i q^{79} +(1.84701 + 8.75149i) q^{80} +7.41882 q^{81} +(-2.71707 - 9.59861i) q^{82} -4.32876i q^{83} +(-8.92534 + 7.14971i) q^{85} +(-14.6675 + 4.15191i) q^{86} +0.800024i q^{87} +(10.1950 + 9.36967i) q^{88} -2.18254i q^{89} +(-5.17961 + 7.26206i) q^{90} +(7.88798 - 4.85468i) q^{92} +0.625583i q^{93} +(4.70485 + 16.6208i) q^{94} +(-10.9353 + 8.75979i) q^{95} +(-2.35125 - 0.455934i) q^{96} -3.42330 q^{97} +13.8090i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 16 q^{4} - 64 q^{9} + 16 q^{16} - 16 q^{25} - 48 q^{29} - 8 q^{30} + 176 q^{36} - 48 q^{44} - 32 q^{46} + 32 q^{50} + 24 q^{60} - 80 q^{64} - 16 q^{65} - 112 q^{74} - 48 q^{81} - 64 q^{85} - 112 q^{86}+O(q^{100}) \) 48 * q + 16 * q^4 - 64 * q^9 + 16 * q^16 - 16 * q^25 - 48 * q^29 - 8 * q^30 + 176 * q^36 - 48 * q^44 - 32 * q^46 + 32 * q^50 + 24 * q^60 - 80 * q^64 - 16 * q^65 - 112 * q^74 - 48 * q^81 - 64 * q^85 - 112 * q^86

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more