LMFDB - Embedded newform 980.2.c.e.979.22

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			979.22
Character	$\chi$	$=$	980.979
Dual form			980.2.c.e.979.23

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.255919 - 1.39086i) q^{2} +3.18626i q^{3} +(-1.86901 + 0.711898i) q^{4} +(1.80715 + 1.31689i) q^{5} +(4.43165 - 0.815425i) q^{6} +(1.46847 + 2.41735i) q^{8} -7.15223 q^{9} +O(q^{10})$	\(q+(-0.255919 - 1.39086i) q^{2} +3.18626i q^{3} +(-1.86901 + 0.711898i) q^{4} +(1.80715 + 1.31689i) q^{5} +(4.43165 - 0.815425i) q^{6} +(1.46847 + 2.41735i) q^{8} -7.15223 q^{9} +(1.36913 - 2.85052i) q^{10} +4.51680i q^{11} +(-2.26829 - 5.95515i) q^{12} -2.22528 q^{13} +(-4.19595 + 5.75805i) q^{15} +(2.98640 - 2.66109i) q^{16} -2.52865 q^{17} +(1.83040 + 9.94779i) q^{18} +5.21241 q^{19} +(-4.31508 - 1.17477i) q^{20} +(6.28226 - 1.15594i) q^{22} -1.71481 q^{23} +(-7.70231 + 4.67892i) q^{24} +(1.53160 + 4.75964i) q^{25} +(0.569493 + 3.09507i) q^{26} -13.2301i q^{27} -2.31039 q^{29} +(9.08250 + 4.36240i) q^{30} +4.62540 q^{31} +(-4.46550 - 3.47266i) q^{32} -14.3917 q^{33} +(0.647131 + 3.51701i) q^{34} +(13.3676 - 5.09167i) q^{36} -0.336766i q^{37} +(-1.33396 - 7.24976i) q^{38} -7.09032i q^{39} +(-0.529635 + 6.30234i) q^{40} -3.28064i q^{41} -6.66354 q^{43} +(-3.21551 - 8.44195i) q^{44} +(-12.9252 - 9.41870i) q^{45} +(0.438852 + 2.38506i) q^{46} +1.44644i q^{47} +(8.47892 + 9.51544i) q^{48} +(6.22805 - 3.34834i) q^{50} -8.05693i q^{51} +(4.15908 - 1.58418i) q^{52} -10.0769i q^{53} +(-18.4013 + 3.38584i) q^{54} +(-5.94813 + 8.16255i) q^{55} +16.6081i q^{57} +(0.591274 + 3.21344i) q^{58} +3.20322 q^{59} +(3.74312 - 13.7490i) q^{60} -6.05175i q^{61} +(-1.18373 - 6.43331i) q^{62} +(-3.68719 + 7.09962i) q^{64} +(-4.02143 - 2.93045i) q^{65} +(3.68311 + 20.0169i) q^{66} -11.1495 q^{67} +(4.72608 - 1.80014i) q^{68} -5.46381i q^{69} +9.15549i q^{71} +(-10.5028 - 17.2895i) q^{72} +3.24011 q^{73} +(-0.468396 + 0.0861849i) q^{74} +(-15.1654 + 4.88008i) q^{75} +(-9.74205 + 3.71071i) q^{76} +(-9.86168 + 1.81455i) q^{78} +14.2700i q^{79} +(8.90125 - 0.876239i) q^{80} +20.6978 q^{81} +(-4.56292 + 0.839579i) q^{82} +11.3059i q^{83} +(-4.56966 - 3.32995i) q^{85} +(1.70533 + 9.26808i) q^{86} -7.36150i q^{87} +(-10.9187 + 6.63279i) q^{88} +15.2152i q^{89} +(-9.79234 + 20.3876i) q^{90} +(3.20499 - 1.22077i) q^{92} +14.7377i q^{93} +(2.01181 - 0.370173i) q^{94} +(9.41962 + 6.86417i) q^{95} +(11.0648 - 14.2282i) q^{96} -4.49303 q^{97} -32.3052i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 16 q^{4} - 64 q^{9}+O(q^{10}) $ 48 * q + 16 * q^4 - 64 * q^9	$ 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

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 $

$2$	−0.255919	−	1.39086i	−0.180962	−	0.983490i
$2$	−0.255919	−	1.39086i	−0.180962	−	0.983490i
$3$			3.18626i			1.83959i	0.392403	+	0.919793i	$0.371644\pi$
$3$			3.18626i			1.83959i	−0.392403	+	0.919793i	$0.628356\pi$
$4$	−1.86901	+	0.711898i	−0.934505	+	0.355949i
$5$	1.80715	+	1.31689i	0.808183	+	0.588931i
$5$	1.80715	+	1.31689i	0.808183	+	0.588931i
$6$	4.43165	−	0.815425i	1.80921	−	0.332896i
$7$		0			0
$7$		0			0
$8$	1.46847	+	2.41735i	0.519183	+	0.854663i
$9$	−7.15223			−2.38408
$10$	1.36913	−	2.85052i	0.432957	−	0.901415i
$11$			4.51680i			1.36187i	0.732345	+	0.680934i	$0.238426\pi$
$11$			4.51680i			1.36187i	−0.732345	+	0.680934i	$0.761574\pi$
$12$	−2.26829	−	5.95515i	−0.654799	−	1.71910i
$13$	−2.22528			−0.617182			−0.308591	−	0.951195i	$-0.599858\pi$
$13$	−2.22528			−0.617182			−0.308591	+	0.951195i	$0.599858\pi$
$14$		0			0
$15$	−4.19595	+	5.75805i	−1.08339	+	1.48672i
$16$	2.98640	−	2.66109i	0.746600	−	0.665273i
$17$	−2.52865			−0.613288			−0.306644	−	0.951824i	$-0.599206\pi$
$17$	−2.52865			−0.613288			−0.306644	+	0.951824i	$0.599206\pi$
$18$	1.83040	+	9.94779i	0.431428	+	2.34472i
$19$	5.21241			1.19581			0.597904	−	0.801568i	$-0.296000\pi$
$19$	5.21241			1.19581			0.597904	+	0.801568i	$0.296000\pi$
$20$	−4.31508	−	1.17477i	−0.964881	−	0.262687i
$21$		0			0
$22$	6.28226	−	1.15594i	1.33938	−	0.246447i
$23$	−1.71481			−0.357562			−0.178781	−	0.983889i	$-0.557215\pi$
$23$	−1.71481			−0.357562			−0.178781	+	0.983889i	$0.557215\pi$
$24$	−7.70231	+	4.67892i	−1.57223	+	0.955082i
$25$	1.53160	+	4.75964i	0.306321	+	0.951928i
$26$	0.569493	+	3.09507i	0.111687	+	0.606993i
$27$		−	13.2301i		−	2.54613i
$28$		0			0
$29$	−2.31039			−0.429029			−0.214514	−	0.976721i	$-0.568817\pi$
$29$	−2.31039			−0.429029			−0.214514	+	0.976721i	$0.568817\pi$
$30$	9.08250	+	4.36240i	1.65823	+	0.796462i
$31$	4.62540			0.830747			0.415373	−	0.909651i	$-0.363651\pi$
$31$	4.62540			0.830747			0.415373	+	0.909651i	$0.363651\pi$
$32$	−4.46550	−	3.47266i	−0.789396	−	0.613885i
$33$	−14.3917			−2.50527
$34$	0.647131	+	3.51701i	0.110982	+	0.603163i
$35$		0			0
$36$	13.3676	−	5.09167i	2.22793	−	0.848611i
$37$		−	0.336766i		−	0.0553640i	−0.999617	−	0.0276820i	$-0.991187\pi$
$37$		−	0.336766i		−	0.0553640i	0.999617	−	0.0276820i	$-0.00881258\pi$
$38$	−1.33396	−	7.24976i	−0.216396	−	1.17607i
$39$		−	7.09032i		−	1.13536i
$40$	−0.529635	+	6.30234i	−0.0837427	+	0.996487i
$41$		−	3.28064i		−	0.512350i	−0.966630	−	0.256175i	$-0.917538\pi$
$41$		−	3.28064i		−	0.512350i	0.966630	−	0.256175i	$-0.0824623\pi$
$42$		0			0
$43$	−6.66354			−1.01618			−0.508090	−	0.861304i	$-0.669648\pi$
$43$	−6.66354			−1.01618			−0.508090	+	0.861304i	$0.669648\pi$
$44$	−3.21551	−	8.44195i	−0.484756	−	1.27267i
$45$	−12.9252	−	9.41870i	−1.92677	−	1.40406i
$46$	0.438852	+	2.38506i	0.0647052	+	0.351659i
$47$			1.44644i			0.210985i	0.994420	+	0.105493i	$0.0336420\pi$
$47$			1.44644i			0.210985i	−0.994420	+	0.105493i	$0.966358\pi$
$48$	8.47892	+	9.51544i	1.22383	+	1.37344i
$49$		0			0
$50$	6.22805	−	3.34834i	0.880780	−	0.473527i
$51$		−	8.05693i		−	1.12820i
$52$	4.15908	−	1.58418i	0.576760	−	0.219686i
$53$		−	10.0769i		−	1.38416i	−0.721819	−	0.692082i	$-0.756694\pi$
$53$		−	10.0769i		−	1.38416i	0.721819	−	0.692082i	$-0.243306\pi$
$54$	−18.4013	+	3.38584i	−2.50410	+	0.460754i
$55$	−5.94813	+	8.16255i	−0.802046	+	1.10064i
$56$		0			0
$57$			16.6081i			2.19979i
$58$	0.591274	+	3.21344i	0.0776380	+	0.421945i
$59$	3.20322			0.417023			0.208512	−	0.978020i	$-0.433138\pi$
$59$	3.20322			0.417023			0.208512	+	0.978020i	$0.433138\pi$
$60$	3.74312	−	13.7490i	0.483235	−	1.77498i
$61$		−	6.05175i		−	0.774847i	−0.921902	−	0.387424i	$-0.873365\pi$
$61$		−	6.05175i		−	0.774847i	0.921902	−	0.387424i	$-0.126635\pi$
$62$	−1.18373	−	6.43331i	−0.150334	−	0.817031i
$63$		0			0
$64$	−3.68719	+	7.09962i	−0.460899	+	0.887453i
$65$	−4.02143	−	2.93045i	−0.498797	−	0.363478i
$66$	3.68311	+	20.0169i	0.453360	+	2.46391i
$67$	−11.1495			−1.36213			−0.681067	−	0.732221i	$-0.738484\pi$
$67$	−11.1495			−1.36213			−0.681067	+	0.732221i	$0.738484\pi$
$68$	4.72608	−	1.80014i	0.573121	−	0.218299i
$69$		−	5.46381i		−	0.657766i
$70$		0			0
$71$			9.15549i			1.08656i	0.839553	+	0.543278i	$0.182817\pi$
$71$			9.15549i			1.08656i	−0.839553	+	0.543278i	$0.817183\pi$
$72$	−10.5028	−	17.2895i	−1.23777	−	2.03758i
$73$	3.24011			0.379226			0.189613	−	0.981859i	$-0.439277\pi$
$73$	3.24011			0.379226			0.189613	+	0.981859i	$0.439277\pi$
$74$	−0.468396	+	0.0861849i	−0.0544499	+	0.0100188i
$75$	−15.1654	+	4.88008i	−1.75115	+	0.563504i
$76$	−9.74205	+	3.71071i	−1.11749	+	0.425647i
$77$		0			0
$78$	−9.86168	+	1.81455i	−1.11662	+	0.205457i
$79$			14.2700i			1.60550i	0.596318	+	0.802748i	$0.296630\pi$
$79$			14.2700i			1.60550i	−0.596318	+	0.802748i	$0.703370\pi$
$80$	8.90125	−	0.876239i	0.995190	−	0.0979666i
$81$	20.6978			2.29975
$82$	−4.56292	+	0.839579i	−0.503891	+	0.0927160i
$83$			11.3059i			1.24099i	0.784212	+	0.620493i	$0.213067\pi$
$83$			11.3059i			1.24099i	−0.784212	+	0.620493i	$0.786933\pi$
$84$		0			0
$85$	−4.56966	−	3.32995i	−0.495649	−	0.361184i
$86$	1.70533	+	9.26808i	0.183890	+	0.999403i
$87$		−	7.36150i		−	0.789235i
$88$	−10.9187	+	6.63279i	−1.16394	+	0.707058i
$89$			15.2152i			1.61281i	0.591364	+	0.806405i	$0.298590\pi$
$89$			15.2152i			1.61281i	−0.591364	+	0.806405i	$0.701410\pi$
$90$	−9.79234	+	20.3876i	−1.03220	+	2.14904i
$91$		0			0
$92$	3.20499	−	1.22077i	0.334143	−	0.127274i
$93$			14.7377i			1.52823i
$94$	2.01181	−	0.370173i	0.207502	−	0.0381804i
$95$	9.41962	+	6.86417i	0.966433	+	0.704249i
$96$	11.0648	−	14.2282i	1.12929	−	1.45216i
$97$	−4.49303			−0.456198			−0.228099	−	0.973638i	$-0.573251\pi$
$97$	−4.49303			−0.456198			−0.228099	+	0.973638i	$0.573251\pi$
$98$		0			0
$99$		−	32.3052i		−	3.24680i
$100$	−6.25097	−	7.80547i	−0.625097	−	0.780547i
$101$		−	0.734445i		−	0.0730800i	−0.999332	−	0.0365400i	$-0.988366\pi$
$101$		−	0.734445i		−	0.0730800i	0.999332	−	0.0365400i	$-0.0116336\pi$
$102$	−11.2061	+	2.06193i	−1.10957	+	0.204161i
$103$		−	11.8422i		−	1.16685i	−0.812167	−	0.583424i	$-0.801712\pi$
$103$		−	11.8422i		−	1.16685i	0.812167	−	0.583424i	$-0.198288\pi$
$104$	−3.26776	−	5.37929i	−0.320430	−	0.527483i
$105$		0			0
$106$	−14.0155	+	2.57886i	−1.36131	+	0.250481i
$107$	−4.98954			−0.482357			−0.241179	−	0.970481i	$-0.577534\pi$
$107$	−4.98954			−0.482357			−0.241179	+	0.970481i	$0.577534\pi$
$108$	9.41848	+	24.7272i	0.906294	+	2.37937i
$109$	11.3159			1.08386			0.541931	−	0.840423i	$-0.317693\pi$
$109$	11.3159			1.08386			0.541931	+	0.840423i	$0.317693\pi$
$110$	12.8753	+	6.18409i	1.22761	+	0.589630i
$111$	1.07302			0.101847
$112$		0			0
$113$		−	1.57514i		−	0.148177i	−0.997252	−	0.0740883i	$-0.976395\pi$
$113$		−	1.57514i		−	0.148177i	0.997252	−	0.0740883i	$-0.0236047\pi$
$114$	23.0996	−	4.25033i	2.16347	−	0.398080i
$115$	−3.09892	−	2.25821i	−0.288976	−	0.210579i
$116$	4.31814	−	1.64476i	0.400930	−	0.152712i
$117$	15.9157			1.47141
$118$	−0.819765	−	4.45524i	−0.0754655	−	0.410138i
$119$		0			0
$120$	−20.0809	−	1.68755i	−1.83312	−	0.154052i
$121$	−9.40151			−0.854683
$122$	−8.41717	+	1.54876i	−0.762054	+	0.140218i
$123$	10.4530			0.942511
$124$	−8.64493	+	3.29282i	−0.776337	+	0.295704i
$125$	−3.50008	+	10.6184i	−0.313057	+	0.949734i
$126$		0			0
$127$	17.0124			1.50960			0.754801	−	0.655954i	$-0.227733\pi$
$127$	17.0124			1.50960			0.754801	+	0.655954i	$0.227733\pi$
$128$	10.8182	+	3.31145i	0.956206	+	0.292694i
$129$		−	21.2317i		−	1.86935i
$130$	−3.04670	+	6.34322i	−0.267213	+	0.556337i
$131$	−8.95868			−0.782723			−0.391362	−	0.920237i	$-0.627996\pi$
$131$	−8.95868			−0.782723			−0.391362	+	0.920237i	$0.627996\pi$
$132$	26.8982	−	10.2454i	2.34119	−	0.891750i
$133$		0			0
$134$	2.85339	+	15.5075i	0.246495	+	1.33965i
$135$	17.4226	−	23.9088i	1.49950	−	2.05774i
$136$	−3.71325	−	6.11264i	−0.318409	−	0.524155i
$137$		−	8.32232i		−	0.711023i	−0.934672	−	0.355512i	$-0.884307\pi$
$137$		−	8.32232i		−	0.711023i	0.934672	−	0.355512i	$-0.115693\pi$
$138$	−7.59943	+	1.39830i	−0.646906	+	0.119031i
$139$	15.5985			1.32305			0.661524	−	0.749924i	$-0.269910\pi$
$139$	15.5985			1.32305			0.661524	+	0.749924i	$0.269910\pi$
$140$		0			0
$141$	−4.60874			−0.388126
$142$	12.7341	−	2.34307i	1.06862	−	0.196626i
$143$		−	10.0512i		−	0.840521i
$144$	−21.3594	+	19.0328i	−1.77995	+	1.58606i
$145$	−4.17523	−	3.04253i	−0.346734	−	0.252668i
$146$	−0.829206	−	4.50655i	−0.0686256	−	0.372965i
$147$		0			0
$148$	0.239743	+	0.629419i	0.0197068	+	0.0517379i
$149$	2.51385			0.205943			0.102971	−	0.994684i	$-0.467165\pi$
$149$	2.51385			0.205943			0.102971	+	0.994684i	$0.467165\pi$
$150$	10.6687	+	19.8442i	0.871093	+	1.62027i
$151$			12.7350i			1.03636i	0.855271	+	0.518181i	$0.173391\pi$
$151$			12.7350i			1.03636i	−0.855271	+	0.518181i	$0.826609\pi$
$152$	7.65427	+	12.6002i	0.620843	+	1.02201i
$153$	18.0855			1.46213
$154$		0			0
$155$	8.35881	+	6.09114i	0.671396	+	0.489253i
$156$	5.04759	+	13.2519i	0.404131	+	1.06100i
$157$	8.64749			0.690145			0.345073	−	0.938576i	$-0.387854\pi$
$157$	8.64749			0.690145			0.345073	+	0.938576i	$0.387854\pi$
$158$	19.8476	−	3.65196i	1.57899	−	0.290534i
$159$	32.1075			2.54629
$160$	−3.49673	−	12.1562i	−0.276441	−	0.961031i
$161$		0			0
$162$	−5.29696	−	28.7878i	−0.416168	−	2.26178i
$163$	−3.41606			−0.267566			−0.133783	−	0.991011i	$-0.542713\pi$
$163$	−3.41606			−0.267566			−0.133783	+	0.991011i	$0.542713\pi$
$164$	2.33548	+	6.13155i	0.182370	+	0.478793i
$165$	−26.0080	−	18.9523i	−2.02472	−	1.47543i
$166$	15.7250	−	2.89340i	1.22050	−	0.224572i
$167$			11.6381i			0.900581i	0.892882	+	0.450290i	$0.148680\pi$
$167$			11.6381i			0.900581i	−0.892882	+	0.450290i	$0.851320\pi$
$168$		0			0
$169$	−8.04812			−0.619086
$170$	−3.46205	+	7.20798i	−0.265527	+	0.552827i
$171$	−37.2804			−2.85090
$172$	12.4542	−	4.74376i	0.949626	−	0.361708i
$173$	8.21670			0.624704			0.312352	−	0.949966i	$-0.398883\pi$
$173$	8.21670			0.624704			0.312352	+	0.949966i	$0.398883\pi$
$174$	−10.2388	+	1.88395i	−0.776205	+	0.142822i
$175$		0			0
$176$	12.0196	+	13.4890i	0.906013	+	1.01677i
$177$			10.2063i			0.767151i
$178$	21.1623	−	3.89387i	1.58618	−	0.291858i
$179$		−	15.5937i		−	1.16553i	−0.812641	−	0.582764i	$-0.801971\pi$
$179$		−	15.5937i		−	1.16553i	0.812641	−	0.582764i	$-0.198029\pi$
$180$	30.8625	+	8.40224i	2.30035	+	0.626266i
$181$		−	15.8536i		−	1.17839i	−0.807990	−	0.589196i	$-0.799445\pi$
$181$		−	15.8536i		−	1.17839i	0.807990	−	0.589196i	$-0.200555\pi$
$182$		0			0
$183$	19.2824			1.42540
$184$	−2.51814	−	4.14529i	−0.185640	−	0.305595i
$185$	0.443484	−	0.608588i	0.0326056	−	0.0447442i
$186$	20.4982	−	3.77167i	1.50300	−	0.276552i
$187$		−	11.4214i		−	0.835217i
$188$	−1.02972	−	2.70342i	−0.0751001	−	0.197167i
$189$		0			0
$190$	7.13647	−	14.8581i	0.517734	−	1.07792i
$191$			11.2516i			0.814137i	0.913398	+	0.407068i	$0.133449\pi$
$191$			11.2516i			0.814137i	−0.913398	+	0.407068i	$0.866551\pi$
$192$	−22.6212	−	11.7483i	−1.63255	−	0.847863i
$193$			24.8339i			1.78758i	0.448484	+	0.893791i	$0.351964\pi$
$193$			24.8339i			1.78758i	−0.448484	+	0.893791i	$0.648036\pi$
$194$	1.14985	+	6.24919i	0.0825546	+	0.448666i
$195$	9.33717	−	12.8133i	0.668649	−	0.917579i
$196$		0			0
$197$			13.9890i			0.996672i	0.866984	+	0.498336i	$0.166055\pi$
$197$			13.9890i			0.996672i	−0.866984	+	0.498336i	$0.833945\pi$
$198$	−44.9322	+	8.26753i	−3.19319	+	0.587548i
$199$	19.5440			1.38544			0.692719	−	0.721208i	$-0.256413\pi$
$199$	19.5440			1.38544			0.692719	+	0.721208i	$0.256413\pi$
$200$	−9.25662	+	10.6918i	−0.654542	+	0.756026i
$201$		−	35.5253i		−	2.50576i
$202$	−1.02151	+	0.187959i	−0.0718734	+	0.0132247i
$203$		0			0
$204$	5.73572	+	15.0585i	0.401581	+	1.05431i
$205$	4.32024	−	5.92862i	0.301739	−	0.414072i
$206$	−16.4709	+	3.03065i	−1.14758	+	0.211156i
$207$	12.2647			0.852455
$208$	−6.64559	+	5.92168i	−0.460789	+	0.410595i
$209$			23.5434i			1.62853i
$210$		0			0
$211$		−	3.60453i		−	0.248146i	−0.992273	−	0.124073i	$-0.960404\pi$
$211$		−	3.60453i		−	0.248146i	0.992273	−	0.124073i	$-0.0395957\pi$
$212$	7.17370	+	18.8338i	0.492692	+	1.29351i
$213$	−29.1717			−1.99882
$214$	1.27692	+	6.93978i	0.0872885	+	0.474394i
$215$	−12.0420	−	8.77514i	−0.821260	−	0.598460i
$216$	31.9818	−	19.4280i	2.17609	−	1.32191i
$217$		0			0
$218$	−2.89595	−	15.7388i	−0.196138	−	1.06597i
$219$			10.3238i			0.697619i
$220$	5.30621	−	19.4904i	0.357745	−	1.31404i
$221$	5.62696			0.378511
$222$	−0.274607	−	1.49243i	−0.0184304	−	0.100165i
$223$		−	1.51767i		−	0.101631i	−0.998708	−	0.0508154i	$-0.983818\pi$
$223$		−	1.51767i		−	0.101631i	0.998708	−	0.0508154i	$-0.0161820\pi$
$224$		0			0
$225$	−10.9544	−	34.0421i	−0.730293	−	2.26947i
$226$	−2.19080	+	0.403108i	−0.145730	+	0.0268144i
$227$			15.5593i			1.03271i	0.856375	+	0.516354i	$0.172711\pi$
$227$			15.5593i			1.03271i	−0.856375	+	0.516354i	$0.827289\pi$
$228$	−11.8233	−	31.0407i	−0.783015	−	2.05572i
$229$		−	19.2013i		−	1.26885i	−0.772982	−	0.634427i	$-0.781236\pi$
$229$		−	19.2013i		−	1.26885i	0.772982	−	0.634427i	$-0.218764\pi$
$230$	−2.34779	+	4.88810i	−0.154809	+	0.322311i
$231$		0			0
$232$	−3.39274	−	5.58503i	−0.222744	−	0.366675i
$233$			3.14543i			0.206064i	0.994678	+	0.103032i	$0.0328544\pi$
$233$			3.14543i			0.206064i	−0.994678	+	0.103032i	$0.967146\pi$
$234$	−4.07315	−	22.1367i	−0.266270	−	1.44712i
$235$	−1.90481	+	2.61394i	−0.124256	+	0.170515i
$236$	−5.98685	+	2.28037i	−0.389711	+	0.148439i
$237$	−45.4678			−2.95345
$238$		0			0
$239$			3.75292i			0.242756i	0.992606	+	0.121378i	$0.0387314\pi$
$239$			3.75292i			0.242756i	−0.992606	+	0.121378i	$0.961269\pi$
$240$	2.79192	+	28.3617i	0.180218	+	1.83074i
$241$			7.43129i			0.478691i	0.970934	+	0.239346i	$0.0769329\pi$
$241$			7.43129i			0.478691i	−0.970934	+	0.239346i	$0.923067\pi$
$242$	2.40603	+	13.0762i	0.154665	+	0.840572i
$243$			26.2581i			1.68446i
$244$	4.30823	+	11.3108i	0.275806	+	0.724099i
$245$		0			0
$246$	−2.67511	−	14.5387i	−0.170559	−	0.926951i
$247$	−11.5991			−0.738032
$248$	6.79227	+	11.1812i	0.431309	+	0.710009i
$249$	−36.0236			−2.28290
$250$	15.6644	+	2.15070i	0.990706	+	0.136022i
$251$	5.77378			0.364438			0.182219	−	0.983258i	$-0.441672\pi$
$251$	5.77378			0.364438			0.182219	+	0.983258i	$0.441672\pi$
$252$		0			0
$253$		−	7.74544i		−	0.486952i
$254$	−4.35379	−	23.6619i	−0.273181	−	1.48468i
$255$	10.6101	−	14.5601i	0.664430	−	0.911790i
$256$	1.83718	−	15.8942i	0.114824	−	0.993386i
$257$	14.8503			0.926336			0.463168	−	0.886270i	$-0.346713\pi$
$257$	14.8503			0.926336			0.463168	+	0.886270i	$0.346713\pi$
$258$	−29.5305	+	5.43361i	−1.83849	+	0.338282i
$259$		0			0
$260$	9.60227	+	2.61420i	0.595508	+	0.162126i
$261$	16.5245			1.02284
$262$	2.29270	+	12.4603i	0.141643	+	0.769800i
$263$	−25.0905			−1.54715			−0.773573	−	0.633707i	$-0.781533\pi$
$263$	−25.0905			−1.54715			−0.773573	+	0.633707i	$0.781533\pi$
$264$	−21.1338	−	34.7898i	−1.30069	−	2.14116i
$265$	13.2701	−	18.2104i	0.815176	−	1.11866i
$266$		0			0
$267$	−48.4796			−2.96690
$268$	20.8386	−	7.93735i	1.27292	−	0.484851i
$269$			29.7861i			1.81609i	0.418871	+	0.908046i	$0.362426\pi$
$269$			29.7861i			1.81609i	−0.418871	+	0.908046i	$0.637574\pi$
$270$	−37.7127	−	18.1137i	−2.29512	−	1.10237i
$271$	1.90002			0.115418			0.0577091	−	0.998333i	$-0.481620\pi$
$271$	1.90002			0.115418			0.0577091	+	0.998333i	$0.481620\pi$
$272$	−7.55157	+	6.72897i	−0.457881	+	0.408004i
$273$		0			0
$274$	−11.5752	+	2.12984i	−0.699284	+	0.128668i
$275$	−21.4984	+	6.91795i	−1.29640	+	0.417168i
$276$	3.88968	+	10.2119i	0.234131	+	0.614686i
$277$			0.261529i			0.0157138i	0.999969	+	0.00785689i	$0.00250095\pi$
$277$			0.261529i			0.0157138i	−0.999969	+	0.00785689i	$0.997499\pi$
$278$	−3.99196	−	21.6954i	−0.239422	−	1.30120i
$279$	−33.0820			−1.98057
$280$		0			0
$281$	5.36553			0.320080			0.160040	−	0.987110i	$-0.448838\pi$
$281$	5.36553			0.320080			0.160040	+	0.987110i	$0.448838\pi$
$282$	1.17947	+	6.41013i	0.0702361	+	0.381718i
$283$			14.9849i			0.890757i	0.895342	+	0.445378i	$0.146931\pi$
$283$			14.9849i			0.890757i	−0.895342	+	0.445378i	$0.853069\pi$
$284$	−6.51778	−	17.1117i	−0.386759	−	1.01539i
$285$	−21.8710	+	30.0133i	−1.29553	+	1.77784i
$286$	−13.9798	+	2.57229i	−0.826644	+	0.152103i
$287$		0			0
$288$	31.9383	+	24.8372i	1.88198	+	1.46355i
$289$	−10.6059			−0.623878
$290$	−3.16322	+	6.58582i	−0.185751	+	0.386733i
$291$		−	14.3159i		−	0.839215i
$292$	−6.05579	+	2.30663i	−0.354388	+	0.134985i
$293$	23.2770			1.35986			0.679928	−	0.733279i	$-0.262011\pi$
$293$	23.2770			1.35986			0.679928	+	0.733279i	$0.262011\pi$
$294$		0			0
$295$	5.78871	+	4.21828i	0.337031	+	0.245598i
$296$	0.814082	−	0.494531i	0.0473176	−	0.0287440i
$297$	59.7577			3.46749
$298$	−0.643344	−	3.49643i	−0.0372679	−	0.202543i
$299$	3.81593			0.220681
$300$	24.8702	−	19.9172i	1.43588	−	1.14992i
$301$		0			0
$302$	17.7127	−	3.25914i	1.01925	−	0.187542i
$303$	2.34013			0.134437
$304$	15.5663	−	13.8707i	0.892791	−	0.795539i
$305$	7.96948	−	10.9364i	0.456331	−	0.626219i
$306$	−4.62843	−	25.1545i	−0.264590	−	1.43799i
$307$			5.70758i			0.325749i	0.986647	+	0.162874i	$0.0520765\pi$
$307$			5.70758i			0.325749i	−0.986647	+	0.162874i	$0.947923\pi$
$308$		0			0
$309$	37.7324			2.14652
$310$	6.33278	−	13.1848i	0.359678	−	0.748847i
$311$	32.0916			1.81975			0.909873	−	0.414886i	$-0.136179\pi$
$311$	32.0916			1.81975			0.909873	+	0.414886i	$0.136179\pi$
$312$	17.1398	−	10.4119i	0.970351	−	0.589460i
$313$	28.1435			1.59077			0.795384	−	0.606106i	$-0.207269\pi$
$313$	28.1435			1.59077			0.795384	+	0.606106i	$0.207269\pi$
$314$	−2.21306	−	12.0275i	−0.124890	−	0.678751i
$315$		0			0
$316$	−10.1588	−	26.6707i	−0.571475	−	1.50034i
$317$			13.3985i			0.752533i	0.926511	+	0.376267i	$0.122792\pi$
$317$			13.3985i			0.752533i	−0.926511	+	0.376267i	$0.877208\pi$
$318$	−8.21692	−	44.6571i	−0.460782	−	2.50425i
$319$		−	10.4356i		−	0.584280i
$320$	−16.0127	+	7.97449i	−0.895139	+	0.445787i
$321$		−	15.8980i		−	0.887338i
$322$		0			0
$323$	−13.1804			−0.733375
$324$	−38.6843	+	14.7347i	−2.14913	+	0.818595i
$325$	−3.40825	−	10.5915i	−0.189056	−	0.587513i
$326$	0.874236	+	4.75128i	0.0484194	+	0.263149i
$327$			36.0552i			1.99386i
$328$	7.93046	−	4.81752i	0.437886	−	0.266003i
$329$		0			0
$330$	−19.7041	+	41.0239i	−1.08468	+	2.25829i
$331$		−	22.7117i		−	1.24835i	−0.781286	−	0.624173i	$-0.785436\pi$
$331$		−	22.7117i		−	1.24835i	0.781286	−	0.624173i	$-0.214564\pi$
$332$	−8.04867	−	21.1309i	−0.441728	−	1.15971i
$333$			2.40863i			0.131992i
$334$	16.1870	−	2.97841i	0.885712	−	0.162971i
$335$	−20.1489	−	14.6827i	−1.10085	−	0.802203i
$336$		0			0
$337$		−	8.84953i		−	0.482065i	−0.970517	−	0.241032i	$-0.922514\pi$
$337$		−	8.84953i		−	0.482065i	0.970517	−	0.241032i	$-0.0774860\pi$
$338$	2.05967	+	11.1938i	0.112031	+	0.608865i
$339$	5.01880			0.272584
$340$	10.9113	+	2.97059i	0.591750	+	0.161103i
$341$			20.8920i			1.13137i
$342$	9.54077	+	51.8520i	0.515906	+	2.80383i
$343$		0			0
$344$	−9.78521	−	16.1081i	−0.527583	−	0.868492i
$345$	7.19524	−	9.87395i	0.387379	−	0.531596i
$346$	−2.10281	−	11.4283i	−0.113048	−	0.614390i
$347$	16.7339			0.898325			0.449163	−	0.893450i	$-0.351722\pi$
$347$	16.7339			0.898325			0.449163	+	0.893450i	$0.351722\pi$
$348$	5.24064	+	13.7587i	0.280928	+	0.737545i
$349$		−	3.86908i		−	0.207107i	−0.994624	−	0.103554i	$-0.966979\pi$
$349$		−	3.86908i		−	0.207107i	0.994624	−	0.103554i	$-0.0330213\pi$
$350$		0			0
$351$			29.4407i			1.57143i
$352$	15.6853	−	20.1698i	0.836029	−	1.07505i
$353$	7.90229			0.420597			0.210298	−	0.977637i	$-0.432556\pi$
$353$	7.90229			0.420597			0.210298	+	0.977637i	$0.432556\pi$
$354$	14.1956	−	2.61198i	0.754485	−	0.138825i
$355$	−12.0568	+	16.5454i	−0.639907	+	0.878137i
$356$	−10.8317	−	28.4374i	−0.574079	−	1.50718i
$357$		0			0
$358$	−21.6887	+	3.99073i	−1.14629	+	0.210917i
$359$			4.16127i			0.219623i	0.993952	+	0.109812i	$0.0350248\pi$
$359$			4.16127i			0.219623i	−0.993952	+	0.109812i	$0.964975\pi$
$360$	3.78808	−	45.0758i	0.199649	−	2.37570i
$361$	8.16920			0.429958
$362$	−22.0503	+	4.05725i	−1.15894	+	0.213244i
$363$		−	29.9556i		−	1.57226i
$364$		0			0
$365$	5.85537	+	4.26686i	0.306484	+	0.223338i
$366$	−4.93475	−	26.8193i	−0.257943	−	1.40186i
$367$			27.3777i			1.42910i	0.699583	+	0.714551i	$0.253369\pi$
$367$			27.3777i			1.42910i	−0.699583	+	0.714551i	$0.746631\pi$
$368$	−5.12110	+	4.56326i	−0.266956	+	0.237876i
$369$			23.4639i			1.22148i
$370$	−0.959959	−	0.461076i	−0.0499059	−	0.0239702i
$371$		0			0
$372$	−10.4918	−	27.5450i	−0.543973	−	1.42814i
$373$		−	29.3085i		−	1.51754i	−0.651360	−	0.758768i	$-0.725801\pi$
$373$		−	29.3085i		−	1.51754i	0.651360	−	0.758768i	$-0.274199\pi$
$374$	−15.8857	+	2.92296i	−0.821428	+	0.151143i
$375$	−33.8328	−	11.1522i	−1.74712	−	0.575895i
$376$	−3.49656	+	2.12406i	−0.180321	+	0.109540i
$377$	5.14127			0.264789
$378$		0			0
$379$			21.4131i			1.09992i	0.835192	+	0.549958i	$0.185356\pi$
$379$			21.4131i			1.09992i	−0.835192	+	0.549958i	$0.814644\pi$
$380$	−22.4920	−	6.12339i	−1.15381	−	0.314123i
$381$			54.2057i			2.77704i
$382$	15.6494	−	2.87950i	0.800695	−	0.147328i
$383$		−	19.2892i		−	0.985633i	−0.870133	−	0.492817i	$-0.835967\pi$
$383$		−	19.2892i		−	0.985633i	0.870133	−	0.492817i	$-0.164033\pi$
$384$	−10.5511	+	34.4697i	−0.538435	+	1.75902i
$385$		0			0
$386$	34.5406	−	6.35547i	1.75807	−	0.323485i
$387$	47.6592			2.42265
$388$	8.39751	−	3.19858i	0.426319	−	0.162383i
$389$	15.5064			0.786203			0.393102	−	0.919495i	$-0.371402\pi$
$389$	15.5064			0.786203			0.393102	+	0.919495i	$0.371402\pi$
$390$	−20.2111	−	9.70758i	−1.02343	−	0.491562i
$391$	4.33615			0.219288
$392$		0			0
$393$		−	28.5446i		−	1.43989i
$394$	19.4567	−	3.58004i	0.980217	−	0.180360i
$395$	−18.7920	+	25.7880i	−0.945526	+	1.29754i
$396$	22.9980	+	60.3788i	1.15570	+	3.03415i
$397$	−23.0690			−1.15780			−0.578899	−	0.815399i	$-0.696518\pi$
$397$	−23.0690			−1.15780			−0.578899	+	0.815399i	$0.696518\pi$
$398$	−5.00169	−	27.1831i	−0.250712	−	1.36256i
$399$		0			0
$400$	17.2398	+	10.1385i	0.861991	+	0.506923i
$401$	36.6133			1.82838			0.914191	−	0.405283i	$-0.132827\pi$
$401$	36.6133			1.82838			0.914191	+	0.405283i	$0.132827\pi$
$402$	−49.4109	+	9.09162i	−2.46439	+	0.453449i
$403$	−10.2928			−0.512722
$404$	0.522850	+	1.37268i	0.0260128	+	0.0682936i
$405$	37.4040	+	27.2567i	1.85862	+	1.35439i
$406$		0			0
$407$	1.52111			0.0753984
$408$	19.4764	−	11.8314i	0.964228	−	0.585740i
$409$		−	30.9997i		−	1.53284i	−0.642341	−	0.766419i	$-0.722037\pi$
$409$		−	30.9997i		−	1.53284i	0.642341	−	0.766419i	$-0.277963\pi$
$410$	−9.35154	−	4.49162i	−0.461839	−	0.221825i
$411$	26.5170			1.30799
$412$	8.43046	+	22.1332i	0.415339	+	1.09043i
$413$		0			0
$414$	−3.13877	−	17.0585i	−0.154262	−	0.838381i
$415$	−14.8886	+	20.4315i	−0.730855	+	1.00294i
$416$	9.93699	+	7.72764i	0.487201	+	0.378879i
$417$			49.7008i			2.43386i
$418$	32.7457	−	6.02522i	1.60165	−	0.294703i
$419$	11.9532			0.583953			0.291977	−	0.956425i	$-0.405687\pi$
$419$	11.9532			0.583953			0.291977	+	0.956425i	$0.405687\pi$
$420$		0			0
$421$	13.5052			0.658205			0.329103	−	0.944294i	$-0.393254\pi$
$421$	13.5052			0.658205			0.329103	+	0.944294i	$0.393254\pi$
$422$	−5.01341	+	0.922469i	−0.244049	+	0.0449051i
$423$		−	10.3453i		−	0.503006i
$424$	24.3593	−	14.7976i	1.18299	−	0.718634i
$425$	−3.87289	−	12.0355i	−0.187863	−	0.583806i
$426$	7.46561	+	40.5740i	0.361710	+	1.96581i
$427$		0			0
$428$	9.32551	−	3.55205i	0.450765	−	0.171695i
$429$	32.0256			1.54621
$430$	−9.12325	+	18.9946i	−0.439962	+	0.915999i
$431$			35.5892i			1.71427i	0.515090	+	0.857136i	$0.327758\pi$
$431$			35.5892i			1.71427i	−0.515090	+	0.857136i	$0.672242\pi$
$432$	−35.2065	−	39.5103i	−1.69387	−	1.90094i
$433$	−16.8799			−0.811199			−0.405599	−	0.914051i	$-0.632937\pi$
$433$	−16.8799			−0.811199			−0.405599	+	0.914051i	$0.632937\pi$
$434$		0			0
$435$	9.69428	−	13.3034i	0.464805	−	0.637847i
$436$	−21.1495	+	8.05574i	−1.01288	+	0.385800i
$437$	−8.93827			−0.427576
$438$	14.3590	−	2.64206i	0.686101	−	0.126243i
$439$	−23.5676			−1.12482			−0.562410	−	0.826858i	$-0.690126\pi$
$439$	−23.5676			−1.12482			−0.562410	+	0.826858i	$0.690126\pi$
$440$	−28.4664	−	2.39226i	−1.35708	−	0.114046i
$441$		0			0
$442$	−1.44005	−	7.82635i	−0.0684962	−	0.372261i
$443$	−8.93347			−0.424442			−0.212221	−	0.977222i	$-0.568070\pi$
$443$	−8.93347			−0.424442			−0.212221	+	0.977222i	$0.568070\pi$
$444$	−2.00549	+	0.763883i	−0.0951764	+	0.0362523i
$445$	−20.0368	+	27.4962i	−0.949834	+	1.30345i
$446$	−2.11087	+	0.388401i	−0.0999528	+	0.0183913i
$447$			8.00978i			0.378850i
$448$		0			0
$449$	−33.1350			−1.56374			−0.781868	−	0.623445i	$-0.785733\pi$
$449$	−33.1350			−1.56374			−0.781868	+	0.623445i	$0.785733\pi$
$450$	−44.5445	+	23.9481i	−2.09985	+	1.12892i
$451$	14.8180			0.697752
$452$	1.12134	+	2.94395i	0.0527433	+	0.138472i
$453$	−40.5771			−1.90648
$454$	21.6409	−	3.98193i	1.01566	−	0.186881i
$455$		0			0
$456$	−40.1476	+	24.3885i	−1.88008	+	1.14209i
$457$		−	24.6492i		−	1.15304i	−0.817082	−	0.576521i	$-0.804410\pi$
$457$		−	24.6492i		−	1.15304i	0.817082	−	0.576521i	$-0.195590\pi$
$458$	−26.7064	+	4.91397i	−1.24791	+	0.229615i
$459$			33.4543i			1.56151i
$460$	7.39953	+	2.01450i	0.345005	+	0.0939268i
$461$			38.2341i			1.78074i	0.455239	+	0.890369i	$0.349554\pi$
$461$			38.2341i			1.78074i	−0.455239	+	0.890369i	$0.650446\pi$
$462$		0			0
$463$	−14.6319			−0.680004			−0.340002	−	0.940425i	$-0.610428\pi$
$463$	−14.6319			−0.680004			−0.340002	+	0.940425i	$0.610428\pi$
$464$	−6.89975	+	6.14816i	−0.320313	+	0.285421i
$465$	−19.4080	+	26.6333i	−0.900022	+	1.23509i
$466$	4.37487	−	0.804976i	0.202662	−	0.0372898i
$467$		−	8.52322i		−	0.394408i	−0.980363	−	0.197204i	$-0.936814\pi$
$467$		−	8.52322i		−	0.394408i	0.980363	−	0.197204i	$-0.0631861\pi$
$468$	−29.7467	+	11.3304i	−1.37504	+	0.523748i
$469$		0			0
$470$	4.12312	+	1.98037i	0.190185	+	0.0913476i
$471$			27.5531i			1.26958i
$472$	4.70383	+	7.74331i	0.216511	+	0.356415i
$473$		−	30.0979i		−	1.38390i
$474$	11.6361	+	63.2395i	0.534463	+	2.90469i
$475$	7.98335	+	24.8092i	0.366301	+	1.13832i
$476$		0			0
$477$			72.0721i			3.29995i
$478$	5.21981	−	0.960446i	0.238748	−	0.0439298i
$479$	−39.2249			−1.79223			−0.896115	−	0.443823i	$-0.853622\pi$
$479$	−39.2249			−1.79223			−0.896115	+	0.443823i	$0.853622\pi$
$480$	38.7327	−	11.1415i	1.76790	−	0.508537i
$481$			0.749400i			0.0341697i
$482$	10.3359	−	1.90181i	0.470788	−	0.0866251i
$483$		0			0
$484$	17.5715	−	6.69292i	0.798706	−	0.304224i
$485$	−8.11959	−	5.91682i	−0.368691	−	0.268669i
$486$	36.5215	−	6.71996i	1.65665	−	0.304824i
$487$	25.5876			1.15948			0.579742	−	0.814800i	$-0.303153\pi$
$487$	25.5876			1.15948			0.579742	+	0.814800i	$0.303153\pi$
$488$	14.6292	−	8.88682i	0.662233	−	0.402287i
$489$		−	10.8844i		−	0.492212i
$490$		0			0
$491$		−	40.7008i		−	1.83680i	−0.395654	−	0.918400i	$-0.629482\pi$
$491$		−	40.7008i		−	1.83680i	0.395654	−	0.918400i	$-0.370518\pi$
$492$	−19.5367	+	7.44144i	−0.880782	+	0.335486i
$493$	5.84217			0.263118
$494$	2.96843	+	16.1328i	0.133556	+	0.725847i
$495$	42.5424	−	58.3805i	1.91214	−	2.62401i
$496$	13.8133	−	12.3086i	0.620236	−	0.552673i
$497$		0			0
$498$	9.21913	+	50.1039i	0.413119	+	2.24521i
$499$		−	15.9072i		−	0.712106i	−0.934466	−	0.356053i	$-0.884122\pi$
$499$		−	15.9072i		−	0.712106i	0.934466	−	0.356053i	$-0.115878\pi$
$500$	−1.01751	−	22.3375i	−0.0455042	−	0.998964i
$501$	−37.0819			−1.65670
$502$	−1.47762	−	8.03055i	−0.0659495	−	0.358421i
$503$			9.64379i			0.429995i	0.976615	+	0.214998i	$0.0689744\pi$
$503$			9.64379i			0.429995i	−0.976615	+	0.214998i	$0.931026\pi$
$504$		0			0
$505$	0.967182	−	1.32725i	0.0430391	−	0.0590620i
$506$	−10.7729	+	1.98221i	−0.478912	+	0.0881199i
$507$		−	25.6434i		−	1.13886i
$508$	−31.7963	+	12.1111i	−1.41073	+	0.537342i
$509$			3.77669i			0.167399i	0.996491	+	0.0836995i	$0.0266736\pi$
$509$			3.77669i			0.167399i	−0.996491	+	0.0836995i	$0.973326\pi$
$510$	−22.9665	−	11.0310i	−1.01697	−	0.488460i
$511$		0			0
$512$	−22.5768	+	1.51235i	−0.997764	+	0.0668372i
$513$		−	68.9606i		−	3.04469i
$514$	−3.80048	−	20.6548i	−0.167632	−	0.911043i
$515$	15.5949	−	21.4007i	0.687193	−	0.943028i
$516$	15.1148	+	39.6824i	0.665394	+	1.74692i
$517$	−6.53330			−0.287334
$518$		0			0
$519$			26.1805i			1.14920i
$520$	1.17859	−	14.0245i	0.0516845	−	0.615015i
$521$		−	0.0914926i		−	0.00400837i	−0.999998	−	0.00200418i	$-0.999362\pi$
$521$		−	0.0914926i		−	0.00400837i	0.999998	−	0.00200418i	$-0.000637952\pi$
$522$	−4.22893	−	22.9833i	−0.185095	−	1.00595i
$523$		−	15.0818i		−	0.659480i	−0.944072	−	0.329740i	$-0.893039\pi$
$523$		−	15.0818i		−	0.659480i	0.944072	−	0.329740i	$-0.106961\pi$
$524$	16.7439	−	6.37767i	0.731459	−	0.278610i
$525$		0			0
$526$	6.42115	+	34.8975i	0.279975	+	1.52160i
$527$	−11.6960			−0.509487
$528$	−42.9794	+	38.2976i	−1.87044	+	1.66669i
$529$	−20.0594			−0.872150
$530$	−28.7243	−	13.7965i	−1.24770	−	0.599283i
$531$	−22.9102			−0.994217
$532$		0			0
$533$			7.30035i			0.316213i
$534$	12.4069	+	67.4286i	0.536898	+	2.91792i
$535$	−9.01687	−	6.57068i	−0.389833	−	0.284075i
$536$	−16.3728	−	26.9524i	−0.707197	−	1.16417i
$537$	49.6855			2.14409
$538$	41.4285	−	7.62284i	1.78611	−	0.328644i
$539$		0			0
$540$	−15.5423	+	57.0889i	−0.668835	+	2.45671i
$541$	−27.4738			−1.18119			−0.590596	−	0.806968i	$-0.701107\pi$
$541$	−27.4738			−1.18119			−0.590596	+	0.806968i	$0.701107\pi$
$542$	−0.486253	−	2.64268i	−0.0208864	−	0.113513i
$543$	50.5138			2.16775
$544$	11.2917	+	8.78114i	0.484127	+	0.376488i
$545$	20.4495	+	14.9017i	0.875960	+	0.638320i
$546$		0			0
$547$	−18.3722			−0.785540			−0.392770	−	0.919637i	$-0.628483\pi$
$547$	−18.3722			−0.785540			−0.392770	+	0.919637i	$0.628483\pi$
$548$	5.92464	+	15.5545i	0.253088	+	0.664455i
$549$			43.2835i			1.84730i
$550$	15.1238	+	28.1309i	0.644880	+	1.19950i
$551$	−12.0427			−0.513036
$552$	13.2080	−	8.02345i	0.562168	−	0.341501i
$553$		0			0
$554$	0.363752	−	0.0669304i	0.0154543	−	0.00284360i
$555$	1.93912	+	1.41305i	0.0823109	+	0.0599807i
$556$	−29.1538	+	11.1045i	−1.23640	+	0.470938i
$557$			13.9550i			0.591294i	0.955297	+	0.295647i	$0.0955351\pi$
$557$			13.9550i			0.591294i	−0.955297	+	0.295647i	$0.904465\pi$
$558$	8.46632	+	46.0126i	0.358408	+	1.94787i
$559$	14.8283			0.627168
$560$		0			0
$561$	36.3916			1.53645
$562$	−1.37314	−	7.46272i	−0.0579225	−	0.314796i
$563$		−	18.5730i		−	0.782760i	−0.920229	−	0.391380i	$-0.871998\pi$
$563$		−	18.5730i		−	0.782760i	0.920229	−	0.391380i	$-0.128002\pi$
$564$	8.61378	−	3.28095i	0.362706	−	0.138153i
$565$	2.07428	−	2.84652i	0.0872657	−	0.119754i
$566$	20.8419	−	3.83491i	0.876051	−	0.161193i
$567$		0			0
$568$	−22.1320	+	13.4446i	−0.928640	+	0.564122i
$569$	8.08905			0.339111			0.169555	−	0.985521i	$-0.445767\pi$
$569$	8.08905			0.339111			0.169555	+	0.985521i	$0.445767\pi$
$570$	47.3417	+	22.7386i	1.98293	+	0.952416i
$571$		−	0.840877i		−	0.0351896i	−0.999845	−	0.0175948i	$-0.994399\pi$
$571$		−	0.840877i		−	0.0351896i	0.999845	−	0.0175948i	$-0.00560089\pi$
$572$	7.15541	+	18.7857i	0.299183	+	0.785471i
$573$	−35.8505			−1.49767
$574$		0			0
$575$	−2.62640	−	8.16186i	−0.109529	−	0.340373i
$576$	26.3716	−	50.7782i	1.09882	−	2.11576i
$577$	46.1975			1.92323			0.961614	−	0.274404i	$-0.0884807\pi$
$577$	46.1975			1.92323			0.961614	+	0.274404i	$0.0884807\pi$
$578$	2.71426	+	14.7514i	0.112898	+	0.613578i
$579$	−79.1271			−3.28841
$580$	9.96952	+	2.71418i	0.413962	+	0.112700i
$581$		0			0
$582$	−19.9115	+	3.66373i	−0.825360	+	0.151866i
$583$	45.5152			1.88505
$584$	4.75800	+	7.83248i	0.196887	+	0.324110i
$585$	28.7622	+	20.9593i	1.18917	+	0.866560i
$586$	−5.95703	−	32.3751i	−0.246083	−	1.33740i
$587$			2.72072i			0.112296i	0.998422	+	0.0561482i	$0.0178819\pi$
$587$			2.72072i			0.112296i	−0.998422	+	0.0561482i	$0.982118\pi$
$588$		0			0
$589$	24.1095			0.993414
$590$	4.38562	−	9.13085i	0.180553	−	0.375911i
$591$	−44.5724			−1.83346
$592$	−0.896165	−	1.00572i	−0.0368322	−	0.0413348i
$593$	−34.7891			−1.42862			−0.714308	−	0.699831i	$-0.753259\pi$
$593$	−34.7891			−1.42862			−0.714308	+	0.699831i	$0.753259\pi$
$594$	−15.2932	−	83.1149i	−0.627486	−	3.41025i
$595$		0			0
$596$	−4.69842	+	1.78961i	−0.192455	+	0.0733052i
$597$			62.2722i			2.54863i
$598$	−0.976570	−	5.30744i	−0.0399349	−	0.217037i
$599$			11.7189i			0.478821i	0.970918	+	0.239411i	$0.0769542\pi$
$599$			11.7189i			0.478821i	−0.970918	+	0.239411i	$0.923046\pi$
$600$	−34.0669	−	29.4940i	−1.39078	−	1.20409i
$601$			17.1738i			0.700532i	0.936650	+	0.350266i	$0.113909\pi$
$601$			17.1738i			0.700532i	−0.936650	+	0.350266i	$0.886091\pi$
$602$		0			0
$603$	79.7442			3.24743
$604$	−9.06605	−	23.8019i	−0.368892	−	0.968485i
$605$	−16.9900	−	12.3808i	−0.690740	−	0.503349i
$606$	−0.598884	−	3.25480i	−0.0243280	−	0.132217i
$607$			16.6117i			0.674247i	0.941460	+	0.337123i	$0.109454\pi$
$607$			16.6117i			0.674247i	−0.941460	+	0.337123i	$0.890546\pi$
$608$	−23.2760	−	18.1009i	−0.943966	−	0.734088i
$609$		0			0
$610$	−17.2507	−	8.28563i	−0.698458	−	0.335475i
$611$		−	3.21874i		−	0.130216i
$612$	−33.8020	+	12.8750i	−1.36637	+	0.520443i
$613$		−	32.9900i		−	1.33245i	−0.745750	−	0.666226i	$-0.767908\pi$
$613$		−	32.9900i		−	1.33245i	0.745750	−	0.666226i	$-0.232092\pi$
$614$	7.93847	−	1.46068i	0.320371	−	0.0589483i
$615$	18.8901	+	13.7654i	0.761722	+	0.555074i
$616$		0			0
$617$			23.9885i			0.965739i	0.875692	+	0.482870i	$0.160405\pi$
$617$			23.9885i			0.965739i	−0.875692	+	0.482870i	$0.839595\pi$
$618$	−9.65644	−	52.4806i	−0.388439	−	2.11108i
$619$	−31.3184			−1.25879			−0.629396	−	0.777085i	$-0.716698\pi$
$619$	−31.3184			−1.25879			−0.629396	+	0.777085i	$0.716698\pi$
$620$	−19.9590	−	5.43379i	−0.801572	−	0.218226i
$621$			22.6870i			0.910400i
$622$	−8.21286	−	44.6351i	−0.329306	−	1.78970i
$623$		0			0
$624$	−18.8680	−	21.1746i	−0.755325	−	0.847660i
$625$	−20.3084	+	14.5798i	−0.812335	+	0.583191i
$626$	−7.20248	−	39.1439i	−0.287869	−	1.56450i
$627$	−75.0154			−2.99583
$628$	−16.1623	+	6.15614i	−0.644944	+	0.245657i
$629$			0.851564i			0.0339541i
$630$		0			0
$631$		−	37.4842i		−	1.49222i	−0.665821	−	0.746112i	$-0.731919\pi$
$631$		−	37.4842i		−	1.49222i	0.665821	−	0.746112i	$-0.268081\pi$
$632$	−34.4955	+	20.9550i	−1.37216	+	0.833546i
$633$	11.4850			0.456486
$634$	18.6355	−	3.42893i	0.740109	−	0.136180i
$635$	30.7439	+	22.4034i	1.22004	+	0.889051i
$636$	−60.0092	+	22.8573i	−2.37952	+	0.906349i
$637$		0			0
$638$	−14.5145	+	2.67067i	−0.574634	+	0.105733i
$639$		−	65.4822i		−	2.59044i
$640$	15.1894	+	20.2307i	0.600414	+	0.799690i
$641$	35.6213			1.40696			0.703479	−	0.710716i	$-0.251629\pi$
$641$	35.6213			1.40696			0.703479	+	0.710716i	$0.251629\pi$
$642$	−22.1119	+	4.06860i	−0.872688	+	0.160575i
$643$			2.55684i			0.100832i	0.998728	+	0.0504159i	$0.0160547\pi$
$643$			2.55684i			0.100832i	−0.998728	+	0.0504159i	$0.983945\pi$
$644$		0			0
$645$	27.9599	−	38.3690i	1.10092	−	1.51078i
$646$	3.37311	+	18.3321i	0.132713	+	0.721267i
$647$		−	17.7876i		−	0.699301i	−0.936880	−	0.349651i	$-0.886300\pi$
$647$		−	17.7876i		−	0.699301i	0.936880	−	0.349651i	$-0.113700\pi$
$648$	30.3940	+	50.0338i	1.19399	+	1.96551i
$649$			14.4683i			0.567931i
$650$	−13.8592	+	7.45100i	−0.543602	+	0.292252i
$651$		0			0
$652$	6.38465	−	2.43189i	0.250042	−	0.0952401i
$653$			13.0090i			0.509081i	0.967062	+	0.254541i	$0.0819242\pi$
$653$			13.0090i			0.509081i	−0.967062	+	0.254541i	$0.918076\pi$
$654$	50.1480	−	9.22723i	1.96094	−	0.360813i
$655$	−16.1897	−	11.7976i	−0.632584	−	0.460970i
$656$	−8.73008	−	9.79730i	−0.340852	−	0.382520i
$657$	−23.1740			−0.904104
$658$		0			0
$659$			5.68280i			0.221370i	0.993856	+	0.110685i	$0.0353045\pi$
$659$			5.68280i			0.221370i	−0.993856	+	0.110685i	$0.964695\pi$
$660$	62.1013	+	16.9069i	2.41729	+	0.658102i
$661$		−	16.1645i		−	0.628727i	−0.949303	−	0.314364i	$-0.898209\pi$
$661$		−	16.1645i		−	0.628727i	0.949303	−	0.314364i	$-0.101791\pi$
$662$	−31.5889	+	5.81235i	−1.22774	+	0.225904i
$663$			17.9290i			0.696303i
$664$	−27.3304	+	16.6024i	−1.06063	+	0.644299i
$665$		0			0
$666$	3.35008	−	0.616415i	0.129813	−	0.0238856i
$667$	3.96187			0.153404
$668$	−8.28512	−	21.7517i	−0.320561	−	0.841597i
$669$	4.83569			0.186959
$670$	−15.2652	+	31.7820i	−0.589745	+	1.22785i
$671$	27.3346			1.05524
$672$		0			0
$673$		−	32.4901i		−	1.25240i	−0.779662	−	0.626200i	$-0.784609\pi$
$673$		−	32.4901i		−	1.25240i	0.779662	−	0.626200i	$-0.215391\pi$
$674$	−12.3085	+	2.26477i	−0.474106	+	0.0872355i
$675$	62.9705	−	20.2633i	2.42373	−	0.779933i
$676$	15.0420	−	5.72944i	0.578539	−	0.220363i
$677$	18.1326			0.696891			0.348446	−	0.937329i	$-0.386710\pi$
$677$	18.1326			0.696891			0.348446	+	0.937329i	$0.386710\pi$
$678$	−1.28441	−	6.98047i	−0.0493273	−	0.268083i
$679$		0			0
$680$	1.33926	−	15.9364i	0.0513584	−	0.611134i
$681$	−49.5760			−1.89976
$682$	29.0580	−	5.34668i	1.11269	−	0.204735i
$683$	−8.81555			−0.337318			−0.168659	−	0.985674i	$-0.553944\pi$
$683$	−8.81555			−0.337318			−0.168659	+	0.985674i	$0.553944\pi$
$684$	69.6774	−	26.5398i	2.66418	−	1.01478i
$685$	10.9596	−	15.0397i	0.418744	−	0.574637i
$686$		0			0
$687$	61.1801			2.33417
$688$	−19.9000	+	17.7323i	−0.758680	+	0.676037i
$689$			22.4239i			0.854281i
$690$	−15.5747	−	7.48067i	−0.592920	−	0.284784i
$691$	9.13188			0.347393			0.173697	−	0.984799i	$-0.444429\pi$
$691$	9.13188			0.347393			0.173697	+	0.984799i	$0.444429\pi$
$692$	−15.3571	+	5.84945i	−0.583789	+	0.222363i
$693$		0			0
$694$	−4.28254	−	23.2747i	−0.162563	−	0.883494i
$695$	28.1889	+	20.5415i	1.06927	+	0.779184i
$696$	17.7953	−	10.8101i	0.674530	−	0.409757i
$697$			8.29559i			0.314218i
$698$	−5.38137	+	0.990173i	−0.203688	+	0.0374786i
$699$	−10.0221			−0.379072
$700$		0			0
$701$	−23.3178			−0.880700			−0.440350	−	0.897826i	$-0.645146\pi$
$701$	−23.3178			−0.880700			−0.440350	+	0.897826i	$0.645146\pi$
$702$	40.9480	−	7.53444i	1.54548	−	0.284369i
$703$		−	1.75536i		−	0.0662047i
$704$	−32.0676	−	16.6543i	−1.20859	−	0.627683i
$705$	−8.32870	−	6.06920i	−0.313677	−	0.228579i
$706$	−2.02235	−	10.9910i	−0.0761121	−	0.413653i
$707$		0			0
$708$	−7.26583	−	19.0756i	−0.273067	−	0.716906i
$709$	0.346485			0.0130125			0.00650625	−	0.999979i	$-0.497929\pi$
$709$	0.346485			0.0130125			0.00650625	+	0.999979i	$0.497929\pi$
$710$	26.0979	+	12.5351i	0.979438	+	0.470432i
$711$		−	102.062i		−	3.82763i
$712$	−36.7806	+	22.3431i	−1.37841	+	0.837343i
$713$	−7.93167			−0.297043
$714$		0			0
$715$	13.2363	−	18.1640i	0.495009	−	0.679295i
$716$	11.1011	+	29.1448i	0.414869	+	1.08919i
$717$	−11.9578			−0.446571
$718$	5.78776	−	1.06495i	0.215997	−	0.0397436i
$719$	−40.3315			−1.50411			−0.752056	−	0.659099i	$-0.770938\pi$
$719$	−40.3315			−1.50411			−0.752056	+	0.659099i	$0.770938\pi$
$720$	−63.6638	+	6.26707i	−2.37261	+	0.233560i
$721$		0			0
$722$	−2.09066	−	11.3623i	−0.0778062	−	0.422859i
$723$	−23.6780			−0.880594
$724$	11.2862	+	29.6306i	0.419448	+	1.10121i
$725$	−3.53860	−	10.9966i	−0.131420	−	0.408405i
$726$	−41.6642	+	7.66623i	−1.54630	+	0.284520i
$727$		−	19.5590i		−	0.725402i	−0.931906	−	0.362701i	$-0.881855\pi$
$727$		−	19.5590i		−	0.725402i	0.931906	−	0.362701i	$-0.118145\pi$
$728$		0			0
$729$	−21.5718			−0.798957
$730$	4.43613	−	9.23600i	0.164188	−	0.341840i
$731$	16.8498			0.623211
$732$	−36.0391	+	13.7271i	−1.33204	+	0.507369i
$733$	19.6314			0.725101			0.362550	−	0.931964i	$-0.381906\pi$
$733$	19.6314			0.725101			0.362550	+	0.931964i	$0.381906\pi$
$734$	38.0786	−	7.00647i	1.40551	−	0.258614i
$735$		0			0
$736$	7.65746	+	5.95493i	0.282258	+	0.219502i
$737$		−	50.3603i		−	1.85505i
$738$	32.6351	−	6.00486i	1.20131	−	0.221042i
$739$			0.386471i			0.0142166i	0.999975	+	0.00710828i	$0.00226265\pi$
$739$			0.386471i			0.0142166i	−0.999975	+	0.00710828i	$0.997737\pi$
$740$	−0.395623	+	1.45317i	−0.0145434	+	0.0534197i
$741$		−	36.9577i		−	1.35767i
$742$		0			0
$743$	−51.2724			−1.88100			−0.940502	−	0.339789i	$-0.889644\pi$
$743$	−51.2724			−1.88100			−0.940502	+	0.339789i	$0.889644\pi$
$744$	−35.6263	+	21.6419i	−1.30612	+	0.793431i
$745$	4.54292	+	3.31047i	0.166440	+	0.121286i
$746$	−40.7642	+	7.50061i	−1.49248	+	0.274617i
$747$		−	80.8626i		−	2.95861i
$748$	8.13089	+	21.3468i	0.297295	+	0.780515i
$749$		0			0
$750$	−6.85267	+	49.9109i	−0.250224	+	1.82249i
$751$		−	6.96844i		−	0.254282i	−0.991885	−	0.127141i	$-0.959420\pi$
$751$		−	6.96844i		−	0.254282i	0.991885	−	0.127141i	$-0.0405801\pi$
$752$	3.84912	+	4.31966i	0.140363	+	0.157522i
$753$			18.3967i			0.670415i
$754$	−1.31575	−	7.15082i	−0.0479168	−	0.260417i
$755$	−16.7706	+	23.0141i	−0.610345	+	0.837570i
$756$		0			0
$757$		−	15.8945i		−	0.577696i	−0.957375	−	0.288848i	$-0.906728\pi$
$757$		−	15.8945i		−	0.577696i	0.957375	−	0.288848i	$-0.0932722\pi$
$758$	29.7827	−	5.48003i	1.08176	−	0.199044i
$759$	24.6790			0.895790
$760$	−2.76068	+	32.8504i	−0.100140	+	1.19161i
$761$		−	15.2848i		−	0.554074i	−0.960859	−	0.277037i	$-0.910648\pi$
$761$		−	15.2848i		−	0.554074i	0.960859	−	0.277037i	$-0.0893524\pi$
$762$	75.3929	−	13.8723i	2.73120	−	0.502540i
$763$		0			0
$764$	−8.00999	−	21.0293i	−0.289791	−	0.760815i
$765$	32.6833	+	23.8166i	1.18167	+	0.861092i
$766$	−26.8287	+	4.93649i	−0.969360	+	0.178362i
$767$	−7.12807			−0.257380
$768$	50.6429	+	5.85374i	1.82742	+	0.211229i
$769$		−	7.67597i		−	0.276803i	−0.990376	−	0.138401i	$-0.955804\pi$
$769$		−	7.67597i		−	0.276803i	0.990376	−	0.138401i	$-0.0441964\pi$
$770$		0			0
$771$			47.3169i			1.70408i
$772$	−17.6792	−	46.4148i	−0.636288	−	1.67050i
$773$	−18.7437			−0.674162			−0.337081	−	0.941476i	$-0.609440\pi$
$773$	−18.7437			−0.674162			−0.337081	+	0.941476i	$0.609440\pi$
$774$	−12.1969	−	66.2875i	−0.438409	−	2.38265i
$775$	7.08429	+	22.0153i	0.254475	+	0.790812i
$776$	−6.59788	−	10.8612i	−0.236850	−	0.389895i
$777$		0			0
$778$	−3.96837	−	21.5672i	−0.142273	−	0.773223i
$779$		−	17.1000i		−	0.612672i
$780$	−8.32951	+	30.5953i	−0.298244	+	1.09549i
$781$	−41.3535			−1.47975
$782$	−1.10970	−	6.03100i	−0.0396829	−	0.215668i
$783$			30.5667i			1.09236i
$784$		0			0
$785$	15.6273	+	11.3878i	0.557764	+	0.406448i
$786$	−39.7017	+	7.30513i	−1.41611	+	0.260565i
$787$		−	4.41739i		−	0.157463i	−0.996896	−	0.0787315i	$-0.974913\pi$
$787$		−	4.41739i		−	0.157463i	0.996896	−	0.0787315i	$-0.0250870\pi$
$788$	−9.95872	−	26.1455i	−0.354765	−	0.931395i
$789$		−	79.9448i		−	2.84611i
$790$	40.6769	+	19.5374i	1.44722	+	0.695111i
$791$		0			0
$792$	78.0932	−	47.4393i	2.77492	−	1.68568i
$793$			13.4669i			0.478222i
$794$	5.90380	+	32.0858i	0.209518	+	1.13868i
$795$	58.0231	+	42.2820i	2.05787	+	1.49959i
$796$	−36.5279	+	13.9133i	−1.29470	+	0.493145i
$797$	35.0449			1.24135			0.620677	−	0.784066i	$-0.286858\pi$
$797$	35.0449			1.24135			0.620677	+	0.784066i	$0.286858\pi$
$798$		0			0
$799$		−	3.65755i		−	0.129395i
$800$	9.68922	−	26.5729i	0.342566	−	0.939494i
$801$		−	108.823i		−	3.84507i
$802$	−9.37006	−	50.9242i	−0.330868	−	1.79820i
$803$			14.6349i			0.516455i
$804$	25.2904	+	66.3972i	0.891925	+	2.34165i
$805$		0			0
$806$	2.63413	+	14.3159i	0.0927834	+	0.504257i
$807$	−94.9062			−3.34086
$808$	1.77541	−	1.07851i	0.0624588	−	0.0379419i
$809$	21.0185			0.738971			0.369485	−	0.929237i	$-0.379534\pi$
$809$	21.0185			0.738971			0.369485	+	0.929237i	$0.379534\pi$
$810$	28.3379	−	58.9994i	0.995693	−	2.07303i
$811$	14.1034			0.495239			0.247619	−	0.968857i	$-0.420352\pi$
$811$	14.1034			0.495239			0.247619	+	0.968857i	$0.420352\pi$
$812$		0			0
$813$			6.05397i			0.212322i
$814$	−0.389280	−	2.11565i	−0.0136443	−	0.0741536i
$815$	−6.17334	−	4.49857i	−0.216243	−	0.157578i
$816$	−21.4402	−	24.0612i	−0.750558	−	0.842312i
$817$	−34.7331			−1.21516
$818$	−43.1164	+	7.93343i	−1.50753	+	0.277386i
$819$		0			0
$820$	−3.85400	+	14.1562i	−0.134587	+	0.494356i
$821$	55.4469			1.93511			0.967556	−	0.252657i	$-0.0813045\pi$
$821$	55.4469			1.93511			0.967556	+	0.252657i	$0.0813045\pi$
$822$	−6.78622	−	36.8816i	−0.236697	−	1.28639i
$823$	−29.6364			−1.03306			−0.516529	−	0.856269i	$-0.672776\pi$
$823$	−29.6364			−1.03306			−0.516529	+	0.856269i	$0.672776\pi$
$824$	28.6268	−	17.3900i	0.997263	−	0.605808i
$825$	−22.0424	−	68.4993i	−0.767417	−	2.38484i
$826$		0			0
$827$	−10.1475			−0.352865			−0.176432	−	0.984313i	$-0.556456\pi$
$827$	−10.1475			−0.352865			−0.176432	+	0.984313i	$0.556456\pi$
$828$	−22.9229	+	8.73122i	−0.796624	+	0.303431i
$829$		−	28.7775i		−	0.999485i	−0.866174	−	0.499742i	$-0.833428\pi$
$829$		−	28.7775i		−	0.999485i	0.866174	−	0.499742i	$-0.166572\pi$
$830$	32.2278	+	15.4793i	1.11864	+	0.537294i
$831$	−0.833300			−0.0289069
$832$	8.20504	−	15.7987i	0.284458	−	0.547720i
$833$		0			0
$834$	69.1272	−	12.7194i	2.39368	−	0.440437i
$835$	−15.3260	+	21.0318i	−0.530380	+	0.727834i
$836$	−16.7605	−	44.0029i	−0.579675	−	1.52187i
$837$		−	61.1945i		−	2.11519i
$838$	−3.05906	−	16.6253i	−0.105674	−	0.574312i
$839$	5.90481			0.203857			0.101928	−	0.994792i	$-0.467499\pi$
$839$	5.90481			0.203857			0.101928	+	0.994792i	$0.467499\pi$
$840$		0			0
$841$	−23.6621			−0.815934
$842$	−3.45625	−	18.7840i	−0.119110	−	0.647338i
$843$			17.0959i			0.588816i
$844$	2.56606	+	6.73690i	0.0883274	+	0.231894i
$845$	−14.5442	−	10.5985i	−0.500335	−	0.364599i
$846$	−14.3889	+	2.64756i	−0.494701	+	0.0910251i
$847$		0			0
$848$	−26.8154	−	30.0935i	−0.920846	−	1.03342i
$849$	−47.7456			−1.63862
$850$	−15.7486	+	8.46678i	−0.540172	+	0.290408i
$851$			0.577488i			0.0197960i
$852$	54.5223	−	20.7673i	1.86790	−	0.711477i
$853$	4.83687			0.165611			0.0828057	−	0.996566i	$-0.473612\pi$
$853$	4.83687			0.165611			0.0828057	+	0.996566i	$0.473612\pi$
$854$		0			0
$855$	−67.3713	−	49.0941i	−2.30405	−	1.67898i
$856$	−7.32700	−	12.0615i	−0.250432	−	0.412253i
$857$	−6.11967			−0.209044			−0.104522	−	0.994523i	$-0.533331\pi$
$857$	−6.11967			−0.209044			−0.104522	+	0.994523i	$0.533331\pi$
$858$	−8.19597	−	44.5433i	−0.279806	−	1.52068i
$859$	33.1953			1.13261			0.566304	−	0.824196i	$-0.308373\pi$
$859$	33.1953			1.13261			0.566304	+	0.824196i	$0.308373\pi$
$860$	28.7537	+	7.82813i	0.980493	+	0.266937i
$861$		0			0
$862$	49.4998	−	9.10797i	1.68597	−	0.310219i
$863$	44.4654			1.51362			0.756809	−	0.653636i	$-0.226757\pi$
$863$	44.4654			1.51362			0.756809	+	0.653636i	$0.226757\pi$
$864$	−45.9435	+	59.0789i	−1.56303	+	2.00991i
$865$	14.8488	+	10.8205i	0.504875	+	0.367907i
$866$	4.31991	+	23.4777i	0.146796	+	0.797806i
$867$		−	33.7932i		−	1.14768i
$868$		0			0
$869$	−64.4546			−2.18647
$870$	−20.9841	−	10.0788i	−0.711428	−	0.341705i
$871$	24.8109			0.840685
$872$	16.6170	+	27.3544i	0.562723	+	0.926338i
$873$	32.1352			1.08761
$874$	2.28748	+	12.4319i	0.0773751	+	0.420516i
$875$		0			0
$876$	−7.34951	−	19.2953i	−0.248317	−	0.651928i
$877$			34.5612i			1.16705i	0.812095	+	0.583525i	$0.198327\pi$
$877$			34.5612i			1.16705i	−0.812095	+	0.583525i	$0.801673\pi$
$878$	6.03141	+	32.7794i	0.203550	+	1.10625i
$879$			74.1665i			2.50157i
$880$	3.95780	+	40.2052i	0.133417	+	1.35532i
$881$			10.5105i			0.354109i	0.984201	+	0.177055i	$0.0566569\pi$
$881$			10.5105i			0.354109i	−0.984201	+	0.177055i	$0.943343\pi$
$882$		0			0
$883$	−9.49737			−0.319612			−0.159806	−	0.987148i	$-0.551087\pi$
$883$	−9.49737			−0.319612			−0.159806	+	0.987148i	$0.551087\pi$
$884$	−10.5169	+	4.00583i	−0.353720	+	0.134731i
$885$	−13.4405	+	18.4443i	−0.451799	+	0.619998i
$886$	2.28625	+	12.4253i	0.0768080	+	0.417435i
$887$			53.1500i			1.78460i	0.451442	+	0.892301i	$0.350910\pi$
$887$			53.1500i			1.78460i	−0.451442	+	0.892301i	$0.649090\pi$
$888$	1.57570	+	2.59387i	0.0528771	+	0.0870447i
$889$		0			0
$890$	43.3713	+	20.8316i	1.45381	+	0.698277i
$891$			93.4877i			3.13196i
$892$	1.08043	+	2.83654i	0.0361754	+	0.0949745i
$893$			7.53945i			0.252298i
$894$	11.1405	−	2.04986i	0.372595	−	0.0685575i
$895$	20.5352	−	28.1802i	0.686415	−	0.941960i
$896$		0			0
$897$			12.1585i			0.405962i
$898$	8.47988	+	46.0862i	0.282977	+	1.53792i
$899$	−10.6865			−0.356414
$900$	44.7084	+	55.8266i	1.49028	+	1.86089i
$901$			25.4809i			0.848891i
$902$	−3.79221	−	20.6098i	−0.126267	−	0.686232i
$903$		0			0
$904$	3.80766	−	2.31304i	0.126641	−	0.0769307i
$905$	20.8775	−	28.6500i	0.693991	−	0.952357i
$906$	10.3845	+	56.4372i	0.345000	+	1.87500i
$907$	10.1694			0.337668			0.168834	−	0.985644i	$-0.446000\pi$
$907$	10.1694			0.337668			0.168834	+	0.985644i	$0.446000\pi$
$908$	−11.0767	−	29.0805i	−0.367592	−	0.965072i
$909$			5.25292i			0.174228i
$910$		0			0
$911$		−	10.2186i		−	0.338556i	−0.985568	−	0.169278i	$-0.945856\pi$
$911$		−	10.2186i		−	0.338556i	0.985568	−	0.169278i	$-0.0541436\pi$
$912$	44.1956	+	49.5984i	1.46346	+	1.64237i
$913$	−51.0666			−1.69006
$914$	−34.2837	+	6.30821i	−1.13401	+	0.208657i
$915$	34.8463	+	25.3928i	1.15198	+	0.839461i
$916$	13.6693	+	35.8874i	0.451648	+	1.18575i
$917$		0			0
$918$	46.5304	−	8.56160i	1.53573	−	0.282575i
$919$		−	20.5705i		−	0.678557i	−0.940686	−	0.339278i	$-0.889817\pi$
$919$		−	20.5705i		−	0.678557i	0.940686	−	0.339278i	$-0.110183\pi$
$920$	0.908222	−	10.8073i	0.0299432	−	0.356306i
$921$	−18.1858			−0.599243
$922$	53.1784	−	9.78484i	1.75134	−	0.322247i
$923$		−	20.3736i		−	0.670604i
$924$		0			0
$925$	1.60289	−	0.515792i	0.0527025	−	0.0169591i
$926$	3.74459	+	20.3510i	0.123055	+	0.668777i
$927$			84.6984i			2.78186i
$928$	10.3170	+	8.02319i	0.338673	+	0.263374i
$929$		−	9.03122i		−	0.296305i	−0.988965	−	0.148152i	$-0.952667\pi$
$929$		−	9.03122i		−	0.296305i	0.988965	−	0.148152i	$-0.0473326\pi$
$930$	42.0102	+	20.1779i	1.37757	+	0.661658i
$931$		0			0
$932$	−2.23923	−	5.87884i	−0.0733483	−	0.192568i
$933$			102.252i			3.34758i
$934$	−11.8546	+	2.18126i	−0.387896	+	0.0713729i
$935$	15.0407	−	20.6403i	0.491885	−	0.675008i
$936$	23.3718	+	38.4740i	0.763931	+	1.25756i
$937$	−29.3531			−0.958923			−0.479462	−	0.877563i	$-0.659168\pi$
$937$	−29.3531			−0.958923			−0.479462	+	0.877563i	$0.659168\pi$
$938$		0			0
$939$			89.6726i			2.92635i
$940$	1.69924	−	6.24152i	0.0554231	−	0.203576i
$941$			3.97875i			0.129704i	0.997895	+	0.0648518i	$0.0206575\pi$
$941$			3.97875i			0.129704i	−0.997895	+	0.0648518i	$0.979343\pi$
$942$	38.3227	−	7.05138i	1.24862	−	0.229746i
$943$			5.62566i			0.183197i
$944$	9.56609	−	8.52406i	0.311350	−	0.277434i
$945$		0			0
$946$	−41.8621	+	7.70263i	−1.36105	+	0.250434i
$947$	−7.82851			−0.254392			−0.127196	−	0.991878i	$-0.540598\pi$
$947$	−7.82851			−0.254392			−0.127196	+	0.991878i	$0.540598\pi$
$948$	84.9797	−	32.3684i	2.76001	−	1.05128i
$949$	−7.21015			−0.234051
$950$	32.4632	−	17.4529i	1.05324	−	0.566247i
$951$	−42.6910			−1.38435
$952$		0			0
$953$			6.08169i			0.197005i	0.995137	+	0.0985026i	$0.0314053\pi$
$953$			6.08169i			0.197005i	−0.995137	+	0.0985026i	$0.968595\pi$
$954$	100.243	−	18.4446i	3.24547	−	0.597167i
$955$	−14.8171	+	20.3333i	−0.479470	+	0.657972i
$956$	−2.67170	−	7.01425i	−0.0864090	−	0.226857i
$957$	33.2504			1.07483
$958$	10.0384	+	54.5565i	0.324326	+	1.76264i
$959$		0			0
$960$	−25.4088	−	51.0207i	−0.820064	−	1.64669i
$961$	−9.60565			−0.309860
$962$	1.04231	−	0.191786i	0.0336055	−	0.00618342i
$963$	35.6864			1.14998
$964$	−5.29032	−	13.8892i	−0.170390	−	0.447340i
$965$	−32.7035	+	44.8786i	−1.05276	+	1.44469i
$966$		0			0
$967$	17.5988			0.565940			0.282970	−	0.959129i	$-0.408680\pi$
$967$	17.5988			0.565940			0.282970	+	0.959129i	$0.408680\pi$
$968$	−13.8058	−	22.7268i	−0.443737	−	0.730466i
$969$		−	41.9960i		−	1.34911i
$970$	−6.15154	+	12.8075i	−0.197514	+	0.411223i
$971$	40.5317			1.30073			0.650363	−	0.759624i	$-0.274617\pi$
$971$	40.5317			1.30073			0.650363	+	0.759624i	$0.274617\pi$
$972$	−18.6931	−	49.0767i	−0.599582	−	1.57414i
$973$		0			0
$974$	−6.54835	−	35.5888i	−0.209823	−	1.14034i
$975$	33.7474	−	10.8596i	1.08078	−	0.347785i
$976$	−16.1043	−	18.0729i	−0.515485	−	0.578501i
$977$		−	42.5787i		−	1.36221i	−0.732184	−	0.681107i	$-0.761499\pi$
$977$		−	42.5787i		−	1.36221i	0.732184	−	0.681107i	$-0.238501\pi$
$978$	−15.1388	+	2.78554i	−0.484085	+	0.0890717i
$979$	−68.7242			−2.19643
$980$		0			0
$981$	−80.9337			−2.58401
$982$	−56.6092	+	10.4161i	−1.80647	+	0.332391i
$983$			21.4753i			0.684954i	0.939526	+	0.342477i	$0.111266\pi$
$983$			21.4753i			0.684954i	−0.939526	+	0.342477i	$0.888734\pi$
$984$	15.3499	+	25.2685i	0.489336	+	0.805530i
$985$	−18.4219	+	25.2802i	−0.586971	+	0.805494i
$986$	−1.49512	−	8.12567i	−0.0476145	−	0.258774i
$987$		0			0
$988$	21.6788	−	8.25737i	0.689695	−	0.262702i
$989$	11.4267			0.363347
$990$	−92.0868	−	44.2301i	−2.92671	−	1.40572i
$991$			46.8099i			1.48696i	0.668756	+	0.743482i	$0.266827\pi$
$991$			46.8099i			1.48696i	−0.668756	+	0.743482i	$0.733173\pi$
$992$	−20.6547	−	16.0624i	−0.655788	−	0.509983i
$993$	72.3652			2.29644
$994$		0			0
$995$	35.3190	+	25.7373i	1.11969	+	0.815927i
$996$	67.3284	−	25.6451i	2.13338	−	0.812597i
$997$	34.0519			1.07843			0.539217	−	0.842167i	$-0.318720\pi$
$997$	34.0519			1.07843			0.539217	+	0.842167i	$0.318720\pi$
$998$	−22.1248	+	4.07097i	−0.700349	+	0.128864i
$999$	−4.45544			−0.140964

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	980.2.c.e.979.22	yes	48
4.3	odd	2	inner	980.2.c.e.979.25	yes	48
5.4	even	2	inner	980.2.c.e.979.27	yes	48
7.2	even	3		980.2.s.g.619.9		96
7.3	odd	6		980.2.s.g.19.45		96
7.4	even	3		980.2.s.g.19.46		96
7.5	odd	6		980.2.s.g.619.10		96
7.6	odd	2	inner	980.2.c.e.979.21	✓	48
20.19	odd	2	inner	980.2.c.e.979.24	yes	48
28.3	even	6		980.2.s.g.19.40		96
28.11	odd	6		980.2.s.g.19.39		96
28.19	even	6		980.2.s.g.619.3		96
28.23	odd	6		980.2.s.g.619.4		96
28.27	even	2	inner	980.2.c.e.979.26	yes	48
35.4	even	6		980.2.s.g.19.3		96
35.9	even	6		980.2.s.g.619.40		96
35.19	odd	6		980.2.s.g.619.39		96
35.24	odd	6		980.2.s.g.19.4		96
35.34	odd	2	inner	980.2.c.e.979.28	yes	48
140.19	even	6		980.2.s.g.619.46		96
140.39	odd	6		980.2.s.g.19.10		96
140.59	even	6		980.2.s.g.19.9		96
140.79	odd	6		980.2.s.g.619.45		96
140.139	even	2	inner	980.2.c.e.979.23	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
980.2.c.e.979.21	✓	48	7.6	odd	2	inner
980.2.c.e.979.22	yes	48	1.1	even	1	trivial
980.2.c.e.979.23	yes	48	140.139	even	2	inner
980.2.c.e.979.24	yes	48	20.19	odd	2	inner
980.2.c.e.979.25	yes	48	4.3	odd	2	inner
980.2.c.e.979.26	yes	48	28.27	even	2	inner
980.2.c.e.979.27	yes	48	5.4	even	2	inner
980.2.c.e.979.28	yes	48	35.34	odd	2	inner
980.2.s.g.19.3		96	35.4	even	6
980.2.s.g.19.4		96	35.24	odd	6
980.2.s.g.19.9		96	140.59	even	6
980.2.s.g.19.10		96	140.39	odd	6
980.2.s.g.19.39		96	28.11	odd	6
980.2.s.g.19.40		96	28.3	even	6
980.2.s.g.19.45		96	7.3	odd	6
980.2.s.g.19.46		96	7.4	even	3
980.2.s.g.619.3		96	28.19	even	6
980.2.s.g.619.4		96	28.23	odd	6
980.2.s.g.619.9		96	7.2	even	3
980.2.s.g.619.10		96	7.5	odd	6
980.2.s.g.619.39		96	35.19	odd	6
980.2.s.g.619.40		96	35.9	even	6
980.2.s.g.619.45		96	140.79	odd	6
980.2.s.g.619.46		96	140.19	even	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)

\(f(q)\)	\(=\)	\(q+(-0.255919 - 1.39086i) q^{2} +3.18626i q^{3} +(-1.86901 + 0.711898i) q^{4} +(1.80715 + 1.31689i) q^{5} +(4.43165 - 0.815425i) q^{6} +(1.46847 + 2.41735i) q^{8} -7.15223 q^{9} +O(q^{10})\)	\(q+(-0.255919 - 1.39086i) q^{2} +3.18626i q^{3} +(-1.86901 + 0.711898i) q^{4} +(1.80715 + 1.31689i) q^{5} +(4.43165 - 0.815425i) q^{6} +(1.46847 + 2.41735i) q^{8} -7.15223 q^{9} +(1.36913 - 2.85052i) q^{10} +4.51680i q^{11} +(-2.26829 - 5.95515i) q^{12} -2.22528 q^{13} +(-4.19595 + 5.75805i) q^{15} +(2.98640 - 2.66109i) q^{16} -2.52865 q^{17} +(1.83040 + 9.94779i) q^{18} +5.21241 q^{19} +(-4.31508 - 1.17477i) q^{20} +(6.28226 - 1.15594i) q^{22} -1.71481 q^{23} +(-7.70231 + 4.67892i) q^{24} +(1.53160 + 4.75964i) q^{25} +(0.569493 + 3.09507i) q^{26} -13.2301i q^{27} -2.31039 q^{29} +(9.08250 + 4.36240i) q^{30} +4.62540 q^{31} +(-4.46550 - 3.47266i) q^{32} -14.3917 q^{33} +(0.647131 + 3.51701i) q^{34} +(13.3676 - 5.09167i) q^{36} -0.336766i q^{37} +(-1.33396 - 7.24976i) q^{38} -7.09032i q^{39} +(-0.529635 + 6.30234i) q^{40} -3.28064i q^{41} -6.66354 q^{43} +(-3.21551 - 8.44195i) q^{44} +(-12.9252 - 9.41870i) q^{45} +(0.438852 + 2.38506i) q^{46} +1.44644i q^{47} +(8.47892 + 9.51544i) q^{48} +(6.22805 - 3.34834i) q^{50} -8.05693i q^{51} +(4.15908 - 1.58418i) q^{52} -10.0769i q^{53} +(-18.4013 + 3.38584i) q^{54} +(-5.94813 + 8.16255i) q^{55} +16.6081i q^{57} +(0.591274 + 3.21344i) q^{58} +3.20322 q^{59} +(3.74312 - 13.7490i) q^{60} -6.05175i q^{61} +(-1.18373 - 6.43331i) q^{62} +(-3.68719 + 7.09962i) q^{64} +(-4.02143 - 2.93045i) q^{65} +(3.68311 + 20.0169i) q^{66} -11.1495 q^{67} +(4.72608 - 1.80014i) q^{68} -5.46381i q^{69} +9.15549i q^{71} +(-10.5028 - 17.2895i) q^{72} +3.24011 q^{73} +(-0.468396 + 0.0861849i) q^{74} +(-15.1654 + 4.88008i) q^{75} +(-9.74205 + 3.71071i) q^{76} +(-9.86168 + 1.81455i) q^{78} +14.2700i q^{79} +(8.90125 - 0.876239i) q^{80} +20.6978 q^{81} +(-4.56292 + 0.839579i) q^{82} +11.3059i q^{83} +(-4.56966 - 3.32995i) q^{85} +(1.70533 + 9.26808i) q^{86} -7.36150i q^{87} +(-10.9187 + 6.63279i) q^{88} +15.2152i q^{89} +(-9.79234 + 20.3876i) q^{90} +(3.20499 - 1.22077i) q^{92} +14.7377i q^{93} +(2.01181 - 0.370173i) q^{94} +(9.41962 + 6.86417i) q^{95} +(11.0648 - 14.2282i) q^{96} -4.49303 q^{97} -32.3052i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 16 q^{4} - 64 q^{9}+O(q^{10}) \) 48 * q + 16 * q^4 - 64 * q^9	\( 48 q + 16 q^{4} - 64 q^{9} + 16 q^{16} - 16 q^{25} - 48 q^{29} - 8 q^{30} + 176 q^{36} - 48 q^{44} - 32 q^{46} + 32 q^{50} + 24 q^{60} - 80 q^{64} - 16 q^{65} - 112 q^{74} - 48 q^{81} - 64 q^{85} - 112 q^{86}+O(q^{100}) \) 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