LMFDB - Embedded newform 966.2.f.b.461.15

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			461.15
Character	$\chi$	$=$	966.461
Dual form			966.2.f.b.461.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000i q^{2} +(-1.62776 - 0.591954i) q^{3} -1.00000 q^{4} +2.12506 q^{5} +(0.591954 - 1.62776i) q^{6} +(2.32692 - 1.25915i) q^{7} -1.00000i q^{8} +(2.29918 + 1.92711i) q^{9} +O(q^{10})$	\(q+1.00000i q^{2} +(-1.62776 - 0.591954i) q^{3} -1.00000 q^{4} +2.12506 q^{5} +(0.591954 - 1.62776i) q^{6} +(2.32692 - 1.25915i) q^{7} -1.00000i q^{8} +(2.29918 + 1.92711i) q^{9} +2.12506i q^{10} +1.02515i q^{11} +(1.62776 + 0.591954i) q^{12} -0.150487i q^{13} +(1.25915 + 2.32692i) q^{14} +(-3.45908 - 1.25794i) q^{15} +1.00000 q^{16} +0.704599 q^{17} +(-1.92711 + 2.29918i) q^{18} -6.24091i q^{19} -2.12506 q^{20} +(-4.53301 + 0.672165i) q^{21} -1.02515 q^{22} -1.00000i q^{23} +(-0.591954 + 1.62776i) q^{24} -0.484125 q^{25} +0.150487 q^{26} +(-2.60174 - 4.49788i) q^{27} +(-2.32692 + 1.25915i) q^{28} +2.79030i q^{29} +(1.25794 - 3.45908i) q^{30} -1.14509i q^{31} +1.00000i q^{32} +(0.606844 - 1.66870i) q^{33} +0.704599i q^{34} +(4.94483 - 2.67577i) q^{35} +(-2.29918 - 1.92711i) q^{36} +9.94331 q^{37} +6.24091 q^{38} +(-0.0890814 + 0.244956i) q^{39} -2.12506i q^{40} +3.85795 q^{41} +(-0.672165 - 4.53301i) q^{42} -2.35341 q^{43} -1.02515i q^{44} +(4.88589 + 4.09523i) q^{45} +1.00000 q^{46} +4.30515 q^{47} +(-1.62776 - 0.591954i) q^{48} +(3.82907 - 5.85988i) q^{49} -0.484125i q^{50} +(-1.14692 - 0.417090i) q^{51} +0.150487i q^{52} +0.984948i q^{53} +(4.49788 - 2.60174i) q^{54} +2.17851i q^{55} +(-1.25915 - 2.32692i) q^{56} +(-3.69433 + 10.1587i) q^{57} -2.79030 q^{58} +11.2629 q^{59} +(3.45908 + 1.25794i) q^{60} -4.52548i q^{61} +1.14509 q^{62} +(7.77653 + 1.58921i) q^{63} -1.00000 q^{64} -0.319794i q^{65} +(1.66870 + 0.606844i) q^{66} -3.75504 q^{67} -0.704599 q^{68} +(-0.591954 + 1.62776i) q^{69} +(2.67577 + 4.94483i) q^{70} -1.06393i q^{71} +(1.92711 - 2.29918i) q^{72} +6.03172i q^{73} +9.94331i q^{74} +(0.788038 + 0.286580i) q^{75} +6.24091i q^{76} +(1.29082 + 2.38545i) q^{77} +(-0.244956 - 0.0890814i) q^{78} +15.1258 q^{79} +2.12506 q^{80} +(1.57246 + 8.86157i) q^{81} +3.85795i q^{82} -1.50906 q^{83} +(4.53301 - 0.672165i) q^{84} +1.49731 q^{85} -2.35341i q^{86} +(1.65173 - 4.54193i) q^{87} +1.02515 q^{88} -9.18507 q^{89} +(-4.09523 + 4.88589i) q^{90} +(-0.189486 - 0.350171i) q^{91} +1.00000i q^{92} +(-0.677842 + 1.86393i) q^{93} +4.30515i q^{94} -13.2623i q^{95} +(0.591954 - 1.62776i) q^{96} +15.7292i q^{97} +(5.85988 + 3.82907i) q^{98} +(-1.97559 + 2.35702i) 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
$3$	−1.62776	−	0.591954i	−0.939785	−	0.341765i
$3$	−1.62776	−	0.591954i	−0.939785	−	0.341765i
$4$	−1.00000			−0.500000
$5$	2.12506			0.950355			0.475178	−	0.879890i	$-0.342384\pi$
$5$	2.12506			0.950355			0.475178	+	0.879890i	$0.342384\pi$
$6$	0.591954	−	1.62776i	0.241664	−	0.664529i
$7$	2.32692	−	1.25915i	0.879491	−	0.475915i
$7$	2.32692	−	1.25915i	0.879491	−	0.475915i
$8$		−	1.00000i		−	0.353553i
$9$	2.29918	+	1.92711i	0.766394	+	0.642371i
$10$			2.12506i			0.672003i
$11$			1.02515i			0.309096i	0.987985	+	0.154548i	$0.0493921\pi$
$11$			1.02515i			0.309096i	−0.987985	+	0.154548i	$0.950608\pi$
$12$	1.62776	+	0.591954i	0.469893	+	0.170882i
$13$		−	0.150487i		−	0.0417376i	−0.999782	−	0.0208688i	$-0.993357\pi$
$13$		−	0.150487i		−	0.0417376i	0.999782	−	0.0208688i	$-0.00664323\pi$
$14$	1.25915	+	2.32692i	0.336522	+	0.621894i
$15$	−3.45908	−	1.25794i	−0.893130	−	0.324798i
$16$	1.00000			0.250000
$17$	0.704599			0.170890			0.0854452	−	0.996343i	$-0.472769\pi$
$17$	0.704599			0.170890			0.0854452	+	0.996343i	$0.472769\pi$
$18$	−1.92711	+	2.29918i	−0.454225	+	0.541922i
$19$		−	6.24091i		−	1.43176i	−0.698222	−	0.715881i	$-0.746025\pi$
$19$		−	6.24091i		−	1.43176i	0.698222	−	0.715881i	$-0.253975\pi$
$20$	−2.12506			−0.475178
$21$	−4.53301	+	0.672165i	−0.989184	+	0.146678i
$22$	−1.02515			−0.218564
$23$		−	1.00000i		−	0.208514i
$23$		−	1.00000i		−	0.208514i
$24$	−0.591954	+	1.62776i	−0.120832	+	0.332264i
$25$	−0.484125			−0.0968251
$26$	0.150487			0.0295129
$27$	−2.60174	−	4.49788i	−0.500706	−	0.865618i
$28$	−2.32692	+	1.25915i	−0.439746	+	0.237957i
$29$			2.79030i			0.518146i	0.965858	+	0.259073i	$0.0834170\pi$
$29$			2.79030i			0.518146i	−0.965858	+	0.259073i	$0.916583\pi$
$30$	1.25794	−	3.45908i	0.229667	−	0.631538i
$31$		−	1.14509i		−	0.205665i	−0.994699	−	0.102832i	$-0.967209\pi$
$31$		−	1.14509i		−	0.205665i	0.994699	−	0.102832i	$-0.0327905\pi$
$32$			1.00000i			0.176777i
$33$	0.606844	−	1.66870i	0.105638	−	0.290484i
$34$			0.704599i			0.120838i
$35$	4.94483	−	2.67577i	0.835829	−	0.452288i
$36$	−2.29918	−	1.92711i	−0.383197	−	0.321186i
$37$	9.94331			1.63467			0.817335	−	0.576163i	$-0.195451\pi$
$37$	9.94331			1.63467			0.817335	+	0.576163i	$0.195451\pi$
$38$	6.24091			1.01241
$39$	−0.0890814	+	0.244956i	−0.0142644	+	0.0392244i
$40$		−	2.12506i		−	0.336001i
$41$	3.85795			0.602510			0.301255	−	0.953544i	$-0.402594\pi$
$41$	3.85795			0.602510			0.301255	+	0.953544i	$0.402594\pi$
$42$	−0.672165	−	4.53301i	−0.103717	−	0.699459i
$43$	−2.35341			−0.358891			−0.179445	−	0.983768i	$-0.557430\pi$
$43$	−2.35341			−0.358891			−0.179445	+	0.983768i	$0.557430\pi$
$44$		−	1.02515i		−	0.154548i
$45$	4.88589	+	4.09523i	0.728346	+	0.610481i
$46$	1.00000			0.147442
$47$	4.30515			0.627971			0.313986	−	0.949428i	$-0.398336\pi$
$47$	4.30515			0.627971			0.313986	+	0.949428i	$0.398336\pi$
$48$	−1.62776	−	0.591954i	−0.234946	−	0.0854412i
$49$	3.82907	−	5.85988i	0.547011	−	0.837126i
$50$		−	0.484125i		−	0.0684657i
$51$	−1.14692	−	0.417090i	−0.160600	−	0.0584043i
$52$			0.150487i			0.0208688i
$53$			0.984948i			0.135293i	0.997709	+	0.0676465i	$0.0215490\pi$
$53$			0.984948i			0.135293i	−0.997709	+	0.0676465i	$0.978451\pi$
$54$	4.49788	−	2.60174i	0.612084	−	0.354052i
$55$			2.17851i			0.293751i
$56$	−1.25915	−	2.32692i	−0.168261	−	0.310947i
$57$	−3.69433	+	10.1587i	−0.489326	+	1.34555i
$58$	−2.79030			−0.366384
$59$	11.2629			1.46630			0.733151	−	0.680066i	$-0.238049\pi$
$59$	11.2629			1.46630			0.733151	+	0.680066i	$0.238049\pi$
$60$	3.45908	+	1.25794i	0.446565	+	0.162399i
$61$		−	4.52548i		−	0.579429i	−0.957113	−	0.289714i	$-0.906440\pi$
$61$		−	4.52548i		−	0.579429i	0.957113	−	0.289714i	$-0.0935604\pi$
$62$	1.14509			0.145427
$63$	7.77653	+	1.58921i	0.979751	+	0.200222i
$64$	−1.00000			−0.125000
$65$		−	0.319794i		−	0.0396655i
$66$	1.66870	+	0.606844i	0.205403	+	0.0746974i
$67$	−3.75504			−0.458752			−0.229376	−	0.973338i	$-0.573668\pi$
$67$	−3.75504			−0.458752			−0.229376	+	0.973338i	$0.573668\pi$
$68$	−0.704599			−0.0854452
$69$	−0.591954	+	1.62776i	−0.0712629	+	0.195959i
$70$	2.67577	+	4.94483i	0.319816	+	0.591021i
$71$		−	1.06393i		−	0.126265i	−0.998005	−	0.0631325i	$-0.979891\pi$
$71$		−	1.06393i		−	0.126265i	0.998005	−	0.0631325i	$-0.0201091\pi$
$72$	1.92711	−	2.29918i	0.227113	−	0.270961i
$73$			6.03172i			0.705959i	0.935631	+	0.352979i	$0.114831\pi$
$73$			6.03172i			0.705959i	−0.935631	+	0.352979i	$0.885169\pi$
$74$			9.94331i			1.15589i
$75$	0.788038	+	0.286580i	0.0909948	+	0.0330914i
$76$			6.24091i			0.715881i
$77$	1.29082	+	2.38545i	0.147103	+	0.271847i
$78$	−0.244956	−	0.0890814i	−0.0277358	−	0.0100865i
$79$	15.1258			1.70179			0.850894	−	0.525337i	$-0.176061\pi$
$79$	15.1258			1.70179			0.850894	+	0.525337i	$0.176061\pi$
$80$	2.12506			0.237589
$81$	1.57246	+	8.86157i	0.174718	+	0.984618i
$82$			3.85795i			0.426039i
$83$	−1.50906			−0.165641			−0.0828204	−	0.996564i	$-0.526393\pi$
$83$	−1.50906			−0.165641			−0.0828204	+	0.996564i	$0.526393\pi$
$84$	4.53301	−	0.672165i	0.494592	−	0.0733392i
$85$	1.49731			0.162407
$86$		−	2.35341i		−	0.253774i
$87$	1.65173	−	4.54193i	0.177084	−	0.486946i
$88$	1.02515			0.109282
$89$	−9.18507			−0.973615			−0.486808	−	0.873509i	$-0.661839\pi$
$89$	−9.18507			−0.973615			−0.486808	+	0.873509i	$0.661839\pi$
$90$	−4.09523	+	4.88589i	−0.431675	+	0.515018i
$91$	−0.189486	−	0.350171i	−0.0198635	−	0.0367079i
$92$			1.00000i			0.104257i
$93$	−0.677842	+	1.86393i	−0.0702889	+	0.193281i
$94$			4.30515i			0.444043i
$95$		−	13.2623i		−	1.36068i
$96$	0.591954	−	1.62776i	0.0604161	−	0.166132i
$97$			15.7292i			1.59705i	0.601959	+	0.798527i	$0.294387\pi$
$97$			15.7292i			1.59705i	−0.601959	+	0.798527i	$0.705613\pi$
$98$	5.85988	+	3.82907i	0.591937	+	0.386795i
$99$	−1.97559	+	2.35702i	−0.198554	+	0.236889i
$100$	0.484125			0.0484125
$101$	−3.35178			−0.333515			−0.166758	−	0.985998i	$-0.553330\pi$
$101$	−3.35178			−0.333515			−0.166758	+	0.985998i	$0.553330\pi$
$102$	0.417090	−	1.14692i	0.0412981	−	0.113562i
$103$			3.14101i			0.309493i	0.987954	+	0.154747i	$0.0494561\pi$
$103$			3.14101i			0.309493i	−0.987954	+	0.154747i	$0.950544\pi$
$104$	−0.150487			−0.0147565
$105$	−9.63292	+	1.42839i	−0.940076	+	0.139397i
$106$	−0.984948			−0.0956667
$107$		−	16.6988i		−	1.61433i	−0.590325	−	0.807166i	$-0.701000\pi$
$107$		−	16.6988i		−	1.61433i	0.590325	−	0.807166i	$-0.299000\pi$
$108$	2.60174	+	4.49788i	0.250353	+	0.432809i
$109$	11.0728			1.06058			0.530291	−	0.847815i	$-0.322083\pi$
$109$	11.0728			1.06058			0.530291	+	0.847815i	$0.322083\pi$
$110$	−2.17851			−0.207713
$111$	−16.1853	−	5.88598i	−1.53624	−	0.558673i
$112$	2.32692	−	1.25915i	0.219873	−	0.118979i
$113$		−	1.21980i		−	0.114749i	−0.998353	−	0.0573747i	$-0.981727\pi$
$113$		−	1.21980i		−	0.114749i	0.998353	−	0.0573747i	$-0.0182730\pi$
$114$	−10.1587	−	3.69433i	−0.951447	−	0.346006i
$115$		−	2.12506i		−	0.198163i
$116$		−	2.79030i		−	0.259073i
$117$	0.290006	−	0.345997i	0.0268110	−	0.0319874i
$118$			11.2629i			1.03683i
$119$	1.63954	−	0.887197i	0.150297	−	0.0813293i
$120$	−1.25794	+	3.45908i	−0.114833	+	0.315769i
$121$	9.94906			0.904460
$122$	4.52548			0.409718
$123$	−6.27980	−	2.28373i	−0.566231	−	0.205917i
$124$			1.14509i			0.102832i
$125$	−11.6541			−1.04237
$126$	−1.58921	+	7.77653i	−0.141578	+	0.692788i
$127$	2.14806			0.190609			0.0953047	−	0.995448i	$-0.469617\pi$
$127$	2.14806			0.190609			0.0953047	+	0.995448i	$0.469617\pi$
$128$		−	1.00000i		−	0.0883883i
$129$	3.83077	+	1.39311i	0.337280	+	0.122656i
$130$	0.319794			0.0280478
$131$	3.35362			0.293007			0.146504	−	0.989210i	$-0.453198\pi$
$131$	3.35362			0.293007			0.146504	+	0.989210i	$0.453198\pi$
$132$	−0.606844	+	1.66870i	−0.0528190	+	0.145242i
$133$	−7.85825	−	14.5221i	−0.681397	−	1.25922i
$134$		−	3.75504i		−	0.324386i
$135$	−5.52886	−	9.55826i	−0.475848	−	0.822644i
$136$		−	0.704599i		−	0.0604189i
$137$		−	12.3169i		−	1.05231i	−0.850390	−	0.526153i	$-0.823634\pi$
$137$		−	12.3169i		−	1.05231i	0.850390	−	0.526153i	$-0.176366\pi$
$138$	−1.62776	−	0.591954i	−0.138564	−	0.0503905i
$139$		−	9.80157i		−	0.831358i	−0.909511	−	0.415679i	$-0.863544\pi$
$139$		−	9.80157i		−	0.831358i	0.909511	−	0.415679i	$-0.136456\pi$
$140$	−4.94483	+	2.67577i	−0.417915	+	0.226144i
$141$	−7.00774	−	2.54845i	−0.590158	−	0.214618i
$142$	1.06393			0.0892828
$143$	0.154272			0.0129009
$144$	2.29918	+	1.92711i	0.191598	+	0.160593i
$145$			5.92955i			0.492423i
$146$	−6.03172			−0.499188
$147$	−9.70158	+	7.27182i	−0.800173	+	0.599770i
$148$	−9.94331			−0.817335
$149$			8.98495i			0.736076i	0.929811	+	0.368038i	$0.119970\pi$
$149$			8.98495i			0.736076i	−0.929811	+	0.368038i	$0.880030\pi$
$150$	−0.286580	+	0.788038i	−0.0233992	+	0.0643431i
$151$	−19.9961			−1.62726			−0.813629	−	0.581385i	$-0.802511\pi$
$151$	−19.9961			−1.62726			−0.813629	+	0.581385i	$0.802511\pi$
$152$	−6.24091			−0.506204
$153$	1.62000	+	1.35784i	0.130969	+	0.109775i
$154$	−2.38545	+	1.29082i	−0.192225	+	0.104018i
$155$		−	2.43339i		−	0.195454i
$156$	0.0890814	−	0.244956i	0.00713222	−	0.0196122i
$157$		−	9.71340i		−	0.775214i	−0.921825	−	0.387607i	$-0.873302\pi$
$157$		−	9.71340i		−	0.775214i	0.921825	−	0.387607i	$-0.126698\pi$
$158$			15.1258i			1.20335i
$159$	0.583044	−	1.60326i	0.0462384	−	0.127146i
$160$			2.12506i			0.168001i
$161$	−1.25915	−	2.32692i	−0.0992351	−	0.183387i
$162$	−8.86157	+	1.57246i	−0.696230	+	0.123544i
$163$	8.17816			0.640563			0.320282	−	0.947322i	$-0.396222\pi$
$163$	8.17816			0.640563			0.320282	+	0.947322i	$0.396222\pi$
$164$	−3.85795			−0.301255
$165$	1.28958	−	3.54609i	0.100394	−	0.276063i
$166$		−	1.50906i		−	0.117126i
$167$	−16.3259			−1.26334			−0.631668	−	0.775239i	$-0.717629\pi$
$167$	−16.3259			−1.26334			−0.631668	+	0.775239i	$0.717629\pi$
$168$	0.672165	+	4.53301i	0.0518586	+	0.349729i
$169$	12.9774			0.998258
$170$			1.49731i			0.114839i
$171$	12.0269	−	14.3490i	0.919723	−	1.09729i
$172$	2.35341			0.179445
$173$	−20.9020			−1.58915			−0.794575	−	0.607166i	$-0.792306\pi$
$173$	−20.9020			−1.58915			−0.794575	+	0.607166i	$0.792306\pi$
$174$	4.54193	+	1.65173i	0.344323	+	0.125217i
$175$	−1.12652	+	0.609587i	−0.0851568	+	0.0460805i
$176$			1.02515i			0.0772739i
$177$	−18.3332	−	6.66711i	−1.37801	−	0.501130i
$178$		−	9.18507i		−	0.688450i
$179$		−	23.9976i		−	1.79366i	−0.442374	−	0.896831i	$-0.645863\pi$
$179$		−	23.9976i		−	1.79366i	0.442374	−	0.896831i	$-0.354137\pi$
$180$	−4.88589	−	4.09523i	−0.364173	−	0.305240i
$181$			14.9737i			1.11299i	0.830852	+	0.556493i	$0.187853\pi$
$181$			14.9737i			1.11299i	−0.830852	+	0.556493i	$0.812147\pi$
$182$	0.350171	−	0.189486i	0.0259564	−	0.0140456i
$183$	−2.67888	+	7.36639i	−0.198028	+	0.544539i
$184$	−1.00000			−0.0737210
$185$	21.1301			1.55352
$186$	−1.86393	−	0.677842i	−0.136670	−	0.0497018i
$187$			0.722323i			0.0528215i
$188$	−4.30515			−0.313986
$189$	−11.7176	−	7.19020i	−0.852326	−	0.523010i
$190$	13.2623			0.962148
$191$			22.4940i			1.62761i	0.581137	+	0.813805i	$0.302608\pi$
$191$			22.4940i			1.62761i	−0.581137	+	0.813805i	$0.697392\pi$
$192$	1.62776	+	0.591954i	0.117473	+	0.0427206i
$193$	−22.1441			−1.59397			−0.796985	−	0.603999i	$-0.793573\pi$
$193$	−22.1441			−1.59397			−0.796985	+	0.603999i	$0.793573\pi$
$194$	−15.7292			−1.12929
$195$	−0.189303	+	0.520546i	−0.0135563	+	0.0372771i
$196$	−3.82907	+	5.85988i	−0.273505	+	0.418563i
$197$			3.40063i			0.242285i	0.992635	+	0.121143i	$0.0386558\pi$
$197$			3.40063i			0.242285i	−0.992635	+	0.121143i	$0.961344\pi$
$198$	−2.35702	−	1.97559i	−0.167506	−	0.140399i
$199$			13.2597i			0.939954i	0.882679	+	0.469977i	$0.155738\pi$
$199$			13.2597i			0.939954i	−0.882679	+	0.469977i	$0.844262\pi$
$200$			0.484125i			0.0342328i
$201$	6.11230	+	2.22281i	0.431128	+	0.156785i
$202$		−	3.35178i		−	0.235831i
$203$	3.51341	+	6.49280i	0.246593	+	0.455705i
$204$	1.14692	+	0.417090i	0.0803002	+	0.0292022i
$205$	8.19837			0.572599
$206$	−3.14101			−0.218845
$207$	1.92711	−	2.29918i	0.133944	−	0.159804i
$208$		−	0.150487i		−	0.0104344i
$209$	6.39789			0.442552
$210$	−1.42839	−	9.63292i	−0.0985682	−	0.664734i
$211$	−5.52971			−0.380681			−0.190340	−	0.981718i	$-0.560959\pi$
$211$	−5.52971			−0.380681			−0.190340	+	0.981718i	$0.560959\pi$
$212$		−	0.984948i		−	0.0676465i
$213$	−0.629796	+	1.73181i	−0.0431529	+	0.118662i
$214$	16.6988			1.14151
$215$	−5.00112			−0.341074
$216$	−4.49788	+	2.60174i	−0.306042	+	0.177026i
$217$	−1.44184	−	2.66453i	−0.0978788	−	0.180880i
$218$			11.0728i			0.749945i
$219$	3.57050	−	9.81816i	0.241272	−	0.663450i
$220$		−	2.17851i		−	0.146875i
$221$		−	0.106033i		−	0.00713256i
$222$	5.88598	−	16.1853i	0.395041	−	1.08629i
$223$		−	11.7686i		−	0.788083i	−0.919093	−	0.394041i	$-0.871077\pi$
$223$		−	11.7686i		−	0.788083i	0.919093	−	0.394041i	$-0.128923\pi$
$224$	1.25915	+	2.32692i	0.0841306	+	0.155474i
$225$	−1.11309	−	0.932965i	−0.0742061	−	0.0621977i
$226$	1.21980			0.0811400
$227$	−20.3164			−1.34844			−0.674222	−	0.738529i	$-0.735521\pi$
$227$	−20.3164			−1.34844			−0.674222	+	0.738529i	$0.735521\pi$
$228$	3.69433	−	10.1587i	0.244663	−	0.672775i
$229$			24.2391i			1.60177i	0.598820	+	0.800884i	$0.295637\pi$
$229$			24.2391i			1.60177i	−0.598820	+	0.800884i	$0.704363\pi$
$230$	2.12506			0.140122
$231$	−0.689073	−	4.64704i	−0.0453377	−	0.305753i
$232$	2.79030			0.183192
$233$			9.69298i			0.635008i	0.948257	+	0.317504i	$0.102845\pi$
$233$			9.69298i			0.635008i	−0.948257	+	0.317504i	$0.897155\pi$
$234$	0.345997	+	0.290006i	0.0226185	+	0.0189583i
$235$	9.14870			0.596795
$236$	−11.2629			−0.733151
$237$	−24.6212	−	8.95380i	−1.59932	−	0.581611i
$238$	0.887197	+	1.63954i	0.0575085	+	0.106276i
$239$			3.15960i			0.204378i	0.994765	+	0.102189i	$0.0325846\pi$
$239$			3.15960i			0.204378i	−0.994765	+	0.102189i	$0.967415\pi$
$240$	−3.45908	−	1.25794i	−0.223282	−	0.0811995i
$241$			25.7775i			1.66047i	0.557411	+	0.830237i	$0.311795\pi$
$241$			25.7775i			1.66047i	−0.557411	+	0.830237i	$0.688205\pi$
$242$			9.94906i			0.639550i
$243$	2.68605	−	15.3553i	0.172310	−	0.985043i
$244$			4.52548i			0.289714i
$245$	8.13701	−	12.4526i	0.519854	−	0.795567i
$246$	2.28373	−	6.27980i	0.145605	−	0.400385i
$247$	−0.939176			−0.0597583
$248$	−1.14509			−0.0727134
$249$	2.45638	+	0.893294i	0.155667	+	0.0566102i
$250$		−	11.6541i		−	0.737069i
$251$	−24.1586			−1.52488			−0.762438	−	0.647061i	$-0.775998\pi$
$251$	−24.1586			−1.52488			−0.762438	+	0.647061i	$0.775998\pi$
$252$	−7.77653	−	1.58921i	−0.489875	−	0.100111i
$253$	1.02515			0.0644509
$254$			2.14806i			0.134781i
$255$	−2.43726	−	0.886342i	−0.152627	−	0.0555049i
$256$	1.00000			0.0625000
$257$	5.49615			0.342840			0.171420	−	0.985198i	$-0.445164\pi$
$257$	5.49615			0.342840			0.171420	+	0.985198i	$0.445164\pi$
$258$	−1.39311	+	3.83077i	−0.0867311	+	0.238493i
$259$	23.1372	−	12.5201i	1.43768	−	0.777963i
$260$			0.319794i			0.0198328i
$261$	−5.37723	+	6.41541i	−0.332842	+	0.397104i
$262$			3.35362i			0.207187i
$263$		−	2.15233i		−	0.132718i	−0.997796	−	0.0663591i	$-0.978862\pi$
$263$		−	2.15233i		−	0.132718i	0.997796	−	0.0663591i	$-0.0211383\pi$
$264$	−1.66870	−	0.606844i	−0.102701	−	0.0373487i
$265$			2.09307i			0.128576i
$266$	14.5221	−	7.85825i	0.890405	−	0.481820i
$267$	14.9510	+	5.43714i	0.914989	+	0.332747i
$268$	3.75504			0.229376
$269$	7.82524			0.477114			0.238557	−	0.971129i	$-0.423326\pi$
$269$	7.82524			0.477114			0.238557	+	0.971129i	$0.423326\pi$
$270$	9.55826	−	5.52886i	0.581697	−	0.336475i
$271$			6.59149i			0.400404i	0.979755	+	0.200202i	$0.0641599\pi$
$271$			6.59149i			0.400404i	−0.979755	+	0.200202i	$0.935840\pi$
$272$	0.704599			0.0427226
$273$	0.101152	+	0.682160i	0.00612200	+	0.0412862i
$274$	12.3169			0.744092
$275$		−	0.496303i		−	0.0299282i
$276$	0.591954	−	1.62776i	0.0356315	−	0.0979794i
$277$	10.0170			0.601861			0.300931	−	0.953646i	$-0.402703\pi$
$277$	10.0170			0.601861			0.300931	+	0.953646i	$0.402703\pi$
$278$	9.80157			0.587859
$279$	2.20672	−	2.63277i	0.132113	−	0.157620i
$280$	−2.67577	−	4.94483i	−0.159908	−	0.295510i
$281$		−	13.9833i		−	0.834177i	−0.908866	−	0.417088i	$-0.863051\pi$
$281$		−	13.9833i		−	0.834177i	0.908866	−	0.417088i	$-0.136949\pi$
$282$	2.54845	−	7.00774i	0.151758	−	0.417305i
$283$			10.5457i			0.626879i	0.949608	+	0.313440i	$0.101481\pi$
$283$			10.5457i			0.626879i	−0.949608	+	0.313440i	$0.898519\pi$
$284$			1.06393i			0.0631325i
$285$	−7.85067	+	21.5878i	−0.465034	+	1.27875i
$286$			0.154272i			0.00912232i
$287$	8.97712	−	4.85774i	0.529903	−	0.286744i
$288$	−1.92711	+	2.29918i	−0.113556	+	0.135481i
$289$	−16.5035			−0.970796
$290$	−5.92955			−0.348195
$291$	9.31094	−	25.6032i	0.545817	−	1.50089i
$292$		−	6.03172i		−	0.352979i
$293$	−5.81769			−0.339873			−0.169936	−	0.985455i	$-0.554356\pi$
$293$	−5.81769			−0.339873			−0.169936	+	0.985455i	$0.554356\pi$
$294$	−7.27182	−	9.70158i	−0.424101	−	0.565808i
$295$	23.9343			1.39351
$296$		−	9.94331i		−	0.577943i
$297$	4.61102	−	2.66719i	0.267559	−	0.154766i
$298$	−8.98495			−0.520484
$299$	−0.150487			−0.00870289
$300$	−0.788038	−	0.286580i	−0.0454974	−	0.0165457i
$301$	−5.47618	+	2.96329i	−0.315641	+	0.170801i
$302$		−	19.9961i		−	1.15064i
$303$	5.45589	+	1.98410i	0.313433	+	0.113984i
$304$		−	6.24091i		−	0.357941i
$305$		−	9.61692i		−	0.550663i
$306$	−1.35784	+	1.62000i	−0.0776227	+	0.0926093i
$307$		−	10.5468i		−	0.601939i	−0.953634	−	0.300969i	$-0.902690\pi$
$307$		−	10.5468i		−	0.601939i	0.953634	−	0.300969i	$-0.0973102\pi$
$308$	−1.29082	−	2.38545i	−0.0735516	−	0.135924i
$309$	1.85934	−	5.11280i	0.105774	−	0.290857i
$310$	2.43339			0.138207
$311$	−3.92395			−0.222507			−0.111253	−	0.993792i	$-0.535487\pi$
$311$	−3.92395			−0.222507			−0.111253	+	0.993792i	$0.535487\pi$
$312$	0.244956	+	0.0890814i	0.0138679	+	0.00504324i
$313$			10.4652i			0.591531i	0.955261	+	0.295765i	$0.0955746\pi$
$313$			10.4652i			0.591531i	−0.955261	+	0.295765i	$0.904425\pi$
$314$	9.71340			0.548159
$315$	16.5256	+	3.37717i	0.931111	+	0.190282i
$316$	−15.1258			−0.850894
$317$		−	17.5779i		−	0.987276i	−0.869667	−	0.493638i	$-0.835667\pi$
$317$		−	17.5779i		−	0.987276i	0.869667	−	0.493638i	$-0.164333\pi$
$318$	1.60326	+	0.583044i	0.0899061	+	0.0326955i
$319$	−2.86049			−0.160157
$320$	−2.12506			−0.118794
$321$	−9.88491	+	27.1815i	−0.551722	+	1.51713i
$322$	2.32692	−	1.25915i	0.129674	−	0.0701698i
$323$		−	4.39734i		−	0.244674i
$324$	−1.57246	−	8.86157i	−0.0873591	−	0.492309i
$325$			0.0728546i			0.00404125i
$326$			8.17816i			0.452947i
$327$	−18.0238	−	6.55460i	−0.996720	−	0.362470i
$328$		−	3.85795i		−	0.213020i
$329$	10.0177	−	5.42084i	0.552295	−	0.298861i
$330$	3.54609	+	1.28958i	0.195206	+	0.0709890i
$331$	−4.91032			−0.269896			−0.134948	−	0.990853i	$-0.543087\pi$
$331$	−4.91032			−0.269896			−0.134948	+	0.990853i	$0.543087\pi$
$332$	1.50906			0.0828204
$333$	22.8615	+	19.1619i	1.25280	+	1.05007i
$334$		−	16.3259i		−	0.893313i
$335$	−7.97969			−0.435977
$336$	−4.53301	+	0.672165i	−0.247296	+	0.0366696i
$337$	−27.5273			−1.49951			−0.749753	−	0.661718i	$-0.769828\pi$
$337$	−27.5273			−1.49951			−0.749753	+	0.661718i	$0.769828\pi$
$338$			12.9774i			0.705875i
$339$	−0.722067	+	1.98554i	−0.0392173	+	0.107840i
$340$	−1.49731			−0.0812033
$341$	1.17390			0.0635700
$342$	14.3490	+	12.0269i	0.775904	+	0.650342i
$343$	1.53145	−	18.4568i	0.0826907	−	0.996575i
$344$			2.35341i			0.126887i
$345$	−1.25794	+	3.45908i	−0.0677251	+	0.186230i
$346$		−	20.9020i		−	1.12370i
$347$			20.9489i			1.12460i	0.826935	+	0.562298i	$0.190083\pi$
$347$			20.9489i			1.12460i	−0.826935	+	0.562298i	$0.809917\pi$
$348$	−1.65173	+	4.54193i	−0.0885420	+	0.243473i
$349$			1.39806i			0.0748363i	0.999300	+	0.0374182i	$0.0119134\pi$
$349$			1.39806i			0.0748363i	−0.999300	+	0.0374182i	$0.988087\pi$
$350$	−0.609587	−	1.12652i	−0.0325838	−	0.0602150i
$351$	−0.676873	+	0.391529i	−0.0361288	+	0.0208982i
$352$	−1.02515			−0.0546409
$353$	26.9272			1.43319			0.716596	−	0.697488i	$-0.245699\pi$
$353$	26.9272			1.43319			0.716596	+	0.697488i	$0.245699\pi$
$354$	6.66711	−	18.3332i	0.354353	−	0.974400i
$355$		−	2.26091i		−	0.119997i
$356$	9.18507			0.486808
$357$	−3.19396	+	0.473607i	−0.169042	+	0.0250659i
$358$	23.9976			1.26831
$359$			23.2582i			1.22752i	0.789493	+	0.613759i	$0.210343\pi$
$359$			23.2582i			1.22752i	−0.789493	+	0.613759i	$0.789657\pi$
$360$	4.09523	−	4.88589i	0.215838	−	0.257509i
$361$	−19.9489			−1.04994
$362$	−14.9737			−0.787000
$363$	−16.1946	−	5.88939i	−0.849998	−	0.309113i
$364$	0.189486	+	0.350171i	0.00993177	+	0.0183539i
$365$			12.8178i			0.670912i
$366$	−7.36639	−	2.67888i	−0.385047	−	0.140027i
$367$			20.4322i			1.06655i	0.845941	+	0.533276i	$0.179039\pi$
$367$			20.4322i			1.06655i	−0.845941	+	0.533276i	$0.820961\pi$
$368$		−	1.00000i		−	0.0521286i
$369$	8.87012	+	7.43471i	0.461760	+	0.387035i
$370$			21.1301i			1.09850i
$371$	1.24020	+	2.29189i	0.0643880	+	0.118989i
$372$	0.677842	−	1.86393i	0.0351445	−	0.0966403i
$373$	−3.92149			−0.203047			−0.101523	−	0.994833i	$-0.532372\pi$
$373$	−3.92149			−0.203047			−0.101523	+	0.994833i	$0.532372\pi$
$374$	−0.722323			−0.0373504
$375$	18.9700	+	6.89869i	0.979607	+	0.356247i
$376$		−	4.30515i		−	0.222021i
$377$	0.419904			0.0216262
$378$	7.19020	−	11.7176i	0.369824	−	0.602686i
$379$	14.3472			0.736966			0.368483	−	0.929635i	$-0.379877\pi$
$379$	14.3472			0.736966			0.368483	+	0.929635i	$0.379877\pi$
$380$			13.2623i			0.680341i
$381$	−3.49652	−	1.27155i	−0.179132	−	0.0651436i
$382$	−22.4940			−1.15089
$383$	−11.2269			−0.573667			−0.286834	−	0.957980i	$-0.592603\pi$
$383$	−11.2269			−0.573667			−0.286834	+	0.957980i	$0.592603\pi$
$384$	−0.591954	+	1.62776i	−0.0302080	+	0.0830661i
$385$	2.74308	+	5.06922i	0.139800	+	0.258351i
$386$		−	22.1441i		−	1.12711i
$387$	−5.41090	−	4.53528i	−0.275052	−	0.230541i
$388$		−	15.7292i		−	0.798527i
$389$			20.0180i			1.01495i	0.861666	+	0.507476i	$0.169421\pi$
$389$			20.0180i			1.01495i	−0.861666	+	0.507476i	$0.830579\pi$
$390$	−0.520546	−	0.189303i	−0.0263589	−	0.00958574i
$391$		−	0.704599i		−	0.0356331i
$392$	−5.85988	−	3.82907i	−0.295969	−	0.193397i
$393$	−5.45888	−	1.98519i	−0.275364	−	0.100140i
$394$	−3.40063			−0.171321
$395$	32.1433			1.61730
$396$	1.97559	−	2.35702i	0.0992771	−	0.118444i
$397$		−	15.0096i		−	0.753312i	−0.926353	−	0.376656i	$-0.877074\pi$
$397$		−	15.0096i		−	0.753312i	0.926353	−	0.376656i	$-0.122926\pi$
$398$	−13.2597			−0.664648
$399$	4.19492	+	28.2901i	0.210009	+	1.41628i
$400$	−0.484125			−0.0242063
$401$			9.92661i			0.495711i	0.968797	+	0.247856i	$0.0797259\pi$
$401$			9.92661i			0.495711i	−0.968797	+	0.247856i	$0.920274\pi$
$402$	−2.22281	+	6.11230i	−0.110864	+	0.304854i
$403$	−0.172322			−0.00858395
$404$	3.35178			0.166758
$405$	3.34158	+	18.8313i	0.166044	+	0.935737i
$406$	−6.49280	+	3.51341i	−0.322232	+	0.174368i
$407$			10.1934i			0.505269i
$408$	−0.417090	+	1.14692i	−0.0206491	+	0.0567808i
$409$		−	10.3230i		−	0.510438i	−0.966883	−	0.255219i	$-0.917852\pi$
$409$		−	10.3230i		−	0.510438i	0.966883	−	0.255219i	$-0.0821476\pi$
$410$			8.19837i			0.404889i
$411$	−7.29105	+	20.0489i	−0.359641	+	0.988941i
$412$		−	3.14101i		−	0.154747i
$413$	26.2078	−	14.1817i	1.28960	−	0.697834i
$414$	2.29918	+	1.92711i	0.112999	+	0.0947125i
$415$	−3.20684			−0.157418
$416$	0.150487			0.00737823
$417$	−5.80208	+	15.9546i	−0.284129	+	0.781298i
$418$			6.39789i			0.312931i
$419$	−17.8007			−0.869620			−0.434810	−	0.900522i	$-0.643184\pi$
$419$	−17.8007			−0.869620			−0.434810	+	0.900522i	$0.643184\pi$
$420$	9.63292	−	1.42839i	0.470038	−	0.0696983i
$421$	−19.1783			−0.934695			−0.467347	−	0.884074i	$-0.654790\pi$
$421$	−19.1783			−0.934695			−0.467347	+	0.884074i	$0.654790\pi$
$422$		−	5.52971i		−	0.269182i
$423$	9.89832	+	8.29652i	0.481273	+	0.403391i
$424$	0.984948			0.0478333
$425$	−0.341114			−0.0165465
$426$	−1.73181	−	0.629796i	−0.0839067	−	0.0305137i
$427$	−5.69827	−	10.5304i	−0.275759	−	0.509603i
$428$			16.6988i			0.807166i
$429$	−0.251118	−	0.0913222i	−0.0121241	−	0.00440908i
$430$		−	5.00112i		−	0.241176i
$431$			13.2557i			0.638503i	0.947670	+	0.319251i	$0.103431\pi$
$431$			13.2557i			0.638503i	−0.947670	+	0.319251i	$0.896569\pi$
$432$	−2.60174	−	4.49788i	−0.125176	−	0.216404i
$433$		−	13.6697i		−	0.656922i	−0.944517	−	0.328461i	$-0.893470\pi$
$433$		−	13.6697i		−	0.656922i	0.944517	−	0.328461i	$-0.106530\pi$
$434$	2.66453	−	1.44184i	0.127902	−	0.0692108i
$435$	3.51002	−	9.65187i	0.168293	−	0.462772i
$436$	−11.0728			−0.530291
$437$	−6.24091			−0.298543
$438$	9.81816	+	3.57050i	0.469130	+	0.170605i
$439$			21.9429i			1.04728i	0.851940	+	0.523639i	$0.175426\pi$
$439$			21.9429i			1.04728i	−0.851940	+	0.523639i	$0.824574\pi$
$440$	2.17851			0.103857
$441$	20.0964	−	6.09386i	0.956971	−	0.290184i
$442$	0.106033			0.00504348
$443$			31.3991i			1.49182i	0.666049	+	0.745908i	$0.267984\pi$
$443$			31.3991i			1.49182i	−0.666049	+	0.745908i	$0.732016\pi$
$444$	16.1853	+	5.88598i	0.768120	+	0.279336i
$445$	−19.5188			−0.925280
$446$	11.7686			0.557259
$447$	5.31868	−	14.6253i	0.251565	−	0.691753i
$448$	−2.32692	+	1.25915i	−0.109936	+	0.0594893i
$449$		−	30.4995i		−	1.43936i	−0.694307	−	0.719679i	$-0.744289\pi$
$449$		−	30.4995i		−	1.43936i	0.694307	−	0.719679i	$-0.255711\pi$
$450$	0.932965	−	1.11309i	0.0439804	−	0.0524717i
$451$			3.95499i			0.186233i
$452$			1.21980i			0.0573747i
$453$	32.5487	+	11.8368i	1.52927	+	0.556139i
$454$		−	20.3164i		−	0.953494i
$455$	−0.402669	−	0.744133i	−0.0188774	−	0.0348855i
$456$	10.1587	+	3.69433i	0.475724	+	0.173003i
$457$	−0.225335			−0.0105407			−0.00527036	−	0.999986i	$-0.501678\pi$
$457$	−0.225335			−0.0105407			−0.00527036	+	0.999986i	$0.501678\pi$
$458$	−24.2391			−1.13262
$459$	−1.83319	−	3.16920i	−0.0855658	−	0.147926i
$460$			2.12506i			0.0990814i
$461$	19.3057			0.899158			0.449579	−	0.893241i	$-0.351574\pi$
$461$	19.3057			0.899158			0.449579	+	0.893241i	$0.351574\pi$
$462$	4.64704	−	0.689073i	0.216200	−	0.0320586i
$463$	−23.8528			−1.10853			−0.554267	−	0.832339i	$-0.687001\pi$
$463$	−23.8528			−1.10853			−0.554267	+	0.832339i	$0.687001\pi$
$464$			2.79030i			0.129536i
$465$	−1.44045	+	3.96096i	−0.0667995	+	0.183685i
$466$	−9.69298			−0.449019
$467$	1.23736			0.0572583			0.0286292	−	0.999590i	$-0.490886\pi$
$467$	1.23736			0.0572583			0.0286292	+	0.999590i	$0.490886\pi$
$468$	−0.290006	+	0.345997i	−0.0134055	+	0.0159937i
$469$	−8.73767	+	4.72817i	−0.403468	+	0.218327i
$470$			9.14870i			0.421998i
$471$	−5.74989	+	15.8110i	−0.264941	+	0.728535i
$472$		−	11.2629i		−	0.518416i
$473$		−	2.41260i		−	0.110932i
$474$	8.95380	−	24.6212i	0.411261	−	1.13089i
$475$			3.02138i			0.138631i
$476$	−1.63954	+	0.887197i	−0.0751483	+	0.0406646i
$477$	−1.89811	+	2.26457i	−0.0869084	+	0.103688i
$478$	−3.15960			−0.144517
$479$	24.5462			1.12155			0.560773	−	0.827969i	$-0.310504\pi$
$479$	24.5462			1.12155			0.560773	+	0.827969i	$0.310504\pi$
$480$	1.25794	−	3.45908i	0.0574167	−	0.157885i
$481$		−	1.49634i		−	0.0682272i
$482$	−25.7775			−1.17413
$483$	0.672165	+	4.53301i	0.0305846	+	0.206259i
$484$	−9.94906			−0.452230
$485$			33.4254i			1.51777i
$486$	15.3553	+	2.68605i	0.696530	+	0.121842i
$487$	−11.9122			−0.539795			−0.269898	−	0.962889i	$-0.586990\pi$
$487$	−11.9122			−0.539795			−0.269898	+	0.962889i	$0.586990\pi$
$488$	−4.52548			−0.204859
$489$	−13.3121	−	4.84110i	−0.601992	−	0.218922i
$490$	12.4526	+	8.13701i	0.562551	+	0.367592i
$491$		−	16.5262i		−	0.745817i	−0.927868	−	0.372909i	$-0.878360\pi$
$491$		−	16.5262i		−	0.745817i	0.927868	−	0.372909i	$-0.121640\pi$
$492$	6.27980	+	2.28373i	0.283115	+	0.102958i
$493$			1.96604i			0.0885462i
$494$		−	0.939176i		−	0.0422555i
$495$	−4.19824	+	5.00880i	−0.188697	+	0.225129i
$496$		−	1.14509i		−	0.0514161i
$497$	−1.33965	−	2.47567i	−0.0600913	−	0.111049i
$498$	−0.893294	+	2.45638i	−0.0400295	+	0.110073i
$499$	−12.4640			−0.557963			−0.278982	−	0.960296i	$-0.589997\pi$
$499$	−12.4640			−0.557963			−0.278982	+	0.960296i	$0.589997\pi$
$500$	11.6541			0.521187
$501$	26.5746	+	9.66418i	1.18726	+	0.431764i
$502$		−	24.1586i		−	1.07825i
$503$	−6.05769			−0.270099			−0.135050	−	0.990839i	$-0.543119\pi$
$503$	−6.05769			−0.270099			−0.135050	+	0.990839i	$0.543119\pi$
$504$	1.58921	−	7.77653i	0.0707892	−	0.346394i
$505$	−7.12274			−0.316958
$506$			1.02515i			0.0455737i
$507$	−21.1240	−	7.68200i	−0.938148	−	0.341170i
$508$	−2.14806			−0.0953047
$509$	−4.38489			−0.194357			−0.0971784	−	0.995267i	$-0.530982\pi$
$509$	−4.38489			−0.194357			−0.0971784	+	0.995267i	$0.530982\pi$
$510$	0.886342	−	2.43726i	0.0392479	−	0.107924i
$511$	7.59485	+	14.0353i	0.335976	+	0.620885i
$512$			1.00000i			0.0441942i
$513$	−28.0709	+	16.2372i	−1.23936	+	0.716891i
$514$			5.49615i			0.242425i
$515$			6.67484i			0.294128i
$516$	−3.83077	−	1.39311i	−0.168640	−	0.0613282i
$517$			4.41345i			0.194103i
$518$	12.5201	+	23.1372i	0.550103	+	1.01659i
$519$	34.0234	+	12.3730i	1.49346	+	0.543115i
$520$	−0.319794			−0.0140239
$521$	8.98121			0.393474			0.196737	−	0.980456i	$-0.436966\pi$
$521$	8.98121			0.393474			0.196737	+	0.980456i	$0.436966\pi$
$522$	−6.41541	−	5.37723i	−0.280795	−	0.235355i
$523$		−	42.9160i		−	1.87658i	−0.345845	−	0.938292i	$-0.612408\pi$
$523$		−	42.9160i		−	1.87658i	0.345845	−	0.938292i	$-0.387592\pi$
$524$	−3.35362			−0.146504
$525$	2.19455	−	0.325412i	0.0957779	−	0.0142021i
$526$	2.15233			0.0938460
$527$		−	0.806831i		−	0.0351461i
$528$	0.606844	−	1.66870i	0.0264095	−	0.0726209i
$529$	−1.00000			−0.0434783
$530$	−2.09307			−0.0909173
$531$	25.8954	+	21.7048i	1.12376	+	0.941910i
$532$	7.85825	+	14.5221i	0.340698	+	0.629611i
$533$		−	0.580571i		−	0.0251473i
$534$	−5.43714	+	14.9510i	−0.235288	+	0.646995i
$535$		−	35.4859i		−	1.53419i
$536$			3.75504i			0.162193i
$537$	−14.2055	+	39.0622i	−0.613011	+	1.68566i
$538$			7.82524i			0.337370i
$539$	6.00728	+	3.92539i	0.258752	+	0.169079i
$540$	5.52886	+	9.55826i	0.237924	+	0.411322i
$541$	17.5189			0.753198			0.376599	−	0.926376i	$-0.377094\pi$
$541$	17.5189			0.753198			0.376599	+	0.926376i	$0.377094\pi$
$542$	−6.59149			−0.283129
$543$	8.86374	−	24.3735i	0.380379	−	1.04597i
$544$			0.704599i			0.0302094i
$545$	23.5304			1.00793
$546$	−0.682160	+	0.101152i	−0.0291937	+	0.00432891i
$547$	11.6980			0.500169			0.250085	−	0.968224i	$-0.419542\pi$
$547$	11.6980			0.500169			0.250085	+	0.968224i	$0.419542\pi$
$548$			12.3169i			0.526153i
$549$	8.72113	−	10.4049i	0.372209	−	0.444071i
$550$	0.496303			0.0211624
$551$	17.4140			0.741862
$552$	1.62776	+	0.591954i	0.0692819	+	0.0251952i
$553$	35.1965	−	19.0457i	1.49671	−	0.809906i
$554$			10.0170i			0.425580i
$555$	−34.3947	−	12.5081i	−1.45997	−	0.530938i
$556$			9.80157i			0.415679i
$557$		−	27.6337i		−	1.17088i	−0.810717	−	0.585438i	$-0.800923\pi$
$557$		−	27.6337i		−	1.17088i	0.810717	−	0.585438i	$-0.199077\pi$
$558$	2.63277	+	2.20672i	0.111454	+	0.0934180i
$559$			0.354157i			0.0149792i
$560$	4.94483	−	2.67577i	0.208957	−	0.113072i
$561$	0.427582	−	1.17577i	0.0180525	−	0.0496409i
$562$	13.9833			0.589852
$563$	6.35644			0.267892			0.133946	−	0.990989i	$-0.457235\pi$
$563$	6.35644			0.267892			0.133946	+	0.990989i	$0.457235\pi$
$564$	7.00774	+	2.54845i	0.295079	+	0.107309i
$565$		−	2.59215i		−	0.109053i
$566$	−10.5457			−0.443271
$567$	14.8170	+	18.6401i	0.622257	+	0.782813i
$568$	−1.06393			−0.0446414
$569$		−	34.3782i		−	1.44121i	−0.693345	−	0.720606i	$-0.743864\pi$
$569$		−	34.3782i		−	1.44121i	0.693345	−	0.720606i	$-0.256136\pi$
$570$	−21.5878	−	7.85067i	−0.904213	−	0.328828i
$571$	−19.8190			−0.829400			−0.414700	−	0.909958i	$-0.636114\pi$
$571$	−19.8190			−0.829400			−0.414700	+	0.909958i	$0.636114\pi$
$572$	−0.154272			−0.00645046
$573$	13.3154	−	36.6148i	0.556260	−	1.52960i
$574$	4.85774	+	8.97712i	0.202758	+	0.374698i
$575$			0.484125i			0.0201894i
$576$	−2.29918	−	1.92711i	−0.0957992	−	0.0802964i
$577$			21.0500i			0.876322i	0.898897	+	0.438161i	$0.144370\pi$
$577$			21.0500i			0.876322i	−0.898897	+	0.438161i	$0.855630\pi$
$578$		−	16.5035i		−	0.686457i
$579$	36.0452	+	13.1083i	1.49799	+	0.544763i
$580$		−	5.92955i		−	0.246211i
$581$	−3.51146	+	1.90014i	−0.145680	+	0.0788309i
$582$	25.6032	+	9.31094i	1.06129	+	0.385951i
$583$	−1.00972			−0.0418185
$584$	6.03172			0.249594
$585$	0.616279	−	0.735264i	0.0254800	−	0.0303994i
$586$		−	5.81769i		−	0.240326i
$587$	−13.1776			−0.543898			−0.271949	−	0.962312i	$-0.587668\pi$
$587$	−13.1776			−0.543898			−0.271949	+	0.962312i	$0.587668\pi$
$588$	9.70158	−	7.27182i	0.400086	−	0.299885i
$589$	−7.14641			−0.294463
$590$			23.9343i			0.985358i
$591$	2.01302	−	5.53540i	0.0828046	−	0.227696i
$592$	9.94331			0.408668
$593$	33.7881			1.38751			0.693756	−	0.720210i	$-0.255955\pi$
$593$	33.7881			1.38751			0.693756	+	0.720210i	$0.255955\pi$
$594$	2.66719	+	4.61102i	0.109436	+	0.189193i
$595$	3.48413	−	1.88535i	0.142835	−	0.0772917i
$596$		−	8.98495i		−	0.368038i
$597$	7.84912	−	21.5835i	0.321243	−	0.883355i
$598$		−	0.150487i		−	0.00615387i
$599$			6.71838i			0.274506i	0.990536	+	0.137253i	$0.0438273\pi$
$599$			6.71838i			0.274506i	−0.990536	+	0.137253i	$0.956173\pi$
$600$	0.286580	−	0.788038i	0.0116996	−	0.0321715i
$601$			28.0261i			1.14321i	0.820530	+	0.571604i	$0.193679\pi$
$601$			28.0261i			1.14321i	−0.820530	+	0.571604i	$0.806321\pi$
$602$	−2.96329	−	5.47618i	−0.120775	−	0.223192i
$603$	−8.63352	−	7.23640i	−0.351584	−	0.294689i
$604$	19.9961			0.813629
$605$	21.1423			0.859558
$606$	−1.98410	+	5.45589i	−0.0805987	+	0.221630i
$607$			43.9968i			1.78578i	0.450278	+	0.892888i	$0.351325\pi$
$607$			43.9968i			1.78578i	−0.450278	+	0.892888i	$0.648675\pi$
$608$	6.24091			0.253102
$609$	−1.87554	−	12.6485i	−0.0760008	−	0.512542i
$610$	9.61692			0.389378
$611$		−	0.647870i		−	0.0262100i
$612$	−1.62000	−	1.35784i	−0.0654847	−	0.0548876i
$613$	−41.4712			−1.67500			−0.837502	−	0.546434i	$-0.815985\pi$
$613$	−41.4712			−1.67500			−0.837502	+	0.546434i	$0.815985\pi$
$614$	10.5468			0.425635
$615$	−13.3449	−	4.85306i	−0.538120	−	0.195694i
$616$	2.38545	−	1.29082i	0.0961124	−	0.0520088i
$617$		−	41.2660i		−	1.66131i	−0.556791	−	0.830653i	$-0.687967\pi$
$617$		−	41.2660i		−	1.66131i	0.556791	−	0.830653i	$-0.312033\pi$
$618$	5.11280	+	1.85934i	0.205667	+	0.0747934i
$619$		−	7.01983i		−	0.282151i	−0.989999	−	0.141075i	$-0.954944\pi$
$619$		−	7.01983i		−	0.282151i	0.989999	−	0.141075i	$-0.0450560\pi$
$620$			2.43339i			0.0977272i
$621$	−4.49788	+	2.60174i	−0.180494	+	0.104404i
$622$		−	3.92395i		−	0.157336i
$623$	−21.3729	+	11.5654i	−0.856286	+	0.463358i
$624$	−0.0890814	+	0.244956i	−0.00356611	+	0.00980610i
$625$	−22.3450			−0.893800
$626$	−10.4652			−0.418275
$627$	−10.4142	−	3.78726i	−0.415904	−	0.151249i
$628$			9.71340i			0.387607i
$629$	7.00605			0.279349
$630$	−3.37717	+	16.5256i	−0.134550	+	0.658395i
$631$	2.94766			0.117345			0.0586723	−	0.998277i	$-0.481313\pi$
$631$	2.94766			0.117345			0.0586723	+	0.998277i	$0.481313\pi$
$632$		−	15.1258i		−	0.601673i
$633$	9.00101	+	3.27333i	0.357758	+	0.130103i
$634$	17.5779			0.698110
$635$	4.56475			0.181147
$636$	−0.583044	+	1.60326i	−0.0231192	+	0.0635732i
$637$	−0.881836	−	0.576226i	−0.0349396	−	0.0228309i
$638$		−	2.86049i		−	0.113248i
$639$	2.05031	−	2.44616i	0.0811090	−	0.0967686i
$640$		−	2.12506i		−	0.0840003i
$641$			42.0920i			1.66253i	0.555873	+	0.831267i	$0.312384\pi$
$641$			42.0920i			1.66253i	−0.555873	+	0.831267i	$0.687616\pi$
$642$	−27.1815	−	9.88491i	−1.07277	−	0.390126i
$643$		−	35.2004i		−	1.38817i	−0.719894	−	0.694084i	$-0.755810\pi$
$643$		−	35.2004i		−	1.38817i	0.719894	−	0.694084i	$-0.244190\pi$
$644$	1.25915	+	2.32692i	0.0496175	+	0.0916933i
$645$	8.14061	+	2.96044i	0.320536	+	0.116567i
$646$	4.39734			0.173011
$647$	−48.3518			−1.90091			−0.950453	−	0.310868i	$-0.899380\pi$
$647$	−48.3518			−1.90091			−0.950453	+	0.310868i	$0.899380\pi$
$648$	8.86157	−	1.57246i	0.348115	−	0.0617722i
$649$			11.5462i			0.453227i
$650$	−0.0728546			−0.00285759
$651$	0.769691	+	5.19072i	0.0301665	+	0.203440i
$652$	−8.17816			−0.320282
$653$		−	21.8658i		−	0.855674i	−0.903856	−	0.427837i	$-0.859276\pi$
$653$		−	21.8658i		−	0.855674i	0.903856	−	0.427837i	$-0.140724\pi$
$654$	6.55460	−	18.0238i	0.256305	−	0.704788i
$655$	7.12664			0.278461
$656$	3.85795			0.150628
$657$	−11.6238	+	13.8680i	−0.453488	+	0.541042i
$658$	5.42084	+	10.0177i	0.211326	+	0.390532i
$659$			21.5374i			0.838977i	0.907761	+	0.419488i	$0.137791\pi$
$659$			21.5374i			0.838977i	−0.907761	+	0.419488i	$0.862209\pi$
$660$	−1.28958	+	3.54609i	−0.0501968	+	0.138031i
$661$		−	36.1185i		−	1.40485i	−0.711760	−	0.702423i	$-0.752101\pi$
$661$		−	36.1185i		−	1.40485i	0.711760	−	0.702423i	$-0.247899\pi$
$662$		−	4.91032i		−	0.190845i
$663$	−0.0627667	+	0.172596i	−0.00243766	+	0.00670307i
$664$			1.50906i			0.0585629i
$665$	−16.6992	−	30.8602i	−0.647569	−	1.19671i
$666$	−19.1619	+	22.8615i	−0.742508	+	0.885864i
$667$	2.79030			0.108041
$668$	16.3259			0.631668
$669$	−6.96646	+	19.1564i	−0.269339	+	0.740629i
$670$		−	7.97969i		−	0.308282i
$671$	4.63932			0.179099
$672$	−0.672165	−	4.53301i	−0.0259293	−	0.174865i
$673$	−20.5559			−0.792371			−0.396186	−	0.918170i	$-0.629666\pi$
$673$	−20.5559			−0.792371			−0.396186	+	0.918170i	$0.629666\pi$
$674$		−	27.5273i		−	1.06031i
$675$	1.25957	+	2.17754i	0.0484809	+	0.0838135i
$676$	−12.9774			−0.499129
$677$	−15.1906			−0.583821			−0.291910	−	0.956446i	$-0.594291\pi$
$677$	−15.1906			−0.583821			−0.291910	+	0.956446i	$0.594291\pi$
$678$	−1.98554	−	0.722067i	−0.0762542	−	0.0277308i
$679$	19.8054	+	36.6004i	0.760061	+	1.40459i
$680$		−	1.49731i		−	0.0574194i
$681$	33.0701	+	12.0263i	1.26725	+	0.460851i
$682$			1.17390i			0.0449508i
$683$		−	9.31273i		−	0.356342i	−0.984000	−	0.178171i	$-0.942982\pi$
$683$		−	9.31273i		−	0.356342i	0.984000	−	0.178171i	$-0.0570180\pi$
$684$	−12.0269	+	14.3490i	−0.459862	+	0.548647i
$685$		−	26.1742i		−	1.00006i
$686$	18.4568	+	1.53145i	0.704685	+	0.0584712i
$687$	14.3485	−	39.4554i	0.547428	−	1.50532i
$688$	−2.35341			−0.0897227
$689$	0.148222			0.00564681
$690$	−3.45908	−	1.25794i	−0.131685	−	0.0478889i
$691$			28.0109i			1.06558i	0.846246	+	0.532792i	$0.178857\pi$
$691$			28.0109i			1.06558i	−0.846246	+	0.532792i	$0.821143\pi$
$692$	20.9020			0.794575
$693$	−1.62919	+	7.97214i	−0.0618878	+	0.302837i
$694$	−20.9489			−0.795209
$695$		−	20.8289i		−	0.790086i
$696$	−4.54193	−	1.65173i	−0.172161	−	0.0626087i
$697$	2.71831			0.102963
$698$	−1.39806			−0.0529173
$699$	5.73780	−	15.7778i	0.217023	−	0.596771i
$700$	1.12652	−	0.609587i	0.0425784	−	0.0230402i
$701$		−	5.41348i		−	0.204464i	−0.994761	−	0.102232i	$-0.967402\pi$
$701$		−	5.41348i		−	0.204464i	0.994761	−	0.102232i	$-0.0325985\pi$
$702$	−0.391529	−	0.676873i	−0.0147773	−	0.0255469i
$703$		−	62.0553i		−	2.34046i
$704$		−	1.02515i		−	0.0386370i
$705$	−14.8919	−	5.41561i	−0.560860	−	0.203964i
$706$			26.9272i			1.01342i
$707$	−7.79932	+	4.22041i	−0.293324	+	0.158725i
$708$	18.3332	+	6.66711i	0.689005	+	0.250565i
$709$	30.5487			1.14728			0.573641	−	0.819107i	$-0.305530\pi$
$709$	30.5487			1.14728			0.573641	+	0.819107i	$0.305530\pi$
$710$	2.26091			0.0848503
$711$	34.7770	+	29.1492i	1.30424	+	1.09318i
$712$			9.18507i			0.344225i
$713$	−1.14509			−0.0428840
$714$	−0.473607	−	3.19396i	−0.0177243	−	0.119531i
$715$	0.327838			0.0122604
$716$			23.9976i			0.896831i
$717$	1.87034	−	5.14306i	0.0698491	−	0.192071i
$718$	−23.2582			−0.867987
$719$	28.1362			1.04930			0.524652	−	0.851317i	$-0.324195\pi$
$719$	28.1362			1.04930			0.524652	+	0.851317i	$0.324195\pi$
$720$	4.88589	+	4.09523i	0.182087	+	0.152620i
$721$	3.95501	+	7.30887i	0.147292	+	0.272197i
$722$		−	19.9489i		−	0.742422i
$723$	15.2591	−	41.9595i	0.567492	−	1.56049i
$724$		−	14.9737i		−	0.556493i
$725$		−	1.35086i		−	0.0501695i
$726$	5.88939	−	16.1946i	0.218576	−	0.601040i
$727$			0.939489i			0.0348437i	0.999848	+	0.0174219i	$0.00554583\pi$
$727$			0.939489i			0.0348437i	−0.999848	+	0.0174219i	$0.994454\pi$
$728$	−0.350171	+	0.189486i	−0.0129782	+	0.00702282i
$729$	−13.4619	+	23.4047i	−0.498588	+	0.866839i
$730$	−12.8178			−0.474406
$731$	−1.65821			−0.0613310
$732$	2.67888	−	7.36639i	0.0990142	−	0.272269i
$733$		−	27.7481i		−	1.02490i	−0.858718	−	0.512449i	$-0.828738\pi$
$733$		−	27.7481i		−	1.02490i	0.858718	−	0.512449i	$-0.171262\pi$
$734$	−20.4322			−0.754166
$735$	−20.6164	+	15.4530i	−0.760448	+	0.569994i
$736$	1.00000			0.0368605
$737$		−	3.84950i		−	0.141798i
$738$	−7.43471	+	8.87012i	−0.273675	+	0.326514i
$739$	−35.0583			−1.28964			−0.644820	−	0.764334i	$-0.723068\pi$
$739$	−35.0583			−1.28964			−0.644820	+	0.764334i	$0.723068\pi$
$740$	−21.1301			−0.776759
$741$	1.52875	+	0.555949i	0.0561600	+	0.0204233i
$742$	−2.29189	+	1.24020i	−0.0841380	+	0.0455292i
$743$		−	5.75510i		−	0.211134i	−0.994412	−	0.105567i	$-0.966334\pi$
$743$		−	5.75510i		−	0.211134i	0.994412	−	0.105567i	$-0.0336658\pi$
$744$	1.86393	+	0.677842i	0.0683350	+	0.0248509i
$745$			19.0935i			0.699533i
$746$		−	3.92149i		−	0.143576i
$747$	−3.46960	−	2.90813i	−0.126946	−	0.106403i
$748$		−	0.722323i		−	0.0264107i
$749$	−21.0263	−	38.8567i	−0.768284	−	1.41979i
$750$	−6.89869	+	18.9700i	−0.251904	+	0.692687i
$751$	−11.3916			−0.415685			−0.207842	−	0.978162i	$-0.566644\pi$
$751$	−11.3916			−0.415685			−0.207842	+	0.978162i	$0.566644\pi$
$752$	4.30515			0.156993
$753$	39.3243	+	14.3008i	1.43306	+	0.521149i
$754$			0.419904i			0.0152920i
$755$	−42.4928			−1.54647
$756$	11.7176	+	7.19020i	0.426163	+	0.261505i
$757$	33.4679			1.21641			0.608205	−	0.793780i	$-0.291890\pi$
$757$	33.4679			1.21641			0.608205	+	0.793780i	$0.291890\pi$
$758$			14.3472i			0.521113i
$759$	−1.66870	−	0.606844i	−0.0605700	−	0.0220271i
$760$	−13.2623			−0.481074
$761$	7.00540			0.253946			0.126973	−	0.991906i	$-0.459474\pi$
$761$	7.00540			0.253946			0.126973	+	0.991906i	$0.459474\pi$
$762$	1.27155	−	3.49652i	0.0460635	−	0.126665i
$763$	25.7655	−	13.9423i	0.932774	−	0.504747i
$764$		−	22.4940i		−	0.813805i
$765$	3.44260	+	2.88550i	0.124467	+	0.104325i
$766$		−	11.2269i		−	0.405644i
$767$		−	1.69492i		−	0.0611999i
$768$	−1.62776	−	0.591954i	−0.0587366	−	0.0213603i
$769$		−	4.28914i		−	0.154670i	−0.997005	−	0.0773351i	$-0.975359\pi$
$769$		−	4.28914i		−	0.154670i	0.997005	−	0.0773351i	$-0.0246411\pi$
$770$	−5.06922	+	2.74308i	−0.182682	+	0.0988537i
$771$	−8.94639	−	3.25347i	−0.322196	−	0.117171i
$772$	22.1441			0.796985
$773$	−15.0925			−0.542838			−0.271419	−	0.962461i	$-0.587493\pi$
$773$	−15.0925			−0.542838			−0.271419	+	0.962461i	$0.587493\pi$
$774$	4.53528	−	5.41090i	0.163017	−	0.194491i
$775$			0.554368i			0.0199135i
$776$	15.7292			0.564644
$777$	−45.0731	+	6.68354i	−1.61699	+	0.239771i
$778$	−20.0180			−0.717679
$779$		−	24.0771i		−	0.862652i
$780$	0.189303	−	0.520546i	0.00677814	−	0.0186385i
$781$	1.09069			0.0390279
$782$	0.704599			0.0251964
$783$	12.5504	−	7.25964i	0.448516	−	0.259439i
$784$	3.82907	−	5.85988i	0.136753	−	0.209281i
$785$		−	20.6415i		−	0.736728i
$786$	1.98519	−	5.45888i	0.0708094	−	0.194712i
$787$			2.70531i			0.0964337i	0.998837	+	0.0482169i	$0.0153539\pi$
$787$			2.70531i			0.0964337i	−0.998837	+	0.0482169i	$0.984646\pi$
$788$		−	3.40063i		−	0.121143i
$789$	−1.27408	+	3.50347i	−0.0453584	+	0.124727i
$790$			32.1433i			1.14361i
$791$	−1.53592	−	2.83838i	−0.0546109	−	0.100921i
$792$	2.35702	+	1.97559i	0.0837529	+	0.0701995i
$793$	−0.681027			−0.0241840
$794$	15.0096			0.532672
$795$	1.23900	−	3.40701i	0.0439429	−	0.120834i
$796$		−	13.2597i		−	0.469977i
$797$	−19.0820			−0.675920			−0.337960	−	0.941160i	$-0.609737\pi$
$797$	−19.0820			−0.675920			−0.337960	+	0.941160i	$0.609737\pi$
$798$	−28.2901	+	4.19492i	−1.00146	+	0.148498i
$799$	3.03341			0.107314
$800$		−	0.484125i		−	0.0171164i
$801$	−21.1181	−	17.7007i	−0.746172	−	0.625422i
$802$	−9.92661			−0.350521
$803$	−6.18344			−0.218209
$804$	−6.11230	−	2.22281i	−0.215564	−	0.0783926i
$805$	−2.67577	−	4.94483i	−0.0943086	−	0.174282i
$806$		−	0.172322i		−	0.00606977i
$807$	−12.7376	−	4.63219i	−0.448384	−	0.163061i
$808$			3.35178i			0.117915i
$809$			50.6461i			1.78062i	0.455354	+	0.890311i	$0.349513\pi$
$809$			50.6461i			1.78062i	−0.455354	+	0.890311i	$0.650487\pi$
$810$	−18.8313	+	3.34158i	−0.661666	+	0.117411i
$811$		−	41.9260i		−	1.47222i	−0.676862	−	0.736110i	$-0.736660\pi$
$811$		−	41.9260i		−	1.47222i	0.676862	−	0.736110i	$-0.263340\pi$
$812$	−3.51341	−	6.49280i	−0.123297	−	0.227852i
$813$	3.90186	−	10.7293i	0.136844	−	0.376294i
$814$	−10.1934			−0.357279
$815$	17.3791			0.608762
$816$	−1.14692	−	0.417090i	−0.0401501	−	0.0146011i
$817$			14.6874i			0.513847i
$818$	10.3230			0.360934
$819$	0.239156	−	1.17027i	0.00835679	−	0.0408924i
$820$	−8.19837			−0.286299
$821$			19.2850i			0.673049i	0.941675	+	0.336525i	$0.109252\pi$
$821$			19.2850i			0.673049i	−0.941675	+	0.336525i	$0.890748\pi$
$822$	−20.0489	−	7.29105i	−0.699287	−	0.254305i
$823$	26.4873			0.923288			0.461644	−	0.887065i	$-0.347260\pi$
$823$	26.4873			0.923288			0.461644	+	0.887065i	$0.347260\pi$
$824$	3.14101			0.109422
$825$	−0.293789	+	0.807861i	−0.0102284	+	0.0281261i
$826$	14.1817	+	26.2078i	0.493443	+	0.911885i
$827$			51.7766i			1.80045i	0.435427	+	0.900224i	$0.356598\pi$
$827$			51.7766i			1.80045i	−0.435427	+	0.900224i	$0.643402\pi$
$828$	−1.92711	+	2.29918i	−0.0669718	+	0.0799021i
$829$		−	34.7022i		−	1.20526i	−0.798022	−	0.602628i	$-0.794120\pi$
$829$		−	34.7022i		−	1.20526i	0.798022	−	0.602628i	$-0.205880\pi$
$830$		−	3.20684i		−	0.111311i
$831$	−16.3052	−	5.92958i	−0.565620	−	0.205695i
$832$			0.150487i			0.00521720i
$833$	2.69796	−	4.12887i	0.0934789	−	0.143057i
$834$	−15.9546	−	5.80208i	−0.552461	−	0.200910i
$835$	−34.6935			−1.20062
$836$	−6.39789			−0.221276
$837$	−5.15049	+	2.97923i	−0.178027	+	0.102977i
$838$		−	17.8007i		−	0.614914i
$839$	40.7756			1.40773			0.703865	−	0.710334i	$-0.251456\pi$
$839$	40.7756			1.40773			0.703865	+	0.710334i	$0.251456\pi$
$840$	1.42839	+	9.63292i	0.0492841	+	0.332367i
$841$	21.2142			0.731525
$842$		−	19.1783i		−	0.660929i
$843$	−8.27750	+	22.7615i	−0.285092	+	0.783947i
$844$	5.52971			0.190340
$845$	27.5776			0.948700
$846$	−8.29652	+	9.89832i	−0.285240	+	0.340311i
$847$	23.1506	−	12.5274i	0.795465	−	0.430446i
$848$			0.984948i			0.0338233i
$849$	6.24260	−	17.1659i	0.214245	−	0.589132i
$850$		−	0.341114i		−	0.0117001i
$851$		−	9.94331i		−	0.340852i
$852$	0.629796	−	1.73181i	0.0215765	−	0.0593310i
$853$			50.1877i			1.71839i	0.511645	+	0.859197i	$0.329036\pi$
$853$			50.1877i			1.71839i	−0.511645	+	0.859197i	$0.670964\pi$
$854$	10.5304	−	5.69827i	0.360344	−	0.194991i
$855$	25.5580	−	30.4924i	0.874064	−	1.04282i
$856$	−16.6988			−0.570753
$857$	−26.2496			−0.896668			−0.448334	−	0.893866i	$-0.647983\pi$
$857$	−26.2496			−0.896668			−0.448334	+	0.893866i	$0.647983\pi$
$858$	0.0913222	−	0.251118i	0.00311769	−	0.00857303i
$859$			36.0465i			1.22989i	0.788570	+	0.614945i	$0.210822\pi$
$859$			36.0465i			1.22989i	−0.788570	+	0.614945i	$0.789178\pi$
$860$	5.00112			0.170537
$861$	−17.4881	+	2.59318i	−0.595994	+	0.0883753i
$862$	−13.2557			−0.451490
$863$		−	12.1410i		−	0.413285i	−0.978416	−	0.206643i	$-0.933746\pi$
$863$		−	12.1410i		−	0.413285i	0.978416	−	0.206643i	$-0.0662538\pi$
$864$	4.49788	−	2.60174i	0.153021	−	0.0885131i
$865$	−44.4180			−1.51026
$866$	13.6697			0.464514
$867$	26.8637	+	9.76934i	0.912340	+	0.331784i
$868$	1.44184	+	2.66453i	0.0489394	+	0.0904401i
$869$			15.5063i			0.526015i
$870$	9.65187	+	3.51002i	0.327229	+	0.119001i
$871$			0.565085i			0.0191472i
$872$		−	11.0728i		−	0.374973i
$873$	−30.3119	+	36.1642i	−1.02590	+	1.22397i
$874$		−	6.24091i		−	0.211102i
$875$	−27.1181	+	14.6743i	−0.916758	+	0.496081i
$876$	−3.57050	+	9.81816i	−0.120636	+	0.331725i
$877$	6.74642			0.227810			0.113905	−	0.993492i	$-0.463664\pi$
$877$	6.74642			0.227810			0.113905	+	0.993492i	$0.463664\pi$
$878$	−21.9429			−0.740537
$879$	9.46978	+	3.44380i	0.319408	+	0.116157i
$880$			2.17851i			0.0734377i
$881$	−45.6535			−1.53810			−0.769052	−	0.639186i	$-0.779272\pi$
$881$	−45.6535			−1.53810			−0.769052	+	0.639186i	$0.779272\pi$
$882$	6.09386	+	20.0964i	0.205191	+	0.676681i
$883$	−49.4263			−1.66333			−0.831664	−	0.555279i	$-0.812611\pi$
$883$	−49.4263			−1.66333			−0.831664	+	0.555279i	$0.812611\pi$
$884$			0.106033i			0.00356628i
$885$	−38.9592	−	14.1680i	−1.30960	−	0.476252i
$886$	−31.3991			−1.05487
$887$	−53.0830			−1.78235			−0.891176	−	0.453659i	$-0.850119\pi$
$887$	−53.0830			−1.78235			−0.891176	+	0.453659i	$0.850119\pi$
$888$	−5.88598	+	16.1853i	−0.197521	+	0.543143i
$889$	4.99835	−	2.70473i	0.167639	−	0.0907138i
$890$		−	19.5188i		−	0.654272i
$891$	−9.08447	+	1.61202i	−0.304341	+	0.0540046i
$892$			11.7686i			0.394041i
$893$		−	26.8681i		−	0.899105i
$894$	14.6253	+	5.31868i	0.489143	+	0.177883i
$895$		−	50.9962i		−	1.70462i
$896$	−1.25915	−	2.32692i	−0.0420653	−	0.0777368i
$897$	0.244956	+	0.0890814i	0.00817885	+	0.00297434i
$898$	30.4995			1.01778
$899$	3.19515			0.106564
$900$	1.11309	+	0.932965i	0.0371031	+	0.0310988i
$901$			0.693994i			0.0231203i
$902$	−3.95499			−0.131687
$903$	10.6680	−	1.58188i	0.355009	−	0.0526415i
$904$	−1.21980			−0.0405700
$905$			31.8200i			1.05773i
$906$	−11.8368	+	32.5487i	−0.393250	+	1.08136i
$907$	10.5462			0.350182			0.175091	−	0.984552i	$-0.443978\pi$
$907$	10.5462			0.350182			0.175091	+	0.984552i	$0.443978\pi$
$908$	20.3164			0.674222
$909$	−7.70636	−	6.45927i	−0.255604	−	0.214241i
$910$	0.744133	−	0.402669i	0.0246678	−	0.0133483i
$911$			20.5456i			0.680706i	0.940298	+	0.340353i	$0.110547\pi$
$911$			20.5456i			0.680706i	−0.940298	+	0.340353i	$0.889453\pi$
$912$	−3.69433	+	10.1587i	−0.122332	+	0.336387i
$913$		−	1.54702i		−	0.0511989i
$914$		−	0.225335i		−	0.00745341i
$915$	−5.69278	+	15.6540i	−0.188197	+	0.517505i
$916$		−	24.2391i		−	0.800884i
$917$	7.80359	−	4.22272i	0.257697	−	0.139446i
$918$	3.16920	−	1.83319i	0.104599	−	0.0605042i
$919$	41.4145			1.36614			0.683069	−	0.730354i	$-0.260645\pi$
$919$	41.4145			1.36614			0.683069	+	0.730354i	$0.260645\pi$
$920$	−2.12506			−0.0700611
$921$	−6.24323	+	17.1677i	−0.205722	+	0.565693i
$922$			19.3057i			0.635801i
$923$	−0.160107			−0.00526999
$924$	0.689073	+	4.64704i	0.0226688	+	0.152876i
$925$	−4.81381			−0.158277
$926$		−	23.8528i		−	0.783851i
$927$	−6.05309	+	7.22176i	−0.198810	+	0.237194i
$928$	−2.79030			−0.0915961
$929$	42.3536			1.38958			0.694788	−	0.719215i	$-0.255498\pi$
$929$	42.3536			1.38958			0.694788	+	0.719215i	$0.255498\pi$
$930$	−3.96096	−	1.44045i	−0.129885	−	0.0472343i
$931$	−36.5710	−	23.8969i	−1.19857	−	0.783189i
$932$		−	9.69298i		−	0.317504i
$933$	6.38724	+	2.32280i	0.209109	+	0.0760451i
$934$			1.23736i			0.0404877i
$935$			1.53498i			0.0501992i
$936$	−0.345997	−	0.290006i	−0.0113093	−	0.00947913i
$937$			11.5089i			0.375978i	0.982171	+	0.187989i	$0.0601970\pi$
$937$			11.5089i			0.375978i	−0.982171	+	0.187989i	$0.939803\pi$
$938$	−4.72817	−	8.73767i	−0.154380	−	0.285295i
$939$	6.19495	−	17.0349i	0.202164	−	0.555912i
$940$	−9.14870			−0.298398
$941$	−34.5015			−1.12472			−0.562359	−	0.826893i	$-0.690106\pi$
$941$	−34.5015			−1.12472			−0.562359	+	0.826893i	$0.690106\pi$
$942$	−15.8110	−	5.74989i	−0.515152	−	0.187341i
$943$		−	3.85795i		−	0.125632i
$944$	11.2629			0.366575
$945$	−24.9005	−	15.2796i	−0.810013	−	0.497045i
$946$	2.41260			0.0784405
$947$			16.6401i			0.540730i	0.962758	+	0.270365i	$0.0871444\pi$
$947$			16.6401i			0.540730i	−0.962758	+	0.270365i	$0.912856\pi$
$948$	24.6212	+	8.95380i	0.799658	+	0.290806i
$949$	0.907695			0.0294650
$950$	−3.02138			−0.0980266
$951$	−10.4053	+	28.6126i	−0.337416	+	0.927828i
$952$	−0.887197	−	1.63954i	−0.0287542	−	0.0531379i
$953$			49.3693i			1.59923i	0.600513	+	0.799615i	$0.294963\pi$
$953$			49.3693i			1.59923i	−0.600513	+	0.799615i	$0.705037\pi$
$954$	−2.26457	−	1.89811i	−0.0733183	−	0.0614535i
$955$			47.8011i			1.54681i
$956$		−	3.15960i		−	0.102189i
$957$	4.65618	+	1.69328i	0.150513	+	0.0547359i
$958$			24.5462i			0.793053i
$959$	−15.5089	−	28.6604i	−0.500808	−	0.925494i
$960$	3.45908	+	1.25794i	0.111641	+	0.0405998i
$961$	29.6888			0.957702
$962$	1.49634			0.0482439
$963$	32.1805	−	38.3935i	1.03700	−	1.23721i
$964$		−	25.7775i		−	0.830237i
$965$	−47.0576			−1.51484
$966$	−4.53301	+	0.672165i	−0.145847	+	0.0216265i
$967$	−23.6682			−0.761119			−0.380560	−	0.924756i	$-0.624269\pi$
$967$	−23.6682			−0.761119			−0.380560	+	0.924756i	$0.624269\pi$
$968$		−	9.94906i		−	0.319775i
$969$	−2.60302	+	7.15780i	−0.0836211	+	0.229942i
$970$	−33.4254			−1.07322
$971$	53.0160			1.70136			0.850682	−	0.525680i	$-0.176189\pi$
$971$	53.0160			1.70136			0.850682	+	0.525680i	$0.176189\pi$
$972$	−2.68605	+	15.3553i	−0.0861552	+	0.492521i
$973$	−12.3417	−	22.8074i	−0.395656	−	0.731172i
$974$		−	11.9122i		−	0.381693i
$975$	0.0431266	−	0.118590i	0.00138116	−	0.00379791i
$976$		−	4.52548i		−	0.144857i
$977$		−	49.4184i		−	1.58104i	−0.612439	−	0.790518i	$-0.709811\pi$
$977$		−	49.4184i		−	1.58104i	0.612439	−	0.790518i	$-0.290189\pi$
$978$	4.84110	−	13.3121i	0.154801	−	0.425673i
$979$		−	9.41611i		−	0.300940i
$980$	−8.13701	+	12.4526i	−0.259927	+	0.397783i
$981$	25.4584	+	21.3386i	0.812824	+	0.681288i
$982$	16.5262			0.527372
$983$	−39.5517			−1.26150			−0.630751	−	0.775985i	$-0.717253\pi$
$983$	−39.5517			−1.26150			−0.630751	+	0.775985i	$0.717253\pi$
$984$	−2.28373	+	6.27980i	−0.0728026	+	0.200193i
$985$			7.22655i			0.230257i
$986$	−1.96604			−0.0626116
$987$	−19.5153	+	2.89377i	−0.621179	+	0.0921098i
$988$	0.939176			0.0298792
$989$			2.35341i			0.0748339i
$990$	−5.00880	−	4.19824i	−0.159190	−	0.133429i
$991$	−25.9400			−0.824012			−0.412006	−	0.911181i	$-0.635172\pi$
$991$	−25.9400			−0.824012			−0.412006	+	0.911181i	$0.635172\pi$
$992$	1.14509			0.0363567
$993$	7.99281	+	2.90669i	0.253644	+	0.0922409i
$994$	2.47567	−	1.33965i	0.0785234	−	0.0424910i
$995$			28.1776i			0.893290i
$996$	−2.45638	−	0.893294i	−0.0778334	−	0.0283051i
$997$		−	39.4425i		−	1.24916i	−0.780963	−	0.624578i	$-0.785271\pi$
$997$		−	39.4425i		−	1.24916i	0.780963	−	0.624578i	$-0.214729\pi$
$998$		−	12.4640i		−	0.394540i
$999$	−25.8699	−	44.7238i	−0.818488	−	1.41500i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	966.2.f.b.461.15	yes	24
3.2	odd	2	inner	966.2.f.b.461.10	yes	24
7.6	odd	2	inner	966.2.f.b.461.22	yes	24
21.20	even	2	inner	966.2.f.b.461.3	✓	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
966.2.f.b.461.3	✓	24	21.20	even	2	inner
966.2.f.b.461.10	yes	24	3.2	odd	2	inner
966.2.f.b.461.15	yes	24	1.1	even	1	trivial
966.2.f.b.461.22	yes	24	7.6	odd	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)

\(f(q)\)	\(=\)	\(q+1.00000i q^{2} +(-1.62776 - 0.591954i) q^{3} -1.00000 q^{4} +2.12506 q^{5} +(0.591954 - 1.62776i) q^{6} +(2.32692 - 1.25915i) q^{7} -1.00000i q^{8} +(2.29918 + 1.92711i) q^{9} +O(q^{10})\)	\(q+1.00000i q^{2} +(-1.62776 - 0.591954i) q^{3} -1.00000 q^{4} +2.12506 q^{5} +(0.591954 - 1.62776i) q^{6} +(2.32692 - 1.25915i) q^{7} -1.00000i q^{8} +(2.29918 + 1.92711i) q^{9} +2.12506i q^{10} +1.02515i q^{11} +(1.62776 + 0.591954i) q^{12} -0.150487i q^{13} +(1.25915 + 2.32692i) q^{14} +(-3.45908 - 1.25794i) q^{15} +1.00000 q^{16} +0.704599 q^{17} +(-1.92711 + 2.29918i) q^{18} -6.24091i q^{19} -2.12506 q^{20} +(-4.53301 + 0.672165i) q^{21} -1.02515 q^{22} -1.00000i q^{23} +(-0.591954 + 1.62776i) q^{24} -0.484125 q^{25} +0.150487 q^{26} +(-2.60174 - 4.49788i) q^{27} +(-2.32692 + 1.25915i) q^{28} +2.79030i q^{29} +(1.25794 - 3.45908i) q^{30} -1.14509i q^{31} +1.00000i q^{32} +(0.606844 - 1.66870i) q^{33} +0.704599i q^{34} +(4.94483 - 2.67577i) q^{35} +(-2.29918 - 1.92711i) q^{36} +9.94331 q^{37} +6.24091 q^{38} +(-0.0890814 + 0.244956i) q^{39} -2.12506i q^{40} +3.85795 q^{41} +(-0.672165 - 4.53301i) q^{42} -2.35341 q^{43} -1.02515i q^{44} +(4.88589 + 4.09523i) q^{45} +1.00000 q^{46} +4.30515 q^{47} +(-1.62776 - 0.591954i) q^{48} +(3.82907 - 5.85988i) q^{49} -0.484125i q^{50} +(-1.14692 - 0.417090i) q^{51} +0.150487i q^{52} +0.984948i q^{53} +(4.49788 - 2.60174i) q^{54} +2.17851i q^{55} +(-1.25915 - 2.32692i) q^{56} +(-3.69433 + 10.1587i) q^{57} -2.79030 q^{58} +11.2629 q^{59} +(3.45908 + 1.25794i) q^{60} -4.52548i q^{61} +1.14509 q^{62} +(7.77653 + 1.58921i) q^{63} -1.00000 q^{64} -0.319794i q^{65} +(1.66870 + 0.606844i) q^{66} -3.75504 q^{67} -0.704599 q^{68} +(-0.591954 + 1.62776i) q^{69} +(2.67577 + 4.94483i) q^{70} -1.06393i q^{71} +(1.92711 - 2.29918i) q^{72} +6.03172i q^{73} +9.94331i q^{74} +(0.788038 + 0.286580i) q^{75} +6.24091i q^{76} +(1.29082 + 2.38545i) q^{77} +(-0.244956 - 0.0890814i) q^{78} +15.1258 q^{79} +2.12506 q^{80} +(1.57246 + 8.86157i) q^{81} +3.85795i q^{82} -1.50906 q^{83} +(4.53301 - 0.672165i) q^{84} +1.49731 q^{85} -2.35341i q^{86} +(1.65173 - 4.54193i) q^{87} +1.02515 q^{88} -9.18507 q^{89} +(-4.09523 + 4.88589i) q^{90} +(-0.189486 - 0.350171i) q^{91} +1.00000i q^{92} +(-0.677842 + 1.86393i) q^{93} +4.30515i q^{94} -13.2623i q^{95} +(0.591954 - 1.62776i) q^{96} +15.7292i q^{97} +(5.85988 + 3.82907i) q^{98} +(-1.97559 + 2.35702i) 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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