LMFDB - Embedded newform 65.2.e.a.16.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [65,2,Mod(16,65)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(65, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 2]))

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

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

chi := DirichletCharacter("65.16");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 65 = 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	65.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:	$0.519027613138$
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			16.1
Root			$0.809017 + 1.40126i$ of defining polynomial
Character	$\chi$	$=$	65.16
Dual form			65.2.e.a.61.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.809017 - 1.40126i) q^{2} +(1.11803 + 1.93649i) q^{3} +(-0.309017 + 0.535233i) q^{4} +1.00000 q^{5} +(1.80902 - 3.13331i) q^{6} +(0.118034 - 0.204441i) q^{7} -2.23607 q^{8} +(-1.00000 + 1.73205i) q^{9} +O(q^{10})$	\(q+(-0.809017 - 1.40126i) q^{2} +(1.11803 + 1.93649i) q^{3} +(-0.309017 + 0.535233i) q^{4} +1.00000 q^{5} +(1.80902 - 3.13331i) q^{6} +(0.118034 - 0.204441i) q^{7} -2.23607 q^{8} +(-1.00000 + 1.73205i) q^{9} +(-0.809017 - 1.40126i) q^{10} +(-2.11803 - 3.66854i) q^{11} -1.38197 q^{12} +(-1.00000 + 3.46410i) q^{13} -0.381966 q^{14} +(1.11803 + 1.93649i) q^{15} +(2.42705 + 4.20378i) q^{16} +(-2.73607 + 4.73901i) q^{17} +3.23607 q^{18} +(0.118034 - 0.204441i) q^{19} +(-0.309017 + 0.535233i) q^{20} +0.527864 q^{21} +(-3.42705 + 5.93583i) q^{22} +(-4.11803 - 7.13264i) q^{23} +(-2.50000 - 4.33013i) q^{24} +1.00000 q^{25} +(5.66312 - 1.40126i) q^{26} +2.23607 q^{27} +(0.0729490 + 0.126351i) q^{28} +(-0.736068 - 1.27491i) q^{29} +(1.80902 - 3.13331i) q^{30} +(1.69098 - 2.92887i) q^{32} +(4.73607 - 8.20311i) q^{33} +8.85410 q^{34} +(0.118034 - 0.204441i) q^{35} +(-0.618034 - 1.07047i) q^{36} +(-1.50000 - 2.59808i) q^{37} -0.381966 q^{38} +(-7.82624 + 1.93649i) q^{39} -2.23607 q^{40} +(2.97214 + 5.14789i) q^{41} +(-0.427051 - 0.739674i) q^{42} +(0.881966 - 1.52761i) q^{43} +2.61803 q^{44} +(-1.00000 + 1.73205i) q^{45} +(-6.66312 + 11.5409i) q^{46} +12.9443 q^{47} +(-5.42705 + 9.39993i) q^{48} +(3.47214 + 6.01392i) q^{49} +(-0.809017 - 1.40126i) q^{50} -12.2361 q^{51} +(-1.54508 - 1.60570i) q^{52} +6.00000 q^{53} +(-1.80902 - 3.13331i) q^{54} +(-2.11803 - 3.66854i) q^{55} +(-0.263932 + 0.457144i) q^{56} +0.527864 q^{57} +(-1.19098 + 2.06284i) q^{58} +(-6.35410 + 11.0056i) q^{59} -1.38197 q^{60} +(6.20820 - 10.7529i) q^{61} +(0.236068 + 0.408882i) q^{63} +4.23607 q^{64} +(-1.00000 + 3.46410i) q^{65} -15.3262 q^{66} +(-5.35410 - 9.27358i) q^{67} +(-1.69098 - 2.92887i) q^{68} +(9.20820 - 15.9491i) q^{69} -0.381966 q^{70} +(0.881966 - 1.52761i) q^{71} +(2.23607 - 3.87298i) q^{72} -6.00000 q^{73} +(-2.42705 + 4.20378i) q^{74} +(1.11803 + 1.93649i) q^{75} +(0.0729490 + 0.126351i) q^{76} -1.00000 q^{77} +(9.04508 + 9.39993i) q^{78} +(2.42705 + 4.20378i) q^{80} +(5.50000 + 9.52628i) q^{81} +(4.80902 - 8.32946i) q^{82} -8.94427 q^{83} +(-0.163119 + 0.282530i) q^{84} +(-2.73607 + 4.73901i) q^{85} -2.85410 q^{86} +(1.64590 - 2.85078i) q^{87} +(4.73607 + 8.20311i) q^{88} +(4.50000 + 7.79423i) q^{89} +3.23607 q^{90} +(0.590170 + 0.613323i) q^{91} +5.09017 q^{92} +(-10.4721 - 18.1383i) q^{94} +(0.118034 - 0.204441i) q^{95} +7.56231 q^{96} +(-2.73607 + 4.73901i) q^{97} +(5.61803 - 9.73072i) q^{98} +8.47214 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - q^{2} + q^{4} + 4 q^{5} + 5 q^{6} - 4 q^{7} - 4 q^{9}+O(q^{10}) $ 4 * q - q^2 + q^4 + 4 * q^5 + 5 * q^6 - 4 * q^7 - 4 * q^9	$ 4 q - q^{2} + q^{4} + 4 q^{5} + 5 q^{6} - 4 q^{7} - 4 q^{9} - q^{10} - 4 q^{11} - 10 q^{12} - 4 q^{13} - 6 q^{14} + 3 q^{16} - 2 q^{17} + 4 q^{18} - 4 q^{19} + q^{20} + 20 q^{21} - 7 q^{22} - 12 q^{23} - 10 q^{24} + 4 q^{25} + 7 q^{26} + 7 q^{28} + 6 q^{29} + 5 q^{30} + 9 q^{32} + 10 q^{33} + 22 q^{34} - 4 q^{35} + 2 q^{36} - 6 q^{37} - 6 q^{38} - 6 q^{41} + 5 q^{42} + 8 q^{43} + 6 q^{44} - 4 q^{45} - 11 q^{46} + 16 q^{47} - 15 q^{48} - 4 q^{49} - q^{50} - 40 q^{51} + 5 q^{52} + 24 q^{53} - 5 q^{54} - 4 q^{55} - 10 q^{56} + 20 q^{57} - 7 q^{58} - 12 q^{59} - 10 q^{60} - 2 q^{61} - 8 q^{63} + 8 q^{64} - 4 q^{65} - 30 q^{66} - 8 q^{67} - 9 q^{68} + 10 q^{69} - 6 q^{70} + 8 q^{71} - 24 q^{73} - 3 q^{74} + 7 q^{76} - 4 q^{77} + 25 q^{78} + 3 q^{80} + 22 q^{81} + 17 q^{82} + 15 q^{84} - 2 q^{85} + 2 q^{86} + 20 q^{87} + 10 q^{88} + 18 q^{89} + 4 q^{90} - 20 q^{91} - 2 q^{92} - 24 q^{94} - 4 q^{95} - 10 q^{96} - 2 q^{97} + 18 q^{98} + 16 q^{99}+O(q^{100}) $ 4 * q - q^2 + q^4 + 4 * q^5 + 5 * q^6 - 4 * q^7 - 4 * q^9 - q^10 - 4 * q^11 - 10 * q^12 - 4 * q^13 - 6 * q^14 + 3 * q^16 - 2 * q^17 + 4 * q^18 - 4 * q^19 + q^20 + 20 * q^21 - 7 * q^22 - 12 * q^23 - 10 * q^24 + 4 * q^25 + 7 * q^26 + 7 * q^28 + 6 * q^29 + 5 * q^30 + 9 * q^32 + 10 * q^33 + 22 * q^34 - 4 * q^35 + 2 * q^36 - 6 * q^37 - 6 * q^38 - 6 * q^41 + 5 * q^42 + 8 * q^43 + 6 * q^44 - 4 * q^45 - 11 * q^46 + 16 * q^47 - 15 * q^48 - 4 * q^49 - q^50 - 40 * q^51 + 5 * q^52 + 24 * q^53 - 5 * q^54 - 4 * q^55 - 10 * q^56 + 20 * q^57 - 7 * q^58 - 12 * q^59 - 10 * q^60 - 2 * q^61 - 8 * q^63 + 8 * q^64 - 4 * q^65 - 30 * q^66 - 8 * q^67 - 9 * q^68 + 10 * q^69 - 6 * q^70 + 8 * q^71 - 24 * q^73 - 3 * q^74 + 7 * q^76 - 4 * q^77 + 25 * q^78 + 3 * q^80 + 22 * q^81 + 17 * q^82 + 15 * q^84 - 2 * q^85 + 2 * q^86 + 20 * q^87 + 10 * q^88 + 18 * q^89 + 4 * q^90 - 20 * q^91 - 2 * q^92 - 24 * q^94 - 4 * q^95 - 10 * q^96 - 2 * q^97 + 18 * q^98 + 16 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/65\mathbb{Z}\right)^\times$.

$n$	$27$	$41$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$

Coefficient data

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

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

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

$2$	−0.809017	−	1.40126i	−0.572061	−	0.990839i	−0.996354	−	0.0853143i	$-0.972811\pi$
$2$	−0.809017	−	1.40126i	−0.572061	−	0.990839i	0.424293	−	0.905525i	$-0.360523\pi$
$3$	1.11803	+	1.93649i	0.645497	+	1.11803i	0.984186	+	0.177136i	$0.0566831\pi$
$3$	1.11803	+	1.93649i	0.645497	+	1.11803i	−0.338689	+	0.940898i	$0.609984\pi$
$4$	−0.309017	+	0.535233i	−0.154508	+	0.267617i
$5$	1.00000			0.447214
$5$	1.00000			0.447214
$6$	1.80902	−	3.13331i	0.738528	−	1.27917i
$7$	0.118034	−	0.204441i	0.0446127	−	0.0772714i	−0.842857	−	0.538138i	$-0.819128\pi$
$7$	0.118034	−	0.204441i	0.0446127	−	0.0772714i	0.887469	+	0.460866i	$0.152461\pi$
$8$	−2.23607			−0.790569
$9$	−1.00000	+	1.73205i	−0.333333	+	0.577350i
$10$	−0.809017	−	1.40126i	−0.255834	−	0.443117i
$11$	−2.11803	−	3.66854i	−0.638611	−	1.10611i	−0.985738	−	0.168289i	$-0.946176\pi$
$11$	−2.11803	−	3.66854i	−0.638611	−	1.10611i	0.347126	−	0.937818i	$-0.387157\pi$
$12$	−1.38197			−0.398939
$13$	−1.00000	+	3.46410i	−0.277350	+	0.960769i
$13$	−1.00000	+	3.46410i	−0.277350	+	0.960769i
$14$	−0.381966			−0.102085
$15$	1.11803	+	1.93649i	0.288675	+	0.500000i
$16$	2.42705	+	4.20378i	0.606763	+	1.05094i
$17$	−2.73607	+	4.73901i	−0.663594	+	1.14938i	0.316071	+	0.948736i	$0.397636\pi$
$17$	−2.73607	+	4.73901i	−0.663594	+	1.14938i	−0.979664	+	0.200643i	$0.935697\pi$
$18$	3.23607			0.762749
$19$	0.118034	−	0.204441i	0.0270789	−	0.0469020i	−0.852168	−	0.523268i	$-0.824713\pi$
$19$	0.118034	−	0.204441i	0.0270789	−	0.0469020i	0.879247	+	0.476366i	$0.158046\pi$
$20$	−0.309017	+	0.535233i	−0.0690983	+	0.119682i
$21$	0.527864			0.115189
$22$	−3.42705	+	5.93583i	−0.730650	+	1.26552i
$23$	−4.11803	−	7.13264i	−0.858669	−	1.48726i	−0.873199	−	0.487365i	$-0.837958\pi$
$23$	−4.11803	−	7.13264i	−0.858669	−	1.48726i	0.0145291	−	0.999894i	$-0.495375\pi$
$24$	−2.50000	−	4.33013i	−0.510310	−	0.883883i
$25$	1.00000			0.200000
$26$	5.66312	−	1.40126i	1.11063	−	0.274809i
$27$	2.23607			0.430331
$28$	0.0729490	+	0.126351i	0.0137861	+	0.0238782i
$29$	−0.736068	−	1.27491i	−0.136684	−	0.236744i	0.789555	−	0.613679i	$-0.210311\pi$
$29$	−0.736068	−	1.27491i	−0.136684	−	0.236744i	−0.926240	+	0.376935i	$0.876978\pi$
$30$	1.80902	−	3.13331i	0.330280	−	0.572061i
$31$		0			0			−	1.00000i	$-0.5\pi$
$31$		0			0				1.00000i	$0.5\pi$
$32$	1.69098	−	2.92887i	0.298926	−	0.517756i
$33$	4.73607	−	8.20311i	0.824444	−	1.42798i
$34$	8.85410			1.51847
$35$	0.118034	−	0.204441i	0.0199514	−	0.0345568i
$36$	−0.618034	−	1.07047i	−0.103006	−	0.178411i
$37$	−1.50000	−	2.59808i	−0.246598	−	0.427121i	0.715981	−	0.698119i	$-0.245980\pi$
$37$	−1.50000	−	2.59808i	−0.246598	−	0.427121i	−0.962580	+	0.270998i	$0.912646\pi$
$38$	−0.381966			−0.0619631
$39$	−7.82624	+	1.93649i	−1.25320	+	0.310087i
$40$	−2.23607			−0.353553
$41$	2.97214	+	5.14789i	0.464170	+	0.803965i	0.999164	−	0.0408904i	$-0.0130195\pi$
$41$	2.97214	+	5.14789i	0.464170	+	0.803965i	−0.534994	+	0.844856i	$0.679686\pi$
$42$	−0.427051	−	0.739674i	−0.0658954	−	0.114134i
$43$	0.881966	−	1.52761i	0.134499	−	0.232958i	−0.790907	−	0.611936i	$-0.790391\pi$
$43$	0.881966	−	1.52761i	0.134499	−	0.232958i	0.925406	+	0.378978i	$0.123724\pi$
$44$	2.61803			0.394683
$45$	−1.00000	+	1.73205i	−0.149071	+	0.258199i
$46$	−6.66312	+	11.5409i	−0.982423	+	1.70161i
$47$	12.9443			1.88812			0.944058	−	0.329779i	$-0.106974\pi$
$47$	12.9443			1.88812			0.944058	+	0.329779i	$0.106974\pi$
$48$	−5.42705	+	9.39993i	−0.783327	+	1.35676i
$49$	3.47214	+	6.01392i	0.496019	+	0.859131i
$50$	−0.809017	−	1.40126i	−0.114412	−	0.198168i
$51$	−12.2361			−1.71339
$52$	−1.54508	−	1.60570i	−0.214265	−	0.222670i
$53$	6.00000			0.824163			0.412082	−	0.911147i	$-0.364802\pi$
$53$	6.00000			0.824163			0.412082	+	0.911147i	$0.364802\pi$
$54$	−1.80902	−	3.13331i	−0.246176	−	0.426389i
$55$	−2.11803	−	3.66854i	−0.285596	−	0.494666i
$56$	−0.263932	+	0.457144i	−0.0352694	+	0.0610884i
$57$	0.527864			0.0699173
$58$	−1.19098	+	2.06284i	−0.156384	+	0.270865i
$59$	−6.35410	+	11.0056i	−0.827234	+	1.43281i	0.0729666	+	0.997334i	$0.476753\pi$
$59$	−6.35410	+	11.0056i	−0.827234	+	1.43281i	−0.900200	+	0.435476i	$0.856580\pi$
$60$	−1.38197			−0.178411
$61$	6.20820	−	10.7529i	0.794879	−	1.37677i	−0.128037	−	0.991769i	$-0.540868\pi$
$61$	6.20820	−	10.7529i	0.794879	−	1.37677i	0.922916	−	0.385002i	$-0.125799\pi$
$62$		0			0
$63$	0.236068	+	0.408882i	0.0297418	+	0.0515143i
$64$	4.23607			0.529508
$65$	−1.00000	+	3.46410i	−0.124035	+	0.429669i
$66$	−15.3262			−1.88653
$67$	−5.35410	−	9.27358i	−0.654108	−	1.13295i	−0.982117	−	0.188273i	$-0.939711\pi$
$67$	−5.35410	−	9.27358i	−0.654108	−	1.13295i	0.328009	−	0.944675i	$-0.393622\pi$
$68$	−1.69098	−	2.92887i	−0.205062	−	0.355177i
$69$	9.20820	−	15.9491i	1.10854	−	1.92004i
$70$	−0.381966			−0.0456537
$71$	0.881966	−	1.52761i	0.104670	−	0.181294i	−0.808933	−	0.587900i	$-0.799955\pi$
$71$	0.881966	−	1.52761i	0.104670	−	0.181294i	0.913603	+	0.406607i	$0.133288\pi$
$72$	2.23607	−	3.87298i	0.263523	−	0.456435i
$73$	−6.00000			−0.702247			−0.351123	−	0.936329i	$-0.614200\pi$
$73$	−6.00000			−0.702247			−0.351123	+	0.936329i	$0.614200\pi$
$74$	−2.42705	+	4.20378i	−0.282139	+	0.488679i
$75$	1.11803	+	1.93649i	0.129099	+	0.223607i
$76$	0.0729490	+	0.126351i	0.00836783	+	0.0144935i
$77$	−1.00000			−0.113961
$78$	9.04508	+	9.39993i	1.02415	+	1.06433i
$79$		0			0			−	1.00000i	$-0.5\pi$
$79$		0			0				1.00000i	$0.5\pi$
$80$	2.42705	+	4.20378i	0.271353	+	0.469996i
$81$	5.50000	+	9.52628i	0.611111	+	1.05848i
$82$	4.80902	−	8.32946i	0.531067	−	0.919835i
$83$	−8.94427			−0.981761			−0.490881	−	0.871227i	$-0.663325\pi$
$83$	−8.94427			−0.981761			−0.490881	+	0.871227i	$0.663325\pi$
$84$	−0.163119	+	0.282530i	−0.0177977	+	0.0308266i
$85$	−2.73607	+	4.73901i	−0.296768	+	0.514018i
$86$	−2.85410			−0.307766
$87$	1.64590	−	2.85078i	0.176459	−	0.305636i
$88$	4.73607	+	8.20311i	0.504867	+	0.874455i
$89$	4.50000	+	7.79423i	0.476999	+	0.826187i	0.999653	−	0.0263586i	$-0.00839118\pi$
$89$	4.50000	+	7.79423i	0.476999	+	0.826187i	−0.522654	+	0.852545i	$0.675058\pi$
$90$	3.23607			0.341112
$91$	0.590170	+	0.613323i	0.0618666	+	0.0642937i
$92$	5.09017			0.530687
$93$		0			0
$94$	−10.4721	−	18.1383i	−1.08012	−	1.87082i
$95$	0.118034	−	0.204441i	0.0121100	−	0.0209752i
$96$	7.56231			0.771825
$97$	−2.73607	+	4.73901i	−0.277806	+	0.481173i	−0.970839	−	0.239732i	$-0.922940\pi$
$97$	−2.73607	+	4.73901i	−0.277806	+	0.481173i	0.693034	+	0.720905i	$0.256274\pi$
$98$	5.61803	−	9.73072i	0.567507	−	0.982951i
$99$	8.47214			0.851482
$100$	−0.309017	+	0.535233i	−0.0309017	+	0.0535233i
$101$	−4.73607	−	8.20311i	−0.471256	−	0.816240i	0.528203	−	0.849118i	$-0.322866\pi$
$101$	−4.73607	−	8.20311i	−0.471256	−	0.816240i	−0.999459	+	0.0328781i	$0.989533\pi$
$102$	9.89919	+	17.1459i	0.980166	+	1.69770i
$103$	−4.94427			−0.487174			−0.243587	−	0.969879i	$-0.578324\pi$
$103$	−4.94427			−0.487174			−0.243587	+	0.969879i	$0.578324\pi$
$104$	2.23607	−	7.74597i	0.219265	−	0.759555i
$105$	0.527864			0.0515143
$106$	−4.85410	−	8.40755i	−0.471472	−	0.816614i
$107$	5.11803	+	8.86469i	0.494779	+	0.856982i	0.999982	−	0.00601821i	$-0.00191567\pi$
$107$	5.11803	+	8.86469i	0.494779	+	0.856982i	−0.505203	+	0.863001i	$0.668582\pi$
$108$	−0.690983	+	1.19682i	−0.0664899	+	0.115164i
$109$	−2.00000			−0.191565			−0.0957826	−	0.995402i	$-0.530535\pi$
$109$	−2.00000			−0.191565			−0.0957826	+	0.995402i	$0.530535\pi$
$110$	−3.42705	+	5.93583i	−0.326756	+	0.565959i
$111$	3.35410	−	5.80948i	0.318357	−	0.551411i
$112$	1.14590			0.108277
$113$	3.73607	−	6.47106i	0.351460	−	0.608746i	−0.635046	−	0.772475i	$-0.719019\pi$
$113$	3.73607	−	6.47106i	0.351460	−	0.608746i	0.986505	+	0.163728i	$0.0523521\pi$
$114$	−0.427051	−	0.739674i	−0.0399970	−	0.0692768i
$115$	−4.11803	−	7.13264i	−0.384009	−	0.665122i
$116$	0.909830			0.0844756
$117$	−5.00000	−	5.19615i	−0.462250	−	0.480384i
$118$	20.5623			1.89291
$119$	0.645898	+	1.11873i	0.0592094	+	0.102554i
$120$	−2.50000	−	4.33013i	−0.228218	−	0.395285i
$121$	−3.47214	+	6.01392i	−0.315649	+	0.546720i
$122$	−20.0902			−1.81888
$123$	−6.64590	+	11.5110i	−0.599240	+	1.03791i
$124$		0			0
$125$	1.00000			0.0894427
$126$	0.381966	−	0.661585i	0.0340282	−	0.0589386i
$127$	−0.118034	−	0.204441i	−0.0104738	−	0.0181412i	0.860741	−	0.509043i	$-0.170001\pi$
$127$	−0.118034	−	0.204441i	−0.0104738	−	0.0181412i	−0.871215	+	0.490902i	$0.836667\pi$
$128$	−6.80902	−	11.7936i	−0.601838	−	1.04241i
$129$	3.94427			0.347274
$130$	5.66312	−	1.40126i	0.496688	−	0.122899i
$131$	−12.0000			−1.04844			−0.524222	−	0.851581i	$-0.675644\pi$
$131$	−12.0000			−1.04844			−0.524222	+	0.851581i	$0.675644\pi$
$132$	2.92705	+	5.06980i	0.254767	+	0.441270i
$133$	−0.0278640	−	0.0482619i	−0.00241612	−	0.00418484i
$134$	−8.66312	+	15.0050i	−0.748379	+	1.29623i
$135$	2.23607			0.192450
$136$	6.11803	−	10.5967i	0.524617	−	0.908663i
$137$	3.73607	−	6.47106i	0.319194	−	0.552860i	−0.661126	−	0.750275i	$-0.729921\pi$
$137$	3.73607	−	6.47106i	0.319194	−	0.552860i	0.980320	+	0.197415i	$0.0632546\pi$
$138$	−29.7984			−2.53661
$139$	1.64590	−	2.85078i	0.139603	−	0.241800i	−0.787743	−	0.616004i	$-0.788751\pi$
$139$	1.64590	−	2.85078i	0.139603	−	0.241800i	0.927346	+	0.374204i	$0.122084\pi$
$140$	0.0729490	+	0.126351i	0.00616532	+	0.0106786i
$141$	14.4721	+	25.0665i	1.21877	+	2.11098i
$142$	−2.85410			−0.239511
$143$	14.8262	−	3.66854i	1.23983	−	0.306779i
$144$	−9.70820			−0.809017
$145$	−0.736068	−	1.27491i	−0.0611271	−	0.105875i
$146$	4.85410	+	8.40755i	0.401728	+	0.695814i
$147$	−7.76393	+	13.4475i	−0.640358	+	1.10913i
$148$	1.85410			0.152406
$149$	−6.73607	+	11.6672i	−0.551840	+	0.955815i	0.446302	+	0.894883i	$0.352741\pi$
$149$	−6.73607	+	11.6672i	−0.551840	+	0.955815i	−0.998142	+	0.0609327i	$0.980593\pi$
$150$	1.80902	−	3.13331i	0.147706	−	0.255834i
$151$	8.00000			0.651031			0.325515	−	0.945537i	$-0.394462\pi$
$151$	8.00000			0.651031			0.325515	+	0.945537i	$0.394462\pi$
$152$	−0.263932	+	0.457144i	−0.0214077	+	0.0370792i
$153$	−5.47214	−	9.47802i	−0.442396	−	0.766252i
$154$	0.809017	+	1.40126i	0.0651924	+	0.112917i
$155$		0			0
$156$	1.38197	−	4.78727i	0.110646	−	0.383288i
$157$	−18.0000			−1.43656			−0.718278	−	0.695756i	$-0.755069\pi$
$157$	−18.0000			−1.43656			−0.718278	+	0.695756i	$0.755069\pi$
$158$		0			0
$159$	6.70820	+	11.6190i	0.531995	+	0.921443i
$160$	1.69098	−	2.92887i	0.133684	−	0.231547i
$161$	−1.94427			−0.153230
$162$	8.89919	−	15.4138i	0.699186	−	1.21103i
$163$	−0.645898	+	1.11873i	−0.0505906	+	0.0876256i	−0.890212	−	0.455547i	$-0.849444\pi$
$163$	−0.645898	+	1.11873i	−0.0505906	+	0.0876256i	0.839621	+	0.543173i	$0.182777\pi$
$164$	−3.67376			−0.286873
$165$	4.73607	−	8.20311i	0.368702	−	0.638611i
$166$	7.23607	+	12.5332i	0.561628	+	0.972768i
$167$	−2.59017	−	4.48631i	−0.200433	−	0.347161i	0.748235	−	0.663434i	$-0.230902\pi$
$167$	−2.59017	−	4.48631i	−0.200433	−	0.347161i	−0.948668	+	0.316273i	$0.897568\pi$
$168$	−1.18034			−0.0910652
$169$	−11.0000	−	6.92820i	−0.846154	−	0.532939i
$170$	8.85410			0.679079
$171$	0.236068	+	0.408882i	0.0180526	+	0.0312680i
$172$	0.545085	+	0.944115i	0.0415623	+	0.0719881i
$173$	−8.44427	+	14.6259i	−0.642006	+	1.11199i	0.342978	+	0.939343i	$0.388564\pi$
$173$	−8.44427	+	14.6259i	−0.642006	+	1.11199i	−0.984984	+	0.172644i	$0.944769\pi$
$174$	−5.32624			−0.403781
$175$	0.118034	−	0.204441i	0.00892253	−	0.0154543i
$176$	10.2812	−	17.8075i	0.774971	−	1.34229i
$177$	−28.4164			−2.13591
$178$	7.28115	−	12.6113i	0.545745	−	0.945259i
$179$	1.88197	+	3.25966i	0.140665	+	0.243638i	0.927747	−	0.373209i	$-0.121743\pi$
$179$	1.88197	+	3.25966i	0.140665	+	0.243638i	−0.787082	+	0.616848i	$0.788409\pi$
$180$	−0.618034	−	1.07047i	−0.0460655	−	0.0797878i
$181$	6.00000			0.445976			0.222988	−	0.974821i	$-0.428419\pi$
$181$	6.00000			0.445976			0.222988	+	0.974821i	$0.428419\pi$
$182$	0.381966	−	1.32317i	0.0283132	−	0.0980798i
$183$	27.7639			2.05237
$184$	9.20820	+	15.9491i	0.678838	+	1.17578i
$185$	−1.50000	−	2.59808i	−0.110282	−	0.191014i
$186$		0			0
$187$	23.1803			1.69511
$188$	−4.00000	+	6.92820i	−0.291730	+	0.505291i
$189$	0.263932	−	0.457144i	0.0191982	−	0.0332523i
$190$	−0.381966			−0.0277107
$191$	2.40983	−	4.17395i	0.174369	−	0.302016i	−0.765574	−	0.643348i	$-0.777545\pi$
$191$	2.40983	−	4.17395i	0.174369	−	0.302016i	0.939943	+	0.341332i	$0.110878\pi$
$192$	4.73607	+	8.20311i	0.341796	+	0.592008i
$193$	−2.73607	−	4.73901i	−0.196946	−	0.341121i	0.750590	−	0.660768i	$-0.229769\pi$
$193$	−2.73607	−	4.73901i	−0.196946	−	0.341121i	−0.947537	+	0.319646i	$0.896436\pi$
$194$	8.85410			0.635687
$195$	−7.82624	+	1.93649i	−0.560449	+	0.138675i
$196$	−4.29180			−0.306557
$197$	−1.50000	−	2.59808i	−0.106871	−	0.185105i	0.807630	−	0.589689i	$-0.200750\pi$
$197$	−1.50000	−	2.59808i	−0.106871	−	0.185105i	−0.914501	+	0.404584i	$0.867416\pi$
$198$	−6.85410	−	11.8717i	−0.487100	−	0.843682i
$199$	7.35410	−	12.7377i	0.521318	−	0.902950i	−0.478374	−	0.878156i	$-0.658774\pi$
$199$	7.35410	−	12.7377i	0.521318	−	0.902950i	0.999693	−	0.0247939i	$-0.00789296\pi$
$200$	−2.23607			−0.158114
$201$	11.9721	−	20.7363i	0.844449	−	1.46263i
$202$	−7.66312	+	13.2729i	−0.539175	+	0.933879i
$203$	−0.347524			−0.0243914
$204$	3.78115	−	6.54915i	0.264734	−	0.458532i
$205$	2.97214	+	5.14789i	0.207583	+	0.359544i
$206$	4.00000	+	6.92820i	0.278693	+	0.482711i
$207$	16.4721			1.14489
$208$	−16.9894	+	4.20378i	−1.17800	+	0.291479i
$209$	−1.00000			−0.0691714
$210$	−0.427051	−	0.739674i	−0.0294693	−	0.0510424i
$211$	−4.59017	−	7.95041i	−0.316000	−	0.547329i	0.663649	−	0.748044i	$-0.269007\pi$
$211$	−4.59017	−	7.95041i	−0.316000	−	0.547329i	−0.979650	+	0.200715i	$0.935673\pi$
$212$	−1.85410	+	3.21140i	−0.127340	+	0.220560i
$213$	3.94427			0.270257
$214$	8.28115	−	14.3434i	0.566088	−	0.980493i
$215$	0.881966	−	1.52761i	0.0601496	−	0.104182i
$216$	−5.00000			−0.340207
$217$		0			0
$218$	1.61803	+	2.80252i	0.109587	+	0.189810i
$219$	−6.70820	−	11.6190i	−0.453298	−	0.785136i
$220$	2.61803			0.176508
$221$	−13.6803	−	14.2170i	−0.920239	−	0.956341i
$222$	−10.8541			−0.728480
$223$	6.35410	+	11.0056i	0.425502	+	0.736991i	0.996467	−	0.0839830i	$-0.0267642\pi$
$223$	6.35410	+	11.0056i	0.425502	+	0.736991i	−0.570965	+	0.820974i	$0.693431\pi$
$224$	−0.399187	−	0.691412i	−0.0266718	−	0.0461969i
$225$	−1.00000	+	1.73205i	−0.0666667	+	0.115470i
$226$	−12.0902			−0.804226
$227$	0.881966	−	1.52761i	0.0585381	−	0.101391i	−0.835271	−	0.549838i	$-0.814689\pi$
$227$	0.881966	−	1.52761i	0.0585381	−	0.101391i	0.893809	+	0.448447i	$0.148023\pi$
$228$	−0.163119	+	0.282530i	−0.0108028	+	0.0187110i
$229$	−19.8885			−1.31427			−0.657136	−	0.753772i	$-0.728232\pi$
$229$	−19.8885			−1.31427			−0.657136	+	0.753772i	$0.728232\pi$
$230$	−6.66312	+	11.5409i	−0.439353	+	0.760982i
$231$	−1.11803	−	1.93649i	−0.0735612	−	0.127412i
$232$	1.64590	+	2.85078i	0.108058	+	0.187163i
$233$	19.8885			1.30294			0.651471	−	0.758674i	$-0.274152\pi$
$233$	19.8885			1.30294			0.651471	+	0.758674i	$0.274152\pi$
$234$	−3.23607	+	11.2101i	−0.211548	+	0.732825i
$235$	12.9443			0.844391
$236$	−3.92705	−	6.80185i	−0.255629	−	0.442763i
$237$		0			0
$238$	1.04508	−	1.81014i	0.0677428	−	0.117334i
$239$	9.88854			0.639637			0.319818	−	0.947479i	$-0.396378\pi$
$239$	9.88854			0.639637			0.319818	+	0.947479i	$0.396378\pi$
$240$	−5.42705	+	9.39993i	−0.350315	+	0.606763i
$241$	−7.50000	+	12.9904i	−0.483117	+	0.836784i	−0.999812	−	0.0193858i	$-0.993829\pi$
$241$	−7.50000	+	12.9904i	−0.483117	+	0.836784i	0.516695	+	0.856170i	$0.327162\pi$
$242$	11.2361			0.722282
$243$	−8.94427	+	15.4919i	−0.573775	+	0.993808i
$244$	3.83688	+	6.64567i	0.245631	+	0.425446i
$245$	3.47214	+	6.01392i	0.221827	+	0.384215i
$246$	21.5066			1.37121
$247$	0.590170	+	0.613323i	0.0375516	+	0.0390248i
$248$		0			0
$249$	−10.0000	−	17.3205i	−0.633724	−	1.09764i
$250$	−0.809017	−	1.40126i	−0.0511667	−	0.0886234i
$251$	−7.88197	+	13.6520i	−0.497505	+	0.861704i	−0.999996	−	0.00287826i	$-0.999084\pi$
$251$	−7.88197	+	13.6520i	−0.497505	+	0.861704i	0.502491	+	0.864583i	$0.332417\pi$
$252$	−0.291796			−0.0183814
$253$	−17.4443	+	30.2144i	−1.09671	+	1.89956i
$254$	−0.190983	+	0.330792i	−0.0119833	+	0.0207558i
$255$	−12.2361			−0.766252
$256$	−6.78115	+	11.7453i	−0.423822	+	0.734081i
$257$	−4.26393	−	7.38535i	−0.265977	−	0.460685i	0.701842	−	0.712332i	$-0.252361\pi$
$257$	−4.26393	−	7.38535i	−0.265977	−	0.460685i	−0.967819	+	0.251647i	$0.919028\pi$
$258$	−3.19098	−	5.52694i	−0.198662	−	0.344093i
$259$	−0.708204			−0.0440057
$260$	−1.54508	−	1.60570i	−0.0958221	−	0.0995812i
$261$	2.94427			0.182246
$262$	9.70820	+	16.8151i	0.599775	+	1.03884i
$263$	−4.11803	−	7.13264i	−0.253929	−	0.439818i	0.710675	−	0.703520i	$-0.248390\pi$
$263$	−4.11803	−	7.13264i	−0.253929	−	0.439818i	−0.964604	+	0.263703i	$0.915056\pi$
$264$	−10.5902	+	18.3427i	−0.651780	+	1.12892i
$265$	6.00000			0.368577
$266$	−0.0450850	+	0.0780895i	−0.00276434	+	0.00478797i
$267$	−10.0623	+	17.4284i	−0.615803	+	1.06660i
$268$	6.61803			0.404261
$269$	7.73607	−	13.3993i	0.471676	−	0.816967i	−0.527799	−	0.849370i	$-0.676982\pi$
$269$	7.73607	−	13.3993i	0.471676	−	0.816967i	0.999475	+	0.0324021i	$0.0103157\pi$
$270$	−1.80902	−	3.13331i	−0.110093	−	0.190687i
$271$	−7.35410	−	12.7377i	−0.446730	−	0.773759i	0.551441	−	0.834214i	$-0.314078\pi$
$271$	−7.35410	−	12.7377i	−0.446730	−	0.773759i	−0.998171	+	0.0604550i	$0.980745\pi$
$272$	−26.5623			−1.61058
$273$	−0.527864	+	1.82857i	−0.0319478	+	0.110670i
$274$	−12.0902			−0.730394
$275$	−2.11803	−	3.66854i	−0.127722	−	0.221221i
$276$	5.69098	+	9.85707i	0.342557	+	0.593326i
$277$	9.44427	−	16.3580i	0.567451	−	0.982854i	−0.429366	−	0.903131i	$-0.641263\pi$
$277$	9.44427	−	16.3580i	0.567451	−	0.982854i	0.996817	−	0.0797238i	$-0.0254038\pi$
$278$	−5.32624			−0.319447
$279$		0			0
$280$	−0.263932	+	0.457144i	−0.0157730	+	0.0273196i
$281$	19.8885			1.18645			0.593226	−	0.805036i	$-0.297854\pi$
$281$	19.8885			1.18645			0.593226	+	0.805036i	$0.297854\pi$
$282$	23.4164	−	40.5584i	1.39443	−	2.41522i
$283$	−1.35410	−	2.34537i	−0.0804930	−	0.139418i	0.822969	−	0.568087i	$-0.192316\pi$
$283$	−1.35410	−	2.34537i	−0.0804930	−	0.139418i	−0.903462	+	0.428669i	$0.858983\pi$
$284$	0.545085	+	0.944115i	0.0323448	+	0.0560229i
$285$	0.527864			0.0312680
$286$	−17.1353	−	17.8075i	−1.01323	−	1.05298i
$287$	1.40325			0.0828314
$288$	3.38197	+	5.85774i	0.199284	+	0.345170i
$289$	−6.47214	−	11.2101i	−0.380714	−	0.659416i
$290$	−1.19098	+	2.06284i	−0.0699369	+	0.121134i
$291$	−12.2361			−0.717291
$292$	1.85410	−	3.21140i	0.108503	−	0.187933i
$293$	6.02786	−	10.4406i	0.352152	−	0.609944i	−0.634475	−	0.772944i	$-0.718783\pi$
$293$	6.02786	−	10.4406i	0.352152	−	0.609944i	0.986626	+	0.162999i	$0.0521168\pi$
$294$	25.1246			1.46530
$295$	−6.35410	+	11.0056i	−0.369950	+	0.640772i
$296$	3.35410	+	5.80948i	0.194953	+	0.337669i
$297$	−4.73607	−	8.20311i	−0.274815	−	0.475993i
$298$	21.7984			1.26275
$299$	28.8262	−	7.13264i	1.66706	−	0.412491i
$300$	−1.38197			−0.0797878
$301$	−0.208204	−	0.360620i	−0.0120007	−	0.0207858i
$302$	−6.47214	−	11.2101i	−0.372430	−	0.645067i
$303$	10.5902	−	18.3427i	0.608389	−	1.05376i
$304$	1.14590			0.0657218
$305$	6.20820	−	10.7529i	0.355481	−	0.615711i
$306$	−8.85410	+	15.3358i	−0.506155	+	0.876687i
$307$	7.05573			0.402692			0.201346	−	0.979520i	$-0.435468\pi$
$307$	7.05573			0.402692			0.201346	+	0.979520i	$0.435468\pi$
$308$	0.309017	−	0.535233i	0.0176079	−	0.0304977i
$309$	−5.52786	−	9.57454i	−0.314469	−	0.544677i
$310$		0			0
$311$	−24.0000			−1.36092			−0.680458	−	0.732787i	$-0.738219\pi$
$311$	−24.0000			−1.36092			−0.680458	+	0.732787i	$0.738219\pi$
$312$	17.5000	−	4.33013i	0.990742	−	0.245145i
$313$	−31.8885			−1.80245			−0.901224	−	0.433355i	$-0.857330\pi$
$313$	−31.8885			−1.80245			−0.901224	+	0.433355i	$0.857330\pi$
$314$	14.5623	+	25.2227i	0.821798	+	1.42340i
$315$	0.236068	+	0.408882i	0.0133009	+	0.0230379i
$316$		0			0
$317$	23.8885			1.34171			0.670857	−	0.741587i	$-0.265926\pi$
$317$	23.8885			1.34171			0.670857	+	0.741587i	$0.265926\pi$
$318$	10.8541	−	18.7999i	0.608668	−	1.05424i
$319$	−3.11803	+	5.40059i	−0.174576	+	0.302375i
$320$	4.23607			0.236803
$321$	−11.4443	+	19.8221i	−0.638757	+	1.10636i
$322$	1.57295	+	2.72443i	0.0876570	+	0.151826i
$323$	0.645898	+	1.11873i	0.0359387	+	0.0622477i
$324$	−6.79837			−0.377687
$325$	−1.00000	+	3.46410i	−0.0554700	+	0.192154i
$326$	2.09017			0.115764
$327$	−2.23607	−	3.87298i	−0.123655	−	0.214176i
$328$	−6.64590	−	11.5110i	−0.366958	−	0.635590i
$329$	1.52786	−	2.64634i	0.0842339	−	0.145897i
$330$	−15.3262			−0.843682
$331$	−12.8262	+	22.2157i	−0.704994	+	1.22109i	0.261700	+	0.965149i	$0.415717\pi$
$331$	−12.8262	+	22.2157i	−0.704994	+	1.22109i	−0.966694	+	0.255936i	$0.917616\pi$
$332$	2.76393	−	4.78727i	0.151690	−	0.262736i
$333$	6.00000			0.328798
$334$	−4.19098	+	7.25900i	−0.229320	+	0.397195i
$335$	−5.35410	−	9.27358i	−0.292526	−	0.506670i
$336$	1.28115	+	2.21902i	0.0698926	+	0.121058i
$337$	27.8885			1.51919			0.759593	−	0.650399i	$-0.225398\pi$
$337$	27.8885			1.51919			0.759593	+	0.650399i	$0.225398\pi$
$338$	−0.809017	+	21.0189i	−0.0440047	+	1.14328i
$339$	16.7082			0.907465
$340$	−1.69098	−	2.92887i	−0.0917064	−	0.158840i
$341$		0			0
$342$	0.381966	−	0.661585i	0.0206544	−	0.0357744i
$343$	3.29180			0.177740
$344$	−1.97214	+	3.41584i	−0.106330	+	0.184170i
$345$	9.20820	−	15.9491i	0.495753	−	0.858669i
$346$	27.3262			1.46907
$347$	−8.64590	+	14.9751i	−0.464136	+	0.803907i	−0.999162	−	0.0409283i	$-0.986968\pi$
$347$	−8.64590	+	14.9751i	−0.464136	+	0.803907i	0.535026	+	0.844836i	$0.320302\pi$
$348$	1.01722	+	1.76188i	0.0545288	+	0.0944466i
$349$	12.2082	+	21.1452i	0.653490	+	1.13188i	0.982270	+	0.187472i	$0.0600293\pi$
$349$	12.2082	+	21.1452i	0.653490	+	1.13188i	−0.328780	+	0.944407i	$0.606637\pi$
$350$	−0.381966			−0.0204169
$351$	−2.23607	+	7.74597i	−0.119352	+	0.413449i
$352$	−14.3262			−0.763591
$353$	5.26393	+	9.11740i	0.280171	+	0.485270i	0.971427	−	0.237340i	$-0.0762756\pi$
$353$	5.26393	+	9.11740i	0.280171	+	0.485270i	−0.691256	+	0.722610i	$0.742942\pi$
$354$	22.9894	+	39.8187i	1.22187	+	2.11634i
$355$	0.881966	−	1.52761i	0.0468099	−	0.0810771i
$356$	−5.56231			−0.294802
$357$	−1.44427	+	2.50155i	−0.0764390	+	0.132396i
$358$	3.04508	−	5.27424i	0.160938	−	0.278752i
$359$	−17.8885			−0.944121			−0.472061	−	0.881566i	$-0.656490\pi$
$359$	−17.8885			−0.944121			−0.472061	+	0.881566i	$0.656490\pi$
$360$	2.23607	−	3.87298i	0.117851	−	0.204124i
$361$	9.47214	+	16.4062i	0.498533	+	0.863485i
$362$	−4.85410	−	8.40755i	−0.255126	−	0.441891i
$363$	−15.5279			−0.815001
$364$	−0.510643	+	0.126351i	−0.0267650	+	0.00662261i
$365$	−6.00000			−0.314054
$366$	−22.4615	−	38.9044i	−1.17408	−	2.03357i
$367$	12.8262	+	22.2157i	0.669524	+	1.15965i	0.978037	+	0.208430i	$0.0668353\pi$
$367$	12.8262	+	22.2157i	0.669524	+	1.15965i	−0.308513	+	0.951220i	$0.599831\pi$
$368$	19.9894	−	34.6226i	1.04202	−	1.80483i
$369$	−11.8885			−0.618893
$370$	−2.42705	+	4.20378i	−0.126176	+	0.218544i
$371$	0.708204	−	1.22665i	0.0367681	−	0.0636842i
$372$		0			0
$373$	−5.02786	+	8.70852i	−0.260333	+	0.450910i	−0.966330	−	0.257305i	$-0.917166\pi$
$373$	−5.02786	+	8.70852i	−0.260333	+	0.450910i	0.705997	+	0.708214i	$0.250499\pi$
$374$	−18.7533	−	32.4816i	−0.969709	−	1.67959i
$375$	1.11803	+	1.93649i	0.0577350	+	0.100000i
$376$	−28.9443			−1.49269
$377$	5.15248	−	1.27491i	0.265366	−	0.0656611i
$378$	−0.854102			−0.0439303
$379$	−16.5902	−	28.7350i	−0.852180	−	1.47602i	−0.879237	−	0.476385i	$-0.841947\pi$
$379$	−16.5902	−	28.7350i	−0.852180	−	1.47602i	0.0270571	−	0.999634i	$-0.491386\pi$
$380$	0.0729490	+	0.126351i	0.00374221	+	0.00648169i
$381$	0.263932	−	0.457144i	0.0135216	−	0.0234202i
$382$	−7.79837			−0.399000
$383$	0.118034	−	0.204441i	0.00603126	−	0.0104464i	−0.862994	−	0.505214i	$-0.831414\pi$
$383$	0.118034	−	0.204441i	0.00603126	−	0.0104464i	0.869025	+	0.494768i	$0.164747\pi$
$384$	15.2254	−	26.3712i	0.776969	−	1.34575i
$385$	−1.00000			−0.0509647
$386$	−4.42705	+	7.66788i	−0.225331	+	0.390285i
$387$	1.76393	+	3.05522i	0.0896657	+	0.155306i
$388$	−1.69098	−	2.92887i	−0.0858467	−	0.148691i
$389$	−35.8885			−1.81962			−0.909811	−	0.415023i	$-0.863773\pi$
$389$	−35.8885			−1.81962			−0.909811	+	0.415023i	$0.863773\pi$
$390$	9.04508	+	9.39993i	0.458016	+	0.475984i
$391$	45.0689			2.27923
$392$	−7.76393	−	13.4475i	−0.392138	−	0.679203i
$393$	−13.4164	−	23.2379i	−0.676768	−	1.17220i
$394$	−2.42705	+	4.20378i	−0.122273	+	0.211783i
$395$		0			0
$396$	−2.61803	+	4.53457i	−0.131561	+	0.227871i
$397$	−5.02786	+	8.70852i	−0.252341	+	0.437068i	−0.964170	−	0.265285i	$-0.914534\pi$
$397$	−5.02786	+	8.70852i	−0.252341	+	0.437068i	0.711829	+	0.702353i	$0.247867\pi$
$398$	−23.7984			−1.19290
$399$	0.0623059	−	0.107917i	0.00311920	−	0.00540261i
$400$	2.42705	+	4.20378i	0.121353	+	0.210189i
$401$	13.4443	+	23.2862i	0.671375	+	1.16286i	0.977514	+	0.210869i	$0.0676293\pi$
$401$	13.4443	+	23.2862i	0.671375	+	1.16286i	−0.306139	+	0.951987i	$0.599037\pi$
$402$	−38.7426			−1.93231
$403$		0			0
$404$	5.85410			0.291252
$405$	5.50000	+	9.52628i	0.273297	+	0.473365i
$406$	0.281153	+	0.486971i	0.0139534	+	0.0241680i
$407$	−6.35410	+	11.0056i	−0.314961	+	0.545529i
$408$	27.3607			1.35456
$409$	5.44427	−	9.42976i	0.269202	−	0.466271i	−0.699454	−	0.714678i	$-0.746573\pi$
$409$	5.44427	−	9.42976i	0.269202	−	0.466271i	0.968656	+	0.248406i	$0.0799068\pi$
$410$	4.80902	−	8.32946i	0.237500	−	0.411363i
$411$	16.7082			0.824155
$412$	1.52786	−	2.64634i	0.0752725	−	0.130376i
$413$	1.50000	+	2.59808i	0.0738102	+	0.127843i
$414$	−13.3262	−	23.0817i	−0.654949	−	1.13440i
$415$	−8.94427			−0.439057
$416$	8.45492	+	8.78661i	0.414536	+	0.430799i
$417$	7.36068			0.360454
$418$	0.809017	+	1.40126i	0.0395703	+	0.0685378i
$419$	6.82624	+	11.8234i	0.333484	+	0.577610i	0.983192	−	0.182573i	$-0.0584425\pi$
$419$	6.82624	+	11.8234i	0.333484	+	0.577610i	−0.649709	+	0.760183i	$0.725109\pi$
$420$	−0.163119	+	0.282530i	−0.00795939	+	0.0137861i
$421$	6.00000			0.292422			0.146211	−	0.989253i	$-0.453292\pi$
$421$	6.00000			0.292422			0.146211	+	0.989253i	$0.453292\pi$
$422$	−7.42705	+	12.8640i	−0.361543	+	0.626211i
$423$	−12.9443	+	22.4201i	−0.629372	+	1.09010i
$424$	−13.4164			−0.651558
$425$	−2.73607	+	4.73901i	−0.132719	+	0.229876i
$426$	−3.19098	−	5.52694i	−0.154604	−	0.267781i
$427$	−1.46556	−	2.53842i	−0.0709233	−	0.122843i
$428$	−6.32624			−0.305790
$429$	23.6803	+	24.6093i	1.14330	+	1.18815i
$430$	−2.85410			−0.137637
$431$	−2.40983	−	4.17395i	−0.116077	−	0.201052i	0.802133	−	0.597146i	$-0.203699\pi$
$431$	−2.40983	−	4.17395i	−0.116077	−	0.201052i	−0.918210	+	0.396094i	$0.870365\pi$
$432$	5.42705	+	9.39993i	0.261109	+	0.452254i
$433$	11.7361	−	20.3275i	0.563999	−	0.976876i	−0.433143	−	0.901325i	$-0.642595\pi$
$433$	11.7361	−	20.3275i	0.563999	−	0.976876i	0.997142	−	0.0755503i	$-0.0240713\pi$
$434$		0			0
$435$	1.64590	−	2.85078i	0.0789148	−	0.136684i
$436$	0.618034	−	1.07047i	0.0295985	−	0.0512660i
$437$	−1.94427			−0.0930071
$438$	−10.8541	+	18.7999i	−0.518629	+	0.898292i
$439$	4.64590	+	8.04693i	0.221737	+	0.384059i	0.955335	−	0.295524i	$-0.0954941\pi$
$439$	4.64590	+	8.04693i	0.221737	+	0.384059i	−0.733599	+	0.679583i	$0.762161\pi$
$440$	4.73607	+	8.20311i	0.225783	+	0.391068i
$441$	−13.8885			−0.661359
$442$	−8.85410	+	30.6715i	−0.421147	+	1.45889i
$443$	−16.9443			−0.805047			−0.402523	−	0.915410i	$-0.631867\pi$
$443$	−16.9443			−0.805047			−0.402523	+	0.915410i	$0.631867\pi$
$444$	2.07295	+	3.59045i	0.0983778	+	0.170395i
$445$	4.50000	+	7.79423i	0.213320	+	0.369482i
$446$	10.2812	−	17.8075i	0.486827	−	0.843209i
$447$	−30.1246			−1.42485
$448$	0.500000	−	0.866025i	0.0236228	−	0.0409159i
$449$	6.97214	−	12.0761i	0.329035	−	0.569906i	−0.653285	−	0.757112i	$-0.726610\pi$
$449$	6.97214	−	12.0761i	0.329035	−	0.569906i	0.982321	+	0.187206i	$0.0599431\pi$
$450$	3.23607			0.152550
$451$	12.5902	−	21.8068i	0.592848	−	1.02684i
$452$	2.30902	+	3.99933i	0.108607	+	0.188113i
$453$	8.94427	+	15.4919i	0.420239	+	0.727875i
$454$	−2.85410			−0.133950
$455$	0.590170	+	0.613323i	0.0276676	+	0.0287530i
$456$	−1.18034			−0.0552745
$457$	14.2082	+	24.6093i	0.664632	+	1.15118i	0.979385	+	0.202002i	$0.0647449\pi$
$457$	14.2082	+	24.6093i	0.664632	+	1.15118i	−0.314753	+	0.949174i	$0.601922\pi$
$458$	16.0902	+	27.8690i	0.751844	+	1.30223i
$459$	−6.11803	+	10.5967i	−0.285565	+	0.494614i
$460$	5.09017			0.237330
$461$	14.2082	−	24.6093i	0.661742	−	1.14617i	−0.318416	−	0.947951i	$-0.603151\pi$
$461$	14.2082	−	24.6093i	0.661742	−	1.14617i	0.980158	−	0.198220i	$-0.0635159\pi$
$462$	−1.80902	+	3.13331i	−0.0841631	+	0.145775i
$463$	28.9443			1.34515			0.672577	−	0.740027i	$-0.265187\pi$
$463$	28.9443			1.34515			0.672577	+	0.740027i	$0.265187\pi$
$464$	3.57295	−	6.18853i	0.165870	−	0.287295i
$465$		0			0
$466$	−16.0902	−	27.8690i	−0.745363	−	1.29101i
$467$	−8.94427			−0.413892			−0.206946	−	0.978352i	$-0.566352\pi$
$467$	−8.94427			−0.413892			−0.206946	+	0.978352i	$0.566352\pi$
$468$	4.32624	−	1.07047i	0.199980	−	0.0494823i
$469$	−2.52786			−0.116726
$470$	−10.4721	−	18.1383i	−0.483044	−	0.836656i
$471$	−20.1246	−	34.8569i	−0.927293	−	1.60612i
$472$	14.2082	−	24.6093i	0.653986	−	1.13274i
$473$	−7.47214			−0.343569
$474$		0			0
$475$	0.118034	−	0.204441i	0.00541577	−	0.00938039i
$476$	−0.798374			−0.0365934
$477$	−6.00000	+	10.3923i	−0.274721	+	0.475831i
$478$	−8.00000	−	13.8564i	−0.365911	−	0.633777i
$479$	4.06231	+	7.03612i	0.185611	+	0.321489i	0.943782	−	0.330567i	$-0.107240\pi$
$479$	4.06231	+	7.03612i	0.185611	+	0.321489i	−0.758171	+	0.652056i	$0.773907\pi$
$480$	7.56231			0.345170
$481$	10.5000	−	2.59808i	0.478759	−	0.118462i
$482$	24.2705			1.10549
$483$	−2.17376	−	3.76507i	−0.0989096	−	0.171316i
$484$	−2.14590	−	3.71680i	−0.0975408	−	0.168946i
$485$	−2.73607	+	4.73901i	−0.124238	+	0.215187i
$486$	28.9443			1.31294
$487$	13.0623	−	22.6246i	0.591910	−	1.02522i	−0.402065	−	0.915611i	$-0.631708\pi$
$487$	13.0623	−	22.6246i	0.591910	−	1.02522i	0.993975	−	0.109607i	$-0.0349591\pi$
$488$	−13.8820	+	24.0443i	−0.628407	+	1.08843i
$489$	−2.88854			−0.130624
$490$	5.61803	−	9.73072i	0.253797	−	0.439589i
$491$	−2.11803	−	3.66854i	−0.0955855	−	0.165559i	0.814267	−	0.580490i	$-0.197139\pi$
$491$	−2.11803	−	3.66854i	−0.0955855	−	0.165559i	−0.909853	+	0.414931i	$0.863806\pi$
$492$	−4.10739	−	7.11421i	−0.185175	−	0.320733i
$493$	8.05573			0.362812
$494$	0.381966	−	1.32317i	0.0171855	−	0.0595322i
$495$	8.47214			0.380794
$496$		0			0
$497$	−0.208204	−	0.360620i	−0.00933922	−	0.0161760i
$498$	−16.1803	+	28.0252i	−0.725058	+	1.25584i
$499$	13.8885			0.621737			0.310868	−	0.950453i	$-0.399380\pi$
$499$	13.8885			0.621737			0.310868	+	0.950453i	$0.399380\pi$
$500$	−0.309017	+	0.535233i	−0.0138197	+	0.0239364i
$501$	5.79180	−	10.0317i	0.258758	−	0.448183i
$502$	25.5066			1.13841
$503$	6.59017	−	11.4145i	0.293841	−	0.508948i	−0.680873	−	0.732401i	$-0.738400\pi$
$503$	6.59017	−	11.4145i	0.293841	−	0.508948i	0.974715	+	0.223453i	$0.0717330\pi$
$504$	−0.527864	−	0.914287i	−0.0235129	−	0.0407256i
$505$	−4.73607	−	8.20311i	−0.210752	−	0.365034i
$506$	56.4508			2.50955
$507$	1.11803	−	29.0474i	0.0496536	−	1.29004i
$508$	0.145898			0.00647318
$509$	−5.68034	−	9.83864i	−0.251777	−	0.436090i	0.712238	−	0.701938i	$-0.247681\pi$
$509$	−5.68034	−	9.83864i	−0.251777	−	0.436090i	−0.964015	+	0.265848i	$0.914348\pi$
$510$	9.89919	+	17.1459i	0.438343	+	0.759233i
$511$	−0.708204	+	1.22665i	−0.0313291	+	0.0542636i
$512$	−5.29180			−0.233867
$513$	0.263932	−	0.457144i	0.0116529	−	0.0201834i
$514$	−6.89919	+	11.9497i	−0.304310	+	0.527081i
$515$	−4.94427			−0.217871
$516$	−1.21885	+	2.11111i	−0.0536567	+	0.0929362i
$517$	−27.4164	−	47.4866i	−1.20577	−	2.08846i
$518$	0.572949	+	0.992377i	0.0251739	+	0.0436025i
$519$	−37.7639			−1.65765
$520$	2.23607	−	7.74597i	0.0980581	−	0.339683i
$521$	−41.7771			−1.83029			−0.915144	−	0.403128i	$-0.867923\pi$
$521$	−41.7771			−1.83029			−0.915144	+	0.403128i	$0.867923\pi$
$522$	−2.38197	−	4.12569i	−0.104256	−	0.180576i
$523$	−9.35410	−	16.2018i	−0.409026	−	0.708454i	0.585755	−	0.810488i	$-0.300798\pi$
$523$	−9.35410	−	16.2018i	−0.409026	−	0.708454i	−0.994781	+	0.102034i	$0.967465\pi$
$524$	3.70820	−	6.42280i	0.161994	−	0.280581i
$525$	0.527864			0.0230379
$526$	−6.66312	+	11.5409i	−0.290526	+	0.503205i
$527$		0			0
$528$	45.9787			2.00097
$529$	−22.4164	+	38.8264i	−0.974626	+	1.68810i
$530$	−4.85410	−	8.40755i	−0.210849	−	0.365201i
$531$	−12.7082	−	22.0113i	−0.551489	−	0.955207i
$532$	0.0344419			0.00149324
$533$	−20.8050	+	5.14789i	−0.901162	+	0.222980i
$534$	32.5623			1.40911
$535$	5.11803	+	8.86469i	0.221272	+	0.383254i
$536$	11.9721	+	20.7363i	0.517118	+	0.895674i
$537$	−4.20820	+	7.28882i	−0.181597	+	0.314536i
$538$	−25.0344			−1.07931
$539$	14.7082	−	25.4754i	0.633527	−	1.09730i
$540$	−0.690983	+	1.19682i	−0.0297352	+	0.0515028i
$541$	7.88854			0.339155			0.169577	−	0.985517i	$-0.445760\pi$
$541$	7.88854			0.339155			0.169577	+	0.985517i	$0.445760\pi$
$542$	−11.8992	+	20.6100i	−0.511114	+	0.885275i
$543$	6.70820	+	11.6190i	0.287877	+	0.498617i
$544$	9.25329	+	16.0272i	0.396731	+	0.687159i
$545$	−2.00000			−0.0856706
$546$	2.98936	−	0.739674i	0.127933	−	0.0316551i
$547$	−34.8328			−1.48934			−0.744672	−	0.667431i	$-0.767394\pi$
$547$	−34.8328			−1.48934			−0.744672	+	0.667431i	$0.767394\pi$
$548$	2.30902	+	3.99933i	0.0986363	+	0.170843i
$549$	12.4164	+	21.5058i	0.529919	+	0.917847i
$550$	−3.42705	+	5.93583i	−0.146130	+	0.253104i
$551$	−0.347524			−0.0148050
$552$	−20.5902	+	35.6632i	−0.876376	+	1.51793i
$553$		0			0
$554$	−30.5623			−1.29847
$555$	3.35410	−	5.80948i	0.142374	−	0.246598i
$556$	1.01722	+	1.76188i	0.0431398	+	0.0747203i
$557$	−3.97214	−	6.87994i	−0.168305	−	0.291512i	0.769519	−	0.638624i	$-0.220496\pi$
$557$	−3.97214	−	6.87994i	−0.168305	−	0.291512i	−0.937824	+	0.347111i	$0.887163\pi$
$558$		0			0
$559$	4.40983	+	4.58283i	0.186516	+	0.193833i
$560$	1.14590			0.0484230
$561$	25.9164	+	44.8885i	1.09419	+	1.89520i
$562$	−16.0902	−	27.8690i	−0.678723	−	1.17558i
$563$	−8.64590	+	14.9751i	−0.364381	+	0.631127i	−0.988677	−	0.150062i	$-0.952053\pi$
$563$	−8.64590	+	14.9751i	−0.364381	+	0.631127i	0.624295	+	0.781188i	$0.285386\pi$
$564$	−17.8885			−0.753244
$565$	3.73607	−	6.47106i	0.157178	−	0.272240i
$566$	−2.19098	+	3.79489i	−0.0920939	+	0.159511i
$567$	2.59675			0.109053
$568$	−1.97214	+	3.41584i	−0.0827490	+	0.143325i
$569$	9.44427	+	16.3580i	0.395924	+	0.685761i	0.993219	−	0.116261i	$-0.0370909\pi$
$569$	9.44427	+	16.3580i	0.395924	+	0.685761i	−0.597294	+	0.802022i	$0.703758\pi$
$570$	−0.427051	−	0.739674i	−0.0178872	−	0.0309815i
$571$	28.0000			1.17176			0.585882	−	0.810397i	$-0.300748\pi$
$571$	28.0000			1.17176			0.585882	+	0.810397i	$0.300748\pi$
$572$	−2.61803	+	9.06914i	−0.109466	+	0.379200i
$573$	10.7771			0.450219
$574$	−1.13525	−	1.96632i	−0.0473846	−	0.0820726i
$575$	−4.11803	−	7.13264i	−0.171734	−	0.297452i
$576$	−4.23607	+	7.33708i	−0.176503	+	0.305712i
$577$	−7.88854			−0.328404			−0.164202	−	0.986427i	$-0.552505\pi$
$577$	−7.88854			−0.328404			−0.164202	+	0.986427i	$0.552505\pi$
$578$	−10.4721	+	18.1383i	−0.435583	+	0.754453i
$579$	6.11803	−	10.5967i	0.254257	−	0.440386i
$580$	0.909830			0.0377786
$581$	−1.05573	+	1.82857i	−0.0437990	+	0.0758621i
$582$	9.89919	+	17.1459i	0.410335	+	0.710720i
$583$	−12.7082	−	22.0113i	−0.526320	−	0.911613i
$584$	13.4164			0.555175
$585$	−5.00000	−	5.19615i	−0.206725	−	0.214834i
$586$	−19.5066			−0.805809
$587$	−2.88197	−	4.99171i	−0.118951	−	0.206030i	0.800401	−	0.599465i	$-0.204620\pi$
$587$	−2.88197	−	4.99171i	−0.118951	−	0.206030i	−0.919352	+	0.393435i	$0.871287\pi$
$588$	−4.79837	−	8.31103i	−0.197882	−	0.342741i
$589$		0			0
$590$	20.5623			0.846537
$591$	3.35410	−	5.80948i	0.137969	−	0.238970i
$592$	7.28115	−	12.6113i	0.299254	−	0.518322i
$593$	27.8885			1.14525			0.572623	−	0.819819i	$-0.305926\pi$
$593$	27.8885			1.14525			0.572623	+	0.819819i	$0.305926\pi$
$594$	−7.66312	+	13.2729i	−0.314422	+	0.544594i
$595$	0.645898	+	1.11873i	0.0264792	+	0.0458634i
$596$	−4.16312	−	7.21073i	−0.170528	−	0.295363i
$597$	32.8885			1.34604
$598$	−33.3156	−	34.6226i	−1.36238	−	1.41582i
$599$	−24.0000			−0.980613			−0.490307	−	0.871550i	$-0.663115\pi$
$599$	−24.0000			−0.980613			−0.490307	+	0.871550i	$0.663115\pi$
$600$	−2.50000	−	4.33013i	−0.102062	−	0.176777i
$601$	−13.0279	−	22.5649i	−0.531418	−	0.920442i	−0.999328	−	0.0366662i	$-0.988326\pi$
$601$	−13.0279	−	22.5649i	−0.531418	−	0.920442i	0.467910	−	0.883776i	$-0.345007\pi$
$602$	−0.336881	+	0.583495i	−0.0137302	+	0.0237815i
$603$	21.4164			0.872144
$604$	−2.47214	+	4.28187i	−0.100590	+	0.174227i
$605$	−3.47214	+	6.01392i	−0.141162	+	0.244500i
$606$	−34.2705			−1.39214
$607$	−6.35410	+	11.0056i	−0.257905	+	0.446705i	−0.965681	−	0.259733i	$-0.916366\pi$
$607$	−6.35410	+	11.0056i	−0.257905	+	0.446705i	0.707775	+	0.706437i	$0.249699\pi$
$608$	−0.399187	−	0.691412i	−0.0161892	−	0.0280405i
$609$	−0.388544	−	0.672978i	−0.0157446	−	0.0272704i
$610$	−20.0902			−0.813427
$611$	−12.9443	+	44.8403i	−0.523669	+	1.81404i
$612$	6.76393			0.273416
$613$	−11.0279	−	19.1008i	−0.445411	−	0.771475i	0.552670	−	0.833400i	$-0.313609\pi$
$613$	−11.0279	−	19.1008i	−0.445411	−	0.771475i	−0.998081	+	0.0619256i	$0.980276\pi$
$614$	−5.70820	−	9.88690i	−0.230364	−	0.399003i
$615$	−6.64590	+	11.5110i	−0.267988	+	0.464170i
$616$	2.23607			0.0900937
$617$	6.79180	−	11.7637i	0.273427	−	0.473590i	−0.696310	−	0.717741i	$-0.745176\pi$
$617$	6.79180	−	11.7637i	0.273427	−	0.473590i	0.969737	+	0.244151i	$0.0785093\pi$
$618$	−8.94427	+	15.4919i	−0.359791	+	0.623177i
$619$	12.0000			0.482321			0.241160	−	0.970485i	$-0.422472\pi$
$619$	12.0000			0.482321			0.241160	+	0.970485i	$0.422472\pi$
$620$		0			0
$621$	−9.20820	−	15.9491i	−0.369512	−	0.640014i
$622$	19.4164	+	33.6302i	0.778527	+	1.34845i
$623$	2.12461			0.0851208
$624$	−27.1353	−	28.1998i	−1.08628	−	1.12889i
$625$	1.00000			0.0400000
$626$	25.7984	+	44.6841i	1.03111	+	1.78594i
$627$	−1.11803	−	1.93649i	−0.0446500	−	0.0773360i
$628$	5.56231	−	9.63420i	0.221960	−	0.384446i
$629$	16.4164			0.654565
$630$	0.381966	−	0.661585i	0.0152179	−	0.0263582i
$631$	−12.0623	+	20.8925i	−0.480193	+	0.831718i	−0.999742	−	0.0227223i	$-0.992767\pi$
$631$	−12.0623	+	20.8925i	−0.480193	+	0.831718i	0.519549	+	0.854441i	$0.326100\pi$
$632$		0			0
$633$	10.2639	−	17.7777i	0.407955	−	0.706598i
$634$	−19.3262	−	33.4740i	−0.767543	−	1.32942i
$635$	−0.118034	−	0.204441i	−0.00468404	−	0.00811299i
$636$	−8.29180			−0.328791
$637$	−24.3050	+	6.01392i	−0.962997	+	0.238280i
$638$	10.0902			0.399474
$639$	1.76393	+	3.05522i	0.0697801	+	0.120863i
$640$	−6.80902	−	11.7936i	−0.269150	−	0.466182i
$641$	13.4443	−	23.2862i	0.531017	−	0.919748i	−0.468328	−	0.883555i	$-0.655143\pi$
$641$	13.4443	−	23.2862i	0.531017	−	0.919748i	0.999345	−	0.0361934i	$-0.0115232\pi$
$642$	37.0344			1.46163
$643$	15.3541	−	26.5941i	0.605507	−	1.04877i	−0.386465	−	0.922304i	$-0.626304\pi$
$643$	15.3541	−	26.5941i	0.605507	−	1.04877i	0.991971	−	0.126464i	$-0.0403628\pi$
$644$	0.600813	−	1.04064i	0.0236754	−	0.0410069i
$645$	3.94427			0.155306
$646$	1.04508	−	1.81014i	0.0411183	−	0.0712190i
$647$	23.2984	+	40.3540i	0.915954	+	1.58648i	0.805499	+	0.592597i	$0.201897\pi$
$647$	23.2984	+	40.3540i	0.915954	+	1.58648i	0.110454	+	0.993881i	$0.464769\pi$
$648$	−12.2984	−	21.3014i	−0.483126	−	0.836798i
$649$	53.8328			2.11312
$650$	5.66312	−	1.40126i	0.222126	−	0.0549619i
$651$		0			0
$652$	−0.399187	−	0.691412i	−0.0156334	−	0.0270778i
$653$	10.5000	+	18.1865i	0.410897	+	0.711694i	0.994988	−	0.0999939i	$-0.0318823\pi$
$653$	10.5000	+	18.1865i	0.410897	+	0.711694i	−0.584091	+	0.811688i	$0.698549\pi$
$654$	−3.61803	+	6.26662i	−0.141476	+	0.245044i
$655$	−12.0000			−0.468879
$656$	−14.4271	+	24.9884i	−0.563282	+	0.975633i
$657$	6.00000	−	10.3923i	0.234082	−	0.405442i
$658$	−4.94427			−0.192748
$659$	24.1180	−	41.7737i	0.939505	−	1.62727i	0.173109	−	0.984903i	$-0.444619\pi$
$659$	24.1180	−	41.7737i	0.939505	−	1.62727i	0.766396	−	0.642368i	$-0.222048\pi$
$660$	2.92705	+	5.06980i	0.113935	+	0.197342i
$661$	−1.68034	−	2.91043i	−0.0653576	−	0.113203i	0.831495	−	0.555532i	$-0.187485\pi$
$661$	−1.68034	−	2.91043i	−0.0653576	−	0.113203i	−0.896853	+	0.442330i	$0.854152\pi$
$662$	41.5066			1.61320
$663$	12.2361	−	42.3870i	0.475210	−	1.64617i
$664$	20.0000			0.776151
$665$	−0.0278640	−	0.0482619i	−0.00108052	−	0.00187152i
$666$	−4.85410	−	8.40755i	−0.188093	−	0.325786i
$667$	−6.06231	+	10.5002i	−0.234733	+	0.406570i
$668$	3.20163			0.123875
$669$	−14.2082	+	24.6093i	−0.549321	+	0.951452i
$670$	−8.66312	+	15.0050i	−0.334685	+	0.579692i
$671$	−52.5967			−2.03047
$672$	0.892609	−	1.54604i	0.0344331	−	0.0596400i
$673$	18.2082	+	31.5375i	0.701875	+	1.21568i	0.967808	+	0.251691i	$0.0809867\pi$
$673$	18.2082	+	31.5375i	0.701875	+	1.21568i	−0.265933	+	0.963992i	$0.585680\pi$
$674$	−22.5623	−	39.0791i	−0.869068	−	1.50527i
$675$	2.23607			0.0860663
$676$	7.10739	−	3.74663i	0.273361	−	0.144101i
$677$	47.8885			1.84051			0.920253	−	0.391324i	$-0.127983\pi$
$677$	47.8885			1.84051			0.920253	+	0.391324i	$0.127983\pi$
$678$	−13.5172	−	23.4125i	−0.519126	−	0.899152i
$679$	0.645898	+	1.11873i	0.0247873	+	0.0429328i
$680$	6.11803	−	10.5967i	0.234616	−	0.406367i
$681$	3.94427			0.151145
$682$		0			0
$683$	−15.1180	+	26.1852i	−0.578475	+	1.00195i	0.417179	+	0.908824i	$0.363019\pi$
$683$	−15.1180	+	26.1852i	−0.578475	+	1.00195i	−0.995654	+	0.0931246i	$0.970315\pi$
$684$	−0.291796			−0.0111571
$685$	3.73607	−	6.47106i	0.142748	−	0.247246i
$686$	−2.66312	−	4.61266i	−0.101678	−	0.176112i
$687$	−22.2361	−	38.5140i	−0.848359	−	1.46940i
$688$	8.56231			0.326435
$689$	−6.00000	+	20.7846i	−0.228582	+	0.791831i
$690$	−29.7984			−1.13440
$691$	5.29837	+	9.17705i	0.201560	+	0.349112i	0.949031	−	0.315182i	$-0.102066\pi$
$691$	5.29837	+	9.17705i	0.201560	+	0.349112i	−0.747471	+	0.664294i	$0.768732\pi$
$692$	−5.21885	−	9.03931i	−0.198391	−	0.343623i
$693$	1.00000	−	1.73205i	0.0379869	−	0.0657952i
$694$	27.9787			1.06206
$695$	1.64590	−	2.85078i	0.0624325	−	0.108136i
$696$	−3.68034	+	6.37454i	−0.139503	+	0.241626i
$697$	−32.5279			−1.23208
$698$	19.7533	−	34.2137i	0.747673	−	1.29501i
$699$	22.2361	+	38.5140i	0.841045	+	1.45673i
$700$	0.0729490	+	0.126351i	0.00275721	+	0.00477563i
$701$	−27.8885			−1.05334			−0.526668	−	0.850071i	$-0.676559\pi$
$701$	−27.8885			−1.05334			−0.526668	+	0.850071i	$0.676559\pi$
$702$	12.6631	−	3.13331i	0.477939	−	0.118259i
$703$	−0.708204			−0.0267104
$704$	−8.97214	−	15.5402i	−0.338150	−	0.585693i
$705$	14.4721	+	25.0665i	0.545052	+	0.944058i
$706$	8.51722	−	14.7523i	0.320550	−	0.555209i
$707$	−2.23607			−0.0840960
$708$	8.78115	−	15.2094i	0.330016	−	0.571604i
$709$	19.1525	−	33.1731i	0.719286	−	1.24584i	−0.241997	−	0.970277i	$-0.577802\pi$
$709$	19.1525	−	33.1731i	0.719286	−	1.24584i	0.961283	−	0.275563i	$-0.0888644\pi$
$710$	−2.85410			−0.107113
$711$		0			0
$712$	−10.0623	−	17.4284i	−0.377101	−	0.653158i
$713$		0			0
$714$	4.67376			0.174911
$715$	14.8262	−	3.66854i	0.554470	−	0.137196i
$716$	−2.32624			−0.0869356
$717$	11.0557	+	19.1491i	0.412884	+	0.715136i
$718$	14.4721	+	25.0665i	0.540095	+	0.935473i
$719$	−4.06231	+	7.03612i	−0.151498	+	0.262403i	−0.931779	−	0.363027i	$-0.881743\pi$
$719$	−4.06231	+	7.03612i	−0.151498	+	0.262403i	0.780280	+	0.625430i	$0.215077\pi$
$720$	−9.70820			−0.361803
$721$	−0.583592	+	1.01081i	−0.0217341	+	0.0376446i
$722$	15.3262	−	26.5458i	0.570384	−	0.987933i
$723$	−33.5410			−1.24740
$724$	−1.85410	+	3.21140i	−0.0689072	+	0.119351i
$725$	−0.736068	−	1.27491i	−0.0273369	−	0.0473489i
$726$	12.5623	+	21.7586i	0.466231	+	0.807536i
$727$	11.0557			0.410034			0.205017	−	0.978758i	$-0.434275\pi$
$727$	11.0557			0.410034			0.205017	+	0.978758i	$0.434275\pi$
$728$	−1.31966	−	1.37143i	−0.0489099	−	0.0508286i
$729$	−7.00000			−0.259259
$730$	4.85410	+	8.40755i	0.179658	+	0.311177i
$731$	4.82624	+	8.35929i	0.178505	+	0.309179i
$732$	−8.57953	+	14.8602i	−0.317108	+	0.549248i
$733$	−8.11146			−0.299603			−0.149802	−	0.988716i	$-0.547864\pi$
$733$	−8.11146			−0.299603			−0.149802	+	0.988716i	$0.547864\pi$
$734$	20.7533	−	35.9458i	0.766018	−	1.32678i
$735$	−7.76393	+	13.4475i	−0.286377	+	0.496019i
$736$	−27.8541			−1.02672
$737$	−22.6803	+	39.2835i	−0.835441	+	1.44703i
$738$	9.61803	+	16.6589i	0.354045	+	0.613223i
$739$	19.7705	+	34.2435i	0.727270	+	1.25967i	0.958033	+	0.286659i	$0.0925445\pi$
$739$	19.7705	+	34.2435i	0.727270	+	1.25967i	−0.230763	+	0.973010i	$0.574122\pi$
$740$	1.85410			0.0681581
$741$	−0.527864	+	1.82857i	−0.0193916	+	0.0671744i
$742$	−2.29180			−0.0841345
$743$	−1.06231	−	1.83997i	−0.0389722	−	0.0675019i	0.845881	−	0.533371i	$-0.179075\pi$
$743$	−1.06231	−	1.83997i	−0.0389722	−	0.0675019i	−0.884854	+	0.465869i	$0.845742\pi$
$744$		0			0
$745$	−6.73607	+	11.6672i	−0.246790	+	0.427454i
$746$	16.2705			0.595706
$747$	8.94427	−	15.4919i	0.327254	−	0.566820i
$748$	−7.16312	+	12.4069i	−0.261910	+	0.453641i
$749$	2.41641			0.0882936
$750$	1.80902	−	3.13331i	0.0660560	−	0.114412i
$751$	8.64590	+	14.9751i	0.315493	+	0.546450i	0.979542	−	0.201239i	$-0.0644967\pi$
$751$	8.64590	+	14.9751i	0.315493	+	0.546450i	−0.664049	+	0.747689i	$0.731163\pi$
$752$	31.4164	+	54.4148i	1.14564	+	1.98430i
$753$	−35.2492			−1.28455
$754$	−5.95492	−	6.18853i	−0.216865	−	0.225373i
$755$	8.00000			0.291150
$756$	0.163119	+	0.282530i	0.00593258	+	0.0102755i
$757$	−14.4443	−	25.0182i	−0.524986	−	0.909302i	−0.999577	−	0.0290958i	$-0.990737\pi$
$757$	−14.4443	−	25.0182i	−0.524986	−	0.909302i	0.474591	−	0.880207i	$-0.342596\pi$
$758$	−26.8435	+	46.4942i	−0.974998	+	1.68875i
$759$	−78.0132			−2.83170
$760$	−0.263932	+	0.457144i	−0.00957382	+	0.0165823i
$761$	10.0279	−	17.3688i	0.363510	−	0.629617i	−0.625026	−	0.780604i	$-0.714912\pi$
$761$	10.0279	−	17.3688i	0.363510	−	0.629617i	0.988536	+	0.150986i	$0.0482450\pi$
$762$	−0.854102			−0.0309408
$763$	−0.236068	+	0.408882i	−0.00854623	+	0.0148025i
$764$	1.48936	+	2.57964i	0.0538830	+	0.0933282i
$765$	−5.47214	−	9.47802i	−0.197845	−	0.342678i
$766$	−0.381966			−0.0138010
$767$	−31.7705	−	33.0169i	−1.14717	−	1.19217i
$768$	−30.3262			−1.09430
$769$	11.9164	+	20.6398i	0.429717	+	0.744291i	0.996848	−	0.0793363i	$-0.0252801\pi$
$769$	11.9164	+	20.6398i	0.429717	+	0.744291i	−0.567131	+	0.823627i	$0.691947\pi$
$770$	0.809017	+	1.40126i	0.0291549	+	0.0504979i
$771$	9.53444	−	16.5141i	0.343375	−	0.594742i
$772$	3.38197			0.121720
$773$	18.9721	−	32.8607i	0.682380	−	1.18192i	−0.291872	−	0.956457i	$-0.594278\pi$
$773$	18.9721	−	32.8607i	0.682380	−	1.18192i	0.974252	−	0.225460i	$-0.0723885\pi$
$774$	2.85410	−	4.94345i	0.102589	−	0.177689i
$775$		0			0
$776$	6.11803	−	10.5967i	0.219625	−	0.380401i
$777$	−0.791796	−	1.37143i	−0.0284055	−	0.0491998i
$778$	29.0344	+	50.2891i	1.04094	+	1.80295i
$779$	1.40325			0.0502767
$780$	1.38197	−	4.78727i	0.0494823	−	0.171412i
$781$	−7.47214			−0.267374
$782$	−36.4615	−	63.1532i	−1.30386	−	2.25835i
$783$	−1.64590	−	2.85078i	−0.0588196	−	0.101879i
$784$	−16.8541	+	29.1922i	−0.601932	+	1.04258i
$785$	−18.0000			−0.642448
$786$	−21.7082	+	37.5997i	−0.774306	+	1.34114i
$787$	18.7705	−	32.5115i	0.669096	−	1.15891i	−0.309061	−	0.951042i	$-0.600015\pi$
$787$	18.7705	−	32.5115i	0.669096	−	1.15891i	0.978157	−	0.207867i	$-0.0666520\pi$
$788$	1.85410			0.0660496
$789$	9.20820	−	15.9491i	0.327821	−	0.567802i
$790$		0			0
$791$	−0.881966	−	1.52761i	−0.0313591	−	0.0543156i
$792$	−18.9443			−0.673155
$793$	31.0410	+	32.2588i	1.10230	+	1.14554i
$794$	16.2705			0.577419
$795$	6.70820	+	11.6190i	0.237915	+	0.412082i
$796$	4.54508	+	7.87232i	0.161096	+	0.279027i
$797$	−0.0835921	+	0.144786i	−0.00296099	+	0.00512858i	−0.867502	−	0.497434i	$-0.834276\pi$
$797$	−0.0835921	+	0.144786i	−0.00296099	+	0.00512858i	0.864541	+	0.502562i	$0.167609\pi$
$798$	−0.201626			−0.00713749
$799$	−35.4164	+	61.3430i	−1.25294	+	2.17016i
$800$	1.69098	−	2.92887i	0.0597853	−	0.103551i
$801$	−18.0000			−0.635999
$802$	21.7533	−	37.6778i	0.768135	−	1.33045i
$803$	12.7082	+	22.0113i	0.448463	+	0.776760i
$804$	7.39919	+	12.8158i	0.260949	+	0.451977i
$805$	−1.94427			−0.0685266
$806$		0			0
$807$	34.5967			1.21786
$808$	10.5902	+	18.3427i	0.372561	+	0.645294i
$809$	−16.4443	−	28.4823i	−0.578150	−	1.00138i	−0.995692	−	0.0927271i	$-0.970442\pi$
$809$	−16.4443	−	28.4823i	−0.578150	−	1.00138i	0.417542	−	0.908658i	$-0.362892\pi$
$810$	8.89919	−	15.4138i	0.312686	−	0.541587i
$811$	−39.7771			−1.39676			−0.698381	−	0.715726i	$-0.746096\pi$
$811$	−39.7771			−1.39676			−0.698381	+	0.715726i	$0.746096\pi$
$812$	0.107391	−	0.186006i	0.00376868	−	0.00652755i
$813$	16.4443	−	28.4823i	0.576726	−	0.998918i
$814$	20.5623			0.720708
$815$	−0.645898	+	1.11873i	−0.0226248	+	0.0391873i
$816$	−29.6976	−	51.4377i	−1.03962	−	1.80068i
$817$	−0.208204	−	0.360620i	−0.00728413	−	0.0126165i
$818$	−17.6180			−0.616000
$819$	−1.65248	+	0.408882i	−0.0577422	+	0.0142875i
$820$	−3.67376			−0.128293
$821$	−9.68034	−	16.7668i	−0.337846	−	0.585167i	0.646181	−	0.763184i	$-0.276365\pi$
$821$	−9.68034	−	16.7668i	−0.337846	−	0.585167i	−0.984027	+	0.178017i	$0.943032\pi$
$822$	−13.5172	−	23.4125i	−0.471467	−	0.816605i
$823$	−11.2984	+	19.5694i	−0.393837	+	0.682145i	−0.992952	−	0.118518i	$-0.962186\pi$
$823$	−11.2984	+	19.5694i	−0.393837	+	0.682145i	0.599115	+	0.800663i	$0.295519\pi$
$824$	11.0557			0.385145
$825$	4.73607	−	8.20311i	0.164889	−	0.285596i
$826$	2.42705	−	4.20378i	0.0844479	−	0.146268i
$827$	8.94427			0.311023			0.155511	−	0.987834i	$-0.450297\pi$
$827$	8.94427			0.311023			0.155511	+	0.987834i	$0.450297\pi$
$828$	−5.09017	+	8.81643i	−0.176896	+	0.306392i
$829$	−18.6246	−	32.2588i	−0.646860	−	1.12039i	−0.983869	−	0.178892i	$-0.942749\pi$
$829$	−18.6246	−	32.2588i	−0.646860	−	1.12039i	0.337009	−	0.941501i	$-0.390585\pi$
$830$	7.23607	+	12.5332i	0.251168	+	0.435035i
$831$	42.2361			1.46515
$832$	−4.23607	+	14.6742i	−0.146859	+	0.508735i
$833$	−38.0000			−1.31662
$834$	−5.95492	−	10.3142i	−0.206202	−	0.357152i
$835$	−2.59017	−	4.48631i	−0.0896365	−	0.155255i
$836$	0.309017	−	0.535233i	0.0106876	−	0.0185114i
$837$		0			0
$838$	11.0451	−	19.1306i	0.381546	−	0.660857i
$839$	−8.64590	+	14.9751i	−0.298490	+	0.516999i	−0.975791	−	0.218707i	$-0.929816\pi$
$839$	−8.64590	+	14.9751i	−0.298490	+	0.516999i	0.677301	+	0.735706i	$0.263149\pi$
$840$	−1.18034			−0.0407256
$841$	13.4164	−	23.2379i	0.462635	−	0.801307i
$842$	−4.85410	−	8.40755i	−0.167283	−	0.289743i
$843$	22.2361	+	38.5140i	0.765851	+	1.32649i
$844$	5.67376			0.195299
$845$	−11.0000	−	6.92820i	−0.378412	−	0.238337i
$846$	41.8885			1.44016
$847$	0.819660	+	1.41969i	0.0281639	+	0.0487812i
$848$	14.5623	+	25.2227i	0.500072	+	0.866149i
$849$	3.02786	−	5.24441i	0.103916	−	0.179988i
$850$	8.85410			0.303693
$851$	−12.3541	+	21.3979i	−0.423493	+	0.733512i
$852$	−1.21885	+	2.11111i	−0.0417570	+	0.0723253i
$853$	6.00000			0.205436			0.102718	−	0.994711i	$-0.467246\pi$
$853$	6.00000			0.205436			0.102718	+	0.994711i	$0.467246\pi$
$854$	−2.37132	+	4.10725i	−0.0811450	+	0.140547i
$855$	0.236068	+	0.408882i	0.00807335	+	0.0139835i
$856$	−11.4443	−	19.8221i	−0.391157	−	0.677504i
$857$	0.111456			0.00380727			0.00190364	−	0.999998i	$-0.499394\pi$
$857$	0.111456			0.00380727			0.00190364	+	0.999998i	$0.499394\pi$
$858$	15.3262	−	53.0916i	0.523229	−	1.81252i
$859$	−13.8885			−0.473871			−0.236935	−	0.971525i	$-0.576143\pi$
$859$	−13.8885			−0.473871			−0.236935	+	0.971525i	$0.576143\pi$
$860$	0.545085	+	0.944115i	0.0185872	+	0.0321940i
$861$	1.56888	+	2.71739i	0.0534674	+	0.0926083i
$862$	−3.89919	+	6.75359i	−0.132807	+	0.230028i
$863$	−38.8328			−1.32188			−0.660942	−	0.750437i	$-0.729843\pi$
$863$	−38.8328			−1.32188			−0.660942	+	0.750437i	$0.729843\pi$
$864$	3.78115	−	6.54915i	0.128637	−	0.222807i
$865$	−8.44427	+	14.6259i	−0.287114	+	0.497296i
$866$	−37.9787			−1.29057
$867$	14.4721	−	25.0665i	0.491500	−	0.851302i
$868$		0			0
$869$		0			0
$870$	−5.32624			−0.180576
$871$	37.4787	−	9.27358i	1.26992	−	0.314223i
$872$	4.47214			0.151446
$873$	−5.47214	−	9.47802i	−0.185204	−	0.320782i
$874$	1.57295	+	2.72443i	0.0532058	+	0.0921551i
$875$	0.118034	−	0.204441i	0.00399028	−	0.00691136i
$876$	8.29180			0.280154
$877$	−27.8607	+	48.2561i	−0.940788	+	1.62949i	−0.176816	+	0.984244i	$0.556580\pi$
$877$	−27.8607	+	48.2561i	−0.940788	+	1.62949i	−0.763972	+	0.645249i	$0.776754\pi$
$878$	7.51722	−	13.0202i	0.253694	−	0.439411i
$879$	26.9574			0.909251
$880$	10.2812	−	17.8075i	0.346578	−	0.600290i
$881$	−7.50000	−	12.9904i	−0.252681	−	0.437657i	0.711582	−	0.702603i	$-0.247979\pi$
$881$	−7.50000	−	12.9904i	−0.252681	−	0.437657i	−0.964263	+	0.264946i	$0.914646\pi$
$882$	11.2361	+	19.4614i	0.378338	+	0.655301i
$883$	10.8328			0.364553			0.182277	−	0.983247i	$-0.441653\pi$
$883$	10.8328			0.364553			0.182277	+	0.983247i	$0.441653\pi$
$884$	11.8369	−	2.92887i	0.398117	−	0.0985085i
$885$	−28.4164			−0.955207
$886$	13.7082	+	23.7433i	0.460536	+	0.797672i
$887$	20.2426	+	35.0613i	0.679682	+	1.17724i	0.975077	+	0.221868i	$0.0712153\pi$
$887$	20.2426	+	35.0613i	0.679682	+	1.17724i	−0.295395	+	0.955375i	$0.595451\pi$
$888$	−7.50000	+	12.9904i	−0.251684	+	0.435929i
$889$	−0.0557281			−0.00186906
$890$	7.28115	−	12.6113i	0.244065	−	0.422733i
$891$	23.2984	−	40.3540i	0.780525	−	1.35191i
$892$	−7.85410			−0.262975
$893$	1.52786	−	2.64634i	0.0511280	−	0.0885563i
$894$	24.3713	+	42.2124i	0.815099	+	1.41179i
$895$	1.88197	+	3.25966i	0.0629072	+	0.108958i
$896$	−3.21478			−0.107398
$897$	46.0410	+	47.8472i	1.53726	+	1.59757i
$898$	−22.5623			−0.752914
$899$		0			0
$900$	−0.618034	−	1.07047i	−0.0206011	−	0.0356822i
$901$	−16.4164	+	28.4341i	−0.546910	+	0.947276i
$902$	−40.7426			−1.35658
$903$	0.465558	−	0.806370i	0.0154928	−	0.0268343i
$904$	−8.35410	+	14.4697i	−0.277853	+	0.481256i
$905$	6.00000			0.199447
$906$	14.4721	−	25.0665i	0.480805	−	0.832778i
$907$	10.0623	+	17.4284i	0.334113	+	0.578701i	0.983314	−	0.181916i	$-0.0582298\pi$
$907$	10.0623	+	17.4284i	0.334113	+	0.578701i	−0.649201	+	0.760617i	$0.724896\pi$
$908$	0.545085	+	0.944115i	0.0180893	+	0.0313316i
$909$	18.9443			0.628342
$910$	0.381966	−	1.32317i	0.0126620	−	0.0438626i
$911$	48.0000			1.59031			0.795155	−	0.606406i	$-0.207389\pi$
$911$	48.0000			1.59031			0.795155	+	0.606406i	$0.207389\pi$
$912$	1.28115	+	2.21902i	0.0424232	+	0.0734792i
$913$	18.9443	+	32.8124i	0.626964	+	1.08593i
$914$	22.9894	−	39.8187i	0.760420	−	1.31709i
$915$	27.7639			0.917847
$916$	6.14590	−	10.6450i	0.203066	−	0.351721i
$917$	−1.41641	+	2.45329i	−0.0467739	+	0.0810148i
$918$	19.7984			0.653444
$919$	−16.6459	+	28.8315i	−0.549098	+	0.951065i	0.449239	+	0.893412i	$0.351695\pi$
$919$	−16.6459	+	28.8315i	−0.549098	+	0.951065i	−0.998337	+	0.0576532i	$0.981638\pi$
$920$	9.20820	+	15.9491i	0.303585	+	0.525825i
$921$	7.88854	+	13.6634i	0.259936	+	0.450223i
$922$	−45.9787			−1.51423
$923$	4.40983	+	4.58283i	0.145151	+	0.150846i
$924$	1.38197			0.0454633
$925$	−1.50000	−	2.59808i	−0.0493197	−	0.0854242i
$926$	−23.4164	−	40.5584i	−0.769511	−	1.33283i
$927$	4.94427	−	8.56373i	0.162391	−	0.281270i
$928$	−4.97871			−0.163434
$929$	−1.02786	+	1.78031i	−0.0337231	+	0.0584102i	−0.882394	−	0.470511i	$-0.844070\pi$
$929$	−1.02786	+	1.78031i	−0.0337231	+	0.0584102i	0.848671	+	0.528921i	$0.177403\pi$
$930$		0			0
$931$	1.63932			0.0537266
$932$	−6.14590	+	10.6450i	−0.201316	+	0.348689i
$933$	−26.8328	−	46.4758i	−0.878467	−	1.52155i
$934$	7.23607	+	12.5332i	0.236771	+	0.410100i
$935$	23.1803			0.758078
$936$	11.1803	+	11.6190i	0.365441	+	0.379777i
$937$	−6.00000			−0.196011			−0.0980057	−	0.995186i	$-0.531246\pi$
$937$	−6.00000			−0.196011			−0.0980057	+	0.995186i	$0.531246\pi$
$938$	2.04508	+	3.54219i	0.0667744	+	0.115657i
$939$	−35.6525	−	61.7519i	−1.16347	−	2.01520i
$940$	−4.00000	+	6.92820i	−0.130466	+	0.225973i
$941$	23.8885			0.778744			0.389372	−	0.921081i	$-0.372692\pi$
$941$	23.8885			0.778744			0.389372	+	0.921081i	$0.372692\pi$
$942$	−32.5623	+	56.3996i	−1.06094	+	1.83760i
$943$	24.4787	−	42.3984i	0.797137	−	1.38068i
$944$	−61.6869			−2.00774
$945$	0.263932	−	0.457144i	0.00858571	−	0.0148709i
$946$	6.04508	+	10.4704i	0.196543	+	0.340422i
$947$	−8.40983	−	14.5663i	−0.273283	−	0.473340i	0.696418	−	0.717637i	$-0.254776\pi$
$947$	−8.40983	−	14.5663i	−0.273283	−	0.473340i	−0.969700	+	0.244297i	$0.921443\pi$
$948$		0			0
$949$	6.00000	−	20.7846i	0.194768	−	0.674697i
$950$	−0.381966			−0.0123926
$951$	26.7082	+	46.2600i	0.866073	+	1.50008i
$952$	−1.44427	−	2.50155i	−0.0468091	−	0.0810758i
$953$	28.0967	−	48.6650i	0.910143	−	1.57641i	0.0962820	−	0.995354i	$-0.469305\pi$
$953$	28.0967	−	48.6650i	0.910143	−	1.57641i	0.813861	−	0.581060i	$-0.197362\pi$
$954$	19.4164			0.628629
$955$	2.40983	−	4.17395i	0.0779803	−	0.135066i
$956$	−3.05573	+	5.29268i	−0.0988293	+	0.171177i
$957$	−13.9443			−0.450754
$958$	6.57295	−	11.3847i	0.212362	−	0.367822i
$959$	−0.881966	−	1.52761i	−0.0284802	−	0.0493291i
$960$	4.73607	+	8.20311i	0.152856	+	0.264754i
$961$	−31.0000			−1.00000
$962$	−12.1353	−	12.6113i	−0.391256	−	0.406605i
$963$	−20.4721			−0.659705
$964$	−4.63525	−	8.02850i	−0.149292	−	0.258580i
$965$	−2.73607	−	4.73901i	−0.0880771	−	0.152554i
$966$	−3.51722	+	6.09201i	−0.113165	+	0.196007i
$967$	−1.16718			−0.0375341			−0.0187671	−	0.999824i	$-0.505974\pi$
$967$	−1.16718			−0.0375341			−0.0187671	+	0.999824i	$0.505974\pi$
$968$	7.76393	−	13.4475i	0.249542	−	0.432220i
$969$	−1.44427	+	2.50155i	−0.0463967	+	0.0803614i
$970$	8.85410			0.284288
$971$	8.11803	−	14.0608i	0.260520	−	0.451234i	−0.705860	−	0.708351i	$-0.749439\pi$
$971$	8.11803	−	14.0608i	0.260520	−	0.451234i	0.966380	+	0.257117i	$0.0827726\pi$
$972$	−5.52786	−	9.57454i	−0.177306	−	0.307104i
$973$	−0.388544	−	0.672978i	−0.0124561	−	0.0215747i
$974$	−42.2705			−1.35443
$975$	−7.82624	+	1.93649i	−0.250640	+	0.0620174i
$976$	60.2705			1.92921
$977$	−17.2082	−	29.8055i	−0.550539	−	0.953562i	−0.998236	−	0.0593763i	$-0.981089\pi$
$977$	−17.2082	−	29.8055i	−0.550539	−	0.953562i	0.447696	−	0.894186i	$-0.352245\pi$
$978$	2.33688	+	4.04760i	0.0747252	+	0.129428i
$979$	19.0623	−	33.0169i	0.609234	−	1.05522i
$980$	−4.29180			−0.137096
$981$	2.00000	−	3.46410i	0.0638551	−	0.110600i
$982$	−3.42705	+	5.93583i	−0.109362	+	0.189420i
$983$	−14.8328			−0.473093			−0.236547	−	0.971620i	$-0.576016\pi$
$983$	−14.8328			−0.473093			−0.236547	+	0.971620i	$0.576016\pi$
$984$	14.8607	−	25.7395i	0.473741	−	0.820544i
$985$	−1.50000	−	2.59808i	−0.0477940	−	0.0827816i
$986$	−6.51722	−	11.2882i	−0.207551	−	0.359488i
$987$	6.83282			0.217491
$988$	−0.510643	+	0.126351i	−0.0162457	+	0.00401977i
$989$	−14.5279			−0.461959
$990$	−6.85410	−	11.8717i	−0.217838	−	0.377306i
$991$	16.6459	+	28.8315i	0.528774	+	0.915864i	0.999437	+	0.0335508i	$0.0106816\pi$
$991$	16.6459	+	28.8315i	0.528774	+	0.915864i	−0.470663	+	0.882313i	$0.655985\pi$
$992$		0			0
$993$	−57.3607			−1.82029
$994$	−0.336881	+	0.583495i	−0.0106852	+	0.0185073i
$995$	7.35410	−	12.7377i	0.233141	−	0.403812i
$996$	12.3607			0.391663
$997$	−8.44427	+	14.6259i	−0.267433	+	0.463207i	−0.968198	−	0.250185i	$-0.919509\pi$
$997$	−8.44427	+	14.6259i	−0.267433	+	0.463207i	0.700765	+	0.713392i	$0.252842\pi$
$998$	−11.2361	−	19.4614i	−0.355672	−	0.616041i
$999$	−3.35410	−	5.80948i	−0.106119	−	0.183804i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	65.2.e.a.16.1	✓	4
3.2	odd	2		585.2.j.e.406.2		4
4.3	odd	2		1040.2.q.n.81.1		4
5.2	odd	4		325.2.o.a.224.4		8
5.3	odd	4		325.2.o.a.224.1		8
5.4	even	2		325.2.e.b.276.2		4
13.2	odd	12		845.2.c.c.506.1		4
13.3	even	3		845.2.a.e.1.2		2
13.4	even	6		845.2.e.g.191.2		4
13.5	odd	4		845.2.m.e.361.1		8
13.6	odd	12		845.2.m.e.316.4		8
13.7	odd	12		845.2.m.e.316.1		8
13.8	odd	4		845.2.m.e.361.4		8
13.9	even	3	inner	65.2.e.a.61.1	yes	4
13.10	even	6		845.2.a.b.1.1		2
13.11	odd	12		845.2.c.c.506.4		4
13.12	even	2		845.2.e.g.146.2		4
39.23	odd	6		7605.2.a.bf.1.2		2
39.29	odd	6		7605.2.a.ba.1.1		2
39.35	odd	6		585.2.j.e.451.2		4
52.35	odd	6		1040.2.q.n.321.1		4
65.9	even	6		325.2.e.b.126.2		4
65.22	odd	12		325.2.o.a.74.1		8
65.29	even	6		4225.2.a.u.1.1		2
65.48	odd	12		325.2.o.a.74.4		8
65.49	even	6		4225.2.a.y.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
65.2.e.a.16.1	✓	4	1.1	even	1	trivial
65.2.e.a.61.1	yes	4	13.9	even	3	inner
325.2.e.b.126.2		4	65.9	even	6
325.2.e.b.276.2		4	5.4	even	2
325.2.o.a.74.1		8	65.22	odd	12
325.2.o.a.74.4		8	65.48	odd	12
325.2.o.a.224.1		8	5.3	odd	4
325.2.o.a.224.4		8	5.2	odd	4
585.2.j.e.406.2		4	3.2	odd	2
585.2.j.e.451.2		4	39.35	odd	6
845.2.a.b.1.1		2	13.10	even	6
845.2.a.e.1.2		2	13.3	even	3
845.2.c.c.506.1		4	13.2	odd	12
845.2.c.c.506.4		4	13.11	odd	12
845.2.e.g.146.2		4	13.12	even	2
845.2.e.g.191.2		4	13.4	even	6
845.2.m.e.316.1		8	13.7	odd	12
845.2.m.e.316.4		8	13.6	odd	12
845.2.m.e.361.1		8	13.5	odd	4
845.2.m.e.361.4		8	13.8	odd	4
1040.2.q.n.81.1		4	4.3	odd	2
1040.2.q.n.321.1		4	52.35	odd	6
4225.2.a.u.1.1		2	65.29	even	6
4225.2.a.y.1.2		2	65.49	even	6
7605.2.a.ba.1.1		2	39.29	odd	6
7605.2.a.bf.1.2		2	39.23	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 65 = 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	65.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.809017 - 1.40126i) q^{2} +(1.11803 + 1.93649i) q^{3} +(-0.309017 + 0.535233i) q^{4} +1.00000 q^{5} +(1.80902 - 3.13331i) q^{6} +(0.118034 - 0.204441i) q^{7} -2.23607 q^{8} +(-1.00000 + 1.73205i) q^{9} +O(q^{10})\)	\(q+(-0.809017 - 1.40126i) q^{2} +(1.11803 + 1.93649i) q^{3} +(-0.309017 + 0.535233i) q^{4} +1.00000 q^{5} +(1.80902 - 3.13331i) q^{6} +(0.118034 - 0.204441i) q^{7} -2.23607 q^{8} +(-1.00000 + 1.73205i) q^{9} +(-0.809017 - 1.40126i) q^{10} +(-2.11803 - 3.66854i) q^{11} -1.38197 q^{12} +(-1.00000 + 3.46410i) q^{13} -0.381966 q^{14} +(1.11803 + 1.93649i) q^{15} +(2.42705 + 4.20378i) q^{16} +(-2.73607 + 4.73901i) q^{17} +3.23607 q^{18} +(0.118034 - 0.204441i) q^{19} +(-0.309017 + 0.535233i) q^{20} +0.527864 q^{21} +(-3.42705 + 5.93583i) q^{22} +(-4.11803 - 7.13264i) q^{23} +(-2.50000 - 4.33013i) q^{24} +1.00000 q^{25} +(5.66312 - 1.40126i) q^{26} +2.23607 q^{27} +(0.0729490 + 0.126351i) q^{28} +(-0.736068 - 1.27491i) q^{29} +(1.80902 - 3.13331i) q^{30} +(1.69098 - 2.92887i) q^{32} +(4.73607 - 8.20311i) q^{33} +8.85410 q^{34} +(0.118034 - 0.204441i) q^{35} +(-0.618034 - 1.07047i) q^{36} +(-1.50000 - 2.59808i) q^{37} -0.381966 q^{38} +(-7.82624 + 1.93649i) q^{39} -2.23607 q^{40} +(2.97214 + 5.14789i) q^{41} +(-0.427051 - 0.739674i) q^{42} +(0.881966 - 1.52761i) q^{43} +2.61803 q^{44} +(-1.00000 + 1.73205i) q^{45} +(-6.66312 + 11.5409i) q^{46} +12.9443 q^{47} +(-5.42705 + 9.39993i) q^{48} +(3.47214 + 6.01392i) q^{49} +(-0.809017 - 1.40126i) q^{50} -12.2361 q^{51} +(-1.54508 - 1.60570i) q^{52} +6.00000 q^{53} +(-1.80902 - 3.13331i) q^{54} +(-2.11803 - 3.66854i) q^{55} +(-0.263932 + 0.457144i) q^{56} +0.527864 q^{57} +(-1.19098 + 2.06284i) q^{58} +(-6.35410 + 11.0056i) q^{59} -1.38197 q^{60} +(6.20820 - 10.7529i) q^{61} +(0.236068 + 0.408882i) q^{63} +4.23607 q^{64} +(-1.00000 + 3.46410i) q^{65} -15.3262 q^{66} +(-5.35410 - 9.27358i) q^{67} +(-1.69098 - 2.92887i) q^{68} +(9.20820 - 15.9491i) q^{69} -0.381966 q^{70} +(0.881966 - 1.52761i) q^{71} +(2.23607 - 3.87298i) q^{72} -6.00000 q^{73} +(-2.42705 + 4.20378i) q^{74} +(1.11803 + 1.93649i) q^{75} +(0.0729490 + 0.126351i) q^{76} -1.00000 q^{77} +(9.04508 + 9.39993i) q^{78} +(2.42705 + 4.20378i) q^{80} +(5.50000 + 9.52628i) q^{81} +(4.80902 - 8.32946i) q^{82} -8.94427 q^{83} +(-0.163119 + 0.282530i) q^{84} +(-2.73607 + 4.73901i) q^{85} -2.85410 q^{86} +(1.64590 - 2.85078i) q^{87} +(4.73607 + 8.20311i) q^{88} +(4.50000 + 7.79423i) q^{89} +3.23607 q^{90} +(0.590170 + 0.613323i) q^{91} +5.09017 q^{92} +(-10.4721 - 18.1383i) q^{94} +(0.118034 - 0.204441i) q^{95} +7.56231 q^{96} +(-2.73607 + 4.73901i) q^{97} +(5.61803 - 9.73072i) q^{98} +8.47214 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - q^{2} + q^{4} + 4 q^{5} + 5 q^{6} - 4 q^{7} - 4 q^{9}+O(q^{10}) \) 4 * q - q^2 + q^4 + 4 * q^5 + 5 * q^6 - 4 * q^7 - 4 * q^9	\( 4 q - q^{2} + q^{4} + 4 q^{5} + 5 q^{6} - 4 q^{7} - 4 q^{9} - q^{10} - 4 q^{11} - 10 q^{12} - 4 q^{13} - 6 q^{14} + 3 q^{16} - 2 q^{17} + 4 q^{18} - 4 q^{19} + q^{20} + 20 q^{21} - 7 q^{22} - 12 q^{23} - 10 q^{24} + 4 q^{25} + 7 q^{26} + 7 q^{28} + 6 q^{29} + 5 q^{30} + 9 q^{32} + 10 q^{33} + 22 q^{34} - 4 q^{35} + 2 q^{36} - 6 q^{37} - 6 q^{38} - 6 q^{41} + 5 q^{42} + 8 q^{43} + 6 q^{44} - 4 q^{45} - 11 q^{46} + 16 q^{47} - 15 q^{48} - 4 q^{49} - q^{50} - 40 q^{51} + 5 q^{52} + 24 q^{53} - 5 q^{54} - 4 q^{55} - 10 q^{56} + 20 q^{57} - 7 q^{58} - 12 q^{59} - 10 q^{60} - 2 q^{61} - 8 q^{63} + 8 q^{64} - 4 q^{65} - 30 q^{66} - 8 q^{67} - 9 q^{68} + 10 q^{69} - 6 q^{70} + 8 q^{71} - 24 q^{73} - 3 q^{74} + 7 q^{76} - 4 q^{77} + 25 q^{78} + 3 q^{80} + 22 q^{81} + 17 q^{82} + 15 q^{84} - 2 q^{85} + 2 q^{86} + 20 q^{87} + 10 q^{88} + 18 q^{89} + 4 q^{90} - 20 q^{91} - 2 q^{92} - 24 q^{94} - 4 q^{95} - 10 q^{96} - 2 q^{97} + 18 q^{98} + 16 q^{99}+O(q^{100}) \) 4 * q - q^2 + q^4 + 4 * q^5 + 5 * q^6 - 4 * q^7 - 4 * q^9 - q^10 - 4 * q^11 - 10 * q^12 - 4 * q^13 - 6 * q^14 + 3 * q^16 - 2 * q^17 + 4 * q^18 - 4 * q^19 + q^20 + 20 * q^21 - 7 * q^22 - 12 * q^23 - 10 * q^24 + 4 * q^25 + 7 * q^26 + 7 * q^28 + 6 * q^29 + 5 * q^30 + 9 * q^32 + 10 * q^33 + 22 * q^34 - 4 * q^35 + 2 * q^36 - 6 * q^37 - 6 * q^38 - 6 * q^41 + 5 * q^42 + 8 * q^43 + 6 * q^44 - 4 * q^45 - 11 * q^46 + 16 * q^47 - 15 * q^48 - 4 * q^49 - q^50 - 40 * q^51 + 5 * q^52 + 24 * q^53 - 5 * q^54 - 4 * q^55 - 10 * q^56 + 20 * q^57 - 7 * q^58 - 12 * q^59 - 10 * q^60 - 2 * q^61 - 8 * q^63 + 8 * q^64 - 4 * q^65 - 30 * q^66 - 8 * q^67 - 9 * q^68 + 10 * q^69 - 6 * q^70 + 8 * q^71 - 24 * q^73 - 3 * q^74 + 7 * q^76 - 4 * q^77 + 25 * q^78 + 3 * q^80 + 22 * q^81 + 17 * q^82 + 15 * q^84 - 2 * q^85 + 2 * q^86 + 20 * q^87 + 10 * q^88 + 18 * q^89 + 4 * q^90 - 20 * q^91 - 2 * q^92 - 24 * q^94 - 4 * q^95 - 10 * q^96 - 2 * q^97 + 18 * q^98 + 16 * q^99

Introduction

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