LMFDB - Embedded newform 630.2.i.i.121.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [630,2,Mod(121,630)]

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, 2]))

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

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

chi := DirichletCharacter("630.121");

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.i (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:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - x^{15} + 2 x^{14} - 4 x^{13} + 5 x^{12} + 2 x^{11} - 35 x^{10} + 81 x^{9} - 66 x^{8} + \cdots + 6561 $ x^16 - x^15 + 2x^14 - 4x^13 + 5x^12 + 2x^11 - 35x^10 + 81x^9 - 66x^8 + 243x^7 - 315x^6 + 54x^5 + 405x^4 - 972x^3 + 1458x^2 - 2187x + 6561
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 3 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			121.3
Root			$-1.73198 - 0.0153002i$ of defining polynomial
Character	$\chi$	$=$	630.121
Dual form			630.2.i.i.151.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} +(-0.879242 - 1.49229i) q^{3} +1.00000 q^{4} +(0.500000 + 0.866025i) q^{5} +(0.879242 + 1.49229i) q^{6} +(2.58337 - 0.571125i) q^{7} -1.00000 q^{8} +(-1.45387 + 2.62417i) q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +(-0.879242 - 1.49229i) q^{3} +1.00000 q^{4} +(0.500000 + 0.866025i) q^{5} +(0.879242 + 1.49229i) q^{6} +(2.58337 - 0.571125i) q^{7} -1.00000 q^{8} +(-1.45387 + 2.62417i) q^{9} +(-0.500000 - 0.866025i) q^{10} +(-0.0955935 + 0.165573i) q^{11} +(-0.879242 - 1.49229i) q^{12} +(2.58891 - 4.48412i) q^{13} +(-2.58337 + 0.571125i) q^{14} +(0.852741 - 1.50759i) q^{15} +1.00000 q^{16} +(2.72213 + 4.71486i) q^{17} +(1.45387 - 2.62417i) q^{18} +(-2.06598 + 3.57838i) q^{19} +(0.500000 + 0.866025i) q^{20} +(-3.12369 - 3.35299i) q^{21} +(0.0955935 - 0.165573i) q^{22} +(4.25533 + 7.37044i) q^{23} +(0.879242 + 1.49229i) q^{24} +(-0.500000 + 0.866025i) q^{25} +(-2.58891 + 4.48412i) q^{26} +(5.19433 - 0.137687i) q^{27} +(2.58337 - 0.571125i) q^{28} +(-3.67720 - 6.36910i) q^{29} +(-0.852741 + 1.50759i) q^{30} +2.19119 q^{31} -1.00000 q^{32} +(0.331133 - 0.00292520i) q^{33} +(-2.72213 - 4.71486i) q^{34} +(1.78630 + 1.95170i) q^{35} +(-1.45387 + 2.62417i) q^{36} +(4.44983 - 7.70732i) q^{37} +(2.06598 - 3.57838i) q^{38} +(-8.96788 + 0.0792214i) q^{39} +(-0.500000 - 0.866025i) q^{40} +(3.65913 - 6.33779i) q^{41} +(3.12369 + 3.35299i) q^{42} +(-0.180602 - 0.312813i) q^{43} +(-0.0955935 + 0.165573i) q^{44} +(-2.99953 + 0.0529993i) q^{45} +(-4.25533 - 7.37044i) q^{46} +2.60078 q^{47} +(-0.879242 - 1.49229i) q^{48} +(6.34763 - 2.95086i) q^{49} +(0.500000 - 0.866025i) q^{50} +(4.64254 - 8.20771i) q^{51} +(2.58891 - 4.48412i) q^{52} +(-3.12346 - 5.40999i) q^{53} +(-5.19433 + 0.137687i) q^{54} -0.191187 q^{55} +(-2.58337 + 0.571125i) q^{56} +(7.15648 - 0.0632196i) q^{57} +(3.67720 + 6.36910i) q^{58} +8.01684 q^{59} +(0.852741 - 1.50759i) q^{60} +2.86896 q^{61} -2.19119 q^{62} +(-2.25715 + 7.60955i) q^{63} +1.00000 q^{64} +5.17781 q^{65} +(-0.331133 + 0.00292520i) q^{66} +5.95735 q^{67} +(2.72213 + 4.71486i) q^{68} +(7.25739 - 12.8306i) q^{69} +(-1.78630 - 1.95170i) q^{70} -9.49986 q^{71} +(1.45387 - 2.62417i) q^{72} +(-2.71302 - 4.69909i) q^{73} +(-4.44983 + 7.70732i) q^{74} +(1.73198 - 0.0153002i) q^{75} +(-2.06598 + 3.57838i) q^{76} +(-0.152391 + 0.482332i) q^{77} +(8.96788 - 0.0792214i) q^{78} +2.95806 q^{79} +(0.500000 + 0.866025i) q^{80} +(-4.77254 - 7.63039i) q^{81} +(-3.65913 + 6.33779i) q^{82} +(1.58717 + 2.74906i) q^{83} +(-3.12369 - 3.35299i) q^{84} +(-2.72213 + 4.71486i) q^{85} +(0.180602 + 0.312813i) q^{86} +(-6.27141 + 11.0874i) q^{87} +(0.0955935 - 0.165573i) q^{88} +(-8.43118 + 14.6032i) q^{89} +(2.99953 - 0.0529993i) q^{90} +(4.12712 - 13.0627i) q^{91} +(4.25533 + 7.37044i) q^{92} +(-1.92658 - 3.26989i) q^{93} -2.60078 q^{94} -4.13196 q^{95} +(0.879242 + 1.49229i) q^{96} +(7.26779 + 12.5882i) q^{97} +(-6.34763 + 2.95086i) q^{98} +(-0.295511 - 0.491575i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 16 q^{2} + 2 q^{3} + 16 q^{4} + 8 q^{5} - 2 q^{6} + 4 q^{7} - 16 q^{8} - 6 q^{9}+O(q^{10}) $ 16 * q - 16 * q^2 + 2 * q^3 + 16 * q^4 + 8 * q^5 - 2 * q^6 + 4 * q^7 - 16 * q^8 - 6 * q^9	\( 16 q - 16 q^{2} + 2 q^{3} + 16 q^{4} + 8 q^{5} - 2 q^{6} + 4 q^{7} - 16 q^{8} - 6 q^{9} - 8 q^{10} + q^{11} + 2 q^{12} + 2 q^{13} - 4 q^{14} + q^{15} + 16 q^{16} + 11 q^{17} + 6 q^{18} - 2 q^{19} + 8 q^{20} - 15 q^{21} - q^{22} + 11 q^{23} - 2 q^{24} - 8 q^{25} - 2 q^{26} - 7 q^{27} + 4 q^{28} + 17 q^{29} - q^{30} + 30 q^{31} - 16 q^{32} + 5 q^{33} - 11 q^{34} - 4 q^{35} - 6 q^{36} - 2 q^{37} + 2 q^{38} - 8 q^{40} + 7 q^{41} + 15 q^{42} - 13 q^{43} + q^{44} + 3 q^{45} - 11 q^{46} + 10 q^{47} + 2 q^{48} - 14 q^{49} + 8 q^{50} - 3 q^{51} + 2 q^{52} + 18 q^{53} + 7 q^{54} + 2 q^{55} - 4 q^{56} - 4 q^{57} - 17 q^{58} - 2 q^{59} + q^{60} + 54 q^{61} - 30 q^{62} + 41 q^{63} + 16 q^{64} + 4 q^{65} - 5 q^{66} + 20 q^{67} + 11 q^{68} - 14 q^{69} + 4 q^{70} - 38 q^{71} + 6 q^{72} - 8 q^{73} + 2 q^{74} - q^{75} - 2 q^{76} - 7 q^{77} + 50 q^{79} + 8 q^{80} - 6 q^{81} - 7 q^{82} + 2 q^{83} - 15 q^{84} - 11 q^{85} + 13 q^{86} - 32 q^{87} - q^{88} - 6 q^{89} - 3 q^{90} + 14 q^{91} + 11 q^{92} - 6 q^{93} - 10 q^{94} - 4 q^{95} - 2 q^{96} + 26 q^{97} + 14 q^{98} - 5 q^{99}+O(q^{100}) \) 16 * q - 16 * q^2 + 2 * q^3 + 16 * q^4 + 8 * q^5 - 2 * q^6 + 4 * q^7 - 16 * q^8 - 6 * q^9 - 8 * q^10 + q^11 + 2 * q^12 + 2 * q^13 - 4 * q^14 + q^15 + 16 * q^16 + 11 * q^17 + 6 * q^18 - 2 * q^19 + 8 * q^20 - 15 * q^21 - q^22 + 11 * q^23 - 2 * q^24 - 8 * q^25 - 2 * q^26 - 7 * q^27 + 4 * q^28 + 17 * q^29 - q^30 + 30 * q^31 - 16 * q^32 + 5 * q^33 - 11 * q^34 - 4 * q^35 - 6 * q^36 - 2 * q^37 + 2 * q^38 - 8 * q^40 + 7 * q^41 + 15 * q^42 - 13 * q^43 + q^44 + 3 * q^45 - 11 * q^46 + 10 * q^47 + 2 * q^48 - 14 * q^49 + 8 * q^50 - 3 * q^51 + 2 * q^52 + 18 * q^53 + 7 * q^54 + 2 * q^55 - 4 * q^56 - 4 * q^57 - 17 * q^58 - 2 * q^59 + q^60 + 54 * q^61 - 30 * q^62 + 41 * q^63 + 16 * q^64 + 4 * q^65 - 5 * q^66 + 20 * q^67 + 11 * q^68 - 14 * q^69 + 4 * q^70 - 38 * q^71 + 6 * q^72 - 8 * q^73 + 2 * q^74 - q^75 - 2 * q^76 - 7 * q^77 + 50 * q^79 + 8 * q^80 - 6 * q^81 - 7 * q^82 + 2 * q^83 - 15 * q^84 - 11 * q^85 + 13 * q^86 - 32 * q^87 - q^88 - 6 * q^89 - 3 * q^90 + 14 * q^91 + 11 * q^92 - 6 * q^93 - 10 * q^94 - 4 * q^95 - 2 * q^96 + 26 * q^97 + 14 * q^98 - 5 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−1.00000			−0.707107
$2$	−1.00000			−0.707107
$3$	−0.879242	−	1.49229i	−0.507631	−	0.861575i
$3$	−0.879242	−	1.49229i	−0.507631	−	0.861575i
$4$	1.00000			0.500000
$5$	0.500000	+	0.866025i	0.223607	+	0.387298i
$5$	0.500000	+	0.866025i	0.223607	+	0.387298i
$6$	0.879242	+	1.49229i	0.358949	+	0.609225i
$7$	2.58337	−	0.571125i	0.976423	−	0.215865i
$7$	2.58337	−	0.571125i	0.976423	−	0.215865i
$8$	−1.00000			−0.353553
$9$	−1.45387	+	2.62417i	−0.484622	+	0.874723i
$10$	−0.500000	−	0.866025i	−0.158114	−	0.273861i
$11$	−0.0955935	+	0.165573i	−0.0288225	+	0.0499221i	−0.880077	−	0.474831i	$-0.842509\pi$
$11$	−0.0955935	+	0.165573i	−0.0288225	+	0.0499221i	0.851254	+	0.524753i	$0.175842\pi$
$12$	−0.879242	−	1.49229i	−0.253815	−	0.430787i
$13$	2.58891	−	4.48412i	0.718033	−	1.24367i	−0.243745	−	0.969839i	$-0.578376\pi$
$13$	2.58891	−	4.48412i	0.718033	−	1.24367i	0.961778	−	0.273831i	$-0.0882907\pi$
$14$	−2.58337	+	0.571125i	−0.690435	+	0.152640i
$15$	0.852741	−	1.50759i	0.220177	−	0.389258i
$16$	1.00000			0.250000
$17$	2.72213	+	4.71486i	0.660213	+	1.14352i	0.980560	+	0.196222i	$0.0628672\pi$
$17$	2.72213	+	4.71486i	0.660213	+	1.14352i	−0.320347	+	0.947300i	$0.603799\pi$
$18$	1.45387	−	2.62417i	0.342680	−	0.618523i
$19$	−2.06598	+	3.57838i	−0.473968	+	0.820936i	−0.999556	−	0.0298029i	$-0.990512\pi$
$19$	−2.06598	+	3.57838i	−0.473968	+	0.820936i	0.525588	+	0.850739i	$0.323845\pi$
$20$	0.500000	+	0.866025i	0.111803	+	0.193649i
$21$	−3.12369	−	3.35299i	−0.681646	−	0.731682i
$22$	0.0955935	−	0.165573i	0.0203806	−	0.0353002i
$23$	4.25533	+	7.37044i	0.887297	+	1.53684i	0.843058	+	0.537823i	$0.180753\pi$
$23$	4.25533	+	7.37044i	0.887297	+	1.53684i	0.0442394	+	0.999021i	$0.485914\pi$
$24$	0.879242	+	1.49229i	0.179475	+	0.304613i
$25$	−0.500000	+	0.866025i	−0.100000	+	0.173205i
$26$	−2.58891	+	4.48412i	−0.507726	+	0.879407i
$27$	5.19433	−	0.137687i	0.999649	−	0.0264979i
$28$	2.58337	−	0.571125i	0.488212	−	0.107932i
$29$	−3.67720	−	6.36910i	−0.682839	−	1.18271i	−0.974111	−	0.226072i	$-0.927412\pi$
$29$	−3.67720	−	6.36910i	−0.682839	−	1.18271i	0.291271	−	0.956641i	$-0.405922\pi$
$30$	−0.852741	+	1.50759i	−0.155689	+	0.275247i
$31$	2.19119			0.393549			0.196774	−	0.980449i	$-0.436953\pi$
$31$	2.19119			0.393549			0.196774	+	0.980449i	$0.436953\pi$
$32$	−1.00000			−0.176777
$33$	0.331133	−	0.00292520i	0.0576428	−	0.000509211i
$34$	−2.72213	−	4.71486i	−0.466841	−	0.808592i
$35$	1.78630	+	1.95170i	0.301939	+	0.329898i
$36$	−1.45387	+	2.62417i	−0.242311	+	0.437362i
$37$	4.44983	−	7.70732i	0.731547	−	1.26708i	−0.224675	−	0.974434i	$-0.572132\pi$
$37$	4.44983	−	7.70732i	0.731547	−	1.26708i	0.956222	−	0.292643i	$-0.0945346\pi$
$38$	2.06598	−	3.57838i	0.335146	−	0.580490i
$39$	−8.96788	+	0.0792214i	−1.43601	+	0.0126856i
$40$	−0.500000	−	0.866025i	−0.0790569	−	0.136931i
$41$	3.65913	−	6.33779i	0.571460	−	0.989797i	−0.424957	−	0.905214i	$-0.639711\pi$
$41$	3.65913	−	6.33779i	0.571460	−	0.989797i	0.996416	−	0.0845834i	$-0.0269559\pi$
$42$	3.12369	+	3.35299i	0.481997	+	0.517377i
$43$	−0.180602	−	0.312813i	−0.0275416	−	0.0477035i	0.851926	−	0.523662i	$-0.175435\pi$
$43$	−0.180602	−	0.312813i	−0.0275416	−	0.0477035i	−0.879468	+	0.475959i	$0.842101\pi$
$44$	−0.0955935	+	0.165573i	−0.0144113	+	0.0249610i
$45$	−2.99953	+	0.0529993i	−0.447144	+	0.00790067i
$46$	−4.25533	−	7.37044i	−0.627414	−	1.08671i
$47$	2.60078			0.379362			0.189681	−	0.981846i	$-0.439255\pi$
$47$	2.60078			0.379362			0.189681	+	0.981846i	$0.439255\pi$
$48$	−0.879242	−	1.49229i	−0.126908	−	0.215394i
$49$	6.34763	−	2.95086i	0.906805	−	0.421551i
$50$	0.500000	−	0.866025i	0.0707107	−	0.122474i
$51$	4.64254	−	8.20771i	0.650086	−	1.14931i
$52$	2.58891	−	4.48412i	0.359017	−	0.621835i
$53$	−3.12346	−	5.40999i	−0.429040	−	0.743119i	0.567748	−	0.823202i	$-0.307815\pi$
$53$	−3.12346	−	5.40999i	−0.429040	−	0.743119i	−0.996788	+	0.0800833i	$0.974481\pi$
$54$	−5.19433	+	0.137687i	−0.706858	+	0.0187369i
$55$	−0.191187			−0.0257797
$56$	−2.58337	+	0.571125i	−0.345218	+	0.0763198i
$57$	7.15648	−	0.0632196i	0.947899	−	0.00837365i
$58$	3.67720	+	6.36910i	0.482840	+	0.836304i
$59$	8.01684			1.04370			0.521852	−	0.853036i	$-0.325241\pi$
$59$	8.01684			1.04370			0.521852	+	0.853036i	$0.325241\pi$
$60$	0.852741	−	1.50759i	0.110088	−	0.194629i
$61$	2.86896			0.367333			0.183666	−	0.982989i	$-0.441203\pi$
$61$	2.86896			0.367333			0.183666	+	0.982989i	$0.441203\pi$
$62$	−2.19119			−0.278281
$63$	−2.25715	+	7.60955i	−0.284374	+	0.958713i
$64$	1.00000			0.125000
$65$	5.17781			0.642228
$66$	−0.331133	+	0.00292520i	−0.0407596	+	0.000360067i
$67$	5.95735			0.727806			0.363903	−	0.931437i	$-0.381444\pi$
$67$	5.95735			0.727806			0.363903	+	0.931437i	$0.381444\pi$
$68$	2.72213	+	4.71486i	0.330106	+	0.571761i
$69$	7.25739	−	12.8306i	0.873687	−	1.54462i
$70$	−1.78630	−	1.95170i	−0.213503	−	0.233273i
$71$	−9.49986			−1.12743			−0.563713	−	0.825971i	$-0.690628\pi$
$71$	−9.49986			−1.12743			−0.563713	+	0.825971i	$0.690628\pi$
$72$	1.45387	−	2.62417i	0.171340	−	0.309261i
$73$	−2.71302	−	4.69909i	−0.317535	−	0.549987i	0.662438	−	0.749117i	$-0.269522\pi$
$73$	−2.71302	−	4.69909i	−0.317535	−	0.549987i	−0.979973	+	0.199130i	$0.936188\pi$
$74$	−4.44983	+	7.70732i	−0.517282	+	0.895958i
$75$	1.73198	−	0.0153002i	0.199992	−	0.00176671i
$76$	−2.06598	+	3.57838i	−0.236984	+	0.410468i
$77$	−0.152391	+	0.482332i	−0.0173666	+	0.0549669i
$78$	8.96788	−	0.0792214i	1.01541	−	0.00897006i
$79$	2.95806			0.332808			0.166404	−	0.986058i	$-0.446784\pi$
$79$	2.95806			0.332808			0.166404	+	0.986058i	$0.446784\pi$
$80$	0.500000	+	0.866025i	0.0559017	+	0.0968246i
$81$	−4.77254	−	7.63039i	−0.530282	−	0.847821i
$82$	−3.65913	+	6.33779i	−0.404083	+	0.699892i
$83$	1.58717	+	2.74906i	0.174214	+	0.301748i	0.939889	−	0.341480i	$-0.110928\pi$
$83$	1.58717	+	2.74906i	0.174214	+	0.301748i	−0.765675	+	0.643228i	$0.777595\pi$
$84$	−3.12369	−	3.35299i	−0.340823	−	0.365841i
$85$	−2.72213	+	4.71486i	−0.295256	+	0.511399i
$86$	0.180602	+	0.312813i	0.0194749	+	0.0337315i
$87$	−6.27141	+	11.0874i	−0.672365	+	1.18870i
$88$	0.0955935	−	0.165573i	0.0101903	−	0.0176501i
$89$	−8.43118	+	14.6032i	−0.893703	+	1.54794i	−0.0583019	+	0.998299i	$0.518569\pi$
$89$	−8.43118	+	14.6032i	−0.893703	+	1.54794i	−0.835401	+	0.549640i	$0.814765\pi$
$90$	2.99953	−	0.0529993i	0.316178	−	0.00558662i
$91$	4.12712	−	13.0627i	0.432639	−	1.36935i
$92$	4.25533	+	7.37044i	0.443649	+	0.768422i
$93$	−1.92658	−	3.26989i	−0.199777	−	0.339072i
$94$	−2.60078			−0.268250
$95$	−4.13196			−0.423930
$96$	0.879242	+	1.49229i	0.0897373	+	0.152306i
$97$	7.26779	+	12.5882i	0.737932	+	1.27814i	0.953425	+	0.301630i	$0.0975307\pi$
$97$	7.26779	+	12.5882i	0.737932	+	1.27814i	−0.215493	+	0.976505i	$0.569136\pi$
$98$	−6.34763	+	2.95086i	−0.641208	+	0.298082i
$99$	−0.295511	−	0.491575i	−0.0297000	−	0.0494051i
$100$	−0.500000	+	0.866025i	−0.0500000	+	0.0866025i
$101$	−4.58848	+	7.94749i	−0.456571	+	0.790805i	−0.998777	−	0.0494411i	$-0.984256\pi$
$101$	−4.58848	+	7.94749i	−0.456571	+	0.790805i	0.542206	+	0.840246i	$0.317589\pi$
$102$	−4.64254	+	8.20771i	−0.459680	+	0.812685i
$103$	−9.81248	−	16.9957i	−0.966853	−	1.67464i	−0.704552	−	0.709652i	$-0.748852\pi$
$103$	−9.81248	−	16.9957i	−0.966853	−	1.67464i	−0.262300	−	0.964986i	$-0.584481\pi$
$104$	−2.58891	+	4.48412i	−0.253863	+	0.439704i
$105$	1.34193	−	4.38169i	0.130959	−	0.427609i
$106$	3.12346	+	5.40999i	0.303377	+	0.525464i
$107$	−0.990672	+	1.71589i	−0.0957718	+	0.165882i	−0.909930	−	0.414761i	$-0.863865\pi$
$107$	−0.990672	+	1.71589i	−0.0957718	+	0.165882i	0.814159	+	0.580642i	$0.197199\pi$
$108$	5.19433	−	0.137687i	0.499824	−	0.0132490i
$109$	−4.35266	−	7.53902i	−0.416909	−	0.722108i	0.578718	−	0.815528i	$-0.303553\pi$
$109$	−4.35266	−	7.53902i	−0.416909	−	0.722108i	−0.995627	+	0.0934203i	$0.970220\pi$
$110$	0.191187			0.0182290
$111$	−15.4140	+	0.136166i	−1.46304	+	0.0129243i
$112$	2.58337	−	0.571125i	0.244106	−	0.0539662i
$113$	7.64837	−	13.2474i	0.719498	−	1.24621i	−0.241701	−	0.970351i	$-0.577705\pi$
$113$	7.64837	−	13.2474i	0.719498	−	1.24621i	0.961199	−	0.275856i	$-0.0889614\pi$
$114$	−7.15648	+	0.0632196i	−0.670266	+	0.00592106i
$115$	−4.25533	+	7.37044i	−0.396811	+	0.687297i
$116$	−3.67720	−	6.36910i	−0.341420	−	0.591356i
$117$	8.00316	+	13.3130i	0.739892	+	1.23079i
$118$	−8.01684			−0.738010
$119$	9.72505	+	10.6256i	0.891493	+	0.974045i
$120$	−0.852741	+	1.50759i	−0.0778443	+	0.137624i
$121$	5.48172	+	9.49462i	0.498339	+	0.863148i
$122$	−2.86896			−0.259743
$123$	−12.6751	+	0.111971i	−1.14287	+	0.0100960i
$124$	2.19119			0.196774
$125$	−1.00000			−0.0894427
$126$	2.25715	−	7.60955i	0.201083	−	0.677913i
$127$	10.0972			0.895981			0.447990	−	0.894038i	$-0.352140\pi$
$127$	10.0972			0.895981			0.447990	+	0.894038i	$0.352140\pi$
$128$	−1.00000			−0.0883883
$129$	−0.308014	+	0.544550i	−0.0271192	+	0.0479449i
$130$	−5.17781			−0.454124
$131$	2.74578	+	4.75582i	0.239899	+	0.415518i	0.960685	−	0.277640i	$-0.0895522\pi$
$131$	2.74578	+	4.75582i	0.239899	+	0.415518i	−0.720786	+	0.693158i	$0.756219\pi$
$132$	0.331133	−	0.00292520i	0.0288214	−	0.000254606i
$133$	−3.29349	+	10.4242i	−0.285582	+	0.903894i
$134$	−5.95735			−0.514636
$135$	2.71640	+	4.42958i	0.233791	+	0.381237i
$136$	−2.72213	−	4.71486i	−0.233420	−	0.404296i
$137$	6.02980	−	10.4439i	0.515161	−	0.892285i	−0.484684	−	0.874689i	$-0.661066\pi$
$137$	6.02980	−	10.4439i	0.515161	−	0.892285i	0.999845	−	0.0175955i	$-0.00560110\pi$
$138$	−7.25739	+	12.8306i	−0.617790	+	1.09221i
$139$	−7.21354	+	12.4942i	−0.611845	+	1.05975i	0.379085	+	0.925362i	$0.376239\pi$
$139$	−7.21354	+	12.4942i	−0.611845	+	1.05975i	−0.990929	+	0.134384i	$0.957094\pi$
$140$	1.78630	+	1.95170i	0.150970	+	0.164949i
$141$	−2.28671	−	3.88112i	−0.192576	−	0.326849i
$142$	9.49986			0.797211
$143$	0.494965	+	0.857305i	0.0413911	+	0.0716914i
$144$	−1.45387	+	2.62417i	−0.121156	+	0.218681i
$145$	3.67720	−	6.36910i	0.305375	−	0.528925i
$146$	2.71302	+	4.69909i	0.224531	+	0.388900i
$147$	−9.98464	−	6.87800i	−0.823520	−	0.567288i
$148$	4.44983	−	7.70732i	0.365773	−	0.633538i
$149$	−3.07958	−	5.33398i	−0.252289	−	0.436977i	0.711867	−	0.702314i	$-0.247850\pi$
$149$	−3.07958	−	5.33398i	−0.252289	−	0.436977i	−0.964156	+	0.265338i	$0.914517\pi$
$150$	−1.73198	+	0.0153002i	−0.141416	+	0.00124925i
$151$	−9.53198	+	16.5099i	−0.775702	+	1.34356i	0.158697	+	0.987327i	$0.449271\pi$
$151$	−9.53198	+	16.5099i	−0.775702	+	1.34356i	−0.934399	+	0.356228i	$0.884063\pi$
$152$	2.06598	−	3.57838i	0.167573	−	0.290245i
$153$	−16.3302	+	0.288542i	−1.32022	+	0.0233272i
$154$	0.152391	−	0.482332i	0.0122800	−	0.0388674i
$155$	1.09559	+	1.89762i	0.0880002	+	0.152421i
$156$	−8.96788	+	0.0792214i	−0.718005	+	0.00634279i
$157$	15.0459			1.20079			0.600395	−	0.799704i	$-0.295010\pi$
$157$	15.0459			1.20079			0.600395	+	0.799704i	$0.295010\pi$
$158$	−2.95806			−0.235331
$159$	−5.32700	+	9.41780i	−0.422459	+	0.746880i
$160$	−0.500000	−	0.866025i	−0.0395285	−	0.0684653i
$161$	15.2025	+	16.6103i	1.19813	+	1.30907i
$162$	4.77254	+	7.63039i	0.374966	+	0.599500i
$163$	−9.50876	+	16.4697i	−0.744783	+	1.29000i	0.205512	+	0.978654i	$0.434114\pi$
$163$	−9.50876	+	16.4697i	−0.744783	+	1.29000i	−0.950296	+	0.311348i	$0.899219\pi$
$164$	3.65913	−	6.33779i	0.285730	−	0.494899i
$165$	0.168100	+	0.285307i	0.0130865	+	0.0222111i
$166$	−1.58717	−	2.74906i	−0.123188	−	0.213368i
$167$	−4.30085	+	7.44928i	−0.332809	+	0.576443i	−0.983062	−	0.183276i	$-0.941330\pi$
$167$	−4.30085	+	7.44928i	−0.332809	+	0.576443i	0.650252	+	0.759719i	$0.274663\pi$
$168$	3.12369	+	3.35299i	0.240998	+	0.258689i
$169$	−6.90486	−	11.9596i	−0.531143	−	0.919967i
$170$	2.72213	−	4.71486i	0.208778	−	0.361613i
$171$	−6.38662	−	10.6240i	−0.488397	−	0.812435i
$172$	−0.180602	−	0.312813i	−0.0137708	−	0.0238517i
$173$	−3.92905			−0.298720			−0.149360	−	0.988783i	$-0.547721\pi$
$173$	−3.92905			−0.298720			−0.149360	+	0.988783i	$0.547721\pi$
$174$	6.27141	−	11.0874i	0.475434	−	0.840537i
$175$	−0.797078	+	2.52283i	−0.0602534	+	0.190708i
$176$	−0.0955935	+	0.165573i	−0.00720563	+	0.0124805i
$177$	−7.04875	−	11.9635i	−0.529816	−	0.899229i
$178$	8.43118	−	14.6032i	0.631944	−	1.09456i
$179$	−7.65542	−	13.2596i	−0.572193	−	0.991067i	−0.996340	−	0.0854737i	$-0.972760\pi$
$179$	−7.65542	−	13.2596i	−0.572193	−	0.991067i	0.424148	−	0.905593i	$-0.360574\pi$
$180$	−2.99953	+	0.0529993i	−0.223572	+	0.00395033i
$181$	−2.42858			−0.180515			−0.0902575	−	0.995918i	$-0.528769\pi$
$181$	−2.42858			−0.180515			−0.0902575	+	0.995918i	$0.528769\pi$
$182$	−4.12712	+	13.0627i	−0.305922	+	0.968274i
$183$	−2.52251	−	4.28132i	−0.186469	−	0.316485i
$184$	−4.25533	−	7.37044i	−0.313707	−	0.543356i
$185$	8.89965			0.654315
$186$	1.92658	+	3.26989i	0.141264	+	0.239760i
$187$	−1.04087			−0.0761160
$188$	2.60078			0.189681
$189$	13.3402	−	3.32231i	0.970360	−	0.241662i
$190$	4.13196			0.299764
$191$	−22.2685			−1.61130			−0.805648	−	0.592395i	$-0.798183\pi$
$191$	−22.2685			−1.61130			−0.805648	+	0.592395i	$0.798183\pi$
$192$	−0.879242	−	1.49229i	−0.0634538	−	0.107697i
$193$	−17.9136			−1.28945			−0.644725	−	0.764414i	$-0.723028\pi$
$193$	−17.9136			−1.28945			−0.644725	+	0.764414i	$0.723028\pi$
$194$	−7.26779	−	12.5882i	−0.521797	−	0.903778i
$195$	−4.55255	−	7.72680i	−0.326015	−	0.553328i
$196$	6.34763	−	2.95086i	0.453402	−	0.210776i
$197$	−13.7326			−0.978404			−0.489202	−	0.872170i	$-0.662712\pi$
$197$	−13.7326			−0.978404			−0.489202	+	0.872170i	$0.662712\pi$
$198$	0.295511	+	0.491575i	0.0210011	+	0.0349347i
$199$	3.22427	+	5.58461i	0.228563	+	0.395882i	0.957382	−	0.288824i	$-0.0932641\pi$
$199$	3.22427	+	5.58461i	0.228563	+	0.395882i	−0.728820	+	0.684706i	$0.759931\pi$
$200$	0.500000	−	0.866025i	0.0353553	−	0.0612372i
$201$	−5.23795	−	8.89010i	−0.369457	−	0.627059i
$202$	4.58848	−	7.94749i	0.322845	−	0.559183i
$203$	−13.1371	−	14.3536i	−0.922047	−	1.00743i
$204$	4.64254	−	8.20771i	0.325043	−	0.574655i
$205$	7.31825			0.511129
$206$	9.81248	+	16.9957i	0.683668	+	1.18415i
$207$	−25.5280	+	0.451059i	−1.77432	+	0.0313508i
$208$	2.58891	−	4.48412i	0.179508	−	0.310917i
$209$	−0.394988	−	0.684140i	−0.0273219	−	0.0473229i
$210$	−1.34193	+	4.38169i	−0.0926017	+	0.302366i
$211$	−4.90482	+	8.49539i	−0.337661	+	0.584847i	−0.983992	−	0.178210i	$-0.942969\pi$
$211$	−4.90482	+	8.49539i	−0.337661	+	0.584847i	0.646331	+	0.763057i	$0.276303\pi$
$212$	−3.12346	−	5.40999i	−0.214520	−	0.371559i
$213$	8.35268	+	14.1766i	0.572316	+	0.971362i
$214$	0.990672	−	1.71589i	0.0677209	−	0.117296i
$215$	0.180602	−	0.312813i	0.0123170	−	0.0213336i
$216$	−5.19433	+	0.137687i	−0.353429	+	0.00936843i
$217$	5.66065	−	1.25144i	0.384270	−	0.0849534i
$218$	4.35266	+	7.53902i	0.294799	+	0.510607i
$219$	−4.62701	+	8.18026i	−0.312664	+	0.552771i
$220$	−0.191187			−0.0128898
$221$	28.1893			1.89622
$222$	15.4140	−	0.136166i	1.03452	−	0.00913888i
$223$	3.43638	+	5.95198i	0.230117	+	0.398574i	0.957842	−	0.287295i	$-0.0927559\pi$
$223$	3.43638	+	5.95198i	0.230117	+	0.398574i	−0.727726	+	0.685868i	$0.759423\pi$
$224$	−2.58337	+	0.571125i	−0.172609	+	0.0381599i
$225$	−1.54566	−	2.57117i	−0.103044	−	0.171411i
$226$	−7.64837	+	13.2474i	−0.508762	+	0.881202i
$227$	−3.38526	+	5.86344i	−0.224688	+	0.389170i	−0.956226	−	0.292630i	$-0.905469\pi$
$227$	−3.38526	+	5.86344i	−0.224688	+	0.389170i	0.731538	+	0.681801i	$0.238803\pi$
$228$	7.15648	−	0.0632196i	0.473949	−	0.00418682i
$229$	7.68998	+	13.3194i	0.508168	+	0.880173i	0.999955	+	0.00945765i	$0.00301051\pi$
$229$	7.68998	+	13.3194i	0.508168	+	0.880173i	−0.491787	+	0.870715i	$0.663656\pi$
$230$	4.25533	−	7.37044i	0.280588	−	0.485993i
$231$	0.853769	−	0.196675i	0.0561739	−	0.0129403i
$232$	3.67720	+	6.36910i	0.241420	+	0.418152i
$233$	−0.451961	+	0.782819i	−0.0296089	+	0.0512842i	−0.880450	−	0.474139i	$-0.842760\pi$
$233$	−0.451961	+	0.782819i	−0.0296089	+	0.0512842i	0.850841	+	0.525423i	$0.176093\pi$
$234$	−8.00316	−	13.3130i	−0.523183	−	0.870300i
$235$	1.30039	+	2.25234i	0.0848280	+	0.146926i
$236$	8.01684			0.521852
$237$	−2.60085	−	4.41429i	−0.168944	−	0.286739i
$238$	−9.72505	−	10.6256i	−0.630381	−	0.688754i
$239$	10.1769	−	17.6269i	0.658287	−	1.14019i	−0.322772	−	0.946477i	$-0.604615\pi$
$239$	10.1769	−	17.6269i	0.658287	−	1.14019i	0.981059	−	0.193710i	$-0.0620520\pi$
$240$	0.852741	−	1.50759i	0.0550442	−	0.0973146i
$241$	−8.22393	+	14.2443i	−0.529750	+	0.917554i	0.469648	+	0.882854i	$0.344381\pi$
$241$	−8.22393	+	14.2443i	−0.529750	+	0.917554i	−0.999398	+	0.0346998i	$0.988952\pi$
$242$	−5.48172	−	9.49462i	−0.352379	−	0.610338i
$243$	−7.19055	+	13.8310i	−0.461274	+	0.887258i
$244$	2.86896			0.183666
$245$	5.72933	+	4.02178i	0.366034	+	0.256942i
$246$	12.6751	−	0.111971i	0.808134	−	0.00713898i
$247$	10.6972	+	18.5282i	0.680649	+	1.17892i
$248$	−2.19119			−0.139141
$249$	2.70689	−	4.78561i	0.171542	−	0.303275i
$250$	1.00000			0.0632456
$251$	13.8668			0.875266			0.437633	−	0.899154i	$-0.355817\pi$
$251$	13.8668			0.875266			0.437633	+	0.899154i	$0.355817\pi$
$252$	−2.25715	+	7.60955i	−0.142187	+	0.479357i
$253$	−1.62713			−0.102297
$254$	−10.0972			−0.633554
$255$	9.42936	−	0.0832980i	0.590489	−	0.00521633i
$256$	1.00000			0.0625000
$257$	−1.53715	−	2.66242i	−0.0958847	−	0.166077i	0.814093	−	0.580735i	$-0.197235\pi$
$257$	−1.53715	−	2.66242i	−0.0958847	−	0.166077i	−0.909977	+	0.414658i	$0.863901\pi$
$258$	0.308014	−	0.544550i	0.0191761	−	0.0339022i
$259$	7.09371	−	22.4523i	0.440782	−	1.39512i
$260$	5.17781			0.321114
$261$	22.0598	−	0.389778i	1.36547	−	0.0241267i
$262$	−2.74578	−	4.75582i	−0.169635	−	0.293816i
$263$	8.64009	−	14.9651i	0.532771	−	0.922787i	−0.466497	−	0.884523i	$-0.654484\pi$
$263$	8.64009	−	14.9651i	0.532771	−	0.922787i	0.999268	−	0.0382636i	$-0.0121826\pi$
$264$	−0.331133	+	0.00292520i	−0.0203798	+	0.000180033i
$265$	3.12346	−	5.40999i	0.191872	−	0.332333i
$266$	3.29349	−	10.4242i	0.201937	−	0.639150i
$267$	29.2053	−	0.257997i	1.78734	−	0.0157892i
$268$	5.95735			0.363903
$269$	−4.35721	−	7.54691i	−0.265664	−	0.460143i	0.702074	−	0.712104i	$-0.252258\pi$
$269$	−4.35721	−	7.54691i	−0.265664	−	0.460143i	−0.967737	+	0.251961i	$0.918924\pi$
$270$	−2.71640	−	4.42958i	−0.165315	−	0.269575i
$271$	−3.71843	+	6.44051i	−0.225879	+	0.391233i	−0.956583	−	0.291461i	$-0.905859\pi$
$271$	−3.71843	+	6.44051i	−0.225879	+	0.391233i	0.730704	+	0.682694i	$0.239192\pi$
$272$	2.72213	+	4.71486i	0.165053	+	0.285881i
$273$	−23.1221	+	5.32644i	−1.39942	+	0.322371i
$274$	−6.02980	+	10.4439i	−0.364274	+	0.630940i
$275$	−0.0955935	−	0.165573i	−0.00576451	−	0.00998442i
$276$	7.25739	−	12.8306i	0.436843	−	0.772311i
$277$	3.78667	−	6.55870i	0.227519	−	0.394074i	−0.729553	−	0.683924i	$-0.760272\pi$
$277$	3.78667	−	6.55870i	0.227519	−	0.394074i	0.957072	+	0.289850i	$0.0936054\pi$
$278$	7.21354	−	12.4942i	0.432639	−	0.749353i
$279$	−3.18569	+	5.75005i	−0.190723	+	0.344246i
$280$	−1.78630	−	1.95170i	−0.106752	−	0.116637i
$281$	0.170693	+	0.295650i	0.0101827	+	0.0176370i	0.871072	−	0.491156i	$-0.163425\pi$
$281$	0.170693	+	0.295650i	0.0101827	+	0.0176370i	−0.860889	+	0.508793i	$0.830092\pi$
$282$	2.28671	+	3.88112i	0.136172	+	0.231117i
$283$	20.4280			1.21432			0.607159	−	0.794580i	$-0.292309\pi$
$283$	20.4280			1.21432			0.607159	+	0.794580i	$0.292309\pi$
$284$	−9.49986			−0.563713
$285$	3.63299	+	6.16608i	0.215200	+	0.365247i
$286$	−0.494965	−	0.857305i	−0.0292679	−	0.0506935i
$287$	5.83322	−	18.4627i	0.344324	−	1.08982i
$288$	1.45387	−	2.62417i	0.0856699	−	0.154631i
$289$	−6.31995	+	10.9465i	−0.371762	+	0.643910i
$290$	−3.67720	+	6.36910i	−0.215933	+	0.374007i
$291$	12.3951	−	21.9137i	0.726613	−	1.28460i
$292$	−2.71302	−	4.69909i	−0.158768	−	0.274994i
$293$	−3.99479	+	6.91917i	−0.233378	+	0.404222i	−0.958800	−	0.284082i	$-0.908311\pi$
$293$	−3.99479	+	6.91917i	−0.233378	+	0.404222i	0.725422	+	0.688304i	$0.241645\pi$
$294$	9.98464	+	6.87800i	0.582316	+	0.401133i
$295$	4.00842	+	6.94279i	0.233379	+	0.404225i
$296$	−4.44983	+	7.70732i	−0.258641	+	0.447979i
$297$	−0.473747	+	0.873202i	−0.0274896	+	0.0506683i
$298$	3.07958	+	5.33398i	0.178395	+	0.308989i
$299$	44.0666			2.54844
$300$	1.73198	−	0.0153002i	0.0999961	−	0.000883356i
$301$	−0.645219	−	0.704965i	−0.0371898	−	0.0406335i
$302$	9.53198	−	16.5099i	0.548504	−	0.950037i
$303$	15.8944	−	0.140409i	0.913107	−	0.00806630i
$304$	−2.06598	+	3.57838i	−0.118492	+	0.205234i
$305$	1.43448	+	2.48459i	0.0821381	+	0.142267i
$306$	16.3302	−	0.288542i	0.933536	−	0.0164948i
$307$	−21.5270			−1.22861			−0.614306	−	0.789068i	$-0.710564\pi$
$307$	−21.5270			−1.22861			−0.614306	+	0.789068i	$0.710564\pi$
$308$	−0.152391	+	0.482332i	−0.00868328	+	0.0274834i
$309$	−16.7350	+	29.5864i	−0.952022	+	1.68311i
$310$	−1.09559	−	1.89762i	−0.0622255	−	0.107778i
$311$	6.04973			0.343049			0.171524	−	0.985180i	$-0.445131\pi$
$311$	6.04973			0.343049			0.171524	+	0.985180i	$0.445131\pi$
$312$	8.96788	−	0.0792214i	0.507706	−	0.00448503i
$313$	−24.8404			−1.40406			−0.702032	−	0.712146i	$-0.747724\pi$
$313$	−24.8404			−1.40406			−0.702032	+	0.712146i	$0.747724\pi$
$314$	−15.0459			−0.849086
$315$	−7.71864	+	1.85002i	−0.434896	+	0.104237i
$316$	2.95806			0.166404
$317$	16.5528			0.929700			0.464850	−	0.885390i	$-0.346108\pi$
$317$	16.5528			0.929700			0.464850	+	0.885390i	$0.346108\pi$
$318$	5.32700	−	9.41780i	0.298723	−	0.528124i
$319$	1.40607			0.0787246
$320$	0.500000	+	0.866025i	0.0279508	+	0.0484123i
$321$	3.43165	−	0.0303149i	0.191536	−	0.00169201i
$322$	−15.2025	−	16.6103i	−0.847205	−	0.925655i
$323$	−22.4954			−1.25168
$324$	−4.77254	−	7.63039i	−0.265141	−	0.423911i
$325$	2.58891	+	4.48412i	0.143607	+	0.248734i
$326$	9.50876	−	16.4697i	0.526641	−	0.912170i
$327$	−7.42338	+	13.1241i	−0.410514	+	0.725762i
$328$	−3.65913	+	6.33779i	−0.202041	+	0.349946i
$329$	6.71878	−	1.48537i	0.370418	−	0.0818910i
$330$	−0.168100	−	0.285307i	−0.00925358	−	0.0157056i
$331$	−27.5589			−1.51477			−0.757387	−	0.652966i	$-0.773524\pi$
$331$	−27.5589			−1.51477			−0.757387	+	0.652966i	$0.773524\pi$
$332$	1.58717	+	2.74906i	0.0871072	+	0.150874i
$333$	13.7559	+	22.8825i	0.753817	+	1.25395i
$334$	4.30085	−	7.44928i	0.235332	−	0.407607i
$335$	2.97867	+	5.15921i	0.162742	+	0.281878i
$336$	−3.12369	−	3.35299i	−0.170412	−	0.182921i
$337$	5.26173	−	9.11358i	0.286625	−	0.496449i	−0.686377	−	0.727246i	$-0.740800\pi$
$337$	5.26173	−	9.11358i	0.286625	−	0.496449i	0.973002	+	0.230797i	$0.0741334\pi$
$338$	6.90486	+	11.9596i	0.375575	+	0.650515i
$339$	−26.4937	+	0.234043i	−1.43894	+	0.0127115i
$340$	−2.72213	+	4.71486i	−0.147628	+	0.255699i
$341$	−0.209463	+	0.362801i	−0.0113431	+	0.0196468i
$342$	6.38662	+	10.6240i	0.345349	+	0.574478i
$343$	14.7130	−	11.2485i	0.794427	−	0.607360i
$344$	0.180602	+	0.312813i	0.00973743	+	0.0168657i
$345$	14.7403	−	0.130215i	0.793592	−	0.00701052i
$346$	3.92905			0.211227
$347$	−21.4162			−1.14968			−0.574841	−	0.818265i	$-0.694936\pi$
$347$	−21.4162			−1.14968			−0.574841	+	0.818265i	$0.694936\pi$
$348$	−6.27141	+	11.0874i	−0.336183	+	0.594349i
$349$	−9.67929	−	16.7650i	−0.518120	−	0.897411i	−0.999778	−	0.0210515i	$-0.993299\pi$
$349$	−9.67929	−	16.7650i	−0.518120	−	0.897411i	0.481658	−	0.876359i	$-0.340035\pi$
$350$	0.797078	−	2.52283i	0.0426056	−	0.134851i
$351$	12.8302	−	23.6484i	0.684826	−	1.26226i
$352$	0.0955935	−	0.165573i	0.00509515	−	0.00882506i
$353$	0.0756056	−	0.130953i	0.00402408	−	0.00696991i	−0.864006	−	0.503481i	$-0.832052\pi$
$353$	0.0756056	−	0.130953i	0.00402408	−	0.00696991i	0.868030	+	0.496511i	$0.165386\pi$
$354$	7.04875	+	11.9635i	0.374637	+	0.635851i
$355$	−4.74993	−	8.22712i	−0.252100	−	0.436650i
$356$	−8.43118	+	14.6032i	−0.446852	+	0.773970i
$357$	7.30578	−	23.8551i	0.386663	−	1.26254i
$358$	7.65542	+	13.2596i	0.404601	+	0.700790i
$359$	4.21049	−	7.29279i	0.222221	−	0.384899i	−0.733261	−	0.679947i	$-0.762003\pi$
$359$	4.21049	−	7.29279i	0.222221	−	0.384899i	0.955482	+	0.295049i	$0.0953359\pi$
$360$	2.99953	−	0.0529993i	0.158089	−	0.00279331i
$361$	0.963472	+	1.66878i	0.0507090	+	0.0878306i
$362$	2.42858			0.127643
$363$	9.34898	−	16.5284i	0.490694	−	0.867516i
$364$	4.12712	−	13.0627i	0.216320	−	0.684673i
$365$	2.71302	−	4.69909i	0.142006	−	0.245962i
$366$	2.52251	+	4.28132i	0.131854	+	0.223788i
$367$	−7.27037	+	12.5926i	−0.379510	+	0.657331i	−0.990991	−	0.133928i	$-0.957241\pi$
$367$	−7.27037	+	12.5926i	−0.379510	+	0.657331i	0.611481	+	0.791259i	$0.290574\pi$
$368$	4.25533	+	7.37044i	0.221824	+	0.384211i
$369$	11.3116	+	18.8165i	0.588857	+	0.979547i
$370$	−8.89965			−0.462671
$371$	−11.1588	−	12.1921i	−0.579338	−	0.632984i
$372$	−1.92658	−	3.26989i	−0.0998887	−	0.169536i
$373$	−8.81157	−	15.2621i	−0.456246	−	0.790241i	0.542513	−	0.840047i	$-0.317473\pi$
$373$	−8.81157	−	15.2621i	−0.456246	−	0.790241i	−0.998759	+	0.0498064i	$0.984140\pi$
$374$	1.04087			0.0538221
$375$	0.879242	+	1.49229i	0.0454039	+	0.0770616i
$376$	−2.60078			−0.134125
$377$	−38.0797			−1.96121
$378$	−13.3402	+	3.32231i	−0.686148	+	0.170881i
$379$	18.9287			0.972301			0.486151	−	0.873875i	$-0.338401\pi$
$379$	18.9287			0.972301			0.486151	+	0.873875i	$0.338401\pi$
$380$	−4.13196			−0.211965
$381$	−8.87787	−	15.0679i	−0.454827	−	0.771954i
$382$	22.2685			1.13936
$383$	−10.7236	−	18.5738i	−0.547950	−	0.949077i	−0.998415	−	0.0562829i	$-0.982075\pi$
$383$	−10.7236	−	18.5738i	−0.547950	−	0.949077i	0.450465	−	0.892794i	$-0.351258\pi$
$384$	0.879242	+	1.49229i	0.0448686	+	0.0761532i
$385$	−0.493907	+	0.109192i	−0.0251719	+	0.00556492i
$386$	17.9136			0.911779
$387$	1.08345	−	0.0191436i	0.0550746	−	0.000973124i
$388$	7.26779	+	12.5882i	0.368966	+	0.639068i
$389$	−6.45188	+	11.1750i	−0.327123	+	0.566594i	−0.981940	−	0.189194i	$-0.939413\pi$
$389$	−6.45188	+	11.1750i	−0.327123	+	0.566594i	0.654816	+	0.755788i	$0.272746\pi$
$390$	4.55255	+	7.72680i	0.230527	+	0.391262i
$391$	−23.1671	+	40.1266i	−1.17161	+	2.02929i
$392$	−6.34763	+	2.95086i	−0.320604	+	0.149041i
$393$	4.68287	−	8.27901i	0.236220	−	0.417621i
$394$	13.7326			0.691836
$395$	1.47903	+	2.56176i	0.0744182	+	0.128896i
$396$	−0.295511	−	0.491575i	−0.0148500	−	0.0247026i
$397$	10.2010	−	17.6686i	0.511972	−	0.886762i	−0.487931	−	0.872882i	$-0.662248\pi$
$397$	10.2010	−	17.6686i	0.511972	−	0.886762i	0.999904	−	0.0138799i	$-0.00441826\pi$
$398$	−3.22427	−	5.58461i	−0.161618	−	0.279931i
$399$	18.4517	−	4.25056i	0.923743	−	0.212794i
$400$	−0.500000	+	0.866025i	−0.0250000	+	0.0433013i
$401$	−7.98902	−	13.8374i	−0.398952	−	0.691006i	0.594644	−	0.803989i	$-0.297293\pi$
$401$	−7.98902	−	13.8374i	−0.398952	−	0.691006i	−0.993597	+	0.112983i	$0.963959\pi$
$402$	5.23795	+	8.89010i	0.261245	+	0.443398i
$403$	5.67278	−	9.82554i	0.282581	−	0.489445i
$404$	−4.58848	+	7.94749i	−0.228286	+	0.395402i
$405$	4.22184	−	7.94834i	0.209785	−	0.394956i
$406$	13.1371	+	14.3536i	0.651985	+	0.712358i
$407$	0.850749	+	1.47354i	0.0421701	+	0.0730407i
$408$	−4.64254	+	8.20771i	−0.229840	+	0.406342i
$409$	25.1983			1.24597			0.622987	−	0.782232i	$-0.285919\pi$
$409$	25.1983			1.24597			0.622987	+	0.782232i	$0.285919\pi$
$410$	−7.31825			−0.361423
$411$	−20.8870	+	0.184514i	−1.03028	+	0.00910141i
$412$	−9.81248	−	16.9957i	−0.483426	−	0.837319i
$413$	20.7105	−	4.57862i	1.01910	−	0.225299i
$414$	25.5280	−	0.451059i	1.25463	−	0.0221683i
$415$	−1.58717	+	2.74906i	−0.0779111	+	0.134946i
$416$	−2.58891	+	4.48412i	−0.126932	+	0.219852i
$417$	24.9875	−	0.220737i	1.22364	−	0.0108095i
$418$	0.394988	+	0.684140i	0.0193195	+	0.0334624i
$419$	6.33650	−	10.9751i	0.309559	−	0.536171i	−0.668707	−	0.743526i	$-0.733152\pi$
$419$	6.33650	−	10.9751i	0.309559	−	0.536171i	0.978266	+	0.207355i	$0.0664854\pi$
$420$	1.34193	−	4.38169i	0.0654793	−	0.213805i
$421$	2.09991	+	3.63715i	0.102343	+	0.177264i	0.912650	−	0.408743i	$-0.134033\pi$
$421$	2.09991	+	3.63715i	0.102343	+	0.177264i	−0.810306	+	0.586006i	$0.800699\pi$
$422$	4.90482	−	8.49539i	0.238763	−	0.413549i
$423$	−3.78118	+	6.82488i	−0.183847	+	0.331837i
$424$	3.12346	+	5.40999i	0.151689	+	0.262732i
$425$	−5.44425			−0.264085
$426$	−8.35268	−	14.1766i	−0.404689	−	0.686857i
$427$	7.41160	−	1.63854i	0.358672	−	0.0792943i
$428$	−0.990672	+	1.71589i	−0.0478859	+	0.0829408i
$429$	0.844154	−	1.49241i	0.0407562	−	0.0720543i
$430$	−0.180602	+	0.312813i	−0.00870943	+	0.0150852i
$431$	5.75441	+	9.96694i	0.277180	+	0.480090i	0.970683	−	0.240364i	$-0.0772667\pi$
$431$	5.75441	+	9.96694i	0.277180	+	0.480090i	−0.693503	+	0.720454i	$0.743933\pi$
$432$	5.19433	−	0.137687i	0.249912	−	0.00662448i
$433$	−8.34590			−0.401078			−0.200539	−	0.979686i	$-0.564269\pi$
$433$	−8.34590			−0.401078			−0.200539	+	0.979686i	$0.564269\pi$
$434$	−5.66065	+	1.25144i	−0.271720	+	0.0600711i
$435$	−12.7377	+	0.112524i	−0.610726	+	0.00539510i
$436$	−4.35266	−	7.53902i	−0.208455	−	0.361054i
$437$	−35.1657			−1.68220
$438$	4.62701	−	8.18026i	0.221087	−	0.390868i
$439$	−31.6786			−1.51194			−0.755969	−	0.654607i	$-0.772834\pi$
$439$	−31.6786			−1.51194			−0.755969	+	0.654607i	$0.772834\pi$
$440$	0.191187			0.00911448
$441$	−1.48506	+	20.9474i	−0.0707171	+	0.997496i
$442$	−28.1893			−1.34083
$443$	33.7313			1.60262			0.801311	−	0.598248i	$-0.204136\pi$
$443$	33.7313			1.60262			0.801311	+	0.598248i	$0.204136\pi$
$444$	−15.4140	+	0.136166i	−0.731518	+	0.00646216i
$445$	−16.8624			−0.799352
$446$	−3.43638	−	5.95198i	−0.162717	−	0.281834i
$447$	−5.25216	+	9.28549i	−0.248419	+	0.439189i
$448$	2.58337	−	0.571125i	0.122053	−	0.0269831i
$449$	−38.8454			−1.83323			−0.916615	−	0.399772i	$-0.869089\pi$
$449$	−38.8454			−1.83323			−0.916615	+	0.399772i	$0.869089\pi$
$450$	1.54566	+	2.57117i	0.0728633	+	0.121206i
$451$	0.699578	+	1.21170i	0.0329418	+	0.0570569i
$452$	7.64837	−	13.2474i	0.359749	−	0.623104i
$453$	33.0185	−	0.291682i	1.55134	−	0.0137044i
$454$	3.38526	−	5.86344i	0.158878	−	0.275185i
$455$	13.3762	−	2.95718i	0.627087	−	0.138635i
$456$	−7.15648	+	0.0632196i	−0.335133	+	0.00296053i
$457$	−16.8141			−0.786529			−0.393264	−	0.919425i	$-0.628654\pi$
$457$	−16.8141			−0.786529			−0.393264	+	0.919425i	$0.628654\pi$
$458$	−7.68998	−	13.3194i	−0.359329	−	0.622376i
$459$	14.7888	+	24.1157i	0.690282	+	1.12563i
$460$	−4.25533	+	7.37044i	−0.198406	+	0.343649i
$461$	18.5721	+	32.1678i	0.864987	+	1.49820i	0.867060	+	0.498204i	$0.166007\pi$
$461$	18.5721	+	32.1678i	0.864987	+	1.49820i	−0.00207255	+	0.999998i	$0.500660\pi$
$462$	−0.853769	+	0.196675i	−0.0397209	+	0.00915015i
$463$	−4.73848	+	8.20729i	−0.220216	+	0.381425i	−0.954873	−	0.297013i	$-0.904010\pi$
$463$	−4.73848	+	8.20729i	−0.220216	+	0.381425i	0.734657	+	0.678438i	$0.237343\pi$
$464$	−3.67720	−	6.36910i	−0.170710	−	0.295678i
$465$	1.86852	−	3.30342i	0.0866503	−	0.153192i
$466$	0.451961	−	0.782819i	0.0209367	−	0.0362634i
$467$	−8.72166	+	15.1064i	−0.403590	+	0.699039i	−0.994156	−	0.107950i	$-0.965571\pi$
$467$	−8.72166	+	15.1064i	−0.403590	+	0.699039i	0.590566	+	0.806989i	$0.298905\pi$
$468$	8.00316	+	13.3130i	0.369946	+	0.615395i
$469$	15.3901	−	3.40239i	0.710647	−	0.157108i
$470$	−1.30039	−	2.25234i	−0.0599824	−	0.103893i
$471$	−13.2289	−	22.4528i	−0.609558	−	1.03457i
$472$	−8.01684			−0.369005
$473$	0.0690577			0.00317528
$474$	2.60085	+	4.41429i	0.119461	+	0.202755i
$475$	−2.06598	−	3.57838i	−0.0947936	−	0.164187i
$476$	9.72505	+	10.6256i	0.445747	+	0.487022i
$477$	18.7378	−	0.331082i	0.857946	−	0.0151592i
$478$	−10.1769	+	17.6269i	−0.465479	+	0.806234i
$479$	0.469756	−	0.813641i	0.0214637	−	0.0371762i	−0.855094	−	0.518473i	$-0.826501\pi$
$479$	0.469756	−	0.813641i	0.0214637	−	0.0371762i	0.876558	+	0.481297i	$0.159834\pi$
$480$	−0.852741	+	1.50759i	−0.0389221	+	0.0688118i
$481$	−23.0404	−	39.9071i	−1.05055	−	1.81961i
$482$	8.22393	−	14.2443i	0.374590	−	0.648808i
$483$	11.4207	−	37.2911i	0.519658	−	1.69680i
$484$	5.48172	+	9.49462i	0.249169	+	0.431574i
$485$	−7.26779	+	12.5882i	−0.330013	+	0.571600i
$486$	7.19055	−	13.8310i	0.326170	−	0.627386i
$487$	12.3343	+	21.3637i	0.558922	+	0.968082i	0.997587	+	0.0694311i	$0.0221184\pi$
$487$	12.3343	+	21.3637i	0.558922	+	0.968082i	−0.438664	+	0.898651i	$0.644548\pi$
$488$	−2.86896			−0.129872
$489$	32.9380	−	0.290971i	1.48951	−	0.0131582i
$490$	−5.72933	−	4.02178i	−0.258825	−	0.181686i
$491$	7.85545	−	13.6060i	0.354512	−	0.614032i	−0.632523	−	0.774542i	$-0.717980\pi$
$491$	7.85545	−	13.6060i	0.354512	−	0.614032i	0.987034	+	0.160510i	$0.0513138\pi$
$492$	−12.6751	+	0.111971i	−0.571437	+	0.00504802i
$493$	20.0196	−	34.6750i	0.901639	−	1.56168i
$494$	−10.6972	−	18.5282i	−0.481292	−	0.833622i
$495$	0.277961	−	0.501707i	0.0124934	−	0.0225501i
$496$	2.19119			0.0983872
$497$	−24.5417	+	5.42561i	−1.10085	+	0.243372i
$498$	−2.70689	+	4.78561i	−0.121299	+	0.214448i
$499$	−11.5312	−	19.9727i	−0.516209	−	0.894100i	−0.999823	−	0.0188188i	$-0.994009\pi$
$499$	−11.5312	−	19.9727i	−0.516209	−	0.894100i	0.483614	−	0.875281i	$-0.339324\pi$
$500$	−1.00000			−0.0447214
$501$	14.8980	−	0.131607i	0.665593	−	0.00587979i
$502$	−13.8668			−0.618907
$503$	23.3244			1.03998			0.519992	−	0.854171i	$-0.325935\pi$
$503$	23.3244			1.03998			0.519992	+	0.854171i	$0.325935\pi$
$504$	2.25715	−	7.60955i	0.100542	−	0.338956i
$505$	−9.17697			−0.408370
$506$	1.62713			0.0723346
$507$	−11.7761	+	20.8194i	−0.522996	+	0.924623i
$508$	10.0972			0.447990
$509$	−3.67052	−	6.35753i	−0.162693	−	0.281792i	0.773141	−	0.634235i	$-0.218685\pi$
$509$	−3.67052	−	6.35753i	−0.162693	−	0.281792i	−0.935834	+	0.352442i	$0.885351\pi$
$510$	−9.42936	+	0.0832980i	−0.417539	+	0.00368850i
$511$	−9.69252	−	10.5900i	−0.428772	−	0.468475i
$512$	−1.00000			−0.0441942
$513$	−10.2387	+	18.8717i	−0.452048	+	0.833207i
$514$	1.53715	+	2.66242i	0.0678007	+	0.117434i
$515$	9.81248	−	16.9957i	0.432390	−	0.748921i
$516$	−0.308014	+	0.544550i	−0.0135596	+	0.0239725i
$517$	−0.248617	+	0.430618i	−0.0109342	+	0.0189386i
$518$	−7.09371	+	22.4523i	−0.311680	+	0.986497i
$519$	3.45459	+	5.86329i	0.151640	+	0.257370i
$520$	−5.17781			−0.227062
$521$	2.73136	+	4.73085i	0.119663	+	0.207262i	0.919634	−	0.392776i	$-0.128485\pi$
$521$	2.73136	+	4.73085i	0.119663	+	0.207262i	−0.799971	+	0.600038i	$0.795152\pi$
$522$	−22.0598	+	0.389778i	−0.965530	+	0.0170601i
$523$	−17.7135	+	30.6806i	−0.774556	+	1.34157i	0.160488	+	0.987038i	$0.448693\pi$
$523$	−17.7135	+	30.6806i	−0.774556	+	1.34157i	−0.935044	+	0.354532i	$0.884640\pi$
$524$	2.74578	+	4.75582i	0.119950	+	0.207759i
$525$	4.46562	−	1.02871i	0.194896	−	0.0448964i
$526$	−8.64009	+	14.9651i	−0.376726	+	0.652509i
$527$	5.96469	+	10.3311i	0.259826	+	0.450032i
$528$	0.331133	−	0.00292520i	0.0144107	−	0.000127303i
$529$	−24.7156	+	42.8087i	−1.07459	+	1.86125i
$530$	−3.12346	+	5.40999i	−0.135674	+	0.234995i
$531$	−11.6554	+	21.0376i	−0.505802	+	0.912953i
$532$	−3.29349	+	10.4242i	−0.142791	+	0.451947i
$533$	−18.9463	−	32.8159i	−0.820654	−	1.42141i
$534$	−29.2053	+	0.257997i	−1.26384	+	0.0111646i
$535$	−1.98134			−0.0856609
$536$	−5.95735			−0.257318
$537$	−13.0562	+	23.0825i	−0.563416	+	0.996082i
$538$	4.35721	+	7.54691i	0.187853	+	0.325370i
$539$	−0.118211	+	1.33308i	−0.00509169	+	0.0574198i
$540$	2.71640	+	4.42958i	0.116895	+	0.190619i
$541$	11.7539	−	20.3584i	0.505340	−	0.875275i	−0.494641	−	0.869098i	$-0.664700\pi$
$541$	11.7539	−	20.3584i	0.505340	−	0.875275i	0.999981	−	0.00617730i	$-0.00196631\pi$
$542$	3.71843	−	6.44051i	0.159720	−	0.276644i
$543$	2.13531	+	3.62415i	0.0916349	+	0.155527i
$544$	−2.72213	−	4.71486i	−0.116710	−	0.202148i
$545$	4.35266	−	7.53902i	0.186447	−	0.322936i
$546$	23.1221	−	5.32644i	0.989536	−	0.227951i
$547$	−0.992007	−	1.71821i	−0.0424152	−	0.0734652i	0.844038	−	0.536283i	$-0.180172\pi$
$547$	−0.992007	−	1.71821i	−0.0424152	−	0.0734652i	−0.886454	+	0.462817i	$0.846839\pi$
$548$	6.02980	−	10.4439i	0.257580	−	0.446142i
$549$	−4.17109	+	7.52864i	−0.178018	+	0.321315i
$550$	0.0955935	+	0.165573i	0.00407612	+	0.00706005i
$551$	30.3881			1.29458
$552$	−7.25739	+	12.8306i	−0.308895	+	0.546106i
$553$	7.64178	−	1.68942i	0.324962	−	0.0718416i
$554$	−3.78667	+	6.55870i	−0.160880	+	0.278652i
$555$	−7.82495	−	13.2809i	−0.332151	−	0.563742i
$556$	−7.21354	+	12.4942i	−0.305922	+	0.529873i
$557$	−19.8048	−	34.3029i	−0.839155	−	1.45346i	−0.890602	−	0.454784i	$-0.849716\pi$
$557$	−19.8048	−	34.3029i	−0.839155	−	1.45346i	0.0514464	−	0.998676i	$-0.483617\pi$
$558$	3.18569	−	5.75005i	0.134861	−	0.243419i
$559$	−1.87025			−0.0791032
$560$	1.78630	+	1.95170i	0.0754848	+	0.0824746i
$561$	0.915177	+	1.55328i	0.0386388	+	0.0655796i
$562$	−0.170693	−	0.295650i	−0.00720027	−	0.0124712i
$563$	−31.4651			−1.32610			−0.663048	−	0.748577i	$-0.730737\pi$
$563$	−31.4651			−1.32610			−0.663048	+	0.748577i	$0.730737\pi$
$564$	−2.28671	−	3.88112i	−0.0962880	−	0.163425i
$565$	15.2967			0.643539
$566$	−20.4280			−0.858653
$567$	−16.6872	−	16.9864i	−0.700795	−	0.713363i
$568$	9.49986			0.398605
$569$	−39.0005			−1.63499			−0.817493	−	0.575938i	$-0.804637\pi$
$569$	−39.0005			−1.63499			−0.817493	+	0.575938i	$0.804637\pi$
$570$	−3.63299	−	6.16608i	−0.152169	−	0.258269i
$571$	0.00538800			0.000225481			0.000112740	−	1.00000i	$-0.499964\pi$
$571$	0.00538800			0.000225481			0.000112740		1.00000i	$0.499964\pi$
$572$	0.494965	+	0.857305i	0.0206955	+	0.0358457i
$573$	19.5794	+	33.2312i	0.817943	+	1.38825i
$574$	−5.83322	+	18.4627i	−0.243474	+	0.770618i
$575$	−8.51066			−0.354919
$576$	−1.45387	+	2.62417i	−0.0605778	+	0.109340i
$577$	3.27457	+	5.67172i	0.136322	+	0.236117i	0.926102	−	0.377274i	$-0.123138\pi$
$577$	3.27457	+	5.67172i	0.136322	+	0.236117i	−0.789780	+	0.613391i	$0.789805\pi$
$578$	6.31995	−	10.9465i	0.262875	−	0.455313i
$579$	15.7504	+	26.7323i	0.654565	+	1.11096i
$580$	3.67720	−	6.36910i	0.152688	−	0.264463i
$581$	5.67031	+	6.19537i	0.235244	+	0.257027i
$582$	−12.3951	+	21.9137i	−0.513793	+	0.908352i
$583$	1.19433			0.0494641
$584$	2.71302	+	4.69909i	0.112266	+	0.194450i
$585$	−7.52785	+	13.5875i	−0.311238	+	0.561772i
$586$	3.99479	−	6.91917i	0.165023	−	0.285828i
$587$	−11.9758	−	20.7427i	−0.494295	−	0.856144i	0.505683	−	0.862719i	$-0.331240\pi$
$587$	−11.9758	−	20.7427i	−0.494295	−	0.856144i	−0.999978	+	0.00657508i	$0.997907\pi$
$588$	−9.98464	−	6.87800i	−0.411760	−	0.283644i
$589$	−4.52694	+	7.84090i	−0.186529	+	0.323079i
$590$	−4.00842	−	6.94279i	−0.165024	−	0.285830i
$591$	12.0742	+	20.4930i	0.496668	+	0.842968i
$592$	4.44983	−	7.70732i	0.182887	−	0.316769i
$593$	18.9156	−	32.7627i	0.776769	−	1.34540i	−0.157026	−	0.987594i	$-0.550191\pi$
$593$	18.9156	−	32.7627i	0.776769	−	1.34540i	0.933795	−	0.357809i	$-0.116476\pi$
$594$	0.473747	−	0.873202i	0.0194381	−	0.0358279i
$595$	−4.33949	+	13.7349i	−0.177902	+	0.563077i
$596$	−3.07958	−	5.33398i	−0.126144	−	0.218488i
$597$	5.49894	−	9.72177i	0.225057	−	0.397886i
$598$	−44.0666			−1.80202
$599$	−35.9125			−1.46734			−0.733672	−	0.679504i	$-0.762195\pi$
$599$	−35.9125			−1.46734			−0.733672	+	0.679504i	$0.762195\pi$
$600$	−1.73198	+	0.0153002i	−0.0707079	+	0.000624627i
$601$	23.6055	+	40.8858i	0.962887	+	1.66777i	0.715189	+	0.698931i	$0.246341\pi$
$601$	23.6055	+	40.8858i	0.962887	+	1.66777i	0.247697	+	0.968837i	$0.420326\pi$
$602$	0.645219	+	0.704965i	0.0262972	+	0.0287322i
$603$	−8.66119	+	15.6331i	−0.352711	+	0.636629i
$604$	−9.53198	+	16.5099i	−0.387851	+	0.671778i
$605$	−5.48172	+	9.49462i	−0.222864	+	0.386011i
$606$	−15.8944	+	0.140409i	−0.645664	+	0.00570374i
$607$	0.514058	+	0.890374i	0.0208650	+	0.0361392i	0.876269	−	0.481822i	$-0.160025\pi$
$607$	0.514058	+	0.890374i	0.0208650	+	0.0361392i	−0.855404	+	0.517961i	$0.826691\pi$
$608$	2.06598	−	3.57838i	0.0837865	−	0.145122i
$609$	−9.86906	+	32.2248i	−0.399915	+	1.30581i
$610$	−1.43448	−	2.48459i	−0.0580804	−	0.100598i
$611$	6.73317	−	11.6622i	0.272395	−	0.471802i
$612$	−16.3302	+	0.288542i	−0.660110	+	0.0116636i
$613$	−6.85982	−	11.8815i	−0.277065	−	0.479891i	0.693589	−	0.720371i	$-0.256029\pi$
$613$	−6.85982	−	11.8815i	−0.277065	−	0.479891i	−0.970654	+	0.240480i	$0.922695\pi$
$614$	21.5270			0.868760
$615$	−6.43452	−	10.9210i	−0.259465	−	0.440376i
$616$	0.152391	−	0.482332i	0.00614001	−	0.0194337i
$617$	−12.5539	+	21.7439i	−0.505399	+	0.875377i	0.494581	+	0.869131i	$0.335321\pi$
$617$	−12.5539	+	21.7439i	−0.505399	+	0.875377i	−0.999980	+	0.00624554i	$0.998012\pi$
$618$	16.7350	−	29.5864i	0.673181	−	1.19014i
$619$	16.7647	−	29.0373i	0.673830	−	1.16711i	−0.302979	−	0.952997i	$-0.597981\pi$
$619$	16.7647	−	29.0373i	0.673830	−	1.16711i	0.976809	−	0.214111i	$-0.0686855\pi$
$620$	1.09559	+	1.89762i	0.0440001	+	0.0762104i
$621$	23.1184	+	37.6986i	0.927709	+	1.51279i
$622$	−6.04973			−0.242572
$623$	−13.4406	+	42.5409i	−0.538487	+	1.70436i
$624$	−8.96788	+	0.0792214i	−0.359003	+	0.00317139i
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$	24.8404			0.992823
$627$	−0.673645	+	1.19096i	−0.0269028	+	0.0475624i
$628$	15.0459			0.600395
$629$	48.4520			1.93191
$630$	7.71864	−	1.85002i	0.307518	−	0.0737067i
$631$	−14.3306			−0.570491			−0.285245	−	0.958455i	$-0.592075\pi$
$631$	−14.3306			−0.570491			−0.285245	+	0.958455i	$0.592075\pi$
$632$	−2.95806			−0.117665
$633$	16.9901	−	0.150089i	0.675297	−	0.00596551i
$634$	−16.5528			−0.657397
$635$	5.04859	+	8.74442i	0.200347	+	0.347012i
$636$	−5.32700	+	9.41780i	−0.211229	+	0.373440i
$637$	3.20143	−	36.1030i	0.126845	−	1.43045i
$638$	−1.40607			−0.0556667
$639$	13.8115	−	24.9293i	0.546376	−	0.986186i
$640$	−0.500000	−	0.866025i	−0.0197642	−	0.0342327i
$641$	−12.5946	+	21.8145i	−0.497456	+	0.861619i	−0.999996	−	0.00293483i	$-0.999066\pi$
$641$	−12.5946	+	21.8145i	−0.497456	+	0.861619i	0.502539	+	0.864554i	$0.332399\pi$
$642$	−3.43165	+	0.0303149i	−0.135437	+	0.00119643i
$643$	−14.2009	+	24.5967i	−0.560028	+	0.969997i	0.437465	+	0.899235i	$0.355876\pi$
$643$	−14.2009	+	24.5967i	−0.560028	+	0.969997i	−0.997493	+	0.0707620i	$0.977457\pi$
$644$	15.2025	+	16.6103i	0.599064	+	0.654537i
$645$	−0.625601	+	0.00552650i	−0.0246330	+	0.000217606i
$646$	22.4954			0.885070
$647$	−0.182267	−	0.315696i	−0.00716566	−	0.0124113i	0.862420	−	0.506193i	$-0.168948\pi$
$647$	−0.182267	−	0.315696i	−0.00716566	−	0.0124113i	−0.869586	+	0.493782i	$0.835614\pi$
$648$	4.77254	+	7.63039i	0.187483	+	0.299750i
$649$	−0.766358	+	1.32737i	−0.0300822	+	0.0521039i
$650$	−2.58891	−	4.48412i	−0.101545	−	0.175881i
$651$	−6.84460	−	7.34702i	−0.268261	−	0.287953i
$652$	−9.50876	+	16.4697i	−0.372392	+	0.645001i
$653$	17.1389	+	29.6855i	0.670698	+	1.16168i	0.977706	+	0.209977i	$0.0673388\pi$
$653$	17.1389	+	29.6855i	0.670698	+	1.16168i	−0.307008	+	0.951707i	$0.599328\pi$
$654$	7.42338	−	13.1241i	0.290277	−	0.513191i
$655$	−2.74578	+	4.75582i	−0.107286	+	0.185825i
$656$	3.65913	−	6.33779i	0.142865	−	0.247449i
$657$	16.2756	−	0.287576i	0.634971	−	0.0112194i
$658$	−6.71878	+	1.48537i	−0.261925	+	0.0579057i
$659$	13.5956	+	23.5482i	0.529609	+	0.917309i	0.999404	+	0.0345334i	$0.0109945\pi$
$659$	13.5956	+	23.5482i	0.529609	+	0.917309i	−0.469795	+	0.882776i	$0.655672\pi$
$660$	0.168100	+	0.285307i	0.00654327	+	0.0111056i
$661$	−2.74763			−0.106871			−0.0534353	−	0.998571i	$-0.517017\pi$
$661$	−2.74763			−0.106871			−0.0534353	+	0.998571i	$0.517017\pi$
$662$	27.5589			1.07111
$663$	−24.7852	−	42.0667i	−0.962579	−	1.63373i
$664$	−1.58717	−	2.74906i	−0.0615941	−	0.106684i
$665$	−10.6744	+	2.35986i	−0.413935	+	0.0915116i
$666$	−13.7559	−	22.8825i	−0.533029	−	0.886680i
$667$	31.2954	−	54.2052i	1.21176	−	2.09884i
$668$	−4.30085	+	7.44928i	−0.166405	+	0.288221i
$669$	5.86068	−	10.3613i	0.226587	−	0.400591i
$670$	−2.97867	−	5.15921i	−0.115076	−	0.199318i
$671$	−0.274254	+	0.475022i	−0.0105875	+	0.0183380i
$672$	3.12369	+	3.35299i	0.120499	+	0.129344i
$673$	−0.235989	−	0.408746i	−0.00909672	−	0.0157560i	0.861441	−	0.507857i	$-0.169562\pi$
$673$	−0.235989	−	0.408746i	−0.00909672	−	0.0157560i	−0.870538	+	0.492101i	$0.836229\pi$
$674$	−5.26173	+	9.11358i	−0.202674	+	0.351042i
$675$	−2.47792	+	4.56726i	−0.0953753	+	0.175794i
$676$	−6.90486	−	11.9596i	−0.265572	−	0.459984i
$677$	−30.2327			−1.16194			−0.580969	−	0.813926i	$-0.697326\pi$
$677$	−30.2327			−1.16194			−0.580969	+	0.813926i	$0.697326\pi$
$678$	26.4937	−	0.234043i	1.01748	−	0.00898836i
$679$	25.9648	+	28.3691i	0.996438	+	1.08871i
$680$	2.72213	−	4.71486i	0.104389	−	0.180807i
$681$	11.7264	−	0.103590i	0.449358	−	0.00396958i
$682$	0.209463	−	0.362801i	0.00802076	−	0.0138924i
$683$	13.6495	+	23.6416i	0.522284	+	0.904622i	0.999664	+	0.0259253i	$0.00825320\pi$
$683$	13.6495	+	23.6416i	0.522284	+	0.904622i	−0.477380	+	0.878697i	$0.658413\pi$
$684$	−6.38662	−	10.6240i	−0.244198	−	0.406217i
$685$	12.0596			0.460774
$686$	−14.7130	+	11.2485i	−0.561745	+	0.429468i
$687$	13.1151	−	23.1867i	0.500373	−	0.884628i
$688$	−0.180602	−	0.312813i	−0.00688541	−	0.0119259i
$689$	−32.3453			−1.23226
$690$	−14.7403	+	0.130215i	−0.561154	+	0.00495718i
$691$	−32.2003			−1.22496			−0.612478	−	0.790488i	$-0.709827\pi$
$691$	−32.2003			−1.22496			−0.612478	+	0.790488i	$0.709827\pi$
$692$	−3.92905			−0.149360
$693$	−1.04417	−	1.10115i	−0.0396646	−	0.0418291i
$694$	21.4162			0.812947
$695$	−14.4271			−0.547250
$696$	6.27141	−	11.0874i	0.237717	−	0.420268i
$697$	39.8424			1.50914
$698$	9.67929	+	16.7650i	0.366366	+	0.634565i
$699$	1.56558	−	0.0138302i	0.0592156	−	0.000523105i
$700$	−0.797078	+	2.52283i	−0.0301267	+	0.0953540i
$701$	−10.7282			−0.405198			−0.202599	−	0.979262i	$-0.564939\pi$
$701$	−10.7282			−0.405198			−0.202599	+	0.979262i	$0.564939\pi$
$702$	−12.8302	+	23.6484i	−0.484245	+	0.892552i
$703$	18.3865	+	31.8463i	0.693459	+	1.20111i
$704$	−0.0955935	+	0.165573i	−0.00360282	+	0.00624026i
$705$	2.21779	−	3.92091i	0.0835268	−	0.147670i
$706$	−0.0756056	+	0.130953i	−0.00284546	+	0.00492847i
$707$	−7.31476	+	23.1519i	−0.275100	+	0.870718i
$708$	−7.04875	−	11.9635i	−0.264908	−	0.449615i
$709$	33.4757			1.25721			0.628603	−	0.777726i	$-0.283627\pi$
$709$	33.4757			1.25721			0.628603	+	0.777726i	$0.283627\pi$
$710$	4.74993	+	8.22712i	0.178262	+	0.308758i
$711$	−4.30063	+	7.76246i	−0.161286	+	0.291115i
$712$	8.43118	−	14.6032i	0.315972	−	0.547279i
$713$	9.32422	+	16.1500i	0.349195	+	0.604823i
$714$	−7.30578	+	23.8551i	−0.273412	+	0.892753i
$715$	−0.494965	+	0.857305i	−0.0185106	+	0.0320614i
$716$	−7.65542	−	13.2596i	−0.286096	−	0.495533i
$717$	−35.2523	+	0.311416i	−1.31652	+	0.0116300i
$718$	−4.21049	+	7.29279i	−0.157134	+	0.272164i
$719$	16.0414	−	27.7846i	0.598245	−	1.03619i	−0.394835	−	0.918752i	$-0.629198\pi$
$719$	16.0414	−	27.7846i	0.598245	−	1.03619i	0.993080	−	0.117439i	$-0.0374683\pi$
$720$	−2.99953	+	0.0529993i	−0.111786	+	0.00197517i
$721$	−35.0560	−	38.3021i	−1.30555	−	1.42645i
$722$	−0.963472	−	1.66878i	−0.0358567	−	0.0621056i
$723$	28.4874	−	0.251655i	1.05946	−	0.00935915i
$724$	−2.42858			−0.0902575
$725$	7.35441			0.273136
$726$	−9.34898	+	16.5284i	−0.346973	+	0.613426i
$727$	−1.81612	−	3.14561i	−0.0673562	−	0.116664i	0.830381	−	0.557197i	$-0.188123\pi$
$727$	−1.81612	−	3.14561i	−0.0673562	−	0.116664i	−0.897737	+	0.440532i	$0.854790\pi$
$728$	−4.12712	+	13.0627i	−0.152961	+	0.484137i
$729$	26.9621	−	1.43039i	0.998596	−	0.0529772i
$730$	−2.71302	+	4.69909i	−0.100413	+	0.173921i
$731$	0.983246	−	1.70303i	0.0363667	−	0.0629889i
$732$	−2.52251	−	4.28132i	−0.0932347	−	0.158242i
$733$	−21.5844	−	37.3853i	−0.797239	−	1.38086i	−0.921408	−	0.388597i	$-0.872960\pi$
$733$	−21.5844	−	37.3853i	−0.797239	−	1.38086i	0.124169	−	0.992261i	$-0.460374\pi$
$734$	7.27037	−	12.5926i	0.268354	−	0.464803i
$735$	0.964199	−	12.0860i	0.0355650	−	0.445797i
$736$	−4.25533	−	7.37044i	−0.156853	−	0.271678i
$737$	−0.569484	+	0.986375i	−0.0209772	+	0.0363336i
$738$	−11.3116	−	18.8165i	−0.416384	−	0.692644i
$739$	−14.2568	−	24.6935i	−0.524445	−	0.908365i	−0.999595	−	0.0284605i	$-0.990940\pi$
$739$	−14.2568	−	24.6935i	−0.524445	−	0.908365i	0.475150	−	0.879905i	$-0.342394\pi$
$740$	8.89965			0.327158
$741$	18.2440	−	32.2541i	0.670209	−	1.18489i
$742$	11.1588	+	12.1921i	0.409654	+	0.447587i
$743$	8.86243	−	15.3502i	0.325131	−	0.563144i	−0.656408	−	0.754406i	$-0.727925\pi$
$743$	8.86243	−	15.3502i	0.325131	−	0.563144i	0.981539	+	0.191263i	$0.0612582\pi$
$744$	1.92658	+	3.26989i	0.0706320	+	0.119880i
$745$	3.07958	−	5.33398i	0.112827	−	0.195422i
$746$	8.81157	+	15.2621i	0.322614	+	0.558785i
$747$	−9.52153	+	0.168238i	−0.348374	+	0.00615550i
$748$	−1.04087			−0.0380580
$749$	−1.57928	+	4.99859i	−0.0577058	+	0.182645i
$750$	−0.879242	−	1.49229i	−0.0321054	−	0.0544908i
$751$	16.3113	+	28.2519i	0.595206	+	1.03093i	0.993518	+	0.113677i	$0.0362629\pi$
$751$	16.3113	+	28.2519i	0.595206	+	1.03093i	−0.398312	+	0.917250i	$0.630404\pi$
$752$	2.60078			0.0948406
$753$	−12.1923	−	20.6933i	−0.444312	−	0.754107i
$754$	38.0797			1.38678
$755$	−19.0640			−0.693809
$756$	13.3402	−	3.32231i	0.485180	−	0.120831i
$757$	−31.1176			−1.13099			−0.565493	−	0.824753i	$-0.691314\pi$
$757$	−31.1176			−1.13099			−0.565493	+	0.824753i	$0.691314\pi$
$758$	−18.9287			−0.687521
$759$	1.43064	+	2.42815i	0.0519289	+	0.0881362i
$760$	4.13196			0.149882
$761$	−4.80261	−	8.31836i	−0.174094	−	0.301540i	0.765753	−	0.643135i	$-0.222366\pi$
$761$	−4.80261	−	8.31836i	−0.174094	−	0.301540i	−0.939848	+	0.341594i	$0.889033\pi$
$762$	8.87787	+	15.0679i	0.321611	+	0.545854i
$763$	−15.5503	−	16.9902i	−0.562957	−	0.615087i
$764$	−22.2685			−0.805648
$765$	−8.41499	−	13.9981i	−0.304245	−	0.506103i
$766$	10.7236	+	18.5738i	0.387459	+	0.671099i
$767$	20.7549	−	35.9485i	0.749414	−	1.29802i
$768$	−0.879242	−	1.49229i	−0.0317269	−	0.0538484i
$769$	21.5088	−	37.2544i	0.775629	−	1.34343i	−0.158812	−	0.987309i	$-0.550766\pi$
$769$	21.5088	−	37.2544i	0.775629	−	1.34343i	0.934440	−	0.356119i	$-0.115900\pi$
$770$	0.493907	−	0.109192i	0.0177992	−	0.00393500i
$771$	−2.62158	+	4.63478i	−0.0944139	+	0.166918i
$772$	−17.9136			−0.644725
$773$	17.0080	+	29.4588i	0.611737	+	1.05956i	0.990948	+	0.134249i	$0.0428622\pi$
$773$	17.0080	+	29.4588i	0.611737	+	1.05956i	−0.379211	+	0.925310i	$0.623804\pi$
$774$	−1.08345	+	0.0191436i	−0.0389437	+	0.000688103i
$775$	−1.09559	+	1.89762i	−0.0393549	+	0.0681647i
$776$	−7.26779	−	12.5882i	−0.260898	−	0.451889i
$777$	−39.7425	+	9.15512i	−1.42575	+	0.328438i
$778$	6.45188	−	11.1750i	0.231311	−	0.400643i
$779$	15.1193	+	26.1875i	0.541707	+	0.938264i
$780$	−4.55255	−	7.72680i	−0.163007	−	0.276664i
$781$	0.908125	−	1.57292i	0.0324953	−	0.0562835i
$782$	23.1671	−	40.1266i	0.828453	−	1.43492i
$783$	−19.9775	−	32.5769i	−0.713939	−	1.16420i
$784$	6.34763	−	2.95086i	0.226701	−	0.105388i
$785$	7.52293	+	13.0301i	0.268505	+	0.465064i
$786$	−4.68287	+	8.27901i	−0.167032	+	0.295303i
$787$	37.3421			1.33110			0.665551	−	0.746353i	$-0.268197\pi$
$787$	37.3421			1.33110			0.665551	+	0.746353i	$0.268197\pi$
$788$	−13.7326			−0.489202
$789$	−29.9290	+	0.264390i	−1.06550	+	0.00941253i
$790$	−1.47903	−	2.56176i	−0.0526216	−	0.0911433i
$791$	12.1927	−	38.5911i	0.433522	−	1.37214i
$792$	0.295511	+	0.491575i	0.0105005	+	0.0174673i
$793$	7.42747	−	12.8648i	0.263757	−	0.456841i
$794$	−10.2010	+	17.6686i	−0.362019	+	0.627035i
$795$	−10.8196	+	0.0955789i	−0.383730	+	0.00338983i
$796$	3.22427	+	5.58461i	0.114281	+	0.197941i
$797$	16.6036	−	28.7583i	0.588130	−	1.01867i	−0.406347	−	0.913719i	$-0.633198\pi$
$797$	16.6036	−	28.7583i	0.588130	−	1.01867i	0.994477	−	0.104952i	$-0.0334689\pi$
$798$	−18.4517	+	4.25056i	−0.653185	+	0.150468i
$799$	7.07965	+	12.2623i	0.250460	+	0.433809i
$800$	0.500000	−	0.866025i	0.0176777	−	0.0306186i
$801$	−26.0636	−	43.3560i	−0.920910	−	1.53191i
$802$	7.98902	+	13.8374i	0.282102	+	0.488615i
$803$	1.03739			0.0366087
$804$	−5.23795	−	8.89010i	−0.184728	−	0.313530i
$805$	−6.78365	+	21.4709i	−0.239092	+	0.756751i
$806$	−5.67278	+	9.82554i	−0.199815	+	0.346090i
$807$	−7.43114	+	13.1378i	−0.261589	+	0.462472i
$808$	4.58848	−	7.94749i	0.161422	−	0.279592i
$809$	26.8729	+	46.5453i	0.944803	+	1.63645i	0.756146	+	0.654403i	$0.227080\pi$
$809$	26.8729	+	46.5453i	0.944803	+	1.63645i	0.188657	+	0.982043i	$0.439587\pi$
$810$	−4.22184	+	7.94834i	−0.148340	+	0.279276i
$811$	30.9069			1.08529			0.542644	−	0.839963i	$-0.317423\pi$
$811$	30.9069			1.08529			0.542644	+	0.839963i	$0.317423\pi$
$812$	−13.1371	−	14.3536i	−0.461023	−	0.503713i
$813$	12.8805	−	0.113785i	0.451739	−	0.00399062i
$814$	−0.850749	−	1.47354i	−0.0298187	−	0.0516476i
$815$	−19.0175			−0.666155
$816$	4.64254	−	8.20771i	0.162521	−	0.287327i
$817$	1.49248			0.0522154
$818$	−25.1983			−0.881037
$819$	28.2786	+	29.8217i	0.988133	+	1.04206i
$820$	7.31825			0.255564
$821$	−12.0846			−0.421754			−0.210877	−	0.977513i	$-0.567632\pi$
$821$	−12.0846			−0.421754			−0.210877	+	0.977513i	$0.567632\pi$
$822$	20.8870	−	0.184514i	0.728519	−	0.00643567i
$823$	17.9744			0.626548			0.313274	−	0.949663i	$-0.398574\pi$
$823$	17.9744			0.626548			0.313274	+	0.949663i	$0.398574\pi$
$824$	9.81248	+	16.9957i	0.341834	+	0.592074i
$825$	−0.163033	+	0.288232i	−0.00567608	+	0.0100349i
$826$	−20.7105	+	4.57862i	−0.720610	+	0.159311i
$827$	−11.3191			−0.393603			−0.196802	−	0.980443i	$-0.563055\pi$
$827$	−11.3191			−0.393603			−0.196802	+	0.980443i	$0.563055\pi$
$828$	−25.5280	+	0.451059i	−0.887159	+	0.0156754i
$829$	−15.8922	−	27.5262i	−0.551960	−	0.956023i	−0.998133	−	0.0610761i	$-0.980547\pi$
$829$	−15.8922	−	27.5262i	−0.551960	−	0.956023i	0.446173	−	0.894947i	$-0.352787\pi$
$830$	1.58717	−	2.74906i	0.0550914	−	0.0954212i
$831$	−13.1169	+	0.115873i	−0.455020	+	0.00401960i
$832$	2.58891	−	4.48412i	0.0897541	−	0.155459i
$833$	31.1920	+	21.8956i	1.08074	+	0.758638i
$834$	−24.9875	+	0.220737i	−0.865245	+	0.00764349i
$835$	−8.60169			−0.297674
$836$	−0.394988	−	0.684140i	−0.0136610	−	0.0236615i
$837$	11.3817	−	0.301699i	0.393411	−	0.0104282i
$838$	−6.33650	+	10.9751i	−0.218891	+	0.379130i
$839$	−7.26833	−	12.5891i	−0.250931	−	0.434624i	0.712852	−	0.701315i	$-0.247403\pi$
$839$	−7.26833	−	12.5891i	−0.250931	−	0.434624i	−0.963782	+	0.266690i	$0.914070\pi$
$840$	−1.34193	+	4.38169i	−0.0463008	+	0.151183i
$841$	−12.5436	+	21.7262i	−0.432539	+	0.749180i
$842$	−2.09991	−	3.63715i	−0.0723676	−	0.125344i
$843$	0.291115	−	0.514672i	0.0100265	−	0.0177263i
$844$	−4.90482	+	8.49539i	−0.168831	+	0.292423i
$845$	6.90486	−	11.9596i	0.237534	−	0.411422i
$846$	3.78118	−	6.82488i	0.130000	−	0.234644i
$847$	19.5840	+	21.3974i	0.672913	+	0.735224i
$848$	−3.12346	−	5.40999i	−0.107260	−	0.185780i
$849$	−17.9612	−	30.4845i	−0.616425	−	1.04623i
$850$	5.44425			0.186736
$851$	75.7419			2.59640
$852$	8.35268	+	14.1766i	0.286158	+	0.485681i
$853$	3.35090	+	5.80393i	0.114733	+	0.198723i	0.917673	−	0.397337i	$-0.130066\pi$
$853$	3.35090	+	5.80393i	0.114733	+	0.198723i	−0.802940	+	0.596060i	$0.796732\pi$
$854$	−7.41160	+	1.63854i	−0.253620	+	0.0560695i
$855$	6.00731	−	10.8430i	0.205446	−	0.370821i
$856$	0.990672	−	1.71589i	0.0338605	−	0.0586480i
$857$	−0.945523	+	1.63769i	−0.0322985	+	0.0559426i	−0.881723	−	0.471768i	$-0.843616\pi$
$857$	−0.945523	+	1.63769i	−0.0322985	+	0.0559426i	0.849424	+	0.527710i	$0.176949\pi$
$858$	−0.844154	+	1.49241i	−0.0288190	+	0.0509501i
$859$	4.50007	+	7.79436i	0.153541	+	0.265940i	0.932527	−	0.361101i	$-0.117599\pi$
$859$	4.50007	+	7.79436i	0.153541	+	0.265940i	−0.778986	+	0.627041i	$0.784266\pi$
$860$	0.180602	−	0.312813i	0.00615849	−	0.0106668i
$861$	−32.6805	+	7.52832i	−1.11375	+	0.256565i
$862$	−5.75441	−	9.96694i	−0.195996	−	0.339475i
$863$	−0.483202	+	0.836930i	−0.0164484	+	0.0284894i	−0.874132	−	0.485688i	$-0.838569\pi$
$863$	−0.483202	+	0.836930i	−0.0164484	+	0.0284894i	0.857684	+	0.514177i	$0.171903\pi$
$864$	−5.19433	+	0.137687i	−0.176715	+	0.00468422i
$865$	−1.96453	−	3.40266i	−0.0667959	−	0.115694i
$866$	8.34590			0.283605
$867$	21.8921	−	0.193393i	0.743495	−	0.00656796i
$868$	5.66065	−	1.25144i	0.192135	−	0.0424767i
$869$	−0.282772	+	0.489775i	−0.00959237	+	0.0166145i
$870$	12.7377	−	0.112524i	0.431849	−	0.00381491i
$871$	15.4230	−	26.7134i	0.522589	−	0.905150i
$872$	4.35266	+	7.53902i	0.147400	+	0.255304i
$873$	−43.5999	+	0.770375i	−1.47563	+	0.0260732i
$874$	35.1657			1.18950
$875$	−2.58337	+	0.571125i	−0.0873339	+	0.0193076i
$876$	−4.62701	+	8.18026i	−0.156332	+	0.276385i
$877$	−15.2117	−	26.3474i	−0.513662	−	0.889689i	−0.999874	−	0.0158484i	$-0.994955\pi$
$877$	−15.2117	−	26.3474i	−0.513662	−	0.889689i	0.486212	−	0.873841i	$-0.338378\pi$
$878$	31.6786			1.06910
$879$	13.8378	−	0.122242i	0.466738	−	0.00412312i
$880$	−0.191187			−0.00644491
$881$	17.3361			0.584067			0.292033	−	0.956408i	$-0.405668\pi$
$881$	17.3361			0.584067			0.292033	+	0.956408i	$0.405668\pi$
$882$	1.48506	−	20.9474i	0.0500046	−	0.705336i
$883$	26.4145			0.888920			0.444460	−	0.895799i	$-0.353396\pi$
$883$	26.4145			0.888920			0.444460	+	0.895799i	$0.353396\pi$
$884$	28.1893			0.948109
$885$	6.83629	−	12.0861i	0.229800	−	0.406271i
$886$	−33.7313			−1.13322
$887$	9.63231	+	16.6836i	0.323421	+	0.560182i	0.981192	−	0.193037i	$-0.0618336\pi$
$887$	9.63231	+	16.6836i	0.323421	+	0.560182i	−0.657770	+	0.753219i	$0.728500\pi$
$888$	15.4140	−	0.136166i	0.517262	−	0.00456944i
$889$	26.0848	−	5.76676i	0.874856	−	0.193411i
$890$	16.8624			0.565228
$891$	1.71961	−	0.0607872i	0.0576091	−	0.00203645i
$892$	3.43638	+	5.95198i	0.115058	+	0.199287i
$893$	−5.37315	+	9.30656i	−0.179806	+	0.311432i
$894$	5.25216	−	9.28549i	0.175659	−	0.310553i
$895$	7.65542	−	13.2596i	0.255892	−	0.443218i
$896$	−2.58337	+	0.571125i	−0.0863044	+	0.0190799i
$897$	−38.7452	−	65.7602i	−1.29366	−	2.19567i
$898$	38.8454			1.29629
$899$	−8.05744	−	13.9559i	−0.268731	−	0.465455i
$900$	−1.54566	−	2.57117i	−0.0515222	−	0.0857057i
$901$	17.0049	−	29.4533i	0.566515	−	0.981233i
$902$	−0.699578	−	1.21170i	−0.0232934	−	0.0403453i
$903$	−0.484710	+	1.58269i	−0.0161301	+	0.0526686i
$904$	−7.64837	+	13.2474i	−0.254381	+	0.440601i
$905$	−1.21429	−	2.10321i	−0.0403644	−	0.0699132i
$906$	−33.0185	+	0.291682i	−1.09697	+	0.00969049i
$907$	−13.2708	+	22.9856i	−0.440648	+	0.763225i	−0.997738	−	0.0672274i	$-0.978585\pi$
$907$	−13.2708	+	22.9856i	−0.440648	+	0.763225i	0.557090	+	0.830452i	$0.311918\pi$
$908$	−3.38526	+	5.86344i	−0.112344	+	0.194585i
$909$	−14.1845	−	23.5956i	−0.470471	−	0.782615i
$910$	−13.3762	+	2.95718i	−0.443417	+	0.0980295i
$911$	−6.06577	−	10.5062i	−0.200968	−	0.348087i	0.747873	−	0.663842i	$-0.231075\pi$
$911$	−6.06577	−	10.5062i	−0.200968	−	0.348087i	−0.948841	+	0.315755i	$0.897742\pi$
$912$	7.15648	−	0.0632196i	0.236975	−	0.00209341i
$913$	−0.606892			−0.0200852
$914$	16.8141			0.556160
$915$	2.44648	−	4.32522i	0.0808782	−	0.142987i
$916$	7.68998	+	13.3194i	0.254084	+	0.440087i
$917$	9.80953	+	10.7179i	0.323939	+	0.353936i
$918$	−14.7888	−	24.1157i	−0.488103	−	0.795938i
$919$	−12.6371	+	21.8880i	−0.416858	+	0.722019i	−0.995622	−	0.0934763i	$-0.970202\pi$
$919$	−12.6371	+	21.8880i	−0.416858	+	0.722019i	0.578764	+	0.815495i	$0.303535\pi$
$920$	4.25533	−	7.37044i	0.140294	−	0.242996i
$921$	18.9275	+	32.1246i	0.623681	+	1.05854i
$922$	−18.5721	−	32.1678i	−0.611638	−	1.05939i
$923$	−24.5942	+	42.5985i	−0.809530	+	1.40215i
$924$	0.853769	−	0.196675i	0.0280869	−	0.00647013i
$925$	4.44983	+	7.70732i	0.146309	+	0.253415i
$926$	4.73848	−	8.20729i	0.155716	−	0.269708i
$927$	58.8657	−	1.04011i	1.93340	−	0.0341617i
$928$	3.67720	+	6.36910i	0.120710	+	0.209076i
$929$	44.5198			1.46065			0.730323	−	0.683102i	$-0.239370\pi$
$929$	44.5198			1.46065			0.730323	+	0.683102i	$0.239370\pi$
$930$	−1.86852	+	3.30342i	−0.0612710	+	0.108323i
$931$	−2.55478	+	28.8106i	−0.0837295	+	0.944231i
$932$	−0.451961	+	0.782819i	−0.0148045	+	0.0256421i
$933$	−5.31917	−	9.02795i	−0.174142	−	0.295562i
$934$	8.72166	−	15.1064i	0.285382	−	0.494295i
$935$	−0.520435	−	0.901421i	−0.0170201	−	0.0294796i
$936$	−8.00316	−	13.3130i	−0.261591	−	0.435150i
$937$	−6.11216			−0.199675			−0.0998377	−	0.995004i	$-0.531832\pi$
$937$	−6.11216			−0.199675			−0.0998377	+	0.995004i	$0.531832\pi$
$938$	−15.3901	+	3.40239i	−0.502503	+	0.111092i
$939$	21.8407	+	37.0691i	0.712745	+	1.20971i
$940$	1.30039	+	2.25234i	0.0424140	+	0.0734632i
$941$	−46.0028			−1.49965			−0.749824	−	0.661638i	$-0.769862\pi$
$941$	−46.0028			−1.49965			−0.749824	+	0.661638i	$0.769862\pi$
$942$	13.2289	+	22.4528i	0.431022	+	0.731552i
$943$	62.2831			2.02822
$944$	8.01684			0.260926
$945$	9.54733	+	9.89184i	0.310575	+	0.321782i
$946$	−0.0690577			−0.00224526
$947$	−38.8887			−1.26371			−0.631857	−	0.775085i	$-0.717707\pi$
$947$	−38.8887			−1.26371			−0.631857	+	0.775085i	$0.717707\pi$
$948$	−2.60085	−	4.41429i	−0.0844718	−	0.143370i
$949$	−28.0950			−0.912003
$950$	2.06598	+	3.57838i	0.0670292	+	0.116098i
$951$	−14.5539	−	24.7017i	−0.471944	−	0.801006i
$952$	−9.72505	−	10.6256i	−0.315191	−	0.344377i
$953$	−32.5723			−1.05512			−0.527561	−	0.849517i	$-0.676893\pi$
$953$	−32.5723			−1.05512			−0.527561	+	0.849517i	$0.676893\pi$
$954$	−18.7378	+	0.331082i	−0.606659	+	0.0107192i
$955$	−11.1343	−	19.2851i	−0.360297	−	0.624052i
$956$	10.1769	−	17.6269i	0.329143	−	0.570093i
$957$	−1.23627	−	2.09826i	−0.0399630	−	0.0678272i
$958$	−0.469756	+	0.813641i	−0.0151771	+	0.0262876i
$959$	9.61244	−	30.4243i	0.310402	−	0.982452i
$960$	0.852741	−	1.50759i	0.0275221	−	0.0486573i
$961$	−26.1987			−0.845119
$962$	23.0404	+	39.9071i	0.742851	+	1.28666i
$963$	−3.06249	−	5.09437i	−0.0986874	−	0.164164i
$964$	−8.22393	+	14.2443i	−0.264875	+	0.458777i
$965$	−8.95681	−	15.5137i	−0.288330	−	0.499402i
$966$	−11.4207	+	37.2911i	−0.367454	+	1.19982i
$967$	−24.2156	+	41.9426i	−0.778721	+	1.34878i	0.153959	+	0.988077i	$0.450798\pi$
$967$	−24.2156	+	41.9426i	−0.778721	+	1.34878i	−0.932679	+	0.360707i	$0.882536\pi$
$968$	−5.48172	−	9.49462i	−0.176189	−	0.305169i
$969$	19.7789	+	33.5697i	0.635390	+	1.07841i
$970$	7.26779	−	12.5882i	0.233355	−	0.404182i
$971$	−12.7417	+	22.0692i	−0.408899	+	0.708235i	−0.994767	−	0.102172i	$-0.967421\pi$
$971$	−12.7417	+	22.0692i	−0.408899	+	0.708235i	0.585867	+	0.810407i	$0.300754\pi$
$972$	−7.19055	+	13.8310i	−0.230637	+	0.443629i
$973$	−11.4995	+	36.3971i	−0.368657	+	1.16684i
$974$	−12.3343	−	21.3637i	−0.395218	−	0.684537i
$975$	4.41533	−	7.80602i	0.141404	−	0.249993i
$976$	2.86896			0.0918332
$977$	−16.3861			−0.524238			−0.262119	−	0.965036i	$-0.584421\pi$
$977$	−16.3861			−0.524238			−0.262119	+	0.965036i	$0.584421\pi$
$978$	−32.9380	+	0.290971i	−1.05324	+	0.00930424i
$979$	−1.61193	−	2.79195i	−0.0515176	−	0.0892311i
$980$	5.72933	+	4.02178i	0.183017	+	0.128471i
$981$	26.1119	−	0.461376i	0.833688	−	0.0147306i
$982$	−7.85545	+	13.6060i	−0.250678	+	0.434186i
$983$	−1.05589	+	1.82886i	−0.0336777	+	0.0583315i	−0.882373	−	0.470551i	$-0.844055\pi$
$983$	−1.05589	+	1.82886i	−0.0336777	+	0.0583315i	0.848695	+	0.528882i	$0.177389\pi$
$984$	12.6751	−	0.111971i	0.404067	−	0.00356949i
$985$	−6.86628	−	11.8927i	−0.218778	−	0.378934i
$986$	−20.0196	+	34.6750i	−0.637555	+	1.10428i
$987$	−8.12403	−	8.72037i	−0.258591	−	0.277573i
$988$	10.6972	+	18.5282i	0.340325	+	0.589460i
$989$	1.53705	−	2.66224i	0.0488752	−	0.0846543i
$990$	−0.277961	+	0.501707i	−0.00883417	+	0.0159453i
$991$	−28.3509	−	49.1052i	−0.900597	−	1.55988i	−0.826721	−	0.562612i	$-0.809797\pi$
$991$	−28.3509	−	49.1052i	−0.900597	−	1.55988i	−0.0738758	−	0.997267i	$-0.523537\pi$
$992$	−2.19119			−0.0695703
$993$	24.2309	+	41.1259i	0.768946	+	1.30509i
$994$	24.5417	−	5.42561i	0.778415	−	0.172090i
$995$	−3.22427	+	5.58461i	−0.102216	+	0.177044i
$996$	2.70689	−	4.78561i	0.0857711	−	0.151638i
$997$	8.89880	−	15.4132i	0.281828	−	0.488140i	−0.690007	−	0.723803i	$-0.742393\pi$
$997$	8.89880	−	15.4132i	0.281828	−	0.488140i	0.971835	+	0.235662i	$0.0757260\pi$
$998$	11.5312	+	19.9727i	0.365015	+	0.632224i
$999$	22.0527	−	40.6471i	0.697715	−	1.28602i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	630.2.i.i.121.3	✓	16
3.2	odd	2		1890.2.i.i.1171.8		16
7.4	even	3		630.2.l.i.571.4	yes	16
9.2	odd	6		1890.2.l.i.1801.2		16
9.7	even	3		630.2.l.i.331.4	yes	16
21.11	odd	6		1890.2.l.i.361.2		16
63.11	odd	6		1890.2.i.i.991.8		16
63.25	even	3	inner	630.2.i.i.151.3	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
630.2.i.i.121.3	✓	16	1.1	even	1	trivial
630.2.i.i.151.3	yes	16	63.25	even	3	inner
630.2.l.i.331.4	yes	16	9.7	even	3
630.2.l.i.571.4	yes	16	7.4	even	3
1890.2.i.i.991.8		16	63.11	odd	6
1890.2.i.i.1171.8		16	3.2	odd	2
1890.2.l.i.361.2		16	21.11	odd	6
1890.2.l.i.1801.2		16	9.2	odd	6

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.i (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +(-0.879242 - 1.49229i) q^{3} +1.00000 q^{4} +(0.500000 + 0.866025i) q^{5} +(0.879242 + 1.49229i) q^{6} +(2.58337 - 0.571125i) q^{7} -1.00000 q^{8} +(-1.45387 + 2.62417i) q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +(-0.879242 - 1.49229i) q^{3} +1.00000 q^{4} +(0.500000 + 0.866025i) q^{5} +(0.879242 + 1.49229i) q^{6} +(2.58337 - 0.571125i) q^{7} -1.00000 q^{8} +(-1.45387 + 2.62417i) q^{9} +(-0.500000 - 0.866025i) q^{10} +(-0.0955935 + 0.165573i) q^{11} +(-0.879242 - 1.49229i) q^{12} +(2.58891 - 4.48412i) q^{13} +(-2.58337 + 0.571125i) q^{14} +(0.852741 - 1.50759i) q^{15} +1.00000 q^{16} +(2.72213 + 4.71486i) q^{17} +(1.45387 - 2.62417i) q^{18} +(-2.06598 + 3.57838i) q^{19} +(0.500000 + 0.866025i) q^{20} +(-3.12369 - 3.35299i) q^{21} +(0.0955935 - 0.165573i) q^{22} +(4.25533 + 7.37044i) q^{23} +(0.879242 + 1.49229i) q^{24} +(-0.500000 + 0.866025i) q^{25} +(-2.58891 + 4.48412i) q^{26} +(5.19433 - 0.137687i) q^{27} +(2.58337 - 0.571125i) q^{28} +(-3.67720 - 6.36910i) q^{29} +(-0.852741 + 1.50759i) q^{30} +2.19119 q^{31} -1.00000 q^{32} +(0.331133 - 0.00292520i) q^{33} +(-2.72213 - 4.71486i) q^{34} +(1.78630 + 1.95170i) q^{35} +(-1.45387 + 2.62417i) q^{36} +(4.44983 - 7.70732i) q^{37} +(2.06598 - 3.57838i) q^{38} +(-8.96788 + 0.0792214i) q^{39} +(-0.500000 - 0.866025i) q^{40} +(3.65913 - 6.33779i) q^{41} +(3.12369 + 3.35299i) q^{42} +(-0.180602 - 0.312813i) q^{43} +(-0.0955935 + 0.165573i) q^{44} +(-2.99953 + 0.0529993i) q^{45} +(-4.25533 - 7.37044i) q^{46} +2.60078 q^{47} +(-0.879242 - 1.49229i) q^{48} +(6.34763 - 2.95086i) q^{49} +(0.500000 - 0.866025i) q^{50} +(4.64254 - 8.20771i) q^{51} +(2.58891 - 4.48412i) q^{52} +(-3.12346 - 5.40999i) q^{53} +(-5.19433 + 0.137687i) q^{54} -0.191187 q^{55} +(-2.58337 + 0.571125i) q^{56} +(7.15648 - 0.0632196i) q^{57} +(3.67720 + 6.36910i) q^{58} +8.01684 q^{59} +(0.852741 - 1.50759i) q^{60} +2.86896 q^{61} -2.19119 q^{62} +(-2.25715 + 7.60955i) q^{63} +1.00000 q^{64} +5.17781 q^{65} +(-0.331133 + 0.00292520i) q^{66} +5.95735 q^{67} +(2.72213 + 4.71486i) q^{68} +(7.25739 - 12.8306i) q^{69} +(-1.78630 - 1.95170i) q^{70} -9.49986 q^{71} +(1.45387 - 2.62417i) q^{72} +(-2.71302 - 4.69909i) q^{73} +(-4.44983 + 7.70732i) q^{74} +(1.73198 - 0.0153002i) q^{75} +(-2.06598 + 3.57838i) q^{76} +(-0.152391 + 0.482332i) q^{77} +(8.96788 - 0.0792214i) q^{78} +2.95806 q^{79} +(0.500000 + 0.866025i) q^{80} +(-4.77254 - 7.63039i) q^{81} +(-3.65913 + 6.33779i) q^{82} +(1.58717 + 2.74906i) q^{83} +(-3.12369 - 3.35299i) q^{84} +(-2.72213 + 4.71486i) q^{85} +(0.180602 + 0.312813i) q^{86} +(-6.27141 + 11.0874i) q^{87} +(0.0955935 - 0.165573i) q^{88} +(-8.43118 + 14.6032i) q^{89} +(2.99953 - 0.0529993i) q^{90} +(4.12712 - 13.0627i) q^{91} +(4.25533 + 7.37044i) q^{92} +(-1.92658 - 3.26989i) q^{93} -2.60078 q^{94} -4.13196 q^{95} +(0.879242 + 1.49229i) q^{96} +(7.26779 + 12.5882i) q^{97} +(-6.34763 + 2.95086i) q^{98} +(-0.295511 - 0.491575i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 16 q^{2} + 2 q^{3} + 16 q^{4} + 8 q^{5} - 2 q^{6} + 4 q^{7} - 16 q^{8} - 6 q^{9}+O(q^{10}) \) 16 * q - 16 * q^2 + 2 * q^3 + 16 * q^4 + 8 * q^5 - 2 * q^6 + 4 * q^7 - 16 * q^8 - 6 * q^9	\( 16 q - 16 q^{2} + 2 q^{3} + 16 q^{4} + 8 q^{5} - 2 q^{6} + 4 q^{7} - 16 q^{8} - 6 q^{9} - 8 q^{10} + q^{11} + 2 q^{12} + 2 q^{13} - 4 q^{14} + q^{15} + 16 q^{16} + 11 q^{17} + 6 q^{18} - 2 q^{19} + 8 q^{20} - 15 q^{21} - q^{22} + 11 q^{23} - 2 q^{24} - 8 q^{25} - 2 q^{26} - 7 q^{27} + 4 q^{28} + 17 q^{29} - q^{30} + 30 q^{31} - 16 q^{32} + 5 q^{33} - 11 q^{34} - 4 q^{35} - 6 q^{36} - 2 q^{37} + 2 q^{38} - 8 q^{40} + 7 q^{41} + 15 q^{42} - 13 q^{43} + q^{44} + 3 q^{45} - 11 q^{46} + 10 q^{47} + 2 q^{48} - 14 q^{49} + 8 q^{50} - 3 q^{51} + 2 q^{52} + 18 q^{53} + 7 q^{54} + 2 q^{55} - 4 q^{56} - 4 q^{57} - 17 q^{58} - 2 q^{59} + q^{60} + 54 q^{61} - 30 q^{62} + 41 q^{63} + 16 q^{64} + 4 q^{65} - 5 q^{66} + 20 q^{67} + 11 q^{68} - 14 q^{69} + 4 q^{70} - 38 q^{71} + 6 q^{72} - 8 q^{73} + 2 q^{74} - q^{75} - 2 q^{76} - 7 q^{77} + 50 q^{79} + 8 q^{80} - 6 q^{81} - 7 q^{82} + 2 q^{83} - 15 q^{84} - 11 q^{85} + 13 q^{86} - 32 q^{87} - q^{88} - 6 q^{89} - 3 q^{90} + 14 q^{91} + 11 q^{92} - 6 q^{93} - 10 q^{94} - 4 q^{95} - 2 q^{96} + 26 q^{97} + 14 q^{98} - 5 q^{99}+O(q^{100}) \) 16 * q - 16 * q^2 + 2 * q^3 + 16 * q^4 + 8 * q^5 - 2 * q^6 + 4 * q^7 - 16 * q^8 - 6 * q^9 - 8 * q^10 + q^11 + 2 * q^12 + 2 * q^13 - 4 * q^14 + q^15 + 16 * q^16 + 11 * q^17 + 6 * q^18 - 2 * q^19 + 8 * q^20 - 15 * q^21 - q^22 + 11 * q^23 - 2 * q^24 - 8 * q^25 - 2 * q^26 - 7 * q^27 + 4 * q^28 + 17 * q^29 - q^30 + 30 * q^31 - 16 * q^32 + 5 * q^33 - 11 * q^34 - 4 * q^35 - 6 * q^36 - 2 * q^37 + 2 * q^38 - 8 * q^40 + 7 * q^41 + 15 * q^42 - 13 * q^43 + q^44 + 3 * q^45 - 11 * q^46 + 10 * q^47 + 2 * q^48 - 14 * q^49 + 8 * q^50 - 3 * q^51 + 2 * q^52 + 18 * q^53 + 7 * q^54 + 2 * q^55 - 4 * q^56 - 4 * q^57 - 17 * q^58 - 2 * q^59 + q^60 + 54 * q^61 - 30 * q^62 + 41 * q^63 + 16 * q^64 + 4 * q^65 - 5 * q^66 + 20 * q^67 + 11 * q^68 - 14 * q^69 + 4 * q^70 - 38 * q^71 + 6 * q^72 - 8 * q^73 + 2 * q^74 - q^75 - 2 * q^76 - 7 * q^77 + 50 * q^79 + 8 * q^80 - 6 * q^81 - 7 * q^82 + 2 * q^83 - 15 * q^84 - 11 * q^85 + 13 * q^86 - 32 * q^87 - q^88 - 6 * q^89 - 3 * q^90 + 14 * q^91 + 11 * q^92 - 6 * q^93 - 10 * q^94 - 4 * q^95 - 2 * q^96 + 26 * q^97 + 14 * q^98 - 5 * q^99

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