LMFDB - Embedded newform 980.2.c.e.979.21

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			979.21
Character	$\chi$	$=$	980.979
Dual form			980.2.c.e.979.24

$q$-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	$-0.628356\pi$
$3$		−	3.18626i		−	1.83959i	0.392403	−	0.919793i	$-0.371644\pi$
$4$	−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	$-0.400142\pi$
$13$	2.22528			0.617182			0.308591	+	0.951195i	$0.400142\pi$
$14$		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	$-0.400794\pi$
$17$	2.52865			0.613288			0.306644	+	0.951824i	$0.400794\pi$
$18$	1.83040	+	9.94779i	0.431428	+	2.34472i
$19$	−5.21241			−1.19581			−0.597904	−	0.801568i	$-0.704000\pi$
$19$	−5.21241			−1.19581			−0.597904	+	0.801568i	$0.704000\pi$
$20$	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	$-0.636349\pi$
$31$	−4.62540			−0.830747			−0.415373	+	0.909651i	$0.636349\pi$
$32$	−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	$0.0824623\pi$
$41$			3.28064i			0.512350i	−0.966630	+	0.256175i	$0.917538\pi$
$42$		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	$-0.966358\pi$
$47$		−	1.44644i		−	0.210985i	0.994420	−	0.105493i	$-0.0336420\pi$
$48$	−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	$-0.566862\pi$
$59$	−3.20322			−0.417023			−0.208512	+	0.978020i	$0.566862\pi$
$60$	3.74312	−	13.7490i	0.483235	−	1.77498i
$61$			6.05175i			0.774847i	0.921902	+	0.387424i	$0.126635\pi$
$61$			6.05175i			0.774847i	−0.921902	+	0.387424i	$0.873365\pi$
$62$	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	$-0.560723\pi$
$73$	−3.24011			−0.379226			−0.189613	+	0.981859i	$0.560723\pi$
$74$	−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	$-0.786933\pi$
$83$		−	11.3059i		−	1.24099i	0.784212	−	0.620493i	$-0.213067\pi$
$84$		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	$-0.701410\pi$
$89$		−	15.2152i		−	1.61281i	0.591364	−	0.806405i	$-0.298590\pi$
$90$	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	$-0.426749\pi$
$97$	4.49303			0.456198			0.228099	+	0.973638i	$0.426749\pi$
$98$		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	$0.0116336\pi$
$101$			0.734445i			0.0730800i	−0.999332	+	0.0365400i	$0.988366\pi$
$102$	−11.2061	+	2.06193i	−1.10957	+	0.204161i
$103$			11.8422i			1.16685i	0.812167	+	0.583424i	$0.198288\pi$
$103$			11.8422i			1.16685i	−0.812167	+	0.583424i	$0.801712\pi$
$104$	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	$-0.372004\pi$
$131$	8.95868			0.782723			0.391362	+	0.920237i	$0.372004\pi$
$132$	−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	$-0.730090\pi$
$139$	−15.5985			−1.32305			−0.661524	+	0.749924i	$0.730090\pi$
$140$		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	$-0.612146\pi$
$157$	−8.64749			−0.690145			−0.345073	+	0.938576i	$0.612146\pi$
$158$	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	$-0.851320\pi$
$167$		−	11.6381i		−	0.900581i	0.892882	−	0.450290i	$-0.148680\pi$
$168$		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	$-0.601117\pi$
$173$	−8.21670			−0.624704			−0.312352	+	0.949966i	$0.601117\pi$
$174$	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	$0.200555\pi$
$181$			15.8536i			1.17839i	−0.807990	+	0.589196i	$0.799445\pi$
$182$		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	$-0.743587\pi$
$199$	−19.5440			−1.38544			−0.692719	+	0.721208i	$0.743587\pi$
$200$	−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	$0.0161820\pi$
$223$			1.51767i			0.101631i	−0.998708	+	0.0508154i	$0.983818\pi$
$224$		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	$-0.827289\pi$
$227$		−	15.5593i		−	1.03271i	0.856375	−	0.516354i	$-0.172711\pi$
$228$	−11.8233	−	31.0407i	−0.783015	−	2.05572i
$229$			19.2013i			1.26885i	0.772982	+	0.634427i	$0.218764\pi$
$229$			19.2013i			1.26885i	−0.772982	+	0.634427i	$0.781236\pi$
$230$	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	$-0.923067\pi$
$241$		−	7.43129i		−	0.478691i	0.970934	−	0.239346i	$-0.0769329\pi$
$242$	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	$-0.558328\pi$
$251$	−5.77378			−0.364438			−0.182219	+	0.983258i	$0.558328\pi$
$252$		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	$-0.653287\pi$
$257$	−14.8503			−0.926336			−0.463168	+	0.886270i	$0.653287\pi$
$258$	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	$-0.637574\pi$
$269$		−	29.7861i		−	1.81609i	0.418871	−	0.908046i	$-0.362426\pi$
$270$	−37.7127	−	18.1137i	−2.29512	−	1.10237i
$271$	−1.90002			−0.115418			−0.0577091	−	0.998333i	$-0.518380\pi$
$271$	−1.90002			−0.115418			−0.0577091	+	0.998333i	$0.518380\pi$
$272$	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	$-0.853069\pi$
$283$		−	14.9849i		−	0.890757i	0.895342	−	0.445378i	$-0.146931\pi$
$284$	−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	$-0.737989\pi$
$293$	−23.2770			−1.35986			−0.679928	+	0.733279i	$0.737989\pi$
$294$		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	$-0.947923\pi$
$307$		−	5.70758i		−	0.325749i	0.986647	−	0.162874i	$-0.0520765\pi$
$308$		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	$-0.863821\pi$
$311$	−32.0916			−1.81975			−0.909873	+	0.414886i	$0.863821\pi$
$312$	17.1398	−	10.4119i	0.970351	−	0.589460i
$313$	−28.1435			−1.59077			−0.795384	−	0.606106i	$-0.792731\pi$
$313$	−28.1435			−1.59077			−0.795384	+	0.606106i	$0.792731\pi$
$314$	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	$0.0330213\pi$
$349$			3.86908i			0.207107i	−0.994624	+	0.103554i	$0.966979\pi$
$350$		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	$-0.567444\pi$
$353$	−7.90229			−0.420597			−0.210298	+	0.977637i	$0.567444\pi$
$354$	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	$-0.746631\pi$
$367$		−	27.3777i		−	1.42910i	0.699583	−	0.714551i	$-0.253369\pi$
$368$	−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	$0.164033\pi$
$383$			19.2892i			0.985633i	−0.870133	+	0.492817i	$0.835967\pi$
$384$	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	$-0.303482\pi$
$397$	23.0690			1.15780			0.578899	+	0.815399i	$0.303482\pi$
$398$	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	$0.277963\pi$
$409$			30.9997i			1.53284i	−0.642341	+	0.766419i	$0.722037\pi$
$410$	−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	$-0.594313\pi$
$419$	−11.9532			−0.583953			−0.291977	+	0.956425i	$0.594313\pi$
$420$		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	$-0.367063\pi$
$433$	16.8799			0.811199			0.405599	+	0.914051i	$0.367063\pi$
$434$		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	$-0.309874\pi$
$439$	23.5676			1.12482			0.562410	+	0.826858i	$0.309874\pi$
$440$	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	$-0.650446\pi$
$461$		−	38.2341i		−	1.78074i	0.455239	−	0.890369i	$-0.349554\pi$
$462$		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	$0.0631861\pi$
$467$			8.52322i			0.394408i	−0.980363	+	0.197204i	$0.936814\pi$
$468$	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	$-0.146378\pi$
$479$	39.2249			1.79223			0.896115	+	0.443823i	$0.146378\pi$
$480$	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	$-0.931026\pi$
$503$		−	9.64379i		−	0.429995i	0.976615	−	0.214998i	$-0.0689744\pi$
$504$		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	$-0.973326\pi$
$509$		−	3.77669i		−	0.167399i	0.996491	−	0.0836995i	$-0.0266736\pi$
$510$	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	$0.000637952\pi$
$521$			0.0914926i			0.00400837i	−0.999998	+	0.00200418i	$0.999362\pi$
$522$	−4.22893	−	22.9833i	−0.185095	−	1.00595i
$523$			15.0818i			0.659480i	0.944072	+	0.329740i	$0.106961\pi$
$523$			15.0818i			0.659480i	−0.944072	+	0.329740i	$0.893039\pi$
$524$	−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	$0.128002\pi$
$563$			18.5730i			0.782760i	−0.920229	+	0.391380i	$0.871998\pi$
$564$	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	$-0.911519\pi$
$577$	−46.1975			−1.92323			−0.961614	+	0.274404i	$0.911519\pi$
$578$	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	$-0.982118\pi$
$587$		−	2.72072i		−	0.112296i	0.998422	−	0.0561482i	$-0.0178819\pi$
$588$		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	$-0.246741\pi$
$593$	34.7891			1.42862			0.714308	+	0.699831i	$0.246741\pi$
$594$	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	$-0.886091\pi$
$601$		−	17.1738i		−	0.700532i	0.936650	−	0.350266i	$-0.113909\pi$
$602$		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	$-0.890546\pi$
$607$		−	16.6117i		−	0.674247i	0.941460	−	0.337123i	$-0.109454\pi$
$608$	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	$-0.283302\pi$
$619$	31.3184			1.25879			0.629396	+	0.777085i	$0.283302\pi$
$620$	−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	$-0.983945\pi$
$643$		−	2.55684i		−	0.100832i	0.998728	−	0.0504159i	$-0.0160547\pi$
$644$		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	$0.113700\pi$
$647$			17.7876i			0.699301i	−0.936880	+	0.349651i	$0.886300\pi$
$648$	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	$0.101791\pi$
$661$			16.1645i			0.628727i	−0.949303	+	0.314364i	$0.898209\pi$
$662$	−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	$-0.613290\pi$
$677$	−18.1326			−0.696891			−0.348446	+	0.937329i	$0.613290\pi$
$678$	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	$-0.555571\pi$
$691$	−9.13188			−0.347393			−0.173697	+	0.984799i	$0.555571\pi$
$692$	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	$-0.229062\pi$
$719$	40.3315			1.50411			0.752056	+	0.659099i	$0.229062\pi$
$720$	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	$0.118145\pi$
$727$			19.5590i			0.725402i	−0.931906	+	0.362701i	$0.881855\pi$
$728$		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	$-0.618094\pi$
$733$	−19.6314			−0.725101			−0.362550	+	0.931964i	$0.618094\pi$
$734$	−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	$0.0893524\pi$
$761$			15.2848i			0.554074i	−0.960859	+	0.277037i	$0.910648\pi$
$762$	−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	$0.0441964\pi$
$769$			7.67597i			0.276803i	−0.990376	+	0.138401i	$0.955804\pi$
$770$		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	$-0.390560\pi$
$773$	18.7437			0.674162			0.337081	+	0.941476i	$0.390560\pi$
$774$	−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	$0.0250870\pi$
$787$			4.41739i			0.157463i	−0.996896	+	0.0787315i	$0.974913\pi$
$788$	−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	$-0.713142\pi$
$797$	−35.0449			−1.24135			−0.620677	+	0.784066i	$0.713142\pi$
$798$		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	$-0.579648\pi$
$811$	−14.1034			−0.495239			−0.247619	+	0.968857i	$0.579648\pi$
$812$		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	$0.166572\pi$
$829$			28.7775i			0.999485i	−0.866174	+	0.499742i	$0.833428\pi$
$830$	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	$-0.532501\pi$
$839$	−5.90481			−0.203857			−0.101928	+	0.994792i	$0.532501\pi$
$840$		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	$-0.526388\pi$
$853$	−4.83687			−0.165611			−0.0828057	+	0.996566i	$0.526388\pi$
$854$		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	$-0.466669\pi$
$857$	6.11967			0.209044			0.104522	+	0.994523i	$0.466669\pi$
$858$	−8.19597	−	44.5433i	−0.279806	−	1.52068i
$859$	−33.1953			−1.13261			−0.566304	−	0.824196i	$-0.691627\pi$
$859$	−33.1953			−1.13261			−0.566304	+	0.824196i	$0.691627\pi$
$860$	−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	$-0.943343\pi$
$881$		−	10.5105i		−	0.354109i	0.984201	−	0.177055i	$-0.0566569\pi$
$882$		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	$-0.649090\pi$
$887$		−	53.1500i		−	1.78460i	0.451442	−	0.892301i	$-0.350910\pi$
$888$	−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	$0.0473326\pi$
$929$			9.03122i			0.296305i	−0.988965	+	0.148152i	$0.952667\pi$
$930$	−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	$-0.340832\pi$
$937$	29.3531			0.958923			0.479462	+	0.877563i	$0.340832\pi$
$938$		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	$-0.979343\pi$
$941$		−	3.97875i		−	0.129704i	0.997895	−	0.0648518i	$-0.0206575\pi$
$942$	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	$-0.725383\pi$
$971$	−40.5317			−1.30073			−0.650363	+	0.759624i	$0.725383\pi$
$972$	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	$-0.888734\pi$
$983$		−	21.4753i		−	0.684954i	0.939526	−	0.342477i	$-0.111266\pi$
$984$	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	$-0.681280\pi$
$997$	−34.0519			−1.07843			−0.539217	+	0.842167i	$0.681280\pi$
$998$	−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.979.21	✓	48
4.3	odd	2	inner	980.2.c.e.979.26	yes	48
5.4	even	2	inner	980.2.c.e.979.28	yes	48
7.2	even	3		980.2.s.g.619.10		96
7.3	odd	6		980.2.s.g.19.46		96
7.4	even	3		980.2.s.g.19.45		96
7.5	odd	6		980.2.s.g.619.9		96
7.6	odd	2	inner	980.2.c.e.979.22	yes	48
20.19	odd	2	inner	980.2.c.e.979.23	yes	48
28.3	even	6		980.2.s.g.19.39		96
28.11	odd	6		980.2.s.g.19.40		96
28.19	even	6		980.2.s.g.619.4		96
28.23	odd	6		980.2.s.g.619.3		96
28.27	even	2	inner	980.2.c.e.979.25	yes	48
35.4	even	6		980.2.s.g.19.4		96
35.9	even	6		980.2.s.g.619.39		96
35.19	odd	6		980.2.s.g.619.40		96
35.24	odd	6		980.2.s.g.19.3		96
35.34	odd	2	inner	980.2.c.e.979.27	yes	48
140.19	even	6		980.2.s.g.619.45		96
140.39	odd	6		980.2.s.g.19.9		96
140.59	even	6		980.2.s.g.19.10		96
140.79	odd	6		980.2.s.g.619.46		96
140.139	even	2	inner	980.2.c.e.979.24	yes	48

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

Overview	Random
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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

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