LMFDB - Embedded newform 65.2.e.b.61.1

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:	$\Q(\sqrt{-3}, \sqrt{13})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} + 4x^{2} + 3x + 9 $ x^4 - x^3 + 4x^2 + 3x + 9
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			61.1
Root			$-0.651388 + 1.12824i$ of defining polynomial
Character	$\chi$	$=$	65.61
Dual form			65.2.e.b.16.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.651388 + 1.12824i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(0.151388 + 0.262211i) q^{4} -1.00000 q^{5} +(-0.651388 - 1.12824i) q^{6} +(0.500000 + 0.866025i) q^{7} -3.00000 q^{8} +(1.00000 + 1.73205i) q^{9} +O(q^{10})$	\(q+(-0.651388 + 1.12824i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(0.151388 + 0.262211i) q^{4} -1.00000 q^{5} +(-0.651388 - 1.12824i) q^{6} +(0.500000 + 0.866025i) q^{7} -3.00000 q^{8} +(1.00000 + 1.73205i) q^{9} +(0.651388 - 1.12824i) q^{10} +(2.80278 - 4.85455i) q^{11} -0.302776 q^{12} +3.60555 q^{13} -1.30278 q^{14} +(0.500000 - 0.866025i) q^{15} +(1.65139 - 2.86029i) q^{16} +(-0.197224 - 0.341603i) q^{17} -2.60555 q^{18} +(-0.802776 - 1.39045i) q^{19} +(-0.151388 - 0.262211i) q^{20} -1.00000 q^{21} +(3.65139 + 6.32439i) q^{22} +(1.50000 - 2.59808i) q^{23} +(1.50000 - 2.59808i) q^{24} +1.00000 q^{25} +(-2.34861 + 4.06792i) q^{26} -5.00000 q^{27} +(-0.151388 + 0.262211i) q^{28} +(-4.10555 + 7.11102i) q^{29} +(0.651388 + 1.12824i) q^{30} -4.00000 q^{31} +(-0.848612 - 1.46984i) q^{32} +(2.80278 + 4.85455i) q^{33} +0.513878 q^{34} +(-0.500000 - 0.866025i) q^{35} +(-0.302776 + 0.524423i) q^{36} +(1.80278 - 3.12250i) q^{37} +2.09167 q^{38} +(-1.80278 + 3.12250i) q^{39} +3.00000 q^{40} +(-1.50000 + 2.59808i) q^{41} +(0.651388 - 1.12824i) q^{42} +(-2.10555 - 3.64692i) q^{43} +1.69722 q^{44} +(-1.00000 - 1.73205i) q^{45} +(1.95416 + 3.38471i) q^{46} -5.21110 q^{47} +(1.65139 + 2.86029i) q^{48} +(3.00000 - 5.19615i) q^{49} +(-0.651388 + 1.12824i) q^{50} +0.394449 q^{51} +(0.545837 + 0.945417i) q^{52} +11.2111 q^{53} +(3.25694 - 5.64118i) q^{54} +(-2.80278 + 4.85455i) q^{55} +(-1.50000 - 2.59808i) q^{56} +1.60555 q^{57} +(-5.34861 - 9.26407i) q^{58} +(-5.40833 - 9.36750i) q^{59} +0.302776 q^{60} +(0.500000 + 0.866025i) q^{61} +(2.60555 - 4.51295i) q^{62} +(-1.00000 + 1.73205i) q^{63} +8.81665 q^{64} -3.60555 q^{65} -7.30278 q^{66} +(3.50000 - 6.06218i) q^{67} +(0.0597147 - 0.103429i) q^{68} +(1.50000 + 2.59808i) q^{69} +1.30278 q^{70} +(8.40833 + 14.5636i) q^{71} +(-3.00000 - 5.19615i) q^{72} -15.2111 q^{73} +(2.34861 + 4.06792i) q^{74} +(-0.500000 + 0.866025i) q^{75} +(0.243061 - 0.420994i) q^{76} +5.60555 q^{77} +(-2.34861 - 4.06792i) q^{78} -9.21110 q^{79} +(-1.65139 + 2.86029i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(-1.95416 - 3.38471i) q^{82} +5.21110 q^{83} +(-0.151388 - 0.262211i) q^{84} +(0.197224 + 0.341603i) q^{85} +5.48612 q^{86} +(-4.10555 - 7.11102i) q^{87} +(-8.40833 + 14.5636i) q^{88} +(-4.10555 + 7.11102i) q^{89} +2.60555 q^{90} +(1.80278 + 3.12250i) q^{91} +0.908327 q^{92} +(2.00000 - 3.46410i) q^{93} +(3.39445 - 5.87936i) q^{94} +(0.802776 + 1.39045i) q^{95} +1.69722 q^{96} +(7.80278 + 13.5148i) q^{97} +(3.90833 + 6.76942i) q^{98} +11.2111 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + q^{2} - 2 q^{3} - 3 q^{4} - 4 q^{5} + q^{6} + 2 q^{7} - 12 q^{8} + 4 q^{9}+O(q^{10}) $ 4 * q + q^2 - 2 * q^3 - 3 * q^4 - 4 * q^5 + q^6 + 2 * q^7 - 12 * q^8 + 4 * q^9	\( 4 q + q^{2} - 2 q^{3} - 3 q^{4} - 4 q^{5} + q^{6} + 2 q^{7} - 12 q^{8} + 4 q^{9} - q^{10} + 4 q^{11} + 6 q^{12} + 2 q^{14} + 2 q^{15} + 3 q^{16} - 8 q^{17} + 4 q^{18} + 4 q^{19} + 3 q^{20} - 4 q^{21} + 11 q^{22} + 6 q^{23} + 6 q^{24} + 4 q^{25} - 13 q^{26} - 20 q^{27} + 3 q^{28} - 2 q^{29} - q^{30} - 16 q^{31} - 7 q^{32} + 4 q^{33} - 34 q^{34} - 2 q^{35} + 6 q^{36} + 30 q^{38} + 12 q^{40} - 6 q^{41} - q^{42} + 6 q^{43} + 14 q^{44} - 4 q^{45} - 3 q^{46} + 8 q^{47} + 3 q^{48} + 12 q^{49} + q^{50} + 16 q^{51} + 13 q^{52} + 16 q^{53} - 5 q^{54} - 4 q^{55} - 6 q^{56} - 8 q^{57} - 25 q^{58} - 6 q^{60} + 2 q^{61} - 4 q^{62} - 4 q^{63} - 8 q^{64} - 22 q^{66} + 14 q^{67} - 25 q^{68} + 6 q^{69} - 2 q^{70} + 12 q^{71} - 12 q^{72} - 32 q^{73} + 13 q^{74} - 2 q^{75} + 19 q^{76} + 8 q^{77} - 13 q^{78} - 8 q^{79} - 3 q^{80} - 2 q^{81} + 3 q^{82} - 8 q^{83} + 3 q^{84} + 8 q^{85} + 58 q^{86} - 2 q^{87} - 12 q^{88} - 2 q^{89} - 4 q^{90} - 18 q^{92} + 8 q^{93} + 28 q^{94} - 4 q^{95} + 14 q^{96} + 24 q^{97} - 6 q^{98} + 16 q^{99}+O(q^{100}) \) 4 * q + q^2 - 2 * q^3 - 3 * q^4 - 4 * q^5 + q^6 + 2 * q^7 - 12 * q^8 + 4 * q^9 - q^10 + 4 * q^11 + 6 * q^12 + 2 * q^14 + 2 * q^15 + 3 * q^16 - 8 * q^17 + 4 * q^18 + 4 * q^19 + 3 * q^20 - 4 * q^21 + 11 * q^22 + 6 * q^23 + 6 * q^24 + 4 * q^25 - 13 * q^26 - 20 * q^27 + 3 * q^28 - 2 * q^29 - q^30 - 16 * q^31 - 7 * q^32 + 4 * q^33 - 34 * q^34 - 2 * q^35 + 6 * q^36 + 30 * q^38 + 12 * q^40 - 6 * q^41 - q^42 + 6 * q^43 + 14 * q^44 - 4 * q^45 - 3 * q^46 + 8 * q^47 + 3 * q^48 + 12 * q^49 + q^50 + 16 * q^51 + 13 * q^52 + 16 * q^53 - 5 * q^54 - 4 * q^55 - 6 * q^56 - 8 * q^57 - 25 * q^58 - 6 * q^60 + 2 * q^61 - 4 * q^62 - 4 * q^63 - 8 * q^64 - 22 * q^66 + 14 * q^67 - 25 * q^68 + 6 * q^69 - 2 * q^70 + 12 * q^71 - 12 * q^72 - 32 * q^73 + 13 * q^74 - 2 * q^75 + 19 * q^76 + 8 * q^77 - 13 * q^78 - 8 * q^79 - 3 * q^80 - 2 * q^81 + 3 * q^82 - 8 * q^83 + 3 * q^84 + 8 * q^85 + 58 * q^86 - 2 * q^87 - 12 * q^88 - 2 * q^89 - 4 * q^90 - 18 * q^92 + 8 * q^93 + 28 * q^94 - 4 * q^95 + 14 * q^96 + 24 * q^97 - 6 * q^98 + 16 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$27$	$41$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$

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 $

$2$	−0.651388	+	1.12824i	−0.460601	+	0.797784i	−0.998991	−	0.0449118i	$-0.985699\pi$
$2$	−0.651388	+	1.12824i	−0.460601	+	0.797784i	0.538390	+	0.842696i	$0.319033\pi$
$3$	−0.500000	+	0.866025i	−0.288675	+	0.500000i	−0.973494	−	0.228714i	$-0.926548\pi$
$3$	−0.500000	+	0.866025i	−0.288675	+	0.500000i	0.684819	+	0.728714i	$0.259881\pi$
$4$	0.151388	+	0.262211i	0.0756939	+	0.131106i
$5$	−1.00000			−0.447214
$5$	−1.00000			−0.447214
$6$	−0.651388	−	1.12824i	−0.265928	−	0.460601i
$7$	0.500000	+	0.866025i	0.188982	+	0.327327i	0.944911	−	0.327327i	$-0.106148\pi$
$7$	0.500000	+	0.866025i	0.188982	+	0.327327i	−0.755929	+	0.654654i	$0.772814\pi$
$8$	−3.00000			−1.06066
$9$	1.00000	+	1.73205i	0.333333	+	0.577350i
$10$	0.651388	−	1.12824i	0.205987	−	0.356780i
$11$	2.80278	−	4.85455i	0.845069	−	1.46370i	−0.0404929	−	0.999180i	$-0.512893\pi$
$11$	2.80278	−	4.85455i	0.845069	−	1.46370i	0.885562	−	0.464522i	$-0.153774\pi$
$12$	−0.302776			−0.0874038
$13$	3.60555			1.00000
$13$	3.60555			1.00000
$14$	−1.30278			−0.348181
$15$	0.500000	−	0.866025i	0.129099	−	0.223607i
$16$	1.65139	−	2.86029i	0.412847	−	0.715072i
$17$	−0.197224	−	0.341603i	−0.0478339	−	0.0828508i	0.841117	−	0.540853i	$-0.181898\pi$
$17$	−0.197224	−	0.341603i	−0.0478339	−	0.0828508i	−0.888951	+	0.458002i	$0.848565\pi$
$18$	−2.60555			−0.614134
$19$	−0.802776	−	1.39045i	−0.184169	−	0.318991i	0.759127	−	0.650943i	$-0.225626\pi$
$19$	−0.802776	−	1.39045i	−0.184169	−	0.318991i	−0.943296	+	0.331952i	$0.892293\pi$
$20$	−0.151388	−	0.262211i	−0.0338513	−	0.0586323i
$21$	−1.00000			−0.218218
$22$	3.65139	+	6.32439i	0.778478	+	1.34836i
$23$	1.50000	−	2.59808i	0.312772	−	0.541736i	−0.666190	−	0.745782i	$-0.732076\pi$
$23$	1.50000	−	2.59808i	0.312772	−	0.541736i	0.978961	+	0.204046i	$0.0654092\pi$
$24$	1.50000	−	2.59808i	0.306186	−	0.530330i
$25$	1.00000			0.200000
$26$	−2.34861	+	4.06792i	−0.460601	+	0.797784i
$27$	−5.00000			−0.962250
$28$	−0.151388	+	0.262211i	−0.0286096	+	0.0495533i
$29$	−4.10555	+	7.11102i	−0.762382	+	1.32048i	0.179238	+	0.983806i	$0.442637\pi$
$29$	−4.10555	+	7.11102i	−0.762382	+	1.32048i	−0.941620	+	0.336678i	$0.890697\pi$
$30$	0.651388	+	1.12824i	0.118927	+	0.205987i
$31$	−4.00000			−0.718421			−0.359211	−	0.933257i	$-0.616954\pi$
$31$	−4.00000			−0.718421			−0.359211	+	0.933257i	$0.616954\pi$
$32$	−0.848612	−	1.46984i	−0.150015	−	0.259833i
$33$	2.80278	+	4.85455i	0.487901	+	0.845069i
$34$	0.513878			0.0881294
$35$	−0.500000	−	0.866025i	−0.0845154	−	0.146385i
$36$	−0.302776	+	0.524423i	−0.0504626	+	0.0874038i
$37$	1.80278	−	3.12250i	0.296374	−	0.513336i	−0.678929	−	0.734204i	$-0.737556\pi$
$37$	1.80278	−	3.12250i	0.296374	−	0.513336i	0.975304	+	0.220868i	$0.0708890\pi$
$38$	2.09167			0.339314
$39$	−1.80278	+	3.12250i	−0.288675	+	0.500000i
$40$	3.00000			0.474342
$41$	−1.50000	+	2.59808i	−0.234261	+	0.405751i	−0.959058	−	0.283211i	$-0.908600\pi$
$41$	−1.50000	+	2.59808i	−0.234261	+	0.405751i	0.724797	+	0.688963i	$0.241934\pi$
$42$	0.651388	−	1.12824i	0.100511	−	0.174091i
$43$	−2.10555	−	3.64692i	−0.321094	−	0.556150i	0.659620	−	0.751599i	$-0.270717\pi$
$43$	−2.10555	−	3.64692i	−0.321094	−	0.556150i	−0.980714	+	0.195449i	$0.937384\pi$
$44$	1.69722			0.255866
$45$	−1.00000	−	1.73205i	−0.149071	−	0.258199i
$46$	1.95416	+	3.38471i	0.288126	+	0.499048i
$47$	−5.21110			−0.760117			−0.380059	−	0.924962i	$-0.624096\pi$
$47$	−5.21110			−0.760117			−0.380059	+	0.924962i	$0.624096\pi$
$48$	1.65139	+	2.86029i	0.238357	+	0.412847i
$49$	3.00000	−	5.19615i	0.428571	−	0.742307i
$50$	−0.651388	+	1.12824i	−0.0921201	+	0.159557i
$51$	0.394449			0.0552339
$52$	0.545837	+	0.945417i	0.0756939	+	0.131106i
$53$	11.2111			1.53996			0.769982	−	0.638066i	$-0.220265\pi$
$53$	11.2111			1.53996			0.769982	+	0.638066i	$0.220265\pi$
$54$	3.25694	−	5.64118i	0.443213	−	0.767668i
$55$	−2.80278	+	4.85455i	−0.377926	+	0.654587i
$56$	−1.50000	−	2.59808i	−0.200446	−	0.347183i
$57$	1.60555			0.212660
$58$	−5.34861	−	9.26407i	−0.702307	−	1.21643i
$59$	−5.40833	−	9.36750i	−0.704104	−	1.21954i	−0.967014	−	0.254724i	$-0.918015\pi$
$59$	−5.40833	−	9.36750i	−0.704104	−	1.21954i	0.262910	−	0.964820i	$-0.415318\pi$
$60$	0.302776			0.0390882
$61$	0.500000	+	0.866025i	0.0640184	+	0.110883i	0.896258	−	0.443533i	$-0.146275\pi$
$61$	0.500000	+	0.866025i	0.0640184	+	0.110883i	−0.832240	+	0.554416i	$0.812942\pi$
$62$	2.60555	−	4.51295i	0.330905	−	0.573145i
$63$	−1.00000	+	1.73205i	−0.125988	+	0.218218i
$64$	8.81665			1.10208
$65$	−3.60555			−0.447214
$66$	−7.30278			−0.898910
$67$	3.50000	−	6.06218i	0.427593	−	0.740613i	−0.569066	−	0.822292i	$-0.692695\pi$
$67$	3.50000	−	6.06218i	0.427593	−	0.740613i	0.996659	+	0.0816792i	$0.0260283\pi$
$68$	0.0597147	−	0.103429i	0.00724147	−	0.0125426i
$69$	1.50000	+	2.59808i	0.180579	+	0.312772i
$70$	1.30278			0.155711
$71$	8.40833	+	14.5636i	0.997885	+	1.72839i	0.555240	+	0.831690i	$0.312626\pi$
$71$	8.40833	+	14.5636i	0.997885	+	1.72839i	0.442645	+	0.896697i	$0.354040\pi$
$72$	−3.00000	−	5.19615i	−0.353553	−	0.612372i
$73$	−15.2111			−1.78032			−0.890162	−	0.455643i	$-0.849409\pi$
$73$	−15.2111			−1.78032			−0.890162	+	0.455643i	$0.849409\pi$
$74$	2.34861	+	4.06792i	0.273021	+	0.472886i
$75$	−0.500000	+	0.866025i	−0.0577350	+	0.100000i
$76$	0.243061	−	0.420994i	0.0278810	−	0.0482913i
$77$	5.60555			0.638812
$78$	−2.34861	−	4.06792i	−0.265928	−	0.460601i
$79$	−9.21110			−1.03633			−0.518165	−	0.855281i	$-0.673385\pi$
$79$	−9.21110			−1.03633			−0.518165	+	0.855281i	$0.673385\pi$
$80$	−1.65139	+	2.86029i	−0.184631	+	0.319790i
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$	−1.95416	−	3.38471i	−0.215801	−	0.373779i
$83$	5.21110			0.571993			0.285996	−	0.958231i	$-0.407675\pi$
$83$	5.21110			0.571993			0.285996	+	0.958231i	$0.407675\pi$
$84$	−0.151388	−	0.262211i	−0.0165178	−	0.0286096i
$85$	0.197224	+	0.341603i	0.0213920	+	0.0370520i
$86$	5.48612			0.591584
$87$	−4.10555	−	7.11102i	−0.440161	−	0.762382i
$88$	−8.40833	+	14.5636i	−0.896331	+	1.55249i
$89$	−4.10555	+	7.11102i	−0.435188	+	0.753767i	−0.997311	−	0.0732864i	$-0.976651\pi$
$89$	−4.10555	+	7.11102i	−0.435188	+	0.753767i	0.562123	+	0.827053i	$0.309985\pi$
$90$	2.60555			0.274649
$91$	1.80278	+	3.12250i	0.188982	+	0.327327i
$92$	0.908327			0.0946996
$93$	2.00000	−	3.46410i	0.207390	−	0.359211i
$94$	3.39445	−	5.87936i	0.350111	−	0.606409i
$95$	0.802776	+	1.39045i	0.0823630	+	0.142657i
$96$	1.69722			0.173222
$97$	7.80278	+	13.5148i	0.792252	+	1.37222i	0.924570	+	0.381013i	$0.124425\pi$
$97$	7.80278	+	13.5148i	0.792252	+	1.37222i	−0.132318	+	0.991207i	$0.542242\pi$
$98$	3.90833	+	6.76942i	0.394801	+	0.683815i
$99$	11.2111			1.12676
$100$	0.151388	+	0.262211i	0.0151388	+	0.0262211i
$101$	4.50000	−	7.79423i	0.447767	−	0.775555i	−0.550474	−	0.834853i	$-0.685553\pi$
$101$	4.50000	−	7.79423i	0.447767	−	0.775555i	0.998240	+	0.0592978i	$0.0188862\pi$
$102$	−0.256939	+	0.445032i	−0.0254408	+	0.0440647i
$103$	−4.00000			−0.394132			−0.197066	−	0.980390i	$-0.563141\pi$
$103$	−4.00000			−0.394132			−0.197066	+	0.980390i	$0.563141\pi$
$104$	−10.8167			−1.06066
$105$	1.00000			0.0975900
$106$	−7.30278	+	12.6488i	−0.709308	+	1.22856i
$107$	4.10555	−	7.11102i	0.396899	−	0.687449i	−0.596443	−	0.802656i	$-0.703420\pi$
$107$	4.10555	−	7.11102i	0.396899	−	0.687449i	0.993342	+	0.115207i	$0.0367531\pi$
$108$	−0.756939	−	1.31106i	−0.0728365	−	0.126157i
$109$	−4.78890			−0.458693			−0.229347	−	0.973345i	$-0.573659\pi$
$109$	−4.78890			−0.458693			−0.229347	+	0.973345i	$0.573659\pi$
$110$	−3.65139	−	6.32439i	−0.348146	−	0.603007i
$111$	1.80278	+	3.12250i	0.171112	+	0.296374i
$112$	3.30278			0.312083
$113$	−2.80278	−	4.85455i	−0.263663	−	0.456678i	0.703550	−	0.710646i	$-0.251597\pi$
$113$	−2.80278	−	4.85455i	−0.263663	−	0.456678i	−0.967212	+	0.253969i	$0.918264\pi$
$114$	−1.04584	+	1.81144i	−0.0979516	+	0.169657i
$115$	−1.50000	+	2.59808i	−0.139876	+	0.242272i
$116$	−2.48612			−0.230831
$117$	3.60555	+	6.24500i	0.333333	+	0.577350i
$118$	14.0917			1.29724
$119$	0.197224	−	0.341603i	0.0180795	−	0.0313147i
$120$	−1.50000	+	2.59808i	−0.136931	+	0.237171i
$121$	−10.2111	−	17.6861i	−0.928282	−	1.60783i
$122$	−1.30278			−0.117948
$123$	−1.50000	−	2.59808i	−0.135250	−	0.234261i
$124$	−0.605551	−	1.04885i	−0.0543801	−	0.0941891i
$125$	−1.00000			−0.0894427
$126$	−1.30278	−	2.25647i	−0.116060	−	0.201023i
$127$	−5.10555	+	8.84307i	−0.453044	+	0.784696i	−0.998573	−	0.0533960i	$-0.982995\pi$
$127$	−5.10555	+	8.84307i	−0.453044	+	0.784696i	0.545529	+	0.838092i	$0.316329\pi$
$128$	−4.04584	+	7.00759i	−0.357605	+	0.619390i
$129$	4.21110			0.370767
$130$	2.34861	−	4.06792i	0.205987	−	0.356780i
$131$	−6.78890			−0.593149			−0.296574	−	0.955010i	$-0.595844\pi$
$131$	−6.78890			−0.593149			−0.296574	+	0.955010i	$0.595844\pi$
$132$	−0.848612	+	1.46984i	−0.0738622	+	0.127933i
$133$	0.802776	−	1.39045i	0.0696095	−	0.120567i
$134$	4.55971	+	7.89766i	0.393899	+	0.682254i
$135$	5.00000			0.430331
$136$	0.591673	+	1.02481i	0.0507355	+	0.0878765i
$137$	−2.80278	−	4.85455i	−0.239457	−	0.414752i	0.721101	−	0.692830i	$-0.243636\pi$
$137$	−2.80278	−	4.85455i	−0.239457	−	0.414752i	−0.960559	+	0.278077i	$0.910303\pi$
$138$	−3.90833			−0.332699
$139$	−6.80278	−	11.7828i	−0.577004	−	0.999400i	−0.995821	−	0.0913293i	$-0.970888\pi$
$139$	−6.80278	−	11.7828i	−0.577004	−	0.999400i	0.418817	−	0.908071i	$-0.362445\pi$
$140$	0.151388	−	0.262211i	0.0127946	−	0.0221609i
$141$	2.60555	−	4.51295i	0.219427	−	0.380059i
$142$	−21.9083			−1.83851
$143$	10.1056	−	17.5033i	0.845069	−	1.46370i
$144$	6.60555			0.550463
$145$	4.10555	−	7.11102i	0.340947	−	0.590538i
$146$	9.90833	−	17.1617i	0.820019	−	1.42031i
$147$	3.00000	+	5.19615i	0.247436	+	0.428571i
$148$	1.09167			0.0897350
$149$	−1.50000	−	2.59808i	−0.122885	−	0.212843i	0.798019	−	0.602632i	$-0.205881\pi$
$149$	−1.50000	−	2.59808i	−0.122885	−	0.212843i	−0.920904	+	0.389789i	$0.872548\pi$
$150$	−0.651388	−	1.12824i	−0.0531856	−	0.0921201i
$151$	13.2111			1.07510			0.537552	−	0.843231i	$-0.319349\pi$
$151$	13.2111			1.07510			0.537552	+	0.843231i	$0.319349\pi$
$152$	2.40833	+	4.17134i	0.195341	+	0.338341i
$153$	0.394449	−	0.683205i	0.0318893	−	0.0552339i
$154$	−3.65139	+	6.32439i	−0.294237	+	0.509634i
$155$	4.00000			0.321288
$156$	−1.09167			−0.0874038
$157$	−3.21110			−0.256274			−0.128137	−	0.991756i	$-0.540900\pi$
$157$	−3.21110			−0.256274			−0.128137	+	0.991756i	$0.540900\pi$
$158$	6.00000	−	10.3923i	0.477334	−	0.826767i
$159$	−5.60555	+	9.70910i	−0.444549	+	0.769982i
$160$	0.848612	+	1.46984i	0.0670887	+	0.116201i
$161$	3.00000			0.236433
$162$	−0.651388	−	1.12824i	−0.0511779	−	0.0886427i
$163$	9.10555	+	15.7713i	0.713202	+	1.23530i	0.963649	+	0.267172i	$0.0860890\pi$
$163$	9.10555	+	15.7713i	0.713202	+	1.23530i	−0.250447	+	0.968130i	$0.580578\pi$
$164$	−0.908327			−0.0709284
$165$	−2.80278	−	4.85455i	−0.218196	−	0.377926i
$166$	−3.39445	+	5.87936i	−0.263460	+	0.456327i
$167$	−4.50000	+	7.79423i	−0.348220	+	0.603136i	−0.985933	−	0.167139i	$-0.946547\pi$
$167$	−4.50000	+	7.79423i	−0.348220	+	0.603136i	0.637713	+	0.770274i	$0.279881\pi$
$168$	3.00000			0.231455
$169$	13.0000			1.00000
$170$	−0.513878			−0.0394127
$171$	1.60555	−	2.78090i	0.122780	−	0.212660i
$172$	0.637510	−	1.10420i	0.0486097	−	0.0841944i
$173$	8.40833	+	14.5636i	0.639273	+	1.10725i	0.985593	+	0.169137i	$0.0540981\pi$
$173$	8.40833	+	14.5636i	0.639273	+	1.10725i	−0.346319	+	0.938117i	$0.612569\pi$
$174$	10.6972			0.810954
$175$	0.500000	+	0.866025i	0.0377964	+	0.0654654i
$176$	−9.25694	−	16.0335i	−0.697768	−	1.20857i
$177$	10.8167			0.813029
$178$	−5.34861	−	9.26407i	−0.400895	−	0.694371i
$179$	−0.591673	+	1.02481i	−0.0442237	+	0.0765977i	−0.887290	−	0.461212i	$-0.847415\pi$
$179$	−0.591673	+	1.02481i	−0.0442237	+	0.0765977i	0.843066	+	0.537810i	$0.180748\pi$
$180$	0.302776	−	0.524423i	0.0225676	−	0.0390882i
$181$	−25.6333			−1.90531			−0.952654	−	0.304055i	$-0.901659\pi$
$181$	−25.6333			−1.90531			−0.952654	+	0.304055i	$0.901659\pi$
$182$	−4.69722			−0.348181
$183$	−1.00000			−0.0739221
$184$	−4.50000	+	7.79423i	−0.331744	+	0.574598i
$185$	−1.80278	+	3.12250i	−0.132543	+	0.229571i
$186$	2.60555	+	4.51295i	0.191048	+	0.330905i
$187$	−2.21110			−0.161692
$188$	−0.788897	−	1.36641i	−0.0575363	−	0.0996557i
$189$	−2.50000	−	4.33013i	−0.181848	−	0.314970i
$190$	−2.09167			−0.151746
$191$	2.40833	+	4.17134i	0.174260	+	0.301828i	0.939905	−	0.341436i	$-0.110913\pi$
$191$	2.40833	+	4.17134i	0.174260	+	0.301828i	−0.765645	+	0.643264i	$0.777580\pi$
$192$	−4.40833	+	7.63545i	−0.318144	+	0.551041i
$193$	−4.19722	+	7.26981i	−0.302123	+	0.523292i	−0.976617	−	0.214988i	$-0.931029\pi$
$193$	−4.19722	+	7.26981i	−0.302123	+	0.523292i	0.674494	+	0.738281i	$0.264362\pi$
$194$	−20.3305			−1.45965
$195$	1.80278	−	3.12250i	0.129099	−	0.223607i
$196$	1.81665			0.129761
$197$	−11.4083	+	19.7598i	−0.812810	+	1.40783i	0.0980804	+	0.995178i	$0.468730\pi$
$197$	−11.4083	+	19.7598i	−0.812810	+	1.40783i	−0.910890	+	0.412649i	$0.864604\pi$
$198$	−7.30278	+	12.6488i	−0.518986	+	0.898910i
$199$	4.40833	+	7.63545i	0.312498	+	0.541262i	0.978902	−	0.204328i	$-0.0655009\pi$
$199$	4.40833	+	7.63545i	0.312498	+	0.541262i	−0.666404	+	0.745590i	$0.732168\pi$
$200$	−3.00000			−0.212132
$201$	3.50000	+	6.06218i	0.246871	+	0.427593i
$202$	5.86249	+	10.1541i	0.412483	+	0.714442i
$203$	−8.21110			−0.576306
$204$	0.0597147	+	0.103429i	0.00418087	+	0.00724147i
$205$	1.50000	−	2.59808i	0.104765	−	0.181458i
$206$	2.60555	−	4.51295i	0.181537	−	0.314432i
$207$	6.00000			0.417029
$208$	5.95416	−	10.3129i	0.412847	−	0.715072i
$209$	−9.00000			−0.622543
$210$	−0.651388	+	1.12824i	−0.0449500	+	0.0778557i
$211$	8.19722	−	14.1980i	0.564320	−	0.977431i	−0.432792	−	0.901494i	$-0.642472\pi$
$211$	8.19722	−	14.1980i	0.564320	−	0.977431i	0.997113	−	0.0759376i	$-0.0241950\pi$
$212$	1.69722	+	2.93968i	0.116566	+	0.201898i
$213$	−16.8167			−1.15226
$214$	5.34861	+	9.26407i	0.365624	+	0.633279i
$215$	2.10555	+	3.64692i	0.143597	+	0.248718i
$216$	15.0000			1.02062
$217$	−2.00000	−	3.46410i	−0.135769	−	0.235159i
$218$	3.11943	−	5.40301i	0.211274	−	0.365938i
$219$	7.60555	−	13.1732i	0.513936	−	0.890162i
$220$	−1.69722			−0.114427
$221$	−0.711103	−	1.23167i	−0.0478339	−	0.0828508i
$222$	−4.69722			−0.315257
$223$	−5.10555	+	8.84307i	−0.341893	+	0.592176i	−0.984784	−	0.173781i	$-0.944401\pi$
$223$	−5.10555	+	8.84307i	−0.341893	+	0.592176i	0.642891	+	0.765957i	$0.277735\pi$
$224$	0.848612	−	1.46984i	0.0567003	−	0.0982078i
$225$	1.00000	+	1.73205i	0.0666667	+	0.115470i
$226$	7.30278			0.485773
$227$	−0.711103	−	1.23167i	−0.0471975	−	0.0817485i	0.841462	−	0.540317i	$-0.181696\pi$
$227$	−0.711103	−	1.23167i	−0.0471975	−	0.0817485i	−0.888659	+	0.458569i	$0.848362\pi$
$228$	0.243061	+	0.420994i	0.0160971	+	0.0278810i
$229$	14.0000			0.925146			0.462573	−	0.886581i	$-0.346926\pi$
$229$	14.0000			0.925146			0.462573	+	0.886581i	$0.346926\pi$
$230$	−1.95416	−	3.38471i	−0.128854	−	0.223181i
$231$	−2.80278	+	4.85455i	−0.184409	+	0.319406i
$232$	12.3167	−	21.3331i	0.808628	−	1.40058i
$233$	0.788897			0.0516824			0.0258412	−	0.999666i	$-0.491774\pi$
$233$	0.788897			0.0516824			0.0258412	+	0.999666i	$0.491774\pi$
$234$	−9.39445			−0.614134
$235$	5.21110			0.339935
$236$	1.63751	−	2.83625i	0.106593	−	0.184624i
$237$	4.60555	−	7.97705i	0.299163	−	0.518165i
$238$	0.256939	+	0.445032i	0.0166549	+	0.0288471i
$239$		0			0			−	1.00000i	$-0.5\pi$
$239$		0			0				1.00000i	$0.5\pi$
$240$	−1.65139	−	2.86029i	−0.106597	−	0.184631i
$241$	−8.10555	−	14.0392i	−0.522124	−	0.904346i	−0.999669	−	0.0257384i	$-0.991806\pi$
$241$	−8.10555	−	14.0392i	−0.522124	−	0.904346i	0.477544	−	0.878608i	$-0.341527\pi$
$242$	26.6056			1.71027
$243$	−8.00000	−	13.8564i	−0.513200	−	0.888889i
$244$	−0.151388	+	0.262211i	−0.00969161	+	0.0167864i
$245$	−3.00000	+	5.19615i	−0.191663	+	0.331970i
$246$	3.90833			0.249186
$247$	−2.89445	−	5.01333i	−0.184169	−	0.318991i
$248$	12.0000			0.762001
$249$	−2.60555	+	4.51295i	−0.165120	+	0.285996i
$250$	0.651388	−	1.12824i	0.0411974	−	0.0713560i
$251$	14.4083	+	24.9560i	0.909446	+	1.57521i	0.814836	+	0.579691i	$0.196827\pi$
$251$	14.4083	+	24.9560i	0.909446	+	1.57521i	0.0946094	+	0.995514i	$0.469840\pi$
$252$	−0.605551			−0.0381461
$253$	−8.40833	−	14.5636i	−0.528627	−	0.915609i
$254$	−6.65139	−	11.5205i	−0.417345	−	0.722863i
$255$	−0.394449			−0.0247013
$256$	3.54584	+	6.14157i	0.221615	+	0.383848i
$257$	11.8028	−	20.4430i	0.736237	−	1.27520i	−0.217942	−	0.975962i	$-0.569934\pi$
$257$	11.8028	−	20.4430i	0.736237	−	1.27520i	0.954179	−	0.299238i	$-0.0967324\pi$
$258$	−2.74306	+	4.75112i	−0.170776	+	0.295792i
$259$	3.60555			0.224038
$260$	−0.545837	−	0.945417i	−0.0338513	−	0.0586323i
$261$	−16.4222			−1.01651
$262$	4.42221	−	7.65948i	0.273205	−	0.473204i
$263$	−13.1056	+	22.6995i	−0.808123	+	1.39971i	0.106040	+	0.994362i	$0.466183\pi$
$263$	−13.1056	+	22.6995i	−0.808123	+	1.39971i	−0.914162	+	0.405348i	$0.867150\pi$
$264$	−8.40833	−	14.5636i	−0.517497	−	0.896331i
$265$	−11.2111			−0.688693
$266$	1.04584	+	1.81144i	0.0641244	+	0.111067i
$267$	−4.10555	−	7.11102i	−0.251256	−	0.435188i
$268$	2.11943			0.129465
$269$	4.50000	+	7.79423i	0.274370	+	0.475223i	0.969976	−	0.243201i	$-0.0781974\pi$
$269$	4.50000	+	7.79423i	0.274370	+	0.475223i	−0.695606	+	0.718423i	$0.744864\pi$
$270$	−3.25694	+	5.64118i	−0.198211	+	0.343312i
$271$	−0.408327	+	0.707243i	−0.0248041	+	0.0429620i	−0.878161	−	0.478365i	$-0.841230\pi$
$271$	−0.408327	+	0.707243i	−0.0248041	+	0.0429620i	0.853357	+	0.521327i	$0.174563\pi$
$272$	−1.30278			−0.0789924
$273$	−3.60555			−0.218218
$274$	7.30278			0.441177
$275$	2.80278	−	4.85455i	0.169014	−	0.292740i
$276$	−0.454163	+	0.786634i	−0.0273374	+	0.0473498i
$277$	−10.1972	−	17.6621i	−0.612692	−	1.06121i	−0.990785	−	0.135446i	$-0.956753\pi$
$277$	−10.1972	−	17.6621i	−0.612692	−	1.06121i	0.378093	−	0.925768i	$-0.376580\pi$
$278$	17.7250			1.06307
$279$	−4.00000	−	6.92820i	−0.239474	−	0.414781i
$280$	1.50000	+	2.59808i	0.0896421	+	0.155265i
$281$	−6.00000			−0.357930			−0.178965	−	0.983855i	$-0.557275\pi$
$281$	−6.00000			−0.357930			−0.178965	+	0.983855i	$0.557275\pi$
$282$	3.39445	+	5.87936i	0.202136	+	0.350111i
$283$	−2.50000	+	4.33013i	−0.148610	+	0.257399i	−0.930714	−	0.365748i	$-0.880813\pi$
$283$	−2.50000	+	4.33013i	−0.148610	+	0.257399i	0.782104	+	0.623148i	$0.214146\pi$
$284$	−2.54584	+	4.40952i	−0.151068	+	0.261657i
$285$	−1.60555			−0.0951046
$286$	13.1653	+	22.8029i	0.778478	+	1.34836i
$287$	−3.00000			−0.177084
$288$	1.69722	−	2.93968i	0.100010	−	0.173222i
$289$	8.42221	−	14.5877i	0.495424	−	0.858099i
$290$	5.34861	+	9.26407i	0.314081	+	0.544005i
$291$	−15.6056			−0.914814
$292$	−2.30278	−	3.98852i	−0.134760	−	0.233411i
$293$	−8.80278	−	15.2469i	−0.514264	−	0.890731i	−0.999863	−	0.0165493i	$-0.994732\pi$
$293$	−8.80278	−	15.2469i	−0.514264	−	0.890731i	0.485599	−	0.874181i	$-0.338601\pi$
$294$	−7.81665			−0.455877
$295$	5.40833	+	9.36750i	0.314885	+	0.545397i
$296$	−5.40833	+	9.36750i	−0.314353	+	0.544475i
$297$	−14.0139	+	24.2727i	−0.813168	+	1.40845i
$298$	3.90833			0.226403
$299$	5.40833	−	9.36750i	0.312772	−	0.541736i
$300$	−0.302776			−0.0174808
$301$	2.10555	−	3.64692i	0.121362	−	0.210205i
$302$	−8.60555	+	14.9053i	−0.495194	+	0.857701i
$303$	4.50000	+	7.79423i	0.258518	+	0.447767i
$304$	−5.30278			−0.304135
$305$	−0.500000	−	0.866025i	−0.0286299	−	0.0495885i
$306$	0.513878	+	0.890063i	0.0293765	+	0.0508815i
$307$	−16.0000			−0.913168			−0.456584	−	0.889680i	$-0.650927\pi$
$307$	−16.0000			−0.913168			−0.456584	+	0.889680i	$0.650927\pi$
$308$	0.848612	+	1.46984i	0.0483542	+	0.0837519i
$309$	2.00000	−	3.46410i	0.113776	−	0.197066i
$310$	−2.60555	+	4.51295i	−0.147985	+	0.256318i
$311$	5.21110			0.295495			0.147747	−	0.989025i	$-0.452798\pi$
$311$	5.21110			0.295495			0.147747	+	0.989025i	$0.452798\pi$
$312$	5.40833	−	9.36750i	0.306186	−	0.530330i
$313$	14.0000			0.791327			0.395663	−	0.918396i	$-0.370515\pi$
$313$	14.0000			0.791327			0.395663	+	0.918396i	$0.370515\pi$
$314$	2.09167	−	3.62288i	0.118040	−	0.204451i
$315$	1.00000	−	1.73205i	0.0563436	−	0.0975900i
$316$	−1.39445	−	2.41526i	−0.0784439	−	0.135869i
$317$	6.00000			0.336994			0.168497	−	0.985702i	$-0.446109\pi$
$317$	6.00000			0.336994			0.168497	+	0.985702i	$0.446109\pi$
$318$	−7.30278	−	12.6488i	−0.409519	−	0.709308i
$319$	23.0139	+	39.8612i	1.28853	+	2.23180i
$320$	−8.81665			−0.492866
$321$	4.10555	+	7.11102i	0.229150	+	0.396899i
$322$	−1.95416	+	3.38471i	−0.108901	+	0.188623i
$323$	−0.316654	+	0.548461i	−0.0176191	+	0.0305172i
$324$	−0.302776			−0.0168209
$325$	3.60555			0.200000
$326$	−23.7250			−1.31401
$327$	2.39445	−	4.14731i	0.132413	−	0.229347i
$328$	4.50000	−	7.79423i	0.248471	−	0.430364i
$329$	−2.60555	−	4.51295i	−0.143649	−	0.248807i
$330$	7.30278			0.402005
$331$	13.0139	+	22.5407i	0.715307	+	1.23895i	0.962841	+	0.270069i	$0.0870467\pi$
$331$	13.0139	+	22.5407i	0.715307	+	1.23895i	−0.247533	+	0.968879i	$0.579620\pi$
$332$	0.788897	+	1.36641i	0.0432964	+	0.0749915i
$333$	7.21110			0.395166
$334$	−5.86249	−	10.1541i	−0.320781	−	0.555609i
$335$	−3.50000	+	6.06218i	−0.191225	+	0.331212i
$336$	−1.65139	+	2.86029i	−0.0900906	+	0.156041i
$337$	17.6333			0.960547			0.480274	−	0.877119i	$-0.340537\pi$
$337$	17.6333			0.960547			0.480274	+	0.877119i	$0.340537\pi$
$338$	−8.46804	+	14.6671i	−0.460601	+	0.797784i
$339$	5.60555			0.304452
$340$	−0.0597147	+	0.103429i	−0.00323849	+	0.00560922i
$341$	−11.2111	+	19.4182i	−0.607115	+	1.05155i
$342$	2.09167	+	3.62288i	0.113105	+	0.195903i
$343$	13.0000			0.701934
$344$	6.31665	+	10.9408i	0.340571	+	0.589887i
$345$	−1.50000	−	2.59808i	−0.0807573	−	0.139876i
$346$	−21.9083			−1.17780
$347$	−10.1056	−	17.5033i	−0.542494	−	0.939628i	−0.998760	−	0.0497842i	$-0.984147\pi$
$347$	−10.1056	−	17.5033i	−0.542494	−	0.939628i	0.456266	−	0.889844i	$-0.349187\pi$
$348$	1.24306	−	2.15304i	0.0666351	−	0.115415i
$349$	9.10555	−	15.7713i	0.487409	−	0.844217i	−0.512486	−	0.858695i	$-0.671275\pi$
$349$	9.10555	−	15.7713i	0.487409	−	0.844217i	0.999895	+	0.0144783i	$0.00460876\pi$
$350$	−1.30278			−0.0696363
$351$	−18.0278			−0.962250
$352$	−9.51388			−0.507091
$353$	2.40833	−	4.17134i	0.128182	−	0.222018i	−0.794790	−	0.606884i	$-0.792419\pi$
$353$	2.40833	−	4.17134i	0.128182	−	0.222018i	0.922972	+	0.384866i	$0.125752\pi$
$354$	−7.04584	+	12.2037i	−0.374482	+	0.648622i
$355$	−8.40833	−	14.5636i	−0.446268	−	0.772958i
$356$	−2.48612			−0.131764
$357$	0.197224	+	0.341603i	0.0104382	+	0.0180795i
$358$	−0.770817	−	1.33509i	−0.0407390	−	0.0705619i
$359$	−10.4222			−0.550063			−0.275031	−	0.961435i	$-0.588688\pi$
$359$	−10.4222			−0.550063			−0.275031	+	0.961435i	$0.588688\pi$
$360$	3.00000	+	5.19615i	0.158114	+	0.273861i
$361$	8.21110	−	14.2220i	0.432163	−	0.748529i
$362$	16.6972	−	28.9204i	0.877587	−	1.52002i
$363$	20.4222			1.07189
$364$	−0.545837	+	0.945417i	−0.0286096	+	0.0495533i
$365$	15.2111			0.796185
$366$	0.651388	−	1.12824i	0.0340486	−	0.0589739i
$367$	8.71110	−	15.0881i	0.454716	−	0.787591i	−0.543956	−	0.839114i	$-0.683074\pi$
$367$	8.71110	−	15.0881i	0.454716	−	0.787591i	0.998672	+	0.0515228i	$0.0164075\pi$
$368$	−4.95416	−	8.58086i	−0.258254	−	0.447308i
$369$	−6.00000			−0.312348
$370$	−2.34861	−	4.06792i	−0.122099	−	0.211481i
$371$	5.60555	+	9.70910i	0.291026	+	0.504071i
$372$	1.21110			0.0627927
$373$	13.8028	+	23.9071i	0.714681	+	1.23786i	0.963083	+	0.269206i	$0.0867613\pi$
$373$	13.8028	+	23.9071i	0.714681	+	1.23786i	−0.248402	+	0.968657i	$0.579905\pi$
$374$	1.44029	−	2.49465i	0.0744754	−	0.128995i
$375$	0.500000	−	0.866025i	0.0258199	−	0.0447214i
$376$	15.6333			0.806226
$377$	−14.8028	+	25.6392i	−0.762382	+	1.32048i
$378$	6.51388			0.335038
$379$	−1.19722	+	2.07365i	−0.0614973	+	0.106516i	−0.895135	−	0.445795i	$-0.852921\pi$
$379$	−1.19722	+	2.07365i	−0.0614973	+	0.106516i	0.833638	+	0.552312i	$0.186254\pi$
$380$	−0.243061	+	0.420994i	−0.0124688	+	0.0215965i
$381$	−5.10555	−	8.84307i	−0.261565	−	0.453044i
$382$	−6.27502			−0.321058
$383$	−9.31665	−	16.1369i	−0.476059	−	0.824558i	0.523565	−	0.851986i	$-0.324602\pi$
$383$	−9.31665	−	16.1369i	−0.476059	−	0.824558i	−0.999624	+	0.0274277i	$0.991268\pi$
$384$	−4.04584	−	7.00759i	−0.206463	−	0.357605i
$385$	−5.60555			−0.285685
$386$	−5.46804	−	9.47093i	−0.278316	−	0.482057i
$387$	4.21110	−	7.29384i	0.214062	−	0.370767i
$388$	−2.36249	+	4.09195i	−0.119937	+	0.207737i
$389$	−0.788897			−0.0399987			−0.0199993	−	0.999800i	$-0.506366\pi$
$389$	−0.788897			−0.0399987			−0.0199993	+	0.999800i	$0.506366\pi$
$390$	2.34861	+	4.06792i	0.118927	+	0.205987i
$391$	−1.18335			−0.0598444
$392$	−9.00000	+	15.5885i	−0.454569	+	0.787336i
$393$	3.39445	−	5.87936i	0.171227	−	0.296574i
$394$	−14.8625	−	25.7426i	−0.748761	−	1.29689i
$395$	9.21110			0.463461
$396$	1.69722	+	2.93968i	0.0852887	+	0.147724i
$397$	7.01388	+	12.1484i	0.352016	+	0.609710i	0.986603	−	0.163142i	$-0.0521628\pi$
$397$	7.01388	+	12.1484i	0.352016	+	0.609710i	−0.634586	+	0.772852i	$0.718829\pi$
$398$	−11.4861			−0.575747
$399$	0.802776	+	1.39045i	0.0401890	+	0.0696095i
$400$	1.65139	−	2.86029i	0.0825694	−	0.143014i
$401$	1.10555	−	1.91487i	0.0552086	−	0.0956241i	−0.837100	−	0.547049i	$-0.815751\pi$
$401$	1.10555	−	1.91487i	0.0552086	−	0.0956241i	0.892309	+	0.451425i	$0.149084\pi$
$402$	−9.11943			−0.454836
$403$	−14.4222			−0.718421
$404$	2.72498			0.135573
$405$	0.500000	−	0.866025i	0.0248452	−	0.0430331i
$406$	5.34861	−	9.26407i	0.265447	−	0.459768i
$407$	−10.1056	−	17.5033i	−0.500914	−	0.867608i
$408$	−1.18335			−0.0585844
$409$	3.10555	+	5.37897i	0.153560	+	0.265973i	0.932534	−	0.361083i	$-0.117593\pi$
$409$	3.10555	+	5.37897i	0.153560	+	0.265973i	−0.778974	+	0.627056i	$0.784260\pi$
$410$	1.95416	+	3.38471i	0.0965093	+	0.167159i
$411$	5.60555			0.276501
$412$	−0.605551	−	1.04885i	−0.0298334	−	0.0516729i
$413$	5.40833	−	9.36750i	0.266126	−	0.460944i
$414$	−3.90833	+	6.76942i	−0.192084	+	0.332699i
$415$	−5.21110			−0.255803
$416$	−3.05971	−	5.29958i	−0.150015	−	0.259833i
$417$	13.6056			0.666267
$418$	5.86249	−	10.1541i	0.286744	−	0.496655i
$419$	16.6194	−	28.7857i	0.811912	−	1.40627i	−0.0996117	−	0.995026i	$-0.531760\pi$
$419$	16.6194	−	28.7857i	0.811912	−	1.40627i	0.911524	−	0.411247i	$-0.134907\pi$
$420$	0.151388	+	0.262211i	0.00738697	+	0.0127946i
$421$	3.57779			0.174371			0.0871855	−	0.996192i	$-0.472213\pi$
$421$	3.57779			0.174371			0.0871855	+	0.996192i	$0.472213\pi$
$422$	10.6791	+	18.4968i	0.519853	+	0.900411i
$423$	−5.21110	−	9.02589i	−0.253372	−	0.438854i
$424$	−33.6333			−1.63338
$425$	−0.197224	−	0.341603i	−0.00956679	−	0.0165702i
$426$	10.9542	−	18.9732i	0.530731	−	0.919253i
$427$	−0.500000	+	0.866025i	−0.0241967	+	0.0419099i
$428$	2.48612			0.120171
$429$	10.1056	+	17.5033i	0.487901	+	0.845069i
$430$	−5.48612			−0.264564
$431$	10.6194	−	18.3934i	0.511520	−	0.885978i	−0.488391	−	0.872625i	$-0.662416\pi$
$431$	10.6194	−	18.3934i	0.511520	−	0.885978i	0.999911	−	0.0133535i	$-0.00425069\pi$
$432$	−8.25694	+	14.3014i	−0.397262	+	0.688078i
$433$	1.80278	+	3.12250i	0.0866359	+	0.150058i	0.906087	−	0.423091i	$-0.139055\pi$
$433$	1.80278	+	3.12250i	0.0866359	+	0.150058i	−0.819451	+	0.573149i	$0.805722\pi$
$434$	5.21110			0.250141
$435$	4.10555	+	7.11102i	0.196846	+	0.340947i
$436$	−0.724981	−	1.25570i	−0.0347203	−	0.0601373i
$437$	−4.81665			−0.230412
$438$	9.90833	+	17.1617i	0.473438	+	0.820019i
$439$	−11.6194	+	20.1254i	−0.554565	+	0.960535i	0.443372	+	0.896338i	$0.353782\pi$
$439$	−11.6194	+	20.1254i	−0.554565	+	0.960535i	−0.997937	+	0.0641973i	$0.979551\pi$
$440$	8.40833	−	14.5636i	0.400851	−	0.694295i
$441$	12.0000			0.571429
$442$	1.85281			0.0881294
$443$	−22.4222			−1.06531			−0.532656	−	0.846332i	$-0.678806\pi$
$443$	−22.4222			−1.06531			−0.532656	+	0.846332i	$0.678806\pi$
$444$	−0.545837	+	0.945417i	−0.0259043	+	0.0448675i
$445$	4.10555	−	7.11102i	0.194622	−	0.337095i
$446$	−6.65139	−	11.5205i	−0.314952	−	0.545513i
$447$	3.00000			0.141895
$448$	4.40833	+	7.63545i	0.208274	+	0.360741i
$449$	6.31665	+	10.9408i	0.298101	+	0.516327i	0.975702	−	0.219104i	$-0.0703133\pi$
$449$	6.31665	+	10.9408i	0.298101	+	0.516327i	−0.677600	+	0.735430i	$0.736980\pi$
$450$	−2.60555			−0.122827
$451$	8.40833	+	14.5636i	0.395933	+	0.685775i
$452$	0.848612	−	1.46984i	0.0399154	−	0.0691354i
$453$	−6.60555	+	11.4412i	−0.310356	+	0.537552i
$454$	1.85281			0.0869569
$455$	−1.80278	−	3.12250i	−0.0845154	−	0.146385i
$456$	−4.81665			−0.225560
$457$	2.59167	−	4.48891i	0.121233	−	0.209982i	−0.799021	−	0.601303i	$-0.794648\pi$
$457$	2.59167	−	4.48891i	0.121233	−	0.209982i	0.920254	+	0.391321i	$0.127982\pi$
$458$	−9.11943	+	15.7953i	−0.426123	+	0.738067i
$459$	0.986122	+	1.70801i	0.0460282	+	0.0797232i
$460$	−0.908327			−0.0423510
$461$	−10.8944	−	18.8697i	−0.507405	−	0.878851i	−0.999963	−	0.00857184i	$-0.997271\pi$
$461$	−10.8944	−	18.8697i	−0.507405	−	0.878851i	0.492558	−	0.870280i	$-0.336062\pi$
$462$	−3.65139	−	6.32439i	−0.169878	−	0.294237i
$463$	−5.57779			−0.259222			−0.129611	−	0.991565i	$-0.541373\pi$
$463$	−5.57779			−0.259222			−0.129611	+	0.991565i	$0.541373\pi$
$464$	13.5597	+	23.4861i	0.629494	+	1.09032i
$465$	−2.00000	+	3.46410i	−0.0927478	+	0.160644i
$466$	−0.513878	+	0.890063i	−0.0238049	+	0.0412314i
$467$	17.2111			0.796435			0.398217	−	0.917291i	$-0.369629\pi$
$467$	17.2111			0.796435			0.398217	+	0.917291i	$0.369629\pi$
$468$	−1.09167	+	1.89083i	−0.0504626	+	0.0874038i
$469$	7.00000			0.323230
$470$	−3.39445	+	5.87936i	−0.156574	+	0.271195i
$471$	1.60555	−	2.78090i	0.0739799	−	0.128137i
$472$	16.2250	+	28.1025i	0.746815	+	1.29352i
$473$	−23.6056			−1.08538
$474$	6.00000	+	10.3923i	0.275589	+	0.477334i
$475$	−0.802776	−	1.39045i	−0.0368339	−	0.0637981i
$476$	0.119429			0.00547404
$477$	11.2111	+	19.4182i	0.513321	+	0.889098i
$478$		0			0
$479$	3.59167	−	6.22096i	0.164108	−	0.284243i	−0.772230	−	0.635343i	$-0.780859\pi$
$479$	3.59167	−	6.22096i	0.164108	−	0.284243i	0.936338	+	0.351100i	$0.114192\pi$
$480$	−1.69722			−0.0774673
$481$	6.50000	−	11.2583i	0.296374	−	0.513336i
$482$	21.1194			0.961964
$483$	−1.50000	+	2.59808i	−0.0682524	+	0.118217i
$484$	3.09167	−	5.35493i	0.140531	−	0.243406i
$485$	−7.80278	−	13.5148i	−0.354306	−	0.613676i
$486$	20.8444			0.945522
$487$	0.500000	+	0.866025i	0.0226572	+	0.0392434i	0.877132	−	0.480250i	$-0.159454\pi$
$487$	0.500000	+	0.866025i	0.0226572	+	0.0392434i	−0.854475	+	0.519493i	$0.826121\pi$
$488$	−1.50000	−	2.59808i	−0.0679018	−	0.117609i
$489$	−18.2111			−0.823535
$490$	−3.90833	−	6.76942i	−0.176560	−	0.305811i
$491$	−2.40833	+	4.17134i	−0.108686	+	0.188250i	−0.915238	−	0.402913i	$-0.867998\pi$
$491$	−2.40833	+	4.17134i	−0.108686	+	0.188250i	0.806552	+	0.591163i	$0.201331\pi$
$492$	0.454163	−	0.786634i	0.0204753	−	0.0354642i
$493$	3.23886			0.145871
$494$	7.54163			0.339314
$495$	−11.2111			−0.503902
$496$	−6.60555	+	11.4412i	−0.296598	+	0.513723i
$497$	−8.40833	+	14.5636i	−0.377165	+	0.653269i
$498$	−3.39445	−	5.87936i	−0.152109	−	0.263460i
$499$	−26.4222			−1.18282			−0.591410	−	0.806371i	$-0.701429\pi$
$499$	−26.4222			−1.18282			−0.591410	+	0.806371i	$0.701429\pi$
$500$	−0.151388	−	0.262211i	−0.00677027	−	0.0117265i
$501$	−4.50000	−	7.79423i	−0.201045	−	0.348220i
$502$	−37.5416			−1.67557
$503$	−1.50000	−	2.59808i	−0.0668817	−	0.115842i	0.830645	−	0.556802i	$-0.187972\pi$
$503$	−1.50000	−	2.59808i	−0.0668817	−	0.115842i	−0.897527	+	0.440959i	$0.854638\pi$
$504$	3.00000	−	5.19615i	0.133631	−	0.231455i
$505$	−4.50000	+	7.79423i	−0.200247	+	0.346839i
$506$	21.9083			0.973944
$507$	−6.50000	+	11.2583i	−0.288675	+	0.500000i
$508$	−3.09167			−0.137171
$509$	−1.50000	+	2.59808i	−0.0664863	+	0.115158i	−0.897352	−	0.441315i	$-0.854512\pi$
$509$	−1.50000	+	2.59808i	−0.0664863	+	0.115158i	0.830866	+	0.556473i	$0.187846\pi$
$510$	0.256939	−	0.445032i	0.0113775	−	0.0197063i
$511$	−7.60555	−	13.1732i	−0.336450	−	0.582748i
$512$	−25.4222			−1.12351
$513$	4.01388	+	6.95224i	0.177217	+	0.306949i
$514$	15.3764	+	26.6327i	0.678223	+	1.17472i
$515$	4.00000			0.176261
$516$	0.637510	+	1.10420i	0.0280648	+	0.0486097i
$517$	−14.6056	+	25.2976i	−0.642351	+	1.11259i
$518$	−2.34861	+	4.06792i	−0.103192	+	0.178734i
$519$	−16.8167			−0.738169
$520$	10.8167			0.474342
$521$	18.0000			0.788594			0.394297	−	0.918983i	$-0.370988\pi$
$521$	18.0000			0.788594			0.394297	+	0.918983i	$0.370988\pi$
$522$	10.6972	−	18.5281i	0.468205	−	0.810954i
$523$	−13.7111	+	23.7483i	−0.599545	+	1.03844i	0.393344	+	0.919392i	$0.371318\pi$
$523$	−13.7111	+	23.7483i	−0.599545	+	1.03844i	−0.992888	+	0.119050i	$0.962015\pi$
$524$	−1.02776	−	1.78013i	−0.0448977	−	0.0777652i
$525$	−1.00000			−0.0436436
$526$	−17.0736	−	29.5723i	−0.744444	−	1.28941i
$527$	0.788897	+	1.36641i	0.0343649	+	0.0595218i
$528$	18.5139			0.805713
$529$	7.00000	+	12.1244i	0.304348	+	0.527146i
$530$	7.30278	−	12.6488i	0.317212	−	0.549428i
$531$	10.8167	−	18.7350i	0.469403	−	0.813029i
$532$	0.486122			0.0210761
$533$	−5.40833	+	9.36750i	−0.234261	+	0.405751i
$534$	10.6972			0.462914
$535$	−4.10555	+	7.11102i	−0.177498	+	0.307436i
$536$	−10.5000	+	18.1865i	−0.453531	+	0.785539i
$537$	−0.591673	−	1.02481i	−0.0255326	−	0.0442237i
$538$	−11.7250			−0.505500
$539$	−16.8167	−	29.1273i	−0.724345	−	1.25460i
$540$	0.756939	+	1.31106i	0.0325735	+	0.0564189i
$541$	17.6333			0.758115			0.379058	−	0.925373i	$-0.376248\pi$
$541$	17.6333			0.758115			0.379058	+	0.925373i	$0.376248\pi$
$542$	−0.531958	−	0.921379i	−0.0228496	−	0.0395766i
$543$	12.8167	−	22.1991i	0.550015	−	0.952654i
$544$	−0.334734	+	0.579776i	−0.0143516	+	0.0248577i
$545$	4.78890			0.205134
$546$	2.34861	−	4.06792i	0.100511	−	0.174091i
$547$	−24.8444			−1.06227			−0.531135	−	0.847287i	$-0.678234\pi$
$547$	−24.8444			−1.06227			−0.531135	+	0.847287i	$0.678234\pi$
$548$	0.848612	−	1.46984i	0.0362509	−	0.0627884i
$549$	−1.00000	+	1.73205i	−0.0426790	+	0.0739221i
$550$	3.65139	+	6.32439i	0.155696	+	0.269673i
$551$	13.1833			0.561629
$552$	−4.50000	−	7.79423i	−0.191533	−	0.331744i
$553$	−4.60555	−	7.97705i	−0.195848	−	0.339219i
$554$	26.5694			1.12883
$555$	−1.80278	−	3.12250i	−0.0765236	−	0.132543i
$556$	2.05971	−	3.56753i	0.0873514	−	0.151297i
$557$	−2.80278	+	4.85455i	−0.118757	+	0.205694i	−0.919276	−	0.393615i	$-0.871224\pi$
$557$	−2.80278	+	4.85455i	−0.118757	+	0.205694i	0.800518	+	0.599309i	$0.204558\pi$
$558$	10.4222			0.441207
$559$	−7.59167	−	13.1492i	−0.321094	−	0.556150i
$560$	−3.30278			−0.139568
$561$	1.10555	−	1.91487i	0.0466764	−	0.0808459i
$562$	3.90833	−	6.76942i	0.164863	−	0.285551i
$563$	9.71110	+	16.8201i	0.409274	+	0.708884i	0.994809	−	0.101764i	$-0.0324486\pi$
$563$	9.71110	+	16.8201i	0.409274	+	0.708884i	−0.585534	+	0.810648i	$0.699115\pi$
$564$	1.57779			0.0664372
$565$	2.80278	+	4.85455i	0.117914	+	0.204232i
$566$	−3.25694	−	5.64118i	−0.136899	−	0.237117i
$567$	−1.00000			−0.0419961
$568$	−25.2250	−	43.6909i	−1.05842	−	1.83323i
$569$	−0.711103	+	1.23167i	−0.0298110	+	0.0516341i	−0.880546	−	0.473961i	$-0.842824\pi$
$569$	−0.711103	+	1.23167i	−0.0298110	+	0.0516341i	0.850735	+	0.525595i	$0.176157\pi$
$570$	1.04584	−	1.81144i	0.0438053	−	0.0758730i
$571$	−36.8444			−1.54189			−0.770945	−	0.636901i	$-0.780216\pi$
$571$	−36.8444			−1.54189			−0.770945	+	0.636901i	$0.780216\pi$
$572$	6.11943			0.255866
$573$	−4.81665			−0.201219
$574$	1.95416	−	3.38471i	0.0815652	−	0.141275i
$575$	1.50000	−	2.59808i	0.0625543	−	0.108347i
$576$	8.81665	+	15.2709i	0.367361	+	0.636287i
$577$	29.6333			1.23365			0.616825	−	0.787100i	$-0.288418\pi$
$577$	29.6333			1.23365			0.616825	+	0.787100i	$0.288418\pi$
$578$	10.9722	+	19.0045i	0.456385	+	0.790482i
$579$	−4.19722	−	7.26981i	−0.174431	−	0.302123i
$580$	2.48612			0.103231
$581$	2.60555	+	4.51295i	0.108096	+	0.187229i
$582$	10.1653	−	17.6068i	0.421364	−	0.729824i
$583$	31.4222	−	54.4249i	1.30137	−	2.25405i
$584$	45.6333			1.88832
$585$	−3.60555	−	6.24500i	−0.149071	−	0.258199i
$586$	22.9361			0.947481
$587$	2.28890	−	3.96449i	0.0944729	−	0.163632i	−0.814916	−	0.579580i	$-0.803217\pi$
$587$	2.28890	−	3.96449i	0.0944729	−	0.163632i	0.909389	+	0.415948i	$0.136550\pi$
$588$	−0.908327	+	1.57327i	−0.0374588	+	0.0648805i
$589$	3.21110	+	5.56179i	0.132311	+	0.229170i
$590$	−14.0917			−0.580145
$591$	−11.4083	−	19.7598i	−0.469276	−	0.812810i
$592$	−5.95416	−	10.3129i	−0.244715	−	0.423858i
$593$	35.2111			1.44595			0.722973	−	0.690876i	$-0.242775\pi$
$593$	35.2111			1.44595			0.722973	+	0.690876i	$0.242775\pi$
$594$	−18.2569	−	31.6219i	−0.749091	−	1.29746i
$595$	−0.197224	+	0.341603i	−0.00808541	+	0.0140043i
$596$	0.454163	−	0.786634i	0.0186033	−	0.0322218i
$597$	−8.81665			−0.360842
$598$	7.04584	+	12.2037i	0.288126	+	0.499048i
$599$	−6.78890			−0.277387			−0.138693	−	0.990335i	$-0.544290\pi$
$599$	−6.78890			−0.277387			−0.138693	+	0.990335i	$0.544290\pi$
$600$	1.50000	−	2.59808i	0.0612372	−	0.106066i
$601$	−14.1056	+	24.4315i	−0.575377	+	0.996583i	0.420623	+	0.907235i	$0.361811\pi$
$601$	−14.1056	+	24.4315i	−0.575377	+	0.996583i	−0.996001	+	0.0893475i	$0.971522\pi$
$602$	2.74306	+	4.75112i	0.111799	+	0.193641i
$603$	14.0000			0.570124
$604$	2.00000	+	3.46410i	0.0813788	+	0.140952i
$605$	10.2111	+	17.6861i	0.415140	+	0.719044i
$606$	−11.7250			−0.476295
$607$	9.89445	+	17.1377i	0.401603	+	0.695597i	0.993920	−	0.110108i	$-0.0351197\pi$
$607$	9.89445	+	17.1377i	0.401603	+	0.695597i	−0.592316	+	0.805706i	$0.701786\pi$
$608$	−1.36249	+	2.35990i	−0.0552563	+	0.0957067i
$609$	4.10555	−	7.11102i	0.166365	−	0.288153i
$610$	1.30278			0.0527478
$611$	−18.7889			−0.760117
$612$	0.238859			0.00965530
$613$	−0.802776	+	1.39045i	−0.0324238	+	0.0561597i	−0.881782	−	0.471657i	$-0.843656\pi$
$613$	−0.802776	+	1.39045i	−0.0324238	+	0.0561597i	0.849358	+	0.527817i	$0.176989\pi$
$614$	10.4222	−	18.0518i	0.420606	−	0.728511i
$615$	1.50000	+	2.59808i	0.0604858	+	0.104765i
$616$	−16.8167			−0.677562
$617$	−13.2250	−	22.9063i	−0.532418	−	0.922174i	−0.999284	−	0.0378463i	$-0.987950\pi$
$617$	−13.2250	−	22.9063i	−0.532418	−	0.922174i	0.466866	−	0.884328i	$-0.345383\pi$
$618$	2.60555	+	4.51295i	0.104811	+	0.181537i
$619$	−14.4222			−0.579677			−0.289839	−	0.957076i	$-0.593602\pi$
$619$	−14.4222			−0.579677			−0.289839	+	0.957076i	$0.593602\pi$
$620$	0.605551	+	1.04885i	0.0243195	+	0.0421227i
$621$	−7.50000	+	12.9904i	−0.300965	+	0.521286i
$622$	−3.39445	+	5.87936i	−0.136105	+	0.235741i
$623$	−8.21110			−0.328971
$624$	5.95416	+	10.3129i	0.238357	+	0.412847i
$625$	1.00000			0.0400000
$626$	−9.11943	+	15.7953i	−0.364486	+	0.631308i
$627$	4.50000	−	7.79423i	0.179713	−	0.311272i
$628$	−0.486122	−	0.841988i	−0.0193984	−	0.0335990i
$629$	−1.42221			−0.0567070
$630$	1.30278	+	2.25647i	0.0519038	+	0.0899001i
$631$	−0.0138782	−	0.0240377i	−0.000552482	−	0.000956927i	0.865749	−	0.500478i	$-0.166843\pi$
$631$	−0.0138782	−	0.0240377i	−0.000552482	−	0.000956927i	−0.866302	+	0.499521i	$0.833509\pi$
$632$	27.6333			1.09919
$633$	8.19722	+	14.1980i	0.325810	+	0.564320i
$634$	−3.90833	+	6.76942i	−0.155219	+	0.268848i
$635$	5.10555	−	8.84307i	0.202608	−	0.350927i
$636$	−3.39445			−0.134599
$637$	10.8167	−	18.7350i	0.428571	−	0.742307i
$638$	−59.9638			−2.37399
$639$	−16.8167	+	29.1273i	−0.665257	+	1.15226i
$640$	4.04584	−	7.00759i	0.159926	−	0.276999i
$641$	9.71110	+	16.8201i	0.383565	+	0.664355i	0.991569	−	0.129579i	$-0.0413627\pi$
$641$	9.71110	+	16.8201i	0.383565	+	0.664355i	−0.608004	+	0.793934i	$0.708029\pi$
$642$	−10.6972			−0.422186
$643$	20.3167	+	35.1895i	0.801211	+	1.38774i	0.918820	+	0.394678i	$0.129144\pi$
$643$	20.3167	+	35.1895i	0.801211	+	1.38774i	−0.117609	+	0.993060i	$0.537523\pi$
$644$	0.454163	+	0.786634i	0.0178965	+	0.0309977i
$645$	−4.21110			−0.165812
$646$	−0.412529	−	0.714521i	−0.0162307	−	0.0281125i
$647$	−5.28890	+	9.16064i	−0.207928	+	0.360142i	−0.951062	−	0.309001i	$-0.900005\pi$
$647$	−5.28890	+	9.16064i	−0.207928	+	0.360142i	0.743134	+	0.669143i	$0.233339\pi$
$648$	1.50000	−	2.59808i	0.0589256	−	0.102062i
$649$	−60.6333			−2.38007
$650$	−2.34861	+	4.06792i	−0.0921201	+	0.159557i
$651$	4.00000			0.156772
$652$	−2.75694	+	4.77516i	−0.107970	+	0.187010i
$653$	14.4083	−	24.9560i	0.563841	−	0.976602i	−0.433315	−	0.901243i	$-0.642656\pi$
$653$	14.4083	−	24.9560i	0.563841	−	0.976602i	0.997156	−	0.0753594i	$-0.0240104\pi$
$654$	3.11943	+	5.40301i	0.121979	+	0.211274i
$655$	6.78890			0.265264
$656$	4.95416	+	8.58086i	0.193428	+	0.335026i
$657$	−15.2111	−	26.3464i	−0.593442	−	1.02787i
$658$	6.78890			0.264659
$659$	6.59167	+	11.4171i	0.256775	+	0.444748i	0.965376	−	0.260862i	$-0.0840067\pi$
$659$	6.59167	+	11.4171i	0.256775	+	0.444748i	−0.708601	+	0.705609i	$0.750673\pi$
$660$	0.848612	−	1.46984i	0.0330322	−	0.0572134i
$661$	−19.3167	+	33.4574i	−0.751331	+	1.30134i	0.195847	+	0.980634i	$0.437254\pi$
$661$	−19.3167	+	33.4574i	−0.751331	+	1.30134i	−0.947178	+	0.320709i	$0.896079\pi$
$662$	−33.9083			−1.31788
$663$	1.42221			0.0552339
$664$	−15.6333			−0.606690
$665$	−0.802776	+	1.39045i	−0.0311303	+	0.0539193i
$666$	−4.69722	+	8.13583i	−0.182014	+	0.315257i
$667$	12.3167	+	21.3331i	0.476903	+	0.826020i
$668$	−2.72498			−0.105433
$669$	−5.10555	−	8.84307i	−0.197392	−	0.341893i
$670$	−4.55971	−	7.89766i	−0.176157	−	0.305113i
$671$	5.60555			0.216400
$672$	0.848612	+	1.46984i	0.0327359	+	0.0567003i
$673$	5.19722	−	9.00186i	0.200338	−	0.346996i	−0.748299	−	0.663361i	$-0.769129\pi$
$673$	5.19722	−	9.00186i	0.200338	−	0.346996i	0.948637	+	0.316365i	$0.102463\pi$
$674$	−11.4861	+	19.8945i	−0.442429	+	0.766309i
$675$	−5.00000			−0.192450
$676$	1.96804	+	3.40875i	0.0756939	+	0.131106i
$677$	33.6333			1.29263			0.646317	−	0.763069i	$-0.276309\pi$
$677$	33.6333			1.29263			0.646317	+	0.763069i	$0.276309\pi$
$678$	−3.65139	+	6.32439i	−0.140231	+	0.242887i
$679$	−7.80278	+	13.5148i	−0.299443	+	0.518651i
$680$	−0.591673	−	1.02481i	−0.0226896	−	0.0392996i
$681$	1.42221			0.0544990
$682$	−14.6056	−	25.2976i	−0.559275	−	0.968694i
$683$	−10.8944	−	18.8697i	−0.416864	−	0.722030i	0.578758	−	0.815500i	$-0.303538\pi$
$683$	−10.8944	−	18.8697i	−0.416864	−	0.722030i	−0.995622	+	0.0934691i	$0.970204\pi$
$684$	0.972244			0.0371747
$685$	2.80278	+	4.85455i	0.107089	+	0.185483i
$686$	−8.46804	+	14.6671i	−0.323311	+	0.559992i
$687$	−7.00000	+	12.1244i	−0.267067	+	0.462573i
$688$	−13.9083			−0.530250
$689$	40.4222			1.53996
$690$	3.90833			0.148787
$691$	−3.01388	+	5.22019i	−0.114653	+	0.198585i	−0.917641	−	0.397410i	$-0.869909\pi$
$691$	−3.01388	+	5.22019i	−0.114653	+	0.198585i	0.802988	+	0.595995i	$0.203242\pi$
$692$	−2.54584	+	4.40952i	−0.0967782	+	0.167625i
$693$	5.60555	+	9.70910i	0.212937	+	0.368818i
$694$	26.3305			0.999493
$695$	6.80278	+	11.7828i	0.258044	+	0.446945i
$696$	12.3167	+	21.3331i	0.466862	+	0.808628i
$697$	1.18335			0.0448224
$698$	11.8625	+	20.5464i	0.449002	+	0.777694i
$699$	−0.394449	+	0.683205i	−0.0149194	+	0.0258412i
$700$	−0.151388	+	0.262211i	−0.00572192	+	0.00991066i
$701$	−7.57779			−0.286209			−0.143105	−	0.989708i	$-0.545709\pi$
$701$	−7.57779			−0.286209			−0.143105	+	0.989708i	$0.545709\pi$
$702$	11.7431	−	20.3396i	0.443213	−	0.767668i
$703$	−5.78890			−0.218332
$704$	24.7111	−	42.8009i	0.931335	−	1.61312i
$705$	−2.60555	+	4.51295i	−0.0981307	+	0.169967i
$706$	3.13751	+	5.43433i	0.118082	+	0.204524i
$707$	9.00000			0.338480
$708$	1.63751	+	2.83625i	0.0615414	+	0.106593i
$709$	−21.9222	−	37.9704i	−0.823306	−	1.42601i	−0.903207	−	0.429205i	$-0.858794\pi$
$709$	−21.9222	−	37.9704i	−0.823306	−	1.42601i	0.0799016	−	0.996803i	$-0.474539\pi$
$710$	21.9083			0.822205
$711$	−9.21110	−	15.9541i	−0.345443	−	0.598325i
$712$	12.3167	−	21.3331i	0.461586	−	0.799491i
$713$	−6.00000	+	10.3923i	−0.224702	+	0.389195i
$714$	−0.513878			−0.0192314
$715$	−10.1056	+	17.5033i	−0.377926	+	0.654587i
$716$	−0.358288			−0.0133899
$717$		0			0
$718$	6.78890	−	11.7587i	0.253359	−	0.438831i
$719$	9.19722	+	15.9301i	0.342999	+	0.594091i	0.984988	−	0.172622i	$-0.0552241\pi$
$719$	9.19722	+	15.9301i	0.342999	+	0.594091i	−0.641989	+	0.766713i	$0.721891\pi$
$720$	−6.60555			−0.246174
$721$	−2.00000	−	3.46410i	−0.0744839	−	0.129010i
$722$	10.6972	+	18.5281i	0.398109	+	0.689546i
$723$	16.2111			0.602897
$724$	−3.88057	−	6.72135i	−0.144220	−	0.249797i
$725$	−4.10555	+	7.11102i	−0.152476	+	0.264097i
$726$	−13.3028	+	23.0411i	−0.493712	+	0.855135i
$727$	42.4222			1.57335			0.786676	−	0.617366i	$-0.211800\pi$
$727$	42.4222			1.57335			0.786676	+	0.617366i	$0.211800\pi$
$728$	−5.40833	−	9.36750i	−0.200446	−	0.347183i
$729$	13.0000			0.481481
$730$	−9.90833	+	17.1617i	−0.366724	+	0.635184i
$731$	−0.830532	+	1.43852i	−0.0307183	+	0.0532057i
$732$	−0.151388	−	0.262211i	−0.00559545	−	0.00969161i
$733$	10.8444			0.400547			0.200274	−	0.979740i	$-0.435817\pi$
$733$	10.8444			0.400547			0.200274	+	0.979740i	$0.435817\pi$
$734$	11.3486	+	19.6564i	0.418885	+	0.725530i
$735$	−3.00000	−	5.19615i	−0.110657	−	0.191663i
$736$	−5.09167			−0.187682
$737$	−19.6194	−	33.9818i	−0.722691	−	1.25174i
$738$	3.90833	−	6.76942i	0.143868	−	0.249186i
$739$	14.1972	−	24.5903i	0.522253	−	0.904569i	−0.477411	−	0.878680i	$-0.658425\pi$
$739$	14.1972	−	24.5903i	0.522253	−	0.904569i	0.999665	−	0.0258895i	$-0.00824179\pi$
$740$	−1.09167			−0.0401307
$741$	5.78890			0.212660
$742$	−14.6056			−0.536187
$743$	3.31665	−	5.74461i	0.121676	−	0.210749i	−0.798753	−	0.601660i	$-0.794506\pi$
$743$	3.31665	−	5.74461i	0.121676	−	0.210749i	0.920429	+	0.390910i	$0.127840\pi$
$744$	−6.00000	+	10.3923i	−0.219971	+	0.381000i
$745$	1.50000	+	2.59808i	0.0549557	+	0.0951861i
$746$	−35.9638			−1.31673
$747$	5.21110	+	9.02589i	0.190664	+	0.330240i
$748$	−0.334734	−	0.579776i	−0.0122391	−	0.0211987i
$749$	8.21110			0.300027
$750$	0.651388	+	1.12824i	0.0237853	+	0.0411974i
$751$	9.22498	−	15.9781i	0.336624	−	0.583050i	−0.647171	−	0.762345i	$-0.724048\pi$
$751$	9.22498	−	15.9781i	0.336624	−	0.583050i	0.983795	+	0.179294i	$0.0573814\pi$
$752$	−8.60555	+	14.9053i	−0.313812	+	0.543539i
$753$	−28.8167			−1.05014
$754$	−19.2847	−	33.4021i	−0.702307	−	1.21643i
$755$	−13.2111			−0.480801
$756$	0.756939	−	1.31106i	0.0275296	−	0.0476827i
$757$	10.4083	−	18.0278i	0.378297	−	0.655230i	−0.612518	−	0.790457i	$-0.709843\pi$
$757$	10.4083	−	18.0278i	0.378297	−	0.655230i	0.990815	+	0.135227i	$0.0431764\pi$
$758$	−1.55971	−	2.70151i	−0.0566514	−	0.0981231i
$759$	16.8167			0.610406
$760$	−2.40833	−	4.17134i	−0.0873592	−	0.151311i
$761$	12.3167	+	21.3331i	0.446478	+	0.773323i	0.998154	−	0.0607356i	$-0.0193447\pi$
$761$	12.3167	+	21.3331i	0.446478	+	0.773323i	−0.551676	+	0.834059i	$0.686011\pi$
$762$	13.3028			0.481909
$763$	−2.39445	−	4.14731i	−0.0866849	−	0.150143i
$764$	−0.729183	+	1.26298i	−0.0263809	+	0.0456931i
$765$	−0.394449	+	0.683205i	−0.0142613	+	0.0247013i
$766$	24.2750			0.877092
$767$	−19.5000	−	33.7750i	−0.704104	−	1.21954i
$768$	−7.09167			−0.255899
$769$	−5.50000	+	9.52628i	−0.198335	+	0.343526i	−0.947989	−	0.318304i	$-0.896887\pi$
$769$	−5.50000	+	9.52628i	−0.198335	+	0.343526i	0.749654	+	0.661830i	$0.230220\pi$
$770$	3.65139	−	6.32439i	0.131587	−	0.227915i
$771$	11.8028	+	20.4430i	0.425067	+	0.736237i
$772$	−2.54163			−0.0914754
$773$	−14.8028	−	25.6392i	−0.532419	−	0.922176i	−0.999284	−	0.0378477i	$-0.987950\pi$
$773$	−14.8028	−	25.6392i	−0.532419	−	0.922176i	0.466865	−	0.884329i	$-0.345384\pi$
$774$	5.48612	+	9.50224i	0.197195	+	0.341551i
$775$	−4.00000			−0.143684
$776$	−23.4083	−	40.5444i	−0.840310	−	1.45546i
$777$	−1.80278	+	3.12250i	−0.0646742	+	0.112019i
$778$	0.513878	−	0.890063i	0.0184234	−	0.0319103i
$779$	4.81665			0.172575
$780$	1.09167			0.0390882
$781$	94.2666			3.37312
$782$	0.770817	−	1.33509i	0.0275644	−	0.0477429i
$783$	20.5278	−	35.5551i	0.733602	−	1.27064i
$784$	−9.90833	−	17.1617i	−0.353869	−	0.612919i
$785$	3.21110			0.114609
$786$	4.42221	+	7.65948i	0.157735	+	0.273205i
$787$	14.3167	+	24.7972i	0.510334	+	0.883924i	0.999928	+	0.0119736i	$0.00381140\pi$
$787$	14.3167	+	24.7972i	0.510334	+	0.883924i	−0.489595	+	0.871950i	$0.662855\pi$
$788$	−6.90833			−0.246099
$789$	−13.1056	−	22.6995i	−0.466570	−	0.808123i
$790$	−6.00000	+	10.3923i	−0.213470	+	0.369742i
$791$	2.80278	−	4.85455i	0.0996552	−	0.172608i
$792$	−33.6333			−1.19511
$793$	1.80278	+	3.12250i	0.0640184	+	0.110883i
$794$	−18.2750			−0.648556
$795$	5.60555	−	9.70910i	0.198808	−	0.344346i
$796$	−1.33473	+	2.31183i	−0.0473084	+	0.0819405i
$797$	−25.2250	−	43.6909i	−0.893515	−	1.54761i	−0.835632	−	0.549289i	$-0.814898\pi$
$797$	−25.2250	−	43.6909i	−0.893515	−	1.54761i	−0.0578825	−	0.998323i	$-0.518435\pi$
$798$	−2.09167			−0.0740444
$799$	1.02776	+	1.78013i	0.0363594	+	0.0629763i
$800$	−0.848612	−	1.46984i	−0.0300030	−	0.0519667i
$801$	−16.4222			−0.580250
$802$	1.44029	+	2.49465i	0.0508582	+	0.0880891i
$803$	−42.6333	+	73.8431i	−1.50450	+	2.60586i
$804$	−1.05971	+	1.83548i	−0.0373733	+	0.0647324i
$805$	−3.00000			−0.105736
$806$	9.39445	−	16.2717i	0.330905	−	0.573145i
$807$	−9.00000			−0.316815
$808$	−13.5000	+	23.3827i	−0.474928	+	0.822600i
$809$	−8.52776	+	14.7705i	−0.299820	+	0.519303i	−0.976095	−	0.217346i	$-0.930260\pi$
$809$	−8.52776	+	14.7705i	−0.299820	+	0.519303i	0.676275	+	0.736650i	$0.263593\pi$
$810$	0.651388	+	1.12824i	0.0228874	+	0.0396422i
$811$	−17.5778			−0.617240			−0.308620	−	0.951185i	$-0.599867\pi$
$811$	−17.5778			−0.617240			−0.308620	+	0.951185i	$0.599867\pi$
$812$	−1.24306	−	2.15304i	−0.0436229	−	0.0755571i
$813$	−0.408327	−	0.707243i	−0.0143207	−	0.0248041i
$814$	26.3305			0.922885
$815$	−9.10555	−	15.7713i	−0.318954	−	0.552444i
$816$	0.651388	−	1.12824i	0.0228031	−	0.0394962i
$817$	−3.38057	+	5.85532i	−0.118271	+	0.204852i
$818$	−8.09167			−0.282919
$819$	−3.60555	+	6.24500i	−0.125988	+	0.218218i
$820$	0.908327			0.0317202
$821$	3.71110	−	6.42782i	0.129518	−	0.224332i	−0.793972	−	0.607955i	$-0.791990\pi$
$821$	3.71110	−	6.42782i	0.129518	−	0.224332i	0.923490	+	0.383622i	$0.125324\pi$
$822$	−3.65139	+	6.32439i	−0.127357	+	0.220588i
$823$	−13.3167	−	23.0651i	−0.464189	−	0.804000i	0.534975	−	0.844868i	$-0.320321\pi$
$823$	−13.3167	−	23.0651i	−0.464189	−	0.804000i	−0.999165	+	0.0408682i	$0.986988\pi$
$824$	12.0000			0.418040
$825$	2.80278	+	4.85455i	0.0975801	+	0.169014i
$826$	7.04584	+	12.2037i	0.245156	+	0.424623i
$827$	−13.5778			−0.472146			−0.236073	−	0.971735i	$-0.575860\pi$
$827$	−13.5778			−0.472146			−0.236073	+	0.971735i	$0.575860\pi$
$828$	0.908327	+	1.57327i	0.0315665	+	0.0546749i
$829$	−0.288897	+	0.500385i	−0.0100338	+	0.0173791i	−0.870999	−	0.491285i	$-0.836527\pi$
$829$	−0.288897	+	0.500385i	−0.0100338	+	0.0173791i	0.860965	+	0.508664i	$0.169861\pi$
$830$	3.39445	−	5.87936i	0.117823	−	0.204075i
$831$	20.3944			0.707476
$832$	31.7889			1.10208
$833$	−2.36669			−0.0820010
$834$	−8.86249	+	15.3503i	−0.306883	+	0.531537i
$835$	4.50000	−	7.79423i	0.155729	−	0.269730i
$836$	−1.36249	−	2.35990i	−0.0471227	−	0.0816189i
$837$	20.0000			0.691301
$838$	21.6514	+	37.5013i	0.747935	+	1.29546i
$839$	−8.01388	−	13.8804i	−0.276670	−	0.479206i	0.693885	−	0.720086i	$-0.255897\pi$
$839$	−8.01388	−	13.8804i	−0.276670	−	0.479206i	−0.970555	+	0.240879i	$0.922564\pi$
$840$	−3.00000			−0.103510
$841$	−19.2111	−	33.2746i	−0.662452	−	1.14740i
$842$	−2.33053	+	4.03660i	−0.0803154	+	0.139110i
$843$	3.00000	−	5.19615i	0.103325	−	0.178965i
$844$	4.96384			0.170862
$845$	−13.0000			−0.447214
$846$	13.5778			0.466814
$847$	10.2111	−	17.6861i	0.350858	−	0.607703i
$848$	18.5139	−	32.0670i	0.635769	−	1.10118i
$849$	−2.50000	−	4.33013i	−0.0857998	−	0.148610i
$850$	0.513878			0.0176259
$851$	−5.40833	−	9.36750i	−0.185395	−	0.321114i
$852$	−2.54584	−	4.40952i	−0.0872189	−	0.151068i
$853$	32.7889			1.12267			0.561335	−	0.827589i	$-0.310288\pi$
$853$	32.7889			1.12267			0.561335	+	0.827589i	$0.310288\pi$
$854$	−0.651388	−	1.12824i	−0.0222900	−	0.0386075i
$855$	−1.60555	+	2.78090i	−0.0549087	+	0.0951046i
$856$	−12.3167	+	21.3331i	−0.420975	+	0.729149i
$857$	6.00000			0.204956			0.102478	−	0.994735i	$-0.467323\pi$
$857$	6.00000			0.204956			0.102478	+	0.994735i	$0.467323\pi$
$858$	−26.3305			−0.898910
$859$	25.2111			0.860192			0.430096	−	0.902783i	$-0.358480\pi$
$859$	25.2111			0.860192			0.430096	+	0.902783i	$0.358480\pi$
$860$	−0.637510	+	1.10420i	−0.0217389	+	0.0376529i
$861$	1.50000	−	2.59808i	0.0511199	−	0.0885422i
$862$	13.8347	+	23.9625i	0.471213	+	0.816165i
$863$	36.0000			1.22545			0.612727	−	0.790295i	$-0.290072\pi$
$863$	36.0000			1.22545			0.612727	+	0.790295i	$0.290072\pi$
$864$	4.24306	+	7.34920i	0.144352	+	0.250025i
$865$	−8.40833	−	14.5636i	−0.285892	−	0.495179i
$866$	−4.69722			−0.159618
$867$	8.42221	+	14.5877i	0.286033	+	0.495424i
$868$	0.605551	−	1.04885i	0.0205537	−	0.0356001i
$869$	−25.8167	+	44.7158i	−0.875770	+	1.51688i
$870$	−10.6972			−0.362670
$871$	12.6194	−	21.8575i	0.427593	−	0.740613i
$872$	14.3667			0.486518
$873$	−15.6056	+	27.0296i	−0.528168	+	0.914814i
$874$	3.13751	−	5.43433i	0.106128	−	0.183819i
$875$	−0.500000	−	0.866025i	−0.0169031	−	0.0292770i
$876$	4.60555			0.155607
$877$	19.0139	+	32.9330i	0.642053	+	1.11207i	0.984974	+	0.172704i	$0.0552504\pi$
$877$	19.0139	+	32.9330i	0.642053	+	1.11207i	−0.342921	+	0.939364i	$0.611416\pi$
$878$	−15.1375	−	26.2189i	−0.510866	−	0.884846i
$879$	17.6056			0.593821
$880$	9.25694	+	16.0335i	0.312051	+	0.540489i
$881$	−17.9222	+	31.0422i	−0.603814	+	1.04584i	0.388423	+	0.921481i	$0.373020\pi$
$881$	−17.9222	+	31.0422i	−0.603814	+	1.04584i	−0.992238	+	0.124356i	$0.960313\pi$
$882$	−7.81665	+	13.5388i	−0.263200	+	0.455877i
$883$	−31.6333			−1.06455			−0.532273	−	0.846573i	$-0.678662\pi$
$883$	−31.6333			−1.06455			−0.532273	+	0.846573i	$0.678662\pi$
$884$	0.215305	−	0.372918i	0.00724147	−	0.0125426i
$885$	−10.8167			−0.363598
$886$	14.6056	−	25.2976i	0.490683	−	0.849888i
$887$	−17.5278	+	30.3590i	−0.588524	+	1.01935i	0.405901	+	0.913917i	$0.366958\pi$
$887$	−17.5278	+	30.3590i	−0.588524	+	1.01935i	−0.994426	+	0.105437i	$0.966376\pi$
$888$	−5.40833	−	9.36750i	−0.181492	−	0.314353i
$889$	−10.2111			−0.342469
$890$	5.34861	+	9.26407i	0.179286	+	0.310532i
$891$	2.80278	+	4.85455i	0.0938965	+	0.162634i
$892$	−3.09167			−0.103517
$893$	4.18335	+	7.24577i	0.139990	+	0.242470i
$894$	−1.95416	+	3.38471i	−0.0653570	+	0.113202i
$895$	0.591673	−	1.02481i	0.0197775	−	0.0342555i
$896$	−8.09167			−0.270324
$897$	5.40833	+	9.36750i	0.180579	+	0.312772i
$898$	−16.4584			−0.549223
$899$	16.4222	−	28.4441i	0.547711	−	0.948664i
$900$	−0.302776	+	0.524423i	−0.0100925	+	0.0174808i
$901$	−2.21110	−	3.82974i	−0.0736625	−	0.127587i
$902$	−21.9083			−0.729467
$903$	2.10555	+	3.64692i	0.0700684	+	0.121362i
$904$	8.40833	+	14.5636i	0.279657	+	0.484380i
$905$	25.6333			0.852080
$906$	−8.60555	−	14.9053i	−0.285900	−	0.495194i
$907$	−24.1333	+	41.8001i	−0.801333	+	1.38795i	0.117405	+	0.993084i	$0.462542\pi$
$907$	−24.1333	+	41.8001i	−0.801333	+	1.38795i	−0.918739	+	0.394866i	$0.870791\pi$
$908$	0.215305	−	0.372918i	0.00714513	−	0.0123757i
$909$	18.0000			0.597022
$910$	4.69722			0.155711
$911$	−36.0000			−1.19273			−0.596367	−	0.802712i	$-0.703390\pi$
$911$	−36.0000			−1.19273			−0.596367	+	0.802712i	$0.703390\pi$
$912$	2.65139	−	4.59234i	0.0877962	−	0.152068i
$913$	14.6056	−	25.2976i	0.483373	−	0.837227i
$914$	3.37637	+	5.84804i	0.111680	+	0.193436i
$915$	1.00000			0.0330590
$916$	2.11943	+	3.67096i	0.0700279	+	0.121292i
$917$	−3.39445	−	5.87936i	−0.112095	−	0.194153i
$918$	−2.56939			−0.0848025
$919$	8.59167	+	14.8812i	0.283413	+	0.490886i	0.972223	−	0.234056i	$-0.0751999\pi$
$919$	8.59167	+	14.8812i	0.283413	+	0.490886i	−0.688810	+	0.724942i	$0.741867\pi$
$920$	4.50000	−	7.79423i	0.148361	−	0.256968i
$921$	8.00000	−	13.8564i	0.263609	−	0.456584i
$922$	28.3860			0.934845
$923$	30.3167	+	52.5100i	0.997885	+	1.72839i
$924$	−1.69722			−0.0558346
$925$	1.80278	−	3.12250i	0.0592749	−	0.102667i
$926$	3.63331	−	6.29307i	0.119398	−	0.206803i
$927$	−4.00000	−	6.92820i	−0.131377	−	0.227552i
$928$	13.9361			0.457474
$929$	−6.71110	−	11.6240i	−0.220184	−	0.381370i	0.734680	−	0.678414i	$-0.237332\pi$
$929$	−6.71110	−	11.6240i	−0.220184	−	0.381370i	−0.954864	+	0.297044i	$0.903999\pi$
$930$	−2.60555	−	4.51295i	−0.0854394	−	0.147985i
$931$	−9.63331			−0.315719
$932$	0.119429	+	0.206858i	0.00391204	+	0.00677586i
$933$	−2.60555	+	4.51295i	−0.0853019	+	0.147747i
$934$	−11.2111	+	19.4182i	−0.366838	+	0.635383i
$935$	2.21110			0.0723108
$936$	−10.8167	−	18.7350i	−0.353553	−	0.612372i
$937$	−46.4777			−1.51836			−0.759180	−	0.650880i	$-0.774400\pi$
$937$	−46.4777			−1.51836			−0.759180	+	0.650880i	$0.774400\pi$
$938$	−4.55971	+	7.89766i	−0.148880	+	0.257868i
$939$	−7.00000	+	12.1244i	−0.228436	+	0.395663i
$940$	0.788897	+	1.36641i	0.0257310	+	0.0445674i
$941$	33.6333			1.09641			0.548207	−	0.836343i	$-0.315311\pi$
$941$	33.6333			1.09641			0.548207	+	0.836343i	$0.315311\pi$
$942$	2.09167	+	3.62288i	0.0681504	+	0.118040i
$943$	4.50000	+	7.79423i	0.146540	+	0.253815i
$944$	−35.7250			−1.16275
$945$	2.50000	+	4.33013i	0.0813250	+	0.140859i
$946$	15.3764	−	26.6327i	0.499929	−	0.865902i
$947$	−12.3167	+	21.3331i	−0.400237	+	0.693232i	−0.993754	−	0.111590i	$-0.964406\pi$
$947$	−12.3167	+	21.3331i	−0.400237	+	0.693232i	0.593517	+	0.804822i	$0.297739\pi$
$948$	2.78890			0.0905792
$949$	−54.8444			−1.78032
$950$	2.09167			0.0678628
$951$	−3.00000	+	5.19615i	−0.0972817	+	0.168497i
$952$	−0.591673	+	1.02481i	−0.0191762	+	0.0332142i
$953$	−25.2250	−	43.6909i	−0.817117	−	1.41529i	−0.907798	−	0.419409i	$-0.862237\pi$
$953$	−25.2250	−	43.6909i	−0.817117	−	1.41529i	0.0906803	−	0.995880i	$-0.471096\pi$
$954$	−29.2111			−0.945744
$955$	−2.40833	−	4.17134i	−0.0779316	−	0.134982i
$956$		0			0
$957$	−46.0278			−1.48787
$958$	4.67914	+	8.10452i	0.151176	+	0.261845i
$959$	2.80278	−	4.85455i	0.0905063	−	0.156762i
$960$	4.40833	−	7.63545i	0.142278	−	0.246433i
$961$	−15.0000			−0.483871
$962$	8.46804	+	14.6671i	0.273021	+	0.472886i
$963$	16.4222			0.529198
$964$	2.45416	−	4.25074i	0.0790433	−	0.136907i
$965$	4.19722	−	7.26981i	0.135113	−	0.234023i
$966$	−1.95416	−	3.38471i	−0.0628742	−	0.108901i
$967$	56.4777			1.81620			0.908100	−	0.418752i	$-0.137532\pi$
$967$	56.4777			1.81620			0.908100	+	0.418752i	$0.137532\pi$
$968$	30.6333	+	53.0584i	0.984592	+	1.70536i
$969$	−0.316654	−	0.548461i	−0.0101724	−	0.0176191i
$970$	20.3305			0.652774
$971$	3.98612	+	6.90417i	0.127921	+	0.221565i	0.922871	−	0.385110i	$-0.125836\pi$
$971$	3.98612	+	6.90417i	0.127921	+	0.221565i	−0.794950	+	0.606675i	$0.792503\pi$
$972$	2.42221	−	4.19538i	0.0776923	−	0.134567i
$973$	6.80278	−	11.7828i	0.218087	−	0.377738i
$974$	−1.30278			−0.0417436
$975$	−1.80278	+	3.12250i	−0.0577350	+	0.100000i
$976$	3.30278			0.105719
$977$	−3.59167	+	6.22096i	−0.114908	+	0.199026i	−0.917743	−	0.397175i	$-0.869991\pi$
$977$	−3.59167	+	6.22096i	−0.114908	+	0.199026i	0.802835	+	0.596201i	$0.203324\pi$
$978$	11.8625	−	20.5464i	0.379321	−	0.657003i
$979$	23.0139	+	39.8612i	0.735527	+	1.27397i
$980$	−1.81665			−0.0580309
$981$	−4.78890	−	8.29461i	−0.152898	−	0.264827i
$982$	−3.13751	−	5.43433i	−0.100122	−	0.173416i
$983$	−10.4222			−0.332417			−0.166208	−	0.986091i	$-0.553152\pi$
$983$	−10.4222			−0.332417			−0.166208	+	0.986091i	$0.553152\pi$
$984$	4.50000	+	7.79423i	0.143455	+	0.248471i
$985$	11.4083	−	19.7598i	0.363500	−	0.629600i
$986$	−2.10975	+	3.65420i	−0.0671882	+	0.116373i
$987$	5.21110			0.165871
$988$	0.876369	−	1.51791i	0.0278810	−	0.0482913i
$989$	−12.6333			−0.401716
$990$	7.30278	−	12.6488i	0.232097	−	0.402005i
$991$	−1.98612	+	3.44006i	−0.0630912	+	0.109277i	−0.895846	−	0.444365i	$-0.853429\pi$
$991$	−1.98612	+	3.44006i	−0.0630912	+	0.109277i	0.832754	+	0.553642i	$0.186763\pi$
$992$	3.39445	+	5.87936i	0.107774	+	0.186670i
$993$	−26.0278			−0.825966
$994$	−10.9542	−	18.9732i	−0.347445	−	0.601792i
$995$	−4.40833	−	7.63545i	−0.139753	−	0.242060i
$996$	−1.57779			−0.0499943
$997$	−23.2250	−	40.2268i	−0.735543	−	1.27400i	−0.954485	−	0.298259i	$-0.903594\pi$
$997$	−23.2250	−	40.2268i	−0.735543	−	1.27400i	0.218942	−	0.975738i	$-0.429739\pi$
$998$	17.2111	−	29.8105i	0.544808	−	0.943635i
$999$	−9.01388	+	15.6125i	−0.285186	+	0.493957i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	65.2.e.b.61.1	yes	4
3.2	odd	2		585.2.j.d.451.2		4
4.3	odd	2		1040.2.q.o.321.1		4
5.2	odd	4		325.2.o.b.74.2		8
5.3	odd	4		325.2.o.b.74.3		8
5.4	even	2		325.2.e.a.126.2		4
13.2	odd	12		845.2.m.d.361.2		8
13.3	even	3	inner	65.2.e.b.16.1	✓	4
13.4	even	6		845.2.a.f.1.1		2
13.5	odd	4		845.2.m.d.316.3		8
13.6	odd	12		845.2.c.d.506.2		4
13.7	odd	12		845.2.c.d.506.3		4
13.8	odd	4		845.2.m.d.316.2		8
13.9	even	3		845.2.a.c.1.2		2
13.10	even	6		845.2.e.d.146.2		4
13.11	odd	12		845.2.m.d.361.3		8
13.12	even	2		845.2.e.d.191.2		4
39.17	odd	6		7605.2.a.bb.1.2		2
39.29	odd	6		585.2.j.d.406.2		4
39.35	odd	6		7605.2.a.bg.1.1		2
52.3	odd	6		1040.2.q.o.81.1		4
65.3	odd	12		325.2.o.b.224.2		8
65.4	even	6		4225.2.a.t.1.2		2
65.9	even	6		4225.2.a.x.1.1		2
65.29	even	6		325.2.e.a.276.2		4
65.42	odd	12		325.2.o.b.224.3		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
65.2.e.b.16.1	✓	4	13.3	even	3	inner
65.2.e.b.61.1	yes	4	1.1	even	1	trivial
325.2.e.a.126.2		4	5.4	even	2
325.2.e.a.276.2		4	65.29	even	6
325.2.o.b.74.2		8	5.2	odd	4
325.2.o.b.74.3		8	5.3	odd	4
325.2.o.b.224.2		8	65.3	odd	12
325.2.o.b.224.3		8	65.42	odd	12
585.2.j.d.406.2		4	39.29	odd	6
585.2.j.d.451.2		4	3.2	odd	2
845.2.a.c.1.2		2	13.9	even	3
845.2.a.f.1.1		2	13.4	even	6
845.2.c.d.506.2		4	13.6	odd	12
845.2.c.d.506.3		4	13.7	odd	12
845.2.e.d.146.2		4	13.10	even	6
845.2.e.d.191.2		4	13.12	even	2
845.2.m.d.316.2		8	13.8	odd	4
845.2.m.d.316.3		8	13.5	odd	4
845.2.m.d.361.2		8	13.2	odd	12
845.2.m.d.361.3		8	13.11	odd	12
1040.2.q.o.81.1		4	52.3	odd	6
1040.2.q.o.321.1		4	4.3	odd	2
4225.2.a.t.1.2		2	65.4	even	6
4225.2.a.x.1.1		2	65.9	even	6
7605.2.a.bb.1.2		2	39.17	odd	6
7605.2.a.bg.1.1		2	39.35	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)

\(f(q)\)	\(=\)	\(q+(-0.651388 + 1.12824i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(0.151388 + 0.262211i) q^{4} -1.00000 q^{5} +(-0.651388 - 1.12824i) q^{6} +(0.500000 + 0.866025i) q^{7} -3.00000 q^{8} +(1.00000 + 1.73205i) q^{9} +O(q^{10})\)	\(q+(-0.651388 + 1.12824i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(0.151388 + 0.262211i) q^{4} -1.00000 q^{5} +(-0.651388 - 1.12824i) q^{6} +(0.500000 + 0.866025i) q^{7} -3.00000 q^{8} +(1.00000 + 1.73205i) q^{9} +(0.651388 - 1.12824i) q^{10} +(2.80278 - 4.85455i) q^{11} -0.302776 q^{12} +3.60555 q^{13} -1.30278 q^{14} +(0.500000 - 0.866025i) q^{15} +(1.65139 - 2.86029i) q^{16} +(-0.197224 - 0.341603i) q^{17} -2.60555 q^{18} +(-0.802776 - 1.39045i) q^{19} +(-0.151388 - 0.262211i) q^{20} -1.00000 q^{21} +(3.65139 + 6.32439i) q^{22} +(1.50000 - 2.59808i) q^{23} +(1.50000 - 2.59808i) q^{24} +1.00000 q^{25} +(-2.34861 + 4.06792i) q^{26} -5.00000 q^{27} +(-0.151388 + 0.262211i) q^{28} +(-4.10555 + 7.11102i) q^{29} +(0.651388 + 1.12824i) q^{30} -4.00000 q^{31} +(-0.848612 - 1.46984i) q^{32} +(2.80278 + 4.85455i) q^{33} +0.513878 q^{34} +(-0.500000 - 0.866025i) q^{35} +(-0.302776 + 0.524423i) q^{36} +(1.80278 - 3.12250i) q^{37} +2.09167 q^{38} +(-1.80278 + 3.12250i) q^{39} +3.00000 q^{40} +(-1.50000 + 2.59808i) q^{41} +(0.651388 - 1.12824i) q^{42} +(-2.10555 - 3.64692i) q^{43} +1.69722 q^{44} +(-1.00000 - 1.73205i) q^{45} +(1.95416 + 3.38471i) q^{46} -5.21110 q^{47} +(1.65139 + 2.86029i) q^{48} +(3.00000 - 5.19615i) q^{49} +(-0.651388 + 1.12824i) q^{50} +0.394449 q^{51} +(0.545837 + 0.945417i) q^{52} +11.2111 q^{53} +(3.25694 - 5.64118i) q^{54} +(-2.80278 + 4.85455i) q^{55} +(-1.50000 - 2.59808i) q^{56} +1.60555 q^{57} +(-5.34861 - 9.26407i) q^{58} +(-5.40833 - 9.36750i) q^{59} +0.302776 q^{60} +(0.500000 + 0.866025i) q^{61} +(2.60555 - 4.51295i) q^{62} +(-1.00000 + 1.73205i) q^{63} +8.81665 q^{64} -3.60555 q^{65} -7.30278 q^{66} +(3.50000 - 6.06218i) q^{67} +(0.0597147 - 0.103429i) q^{68} +(1.50000 + 2.59808i) q^{69} +1.30278 q^{70} +(8.40833 + 14.5636i) q^{71} +(-3.00000 - 5.19615i) q^{72} -15.2111 q^{73} +(2.34861 + 4.06792i) q^{74} +(-0.500000 + 0.866025i) q^{75} +(0.243061 - 0.420994i) q^{76} +5.60555 q^{77} +(-2.34861 - 4.06792i) q^{78} -9.21110 q^{79} +(-1.65139 + 2.86029i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(-1.95416 - 3.38471i) q^{82} +5.21110 q^{83} +(-0.151388 - 0.262211i) q^{84} +(0.197224 + 0.341603i) q^{85} +5.48612 q^{86} +(-4.10555 - 7.11102i) q^{87} +(-8.40833 + 14.5636i) q^{88} +(-4.10555 + 7.11102i) q^{89} +2.60555 q^{90} +(1.80278 + 3.12250i) q^{91} +0.908327 q^{92} +(2.00000 - 3.46410i) q^{93} +(3.39445 - 5.87936i) q^{94} +(0.802776 + 1.39045i) q^{95} +1.69722 q^{96} +(7.80278 + 13.5148i) q^{97} +(3.90833 + 6.76942i) q^{98} +11.2111 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + q^{2} - 2 q^{3} - 3 q^{4} - 4 q^{5} + q^{6} + 2 q^{7} - 12 q^{8} + 4 q^{9}+O(q^{10}) \) 4 * q + q^2 - 2 * q^3 - 3 * q^4 - 4 * q^5 + q^6 + 2 * q^7 - 12 * q^8 + 4 * q^9	\( 4 q + q^{2} - 2 q^{3} - 3 q^{4} - 4 q^{5} + q^{6} + 2 q^{7} - 12 q^{8} + 4 q^{9} - q^{10} + 4 q^{11} + 6 q^{12} + 2 q^{14} + 2 q^{15} + 3 q^{16} - 8 q^{17} + 4 q^{18} + 4 q^{19} + 3 q^{20} - 4 q^{21} + 11 q^{22} + 6 q^{23} + 6 q^{24} + 4 q^{25} - 13 q^{26} - 20 q^{27} + 3 q^{28} - 2 q^{29} - q^{30} - 16 q^{31} - 7 q^{32} + 4 q^{33} - 34 q^{34} - 2 q^{35} + 6 q^{36} + 30 q^{38} + 12 q^{40} - 6 q^{41} - q^{42} + 6 q^{43} + 14 q^{44} - 4 q^{45} - 3 q^{46} + 8 q^{47} + 3 q^{48} + 12 q^{49} + q^{50} + 16 q^{51} + 13 q^{52} + 16 q^{53} - 5 q^{54} - 4 q^{55} - 6 q^{56} - 8 q^{57} - 25 q^{58} - 6 q^{60} + 2 q^{61} - 4 q^{62} - 4 q^{63} - 8 q^{64} - 22 q^{66} + 14 q^{67} - 25 q^{68} + 6 q^{69} - 2 q^{70} + 12 q^{71} - 12 q^{72} - 32 q^{73} + 13 q^{74} - 2 q^{75} + 19 q^{76} + 8 q^{77} - 13 q^{78} - 8 q^{79} - 3 q^{80} - 2 q^{81} + 3 q^{82} - 8 q^{83} + 3 q^{84} + 8 q^{85} + 58 q^{86} - 2 q^{87} - 12 q^{88} - 2 q^{89} - 4 q^{90} - 18 q^{92} + 8 q^{93} + 28 q^{94} - 4 q^{95} + 14 q^{96} + 24 q^{97} - 6 q^{98} + 16 q^{99}+O(q^{100}) \) 4 * q + q^2 - 2 * q^3 - 3 * q^4 - 4 * q^5 + q^6 + 2 * q^7 - 12 * q^8 + 4 * q^9 - q^10 + 4 * q^11 + 6 * q^12 + 2 * q^14 + 2 * q^15 + 3 * q^16 - 8 * q^17 + 4 * q^18 + 4 * q^19 + 3 * q^20 - 4 * q^21 + 11 * q^22 + 6 * q^23 + 6 * q^24 + 4 * q^25 - 13 * q^26 - 20 * q^27 + 3 * q^28 - 2 * q^29 - q^30 - 16 * q^31 - 7 * q^32 + 4 * q^33 - 34 * q^34 - 2 * q^35 + 6 * q^36 + 30 * q^38 + 12 * q^40 - 6 * q^41 - q^42 + 6 * q^43 + 14 * q^44 - 4 * q^45 - 3 * q^46 + 8 * q^47 + 3 * q^48 + 12 * q^49 + q^50 + 16 * q^51 + 13 * q^52 + 16 * q^53 - 5 * q^54 - 4 * q^55 - 6 * q^56 - 8 * q^57 - 25 * q^58 - 6 * q^60 + 2 * q^61 - 4 * q^62 - 4 * q^63 - 8 * q^64 - 22 * q^66 + 14 * q^67 - 25 * q^68 + 6 * q^69 - 2 * q^70 + 12 * q^71 - 12 * q^72 - 32 * q^73 + 13 * q^74 - 2 * q^75 + 19 * q^76 + 8 * q^77 - 13 * q^78 - 8 * q^79 - 3 * q^80 - 2 * q^81 + 3 * q^82 - 8 * q^83 + 3 * q^84 + 8 * q^85 + 58 * q^86 - 2 * q^87 - 12 * q^88 - 2 * q^89 - 4 * q^90 - 18 * q^92 + 8 * q^93 + 28 * q^94 - 4 * q^95 + 14 * q^96 + 24 * q^97 - 6 * q^98 + 16 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more