LMFDB - Embedded newform 966.2.y.d.193.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [966,2,Mod(25,966)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(966, base_ring=CyclotomicField(66))

chi = DirichletCharacter(H, H._module([0, 44, 6]))

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

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

chi := DirichletCharacter("966.25");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 966 = 2 \cdot 3 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	966.y (of order $33$, degree $20$, 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:	$160$
Relative dimension:	$8$ over $\Q(\zeta_{33})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{33}]$

Embedding invariants

Embedding label			193.3
Character	$\chi$	$=$	966.193
Dual form			966.2.y.d.961.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.723734 + 0.690079i) q^{2} +(0.981929 - 0.189251i) q^{3} +(0.0475819 + 0.998867i) q^{4} +(-0.487084 + 0.383047i) q^{5} +(0.841254 + 0.540641i) q^{6} +(-2.45437 + 0.987961i) q^{7} +(-0.654861 + 0.755750i) q^{8} +(0.928368 - 0.371662i) q^{9} +O(q^{10})$	\(q+(0.723734 + 0.690079i) q^{2} +(0.981929 - 0.189251i) q^{3} +(0.0475819 + 0.998867i) q^{4} +(-0.487084 + 0.383047i) q^{5} +(0.841254 + 0.540641i) q^{6} +(-2.45437 + 0.987961i) q^{7} +(-0.654861 + 0.755750i) q^{8} +(0.928368 - 0.371662i) q^{9} +(-0.616852 - 0.0589023i) q^{10} +(-2.95541 + 2.81798i) q^{11} +(0.235759 + 0.971812i) q^{12} +(2.24769 + 4.92175i) q^{13} +(-2.45808 - 0.978688i) q^{14} +(-0.405790 + 0.468306i) q^{15} +(-0.995472 + 0.0950560i) q^{16} +(0.348009 - 0.179411i) q^{17} +(0.928368 + 0.371662i) q^{18} +(-4.63739 - 2.39074i) q^{19} +(-0.405790 - 0.468306i) q^{20} +(-2.22304 + 1.43460i) q^{21} -4.08355 q^{22} +(0.865497 - 4.71709i) q^{23} +(-0.500000 + 0.866025i) q^{24} +(-1.08827 + 4.48591i) q^{25} +(-1.76967 + 5.11312i) q^{26} +(0.841254 - 0.540641i) q^{27} +(-1.10363 - 2.40458i) q^{28} +(2.23536 + 1.43658i) q^{29} +(-0.616852 + 0.0589023i) q^{30} +(-0.168242 - 0.486104i) q^{31} +(-0.786053 - 0.618159i) q^{32} +(-2.36869 + 3.32637i) q^{33} +(0.375673 + 0.110308i) q^{34} +(0.817049 - 1.42136i) q^{35} +(0.415415 + 0.909632i) q^{36} +(-7.21529 + 2.88857i) q^{37} +(-1.70644 - 4.93042i) q^{38} +(3.13852 + 4.40743i) q^{39} +(0.0294845 - 0.618956i) q^{40} +(1.67842 + 11.6737i) q^{41} +(-2.59888 - 0.495807i) q^{42} +(2.26140 + 2.60980i) q^{43} +(-2.95541 - 2.81798i) q^{44} +(-0.309829 + 0.536640i) q^{45} +(3.88155 - 2.81666i) q^{46} +(0.662957 + 1.14828i) q^{47} +(-0.959493 + 0.281733i) q^{48} +(5.04787 - 4.84965i) q^{49} +(-3.88325 + 2.49561i) q^{50} +(0.307766 - 0.242030i) q^{51} +(-4.80923 + 2.47933i) q^{52} +(0.801915 + 1.12613i) q^{53} +(0.981929 + 0.189251i) q^{54} +(0.360115 - 2.50465i) q^{55} +(0.860619 - 2.50187i) q^{56} +(-5.00603 - 1.46990i) q^{57} +(0.626454 + 2.58228i) q^{58} +(5.77777 + 0.551710i) q^{59} +(-0.487084 - 0.383047i) q^{60} +(0.991878 + 0.191169i) q^{61} +(0.213688 - 0.467911i) q^{62} +(-1.91137 + 1.82939i) q^{63} +(-0.142315 - 0.989821i) q^{64} +(-2.98008 - 1.53634i) q^{65} +(-4.00976 + 0.772818i) q^{66} +(1.87816 - 7.74188i) q^{67} +(0.195767 + 0.339078i) q^{68} +(-0.0428585 - 4.79564i) q^{69} +(1.57218 - 0.464858i) q^{70} +(8.24093 - 2.41975i) q^{71} +(-0.327068 + 0.945001i) q^{72} +(0.0885673 + 1.85926i) q^{73} +(-7.21529 - 2.88857i) q^{74} +(-0.219639 + 4.61080i) q^{75} +(2.16738 - 4.74589i) q^{76} +(4.46961 - 9.83618i) q^{77} +(-0.770024 + 5.35563i) q^{78} +(4.86167 - 6.82726i) q^{79} +(0.448468 - 0.427613i) q^{80} +(0.723734 - 0.690079i) q^{81} +(-6.84102 + 9.60686i) q^{82} +(0.685741 - 4.76943i) q^{83} +(-1.53875 - 2.15226i) q^{84} +(-0.100787 + 0.220692i) q^{85} +(-0.164312 + 3.44934i) q^{86} +(2.46684 + 0.987575i) q^{87} +(-0.194303 - 4.07893i) q^{88} +(0.118557 - 0.342548i) q^{89} +(-0.594558 + 0.174578i) q^{90} +(-10.3792 - 9.85917i) q^{91} +(4.75293 + 0.640068i) q^{92} +(-0.257198 - 0.445480i) q^{93} +(-0.312596 + 1.28854i) q^{94} +(3.17457 - 0.611847i) q^{95} +(-0.888835 - 0.458227i) q^{96} +(1.80078 + 12.5247i) q^{97} +(6.99995 - 0.0264275i) q^{98} +(-1.69637 + 3.71453i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 160 q + 8 q^{2} + 8 q^{3} + 8 q^{4} - 2 q^{5} - 16 q^{6} + 6 q^{7} - 16 q^{8} + 8 q^{9}+O(q^{10}) $ 160 * q + 8 * q^2 + 8 * q^3 + 8 * q^4 - 2 * q^5 - 16 * q^6 + 6 * q^7 - 16 * q^8 + 8 * q^9	\( 160 q + 8 q^{2} + 8 q^{3} + 8 q^{4} - 2 q^{5} - 16 q^{6} + 6 q^{7} - 16 q^{8} + 8 q^{9} - 2 q^{10} - 4 q^{11} + 8 q^{12} - 4 q^{13} + 5 q^{14} + 26 q^{15} + 8 q^{16} - 13 q^{17} + 8 q^{18} + 4 q^{19} + 26 q^{20} + 11 q^{21} - 124 q^{22} + 26 q^{23} - 80 q^{24} + 14 q^{25} + 2 q^{26} - 16 q^{27} - 22 q^{28} + 54 q^{29} - 2 q^{30} + 15 q^{31} + 8 q^{32} - 4 q^{33} + 4 q^{34} - 2 q^{35} - 16 q^{36} + 7 q^{37} - 7 q^{38} + 2 q^{39} + 9 q^{40} - 30 q^{41} + 6 q^{42} + 36 q^{43} - 4 q^{44} + 20 q^{45} + 4 q^{46} - 6 q^{47} - 16 q^{48} + 14 q^{49} - 28 q^{50} + 9 q^{51} + 2 q^{52} - 24 q^{53} + 8 q^{54} - 14 q^{55} + 6 q^{56} - 30 q^{57} - 5 q^{58} + 4 q^{59} - 2 q^{60} + 32 q^{61} - 8 q^{62} - 6 q^{63} - 16 q^{64} + 38 q^{65} - 4 q^{66} + 6 q^{67} + 42 q^{68} - 30 q^{69} - 8 q^{70} - 180 q^{71} + 8 q^{72} - 32 q^{73} + 7 q^{74} + 14 q^{75} - 8 q^{76} + 61 q^{77} + 18 q^{78} - 66 q^{79} - 2 q^{80} + 8 q^{81} - 7 q^{82} + 130 q^{83} + 5 q^{84} - 70 q^{85} - 40 q^{86} + 6 q^{87} - 15 q^{88} - 4 q^{89} + 4 q^{90} - 6 q^{91} + 58 q^{92} - 18 q^{93} + 16 q^{94} + 19 q^{95} + 8 q^{96} + 40 q^{97} + 43 q^{98} + 8 q^{99}+O(q^{100}) \) 160 * q + 8 * q^2 + 8 * q^3 + 8 * q^4 - 2 * q^5 - 16 * q^6 + 6 * q^7 - 16 * q^8 + 8 * q^9 - 2 * q^10 - 4 * q^11 + 8 * q^12 - 4 * q^13 + 5 * q^14 + 26 * q^15 + 8 * q^16 - 13 * q^17 + 8 * q^18 + 4 * q^19 + 26 * q^20 + 11 * q^21 - 124 * q^22 + 26 * q^23 - 80 * q^24 + 14 * q^25 + 2 * q^26 - 16 * q^27 - 22 * q^28 + 54 * q^29 - 2 * q^30 + 15 * q^31 + 8 * q^32 - 4 * q^33 + 4 * q^34 - 2 * q^35 - 16 * q^36 + 7 * q^37 - 7 * q^38 + 2 * q^39 + 9 * q^40 - 30 * q^41 + 6 * q^42 + 36 * q^43 - 4 * q^44 + 20 * q^45 + 4 * q^46 - 6 * q^47 - 16 * q^48 + 14 * q^49 - 28 * q^50 + 9 * q^51 + 2 * q^52 - 24 * q^53 + 8 * q^54 - 14 * q^55 + 6 * q^56 - 30 * q^57 - 5 * q^58 + 4 * q^59 - 2 * q^60 + 32 * q^61 - 8 * q^62 - 6 * q^63 - 16 * q^64 + 38 * q^65 - 4 * q^66 + 6 * q^67 + 42 * q^68 - 30 * q^69 - 8 * q^70 - 180 * q^71 + 8 * q^72 - 32 * q^73 + 7 * q^74 + 14 * q^75 - 8 * q^76 + 61 * q^77 + 18 * q^78 - 66 * q^79 - 2 * q^80 + 8 * q^81 - 7 * q^82 + 130 * q^83 + 5 * q^84 - 70 * q^85 - 40 * q^86 + 6 * q^87 - 15 * q^88 - 4 * q^89 + 4 * q^90 - 6 * q^91 + 58 * q^92 - 18 * q^93 + 16 * q^94 + 19 * q^95 + 8 * q^96 + 40 * q^97 + 43 * q^98 + 8 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$323$	$829$	$925$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{5}{11}\right)$

Coefficient data

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

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

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

$2$	0.723734	+	0.690079i	0.511757	+	0.487960i
$2$	0.723734	+	0.690079i	0.511757	+	0.487960i
$3$	0.981929	−	0.189251i	0.566917	−	0.109264i
$3$	0.981929	−	0.189251i	0.566917	−	0.109264i
$4$	0.0475819	+	0.998867i	0.0237910	+	0.499434i
$5$	−0.487084	+	0.383047i	−0.217831	+	0.171304i	−0.721112	−	0.692819i	$-0.756369\pi$
$5$	−0.487084	+	0.383047i	−0.217831	+	0.171304i	0.503281	+	0.864123i	$0.332126\pi$
$6$	0.841254	+	0.540641i	0.343440	+	0.220716i
$7$	−2.45437	+	0.987961i	−0.927665	+	0.373414i
$7$	−2.45437	+	0.987961i	−0.927665	+	0.373414i
$8$	−0.654861	+	0.755750i	−0.231528	+	0.267198i
$9$	0.928368	−	0.371662i	0.309456	−	0.123887i
$10$	−0.616852	−	0.0589023i	−0.195066	−	0.0186265i
$11$	−2.95541	+	2.81798i	−0.891089	+	0.849652i	−0.989357	−	0.145508i	$-0.953518\pi$
$11$	−2.95541	+	2.81798i	−0.891089	+	0.849652i	0.0982681	+	0.995160i	$0.468670\pi$
$12$	0.235759	+	0.971812i	0.0680577	+	0.280538i
$13$	2.24769	+	4.92175i	0.623397	+	1.36505i	0.913023	+	0.407908i	$0.133742\pi$
$13$	2.24769	+	4.92175i	0.623397	+	1.36505i	−0.289626	+	0.957140i	$0.593531\pi$
$14$	−2.45808	−	0.978688i	−0.656950	−	0.261565i
$15$	−0.405790	+	0.468306i	−0.104774	+	0.120916i
$16$	−0.995472	+	0.0950560i	−0.248868	+	0.0237640i
$17$	0.348009	−	0.179411i	0.0844045	−	0.0435135i	−0.415507	−	0.909590i	$-0.636396\pi$
$17$	0.348009	−	0.179411i	0.0844045	−	0.0435135i	0.499912	+	0.866076i	$0.333366\pi$
$18$	0.928368	+	0.371662i	0.218818	+	0.0876017i
$19$	−4.63739	−	2.39074i	−1.06389	−	0.548473i	−0.164840	−	0.986320i	$-0.552711\pi$
$19$	−4.63739	−	2.39074i	−1.06389	−	0.548473i	−0.899050	+	0.437847i	$0.855741\pi$
$20$	−0.405790	−	0.468306i	−0.0907374	−	0.104717i
$21$	−2.22304	+	1.43460i	−0.485108	+	0.313055i
$22$	−4.08355			−0.870617
$23$	0.865497	−	4.71709i	0.180469	−	0.983581i
$23$	0.865497	−	4.71709i	0.180469	−	0.983581i
$24$	−0.500000	+	0.866025i	−0.102062	+	0.176777i
$25$	−1.08827	+	4.48591i	−0.217654	+	0.897181i
$26$	−1.76967	+	5.11312i	−0.347061	+	1.00277i
$27$	0.841254	−	0.540641i	0.161899	−	0.104046i
$28$	−1.10363	−	2.40458i	−0.208566	−	0.454423i
$29$	2.23536	+	1.43658i	0.415097	+	0.266766i	0.731477	−	0.681866i	$-0.238831\pi$
$29$	2.23536	+	1.43658i	0.415097	+	0.266766i	−0.316381	+	0.948632i	$0.602468\pi$
$30$	−0.616852	+	0.0589023i	−0.112621	+	0.0107540i
$31$	−0.168242	−	0.486104i	−0.0302172	−	0.0873069i	0.928883	−	0.370372i	$-0.120770\pi$
$31$	−0.168242	−	0.486104i	−0.0302172	−	0.0873069i	−0.959101	+	0.283065i	$0.908649\pi$
$32$	−0.786053	−	0.618159i	−0.138956	−	0.109276i
$33$	−2.36869	+	3.32637i	−0.412337	+	0.579046i
$34$	0.375673	+	0.110308i	0.0644274	+	0.0189176i
$35$	0.817049	−	1.42136i	0.138107	−	0.240254i
$36$	0.415415	+	0.909632i	0.0692358	+	0.151605i
$37$	−7.21529	+	2.88857i	−1.18619	+	0.474878i	−0.879023	−	0.476779i	$-0.841804\pi$
$37$	−7.21529	+	2.88857i	−1.18619	+	0.474878i	−0.307164	+	0.951657i	$0.599380\pi$
$38$	−1.70644	−	4.93042i	−0.276821	−	0.799820i
$39$	3.13852	+	4.40743i	0.502565	+	0.705754i
$40$	0.0294845	−	0.618956i	0.00466191	−	0.0978656i
$41$	1.67842	+	11.6737i	0.262125	+	1.82312i	0.516816	+	0.856096i	$0.327117\pi$
$41$	1.67842	+	11.6737i	0.262125	+	1.82312i	−0.254691	+	0.967022i	$0.581974\pi$
$42$	−2.59888	−	0.495807i	−0.401016	−	0.0765046i
$43$	2.26140	+	2.60980i	0.344860	+	0.397990i	0.901511	−	0.432757i	$-0.142459\pi$
$43$	2.26140	+	2.60980i	0.344860	+	0.397990i	−0.556650	+	0.830747i	$0.687914\pi$
$44$	−2.95541	−	2.81798i	−0.445544	−	0.424826i
$45$	−0.309829	+	0.536640i	−0.0461866	+	0.0799975i
$46$	3.88155	−	2.81666i	0.572304	−	0.415293i
$47$	0.662957	+	1.14828i	0.0967023	+	0.167493i	0.910318	−	0.413910i	$-0.135837\pi$
$47$	0.662957	+	1.14828i	0.0967023	+	0.167493i	−0.813616	+	0.581403i	$0.802504\pi$
$48$	−0.959493	+	0.281733i	−0.138491	+	0.0406646i
$49$	5.04787	−	4.84965i	0.721124	−	0.692806i
$50$	−3.88325	+	2.49561i	−0.549174	+	0.352933i
$51$	0.307766	−	0.242030i	0.0430958	−	0.0338909i
$52$	−4.80923	+	2.47933i	−0.666920	+	0.343821i
$53$	0.801915	+	1.12613i	0.110151	+	0.154686i	0.865972	−	0.500093i	$-0.166701\pi$
$53$	0.801915	+	1.12613i	0.110151	+	0.154686i	−0.755820	+	0.654779i	$0.772762\pi$
$54$	0.981929	+	0.189251i	0.133624	+	0.0257538i
$55$	0.360115	−	2.50465i	0.0485578	−	0.337727i
$56$	0.860619	−	2.50187i	0.115005	−	0.334326i
$57$	−5.00603	−	1.46990i	−0.663066	−	0.194694i
$58$	0.626454	+	2.58228i	0.0822575	+	0.339070i
$59$	5.77777	+	0.551710i	0.752202	+	0.0718265i	0.464112	−	0.885777i	$-0.346374\pi$
$59$	5.77777	+	0.551710i	0.752202	+	0.0718265i	0.288090	+	0.957603i	$0.406980\pi$
$60$	−0.487084	−	0.383047i	−0.0628823	−	0.0494512i
$61$	0.991878	+	0.191169i	0.126997	+	0.0244767i	0.252354	−	0.967635i	$-0.418795\pi$
$61$	0.991878	+	0.191169i	0.126997	+	0.0244767i	−0.125357	+	0.992112i	$0.540008\pi$
$62$	0.213688	−	0.467911i	0.0271384	−	0.0594247i
$63$	−1.91137	+	1.82939i	−0.240810	+	0.230481i
$64$	−0.142315	−	0.989821i	−0.0177894	−	0.123728i
$65$	−2.98008	−	1.53634i	−0.369633	−	0.190559i
$66$	−4.00976	+	0.772818i	−0.493567	+	0.0951273i
$67$	1.87816	−	7.74188i	0.229454	−	0.945821i	−0.734257	−	0.678872i	$-0.762469\pi$
$67$	1.87816	−	7.74188i	0.229454	−	0.945821i	0.963711	−	0.266949i	$-0.0860156\pi$
$68$	0.195767	+	0.339078i	0.0237402	+	0.0411192i
$69$	−0.0428585	−	4.79564i	−0.00515956	−	0.577327i
$70$	1.57218	−	0.464858i	0.187911	−	0.0555612i
$71$	8.24093	−	2.41975i	0.978018	−	0.287172i	0.246612	−	0.969114i	$-0.420683\pi$
$71$	8.24093	−	2.41975i	0.978018	−	0.287172i	0.731406	+	0.681942i	$0.238864\pi$
$72$	−0.327068	+	0.945001i	−0.0385453	+	0.111369i
$73$	0.0885673	+	1.85926i	0.0103660	+	0.217610i	0.998107	+	0.0615060i	$0.0195903\pi$
$73$	0.0885673	+	1.85926i	0.0103660	+	0.217610i	−0.987741	+	0.156104i	$0.950107\pi$
$74$	−7.21529	−	2.88857i	−0.838761	−	0.335789i
$75$	−0.219639	+	4.61080i	−0.0253618	+	0.532409i
$76$	2.16738	−	4.74589i	0.248615	−	0.544391i
$77$	4.46961	−	9.83618i	0.509360	−	1.12094i
$78$	−0.770024	+	5.35563i	−0.0871880	+	0.606406i
$79$	4.86167	−	6.82726i	0.546981	−	0.768127i	−0.444861	−	0.895599i	$-0.646747\pi$
$79$	4.86167	−	6.82726i	0.546981	−	0.768127i	0.991842	+	0.127472i	$0.0406864\pi$
$80$	0.448468	−	0.427613i	0.0501402	−	0.0478086i
$81$	0.723734	−	0.690079i	0.0804149	−	0.0766754i
$82$	−6.84102	+	9.60686i	−0.755464	+	1.06090i
$83$	0.685741	−	4.76943i	0.0752698	−	0.523513i	−0.916949	−	0.399005i	$-0.869356\pi$
$83$	0.685741	−	4.76943i	0.0752698	−	0.523513i	0.992219	−	0.124508i	$-0.0397353\pi$
$84$	−1.53875	−	2.15226i	−0.167892	−	0.234831i
$85$	−0.100787	+	0.220692i	−0.0109318	+	0.0239374i
$86$	−0.164312	+	3.44934i	−0.0177183	+	0.371952i
$87$	2.46684	+	0.987575i	0.264473	+	0.105879i
$88$	−0.194303	−	4.07893i	−0.0207128	−	0.434815i
$89$	0.118557	−	0.342548i	0.0125670	−	0.0363100i	−0.938543	−	0.345163i	$-0.887824\pi$
$89$	0.118557	−	0.342548i	0.0125670	−	0.0363100i	0.951110	+	0.308853i	$0.0999450\pi$
$90$	−0.594558	+	0.174578i	−0.0626719	+	0.0184021i
$91$	−10.3792	−	9.85917i	−1.08803	−	1.03352i
$92$	4.75293	+	0.640068i	0.495527	+	0.0667317i
$93$	−0.257198	−	0.445480i	−0.0266702	−	0.0461941i
$94$	−0.312596	+	1.28854i	−0.0322418	+	0.132903i
$95$	3.17457	−	0.611847i	0.325704	−	0.0627742i
$96$	−0.888835	−	0.458227i	−0.0907164	−	0.0467675i
$97$	1.80078	+	12.5247i	0.182842	+	1.27169i	0.850003	+	0.526778i	$0.176600\pi$
$97$	1.80078	+	12.5247i	0.182842	+	1.27169i	−0.667161	+	0.744914i	$0.732491\pi$
$98$	6.99995	−	0.0264275i	0.707102	−	0.00266958i
$99$	−1.69637	+	3.71453i	−0.170492	+	0.373325i
$100$	−4.53261	−	0.873588i	−0.453261	−	0.0873588i
$101$	−11.3366	−	8.91519i	−1.12803	−	0.887094i	−0.133451	−	0.991055i	$-0.542606\pi$
$101$	−11.3366	−	8.91519i	−1.12803	−	0.887094i	−0.994581	+	0.103961i	$0.966848\pi$
$102$	0.389760	+	0.0372176i	0.0385920	+	0.00368509i
$103$	3.53453	+	14.5696i	0.348268	+	1.43558i	0.829264	+	0.558858i	$0.188760\pi$
$103$	3.53453	+	14.5696i	0.348268	+	1.43558i	−0.480996	+	0.876723i	$0.659725\pi$
$104$	−5.19153	−	1.52437i	−0.509072	−	0.149477i
$105$	0.533290	−	1.55030i	0.0520438	−	0.151294i
$106$	−0.196747	+	1.36840i	−0.0191097	+	0.132911i
$107$	15.0234	+	2.89552i	1.45237	+	0.279921i	0.853569	−	0.520979i	$-0.174433\pi$
$107$	15.0234	+	2.89552i	1.45237	+	0.279921i	0.598798	+	0.800900i	$0.295645\pi$
$108$	0.580057	+	0.814576i	0.0558160	+	0.0783826i
$109$	−2.31098	+	1.19139i	−0.221352	+	0.114115i	−0.565336	−	0.824861i	$-0.691254\pi$
$109$	−2.31098	+	1.19139i	−0.221352	+	0.114115i	0.343984	+	0.938975i	$0.388223\pi$
$110$	1.98904	−	1.56419i	0.189647	−	0.149140i
$111$	−6.53824	+	4.20187i	−0.620582	+	0.398824i
$112$	2.34934	−	1.21679i	0.221992	−	0.114976i
$113$	13.6999	−	4.02264i	1.28877	−	0.378418i	0.435645	−	0.900119i	$-0.356520\pi$
$113$	13.6999	−	4.02264i	1.28877	−	0.378418i	0.853129	+	0.521701i	$0.174702\pi$
$114$	−2.60869	−	4.51838i	−0.244326	−	0.423185i
$115$	1.38530	+	2.62915i	0.129180	+	0.245169i
$116$	−1.32859	+	2.30119i	−0.123357	+	0.213660i
$117$	3.91591	+	3.73381i	0.362026	+	0.345191i
$118$	3.80085	+	4.38641i	0.349896	+	0.403802i
$119$	−0.676891	+	0.784160i	−0.0620505	+	0.0718838i
$120$	−0.0881866	−	0.613351i	−0.00805029	−	0.0559910i
$121$	0.270047	−	5.66899i	0.0245498	−	0.515363i
$122$	0.585934	+	0.822829i	0.0530480	+	0.0744955i
$123$	3.85734	+	11.1451i	0.347805	+	1.00492i
$124$	0.477548	−	0.191181i	0.0428851	−	0.0171686i
$125$	−2.47531	−	5.42018i	−0.221399	−	0.484795i
$126$	−2.64575	+	0.00499434i	−0.235702	+	0.000444931i
$127$	−9.45199	−	2.77535i	−0.838728	−	0.246273i	−0.165966	−	0.986131i	$-0.553074\pi$
$127$	−9.45199	−	2.77535i	−0.838728	−	0.246273i	−0.672762	+	0.739859i	$0.734892\pi$
$128$	0.580057	−	0.814576i	0.0512703	−	0.0719990i
$129$	2.71444	+	2.13466i	0.238993	+	0.187946i
$130$	−1.09659	−	3.16839i	−0.0961773	−	0.277886i
$131$	14.1822	−	1.35424i	1.23911	−	0.118320i	0.545151	−	0.838338i	$-0.316472\pi$
$131$	14.1822	−	1.35424i	1.23911	−	0.118320i	0.693956	+	0.720018i	$0.255866\pi$
$132$	−3.43530	−	2.20774i	−0.299005	−	0.192159i
$133$	13.7438	+	1.28620i	1.19174	+	0.111528i
$134$	6.70179	−	4.30698i	0.578947	−	0.372066i
$135$	−0.202670	+	0.585578i	−0.0174431	+	0.0503985i
$136$	−0.0923074	+	0.380496i	−0.00791530	+	0.0326273i
$137$	5.48719	−	9.50410i	0.468803	−	0.811990i	−0.530561	−	0.847646i	$-0.678019\pi$
$137$	5.48719	−	9.50410i	0.468803	−	0.811990i	0.999364	+	0.0356565i	$0.0113522\pi$
$138$	3.27835	−	3.50034i	0.279072	−	0.297969i
$139$	−21.2672			−1.80386			−0.901932	−	0.431879i	$-0.857851\pi$
$139$	−21.2672			−1.80386			−0.901932	+	0.431879i	$0.857851\pi$
$140$	1.45863	+	0.748493i	0.123276	+	0.0632592i
$141$	0.868289	+	1.00206i	0.0731232	+	0.0843886i
$142$	7.63406	+	3.93563i	0.640636	+	0.330271i
$143$	−20.5122	−	8.21185i	−1.71532	−	0.686709i
$144$	−0.888835	+	0.458227i	−0.0740696	+	0.0381855i
$145$	−1.63909	+	0.156514i	−0.136119	+	0.0129978i
$146$	−1.21893	+	1.40673i	−0.100880	+	0.116421i
$147$	4.03884	−	5.71732i	0.333118	−	0.471557i
$148$	−3.22861	−	7.06968i	−0.265390	−	0.581124i
$149$	−4.01610	−	16.5546i	−0.329012	−	1.35621i	−0.860634	−	0.509224i	$-0.829932\pi$
$149$	−4.01610	−	16.5546i	−0.329012	−	1.35621i	0.531622	−	0.846982i	$-0.321583\pi$
$150$	−3.34077	+	3.18542i	−0.272773	+	0.260089i
$151$	−7.89752	−	0.754122i	−0.642691	−	0.0613696i	−0.231378	−	0.972864i	$-0.574324\pi$
$151$	−7.89752	−	0.754122i	−0.642691	−	0.0613696i	−0.411313	+	0.911494i	$0.634930\pi$
$152$	4.84364	−	1.93910i	0.392871	−	0.157282i
$153$	0.256400	−	0.295901i	0.0207287	−	0.0239222i
$154$	10.0226	−	4.03439i	0.807640	−	0.325101i
$155$	0.268149	+	0.172329i	0.0215383	+	0.0138418i
$156$	−4.25310	+	3.34468i	−0.340521	+	0.267788i
$157$	−0.228907	−	4.80535i	−0.0182688	−	0.383509i	−0.989423	−	0.145058i	$-0.953663\pi$
$157$	−0.228907	−	4.80535i	−0.0182688	−	0.383509i	0.971154	−	0.238451i	$-0.0766398\pi$
$158$	8.22991	−	1.58618i	0.654736	−	0.126190i
$159$	1.00054	+	0.954018i	0.0793484	+	0.0756585i
$160$	0.619658			0.0489883
$161$	2.53605	+	12.4326i	0.199869	+	0.979823i
$162$	1.00000			0.0785674
$163$	−5.83647	−	5.56506i	−0.457148	−	0.435889i	0.426185	−	0.904636i	$-0.359857\pi$
$163$	−5.83647	−	5.56506i	−0.457148	−	0.435889i	−0.883333	+	0.468747i	$0.844706\pi$
$164$	−11.5806	+	2.23197i	−0.904291	+	0.174288i
$165$	−0.120402	−	2.52754i	−0.00937326	−	0.196769i
$166$	3.78758	−	2.97859i	0.293973	−	0.231183i
$167$	4.18462	+	2.68929i	0.323816	+	0.208104i	0.692441	−	0.721474i	$-0.256535\pi$
$167$	4.18462	+	2.68929i	0.323816	+	0.208104i	−0.368625	+	0.929578i	$0.620172\pi$
$168$	0.371585	−	2.61953i	0.0286684	−	0.202101i
$169$	−10.6583	+	12.3004i	−0.819873	+	0.946184i
$170$	−0.225238	+	0.0901715i	−0.0172749	+	0.00691584i
$171$	−5.19375	−	0.495943i	−0.397176	−	0.0379257i
$172$	−2.49924	+	2.38302i	−0.190565	+	0.181703i
$173$	3.29726	+	13.5915i	0.250686	+	1.03334i	0.948428	+	0.316992i	$0.102673\pi$
$173$	3.29726	+	13.5915i	0.250686	+	1.03334i	−0.697742	+	0.716349i	$0.745812\pi$
$174$	1.10383	+	2.41706i	0.0836814	+	0.183237i
$175$	−1.76089	−	12.0852i	−0.133110	−	0.913558i
$176$	2.67416	−	3.08614i	0.201572	−	0.232627i
$177$	5.77777	−	0.551710i	0.434284	−	0.0414691i
$178$	0.322189	−	0.166100i	0.0241491	−	0.0124497i
$179$	10.8169	+	4.33043i	0.808492	+	0.323671i	0.738824	−	0.673899i	$-0.235382\pi$
$179$	10.8169	+	4.33043i	0.808492	+	0.323671i	0.0696684	+	0.997570i	$0.477806\pi$
$180$	−0.550774	−	0.283944i	−0.0410523	−	0.0211639i
$181$	−2.20740	−	2.54747i	−0.164075	−	0.189352i	0.667759	−	0.744378i	$-0.267254\pi$
$181$	−2.20740	−	2.54747i	−0.164075	−	0.189352i	−0.831833	+	0.555026i	$0.812708\pi$
$182$	−0.708144	−	14.2979i	−0.0524912	−	1.05983i
$183$	1.01013			0.0746711
$184$	2.99816	+	3.74313i	0.221027	+	0.275948i
$185$	2.40800	−	4.17077i	0.177039	−	0.306641i
$186$	0.121273	−	0.499896i	0.00889219	−	0.0366541i
$187$	−0.522932	+	1.51091i	−0.0382406	+	0.110489i
$188$	−1.11543	+	0.716844i	−0.0813511	+	0.0522812i
$189$	−1.53062	+	2.15806i	−0.111336	+	0.156976i
$190$	2.71976	+	1.74789i	0.197312	+	0.126805i
$191$	18.2973	−	1.74718i	1.32395	−	0.126422i	0.590982	−	0.806685i	$-0.298741\pi$
$191$	18.2973	−	1.74718i	1.32395	−	0.126422i	0.732968	+	0.680263i	$0.238135\pi$
$192$	−0.327068	−	0.945001i	−0.0236041	−	0.0681996i
$193$	−0.824206	−	0.648162i	−0.0593276	−	0.0466558i	0.588055	−	0.808821i	$-0.299894\pi$
$193$	−0.824206	−	0.648162i	−0.0593276	−	0.0466558i	−0.647382	+	0.762165i	$0.724136\pi$
$194$	−7.33975	+	10.3072i	−0.526964	+	0.740017i
$195$	−3.21698	−	0.944590i	−0.230373	−	0.0676435i
$196$	5.08434	+	4.81139i	0.363167	+	0.343671i
$197$	−2.80661	−	6.14561i	−0.199962	−	0.437857i	0.782912	−	0.622132i	$-0.213733\pi$
$197$	−2.80661	−	6.14561i	−0.199962	−	0.437857i	−0.982875	+	0.184276i	$0.941006\pi$
$198$	−3.79104	+	1.51770i	−0.269418	+	0.107859i
$199$	6.09240	+	17.6028i	0.431879	+	1.24783i	0.925697	+	0.378266i	$0.123480\pi$
$199$	6.09240	+	17.6028i	0.431879	+	1.24783i	−0.493818	+	0.869565i	$0.664399\pi$
$200$	−2.67756	−	3.76010i	−0.189332	−	0.265879i
$201$	0.379058	−	7.95741i	0.0267367	−	0.561273i
$202$	−2.05249	−	14.2754i	−0.144412	−	1.00441i
$203$	−6.90570	−	1.31745i	−0.484685	−	0.0924668i
$204$	0.256400	+	0.295901i	0.0179516	+	0.0207172i
$205$	−5.28909	−	5.04314i	−0.369406	−	0.352228i
$206$	−7.49608	+	12.9836i	−0.522277	+	0.904609i
$207$	−0.949665	−	4.70087i	−0.0660063	−	0.326733i
$208$	−2.70535	−	4.68581i	−0.187582	−	0.324902i
$209$	20.4424	−	6.00244i	1.41403	−	0.415197i
$210$	1.45579	−	0.753994i	0.100459	−	0.0520305i
$211$	17.8773	−	11.4891i	1.23073	−	0.790941i	0.246723	−	0.969086i	$-0.420646\pi$
$211$	17.8773	−	11.4891i	1.23073	−	0.790941i	0.984004	+	0.178145i	$0.0570098\pi$
$212$	−1.08670	+	0.854590i	−0.0746348	+	0.0586935i
$213$	7.63406	−	3.93563i	0.523077	−	0.269665i
$214$	8.87481	+	12.4629i	0.606669	+	0.851948i
$215$	−2.10117	−	0.404967i	−0.143298	−	0.0276185i
$216$	−0.142315	+	0.989821i	−0.00968330	+	0.0673488i
$217$	0.893181	+	1.02686i	0.0606331	+	0.0697080i
$218$	−2.49469	−	0.732508i	−0.168962	−	0.0496117i
$219$	0.438833	+	1.80890i	0.0296536	+	0.122234i
$220$	2.51895	+	0.240531i	0.169828	+	0.0162166i
$221$	1.66523	+	1.30955i	0.112016	+	0.0880900i
$222$	−7.63157	−	1.47086i	−0.512197	−	0.0987179i
$223$	4.37701	−	9.58431i	0.293106	−	0.641813i	−0.704593	−	0.709612i	$-0.748870\pi$
$223$	4.37701	−	9.58431i	0.293106	−	0.641813i	0.997699	+	0.0677987i	$0.0215976\pi$
$224$	2.53998	+	0.740601i	0.169710	+	0.0494835i
$225$	0.656929	+	4.56904i	0.0437952	+	0.304603i
$226$	12.6910	+	6.54266i	0.844192	+	0.435211i
$227$	−17.5743	+	3.38718i	−1.16645	+	0.224815i	−0.735477	−	0.677550i	$-0.763042\pi$
$227$	−17.5743	+	3.38718i	−1.16645	+	0.224815i	−0.430973	+	0.902365i	$0.641830\pi$
$228$	1.23004	−	5.07031i	0.0814616	−	0.335789i
$229$	4.44632	+	7.70126i	0.293821	+	0.508913i	0.974710	−	0.223474i	$-0.0717396\pi$
$229$	4.44632	+	7.70126i	0.293821	+	0.508913i	−0.680889	+	0.732387i	$0.738406\pi$
$230$	−0.811731	+	2.85877i	−0.0535239	+	0.188502i
$231$	2.52733	−	10.5043i	0.166286	−	0.691133i
$232$	−2.54955	+	0.748615i	−0.167386	+	0.0491490i
$233$	−1.38612	+	4.00492i	−0.0908075	+	0.262371i	−0.981255	−	0.192716i	$-0.938271\pi$
$233$	−1.38612	+	4.00492i	−0.0908075	+	0.262371i	0.890447	+	0.455087i	$0.150392\pi$
$234$	0.257452	+	5.40458i	0.0168301	+	0.353308i
$235$	−0.762760	−	0.305363i	−0.0497570	−	0.0199197i
$236$	−0.276168	+	5.79748i	−0.0179770	+	0.377384i
$237$	3.48175	−	7.62396i	0.226164	−	0.495230i
$238$	−1.03102	+	0.100415i	−0.0668312	+	0.00650893i
$239$	−1.36093	+	9.46548i	−0.0880313	+	0.612271i	0.897275	+	0.441473i	$0.145544\pi$
$239$	−1.36093	+	9.46548i	−0.0880313	+	0.612271i	−0.985306	+	0.170798i	$0.945365\pi$
$240$	0.359437	−	0.504759i	0.0232016	−	0.0325820i
$241$	−7.72221	+	7.36311i	−0.497431	+	0.474300i	−0.896766	−	0.442506i	$-0.854090\pi$
$241$	−7.72221	+	7.36311i	−0.497431	+	0.474300i	0.399335	+	0.916805i	$0.369241\pi$
$242$	4.10749	−	3.91649i	0.264040	−	0.251761i
$243$	0.580057	−	0.814576i	0.0372107	−	0.0522551i
$244$	−0.143757	+	0.999851i	−0.00920309	+	0.0640089i
$245$	−0.601092	+	4.29576i	−0.0384024	+	0.274446i
$246$	−4.89928	+	10.7279i	−0.312367	+	0.683988i
$247$	1.34322	−	28.1977i	0.0854672	−	1.79418i
$248$	0.477548	+	0.191181i	0.0303243	+	0.0121400i
$249$	−0.229272	−	4.81302i	−0.0145295	−	0.305013i
$250$	1.94888	−	5.63093i	0.123258	−	0.356131i
$251$	−1.14715	+	0.336833i	−0.0724073	+	0.0212607i	−0.317736	−	0.948179i	$-0.602922\pi$
$251$	−1.14715	+	0.336833i	−0.0724073	+	0.0212607i	0.245328	+	0.969440i	$0.421104\pi$
$252$	−1.91826	−	1.82216i	−0.120839	−	0.114785i
$253$	10.7347	+	16.3799i	0.674887	+	1.02979i
$254$	−4.92551	−	8.53124i	−0.309054	−	0.535297i
$255$	−0.0571991	+	0.235778i	−0.00358194	+	0.0147650i
$256$	0.981929	−	0.189251i	0.0613705	−	0.0118282i
$257$	27.4364	+	14.1444i	1.71144	+	0.882306i	0.979635	+	0.200788i	$0.0643503\pi$
$257$	27.4364	+	14.1444i	1.71144	+	0.882306i	0.731801	+	0.681518i	$0.238680\pi$
$258$	0.491449	+	3.41810i	0.0305963	+	0.212802i
$259$	14.8552	−	14.2180i	0.923058	−	0.883466i
$260$	1.39280	−	3.04980i	0.0863777	−	0.189141i
$261$	2.60916	+	0.502875i	0.161503	+	0.0311272i
$262$	11.1987	+	8.80674i	0.691857	+	0.544082i
$263$	11.0705	+	1.05710i	0.682636	+	0.0651838i	0.430612	−	0.902537i	$-0.358298\pi$
$263$	11.0705	+	1.05710i	0.682636	+	0.0651838i	0.252024	+	0.967721i	$0.418904\pi$
$264$	−0.962735	−	3.96845i	−0.0592522	−	0.244241i
$265$	−0.821962	−	0.241350i	−0.0504927	−	0.0148260i
$266$	9.05929	+	10.4152i	0.555461	+	0.638596i
$267$	0.0515868	−	0.358794i	0.00315706	−	0.0219579i
$268$	7.82247	+	1.50766i	0.477834	+	0.0920949i
$269$	−11.9751	−	16.8166i	−0.730133	−	1.02533i	−0.998083	−	0.0618952i	$-0.980286\pi$
$269$	−11.9751	−	16.8166i	−0.730133	−	1.02533i	0.267950	−	0.963433i	$-0.413654\pi$
$270$	−0.550774	+	0.283944i	−0.0335191	+	0.0172803i
$271$	−22.8713	+	17.9862i	−1.38933	+	1.09258i	−0.405380	+	0.914148i	$0.632861\pi$
$271$	−22.8713	+	17.9862i	−1.38933	+	1.09258i	−0.983952	+	0.178435i	$0.942897\pi$
$272$	−0.329379	+	0.211679i	−0.0199715	+	0.0128349i
$273$	−12.0575	−	7.71673i	−0.729750	−	0.467038i
$274$	10.5298	−	3.09184i	0.636131	−	0.186785i
$275$	−9.42489	−	16.3244i	−0.568342	−	0.984398i
$276$	4.78817	−	0.270996i	0.288214	−	0.0163120i
$277$	−13.3052	+	23.0452i	−0.799430	+	1.38465i	0.120558	+	0.992706i	$0.461532\pi$
$277$	−13.3052	+	23.0452i	−0.799430	+	1.38465i	−0.919988	+	0.391947i	$0.871802\pi$
$278$	−15.3918	−	14.6761i	−0.923140	−	0.880212i
$279$	−0.336857	−	0.388754i	−0.0201671	−	0.0232741i
$280$	0.539139	+	1.54828i	0.0322197	+	0.0925273i
$281$	1.39717	+	9.71750i	0.0833479	+	0.579697i	0.988106	+	0.153772i	$0.0491422\pi$
$281$	1.39717	+	9.71750i	0.0833479	+	0.579697i	−0.904758	+	0.425925i	$0.859949\pi$
$282$	−0.0630896	+	1.32441i	−0.00375693	+	0.0788676i
$283$	16.0687	+	22.5653i	0.955183	+	1.34137i	0.939888	+	0.341484i	$0.110930\pi$
$283$	16.0687	+	22.5653i	0.955183	+	1.34137i	0.0152956	+	0.999883i	$0.495131\pi$
$284$	2.80913	+	8.11646i	0.166691	+	0.481623i
$285$	3.00140	−	1.20158i	0.177788	−	0.0711755i
$286$	−9.17856	−	20.0982i	−0.542740	−	1.18843i
$287$	−15.6526	−	26.9933i	−0.923943	−	1.59336i
$288$	−0.959493	−	0.281733i	−0.0565387	−	0.0166013i
$289$	−9.77205	+	13.7229i	−0.574826	+	0.807230i
$290$	−1.29427	−	1.01783i	−0.0760022	−	0.0597688i
$291$	4.13856	+	11.9576i	0.242607	+	0.700965i
$292$	−1.85294	+	0.176934i	−0.108435	+	0.0103543i
$293$	1.05563	+	0.678412i	0.0616706	+	0.0396333i	0.571113	−	0.820872i	$-0.306512\pi$
$293$	1.05563	+	0.678412i	0.0616706	+	0.0396333i	−0.509442	+	0.860505i	$0.670148\pi$
$294$	6.86845	−	1.35070i	0.400576	−	0.0787744i
$295$	−3.02559	+	1.94443i	−0.176157	+	0.113209i
$296$	2.54198	−	7.34456i	0.147749	−	0.426894i
$297$	−0.962735	+	3.96845i	−0.0558635	+	0.230273i
$298$	8.51740	−	14.7526i	0.493400	−	0.854593i
$299$	25.1617	−	6.34278i	1.45514	−	0.366813i
$300$	−4.61602			−0.266506
$301$	−8.12869	−	4.17123i	−0.468530	−	0.240426i
$302$	−5.19530	−	5.99570i	−0.298956	−	0.345014i
$303$	−12.8189	−	6.60862i	−0.736428	−	0.379655i
$304$	4.84364	+	1.93910i	0.277802	+	0.111215i
$305$	−0.556355	+	0.286821i	−0.0318568	+	0.0164233i
$306$	0.389760	−	0.0372176i	0.0222811	−	0.00212759i
$307$	3.17657	−	3.66596i	0.181296	−	0.209227i	−0.657826	−	0.753170i	$-0.728524\pi$
$307$	3.17657	−	3.66596i	0.181296	−	0.209227i	0.839122	+	0.543943i	$0.183069\pi$
$308$	10.0377	+	3.99653i	0.571952	+	0.227723i
$309$	6.22797	+	13.6373i	0.354297	+	0.775801i
$310$	0.0751480	+	0.309764i	0.00426812	+	0.0175934i
$311$	−4.03356	+	3.84599i	−0.228722	+	0.218086i	−0.795770	−	0.605598i	$-0.792934\pi$
$311$	−4.03356	+	3.84599i	−0.228722	+	0.218086i	0.567048	+	0.823685i	$0.308085\pi$
$312$	−5.38621	−	0.514320i	−0.304934	−	0.0291177i
$313$	−17.0236	+	6.81522i	−0.962230	+	0.385219i	−0.798975	−	0.601365i	$-0.794624\pi$
$313$	−17.0236	+	6.81522i	−0.962230	+	0.385219i	−0.163256	+	0.986584i	$0.552200\pi$
$314$	3.15041	−	3.63576i	0.177788	−	0.205178i
$315$	0.230256	−	1.62321i	0.0129735	−	0.0914576i
$316$	7.05086	+	4.53131i	0.396642	+	0.254906i
$317$	15.1259	−	11.8951i	0.849555	−	0.668097i	−0.0953497	−	0.995444i	$-0.530397\pi$
$317$	15.1259	−	11.8951i	0.849555	−	0.668097i	0.944904	+	0.327347i	$0.106155\pi$
$318$	0.0657809	+	1.38091i	0.00368881	+	0.0774376i
$319$	−10.6547	+	2.05352i	−0.596546	+	0.114975i
$320$	0.448468	+	0.427613i	0.0250701	+	0.0239043i
$321$	15.2999			0.853957
$322$	−6.74402	+	10.7479i	−0.375830	+	0.598959i
$323$	−2.04278			−0.113663
$324$	0.723734	+	0.690079i	0.0402074	+	0.0383377i
$325$	−24.5246	+	4.72673i	−1.36038	+	0.262192i
$326$	−0.383719	−	8.05525i	−0.0212522	−	0.446139i
$327$	−2.04375	+	1.60722i	−0.113019	+	0.0888795i
$328$	−9.92149	−	6.37616i	−0.547823	−	0.352064i
$329$	−2.76159	−	2.16332i	−0.152252	−	0.119268i
$330$	1.65706	−	1.91235i	0.0912184	−	0.105272i
$331$	14.6619	−	5.86974i	0.805892	−	0.322630i	0.0681169	−	0.997677i	$-0.478301\pi$
$331$	14.6619	−	5.86974i	0.805892	−	0.322630i	0.737775	+	0.675047i	$0.235877\pi$
$332$	4.79666	+	0.458025i	0.263251	+	0.0251374i
$333$	−5.62487	+	5.36331i	−0.308241	+	0.293907i
$334$	1.17273	+	4.83405i	0.0641689	+	0.264508i
$335$	2.05068	+	4.49037i	0.112041	+	0.245335i
$336$	2.07661	−	1.63942i	0.113288	−	0.0894376i
$337$	16.6570	−	19.2232i	0.907363	−	1.04715i	−0.0913187	−	0.995822i	$-0.529108\pi$
$337$	16.6570	−	19.2232i	0.907363	−	1.04715i	0.998682	−	0.0513310i	$-0.0163463\pi$
$338$	−16.2020	+	1.54711i	−0.881275	+	0.0841516i
$339$	12.6910	−	6.54266i	0.689280	−	0.355348i
$340$	−0.225238	−	0.0901715i	−0.0122152	−	0.00489024i
$341$	1.86705	+	0.962533i	0.101107	+	0.0521241i
$342$	−3.41665	−	3.94303i	−0.184751	−	0.213215i
$343$	−7.59807	+	16.8899i	−0.410257	+	0.911970i
$344$	−3.45325			−0.186187
$345$	1.85783	+	2.31946i	0.100022	+	0.124876i
$346$	−6.99286	+	12.1120i	−0.375938	+	0.651144i
$347$	3.46270	−	14.2734i	0.185887	−	0.766238i	−0.800162	−	0.599784i	$-0.795253\pi$
$347$	3.46270	−	14.2734i	0.185887	−	0.766238i	0.986049	−	0.166454i	$-0.0532317\pi$
$348$	−0.869079	+	2.51104i	−0.0465875	+	0.134606i
$349$	−1.74669	+	1.12253i	−0.0934981	+	0.0600876i	−0.586554	−	0.809910i	$-0.699516\pi$
$349$	−1.74669	+	1.12253i	−0.0934981	+	0.0600876i	0.493056	+	0.869997i	$0.335880\pi$
$350$	7.06536	−	9.96165i	0.377659	−	0.532473i
$351$	4.55178	+	2.92525i	0.242956	+	0.156138i
$352$	4.06506	−	0.388167i	0.216669	−	0.0206893i
$353$	−4.88736	−	14.1211i	−0.260128	−	0.751590i	−0.997131	−	0.0757004i	$-0.975881\pi$
$353$	−4.88736	−	14.1211i	−0.260128	−	0.751590i	0.737003	−	0.675890i	$-0.236240\pi$
$354$	4.56229	+	3.58783i	0.242483	+	0.190691i
$355$	−3.08715	+	4.33529i	−0.163849	+	0.230093i
$356$	0.347801	+	0.102124i	0.0184334	+	0.00541254i
$357$	−0.516255	+	0.898091i	−0.0273231	+	0.0475320i
$358$	4.84021	+	10.5986i	0.255813	+	0.560153i
$359$	−20.5507	+	8.22727i	−1.08463	+	0.434219i	−0.843969	−	0.536392i	$-0.819787\pi$
$359$	−20.5507	+	8.22727i	−1.08463	+	0.434219i	−0.240656	+	0.970610i	$0.577363\pi$
$360$	−0.202670	−	0.585578i	−0.0106817	−	0.0308626i
$361$	4.76865	+	6.69663i	0.250982	+	0.352454i
$362$	0.160389	−	3.36697i	0.00842984	−	0.176964i
$363$	−0.807696	−	5.61765i	−0.0423931	−	0.294850i
$364$	9.35414	−	10.8365i	0.490290	−	0.567988i
$365$	−0.755323	−	0.871689i	−0.0395354	−	0.0456263i
$366$	0.731067	+	0.697071i	0.0382135	+	0.0364365i
$367$	10.8894	−	18.8610i	0.568423	−	0.984537i	−0.428300	−	0.903637i	$-0.640887\pi$
$367$	10.8894	−	18.8610i	0.568423	−	0.984537i	0.996722	−	0.0809001i	$-0.0257795\pi$
$368$	−0.413190	+	4.77800i	−0.0215390	+	0.249070i
$369$	5.89685	+	10.2136i	0.306978	+	0.531701i
$370$	4.62091	−	1.35682i	0.240230	−	0.0705378i
$371$	−3.08077	−	1.97168i	−0.159946	−	0.102365i
$372$	0.432737	−	0.278103i	0.0224364	−	0.0144190i
$373$	−21.0741	+	16.5728i	−1.09117	+	0.858109i	−0.990596	−	0.136820i	$-0.956312\pi$
$373$	−21.0741	+	16.5728i	−1.09117	+	0.858109i	−0.100579	+	0.994929i	$0.532069\pi$
$374$	−1.42111	+	0.732634i	−0.0734840	+	0.0378836i
$375$	−3.45636	−	4.85377i	−0.178485	−	0.250648i
$376$	−1.30195	−	0.250931i	−0.0671431	−	0.0129408i
$377$	−2.04609	+	14.2309i	−0.105379	+	0.732928i
$378$	−2.59699	+	0.505615i	−0.133575	+	0.0260060i
$379$	24.7111	+	7.25585i	1.26933	+	0.372708i	0.845958	−	0.533250i	$-0.179029\pi$
$379$	24.7111	+	7.25585i	1.26933	+	0.372708i	0.423369	+	0.905958i	$0.360848\pi$
$380$	0.762206	+	3.14186i	0.0391004	+	0.161174i
$381$	−9.80642	−	0.936399i	−0.502398	−	0.0479732i
$382$	14.4481	+	11.3621i	0.739230	+	0.581337i
$383$	−23.2556	−	4.48215i	−1.18831	−	0.229027i	−0.443479	−	0.896285i	$-0.646256\pi$
$383$	−23.2556	−	4.48215i	−1.18831	−	0.229027i	−0.744827	+	0.667258i	$0.767468\pi$
$384$	0.415415	−	0.909632i	0.0211991	−	0.0464195i
$385$	1.59064	+	6.50312i	0.0810668	+	0.331430i
$386$	−0.149222	−	1.03786i	−0.00759522	−	0.0528259i
$387$	3.06937	+	1.58237i	0.156025	+	0.0804365i
$388$	−12.4248	+	2.39469i	−0.630776	+	0.121572i
$389$	0.364535	−	1.50263i	0.0184827	−	0.0761866i	−0.961823	−	0.273671i	$-0.911762\pi$
$389$	0.364535	−	1.50263i	0.0184827	−	0.0761866i	0.980306	+	0.197484i	$0.0632772\pi$
$390$	−1.67639	−	2.90360i	−0.0848875	−	0.147030i
$391$	−0.545097	−	1.79687i	−0.0275667	−	0.0908714i
$392$	0.359469	+	6.99076i	0.0181559	+	0.353087i
$393$	13.6696	−	4.01377i	0.689542	−	0.202468i
$394$	2.20972	−	6.38457i	0.111324	−	0.321650i
$395$	0.247121	+	5.18770i	0.0124340	+	0.261022i
$396$	−3.79104	−	1.51770i	−0.190507	−	0.0762675i
$397$	−0.458571	+	9.62659i	−0.0230150	+	0.483144i	0.957708	+	0.287742i	$0.0929045\pi$
$397$	−0.458571	+	9.62659i	−0.0230150	+	0.483144i	−0.980723	+	0.195403i	$0.937399\pi$
$398$	−7.73807	+	16.9440i	−0.387874	+	0.849326i
$399$	13.7389	−	1.33808i	0.687804	−	0.0669877i
$400$	0.656929	−	4.56904i	0.0328464	−	0.228452i
$401$	−7.80783	+	10.9646i	−0.389905	+	0.547544i	−0.962144	−	0.272542i	$-0.912135\pi$
$401$	−7.80783	+	10.9646i	−0.389905	+	0.547544i	0.572239	+	0.820087i	$0.306075\pi$
$402$	5.76558	−	5.49747i	0.287561	−	0.274189i
$403$	2.01433	−	1.92066i	0.100341	−	0.0956748i
$404$	8.36567	−	11.7479i	0.416208	−	0.584482i
$405$	−0.0881866	+	0.613351i	−0.00438203	+	0.0304777i
$406$	−4.08874	−	5.71896i	−0.202921	−	0.283827i
$407$	13.1842	−	28.8694i	0.653517	−	1.43100i
$408$	−0.0186299	+	0.391090i	−0.000922317	+	0.0193618i
$409$	20.5766	+	8.23761i	1.01744	+	0.407324i	0.819616	−	0.572913i	$-0.194187\pi$
$409$	20.5766	+	8.23761i	1.01744	+	0.407324i	0.197829	+	0.980237i	$0.436611\pi$
$410$	−0.347732	−	7.29979i	−0.0171732	−	0.360511i
$411$	3.58937	−	10.3708i	0.177051	−	0.511554i
$412$	−14.3849	+	4.22378i	−0.708692	+	0.208091i
$413$	−14.7259	+	4.35411i	−0.724612	+	0.214252i
$414$	2.55666	−	4.05752i	0.125653	−	0.199416i
$415$	1.49290	+	2.58579i	0.0732838	+	0.126931i
$416$	1.27562	−	5.25819i	0.0625425	−	0.257804i
$417$	−20.8829	+	4.02485i	−1.02264	+	0.197098i
$418$	18.9370	+	9.76272i	0.926240	+	0.477510i
$419$	4.37559	+	30.4329i	0.213761	+	1.48674i	0.760444	+	0.649403i	$0.224981\pi$
$419$	4.37559	+	30.4329i	0.213761	+	1.48674i	−0.546683	+	0.837340i	$0.684110\pi$
$420$	1.57392	+	0.458919i	0.0767995	+	0.0223930i
$421$	−6.36614	+	13.9399i	−0.310267	+	0.679389i	−0.998957	−	0.0456667i	$-0.985459\pi$
$421$	−6.36614	+	13.9399i	−0.310267	+	0.679389i	0.688690	+	0.725056i	$0.258186\pi$
$422$	20.8668	+	4.02175i	1.01578	+	0.195776i
$423$	1.04224	+	0.819626i	0.0506754	+	0.0398516i
$424$	−1.37622	−	0.131413i	−0.0668350	−	0.00638196i
$425$	0.426093	+	1.75638i	0.0206686	+	0.0851970i
$426$	8.24093	+	2.41975i	0.399274	+	0.117237i
$427$	−2.62330	+	0.510738i	−0.126951	+	0.0247163i
$428$	−2.17740	+	15.1442i	−0.105249	+	0.732021i
$429$	−21.6956	−	4.18149i	−1.04747	−	0.201884i
$430$	−1.24123	−	1.74306i	−0.0598573	−	0.0840578i
$431$	−16.8082	+	8.66524i	−0.809624	+	0.417390i	−0.812755	−	0.582605i	$-0.802033\pi$
$431$	−16.8082	+	8.66524i	−0.809624	+	0.417390i	0.00313180	+	0.999995i	$0.499003\pi$
$432$	−0.786053	+	0.618159i	−0.0378190	+	0.0297412i
$433$	10.2320	−	6.57571i	0.491719	−	0.316008i	−0.271178	−	0.962529i	$-0.587413\pi$
$433$	10.2320	−	6.57571i	0.491719	−	0.316008i	0.762896	+	0.646521i	$0.223777\pi$
$434$	−0.0621909	+	1.35954i	−0.00298526	+	0.0652601i
$435$	−1.57985	+	0.463885i	−0.0757479	+	0.0222416i
$436$	−1.30001	−	2.25168i	−0.0622590	−	0.107836i
$437$	−15.2910	+	19.8058i	−0.731466	+	0.947439i
$438$	−0.930682	+	1.61199i	−0.0444697	+	0.0770238i
$439$	−22.1695	−	21.1386i	−1.05809	−	1.00889i	−0.999944	−	0.0105815i	$-0.996632\pi$
$439$	−22.1695	−	21.1386i	−1.05809	−	1.00889i	−0.0581488	−	0.998308i	$-0.518520\pi$
$440$	1.65706	+	1.91235i	0.0789975	+	0.0911679i
$441$	2.88385	−	6.37836i	0.137326	−	0.303731i
$442$	0.301490	+	2.09691i	0.0143404	+	0.0997397i
$443$	0.900874	−	18.9117i	0.0428018	−	0.898521i	−0.870732	−	0.491758i	$-0.836354\pi$
$443$	0.900874	−	18.9117i	0.0428018	−	0.898521i	0.913534	−	0.406763i	$-0.133342\pi$
$444$	−4.50821	−	6.33090i	−0.213950	−	0.300451i
$445$	0.0734647	+	0.212262i	0.00348256	+	0.0100622i
$446$	9.78172	−	3.91601i	0.463178	−	0.185429i
$447$	−7.07651	−	15.4954i	−0.334707	−	0.732907i
$448$	1.32720	+	2.28879i	0.0627042	+	0.108135i
$449$	34.6708	+	10.1803i	1.63622	+	0.480437i	0.965310	−	0.261105i	$-0.0840869\pi$
$449$	34.6708	+	10.1803i	1.63622	+	0.480437i	0.670907	+	0.741542i	$0.265905\pi$
$450$	−2.67756	+	3.76010i	−0.126221	+	0.177253i
$451$	−37.8565	−	29.7707i	−1.78259	−	1.40185i
$452$	4.66995	+	13.4929i	0.219656	+	0.634654i
$453$	−7.89752	+	0.754122i	−0.371058	+	0.0354317i
$454$	−15.0566	−	9.67627i	−0.706640	−	0.454130i
$455$	8.83205	+	0.826538i	0.414053	+	0.0387487i
$456$	4.38914	−	2.82073i	0.205540	−	0.132093i
$457$	2.95046	−	8.52478i	0.138017	−	0.398773i	−0.854719	−	0.519091i	$-0.826270\pi$
$457$	2.95046	−	8.52478i	0.138017	−	0.398773i	0.992735	+	0.120319i	$0.0383917\pi$
$458$	−2.09652	+	8.64197i	−0.0979640	+	0.403813i
$459$	0.195767	−	0.339078i	0.00913760	−	0.0158268i
$460$	−2.56025	+	1.50883i	−0.119372	+	0.0703495i
$461$	−23.0532			−1.07369			−0.536847	−	0.843680i	$-0.680385\pi$
$461$	−23.0532			−1.07369			−0.536847	+	0.843680i	$0.680385\pi$
$462$	9.07792	−	5.85827i	0.422343	−	0.272551i
$463$	−12.1909	−	14.0691i	−0.566560	−	0.653845i	0.398101	−	0.917342i	$-0.369669\pi$
$463$	−12.1909	−	14.0691i	−0.566560	−	0.653845i	−0.964660	+	0.263497i	$0.915124\pi$
$464$	−2.36180	−	1.21759i	−0.109644	−	0.0565253i
$465$	0.295917	+	0.118467i	0.0137228	+	0.00549378i
$466$	−3.76689	+	1.94197i	−0.174498	+	0.0899599i
$467$	−31.6643	+	3.02358i	−1.46525	+	0.139915i	−0.796981	−	0.604004i	$-0.793571\pi$
$467$	−31.6643	+	3.02358i	−1.46525	+	0.139915i	−0.668270	+	0.743919i	$0.732965\pi$
$468$	−3.54326	+	4.08914i	−0.163787	+	0.189021i
$469$	3.03898	+	20.8570i	0.140327	+	0.963086i
$470$	−0.341311	−	0.747366i	−0.0157435	−	0.0344734i
$471$	−1.13419	−	4.67519i	−0.0522607	−	0.215422i
$472$	−4.20059	+	4.00525i	−0.193348	+	0.184357i
$473$	−14.0377	−	1.34044i	−0.645454	−	0.0616334i
$474$	7.78099	−	3.11504i	0.357393	−	0.143079i
$475$	15.7714	−	18.2011i	0.723639	−	0.835124i
$476$	−0.815479	−	0.638812i	−0.0373774	−	0.0292799i
$477$	1.16301	+	0.747423i	0.0532507	+	0.0342221i
$478$	−7.51688	+	5.91134i	−0.343814	+	0.270378i
$479$	0.233200	+	4.89546i	0.0106552	+	0.223679i	0.997914	+	0.0645570i	$0.0205634\pi$
$479$	0.233200	+	4.89546i	0.0106552	+	0.223679i	−0.987259	+	0.159122i	$0.949134\pi$
$480$	0.608460	−	0.117271i	0.0277723	−	0.00535267i
$481$	−30.4345	−	29.0193i	−1.38770	−	1.32317i
$482$	−10.6700			−0.486003
$483$	4.84310	+	11.7279i	0.220369	+	0.533639i
$484$	5.67542			0.257974
$485$	−5.67469	−	5.41081i	−0.257674	−	0.245692i
$486$	0.981929	−	0.189251i	0.0445412	−	0.00858461i
$487$	−1.47606	−	30.9864i	−0.0668868	−	1.40413i	−0.743967	−	0.668217i	$-0.767058\pi$
$487$	−1.47606	−	30.9864i	−0.0668868	−	1.40413i	0.677080	−	0.735909i	$-0.263245\pi$
$488$	−0.794018	+	0.624422i	−0.0359435	+	0.0282663i
$489$	−6.78419	−	4.35994i	−0.306792	−	0.197163i
$490$	−3.39944	+	2.69418i	−0.153571	+	0.121711i
$491$	2.44840	−	2.82561i	0.110495	−	0.127518i	−0.697808	−	0.716285i	$-0.745841\pi$
$491$	2.44840	−	2.82561i	0.110495	−	0.127518i	0.808303	+	0.588767i	$0.200386\pi$
$492$	−10.9489	+	4.38328i	−0.493614	+	0.197613i
$493$	1.03566	+	0.0988939i	0.0466440	+	0.00445396i
$494$	20.4308	−	19.4807i	0.919224	−	0.876479i
$495$	−0.596566	−	2.45908i	−0.0268137	−	0.110527i
$496$	0.213688	+	0.467911i	0.00959486	+	0.0210098i
$497$	−17.8357	+	14.0807i	−0.800039	+	0.631605i
$498$	3.15543	−	3.64156i	0.141398	−	0.163182i
$499$	5.00116	−	0.477553i	0.223883	−	0.0213782i	0.0174882	−	0.999847i	$-0.494433\pi$
$499$	5.00116	−	0.477553i	0.223883	−	0.0213782i	0.206394	+	0.978469i	$0.433827\pi$
$500$	5.29626	−	2.73041i	0.236856	−	0.122108i
$501$	4.61795	+	1.84875i	0.206315	+	0.0825960i
$502$	−1.06267	−	0.547845i	−0.0474293	−	0.0244515i
$503$	3.53900	+	4.08423i	0.157796	+	0.182107i	0.829143	−	0.559037i	$-0.188829\pi$
$503$	3.53900	+	4.08423i	0.157796	+	0.182107i	−0.671346	+	0.741144i	$0.734284\pi$
$504$	−0.130878	−	2.64251i	−0.00582979	−	0.117707i
$505$	8.93681			0.397683
$506$	−3.53430	+	19.2625i	−0.157119	+	0.856322i
$507$	−8.13787	+	14.0952i	−0.361416	+	0.625990i
$508$	2.32247	−	9.57334i	0.103043	−	0.424748i
$509$	−7.59033	+	21.9308i	−0.336436	+	0.972067i	0.642213	+	0.766526i	$0.278016\pi$
$509$	−7.59033	+	21.9308i	−0.336436	+	0.972067i	−0.978649	+	0.205540i	$0.934105\pi$
$510$	−0.204102	+	0.131169i	−0.00903780	+	0.00580824i
$511$	−2.05425	−	4.47580i	−0.0908747	−	0.197998i
$512$	0.841254	+	0.540641i	0.0371785	+	0.0238932i
$513$	−5.19375	+	0.495943i	−0.229310	+	0.0218964i
$514$	10.0959	+	29.1701i	0.445310	+	1.28664i
$515$	−7.30244	−	5.74271i	−0.321784	−	0.253054i
$516$	−2.00308	+	2.81294i	−0.0881809	+	0.123833i
$517$	−5.19512	−	1.52543i	−0.228481	−	0.0670881i
$518$	20.5628	−	0.0388161i	0.903477	−	0.00170548i
$519$	5.80987	+	12.7219i	0.255025	+	0.558427i
$520$	3.11262	−	1.24611i	0.136497	−	0.0546453i
$521$	−1.58945	−	4.59242i	−0.0696351	−	0.201197i	0.904813	−	0.425808i	$-0.140010\pi$
$521$	−1.58945	−	4.59242i	−0.0696351	−	0.201197i	−0.974449	+	0.224611i	$0.927889\pi$
$522$	1.54132	+	2.16448i	0.0674616	+	0.0947366i
$523$	−1.34057	+	28.1419i	−0.0586188	+	1.23056i	0.757562	+	0.652764i	$0.226390\pi$
$523$	−1.34057	+	28.1419i	−0.0586188	+	1.23056i	−0.816181	+	0.577797i	$0.803913\pi$
$524$	2.02752	+	14.1017i	0.0885727	+	0.616036i
$525$	−4.01621	−	11.5336i	−0.175282	−	0.503367i
$526$	7.28261	+	8.40458i	0.317537	+	0.366457i
$527$	−0.145762	−	0.138984i	−0.00634950	−	0.00605423i
$528$	2.04178	−	3.53646i	0.0888570	−	0.153905i
$529$	−21.5018	−	8.16525i	−0.934862	−	0.355011i
$530$	−0.428331	−	0.741892i	−0.0186055	−	0.0322257i
$531$	5.56895	−	1.63519i	0.241672	−	0.0709612i
$532$	−0.630786	+	13.7895i	−0.0273480	+	0.597849i
$533$	−53.6823	+	34.4995i	−2.32524	+	1.49434i
$534$	0.284932	−	0.224073i	0.0123302	−	0.00969657i
$535$	−8.42679	+	4.34431i	−0.364322	+	0.187821i
$536$	4.62099	+	6.48927i	0.199596	+	0.280294i
$537$	11.4410	+	2.20506i	0.493713	+	0.0951555i
$538$	2.93804	−	20.4345i	0.126668	−	0.880994i
$539$	−1.25232	+	28.5574i	−0.0539411	+	1.23006i
$540$	−0.594558	−	0.174578i	−0.0255857	−	0.00751264i
$541$	6.98772	+	28.8038i	0.300426	+	1.23837i	0.899230	+	0.437476i	$0.144128\pi$
$541$	6.98772	+	28.8038i	0.300426	+	1.23837i	−0.598804	+	0.800895i	$0.704357\pi$
$542$	−28.9646	−	2.76579i	−1.24414	−	0.118801i
$543$	−2.64962	−	2.08368i	−0.113706	−	0.0894194i
$544$	−0.384458	−	0.0740981i	−0.0164835	−	0.00317693i
$545$	0.669283	−	1.46553i	0.0286689	−	0.0627762i
$546$	−3.40123	−	13.9055i	−0.145559	−	0.595099i
$547$	−5.13933	−	35.7448i	−0.219742	−	1.52834i	−0.738991	−	0.673715i	$-0.764697\pi$
$547$	−5.13933	−	35.7448i	−0.219742	−	1.52834i	0.519249	−	0.854623i	$-0.326212\pi$
$548$	9.75443	+	5.02876i	0.416688	+	0.214818i
$549$	0.991878	−	0.191169i	0.0423323	−	0.00815889i
$550$	4.44401	−	18.3184i	0.189493	−	0.781101i
$551$	−6.93176	−	12.0062i	−0.295303	−	0.511479i
$552$	3.65237	+	3.10809i	0.155455	+	0.132289i
$553$	−5.18727	+	21.5598i	−0.220585	+	0.916815i
$554$	−25.5324	+	7.49700i	−1.08477	+	0.318517i
$555$	1.57516	−	4.55112i	0.0668617	−	0.193184i
$556$	−1.01194	−	21.2431i	−0.0429156	−	0.900910i
$557$	−23.8611	−	9.55253i	−1.01103	−	0.404754i	−0.193781	−	0.981045i	$-0.562075\pi$
$557$	−23.8611	−	9.55253i	−1.01103	−	0.404754i	−0.817245	+	0.576291i	$0.804499\pi$
$558$	0.0244759	−	0.513813i	0.00103615	−	0.0217514i
$559$	−7.76184	+	16.9961i	−0.328291	+	0.718857i
$560$	−0.678241	+	1.49259i	−0.0286609	+	0.0630734i
$561$	−0.227540	+	1.58257i	−0.00960673	+	0.0668163i
$562$	−5.69467	+	7.99704i	−0.240215	+	0.337335i
$563$	−29.7810	+	28.3961i	−1.25512	+	1.19675i	−0.283826	+	0.958876i	$0.591604\pi$
$563$	−29.7810	+	28.3961i	−1.25512	+	1.19675i	−0.971295	+	0.237879i	$0.923548\pi$
$564$	−0.959610	+	0.914986i	−0.0404069	+	0.0385279i
$565$	−5.13212	+	7.20706i	−0.215910	+	0.303203i
$566$	−3.94239	+	27.4199i	−0.165711	+	1.15255i
$567$	−1.09454	+	2.40873i	−0.0459664	+	0.101157i
$568$	−3.56793	+	7.81268i	−0.149707	+	0.327813i
$569$	1.59162	−	33.4123i	0.0667243	−	1.40072i	−0.678842	−	0.734284i	$-0.737518\pi$
$569$	1.59162	−	33.4123i	0.0667243	−	1.40072i	0.745566	−	0.666431i	$-0.232179\pi$
$570$	3.00140	+	1.20158i	0.125715	+	0.0503287i
$571$	−0.833737	−	17.5023i	−0.0348908	−	0.732448i	−0.946755	−	0.321956i	$-0.895660\pi$
$571$	−0.833737	−	17.5023i	−0.0348908	−	0.732448i	0.911864	−	0.410493i	$-0.134643\pi$
$572$	7.22654	−	20.8797i	0.302157	−	0.873025i
$573$	17.6360	−	5.17841i	0.736756	−	0.216331i
$574$	7.29918	−	30.3375i	0.304662	−	1.26626i
$575$	20.2185	+	9.01600i	0.843170	+	0.375993i
$576$	−0.500000	−	0.866025i	−0.0208333	−	0.0360844i
$577$	3.33030	−	13.7277i	0.138642	−	0.571491i	−0.859532	−	0.511083i	$-0.829245\pi$
$577$	3.33030	−	13.7277i	0.138642	−	0.571491i	0.998174	−	0.0604082i	$-0.0192402\pi$
$578$	−16.5423	+	3.18826i	−0.688067	+	0.132614i
$579$	−0.931977	−	0.480467i	−0.0387316	−	0.0199675i
$580$	−0.234328	−	1.62979i	−0.00972993	−	0.0676731i
$581$	3.02895	+	12.3834i	0.125662	+	0.513752i
$582$	−5.25646	+	11.5100i	−0.217887	+	0.477106i
$583$	−5.54340	−	1.06840i	−0.229584	−	0.0442487i
$584$	−1.46313	−	1.15062i	−0.0605448	−	0.0476130i
$585$	−3.33761	−	0.318703i	−0.137993	−	0.0131767i
$586$	0.295837	+	1.21946i	0.0122209	+	0.0503753i
$587$	−20.0856	−	5.89766i	−0.829020	−	0.243422i	−0.160424	−	0.987048i	$-0.551286\pi$
$587$	−20.0856	−	5.89766i	−0.829020	−	0.243422i	−0.668596	+	0.743626i	$0.733104\pi$
$588$	5.90302	+	3.76223i	0.243436	+	0.155152i
$589$	−0.381944	+	2.65648i	−0.0157377	+	0.109458i
$590$	−3.53153	−	0.680647i	−0.145391	−	0.0280218i
$591$	−3.91895	−	5.50340i	−0.161204	−	0.226380i
$592$	6.90805	−	3.56134i	0.283919	−	0.146370i
$593$	13.6260	−	10.7156i	0.559554	−	0.440038i	−0.297901	−	0.954597i	$-0.596287\pi$
$593$	13.6260	−	10.7156i	0.559554	−	0.440038i	0.857455	+	0.514559i	$0.172044\pi$
$594$	−3.43530	+	2.20774i	−0.140952	+	0.0905845i
$595$	0.0293326	−	0.641233i	0.00120252	−	0.0262880i
$596$	16.3448	−	4.79926i	0.669508	−	0.196585i
$597$	9.31366	+	16.1317i	0.381183	+	0.660228i
$598$	22.5874	+	12.7731i	0.923668	+	0.522330i
$599$	−21.3751	+	37.0227i	−0.873363	+	1.51271i	−0.0148659	+	0.999889i	$0.504732\pi$
$599$	−21.3751	+	37.0227i	−0.873363	+	1.51271i	−0.858497	+	0.512819i	$0.828601\pi$
$600$	−3.34077	−	3.18542i	−0.136387	−	0.130044i
$601$	9.42015	+	10.8714i	0.384256	+	0.443455i	0.914620	−	0.404315i	$-0.132490\pi$
$601$	9.42015	+	10.8714i	0.384256	+	0.443455i	−0.530364	+	0.847770i	$0.677945\pi$
$602$	−3.00453	−	8.62830i	−0.122456	−	0.351663i
$603$	−1.13374	−	7.88535i	−0.0461696	−	0.321116i
$604$	0.377488	−	7.92446i	0.0153598	−	0.322442i
$605$	2.03996	+	2.86472i	0.0829360	+	0.116467i
$606$	−4.71703	−	13.6290i	−0.191616	−	0.553638i
$607$	36.1251	−	14.4623i	1.46627	−	0.587008i	0.505127	−	0.863045i	$-0.331445\pi$
$607$	36.1251	−	14.4623i	1.46627	−	0.587008i	0.961147	+	0.276037i	$0.0890212\pi$
$608$	2.16738	+	4.74589i	0.0878987	+	0.192471i
$609$	−7.03023	+	0.0132709i	−0.284879	+	0.000537763i
$610$	−0.600582	−	0.176347i	−0.0243169	−	0.00714007i
$611$	−4.16141	+	5.84388i	−0.168352	+	0.236418i
$612$	0.307766	+	0.242030i	0.0124407	+	0.00978347i
$613$	5.25431	+	15.1813i	0.212220	+	0.613168i	0.999996	−	0.00279301i	$-0.000889042\pi$
$613$	5.25431	+	15.1813i	0.212220	+	0.613168i	−0.787777	+	0.615961i	$0.788768\pi$
$614$	4.82879	−	0.461094i	0.194874	−	0.0186082i
$615$	−6.14793	−	3.95104i	−0.247909	−	0.159321i
$616$	4.50672	+	9.81924i	0.181581	+	0.395628i
$617$	−6.66961	+	4.28630i	−0.268508	+	0.172560i	−0.667966	−	0.744192i	$-0.732835\pi$
$617$	−6.66961	+	4.28630i	−0.268508	+	0.172560i	0.399458	+	0.916752i	$0.369198\pi$
$618$	−4.90345	+	14.1676i	−0.197246	+	0.569904i
$619$	−3.13085	+	12.9055i	−0.125840	+	0.518718i	0.873644	+	0.486567i	$0.161751\pi$
$619$	−3.13085	+	12.9055i	−0.125840	+	0.518718i	−0.999483	+	0.0321510i	$0.989764\pi$
$620$	−0.159375	+	0.276045i	−0.00640064	+	0.0110862i
$621$	−1.82215	−	4.43619i	−0.0731203	−	0.178018i
$622$	−5.57326			−0.223468
$623$	0.0474413	+	0.957868i	0.00190070	+	0.0383762i
$624$	−3.54326	−	4.08914i	−0.141844	−	0.163697i
$625$	−17.2326	−	8.88400i	−0.689302	−	0.355360i
$626$	−17.0236	−	6.81522i	−0.680400	−	0.272391i
$627$	18.9370	−	9.76272i	0.756272	−	0.389885i
$628$	4.78902	−	0.457296i	0.191103	−	0.0182481i
$629$	−1.99274	+	2.29975i	−0.0794559	+	0.0916970i
$630$	1.28679	−	1.01588i	0.0512669	−	0.0404736i
$631$	10.1562	+	22.2390i	0.404313	+	0.885322i	0.996815	+	0.0797528i	$0.0254131\pi$
$631$	10.1562	+	22.2390i	0.404313	+	0.885322i	−0.592502	+	0.805569i	$0.701860\pi$
$632$	1.97598	+	8.14511i	0.0786004	+	0.323995i
$633$	15.3800	−	14.6648i	0.611299	−	0.582872i
$634$	19.1557	+	1.82915i	0.760770	+	0.0726447i
$635$	5.66701	−	2.26873i	0.224888	−	0.0900317i
$636$	−0.905329	+	1.04481i	−0.0358986	+	0.0414292i
$637$	35.2148	+	13.9438i	1.39526	+	0.552475i
$638$	−9.12823	−	5.86636i	−0.361390	−	0.232251i
$639$	6.75128	−	5.30927i	0.267076	−	0.210031i
$640$	0.0294845	+	0.618956i	0.00116548	+	0.0244664i
$641$	29.9540	−	5.77317i	1.18311	−	0.228026i	0.440504	−	0.897751i	$-0.354800\pi$
$641$	29.9540	−	5.77317i	1.18311	−	0.228026i	0.742610	+	0.669724i	$0.233588\pi$
$642$	11.0731	+	10.5581i	0.437019	+	0.416696i
$643$	1.62659			0.0641466			0.0320733	−	0.999486i	$-0.489789\pi$
$643$	1.62659			0.0641466			0.0320733	+	0.999486i	$0.489789\pi$
$644$	−12.2978	+	3.12474i	−0.484601	+	0.123132i
$645$	−2.13984			−0.0842560
$646$	−1.47843	−	1.40968i	−0.0581679	−	0.0554630i
$647$	−0.562454	+	0.108404i	−0.0221124	+	0.00426181i	−0.200295	−	0.979736i	$-0.564190\pi$
$647$	−0.562454	+	0.108404i	−0.0221124	+	0.00426181i	0.178183	+	0.983997i	$0.442978\pi$
$648$	0.0475819	+	0.998867i	0.00186919	+	0.0392392i
$649$	−18.6304	+	14.6511i	−0.731306	+	0.575105i
$650$	−21.0111	−	13.5030i	−0.824123	−	0.529632i
$651$	1.07138	+	0.839270i	0.0419905	+	0.0328936i
$652$	5.28105	−	6.09466i	0.206822	−	0.238685i
$653$	33.6085	−	13.4548i	1.31520	−	0.526528i	0.395257	−	0.918571i	$-0.370656\pi$
$653$	33.6085	−	13.4548i	1.31520	−	0.526528i	0.919947	+	0.392042i	$0.128231\pi$
$654$	−2.58824	−	0.247147i	−0.101208	−	0.00966421i
$655$	−6.38920	+	6.09209i	−0.249647	+	0.238038i
$656$	−2.78047	−	11.4613i	−0.108559	−	0.447487i
$657$	0.773239	+	1.69316i	0.0301669	+	0.0660563i
$658$	−0.505800	−	3.47139i	−0.0197181	−	0.135329i
$659$	24.0407	−	27.7445i	0.936495	−	1.08077i	−0.0600899	−	0.998193i	$-0.519139\pi$
$659$	24.0407	−	27.7445i	0.936495	−	1.08077i	0.996584	−	0.0825794i	$-0.0263158\pi$
$660$	2.51895	−	0.240531i	0.0980500	−	0.00936264i
$661$	35.2179	−	18.1561i	1.36982	−	0.706191i	0.392856	−	0.919600i	$-0.371487\pi$
$661$	35.2179	−	18.1561i	1.36982	−	0.706191i	0.976963	+	0.213409i	$0.0684568\pi$
$662$	14.6619	+	5.86974i	0.569851	+	0.228134i
$663$	1.88297	+	0.970740i	0.0731286	+	0.0377004i
$664$	3.15543	+	3.64156i	0.122455	+	0.141320i
$665$	−7.18708	+	4.63805i	−0.278703	+	0.179856i
$666$	−7.77202			−0.301160
$667$	8.71118	−	9.30105i	0.337298	−	0.360138i
$668$	−2.48714	+	4.30785i	−0.0962302	+	0.166676i
$669$	2.48407	−	10.2395i	0.0960396	−	0.395881i
$670$	−1.61456	+	4.66497i	−0.0623759	+	0.180223i
$671$	−3.47011	+	2.23011i	−0.133962	+	0.0860923i
$672$	2.63424	+	0.246522i	0.101618	+	0.00950981i
$673$	40.6835	+	26.1457i	1.56824	+	1.00784i	0.979963	+	0.199181i	$0.0638281\pi$
$673$	40.6835	+	26.1457i	1.56824	+	1.00784i	0.588273	+	0.808663i	$0.299808\pi$
$674$	25.3207	−	2.41784i	0.975318	−	0.0931316i
$675$	1.50975	+	4.36215i	0.0581104	+	0.167899i
$676$	−12.7936	−	10.0610i	−0.492061	−	0.386961i
$677$	−3.56088	+	5.00055i	−0.136856	+	0.192187i	−0.877316	−	0.479913i	$-0.840668\pi$
$677$	−3.56088	+	5.00055i	−0.136856	+	0.192187i	0.740460	+	0.672100i	$0.234608\pi$
$678$	13.6999	+	4.02264i	0.526140	+	0.154489i
$679$	−16.7937	−	28.9612i	−0.644484	−	1.11143i
$680$	−0.100787	−	0.220692i	−0.00386499	−	0.00846315i
$681$	−16.6157	+	6.65193i	−0.636716	+	0.254903i
$682$	0.687027	+	1.98503i	0.0263076	+	0.0760108i
$683$	20.2915	+	28.4954i	0.776432	+	1.09035i	0.993460	+	0.114181i	$0.0364244\pi$
$683$	20.2915	+	28.4954i	0.776432	+	1.09035i	−0.217028	+	0.976165i	$0.569636\pi$
$684$	0.248253	−	5.21147i	0.00949218	−	0.199265i
$685$	0.967794	+	6.73115i	0.0369775	+	0.257184i
$686$	−17.1544	+	6.98054i	−0.654956	+	0.266518i
$687$	5.82344	+	6.72061i	0.222178	+	0.256407i
$688$	−2.49924	−	2.38302i	−0.0952825	−	0.0908517i
$689$	−3.74009	+	6.47802i	−0.142486	+	0.246793i
$690$	−0.256037	+	2.96073i	−0.00974715	+	0.112713i
$691$	−9.85886	−	17.0760i	−0.375049	−	0.649603i	0.615286	−	0.788304i	$-0.289041\pi$
$691$	−9.85886	−	17.0760i	−0.375049	−	0.649603i	−0.990334	+	0.138701i	$0.955707\pi$
$692$	−13.4192	+	3.94023i	−0.510121	+	0.149785i
$693$	0.493706	−	10.7928i	0.0187543	−	0.409984i
$694$	12.3559	−	7.94063i	0.469022	−	0.301422i
$695$	10.3589	−	8.14636i	0.392937	−	0.309009i
$696$	−2.36180	+	1.21759i	−0.0895237	+	0.0461527i
$697$	2.67849	+	3.76141i	0.101455	+	0.142473i
$698$	−2.03877	−	0.392941i	−0.0771686	−	0.0148730i
$699$	−0.603131	+	4.19487i	−0.0228125	+	0.158665i
$700$	11.9878	−	2.33393i	0.453095	−	0.0882143i
$701$	−9.47587	−	2.78237i	−0.357899	−	0.105089i	0.0978400	−	0.995202i	$-0.468807\pi$
$701$	−9.47587	−	2.78237i	−0.357899	−	0.105089i	−0.455739	+	0.890114i	$0.650625\pi$
$702$	1.27562	+	5.25819i	0.0481453	+	0.198457i
$703$	40.3659	+	3.85448i	1.52243	+	0.145374i
$704$	3.20989	+	2.52429i	0.120977	+	0.0951376i
$705$	−0.806766	−	0.155491i	−0.0303846	−	0.00585615i
$706$	6.20752	−	13.5926i	0.233623	−	0.511564i
$707$	36.6320	+	10.6811i	1.37769	+	0.401703i
$708$	0.826003	+	5.74497i	0.0310431	+	0.215909i
$709$	−11.3582	−	5.85556i	−0.426566	−	0.219910i	0.231556	−	0.972822i	$-0.425618\pi$
$709$	−11.3582	−	5.85556i	−0.426566	−	0.219910i	−0.658122	+	0.752912i	$0.728649\pi$
$710$	−5.22596	+	1.00722i	−0.196127	+	0.0378004i
$711$	1.97598	−	8.14511i	0.0741051	−	0.305466i
$712$	0.181242	+	0.313920i	0.00679233	+	0.0117647i
$713$	−2.43861	+	0.372892i	−0.0913266	+	0.0139649i
$714$	−0.993386	+	0.293722i	−0.0371765	+	0.0109923i
$715$	13.1367	−	3.85728i	0.491285	−	0.144254i
$716$	−3.81084	+	11.0107i	−0.142418	+	0.411489i
$717$	0.455017	+	9.55199i	0.0169929	+	0.356725i
$718$	−20.5507	−	8.22727i	−0.766946	−	0.307039i
$719$	0.554194	−	11.6340i	0.0206680	−	0.433874i	−0.964691	−	0.263383i	$-0.915162\pi$
$719$	0.554194	−	11.6340i	0.0206680	−	0.433874i	0.985359	−	0.170491i	$-0.0545353\pi$
$720$	0.257415	−	0.563661i	0.00959330	−	0.0210064i
$721$	−23.0692	−	32.2671i	−0.859142	−	1.20169i
$722$	−1.16997	+	8.13733i	−0.0435418	+	0.302840i
$723$	−6.18918	+	8.69149i	−0.230178	+	0.323240i
$724$	2.43955	−	2.32611i	0.0906653	−	0.0864492i
$725$	−8.87704	+	8.46424i	−0.329685	+	0.314354i
$726$	3.29207	−	4.62306i	0.122180	−	0.171578i
$727$	6.63417	−	46.1417i	0.246048	−	1.71130i	−0.374580	−	0.927195i	$-0.622213\pi$
$727$	6.63417	−	46.1417i	0.246048	−	1.71130i	0.620628	−	0.784105i	$-0.286878\pi$
$728$	14.2480	−	1.38766i	0.528065	−	0.0514302i
$729$	0.415415	−	0.909632i	0.0153857	−	0.0336901i
$730$	0.0548815	−	1.15210i	0.00203125	−	0.0426413i
$731$	1.25521	+	0.502511i	0.0464257	+	0.0185861i
$732$	0.0480640	+	1.00899i	0.00177650	+	0.0372933i
$733$	14.7943	−	42.7453i	0.546440	−	1.57884i	−0.246247	−	0.969207i	$-0.579197\pi$
$733$	14.7943	−	42.7453i	0.546440	−	1.57884i	0.792687	−	0.609628i	$-0.208681\pi$
$734$	20.8966	−	6.13580i	0.771309	−	0.226477i
$735$	0.222748	+	4.33188i	0.00821617	+	0.159784i
$736$	−3.59624	+	3.17287i	−0.132559	+	0.116953i
$737$	16.2657	+	28.1730i	0.599154	+	1.03777i
$738$	−2.78047	+	11.4613i	−0.102351	+	0.421895i
$739$	−47.8370	+	9.21982i	−1.75971	+	0.339157i	−0.963875	−	0.266355i	$-0.914181\pi$
$739$	−47.8370	+	9.21982i	−1.75971	+	0.339157i	−0.795836	+	0.605512i	$0.792968\pi$
$740$	4.28063	+	2.20682i	0.157359	+	0.0811242i
$741$	−4.01750	−	27.9423i	−0.147587	−	1.02649i
$742$	−0.869041	−	3.55295i	−0.0319035	−	0.130433i
$743$	−18.4766	+	40.4581i	−0.677840	+	1.48426i	0.187075	+	0.982346i	$0.440099\pi$
$743$	−18.4766	+	40.4581i	−0.677840	+	1.48426i	−0.864915	+	0.501918i	$0.832628\pi$
$744$	0.505100	+	0.0973500i	0.0185179	+	0.00356902i
$745$	8.29738	+	6.52513i	0.303992	+	0.239062i
$746$	−26.6886	−	2.54845i	−0.977139	−	0.0933055i
$747$	−1.13600	−	4.68265i	−0.0415640	−	0.171329i
$748$	−1.53408	−	0.450447i	−0.0560916	−	0.0164700i
$749$	−39.7337	+	7.73585i	−1.45184	+	0.282662i
$750$	0.848004	−	5.89800i	0.0309647	−	0.215364i
$751$	−26.8621	−	5.17725i	−0.980212	−	0.188920i	−0.326114	−	0.945330i	$-0.605739\pi$
$751$	−26.8621	−	5.17725i	−0.980212	−	0.188920i	−0.654098	+	0.756410i	$0.726952\pi$
$752$	−0.769106	−	1.08006i	−0.0280464	−	0.0393857i
$753$	−1.06267	+	0.547845i	−0.0387259	+	0.0199646i
$754$	−11.3013	+	8.88741i	−0.411568	+	0.323661i
$755$	4.13562	−	2.65780i	0.150511	−	0.0967274i
$756$	−2.22844	−	1.42620i	−0.0810477	−	0.0518703i
$757$	−37.5598	+	11.0286i	−1.36514	+	0.400840i	−0.880570	−	0.473916i	$-0.842840\pi$
$757$	−37.5598	+	11.0286i	−1.36514	+	0.400840i	−0.484565	+	0.874755i	$0.661022\pi$
$758$	12.8772	+	22.3039i	0.467721	+	0.810116i
$759$	13.6407	+	14.0523i	0.495125	+	0.510066i
$760$	−1.61649	+	2.79985i	−0.0586364	+	0.101561i
$761$	9.12388	+	8.69960i	0.330740	+	0.315360i	0.837193	−	0.546907i	$-0.184195\pi$
$761$	9.12388	+	8.69960i	0.330740	+	0.315360i	−0.506453	+	0.862268i	$0.669044\pi$
$762$	−6.45105	−	7.44491i	−0.233697	−	0.269700i
$763$	4.49495	−	5.20728i	0.162728	−	0.188516i
$764$	2.61583	+	18.1935i	0.0946374	+	0.658217i
$765$	−0.0115442	+	0.242342i	−0.000417380	+	0.00876189i
$766$	−13.7378	−	19.2921i	−0.496368	−	0.697051i
$767$	10.2712	+	29.6768i	0.370873	+	1.07157i
$768$	0.928368	−	0.371662i	0.0334996	−	0.0134112i
$769$	18.6726	+	40.8872i	0.673350	+	1.47443i	0.869539	+	0.493864i	$0.164416\pi$
$769$	18.6726	+	40.8872i	0.673350	+	1.47443i	−0.196189	+	0.980566i	$0.562857\pi$
$770$	−3.33646	+	5.80420i	−0.120238	+	0.209169i
$771$	29.6174	+	8.69647i	1.06665	+	0.313196i
$772$	0.608211	−	0.854113i	0.0218900	−	0.0307402i
$773$	−0.959593	−	0.754632i	−0.0345142	−	0.0271422i	0.600753	−	0.799435i	$-0.294868\pi$
$773$	−0.959593	−	0.754632i	−0.0345142	−	0.0271422i	−0.635267	+	0.772293i	$0.719110\pi$
$774$	1.12945	+	3.26333i	0.0405972	+	0.117298i
$775$	2.36371	−	0.225707i	0.0849070	−	0.00810763i
$776$	−10.6448	−	6.84100i	−0.382126	−	0.245578i
$777$	11.8960	−	16.7725i	0.426766	−	0.601709i
$778$	1.30076	−	0.835949i	0.0466346	−	0.0299702i
$779$	20.1252	−	58.1479i	0.721060	−	2.08337i
$780$	0.790450	−	3.25828i	0.0283026	−	0.116665i
$781$	−17.5365	+	30.3741i	−0.627505	+	1.08687i
$782$	0.845475	−	1.67661i	0.0302341	−	0.0599556i
$783$	2.65718			0.0949599
$784$	−4.56402	+	5.30752i	−0.163001	+	0.189554i
$785$	1.95218	+	2.25293i	0.0696761	+	0.0804105i
$786$	12.6630	+	6.52823i	0.451674	+	0.232854i
$787$	−10.9226	−	4.37274i	−0.389348	−	0.155871i	0.168725	−	0.985663i	$-0.446035\pi$
$787$	−10.9226	−	4.37274i	−0.389348	−	0.155871i	−0.558073	+	0.829792i	$0.688459\pi$
$788$	6.00511	−	3.09585i	0.213923	−	0.110285i
$789$	11.0705	−	1.05710i	0.394120	−	0.0376339i
$790$	−3.40107	+	3.92505i	−0.121005	+	0.139647i
$791$	−29.6503	+	23.4080i	−1.05424	+	0.832292i
$792$	−1.69637	−	3.71453i	−0.0602779	−	0.131990i
$793$	1.28855	+	5.31146i	0.0457577	+	0.188616i
$794$	−6.97499	+	6.65064i	−0.247533	+	0.236022i
$795$	−0.852784	−	0.0814310i	−0.0302451	−	0.00288806i
$796$	−17.2930	+	6.92307i	−0.612934	+	0.245382i
$797$	−0.134567	+	0.155299i	−0.00476662	+	0.00550098i	−0.758128	−	0.652106i	$-0.773886\pi$
$797$	−0.134567	+	0.155299i	−0.00476662	+	0.00550098i	0.753361	+	0.657607i	$0.228431\pi$
$798$	10.8667	+	8.51249i	0.384676	+	0.301339i
$799$	0.436728	+	0.280668i	0.0154503	+	0.00992932i
$800$	3.62844	−	2.85344i	0.128285	−	0.100884i
$801$	−0.0172477	−	0.362073i	−0.000609417	−	0.0127932i
$802$	−13.2172	+	2.54741i	−0.466716	+	0.0899521i
$803$	−5.50109	−	5.24528i	−0.194129	−	0.185102i
$804$	7.96644			0.280955
$805$	−5.99753	−	5.08428i	−0.211385	−	0.179197i
$806$	2.78324			0.0980356
$807$	−14.9412	−	14.2464i	−0.525956	−	0.501498i
$808$	14.1615	−	2.72941i	0.498201	−	0.0960204i
$809$	2.00108	+	42.0079i	0.0703543	+	1.47692i	0.707794	+	0.706419i	$0.249691\pi$
$809$	2.00108	+	42.0079i	0.0703543	+	1.47692i	−0.637439	+	0.770500i	$0.720006\pi$
$810$	−0.487084	+	0.383047i	−0.0171144	+	0.0134589i
$811$	5.72204	+	3.67733i	0.200928	+	0.129129i	0.637236	−	0.770669i	$-0.280078\pi$
$811$	5.72204	+	3.67733i	0.200928	+	0.129129i	−0.436308	+	0.899798i	$0.643714\pi$
$812$	0.987370	−	6.96056i	0.0346499	−	0.244268i
$813$	−19.0541	+	21.9896i	−0.668255	+	0.771208i
$814$	29.4640	−	11.7956i	1.03271	−	0.413436i
$815$	4.97454	+	0.475011i	0.174250	+	0.0166389i
$816$	−0.283366	+	0.270189i	−0.00991979	+	0.00945850i
$817$	−4.24765	−	17.5091i	−0.148606	−	0.612564i
$818$	9.20735	+	20.1613i	0.321927	+	0.704923i
$819$	−13.3000	−	5.29539i	−0.464738	−	0.185036i
$820$	4.78576	−	5.52307i	0.167126	−	0.192874i
$821$	38.8594	−	3.71062i	1.35620	−	0.129502i	0.608510	−	0.793546i	$-0.291768\pi$
$821$	38.8594	−	3.71062i	1.35620	−	0.129502i	0.747693	+	0.664045i	$0.231162\pi$
$822$	9.75443	−	5.02876i	0.340225	−	0.175398i
$823$	−14.2511	−	5.70526i	−0.496761	−	0.198873i	0.109733	−	0.993961i	$-0.465000\pi$
$823$	−14.2511	−	5.70526i	−0.496761	−	0.198873i	−0.606494	+	0.795088i	$0.707425\pi$
$824$	−13.3256	−	6.86980i	−0.464218	−	0.239321i
$825$	−12.3440	−	14.2457i	−0.429762	−	0.495972i
$826$	−13.6623	−	7.01078i	−0.475372	−	0.243936i
$827$	−7.13596			−0.248142			−0.124071	−	0.992273i	$-0.539595\pi$
$827$	−7.13596			−0.248142			−0.124071	+	0.992273i	$0.539595\pi$
$828$	4.65035	−	1.17227i	0.161611	−	0.0407390i
$829$	19.1291	−	33.1325i	0.664380	−	1.15074i	−0.315073	−	0.949067i	$-0.602029\pi$
$829$	19.1291	−	33.1325i	0.664380	−	1.15074i	0.979453	−	0.201672i	$-0.0646376\pi$
$830$	−0.703931	+	2.90164i	−0.0244338	+	0.100718i
$831$	−8.70339	+	25.1468i	−0.301917	+	0.872332i
$832$	4.55178	−	2.92525i	0.157804	−	0.101415i
$833$	0.886621	−	2.59336i	0.0307196	−	0.0898546i
$834$	−17.8911	−	11.4979i	−0.619519	−	0.398141i
$835$	−3.06839	+	0.292996i	−0.106186	+	0.0101395i
$836$	6.96833	+	20.1337i	0.241005	+	0.696337i
$837$	−0.404342	−	0.317978i	−0.0139761	−	0.0109909i
$838$	−17.8343	+	25.0448i	−0.616076	+	0.865158i
$839$	7.10565	+	2.08641i	0.245314	+	0.0720308i	0.402078	−	0.915605i	$-0.368288\pi$
$839$	7.10565	+	2.08641i	0.245314	+	0.0720308i	−0.156764	+	0.987636i	$0.550106\pi$
$840$	0.822409	+	1.41827i	0.0283758	+	0.0489348i
$841$	−9.11395	−	19.9568i	−0.314274	−	0.688164i
$842$	−14.2270	+	5.69564i	−0.490296	+	0.196285i
$843$	3.21097	+	9.27748i	0.110592	+	0.319533i
$844$	12.3267	+	17.3104i	0.424303	+	0.595850i
$845$	0.479883	−	10.0740i	0.0165085	−	0.346555i
$846$	0.188697	+	1.31242i	0.00648755	+	0.0451219i
$847$	4.93795	+	14.1806i	0.169670	+	0.487251i
$848$	−0.905329	−	1.04481i	−0.0310891	−	0.0358788i
$849$	20.0488	+	19.1165i	0.688073	+	0.656076i
$850$	−0.903663	+	1.56519i	−0.0309954	+	0.0536856i
$851$	7.38081	+	36.5352i	0.253011	+	1.25241i
$852$	4.29442	+	7.43815i	0.147124	+	0.254827i
$853$	38.2595	−	11.2340i	1.30998	−	0.384645i	0.449114	−	0.893475i	$-0.351740\pi$
$853$	38.2595	−	11.2340i	1.30998	−	0.384645i	0.860867	+	0.508829i	$0.169922\pi$
$854$	−2.25102	−	1.44065i	−0.0770284	−	0.0492979i
$855$	2.71976	−	1.74789i	0.0930140	−	0.0597764i
$856$	−12.0265	+	9.45777i	−0.411058	+	0.323260i
$857$	31.3246	−	16.1489i	1.07003	−	0.551637i	0.169096	−	0.985600i	$-0.445915\pi$
$857$	31.3246	−	16.1489i	1.07003	−	0.551637i	0.900931	+	0.433963i	$0.142885\pi$
$858$	−12.8163	−	17.9980i	−0.437542	−	0.614441i
$859$	16.3799	+	3.15696i	0.558874	+	0.107714i	0.460863	−	0.887471i	$-0.347540\pi$
$859$	16.3799	+	3.15696i	0.558874	+	0.107714i	0.0980111	+	0.995185i	$0.468752\pi$
$860$	0.304531	−	2.11806i	0.0103844	−	0.0722251i
$861$	−20.4782	−	23.5432i	−0.697896	−	0.802350i
$862$	−18.1444	−	5.32767i	−0.618000	−	0.181461i
$863$	−12.0477	−	49.6614i	−0.410109	−	1.69049i	−0.684612	−	0.728907i	$-0.740029\pi$
$863$	−12.0477	−	49.6614i	−0.410109	−	1.69049i	0.274503	−	0.961586i	$-0.411487\pi$
$864$	−0.995472	−	0.0950560i	−0.0338666	−	0.00323387i
$865$	−6.81222	−	5.35719i	−0.231622	−	0.182150i
$866$	11.9430	+	2.30183i	0.405840	+	0.0782192i
$867$	−6.99837	+	15.3243i	−0.237677	+	0.520440i
$868$	−0.983200	+	0.941029i	−0.0333720	+	0.0319406i
$869$	4.87084	+	33.8774i	0.165232	+	1.14921i
$870$	−1.46351	−	0.754490i	−0.0496175	−	0.0255796i
$871$	42.3251	−	8.15750i	1.43413	−	0.276406i
$872$	0.612976	−	2.52672i	0.0207580	−	0.0855656i
$873$	6.32675	+	10.9583i	0.214128	+	0.370881i
$874$	−24.7342	+	3.78214i	−0.836645	+	0.127933i
$875$	11.4303	+	10.8576i	0.386413	+	0.367054i
$876$	−1.78597	+	0.524407i	−0.0603422	+	0.0177181i
$877$	12.2982	−	35.5333i	0.415280	−	1.19987i	−0.522498	−	0.852640i	$-0.675000\pi$
$877$	12.2982	−	35.5333i	0.415280	−	1.19987i	0.937779	−	0.347234i	$-0.112879\pi$
$878$	−1.45753	−	30.5974i	−0.0491894	−	1.03261i
$879$	1.16494	+	0.466373i	0.0392926	+	0.0157304i
$880$	−0.120402	+	2.52754i	−0.00405874	+	0.0852034i
$881$	8.87338	−	19.4300i	0.298952	−	0.654613i	−0.699229	−	0.714897i	$-0.746473\pi$
$881$	8.87338	−	19.4300i	0.298952	−	0.654613i	0.998181	+	0.0602842i	$0.0192007\pi$
$882$	6.48871	−	2.62615i	0.218486	−	0.0884272i
$883$	6.40164	−	44.5244i	0.215432	−	1.49837i	−0.539178	−	0.842192i	$-0.681265\pi$
$883$	6.40164	−	44.5244i	0.215432	−	1.49837i	0.754610	−	0.656173i	$-0.227826\pi$
$884$	−1.22883	+	1.72566i	−0.0413302	+	0.0580401i
$885$	−2.60293	+	2.48189i	−0.0874965	+	0.0834278i
$886$	13.7025	−	13.0654i	0.460346	−	0.438939i
$887$	14.7982	−	20.7811i	0.496874	−	0.697762i	−0.487644	−	0.873042i	$-0.662144\pi$
$887$	14.7982	−	20.7811i	0.496874	−	0.697762i	0.984519	+	0.175280i	$0.0560831\pi$
$888$	1.10607	−	7.69291i	0.0371174	−	0.258157i
$889$	25.9406	−	2.52645i	0.870020	−	0.0847345i
$890$	−0.0933089	+	0.204318i	−0.00312772	+	0.00684876i
$891$	−0.194303	+	4.07893i	−0.00650941	+	0.136649i
$892$	9.78172	+	3.91601i	0.327516	+	0.131118i
$893$	−0.329162	−	6.90996i	−0.0110150	−	0.231233i
$894$	5.57154	−	16.0979i	0.186340	−	0.538394i
$895$	−6.92749	+	2.03410i	−0.231561	+	0.0679923i
$896$	−0.618905	+	2.57234i	−0.0206762	+	0.0859360i
$897$	23.5066	−	10.9900i	0.784863	−	0.366947i
$898$	18.0673	+	31.2934i	0.602912	+	1.04427i
$899$	0.322245	−	1.32831i	0.0107475	−	0.0443017i
$900$	−4.53261	+	0.873588i	−0.151087	+	0.0291196i
$901$	0.481113	+	0.248031i	0.0160282	+	0.00826312i
$902$	−6.85391	−	47.6700i	−0.228210	−	1.58724i
$903$	−8.77120	−	2.55748i	−0.291887	−	0.0851077i
$904$	−5.93139	+	12.9879i	−0.197275	+	0.431972i
$905$	2.05099	+	0.395296i	0.0681772	+	0.0131401i
$906$	−6.23611	−	4.90413i	−0.207181	−	0.162929i
$907$	−49.7840	−	4.75380i	−1.65305	−	0.157847i	−0.773547	−	0.633739i	$-0.781519\pi$
$907$	−49.7840	−	4.75380i	−1.65305	−	0.157847i	−0.879504	+	0.475892i	$0.842125\pi$
$908$	−4.21956	−	17.3933i	−0.140031	−	0.577216i
$909$	−13.8380	−	4.06319i	−0.458976	−	0.134768i
$910$	5.82168	+	6.69301i	0.192987	+	0.221871i
$911$	2.75887	−	19.1884i	0.0914056	−	0.635740i	−0.891690	−	0.452647i	$-0.850480\pi$
$911$	2.75887	−	19.1884i	0.0914056	−	0.635740i	0.983096	−	0.183093i	$-0.0586110\pi$
$912$	5.12309	+	0.987395i	0.169642	+	0.0326959i
$913$	11.4135	+	16.0280i	0.377732	+	0.530450i
$914$	8.01812	−	4.13363i	0.265216	−	0.136728i
$915$	−0.492020	+	0.386928i	−0.0162657	+	0.0127915i
$916$	−7.48097	+	4.80773i	−0.247178	+	0.158852i
$917$	−33.4705	+	17.3353i	−1.10529	+	0.572461i
$918$	0.375673	−	0.110308i	0.0123991	−	0.00364069i
$919$	2.18368	+	3.78225i	0.0720331	+	0.124765i	0.899792	−	0.436319i	$-0.143718\pi$
$919$	2.18368	+	3.78225i	0.0720331	+	0.124765i	−0.827759	+	0.561084i	$0.810385\pi$
$920$	−2.89415	−	0.674786i	−0.0954174	−	0.0222470i
$921$	2.42538	−	4.20088i	0.0799189	−	0.138424i
$922$	−16.6844	−	15.9085i	−0.549471	−	0.523919i
$923$	30.4325	+	35.1209i	1.00170	+	1.15602i
$924$	10.6127	+	2.02465i	0.349131	+	0.0666062i
$925$	−5.10566	−	35.5107i	−0.167873	−	1.16758i
$926$	0.885786	−	18.5949i	0.0291087	−	0.611068i
$927$	8.69630	+	12.2123i	0.285624	+	0.401103i
$928$	−0.869079	−	2.51104i	−0.0285289	−	0.0824289i
$929$	12.8180	−	5.13157i	0.420546	−	0.168361i	−0.151730	−	0.988422i	$-0.548485\pi$
$929$	12.8180	−	5.13157i	0.420546	−	0.168361i	0.572277	+	0.820061i	$0.306060\pi$
$930$	0.132413	+	0.289945i	0.00434200	+	0.00950766i
$931$	−35.0031	+	10.4216i	−1.14718	+	0.341553i
$932$	−4.06634	−	1.19398i	−0.133197	−	0.0391103i
$933$	−3.23281	+	4.53985i	−0.105837	+	0.148628i
$934$	−25.0031	−	19.6626i	−0.818126	−	0.643381i
$935$	−0.324039	−	0.936249i	−0.0105972	−	0.0306186i
$936$	−5.38621	+	0.514320i	−0.176054	+	0.0168111i
$937$	39.9434	+	25.6701i	1.30489	+	0.838605i	0.993736	−	0.111753i	$-0.0356465\pi$
$937$	39.9434	+	25.6701i	1.30489	+	0.838605i	0.311159	+	0.950358i	$0.399283\pi$
$938$	−12.1936	+	17.1920i	−0.398134	+	0.561340i
$939$	−15.4262	+	9.91379i	−0.503414	+	0.323524i
$940$	0.268724	−	0.776426i	0.00876480	−	0.0253242i
$941$	6.56695	−	27.0693i	0.214076	−	0.882435i	−0.758840	−	0.651277i	$-0.774233\pi$
$941$	6.56695	−	27.0693i	0.214076	−	0.882435i	0.972916	−	0.231158i	$-0.0742514\pi$
$942$	2.40540	−	4.16628i	0.0783722	−	0.135745i
$943$	56.5183	+	2.18627i	1.84049	+	0.0711946i
$944$	−5.80405			−0.188906
$945$	−0.0810999	−	1.63745i	−0.00263818	−	0.0532664i
$946$	−9.23455	−	10.6572i	−0.300241	−	0.346497i
$947$	−39.4268	−	20.3259i	−1.28120	−	0.660504i	−0.322944	−	0.946418i	$-0.604673\pi$
$947$	−39.4268	−	20.3259i	−1.28120	−	0.660504i	−0.958255	+	0.285914i	$0.907703\pi$
$948$	7.78099	+	3.11504i	0.252715	+	0.101172i
$949$	−8.95173	+	4.61494i	−0.290585	+	0.149807i
$950$	23.9745	−	2.28928i	0.777835	−	0.0742742i
$951$	12.6014	−	14.5428i	0.408628	−	0.471581i
$952$	−0.149359	−	1.02508i	−0.00484076	−	0.0332229i
$953$	−23.1191	−	50.6238i	−0.748902	−	1.63987i	−0.768329	−	0.640055i	$-0.778911\pi$
$953$	−23.1191	−	50.6238i	−0.748902	−	1.63987i	0.0194268	−	0.999811i	$-0.493816\pi$
$954$	0.325931	+	1.34351i	0.0105524	+	0.0434976i
$955$	−8.24310	+	7.85978i	−0.266740	+	0.254336i
$956$	−9.51952	−	0.909004i	−0.307883	−	0.0293993i
$957$	−10.0735	+	4.03282i	−0.325630	+	0.130362i
$958$	−3.20948	+	3.70394i	−0.103694	+	0.119669i
$959$	−4.07792	+	28.7477i	−0.131683	+	0.928312i
$960$	0.521290	+	0.335013i	0.0168246	+	0.0108125i
$961$	24.1597	−	18.9994i	0.779344	−	0.612883i
$962$	−2.00092	−	42.0045i	−0.0645122	−	1.35428i
$963$	15.0234	−	2.89552i	0.484122	−	0.0933069i
$964$	−7.72221	−	7.36311i	−0.248716	−	0.237150i
$965$	0.649734			0.0209157
$966$	−4.58809	+	11.8300i	−0.147619	+	0.380625i
$967$	−13.1580			−0.423132			−0.211566	−	0.977364i	$-0.567856\pi$
$967$	−13.1580			−0.423132			−0.211566	+	0.977364i	$0.567856\pi$
$968$	4.10749	+	3.91649i	0.132020	+	0.125881i
$969$	−2.00586	+	0.386598i	−0.0644375	+	0.0124193i
$970$	−0.373083	−	7.83197i	−0.0119790	−	0.251469i
$971$	−8.67279	+	6.82036i	−0.278323	+	0.218876i	−0.747556	−	0.664199i	$-0.768773\pi$
$971$	−8.67279	+	6.82036i	−0.278323	+	0.218876i	0.469233	+	0.883074i	$0.344530\pi$
$972$	0.841254	+	0.540641i	0.0269832	+	0.0173411i
$973$	52.1977	−	21.0112i	1.67338	−	0.673588i
$974$	20.3148	−	23.4445i	0.650927	−	0.751210i
$975$	−23.1869	+	9.28262i	−0.742574	+	0.297282i
$976$	−1.00556	−	0.0960192i	−0.0321871	−	0.00307350i
$977$	3.38798	−	3.23043i	0.108391	−	0.103351i	−0.633946	−	0.773377i	$-0.718566\pi$
$977$	3.38798	−	3.23043i	0.108391	−	0.103351i	0.742337	+	0.670027i	$0.233717\pi$
$978$	−1.90125	−	7.83706i	−0.0607953	−	0.250602i
$979$	0.614907	+	1.34646i	0.0196525	+	0.0430330i
$980$	−4.31949	−	0.396011i	−0.137981	−	0.0126501i
$981$	−1.70265	+	1.96496i	−0.0543613	+	0.0627363i
$982$	3.72189	−	0.355397i	0.118770	−	0.0113412i
$983$	48.8510	−	25.1844i	1.55811	−	0.803259i	0.558451	−	0.829538i	$-0.311396\pi$
$983$	48.8510	−	25.1844i	1.55811	−	0.803259i	0.999655	+	0.0262786i	$0.00836570\pi$
$984$	−10.9489	−	4.38328i	−0.349038	−	0.139734i
$985$	3.72111	+	1.91837i	0.118565	+	0.0611243i
$986$	0.681301	+	0.786263i	0.0216970	+	0.0250397i
$987$	−3.12110	−	1.60159i	−0.0993457	−	0.0509791i
$988$	28.2297			0.898106
$989$	14.2679	−	8.40845i	0.453692	−	0.267373i
$990$	1.26520	−	2.19140i	0.0402108	−	0.0696472i
$991$	9.81110	−	40.4419i	0.311660	−	1.28468i	−0.573428	−	0.819256i	$-0.694387\pi$
$991$	9.81110	−	40.4419i	0.311660	−	1.28468i	0.885088	−	0.465424i	$-0.154098\pi$
$992$	−0.168242	+	0.486104i	−0.00534170	+	0.0154338i
$993$	13.2861	−	8.53846i	0.421622	−	0.270960i
$994$	−22.6251	−	2.11734i	−0.717623	−	0.0671580i
$995$	−9.71023	−	6.24039i	−0.307835	−	0.197834i
$996$	4.79666	−	0.458025i	0.151988	−	0.0145131i
$997$	−0.251374	−	0.726298i	−0.00796110	−	0.0230021i	0.940950	−	0.338545i	$-0.109935\pi$
$997$	−0.251374	−	0.726298i	−0.00796110	−	0.0230021i	−0.948911	+	0.315543i	$0.897813\pi$
$998$	3.94906	+	3.10557i	0.125005	+	0.0983052i
$999$	−4.50821	+	6.33090i	−0.142634	+	0.200301i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	966.2.y.d.193.3	✓	160
7.2	even	3	inner	966.2.y.d.331.6	yes	160
23.18	even	11	inner	966.2.y.d.823.6	yes	160
161.156	even	33	inner	966.2.y.d.961.3	yes	160

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
966.2.y.d.193.3	✓	160	1.1	even	1	trivial
966.2.y.d.331.6	yes	160	7.2	even	3	inner
966.2.y.d.823.6	yes	160	23.18	even	11	inner
966.2.y.d.961.3	yes	160	161.156	even	33	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.y (of order \(33\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(0.723734 + 0.690079i) q^{2} +(0.981929 - 0.189251i) q^{3} +(0.0475819 + 0.998867i) q^{4} +(-0.487084 + 0.383047i) q^{5} +(0.841254 + 0.540641i) q^{6} +(-2.45437 + 0.987961i) q^{7} +(-0.654861 + 0.755750i) q^{8} +(0.928368 - 0.371662i) q^{9} +O(q^{10})\)	\(q+(0.723734 + 0.690079i) q^{2} +(0.981929 - 0.189251i) q^{3} +(0.0475819 + 0.998867i) q^{4} +(-0.487084 + 0.383047i) q^{5} +(0.841254 + 0.540641i) q^{6} +(-2.45437 + 0.987961i) q^{7} +(-0.654861 + 0.755750i) q^{8} +(0.928368 - 0.371662i) q^{9} +(-0.616852 - 0.0589023i) q^{10} +(-2.95541 + 2.81798i) q^{11} +(0.235759 + 0.971812i) q^{12} +(2.24769 + 4.92175i) q^{13} +(-2.45808 - 0.978688i) q^{14} +(-0.405790 + 0.468306i) q^{15} +(-0.995472 + 0.0950560i) q^{16} +(0.348009 - 0.179411i) q^{17} +(0.928368 + 0.371662i) q^{18} +(-4.63739 - 2.39074i) q^{19} +(-0.405790 - 0.468306i) q^{20} +(-2.22304 + 1.43460i) q^{21} -4.08355 q^{22} +(0.865497 - 4.71709i) q^{23} +(-0.500000 + 0.866025i) q^{24} +(-1.08827 + 4.48591i) q^{25} +(-1.76967 + 5.11312i) q^{26} +(0.841254 - 0.540641i) q^{27} +(-1.10363 - 2.40458i) q^{28} +(2.23536 + 1.43658i) q^{29} +(-0.616852 + 0.0589023i) q^{30} +(-0.168242 - 0.486104i) q^{31} +(-0.786053 - 0.618159i) q^{32} +(-2.36869 + 3.32637i) q^{33} +(0.375673 + 0.110308i) q^{34} +(0.817049 - 1.42136i) q^{35} +(0.415415 + 0.909632i) q^{36} +(-7.21529 + 2.88857i) q^{37} +(-1.70644 - 4.93042i) q^{38} +(3.13852 + 4.40743i) q^{39} +(0.0294845 - 0.618956i) q^{40} +(1.67842 + 11.6737i) q^{41} +(-2.59888 - 0.495807i) q^{42} +(2.26140 + 2.60980i) q^{43} +(-2.95541 - 2.81798i) q^{44} +(-0.309829 + 0.536640i) q^{45} +(3.88155 - 2.81666i) q^{46} +(0.662957 + 1.14828i) q^{47} +(-0.959493 + 0.281733i) q^{48} +(5.04787 - 4.84965i) q^{49} +(-3.88325 + 2.49561i) q^{50} +(0.307766 - 0.242030i) q^{51} +(-4.80923 + 2.47933i) q^{52} +(0.801915 + 1.12613i) q^{53} +(0.981929 + 0.189251i) q^{54} +(0.360115 - 2.50465i) q^{55} +(0.860619 - 2.50187i) q^{56} +(-5.00603 - 1.46990i) q^{57} +(0.626454 + 2.58228i) q^{58} +(5.77777 + 0.551710i) q^{59} +(-0.487084 - 0.383047i) q^{60} +(0.991878 + 0.191169i) q^{61} +(0.213688 - 0.467911i) q^{62} +(-1.91137 + 1.82939i) q^{63} +(-0.142315 - 0.989821i) q^{64} +(-2.98008 - 1.53634i) q^{65} +(-4.00976 + 0.772818i) q^{66} +(1.87816 - 7.74188i) q^{67} +(0.195767 + 0.339078i) q^{68} +(-0.0428585 - 4.79564i) q^{69} +(1.57218 - 0.464858i) q^{70} +(8.24093 - 2.41975i) q^{71} +(-0.327068 + 0.945001i) q^{72} +(0.0885673 + 1.85926i) q^{73} +(-7.21529 - 2.88857i) q^{74} +(-0.219639 + 4.61080i) q^{75} +(2.16738 - 4.74589i) q^{76} +(4.46961 - 9.83618i) q^{77} +(-0.770024 + 5.35563i) q^{78} +(4.86167 - 6.82726i) q^{79} +(0.448468 - 0.427613i) q^{80} +(0.723734 - 0.690079i) q^{81} +(-6.84102 + 9.60686i) q^{82} +(0.685741 - 4.76943i) q^{83} +(-1.53875 - 2.15226i) q^{84} +(-0.100787 + 0.220692i) q^{85} +(-0.164312 + 3.44934i) q^{86} +(2.46684 + 0.987575i) q^{87} +(-0.194303 - 4.07893i) q^{88} +(0.118557 - 0.342548i) q^{89} +(-0.594558 + 0.174578i) q^{90} +(-10.3792 - 9.85917i) q^{91} +(4.75293 + 0.640068i) q^{92} +(-0.257198 - 0.445480i) q^{93} +(-0.312596 + 1.28854i) q^{94} +(3.17457 - 0.611847i) q^{95} +(-0.888835 - 0.458227i) q^{96} +(1.80078 + 12.5247i) q^{97} +(6.99995 - 0.0264275i) q^{98} +(-1.69637 + 3.71453i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 160 q + 8 q^{2} + 8 q^{3} + 8 q^{4} - 2 q^{5} - 16 q^{6} + 6 q^{7} - 16 q^{8} + 8 q^{9}+O(q^{10}) \) 160 * q + 8 * q^2 + 8 * q^3 + 8 * q^4 - 2 * q^5 - 16 * q^6 + 6 * q^7 - 16 * q^8 + 8 * q^9	\( 160 q + 8 q^{2} + 8 q^{3} + 8 q^{4} - 2 q^{5} - 16 q^{6} + 6 q^{7} - 16 q^{8} + 8 q^{9} - 2 q^{10} - 4 q^{11} + 8 q^{12} - 4 q^{13} + 5 q^{14} + 26 q^{15} + 8 q^{16} - 13 q^{17} + 8 q^{18} + 4 q^{19} + 26 q^{20} + 11 q^{21} - 124 q^{22} + 26 q^{23} - 80 q^{24} + 14 q^{25} + 2 q^{26} - 16 q^{27} - 22 q^{28} + 54 q^{29} - 2 q^{30} + 15 q^{31} + 8 q^{32} - 4 q^{33} + 4 q^{34} - 2 q^{35} - 16 q^{36} + 7 q^{37} - 7 q^{38} + 2 q^{39} + 9 q^{40} - 30 q^{41} + 6 q^{42} + 36 q^{43} - 4 q^{44} + 20 q^{45} + 4 q^{46} - 6 q^{47} - 16 q^{48} + 14 q^{49} - 28 q^{50} + 9 q^{51} + 2 q^{52} - 24 q^{53} + 8 q^{54} - 14 q^{55} + 6 q^{56} - 30 q^{57} - 5 q^{58} + 4 q^{59} - 2 q^{60} + 32 q^{61} - 8 q^{62} - 6 q^{63} - 16 q^{64} + 38 q^{65} - 4 q^{66} + 6 q^{67} + 42 q^{68} - 30 q^{69} - 8 q^{70} - 180 q^{71} + 8 q^{72} - 32 q^{73} + 7 q^{74} + 14 q^{75} - 8 q^{76} + 61 q^{77} + 18 q^{78} - 66 q^{79} - 2 q^{80} + 8 q^{81} - 7 q^{82} + 130 q^{83} + 5 q^{84} - 70 q^{85} - 40 q^{86} + 6 q^{87} - 15 q^{88} - 4 q^{89} + 4 q^{90} - 6 q^{91} + 58 q^{92} - 18 q^{93} + 16 q^{94} + 19 q^{95} + 8 q^{96} + 40 q^{97} + 43 q^{98} + 8 q^{99}+O(q^{100}) \) 160 * q + 8 * q^2 + 8 * q^3 + 8 * q^4 - 2 * q^5 - 16 * q^6 + 6 * q^7 - 16 * q^8 + 8 * q^9 - 2 * q^10 - 4 * q^11 + 8 * q^12 - 4 * q^13 + 5 * q^14 + 26 * q^15 + 8 * q^16 - 13 * q^17 + 8 * q^18 + 4 * q^19 + 26 * q^20 + 11 * q^21 - 124 * q^22 + 26 * q^23 - 80 * q^24 + 14 * q^25 + 2 * q^26 - 16 * q^27 - 22 * q^28 + 54 * q^29 - 2 * q^30 + 15 * q^31 + 8 * q^32 - 4 * q^33 + 4 * q^34 - 2 * q^35 - 16 * q^36 + 7 * q^37 - 7 * q^38 + 2 * q^39 + 9 * q^40 - 30 * q^41 + 6 * q^42 + 36 * q^43 - 4 * q^44 + 20 * q^45 + 4 * q^46 - 6 * q^47 - 16 * q^48 + 14 * q^49 - 28 * q^50 + 9 * q^51 + 2 * q^52 - 24 * q^53 + 8 * q^54 - 14 * q^55 + 6 * q^56 - 30 * q^57 - 5 * q^58 + 4 * q^59 - 2 * q^60 + 32 * q^61 - 8 * q^62 - 6 * q^63 - 16 * q^64 + 38 * q^65 - 4 * q^66 + 6 * q^67 + 42 * q^68 - 30 * q^69 - 8 * q^70 - 180 * q^71 + 8 * q^72 - 32 * q^73 + 7 * q^74 + 14 * q^75 - 8 * q^76 + 61 * q^77 + 18 * q^78 - 66 * q^79 - 2 * q^80 + 8 * q^81 - 7 * q^82 + 130 * q^83 + 5 * q^84 - 70 * q^85 - 40 * q^86 + 6 * q^87 - 15 * q^88 - 4 * q^89 + 4 * q^90 - 6 * q^91 + 58 * q^92 - 18 * q^93 + 16 * q^94 + 19 * q^95 + 8 * q^96 + 40 * q^97 + 43 * q^98 + 8 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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