LMFDB - Embedded newform 570.2.i.j.121.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [570,2,Mod(121,570)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(570, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 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("570.121");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 570 = 2 \cdot 3 \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	570.i (of order $3$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$4.55147291521$
Analytic rank:	$0$
Dimension:	$6$
Relative dimension:	$3$ over $\Q(\zeta_{3})$
Coefficient field:	6.0.29654208.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} + 14x^{4} + 49x^{2} + 12 $ x^6 + 14x^4 + 49x^2 + 12
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 3 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			121.1
Root			$-2.35084i$ of defining polynomial
Character	$\chi$	$=$	570.121
Dual form			570.2.i.j.391.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-0.500000 - 0.866025i) q^{5} +(-0.500000 + 0.866025i) q^{6} -4.59821 q^{7} +1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-0.500000 - 0.866025i) q^{5} +(-0.500000 + 0.866025i) q^{6} -4.59821 q^{7} +1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +(-0.500000 + 0.866025i) q^{10} +0.473560 q^{11} +1.00000 q^{12} +(0.263220 - 0.455910i) q^{13} +(2.29911 + 3.98217i) q^{14} +(-0.500000 + 0.866025i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(2.27267 + 3.93637i) q^{17} +1.00000 q^{18} +(2.56233 + 3.52626i) q^{19} +1.00000 q^{20} +(2.29911 + 3.98217i) q^{21} +(-0.236780 - 0.410115i) q^{22} +(0.236780 - 0.410115i) q^{23} +(-0.500000 - 0.866025i) q^{24} +(-0.500000 + 0.866025i) q^{25} -0.526440 q^{26} +1.00000 q^{27} +(2.29911 - 3.98217i) q^{28} +(-4.32555 + 7.49206i) q^{29} +1.00000 q^{30} -0.526440 q^{31} +(-0.500000 + 0.866025i) q^{32} +(-0.236780 - 0.410115i) q^{33} +(2.27267 - 3.93637i) q^{34} +(2.29911 + 3.98217i) q^{35} +(-0.500000 - 0.866025i) q^{36} -1.00000 q^{37} +(1.77267 - 3.98217i) q^{38} -0.526440 q^{39} +(-0.500000 - 0.866025i) q^{40} +(5.63410 + 9.75854i) q^{41} +(2.29911 - 3.98217i) q^{42} +(-6.33499 - 10.9725i) q^{43} +(-0.236780 + 0.410115i) q^{44} +1.00000 q^{45} -0.473560 q^{46} +(-4.07177 + 7.05251i) q^{47} +(-0.500000 + 0.866025i) q^{48} +14.1435 q^{49} +1.00000 q^{50} +(2.27267 - 3.93637i) q^{51} +(0.263220 + 0.455910i) q^{52} +(-0.964114 + 1.66990i) q^{53} +(-0.500000 - 0.866025i) q^{54} +(-0.236780 - 0.410115i) q^{55} -4.59821 q^{56} +(1.77267 - 3.98217i) q^{57} +8.65109 q^{58} +(-3.00000 - 5.19615i) q^{59} +(-0.500000 - 0.866025i) q^{60} +(-1.53589 + 2.66023i) q^{61} +(0.263220 + 0.455910i) q^{62} +(2.29911 - 3.98217i) q^{63} +1.00000 q^{64} -0.526440 q^{65} +(-0.236780 + 0.410115i) q^{66} +(-4.53589 + 7.85638i) q^{67} -4.54533 q^{68} -0.473560 q^{69} +(2.29911 - 3.98217i) q^{70} +(2.27267 + 3.93637i) q^{71} +(-0.500000 + 0.866025i) q^{72} +(1.46411 + 2.53592i) q^{73} +(0.500000 + 0.866025i) q^{74} +1.00000 q^{75} +(-4.33499 + 0.455910i) q^{76} -2.17753 q^{77} +(0.263220 + 0.455910i) q^{78} +(0.736780 + 1.27614i) q^{79} +(-0.500000 + 0.866025i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(5.63410 - 9.75854i) q^{82} +4.10576 q^{83} -4.59821 q^{84} +(2.27267 - 3.93637i) q^{85} +(-6.33499 + 10.9725i) q^{86} +8.65109 q^{87} +0.473560 q^{88} +(0.964114 - 1.66990i) q^{89} +(-0.500000 - 0.866025i) q^{90} +(-1.21034 + 2.09637i) q^{91} +(0.236780 + 0.410115i) q^{92} +(0.263220 + 0.455910i) q^{93} +8.14354 q^{94} +(1.77267 - 3.98217i) q^{95} +1.00000 q^{96} +(-8.79911 - 15.2405i) q^{97} +(-7.07177 - 12.2487i) q^{98} +(-0.236780 + 0.410115i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 3 q^{2} - 3 q^{3} - 3 q^{4} - 3 q^{5} - 3 q^{6} + 2 q^{7} + 6 q^{8} - 3 q^{9}+O(q^{10}) $ 6 * q - 3 * q^2 - 3 * q^3 - 3 * q^4 - 3 * q^5 - 3 * q^6 + 2 * q^7 + 6 * q^8 - 3 * q^9	\( 6 q - 3 q^{2} - 3 q^{3} - 3 q^{4} - 3 q^{5} - 3 q^{6} + 2 q^{7} + 6 q^{8} - 3 q^{9} - 3 q^{10} + 8 q^{11} + 6 q^{12} - q^{13} - q^{14} - 3 q^{15} - 3 q^{16} + 4 q^{17} + 6 q^{18} - 2 q^{19} + 6 q^{20} - q^{21} - 4 q^{22} + 4 q^{23} - 3 q^{24} - 3 q^{25} + 2 q^{26} + 6 q^{27} - q^{28} - 6 q^{29} + 6 q^{30} + 2 q^{31} - 3 q^{32} - 4 q^{33} + 4 q^{34} - q^{35} - 3 q^{36} - 6 q^{37} + q^{38} + 2 q^{39} - 3 q^{40} - 8 q^{41} - q^{42} - 11 q^{43} - 4 q^{44} + 6 q^{45} - 8 q^{46} - 3 q^{48} + 36 q^{49} + 6 q^{50} + 4 q^{51} - q^{52} - 18 q^{53} - 3 q^{54} - 4 q^{55} + 2 q^{56} + q^{57} + 12 q^{58} - 18 q^{59} - 3 q^{60} + 3 q^{61} - q^{62} - q^{63} + 6 q^{64} + 2 q^{65} - 4 q^{66} - 15 q^{67} - 8 q^{68} - 8 q^{69} - q^{70} + 4 q^{71} - 3 q^{72} + 21 q^{73} + 3 q^{74} + 6 q^{75} + q^{76} + 32 q^{77} - q^{78} + 7 q^{79} - 3 q^{80} - 3 q^{81} - 8 q^{82} + 4 q^{83} + 2 q^{84} + 4 q^{85} - 11 q^{86} + 12 q^{87} + 8 q^{88} + 18 q^{89} - 3 q^{90} - 15 q^{91} + 4 q^{92} - q^{93} + q^{95} + 6 q^{96} - 38 q^{97} - 18 q^{98} - 4 q^{99}+O(q^{100}) \) 6 * q - 3 * q^2 - 3 * q^3 - 3 * q^4 - 3 * q^5 - 3 * q^6 + 2 * q^7 + 6 * q^8 - 3 * q^9 - 3 * q^10 + 8 * q^11 + 6 * q^12 - q^13 - q^14 - 3 * q^15 - 3 * q^16 + 4 * q^17 + 6 * q^18 - 2 * q^19 + 6 * q^20 - q^21 - 4 * q^22 + 4 * q^23 - 3 * q^24 - 3 * q^25 + 2 * q^26 + 6 * q^27 - q^28 - 6 * q^29 + 6 * q^30 + 2 * q^31 - 3 * q^32 - 4 * q^33 + 4 * q^34 - q^35 - 3 * q^36 - 6 * q^37 + q^38 + 2 * q^39 - 3 * q^40 - 8 * q^41 - q^42 - 11 * q^43 - 4 * q^44 + 6 * q^45 - 8 * q^46 - 3 * q^48 + 36 * q^49 + 6 * q^50 + 4 * q^51 - q^52 - 18 * q^53 - 3 * q^54 - 4 * q^55 + 2 * q^56 + q^57 + 12 * q^58 - 18 * q^59 - 3 * q^60 + 3 * q^61 - q^62 - q^63 + 6 * q^64 + 2 * q^65 - 4 * q^66 - 15 * q^67 - 8 * q^68 - 8 * q^69 - q^70 + 4 * q^71 - 3 * q^72 + 21 * q^73 + 3 * q^74 + 6 * q^75 + q^76 + 32 * q^77 - q^78 + 7 * q^79 - 3 * q^80 - 3 * q^81 - 8 * q^82 + 4 * q^83 + 2 * q^84 + 4 * q^85 - 11 * q^86 + 12 * q^87 + 8 * q^88 + 18 * q^89 - 3 * q^90 - 15 * q^91 + 4 * q^92 - q^93 + q^95 + 6 * q^96 - 38 * q^97 - 18 * q^98 - 4 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/570\mathbb{Z}\right)^\times$.

$n$	$191$	$211$	$457$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$	$1$

Coefficient data

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

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

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

$2$	−0.500000	−	0.866025i	−0.353553	−	0.612372i
$2$	−0.500000	−	0.866025i	−0.353553	−	0.612372i
$3$	−0.500000	−	0.866025i	−0.288675	−	0.500000i
$3$	−0.500000	−	0.866025i	−0.288675	−	0.500000i
$4$	−0.500000	+	0.866025i	−0.250000	+	0.433013i
$5$	−0.500000	−	0.866025i	−0.223607	−	0.387298i
$5$	−0.500000	−	0.866025i	−0.223607	−	0.387298i
$6$	−0.500000	+	0.866025i	−0.204124	+	0.353553i
$7$	−4.59821			−1.73796			−0.868980	−	0.494847i	$-0.835224\pi$
$7$	−4.59821			−1.73796			−0.868980	+	0.494847i	$0.835224\pi$
$8$	1.00000			0.353553
$9$	−0.500000	+	0.866025i	−0.166667	+	0.288675i
$10$	−0.500000	+	0.866025i	−0.158114	+	0.273861i
$11$	0.473560			0.142784			0.0713919	−	0.997448i	$-0.477256\pi$
$11$	0.473560			0.142784			0.0713919	+	0.997448i	$0.477256\pi$
$12$	1.00000			0.288675
$13$	0.263220	−	0.455910i	0.0730041	−	0.126447i	−0.827213	−	0.561889i	$-0.810075\pi$
$13$	0.263220	−	0.455910i	0.0730041	−	0.126447i	0.900217	+	0.435442i	$0.143408\pi$
$14$	2.29911	+	3.98217i	0.614462	+	1.06428i
$15$	−0.500000	+	0.866025i	−0.129099	+	0.223607i
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	2.27267	+	3.93637i	0.551202	+	0.954711i	0.998188	+	0.0601695i	$0.0191641\pi$
$17$	2.27267	+	3.93637i	0.551202	+	0.954711i	−0.446986	+	0.894541i	$0.647503\pi$
$18$	1.00000			0.235702
$19$	2.56233	+	3.52626i	0.587838	+	0.808979i
$19$	2.56233	+	3.52626i	0.587838	+	0.808979i
$20$	1.00000			0.223607
$21$	2.29911	+	3.98217i	0.501706	+	0.868980i
$22$	−0.236780	−	0.410115i	−0.0504817	−	0.0874369i
$23$	0.236780	−	0.410115i	0.0493721	−	0.0855149i	−0.840283	−	0.542148i	$-0.817611\pi$
$23$	0.236780	−	0.410115i	0.0493721	−	0.0855149i	0.889655	+	0.456633i	$0.150945\pi$
$24$	−0.500000	−	0.866025i	−0.102062	−	0.176777i
$25$	−0.500000	+	0.866025i	−0.100000	+	0.173205i
$26$	−0.526440			−0.103243
$27$	1.00000			0.192450
$28$	2.29911	−	3.98217i	0.434490	−	0.752559i
$29$	−4.32555	+	7.49206i	−0.803234	+	1.39124i	0.114244	+	0.993453i	$0.463556\pi$
$29$	−4.32555	+	7.49206i	−0.803234	+	1.39124i	−0.917477	+	0.397789i	$0.869778\pi$
$30$	1.00000			0.182574
$31$	−0.526440			−0.0945514			−0.0472757	−	0.998882i	$-0.515054\pi$
$31$	−0.526440			−0.0945514			−0.0472757	+	0.998882i	$0.515054\pi$
$32$	−0.500000	+	0.866025i	−0.0883883	+	0.153093i
$33$	−0.236780	−	0.410115i	−0.0412181	−	0.0713919i
$34$	2.27267	−	3.93637i	0.389759	−	0.675082i
$35$	2.29911	+	3.98217i	0.388620	+	0.673109i
$36$	−0.500000	−	0.866025i	−0.0833333	−	0.144338i
$37$	−1.00000			−0.164399			−0.0821995	−	0.996616i	$-0.526194\pi$
$37$	−1.00000			−0.164399			−0.0821995	+	0.996616i	$0.526194\pi$
$38$	1.77267	−	3.98217i	0.287564	−	0.645993i
$39$	−0.526440			−0.0842978
$40$	−0.500000	−	0.866025i	−0.0790569	−	0.136931i
$41$	5.63410	+	9.75854i	0.879898	+	1.52403i	0.851452	+	0.524433i	$0.175723\pi$
$41$	5.63410	+	9.75854i	0.879898	+	1.52403i	0.0284461	+	0.999595i	$0.490944\pi$
$42$	2.29911	−	3.98217i	0.354760	−	0.614462i
$43$	−6.33499	−	10.9725i	−0.966077	−	1.67329i	−0.706693	−	0.707520i	$-0.749814\pi$
$43$	−6.33499	−	10.9725i	−0.966077	−	1.67329i	−0.259384	−	0.965774i	$-0.583520\pi$
$44$	−0.236780	+	0.410115i	−0.0356959	+	0.0618272i
$45$	1.00000			0.149071
$46$	−0.473560			−0.0698227
$47$	−4.07177	+	7.05251i	−0.593929	+	1.02871i	0.399768	+	0.916616i	$0.369091\pi$
$47$	−4.07177	+	7.05251i	−0.593929	+	1.02871i	−0.993697	+	0.112099i	$0.964243\pi$
$48$	−0.500000	+	0.866025i	−0.0721688	+	0.125000i
$49$	14.1435			2.02051
$50$	1.00000			0.141421
$51$	2.27267	−	3.93637i	0.318237	−	0.551202i
$52$	0.263220	+	0.455910i	0.0365020	+	0.0632234i
$53$	−0.964114	+	1.66990i	−0.132431	+	0.229378i	−0.924613	−	0.380907i	$-0.875612\pi$
$53$	−0.964114	+	1.66990i	−0.132431	+	0.229378i	0.792182	+	0.610285i	$0.208945\pi$
$54$	−0.500000	−	0.866025i	−0.0680414	−	0.117851i
$55$	−0.236780	−	0.410115i	−0.0319274	−	0.0552999i
$56$	−4.59821			−0.614462
$57$	1.77267	−	3.98217i	0.234795	−	0.527451i
$58$	8.65109			1.13594
$59$	−3.00000	−	5.19615i	−0.390567	−	0.676481i	0.601958	−	0.798528i	$-0.294388\pi$
$59$	−3.00000	−	5.19615i	−0.390567	−	0.676481i	−0.992524	+	0.122047i	$0.961054\pi$
$60$	−0.500000	−	0.866025i	−0.0645497	−	0.111803i
$61$	−1.53589	+	2.66023i	−0.196650	+	0.340608i	−0.947440	−	0.319933i	$-0.896340\pi$
$61$	−1.53589	+	2.66023i	−0.196650	+	0.340608i	0.750790	+	0.660541i	$0.229673\pi$
$62$	0.263220	+	0.455910i	0.0334290	+	0.0579007i
$63$	2.29911	−	3.98217i	0.289660	−	0.501706i
$64$	1.00000			0.125000
$65$	−0.526440			−0.0652968
$66$	−0.236780	+	0.410115i	−0.0291456	+	0.0504817i
$67$	−4.53589	+	7.85638i	−0.554147	+	0.959810i	0.443823	+	0.896115i	$0.353622\pi$
$67$	−4.53589	+	7.85638i	−0.554147	+	0.959810i	−0.997969	+	0.0636955i	$0.979711\pi$
$68$	−4.54533			−0.551202
$69$	−0.473560			−0.0570100
$70$	2.29911	−	3.98217i	0.274796	−	0.475960i
$71$	2.27267	+	3.93637i	0.269716	+	0.467161i	0.968788	−	0.247889i	$-0.0797369\pi$
$71$	2.27267	+	3.93637i	0.269716	+	0.467161i	−0.699073	+	0.715051i	$0.746404\pi$
$72$	−0.500000	+	0.866025i	−0.0589256	+	0.102062i
$73$	1.46411	+	2.53592i	0.171362	+	0.296807i	0.938896	−	0.344201i	$-0.111850\pi$
$73$	1.46411	+	2.53592i	0.171362	+	0.296807i	−0.767535	+	0.641008i	$0.778517\pi$
$74$	0.500000	+	0.866025i	0.0581238	+	0.100673i
$75$	1.00000			0.115470
$76$	−4.33499	+	0.455910i	−0.497258	+	0.0522965i
$77$	−2.17753			−0.248153
$78$	0.263220	+	0.455910i	0.0298038	+	0.0516217i
$79$	0.736780	+	1.27614i	0.0828942	+	0.143577i	0.904492	−	0.426491i	$-0.140250\pi$
$79$	0.736780	+	1.27614i	0.0828942	+	0.143577i	−0.821598	+	0.570068i	$0.806917\pi$
$80$	−0.500000	+	0.866025i	−0.0559017	+	0.0968246i
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	5.63410	−	9.75854i	0.622182	−	1.07765i
$83$	4.10576			0.450666			0.225333	−	0.974282i	$-0.427653\pi$
$83$	4.10576			0.450666			0.225333	+	0.974282i	$0.427653\pi$
$84$	−4.59821			−0.501706
$85$	2.27267	−	3.93637i	0.246505	−	0.426960i
$86$	−6.33499	+	10.9725i	−0.683120	+	1.18320i
$87$	8.65109			0.927494
$88$	0.473560			0.0504817
$89$	0.964114	−	1.66990i	0.102196	−	0.177009i	−0.810393	−	0.585886i	$-0.800746\pi$
$89$	0.964114	−	1.66990i	0.102196	−	0.177009i	0.912589	+	0.408878i	$0.134080\pi$
$90$	−0.500000	−	0.866025i	−0.0527046	−	0.0912871i
$91$	−1.21034	+	2.09637i	−0.126878	+	0.219759i
$92$	0.236780	+	0.410115i	0.0246860	+	0.0427575i
$93$	0.263220	+	0.455910i	0.0272946	+	0.0472757i
$94$	8.14354			0.839942
$95$	1.77267	−	3.98217i	0.181872	−	0.408562i
$96$	1.00000			0.102062
$97$	−8.79911	−	15.2405i	−0.893414	−	1.54744i	−0.835756	−	0.549102i	$-0.814970\pi$
$97$	−8.79911	−	15.2405i	−0.893414	−	1.54744i	−0.0576582	−	0.998336i	$-0.518363\pi$
$98$	−7.07177	−	12.2487i	−0.714357	−	1.23730i
$99$	−0.236780	+	0.410115i	−0.0237973	+	0.0412181i
$100$	−0.500000	−	0.866025i	−0.0500000	−	0.0866025i
$101$	−6.59821	+	11.4284i	−0.656547	+	1.13717i	0.324957	+	0.945729i	$0.394650\pi$
$101$	−6.59821	+	11.4284i	−0.656547	+	1.13717i	−0.981504	+	0.191443i	$0.938683\pi$
$102$	−4.54533			−0.450055
$103$	−12.7418			−1.25548			−0.627741	−	0.778422i	$-0.716020\pi$
$103$	−12.7418			−1.25548			−0.627741	+	0.778422i	$0.716020\pi$
$104$	0.263220	−	0.455910i	0.0258108	−	0.0447057i
$105$	2.29911	−	3.98217i	0.224370	−	0.388620i
$106$	1.92823			0.187286
$107$	−10.7946			−1.04356			−0.521778	−	0.853081i	$-0.674731\pi$
$107$	−10.7946			−1.04356			−0.521778	+	0.853081i	$0.674731\pi$
$108$	−0.500000	+	0.866025i	−0.0481125	+	0.0833333i
$109$	−3.27267	−	5.66842i	−0.313465	−	0.542936i	0.665645	−	0.746268i	$-0.268156\pi$
$109$	−3.27267	−	5.66842i	−0.313465	−	0.542936i	−0.979110	+	0.203332i	$0.934823\pi$
$110$	−0.236780	+	0.410115i	−0.0225761	+	0.0391030i
$111$	0.500000	+	0.866025i	0.0474579	+	0.0821995i
$112$	2.29911	+	3.98217i	0.217245	+	0.376279i
$113$	16.7946			1.57991			0.789953	−	0.613167i	$-0.210105\pi$
$113$	16.7946			1.57991			0.789953	+	0.613167i	$0.210105\pi$
$114$	−4.33499	+	0.455910i	−0.406009	+	0.0426999i
$115$	−0.473560			−0.0441597
$116$	−4.32555	−	7.49206i	−0.401617	−	0.695621i
$117$	0.263220	+	0.455910i	0.0243347	+	0.0421489i
$118$	−3.00000	+	5.19615i	−0.276172	+	0.478345i
$119$	−10.4502	−	18.1003i	−0.957968	−	1.65925i
$120$	−0.500000	+	0.866025i	−0.0456435	+	0.0790569i
$121$	−10.7757			−0.979613
$122$	3.07177			0.278105
$123$	5.63410	−	9.75854i	0.508009	−	0.879898i
$124$	0.263220	−	0.455910i	0.0236378	−	0.0409419i
$125$	1.00000			0.0894427
$126$	−4.59821			−0.409641
$127$	−7.10766	+	12.3108i	−0.630703	+	1.09241i	0.356706	+	0.934217i	$0.383900\pi$
$127$	−7.10766	+	12.3108i	−0.630703	+	1.09241i	−0.987408	+	0.158192i	$0.949433\pi$
$128$	−0.500000	−	0.866025i	−0.0441942	−	0.0765466i
$129$	−6.33499	+	10.9725i	−0.557765	+	0.966077i
$130$	0.263220	+	0.455910i	0.0230859	+	0.0399860i
$131$	−7.43320	−	12.8747i	−0.649442	−	1.12487i	−0.983256	−	0.182227i	$-0.941669\pi$
$131$	−7.43320	−	12.8747i	−0.649442	−	1.12487i	0.333815	−	0.942639i	$-0.391664\pi$
$132$	0.473560			0.0412181
$133$	−11.7821	−	16.2145i	−1.02164	−	1.40597i
$134$	9.07177			0.783682
$135$	−0.500000	−	0.866025i	−0.0430331	−	0.0745356i
$136$	2.27267	+	3.93637i	0.194879	+	0.337541i
$137$	−4.66998	+	8.08865i	−0.398983	+	0.691060i	−0.993601	−	0.112949i	$-0.963970\pi$
$137$	−4.66998	+	8.08865i	−0.398983	+	0.691060i	0.594617	+	0.804009i	$0.297304\pi$
$138$	0.236780	+	0.410115i	0.0201561	+	0.0349113i
$139$	−2.26322	+	3.92001i	−0.191964	+	0.332491i	−0.945901	−	0.324455i	$-0.894819\pi$
$139$	−2.26322	+	3.92001i	−0.191964	+	0.332491i	0.753937	+	0.656947i	$0.228152\pi$
$140$	−4.59821			−0.388620
$141$	8.14354			0.685810
$142$	2.27267	−	3.93637i	0.190718	−	0.330333i
$143$	0.124650	−	0.215901i	0.0104238	−	0.0180545i
$144$	1.00000			0.0833333
$145$	8.65109			0.718434
$146$	1.46411	−	2.53592i	0.121171	−	0.209874i
$147$	−7.07177	−	12.2487i	−0.583270	−	1.01025i
$148$	0.500000	−	0.866025i	0.0410997	−	0.0711868i
$149$	1.20089	+	2.08001i	0.0983811	+	0.170401i	0.911015	−	0.412374i	$-0.135300\pi$
$149$	1.20089	+	2.08001i	0.0983811	+	0.170401i	−0.812634	+	0.582775i	$0.801967\pi$
$150$	−0.500000	−	0.866025i	−0.0408248	−	0.0707107i
$151$	−15.7418			−1.28105			−0.640523	−	0.767939i	$-0.721282\pi$
$151$	−15.7418			−1.28105			−0.640523	+	0.767939i	$0.721282\pi$
$152$	2.56233	+	3.52626i	0.207832	+	0.286017i
$153$	−4.54533			−0.367468
$154$	1.08876	+	1.88580i	0.0877352	+	0.151962i
$155$	0.263220	+	0.455910i	0.0211423	+	0.0366196i
$156$	0.263220	−	0.455910i	0.0210745	−	0.0365020i
$157$	4.09821	+	7.09831i	0.327073	+	0.566507i	0.981930	−	0.189246i	$-0.0606044\pi$
$157$	4.09821	+	7.09831i	0.327073	+	0.566507i	−0.654857	+	0.755753i	$0.727271\pi$
$158$	0.736780	−	1.27614i	0.0586151	−	0.101524i
$159$	1.92823			0.152919
$160$	1.00000			0.0790569
$161$	−1.08876	+	1.88580i	−0.0858067	+	0.148622i
$162$	−0.500000	+	0.866025i	−0.0392837	+	0.0680414i
$163$	15.5793			1.22027			0.610133	−	0.792299i	$-0.291116\pi$
$163$	15.5793			1.22027			0.610133	+	0.792299i	$0.291116\pi$
$164$	−11.2682			−0.879898
$165$	−0.236780	+	0.410115i	−0.0184333	+	0.0319274i
$166$	−2.05288	−	3.55569i	−0.159334	−	0.275975i
$167$	−6.23678	+	10.8024i	−0.482617	+	0.835916i	−0.999801	−	0.0199577i	$-0.993647\pi$
$167$	−6.23678	+	10.8024i	−0.482617	+	0.835916i	0.517184	+	0.855874i	$0.326980\pi$
$168$	2.29911	+	3.98217i	0.177380	+	0.307231i
$169$	6.36143	+	11.0183i	0.489341	+	0.847563i
$170$	−4.54533			−0.348611
$171$	−4.33499	+	0.455910i	−0.331505	+	0.0348643i
$172$	12.6700			0.966077
$173$	−7.56233	−	13.0983i	−0.574953	−	0.995848i	−0.996047	−	0.0888306i	$-0.971687\pi$
$173$	−7.56233	−	13.0983i	−0.574953	−	0.995848i	0.421094	−	0.907017i	$-0.361646\pi$
$174$	−4.32555	−	7.49206i	−0.327919	−	0.567972i
$175$	2.29911	−	3.98217i	0.173796	−	0.301024i
$176$	−0.236780	−	0.410115i	−0.0178480	−	0.0309136i
$177$	−3.00000	+	5.19615i	−0.225494	+	0.390567i
$178$	−1.92823			−0.144527
$179$	−1.42068			−0.106187			−0.0530933	−	0.998590i	$-0.516908\pi$
$179$	−1.42068			−0.106187			−0.0530933	+	0.998590i	$0.516908\pi$
$180$	−0.500000	+	0.866025i	−0.0372678	+	0.0645497i
$181$	4.39732	−	7.61637i	0.326850	−	0.566121i	−0.655035	−	0.755598i	$-0.727346\pi$
$181$	4.39732	−	7.61637i	0.326850	−	0.566121i	0.981885	+	0.189478i	$0.0606795\pi$
$182$	2.42068			0.179433
$183$	3.07177			0.227072
$184$	0.236780	−	0.410115i	0.0174557	−	0.0302341i
$185$	0.500000	+	0.866025i	0.0367607	+	0.0636715i
$186$	0.263220	−	0.455910i	0.0193002	−	0.0334290i
$187$	1.07624	+	1.86411i	0.0787028	+	0.136317i
$188$	−4.07177	−	7.05251i	−0.296964	−	0.514357i
$189$	−4.59821			−0.334471
$190$	−4.33499	+	0.455910i	−0.314493	+	0.0330752i
$191$	9.15864			0.662696			0.331348	−	0.943509i	$-0.392497\pi$
$191$	9.15864			0.662696			0.331348	+	0.943509i	$0.392497\pi$
$192$	−0.500000	−	0.866025i	−0.0360844	−	0.0625000i
$193$	−0.588765	−	1.01977i	−0.0423802	−	0.0734047i	0.844057	−	0.536253i	$-0.180161\pi$
$193$	−0.588765	−	1.01977i	−0.0423802	−	0.0734047i	−0.886437	+	0.462848i	$0.846827\pi$
$194$	−8.79911	+	15.2405i	−0.631739	+	1.09420i
$195$	0.263220	+	0.455910i	0.0188496	+	0.0326484i
$196$	−7.07177	+	12.2487i	−0.505127	+	0.874905i
$197$	12.2153			0.870305			0.435153	−	0.900357i	$-0.356694\pi$
$197$	12.2153			0.870305			0.435153	+	0.900357i	$0.356694\pi$
$198$	0.473560			0.0336545
$199$	−1.06233	+	1.84000i	−0.0753062	+	0.130434i	−0.901219	−	0.433363i	$-0.857327\pi$
$199$	−1.06233	+	1.84000i	−0.0753062	+	0.130434i	0.825913	+	0.563797i	$0.190660\pi$
$200$	−0.500000	+	0.866025i	−0.0353553	+	0.0612372i
$201$	9.07177			0.639873
$202$	13.1964			0.928497
$203$	19.8898	−	34.4501i	1.39599	−	2.41792i
$204$	2.27267	+	3.93637i	0.159118	+	0.275601i
$205$	5.63410	−	9.75854i	0.393502	−	0.681566i
$206$	6.37088	+	11.0347i	0.443880	+	0.768823i
$207$	0.236780	+	0.410115i	0.0164574	+	0.0285050i
$208$	−0.526440			−0.0365020
$209$	1.21342	+	1.66990i	0.0839337	+	0.115509i
$210$	−4.59821			−0.317307
$211$	9.49553	+	16.4467i	0.653699	+	1.13224i	0.982218	+	0.187743i	$0.0601171\pi$
$211$	9.49553	+	16.4467i	0.653699	+	1.13224i	−0.328519	+	0.944497i	$0.606550\pi$
$212$	−0.964114	−	1.66990i	−0.0662157	−	0.114689i
$213$	2.27267	−	3.93637i	0.155720	−	0.269716i
$214$	5.39732	+	9.34843i	0.368953	+	0.639045i
$215$	−6.33499	+	10.9725i	−0.432043	+	0.748320i
$216$	1.00000			0.0680414
$217$	2.42068			0.164327
$218$	−3.27267	+	5.66842i	−0.221653	+	0.383914i
$219$	1.46411	−	2.53592i	0.0989357	−	0.171362i
$220$	0.473560			0.0319274
$221$	2.39284			0.160960
$222$	0.500000	−	0.866025i	0.0335578	−	0.0581238i
$223$	−10.4238	−	18.0545i	−0.698026	−	1.20902i	−0.969150	−	0.246472i	$-0.920729\pi$
$223$	−10.4238	−	18.0545i	−0.698026	−	1.20902i	0.271123	−	0.962545i	$-0.412605\pi$
$224$	2.29911	−	3.98217i	0.153615	−	0.266070i
$225$	−0.500000	−	0.866025i	−0.0333333	−	0.0577350i
$226$	−8.39732	−	14.5446i	−0.558581	−	0.967491i
$227$	4.79463			0.318231			0.159115	−	0.987260i	$-0.449136\pi$
$227$	4.79463			0.318231			0.159115	+	0.987260i	$0.449136\pi$
$228$	2.56233	+	3.52626i	0.169694	+	0.233532i
$229$	−18.5264			−1.22426			−0.612131	−	0.790757i	$-0.709687\pi$
$229$	−18.5264			−1.22426			−0.612131	+	0.790757i	$0.709687\pi$
$230$	0.236780	+	0.410115i	0.0156128	+	0.0270422i
$231$	1.08876	+	1.88580i	0.0716355	+	0.124076i
$232$	−4.32555	+	7.49206i	−0.283986	+	0.491878i
$233$	12.7229	+	22.0366i	0.833502	+	1.44367i	0.895244	+	0.445576i	$0.147001\pi$
$233$	12.7229	+	22.0366i	0.833502	+	1.44367i	−0.0617416	+	0.998092i	$0.519665\pi$
$234$	0.263220	−	0.455910i	0.0172072	−	0.0298038i
$235$	8.14354			0.531226
$236$	6.00000			0.390567
$237$	0.736780	−	1.27614i	0.0478590	−	0.0828942i
$238$	−10.4502	+	18.1003i	−0.677386	+	1.17327i
$239$	−9.33996			−0.604152			−0.302076	−	0.953284i	$-0.597680\pi$
$239$	−9.33996			−0.604152			−0.302076	+	0.953284i	$0.597680\pi$
$240$	1.00000			0.0645497
$241$	7.21034	−	12.4887i	0.464459	−	0.804466i	−0.534718	−	0.845031i	$-0.679582\pi$
$241$	7.21034	−	12.4887i	0.464459	−	0.804466i	0.999177	+	0.0405642i	$0.0129155\pi$
$242$	5.38787	+	9.33207i	0.346345	+	0.599888i
$243$	−0.500000	+	0.866025i	−0.0320750	+	0.0555556i
$244$	−1.53589	−	2.66023i	−0.0983250	−	0.170304i
$245$	−7.07177	−	12.2487i	−0.451799	−	0.782539i
$246$	−11.2682			−0.718434
$247$	2.28211	−	0.240009i	0.145207	−	0.0152714i
$248$	−0.526440			−0.0334290
$249$	−2.05288	−	3.55569i	−0.130096	−	0.225333i
$250$	−0.500000	−	0.866025i	−0.0316228	−	0.0547723i
$251$	11.6171	−	20.1214i	0.733265	−	1.27005i	−0.222215	−	0.974998i	$-0.571329\pi$
$251$	11.6171	−	20.1214i	0.733265	−	1.27005i	0.955480	−	0.295055i	$-0.0953379\pi$
$252$	2.29911	+	3.98217i	0.144830	+	0.250853i
$253$	0.112130	−	0.194214i	0.00704953	−	0.0122101i
$254$	14.2153			0.891948
$255$	−4.54533			−0.284640
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−3.00000	+	5.19615i	−0.187135	+	0.324127i	−0.944294	−	0.329104i	$-0.893253\pi$
$257$	−3.00000	+	5.19615i	−0.187135	+	0.324127i	0.757159	+	0.653231i	$0.226587\pi$
$258$	12.6700			0.788799
$259$	4.59821			0.285719
$260$	0.263220	−	0.455910i	0.0163242	−	0.0282743i
$261$	−4.32555	−	7.49206i	−0.267745	−	0.463747i
$262$	−7.43320	+	12.8747i	−0.459225	+	0.795401i
$263$	11.2897	+	19.5543i	0.696150	+	1.20577i	0.969791	+	0.243936i	$0.0784386\pi$
$263$	11.2897	+	19.5543i	0.696150	+	1.20577i	−0.273641	+	0.961832i	$0.588228\pi$
$264$	−0.236780	−	0.410115i	−0.0145728	−	0.0252408i
$265$	1.92823			0.118450
$266$	−8.15109	+	18.3108i	−0.499775	+	1.12271i
$267$	−1.92823			−0.118006
$268$	−4.53589	−	7.85638i	−0.277073	−	0.479905i
$269$	0.253774	+	0.439550i	0.0154729	+	0.0267998i	0.873658	−	0.486540i	$-0.161741\pi$
$269$	0.253774	+	0.439550i	0.0154729	+	0.0267998i	−0.858185	+	0.513340i	$0.828408\pi$
$270$	−0.500000	+	0.866025i	−0.0304290	+	0.0527046i
$271$	−13.1247	−	22.7326i	−0.797266	−	1.38090i	−0.921390	−	0.388638i	$-0.872946\pi$
$271$	−13.1247	−	22.7326i	−0.797266	−	1.38090i	0.124125	−	0.992267i	$-0.460388\pi$
$272$	2.27267	−	3.93637i	0.137801	−	0.238678i
$273$	2.42068			0.146506
$274$	9.33996			0.564248
$275$	−0.236780	+	0.410115i	−0.0142784	+	0.0247309i
$276$	0.236780	−	0.410115i	0.0142525	−	0.0246860i
$277$	32.2493			1.93767			0.968836	−	0.247702i	$-0.0796753\pi$
$277$	32.2493			1.93767			0.968836	+	0.247702i	$0.0796753\pi$
$278$	4.52644			0.271478
$279$	0.263220	−	0.455910i	0.0157586	−	0.0272946i
$280$	2.29911	+	3.98217i	0.137398	+	0.237980i
$281$	0.107657	−	0.186467i	0.00642225	−	0.0111237i	−0.862796	−	0.505552i	$-0.831289\pi$
$281$	0.107657	−	0.186467i	0.00642225	−	0.0111237i	0.869219	+	0.494428i	$0.164622\pi$
$282$	−4.07177	−	7.05251i	−0.242470	−	0.419971i
$283$	14.2153	+	24.6216i	0.845013	+	1.46360i	0.885610	+	0.464429i	$0.153741\pi$
$283$	14.2153	+	24.6216i	0.845013	+	1.46360i	−0.0405976	+	0.999176i	$0.512926\pi$
$284$	−4.54533			−0.269716
$285$	−4.33499	+	0.455910i	−0.256783	+	0.0270058i
$286$	−0.249301			−0.0147415
$287$	−25.9068	−	44.8718i	−1.52923	−	2.64870i
$288$	−0.500000	−	0.866025i	−0.0294628	−	0.0510310i
$289$	−1.83002	+	3.16968i	−0.107648	+	0.186452i
$290$	−4.32555	−	7.49206i	−0.254005	−	0.439949i
$291$	−8.79911	+	15.2405i	−0.515813	+	0.893414i
$292$	−2.92823			−0.171362
$293$	23.2682			1.35934			0.679671	−	0.733517i	$-0.262122\pi$
$293$	23.2682			1.35934			0.679671	+	0.733517i	$0.262122\pi$
$294$	−7.07177	+	12.2487i	−0.412434	+	0.714357i
$295$	−3.00000	+	5.19615i	−0.174667	+	0.302532i
$296$	−1.00000			−0.0581238
$297$	0.473560			0.0274788
$298$	1.20089	−	2.08001i	0.0695660	−	0.120492i
$299$	−0.124650	−	0.215901i	−0.00720872	−	0.0124859i
$300$	−0.500000	+	0.866025i	−0.0288675	+	0.0500000i
$301$	29.1296	+	50.4540i	1.67900	+	2.90812i
$302$	7.87088	+	13.6328i	0.452918	+	0.784477i
$303$	13.1964			0.758115
$304$	1.77267	−	3.98217i	0.101669	−	0.228393i
$305$	3.07177			0.175889
$306$	2.27267	+	3.93637i	0.129920	+	0.225027i
$307$	−6.99553	−	12.1166i	−0.399256	−	0.691531i	0.594378	−	0.804185i	$-0.297398\pi$
$307$	−6.99553	−	12.1166i	−0.399256	−	0.691531i	−0.993634	+	0.112654i	$0.964065\pi$
$308$	1.08876	−	1.88580i	0.0620381	−	0.107453i
$309$	6.37088	+	11.0347i	0.362426	+	0.627741i
$310$	0.263220	−	0.455910i	0.0149499	−	0.0258940i
$311$	31.4457			1.78312			0.891562	−	0.452899i	$-0.149610\pi$
$311$	31.4457			1.78312			0.891562	+	0.452899i	$0.149610\pi$
$312$	−0.526440			−0.0298038
$313$	−15.6171	+	27.0496i	−0.882731	+	1.52893i	−0.0344382	+	0.999407i	$0.510964\pi$
$313$	−15.6171	+	27.0496i	−0.882731	+	1.52893i	−0.848293	+	0.529528i	$0.822369\pi$
$314$	4.09821	−	7.09831i	0.231275	−	0.400581i
$315$	−4.59821			−0.259080
$316$	−1.47356			−0.0828942
$317$	−10.1794	+	17.6313i	−0.571734	+	0.990272i	0.424654	+	0.905355i	$0.360396\pi$
$317$	−10.1794	+	17.6313i	−0.571734	+	0.990272i	−0.996388	+	0.0849162i	$0.972938\pi$
$318$	−0.964114	−	1.66990i	−0.0540649	−	0.0936431i
$319$	−2.04841	+	3.54794i	−0.114689	+	0.198647i
$320$	−0.500000	−	0.866025i	−0.0279508	−	0.0484123i
$321$	5.39732	+	9.34843i	0.301249	+	0.521778i
$322$	2.17753			0.121349
$323$	−8.05735	+	18.1003i	−0.448323	+	1.00713i
$324$	1.00000			0.0555556
$325$	0.263220	+	0.455910i	0.0146008	+	0.0252893i
$326$	−7.78966	−	13.4921i	−0.431429	−	0.747258i
$327$	−3.27267	+	5.66842i	−0.180979	+	0.313465i
$328$	5.63410	+	9.75854i	0.311091	+	0.538825i
$329$	18.7229	−	32.4289i	1.03222	−	1.78787i
$330$	0.473560			0.0260686
$331$	−3.40179			−0.186979			−0.0934896	−	0.995620i	$-0.529802\pi$
$331$	−3.40179			−0.186979			−0.0934896	+	0.995620i	$0.529802\pi$
$332$	−2.05288	+	3.55569i	−0.112666	+	0.195144i
$333$	0.500000	−	0.866025i	0.0273998	−	0.0474579i
$334$	12.4736			0.682523
$335$	9.07177			0.495644
$336$	2.29911	−	3.98217i	0.125426	−	0.217245i
$337$	5.40676	+	9.36479i	0.294525	+	0.510132i	0.974874	−	0.222756i	$-0.0715052\pi$
$337$	5.40676	+	9.36479i	0.294525	+	0.510132i	−0.680349	+	0.732888i	$0.738172\pi$
$338$	6.36143	−	11.0183i	0.346016	−	0.599318i
$339$	−8.39732	−	14.5446i	−0.456080	−	0.789953i
$340$	2.27267	+	3.93637i	0.123253	+	0.213480i
$341$	−0.249301			−0.0135004
$342$	2.56233	+	3.52626i	0.138555	+	0.190678i
$343$	−32.8475			−1.77360
$344$	−6.33499	−	10.9725i	−0.341560	−	0.591599i
$345$	0.236780	+	0.410115i	0.0127478	+	0.0220799i
$346$	−7.56233	+	13.0983i	−0.406553	+	0.704171i
$347$	4.57932	+	7.93161i	0.245831	+	0.425791i	0.962365	−	0.271761i	$-0.0876059\pi$
$347$	4.57932	+	7.93161i	0.245831	+	0.425791i	−0.716534	+	0.697552i	$0.754273\pi$
$348$	−4.32555	+	7.49206i	−0.231874	+	0.401617i
$349$	4.08687			0.218765			0.109382	−	0.994000i	$-0.465113\pi$
$349$	4.08687			0.218765			0.109382	+	0.994000i	$0.465113\pi$
$350$	−4.59821			−0.245785
$351$	0.263220	−	0.455910i	0.0140496	−	0.0243347i
$352$	−0.236780	+	0.410115i	−0.0126204	+	0.0218592i
$353$	−17.8097			−0.947916			−0.473958	−	0.880547i	$-0.657175\pi$
$353$	−17.8097			−0.947916			−0.473958	+	0.880547i	$0.657175\pi$
$354$	6.00000			0.318896
$355$	2.27267	−	3.93637i	0.120621	−	0.208921i
$356$	0.964114	+	1.66990i	0.0510980	+	0.0885043i
$357$	−10.4502	+	18.1003i	−0.553083	+	0.957968i
$358$	0.710340	+	1.23035i	0.0375427	+	0.0650258i
$359$	4.79911	+	8.31229i	0.253287	+	0.438706i	0.964429	−	0.264343i	$-0.0851549\pi$
$359$	4.79911	+	8.31229i	0.253287	+	0.438706i	−0.711142	+	0.703049i	$0.751822\pi$
$360$	1.00000			0.0527046
$361$	−5.86898	+	18.0708i	−0.308894	+	0.951097i
$362$	−8.79463			−0.462236
$363$	5.38787	+	9.33207i	0.282790	+	0.489806i
$364$	−1.21034	−	2.09637i	−0.0634391	−	0.109880i
$365$	1.46411	−	2.53592i	0.0766353	−	0.132736i
$366$	−1.53589	−	2.66023i	−0.0802820	−	0.139053i
$367$	−0.683901	+	1.18455i	−0.0356993	+	0.0618330i	−0.883323	−	0.468765i	$-0.844699\pi$
$367$	−0.683901	+	1.18455i	−0.0356993	+	0.0618330i	0.847624	+	0.530598i	$0.178033\pi$
$368$	−0.473560			−0.0246860
$369$	−11.2682			−0.586599
$370$	0.500000	−	0.866025i	0.0259938	−	0.0450225i
$371$	4.43320	−	7.67853i	0.230160	−	0.398649i
$372$	−0.526440			−0.0272946
$373$	−24.6171			−1.27463			−0.637313	−	0.770605i	$-0.719954\pi$
$373$	−24.6171			−1.27463			−0.637313	+	0.770605i	$0.719954\pi$
$374$	1.07624	−	1.86411i	0.0556513	−	0.0963908i
$375$	−0.500000	−	0.866025i	−0.0258199	−	0.0447214i
$376$	−4.07177	+	7.05251i	−0.209986	+	0.363706i
$377$	2.27714	+	3.94412i	0.117279	+	0.203133i
$378$	2.29911	+	3.98217i	0.118253	+	0.204821i
$379$	15.7606			0.809570			0.404785	−	0.914412i	$-0.367346\pi$
$379$	15.7606			0.809570			0.404785	+	0.914412i	$0.367346\pi$
$380$	2.56233	+	3.52626i	0.131445	+	0.180893i
$381$	14.2153			0.728273
$382$	−4.57932	−	7.93161i	−0.234298	−	0.405817i
$383$	−10.0718	−	17.4448i	−0.514643	−	0.891389i	−0.999856	−	0.0169922i	$-0.994591\pi$
$383$	−10.0718	−	17.4448i	−0.514643	−	0.891389i	0.485212	−	0.874396i	$-0.338742\pi$
$384$	−0.500000	+	0.866025i	−0.0255155	+	0.0441942i
$385$	1.08876	+	1.88580i	0.0554886	+	0.0961091i
$386$	−0.588765	+	1.01977i	−0.0299673	+	0.0519050i
$387$	12.6700			0.644051
$388$	17.5982			0.893414
$389$	10.3255	−	17.8844i	0.523526	−	0.906773i	−0.476099	−	0.879392i	$-0.657950\pi$
$389$	10.3255	−	17.8844i	0.523526	−	0.906773i	0.999625	−	0.0273819i	$-0.00871701\pi$
$390$	0.263220	−	0.455910i	0.0133287	−	0.0230859i
$391$	2.15249			0.108856
$392$	14.1435			0.714357
$393$	−7.43320	+	12.8747i	−0.374955	+	0.649442i
$394$	−6.10766	−	10.5788i	−0.307699	−	0.532951i
$395$	0.736780	−	1.27614i	0.0370714	−	0.0642096i
$396$	−0.236780	−	0.410115i	−0.0118986	−	0.0206091i
$397$	−13.6435	−	23.6313i	−0.684750	−	1.18602i	−0.973515	−	0.228622i	$-0.926578\pi$
$397$	−13.6435	−	23.6313i	−0.684750	−	1.18602i	0.288766	−	0.957400i	$-0.406755\pi$
$398$	2.12465			0.106499
$399$	−8.15109	+	18.3108i	−0.408065	+	0.916689i
$400$	1.00000			0.0500000
$401$	−17.1435	−	29.6935i	−0.856108	−	1.48282i	−0.875614	−	0.483012i	$-0.839543\pi$
$401$	−17.1435	−	29.6935i	−0.856108	−	1.48282i	0.0195060	−	0.999810i	$-0.493791\pi$
$402$	−4.53589	−	7.85638i	−0.226229	−	0.391841i
$403$	−0.138569	+	0.240009i	−0.00690263	+	0.0119557i
$404$	−6.59821	−	11.4284i	−0.328273	−	0.568586i
$405$	−0.500000	+	0.866025i	−0.0248452	+	0.0430331i
$406$	−39.7795			−1.97423
$407$	−0.473560			−0.0234735
$408$	2.27267	−	3.93637i	0.112514	−	0.194879i
$409$	10.3803	−	17.9792i	0.513274	−	0.889016i	−0.486608	−	0.873621i	$-0.661766\pi$
$409$	10.3803	−	17.9792i	0.513274	−	0.889016i	0.999881	−	0.0153958i	$-0.00490083\pi$
$410$	−11.2682			−0.556496
$411$	9.33996			0.460706
$412$	6.37088	−	11.0347i	0.313871	−	0.543640i
$413$	13.7946	+	23.8930i	0.678789	+	1.17570i
$414$	0.236780	−	0.410115i	0.0116371	−	0.0201561i
$415$	−2.05288	−	3.55569i	−0.100772	−	0.174542i
$416$	0.263220	+	0.455910i	0.0129054	+	0.0223528i
$417$	4.52644			0.221661
$418$	0.839464	−	1.88580i	0.0410595	−	0.0922373i
$419$	−27.5642			−1.34660			−0.673300	−	0.739369i	$-0.735124\pi$
$419$	−27.5642			−1.34660			−0.673300	+	0.739369i	$0.735124\pi$
$420$	2.29911	+	3.98217i	0.112185	+	0.194310i
$421$	2.72733	+	4.72388i	0.132922	+	0.230228i	0.924802	−	0.380449i	$-0.124231\pi$
$421$	2.72733	+	4.72388i	0.132922	+	0.230228i	−0.791880	+	0.610677i	$0.790897\pi$
$422$	9.49553	−	16.4467i	0.462235	−	0.800615i
$423$	−4.07177	−	7.05251i	−0.197976	−	0.342905i
$424$	−0.964114	+	1.66990i	−0.0468215	+	0.0810973i
$425$	−4.54533			−0.220481
$426$	−4.54533			−0.220222
$427$	7.06233	−	12.2323i	0.341770	−	0.591963i
$428$	5.39732	−	9.34843i	0.260889	−	0.451873i
$429$	−0.249301			−0.0120364
$430$	12.6700			0.611001
$431$	20.0484	−	34.7249i	0.965698	−	1.67264i	0.257969	−	0.966153i	$-0.416947\pi$
$431$	20.0484	−	34.7249i	0.965698	−	1.67264i	0.707729	−	0.706484i	$-0.249720\pi$
$432$	−0.500000	−	0.866025i	−0.0240563	−	0.0416667i
$433$	−5.60766	+	9.71275i	−0.269487	+	0.466765i	−0.968729	−	0.248120i	$-0.920187\pi$
$433$	−5.60766	+	9.71275i	−0.269487	+	0.466765i	0.699243	+	0.714884i	$0.253521\pi$
$434$	−1.21034	−	2.09637i	−0.0580982	−	0.100629i
$435$	−4.32555	−	7.49206i	−0.207394	−	0.359217i
$436$	6.54533			0.313465
$437$	2.05288	−	0.215901i	0.0982025	−	0.0103279i
$438$	−2.92823			−0.139916
$439$	−7.18698	−	12.4482i	−0.343016	−	0.594121i	0.641976	−	0.766725i	$-0.278115\pi$
$439$	−7.18698	−	12.4482i	−0.343016	−	0.594121i	−0.984991	+	0.172605i	$0.944782\pi$
$440$	−0.236780	−	0.410115i	−0.0112881	−	0.0195515i
$441$	−7.07177	+	12.2487i	−0.336751	+	0.583270i
$442$	−1.19642	−	2.07226i	−0.0569080	−	0.0985675i
$443$	3.25377	−	5.63570i	0.154591	−	0.267760i	−0.778319	−	0.627869i	$-0.783927\pi$
$443$	3.25377	−	5.63570i	0.154591	−	0.267760i	0.932910	+	0.360109i	$0.117261\pi$
$444$	−1.00000			−0.0474579
$445$	−1.92823			−0.0914068
$446$	−10.4238	+	18.0545i	−0.493579	+	0.854904i
$447$	1.20089	−	2.08001i	0.0568004	−	0.0983811i
$448$	−4.59821			−0.217245
$449$	−1.92823			−0.0909988			−0.0454994	−	0.998964i	$-0.514488\pi$
$449$	−1.92823			−0.0909988			−0.0454994	+	0.998964i	$0.514488\pi$
$450$	−0.500000	+	0.866025i	−0.0235702	+	0.0408248i
$451$	2.66808	+	4.62126i	0.125635	+	0.217607i
$452$	−8.39732	+	14.5446i	−0.394977	+	0.684119i
$453$	7.87088	+	13.6328i	0.369806	+	0.640523i
$454$	−2.39732	−	4.15227i	−0.112512	−	0.194876i
$455$	2.42068			0.113483
$456$	1.77267	−	3.98217i	0.0830127	−	0.186482i
$457$	−29.2531			−1.36840			−0.684201	−	0.729293i	$-0.739849\pi$
$457$	−29.2531			−1.36840			−0.684201	+	0.729293i	$0.739849\pi$
$458$	9.26322	+	16.0444i	0.432842	+	0.749704i
$459$	2.27267	+	3.93637i	0.106079	+	0.183734i
$460$	0.236780	−	0.410115i	0.0110399	−	0.0191217i
$461$	0.473560	+	0.820230i	0.0220559	+	0.0382019i	0.876843	−	0.480777i	$-0.159645\pi$
$461$	0.473560	+	0.820230i	0.0220559	+	0.0382019i	−0.854787	+	0.518979i	$0.826312\pi$
$462$	1.08876	−	1.88580i	0.0506539	−	0.0877352i
$463$	16.7418			0.778055			0.389028	−	0.921226i	$-0.372811\pi$
$463$	16.7418			0.778055			0.389028	+	0.921226i	$0.372811\pi$
$464$	8.65109			0.401617
$465$	0.263220	−	0.455910i	0.0122065	−	0.0211423i
$466$	12.7229	−	22.0366i	0.589375	−	1.02083i
$467$	19.7040			0.911791			0.455895	−	0.890033i	$-0.349319\pi$
$467$	19.7040			0.911791			0.455895	+	0.890033i	$0.349319\pi$
$468$	−0.526440			−0.0243347
$469$	20.8570	−	36.1253i	0.963085	−	1.66811i
$470$	−4.07177	−	7.05251i	−0.187817	−	0.325308i
$471$	4.09821	−	7.09831i	0.188836	−	0.327073i
$472$	−3.00000	−	5.19615i	−0.138086	−	0.239172i
$473$	−3.00000	−	5.19615i	−0.137940	−	0.238919i
$474$	−1.47356			−0.0676829
$475$	−4.33499	+	0.455910i	−0.198903	+	0.0209186i
$476$	20.9004			0.957968
$477$	−0.964114	−	1.66990i	−0.0441438	−	0.0764593i
$478$	4.66998	+	8.08865i	0.213600	+	0.369966i
$479$	−15.3444	+	26.5773i	−0.701105	+	1.21435i	0.266974	+	0.963704i	$0.413976\pi$
$479$	−15.3444	+	26.5773i	−0.701105	+	1.21435i	−0.968079	+	0.250646i	$0.919357\pi$
$480$	−0.500000	−	0.866025i	−0.0228218	−	0.0395285i
$481$	−0.263220	+	0.455910i	−0.0120018	+	0.0207877i
$482$	−14.4207			−0.656844
$483$	2.17753			0.0990810
$484$	5.38787	−	9.33207i	0.244903	−	0.424185i
$485$	−8.79911	+	15.2405i	−0.399547	+	0.692035i
$486$	1.00000			0.0453609
$487$	−41.9103			−1.89914			−0.949569	−	0.313557i	$-0.898479\pi$
$487$	−41.9103			−1.89914			−0.949569	+	0.313557i	$0.898479\pi$
$488$	−1.53589	+	2.66023i	−0.0695263	+	0.120423i
$489$	−7.78966	−	13.4921i	−0.352261	−	0.610133i
$490$	−7.07177	+	12.2487i	−0.319470	+	0.553338i
$491$	7.81610	+	13.5379i	0.352736	+	0.610956i	0.986728	−	0.162384i	$-0.0519182\pi$
$491$	7.81610	+	13.5379i	0.352736	+	0.610956i	−0.633992	+	0.773340i	$0.718585\pi$
$492$	5.63410	+	9.75854i	0.254005	+	0.439949i
$493$	−39.3221			−1.77098
$494$	−1.34891	−	1.85636i	−0.0606903	−	0.0835217i
$495$	0.473560			0.0212850
$496$	0.263220	+	0.455910i	0.0118189	+	0.0204710i
$497$	−10.4502	−	18.1003i	−0.468755	−	0.811908i
$498$	−2.05288	+	3.55569i	−0.0919917	+	0.159334i
$499$	−0.102684	−	0.177854i	−0.00459676	−	0.00796183i	0.863718	−	0.503976i	$-0.168130\pi$
$499$	−0.102684	−	0.177854i	−0.00459676	−	0.00796183i	−0.868315	+	0.496014i	$0.834797\pi$
$500$	−0.500000	+	0.866025i	−0.0223607	+	0.0387298i
$501$	12.4736			0.557278
$502$	−23.2342			−1.03699
$503$	−1.81610	+	3.14558i	−0.0809759	+	0.140254i	−0.903669	−	0.428231i	$-0.859137\pi$
$503$	−1.81610	+	3.14558i	−0.0809759	+	0.140254i	0.822693	+	0.568485i	$0.192470\pi$
$504$	2.29911	−	3.98217i	0.102410	−	0.177380i
$505$	13.1964			0.587233
$506$	−0.224259			−0.00996954
$507$	6.36143	−	11.0183i	0.282521	−	0.489341i
$508$	−7.10766	−	12.3108i	−0.315351	−	0.546204i
$509$	−5.01889	+	8.69298i	−0.222458	+	0.385309i	−0.955554	−	0.294816i	$-0.904742\pi$
$509$	−5.01889	+	8.69298i	−0.222458	+	0.385309i	0.733095	+	0.680126i	$0.238075\pi$
$510$	2.27267	+	3.93637i	0.100635	+	0.174305i
$511$	−6.73231	−	11.6607i	−0.297820	−	0.515839i
$512$	1.00000			0.0441942
$513$	2.56233	+	3.52626i	0.113129	+	0.155688i
$514$	6.00000			0.264649
$515$	6.37088	+	11.0347i	0.280734	+	0.486246i
$516$	−6.33499	−	10.9725i	−0.278882	−	0.483039i
$517$	−1.92823	+	3.33979i	−0.0848034	+	0.146884i
$518$	−2.29911	−	3.98217i	−0.101017	−	0.174966i
$519$	−7.56233	+	13.0983i	−0.331949	+	0.574953i
$520$	−0.526440			−0.0230859
$521$	−6.24930			−0.273787			−0.136893	−	0.990586i	$-0.543712\pi$
$521$	−6.24930			−0.273787			−0.136893	+	0.990586i	$0.543712\pi$
$522$	−4.32555	+	7.49206i	−0.189324	+	0.327919i
$523$	−13.2776	+	22.9975i	−0.580591	+	1.00561i	0.414819	+	0.909904i	$0.363845\pi$
$523$	−13.2776	+	22.9975i	−0.580591	+	1.00561i	−0.995409	+	0.0957084i	$0.969488\pi$
$524$	14.8664			0.649442
$525$	−4.59821			−0.200682
$526$	11.2897	−	19.5543i	0.492253	−	0.852606i
$527$	−1.19642	−	2.07226i	−0.0521169	−	0.0902692i
$528$	−0.236780	+	0.410115i	−0.0103045	+	0.0178480i
$529$	11.3879	+	19.7244i	0.495125	+	0.857581i
$530$	−0.964114	−	1.66990i	−0.0418785	−	0.0725356i
$531$	6.00000			0.260378
$532$	19.9332	−	2.09637i	0.864214	−	0.0908892i
$533$	5.93202			0.256944
$534$	0.964114	+	1.66990i	0.0417213	+	0.0722634i
$535$	5.39732	+	9.34843i	0.233346	+	0.404168i
$536$	−4.53589	+	7.85638i	−0.195920	+	0.339344i
$537$	0.710340	+	1.23035i	0.0306535	+	0.0530933i
$538$	0.253774	−	0.439550i	0.0109410	−	0.0189503i
$539$	6.69782			0.288496
$540$	1.00000			0.0430331
$541$	15.0390	−	26.0482i	0.646575	−	1.11990i	−0.337360	−	0.941376i	$-0.609534\pi$
$541$	15.0390	−	26.0482i	0.646575	−	1.11990i	0.983935	−	0.178526i	$-0.0571328\pi$
$542$	−13.1247	+	22.7326i	−0.563752	+	0.976447i
$543$	−8.79463			−0.377414
$544$	−4.54533			−0.194879
$545$	−3.27267	+	5.66842i	−0.140186	+	0.242809i
$546$	−1.21034	−	2.09637i	−0.0517978	−	0.0897164i
$547$	3.26322	−	5.65206i	0.139525	−	0.241665i	−0.787792	−	0.615942i	$-0.788776\pi$
$547$	3.26322	−	5.65206i	0.139525	−	0.241665i	0.927317	+	0.374277i	$0.122109\pi$
$548$	−4.66998	−	8.08865i	−0.199492	−	0.345530i
$549$	−1.53589	−	2.66023i	−0.0655500	−	0.113536i
$550$	0.473560			0.0201927
$551$	−37.5024	+	3.94412i	−1.59766	+	0.168025i
$552$	−0.473560			−0.0201561
$553$	−3.38787	−	5.86796i	−0.144067	−	0.249531i
$554$	−16.1247	−	27.9287i	−0.685071	−	1.18658i
$555$	0.500000	−	0.866025i	0.0212238	−	0.0367607i
$556$	−2.26322	−	3.92001i	−0.0959819	−	0.166246i
$557$	15.1077	−	26.1672i	0.640132	−	1.10874i	−0.345271	−	0.938503i	$-0.612213\pi$
$557$	15.1077	−	26.1672i	0.640132	−	1.10874i	0.985403	−	0.170238i	$-0.0544537\pi$
$558$	−0.526440			−0.0222860
$559$	−6.66998			−0.282110
$560$	2.29911	−	3.98217i	0.0971549	−	0.168277i
$561$	1.07624	−	1.86411i	0.0454391	−	0.0787028i
$562$	−0.215313			−0.00908243
$563$	11.2342			0.473465			0.236733	−	0.971575i	$-0.423923\pi$
$563$	11.2342			0.473465			0.236733	+	0.971575i	$0.423923\pi$
$564$	−4.07177	+	7.05251i	−0.171452	+	0.296964i
$565$	−8.39732	−	14.5446i	−0.353278	−	0.611895i
$566$	14.2153	−	24.6216i	0.597514	−	1.03492i
$567$	2.29911	+	3.98217i	0.0965533	+	0.167235i
$568$	2.27267	+	3.93637i	0.0953589	+	0.165167i
$569$	−15.3740			−0.644510			−0.322255	−	0.946653i	$-0.604441\pi$
$569$	−15.3740			−0.644510			−0.322255	+	0.946653i	$0.604441\pi$
$570$	2.56233	+	3.52626i	0.107324	+	0.147699i
$571$	18.8513			0.788903			0.394451	−	0.918917i	$-0.370935\pi$
$571$	18.8513			0.788903			0.394451	+	0.918917i	$0.370935\pi$
$572$	0.124650	+	0.215901i	0.00521190	+	0.00902727i
$573$	−4.57932	−	7.93161i	−0.191304	−	0.331348i
$574$	−25.9068	+	44.8718i	−1.08133	+	1.87291i
$575$	0.236780	+	0.410115i	0.00987441	+	0.0171030i
$576$	−0.500000	+	0.866025i	−0.0208333	+	0.0360844i
$577$	−19.3489			−0.805506			−0.402753	−	0.915309i	$-0.631947\pi$
$577$	−19.3489			−0.805506			−0.402753	+	0.915309i	$0.631947\pi$
$578$	3.66004			0.152237
$579$	−0.588765	+	1.01977i	−0.0244682	+	0.0423802i
$580$	−4.32555	+	7.49206i	−0.179608	+	0.311091i
$581$	−18.8791			−0.783239
$582$	17.5982			0.729469
$583$	−0.456566	+	0.790796i	−0.0189090	+	0.0327514i
$584$	1.46411	+	2.53592i	0.0605855	+	0.104937i
$585$	0.263220	−	0.455910i	0.0108828	−	0.0188496i
$586$	−11.6341	−	20.1508i	−0.480600	−	0.832424i
$587$	−8.01889	−	13.8891i	−0.330975	−	0.573266i	0.651728	−	0.758453i	$-0.274044\pi$
$587$	−8.01889	−	13.8891i	−0.330975	−	0.573266i	−0.982703	+	0.185187i	$0.940711\pi$
$588$	14.1435			0.583270
$589$	−1.34891	−	1.85636i	−0.0555809	−	0.0764901i
$590$	6.00000			0.247016
$591$	−6.10766	−	10.5788i	−0.251235	−	0.435153i
$592$	0.500000	+	0.866025i	0.0205499	+	0.0355934i
$593$	−14.4880	+	25.0939i	−0.594950	+	1.03048i	0.398604	+	0.917123i	$0.369495\pi$
$593$	−14.4880	+	25.0939i	−0.594950	+	1.03048i	−0.993554	+	0.113360i	$0.963839\pi$
$594$	−0.236780	−	0.410115i	−0.00971521	−	0.0168272i
$595$	−10.4502	+	18.1003i	−0.428416	+	0.742039i
$596$	−2.40179			−0.0983811
$597$	2.12465			0.0869562
$598$	−0.124650	+	0.215901i	−0.00509734	+	0.00882885i
$599$	−23.1391	+	40.0780i	−0.945437	+	1.63754i	−0.190562	+	0.981675i	$0.561031\pi$
$599$	−23.1391	+	40.0780i	−0.945437	+	1.63754i	−0.754874	+	0.655869i	$0.772302\pi$
$600$	1.00000			0.0408248
$601$	−10.6072			−0.432675			−0.216337	−	0.976319i	$-0.569411\pi$
$601$	−10.6072			−0.432675			−0.216337	+	0.976319i	$0.569411\pi$
$602$	29.1296	−	50.4540i	1.18723	−	2.05635i
$603$	−4.53589	−	7.85638i	−0.184716	−	0.319937i
$604$	7.87088	−	13.6328i	0.320261	−	0.554709i
$605$	5.38787	+	9.33207i	0.219048	+	0.379402i
$606$	−6.59821	−	11.4284i	−0.268034	−	0.464248i
$607$	28.0439			1.13827			0.569134	−	0.822245i	$-0.307279\pi$
$607$	28.0439			1.13827			0.569134	+	0.822245i	$0.307279\pi$
$608$	−4.33499	+	0.455910i	−0.175807	+	0.0184896i
$609$	−39.7795			−1.61195
$610$	−1.53589	−	2.66023i	−0.0621862	−	0.107710i
$611$	2.14354	+	3.71272i	0.0867184	+	0.150201i
$612$	2.27267	−	3.93637i	0.0918671	−	0.159118i
$613$	−12.4143	−	21.5022i	−0.501409	−	0.868466i	−0.999999	−	0.00162804i	$-0.999482\pi$
$613$	−12.4143	−	21.5022i	−0.501409	−	0.868466i	0.498589	−	0.866838i	$-0.333852\pi$
$614$	−6.99553	+	12.1166i	−0.282316	+	0.488987i
$615$	−11.2682			−0.454377
$616$	−2.17753			−0.0877352
$617$	6.00000	−	10.3923i	0.241551	−	0.418378i	−0.719605	−	0.694383i	$-0.755677\pi$
$617$	6.00000	−	10.3923i	0.241551	−	0.418378i	0.961156	+	0.276005i	$0.0890106\pi$
$618$	6.37088	−	11.0347i	0.256274	−	0.443880i
$619$	33.7946			1.35832			0.679160	−	0.733990i	$-0.262344\pi$
$619$	33.7946			1.35832			0.679160	+	0.733990i	$0.262344\pi$
$620$	−0.526440			−0.0211423
$621$	0.236780	−	0.410115i	0.00950166	−	0.0164574i
$622$	−15.7229	−	27.2328i	−0.630429	−	1.09194i
$623$	−4.43320	+	7.67853i	−0.177612	+	0.307634i
$624$	0.263220	+	0.455910i	0.0105372	+	0.0182510i
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$	31.2342			1.24837
$627$	0.839464	−	1.88580i	0.0335250	−	0.0753114i
$628$	−8.19642			−0.327073
$629$	−2.27267	−	3.93637i	−0.0906171	−	0.156953i
$630$	2.29911	+	3.98217i	0.0915986	+	0.158653i
$631$	7.11520	−	12.3239i	0.283252	−	0.490607i	−0.688932	−	0.724826i	$-0.741920\pi$
$631$	7.11520	−	12.3239i	0.283252	−	0.490607i	0.972184	+	0.234220i	$0.0752534\pi$
$632$	0.736780	+	1.27614i	0.0293075	+	0.0507621i
$633$	9.49553	−	16.4467i	0.377413	−	0.653699i
$634$	20.3589			0.808553
$635$	14.2153			0.564117
$636$	−0.964114	+	1.66990i	−0.0382296	+	0.0662157i
$637$	3.72286	−	6.44818i	0.147505	−	0.255486i
$638$	4.09681			0.162194
$639$	−4.54533			−0.179811
$640$	−0.500000	+	0.866025i	−0.0197642	+	0.0342327i
$641$	−13.1624	−	22.7980i	−0.519885	−	0.900467i	−0.999733	−	0.0231153i	$-0.992642\pi$
$641$	−13.1624	−	22.7980i	−0.519885	−	0.900467i	0.479848	−	0.877352i	$-0.340692\pi$
$642$	5.39732	−	9.34843i	0.213015	−	0.368953i
$643$	−8.25875	−	14.3046i	−0.325693	−	0.564117i	0.655959	−	0.754796i	$-0.272264\pi$
$643$	−8.25875	−	14.3046i	−0.325693	−	0.564117i	−0.981652	+	0.190679i	$0.938931\pi$
$644$	−1.08876	−	1.88580i	−0.0429033	−	0.0743108i
$645$	12.6700			0.498880
$646$	19.7040	−	2.07226i	0.775242	−	0.0815321i
$647$	29.2592			1.15030			0.575150	−	0.818048i	$-0.304944\pi$
$647$	29.2592			1.15030			0.575150	+	0.818048i	$0.304944\pi$
$648$	−0.500000	−	0.866025i	−0.0196419	−	0.0340207i
$649$	−1.42068	−	2.46069i	−0.0557666	−	0.0965906i
$650$	0.263220	−	0.455910i	0.0103243	−	0.0178823i
$651$	−1.21034	−	2.09637i	−0.0474370	−	0.0821633i
$652$	−7.78966	+	13.4921i	−0.305067	+	0.528391i
$653$	−41.7668			−1.63446			−0.817230	−	0.576311i	$-0.804492\pi$
$653$	−41.7668			−1.63446			−0.817230	+	0.576311i	$0.804492\pi$
$654$	6.54533			0.255943
$655$	−7.43320	+	12.8747i	−0.290439	+	0.503055i
$656$	5.63410	−	9.75854i	0.219975	−	0.381007i
$657$	−2.92823			−0.114241
$658$	−37.4457			−1.45979
$659$	−12.9596	+	22.4468i	−0.504836	+	0.874402i	0.495148	+	0.868808i	$0.335114\pi$
$659$	−12.9596	+	22.4468i	−0.504836	+	0.874402i	−0.999984	+	0.00559311i	$0.998220\pi$
$660$	−0.236780	−	0.410115i	−0.00921665	−	0.0159637i
$661$	14.8135	−	25.6578i	0.576179	−	0.997972i	−0.419733	−	0.907648i	$-0.637876\pi$
$661$	14.8135	−	25.6578i	0.576179	−	0.997972i	0.995912	−	0.0903242i	$-0.0287903\pi$
$662$	1.70089	+	2.94604i	0.0661071	+	0.114501i
$663$	−1.19642	−	2.07226i	−0.0464652	−	0.0804800i
$664$	4.10576			0.159334
$665$	−8.15109	+	18.3108i	−0.316086	+	0.710064i
$666$	−1.00000			−0.0387492
$667$	2.04841	+	3.54794i	0.0793146	+	0.137377i
$668$	−6.23678	−	10.8024i	−0.241308	−	0.417958i
$669$	−10.4238	+	18.0545i	−0.403006	+	0.698026i
$670$	−4.53589	−	7.85638i	−0.175237	−	0.303519i
$671$	−0.727334	+	1.25978i	−0.0280784	+	0.0486333i
$672$	−4.59821			−0.177380
$673$	39.7606			1.53266			0.766330	−	0.642447i	$-0.222081\pi$
$673$	39.7606			1.53266			0.766330	+	0.642447i	$0.222081\pi$
$674$	5.40676	−	9.36479i	0.208261	−	0.360718i
$675$	−0.500000	+	0.866025i	−0.0192450	+	0.0333333i
$676$	−12.7229			−0.489341
$677$	−14.3589			−0.551856			−0.275928	−	0.961178i	$-0.588985\pi$
$677$	−14.3589			−0.551856			−0.275928	+	0.961178i	$0.588985\pi$
$678$	−8.39732	+	14.5446i	−0.322497	+	0.558581i
$679$	40.4601	+	70.0790i	1.55272	+	2.68939i
$680$	2.27267	−	3.93637i	0.0871527	−	0.150953i
$681$	−2.39732	−	4.15227i	−0.0918654	−	0.159115i
$682$	0.124650	+	0.215901i	0.00477311	+	0.00826727i
$683$	10.7946			0.413045			0.206523	−	0.978442i	$-0.433785\pi$
$683$	10.7946			0.413045			0.206523	+	0.978442i	$0.433785\pi$
$684$	1.77267	−	3.98217i	0.0677796	−	0.152262i
$685$	9.33996			0.356862
$686$	16.4238	+	28.4468i	0.627062	+	1.08610i
$687$	9.26322	+	16.0444i	0.353414	+	0.612131i
$688$	−6.33499	+	10.9725i	−0.241519	+	0.418324i
$689$	0.507548	+	0.879099i	0.0193360	+	0.0334910i
$690$	0.236780	−	0.410115i	0.00901407	−	0.0156128i
$691$	−28.4646			−1.08284			−0.541422	−	0.840751i	$-0.682114\pi$
$691$	−28.4646			−1.08284			−0.541422	+	0.840751i	$0.682114\pi$
$692$	15.1247			0.574953
$693$	1.08876	−	1.88580i	0.0413588	−	0.0716355i
$694$	4.57932	−	7.93161i	0.173829	−	0.301080i
$695$	4.52644			0.171698
$696$	8.65109			0.327919
$697$	−25.6088	+	44.3558i	−0.970004	+	1.68010i
$698$	−2.04343	−	3.53933i	−0.0773451	−	0.133966i
$699$	12.7229	−	22.0366i	0.481223	−	0.833502i
$700$	2.29911	+	3.98217i	0.0868980	+	0.150512i
$701$	16.7606	+	29.0303i	0.633041	+	1.09646i	0.986927	+	0.161170i	$0.0515268\pi$
$701$	16.7606	+	29.0303i	0.633041	+	1.09646i	−0.353886	+	0.935289i	$0.615140\pi$
$702$	−0.526440			−0.0198692
$703$	−2.56233	−	3.52626i	−0.0966399	−	0.132995i
$704$	0.473560			0.0178480
$705$	−4.07177	−	7.05251i	−0.153352	−	0.265613i
$706$	8.90486	+	15.4237i	0.335139	+	0.580478i
$707$	30.3400	−	52.5504i	1.14105	−	1.97636i
$708$	−3.00000	−	5.19615i	−0.112747	−	0.195283i
$709$	20.8758	−	36.1580i	0.784009	−	1.35794i	−0.145580	−	0.989346i	$-0.546505\pi$
$709$	20.8758	−	36.1580i	0.784009	−	1.35794i	0.929589	−	0.368597i	$-0.120162\pi$
$710$	−4.54533			−0.170583
$711$	−1.47356			−0.0552628
$712$	0.964114	−	1.66990i	0.0361317	−	0.0625820i
$713$	−0.124650	+	0.215901i	−0.00466820	+	0.00808555i
$714$	20.9004			0.782177
$715$	−0.249301			−0.00932333
$716$	0.710340	−	1.23035i	0.0265467	−	0.0459802i
$717$	4.66998	+	8.08865i	0.174404	+	0.302076i
$718$	4.79911	−	8.31229i	0.179101	−	0.310212i
$719$	−3.03399	−	5.25502i	−0.113149	−	0.195979i	0.803890	−	0.594779i	$-0.202760\pi$
$719$	−3.03399	−	5.25502i	−0.113149	−	0.195979i	−0.917038	+	0.398799i	$0.869427\pi$
$720$	−0.500000	−	0.866025i	−0.0186339	−	0.0322749i
$721$	58.5893			2.18198
$722$	18.5843	−	3.95273i	0.691636	−	0.147105i
$723$	−14.4207			−0.536311
$724$	4.39732	+	7.61637i	0.163425	+	0.283060i
$725$	−4.32555	−	7.49206i	−0.160647	−	0.278248i
$726$	5.38787	−	9.33207i	0.199963	−	0.346345i
$727$	7.80855	+	13.5248i	0.289603	+	0.501607i	0.973715	−	0.227770i	$-0.0731433\pi$
$727$	7.80855	+	13.5248i	0.289603	+	0.501607i	−0.684112	+	0.729377i	$0.739810\pi$
$728$	−1.21034	+	2.09637i	−0.0448582	+	0.0776967i
$729$	1.00000			0.0370370
$730$	−2.92823			−0.108379
$731$	28.7946	−	49.8738i	1.06501	−	1.84465i
$732$	−1.53589	+	2.66023i	−0.0567680	+	0.0983250i
$733$	20.4736			0.756208			0.378104	−	0.925763i	$-0.376576\pi$
$733$	20.4736			0.756208			0.378104	+	0.925763i	$0.376576\pi$
$734$	1.36780			0.0504865
$735$	−7.07177	+	12.2487i	−0.260846	+	0.451799i
$736$	0.236780	+	0.410115i	0.00872783	+	0.0151170i
$737$	−2.14802	+	3.72047i	−0.0791232	+	0.137045i
$738$	5.63410	+	9.75854i	0.207394	+	0.359217i
$739$	14.8973	+	25.8029i	0.548007	+	0.949175i	0.998411	+	0.0563507i	$0.0179465\pi$
$739$	14.8973	+	25.8029i	0.548007	+	0.949175i	−0.450404	+	0.892825i	$0.648720\pi$
$740$	−1.00000			−0.0367607
$741$	−1.34891	−	1.85636i	−0.0495534	−	0.0681952i
$742$	−8.86640			−0.325496
$743$	15.5767	+	26.9797i	0.571455	+	0.989790i	0.996417	+	0.0845782i	$0.0269543\pi$
$743$	15.5767	+	26.9797i	0.571455	+	0.989790i	−0.424962	+	0.905211i	$0.639712\pi$
$744$	0.263220	+	0.455910i	0.00965011	+	0.0167145i
$745$	1.20089	−	2.08001i	0.0439974	−	0.0762057i
$746$	12.3086	+	21.3190i	0.450648	+	0.780545i
$747$	−2.05288	+	3.55569i	−0.0751109	+	0.130096i
$748$	−2.15249			−0.0787028
$749$	49.6360			1.81366
$750$	−0.500000	+	0.866025i	−0.0182574	+	0.0316228i
$751$	−14.3879	+	24.9205i	−0.525021	+	0.909363i	0.474555	+	0.880226i	$0.342609\pi$
$751$	−14.3879	+	24.9205i	−0.525021	+	0.909363i	−0.999575	+	0.0291367i	$0.990724\pi$
$752$	8.14354			0.296964
$753$	−23.2342			−0.846701
$754$	2.27714	−	3.94412i	0.0829285	−	0.143636i
$755$	7.87088	+	13.6328i	0.286451	+	0.496147i
$756$	2.29911	−	3.98217i	0.0836177	−	0.144830i
$757$	11.2040	+	19.4058i	0.407215	+	0.705317i	0.994577	−	0.104007i	$-0.0331666\pi$
$757$	11.2040	+	19.4058i	0.407215	+	0.705317i	−0.587361	+	0.809325i	$0.699833\pi$
$758$	−7.88032	−	13.6491i	−0.286226	−	0.495758i
$759$	−0.224259			−0.00814010
$760$	1.77267	−	3.98217i	0.0643013	−	0.144448i
$761$	−17.5175			−0.635009			−0.317504	−	0.948257i	$-0.602845\pi$
$761$	−17.5175			−0.635009			−0.317504	+	0.948257i	$0.602845\pi$
$762$	−7.10766	−	12.3108i	−0.257483	−	0.445974i
$763$	15.0484	+	26.0646i	0.544789	+	0.943602i
$764$	−4.57932	+	7.93161i	−0.165674	+	0.286956i
$765$	2.27267	+	3.93637i	0.0821684	+	0.142320i
$766$	−10.0718	+	17.4448i	−0.363908	+	0.630307i
$767$	−3.15864			−0.114052
$768$	1.00000			0.0360844
$769$	20.2821	−	35.1296i	0.731392	−	1.26681i	−0.224897	−	0.974383i	$-0.572205\pi$
$769$	20.2821	−	35.1296i	0.731392	−	1.26681i	0.956288	−	0.292425i	$-0.0944622\pi$
$770$	1.08876	−	1.88580i	0.0392364	−	0.0679594i
$771$	6.00000			0.216085
$772$	1.17753			0.0423802
$773$	−7.30408	+	12.6510i	−0.262709	+	0.455026i	−0.966961	−	0.254924i	$-0.917949\pi$
$773$	−7.30408	+	12.6510i	−0.262709	+	0.455026i	0.704252	+	0.709951i	$0.251283\pi$
$774$	−6.33499	−	10.9725i	−0.227707	−	0.394399i
$775$	0.263220	−	0.455910i	0.00945514	−	0.0163768i
$776$	−8.79911	−	15.2405i	−0.315869	−	0.547102i
$777$	−2.29911	−	3.98217i	−0.0824799	−	0.142859i
$778$	−20.6511			−0.740377
$779$	−19.9747	+	44.8718i	−0.715669	+	1.60770i
$780$	−0.526440			−0.0188496
$781$	1.07624	+	1.86411i	0.0385110	+	0.0667031i
$782$	−1.07624	−	1.86411i	−0.0384864	−	0.0666604i
$783$	−4.32555	+	7.49206i	−0.154582	+	0.267745i
$784$	−7.07177	−	12.2487i	−0.252563	−	0.437452i
$785$	4.09821	−	7.09831i	0.146271	−	0.253350i
$786$	14.8664			0.530267
$787$	9.25310			0.329837			0.164919	−	0.986307i	$-0.447264\pi$
$787$	9.25310			0.329837			0.164919	+	0.986307i	$0.447264\pi$
$788$	−6.10766	+	10.5788i	−0.217576	+	0.376853i
$789$	11.2897	−	19.5543i	0.401923	−	0.696150i
$790$	−1.47356			−0.0524269
$791$	−77.2253			−2.74581
$792$	−0.236780	+	0.410115i	−0.00841362	+	0.0145728i
$793$	0.808551	+	1.40045i	0.0287125	+	0.0497315i
$794$	−13.6435	+	23.6313i	−0.484191	+	0.838644i
$795$	−0.964114	−	1.66990i	−0.0341936	−	0.0592251i
$796$	−1.06233	−	1.84000i	−0.0376531	−	0.0652171i
$797$	−17.9660			−0.636389			−0.318194	−	0.948025i	$-0.603076\pi$
$797$	−17.9660			−0.636389			−0.318194	+	0.948025i	$0.603076\pi$
$798$	19.9332	−	2.09637i	0.705628	−	0.0742107i
$799$	−37.0151			−1.30950
$800$	−0.500000	−	0.866025i	−0.0176777	−	0.0306186i
$801$	0.964114	+	1.66990i	0.0340653	+	0.0590028i
$802$	−17.1435	+	29.6935i	−0.605360	+	1.04851i
$803$	0.693346	+	1.20091i	0.0244677	+	0.0423792i
$804$	−4.53589	+	7.85638i	−0.159968	+	0.277073i
$805$	2.17753			0.0767478
$806$	0.277139			0.00976180
$807$	0.253774	−	0.439550i	0.00893327	−	0.0154729i
$808$	−6.59821	+	11.4284i	−0.232124	+	0.402051i
$809$	−21.8565			−0.768432			−0.384216	−	0.923243i	$-0.625528\pi$
$809$	−21.8565			−0.768432			−0.384216	+	0.923243i	$0.625528\pi$
$810$	1.00000			0.0351364
$811$	−10.2323	+	17.7229i	−0.359305	+	0.622334i	−0.987845	−	0.155443i	$-0.950320\pi$
$811$	−10.2323	+	17.7229i	−0.359305	+	0.622334i	0.628540	+	0.777777i	$0.283653\pi$
$812$	19.8898	+	34.4501i	0.697994	+	1.20896i
$813$	−13.1247	+	22.7326i	−0.460302	+	0.797266i
$814$	0.236780	+	0.410115i	0.00829914	+	0.0143745i
$815$	−7.78966	−	13.4921i	−0.272860	−	0.472607i
$816$	−4.54533			−0.159118
$817$	22.4596	−	50.4540i	0.785763	−	1.76516i
$818$	−20.7606			−0.725879
$819$	−1.21034	−	2.09637i	−0.0422927	−	0.0732531i
$820$	5.63410	+	9.75854i	0.196751	+	0.340783i
$821$	15.9471	−	27.6212i	0.556558	−	0.963987i	−0.441222	−	0.897398i	$-0.645455\pi$
$821$	15.9471	−	27.6212i	0.556558	−	0.963987i	0.997780	−	0.0665894i	$-0.0212118\pi$
$822$	−4.66998	−	8.08865i	−0.162884	−	0.282124i
$823$	8.01699	−	13.8858i	0.279455	−	0.484030i	−0.691795	−	0.722094i	$-0.743180\pi$
$823$	8.01699	−	13.8858i	0.279455	−	0.484030i	0.971249	+	0.238064i	$0.0765129\pi$
$824$	−12.7418			−0.443880
$825$	0.473560			0.0164873
$826$	13.7946	−	23.8930i	0.479977	−	0.831344i
$827$	−19.4502	+	33.6887i	−0.676350	+	1.17147i	0.299723	+	0.954026i	$0.403106\pi$
$827$	−19.4502	+	33.6887i	−0.676350	+	1.17147i	−0.976072	+	0.217446i	$0.930228\pi$
$828$	−0.473560			−0.0164574
$829$	0.602006			0.0209085			0.0104543	−	0.999945i	$-0.496672\pi$
$829$	0.602006			0.0209085			0.0104543	+	0.999945i	$0.496672\pi$
$830$	−2.05288	+	3.55569i	−0.0712565	+	0.123420i
$831$	−16.1247	−	27.9287i	−0.559358	−	0.968836i
$832$	0.263220	−	0.455910i	0.00912551	−	0.0158058i
$833$	32.1435	+	55.6742i	1.11371	+	1.92900i
$834$	−2.26322	−	3.92001i	−0.0783689	−	0.135739i
$835$	12.4736			0.431665
$836$	−2.05288	+	0.215901i	−0.0710003	+	0.00746709i
$837$	−0.526440			−0.0181964
$838$	13.7821	+	23.8713i	0.476095	+	0.824621i
$839$	−0.0339879	−	0.0588688i	−0.00117339	−	0.00203238i	0.865438	−	0.501016i	$-0.167040\pi$
$839$	−0.0339879	−	0.0588688i	−0.00117339	−	0.00203238i	−0.866612	+	0.498983i	$0.833707\pi$
$840$	2.29911	−	3.98217i	0.0793267	−	0.137398i
$841$	−22.9207	−	39.6998i	−0.790368	−	1.36896i
$842$	2.72733	−	4.72388i	0.0939901	−	0.162796i
$843$	−0.215313			−0.00741578
$844$	−18.9911			−0.653699
$845$	6.36143	−	11.0183i	0.218840	−	0.379042i
$846$	−4.07177	+	7.05251i	−0.139990	+	0.242470i
$847$	49.5491			1.70253
$848$	1.92823			0.0662157
$849$	14.2153	−	24.6216i	0.487868	−	0.845013i
$850$	2.27267	+	3.93637i	0.0779518	+	0.135016i
$851$	−0.236780	+	0.410115i	−0.00811672	+	0.0140586i
$852$	2.27267	+	3.93637i	0.0778602	+	0.134858i
$853$	−1.28211	−	2.22068i	−0.0438987	−	0.0760347i	0.843241	−	0.537535i	$-0.180645\pi$
$853$	−1.28211	−	2.22068i	−0.0438987	−	0.0760347i	−0.887140	+	0.461501i	$0.847311\pi$
$854$	−14.1247			−0.483336
$855$	2.56233	+	3.52626i	0.0876297	+	0.120595i
$856$	−10.7946			−0.368953
$857$	−9.85646	−	17.0719i	−0.336690	−	0.583165i	0.647118	−	0.762390i	$-0.275974\pi$
$857$	−9.85646	−	17.0719i	−0.336690	−	0.583165i	−0.983808	+	0.179225i	$0.942641\pi$
$858$	0.124650	+	0.215901i	0.00425550	+	0.00737074i
$859$	−5.75377	+	9.96583i	−0.196316	+	0.340030i	−0.947331	−	0.320255i	$-0.896231\pi$
$859$	−5.75377	+	9.96583i	−0.196316	+	0.340030i	0.751015	+	0.660285i	$0.229565\pi$
$860$	−6.33499	−	10.9725i	−0.216021	−	0.374160i
$861$	−25.9068	+	44.8718i	−0.882900	+	1.52923i
$862$	−40.0968			−1.36570
$863$	−33.1157			−1.12727			−0.563636	−	0.826023i	$-0.690598\pi$
$863$	−33.1157			−1.12727			−0.563636	+	0.826023i	$0.690598\pi$
$864$	−0.500000	+	0.866025i	−0.0170103	+	0.0294628i
$865$	−7.56233	+	13.0983i	−0.257127	+	0.445357i
$866$	11.2153			0.381112
$867$	3.66004			0.124301
$868$	−1.21034	+	2.09637i	−0.0410816	+	0.0711555i
$869$	0.348910	+	0.604330i	0.0118360	+	0.0205005i
$870$	−4.32555	+	7.49206i	−0.146650	+	0.254005i
$871$	2.38787	+	4.13591i	0.0809099	+	0.140140i
$872$	−3.27267	−	5.66842i	−0.110826	−	0.191957i
$873$	17.5982			0.595609
$874$	−1.21342	−	1.66990i	−0.0410444	−	0.0564851i
$875$	−4.59821			−0.155448
$876$	1.46411	+	2.53592i	0.0494678	+	0.0856808i
$877$	20.1700	+	34.9354i	0.681092	+	1.17969i	0.974648	+	0.223744i	$0.0718279\pi$
$877$	20.1700	+	34.9354i	0.681092	+	1.17969i	−0.293556	+	0.955942i	$0.594839\pi$
$878$	−7.18698	+	12.4482i	−0.242549	+	0.420107i
$879$	−11.6341	−	20.1508i	−0.392408	−	0.679671i
$880$	−0.236780	+	0.410115i	−0.00798186	+	0.0138250i
$881$	−5.51749			−0.185889			−0.0929445	−	0.995671i	$-0.529628\pi$
$881$	−5.51749			−0.185889			−0.0929445	+	0.995671i	$0.529628\pi$
$882$	14.1435			0.476238
$883$	−23.2927	+	40.3442i	−0.783863	+	1.35769i	0.145813	+	0.989312i	$0.453420\pi$
$883$	−23.2927	+	40.3442i	−0.783863	+	1.35769i	−0.929676	+	0.368378i	$0.879913\pi$
$884$	−1.19642	+	2.07226i	−0.0402400	+	0.0696977i
$885$	6.00000			0.201688
$886$	−6.50755			−0.218625
$887$	−10.5793	+	18.3239i	−0.355219	+	0.615257i	−0.987155	−	0.159763i	$-0.948927\pi$
$887$	−10.5793	+	18.3239i	−0.355219	+	0.615257i	0.631937	+	0.775020i	$0.282260\pi$
$888$	0.500000	+	0.866025i	0.0167789	+	0.0290619i
$889$	32.6825	−	56.6078i	1.09614	−	1.89856i
$890$	0.964114	+	1.66990i	0.0323172	+	0.0559750i
$891$	−0.236780	−	0.410115i	−0.00793243	−	0.0137394i
$892$	20.8475			0.698026
$893$	−35.3022	+	3.71272i	−1.18134	+	0.124242i
$894$	−2.40179			−0.0803278
$895$	0.710340	+	1.23035i	0.0237441	+	0.0411259i
$896$	2.29911	+	3.98217i	0.0768077	+	0.133035i
$897$	−0.124650	+	0.215901i	−0.00416196	+	0.00720872i
$898$	0.964114	+	1.66990i	0.0321729	+	0.0557251i
$899$	2.27714	−	3.94412i	0.0759468	−	0.131544i
$900$	1.00000			0.0333333
$901$	−8.76444			−0.291986
$902$	2.66808	−	4.62126i	0.0888375	−	0.153871i
$903$	29.1296	−	50.4540i	0.969373	−	1.67900i
$904$	16.7946			0.558581
$905$	−8.79463			−0.292343
$906$	7.87088	−	13.6328i	0.261492	−	0.452918i
$907$	−1.38290	−	2.39525i	−0.0459184	−	0.0795329i	0.842153	−	0.539239i	$-0.181288\pi$
$907$	−1.38290	−	2.39525i	−0.0459184	−	0.0795329i	−0.888071	+	0.459706i	$0.847955\pi$
$908$	−2.39732	+	4.15227i	−0.0795577	+	0.137798i
$909$	−6.59821	−	11.4284i	−0.218849	−	0.379057i
$910$	−1.21034	−	2.09637i	−0.0401224	−	0.0694940i
$911$	−7.37775			−0.244436			−0.122218	−	0.992503i	$-0.539001\pi$
$911$	−7.37775			−0.244436			−0.122218	+	0.992503i	$0.539001\pi$
$912$	−4.33499	+	0.455910i	−0.143546	+	0.0150967i
$913$	1.94432			0.0643477
$914$	14.6265	+	25.3339i	0.483803	+	0.837972i
$915$	−1.53589	−	2.66023i	−0.0507748	−	0.0879445i
$916$	9.26322	−	16.0444i	0.306065	−	0.530121i
$917$	34.1794	+	59.2005i	1.12870	+	1.95497i
$918$	2.27267	−	3.93637i	0.0750091	−	0.129920i
$919$	10.0189			0.330493			0.165246	−	0.986252i	$-0.447158\pi$
$919$	10.0189			0.330493			0.165246	+	0.986252i	$0.447158\pi$
$920$	−0.473560			−0.0156128
$921$	−6.99553	+	12.1166i	−0.230510	+	0.399256i
$922$	0.473560	−	0.820230i	0.0155959	−	0.0270129i
$923$	2.39284			0.0787614
$924$	−2.17753			−0.0716355
$925$	0.500000	−	0.866025i	0.0164399	−	0.0284747i
$926$	−8.37088	−	14.4988i	−0.275084	−	0.476460i
$927$	6.37088	−	11.0347i	0.209247	−	0.362426i
$928$	−4.32555	−	7.49206i	−0.141993	−	0.245939i
$929$	20.4098	+	35.3509i	0.669625	+	1.15982i	0.978009	+	0.208563i	$0.0668785\pi$
$929$	20.4098	+	35.3509i	0.669625	+	1.15982i	−0.308384	+	0.951262i	$0.599788\pi$
$930$	−0.526440			−0.0172626
$931$	36.2404	+	49.8738i	1.18773	+	1.63455i
$932$	−25.4457			−0.833502
$933$	−15.7229	−	27.2328i	−0.514743	−	0.891562i
$934$	−9.85198	−	17.0641i	−0.322367	−	0.558356i
$935$	1.07624	−	1.86411i	0.0351969	−	0.0609629i
$936$	0.263220	+	0.455910i	0.00860361	+	0.0149019i
$937$	−14.6983	+	25.4582i	−0.480173	+	0.831684i	−0.999741	−	0.0227447i	$-0.992760\pi$
$937$	−14.6983	+	25.4582i	−0.480173	+	0.831684i	0.519568	+	0.854429i	$0.326093\pi$
$938$	−41.7139			−1.36201
$939$	31.2342			1.01929
$940$	−4.07177	+	7.05251i	−0.132807	+	0.230028i
$941$	−29.0144	+	50.2544i	−0.945843	+	1.63825i	−0.191789	+	0.981436i	$0.561429\pi$
$941$	−29.0144	+	50.2544i	−0.945843	+	1.63825i	−0.754054	+	0.656812i	$0.771905\pi$
$942$	−8.19642			−0.267054
$943$	5.33617			0.173770
$944$	−3.00000	+	5.19615i	−0.0976417	+	0.169120i
$945$	2.29911	+	3.98217i	0.0747899	+	0.129540i
$946$	−3.00000	+	5.19615i	−0.0975384	+	0.168941i
$947$	14.8709	+	25.7571i	0.483239	+	0.836994i	0.999815	−	0.0192475i	$-0.00612705\pi$
$947$	14.8709	+	25.7571i	0.483239	+	0.836994i	−0.516576	+	0.856241i	$0.672794\pi$
$948$	0.736780	+	1.27614i	0.0239295	+	0.0414471i
$949$	1.54154			0.0500404
$950$	2.56233	+	3.52626i	0.0831328	+	0.114407i
$951$	20.3589			0.660181
$952$	−10.4502	−	18.1003i	−0.338693	−	0.586633i
$953$	20.3928	+	35.3214i	0.660589	+	1.14417i	0.980461	+	0.196713i	$0.0630267\pi$
$953$	20.3928	+	35.3214i	0.660589	+	1.14417i	−0.319872	+	0.947461i	$0.603640\pi$
$954$	−0.964114	+	1.66990i	−0.0312144	+	0.0540649i
$955$	−4.57932	−	7.93161i	−0.148183	−	0.256661i
$956$	4.66998	−	8.08865i	0.151038	−	0.261605i
$957$	4.09681			0.132431
$958$	30.6889			0.991512
$959$	21.4736	−	37.1933i	0.693417	−	1.20103i
$960$	−0.500000	+	0.866025i	−0.0161374	+	0.0279508i
$961$	−30.7229			−0.991060
$962$	0.526440			0.0169731
$963$	5.39732	−	9.34843i	0.173926	−	0.301249i
$964$	7.21034	+	12.4887i	0.232229	+	0.402233i
$965$	−0.588765	+	1.01977i	−0.0189530	+	0.0328276i
$966$	−1.08876	−	1.88580i	−0.0350304	−	0.0606745i
$967$	−17.7368	−	30.7210i	−0.570376	−	0.987921i	−0.996527	−	0.0832687i	$-0.973464\pi$
$967$	−17.7368	−	30.7210i	−0.570376	−	0.987921i	0.426151	−	0.904652i	$-0.359869\pi$
$968$	−10.7757			−0.346345
$969$	19.7040	−	2.07226i	0.632983	−	0.0665707i
$970$	17.5982			0.565044
$971$	12.2153	+	21.1575i	0.392008	+	0.678978i	0.992714	−	0.120492i	$-0.0384472\pi$
$971$	12.2153	+	21.1575i	0.392008	+	0.678978i	−0.600706	+	0.799470i	$0.705114\pi$
$972$	−0.500000	−	0.866025i	−0.0160375	−	0.0277778i
$973$	10.4068	−	18.0250i	0.333625	−	0.577856i
$974$	20.9552	+	36.2954i	0.671447	+	1.16298i
$975$	0.263220	−	0.455910i	0.00842978	−	0.0146008i
$976$	3.07177			0.0983250
$977$	−45.0137			−1.44012			−0.720059	−	0.693913i	$-0.755885\pi$
$977$	−45.0137			−1.44012			−0.720059	+	0.693913i	$0.755885\pi$
$978$	−7.78966	+	13.4921i	−0.249086	+	0.431429i
$979$	0.456566	−	0.790796i	0.0145919	−	0.0252740i
$980$	14.1435			0.451799
$981$	6.54533			0.208976
$982$	7.81610	−	13.5379i	0.249422	−	0.432011i
$983$	18.3614	+	31.8029i	0.585639	+	1.01436i	0.994795	+	0.101892i	$0.0324896\pi$
$983$	18.3614	+	31.8029i	0.585639	+	1.01436i	−0.409157	+	0.912464i	$0.634177\pi$
$984$	5.63410	−	9.75854i	0.179608	−	0.311091i
$985$	−6.10766	−	10.5788i	−0.194606	−	0.337068i
$986$	19.6610	+	34.0539i	0.626135	+	1.08450i
$987$	−37.4457			−1.19191
$988$	−0.933202	+	2.09637i	−0.0296891	+	0.0666944i
$989$	−6.00000			−0.190789
$990$	−0.236780	−	0.410115i	−0.00752537	−	0.0130343i
$991$	−17.0005	−	29.4457i	−0.540039	−	0.935374i	−0.998901	−	0.0468671i	$-0.985076\pi$
$991$	−17.0005	−	29.4457i	−0.540039	−	0.935374i	0.458862	−	0.888507i	$-0.348257\pi$
$992$	0.263220	−	0.455910i	0.00835724	−	0.0144752i
$993$	1.70089	+	2.94604i	0.0539763	+	0.0934896i
$994$	−10.4502	+	18.1003i	−0.331460	+	0.574106i
$995$	2.12465			0.0673559
$996$	4.10576			0.130096
$997$	8.60955	−	14.9122i	0.272667	−	0.472274i	−0.696877	−	0.717191i	$-0.745428\pi$
$997$	8.60955	−	14.9122i	0.272667	−	0.472274i	0.969544	+	0.244917i	$0.0787608\pi$
$998$	−0.102684	+	0.177854i	−0.00325040	+	0.00562986i
$999$	−1.00000			−0.0316386

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	570.2.i.j.121.1	✓	6
3.2	odd	2		1710.2.l.q.1261.1		6
19.11	even	3	inner	570.2.i.j.391.1	yes	6
57.11	odd	6		1710.2.l.q.1531.1		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
570.2.i.j.121.1	✓	6	1.1	even	1	trivial
570.2.i.j.391.1	yes	6	19.11	even	3	inner
1710.2.l.q.1261.1		6	3.2	odd	2
1710.2.l.q.1531.1		6	57.11	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:	\( N \)	\(=\)	\( 570 = 2 \cdot 3 \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	570.i (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-0.500000 - 0.866025i) q^{5} +(-0.500000 + 0.866025i) q^{6} -4.59821 q^{7} +1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-0.500000 - 0.866025i) q^{5} +(-0.500000 + 0.866025i) q^{6} -4.59821 q^{7} +1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +(-0.500000 + 0.866025i) q^{10} +0.473560 q^{11} +1.00000 q^{12} +(0.263220 - 0.455910i) q^{13} +(2.29911 + 3.98217i) q^{14} +(-0.500000 + 0.866025i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(2.27267 + 3.93637i) q^{17} +1.00000 q^{18} +(2.56233 + 3.52626i) q^{19} +1.00000 q^{20} +(2.29911 + 3.98217i) q^{21} +(-0.236780 - 0.410115i) q^{22} +(0.236780 - 0.410115i) q^{23} +(-0.500000 - 0.866025i) q^{24} +(-0.500000 + 0.866025i) q^{25} -0.526440 q^{26} +1.00000 q^{27} +(2.29911 - 3.98217i) q^{28} +(-4.32555 + 7.49206i) q^{29} +1.00000 q^{30} -0.526440 q^{31} +(-0.500000 + 0.866025i) q^{32} +(-0.236780 - 0.410115i) q^{33} +(2.27267 - 3.93637i) q^{34} +(2.29911 + 3.98217i) q^{35} +(-0.500000 - 0.866025i) q^{36} -1.00000 q^{37} +(1.77267 - 3.98217i) q^{38} -0.526440 q^{39} +(-0.500000 - 0.866025i) q^{40} +(5.63410 + 9.75854i) q^{41} +(2.29911 - 3.98217i) q^{42} +(-6.33499 - 10.9725i) q^{43} +(-0.236780 + 0.410115i) q^{44} +1.00000 q^{45} -0.473560 q^{46} +(-4.07177 + 7.05251i) q^{47} +(-0.500000 + 0.866025i) q^{48} +14.1435 q^{49} +1.00000 q^{50} +(2.27267 - 3.93637i) q^{51} +(0.263220 + 0.455910i) q^{52} +(-0.964114 + 1.66990i) q^{53} +(-0.500000 - 0.866025i) q^{54} +(-0.236780 - 0.410115i) q^{55} -4.59821 q^{56} +(1.77267 - 3.98217i) q^{57} +8.65109 q^{58} +(-3.00000 - 5.19615i) q^{59} +(-0.500000 - 0.866025i) q^{60} +(-1.53589 + 2.66023i) q^{61} +(0.263220 + 0.455910i) q^{62} +(2.29911 - 3.98217i) q^{63} +1.00000 q^{64} -0.526440 q^{65} +(-0.236780 + 0.410115i) q^{66} +(-4.53589 + 7.85638i) q^{67} -4.54533 q^{68} -0.473560 q^{69} +(2.29911 - 3.98217i) q^{70} +(2.27267 + 3.93637i) q^{71} +(-0.500000 + 0.866025i) q^{72} +(1.46411 + 2.53592i) q^{73} +(0.500000 + 0.866025i) q^{74} +1.00000 q^{75} +(-4.33499 + 0.455910i) q^{76} -2.17753 q^{77} +(0.263220 + 0.455910i) q^{78} +(0.736780 + 1.27614i) q^{79} +(-0.500000 + 0.866025i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(5.63410 - 9.75854i) q^{82} +4.10576 q^{83} -4.59821 q^{84} +(2.27267 - 3.93637i) q^{85} +(-6.33499 + 10.9725i) q^{86} +8.65109 q^{87} +0.473560 q^{88} +(0.964114 - 1.66990i) q^{89} +(-0.500000 - 0.866025i) q^{90} +(-1.21034 + 2.09637i) q^{91} +(0.236780 + 0.410115i) q^{92} +(0.263220 + 0.455910i) q^{93} +8.14354 q^{94} +(1.77267 - 3.98217i) q^{95} +1.00000 q^{96} +(-8.79911 - 15.2405i) q^{97} +(-7.07177 - 12.2487i) q^{98} +(-0.236780 + 0.410115i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 3 q^{2} - 3 q^{3} - 3 q^{4} - 3 q^{5} - 3 q^{6} + 2 q^{7} + 6 q^{8} - 3 q^{9}+O(q^{10}) \) 6 * q - 3 * q^2 - 3 * q^3 - 3 * q^4 - 3 * q^5 - 3 * q^6 + 2 * q^7 + 6 * q^8 - 3 * q^9	\( 6 q - 3 q^{2} - 3 q^{3} - 3 q^{4} - 3 q^{5} - 3 q^{6} + 2 q^{7} + 6 q^{8} - 3 q^{9} - 3 q^{10} + 8 q^{11} + 6 q^{12} - q^{13} - q^{14} - 3 q^{15} - 3 q^{16} + 4 q^{17} + 6 q^{18} - 2 q^{19} + 6 q^{20} - q^{21} - 4 q^{22} + 4 q^{23} - 3 q^{24} - 3 q^{25} + 2 q^{26} + 6 q^{27} - q^{28} - 6 q^{29} + 6 q^{30} + 2 q^{31} - 3 q^{32} - 4 q^{33} + 4 q^{34} - q^{35} - 3 q^{36} - 6 q^{37} + q^{38} + 2 q^{39} - 3 q^{40} - 8 q^{41} - q^{42} - 11 q^{43} - 4 q^{44} + 6 q^{45} - 8 q^{46} - 3 q^{48} + 36 q^{49} + 6 q^{50} + 4 q^{51} - q^{52} - 18 q^{53} - 3 q^{54} - 4 q^{55} + 2 q^{56} + q^{57} + 12 q^{58} - 18 q^{59} - 3 q^{60} + 3 q^{61} - q^{62} - q^{63} + 6 q^{64} + 2 q^{65} - 4 q^{66} - 15 q^{67} - 8 q^{68} - 8 q^{69} - q^{70} + 4 q^{71} - 3 q^{72} + 21 q^{73} + 3 q^{74} + 6 q^{75} + q^{76} + 32 q^{77} - q^{78} + 7 q^{79} - 3 q^{80} - 3 q^{81} - 8 q^{82} + 4 q^{83} + 2 q^{84} + 4 q^{85} - 11 q^{86} + 12 q^{87} + 8 q^{88} + 18 q^{89} - 3 q^{90} - 15 q^{91} + 4 q^{92} - q^{93} + q^{95} + 6 q^{96} - 38 q^{97} - 18 q^{98} - 4 q^{99}+O(q^{100}) \) 6 * q - 3 * q^2 - 3 * q^3 - 3 * q^4 - 3 * q^5 - 3 * q^6 + 2 * q^7 + 6 * q^8 - 3 * q^9 - 3 * q^10 + 8 * q^11 + 6 * q^12 - q^13 - q^14 - 3 * q^15 - 3 * q^16 + 4 * q^17 + 6 * q^18 - 2 * q^19 + 6 * q^20 - q^21 - 4 * q^22 + 4 * q^23 - 3 * q^24 - 3 * q^25 + 2 * q^26 + 6 * q^27 - q^28 - 6 * q^29 + 6 * q^30 + 2 * q^31 - 3 * q^32 - 4 * q^33 + 4 * q^34 - q^35 - 3 * q^36 - 6 * q^37 + q^38 + 2 * q^39 - 3 * q^40 - 8 * q^41 - q^42 - 11 * q^43 - 4 * q^44 + 6 * q^45 - 8 * q^46 - 3 * q^48 + 36 * q^49 + 6 * q^50 + 4 * q^51 - q^52 - 18 * q^53 - 3 * q^54 - 4 * q^55 + 2 * q^56 + q^57 + 12 * q^58 - 18 * q^59 - 3 * q^60 + 3 * q^61 - q^62 - q^63 + 6 * q^64 + 2 * q^65 - 4 * q^66 - 15 * q^67 - 8 * q^68 - 8 * q^69 - q^70 + 4 * q^71 - 3 * q^72 + 21 * q^73 + 3 * q^74 + 6 * q^75 + q^76 + 32 * q^77 - q^78 + 7 * q^79 - 3 * q^80 - 3 * q^81 - 8 * q^82 + 4 * q^83 + 2 * q^84 + 4 * q^85 - 11 * q^86 + 12 * q^87 + 8 * q^88 + 18 * q^89 - 3 * q^90 - 15 * q^91 + 4 * q^92 - q^93 + q^95 + 6 * q^96 - 38 * q^97 - 18 * q^98 - 4 * q^99

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