LMFDB - Embedded newform 2010.2.d.d.401.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2010,2,Mod(401,2010)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2010, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("2010.401");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2010 = 2 \cdot 3 \cdot 5 \cdot 67 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2010.d (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:	$16.0499308063$
Analytic rank:	$0$
Dimension:	$20$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - 2 x^{19} + 2 x^{18} + 2 x^{17} - 9 x^{16} + 4 x^{15} + 14 x^{14} - 28 x^{13} - 16 x^{12} + \cdots + 59049 $ x^20 - 2x^19 + 2x^18 + 2x^17 - 9x^16 + 4x^15 + 14x^14 - 28x^13 - 16x^12 + 188x^11 - 288x^10 + 564x^9 - 144x^8 - 756x^7 + 1134x^6 + 972x^5 - 6561x^4 + 4374x^3 + 13122x^2 - 39366*x + 59049
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{5} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			401.2
Root			$1.68704 + 0.392308i$ of defining polynomial
Character	$\chi$	$=$	2010.401
Dual form			2010.2.d.d.401.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} +(-1.68704 + 0.392308i) q^{3} +1.00000 q^{4} +1.00000 q^{5} +(-1.68704 + 0.392308i) q^{6} -2.72263i q^{7} +1.00000 q^{8} +(2.69219 - 1.32367i) q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +(-1.68704 + 0.392308i) q^{3} +1.00000 q^{4} +1.00000 q^{5} +(-1.68704 + 0.392308i) q^{6} -2.72263i q^{7} +1.00000 q^{8} +(2.69219 - 1.32367i) q^{9} +1.00000 q^{10} +5.40581 q^{11} +(-1.68704 + 0.392308i) q^{12} +1.90134i q^{13} -2.72263i q^{14} +(-1.68704 + 0.392308i) q^{15} +1.00000 q^{16} -1.89478i q^{17} +(2.69219 - 1.32367i) q^{18} -2.89310 q^{19} +1.00000 q^{20} +(1.06811 + 4.59318i) q^{21} +5.40581 q^{22} +0.0386030i q^{23} +(-1.68704 + 0.392308i) q^{24} +1.00000 q^{25} +1.90134i q^{26} +(-4.02254 + 3.28926i) q^{27} -2.72263i q^{28} -9.54907i q^{29} +(-1.68704 + 0.392308i) q^{30} +0.791170i q^{31} +1.00000 q^{32} +(-9.11980 + 2.12074i) q^{33} -1.89478i q^{34} -2.72263i q^{35} +(2.69219 - 1.32367i) q^{36} -4.33807 q^{37} -2.89310 q^{38} +(-0.745909 - 3.20763i) q^{39} +1.00000 q^{40} +2.80538 q^{41} +(1.06811 + 4.59318i) q^{42} +9.14619i q^{43} +5.40581 q^{44} +(2.69219 - 1.32367i) q^{45} +0.0386030i q^{46} -3.02549i q^{47} +(-1.68704 + 0.392308i) q^{48} -0.412733 q^{49} +1.00000 q^{50} +(0.743337 + 3.19657i) q^{51} +1.90134i q^{52} +3.05084 q^{53} +(-4.02254 + 3.28926i) q^{54} +5.40581 q^{55} -2.72263i q^{56} +(4.88076 - 1.13498i) q^{57} -9.54907i q^{58} -8.27799i q^{59} +(-1.68704 + 0.392308i) q^{60} -14.8383i q^{61} +0.791170i q^{62} +(-3.60388 - 7.32985i) q^{63} +1.00000 q^{64} +1.90134i q^{65} +(-9.11980 + 2.12074i) q^{66} +(5.24905 + 6.28072i) q^{67} -1.89478i q^{68} +(-0.0151442 - 0.0651246i) q^{69} -2.72263i q^{70} -14.3117i q^{71} +(2.69219 - 1.32367i) q^{72} +11.1356 q^{73} -4.33807 q^{74} +(-1.68704 + 0.392308i) q^{75} -2.89310 q^{76} -14.7180i q^{77} +(-0.745909 - 3.20763i) q^{78} +15.7714i q^{79} +1.00000 q^{80} +(5.49577 - 7.12717i) q^{81} +2.80538 q^{82} +4.38087i q^{83} +(1.06811 + 4.59318i) q^{84} -1.89478i q^{85} +9.14619i q^{86} +(3.74617 + 16.1096i) q^{87} +5.40581 q^{88} +13.1250i q^{89} +(2.69219 - 1.32367i) q^{90} +5.17665 q^{91} +0.0386030i q^{92} +(-0.310382 - 1.33473i) q^{93} -3.02549i q^{94} -2.89310 q^{95} +(-1.68704 + 0.392308i) q^{96} +5.86842i q^{97} -0.412733 q^{98} +(14.5535 - 7.15553i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + 20 q^{2} - 2 q^{3} + 20 q^{4} + 20 q^{5} - 2 q^{6} + 20 q^{8}+O(q^{10}) $ 20 * q + 20 * q^2 - 2 * q^3 + 20 * q^4 + 20 * q^5 - 2 * q^6 + 20 * q^8	$ 20 q + 20 q^{2} - 2 q^{3} + 20 q^{4} + 20 q^{5} - 2 q^{6} + 20 q^{8} + 20 q^{10} - 2 q^{12} - 2 q^{15} + 20 q^{16} + 16 q^{19} + 20 q^{20} - 2 q^{21} - 2 q^{24} + 20 q^{25} + 10 q^{27} - 2 q^{30} + 20 q^{32} + 2 q^{33} + 20 q^{37} + 16 q^{38} + 16 q^{39} + 20 q^{40} + 8 q^{41} - 2 q^{42} - 2 q^{48} - 48 q^{49} + 20 q^{50} + 32 q^{51} - 36 q^{53} + 10 q^{54} + 16 q^{57} - 2 q^{60} - 4 q^{63} + 20 q^{64} + 2 q^{66} + 16 q^{67} - 28 q^{69} - 4 q^{73} + 20 q^{74} - 2 q^{75} + 16 q^{76} + 16 q^{78} + 20 q^{80} + 12 q^{81} + 8 q^{82} - 2 q^{84} + 32 q^{87} + 12 q^{91} - 12 q^{93} + 16 q^{95} - 2 q^{96} - 48 q^{98} + 12 q^{99}+O(q^{100}) $ 20 * q + 20 * q^2 - 2 * q^3 + 20 * q^4 + 20 * q^5 - 2 * q^6 + 20 * q^8 + 20 * q^10 - 2 * q^12 - 2 * q^15 + 20 * q^16 + 16 * q^19 + 20 * q^20 - 2 * q^21 - 2 * q^24 + 20 * q^25 + 10 * q^27 - 2 * q^30 + 20 * q^32 + 2 * q^33 + 20 * q^37 + 16 * q^38 + 16 * q^39 + 20 * q^40 + 8 * q^41 - 2 * q^42 - 2 * q^48 - 48 * q^49 + 20 * q^50 + 32 * q^51 - 36 * q^53 + 10 * q^54 + 16 * q^57 - 2 * q^60 - 4 * q^63 + 20 * q^64 + 2 * q^66 + 16 * q^67 - 28 * q^69 - 4 * q^73 + 20 * q^74 - 2 * q^75 + 16 * q^76 + 16 * q^78 + 20 * q^80 + 12 * q^81 + 8 * q^82 - 2 * q^84 + 32 * q^87 + 12 * q^91 - 12 * q^93 + 16 * q^95 - 2 * q^96 - 48 * q^98 + 12 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/2010\mathbb{Z}\right)^\times$.

$n$	$671$	$1141$	$1207$
$\chi(n)$	$-1$	$-1$	$1$

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 $

$2$	1.00000			0.707107
$2$	1.00000			0.707107
$3$	−1.68704	+	0.392308i	−0.974011	+	0.226499i
$3$	−1.68704	+	0.392308i	−0.974011	+	0.226499i
$4$	1.00000			0.500000
$5$	1.00000			0.447214
$5$	1.00000			0.447214
$6$	−1.68704	+	0.392308i	−0.688730	+	0.160159i
$7$		−	2.72263i		−	1.02906i	−0.857473	−	0.514529i	$-0.827967\pi$
$7$		−	2.72263i		−	1.02906i	0.857473	−	0.514529i	$-0.172033\pi$
$8$	1.00000			0.353553
$9$	2.69219	−	1.32367i	0.897397	−	0.441225i
$10$	1.00000			0.316228
$11$	5.40581			1.62991			0.814956	−	0.579523i	$-0.196761\pi$
$11$	5.40581			1.62991			0.814956	+	0.579523i	$0.196761\pi$
$12$	−1.68704	+	0.392308i	−0.487006	+	0.113249i
$13$			1.90134i			0.527336i	0.964613	+	0.263668i	$0.0849324\pi$
$13$			1.90134i			0.527336i	−0.964613	+	0.263668i	$0.915068\pi$
$14$		−	2.72263i		−	0.727654i
$15$	−1.68704	+	0.392308i	−0.435591	+	0.101293i
$16$	1.00000			0.250000
$17$		−	1.89478i		−	0.459552i	−0.973244	−	0.229776i	$-0.926201\pi$
$17$		−	1.89478i		−	0.459552i	0.973244	−	0.229776i	$-0.0737994\pi$
$18$	2.69219	−	1.32367i	0.634555	−	0.311993i
$19$	−2.89310			−0.663722			−0.331861	−	0.943328i	$-0.607676\pi$
$19$	−2.89310			−0.663722			−0.331861	+	0.943328i	$0.607676\pi$
$20$	1.00000			0.223607
$21$	1.06811	+	4.59318i	0.233081	+	1.00231i
$22$	5.40581			1.15252
$23$			0.0386030i			0.00804927i	0.999992	+	0.00402464i	$0.00128109\pi$
$23$			0.0386030i			0.00804927i	−0.999992	+	0.00402464i	$0.998719\pi$
$24$	−1.68704	+	0.392308i	−0.344365	+	0.0800794i
$25$	1.00000			0.200000
$26$			1.90134i			0.372883i
$27$	−4.02254	+	3.28926i	−0.774138	+	0.633017i
$28$		−	2.72263i		−	0.514529i
$29$		−	9.54907i		−	1.77322i	−0.462521	−	0.886608i	$-0.653055\pi$
$29$		−	9.54907i		−	1.77322i	0.462521	−	0.886608i	$-0.346945\pi$
$30$	−1.68704	+	0.392308i	−0.308009	+	0.0716252i
$31$			0.791170i			0.142098i	0.997473	+	0.0710492i	$0.0226347\pi$
$31$			0.791170i			0.142098i	−0.997473	+	0.0710492i	$0.977365\pi$
$32$	1.00000			0.176777
$33$	−9.11980	+	2.12074i	−1.58755	+	0.369173i
$34$		−	1.89478i		−	0.324953i
$35$		−	2.72263i		−	0.460209i
$36$	2.69219	−	1.32367i	0.448698	−	0.220612i
$37$	−4.33807			−0.713174			−0.356587	−	0.934262i	$-0.616060\pi$
$37$	−4.33807			−0.713174			−0.356587	+	0.934262i	$0.616060\pi$
$38$	−2.89310			−0.469322
$39$	−0.745909	−	3.20763i	−0.119441	−	0.513631i
$40$	1.00000			0.158114
$41$	2.80538			0.438126			0.219063	−	0.975711i	$-0.429700\pi$
$41$	2.80538			0.438126			0.219063	+	0.975711i	$0.429700\pi$
$42$	1.06811	+	4.59318i	0.164813	+	0.708744i
$43$			9.14619i			1.39478i	0.716691	+	0.697390i	$0.245656\pi$
$43$			9.14619i			1.39478i	−0.716691	+	0.697390i	$0.754344\pi$
$44$	5.40581			0.814956
$45$	2.69219	−	1.32367i	0.401328	−	0.197322i
$46$			0.0386030i			0.00569170i
$47$		−	3.02549i		−	0.441313i	−0.975352	−	0.220657i	$-0.929180\pi$
$47$		−	3.02549i		−	0.441313i	0.975352	−	0.220657i	$-0.0708200\pi$
$48$	−1.68704	+	0.392308i	−0.243503	+	0.0566247i
$49$	−0.412733			−0.0589618
$50$	1.00000			0.141421
$51$	0.743337	+	3.19657i	0.104088	+	0.447609i
$52$			1.90134i			0.263668i
$53$	3.05084			0.419065			0.209532	−	0.977802i	$-0.432806\pi$
$53$	3.05084			0.419065			0.209532	+	0.977802i	$0.432806\pi$
$54$	−4.02254	+	3.28926i	−0.547398	+	0.447611i
$55$	5.40581			0.728919
$56$		−	2.72263i		−	0.363827i
$57$	4.88076	−	1.13498i	0.646473	−	0.150332i
$58$		−	9.54907i		−	1.25385i
$59$		−	8.27799i		−	1.07770i	−0.842401	−	0.538851i	$-0.818858\pi$
$59$		−	8.27799i		−	1.07770i	0.842401	−	0.538851i	$-0.181142\pi$
$60$	−1.68704	+	0.392308i	−0.217796	+	0.0506467i
$61$		−	14.8383i		−	1.89985i	−0.312476	−	0.949926i	$-0.601158\pi$
$61$		−	14.8383i		−	1.89985i	0.312476	−	0.949926i	$-0.398842\pi$
$62$			0.791170i			0.100479i
$63$	−3.60388	−	7.32985i	−0.454046	−	0.923474i
$64$	1.00000			0.125000
$65$			1.90134i			0.235832i
$66$	−9.11980	+	2.12074i	−1.12257	+	0.261045i
$67$	5.24905	+	6.28072i	0.641274	+	0.767312i
$67$	5.24905	+	6.28072i	0.641274	+	0.767312i
$68$		−	1.89478i		−	0.229776i
$69$	−0.0151442	−	0.0651246i	−0.00182315	−	0.00784008i
$70$		−	2.72263i		−	0.325417i
$71$		−	14.3117i		−	1.69849i	−0.527998	−	0.849246i	$-0.677057\pi$
$71$		−	14.3117i		−	1.69849i	0.527998	−	0.849246i	$-0.322943\pi$
$72$	2.69219	−	1.32367i	0.317278	−	0.155997i
$73$	11.1356			1.30332			0.651662	−	0.758510i	$-0.274072\pi$
$73$	11.1356			1.30332			0.651662	+	0.758510i	$0.274072\pi$
$74$	−4.33807			−0.504291
$75$	−1.68704	+	0.392308i	−0.194802	+	0.0452998i
$76$	−2.89310			−0.331861
$77$		−	14.7180i		−	1.67728i
$78$	−0.745909	−	3.20763i	−0.0844576	−	0.363192i
$79$			15.7714i			1.77442i	0.461361	+	0.887212i	$0.347361\pi$
$79$			15.7714i			1.77442i	−0.461361	+	0.887212i	$0.652639\pi$
$80$	1.00000			0.111803
$81$	5.49577	−	7.12717i	0.610641	−	0.791908i
$82$	2.80538			0.309802
$83$			4.38087i			0.480863i	0.970666	+	0.240432i	$0.0772889\pi$
$83$			4.38087i			0.480863i	−0.970666	+	0.240432i	$0.922711\pi$
$84$	1.06811	+	4.59318i	0.116540	+	0.501157i
$85$		−	1.89478i		−	0.205518i
$86$			9.14619i			0.986259i
$87$	3.74617	+	16.1096i	0.401632	+	1.72713i
$88$	5.40581			0.576261
$89$			13.1250i			1.39125i	0.718407	+	0.695623i	$0.244872\pi$
$89$			13.1250i			1.39125i	−0.718407	+	0.695623i	$0.755128\pi$
$90$	2.69219	−	1.32367i	0.283782	−	0.139528i
$91$	5.17665			0.542660
$92$			0.0386030i			0.00402464i
$93$	−0.310382	−	1.33473i	−0.0321851	−	0.138405i
$94$		−	3.02549i		−	0.312056i
$95$	−2.89310			−0.296825
$96$	−1.68704	+	0.392308i	−0.172183	+	0.0400397i
$97$			5.86842i			0.595848i	0.954590	+	0.297924i	$0.0962942\pi$
$97$			5.86842i			0.595848i	−0.954590	+	0.297924i	$0.903706\pi$
$98$	−0.412733			−0.0416923
$99$	14.5535	−	7.15553i	1.46268	−	0.719158i
$100$	1.00000			0.100000
$101$	15.3102			1.52342			0.761709	−	0.647919i	$-0.224361\pi$
$101$	15.3102			1.52342			0.761709	+	0.647919i	$0.224361\pi$
$102$	0.743337	+	3.19657i	0.0736014	+	0.316507i
$103$	−18.0881			−1.78228			−0.891139	−	0.453731i	$-0.850093\pi$
$103$	−18.0881			−1.78228			−0.891139	+	0.453731i	$0.850093\pi$
$104$			1.90134i			0.186441i
$105$	1.06811	+	4.59318i	0.104237	+	0.448249i
$106$	3.05084			0.296323
$107$		−	9.59519i		−	0.927602i	−0.885939	−	0.463801i	$-0.846485\pi$
$107$		−	9.59519i		−	0.927602i	0.885939	−	0.463801i	$-0.153515\pi$
$108$	−4.02254	+	3.28926i	−0.387069	+	0.316509i
$109$		−	19.6347i		−	1.88066i	−0.340259	−	0.940332i	$-0.610515\pi$
$109$		−	19.6347i		−	1.88066i	0.340259	−	0.940332i	$-0.389485\pi$
$110$	5.40581			0.515423
$111$	7.31849	−	1.70186i	0.694640	−	0.161533i
$112$		−	2.72263i		−	0.257265i
$113$	−3.45430			−0.324954			−0.162477	−	0.986712i	$-0.551948\pi$
$113$	−3.45430			−0.324954			−0.162477	+	0.986712i	$0.551948\pi$
$114$	4.88076	−	1.13498i	0.457125	−	0.106301i
$115$			0.0386030i			0.00359974i
$116$		−	9.54907i		−	0.886608i
$117$	2.51675	+	5.11876i	0.232674	+	0.473230i
$118$		−	8.27799i		−	0.762051i
$119$	−5.15880			−0.472906
$120$	−1.68704	+	0.392308i	−0.154005	+	0.0358126i
$121$	18.2227			1.65661
$122$		−	14.8383i		−	1.34340i
$123$	−4.73277	+	1.10057i	−0.426740	+	0.0992351i
$124$			0.791170i			0.0710492i
$125$	1.00000			0.0894427
$126$	−3.60388	−	7.32985i	−0.321059	−	0.652995i
$127$	12.0151			1.06616			0.533082	−	0.846064i	$-0.321034\pi$
$127$	12.0151			1.06616			0.533082	+	0.846064i	$0.321034\pi$
$128$	1.00000			0.0883883
$129$	−3.58812	−	15.4300i	−0.315916	−	1.35853i
$130$			1.90134i			0.166758i
$131$			4.98232i			0.435307i	0.976026	+	0.217653i	$0.0698403\pi$
$131$			4.98232i			0.435307i	−0.976026	+	0.217653i	$0.930160\pi$
$132$	−9.11980	+	2.12074i	−0.793777	+	0.184587i
$133$			7.87684i			0.683009i
$134$	5.24905	+	6.28072i	0.453449	+	0.542572i
$135$	−4.02254	+	3.28926i	−0.346205	+	0.283094i
$136$		−	1.89478i		−	0.162476i
$137$	16.2254			1.38623			0.693115	−	0.720827i	$-0.256238\pi$
$137$	16.2254			1.38623			0.693115	+	0.720827i	$0.256238\pi$
$138$	−0.0151442	−	0.0651246i	−0.00128916	−	0.00554378i
$139$			3.95684i			0.335615i	0.985820	+	0.167807i	$0.0536687\pi$
$139$			3.95684i			0.335615i	−0.985820	+	0.167807i	$0.946331\pi$
$140$		−	2.72263i		−	0.230105i
$141$	1.18692	+	5.10412i	0.0999569	+	0.429844i
$142$		−	14.3117i		−	1.20101i
$143$			10.2783i			0.859512i
$144$	2.69219	−	1.32367i	0.224349	−	0.110306i
$145$		−	9.54907i		−	0.793007i
$146$	11.1356			0.921589
$147$	0.696295	−	0.161918i	0.0574295	−	0.0133548i
$148$	−4.33807			−0.356587
$149$			14.1824i			1.16187i	0.813951	+	0.580933i	$0.197312\pi$
$149$			14.1824i			1.16187i	−0.813951	+	0.580933i	$0.802688\pi$
$150$	−1.68704	+	0.392308i	−0.137746	+	0.0320318i
$151$	22.3784			1.82113			0.910566	−	0.413365i	$-0.135646\pi$
$151$	22.3784			1.82113			0.910566	+	0.413365i	$0.135646\pi$
$152$	−2.89310			−0.234661
$153$	−2.50808	−	5.10111i	−0.202766	−	0.412401i
$154$		−	14.7180i		−	1.18601i
$155$			0.791170i			0.0635483i
$156$	−0.745909	−	3.20763i	−0.0597205	−	0.256816i
$157$	−16.5589			−1.32155			−0.660773	−	0.750585i	$-0.729772\pi$
$157$	−16.5589			−1.32155			−0.660773	+	0.750585i	$0.729772\pi$
$158$			15.7714i			1.25471i
$159$	−5.14688	+	1.19687i	−0.408174	+	0.0949177i
$160$	1.00000			0.0790569
$161$	0.105102			0.00828317
$162$	5.49577	−	7.12717i	0.431788	−	0.559963i
$163$	−15.1187			−1.18419			−0.592094	−	0.805869i	$-0.701699\pi$
$163$	−15.1187			−1.18419			−0.592094	+	0.805869i	$0.701699\pi$
$164$	2.80538			0.219063
$165$	−9.11980	+	2.12074i	−0.709975	+	0.165099i
$166$			4.38087i			0.340022i
$167$			5.29268i			0.409560i	0.978808	+	0.204780i	$0.0656478\pi$
$167$			5.29268i			0.409560i	−0.978808	+	0.204780i	$0.934352\pi$
$168$	1.06811	+	4.59318i	0.0824064	+	0.354372i
$169$	9.38492			0.721917
$170$		−	1.89478i		−	0.145323i
$171$	−7.78877	+	3.82952i	−0.595622	+	0.292851i
$172$			9.14619i			0.697390i
$173$		−	11.1065i		−	0.844412i	−0.906500	−	0.422206i	$-0.861256\pi$
$173$		−	11.1065i		−	0.844412i	0.906500	−	0.422206i	$-0.138744\pi$
$174$	3.74617	+	16.1096i	0.283996	+	1.22127i
$175$		−	2.72263i		−	0.205812i
$176$	5.40581			0.407478
$177$	3.24752	+	13.9653i	0.244098	+	1.04969i
$178$			13.1250i			0.983760i
$179$	−11.5773			−0.865328			−0.432664	−	0.901555i	$-0.642426\pi$
$179$	−11.5773			−0.865328			−0.432664	+	0.901555i	$0.642426\pi$
$180$	2.69219	−	1.32367i	0.200664	−	0.0986609i
$181$	−17.7578			−1.31993			−0.659963	−	0.751298i	$-0.729428\pi$
$181$	−17.7578			−1.31993			−0.659963	+	0.751298i	$0.729428\pi$
$182$	5.17665			0.383718
$183$	5.82118	+	25.0328i	0.430314	+	1.85048i
$184$			0.0386030i			0.00284585i
$185$	−4.33807			−0.318941
$186$	−0.310382	−	1.33473i	−0.0227583	−	0.0978674i
$187$		−	10.2428i		−	0.749030i
$188$		−	3.02549i		−	0.220657i
$189$	8.95544	+	10.9519i	0.651412	+	0.796633i
$190$	−2.89310			−0.209887
$191$	6.19632			0.448350			0.224175	−	0.974549i	$-0.428031\pi$
$191$	6.19632			0.448350			0.224175	+	0.974549i	$0.428031\pi$
$192$	−1.68704	+	0.392308i	−0.121751	+	0.0283124i
$193$	2.41446			0.173796			0.0868982	−	0.996217i	$-0.472305\pi$
$193$	2.41446			0.173796			0.0868982	+	0.996217i	$0.472305\pi$
$194$			5.86842i			0.421328i
$195$	−0.745909	−	3.20763i	−0.0534157	−	0.229703i
$196$	−0.412733			−0.0294809
$197$	−0.773294			−0.0550949			−0.0275475	−	0.999620i	$-0.508770\pi$
$197$	−0.773294			−0.0550949			−0.0275475	+	0.999620i	$0.508770\pi$
$198$	14.5535	−	7.15553i	1.03427	−	0.508521i
$199$	−3.51882			−0.249443			−0.124721	−	0.992192i	$-0.539804\pi$
$199$	−3.51882			−0.249443			−0.124721	+	0.992192i	$0.539804\pi$
$200$	1.00000			0.0707107
$201$	−11.3193	−	8.53657i	−0.798403	−	0.602123i
$202$	15.3102			1.07722
$203$	−25.9986			−1.82474
$204$	0.743337	+	3.19657i	0.0520440	+	0.223805i
$205$	2.80538			0.195936
$206$	−18.0881			−1.26026
$207$	0.0510978	+	0.103926i	0.00355154	+	0.00722339i
$208$			1.90134i			0.131834i
$209$	−15.6395			−1.08181
$210$	1.06811	+	4.59318i	0.0737066	+	0.316960i
$211$	−20.4823			−1.41006			−0.705030	−	0.709178i	$-0.749066\pi$
$211$	−20.4823			−1.41006			−0.705030	+	0.709178i	$0.749066\pi$
$212$	3.05084			0.209532
$213$	5.61461	+	24.1444i	0.384706	+	1.65435i
$214$		−	9.59519i		−	0.655914i
$215$			9.14619i			0.623765i
$216$	−4.02254	+	3.28926i	−0.273699	+	0.223805i
$217$	2.15407			0.146228
$218$		−	19.6347i		−	1.32983i
$219$	−18.7862	+	4.36858i	−1.26945	+	0.295201i
$220$	5.40581			0.364459
$221$	3.60262			0.242339
$222$	7.31849	−	1.70186i	0.491185	−	0.114221i
$223$	−11.4575			−0.767254			−0.383627	−	0.923488i	$-0.625325\pi$
$223$	−11.4575			−0.767254			−0.383627	+	0.923488i	$0.625325\pi$
$224$		−	2.72263i		−	0.181914i
$225$	2.69219	−	1.32367i	0.179479	−	0.0882450i
$226$	−3.45430			−0.229777
$227$		−	12.8804i		−	0.854902i	−0.904039	−	0.427451i	$-0.859412\pi$
$227$		−	12.8804i		−	0.854902i	0.904039	−	0.427451i	$-0.140588\pi$
$228$	4.88076	−	1.13498i	0.323236	−	0.0751661i
$229$		−	0.324447i		−	0.0214401i	−0.999943	−	0.0107200i	$-0.996588\pi$
$229$		−	0.324447i		−	0.0214401i	0.999943	−	0.0107200i	$-0.00341236\pi$
$230$			0.0386030i			0.00254540i
$231$	5.77399	+	24.8299i	0.379901	+	1.63369i
$232$		−	9.54907i		−	0.626927i
$233$	14.5074			0.950414			0.475207	−	0.879874i	$-0.342373\pi$
$233$	14.5074			0.950414			0.475207	+	0.879874i	$0.342373\pi$
$234$	2.51675	+	5.11876i	0.164525	+	0.334624i
$235$		−	3.02549i		−	0.197361i
$236$		−	8.27799i		−	0.538851i
$237$	−6.18725	−	26.6070i	−0.401905	−	1.72831i
$238$	−5.15880			−0.334395
$239$	−8.86410			−0.573371			−0.286685	−	0.958025i	$-0.592553\pi$
$239$	−8.86410			−0.573371			−0.286685	+	0.958025i	$0.592553\pi$
$240$	−1.68704	+	0.392308i	−0.108898	+	0.0253233i
$241$	−16.8565			−1.08582			−0.542912	−	0.839790i	$-0.682678\pi$
$241$	−16.8565			−1.08582			−0.542912	+	0.839790i	$0.682678\pi$
$242$	18.2227			1.17140
$243$	−6.47553	+	14.1798i	−0.415405	+	0.909636i
$244$		−	14.8383i		−	0.949926i
$245$	−0.412733			−0.0263685
$246$	−4.73277	+	1.10057i	−0.301751	+	0.0701698i
$247$		−	5.50075i		−	0.350005i
$248$			0.791170i			0.0502394i
$249$	−1.71865	−	7.39069i	−0.108915	−	0.468366i
$250$	1.00000			0.0632456
$251$	2.14685			0.135508			0.0677540	−	0.997702i	$-0.478417\pi$
$251$	2.14685			0.135508			0.0677540	+	0.997702i	$0.478417\pi$
$252$	−3.60388	−	7.32985i	−0.227023	−	0.461737i
$253$			0.208680i			0.0131196i
$254$	12.0151			0.753891
$255$	0.743337	+	3.19657i	0.0465496	+	0.200177i
$256$	1.00000			0.0625000
$257$			6.61736i			0.412780i	0.978470	+	0.206390i	$0.0661715\pi$
$257$			6.61736i			0.412780i	−0.978470	+	0.206390i	$0.933829\pi$
$258$	−3.58812	−	15.4300i	−0.223387	−	0.960628i
$259$			11.8110i			0.733898i
$260$			1.90134i			0.117916i
$261$	−12.6399	−	25.7079i	−0.782388	−	1.59128i
$262$			4.98232i			0.307808i
$263$		−	3.09139i		−	0.190623i	−0.995447	−	0.0953115i	$-0.969615\pi$
$263$		−	3.09139i		−	0.190623i	0.995447	−	0.0953115i	$-0.0303847\pi$
$264$	−9.11980	+	2.12074i	−0.561285	+	0.130522i
$265$	3.05084			0.187411
$266$			7.87684i			0.482960i
$267$	−5.14903	−	22.1423i	−0.315116	−	1.35509i
$268$	5.24905	+	6.28072i	0.320637	+	0.383656i
$269$			13.1196i			0.799913i	0.916534	+	0.399957i	$0.130975\pi$
$269$			13.1196i			0.799913i	−0.916534	+	0.399957i	$0.869025\pi$
$270$	−4.02254	+	3.28926i	−0.244804	+	0.200178i
$271$			1.86399i			0.113229i	0.998396	+	0.0566145i	$0.0180306\pi$
$271$			1.86399i			0.113229i	−0.998396	+	0.0566145i	$0.981969\pi$
$272$		−	1.89478i		−	0.114888i
$273$	−8.73319	+	2.03084i	−0.528557	+	0.122912i
$274$	16.2254			0.980212
$275$	5.40581			0.325982
$276$	−0.0151442	−	0.0651246i	−0.000911576	−	0.00392004i
$277$	−3.82021			−0.229534			−0.114767	−	0.993392i	$-0.536612\pi$
$277$	−3.82021			−0.229534			−0.114767	+	0.993392i	$0.536612\pi$
$278$			3.95684i			0.237316i
$279$	1.04725	+	2.12998i	0.0626974	+	0.127519i
$280$		−	2.72263i		−	0.162708i
$281$	−1.45613			−0.0868655			−0.0434327	−	0.999056i	$-0.513829\pi$
$281$	−1.45613			−0.0868655			−0.0434327	+	0.999056i	$0.513829\pi$
$282$	1.18692	+	5.10412i	0.0706802	+	0.303946i
$283$	−11.7886			−0.700761			−0.350381	−	0.936607i	$-0.613948\pi$
$283$	−11.7886			−0.700761			−0.350381	+	0.936607i	$0.613948\pi$
$284$		−	14.3117i		−	0.849246i
$285$	4.88076	−	1.13498i	0.289111	−	0.0672306i
$286$			10.2783i			0.607767i
$287$		−	7.63801i		−	0.450857i
$288$	2.69219	−	1.32367i	0.158639	−	0.0779983i
$289$	13.4098			0.788812
$290$		−	9.54907i		−	0.560740i
$291$	−2.30223	−	9.90024i	−0.134959	−	0.580363i
$292$	11.1356			0.651662
$293$			15.1973i			0.887837i	0.896067	+	0.443918i	$0.146412\pi$
$293$			15.1973i			0.887837i	−0.896067	+	0.443918i	$0.853588\pi$
$294$	0.696295	−	0.161918i	0.0406088	−	0.00944326i
$295$		−	8.27799i		−	0.481963i
$296$	−4.33807			−0.252145
$297$	−21.7451	+	17.7811i	−1.26178	+	1.03176i
$298$			14.1824i			0.821564i
$299$	−0.0733973			−0.00424467
$300$	−1.68704	+	0.392308i	−0.0974011	+	0.0226499i
$301$	24.9017			1.43531
$302$	22.3784			1.28773
$303$	−25.8288	+	6.00629i	−1.48383	+	0.345052i
$304$	−2.89310			−0.165930
$305$		−	14.8383i		−	0.849639i
$306$	−2.50808	−	5.10111i	−0.143377	−	0.291611i
$307$	−20.1208			−1.14836			−0.574178	−	0.818731i	$-0.694678\pi$
$307$	−20.1208			−1.14836			−0.574178	+	0.818731i	$0.694678\pi$
$308$		−	14.7180i		−	0.838638i
$309$	30.5154	−	7.09611i	1.73596	−	0.403684i
$310$			0.791170i			0.0449355i
$311$	−18.6317			−1.05651			−0.528254	−	0.849086i	$-0.677153\pi$
$311$	−18.6317			−1.05651			−0.528254	+	0.849086i	$0.677153\pi$
$312$	−0.745909	−	3.20763i	−0.0422288	−	0.181596i
$313$			12.9623i			0.732672i	0.930483	+	0.366336i	$0.119388\pi$
$313$			12.9623i			0.732672i	−0.930483	+	0.366336i	$0.880612\pi$
$314$	−16.5589			−0.934475
$315$	−3.60388	−	7.32985i	−0.203056	−	0.412990i
$316$			15.7714i			0.887212i
$317$		−	25.4987i		−	1.43215i	−0.698024	−	0.716075i	$-0.745937\pi$
$317$		−	25.4987i		−	1.43215i	0.698024	−	0.716075i	$-0.254063\pi$
$318$	−5.14688	+	1.19687i	−0.288622	+	0.0671169i
$319$		−	51.6204i		−	2.89019i
$320$	1.00000			0.0559017
$321$	3.76427	+	16.1874i	0.210101	+	0.903495i
$322$	0.105102			0.00585709
$323$			5.48179i			0.305015i
$324$	5.49577	−	7.12717i	0.305321	−	0.395954i
$325$			1.90134i			0.105467i
$326$	−15.1187			−0.837348
$327$	7.70284	+	33.1245i	0.425968	+	1.83179i
$328$	2.80538			0.154901
$329$	−8.23730			−0.454137
$330$	−9.11980	+	2.12074i	−0.502028	+	0.116743i
$331$			26.4069i			1.45145i	0.687984	+	0.725726i	$0.258496\pi$
$331$			26.4069i			1.45145i	−0.687984	+	0.725726i	$0.741504\pi$
$332$			4.38087i			0.240432i
$333$	−11.6789	+	5.74220i	−0.640000	+	0.314670i
$334$			5.29268i			0.289602i
$335$	5.24905	+	6.28072i	0.286786	+	0.343153i
$336$	1.06811	+	4.59318i	0.0582702	+	0.250579i
$337$			14.2377i			0.775577i	0.921748	+	0.387788i	$0.126761\pi$
$337$			14.2377i			0.775577i	−0.921748	+	0.387788i	$0.873239\pi$
$338$	9.38492			0.510472
$339$	5.82754	−	1.35515i	0.316509	−	0.0736016i
$340$		−	1.89478i		−	0.102759i
$341$			4.27691i			0.231608i
$342$	−7.78877	+	3.82952i	−0.421168	+	0.207077i
$343$		−	17.9347i		−	0.968384i
$344$			9.14619i			0.493129i
$345$	−0.0151442	−	0.0651246i	−0.000815338	−	0.00350619i
$346$		−	11.1065i		−	0.597090i
$347$	5.56480			0.298734			0.149367	−	0.988782i	$-0.452276\pi$
$347$	5.56480			0.298734			0.149367	+	0.988782i	$0.452276\pi$
$348$	3.74617	+	16.1096i	0.200816	+	0.863567i
$349$	35.7961			1.91612			0.958062	−	0.286561i	$-0.0925122\pi$
$349$	35.7961			1.91612			0.958062	+	0.286561i	$0.0925122\pi$
$350$		−	2.72263i		−	0.145531i
$351$	−6.25398	−	7.64820i	−0.333813	−	0.408231i
$352$	5.40581			0.288130
$353$	−2.34453			−0.124786			−0.0623932	−	0.998052i	$-0.519873\pi$
$353$	−2.34453			−0.124786			−0.0623932	+	0.998052i	$0.519873\pi$
$354$	3.24752	+	13.9653i	0.172604	+	0.742246i
$355$		−	14.3117i		−	0.759589i
$356$			13.1250i			0.695623i
$357$	8.70308	−	2.02384i	0.460616	−	0.107113i
$358$	−11.5773			−0.611879
$359$			19.9473i			1.05278i	0.850244	+	0.526389i	$0.176454\pi$
$359$			19.9473i			1.05278i	−0.850244	+	0.526389i	$0.823546\pi$
$360$	2.69219	−	1.32367i	0.141891	−	0.0697638i
$361$	−10.6300			−0.559473
$362$	−17.7578			−0.933329
$363$	−30.7425	+	7.14892i	−1.61356	+	0.375221i
$364$	5.17665			0.271330
$365$	11.1356			0.582864
$366$	5.82118	+	25.0328i	0.304278	+	1.30848i
$367$			32.9954i			1.72235i	0.508311	+	0.861174i	$0.330270\pi$
$367$			32.9954i			1.72235i	−0.508311	+	0.861174i	$0.669730\pi$
$368$			0.0386030i			0.00201232i
$369$	7.55260	−	3.71341i	0.393173	−	0.193312i
$370$	−4.33807			−0.225526
$371$		−	8.30631i		−	0.431242i
$372$	−0.310382	−	1.33473i	−0.0160926	−	0.0692027i
$373$		−	10.7810i		−	0.558218i	−0.960259	−	0.279109i	$-0.909961\pi$
$373$		−	10.7810i		−	0.558218i	0.960259	−	0.279109i	$-0.0900391\pi$
$374$		−	10.2428i		−	0.529644i
$375$	−1.68704	+	0.392308i	−0.0871182	+	0.0202587i
$376$		−	3.02549i		−	0.156028i
$377$	18.1560			0.935081
$378$	8.95544	+	10.9519i	0.460618	+	0.563305i
$379$			29.7333i			1.52730i	0.645631	+	0.763649i	$0.276594\pi$
$379$			29.7333i			1.52730i	−0.645631	+	0.763649i	$0.723406\pi$
$380$	−2.89310			−0.148413
$381$	−20.2698	+	4.71360i	−1.03846	+	0.241485i
$382$	6.19632			0.317031
$383$	−25.0490			−1.27994			−0.639971	−	0.768399i	$-0.721054\pi$
$383$	−25.0490			−1.27994			−0.639971	+	0.768399i	$0.721054\pi$
$384$	−1.68704	+	0.392308i	−0.0860913	+	0.0200199i
$385$		−	14.7180i		−	0.750100i
$386$	2.41446			0.122893
$387$	12.1066	+	24.6233i	0.615412	+	1.25167i
$388$			5.86842i			0.297924i
$389$			8.57535i			0.434788i	0.976084	+	0.217394i	$0.0697556\pi$
$389$			8.57535i			0.434788i	−0.976084	+	0.217394i	$0.930244\pi$
$390$	−0.745909	−	3.20763i	−0.0377706	−	0.162425i
$391$	0.0731442			0.00369906
$392$	−0.412733			−0.0208461
$393$	−1.95460	−	8.40535i	−0.0985965	−	0.423994i
$394$	−0.773294			−0.0389580
$395$			15.7714i			0.793547i
$396$	14.5535	−	7.15553i	0.731339	−	0.359579i
$397$	4.06430			0.203982			0.101991	−	0.994785i	$-0.467479\pi$
$397$	4.06430			0.203982			0.101991	+	0.994785i	$0.467479\pi$
$398$	−3.51882			−0.176383
$399$	−3.09014	−	13.2885i	−0.154701	−	0.665258i
$400$	1.00000			0.0500000
$401$	−15.5754			−0.777799			−0.388900	−	0.921280i	$-0.627145\pi$
$401$	−15.5754			−0.777799			−0.388900	+	0.921280i	$0.627145\pi$
$402$	−11.3193	−	8.53657i	−0.564556	−	0.425765i
$403$	−1.50428			−0.0749336
$404$	15.3102			0.761709
$405$	5.49577	−	7.12717i	0.273087	−	0.354152i
$406$	−25.9986			−1.29029
$407$	−23.4508			−1.16241
$408$	0.743337	+	3.19657i	0.0368007	+	0.158254i
$409$		−	14.0044i		−	0.692474i	−0.938147	−	0.346237i	$-0.887459\pi$
$409$		−	14.0044i		−	0.692474i	0.938147	−	0.346237i	$-0.112541\pi$
$410$	2.80538			0.138548
$411$	−27.3729	+	6.36535i	−1.35020	+	0.313979i
$412$	−18.0881			−0.891139
$413$	−22.5379			−1.10902
$414$	0.0510978	+	0.103926i	0.00251132	+	0.00510771i
$415$			4.38087i			0.215048i
$416$			1.90134i			0.0932207i
$417$	−1.55230	−	6.67534i	−0.0760164	−	0.326893i
$418$	−15.6395			−0.764954
$419$			22.0846i			1.07890i	0.842017	+	0.539452i	$0.181368\pi$
$419$			22.0846i			1.07890i	−0.842017	+	0.539452i	$0.818632\pi$
$420$	1.06811	+	4.59318i	0.0521184	+	0.224124i
$421$	22.3648			1.09000			0.544998	−	0.838437i	$-0.316530\pi$
$421$	22.3648			1.09000			0.544998	+	0.838437i	$0.316530\pi$
$422$	−20.4823			−0.997063
$423$	−4.00477	−	8.14519i	−0.194718	−	0.396033i
$424$	3.05084			0.148162
$425$		−	1.89478i		−	0.0919104i
$426$	5.61461	+	24.1444i	0.272029	+	1.16980i
$427$	−40.3993			−1.95506
$428$		−	9.59519i		−	0.463801i
$429$	−4.03224	−	17.3398i	−0.194678	−	0.837174i
$430$			9.14619i			0.441068i
$431$			27.7365i			1.33602i	0.744153	+	0.668009i	$0.232853\pi$
$431$			27.7365i			1.33602i	−0.744153	+	0.668009i	$0.767147\pi$
$432$	−4.02254	+	3.28926i	−0.193534	+	0.158254i
$433$			6.52152i			0.313404i	0.987646	+	0.156702i	$0.0500863\pi$
$433$			6.52152i			0.313404i	−0.987646	+	0.156702i	$0.949914\pi$
$434$	2.15407			0.103399
$435$	3.74617	+	16.1096i	0.179615	+	0.772398i
$436$		−	19.6347i		−	0.940332i
$437$		−	0.111682i		−	0.00534248i
$438$	−18.7862	+	4.36858i	−0.897638	+	0.208739i
$439$	1.00739			0.0480802			0.0240401	−	0.999711i	$-0.492347\pi$
$439$	1.00739			0.0480802			0.0240401	+	0.999711i	$0.492347\pi$
$440$	5.40581			0.257712
$441$	−1.11115	+	0.546324i	−0.0529121	+	0.0260154i
$442$	3.60262			0.171359
$443$	9.04482			0.429733			0.214866	−	0.976643i	$-0.431068\pi$
$443$	9.04482			0.429733			0.214866	+	0.976643i	$0.431068\pi$
$444$	7.31849	−	1.70186i	0.347320	−	0.0807666i
$445$			13.1250i			0.622184i
$446$	−11.4575			−0.542531
$447$	−5.56386	−	23.9262i	−0.263161	−	1.13167i
$448$		−	2.72263i		−	0.128632i
$449$			3.00648i			0.141884i	0.997480	+	0.0709422i	$0.0226006\pi$
$449$			3.00648i			0.141884i	−0.997480	+	0.0709422i	$0.977399\pi$
$450$	2.69219	−	1.32367i	0.126911	−	0.0623986i
$451$	15.1653			0.714107
$452$	−3.45430			−0.162477
$453$	−37.7533	+	8.77923i	−1.77380	+	0.412484i
$454$		−	12.8804i		−	0.604507i
$455$	5.17665			0.242685
$456$	4.88076	−	1.13498i	0.228563	−	0.0531505i
$457$	−4.40716			−0.206158			−0.103079	−	0.994673i	$-0.532870\pi$
$457$	−4.40716			−0.206158			−0.103079	+	0.994673i	$0.532870\pi$
$458$		−	0.324447i		−	0.0151604i
$459$	6.23242	+	7.62183i	0.290905	+	0.355757i
$460$			0.0386030i			0.00179987i
$461$			19.7207i			0.918485i	0.888311	+	0.459242i	$0.151879\pi$
$461$			19.7207i			0.918485i	−0.888311	+	0.459242i	$0.848121\pi$
$462$	5.77399	+	24.8299i	0.268631	+	1.15519i
$463$			22.7061i			1.05524i	0.849481	+	0.527620i	$0.176915\pi$
$463$			22.7061i			1.05524i	−0.849481	+	0.527620i	$0.823085\pi$
$464$		−	9.54907i		−	0.443304i
$465$	−0.310382	−	1.33473i	−0.0143936	−	0.0618968i
$466$	14.5074			0.672044
$467$		−	20.0471i		−	0.927668i	−0.885922	−	0.463834i	$-0.846473\pi$
$467$		−	20.0471i		−	0.927668i	0.885922	−	0.463834i	$-0.153527\pi$
$468$	2.51675	+	5.11876i	0.116337	+	0.236615i
$469$	17.1001	−	14.2912i	0.789609	−	0.659908i
$470$		−	3.02549i		−	0.139555i
$471$	27.9355	−	6.49620i	1.28720	−	0.299329i
$472$		−	8.27799i		−	0.381025i
$473$			49.4425i			2.27337i
$474$	−6.18725	−	26.6070i	−0.284190	−	1.22210i
$475$	−2.89310			−0.132744
$476$	−5.15880			−0.236453
$477$	8.21343	−	4.03832i	0.376067	−	0.184902i
$478$	−8.86410			−0.405434
$479$			30.3787i			1.38804i	0.719957	+	0.694018i	$0.244161\pi$
$479$			30.3787i			1.38804i	−0.719957	+	0.694018i	$0.755839\pi$
$480$	−1.68704	+	0.392308i	−0.0770024	+	0.0179063i
$481$		−	8.24814i		−	0.376083i
$482$	−16.8565			−0.767793
$483$	−0.177310	+	0.0412322i	−0.00806791	+	0.00187613i
$484$	18.2227			0.828307
$485$			5.86842i			0.266471i
$486$	−6.47553	+	14.1798i	−0.293736	+	0.643210i
$487$		−	14.7820i		−	0.669836i	−0.942247	−	0.334918i	$-0.891291\pi$
$487$		−	14.7820i		−	0.669836i	0.942247	−	0.334918i	$-0.108709\pi$
$488$		−	14.8383i		−	0.671699i
$489$	25.5058	−	5.93118i	1.15341	−	0.268217i
$490$	−0.412733			−0.0186454
$491$			28.9541i			1.30668i	0.757064	+	0.653341i	$0.226633\pi$
$491$			28.9541i			1.30668i	−0.757064	+	0.653341i	$0.773367\pi$
$492$	−4.73277	+	1.10057i	−0.213370	+	0.0496175i
$493$	−18.0934			−0.814886
$494$		−	5.50075i		−	0.247491i
$495$	14.5535	−	7.15553i	0.654129	−	0.321617i
$496$			0.791170i			0.0355246i
$497$	−38.9656			−1.74785
$498$	−1.71865	−	7.39069i	−0.0770145	−	0.331185i
$499$		−	13.4078i		−	0.600214i	−0.953906	−	0.300107i	$-0.902978\pi$
$499$		−	13.4078i		−	0.600214i	0.953906	−	0.300107i	$-0.0970224\pi$
$500$	1.00000			0.0447214
$501$	−2.07636	−	8.92895i	−0.0927648	−	0.398916i
$502$	2.14685			0.0958186
$503$	−19.2034			−0.856237			−0.428118	−	0.903723i	$-0.640823\pi$
$503$	−19.2034			−0.856237			−0.428118	+	0.903723i	$0.640823\pi$
$504$	−3.60388	−	7.32985i	−0.160530	−	0.326497i
$505$	15.3102			0.681293
$506$			0.208680i			0.00927696i
$507$	−15.8327	+	3.68177i	−0.703155	+	0.163513i
$508$	12.0151			0.533082
$509$			1.44202i			0.0639163i	0.999489	+	0.0319581i	$0.0101743\pi$
$509$			1.44202i			0.0639163i	−0.999489	+	0.0319581i	$0.989826\pi$
$510$	0.743337	+	3.19657i	0.0329155	+	0.141546i
$511$		−	30.3182i		−	1.34120i
$512$	1.00000			0.0441942
$513$	11.6376	−	9.51613i	0.513812	−	0.420148i
$514$			6.61736i			0.291879i
$515$	−18.0881			−0.797059
$516$	−3.58812	−	15.4300i	−0.157958	−	0.679266i
$517$		−	16.3552i		−	0.719302i
$518$			11.8110i			0.518945i
$519$	4.35717	+	18.7371i	0.191258	+	0.822467i
$520$			1.90134i			0.0833792i
$521$	−13.7548			−0.602607			−0.301304	−	0.953528i	$-0.597422\pi$
$521$	−13.7548			−0.602607			−0.301304	+	0.953528i	$0.597422\pi$
$522$	−12.6399	−	25.7079i	−0.553232	−	1.12520i
$523$	13.7013			0.599118			0.299559	−	0.954078i	$-0.403161\pi$
$523$	13.7013			0.599118			0.299559	+	0.954078i	$0.403161\pi$
$524$			4.98232i			0.217653i
$525$	1.06811	+	4.59318i	0.0466161	+	0.200463i
$526$		−	3.09139i		−	0.134791i
$527$	1.49910			0.0653016
$528$	−9.11980	+	2.12074i	−0.396888	+	0.0922933i
$529$	22.9985			0.999935
$530$	3.05084			0.132520
$531$	−10.9574	−	22.2859i	−0.475509	−	0.967126i
$532$			7.87684i			0.341504i
$533$			5.33397i			0.231040i
$534$	−5.14903	−	22.1423i	−0.222820	−	0.958193i
$535$		−	9.59519i		−	0.414836i
$536$	5.24905	+	6.28072i	0.226724	+	0.271286i
$537$	19.5313	−	4.54186i	0.842839	−	0.195996i
$538$			13.1196i			0.565624i
$539$	−2.23115			−0.0961026
$540$	−4.02254	+	3.28926i	−0.173102	+	0.141547i
$541$		−	6.13962i		−	0.263963i	−0.991252	−	0.131981i	$-0.957866\pi$
$541$		−	6.13962i		−	0.263963i	0.991252	−	0.131981i	$-0.0421339\pi$
$542$			1.86399i			0.0800651i
$543$	29.9581	−	6.96651i	1.28562	−	0.298962i
$544$		−	1.89478i		−	0.0812381i
$545$		−	19.6347i		−	0.841058i
$546$	−8.73319	+	2.03084i	−0.373746	+	0.0869118i
$547$			10.1043i			0.432029i	0.976390	+	0.216014i	$0.0693058\pi$
$547$			10.1043i			0.432029i	−0.976390	+	0.216014i	$0.930694\pi$
$548$	16.2254			0.693115
$549$	−19.6411	−	39.9476i	−0.838262	−	1.70492i
$550$	5.40581			0.230504
$551$			27.6264i			1.17692i
$552$	−0.0151442	−	0.0651246i	−0.000644581	−	0.00277189i
$553$	42.9398			1.82599
$554$	−3.82021			−0.162305
$555$	7.31849	−	1.70186i	0.310652	−	0.0722398i
$556$			3.95684i			0.167807i
$557$			41.0771i			1.74049i	0.492616	+	0.870247i	$0.336041\pi$
$557$			41.0771i			1.74049i	−0.492616	+	0.870247i	$0.663959\pi$
$558$	1.04725	+	2.12998i	0.0443337	+	0.0901693i
$559$	−17.3900			−0.735518
$560$		−	2.72263i		−	0.115052i
$561$	4.01834	+	17.2800i	0.169654	+	0.729564i
$562$	−1.45613			−0.0614231
$563$	−31.5014			−1.32763			−0.663813	−	0.747898i	$-0.731063\pi$
$563$	−31.5014			−1.32763			−0.663813	+	0.747898i	$0.731063\pi$
$564$	1.18692	+	5.10412i	0.0499785	+	0.214922i
$565$	−3.45430			−0.145324
$566$	−11.7886			−0.495513
$567$	−19.4047	−	14.9630i	−0.814919	−	0.628385i
$568$		−	14.3117i		−	0.600507i
$569$			19.6646i			0.824384i	0.911097	+	0.412192i	$0.135237\pi$
$569$			19.6646i			0.824384i	−0.911097	+	0.412192i	$0.864763\pi$
$570$	4.88076	−	1.13498i	0.204433	−	0.0475392i
$571$	−24.4769			−1.02432			−0.512162	−	0.858889i	$-0.671155\pi$
$571$	−24.4769			−1.02432			−0.512162	+	0.858889i	$0.671155\pi$
$572$			10.2783i			0.429756i
$573$	−10.4534	+	2.43086i	−0.436698	+	0.101551i
$574$		−	7.63801i		−	0.318804i
$575$			0.0386030i			0.00160985i
$576$	2.69219	−	1.32367i	0.112175	−	0.0551531i
$577$			18.2904i			0.761438i	0.924691	+	0.380719i	$0.124323\pi$
$577$			18.2904i			0.761438i	−0.924691	+	0.380719i	$0.875677\pi$
$578$	13.4098			0.557774
$579$	−4.07328	+	0.947209i	−0.169280	+	0.0393647i
$580$		−	9.54907i		−	0.396503i
$581$	11.9275			0.494836
$582$	−2.30223	−	9.90024i	−0.0954303	−	0.410378i
$583$	16.4922			0.683039
$584$	11.1356			0.460794
$585$	2.51675	+	5.11876i	0.104055	+	0.211635i
$586$			15.1973i			0.627795i
$587$	32.4075			1.33760			0.668800	−	0.743442i	$-0.266808\pi$
$587$	32.4075			1.33760			0.668800	+	0.743442i	$0.266808\pi$
$588$	0.696295	−	0.161918i	0.0287147	−	0.00667739i
$589$		−	2.28893i		−	0.0943138i
$590$		−	8.27799i		−	0.340799i
$591$	1.30458	−	0.303369i	0.0536631	−	0.0124789i
$592$	−4.33807			−0.178294
$593$	−3.34951			−0.137548			−0.0687740	−	0.997632i	$-0.521909\pi$
$593$	−3.34951			−0.137548			−0.0687740	+	0.997632i	$0.521909\pi$
$594$	−21.7451	+	17.7811i	−0.892210	+	0.729567i
$595$	−5.15880			−0.211490
$596$			14.1824i			0.580933i
$597$	5.93639	−	1.38046i	0.242960	−	0.0564985i
$598$	−0.0733973			−0.00300144
$599$	30.9854			1.26603			0.633015	−	0.774140i	$-0.281817\pi$
$599$	30.9854			1.26603			0.633015	+	0.774140i	$0.281817\pi$
$600$	−1.68704	+	0.392308i	−0.0688730	+	0.0160159i
$601$	8.14507			0.332244			0.166122	−	0.986105i	$-0.446875\pi$
$601$	8.14507			0.332244			0.166122	+	0.986105i	$0.446875\pi$
$602$	24.9017			1.01492
$603$	22.4451	+	9.96086i	0.914034	+	0.405638i
$604$	22.3784			0.910566
$605$	18.2227			0.740860
$606$	−25.8288	+	6.00629i	−1.04922	+	0.243989i
$607$	43.0766			1.74843			0.874214	−	0.485542i	$-0.161378\pi$
$607$	43.0766			1.74843			0.874214	+	0.485542i	$0.161378\pi$
$608$	−2.89310			−0.117331
$609$	43.8606	−	10.1994i	1.77732	−	0.413303i
$610$		−	14.8383i		−	0.600786i
$611$	5.75248			0.232720
$612$	−2.50808	−	5.10111i	−0.101383	−	0.206200i
$613$	−34.5080			−1.39376			−0.696882	−	0.717186i	$-0.745430\pi$
$613$	−34.5080			−1.39376			−0.696882	+	0.717186i	$0.745430\pi$
$614$	−20.1208			−0.812010
$615$	−4.73277	+	1.10057i	−0.190844	+	0.0443793i
$616$		−	14.7180i		−	0.593006i
$617$			9.63115i			0.387736i	0.981028	+	0.193868i	$0.0621033\pi$
$617$			9.63115i			0.387736i	−0.981028	+	0.193868i	$0.937897\pi$
$618$	30.5154	−	7.09611i	1.22751	−	0.285448i
$619$	−24.1831			−0.972001			−0.486001	−	0.873959i	$-0.661545\pi$
$619$	−24.1831			−0.972001			−0.486001	+	0.873959i	$0.661545\pi$
$620$			0.791170i			0.0317742i
$621$	−0.126975	−	0.155282i	−0.00509533	−	0.00623124i
$622$	−18.6317			−0.747064
$623$	35.7345			1.43167
$624$	−0.745909	−	3.20763i	−0.0298603	−	0.128408i
$625$	1.00000			0.0400000
$626$			12.9623i			0.518078i
$627$	26.3845	−	6.13550i	1.05369	−	0.245028i
$628$	−16.5589			−0.660773
$629$			8.21970i			0.327741i
$630$	−3.60388	−	7.32985i	−0.143582	−	0.292028i
$631$		−	44.5797i		−	1.77469i	−0.461105	−	0.887345i	$-0.652547\pi$
$631$		−	44.5797i		−	1.77469i	0.461105	−	0.887345i	$-0.347453\pi$
$632$			15.7714i			0.627354i
$633$	34.5544	−	8.03536i	1.37341	−	0.319377i
$634$		−	25.4987i		−	1.01268i
$635$	12.0151			0.476803
$636$	−5.14688	+	1.19687i	−0.204087	+	0.0474588i
$637$		−	0.784744i		−	0.0310927i
$638$		−	51.6204i		−	2.04367i
$639$	−18.9441	−	38.5299i	−0.749417	−	1.52422i
$640$	1.00000			0.0395285
$641$	−25.7775			−1.01815			−0.509075	−	0.860722i	$-0.670012\pi$
$641$	−25.7775			−1.01815			−0.509075	+	0.860722i	$0.670012\pi$
$642$	3.76427	+	16.1874i	0.148564	+	0.638867i
$643$	41.2128			1.62527			0.812637	−	0.582771i	$-0.198031\pi$
$643$	41.2128			1.62527			0.812637	+	0.582771i	$0.198031\pi$
$644$	0.105102			0.00414159
$645$	−3.58812	−	15.4300i	−0.141282	−	0.607554i
$646$			5.48179i			0.215678i
$647$	−21.6690			−0.851897			−0.425949	−	0.904747i	$-0.640060\pi$
$647$	−21.6690			−0.851897			−0.425949	+	0.904747i	$0.640060\pi$
$648$	5.49577	−	7.12717i	0.215894	−	0.279982i
$649$		−	44.7492i		−	1.75656i
$650$			1.90134i			0.0745766i
$651$	−3.63399	+	0.845057i	−0.142427	+	0.0331204i
$652$	−15.1187			−0.592094
$653$	−18.2586			−0.714514			−0.357257	−	0.934006i	$-0.616288\pi$
$653$	−18.2586			−0.714514			−0.357257	+	0.934006i	$0.616288\pi$
$654$	7.70284	+	33.1245i	0.301205	+	1.29527i
$655$			4.98232i			0.194675i
$656$	2.80538			0.109532
$657$	29.9791	−	14.7399i	1.16960	−	0.575059i
$658$	−8.23730			−0.321123
$659$		−	47.1422i		−	1.83640i	−0.396116	−	0.918201i	$-0.629642\pi$
$659$		−	47.1422i		−	1.83640i	0.396116	−	0.918201i	$-0.370358\pi$
$660$	−9.11980	+	2.12074i	−0.354988	+	0.0825496i
$661$		−	4.94024i		−	0.192153i	−0.995374	−	0.0960765i	$-0.969371\pi$
$661$		−	4.94024i		−	0.192153i	0.995374	−	0.0960765i	$-0.0306294\pi$
$662$			26.4069i			1.02633i
$663$	−6.07776	+	1.41334i	−0.236040	+	0.0548894i
$664$			4.38087i			0.170011i
$665$			7.87684i			0.305451i
$666$	−11.6789	+	5.74220i	−0.452549	+	0.222506i
$667$	0.368622			0.0142731
$668$			5.29268i			0.204780i
$669$	19.3293	−	4.49488i	0.747314	−	0.173782i
$670$	5.24905	+	6.28072i	0.202788	+	0.242645i
$671$		−	80.2131i		−	3.09659i
$672$	1.06811	+	4.59318i	0.0412032	+	0.177186i
$673$		−	23.0687i		−	0.889233i	−0.895721	−	0.444617i	$-0.853340\pi$
$673$		−	23.0687i		−	0.889233i	0.895721	−	0.444617i	$-0.146660\pi$
$674$			14.2377i			0.548416i
$675$	−4.02254	+	3.28926i	−0.154828	+	0.126603i
$676$	9.38492			0.360958
$677$	13.9700			0.536912			0.268456	−	0.963292i	$-0.413487\pi$
$677$	13.9700			0.536912			0.268456	+	0.963292i	$0.413487\pi$
$678$	5.82754	−	1.35515i	0.223805	−	0.0520442i
$679$	15.9776			0.613162
$680$		−	1.89478i		−	0.0726616i
$681$	5.05308	+	21.7297i	0.193634	+	0.832684i
$682$			4.27691i			0.163772i
$683$	−34.9517			−1.33739			−0.668694	−	0.743538i	$-0.733146\pi$
$683$	−34.9517			−1.33739			−0.668694	+	0.743538i	$0.733146\pi$
$684$	−7.78877	+	3.82952i	−0.297811	+	0.146425i
$685$	16.2254			0.619941
$686$		−	17.9347i		−	0.684751i
$687$	0.127283	+	0.547355i	0.00485616	+	0.0208829i
$688$			9.14619i			0.348695i
$689$			5.80067i			0.220988i
$690$	−0.0151442	−	0.0651246i	−0.000576531	−	0.00247925i
$691$	12.7491			0.484999			0.242499	−	0.970152i	$-0.422033\pi$
$691$	12.7491			0.484999			0.242499	+	0.970152i	$0.422033\pi$
$692$		−	11.1065i		−	0.422206i
$693$	−19.4819	−	39.6237i	−0.740056	−	1.50518i
$694$	5.56480			0.211237
$695$			3.95684i			0.150092i
$696$	3.74617	+	16.1096i	0.141998	+	0.610634i
$697$		−	5.31558i		−	0.201342i
$698$	35.7961			1.35490
$699$	−24.4746	+	5.69138i	−0.925714	+	0.215268i
$700$		−	2.72263i		−	0.102906i
$701$	−12.2647			−0.463233			−0.231616	−	0.972807i	$-0.574401\pi$
$701$	−12.2647			−0.463233			−0.231616	+	0.972807i	$0.574401\pi$
$702$	−6.25398	−	7.64820i	−0.236041	−	0.288663i
$703$	12.5505			0.473350
$704$	5.40581			0.203739
$705$	1.18692	+	5.10412i	0.0447021	+	0.192232i
$706$	−2.34453			−0.0882374
$707$		−	41.6840i		−	1.56769i
$708$	3.24752	+	13.9653i	0.122049	+	0.524847i
$709$	−25.9179			−0.973366			−0.486683	−	0.873579i	$-0.661793\pi$
$709$	−25.9179			−0.973366			−0.486683	+	0.873579i	$0.661793\pi$
$710$		−	14.3117i		−	0.537110i
$711$	20.8763	+	42.4597i	0.782921	+	1.59236i
$712$			13.1250i			0.491880i
$713$	−0.0305415			−0.00114379
$714$	8.70308	−	2.02384i	0.325705	−	0.0757401i
$715$			10.2783i			0.384385i
$716$	−11.5773			−0.432664
$717$	14.9541	−	3.47745i	0.558470	−	0.129868i
$718$			19.9473i			0.744427i
$719$			7.67717i			0.286310i	0.989700	+	0.143155i	$0.0457248\pi$
$719$			7.67717i			0.286310i	−0.989700	+	0.143155i	$0.954275\pi$
$720$	2.69219	−	1.32367i	0.100332	−	0.0493305i
$721$			49.2474i			1.83407i
$722$	−10.6300			−0.395607
$723$	28.4376	−	6.61293i	1.05760	−	0.245938i
$724$	−17.7578			−0.659963
$725$		−	9.54907i		−	0.354643i
$726$	−30.7425	+	7.14892i	−1.14096	+	0.265321i
$727$			32.2446i			1.19589i	0.801538	+	0.597943i	$0.204015\pi$
$727$			32.2446i			1.19589i	−0.801538	+	0.597943i	$0.795985\pi$
$728$	5.17665			0.191859
$729$	5.36160	−	26.4623i	0.198578	−	0.980085i
$730$	11.1356			0.412147
$731$	17.3300			0.640975
$732$	5.82118	+	25.0328i	0.215157	+	0.925239i
$733$		−	1.96666i		−	0.0726402i	−0.999340	−	0.0363201i	$-0.988436\pi$
$733$		−	1.96666i		−	0.0726402i	0.999340	−	0.0363201i	$-0.0115636\pi$
$734$			32.9954i			1.21788i
$735$	0.696295	−	0.161918i	0.0256832	−	0.00597244i
$736$			0.0386030i			0.00142292i
$737$	28.3754	+	33.9524i	1.04522	+	1.25065i
$738$	7.55260	−	3.71341i	0.278015	−	0.136692i
$739$			3.70724i			0.136373i	0.997673	+	0.0681866i	$0.0217213\pi$
$739$			3.70724i			0.136373i	−0.997673	+	0.0681866i	$0.978279\pi$
$740$	−4.33807			−0.159471
$741$	2.15799	+	9.27998i	0.0792756	+	0.340908i
$742$		−	8.30631i		−	0.304934i
$743$		−	20.7107i		−	0.759801i	−0.925027	−	0.379901i	$-0.875958\pi$
$743$		−	20.7107i		−	0.759801i	0.925027	−	0.379901i	$-0.124042\pi$
$744$	−0.310382	−	1.33473i	−0.0113792	−	0.0489337i
$745$			14.1824i			0.519603i
$746$		−	10.7810i		−	0.394720i
$747$	5.79885	+	11.7941i	0.212169	+	0.431525i
$748$		−	10.2428i		−	0.374515i
$749$	−26.1242			−0.954557
$750$	−1.68704	+	0.392308i	−0.0616019	+	0.0143250i
$751$	28.9926			1.05796			0.528978	−	0.848636i	$-0.322575\pi$
$751$	28.9926			1.05796			0.528978	+	0.848636i	$0.322575\pi$
$752$		−	3.02549i		−	0.110328i
$753$	−3.62182	+	0.842225i	−0.131986	+	0.0306924i
$754$	18.1560			0.661202
$755$	22.3784			0.814435
$756$	8.95544	+	10.9519i	0.325706	+	0.398316i
$757$			22.4777i			0.816967i	0.912766	+	0.408484i	$0.133942\pi$
$757$			22.4777i			0.816967i	−0.912766	+	0.408484i	$0.866058\pi$
$758$			29.7333i			1.07996i
$759$	−0.0818668	−	0.352051i	−0.00297158	−	0.0127786i
$760$	−2.89310			−0.104944
$761$		−	40.3796i		−	1.46376i	−0.681433	−	0.731880i	$-0.738643\pi$
$761$		−	40.3796i		−	1.46376i	0.681433	−	0.731880i	$-0.261357\pi$
$762$	−20.2698	+	4.71360i	−0.734299	+	0.170756i
$763$	−53.4581			−1.93531
$764$	6.19632			0.224175
$765$	−2.50808	−	5.10111i	−0.0906797	−	0.184431i
$766$	−25.0490			−0.905056
$767$	15.7393			0.568312
$768$	−1.68704	+	0.392308i	−0.0608757	+	0.0141562i
$769$			12.9369i			0.466516i	0.972415	+	0.233258i	$0.0749387\pi$
$769$			12.9369i			0.466516i	−0.972415	+	0.233258i	$0.925061\pi$
$770$		−	14.7180i		−	0.530401i
$771$	−2.59604	−	11.1637i	−0.0934941	−	0.402052i
$772$	2.41446			0.0868982
$773$		−	27.6422i		−	0.994220i	−0.867688	−	0.497110i	$-0.834395\pi$
$773$		−	27.6422i		−	0.994220i	0.867688	−	0.497110i	$-0.165605\pi$
$774$	12.1066	+	24.6233i	0.435162	+	0.885065i
$775$			0.791170i			0.0284197i
$776$			5.86842i			0.210664i
$777$	−4.63354	−	19.9256i	−0.166227	−	0.714825i
$778$			8.57535i			0.307441i
$779$	−8.11622			−0.290794
$780$	−0.745909	−	3.20763i	−0.0267078	−	0.114851i
$781$		−	77.3665i		−	2.76839i
$782$	0.0731442			0.00261563
$783$	31.4093	+	38.4115i	1.12248	+	1.37271i
$784$	−0.412733			−0.0147405
$785$	−16.5589			−0.591014
$786$	−1.95460	−	8.40535i	−0.0697183	−	0.299809i
$787$			1.90392i			0.0678674i	0.999424	+	0.0339337i	$0.0108035\pi$
$787$			1.90392i			0.0678674i	−0.999424	+	0.0339337i	$0.989196\pi$
$788$	−0.773294			−0.0275475
$789$	1.21277	+	5.21528i	0.0431759	+	0.185669i
$790$			15.7714i			0.561122i
$791$			9.40481i			0.334396i
$792$	14.5535	−	7.15553i	0.517135	−	0.254261i
$793$	28.2126			1.00186
$794$	4.06430			0.144237
$795$	−5.14688	+	1.19687i	−0.182541	+	0.0424485i
$796$	−3.51882			−0.124721
$797$			17.5534i			0.621773i	0.950447	+	0.310886i	$0.100626\pi$
$797$			17.5534i			0.621773i	−0.950447	+	0.310886i	$0.899374\pi$
$798$	−3.09014	−	13.2885i	−0.109390	−	0.470409i
$799$	−5.73265			−0.202806
$800$	1.00000			0.0353553
$801$	17.3732	+	35.3350i	0.613852	+	1.24850i
$802$	−15.5754			−0.549987
$803$	60.1969			2.12430
$804$	−11.3193	−	8.53657i	−0.399202	−	0.301062i
$805$	0.105102			0.00370435
$806$	−1.50428			−0.0529861
$807$	−5.14690	−	22.1332i	−0.181179	−	0.779125i
$808$	15.3102			0.538610
$809$	−5.03980			−0.177190			−0.0885950	−	0.996068i	$-0.528238\pi$
$809$	−5.03980			−0.177190			−0.0885950	+	0.996068i	$0.528238\pi$
$810$	5.49577	−	7.12717i	0.193102	−	0.250423i
$811$			24.9806i			0.877186i	0.898686	+	0.438593i	$0.144523\pi$
$811$			24.9806i			0.877186i	−0.898686	+	0.438593i	$0.855477\pi$
$812$	−25.9986			−0.912372
$813$	−0.731256	−	3.14461i	−0.0256463	−	0.110286i
$814$	−23.4508			−0.821949
$815$	−15.1187			−0.529585
$816$	0.743337	+	3.19657i	0.0260220	+	0.111902i
$817$		−	26.4608i		−	0.925747i
$818$		−	14.0044i		−	0.489653i
$819$	13.9365	−	6.85220i	0.486981	−	0.239435i
$820$	2.80538			0.0979680
$821$			10.8968i			0.380302i	0.981755	+	0.190151i	$0.0608978\pi$
$821$			10.8968i			0.380302i	−0.981755	+	0.190151i	$0.939102\pi$
$822$	−27.3729	+	6.36535i	−0.954738	+	0.222017i
$823$	18.3723			0.640420			0.320210	−	0.947347i	$-0.396247\pi$
$823$	18.3723			0.640420			0.320210	+	0.947347i	$0.396247\pi$
$824$	−18.0881			−0.630130
$825$	−9.11980	+	2.12074i	−0.317511	+	0.0738347i
$826$	−22.5379			−0.784195
$827$		−	30.6359i		−	1.06532i	−0.846331	−	0.532658i	$-0.821193\pi$
$827$		−	30.6359i		−	1.06532i	0.846331	−	0.532658i	$-0.178807\pi$
$828$	0.0510978	+	0.103926i	0.00177577	+	0.00361169i
$829$	−17.8494			−0.619935			−0.309967	−	0.950747i	$-0.600318\pi$
$829$	−17.8494			−0.619935			−0.309967	+	0.950747i	$0.600318\pi$
$830$			4.38087i			0.152062i
$831$	6.44483	−	1.49870i	0.223569	−	0.0519892i
$832$			1.90134i			0.0659170i
$833$			0.782039i			0.0270960i
$834$	−1.55230	−	6.67534i	−0.0537517	−	0.231148i
$835$			5.29268i			0.183161i
$836$	−15.6395			−0.540904
$837$	−2.60236	−	3.18251i	−0.0899508	−	0.110004i
$838$			22.0846i			0.762900i
$839$		−	0.988106i		−	0.0341132i	−0.999855	−	0.0170566i	$-0.994570\pi$
$839$		−	0.988106i		−	0.0341132i	0.999855	−	0.0170566i	$-0.00542955\pi$
$840$	1.06811	+	4.59318i	0.0368533	+	0.158480i
$841$	−62.1846			−2.14430
$842$	22.3648			0.770744
$843$	2.45655	−	0.571251i	0.0846079	−	0.0196749i
$844$	−20.4823			−0.705030
$845$	9.38492			0.322851
$846$	−4.00477	−	8.14519i	−0.137687	−	0.280038i
$847$		−	49.6139i		−	1.70475i
$848$	3.05084			0.104766
$849$	19.8879	−	4.62477i	0.682550	−	0.158722i
$850$		−	1.89478i		−	0.0649905i
$851$		−	0.167462i		−	0.00574054i
$852$	5.61461	+	24.1444i	0.192353	+	0.827175i
$853$	−43.2497			−1.48084			−0.740421	−	0.672143i	$-0.765374\pi$
$853$	−43.2497			−1.48084			−0.740421	+	0.672143i	$0.765374\pi$
$854$	−40.3993			−1.38244
$855$	−7.78877	+	3.82952i	−0.266370	+	0.130967i
$856$		−	9.59519i		−	0.327957i
$857$	32.9357			1.12506			0.562530	−	0.826777i	$-0.309828\pi$
$857$	32.9357			1.12506			0.562530	+	0.826777i	$0.309828\pi$
$858$	−4.03224	−	17.3398i	−0.137658	−	0.591972i
$859$	46.0114			1.56989			0.784944	−	0.619566i	$-0.212691\pi$
$859$	46.0114			1.56989			0.784944	+	0.619566i	$0.212691\pi$
$860$			9.14619i			0.311882i
$861$	2.99645	+	12.8856i	0.102119	+	0.439140i
$862$			27.7365i			0.944708i
$863$		−	50.5151i		−	1.71955i	−0.510670	−	0.859777i	$-0.670603\pi$
$863$		−	50.5151i		−	1.71955i	0.510670	−	0.859777i	$-0.329397\pi$
$864$	−4.02254	+	3.28926i	−0.136849	+	0.111903i
$865$		−	11.1065i		−	0.377633i
$866$			6.52152i			0.221610i
$867$	−22.6228	+	5.26077i	−0.768312	+	0.178665i
$868$	2.15407			0.0731138
$869$			85.2573i			2.89216i
$870$	3.74617	+	16.1096i	0.127007	+	0.546168i
$871$	−11.9418	+	9.98022i	−0.404632	+	0.338167i
$872$		−	19.6347i		−	0.664915i
$873$	7.76788	+	15.7989i	0.262903	+	0.534712i
$874$		−	0.111682i		−	0.00377770i
$875$		−	2.72263i		−	0.0920418i
$876$	−18.7862	+	4.36858i	−0.634726	+	0.147601i
$877$	8.50909			0.287331			0.143666	−	0.989626i	$-0.454111\pi$
$877$	8.50909			0.287331			0.143666	+	0.989626i	$0.454111\pi$
$878$	1.00739			0.0339978
$879$	−5.96202	−	25.6384i	−0.201094	−	0.864763i
$880$	5.40581			0.182230
$881$		−	57.2596i		−	1.92913i	−0.263854	−	0.964563i	$-0.584994\pi$
$881$		−	57.2596i		−	1.92913i	0.263854	−	0.964563i	$-0.415006\pi$
$882$	−1.11115	+	0.546324i	−0.0374145	+	0.0183957i
$883$			14.0639i			0.473287i	0.971597	+	0.236644i	$0.0760474\pi$
$883$			14.0639i			0.473287i	−0.971597	+	0.236644i	$0.923953\pi$
$884$	3.60262			0.121169
$885$	3.24752	+	13.9653i	0.109164	+	0.469438i
$886$	9.04482			0.303867
$887$			21.9779i			0.737946i	0.929440	+	0.368973i	$0.120290\pi$
$887$			21.9779i			0.737946i	−0.929440	+	0.368973i	$0.879710\pi$
$888$	7.31849	−	1.70186i	0.245592	−	0.0571106i
$889$		−	32.7126i		−	1.09714i
$890$			13.1250i			0.439951i
$891$	29.7091	−	38.5281i	0.995291	−	1.29074i
$892$	−11.4575			−0.383627
$893$			8.75304i			0.292909i
$894$	−5.56386	−	23.9262i	−0.186083	−	0.800212i
$895$	−11.5773			−0.386986
$896$		−	2.72263i		−	0.0909568i
$897$	0.123824	−	0.0287943i	0.00413436	−	0.000961414i
$898$			3.00648i			0.100327i
$899$	7.55494			0.251971
$900$	2.69219	−	1.32367i	0.0897397	−	0.0441225i
$901$		−	5.78067i		−	0.192582i
$902$	15.1653			0.504950
$903$	−42.0101	+	9.76913i	−1.39801	+	0.325096i
$904$	−3.45430			−0.114888
$905$	−17.7578			−0.590289
$906$	−37.7533	+	8.77923i	−1.25427	+	0.291670i
$907$	−3.61662			−0.120088			−0.0600440	−	0.998196i	$-0.519124\pi$
$907$	−3.61662			−0.120088			−0.0600440	+	0.998196i	$0.519124\pi$
$908$		−	12.8804i		−	0.427451i
$909$	41.2179	−	20.2657i	1.36711	−	0.672170i
$910$	5.17665			0.171604
$911$		−	5.80383i		−	0.192289i	−0.995367	−	0.0961447i	$-0.969349\pi$
$911$		−	5.80383i		−	0.192289i	0.995367	−	0.0961447i	$-0.0306512\pi$
$912$	4.88076	−	1.13498i	0.161618	−	0.0375831i
$913$			23.6821i			0.783765i
$914$	−4.40716			−0.145776
$915$	5.82118	+	25.0328i	0.192442	+	0.827558i
$916$		−	0.324447i		−	0.0107200i
$917$	13.5650			0.447956
$918$	6.23242	+	7.62183i	0.205701	+	0.251558i
$919$		−	6.86428i		−	0.226432i	−0.993570	−	0.113216i	$-0.963885\pi$
$919$		−	6.86428i		−	0.226432i	0.993570	−	0.113216i	$-0.0361151\pi$
$920$			0.0386030i			0.00127270i
$921$	33.9446	−	7.89355i	1.11851	−	0.260101i
$922$			19.7207i			0.649467i
$923$	27.2115			0.895676
$924$	5.77399	+	24.8299i	0.189950	+	0.816843i
$925$	−4.33807			−0.142635
$926$			22.7061i			0.746167i
$927$	−48.6967	+	23.9428i	−1.59941	+	0.786385i
$928$		−	9.54907i		−	0.313463i
$929$	27.7659			0.910968			0.455484	−	0.890244i	$-0.349466\pi$
$929$	27.7659			0.910968			0.455484	+	0.890244i	$0.349466\pi$
$930$	−0.310382	−	1.33473i	−0.0101778	−	0.0437676i
$931$	1.19408			0.0391342
$932$	14.5074			0.475207
$933$	31.4324	−	7.30937i	1.02905	−	0.239298i
$934$		−	20.0471i		−	0.655960i
$935$		−	10.2428i		−	0.334976i
$936$	2.51675	+	5.11876i	0.0822626	+	0.167312i
$937$			51.0458i			1.66759i	0.552071	+	0.833797i	$0.313838\pi$
$937$			51.0458i			1.66759i	−0.552071	+	0.833797i	$0.686162\pi$
$938$	17.1001	−	14.2912i	0.558338	−	0.466625i
$939$	−5.08521	−	21.8679i	−0.165949	−	0.713631i
$940$		−	3.02549i		−	0.0986806i
$941$	−13.3559			−0.435390			−0.217695	−	0.976017i	$-0.569854\pi$
$941$	−13.3559			−0.435390			−0.217695	+	0.976017i	$0.569854\pi$
$942$	27.9355	−	6.49620i	0.910189	−	0.211657i
$943$			0.108296i			0.00352660i
$944$		−	8.27799i		−	0.269426i
$945$	8.95544	+	10.9519i	0.291320	+	0.356265i
$946$			49.4425i			1.60752i
$947$			5.66956i			0.184236i	0.995748	+	0.0921181i	$0.0293637\pi$
$947$			5.66956i			0.184236i	−0.995748	+	0.0921181i	$0.970636\pi$
$948$	−6.18725	−	26.6070i	−0.200953	−	0.864155i
$949$			21.1725i			0.687290i
$950$	−2.89310			−0.0938645
$951$	10.0033	+	43.0173i	0.324380	+	1.39493i
$952$	−5.15880			−0.167198
$953$			21.4456i			0.694692i	0.937737	+	0.347346i	$0.112917\pi$
$953$			21.4456i			0.694692i	−0.937737	+	0.347346i	$0.887083\pi$
$954$	8.21343	−	4.03832i	0.265920	−	0.130745i
$955$	6.19632			0.200508
$956$	−8.86410			−0.286685
$957$	20.2511	+	87.0855i	0.654624	+	2.81508i
$958$			30.3787i			0.981490i
$959$		−	44.1758i		−	1.42651i
$960$	−1.68704	+	0.392308i	−0.0544489	+	0.0126617i
$961$	30.3740			0.979808
$962$		−	8.24814i		−	0.265931i
$963$	−12.7009	−	25.8321i	−0.409281	−	0.832427i
$964$	−16.8565			−0.542912
$965$	2.41446			0.0777241
$966$	−0.177310	+	0.0412322i	−0.00570487	+	0.00132662i
$967$	−23.8399			−0.766639			−0.383319	−	0.923616i	$-0.625219\pi$
$967$	−23.8399			−0.766639			−0.383319	+	0.923616i	$0.625219\pi$
$968$	18.2227			0.585701
$969$	−2.15055	−	9.24798i	−0.0690855	−	0.297088i
$970$			5.86842i			0.188424i
$971$			43.2474i			1.38788i	0.720035	+	0.693938i	$0.244126\pi$
$971$			43.2474i			1.38788i	−0.720035	+	0.693938i	$0.755874\pi$
$972$	−6.47553	+	14.1798i	−0.207703	+	0.454818i
$973$	10.7730			0.345367
$974$		−	14.7820i		−	0.473646i
$975$	−0.745909	−	3.20763i	−0.0238882	−	0.102726i
$976$		−	14.8383i		−	0.474963i
$977$		−	57.1350i		−	1.82791i	−0.405815	−	0.913955i	$-0.633012\pi$
$977$		−	57.1350i		−	1.82791i	0.405815	−	0.913955i	$-0.366988\pi$
$978$	25.5058	−	5.93118i	0.815586	−	0.189658i
$979$			70.9512i			2.26761i
$980$	−0.412733			−0.0131843
$981$	−25.9900	−	52.8604i	−0.829796	−	1.68770i
$982$			28.9541i			0.923963i
$983$	−45.1003			−1.43848			−0.719238	−	0.694764i	$-0.755509\pi$
$983$	−45.1003			−1.43848			−0.719238	+	0.694764i	$0.755509\pi$
$984$	−4.73277	+	1.10057i	−0.150875	+	0.0350849i
$985$	−0.773294			−0.0246392
$986$	−18.0934			−0.576211
$987$	13.8966	−	3.23156i	0.442335	−	0.102862i
$988$		−	5.50075i		−	0.175002i
$989$	−0.353070			−0.0112270
$990$	14.5535	−	7.15553i	0.462539	−	0.227418i
$991$			20.6844i			0.657061i	0.944493	+	0.328531i	$0.106553\pi$
$991$			20.6844i			0.657061i	−0.944493	+	0.328531i	$0.893447\pi$
$992$			0.791170i			0.0251197i
$993$	−10.3596	−	44.5493i	−0.328752	−	1.41373i
$994$	−38.9656			−1.23591
$995$	−3.51882			−0.111554
$996$	−1.71865	−	7.39069i	−0.0544575	−	0.234183i
$997$	38.1235			1.20738			0.603691	−	0.797218i	$-0.293696\pi$
$997$	38.1235			1.20738			0.603691	+	0.797218i	$0.293696\pi$
$998$		−	13.4078i		−	0.424415i
$999$	17.4500	−	14.2690i	0.552095	−	0.451452i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2010.2.d.d.401.2	yes	20
3.2	odd	2		2010.2.d.c.401.20	yes	20
67.66	odd	2		2010.2.d.c.401.19	✓	20
201.200	even	2	inner	2010.2.d.d.401.1	yes	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2010.2.d.c.401.19	✓	20	67.66	odd	2
2010.2.d.c.401.20	yes	20	3.2	odd	2
2010.2.d.d.401.1	yes	20	201.200	even	2	inner
2010.2.d.d.401.2	yes	20	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 2010 = 2 \cdot 3 \cdot 5 \cdot 67 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2010.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +(-1.68704 + 0.392308i) q^{3} +1.00000 q^{4} +1.00000 q^{5} +(-1.68704 + 0.392308i) q^{6} -2.72263i q^{7} +1.00000 q^{8} +(2.69219 - 1.32367i) q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +(-1.68704 + 0.392308i) q^{3} +1.00000 q^{4} +1.00000 q^{5} +(-1.68704 + 0.392308i) q^{6} -2.72263i q^{7} +1.00000 q^{8} +(2.69219 - 1.32367i) q^{9} +1.00000 q^{10} +5.40581 q^{11} +(-1.68704 + 0.392308i) q^{12} +1.90134i q^{13} -2.72263i q^{14} +(-1.68704 + 0.392308i) q^{15} +1.00000 q^{16} -1.89478i q^{17} +(2.69219 - 1.32367i) q^{18} -2.89310 q^{19} +1.00000 q^{20} +(1.06811 + 4.59318i) q^{21} +5.40581 q^{22} +0.0386030i q^{23} +(-1.68704 + 0.392308i) q^{24} +1.00000 q^{25} +1.90134i q^{26} +(-4.02254 + 3.28926i) q^{27} -2.72263i q^{28} -9.54907i q^{29} +(-1.68704 + 0.392308i) q^{30} +0.791170i q^{31} +1.00000 q^{32} +(-9.11980 + 2.12074i) q^{33} -1.89478i q^{34} -2.72263i q^{35} +(2.69219 - 1.32367i) q^{36} -4.33807 q^{37} -2.89310 q^{38} +(-0.745909 - 3.20763i) q^{39} +1.00000 q^{40} +2.80538 q^{41} +(1.06811 + 4.59318i) q^{42} +9.14619i q^{43} +5.40581 q^{44} +(2.69219 - 1.32367i) q^{45} +0.0386030i q^{46} -3.02549i q^{47} +(-1.68704 + 0.392308i) q^{48} -0.412733 q^{49} +1.00000 q^{50} +(0.743337 + 3.19657i) q^{51} +1.90134i q^{52} +3.05084 q^{53} +(-4.02254 + 3.28926i) q^{54} +5.40581 q^{55} -2.72263i q^{56} +(4.88076 - 1.13498i) q^{57} -9.54907i q^{58} -8.27799i q^{59} +(-1.68704 + 0.392308i) q^{60} -14.8383i q^{61} +0.791170i q^{62} +(-3.60388 - 7.32985i) q^{63} +1.00000 q^{64} +1.90134i q^{65} +(-9.11980 + 2.12074i) q^{66} +(5.24905 + 6.28072i) q^{67} -1.89478i q^{68} +(-0.0151442 - 0.0651246i) q^{69} -2.72263i q^{70} -14.3117i q^{71} +(2.69219 - 1.32367i) q^{72} +11.1356 q^{73} -4.33807 q^{74} +(-1.68704 + 0.392308i) q^{75} -2.89310 q^{76} -14.7180i q^{77} +(-0.745909 - 3.20763i) q^{78} +15.7714i q^{79} +1.00000 q^{80} +(5.49577 - 7.12717i) q^{81} +2.80538 q^{82} +4.38087i q^{83} +(1.06811 + 4.59318i) q^{84} -1.89478i q^{85} +9.14619i q^{86} +(3.74617 + 16.1096i) q^{87} +5.40581 q^{88} +13.1250i q^{89} +(2.69219 - 1.32367i) q^{90} +5.17665 q^{91} +0.0386030i q^{92} +(-0.310382 - 1.33473i) q^{93} -3.02549i q^{94} -2.89310 q^{95} +(-1.68704 + 0.392308i) q^{96} +5.86842i q^{97} -0.412733 q^{98} +(14.5535 - 7.15553i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 20 q^{2} - 2 q^{3} + 20 q^{4} + 20 q^{5} - 2 q^{6} + 20 q^{8}+O(q^{10}) \) 20 * q + 20 * q^2 - 2 * q^3 + 20 * q^4 + 20 * q^5 - 2 * q^6 + 20 * q^8	\( 20 q + 20 q^{2} - 2 q^{3} + 20 q^{4} + 20 q^{5} - 2 q^{6} + 20 q^{8} + 20 q^{10} - 2 q^{12} - 2 q^{15} + 20 q^{16} + 16 q^{19} + 20 q^{20} - 2 q^{21} - 2 q^{24} + 20 q^{25} + 10 q^{27} - 2 q^{30} + 20 q^{32} + 2 q^{33} + 20 q^{37} + 16 q^{38} + 16 q^{39} + 20 q^{40} + 8 q^{41} - 2 q^{42} - 2 q^{48} - 48 q^{49} + 20 q^{50} + 32 q^{51} - 36 q^{53} + 10 q^{54} + 16 q^{57} - 2 q^{60} - 4 q^{63} + 20 q^{64} + 2 q^{66} + 16 q^{67} - 28 q^{69} - 4 q^{73} + 20 q^{74} - 2 q^{75} + 16 q^{76} + 16 q^{78} + 20 q^{80} + 12 q^{81} + 8 q^{82} - 2 q^{84} + 32 q^{87} + 12 q^{91} - 12 q^{93} + 16 q^{95} - 2 q^{96} - 48 q^{98} + 12 q^{99}+O(q^{100}) \) 20 * q + 20 * q^2 - 2 * q^3 + 20 * q^4 + 20 * q^5 - 2 * q^6 + 20 * q^8 + 20 * q^10 - 2 * q^12 - 2 * q^15 + 20 * q^16 + 16 * q^19 + 20 * q^20 - 2 * q^21 - 2 * q^24 + 20 * q^25 + 10 * q^27 - 2 * q^30 + 20 * q^32 + 2 * q^33 + 20 * q^37 + 16 * q^38 + 16 * q^39 + 20 * q^40 + 8 * q^41 - 2 * q^42 - 2 * q^48 - 48 * q^49 + 20 * q^50 + 32 * q^51 - 36 * q^53 + 10 * q^54 + 16 * q^57 - 2 * q^60 - 4 * q^63 + 20 * q^64 + 2 * q^66 + 16 * q^67 - 28 * q^69 - 4 * q^73 + 20 * q^74 - 2 * q^75 + 16 * q^76 + 16 * q^78 + 20 * q^80 + 12 * q^81 + 8 * q^82 - 2 * q^84 + 32 * q^87 + 12 * q^91 - 12 * q^93 + 16 * q^95 - 2 * q^96 - 48 * q^98 + 12 * q^99

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