LMFDB - Embedded newform 287.2.e.a.165.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [287,2,Mod(165,287)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(287, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([4, 0]))

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

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

chi := DirichletCharacter("287.165");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 287 = 7 \cdot 41 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	287.e (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:	$2.29170653801$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\sqrt{-3}, \sqrt{5})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} + 2x^{2} + x + 1 $ x^4 - x^3 + 2*x^2 + x + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			165.2
Root			$-0.309017 - 0.535233i$ of defining polynomial
Character	$\chi$	$=$	287.165
Dual form			287.2.e.a.247.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.309017 + 0.535233i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(0.809017 - 1.40126i) q^{4} +(0.500000 + 0.866025i) q^{5} -0.618034 q^{6} +(-2.00000 + 1.73205i) q^{7} +2.23607 q^{8} +(1.00000 + 1.73205i) q^{9} +O(q^{10})$	\(q+(0.309017 + 0.535233i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(0.809017 - 1.40126i) q^{4} +(0.500000 + 0.866025i) q^{5} -0.618034 q^{6} +(-2.00000 + 1.73205i) q^{7} +2.23607 q^{8} +(1.00000 + 1.73205i) q^{9} +(-0.309017 + 0.535233i) q^{10} +(-0.500000 + 0.866025i) q^{11} +(0.809017 + 1.40126i) q^{12} +4.47214 q^{13} +(-1.54508 - 0.535233i) q^{14} -1.00000 q^{15} +(-0.927051 - 1.60570i) q^{16} +(0.118034 - 0.204441i) q^{17} +(-0.618034 + 1.07047i) q^{18} +(3.73607 + 6.47106i) q^{19} +1.61803 q^{20} +(-0.500000 - 2.59808i) q^{21} -0.618034 q^{22} +(-2.35410 - 4.07742i) q^{23} +(-1.11803 + 1.93649i) q^{24} +(2.00000 - 3.46410i) q^{25} +(1.38197 + 2.39364i) q^{26} -5.00000 q^{27} +(0.809017 + 4.20378i) q^{28} -4.47214 q^{29} +(-0.309017 - 0.535233i) q^{30} +(-2.11803 + 3.66854i) q^{31} +(2.80902 - 4.86536i) q^{32} +(-0.500000 - 0.866025i) q^{33} +0.145898 q^{34} +(-2.50000 - 0.866025i) q^{35} +3.23607 q^{36} +(-2.73607 - 4.73901i) q^{37} +(-2.30902 + 3.99933i) q^{38} +(-2.23607 + 3.87298i) q^{39} +(1.11803 + 1.93649i) q^{40} -1.00000 q^{41} +(1.23607 - 1.07047i) q^{42} +2.47214 q^{43} +(0.809017 + 1.40126i) q^{44} +(-1.00000 + 1.73205i) q^{45} +(1.45492 - 2.51999i) q^{46} +(-2.73607 - 4.73901i) q^{47} +1.85410 q^{48} +(1.00000 - 6.92820i) q^{49} +2.47214 q^{50} +(0.118034 + 0.204441i) q^{51} +(3.61803 - 6.26662i) q^{52} +(2.88197 - 4.99171i) q^{53} +(-1.54508 - 2.67617i) q^{54} -1.00000 q^{55} +(-4.47214 + 3.87298i) q^{56} -7.47214 q^{57} +(-1.38197 - 2.39364i) q^{58} +(2.35410 - 4.07742i) q^{59} +(-0.809017 + 1.40126i) q^{60} +(-0.263932 - 0.457144i) q^{61} -2.61803 q^{62} +(-5.00000 - 1.73205i) q^{63} -0.236068 q^{64} +(2.23607 + 3.87298i) q^{65} +(0.309017 - 0.535233i) q^{66} +(5.97214 - 10.3440i) q^{67} +(-0.190983 - 0.330792i) q^{68} +4.70820 q^{69} +(-0.309017 - 1.60570i) q^{70} -5.52786 q^{71} +(2.23607 + 3.87298i) q^{72} +(5.73607 - 9.93516i) q^{73} +(1.69098 - 2.92887i) q^{74} +(2.00000 + 3.46410i) q^{75} +12.0902 q^{76} +(-0.500000 - 2.59808i) q^{77} -2.76393 q^{78} +(0.500000 + 0.866025i) q^{79} +(0.927051 - 1.60570i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(-0.309017 - 0.535233i) q^{82} -10.4721 q^{83} +(-4.04508 - 1.40126i) q^{84} +0.236068 q^{85} +(0.763932 + 1.32317i) q^{86} +(2.23607 - 3.87298i) q^{87} +(-1.11803 + 1.93649i) q^{88} +(4.88197 + 8.45581i) q^{89} -1.23607 q^{90} +(-8.94427 + 7.74597i) q^{91} -7.61803 q^{92} +(-2.11803 - 3.66854i) q^{93} +(1.69098 - 2.92887i) q^{94} +(-3.73607 + 6.47106i) q^{95} +(2.80902 + 4.86536i) q^{96} -0.472136 q^{97} +(4.01722 - 1.60570i) q^{98} -2.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - q^{2} - 2 q^{3} + q^{4} + 2 q^{5} + 2 q^{6} - 8 q^{7} + 4 q^{9}+O(q^{10}) $ 4 * q - q^2 - 2 * q^3 + q^4 + 2 * q^5 + 2 * q^6 - 8 * q^7 + 4 * q^9	$ 4 q - q^{2} - 2 q^{3} + q^{4} + 2 q^{5} + 2 q^{6} - 8 q^{7} + 4 q^{9} + q^{10} - 2 q^{11} + q^{12} + 5 q^{14} - 4 q^{15} + 3 q^{16} - 4 q^{17} + 2 q^{18} + 6 q^{19} + 2 q^{20} - 2 q^{21} + 2 q^{22} + 4 q^{23} + 8 q^{25} + 10 q^{26} - 20 q^{27} + q^{28} + q^{30} - 4 q^{31} + 9 q^{32} - 2 q^{33} + 14 q^{34} - 10 q^{35} + 4 q^{36} - 2 q^{37} - 7 q^{38} - 4 q^{41} - 4 q^{42} - 8 q^{43} + q^{44} - 4 q^{45} + 17 q^{46} - 2 q^{47} - 6 q^{48} + 4 q^{49} - 8 q^{50} - 4 q^{51} + 10 q^{52} + 16 q^{53} + 5 q^{54} - 4 q^{55} - 12 q^{57} - 10 q^{58} - 4 q^{59} - q^{60} - 10 q^{61} - 6 q^{62} - 20 q^{63} + 8 q^{64} - q^{66} + 6 q^{67} - 3 q^{68} - 8 q^{69} + q^{70} - 40 q^{71} + 14 q^{73} + 9 q^{74} + 8 q^{75} + 26 q^{76} - 2 q^{77} - 20 q^{78} + 2 q^{79} - 3 q^{80} - 2 q^{81} + q^{82} - 24 q^{83} - 5 q^{84} - 8 q^{85} + 12 q^{86} + 24 q^{89} + 4 q^{90} - 26 q^{92} - 4 q^{93} + 9 q^{94} - 6 q^{95} + 9 q^{96} + 16 q^{97} - 13 q^{98} - 8 q^{99}+O(q^{100}) $ 4 * q - q^2 - 2 * q^3 + q^4 + 2 * q^5 + 2 * q^6 - 8 * q^7 + 4 * q^9 + q^10 - 2 * q^11 + q^12 + 5 * q^14 - 4 * q^15 + 3 * q^16 - 4 * q^17 + 2 * q^18 + 6 * q^19 + 2 * q^20 - 2 * q^21 + 2 * q^22 + 4 * q^23 + 8 * q^25 + 10 * q^26 - 20 * q^27 + q^28 + q^30 - 4 * q^31 + 9 * q^32 - 2 * q^33 + 14 * q^34 - 10 * q^35 + 4 * q^36 - 2 * q^37 - 7 * q^38 - 4 * q^41 - 4 * q^42 - 8 * q^43 + q^44 - 4 * q^45 + 17 * q^46 - 2 * q^47 - 6 * q^48 + 4 * q^49 - 8 * q^50 - 4 * q^51 + 10 * q^52 + 16 * q^53 + 5 * q^54 - 4 * q^55 - 12 * q^57 - 10 * q^58 - 4 * q^59 - q^60 - 10 * q^61 - 6 * q^62 - 20 * q^63 + 8 * q^64 - q^66 + 6 * q^67 - 3 * q^68 - 8 * q^69 + q^70 - 40 * q^71 + 14 * q^73 + 9 * q^74 + 8 * q^75 + 26 * q^76 - 2 * q^77 - 20 * q^78 + 2 * q^79 - 3 * q^80 - 2 * q^81 + q^82 - 24 * q^83 - 5 * q^84 - 8 * q^85 + 12 * q^86 + 24 * q^89 + 4 * q^90 - 26 * q^92 - 4 * q^93 + 9 * q^94 - 6 * q^95 + 9 * q^96 + 16 * q^97 - 13 * q^98 - 8 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/287\mathbb{Z}\right)^\times$.

$n$	$206$	$211$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$

Coefficient data

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

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

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

$2$	0.309017	+	0.535233i	0.218508	+	0.378467i	0.954352	−	0.298684i	$-0.0965477\pi$
$2$	0.309017	+	0.535233i	0.218508	+	0.378467i	−0.735844	+	0.677151i	$0.763214\pi$
$3$	−0.500000	+	0.866025i	−0.288675	+	0.500000i	−0.973494	−	0.228714i	$-0.926548\pi$
$3$	−0.500000	+	0.866025i	−0.288675	+	0.500000i	0.684819	+	0.728714i	$0.259881\pi$
$4$	0.809017	−	1.40126i	0.404508	−	0.700629i
$5$	0.500000	+	0.866025i	0.223607	+	0.387298i	0.955901	−	0.293691i	$-0.0948835\pi$
$5$	0.500000	+	0.866025i	0.223607	+	0.387298i	−0.732294	+	0.680989i	$0.761550\pi$
$6$	−0.618034			−0.252311
$7$	−2.00000	+	1.73205i	−0.755929	+	0.654654i
$7$	−2.00000	+	1.73205i	−0.755929	+	0.654654i
$8$	2.23607			0.790569
$9$	1.00000	+	1.73205i	0.333333	+	0.577350i
$10$	−0.309017	+	0.535233i	−0.0977198	+	0.169256i
$11$	−0.500000	+	0.866025i	−0.150756	+	0.261116i	−0.931505	−	0.363727i	$-0.881504\pi$
$11$	−0.500000	+	0.866025i	−0.150756	+	0.261116i	0.780750	+	0.624844i	$0.214837\pi$
$12$	0.809017	+	1.40126i	0.233543	+	0.404508i
$13$	4.47214			1.24035			0.620174	−	0.784465i	$-0.287062\pi$
$13$	4.47214			1.24035			0.620174	+	0.784465i	$0.287062\pi$
$14$	−1.54508	−	0.535233i	−0.412941	−	0.143047i
$15$	−1.00000			−0.258199
$16$	−0.927051	−	1.60570i	−0.231763	−	0.401425i
$17$	0.118034	−	0.204441i	0.0286274	−	0.0495842i	−0.851357	−	0.524587i	$-0.824220\pi$
$17$	0.118034	−	0.204441i	0.0286274	−	0.0495842i	0.879984	+	0.475003i	$0.157553\pi$
$18$	−0.618034	+	1.07047i	−0.145672	+	0.252311i
$19$	3.73607	+	6.47106i	0.857113	+	1.48456i	0.874671	+	0.484717i	$0.161077\pi$
$19$	3.73607	+	6.47106i	0.857113	+	1.48456i	−0.0175582	+	0.999846i	$0.505589\pi$
$20$	1.61803			0.361803
$21$	−0.500000	−	2.59808i	−0.109109	−	0.566947i
$22$	−0.618034			−0.131765
$23$	−2.35410	−	4.07742i	−0.490864	−	0.850202i	0.509081	−	0.860719i	$-0.329986\pi$
$23$	−2.35410	−	4.07742i	−0.490864	−	0.850202i	−0.999945	+	0.0105172i	$0.996652\pi$
$24$	−1.11803	+	1.93649i	−0.228218	+	0.395285i
$25$	2.00000	−	3.46410i	0.400000	−	0.692820i
$26$	1.38197	+	2.39364i	0.271026	+	0.469431i
$27$	−5.00000			−0.962250
$28$	0.809017	+	4.20378i	0.152890	+	0.794439i
$29$	−4.47214			−0.830455			−0.415227	−	0.909718i	$-0.636298\pi$
$29$	−4.47214			−0.830455			−0.415227	+	0.909718i	$0.636298\pi$
$30$	−0.309017	−	0.535233i	−0.0564185	−	0.0977198i
$31$	−2.11803	+	3.66854i	−0.380410	+	0.658890i	−0.991121	−	0.132964i	$-0.957550\pi$
$31$	−2.11803	+	3.66854i	−0.380410	+	0.658890i	0.610711	+	0.791854i	$0.290884\pi$
$32$	2.80902	−	4.86536i	0.496569	−	0.860082i
$33$	−0.500000	−	0.866025i	−0.0870388	−	0.150756i
$34$	0.145898			0.0250213
$35$	−2.50000	−	0.866025i	−0.422577	−	0.146385i
$36$	3.23607			0.539345
$37$	−2.73607	−	4.73901i	−0.449807	−	0.779088i	0.548566	−	0.836107i	$-0.315174\pi$
$37$	−2.73607	−	4.73901i	−0.449807	−	0.779088i	−0.998373	+	0.0570188i	$0.981840\pi$
$38$	−2.30902	+	3.99933i	−0.374572	+	0.648778i
$39$	−2.23607	+	3.87298i	−0.358057	+	0.620174i
$40$	1.11803	+	1.93649i	0.176777	+	0.306186i
$41$	−1.00000			−0.156174
$41$	−1.00000			−0.156174
$42$	1.23607	−	1.07047i	0.190729	−	0.165177i
$43$	2.47214			0.376997			0.188499	−	0.982073i	$-0.439638\pi$
$43$	2.47214			0.376997			0.188499	+	0.982073i	$0.439638\pi$
$44$	0.809017	+	1.40126i	0.121964	+	0.211248i
$45$	−1.00000	+	1.73205i	−0.149071	+	0.258199i
$46$	1.45492	−	2.51999i	0.214516	−	0.371552i
$47$	−2.73607	−	4.73901i	−0.399097	−	0.691255i	0.594518	−	0.804082i	$-0.297343\pi$
$47$	−2.73607	−	4.73901i	−0.399097	−	0.691255i	−0.993615	+	0.112827i	$0.964010\pi$
$48$	1.85410			0.267617
$49$	1.00000	−	6.92820i	0.142857	−	0.989743i
$50$	2.47214			0.349613
$51$	0.118034	+	0.204441i	0.0165281	+	0.0286274i
$52$	3.61803	−	6.26662i	0.501731	−	0.869024i
$53$	2.88197	−	4.99171i	0.395868	−	0.685664i	−0.597343	−	0.801986i	$-0.703777\pi$
$53$	2.88197	−	4.99171i	0.395868	−	0.685664i	0.993212	+	0.116321i	$0.0371103\pi$
$54$	−1.54508	−	2.67617i	−0.210259	−	0.364180i
$55$	−1.00000			−0.134840
$56$	−4.47214	+	3.87298i	−0.597614	+	0.517549i
$57$	−7.47214			−0.989709
$58$	−1.38197	−	2.39364i	−0.181461	−	0.314300i
$59$	2.35410	−	4.07742i	0.306478	−	0.530835i	−0.671111	−	0.741357i	$-0.734183\pi$
$59$	2.35410	−	4.07742i	0.306478	−	0.530835i	0.977589	+	0.210521i	$0.0675161\pi$
$60$	−0.809017	+	1.40126i	−0.104444	+	0.180902i
$61$	−0.263932	−	0.457144i	−0.0337930	−	0.0585312i	0.848634	−	0.528980i	$-0.177425\pi$
$61$	−0.263932	−	0.457144i	−0.0337930	−	0.0585312i	−0.882427	+	0.470449i	$0.844092\pi$
$62$	−2.61803			−0.332491
$63$	−5.00000	−	1.73205i	−0.629941	−	0.218218i
$64$	−0.236068			−0.0295085
$65$	2.23607	+	3.87298i	0.277350	+	0.480384i
$66$	0.309017	−	0.535233i	0.0380374	−	0.0658826i
$67$	5.97214	−	10.3440i	0.729613	−	1.26373i	−0.227435	−	0.973793i	$-0.573034\pi$
$67$	5.97214	−	10.3440i	0.729613	−	1.26373i	0.957047	−	0.289933i	$-0.0936329\pi$
$68$	−0.190983	−	0.330792i	−0.0231601	−	0.0401145i
$69$	4.70820			0.566801
$70$	−0.309017	−	1.60570i	−0.0369346	−	0.191918i
$71$	−5.52786			−0.656037			−0.328018	−	0.944671i	$-0.606381\pi$
$71$	−5.52786			−0.656037			−0.328018	+	0.944671i	$0.606381\pi$
$72$	2.23607	+	3.87298i	0.263523	+	0.456435i
$73$	5.73607	−	9.93516i	0.671356	−	1.16282i	−0.306164	−	0.951979i	$-0.599046\pi$
$73$	5.73607	−	9.93516i	0.671356	−	1.16282i	0.977520	−	0.210844i	$-0.0676211\pi$
$74$	1.69098	−	2.92887i	0.196573	−	0.340474i
$75$	2.00000	+	3.46410i	0.230940	+	0.400000i
$76$	12.0902			1.38684
$77$	−0.500000	−	2.59808i	−0.0569803	−	0.296078i
$78$	−2.76393			−0.312954
$79$	0.500000	+	0.866025i	0.0562544	+	0.0974355i	0.892781	−	0.450490i	$-0.148751\pi$
$79$	0.500000	+	0.866025i	0.0562544	+	0.0974355i	−0.836527	+	0.547926i	$0.815418\pi$
$80$	0.927051	−	1.60570i	0.103647	−	0.179523i
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$	−0.309017	−	0.535233i	−0.0341252	−	0.0591066i
$83$	−10.4721			−1.14947			−0.574733	−	0.818341i	$-0.694894\pi$
$83$	−10.4721			−1.14947			−0.574733	+	0.818341i	$0.694894\pi$
$84$	−4.04508	−	1.40126i	−0.441355	−	0.152890i
$85$	0.236068			0.0256052
$86$	0.763932	+	1.32317i	0.0823769	+	0.142681i
$87$	2.23607	−	3.87298i	0.239732	−	0.415227i
$88$	−1.11803	+	1.93649i	−0.119183	+	0.206431i
$89$	4.88197	+	8.45581i	0.517487	+	0.896314i	0.999794	+	0.0203118i	$0.00646588\pi$
$89$	4.88197	+	8.45581i	0.517487	+	0.896314i	−0.482306	+	0.876003i	$0.660201\pi$
$90$	−1.23607			−0.130293
$91$	−8.94427	+	7.74597i	−0.937614	+	0.811998i
$92$	−7.61803			−0.794235
$93$	−2.11803	−	3.66854i	−0.219630	−	0.380410i
$94$	1.69098	−	2.92887i	0.174412	−	0.302090i
$95$	−3.73607	+	6.47106i	−0.383312	+	0.663917i
$96$	2.80902	+	4.86536i	0.286694	+	0.496569i
$97$	−0.472136			−0.0479381			−0.0239691	−	0.999713i	$-0.507630\pi$
$97$	−0.472136			−0.0479381			−0.0239691	+	0.999713i	$0.507630\pi$
$98$	4.01722	−	1.60570i	0.405801	−	0.162200i
$99$	−2.00000			−0.201008
$100$	−3.23607	−	5.60503i	−0.323607	−	0.560503i
$101$	−8.35410	+	14.4697i	−0.831264	+	1.43979i	0.0657719	+	0.997835i	$0.479049\pi$
$101$	−8.35410	+	14.4697i	−0.831264	+	1.43979i	−0.897036	+	0.441957i	$0.854284\pi$
$102$	−0.0729490	+	0.126351i	−0.00722303	+	0.0125107i
$103$	2.59017	+	4.48631i	0.255217	+	0.442049i	0.964954	−	0.262417i	$-0.0845197\pi$
$103$	2.59017	+	4.48631i	0.255217	+	0.442049i	−0.709737	+	0.704466i	$0.751186\pi$
$104$	10.0000			0.980581
$105$	2.00000	−	1.73205i	0.195180	−	0.169031i
$106$	3.56231			0.346002
$107$	7.35410	+	12.7377i	0.710948	+	1.23140i	0.964502	+	0.264077i	$0.0850672\pi$
$107$	7.35410	+	12.7377i	0.710948	+	1.23140i	−0.253554	+	0.967321i	$0.581600\pi$
$108$	−4.04508	+	7.00629i	−0.389238	+	0.674181i
$109$	4.88197	−	8.45581i	0.467608	−	0.809920i	−0.531707	−	0.846928i	$-0.678449\pi$
$109$	4.88197	−	8.45581i	0.467608	−	0.809920i	0.999315	+	0.0370081i	$0.0117827\pi$
$110$	−0.309017	−	0.535233i	−0.0294636	−	0.0510325i
$111$	5.47214			0.519392
$112$	4.63525	+	1.60570i	0.437990	+	0.151724i
$113$	−15.8885			−1.49467			−0.747334	−	0.664448i	$-0.768667\pi$
$113$	−15.8885			−1.49467			−0.747334	+	0.664448i	$0.768667\pi$
$114$	−2.30902	−	3.99933i	−0.216259	−	0.374572i
$115$	2.35410	−	4.07742i	0.219521	−	0.380222i
$116$	−3.61803	+	6.26662i	−0.335926	+	0.581841i
$117$	4.47214	+	7.74597i	0.413449	+	0.716115i
$118$	2.90983			0.267872
$119$	0.118034	+	0.613323i	0.0108202	+	0.0562232i
$120$	−2.23607			−0.204124
$121$	5.00000	+	8.66025i	0.454545	+	0.787296i
$122$	0.163119	−	0.282530i	0.0147681	−	0.0255791i
$123$	0.500000	−	0.866025i	0.0450835	−	0.0780869i
$124$	3.42705	+	5.93583i	0.307758	+	0.533053i
$125$	9.00000			0.804984
$126$	−0.618034	−	3.21140i	−0.0550588	−	0.286094i
$127$	−11.4164			−1.01304			−0.506521	−	0.862228i	$-0.669069\pi$
$127$	−11.4164			−1.01304			−0.506521	+	0.862228i	$0.669069\pi$
$128$	−5.69098	−	9.85707i	−0.503017	−	0.871250i
$129$	−1.23607	+	2.14093i	−0.108830	+	0.188499i
$130$	−1.38197	+	2.39364i	−0.121206	+	0.209936i
$131$	−8.82624	−	15.2875i	−0.771152	−	1.33567i	−0.936932	−	0.349512i	$-0.886348\pi$
$131$	−8.82624	−	15.2875i	−0.771152	−	1.33567i	0.165780	−	0.986163i	$-0.446986\pi$
$132$	−1.61803			−0.140832
$133$	−18.6803	−	6.47106i	−1.61979	−	0.561112i
$134$	7.38197			0.637705
$135$	−2.50000	−	4.33013i	−0.215166	−	0.372678i
$136$	0.263932	−	0.457144i	0.0226320	−	0.0391997i
$137$	7.82624	−	13.5554i	0.668641	−	1.15812i	−0.309644	−	0.950853i	$-0.600210\pi$
$137$	7.82624	−	13.5554i	0.668641	−	1.15812i	0.978284	−	0.207267i	$-0.0664569\pi$
$138$	1.45492	+	2.51999i	0.123851	+	0.214516i
$139$	−0.944272			−0.0800921			−0.0400460	−	0.999198i	$-0.512750\pi$
$139$	−0.944272			−0.0800921			−0.0400460	+	0.999198i	$0.512750\pi$
$140$	−3.23607	+	2.80252i	−0.273498	+	0.236856i
$141$	5.47214			0.460837
$142$	−1.70820	−	2.95870i	−0.143349	−	0.248288i
$143$	−2.23607	+	3.87298i	−0.186989	+	0.323875i
$144$	1.85410	−	3.21140i	0.154508	−	0.267617i
$145$	−2.23607	−	3.87298i	−0.185695	−	0.321634i
$146$	7.09017			0.586787
$147$	5.50000	+	4.33013i	0.453632	+	0.357143i
$148$	−8.85410			−0.727803
$149$	10.5902	+	18.3427i	0.867581	+	1.50269i	0.864462	+	0.502698i	$0.167659\pi$
$149$	10.5902	+	18.3427i	0.867581	+	1.50269i	0.00311867	+	0.999995i	$0.499007\pi$
$150$	−1.23607	+	2.14093i	−0.100925	+	0.174806i
$151$	5.97214	−	10.3440i	0.486006	−	0.841786i	−0.513865	−	0.857871i	$-0.671787\pi$
$151$	5.97214	−	10.3440i	0.486006	−	0.841786i	0.999871	+	0.0160847i	$0.00512015\pi$
$152$	8.35410	+	14.4697i	0.677607	+	1.17365i
$153$	0.472136			0.0381699
$154$	1.23607	−	1.07047i	0.0996052	−	0.0862606i
$155$	−4.23607			−0.340249
$156$	3.61803	+	6.26662i	0.289675	+	0.501731i
$157$	−1.11803	+	1.93649i	−0.0892288	+	0.154549i	−0.907185	−	0.420731i	$-0.861774\pi$
$157$	−1.11803	+	1.93649i	−0.0892288	+	0.154549i	0.817957	+	0.575280i	$0.195107\pi$
$158$	−0.309017	+	0.535233i	−0.0245841	+	0.0425809i
$159$	2.88197	+	4.99171i	0.228555	+	0.395868i
$160$	5.61803			0.444145
$161$	11.7705	+	4.07742i	0.927646	+	0.321346i
$162$	−0.618034			−0.0485573
$163$	9.35410	+	16.2018i	0.732670	+	1.26902i	0.955738	+	0.294219i	$0.0950594\pi$
$163$	9.35410	+	16.2018i	0.732670	+	1.26902i	−0.223068	+	0.974803i	$0.571607\pi$
$164$	−0.809017	+	1.40126i	−0.0631736	+	0.109420i
$165$	0.500000	−	0.866025i	0.0389249	−	0.0674200i
$166$	−3.23607	−	5.60503i	−0.251168	−	0.435035i
$167$	6.47214			0.500829			0.250414	−	0.968139i	$-0.419433\pi$
$167$	6.47214			0.500829			0.250414	+	0.968139i	$0.419433\pi$
$168$	−1.11803	−	5.80948i	−0.0862582	−	0.448211i
$169$	7.00000			0.538462
$170$	0.0729490	+	0.126351i	0.00559493	+	0.00969071i
$171$	−7.47214	+	12.9421i	−0.571409	+	0.989709i
$172$	2.00000	−	3.46410i	0.152499	−	0.264135i
$173$	−8.44427	−	14.6259i	−0.642006	−	1.11199i	−0.984984	−	0.172644i	$-0.944769\pi$
$173$	−8.44427	−	14.6259i	−0.642006	−	1.11199i	0.342978	−	0.939343i	$-0.388564\pi$
$174$	2.76393			0.209533
$175$	2.00000	+	10.3923i	0.151186	+	0.785584i
$176$	1.85410			0.139758
$177$	2.35410	+	4.07742i	0.176945	+	0.306478i
$178$	−3.01722	+	5.22598i	−0.226150	+	0.391704i
$179$	−8.20820	+	14.2170i	−0.613510	+	1.06263i	0.377134	+	0.926159i	$0.376910\pi$
$179$	−8.20820	+	14.2170i	−0.613510	+	1.06263i	−0.990644	+	0.136472i	$0.956424\pi$
$180$	1.61803	+	2.80252i	0.120601	+	0.208887i
$181$	5.41641			0.402598			0.201299	−	0.979530i	$-0.435484\pi$
$181$	5.41641			0.402598			0.201299	+	0.979530i	$0.435484\pi$
$182$	−6.90983	−	2.39364i	−0.512191	−	0.177428i
$183$	0.527864			0.0390208
$184$	−5.26393	−	9.11740i	−0.388062	−	0.672143i
$185$	2.73607	−	4.73901i	0.201160	−	0.348419i
$186$	1.30902	−	2.26728i	0.0959818	−	0.166245i
$187$	0.118034	+	0.204441i	0.00863150	+	0.0149502i
$188$	−8.85410			−0.645752
$189$	10.0000	−	8.66025i	0.727393	−	0.629941i
$190$	−4.61803			−0.335027
$191$	1.73607	+	3.00696i	0.125617	+	0.217576i	0.921974	−	0.387251i	$-0.126575\pi$
$191$	1.73607	+	3.00696i	0.125617	+	0.217576i	−0.796357	+	0.604827i	$0.793242\pi$
$192$	0.118034	−	0.204441i	0.00851837	−	0.0147542i
$193$	−11.5902	+	20.0748i	−0.834279	+	1.44501i	0.0603377	+	0.998178i	$0.480782\pi$
$193$	−11.5902	+	20.0748i	−0.834279	+	1.44501i	−0.894616	+	0.446835i	$0.852551\pi$
$194$	−0.145898	−	0.252703i	−0.0104749	−	0.0181430i
$195$	−4.47214			−0.320256
$196$	−8.89919	−	7.00629i	−0.635656	−	0.500449i
$197$	14.9443			1.06474			0.532368	−	0.846513i	$-0.321302\pi$
$197$	14.9443			1.06474			0.532368	+	0.846513i	$0.321302\pi$
$198$	−0.618034	−	1.07047i	−0.0439218	−	0.0760747i
$199$	−0.0278640	+	0.0482619i	−0.00197523	+	0.00342120i	−0.867011	−	0.498288i	$-0.833962\pi$
$199$	−0.0278640	+	0.0482619i	−0.00197523	+	0.00342120i	0.865036	+	0.501710i	$0.167295\pi$
$200$	4.47214	−	7.74597i	0.316228	−	0.547723i
$201$	5.97214	+	10.3440i	0.421242	+	0.729613i
$202$	−10.3262			−0.726552
$203$	8.94427	−	7.74597i	0.627765	−	0.543660i
$204$	0.381966			0.0267430
$205$	−0.500000	−	0.866025i	−0.0349215	−	0.0604858i
$206$	−1.60081	+	2.77269i	−0.111534	+	0.193182i
$207$	4.70820	−	8.15485i	0.327243	−	0.566801i
$208$	−4.14590	−	7.18091i	−0.287466	−	0.497906i
$209$	−7.47214			−0.516858
$210$	1.54508	+	0.535233i	0.106621	+	0.0369346i
$211$		0			0			−	1.00000i	$-0.5\pi$
$211$		0			0				1.00000i	$0.5\pi$
$212$	−4.66312	−	8.07676i	−0.320264	−	0.554714i
$213$	2.76393	−	4.78727i	0.189382	−	0.328018i
$214$	−4.54508	+	7.87232i	−0.310696	+	0.538141i
$215$	1.23607	+	2.14093i	0.0842991	+	0.146010i
$216$	−11.1803			−0.760726
$217$	−2.11803	−	11.0056i	−0.143782	−	0.747111i
$218$	6.03444			0.408704
$219$	5.73607	+	9.93516i	0.387608	+	0.671356i
$220$	−0.809017	+	1.40126i	−0.0545439	+	0.0944728i
$221$	0.527864	−	0.914287i	0.0355080	−	0.0615016i
$222$	1.69098	+	2.92887i	0.113491	+	0.196573i
$223$	0.944272			0.0632331			0.0316166	−	0.999500i	$-0.489934\pi$
$223$	0.944272			0.0632331			0.0316166	+	0.999500i	$0.489934\pi$
$224$	2.80902	+	14.5961i	0.187685	+	0.975242i
$225$	8.00000			0.533333
$226$	−4.90983	−	8.50408i	−0.326597	−	0.565683i
$227$	−1.73607	+	3.00696i	−0.115227	+	0.199579i	−0.917870	−	0.396880i	$-0.870093\pi$
$227$	−1.73607	+	3.00696i	−0.115227	+	0.199579i	0.802644	+	0.596459i	$0.203426\pi$
$228$	−6.04508	+	10.4704i	−0.400346	+	0.693419i
$229$	−10.0623	−	17.4284i	−0.664936	−	1.15170i	−0.979303	−	0.202401i	$-0.935126\pi$
$229$	−10.0623	−	17.4284i	−0.664936	−	1.15170i	0.314367	−	0.949302i	$-0.398208\pi$
$230$	2.90983			0.191869
$231$	2.50000	+	0.866025i	0.164488	+	0.0569803i
$232$	−10.0000			−0.656532
$233$	−8.35410	−	14.4697i	−0.547295	−	0.947943i	−0.998459	−	0.0555020i	$-0.982324\pi$
$233$	−8.35410	−	14.4697i	−0.547295	−	0.947943i	0.451163	−	0.892441i	$-0.351009\pi$
$234$	−2.76393	+	4.78727i	−0.180684	+	0.312954i
$235$	2.73607	−	4.73901i	0.178481	−	0.309139i
$236$	−3.80902	−	6.59741i	−0.247946	−	0.429455i
$237$	−1.00000			−0.0649570
$238$	−0.291796	+	0.252703i	−0.0189143	+	0.0163803i
$239$	6.47214			0.418648			0.209324	−	0.977846i	$-0.432874\pi$
$239$	6.47214			0.418648			0.209324	+	0.977846i	$0.432874\pi$
$240$	0.927051	+	1.60570i	0.0598409	+	0.103647i
$241$	3.73607	−	6.47106i	0.240661	−	0.416838i	−0.720242	−	0.693723i	$-0.755969\pi$
$241$	3.73607	−	6.47106i	0.240661	−	0.416838i	0.960903	+	0.276886i	$0.0893024\pi$
$242$	−3.09017	+	5.35233i	−0.198644	+	0.344061i
$243$	−8.00000	−	13.8564i	−0.513200	−	0.888889i
$244$	−0.854102			−0.0546783
$245$	6.50000	−	2.59808i	0.415270	−	0.165985i
$246$	0.618034			0.0394044
$247$	16.7082	+	28.9395i	1.06312	+	1.84137i
$248$	−4.73607	+	8.20311i	−0.300741	+	0.520898i
$249$	5.23607	−	9.06914i	0.331822	−	0.574733i
$250$	2.78115	+	4.81710i	0.175896	+	0.304660i
$251$	−26.8328			−1.69367			−0.846836	−	0.531854i	$-0.821496\pi$
$251$	−26.8328			−1.69367			−0.846836	+	0.531854i	$0.821496\pi$
$252$	−6.47214	+	5.60503i	−0.407706	+	0.353084i
$253$	4.70820			0.296002
$254$	−3.52786	−	6.11044i	−0.221358	−	0.383403i
$255$	−0.118034	+	0.204441i	−0.00739158	+	0.0128026i
$256$	3.28115	−	5.68312i	0.205072	−	0.355195i
$257$	7.35410	+	12.7377i	0.458736	+	0.794555i	0.998894	−	0.0470090i	$-0.0149689\pi$
$257$	7.35410	+	12.7377i	0.458736	+	0.794555i	−0.540158	+	0.841564i	$0.681636\pi$
$258$	−1.52786			−0.0951207
$259$	13.6803	+	4.73901i	0.850055	+	0.294468i
$260$	7.23607			0.448762
$261$	−4.47214	−	7.74597i	−0.276818	−	0.479463i
$262$	5.45492	−	9.44819i	0.337006	−	0.583711i
$263$	0.736068	−	1.27491i	0.0453879	−	0.0786141i	−0.842439	−	0.538792i	$-0.818881\pi$
$263$	0.736068	−	1.27491i	0.0453879	−	0.0786141i	0.887827	+	0.460178i	$0.152214\pi$
$264$	−1.11803	−	1.93649i	−0.0688102	−	0.119183i
$265$	5.76393			0.354076
$266$	−2.30902	−	11.9980i	−0.141575	−	0.735645i
$267$	−9.76393			−0.597543
$268$	−9.66312	−	16.7370i	−0.590269	−	1.02238i
$269$	5.26393	−	9.11740i	0.320948	−	0.555898i	−0.659736	−	0.751497i	$-0.729332\pi$
$269$	5.26393	−	9.11740i	0.320948	−	0.555898i	0.980684	+	0.195600i	$0.0626653\pi$
$270$	1.54508	−	2.67617i	0.0940309	−	0.162866i
$271$	−4.82624	−	8.35929i	−0.293173	−	0.507791i	0.681385	−	0.731925i	$-0.261378\pi$
$271$	−4.82624	−	8.35929i	−0.293173	−	0.507791i	−0.974558	+	0.224134i	$0.928045\pi$
$272$	−0.437694			−0.0265391
$273$	−2.23607	−	11.6190i	−0.135333	−	0.703211i
$274$	9.67376			0.584413
$275$	2.00000	+	3.46410i	0.120605	+	0.208893i
$276$	3.80902	−	6.59741i	0.229276	−	0.397117i
$277$	10.9721	−	19.0043i	0.659252	−	1.14186i	−0.321558	−	0.946890i	$-0.604206\pi$
$277$	10.9721	−	19.0043i	0.659252	−	1.14186i	0.980810	−	0.194968i	$-0.0624602\pi$
$278$	−0.291796	−	0.505406i	−0.0175008	−	0.0303122i
$279$	−8.47214			−0.507214
$280$	−5.59017	−	1.93649i	−0.334077	−	0.115728i
$281$	4.47214			0.266785			0.133393	−	0.991063i	$-0.457413\pi$
$281$	4.47214			0.266785			0.133393	+	0.991063i	$0.457413\pi$
$282$	1.69098	+	2.92887i	0.100697	+	0.174412i
$283$	5.59017	−	9.68246i	0.332301	−	0.575562i	−0.650662	−	0.759368i	$-0.725508\pi$
$283$	5.59017	−	9.68246i	0.332301	−	0.575562i	0.982963	+	0.183805i	$0.0588416\pi$
$284$	−4.47214	+	7.74597i	−0.265372	+	0.459639i
$285$	−3.73607	−	6.47106i	−0.221306	−	0.383312i
$286$	−2.76393			−0.163435
$287$	2.00000	−	1.73205i	0.118056	−	0.102240i
$288$	11.2361			0.662092
$289$	8.47214	+	14.6742i	0.498361	+	0.863186i
$290$	1.38197	−	2.39364i	0.0811518	−	0.140559i
$291$	0.236068	−	0.408882i	0.0138385	−	0.0239691i
$292$	−9.28115	−	16.0754i	−0.543138	−	0.940743i
$293$	−24.8328			−1.45075			−0.725374	−	0.688355i	$-0.758333\pi$
$293$	−24.8328			−1.45075			−0.725374	+	0.688355i	$0.758333\pi$
$294$	−0.618034	+	4.28187i	−0.0360445	+	0.249723i
$295$	4.70820			0.274122
$296$	−6.11803	−	10.5967i	−0.355604	−	0.615923i
$297$	2.50000	−	4.33013i	0.145065	−	0.251259i
$298$	−6.54508	+	11.3364i	−0.379147	+	0.656701i
$299$	−10.5279	−	18.2348i	−0.608842	−	1.05455i
$300$	6.47214			0.373669
$301$	−4.94427	+	4.28187i	−0.284983	+	0.246803i
$302$	7.38197			0.424784
$303$	−8.35410	−	14.4697i	−0.479931	−	0.831264i
$304$	6.92705	−	11.9980i	0.397294	−	0.688133i
$305$	0.263932	−	0.457144i	0.0151127	−	0.0261760i
$306$	0.145898	+	0.252703i	0.00834044	+	0.0144461i
$307$	25.8885			1.47754			0.738769	−	0.673959i	$-0.235408\pi$
$307$	25.8885			1.47754			0.738769	+	0.673959i	$0.235408\pi$
$308$	−4.04508	−	1.40126i	−0.230490	−	0.0798441i
$309$	−5.18034			−0.294699
$310$	−1.30902	−	2.26728i	−0.0743472	−	0.128773i
$311$	−15.9164	+	27.5680i	−0.902537	+	1.56324i	−0.0783466	+	0.996926i	$0.524964\pi$
$311$	−15.9164	+	27.5680i	−0.902537	+	1.56324i	−0.824190	+	0.566313i	$0.808369\pi$
$312$	−5.00000	+	8.66025i	−0.283069	+	0.490290i
$313$	15.3541	+	26.5941i	0.867865	+	1.50319i	0.864174	+	0.503193i	$0.167842\pi$
$313$	15.3541	+	26.5941i	0.867865	+	1.50319i	0.00369130	+	0.999993i	$0.498825\pi$
$314$	−1.38197			−0.0779889
$315$	−1.00000	−	5.19615i	−0.0563436	−	0.292770i
$316$	1.61803			0.0910215
$317$	−15.1180	−	26.1852i	−0.849113	−	1.47071i	−0.882001	−	0.471248i	$-0.843804\pi$
$317$	−15.1180	−	26.1852i	−0.849113	−	1.47071i	0.0328871	−	0.999459i	$-0.489530\pi$
$318$	−1.78115	+	3.08505i	−0.0998821	+	0.173001i
$319$	2.23607	−	3.87298i	0.125196	−	0.216845i
$320$	−0.118034	−	0.204441i	−0.00659830	−	0.0114286i
$321$	−14.7082			−0.820932
$322$	1.45492	+	7.55996i	0.0810792	+	0.421300i
$323$	1.76393			0.0981478
$324$	0.809017	+	1.40126i	0.0449454	+	0.0778477i
$325$	8.94427	−	15.4919i	0.496139	−	0.859338i
$326$	−5.78115	+	10.0133i	−0.320188	+	0.554583i
$327$	4.88197	+	8.45581i	0.269973	+	0.467608i
$328$	−2.23607			−0.123466
$329$	13.6803	+	4.73901i	0.754222	+	0.261270i
$330$	0.618034			0.0340217
$331$	−10.9164	−	18.9078i	−0.600020	−	1.03927i	−0.992817	−	0.119640i	$-0.961826\pi$
$331$	−10.9164	−	18.9078i	−0.600020	−	1.03927i	0.392797	−	0.919625i	$-0.371507\pi$
$332$	−8.47214	+	14.6742i	−0.464969	+	0.805350i
$333$	5.47214	−	9.47802i	0.299871	−	0.519392i
$334$	2.00000	+	3.46410i	0.109435	+	0.189547i
$335$	11.9443			0.652585
$336$	−3.70820	+	3.21140i	−0.202299	+	0.175196i
$337$	0.472136			0.0257189			0.0128594	−	0.999917i	$-0.495907\pi$
$337$	0.472136			0.0257189			0.0128594	+	0.999917i	$0.495907\pi$
$338$	2.16312	+	3.74663i	0.117658	+	0.203790i
$339$	7.94427	−	13.7599i	0.431474	−	0.747334i
$340$	0.190983	−	0.330792i	0.0103575	−	0.0179397i
$341$	−2.11803	−	3.66854i	−0.114698	−	0.198663i
$342$	−9.23607			−0.499429
$343$	10.0000	+	15.5885i	0.539949	+	0.841698i
$344$	5.52786			0.298042
$345$	2.35410	+	4.07742i	0.126741	+	0.219521i
$346$	5.21885	−	9.03931i	0.280567	−	0.485956i
$347$	1.50000	−	2.59808i	0.0805242	−	0.139472i	−0.822951	−	0.568112i	$-0.807674\pi$
$347$	1.50000	−	2.59808i	0.0805242	−	0.139472i	0.903475	+	0.428640i	$0.141007\pi$
$348$	−3.61803	−	6.26662i	−0.193947	−	0.335926i
$349$	−11.5279			−0.617072			−0.308536	−	0.951213i	$-0.599839\pi$
$349$	−11.5279			−0.617072			−0.308536	+	0.951213i	$0.599839\pi$
$350$	−4.94427	+	4.28187i	−0.264282	+	0.228875i
$351$	−22.3607			−1.19352
$352$	2.80902	+	4.86536i	0.149721	+	0.259325i
$353$	−8.26393	+	14.3136i	−0.439845	+	0.761833i	−0.997677	−	0.0681202i	$-0.978300\pi$
$353$	−8.26393	+	14.3136i	−0.439845	+	0.761833i	0.557832	+	0.829954i	$0.311633\pi$
$354$	−1.45492	+	2.51999i	−0.0773279	+	0.133936i
$355$	−2.76393	−	4.78727i	−0.146694	−	0.254082i
$356$	15.7984			0.837312
$357$	−0.590170	−	0.204441i	−0.0312351	−	0.0108202i
$358$	−10.1459			−0.536227
$359$	−8.82624	−	15.2875i	−0.465831	−	0.806843i	0.533408	−	0.845858i	$-0.320911\pi$
$359$	−8.82624	−	15.2875i	−0.465831	−	0.806843i	−0.999239	+	0.0390154i	$0.987578\pi$
$360$	−2.23607	+	3.87298i	−0.117851	+	0.204124i
$361$	−18.4164	+	31.8982i	−0.969285	+	1.67885i
$362$	1.67376	+	2.89904i	0.0879710	+	0.152370i
$363$	−10.0000			−0.524864
$364$	3.61803	+	18.7999i	0.189637	+	0.985380i
$365$	11.4721			0.600479
$366$	0.163119	+	0.282530i	0.00852636	+	0.0147681i
$367$	−8.59017	+	14.8786i	−0.448403	+	0.776657i	−0.998282	−	0.0585871i	$-0.981340\pi$
$367$	−8.59017	+	14.8786i	−0.448403	+	0.776657i	0.549879	+	0.835244i	$0.314674\pi$
$368$	−4.36475	+	7.55996i	−0.227528	+	0.394090i
$369$	−1.00000	−	1.73205i	−0.0520579	−	0.0901670i
$370$	3.38197			0.175820
$371$	2.88197	+	14.9751i	0.149624	+	0.777470i
$372$	−6.85410			−0.355369
$373$	8.97214	+	15.5402i	0.464560	+	0.804641i	0.999182	−	0.0404505i	$-0.0128793\pi$
$373$	8.97214	+	15.5402i	0.464560	+	0.804641i	−0.534622	+	0.845091i	$0.679546\pi$
$374$	−0.0729490	+	0.126351i	−0.00377210	+	0.00653348i
$375$	−4.50000	+	7.79423i	−0.232379	+	0.402492i
$376$	−6.11803	−	10.5967i	−0.315514	−	0.546485i
$377$	−20.0000			−1.03005
$378$	7.72542	+	2.67617i	0.397353	+	0.137647i
$379$	4.58359			0.235443			0.117722	−	0.993047i	$-0.462441\pi$
$379$	4.58359			0.235443			0.117722	+	0.993047i	$0.462441\pi$
$380$	6.04508	+	10.4704i	0.310106	+	0.537120i
$381$	5.70820	−	9.88690i	0.292440	−	0.506521i
$382$	−1.07295	+	1.85840i	−0.0548968	+	0.0950841i
$383$	7.44427	+	12.8939i	0.380385	+	0.658845i	0.991117	−	0.132992i	$-0.0424583\pi$
$383$	7.44427	+	12.8939i	0.380385	+	0.658845i	−0.610733	+	0.791837i	$0.709125\pi$
$384$	11.3820			0.580834
$385$	2.00000	−	1.73205i	0.101929	−	0.0882735i
$386$	−14.3262			−0.729186
$387$	2.47214	+	4.28187i	0.125666	+	0.217659i
$388$	−0.381966	+	0.661585i	−0.0193914	+	0.0335869i
$389$	0.500000	−	0.866025i	0.0253510	−	0.0439092i	−0.853072	−	0.521794i	$-0.825263\pi$
$389$	0.500000	−	0.866025i	0.0253510	−	0.0439092i	0.878423	+	0.477885i	$0.158596\pi$
$390$	−1.38197	−	2.39364i	−0.0699786	−	0.121206i
$391$	−1.11146			−0.0562088
$392$	2.23607	−	15.4919i	0.112938	−	0.782461i
$393$	17.6525			0.890450
$394$	4.61803	+	7.99867i	0.232653	+	0.402967i
$395$	−0.500000	+	0.866025i	−0.0251577	+	0.0435745i
$396$	−1.61803	+	2.80252i	−0.0813093	+	0.140832i
$397$	1.82624	+	3.16314i	0.0916563	+	0.158753i	0.908208	−	0.418519i	$-0.137451\pi$
$397$	1.82624	+	3.16314i	0.0916563	+	0.158753i	−0.816552	+	0.577272i	$0.804117\pi$
$398$	−0.0344419			−0.00172641
$399$	14.9443	−	12.9421i	0.748149	−	0.647916i
$400$	−7.41641			−0.370820
$401$	4.97214	+	8.61199i	0.248297	+	0.430062i	0.963053	−	0.269311i	$-0.0867959\pi$
$401$	4.97214	+	8.61199i	0.248297	+	0.430062i	−0.714757	+	0.699373i	$0.753463\pi$
$402$	−3.69098	+	6.39297i	−0.184090	+	0.318852i
$403$	−9.47214	+	16.4062i	−0.471841	+	0.817252i
$404$	13.5172	+	23.4125i	0.672507	+	1.16482i
$405$	−1.00000			−0.0496904
$406$	6.90983	+	2.39364i	0.342929	+	0.118794i
$407$	5.47214			0.271244
$408$	0.263932	+	0.457144i	0.0130666	+	0.0226320i
$409$	−6.44427	+	11.1618i	−0.318649	+	0.551916i	−0.980206	−	0.197979i	$-0.936562\pi$
$409$	−6.44427	+	11.1618i	−0.318649	+	0.551916i	0.661558	+	0.749894i	$0.269896\pi$
$410$	0.309017	−	0.535233i	0.0152613	−	0.0264333i
$411$	7.82624	+	13.5554i	0.386040	+	0.668641i
$412$	8.38197			0.412950
$413$	2.35410	+	12.2323i	0.115838	+	0.601911i
$414$	5.81966			0.286021
$415$	−5.23607	−	9.06914i	−0.257028	−	0.445186i
$416$	12.5623	−	21.7586i	0.615918	−	1.06680i
$417$	0.472136	−	0.817763i	0.0231206	−	0.0400460i
$418$	−2.30902	−	3.99933i	−0.112938	−	0.195614i
$419$	17.8885			0.873913			0.436956	−	0.899483i	$-0.356056\pi$
$419$	17.8885			0.873913			0.436956	+	0.899483i	$0.356056\pi$
$420$	−0.809017	−	4.20378i	−0.0394760	−	0.205123i
$421$	−7.52786			−0.366886			−0.183443	−	0.983030i	$-0.558724\pi$
$421$	−7.52786			−0.366886			−0.183443	+	0.983030i	$0.558724\pi$
$422$		0			0
$423$	5.47214	−	9.47802i	0.266064	−	0.460837i
$424$	6.44427	−	11.1618i	0.312962	−	0.542065i
$425$	−0.472136	−	0.817763i	−0.0229020	−	0.0396674i
$426$	3.41641			0.165526
$427$	1.31966	+	0.457144i	0.0638628	+	0.0221227i
$428$	23.7984			1.15034
$429$	−2.23607	−	3.87298i	−0.107958	−	0.186989i
$430$	−0.763932	+	1.32317i	−0.0368401	+	0.0638089i
$431$	16.8262	−	29.1439i	0.810491	−	1.40381i	−0.102029	−	0.994781i	$-0.532534\pi$
$431$	16.8262	−	29.1439i	0.810491	−	1.40381i	0.912521	−	0.409031i	$-0.134133\pi$
$432$	4.63525	+	8.02850i	0.223014	+	0.386271i
$433$	−10.9443			−0.525948			−0.262974	−	0.964803i	$-0.584703\pi$
$433$	−10.9443			−0.525948			−0.262974	+	0.964803i	$0.584703\pi$
$434$	5.23607	−	4.53457i	0.251339	−	0.217666i
$435$	4.47214			0.214423
$436$	−7.89919	−	13.6818i	−0.378302	−	0.655239i
$437$	17.5902	−	30.4671i	0.841452	−	1.45744i
$438$	−3.54508	+	6.14027i	−0.169391	+	0.293393i
$439$	4.79180	+	8.29963i	0.228700	+	0.396120i	0.957423	−	0.288689i	$-0.0932192\pi$
$439$	4.79180	+	8.29963i	0.228700	+	0.396120i	−0.728723	+	0.684808i	$0.759886\pi$
$440$	−2.23607			−0.106600
$441$	13.0000	−	5.19615i	0.619048	−	0.247436i
$442$	0.652476			0.0310351
$443$	6.11803	+	10.5967i	0.290677	+	0.503467i	0.973970	−	0.226677i	$-0.0727863\pi$
$443$	6.11803	+	10.5967i	0.290677	+	0.503467i	−0.683293	+	0.730144i	$0.739453\pi$
$444$	4.42705	−	7.66788i	0.210099	−	0.363901i
$445$	−4.88197	+	8.45581i	−0.231427	+	0.400844i
$446$	0.291796	+	0.505406i	0.0138169	+	0.0239316i
$447$	−21.1803			−1.00180
$448$	0.472136	−	0.408882i	0.0223063	−	0.0193178i
$449$	38.9443			1.83789			0.918947	−	0.394381i	$-0.129041\pi$
$449$	38.9443			1.83789			0.918947	+	0.394381i	$0.129041\pi$
$450$	2.47214	+	4.28187i	0.116538	+	0.201849i
$451$	0.500000	−	0.866025i	0.0235441	−	0.0407795i
$452$	−12.8541	+	22.2640i	−0.604606	+	1.04721i
$453$	5.97214	+	10.3440i	0.280595	+	0.486006i
$454$	−2.14590			−0.100712
$455$	−11.1803	−	3.87298i	−0.524142	−	0.181568i
$456$	−16.7082			−0.782433
$457$	10.8820	+	18.8481i	0.509037	+	0.881678i	0.999945	+	0.0104665i	$0.00333166\pi$
$457$	10.8820	+	18.8481i	0.509037	+	0.881678i	−0.490908	+	0.871211i	$0.663335\pi$
$458$	6.21885	−	10.7714i	0.290588	−	0.503313i
$459$	−0.590170	+	1.02220i	−0.0275468	+	0.0477124i
$460$	−3.80902	−	6.59741i	−0.177596	−	0.307606i
$461$	−21.0557			−0.980663			−0.490332	−	0.871536i	$-0.663124\pi$
$461$	−21.0557			−0.980663			−0.490332	+	0.871536i	$0.663124\pi$
$462$	0.309017	+	1.60570i	0.0143768	+	0.0747039i
$463$	−37.8885			−1.76083			−0.880415	−	0.474204i	$-0.842736\pi$
$463$	−37.8885			−1.76083			−0.880415	+	0.474204i	$0.842736\pi$
$464$	4.14590	+	7.18091i	0.192468	+	0.333365i
$465$	2.11803	−	3.66854i	0.0982215	−	0.170125i
$466$	5.16312	−	8.94278i	0.239177	−	0.414266i
$467$	−15.5902	−	27.0030i	−0.721427	−	1.24955i	−0.960428	−	0.278529i	$-0.910153\pi$
$467$	−15.5902	−	27.0030i	−0.721427	−	1.24955i	0.239001	−	0.971019i	$-0.423180\pi$
$468$	14.4721			0.668975
$469$	5.97214	+	31.0321i	0.275768	+	1.43293i
$470$	3.38197			0.155998
$471$	−1.11803	−	1.93649i	−0.0515163	−	0.0892288i
$472$	5.26393	−	9.11740i	0.242292	−	0.419662i
$473$	−1.23607	+	2.14093i	−0.0568345	+	0.0984402i
$474$	−0.309017	−	0.535233i	−0.0141936	−	0.0245841i
$475$	29.8885			1.37138
$476$	0.954915	+	0.330792i	0.0437685	+	0.0151618i
$477$	11.5279			0.527825
$478$	2.00000	+	3.46410i	0.0914779	+	0.158444i
$479$	−10.5000	+	18.1865i	−0.479757	+	0.830964i	−0.999730	−	0.0232187i	$-0.992609\pi$
$479$	−10.5000	+	18.1865i	−0.479757	+	0.830964i	0.519973	+	0.854183i	$0.325942\pi$
$480$	−2.80902	+	4.86536i	−0.128213	+	0.222072i
$481$	−12.2361	−	21.1935i	−0.557917	−	0.966340i
$482$	4.61803			0.210346
$483$	−9.41641	+	8.15485i	−0.428461	+	0.371058i
$484$	16.1803			0.735470
$485$	−0.236068	−	0.408882i	−0.0107193	−	0.0185664i
$486$	4.94427	−	8.56373i	0.224277	−	0.388459i
$487$	−20.7705	+	35.9756i	−0.941202	+	1.63021i	−0.178018	+	0.984027i	$0.556969\pi$
$487$	−20.7705	+	35.9756i	−0.941202	+	1.63021i	−0.763183	+	0.646182i	$0.776365\pi$
$488$	−0.590170	−	1.02220i	−0.0267157	−	0.0462730i
$489$	−18.7082			−0.846014
$490$	3.39919	+	2.67617i	0.153560	+	0.120897i
$491$	32.3607			1.46042			0.730209	−	0.683224i	$-0.239423\pi$
$491$	32.3607			1.46042			0.730209	+	0.683224i	$0.239423\pi$
$492$	−0.809017	−	1.40126i	−0.0364733	−	0.0631736i
$493$	−0.527864	+	0.914287i	−0.0237738	+	0.0411774i
$494$	−10.3262	+	17.8856i	−0.464599	+	0.804710i
$495$	−1.00000	−	1.73205i	−0.0449467	−	0.0778499i
$496$	7.85410			0.352660
$497$	11.0557	−	9.57454i	0.495917	−	0.429477i
$498$	6.47214			0.290023
$499$	16.9721	+	29.3966i	0.759777	+	1.31597i	0.942964	+	0.332895i	$0.108025\pi$
$499$	16.9721	+	29.3966i	0.759777	+	1.31597i	−0.183187	+	0.983078i	$0.558641\pi$
$500$	7.28115	−	12.6113i	0.325623	−	0.563996i
$501$	−3.23607	+	5.60503i	−0.144577	+	0.250414i
$502$	−8.29180	−	14.3618i	−0.370081	−	0.640999i
$503$	4.00000			0.178351			0.0891756	−	0.996016i	$-0.471577\pi$
$503$	4.00000			0.178351			0.0891756	+	0.996016i	$0.471577\pi$
$504$	−11.1803	−	3.87298i	−0.498012	−	0.172516i
$505$	−16.7082			−0.743505
$506$	1.45492	+	2.51999i	0.0646789	+	0.112027i
$507$	−3.50000	+	6.06218i	−0.155440	+	0.269231i
$508$	−9.23607	+	15.9973i	−0.409784	+	0.709767i
$509$	−13.5902	−	23.5389i	−0.602374	−	1.04334i	−0.992461	−	0.122564i	$-0.960888\pi$
$509$	−13.5902	−	23.5389i	−0.602374	−	1.04334i	0.390087	−	0.920778i	$-0.372445\pi$
$510$	−0.145898			−0.00646047
$511$	5.73607	+	29.8055i	0.253749	+	1.31852i
$512$	−18.7082			−0.826794
$513$	−18.6803	−	32.3553i	−0.824757	−	1.42852i
$514$	−4.54508	+	7.87232i	−0.200475	+	0.347233i
$515$	−2.59017	+	4.48631i	−0.114137	+	0.197690i
$516$	2.00000	+	3.46410i	0.0880451	+	0.152499i
$517$	5.47214			0.240664
$518$	1.69098	+	8.78661i	0.0742975	+	0.386061i
$519$	16.8885			0.741325
$520$	5.00000	+	8.66025i	0.219265	+	0.379777i
$521$	−4.17376	+	7.22917i	−0.182856	+	0.316716i	−0.942852	−	0.333212i	$-0.891867\pi$
$521$	−4.17376	+	7.22917i	−0.182856	+	0.316716i	0.759996	+	0.649928i	$0.225201\pi$
$522$	2.76393	−	4.78727i	0.120974	−	0.209533i
$523$	−5.88197	−	10.1879i	−0.257200	−	0.445484i	0.708290	−	0.705921i	$-0.249467\pi$
$523$	−5.88197	−	10.1879i	−0.257200	−	0.445484i	−0.965491	+	0.260437i	$0.916133\pi$
$524$	−28.5623			−1.24775
$525$	−10.0000	−	3.46410i	−0.436436	−	0.151186i
$526$	0.909830			0.0396705
$527$	0.500000	+	0.866025i	0.0217803	+	0.0377247i
$528$	−0.927051	+	1.60570i	−0.0403447	+	0.0698791i
$529$	0.416408	−	0.721240i	0.0181047	−	0.0313582i
$530$	1.78115	+	3.08505i	0.0773683	+	0.134006i
$531$	9.41641			0.408637
$532$	−24.1803	+	20.9408i	−1.04835	+	0.907898i
$533$	−4.47214			−0.193710
$534$	−3.01722	−	5.22598i	−0.130568	−	0.226150i
$535$	−7.35410	+	12.7377i	−0.317946	+	0.550698i
$536$	13.3541	−	23.1300i	0.576809	−	0.999063i
$537$	−8.20820	−	14.2170i	−0.354210	−	0.613510i
$538$	6.50658			0.280518
$539$	5.50000	+	4.33013i	0.236902	+	0.186512i
$540$	−8.09017			−0.348145
$541$	−14.7361	−	25.5236i	−0.633553	−	1.09735i	−0.986820	−	0.161823i	$-0.948263\pi$
$541$	−14.7361	−	25.5236i	−0.633553	−	1.09735i	0.353267	−	0.935523i	$-0.385071\pi$
$542$	2.98278	−	5.16632i	0.128121	−	0.221913i
$543$	−2.70820	+	4.69075i	−0.116220	+	0.201299i
$544$	−0.663119	−	1.14856i	−0.0284310	−	0.0492439i
$545$	9.76393			0.418241
$546$	5.52786	−	4.78727i	0.236571	−	0.204876i
$547$	−18.4721			−0.789812			−0.394906	−	0.918722i	$-0.629223\pi$
$547$	−18.4721			−0.789812			−0.394906	+	0.918722i	$0.629223\pi$
$548$	−12.6631	−	21.9332i	−0.540942	−	0.936938i
$549$	0.527864	−	0.914287i	0.0225287	−	0.0390208i
$550$	−1.23607	+	2.14093i	−0.0527061	+	0.0912897i
$551$	−16.7082	−	28.9395i	−0.711793	−	1.23286i
$552$	10.5279			0.448096
$553$	−2.50000	−	0.866025i	−0.106311	−	0.0368271i
$554$	13.5623			0.576207
$555$	2.73607	+	4.73901i	0.116140	+	0.201160i
$556$	−0.763932	+	1.32317i	−0.0323979	+	0.0561149i
$557$	−3.59017	+	6.21836i	−0.152120	+	0.263480i	−0.932007	−	0.362441i	$-0.881943\pi$
$557$	−3.59017	+	6.21836i	−0.152120	+	0.263480i	0.779886	+	0.625921i	$0.215277\pi$
$558$	−2.61803	−	4.53457i	−0.110830	−	0.191964i
$559$	11.0557			0.467607
$560$	0.927051	+	4.81710i	0.0391751	+	0.203560i
$561$	−0.236068			−0.00996680
$562$	1.38197	+	2.39364i	0.0582947	+	0.100969i
$563$	5.50000	−	9.52628i	0.231797	−	0.401485i	−0.726540	−	0.687124i	$-0.758873\pi$
$563$	5.50000	−	9.52628i	0.231797	−	0.401485i	0.958337	+	0.285640i	$0.0922060\pi$
$564$	4.42705	−	7.66788i	0.186412	−	0.322876i
$565$	−7.94427	−	13.7599i	−0.334218	−	0.578883i
$566$	6.90983			0.290442
$567$	−0.500000	−	2.59808i	−0.0209980	−	0.109109i
$568$	−12.3607			−0.518643
$569$	6.02786	+	10.4406i	0.252701	+	0.437691i	0.964269	−	0.264927i	$-0.0853477\pi$
$569$	6.02786	+	10.4406i	0.252701	+	0.437691i	−0.711567	+	0.702618i	$0.752014\pi$
$570$	2.30902	−	3.99933i	0.0967141	−	0.167514i
$571$	18.7361	−	32.4518i	0.784080	−	1.35807i	−0.145467	−	0.989363i	$-0.546468\pi$
$571$	18.7361	−	32.4518i	0.784080	−	1.35807i	0.929547	−	0.368703i	$-0.120198\pi$
$572$	3.61803	+	6.26662i	0.151278	+	0.262020i
$573$	−3.47214			−0.145051
$574$	1.54508	+	0.535233i	0.0644906	+	0.0223402i
$575$	−18.8328			−0.785383
$576$	−0.236068	−	0.408882i	−0.00983617	−	0.0170367i
$577$	−17.7705	+	30.7794i	−0.739796	+	1.28136i	0.212791	+	0.977098i	$0.431745\pi$
$577$	−17.7705	+	30.7794i	−0.739796	+	1.28136i	−0.952587	+	0.304267i	$0.901589\pi$
$578$	−5.23607	+	9.06914i	−0.217792	+	0.377226i
$579$	−11.5902	−	20.0748i	−0.481671	−	0.834279i
$580$	−7.23607			−0.300461
$581$	20.9443	−	18.1383i	0.868915	−	0.752502i
$582$	0.291796			0.0120953
$583$	2.88197	+	4.99171i	0.119359	+	0.206736i
$584$	12.8262	−	22.2157i	0.530754	−	0.919292i
$585$	−4.47214	+	7.74597i	−0.184900	+	0.320256i
$586$	−7.67376	−	13.2913i	−0.317000	−	0.549060i
$587$	−16.0000			−0.660391			−0.330195	−	0.943913i	$-0.607115\pi$
$587$	−16.0000			−0.660391			−0.330195	+	0.943913i	$0.607115\pi$
$588$	10.5172	−	4.20378i	0.433723	−	0.173361i
$589$	−31.6525			−1.30422
$590$	1.45492	+	2.51999i	0.0598979	+	0.103746i
$591$	−7.47214	+	12.9421i	−0.307363	+	0.532368i
$592$	−5.07295	+	8.78661i	−0.208497	+	0.361127i
$593$	6.11803	+	10.5967i	0.251238	+	0.435156i	0.963867	−	0.266385i	$-0.0858291\pi$
$593$	6.11803	+	10.5967i	0.251238	+	0.435156i	−0.712629	+	0.701541i	$0.752496\pi$
$594$	3.09017			0.126791
$595$	−0.472136	+	0.408882i	−0.0193557	+	0.0167625i
$596$	34.2705			1.40377
$597$	−0.0278640	−	0.0482619i	−0.00114040	−	0.00197523i
$598$	6.50658	−	11.2697i	0.266074	−	0.460853i
$599$	−11.0623	+	19.1605i	−0.451994	+	0.782876i	−0.998510	−	0.0545727i	$-0.982620\pi$
$599$	−11.0623	+	19.1605i	−0.451994	+	0.782876i	0.546516	+	0.837449i	$0.315954\pi$
$600$	4.47214	+	7.74597i	0.182574	+	0.316228i
$601$	−8.47214			−0.345586			−0.172793	−	0.984958i	$-0.555279\pi$
$601$	−8.47214			−0.345586			−0.172793	+	0.984958i	$0.555279\pi$
$602$	−3.81966	−	1.32317i	−0.155678	−	0.0539283i
$603$	23.8885			0.972817
$604$	−9.66312	−	16.7370i	−0.393187	−	0.681019i
$605$	−5.00000	+	8.66025i	−0.203279	+	0.352089i
$606$	5.16312	−	8.94278i	0.209737	−	0.363276i
$607$	−3.40983	−	5.90600i	−0.138401	−	0.239717i	0.788491	−	0.615047i	$-0.210863\pi$
$607$	−3.40983	−	5.90600i	−0.138401	−	0.239717i	−0.926891	+	0.375330i	$0.877530\pi$
$608$	41.9787			1.70246
$609$	2.23607	+	11.6190i	0.0906100	+	0.470824i
$610$	0.326238			0.0132090
$611$	−12.2361	−	21.1935i	−0.495018	−	0.857397i
$612$	0.381966	−	0.661585i	0.0154401	−	0.0267430i
$613$	−4.55573	+	7.89075i	−0.184004	+	0.318704i	−0.943240	−	0.332110i	$-0.892239\pi$
$613$	−4.55573	+	7.89075i	−0.184004	+	0.318704i	0.759236	+	0.650815i	$0.225573\pi$
$614$	8.00000	+	13.8564i	0.322854	+	0.559199i
$615$	1.00000			0.0403239
$616$	−1.11803	−	5.80948i	−0.0450469	−	0.234070i
$617$	−1.41641			−0.0570224			−0.0285112	−	0.999593i	$-0.509077\pi$
$617$	−1.41641			−0.0570224			−0.0285112	+	0.999593i	$0.509077\pi$
$618$	−1.60081	−	2.77269i	−0.0643941	−	0.111534i
$619$	13.1180	−	22.7211i	0.527258	−	0.913238i	−0.472237	−	0.881472i	$-0.656553\pi$
$619$	13.1180	−	22.7211i	0.527258	−	0.913238i	0.999495	−	0.0317666i	$-0.0101133\pi$
$620$	−3.42705	+	5.93583i	−0.137634	+	0.238389i
$621$	11.7705	+	20.3871i	0.472334	+	0.818107i
$622$	−19.6738			−0.788846
$623$	−24.4098	−	8.45581i	−0.977959	−	0.338775i
$624$	8.29180			0.331937
$625$	−5.50000	−	9.52628i	−0.220000	−	0.381051i
$626$	−9.48936	+	16.4360i	−0.379271	+	0.656917i
$627$	3.73607	−	6.47106i	0.149204	−	0.258429i
$628$	1.80902	+	3.13331i	0.0721876	+	0.125033i
$629$	−1.29180			−0.0515073
$630$	2.47214	−	2.14093i	0.0984923	−	0.0852968i
$631$	−32.0000			−1.27390			−0.636950	−	0.770905i	$-0.719804\pi$
$631$	−32.0000			−1.27390			−0.636950	+	0.770905i	$0.719804\pi$
$632$	1.11803	+	1.93649i	0.0444730	+	0.0770295i
$633$		0			0
$634$	9.34346	−	16.1833i	0.371076	−	0.642723i
$635$	−5.70820	−	9.88690i	−0.226523	−	0.392350i
$636$	9.32624			0.369809
$637$	4.47214	−	30.9839i	0.177192	−	1.22763i
$638$	2.76393			0.109425
$639$	−5.52786	−	9.57454i	−0.218679	−	0.378763i
$640$	5.69098	−	9.85707i	0.224956	−	0.389635i
$641$	−19.8820	+	34.4366i	−0.785290	+	1.36016i	0.143535	+	0.989645i	$0.454153\pi$
$641$	−19.8820	+	34.4366i	−0.785290	+	1.36016i	−0.928825	+	0.370518i	$0.879180\pi$
$642$	−4.54508	−	7.87232i	−0.179380	−	0.310696i
$643$	−43.7771			−1.72640			−0.863200	−	0.504862i	$-0.831543\pi$
$643$	−43.7771			−1.72640			−0.863200	+	0.504862i	$0.831543\pi$
$644$	15.2361	−	13.1948i	0.600385	−	0.519949i
$645$	−2.47214			−0.0973403
$646$	0.545085	+	0.944115i	0.0214461	+	0.0371457i
$647$	11.1180	−	19.2570i	0.437095	−	0.757071i	−0.560369	−	0.828243i	$-0.689341\pi$
$647$	11.1180	−	19.2570i	0.437095	−	0.757071i	0.997464	+	0.0711723i	$0.0226740\pi$
$648$	−1.11803	+	1.93649i	−0.0439205	+	0.0760726i
$649$	2.35410	+	4.07742i	0.0924066	+	0.160053i
$650$	11.0557			0.433641
$651$	10.5902	+	3.66854i	0.415061	+	0.143782i
$652$	30.2705			1.18548
$653$	−22.5344	−	39.0308i	−0.881841	−	1.52739i	−0.849292	−	0.527923i	$-0.822971\pi$
$653$	−22.5344	−	39.0308i	−0.881841	−	1.52739i	−0.0325486	−	0.999470i	$-0.510362\pi$
$654$	−3.01722	+	5.22598i	−0.117983	+	0.204352i
$655$	8.82624	−	15.2875i	0.344870	−	0.597332i
$656$	0.927051	+	1.60570i	0.0361953	+	0.0626920i
$657$	22.9443			0.895141
$658$	1.69098	+	8.78661i	0.0659214	+	0.342538i
$659$	−7.05573			−0.274852			−0.137426	−	0.990512i	$-0.543883\pi$
$659$	−7.05573			−0.274852			−0.137426	+	0.990512i	$0.543883\pi$
$660$	−0.809017	−	1.40126i	−0.0314909	−	0.0545439i
$661$	−23.6803	+	41.0156i	−0.921058	+	1.59532i	−0.123278	+	0.992372i	$0.539341\pi$
$661$	−23.6803	+	41.0156i	−0.921058	+	1.59532i	−0.797781	+	0.602948i	$0.793993\pi$
$662$	6.74671	−	11.6856i	0.262218	−	0.454176i
$663$	0.527864	+	0.914287i	0.0205005	+	0.0355080i
$664$	−23.4164			−0.908733
$665$	−3.73607	−	19.4132i	−0.144879	−	0.752811i
$666$	6.76393			0.262097
$667$	10.5279	+	18.2348i	0.407641	+	0.706054i
$668$	5.23607	−	9.06914i	0.202590	−	0.350895i
$669$	−0.472136	+	0.817763i	−0.0182538	+	0.0316166i
$670$	3.69098	+	6.39297i	0.142595	+	0.246982i
$671$	0.527864			0.0203780
$672$	−14.0451	−	4.86536i	−0.541801	−	0.187685i
$673$	−18.5836			−0.716345			−0.358172	−	0.933655i	$-0.616600\pi$
$673$	−18.5836			−0.716345			−0.358172	+	0.933655i	$0.616600\pi$
$674$	0.145898	+	0.252703i	0.00561978	+	0.00973375i
$675$	−10.0000	+	17.3205i	−0.384900	+	0.666667i
$676$	5.66312	−	9.80881i	0.217812	−	0.377262i
$677$	0.972136	+	1.68379i	0.0373622	+	0.0647133i	0.884102	−	0.467294i	$-0.154771\pi$
$677$	0.972136	+	1.68379i	0.0373622	+	0.0647133i	−0.846740	+	0.532008i	$0.821438\pi$
$678$	9.81966			0.377122
$679$	0.944272	−	0.817763i	0.0362378	−	0.0313829i
$680$	0.527864			0.0202427
$681$	−1.73607	−	3.00696i	−0.0665263	−	0.115227i
$682$	1.30902	−	2.26728i	0.0501249	−	0.0868188i
$683$	−3.26393	+	5.65330i	−0.124891	+	0.216317i	−0.921690	−	0.387927i	$-0.873191\pi$
$683$	−3.26393	+	5.65330i	−0.124891	+	0.216317i	0.796799	+	0.604244i	$0.206525\pi$
$684$	12.0902	+	20.9408i	0.462279	+	0.800691i
$685$	15.6525			0.598050
$686$	−5.25329	+	10.1694i	−0.200572	+	0.388271i
$687$	20.1246			0.767802
$688$	−2.29180	−	3.96951i	−0.0873739	−	0.151336i
$689$	12.8885	−	22.3236i	0.491014	−	0.850462i
$690$	−1.45492	+	2.51999i	−0.0553877	+	0.0959343i
$691$	−1.31966	−	2.28572i	−0.0502022	−	0.0869528i	0.839832	−	0.542846i	$-0.182653\pi$
$691$	−1.31966	−	2.28572i	−0.0502022	−	0.0869528i	−0.890035	+	0.455893i	$0.849320\pi$
$692$	−27.3262			−1.03879
$693$	4.00000	−	3.46410i	0.151947	−	0.131590i
$694$	1.85410			0.0703807
$695$	−0.472136	−	0.817763i	−0.0179091	−	0.0310195i
$696$	5.00000	−	8.66025i	0.189525	−	0.328266i
$697$	−0.118034	+	0.204441i	−0.00447086	+	0.00774375i
$698$	−3.56231	−	6.17009i	−0.134835	−	0.233542i
$699$	16.7082			0.631962
$700$	16.1803	+	5.60503i	0.611559	+	0.211850i
$701$	2.36068			0.0891616			0.0445808	−	0.999006i	$-0.485805\pi$
$701$	2.36068			0.0891616			0.0445808	+	0.999006i	$0.485805\pi$
$702$	−6.90983	−	11.9682i	−0.260795	−	0.451710i
$703$	20.4443	−	35.4105i	0.771070	−	1.33553i
$704$	0.118034	−	0.204441i	0.00444857	−	0.00770516i
$705$	2.73607	+	4.73901i	0.103046	+	0.178481i
$706$	−10.2148			−0.384438
$707$	−8.35410	−	43.4092i	−0.314188	−	1.63257i
$708$	7.61803			0.286303
$709$	1.06231	+	1.83997i	0.0398957	+	0.0691014i	0.885284	−	0.465051i	$-0.153964\pi$
$709$	1.06231	+	1.83997i	0.0398957	+	0.0691014i	−0.845388	+	0.534153i	$0.820631\pi$
$710$	1.70820	−	2.95870i	0.0641078	−	0.111038i
$711$	−1.00000	+	1.73205i	−0.0375029	+	0.0649570i
$712$	10.9164	+	18.9078i	0.409110	+	0.708599i
$713$	19.9443			0.746919
$714$	−0.0729490	−	0.379054i	−0.00273005	−	0.0141857i
$715$	−4.47214			−0.167248
$716$	13.2812	+	23.0036i	0.496340	+	0.859686i
$717$	−3.23607	+	5.60503i	−0.120853	+	0.209324i
$718$	5.45492	−	9.44819i	0.203576	−	0.352603i
$719$	−21.6803	−	37.5515i	−0.808540	−	1.40043i	−0.913875	−	0.405996i	$-0.866925\pi$
$719$	−21.6803	−	37.5515i	−0.808540	−	1.40043i	0.105335	−	0.994437i	$-0.466409\pi$
$720$	3.70820			0.138197
$721$	−12.9508	−	4.48631i	−0.482315	−	0.167079i
$722$	−22.7639			−0.847186
$723$	3.73607	+	6.47106i	0.138946	+	0.240661i
$724$	4.38197	−	7.58979i	0.162854	−	0.282072i
$725$	−8.94427	+	15.4919i	−0.332182	+	0.575356i
$726$	−3.09017	−	5.35233i	−0.114687	−	0.198644i
$727$	24.9443			0.925132			0.462566	−	0.886585i	$-0.346929\pi$
$727$	24.9443			0.925132			0.462566	+	0.886585i	$0.346929\pi$
$728$	−20.0000	+	17.3205i	−0.741249	+	0.641941i
$729$	13.0000			0.481481
$730$	3.54508	+	6.14027i	0.131209	+	0.227261i
$731$	0.291796	−	0.505406i	0.0107925	−	0.0186931i
$732$	0.427051	−	0.739674i	0.0157843	−	0.0273391i
$733$	17.9164	+	31.0321i	0.661758	+	1.14620i	0.980154	+	0.198240i	$0.0635225\pi$
$733$	17.9164	+	31.0321i	0.661758	+	1.14620i	−0.318396	+	0.947958i	$0.603144\pi$
$734$	−10.6180			−0.391919
$735$	−1.00000	+	6.92820i	−0.0368856	+	0.255551i
$736$	−26.4508			−0.974991
$737$	5.97214	+	10.3440i	0.219986	+	0.381028i
$738$	0.618034	−	1.07047i	0.0227501	−	0.0394044i
$739$	6.17376	−	10.6933i	0.227106	−	0.393358i	−0.729844	−	0.683614i	$-0.760407\pi$
$739$	6.17376	−	10.6933i	0.227106	−	0.393358i	0.956949	+	0.290256i	$0.0937404\pi$
$740$	−4.42705	−	7.66788i	−0.162742	−	0.281877i
$741$	−33.4164			−1.22758
$742$	−7.12461	+	6.17009i	−0.261553	+	0.226511i
$743$	44.7214			1.64067			0.820334	−	0.571885i	$-0.193788\pi$
$743$	44.7214			1.64067			0.820334	+	0.571885i	$0.193788\pi$
$744$	−4.73607	−	8.20311i	−0.173633	−	0.300741i
$745$	−10.5902	+	18.3427i	−0.387994	+	0.672025i
$746$	−5.54508	+	9.60437i	−0.203020	+	0.351641i
$747$	−10.4721	−	18.1383i	−0.383155	−	0.663645i
$748$	0.381966			0.0139661
$749$	−36.7705	−	12.7377i	−1.34357	−	0.465425i
$750$	−5.56231			−0.203107
$751$	15.7361	+	27.2557i	0.574217	+	0.994573i	0.996126	+	0.0879353i	$0.0280269\pi$
$751$	15.7361	+	27.2557i	0.574217	+	0.994573i	−0.421909	+	0.906638i	$0.638640\pi$
$752$	−5.07295	+	8.78661i	−0.184991	+	0.320415i
$753$	13.4164	−	23.2379i	0.488921	−	0.846836i
$754$	−6.18034	−	10.7047i	−0.225075	−	0.389841i
$755$	11.9443			0.434697
$756$	−4.04508	−	21.0189i	−0.147118	−	0.764449i
$757$	14.9443			0.543159			0.271579	−	0.962416i	$-0.412454\pi$
$757$	14.9443			0.543159			0.271579	+	0.962416i	$0.412454\pi$
$758$	1.41641	+	2.45329i	0.0514463	+	0.0891075i
$759$	−2.35410	+	4.07742i	−0.0854485	+	0.148001i
$760$	−8.35410	+	14.4697i	−0.303035	+	0.524872i
$761$	23.1525	+	40.1013i	0.839277	+	1.45367i	0.890500	+	0.454983i	$0.150354\pi$
$761$	23.1525	+	40.1013i	0.839277	+	1.45367i	−0.0512238	+	0.998687i	$0.516312\pi$
$762$	7.05573			0.255602
$763$	4.88197	+	25.3674i	0.176739	+	0.918363i
$764$	5.61803			0.203253
$765$	0.236068	+	0.408882i	0.00853506	+	0.0147832i
$766$	−4.60081	+	7.96884i	−0.166234	+	0.287926i
$767$	10.5279	−	18.2348i	0.380139	−	0.658420i
$768$	3.28115	+	5.68312i	0.118398	+	0.205072i
$769$	36.8328			1.32823			0.664113	−	0.747633i	$-0.268810\pi$
$769$	36.8328			1.32823			0.664113	+	0.747633i	$0.268810\pi$
$770$	1.54508	+	0.535233i	0.0556810	+	0.0192885i
$771$	−14.7082			−0.529703
$772$	18.7533	+	32.4816i	0.674946	+	1.16904i
$773$	−10.8262	+	18.7516i	−0.389393	+	0.674448i	−0.992368	−	0.123312i	$-0.960648\pi$
$773$	−10.8262	+	18.7516i	−0.389393	+	0.674448i	0.602975	+	0.797760i	$0.293982\pi$
$774$	−1.52786	+	2.64634i	−0.0549179	+	0.0951207i
$775$	8.47214	+	14.6742i	0.304328	+	0.527112i
$776$	−1.05573			−0.0378984
$777$	−10.9443	+	9.47802i	−0.392624	+	0.340022i
$778$	0.618034			0.0221576
$779$	−3.73607	−	6.47106i	−0.133859	−	0.231850i
$780$	−3.61803	+	6.26662i	−0.129546	+	0.224381i
$781$	2.76393	−	4.78727i	0.0989013	−	0.171302i
$782$	−0.343459	−	0.594888i	−0.0122821	−	0.0212732i
$783$	22.3607			0.799106
$784$	−12.0517	+	4.81710i	−0.430417	+	0.172039i
$785$	−2.23607			−0.0798087
$786$	5.45492	+	9.44819i	0.194570	+	0.337006i
$787$	10.8262	−	18.7516i	0.385914	−	0.668422i	−0.605982	−	0.795479i	$-0.707220\pi$
$787$	10.8262	−	18.7516i	0.385914	−	0.668422i	0.991895	+	0.127056i	$0.0405529\pi$
$788$	12.0902	−	20.9408i	0.430694	−	0.745985i
$789$	0.736068	+	1.27491i	0.0262047	+	0.0453879i
$790$	−0.618034			−0.0219887
$791$	31.7771	−	27.5198i	1.12986	−	0.978490i
$792$	−4.47214			−0.158910
$793$	−1.18034	−	2.04441i	−0.0419151	−	0.0725991i
$794$	−1.12868	+	1.95493i	−0.0400553	+	0.0693777i
$795$	−2.88197	+	4.99171i	−0.102213	+	0.177038i
$796$	0.0450850	+	0.0780895i	0.00159799	+	0.00276781i
$797$	−28.8328			−1.02131			−0.510655	−	0.859785i	$-0.670597\pi$
$797$	−28.8328			−1.02131			−0.510655	+	0.859785i	$0.670597\pi$
$798$	11.5451	+	3.99933i	0.408692	+	0.141575i
$799$	−1.29180			−0.0457005
$800$	−11.2361	−	19.4614i	−0.397255	−	0.688066i
$801$	−9.76393	+	16.9116i	−0.344992	+	0.597543i
$802$	−3.07295	+	5.32250i	−0.108510	+	0.187944i
$803$	5.73607	+	9.93516i	0.202421	+	0.350604i
$804$	19.3262			0.681584
$805$	2.35410	+	12.2323i	0.0829712	+	0.431131i
$806$	−11.7082			−0.412404
$807$	5.26393	+	9.11740i	0.185299	+	0.320948i
$808$	−18.6803	+	32.3553i	−0.657172	+	1.13826i
$809$	−12.8262	+	22.2157i	−0.450947	+	0.781062i	−0.998445	−	0.0557444i	$-0.982247\pi$
$809$	−12.8262	+	22.2157i	−0.450947	+	0.781062i	0.547499	+	0.836807i	$0.315580\pi$
$810$	−0.309017	−	0.535233i	−0.0108578	−	0.0188062i
$811$	−36.7214			−1.28946			−0.644731	−	0.764410i	$-0.723030\pi$
$811$	−36.7214			−1.28946			−0.644731	+	0.764410i	$0.723030\pi$
$812$	−3.61803	−	18.7999i	−0.126968	−	0.659746i
$813$	9.65248			0.338527
$814$	1.69098	+	2.92887i	0.0592689	+	0.102657i
$815$	−9.35410	+	16.2018i	−0.327660	+	0.567524i
$816$	0.218847	−	0.379054i	0.00766118	−	0.0132696i
$817$	9.23607	+	15.9973i	0.323129	+	0.559676i
$818$	−7.96556			−0.278509
$819$	−22.3607	−	7.74597i	−0.781345	−	0.270666i
$820$	−1.61803			−0.0565042
$821$	10.5000	+	18.1865i	0.366453	+	0.634714i	0.989008	−	0.147861i	$-0.0472389\pi$
$821$	10.5000	+	18.1865i	0.366453	+	0.634714i	−0.622556	+	0.782576i	$0.713906\pi$
$822$	−4.83688	+	8.37772i	−0.168706	+	0.292207i
$823$	2.26393	−	3.92125i	0.0789157	−	0.136686i	−0.823867	−	0.566784i	$-0.808188\pi$
$823$	2.26393	−	3.92125i	0.0789157	−	0.136686i	0.902782	+	0.430098i	$0.141521\pi$
$824$	5.79180	+	10.0317i	0.201767	+	0.349470i
$825$	−4.00000			−0.139262
$826$	−5.81966	+	5.03997i	−0.202492	+	0.175363i
$827$	36.0000			1.25184			0.625921	−	0.779886i	$-0.284723\pi$
$827$	36.0000			1.25184			0.625921	+	0.779886i	$0.284723\pi$
$828$	−7.61803	−	13.1948i	−0.264745	−	0.458552i
$829$	6.97214	−	12.0761i	0.242152	−	0.419420i	−0.719175	−	0.694829i	$-0.755480\pi$
$829$	6.97214	−	12.0761i	0.242152	−	0.419420i	0.961327	+	0.275409i	$0.0888133\pi$
$830$	3.23607	−	5.60503i	0.112326	−	0.194554i
$831$	10.9721	+	19.0043i	0.380619	+	0.659252i
$832$	−1.05573			−0.0366008
$833$	−1.29837	−	1.02220i	−0.0449860	−	0.0354173i
$834$	0.583592			0.0202081
$835$	3.23607	+	5.60503i	0.111989	+	0.193970i
$836$	−6.04508	+	10.4704i	−0.209074	+	0.362126i
$837$	10.5902	−	18.3427i	0.366050	−	0.634017i
$838$	5.52786	+	9.57454i	0.190957	+	0.330747i
$839$	3.05573			0.105495			0.0527477	−	0.998608i	$-0.483202\pi$
$839$	3.05573			0.105495			0.0527477	+	0.998608i	$0.483202\pi$
$840$	4.47214	−	3.87298i	0.154303	−	0.133631i
$841$	−9.00000			−0.310345
$842$	−2.32624	−	4.02916i	−0.0801675	−	0.138854i
$843$	−2.23607	+	3.87298i	−0.0770143	+	0.133393i
$844$		0			0
$845$	3.50000	+	6.06218i	0.120404	+	0.208545i
$846$	6.76393			0.232549
$847$	−25.0000	−	8.66025i	−0.859010	−	0.297570i
$848$	−10.6869			−0.366990
$849$	5.59017	+	9.68246i	0.191854	+	0.332301i
$850$	0.291796	−	0.505406i	0.0100085	−	0.0173353i
$851$	−12.8820	+	22.3122i	−0.441588	+	0.764853i
$852$	−4.47214	−	7.74597i	−0.153213	−	0.265372i
$853$	1.05573			0.0361474			0.0180737	−	0.999837i	$-0.494247\pi$
$853$	1.05573			0.0361474			0.0180737	+	0.999837i	$0.494247\pi$
$854$	0.163119	+	0.847591i	0.00558182	+	0.0290040i
$855$	−14.9443			−0.511083
$856$	16.4443	+	28.4823i	0.562054	+	0.973505i
$857$	−26.1525	+	45.2974i	−0.893352	+	1.54733i	−0.0575200	+	0.998344i	$0.518319\pi$
$857$	−26.1525	+	45.2974i	−0.893352	+	1.54733i	−0.835832	+	0.548986i	$0.815014\pi$
$858$	1.38197	−	2.39364i	0.0471795	−	0.0817174i
$859$	21.3541	+	36.9864i	0.728593	+	1.26196i	0.957478	+	0.288506i	$0.0931585\pi$
$859$	21.3541	+	36.9864i	0.728593	+	1.26196i	−0.228886	+	0.973453i	$0.573508\pi$
$860$	4.00000			0.136399
$861$	0.500000	+	2.59808i	0.0170400	+	0.0885422i
$862$	20.7984			0.708395
$863$	−11.5902	−	20.0748i	−0.394534	−	0.683353i	0.598508	−	0.801117i	$-0.295761\pi$
$863$	−11.5902	−	20.0748i	−0.394534	−	0.683353i	−0.993042	+	0.117764i	$0.962427\pi$
$864$	−14.0451	+	24.3268i	−0.477823	+	0.827615i
$865$	8.44427	−	14.6259i	0.287114	−	0.497296i
$866$	−3.38197	−	5.85774i	−0.114924	−	0.199054i
$867$	−16.9443			−0.575458
$868$	−17.1353	−	5.93583i	−0.581608	−	0.201475i
$869$	−1.00000			−0.0339227
$870$	1.38197	+	2.39364i	0.0468530	+	0.0811518i
$871$	26.7082	−	46.2600i	0.904973	−	1.56746i
$872$	10.9164	−	18.9078i	0.369676	−	0.640298i
$873$	−0.472136	−	0.817763i	−0.0159794	−	0.0276771i
$874$	21.7426			0.735456
$875$	−18.0000	+	15.5885i	−0.608511	+	0.526986i
$876$	18.5623			0.627162
$877$	3.73607	+	6.47106i	0.126158	+	0.218512i	0.922185	−	0.386749i	$-0.126402\pi$
$877$	3.73607	+	6.47106i	0.126158	+	0.218512i	−0.796027	+	0.605261i	$0.793069\pi$
$878$	−2.96149	+	5.12946i	−0.0999455	+	0.173111i
$879$	12.4164	−	21.5058i	0.418795	−	0.725374i
$880$	0.927051	+	1.60570i	0.0312509	+	0.0541281i
$881$	15.5279			0.523147			0.261574	−	0.965184i	$-0.415759\pi$
$881$	15.5279			0.523147			0.261574	+	0.965184i	$0.415759\pi$
$882$	6.79837	+	5.35233i	0.228913	+	0.180222i
$883$	−43.4164			−1.46108			−0.730539	−	0.682871i	$-0.760731\pi$
$883$	−43.4164			−1.46108			−0.730539	+	0.682871i	$0.760731\pi$
$884$	−0.854102	−	1.47935i	−0.0287266	−	0.0497559i
$885$	−2.35410	+	4.07742i	−0.0791323	+	0.137061i
$886$	−3.78115	+	6.54915i	−0.127030	+	0.220023i
$887$	5.55573	+	9.62280i	0.186543	+	0.323102i	0.944095	−	0.329672i	$-0.106938\pi$
$887$	5.55573	+	9.62280i	0.186543	+	0.323102i	−0.757552	+	0.652774i	$0.773605\pi$
$888$	12.2361			0.410616
$889$	22.8328	−	19.7738i	0.765788	−	0.663192i
$890$	−6.03444			−0.202275
$891$	−0.500000	−	0.866025i	−0.0167506	−	0.0290129i
$892$	0.763932	−	1.32317i	0.0255783	−	0.0443030i
$893$	20.4443	−	35.4105i	0.684141	−	1.18497i
$894$	−6.54508	−	11.3364i	−0.218900	−	0.379147i
$895$	−16.4164			−0.548740
$896$	28.4549	+	9.85707i	0.950612	+	0.329302i
$897$	21.0557			0.703030
$898$	12.0344	+	20.8443i	0.401595	+	0.695582i
$899$	9.47214	−	16.4062i	0.315913	−	0.547178i
$900$	6.47214	−	11.2101i	0.215738	−	0.373669i
$901$	−0.680340	−	1.17838i	−0.0226654	−	0.0392576i
$902$	0.618034			0.0205783
$903$	−1.23607	−	6.42280i	−0.0411338	−	0.213737i
$904$	−35.5279			−1.18164
$905$	2.70820	+	4.69075i	0.0900237	+	0.155926i
$906$	−3.69098	+	6.39297i	−0.122625	+	0.212392i
$907$	22.8262	−	39.5362i	0.757933	−	1.31278i	−0.185970	−	0.982555i	$-0.559543\pi$
$907$	22.8262	−	39.5362i	0.757933	−	1.31278i	0.943903	−	0.330223i	$-0.107124\pi$
$908$	2.80902	+	4.86536i	0.0932205	+	0.161463i
$909$	−33.4164			−1.10835
$910$	−1.38197	−	7.18091i	−0.0458117	−	0.238045i
$911$	−20.5836			−0.681965			−0.340982	−	0.940070i	$-0.610760\pi$
$911$	−20.5836			−0.681965			−0.340982	+	0.940070i	$0.610760\pi$
$912$	6.92705	+	11.9980i	0.229378	+	0.397294i
$913$	5.23607	−	9.06914i	0.173289	−	0.300145i
$914$	−6.72542	+	11.6488i	−0.222457	+	0.385307i
$915$	0.263932	+	0.457144i	0.00872532	+	0.0151127i
$916$	−32.5623			−1.07589
$917$	44.1312	+	15.2875i	1.45734	+	0.504837i
$918$	−0.729490			−0.0240768
$919$	10.9721	+	19.0043i	0.361937	+	0.626894i	0.988280	−	0.152654i	$-0.0487821\pi$
$919$	10.9721	+	19.0043i	0.361937	+	0.626894i	−0.626342	+	0.779548i	$0.715449\pi$
$920$	5.26393	−	9.11740i	0.173547	−	0.300592i
$921$	−12.9443	+	22.4201i	−0.426528	+	0.738769i
$922$	−6.50658	−	11.2697i	−0.214283	−	0.371149i
$923$	−24.7214			−0.813713
$924$	3.23607	−	2.80252i	0.106459	−	0.0921960i
$925$	−21.8885			−0.719691
$926$	−11.7082	−	20.2792i	−0.384755	−	0.666416i
$927$	−5.18034	+	8.97261i	−0.170145	+	0.294699i
$928$	−12.5623	+	21.7586i	−0.412378	+	0.714259i
$929$	−13.7705	−	23.8512i	−0.451796	−	0.782533i	0.546702	−	0.837327i	$-0.315883\pi$
$929$	−13.7705	−	23.8512i	−0.451796	−	0.782533i	−0.998498	+	0.0547941i	$0.982550\pi$
$930$	2.61803			0.0858487
$931$	48.5689	−	19.4132i	1.59178	−	0.636241i
$932$	−27.0344			−0.885543
$933$	−15.9164	−	27.5680i	−0.521080	−	0.902537i
$934$	9.63525	−	16.6888i	0.315275	−	0.546073i
$935$	−0.118034	+	0.204441i	−0.00386012	+	0.00668593i
$936$	10.0000	+	17.3205i	0.326860	+	0.566139i
$937$	2.58359			0.0844023			0.0422011	−	0.999109i	$-0.486563\pi$
$937$	2.58359			0.0844023			0.0422011	+	0.999109i	$0.486563\pi$
$938$	−14.7639	+	12.7859i	−0.482059	+	0.417476i
$939$	−30.7082			−1.00212
$940$	−4.42705	−	7.66788i	−0.144394	−	0.250099i
$941$	−3.79180	+	6.56758i	−0.123609	+	0.214097i	−0.921188	−	0.389117i	$-0.872780\pi$
$941$	−3.79180	+	6.56758i	−0.123609	+	0.214097i	0.797579	+	0.603214i	$0.206114\pi$
$942$	0.690983	−	1.19682i	0.0225134	−	0.0389944i
$943$	2.35410	+	4.07742i	0.0766601	+	0.132779i
$944$	−8.72949			−0.284121
$945$	12.5000	+	4.33013i	0.406625	+	0.140859i
$946$	−1.52786			−0.0496751
$947$	−8.64590	−	14.9751i	−0.280954	−	0.486626i	0.690666	−	0.723174i	$-0.257317\pi$
$947$	−8.64590	−	14.9751i	−0.280954	−	0.486626i	−0.971620	+	0.236547i	$0.923984\pi$
$948$	−0.809017	+	1.40126i	−0.0262757	+	0.0455108i
$949$	25.6525	−	44.4314i	0.832715	−	1.44230i
$950$	9.23607	+	15.9973i	0.299658	+	0.519022i
$951$	30.2361			0.980472
$952$	0.263932	+	1.37143i	0.00855409	+	0.0444483i
$953$	8.11146			0.262756			0.131378	−	0.991332i	$-0.458060\pi$
$953$	8.11146			0.262756			0.131378	+	0.991332i	$0.458060\pi$
$954$	3.56231	+	6.17009i	0.115334	+	0.199764i
$955$	−1.73607	+	3.00696i	−0.0561778	+	0.0973029i
$956$	5.23607	−	9.06914i	0.169347	−	0.293317i
$957$	2.23607	+	3.87298i	0.0722818	+	0.125196i
$958$	−12.9787			−0.419323
$959$	7.82624	+	40.6663i	0.252722	+	1.31318i
$960$	0.236068			0.00761906
$961$	6.52786	+	11.3066i	0.210576	+	0.364729i
$962$	7.56231	−	13.0983i	0.243819	−	0.422306i
$963$	−14.7082	+	25.4754i	−0.473965	+	0.820932i
$964$	−6.04508	−	10.4704i	−0.194699	−	0.337229i
$965$	−23.1803			−0.746202
$966$	−7.27458	−	2.51999i	−0.234056	−	0.0810792i
$967$	−41.3050			−1.32828			−0.664139	−	0.747609i	$-0.731202\pi$
$967$	−41.3050			−1.32828			−0.664139	+	0.747609i	$0.731202\pi$
$968$	11.1803	+	19.3649i	0.359350	+	0.622412i
$969$	−0.881966	+	1.52761i	−0.0283328	+	0.0490739i
$970$	0.145898	−	0.252703i	0.00468450	−	0.00811380i
$971$	12.3885	+	21.4576i	0.397567	+	0.688607i	0.993425	−	0.114483i	$-0.0365212\pi$
$971$	12.3885	+	21.4576i	0.397567	+	0.688607i	−0.595858	+	0.803090i	$0.703188\pi$
$972$	−25.8885			−0.830375
$973$	1.88854	−	1.63553i	0.0605439	−	0.0524326i
$974$	−25.6738			−0.822640
$975$	8.94427	+	15.4919i	0.286446	+	0.496139i
$976$	−0.489357	+	0.847591i	−0.0156639	+	0.0271307i
$977$	3.82624	−	6.62724i	0.122412	−	0.212024i	−0.798306	−	0.602252i	$-0.794270\pi$
$977$	3.82624	−	6.62724i	0.122412	−	0.212024i	0.920718	+	0.390228i	$0.127604\pi$
$978$	−5.78115	−	10.0133i	−0.184861	−	0.320188i
$979$	−9.76393			−0.312057
$980$	1.61803	−	11.2101i	0.0516862	−	0.358092i
$981$	19.5279			0.623477
$982$	10.0000	+	17.3205i	0.319113	+	0.552720i
$983$	4.93769	−	8.55234i	0.157488	−	0.272777i	−0.776474	−	0.630149i	$-0.782994\pi$
$983$	4.93769	−	8.55234i	0.157488	−	0.272777i	0.933962	+	0.357372i	$0.116327\pi$
$984$	1.11803	−	1.93649i	0.0356416	−	0.0617331i
$985$	7.47214	+	12.9421i	0.238082	+	0.412370i
$986$	−0.652476			−0.0207791
$987$	−10.9443	+	9.47802i	−0.348360	+	0.301689i
$988$	54.0689			1.72016
$989$	−5.81966	−	10.0799i	−0.185054	−	0.320524i
$990$	0.618034	−	1.07047i	0.0196424	−	0.0340217i
$991$	9.79180	−	16.9599i	0.311047	−	0.538749i	−0.667543	−	0.744572i	$-0.732654\pi$
$991$	9.79180	−	16.9599i	0.311047	−	0.538749i	0.978589	+	0.205823i	$0.0659871\pi$
$992$	11.8992	+	20.6100i	0.377800	+	0.654368i
$993$	21.8328			0.692843
$994$	8.54102	+	2.95870i	0.270905	+	0.0938441i
$995$	−0.0557281			−0.00176670
$996$	−8.47214	−	14.6742i	−0.268450	−	0.464969i
$997$	−8.53444	+	14.7821i	−0.270288	+	0.468153i	−0.968936	−	0.247313i	$-0.920452\pi$
$997$	−8.53444	+	14.7821i	−0.270288	+	0.468153i	0.698647	+	0.715466i	$0.253786\pi$
$998$	−10.4894	+	18.1681i	−0.332035	+	0.575101i
$999$	13.6803	+	23.6950i	0.432827	+	0.749678i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	287.2.e.a.165.2	✓	4
7.2	even	3	inner	287.2.e.a.247.2	yes	4
7.3	odd	6		2009.2.a.e.1.1		2
7.4	even	3		2009.2.a.f.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
287.2.e.a.165.2	✓	4	1.1	even	1	trivial
287.2.e.a.247.2	yes	4	7.2	even	3	inner
2009.2.a.e.1.1		2	7.3	odd	6
2009.2.a.f.1.1		2	7.4	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:	\( N \)	\(=\)	\( 287 = 7 \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	287.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.309017 + 0.535233i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(0.809017 - 1.40126i) q^{4} +(0.500000 + 0.866025i) q^{5} -0.618034 q^{6} +(-2.00000 + 1.73205i) q^{7} +2.23607 q^{8} +(1.00000 + 1.73205i) q^{9} +O(q^{10})\)	\(q+(0.309017 + 0.535233i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(0.809017 - 1.40126i) q^{4} +(0.500000 + 0.866025i) q^{5} -0.618034 q^{6} +(-2.00000 + 1.73205i) q^{7} +2.23607 q^{8} +(1.00000 + 1.73205i) q^{9} +(-0.309017 + 0.535233i) q^{10} +(-0.500000 + 0.866025i) q^{11} +(0.809017 + 1.40126i) q^{12} +4.47214 q^{13} +(-1.54508 - 0.535233i) q^{14} -1.00000 q^{15} +(-0.927051 - 1.60570i) q^{16} +(0.118034 - 0.204441i) q^{17} +(-0.618034 + 1.07047i) q^{18} +(3.73607 + 6.47106i) q^{19} +1.61803 q^{20} +(-0.500000 - 2.59808i) q^{21} -0.618034 q^{22} +(-2.35410 - 4.07742i) q^{23} +(-1.11803 + 1.93649i) q^{24} +(2.00000 - 3.46410i) q^{25} +(1.38197 + 2.39364i) q^{26} -5.00000 q^{27} +(0.809017 + 4.20378i) q^{28} -4.47214 q^{29} +(-0.309017 - 0.535233i) q^{30} +(-2.11803 + 3.66854i) q^{31} +(2.80902 - 4.86536i) q^{32} +(-0.500000 - 0.866025i) q^{33} +0.145898 q^{34} +(-2.50000 - 0.866025i) q^{35} +3.23607 q^{36} +(-2.73607 - 4.73901i) q^{37} +(-2.30902 + 3.99933i) q^{38} +(-2.23607 + 3.87298i) q^{39} +(1.11803 + 1.93649i) q^{40} -1.00000 q^{41} +(1.23607 - 1.07047i) q^{42} +2.47214 q^{43} +(0.809017 + 1.40126i) q^{44} +(-1.00000 + 1.73205i) q^{45} +(1.45492 - 2.51999i) q^{46} +(-2.73607 - 4.73901i) q^{47} +1.85410 q^{48} +(1.00000 - 6.92820i) q^{49} +2.47214 q^{50} +(0.118034 + 0.204441i) q^{51} +(3.61803 - 6.26662i) q^{52} +(2.88197 - 4.99171i) q^{53} +(-1.54508 - 2.67617i) q^{54} -1.00000 q^{55} +(-4.47214 + 3.87298i) q^{56} -7.47214 q^{57} +(-1.38197 - 2.39364i) q^{58} +(2.35410 - 4.07742i) q^{59} +(-0.809017 + 1.40126i) q^{60} +(-0.263932 - 0.457144i) q^{61} -2.61803 q^{62} +(-5.00000 - 1.73205i) q^{63} -0.236068 q^{64} +(2.23607 + 3.87298i) q^{65} +(0.309017 - 0.535233i) q^{66} +(5.97214 - 10.3440i) q^{67} +(-0.190983 - 0.330792i) q^{68} +4.70820 q^{69} +(-0.309017 - 1.60570i) q^{70} -5.52786 q^{71} +(2.23607 + 3.87298i) q^{72} +(5.73607 - 9.93516i) q^{73} +(1.69098 - 2.92887i) q^{74} +(2.00000 + 3.46410i) q^{75} +12.0902 q^{76} +(-0.500000 - 2.59808i) q^{77} -2.76393 q^{78} +(0.500000 + 0.866025i) q^{79} +(0.927051 - 1.60570i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(-0.309017 - 0.535233i) q^{82} -10.4721 q^{83} +(-4.04508 - 1.40126i) q^{84} +0.236068 q^{85} +(0.763932 + 1.32317i) q^{86} +(2.23607 - 3.87298i) q^{87} +(-1.11803 + 1.93649i) q^{88} +(4.88197 + 8.45581i) q^{89} -1.23607 q^{90} +(-8.94427 + 7.74597i) q^{91} -7.61803 q^{92} +(-2.11803 - 3.66854i) q^{93} +(1.69098 - 2.92887i) q^{94} +(-3.73607 + 6.47106i) q^{95} +(2.80902 + 4.86536i) q^{96} -0.472136 q^{97} +(4.01722 - 1.60570i) q^{98} -2.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - q^{2} - 2 q^{3} + q^{4} + 2 q^{5} + 2 q^{6} - 8 q^{7} + 4 q^{9}+O(q^{10}) \) 4 * q - q^2 - 2 * q^3 + q^4 + 2 * q^5 + 2 * q^6 - 8 * q^7 + 4 * q^9	\( 4 q - q^{2} - 2 q^{3} + q^{4} + 2 q^{5} + 2 q^{6} - 8 q^{7} + 4 q^{9} + q^{10} - 2 q^{11} + q^{12} + 5 q^{14} - 4 q^{15} + 3 q^{16} - 4 q^{17} + 2 q^{18} + 6 q^{19} + 2 q^{20} - 2 q^{21} + 2 q^{22} + 4 q^{23} + 8 q^{25} + 10 q^{26} - 20 q^{27} + q^{28} + q^{30} - 4 q^{31} + 9 q^{32} - 2 q^{33} + 14 q^{34} - 10 q^{35} + 4 q^{36} - 2 q^{37} - 7 q^{38} - 4 q^{41} - 4 q^{42} - 8 q^{43} + q^{44} - 4 q^{45} + 17 q^{46} - 2 q^{47} - 6 q^{48} + 4 q^{49} - 8 q^{50} - 4 q^{51} + 10 q^{52} + 16 q^{53} + 5 q^{54} - 4 q^{55} - 12 q^{57} - 10 q^{58} - 4 q^{59} - q^{60} - 10 q^{61} - 6 q^{62} - 20 q^{63} + 8 q^{64} - q^{66} + 6 q^{67} - 3 q^{68} - 8 q^{69} + q^{70} - 40 q^{71} + 14 q^{73} + 9 q^{74} + 8 q^{75} + 26 q^{76} - 2 q^{77} - 20 q^{78} + 2 q^{79} - 3 q^{80} - 2 q^{81} + q^{82} - 24 q^{83} - 5 q^{84} - 8 q^{85} + 12 q^{86} + 24 q^{89} + 4 q^{90} - 26 q^{92} - 4 q^{93} + 9 q^{94} - 6 q^{95} + 9 q^{96} + 16 q^{97} - 13 q^{98} - 8 q^{99}+O(q^{100}) \) 4 * q - q^2 - 2 * q^3 + q^4 + 2 * q^5 + 2 * q^6 - 8 * q^7 + 4 * q^9 + q^10 - 2 * q^11 + q^12 + 5 * q^14 - 4 * q^15 + 3 * q^16 - 4 * q^17 + 2 * q^18 + 6 * q^19 + 2 * q^20 - 2 * q^21 + 2 * q^22 + 4 * q^23 + 8 * q^25 + 10 * q^26 - 20 * q^27 + q^28 + q^30 - 4 * q^31 + 9 * q^32 - 2 * q^33 + 14 * q^34 - 10 * q^35 + 4 * q^36 - 2 * q^37 - 7 * q^38 - 4 * q^41 - 4 * q^42 - 8 * q^43 + q^44 - 4 * q^45 + 17 * q^46 - 2 * q^47 - 6 * q^48 + 4 * q^49 - 8 * q^50 - 4 * q^51 + 10 * q^52 + 16 * q^53 + 5 * q^54 - 4 * q^55 - 12 * q^57 - 10 * q^58 - 4 * q^59 - q^60 - 10 * q^61 - 6 * q^62 - 20 * q^63 + 8 * q^64 - q^66 + 6 * q^67 - 3 * q^68 - 8 * q^69 + q^70 - 40 * q^71 + 14 * q^73 + 9 * q^74 + 8 * q^75 + 26 * q^76 - 2 * q^77 - 20 * q^78 + 2 * q^79 - 3 * q^80 - 2 * q^81 + q^82 - 24 * q^83 - 5 * q^84 - 8 * q^85 + 12 * q^86 + 24 * q^89 + 4 * q^90 - 26 * q^92 - 4 * q^93 + 9 * q^94 - 6 * q^95 + 9 * q^96 + 16 * q^97 - 13 * q^98 - 8 * q^99

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