LMFDB - Embedded newform 287.2.e.a.247.1

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			247.1
Root			$0.809017 - 1.40126i$ of defining polynomial
Character	$\chi$	$=$	287.247
Dual form			287.2.e.a.165.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.809017 + 1.40126i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(-0.309017 - 0.535233i) q^{4} +(0.500000 - 0.866025i) q^{5} +1.61803 q^{6} +(-2.00000 - 1.73205i) q^{7} -2.23607 q^{8} +(1.00000 - 1.73205i) q^{9} +O(q^{10})$	\(q+(-0.809017 + 1.40126i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(-0.309017 - 0.535233i) q^{4} +(0.500000 - 0.866025i) q^{5} +1.61803 q^{6} +(-2.00000 - 1.73205i) q^{7} -2.23607 q^{8} +(1.00000 - 1.73205i) q^{9} +(0.809017 + 1.40126i) q^{10} +(-0.500000 - 0.866025i) q^{11} +(-0.309017 + 0.535233i) q^{12} -4.47214 q^{13} +(4.04508 - 1.40126i) q^{14} -1.00000 q^{15} +(2.42705 - 4.20378i) q^{16} +(-2.11803 - 3.66854i) q^{17} +(1.61803 + 2.80252i) q^{18} +(-0.736068 + 1.27491i) q^{19} -0.618034 q^{20} +(-0.500000 + 2.59808i) q^{21} +1.61803 q^{22} +(4.35410 - 7.54153i) q^{23} +(1.11803 + 1.93649i) q^{24} +(2.00000 + 3.46410i) q^{25} +(3.61803 - 6.26662i) q^{26} -5.00000 q^{27} +(-0.309017 + 1.60570i) q^{28} +4.47214 q^{29} +(0.809017 - 1.40126i) q^{30} +(0.118034 + 0.204441i) q^{31} +(1.69098 + 2.92887i) q^{32} +(-0.500000 + 0.866025i) q^{33} +6.85410 q^{34} +(-2.50000 + 0.866025i) q^{35} -1.23607 q^{36} +(1.73607 - 3.00696i) q^{37} +(-1.19098 - 2.06284i) q^{38} +(2.23607 + 3.87298i) q^{39} +(-1.11803 + 1.93649i) q^{40} -1.00000 q^{41} +(-3.23607 - 2.80252i) q^{42} -6.47214 q^{43} +(-0.309017 + 0.535233i) q^{44} +(-1.00000 - 1.73205i) q^{45} +(7.04508 + 12.2024i) q^{46} +(1.73607 - 3.00696i) q^{47} -4.85410 q^{48} +(1.00000 + 6.92820i) q^{49} -6.47214 q^{50} +(-2.11803 + 3.66854i) q^{51} +(1.38197 + 2.39364i) q^{52} +(5.11803 + 8.86469i) q^{53} +(4.04508 - 7.00629i) q^{54} -1.00000 q^{55} +(4.47214 + 3.87298i) q^{56} +1.47214 q^{57} +(-3.61803 + 6.26662i) q^{58} +(-4.35410 - 7.54153i) q^{59} +(0.309017 + 0.535233i) q^{60} +(-4.73607 + 8.20311i) q^{61} -0.381966 q^{62} +(-5.00000 + 1.73205i) q^{63} +4.23607 q^{64} +(-2.23607 + 3.87298i) q^{65} +(-0.809017 - 1.40126i) q^{66} +(-2.97214 - 5.14789i) q^{67} +(-1.30902 + 2.26728i) q^{68} -8.70820 q^{69} +(0.809017 - 4.20378i) q^{70} -14.4721 q^{71} +(-2.23607 + 3.87298i) q^{72} +(1.26393 + 2.18919i) q^{73} +(2.80902 + 4.86536i) q^{74} +(2.00000 - 3.46410i) q^{75} +0.909830 q^{76} +(-0.500000 + 2.59808i) q^{77} -7.23607 q^{78} +(0.500000 - 0.866025i) q^{79} +(-2.42705 - 4.20378i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(0.809017 - 1.40126i) q^{82} -1.52786 q^{83} +(1.54508 - 0.535233i) q^{84} -4.23607 q^{85} +(5.23607 - 9.06914i) q^{86} +(-2.23607 - 3.87298i) q^{87} +(1.11803 + 1.93649i) q^{88} +(7.11803 - 12.3288i) q^{89} +3.23607 q^{90} +(8.94427 + 7.74597i) q^{91} -5.38197 q^{92} +(0.118034 - 0.204441i) q^{93} +(2.80902 + 4.86536i) q^{94} +(0.736068 + 1.27491i) q^{95} +(1.69098 - 2.92887i) q^{96} +8.47214 q^{97} +(-10.5172 - 4.20378i) 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 $\left(\mathbb{Z}/287\mathbb{Z}\right)^\times$.

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

Coefficient data

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

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

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

$2$	−0.809017	+	1.40126i	−0.572061	+	0.990839i	0.424293	+	0.905525i	$0.360523\pi$
$2$	−0.809017	+	1.40126i	−0.572061	+	0.990839i	−0.996354	+	0.0853143i	$0.972811\pi$
$3$	−0.500000	−	0.866025i	−0.288675	−	0.500000i	0.684819	−	0.728714i	$-0.259881\pi$
$3$	−0.500000	−	0.866025i	−0.288675	−	0.500000i	−0.973494	+	0.228714i	$0.926548\pi$
$4$	−0.309017	−	0.535233i	−0.154508	−	0.267617i
$5$	0.500000	−	0.866025i	0.223607	−	0.387298i	−0.732294	−	0.680989i	$-0.761550\pi$
$5$	0.500000	−	0.866025i	0.223607	−	0.387298i	0.955901	+	0.293691i	$0.0948835\pi$
$6$	1.61803			0.660560
$7$	−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
$10$	0.809017	+	1.40126i	0.255834	+	0.443117i
$11$	−0.500000	−	0.866025i	−0.150756	−	0.261116i	0.780750	−	0.624844i	$-0.214837\pi$
$11$	−0.500000	−	0.866025i	−0.150756	−	0.261116i	−0.931505	+	0.363727i	$0.881504\pi$
$12$	−0.309017	+	0.535233i	−0.0892055	+	0.154508i
$13$	−4.47214			−1.24035			−0.620174	−	0.784465i	$-0.712938\pi$
$13$	−4.47214			−1.24035			−0.620174	+	0.784465i	$0.712938\pi$
$14$	4.04508	−	1.40126i	1.08109	−	0.374502i
$15$	−1.00000			−0.258199
$16$	2.42705	−	4.20378i	0.606763	−	1.05094i
$17$	−2.11803	−	3.66854i	−0.513699	−	0.889752i	−0.999874	−	0.0158908i	$-0.994942\pi$
$17$	−2.11803	−	3.66854i	−0.513699	−	0.889752i	0.486175	−	0.873861i	$-0.338392\pi$
$18$	1.61803	+	2.80252i	0.381374	+	0.660560i
$19$	−0.736068	+	1.27491i	−0.168866	+	0.292484i	−0.938021	−	0.346578i	$-0.887344\pi$
$19$	−0.736068	+	1.27491i	−0.168866	+	0.292484i	0.769156	+	0.639061i	$0.220677\pi$
$20$	−0.618034			−0.138197
$21$	−0.500000	+	2.59808i	−0.109109	+	0.566947i
$22$	1.61803			0.344966
$23$	4.35410	−	7.54153i	0.907893	−	1.57252i	0.0909070	−	0.995859i	$-0.471023\pi$
$23$	4.35410	−	7.54153i	0.907893	−	1.57252i	0.816986	−	0.576657i	$-0.195643\pi$
$24$	1.11803	+	1.93649i	0.228218	+	0.395285i
$25$	2.00000	+	3.46410i	0.400000	+	0.692820i
$26$	3.61803	−	6.26662i	0.709555	−	1.22899i
$27$	−5.00000			−0.962250
$28$	−0.309017	+	1.60570i	−0.0583987	+	0.303449i
$29$	4.47214			0.830455			0.415227	−	0.909718i	$-0.363702\pi$
$29$	4.47214			0.830455			0.415227	+	0.909718i	$0.363702\pi$
$30$	0.809017	−	1.40126i	0.147706	−	0.255834i
$31$	0.118034	+	0.204441i	0.0211995	+	0.0367187i	0.876431	−	0.481528i	$-0.159918\pi$
$31$	0.118034	+	0.204441i	0.0211995	+	0.0367187i	−0.855231	+	0.518247i	$0.826585\pi$
$32$	1.69098	+	2.92887i	0.298926	+	0.517756i
$33$	−0.500000	+	0.866025i	−0.0870388	+	0.150756i
$34$	6.85410			1.17547
$35$	−2.50000	+	0.866025i	−0.422577	+	0.146385i
$36$	−1.23607			−0.206011
$37$	1.73607	−	3.00696i	0.285408	−	0.494341i	−0.687300	−	0.726374i	$-0.741204\pi$
$37$	1.73607	−	3.00696i	0.285408	−	0.494341i	0.972708	+	0.232033i	$0.0745376\pi$
$38$	−1.19098	−	2.06284i	−0.193203	−	0.334637i
$39$	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
$42$	−3.23607	−	2.80252i	−0.499336	−	0.432438i
$43$	−6.47214			−0.986991			−0.493496	−	0.869748i	$-0.664281\pi$
$43$	−6.47214			−0.986991			−0.493496	+	0.869748i	$0.664281\pi$
$44$	−0.309017	+	0.535233i	−0.0465861	+	0.0806894i
$45$	−1.00000	−	1.73205i	−0.149071	−	0.258199i
$46$	7.04508	+	12.2024i	1.03874	+	1.79915i
$47$	1.73607	−	3.00696i	0.253232	−	0.438610i	−0.711182	−	0.703008i	$-0.751840\pi$
$47$	1.73607	−	3.00696i	0.253232	−	0.438610i	0.964414	+	0.264398i	$0.0851732\pi$
$48$	−4.85410			−0.700629
$49$	1.00000	+	6.92820i	0.142857	+	0.989743i
$50$	−6.47214			−0.915298
$51$	−2.11803	+	3.66854i	−0.296584	+	0.513699i
$52$	1.38197	+	2.39364i	0.191644	+	0.331937i
$53$	5.11803	+	8.86469i	0.703016	+	1.21766i	0.967403	+	0.253243i	$0.0814971\pi$
$53$	5.11803	+	8.86469i	0.703016	+	1.21766i	−0.264387	+	0.964417i	$0.585170\pi$
$54$	4.04508	−	7.00629i	0.550466	−	0.953436i
$55$	−1.00000			−0.134840
$56$	4.47214	+	3.87298i	0.597614	+	0.517549i
$57$	1.47214			0.194989
$58$	−3.61803	+	6.26662i	−0.475071	+	0.822847i
$59$	−4.35410	−	7.54153i	−0.566856	−	0.981823i	−0.996874	−	0.0790030i	$-0.974826\pi$
$59$	−4.35410	−	7.54153i	−0.566856	−	0.981823i	0.430019	−	0.902820i	$-0.358507\pi$
$60$	0.309017	+	0.535233i	0.0398939	+	0.0690983i
$61$	−4.73607	+	8.20311i	−0.606391	+	1.05030i	0.385439	+	0.922733i	$0.374050\pi$
$61$	−4.73607	+	8.20311i	−0.606391	+	1.05030i	−0.991830	+	0.127567i	$0.959283\pi$
$62$	−0.381966			−0.0485097
$63$	−5.00000	+	1.73205i	−0.629941	+	0.218218i
$64$	4.23607			0.529508
$65$	−2.23607	+	3.87298i	−0.277350	+	0.480384i
$66$	−0.809017	−	1.40126i	−0.0995831	−	0.172483i
$67$	−2.97214	−	5.14789i	−0.363104	−	0.628915i	0.625366	−	0.780332i	$-0.284950\pi$
$67$	−2.97214	−	5.14789i	−0.363104	−	0.628915i	−0.988470	+	0.151417i	$0.951616\pi$
$68$	−1.30902	+	2.26728i	−0.158742	+	0.274949i
$69$	−8.70820			−1.04834
$70$	0.809017	−	4.20378i	0.0966960	−	0.502447i
$71$	−14.4721			−1.71753			−0.858763	−	0.512373i	$-0.828767\pi$
$71$	−14.4721			−1.71753			−0.858763	+	0.512373i	$0.828767\pi$
$72$	−2.23607	+	3.87298i	−0.263523	+	0.456435i
$73$	1.26393	+	2.18919i	0.147932	+	0.256226i	0.930463	−	0.366386i	$-0.119405\pi$
$73$	1.26393	+	2.18919i	0.147932	+	0.256226i	−0.782531	+	0.622612i	$0.786072\pi$
$74$	2.80902	+	4.86536i	0.326542	+	0.565587i
$75$	2.00000	−	3.46410i	0.230940	−	0.400000i
$76$	0.909830			0.104365
$77$	−0.500000	+	2.59808i	−0.0569803	+	0.296078i
$78$	−7.23607			−0.819323
$79$	0.500000	−	0.866025i	0.0562544	−	0.0974355i	−0.836527	−	0.547926i	$-0.815418\pi$
$79$	0.500000	−	0.866025i	0.0562544	−	0.0974355i	0.892781	+	0.450490i	$0.148751\pi$
$80$	−2.42705	−	4.20378i	−0.271353	−	0.469996i
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	0.809017	−	1.40126i	0.0893410	−	0.154743i
$83$	−1.52786			−0.167705			−0.0838524	−	0.996478i	$-0.526722\pi$
$83$	−1.52786			−0.167705			−0.0838524	+	0.996478i	$0.526722\pi$
$84$	1.54508	−	0.535233i	0.168583	−	0.0583987i
$85$	−4.23607			−0.459466
$86$	5.23607	−	9.06914i	0.564620	−	0.977950i
$87$	−2.23607	−	3.87298i	−0.239732	−	0.415227i
$88$	1.11803	+	1.93649i	0.119183	+	0.206431i
$89$	7.11803	−	12.3288i	0.754510	−	1.30685i	−0.191107	−	0.981569i	$-0.561208\pi$
$89$	7.11803	−	12.3288i	0.754510	−	1.30685i	0.945618	−	0.325281i	$-0.105459\pi$
$90$	3.23607			0.341112
$91$	8.94427	+	7.74597i	0.937614	+	0.811998i
$92$	−5.38197			−0.561109
$93$	0.118034	−	0.204441i	0.0122396	−	0.0211995i
$94$	2.80902	+	4.86536i	0.289728	+	0.501824i
$95$	0.736068	+	1.27491i	0.0755190	+	0.130803i
$96$	1.69098	−	2.92887i	0.172585	−	0.298926i
$97$	8.47214			0.860215			0.430108	−	0.902778i	$-0.358476\pi$
$97$	8.47214			0.860215			0.430108	+	0.902778i	$0.358476\pi$
$98$	−10.5172	−	4.20378i	−1.06240	−	0.424645i
$99$	−2.00000			−0.201008
$100$	1.23607	−	2.14093i	0.123607	−	0.214093i
$101$	−1.64590	−	2.85078i	−0.163773	−	0.283663i	0.772446	−	0.635081i	$-0.219033\pi$
$101$	−1.64590	−	2.85078i	−0.163773	−	0.283663i	−0.936219	+	0.351417i	$0.885700\pi$
$102$	−3.42705	−	5.93583i	−0.339329	−	0.587734i
$103$	−8.59017	+	14.8786i	−0.846415	+	1.46603i	0.0379724	+	0.999279i	$0.487910\pi$
$103$	−8.59017	+	14.8786i	−0.846415	+	1.46603i	−0.884387	+	0.466754i	$0.845423\pi$
$104$	10.0000			0.980581
$105$	2.00000	+	1.73205i	0.195180	+	0.169031i
$106$	−16.5623			−1.60867
$107$	0.645898	−	1.11873i	0.0624413	−	0.108152i	−0.833115	−	0.553100i	$-0.813445\pi$
$107$	0.645898	−	1.11873i	0.0624413	−	0.108152i	0.895556	+	0.444949i	$0.146778\pi$
$108$	1.54508	+	2.67617i	0.148676	+	0.257514i
$109$	7.11803	+	12.3288i	0.681784	+	1.18088i	0.974436	+	0.224666i	$0.0721289\pi$
$109$	7.11803	+	12.3288i	0.681784	+	1.18088i	−0.292652	+	0.956219i	$0.594538\pi$
$110$	0.809017	−	1.40126i	0.0771367	−	0.133605i
$111$	−3.47214			−0.329561
$112$	−12.1353	+	4.20378i	−1.14667	+	0.397219i
$113$	19.8885			1.87096			0.935478	−	0.353384i	$-0.114969\pi$
$113$	19.8885			1.87096			0.935478	+	0.353384i	$0.114969\pi$
$114$	−1.19098	+	2.06284i	−0.111546	+	0.193203i
$115$	−4.35410	−	7.54153i	−0.406022	−	0.703251i
$116$	−1.38197	−	2.39364i	−0.128312	−	0.222243i
$117$	−4.47214	+	7.74597i	−0.413449	+	0.716115i
$118$	14.0902			1.29711
$119$	−2.11803	+	11.0056i	−0.194160	+	1.00888i
$120$	2.23607			0.204124
$121$	5.00000	−	8.66025i	0.454545	−	0.787296i
$122$	−7.66312	−	13.2729i	−0.693786	−	1.20167i
$123$	0.500000	+	0.866025i	0.0450835	+	0.0780869i
$124$	0.0729490	−	0.126351i	0.00655102	−	0.0113467i
$125$	9.00000			0.804984
$126$	1.61803	−	8.40755i	0.144146	−	0.749004i
$127$	15.4164			1.36798			0.683992	−	0.729489i	$-0.260242\pi$
$127$	15.4164			1.36798			0.683992	+	0.729489i	$0.260242\pi$
$128$	−6.80902	+	11.7936i	−0.601838	+	1.04241i
$129$	3.23607	+	5.60503i	0.284920	+	0.493496i
$130$	−3.61803	−	6.26662i	−0.317323	−	0.549619i
$131$	6.82624	−	11.8234i	0.596411	−	1.03301i	−0.396935	−	0.917847i	$-0.629926\pi$
$131$	6.82624	−	11.8234i	0.596411	−	1.03301i	0.993346	−	0.115168i	$-0.0367405\pi$
$132$	0.618034			0.0537930
$133$	3.68034	−	1.27491i	0.319126	−	0.110548i
$134$	9.61803			0.830872
$135$	−2.50000	+	4.33013i	−0.215166	+	0.372678i
$136$	4.73607	+	8.20311i	0.406114	+	0.703411i
$137$	−7.82624	−	13.5554i	−0.668641	−	1.15812i	−0.978284	−	0.207267i	$-0.933543\pi$
$137$	−7.82624	−	13.5554i	−0.668641	−	1.15812i	0.309644	−	0.950853i	$-0.399790\pi$
$138$	7.04508	−	12.2024i	0.599717	−	1.03874i
$139$	16.9443			1.43719			0.718597	−	0.695427i	$-0.244785\pi$
$139$	16.9443			1.43719			0.718597	+	0.695427i	$0.244785\pi$
$140$	1.23607	+	1.07047i	0.104467	+	0.0904709i
$141$	−3.47214			−0.292407
$142$	11.7082	−	20.2792i	0.982531	−	1.70179i
$143$	2.23607	+	3.87298i	0.186989	+	0.323875i
$144$	−4.85410	−	8.40755i	−0.404508	−	0.700629i
$145$	2.23607	−	3.87298i	0.185695	−	0.321634i
$146$	−4.09017			−0.338505
$147$	5.50000	−	4.33013i	0.453632	−	0.357143i
$148$	−2.14590			−0.176392
$149$	−0.590170	+	1.02220i	−0.0483486	+	0.0837422i	−0.889187	−	0.457544i	$-0.848729\pi$
$149$	−0.590170	+	1.02220i	−0.0483486	+	0.0837422i	0.840838	+	0.541286i	$0.182063\pi$
$150$	3.23607	+	5.60503i	0.264224	+	0.457649i
$151$	−2.97214	−	5.14789i	−0.241869	−	0.418929i	0.719378	−	0.694619i	$-0.244427\pi$
$151$	−2.97214	−	5.14789i	−0.241869	−	0.418929i	−0.961247	+	0.275690i	$0.911094\pi$
$152$	1.64590	−	2.85078i	0.133500	−	0.231229i
$153$	−8.47214			−0.684932
$154$	−3.23607	−	2.80252i	−0.260770	−	0.225833i
$155$	0.236068			0.0189614
$156$	1.38197	−	2.39364i	0.110646	−	0.191644i
$157$	1.11803	+	1.93649i	0.0892288	+	0.154549i	0.907185	−	0.420731i	$-0.138226\pi$
$157$	1.11803	+	1.93649i	0.0892288	+	0.154549i	−0.817957	+	0.575280i	$0.804893\pi$
$158$	0.809017	+	1.40126i	0.0643619	+	0.111478i
$159$	5.11803	−	8.86469i	0.405886	−	0.703016i
$160$	3.38197			0.267368
$161$	−21.7705	+	7.54153i	−1.71576	+	0.594355i
$162$	1.61803			0.127125
$163$	2.64590	−	4.58283i	0.207243	−	0.358955i	−0.743602	−	0.668622i	$-0.766884\pi$
$163$	2.64590	−	4.58283i	0.207243	−	0.358955i	0.950845	+	0.309667i	$0.100218\pi$
$164$	0.309017	+	0.535233i	0.0241302	+	0.0417947i
$165$	0.500000	+	0.866025i	0.0389249	+	0.0674200i
$166$	1.23607	−	2.14093i	0.0959375	−	0.166169i
$167$	−2.47214			−0.191300			−0.0956498	−	0.995415i	$-0.530493\pi$
$167$	−2.47214			−0.191300			−0.0956498	+	0.995415i	$0.530493\pi$
$168$	1.11803	−	5.80948i	0.0862582	−	0.448211i
$169$	7.00000			0.538462
$170$	3.42705	−	5.93583i	0.262843	−	0.455257i
$171$	1.47214	+	2.54981i	0.112577	+	0.194989i
$172$	2.00000	+	3.46410i	0.152499	+	0.264135i
$173$	9.44427	−	16.3580i	0.718035	−	1.24367i	−0.243743	−	0.969840i	$-0.578375\pi$
$173$	9.44427	−	16.3580i	0.718035	−	1.24367i	0.961777	−	0.273833i	$-0.0882914\pi$
$174$	7.23607			0.548565
$175$	2.00000	−	10.3923i	0.151186	−	0.785584i
$176$	−4.85410			−0.365892
$177$	−4.35410	+	7.54153i	−0.327274	+	0.566856i
$178$	11.5172	+	19.9484i	0.863252	+	1.49520i
$179$	5.20820	+	9.02087i	0.389279	+	0.674252i	0.992353	−	0.123434i	$-0.0393907\pi$
$179$	5.20820	+	9.02087i	0.389279	+	0.674252i	−0.603073	+	0.797686i	$0.706057\pi$
$180$	−0.618034	+	1.07047i	−0.0460655	+	0.0797878i
$181$	−21.4164			−1.59187			−0.795935	−	0.605383i	$-0.793020\pi$
$181$	−21.4164			−1.59187			−0.795935	+	0.605383i	$0.793020\pi$
$182$	−18.0902	+	6.26662i	−1.34093	+	0.464513i
$183$	9.47214			0.700200
$184$	−9.73607	+	16.8634i	−0.717752	+	1.24318i
$185$	−1.73607	−	3.00696i	−0.127638	−	0.221076i
$186$	0.190983	+	0.330792i	0.0140036	+	0.0242549i
$187$	−2.11803	+	3.66854i	−0.154886	+	0.268270i
$188$	−2.14590			−0.156506
$189$	10.0000	+	8.66025i	0.727393	+	0.629941i
$190$	−2.38197			−0.172806
$191$	−2.73607	+	4.73901i	−0.197975	+	0.342903i	−0.947872	−	0.318652i	$-0.896770\pi$
$191$	−2.73607	+	4.73901i	−0.197975	+	0.342903i	0.749897	+	0.661555i	$0.230103\pi$
$192$	−2.11803	−	3.66854i	−0.152856	−	0.264754i
$193$	−0.409830	−	0.709846i	−0.0295002	−	0.0510959i	0.850898	−	0.525330i	$-0.176058\pi$
$193$	−0.409830	−	0.709846i	−0.0295002	−	0.0510959i	−0.880399	+	0.474234i	$0.842725\pi$
$194$	−6.85410	+	11.8717i	−0.492096	+	0.852335i
$195$	4.47214			0.320256
$196$	3.39919	−	2.67617i	0.242799	−	0.191155i
$197$	−2.94427			−0.209771			−0.104885	−	0.994484i	$-0.533448\pi$
$197$	−2.94427			−0.209771			−0.104885	+	0.994484i	$0.533448\pi$
$198$	1.61803	−	2.80252i	0.114989	−	0.199166i
$199$	−8.97214	−	15.5402i	−0.636018	−	1.10162i	−0.986299	−	0.164970i	$-0.947247\pi$
$199$	−8.97214	−	15.5402i	−0.636018	−	1.10162i	0.350281	−	0.936645i	$-0.386086\pi$
$200$	−4.47214	−	7.74597i	−0.316228	−	0.547723i
$201$	−2.97214	+	5.14789i	−0.209638	+	0.363104i
$202$	5.32624			0.374753
$203$	−8.94427	−	7.74597i	−0.627765	−	0.543660i
$204$	2.61803			0.183299
$205$	−0.500000	+	0.866025i	−0.0349215	+	0.0604858i
$206$	−13.8992	−	24.0741i	−0.968402	−	1.67732i
$207$	−8.70820	−	15.0831i	−0.605262	−	1.04834i
$208$	−10.8541	+	18.7999i	−0.752597	+	1.30354i
$209$	1.47214			0.101830
$210$	−4.04508	+	1.40126i	−0.279137	+	0.0966960i
$211$		0			0			−	1.00000i	$-0.5\pi$
$211$		0			0				1.00000i	$0.5\pi$
$212$	3.16312	−	5.47868i	0.217244	−	0.376277i
$213$	7.23607	+	12.5332i	0.495807	+	0.858763i
$214$	1.04508	+	1.81014i	0.0714405	+	0.123739i
$215$	−3.23607	+	5.60503i	−0.220698	+	0.382260i
$216$	11.1803			0.760726
$217$	0.118034	−	0.613323i	0.00801267	−	0.0416351i
$218$	−23.0344			−1.56009
$219$	1.26393	−	2.18919i	0.0854086	−	0.147932i
$220$	0.309017	+	0.535233i	0.0208339	+	0.0360854i
$221$	9.47214	+	16.4062i	0.637165	+	1.10360i
$222$	2.80902	−	4.86536i	0.188529	−	0.326542i
$223$	−16.9443			−1.13467			−0.567336	−	0.823486i	$-0.692026\pi$
$223$	−16.9443			−1.13467			−0.567336	+	0.823486i	$0.692026\pi$
$224$	1.69098	−	8.78661i	0.112984	−	0.587080i
$225$	8.00000			0.533333
$226$	−16.0902	+	27.8690i	−1.07030	+	1.85382i
$227$	2.73607	+	4.73901i	0.181599	+	0.314539i	0.942425	−	0.334417i	$-0.108539\pi$
$227$	2.73607	+	4.73901i	0.181599	+	0.314539i	−0.760826	+	0.648956i	$0.775206\pi$
$228$	−0.454915	−	0.787936i	−0.0301275	−	0.0521823i
$229$	10.0623	−	17.4284i	0.664936	−	1.15170i	−0.314367	−	0.949302i	$-0.601792\pi$
$229$	10.0623	−	17.4284i	0.664936	−	1.15170i	0.979303	−	0.202401i	$-0.0648745\pi$
$230$	14.0902			0.929078
$231$	2.50000	−	0.866025i	0.164488	−	0.0569803i
$232$	−10.0000			−0.656532
$233$	−1.64590	+	2.85078i	−0.107826	+	0.186761i	−0.914889	−	0.403704i	$-0.867722\pi$
$233$	−1.64590	+	2.85078i	−0.107826	+	0.186761i	0.807063	+	0.590465i	$0.201056\pi$
$234$	−7.23607	−	12.5332i	−0.473037	−	0.819323i
$235$	−1.73607	−	3.00696i	−0.113249	−	0.196152i
$236$	−2.69098	+	4.66092i	−0.175168	+	0.303400i
$237$	−1.00000			−0.0649570
$238$	−13.7082	−	11.8717i	−0.888571	−	0.769525i
$239$	−2.47214			−0.159909			−0.0799546	−	0.996799i	$-0.525478\pi$
$239$	−2.47214			−0.159909			−0.0799546	+	0.996799i	$0.525478\pi$
$240$	−2.42705	+	4.20378i	−0.156665	+	0.271353i
$241$	−0.736068	−	1.27491i	−0.0474143	−	0.0821240i	0.841344	−	0.540500i	$-0.181765\pi$
$241$	−0.736068	−	1.27491i	−0.0474143	−	0.0821240i	−0.888759	+	0.458376i	$0.848431\pi$
$242$	8.09017	+	14.0126i	0.520056	+	0.900763i
$243$	−8.00000	+	13.8564i	−0.513200	+	0.888889i
$244$	5.85410			0.374770
$245$	6.50000	+	2.59808i	0.415270	+	0.165985i
$246$	−1.61803			−0.103162
$247$	3.29180	−	5.70156i	0.209452	−	0.362781i
$248$	−0.263932	−	0.457144i	−0.0167597	−	0.0290287i
$249$	0.763932	+	1.32317i	0.0484122	+	0.0838524i
$250$	−7.28115	+	12.6113i	−0.460501	+	0.797610i
$251$	26.8328			1.69367			0.846836	−	0.531854i	$-0.178504\pi$
$251$	26.8328			1.69367			0.846836	+	0.531854i	$0.178504\pi$
$252$	2.47214	+	2.14093i	0.155730	+	0.134866i
$253$	−8.70820			−0.547480
$254$	−12.4721	+	21.6024i	−0.782571	+	1.35545i
$255$	2.11803	+	3.66854i	0.132636	+	0.229733i
$256$	−6.78115	−	11.7453i	−0.423822	−	0.734081i
$257$	0.645898	−	1.11873i	0.0402900	−	0.0697843i	−0.845177	−	0.534486i	$-0.820505\pi$
$257$	0.645898	−	1.11873i	0.0402900	−	0.0697843i	0.885467	+	0.464702i	$0.153838\pi$
$258$	−10.4721			−0.651967
$259$	−8.68034	+	3.00696i	−0.539370	+	0.186843i
$260$	2.76393			0.171412
$261$	4.47214	−	7.74597i	0.276818	−	0.479463i
$262$	11.0451	+	19.1306i	0.682368	+	1.18190i
$263$	−3.73607	−	6.47106i	−0.230376	−	0.399023i	0.727543	−	0.686062i	$-0.240662\pi$
$263$	−3.73607	−	6.47106i	−0.230376	−	0.399023i	−0.957919	+	0.287040i	$0.907329\pi$
$264$	1.11803	−	1.93649i	0.0688102	−	0.119183i
$265$	10.2361			0.628797
$266$	−1.19098	+	6.18853i	−0.0730239	+	0.379443i
$267$	−14.2361			−0.871233
$268$	−1.83688	+	3.18157i	−0.112205	+	0.194345i
$269$	9.73607	+	16.8634i	0.593619	+	1.02818i	0.993740	+	0.111715i	$0.0356345\pi$
$269$	9.73607	+	16.8634i	0.593619	+	1.02818i	−0.400122	+	0.916462i	$0.631032\pi$
$270$	−4.04508	−	7.00629i	−0.246176	−	0.426389i
$271$	10.8262	−	18.7516i	0.657647	−	1.13908i	−0.323576	−	0.946202i	$-0.604885\pi$
$271$	10.8262	−	18.7516i	0.657647	−	1.13908i	0.981223	−	0.192876i	$-0.0617815\pi$
$272$	−20.5623			−1.24677
$273$	2.23607	−	11.6190i	0.135333	−	0.703211i
$274$	25.3262			1.53001
$275$	2.00000	−	3.46410i	0.120605	−	0.208893i
$276$	2.69098	+	4.66092i	0.161978	+	0.280554i
$277$	2.02786	+	3.51236i	0.121843	+	0.211037i	0.920494	−	0.390756i	$-0.127786\pi$
$277$	2.02786	+	3.51236i	0.121843	+	0.211037i	−0.798652	+	0.601793i	$0.794453\pi$
$278$	−13.7082	+	23.7433i	−0.822163	+	1.42403i
$279$	0.472136			0.0282660
$280$	5.59017	−	1.93649i	0.334077	−	0.115728i
$281$	−4.47214			−0.266785			−0.133393	−	0.991063i	$-0.542587\pi$
$281$	−4.47214			−0.266785			−0.133393	+	0.991063i	$0.542587\pi$
$282$	2.80902	−	4.86536i	0.167275	−	0.289728i
$283$	−5.59017	−	9.68246i	−0.332301	−	0.575562i	0.650662	−	0.759368i	$-0.274492\pi$
$283$	−5.59017	−	9.68246i	−0.332301	−	0.575562i	−0.982963	+	0.183805i	$0.941158\pi$
$284$	4.47214	+	7.74597i	0.265372	+	0.459639i
$285$	0.736068	−	1.27491i	0.0436009	−	0.0755190i
$286$	−7.23607			−0.427878
$287$	2.00000	+	1.73205i	0.118056	+	0.102240i
$288$	6.76393			0.398569
$289$	−0.472136	+	0.817763i	−0.0277727	+	0.0481037i
$290$	3.61803	+	6.26662i	0.212458	+	0.367989i
$291$	−4.23607	−	7.33708i	−0.248323	−	0.430108i
$292$	0.781153	−	1.35300i	0.0457135	−	0.0791781i
$293$	28.8328			1.68443			0.842216	−	0.539141i	$-0.181251\pi$
$293$	28.8328			1.68443			0.842216	+	0.539141i	$0.181251\pi$
$294$	1.61803	+	11.2101i	0.0943657	+	0.653784i
$295$	−8.70820			−0.507011
$296$	−3.88197	+	6.72376i	−0.225635	+	0.390811i
$297$	2.50000	+	4.33013i	0.145065	+	0.251259i
$298$	−0.954915	−	1.65396i	−0.0553167	−	0.0958114i
$299$	−19.4721	+	33.7267i	−1.12610	+	1.95047i
$300$	−2.47214			−0.142729
$301$	12.9443	+	11.2101i	0.746095	+	0.646138i
$302$	9.61803			0.553456
$303$	−1.64590	+	2.85078i	−0.0945544	+	0.163773i
$304$	3.57295	+	6.18853i	0.204923	+	0.354936i
$305$	4.73607	+	8.20311i	0.271186	+	0.469709i
$306$	6.85410	−	11.8717i	0.391823	−	0.678657i
$307$	−9.88854			−0.564369			−0.282185	−	0.959360i	$-0.591059\pi$
$307$	−9.88854			−0.564369			−0.282185	+	0.959360i	$0.591059\pi$
$308$	1.54508	−	0.535233i	0.0880394	−	0.0304977i
$309$	17.1803			0.977355
$310$	−0.190983	+	0.330792i	−0.0108471	+	0.0187877i
$311$	10.9164	+	18.9078i	0.619013	+	1.07216i	0.989666	+	0.143390i	$0.0458004\pi$
$311$	10.9164	+	18.9078i	0.619013	+	1.07216i	−0.370654	+	0.928771i	$0.620866\pi$
$312$	−5.00000	−	8.66025i	−0.283069	−	0.490290i
$313$	8.64590	−	14.9751i	0.488695	−	0.846445i	−0.511220	−	0.859450i	$-0.670806\pi$
$313$	8.64590	−	14.9751i	0.488695	−	0.846445i	0.999915	+	0.0130050i	$0.00413974\pi$
$314$	−3.61803			−0.204177
$315$	−1.00000	+	5.19615i	−0.0563436	+	0.292770i
$316$	−0.618034			−0.0347671
$317$	−12.8820	+	22.3122i	−0.723523	+	1.25318i	0.236056	+	0.971740i	$0.424145\pi$
$317$	−12.8820	+	22.3122i	−0.723523	+	1.25318i	−0.959579	+	0.281440i	$0.909188\pi$
$318$	8.28115	+	14.3434i	0.464384	+	0.804337i
$319$	−2.23607	−	3.87298i	−0.125196	−	0.216845i
$320$	2.11803	−	3.66854i	0.118402	−	0.205078i
$321$	−1.29180			−0.0721010
$322$	7.04508	−	36.6073i	0.392607	−	2.04005i
$323$	6.23607			0.346984
$324$	−0.309017	+	0.535233i	−0.0171676	+	0.0297352i
$325$	−8.94427	−	15.4919i	−0.496139	−	0.859338i
$326$	4.28115	+	7.41517i	0.237111	+	0.410689i
$327$	7.11803	−	12.3288i	0.393628	−	0.681784i
$328$	2.23607			0.123466
$329$	−8.68034	+	3.00696i	−0.478563	+	0.165779i
$330$	−1.61803			−0.0890698
$331$	15.9164	−	27.5680i	0.874845	−	1.51528i	0.0179170	−	0.999839i	$-0.494297\pi$
$331$	15.9164	−	27.5680i	0.874845	−	1.51528i	0.856928	−	0.515436i	$-0.172370\pi$
$332$	0.472136	+	0.817763i	0.0259118	+	0.0448806i
$333$	−3.47214	−	6.01392i	−0.190272	−	0.329561i
$334$	2.00000	−	3.46410i	0.109435	−	0.189547i
$335$	−5.94427			−0.324770
$336$	9.70820	+	8.40755i	0.529626	+	0.458670i
$337$	−8.47214			−0.461507			−0.230753	−	0.973012i	$-0.574119\pi$
$337$	−8.47214			−0.461507			−0.230753	+	0.973012i	$0.574119\pi$
$338$	−5.66312	+	9.80881i	−0.308033	+	0.533529i
$339$	−9.94427	−	17.2240i	−0.540099	−	0.935478i
$340$	1.30902	+	2.26728i	0.0709914	+	0.122961i
$341$	0.118034	−	0.204441i	0.00639190	−	0.0110711i
$342$	−4.76393			−0.257604
$343$	10.0000	−	15.5885i	0.539949	−	0.841698i
$344$	14.4721			0.780285
$345$	−4.35410	+	7.54153i	−0.234417	+	0.406022i
$346$	15.2812	+	26.4677i	0.821520	+	1.42291i
$347$	1.50000	+	2.59808i	0.0805242	+	0.139472i	0.903475	−	0.428640i	$-0.141007\pi$
$347$	1.50000	+	2.59808i	0.0805242	+	0.139472i	−0.822951	+	0.568112i	$0.807674\pi$
$348$	−1.38197	+	2.39364i	−0.0740812	+	0.128312i
$349$	−20.4721			−1.09585			−0.547924	−	0.836528i	$-0.684582\pi$
$349$	−20.4721			−1.09585			−0.547924	+	0.836528i	$0.684582\pi$
$350$	12.9443	+	11.2101i	0.691900	+	0.599203i
$351$	22.3607			1.19352
$352$	1.69098	−	2.92887i	0.0901297	−	0.156109i
$353$	−12.7361	−	22.0595i	−0.677872	−	1.17411i	−0.975620	−	0.219465i	$-0.929569\pi$
$353$	−12.7361	−	22.0595i	−0.677872	−	1.17411i	0.297748	−	0.954645i	$-0.403765\pi$
$354$	−7.04508	−	12.2024i	−0.374442	−	0.648553i
$355$	−7.23607	+	12.5332i	−0.384051	+	0.665195i
$356$	−8.79837			−0.466313
$357$	10.5902	−	3.66854i	0.560491	−	0.194160i
$358$	−16.8541			−0.890767
$359$	6.82624	−	11.8234i	0.360275	−	0.624015i	−0.627731	−	0.778430i	$-0.716016\pi$
$359$	6.82624	−	11.8234i	0.360275	−	0.624015i	0.988006	+	0.154416i	$0.0493495\pi$
$360$	2.23607	+	3.87298i	0.117851	+	0.204124i
$361$	8.41641	+	14.5776i	0.442969	+	0.767245i
$362$	17.3262	−	30.0099i	0.910647	−	1.57729i
$363$	−10.0000			−0.524864
$364$	1.38197	−	7.18091i	0.0724347	−	0.376382i
$365$	2.52786			0.132314
$366$	−7.66312	+	13.2729i	−0.400558	+	0.693786i
$367$	2.59017	+	4.48631i	0.135206	+	0.234183i	0.925676	−	0.378317i	$-0.123497\pi$
$367$	2.59017	+	4.48631i	0.135206	+	0.234183i	−0.790470	+	0.612500i	$0.790164\pi$
$368$	−21.1353	−	36.6073i	−1.10175	−	1.90829i
$369$	−1.00000	+	1.73205i	−0.0520579	+	0.0901670i
$370$	5.61803			0.292068
$371$	5.11803	−	26.5941i	0.265715	−	1.38070i
$372$	−0.145898			−0.00756446
$373$	0.0278640	−	0.0482619i	0.00144275	−	0.00249891i	−0.865303	−	0.501249i	$-0.832874\pi$
$373$	0.0278640	−	0.0482619i	0.00144275	−	0.00249891i	0.866746	+	0.498750i	$0.166207\pi$
$374$	−3.42705	−	5.93583i	−0.177209	−	0.306934i
$375$	−4.50000	−	7.79423i	−0.232379	−	0.402492i
$376$	−3.88197	+	6.72376i	−0.200197	+	0.346752i
$377$	−20.0000			−1.03005
$378$	−20.2254	+	7.00629i	−1.04028	+	0.360365i
$379$	31.4164			1.61375			0.806876	−	0.590721i	$-0.201156\pi$
$379$	31.4164			1.61375			0.806876	+	0.590721i	$0.201156\pi$
$380$	0.454915	−	0.787936i	0.0233366	−	0.0404203i
$381$	−7.70820	−	13.3510i	−0.394903	−	0.683992i
$382$	−4.42705	−	7.66788i	−0.226508	−	0.392323i
$383$	−10.4443	+	18.0900i	−0.533677	+	0.924356i	0.465549	+	0.885022i	$0.345857\pi$
$383$	−10.4443	+	18.0900i	−0.533677	+	0.924356i	−0.999226	+	0.0393341i	$0.987476\pi$
$384$	13.6180			0.694942
$385$	2.00000	+	1.73205i	0.101929	+	0.0882735i
$386$	1.32624			0.0675037
$387$	−6.47214	+	11.2101i	−0.328997	+	0.569840i
$388$	−2.61803	−	4.53457i	−0.132911	−	0.230208i
$389$	0.500000	+	0.866025i	0.0253510	+	0.0439092i	0.878423	−	0.477885i	$-0.158596\pi$
$389$	0.500000	+	0.866025i	0.0253510	+	0.0439092i	−0.853072	+	0.521794i	$0.825263\pi$
$390$	−3.61803	+	6.26662i	−0.183206	+	0.317323i
$391$	−36.8885			−1.86553
$392$	−2.23607	−	15.4919i	−0.112938	−	0.782461i
$393$	−13.6525			−0.688676
$394$	2.38197	−	4.12569i	0.120002	−	0.207849i
$395$	−0.500000	−	0.866025i	−0.0251577	−	0.0435745i
$396$	0.618034	+	1.07047i	0.0310574	+	0.0537930i
$397$	−13.8262	+	23.9477i	−0.693919	+	1.20190i	0.276625	+	0.960978i	$0.410784\pi$
$397$	−13.8262	+	23.9477i	−0.693919	+	1.20190i	−0.970544	+	0.240925i	$0.922549\pi$
$398$	29.0344			1.45537
$399$	−2.94427	−	2.54981i	−0.147398	−	0.127650i
$400$	19.4164			0.970820
$401$	−3.97214	+	6.87994i	−0.198359	+	0.343568i	−0.947996	−	0.318281i	$-0.896895\pi$
$401$	−3.97214	+	6.87994i	−0.198359	+	0.343568i	0.749637	+	0.661849i	$0.230228\pi$
$402$	−4.80902	−	8.32946i	−0.239852	−	0.415436i
$403$	−0.527864	−	0.914287i	−0.0262948	−	0.0455439i
$404$	−1.01722	+	1.76188i	−0.0506086	+	0.0876567i
$405$	−1.00000			−0.0496904
$406$	18.0902	−	6.26662i	0.897800	−	0.311007i
$407$	−3.47214			−0.172107
$408$	4.73607	−	8.20311i	0.234470	−	0.406114i
$409$	11.4443	+	19.8221i	0.565883	+	0.980138i	0.996967	+	0.0778261i	$0.0247979\pi$
$409$	11.4443	+	19.8221i	0.565883	+	0.980138i	−0.431084	+	0.902312i	$0.641869\pi$
$410$	−0.809017	−	1.40126i	−0.0399545	−	0.0692032i
$411$	−7.82624	+	13.5554i	−0.386040	+	0.668641i
$412$	10.6180			0.523113
$413$	−4.35410	+	22.6246i	−0.214251	+	1.11328i
$414$	28.1803			1.38499
$415$	−0.763932	+	1.32317i	−0.0374999	+	0.0649518i
$416$	−7.56231	−	13.0983i	−0.370773	−	0.642197i
$417$	−8.47214	−	14.6742i	−0.414882	−	0.718597i
$418$	−1.19098	+	2.06284i	−0.0582529	+	0.100897i
$419$	−17.8885			−0.873913			−0.436956	−	0.899483i	$-0.643944\pi$
$419$	−17.8885			−0.873913			−0.436956	+	0.899483i	$0.643944\pi$
$420$	0.309017	−	1.60570i	0.0150785	−	0.0783501i
$421$	−16.4721			−0.802803			−0.401401	−	0.915902i	$-0.631477\pi$
$421$	−16.4721			−0.802803			−0.401401	+	0.915902i	$0.631477\pi$
$422$		0			0
$423$	−3.47214	−	6.01392i	−0.168821	−	0.292407i
$424$	−11.4443	−	19.8221i	−0.555783	−	0.962644i
$425$	8.47214	−	14.6742i	0.410959	−	0.711802i
$426$	−23.4164			−1.13453
$427$	23.6803	−	8.20311i	1.14597	−	0.396976i
$428$	−0.798374			−0.0385909
$429$	2.23607	−	3.87298i	0.107958	−	0.186989i
$430$	−5.23607	−	9.06914i	−0.252506	−	0.437353i
$431$	1.17376	+	2.03302i	0.0565381	+	0.0979269i	0.892909	−	0.450237i	$-0.148660\pi$
$431$	1.17376	+	2.03302i	0.0565381	+	0.0979269i	−0.836371	+	0.548164i	$0.815327\pi$
$432$	−12.1353	+	21.0189i	−0.583858	+	1.01127i
$433$	6.94427			0.333720			0.166860	−	0.985981i	$-0.446637\pi$
$433$	6.94427			0.333720			0.166860	+	0.985981i	$0.446637\pi$
$434$	0.763932	+	0.661585i	0.0366699	+	0.0317571i
$435$	−4.47214			−0.214423
$436$	4.39919	−	7.61962i	0.210683	−	0.364913i
$437$	6.40983	+	11.1022i	0.306624	+	0.531088i
$438$	2.04508	+	3.54219i	0.0977179	+	0.169252i
$439$	18.2082	−	31.5375i	0.869030	−	1.50520i	0.00604112	−	0.999982i	$-0.498077\pi$
$439$	18.2082	−	31.5375i	0.869030	−	1.50520i	0.862989	−	0.505223i	$-0.168590\pi$
$440$	2.23607			0.106600
$441$	13.0000	+	5.19615i	0.619048	+	0.247436i
$442$	−30.6525			−1.45799
$443$	3.88197	−	6.72376i	0.184438	−	0.319456i	−0.758949	−	0.651150i	$-0.774287\pi$
$443$	3.88197	−	6.72376i	0.184438	−	0.319456i	0.943387	+	0.331694i	$0.107620\pi$
$444$	1.07295	+	1.85840i	0.0509199	+	0.0881959i
$445$	−7.11803	−	12.3288i	−0.337427	−	0.584441i
$446$	13.7082	−	23.7433i	0.649102	−	1.12428i
$447$	1.18034			0.0558282
$448$	−8.47214	−	7.33708i	−0.400271	−	0.346645i
$449$	21.0557			0.993681			0.496841	−	0.867842i	$-0.334493\pi$
$449$	21.0557			0.993681			0.496841	+	0.867842i	$0.334493\pi$
$450$	−6.47214	+	11.2101i	−0.305099	+	0.528448i
$451$	0.500000	+	0.866025i	0.0235441	+	0.0407795i
$452$	−6.14590	−	10.6450i	−0.289079	−	0.500699i
$453$	−2.97214	+	5.14789i	−0.139643	+	0.241869i
$454$	−8.85410			−0.415544
$455$	11.1803	−	3.87298i	0.524142	−	0.181568i
$456$	−3.29180			−0.154152
$457$	13.1180	−	22.7211i	0.613636	−	1.06285i	−0.376986	−	0.926219i	$-0.623040\pi$
$457$	13.1180	−	22.7211i	0.613636	−	1.06285i	0.990622	−	0.136630i	$-0.0436270\pi$
$458$	16.2812	+	28.1998i	0.760768	+	1.31769i
$459$	10.5902	+	18.3427i	0.494307	+	0.856164i
$460$	−2.69098	+	4.66092i	−0.125468	+	0.217316i
$461$	−38.9443			−1.81382			−0.906908	−	0.421329i	$-0.861564\pi$
$461$	−38.9443			−1.81382			−0.906908	+	0.421329i	$0.861564\pi$
$462$	−0.809017	+	4.20378i	−0.0376389	+	0.195577i
$463$	−2.11146			−0.0981277			−0.0490638	−	0.998796i	$-0.515624\pi$
$463$	−2.11146			−0.0981277			−0.0490638	+	0.998796i	$0.515624\pi$
$464$	10.8541	−	18.7999i	0.503889	−	0.872761i
$465$	−0.118034	−	0.204441i	−0.00547370	−	0.00948072i
$466$	−2.66312	−	4.61266i	−0.123367	−	0.213677i
$467$	−4.40983	+	7.63805i	−0.204063	+	0.353447i	−0.949834	−	0.312756i	$-0.898748\pi$
$467$	−4.40983	+	7.63805i	−0.204063	+	0.353447i	0.745771	+	0.666202i	$0.232081\pi$
$468$	5.52786			0.255526
$469$	−2.97214	+	15.4437i	−0.137240	+	0.713122i
$470$	5.61803			0.259141
$471$	1.11803	−	1.93649i	0.0515163	−	0.0892288i
$472$	9.73607	+	16.8634i	0.448139	+	0.776199i
$473$	3.23607	+	5.60503i	0.148795	+	0.257720i
$474$	0.809017	−	1.40126i	0.0371594	−	0.0643619i
$475$	−5.88854			−0.270185
$476$	6.54508	−	2.26728i	0.299993	−	0.103921i
$477$	20.4721			0.937355
$478$	2.00000	−	3.46410i	0.0914779	−	0.158444i
$479$	−10.5000	−	18.1865i	−0.479757	−	0.830964i	0.519973	−	0.854183i	$-0.325942\pi$
$479$	−10.5000	−	18.1865i	−0.479757	−	0.830964i	−0.999730	+	0.0232187i	$0.992609\pi$
$480$	−1.69098	−	2.92887i	−0.0771825	−	0.133684i
$481$	−7.76393	+	13.4475i	−0.354005	+	0.613154i
$482$	2.38197			0.108496
$483$	17.4164	+	15.0831i	0.792474	+	0.686303i
$484$	−6.18034			−0.280925
$485$	4.23607	−	7.33708i	0.192350	−	0.333160i
$486$	−12.9443	−	22.4201i	−0.587164	−	1.01700i
$487$	12.7705	+	22.1192i	0.578687	+	1.00232i	0.995630	+	0.0933828i	$0.0297680\pi$
$487$	12.7705	+	22.1192i	0.578687	+	1.00232i	−0.416943	+	0.908933i	$0.636899\pi$
$488$	10.5902	−	18.3427i	0.479394	−	0.830336i
$489$	−5.29180			−0.239303
$490$	−8.89919	+	7.00629i	−0.402024	+	0.316512i
$491$	−12.3607			−0.557830			−0.278915	−	0.960316i	$-0.589975\pi$
$491$	−12.3607			−0.557830			−0.278915	+	0.960316i	$0.589975\pi$
$492$	0.309017	−	0.535233i	0.0139316	−	0.0241302i
$493$	−9.47214	−	16.4062i	−0.426604	−	0.738899i
$494$	5.32624	+	9.22531i	0.239639	+	0.415067i
$495$	−1.00000	+	1.73205i	−0.0449467	+	0.0778499i
$496$	1.14590			0.0514523
$497$	28.9443	+	25.0665i	1.29833	+	1.12439i
$498$	−2.47214			−0.110779
$499$	8.02786	−	13.9047i	0.359377	−	0.622458i	−0.628480	−	0.777826i	$-0.716323\pi$
$499$	8.02786	−	13.9047i	0.359377	−	0.622458i	0.987857	+	0.155367i	$0.0496560\pi$
$500$	−2.78115	−	4.81710i	−0.124377	−	0.215427i
$501$	1.23607	+	2.14093i	0.0552234	+	0.0956498i
$502$	−21.7082	+	37.5997i	−0.968885	+	1.67816i
$503$	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
$505$	−3.29180			−0.146483
$506$	7.04508	−	12.2024i	0.313192	−	0.542465i
$507$	−3.50000	−	6.06218i	−0.155440	−	0.269231i
$508$	−4.76393	−	8.25137i	−0.211365	−	0.366095i
$509$	−2.40983	+	4.17395i	−0.106814	+	0.185007i	−0.914478	−	0.404636i	$-0.867398\pi$
$509$	−2.40983	+	4.17395i	−0.106814	+	0.185007i	0.807664	+	0.589643i	$0.200732\pi$
$510$	−6.85410			−0.303505
$511$	1.26393	−	6.56758i	0.0559131	−	0.290533i
$512$	−5.29180			−0.233867
$513$	3.68034	−	6.37454i	0.162491	−	0.281443i
$514$	1.04508	+	1.81014i	0.0460967	+	0.0798419i
$515$	8.59017	+	14.8786i	0.378528	+	0.655630i
$516$	2.00000	−	3.46410i	0.0880451	−	0.152499i
$517$	−3.47214			−0.152704
$518$	2.80902	−	14.5961i	0.123421	−	0.641315i
$519$	−18.8885			−0.829115
$520$	5.00000	−	8.66025i	0.219265	−	0.379777i
$521$	−19.8262	−	34.3401i	−0.868603	−	1.50446i	−0.863424	−	0.504478i	$-0.831685\pi$
$521$	−19.8262	−	34.3401i	−0.868603	−	1.50446i	−0.00517893	−	0.999987i	$-0.501649\pi$
$522$	7.23607	+	12.5332i	0.316714	+	0.548565i
$523$	−8.11803	+	14.0608i	−0.354977	+	0.614838i	−0.987114	−	0.160019i	$-0.948845\pi$
$523$	−8.11803	+	14.0608i	−0.354977	+	0.614838i	0.632137	+	0.774857i	$0.282178\pi$
$524$	−8.43769			−0.368602
$525$	−10.0000	+	3.46410i	−0.436436	+	0.151186i
$526$	12.0902			0.527156
$527$	0.500000	−	0.866025i	0.0217803	−	0.0377247i
$528$	2.42705	+	4.20378i	0.105624	+	0.182946i
$529$	−26.4164	−	45.7546i	−1.14854	−	1.98933i
$530$	−8.28115	+	14.3434i	−0.359710	+	0.623037i
$531$	−17.4164			−0.755808
$532$	−1.81966	−	1.57587i	−0.0788923	−	0.0683227i
$533$	4.47214			0.193710
$534$	11.5172	−	19.9484i	0.498399	−	0.863252i
$535$	−0.645898	−	1.11873i	−0.0279246	−	0.0483668i
$536$	6.64590	+	11.5110i	0.287059	+	0.497201i
$537$	5.20820	−	9.02087i	0.224751	−	0.389279i
$538$	−31.5066			−1.35835
$539$	5.50000	−	4.33013i	0.236902	−	0.186512i
$540$	3.09017			0.132980
$541$	−10.2639	+	17.7777i	−0.441281	+	0.764321i	−0.997785	−	0.0665240i	$-0.978809\pi$
$541$	−10.2639	+	17.7777i	−0.441281	+	0.764321i	0.556504	+	0.830845i	$0.312142\pi$
$542$	17.5172	+	30.3407i	0.752429	+	1.30325i
$543$	10.7082	+	18.5472i	0.459533	+	0.795935i
$544$	7.16312	−	12.4069i	0.307116	−	0.531941i
$545$	14.2361			0.609806
$546$	14.4721	+	12.5332i	0.619350	+	0.536373i
$547$	−9.52786			−0.407382			−0.203691	−	0.979035i	$-0.565294\pi$
$547$	−9.52786			−0.407382			−0.203691	+	0.979035i	$0.565294\pi$
$548$	−4.83688	+	8.37772i	−0.206621	+	0.357879i
$549$	9.47214	+	16.4062i	0.404261	+	0.700200i
$550$	3.23607	+	5.60503i	0.137986	+	0.238999i
$551$	−3.29180	+	5.70156i	−0.140235	+	0.242895i
$552$	19.4721			0.828789
$553$	−2.50000	+	0.866025i	−0.106311	+	0.0368271i
$554$	−6.56231			−0.278806
$555$	−1.73607	+	3.00696i	−0.0736920	+	0.127638i
$556$	−5.23607	−	9.06914i	−0.222059	−	0.384617i
$557$	7.59017	+	13.1466i	0.321606	+	0.557038i	0.980820	−	0.194918i	$-0.0624441\pi$
$557$	7.59017	+	13.1466i	0.321606	+	0.557038i	−0.659214	+	0.751956i	$0.729111\pi$
$558$	−0.381966	+	0.661585i	−0.0161699	+	0.0280071i
$559$	28.9443			1.22421
$560$	−2.42705	+	12.6113i	−0.102562	+	0.532926i
$561$	4.23607			0.178847
$562$	3.61803	−	6.26662i	0.152618	−	0.264341i
$563$	5.50000	+	9.52628i	0.231797	+	0.401485i	0.958337	−	0.285640i	$-0.0922060\pi$
$563$	5.50000	+	9.52628i	0.231797	+	0.401485i	−0.726540	+	0.687124i	$0.758873\pi$
$564$	1.07295	+	1.85840i	0.0451793	+	0.0782528i
$565$	9.94427	−	17.2240i	0.418359	−	0.724618i
$566$	18.0902			0.760387
$567$	−0.500000	+	2.59808i	−0.0209980	+	0.109109i
$568$	32.3607			1.35782
$569$	14.9721	−	25.9325i	0.627665	−	1.08715i	−0.360355	−	0.932815i	$-0.617344\pi$
$569$	14.9721	−	25.9325i	0.627665	−	1.08715i	0.988019	−	0.154332i	$-0.0493224\pi$
$570$	1.19098	+	2.06284i	0.0498848	+	0.0864030i
$571$	14.2639	+	24.7059i	0.596927	+	1.03391i	0.993272	+	0.115806i	$0.0369451\pi$
$571$	14.2639	+	24.7059i	0.596927	+	1.03391i	−0.396345	+	0.918102i	$0.629722\pi$
$572$	1.38197	−	2.39364i	0.0577829	−	0.100083i
$573$	5.47214			0.228602
$574$	−4.04508	+	1.40126i	−0.168839	+	0.0584874i
$575$	34.8328			1.45263
$576$	4.23607	−	7.33708i	0.176503	−	0.305712i
$577$	15.7705	+	27.3153i	0.656535	+	1.13715i	0.981507	+	0.191428i	$0.0613119\pi$
$577$	15.7705	+	27.3153i	0.656535	+	1.13715i	−0.324972	+	0.945724i	$0.605355\pi$
$578$	−0.763932	−	1.32317i	−0.0317754	−	0.0550366i
$579$	−0.409830	+	0.709846i	−0.0170320	+	0.0295002i
$580$	−2.76393			−0.114766
$581$	3.05573	+	2.64634i	0.126773	+	0.109789i
$582$	13.7082			0.568223
$583$	5.11803	−	8.86469i	0.211967	−	0.367138i
$584$	−2.82624	−	4.89519i	−0.116951	−	0.202564i
$585$	4.47214	+	7.74597i	0.184900	+	0.320256i
$586$	−23.3262	+	40.4022i	−0.963598	+	1.66900i
$587$	−16.0000			−0.660391			−0.330195	−	0.943913i	$-0.607115\pi$
$587$	−16.0000			−0.660391			−0.330195	+	0.943913i	$0.607115\pi$
$588$	−4.01722	−	1.60570i	−0.165667	−	0.0662179i
$589$	−0.347524			−0.0143195
$590$	7.04508	−	12.2024i	0.290042	−	0.502367i
$591$	1.47214	+	2.54981i	0.0605556	+	0.104885i
$592$	−8.42705	−	14.5961i	−0.346350	−	0.599895i
$593$	3.88197	−	6.72376i	0.159413	−	0.276112i	−0.775244	−	0.631662i	$-0.782373\pi$
$593$	3.88197	−	6.72376i	0.159413	−	0.276112i	0.934657	+	0.355550i	$0.115706\pi$
$594$	−8.09017			−0.331944
$595$	8.47214	+	7.33708i	0.347324	+	0.300791i
$596$	0.729490			0.0298811
$597$	−8.97214	+	15.5402i	−0.367205	+	0.636018i
$598$	−31.5066	−	54.5710i	−1.28840	−	2.23157i
$599$	9.06231	+	15.6964i	0.370276	+	0.641336i	0.989608	−	0.143793i	$-0.0459299\pi$
$599$	9.06231	+	15.6964i	0.370276	+	0.641336i	−0.619332	+	0.785129i	$0.712597\pi$
$600$	−4.47214	+	7.74597i	−0.182574	+	0.316228i
$601$	0.472136			0.0192588			0.00962941	−	0.999954i	$-0.496935\pi$
$601$	0.472136			0.0192588			0.00962941	+	0.999954i	$0.496935\pi$
$602$	−26.1803	+	9.06914i	−1.06703	+	0.369630i
$603$	−11.8885			−0.484139
$604$	−1.83688	+	3.18157i	−0.0747416	+	0.129456i
$605$	−5.00000	−	8.66025i	−0.203279	−	0.352089i
$606$	−2.66312	−	4.61266i	−0.108182	−	0.187376i
$607$	−14.5902	+	25.2709i	−0.592197	+	1.02571i	0.401739	+	0.915754i	$0.368406\pi$
$607$	−14.5902	+	25.2709i	−0.592197	+	1.02571i	−0.993936	+	0.109961i	$0.964927\pi$
$608$	−4.97871			−0.201914
$609$	−2.23607	+	11.6190i	−0.0906100	+	0.470824i
$610$	−15.3262			−0.620541
$611$	−7.76393	+	13.4475i	−0.314095	+	0.544029i
$612$	2.61803	+	4.53457i	0.105828	+	0.183299i
$613$	−22.4443	−	38.8746i	−0.906516	−	1.57013i	−0.818870	−	0.573979i	$-0.805399\pi$
$613$	−22.4443	−	38.8746i	−0.906516	−	1.57013i	−0.0876459	−	0.996152i	$-0.527934\pi$
$614$	8.00000	−	13.8564i	0.322854	−	0.559199i
$615$	1.00000			0.0403239
$616$	1.11803	−	5.80948i	0.0450469	−	0.234070i
$617$	25.4164			1.02323			0.511613	−	0.859216i	$-0.329048\pi$
$617$	25.4164			1.02323			0.511613	+	0.859216i	$0.329048\pi$
$618$	−13.8992	+	24.0741i	−0.559107	+	0.968402i
$619$	10.8820	+	18.8481i	0.437383	+	0.757570i	0.997487	−	0.0708527i	$-0.0225720\pi$
$619$	10.8820	+	18.8481i	0.437383	+	0.757570i	−0.560104	+	0.828423i	$0.689239\pi$
$620$	−0.0729490	−	0.126351i	−0.00292970	−	0.00507439i
$621$	−21.7705	+	37.7076i	−0.873620	+	1.51316i
$622$	−35.3262			−1.41645
$623$	−35.5902	+	12.3288i	−1.42589	+	0.493943i
$624$	21.7082			0.869024
$625$	−5.50000	+	9.52628i	−0.220000	+	0.381051i
$626$	13.9894	+	24.2303i	0.559127	+	0.968437i
$627$	−0.736068	−	1.27491i	−0.0293957	−	0.0509149i
$628$	0.690983	−	1.19682i	0.0275732	−	0.0477582i
$629$	−14.7082			−0.586454
$630$	−6.47214	−	5.60503i	−0.257856	−	0.223310i
$631$	−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
$634$	−20.8435	−	36.1019i	−0.827800	−	1.43379i
$635$	7.70820	−	13.3510i	0.305891	−	0.529818i
$636$	−6.32624			−0.250852
$637$	−4.47214	−	30.9839i	−0.177192	−	1.22763i
$638$	7.23607			0.286479
$639$	−14.4721	+	25.0665i	−0.572509	+	0.991614i
$640$	6.80902	+	11.7936i	0.269150	+	0.466182i
$641$	−22.1180	−	38.3096i	−0.873610	−	1.51314i	−0.858236	−	0.513255i	$-0.828440\pi$
$641$	−22.1180	−	38.3096i	−0.873610	−	1.51314i	−0.0153735	−	0.999882i	$-0.504894\pi$
$642$	1.04508	−	1.81014i	0.0412462	−	0.0714405i
$643$	27.7771			1.09542			0.547711	−	0.836668i	$-0.315499\pi$
$643$	27.7771			1.09542			0.547711	+	0.836668i	$0.315499\pi$
$644$	10.7639	+	9.32184i	0.424158	+	0.367332i
$645$	6.47214			0.254840
$646$	−5.04508	+	8.73834i	−0.198496	+	0.343806i
$647$	8.88197	+	15.3840i	0.349186	+	0.604808i	0.986105	−	0.166123i	$-0.0531248\pi$
$647$	8.88197	+	15.3840i	0.349186	+	0.604808i	−0.636919	+	0.770931i	$0.719791\pi$
$648$	1.11803	+	1.93649i	0.0439205	+	0.0760726i
$649$	−4.35410	+	7.54153i	−0.170913	+	0.296031i
$650$	28.9443			1.13529
$651$	−0.590170	+	0.204441i	−0.0231306	+	0.00801267i
$652$	−3.27051			−0.128083
$653$	6.53444	−	11.3180i	0.255712	−	0.442907i	−0.709376	−	0.704830i	$-0.751023\pi$
$653$	6.53444	−	11.3180i	0.255712	−	0.442907i	0.965089	+	0.261923i	$0.0843566\pi$
$654$	11.5172	+	19.9484i	0.450359	+	0.780045i
$655$	−6.82624	−	11.8234i	−0.266723	−	0.461978i
$656$	−2.42705	+	4.20378i	−0.0947604	+	0.164130i
$657$	5.05573			0.197243
$658$	2.80902	−	14.5961i	0.109507	−	0.569014i
$659$	−24.9443			−0.971691			−0.485845	−	0.874045i	$-0.661488\pi$
$659$	−24.9443			−0.971691			−0.485845	+	0.874045i	$0.661488\pi$
$660$	0.309017	−	0.535233i	0.0120285	−	0.0208339i
$661$	−1.31966	−	2.28572i	−0.0513288	−	0.0889041i	0.839219	−	0.543793i	$-0.183012\pi$
$661$	−1.31966	−	2.28572i	−0.0513288	−	0.0889041i	−0.890548	+	0.454889i	$0.849679\pi$
$662$	25.7533	+	44.6060i	1.00093	+	1.73366i
$663$	9.47214	−	16.4062i	0.367867	−	0.637165i
$664$	3.41641			0.132582
$665$	0.736068	−	3.82472i	0.0285435	−	0.148316i
$666$	11.2361			0.435389
$667$	19.4721	−	33.7267i	0.753964	−	1.30590i
$668$	0.763932	+	1.32317i	0.0295574	+	0.0511949i
$669$	8.47214	+	14.6742i	0.327552	+	0.567336i
$670$	4.80902	−	8.32946i	0.185789	−	0.321795i
$671$	9.47214			0.365668
$672$	−8.45492	+	2.92887i	−0.326155	+	0.112984i
$673$	−45.4164			−1.75067			−0.875337	−	0.483513i	$-0.839360\pi$
$673$	−45.4164			−1.75067			−0.875337	+	0.483513i	$0.839360\pi$
$674$	6.85410	−	11.8717i	0.264010	−	0.457279i
$675$	−10.0000	−	17.3205i	−0.384900	−	0.666667i
$676$	−2.16312	−	3.74663i	−0.0831969	−	0.144101i
$677$	−7.97214	+	13.8081i	−0.306394	+	0.530690i	−0.977571	−	0.210607i	$-0.932456\pi$
$677$	−7.97214	+	13.8081i	−0.306394	+	0.530690i	0.671177	+	0.741297i	$0.265789\pi$
$678$	32.1803			1.23588
$679$	−16.9443	−	14.6742i	−0.650261	−	0.563143i
$680$	9.47214			0.363240
$681$	2.73607	−	4.73901i	0.104846	−	0.181599i
$682$	0.190983	+	0.330792i	0.00731312	+	0.0126667i
$683$	−7.73607	−	13.3993i	−0.296012	−	0.512709i	0.679207	−	0.733946i	$-0.262324\pi$
$683$	−7.73607	−	13.3993i	−0.296012	−	0.512709i	−0.975220	+	0.221238i	$0.928990\pi$
$684$	0.909830	−	1.57587i	0.0347882	−	0.0602550i
$685$	−15.6525			−0.598050
$686$	13.7533	+	26.6239i	0.525103	+	1.01651i
$687$	−20.1246			−0.767802
$688$	−15.7082	+	27.2074i	−0.598870	+	1.03727i
$689$	−22.8885	−	39.6441i	−0.871984	−	1.51032i
$690$	−7.04508	−	12.2024i	−0.268202	−	0.464539i
$691$	−23.6803	+	41.0156i	−0.900843	+	1.56031i	−0.0744399	+	0.997225i	$0.523717\pi$
$691$	−23.6803	+	41.0156i	−0.900843	+	1.56031i	−0.826403	+	0.563080i	$0.809616\pi$
$692$	−11.6738			−0.443770
$693$	4.00000	+	3.46410i	0.151947	+	0.131590i
$694$	−4.85410			−0.184259
$695$	8.47214	−	14.6742i	0.321366	−	0.556623i
$696$	5.00000	+	8.66025i	0.189525	+	0.328266i
$697$	2.11803	+	3.66854i	0.0802263	+	0.138956i
$698$	16.5623	−	28.6868i	0.626893	−	1.08581i
$699$	3.29180			0.124507
$700$	−6.18034	+	2.14093i	−0.233595	+	0.0809196i
$701$	−42.3607			−1.59994			−0.799970	−	0.600039i	$-0.795152\pi$
$701$	−42.3607			−1.59994			−0.799970	+	0.600039i	$0.795152\pi$
$702$	−18.0902	+	31.3331i	−0.682769	+	1.18259i
$703$	2.55573	+	4.42665i	0.0963911	+	0.166954i
$704$	−2.11803	−	3.66854i	−0.0798264	−	0.138263i
$705$	−1.73607	+	3.00696i	−0.0653841	+	0.113249i
$706$	41.2148			1.55114
$707$	−1.64590	+	8.55234i	−0.0619004	+	0.321644i
$708$	5.38197			0.202267
$709$	−19.0623	+	33.0169i	−0.715900	+	1.23998i	0.246711	+	0.969089i	$0.420650\pi$
$709$	−19.0623	+	33.0169i	−0.715900	+	1.23998i	−0.962611	+	0.270886i	$0.912683\pi$
$710$	−11.7082	−	20.2792i	−0.439401	−	0.761065i
$711$	−1.00000	−	1.73205i	−0.0375029	−	0.0649570i
$712$	−15.9164	+	27.5680i	−0.596493	+	1.03316i
$713$	2.05573			0.0769876
$714$	−3.42705	+	17.8075i	−0.128254	+	0.666428i
$715$	4.47214			0.167248
$716$	3.21885	−	5.57521i	0.120294	−	0.208355i
$717$	1.23607	+	2.14093i	0.0461618	+	0.0799546i
$718$	11.0451	+	19.1306i	0.412199	+	0.713949i
$719$	0.680340	−	1.17838i	0.0253724	−	0.0439463i	−0.853060	−	0.521812i	$-0.825256\pi$
$719$	0.680340	−	1.17838i	0.0253724	−	0.0439463i	0.878433	+	0.477866i	$0.158590\pi$
$720$	−9.70820			−0.361803
$721$	42.9508	−	14.8786i	1.59957	−	0.554108i
$722$	−27.2361			−1.01362
$723$	−0.736068	+	1.27491i	−0.0273747	+	0.0474143i
$724$	6.61803	+	11.4628i	0.245957	+	0.426011i
$725$	8.94427	+	15.4919i	0.332182	+	0.575356i
$726$	8.09017	−	14.0126i	0.300254	−	0.520056i
$727$	7.05573			0.261682			0.130841	−	0.991403i	$-0.458232\pi$
$727$	7.05573			0.261682			0.130841	+	0.991403i	$0.458232\pi$
$728$	−20.0000	−	17.3205i	−0.741249	−	0.641941i
$729$	13.0000			0.481481
$730$	−2.04508	+	3.54219i	−0.0756920	+	0.131102i
$731$	13.7082	+	23.7433i	0.507016	+	0.878178i
$732$	−2.92705	−	5.06980i	−0.108187	−	0.187385i
$733$	−8.91641	+	15.4437i	−0.329335	+	0.570425i	−0.982380	−	0.186894i	$-0.940158\pi$
$733$	−8.91641	+	15.4437i	−0.329335	+	0.570425i	0.653045	+	0.757319i	$0.273491\pi$
$734$	−8.38197			−0.309384
$735$	−1.00000	−	6.92820i	−0.0368856	−	0.255551i
$736$	29.4508			1.08557
$737$	−2.97214	+	5.14789i	−0.109480	+	0.189625i
$738$	−1.61803	−	2.80252i	−0.0595607	−	0.103162i
$739$	21.8262	+	37.8042i	0.802891	+	1.39065i	0.917706	+	0.397261i	$0.130039\pi$
$739$	21.8262	+	37.8042i	0.802891	+	1.39065i	−0.114814	+	0.993387i	$0.536627\pi$
$740$	−1.07295	+	1.85840i	−0.0394424	+	0.0683162i
$741$	−6.58359			−0.241854
$742$	33.1246	+	28.6868i	1.21604	+	1.05312i
$743$	−44.7214			−1.64067			−0.820334	−	0.571885i	$-0.806212\pi$
$743$	−44.7214			−1.64067			−0.820334	+	0.571885i	$0.806212\pi$
$744$	−0.263932	+	0.457144i	−0.00967622	+	0.0167597i
$745$	0.590170	+	1.02220i	0.0216222	+	0.0374507i
$746$	0.0450850	+	0.0780895i	0.00165068	+	0.00285906i
$747$	−1.52786	+	2.64634i	−0.0559016	+	0.0968244i
$748$	2.61803			0.0957248
$749$	−3.22949	+	1.11873i	−0.118003	+	0.0408774i
$750$	14.5623			0.531740
$751$	11.2639	−	19.5097i	0.411027	−	0.711919i	−0.583976	−	0.811771i	$-0.698504\pi$
$751$	11.2639	−	19.5097i	0.411027	−	0.711919i	0.995002	+	0.0998521i	$0.0318370\pi$
$752$	−8.42705	−	14.5961i	−0.307303	−	0.532264i
$753$	−13.4164	−	23.2379i	−0.488921	−	0.846836i
$754$	16.1803	−	28.0252i	0.589253	−	1.02062i
$755$	−5.94427			−0.216334
$756$	1.54508	−	8.02850i	0.0561942	−	0.291994i
$757$	−2.94427			−0.107011			−0.0535057	−	0.998568i	$-0.517040\pi$
$757$	−2.94427			−0.107011			−0.0535057	+	0.998568i	$0.517040\pi$
$758$	−25.4164	+	44.0225i	−0.923166	+	1.59897i
$759$	4.35410	+	7.54153i	0.158044	+	0.273740i
$760$	−1.64590	−	2.85078i	−0.0597030	−	0.103409i
$761$	−8.15248	+	14.1205i	−0.295527	+	0.511868i	−0.975107	−	0.221733i	$-0.928829\pi$
$761$	−8.15248	+	14.1205i	−0.295527	+	0.511868i	0.679580	+	0.733601i	$0.262162\pi$
$762$	24.9443			0.903636
$763$	7.11803	−	36.9864i	0.257690	−	1.33900i
$764$	3.38197			0.122355
$765$	−4.23607	+	7.33708i	−0.153155	+	0.265273i
$766$	−16.8992	−	29.2703i	−0.610592	−	1.05758i
$767$	19.4721	+	33.7267i	0.703098	+	1.21780i
$768$	−6.78115	+	11.7453i	−0.244694	+	0.423822i
$769$	−16.8328			−0.607007			−0.303503	−	0.952830i	$-0.598156\pi$
$769$	−16.8328			−0.607007			−0.303503	+	0.952830i	$0.598156\pi$
$770$	−4.04508	+	1.40126i	−0.145775	+	0.0504979i
$771$	−1.29180			−0.0465229
$772$	−0.253289	+	0.438709i	−0.00911607	+	0.0157895i
$773$	4.82624	+	8.35929i	0.173588	+	0.300663i	0.939672	−	0.342078i	$-0.111131\pi$
$773$	4.82624	+	8.35929i	0.173588	+	0.300663i	−0.766084	+	0.642741i	$0.777797\pi$
$774$	−10.4721	−	18.1383i	−0.376413	−	0.651967i
$775$	−0.472136	+	0.817763i	−0.0169596	+	0.0293749i
$776$	−18.9443			−0.680060
$777$	6.94427	+	6.01392i	0.249124	+	0.215748i
$778$	−1.61803			−0.0580093
$779$	0.736068	−	1.27491i	0.0263724	−	0.0456783i
$780$	−1.38197	−	2.39364i	−0.0494823	−	0.0857059i
$781$	7.23607	+	12.5332i	0.258927	+	0.448474i
$782$	29.8435	−	51.6904i	1.06720	−	1.84844i
$783$	−22.3607			−0.799106
$784$	31.5517	+	12.6113i	1.12685	+	0.450405i
$785$	2.23607			0.0798087
$786$	11.0451	−	19.1306i	0.393965	−	0.682368i
$787$	−4.82624	−	8.35929i	−0.172037	−	0.297976i	0.767095	−	0.641534i	$-0.221701\pi$
$787$	−4.82624	−	8.35929i	−0.172037	−	0.297976i	−0.939132	+	0.343557i	$0.888368\pi$
$788$	0.909830	+	1.57587i	0.0324114	+	0.0561381i
$789$	−3.73607	+	6.47106i	−0.133008	+	0.230376i
$790$	1.61803			0.0575671
$791$	−39.7771	−	34.4480i	−1.41431	−	1.22483i
$792$	4.47214			0.158910
$793$	21.1803	−	36.6854i	0.752136	−	1.30274i
$794$	−22.3713	−	38.7483i	−0.793929	−	1.37512i
$795$	−5.11803	−	8.86469i	−0.181518	−	0.314398i
$796$	−5.54508	+	9.60437i	−0.196540	+	0.340418i
$797$	24.8328			0.879623			0.439812	−	0.898090i	$-0.355045\pi$
$797$	24.8328			0.879623			0.439812	+	0.898090i	$0.355045\pi$
$798$	5.95492	−	2.06284i	0.210802	−	0.0730239i
$799$	−14.7082			−0.520339
$800$	−6.76393	+	11.7155i	−0.239141	+	0.414205i
$801$	−14.2361	−	24.6576i	−0.503007	−	0.871233i
$802$	−6.42705	−	11.1320i	−0.226947	−	0.393084i
$803$	1.26393	−	2.18919i	0.0446032	−	0.0772550i
$804$	3.67376			0.129564
$805$	−4.35410	+	22.6246i	−0.153462	+	0.797412i
$806$	1.70820			0.0601689
$807$	9.73607	−	16.8634i	0.342726	−	0.593619i
$808$	3.68034	+	6.37454i	0.129474	+	0.224255i
$809$	2.82624	+	4.89519i	0.0993652	+	0.172106i	0.911422	−	0.411473i	$-0.134985\pi$
$809$	2.82624	+	4.89519i	0.0993652	+	0.172106i	−0.812057	+	0.583578i	$0.801652\pi$
$810$	0.809017	−	1.40126i	0.0284260	−	0.0492352i
$811$	52.7214			1.85130			0.925649	−	0.378384i	$-0.123520\pi$
$811$	52.7214			1.85130			0.925649	+	0.378384i	$0.123520\pi$
$812$	−1.38197	+	7.18091i	−0.0484975	+	0.252000i
$813$	−21.6525			−0.759385
$814$	2.80902	−	4.86536i	0.0984560	−	0.170531i
$815$	−2.64590	−	4.58283i	−0.0926818	−	0.160530i
$816$	10.2812	+	17.8075i	0.359912	+	0.623386i
$817$	4.76393	−	8.25137i	0.166669	−	0.288679i
$818$	−37.0344			−1.29488
$819$	22.3607	−	7.74597i	0.781345	−	0.270666i
$820$	0.618034			0.0215827
$821$	10.5000	−	18.1865i	0.366453	−	0.634714i	−0.622556	−	0.782576i	$-0.713906\pi$
$821$	10.5000	−	18.1865i	0.366453	−	0.634714i	0.989008	+	0.147861i	$0.0472389\pi$
$822$	−12.6631	−	21.9332i	−0.441677	−	0.765007i
$823$	6.73607	+	11.6672i	0.234805	+	0.406693i	0.959216	−	0.282675i	$-0.0912216\pi$
$823$	6.73607	+	11.6672i	0.234805	+	0.406693i	−0.724411	+	0.689368i	$0.757888\pi$
$824$	19.2082	−	33.2696i	0.669149	−	1.15900i
$825$	−4.00000			−0.139262
$826$	−28.1803	−	24.4049i	−0.980519	−	0.849155i
$827$	36.0000			1.25184			0.625921	−	0.779886i	$-0.284723\pi$
$827$	36.0000			1.25184			0.625921	+	0.779886i	$0.284723\pi$
$828$	−5.38197	+	9.32184i	−0.187036	+	0.323956i
$829$	−1.97214	−	3.41584i	−0.0684951	−	0.118637i	0.829744	−	0.558144i	$-0.188486\pi$
$829$	−1.97214	−	3.41584i	−0.0684951	−	0.118637i	−0.898239	+	0.439507i	$0.855153\pi$
$830$	−1.23607	−	2.14093i	−0.0429045	−	0.0743129i
$831$	2.02786	−	3.51236i	0.0703458	−	0.121843i
$832$	−18.9443			−0.656774
$833$	23.2984	−	18.3427i	0.807241	−	0.635537i
$834$	27.4164			0.949353
$835$	−1.23607	+	2.14093i	−0.0427759	+	0.0740900i
$836$	−0.454915	−	0.787936i	−0.0157336	−	0.0272513i
$837$	−0.590170	−	1.02220i	−0.0203993	−	0.0353326i
$838$	14.4721	−	25.0665i	0.499932	−	0.865907i
$839$	20.9443			0.723077			0.361538	−	0.932357i	$-0.382252\pi$
$839$	20.9443			0.723077			0.361538	+	0.932357i	$0.382252\pi$
$840$	−4.47214	−	3.87298i	−0.154303	−	0.133631i
$841$	−9.00000			−0.310345
$842$	13.3262	−	23.0817i	0.459252	−	0.795449i
$843$	2.23607	+	3.87298i	0.0770143	+	0.133393i
$844$		0			0
$845$	3.50000	−	6.06218i	0.120404	−	0.208545i
$846$	11.2361			0.386304
$847$	−25.0000	+	8.66025i	−0.859010	+	0.297570i
$848$	49.6869			1.70626
$849$	−5.59017	+	9.68246i	−0.191854	+	0.332301i
$850$	13.7082	+	23.7433i	0.470188	+	0.814389i
$851$	−15.1180	−	26.1852i	−0.518240	−	0.897617i
$852$	4.47214	−	7.74597i	0.153213	−	0.265372i
$853$	18.9443			0.648640			0.324320	−	0.945948i	$-0.394865\pi$
$853$	18.9443			0.648640			0.324320	+	0.945948i	$0.394865\pi$
$854$	−7.66312	+	39.8187i	−0.262227	+	1.36257i
$855$	2.94427			0.100692
$856$	−1.44427	+	2.50155i	−0.0493642	+	0.0855013i
$857$	5.15248	+	8.92435i	0.176005	+	0.304850i	0.940509	−	0.339770i	$-0.110349\pi$
$857$	5.15248	+	8.92435i	0.176005	+	0.304850i	−0.764503	+	0.644620i	$0.777016\pi$
$858$	3.61803	+	6.26662i	0.123518	+	0.213939i
$859$	14.6459	−	25.3674i	0.499712	−	0.865526i	−0.500288	−	0.865859i	$-0.666773\pi$
$859$	14.6459	−	25.3674i	0.499712	−	0.865526i	1.00000		0.000332993i	$0.000105995\pi$
$860$	4.00000			0.136399
$861$	0.500000	−	2.59808i	0.0170400	−	0.0885422i
$862$	−3.79837			−0.129373
$863$	−0.409830	+	0.709846i	−0.0139508	+	0.0241635i	−0.872917	−	0.487870i	$-0.837774\pi$
$863$	−0.409830	+	0.709846i	−0.0139508	+	0.0241635i	0.858966	+	0.512033i	$0.171107\pi$
$864$	−8.45492	−	14.6443i	−0.287642	−	0.498211i
$865$	−9.44427	−	16.3580i	−0.321115	−	0.556187i
$866$	−5.61803	+	9.73072i	−0.190909	+	0.330663i
$867$	0.944272			0.0320692
$868$	−0.364745	+	0.126351i	−0.0123803	+	0.00428865i
$869$	−1.00000			−0.0339227
$870$	3.61803	−	6.26662i	0.122663	−	0.212458i
$871$	13.2918	+	23.0221i	0.450375	+	0.780073i
$872$	−15.9164	−	27.5680i	−0.538998	−	0.933571i
$873$	8.47214	−	14.6742i	0.286738	−	0.496645i
$874$	−20.7426			−0.701630
$875$	−18.0000	−	15.5885i	−0.608511	−	0.526986i
$876$	−1.56231			−0.0527854
$877$	−0.736068	+	1.27491i	−0.0248552	+	0.0430506i	−0.878185	−	0.478320i	$-0.841246\pi$
$877$	−0.736068	+	1.27491i	−0.0248552	+	0.0430506i	0.853330	+	0.521371i	$0.174579\pi$
$878$	29.4615	+	51.0288i	0.994277	+	1.72214i
$879$	−14.4164	−	24.9700i	−0.486253	−	0.842216i
$880$	−2.42705	+	4.20378i	−0.0818159	+	0.141709i
$881$	24.4721			0.824487			0.412244	−	0.911074i	$-0.364745\pi$
$881$	24.4721			0.824487			0.412244	+	0.911074i	$0.364745\pi$
$882$	−17.7984	+	14.0126i	−0.599302	+	0.471828i
$883$	−16.5836			−0.558082			−0.279041	−	0.960279i	$-0.590017\pi$
$883$	−16.5836			−0.558082			−0.279041	+	0.960279i	$0.590017\pi$
$884$	5.85410	−	10.1396i	0.196895	−	0.341032i
$885$	4.35410	+	7.54153i	0.146362	+	0.253506i
$886$	6.28115	+	10.8793i	0.211019	+	0.365496i
$887$	23.4443	−	40.6067i	0.787182	−	1.36344i	−0.140505	−	0.990080i	$-0.544873\pi$
$887$	23.4443	−	40.6067i	0.787182	−	1.36344i	0.927687	−	0.373359i	$-0.121794\pi$
$888$	7.76393			0.260540
$889$	−30.8328	−	26.7020i	−1.03410	−	0.895556i
$890$	23.0344			0.772116
$891$	−0.500000	+	0.866025i	−0.0167506	+	0.0290129i
$892$	5.23607	+	9.06914i	0.175317	+	0.303657i
$893$	2.55573	+	4.42665i	0.0855242	+	0.148132i
$894$	−0.954915	+	1.65396i	−0.0319371	+	0.0553167i
$895$	10.4164			0.348182
$896$	34.0451	−	11.7936i	1.13737	−	0.393995i
$897$	38.9443			1.30031
$898$	−17.0344	+	29.5045i	−0.568447	+	0.984579i
$899$	0.527864	+	0.914287i	0.0176053	+	0.0304932i
$900$	−2.47214	−	4.28187i	−0.0824045	−	0.142729i
$901$	21.6803	−	37.5515i	0.722277	−	1.25102i
$902$	−1.61803			−0.0538746
$903$	3.23607	−	16.8151i	0.107690	−	0.559572i
$904$	−44.4721			−1.47912
$905$	−10.7082	+	18.5472i	−0.355953	+	0.616528i
$906$	−4.80902	−	8.32946i	−0.159769	−	0.276728i
$907$	7.17376	+	12.4253i	0.238201	+	0.412576i	0.960198	−	0.279320i	$-0.0901090\pi$
$907$	7.17376	+	12.4253i	0.238201	+	0.412576i	−0.721997	+	0.691896i	$0.756776\pi$
$908$	1.69098	−	2.92887i	0.0561172	−	0.0971979i
$909$	−6.58359			−0.218364
$910$	−3.61803	+	18.7999i	−0.119937	+	0.623209i
$911$	−47.4164			−1.57098			−0.785488	−	0.618877i	$-0.787588\pi$
$911$	−47.4164			−1.57098			−0.785488	+	0.618877i	$0.787588\pi$
$912$	3.57295	−	6.18853i	0.118312	−	0.204923i
$913$	0.763932	+	1.32317i	0.0252825	+	0.0437905i
$914$	21.2254	+	36.7635i	0.702075	+	1.21603i
$915$	4.73607	−	8.20311i	0.156570	−	0.271186i
$916$	−12.4377			−0.410953
$917$	−34.1312	+	11.8234i	−1.12711	+	0.390443i
$918$	−34.2705			−1.13110
$919$	2.02786	−	3.51236i	0.0668931	−	0.115862i	−0.830639	−	0.556811i	$-0.812025\pi$
$919$	2.02786	−	3.51236i	0.0668931	−	0.115862i	0.897532	+	0.440949i	$0.145358\pi$
$920$	9.73607	+	16.8634i	0.320989	+	0.555969i
$921$	4.94427	+	8.56373i	0.162919	+	0.282185i
$922$	31.5066	−	54.5710i	1.03761	−	1.79720i
$923$	64.7214			2.13033
$924$	−1.23607	−	1.07047i	−0.0406637	−	0.0352158i
$925$	13.8885			0.456653
$926$	1.70820	−	2.95870i	0.0561351	−	0.0972288i
$927$	17.1803	+	29.7572i	0.564276	+	0.977355i
$928$	7.56231	+	13.0983i	0.248245	+	0.429973i
$929$	19.7705	−	34.2435i	0.648649	−	1.12349i	−0.334796	−	0.942291i	$-0.608668\pi$
$929$	19.7705	−	34.2435i	0.648649	−	1.12349i	0.983446	−	0.181203i	$-0.0579992\pi$
$930$	0.381966			0.0125252
$931$	−9.56888	−	3.82472i	−0.313607	−	0.125350i
$932$	2.03444			0.0666404
$933$	10.9164	−	18.9078i	0.357387	−	0.619013i
$934$	−7.13525	−	12.3586i	−0.233473	−	0.404387i
$935$	2.11803	+	3.66854i	0.0692671	+	0.119974i
$936$	10.0000	−	17.3205i	0.326860	−	0.566139i
$937$	29.4164			0.960992			0.480496	−	0.876997i	$-0.340457\pi$
$937$	29.4164			0.960992			0.480496	+	0.876997i	$0.340457\pi$
$938$	−19.2361	−	16.6589i	−0.628080	−	0.543933i
$939$	−17.2918			−0.564296
$940$	−1.07295	+	1.85840i	−0.0349957	+	0.0606144i
$941$	−17.2082	−	29.8055i	−0.560971	−	0.971631i	−0.997412	−	0.0718979i	$-0.977094\pi$
$941$	−17.2082	−	29.8055i	−0.560971	−	0.971631i	0.436441	−	0.899733i	$-0.356239\pi$
$942$	1.80902	+	3.13331i	0.0589410	+	0.102089i
$943$	−4.35410	+	7.54153i	−0.141789	+	0.245586i
$944$	−42.2705			−1.37579
$945$	12.5000	−	4.33013i	0.406625	−	0.140859i
$946$	−10.4721			−0.340479
$947$	−15.3541	+	26.5941i	−0.498941	+	0.864192i	−0.999999	−	0.00122208i	$-0.999611\pi$
$947$	−15.3541	+	26.5941i	−0.498941	+	0.864192i	0.501058	+	0.865414i	$0.332944\pi$
$948$	0.309017	+	0.535233i	0.0100364	+	0.0173836i
$949$	−5.65248	−	9.79038i	−0.183487	−	0.317809i
$950$	4.76393	−	8.25137i	0.154562	−	0.267710i
$951$	25.7639			0.835453
$952$	4.73607	−	24.6093i	0.153497	−	0.797593i
$953$	43.8885			1.42169			0.710845	−	0.703349i	$-0.248313\pi$
$953$	43.8885			1.42169			0.710845	+	0.703349i	$0.248313\pi$
$954$	−16.5623	+	28.6868i	−0.536224	+	0.928768i
$955$	2.73607	+	4.73901i	0.0885371	+	0.153351i
$956$	0.763932	+	1.32317i	0.0247073	+	0.0427943i
$957$	−2.23607	+	3.87298i	−0.0722818	+	0.125196i
$958$	33.9787			1.09780
$959$	−7.82624	+	40.6663i	−0.252722	+	1.31318i
$960$	−4.23607			−0.136719
$961$	15.4721	−	26.7985i	0.499101	−	0.864469i
$962$	−12.5623	−	21.7586i	−0.405025	−	0.701524i
$963$	−1.29180	−	2.23746i	−0.0416275	−	0.0721010i
$964$	−0.454915	+	0.787936i	−0.0146518	+	0.0253777i
$965$	−0.819660			−0.0263858
$966$	−35.2254	+	12.2024i	−1.13336	+	0.392607i
$967$	21.3050			0.685121			0.342561	−	0.939496i	$-0.388706\pi$
$967$	21.3050			0.685121			0.342561	+	0.939496i	$0.388706\pi$
$968$	−11.1803	+	19.3649i	−0.359350	+	0.622412i
$969$	−3.11803	−	5.40059i	−0.100166	−	0.173492i
$970$	6.85410	+	11.8717i	0.220072	+	0.381176i
$971$	−23.3885	+	40.5101i	−0.750574	+	1.30003i	0.196971	+	0.980409i	$0.436890\pi$
$971$	−23.3885	+	40.5101i	−0.750574	+	1.30003i	−0.947545	+	0.319623i	$0.896444\pi$
$972$	9.88854			0.317175
$973$	−33.8885	−	29.3483i	−1.08642	−	0.940865i
$974$	−41.3262			−1.32418
$975$	−8.94427	+	15.4919i	−0.286446	+	0.496139i
$976$	22.9894	+	39.8187i	0.735871	+	1.27457i
$977$	−11.8262	−	20.4836i	−0.378355	−	0.655330i	0.612468	−	0.790495i	$-0.290177\pi$
$977$	−11.8262	−	20.4836i	−0.378355	−	0.655330i	−0.990823	+	0.135165i	$0.956843\pi$
$978$	4.28115	−	7.41517i	0.136896	−	0.237111i
$979$	−14.2361			−0.454987
$980$	−0.618034	−	4.28187i	−0.0197424	−	0.136779i
$981$	28.4721			0.909045
$982$	10.0000	−	17.3205i	0.319113	−	0.552720i
$983$	25.0623	+	43.4092i	0.799363	+	1.38454i	0.920031	+	0.391845i	$0.128163\pi$
$983$	25.0623	+	43.4092i	0.799363	+	1.38454i	−0.120668	+	0.992693i	$0.538504\pi$
$984$	−1.11803	−	1.93649i	−0.0356416	−	0.0617331i
$985$	−1.47214	+	2.54981i	−0.0469062	+	0.0812438i
$986$	30.6525			0.976174
$987$	6.94427	+	6.01392i	0.221039	+	0.191425i
$988$	−4.06888			−0.129448
$989$	−28.1803	+	48.8098i	−0.896083	+	1.55206i
$990$	−1.61803	−	2.80252i	−0.0514245	−	0.0890698i
$991$	23.2082	+	40.1978i	0.737233	+	1.27692i	0.953737	+	0.300643i	$0.0972013\pi$
$991$	23.2082	+	40.1978i	0.737233	+	1.27692i	−0.216504	+	0.976282i	$0.569465\pi$
$992$	−0.399187	+	0.691412i	−0.0126742	+	0.0219524i
$993$	−31.8328			−1.01018
$994$	−58.5410	+	20.2792i	−1.85681	+	0.643217i
$995$	−17.9443			−0.568872
$996$	0.472136	−	0.817763i	0.0149602	−	0.0259118i
$997$	20.5344	+	35.5667i	0.650332	+	1.12641i	0.983042	+	0.183379i	$0.0587037\pi$
$997$	20.5344	+	35.5667i	0.650332	+	1.12641i	−0.332710	+	0.943029i	$0.607963\pi$
$998$	12.9894	+	22.4982i	0.411171	+	0.712169i
$999$	−8.68034	+	15.0348i	−0.274634	+	0.475680i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	287.2.e.a.247.1	yes	4
7.2	even	3		2009.2.a.f.1.2		2
7.4	even	3	inner	287.2.e.a.165.1	✓	4
7.5	odd	6		2009.2.a.e.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
287.2.e.a.165.1	✓	4	7.4	even	3	inner
287.2.e.a.247.1	yes	4	1.1	even	1	trivial
2009.2.a.e.1.2		2	7.5	odd	6
2009.2.a.f.1.2		2	7.2	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)

\(f(q)\)	\(=\)	\(q+(-0.809017 + 1.40126i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(-0.309017 - 0.535233i) q^{4} +(0.500000 - 0.866025i) q^{5} +1.61803 q^{6} +(-2.00000 - 1.73205i) q^{7} -2.23607 q^{8} +(1.00000 - 1.73205i) q^{9} +O(q^{10})\)	\(q+(-0.809017 + 1.40126i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(-0.309017 - 0.535233i) q^{4} +(0.500000 - 0.866025i) q^{5} +1.61803 q^{6} +(-2.00000 - 1.73205i) q^{7} -2.23607 q^{8} +(1.00000 - 1.73205i) q^{9} +(0.809017 + 1.40126i) q^{10} +(-0.500000 - 0.866025i) q^{11} +(-0.309017 + 0.535233i) q^{12} -4.47214 q^{13} +(4.04508 - 1.40126i) q^{14} -1.00000 q^{15} +(2.42705 - 4.20378i) q^{16} +(-2.11803 - 3.66854i) q^{17} +(1.61803 + 2.80252i) q^{18} +(-0.736068 + 1.27491i) q^{19} -0.618034 q^{20} +(-0.500000 + 2.59808i) q^{21} +1.61803 q^{22} +(4.35410 - 7.54153i) q^{23} +(1.11803 + 1.93649i) q^{24} +(2.00000 + 3.46410i) q^{25} +(3.61803 - 6.26662i) q^{26} -5.00000 q^{27} +(-0.309017 + 1.60570i) q^{28} +4.47214 q^{29} +(0.809017 - 1.40126i) q^{30} +(0.118034 + 0.204441i) q^{31} +(1.69098 + 2.92887i) q^{32} +(-0.500000 + 0.866025i) q^{33} +6.85410 q^{34} +(-2.50000 + 0.866025i) q^{35} -1.23607 q^{36} +(1.73607 - 3.00696i) q^{37} +(-1.19098 - 2.06284i) q^{38} +(2.23607 + 3.87298i) q^{39} +(-1.11803 + 1.93649i) q^{40} -1.00000 q^{41} +(-3.23607 - 2.80252i) q^{42} -6.47214 q^{43} +(-0.309017 + 0.535233i) q^{44} +(-1.00000 - 1.73205i) q^{45} +(7.04508 + 12.2024i) q^{46} +(1.73607 - 3.00696i) q^{47} -4.85410 q^{48} +(1.00000 + 6.92820i) q^{49} -6.47214 q^{50} +(-2.11803 + 3.66854i) q^{51} +(1.38197 + 2.39364i) q^{52} +(5.11803 + 8.86469i) q^{53} +(4.04508 - 7.00629i) q^{54} -1.00000 q^{55} +(4.47214 + 3.87298i) q^{56} +1.47214 q^{57} +(-3.61803 + 6.26662i) q^{58} +(-4.35410 - 7.54153i) q^{59} +(0.309017 + 0.535233i) q^{60} +(-4.73607 + 8.20311i) q^{61} -0.381966 q^{62} +(-5.00000 + 1.73205i) q^{63} +4.23607 q^{64} +(-2.23607 + 3.87298i) q^{65} +(-0.809017 - 1.40126i) q^{66} +(-2.97214 - 5.14789i) q^{67} +(-1.30902 + 2.26728i) q^{68} -8.70820 q^{69} +(0.809017 - 4.20378i) q^{70} -14.4721 q^{71} +(-2.23607 + 3.87298i) q^{72} +(1.26393 + 2.18919i) q^{73} +(2.80902 + 4.86536i) q^{74} +(2.00000 - 3.46410i) q^{75} +0.909830 q^{76} +(-0.500000 + 2.59808i) q^{77} -7.23607 q^{78} +(0.500000 - 0.866025i) q^{79} +(-2.42705 - 4.20378i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(0.809017 - 1.40126i) q^{82} -1.52786 q^{83} +(1.54508 - 0.535233i) q^{84} -4.23607 q^{85} +(5.23607 - 9.06914i) q^{86} +(-2.23607 - 3.87298i) q^{87} +(1.11803 + 1.93649i) q^{88} +(7.11803 - 12.3288i) q^{89} +3.23607 q^{90} +(8.94427 + 7.74597i) q^{91} -5.38197 q^{92} +(0.118034 - 0.204441i) q^{93} +(2.80902 + 4.86536i) q^{94} +(0.736068 + 1.27491i) q^{95} +(1.69098 - 2.92887i) q^{96} +8.47214 q^{97} +(-10.5172 - 4.20378i) 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

Introduction

L-functions

Modular forms

Varieties

Fields

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