LMFDB - Embedded newform 630.2.j.j.421.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [630,2,Mod(211,630)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(630, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([2, 0, 0]))

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

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

chi := DirichletCharacter("630.211");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 630 = 2 \cdot 3^{2} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	630.j (of order $3$, degree $2$, 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:	$5.03057532734$
Analytic rank:	$0$
Dimension:	$6$
Relative dimension:	$3$ over $\Q(\zeta_{3})$
Coefficient field:	6.0.954288.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{5} - 2x^{4} + 3x^{3} - 6x^{2} - 9x + 27 $ x^6 - x^5 - 2x^4 + 3x^3 - 6x^2 - 9x + 27
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 3 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			421.3
Root			$1.71903 + 0.211943i$ of defining polynomial
Character	$\chi$	$=$	630.421
Dual form			630.2.j.j.211.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 + 0.866025i) q^{2} +(1.04307 + 1.38276i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(0.500000 + 0.866025i) q^{5} +(-1.71903 + 0.211943i) q^{6} +(-0.500000 + 0.866025i) q^{7} +1.00000 q^{8} +(-0.824030 + 2.88461i) q^{9} +O(q^{10})$	\(q+(-0.500000 + 0.866025i) q^{2} +(1.04307 + 1.38276i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(0.500000 + 0.866025i) q^{5} +(-1.71903 + 0.211943i) q^{6} +(-0.500000 + 0.866025i) q^{7} +1.00000 q^{8} +(-0.824030 + 2.88461i) q^{9} -1.00000 q^{10} +(-0.367095 + 0.635828i) q^{11} +(0.675970 - 1.59470i) q^{12} +(0.867095 + 1.50185i) q^{13} +(-0.500000 - 0.866025i) q^{14} +(-0.675970 + 1.59470i) q^{15} +(-0.500000 + 0.866025i) q^{16} +2.52420 q^{17} +(-2.08613 - 2.15594i) q^{18} -6.52420 q^{19} +(0.500000 - 0.866025i) q^{20} +(-1.71903 + 0.211943i) q^{21} +(-0.367095 - 0.635828i) q^{22} +(1.86710 + 3.23390i) q^{23} +(1.04307 + 1.38276i) q^{24} +(-0.500000 + 0.866025i) q^{25} -1.73419 q^{26} +(-4.84823 + 1.86940i) q^{27} +1.00000 q^{28} +(1.13290 - 1.96225i) q^{29} +(-1.04307 - 1.38276i) q^{30} +(2.00000 + 3.46410i) q^{31} +(-0.500000 - 0.866025i) q^{32} +(-1.26210 + 0.155606i) q^{33} +(-1.26210 + 2.18602i) q^{34} -1.00000 q^{35} +(2.91016 - 0.728674i) q^{36} -7.25839 q^{37} +(3.26210 - 5.65012i) q^{38} +(-1.17226 + 2.76551i) q^{39} +(0.500000 + 0.866025i) q^{40} +(3.36710 + 5.83198i) q^{41} +(0.675970 - 1.59470i) q^{42} +(0.500000 - 0.866025i) q^{43} +0.734191 q^{44} +(-2.91016 + 0.728674i) q^{45} -3.73419 q^{46} +(4.79001 - 8.29654i) q^{47} +(-1.71903 + 0.211943i) q^{48} +(-0.500000 - 0.866025i) q^{49} +(-0.500000 - 0.866025i) q^{50} +(2.63290 + 3.49035i) q^{51} +(0.867095 - 1.50185i) q^{52} +3.25839 q^{53} +(0.805165 - 5.13339i) q^{54} -0.734191 q^{55} +(-0.500000 + 0.866025i) q^{56} +(-6.80516 - 9.02138i) q^{57} +(1.13290 + 1.96225i) q^{58} +(-0.527909 - 0.914365i) q^{59} +(1.71903 - 0.211943i) q^{60} +(-1.89500 + 3.28224i) q^{61} -4.00000 q^{62} +(-2.08613 - 2.15594i) q^{63} +1.00000 q^{64} +(-0.867095 + 1.50185i) q^{65} +(0.496291 - 1.17081i) q^{66} +(-2.99629 - 5.18973i) q^{67} +(-1.26210 - 2.18602i) q^{68} +(-2.52420 + 5.95491i) q^{69} +(0.500000 - 0.866025i) q^{70} -3.25839 q^{71} +(-0.824030 + 2.88461i) q^{72} +10.0484 q^{73} +(3.62920 - 6.28595i) q^{74} +(-1.71903 + 0.211943i) q^{75} +(3.26210 + 5.65012i) q^{76} +(-0.367095 - 0.635828i) q^{77} +(-1.80887 - 2.39796i) q^{78} +(-6.52420 + 11.3002i) q^{79} -1.00000 q^{80} +(-7.64195 - 4.75401i) q^{81} -6.73419 q^{82} +(7.79001 - 13.4927i) q^{83} +(1.04307 + 1.38276i) q^{84} +(1.26210 + 2.18602i) q^{85} +(0.500000 + 0.866025i) q^{86} +(3.89500 - 0.480222i) q^{87} +(-0.367095 + 0.635828i) q^{88} +5.04840 q^{89} +(0.824030 - 2.88461i) q^{90} -1.73419 q^{91} +(1.86710 - 3.23390i) q^{92} +(-2.70388 + 6.37880i) q^{93} +(4.79001 + 8.29654i) q^{94} +(-3.26210 - 5.65012i) q^{95} +(0.675970 - 1.59470i) q^{96} +(-0.234191 + 0.405631i) q^{97} +1.00000 q^{98} +(-1.53162 - 1.58287i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 3 q^{2} - q^{3} - 3 q^{4} + 3 q^{5} - q^{6} - 3 q^{7} + 6 q^{8} - 7 q^{9}+O(q^{10}) $ 6 * q - 3 * q^2 - q^3 - 3 * q^4 + 3 * q^5 - q^6 - 3 * q^7 + 6 * q^8 - 7 * q^9	$ 6 q - 3 q^{2} - q^{3} - 3 q^{4} + 3 q^{5} - q^{6} - 3 q^{7} + 6 q^{8} - 7 q^{9} - 6 q^{10} + 3 q^{11} + 2 q^{12} - 3 q^{14} - 2 q^{15} - 3 q^{16} - 18 q^{17} + 2 q^{18} - 6 q^{19} + 3 q^{20} - q^{21} + 3 q^{22} + 6 q^{23} - q^{24} - 3 q^{25} + 2 q^{27} + 6 q^{28} + 12 q^{29} + q^{30} + 12 q^{31} - 3 q^{32} + 9 q^{33} + 9 q^{34} - 6 q^{35} + 5 q^{36} + 3 q^{38} + 22 q^{39} + 3 q^{40} + 15 q^{41} + 2 q^{42} + 3 q^{43} - 6 q^{44} - 5 q^{45} - 12 q^{46} + 6 q^{47} - q^{48} - 3 q^{49} - 3 q^{50} + 21 q^{51} - 24 q^{53} - 19 q^{54} + 6 q^{55} - 3 q^{56} - 17 q^{57} + 12 q^{58} + 3 q^{59} + q^{60} - 24 q^{62} + 2 q^{63} + 6 q^{64} - 24 q^{66} + 9 q^{67} + 9 q^{68} + 18 q^{69} + 3 q^{70} + 24 q^{71} - 7 q^{72} - 6 q^{73} - q^{75} + 3 q^{76} + 3 q^{77} - 14 q^{78} - 6 q^{79} - 6 q^{80} - 19 q^{81} - 30 q^{82} + 24 q^{83} - q^{84} - 9 q^{85} + 3 q^{86} + 12 q^{87} + 3 q^{88} - 36 q^{89} + 7 q^{90} + 6 q^{92} - 8 q^{93} + 6 q^{94} - 3 q^{95} + 2 q^{96} + 9 q^{97} + 6 q^{98} - 30 q^{99}+O(q^{100}) $ 6 * q - 3 * q^2 - q^3 - 3 * q^4 + 3 * q^5 - q^6 - 3 * q^7 + 6 * q^8 - 7 * q^9 - 6 * q^10 + 3 * q^11 + 2 * q^12 - 3 * q^14 - 2 * q^15 - 3 * q^16 - 18 * q^17 + 2 * q^18 - 6 * q^19 + 3 * q^20 - q^21 + 3 * q^22 + 6 * q^23 - q^24 - 3 * q^25 + 2 * q^27 + 6 * q^28 + 12 * q^29 + q^30 + 12 * q^31 - 3 * q^32 + 9 * q^33 + 9 * q^34 - 6 * q^35 + 5 * q^36 + 3 * q^38 + 22 * q^39 + 3 * q^40 + 15 * q^41 + 2 * q^42 + 3 * q^43 - 6 * q^44 - 5 * q^45 - 12 * q^46 + 6 * q^47 - q^48 - 3 * q^49 - 3 * q^50 + 21 * q^51 - 24 * q^53 - 19 * q^54 + 6 * q^55 - 3 * q^56 - 17 * q^57 + 12 * q^58 + 3 * q^59 + q^60 - 24 * q^62 + 2 * q^63 + 6 * q^64 - 24 * q^66 + 9 * q^67 + 9 * q^68 + 18 * q^69 + 3 * q^70 + 24 * q^71 - 7 * q^72 - 6 * q^73 - q^75 + 3 * q^76 + 3 * q^77 - 14 * q^78 - 6 * q^79 - 6 * q^80 - 19 * q^81 - 30 * q^82 + 24 * q^83 - q^84 - 9 * q^85 + 3 * q^86 + 12 * q^87 + 3 * q^88 - 36 * q^89 + 7 * q^90 + 6 * q^92 - 8 * q^93 + 6 * q^94 - 3 * q^95 + 2 * q^96 + 9 * q^97 + 6 * q^98 - 30 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/630\mathbb{Z}\right)^\times$.

$n$	$127$	$281$	$451$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$	$1$

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 $

$2$	−0.500000	+	0.866025i	−0.353553	+	0.612372i
$2$	−0.500000	+	0.866025i	−0.353553	+	0.612372i
$3$	1.04307	+	1.38276i	0.602214	+	0.798335i
$3$	1.04307	+	1.38276i	0.602214	+	0.798335i
$4$	−0.500000	−	0.866025i	−0.250000	−	0.433013i
$5$	0.500000	+	0.866025i	0.223607	+	0.387298i
$5$	0.500000	+	0.866025i	0.223607	+	0.387298i
$6$	−1.71903	+	0.211943i	−0.701793	+	0.0865252i
$7$	−0.500000	+	0.866025i	−0.188982	+	0.327327i
$7$	−0.500000	+	0.866025i	−0.188982	+	0.327327i
$8$	1.00000			0.353553
$9$	−0.824030	+	2.88461i	−0.274677	+	0.961537i
$10$	−1.00000			−0.316228
$11$	−0.367095	+	0.635828i	−0.110683	+	0.191709i	−0.916046	−	0.401073i	$-0.868637\pi$
$11$	−0.367095	+	0.635828i	−0.110683	+	0.191709i	0.805363	+	0.592783i	$0.201971\pi$
$12$	0.675970	−	1.59470i	0.195136	−	0.460350i
$13$	0.867095	+	1.50185i	0.240489	+	0.416539i	0.960854	−	0.277056i	$-0.0893589\pi$
$13$	0.867095	+	1.50185i	0.240489	+	0.416539i	−0.720365	+	0.693596i	$0.756026\pi$
$14$	−0.500000	−	0.866025i	−0.133631	−	0.231455i
$15$	−0.675970	+	1.59470i	−0.174535	+	0.411750i
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	2.52420			0.612208			0.306104	−	0.951998i	$-0.400974\pi$
$17$	2.52420			0.612208			0.306104	+	0.951998i	$0.400974\pi$
$18$	−2.08613	−	2.15594i	−0.491706	−	0.508159i
$19$	−6.52420			−1.49675			−0.748377	−	0.663274i	$-0.769167\pi$
$19$	−6.52420			−1.49675			−0.748377	+	0.663274i	$0.769167\pi$
$20$	0.500000	−	0.866025i	0.111803	−	0.193649i
$21$	−1.71903	+	0.211943i	−0.375124	+	0.0462497i
$22$	−0.367095	−	0.635828i	−0.0782650	−	0.135559i
$23$	1.86710	+	3.23390i	0.389316	+	0.674316i	0.992358	−	0.123394i	$-0.0393780\pi$
$23$	1.86710	+	3.23390i	0.389316	+	0.674316i	−0.603041	+	0.797710i	$0.706045\pi$
$24$	1.04307	+	1.38276i	0.212915	+	0.282254i
$25$	−0.500000	+	0.866025i	−0.100000	+	0.173205i
$26$	−1.73419			−0.340103
$27$	−4.84823	+	1.86940i	−0.933042	+	0.359767i
$28$	1.00000			0.188982
$29$	1.13290	−	1.96225i	0.210375	−	0.364380i	−0.741457	−	0.671001i	$-0.765865\pi$
$29$	1.13290	−	1.96225i	0.210375	−	0.364380i	0.951832	+	0.306620i	$0.0991981\pi$
$30$	−1.04307	−	1.38276i	−0.190437	−	0.252456i
$31$	2.00000	+	3.46410i	0.359211	+	0.622171i	0.987829	−	0.155543i	$-0.0497126\pi$
$31$	2.00000	+	3.46410i	0.359211	+	0.622171i	−0.628619	+	0.777714i	$0.716379\pi$
$32$	−0.500000	−	0.866025i	−0.0883883	−	0.153093i
$33$	−1.26210	+	0.155606i	−0.219703	+	0.0270876i
$34$	−1.26210	+	2.18602i	−0.216448	+	0.374900i
$35$	−1.00000			−0.169031
$36$	2.91016	−	0.728674i	0.485027	−	0.121446i
$37$	−7.25839			−1.19327			−0.596636	−	0.802512i	$-0.703496\pi$
$37$	−7.25839			−1.19327			−0.596636	+	0.802512i	$0.703496\pi$
$38$	3.26210	−	5.65012i	0.529182	−	0.916571i
$39$	−1.17226	+	2.76551i	−0.187712	+	0.442836i
$40$	0.500000	+	0.866025i	0.0790569	+	0.136931i
$41$	3.36710	+	5.83198i	0.525852	+	0.910802i	0.999546	+	0.0301131i	$0.00958675\pi$
$41$	3.36710	+	5.83198i	0.525852	+	0.910802i	−0.473695	+	0.880689i	$0.657080\pi$
$42$	0.675970	−	1.59470i	0.104304	−	0.246067i
$43$	0.500000	−	0.866025i	0.0762493	−	0.132068i	−0.825380	−	0.564578i	$-0.809039\pi$
$43$	0.500000	−	0.866025i	0.0762493	−	0.132068i	0.901629	+	0.432511i	$0.142372\pi$
$44$	0.734191			0.110683
$45$	−2.91016	+	0.728674i	−0.433821	+	0.108624i
$46$	−3.73419			−0.550576
$47$	4.79001	−	8.29654i	0.698695	−	1.21017i	−0.270225	−	0.962797i	$-0.587098\pi$
$47$	4.79001	−	8.29654i	0.698695	−	1.21017i	0.968919	−	0.247377i	$-0.0795687\pi$
$48$	−1.71903	+	0.211943i	−0.248121	+	0.0305913i
$49$	−0.500000	−	0.866025i	−0.0714286	−	0.123718i
$50$	−0.500000	−	0.866025i	−0.0707107	−	0.122474i
$51$	2.63290	+	3.49035i	0.368680	+	0.488747i
$52$	0.867095	−	1.50185i	0.120245	−	0.208270i
$53$	3.25839			0.447574			0.223787	−	0.974638i	$-0.428158\pi$
$53$	3.25839			0.447574			0.223787	+	0.974638i	$0.428158\pi$
$54$	0.805165	−	5.13339i	0.109569	−	0.698566i
$55$	−0.734191			−0.0989983
$56$	−0.500000	+	0.866025i	−0.0668153	+	0.115728i
$57$	−6.80516	−	9.02138i	−0.901366	−	1.19491i
$58$	1.13290	+	1.96225i	0.148758	+	0.257656i
$59$	−0.527909	−	0.914365i	−0.0687279	−	0.119040i	0.829614	−	0.558338i	$-0.188561\pi$
$59$	−0.527909	−	0.914365i	−0.0687279	−	0.119040i	−0.898342	+	0.439298i	$0.855227\pi$
$60$	1.71903	−	0.211943i	0.221926	−	0.0273617i
$61$	−1.89500	+	3.28224i	−0.242630	+	0.420248i	−0.961463	−	0.274935i	$-0.911344\pi$
$61$	−1.89500	+	3.28224i	−0.242630	+	0.420248i	0.718832	+	0.695184i	$0.244677\pi$
$62$	−4.00000			−0.508001
$63$	−2.08613	−	2.15594i	−0.262828	−	0.271622i
$64$	1.00000			0.125000
$65$	−0.867095	+	1.50185i	−0.107550	+	0.186282i
$66$	0.496291	−	1.17081i	0.0610892	−	0.144117i
$67$	−2.99629	−	5.18973i	−0.366055	−	0.634026i	0.622890	−	0.782310i	$-0.285959\pi$
$67$	−2.99629	−	5.18973i	−0.366055	−	0.634026i	−0.988945	+	0.148283i	$0.952625\pi$
$68$	−1.26210	−	2.18602i	−0.153052	−	0.265094i
$69$	−2.52420	+	5.95491i	−0.303878	+	0.716887i
$70$	0.500000	−	0.866025i	0.0597614	−	0.103510i
$71$	−3.25839			−0.386700			−0.193350	−	0.981130i	$-0.561935\pi$
$71$	−3.25839			−0.386700			−0.193350	+	0.981130i	$0.561935\pi$
$72$	−0.824030	+	2.88461i	−0.0971129	+	0.339955i
$73$	10.0484			1.17608			0.588038	−	0.808833i	$-0.299901\pi$
$73$	10.0484			1.17608			0.588038	+	0.808833i	$0.299901\pi$
$74$	3.62920	−	6.28595i	0.421885	−	0.730727i
$75$	−1.71903	+	0.211943i	−0.198497	+	0.0244730i
$76$	3.26210	+	5.65012i	0.374189	+	0.648114i
$77$	−0.367095	−	0.635828i	−0.0418344	−	0.0724593i
$78$	−1.80887	−	2.39796i	−0.204815	−	0.271516i
$79$	−6.52420	+	11.3002i	−0.734030	+	1.27138i	0.221118	+	0.975247i	$0.429029\pi$
$79$	−6.52420	+	11.3002i	−0.734030	+	1.27138i	−0.955148	+	0.296130i	$0.904304\pi$
$80$	−1.00000			−0.111803
$81$	−7.64195	−	4.75401i	−0.849105	−	0.528224i
$82$	−6.73419			−0.743667
$83$	7.79001	−	13.4927i	0.855065	−	1.48102i	−0.0215206	−	0.999768i	$-0.506851\pi$
$83$	7.79001	−	13.4927i	0.855065	−	1.48102i	0.876585	−	0.481247i	$-0.159816\pi$
$84$	1.04307	+	1.38276i	0.113808	+	0.150871i
$85$	1.26210	+	2.18602i	0.136894	+	0.237107i
$86$	0.500000	+	0.866025i	0.0539164	+	0.0933859i
$87$	3.89500	−	0.480222i	0.417588	−	0.0514852i
$88$	−0.367095	+	0.635828i	−0.0391325	+	0.0677795i
$89$	5.04840			0.535129			0.267565	−	0.963540i	$-0.413781\pi$
$89$	5.04840			0.535129			0.267565	+	0.963540i	$0.413781\pi$
$90$	0.824030	−	2.88461i	0.0868604	−	0.304065i
$91$	−1.73419			−0.181793
$92$	1.86710	−	3.23390i	0.194658	−	0.337158i
$93$	−2.70388	+	6.37880i	−0.280379	+	0.661450i
$94$	4.79001	+	8.29654i	0.494052	+	0.855723i
$95$	−3.26210	−	5.65012i	−0.334684	−	0.579690i
$96$	0.675970	−	1.59470i	0.0689909	−	0.162758i
$97$	−0.234191	+	0.405631i	−0.0237785	+	0.0411856i	−0.877670	−	0.479266i	$-0.840903\pi$
$97$	−0.234191	+	0.405631i	−0.0237785	+	0.0411856i	0.853891	+	0.520451i	$0.174236\pi$
$98$	1.00000			0.101015
$99$	−1.53162	−	1.58287i	−0.153933	−	0.159084i
$100$	1.00000			0.100000
$101$	4.46838	−	7.73946i	0.444621	−	0.770106i	−0.553405	−	0.832912i	$-0.686672\pi$
$101$	4.46838	−	7.73946i	0.444621	−	0.770106i	0.998026	+	0.0628067i	$0.0200052\pi$
$102$	−4.33919	+	0.534986i	−0.429644	+	0.0529715i
$103$	−0.104996	−	0.181858i	−0.0103455	−	0.0179190i	0.860806	−	0.508933i	$-0.169960\pi$
$103$	−0.104996	−	0.181858i	−0.0103455	−	0.0179190i	−0.871152	+	0.491014i	$0.836626\pi$
$104$	0.867095	+	1.50185i	0.0850257	+	0.147269i
$105$	−1.04307	−	1.38276i	−0.101793	−	0.134943i
$106$	−1.62920	+	2.82185i	−0.158241	+	0.274082i
$107$	1.05582			0.102070			0.0510349	−	0.998697i	$-0.483748\pi$
$107$	1.05582			0.102070			0.0510349	+	0.998697i	$0.483748\pi$
$108$	4.04307	+	3.26399i	0.389044	+	0.314077i
$109$	18.2510			1.74813			0.874063	−	0.485813i	$-0.161476\pi$
$109$	18.2510			1.74813			0.874063	+	0.485813i	$0.161476\pi$
$110$	0.367095	−	0.635828i	0.0350012	−	0.0606238i
$111$	−7.57097	−	10.0366i	−0.718605	−	0.952631i
$112$	−0.500000	−	0.866025i	−0.0472456	−	0.0818317i
$113$	8.28630	+	14.3523i	0.779509	+	1.35015i	0.932225	+	0.361880i	$0.117865\pi$
$113$	8.28630	+	14.3523i	0.779509	+	1.35015i	−0.152715	+	0.988270i	$0.548802\pi$
$114$	11.2153	−	1.38276i	1.05041	−	0.129507i
$115$	−1.86710	+	3.23390i	−0.174108	+	0.301563i
$116$	−2.26581			−0.210375
$117$	−5.04677	+	1.26366i	−0.466574	+	0.116825i
$118$	1.05582			0.0971959
$119$	−1.26210	+	2.18602i	−0.115696	+	0.200392i
$120$	−0.675970	+	1.59470i	−0.0617073	+	0.145575i
$121$	5.23048	+	9.05946i	0.475498	+	0.823587i
$122$	−1.89500	−	3.28224i	−0.171566	−	0.297160i
$123$	−4.55211	+	10.7390i	−0.410450	+	0.968304i
$124$	2.00000	−	3.46410i	0.179605	−	0.311086i
$125$	−1.00000			−0.0894427
$126$	2.91016	−	0.728674i	0.259258	−	0.0649154i
$127$	−9.84583			−0.873676			−0.436838	−	0.899540i	$-0.643902\pi$
$127$	−9.84583			−0.873676			−0.436838	+	0.899540i	$0.643902\pi$
$128$	−0.500000	+	0.866025i	−0.0441942	+	0.0765466i
$129$	1.71903	−	0.211943i	0.151353	−	0.0186605i
$130$	−0.867095	−	1.50185i	−0.0760493	−	0.131721i
$131$	8.28630	+	14.3523i	0.723977	+	1.25397i	0.959394	+	0.282071i	$0.0910213\pi$
$131$	8.28630	+	14.3523i	0.723977	+	1.25397i	−0.235416	+	0.971895i	$0.575645\pi$
$132$	0.765809	+	1.01521i	0.0666551	+	0.0883625i
$133$	3.26210	−	5.65012i	0.282860	−	0.489928i
$134$	5.99258			0.517680
$135$	−4.04307	−	3.26399i	−0.347972	−	0.280919i
$136$	2.52420			0.216448
$137$	5.39500	−	9.34442i	0.460926	−	0.798348i	−0.538081	−	0.842893i	$-0.680851\pi$
$137$	5.39500	−	9.34442i	0.460926	−	0.798348i	0.999007	+	0.0445453i	$0.0141839\pi$
$138$	−3.89500	−	5.16348i	−0.331565	−	0.439544i
$139$	3.50000	+	6.06218i	0.296866	+	0.514187i	0.975417	−	0.220366i	$-0.0707252\pi$
$139$	3.50000	+	6.06218i	0.296866	+	0.514187i	−0.678551	+	0.734553i	$0.737392\pi$
$140$	0.500000	+	0.866025i	0.0422577	+	0.0731925i
$141$	16.4684	−	2.03041i	1.38689	−	0.170992i
$142$	1.62920	−	2.82185i	0.136719	−	0.236804i
$143$	−1.27323			−0.106473
$144$	−2.08613	−	2.15594i	−0.173844	−	0.179661i
$145$	2.26581			0.188165
$146$	−5.02420	+	8.70217i	−0.415806	+	0.720197i
$147$	0.675970	−	1.59470i	0.0557530	−	0.131529i
$148$	3.62920	+	6.28595i	0.298318	+	0.516702i
$149$	4.46838	+	7.73946i	0.366064	+	0.634042i	0.988946	−	0.148274i	$-0.0473718\pi$
$149$	4.46838	+	7.73946i	0.366064	+	0.634042i	−0.622882	+	0.782316i	$0.714038\pi$
$150$	0.675970	−	1.59470i	0.0551927	−	0.130207i
$151$	9.79001	−	16.9568i	0.796700	−	1.37992i	−0.125055	−	0.992150i	$-0.539911\pi$
$151$	9.79001	−	16.9568i	0.796700	−	1.37992i	0.921754	−	0.387774i	$-0.126756\pi$
$152$	−6.52420			−0.529182
$153$	−2.08002	+	7.28133i	−0.168159	+	0.588661i
$154$	0.734191			0.0591628
$155$	−2.00000	+	3.46410i	−0.160644	+	0.278243i
$156$	2.98113	−	0.367549i	0.238682	−	0.0294275i
$157$	−7.33548	−	12.7054i	−0.585435	−	1.01400i	−0.994821	−	0.101642i	$-0.967590\pi$
$157$	−7.33548	−	12.7054i	−0.585435	−	1.01400i	0.409386	−	0.912361i	$-0.365743\pi$
$158$	−6.52420	−	11.3002i	−0.519037	−	0.898999i
$159$	3.39871	+	4.50556i	0.269536	+	0.357314i
$160$	0.500000	−	0.866025i	0.0395285	−	0.0684653i
$161$	−3.73419			−0.294295
$162$	7.93807	−	4.24111i	0.623674	−	0.333213i
$163$	9.94418			0.778888			0.389444	−	0.921050i	$-0.372667\pi$
$163$	9.94418			0.778888			0.389444	+	0.921050i	$0.372667\pi$
$164$	3.36710	−	5.83198i	0.262926	−	0.455401i
$165$	−0.765809	−	1.01521i	−0.0596182	−	0.0790338i
$166$	7.79001	+	13.4927i	0.604622	+	1.04724i
$167$	2.10500	+	3.64596i	0.162889	+	0.282133i	0.935904	−	0.352256i	$-0.114585\pi$
$167$	2.10500	+	3.64596i	0.162889	+	0.282133i	−0.773014	+	0.634389i	$0.781252\pi$
$168$	−1.71903	+	0.211943i	−0.132626	+	0.0163517i
$169$	4.99629	−	8.65383i	0.384330	−	0.665679i
$170$	−2.52420			−0.193597
$171$	5.37614	−	18.8198i	0.411124	−	1.43918i
$172$	−1.00000			−0.0762493
$173$	6.00000	−	10.3923i	0.456172	−	0.790112i	−0.542583	−	0.840002i	$-0.682554\pi$
$173$	6.00000	−	10.3923i	0.456172	−	0.790112i	0.998755	+	0.0498898i	$0.0158870\pi$
$174$	−1.53162	+	3.61328i	−0.116112	+	0.273922i
$175$	−0.500000	−	0.866025i	−0.0377964	−	0.0654654i
$176$	−0.367095	−	0.635828i	−0.0276709	−	0.0479273i
$177$	0.713701	−	1.68371i	0.0536450	−	0.126555i
$178$	−2.52420	+	4.37204i	−0.189197	+	0.327698i
$179$	18.9926			1.41957			0.709786	−	0.704417i	$-0.248792\pi$
$179$	18.9926			1.41957			0.709786	+	0.704417i	$0.248792\pi$
$180$	2.08613	+	2.15594i	0.155491	+	0.160694i
$181$	16.6284			1.23598			0.617990	−	0.786186i	$-0.287947\pi$
$181$	16.6284			1.23598			0.617990	+	0.786186i	$0.287947\pi$
$182$	0.867095	−	1.50185i	0.0642734	−	0.111325i
$183$	−6.51516	+	0.803265i	−0.481614	+	0.0593790i
$184$	1.86710	+	3.23390i	0.137644	+	0.238407i
$185$	−3.62920	−	6.28595i	−0.266824	−	0.462152i
$186$	−4.17226	−	5.53103i	−0.305925	−	0.405554i
$187$	−0.926622	+	1.60496i	−0.0677613	+	0.117366i
$188$	−9.58002			−0.698695
$189$	0.805165	−	5.13339i	0.0585671	−	0.373399i
$190$	6.52420			0.473315
$191$	−8.04840	+	13.9402i	−0.582362	+	1.00868i	0.412837	+	0.910805i	$0.364538\pi$
$191$	−8.04840	+	13.9402i	−0.582362	+	1.00868i	−0.995199	+	0.0978752i	$0.968795\pi$
$192$	1.04307	+	1.38276i	0.0752767	+	0.0997918i
$193$	8.38759	+	14.5277i	0.603752	+	1.04573i	0.992247	+	0.124278i	$0.0396615\pi$
$193$	8.38759	+	14.5277i	0.603752	+	1.04573i	−0.388496	+	0.921450i	$0.627005\pi$
$194$	−0.234191	−	0.405631i	−0.0168139	−	0.0291226i
$195$	−2.98113	+	0.367549i	−0.213483	+	0.0263207i
$196$	−0.500000	+	0.866025i	−0.0357143	+	0.0618590i
$197$	11.3700			0.810081			0.405040	−	0.914299i	$-0.367257\pi$
$197$	11.3700			0.810081			0.405040	+	0.914299i	$0.367257\pi$
$198$	2.13661	−	0.534986i	0.151843	−	0.0380198i
$199$	−18.7826			−1.33146			−0.665731	−	0.746192i	$-0.731880\pi$
$199$	−18.7826			−1.33146			−0.665731	+	0.746192i	$0.731880\pi$
$200$	−0.500000	+	0.866025i	−0.0353553	+	0.0612372i
$201$	4.05080	−	9.55636i	0.285722	−	0.674054i
$202$	4.46838	+	7.73946i	0.314394	+	0.544547i
$203$	1.13290	+	1.96225i	0.0795143	+	0.137723i
$204$	1.70628	−	4.02534i	0.119464	−	0.281830i
$205$	−3.36710	+	5.83198i	−0.235168	+	0.407323i
$206$	0.209991			0.0146308
$207$	−10.8671	+	2.72101i	−0.755315	+	0.189123i
$208$	−1.73419			−0.120245
$209$	2.39500	−	4.14827i	0.165666	−	0.286942i
$210$	1.71903	−	0.211943i	0.118625	−	0.0146254i
$211$	−3.52420	−	6.10409i	−0.242616	−	0.420223i	0.718843	−	0.695173i	$-0.244672\pi$
$211$	−3.52420	−	6.10409i	−0.242616	−	0.420223i	−0.961459	+	0.274950i	$0.911339\pi$
$212$	−1.62920	−	2.82185i	−0.111894	−	0.193805i
$213$	−3.39871	−	4.50556i	−0.232876	−	0.308716i
$214$	−0.527909	+	0.914365i	−0.0360871	+	0.0625047i
$215$	1.00000			0.0681994
$216$	−4.84823	+	1.86940i	−0.329880	+	0.127197i
$217$	−4.00000			−0.271538
$218$	−9.12549	+	15.8058i	−0.618056	+	1.07050i
$219$	10.4811	+	13.8945i	0.708249	+	0.938902i
$220$	0.367095	+	0.635828i	0.0247496	+	0.0428675i
$221$	2.18872	+	3.79098i	0.147229	+	0.255009i
$222$	12.4774	−	1.53836i	0.837430	−	0.103248i
$223$	−3.83919	+	6.64967i	−0.257091	+	0.445295i	−0.965461	−	0.260546i	$-0.916097\pi$
$223$	−3.83919	+	6.64967i	−0.257091	+	0.445295i	0.708370	+	0.705841i	$0.249431\pi$
$224$	1.00000			0.0668153
$225$	−2.08613	−	2.15594i	−0.139075	−	0.143729i
$226$	−16.5726			−1.10239
$227$	10.4434	−	18.0885i	0.693153	−	1.20058i	−0.277646	−	0.960683i	$-0.589554\pi$
$227$	10.4434	−	18.0885i	0.693153	−	1.20058i	0.970799	−	0.239893i	$-0.0771123\pi$
$228$	−4.41016	+	10.4041i	−0.292070	+	0.689031i
$229$	−10.6776	−	18.4941i	−0.705595	−	1.22213i	−0.966476	−	0.256756i	$-0.917346\pi$
$229$	−10.6776	−	18.4941i	−0.705595	−	1.22213i	0.260881	−	0.965371i	$-0.415987\pi$
$230$	−1.86710	−	3.23390i	−0.123113	−	0.213237i
$231$	0.496291	−	1.17081i	0.0326535	−	0.0770339i
$232$	1.13290	−	1.96225i	0.0743788	−	0.128828i
$233$	−4.31421			−0.282633			−0.141317	−	0.989964i	$-0.545134\pi$
$233$	−4.31421			−0.282633			−0.141317	+	0.989964i	$0.545134\pi$
$234$	1.42903	−	5.00246i	0.0934184	−	0.327021i
$235$	9.58002			0.624931
$236$	−0.527909	+	0.914365i	−0.0343639	+	0.0595201i
$237$	−22.4307	+	2.76551i	−1.45703	+	0.179639i
$238$	−1.26210	−	2.18602i	−0.0818098	−	0.141699i
$239$	4.05582	+	7.02488i	0.262349	+	0.454402i	0.966866	−	0.255286i	$-0.0821695\pi$
$239$	4.05582	+	7.02488i	0.262349	+	0.454402i	−0.704517	+	0.709687i	$0.748836\pi$
$240$	−1.04307	−	1.38276i	−0.0673296	−	0.0892565i
$241$	11.1292	−	19.2763i	0.716894	−	1.24170i	−0.245330	−	0.969440i	$-0.578896\pi$
$241$	11.1292	−	19.2763i	0.716894	−	1.24170i	0.962224	−	0.272258i	$-0.0877704\pi$
$242$	−10.4610			−0.672456
$243$	−1.39741	−	15.5257i	−0.0896438	−	0.995974i
$244$	3.79001			0.242630
$245$	0.500000	−	0.866025i	0.0319438	−	0.0553283i
$246$	−7.02420	−	9.31175i	−0.447847	−	0.593695i
$247$	−5.65710	−	9.79839i	−0.359953	−	0.623457i
$248$	2.00000	+	3.46410i	0.127000	+	0.219971i
$249$	26.7826	−	3.30207i	1.69728	−	0.209260i
$250$	0.500000	−	0.866025i	0.0316228	−	0.0547723i
$251$	−22.4684			−1.41819			−0.709096	−	0.705112i	$-0.750897\pi$
$251$	−22.4684			−1.41819			−0.709096	+	0.705112i	$0.750897\pi$
$252$	−0.824030	+	2.88461i	−0.0519090	+	0.181713i
$253$	−2.74161			−0.172364
$254$	4.92291	−	8.52674i	0.308891	−	0.535015i
$255$	−1.70628	+	4.02534i	−0.106852	+	0.252076i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	1.75839	+	3.04562i	0.109685	+	0.189981i	0.915643	−	0.401993i	$-0.131682\pi$
$257$	1.75839	+	3.04562i	0.109685	+	0.189981i	−0.805957	+	0.591974i	$0.798349\pi$
$258$	−0.675970	+	1.59470i	−0.0420840	+	0.0992816i
$259$	3.62920	−	6.28595i	0.225507	−	0.390590i
$260$	1.73419			0.107550
$261$	4.72677	+	4.88494i	0.292580	+	0.302370i
$262$	−16.5726			−1.02386
$263$	−5.92291	+	10.2588i	−0.365222	+	0.632584i	−0.988812	−	0.149168i	$-0.952340\pi$
$263$	−5.92291	+	10.2588i	−0.365222	+	0.632584i	0.623589	+	0.781752i	$0.285674\pi$
$264$	−1.26210	+	0.155606i	−0.0776769	+	0.00957691i
$265$	1.62920	+	2.82185i	0.100081	+	0.173345i
$266$	3.26210	+	5.65012i	0.200012	+	0.346431i
$267$	5.26581	+	6.98071i	0.322262	+	0.427212i
$268$	−2.99629	+	5.18973i	−0.183028	+	0.317013i
$269$	−23.2436			−1.41718			−0.708592	−	0.705618i	$-0.750669\pi$
$269$	−23.2436			−1.41718			−0.708592	+	0.705618i	$0.750669\pi$
$270$	4.84823	−	1.86940i	0.295054	−	0.113768i
$271$	−23.3142			−1.41624			−0.708119	−	0.706093i	$-0.750456\pi$
$271$	−23.3142			−1.41624			−0.708119	+	0.706093i	$0.750456\pi$
$272$	−1.26210	+	2.18602i	−0.0765260	+	0.132547i
$273$	−1.80887	−	2.39796i	−0.109478	−	0.145131i
$274$	5.39500	+	9.34442i	0.325924	+	0.564517i
$275$	−0.367095	−	0.635828i	−0.0221367	−	0.0383419i
$276$	6.41920	−	0.791434i	0.386391	−	0.0476388i
$277$	−1.47580	+	2.55616i	−0.0886723	+	0.153585i	−0.906950	−	0.421238i	$-0.861596\pi$
$277$	−1.47580	+	2.55616i	−0.0886723	+	0.153585i	0.818278	+	0.574823i	$0.194929\pi$
$278$	−7.00000			−0.419832
$279$	−11.6406	+	2.91469i	−0.696907	+	0.174498i
$280$	−1.00000			−0.0597614
$281$	−13.0763	+	22.6488i	−0.780067	+	1.35112i	0.151835	+	0.988406i	$0.451482\pi$
$281$	−13.0763	+	22.6488i	−0.780067	+	1.35112i	−0.931902	+	0.362710i	$0.881852\pi$
$282$	−6.47580	+	15.2772i	−0.385628	+	0.909747i
$283$	−1.73419	−	3.00371i	−0.103087	−	0.178552i	0.809868	−	0.586612i	$-0.199539\pi$
$283$	−1.73419	−	3.00371i	−0.103087	−	0.178552i	−0.912955	+	0.408060i	$0.866205\pi$
$284$	1.62920	+	2.82185i	0.0966750	+	0.167446i
$285$	4.41016	−	10.4041i	0.261235	−	0.616288i
$286$	0.636614	−	1.10265i	0.0376438	−	0.0652009i
$287$	−6.73419			−0.397507
$288$	2.91016	−	0.728674i	0.171483	−	0.0429375i
$289$	−10.6284			−0.625201
$290$	−1.13290	+	1.96225i	−0.0665264	+	0.115227i
$291$	−0.805165	+	0.0992701i	−0.0471996	+	0.00581932i
$292$	−5.02420	−	8.70217i	−0.294019	−	0.509256i
$293$	−3.18130	−	5.51018i	−0.185854	−	0.321908i	0.758010	−	0.652243i	$-0.226172\pi$
$293$	−3.18130	−	5.51018i	−0.185854	−	0.321908i	−0.943864	+	0.330335i	$0.892838\pi$
$294$	1.04307	+	1.38276i	0.0608328	+	0.0806440i
$295$	0.527909	−	0.914365i	0.0307360	−	0.0532364i
$296$	−7.25839			−0.421885
$297$	0.591145	−	3.76889i	0.0343017	−	0.218693i
$298$	−8.93676			−0.517693
$299$	−3.23790	+	5.60821i	−0.187253	+	0.324331i
$300$	1.04307	+	1.38276i	0.0602214	+	0.0798335i
$301$	0.500000	+	0.866025i	0.0288195	+	0.0499169i
$302$	9.79001	+	16.9568i	0.563352	+	0.975754i
$303$	15.3626	−	1.89408i	0.882559	−	0.108812i
$304$	3.26210	−	5.65012i	0.187094	−	0.324057i
$305$	−3.79001			−0.217015
$306$	−5.26581	−	5.44201i	−0.301026	−	0.311099i
$307$	12.3142			0.702809			0.351404	−	0.936224i	$-0.385704\pi$
$307$	12.3142			0.702809			0.351404	+	0.936224i	$0.385704\pi$
$308$	−0.367095	+	0.635828i	−0.0209172	+	0.0362297i
$309$	0.141948	−	0.334873i	0.00807513	−	0.0190503i
$310$	−2.00000	−	3.46410i	−0.113592	−	0.196748i
$311$	−10.7268	−	18.5793i	−0.608259	−	1.05354i	−0.991527	−	0.129899i	$-0.958535\pi$
$311$	−10.7268	−	18.5793i	−0.608259	−	1.05354i	0.383268	−	0.923637i	$-0.374799\pi$
$312$	−1.17226	+	2.76551i	−0.0663662	+	0.156566i
$313$	7.73048	−	13.3896i	0.436953	−	0.756824i	−0.560500	−	0.828154i	$-0.689391\pi$
$313$	7.73048	−	13.3896i	0.436953	−	0.756824i	0.997453	+	0.0713301i	$0.0227244\pi$
$314$	14.6710			0.827930
$315$	0.824030	−	2.88461i	0.0464289	−	0.162529i
$316$	13.0484			0.734030
$317$	−10.8876	+	18.8579i	−0.611508	+	1.05916i	0.379479	+	0.925200i	$0.376103\pi$
$317$	−10.8876	+	18.8579i	−0.611508	+	1.05916i	−0.990986	+	0.133962i	$0.957230\pi$
$318$	−5.60129	+	0.690592i	−0.314105	+	0.0387265i
$319$	0.831768	+	1.44066i	0.0465701	+	0.0806618i
$320$	0.500000	+	0.866025i	0.0279508	+	0.0484123i
$321$	1.10129	+	1.45994i	0.0614678	+	0.0814858i
$322$	1.86710	−	3.23390i	0.104049	−	0.180218i
$323$	−16.4684			−0.916325
$324$	−0.296122	+	8.99513i	−0.0164512	+	0.499729i
$325$	−1.73419			−0.0961956
$326$	−4.97209	+	8.61191i	−0.275379	+	0.476970i
$327$	19.0370	+	25.2366i	1.05275	+	1.39559i
$328$	3.36710	+	5.83198i	0.185917	+	0.322017i
$329$	4.79001	+	8.29654i	0.264082	+	0.457403i
$330$	1.26210	−	0.155606i	0.0694763	−	0.00856585i
$331$	−11.7900	+	20.4209i	−0.648037	+	1.12243i	0.335554	+	0.942021i	$0.391077\pi$
$331$	−11.7900	+	20.4209i	−0.648037	+	1.12243i	−0.983591	+	0.180413i	$0.942257\pi$
$332$	−15.5800			−0.855065
$333$	5.98113	−	20.9376i	0.327764	−	1.14737i
$334$	−4.20999			−0.230360
$335$	2.99629	−	5.18973i	0.163705	−	0.283545i
$336$	0.675970	−	1.59470i	0.0368772	−	0.0869980i
$337$	−8.44340	−	14.6244i	−0.459941	−	0.796642i	0.539016	−	0.842296i	$-0.318796\pi$
$337$	−8.44340	−	14.6244i	−0.459941	−	0.796642i	−0.998957	+	0.0456536i	$0.985463\pi$
$338$	4.99629	+	8.65383i	0.271762	+	0.470706i
$339$	−11.2026	+	26.4283i	−0.608440	+	1.43539i
$340$	1.26210	−	2.18602i	0.0684470	−	0.118554i
$341$	−2.93676			−0.159035
$342$	13.6103	+	14.0658i	0.735962	+	0.760589i
$343$	1.00000			0.0539949
$344$	0.500000	−	0.866025i	0.0269582	−	0.0466930i
$345$	−6.41920	+	0.791434i	−0.345598	+	0.0426094i
$346$	6.00000	+	10.3923i	0.322562	+	0.558694i
$347$	3.94047	+	6.82510i	0.211536	+	0.366391i	0.952195	−	0.305490i	$-0.0988202\pi$
$347$	3.94047	+	6.82510i	0.211536	+	0.366391i	−0.740660	+	0.671880i	$0.765487\pi$
$348$	−2.36339	−	3.13306i	−0.126691	−	0.167950i
$349$	4.68501	−	8.11468i	0.250783	−	0.434369i	−0.712959	−	0.701206i	$-0.752645\pi$
$349$	4.68501	−	8.11468i	0.250783	−	0.434369i	0.963742	+	0.266837i	$0.0859786\pi$
$350$	1.00000			0.0534522
$351$	−7.01145	−	5.66038i	−0.374243	−	0.302129i
$352$	0.734191			0.0391325
$353$	14.2342	−	24.6543i	0.757610	−	1.31222i	−0.186457	−	0.982463i	$-0.559700\pi$
$353$	14.2342	−	24.6543i	0.757610	−	1.31222i	0.944067	−	0.329755i	$-0.106966\pi$
$354$	1.10129	+	1.45994i	0.0585327	+	0.0775949i
$355$	−1.62920	−	2.82185i	−0.0864687	−	0.149768i
$356$	−2.52420	−	4.37204i	−0.133782	−	0.231718i
$357$	−4.33919	+	0.534986i	−0.229654	+	0.0283144i
$358$	−9.49629	+	16.4481i	−0.501895	+	0.869307i
$359$	−14.3068			−0.755083			−0.377542	−	0.925993i	$-0.623231\pi$
$359$	−14.3068			−0.755083			−0.377542	+	0.925993i	$0.623231\pi$
$360$	−2.91016	+	0.728674i	−0.153379	+	0.0384045i
$361$	23.5652			1.24027
$362$	−8.31421	+	14.4006i	−0.436985	+	0.756880i
$363$	−7.07129	+	16.6821i	−0.371147	+	0.875583i
$364$	0.867095	+	1.50185i	0.0454482	+	0.0787185i
$365$	5.02420	+	8.70217i	0.262979	+	0.455492i
$366$	2.56193	−	6.04392i	0.133914	−	0.315921i
$367$	−12.9434	+	22.4186i	−0.675640	+	1.17024i	0.300641	+	0.953737i	$0.402799\pi$
$367$	−12.9434	+	22.4186i	−0.675640	+	1.17024i	−0.976281	+	0.216506i	$0.930534\pi$
$368$	−3.73419			−0.194658
$369$	−19.5976	+	4.90703i	−1.02021	+	0.255450i
$370$	7.25839			0.377346
$371$	−1.62920	+	2.82185i	−0.0845836	+	0.146503i
$372$	6.87614	−	0.847771i	0.356511	−	0.0439549i
$373$	−15.5242	−	26.8887i	−0.803813	−	1.39224i	−0.917090	−	0.398681i	$-0.869468\pi$
$373$	−15.5242	−	26.8887i	−0.803813	−	1.39224i	0.113277	−	0.993563i	$-0.463865\pi$
$374$	−0.926622	−	1.60496i	−0.0479145	−	0.0829903i
$375$	−1.04307	−	1.38276i	−0.0538637	−	0.0714052i
$376$	4.79001	−	8.29654i	0.247026	−	0.427861i
$377$	3.92935			0.202372
$378$	4.04307	+	3.26399i	0.207953	+	0.167881i
$379$	−30.8868			−1.58655			−0.793274	−	0.608864i	$-0.791625\pi$
$379$	−30.8868			−1.58655			−0.793274	+	0.608864i	$0.791625\pi$
$380$	−3.26210	+	5.65012i	−0.167342	+	0.289845i
$381$	−10.2698	−	13.6144i	−0.526140	−	0.697486i
$382$	−8.04840	−	13.9402i	−0.411792	−	0.713245i
$383$	−8.04840	−	13.9402i	−0.411254	−	0.712313i	0.583773	−	0.811917i	$-0.301576\pi$
$383$	−8.04840	−	13.9402i	−0.411254	−	0.712313i	−0.995027	+	0.0996040i	$0.968242\pi$
$384$	−1.71903	+	0.211943i	−0.0877241	+	0.0108157i
$385$	0.367095	−	0.635828i	0.0187089	−	0.0324048i
$386$	−16.7752			−0.853834
$387$	2.08613	+	2.15594i	0.106044	+	0.109592i
$388$	0.468382			0.0237785
$389$	−10.0558	+	17.4172i	−0.509850	+	0.883086i	0.490085	+	0.871675i	$0.336966\pi$
$389$	−10.0558	+	17.4172i	−0.509850	+	0.883086i	−0.999935	+	0.0114116i	$0.996367\pi$
$390$	1.17226	−	2.76551i	0.0593597	−	0.140037i
$391$	4.71292	+	8.16302i	0.238343	+	0.412822i
$392$	−0.500000	−	0.866025i	−0.0252538	−	0.0437409i
$393$	−11.2026	+	26.4283i	−0.565095	+	1.33313i
$394$	−5.68501	+	9.84673i	−0.286407	+	0.496071i
$395$	−13.0484			−0.656536
$396$	−0.604996	+	2.11785i	−0.0304022	+	0.106426i
$397$	−7.42584			−0.372692			−0.186346	−	0.982484i	$-0.559665\pi$
$397$	−7.42584			−0.372692			−0.186346	+	0.982484i	$0.559665\pi$
$398$	9.39130	−	16.2662i	0.470743	−	0.815351i
$399$	11.2153	−	1.38276i	0.561469	−	0.0692244i
$400$	−0.500000	−	0.866025i	−0.0250000	−	0.0433013i
$401$	17.0800	+	29.5835i	0.852935	+	1.47733i	0.878547	+	0.477655i	$0.158513\pi$
$401$	17.0800	+	29.5835i	0.852935	+	1.47733i	−0.0256119	+	0.999672i	$0.508153\pi$
$402$	6.25065	+	8.28628i	0.311754	+	0.413282i
$403$	−3.46838	+	6.00741i	−0.172772	+	0.299251i
$404$	−8.93676			−0.444621
$405$	0.296122	−	8.99513i	0.0147144	−	0.446971i
$406$	−2.26581			−0.112450
$407$	2.66452	−	4.61509i	0.132075	−	0.228761i
$408$	2.63290	+	3.49035i	0.130348	+	0.172798i
$409$	−4.21292	−	7.29699i	−0.208316	−	0.360813i	0.742868	−	0.669437i	$-0.233465\pi$
$409$	−4.21292	−	7.29699i	−0.208316	−	0.360813i	−0.951184	+	0.308624i	$0.900131\pi$
$410$	−3.36710	−	5.83198i	−0.166289	−	0.288021i
$411$	18.5484	−	2.28686i	0.914925	−	0.112803i
$412$	−0.104996	+	0.181858i	−0.00517277	+	0.00895949i
$413$	1.05582			0.0519534
$414$	3.07709	−	10.7717i	0.151231	−	0.529399i
$415$	15.5800			0.764793
$416$	0.867095	−	1.50185i	0.0425129	−	0.0736344i
$417$	−4.73179	+	11.1629i	−0.231717	+	0.546649i
$418$	2.39500	+	4.14827i	0.117143	+	0.202898i
$419$	−12.8179	−	22.2013i	−0.626196	−	1.08460i	−0.988308	−	0.152469i	$-0.951278\pi$
$419$	−12.8179	−	22.2013i	−0.626196	−	1.08460i	0.362112	−	0.932135i	$-0.382056\pi$
$420$	−0.675970	+	1.59470i	−0.0329839	+	0.0778133i
$421$	12.9713	−	22.4670i	0.632183	−	1.09497i	−0.354921	−	0.934896i	$-0.615492\pi$
$421$	12.9713	−	22.4670i	0.632183	−	1.09497i	0.987105	−	0.160077i	$-0.0511743\pi$
$422$	7.04840			0.343111
$423$	19.9852	+	20.6539i	0.971712	+	1.00423i
$424$	3.25839			0.158241
$425$	−1.26210	+	2.18602i	−0.0612208	+	0.106038i
$426$	5.60129	−	0.690592i	0.271383	−	0.0334593i
$427$	−1.89500	−	3.28224i	−0.0917057	−	0.158839i
$428$	−0.527909	−	0.914365i	−0.0255174	−	0.0441975i
$429$	−1.32806	−	1.76056i	−0.0641193	−	0.0850008i
$430$	−0.500000	+	0.866025i	−0.0241121	+	0.0417635i
$431$	−14.6284			−0.704626			−0.352313	−	0.935882i	$-0.614605\pi$
$431$	−14.6284			−0.704626			−0.352313	+	0.935882i	$0.614605\pi$
$432$	0.805165	−	5.13339i	0.0387385	−	0.246980i
$433$	29.0000			1.39365			0.696826	−	0.717241i	$-0.254595\pi$
$433$	29.0000			1.39365			0.696826	+	0.717241i	$0.254595\pi$
$434$	2.00000	−	3.46410i	0.0960031	−	0.166282i
$435$	2.36339	+	3.13306i	0.113316	+	0.150219i
$436$	−9.12549	−	15.8058i	−0.437032	−	0.756961i
$437$	−12.1813	−	21.0986i	−0.582711	−	1.00928i
$438$	−17.2735	+	2.12968i	−0.825362	+	0.101760i
$439$	5.65710	−	9.79839i	0.269999	−	0.467652i	−0.698862	−	0.715256i	$-0.746310\pi$
$439$	5.65710	−	9.79839i	0.269999	−	0.467652i	0.968861	+	0.247604i	$0.0796433\pi$
$440$	−0.734191			−0.0350012
$441$	2.91016	−	0.728674i	0.138579	−	0.0346987i
$442$	−4.37744			−0.208214
$443$	12.9610	−	22.4490i	0.615794	−	1.06659i	−0.374451	−	0.927247i	$-0.622169\pi$
$443$	12.9610	−	22.4490i	0.615794	−	1.06659i	0.990245	−	0.139340i	$-0.0444980\pi$
$444$	−4.90645	+	11.5749i	−0.232850	+	0.549323i
$445$	2.52420	+	4.37204i	0.119659	+	0.207255i
$446$	−3.83919	−	6.64967i	−0.181791	−	0.314871i
$447$	−6.04098	+	14.2514i	−0.285729	+	0.674070i
$448$	−0.500000	+	0.866025i	−0.0236228	+	0.0409159i
$449$	11.5874			0.546845			0.273422	−	0.961894i	$-0.411844\pi$
$449$	11.5874			0.546845			0.273422	+	0.961894i	$0.411844\pi$
$450$	2.91016	−	0.728674i	0.137186	−	0.0343500i
$451$	−4.94418			−0.232812
$452$	8.28630	−	14.3523i	0.389755	−	0.675075i
$453$	33.6587	−	4.14984i	1.58143	−	0.194977i
$454$	10.4434	+	18.0885i	0.490133	+	0.848936i
$455$	−0.867095	−	1.50185i	−0.0406501	−	0.0704080i
$456$	−6.80516	−	9.02138i	−0.318681	−	0.422465i
$457$	4.89130	−	8.47197i	0.228805	−	0.396302i	−0.728649	−	0.684887i	$-0.759851\pi$
$457$	4.89130	−	8.47197i	0.228805	−	0.396302i	0.957454	+	0.288585i	$0.0931848\pi$
$458$	21.3552			0.997862
$459$	−12.2379	+	4.71875i	−0.571216	+	0.220252i
$460$	3.73419			0.174108
$461$	15.0976	−	26.1498i	0.703164	−	1.21792i	−0.264186	−	0.964472i	$-0.585103\pi$
$461$	15.0976	−	26.1498i	0.703164	−	1.21792i	0.967350	−	0.253444i	$-0.0815635\pi$
$462$	0.765809	+	1.01521i	0.0356287	+	0.0472317i
$463$	−12.0484	−	20.8684i	−0.559937	−	0.969839i	−0.997501	−	0.0706516i	$-0.977492\pi$
$463$	−12.0484	−	20.8684i	−0.559937	−	0.969839i	0.437564	−	0.899187i	$-0.355841\pi$
$464$	1.13290	+	1.96225i	0.0525938	+	0.0910951i
$465$	−6.87614	+	0.847771i	−0.318873	+	0.0393144i
$466$	2.15710	−	3.73621i	0.0999259	−	0.173077i
$467$	41.1803			1.90560			0.952799	−	0.303602i	$-0.0981893\pi$
$467$	41.1803			1.90560			0.952799	+	0.303602i	$0.0981893\pi$
$468$	3.61775	+	3.73881i	0.167230	+	0.172826i
$469$	5.99258			0.276712
$470$	−4.79001	+	8.29654i	−0.220947	+	0.382691i
$471$	9.91712	−	23.3958i	0.456957	−	1.07802i
$472$	−0.527909	−	0.914365i	−0.0242990	−	0.0420871i
$473$	0.367095	+	0.635828i	0.0168791	+	0.0292354i
$474$	8.82032	−	20.8083i	0.405131	−	0.955755i
$475$	3.26210	−	5.65012i	0.149675	−	0.259245i
$476$	2.52420			0.115696
$477$	−2.68501	+	9.39919i	−0.122938	+	0.430359i
$478$	−8.11164			−0.371018
$479$	−18.5939	+	32.2055i	−0.849576	+	1.47151i	0.0320121	+	0.999487i	$0.489809\pi$
$479$	−18.5939	+	32.2055i	−0.849576	+	1.47151i	−0.881588	+	0.472020i	$0.843525\pi$
$480$	1.71903	−	0.211943i	0.0784628	−	0.00967382i
$481$	−6.29372	−	10.9010i	−0.286969	−	0.497045i
$482$	11.1292	+	19.2763i	0.506921	+	0.878013i
$483$	−3.89500	−	5.16348i	−0.177229	−	0.234946i
$484$	5.23048	−	9.05946i	0.237749	−	0.411794i
$485$	−0.468382			−0.0212681
$486$	14.1444	+	6.55266i	0.641601	+	0.297235i
$487$	−4.51678			−0.204675			−0.102337	−	0.994750i	$-0.532632\pi$
$487$	−4.51678			−0.204675			−0.102337	+	0.994750i	$0.532632\pi$
$488$	−1.89500	+	3.28224i	−0.0857828	+	0.148580i
$489$	10.3724	+	13.7504i	0.469057	+	0.621814i
$490$	0.500000	+	0.866025i	0.0225877	+	0.0391230i
$491$	−5.17759	−	8.96786i	−0.233662	−	0.404714i	0.725221	−	0.688516i	$-0.241737\pi$
$491$	−5.17759	−	8.96786i	−0.233662	−	0.404714i	−0.958883	+	0.283802i	$0.908404\pi$
$492$	11.5763	−	1.42726i	0.521900	−	0.0643460i
$493$	2.85968	−	4.95311i	0.128793	−	0.223077i
$494$	11.3142			0.509050
$495$	0.604996	−	2.11785i	0.0271925	−	0.0951905i
$496$	−4.00000			−0.179605
$497$	1.62920	−	2.82185i	0.0730794	−	0.126577i
$498$	−10.5316	+	24.8454i	−0.471933	+	1.11335i
$499$	−14.3597	−	24.8717i	−0.642827	−	1.11341i	−0.984799	−	0.173699i	$-0.944428\pi$
$499$	−14.3597	−	24.8717i	−0.642827	−	1.11341i	0.341971	−	0.939710i	$-0.388905\pi$
$500$	0.500000	+	0.866025i	0.0223607	+	0.0387298i
$501$	−2.84583	+	6.71367i	−0.127142	+	0.299945i
$502$	11.2342	−	19.4582i	0.501406	−	0.868462i
$503$	−15.5800			−0.694679			−0.347339	−	0.937740i	$-0.612915\pi$
$503$	−15.5800			−0.694679			−0.347339	+	0.937740i	$0.612915\pi$
$504$	−2.08613	−	2.15594i	−0.0929236	−	0.0960330i
$505$	8.93676			0.397681
$506$	1.37080	−	2.37430i	0.0609397	−	0.105551i
$507$	17.1776	−	2.11785i	0.762884	−	0.0940572i
$508$	4.92291	+	8.52674i	0.218419	+	0.378313i
$509$	−1.30757	−	2.26478i	−0.0579570	−	0.100384i	0.835591	−	0.549352i	$-0.185125\pi$
$509$	−1.30757	−	2.26478i	−0.0579570	−	0.100384i	−0.893548	+	0.448967i	$0.851792\pi$
$510$	−2.63290	−	3.49035i	−0.116587	−	0.154555i
$511$	−5.02420	+	8.70217i	−0.222258	+	0.384961i
$512$	1.00000			0.0441942
$513$	31.6308	−	12.1964i	1.39653	−	0.538482i
$514$	−3.51678			−0.155119
$515$	0.104996	−	0.181858i	0.00462666	−	0.00801362i
$516$	−1.04307	−	1.38276i	−0.0459184	−	0.0608725i
$517$	3.51678	+	6.09124i	0.154668	+	0.267893i
$518$	3.62920	+	6.28595i	0.159458	+	0.276189i
$519$	20.6284	−	2.54331i	0.905487	−	0.111639i
$520$	−0.867095	+	1.50185i	−0.0380247	+	0.0658606i
$521$	−22.4817			−0.984939			−0.492470	−	0.870330i	$-0.663906\pi$
$521$	−22.4817			−0.984939			−0.492470	+	0.870330i	$0.663906\pi$
$522$	−6.59387	+	1.65104i	−0.288606	+	0.0722639i
$523$	−4.16745			−0.182230			−0.0911150	−	0.995840i	$-0.529043\pi$
$523$	−4.16745			−0.182230			−0.0911150	+	0.995840i	$0.529043\pi$
$524$	8.28630	−	14.3523i	0.361989	−	0.626983i
$525$	0.675970	−	1.59470i	0.0295017	−	0.0695984i
$526$	−5.92291	−	10.2588i	−0.258251	−	0.447304i
$527$	5.04840	+	8.74408i	0.219912	+	0.380898i
$528$	0.496291	−	1.17081i	0.0215983	−	0.0509531i
$529$	4.52791	−	7.84257i	0.196866	−	0.340981i
$530$	−3.25839			−0.141535
$531$	3.07260	−	0.769346i	0.133339	−	0.0333868i
$532$	−6.52420			−0.282860
$533$	−5.83919	+	10.1138i	−0.252923	+	0.438076i
$534$	−8.67837	+	1.06997i	−0.375550	+	0.0463022i
$535$	0.527909	+	0.914365i	0.0228235	+	0.0395314i
$536$	−2.99629	−	5.18973i	−0.129420	−	0.224162i
$537$	19.8105	+	26.2621i	0.854886	+	1.13329i
$538$	11.6218	−	20.1295i	0.501050	−	0.867845i
$539$	0.734191			0.0316238
$540$	−0.805165	+	5.13339i	−0.0346488	+	0.220906i
$541$	32.5168			1.39801			0.699003	−	0.715119i	$-0.253627\pi$
$541$	32.5168			1.39801			0.699003	+	0.715119i	$0.253627\pi$
$542$	11.6571	−	20.1907i	0.500715	−	0.867265i
$543$	17.3445	+	22.9930i	0.744325	+	0.986726i
$544$	−1.26210	−	2.18602i	−0.0541121	−	0.0937249i
$545$	9.12549	+	15.8058i	0.390893	+	0.677046i
$546$	2.98113	−	0.367549i	0.127581	−	0.0157296i
$547$	−10.8700	+	18.8274i	−0.464769	+	0.805003i	−0.999191	−	0.0402145i	$-0.987196\pi$
$547$	−10.8700	+	18.8274i	−0.464769	+	0.805003i	0.534422	+	0.845218i	$0.320529\pi$
$548$	−10.7900			−0.460926
$549$	−7.90645	−	8.17102i	−0.337439	−	0.348730i
$550$	0.734191			0.0313060
$551$	−7.39130	+	12.8021i	−0.314880	+	0.545388i
$552$	−2.52420	+	5.95491i	−0.107437	+	0.253458i
$553$	−6.52420	−	11.3002i	−0.277437	−	0.480535i
$554$	−1.47580	−	2.55616i	−0.0627008	−	0.108601i
$555$	4.90645	−	11.5749i	0.208267	−	0.491329i
$556$	3.50000	−	6.06218i	0.148433	−	0.257094i
$557$	9.58002			0.405918			0.202959	−	0.979187i	$-0.434944\pi$
$557$	9.58002			0.405918			0.202959	+	0.979187i	$0.434944\pi$
$558$	3.29612	−	11.5384i	0.139536	−	0.488461i
$559$	1.73419			0.0733485
$560$	0.500000	−	0.866025i	0.0211289	−	0.0365963i
$561$	−3.18579	+	0.392782i	−0.134504	+	0.0165833i
$562$	−13.0763	−	22.6488i	−0.551591	−	0.955383i
$563$	10.8355	+	18.7676i	0.456661	+	0.790960i	0.998782	−	0.0493404i	$-0.0157119\pi$
$563$	10.8355	+	18.7676i	0.456661	+	0.790960i	−0.542121	+	0.840300i	$0.682379\pi$
$564$	−9.99258	−	13.2468i	−0.420764	−	0.557792i
$565$	−8.28630	+	14.3523i	−0.348607	+	0.603805i
$566$	3.46838			0.145787
$567$	7.93807	−	4.24111i	0.333368	−	0.178110i
$568$	−3.25839			−0.136719
$569$	−3.52791	+	6.11052i	−0.147898	+	0.256166i	−0.930450	−	0.366418i	$-0.880584\pi$
$569$	−3.52791	+	6.11052i	−0.147898	+	0.256166i	0.782553	+	0.622584i	$0.213917\pi$
$570$	6.80516	+	9.02138i	0.285037	+	0.377864i
$571$	14.1292	+	24.4725i	0.591288	+	1.02414i	0.994059	+	0.108841i	$0.0347138\pi$
$571$	14.1292	+	24.4725i	0.591288	+	1.02414i	−0.402771	+	0.915301i	$0.631953\pi$
$572$	0.636614	+	1.10265i	0.0266182	+	0.0461040i
$573$	−27.6710	+	3.41160i	−1.15597	+	0.142522i
$574$	3.36710	−	5.83198i	0.140540	−	0.243422i
$575$	−3.73419			−0.155727
$576$	−0.824030	+	2.88461i	−0.0343346	+	0.120192i
$577$	−17.5726			−0.731557			−0.365778	−	0.930702i	$-0.619197\pi$
$577$	−17.5726			−0.731557			−0.365778	+	0.930702i	$0.619197\pi$
$578$	5.31421	−	9.20448i	0.221042	−	0.382856i
$579$	−11.3395	+	26.7514i	−0.471254	+	1.11175i
$580$	−1.13290	−	1.96225i	−0.0470413	−	0.0814779i
$581$	7.79001	+	13.4927i	0.323184	+	0.559771i
$582$	0.316612	−	0.746928i	0.0131240	−	0.0309612i
$583$	−1.19614	+	2.07178i	−0.0495391	+	0.0858042i
$584$	10.0484			0.415806
$585$	−3.61775	−	3.73881i	−0.149575	−	0.154581i
$586$	6.36261			0.262837
$587$	19.6813	−	34.0890i	0.812334	−	1.40700i	−0.0988919	−	0.995098i	$-0.531530\pi$
$587$	19.6813	−	34.0890i	0.812334	−	1.40700i	0.911226	−	0.411906i	$-0.135137\pi$
$588$	−1.71903	+	0.211943i	−0.0708918	+	0.00874037i
$589$	−13.0484	−	22.6005i	−0.537650	−	0.931237i
$590$	0.527909	+	0.914365i	0.0217337	+	0.0376438i
$591$	11.8597	+	15.7220i	0.487842	+	0.646716i
$592$	3.62920	−	6.28595i	0.149159	−	0.258351i
$593$	15.1042			0.620256			0.310128	−	0.950695i	$-0.399628\pi$
$593$	15.1042			0.620256			0.310128	+	0.950695i	$0.399628\pi$
$594$	2.96838	+	2.39639i	0.121794	+	0.0983251i
$595$	−2.52420			−0.103482
$596$	4.46838	−	7.73946i	0.183032	−	0.317021i
$597$	−19.5915	−	25.9717i	−0.801825	−	1.06295i
$598$	−3.23790	−	5.60821i	−0.132408	−	0.229337i
$599$	−12.4758	−	21.6087i	−0.509747	−	0.882908i	−0.999936	−	0.0112921i	$-0.996406\pi$
$599$	−12.4758	−	21.6087i	−0.509747	−	0.882908i	0.490189	−	0.871616i	$-0.336928\pi$
$600$	−1.71903	+	0.211943i	−0.0701793	+	0.00865252i
$601$	−12.5697	+	21.7713i	−0.512727	+	0.888070i	0.487164	+	0.873311i	$0.338032\pi$
$601$	−12.5697	+	21.7713i	−0.512727	+	0.888070i	−0.999891	+	0.0147593i	$0.995302\pi$
$602$	−1.00000			−0.0407570
$603$	17.4394	−	4.36664i	0.710186	−	0.177823i
$604$	−19.5800			−0.796700
$605$	−5.23048	+	9.05946i	−0.212649	+	0.368319i
$606$	−6.04098	+	14.2514i	−0.245398	+	0.578926i
$607$	20.5168	+	35.5361i	0.832750	+	1.44237i	0.895849	+	0.444359i	$0.146568\pi$
$607$	20.5168	+	35.5361i	0.832750	+	1.44237i	−0.0630984	+	0.998007i	$0.520098\pi$
$608$	3.26210	+	5.65012i	0.132296	+	0.229143i
$609$	−1.53162	+	3.61328i	−0.0620643	+	0.146418i
$610$	1.89500	−	3.28224i	0.0767265	−	0.132894i
$611$	16.6136			0.672113
$612$	7.34583	−	1.83932i	0.296937	−	0.0743500i
$613$	9.59485			0.387533			0.193766	−	0.981048i	$-0.437930\pi$
$613$	9.59485			0.387533			0.193766	+	0.981048i	$0.437930\pi$
$614$	−6.15710	+	10.6644i	−0.248480	+	0.430381i
$615$	−11.5763	+	1.42726i	−0.466802	+	0.0575528i
$616$	−0.367095	−	0.635828i	−0.0147907	−	0.0256182i
$617$	14.9118	+	25.8280i	0.600326	+	1.03979i	0.992772	+	0.120020i	$0.0382958\pi$
$617$	14.9118	+	25.8280i	0.600326	+	1.03979i	−0.392446	+	0.919775i	$0.628371\pi$
$618$	0.219035	+	0.290367i	0.00881087	+	0.0116803i
$619$	−7.44418	+	12.8937i	−0.299207	+	0.518242i	−0.975955	−	0.217973i	$-0.930055\pi$
$619$	−7.44418	+	12.8937i	−0.299207	+	0.518242i	0.676748	+	0.736215i	$0.263389\pi$
$620$	4.00000			0.160644
$621$	−15.0976	−	12.1884i	−0.605845	−	0.489102i
$622$	21.4535			0.860209
$623$	−2.52420	+	4.37204i	−0.101130	+	0.175162i
$624$	−1.80887	−	2.39796i	−0.0724129	−	0.0959954i
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$	7.73048	+	13.3896i	0.308972	+	0.535156i
$627$	8.23419	−	1.01521i	0.328842	−	0.0405435i
$628$	−7.33548	+	12.7054i	−0.292717	+	0.507001i
$629$	−18.3216			−0.730531
$630$	2.08613	+	2.15594i	0.0831134	+	0.0858946i
$631$	6.85324			0.272823			0.136412	−	0.990652i	$-0.456443\pi$
$631$	6.85324			0.272823			0.136412	+	0.990652i	$0.456443\pi$
$632$	−6.52420	+	11.3002i	−0.259519	+	0.449500i
$633$	4.76450	−	11.2401i	0.189372	−	0.446753i
$634$	−10.8876	−	18.8579i	−0.432401	−	0.748941i
$635$	−4.92291	−	8.52674i	−0.195360	−	0.338373i
$636$	2.20257	−	5.19615i	0.0873377	−	0.206041i
$637$	0.867095	−	1.50185i	0.0343556	−	0.0595056i
$638$	−1.66354			−0.0658600
$639$	2.68501	−	9.39919i	0.106217	−	0.371826i
$640$	−1.00000			−0.0395285
$641$	−3.05211	+	5.28641i	−0.120551	+	0.208801i	−0.919985	−	0.391953i	$-0.871799\pi$
$641$	−3.05211	+	5.28641i	−0.120551	+	0.208801i	0.799434	+	0.600754i	$0.205133\pi$
$642$	−1.81499	+	0.223773i	−0.0716318	+	0.00883161i
$643$	−23.1850	−	40.1576i	−0.914328	−	1.58366i	−0.807883	−	0.589343i	$-0.799387\pi$
$643$	−23.1850	−	40.1576i	−0.914328	−	1.58366i	−0.106445	−	0.994319i	$-0.533947\pi$
$644$	1.86710	+	3.23390i	0.0735739	+	0.127434i
$645$	1.04307	+	1.38276i	0.0410706	+	0.0544460i
$646$	8.23419	−	14.2620i	0.323970	−	0.561132i
$647$	38.1803			1.50102			0.750512	−	0.660857i	$-0.229807\pi$
$647$	38.1803			1.50102			0.750512	+	0.660857i	$0.229807\pi$
$648$	−7.64195	−	4.75401i	−0.300204	−	0.186755i
$649$	0.775172			0.0304282
$650$	0.867095	−	1.50185i	0.0340103	−	0.0589075i
$651$	−4.17226	−	5.53103i	−0.163524	−	0.216778i
$652$	−4.97209	−	8.61191i	−0.194722	−	0.337269i
$653$	−0.888365	−	1.53869i	−0.0347644	−	0.0602137i	0.848120	−	0.529805i	$-0.177735\pi$
$653$	−0.888365	−	1.53869i	−0.0347644	−	0.0602137i	−0.882884	+	0.469591i	$0.844401\pi$
$654$	−31.3741	+	3.86816i	−1.22682	+	0.151257i
$655$	−8.28630	+	14.3523i	−0.323773	+	0.560790i
$656$	−6.73419			−0.262926
$657$	−8.28019	+	28.9857i	−0.323041	+	1.13084i
$658$	−9.58002			−0.373468
$659$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$659$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$660$	−0.496291	+	1.17081i	−0.0193181	+	0.0455739i
$661$	20.3626	+	35.2691i	0.792014	+	1.37181i	0.924718	+	0.380652i	$0.124300\pi$
$661$	20.3626	+	35.2691i	0.792014	+	1.37181i	−0.132705	+	0.991156i	$0.542366\pi$
$662$	−11.7900	−	20.4209i	−0.458232	−	0.793681i
$663$	−2.95902	+	6.98071i	−0.114919	+	0.271108i
$664$	7.79001	−	13.4927i	0.302311	−	0.523618i
$665$	6.52420			0.252998
$666$	15.1419	+	15.6486i	0.586739	+	0.606372i
$667$	8.46096			0.327610
$668$	2.10500	−	3.64596i	0.0814447	−	0.141066i
$669$	−13.1994	+	1.62738i	−0.510318	+	0.0629180i
$670$	2.99629	+	5.18973i	0.115757	+	0.200497i
$671$	−1.39130	−	2.40979i	−0.0537104	−	0.0930291i
$672$	1.04307	+	1.38276i	0.0402371	+	0.0533410i
$673$	−20.7900	+	36.0094i	−0.801396	+	1.38806i	0.117301	+	0.993096i	$0.462576\pi$
$673$	−20.7900	+	36.0094i	−0.801396	+	1.38806i	−0.918697	+	0.394962i	$0.870758\pi$
$674$	16.8868			0.650456
$675$	0.805165	−	5.13339i	0.0309908	−	0.197584i
$676$	−9.99258			−0.384330
$677$	8.44711	−	14.6308i	0.324649	−	0.562308i	−0.656792	−	0.754072i	$-0.728087\pi$
$677$	8.44711	−	14.6308i	0.324649	−	0.562308i	0.981441	+	0.191763i	$0.0614205\pi$
$678$	−17.2863	−	22.9159i	−0.663876	−	0.880079i
$679$	−0.234191	−	0.405631i	−0.00898743	−	0.0155667i
$680$	1.26210	+	2.18602i	0.0483993	+	0.0838301i
$681$	35.9051	−	4.42681i	1.37589	−	0.169636i
$682$	1.46838	−	2.54331i	0.0562273	−	0.0973885i
$683$	−23.6694			−0.905684			−0.452842	−	0.891591i	$-0.649590\pi$
$683$	−23.6694			−0.905684			−0.452842	+	0.891591i	$0.649590\pi$
$684$	−18.9865	+	4.75401i	−0.725966	+	0.181774i
$685$	10.7900			0.412265
$686$	−0.500000	+	0.866025i	−0.0190901	+	0.0330650i
$687$	14.4355	−	34.0551i	0.550747	−	1.29928i
$688$	0.500000	+	0.866025i	0.0190623	+	0.0330169i
$689$	2.82534	+	4.89363i	0.107637	+	0.186432i
$690$	2.52420	−	5.95491i	0.0960946	−	0.226700i
$691$	−1.58002	+	2.73667i	−0.0601067	+	0.104108i	−0.894513	−	0.447042i	$-0.852477\pi$
$691$	−1.58002	+	2.73667i	−0.0601067	+	0.104108i	0.834406	+	0.551150i	$0.185811\pi$
$692$	−12.0000			−0.456172
$693$	2.13661	−	0.534986i	0.0811632	−	0.0203224i
$694$	−7.88095			−0.299157
$695$	−3.50000	+	6.06218i	−0.132763	+	0.229952i
$696$	3.89500	−	0.480222i	0.147640	−	0.0182028i
$697$	8.49922	+	14.7211i	0.321931	+	0.557601i
$698$	4.68501	+	8.11468i	0.177330	+	0.307145i
$699$	−4.50000	−	5.96550i	−0.170206	−	0.225636i
$700$	−0.500000	+	0.866025i	−0.0188982	+	0.0327327i
$701$	−47.4110			−1.79069			−0.895345	−	0.445374i	$-0.853071\pi$
$701$	−47.4110			−1.79069			−0.895345	+	0.445374i	$0.853071\pi$
$702$	8.40776	−	3.24190i	0.317330	−	0.122358i
$703$	47.3552			1.78603
$704$	−0.367095	+	0.635828i	−0.0138354	+	0.0239637i
$705$	9.99258	+	13.2468i	0.376342	+	0.498904i
$706$	14.2342	+	24.6543i	0.535711	+	0.927878i
$707$	4.46838	+	7.73946i	0.168051	+	0.291073i
$708$	−1.81499	+	0.223773i	−0.0682114	+	0.00840990i
$709$	−23.3913	+	40.5149i	−0.878479	+	1.52157i	−0.0254681	+	0.999676i	$0.508108\pi$
$709$	−23.3913	+	40.5149i	−0.878479	+	1.52157i	−0.853010	+	0.521894i	$0.825226\pi$
$710$	3.25839			0.122285
$711$	−27.2207	−	28.1315i	−1.02085	−	1.05501i
$712$	5.04840			0.189197
$713$	−7.46838	+	12.9356i	−0.279693	+	0.484443i
$714$	1.70628	−	4.02534i	0.0638560	−	0.150645i
$715$	−0.636614	−	1.10265i	−0.0238080	−	0.0412367i
$716$	−9.49629	−	16.4481i	−0.354893	−	0.614693i
$717$	−5.48322	+	12.9356i	−0.204775	+	0.483089i
$718$	7.15339	−	12.3900i	0.266962	−	0.462392i
$719$	−24.8794			−0.927845			−0.463922	−	0.885876i	$-0.653558\pi$
$719$	−24.8794			−0.927845			−0.463922	+	0.885876i	$0.653558\pi$
$720$	0.824030	−	2.88461i	0.0307098	−	0.107503i
$721$	0.209991			0.00782049
$722$	−11.7826	+	20.4080i	−0.438503	+	0.759509i
$723$	38.2629	−	4.71750i	1.42301	−	0.175446i
$724$	−8.31421	−	14.4006i	−0.308995	−	0.535195i
$725$	1.13290	+	1.96225i	0.0420750	+	0.0728761i
$726$	−10.9115	−	14.4650i	−0.404962	−	0.536845i
$727$	3.62920	−	6.28595i	0.134599	−	0.233133i	−0.790845	−	0.612017i	$-0.790359\pi$
$727$	3.62920	−	6.28595i	0.134599	−	0.233133i	0.925444	+	0.378884i	$0.123692\pi$
$728$	−1.73419			−0.0642734
$729$	20.0107	−	18.1266i	0.741136	−	0.671355i
$730$	−10.0484			−0.371908
$731$	1.26210	−	2.18602i	0.0466804	−	0.0808529i
$732$	3.95323	+	5.24066i	0.146115	+	0.193700i
$733$	−23.9081	−	41.4100i	−0.883065	−	1.52951i	−0.847916	−	0.530131i	$-0.822143\pi$
$733$	−23.9081	−	41.4100i	−0.883065	−	1.52951i	−0.0351494	−	0.999382i	$-0.511191\pi$
$734$	−12.9434	−	22.4186i	−0.477750	−	0.827487i
$735$	1.71903	−	0.211943i	0.0634076	−	0.00781762i
$736$	1.86710	−	3.23390i	0.0688221	−	0.119203i
$737$	4.39970			0.162065
$738$	5.54918	−	19.4255i	0.204268	−	0.715063i
$739$	40.4110			1.48654			0.743271	−	0.668990i	$-0.233273\pi$
$739$	40.4110			1.48654			0.743271	+	0.668990i	$0.233273\pi$
$740$	−3.62920	+	6.28595i	−0.133412	+	0.231076i
$741$	7.64806	−	18.0428i	0.280959	−	0.662817i
$742$	−1.62920	−	2.82185i	−0.0598096	−	0.103593i
$743$	−4.46838	−	7.73946i	−0.163929	−	0.283933i	0.772345	−	0.635203i	$-0.219083\pi$
$743$	−4.46838	−	7.73946i	−0.163929	−	0.283933i	−0.936274	+	0.351269i	$0.885750\pi$
$744$	−2.70388	+	6.37880i	−0.0991290	+	0.233858i
$745$	−4.46838	+	7.73946i	−0.163709	+	0.283552i
$746$	31.0484			1.13676
$747$	32.5019	+	33.5895i	1.18918	+	1.22898i
$748$	1.85324			0.0677613
$749$	−0.527909	+	0.914365i	−0.0192894	+	0.0334102i
$750$	1.71903	−	0.211943i	0.0627703	−	0.00773905i
$751$	−0.517560	−	0.896440i	−0.0188860	−	0.0327116i	0.856428	−	0.516267i	$-0.172679\pi$
$751$	−0.517560	−	0.896440i	−0.0188860	−	0.0327116i	−0.875314	+	0.483555i	$0.839345\pi$
$752$	4.79001	+	8.29654i	0.174674	+	0.302544i
$753$	−23.4360	−	31.0683i	−0.854055	−	1.13219i
$754$	−1.96467	+	3.40291i	−0.0715492	+	0.123927i
$755$	19.5800			0.712590
$756$	−4.84823	+	1.86940i	−0.176328	+	0.0679895i
$757$	3.27323			0.118967			0.0594837	−	0.998229i	$-0.481055\pi$
$757$	3.27323			0.118967			0.0594837	+	0.998229i	$0.481055\pi$
$758$	15.4434	−	26.7488i	0.560930	−	0.971559i
$759$	−2.85968	−	3.79098i	−0.103800	−	0.137604i
$760$	−3.26210	−	5.65012i	−0.118329	−	0.204951i
$761$	11.4610	+	19.8510i	0.415460	+	0.719597i	0.995477	−	0.0950072i	$-0.0302874\pi$
$761$	11.4610	+	19.8510i	0.415460	+	0.719597i	−0.580017	+	0.814604i	$0.696954\pi$
$762$	16.9253	−	2.08675i	0.613140	−	0.0755950i
$763$	−9.12549	+	15.8058i	−0.330365	+	0.572209i
$764$	16.0968			0.582362
$765$	−7.34583	+	1.83932i	−0.265589	+	0.0665007i
$766$	16.0968			0.581601
$767$	0.915495	−	1.58568i	0.0330566	−	0.0572557i
$768$	0.675970	−	1.59470i	0.0243920	−	0.0575437i
$769$	−10.1747	−	17.6230i	−0.366908	−	0.635503i	0.622173	−	0.782880i	$-0.286250\pi$
$769$	−10.1747	−	17.6230i	−0.366908	−	0.635503i	−0.989080	+	0.147377i	$0.952917\pi$
$770$	0.367095	+	0.635828i	0.0132292	+	0.0229137i
$771$	−2.37724	+	5.60821i	−0.0856141	+	0.201975i
$772$	8.38759	−	14.5277i	0.301876	−	0.522864i
$773$	4.89423			0.176033			0.0880165	−	0.996119i	$-0.471947\pi$
$773$	4.89423			0.176033			0.0880165	+	0.996119i	$0.471947\pi$
$774$	−2.91016	+	0.728674i	−0.104604	+	0.0261916i
$775$	−4.00000			−0.143684
$776$	−0.234191	+	0.405631i	−0.00840697	+	0.0145613i
$777$	12.4774	−	1.53836i	0.447625	−	0.0551885i
$778$	−10.0558	−	17.4172i	−0.360519	−	0.624436i
$779$	−21.9676	−	38.0490i	−0.787071	−	1.36325i
$780$	1.80887	+	2.39796i	0.0647681	+	0.0858609i
$781$	1.19614	−	2.07178i	0.0428013	−	0.0741340i
$782$	−9.42584			−0.337067
$783$	−1.82435	+	11.6313i	−0.0651969	+	0.415668i
$784$	1.00000			0.0357143
$785$	7.33548	−	12.7054i	0.261814	−	0.453476i
$786$	−17.2863	−	22.9159i	−0.616582	−	0.817382i
$787$	19.8458	+	34.3740i	0.707427	+	1.22530i	0.965808	+	0.259257i	$0.0834777\pi$
$787$	19.8458	+	34.3740i	0.707427	+	1.22530i	−0.258381	+	0.966043i	$0.583189\pi$
$788$	−5.68501	−	9.84673i	−0.202520	−	0.350775i
$789$	−20.3634	+	2.51064i	−0.724956	+	0.0893810i
$790$	6.52420	−	11.3002i	0.232121	−	0.402045i
$791$	−16.5726			−0.589254
$792$	−1.53162	−	1.58287i	−0.0544237	−	0.0562448i
$793$	−6.57260			−0.233400
$794$	3.71292	−	6.43097i	0.131767	−	0.228227i
$795$	−2.20257	+	5.19615i	−0.0781172	+	0.184289i
$796$	9.39130	+	16.2662i	0.332866	+	0.576540i
$797$	−25.0968	−	43.4689i	−0.888974	−	1.53975i	−0.841090	−	0.540896i	$-0.818085\pi$
$797$	−25.0968	−	43.4689i	−0.888974	−	1.53975i	−0.0478845	−	0.998853i	$-0.515248\pi$
$798$	−4.41016	+	10.4041i	−0.156118	+	0.368302i
$799$	12.0909	−	20.9421i	0.427747	−	0.740879i
$800$	1.00000			0.0353553
$801$	−4.16003	+	14.5627i	−0.146988	+	0.514546i
$802$	−34.1600			−1.20623
$803$	−3.68872	+	6.38905i	−0.130172	+	0.225465i
$804$	−10.3015	+	1.27008i	−0.363304	+	0.0447924i
$805$	−1.86710	−	3.23390i	−0.0658065	−	0.113980i
$806$	−3.46838	−	6.00741i	−0.122169	−	0.211602i
$807$	−24.2445	−	32.1402i	−0.853448	−	1.13139i
$808$	4.46838	−	7.73946i	0.157197	−	0.272273i
$809$	22.9442			0.806674			0.403337	−	0.915051i	$-0.367850\pi$
$809$	22.9442			0.806674			0.403337	+	0.915051i	$0.367850\pi$
$810$	7.64195	+	4.75401i	0.268511	+	0.167039i
$811$	−22.9293			−0.805158			−0.402579	−	0.915385i	$-0.631886\pi$
$811$	−22.9293			−0.805158			−0.402579	+	0.915385i	$0.631886\pi$
$812$	1.13290	−	1.96225i	0.0397572	−	0.0688614i
$813$	−24.3182	−	32.2379i	−0.852878	−	1.13063i
$814$	2.66452	+	4.61509i	0.0933915	+	0.161759i
$815$	4.97209	+	8.61191i	0.174165	+	0.301662i
$816$	−4.33919	+	0.534986i	−0.151902	+	0.0187282i
$817$	−3.26210	+	5.65012i	−0.114126	+	0.197673i
$818$	8.42584			0.294603
$819$	1.42903	−	5.00246i	0.0499342	−	0.174800i
$820$	6.73419			0.235168
$821$	−17.1255	+	29.6622i	−0.597684	+	1.03522i	0.395479	+	0.918475i	$0.370579\pi$
$821$	−17.1255	+	29.6622i	−0.597684	+	1.03522i	−0.993162	+	0.116743i	$0.962755\pi$
$822$	−7.29372	+	17.2068i	−0.254398	+	0.600157i
$823$	12.3913	+	21.4624i	0.431933	+	0.748131i	0.997040	−	0.0768875i	$-0.0244982\pi$
$823$	12.3913	+	21.4624i	0.431933	+	0.748131i	−0.565106	+	0.825018i	$0.691165\pi$
$824$	−0.104996	−	0.181858i	−0.00365770	−	0.00633532i
$825$	0.496291	−	1.17081i	0.0172786	−	0.0407625i
$826$	−0.527909	+	0.914365i	−0.0183683	+	0.0318148i
$827$	36.0410			1.25327			0.626634	−	0.779314i	$-0.284432\pi$
$827$	36.0410			1.25327			0.626634	+	0.779314i	$0.284432\pi$
$828$	7.79001	+	8.05068i	0.270722	+	0.279780i
$829$	−17.3419			−0.602309			−0.301155	−	0.953575i	$-0.597372\pi$
$829$	−17.3419			−0.602309			−0.301155	+	0.953575i	$0.597372\pi$
$830$	−7.79001	+	13.4927i	−0.270395	+	0.468338i
$831$	−5.07390	+	0.625570i	−0.176012	+	0.0217008i
$832$	0.867095	+	1.50185i	0.0300611	+	0.0520674i
$833$	−1.26210	−	2.18602i	−0.0437292	−	0.0757411i
$834$	−7.30146	−	9.67929i	−0.252829	−	0.335167i
$835$	−2.10500	+	3.64596i	−0.0728464	+	0.126174i
$836$	−4.79001			−0.165666
$837$	−16.1723	−	13.0560i	−0.558995	−	0.451280i
$838$	25.6358			0.885575
$839$	24.3765	−	42.2213i	0.841569	−	1.45764i	−0.0469992	−	0.998895i	$-0.514966\pi$
$839$	24.3765	−	42.2213i	0.841569	−	1.45764i	0.888568	−	0.458745i	$-0.151701\pi$
$840$	−1.04307	−	1.38276i	−0.0359892	−	0.0477096i
$841$	11.9331	+	20.6687i	0.411485	+	0.712712i
$842$	12.9713	+	22.4670i	0.447021	+	0.774263i
$843$	−44.9573	+	5.54286i	−1.54841	+	0.190906i
$844$	−3.52420	+	6.10409i	−0.121308	+	0.210112i
$845$	9.99258			0.343755
$846$	−27.8794	+	6.98071i	−0.958513	+	0.240002i
$847$	−10.4610			−0.359443
$848$	−1.62920	+	2.82185i	−0.0559468	+	0.0969027i
$849$	2.34452	−	5.53103i	0.0804637	−	0.189824i
$850$	−1.26210	−	2.18602i	−0.0432897	−	0.0749799i
$851$	−13.5521	−	23.4729i	−0.464560	−	0.804642i
$852$	−2.20257	+	5.19615i	−0.0754589	+	0.178017i
$853$	−27.7194	+	48.0113i	−0.949093	+	1.64388i	−0.201751	+	0.979437i	$0.564663\pi$
$853$	−27.7194	+	48.0113i	−0.949093	+	1.64388i	−0.747342	+	0.664440i	$0.768670\pi$
$854$	3.79001			0.129691
$855$	18.9865	−	4.75401i	0.649324	−	0.162584i
$856$	1.05582			0.0360871
$857$	−2.97951	+	5.16066i	−0.101778	+	0.176285i	−0.912417	−	0.409261i	$-0.865787\pi$
$857$	−2.97951	+	5.16066i	−0.101778	+	0.176285i	0.810639	+	0.585546i	$0.199120\pi$
$858$	2.18872	−	0.269851i	0.0747217	−	0.00921257i
$859$	1.47209	+	2.54974i	0.0502271	+	0.0869959i	0.890046	−	0.455871i	$-0.150672\pi$
$859$	1.47209	+	2.54974i	0.0502271	+	0.0869959i	−0.839819	+	0.542867i	$0.817339\pi$
$860$	−0.500000	−	0.866025i	−0.0170499	−	0.0295312i
$861$	−7.02420	−	9.31175i	−0.239384	−	0.317343i
$862$	7.31421	−	12.6686i	0.249123	−	0.431494i
$863$	−3.58002			−0.121865			−0.0609326	−	0.998142i	$-0.519407\pi$
$863$	−3.58002			−0.121865			−0.0609326	+	0.998142i	$0.519407\pi$
$864$	4.04307	+	3.26399i	0.137548	+	0.111043i
$865$	12.0000			0.408012
$866$	−14.5000	+	25.1147i	−0.492730	+	0.853433i
$867$	−11.0861	−	14.6965i	−0.376505	−	0.499120i
$868$	2.00000	+	3.46410i	0.0678844	+	0.117579i
$869$	−4.79001	−	8.29654i	−0.162490	−	0.281441i
$870$	−3.89500	+	0.480222i	−0.132053	+	0.0162810i
$871$	5.19614	−	8.99998i	0.176065	−	0.304953i
$872$	18.2510			0.618056
$873$	−0.977106	−	1.00980i	−0.0330700	−	0.0341766i
$874$	24.3626			0.824077
$875$	0.500000	−	0.866025i	0.0169031	−	0.0292770i
$876$	6.79241	−	16.0242i	0.229494	−	0.541407i
$877$	2.83177	+	4.90477i	0.0956220	+	0.165622i	0.909868	−	0.414898i	$-0.136183\pi$
$877$	2.83177	+	4.90477i	0.0956220	+	0.165622i	−0.814246	+	0.580520i	$0.802849\pi$
$878$	5.65710	+	9.79839i	0.190918	+	0.330680i
$879$	4.30093	−	10.1464i	0.145067	−	0.342231i
$880$	0.367095	−	0.635828i	0.0123748	−	0.0214338i
$881$	−25.6358			−0.863693			−0.431847	−	0.901947i	$-0.642138\pi$
$881$	−25.6358			−0.863693			−0.431847	+	0.901947i	$0.642138\pi$
$882$	−0.824030	+	2.88461i	−0.0277465	+	0.0971299i
$883$	−44.0745			−1.48323			−0.741613	−	0.670828i	$-0.765939\pi$
$883$	−44.0745			−1.48323			−0.741613	+	0.670828i	$0.765939\pi$
$884$	2.18872	−	3.79098i	0.0736147	−	0.127504i
$885$	1.81499	−	0.223773i	0.0610101	−	0.00752204i
$886$	12.9610	+	22.4490i	0.435432	+	0.754190i
$887$	−10.6358	−	18.4218i	−0.357116	−	0.618544i	0.630361	−	0.776302i	$-0.282907\pi$
$887$	−10.6358	−	18.4218i	−0.357116	−	0.618544i	−0.987478	+	0.157758i	$0.949573\pi$
$888$	−7.57097	−	10.0366i	−0.254065	−	0.336806i
$889$	4.92291	−	8.52674i	0.165109	−	0.285978i
$890$	−5.04840			−0.169223
$891$	5.82806	−	3.11379i	0.195247	−	0.104316i
$892$	7.67837			0.257091
$893$	−31.2510	+	54.1283i	−1.04577	+	1.81133i
$894$	−9.32163	−	12.3574i	−0.311762	−	0.413292i
$895$	9.49629	+	16.4481i	0.317426	+	0.549798i
$896$	−0.500000	−	0.866025i	−0.0167038	−	0.0289319i
$897$	−11.1321	+	1.37250i	−0.371691	+	0.0458264i
$898$	−5.79372	+	10.0350i	−0.193339	+	0.334873i
$899$	9.06324			0.302276
$900$	−0.824030	+	2.88461i	−0.0274677	+	0.0961537i
$901$	8.22483			0.274009
$902$	2.47209	−	4.28179i	0.0823116	−	0.142568i
$903$	−0.675970	+	1.59470i	−0.0224949	+	0.0530683i
$904$	8.28630	+	14.3523i	0.275598	+	0.477350i
$905$	8.31421	+	14.4006i	0.276374	+	0.478693i
$906$	−13.2355	+	31.2242i	−0.439720	+	1.03736i
$907$	−7.56889	+	13.1097i	−0.251321	+	0.435300i	−0.963890	−	0.266302i	$-0.914198\pi$
$907$	−7.56889	+	13.1097i	−0.251321	+	0.435300i	0.712569	+	0.701602i	$0.247532\pi$
$908$	−20.8868			−0.693153
$909$	18.6433	+	19.2671i	0.618358	+	0.639049i
$910$	1.73419			0.0574879
$911$	15.8318	−	27.4214i	0.524530	−	0.908512i	−0.475062	−	0.879952i	$-0.657574\pi$
$911$	15.8318	−	27.4214i	0.524530	−	0.908512i	0.999592	−	0.0285602i	$-0.00909223\pi$
$912$	11.2153	−	1.38276i	0.371377	−	0.0457876i
$913$	5.71935	+	9.90621i	0.189283	+	0.327848i
$914$	4.89130	+	8.47197i	0.161790	+	0.280228i
$915$	−3.95323	−	5.24066i	−0.130690	−	0.173251i
$916$	−10.6776	+	18.4941i	−0.352798	+	0.611063i
$917$	−16.5726			−0.547275
$918$	2.03240	−	12.9577i	0.0670791	−	0.427668i
$919$	0.336463			0.0110989			0.00554945	−	0.999985i	$-0.498234\pi$
$919$	0.336463			0.0110989			0.00554945	+	0.999985i	$0.498234\pi$
$920$	−1.86710	+	3.23390i	−0.0615563	+	0.106619i
$921$	12.8445	+	17.0275i	0.423241	+	0.561077i
$922$	15.0976	+	26.1498i	0.497212	+	0.861197i
$923$	−2.82534	−	4.89363i	−0.0929971	−	0.161076i
$924$	−1.26210	+	0.155606i	−0.0415200	+	0.00511908i
$925$	3.62920	−	6.28595i	0.119327	−	0.206681i
$926$	24.0968			0.791870
$927$	0.611109	−	0.153015i	0.0200714	−	0.00502568i
$928$	−2.26581			−0.0743788
$929$	−15.1952	+	26.3188i	−0.498537	+	0.863491i	−0.999999	−	0.00168868i	$-0.999462\pi$
$929$	−15.1952	+	26.3188i	−0.498537	+	0.863491i	0.501462	+	0.865180i	$0.332796\pi$
$930$	2.70388	−	6.37880i	0.0886637	−	0.209169i
$931$	3.26210	+	5.65012i	0.106911	+	0.185175i
$932$	2.15710	+	3.73621i	0.0706583	+	0.122384i
$933$	14.5019	−	34.2119i	0.474772	−	1.12005i
$934$	−20.5902	+	35.6632i	−0.673731	+	1.16694i
$935$	−1.85324			−0.0606076
$936$	−5.04677	+	1.26366i	−0.164959	+	0.0413040i
$937$	42.9075			1.40173			0.700864	−	0.713295i	$-0.252798\pi$
$937$	42.9075			1.40173			0.700864	+	0.713295i	$0.252798\pi$
$938$	−2.99629	+	5.18973i	−0.0978324	+	0.169451i
$939$	26.5779	−	3.27684i	0.867338	−	0.106936i
$940$	−4.79001	−	8.29654i	−0.156233	−	0.270603i
$941$	−6.32163	−	10.9494i	−0.206079	−	0.356940i	0.744397	−	0.667737i	$-0.232737\pi$
$941$	−6.32163	−	10.9494i	−0.206079	−	0.356940i	−0.950476	+	0.310798i	$0.899404\pi$
$942$	15.3028	+	20.2864i	0.498591	+	0.660965i
$943$	−12.5734	+	21.7777i	−0.409446	+	0.709180i
$944$	1.05582			0.0343639
$945$	4.84823	−	1.86940i	0.157713	−	0.0608117i
$946$	−0.734191			−0.0238706
$947$	1.91256	−	3.31266i	0.0621500	−	0.107647i	−0.833276	−	0.552857i	$-0.813538\pi$
$947$	1.91256	−	3.31266i	0.0621500	−	0.107647i	0.895426	+	0.445210i	$0.146871\pi$
$948$	13.6103	+	18.0428i	0.442043	+	0.586002i
$949$	8.71292	+	15.0912i	0.282833	+	0.489882i
$950$	3.26210	+	5.65012i	0.105836	+	0.183314i
$951$	−37.4323	+	4.61509i	−1.21382	+	0.149654i
$952$	−1.26210	+	2.18602i	−0.0409049	+	0.0708493i
$953$	−3.15417			−0.102174			−0.0510869	−	0.998694i	$-0.516269\pi$
$953$	−3.15417			−0.102174			−0.0510869	+	0.998694i	$0.516269\pi$
$954$	−6.79743	−	7.02488i	−0.220075	−	0.227439i
$955$	−16.0968			−0.520880
$956$	4.05582	−	7.02488i	0.131175	−	0.227201i
$957$	−1.12450	+	2.65284i	−0.0363499	+	0.0857541i
$958$	−18.5939	−	32.2055i	−0.600741	−	1.04051i
$959$	5.39500	+	9.34442i	0.174214	+	0.301747i
$960$	−0.675970	+	1.59470i	−0.0218168	+	0.0514687i
$961$	7.50000	−	12.9904i	0.241935	−	0.419045i
$962$	12.5874			0.405835
$963$	−0.870026	+	3.04562i	−0.0280362	+	0.0981438i
$964$	−22.2584			−0.716894
$965$	−8.38759	+	14.5277i	−0.270006	+	0.467664i
$966$	6.41920	−	0.791434i	0.206534	−	0.0254640i
$967$	19.6917	+	34.1069i	0.633241	+	1.09681i	0.986885	+	0.161425i	$0.0516091\pi$
$967$	19.6917	+	34.1069i	0.633241	+	1.09681i	−0.353644	+	0.935380i	$0.615058\pi$
$968$	5.23048	+	9.05946i	0.168114	+	0.291182i
$969$	−17.1776	−	22.7718i	−0.551824	−	0.731534i
$970$	0.234191	−	0.405631i	0.00751942	−	0.0130240i
$971$	28.2233			0.905728			0.452864	−	0.891580i	$-0.350402\pi$
$971$	28.2233			0.905728			0.452864	+	0.891580i	$0.350402\pi$
$972$	−12.7469	+	8.97304i	−0.408858	+	0.287810i
$973$	−7.00000			−0.224410
$974$	2.25839	−	3.91165i	0.0723635	−	0.125337i
$975$	−1.80887	−	2.39796i	−0.0579303	−	0.0767963i
$976$	−1.89500	−	3.28224i	−0.0606576	−	0.105062i
$977$	−18.4508	−	31.9578i	−0.590294	−	1.02242i	−0.994193	−	0.107616i	$-0.965678\pi$
$977$	−18.4508	−	31.9578i	−0.590294	−	1.02242i	0.403898	−	0.914804i	$-0.367655\pi$
$978$	−17.0944	+	2.10760i	−0.546618	+	0.0673935i
$979$	−1.85324	+	3.20991i	−0.0592300	+	0.102589i
$980$	−1.00000			−0.0319438
$981$	−15.0394	+	52.6469i	−0.480170	+	1.68089i
$982$	10.3552			0.330447
$983$	2.41998	−	4.19153i	0.0771855	−	0.133689i	−0.824849	−	0.565353i	$-0.808740\pi$
$983$	2.41998	−	4.19153i	0.0771855	−	0.133689i	0.902035	+	0.431664i	$0.142073\pi$
$984$	−4.55211	+	10.7390i	−0.145116	+	0.342347i
$985$	5.68501	+	9.84673i	0.181140	+	0.313743i
$986$	2.85968	+	4.95311i	0.0910707	+	0.157739i
$987$	−6.47580	+	15.2772i	−0.206127	+	0.486280i
$988$	−5.65710	+	9.79839i	−0.179976	+	0.311728i
$989$	3.73419			0.118740
$990$	1.53162	+	1.58287i	0.0486780	+	0.0503069i
$991$	−37.8884			−1.20356			−0.601782	−	0.798661i	$-0.705542\pi$
$991$	−37.8884			−1.20356			−0.601782	+	0.798661i	$0.705542\pi$
$992$	2.00000	−	3.46410i	0.0635001	−	0.109985i
$993$	−40.5349	+	4.99761i	−1.28634	+	0.158594i
$994$	1.62920	+	2.82185i	0.0516749	+	0.0895036i
$995$	−9.39130	−	16.2662i	−0.297724	−	0.515673i
$996$	−16.2510	−	21.5434i	−0.514932	−	0.682628i
$997$	−16.5168	+	28.6079i	−0.523092	+	0.906021i	0.476547	+	0.879149i	$0.341888\pi$
$997$	−16.5168	+	28.6079i	−0.523092	+	0.906021i	−0.999639	+	0.0268725i	$0.991445\pi$
$998$	28.7194			0.909095
$999$	35.1903	−	13.5689i	1.11337	−	0.429300i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	630.2.j.j.421.3	yes	6
3.2	odd	2		1890.2.j.i.1261.2		6
9.2	odd	6		5670.2.a.bq.1.2		3
9.4	even	3	inner	630.2.j.j.211.3	✓	6
9.5	odd	6		1890.2.j.i.631.2		6
9.7	even	3		5670.2.a.br.1.2		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
630.2.j.j.211.3	✓	6	9.4	even	3	inner
630.2.j.j.421.3	yes	6	1.1	even	1	trivial
1890.2.j.i.631.2		6	9.5	odd	6
1890.2.j.i.1261.2		6	3.2	odd	2
5670.2.a.bq.1.2		3	9.2	odd	6
5670.2.a.br.1.2		3	9.7	even	3

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:	\( N \)	\(=\)	\( 630 = 2 \cdot 3^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	630.j (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 + 0.866025i) q^{2} +(1.04307 + 1.38276i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(0.500000 + 0.866025i) q^{5} +(-1.71903 + 0.211943i) q^{6} +(-0.500000 + 0.866025i) q^{7} +1.00000 q^{8} +(-0.824030 + 2.88461i) q^{9} +O(q^{10})\)	\(q+(-0.500000 + 0.866025i) q^{2} +(1.04307 + 1.38276i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(0.500000 + 0.866025i) q^{5} +(-1.71903 + 0.211943i) q^{6} +(-0.500000 + 0.866025i) q^{7} +1.00000 q^{8} +(-0.824030 + 2.88461i) q^{9} -1.00000 q^{10} +(-0.367095 + 0.635828i) q^{11} +(0.675970 - 1.59470i) q^{12} +(0.867095 + 1.50185i) q^{13} +(-0.500000 - 0.866025i) q^{14} +(-0.675970 + 1.59470i) q^{15} +(-0.500000 + 0.866025i) q^{16} +2.52420 q^{17} +(-2.08613 - 2.15594i) q^{18} -6.52420 q^{19} +(0.500000 - 0.866025i) q^{20} +(-1.71903 + 0.211943i) q^{21} +(-0.367095 - 0.635828i) q^{22} +(1.86710 + 3.23390i) q^{23} +(1.04307 + 1.38276i) q^{24} +(-0.500000 + 0.866025i) q^{25} -1.73419 q^{26} +(-4.84823 + 1.86940i) q^{27} +1.00000 q^{28} +(1.13290 - 1.96225i) q^{29} +(-1.04307 - 1.38276i) q^{30} +(2.00000 + 3.46410i) q^{31} +(-0.500000 - 0.866025i) q^{32} +(-1.26210 + 0.155606i) q^{33} +(-1.26210 + 2.18602i) q^{34} -1.00000 q^{35} +(2.91016 - 0.728674i) q^{36} -7.25839 q^{37} +(3.26210 - 5.65012i) q^{38} +(-1.17226 + 2.76551i) q^{39} +(0.500000 + 0.866025i) q^{40} +(3.36710 + 5.83198i) q^{41} +(0.675970 - 1.59470i) q^{42} +(0.500000 - 0.866025i) q^{43} +0.734191 q^{44} +(-2.91016 + 0.728674i) q^{45} -3.73419 q^{46} +(4.79001 - 8.29654i) q^{47} +(-1.71903 + 0.211943i) q^{48} +(-0.500000 - 0.866025i) q^{49} +(-0.500000 - 0.866025i) q^{50} +(2.63290 + 3.49035i) q^{51} +(0.867095 - 1.50185i) q^{52} +3.25839 q^{53} +(0.805165 - 5.13339i) q^{54} -0.734191 q^{55} +(-0.500000 + 0.866025i) q^{56} +(-6.80516 - 9.02138i) q^{57} +(1.13290 + 1.96225i) q^{58} +(-0.527909 - 0.914365i) q^{59} +(1.71903 - 0.211943i) q^{60} +(-1.89500 + 3.28224i) q^{61} -4.00000 q^{62} +(-2.08613 - 2.15594i) q^{63} +1.00000 q^{64} +(-0.867095 + 1.50185i) q^{65} +(0.496291 - 1.17081i) q^{66} +(-2.99629 - 5.18973i) q^{67} +(-1.26210 - 2.18602i) q^{68} +(-2.52420 + 5.95491i) q^{69} +(0.500000 - 0.866025i) q^{70} -3.25839 q^{71} +(-0.824030 + 2.88461i) q^{72} +10.0484 q^{73} +(3.62920 - 6.28595i) q^{74} +(-1.71903 + 0.211943i) q^{75} +(3.26210 + 5.65012i) q^{76} +(-0.367095 - 0.635828i) q^{77} +(-1.80887 - 2.39796i) q^{78} +(-6.52420 + 11.3002i) q^{79} -1.00000 q^{80} +(-7.64195 - 4.75401i) q^{81} -6.73419 q^{82} +(7.79001 - 13.4927i) q^{83} +(1.04307 + 1.38276i) q^{84} +(1.26210 + 2.18602i) q^{85} +(0.500000 + 0.866025i) q^{86} +(3.89500 - 0.480222i) q^{87} +(-0.367095 + 0.635828i) q^{88} +5.04840 q^{89} +(0.824030 - 2.88461i) q^{90} -1.73419 q^{91} +(1.86710 - 3.23390i) q^{92} +(-2.70388 + 6.37880i) q^{93} +(4.79001 + 8.29654i) q^{94} +(-3.26210 - 5.65012i) q^{95} +(0.675970 - 1.59470i) q^{96} +(-0.234191 + 0.405631i) q^{97} +1.00000 q^{98} +(-1.53162 - 1.58287i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 3 q^{2} - q^{3} - 3 q^{4} + 3 q^{5} - q^{6} - 3 q^{7} + 6 q^{8} - 7 q^{9}+O(q^{10}) \) 6 * q - 3 * q^2 - q^3 - 3 * q^4 + 3 * q^5 - q^6 - 3 * q^7 + 6 * q^8 - 7 * q^9	\( 6 q - 3 q^{2} - q^{3} - 3 q^{4} + 3 q^{5} - q^{6} - 3 q^{7} + 6 q^{8} - 7 q^{9} - 6 q^{10} + 3 q^{11} + 2 q^{12} - 3 q^{14} - 2 q^{15} - 3 q^{16} - 18 q^{17} + 2 q^{18} - 6 q^{19} + 3 q^{20} - q^{21} + 3 q^{22} + 6 q^{23} - q^{24} - 3 q^{25} + 2 q^{27} + 6 q^{28} + 12 q^{29} + q^{30} + 12 q^{31} - 3 q^{32} + 9 q^{33} + 9 q^{34} - 6 q^{35} + 5 q^{36} + 3 q^{38} + 22 q^{39} + 3 q^{40} + 15 q^{41} + 2 q^{42} + 3 q^{43} - 6 q^{44} - 5 q^{45} - 12 q^{46} + 6 q^{47} - q^{48} - 3 q^{49} - 3 q^{50} + 21 q^{51} - 24 q^{53} - 19 q^{54} + 6 q^{55} - 3 q^{56} - 17 q^{57} + 12 q^{58} + 3 q^{59} + q^{60} - 24 q^{62} + 2 q^{63} + 6 q^{64} - 24 q^{66} + 9 q^{67} + 9 q^{68} + 18 q^{69} + 3 q^{70} + 24 q^{71} - 7 q^{72} - 6 q^{73} - q^{75} + 3 q^{76} + 3 q^{77} - 14 q^{78} - 6 q^{79} - 6 q^{80} - 19 q^{81} - 30 q^{82} + 24 q^{83} - q^{84} - 9 q^{85} + 3 q^{86} + 12 q^{87} + 3 q^{88} - 36 q^{89} + 7 q^{90} + 6 q^{92} - 8 q^{93} + 6 q^{94} - 3 q^{95} + 2 q^{96} + 9 q^{97} + 6 q^{98} - 30 q^{99}+O(q^{100}) \) 6 * q - 3 * q^2 - q^3 - 3 * q^4 + 3 * q^5 - q^6 - 3 * q^7 + 6 * q^8 - 7 * q^9 - 6 * q^10 + 3 * q^11 + 2 * q^12 - 3 * q^14 - 2 * q^15 - 3 * q^16 - 18 * q^17 + 2 * q^18 - 6 * q^19 + 3 * q^20 - q^21 + 3 * q^22 + 6 * q^23 - q^24 - 3 * q^25 + 2 * q^27 + 6 * q^28 + 12 * q^29 + q^30 + 12 * q^31 - 3 * q^32 + 9 * q^33 + 9 * q^34 - 6 * q^35 + 5 * q^36 + 3 * q^38 + 22 * q^39 + 3 * q^40 + 15 * q^41 + 2 * q^42 + 3 * q^43 - 6 * q^44 - 5 * q^45 - 12 * q^46 + 6 * q^47 - q^48 - 3 * q^49 - 3 * q^50 + 21 * q^51 - 24 * q^53 - 19 * q^54 + 6 * q^55 - 3 * q^56 - 17 * q^57 + 12 * q^58 + 3 * q^59 + q^60 - 24 * q^62 + 2 * q^63 + 6 * q^64 - 24 * q^66 + 9 * q^67 + 9 * q^68 + 18 * q^69 + 3 * q^70 + 24 * q^71 - 7 * q^72 - 6 * q^73 - q^75 + 3 * q^76 + 3 * q^77 - 14 * q^78 - 6 * q^79 - 6 * q^80 - 19 * q^81 - 30 * q^82 + 24 * q^83 - q^84 - 9 * q^85 + 3 * q^86 + 12 * q^87 + 3 * q^88 - 36 * q^89 + 7 * q^90 + 6 * q^92 - 8 * q^93 + 6 * q^94 - 3 * q^95 + 2 * q^96 + 9 * q^97 + 6 * q^98 - 30 * q^99

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