LMFDB - Embedded newform 966.2.f.b.461.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [966,2,Mod(461,966)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(966, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 1, 0]))

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

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

chi := DirichletCharacter("966.461");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 966 = 2 \cdot 3 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	966.f (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:	$7.71354883526$
Analytic rank:	$0$
Dimension:	$24$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			461.11
Character	$\chi$	$=$	966.461
Dual form			966.2.f.b.461.23

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000i q^{2} +(1.66919 + 0.462387i) q^{3} -1.00000 q^{4} +1.95027 q^{5} +(0.462387 - 1.66919i) q^{6} +(-0.602835 - 2.57616i) q^{7} +1.00000i q^{8} +(2.57240 + 1.54363i) q^{9} +O(q^{10})$	\(q-1.00000i q^{2} +(1.66919 + 0.462387i) q^{3} -1.00000 q^{4} +1.95027 q^{5} +(0.462387 - 1.66919i) q^{6} +(-0.602835 - 2.57616i) q^{7} +1.00000i q^{8} +(2.57240 + 1.54363i) q^{9} -1.95027i q^{10} -4.18593i q^{11} +(-1.66919 - 0.462387i) q^{12} -7.00187i q^{13} +(-2.57616 + 0.602835i) q^{14} +(3.25538 + 0.901781i) q^{15} +1.00000 q^{16} -3.56933 q^{17} +(1.54363 - 2.57240i) q^{18} +8.08958i q^{19} -1.95027 q^{20} +(0.184936 - 4.57884i) q^{21} -4.18593 q^{22} +1.00000i q^{23} +(-0.462387 + 1.66919i) q^{24} -1.19644 q^{25} -7.00187 q^{26} +(3.58007 + 3.76605i) q^{27} +(0.602835 + 2.57616i) q^{28} -2.33625i q^{29} +(0.901781 - 3.25538i) q^{30} +0.237061i q^{31} -1.00000i q^{32} +(1.93552 - 6.98711i) q^{33} +3.56933i q^{34} +(-1.17569 - 5.02421i) q^{35} +(-2.57240 - 1.54363i) q^{36} -0.324825 q^{37} +8.08958 q^{38} +(3.23757 - 11.6874i) q^{39} +1.95027i q^{40} +8.81948 q^{41} +(-4.57884 - 0.184936i) q^{42} +8.54266 q^{43} +4.18593i q^{44} +(5.01687 + 3.01049i) q^{45} +1.00000 q^{46} -0.174840 q^{47} +(1.66919 + 0.462387i) q^{48} +(-6.27318 + 3.10600i) q^{49} +1.19644i q^{50} +(-5.95790 - 1.65041i) q^{51} +7.00187i q^{52} -5.65184i q^{53} +(3.76605 - 3.58007i) q^{54} -8.16370i q^{55} +(2.57616 - 0.602835i) q^{56} +(-3.74052 + 13.5031i) q^{57} -2.33625 q^{58} -7.74076 q^{59} +(-3.25538 - 0.901781i) q^{60} +9.18309i q^{61} +0.237061 q^{62} +(2.42589 - 7.55745i) q^{63} -1.00000 q^{64} -13.6555i q^{65} +(-6.98711 - 1.93552i) q^{66} +7.68745 q^{67} +3.56933 q^{68} +(-0.462387 + 1.66919i) q^{69} +(-5.02421 + 1.17569i) q^{70} -5.42350i q^{71} +(-1.54363 + 2.57240i) q^{72} +11.1709i q^{73} +0.324825i q^{74} +(-1.99708 - 0.553217i) q^{75} -8.08958i q^{76} +(-10.7836 + 2.52342i) q^{77} +(-11.6874 - 3.23757i) q^{78} +12.2350 q^{79} +1.95027 q^{80} +(4.23444 + 7.94163i) q^{81} -8.81948i q^{82} +17.9170 q^{83} +(-0.184936 + 4.57884i) q^{84} -6.96117 q^{85} -8.54266i q^{86} +(1.08025 - 3.89965i) q^{87} +4.18593 q^{88} -1.21795 q^{89} +(3.01049 - 5.01687i) q^{90} +(-18.0379 + 4.22097i) q^{91} -1.00000i q^{92} +(-0.109614 + 0.395700i) q^{93} +0.174840i q^{94} +15.7769i q^{95} +(0.462387 - 1.66919i) q^{96} +16.7148i q^{97} +(3.10600 + 6.27318i) q^{98} +(6.46151 - 10.7679i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 24 q^{4} - 4 q^{7} + 8 q^{9}+O(q^{10}) $ 24 * q - 24 * q^4 - 4 * q^7 + 8 * q^9	$ 24 q - 24 q^{4} - 4 q^{7} + 8 q^{9} + 24 q^{16} + 16 q^{18} - 28 q^{21} + 8 q^{22} - 24 q^{25} + 4 q^{28} + 24 q^{30} - 8 q^{36} + 40 q^{37} + 72 q^{39} + 64 q^{43} + 24 q^{46} - 24 q^{51} + 16 q^{58} + 12 q^{63} - 24 q^{64} - 64 q^{67} + 16 q^{70} - 16 q^{72} - 32 q^{78} + 88 q^{79} + 48 q^{81} + 28 q^{84} + 64 q^{85} - 8 q^{88} - 56 q^{91} + 8 q^{93} - 8 q^{99}+O(q^{100}) $ 24 * q - 24 * q^4 - 4 * q^7 + 8 * q^9 + 24 * q^16 + 16 * q^18 - 28 * q^21 + 8 * q^22 - 24 * q^25 + 4 * q^28 + 24 * q^30 - 8 * q^36 + 40 * q^37 + 72 * q^39 + 64 * q^43 + 24 * q^46 - 24 * q^51 + 16 * q^58 + 12 * q^63 - 24 * q^64 - 64 * q^67 + 16 * q^70 - 16 * q^72 - 32 * q^78 + 88 * q^79 + 48 * q^81 + 28 * q^84 + 64 * q^85 - 8 * q^88 - 56 * q^91 + 8 * q^93 - 8 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/966\mathbb{Z}\right)^\times$.

$n$	$323$	$829$	$925$
$\chi(n)$	$-1$	$-1$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$		−	1.00000i		−	0.707107i
$2$		−	1.00000i		−	0.707107i
$3$	1.66919	+	0.462387i	0.963708	+	0.266959i
$3$	1.66919	+	0.462387i	0.963708	+	0.266959i
$4$	−1.00000			−0.500000
$5$	1.95027			0.872188			0.436094	−	0.899901i	$-0.356361\pi$
$5$	1.95027			0.872188			0.436094	+	0.899901i	$0.356361\pi$
$6$	0.462387	−	1.66919i	0.188769	−	0.681444i
$7$	−0.602835	−	2.57616i	−0.227850	−	0.973696i
$7$	−0.602835	−	2.57616i	−0.227850	−	0.973696i
$8$			1.00000i			0.353553i
$9$	2.57240	+	1.54363i	0.857465	+	0.514542i
$10$		−	1.95027i		−	0.616730i
$11$		−	4.18593i		−	1.26210i	−0.775740	−	0.631052i	$-0.782623\pi$
$11$		−	4.18593i		−	1.26210i	0.775740	−	0.631052i	$-0.217377\pi$
$12$	−1.66919	−	0.462387i	−0.481854	−	0.133480i
$13$		−	7.00187i		−	1.94197i	−0.239144	−	0.970984i	$-0.576867\pi$
$13$		−	7.00187i		−	1.94197i	0.239144	−	0.970984i	$-0.423133\pi$
$14$	−2.57616	+	0.602835i	−0.688507	+	0.161114i
$15$	3.25538	+	0.901781i	0.840535	+	0.232839i
$16$	1.00000			0.250000
$17$	−3.56933			−0.865690			−0.432845	−	0.901468i	$-0.642490\pi$
$17$	−3.56933			−0.865690			−0.432845	+	0.901468i	$0.642490\pi$
$18$	1.54363	−	2.57240i	0.363836	−	0.606320i
$19$			8.08958i			1.85588i	0.372732	+	0.927939i	$0.378421\pi$
$19$			8.08958i			1.85588i	−0.372732	+	0.927939i	$0.621579\pi$
$20$	−1.95027			−0.436094
$21$	0.184936	−	4.57884i	0.0403564	−	0.999185i
$22$	−4.18593			−0.892443
$23$			1.00000i			0.208514i
$23$			1.00000i			0.208514i
$24$	−0.462387	+	1.66919i	−0.0943844	+	0.340722i
$25$	−1.19644			−0.239287
$26$	−7.00187			−1.37318
$27$	3.58007	+	3.76605i	0.688984	+	0.724776i
$28$	0.602835	+	2.57616i	0.113925	+	0.486848i
$29$		−	2.33625i		−	0.433831i	−0.976190	−	0.216916i	$-0.930400\pi$
$29$		−	2.33625i		−	0.433831i	0.976190	−	0.216916i	$-0.0695996\pi$
$30$	0.901781	−	3.25538i	0.164642	−	0.594348i
$31$			0.237061i			0.0425774i	0.999773	+	0.0212887i	$0.00677692\pi$
$31$			0.237061i			0.0425774i	−0.999773	+	0.0212887i	$0.993223\pi$
$32$		−	1.00000i		−	0.176777i
$33$	1.93552	−	6.98711i	0.336931	−	1.21630i
$34$			3.56933i			0.612135i
$35$	−1.17569	−	5.02421i	−0.198728	−	0.849246i
$36$	−2.57240	−	1.54363i	−0.428733	−	0.257271i
$37$	−0.324825			−0.0534009			−0.0267005	−	0.999643i	$-0.508500\pi$
$37$	−0.324825			−0.0534009			−0.0267005	+	0.999643i	$0.508500\pi$
$38$	8.08958			1.31230
$39$	3.23757	−	11.6874i	0.518427	−	1.87149i
$40$			1.95027i			0.308365i
$41$	8.81948			1.37737			0.688686	−	0.725060i	$-0.258188\pi$
$41$	8.81948			1.37737			0.688686	+	0.725060i	$0.258188\pi$
$42$	−4.57884	−	0.184936i	−0.706531	−	0.0285363i
$43$	8.54266			1.30274			0.651372	−	0.758759i	$-0.274194\pi$
$43$	8.54266			1.30274			0.651372	+	0.758759i	$0.274194\pi$
$44$			4.18593i			0.631052i
$45$	5.01687	+	3.01049i	0.747871	+	0.448777i
$46$	1.00000			0.147442
$47$	−0.174840			−0.0255030			−0.0127515	−	0.999919i	$-0.504059\pi$
$47$	−0.174840			−0.0255030			−0.0127515	+	0.999919i	$0.504059\pi$
$48$	1.66919	+	0.462387i	0.240927	+	0.0667399i
$49$	−6.27318	+	3.10600i	−0.896169	+	0.443714i
$50$			1.19644i			0.169202i
$51$	−5.95790	−	1.65041i	−0.834272	−	0.231104i
$52$			7.00187i			0.970984i
$53$		−	5.65184i		−	0.776340i	−0.921588	−	0.388170i	$-0.873107\pi$
$53$		−	5.65184i		−	0.776340i	0.921588	−	0.388170i	$-0.126893\pi$
$54$	3.76605	−	3.58007i	0.512494	−	0.487185i
$55$		−	8.16370i		−	1.10079i
$56$	2.57616	−	0.602835i	0.344254	−	0.0805572i
$57$	−3.74052	+	13.5031i	−0.495444	+	1.78852i
$58$	−2.33625			−0.306765
$59$	−7.74076			−1.00776			−0.503881	−	0.863773i	$-0.668095\pi$
$59$	−7.74076			−1.00776			−0.503881	+	0.863773i	$0.668095\pi$
$60$	−3.25538	−	0.901781i	−0.420267	−	0.116419i
$61$			9.18309i			1.17577i	0.808943	+	0.587887i	$0.200040\pi$
$61$			9.18309i			1.17577i	−0.808943	+	0.587887i	$0.799960\pi$
$62$	0.237061			0.0301068
$63$	2.42589	−	7.55745i	0.305634	−	0.952149i
$64$	−1.00000			−0.125000
$65$		−	13.6555i		−	1.69376i
$66$	−6.98711	−	1.93552i	−0.860054	−	0.238246i
$67$	7.68745			0.939171			0.469586	−	0.882887i	$-0.344403\pi$
$67$	7.68745			0.939171			0.469586	+	0.882887i	$0.344403\pi$
$68$	3.56933			0.432845
$69$	−0.462387	+	1.66919i	−0.0556649	+	0.200947i
$70$	−5.02421	+	1.17569i	−0.600508	+	0.140522i
$71$		−	5.42350i		−	0.643651i	−0.946799	−	0.321826i	$-0.895703\pi$
$71$		−	5.42350i		−	0.643651i	0.946799	−	0.321826i	$-0.104297\pi$
$72$	−1.54363	+	2.57240i	−0.181918	+	0.303160i
$73$			11.1709i			1.30745i	0.756732	+	0.653726i	$0.226795\pi$
$73$			11.1709i			1.30745i	−0.756732	+	0.653726i	$0.773205\pi$
$74$			0.324825i			0.0377602i
$75$	−1.99708	−	0.553217i	−0.230603	−	0.0638801i
$76$		−	8.08958i		−	0.927939i
$77$	−10.7836	+	2.52342i	−1.22891	+	0.287571i
$78$	−11.6874	−	3.23757i	−1.32334	−	0.366583i
$79$	12.2350			1.37654			0.688271	−	0.725454i	$-0.258370\pi$
$79$	12.2350			1.37654			0.688271	+	0.725454i	$0.258370\pi$
$80$	1.95027			0.218047
$81$	4.23444	+	7.94163i	0.470493	+	0.882404i
$82$		−	8.81948i		−	0.973949i
$83$	17.9170			1.96664			0.983321	−	0.181880i	$-0.0582181\pi$
$83$	17.9170			1.96664			0.983321	+	0.181880i	$0.0582181\pi$
$84$	−0.184936	+	4.57884i	−0.0201782	+	0.499593i
$85$	−6.96117			−0.755045
$86$		−	8.54266i		−	0.921178i
$87$	1.08025	−	3.89965i	0.115815	−	0.418086i
$88$	4.18593			0.446221
$89$	−1.21795			−0.129102			−0.0645510	−	0.997914i	$-0.520562\pi$
$89$	−1.21795			−0.129102			−0.0645510	+	0.997914i	$0.520562\pi$
$90$	3.01049	−	5.01687i	0.317334	−	0.528825i
$91$	−18.0379	+	4.22097i	−1.89089	+	0.442478i
$92$		−	1.00000i		−	0.104257i
$93$	−0.109614	+	0.395700i	−0.0113665	+	0.0410322i
$94$			0.174840i			0.0180334i
$95$			15.7769i			1.61868i
$96$	0.462387	−	1.66919i	0.0471922	−	0.170361i
$97$			16.7148i			1.69713i	0.529088	+	0.848567i	$0.322534\pi$
$97$			16.7148i			1.69713i	−0.529088	+	0.848567i	$0.677466\pi$
$98$	3.10600	+	6.27318i	0.313753	+	0.633687i
$99$	6.46151	−	10.7679i	0.649406	−	1.08221i
$100$	1.19644			0.119644
$101$	−10.8858			−1.08318			−0.541591	−	0.840642i	$-0.682178\pi$
$101$	−10.8858			−1.08318			−0.541591	+	0.840642i	$0.682178\pi$
$102$	−1.65041	+	5.95790i	−0.163415	+	0.589920i
$103$		−	1.91420i		−	0.188612i	−0.995543	−	0.0943058i	$-0.969937\pi$
$103$		−	1.91420i		−	0.188612i	0.995543	−	0.0943058i	$-0.0300631\pi$
$104$	7.00187			0.686589
$105$	0.360676	−	8.92999i	0.0351983	−	0.871478i
$106$	−5.65184			−0.548956
$107$		−	13.7767i		−	1.33185i	−0.746019	−	0.665924i	$-0.768037\pi$
$107$		−	13.7767i		−	1.33185i	0.746019	−	0.665924i	$-0.231963\pi$
$108$	−3.58007	−	3.76605i	−0.344492	−	0.362388i
$109$	−4.26102			−0.408131			−0.204066	−	0.978957i	$-0.565416\pi$
$109$	−4.26102			−0.408131			−0.204066	+	0.978957i	$0.565416\pi$
$110$	−8.16370			−0.778378
$111$	−0.542195	−	0.150195i	−0.0514629	−	0.0142559i
$112$	−0.602835	−	2.57616i	−0.0569626	−	0.243424i
$113$			9.50152i			0.893828i	0.894577	+	0.446914i	$0.147477\pi$
$113$			9.50152i			0.893828i	−0.894577	+	0.446914i	$0.852523\pi$
$114$	13.5031	+	3.74052i	1.26468	+	0.350332i
$115$			1.95027i			0.181864i
$116$			2.33625i			0.216916i
$117$	10.8083	−	18.0116i	0.999224	−	1.66517i
$118$			7.74076i			0.712595i
$119$	2.15172	+	9.19516i	0.197248	+	0.842919i
$120$	−0.901781	+	3.25538i	−0.0823210	+	0.297174i
$121$	−6.52200			−0.592909
$122$	9.18309			0.831398
$123$	14.7214	+	4.07802i	1.32738	+	0.367702i
$124$		−	0.237061i		−	0.0212887i
$125$	−12.0847			−1.08089
$126$	−7.55745	−	2.42589i	−0.673271	−	0.216116i
$127$	4.82854			0.428464			0.214232	−	0.976783i	$-0.431275\pi$
$127$	4.82854			0.428464			0.214232	+	0.976783i	$0.431275\pi$
$128$			1.00000i			0.0883883i
$129$	14.2593	+	3.95002i	1.25546	+	0.347780i
$130$	−13.6555			−1.19767
$131$	−18.7373			−1.63709			−0.818544	−	0.574444i	$-0.805218\pi$
$131$	−18.7373			−1.63709			−0.818544	+	0.574444i	$0.805218\pi$
$132$	−1.93552	+	6.98711i	−0.168465	+	0.608150i
$133$	20.8400	−	4.87669i	1.80706	−	0.422862i
$134$		−	7.68745i		−	0.664094i
$135$	6.98211	+	7.34482i	0.600924	+	0.632142i
$136$		−	3.56933i		−	0.306068i
$137$			6.80806i			0.581652i	0.956776	+	0.290826i	$0.0939301\pi$
$137$			6.80806i			0.581652i	−0.956776	+	0.290826i	$0.906070\pi$
$138$	1.66919	+	0.462387i	0.142091	+	0.0393610i
$139$			12.9800i			1.10095i	0.834852	+	0.550475i	$0.185553\pi$
$139$			12.9800i			1.10095i	−0.834852	+	0.550475i	$0.814447\pi$
$140$	1.17569	+	5.02421i	0.0993642	+	0.424623i
$141$	−0.291841	−	0.0808438i	−0.0245775	−	0.00680827i
$142$	−5.42350			−0.455130
$143$	−29.3093			−2.45097
$144$	2.57240	+	1.54363i	0.214366	+	0.128635i
$145$		−	4.55633i		−	0.378382i
$146$	11.1709			0.924508
$147$	−11.9073	+	2.28386i	−0.982098	+	0.188370i
$148$	0.324825			0.0267005
$149$		−	13.6518i		−	1.11840i	−0.829032	−	0.559201i	$-0.811108\pi$
$149$		−	13.6518i		−	1.11840i	0.829032	−	0.559201i	$-0.188892\pi$
$150$	−0.553217	+	1.99708i	−0.0451700	+	0.163061i
$151$	2.79942			0.227814			0.113907	−	0.993491i	$-0.463663\pi$
$151$	2.79942			0.227814			0.113907	+	0.993491i	$0.463663\pi$
$152$	−8.08958			−0.656152
$153$	−9.18173	−	5.50971i	−0.742299	−	0.445434i
$154$	2.52342	+	10.7836i	0.203343	+	0.868968i
$155$			0.462334i			0.0371355i
$156$	−3.23757	+	11.6874i	−0.259213	+	0.935745i
$157$			9.02729i			0.720456i	0.932864	+	0.360228i	$0.117301\pi$
$157$			9.02729i			0.720456i	−0.932864	+	0.360228i	$0.882699\pi$
$158$		−	12.2350i		−	0.973362i
$159$	2.61334	−	9.43401i	0.207251	−	0.748165i
$160$		−	1.95027i		−	0.154183i
$161$	2.57616	−	0.602835i	0.203030	−	0.0475101i
$162$	7.94163	−	4.23444i	0.623954	−	0.332689i
$163$	1.52485			0.119436			0.0597178	−	0.998215i	$-0.480980\pi$
$163$	1.52485			0.119436			0.0597178	+	0.998215i	$0.480980\pi$
$164$	−8.81948			−0.688686
$165$	3.77479	−	13.6268i	0.293867	−	1.06084i
$166$		−	17.9170i		−	1.39063i
$167$	7.96658			0.616472			0.308236	−	0.951310i	$-0.400261\pi$
$167$	7.96658			0.616472			0.308236	+	0.951310i	$0.400261\pi$
$168$	4.57884	+	0.184936i	0.353265	+	0.0142681i
$169$	−36.0261			−2.77124
$170$			6.96117i			0.533897i
$171$	−12.4873	+	20.8096i	−0.954927	+	1.59135i
$172$	−8.54266			−0.651372
$173$	−4.99294			−0.379606			−0.189803	−	0.981822i	$-0.560785\pi$
$173$	−4.99294			−0.379606			−0.189803	+	0.981822i	$0.560785\pi$
$174$	−3.89965	−	1.08025i	−0.295632	−	0.0818938i
$175$	0.721254	+	3.08221i	0.0545217	+	0.232993i
$176$		−	4.18593i		−	0.315526i
$177$	−12.9208	−	3.57923i	−0.971188	−	0.269031i
$178$			1.21795i			0.0912889i
$179$		−	9.35057i		−	0.698895i	−0.936956	−	0.349447i	$-0.886369\pi$
$179$		−	9.35057i		−	0.698895i	0.936956	−	0.349447i	$-0.113631\pi$
$180$	−5.01687	−	3.01049i	−0.373936	−	0.224389i
$181$		−	13.1624i		−	0.978355i	−0.872184	−	0.489178i	$-0.837297\pi$
$181$		−	13.1624i		−	0.978355i	0.872184	−	0.489178i	$-0.162703\pi$
$182$	4.22097	+	18.0379i	0.312879	+	1.33706i
$183$	−4.24614	+	15.3283i	−0.313884	+	1.13310i
$184$	−1.00000			−0.0737210
$185$	−0.633498			−0.0465757
$186$	0.395700	+	0.109614i	0.0290142	+	0.00803729i
$187$			14.9410i			1.09259i
$188$	0.174840			0.0127515
$189$	7.54375	−	11.4931i	0.548727	−	0.836002i
$190$	15.7769			1.14458
$191$			20.9301i			1.51445i	0.653154	+	0.757225i	$0.273445\pi$
$191$			20.9301i			1.51445i	−0.653154	+	0.757225i	$0.726555\pi$
$192$	−1.66919	−	0.462387i	−0.120463	−	0.0333699i
$193$	−2.02912			−0.146059			−0.0730296	−	0.997330i	$-0.523267\pi$
$193$	−2.02912			−0.146059			−0.0730296	+	0.997330i	$0.523267\pi$
$194$	16.7148			1.20005
$195$	6.31415	−	22.7937i	0.452166	−	1.63229i
$196$	6.27318	−	3.10600i	0.448084	−	0.221857i
$197$			17.2251i			1.22724i	0.789602	+	0.613620i	$0.210287\pi$
$197$			17.2251i			1.22724i	−0.789602	+	0.613620i	$0.789713\pi$
$198$	−10.7679	−	6.46151i	−0.765239	−	0.459199i
$199$			10.9423i			0.775682i	0.921726	+	0.387841i	$0.126779\pi$
$199$			10.9423i			0.775682i	−0.921726	+	0.387841i	$0.873221\pi$
$200$		−	1.19644i		−	0.0846009i
$201$	12.8318	+	3.55458i	0.905087	+	0.250721i
$202$			10.8858i			0.765925i
$203$	−6.01855	+	1.40837i	−0.422420	+	0.0988485i
$204$	5.95790	+	1.65041i	0.417136	+	0.115552i
$205$	17.2004			1.20133
$206$	−1.91420			−0.133368
$207$	−1.54363	+	2.57240i	−0.107289	+	0.178794i
$208$		−	7.00187i		−	0.485492i
$209$	33.8624			2.34231
$210$	−8.92999	−	0.360676i	−0.616228	−	0.0248890i
$211$	16.5236			1.13753			0.568765	−	0.822500i	$-0.307422\pi$
$211$	16.5236			1.13753			0.568765	+	0.822500i	$0.307422\pi$
$212$			5.65184i			0.388170i
$213$	2.50776	−	9.05286i	0.171829	−	0.620292i
$214$	−13.7767			−0.941759
$215$	16.6605			1.13624
$216$	−3.76605	+	3.58007i	−0.256247	+	0.243593i
$217$	0.610707	−	0.142909i	0.0414575	−	0.00970128i
$218$			4.26102i			0.288593i
$219$	−5.16527	+	18.6463i	−0.349037	+	1.26000i
$220$			8.16370i			0.550397i
$221$			24.9920i			1.68114i
$222$	−0.150195	+	0.542195i	−0.0100804	+	0.0363898i
$223$			6.83216i			0.457515i	0.973483	+	0.228758i	$0.0734663\pi$
$223$			6.83216i			0.457515i	−0.973483	+	0.228758i	$0.926534\pi$
$224$	−2.57616	+	0.602835i	−0.172127	+	0.0402786i
$225$	−3.07771	−	1.84685i	−0.205181	−	0.123123i
$226$	9.50152			0.632032
$227$	6.00651			0.398666			0.199333	−	0.979932i	$-0.436122\pi$
$227$	6.00651			0.398666			0.199333	+	0.979932i	$0.436122\pi$
$228$	3.74052	−	13.5031i	0.247722	−	0.894262i
$229$		−	10.3531i		−	0.684150i	−0.939673	−	0.342075i	$-0.888870\pi$
$229$		−	10.3531i		−	0.684150i	0.939673	−	0.342075i	$-0.111130\pi$
$230$	1.95027			0.128597
$231$	−19.1667	−	0.774129i	−1.26108	−	0.0509340i
$232$	2.33625			0.153382
$233$		−	9.24182i		−	0.605451i	−0.953078	−	0.302726i	$-0.902103\pi$
$233$		−	9.24182i		−	0.605451i	0.953078	−	0.302726i	$-0.0978966\pi$
$234$	−18.0116	−	10.8083i	−1.17745	−	0.706558i
$235$	−0.340985			−0.0222434
$236$	7.74076			0.503881
$237$	20.4225	+	5.65730i	1.32658	+	0.367481i
$238$	9.19516	−	2.15172i	0.596034	−	0.139475i
$239$			11.2399i			0.727047i	0.931585	+	0.363524i	$0.118426\pi$
$239$			11.2399i			0.727047i	−0.931585	+	0.363524i	$0.881574\pi$
$240$	3.25538	+	0.901781i	0.210134	+	0.0582097i
$241$		−	3.48754i		−	0.224652i	−0.993671	−	0.112326i	$-0.964170\pi$
$241$		−	3.48754i		−	0.224652i	0.993671	−	0.112326i	$-0.0358301\pi$
$242$			6.52200i			0.419250i
$243$	3.39598	+	15.2141i	0.217852	+	0.975982i
$244$		−	9.18309i		−	0.587887i
$245$	−12.2344	+	6.05754i	−0.781628	+	0.387002i
$246$	4.07802	−	14.7214i	0.260005	−	0.938602i
$247$	56.6422			3.60406
$248$	−0.237061			−0.0150534
$249$	29.9068	+	8.28458i	1.89527	+	0.525014i
$250$			12.0847i			0.764306i
$251$	0.529091			0.0333959			0.0166979	−	0.999861i	$-0.494685\pi$
$251$	0.529091			0.0333959			0.0166979	+	0.999861i	$0.494685\pi$
$252$	−2.42589	+	7.55745i	−0.152817	+	0.476075i
$253$	4.18593			0.263167
$254$		−	4.82854i		−	0.302970i
$255$	−11.6195	−	3.21876i	−0.727643	−	0.201566i
$256$	1.00000			0.0625000
$257$	−8.82434			−0.550447			−0.275224	−	0.961380i	$-0.588752\pi$
$257$	−8.82434			−0.550447			−0.275224	+	0.961380i	$0.588752\pi$
$258$	3.95002	−	14.2593i	0.245917	−	0.887747i
$259$	0.195816	+	0.836801i	0.0121674	+	0.0519963i
$260$			13.6555i			0.846881i
$261$	3.60630	−	6.00976i	0.223224	−	0.371995i
$262$			18.7373i			1.15760i
$263$		−	23.8672i		−	1.47171i	−0.677137	−	0.735857i	$-0.736780\pi$
$263$		−	23.8672i		−	1.47171i	0.677137	−	0.735857i	$-0.263220\pi$
$264$	6.98711	+	1.93552i	0.430027	+	0.119123i
$265$		−	11.0226i		−	0.677115i
$266$	−4.87669	−	20.8400i	−0.299009	−	1.27779i
$267$	−2.03298	−	0.563163i	−0.124417	−	0.0344650i
$268$	−7.68745			−0.469586
$269$	−0.592775			−0.0361421			−0.0180711	−	0.999837i	$-0.505753\pi$
$269$	−0.592775			−0.0361421			−0.0180711	+	0.999837i	$0.505753\pi$
$270$	7.34482	−	6.98211i	0.446992	−	0.424917i
$271$			2.86434i			0.173996i	0.996208	+	0.0869980i	$0.0277274\pi$
$271$			2.86434i			0.173996i	−0.996208	+	0.0869980i	$0.972273\pi$
$272$	−3.56933			−0.216423
$273$	−32.0604	−	1.29490i	−1.94039	−	0.0783707i
$274$	6.80806			0.411290
$275$			5.00820i			0.302006i
$276$	0.462387	−	1.66919i	0.0278324	−	0.100473i
$277$	−13.9675			−0.839224			−0.419612	−	0.907704i	$-0.637834\pi$
$277$	−13.9675			−0.839224			−0.419612	+	0.907704i	$0.637834\pi$
$278$	12.9800			0.778489
$279$	−0.365934	+	0.609815i	−0.0219079	+	0.0365087i
$280$	5.02421	−	1.17569i	0.300254	−	0.0702611i
$281$			16.7970i			1.00202i	0.865440	+	0.501012i	$0.167039\pi$
$281$			16.7970i			1.00202i	−0.865440	+	0.501012i	$0.832961\pi$
$282$	−0.0808438	+	0.291841i	−0.00481418	+	0.0173789i
$283$			17.3411i			1.03082i	0.856943	+	0.515411i	$0.172361\pi$
$283$			17.3411i			1.03082i	−0.856943	+	0.515411i	$0.827639\pi$
$284$			5.42350i			0.321826i
$285$	−7.29504	+	26.3346i	−0.432121	+	1.55993i
$286$			29.3093i			1.73310i
$287$	−5.31669	−	22.7204i	−0.313835	−	1.34114i
$288$	1.54363	−	2.57240i	0.0909590	−	0.151580i
$289$	−4.25987			−0.250581
$290$	−4.55633			−0.267557
$291$	−7.72873	+	27.9002i	−0.453066	+	1.63554i
$292$		−	11.1709i		−	0.653726i
$293$	−9.55084			−0.557966			−0.278983	−	0.960296i	$-0.589997\pi$
$293$	−9.55084			−0.557966			−0.278983	+	0.960296i	$0.589997\pi$
$294$	2.28386	+	11.9073i	0.133198	+	0.694448i
$295$	−15.0966			−0.878958
$296$		−	0.324825i		−	0.0188801i
$297$	15.7644	−	14.9859i	0.914744	−	0.869570i
$298$	−13.6518			−0.790830
$299$	7.00187			0.404928
$300$	1.99708	+	0.553217i	0.115302	+	0.0319400i
$301$	−5.14981	−	22.0072i	−0.296830	−	1.26848i
$302$		−	2.79942i		−	0.161088i
$303$	−18.1705	−	5.03347i	−1.04387	−	0.289166i
$304$			8.08958i			0.463969i
$305$			17.9095i			1.02550i
$306$	−5.50971	+	9.18173i	−0.314969	+	0.524885i
$307$		−	19.5248i		−	1.11434i	−0.830399	−	0.557169i	$-0.811888\pi$
$307$		−	19.5248i		−	1.11434i	0.830399	−	0.557169i	$-0.188112\pi$
$308$	10.7836	−	2.52342i	0.614453	−	0.143785i
$309$	0.885101	−	3.19516i	0.0503516	−	0.181766i
$310$	0.462334			0.0262588
$311$	20.0679			1.13795			0.568973	−	0.822356i	$-0.307341\pi$
$311$	20.0679			1.13795			0.568973	+	0.822356i	$0.307341\pi$
$312$	11.6874	+	3.23757i	0.661672	+	0.183292i
$313$		−	16.3669i		−	0.925114i	−0.886590	−	0.462557i	$-0.846932\pi$
$313$		−	16.3669i		−	0.925114i	0.886590	−	0.462557i	$-0.153068\pi$
$314$	9.02729			0.509439
$315$	4.73115	−	14.7391i	0.266570	−	0.830453i
$316$	−12.2350			−0.688271
$317$		−	8.14630i		−	0.457542i	−0.973480	−	0.228771i	$-0.926529\pi$
$317$		−	8.14630i		−	0.457542i	0.973480	−	0.228771i	$-0.0734707\pi$
$318$	−9.43401	−	2.61334i	−0.529033	−	0.146549i
$319$	−9.77938			−0.547540
$320$	−1.95027			−0.109024
$321$	6.37019	−	22.9960i	0.355550	−	1.28351i
$322$	−0.602835	−	2.57616i	−0.0335947	−	0.143564i
$323$		−	28.8744i		−	1.60662i
$324$	−4.23444	−	7.94163i	−0.235247	−	0.441202i
$325$			8.37729i			0.464689i
$326$		−	1.52485i		−	0.0844537i
$327$	−7.11245	−	1.97024i	−0.393319	−	0.108955i
$328$			8.81948i			0.486975i
$329$	0.105400	+	0.450415i	0.00581087	+	0.0248322i
$330$	−13.6268	−	3.77479i	−0.750129	−	0.207795i
$331$	−26.4631			−1.45454			−0.727271	−	0.686351i	$-0.759212\pi$
$331$	−26.4631			−1.45454			−0.727271	+	0.686351i	$0.759212\pi$
$332$	−17.9170			−0.983321
$333$	−0.835579	−	0.501408i	−0.0457894	−	0.0274770i
$334$		−	7.96658i		−	0.435912i
$335$	14.9926			0.819134
$336$	0.184936	−	4.57884i	0.0100891	−	0.249796i
$337$	27.8741			1.51840			0.759201	−	0.650857i	$-0.225590\pi$
$337$	27.8741			1.51840			0.759201	+	0.650857i	$0.225590\pi$
$338$			36.0261i			1.95956i
$339$	−4.39338	+	15.8599i	−0.238616	+	0.861389i
$340$	6.96117			0.377522
$341$	0.992321			0.0537372
$342$	20.8096	+	12.4873i	1.12526	+	0.675235i
$343$	11.7832	+	14.2883i	0.636235	+	0.771496i
$344$			8.54266i			0.460589i
$345$	−0.901781	+	3.25538i	−0.0485503	+	0.175264i
$346$			4.99294i			0.268422i
$347$			10.8116i			0.580398i	0.956966	+	0.290199i	$0.0937215\pi$
$347$			10.8116i			0.580398i	−0.956966	+	0.290199i	$0.906278\pi$
$348$	−1.08025	+	3.89965i	−0.0579077	+	0.209043i
$349$		−	2.76386i		−	0.147946i	−0.997260	−	0.0739731i	$-0.976432\pi$
$349$		−	2.76386i		−	0.147946i	0.997260	−	0.0739731i	$-0.0235679\pi$
$350$	3.08221	−	0.721254i	0.164751	−	0.0385527i
$351$	26.3694	−	25.0671i	1.40749	−	1.33799i
$352$	−4.18593			−0.223111
$353$	−23.4616			−1.24873			−0.624367	−	0.781131i	$-0.714643\pi$
$353$	−23.4616			−1.24873			−0.624367	+	0.781131i	$0.714643\pi$
$354$	−3.57923	+	12.9208i	−0.190234	+	0.686733i
$355$		−	10.5773i		−	0.561385i
$356$	1.21795			0.0645510
$357$	−0.660098	+	16.3434i	−0.0349361	+	0.864985i
$358$	−9.35057			−0.494193
$359$		−	11.5092i		−	0.607435i	−0.952762	−	0.303717i	$-0.901772\pi$
$359$		−	11.5092i		−	0.607435i	0.952762	−	0.303717i	$-0.0982279\pi$
$360$	−3.01049	+	5.01687i	−0.158667	+	0.264412i
$361$	−46.4414			−2.44428
$362$	−13.1624			−0.691802
$363$	−10.8865	−	3.01569i	−0.571391	−	0.158283i
$364$	18.0379	−	4.22097i	0.945443	−	0.221239i
$365$			21.7862i			1.14034i
$366$	15.3283	+	4.24614i	0.801224	+	0.221949i
$367$		−	8.53645i		−	0.445599i	−0.974864	−	0.222800i	$-0.928480\pi$
$367$		−	8.53645i		−	0.445599i	0.974864	−	0.222800i	$-0.0715196\pi$
$368$			1.00000i			0.0521286i
$369$	22.6872	+	13.6140i	1.18105	+	0.708715i
$370$			0.633498i			0.0329340i
$371$	−14.5600	+	3.40713i	−0.755920	+	0.176889i
$372$	0.109614	−	0.395700i	0.00568323	−	0.0205161i
$373$	−31.5142			−1.63174			−0.815871	−	0.578234i	$-0.803742\pi$
$373$	−31.5142			−1.63174			−0.815871	+	0.578234i	$0.803742\pi$
$374$	14.9410			0.772579
$375$	−20.1717	−	5.58783i	−1.04166	−	0.288554i
$376$		−	0.174840i		−	0.00901668i
$377$	−16.3581			−0.842486
$378$	−11.4931	−	7.54375i	−0.591142	−	0.388008i
$379$	−15.0834			−0.774780			−0.387390	−	0.921916i	$-0.626623\pi$
$379$	−15.0834			−0.774780			−0.387390	+	0.921916i	$0.626623\pi$
$380$		−	15.7769i		−	0.809338i
$381$	8.05975	+	2.23266i	0.412914	+	0.114382i
$382$	20.9301			1.07088
$383$	5.99148			0.306150			0.153075	−	0.988215i	$-0.451082\pi$
$383$	5.99148			0.306150			0.153075	+	0.988215i	$0.451082\pi$
$384$	−0.462387	+	1.66919i	−0.0235961	+	0.0851805i
$385$	−21.0310	+	4.92137i	−1.07184	+	0.250816i
$386$			2.02912i			0.103280i
$387$	21.9751	+	13.1867i	1.11706	+	0.670316i
$388$		−	16.7148i		−	0.848567i
$389$			1.08008i			0.0547622i	0.999625	+	0.0273811i	$0.00871677\pi$
$389$			1.08008i			0.0547622i	−0.999625	+	0.0273811i	$0.991283\pi$
$390$	−22.7937	−	6.31415i	−1.15420	−	0.319730i
$391$		−	3.56933i		−	0.180509i
$392$	−3.10600	−	6.27318i	−0.156877	−	0.316843i
$393$	−31.2762	−	8.66390i	−1.57767	−	0.437036i
$394$	17.2251			0.867789
$395$	23.8615			1.20060
$396$	−6.46151	+	10.7679i	−0.324703	+	0.541106i
$397$			19.0645i			0.956818i	0.878137	+	0.478409i	$0.158786\pi$
$397$			19.0645i			0.956818i	−0.878137	+	0.478409i	$0.841214\pi$
$398$	10.9423			0.548490
$399$	37.0409	+	1.49606i	1.85437	+	0.0748965i
$400$	−1.19644			−0.0598219
$401$			3.58379i			0.178966i	0.995988	+	0.0894831i	$0.0285215\pi$
$401$			3.58379i			0.178966i	−0.995988	+	0.0894831i	$0.971479\pi$
$402$	3.55458	−	12.8318i	0.177286	−	0.639993i
$403$	1.65987			0.0826840
$404$	10.8858			0.541591
$405$	8.25831	+	15.4883i	0.410359	+	0.769622i
$406$	1.40837	+	6.01855i	0.0698965	+	0.298696i
$407$			1.35969i			0.0673976i
$408$	1.65041	−	5.95790i	0.0817077	−	0.294960i
$409$			3.95955i			0.195787i	0.995197	+	0.0978936i	$0.0312105\pi$
$409$			3.95955i			0.195787i	−0.995197	+	0.0978936i	$0.968790\pi$
$410$		−	17.2004i		−	0.849467i
$411$	−3.14796	+	11.3640i	−0.155278	+	0.560543i
$412$			1.91420i			0.0943058i
$413$	4.66640	+	19.9414i	0.229619	+	0.981253i
$414$	2.57240	+	1.54363i	0.126426	+	0.0758651i
$415$	34.9429			1.71528
$416$	−7.00187			−0.343295
$417$	−6.00179	+	21.6661i	−0.293909	+	1.06099i
$418$		−	33.8624i		−	1.65627i
$419$	−13.2658			−0.648078			−0.324039	−	0.946044i	$-0.605041\pi$
$419$	−13.2658			−0.648078			−0.324039	+	0.946044i	$0.605041\pi$
$420$	−0.360676	+	8.92999i	−0.0175992	+	0.435739i
$421$	21.2102			1.03372			0.516861	−	0.856069i	$-0.327100\pi$
$421$	21.2102			1.03372			0.516861	+	0.856069i	$0.327100\pi$
$422$		−	16.5236i		−	0.804355i
$423$	−0.449757	−	0.269887i	−0.0218680	−	0.0131224i
$424$	5.65184			0.274478
$425$	4.27048			0.207149
$426$	−9.05286	−	2.50776i	−0.438613	−	0.121501i
$427$	23.6571	−	5.53589i	1.14485	−	0.267900i
$428$			13.7767i			0.665924i
$429$	−48.9228	−	13.5523i	−2.36202	−	0.654309i
$430$		−	16.6605i		−	0.803441i
$431$			8.01994i			0.386307i	0.981169	+	0.193153i	$0.0618715\pi$
$431$			8.01994i			0.386307i	−0.981169	+	0.193153i	$0.938128\pi$
$432$	3.58007	+	3.76605i	0.172246	+	0.181194i
$433$		−	20.1632i		−	0.968981i	−0.874796	−	0.484491i	$-0.839005\pi$
$433$		−	20.1632i		−	0.968981i	0.874796	−	0.484491i	$-0.160995\pi$
$434$	−0.142909	−	0.610707i	−0.00685984	−	0.0293149i
$435$	2.10679	−	7.60538i	0.101013	−	0.364650i
$436$	4.26102			0.204066
$437$	−8.08958			−0.386977
$438$	18.6463	+	5.16527i	0.890955	+	0.246806i
$439$			39.5350i			1.88690i	0.331508	+	0.943452i	$0.392442\pi$
$439$			39.5350i			1.88690i	−0.331508	+	0.943452i	$0.607558\pi$
$440$	8.16370			0.389189
$441$	−20.9316	−	1.69359i	−0.996743	−	0.0806470i
$442$	24.9920			1.18875
$443$		−	18.1483i		−	0.862254i	−0.902291	−	0.431127i	$-0.858116\pi$
$443$		−	18.1483i		−	0.862254i	0.902291	−	0.431127i	$-0.141884\pi$
$444$	0.542195	+	0.150195i	0.0257314	+	0.00712794i
$445$	−2.37533			−0.112601
$446$	6.83216			0.323512
$447$	6.31244	−	22.7875i	0.298568	−	1.07781i
$448$	0.602835	+	2.57616i	0.0284813	+	0.121712i
$449$		−	23.0015i		−	1.08551i	−0.839892	−	0.542754i	$-0.817381\pi$
$449$		−	23.0015i		−	1.08551i	0.839892	−	0.542754i	$-0.182619\pi$
$450$	−1.84685	+	3.07771i	−0.0870614	+	0.145085i
$451$		−	36.9177i		−	1.73839i
$452$		−	9.50152i		−	0.446914i
$453$	4.67276	+	1.29442i	0.219546	+	0.0608170i
$454$		−	6.00651i		−	0.281899i
$455$	−35.1788	+	8.23204i	−1.64921	+	0.385924i
$456$	−13.5031	−	3.74052i	−0.632339	−	0.175166i
$457$	−5.70940			−0.267074			−0.133537	−	0.991044i	$-0.542634\pi$
$457$	−5.70940			−0.267074			−0.133537	+	0.991044i	$0.542634\pi$
$458$	−10.3531			−0.483767
$459$	−12.7784	−	13.4423i	−0.596447	−	0.627432i
$460$		−	1.95027i		−	0.0909319i
$461$	21.1482			0.984969			0.492485	−	0.870321i	$-0.336089\pi$
$461$	21.1482			0.984969			0.492485	+	0.870321i	$0.336089\pi$
$462$	−0.774129	+	19.1667i	−0.0360157	+	0.891716i
$463$	−3.64251			−0.169282			−0.0846410	−	0.996412i	$-0.526974\pi$
$463$	−3.64251			−0.169282			−0.0846410	+	0.996412i	$0.526974\pi$
$464$		−	2.33625i		−	0.108458i
$465$	−0.213777	+	0.771723i	−0.00991369	+	0.0357878i
$466$	−9.24182			−0.428119
$467$	7.13820			0.330317			0.165158	−	0.986267i	$-0.447186\pi$
$467$	7.13820			0.330317			0.165158	+	0.986267i	$0.447186\pi$
$468$	−10.8083	+	18.0116i	−0.499612	+	0.832585i
$469$	−4.63426	−	19.8041i	−0.213990	−	0.914468i
$470$			0.340985i			0.0157285i
$471$	−4.17411	+	15.0683i	−0.192333	+	0.694309i
$472$		−	7.74076i		−	0.356297i
$473$		−	35.7590i		−	1.64420i
$474$	5.65730	−	20.4225i	0.259848	−	0.938037i
$475$		−	9.67868i		−	0.444088i
$476$	−2.15172	−	9.19516i	−0.0986239	−	0.421460i
$477$	8.72433	−	14.5388i	0.399460	−	0.665685i
$478$	11.2399			0.514100
$479$	25.8976			1.18329			0.591646	−	0.806198i	$-0.298478\pi$
$479$	25.8976			1.18329			0.591646	+	0.806198i	$0.298478\pi$
$480$	0.901781	−	3.25538i	0.0411605	−	0.148587i
$481$			2.27438i			0.103703i
$482$	−3.48754			−0.158853
$483$	4.57884	+	0.184936i	0.208345	+	0.00841488i
$484$	6.52200			0.296454
$485$			32.5985i			1.48022i
$486$	15.2141	−	3.39598i	0.690123	−	0.154045i
$487$	−19.2742			−0.873395			−0.436698	−	0.899608i	$-0.643852\pi$
$487$	−19.2742			−0.873395			−0.436698	+	0.899608i	$0.643852\pi$
$488$	−9.18309			−0.415699
$489$	2.54527	+	0.705072i	0.115101	+	0.0318845i
$490$	6.05754	+	12.2344i	0.273652	+	0.552694i
$491$		−	31.9607i		−	1.44237i	−0.692744	−	0.721184i	$-0.743598\pi$
$491$		−	31.9607i		−	1.44237i	0.692744	−	0.721184i	$-0.256402\pi$
$492$	−14.7214	−	4.07802i	−0.663692	−	0.183851i
$493$			8.33886i			0.375563i
$494$		−	56.6422i		−	2.54845i
$495$	12.6017	−	21.0003i	0.566404	−	0.943892i
$496$			0.237061i			0.0106444i
$497$	−13.9718	+	3.26948i	−0.626721	+	0.146656i
$498$	8.28458	−	29.9068i	0.371241	−	1.34016i
$499$	−36.6266			−1.63963			−0.819815	−	0.572628i	$-0.805924\pi$
$499$	−36.6266			−1.63963			−0.819815	+	0.572628i	$0.805924\pi$
$500$	12.0847			0.540446
$501$	13.2977	+	3.68364i	0.594099	+	0.164573i
$502$		−	0.529091i		−	0.0236145i
$503$	12.8526			0.573070			0.286535	−	0.958070i	$-0.407497\pi$
$503$	12.8526			0.573070			0.286535	+	0.958070i	$0.407497\pi$
$504$	7.55745	+	2.42589i	0.336636	+	0.108058i
$505$	−21.2304			−0.944738
$506$		−	4.18593i		−	0.186087i
$507$	−60.1345	−	16.6580i	−2.67067	−	0.739809i
$508$	−4.82854			−0.214232
$509$	6.44339			0.285598			0.142799	−	0.989752i	$-0.454390\pi$
$509$	6.44339			0.285598			0.142799	+	0.989752i	$0.454390\pi$
$510$	−3.21876	+	11.6195i	−0.142529	+	0.514521i
$511$	28.7779	−	6.73419i	1.27306	−	0.297903i
$512$		−	1.00000i		−	0.0441942i
$513$	−30.4658	+	28.9613i	−1.34510	+	1.27867i
$514$			8.82434i			0.389225i
$515$		−	3.73321i		−	0.164505i
$516$	−14.2593	−	3.95002i	−0.627732	−	0.173890i
$517$			0.731867i			0.0321875i
$518$	0.836801	−	0.195816i	0.0367669	−	0.00860366i
$519$	−8.33417	−	2.30867i	−0.365829	−	0.101339i
$520$	13.6555			0.598835
$521$	−32.2374			−1.41235			−0.706174	−	0.708039i	$-0.749580\pi$
$521$	−32.2374			−1.41235			−0.706174	+	0.708039i	$0.749580\pi$
$522$	−6.00976	−	3.60630i	−0.263040	−	0.157843i
$523$			2.19484i			0.0959735i	0.998848	+	0.0479867i	$0.0152805\pi$
$523$			2.19484i			0.0959735i	−0.998848	+	0.0479867i	$0.984719\pi$
$524$	18.7373			0.818544
$525$	−0.221264	+	5.47830i	−0.00965677	+	0.239093i
$526$	−23.8672			−1.04066
$527$		−	0.846150i		−	0.0368589i
$528$	1.93552	−	6.98711i	0.0842327	−	0.304075i
$529$	−1.00000			−0.0434783
$530$	−11.0226			−0.478793
$531$	−19.9123	−	11.9488i	−0.864120	−	0.518535i
$532$	−20.8400	+	4.87669i	−0.903531	+	0.211431i
$533$		−	61.7528i		−	2.67481i
$534$	−0.563163	+	2.03298i	−0.0243704	+	0.0879758i
$535$		−	26.8684i		−	1.16162i
$536$			7.68745i			0.332047i
$537$	4.32359	−	15.6079i	0.186577	−	0.673530i
$538$			0.592775i			0.0255563i
$539$	13.0015	+	26.2591i	0.560013	+	1.13106i
$540$	−6.98211	−	7.34482i	−0.300462	−	0.316071i
$541$	−42.5880			−1.83100			−0.915502	−	0.402314i	$-0.868206\pi$
$541$	−42.5880			−1.83100			−0.915502	+	0.402314i	$0.868206\pi$
$542$	2.86434			0.123034
$543$	6.08614	−	21.9706i	0.261181	−	0.942849i
$544$			3.56933i			0.153034i
$545$	−8.31014			−0.355968
$546$	−1.29490	+	32.0604i	−0.0554165	+	1.37206i
$547$	7.98052			0.341222			0.170611	−	0.985338i	$-0.445426\pi$
$547$	7.98052			0.341222			0.170611	+	0.985338i	$0.445426\pi$
$548$		−	6.80806i		−	0.290826i
$549$	−14.1752	+	23.6225i	−0.604985	+	1.00819i
$550$	5.00820			0.213550
$551$	18.8993			0.805137
$552$	−1.66919	−	0.462387i	−0.0710455	−	0.0196805i
$553$	−7.37567	−	31.5192i	−0.313645	−	1.34033i
$554$			13.9675i			0.593421i
$555$	−1.05743	−	0.292921i	−0.0448853	−	0.0124338i
$556$		−	12.9800i		−	0.550475i
$557$			15.3471i			0.650278i	0.945666	+	0.325139i	$0.105411\pi$
$557$			15.3471i			0.650278i	−0.945666	+	0.325139i	$0.894589\pi$
$558$	0.609815	+	0.365934i	0.0258155	+	0.0154912i
$559$		−	59.8145i		−	2.52989i
$560$	−1.17569	−	5.02421i	−0.0496821	−	0.212312i
$561$	−6.90851	+	24.9393i	−0.291678	+	1.05294i
$562$	16.7970			0.708539
$563$	33.4328			1.40902			0.704512	−	0.709692i	$-0.251166\pi$
$563$	33.4328			1.40902			0.704512	+	0.709692i	$0.251166\pi$
$564$	0.291841	+	0.0808438i	0.0122887	+	0.00340414i
$565$			18.5306i			0.779586i
$566$	17.3411			0.728902
$567$	17.9062	−	15.6961i	0.751991	−	0.659174i
$568$	5.42350			0.227565
$569$		−	29.4280i		−	1.23369i	−0.787087	−	0.616843i	$-0.788411\pi$
$569$		−	29.4280i		−	1.23369i	0.787087	−	0.616843i	$-0.211589\pi$
$570$	26.3346	+	7.29504i	1.10304	+	0.305555i
$571$	25.1047			1.05060			0.525299	−	0.850918i	$-0.323953\pi$
$571$	25.1047			1.05060			0.525299	+	0.850918i	$0.323953\pi$
$572$	29.3093			1.22548
$573$	−9.67782	+	34.9364i	−0.404297	+	1.45949i
$574$	−22.7204	+	5.31669i	−0.948330	+	0.221915i
$575$		−	1.19644i		−	0.0498949i
$576$	−2.57240	−	1.54363i	−0.107183	−	0.0643177i
$577$		−	20.8099i		−	0.866329i	−0.901315	−	0.433165i	$-0.857397\pi$
$577$		−	20.8099i		−	0.866329i	0.901315	−	0.433165i	$-0.142603\pi$
$578$			4.25987i			0.177187i
$579$	−3.38699	−	0.938240i	−0.140758	−	0.0389919i
$580$			4.55633i			0.189191i
$581$	−10.8010	−	46.1569i	−0.448100	−	1.91491i
$582$	27.9002	+	7.72873i	1.15650	+	0.320366i
$583$	−23.6582			−0.979823
$584$	−11.1709			−0.462254
$585$	21.0790	−	35.1275i	0.871511	−	1.45234i
$586$			9.55084i			0.394541i
$587$	−33.0545			−1.36431			−0.682153	−	0.731209i	$-0.738956\pi$
$587$	−33.0545			−1.36431			−0.682153	+	0.731209i	$0.738956\pi$
$588$	11.9073	−	2.28386i	0.491049	−	0.0941849i
$589$	−1.91773			−0.0790185
$590$			15.0966i			0.621517i
$591$	−7.96468	+	28.7520i	−0.327623	+	1.18270i
$592$	−0.324825			−0.0133502
$593$	−15.1171			−0.620786			−0.310393	−	0.950608i	$-0.600461\pi$
$593$	−15.1171			−0.620786			−0.310393	+	0.950608i	$0.600461\pi$
$594$	−14.9859	−	15.7644i	−0.614879	−	0.646822i
$595$	4.19644	+	17.9331i	0.172037	+	0.735184i
$596$			13.6518i			0.559201i
$597$	−5.05960	+	18.2649i	−0.207076	+	0.747531i
$598$		−	7.00187i		−	0.286328i
$599$		−	29.2716i		−	1.19601i	−0.801494	−	0.598003i	$-0.795961\pi$
$599$		−	29.2716i		−	1.19601i	0.801494	−	0.598003i	$-0.204039\pi$
$600$	0.553217	−	1.99708i	0.0225850	−	0.0815305i
$601$		−	8.67668i		−	0.353929i	−0.984217	−	0.176965i	$-0.943372\pi$
$601$		−	8.67668i		−	0.353929i	0.984217	−	0.176965i	$-0.0566278\pi$
$602$	−22.0072	+	5.14981i	−0.896948	+	0.209891i
$603$	19.7752	+	11.8665i	0.805307	+	0.483243i
$604$	−2.79942			−0.113907
$605$	−12.7197			−0.517128
$606$	−5.03347	+	18.1705i	−0.204471	+	0.738128i
$607$		−	44.4740i		−	1.80515i	−0.430538	−	0.902573i	$-0.641676\pi$
$607$		−	44.4740i		−	1.80515i	0.430538	−	0.902573i	$-0.358324\pi$
$608$	8.08958			0.328076
$609$	−10.6973	−	0.432057i	−0.433478	−	0.0175078i
$610$	17.9095			0.725135
$611$			1.22421i			0.0495260i
$612$	9.18173	+	5.50971i	0.371150	+	0.222717i
$613$	9.37475			0.378643			0.189321	−	0.981915i	$-0.439371\pi$
$613$	9.37475			0.378643			0.189321	+	0.981915i	$0.439371\pi$
$614$	−19.5248			−0.787956
$615$	28.7107	+	7.95325i	1.15773	+	0.320706i
$616$	−2.52342	−	10.7836i	−0.101672	−	0.434484i
$617$			19.2861i			0.776428i	0.921569	+	0.388214i	$0.126908\pi$
$617$			19.2861i			0.776428i	−0.921569	+	0.388214i	$0.873092\pi$
$618$	−3.19516	−	0.885101i	−0.128528	−	0.0356040i
$619$			38.4993i			1.54742i	0.633542	+	0.773709i	$0.281601\pi$
$619$			38.4993i			1.54742i	−0.633542	+	0.773709i	$0.718399\pi$
$620$		−	0.462334i		−	0.0185678i
$621$	−3.76605	+	3.58007i	−0.151126	+	0.143663i
$622$		−	20.0679i		−	0.804649i
$623$	0.734221	+	3.13762i	0.0294159	+	0.125706i
$624$	3.23757	−	11.6874i	0.129607	−	0.467872i
$625$	−17.5864			−0.703454
$626$	−16.3669			−0.654154
$627$	56.5228	+	15.6576i	2.25730	+	0.625303i
$628$		−	9.02729i		−	0.360228i
$629$	1.15941			0.0462287
$630$	−14.7391	−	4.73115i	−0.587219	−	0.188494i
$631$	6.71012			0.267126			0.133563	−	0.991040i	$-0.457358\pi$
$631$	6.71012			0.267126			0.133563	+	0.991040i	$0.457358\pi$
$632$			12.2350i			0.486681i
$633$	27.5810	+	7.64029i	1.09625	+	0.303674i
$634$	−8.14630			−0.323531
$635$	9.41697			0.373701
$636$	−2.61334	+	9.43401i	−0.103626	+	0.374083i
$637$	21.7478	+	43.9240i	0.861678	+	1.74033i
$638$			9.77938i			0.387169i
$639$	8.37186	−	13.9514i	0.331186	−	0.551909i
$640$			1.95027i			0.0770913i
$641$		−	14.0351i		−	0.554354i	−0.960819	−	0.277177i	$-0.910601\pi$
$641$		−	14.0351i		−	0.554354i	0.960819	−	0.277177i	$-0.0893988\pi$
$642$	−22.9960	−	6.37019i	−0.907581	−	0.251412i
$643$			14.3748i			0.566887i	0.958989	+	0.283443i	$0.0914768\pi$
$643$			14.3748i			0.566887i	−0.958989	+	0.283443i	$0.908523\pi$
$644$	−2.57616	+	0.602835i	−0.101515	+	0.0237550i
$645$	27.8096	+	7.70361i	1.09500	+	0.303329i
$646$	−28.8744			−1.13605
$647$	−18.7105			−0.735587			−0.367793	−	0.929908i	$-0.619887\pi$
$647$	−18.7105			−0.735587			−0.367793	+	0.929908i	$0.619887\pi$
$648$	−7.94163	+	4.23444i	−0.311977	+	0.166345i
$649$			32.4023i			1.27190i
$650$	8.37729			0.328584
$651$	1.08547	+	0.0438412i	0.0425428	+	0.00171827i
$652$	−1.52485			−0.0597178
$653$		−	21.3030i		−	0.833650i	−0.908987	−	0.416825i	$-0.863143\pi$
$653$		−	21.3030i		−	0.833650i	0.908987	−	0.416825i	$-0.136857\pi$
$654$	−1.97024	+	7.11245i	−0.0770425	+	0.278119i
$655$	−36.5429			−1.42785
$656$	8.81948			0.344343
$657$	−17.2436	+	28.7359i	−0.672738	+	1.12109i
$658$	0.450415	−	0.105400i	0.0175590	−	0.00410891i
$659$			20.9096i			0.814524i	0.913311	+	0.407262i	$0.133516\pi$
$659$			20.9096i			0.814524i	−0.913311	+	0.407262i	$0.866484\pi$
$660$	−3.77479	+	13.6268i	−0.146934	+	0.530422i
$661$		−	42.4302i		−	1.65035i	−0.564881	−	0.825173i	$-0.691078\pi$
$661$		−	42.4302i		−	1.65035i	0.564881	−	0.825173i	$-0.308922\pi$
$662$			26.4631i			1.02852i
$663$	−11.5560	+	41.7164i	−0.448797	+	1.62013i
$664$			17.9170i			0.695313i
$665$	40.6438	−	9.51087i	1.57610	−	0.368816i
$666$	−0.501408	+	0.835579i	−0.0194292	+	0.0323780i
$667$	2.33625			0.0904600
$668$	−7.96658			−0.308236
$669$	−3.15911	+	11.4042i	−0.122138	+	0.440911i
$670$		−	14.9926i		−	0.579215i
$671$	38.4397			1.48395
$672$	−4.57884	−	0.184936i	−0.176633	−	0.00713406i
$673$	42.5206			1.63905			0.819523	−	0.573046i	$-0.194238\pi$
$673$	42.5206			1.63905			0.819523	+	0.573046i	$0.194238\pi$
$674$		−	27.8741i		−	1.07367i
$675$	−4.28332	−	4.50584i	−0.164865	−	0.173430i
$676$	36.0261			1.38562
$677$	19.5004			0.749460			0.374730	−	0.927134i	$-0.377735\pi$
$677$	19.5004			0.749460			0.374730	+	0.927134i	$0.377735\pi$
$678$	15.8599	+	4.39338i	0.609094	+	0.168727i
$679$	43.0600	−	10.0763i	1.65249	−	0.386692i
$680$		−	6.96117i		−	0.266949i
$681$	10.0260	+	2.77733i	0.384197	+	0.106428i
$682$		−	0.992321i		−	0.0379979i
$683$		−	24.8146i		−	0.949505i	−0.880119	−	0.474753i	$-0.842538\pi$
$683$		−	24.8146i		−	0.949505i	0.880119	−	0.474753i	$-0.157462\pi$
$684$	12.4873	−	20.8096i	0.477463	−	0.795675i
$685$			13.2776i			0.507310i
$686$	14.2883	−	11.7832i	0.545530	−	0.449886i
$687$	4.78713	−	17.2812i	0.182640	−	0.659320i
$688$	8.54266			0.325686
$689$	−39.5735			−1.50763
$690$	3.25538	+	0.901781i	0.123930	+	0.0343302i
$691$			2.77055i			0.105397i	0.998610	+	0.0526983i	$0.0167822\pi$
$691$			2.77055i			0.105397i	−0.998610	+	0.0526983i	$0.983218\pi$
$692$	4.99294			0.189803
$693$	−31.6349	−	10.1546i	−1.20171	−	0.385742i
$694$	10.8116			0.410403
$695$			25.3146i			0.960236i
$696$	3.89965	+	1.08025i	0.147816	+	0.0409469i
$697$	−31.4797			−1.19238
$698$	−2.76386			−0.104614
$699$	4.27330	−	15.4264i	0.161631	−	0.583478i
$700$	−0.721254	−	3.08221i	−0.0272609	−	0.116497i
$701$			21.9857i			0.830388i	0.909733	+	0.415194i	$0.136286\pi$
$701$			21.9857i			0.830388i	−0.909733	+	0.415194i	$0.863714\pi$
$702$	−25.0671	−	26.3694i	−0.946098	−	0.995248i
$703$		−	2.62770i		−	0.0991056i
$704$			4.18593i			0.157763i
$705$	−0.569170	−	0.157667i	−0.0214362	−	0.00593810i
$706$			23.4616i			0.882988i
$707$	6.56237	+	28.0436i	0.246803	+	1.05469i
$708$	12.9208	+	3.57923i	0.485594	+	0.134516i
$709$	21.8317			0.819908			0.409954	−	0.912106i	$-0.365545\pi$
$709$	21.8317			0.819908			0.409954	+	0.912106i	$0.365545\pi$
$710$	−10.5773			−0.396959
$711$	31.4732	+	18.8862i	1.18034	+	0.708288i
$712$		−	1.21795i		−	0.0456445i
$713$	−0.237061			−0.00887801
$714$	16.3434	+	0.660098i	0.611637	+	0.0247035i
$715$	−57.1611			−2.13771
$716$			9.35057i			0.349447i
$717$	−5.19718	+	18.7615i	−0.194092	+	0.700661i
$718$	−11.5092			−0.429521
$719$	−19.3398			−0.721253			−0.360627	−	0.932710i	$-0.617437\pi$
$719$	−19.3398			−0.721253			−0.360627	+	0.932710i	$0.617437\pi$
$720$	5.01687	+	3.01049i	0.186968	+	0.112194i
$721$	−4.93128	+	1.15395i	−0.183650	+	0.0429752i
$722$			46.4414i			1.72837i
$723$	1.61259	−	5.82136i	0.0599730	−	0.216499i
$724$			13.1624i			0.489178i
$725$			2.79518i			0.103810i
$726$	−3.01569	+	10.8865i	−0.111923	+	0.404034i
$727$			44.0259i			1.63283i	0.577465	+	0.816415i	$0.304042\pi$
$727$			44.0259i			1.63283i	−0.577465	+	0.816415i	$0.695958\pi$
$728$	−4.22097	−	18.0379i	−0.156440	−	0.668529i
$729$	−1.36625	+	26.9654i	−0.0506018	+	0.998719i
$730$	21.7862			0.806345
$731$	−30.4916			−1.12777
$732$	4.24614	−	15.3283i	0.156942	−	0.566551i
$733$		−	7.09779i		−	0.262163i	−0.991372	−	0.131082i	$-0.958155\pi$
$733$		−	7.09779i		−	0.262163i	0.991372	−	0.131082i	$-0.0418450\pi$
$734$	−8.53645			−0.315086
$735$	−23.2225	+	4.45415i	−0.856575	+	0.164294i
$736$	1.00000			0.0368605
$737$		−	32.1791i		−	1.18533i
$738$	13.6140	−	22.6872i	0.501138	−	0.835127i
$739$	−2.54034			−0.0934479			−0.0467239	−	0.998908i	$-0.514878\pi$
$739$	−2.54034			−0.0934479			−0.0467239	+	0.998908i	$0.514878\pi$
$740$	0.633498			0.0232878
$741$	94.5466	+	26.1906i	3.47326	+	0.962137i
$742$	3.40713	+	14.5600i	0.125080	+	0.534516i
$743$		−	24.3821i		−	0.894493i	−0.894411	−	0.447247i	$-0.852405\pi$
$743$		−	24.3821i		−	0.894493i	0.894411	−	0.447247i	$-0.147595\pi$
$744$	−0.395700	−	0.109614i	−0.0145071	−	0.00401865i
$745$		−	26.6248i		−	0.975458i
$746$			31.5142i			1.15382i
$747$	46.0895	+	27.6571i	1.68633	+	1.01192i
$748$		−	14.9410i		−	0.546296i
$749$	−35.4911	+	8.30511i	−1.29682	+	0.303462i
$750$	−5.58783	+	20.1717i	−0.204039	+	0.736568i
$751$	20.8040			0.759147			0.379574	−	0.925162i	$-0.376071\pi$
$751$	20.8040			0.759147			0.379574	+	0.925162i	$0.376071\pi$
$752$	−0.174840			−0.00637575
$753$	0.883153	+	0.244645i	0.0321839	+	0.00891535i
$754$			16.3581i			0.595728i
$755$	5.45963			0.198696
$756$	−7.54375	+	11.4931i	−0.274363	+	0.418001i
$757$	32.9030			1.19588			0.597941	−	0.801540i	$-0.295986\pi$
$757$	32.9030			1.19588			0.597941	+	0.801540i	$0.295986\pi$
$758$			15.0834i			0.547852i
$759$	6.98711	+	1.93552i	0.253616	+	0.0702549i
$760$	−15.7769			−0.572288
$761$	−1.08183			−0.0392163			−0.0196081	−	0.999808i	$-0.506242\pi$
$761$	−1.08183			−0.0392163			−0.0196081	+	0.999808i	$0.506242\pi$
$762$	2.23266	−	8.05975i	0.0808806	−	0.291974i
$763$	2.56869	+	10.9771i	0.0929929	+	0.397396i
$764$		−	20.9301i		−	0.757225i
$765$	−17.9069	−	10.7454i	−0.647425	−	0.388502i
$766$		−	5.99148i		−	0.216481i
$767$			54.1998i			1.95704i
$768$	1.66919	+	0.462387i	0.0602317	+	0.0166850i
$769$		−	7.09476i		−	0.255844i	−0.991784	−	0.127922i	$-0.959169\pi$
$769$		−	7.09476i		−	0.255844i	0.991784	−	0.127922i	$-0.0408307\pi$
$770$	4.92137	+	21.0310i	0.177354	+	0.757904i
$771$	−14.7295	−	4.08026i	−0.530470	−	0.146947i
$772$	2.02912			0.0730296
$773$	4.10143			0.147518			0.0737590	−	0.997276i	$-0.476500\pi$
$773$	4.10143			0.147518			0.0737590	+	0.997276i	$0.476500\pi$
$774$	13.1867	−	21.9751i	0.473985	−	0.789879i
$775$		−	0.283629i		−	0.0101882i
$776$	−16.7148			−0.600027
$777$	−0.0600719	+	1.48732i	−0.00215507	+	0.0533574i
$778$	1.08008			0.0387228
$779$			71.3460i			2.55623i
$780$	−6.31415	+	22.7937i	−0.226083	+	0.816146i
$781$	−22.7024			−0.812356
$782$	−3.56933			−0.127639
$783$	8.79844	−	8.36394i	0.314431	−	0.298903i
$784$	−6.27318	+	3.10600i	−0.224042	+	0.110928i
$785$			17.6057i			0.628374i
$786$	−8.66390	+	31.2762i	−0.309031	+	1.11558i
$787$			6.51757i			0.232326i	0.993230	+	0.116163i	$0.0370595\pi$
$787$			6.51757i			0.232326i	−0.993230	+	0.116163i	$0.962940\pi$
$788$		−	17.2251i		−	0.613620i
$789$	11.0359	−	39.8389i	0.392888	−	1.41830i
$790$		−	23.8615i		−	0.848955i
$791$	24.4774	−	5.72785i	0.870317	−	0.203659i
$792$	10.7679	+	6.46151i	0.382619	+	0.229600i
$793$	64.2987			2.28332
$794$	19.0645			0.676573
$795$	5.09673	−	18.3989i	0.180762	−	0.652541i
$796$		−	10.9423i		−	0.387841i
$797$	−18.9228			−0.670280			−0.335140	−	0.942168i	$-0.608784\pi$
$797$	−18.9228			−0.670280			−0.335140	+	0.942168i	$0.608784\pi$
$798$	1.49606	−	37.0409i	0.0529598	−	1.31123i
$799$	0.624062			0.0220777
$800$			1.19644i			0.0423004i
$801$	−3.13304	−	1.88005i	−0.110700	−	0.0664284i
$802$	3.58379			0.126548
$803$	46.7605			1.65014
$804$	−12.8318	−	3.55458i	−0.452543	−	0.125360i
$805$	5.02421	−	1.17569i	0.177080	−	0.0414377i
$806$		−	1.65987i		−	0.0584664i
$807$	−0.989455	−	0.274092i	−0.0348304	−	0.00964848i
$808$		−	10.8858i		−	0.382962i
$809$			13.4432i			0.472638i	0.971676	+	0.236319i	$0.0759411\pi$
$809$			13.4432i			0.472638i	−0.971676	+	0.236319i	$0.924059\pi$
$810$	15.4883	−	8.25831i	0.544205	−	0.290168i
$811$		−	47.7213i		−	1.67572i	−0.545883	−	0.837861i	$-0.683806\pi$
$811$		−	47.7213i		−	1.67572i	0.545883	−	0.837861i	$-0.316194\pi$
$812$	6.01855	−	1.40837i	0.211210	−	0.0494243i
$813$	−1.32443	+	4.78112i	−0.0464499	+	0.167681i
$814$	1.35969			0.0476573
$815$	2.97388			0.104170
$816$	−5.95790	−	1.65041i	−0.208568	−	0.0577760i
$817$			69.1065i			2.41773i
$818$	3.95955			0.138443
$819$	−52.9162	−	16.9858i	−1.84904	−	0.593531i
$820$	−17.2004			−0.600664
$821$		−	48.4833i		−	1.69208i	−0.533119	−	0.846040i	$-0.678980\pi$
$821$		−	48.4833i		−	1.69208i	0.533119	−	0.846040i	$-0.321020\pi$
$822$	11.3640	+	3.14796i	0.396363	+	0.109798i
$823$	2.23643			0.0779570			0.0389785	−	0.999240i	$-0.487590\pi$
$823$	2.23643			0.0779570			0.0389785	+	0.999240i	$0.487590\pi$
$824$	1.91420			0.0666842
$825$	−2.31573	+	8.35964i	−0.0806233	+	0.291045i
$826$	19.9414	−	4.66640i	0.693851	−	0.162365i
$827$			33.5211i			1.16564i	0.812600	+	0.582822i	$0.198051\pi$
$827$			33.5211i			1.16564i	−0.812600	+	0.582822i	$0.801949\pi$
$828$	1.54363	−	2.57240i	0.0536447	−	0.0893969i
$829$			34.7676i			1.20753i	0.797163	+	0.603764i	$0.206333\pi$
$829$			34.7676i			1.20753i	−0.797163	+	0.603764i	$0.793667\pi$
$830$		−	34.9429i		−	1.21289i
$831$	−23.3144	−	6.45838i	−0.808767	−	0.224039i
$832$			7.00187i			0.242746i
$833$	22.3911	−	11.0863i	0.775804	−	0.384119i
$834$	21.6661	+	6.00179i	0.750236	+	0.207825i
$835$	15.5370			0.537680
$836$	−33.8624			−1.17116
$837$	−0.892784	+	0.848695i	−0.0308591	+	0.0293352i
$838$			13.2658i			0.458260i
$839$	−48.1415			−1.66203			−0.831015	−	0.556249i	$-0.812240\pi$
$839$	−48.1415			−1.66203			−0.831015	+	0.556249i	$0.812240\pi$
$840$	8.92999	+	0.360676i	0.308114	+	0.0124445i
$841$	23.5419			0.811791
$842$		−	21.2102i		−	0.730952i
$843$	−7.76672	+	28.0374i	−0.267500	+	0.965659i
$844$	−16.5236			−0.568765
$845$	−70.2607			−2.41704
$846$	−0.269887	+	0.449757i	−0.00927892	+	0.0154630i
$847$	3.93169	+	16.8017i	0.135094	+	0.577313i
$848$		−	5.65184i		−	0.194085i
$849$	−8.01831	+	28.9456i	−0.275188	+	0.993412i
$850$		−	4.27048i		−	0.146476i
$851$		−	0.324825i		−	0.0111349i
$852$	−2.50776	+	9.05286i	−0.0859144	+	0.310146i
$853$		−	8.65410i		−	0.296311i	−0.988964	−	0.148155i	$-0.952666\pi$
$853$		−	8.65410i		−	0.296311i	0.988964	−	0.148155i	$-0.0473336\pi$
$854$	−5.53589	−	23.6571i	−0.189434	−	0.809529i
$855$	−24.3536	+	40.5844i	−0.832876	+	1.38796i
$856$	13.7767			0.470880
$857$	46.3184			1.58221			0.791103	−	0.611682i	$-0.209507\pi$
$857$	46.3184			1.58221			0.791103	+	0.611682i	$0.209507\pi$
$858$	−13.5523	+	48.9228i	−0.462666	+	1.67020i
$859$			6.15224i			0.209912i	0.994477	+	0.104956i	$0.0334701\pi$
$859$			6.15224i			0.209912i	−0.994477	+	0.104956i	$0.966530\pi$
$860$	−16.6605			−0.568119
$861$	1.63104	−	40.3830i	0.0555857	−	1.37625i
$862$	8.01994			0.273160
$863$			56.0948i			1.90949i	0.297427	+	0.954745i	$0.403872\pi$
$863$			56.0948i			1.90949i	−0.297427	+	0.954745i	$0.596128\pi$
$864$	3.76605	−	3.58007i	0.128124	−	0.121796i
$865$	−9.73759			−0.331088
$866$	−20.1632			−0.685173
$867$	−7.11054	−	1.96971i	−0.241487	−	0.0668949i
$868$	−0.610707	+	0.142909i	−0.0207287	+	0.00485064i
$869$		−	51.2147i		−	1.73734i
$870$	−7.60538	−	2.10679i	−0.257847	−	0.0714268i
$871$		−	53.8265i		−	1.82384i
$872$		−	4.26102i		−	0.144296i
$873$	−25.8014	+	42.9972i	−0.873246	+	1.45523i
$874$			8.08958i			0.273634i
$875$	7.28511	+	31.1322i	0.246282	+	1.05246i
$876$	5.16527	−	18.6463i	0.174518	−	0.630001i
$877$	9.97333			0.336775			0.168388	−	0.985721i	$-0.446144\pi$
$877$	9.97333			0.336775			0.168388	+	0.985721i	$0.446144\pi$
$878$	39.5350			1.33424
$879$	−15.9422	−	4.41619i	−0.537716	−	0.148954i
$880$		−	8.16370i		−	0.275198i
$881$	−51.3620			−1.73043			−0.865215	−	0.501401i	$-0.832818\pi$
$881$	−51.3620			−1.73043			−0.865215	+	0.501401i	$0.832818\pi$
$882$	−1.69359	+	20.9316i	−0.0570260	+	0.704804i
$883$	−10.5576			−0.355292			−0.177646	−	0.984094i	$-0.556848\pi$
$883$	−10.5576			−0.355292			−0.177646	+	0.984094i	$0.556848\pi$
$884$		−	24.9920i		−	0.840571i
$885$	−25.1991	−	6.98048i	−0.847058	−	0.234646i
$886$	−18.1483			−0.609705
$887$	−39.3772			−1.32216			−0.661078	−	0.750317i	$-0.729901\pi$
$887$	−39.3772			−1.32216			−0.661078	+	0.750317i	$0.729901\pi$
$888$	0.150195	−	0.542195i	0.00504022	−	0.0181949i
$889$	−2.91081	−	12.4391i	−0.0976255	−	0.417193i
$890$			2.37533i			0.0796211i
$891$	33.2431	−	17.7251i	1.11369	−	0.593812i
$892$		−	6.83216i		−	0.228758i
$893$		−	1.41438i		−	0.0473305i
$894$	−22.7875	−	6.31244i	−0.762129	−	0.211120i
$895$		−	18.2362i		−	0.609568i
$896$	2.57616	−	0.602835i	0.0860634	−	0.0201393i
$897$	11.6874	+	3.23757i	0.390233	+	0.108099i
$898$	−23.0015			−0.767570
$899$	0.553835			0.0184714
$900$	3.07771	+	1.84685i	0.102590	+	0.0615617i
$901$			20.1733i			0.672070i
$902$	−36.9177			−1.22923
$903$	1.57985	−	39.1155i	0.0525740	−	1.30168i
$904$	−9.50152			−0.316016
$905$		−	25.6703i		−	0.853310i
$906$	1.29442	−	4.67276i	0.0430041	−	0.155242i
$907$	39.3728			1.30735			0.653677	−	0.756774i	$-0.273226\pi$
$907$	39.3728			1.30735			0.653677	+	0.756774i	$0.273226\pi$
$908$	−6.00651			−0.199333
$909$	−28.0027	−	16.8037i	−0.928790	−	0.557342i
$910$	8.23204	+	35.1788i	0.272890	+	1.16617i
$911$			18.5776i			0.615505i	0.951467	+	0.307752i	$0.0995768\pi$
$911$			18.5776i			0.615505i	−0.951467	+	0.307752i	$0.900423\pi$
$912$	−3.74052	+	13.5031i	−0.123861	+	0.447131i
$913$		−	74.9991i		−	2.48211i
$914$			5.70940i			0.188850i
$915$	−8.28114	+	29.8944i	−0.273766	+	0.988279i
$916$			10.3531i			0.342075i
$917$	11.2955	+	48.2703i	0.373011	+	1.59403i
$918$	−13.4423	+	12.7784i	−0.443661	+	0.421751i
$919$	19.5243			0.644047			0.322024	−	0.946732i	$-0.395637\pi$
$919$	19.5243			0.644047			0.322024	+	0.946732i	$0.395637\pi$
$920$	−1.95027			−0.0642986
$921$	9.02801	−	32.5906i	0.297483	−	1.07390i
$922$		−	21.1482i		−	0.696478i
$923$	−37.9746			−1.24995
$924$	19.1667	+	0.774129i	0.630538	+	0.0254670i
$925$	0.388633			0.0127782
$926$			3.64251i			0.119700i
$927$	2.95480	−	4.92407i	0.0970485	−	0.161728i
$928$	−2.33625			−0.0766912
$929$	3.45050			0.113207			0.0566036	−	0.998397i	$-0.481973\pi$
$929$	3.45050			0.113207			0.0566036	+	0.998397i	$0.481973\pi$
$930$	0.771723	+	0.213777i	0.0253058	+	0.00701003i
$931$	−25.1262	−	50.7474i	−0.823479	−	1.66318i
$932$			9.24182i			0.302726i
$933$	33.4971	+	9.27914i	1.09665	+	0.303785i
$934$		−	7.13820i		−	0.233569i
$935$			29.1390i			0.952946i
$936$	18.0116	+	10.8083i	0.588727	+	0.353279i
$937$			9.13499i			0.298427i	0.988805	+	0.149214i	$0.0476742\pi$
$937$			9.13499i			0.298427i	−0.988805	+	0.149214i	$0.952326\pi$
$938$	−19.8041	+	4.63426i	−0.646626	+	0.151314i
$939$	7.56787	−	27.3195i	0.246968	−	0.891540i
$940$	0.340985			0.0111217
$941$	−48.2892			−1.57418			−0.787091	−	0.616837i	$-0.788414\pi$
$941$	−48.2892			−1.57418			−0.787091	+	0.616837i	$0.788414\pi$
$942$	15.0683	+	4.17411i	0.490951	+	0.136000i
$943$			8.81948i			0.287202i
$944$	−7.74076			−0.251940
$945$	14.7124	−	22.4147i	0.478593	−	0.729151i
$946$	−35.7590			−1.16262
$947$		−	28.3766i		−	0.922117i	−0.887370	−	0.461058i	$-0.847470\pi$
$947$		−	28.3766i		−	0.922117i	0.887370	−	0.461058i	$-0.152530\pi$
$948$	−20.4225	−	5.65730i	−0.663292	−	0.183740i
$949$	78.2169			2.53903
$950$	−9.67868			−0.314018
$951$	3.76675	−	13.5977i	0.122145	−	0.440937i
$952$	−9.19516	+	2.15172i	−0.298017	+	0.0697376i
$953$			53.1134i			1.72051i	0.509862	+	0.860256i	$0.329696\pi$
$953$			53.1134i			1.72051i	−0.509862	+	0.860256i	$0.670304\pi$
$954$	−14.5388	−	8.72433i	−0.470710	−	0.282461i
$955$			40.8194i			1.32089i
$956$		−	11.2399i		−	0.363524i
$957$	−16.3237	−	4.52186i	−0.527669	−	0.146171i
$958$		−	25.8976i		−	0.836713i
$959$	17.5386	−	4.10414i	0.566352	−	0.132530i
$960$	−3.25538	−	0.901781i	−0.105067	−	0.0291049i
$961$	30.9438			0.998187
$962$	2.27438			0.0733290
$963$	21.2661	−	35.4392i	0.685292	−	1.14201i
$964$			3.48754i			0.112326i
$965$	−3.95734			−0.127391
$966$	0.184936	−	4.57884i	0.00595022	−	0.147322i
$967$	−58.3617			−1.87679			−0.938393	−	0.345569i	$-0.887686\pi$
$967$	−58.3617			−1.87679			−0.938393	+	0.345569i	$0.887686\pi$
$968$		−	6.52200i		−	0.209625i
$969$	13.3512	−	48.1969i	0.428901	−	1.54831i
$970$	32.5985			1.04667
$971$	28.5530			0.916311			0.458155	−	0.888872i	$-0.348510\pi$
$971$	28.5530			0.916311			0.458155	+	0.888872i	$0.348510\pi$
$972$	−3.39598	−	15.2141i	−0.108926	−	0.487991i
$973$	33.4386	−	7.82481i	1.07199	−	0.250852i
$974$			19.2742i			0.617584i
$975$	−3.87355	+	13.9833i	−0.124053	+	0.447824i
$976$			9.18309i			0.293943i
$977$			34.3488i			1.09891i	0.835522	+	0.549457i	$0.185165\pi$
$977$			34.3488i			1.09891i	−0.835522	+	0.549457i	$0.814835\pi$
$978$	0.705072	−	2.54527i	0.0225457	−	0.0813887i
$979$			5.09823i			0.162940i
$980$	12.2344	−	6.05754i	0.390814	−	0.193501i
$981$	−10.9610	−	6.57742i	−0.349959	−	0.210001i
$982$	−31.9607			−1.01991
$983$	40.2620			1.28416			0.642080	−	0.766638i	$-0.278072\pi$
$983$	40.2620			1.28416			0.642080	+	0.766638i	$0.278072\pi$
$984$	−4.07802	+	14.7214i	−0.130002	+	0.469301i
$985$			33.5937i			1.07038i
$986$	8.33886			0.265563
$987$	−0.0323342	+	0.800564i	−0.00102921	+	0.0254822i
$988$	−56.6422			−1.80203
$989$			8.54266i			0.271641i
$990$	−21.0003	−	12.6017i	−0.667432	−	0.400508i
$991$	−13.7559			−0.436972			−0.218486	−	0.975840i	$-0.570112\pi$
$991$	−13.7559			−0.436972			−0.218486	+	0.975840i	$0.570112\pi$
$992$	0.237061			0.00752670
$993$	−44.1719	−	12.2362i	−1.40175	−	0.388304i
$994$	3.26948	+	13.9718i	0.103702	+	0.443159i
$995$			21.3406i			0.676541i
$996$	−29.9068	−	8.28458i	−0.947634	−	0.262507i
$997$		−	36.9900i		−	1.17148i	−0.810497	−	0.585742i	$-0.800803\pi$
$997$		−	36.9900i		−	1.17148i	0.810497	−	0.585742i	$-0.199197\pi$
$998$			36.6266i			1.15939i
$999$	−1.16290	−	1.22331i	−0.0367924	−	0.0387037i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	966.2.f.b.461.11	yes	24
3.2	odd	2	inner	966.2.f.b.461.14	yes	24
7.6	odd	2	inner	966.2.f.b.461.2	✓	24
21.20	even	2	inner	966.2.f.b.461.23	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
966.2.f.b.461.2	✓	24	7.6	odd	2	inner
966.2.f.b.461.11	yes	24	1.1	even	1	trivial
966.2.f.b.461.14	yes	24	3.2	odd	2	inner
966.2.f.b.461.23	yes	24	21.20	even	2	inner

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:	\( N \)	\(=\)	\( 966 = 2 \cdot 3 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	966.f (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-1.00000i q^{2} +(1.66919 + 0.462387i) q^{3} -1.00000 q^{4} +1.95027 q^{5} +(0.462387 - 1.66919i) q^{6} +(-0.602835 - 2.57616i) q^{7} +1.00000i q^{8} +(2.57240 + 1.54363i) q^{9} +O(q^{10})\)	\(q-1.00000i q^{2} +(1.66919 + 0.462387i) q^{3} -1.00000 q^{4} +1.95027 q^{5} +(0.462387 - 1.66919i) q^{6} +(-0.602835 - 2.57616i) q^{7} +1.00000i q^{8} +(2.57240 + 1.54363i) q^{9} -1.95027i q^{10} -4.18593i q^{11} +(-1.66919 - 0.462387i) q^{12} -7.00187i q^{13} +(-2.57616 + 0.602835i) q^{14} +(3.25538 + 0.901781i) q^{15} +1.00000 q^{16} -3.56933 q^{17} +(1.54363 - 2.57240i) q^{18} +8.08958i q^{19} -1.95027 q^{20} +(0.184936 - 4.57884i) q^{21} -4.18593 q^{22} +1.00000i q^{23} +(-0.462387 + 1.66919i) q^{24} -1.19644 q^{25} -7.00187 q^{26} +(3.58007 + 3.76605i) q^{27} +(0.602835 + 2.57616i) q^{28} -2.33625i q^{29} +(0.901781 - 3.25538i) q^{30} +0.237061i q^{31} -1.00000i q^{32} +(1.93552 - 6.98711i) q^{33} +3.56933i q^{34} +(-1.17569 - 5.02421i) q^{35} +(-2.57240 - 1.54363i) q^{36} -0.324825 q^{37} +8.08958 q^{38} +(3.23757 - 11.6874i) q^{39} +1.95027i q^{40} +8.81948 q^{41} +(-4.57884 - 0.184936i) q^{42} +8.54266 q^{43} +4.18593i q^{44} +(5.01687 + 3.01049i) q^{45} +1.00000 q^{46} -0.174840 q^{47} +(1.66919 + 0.462387i) q^{48} +(-6.27318 + 3.10600i) q^{49} +1.19644i q^{50} +(-5.95790 - 1.65041i) q^{51} +7.00187i q^{52} -5.65184i q^{53} +(3.76605 - 3.58007i) q^{54} -8.16370i q^{55} +(2.57616 - 0.602835i) q^{56} +(-3.74052 + 13.5031i) q^{57} -2.33625 q^{58} -7.74076 q^{59} +(-3.25538 - 0.901781i) q^{60} +9.18309i q^{61} +0.237061 q^{62} +(2.42589 - 7.55745i) q^{63} -1.00000 q^{64} -13.6555i q^{65} +(-6.98711 - 1.93552i) q^{66} +7.68745 q^{67} +3.56933 q^{68} +(-0.462387 + 1.66919i) q^{69} +(-5.02421 + 1.17569i) q^{70} -5.42350i q^{71} +(-1.54363 + 2.57240i) q^{72} +11.1709i q^{73} +0.324825i q^{74} +(-1.99708 - 0.553217i) q^{75} -8.08958i q^{76} +(-10.7836 + 2.52342i) q^{77} +(-11.6874 - 3.23757i) q^{78} +12.2350 q^{79} +1.95027 q^{80} +(4.23444 + 7.94163i) q^{81} -8.81948i q^{82} +17.9170 q^{83} +(-0.184936 + 4.57884i) q^{84} -6.96117 q^{85} -8.54266i q^{86} +(1.08025 - 3.89965i) q^{87} +4.18593 q^{88} -1.21795 q^{89} +(3.01049 - 5.01687i) q^{90} +(-18.0379 + 4.22097i) q^{91} -1.00000i q^{92} +(-0.109614 + 0.395700i) q^{93} +0.174840i q^{94} +15.7769i q^{95} +(0.462387 - 1.66919i) q^{96} +16.7148i q^{97} +(3.10600 + 6.27318i) q^{98} +(6.46151 - 10.7679i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 24 q^{4} - 4 q^{7} + 8 q^{9}+O(q^{10}) \) 24 * q - 24 * q^4 - 4 * q^7 + 8 * q^9	\( 24 q - 24 q^{4} - 4 q^{7} + 8 q^{9} + 24 q^{16} + 16 q^{18} - 28 q^{21} + 8 q^{22} - 24 q^{25} + 4 q^{28} + 24 q^{30} - 8 q^{36} + 40 q^{37} + 72 q^{39} + 64 q^{43} + 24 q^{46} - 24 q^{51} + 16 q^{58} + 12 q^{63} - 24 q^{64} - 64 q^{67} + 16 q^{70} - 16 q^{72} - 32 q^{78} + 88 q^{79} + 48 q^{81} + 28 q^{84} + 64 q^{85} - 8 q^{88} - 56 q^{91} + 8 q^{93} - 8 q^{99}+O(q^{100}) \) 24 * q - 24 * q^4 - 4 * q^7 + 8 * q^9 + 24 * q^16 + 16 * q^18 - 28 * q^21 + 8 * q^22 - 24 * q^25 + 4 * q^28 + 24 * q^30 - 8 * q^36 + 40 * q^37 + 72 * q^39 + 64 * q^43 + 24 * q^46 - 24 * q^51 + 16 * q^58 + 12 * q^63 - 24 * q^64 - 64 * q^67 + 16 * q^70 - 16 * q^72 - 32 * q^78 + 88 * q^79 + 48 * q^81 + 28 * q^84 + 64 * q^85 - 8 * q^88 - 56 * q^91 + 8 * q^93 - 8 * q^99

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