LMFDB - Embedded newform 980.2.g.b.391.20

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [980,2,Mod(391,980)]

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, 0, 1]))

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

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

chi := DirichletCharacter("980.391");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 980 = 2^{2} \cdot 5 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	980.g (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			391.20
Character	$\chi$	$=$	980.391
Dual form			980.2.g.b.391.18

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.281497 + 1.38591i) q^{2} +1.31255 q^{3} +(-1.84152 - 0.780262i) q^{4} +1.00000i q^{5} +(-0.369479 + 1.81908i) q^{6} +(1.59976 - 2.33255i) q^{8} -1.27722 q^{9} +O(q^{10})$	\(q+(-0.281497 + 1.38591i) q^{2} +1.31255 q^{3} +(-1.84152 - 0.780262i) q^{4} +1.00000i q^{5} +(-0.369479 + 1.81908i) q^{6} +(1.59976 - 2.33255i) q^{8} -1.27722 q^{9} +(-1.38591 - 0.281497i) q^{10} +0.889067i q^{11} +(-2.41708 - 1.02413i) q^{12} +6.39664i q^{13} +1.31255i q^{15} +(2.78238 + 2.87374i) q^{16} -3.88885i q^{17} +(0.359533 - 1.77011i) q^{18} +0.943374 q^{19} +(0.780262 - 1.84152i) q^{20} +(-1.23217 - 0.250270i) q^{22} +8.79563i q^{23} +(2.09976 - 3.06158i) q^{24} -1.00000 q^{25} +(-8.86520 - 1.80064i) q^{26} -5.61405 q^{27} -0.497418 q^{29} +(-1.81908 - 0.369479i) q^{30} -4.85974 q^{31} +(-4.76598 + 3.04719i) q^{32} +1.16694i q^{33} +(5.38962 + 1.09470i) q^{34} +(2.35202 + 0.996565i) q^{36} -2.66086 q^{37} +(-0.265557 + 1.30744i) q^{38} +8.39590i q^{39} +(2.33255 + 1.59976i) q^{40} -0.823314i q^{41} +9.92015i q^{43} +(0.693705 - 1.63723i) q^{44} -1.27722i q^{45} +(-12.1900 - 2.47595i) q^{46} +7.37488 q^{47} +(3.65201 + 3.77192i) q^{48} +(0.281497 - 1.38591i) q^{50} -5.10431i q^{51} +(4.99106 - 11.7795i) q^{52} -4.70237 q^{53} +(1.58034 - 7.78060i) q^{54} -0.889067 q^{55} +1.23822 q^{57} +(0.140022 - 0.689379i) q^{58} -1.88432 q^{59} +(1.02413 - 2.41708i) q^{60} -0.580462i q^{61} +(1.36800 - 6.73519i) q^{62} +(-2.88154 - 7.46302i) q^{64} -6.39664 q^{65} +(-1.61728 - 0.328491i) q^{66} +9.32852i q^{67} +(-3.03433 + 7.16140i) q^{68} +11.5447i q^{69} +14.3163i q^{71} +(-2.04324 + 2.97917i) q^{72} -9.04450i q^{73} +(0.749025 - 3.68773i) q^{74} -1.31255 q^{75} +(-1.73724 - 0.736079i) q^{76} +(-11.6360 - 2.36342i) q^{78} -14.8831i q^{79} +(-2.87374 + 2.78238i) q^{80} -3.53706 q^{81} +(1.14104 + 0.231761i) q^{82} +4.02691 q^{83} +3.88885 q^{85} +(-13.7485 - 2.79249i) q^{86} -0.652885 q^{87} +(2.07379 + 1.42229i) q^{88} -6.01725i q^{89} +(1.77011 + 0.359533i) q^{90} +(6.86290 - 16.1973i) q^{92} -6.37864 q^{93} +(-2.07601 + 10.2209i) q^{94} +0.943374i q^{95} +(-6.25558 + 3.99959i) q^{96} -14.5252i q^{97} -1.13553i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 8 q^{2} - 8 q^{4} + 8 q^{8} + 48 q^{9}+O(q^{10}) $ 48 * q + 8 * q^2 - 8 * q^4 + 8 * q^8 + 48 * q^9	$ 48 q + 8 q^{2} - 8 q^{4} + 8 q^{8} + 48 q^{9} - 40 q^{16} + 40 q^{18} - 32 q^{22} - 48 q^{25} + 64 q^{29} + 8 q^{32} - 40 q^{36} + 64 q^{37} - 32 q^{46} - 8 q^{50} - 64 q^{53} - 48 q^{58} - 8 q^{64} - 72 q^{72} + 96 q^{74} - 112 q^{78} + 48 q^{81} + 32 q^{88} - 112 q^{92}+O(q^{100}) $ 48 * q + 8 * q^2 - 8 * q^4 + 8 * q^8 + 48 * q^9 - 40 * q^16 + 40 * q^18 - 32 * q^22 - 48 * q^25 + 64 * q^29 + 8 * q^32 - 40 * q^36 + 64 * q^37 - 32 * q^46 - 8 * q^50 - 64 * q^53 - 48 * q^58 - 8 * q^64 - 72 * q^72 + 96 * q^74 - 112 * q^78 + 48 * q^81 + 32 * q^88 - 112 * q^92

Display 100 coefficients 10 coefficients

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 $

$2$	−0.281497	+	1.38591i	−0.199049	+	0.979990i
$2$	−0.281497	+	1.38591i	−0.199049	+	0.979990i
$3$	1.31255			0.757800			0.378900	−	0.925438i	$-0.376302\pi$
$3$	1.31255			0.757800			0.378900	+	0.925438i	$0.376302\pi$
$4$	−1.84152	−	0.780262i	−0.920759	−	0.390131i
$5$			1.00000i			0.447214i
$5$			1.00000i			0.447214i
$6$	−0.369479	+	1.81908i	−0.150839	+	0.742636i
$7$		0			0
$7$		0			0
$8$	1.59976	−	2.33255i	0.565600	−	0.824679i
$9$	−1.27722			−0.425739
$10$	−1.38591	−	0.281497i	−0.438265	−	0.0890173i
$11$			0.889067i			0.268064i	0.990977	+	0.134032i	$0.0427925\pi$
$11$			0.889067i			0.268064i	−0.990977	+	0.134032i	$0.957208\pi$
$12$	−2.41708	−	1.02413i	−0.697751	−	0.295641i
$13$			6.39664i			1.77411i	0.461664	+	0.887055i	$0.347253\pi$
$13$			6.39664i			1.77411i	−0.461664	+	0.887055i	$0.652747\pi$
$14$		0			0
$15$			1.31255i			0.338898i
$16$	2.78238	+	2.87374i	0.695595	+	0.718434i
$17$		−	3.88885i		−	0.943186i	−0.881816	−	0.471593i	$-0.843679\pi$
$17$		−	3.88885i		−	0.943186i	0.881816	−	0.471593i	$-0.156321\pi$
$18$	0.359533	−	1.77011i	0.0847428	−	0.417220i
$19$	0.943374			0.216425			0.108212	−	0.994128i	$-0.465487\pi$
$19$	0.943374			0.216425			0.108212	+	0.994128i	$0.465487\pi$
$20$	0.780262	−	1.84152i	0.174472	−	0.411776i
$21$		0			0
$22$	−1.23217	−	0.250270i	−0.262700	−	0.0533577i
$23$			8.79563i			1.83402i	0.398870	+	0.917008i	$0.369403\pi$
$23$			8.79563i			1.83402i	−0.398870	+	0.917008i	$0.630597\pi$
$24$	2.09976	−	3.06158i	0.428612	−	0.624942i
$25$	−1.00000			−0.200000
$26$	−8.86520	−	1.80064i	−1.73861	−	0.353134i
$27$	−5.61405			−1.08043
$28$		0			0
$29$	−0.497418			−0.0923682			−0.0461841	−	0.998933i	$-0.514706\pi$
$29$	−0.497418			−0.0923682			−0.0461841	+	0.998933i	$0.514706\pi$
$30$	−1.81908	−	0.369479i	−0.332117	−	0.0674573i
$31$	−4.85974			−0.872835			−0.436418	−	0.899744i	$-0.643753\pi$
$31$	−4.85974			−0.872835			−0.436418	+	0.899744i	$0.643753\pi$
$32$	−4.76598	+	3.04719i	−0.842515	+	0.538673i
$33$			1.16694i			0.203139i
$34$	5.38962	+	1.09470i	0.924312	+	0.187740i
$35$		0			0
$36$	2.35202	+	0.996565i	0.392003	+	0.166094i
$37$	−2.66086			−0.437443			−0.218721	−	0.975787i	$-0.570189\pi$
$37$	−2.66086			−0.437443			−0.218721	+	0.975787i	$0.570189\pi$
$38$	−0.265557	+	1.30744i	−0.0430791	+	0.212094i
$39$			8.39590i			1.34442i
$40$	2.33255	+	1.59976i	0.368808	+	0.252944i
$41$		−	0.823314i		−	0.128580i	−0.997931	−	0.0642900i	$-0.979522\pi$
$41$		−	0.823314i		−	0.128580i	0.997931	−	0.0642900i	$-0.0204783\pi$
$42$		0			0
$43$			9.92015i			1.51281i	0.654104	+	0.756404i	$0.273046\pi$
$43$			9.92015i			1.51281i	−0.654104	+	0.756404i	$0.726954\pi$
$44$	0.693705	−	1.63723i	0.104580	−	0.246822i
$45$		−	1.27722i		−	0.190396i
$46$	−12.1900	−	2.47595i	−1.79732	−	0.365058i
$47$	7.37488			1.07574			0.537868	−	0.843029i	$-0.319230\pi$
$47$	7.37488			1.07574			0.537868	+	0.843029i	$0.319230\pi$
$48$	3.65201	+	3.77192i	0.527122	+	0.544429i
$49$		0			0
$50$	0.281497	−	1.38591i	0.0398097	−	0.195998i
$51$		−	5.10431i		−	0.714746i
$52$	4.99106	−	11.7795i	0.692135	−	1.63353i
$53$	−4.70237			−0.645921			−0.322960	−	0.946413i	$-0.604678\pi$
$53$	−4.70237			−0.645921			−0.322960	+	0.946413i	$0.604678\pi$
$54$	1.58034	−	7.78060i	0.215057	−	1.05881i
$55$	−0.889067			−0.119882
$56$		0			0
$57$	1.23822			0.164007
$58$	0.140022	−	0.689379i	0.0183858	−	0.0905199i
$59$	−1.88432			−0.245318			−0.122659	−	0.992449i	$-0.539142\pi$
$59$	−1.88432			−0.245318			−0.122659	+	0.992449i	$0.539142\pi$
$60$	1.02413	−	2.41708i	0.132215	−	0.312044i
$61$		−	0.580462i		−	0.0743206i	−0.999309	−	0.0371603i	$-0.988169\pi$
$61$		−	0.580462i		−	0.0743206i	0.999309	−	0.0371603i	$-0.0118312\pi$
$62$	1.36800	−	6.73519i	0.173737	−	0.855369i
$63$		0			0
$64$	−2.88154	−	7.46302i	−0.360192	−	0.932878i
$65$	−6.39664			−0.793406
$66$	−1.61728	−	0.328491i	−0.199074	−	0.0404345i
$67$			9.32852i			1.13966i	0.821763	+	0.569830i	$0.192991\pi$
$67$			9.32852i			1.13966i	−0.821763	+	0.569830i	$0.807009\pi$
$68$	−3.03433	+	7.16140i	−0.367966	+	0.868447i
$69$			11.5447i			1.38982i
$70$		0			0
$71$			14.3163i			1.69903i	0.527563	+	0.849516i	$0.323106\pi$
$71$			14.3163i			1.69903i	−0.527563	+	0.849516i	$0.676894\pi$
$72$	−2.04324	+	2.97917i	−0.240798	+	0.351098i
$73$		−	9.04450i		−	1.05858i	−0.848442	−	0.529289i	$-0.822459\pi$
$73$		−	9.04450i		−	1.05858i	0.848442	−	0.529289i	$-0.177541\pi$
$74$	0.749025	−	3.68773i	0.0870724	−	0.428690i
$75$	−1.31255			−0.151560
$76$	−1.73724	−	0.736079i	−0.199275	−	0.0844341i
$77$		0			0
$78$	−11.6360	−	2.36342i	−1.31752	−	0.267605i
$79$		−	14.8831i		−	1.67448i	−0.546837	−	0.837239i	$-0.684168\pi$
$79$		−	14.8831i		−	1.67448i	0.546837	−	0.837239i	$-0.315832\pi$
$80$	−2.87374	+	2.78238i	−0.321293	+	0.311080i
$81$	−3.53706			−0.393007
$82$	1.14104	+	0.231761i	0.126007	+	0.0255937i
$83$	4.02691			0.442011			0.221005	−	0.975273i	$-0.429066\pi$
$83$	4.02691			0.442011			0.221005	+	0.975273i	$0.429066\pi$
$84$		0			0
$85$	3.88885			0.421805
$86$	−13.7485	−	2.79249i	−1.48254	−	0.301122i
$87$	−0.652885			−0.0699966
$88$	2.07379	+	1.42229i	0.221067	+	0.151617i
$89$		−	6.01725i		−	0.637828i	−0.947784	−	0.318914i	$-0.896682\pi$
$89$		−	6.01725i		−	0.637828i	0.947784	−	0.318914i	$-0.103318\pi$
$90$	1.77011	+	0.359533i	0.186586	+	0.0378981i
$91$		0			0
$92$	6.86290	−	16.1973i	0.715507	−	1.68869i
$93$	−6.37864			−0.661435
$94$	−2.07601	+	10.2209i	−0.214124	+	1.05421i
$95$			0.943374i			0.0967881i
$96$	−6.25558	+	3.99959i	−0.638458	+	0.408206i
$97$		−	14.5252i		−	1.47481i	−0.675451	−	0.737404i	$-0.736051\pi$
$97$		−	14.5252i		−	1.47481i	0.675451	−	0.737404i	$-0.263949\pi$
$98$		0			0
$99$		−	1.13553i		−	0.114125i
$100$	1.84152	+	0.780262i	0.184152	+	0.0780262i
$101$			14.8231i			1.47496i	0.675371	+	0.737478i	$0.263984\pi$
$101$			14.8231i			1.47496i	−0.675371	+	0.737478i	$0.736016\pi$
$102$	7.07414	+	1.43685i	0.700444	+	0.142269i
$103$	18.3265			1.80577			0.902884	−	0.429884i	$-0.141446\pi$
$103$	18.3265			1.80577			0.902884	+	0.429884i	$0.141446\pi$
$104$	14.9205	+	10.2331i	1.46307	+	1.00344i
$105$		0			0
$106$	1.32371	−	6.51709i	0.128570	−	0.632995i
$107$			8.32630i			0.804934i	0.915435	+	0.402467i	$0.131847\pi$
$107$			8.32630i			0.804934i	−0.915435	+	0.402467i	$0.868153\pi$
$108$	10.3384	+	4.38044i	0.994811	+	0.421508i
$109$	0.994813			0.0952858			0.0476429	−	0.998864i	$-0.484829\pi$
$109$	0.994813			0.0952858			0.0476429	+	0.998864i	$0.484829\pi$
$110$	0.250270	−	1.23217i	0.0238623	−	0.117483i
$111$	−3.49251			−0.331494
$112$		0			0
$113$	0.363411			0.0341868			0.0170934	−	0.999854i	$-0.494559\pi$
$113$	0.363411			0.0341868			0.0170934	+	0.999854i	$0.494559\pi$
$114$	−0.348557	+	1.71607i	−0.0326453	+	0.160725i
$115$	−8.79563			−0.820197
$116$	0.916005	+	0.388117i	0.0850489	+	0.0360357i
$117$		−	8.16990i		−	0.755308i
$118$	0.530432	−	2.61151i	0.0488302	−	0.240409i
$119$		0			0
$120$	3.06158	+	2.09976i	0.279483	+	0.191681i
$121$	10.2096			0.928142
$122$	0.804471	+	0.163399i	0.0728334	+	0.0147934i
$123$		−	1.08064i		−	0.0974379i
$124$	8.94930	+	3.79187i	0.803671	+	0.340520i
$125$		−	1.00000i		−	0.0894427i
$126$		0			0
$127$		−	2.46720i		−	0.218928i	−0.993991	−	0.109464i	$-0.965087\pi$
$127$		−	2.46720i		−	0.218928i	0.993991	−	0.109464i	$-0.0349135\pi$
$128$	11.1543	−	1.89275i	0.985907	−	0.167297i
$129$			13.0207i			1.14641i
$130$	1.80064	−	8.86520i	0.157926	−	0.777530i
$131$	−0.282917			−0.0247186			−0.0123593	−	0.999924i	$-0.503934\pi$
$131$	−0.282917			−0.0247186			−0.0123593	+	0.999924i	$0.503934\pi$
$132$	0.910522	−	2.14895i	0.0792508	−	0.187042i
$133$		0			0
$134$	−12.9285	−	2.62595i	−1.11685	−	0.226848i
$135$		−	5.61405i		−	0.483181i
$136$	−9.07093	−	6.22123i	−0.777826	−	0.533466i
$137$	16.6151			1.41953			0.709764	−	0.704440i	$-0.248802\pi$
$137$	16.6151			1.41953			0.709764	+	0.704440i	$0.248802\pi$
$138$	−15.9999	−	3.24980i	−1.36201	−	0.276641i
$139$	−18.6029			−1.57788			−0.788938	−	0.614473i	$-0.789369\pi$
$139$	−18.6029			−1.57788			−0.788938	+	0.614473i	$0.789369\pi$
$140$		0			0
$141$	9.67988			0.815193
$142$	−19.8412	−	4.03000i	−1.66503	−	0.338190i
$143$	−5.68704			−0.475574
$144$	−3.55370	−	3.67038i	−0.296142	−	0.305865i
$145$		−	0.497418i		−	0.0413083i
$146$	12.5349	+	2.54600i	1.03740	+	0.210709i
$147$		0			0
$148$	4.90003	+	2.07617i	0.402780	+	0.170660i
$149$	15.6654			1.28336			0.641680	−	0.766973i	$-0.278238\pi$
$149$	15.6654			1.28336			0.641680	+	0.766973i	$0.278238\pi$
$150$	0.369479	−	1.81908i	0.0301678	−	0.148527i
$151$		−	11.9875i		−	0.975533i	−0.872974	−	0.487766i	$-0.837812\pi$
$151$		−	11.9875i		−	0.975533i	0.872974	−	0.487766i	$-0.162188\pi$
$152$	1.50917	−	2.20046i	0.122410	−	0.178481i
$153$			4.96691i			0.401551i
$154$		0			0
$155$		−	4.85974i		−	0.390344i
$156$	6.55101	−	15.4612i	0.524500	−	1.23789i
$157$		−	10.6355i		−	0.848804i	−0.905474	−	0.424402i	$-0.860484\pi$
$157$		−	10.6355i		−	0.848804i	0.905474	−	0.424402i	$-0.139516\pi$
$158$	20.6267	+	4.18955i	1.64097	+	0.333303i
$159$	−6.17209			−0.489479
$160$	−3.04719	−	4.76598i	−0.240902	−	0.376784i
$161$		0			0
$162$	0.995674	−	4.90207i	0.0782276	−	0.385143i
$163$		−	7.85089i		−	0.614929i	−0.951560	−	0.307465i	$-0.900519\pi$
$163$		−	7.85089i		−	0.614929i	0.951560	−	0.307465i	$-0.0994806\pi$
$164$	−0.642401	+	1.51615i	−0.0501631	+	0.118391i
$165$	−1.16694			−0.0908464
$166$	−1.13356	+	5.58096i	−0.0879817	+	0.433166i
$167$	−7.90245			−0.611510			−0.305755	−	0.952110i	$-0.598909\pi$
$167$	−7.90245			−0.611510			−0.305755	+	0.952110i	$0.598909\pi$
$168$		0			0
$169$	−27.9170			−2.14746
$170$	−1.09470	+	5.38962i	−0.0839598	+	0.413365i
$171$	−1.20489			−0.0921405
$172$	7.74032	−	18.2681i	0.590194	−	1.39293i
$173$		−	18.6303i		−	1.41643i	−0.705995	−	0.708216i	$-0.749500\pi$
$173$		−	18.6303i		−	1.41643i	0.705995	−	0.708216i	$-0.250500\pi$
$174$	0.183785	−	0.904843i	0.0139327	−	0.0685960i
$175$		0			0
$176$	−2.55494	+	2.47372i	−0.192586	+	0.186464i
$177$	−2.47326			−0.185902
$178$	8.33940	+	1.69384i	0.625065	+	0.126959i
$179$			20.5188i			1.53365i	0.641856	+	0.766825i	$0.278165\pi$
$179$			20.5188i			1.53365i	−0.641856	+	0.766825i	$0.721835\pi$
$180$	−0.996565	+	2.35202i	−0.0742795	+	0.175309i
$181$		−	13.2693i		−	0.986296i	−0.869946	−	0.493148i	$-0.835846\pi$
$181$		−	13.2693i		−	0.986296i	0.869946	−	0.493148i	$-0.164154\pi$
$182$		0			0
$183$		−	0.761885i		−	0.0563202i
$184$	20.5162	+	14.0709i	1.51247	+	1.03732i
$185$		−	2.66086i		−	0.195630i
$186$	1.79557	−	8.84026i	0.131658	−	0.648199i
$187$	3.45745			0.252834
$188$	−13.5810	−	5.75434i	−0.990494	−	0.419678i
$189$		0			0
$190$	−1.30744	−	0.265557i	−0.0948513	−	0.0192655i
$191$			20.7013i			1.49789i	0.662632	+	0.748945i	$0.269439\pi$
$191$			20.7013i			1.49789i	−0.662632	+	0.748945i	$0.730561\pi$
$192$	−3.78216	−	9.79558i	−0.272954	−	0.706935i
$193$	−17.5948			−1.26650			−0.633252	−	0.773945i	$-0.718280\pi$
$193$	−17.5948			−1.26650			−0.633252	+	0.773945i	$0.718280\pi$
$194$	20.1307	+	4.08880i	1.44530	+	0.293559i
$195$	−8.39590			−0.601243
$196$		0			0
$197$	23.8347			1.69815			0.849075	−	0.528272i	$-0.177160\pi$
$197$	23.8347			1.69815			0.849075	+	0.528272i	$0.177160\pi$
$198$	1.57375	+	0.319649i	0.111842	+	0.0227165i
$199$	18.5087			1.31205			0.656023	−	0.754741i	$-0.272238\pi$
$199$	18.5087			1.31205			0.656023	+	0.754741i	$0.272238\pi$
$200$	−1.59976	+	2.33255i	−0.113120	+	0.164936i
$201$			12.2441i			0.863634i
$202$	−20.5436	−	4.17267i	−1.44544	−	0.293588i
$203$		0			0
$204$	−3.98270	+	9.39968i	−0.278845	+	0.658109i
$205$	0.823314			0.0575027
$206$	−5.15887	+	25.3990i	−0.359436	+	1.76963i
$207$		−	11.2339i		−	0.780812i
$208$	−18.3823	+	17.7979i	−1.27458	+	1.23406i
$209$			0.838722i			0.0580156i
$210$		0			0
$211$			8.96174i			0.616952i	0.951232	+	0.308476i	$0.0998189\pi$
$211$			8.96174i			0.616952i	−0.951232	+	0.308476i	$0.900181\pi$
$212$	8.65951	+	3.66908i	0.594737	+	0.251994i
$213$			18.7908i			1.28753i
$214$	−11.5395	−	2.34383i	−0.788827	−	0.160221i
$215$	−9.92015			−0.676548
$216$	−8.98114	+	13.0950i	−0.611089	+	0.891004i
$217$		0			0
$218$	−0.280037	+	1.37873i	−0.0189665	+	0.0933791i
$219$		−	11.8713i		−	0.802191i
$220$	1.63723	+	0.693705i	0.110382	+	0.0467696i
$221$	24.8756			1.67331
$222$	0.983132	−	4.84032i	0.0659835	−	0.324861i
$223$	16.4225			1.09973			0.549865	−	0.835253i	$-0.314679\pi$
$223$	16.4225			1.09973			0.549865	+	0.835253i	$0.314679\pi$
$224$		0			0
$225$	1.27722			0.0851478
$226$	−0.102299	+	0.503656i	−0.00680484	+	0.0335027i
$227$	12.7118			0.843713			0.421857	−	0.906663i	$-0.361379\pi$
$227$	12.7118			0.843713			0.421857	+	0.906663i	$0.361379\pi$
$228$	−2.28021	−	0.966139i	−0.151011	−	0.0639841i
$229$			17.2965i			1.14298i	0.820608	+	0.571491i	$0.193635\pi$
$229$			17.2965i			1.14298i	−0.820608	+	0.571491i	$0.806365\pi$
$230$	2.47595	−	12.1900i	0.163259	−	0.803784i
$231$		0			0
$232$	−0.795749	+	1.16025i	−0.0522435	+	0.0761742i
$233$	23.7478			1.55577			0.777885	−	0.628407i	$-0.216293\pi$
$233$	23.7478			1.55577			0.777885	+	0.628407i	$0.216293\pi$
$234$	11.3228	+	2.29981i	0.740194	+	0.150343i
$235$			7.37488i			0.481084i
$236$	3.47001	+	1.47027i	0.225879	+	0.0957062i
$237$		−	19.5348i		−	1.26892i
$238$		0			0
$239$			10.2033i			0.659997i	0.943981	+	0.329998i	$0.107048\pi$
$239$			10.2033i			0.659997i	−0.943981	+	0.329998i	$0.892952\pi$
$240$	−3.77192	+	3.65201i	−0.243476	+	0.235736i
$241$			2.32844i			0.149988i	0.997184	+	0.0749939i	$0.0238937\pi$
$241$			2.32844i			0.149988i	−0.997184	+	0.0749939i	$0.976106\pi$
$242$	−2.87396	+	14.1496i	−0.184745	+	0.909569i
$243$	12.1996			0.782604
$244$	−0.452913	+	1.06893i	−0.0289948	+	0.0684314i
$245$		0			0
$246$	1.49767	+	0.304197i	0.0954881	+	0.0193949i
$247$			6.03443i			0.383961i
$248$	−7.77442	+	11.3356i	−0.493676	+	0.719809i
$249$	5.28552			0.334956
$250$	1.38591	+	0.281497i	0.0876529	+	0.0178035i
$251$	6.54297			0.412988			0.206494	−	0.978448i	$-0.433795\pi$
$251$	6.54297			0.412988			0.206494	+	0.978448i	$0.433795\pi$
$252$		0			0
$253$	−7.81990			−0.491633
$254$	3.41932	+	0.694509i	0.214547	+	0.0435774i
$255$	5.10431			0.319644
$256$	−0.516710	+	15.9917i	−0.0322944	+	0.999478i
$257$			19.6387i			1.22503i	0.790459	+	0.612515i	$0.209842\pi$
$257$			19.6387i			1.22503i	−0.790459	+	0.612515i	$0.790158\pi$
$258$	−18.0455	−	3.66528i	−1.12347	−	0.228191i
$259$		0			0
$260$	11.7795	+	4.99106i	0.730536	+	0.309532i
$261$	0.635311			0.0393248
$262$	0.0796403	−	0.392099i	0.00492020	−	0.0242239i
$263$		−	10.6800i		−	0.658558i	−0.944233	−	0.329279i	$-0.893194\pi$
$263$		−	10.6800i		−	0.658558i	0.944233	−	0.329279i	$-0.106806\pi$
$264$	2.72195	+	1.86683i	0.167524	+	0.114895i
$265$		−	4.70237i		−	0.288864i
$266$		0			0
$267$		−	7.89794i		−	0.483346i
$268$	7.27869	−	17.1786i	0.444617	−	1.04935i
$269$		−	6.20876i		−	0.378555i	−0.981924	−	0.189278i	$-0.939385\pi$
$269$		−	6.20876i		−	0.378555i	0.981924	−	0.189278i	$-0.0606146\pi$
$270$	7.78060	+	1.58034i	0.473512	+	0.0961765i
$271$	17.4773			1.06167			0.530835	−	0.847475i	$-0.321878\pi$
$271$	17.4773			1.06167			0.530835	+	0.847475i	$0.321878\pi$
$272$	11.1755	−	10.8203i	0.677616	−	0.656075i
$273$		0			0
$274$	−4.67712	+	23.0272i	−0.282555	+	1.39112i
$275$		−	0.889067i		−	0.0536128i
$276$	9.00788	−	21.2598i	0.542211	−	1.27969i
$277$	10.9931			0.660512			0.330256	−	0.943891i	$-0.392865\pi$
$277$	10.9931			0.660512			0.330256	+	0.943891i	$0.392865\pi$
$278$	5.23666	−	25.7820i	0.314074	−	1.54630i
$279$	6.20694			0.371600
$280$		0			0
$281$	−18.5755			−1.10812			−0.554060	−	0.832477i	$-0.686922\pi$
$281$	−18.5755			−1.10812			−0.554060	+	0.832477i	$0.686922\pi$
$282$	−2.72486	+	13.4155i	−0.162263	+	0.798881i
$283$	7.58550			0.450911			0.225456	−	0.974253i	$-0.427613\pi$
$283$	7.58550			0.450911			0.225456	+	0.974253i	$0.427613\pi$
$284$	11.1705	−	26.3637i	0.662845	−	1.56440i
$285$			1.23822i			0.0733460i
$286$	1.60089	−	7.88176i	0.0946625	−	0.466058i
$287$		0			0
$288$	6.08720	−	3.89193i	0.358692	−	0.229334i
$289$	1.87682			0.110401
$290$	0.689379	+	0.140022i	0.0404817	+	0.00822237i
$291$		−	19.0650i		−	1.11761i
$292$	−7.05708	+	16.6556i	−0.412984	+	0.974696i
$293$			5.40695i			0.315878i	0.987449	+	0.157939i	$0.0504849\pi$
$293$			5.40695i			0.315878i	−0.987449	+	0.157939i	$0.949515\pi$
$294$		0			0
$295$		−	1.88432i		−	0.109709i
$296$	−4.25674	+	6.20658i	−0.247418	+	0.360750i
$297$		−	4.99127i		−	0.289623i
$298$	−4.40977	+	21.7109i	−0.255451	+	1.25768i
$299$	−56.2625			−3.25374
$300$	2.41708	+	1.02413i	0.139550	+	0.0591283i
$301$		0			0
$302$	16.6137	+	3.37446i	0.956012	+	0.194178i
$303$			19.4561i			1.11772i
$304$	2.62483	+	2.71101i	0.150544	+	0.155487i
$305$	0.580462			0.0332372
$306$	−6.88371	−	1.39817i	−0.393516	−	0.0799282i
$307$	5.68826			0.324646			0.162323	−	0.986738i	$-0.448101\pi$
$307$	5.68826			0.324646			0.162323	+	0.986738i	$0.448101\pi$
$308$		0			0
$309$	24.0545			1.36841
$310$	6.73519	+	1.36800i	0.382533	+	0.0776974i
$311$	0.125241			0.00710175			0.00355087	−	0.999994i	$-0.498870\pi$
$311$	0.125241			0.00710175			0.00355087	+	0.999994i	$0.498870\pi$
$312$	19.5838	+	13.4314i	1.10872	+	0.760405i
$313$			11.6537i			0.658705i	0.944207	+	0.329352i	$0.106830\pi$
$313$			11.6537i			0.658705i	−0.944207	+	0.329352i	$0.893170\pi$
$314$	14.7399	+	2.99386i	0.831819	+	0.168953i
$315$		0			0
$316$	−11.6127	+	27.4075i	−0.653266	+	1.54179i
$317$	−18.4968			−1.03888			−0.519442	−	0.854505i	$-0.673860\pi$
$317$	−18.4968			−1.03888			−0.519442	+	0.854505i	$0.673860\pi$
$318$	1.73743	−	8.55399i	0.0974301	−	0.479684i
$319$		−	0.442238i		−	0.0247606i
$320$	7.46302	−	2.88154i	0.417196	−	0.161083i
$321$			10.9287i			0.609979i
$322$		0			0
$323$		−	3.66864i		−	0.204129i
$324$	6.51357	+	2.75984i	0.361865	+	0.153324i
$325$		−	6.39664i		−	0.354822i
$326$	10.8807	+	2.21000i	0.602624	+	0.122401i
$327$	1.30574			0.0722076
$328$	−1.92042	−	1.31710i	−0.106037	−	0.0727249i
$329$		0			0
$330$	0.328491	−	1.61728i	0.0180829	−	0.0890285i
$331$		−	6.92396i		−	0.380575i	−0.981728	−	0.190288i	$-0.939058\pi$
$331$		−	6.92396i		−	0.380575i	0.981728	−	0.190288i	$-0.0609421\pi$
$332$	−7.41563	−	3.14205i	−0.406986	−	0.172442i
$333$	3.39850			0.186237
$334$	2.22452	−	10.9521i	0.121720	−	0.599273i
$335$	−9.32852			−0.509671
$336$		0			0
$337$	−15.5483			−0.846970			−0.423485	−	0.905903i	$-0.639193\pi$
$337$	−15.5483			−0.846970			−0.423485	+	0.905903i	$0.639193\pi$
$338$	7.85857	−	38.6906i	0.427450	−	2.10449i
$339$	0.476994			0.0259068
$340$	−7.16140	−	3.03433i	−0.388381	−	0.164559i
$341$		−	4.32063i		−	0.233975i
$342$	0.339174	−	1.66988i	0.0183404	−	0.0902967i
$343$		0			0
$344$	23.1392	+	15.8699i	1.24758	+	0.855645i
$345$	−11.5447			−0.621545
$346$	25.8200	+	5.24437i	1.38809	+	0.281939i
$347$		−	23.4098i		−	1.25671i	−0.777928	−	0.628353i	$-0.783729\pi$
$347$		−	23.4098i		−	1.25671i	0.777928	−	0.628353i	$-0.216271\pi$
$348$	1.20230	+	0.509422i	0.0644501	+	0.0273079i
$349$			31.1435i			1.66707i	0.552465	+	0.833536i	$0.313687\pi$
$349$			31.1435i			1.66707i	−0.552465	+	0.833536i	$0.686313\pi$
$350$		0			0
$351$		−	35.9111i		−	1.91679i
$352$	−2.70916	−	4.23728i	−0.144399	−	0.225848i
$353$		−	10.2234i		−	0.544135i	−0.962278	−	0.272068i	$-0.912293\pi$
$353$		−	10.2234i		−	0.544135i	0.962278	−	0.272068i	$-0.0877074\pi$
$354$	0.696217	−	3.42773i	0.0370035	−	0.182182i
$355$	−14.3163			−0.759830
$356$	−4.69504	+	11.0809i	−0.248836	+	0.587286i
$357$		0			0
$358$	−28.4374	−	5.77600i	−1.50296	−	0.305271i
$359$		−	11.3063i		−	0.596725i	−0.954453	−	0.298363i	$-0.903560\pi$
$359$		−	11.3063i		−	0.596725i	0.954453	−	0.298363i	$-0.0964405\pi$
$360$	−2.97917	−	2.04324i	−0.157016	−	0.107688i
$361$	−18.1100			−0.953160
$362$	18.3900	+	3.73526i	0.966559	+	0.196321i
$363$	13.4005			0.703346
$364$		0			0
$365$	9.04450			0.473411
$366$	1.05591	+	0.214469i	0.0551932	+	0.0112105i
$367$	−22.9155			−1.19618			−0.598090	−	0.801429i	$-0.704073\pi$
$367$	−22.9155			−1.19618			−0.598090	+	0.801429i	$0.704073\pi$
$368$	−25.2763	+	24.4728i	−1.31762	+	1.27573i
$369$			1.05155i			0.0547415i
$370$	3.68773	+	0.749025i	0.191716	+	0.0389400i
$371$		0			0
$372$	11.7464	+	4.97702i	0.609022	+	0.258046i
$373$	−11.2088			−0.580371			−0.290185	−	0.956970i	$-0.593717\pi$
$373$	−11.2088			−0.580371			−0.290185	+	0.956970i	$0.593717\pi$
$374$	−0.973263	+	4.79173i	−0.0503262	+	0.247775i
$375$		−	1.31255i		−	0.0677797i
$376$	11.7980	−	17.2022i	0.608437	−	0.887138i
$377$		−	3.18181i		−	0.163871i
$378$		0			0
$379$		−	24.2647i		−	1.24639i	−0.782065	−	0.623197i	$-0.785834\pi$
$379$		−	24.2647i		−	1.24639i	0.782065	−	0.623197i	$-0.214166\pi$
$380$	0.736079	−	1.73724i	0.0377601	−	0.0891186i
$381$		−	3.23831i		−	0.165904i
$382$	−28.6902	−	5.82735i	−1.46792	−	0.298153i
$383$	−8.06204			−0.411951			−0.205976	−	0.978557i	$-0.566037\pi$
$383$	−8.06204			−0.411951			−0.205976	+	0.978557i	$0.566037\pi$
$384$	14.6405	−	2.48432i	0.747120	−	0.126777i
$385$		0			0
$386$	4.95290	−	24.3850i	0.252096	−	1.24116i
$387$		−	12.6702i		−	0.644062i
$388$	−11.3335	+	26.7484i	−0.575369	+	1.35794i
$389$	13.9714			0.708380			0.354190	−	0.935173i	$-0.384757\pi$
$389$	13.9714			0.708380			0.354190	+	0.935173i	$0.384757\pi$
$390$	2.36342	−	11.6360i	0.119677	−	0.589212i
$391$	34.2049			1.72982
$392$		0			0
$393$	−0.371342			−0.0187317
$394$	−6.70940	+	33.0328i	−0.338015	+	1.66417i
$395$	14.8831			0.748849
$396$	−0.886013	+	2.09110i	−0.0445238	+	0.105082i
$397$		−	11.3650i		−	0.570392i	−0.958469	−	0.285196i	$-0.907941\pi$
$397$		−	11.3650i		−	0.570392i	0.958469	−	0.285196i	$-0.0920586\pi$
$398$	−5.21014	+	25.6514i	−0.261161	+	1.28579i
$399$		0			0
$400$	−2.78238	−	2.87374i	−0.139119	−	0.143687i
$401$	−3.77702			−0.188615			−0.0943076	−	0.995543i	$-0.530064\pi$
$401$	−3.77702			−0.188615			−0.0943076	+	0.995543i	$0.530064\pi$
$402$	−16.9693	−	3.44669i	−0.846353	−	0.171905i
$403$		−	31.0860i		−	1.54851i
$404$	11.5659	−	27.2971i	0.575427	−	1.35808i
$405$		−	3.53706i		−	0.175758i
$406$		0			0
$407$		−	2.36568i		−	0.117263i
$408$	−11.9060	−	8.16567i	−0.589436	−	0.404261i
$409$			13.9788i			0.691207i	0.938381	+	0.345603i	$0.112326\pi$
$409$			13.9788i			0.691207i	−0.938381	+	0.345603i	$0.887674\pi$
$410$	−0.231761	+	1.14104i	−0.0114458	+	0.0563521i
$411$	21.8082			1.07572
$412$	−33.7487	−	14.2995i	−1.66268	−	0.704486i
$413$		0			0
$414$	15.5693	+	3.16232i	0.765188	+	0.155420i
$415$			4.02691i			0.197673i
$416$	−19.4918	−	30.4863i	−0.955665	−	1.49471i
$417$	−24.4172			−1.19571
$418$	−1.16240	−	0.236098i	−0.0568547	−	0.0115479i
$419$	6.23483			0.304591			0.152296	−	0.988335i	$-0.451333\pi$
$419$	6.23483			0.304591			0.152296	+	0.988335i	$0.451333\pi$
$420$		0			0
$421$	−9.67347			−0.471456			−0.235728	−	0.971819i	$-0.575747\pi$
$421$	−9.67347			−0.471456			−0.235728	+	0.971819i	$0.575747\pi$
$422$	−12.4202	−	2.52271i	−0.604606	−	0.122803i
$423$	−9.41932			−0.457983
$424$	−7.52267	+	10.9685i	−0.365333	+	0.532677i
$425$			3.88885i			0.188637i
$426$	−26.0425	−	5.28957i	−1.26176	−	0.256280i
$427$		0			0
$428$	6.49670	−	15.3330i	0.314030	−	0.741150i
$429$	−7.46452			−0.360390
$430$	2.79249	−	13.7485i	0.134666	−	0.663010i
$431$			8.47850i			0.408395i	0.978930	+	0.204197i	$0.0654585\pi$
$431$			8.47850i			0.408395i	−0.978930	+	0.204197i	$0.934542\pi$
$432$	−15.6204	−	16.1333i	−0.751539	−	0.776214i
$433$		−	24.9330i		−	1.19820i	−0.800674	−	0.599101i	$-0.795525\pi$
$433$		−	24.9330i		−	1.19820i	0.800674	−	0.599101i	$-0.204475\pi$
$434$		0			0
$435$		−	0.652885i		−	0.0313035i
$436$	−1.83197	−	0.776215i	−0.0877353	−	0.0371740i
$437$			8.29757i			0.396926i
$438$	16.4527	+	3.34175i	0.786138	+	0.159675i
$439$	−25.4117			−1.21284			−0.606418	−	0.795146i	$-0.707394\pi$
$439$	−25.4117			−1.21284			−0.606418	+	0.795146i	$0.707394\pi$
$440$	−1.42229	+	2.07379i	−0.0678052	+	0.0988640i
$441$		0			0
$442$	−7.00242	+	34.4755i	−0.333071	+	1.63983i
$443$			23.9889i			1.13975i	0.821733	+	0.569873i	$0.193008\pi$
$443$			23.9889i			1.13975i	−0.821733	+	0.569873i	$0.806992\pi$
$444$	6.43152	+	2.72507i	0.305226	+	0.129326i
$445$	6.01725			0.285245
$446$	−4.62288	+	22.7602i	−0.218900	+	1.07772i
$447$	20.5616			0.972530
$448$		0			0
$449$	−17.1281			−0.808326			−0.404163	−	0.914687i	$-0.632437\pi$
$449$	−17.1281			−0.808326			−0.404163	+	0.914687i	$0.632437\pi$
$450$	−0.359533	+	1.77011i	−0.0169486	+	0.0834440i
$451$	0.731981			0.0344676
$452$	−0.669228	−	0.283556i	−0.0314778	−	0.0133373i
$453$		−	15.7342i		−	0.739259i
$454$	−3.57834	+	17.6175i	−0.167940	+	0.826830i
$455$		0			0
$456$	1.98086	−	2.88821i	0.0927623	−	0.135253i
$457$	−11.1835			−0.523144			−0.261572	−	0.965184i	$-0.584241\pi$
$457$	−11.1835			−0.523144			−0.261572	+	0.965184i	$0.584241\pi$
$458$	−23.9714	−	4.86891i	−1.12011	−	0.227509i
$459$			21.8322i			1.01904i
$460$	16.1973	+	6.86290i	0.755204	+	0.319984i
$461$			25.3723i			1.18170i	0.806780	+	0.590852i	$0.201208\pi$
$461$			25.3723i			1.18170i	−0.806780	+	0.590852i	$0.798792\pi$
$462$		0			0
$463$			0.0511973i			0.00237934i	0.999999	+	0.00118967i	$0.000378684\pi$
$463$			0.0511973i			0.00237934i	−0.999999	+	0.00118967i	$0.999621\pi$
$464$	−1.38401	−	1.42945i	−0.0642509	−	0.0663605i
$465$		−	6.37864i		−	0.295803i
$466$	−6.68494	+	32.9124i	−0.309674	+	1.52464i
$467$	−13.2911			−0.615037			−0.307518	−	0.951542i	$-0.599499\pi$
$467$	−13.2911			−0.615037			−0.307518	+	0.951542i	$0.599499\pi$
$468$	−6.37467	+	15.0450i	−0.294669	+	0.695457i
$469$		0			0
$470$	−10.2209	−	2.07601i	−0.471457	−	0.0957591i
$471$		−	13.9596i		−	0.643224i
$472$	−3.01446	+	4.39527i	−0.138752	+	0.202309i
$473$	−8.81968			−0.405529
$474$	27.0735	+	5.49898i	1.24353	+	0.252577i
$475$	−0.943374			−0.0432850
$476$		0			0
$477$	6.00595			0.274994
$478$	−14.1409	−	2.87220i	−0.646790	−	0.131371i
$479$	9.67119			0.441888			0.220944	−	0.975286i	$-0.429086\pi$
$479$	9.67119			0.441888			0.220944	+	0.975286i	$0.429086\pi$
$480$	−3.99959	−	6.25558i	−0.182555	−	0.285527i
$481$		−	17.0206i		−	0.776072i
$482$	−3.22701	−	0.655449i	−0.146986	−	0.0298549i
$483$		0			0
$484$	−18.8011	−	7.96614i	−0.854595	−	0.362097i
$485$	14.5252			0.659555
$486$	−3.43415	+	16.9076i	−0.155776	+	0.766944i
$487$			6.84725i			0.310279i	0.987893	+	0.155139i	$0.0495826\pi$
$487$			6.84725i			0.310279i	−0.987893	+	0.155139i	$0.950417\pi$
$488$	−1.35396	−	0.928600i	−0.0612907	−	0.0420358i
$489$		−	10.3047i		−	0.465993i
$490$		0			0
$491$		−	24.0395i		−	1.08489i	−0.840092	−	0.542444i	$-0.817499\pi$
$491$		−	24.0395i		−	1.08489i	0.840092	−	0.542444i	$-0.182501\pi$
$492$	−0.843182	+	1.99002i	−0.0380136	+	0.0897169i
$493$			1.93439i			0.0871204i
$494$	−8.36320	−	1.69867i	−0.376278	−	0.0764270i
$495$	1.13553			0.0510383
$496$	−13.5217	−	13.9656i	−0.607140	−	0.627074i
$497$		0			0
$498$	−1.48786	+	7.32527i	−0.0666725	+	0.328253i
$499$		−	12.9383i		−	0.579198i	−0.957148	−	0.289599i	$-0.906478\pi$
$499$		−	12.9383i		−	0.579198i	0.957148	−	0.289599i	$-0.0935219\pi$
$500$	−0.780262	+	1.84152i	−0.0348944	+	0.0823552i
$501$	−10.3723			−0.463402
$502$	−1.84183	+	9.06799i	−0.0822048	+	0.404724i
$503$	32.0665			1.42978			0.714888	−	0.699239i	$-0.246478\pi$
$503$	32.0665			1.42978			0.714888	+	0.699239i	$0.246478\pi$
$504$		0			0
$505$	−14.8231			−0.659621
$506$	2.20128	−	10.8377i	0.0978589	−	0.481795i
$507$	−36.6425			−1.62735
$508$	−1.92506	+	4.54339i	−0.0854107	+	0.201580i
$509$			9.41581i			0.417348i	0.977985	+	0.208674i	$0.0669148\pi$
$509$			9.41581i			0.417348i	−0.977985	+	0.208674i	$0.933085\pi$
$510$	−1.43685	+	7.07414i	−0.0636247	+	0.313248i
$511$		0			0
$512$	−22.0176	−	5.21772i	−0.973050	−	0.230593i
$513$	−5.29615			−0.233831
$514$	−27.2176	−	5.52825i	−1.20052	−	0.243840i
$515$			18.3265i			0.807564i
$516$	10.1595	−	23.9778i	0.447249	−	1.05556i
$517$			6.55676i			0.288366i
$518$		0			0
$519$		−	24.4531i		−	1.07337i
$520$	−10.2331	+	14.9205i	−0.448751	+	0.654306i
$521$		−	34.1627i		−	1.49670i	−0.663306	−	0.748348i	$-0.730847\pi$
$521$		−	34.1627i		−	1.49670i	0.663306	−	0.748348i	$-0.269153\pi$
$522$	−0.178838	+	0.880487i	−0.00782754	+	0.0385379i
$523$	33.5013			1.46491			0.732456	−	0.680815i	$-0.238374\pi$
$523$	33.5013			1.46491			0.732456	+	0.680815i	$0.238374\pi$
$524$	0.520997	+	0.220749i	0.0227598	+	0.00964348i
$525$		0			0
$526$	14.8016	+	3.00639i	0.645380	+	0.131085i
$527$			18.8988i			0.823246i
$528$	−3.35349	+	3.24688i	−0.145942	+	0.141302i
$529$	−54.3631			−2.36361
$530$	6.51709	+	1.32371i	0.283084	+	0.0574981i
$531$	2.40669			0.104441
$532$		0			0
$533$	5.26644			0.228115
$534$	10.9459	+	2.22325i	0.473674	+	0.0962093i
$535$	−8.32630			−0.359977
$536$	21.7592	+	14.9234i	0.939854	+	0.644592i
$537$			26.9320i			1.16220i
$538$	8.60482	+	1.74775i	0.370980	+	0.0753509i
$539$		0			0
$540$	−4.38044	+	10.3384i	−0.188504	+	0.444893i
$541$	−17.3065			−0.744065			−0.372033	−	0.928220i	$-0.621339\pi$
$541$	−17.3065			−0.744065			−0.372033	+	0.928220i	$0.621339\pi$
$542$	−4.91981	+	24.2220i	−0.211324	+	1.04043i
$543$		−	17.4165i		−	0.747415i
$544$	11.8501	+	18.5342i	0.508069	+	0.794648i
$545$			0.994813i			0.0426131i
$546$		0			0
$547$		−	12.8897i		−	0.551122i	−0.961284	−	0.275561i	$-0.911136\pi$
$547$		−	12.8897i		−	0.551122i	0.961284	−	0.275561i	$-0.0888636\pi$
$548$	−30.5971	−	12.9642i	−1.30704	−	0.553802i
$549$			0.741377i			0.0316412i
$550$	1.23217	+	0.250270i	0.0525399	+	0.0106715i
$551$	−0.469251			−0.0199908
$552$	26.9285	+	18.4687i	1.14615	+	0.786081i
$553$		0			0
$554$	−3.09453	+	15.2355i	−0.131474	+	0.647295i
$555$		−	3.49251i		−	0.148249i
$556$	34.2576	+	14.5151i	1.45284	+	0.615579i
$557$	−35.1953			−1.49127			−0.745636	−	0.666353i	$-0.767854\pi$
$557$	−35.1953			−1.49127			−0.745636	+	0.666353i	$0.767854\pi$
$558$	−1.74724	+	8.60229i	−0.0739665	+	0.364164i
$559$	−63.4556			−2.68389
$560$		0			0
$561$	4.53807			0.191598
$562$	5.22894	−	25.7440i	0.220570	−	1.08595i
$563$	5.25430			0.221442			0.110721	−	0.993852i	$-0.464684\pi$
$563$	5.25430			0.221442			0.110721	+	0.993852i	$0.464684\pi$
$564$	−17.8257	−	7.55285i	−0.750596	−	0.318032i
$565$			0.363411i			0.0152888i
$566$	−2.13530	+	10.5129i	−0.0897533	+	0.441888i
$567$		0			0
$568$	33.3934	+	22.9026i	1.40116	+	0.960973i
$569$	−14.0506			−0.589033			−0.294517	−	0.955646i	$-0.595159\pi$
$569$	−14.0506			−0.589033			−0.294517	+	0.955646i	$0.595159\pi$
$570$	−1.71607	−	0.348557i	−0.0718784	−	0.0145994i
$571$			13.2349i			0.553862i	0.960890	+	0.276931i	$0.0893173\pi$
$571$			13.2349i			0.553862i	−0.960890	+	0.276931i	$0.910683\pi$
$572$	10.4728	+	4.43739i	0.437890	+	0.185536i
$573$			27.1714i			1.13510i
$574$		0			0
$575$		−	8.79563i		−	0.366803i
$576$	3.68035	+	9.53190i	0.153348	+	0.397163i
$577$		−	9.29642i		−	0.387015i	−0.981099	−	0.193508i	$-0.938014\pi$
$577$		−	9.29642i		−	0.387015i	0.981099	−	0.193508i	$-0.0619864\pi$
$578$	−0.528318	+	2.60111i	−0.0219751	+	0.108192i
$579$	−23.0941			−0.959757
$580$	−0.388117	+	0.916005i	−0.0161157	+	0.0380350i
$581$		0			0
$582$	26.4225	+	5.36675i	1.09525	+	0.222459i
$583$		−	4.18072i		−	0.173148i
$584$	−21.0967	−	14.4690i	−0.872988	−	0.598732i
$585$	8.16990			0.337784
$586$	−7.49358	−	1.52204i	−0.309557	−	0.0628750i
$587$	−7.75382			−0.320034			−0.160017	−	0.987114i	$-0.551155\pi$
$587$	−7.75382			−0.320034			−0.160017	+	0.987114i	$0.551155\pi$
$588$		0			0
$589$	−4.58455			−0.188903
$590$	2.61151	+	0.530432i	0.107514	+	0.0218375i
$591$	31.2842			1.28686
$592$	−7.40353	−	7.64661i	−0.304283	−	0.314274i
$593$		−	3.22407i		−	0.132397i	−0.997806	−	0.0661983i	$-0.978913\pi$
$593$		−	3.22407i		−	0.132397i	0.997806	−	0.0661983i	$-0.0210870\pi$
$594$	6.91747	+	1.40503i	0.283827	+	0.0576490i
$595$		0			0
$596$	−28.8481	−	12.2231i	−1.18167	−	0.500679i
$597$	24.2935			0.994268
$598$	15.8377	−	77.9750i	0.647653	−	3.18864i
$599$		−	18.1351i		−	0.740980i	−0.928836	−	0.370490i	$-0.879190\pi$
$599$		−	18.1351i		−	0.740980i	0.928836	−	0.370490i	$-0.120810\pi$
$600$	−2.09976	+	3.06158i	−0.0857224	+	0.124988i
$601$		−	40.6079i		−	1.65643i	−0.560408	−	0.828216i	$-0.689356\pi$
$601$		−	40.6079i		−	1.65643i	0.560408	−	0.828216i	$-0.310644\pi$
$602$		0			0
$603$		−	11.9145i		−	0.485198i
$604$	−9.35343	+	22.0753i	−0.380586	+	0.898231i
$605$			10.2096i			0.415078i
$606$	−26.9645	−	5.47683i	−1.09536	−	0.222481i
$607$	−18.0687			−0.733384			−0.366692	−	0.930342i	$-0.619510\pi$
$607$	−18.0687			−0.733384			−0.366692	+	0.930342i	$0.619510\pi$
$608$	−4.49611	+	2.87464i	−0.182341	+	0.116582i
$609$		0			0
$610$	−0.163399	+	0.804471i	−0.00661582	+	0.0325721i
$611$			47.1744i			1.90847i
$612$	3.87549	−	9.14666i	0.156658	−	0.369732i
$613$	34.8119			1.40604			0.703020	−	0.711170i	$-0.251834\pi$
$613$	34.8119			1.40604			0.703020	+	0.711170i	$0.251834\pi$
$614$	−1.60123	+	7.88344i	−0.0646203	+	0.318150i
$615$	1.08064			0.0435756
$616$		0			0
$617$	10.5532			0.424854			0.212427	−	0.977177i	$-0.431863\pi$
$617$	10.5532			0.424854			0.212427	+	0.977177i	$0.431863\pi$
$618$	−6.77127	+	33.3374i	−0.272380	+	1.34103i
$619$	−24.6371			−0.990247			−0.495123	−	0.868823i	$-0.664877\pi$
$619$	−24.6371			−0.990247			−0.495123	+	0.868823i	$0.664877\pi$
$620$	−3.79187	+	8.94930i	−0.152285	+	0.359413i
$621$		−	49.3791i		−	1.98152i
$622$	−0.0352549	+	0.173573i	−0.00141359	+	0.00695964i
$623$		0			0
$624$	−24.1276	+	23.3606i	−0.965877	+	0.935172i
$625$	1.00000			0.0400000
$626$	−16.1510	−	3.28048i	−0.645524	−	0.131114i
$627$			1.10086i			0.0439643i
$628$	−8.29847	+	19.5854i	−0.331145	+	0.781544i
$629$			10.3477i			0.412590i
$630$		0			0
$631$			18.9068i			0.752668i	0.926484	+	0.376334i	$0.122815\pi$
$631$			18.9068i			0.752668i	−0.926484	+	0.376334i	$0.877185\pi$
$632$	−34.7155	−	23.8094i	−1.38091	−	0.947086i
$633$			11.7627i			0.467526i
$634$	5.20680	−	25.6350i	0.206789	−	1.01810i
$635$	2.46720			0.0979077
$636$	11.3660	+	4.81585i	0.450692	+	0.190961i
$637$		0			0
$638$	0.612904	+	0.124489i	0.0242651	+	0.00492856i
$639$		−	18.2850i		−	0.723344i
$640$	1.89275	+	11.1543i	0.0748173	+	0.440911i
$641$	−15.2936			−0.604062			−0.302031	−	0.953298i	$-0.597665\pi$
$641$	−15.2936			−0.604062			−0.302031	+	0.953298i	$0.597665\pi$
$642$	−15.1462	−	3.07639i	−0.597773	−	0.121415i
$643$	13.9558			0.550362			0.275181	−	0.961393i	$-0.411262\pi$
$643$	13.9558			0.550362			0.275181	+	0.961393i	$0.411262\pi$
$644$		0			0
$645$	−13.0207			−0.512688
$646$	5.08443	+	1.03271i	0.200044	+	0.0406316i
$647$	28.2293			1.10981			0.554904	−	0.831915i	$-0.312755\pi$
$647$	28.2293			1.10981			0.554904	+	0.831915i	$0.312755\pi$
$648$	−5.65845	+	8.25037i	−0.222285	+	0.324105i
$649$		−	1.67529i		−	0.0657608i
$650$	8.86520	+	1.80064i	0.347722	+	0.0706268i
$651$		0			0
$652$	−6.12576	+	14.4576i	−0.239903	+	0.566202i
$653$	25.3106			0.990480			0.495240	−	0.868756i	$-0.335080\pi$
$653$	25.3106			0.990480			0.495240	+	0.868756i	$0.335080\pi$
$654$	−0.367562	+	1.80964i	−0.0143728	+	0.0707627i
$655$		−	0.282917i		−	0.0110545i
$656$	2.36599	−	2.29077i	0.0923762	−	0.0894396i
$657$			11.5518i			0.450678i
$658$		0			0
$659$			27.5411i			1.07285i	0.843948	+	0.536425i	$0.180226\pi$
$659$			27.5411i			1.07285i	−0.843948	+	0.536425i	$0.819774\pi$
$660$	2.14895	+	0.910522i	0.0836477	+	0.0354420i
$661$		−	22.4848i		−	0.874559i	−0.899326	−	0.437279i	$-0.855942\pi$
$661$		−	22.4848i		−	0.874559i	0.899326	−	0.437279i	$-0.144058\pi$
$662$	9.59602	+	1.94908i	0.372960	+	0.0757530i
$663$	32.6504			1.26804
$664$	6.44209	−	9.39295i	0.250002	−	0.364517i
$665$		0			0
$666$	−0.956668	+	4.71003i	−0.0370701	+	0.182510i
$667$		−	4.37510i		−	0.169405i
$668$	14.5525	+	6.16598i	0.563053	+	0.238569i
$669$	21.5553			0.833376
$670$	2.62595	−	12.9285i	0.101449	−	0.499473i
$671$	0.516070			0.0199227
$672$		0			0
$673$	−11.4276			−0.440501			−0.220251	−	0.975443i	$-0.570688\pi$
$673$	−11.4276			−0.440501			−0.220251	+	0.975443i	$0.570688\pi$
$674$	4.37681	−	21.5486i	0.168588	−	0.830022i
$675$	5.61405			0.216085
$676$	51.4098	+	21.7826i	1.97730	+	0.837793i
$677$		−	46.1169i		−	1.77242i	−0.463286	−	0.886209i	$-0.653330\pi$
$677$		−	46.1169i		−	1.77242i	0.463286	−	0.886209i	$-0.346670\pi$
$678$	−0.134273	+	0.661073i	−0.00515671	+	0.0253884i
$679$		0			0
$680$	6.22123	−	9.07093i	0.238573	−	0.347854i
$681$	16.6849			0.639366
$682$	5.98803	+	1.21625i	0.229294	+	0.0465725i
$683$		−	32.2192i		−	1.23283i	−0.787420	−	0.616416i	$-0.788584\pi$
$683$		−	32.2192i		−	1.23283i	0.787420	−	0.616416i	$-0.211416\pi$
$684$	2.21883	+	0.940133i	0.0848392	+	0.0359469i
$685$			16.6151i			0.634832i
$686$		0			0
$687$			22.7024i			0.866152i
$688$	−28.5079	+	27.6016i	−1.08685	+	1.05230i
$689$		−	30.0794i		−	1.14593i
$690$	3.24980	−	15.9999i	0.123718	−	0.609108i
$691$	−31.0271			−1.18033			−0.590163	−	0.807284i	$-0.700937\pi$
$691$	−31.0271			−1.18033			−0.590163	+	0.807284i	$0.700937\pi$
$692$	−14.5365	+	34.3080i	−0.552595	+	1.30419i
$693$		0			0
$694$	32.4440	+	6.58980i	1.23156	+	0.250146i
$695$		−	18.6029i		−	0.705648i
$696$	−1.04446	+	1.52288i	−0.0395901	+	0.0577248i
$697$	−3.20175			−0.121275
$698$	−43.1622	−	8.76680i	−1.63371	−	0.331828i
$699$	31.1701			1.17896
$700$		0			0
$701$	31.9213			1.20565			0.602826	−	0.797873i	$-0.294041\pi$
$701$	31.9213			1.20565			0.602826	+	0.797873i	$0.294041\pi$
$702$	49.7697	+	10.1089i	1.87844	+	0.381535i
$703$	−2.51019			−0.0946735
$704$	6.63513	−	2.56188i	0.250071	−	0.0965545i
$705$			9.67988i			0.364565i
$706$	14.1687	+	2.87785i	0.533247	+	0.108309i
$707$		0			0
$708$	4.55456	+	1.92979i	0.171171	+	0.0725261i
$709$	−4.98641			−0.187268			−0.0936342	−	0.995607i	$-0.529848\pi$
$709$	−4.98641			−0.187268			−0.0936342	+	0.995607i	$0.529848\pi$
$710$	4.03000	−	19.8412i	0.151243	−	0.744626i
$711$			19.0089i			0.712891i
$712$	−14.0355	−	9.62616i	−0.526003	−	0.360756i
$713$		−	42.7445i		−	1.60079i
$714$		0			0
$715$		−	5.68704i		−	0.212683i
$716$	16.0101	−	37.7858i	0.598325	−	1.41212i
$717$			13.3923i			0.500146i
$718$	15.6696	+	3.18270i	0.584784	+	0.118777i
$719$	−17.2993			−0.645154			−0.322577	−	0.946543i	$-0.604549\pi$
$719$	−17.2993			−0.645154			−0.322577	+	0.946543i	$0.604549\pi$
$720$	3.67038	−	3.55370i	0.136787	−	0.132439i
$721$		0			0
$722$	5.09793	−	25.0990i	0.189725	−	0.934087i
$723$			3.05619i			0.113661i
$724$	−10.3535	+	24.4356i	−0.384785	+	0.908141i
$725$	0.497418			0.0184736
$726$	−3.77222	+	18.5720i	−0.140000	+	0.689272i
$727$	4.42613			0.164156			0.0820780	−	0.996626i	$-0.473844\pi$
$727$	4.42613			0.164156			0.0820780	+	0.996626i	$0.473844\pi$
$728$		0			0
$729$	26.6237			0.986065
$730$	−2.54600	+	12.5349i	−0.0942317	+	0.463937i
$731$	38.5780			1.42686
$732$	−0.594470	+	1.40303i	−0.0219723	+	0.0518573i
$733$			37.4068i			1.38165i	0.723021	+	0.690826i	$0.242753\pi$
$733$			37.4068i			1.38165i	−0.723021	+	0.690826i	$0.757247\pi$
$734$	6.45065	−	31.7589i	0.238098	−	1.17224i
$735$		0			0
$736$	−26.8020	−	41.9198i	−0.987934	−	1.54519i
$737$	−8.29368			−0.305502
$738$	−1.45736	−	0.296009i	−0.0536461	−	0.0108962i
$739$			41.8897i			1.54094i	0.637478	+	0.770469i	$0.279978\pi$
$739$			41.8897i			1.54094i	−0.637478	+	0.770469i	$0.720022\pi$
$740$	−2.07617	+	4.90003i	−0.0763215	+	0.180129i
$741$			7.92048i			0.290966i
$742$		0			0
$743$			33.0690i			1.21318i	0.795014	+	0.606591i	$0.207464\pi$
$743$			33.0690i			1.21318i	−0.795014	+	0.606591i	$0.792536\pi$
$744$	−10.2043	+	14.8785i	−0.374108	+	0.545471i
$745$			15.6654i			0.573936i
$746$	3.15525	−	15.5345i	0.115522	−	0.568757i
$747$	−5.14324			−0.188181
$748$	−6.36696	−	2.69772i	−0.232799	−	0.0986384i
$749$		0			0
$750$	1.81908	+	0.369479i	0.0664234	+	0.0134915i
$751$			6.87464i			0.250859i	0.992103	+	0.125430i	$0.0400309\pi$
$751$			6.87464i			0.250859i	−0.992103	+	0.125430i	$0.959969\pi$
$752$	20.5197	+	21.1934i	0.748277	+	0.772845i
$753$	8.58796			0.312963
$754$	4.40971	+	0.895670i	0.160592	+	0.0326184i
$755$	11.9875			0.436272
$756$		0			0
$757$	18.4550			0.670758			0.335379	−	0.942083i	$-0.391136\pi$
$757$	18.4550			0.670758			0.335379	+	0.942083i	$0.391136\pi$
$758$	33.6288	+	6.83044i	1.22145	+	0.248093i
$759$	−10.2640			−0.372560
$760$	2.20046	+	1.50917i	0.0798192	+	0.0547434i
$761$			40.6962i			1.47524i	0.675218	+	0.737618i	$0.264050\pi$
$761$			40.6962i			1.47524i	−0.675218	+	0.737618i	$0.735950\pi$
$762$	4.48803	+	0.911577i	0.162584	+	0.0330229i
$763$		0			0
$764$	16.1524	−	38.1218i	0.584374	−	1.37920i
$765$	−4.96691			−0.179579
$766$	2.26944	−	11.1733i	0.0819983	−	0.403708i
$767$		−	12.0533i		−	0.435221i
$768$	−0.678207	+	20.9898i	−0.0244727	+	0.757405i
$769$		−	39.5711i		−	1.42697i	−0.700670	−	0.713485i	$-0.747115\pi$
$769$		−	39.5711i		−	1.42697i	0.700670	−	0.713485i	$-0.252885\pi$
$770$		0			0
$771$			25.7768i			0.928327i
$772$	32.4012	+	13.7286i	1.16615	+	0.494103i
$773$			14.9245i			0.536797i	0.963308	+	0.268399i	$0.0864944\pi$
$773$			14.9245i			0.536797i	−0.963308	+	0.268399i	$0.913506\pi$
$774$	17.5598	+	3.56662i	0.631174	+	0.128200i
$775$	4.85974			0.174567
$776$	−33.8807	−	23.2368i	−1.21624	−	0.834153i
$777$		0			0
$778$	−3.93292	+	19.3632i	−0.141002	+	0.694205i
$779$		−	0.776693i		−	0.0278279i
$780$	15.4612	+	6.55101i	0.553600	+	0.234564i
$781$	−12.7281			−0.455449
$782$	−9.62859	+	47.4051i	−0.344318	+	1.69520i
$783$	2.79253			0.0997969
$784$		0			0
$785$	10.6355			0.379597
$786$	0.104532	−	0.514648i	0.00372853	−	0.0183569i
$787$	29.2291			1.04190			0.520952	−	0.853586i	$-0.325577\pi$
$787$	29.2291			1.04190			0.520952	+	0.853586i	$0.325577\pi$
$788$	−43.8920	−	18.5973i	−1.56359	−	0.662502i
$789$		−	14.0180i		−	0.499055i
$790$	−4.18955	+	20.6267i	−0.149057	+	0.733865i
$791$		0			0
$792$	−2.64868	−	1.81658i	−0.0941167	−	0.0645493i
$793$	3.71301			0.131853
$794$	15.7509	+	3.19921i	0.558978	+	0.113536i
$795$		−	6.17209i		−	0.218902i
$796$	−34.0841	−	14.4416i	−1.20808	−	0.511870i
$797$			32.2478i			1.14228i	0.820854	+	0.571138i	$0.193498\pi$
$797$			32.2478i			1.14228i	−0.820854	+	0.571138i	$0.806502\pi$
$798$		0			0
$799$		−	28.6798i		−	1.01462i
$800$	4.76598	−	3.04719i	0.168503	−	0.107735i
$801$			7.68534i			0.271548i
$802$	1.06322	−	5.23462i	0.0375436	−	0.184841i
$803$	8.04116			0.283766
$804$	9.55364	−	22.5478i	0.336931	−	0.795199i
$805$		0			0
$806$	43.0826	+	8.75063i	1.51752	+	0.308228i
$807$		−	8.14930i		−	0.286869i
$808$	34.5756	+	23.7134i	1.21637	+	0.834236i
$809$	18.0629			0.635056			0.317528	−	0.948249i	$-0.397147\pi$
$809$	18.0629			0.635056			0.317528	+	0.948249i	$0.397147\pi$
$810$	4.90207	+	0.995674i	0.172241	+	0.0349844i
$811$	−26.8176			−0.941692			−0.470846	−	0.882215i	$-0.656051\pi$
$811$	−26.8176			−0.941692			−0.470846	+	0.882215i	$0.656051\pi$
$812$		0			0
$813$	22.9398			0.804534
$814$	3.27864	+	0.665934i	0.114916	+	0.0233410i
$815$	7.85089			0.275005
$816$	14.6684	−	14.2021i	0.513498	−	0.497174i
$817$			9.35841i			0.327409i
$818$	−19.3734	−	3.93499i	−0.677375	−	0.137584i
$819$		0			0
$820$	−1.51615	−	0.642401i	−0.0529462	−	0.0224336i
$821$	8.18187			0.285549			0.142775	−	0.989755i	$-0.454398\pi$
$821$	8.18187			0.285549			0.142775	+	0.989755i	$0.454398\pi$
$822$	−6.13894	+	30.2243i	−0.214120	+	1.05419i
$823$			34.3738i			1.19819i	0.800676	+	0.599097i	$0.204474\pi$
$823$			34.3738i			1.19819i	−0.800676	+	0.599097i	$0.795526\pi$
$824$	29.3181	−	42.7475i	1.02134	−	1.48918i
$825$		−	1.16694i		−	0.0406277i
$826$		0			0
$827$			41.6060i			1.44678i	0.690439	+	0.723391i	$0.257418\pi$
$827$			41.6060i			1.44678i	−0.690439	+	0.723391i	$0.742582\pi$
$828$	−8.76541	+	20.6875i	−0.304619	+	0.718940i
$829$			3.42181i			0.118844i	0.998233	+	0.0594222i	$0.0189258\pi$
$829$			3.42181i			0.118844i	−0.998233	+	0.0594222i	$0.981074\pi$
$830$	−5.58096	−	1.13356i	−0.193718	−	0.0393466i
$831$	14.4290			0.500536
$832$	47.7383	−	18.4322i	1.65503	−	0.639021i
$833$		0			0
$834$	6.87337	−	33.8401i	0.238005	−	1.17179i
$835$		−	7.90245i		−	0.273476i
$836$	0.654424	−	1.54452i	0.0226337	−	0.0534184i
$837$	27.2828			0.943033
$838$	−1.75509	+	8.64094i	−0.0606285	+	0.298496i
$839$	−42.9230			−1.48187			−0.740933	−	0.671579i	$-0.765616\pi$
$839$	−42.9230			−1.48187			−0.740933	+	0.671579i	$0.765616\pi$
$840$		0			0
$841$	−28.7526			−0.991468
$842$	2.72305	−	13.4066i	0.0938427	−	0.462022i
$843$	−24.3812			−0.839733
$844$	6.99251	−	16.5032i	0.240692	−	0.568064i
$845$		−	27.9170i		−	0.960375i
$846$	2.65151	−	13.0544i	0.0911609	−	0.448818i
$847$		0			0
$848$	−13.0838	−	13.5134i	−0.449299	−	0.464051i
$849$	9.95634			0.341701
$850$	−5.38962	−	1.09470i	−0.184862	−	0.0375480i
$851$		−	23.4040i		−	0.802277i
$852$	14.6618	−	34.6037i	0.502304	−	1.18550i
$853$		−	31.3541i		−	1.07355i	−0.843727	−	0.536773i	$-0.819643\pi$
$853$		−	31.3541i		−	1.07355i	0.843727	−	0.536773i	$-0.180357\pi$
$854$		0			0
$855$		−	1.20489i		−	0.0412065i
$856$	19.4215	+	13.3201i	0.663812	+	0.455271i
$857$			34.9236i			1.19297i	0.802625	+	0.596484i	$0.203436\pi$
$857$			34.9236i			1.19297i	−0.802625	+	0.596484i	$0.796564\pi$
$858$	2.10124	−	10.3452i	0.0717352	−	0.353179i
$859$	42.3096			1.44359			0.721793	−	0.692109i	$-0.243318\pi$
$859$	42.3096			1.44359			0.721793	+	0.692109i	$0.243318\pi$
$860$	18.2681	+	7.74032i	0.622938	+	0.263943i
$861$		0			0
$862$	−11.7505	−	2.38667i	−0.400223	−	0.0812905i
$863$			24.3442i			0.828688i	0.910120	+	0.414344i	$0.135989\pi$
$863$			24.3442i			0.828688i	−0.910120	+	0.414344i	$0.864011\pi$
$864$	26.7565	−	17.1071i	0.910274	−	0.581996i
$865$	18.6303			0.633448
$866$	34.5549	+	7.01856i	1.17422	+	0.238500i
$867$	2.46341			0.0836618
$868$		0			0
$869$	13.2321			0.448867
$870$	0.904843	+	0.183785i	0.0306771	+	0.00623091i
$871$	−59.6712			−2.02188
$872$	1.59146	−	2.32045i	0.0538937	−	0.0785803i
$873$			18.5518i			0.627884i
$874$	−11.4997	−	2.33574i	−0.388984	−	0.0790077i
$875$		0			0
$876$	−9.26276	+	21.8613i	−0.312960	+	0.738624i
$877$	42.5226			1.43588			0.717942	−	0.696103i	$-0.245084\pi$
$877$	42.5226			1.43588			0.717942	+	0.696103i	$0.245084\pi$
$878$	7.15333	−	35.2185i	0.241413	−	1.18857i
$879$			7.09689i			0.239372i
$880$	−2.47372	−	2.55494i	−0.0833892	−	0.0861271i
$881$			30.5097i			1.02790i	0.857820	+	0.513950i	$0.171818\pi$
$881$			30.5097i			1.02790i	−0.857820	+	0.513950i	$0.828182\pi$
$882$		0			0
$883$			12.7488i			0.429030i	0.976721	+	0.214515i	$0.0688170\pi$
$883$			12.7488i			0.429030i	−0.976721	+	0.214515i	$0.931183\pi$
$884$	−45.8089	−	19.4095i	−1.54072	−	0.652812i
$885$		−	2.47326i		−	0.0831379i
$886$	−33.2466	−	6.75281i	−1.11694	−	0.226865i
$887$	−9.51781			−0.319577			−0.159788	−	0.987151i	$-0.551081\pi$
$887$	−9.51781			−0.319577			−0.159788	+	0.987151i	$0.551081\pi$
$888$	−5.58718	+	8.14644i	−0.187493	+	0.273377i
$889$		0			0
$890$	−1.69384	+	8.33940i	−0.0567777	+	0.279537i
$891$		−	3.14469i		−	0.105351i
$892$	−30.2423	−	12.8138i	−1.01259	−	0.429039i
$893$	6.95727			0.232816
$894$	−5.78803	+	28.4966i	−0.193581	+	0.953069i
$895$	−20.5188			−0.685869
$896$		0			0
$897$	−73.8472			−2.46569
$898$	4.82152	−	23.7381i	0.160896	−	0.792151i
$899$	2.41732			0.0806222
$900$	−2.35202	−	0.996565i	−0.0784006	−	0.0332188i
$901$			18.2868i			0.609223i
$902$	−0.206051	+	1.01446i	−0.00686074	+	0.0337779i
$903$		0			0
$904$	0.581370	−	0.847672i	0.0193361	−	0.0281932i
$905$	13.2693			0.441085
$906$	21.8063	+	4.42914i	0.724466	+	0.147148i
$907$		−	1.54731i		−	0.0513775i	−0.999670	−	0.0256887i	$-0.991822\pi$
$907$		−	1.54731i		−	0.0513775i	0.999670	−	0.0256887i	$-0.00817788\pi$
$908$	−23.4091	−	9.91856i	−0.776857	−	0.329159i
$909$		−	18.9324i		−	0.627947i
$910$		0			0
$911$			19.9439i			0.660769i	0.943846	+	0.330385i	$0.107178\pi$
$911$			19.9439i			0.660769i	−0.943846	+	0.330385i	$0.892822\pi$
$912$	3.44521	+	3.55833i	0.114082	+	0.117828i
$913$			3.58019i			0.118487i
$914$	3.14813	−	15.4994i	0.104131	−	0.512675i
$915$	0.761885			0.0251871
$916$	13.4958	−	31.8517i	0.445913	−	1.05241i
$917$		0			0
$918$	−30.2576	−	6.14571i	−0.998650	−	0.202839i
$919$		−	10.4658i		−	0.345236i	−0.984989	−	0.172618i	$-0.944777\pi$
$919$		−	10.4658i		−	0.345236i	0.984989	−	0.172618i	$-0.0552226\pi$
$920$	−14.0709	+	20.5162i	−0.463904	+	0.676399i
$921$	7.46611			0.246017
$922$	−35.1638	−	7.14222i	−1.15806	−	0.235217i
$923$	−91.5762			−3.01427
$924$		0			0
$925$	2.66086			0.0874886
$926$	−0.0709550	−	0.0144119i	−0.00233173	−	0.000473604i
$927$	−23.4070			−0.768786
$928$	2.37069	−	1.51573i	0.0778216	−	0.0497563i
$929$			32.0214i			1.05059i	0.850921	+	0.525294i	$0.176045\pi$
$929$			32.0214i			1.05059i	−0.850921	+	0.525294i	$0.823955\pi$
$930$	8.84026	+	1.79557i	0.289883	+	0.0588791i
$931$		0			0
$932$	−43.7320	−	18.5295i	−1.43249	−	0.606954i
$933$	0.164384			0.00538171
$934$	3.74140	−	18.4203i	0.122422	−	0.602730i
$935$			3.45745i			0.113071i
$936$	−19.0567	−	13.0699i	−0.622887	−	0.427202i
$937$			47.3389i			1.54649i	0.634106	+	0.773247i	$0.281368\pi$
$937$			47.3389i			1.54649i	−0.634106	+	0.773247i	$0.718632\pi$
$938$		0			0
$939$			15.2960i			0.499167i
$940$	5.75434	−	13.5810i	0.187686	−	0.442962i
$941$		−	5.20892i		−	0.169806i	−0.996389	−	0.0849030i	$-0.972942\pi$
$941$		−	5.20892i		−	0.169806i	0.996389	−	0.0849030i	$-0.0270580\pi$
$942$	19.3468	+	3.92958i	0.630352	+	0.128033i
$943$	7.24156			0.235818
$944$	−5.24290	−	5.41504i	−0.170642	−	0.176245i
$945$		0			0
$946$	2.48271	−	12.2233i	0.0807200	−	0.397414i
$947$		−	0.627790i		−	0.0204004i	−0.999948	−	0.0102002i	$-0.996753\pi$
$947$		−	0.627790i		−	0.0204004i	0.999948	−	0.0102002i	$-0.00324689\pi$
$948$	−15.2422	+	35.9736i	−0.495045	+	1.16837i
$949$	57.8544			1.87803
$950$	0.265557	−	1.30744i	0.00861581	−	0.0424188i
$951$	−24.2780			−0.787267
$952$		0			0
$953$	−4.46691			−0.144697			−0.0723487	−	0.997379i	$-0.523049\pi$
$953$	−4.46691			−0.144697			−0.0723487	+	0.997379i	$0.523049\pi$
$954$	−1.69066	+	8.32373i	−0.0547371	+	0.269491i
$955$	−20.7013			−0.669877
$956$	7.96125	−	18.7896i	0.257485	−	0.607698i
$957$		−	0.580459i		−	0.0187636i
$958$	−2.72242	+	13.4034i	−0.0879572	+	0.433046i
$959$		0			0
$960$	9.79558	−	3.78216i	0.316151	−	0.122069i
$961$	−7.38292			−0.238159
$962$	23.5891	+	4.79125i	0.760542	+	0.154476i
$963$		−	10.6345i		−	0.342692i
$964$	1.81679	−	4.28786i	0.0585149	−	0.138103i
$965$		−	17.5948i		−	0.566398i
$966$		0			0
$967$		−	1.90732i		−	0.0613352i	−0.999530	−	0.0306676i	$-0.990237\pi$
$967$		−	1.90732i		−	0.0613352i	0.999530	−	0.0306676i	$-0.00976333\pi$
$968$	16.3328	−	23.8143i	0.524957	−	0.765419i
$969$		−	4.81527i		−	0.154689i
$970$	−4.08880	+	20.1307i	−0.131283	+	0.646357i
$971$	48.9595			1.57119			0.785593	−	0.618744i	$-0.212358\pi$
$971$	48.9595			1.57119			0.785593	+	0.618744i	$0.212358\pi$
$972$	−22.4658	−	9.51888i	−0.720590	−	0.305318i
$973$		0			0
$974$	−9.48971	−	1.92748i	−0.304070	−	0.0617605i
$975$		−	8.39590i		−	0.268884i
$976$	1.66810	−	1.61507i	0.0533944	−	0.0516971i
$977$	6.31186			0.201934			0.100967	−	0.994890i	$-0.467806\pi$
$977$	6.31186			0.201934			0.100967	+	0.994890i	$0.467806\pi$
$978$	14.2814	+	2.90074i	0.456669	+	0.0927554i
$979$	5.34974			0.170978
$980$		0			0
$981$	−1.27059			−0.0405669
$982$	33.3167	+	6.76706i	1.06318	+	0.215946i
$983$	21.4893			0.685404			0.342702	−	0.939444i	$-0.388658\pi$
$983$	21.4893			0.685404			0.342702	+	0.939444i	$0.388658\pi$
$984$	−2.52064	−	1.72876i	−0.0803550	−	0.0551109i
$985$			23.8347i			0.759436i
$986$	−2.68089	−	0.544524i	−0.0853771	−	0.0173412i
$987$		0			0
$988$	4.70844	−	11.1125i	0.149795	−	0.353536i
$989$	−87.2539			−2.77451
$990$	−0.319649	+	1.57375i	−0.0101591	+	0.0500170i
$991$		−	5.81929i		−	0.184856i	−0.995719	−	0.0924279i	$-0.970537\pi$
$991$		−	5.81929i		−	0.184856i	0.995719	−	0.0924279i	$-0.0294628\pi$
$992$	23.1614	−	14.8086i	0.735377	−	0.470173i
$993$		−	9.08804i		−	0.288400i
$994$		0			0
$995$			18.5087i			0.586765i
$996$	−9.73337	−	4.12409i	−0.308414	−	0.130677i
$997$			24.8679i			0.787574i	0.919202	+	0.393787i	$0.128835\pi$
$997$			24.8679i			0.787574i	−0.919202	+	0.393787i	$0.871165\pi$
$998$	17.9314	+	3.64209i	0.567608	+	0.115288i
$999$	14.9382			0.472624

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	980.2.g.b.391.20	yes	48
4.3	odd	2	inner	980.2.g.b.391.17	✓	48
7.2	even	3		980.2.o.g.31.41		96
7.3	odd	6		980.2.o.g.411.14		96
7.4	even	3		980.2.o.g.411.13		96
7.5	odd	6		980.2.o.g.31.42		96
7.6	odd	2	inner	980.2.g.b.391.19	yes	48
28.3	even	6		980.2.o.g.411.41		96
28.11	odd	6		980.2.o.g.411.42		96
28.19	even	6		980.2.o.g.31.13		96
28.23	odd	6		980.2.o.g.31.14		96
28.27	even	2	inner	980.2.g.b.391.18	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
980.2.g.b.391.17	✓	48	4.3	odd	2	inner
980.2.g.b.391.18	yes	48	28.27	even	2	inner
980.2.g.b.391.19	yes	48	7.6	odd	2	inner
980.2.g.b.391.20	yes	48	1.1	even	1	trivial
980.2.o.g.31.13		96	28.19	even	6
980.2.o.g.31.14		96	28.23	odd	6
980.2.o.g.31.41		96	7.2	even	3
980.2.o.g.31.42		96	7.5	odd	6
980.2.o.g.411.13		96	7.4	even	3
980.2.o.g.411.14		96	7.3	odd	6
980.2.o.g.411.41		96	28.3	even	6
980.2.o.g.411.42		96	28.11	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.g (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.281497 + 1.38591i) q^{2} +1.31255 q^{3} +(-1.84152 - 0.780262i) q^{4} +1.00000i q^{5} +(-0.369479 + 1.81908i) q^{6} +(1.59976 - 2.33255i) q^{8} -1.27722 q^{9} +O(q^{10})\)	\(q+(-0.281497 + 1.38591i) q^{2} +1.31255 q^{3} +(-1.84152 - 0.780262i) q^{4} +1.00000i q^{5} +(-0.369479 + 1.81908i) q^{6} +(1.59976 - 2.33255i) q^{8} -1.27722 q^{9} +(-1.38591 - 0.281497i) q^{10} +0.889067i q^{11} +(-2.41708 - 1.02413i) q^{12} +6.39664i q^{13} +1.31255i q^{15} +(2.78238 + 2.87374i) q^{16} -3.88885i q^{17} +(0.359533 - 1.77011i) q^{18} +0.943374 q^{19} +(0.780262 - 1.84152i) q^{20} +(-1.23217 - 0.250270i) q^{22} +8.79563i q^{23} +(2.09976 - 3.06158i) q^{24} -1.00000 q^{25} +(-8.86520 - 1.80064i) q^{26} -5.61405 q^{27} -0.497418 q^{29} +(-1.81908 - 0.369479i) q^{30} -4.85974 q^{31} +(-4.76598 + 3.04719i) q^{32} +1.16694i q^{33} +(5.38962 + 1.09470i) q^{34} +(2.35202 + 0.996565i) q^{36} -2.66086 q^{37} +(-0.265557 + 1.30744i) q^{38} +8.39590i q^{39} +(2.33255 + 1.59976i) q^{40} -0.823314i q^{41} +9.92015i q^{43} +(0.693705 - 1.63723i) q^{44} -1.27722i q^{45} +(-12.1900 - 2.47595i) q^{46} +7.37488 q^{47} +(3.65201 + 3.77192i) q^{48} +(0.281497 - 1.38591i) q^{50} -5.10431i q^{51} +(4.99106 - 11.7795i) q^{52} -4.70237 q^{53} +(1.58034 - 7.78060i) q^{54} -0.889067 q^{55} +1.23822 q^{57} +(0.140022 - 0.689379i) q^{58} -1.88432 q^{59} +(1.02413 - 2.41708i) q^{60} -0.580462i q^{61} +(1.36800 - 6.73519i) q^{62} +(-2.88154 - 7.46302i) q^{64} -6.39664 q^{65} +(-1.61728 - 0.328491i) q^{66} +9.32852i q^{67} +(-3.03433 + 7.16140i) q^{68} +11.5447i q^{69} +14.3163i q^{71} +(-2.04324 + 2.97917i) q^{72} -9.04450i q^{73} +(0.749025 - 3.68773i) q^{74} -1.31255 q^{75} +(-1.73724 - 0.736079i) q^{76} +(-11.6360 - 2.36342i) q^{78} -14.8831i q^{79} +(-2.87374 + 2.78238i) q^{80} -3.53706 q^{81} +(1.14104 + 0.231761i) q^{82} +4.02691 q^{83} +3.88885 q^{85} +(-13.7485 - 2.79249i) q^{86} -0.652885 q^{87} +(2.07379 + 1.42229i) q^{88} -6.01725i q^{89} +(1.77011 + 0.359533i) q^{90} +(6.86290 - 16.1973i) q^{92} -6.37864 q^{93} +(-2.07601 + 10.2209i) q^{94} +0.943374i q^{95} +(-6.25558 + 3.99959i) q^{96} -14.5252i q^{97} -1.13553i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 8 q^{2} - 8 q^{4} + 8 q^{8} + 48 q^{9}+O(q^{10}) \) 48 * q + 8 * q^2 - 8 * q^4 + 8 * q^8 + 48 * q^9	\( 48 q + 8 q^{2} - 8 q^{4} + 8 q^{8} + 48 q^{9} - 40 q^{16} + 40 q^{18} - 32 q^{22} - 48 q^{25} + 64 q^{29} + 8 q^{32} - 40 q^{36} + 64 q^{37} - 32 q^{46} - 8 q^{50} - 64 q^{53} - 48 q^{58} - 8 q^{64} - 72 q^{72} + 96 q^{74} - 112 q^{78} + 48 q^{81} + 32 q^{88} - 112 q^{92}+O(q^{100}) \) 48 * q + 8 * q^2 - 8 * q^4 + 8 * q^8 + 48 * q^9 - 40 * q^16 + 40 * q^18 - 32 * q^22 - 48 * q^25 + 64 * q^29 + 8 * q^32 - 40 * q^36 + 64 * q^37 - 32 * q^46 - 8 * q^50 - 64 * q^53 - 48 * q^58 - 8 * q^64 - 72 * q^72 + 96 * q^74 - 112 * q^78 + 48 * q^81 + 32 * q^88 - 112 * q^92

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