LMFDB - Embedded newform 630.2.j.k.211.3

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:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			211.3
Root			$1.71903 - 0.211943i$ of defining polynomial
Character	$\chi$	$=$	630.211
Dual form			630.2.j.k.421.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 - 0.866025i) q^{2} +(1.71903 - 0.211943i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-0.500000 + 0.866025i) q^{5} +(-1.04307 - 1.38276i) q^{6} +(-0.500000 - 0.866025i) q^{7} +1.00000 q^{8} +(2.91016 - 0.728674i) q^{9} +O(q^{10})$	\(q+(-0.500000 - 0.866025i) q^{2} +(1.71903 - 0.211943i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-0.500000 + 0.866025i) q^{5} +(-1.04307 - 1.38276i) q^{6} +(-0.500000 - 0.866025i) q^{7} +1.00000 q^{8} +(2.91016 - 0.728674i) q^{9} +1.00000 q^{10} +(-1.04307 - 1.80664i) q^{11} +(-0.675970 + 1.59470i) q^{12} +(1.54307 - 2.67267i) q^{13} +(-0.500000 + 0.866025i) q^{14} +(-0.675970 + 1.59470i) q^{15} +(-0.500000 - 0.866025i) q^{16} +1.64806 q^{17} +(-2.08613 - 2.15594i) q^{18} +4.52420 q^{19} +(-0.500000 - 0.866025i) q^{20} +(-1.04307 - 1.38276i) q^{21} +(-1.04307 + 1.80664i) q^{22} +(1.19113 - 2.06309i) q^{23} +(1.71903 - 0.211943i) q^{24} +(-0.500000 - 0.866025i) q^{25} -3.08613 q^{26} +(4.84823 - 1.86940i) q^{27} +1.00000 q^{28} +(0.895004 + 1.55019i) q^{29} +(1.71903 - 0.211943i) q^{30} +(2.43807 - 4.22286i) q^{31} +(-0.500000 + 0.866025i) q^{32} +(-2.17597 - 2.88461i) q^{33} +(-0.824030 - 1.42726i) q^{34} +1.00000 q^{35} +(-0.824030 + 2.88461i) q^{36} +9.90645 q^{37} +(-2.26210 - 3.91807i) q^{38} +(2.08613 - 4.92145i) q^{39} +(-0.500000 + 0.866025i) q^{40} +(-3.74694 + 6.48990i) q^{41} +(-0.675970 + 1.59470i) q^{42} +(-0.413870 - 0.716844i) q^{43} +2.08613 q^{44} +(-0.824030 + 2.88461i) q^{45} -2.38225 q^{46} +(-1.64806 - 2.85453i) q^{47} +(-1.04307 - 1.38276i) q^{48} +(-0.500000 + 0.866025i) q^{49} +(-0.500000 + 0.866025i) q^{50} +(2.83307 - 0.349294i) q^{51} +(1.54307 + 2.67267i) q^{52} -3.73419 q^{53} +(-4.04307 - 3.26399i) q^{54} +2.08613 q^{55} +(-0.500000 - 0.866025i) q^{56} +(7.77726 - 0.958871i) q^{57} +(0.895004 - 1.55019i) q^{58} +(-5.17597 + 8.96504i) q^{59} +(-1.04307 - 1.38276i) q^{60} +(-1.21903 - 2.11143i) q^{61} -4.87614 q^{62} +(-2.08613 - 2.15594i) q^{63} +1.00000 q^{64} +(1.54307 + 2.67267i) q^{65} +(-1.41016 + 3.32675i) q^{66} +(-5.70017 + 9.87298i) q^{67} +(-0.824030 + 1.42726i) q^{68} +(1.61033 - 3.79897i) q^{69} +(-0.500000 - 0.866025i) q^{70} -15.6587 q^{71} +(2.91016 - 0.728674i) q^{72} +1.70388 q^{73} +(-4.95323 - 8.57924i) q^{74} +(-1.04307 - 1.38276i) q^{75} +(-2.26210 + 3.91807i) q^{76} +(-1.04307 + 1.80664i) q^{77} +(-5.30516 + 0.654083i) q^{78} +(0.351939 + 0.609577i) q^{79} +1.00000 q^{80} +(7.93807 - 4.24111i) q^{81} +7.49389 q^{82} +(-3.73419 - 6.46781i) q^{83} +(1.71903 - 0.211943i) q^{84} +(-0.824030 + 1.42726i) q^{85} +(-0.413870 + 0.716844i) q^{86} +(1.86710 + 2.47515i) q^{87} +(-1.04307 - 1.80664i) q^{88} -2.34452 q^{89} +(2.91016 - 0.728674i) q^{90} -3.08613 q^{91} +(1.19113 + 2.06309i) q^{92} +(3.29612 - 7.77597i) q^{93} +(-1.64806 + 2.85453i) q^{94} +(-2.26210 + 3.91807i) q^{95} +(-0.675970 + 1.59470i) q^{96} +(3.93807 + 6.82094i) q^{97} +1.00000 q^{98} +(-4.35194 - 4.49756i) 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} + 5 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 + 5 * q^9	\( 6 q - 3 q^{2} + q^{3} - 3 q^{4} - 3 q^{5} + q^{6} - 3 q^{7} + 6 q^{8} + 5 q^{9} + 6 q^{10} + q^{11} - 2 q^{12} + 2 q^{13} - 3 q^{14} - 2 q^{15} - 3 q^{16} + 14 q^{17} + 2 q^{18} - 6 q^{19} - 3 q^{20} + q^{21} + q^{22} + 4 q^{23} + q^{24} - 3 q^{25} - 4 q^{26} - 2 q^{27} + 6 q^{28} - 6 q^{29} + q^{30} - 4 q^{31} - 3 q^{32} - 11 q^{33} - 7 q^{34} + 6 q^{35} - 7 q^{36} + 20 q^{37} + 3 q^{38} - 2 q^{39} - 3 q^{40} - 7 q^{41} - 2 q^{42} - 17 q^{43} - 2 q^{44} - 7 q^{45} - 8 q^{46} - 14 q^{47} + q^{48} - 3 q^{49} - 3 q^{50} - 13 q^{51} + 2 q^{52} - 12 q^{53} - 17 q^{54} - 2 q^{55} - 3 q^{56} + 29 q^{57} - 6 q^{58} - 29 q^{59} + q^{60} + 2 q^{61} + 8 q^{62} + 2 q^{63} + 6 q^{64} + 2 q^{65} + 4 q^{66} + q^{67} - 7 q^{68} - 38 q^{69} - 3 q^{70} + 20 q^{71} + 5 q^{72} + 2 q^{73} - 10 q^{74} + q^{75} + 3 q^{76} + q^{77} - 8 q^{78} - 2 q^{79} + 6 q^{80} + 29 q^{81} + 14 q^{82} - 12 q^{83} + q^{84} - 7 q^{85} - 17 q^{86} + 6 q^{87} + q^{88} + 44 q^{89} + 5 q^{90} - 4 q^{91} + 4 q^{92} + 28 q^{93} - 14 q^{94} + 3 q^{95} - 2 q^{96} + 5 q^{97} + 6 q^{98} - 22 q^{99}+O(q^{100}) \) 6 * q - 3 * q^2 + q^3 - 3 * q^4 - 3 * q^5 + q^6 - 3 * q^7 + 6 * q^8 + 5 * q^9 + 6 * q^10 + q^11 - 2 * q^12 + 2 * q^13 - 3 * q^14 - 2 * q^15 - 3 * q^16 + 14 * q^17 + 2 * q^18 - 6 * q^19 - 3 * q^20 + q^21 + q^22 + 4 * q^23 + q^24 - 3 * q^25 - 4 * q^26 - 2 * q^27 + 6 * q^28 - 6 * q^29 + q^30 - 4 * q^31 - 3 * q^32 - 11 * q^33 - 7 * q^34 + 6 * q^35 - 7 * q^36 + 20 * q^37 + 3 * q^38 - 2 * q^39 - 3 * q^40 - 7 * q^41 - 2 * q^42 - 17 * q^43 - 2 * q^44 - 7 * q^45 - 8 * q^46 - 14 * q^47 + q^48 - 3 * q^49 - 3 * q^50 - 13 * q^51 + 2 * q^52 - 12 * q^53 - 17 * q^54 - 2 * q^55 - 3 * q^56 + 29 * q^57 - 6 * q^58 - 29 * q^59 + q^60 + 2 * q^61 + 8 * q^62 + 2 * q^63 + 6 * q^64 + 2 * q^65 + 4 * q^66 + q^67 - 7 * q^68 - 38 * q^69 - 3 * q^70 + 20 * q^71 + 5 * q^72 + 2 * q^73 - 10 * q^74 + q^75 + 3 * q^76 + q^77 - 8 * q^78 - 2 * q^79 + 6 * q^80 + 29 * q^81 + 14 * q^82 - 12 * q^83 + q^84 - 7 * q^85 - 17 * q^86 + 6 * q^87 + q^88 + 44 * q^89 + 5 * q^90 - 4 * q^91 + 4 * q^92 + 28 * q^93 - 14 * q^94 + 3 * q^95 - 2 * q^96 + 5 * q^97 + 6 * q^98 - 22 * 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
$3$	1.71903	−	0.211943i	0.992485	−	0.122365i
$3$	1.71903	−	0.211943i	0.992485	−	0.122365i
$4$	−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
$6$	−1.04307	−	1.38276i	−0.425830	−	0.564508i
$7$	−0.500000	−	0.866025i	−0.188982	−	0.327327i
$7$	−0.500000	−	0.866025i	−0.188982	−	0.327327i
$8$	1.00000			0.353553
$9$	2.91016	−	0.728674i	0.970054	−	0.242891i
$10$	1.00000			0.316228
$11$	−1.04307	−	1.80664i	−0.314496	−	0.544723i	0.664834	−	0.746991i	$-0.268502\pi$
$11$	−1.04307	−	1.80664i	−0.314496	−	0.544723i	−0.979330	+	0.202268i	$0.935169\pi$
$12$	−0.675970	+	1.59470i	−0.195136	+	0.460350i
$13$	1.54307	−	2.67267i	0.427969	−	0.741264i	−0.568723	−	0.822529i	$-0.692562\pi$
$13$	1.54307	−	2.67267i	0.427969	−	0.741264i	0.996693	+	0.0812644i	$0.0258958\pi$
$14$	−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
$17$	1.64806			0.399713			0.199857	−	0.979825i	$-0.435952\pi$
$17$	1.64806			0.399713			0.199857	+	0.979825i	$0.435952\pi$
$18$	−2.08613	−	2.15594i	−0.491706	−	0.508159i
$19$	4.52420			1.03792			0.518961	−	0.854798i	$-0.326319\pi$
$19$	4.52420			1.03792			0.518961	+	0.854798i	$0.326319\pi$
$20$	−0.500000	−	0.866025i	−0.111803	−	0.193649i
$21$	−1.04307	−	1.38276i	−0.227615	−	0.301742i
$22$	−1.04307	+	1.80664i	−0.222382	+	0.385177i
$23$	1.19113	−	2.06309i	0.248367	−	0.430184i	−0.714706	−	0.699425i	$-0.753439\pi$
$23$	1.19113	−	2.06309i	0.248367	−	0.430184i	0.963073	+	0.269241i	$0.0867728\pi$
$24$	1.71903	−	0.211943i	0.350896	−	0.0432626i
$25$	−0.500000	−	0.866025i	−0.100000	−	0.173205i
$26$	−3.08613			−0.605240
$27$	4.84823	−	1.86940i	0.933042	−	0.359767i
$28$	1.00000			0.188982
$29$	0.895004	+	1.55019i	0.166198	+	0.287864i	0.937080	−	0.349114i	$-0.113518\pi$
$29$	0.895004	+	1.55019i	0.166198	+	0.287864i	−0.770882	+	0.636978i	$0.780184\pi$
$30$	1.71903	−	0.211943i	0.313851	−	0.0386953i
$31$	2.43807	−	4.22286i	0.437890	−	0.758448i	−0.559636	−	0.828738i	$-0.689059\pi$
$31$	2.43807	−	4.22286i	0.437890	−	0.758448i	0.997527	+	0.0702902i	$0.0223925\pi$
$32$	−0.500000	+	0.866025i	−0.0883883	+	0.153093i
$33$	−2.17597	−	2.88461i	−0.378788	−	0.502146i
$34$	−0.824030	−	1.42726i	−0.141320	−	0.244774i
$35$	1.00000			0.169031
$36$	−0.824030	+	2.88461i	−0.137338	+	0.480768i
$37$	9.90645			1.62861			0.814305	−	0.580437i	$-0.197118\pi$
$37$	9.90645			1.62861			0.814305	+	0.580437i	$0.197118\pi$
$38$	−2.26210	−	3.91807i	−0.366961	−	0.635595i
$39$	2.08613	−	4.92145i	0.334048	−	0.788063i
$40$	−0.500000	+	0.866025i	−0.0790569	+	0.136931i
$41$	−3.74694	+	6.48990i	−0.585174	+	1.01355i	0.409679	+	0.912230i	$0.365641\pi$
$41$	−3.74694	+	6.48990i	−0.585174	+	1.01355i	−0.994854	+	0.101322i	$0.967693\pi$
$42$	−0.675970	+	1.59470i	−0.104304	+	0.246067i
$43$	−0.413870	−	0.716844i	−0.0631146	−	0.109318i	0.832742	−	0.553662i	$-0.186770\pi$
$43$	−0.413870	−	0.716844i	−0.0631146	−	0.109318i	−0.895856	+	0.444344i	$0.853437\pi$
$44$	2.08613			0.314496
$45$	−0.824030	+	2.88461i	−0.122839	+	0.430012i
$46$	−2.38225			−0.351244
$47$	−1.64806	−	2.85453i	−0.240394	−	0.416375i	0.720432	−	0.693525i	$-0.243943\pi$
$47$	−1.64806	−	2.85453i	−0.240394	−	0.416375i	−0.960827	+	0.277150i	$0.910610\pi$
$48$	−1.04307	−	1.38276i	−0.150553	−	0.199584i
$49$	−0.500000	+	0.866025i	−0.0714286	+	0.123718i
$50$	−0.500000	+	0.866025i	−0.0707107	+	0.122474i
$51$	2.83307	−	0.349294i	0.396710	−	0.0489110i
$52$	1.54307	+	2.67267i	0.213985	+	0.370632i
$53$	−3.73419			−0.512931			−0.256465	−	0.966553i	$-0.582558\pi$
$53$	−3.73419			−0.512931			−0.256465	+	0.966553i	$0.582558\pi$
$54$	−4.04307	−	3.26399i	−0.550191	−	0.444173i
$55$	2.08613			0.281294
$56$	−0.500000	−	0.866025i	−0.0668153	−	0.115728i
$57$	7.77726	−	0.958871i	1.03012	−	0.127006i
$58$	0.895004	−	1.55019i	0.117520	−	0.203550i
$59$	−5.17597	+	8.96504i	−0.673854	+	1.16715i	0.302949	+	0.953007i	$0.402029\pi$
$59$	−5.17597	+	8.96504i	−0.673854	+	1.16715i	−0.976802	+	0.214142i	$0.931304\pi$
$60$	−1.04307	−	1.38276i	−0.134659	−	0.178513i
$61$	−1.21903	−	2.11143i	−0.156081	−	0.270341i	0.777371	−	0.629043i	$-0.216553\pi$
$61$	−1.21903	−	2.11143i	−0.156081	−	0.270341i	−0.933452	+	0.358702i	$0.883220\pi$
$62$	−4.87614			−0.619270
$63$	−2.08613	−	2.15594i	−0.262828	−	0.271622i
$64$	1.00000			0.125000
$65$	1.54307	+	2.67267i	0.191394	+	0.331504i
$66$	−1.41016	+	3.32675i	−0.173579	+	0.409495i
$67$	−5.70017	+	9.87298i	−0.696387	+	1.20618i	0.273325	+	0.961922i	$0.411877\pi$
$67$	−5.70017	+	9.87298i	−0.696387	+	1.20618i	−0.969711	+	0.244255i	$0.921457\pi$
$68$	−0.824030	+	1.42726i	−0.0999284	+	0.173081i
$69$	1.61033	−	3.79897i	0.193861	−	0.457343i
$70$	−0.500000	−	0.866025i	−0.0597614	−	0.103510i
$71$	−15.6587			−1.85835			−0.929175	−	0.369641i	$-0.879481\pi$
$71$	−15.6587			−1.85835			−0.929175	+	0.369641i	$0.879481\pi$
$72$	2.91016	−	0.728674i	0.342966	−	0.0858750i
$73$	1.70388			0.199424			0.0997119	−	0.995016i	$-0.468208\pi$
$73$	1.70388			0.199424			0.0997119	+	0.995016i	$0.468208\pi$
$74$	−4.95323	−	8.57924i	−0.575801	−	0.997316i
$75$	−1.04307	−	1.38276i	−0.120443	−	0.159667i
$76$	−2.26210	+	3.91807i	−0.259481	+	0.449434i
$77$	−1.04307	+	1.80664i	−0.118868	+	0.205886i
$78$	−5.30516	+	0.654083i	−0.600692	+	0.0740603i
$79$	0.351939	+	0.609577i	0.0395963	+	0.0685827i	0.885144	−	0.465317i	$-0.154059\pi$
$79$	0.351939	+	0.609577i	0.0395963	+	0.0685827i	−0.845548	+	0.533899i	$0.820726\pi$
$80$	1.00000			0.111803
$81$	7.93807	−	4.24111i	0.882008	−	0.471235i
$82$	7.49389			0.827561
$83$	−3.73419	−	6.46781i	−0.409881	−	0.709934i	0.584995	−	0.811037i	$-0.301096\pi$
$83$	−3.73419	−	6.46781i	−0.409881	−	0.709934i	−0.994876	+	0.101102i	$0.967763\pi$
$84$	1.71903	−	0.211943i	0.187562	−	0.0231248i
$85$	−0.824030	+	1.42726i	−0.0893786	+	0.154808i
$86$	−0.413870	+	0.716844i	−0.0446287	+	0.0772992i
$87$	1.86710	+	2.47515i	0.200174	+	0.265363i
$88$	−1.04307	−	1.80664i	−0.111191	−	0.192589i
$89$	−2.34452			−0.248519			−0.124259	−	0.992250i	$-0.539655\pi$
$89$	−2.34452			−0.248519			−0.124259	+	0.992250i	$0.539655\pi$
$90$	2.91016	−	0.728674i	0.306758	−	0.0768089i
$91$	−3.08613			−0.323514
$92$	1.19113	+	2.06309i	0.124183	+	0.215092i
$93$	3.29612	−	7.77597i	0.341792	−	0.806331i
$94$	−1.64806	+	2.85453i	−0.169984	+	0.294422i
$95$	−2.26210	+	3.91807i	−0.232087	+	0.401986i
$96$	−0.675970	+	1.59470i	−0.0689909	+	0.162758i
$97$	3.93807	+	6.82094i	0.399850	+	0.692561i	0.993707	−	0.112010i	$-0.0357288\pi$
$97$	3.93807	+	6.82094i	0.399850	+	0.692561i	−0.593857	+	0.804571i	$0.702395\pi$
$98$	1.00000			0.101015
$99$	−4.35194	−	4.49756i	−0.437386	−	0.452022i
$100$	1.00000			0.100000
$101$	−6.25839	−	10.8399i	−0.622733	−	1.07861i	−0.988975	−	0.148086i	$-0.952689\pi$
$101$	−6.25839	−	10.8399i	−0.622733	−	1.07861i	0.366241	−	0.930520i	$-0.380644\pi$
$102$	−1.71903	−	2.27887i	−0.170210	−	0.225641i
$103$	5.65710	−	9.79839i	0.557411	−	0.965464i	−0.440301	−	0.897850i	$-0.645128\pi$
$103$	5.65710	−	9.79839i	0.557411	−	0.965464i	0.997712	−	0.0676138i	$-0.0215386\pi$
$104$	1.54307	−	2.67267i	0.151310	−	0.262077i
$105$	1.71903	−	0.211943i	0.167761	−	0.0206835i
$106$	1.86710	+	3.23390i	0.181348	+	0.314105i
$107$	13.2887			1.28467			0.642334	−	0.766425i	$-0.277966\pi$
$107$	13.2887			1.28467			0.642334	+	0.766425i	$0.277966\pi$
$108$	−0.805165	+	5.13339i	−0.0774770	+	0.493961i
$109$	−15.6029			−1.49449			−0.747244	−	0.664550i	$-0.768623\pi$
$109$	−15.6029			−1.49449			−0.747244	+	0.664550i	$0.768623\pi$
$110$	−1.04307	−	1.80664i	−0.0994524	−	0.172257i
$111$	17.0295	−	2.09960i	1.61637	−	0.199285i
$112$	−0.500000	+	0.866025i	−0.0472456	+	0.0818317i
$113$	−6.93436	+	12.0107i	−0.652330	+	1.12987i	0.330226	+	0.943902i	$0.392875\pi$
$113$	−6.93436	+	12.0107i	−0.652330	+	1.12987i	−0.982556	+	0.185966i	$0.940458\pi$
$114$	−4.71903	−	6.25587i	−0.441978	−	0.585916i
$115$	1.19113	+	2.06309i	0.111073	+	0.192384i
$116$	−1.79001			−0.166198
$117$	2.54307	−	8.90228i	0.235106	−	0.823016i
$118$	10.3519			0.952973
$119$	−0.824030	−	1.42726i	−0.0755387	−	0.130837i
$120$	−0.675970	+	1.59470i	−0.0617073	+	0.145575i
$121$	3.32403	−	5.75739i	0.302185	−	0.523399i
$122$	−1.21903	+	2.11143i	−0.110366	+	0.191160i
$123$	−5.06564	+	11.9505i	−0.456753	+	1.07754i
$124$	2.43807	+	4.22286i	0.218945	+	0.379224i
$125$	1.00000			0.0894427
$126$	−0.824030	+	2.88461i	−0.0734105	+	0.256981i
$127$	−3.96227			−0.351595			−0.175797	−	0.984426i	$-0.556250\pi$
$127$	−3.96227			−0.351595			−0.175797	+	0.984426i	$0.556250\pi$
$128$	−0.500000	−	0.866025i	−0.0441942	−	0.0765466i
$129$	−0.863386	−	1.14456i	−0.0760169	−	0.100773i
$130$	1.54307	−	2.67267i	0.135336	−	0.234408i
$131$	−5.02791	+	8.70859i	−0.439290	+	0.760873i	−0.997635	−	0.0687359i	$-0.978103\pi$
$131$	−5.02791	+	8.70859i	−0.439290	+	0.760873i	0.558344	+	0.829609i	$0.311437\pi$
$132$	3.58613	−	0.442140i	0.312133	−	0.0384834i
$133$	−2.26210	−	3.91807i	−0.196149	−	0.339740i
$134$	11.4003			0.984839
$135$	−0.805165	+	5.13339i	−0.0692976	+	0.441812i
$136$	1.64806			0.141320
$137$	9.92161	+	17.1847i	0.847660	+	1.46819i	0.883291	+	0.468825i	$0.155323\pi$
$137$	9.92161	+	17.1847i	0.847660	+	1.46819i	−0.0356307	+	0.999365i	$0.511344\pi$
$138$	−4.09517	+	0.504901i	−0.348604	+	0.0429800i
$139$	−4.29001	+	7.43051i	−0.363874	+	0.630248i	−0.988595	−	0.150600i	$-0.951879\pi$
$139$	−4.29001	+	7.43051i	−0.363874	+	0.630248i	0.624721	+	0.780848i	$0.285213\pi$
$140$	−0.500000	+	0.866025i	−0.0422577	+	0.0731925i
$141$	−3.43807	−	4.55773i	−0.289538	−	0.383830i
$142$	7.82936	+	13.5609i	0.657026	+	1.13800i
$143$	−6.43807			−0.538378
$144$	−2.08613	−	2.15594i	−0.173844	−	0.179661i
$145$	−1.79001			−0.148652
$146$	−0.851939	−	1.47560i	−0.0705070	−	0.122122i
$147$	−0.675970	+	1.59470i	−0.0557530	+	0.131529i
$148$	−4.95323	+	8.57924i	−0.407153	+	0.705209i
$149$	−0.734191	+	1.27166i	−0.0601473	+	0.104178i	−0.894531	−	0.447006i	$-0.852490\pi$
$149$	−0.734191	+	1.27166i	−0.0601473	+	0.104178i	0.834384	+	0.551184i	$0.185824\pi$
$150$	−0.675970	+	1.59470i	−0.0551927	+	0.130207i
$151$	7.52420	+	13.0323i	0.612311	+	1.06055i	0.990850	+	0.134968i	$0.0430932\pi$
$151$	7.52420	+	13.0323i	0.612311	+	1.06055i	−0.378539	+	0.925585i	$0.623574\pi$
$152$	4.52420			0.366961
$153$	4.79612	−	1.20090i	0.387743	−	0.0970869i
$154$	2.08613			0.168105
$155$	2.43807	+	4.22286i	0.195830	+	0.339188i
$156$	3.21903	+	4.26737i	0.257729	+	0.341663i
$157$	−11.1534	+	19.3182i	−0.890138	+	1.54176i	−0.0504286	+	0.998728i	$0.516059\pi$
$157$	−11.1534	+	19.3182i	−0.890138	+	1.54176i	−0.839709	+	0.543036i	$0.817275\pi$
$158$	0.351939	−	0.609577i	0.0279988	−	0.0484953i
$159$	−6.41920	+	0.791434i	−0.509076	+	0.0627648i
$160$	−0.500000	−	0.866025i	−0.0395285	−	0.0684653i
$161$	−2.38225			−0.187748
$162$	−7.64195	−	4.75401i	−0.600408	−	0.373510i
$163$	9.86872			0.772978			0.386489	−	0.922294i	$-0.373688\pi$
$163$	9.86872			0.772978			0.386489	+	0.922294i	$0.373688\pi$
$164$	−3.74694	−	6.48990i	−0.292587	−	0.506776i
$165$	3.58613	−	0.442140i	0.279180	−	0.0344206i
$166$	−3.73419	+	6.46781i	−0.289829	+	0.501999i
$167$	2.30516	−	3.99266i	0.178379	−	0.308962i	−0.762946	−	0.646462i	$-0.776248\pi$
$167$	2.30516	−	3.99266i	0.178379	−	0.308962i	0.941325	+	0.337500i	$0.109581\pi$
$168$	−1.04307	−	1.38276i	−0.0804742	−	0.106682i
$169$	1.73790	+	3.01013i	0.133685	+	0.231549i
$170$	1.64806			0.126400
$171$	13.1661	−	3.29667i	1.00684	−	0.252102i
$172$	0.827740			0.0631146
$173$	6.43807	+	11.1511i	0.489477	+	0.847800i	0.999927	−	0.0121082i	$-0.00385425\pi$
$173$	6.43807	+	11.1511i	0.489477	+	0.847800i	−0.510449	+	0.859908i	$0.670521\pi$
$174$	1.20999	−	2.85453i	0.0917292	−	0.216401i
$175$	−0.500000	+	0.866025i	−0.0377964	+	0.0654654i
$176$	−1.04307	+	1.80664i	−0.0786240	+	0.136181i
$177$	−6.99760	+	16.5082i	−0.525972	+	1.24083i
$178$	1.17226	+	2.03041i	0.0878646	+	0.152186i
$179$	1.35194			0.101049			0.0505243	−	0.998723i	$-0.483911\pi$
$179$	1.35194			0.101049			0.0505243	+	0.998723i	$0.483911\pi$
$180$	−2.08613	−	2.15594i	−0.155491	−	0.160694i
$181$	−10.0000			−0.743294			−0.371647	−	0.928374i	$-0.621207\pi$
$181$	−10.0000			−0.743294			−0.371647	+	0.928374i	$0.621207\pi$
$182$	1.54307	+	2.67267i	0.114380	+	0.198111i
$183$	−2.54307	−	3.37126i	−0.187989	−	0.249210i
$184$	1.19113	−	2.06309i	0.0878110	−	0.152093i
$185$	−4.95323	+	8.57924i	−0.364168	+	0.630758i
$186$	−8.38225	+	1.03346i	−0.614617	+	0.0757771i
$187$	−1.71903	−	2.97746i	−0.125708	−	0.217733i
$188$	3.29612			0.240394
$189$	−4.04307	−	3.26399i	−0.294090	−	0.237420i
$190$	4.52420			0.328220
$191$	−8.08613	−	14.0056i	−0.585092	−	1.01341i	−0.994864	−	0.101221i	$-0.967725\pi$
$191$	−8.08613	−	14.0056i	−0.585092	−	1.01341i	0.409772	−	0.912188i	$-0.365608\pi$
$192$	1.71903	−	0.211943i	0.124061	−	0.0152956i
$193$	−11.2432	+	19.4739i	−0.809306	+	1.40176i	0.104040	+	0.994573i	$0.466823\pi$
$193$	−11.2432	+	19.4739i	−0.809306	+	1.40176i	−0.913345	+	0.407185i	$0.866510\pi$
$194$	3.93807	−	6.82094i	0.282737	−	0.489715i
$195$	3.21903	+	4.26737i	0.230520	+	0.305592i
$196$	−0.500000	−	0.866025i	−0.0357143	−	0.0618590i
$197$	22.8942			1.63115			0.815573	−	0.578654i	$-0.196422\pi$
$197$	22.8942			1.63115			0.815573	+	0.578654i	$0.196422\pi$
$198$	−1.71903	+	6.01767i	−0.122166	+	0.427657i
$199$	0.853245			0.0604849			0.0302425	−	0.999543i	$-0.490372\pi$
$199$	0.853245			0.0604849			0.0302425	+	0.999543i	$0.490372\pi$
$200$	−0.500000	−	0.866025i	−0.0353553	−	0.0612372i
$201$	−7.70628	+	18.1801i	−0.543559	+	1.28233i
$202$	−6.25839	+	10.8399i	−0.440339	+	0.762689i
$203$	0.895004	−	1.55019i	0.0628170	−	0.108802i
$204$	−1.11404	+	2.62816i	−0.0779983	+	0.184008i
$205$	−3.74694	−	6.48990i	−0.261698	−	0.453274i
$206$	−11.3142			−0.788298
$207$	1.96305	−	6.87187i	0.136441	−	0.477628i
$208$	−3.08613			−0.213985
$209$	−4.71903	−	8.17361i	−0.326422	−	0.565380i
$210$	−1.04307	−	1.38276i	−0.0719783	−	0.0954193i
$211$	13.0484	−	22.6005i	0.898289	−	1.55588i	0.0686081	−	0.997644i	$-0.478144\pi$
$211$	13.0484	−	22.6005i	0.898289	−	1.55588i	0.829681	−	0.558238i	$-0.188522\pi$
$212$	1.86710	−	3.23390i	0.128233	−	0.222105i
$213$	−26.9179	+	3.31875i	−1.84438	+	0.227397i
$214$	−6.64435	−	11.5084i	−0.454199	−	0.786695i
$215$	0.827740			0.0564514
$216$	4.84823	−	1.86940i	0.329880	−	0.127197i
$217$	−4.87614			−0.331014
$218$	7.80146	+	13.5125i	0.528381	+	0.915183i
$219$	2.92903	−	0.361125i	0.197925	−	0.0244025i
$220$	−1.04307	+	1.80664i	−0.0703234	+	0.121804i
$221$	2.54307	−	4.40472i	0.171065	−	0.296293i
$222$	−10.3331	−	13.6982i	−0.693510	−	0.919364i
$223$	1.48484	+	2.57182i	0.0994325	+	0.172222i	0.911450	−	0.411411i	$-0.134964\pi$
$223$	1.48484	+	2.57182i	0.0994325	+	0.172222i	−0.812017	+	0.583633i	$0.801631\pi$
$224$	1.00000			0.0668153
$225$	−2.08613	−	2.15594i	−0.139075	−	0.143729i
$226$	13.8687			0.922534
$227$	−8.15710	−	14.1285i	−0.541406	−	0.937743i	−0.998824	−	0.0484907i	$-0.984559\pi$
$227$	−8.15710	−	14.1285i	−0.541406	−	0.937743i	0.457418	−	0.889252i	$-0.348774\pi$
$228$	−3.05822	+	7.21474i	−0.202536	+	0.477808i
$229$	−2.68742	+	4.65474i	−0.177589	+	0.307594i	−0.941054	−	0.338255i	$-0.890163\pi$
$229$	−2.68742	+	4.65474i	−0.177589	+	0.307594i	0.763465	+	0.645849i	$0.223497\pi$
$230$	1.19113	−	2.06309i	0.0785405	−	0.136036i
$231$	−1.41016	+	3.32675i	−0.0927818	+	0.218884i
$232$	0.895004	+	1.55019i	0.0587599	+	0.101775i
$233$	22.7145			1.48808			0.744040	−	0.668135i	$-0.232907\pi$
$233$	22.7145			1.48808			0.744040	+	0.668135i	$0.232907\pi$
$234$	−8.98113	+	2.24878i	−0.587115	+	0.147007i
$235$	3.29612			0.215015
$236$	−5.17597	−	8.96504i	−0.336927	−	0.583575i
$237$	0.734191	+	0.973292i	0.0476908	+	0.0632221i
$238$	−0.824030	+	1.42726i	−0.0534140	+	0.0925157i
$239$	0.438069	−	0.758758i	0.0283364	−	0.0490800i	−0.851509	−	0.524339i	$-0.824312\pi$
$239$	0.438069	−	0.758758i	0.0283364	−	0.0490800i	0.879846	+	0.475259i	$0.157646\pi$
$240$	1.71903	−	0.211943i	0.110963	−	0.0136808i
$241$	−4.80516	−	8.32279i	−0.309528	−	0.536118i	0.668731	−	0.743504i	$-0.266838\pi$
$241$	−4.80516	−	8.32279i	−0.309528	−	0.536118i	−0.978259	+	0.207386i	$0.933504\pi$
$242$	−6.64806			−0.427354
$243$	12.7469	−	8.97304i	0.817717	−	0.575621i
$244$	2.43807			0.156081
$245$	−0.500000	−	0.866025i	−0.0319438	−	0.0553283i
$246$	12.8823	−	1.58827i	0.821342	−	0.101265i
$247$	6.98113	−	12.0917i	0.444199	−	0.769375i
$248$	2.43807	−	4.22286i	0.154818	−	0.268152i
$249$	−7.79001	−	10.3270i	−0.493672	−	0.654444i
$250$	−0.500000	−	0.866025i	−0.0316228	−	0.0547723i
$251$	−1.81551			−0.114594			−0.0572971	−	0.998357i	$-0.518248\pi$
$251$	−1.81551			−0.114594			−0.0572971	+	0.998357i	$0.518248\pi$
$252$	2.91016	−	0.728674i	0.183323	−	0.0459021i
$253$	−4.96969			−0.312442
$254$	1.98113	+	3.43143i	0.124307	+	0.215307i
$255$	−1.11404	+	2.62816i	−0.0697638	+	0.164582i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−8.05451	+	13.9508i	−0.502427	+	0.870229i	0.497569	+	0.867424i	$0.334226\pi$
$257$	−8.05451	+	13.9508i	−0.502427	+	0.870229i	−0.999996	+	0.00280434i	$0.999107\pi$
$258$	−0.559527	+	1.32000i	−0.0348346	+	0.0821793i
$259$	−4.95323	−	8.57924i	−0.307778	−	0.533088i
$260$	−3.08613			−0.191394
$261$	3.73419	+	3.85914i	0.231141	+	0.238875i
$262$	10.0558			0.621250
$263$	3.89500	+	6.74635i	0.240176	+	0.415997i	0.960764	−	0.277366i	$-0.0894614\pi$
$263$	3.89500	+	6.74635i	0.240176	+	0.415997i	−0.720588	+	0.693363i	$0.756128\pi$
$264$	−2.17597	−	2.88461i	−0.133922	−	0.177535i
$265$	1.86710	−	3.23390i	0.114695	−	0.198657i
$266$	−2.26210	+	3.91807i	−0.138698	+	0.240232i
$267$	−4.03031	+	0.496904i	−0.246651	+	0.0304100i
$268$	−5.70017	−	9.87298i	−0.348193	−	0.603088i
$269$	−19.8310			−1.20912			−0.604558	−	0.796561i	$-0.706650\pi$
$269$	−19.8310			−1.20912			−0.604558	+	0.796561i	$0.706650\pi$
$270$	4.84823	−	1.86940i	0.295054	−	0.113768i
$271$	−3.44549			−0.209298			−0.104649	−	0.994509i	$-0.533372\pi$
$271$	−3.44549			−0.209298			−0.104649	+	0.994509i	$0.533372\pi$
$272$	−0.824030	−	1.42726i	−0.0499642	−	0.0865405i
$273$	−5.30516	+	0.654083i	−0.321083	+	0.0395869i
$274$	9.92161	−	17.1847i	0.599386	−	1.03817i
$275$	−1.04307	+	1.80664i	−0.0628992	+	0.108945i
$276$	2.48484	+	3.29407i	0.149570	+	0.198280i
$277$	9.05582	+	15.6851i	0.544111	+	0.942428i	0.998662	+	0.0517077i	$0.0164664\pi$
$277$	9.05582	+	15.6851i	0.544111	+	0.942428i	−0.454551	+	0.890721i	$0.650200\pi$
$278$	8.58002			0.514595
$279$	4.01809	−	14.0658i	0.240557	−	0.842095i
$280$	1.00000			0.0597614
$281$	11.1699	+	19.3468i	0.666338	+	1.15413i	0.978921	+	0.204240i	$0.0654724\pi$
$281$	11.1699	+	19.3468i	0.666338	+	1.15413i	−0.312583	+	0.949890i	$0.601194\pi$
$282$	−2.22808	+	5.25632i	−0.132680	+	0.313009i
$283$	10.7826	−	18.6760i	0.640958	−	1.11017i	−0.344261	−	0.938874i	$-0.611870\pi$
$283$	10.7826	−	18.6760i	0.640958	−	1.11017i	0.985219	−	0.171299i	$-0.0547963\pi$
$284$	7.82936	−	13.5609i	0.464587	−	0.804689i
$285$	−3.05822	+	7.21474i	−0.181153	+	0.427364i
$286$	3.21903	+	5.57553i	0.190346	+	0.329688i
$287$	7.49389			0.442350
$288$	−0.824030	+	2.88461i	−0.0485565	+	0.169977i
$289$	−14.2839			−0.840229
$290$	0.895004	+	1.55019i	0.0525565	+	0.0910305i
$291$	8.21533	+	10.8908i	0.481591	+	0.638429i
$292$	−0.851939	+	1.47560i	−0.0498560	+	0.0863531i
$293$	3.41920	−	5.92223i	0.199752	−	0.345981i	−0.748696	−	0.662914i	$-0.769320\pi$
$293$	3.41920	−	5.92223i	0.199752	−	0.345981i	0.948448	+	0.316933i	$0.102653\pi$
$294$	1.71903	−	0.211943i	0.100256	−	0.0123607i
$295$	−5.17597	−	8.96504i	−0.301357	−	0.521965i
$296$	9.90645			0.575801
$297$	−8.43436	−	6.80911i	−0.489411	−	0.395104i
$298$	1.46838			0.0850611
$299$	−3.67597	−	6.36697i	−0.212587	−	0.368211i
$300$	1.71903	−	0.211943i	0.0992485	−	0.0122365i
$301$	−0.413870	+	0.716844i	−0.0238551	+	0.0413182i
$302$	7.52420	−	13.0323i	0.432969	−	0.749924i
$303$	−13.0558	−	17.3077i	−0.750037	−	0.994299i
$304$	−2.26210	−	3.91807i	−0.129740	−	0.224717i
$305$	2.43807			0.139603
$306$	−3.43807	−	3.55311i	−0.196541	−	0.203118i
$307$	−17.7268			−1.01172			−0.505860	−	0.862615i	$-0.668825\pi$
$307$	−17.7268			−1.01172			−0.505860	+	0.862615i	$0.668825\pi$
$308$	−1.04307	−	1.80664i	−0.0594341	−	0.102943i
$309$	7.64806	−	18.0428i	0.435083	−	1.02642i
$310$	2.43807	−	4.22286i	0.138473	−	0.239842i
$311$	5.64064	−	9.76988i	0.319851	−	0.553999i	−0.660605	−	0.750733i	$-0.729700\pi$
$311$	5.64064	−	9.76988i	0.319851	−	0.553999i	0.980457	+	0.196734i	$0.0630336\pi$
$312$	2.08613	−	4.92145i	0.118104	−	0.278622i
$313$	−13.9282	−	24.1244i	−0.787271	−	1.36359i	−0.927633	−	0.373493i	$-0.878160\pi$
$313$	−13.9282	−	24.1244i	−0.787271	−	1.36359i	0.140362	−	0.990100i	$-0.455173\pi$
$314$	22.3068			1.25884
$315$	2.91016	−	0.728674i	0.163969	−	0.0410561i
$316$	−0.703878			−0.0395963
$317$	5.56356	+	9.63636i	0.312480	+	0.541232i	0.978899	−	0.204346i	$-0.0655068\pi$
$317$	5.56356	+	9.63636i	0.312480	+	0.541232i	−0.666418	+	0.745578i	$0.732173\pi$
$318$	3.89500	+	5.16348i	0.218421	+	0.289553i
$319$	1.86710	−	3.23390i	0.104537	−	0.181064i
$320$	−0.500000	+	0.866025i	−0.0279508	+	0.0484123i
$321$	22.8437	−	2.81644i	1.27501	−	0.157199i
$322$	1.19113	+	2.06309i	0.0663789	+	0.114972i
$323$	7.45616			0.414872
$324$	−0.296122	+	8.99513i	−0.0164512	+	0.499729i
$325$	−3.08613			−0.171188
$326$	−4.93436	−	8.54656i	−0.273289	−	0.473350i
$327$	−26.8219	+	3.30692i	−1.48326	+	0.182873i
$328$	−3.74694	+	6.48990i	−0.206890	+	0.358345i
$329$	−1.64806	+	2.85453i	−0.0908605	+	0.157375i
$330$	−2.17597	−	2.88461i	−0.119783	−	0.158793i
$331$	−1.14195	−	1.97791i	−0.0627671	−	0.108716i	0.832934	−	0.553372i	$-0.186659\pi$
$331$	−1.14195	−	1.97791i	−0.0627671	−	0.108716i	−0.895701	+	0.444656i	$0.853326\pi$
$332$	7.46838			0.409881
$333$	28.8294	−	7.21857i	1.57984	−	0.395575i
$334$	−4.61033			−0.252266
$335$	−5.70017	−	9.87298i	−0.311434	−	0.539419i
$336$	−0.675970	+	1.59470i	−0.0368772	+	0.0869980i
$337$	3.83548	−	6.64324i	0.208932	−	0.361880i	−0.742447	−	0.669905i	$-0.766335\pi$
$337$	3.83548	−	6.64324i	0.208932	−	0.361880i	0.951378	+	0.308025i	$0.0996680\pi$
$338$	1.73790	−	3.01013i	0.0945293	−	0.163730i
$339$	−9.37483	+	22.1164i	−0.509171	+	1.20120i
$340$	−0.824030	−	1.42726i	−0.0446893	−	0.0774042i
$341$	−10.1723			−0.550859
$342$	−9.43807	−	9.75389i	−0.510352	−	0.527430i
$343$	1.00000			0.0539949
$344$	−0.413870	−	0.716844i	−0.0223144	−	0.0386496i
$345$	2.48484	+	3.29407i	0.133779	+	0.177347i
$346$	6.43807	−	11.1511i	0.346113	−	0.599485i
$347$	12.0521	−	20.8749i	0.646991	−	1.12062i	−0.336847	−	0.941559i	$-0.609360\pi$
$347$	12.0521	−	20.8749i	0.646991	−	1.12062i	0.983838	−	0.179062i	$-0.0573062\pi$
$348$	−3.07709	+	0.379379i	−0.164949	+	0.0203369i
$349$	7.18872	+	12.4512i	0.384803	+	0.666499i	0.991742	−	0.128250i	$-0.0409359\pi$
$349$	7.18872	+	12.4512i	0.384803	+	0.666499i	−0.606938	+	0.794749i	$0.707603\pi$
$350$	1.00000			0.0534522
$351$	2.48484	−	15.8423i	0.132631	−	0.845600i
$352$	2.08613			0.111191
$353$	−11.2342	−	19.4582i	−0.597936	−	1.03565i	−0.993125	−	0.117055i	$-0.962654\pi$
$353$	−11.2342	−	19.4582i	−0.597936	−	1.03565i	0.395190	−	0.918600i	$-0.370679\pi$
$354$	17.7953	−	2.19402i	0.945812	−	0.116611i
$355$	7.82936	−	13.5609i	0.415540	−	0.719736i
$356$	1.17226	−	2.03041i	0.0621297	−	0.107612i
$357$	−1.71903	−	2.27887i	−0.0909810	−	0.120610i
$358$	−0.675970	−	1.17081i	−0.0357261	−	0.0618794i
$359$	24.7220			1.30478			0.652388	−	0.757885i	$-0.273767\pi$
$359$	24.7220			1.30478			0.652388	+	0.757885i	$0.273767\pi$
$360$	−0.824030	+	2.88461i	−0.0434302	+	0.152032i
$361$	1.46838			0.0772833
$362$	5.00000	+	8.66025i	0.262794	+	0.455173i
$363$	4.49389	−	10.6017i	0.235868	−	0.556443i
$364$	1.54307	−	2.67267i	0.0808786	−	0.140086i
$365$	−0.851939	+	1.47560i	−0.0445925	+	0.0772365i
$366$	−1.64806	+	3.88799i	−0.0861455	+	0.203228i
$367$	−12.4216	−	21.5149i	−0.648403	−	1.12307i	−0.983504	−	0.180884i	$-0.942104\pi$
$367$	−12.4216	−	21.5149i	−0.648403	−	1.12307i	0.335102	−	0.942182i	$-0.391229\pi$
$368$	−2.38225			−0.124183
$369$	−6.17519	+	21.6169i	−0.321468	+	1.12533i
$370$	9.90645			0.515012
$371$	1.86710	+	3.23390i	0.0969348	+	0.167896i
$372$	5.08613	+	6.74251i	0.263704	+	0.349583i
$373$	13.2026	−	22.8675i	0.683603	−	1.18404i	−0.290270	−	0.956945i	$-0.593745\pi$
$373$	13.2026	−	22.8675i	0.683603	−	1.18404i	0.973874	−	0.227091i	$-0.0729215\pi$
$374$	−1.71903	+	2.97746i	−0.0888892	+	0.153961i
$375$	1.71903	−	0.211943i	0.0887706	−	0.0109447i
$376$	−1.64806	−	2.85453i	−0.0849922	−	0.147211i
$377$	5.52420			0.284511
$378$	−0.805165	+	5.13339i	−0.0414132	+	0.264033i
$379$	−11.0935			−0.569837			−0.284919	−	0.958552i	$-0.591967\pi$
$379$	−11.0935			−0.569837			−0.284919	+	0.958552i	$0.591967\pi$
$380$	−2.26210	−	3.91807i	−0.116043	−	0.200993i
$381$	−6.81128	+	0.839774i	−0.348952	+	0.0430229i
$382$	−8.08613	+	14.0056i	−0.413722	+	0.716588i
$383$	1.20999	−	2.09577i	0.0618277	−	0.107089i	−0.833455	−	0.552588i	$-0.813640\pi$
$383$	1.20999	−	2.09577i	0.0618277	−	0.107089i	0.895282	+	0.445499i	$0.146974\pi$
$384$	−1.04307	−	1.38276i	−0.0532287	−	0.0705635i
$385$	−1.04307	−	1.80664i	−0.0531595	−	0.0920750i
$386$	22.4865			1.14453
$387$	−1.72677	−	1.78455i	−0.0877768	−	0.0907140i
$388$	−7.87614			−0.399850
$389$	−5.52420	−	9.56819i	−0.280088	−	0.485127i	0.691318	−	0.722551i	$-0.257030\pi$
$389$	−5.52420	−	9.56819i	−0.280088	−	0.485127i	−0.971406	+	0.237424i	$0.923697\pi$
$390$	2.08613	−	4.92145i	0.105635	−	0.249207i
$391$	1.96305	−	3.40010i	0.0992756	−	0.171950i
$392$	−0.500000	+	0.866025i	−0.0252538	+	0.0437409i
$393$	−6.79743	+	16.0360i	−0.342885	+	0.808909i
$394$	−11.4471	−	19.8270i	−0.576697	−	0.998869i
$395$	−0.703878			−0.0354160
$396$	6.07097	−	1.52011i	0.305078	−	0.0763883i
$397$	−32.1345			−1.61279			−0.806393	−	0.591380i	$-0.798583\pi$
$397$	−32.1345			−1.61279			−0.806393	+	0.591380i	$0.798583\pi$
$398$	−0.426622	−	0.738932i	−0.0213846	−	0.0370393i
$399$	−4.71903	−	6.25587i	−0.236247	−	0.313185i
$400$	−0.500000	+	0.866025i	−0.0250000	+	0.0433013i
$401$	−9.54840	+	16.5383i	−0.476824	+	0.825884i	−0.999647	−	0.0265574i	$-0.991546\pi$
$401$	−9.54840	+	16.5383i	−0.476824	+	0.825884i	0.522823	+	0.852441i	$0.324879\pi$
$402$	19.5976	−	2.41622i	0.977438	−	0.120510i
$403$	−7.52420	−	13.0323i	−0.374807	−	0.649185i
$404$	12.5168			0.622733
$405$	−0.296122	+	8.99513i	−0.0147144	+	0.446971i
$406$	−1.79001			−0.0888366
$407$	−10.3331	−	17.8974i	−0.512191	−	0.887142i
$408$	2.83307	−	0.349294i	0.140258	−	0.0172927i
$409$	−16.2079	+	28.0729i	−0.801429	+	1.38812i	0.117246	+	0.993103i	$0.462593\pi$
$409$	−16.2079	+	28.0729i	−0.801429	+	1.38812i	−0.918675	+	0.395014i	$0.870740\pi$
$410$	−3.74694	+	6.48990i	−0.185048	+	0.320513i
$411$	20.6978	+	27.4383i	1.02095	+	1.35343i
$412$	5.65710	+	9.79839i	0.278706	+	0.482732i
$413$	10.3519			0.509386
$414$	−6.93274	+	1.73588i	−0.340725	+	0.0853141i
$415$	7.46838			0.366608
$416$	1.54307	+	2.67267i	0.0756550	+	0.131038i
$417$	−5.79983	+	13.6825i	−0.284019	+	0.670037i
$418$	−4.71903	+	8.17361i	−0.230816	+	0.399784i
$419$	−11.0279	+	19.1009i	−0.538749	+	0.933140i	0.460223	+	0.887803i	$0.347769\pi$
$419$	−11.0279	+	19.1009i	−0.538749	+	0.933140i	−0.998972	+	0.0453367i	$0.985564\pi$
$420$	−0.675970	+	1.59470i	−0.0329839	+	0.0778133i
$421$	−10.5612	−	18.2925i	−0.514719	−	0.891520i	−0.999854	−	0.0170803i	$-0.994563\pi$
$421$	−10.5612	−	18.2925i	−0.514719	−	0.891520i	0.485135	−	0.874439i	$-0.338770\pi$
$422$	−26.0968			−1.27037
$423$	−6.87614	−	7.10623i	−0.334329	−	0.345517i
$424$	−3.73419			−0.181348
$425$	−0.824030	−	1.42726i	−0.0399713	−	0.0692324i
$426$	16.3331	+	21.6522i	0.791340	+	1.04905i
$427$	−1.21903	+	2.11143i	−0.0589932	+	0.102179i
$428$	−6.64435	+	11.5084i	−0.321167	+	0.556277i
$429$	−11.0673	+	1.36450i	−0.534333	+	0.0658788i
$430$	−0.413870	−	0.716844i	−0.0199586	−	0.0345693i
$431$	−12.6433			−0.609004			−0.304502	−	0.952512i	$-0.598490\pi$
$431$	−12.6433			−0.609004			−0.304502	+	0.952512i	$0.598490\pi$
$432$	−4.04307	−	3.26399i	−0.194522	−	0.157039i
$433$	−22.7374			−1.09269			−0.546346	−	0.837560i	$-0.683982\pi$
$433$	−22.7374			−1.09269			−0.546346	+	0.837560i	$0.683982\pi$
$434$	2.43807	+	4.22286i	0.117031	+	0.202704i
$435$	−3.07709	+	0.379379i	−0.147535	+	0.0181898i
$436$	7.80146	−	13.5125i	0.373622	−	0.647132i
$437$	5.38889	−	9.33383i	0.257786	−	0.446498i
$438$	−1.77726	−	2.35605i	−0.0849206	−	0.112576i
$439$	18.5660	+	32.1572i	0.886105	+	1.53478i	0.844442	+	0.535647i	$0.179932\pi$
$439$	18.5660	+	32.1572i	0.886105	+	1.53478i	0.0416629	+	0.999132i	$0.486734\pi$
$440$	2.08613			0.0994524
$441$	−0.824030	+	2.88461i	−0.0392395	+	0.137362i
$442$	−5.08613			−0.241923
$443$	10.9381	+	18.9453i	0.519683	+	0.900118i	0.999738	+	0.0228795i	$0.00728341\pi$
$443$	10.9381	+	18.9453i	0.519683	+	0.900118i	−0.480055	+	0.877238i	$0.659383\pi$
$444$	−6.69646	+	15.7978i	−0.317800	+	0.749731i
$445$	1.17226	−	2.03041i	0.0555705	−	0.0962509i
$446$	1.48484	−	2.57182i	0.0703094	−	0.121779i
$447$	−0.992582	+	2.34163i	−0.0469475	+	0.110755i
$448$	−0.500000	−	0.866025i	−0.0236228	−	0.0409159i
$449$	30.3371			1.43170			0.715848	−	0.698256i	$-0.246040\pi$
$449$	30.3371			1.43170			0.715848	+	0.698256i	$0.246040\pi$
$450$	−0.824030	+	2.88461i	−0.0388452	+	0.135982i
$451$	15.6332			0.736140
$452$	−6.93436	−	12.0107i	−0.326165	−	0.564934i
$453$	15.6965	+	20.8083i	0.737484	+	0.977658i
$454$	−8.15710	+	14.1285i	−0.382832	+	0.663084i
$455$	1.54307	−	2.67267i	0.0723400	−	0.125297i
$456$	7.77726	−	0.958871i	0.364203	−	0.0449032i
$457$	11.2456	+	19.4780i	0.526049	+	0.911143i	0.999540	+	0.0303444i	$0.00966040\pi$
$457$	11.2456	+	19.4780i	0.526049	+	0.911143i	−0.473491	+	0.880799i	$0.657006\pi$
$458$	5.37483			0.251149
$459$	7.99018	−	3.08089i	0.372950	−	0.143804i
$460$	−2.38225			−0.111073
$461$	−12.9532	−	22.4356i	−0.603292	−	1.04493i	−0.992319	−	0.123706i	$-0.960522\pi$
$461$	−12.9532	−	22.4356i	−0.603292	−	1.04493i	0.389027	−	0.921226i	$-0.372811\pi$
$462$	3.58613	−	0.442140i	0.166842	−	0.0205702i
$463$	−4.73419	+	8.19986i	−0.220017	+	0.381080i	−0.954813	−	0.297208i	$-0.903944\pi$
$463$	−4.73419	+	8.19986i	−0.220017	+	0.381080i	0.734796	+	0.678288i	$0.237278\pi$
$464$	0.895004	−	1.55019i	0.0415495	−	0.0719659i
$465$	5.08613	+	6.74251i	0.235864	+	0.312677i
$466$	−11.3573	−	19.6714i	−0.526116	−	0.911259i
$467$	9.72197			0.449879			0.224939	−	0.974373i	$-0.427782\pi$
$467$	9.72197			0.449879			0.224939	+	0.974373i	$0.427782\pi$
$468$	6.43807	+	6.65350i	0.297600	+	0.307558i
$469$	11.4003			0.526419
$470$	−1.64806	−	2.85453i	−0.0760194	−	0.131669i
$471$	−15.0787	+	35.5726i	−0.694790	+	1.63910i
$472$	−5.17597	+	8.96504i	−0.238243	+	0.412650i
$473$	−0.863386	+	1.49543i	−0.0396985	+	0.0687599i
$474$	0.475800	−	1.12247i	0.0218542	−	0.0515569i
$475$	−2.26210	−	3.91807i	−0.103792	−	0.179773i
$476$	1.64806			0.0755387
$477$	−10.8671	+	2.72101i	−0.497570	+	0.124586i
$478$	−0.876139			−0.0400737
$479$	−9.74083	−	16.8716i	−0.445070	−	0.770884i	0.552987	−	0.833190i	$-0.313488\pi$
$479$	−9.74083	−	16.8716i	−0.445070	−	0.770884i	−0.998057	+	0.0623061i	$0.980155\pi$
$480$	−1.04307	−	1.38276i	−0.0476092	−	0.0631139i
$481$	15.2863	−	26.4766i	0.696995	−	1.20723i
$482$	−4.80516	+	8.32279i	−0.218869	+	0.379093i
$483$	−4.09517	+	0.504901i	−0.186337	+	0.0229738i
$484$	3.32403	+	5.75739i	0.151092	+	0.261700i
$485$	−7.87614			−0.357637
$486$	−14.1444	−	6.55266i	−0.641601	−	0.297235i
$487$	−7.22066			−0.327199			−0.163600	−	0.986527i	$-0.552311\pi$
$487$	−7.22066			−0.327199			−0.163600	+	0.986527i	$0.552311\pi$
$488$	−1.21903	−	2.11143i	−0.0551831	−	0.0955799i
$489$	16.9647	−	2.09160i	0.767169	−	0.0945856i
$490$	−0.500000	+	0.866025i	−0.0225877	+	0.0391230i
$491$	−7.68130	+	13.3044i	−0.346652	+	0.600420i	−0.985653	−	0.168787i	$-0.946015\pi$
$491$	−7.68130	+	13.3044i	−0.346652	+	0.600420i	0.639000	+	0.769207i	$0.279348\pi$
$492$	−7.81661	−	10.3622i	−0.352400	−	0.467165i
$493$	1.47502	+	2.55481i	0.0664316	+	0.115063i
$494$	−13.9623			−0.628192
$495$	6.07097	−	1.52011i	0.272870	−	0.0683238i
$496$	−4.87614			−0.218945
$497$	7.82936	+	13.5609i	0.351195	+	0.608288i
$498$	−5.04840	+	11.9098i	−0.226224	+	0.533692i
$499$	3.36469	−	5.82782i	0.150624	−	0.260889i	−0.780833	−	0.624740i	$-0.785205\pi$
$499$	3.36469	−	5.82782i	0.150624	−	0.260889i	0.931457	+	0.363851i	$0.118538\pi$
$500$	−0.500000	+	0.866025i	−0.0223607	+	0.0387298i
$501$	3.11644	−	7.35209i	0.139232	−	0.328467i
$502$	0.907757	+	1.57228i	0.0405152	+	0.0701743i
$503$	−12.8007			−0.570754			−0.285377	−	0.958415i	$-0.592119\pi$
$503$	−12.8007			−0.570754			−0.285377	+	0.958415i	$0.592119\pi$
$504$	−2.08613	−	2.15594i	−0.0929236	−	0.0960330i
$505$	12.5168			0.556989
$506$	2.48484	+	4.30388i	0.110465	+	0.191331i
$507$	3.62549	+	4.80619i	0.161013	+	0.213450i
$508$	1.98113	−	3.43143i	0.0878986	−	0.152245i
$509$	−18.0016	+	31.1797i	−0.797908	+	1.38202i	0.123068	+	0.992398i	$0.460727\pi$
$509$	−18.0016	+	31.1797i	−0.797908	+	1.38202i	−0.920976	+	0.389619i	$0.872607\pi$
$510$	2.83307	−	0.349294i	0.125451	−	0.0154670i
$511$	−0.851939	−	1.47560i	−0.0376876	−	0.0652768i
$512$	1.00000			0.0441942
$513$	21.9344	−	8.45755i	0.968426	−	0.373410i
$514$	16.1090			0.710539
$515$	5.65710	+	9.79839i	0.249282	+	0.431769i
$516$	1.42291	−	0.175433i	0.0626403	−	0.00772302i
$517$	−3.43807	+	5.95491i	−0.151206	+	0.261897i
$518$	−4.95323	+	8.57924i	−0.217632	+	0.376950i
$519$	13.4307	+	17.8046i	0.589540	+	0.781534i
$520$	1.54307	+	2.67267i	0.0676679	+	0.117204i
$521$	−5.78259			−0.253340			−0.126670	−	0.991945i	$-0.540429\pi$
$521$	−5.78259			−0.253340			−0.126670	+	0.991945i	$0.540429\pi$
$522$	1.47502	−	5.16348i	0.0645599	−	0.225999i
$523$	40.9777			1.79183			0.895916	−	0.444224i	$-0.146521\pi$
$523$	40.9777			1.79183			0.895916	+	0.444224i	$0.146521\pi$
$524$	−5.02791	−	8.70859i	−0.219645	−	0.380437i
$525$	−0.675970	+	1.59470i	−0.0295017	+	0.0695984i
$526$	3.89500	−	6.74635i	0.169830	−	0.294155i
$527$	4.01809	−	6.95953i	0.175031	−	0.303162i
$528$	−1.41016	+	3.32675i	−0.0613694	+	0.144778i
$529$	8.66244	+	15.0038i	0.376628	+	0.652338i
$530$	−3.73419			−0.162203
$531$	−8.53031	+	29.8613i	−0.370184	+	1.29587i
$532$	4.52420			0.196149
$533$	11.5636	+	20.0287i	0.500873	+	0.867538i
$534$	2.44549	+	3.24190i	0.105827	+	0.140291i
$535$	−6.64435	+	11.5084i	−0.287260	+	0.497550i
$536$	−5.70017	+	9.87298i	−0.246210	+	0.426448i
$537$	2.32403	−	0.286534i	0.100289	−	0.0123648i
$538$	9.91549	+	17.1741i	0.427487	+	0.740430i
$539$	2.08613			0.0898560
$540$	−4.04307	−	3.26399i	−0.173986	−	0.140460i
$541$	−34.0000			−1.46177			−0.730887	−	0.682498i	$-0.760893\pi$
$541$	−34.0000			−1.46177			−0.730887	+	0.682498i	$0.760893\pi$
$542$	1.72274	+	2.98388i	0.0739982	+	0.128169i
$543$	−17.1903	+	2.11943i	−0.737708	+	0.0909533i
$544$	−0.824030	+	1.42726i	−0.0353300	+	0.0611934i
$545$	7.80146	−	13.5125i	0.334178	−	0.578813i
$546$	3.21903	+	4.26737i	0.137762	+	0.182626i
$547$	−12.8929	−	22.3312i	−0.551261	−	0.954813i	−0.998184	−	0.0602401i	$-0.980813\pi$
$547$	−12.8929	−	22.3312i	−0.551261	−	0.954813i	0.446922	−	0.894573i	$-0.352520\pi$
$548$	−19.8432			−0.847660
$549$	−5.08613	−	5.25632i	−0.217071	−	0.224334i
$550$	2.08613			0.0889529
$551$	4.04918	+	7.01338i	0.172501	+	0.298780i
$552$	1.61033	−	3.79897i	0.0685402	−	0.161695i
$553$	0.351939	−	0.609577i	0.0149660	−	0.0259218i
$554$	9.05582	−	15.6851i	0.384745	−	0.666398i
$555$	−6.69646	+	15.7978i	−0.284249	+	0.670580i
$556$	−4.29001	−	7.43051i	−0.181937	−	0.315124i
$557$	13.3929			0.567476			0.283738	−	0.958902i	$-0.408425\pi$
$557$	13.3929			0.567476			0.283738	+	0.958902i	$0.408425\pi$
$558$	−14.1903	+	3.55311i	−0.600725	+	0.150415i
$559$	−2.55451			−0.108044
$560$	−0.500000	−	0.866025i	−0.0211289	−	0.0365963i
$561$	−3.58613	−	4.75401i	−0.151407	−	0.200715i
$562$	11.1699	−	19.3468i	0.471172	−	0.816094i
$563$	19.3802	−	33.5674i	0.816777	−	1.41470i	−0.0912684	−	0.995826i	$-0.529092\pi$
$563$	19.3802	−	33.5674i	0.816777	−	1.41470i	0.908045	−	0.418872i	$-0.137575\pi$
$564$	5.66615	−	0.698589i	0.238588	−	0.0294159i
$565$	−6.93436	−	12.0107i	−0.291731	−	0.505292i
$566$	−21.5652			−0.906452
$567$	−7.64195	−	4.75401i	−0.320932	−	0.199650i
$568$	−15.6587			−0.657026
$569$	22.3031	+	38.6301i	0.934994	+	1.61946i	0.774645	+	0.632396i	$0.217929\pi$
$569$	22.3031	+	38.6301i	0.934994	+	1.61946i	0.160349	+	0.987060i	$0.448738\pi$
$570$	7.77726	−	0.958871i	0.325753	−	0.0401627i
$571$	1.81258	−	3.13949i	0.0758543	−	0.131383i	−0.825603	−	0.564251i	$-0.809165\pi$
$571$	1.81258	−	3.13949i	0.0758543	−	0.131383i	0.901457	+	0.432868i	$0.142498\pi$
$572$	3.21903	−	5.57553i	0.134595	−	0.233125i
$573$	−16.8687	−	22.3623i	−0.704701	−	0.934198i
$574$	−3.74694	−	6.48990i	−0.156394	−	0.270883i
$575$	−2.38225			−0.0993468
$576$	2.91016	−	0.728674i	0.121257	−	0.0303614i
$577$	−21.1526			−0.880595			−0.440297	−	0.897852i	$-0.645127\pi$
$577$	−21.1526			−0.880595			−0.440297	+	0.897852i	$0.645127\pi$
$578$	7.14195	+	12.3702i	0.297066	+	0.514533i
$579$	−15.2002	+	35.8592i	−0.631697	+	1.49026i
$580$	0.895004	−	1.55019i	0.0371630	−	0.0643683i
$581$	−3.73419	+	6.46781i	−0.154920	+	0.268330i
$582$	5.32403	−	12.5601i	0.220688	−	0.520632i
$583$	3.89500	+	6.74635i	0.161315	+	0.279405i
$584$	1.70388			0.0705070
$585$	6.43807	+	6.65350i	0.266181	+	0.275088i
$586$	−6.83841			−0.282492
$587$	−21.9676	−	38.0490i	−0.906700	−	1.57045i	−0.818619	−	0.574337i	$-0.805260\pi$
$587$	−21.9676	−	38.0490i	−0.906700	−	1.57045i	−0.0880812	−	0.996113i	$-0.528073\pi$
$588$	−1.04307	−	1.38276i	−0.0430153	−	0.0570239i
$589$	11.0303	−	19.1051i	0.454496	−	0.787210i
$590$	−5.17597	+	8.96504i	−0.213091	+	0.369085i
$591$	39.3560	−	4.85226i	1.61889	−	0.199595i
$592$	−4.95323	−	8.57924i	−0.203576	−	0.352605i
$593$	−7.63583			−0.313566			−0.156783	−	0.987633i	$-0.550112\pi$
$593$	−7.63583			−0.313566			−0.156783	+	0.987633i	$0.550112\pi$
$594$	−1.67968	+	10.7089i	−0.0689181	+	0.439392i
$595$	1.64806			0.0675639
$596$	−0.734191	−	1.27166i	−0.0300736	−	0.0520891i
$597$	1.46676	−	0.180839i	0.0600304	−	0.00740125i
$598$	−3.67597	+	6.36697i	−0.150322	+	0.260365i
$599$	6.11644	−	10.5940i	0.249911	−	0.432859i	−0.713590	−	0.700564i	$-0.752932\pi$
$599$	6.11644	−	10.5940i	0.249911	−	0.432859i	0.963501	+	0.267705i	$0.0862653\pi$
$600$	−1.04307	−	1.38276i	−0.0425830	−	0.0564508i
$601$	12.6608	+	21.9292i	0.516445	+	0.894510i	0.999818	+	0.0190947i	$0.00607841\pi$
$601$	12.6608	+	21.9292i	0.516445	+	0.894510i	−0.483372	+	0.875415i	$0.660588\pi$
$602$	0.827740			0.0337361
$603$	−9.39423	+	32.8855i	−0.382562	+	1.33920i
$604$	−15.0484			−0.612311
$605$	3.32403	+	5.75739i	0.135141	+	0.234071i
$606$	−8.46096	+	19.9605i	−0.343703	+	0.810840i
$607$	10.3445	−	17.9172i	0.419871	−	0.727238i	−0.576055	−	0.817411i	$-0.695409\pi$
$607$	10.3445	−	17.9172i	0.419871	−	0.727238i	0.995926	+	0.0901728i	$0.0287419\pi$
$608$	−2.26210	+	3.91807i	−0.0917403	+	0.158899i
$609$	1.20999	−	2.85453i	0.0490313	−	0.115671i
$610$	−1.21903	−	2.11143i	−0.0493573	−	0.0854893i
$611$	−10.1723			−0.411526
$612$	−1.35805	+	4.75401i	−0.0548960	+	0.192170i
$613$	−17.0336			−0.687979			−0.343990	−	0.938973i	$-0.611778\pi$
$613$	−17.0336			−0.687979			−0.343990	+	0.938973i	$0.611778\pi$
$614$	8.86339	+	15.3518i	0.357697	+	0.619550i
$615$	−7.81661	−	10.3622i	−0.315196	−	0.417845i
$616$	−1.04307	+	1.80664i	−0.0420263	+	0.0727917i
$617$	9.03324	−	15.6460i	0.363665	−	0.629886i	−0.624896	−	0.780708i	$-0.714859\pi$
$617$	9.03324	−	15.6460i	0.363665	−	0.629886i	0.988561	+	0.150822i	$0.0481921\pi$
$618$	−19.4495	+	2.39796i	−0.782374	+	0.0964602i
$619$	21.3990	+	37.0642i	0.860100	+	1.48974i	0.871832	+	0.489805i	$0.162932\pi$
$619$	21.3990	+	37.0642i	0.860100	+	1.48974i	−0.0117321	+	0.999931i	$0.503735\pi$
$620$	−4.87614			−0.195830
$621$	1.91811	−	12.2290i	0.0769709	−	0.490734i
$622$	−11.2813			−0.452338
$623$	1.17226	+	2.03041i	0.0469656	+	0.0813468i
$624$	−5.30516	+	0.654083i	−0.212377	+	0.0261843i
$625$	−0.500000	+	0.866025i	−0.0200000	+	0.0346410i
$626$	−13.9282	+	24.1244i	−0.556685	+	0.964206i
$627$	−9.84452	−	13.0506i	−0.393152	−	0.521189i
$628$	−11.1534	−	19.3182i	−0.445069	−	0.770882i
$629$	16.3264			0.650978
$630$	−2.08613	−	2.15594i	−0.0831134	−	0.0858946i
$631$	17.6587			0.702983			0.351491	−	0.936191i	$-0.385675\pi$
$631$	17.6587			0.702983			0.351491	+	0.936191i	$0.385675\pi$
$632$	0.351939	+	0.609577i	0.0139994	+	0.0242477i
$633$	17.6406	−	41.6165i	0.701153	−	1.65411i
$634$	5.56356	−	9.63636i	0.220957	−	0.382709i
$635$	1.98113	−	3.43143i	0.0786189	−	0.136172i
$636$	2.52420	−	5.95491i	0.100091	−	0.236128i
$637$	1.54307	+	2.67267i	0.0611385	+	0.105895i
$638$	−3.73419			−0.147838
$639$	−45.5694	+	11.4101i	−1.80270	+	0.451377i
$640$	1.00000			0.0395285
$641$	5.21370	+	9.03039i	0.205929	+	0.356679i	0.950428	−	0.310944i	$-0.100645\pi$
$641$	5.21370	+	9.03039i	0.205929	+	0.356679i	−0.744499	+	0.667623i	$0.767312\pi$
$642$	−13.8610	−	18.3750i	−0.547049	−	0.725205i
$643$	−20.9142	+	36.2244i	−0.824775	+	1.42855i	0.0773159	+	0.997007i	$0.475365\pi$
$643$	−20.9142	+	36.2244i	−0.824775	+	1.42855i	−0.902091	+	0.431546i	$0.857968\pi$
$644$	1.19113	−	2.06309i	0.0469369	−	0.0812972i
$645$	1.42291	−	0.175433i	0.0560271	−	0.00690768i
$646$	−3.72808	−	6.45722i	−0.146679	−	0.254056i
$647$	48.2871			1.89836			0.949182	−	0.314728i	$-0.101913\pi$
$647$	48.2871			1.89836			0.949182	+	0.314728i	$0.101913\pi$
$648$	7.93807	−	4.24111i	0.311837	−	0.166607i
$649$	21.5955			0.847697
$650$	1.54307	+	2.67267i	0.0605240	+	0.104831i
$651$	−8.38225	+	1.03346i	−0.328526	+	0.0405046i
$652$	−4.93436	+	8.54656i	−0.193244	+	0.334709i
$653$	13.1723	−	22.8150i	0.515470	−	0.892821i	−0.484368	−	0.874864i	$-0.660951\pi$
$653$	13.1723	−	22.8150i	0.515470	−	0.892821i	0.999839	−	0.0179567i	$-0.00571612\pi$
$654$	16.2749	+	21.5750i	0.636397	+	0.843650i
$655$	−5.02791	−	8.70859i	−0.196457	−	0.340273i
$656$	7.49389			0.292587
$657$	4.95856	−	1.24157i	0.193452	−	0.0484383i
$658$	3.29612			0.128496
$659$	−4.64806	−	8.05068i	−0.181063	−	0.313610i	0.761180	−	0.648541i	$-0.224620\pi$
$659$	−4.64806	−	8.05068i	−0.181063	−	0.313610i	−0.942243	+	0.334931i	$0.891287\pi$
$660$	−1.41016	+	3.32675i	−0.0548904	+	0.129494i
$661$	22.3068	−	38.6365i	0.867634	−	1.50279i	0.00322533	−	0.999995i	$-0.498973\pi$
$661$	22.3068	−	38.6365i	0.867634	−	1.50279i	0.864408	−	0.502791i	$-0.167693\pi$
$662$	−1.14195	+	1.97791i	−0.0443831	+	0.0768737i
$663$	3.43807	−	8.11085i	0.133524	−	0.314999i
$664$	−3.73419	−	6.46781i	−0.144915	−	0.251000i
$665$	4.52420			0.175441
$666$	−20.6661	−	21.3577i	−0.800797	−	0.827593i
$667$	4.26425			0.165112
$668$	2.30516	+	3.99266i	0.0891895	+	0.154481i
$669$	3.09758	+	4.10635i	0.119759	+	0.158761i
$670$	−5.70017	+	9.87298i	−0.220217	+	0.381427i
$671$	−2.54307	+	4.40472i	−0.0981739	+	0.170042i
$672$	1.71903	−	0.211943i	0.0663132	−	0.00817587i
$673$	8.25839	+	14.3040i	0.318338	+	0.551377i	0.980141	−	0.198300i	$-0.0635421\pi$
$673$	8.25839	+	14.3040i	0.318338	+	0.551377i	−0.661804	+	0.749677i	$0.730209\pi$
$674$	−7.67095			−0.295474
$675$	−4.04307	−	3.26399i	−0.155618	−	0.125631i
$676$	−3.47580			−0.133685
$677$	−1.04918	−	1.81723i	−0.0403232	−	0.0698418i	0.845159	−	0.534514i	$-0.179505\pi$
$677$	−1.04918	−	1.81723i	−0.0403232	−	0.0698418i	−0.885483	+	0.464672i	$0.846172\pi$
$678$	23.8408	−	2.93937i	0.915601	−	0.112886i
$679$	3.93807	−	6.82094i	0.151129	−	0.261764i
$680$	−0.824030	+	1.42726i	−0.0316001	+	0.0547330i
$681$	−17.0168	−	22.5586i	−0.652084	−	0.864446i
$682$	5.08613	+	8.80944i	0.194758	+	0.337331i
$683$	−30.0288			−1.14902			−0.574509	−	0.818498i	$-0.694807\pi$
$683$	−30.0288			−1.14902			−0.574509	+	0.818498i	$0.694807\pi$
$684$	−3.72808	+	13.0506i	−0.142547	+	0.499000i
$685$	−19.8432			−0.758170
$686$	−0.500000	−	0.866025i	−0.0190901	−	0.0330650i
$687$	−3.63322	+	8.57124i	−0.138616	+	0.327013i
$688$	−0.413870	+	0.716844i	−0.0157786	+	0.0273294i
$689$	−5.76210	+	9.98025i	−0.219519	+	0.380217i
$690$	1.61033	−	3.79897i	0.0613042	−	0.144624i
$691$	−3.40776	−	5.90241i	−0.129637	−	0.224538i	0.793899	−	0.608050i	$-0.208048\pi$
$691$	−3.40776	−	5.90241i	−0.129637	−	0.224538i	−0.923536	+	0.383512i	$0.874715\pi$
$692$	−12.8761			−0.489477
$693$	−1.71903	+	6.01767i	−0.0653007	+	0.228592i
$694$	−24.1042			−0.914984
$695$	−4.29001	−	7.43051i	−0.162729	−	0.281855i
$696$	1.86710	+	2.47515i	0.0707721	+	0.0938202i
$697$	−6.17519	+	10.6957i	−0.233902	+	0.405130i
$698$	7.18872	−	12.4512i	0.272097	−	0.471286i
$699$	39.0471	−	4.81418i	1.47690	−	0.182089i
$700$	−0.500000	−	0.866025i	−0.0188982	−	0.0327327i
$701$	−23.5519			−0.889543			−0.444772	−	0.895644i	$-0.646715\pi$
$701$	−23.5519			−0.889543			−0.444772	+	0.895644i	$0.646715\pi$
$702$	−14.9623	+	5.76922i	−0.564714	+	0.217745i
$703$	44.8188			1.69037
$704$	−1.04307	−	1.80664i	−0.0393120	−	0.0680904i
$705$	5.66615	−	0.698589i	0.213399	−	0.0263104i
$706$	−11.2342	+	19.4582i	−0.422804	+	0.732319i
$707$	−6.25839	+	10.8399i	−0.235371	+	0.407675i
$708$	−10.7977	−	14.3142i	−0.405804	−	0.537961i
$709$	18.8089	+	32.5779i	0.706382	+	1.22349i	0.966190	+	0.257829i	$0.0830073\pi$
$709$	18.8089	+	32.5779i	0.706382	+	1.22349i	−0.259808	+	0.965660i	$0.583659\pi$
$710$	−15.6587			−0.587662
$711$	1.46838	+	1.51752i	0.0550686	+	0.0569113i
$712$	−2.34452			−0.0878646
$713$	−5.80810	−	10.0599i	−0.217515	−	0.376747i
$714$	−1.11404	+	2.62816i	−0.0416919	+	0.0983565i
$715$	3.21903	−	5.57553i	0.120385	−	0.208513i
$716$	−0.675970	+	1.17081i	−0.0252622	+	0.0437554i
$717$	0.592243	−	1.39718i	0.0221177	−	0.0521786i
$718$	−12.3610	−	21.4098i	−0.461308	−	0.799008i
$719$	3.56674			0.133017			0.0665084	−	0.997786i	$-0.478814\pi$
$719$	3.56674			0.133017			0.0665084	+	0.997786i	$0.478814\pi$
$720$	2.91016	−	0.728674i	0.108455	−	0.0271561i
$721$	−11.3142			−0.421363
$722$	−0.734191	−	1.27166i	−0.0273238	−	0.0473261i
$723$	−10.0242	−	13.2887i	−0.372804	−	0.494214i
$724$	5.00000	−	8.66025i	0.185824	−	0.321856i
$725$	0.895004	−	1.55019i	0.0332396	−	0.0575727i
$726$	−11.4282	+	1.40901i	−0.424142	+	0.0522932i
$727$	3.27485	+	5.67221i	0.121458	+	0.210371i	0.920343	−	0.391113i	$-0.127910\pi$
$727$	3.27485	+	5.67221i	0.121458	+	0.210371i	−0.798885	+	0.601484i	$0.794577\pi$
$728$	−3.08613			−0.114380
$729$	20.0107	−	18.1266i	0.741136	−	0.671355i
$730$	1.70388			0.0630634
$731$	−0.682083	−	1.18140i	−0.0252277	−	0.0436957i
$732$	4.19113	−	0.516731i	0.154908	−	0.0190989i
$733$	−6.86469	+	11.8900i	−0.253553	+	0.439167i	−0.964502	−	0.264077i	$-0.914933\pi$
$733$	−6.86469	+	11.8900i	−0.253553	+	0.439167i	0.710948	+	0.703244i	$0.248266\pi$
$734$	−12.4216	+	21.5149i	−0.458490	+	0.794128i
$735$	−1.04307	−	1.38276i	−0.0384740	−	0.0510037i
$736$	1.19113	+	2.06309i	0.0439055	+	0.0760465i
$737$	23.7826			0.876043
$738$	21.8084	−	5.46060i	0.802779	−	0.201007i
$739$	40.8113			1.50127			0.750635	−	0.660717i	$-0.229748\pi$
$739$	40.8113			1.50127			0.750635	+	0.660717i	$0.229748\pi$
$740$	−4.95323	−	8.57924i	−0.182084	−	0.315379i
$741$	9.43807	−	22.2656i	0.346716	−	0.817948i
$742$	1.86710	−	3.23390i	0.0685432	−	0.118720i
$743$	1.53162	−	2.65284i	0.0561896	−	0.0973233i	−0.836562	−	0.547872i	$-0.815438\pi$
$743$	1.53162	−	2.65284i	0.0561896	−	0.0973233i	0.892752	+	0.450548i	$0.148772\pi$
$744$	3.29612	−	7.77597i	0.120842	−	0.285081i
$745$	−0.734191	−	1.27166i	−0.0268987	−	0.0465899i
$746$	−26.4051			−0.966761
$747$	−15.5800	−	16.1014i	−0.570043	−	0.589118i
$748$	3.43807			0.125708
$749$	−6.64435	−	11.5084i	−0.242779	−	0.420506i
$750$	−1.04307	−	1.38276i	−0.0380874	−	0.0504911i
$751$	−3.42161	+	5.92640i	−0.124856	+	0.216257i	−0.921677	−	0.387959i	$-0.873180\pi$
$751$	−3.42161	+	5.92640i	−0.124856	+	0.216257i	0.796821	+	0.604216i	$0.206514\pi$
$752$	−1.64806	+	2.85453i	−0.0600986	+	0.104094i
$753$	−3.12093	+	0.384785i	−0.113733	+	0.0140223i
$754$	−2.76210	−	4.78410i	−0.100590	−	0.174227i
$755$	−15.0484			−0.547667
$756$	4.84823	−	1.86940i	0.176328	−	0.0679895i
$757$	−30.2658			−1.10003			−0.550015	−	0.835155i	$-0.685378\pi$
$757$	−30.2658			−1.10003			−0.550015	+	0.835155i	$0.685378\pi$
$758$	5.54677	+	9.60729i	0.201468	+	0.348953i
$759$	−8.54307	+	1.05329i	−0.310094	+	0.0382320i
$760$	−2.26210	+	3.91807i	−0.0820550	+	0.142123i
$761$	26.1648	−	45.3188i	0.948475	−	1.64281i	0.199835	−	0.979830i	$-0.435959\pi$
$761$	26.1648	−	45.3188i	0.948475	−	1.64281i	0.748640	−	0.662977i	$-0.230707\pi$
$762$	4.13290	+	5.47885i	0.149719	+	0.198478i
$763$	7.80146	+	13.5125i	0.282432	+	0.489186i
$764$	16.1723			0.585092
$765$	−1.35805	+	4.75401i	−0.0491005	+	0.171882i
$766$	−2.41998			−0.0874375
$767$	15.9737	+	27.6673i	0.576777	+	0.999008i
$768$	−0.675970	+	1.59470i	−0.0243920	+	0.0575437i
$769$	−1.16244	+	2.01340i	−0.0419186	+	0.0726051i	−0.886223	−	0.463258i	$-0.846680\pi$
$769$	−1.16244	+	2.01340i	−0.0419186	+	0.0726051i	0.844305	+	0.535863i	$0.180014\pi$
$770$	−1.04307	+	1.80664i	−0.0375895	+	0.0651068i
$771$	−10.8892	+	25.6890i	−0.392165	+	0.925168i
$772$	−11.2432	−	19.4739i	−0.404653	−	0.700879i
$773$	4.65131			0.167296			0.0836480	−	0.996495i	$-0.473343\pi$
$773$	4.65131			0.167296			0.0836480	+	0.996495i	$0.473343\pi$
$774$	−0.682083	+	2.38771i	−0.0245170	+	0.0858243i
$775$	−4.87614			−0.175156
$776$	3.93807	+	6.82094i	0.141368	+	0.244857i
$777$	−10.3331	−	13.6982i	−0.370697	−	0.491421i
$778$	−5.52420	+	9.56819i	−0.198052	+	0.343036i
$779$	−16.9519	+	29.3616i	−0.607366	+	1.05199i
$780$	−5.30516	+	0.654083i	−0.189955	+	0.0234199i
$781$	16.3331	+	28.2897i	0.584443	+	1.01229i
$782$	−3.92610			−0.140397
$783$	7.23712	+	5.84257i	0.258634	+	0.208796i
$784$	1.00000			0.0357143
$785$	−11.1534	−	19.3182i	−0.398082	−	0.689498i
$786$	17.2863	−	2.13126i	0.616582	−	0.0760194i
$787$	−2.37744	+	4.11785i	−0.0847467	+	0.146786i	−0.905283	−	0.424808i	$-0.860341\pi$
$787$	−2.37744	+	4.11785i	−0.0847467	+	0.146786i	0.820537	+	0.571594i	$0.193675\pi$
$788$	−11.4471	+	19.8270i	−0.407787	+	0.706307i
$789$	8.12549	+	10.7717i	0.289275	+	0.383482i
$790$	0.351939	+	0.609577i	0.0125214	+	0.0216878i
$791$	13.8687			0.493115
$792$	−4.35194	−	4.49756i	−0.154639	−	0.159814i
$793$	−7.52420			−0.267192
$794$	16.0673	+	27.8293i	0.570206	+	0.987626i
$795$	2.52420	−	5.95491i	0.0895241	−	0.211199i
$796$	−0.426622	+	0.738932i	−0.0151212	+	0.0261907i
$797$	2.20257	−	3.81497i	0.0780191	−	0.135133i	−0.824376	−	0.566042i	$-0.808474\pi$
$797$	2.20257	−	3.81497i	0.0780191	−	0.135133i	0.902395	+	0.430909i	$0.141807\pi$
$798$	−3.05822	+	7.21474i	−0.108260	+	0.255399i
$799$	−2.71610	−	4.70443i	−0.0960889	−	0.166431i
$800$	1.00000			0.0353553
$801$	−6.82293	+	1.70839i	−0.241076	+	0.0603630i
$802$	19.0968			0.674331
$803$	−1.77726	−	3.07830i	−0.0627180	−	0.108631i
$804$	−11.8913	−	15.7639i	−0.419374	−	0.555950i
$805$	1.19113	−	2.06309i	0.0419817	−	0.0727144i
$806$	−7.52420	+	13.0323i	−0.265029	+	0.459043i
$807$	−34.0902	+	4.20303i	−1.20003	+	0.147954i
$808$	−6.25839	−	10.8399i	−0.220169	−	0.381345i
$809$	1.80548			0.0634775			0.0317387	−	0.999496i	$-0.489896\pi$
$809$	1.80548			0.0634775			0.0317387	+	0.999496i	$0.489896\pi$
$810$	7.93807	−	4.24111i	0.278915	−	0.149018i
$811$	−53.8565			−1.89116			−0.945579	−	0.325394i	$-0.894503\pi$
$811$	−53.8565			−1.89116			−0.945579	+	0.325394i	$0.894503\pi$
$812$	0.895004	+	1.55019i	0.0314085	+	0.0544011i
$813$	−5.92291	+	0.730246i	−0.207726	+	0.0256108i
$814$	−10.3331	+	17.8974i	−0.362174	+	0.627304i
$815$	−4.93436	+	8.54656i	−0.172843	+	0.299373i
$816$	−1.71903	−	2.27887i	−0.0601783	−	0.0797763i
$817$	−1.87243	−	3.24314i	−0.0655080	−	0.113463i
$818$	32.4158			1.13339
$819$	−8.98113	+	2.24878i	−0.313826	+	0.0785788i
$820$	7.49389			0.261698
$821$	1.98855	+	3.44427i	0.0694010	+	0.120206i	0.898638	−	0.438691i	$-0.144558\pi$
$821$	1.98855	+	3.44427i	0.0694010	+	0.120206i	−0.829237	+	0.558897i	$0.811225\pi$
$822$	13.4134	−	31.6440i	0.467846	−	1.10371i
$823$	−28.0221	+	48.5357i	−0.976790	+	1.69185i	−0.302891	+	0.953025i	$0.597952\pi$
$823$	−28.0221	+	48.5357i	−0.976790	+	1.69185i	−0.673899	+	0.738824i	$0.735382\pi$
$824$	5.65710	−	9.79839i	0.197075	−	0.341343i
$825$	−1.41016	+	3.32675i	−0.0490955	+	0.115823i
$826$	−5.17597	−	8.96504i	−0.180095	−	0.311934i
$827$	−14.5874			−0.507255			−0.253627	−	0.967302i	$-0.581624\pi$
$827$	−14.5874			−0.507255			−0.253627	+	0.967302i	$0.581624\pi$
$828$	4.96969	+	5.13598i	0.172709	+	0.178488i
$829$	−1.45355			−0.0504837			−0.0252419	−	0.999681i	$-0.508036\pi$
$829$	−1.45355			−0.0504837			−0.0252419	+	0.999681i	$0.508036\pi$
$830$	−3.73419	−	6.46781i	−0.129616	−	0.224501i
$831$	18.8916	+	25.0440i	0.655343	+	0.868766i
$832$	1.54307	−	2.67267i	0.0534962	−	0.0926581i
$833$	−0.824030	+	1.42726i	−0.0285510	+	0.0494517i
$834$	14.7493	−	1.81847i	0.510728	−	0.0629685i
$835$	2.30516	+	3.99266i	0.0797735	+	0.138172i
$836$	9.43807			0.326422
$837$	3.92610	−	25.0311i	0.135706	−	0.865202i
$838$	22.0558			0.761906
$839$	−27.8318	−	48.2060i	−0.960859	−	1.66426i	−0.720350	−	0.693610i	$-0.756019\pi$
$839$	−27.8318	−	48.2060i	−0.960859	−	1.66426i	−0.240509	−	0.970647i	$-0.577314\pi$
$840$	1.71903	−	0.211943i	0.0593123	−	0.00731272i
$841$	12.8979	−	22.3399i	0.444756	−	0.770341i
$842$	−10.5612	+	18.2925i	−0.363961	+	0.630400i
$843$	23.3018	+	30.8904i	0.802556	+	1.06392i
$844$	13.0484	+	22.6005i	0.449144	+	0.777941i
$845$	−3.47580			−0.119571
$846$	−2.71610	+	9.50802i	−0.0933816	+	0.326893i
$847$	−6.64806			−0.228430
$848$	1.86710	+	3.23390i	0.0641163	+	0.111053i
$849$	14.5774	−	34.3900i	0.500295	−	1.18026i
$850$	−0.824030	+	1.42726i	−0.0282640	+	0.0489547i
$851$	11.7998	−	20.4379i	0.404493	−	0.700602i
$852$	10.5848	−	24.9710i	0.362630	−	0.855491i
$853$	17.5423	+	30.3841i	0.600636	+	1.04033i	0.992725	+	0.120405i	$0.0384194\pi$
$853$	17.5423	+	30.3841i	0.600636	+	1.04033i	−0.392088	+	0.919928i	$0.628247\pi$
$854$	2.43807			0.0834290
$855$	−3.72808	+	13.0506i	−0.127498	+	0.446319i
$856$	13.2887			0.454199
$857$	14.5070	+	25.1268i	0.495548	+	0.858315i	0.999987	−	0.00513280i	$-0.00163383\pi$
$857$	14.5070	+	25.1268i	0.495548	+	0.858315i	−0.504439	+	0.863448i	$0.668300\pi$
$858$	6.71533	+	8.90228i	0.229257	+	0.303919i
$859$	26.6321	−	46.1282i	0.908676	−	1.57387i	0.0927716	−	0.995687i	$-0.470427\pi$
$859$	26.6321	−	46.1282i	0.908676	−	1.57387i	0.815905	−	0.578186i	$-0.196239\pi$
$860$	−0.413870	+	0.716844i	−0.0141128	+	0.0244442i
$861$	12.8823	−	1.58827i	0.439026	−	0.0541283i
$862$	6.32163	+	10.9494i	0.215315	+	0.372937i
$863$	−38.9368			−1.32542			−0.662711	−	0.748875i	$-0.730594\pi$
$863$	−38.9368			−1.32542			−0.662711	+	0.748875i	$0.730594\pi$
$864$	−0.805165	+	5.13339i	−0.0273923	+	0.174642i
$865$	−12.8761			−0.437802
$866$	11.3687	+	19.6912i	0.386325	+	0.669134i
$867$	−24.5545	+	3.02737i	−0.833915	+	0.102815i
$868$	2.43807	−	4.22286i	0.0827535	−	0.143333i
$869$	0.734191	−	1.27166i	0.0249057	−	0.0431380i
$870$	1.86710	+	2.47515i	0.0633005	+	0.0839153i
$871$	17.5915	+	30.4693i	0.596064	+	1.03241i
$872$	−15.6029			−0.528381
$873$	16.4307	+	16.9805i	0.556093	+	0.574701i
$874$	−10.7778			−0.364564
$875$	−0.500000	−	0.866025i	−0.0169031	−	0.0292770i
$876$	−1.15177	+	2.71717i	−0.0389147	+	0.0918048i
$877$	23.5029	−	40.7083i	0.793638	−	1.37462i	−0.130063	−	0.991506i	$-0.541518\pi$
$877$	23.5029	−	40.7083i	0.793638	−	1.37462i	0.923701	−	0.383115i	$-0.125149\pi$
$878$	18.5660	−	32.1572i	0.626571	−	1.08525i
$879$	4.62256	−	10.9052i	0.155915	−	0.367823i
$880$	−1.04307	−	1.80664i	−0.0351617	−	0.0609019i
$881$	−28.5726			−0.962635			−0.481318	−	0.876546i	$-0.659842\pi$
$881$	−28.5726			−0.962635			−0.481318	+	0.876546i	$0.659842\pi$
$882$	2.91016	−	0.728674i	0.0979902	−	0.0245357i
$883$	41.7597			1.40533			0.702663	−	0.711523i	$-0.251994\pi$
$883$	41.7597			1.40533			0.702663	+	0.711523i	$0.251994\pi$
$884$	2.54307	+	4.40472i	0.0855325	+	0.148147i
$885$	−10.7977	−	14.3142i	−0.362962	−	0.481167i
$886$	10.9381	−	18.9453i	0.367472	−	0.636480i
$887$	5.82032	−	10.0811i	0.195427	−	0.338490i	−0.751613	−	0.659604i	$-0.770724\pi$
$887$	5.82032	−	10.0811i	0.195427	−	0.338490i	0.947041	+	0.321114i	$0.104057\pi$
$888$	17.0295	−	2.09960i	0.571474	−	0.0704580i
$889$	1.98113	+	3.43143i	0.0664451	+	0.115086i
$890$	−2.34452			−0.0785885
$891$	−15.9421	−	9.91749i	−0.534080	−	0.332248i
$892$	−2.96969			−0.0994325
$893$	−7.45616	−	12.9144i	−0.249511	−	0.432165i
$894$	2.52420	−	0.311213i	0.0844219	−	0.0104085i
$895$	−0.675970	+	1.17081i	−0.0225952	+	0.0391360i
$896$	−0.500000	+	0.866025i	−0.0167038	+	0.0289319i
$897$	−7.66855	−	10.1659i	−0.256045	−	0.339431i
$898$	−15.1686	−	26.2727i	−0.506181	−	0.876731i
$899$	8.72833			0.291106
$900$	2.91016	−	0.728674i	0.0970054	−	0.0242891i
$901$	−6.15417			−0.205025
$902$	−7.81661	−	13.5388i	−0.260265	−	0.450792i
$903$	−0.559527	+	1.32000i	−0.0186199	+	0.0439267i
$904$	−6.93436	+	12.0107i	−0.230633	+	0.399469i
$905$	5.00000	−	8.66025i	0.166206	−	0.287877i
$906$	10.1723	−	23.9977i	0.337951	−	0.797269i
$907$	−1.12757	−	1.95301i	−0.0374404	−	0.0648486i	0.846698	−	0.532074i	$-0.178587\pi$
$907$	−1.12757	−	1.95301i	−0.0374404	−	0.0648486i	−0.884138	+	0.467225i	$0.845254\pi$
$908$	16.3142			0.541406
$909$	−26.1116	−	26.9854i	−0.866068	−	0.895049i
$910$	−3.08613			−0.102304
$911$	20.1255	+	34.8584i	0.666787	+	1.15491i	0.978797	+	0.204830i	$0.0656643\pi$
$911$	20.1255	+	34.8584i	0.666787	+	1.15491i	−0.312010	+	0.950079i	$0.601002\pi$
$912$	−4.71903	−	6.25587i	−0.156263	−	0.207152i
$913$	−7.79001	+	13.4927i	−0.257812	+	0.446543i
$914$	11.2456	−	19.4780i	0.371973	−	0.644276i
$915$	4.19113	−	0.516731i	0.138554	−	0.0170826i
$916$	−2.68742	−	4.65474i	−0.0887947	−	0.153797i
$917$	10.0558			0.332072
$918$	−6.66322	−	5.37925i	−0.219919	−	0.177542i
$919$	−31.5323			−1.04015			−0.520077	−	0.854120i	$-0.674097\pi$
$919$	−31.5323			−1.04015			−0.520077	+	0.854120i	$0.674097\pi$
$920$	1.19113	+	2.06309i	0.0392703	+	0.0680181i
$921$	−30.4729	+	3.75706i	−1.00412	+	0.123799i
$922$	−12.9532	+	22.4356i	−0.426592	+	0.738879i
$923$	−24.1624	+	41.8506i	−0.795316	+	1.37753i
$924$	−2.17597	−	2.88461i	−0.0715841	−	0.0948967i
$925$	−4.95323	−	8.57924i	−0.162861	−	0.282084i
$926$	9.46838			0.311150
$927$	9.32325	−	32.6371i	0.306216	−	1.07194i
$928$	−1.79001			−0.0587599
$929$	14.0861	+	24.3979i	0.462151	+	0.800469i	0.999068	−	0.0431662i	$-0.0137445\pi$
$929$	14.0861	+	24.3979i	0.462151	+	0.800469i	−0.536917	+	0.843635i	$0.680411\pi$
$930$	3.29612	−	7.77597i	0.108084	−	0.254984i
$931$	−2.26210	+	3.91807i	−0.0741373	+	0.128410i
$932$	−11.3573	+	19.6714i	−0.372020	+	0.644357i
$933$	7.62581	−	17.9903i	0.249658	−	0.588974i
$934$	−4.86098	−	8.41947i	−0.159056	−	0.275493i
$935$	3.43807			0.112437
$936$	2.54307	−	8.90228i	0.0831227	−	0.290980i
$937$	53.5455			1.74926			0.874628	−	0.484794i	$-0.161106\pi$
$937$	53.5455			1.74926			0.874628	+	0.484794i	$0.161106\pi$
$938$	−5.70017	−	9.87298i	−0.186117	−	0.322364i
$939$	−29.0561	−	38.5187i	−0.948211	−	1.25701i
$940$	−1.64806	+	2.85453i	−0.0537538	+	0.0931043i
$941$	−13.3142	+	23.0609i	−0.434031	+	0.751763i	−0.997216	−	0.0745673i	$-0.976242\pi$
$941$	−13.3142	+	23.0609i	−0.434031	+	0.751763i	0.563185	+	0.826331i	$0.309576\pi$
$942$	38.3461	−	4.72776i	1.24938	−	0.154039i
$943$	8.92616	+	15.4606i	0.290676	+	0.503465i
$944$	10.3519			0.336927
$945$	4.84823	−	1.86940i	0.157713	−	0.0608117i
$946$	1.72677			0.0561422
$947$	−20.8552	−	36.1222i	−0.677703	−	1.17382i	−0.975671	−	0.219240i	$-0.929642\pi$
$947$	−20.8552	−	36.1222i	−0.677703	−	1.17382i	0.297968	−	0.954576i	$-0.403691\pi$
$948$	−1.20999	+	0.149182i	−0.0392987	+	0.00484520i
$949$	2.62920	−	4.55390i	0.0853473	−	0.147826i
$950$	−2.26210	+	3.91807i	−0.0733922	+	0.127119i
$951$	11.6063	+	15.3861i	0.376360	+	0.498928i
$952$	−0.824030	−	1.42726i	−0.0267070	−	0.0462578i
$953$	−6.90164			−0.223566			−0.111783	−	0.993733i	$-0.535656\pi$
$953$	−6.90164			−0.223566			−0.111783	+	0.993733i	$0.535656\pi$
$954$	7.79001	+	8.05068i	0.252211	+	0.260650i
$955$	16.1723			0.523322
$956$	0.438069	+	0.758758i	0.0141682	+	0.0245400i
$957$	2.52420	−	5.95491i	0.0815958	−	0.192495i
$958$	−9.74083	+	16.8716i	−0.314712	+	0.545097i
$959$	9.92161	−	17.1847i	0.320385	−	0.554924i
$960$	−0.675970	+	1.59470i	−0.0218168	+	0.0514687i
$961$	3.61164	+	6.25554i	0.116504	+	0.201791i
$962$	−30.5726			−0.985700
$963$	38.6723	−	9.68313i	1.24620	−	0.312034i
$964$	9.61033			0.309528
$965$	−11.2432	−	19.4739i	−0.361933	−	0.626886i
$966$	2.48484	+	3.29407i	0.0799485	+	0.105985i
$967$	−6.49869	+	11.2561i	−0.208984	+	0.361971i	−0.951395	−	0.307974i	$-0.900349\pi$
$967$	−6.49869	+	11.2561i	−0.208984	+	0.361971i	0.742411	+	0.669945i	$0.233682\pi$
$968$	3.32403	−	5.75739i	0.106838	−	0.185050i
$969$	12.8174	−	1.58028i	0.411754	−	0.0507658i
$970$	3.93807	+	6.82094i	0.126444	+	0.219007i
$971$	−28.2233			−0.905728			−0.452864	−	0.891580i	$-0.649598\pi$
$971$	−28.2233			−0.905728			−0.452864	+	0.891580i	$0.649598\pi$
$972$	1.39741	+	15.5257i	0.0448219	+	0.497987i
$973$	8.58002			0.275063
$974$	3.61033	+	6.25327i	0.115682	+	0.200368i
$975$	−5.30516	+	0.654083i	−0.169901	+	0.0209474i
$976$	−1.21903	+	2.11143i	−0.0390203	+	0.0675852i
$977$	24.9471	−	43.2097i	0.798129	−	1.38240i	−0.122704	−	0.992443i	$-0.539157\pi$
$977$	24.9471	−	43.2097i	0.798129	−	1.38240i	0.920833	−	0.389956i	$-0.127510\pi$
$978$	−10.2937	−	13.6460i	−0.329157	−	0.436352i
$979$	2.44549	+	4.23571i	0.0781581	+	0.135374i
$980$	1.00000			0.0319438
$981$	−45.4070	+	11.3694i	−1.44973	+	0.362998i
$982$	15.3626			0.490241
$983$	5.12386	+	8.87479i	0.163426	+	0.283062i	0.936095	−	0.351747i	$-0.114412\pi$
$983$	5.12386	+	8.87479i	0.163426	+	0.283062i	−0.772669	+	0.634809i	$0.781079\pi$
$984$	−5.06564	+	11.9505i	−0.161487	+	0.380968i
$985$	−11.4471	+	19.8270i	−0.364735	+	0.631740i
$986$	1.47502	−	2.55481i	0.0469743	−	0.0813618i
$987$	−2.22808	+	5.25632i	−0.0709205	+	0.167311i
$988$	6.98113	+	12.0917i	0.222099	+	0.384688i
$989$	−1.97188			−0.0627023
$990$	−4.35194	−	4.49756i	−0.138314	−	0.142942i
$991$	54.3807			1.72746			0.863730	−	0.503955i	$-0.168122\pi$
$991$	54.3807			1.72746			0.863730	+	0.503955i	$0.168122\pi$
$992$	2.43807	+	4.22286i	0.0774088	+	0.134076i
$993$	−2.38225	−	3.15807i	−0.0755985	−	0.100218i
$994$	7.82936	−	13.5609i	0.248332	−	0.430124i
$995$	−0.426622	+	0.738932i	−0.0135248	+	0.0234257i
$996$	12.8384	−	1.58287i	0.406801	−	0.0501551i
$997$	2.79743	+	4.84529i	0.0885954	+	0.153452i	0.906918	−	0.421308i	$-0.138429\pi$
$997$	2.79743	+	4.84529i	0.0885954	+	0.153452i	−0.818322	+	0.574760i	$0.805096\pi$
$998$	−6.72938			−0.213015
$999$	48.0288	−	18.5191i	1.51956	−	0.585920i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	630.2.j.k.211.3	✓	6
3.2	odd	2		1890.2.j.j.631.3		6
9.2	odd	6		1890.2.j.j.1261.3		6
9.4	even	3		5670.2.a.bt.1.3		3
9.5	odd	6		5670.2.a.bp.1.1		3
9.7	even	3	inner	630.2.j.k.421.3	yes	6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
630.2.j.k.211.3	✓	6	1.1	even	1	trivial
630.2.j.k.421.3	yes	6	9.7	even	3	inner
1890.2.j.j.631.3		6	3.2	odd	2
1890.2.j.j.1261.3		6	9.2	odd	6
5670.2.a.bp.1.1		3	9.5	odd	6
5670.2.a.bt.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)

\(f(q)\)	\(=\)	\(q+(-0.500000 - 0.866025i) q^{2} +(1.71903 - 0.211943i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-0.500000 + 0.866025i) q^{5} +(-1.04307 - 1.38276i) q^{6} +(-0.500000 - 0.866025i) q^{7} +1.00000 q^{8} +(2.91016 - 0.728674i) q^{9} +O(q^{10})\)	\(q+(-0.500000 - 0.866025i) q^{2} +(1.71903 - 0.211943i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-0.500000 + 0.866025i) q^{5} +(-1.04307 - 1.38276i) q^{6} +(-0.500000 - 0.866025i) q^{7} +1.00000 q^{8} +(2.91016 - 0.728674i) q^{9} +1.00000 q^{10} +(-1.04307 - 1.80664i) q^{11} +(-0.675970 + 1.59470i) q^{12} +(1.54307 - 2.67267i) q^{13} +(-0.500000 + 0.866025i) q^{14} +(-0.675970 + 1.59470i) q^{15} +(-0.500000 - 0.866025i) q^{16} +1.64806 q^{17} +(-2.08613 - 2.15594i) q^{18} +4.52420 q^{19} +(-0.500000 - 0.866025i) q^{20} +(-1.04307 - 1.38276i) q^{21} +(-1.04307 + 1.80664i) q^{22} +(1.19113 - 2.06309i) q^{23} +(1.71903 - 0.211943i) q^{24} +(-0.500000 - 0.866025i) q^{25} -3.08613 q^{26} +(4.84823 - 1.86940i) q^{27} +1.00000 q^{28} +(0.895004 + 1.55019i) q^{29} +(1.71903 - 0.211943i) q^{30} +(2.43807 - 4.22286i) q^{31} +(-0.500000 + 0.866025i) q^{32} +(-2.17597 - 2.88461i) q^{33} +(-0.824030 - 1.42726i) q^{34} +1.00000 q^{35} +(-0.824030 + 2.88461i) q^{36} +9.90645 q^{37} +(-2.26210 - 3.91807i) q^{38} +(2.08613 - 4.92145i) q^{39} +(-0.500000 + 0.866025i) q^{40} +(-3.74694 + 6.48990i) q^{41} +(-0.675970 + 1.59470i) q^{42} +(-0.413870 - 0.716844i) q^{43} +2.08613 q^{44} +(-0.824030 + 2.88461i) q^{45} -2.38225 q^{46} +(-1.64806 - 2.85453i) q^{47} +(-1.04307 - 1.38276i) q^{48} +(-0.500000 + 0.866025i) q^{49} +(-0.500000 + 0.866025i) q^{50} +(2.83307 - 0.349294i) q^{51} +(1.54307 + 2.67267i) q^{52} -3.73419 q^{53} +(-4.04307 - 3.26399i) q^{54} +2.08613 q^{55} +(-0.500000 - 0.866025i) q^{56} +(7.77726 - 0.958871i) q^{57} +(0.895004 - 1.55019i) q^{58} +(-5.17597 + 8.96504i) q^{59} +(-1.04307 - 1.38276i) q^{60} +(-1.21903 - 2.11143i) q^{61} -4.87614 q^{62} +(-2.08613 - 2.15594i) q^{63} +1.00000 q^{64} +(1.54307 + 2.67267i) q^{65} +(-1.41016 + 3.32675i) q^{66} +(-5.70017 + 9.87298i) q^{67} +(-0.824030 + 1.42726i) q^{68} +(1.61033 - 3.79897i) q^{69} +(-0.500000 - 0.866025i) q^{70} -15.6587 q^{71} +(2.91016 - 0.728674i) q^{72} +1.70388 q^{73} +(-4.95323 - 8.57924i) q^{74} +(-1.04307 - 1.38276i) q^{75} +(-2.26210 + 3.91807i) q^{76} +(-1.04307 + 1.80664i) q^{77} +(-5.30516 + 0.654083i) q^{78} +(0.351939 + 0.609577i) q^{79} +1.00000 q^{80} +(7.93807 - 4.24111i) q^{81} +7.49389 q^{82} +(-3.73419 - 6.46781i) q^{83} +(1.71903 - 0.211943i) q^{84} +(-0.824030 + 1.42726i) q^{85} +(-0.413870 + 0.716844i) q^{86} +(1.86710 + 2.47515i) q^{87} +(-1.04307 - 1.80664i) q^{88} -2.34452 q^{89} +(2.91016 - 0.728674i) q^{90} -3.08613 q^{91} +(1.19113 + 2.06309i) q^{92} +(3.29612 - 7.77597i) q^{93} +(-1.64806 + 2.85453i) q^{94} +(-2.26210 + 3.91807i) q^{95} +(-0.675970 + 1.59470i) q^{96} +(3.93807 + 6.82094i) q^{97} +1.00000 q^{98} +(-4.35194 - 4.49756i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 3 q^{2} + q^{3} - 3 q^{4} - 3 q^{5} + q^{6} - 3 q^{7} + 6 q^{8} + 5 q^{9}+O(q^{10}) \) 6 * q - 3 * q^2 + q^3 - 3 * q^4 - 3 * q^5 + q^6 - 3 * q^7 + 6 * q^8 + 5 * q^9	\( 6 q - 3 q^{2} + q^{3} - 3 q^{4} - 3 q^{5} + q^{6} - 3 q^{7} + 6 q^{8} + 5 q^{9} + 6 q^{10} + q^{11} - 2 q^{12} + 2 q^{13} - 3 q^{14} - 2 q^{15} - 3 q^{16} + 14 q^{17} + 2 q^{18} - 6 q^{19} - 3 q^{20} + q^{21} + q^{22} + 4 q^{23} + q^{24} - 3 q^{25} - 4 q^{26} - 2 q^{27} + 6 q^{28} - 6 q^{29} + q^{30} - 4 q^{31} - 3 q^{32} - 11 q^{33} - 7 q^{34} + 6 q^{35} - 7 q^{36} + 20 q^{37} + 3 q^{38} - 2 q^{39} - 3 q^{40} - 7 q^{41} - 2 q^{42} - 17 q^{43} - 2 q^{44} - 7 q^{45} - 8 q^{46} - 14 q^{47} + q^{48} - 3 q^{49} - 3 q^{50} - 13 q^{51} + 2 q^{52} - 12 q^{53} - 17 q^{54} - 2 q^{55} - 3 q^{56} + 29 q^{57} - 6 q^{58} - 29 q^{59} + q^{60} + 2 q^{61} + 8 q^{62} + 2 q^{63} + 6 q^{64} + 2 q^{65} + 4 q^{66} + q^{67} - 7 q^{68} - 38 q^{69} - 3 q^{70} + 20 q^{71} + 5 q^{72} + 2 q^{73} - 10 q^{74} + q^{75} + 3 q^{76} + q^{77} - 8 q^{78} - 2 q^{79} + 6 q^{80} + 29 q^{81} + 14 q^{82} - 12 q^{83} + q^{84} - 7 q^{85} - 17 q^{86} + 6 q^{87} + q^{88} + 44 q^{89} + 5 q^{90} - 4 q^{91} + 4 q^{92} + 28 q^{93} - 14 q^{94} + 3 q^{95} - 2 q^{96} + 5 q^{97} + 6 q^{98} - 22 q^{99}+O(q^{100}) \) 6 * q - 3 * q^2 + q^3 - 3 * q^4 - 3 * q^5 + q^6 - 3 * q^7 + 6 * q^8 + 5 * q^9 + 6 * q^10 + q^11 - 2 * q^12 + 2 * q^13 - 3 * q^14 - 2 * q^15 - 3 * q^16 + 14 * q^17 + 2 * q^18 - 6 * q^19 - 3 * q^20 + q^21 + q^22 + 4 * q^23 + q^24 - 3 * q^25 - 4 * q^26 - 2 * q^27 + 6 * q^28 - 6 * q^29 + q^30 - 4 * q^31 - 3 * q^32 - 11 * q^33 - 7 * q^34 + 6 * q^35 - 7 * q^36 + 20 * q^37 + 3 * q^38 - 2 * q^39 - 3 * q^40 - 7 * q^41 - 2 * q^42 - 17 * q^43 - 2 * q^44 - 7 * q^45 - 8 * q^46 - 14 * q^47 + q^48 - 3 * q^49 - 3 * q^50 - 13 * q^51 + 2 * q^52 - 12 * q^53 - 17 * q^54 - 2 * q^55 - 3 * q^56 + 29 * q^57 - 6 * q^58 - 29 * q^59 + q^60 + 2 * q^61 + 8 * q^62 + 2 * q^63 + 6 * q^64 + 2 * q^65 + 4 * q^66 + q^67 - 7 * q^68 - 38 * q^69 - 3 * q^70 + 20 * q^71 + 5 * q^72 + 2 * q^73 - 10 * q^74 + q^75 + 3 * q^76 + q^77 - 8 * q^78 - 2 * q^79 + 6 * q^80 + 29 * q^81 + 14 * q^82 - 12 * q^83 + q^84 - 7 * q^85 - 17 * q^86 + 6 * q^87 + q^88 + 44 * q^89 + 5 * q^90 - 4 * q^91 + 4 * q^92 + 28 * q^93 - 14 * q^94 + 3 * q^95 - 2 * q^96 + 5 * q^97 + 6 * q^98 - 22 * q^99

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