LMFDB - Embedded newform 462.2.c.b.197.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [462,2,Mod(197,462)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(462, 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("462.197");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 462 = 2 \cdot 3 \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	462.c (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$3.68908857338$
Analytic rank:	$0$
Dimension:	$12$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} + 16x^{10} + 94x^{8} + 246x^{6} + 277x^{4} + 114x^{2} + 9 $ x^12 + 16x^10 + 94x^8 + 246x^6 + 277x^4 + 114*x^2 + 9
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			197.11
Root			$1.88826i$ of defining polynomial
Character	$\chi$	$=$	462.197
Dual form			462.2.c.b.197.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} +(1.72427 - 0.163987i) q^{3} +1.00000 q^{4} +1.55439i q^{5} +(1.72427 - 0.163987i) q^{6} +1.00000i q^{7} +1.00000 q^{8} +(2.94622 - 0.565516i) q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +(1.72427 - 0.163987i) q^{3} +1.00000 q^{4} +1.55439i q^{5} +(1.72427 - 0.163987i) q^{6} +1.00000i q^{7} +1.00000 q^{8} +(2.94622 - 0.565516i) q^{9} +1.55439i q^{10} +(-0.560283 - 3.26896i) q^{11} +(1.72427 - 0.163987i) q^{12} +2.32797i q^{13} +1.00000i q^{14} +(0.254900 + 2.68019i) q^{15} +1.00000 q^{16} -6.13397 q^{17} +(2.94622 - 0.565516i) q^{18} -3.69007i q^{19} +1.55439i q^{20} +(0.163987 + 1.72427i) q^{21} +(-0.560283 - 3.26896i) q^{22} +4.25160i q^{23} +(1.72427 - 0.163987i) q^{24} +2.58387 q^{25} +2.32797i q^{26} +(4.98734 - 1.45825i) q^{27} +1.00000i q^{28} +1.46795 q^{29} +(0.254900 + 2.68019i) q^{30} -1.87190 q^{31} +1.00000 q^{32} +(-1.50215 - 5.54469i) q^{33} -6.13397 q^{34} -1.55439 q^{35} +(2.94622 - 0.565516i) q^{36} -6.88530 q^{37} -3.69007i q^{38} +(0.381758 + 4.01406i) q^{39} +1.55439i q^{40} -2.23355 q^{41} +(0.163987 + 1.72427i) q^{42} -12.1218i q^{43} +(-0.560283 - 3.26896i) q^{44} +(0.879034 + 4.57957i) q^{45} +4.25160i q^{46} -5.48848i q^{47} +(1.72427 - 0.163987i) q^{48} -1.00000 q^{49} +2.58387 q^{50} +(-10.5766 + 1.00589i) q^{51} +2.32797i q^{52} -9.89243i q^{53} +(4.98734 - 1.45825i) q^{54} +(5.08124 - 0.870899i) q^{55} +1.00000i q^{56} +(-0.605125 - 6.36268i) q^{57} +1.46795 q^{58} +6.56911i q^{59} +(0.254900 + 2.68019i) q^{60} +7.35144i q^{61} -1.87190 q^{62} +(0.565516 + 2.94622i) q^{63} +1.00000 q^{64} -3.61858 q^{65} +(-1.50215 - 5.54469i) q^{66} -8.79998 q^{67} -6.13397 q^{68} +(0.697208 + 7.33091i) q^{69} -1.55439 q^{70} +2.88778i q^{71} +(2.94622 - 0.565516i) q^{72} +1.67066i q^{73} -6.88530 q^{74} +(4.45529 - 0.423721i) q^{75} -3.69007i q^{76} +(3.26896 - 0.560283i) q^{77} +(0.381758 + 4.01406i) q^{78} +12.0059i q^{79} +1.55439i q^{80} +(8.36038 - 3.33227i) q^{81} -2.23355 q^{82} +0.338041 q^{83} +(0.163987 + 1.72427i) q^{84} -9.53458i q^{85} -12.1218i q^{86} +(2.53114 - 0.240725i) q^{87} +(-0.560283 - 3.26896i) q^{88} +5.55303i q^{89} +(0.879034 + 4.57957i) q^{90} -2.32797 q^{91} +4.25160i q^{92} +(-3.22766 + 0.306967i) q^{93} -5.48848i q^{94} +5.73582 q^{95} +(1.72427 - 0.163987i) q^{96} -11.8702 q^{97} -1.00000 q^{98} +(-3.49936 - 9.31421i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 12 q^{2} + 4 q^{3} + 12 q^{4} + 4 q^{6} + 12 q^{8}+O(q^{10}) $ 12 * q + 12 * q^2 + 4 * q^3 + 12 * q^4 + 4 * q^6 + 12 * q^8	$ 12 q + 12 q^{2} + 4 q^{3} + 12 q^{4} + 4 q^{6} + 12 q^{8} + 8 q^{11} + 4 q^{12} + 4 q^{15} + 12 q^{16} + 4 q^{17} + 8 q^{22} + 4 q^{24} - 28 q^{25} - 8 q^{27} - 8 q^{29} + 4 q^{30} + 12 q^{31} + 12 q^{32} - 16 q^{33} + 4 q^{34} + 4 q^{35} + 36 q^{39} - 20 q^{41} + 8 q^{44} - 12 q^{45} + 4 q^{48} - 12 q^{49} - 28 q^{50} - 8 q^{51} - 8 q^{54} + 4 q^{55} - 28 q^{57} - 8 q^{58} + 4 q^{60} + 12 q^{62} - 4 q^{63} + 12 q^{64} - 16 q^{66} + 24 q^{67} + 4 q^{68} - 20 q^{69} + 4 q^{70} - 40 q^{75} - 4 q^{77} + 36 q^{78} + 4 q^{81} - 20 q^{82} - 44 q^{83} - 8 q^{87} + 8 q^{88} - 12 q^{90} - 24 q^{91} - 24 q^{93} + 4 q^{96} - 48 q^{97} - 12 q^{98} + 20 q^{99}+O(q^{100}) $ 12 * q + 12 * q^2 + 4 * q^3 + 12 * q^4 + 4 * q^6 + 12 * q^8 + 8 * q^11 + 4 * q^12 + 4 * q^15 + 12 * q^16 + 4 * q^17 + 8 * q^22 + 4 * q^24 - 28 * q^25 - 8 * q^27 - 8 * q^29 + 4 * q^30 + 12 * q^31 + 12 * q^32 - 16 * q^33 + 4 * q^34 + 4 * q^35 + 36 * q^39 - 20 * q^41 + 8 * q^44 - 12 * q^45 + 4 * q^48 - 12 * q^49 - 28 * q^50 - 8 * q^51 - 8 * q^54 + 4 * q^55 - 28 * q^57 - 8 * q^58 + 4 * q^60 + 12 * q^62 - 4 * q^63 + 12 * q^64 - 16 * q^66 + 24 * q^67 + 4 * q^68 - 20 * q^69 + 4 * q^70 - 40 * q^75 - 4 * q^77 + 36 * q^78 + 4 * q^81 - 20 * q^82 - 44 * q^83 - 8 * q^87 + 8 * q^88 - 12 * q^90 - 24 * q^91 - 24 * q^93 + 4 * q^96 - 48 * q^97 - 12 * q^98 + 20 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/462\mathbb{Z}\right)^\times$.

$n$	$155$	$199$	$211$
$\chi(n)$	$-1$	$1$	$-1$

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
$3$	1.72427	−	0.163987i	0.995508	−	0.0946780i
$3$	1.72427	−	0.163987i	0.995508	−	0.0946780i
$4$	1.00000			0.500000
$5$			1.55439i			0.695145i	0.937653	+	0.347572i	$0.112994\pi$
$5$			1.55439i			0.695145i	−0.937653	+	0.347572i	$0.887006\pi$
$6$	1.72427	−	0.163987i	0.703930	−	0.0669475i
$7$			1.00000i			0.377964i
$7$			1.00000i			0.377964i
$8$	1.00000			0.353553
$9$	2.94622	−	0.565516i	0.982072	−	0.188505i
$10$			1.55439i			0.491542i
$11$	−0.560283	−	3.26896i	−0.168932	−	0.985628i
$11$	−0.560283	−	3.26896i	−0.168932	−	0.985628i
$12$	1.72427	−	0.163987i	0.497754	−	0.0473390i
$13$			2.32797i			0.645664i	0.946456	+	0.322832i	$0.104635\pi$
$13$			2.32797i			0.645664i	−0.946456	+	0.322832i	$0.895365\pi$
$14$			1.00000i			0.267261i
$15$	0.254900	+	2.68019i	0.0658150	+	0.692022i
$16$	1.00000			0.250000
$17$	−6.13397			−1.48771			−0.743853	−	0.668344i	$-0.767004\pi$
$17$	−6.13397			−1.48771			−0.743853	+	0.668344i	$0.767004\pi$
$18$	2.94622	−	0.565516i	0.694430	−	0.133294i
$19$		−	3.69007i		−	0.846561i	−0.905999	−	0.423280i	$-0.860879\pi$
$19$		−	3.69007i		−	0.846561i	0.905999	−	0.423280i	$-0.139121\pi$
$20$			1.55439i			0.347572i
$21$	0.163987	+	1.72427i	0.0357849	+	0.376267i
$22$	−0.560283	−	3.26896i	−0.119453	−	0.696944i
$23$			4.25160i			0.886520i	0.896393	+	0.443260i	$0.146178\pi$
$23$			4.25160i			0.886520i	−0.896393	+	0.443260i	$0.853822\pi$
$24$	1.72427	−	0.163987i	0.351965	−	0.0334737i
$25$	2.58387			0.516773
$26$			2.32797i			0.456553i
$27$	4.98734	−	1.45825i	0.959813	−	0.280639i
$28$			1.00000i			0.188982i
$29$	1.46795			0.272591			0.136296	−	0.990668i	$-0.456480\pi$
$29$	1.46795			0.272591			0.136296	+	0.990668i	$0.456480\pi$
$30$	0.254900	+	2.68019i	0.0465382	+	0.489334i
$31$	−1.87190			−0.336203			−0.168102	−	0.985770i	$-0.553764\pi$
$31$	−1.87190			−0.336203			−0.168102	+	0.985770i	$0.553764\pi$
$32$	1.00000			0.176777
$33$	−1.50215	−	5.54469i	−0.261490	−	0.965206i
$34$	−6.13397			−1.05197
$35$	−1.55439			−0.262740
$36$	2.94622	−	0.565516i	0.491036	−	0.0942527i
$37$	−6.88530			−1.13194			−0.565968	−	0.824427i	$-0.691497\pi$
$37$	−6.88530			−1.13194			−0.565968	+	0.824427i	$0.691497\pi$
$38$		−	3.69007i		−	0.598609i
$39$	0.381758	+	4.01406i	0.0611302	+	0.642764i
$40$			1.55439i			0.245771i
$41$	−2.23355			−0.348822			−0.174411	−	0.984673i	$-0.555802\pi$
$41$	−2.23355			−0.348822			−0.174411	+	0.984673i	$0.555802\pi$
$42$	0.163987	+	1.72427i	0.0253038	+	0.266061i
$43$		−	12.1218i		−	1.84855i	−0.381722	−	0.924277i	$-0.624669\pi$
$43$		−	12.1218i		−	1.84855i	0.381722	−	0.924277i	$-0.375331\pi$
$44$	−0.560283	−	3.26896i	−0.0844659	−	0.492814i
$45$	0.879034	+	4.57957i	0.131039	+	0.682683i
$46$			4.25160i			0.626864i
$47$		−	5.48848i		−	0.800578i	−0.916389	−	0.400289i	$-0.868910\pi$
$47$		−	5.48848i		−	0.800578i	0.916389	−	0.400289i	$-0.131090\pi$
$48$	1.72427	−	0.163987i	0.248877	−	0.0236695i
$49$	−1.00000			−0.142857
$50$	2.58387			0.365414
$51$	−10.5766	+	1.00589i	−1.48102	+	0.140853i
$52$			2.32797i			0.322832i
$53$		−	9.89243i		−	1.35883i	−0.733754	−	0.679415i	$-0.762234\pi$
$53$		−	9.89243i		−	1.35883i	0.733754	−	0.679415i	$-0.237766\pi$
$54$	4.98734	−	1.45825i	0.678690	−	0.198442i
$55$	5.08124	−	0.870899i	0.685154	−	0.117432i
$56$			1.00000i			0.133631i
$57$	−0.605125	−	6.36268i	−0.0801507	−	0.842758i
$58$	1.46795			0.192751
$59$			6.56911i			0.855225i	0.903962	+	0.427612i	$0.140645\pi$
$59$			6.56911i			0.855225i	−0.903962	+	0.427612i	$0.859355\pi$
$60$	0.254900	+	2.68019i	0.0329075	+	0.346011i
$61$			7.35144i			0.941255i	0.882332	+	0.470628i	$0.155973\pi$
$61$			7.35144i			0.941255i	−0.882332	+	0.470628i	$0.844027\pi$
$62$	−1.87190			−0.237731
$63$	0.565516	+	2.94622i	0.0712484	+	0.371188i
$64$	1.00000			0.125000
$65$	−3.61858			−0.448830
$66$	−1.50215	−	5.54469i	−0.184901	−	0.682504i
$67$	−8.79998			−1.07509			−0.537544	−	0.843235i	$-0.680648\pi$
$67$	−8.79998			−1.07509			−0.537544	+	0.843235i	$0.680648\pi$
$68$	−6.13397			−0.743853
$69$	0.697208	+	7.33091i	0.0839340	+	0.882537i
$70$	−1.55439			−0.185785
$71$			2.88778i			0.342717i	0.985209	+	0.171358i	$0.0548156\pi$
$71$			2.88778i			0.342717i	−0.985209	+	0.171358i	$0.945184\pi$
$72$	2.94622	−	0.565516i	0.347215	−	0.0666468i
$73$			1.67066i			0.195536i	0.995209	+	0.0977682i	$0.0311704\pi$
$73$			1.67066i			0.195536i	−0.995209	+	0.0977682i	$0.968830\pi$
$74$	−6.88530			−0.800400
$75$	4.45529	−	0.423721i	0.514452	−	0.0489271i
$76$		−	3.69007i		−	0.423280i
$77$	3.26896	−	0.560283i	0.372532	−	0.0638502i
$78$	0.381758	+	4.01406i	0.0432256	+	0.454502i
$79$			12.0059i			1.35077i	0.737467	+	0.675383i	$0.236022\pi$
$79$			12.0059i			1.35077i	−0.737467	+	0.675383i	$0.763978\pi$
$80$			1.55439i			0.173786i
$81$	8.36038	−	3.33227i	0.928931	−	0.370252i
$82$	−2.23355			−0.246655
$83$	0.338041			0.0371049			0.0185524	−	0.999828i	$-0.494094\pi$
$83$	0.338041			0.0371049			0.0185524	+	0.999828i	$0.494094\pi$
$84$	0.163987	+	1.72427i	0.0178925	+	0.188133i
$85$		−	9.53458i		−	1.03417i
$86$		−	12.1218i		−	1.30713i
$87$	2.53114	−	0.240725i	0.271367	−	0.0258084i
$88$	−0.560283	−	3.26896i	−0.0597264	−	0.348472i
$89$			5.55303i			0.588620i	0.955710	+	0.294310i	$0.0950898\pi$
$89$			5.55303i			0.588620i	−0.955710	+	0.294310i	$0.904910\pi$
$90$	0.879034	+	4.57957i	0.0926583	+	0.482729i
$91$	−2.32797			−0.244038
$92$			4.25160i			0.443260i
$93$	−3.22766	+	0.306967i	−0.334693	+	0.0318310i
$94$		−	5.48848i		−	0.566094i
$95$	5.73582			0.588483
$96$	1.72427	−	0.163987i	0.175983	−	0.0167369i
$97$	−11.8702			−1.20523			−0.602617	−	0.798030i	$-0.705875\pi$
$97$	−11.8702			−1.20523			−0.602617	+	0.798030i	$0.705875\pi$
$98$	−1.00000			−0.101015
$99$	−3.49936	−	9.31421i	−0.351699	−	0.936113i
$100$	2.58387			0.258387
$101$	5.50749			0.548016			0.274008	−	0.961727i	$-0.411651\pi$
$101$	5.50749			0.548016			0.274008	+	0.961727i	$0.411651\pi$
$102$	−10.5766	+	1.00589i	−1.04724	+	0.0995981i
$103$	−8.96280			−0.883131			−0.441565	−	0.897229i	$-0.645577\pi$
$103$	−8.96280			−0.883131			−0.441565	+	0.897229i	$0.645577\pi$
$104$			2.32797i			0.228277i
$105$	−2.68019	+	0.254900i	−0.261560	+	0.0248757i
$106$		−	9.89243i		−	0.960838i
$107$	17.3261			1.67498			0.837489	−	0.546454i	$-0.184023\pi$
$107$	17.3261			1.67498			0.837489	+	0.546454i	$0.184023\pi$
$108$	4.98734	−	1.45825i	0.479907	−	0.140320i
$109$			1.24446i			0.119198i	0.998222	+	0.0595990i	$0.0189822\pi$
$109$			1.24446i			0.119198i	−0.998222	+	0.0595990i	$0.981018\pi$
$110$	5.08124	−	0.870899i	0.484477	−	0.0830370i
$111$	−11.8721	+	1.12910i	−1.12685	+	0.107169i
$112$			1.00000i			0.0944911i
$113$			8.92520i			0.839612i	0.907614	+	0.419806i	$0.137902\pi$
$113$			8.92520i			0.839612i	−0.907614	+	0.419806i	$0.862098\pi$
$114$	−0.605125	−	6.36268i	−0.0566751	−	0.595920i
$115$	−6.60865			−0.616260
$116$	1.46795			0.136296
$117$	1.31651	+	6.85872i	0.121711	+	0.634089i
$118$			6.56911i			0.604735i
$119$		−	6.13397i		−	0.562300i
$120$	0.254900	+	2.68019i	0.0232691	+	0.244667i
$121$	−10.3722	+	3.66308i	−0.942924	+	0.333008i
$122$			7.35144i			0.665568i
$123$	−3.85125	+	0.366274i	−0.347255	+	0.0330258i
$124$	−1.87190			−0.168102
$125$			11.7883i			1.05438i
$126$	0.565516	+	2.94622i	0.0503802	+	0.262470i
$127$		−	14.8569i		−	1.31834i	−0.751994	−	0.659170i	$-0.770908\pi$
$127$		−	14.8569i		−	1.31834i	0.751994	−	0.659170i	$-0.229092\pi$
$128$	1.00000			0.0883883
$129$	−1.98782	−	20.9012i	−0.175018	−	1.84025i
$130$	−3.61858			−0.317371
$131$	6.01359			0.525410			0.262705	−	0.964876i	$-0.415385\pi$
$131$	6.01359			0.525410			0.262705	+	0.964876i	$0.415385\pi$
$132$	−1.50215	−	5.54469i	−0.130745	−	0.482603i
$133$	3.69007			0.319970
$134$	−8.79998			−0.760203
$135$	2.26668	+	7.75227i	0.195085	+	0.667209i
$136$	−6.13397			−0.525983
$137$		−	18.0117i		−	1.53885i	−0.638740	−	0.769423i	$-0.720544\pi$
$137$		−	18.0117i		−	1.53885i	0.638740	−	0.769423i	$-0.279456\pi$
$138$	0.697208	+	7.33091i	0.0593503	+	0.624048i
$139$			21.0811i			1.78807i	0.447995	+	0.894036i	$0.352138\pi$
$139$			21.0811i			1.78807i	−0.447995	+	0.894036i	$0.647862\pi$
$140$	−1.55439			−0.131370
$141$	−0.900041	−	9.46363i	−0.0757971	−	0.796981i
$142$			2.88778i			0.242337i
$143$	7.61005	−	1.30432i	0.636384	−	0.109073i
$144$	2.94622	−	0.565516i	0.245518	−	0.0471264i
$145$			2.28177i			0.189491i
$146$			1.67066i			0.138265i
$147$	−1.72427	+	0.163987i	−0.142215	+	0.0135254i
$148$	−6.88530			−0.565968
$149$	3.94691			0.323344			0.161672	−	0.986845i	$-0.448311\pi$
$149$	3.94691			0.323344			0.161672	+	0.986845i	$0.448311\pi$
$150$	4.45529	−	0.423721i	0.363773	−	0.0345967i
$151$		−	15.5811i		−	1.26798i	−0.773343	−	0.633988i	$-0.781417\pi$
$151$		−	15.5811i		−	1.26798i	0.773343	−	0.633988i	$-0.218583\pi$
$152$		−	3.69007i		−	0.299304i
$153$	−18.0720	+	3.46886i	−1.46103	+	0.280441i
$154$	3.26896	−	0.560283i	0.263420	−	0.0451489i
$155$		−	2.90966i		−	0.233710i
$156$	0.381758	+	4.01406i	0.0305651	+	0.321382i
$157$	−5.37080			−0.428637			−0.214318	−	0.976764i	$-0.568753\pi$
$157$	−5.37080			−0.428637			−0.214318	+	0.976764i	$0.568753\pi$
$158$			12.0059i			0.955135i
$159$	−1.62223	−	17.0572i	−0.128651	−	1.35273i
$160$			1.55439i			0.122885i
$161$	−4.25160			−0.335073
$162$	8.36038	−	3.33227i	0.656854	−	0.261808i
$163$	8.20898			0.642977			0.321488	−	0.946914i	$-0.395817\pi$
$163$	8.20898			0.642977			0.321488	+	0.946914i	$0.395817\pi$
$164$	−2.23355			−0.174411
$165$	8.61861	−	2.33492i	0.670958	−	0.181774i
$166$	0.338041			0.0262371
$167$	22.9905			1.77906			0.889530	−	0.456877i	$-0.151032\pi$
$167$	22.9905			1.77906			0.889530	+	0.456877i	$0.151032\pi$
$168$	0.163987	+	1.72427i	0.0126519	+	0.133030i
$169$	7.58054			0.583118
$170$		−	9.53458i		−	0.731269i
$171$	−2.08680	−	10.8718i	−0.159581	−	0.831384i
$172$		−	12.1218i		−	0.924277i
$173$	−18.0429			−1.37178			−0.685889	−	0.727706i	$-0.740586\pi$
$173$	−18.0429			−1.37178			−0.685889	+	0.727706i	$0.740586\pi$
$174$	2.53114	−	0.240725i	0.191885	−	0.0182493i
$175$			2.58387i			0.195322i
$176$	−0.560283	−	3.26896i	−0.0422329	−	0.246407i
$177$	1.07725	+	11.3269i	0.0809710	+	0.851383i
$178$			5.55303i			0.416217i
$179$			14.2005i			1.06139i	0.847561	+	0.530697i	$0.178070\pi$
$179$			14.2005i			1.06139i	−0.847561	+	0.530697i	$0.821930\pi$
$180$	0.879034	+	4.57957i	0.0655193	+	0.341341i
$181$	4.14927			0.308413			0.154207	−	0.988039i	$-0.450718\pi$
$181$	4.14927			0.308413			0.154207	+	0.988039i	$0.450718\pi$
$182$	−2.32797			−0.172561
$183$	1.20554	+	12.6759i	0.0891162	+	0.937027i
$184$			4.25160i			0.313432i
$185$		−	10.7024i		−	0.786860i
$186$	−3.22766	+	0.306967i	−0.236664	+	0.0225079i
$187$	3.43676	+	20.0517i	0.251321	+	1.46632i
$188$		−	5.48848i		−	0.400289i
$189$	1.45825	+	4.98734i	0.106072	+	0.362775i
$190$	5.73582			0.416120
$191$			26.9029i			1.94663i	0.229476	+	0.973314i	$0.426299\pi$
$191$			26.9029i			1.94663i	−0.229476	+	0.973314i	$0.573701\pi$
$192$	1.72427	−	0.163987i	0.124438	−	0.0118348i
$193$		−	14.9456i		−	1.07581i	−0.843007	−	0.537903i	$-0.819217\pi$
$193$		−	14.9456i		−	1.07581i	0.843007	−	0.537903i	$-0.180783\pi$
$194$	−11.8702			−0.852229
$195$	−6.23942	+	0.593401i	−0.446814	+	0.0424944i
$196$	−1.00000			−0.0714286
$197$	0.540638			0.0385188			0.0192594	−	0.999815i	$-0.493869\pi$
$197$	0.540638			0.0385188			0.0192594	+	0.999815i	$0.493869\pi$
$198$	−3.49936	−	9.31421i	−0.248689	−	0.661932i
$199$	25.7890			1.82813			0.914067	−	0.405562i	$-0.132924\pi$
$199$	25.7890			1.82813			0.914067	+	0.405562i	$0.132924\pi$
$200$	2.58387			0.182707
$201$	−15.1735	+	1.44308i	−1.07026	+	0.101787i
$202$	5.50749			0.387506
$203$			1.46795i			0.103030i
$204$	−10.5766	+	1.00589i	−0.740511	+	0.0704265i
$205$		−	3.47181i		−	0.242482i
$206$	−8.96280			−0.624468
$207$	2.40435	+	12.5261i	0.167114	+	0.870626i
$208$			2.32797i			0.161416i
$209$	−12.0627	+	2.06749i	−0.834394	+	0.143011i
$210$	−2.68019	+	0.254900i	−0.184951	+	0.0175898i
$211$		−	7.67730i		−	0.528527i	−0.964451	−	0.264264i	$-0.914871\pi$
$211$		−	7.67730i		−	0.528527i	0.964451	−	0.264264i	$-0.0851289\pi$
$212$		−	9.89243i		−	0.679415i
$213$	0.473560	+	4.97932i	0.0324478	+	0.341177i
$214$	17.3261			1.18439
$215$	18.8420			1.28501
$216$	4.98734	−	1.45825i	0.339345	−	0.0992210i
$217$		−	1.87190i		−	0.127073i
$218$			1.24446i			0.0842858i
$219$	0.273968	+	2.88068i	0.0185130	+	0.194658i
$220$	5.08124	−	0.870899i	0.342577	−	0.0587160i
$221$		−	14.2797i		−	0.960557i
$222$	−11.8721	+	1.12910i	−0.796804	+	0.0757803i
$223$	1.58690			0.106267			0.0531334	−	0.998587i	$-0.483079\pi$
$223$	1.58690			0.106267			0.0531334	+	0.998587i	$0.483079\pi$
$224$			1.00000i			0.0668153i
$225$	7.61263	−	1.46122i	0.507509	−	0.0974146i
$226$			8.92520i			0.593695i
$227$	13.1848			0.875103			0.437552	−	0.899193i	$-0.355846\pi$
$227$	13.1848			0.875103			0.437552	+	0.899193i	$0.355846\pi$
$228$	−0.605125	−	6.36268i	−0.0400754	−	0.421379i
$229$	10.6466			0.703548			0.351774	−	0.936085i	$-0.385579\pi$
$229$	10.6466			0.703548			0.351774	+	0.936085i	$0.385579\pi$
$230$	−6.60865			−0.435761
$231$	5.54469	−	1.50215i	0.364814	−	0.0988340i
$232$	1.46795			0.0963756
$233$	−22.9506			−1.50354			−0.751772	−	0.659423i	$-0.770801\pi$
$233$	−22.9506			−1.50354			−0.751772	+	0.659423i	$0.770801\pi$
$234$	1.31651	+	6.85872i	0.0860628	+	0.448368i
$235$	8.53125			0.556517
$236$			6.56911i			0.427612i
$237$	1.96881	+	20.7014i	0.127888	+	1.34470i
$238$		−	6.13397i		−	0.397606i
$239$	24.5601			1.58866			0.794331	−	0.607486i	$-0.207822\pi$
$239$	24.5601			1.58866			0.794331	+	0.607486i	$0.207822\pi$
$240$	0.254900	+	2.68019i	0.0164537	+	0.173006i
$241$			2.67320i			0.172196i	0.996287	+	0.0860979i	$0.0274398\pi$
$241$			2.67320i			0.172196i	−0.996287	+	0.0860979i	$0.972560\pi$
$242$	−10.3722	+	3.66308i	−0.666748	+	0.235472i
$243$	13.8691	−	7.11673i	0.889704	−	0.456538i
$244$			7.35144i			0.470628i
$245$		−	1.55439i		−	0.0993064i
$246$	−3.85125	+	0.366274i	−0.245547	+	0.0233528i
$247$	8.59040			0.546594
$248$	−1.87190			−0.118866
$249$	0.582875	−	0.0554344i	0.0369382	−	0.00351302i
$250$			11.7883i			0.745557i
$251$		−	10.7048i		−	0.675680i	−0.941204	−	0.337840i	$-0.890304\pi$
$251$		−	10.7048i		−	0.675680i	0.941204	−	0.337840i	$-0.109696\pi$
$252$	0.565516	+	2.94622i	0.0356242	+	0.185594i
$253$	13.8983	−	2.38210i	0.873778	−	0.149761i
$254$		−	14.8569i		−	0.932208i
$255$	−1.56355	−	16.4402i	−0.0979133	−	1.02953i
$256$	1.00000			0.0625000
$257$			23.5380i			1.46826i	0.679010	+	0.734129i	$0.262409\pi$
$257$			23.5380i			1.46826i	−0.679010	+	0.734129i	$0.737591\pi$
$258$	−1.98782	−	20.9012i	−0.123756	−	1.30125i
$259$		−	6.88530i		−	0.427832i
$260$	−3.61858			−0.224415
$261$	4.32490	−	0.830150i	0.267704	−	0.0513850i
$262$	6.01359			0.371521
$263$	20.4719			1.26235			0.631174	−	0.775641i	$-0.282573\pi$
$263$	20.4719			1.26235			0.631174	+	0.775641i	$0.282573\pi$
$264$	−1.50215	−	5.54469i	−0.0924507	−	0.341252i
$265$	15.3767			0.944584
$266$	3.69007			0.226253
$267$	0.910626	+	9.57493i	0.0557294	+	0.585976i
$268$	−8.79998			−0.537544
$269$		−	22.2278i		−	1.35525i	−0.735408	−	0.677625i	$-0.763009\pi$
$269$		−	22.2278i		−	1.35525i	0.735408	−	0.677625i	$-0.236991\pi$
$270$	2.26668	+	7.75227i	0.137946	+	0.471788i
$271$			29.7292i			1.80592i	0.429727	+	0.902959i	$0.358610\pi$
$271$			29.7292i			1.80592i	−0.429727	+	0.902959i	$0.641390\pi$
$272$	−6.13397			−0.371926
$273$	−4.01406	+	0.381758i	−0.242942	+	0.0231050i
$274$		−	18.0117i		−	1.08813i
$275$	−1.44770	−	8.44655i	−0.0872994	−	0.509346i
$276$	0.697208	+	7.33091i	0.0419670	+	0.441269i
$277$		−	0.255479i		−	0.0153502i	−0.999971	−	0.00767511i	$-0.997557\pi$
$277$		−	0.255479i		−	0.0153502i	0.999971	−	0.00767511i	$-0.00244309\pi$
$278$			21.0811i			1.26436i
$279$	−5.51502	+	1.05859i	−0.330176	+	0.0633761i
$280$	−1.55439			−0.0928927
$281$	−23.7042			−1.41408			−0.707038	−	0.707175i	$-0.749969\pi$
$281$	−23.7042			−1.41408			−0.707038	+	0.707175i	$0.749969\pi$
$282$	−0.900041	−	9.46363i	−0.0535967	−	0.563551i
$283$			12.2593i			0.728738i	0.931255	+	0.364369i	$0.118715\pi$
$283$			12.2593i			0.728738i	−0.931255	+	0.364369i	$0.881285\pi$
$284$			2.88778i			0.171358i
$285$	9.89010	−	0.940601i	0.585839	−	0.0557164i
$286$	7.61005	−	1.30432i	0.449992	−	0.0771263i
$287$		−	2.23355i		−	0.131842i
$288$	2.94622	−	0.565516i	0.173607	−	0.0333234i
$289$	20.6255			1.21327
$290$			2.28177i			0.133990i
$291$	−20.4674	+	1.94656i	−1.19982	+	0.114109i
$292$			1.67066i			0.0977682i
$293$	3.94244			0.230320			0.115160	−	0.993347i	$-0.463262\pi$
$293$	3.94244			0.230320			0.115160	+	0.993347i	$0.463262\pi$
$294$	−1.72427	+	0.163987i	−0.100561	+	0.00956393i
$295$	−10.2110			−0.594505
$296$	−6.88530			−0.400200
$297$	−7.56126	−	15.4864i	−0.438749	−	0.898610i
$298$	3.94691			0.228639
$299$	−9.89761			−0.572394
$300$	4.45529	−	0.423721i	0.257226	−	0.0244635i
$301$	12.1218			0.698688
$302$		−	15.5811i		−	0.896594i
$303$	9.49641	−	0.903158i	0.545554	−	0.0518851i
$304$		−	3.69007i		−	0.211640i
$305$	−11.4270			−0.654309
$306$	−18.0720	+	3.46886i	−1.03311	+	0.198301i
$307$			0.116110i			0.00662672i	0.999995	+	0.00331336i	$0.00105468\pi$
$307$			0.116110i			0.00662672i	−0.999995	+	0.00331336i	$0.998945\pi$
$308$	3.26896	−	0.560283i	0.186266	−	0.0319251i
$309$	−15.4543	+	1.46978i	−0.879164	+	0.0836131i
$310$		−	2.90966i		−	0.165258i
$311$		−	5.96425i		−	0.338202i	−0.985599	−	0.169101i	$-0.945914\pi$
$311$		−	5.96425i		−	0.338202i	0.985599	−	0.169101i	$-0.0540863\pi$
$312$	0.381758	+	4.01406i	0.0216128	+	0.227251i
$313$	−4.37295			−0.247174			−0.123587	−	0.992334i	$-0.539440\pi$
$313$	−4.37295			−0.247174			−0.123587	+	0.992334i	$0.539440\pi$
$314$	−5.37080			−0.303092
$315$	−4.57957	+	0.879034i	−0.258030	+	0.0495280i
$316$			12.0059i			0.675383i
$317$			18.0803i			1.01549i	0.861507	+	0.507746i	$0.169521\pi$
$317$			18.0803i			1.01549i	−0.861507	+	0.507746i	$0.830479\pi$
$318$	−1.62223	−	17.0572i	−0.0909703	−	0.956522i
$319$	−0.822467	−	4.79866i	−0.0460493	−	0.268674i
$320$			1.55439i			0.0868931i
$321$	29.8749	−	2.84126i	1.66745	−	0.158584i
$322$	−4.25160			−0.236932
$323$			22.6348i			1.25943i
$324$	8.36038	−	3.33227i	0.464466	−	0.185126i
$325$			6.01518i			0.333662i
$326$	8.20898			0.454653
$327$	0.204076	+	2.14579i	0.0112854	+	0.118663i
$328$	−2.23355			−0.123327
$329$	5.48848			0.302590
$330$	8.61861	−	2.33492i	0.474439	−	0.128533i
$331$	−22.6120			−1.24287			−0.621435	−	0.783466i	$-0.713450\pi$
$331$	−22.6120			−1.24287			−0.621435	+	0.783466i	$0.713450\pi$
$332$	0.338041			0.0185524
$333$	−20.2856	+	3.89375i	−1.11164	+	0.213376i
$334$	22.9905			1.25798
$335$		−	13.6786i		−	0.747343i
$336$	0.163987	+	1.72427i	0.00894623	+	0.0940667i
$337$		−	11.7744i		−	0.641392i	−0.947182	−	0.320696i	$-0.896083\pi$
$337$		−	11.7744i		−	0.641392i	0.947182	−	0.320696i	$-0.103917\pi$
$338$	7.58054			0.412327
$339$	1.46362	+	15.3895i	0.0794928	+	0.835840i
$340$		−	9.53458i		−	0.517085i
$341$	1.04879	+	6.11916i	0.0567954	+	0.331371i
$342$	−2.08680	−	10.8718i	−0.112841	−	0.587877i
$343$		−	1.00000i		−	0.0539949i
$344$		−	12.1218i		−	0.653563i
$345$	−11.3951	+	1.08373i	−0.613491	+	0.0583463i
$346$	−18.0429			−0.969993
$347$	14.4493			0.775680			0.387840	−	0.921727i	$-0.373221\pi$
$347$	14.4493			0.775680			0.387840	+	0.921727i	$0.373221\pi$
$348$	2.53114	−	0.240725i	0.135683	−	0.0129042i
$349$		−	21.4896i		−	1.15031i	−0.818045	−	0.575155i	$-0.804942\pi$
$349$		−	21.4896i		−	1.15031i	0.818045	−	0.575155i	$-0.195058\pi$
$350$			2.58387i			0.138114i
$351$	3.39476	+	11.6104i	0.181199	+	0.619717i
$352$	−0.560283	−	3.26896i	−0.0298632	−	0.174236i
$353$		−	28.2168i		−	1.50183i	−0.660401	−	0.750913i	$-0.729614\pi$
$353$		−	28.2168i		−	1.50183i	0.660401	−	0.750913i	$-0.270386\pi$
$354$	1.07725	+	11.3269i	0.0572552	+	0.602019i
$355$	−4.48875			−0.238238
$356$			5.55303i			0.294310i
$357$	−1.00589	−	10.5766i	−0.0532374	−	0.559774i
$358$			14.2005i			0.750520i
$359$	−16.0750			−0.848408			−0.424204	−	0.905567i	$-0.639446\pi$
$359$	−16.0750			−0.848408			−0.424204	+	0.905567i	$0.639446\pi$
$360$	0.879034	+	4.57957i	0.0463292	+	0.241365i
$361$	5.38336			0.283335
$362$	4.14927			0.218081
$363$	−17.2837	+	8.01705i	−0.907160	+	0.420786i
$364$	−2.32797			−0.122019
$365$	−2.59687			−0.135926
$366$	1.20554	+	12.6759i	0.0630147	+	0.662578i
$367$	−5.46213			−0.285121			−0.142560	−	0.989786i	$-0.545534\pi$
$367$	−5.46213			−0.285121			−0.142560	+	0.989786i	$0.545534\pi$
$368$			4.25160i			0.221630i
$369$	−6.58053	+	1.26311i	−0.342569	+	0.0657549i
$370$		−	10.7024i		−	0.556394i
$371$	9.89243			0.513590
$372$	−3.22766	+	0.306967i	−0.167346	+	0.0159155i
$373$			18.5799i			0.962029i	0.876713	+	0.481015i	$0.159732\pi$
$373$			18.5799i			0.962029i	−0.876713	+	0.481015i	$0.840268\pi$
$374$	3.43676	+	20.0517i	0.177710	+	1.03685i
$375$	1.93313	+	20.3262i	0.0998264	+	1.04964i
$376$		−	5.48848i		−	0.283047i
$377$			3.41735i			0.176002i
$378$	1.45825	+	4.98734i	0.0750040	+	0.256521i
$379$	32.0056			1.64402			0.822008	−	0.569476i	$-0.192854\pi$
$379$	32.0056			1.64402			0.822008	+	0.569476i	$0.192854\pi$
$380$	5.73582			0.294241
$381$	−2.43635	−	25.6174i	−0.124818	−	1.31242i
$382$			26.9029i			1.37647i
$383$		−	23.7095i		−	1.21150i	−0.795656	−	0.605749i	$-0.792874\pi$
$383$		−	23.7095i		−	1.21150i	0.795656	−	0.605749i	$-0.207126\pi$
$384$	1.72427	−	0.163987i	0.0879913	−	0.00836844i
$385$	0.870899	+	5.08124i	0.0443851	+	0.258964i
$386$		−	14.9456i		−	0.760709i
$387$	−6.85507	−	35.7134i	−0.348463	−	1.81541i
$388$	−11.8702			−0.602617
$389$			22.6258i			1.14717i	0.819145	+	0.573586i	$0.194448\pi$
$389$			22.6258i			1.14717i	−0.819145	+	0.573586i	$0.805552\pi$
$390$	−6.23942	+	0.593401i	−0.315945	+	0.0300480i
$391$		−	26.0792i		−	1.31888i
$392$	−1.00000			−0.0505076
$393$	10.3691	−	0.986152i	0.523050	−	0.0497448i
$394$	0.540638			0.0272369
$395$	−18.6618			−0.938978
$396$	−3.49936	−	9.31421i	−0.175850	−	0.468056i
$397$	−4.50324			−0.226011			−0.113006	−	0.993594i	$-0.536048\pi$
$397$	−4.50324			−0.226011			−0.113006	+	0.993594i	$0.536048\pi$
$398$	25.7890			1.29269
$399$	6.36268	−	0.605125i	0.318533	−	0.0302941i
$400$	2.58387			0.129193
$401$			7.24497i			0.361796i	0.983502	+	0.180898i	$0.0579004\pi$
$401$			7.24497i			0.361796i	−0.983502	+	0.180898i	$0.942100\pi$
$402$	−15.1735	+	1.44308i	−0.756788	+	0.0719745i
$403$		−	4.35773i		−	0.217074i
$404$	5.50749			0.274008
$405$	5.17965	+	12.9953i	0.257379	+	0.645742i
$406$			1.46795i			0.0728531i
$407$	3.85772	+	22.5077i	0.191220	+	1.11567i
$408$	−10.5766	+	1.00589i	−0.523620	+	0.0497991i
$409$			37.6611i			1.86222i	0.364738	+	0.931110i	$0.381159\pi$
$409$			37.6611i			1.86222i	−0.364738	+	0.931110i	$0.618841\pi$
$410$		−	3.47181i		−	0.171461i
$411$	−2.95369	−	31.0571i	−0.145695	−	1.53193i
$412$	−8.96280			−0.441565
$413$	−6.56911			−0.323245
$414$	2.40435	+	12.5261i	0.118167	+	0.615626i
$415$			0.525449i			0.0257933i
$416$			2.32797i			0.114138i
$417$	3.45702	+	36.3494i	0.169291	+	1.78004i
$418$	−12.0627	+	2.06749i	−0.590006	+	0.101124i
$419$		−	12.1299i		−	0.592585i	−0.955097	−	0.296292i	$-0.904250\pi$
$419$		−	12.1299i		−	0.592585i	0.955097	−	0.296292i	$-0.0957503\pi$
$420$	−2.68019	+	0.254900i	−0.130780	+	0.0124379i
$421$	−14.3398			−0.698881			−0.349441	−	0.936958i	$-0.613628\pi$
$421$	−14.3398			−0.698881			−0.349441	+	0.936958i	$0.613628\pi$
$422$		−	7.67730i		−	0.373725i
$423$	−3.10383	−	16.1703i	−0.150913	−	0.786225i
$424$		−	9.89243i		−	0.480419i
$425$	−15.8494			−0.768806
$426$	0.473560	+	4.97932i	0.0229440	+	0.241249i
$427$	−7.35144			−0.355761
$428$	17.3261			0.837489
$429$	12.9079	−	3.49696i	0.623199	−	0.168835i
$430$	18.8420			0.908642
$431$	−22.2340			−1.07098			−0.535488	−	0.844543i	$-0.679872\pi$
$431$	−22.2340			−1.07098			−0.535488	+	0.844543i	$0.679872\pi$
$432$	4.98734	−	1.45825i	0.239953	−	0.0701598i
$433$	−22.6153			−1.08682			−0.543411	−	0.839467i	$-0.682868\pi$
$433$	−22.6153			−1.08682			−0.543411	+	0.839467i	$0.682868\pi$
$434$		−	1.87190i		−	0.0898540i
$435$	0.374181	+	3.93438i	0.0179406	+	0.188639i
$436$			1.24446i			0.0595990i
$437$	15.6887			0.750493
$438$	0.273968	+	2.88068i	0.0130907	+	0.137644i
$439$		−	20.3893i		−	0.973127i	−0.873645	−	0.486563i	$-0.838250\pi$
$439$		−	20.3893i		−	0.973127i	0.873645	−	0.486563i	$-0.161750\pi$
$440$	5.08124	−	0.870899i	0.242239	−	0.0415185i
$441$	−2.94622	+	0.565516i	−0.140296	+	0.0269294i
$442$		−	14.2797i		−	0.679217i
$443$			15.4112i			0.732208i	0.930574	+	0.366104i	$0.119309\pi$
$443$			15.4112i			0.732208i	−0.930574	+	0.366104i	$0.880691\pi$
$444$	−11.8721	+	1.12910i	−0.563426	+	0.0535847i
$445$	−8.63158			−0.409176
$446$	1.58690			0.0751419
$447$	6.80554	−	0.647243i	0.321891	−	0.0306136i
$448$			1.00000i			0.0472456i
$449$		−	4.70904i		−	0.222233i	−0.993807	−	0.111117i	$-0.964557\pi$
$449$		−	4.70904i		−	0.222233i	0.993807	−	0.111117i	$-0.0354427\pi$
$450$	7.61263	−	1.46122i	0.358863	−	0.0688825i
$451$	1.25142	+	7.30139i	0.0589271	+	0.343809i
$452$			8.92520i			0.419806i
$453$	−2.55511	−	26.8661i	−0.120049	−	1.26228i
$454$	13.1848			0.618791
$455$		−	3.61858i		−	0.169642i
$456$	−0.605125	−	6.36268i	−0.0283376	−	0.297960i
$457$		−	6.37293i		−	0.298113i	−0.988829	−	0.149057i	$-0.952376\pi$
$457$		−	6.37293i		−	0.298113i	0.988829	−	0.149057i	$-0.0476237\pi$
$458$	10.6466			0.497483
$459$	−30.5921	+	8.94482i	−1.42792	+	0.417509i
$460$	−6.60865			−0.308130
$461$	−31.1985			−1.45306			−0.726530	−	0.687135i	$-0.758868\pi$
$461$	−31.1985			−1.45306			−0.726530	+	0.687135i	$0.758868\pi$
$462$	5.54469	−	1.50215i	0.257962	−	0.0698862i
$463$	−34.7836			−1.61653			−0.808265	−	0.588818i	$-0.799593\pi$
$463$	−34.7836			−1.61653			−0.808265	+	0.588818i	$0.799593\pi$
$464$	1.46795			0.0681478
$465$	−0.477148	−	5.01705i	−0.0221272	−	0.232660i
$466$	−22.9506			−1.06317
$467$		−	16.2040i		−	0.749833i	−0.927059	−	0.374916i	$-0.877671\pi$
$467$		−	16.2040i		−	0.749833i	0.927059	−	0.374916i	$-0.122329\pi$
$468$	1.31651	+	6.85872i	0.0608556	+	0.317044i
$469$		−	8.79998i		−	0.406345i
$470$	8.53125			0.393517
$471$	−9.26072	+	0.880743i	−0.426711	+	0.0405825i
$472$			6.56911i			0.302368i
$473$	−39.6256	+	6.79163i	−1.82199	+	0.312279i
$474$	1.96881	+	20.7014i	0.0904303	+	0.950845i
$475$		−	9.53466i		−	0.437480i
$476$		−	6.13397i		−	0.281150i
$477$	−5.59433	−	29.1452i	−0.256147	−	1.33447i
$478$	24.5601			1.12335
$479$	−29.3852			−1.34264			−0.671322	−	0.741166i	$-0.734273\pi$
$479$	−29.3852			−1.34264			−0.671322	+	0.741166i	$0.734273\pi$
$480$	0.254900	+	2.68019i	0.0116346	+	0.122333i
$481$		−	16.0288i		−	0.730850i
$482$			2.67320i			0.121761i
$483$	−7.33091	+	0.697208i	−0.333568	+	0.0317241i
$484$	−10.3722	+	3.66308i	−0.471462	+	0.166504i
$485$		−	18.4509i		−	0.837813i
$486$	13.8691	−	7.11673i	0.629116	−	0.322821i
$487$	8.31243			0.376672			0.188336	−	0.982105i	$-0.439691\pi$
$487$	8.31243			0.376672			0.188336	+	0.982105i	$0.439691\pi$
$488$			7.35144i			0.332784i
$489$	14.1545	−	1.34617i	0.640089	−	0.0608758i
$490$		−	1.55439i		−	0.0702202i
$491$	−20.2083			−0.911986			−0.455993	−	0.889983i	$-0.650716\pi$
$491$	−20.2083			−0.911986			−0.455993	+	0.889983i	$0.650716\pi$
$492$	−3.85125	+	0.366274i	−0.173628	+	0.0165129i
$493$	−9.00435			−0.405536
$494$	8.59040			0.386500
$495$	14.4779	−	5.43938i	0.650734	−	0.244482i
$496$	−1.87190			−0.0840508
$497$	−2.88778			−0.129535
$498$	0.582875	−	0.0554344i	0.0261192	−	0.00248408i
$499$	15.4409			0.691232			0.345616	−	0.938376i	$-0.387670\pi$
$499$	15.4409			0.691232			0.345616	+	0.938376i	$0.387670\pi$
$500$			11.7883i			0.527189i
$501$	39.6419	−	3.77015i	1.77107	−	0.168438i
$502$		−	10.7048i		−	0.477778i
$503$	−42.6200			−1.90033			−0.950166	−	0.311745i	$-0.899087\pi$
$503$	−42.6200			−1.90033			−0.950166	+	0.311745i	$0.899087\pi$
$504$	0.565516	+	2.94622i	0.0251901	+	0.131235i
$505$			8.56080i			0.380951i
$506$	13.8983	−	2.38210i	0.617855	−	0.105897i
$507$	13.0709	−	1.24311i	0.580499	−	0.0552085i
$508$		−	14.8569i		−	0.659170i
$509$			20.6388i			0.914799i	0.889261	+	0.457400i	$0.151219\pi$
$509$			20.6388i			0.914799i	−0.889261	+	0.457400i	$0.848781\pi$
$510$	−1.56355	−	16.4402i	−0.0692351	−	0.727984i
$511$	−1.67066			−0.0739058
$512$	1.00000			0.0441942
$513$	−5.38103	−	18.4036i	−0.237578	−	0.812540i
$514$			23.5380i			1.03821i
$515$		−	13.9317i		−	0.613904i
$516$	−1.98782	−	20.9012i	−0.0875088	−	0.920125i
$517$	−17.9416	+	3.07510i	−0.789071	+	0.135243i
$518$		−	6.88530i		−	0.302523i
$519$	−31.1109	+	2.95881i	−1.36562	+	0.129877i
$520$	−3.61858			−0.158685
$521$		−	9.41655i		−	0.412547i	−0.978494	−	0.206273i	$-0.933866\pi$
$521$		−	9.41655i		−	0.412547i	0.978494	−	0.206273i	$-0.0661336\pi$
$522$	4.32490	−	0.830150i	0.189296	−	0.0363347i
$523$		−	24.2161i		−	1.05890i	−0.848342	−	0.529449i	$-0.822399\pi$
$523$		−	24.2161i		−	1.05890i	0.848342	−	0.529449i	$-0.177601\pi$
$524$	6.01359			0.262705
$525$	0.423721	+	4.45529i	0.0184927	+	0.194445i
$526$	20.4719			0.892616
$527$	11.4822			0.500171
$528$	−1.50215	−	5.54469i	−0.0653725	−	0.241302i
$529$	4.92390			0.214083
$530$	15.3767			0.667922
$531$	3.71494	+	19.3540i	0.161215	+	0.839893i
$532$	3.69007			0.159985
$533$		−	5.19965i		−	0.225222i
$534$	0.910626	+	9.57493i	0.0394066	+	0.414348i
$535$			26.9316i			1.16435i
$536$	−8.79998			−0.380101
$537$	2.32870	+	24.4855i	0.100491	+	1.05663i
$538$		−	22.2278i		−	0.958306i
$539$	0.560283	+	3.26896i	0.0241331	+	0.140804i
$540$	2.26668	+	7.75227i	0.0975425	+	0.333605i
$541$			18.9497i			0.814710i	0.913270	+	0.407355i	$0.133549\pi$
$541$			18.9497i			0.814710i	−0.913270	+	0.407355i	$0.866451\pi$
$542$			29.7292i			1.27698i
$543$	7.15447	−	0.680428i	0.307028	−	0.0291999i
$544$	−6.13397			−0.262992
$545$	−1.93438			−0.0828599
$546$	−4.01406	+	0.381758i	−0.171786	+	0.0163377i
$547$			14.2802i			0.610579i	0.952260	+	0.305290i	$0.0987533\pi$
$547$			14.2802i			0.610579i	−0.952260	+	0.305290i	$0.901247\pi$
$548$		−	18.0117i		−	0.769423i
$549$	4.15736	+	21.6589i	0.177432	+	0.924381i
$550$	−1.44770	−	8.44655i	−0.0617300	−	0.360162i
$551$		−	5.41684i		−	0.230765i
$552$	0.697208	+	7.33091i	0.0296751	+	0.312024i
$553$	−12.0059			−0.510541
$554$		−	0.255479i		−	0.0108542i
$555$	−1.75506	−	18.4539i	−0.0744983	−	0.783325i
$556$			21.0811i			0.894036i
$557$	29.4827			1.24922			0.624612	−	0.780936i	$-0.285257\pi$
$557$	29.4827			1.24922			0.624612	+	0.780936i	$0.285257\pi$
$558$	−5.51502	+	1.05859i	−0.233469	+	0.0448137i
$559$	28.2192			1.19354
$560$	−1.55439			−0.0656850
$561$	9.21412	+	34.0109i	0.389020	+	1.43594i
$562$	−23.7042			−0.999903
$563$	24.1361			1.01722			0.508609	−	0.860998i	$-0.330160\pi$
$563$	24.1361			1.01722			0.508609	+	0.860998i	$0.330160\pi$
$564$	−0.900041	−	9.46363i	−0.0378986	−	0.398491i
$565$	−13.8732			−0.583652
$566$			12.2593i			0.515296i
$567$	3.33227	+	8.36038i	0.139942	+	0.351103i
$568$			2.88778i			0.121169i
$569$	−17.5648			−0.736353			−0.368176	−	0.929756i	$-0.620018\pi$
$569$	−17.5648			−0.736353			−0.368176	+	0.929756i	$0.620018\pi$
$570$	9.89010	−	0.940601i	0.414251	−	0.0393974i
$571$			7.63928i			0.319694i	0.987142	+	0.159847i	$0.0511001\pi$
$571$			7.63928i			0.319694i	−0.987142	+	0.159847i	$0.948900\pi$
$572$	7.61005	−	1.30432i	0.318192	−	0.0545366i
$573$	4.41174	+	46.3880i	0.184303	+	1.93788i
$574$		−	2.23355i		−	0.0932267i
$575$			10.9856i			0.458130i
$576$	2.94622	−	0.565516i	0.122759	−	0.0235632i
$577$	1.37944			0.0574267			0.0287133	−	0.999588i	$-0.490859\pi$
$577$	1.37944			0.0574267			0.0287133	+	0.999588i	$0.490859\pi$
$578$	20.6255			0.857909
$579$	−2.45088	−	25.7702i	−0.101855	−	1.07097i
$580$			2.28177i			0.0947453i
$581$			0.338041i			0.0140243i
$582$	−20.4674	+	1.94656i	−0.848401	+	0.0806874i
$583$	−32.3379	+	5.54256i	−1.33930	+	0.229550i
$584$			1.67066i			0.0691326i
$585$	−10.6611	+	2.04637i	−0.440783	+	0.0846069i
$586$	3.94244			0.162861
$587$		−	6.71570i		−	0.277187i	−0.990349	−	0.138593i	$-0.955742\pi$
$587$		−	6.71570i		−	0.277187i	0.990349	−	0.138593i	$-0.0442581\pi$
$588$	−1.72427	+	0.163987i	−0.0711077	+	0.00676272i
$589$			6.90744i			0.284616i
$590$	−10.2110			−0.420379
$591$	0.932205	−	0.0886576i	0.0383458	−	0.00364689i
$592$	−6.88530			−0.282984
$593$	10.8458			0.445384			0.222692	−	0.974889i	$-0.428516\pi$
$593$	10.8458			0.445384			0.222692	+	0.974889i	$0.428516\pi$
$594$	−7.56126	−	15.4864i	−0.310242	−	0.635413i
$595$	9.53458			0.390880
$596$	3.94691			0.161672
$597$	44.4672	−	4.22907i	1.81992	−	0.173084i
$598$	−9.89761			−0.404744
$599$			5.77009i			0.235759i	0.993028	+	0.117880i	$0.0376097\pi$
$599$			5.77009i			0.235759i	−0.993028	+	0.117880i	$0.962390\pi$
$600$	4.45529	−	0.423721i	0.181886	−	0.0172983i
$601$		−	36.5608i		−	1.49135i	−0.666312	−	0.745673i	$-0.732128\pi$
$601$		−	36.5608i		−	1.49135i	0.666312	−	0.745673i	$-0.267872\pi$
$602$	12.1218			0.494047
$603$	−25.9266	+	4.97653i	−1.05581	+	0.202660i
$604$		−	15.5811i		−	0.633988i
$605$	−5.69387	−	16.1224i	−0.231489	−	0.655469i
$606$	9.49641	−	0.903158i	0.385765	−	0.0366883i
$607$		−	19.3531i		−	0.785516i	−0.919642	−	0.392758i	$-0.871521\pi$
$607$		−	19.3531i		−	0.785516i	0.919642	−	0.392758i	$-0.128479\pi$
$608$		−	3.69007i		−	0.149652i
$609$	0.240725	+	2.53114i	0.00975466	+	0.102567i
$610$	−11.4270			−0.462666
$611$	12.7770			0.516904
$612$	−18.0720	+	3.46886i	−0.730517	+	0.140220i
$613$			2.22430i			0.0898386i	0.998991	+	0.0449193i	$0.0143031\pi$
$613$			2.22430i			0.0898386i	−0.998991	+	0.0449193i	$0.985697\pi$
$614$			0.116110i			0.00468580i
$615$	−0.569333	−	5.98635i	−0.0229577	−	0.241393i
$616$	3.26896	−	0.560283i	0.131710	−	0.0225745i
$617$		−	6.17157i		−	0.248458i	−0.992254	−	0.124229i	$-0.960354\pi$
$617$		−	6.17157i		−	0.248458i	0.992254	−	0.124229i	$-0.0396457\pi$
$618$	−15.4543	+	1.46978i	−0.621663	+	0.0591234i
$619$	−24.7973			−0.996690			−0.498345	−	0.866979i	$-0.666059\pi$
$619$	−24.7973			−0.996690			−0.498345	+	0.866979i	$0.666059\pi$
$620$		−	2.90966i		−	0.116855i
$621$	6.19987	+	21.2042i	0.248792	+	0.850893i
$622$		−	5.96425i		−	0.239145i
$623$	−5.55303			−0.222477
$624$	0.381758	+	4.01406i	0.0152825	+	0.160691i
$625$	−5.40429			−0.216172
$626$	−4.37295			−0.174778
$627$	−20.4603	+	5.54303i	−0.817106	+	0.221367i
$628$	−5.37080			−0.214318
$629$	42.2342			1.68399
$630$	−4.57957	+	0.879034i	−0.182455	+	0.0350216i
$631$	5.88136			0.234133			0.117067	−	0.993124i	$-0.462651\pi$
$631$	5.88136			0.234133			0.117067	+	0.993124i	$0.462651\pi$
$632$			12.0059i			0.477568i
$633$	−1.25898	−	13.2377i	−0.0500399	−	0.526153i
$634$			18.0803i			0.718062i
$635$	23.0935			0.916438
$636$	−1.62223	−	17.0572i	−0.0643257	−	0.676363i
$637$		−	2.32797i		−	0.0922377i
$638$	−0.822467	−	4.79866i	−0.0325618	−	0.189981i
$639$	1.63309	+	8.50804i	0.0646040	+	0.336573i
$640$			1.55439i			0.0614427i
$641$		−	24.4480i		−	0.965638i	−0.875720	−	0.482819i	$-0.839613\pi$
$641$		−	24.4480i		−	0.965638i	0.875720	−	0.482819i	$-0.160387\pi$
$642$	29.8749	−	2.84126i	1.17907	−	0.112136i
$643$	−0.679843			−0.0268104			−0.0134052	−	0.999910i	$-0.504267\pi$
$643$	−0.679843			−0.0268104			−0.0134052	+	0.999910i	$0.504267\pi$
$644$	−4.25160			−0.167536
$645$	32.4887	−	3.08985i	1.27924	−	0.121663i
$646$			22.6348i			0.890553i
$647$		−	2.53245i		−	0.0995609i	−0.998760	−	0.0497804i	$-0.984148\pi$
$647$		−	2.53245i		−	0.0995609i	0.998760	−	0.0497804i	$-0.0158522\pi$
$648$	8.36038	−	3.33227i	0.328427	−	0.130904i
$649$	21.4741	−	3.68056i	0.842933	−	0.144475i
$650$			6.01518i			0.235935i
$651$	−0.306967	−	3.22766i	−0.0120310	−	0.126502i
$652$	8.20898			0.321488
$653$			1.85882i			0.0727414i	0.999338	+	0.0363707i	$0.0115797\pi$
$653$			1.85882i			0.0727414i	−0.999338	+	0.0363707i	$0.988420\pi$
$654$	0.204076	+	2.14579i	0.00798001	+	0.0839072i
$655$			9.34747i			0.365236i
$656$	−2.23355			−0.0872056
$657$	0.944788	+	4.92214i	0.0368597	+	0.192031i
$658$	5.48848			0.213963
$659$	−21.7156			−0.845920			−0.422960	−	0.906148i	$-0.639009\pi$
$659$	−21.7156			−0.845920			−0.422960	+	0.906148i	$0.639009\pi$
$660$	8.61861	−	2.33492i	0.335479	−	0.0908868i
$661$	−8.05547			−0.313322			−0.156661	−	0.987652i	$-0.550073\pi$
$661$	−8.05547			−0.313322			−0.156661	+	0.987652i	$0.550073\pi$
$662$	−22.6120			−0.878841
$663$	−2.34169	−	24.6221i	−0.0909437	−	0.956243i
$664$	0.338041			0.0131185
$665$			5.73582i			0.222425i
$666$	−20.2856	+	3.89375i	−0.786050	+	0.150880i
$667$			6.24113i			0.241658i
$668$	22.9905			0.889530
$669$	2.73625	−	0.260231i	0.105789	−	0.0100611i
$670$		−	13.6786i		−	0.528451i
$671$	24.0315	−	4.11889i	0.927728	−	0.159008i
$672$	0.163987	+	1.72427i	0.00632594	+	0.0665152i
$673$			16.3214i			0.629144i	0.949234	+	0.314572i	$0.101861\pi$
$673$			16.3214i			0.629144i	−0.949234	+	0.314572i	$0.898139\pi$
$674$		−	11.7744i		−	0.453533i
$675$	12.8866	−	3.76791i	0.496006	−	0.145027i
$676$	7.58054			0.291559
$677$	37.7867			1.45226			0.726131	−	0.687557i	$-0.241317\pi$
$677$	37.7867			1.45226			0.726131	+	0.687557i	$0.241317\pi$
$678$	1.46362	+	15.3895i	0.0562099	+	0.591028i
$679$		−	11.8702i		−	0.455536i
$680$		−	9.53458i		−	0.365635i
$681$	22.7341	−	2.16213i	0.871172	−	0.0828531i
$682$	1.04879	+	6.11916i	0.0401604	+	0.234315i
$683$		−	12.9463i		−	0.495377i	−0.968840	−	0.247688i	$-0.920329\pi$
$683$		−	12.9463i		−	0.495377i	0.968840	−	0.247688i	$-0.0796709\pi$
$684$	−2.08680	−	10.8718i	−0.0797907	−	0.415692i
$685$	27.9973			1.06972
$686$		−	1.00000i		−	0.0381802i
$687$	18.3576	−	1.74591i	0.700387	−	0.0666105i
$688$		−	12.1218i		−	0.462139i
$689$	23.0293			0.877348
$690$	−11.3951	+	1.08373i	−0.433804	+	0.0412570i
$691$	20.5496			0.781745			0.390873	−	0.920445i	$-0.372173\pi$
$691$	20.5496			0.781745			0.390873	+	0.920445i	$0.372173\pi$
$692$	−18.0429			−0.685889
$693$	9.31421	−	3.49936i	0.353817	−	0.132930i
$694$	14.4493			0.548488
$695$	−32.7682			−1.24297
$696$	2.53114	−	0.240725i	0.0959427	−	0.00912465i
$697$	13.7005			0.518945
$698$		−	21.4896i		−	0.813392i
$699$	−39.5731	+	3.76361i	−1.49679	+	0.142353i
$700$			2.58387i			0.0976610i
$701$	13.1555			0.496878			0.248439	−	0.968648i	$-0.420083\pi$
$701$	13.1555			0.496878			0.248439	+	0.968648i	$0.420083\pi$
$702$	3.39476	+	11.6104i	0.128127	+	0.438206i
$703$			25.4073i			0.958253i
$704$	−0.560283	−	3.26896i	−0.0211165	−	0.123203i
$705$	14.7102	−	1.39902i	0.554018	−	0.0526900i
$706$		−	28.2168i		−	1.06195i
$707$			5.50749i			0.207131i
$708$	1.07725	+	11.3269i	0.0404855	+	0.425692i
$709$	−3.20021			−0.120187			−0.0600933	−	0.998193i	$-0.519140\pi$
$709$	−3.20021			−0.120187			−0.0600933	+	0.998193i	$0.519140\pi$
$710$	−4.48875			−0.168460
$711$	6.78951	+	35.3719i	0.254627	+	1.32655i
$712$			5.55303i			0.208109i
$713$		−	7.95857i		−	0.298051i
$714$	−1.00589	−	10.5766i	−0.0376446	−	0.395820i
$715$	2.02743	+	11.8290i	0.0758216	+	0.442379i
$716$			14.2005i			0.530697i
$717$	42.3483	−	4.02754i	1.58153	−	0.150411i
$718$	−16.0750			−0.599915
$719$		−	5.79776i		−	0.216220i	−0.994139	−	0.108110i	$-0.965520\pi$
$719$		−	5.79776i		−	0.216220i	0.994139	−	0.108110i	$-0.0344799\pi$
$720$	0.879034	+	4.57957i	0.0327597	+	0.170671i
$721$		−	8.96280i		−	0.333792i
$722$	5.38336			0.200348
$723$	0.438370	+	4.60931i	0.0163032	+	0.171422i
$724$	4.14927			0.154207
$725$	3.79299			0.140868
$726$	−17.2837	+	8.01705i	−0.641459	+	0.297541i
$727$	−8.38015			−0.310802			−0.155401	−	0.987851i	$-0.549667\pi$
$727$	−8.38015			−0.310802			−0.155401	+	0.987851i	$0.549667\pi$
$728$	−2.32797			−0.0862805
$729$	22.7470	−	14.5455i	0.842483	−	0.538723i
$730$	−2.59687			−0.0961143
$731$			74.3546i			2.75010i
$732$	1.20554	+	12.6759i	0.0445581	+	0.468514i
$733$		−	32.5831i		−	1.20348i	−0.798691	−	0.601742i	$-0.794474\pi$
$733$		−	32.5831i		−	1.20348i	0.798691	−	0.601742i	$-0.205526\pi$
$734$	−5.46213			−0.201611
$735$	−0.254900	−	2.68019i	−0.00940214	−	0.0988603i
$736$			4.25160i			0.156716i
$737$	4.93048	+	28.7668i	0.181617	+	1.05964i
$738$	−6.58053	+	1.26311i	−0.242233	+	0.0464957i
$739$			3.55699i			0.130846i	0.997858	+	0.0654231i	$0.0208397\pi$
$739$			3.55699i			0.130846i	−0.997858	+	0.0654231i	$0.979160\pi$
$740$		−	10.7024i		−	0.393430i
$741$	14.8122	−	1.40871i	0.544138	−	0.0517504i
$742$	9.89243			0.363163
$743$	−39.7069			−1.45671			−0.728353	−	0.685202i	$-0.759714\pi$
$743$	−39.7069			−1.45671			−0.728353	+	0.685202i	$0.759714\pi$
$744$	−3.22766	+	0.306967i	−0.118332	+	0.0112540i
$745$			6.13505i			0.224771i
$746$			18.5799i			0.680258i
$747$	0.995943	−	0.191168i	0.0364396	−	0.00699447i
$748$	3.43676	+	20.0517i	0.125660	+	0.733162i
$749$			17.3261i			0.633082i
$750$	1.93313	+	20.3262i	0.0705879	+	0.742208i
$751$	22.7804			0.831270			0.415635	−	0.909532i	$-0.363559\pi$
$751$	22.7804			0.831270			0.415635	+	0.909532i	$0.363559\pi$
$752$		−	5.48848i		−	0.200144i
$753$	−1.75545	−	18.4579i	−0.0639721	−	0.672645i
$754$			3.41735i			0.124452i
$755$	24.2192			0.881427
$756$	1.45825	+	4.98734i	0.0530359	+	0.181388i
$757$	8.72349			0.317061			0.158530	−	0.987354i	$-0.449324\pi$
$757$	8.72349			0.317061			0.158530	+	0.987354i	$0.449324\pi$
$758$	32.0056			1.16249
$759$	23.5738	−	6.38653i	0.855674	−	0.231816i
$760$	5.73582			0.208060
$761$	−39.4693			−1.43076			−0.715381	−	0.698735i	$-0.753747\pi$
$761$	−39.4693			−1.43076			−0.715381	+	0.698735i	$0.753747\pi$
$762$	−2.43635	−	25.6174i	−0.0882596	−	0.928020i
$763$	−1.24446			−0.0450526
$764$			26.9029i			0.973314i
$765$	−5.39196	−	28.0909i	−0.194947	−	1.01563i
$766$		−	23.7095i		−	0.856658i
$767$	−15.2927			−0.552188
$768$	1.72427	−	0.163987i	0.0622192	−	0.00591738i
$769$			9.19708i			0.331655i	0.986155	+	0.165828i	$0.0530295\pi$
$769$			9.19708i			0.331655i	−0.986155	+	0.165828i	$0.946970\pi$
$770$	0.870899	+	5.08124i	0.0313850	+	0.183115i
$771$	3.85992	+	40.5858i	0.139012	+	1.46166i
$772$		−	14.9456i		−	0.537903i
$773$		−	30.0187i		−	1.07970i	−0.841762	−	0.539848i	$-0.818482\pi$
$773$		−	30.0187i		−	1.07970i	0.841762	−	0.539848i	$-0.181518\pi$
$774$	−6.85507	−	35.7134i	−0.246400	−	1.28369i
$775$	−4.83674			−0.173741
$776$	−11.8702			−0.426115
$777$	−1.12910	−	11.8721i	−0.0405063	−	0.425910i
$778$			22.6258i			0.811174i
$779$			8.24197i			0.295299i
$780$	−6.23942	+	0.593401i	−0.223407	+	0.0212472i
$781$	9.44004	−	1.61798i	0.337791	−	0.0578958i
$782$		−	26.0792i		−	0.932589i
$783$	7.32116	−	2.14063i	0.261637	−	0.0764999i
$784$	−1.00000			−0.0357143
$785$		−	8.34833i		−	0.297965i
$786$	10.3691	−	0.986152i	0.369852	−	0.0351749i
$787$			7.85991i			0.280175i	0.990139	+	0.140088i	$0.0447385\pi$
$787$			7.85991i			0.280175i	−0.990139	+	0.140088i	$0.955262\pi$
$788$	0.540638			0.0192594
$789$	35.2990	−	3.35712i	1.25668	−	0.119517i
$790$	−18.6618			−0.663958
$791$	−8.92520			−0.317343
$792$	−3.49936	−	9.31421i	−0.124345	−	0.330966i
$793$	−17.1140			−0.607735
$794$	−4.50324			−0.159814
$795$	26.5136	−	2.52158i	0.940341	−	0.0894314i
$796$	25.7890			0.914067
$797$			49.3226i			1.74710i	0.486737	+	0.873548i	$0.338187\pi$
$797$			49.3226i			1.74710i	−0.486737	+	0.873548i	$0.661813\pi$
$798$	6.36268	−	0.605125i	0.225237	−	0.0214212i
$799$			33.6662i			1.19102i
$800$	2.58387			0.0913535
$801$	3.14033	+	16.3604i	0.110958	+	0.578067i
$802$			7.24497i			0.255829i
$803$	5.46133	−	0.936045i	0.192726	−	0.0330323i
$804$	−15.1735	+	1.44308i	−0.535130	+	0.0508937i
$805$		−	6.60865i		−	0.232924i
$806$		−	4.35773i		−	0.153495i
$807$	−3.64507	−	38.3267i	−0.128312	−	1.34916i
$808$	5.50749			0.193753
$809$	52.0121			1.82865			0.914325	−	0.404982i	$-0.132722\pi$
$809$	52.0121			1.82865			0.914325	+	0.404982i	$0.132722\pi$
$810$	5.17965	+	12.9953i	0.181994	+	0.456609i
$811$		−	43.8642i		−	1.54028i	−0.637875	−	0.770140i	$-0.720186\pi$
$811$		−	43.8642i		−	1.54028i	0.637875	−	0.770140i	$-0.279814\pi$
$812$			1.46795i			0.0515149i
$813$	4.87520	+	51.2611i	0.170981	+	1.79781i
$814$	3.85772	+	22.5077i	0.135213	+	0.788896i
$815$			12.7600i			0.446962i
$816$	−10.5766	+	1.00589i	−0.370256	+	0.0352133i
$817$	−44.7303			−1.56491
$818$			37.6611i			1.31679i
$819$	−6.85872	+	1.31651i	−0.239663	+	0.0460025i
$820$		−	3.47181i		−	0.121241i
$821$	21.8446			0.762382			0.381191	−	0.924496i	$-0.375514\pi$
$821$	21.8446			0.762382			0.381191	+	0.924496i	$0.375514\pi$
$822$	−2.95369	−	31.0571i	−0.103022	−	1.08324i
$823$	−30.3191			−1.05686			−0.528429	−	0.848977i	$-0.677219\pi$
$823$	−30.3191			−1.05686			−0.528429	+	0.848977i	$0.677219\pi$
$824$	−8.96280			−0.312234
$825$	−3.88135	−	14.3267i	−0.135131	−	0.498793i
$826$	−6.56911			−0.228568
$827$	30.0537			1.04507			0.522535	−	0.852618i	$-0.324987\pi$
$827$	30.0537			1.04507			0.522535	+	0.852618i	$0.324987\pi$
$828$	2.40435	+	12.5261i	0.0835569	+	0.435313i
$829$	45.1267			1.56731			0.783657	−	0.621194i	$-0.213352\pi$
$829$	45.1267			1.56731			0.783657	+	0.621194i	$0.213352\pi$
$830$			0.525449i			0.0182386i
$831$	−0.0418952	−	0.440514i	−0.00145333	−	0.0152813i
$832$			2.32797i			0.0807080i
$833$	6.13397			0.212529
$834$	3.45702	+	36.3494i	0.119707	+	1.25868i
$835$			35.7363i			1.23670i
$836$	−12.0627	+	2.06749i	−0.417197	+	0.0715055i
$837$	−9.33579	+	2.72969i	−0.322692	+	0.0943518i
$838$		−	12.1299i		−	0.419021i
$839$		−	49.8368i		−	1.72056i	−0.509825	−	0.860278i	$-0.670290\pi$
$839$		−	49.8368i		−	1.72056i	0.509825	−	0.860278i	$-0.329710\pi$
$840$	−2.68019	+	0.254900i	−0.0924754	+	0.00879490i
$841$	−26.8451			−0.925694
$842$	−14.3398			−0.494184
$843$	−40.8725	+	3.88719i	−1.40772	+	0.133882i
$844$		−	7.67730i		−	0.264264i
$845$			11.7831i			0.405352i
$846$	−3.10383	−	16.1703i	−0.106712	−	0.555945i
$847$	−3.66308	−	10.3722i	−0.125865	−	0.356392i
$848$		−	9.89243i		−	0.339708i
$849$	2.01036	+	21.1383i	0.0689955	+	0.725465i
$850$	−15.8494			−0.543628
$851$		−	29.2735i		−	1.00348i
$852$	0.473560	+	4.97932i	0.0162239	+	0.170589i
$853$		−	20.7806i		−	0.711514i	−0.934578	−	0.355757i	$-0.884223\pi$
$853$		−	20.7806i		−	0.711514i	0.934578	−	0.355757i	$-0.115777\pi$
$854$	−7.35144			−0.251561
$855$	16.8990	−	3.24370i	0.577932	−	0.110932i
$856$	17.3261			0.592194
$857$	−53.8689			−1.84013			−0.920063	−	0.391770i	$-0.871863\pi$
$857$	−53.8689			−1.84013			−0.920063	+	0.391770i	$0.871863\pi$
$858$	12.9079	−	3.49696i	0.440668	−	0.119384i
$859$	40.4295			1.37944			0.689718	−	0.724078i	$-0.257735\pi$
$859$	40.4295			1.37944			0.689718	+	0.724078i	$0.257735\pi$
$860$	18.8420			0.642507
$861$	−0.366274	−	3.85125i	−0.0124826	−	0.131250i
$862$	−22.2340			−0.757295
$863$			19.8359i			0.675223i	0.941285	+	0.337612i	$0.109619\pi$
$863$			19.8359i			0.675223i	−0.941285	+	0.337612i	$0.890381\pi$
$864$	4.98734	−	1.45825i	0.169673	−	0.0496105i
$865$		−	28.0458i		−	0.953585i
$866$	−22.6153			−0.768500
$867$	35.5640	−	3.38232i	1.20782	−	0.114870i
$868$		−	1.87190i		−	0.0635364i
$869$	39.2467	−	6.72668i	1.33135	−	0.228187i
$870$	0.374181	+	3.93438i	0.0126859	+	0.133388i
$871$		−	20.4861i		−	0.694146i
$872$			1.24446i			0.0421429i
$873$	−34.9721	+	6.71278i	−1.18363	+	0.227193i
$874$	15.6887			0.530679
$875$	−11.7883			−0.398517
$876$	0.273968	+	2.88068i	0.00925651	+	0.0973291i
$877$		−	31.4973i		−	1.06359i	−0.846873	−	0.531795i	$-0.821518\pi$
$877$		−	31.4973i		−	1.06359i	0.846873	−	0.531795i	$-0.178482\pi$
$878$		−	20.3893i		−	0.688104i
$879$	6.79784	−	0.646510i	0.229285	−	0.0218062i
$880$	5.08124	−	0.870899i	0.171289	−	0.0293580i
$881$		−	14.7741i		−	0.497753i	−0.968535	−	0.248877i	$-0.919939\pi$
$881$		−	14.7741i		−	0.497753i	0.968535	−	0.248877i	$-0.0800613\pi$
$882$	−2.94622	+	0.565516i	−0.0992043	+	0.0190419i
$883$	−25.8323			−0.869325			−0.434663	−	0.900593i	$-0.643132\pi$
$883$	−25.8323			−0.869325			−0.434663	+	0.900593i	$0.643132\pi$
$884$		−	14.2797i		−	0.480279i
$885$	−17.6065	+	1.67447i	−0.591835	+	0.0562866i
$886$			15.4112i			0.517749i
$887$	−51.9657			−1.74484			−0.872419	−	0.488758i	$-0.837450\pi$
$887$	−51.9657			−1.74484			−0.872419	+	0.488758i	$0.837450\pi$
$888$	−11.8721	+	1.12910i	−0.398402	+	0.0378901i
$889$	14.8569			0.498286
$890$	−8.63158			−0.289331
$891$	−15.5772	−	25.4627i	−0.521857	−	0.853033i
$892$	1.58690			0.0531334
$893$	−20.2529			−0.677738
$894$	6.80554	−	0.647243i	0.227611	−	0.0216470i
$895$	−22.0731			−0.737823
$896$			1.00000i			0.0334077i
$897$	−17.0662	+	1.62308i	−0.569823	+	0.0541931i
$898$		−	4.70904i		−	0.157143i
$899$	−2.74785			−0.0916460
$900$	7.61263	−	1.46122i	0.253754	−	0.0487073i
$901$			60.6798i			2.02154i
$902$	1.25142	+	7.30139i	0.0416678	+	0.243110i
$903$	20.9012	−	1.98782i	0.695549	−	0.0661504i
$904$			8.92520i			0.296848i
$905$			6.44959i			0.214392i
$906$	−2.55511	−	26.8661i	−0.0848878	−	0.892567i
$907$	−34.5139			−1.14601			−0.573007	−	0.819550i	$-0.694223\pi$
$907$	−34.5139			−1.14601			−0.573007	+	0.819550i	$0.694223\pi$
$908$	13.1848			0.437552
$909$	16.2263	−	3.11458i	0.538191	−	0.103304i
$910$		−	3.61858i		−	0.119955i
$911$			2.20964i			0.0732086i	0.999330	+	0.0366043i	$0.0116541\pi$
$911$			2.20964i			0.0732086i	−0.999330	+	0.0366043i	$0.988346\pi$
$912$	−0.605125	−	6.36268i	−0.0200377	−	0.210690i
$913$	−0.189399	−	1.10504i	−0.00626819	−	0.0365716i
$914$		−	6.37293i		−	0.210798i
$915$	−19.7033	+	1.87388i	−0.651370	+	0.0619487i
$916$	10.6466			0.351774
$917$			6.01359i			0.198586i
$918$	−30.5921	+	8.94482i	−1.00969	+	0.295223i
$919$		−	38.1848i		−	1.25960i	−0.776757	−	0.629800i	$-0.783137\pi$
$919$		−	38.1848i		−	1.25960i	0.776757	−	0.629800i	$-0.216863\pi$
$920$	−6.60865			−0.217881
$921$	0.0190405	+	0.200204i	0.000627405	+	0.00659695i
$922$	−31.1985			−1.02747
$923$	−6.72269			−0.221280
$924$	5.54469	−	1.50215i	0.182407	−	0.0494170i
$925$	−17.7907			−0.584954
$926$	−34.7836			−1.14306
$927$	−26.4063	+	5.06861i	−0.867298	+	0.166475i
$928$	1.46795			0.0481878
$929$			44.5847i			1.46278i	0.681961	+	0.731389i	$0.261127\pi$
$929$			44.5847i			1.46278i	−0.681961	+	0.731389i	$0.738873\pi$
$930$	−0.477148	−	5.01705i	−0.0156463	−	0.164515i
$931$			3.69007i			0.120937i
$932$	−22.9506			−0.751772
$933$	−0.978061	−	10.2840i	−0.0320203	−	0.336682i
$934$		−	16.2040i		−	0.530212i
$935$	−31.1681	+	5.34207i	−1.01931	+	0.174704i
$936$	1.31651	+	6.85872i	0.0430314	+	0.224184i
$937$			42.2209i			1.37930i	0.724145	+	0.689648i	$0.242235\pi$
$937$			42.2209i			1.37930i	−0.724145	+	0.689648i	$0.757765\pi$
$938$		−	8.79998i		−	0.287330i
$939$	−7.54015	+	0.717108i	−0.246063	+	0.0234019i
$940$	8.53125			0.278259
$941$	−5.82020			−0.189733			−0.0948666	−	0.995490i	$-0.530242\pi$
$941$	−5.82020			−0.189733			−0.0948666	+	0.995490i	$0.530242\pi$
$942$	−9.26072	+	0.880743i	−0.301731	+	0.0286962i
$943$		−	9.49617i		−	0.309238i
$944$			6.56911i			0.213806i
$945$	−7.75227	+	2.26668i	−0.252181	+	0.0737352i
$946$	−39.6256	+	6.79163i	−1.28834	+	0.220815i
$947$		−	43.1514i		−	1.40223i	−0.713047	−	0.701116i	$-0.752685\pi$
$947$		−	43.1514i		−	1.40223i	0.713047	−	0.701116i	$-0.247315\pi$
$948$	1.96881	+	20.7014i	0.0639439	+	0.672349i
$949$	−3.88926			−0.126251
$950$		−	9.53466i		−	0.309345i
$951$	2.96494	+	31.1754i	0.0961449	+	1.01093i
$952$		−	6.13397i		−	0.198803i
$953$	−35.7811			−1.15906			−0.579531	−	0.814950i	$-0.696764\pi$
$953$	−35.7811			−1.15906			−0.579531	+	0.814950i	$0.696764\pi$
$954$	−5.59433	−	29.1452i	−0.181123	−	0.943612i
$955$	−41.8177			−1.35319
$956$	24.5601			0.794331
$957$	−2.20508	−	8.13932i	−0.0712800	−	0.263107i
$958$	−29.3852			−0.949393
$959$	18.0117			0.581629
$960$	0.254900	+	2.68019i	0.00822687	+	0.0865028i
$961$	−27.4960			−0.886968
$962$		−	16.0288i		−	0.516789i
$963$	51.0465	−	9.79820i	1.64495	−	0.315743i
$964$			2.67320i			0.0860979i
$965$	23.2313			0.747841
$966$	−7.33091	+	0.697208i	−0.235868	+	0.0224323i
$967$		−	35.5693i		−	1.14383i	−0.820312	−	0.571916i	$-0.806200\pi$
$967$		−	35.5693i		−	1.14383i	0.820312	−	0.571916i	$-0.193800\pi$
$968$	−10.3722	+	3.66308i	−0.333374	+	0.117736i
$969$	3.71181	+	39.0285i	0.119241	+	1.25378i
$970$		−	18.4509i		−	0.592423i
$971$		−	58.2802i		−	1.87030i	−0.354252	−	0.935150i	$-0.615264\pi$
$971$		−	58.2802i		−	1.87030i	0.354252	−	0.935150i	$-0.384736\pi$
$972$	13.8691	−	7.11673i	0.444852	−	0.228269i
$973$	−21.0811			−0.675828
$974$	8.31243			0.266347
$975$	0.986412	+	10.3718i	0.0315905	+	0.332163i
$976$			7.35144i			0.235314i
$977$		−	51.9959i		−	1.66350i	−0.555153	−	0.831748i	$-0.687340\pi$
$977$		−	51.9959i		−	1.66350i	0.555153	−	0.831748i	$-0.312660\pi$
$978$	14.1545	−	1.34617i	0.452611	−	0.0430457i
$979$	18.1526	−	3.11127i	0.580160	−	0.0994366i
$980$		−	1.55439i		−	0.0496532i
$981$	0.703765	+	3.66646i	0.0224695	+	0.117061i
$982$	−20.2083			−0.644872
$983$			27.0667i			0.863294i	0.902043	+	0.431647i	$0.142067\pi$
$983$			27.0667i			0.863294i	−0.902043	+	0.431647i	$0.857933\pi$
$984$	−3.85125	+	0.366274i	−0.122773	+	0.0116764i
$985$			0.840363i			0.0267762i
$986$	−9.00435			−0.286757
$987$	9.46363	−	0.900041i	0.301231	−	0.0286486i
$988$	8.59040			0.273297
$989$	51.5370			1.63878
$990$	14.4779	−	5.43938i	0.460139	−	0.172875i
$991$	32.7286			1.03966			0.519829	−	0.854270i	$-0.325996\pi$
$991$	32.7286			1.03966			0.519829	+	0.854270i	$0.325996\pi$
$992$	−1.87190			−0.0594329
$993$	−38.9892	+	3.70808i	−1.23729	+	0.117672i
$994$	−2.88778			−0.0915950
$995$			40.0862i			1.27082i
$996$	0.582875	−	0.0554344i	0.0184691	−	0.00175651i
$997$			24.2408i			0.767715i	0.923392	+	0.383858i	$0.125405\pi$
$997$			24.2408i			0.767715i	−0.923392	+	0.383858i	$0.874595\pi$
$998$	15.4409			0.488775
$999$	−34.3393	+	10.0405i	−1.08645	+	0.317666i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	462.2.c.b.197.11	yes	12
3.2	odd	2		462.2.c.a.197.12	yes	12
11.10	odd	2		462.2.c.a.197.11	✓	12
33.32	even	2	inner	462.2.c.b.197.12	yes	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
462.2.c.a.197.11	✓	12	11.10	odd	2
462.2.c.a.197.12	yes	12	3.2	odd	2
462.2.c.b.197.11	yes	12	1.1	even	1	trivial
462.2.c.b.197.12	yes	12	33.32	even	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 462 = 2 \cdot 3 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	462.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +(1.72427 - 0.163987i) q^{3} +1.00000 q^{4} +1.55439i q^{5} +(1.72427 - 0.163987i) q^{6} +1.00000i q^{7} +1.00000 q^{8} +(2.94622 - 0.565516i) q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +(1.72427 - 0.163987i) q^{3} +1.00000 q^{4} +1.55439i q^{5} +(1.72427 - 0.163987i) q^{6} +1.00000i q^{7} +1.00000 q^{8} +(2.94622 - 0.565516i) q^{9} +1.55439i q^{10} +(-0.560283 - 3.26896i) q^{11} +(1.72427 - 0.163987i) q^{12} +2.32797i q^{13} +1.00000i q^{14} +(0.254900 + 2.68019i) q^{15} +1.00000 q^{16} -6.13397 q^{17} +(2.94622 - 0.565516i) q^{18} -3.69007i q^{19} +1.55439i q^{20} +(0.163987 + 1.72427i) q^{21} +(-0.560283 - 3.26896i) q^{22} +4.25160i q^{23} +(1.72427 - 0.163987i) q^{24} +2.58387 q^{25} +2.32797i q^{26} +(4.98734 - 1.45825i) q^{27} +1.00000i q^{28} +1.46795 q^{29} +(0.254900 + 2.68019i) q^{30} -1.87190 q^{31} +1.00000 q^{32} +(-1.50215 - 5.54469i) q^{33} -6.13397 q^{34} -1.55439 q^{35} +(2.94622 - 0.565516i) q^{36} -6.88530 q^{37} -3.69007i q^{38} +(0.381758 + 4.01406i) q^{39} +1.55439i q^{40} -2.23355 q^{41} +(0.163987 + 1.72427i) q^{42} -12.1218i q^{43} +(-0.560283 - 3.26896i) q^{44} +(0.879034 + 4.57957i) q^{45} +4.25160i q^{46} -5.48848i q^{47} +(1.72427 - 0.163987i) q^{48} -1.00000 q^{49} +2.58387 q^{50} +(-10.5766 + 1.00589i) q^{51} +2.32797i q^{52} -9.89243i q^{53} +(4.98734 - 1.45825i) q^{54} +(5.08124 - 0.870899i) q^{55} +1.00000i q^{56} +(-0.605125 - 6.36268i) q^{57} +1.46795 q^{58} +6.56911i q^{59} +(0.254900 + 2.68019i) q^{60} +7.35144i q^{61} -1.87190 q^{62} +(0.565516 + 2.94622i) q^{63} +1.00000 q^{64} -3.61858 q^{65} +(-1.50215 - 5.54469i) q^{66} -8.79998 q^{67} -6.13397 q^{68} +(0.697208 + 7.33091i) q^{69} -1.55439 q^{70} +2.88778i q^{71} +(2.94622 - 0.565516i) q^{72} +1.67066i q^{73} -6.88530 q^{74} +(4.45529 - 0.423721i) q^{75} -3.69007i q^{76} +(3.26896 - 0.560283i) q^{77} +(0.381758 + 4.01406i) q^{78} +12.0059i q^{79} +1.55439i q^{80} +(8.36038 - 3.33227i) q^{81} -2.23355 q^{82} +0.338041 q^{83} +(0.163987 + 1.72427i) q^{84} -9.53458i q^{85} -12.1218i q^{86} +(2.53114 - 0.240725i) q^{87} +(-0.560283 - 3.26896i) q^{88} +5.55303i q^{89} +(0.879034 + 4.57957i) q^{90} -2.32797 q^{91} +4.25160i q^{92} +(-3.22766 + 0.306967i) q^{93} -5.48848i q^{94} +5.73582 q^{95} +(1.72427 - 0.163987i) q^{96} -11.8702 q^{97} -1.00000 q^{98} +(-3.49936 - 9.31421i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 12 q^{2} + 4 q^{3} + 12 q^{4} + 4 q^{6} + 12 q^{8}+O(q^{10}) \) 12 * q + 12 * q^2 + 4 * q^3 + 12 * q^4 + 4 * q^6 + 12 * q^8	\( 12 q + 12 q^{2} + 4 q^{3} + 12 q^{4} + 4 q^{6} + 12 q^{8} + 8 q^{11} + 4 q^{12} + 4 q^{15} + 12 q^{16} + 4 q^{17} + 8 q^{22} + 4 q^{24} - 28 q^{25} - 8 q^{27} - 8 q^{29} + 4 q^{30} + 12 q^{31} + 12 q^{32} - 16 q^{33} + 4 q^{34} + 4 q^{35} + 36 q^{39} - 20 q^{41} + 8 q^{44} - 12 q^{45} + 4 q^{48} - 12 q^{49} - 28 q^{50} - 8 q^{51} - 8 q^{54} + 4 q^{55} - 28 q^{57} - 8 q^{58} + 4 q^{60} + 12 q^{62} - 4 q^{63} + 12 q^{64} - 16 q^{66} + 24 q^{67} + 4 q^{68} - 20 q^{69} + 4 q^{70} - 40 q^{75} - 4 q^{77} + 36 q^{78} + 4 q^{81} - 20 q^{82} - 44 q^{83} - 8 q^{87} + 8 q^{88} - 12 q^{90} - 24 q^{91} - 24 q^{93} + 4 q^{96} - 48 q^{97} - 12 q^{98} + 20 q^{99}+O(q^{100}) \) 12 * q + 12 * q^2 + 4 * q^3 + 12 * q^4 + 4 * q^6 + 12 * q^8 + 8 * q^11 + 4 * q^12 + 4 * q^15 + 12 * q^16 + 4 * q^17 + 8 * q^22 + 4 * q^24 - 28 * q^25 - 8 * q^27 - 8 * q^29 + 4 * q^30 + 12 * q^31 + 12 * q^32 - 16 * q^33 + 4 * q^34 + 4 * q^35 + 36 * q^39 - 20 * q^41 + 8 * q^44 - 12 * q^45 + 4 * q^48 - 12 * q^49 - 28 * q^50 - 8 * q^51 - 8 * q^54 + 4 * q^55 - 28 * q^57 - 8 * q^58 + 4 * q^60 + 12 * q^62 - 4 * q^63 + 12 * q^64 - 16 * q^66 + 24 * q^67 + 4 * q^68 - 20 * q^69 + 4 * q^70 - 40 * q^75 - 4 * q^77 + 36 * q^78 + 4 * q^81 - 20 * q^82 - 44 * q^83 - 8 * q^87 + 8 * q^88 - 12 * q^90 - 24 * q^91 - 24 * q^93 + 4 * q^96 - 48 * q^97 - 12 * q^98 + 20 * q^99

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