LMFDB - Embedded newform 630.2.j.j.211.2

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			211.2
Root			$-1.62241 - 0.606458i$ of defining polynomial
Character	$\chi$	$=$	630.211
Dual form			630.2.j.j.421.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 - 0.866025i) q^{2} +(-0.285997 + 1.70828i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(0.500000 - 0.866025i) q^{5} +(1.62241 - 0.606458i) q^{6} +(-0.500000 - 0.866025i) q^{7} +1.00000 q^{8} +(-2.83641 - 0.977122i) q^{9} +O(q^{10})$	\(q+(-0.500000 - 0.866025i) q^{2} +(-0.285997 + 1.70828i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(0.500000 - 0.866025i) q^{5} +(1.62241 - 0.606458i) q^{6} +(-0.500000 - 0.866025i) q^{7} +1.00000 q^{8} +(-2.83641 - 0.977122i) q^{9} -1.00000 q^{10} +(-1.05042 - 1.81937i) q^{11} +(-1.33641 - 1.10182i) q^{12} +(1.55042 - 2.68540i) q^{13} +(-0.500000 + 0.866025i) q^{14} +(1.33641 + 1.10182i) q^{15} +(-0.500000 - 0.866025i) q^{16} -6.81681 q^{17} +(0.571993 + 2.94497i) q^{18} +2.81681 q^{19} +(0.500000 + 0.866025i) q^{20} +(1.62241 - 0.606458i) q^{21} +(-1.05042 + 1.81937i) q^{22} +(2.55042 - 4.41745i) q^{23} +(-0.285997 + 1.70828i) q^{24} +(-0.500000 - 0.866025i) q^{25} -3.10083 q^{26} +(2.48040 - 4.56592i) q^{27} +1.00000 q^{28} +(0.449585 + 0.778704i) q^{29} +(0.285997 - 1.70828i) q^{30} +(2.00000 - 3.46410i) q^{31} +(-0.500000 + 0.866025i) q^{32} +(3.40841 - 1.27406i) q^{33} +(3.40841 + 5.90353i) q^{34} -1.00000 q^{35} +(2.26442 - 1.96784i) q^{36} +0.715980 q^{37} +(-1.40841 - 2.43943i) q^{38} +(4.14399 + 3.41655i) q^{39} +(0.500000 - 0.866025i) q^{40} +(4.05042 - 7.01552i) q^{41} +(-1.33641 - 1.10182i) q^{42} +(0.500000 + 0.866025i) q^{43} +2.10083 q^{44} +(-2.26442 + 1.96784i) q^{45} -5.10083 q^{46} +(-5.91764 - 10.2497i) q^{47} +(1.62241 - 0.606458i) q^{48} +(-0.500000 + 0.866025i) q^{49} +(-0.500000 + 0.866025i) q^{50} +(1.94958 - 11.6450i) q^{51} +(1.55042 + 2.68540i) q^{52} -4.71598 q^{53} +(-5.19440 + 0.134872i) q^{54} -2.10083 q^{55} +(-0.500000 - 0.866025i) q^{56} +(-0.805598 + 4.81189i) q^{57} +(0.449585 - 0.778704i) q^{58} +(5.50924 - 9.54228i) q^{59} +(-1.62241 + 0.606458i) q^{60} +(3.45882 + 5.99085i) q^{61} -4.00000 q^{62} +(0.571993 + 2.94497i) q^{63} +1.00000 q^{64} +(-1.55042 - 2.68540i) q^{65} +(-2.80757 - 2.31473i) q^{66} +(0.307575 - 0.532735i) q^{67} +(3.40841 - 5.90353i) q^{68} +(6.81681 + 5.62019i) q^{69} +(0.500000 + 0.866025i) q^{70} +4.71598 q^{71} +(-2.83641 - 0.977122i) q^{72} -8.63362 q^{73} +(-0.357990 - 0.620057i) q^{74} +(1.62241 - 0.606458i) q^{75} +(-1.40841 + 2.43943i) q^{76} +(-1.05042 + 1.81937i) q^{77} +(0.886827 - 5.29707i) q^{78} +(2.81681 + 4.87886i) q^{79} -1.00000 q^{80} +(7.09046 + 5.54304i) q^{81} -8.10083 q^{82} +(-2.91764 - 5.05350i) q^{83} +(-0.285997 + 1.70828i) q^{84} +(-3.40841 + 5.90353i) q^{85} +(0.500000 - 0.866025i) q^{86} +(-1.45882 + 0.545308i) q^{87} +(-1.05042 - 1.81937i) q^{88} -13.6336 q^{89} +(2.83641 + 0.977122i) q^{90} -3.10083 q^{91} +(2.55042 + 4.41745i) q^{92} +(5.34565 + 4.40727i) q^{93} +(-5.91764 + 10.2497i) q^{94} +(1.40841 - 2.43943i) q^{95} +(-1.33641 - 1.10182i) q^{96} +(-1.60083 - 2.77272i) q^{97} +1.00000 q^{98} +(1.20166 + 6.18687i) 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 $\left(\mathbb{Z}/630\mathbb{Z}\right)^\times$.

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

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
$3$	−0.285997	+	1.70828i	−0.165120	+	0.986273i
$3$	−0.285997	+	1.70828i	−0.165120	+	0.986273i
$4$	−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
$6$	1.62241	−	0.606458i	0.662345	−	0.247585i
$7$	−0.500000	−	0.866025i	−0.188982	−	0.327327i
$7$	−0.500000	−	0.866025i	−0.188982	−	0.327327i
$8$	1.00000			0.353553
$9$	−2.83641	−	0.977122i	−0.945471	−	0.325707i
$10$	−1.00000			−0.316228
$11$	−1.05042	−	1.81937i	−0.316712	−	0.548561i	0.663088	−	0.748542i	$-0.269246\pi$
$11$	−1.05042	−	1.81937i	−0.316712	−	0.548561i	−0.979800	+	0.199980i	$0.935912\pi$
$12$	−1.33641	−	1.10182i	−0.385789	−	0.318068i
$13$	1.55042	−	2.68540i	0.430008	−	0.744795i	−0.566866	−	0.823810i	$-0.691844\pi$
$13$	1.55042	−	2.68540i	0.430008	−	0.744795i	0.996873	+	0.0790149i	$0.0251775\pi$
$14$	−0.500000	+	0.866025i	−0.133631	+	0.231455i
$15$	1.33641	+	1.10182i	0.345060	+	0.284488i
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	−6.81681			−1.65332			−0.826660	−	0.562702i	$-0.809762\pi$
$17$	−6.81681			−1.65332			−0.826660	+	0.562702i	$0.809762\pi$
$18$	0.571993	+	2.94497i	0.134820	+	0.694135i
$19$	2.81681			0.646221			0.323110	−	0.946361i	$-0.395272\pi$
$19$	2.81681			0.646221			0.323110	+	0.946361i	$0.395272\pi$
$20$	0.500000	+	0.866025i	0.111803	+	0.193649i
$21$	1.62241	−	0.606458i	0.354039	−	0.132340i
$22$	−1.05042	+	1.81937i	−0.223949	+	0.387892i
$23$	2.55042	−	4.41745i	0.531798	−	0.921102i	−0.467513	−	0.883986i	$-0.654850\pi$
$23$	2.55042	−	4.41745i	0.531798	−	0.921102i	0.999311	−	0.0371154i	$-0.0118169\pi$
$24$	−0.285997	+	1.70828i	−0.0583788	+	0.348700i
$25$	−0.500000	−	0.866025i	−0.100000	−	0.173205i
$26$	−3.10083			−0.608123
$27$	2.48040	−	4.56592i	0.477353	−	0.878712i
$28$	1.00000			0.188982
$29$	0.449585	+	0.778704i	0.0834858	+	0.144602i	0.904745	−	0.425954i	$-0.140061\pi$
$29$	0.449585	+	0.778704i	0.0834858	+	0.144602i	−0.821259	+	0.570555i	$0.806728\pi$
$30$	0.285997	−	1.70828i	0.0522156	−	0.311887i
$31$	2.00000	−	3.46410i	0.359211	−	0.622171i	−0.628619	−	0.777714i	$-0.716379\pi$
$31$	2.00000	−	3.46410i	0.359211	−	0.622171i	0.987829	+	0.155543i	$0.0497126\pi$
$32$	−0.500000	+	0.866025i	−0.0883883	+	0.153093i
$33$	3.40841	−	1.27406i	0.593327	−	0.221786i
$34$	3.40841	+	5.90353i	0.584537	+	1.01245i
$35$	−1.00000			−0.169031
$36$	2.26442	−	1.96784i	0.377403	−	0.327974i
$37$	0.715980			0.117706			0.0588532	−	0.998267i	$-0.481256\pi$
$37$	0.715980			0.117706			0.0588532	+	0.998267i	$0.481256\pi$
$38$	−1.40841	−	2.43943i	−0.228473	−	0.395728i
$39$	4.14399	+	3.41655i	0.663569	+	0.547086i
$40$	0.500000	−	0.866025i	0.0790569	−	0.136931i
$41$	4.05042	−	7.01552i	0.632569	−	1.09564i	−0.354456	−	0.935073i	$-0.615334\pi$
$41$	4.05042	−	7.01552i	0.632569	−	1.09564i	0.987025	−	0.160568i	$-0.0513327\pi$
$42$	−1.33641	−	1.10182i	−0.206213	−	0.170014i
$43$	0.500000	+	0.866025i	0.0762493	+	0.132068i	0.901629	−	0.432511i	$-0.142372\pi$
$43$	0.500000	+	0.866025i	0.0762493	+	0.132068i	−0.825380	+	0.564578i	$0.809039\pi$
$44$	2.10083			0.316712
$45$	−2.26442	+	1.96784i	−0.337560	+	0.293349i
$46$	−5.10083			−0.752076
$47$	−5.91764	−	10.2497i	−0.863177	−	1.49507i	−0.868846	−	0.495082i	$-0.835138\pi$
$47$	−5.91764	−	10.2497i	−0.863177	−	1.49507i	0.00566976	−	0.999984i	$-0.498195\pi$
$48$	1.62241	−	0.606458i	0.234174	−	0.0875346i
$49$	−0.500000	+	0.866025i	−0.0714286	+	0.123718i
$50$	−0.500000	+	0.866025i	−0.0707107	+	0.122474i
$51$	1.94958	−	11.6450i	0.272996	−	1.63062i
$52$	1.55042	+	2.68540i	0.215004	+	0.372398i
$53$	−4.71598			−0.647790			−0.323895	−	0.946093i	$-0.604992\pi$
$53$	−4.71598			−0.647790			−0.323895	+	0.946093i	$0.604992\pi$
$54$	−5.19440	+	0.134872i	−0.706869	+	0.0183537i
$55$	−2.10083			−0.283276
$56$	−0.500000	−	0.866025i	−0.0668153	−	0.115728i
$57$	−0.805598	+	4.81189i	−0.106704	+	0.637350i
$58$	0.449585	−	0.778704i	0.0590334	−	0.102249i
$59$	5.50924	−	9.54228i	0.717241	−	1.24230i	−0.244847	−	0.969562i	$-0.578738\pi$
$59$	5.50924	−	9.54228i	0.717241	−	1.24230i	0.962089	−	0.272737i	$-0.0879288\pi$
$60$	−1.62241	+	0.606458i	−0.209452	+	0.0782933i
$61$	3.45882	+	5.99085i	0.442857	+	0.767050i	0.997900	−	0.0647712i	$-0.0206318\pi$
$61$	3.45882	+	5.99085i	0.442857	+	0.767050i	−0.555044	+	0.831821i	$0.687298\pi$
$62$	−4.00000			−0.508001
$63$	0.571993	+	2.94497i	0.0720644	+	0.371031i
$64$	1.00000			0.125000
$65$	−1.55042	−	2.68540i	−0.192305	−	0.333083i
$66$	−2.80757	−	2.31473i	−0.345589	−	0.284924i
$67$	0.307575	−	0.532735i	0.0375762	−	0.0650839i	−0.846626	−	0.532189i	$-0.821370\pi$
$67$	0.307575	−	0.532735i	0.0375762	−	0.0650839i	0.884202	+	0.467105i	$0.154703\pi$
$68$	3.40841	−	5.90353i	0.413330	−	0.715908i
$69$	6.81681	+	5.62019i	0.820648	+	0.676591i
$70$	0.500000	+	0.866025i	0.0597614	+	0.103510i
$71$	4.71598			0.559684			0.279842	−	0.960046i	$-0.409718\pi$
$71$	4.71598			0.559684			0.279842	+	0.960046i	$0.409718\pi$
$72$	−2.83641	−	0.977122i	−0.334274	−	0.115155i
$73$	−8.63362			−1.01049			−0.505244	−	0.862976i	$-0.668598\pi$
$73$	−8.63362			−1.01049			−0.505244	+	0.862976i	$0.668598\pi$
$74$	−0.357990	−	0.620057i	−0.0416155	−	0.0720801i
$75$	1.62241	−	0.606458i	0.187340	−	0.0700277i
$76$	−1.40841	+	2.43943i	−0.161555	+	0.279822i
$77$	−1.05042	+	1.81937i	−0.119706	+	0.207337i
$78$	0.886827	−	5.29707i	0.100413	−	0.599775i
$79$	2.81681	+	4.87886i	0.316916	+	0.548914i	0.979843	−	0.199770i	$-0.0640194\pi$
$79$	2.81681	+	4.87886i	0.316916	+	0.548914i	−0.662927	+	0.748684i	$0.730686\pi$
$80$	−1.00000			−0.111803
$81$	7.09046	+	5.54304i	0.787829	+	0.615894i
$82$	−8.10083			−0.894587
$83$	−2.91764	−	5.05350i	−0.320253	−	0.554694i	0.660287	−	0.751013i	$-0.270434\pi$
$83$	−2.91764	−	5.05350i	−0.320253	−	0.554694i	−0.980540	+	0.196319i	$0.937101\pi$
$84$	−0.285997	+	1.70828i	−0.0312048	+	0.186388i
$85$	−3.40841	+	5.90353i	−0.369693	+	0.640328i
$86$	0.500000	−	0.866025i	0.0539164	−	0.0933859i
$87$	−1.45882	+	0.545308i	−0.156402	+	0.0584632i
$88$	−1.05042	−	1.81937i	−0.111975	−	0.193946i
$89$	−13.6336			−1.44516			−0.722580	−	0.691287i	$-0.757044\pi$
$89$	−13.6336			−1.44516			−0.722580	+	0.691287i	$0.757044\pi$
$90$	2.83641	+	0.977122i	0.298984	+	0.102998i
$91$	−3.10083			−0.325055
$92$	2.55042	+	4.41745i	0.265899	+	0.460551i
$93$	5.34565	+	4.40727i	0.554318	+	0.457013i
$94$	−5.91764	+	10.2497i	−0.610358	+	1.05717i
$95$	1.40841	−	2.43943i	0.144499	−	0.250280i
$96$	−1.33641	−	1.10182i	−0.136397	−	0.112454i
$97$	−1.60083	−	2.77272i	−0.162540	−	0.281527i	0.773239	−	0.634115i	$-0.218635\pi$
$97$	−1.60083	−	2.77272i	−0.162540	−	0.281527i	−0.935779	+	0.352587i	$0.885302\pi$
$98$	1.00000			0.101015
$99$	1.20166	+	6.18687i	0.120771	+	0.621804i
$100$	1.00000			0.100000
$101$	7.20166	+	12.4736i	0.716592	+	1.24117i	0.962342	+	0.271841i	$0.0876324\pi$
$101$	7.20166	+	12.4736i	0.716592	+	1.24117i	−0.245750	+	0.969333i	$0.579034\pi$
$102$	−11.0597	+	4.13411i	−1.09507	+	0.409337i
$103$	−5.45882	+	9.45495i	−0.537874	+	0.931624i	0.461145	+	0.887325i	$0.347439\pi$
$103$	−5.45882	+	9.45495i	−0.537874	+	0.931624i	−0.999018	+	0.0442994i	$0.985894\pi$
$104$	1.55042	−	2.68540i	0.152031	−	0.263325i
$105$	0.285997	−	1.70828i	0.0279104	−	0.166711i
$106$	2.35799	+	4.08416i	0.229028	+	0.396689i
$107$	−11.0185			−1.06520			−0.532598	−	0.846368i	$-0.678784\pi$
$107$	−11.0185			−1.06520			−0.532598	+	0.846368i	$0.678784\pi$
$108$	2.71400	+	4.43105i	0.261155	+	0.426378i
$109$	3.66887			0.351414			0.175707	−	0.984442i	$-0.443779\pi$
$109$	3.66887			0.351414			0.175707	+	0.984442i	$0.443779\pi$
$110$	1.05042	+	1.81937i	0.100153	+	0.173470i
$111$	−0.204768	+	1.22309i	−0.0194357	+	0.116091i
$112$	−0.500000	+	0.866025i	−0.0472456	+	0.0818317i
$113$	−5.72522	+	9.91636i	−0.538583	+	0.932853i	0.460398	+	0.887713i	$0.347707\pi$
$113$	−5.72522	+	9.91636i	−0.538583	+	0.932853i	−0.998981	+	0.0451403i	$0.985627\pi$
$114$	4.57002	−	1.70828i	0.428021	−	0.159995i
$115$	−2.55042	−	4.41745i	−0.237827	−	0.411929i
$116$	−0.899170			−0.0834858
$117$	−7.02158	+	6.10195i	−0.649145	+	0.564125i
$118$	−11.0185			−1.01433
$119$	3.40841	+	5.90353i	0.312448	+	0.541176i
$120$	1.33641	+	1.10182i	0.121997	+	0.100582i
$121$	3.29326	−	5.70409i	0.299387	−	0.518553i
$122$	3.45882	−	5.99085i	0.313147	−	0.542386i
$123$	10.8260	+	8.92564i	0.976152	+	0.804798i
$124$	2.00000	+	3.46410i	0.179605	+	0.311086i
$125$	−1.00000			−0.0894427
$126$	2.26442	−	1.96784i	0.201730	−	0.175309i
$127$	12.9361			1.14789			0.573947	−	0.818892i	$-0.305411\pi$
$127$	12.9361			1.14789			0.573947	+	0.818892i	$0.305411\pi$
$128$	−0.500000	−	0.866025i	−0.0441942	−	0.0765466i
$129$	−1.62241	+	0.606458i	−0.142845	+	0.0533956i
$130$	−1.55042	+	2.68540i	−0.135980	+	0.235525i
$131$	−5.72522	+	9.91636i	−0.500214	+	0.866397i	0.499786	+	0.866149i	$0.333412\pi$
$131$	−5.72522	+	9.91636i	−0.500214	+	0.866397i	−1.00000		0.000247572i	$0.999921\pi$
$132$	−0.600830	+	3.58880i	−0.0522956	+	0.312365i
$133$	−1.40841	−	2.43943i	−0.122124	−	0.211525i
$134$	−0.615149			−0.0531408
$135$	−2.71400	−	4.43105i	−0.233584	−	0.381364i
$136$	−6.81681			−0.584537
$137$	0.0411797	+	0.0713253i	0.00351822	+	0.00609373i	0.867779	−	0.496950i	$-0.165547\pi$
$137$	0.0411797	+	0.0713253i	0.00351822	+	0.00609373i	−0.864261	+	0.503044i	$0.832213\pi$
$138$	1.45882	−	8.71362i	0.124183	−	0.741753i
$139$	3.50000	−	6.06218i	0.296866	−	0.514187i	−0.678551	−	0.734553i	$-0.737392\pi$
$139$	3.50000	−	6.06218i	0.296866	−	0.514187i	0.975417	+	0.220366i	$0.0707252\pi$
$140$	0.500000	−	0.866025i	0.0422577	−	0.0731925i
$141$	19.2017	−	7.17760i	1.61707	−	0.604463i
$142$	−2.35799	−	4.08416i	−0.197878	−	0.342735i
$143$	−6.51432			−0.544755
$144$	0.571993	+	2.94497i	0.0476661	+	0.245414i
$145$	0.899170			0.0746720
$146$	4.31681	+	7.47693i	0.357262	+	0.618796i
$147$	−1.33641	−	1.10182i	−0.110225	−	0.0908764i
$148$	−0.357990	+	0.620057i	−0.0294266	+	0.0509683i
$149$	7.20166	−	12.4736i	0.589983	−	1.02188i	−0.404251	−	0.914648i	$-0.632468\pi$
$149$	7.20166	−	12.4736i	0.589983	−	1.02188i	0.994234	−	0.107232i	$-0.0341989\pi$
$150$	−1.33641	−	1.10182i	−0.109118	−	0.0899631i
$151$	−0.917641	−	1.58940i	−0.0746765	−	0.129344i	0.826269	−	0.563276i	$-0.190459\pi$
$151$	−0.917641	−	1.58940i	−0.0746765	−	0.129344i	−0.900946	+	0.433932i	$0.857126\pi$
$152$	2.81681			0.228473
$153$	19.3353	+	6.66086i	1.56316	+	0.538498i
$154$	2.10083			0.169290
$155$	−2.00000	−	3.46410i	−0.160644	−	0.278243i
$156$	−5.03081	+	1.88052i	−0.402787	+	0.150562i
$157$	−10.7521	+	18.6231i	−0.858109	+	1.48629i	0.0156213	+	0.999878i	$0.495027\pi$
$157$	−10.7521	+	18.6231i	−0.858109	+	1.48629i	−0.873730	+	0.486411i	$0.838306\pi$
$158$	2.81681	−	4.87886i	0.224093	−	0.388141i
$159$	1.34875	−	8.05619i	0.106963	−	0.638898i
$160$	0.500000	+	0.866025i	0.0395285	+	0.0684653i
$161$	−5.10083			−0.402002
$162$	1.25518	−	8.91204i	0.0986165	−	0.700196i
$163$	22.0185			1.72462			0.862310	−	0.506381i	$-0.169017\pi$
$163$	22.0185			1.72462			0.862310	+	0.506381i	$0.169017\pi$
$164$	4.05042	+	7.01552i	0.316284	+	0.547820i
$165$	0.600830	−	3.58880i	0.0467746	−	0.279388i
$166$	−2.91764	+	5.05350i	−0.226453	+	0.392228i
$167$	7.45882	−	12.9191i	0.577181	−	0.999707i	−0.418620	−	0.908161i	$-0.637486\pi$
$167$	7.45882	−	12.9191i	0.577181	−	0.999707i	0.995801	−	0.0915451i	$-0.0291806\pi$
$168$	1.62241	−	0.606458i	0.125172	−	0.0467892i
$169$	1.69243	+	2.93137i	0.130187	+	0.225490i
$170$	6.81681			0.522825
$171$	−7.98963	−	2.75237i	−0.610983	−	0.210479i
$172$	−1.00000			−0.0762493
$173$	6.00000	+	10.3923i	0.456172	+	0.790112i	0.998755	−	0.0498898i	$-0.0158870\pi$
$173$	6.00000	+	10.3923i	0.456172	+	0.790112i	−0.542583	+	0.840002i	$0.682554\pi$
$174$	1.20166	+	0.990721i	0.0910977	+	0.0751064i
$175$	−0.500000	+	0.866025i	−0.0377964	+	0.0654654i
$176$	−1.05042	+	1.81937i	−0.0791780	+	0.137140i
$177$	14.7252	+	12.1404i	1.10681	+	0.912525i
$178$	6.81681	+	11.8071i	0.510942	+	0.884977i
$179$	12.3849			0.925687			0.462844	−	0.886440i	$-0.346829\pi$
$179$	12.3849			0.925687			0.462844	+	0.886440i	$0.346829\pi$
$180$	−0.571993	−	2.94497i	−0.0426339	−	0.219505i
$181$	−23.4689			−1.74443			−0.872215	−	0.489123i	$-0.837317\pi$
$181$	−23.4689			−1.74443			−0.872215	+	0.489123i	$0.837317\pi$
$182$	1.55042	+	2.68540i	0.114924	+	0.199055i
$183$	−11.2232	+	4.19526i	−0.829646	+	0.310122i
$184$	2.55042	−	4.41745i	0.188019	−	0.325659i
$185$	0.357990	−	0.620057i	0.0263199	−	0.0455875i
$186$	1.14399	−	6.83310i	0.0838812	−	0.501027i
$187$	7.16048	+	12.4023i	0.523626	+	0.906947i
$188$	11.8353			0.863177
$189$	−5.19440	+	0.134872i	−0.377837	+	0.00981049i
$190$	−2.81681			−0.204353
$191$	10.6336	+	18.4180i	0.769422	+	1.33268i	0.937877	+	0.346968i	$0.112789\pi$
$191$	10.6336	+	18.4180i	0.769422	+	1.33268i	−0.168455	+	0.985709i	$0.553878\pi$
$192$	−0.285997	+	1.70828i	−0.0206400	+	0.123284i
$193$	−3.57397	+	6.19030i	−0.257260	+	0.445587i	−0.965507	−	0.260377i	$-0.916153\pi$
$193$	−3.57397	+	6.19030i	−0.257260	+	0.445587i	0.708247	+	0.705965i	$0.249486\pi$
$194$	−1.60083	+	2.77272i	−0.114933	+	0.199070i
$195$	5.03081	−	1.88052i	0.360264	−	0.134667i
$196$	−0.500000	−	0.866025i	−0.0357143	−	0.0618590i
$197$	−20.7529			−1.47858			−0.739292	−	0.673385i	$-0.764840\pi$
$197$	−20.7529			−1.47858			−0.739292	+	0.673385i	$0.764840\pi$
$198$	4.75716	−	4.13411i	0.338077	−	0.293798i
$199$	−1.46721			−0.104008			−0.0520039	−	0.998647i	$-0.516561\pi$
$199$	−1.46721			−0.104008			−0.0520039	+	0.998647i	$0.516561\pi$
$200$	−0.500000	−	0.866025i	−0.0353553	−	0.0612372i
$201$	0.822093	+	0.677783i	0.0579860	+	0.0478071i
$202$	7.20166	−	12.4736i	0.506707	−	0.877642i
$203$	0.449585	−	0.778704i	0.0315547	−	0.0546543i
$204$	9.11007	+	7.51089i	0.637832	+	0.525867i
$205$	−4.05042	−	7.01552i	−0.282893	−	0.489986i
$206$	10.9176			0.760668
$207$	−11.5504	+	10.0376i	−0.802809	+	0.697664i
$208$	−3.10083			−0.215004
$209$	−2.95882	−	5.12483i	−0.204666	−	0.354492i
$210$	−1.62241	+	0.606458i	−0.111957	+	0.0418495i
$211$	5.81681	−	10.0750i	0.400446	−	0.693592i	−0.593334	−	0.804956i	$-0.702189\pi$
$211$	5.81681	−	10.0750i	0.400446	−	0.693592i	0.993780	+	0.111364i	$0.0355220\pi$
$212$	2.35799	−	4.08416i	0.161947	−	0.280501i
$213$	−1.34875	+	8.05619i	−0.0924151	+	0.552001i
$214$	5.50924	+	9.54228i	0.376604	+	0.652297i
$215$	1.00000			0.0681994
$216$	2.48040	−	4.56592i	0.168770	−	0.310671i
$217$	−4.00000			−0.271538
$218$	−1.83444	−	3.17734i	−0.124244	−	0.215196i
$219$	2.46919	−	14.7486i	0.166852	−	0.996618i
$220$	1.05042	−	1.81937i	0.0708190	−	0.122662i
$221$	−10.5689	+	18.3058i	−0.710940	+	1.23138i
$222$	1.16161	−	0.434211i	0.0779623	−	0.0291424i
$223$	−10.5597	−	18.2899i	−0.707127	−	1.22478i	−0.965919	−	0.258846i	$-0.916658\pi$
$223$	−10.5597	−	18.2899i	−0.707127	−	1.22478i	0.258792	−	0.965933i	$-0.416676\pi$
$224$	1.00000			0.0668153
$225$	0.571993	+	2.94497i	0.0381329	+	0.196331i
$226$	11.4504			0.761671
$227$	−13.5924	−	23.5428i	−0.902162	−	1.56259i	−0.824682	−	0.565596i	$-0.808646\pi$
$227$	−13.5924	−	23.5428i	−0.902162	−	1.56259i	−0.0774798	−	0.996994i	$-0.524687\pi$
$228$	−3.76442	−	3.10361i	−0.249305	−	0.205542i
$229$	11.9916	−	20.7701i	0.792428	−	1.37253i	−0.132032	−	0.991245i	$-0.542150\pi$
$229$	11.9916	−	20.7701i	0.792428	−	1.37253i	0.924460	−	0.381280i	$-0.124517\pi$
$230$	−2.55042	+	4.41745i	−0.168169	+	0.291278i
$231$	−2.80757	−	2.31473i	−0.184725	−	0.152298i
$232$	0.449585	+	0.778704i	0.0295167	+	0.0511244i
$233$	15.7345			1.03080			0.515399	−	0.856950i	$-0.327644\pi$
$233$	15.7345			1.03080			0.515399	+	0.856950i	$0.327644\pi$
$234$	8.79523	+	3.02989i	0.574962	+	0.198070i
$235$	−11.8353			−0.772049
$236$	5.50924	+	9.54228i	0.358621	+	0.621149i
$237$	−9.14003	+	3.41655i	−0.593709	+	0.221929i
$238$	3.40841	−	5.90353i	0.220934	−	0.382669i
$239$	−8.01847	+	13.8884i	−0.518672	+	0.898366i	0.481093	+	0.876670i	$0.340240\pi$
$239$	−8.01847	+	13.8884i	−0.518672	+	0.898366i	−0.999765	+	0.0216962i	$0.993093\pi$
$240$	0.285997	−	1.70828i	0.0184610	−	0.110269i
$241$	7.14201	+	12.3703i	0.460057	+	0.796843i	0.998963	−	0.0455233i	$-0.0144955\pi$
$241$	7.14201	+	12.3703i	0.460057	+	0.796843i	−0.538906	+	0.842366i	$0.681162\pi$
$242$	−6.58651			−0.423397
$243$	−11.4969	+	10.5272i	−0.737526	+	0.675319i
$244$	−6.91764			−0.442857
$245$	0.500000	+	0.866025i	0.0319438	+	0.0553283i
$246$	2.31681	−	13.8385i	0.147714	−	0.882307i
$247$	4.36723	−	7.56426i	0.277880	−	0.481302i
$248$	2.00000	−	3.46410i	0.127000	−	0.219971i
$249$	9.46721	−	3.53885i	0.599960	−	0.224266i
$250$	0.500000	+	0.866025i	0.0316228	+	0.0547723i
$251$	−25.2017			−1.59071			−0.795357	−	0.606141i	$-0.792717\pi$
$251$	−25.2017			−1.59071			−0.795357	+	0.606141i	$0.792717\pi$
$252$	−2.83641	−	0.977122i	−0.178677	−	0.0615529i
$253$	−10.7160			−0.673708
$254$	−6.46806	−	11.2030i	−0.405842	−	0.702939i
$255$	−9.11007	−	7.51089i	−0.570494	−	0.470350i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−6.21598	+	10.7664i	−0.387742	+	0.671589i	−0.992145	−	0.125089i	$-0.960078\pi$
$257$	−6.21598	+	10.7664i	−0.387742	+	0.671589i	0.604403	+	0.796679i	$0.293412\pi$
$258$	1.33641	+	1.10182i	0.0832014	+	0.0685962i
$259$	−0.357990	−	0.620057i	−0.0222444	−	0.0385284i
$260$	3.10083			0.192305
$261$	−0.514319	−	2.64802i	−0.0318355	−	0.163909i
$262$	11.4504			0.707410
$263$	5.46806	+	9.47095i	0.337175	+	0.584004i	0.983900	−	0.178719i	$-0.0571953\pi$
$263$	5.46806	+	9.47095i	0.337175	+	0.584004i	−0.646725	+	0.762723i	$0.723862\pi$
$264$	3.40841	−	1.27406i	0.209773	−	0.0784132i
$265$	−2.35799	+	4.08416i	−0.144850	+	0.250888i
$266$	−1.40841	+	2.43943i	−0.0863549	+	0.149571i
$267$	3.89917	−	23.2900i	0.238625	−	1.42532i
$268$	0.307575	+	0.532735i	0.0187881	+	0.0325420i
$269$	−2.05372			−0.125218			−0.0626088	−	0.998038i	$-0.519942\pi$
$269$	−2.05372			−0.125218			−0.0626088	+	0.998038i	$0.519942\pi$
$270$	−2.48040	+	4.56592i	−0.150952	+	0.277873i
$271$	−3.26555			−0.198368			−0.0991840	−	0.995069i	$-0.531623\pi$
$271$	−3.26555			−0.198368			−0.0991840	+	0.995069i	$0.531623\pi$
$272$	3.40841	+	5.90353i	0.206665	+	0.357954i
$273$	0.886827	−	5.29707i	0.0536732	−	0.320593i
$274$	0.0411797	−	0.0713253i	0.00248775	−	0.00430892i
$275$	−1.05042	+	1.81937i	−0.0633424	+	0.109712i
$276$	−8.27563	+	3.09344i	−0.498134	+	0.186203i
$277$	−10.8168	−	18.7353i	−0.649919	−	1.12569i	−0.983142	−	0.182845i	$-0.941469\pi$
$277$	−10.8168	−	18.7353i	−0.649919	−	1.12569i	0.333223	−	0.942848i	$-0.391864\pi$
$278$	−7.00000			−0.419832
$279$	−9.05767	+	7.87137i	−0.542269	+	0.471247i
$280$	−1.00000			−0.0597614
$281$	11.6429	+	20.1660i	0.694555	+	1.20300i	0.970331	+	0.241782i	$0.0777318\pi$
$281$	11.6429	+	20.1660i	0.694555	+	1.20300i	−0.275776	+	0.961222i	$0.588935\pi$
$282$	−15.8168	−	13.0403i	−0.941877	−	0.776540i
$283$	−3.10083	+	5.37080i	−0.184325	+	0.319261i	−0.943349	−	0.331802i	$-0.892343\pi$
$283$	−3.10083	+	5.37080i	−0.184325	+	0.319261i	0.759024	+	0.651063i	$0.225677\pi$
$284$	−2.35799	+	4.08416i	−0.139921	+	0.242350i
$285$	3.76442	+	3.10361i	0.222985	+	0.183842i
$286$	3.25716	+	5.64157i	0.192600	+	0.333593i
$287$	−8.10083			−0.478177
$288$	2.26442	−	1.96784i	0.133432	−	0.115956i
$289$	29.4689			1.73346
$290$	−0.449585	−	0.778704i	−0.0264005	−	0.0457271i
$291$	5.19440	−	1.94167i	0.304501	−	0.113823i
$292$	4.31681	−	7.47693i	0.252622	−	0.437555i
$293$	16.1840	−	28.0316i	0.945481	−	1.63762i	0.190697	−	0.981649i	$-0.438925\pi$
$293$	16.1840	−	28.0316i	0.945481	−	1.63762i	0.754784	−	0.655973i	$-0.227741\pi$
$294$	−0.285997	+	1.70828i	−0.0166797	+	0.0996287i
$295$	−5.50924	−	9.54228i	−0.320760	−	0.555573i
$296$	0.715980			0.0416155
$297$	−10.9126	+	0.283343i	−0.633211	+	0.0164412i
$298$	−14.4033			−0.834362
$299$	−7.90841	−	13.6978i	−0.457355	−	0.792162i
$300$	−0.285997	+	1.70828i	−0.0165120	+	0.0986273i
$301$	0.500000	−	0.866025i	0.0288195	−	0.0499169i
$302$	−0.917641	+	1.58940i	−0.0528043	+	0.0914597i
$303$	−23.3681	+	8.73500i	−1.34246	+	0.501813i
$304$	−1.40841	−	2.43943i	−0.0807776	−	0.139911i
$305$	6.91764			0.396103
$306$	−3.89917	−	20.0753i	−0.222901	−	1.14763i
$307$	−7.73445			−0.441428			−0.220714	−	0.975339i	$-0.570839\pi$
$307$	−7.73445			−0.441428			−0.220714	+	0.975339i	$0.570839\pi$
$308$	−1.05042	−	1.81937i	−0.0598530	−	0.103668i
$309$	−14.5905	−	12.0293i	−0.830023	−	0.684320i
$310$	−2.00000	+	3.46410i	−0.113592	+	0.196748i
$311$	−5.48568	+	9.50148i	−0.311064	+	0.538779i	−0.978593	−	0.205805i	$-0.934019\pi$
$311$	−5.48568	+	9.50148i	−0.311064	+	0.538779i	0.667529	+	0.744584i	$0.267352\pi$
$312$	4.14399	+	3.41655i	0.234607	+	0.193424i
$313$	5.79326	+	10.0342i	0.327454	+	0.567167i	0.982006	−	0.188850i	$-0.0604760\pi$
$313$	5.79326	+	10.0342i	0.327454	+	0.567167i	−0.654552	+	0.756017i	$0.727143\pi$
$314$	21.5042			1.21355
$315$	2.83641	+	0.977122i	0.159814	+	0.0550546i
$316$	−5.63362			−0.316916
$317$	1.07397	+	1.86017i	0.0603201	+	0.104478i	0.894609	−	0.446851i	$-0.147455\pi$
$317$	1.07397	+	1.86017i	0.0603201	+	0.104478i	−0.834288	+	0.551328i	$0.814121\pi$
$318$	−7.65125	+	2.86004i	−0.429061	+	0.160383i
$319$	0.944501	−	1.63592i	0.0528819	−	0.0915942i
$320$	0.500000	−	0.866025i	0.0279508	−	0.0484123i
$321$	3.15125	−	18.8226i	0.175885	−	1.05057i
$322$	2.55042	+	4.41745i	0.142129	+	0.246175i
$323$	−19.2017			−1.06841
$324$	−8.34565	+	3.36900i	−0.463647	+	0.187167i
$325$	−3.10083			−0.172003
$326$	−11.0092	−	19.0686i	−0.609745	−	1.05611i
$327$	−1.04928	+	6.26744i	−0.0580256	+	0.346590i
$328$	4.05042	−	7.01552i	0.223647	−	0.387368i
$329$	−5.91764	+	10.2497i	−0.326250	+	0.565082i
$330$	−3.40841	+	1.27406i	−0.187627	+	0.0701349i
$331$	−1.08236	−	1.87470i	−0.0594918	−	0.103043i	0.834746	−	0.550636i	$-0.185615\pi$
$331$	−1.08236	−	1.87470i	−0.0594918	−	0.103043i	−0.894237	+	0.447593i	$0.852281\pi$
$332$	5.83528			0.320253
$333$	−2.03081	−	0.699600i	−0.111288	−	0.0383378i
$334$	−14.9176			−0.816257
$335$	−0.307575	−	0.532735i	−0.0168046	−	0.0291064i
$336$	−1.33641	−	1.10182i	−0.0729072	−	0.0601091i
$337$	15.5924	−	27.0069i	0.849374	−	1.47116i	−0.0323931	−	0.999475i	$-0.510313\pi$
$337$	15.5924	−	27.0069i	0.849374	−	1.47116i	0.881767	−	0.471684i	$-0.156354\pi$
$338$	1.69243	−	2.93137i	0.0920558	−	0.159445i
$339$	−15.3025	−	12.6163i	−0.831117	−	0.685223i
$340$	−3.40841	−	5.90353i	−0.184847	−	0.320164i
$341$	−8.40332			−0.455065
$342$	1.61120	+	8.29541i	0.0871235	+	0.448564i
$343$	1.00000			0.0539949
$344$	0.500000	+	0.866025i	0.0269582	+	0.0466930i
$345$	8.27563	−	3.09344i	0.445545	−	0.166545i
$346$	6.00000	−	10.3923i	0.322562	−	0.558694i
$347$	12.7109	−	22.0159i	0.682357	−	1.18188i	−0.291903	−	0.956448i	$-0.594288\pi$
$347$	12.7109	−	22.0159i	0.682357	−	1.18188i	0.974260	−	0.225429i	$-0.0723782\pi$
$348$	0.257159	−	1.53603i	0.0137852	−	0.0823398i
$349$	−11.3765	−	19.7046i	−0.608968	−	1.05476i	−0.991411	−	0.130784i	$-0.958250\pi$
$349$	−11.3765	−	19.7046i	−0.608968	−	1.05476i	0.382443	−	0.923979i	$-0.375083\pi$
$350$	1.00000			0.0534522
$351$	−8.41566	−	13.7399i	−0.449195	−	0.733383i
$352$	2.10083			0.111975
$353$	15.6008	+	27.0214i	0.830348	+	1.43821i	0.897762	+	0.440481i	$0.145192\pi$
$353$	15.6008	+	27.0214i	0.830348	+	1.43821i	−0.0674137	+	0.997725i	$0.521475\pi$
$354$	3.15125	−	18.8226i	0.167487	−	1.00041i
$355$	2.35799	−	4.08416i	0.125149	−	0.216765i
$356$	6.81681	−	11.8071i	0.361290	−	0.625773i
$357$	−11.0597	+	4.13411i	−0.585339	+	0.218800i
$358$	−6.19243	−	10.7256i	−0.327280	−	0.566865i
$359$	12.3496			0.651787			0.325893	−	0.945406i	$-0.394335\pi$
$359$	12.3496			0.651787			0.325893	+	0.945406i	$0.394335\pi$
$360$	−2.26442	+	1.96784i	−0.119345	+	0.103714i
$361$	−11.0656			−0.582399
$362$	11.7345	+	20.3247i	0.616749	+	1.06824i
$363$	8.80229	+	7.25714i	0.462001	+	0.380901i
$364$	1.55042	−	2.68540i	0.0812638	−	0.140753i
$365$	−4.31681	+	7.47693i	−0.225952	+	0.391361i
$366$	9.24482	+	7.62198i	0.483234	+	0.398407i
$367$	11.0924	+	19.2127i	0.579021	+	1.00289i	0.995592	+	0.0937902i	$0.0298983\pi$
$367$	11.0924	+	19.2127i	0.579021	+	1.00289i	−0.416571	+	0.909103i	$0.636768\pi$
$368$	−5.10083			−0.265899
$369$	−18.3437	+	15.9412i	−0.954933	+	0.829864i
$370$	−0.715980			−0.0372220
$371$	2.35799	+	4.08416i	0.122421	+	0.212039i
$372$	−6.48963	+	2.42583i	−0.336472	+	0.125773i
$373$	−6.18319	+	10.7096i	−0.320153	+	0.554522i	−0.980519	−	0.196422i	$-0.937068\pi$
$373$	−6.18319	+	10.7096i	−0.320153	+	0.554522i	0.660366	+	0.750944i	$0.270401\pi$
$374$	7.16048	−	12.4023i	0.370260	−	0.641309i
$375$	0.285997	−	1.70828i	0.0147688	−	0.0882150i
$376$	−5.91764	−	10.2497i	−0.305179	−	0.528586i
$377$	2.78817			0.143598
$378$	2.71400	+	4.43105i	0.139593	+	0.227909i
$379$	17.1849			0.882728			0.441364	−	0.897328i	$-0.354495\pi$
$379$	17.1849			0.882728			0.441364	+	0.897328i	$0.354495\pi$
$380$	1.40841	+	2.43943i	0.0722497	+	0.125140i
$381$	−3.69968	+	22.0984i	−0.189541	+	1.13214i
$382$	10.6336	−	18.4180i	0.544063	−	0.942345i
$383$	10.6336	−	18.4180i	0.543353	−	0.941114i	−0.455356	−	0.890309i	$-0.650488\pi$
$383$	10.6336	−	18.4180i	0.543353	−	0.941114i	0.998709	−	0.0508049i	$-0.0161787\pi$
$384$	1.62241	−	0.606458i	0.0827932	−	0.0309482i
$385$	1.05042	+	1.81937i	0.0535341	+	0.0927238i
$386$	7.14794			0.363821
$387$	−0.571993	−	2.94497i	−0.0290761	−	0.149701i
$388$	3.20166			0.162540
$389$	2.01847	+	3.49609i	0.102341	+	0.177259i	0.912649	−	0.408745i	$-0.134034\pi$
$389$	2.01847	+	3.49609i	0.102341	+	0.177259i	−0.810308	+	0.586004i	$0.800700\pi$
$390$	−4.14399	−	3.41655i	−0.209839	−	0.173004i
$391$	−17.3857	+	30.1129i	−0.879232	+	1.52288i
$392$	−0.500000	+	0.866025i	−0.0252538	+	0.0437409i
$393$	−15.3025	−	12.6163i	−0.771909	−	0.636408i
$394$	10.3765	+	17.9726i	0.522759	+	0.905444i
$395$	5.63362			0.283458
$396$	−5.95882	−	2.05277i	−0.299442	−	0.103155i
$397$	36.7714			1.84550			0.922752	−	0.385395i	$-0.125935\pi$
$397$	36.7714			1.84550			0.922752	+	0.385395i	$0.125935\pi$
$398$	0.733605	+	1.27064i	0.0367723	+	0.0636915i
$399$	4.57002	−	1.70828i	0.228787	−	0.0855208i
$400$	−0.500000	+	0.866025i	−0.0250000	+	0.0433013i
$401$	−4.33528	+	7.50893i	−0.216494	+	0.374978i	−0.953734	−	0.300653i	$-0.902795\pi$
$401$	−4.33528	+	7.50893i	−0.216494	+	0.374978i	0.737240	+	0.675631i	$0.236129\pi$
$402$	0.175931	−	1.05084i	0.00877462	−	0.0524114i
$403$	−6.20166	−	10.7416i	−0.308927	−	0.535077i
$404$	−14.4033			−0.716592
$405$	8.34565	−	3.36900i	0.414699	−	0.167407i
$406$	−0.899170			−0.0446250
$407$	−0.752076	−	1.30263i	−0.0372790	−	0.0645692i
$408$	1.94958	−	11.6450i	0.0965188	−	0.576513i
$409$	17.8857	−	30.9789i	0.884391	−	1.53181i	0.0379804	−	0.999278i	$-0.487908\pi$
$409$	17.8857	−	30.9789i	0.884391	−	1.53181i	0.846410	−	0.532531i	$-0.178759\pi$
$410$	−4.05042	+	7.01552i	−0.200036	+	0.346472i
$411$	−0.133620	+	0.0499474i	−0.00659101	+	0.00246373i
$412$	−5.45882	−	9.45495i	−0.268937	−	0.465812i
$413$	−11.0185			−0.542184
$414$	14.4681	+	4.98413i	0.711066	+	0.244957i
$415$	−5.83528			−0.286443
$416$	1.55042	+	2.68540i	0.0760154	+	0.131662i
$417$	9.35488	+	7.71273i	0.458111	+	0.377694i
$418$	−2.95882	+	5.12483i	−0.144721	+	0.250663i
$419$	3.92688	−	6.80155i	0.191840	−	0.332277i	−0.754020	−	0.656852i	$-0.771888\pi$
$419$	3.92688	−	6.80155i	0.191840	−	0.332277i	0.945860	+	0.324574i	$0.105221\pi$
$420$	1.33641	+	1.10182i	0.0652102	+	0.0537632i
$421$	−17.1017	−	29.6210i	−0.833485	−	1.44364i	−0.895258	−	0.445548i	$-0.853009\pi$
$421$	−17.1017	−	29.6210i	−0.833485	−	1.44364i	0.0617735	−	0.998090i	$-0.480324\pi$
$422$	−11.6336			−0.566316
$423$	6.76970	+	34.8545i	0.329154	+	1.69468i
$424$	−4.71598			−0.229028
$425$	3.40841	+	5.90353i	0.165332	+	0.286363i
$426$	7.65125	−	2.86004i	0.370704	−	0.138569i
$427$	3.45882	−	5.99085i	0.167384	−	0.289918i
$428$	5.50924	−	9.54228i	0.266299	−	0.461243i
$429$	1.86307	−	11.1283i	0.0899500	−	0.537277i
$430$	−0.500000	−	0.866025i	−0.0241121	−	0.0417635i
$431$	25.4689			1.22679			0.613397	−	0.789775i	$-0.289803\pi$
$431$	25.4689			1.22679			0.613397	+	0.789775i	$0.289803\pi$
$432$	−5.19440	+	0.134872i	−0.249916	+	0.00648903i
$433$	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
$435$	−0.257159	+	1.53603i	−0.0123299	+	0.0736470i
$436$	−1.83444	+	3.17734i	−0.0878535	+	0.152167i
$437$	7.18404	−	12.4431i	0.343659	−	0.595235i
$438$	−14.0073	+	5.23592i	−0.669293	+	0.250182i
$439$	−4.36723	−	7.56426i	−0.208436	−	0.361022i	0.742786	−	0.669529i	$-0.233504\pi$
$439$	−4.36723	−	7.56426i	−0.208436	−	0.361022i	−0.951222	+	0.308507i	$0.900171\pi$
$440$	−2.10083			−0.100153
$441$	2.26442	−	1.96784i	0.107829	−	0.0937068i
$442$	21.1378			1.00542
$443$	9.08651	+	15.7383i	0.431713	+	0.747749i	0.997021	−	0.0771309i	$-0.0245759\pi$
$443$	9.08651	+	15.7383i	0.431713	+	0.747749i	−0.565308	+	0.824880i	$0.691243\pi$
$444$	−0.956844	−	0.788880i	−0.0454098	−	0.0374386i
$445$	−6.81681	+	11.8071i	−0.323148	+	0.559708i
$446$	−10.5597	+	18.2899i	−0.500014	+	0.866050i
$447$	19.2488	+	15.8698i	0.910436	+	0.750618i
$448$	−0.500000	−	0.866025i	−0.0236228	−	0.0409159i
$449$	−3.22013			−0.151967			−0.0759837	−	0.997109i	$-0.524210\pi$
$449$	−3.22013			−0.151967			−0.0759837	+	0.997109i	$0.524210\pi$
$450$	2.26442	−	1.96784i	0.106746	−	0.0927650i
$451$	−17.0185			−0.801369
$452$	−5.72522	−	9.91636i	−0.269291	−	0.466427i
$453$	2.97758	−	1.11302i	0.139899	−	0.0522942i
$454$	−13.5924	+	23.5428i	−0.637925	+	1.10492i
$455$	−1.55042	+	2.68540i	−0.0726846	+	0.125893i
$456$	−0.805598	+	4.81189i	−0.0377256	+	0.225337i
$457$	−3.76640	−	6.52359i	−0.176185	−	0.305161i	0.764386	−	0.644759i	$-0.223042\pi$
$457$	−3.76640	−	6.52359i	−0.176185	−	0.305161i	−0.940571	+	0.339598i	$0.889709\pi$
$458$	−23.9832			−1.12066
$459$	−16.9084	+	31.1250i	−0.789217	+	1.45279i
$460$	5.10083			0.237827
$461$	13.8437	+	23.9779i	0.644764	+	1.11676i	0.984356	+	0.176191i	$0.0563777\pi$
$461$	13.8437	+	23.9779i	0.644764	+	1.11676i	−0.339592	+	0.940573i	$0.610289\pi$
$462$	−0.600830	+	3.58880i	−0.0279532	+	0.166966i
$463$	6.63362	−	11.4898i	0.308290	−	0.533975i	−0.669698	−	0.742634i	$-0.733576\pi$
$463$	6.63362	−	11.4898i	0.308290	−	0.533975i	0.977989	+	0.208659i	$0.0669098\pi$
$464$	0.449585	−	0.778704i	0.0208714	−	0.0361504i
$465$	6.48963	−	2.42583i	0.300950	−	0.112495i
$466$	−7.86723	−	13.6264i	−0.364442	−	0.631232i
$467$	25.4570			1.17801			0.589006	−	0.808129i	$-0.299520\pi$
$467$	25.4570			1.17801			0.589006	+	0.808129i	$0.299520\pi$
$468$	−1.77365	−	9.13184i	−0.0819872	−	0.422119i
$469$	−0.615149			−0.0284050
$470$	5.91764	+	10.2497i	0.272960	+	0.472781i
$471$	−28.7384	−	23.6937i	−1.32420	−	1.09175i
$472$	5.50924	−	9.54228i	0.253583	−	0.439219i
$473$	1.05042	−	1.81937i	0.0482981	−	0.0836548i
$474$	7.52884	+	6.20723i	0.345811	+	0.285107i
$475$	−1.40841	−	2.43943i	−0.0646221	−	0.111929i
$476$	−6.81681			−0.312448
$477$	13.3765	+	4.60809i	0.612466	+	0.210990i
$478$	16.0369			0.733513
$479$	−14.0361	−	24.3112i	−0.641326	−	1.11081i	−0.985137	−	0.171770i	$-0.945051\pi$
$479$	−14.0361	−	24.3112i	−0.641326	−	1.11081i	0.343811	−	0.939039i	$-0.388282\pi$
$480$	−1.62241	+	0.606458i	−0.0740525	+	0.0276809i
$481$	1.11007	−	1.92269i	0.0506147	−	0.0876671i
$482$	7.14201	−	12.3703i	0.325310	−	0.563453i
$483$	1.45882	−	8.71362i	0.0663786	−	0.396484i
$484$	3.29326	+	5.70409i	0.149693	+	0.259277i
$485$	−3.20166			−0.145380
$486$	14.8652	+	4.69301i	0.674301	+	0.212879i
$487$	11.4320			0.518032			0.259016	−	0.965873i	$-0.416602\pi$
$487$	11.4320			0.518032			0.259016	+	0.965873i	$0.416602\pi$
$488$	3.45882	+	5.99085i	0.156573	+	0.271193i
$489$	−6.29721	+	37.6136i	−0.284770	+	1.70095i
$490$	0.500000	−	0.866025i	0.0225877	−	0.0391230i
$491$	17.4916	−	30.2964i	0.789385	−	1.36726i	−0.136959	−	0.990577i	$-0.543733\pi$
$491$	17.4916	−	30.2964i	0.789385	−	1.36726i	0.926344	−	0.376679i	$-0.122934\pi$
$492$	−13.1429	+	4.91281i	−0.592526	+	0.221487i
$493$	−3.06473	−	5.30828i	−0.138029	−	0.239073i
$494$	−8.73445			−0.392982
$495$	5.95882	+	2.05277i	0.267829	+	0.0922651i
$496$	−4.00000			−0.179605
$497$	−2.35799	−	4.08416i	−0.105770	−	0.183200i
$498$	−7.79834	−	6.42942i	−0.349452	−	0.288109i
$499$	−8.43527	+	14.6103i	−0.377614	+	0.654047i	−0.990715	−	0.135958i	$-0.956589\pi$
$499$	−8.43527	+	14.6103i	−0.377614	+	0.654047i	0.613100	+	0.790005i	$0.289922\pi$
$500$	0.500000	−	0.866025i	0.0223607	−	0.0387298i
$501$	19.9361	+	16.4365i	0.890680	+	0.734330i
$502$	12.6008	+	21.8253i	0.562403	+	0.974110i
$503$	5.83528			0.260182			0.130091	−	0.991502i	$-0.458473\pi$
$503$	5.83528			0.260182			0.130091	+	0.991502i	$0.458473\pi$
$504$	0.571993	+	2.94497i	0.0254786	+	0.131179i
$505$	14.4033			0.640939
$506$	5.35799	+	9.28031i	0.238192	+	0.412560i
$507$	−5.49161	+	2.05277i	−0.243891	+	0.0911666i
$508$	−6.46806	+	11.2030i	−0.286974	+	0.497053i
$509$	−10.7613	+	18.6391i	−0.476987	+	0.826165i	−0.999652	−	0.0263726i	$-0.991604\pi$
$509$	−10.7613	+	18.6391i	−0.476987	+	0.826165i	0.522665	+	0.852538i	$0.324938\pi$
$510$	−1.94958	+	11.6450i	−0.0863291	+	0.515649i
$511$	4.31681	+	7.47693i	0.190964	+	0.330760i
$512$	1.00000			0.0441942
$513$	6.98681	−	12.8613i	0.308475	−	0.567842i
$514$	12.4320			0.548350
$515$	5.45882	+	9.45495i	0.240544	+	0.416635i
$516$	0.285997	−	1.70828i	0.0125903	−	0.0752026i
$517$	−12.4320	+	21.5328i	−0.546757	+	0.947011i
$518$	−0.357990	+	0.620057i	−0.0157292	+	0.0272437i
$519$	−19.4689	+	7.27749i	−0.854590	+	0.319446i
$520$	−1.55042	−	2.68540i	−0.0679902	−	0.117762i
$521$	33.7899			1.48036			0.740180	−	0.672408i	$-0.234740\pi$
$521$	33.7899			1.48036			0.740180	+	0.672408i	$0.234740\pi$
$522$	−2.03610	+	1.76943i	−0.0891175	+	0.0774456i
$523$	32.0554			1.40169			0.700843	−	0.713316i	$-0.252807\pi$
$523$	32.0554			1.40169			0.700843	+	0.713316i	$0.252807\pi$
$524$	−5.72522	−	9.91636i	−0.250107	−	0.433198i
$525$	−1.33641	−	1.10182i	−0.0583258	−	0.0480873i
$526$	5.46806	−	9.47095i	0.238419	−	0.412953i
$527$	−13.6336	+	23.6141i	−0.593890	+	1.02865i
$528$	−2.80757	−	2.31473i	−0.122184	−	0.100736i
$529$	−1.50924	−	2.61407i	−0.0656189	−	0.113655i
$530$	4.71598			0.204849
$531$	−24.9504	+	21.6826i	−1.08276	+	0.940946i
$532$	2.81681			0.122124
$533$	−12.5597	−	21.7540i	−0.544019	−	0.942268i
$534$	−22.1193	+	8.26821i	−0.957196	+	0.357801i
$535$	−5.50924	+	9.54228i	−0.238185	+	0.412549i
$536$	0.307575	−	0.532735i	0.0132852	−	0.0230106i
$537$	−3.54203	+	21.1567i	−0.152850	+	0.912981i
$538$	1.02686	+	1.77857i	0.0442711	+	0.0766798i
$539$	2.10083			0.0904892
$540$	5.19440	−	0.134872i	0.223531	−	0.00580396i
$541$	16.5680			0.712316			0.356158	−	0.934426i	$-0.384087\pi$
$541$	16.5680			0.712316			0.356158	+	0.934426i	$0.384087\pi$
$542$	1.63277	+	2.82805i	0.0701337	+	0.121475i
$543$	6.71203	−	40.0914i	0.288041	−	1.72048i
$544$	3.40841	−	5.90353i	0.146134	−	0.253112i
$545$	1.83444	−	3.17734i	0.0785786	−	0.136102i
$546$	−5.03081	+	1.88052i	−0.215299	+	0.0804789i
$547$	21.2529	+	36.8111i	0.908709	+	1.57393i	0.815859	+	0.578251i	$0.196264\pi$
$547$	21.2529	+	36.8111i	0.908709	+	1.57393i	0.0928501	+	0.995680i	$0.470402\pi$
$548$	−0.0823593			−0.00351822
$549$	−3.95684	−	20.3722i	−0.168874	−	0.869465i
$550$	2.10083			0.0895797
$551$	1.26640	+	2.19346i	0.0539502	+	0.0934446i
$552$	6.81681	+	5.62019i	0.290143	+	0.239211i
$553$	2.81681	−	4.87886i	0.119783	−	0.207470i
$554$	−10.8168	+	18.7353i	−0.459562	+	0.795985i
$555$	0.956844	+	0.788880i	0.0406158	+	0.0334861i
$556$	3.50000	+	6.06218i	0.148433	+	0.257094i
$557$	−11.8353			−0.501477			−0.250738	−	0.968055i	$-0.580673\pi$
$557$	−11.8353			−0.501477			−0.250738	+	0.968055i	$0.580673\pi$
$558$	11.3456	+	3.90849i	0.480300	+	0.165460i
$559$	3.10083			0.131151
$560$	0.500000	+	0.866025i	0.0211289	+	0.0365963i
$561$	−23.2345	+	8.68506i	−0.980959	+	0.366683i
$562$	11.6429	−	20.1660i	0.491124	−	0.850652i
$563$	14.2521	−	24.6853i	0.600653	−	1.04036i	−0.392069	−	0.919936i	$-0.628241\pi$
$563$	14.2521	−	24.6853i	0.600653	−	1.04036i	0.992722	−	0.120426i	$-0.0384262\pi$
$564$	−3.38485	+	20.2179i	−0.142528	+	0.851328i
$565$	5.72522	+	9.91636i	0.240862	+	0.417185i
$566$	6.20166			0.260675
$567$	1.25518	−	8.91204i	0.0527127	−	0.374271i
$568$	4.71598			0.197878
$569$	2.50924	+	4.34612i	0.105193	+	0.182199i	0.913817	−	0.406126i	$-0.133121\pi$
$569$	2.50924	+	4.34612i	0.105193	+	0.182199i	−0.808624	+	0.588325i	$0.799787\pi$
$570$	0.805598	−	4.81189i	0.0337428	−	0.201548i
$571$	10.1420	−	17.5665i	0.424430	−	0.735134i	−0.571937	−	0.820297i	$-0.693808\pi$
$571$	10.1420	−	17.5665i	0.424430	−	0.735134i	0.996367	+	0.0851633i	$0.0271412\pi$
$572$	3.25716	−	5.64157i	0.136189	−	0.235886i
$573$	−34.5042	+	12.8977i	−1.44143	+	0.538808i
$574$	4.05042	+	7.01552i	0.169061	+	0.292822i
$575$	−5.10083			−0.212719
$576$	−2.83641	−	0.977122i	−0.118184	−	0.0407134i
$577$	10.4504			0.435057			0.217529	−	0.976054i	$-0.430200\pi$
$577$	10.4504			0.435057			0.217529	+	0.976054i	$0.430200\pi$
$578$	−14.7345	−	25.5208i	−0.612872	−	1.06153i
$579$	−9.55259	−	7.87573i	−0.396992	−	0.327304i
$580$	−0.449585	+	0.778704i	−0.0186680	+	0.0323339i
$581$	−2.91764	+	5.05350i	−0.121044	+	0.209655i
$582$	−4.27874	−	3.52765i	−0.177359	−	0.146226i
$583$	4.95374	+	8.58012i	0.205163	+	0.355352i
$584$	−8.63362			−0.357262
$585$	1.77365	+	9.13184i	0.0733316	+	0.377555i
$586$	−32.3681			−1.33711
$587$	0.315964	+	0.547266i	0.0130412	+	0.0225881i	0.872472	−	0.488663i	$-0.162515\pi$
$587$	0.315964	+	0.547266i	0.0130412	+	0.0225881i	−0.859431	+	0.511252i	$0.829182\pi$
$588$	1.62241	−	0.606458i	0.0669070	−	0.0250099i
$589$	5.63362	−	9.75772i	0.232129	−	0.402060i
$590$	−5.50924	+	9.54228i	−0.226812	+	0.392849i
$591$	5.93527	−	35.4517i	0.244144	−	1.45829i
$592$	−0.357990	−	0.620057i	−0.0147133	−	0.0254842i
$593$	−15.6521			−0.642754			−0.321377	−	0.946951i	$-0.604146\pi$
$593$	−15.6521			−0.642754			−0.321377	+	0.946951i	$0.604146\pi$
$594$	5.70166	+	9.30888i	0.233942	+	0.381948i
$595$	6.81681			0.279462
$596$	7.20166	+	12.4736i	0.294992	+	0.510940i
$597$	0.419617	−	2.50640i	0.0171738	−	0.102580i
$598$	−7.90841	+	13.6978i	−0.323399	+	0.560143i
$599$	−21.8168	+	37.7878i	−0.891411	+	1.54397i	−0.0532258	+	0.998583i	$0.516950\pi$
$599$	−21.8168	+	37.7878i	−0.891411	+	1.54397i	−0.838185	+	0.545386i	$0.816383\pi$
$600$	1.62241	−	0.606458i	0.0662345	−	0.0247585i
$601$	−17.3529	−	30.0561i	−0.707840	−	1.22601i	−0.965657	−	0.259821i	$-0.916337\pi$
$601$	−17.3529	−	30.0561i	−0.707840	−	1.22601i	0.257817	−	0.966194i	$-0.416997\pi$
$602$	−1.00000			−0.0407570
$603$	−1.39296	+	1.21052i	−0.0567255	+	0.0492961i
$604$	1.83528			0.0746765
$605$	−3.29326	−	5.70409i	−0.133890	−	0.231904i
$606$	19.2488	+	15.8698i	0.781928	+	0.644668i
$607$	4.56804	−	7.91208i	0.185411	−	0.321141i	−0.758304	−	0.651901i	$-0.773972\pi$
$607$	4.56804	−	7.91208i	0.185411	−	0.321141i	0.943715	+	0.330760i	$0.107305\pi$
$608$	−1.40841	+	2.43943i	−0.0571184	+	0.0989319i
$609$	1.20166	+	0.990721i	0.0486938	+	0.0401461i
$610$	−3.45882	−	5.99085i	−0.140044	−	0.242563i
$611$	−36.6992			−1.48469
$612$	−15.4361	+	13.4144i	−0.623968	+	0.542246i
$613$	1.39502			0.0563442			0.0281721	−	0.999603i	$-0.491031\pi$
$613$	1.39502			0.0563442			0.0281721	+	0.999603i	$0.491031\pi$
$614$	3.86723	+	6.69823i	0.156069	+	0.270319i
$615$	13.1429	−	4.91281i	0.529971	−	0.198104i
$616$	−1.05042	+	1.81937i	−0.0423224	+	0.0733046i
$617$	−6.39078	+	11.0692i	−0.257283	+	0.445627i	−0.965513	−	0.260354i	$-0.916161\pi$
$617$	−6.39078	+	11.0692i	−0.257283	+	0.445627i	0.708230	+	0.705982i	$0.249494\pi$
$618$	−3.12241	+	18.6503i	−0.125602	+	0.750227i
$619$	−19.5185	−	33.8070i	−0.784514	−	1.35882i	−0.929289	−	0.369353i	$-0.879579\pi$
$619$	−19.5185	−	33.8070i	−0.784514	−	1.35882i	0.144776	−	0.989465i	$-0.453754\pi$
$620$	4.00000			0.160644
$621$	−13.8437	−	22.6020i	−0.555527	−	0.906988i
$622$	10.9714			0.439912
$623$	6.81681	+	11.8071i	0.273110	+	0.473040i
$624$	0.886827	−	5.29707i	0.0355015	−	0.212053i
$625$	−0.500000	+	0.866025i	−0.0200000	+	0.0346410i
$626$	5.79326	−	10.0342i	0.231545	−	0.401048i
$627$	9.60083	−	3.58880i	0.383420	−	0.143323i
$628$	−10.7521	−	18.6231i	−0.429055	−	0.743144i
$629$	−4.88070			−0.194606
$630$	−0.571993	−	2.94497i	−0.0227888	−	0.117330i
$631$	−9.32096			−0.371062			−0.185531	−	0.982638i	$-0.559400\pi$
$631$	−9.32096			−0.371062			−0.185531	+	0.982638i	$0.559400\pi$
$632$	2.81681	+	4.87886i	0.112047	+	0.194071i
$633$	15.5473	+	12.8181i	0.617950	+	0.509475i
$634$	1.07397	−	1.86017i	0.0426528	−	0.0738768i
$635$	6.46806	−	11.2030i	0.256677	−	0.444578i
$636$	6.30249	+	5.19615i	0.249910	+	0.206041i
$637$	1.55042	+	2.68540i	0.0614297	+	0.106399i
$638$	−1.88900			−0.0747863
$639$	−13.3765	−	4.60809i	−0.529165	−	0.182293i
$640$	−1.00000			−0.0395285
$641$	12.3260	+	21.3493i	0.486850	+	0.843248i	0.999886	−	0.0151189i	$-0.00481266\pi$
$641$	12.3260	+	21.3493i	0.486850	+	0.843248i	−0.513036	+	0.858367i	$0.671479\pi$
$642$	−17.8765	+	6.68223i	−0.705528	+	0.263727i
$643$	−7.12354	+	12.3383i	−0.280925	+	0.486576i	−0.971613	−	0.236577i	$-0.923975\pi$
$643$	−7.12354	+	12.3383i	−0.280925	+	0.486576i	0.690688	+	0.723153i	$0.257308\pi$
$644$	2.55042	−	4.41745i	0.100500	−	0.174072i
$645$	−0.285997	+	1.70828i	−0.0112611	+	0.0672633i
$646$	9.60083	+	16.6291i	0.377740	+	0.654264i
$647$	22.4570			0.882877			0.441439	−	0.897291i	$-0.354468\pi$
$647$	22.4570			0.882877			0.441439	+	0.897291i	$0.354468\pi$
$648$	7.09046	+	5.54304i	0.278540	+	0.217751i
$649$	−23.1479			−0.908636
$650$	1.55042	+	2.68540i	0.0608123	+	0.105330i
$651$	1.14399	−	6.83310i	0.0448364	−	0.267810i
$652$	−11.0092	+	19.0686i	−0.431155	+	0.746782i
$653$	−25.0369	+	43.3653i	−0.979771	+	1.69701i	−0.316576	+	0.948567i	$0.602533\pi$
$653$	−25.0369	+	43.3653i	−0.979771	+	1.69701i	−0.663195	+	0.748446i	$0.730800\pi$
$654$	5.95241	−	2.22501i	0.232758	−	0.0870049i
$655$	5.72522	+	9.91636i	0.223703	+	0.387464i
$656$	−8.10083			−0.316284
$657$	24.4885	+	8.43610i	0.955388	+	0.329124i
$658$	11.8353			0.461387
$659$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$659$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$660$	2.80757	+	2.31473i	0.109285	+	0.0901009i
$661$	−18.3681	+	31.8144i	−0.714435	+	1.23744i	0.248742	+	0.968570i	$0.419983\pi$
$661$	−18.3681	+	31.8144i	−0.714435	+	1.23744i	−0.963177	+	0.268868i	$0.913350\pi$
$662$	−1.08236	+	1.87470i	−0.0420671	+	0.0728623i
$663$	−28.2488	−	23.2900i	−1.09709	−	0.904508i
$664$	−2.91764	−	5.05350i	−0.113226	−	0.196114i
$665$	−2.81681			−0.109231
$666$	0.409536	+	2.10854i	0.0158692	+	0.0817041i
$667$	4.58651			0.177590
$668$	7.45882	+	12.9191i	0.288590	+	0.499853i
$669$	34.2641	−	12.8080i	1.32473	−	0.495184i
$670$	−0.307575	+	0.532735i	−0.0118826	+	0.0205813i
$671$	7.26640	−	12.5858i	0.280516	−	0.485868i
$672$	−0.285997	+	1.70828i	−0.0110326	+	0.0658982i
$673$	−10.0824	−	17.4632i	−0.388646	−	0.673155i	0.603621	−	0.797271i	$-0.293724\pi$
$673$	−10.0824	−	17.4632i	−0.388646	−	0.673155i	−0.992268	+	0.124116i	$0.960391\pi$
$674$	−31.1849			−1.20120
$675$	−5.19440	+	0.134872i	−0.199933	+	0.00519122i
$676$	−3.38485			−0.130187
$677$	−12.2849	−	21.2780i	−0.472146	−	0.817780i	0.527346	−	0.849650i	$-0.323187\pi$
$677$	−12.2849	−	21.2780i	−0.472146	−	0.817780i	−0.999492	+	0.0318700i	$0.989854\pi$
$678$	−3.27478	+	19.5605i	−0.125767	+	0.751216i
$679$	−1.60083	+	2.77272i	−0.0614342	+	0.106407i
$680$	−3.40841	+	5.90353i	−0.130706	+	0.226390i
$681$	44.1050	−	16.4865i	1.69011	−	0.631763i
$682$	4.20166	+	7.27749i	0.160890	+	0.278669i
$683$	41.7177			1.59628			0.798141	−	0.602470i	$-0.205817\pi$
$683$	41.7177			1.59628			0.798141	+	0.602470i	$0.205817\pi$
$684$	6.37844	−	5.54304i	0.243886	−	0.211944i
$685$	0.0823593			0.00314679
$686$	−0.500000	−	0.866025i	−0.0190901	−	0.0330650i
$687$	32.0515	+	26.4251i	1.22284	+	1.00818i
$688$	0.500000	−	0.866025i	0.0190623	−	0.0330169i
$689$	−7.31173	+	12.6643i	−0.278555	+	0.482471i
$690$	−6.81681	−	5.62019i	−0.259512	−	0.213957i
$691$	19.8353	+	34.3557i	0.754570	+	1.30695i	0.945588	+	0.325367i	$0.105488\pi$
$691$	19.8353	+	34.3557i	0.754570	+	1.30695i	−0.191018	+	0.981586i	$0.561179\pi$
$692$	−12.0000			−0.456172
$693$	4.75716	−	4.13411i	0.180710	−	0.157042i
$694$	−25.4218			−0.964998
$695$	−3.50000	−	6.06218i	−0.132763	−	0.229952i
$696$	−1.45882	+	0.545308i	−0.0552964	+	0.0206699i
$697$	−27.6109	+	47.8235i	−1.04584	+	1.81144i
$698$	−11.3765	+	19.7046i	−0.430605	+	0.745830i
$699$	−4.50000	+	26.8788i	−0.170206	+	1.01665i
$700$	−0.500000	−	0.866025i	−0.0188982	−	0.0327327i
$701$	10.0017			0.377759			0.188879	−	0.982000i	$-0.439514\pi$
$701$	10.0017			0.377759			0.188879	+	0.982000i	$0.439514\pi$
$702$	−7.69129	+	14.1581i	−0.290289	+	0.534365i
$703$	2.01678			0.0760643
$704$	−1.05042	−	1.81937i	−0.0395890	−	0.0685702i
$705$	3.38485	−	20.2179i	0.127481	−	0.761451i
$706$	15.6008	−	27.0214i	0.587145	−	1.01696i
$707$	7.20166	−	12.4736i	0.270846	−	0.469120i
$708$	−17.8765	+	6.68223i	−0.671839	+	0.251134i
$709$	−14.7336	−	25.5194i	−0.553332	−	0.958399i	−0.998031	−	0.0627193i	$-0.980023\pi$
$709$	−14.7336	−	25.5194i	−0.553332	−	0.958399i	0.444699	−	0.895680i	$-0.353311\pi$
$710$	−4.71598			−0.176988
$711$	−3.22239	−	16.5908i	−0.120849	−	0.622204i
$712$	−13.6336			−0.510942
$713$	−10.2017	−	17.6698i	−0.382055	−	0.661739i
$714$	9.11007	+	7.51089i	0.340936	+	0.281088i
$715$	−3.25716	+	5.64157i	−0.121811	+	0.210983i
$716$	−6.19243	+	10.7256i	−0.231422	+	0.400834i
$717$	−21.4320	−	17.6698i	−0.800391	−	0.659891i
$718$	−6.17480	−	10.6951i	−0.230441	−	0.399136i
$719$	29.8000			1.11135			0.555677	−	0.831398i	$-0.312459\pi$
$719$	29.8000			1.11135			0.555677	+	0.831398i	$0.312459\pi$
$720$	2.83641	+	0.977122i	0.105707	+	0.0364152i
$721$	10.9176			0.406594
$722$	5.53279	+	9.58307i	0.205909	+	0.356645i
$723$	−23.1745	+	8.66265i	−0.861870	+	0.322167i
$724$	11.7345	−	20.3247i	0.436107	−	0.755360i
$725$	0.449585	−	0.778704i	0.0166972	−	0.0289203i
$726$	1.88372	−	11.2516i	0.0699114	−	0.417585i
$727$	−0.357990	−	0.620057i	−0.0132771	−	0.0229966i	0.859311	−	0.511454i	$-0.170893\pi$
$727$	−0.357990	−	0.620057i	−0.0132771	−	0.0229966i	−0.872588	+	0.488458i	$0.837560\pi$
$728$	−3.10083			−0.114924
$729$	−14.6952	−	22.6506i	−0.544268	−	0.838911i
$730$	8.63362			0.319545
$731$	−3.40841	−	5.90353i	−0.126064	−	0.218350i
$732$	1.97842	−	11.8172i	0.0731246	−	0.436778i
$733$	0.698355	−	1.20959i	0.0257943	−	0.0446771i	−0.852840	−	0.522172i	$-0.825122\pi$
$733$	0.698355	−	1.20959i	0.0257943	−	0.0446771i	0.878634	+	0.477495i	$0.158455\pi$
$734$	11.0924	−	19.2127i	0.409429	−	0.709153i
$735$	−1.62241	+	0.606458i	−0.0598434	+	0.0223695i
$736$	2.55042	+	4.41745i	0.0940096	+	0.162829i
$737$	−1.29232			−0.0476034
$738$	22.9773	+	7.91550i	0.845806	+	0.291374i
$739$	−17.0017			−0.625417			−0.312709	−	0.949849i	$-0.601236\pi$
$739$	−17.0017			−0.625417			−0.312709	+	0.949849i	$0.601236\pi$
$740$	0.357990	+	0.620057i	0.0131600	+	0.0227937i
$741$	11.6728	+	9.62378i	0.428812	+	0.353538i
$742$	2.35799	−	4.08416i	0.0865645	−	0.149934i
$743$	−7.20166	+	12.4736i	−0.264203	+	0.457614i	−0.967355	−	0.253427i	$-0.918442\pi$
$743$	−7.20166	+	12.4736i	−0.264203	+	0.457614i	0.703151	+	0.711040i	$0.251776\pi$
$744$	5.34565	+	4.40727i	0.195981	+	0.161578i
$745$	−7.20166	−	12.4736i	−0.263848	−	0.456999i
$746$	12.3664			0.452765
$747$	3.33774	+	17.1847i	0.122122	+	0.628755i
$748$	−14.3210			−0.523626
$749$	5.50924	+	9.54228i	0.201303	+	0.348667i
$750$	−1.62241	+	0.606458i	−0.0592420	+	0.0221447i
$751$	−20.6790	+	35.8170i	−0.754586	+	1.30698i	0.190994	+	0.981591i	$0.438829\pi$
$751$	−20.6790	+	35.8170i	−0.754586	+	1.30698i	−0.945580	+	0.325390i	$0.894505\pi$
$752$	−5.91764	+	10.2497i	−0.215794	+	0.373766i
$753$	7.20759	−	43.0514i	0.262659	−	1.56888i
$754$	−1.39409	−	2.41463i	−0.0507696	−	0.0879356i
$755$	−1.83528			−0.0667927
$756$	2.48040	−	4.56592i	0.0902112	−	0.166061i
$757$	8.51432			0.309458			0.154729	−	0.987957i	$-0.450550\pi$
$757$	8.51432			0.309458			0.154729	+	0.987957i	$0.450550\pi$
$758$	−8.59244	−	14.8825i	−0.312092	−	0.540558i
$759$	3.06473	−	18.3058i	0.111243	−	0.664460i
$760$	1.40841	−	2.43943i	0.0510882	−	0.0884874i
$761$	7.58651	−	13.1402i	0.275011	−	0.476333i	−0.695127	−	0.718887i	$-0.744652\pi$
$761$	7.58651	−	13.1402i	0.275011	−	0.476333i	0.970138	+	0.242554i	$0.0779852\pi$
$762$	20.9877	−	7.84520i	0.760303	−	0.284202i
$763$	−1.83444	−	3.17734i	−0.0664110	−	0.115027i
$764$	−21.2672			−0.769422
$765$	15.4361	−	13.4144i	0.558094	−	0.484999i
$766$	−21.2672			−0.768417
$767$	−17.0832	−	29.5890i	−0.616839	−	1.06840i
$768$	−1.33641	−	1.10182i	−0.0482236	−	0.0397584i
$769$	−20.3117	+	35.1809i	−0.732460	+	1.26866i	0.223369	+	0.974734i	$0.428294\pi$
$769$	−20.3117	+	35.1809i	−0.732460	+	1.26866i	−0.955829	+	0.293923i	$0.905039\pi$
$770$	1.05042	−	1.81937i	0.0378543	−	0.0655656i
$771$	−16.6142	−	13.6978i	−0.598346	−	0.493313i
$772$	−3.57397	−	6.19030i	−0.128630	−	0.222794i
$773$	−36.5697			−1.31532			−0.657661	−	0.753314i	$-0.728454\pi$
$773$	−36.5697			−1.31532			−0.657661	+	0.753314i	$0.728454\pi$
$774$	−2.26442	+	1.96784i	−0.0813928	+	0.0707327i
$775$	−4.00000			−0.143684
$776$	−1.60083	−	2.77272i	−0.0574665	−	0.0995348i
$777$	1.16161	−	0.434211i	0.0416726	−	0.0155772i
$778$	2.01847	−	3.49609i	0.0723657	−	0.125341i
$779$	11.4093	−	19.7614i	0.408779	−	0.708026i
$780$	−0.886827	+	5.29707i	−0.0317535	+	0.189666i
$781$	−4.95374	−	8.58012i	−0.177259	−	0.307021i
$782$	34.7714			1.24342
$783$	4.67065	−	0.121273i	0.166915	−	0.00433393i
$784$	1.00000			0.0357143
$785$	10.7521	+	18.6231i	0.383758	+	0.664688i
$786$	−3.27478	+	19.5605i	−0.116808	+	0.697700i
$787$	−2.93611	+	5.08549i	−0.104661	+	0.181278i	−0.913600	−	0.406615i	$-0.866709\pi$
$787$	−2.93611	+	5.08549i	−0.104661	+	0.181278i	0.808939	+	0.587893i	$0.200042\pi$
$788$	10.3765	−	17.9726i	0.369646	−	0.640246i
$789$	−17.7428	+	6.63229i	−0.631662	+	0.236116i
$790$	−2.81681	−	4.87886i	−0.100218	−	0.173582i
$791$	11.4504			0.407130
$792$	1.20166	+	6.18687i	0.0426992	+	0.219841i
$793$	21.4504			0.761727
$794$	−18.3857	−	31.8450i	−0.652484	−	1.13014i
$795$	−6.30249	−	5.19615i	−0.223526	−	0.184289i
$796$	0.733605	−	1.27064i	0.0260019	−	0.0450367i
$797$	12.2672	−	21.2475i	0.434528	−	0.752625i	−0.562729	−	0.826641i	$-0.690249\pi$
$797$	12.2672	−	21.2475i	0.434528	−	0.752625i	0.997257	+	0.0740169i	$0.0235819\pi$
$798$	−3.76442	−	3.10361i	−0.133259	−	0.109867i
$799$	40.3394	+	69.8699i	1.42711	+	2.47182i
$800$	1.00000			0.0353553
$801$	38.6706	+	13.3217i	1.36636	+	0.470700i
$802$	8.67056			0.306168
$803$	9.06889	+	15.7078i	0.320034	+	0.554315i
$804$	−0.998024	+	0.373062i	−0.0351976	+	0.0131569i
$805$	−2.55042	+	4.41745i	−0.0898903	+	0.155695i
$806$	−6.20166	+	10.7416i	−0.218444	+	0.378356i
$807$	0.587357	−	3.50832i	0.0206760	−	0.123499i
$808$	7.20166	+	12.4736i	0.253354	+	0.438821i
$809$	35.0185			1.23118			0.615592	−	0.788065i	$-0.288917\pi$
$809$	35.0185			1.23118			0.615592	+	0.788065i	$0.288917\pi$
$810$	−7.09046	−	5.54304i	−0.249134	−	0.194763i
$811$	−21.7882			−0.765086			−0.382543	−	0.923938i	$-0.624952\pi$
$811$	−21.7882			−0.765086			−0.382543	+	0.923938i	$0.624952\pi$
$812$	0.449585	+	0.778704i	0.0157773	+	0.0273271i
$813$	0.933936	−	5.57846i	0.0327546	−	0.195645i
$814$	−0.752076	+	1.30263i	−0.0263603	+	0.0456573i
$815$	11.0092	−	19.0686i	0.385637	−	0.667942i
$816$	−11.0597	+	4.13411i	−0.387165	+	0.144723i
$817$	1.40841	+	2.43943i	0.0492739	+	0.0853448i
$818$	−35.7714			−1.25072
$819$	8.79523	+	3.02989i	0.307330	+	0.105873i
$820$	8.10083			0.282893
$821$	−9.83444	−	17.0337i	−0.343224	−	0.594482i	0.641805	−	0.766868i	$-0.278186\pi$
$821$	−9.83444	−	17.0337i	−0.343224	−	0.594482i	−0.985029	+	0.172386i	$0.944852\pi$
$822$	0.110066	+	0.0907450i	0.00383899	+	0.00316510i
$823$	3.73360	−	6.46679i	0.130145	−	0.225418i	−0.793587	−	0.608457i	$-0.791789\pi$
$823$	3.73360	−	6.46679i	0.130145	−	0.225418i	0.923732	+	0.383038i	$0.125122\pi$
$824$	−5.45882	+	9.45495i	−0.190167	+	0.329379i
$825$	−2.80757	−	2.31473i	−0.0977472	−	0.0805887i
$826$	5.50924	+	9.54228i	0.191691	+	0.332018i
$827$	10.7512			0.373857			0.186928	−	0.982374i	$-0.440147\pi$
$827$	10.7512			0.373857			0.186928	+	0.982374i	$0.440147\pi$
$828$	−2.91764	−	15.0218i	−0.101395	−	0.522043i
$829$	−31.0083			−1.07696			−0.538481	−	0.842637i	$-0.681002\pi$
$829$	−31.0083			−1.07696			−0.538481	+	0.842637i	$0.681002\pi$
$830$	2.91764	+	5.05350i	0.101273	+	0.175410i
$831$	35.0986	−	13.1199i	1.21756	−	0.455123i
$832$	1.55042	−	2.68540i	0.0537510	−	0.0930994i
$833$	3.40841	−	5.90353i	0.118094	−	0.204545i
$834$	2.00198	−	11.9579i	0.0693228	−	0.414069i
$835$	−7.45882	−	12.9191i	−0.258123	−	0.447082i
$836$	5.91764			0.204666
$837$	−10.8560	−	17.7242i	−0.375239	−	0.612638i
$838$	−7.85375			−0.271303
$839$	2.50331	+	4.33585i	0.0864237	+	0.149690i	0.905997	−	0.423284i	$-0.139123\pi$
$839$	2.50331	+	4.33585i	0.0864237	+	0.149690i	−0.819573	+	0.572974i	$0.805789\pi$
$840$	0.285997	−	1.70828i	0.00986782	−	0.0589411i
$841$	14.0957	−	24.4146i	0.486060	−	0.841881i
$842$	−17.1017	+	29.6210i	−0.589363	+	1.02081i
$843$	−37.7789	+	14.1218i	−1.30118	+	0.486380i
$844$	5.81681	+	10.0750i	0.200223	+	0.346796i
$845$	3.38485			0.116442
$846$	26.8000	−	23.2900i	0.921404	−	0.800726i
$847$	−6.58651			−0.226315
$848$	2.35799	+	4.08416i	0.0809737	+	0.140251i
$849$	−8.28797	−	6.83310i	−0.284442	−	0.234511i
$850$	3.40841	−	5.90353i	0.116907	−	0.202489i
$851$	1.82605	−	3.16280i	0.0625960	−	0.108420i
$852$	−6.30249	−	5.19615i	−0.215920	−	0.178017i
$853$	−15.8705	−	27.4886i	−0.543397	−	0.941191i	−0.998706	−	0.0508573i	$-0.983805\pi$
$853$	−15.8705	−	27.4886i	−0.543397	−	0.941191i	0.455309	−	0.890333i	$-0.349529\pi$
$854$	−6.91764			−0.236717
$855$	−6.37844	+	5.54304i	−0.218138	+	0.189568i
$856$	−11.0185			−0.376604
$857$	−15.6244	−	27.0622i	−0.533719	−	0.924428i	−0.999224	−	0.0393831i	$-0.987461\pi$
$857$	−15.6244	−	27.0622i	−0.533719	−	0.924428i	0.465505	−	0.885045i	$-0.345873\pi$
$858$	−10.5689	+	3.95066i	−0.360816	+	0.134873i
$859$	7.50924	−	13.0064i	0.256212	−	0.443772i	−0.709012	−	0.705196i	$-0.750859\pi$
$859$	7.50924	−	13.0064i	0.256212	−	0.443772i	0.965224	+	0.261424i	$0.0841922\pi$
$860$	−0.500000	+	0.866025i	−0.0170499	+	0.0295312i
$861$	2.31681	−	13.8385i	0.0789567	−	0.471613i
$862$	−12.7345	−	22.0567i	−0.433737	−	0.751255i
$863$	17.8353			0.607120			0.303560	−	0.952812i	$-0.401825\pi$
$863$	17.8353			0.607120			0.303560	+	0.952812i	$0.401825\pi$
$864$	2.71400	+	4.43105i	0.0923323	+	0.150747i
$865$	12.0000			0.408012
$866$	−14.5000	−	25.1147i	−0.492730	−	0.853433i
$867$	−8.42801	+	50.3410i	−0.286230	+	1.70967i
$868$	2.00000	−	3.46410i	0.0678844	−	0.117579i
$869$	5.91764	−	10.2497i	0.200742	−	0.347696i
$870$	1.45882	−	0.545308i	0.0494586	−	0.0184877i
$871$	−0.953737	−	1.65192i	−0.0323161	−	0.0559732i
$872$	3.66887			0.124244
$873$	1.83133	+	9.42878i	0.0619811	+	0.319116i
$874$	−14.3681			−0.486007
$875$	0.500000	+	0.866025i	0.0169031	+	0.0292770i
$876$	11.5381	+	9.51268i	0.389835	+	0.321404i
$877$	2.94450	−	5.10003i	0.0994287	−	0.172216i	−0.812020	−	0.583630i	$-0.801632\pi$
$877$	2.94450	−	5.10003i	0.0994287	−	0.172216i	0.911448	+	0.411415i	$0.134965\pi$
$878$	−4.36723	+	7.56426i	−0.147387	+	0.255281i
$879$	43.2571	+	35.6637i	1.45902	+	1.20291i
$880$	1.05042	+	1.81937i	0.0354095	+	0.0613310i
$881$	7.85375			0.264600			0.132300	−	0.991210i	$-0.457764\pi$
$881$	7.85375			0.264600			0.132300	+	0.991210i	$0.457764\pi$
$882$	−2.83641	−	0.977122i	−0.0955070	−	0.0329014i
$883$	13.1127			0.441277			0.220639	−	0.975356i	$-0.429186\pi$
$883$	13.1127			0.441277			0.220639	+	0.975356i	$0.429186\pi$
$884$	−10.5689	−	18.3058i	−0.355470	−	0.615692i
$885$	17.8765	−	6.68223i	0.600911	−	0.224621i
$886$	9.08651	−	15.7383i	0.305267	−	0.528739i
$887$	22.8538	−	39.5839i	0.767354	−	1.32910i	−0.171639	−	0.985160i	$-0.554906\pi$
$887$	22.8538	−	39.5839i	0.767354	−	1.32910i	0.938993	−	0.343936i	$-0.111760\pi$
$888$	−0.204768	+	1.22309i	−0.00687156	+	0.0410442i
$889$	−6.46806	−	11.2030i	−0.216932	−	0.375737i
$890$	13.6336			0.457000
$891$	2.63693	−	18.7227i	0.0883404	−	0.627234i
$892$	21.1193			0.707127
$893$	−16.6689	−	28.8713i	−0.557802	−	0.966142i
$894$	4.11930	−	24.6048i	0.137770	−	0.822909i
$895$	6.19243	−	10.7256i	0.206990	−	0.358517i
$896$	−0.500000	+	0.866025i	−0.0167038	+	0.0289319i
$897$	25.6613	−	9.59222i	0.856807	−	0.320275i
$898$	1.61007	+	2.78872i	0.0537286	+	0.0930607i
$899$	3.59668			0.119956
$900$	−2.83641	−	0.977122i	−0.0945471	−	0.0325707i
$901$	32.1479			1.07100
$902$	8.50924	+	14.7384i	0.283327	+	0.490736i
$903$	1.33641	+	1.10182i	0.0444730	+	0.0366662i
$904$	−5.72522	+	9.91636i	−0.190418	+	0.329813i
$905$	−11.7345	+	20.3247i	−0.390066	+	0.675615i
$906$	−2.45269	−	2.02215i	−0.0814852	−	0.0671813i
$907$	23.7580	+	41.1501i	0.788872	+	1.36637i	0.926659	+	0.375904i	$0.122668\pi$
$907$	23.7580	+	41.1501i	0.788872	+	1.36637i	−0.137787	+	0.990462i	$0.543999\pi$
$908$	27.1849			0.902162
$909$	−8.23860	−	42.4173i	−0.273257	−	1.40689i
$910$	3.10083			0.102792
$911$	15.9445	+	27.6167i	0.528265	+	0.914982i	0.999457	+	0.0329510i	$0.0104905\pi$
$911$	15.9445	+	27.6167i	0.528265	+	0.914982i	−0.471192	+	0.882031i	$0.656176\pi$
$912$	4.57002	−	1.70828i	0.151328	−	0.0565667i
$913$	−6.12947	+	10.6166i	−0.202856	+	0.351357i
$914$	−3.76640	+	6.52359i	−0.124581	+	0.215781i
$915$	−1.97842	+	11.8172i	−0.0654046	+	0.390666i
$916$	11.9916	+	20.7701i	0.396214	+	0.686263i
$917$	11.4504			0.378127
$918$	35.4093	−	0.919396i	1.16868	−	0.0303446i
$919$	0.110997			0.00366146			0.00183073	−	0.999998i	$-0.499417\pi$
$919$	0.110997			0.00366146			0.00183073	+	0.999998i	$0.499417\pi$
$920$	−2.55042	−	4.41745i	−0.0840847	−	0.145639i
$921$	2.21203	−	13.2126i	0.0728888	−	0.435369i
$922$	13.8437	−	23.9779i	0.455917	−	0.789671i
$923$	7.31173	−	12.6643i	0.240668	−	0.416850i
$924$	3.40841	−	1.27406i	0.112128	−	0.0419136i
$925$	−0.357990	−	0.620057i	−0.0117706	−	0.0203873i
$926$	−13.2672			−0.435989
$927$	24.7221	−	21.4842i	0.811981	−	0.705634i
$928$	−0.899170			−0.0295167
$929$	−12.6873	−	21.9751i	−0.416258	−	0.720980i	0.579301	−	0.815113i	$-0.303325\pi$
$929$	−12.6873	−	21.9751i	−0.416258	−	0.720980i	−0.995560	+	0.0941331i	$0.969992\pi$
$930$	−5.34565	−	4.40727i	−0.175291	−	0.144520i
$931$	−1.40841	+	2.43943i	−0.0461586	+	0.0799491i
$932$	−7.86723	+	13.6264i	−0.257700	+	0.446349i
$933$	−14.6623	−	12.0884i	−0.480021	−	0.395758i
$934$	−12.7285	−	22.0464i	−0.416490	−	0.721382i
$935$	14.3210			0.468346
$936$	−7.02158	+	6.10195i	−0.229507	+	0.199448i
$937$	−57.5613			−1.88044			−0.940222	−	0.340562i	$-0.889383\pi$
$937$	−57.5613			−1.88044			−0.940222	+	0.340562i	$0.889383\pi$
$938$	0.307575	+	0.532735i	0.0100427	+	0.0173944i
$939$	−18.7981	+	7.02673i	−0.613451	+	0.229309i
$940$	5.91764	−	10.2497i	0.193012	−	0.334307i
$941$	7.11930	−	12.3310i	0.232083	−	0.401979i	−0.726338	−	0.687337i	$-0.758779\pi$
$941$	7.11930	−	12.3310i	0.232083	−	0.401979i	0.958421	+	0.285359i	$0.0921127\pi$
$942$	−6.15012	+	36.7350i	−0.200382	+	1.19689i
$943$	−20.6605	−	35.7850i	−0.672798	−	1.16532i
$944$	−11.0185			−0.358621
$945$	−2.48040	+	4.56592i	−0.0806874	+	0.148529i
$946$	−2.10083			−0.0683039
$947$	16.7201	+	28.9601i	0.543331	+	0.941077i	0.998710	+	0.0507795i	$0.0161706\pi$
$947$	16.7201	+	28.9601i	0.543331	+	0.941077i	−0.455379	+	0.890298i	$0.650496\pi$
$948$	1.61120	−	9.62378i	0.0523292	−	0.312566i
$949$	−13.3857	+	23.1847i	−0.434518	+	0.752607i
$950$	−1.40841	+	2.43943i	−0.0456947	+	0.0791455i
$951$	−3.48484	+	1.30263i	−0.113004	+	0.0422408i
$952$	3.40841	+	5.90353i	0.110467	+	0.191335i
$953$	−25.9361			−0.840153			−0.420077	−	0.907489i	$-0.637997\pi$
$953$	−25.9361			−0.840153			−0.420077	+	0.907489i	$0.637997\pi$
$954$	−2.69751	−	13.8884i	−0.0873351	−	0.449654i
$955$	21.2672			0.688192
$956$	−8.01847	−	13.8884i	−0.259336	−	0.449183i
$957$	2.52449	+	2.08134i	0.0816050	+	0.0672801i
$958$	−14.0361	+	24.3112i	−0.453486	+	0.785460i
$959$	0.0411797	−	0.0713253i	0.00132976	−	0.00230321i
$960$	1.33641	+	1.10182i	0.0431325	+	0.0355610i
$961$	7.50000	+	12.9904i	0.241935	+	0.419045i
$962$	−2.22013			−0.0715799
$963$	31.2529	+	10.7664i	1.00711	+	0.346942i
$964$	−14.2840			−0.460057
$965$	3.57397	+	6.19030i	0.115050	+	0.199273i
$966$	−8.27563	+	3.09344i	−0.266264	+	0.0995297i
$967$	−25.8722	+	44.8120i	−0.831995	+	1.44106i	0.0644595	+	0.997920i	$0.479468\pi$
$967$	−25.8722	+	44.8120i	−0.831995	+	1.44106i	−0.896454	+	0.443137i	$0.853866\pi$
$968$	3.29326	−	5.70409i	0.105849	−	0.183336i
$969$	5.49161	−	32.8017i	0.176416	−	1.05374i
$970$	1.60083	+	2.77272i	0.0513996	+	0.0890267i
$971$	−20.0739			−0.644202			−0.322101	−	0.946705i	$-0.604389\pi$
$971$	−20.0739			−0.644202			−0.322101	+	0.946705i	$0.604389\pi$
$972$	−3.36836	−	15.2202i	−0.108040	−	0.488188i
$973$	−7.00000			−0.224410
$974$	−5.71598	−	9.90037i	−0.183152	−	0.317228i
$975$	0.886827	−	5.29707i	0.0284012	−	0.169642i
$976$	3.45882	−	5.99085i	0.110714	−	0.191763i
$977$	−1.02271	+	1.77138i	−0.0327193	+	0.0566716i	−0.881921	−	0.471397i	$-0.843750\pi$
$977$	−1.02271	+	1.77138i	−0.0327193	+	0.0566716i	0.849202	+	0.528068i	$0.177083\pi$
$978$	35.7230	−	13.3533i	1.14229	−	0.426990i
$979$	14.3210	+	24.8046i	0.457700	+	0.792760i
$980$	−1.00000			−0.0319438
$981$	−10.4064	−	3.58494i	−0.332252	−	0.114458i
$982$	−34.9832			−1.11636
$983$	23.8353	+	41.2839i	0.760227	+	1.31675i	0.942733	+	0.333548i	$0.108246\pi$
$983$	23.8353	+	41.2839i	0.760227	+	1.31675i	−0.182506	+	0.983205i	$0.558421\pi$
$984$	10.8260	+	8.92564i	0.345122	+	0.284539i
$985$	−10.3765	+	17.9726i	−0.330622	+	0.572653i
$986$	−3.06473	+	5.30828i	−0.0976010	+	0.169050i
$987$	−15.8168	−	13.0403i	−0.503455	−	0.415078i
$988$	4.36723	+	7.56426i	0.138940	+	0.240651i
$989$	5.10083			0.162197
$990$	−1.20166	−	6.18687i	−0.0381913	−	0.196632i
$991$	−62.0369			−1.97067			−0.985334	−	0.170636i	$-0.945418\pi$
$991$	−62.0369			−1.97067			−0.985334	+	0.170636i	$0.945418\pi$
$992$	2.00000	+	3.46410i	0.0635001	+	0.109985i
$993$	3.51206	−	1.31281i	0.111452	−	0.0416608i
$994$	−2.35799	+	4.08416i	−0.0747909	+	0.129542i
$995$	−0.733605	+	1.27064i	−0.0232568	+	0.0402820i
$996$	−1.66887	+	9.96827i	−0.0528802	+	0.315857i
$997$	−0.568040	−	0.983875i	−0.0179900	−	0.0311596i	0.856890	−	0.515499i	$-0.172393\pi$
$997$	−0.568040	−	0.983875i	−0.0179900	−	0.0311596i	−0.874880	+	0.484339i	$0.839060\pi$
$998$	16.8705			0.534027
$999$	1.77592	−	3.26911i	0.0561875	−	0.103430i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	630.2.j.j.211.2	✓	6
3.2	odd	2		1890.2.j.i.631.3		6
9.2	odd	6		1890.2.j.i.1261.3		6
9.4	even	3		5670.2.a.br.1.3		3
9.5	odd	6		5670.2.a.bq.1.1		3
9.7	even	3	inner	630.2.j.j.421.2	yes	6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
630.2.j.j.211.2	✓	6	1.1	even	1	trivial
630.2.j.j.421.2	yes	6	9.7	even	3	inner
1890.2.j.i.631.3		6	3.2	odd	2
1890.2.j.i.1261.3		6	9.2	odd	6
5670.2.a.bq.1.1		3	9.5	odd	6
5670.2.a.br.1.3		3	9.4	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)

\(f(q)\)	\(=\)	\(q+(-0.500000 - 0.866025i) q^{2} +(-0.285997 + 1.70828i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(0.500000 - 0.866025i) q^{5} +(1.62241 - 0.606458i) q^{6} +(-0.500000 - 0.866025i) q^{7} +1.00000 q^{8} +(-2.83641 - 0.977122i) q^{9} +O(q^{10})\)	\(q+(-0.500000 - 0.866025i) q^{2} +(-0.285997 + 1.70828i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(0.500000 - 0.866025i) q^{5} +(1.62241 - 0.606458i) q^{6} +(-0.500000 - 0.866025i) q^{7} +1.00000 q^{8} +(-2.83641 - 0.977122i) q^{9} -1.00000 q^{10} +(-1.05042 - 1.81937i) q^{11} +(-1.33641 - 1.10182i) q^{12} +(1.55042 - 2.68540i) q^{13} +(-0.500000 + 0.866025i) q^{14} +(1.33641 + 1.10182i) q^{15} +(-0.500000 - 0.866025i) q^{16} -6.81681 q^{17} +(0.571993 + 2.94497i) q^{18} +2.81681 q^{19} +(0.500000 + 0.866025i) q^{20} +(1.62241 - 0.606458i) q^{21} +(-1.05042 + 1.81937i) q^{22} +(2.55042 - 4.41745i) q^{23} +(-0.285997 + 1.70828i) q^{24} +(-0.500000 - 0.866025i) q^{25} -3.10083 q^{26} +(2.48040 - 4.56592i) q^{27} +1.00000 q^{28} +(0.449585 + 0.778704i) q^{29} +(0.285997 - 1.70828i) q^{30} +(2.00000 - 3.46410i) q^{31} +(-0.500000 + 0.866025i) q^{32} +(3.40841 - 1.27406i) q^{33} +(3.40841 + 5.90353i) q^{34} -1.00000 q^{35} +(2.26442 - 1.96784i) q^{36} +0.715980 q^{37} +(-1.40841 - 2.43943i) q^{38} +(4.14399 + 3.41655i) q^{39} +(0.500000 - 0.866025i) q^{40} +(4.05042 - 7.01552i) q^{41} +(-1.33641 - 1.10182i) q^{42} +(0.500000 + 0.866025i) q^{43} +2.10083 q^{44} +(-2.26442 + 1.96784i) q^{45} -5.10083 q^{46} +(-5.91764 - 10.2497i) q^{47} +(1.62241 - 0.606458i) q^{48} +(-0.500000 + 0.866025i) q^{49} +(-0.500000 + 0.866025i) q^{50} +(1.94958 - 11.6450i) q^{51} +(1.55042 + 2.68540i) q^{52} -4.71598 q^{53} +(-5.19440 + 0.134872i) q^{54} -2.10083 q^{55} +(-0.500000 - 0.866025i) q^{56} +(-0.805598 + 4.81189i) q^{57} +(0.449585 - 0.778704i) q^{58} +(5.50924 - 9.54228i) q^{59} +(-1.62241 + 0.606458i) q^{60} +(3.45882 + 5.99085i) q^{61} -4.00000 q^{62} +(0.571993 + 2.94497i) q^{63} +1.00000 q^{64} +(-1.55042 - 2.68540i) q^{65} +(-2.80757 - 2.31473i) q^{66} +(0.307575 - 0.532735i) q^{67} +(3.40841 - 5.90353i) q^{68} +(6.81681 + 5.62019i) q^{69} +(0.500000 + 0.866025i) q^{70} +4.71598 q^{71} +(-2.83641 - 0.977122i) q^{72} -8.63362 q^{73} +(-0.357990 - 0.620057i) q^{74} +(1.62241 - 0.606458i) q^{75} +(-1.40841 + 2.43943i) q^{76} +(-1.05042 + 1.81937i) q^{77} +(0.886827 - 5.29707i) q^{78} +(2.81681 + 4.87886i) q^{79} -1.00000 q^{80} +(7.09046 + 5.54304i) q^{81} -8.10083 q^{82} +(-2.91764 - 5.05350i) q^{83} +(-0.285997 + 1.70828i) q^{84} +(-3.40841 + 5.90353i) q^{85} +(0.500000 - 0.866025i) q^{86} +(-1.45882 + 0.545308i) q^{87} +(-1.05042 - 1.81937i) q^{88} -13.6336 q^{89} +(2.83641 + 0.977122i) q^{90} -3.10083 q^{91} +(2.55042 + 4.41745i) q^{92} +(5.34565 + 4.40727i) q^{93} +(-5.91764 + 10.2497i) q^{94} +(1.40841 - 2.43943i) q^{95} +(-1.33641 - 1.10182i) q^{96} +(-1.60083 - 2.77272i) q^{97} +1.00000 q^{98} +(1.20166 + 6.18687i) 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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