LMFDB - Embedded newform 570.2.i.j.391.1

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			391.1
Root			$2.35084i$ of defining polynomial
Character	$\chi$	$=$	570.391
Dual form			570.2.i.j.121.1

$q$-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 $\left(\mathbb{Z}/570\mathbb{Z}\right)^\times$.

$n$	$191$	$211$	$457$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$	$1$

Coefficient data

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

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

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

$2$	−0.500000	+	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	0.900217	−	0.435442i	$-0.143408\pi$
$13$	0.263220	+	0.455910i	0.0730041	+	0.126447i	−0.827213	+	0.561889i	$0.810075\pi$
$14$	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	−0.446986	−	0.894541i	$-0.647503\pi$
$17$	2.27267	−	3.93637i	0.551202	−	0.954711i	0.998188	−	0.0601695i	$-0.0191641\pi$
$18$	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	0.889655	−	0.456633i	$-0.150945\pi$
$23$	0.236780	+	0.410115i	0.0493721	+	0.0855149i	−0.840283	+	0.542148i	$0.817611\pi$
$24$	−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	−0.917477	−	0.397789i	$-0.869778\pi$
$29$	−4.32555	−	7.49206i	−0.803234	−	1.39124i	0.114244	−	0.993453i	$-0.463556\pi$
$30$	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	0.0284461	−	0.999595i	$-0.490944\pi$
$41$	5.63410	−	9.75854i	0.879898	−	1.52403i	0.851452	−	0.524433i	$-0.175723\pi$
$42$	2.29911	+	3.98217i	0.354760	+	0.614462i
$43$	−6.33499	+	10.9725i	−0.966077	+	1.67329i	−0.259384	+	0.965774i	$0.583520\pi$
$43$	−6.33499	+	10.9725i	−0.966077	+	1.67329i	−0.706693	+	0.707520i	$0.749814\pi$
$44$	−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	−0.993697	−	0.112099i	$-0.964243\pi$
$47$	−4.07177	−	7.05251i	−0.593929	−	1.02871i	0.399768	−	0.916616i	$-0.369091\pi$
$48$	−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	0.792182	−	0.610285i	$-0.208945\pi$
$53$	−0.964114	−	1.66990i	−0.132431	−	0.229378i	−0.924613	+	0.380907i	$0.875612\pi$
$54$	−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	−0.992524	−	0.122047i	$-0.961054\pi$
$59$	−3.00000	+	5.19615i	−0.390567	+	0.676481i	0.601958	+	0.798528i	$0.294388\pi$
$60$	−0.500000	+	0.866025i	−0.0645497	+	0.111803i
$61$	−1.53589	−	2.66023i	−0.196650	−	0.340608i	0.750790	−	0.660541i	$-0.229673\pi$
$61$	−1.53589	−	2.66023i	−0.196650	−	0.340608i	−0.947440	+	0.319933i	$0.896340\pi$
$62$	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	−0.997969	−	0.0636955i	$-0.979711\pi$
$67$	−4.53589	−	7.85638i	−0.554147	−	0.959810i	0.443823	−	0.896115i	$-0.353622\pi$
$68$	−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	−0.699073	−	0.715051i	$-0.746404\pi$
$71$	2.27267	−	3.93637i	0.269716	−	0.467161i	0.968788	+	0.247889i	$0.0797369\pi$
$72$	−0.500000	−	0.866025i	−0.0589256	−	0.102062i
$73$	1.46411	−	2.53592i	0.171362	−	0.296807i	−0.767535	−	0.641008i	$-0.778517\pi$
$73$	1.46411	−	2.53592i	0.171362	−	0.296807i	0.938896	+	0.344201i	$0.111850\pi$
$74$	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	−0.821598	−	0.570068i	$-0.806917\pi$
$79$	0.736780	−	1.27614i	0.0828942	−	0.143577i	0.904492	+	0.426491i	$0.140250\pi$
$80$	−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	0.912589	−	0.408878i	$-0.134080\pi$
$89$	0.964114	+	1.66990i	0.102196	+	0.177009i	−0.810393	+	0.585886i	$0.800746\pi$
$90$	−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	−0.0576582	+	0.998336i	$0.518363\pi$
$97$	−8.79911	+	15.2405i	−0.893414	+	1.54744i	−0.835756	+	0.549102i	$0.814970\pi$
$98$	−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	−0.981504	−	0.191443i	$-0.938683\pi$
$101$	−6.59821	−	11.4284i	−0.656547	−	1.13717i	0.324957	−	0.945729i	$-0.394650\pi$
$102$	−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	−0.979110	−	0.203332i	$-0.934823\pi$
$109$	−3.27267	+	5.66842i	−0.313465	+	0.542936i	0.665645	+	0.746268i	$0.268156\pi$
$110$	−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	−0.987408	−	0.158192i	$-0.949433\pi$
$127$	−7.10766	−	12.3108i	−0.630703	−	1.09241i	0.356706	−	0.934217i	$-0.383900\pi$
$128$	−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	0.333815	+	0.942639i	$0.391664\pi$
$131$	−7.43320	+	12.8747i	−0.649442	+	1.12487i	−0.983256	+	0.182227i	$0.941669\pi$
$132$	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	0.594617	−	0.804009i	$-0.297304\pi$
$137$	−4.66998	−	8.08865i	−0.398983	−	0.691060i	−0.993601	+	0.112949i	$0.963970\pi$
$138$	0.236780	−	0.410115i	0.0201561	−	0.0349113i
$139$	−2.26322	−	3.92001i	−0.191964	−	0.332491i	0.753937	−	0.656947i	$-0.228152\pi$
$139$	−2.26322	−	3.92001i	−0.191964	−	0.332491i	−0.945901	+	0.324455i	$0.894819\pi$
$140$	−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	−0.812634	−	0.582775i	$-0.801967\pi$
$149$	1.20089	−	2.08001i	0.0983811	−	0.170401i	0.911015	+	0.412374i	$0.135300\pi$
$150$	−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	−0.654857	−	0.755753i	$-0.727271\pi$
$157$	4.09821	−	7.09831i	0.327073	−	0.566507i	0.981930	+	0.189246i	$0.0606044\pi$
$158$	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	0.517184	−	0.855874i	$-0.326980\pi$
$167$	−6.23678	−	10.8024i	−0.482617	−	0.835916i	−0.999801	+	0.0199577i	$0.993647\pi$
$168$	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	0.421094	+	0.907017i	$0.361646\pi$
$173$	−7.56233	+	13.0983i	−0.574953	+	0.995848i	−0.996047	+	0.0888306i	$0.971687\pi$
$174$	−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	0.981885	−	0.189478i	$-0.0606795\pi$
$181$	4.39732	+	7.61637i	0.326850	+	0.566121i	−0.655035	+	0.755598i	$0.727346\pi$
$182$	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	−0.886437	−	0.462848i	$-0.846827\pi$
$193$	−0.588765	+	1.01977i	−0.0423802	+	0.0734047i	0.844057	+	0.536253i	$0.180161\pi$
$194$	−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	0.825913	−	0.563797i	$-0.190660\pi$
$199$	−1.06233	−	1.84000i	−0.0753062	−	0.130434i	−0.901219	+	0.433363i	$0.857327\pi$
$200$	−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	−0.328519	−	0.944497i	$-0.606550\pi$
$211$	9.49553	−	16.4467i	0.653699	−	1.13224i	0.982218	−	0.187743i	$-0.0601171\pi$
$212$	−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	0.271123	+	0.962545i	$0.412605\pi$
$223$	−10.4238	+	18.0545i	−0.698026	+	1.20902i	−0.969150	+	0.246472i	$0.920729\pi$
$224$	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	−0.0617416	−	0.998092i	$-0.519665\pi$
$233$	12.7229	−	22.0366i	0.833502	−	1.44367i	0.895244	−	0.445576i	$-0.147001\pi$
$234$	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	0.999177	−	0.0405642i	$-0.0129155\pi$
$241$	7.21034	+	12.4887i	0.464459	+	0.804466i	−0.534718	+	0.845031i	$0.679582\pi$
$242$	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	0.955480	+	0.295055i	$0.0953379\pi$
$251$	11.6171	+	20.1214i	0.733265	+	1.27005i	−0.222215	+	0.974998i	$0.571329\pi$
$252$	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	0.757159	−	0.653231i	$-0.226587\pi$
$257$	−3.00000	−	5.19615i	−0.187135	−	0.324127i	−0.944294	+	0.329104i	$0.893253\pi$
$258$	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	−0.273641	−	0.961832i	$-0.588228\pi$
$263$	11.2897	−	19.5543i	0.696150	−	1.20577i	0.969791	−	0.243936i	$-0.0784386\pi$
$264$	−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	−0.858185	−	0.513340i	$-0.828408\pi$
$269$	0.253774	−	0.439550i	0.0154729	−	0.0267998i	0.873658	+	0.486540i	$0.161741\pi$
$270$	−0.500000	−	0.866025i	−0.0304290	−	0.0527046i
$271$	−13.1247	+	22.7326i	−0.797266	+	1.38090i	0.124125	+	0.992267i	$0.460388\pi$
$271$	−13.1247	+	22.7326i	−0.797266	+	1.38090i	−0.921390	+	0.388638i	$0.872946\pi$
$272$	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	0.869219	−	0.494428i	$-0.164622\pi$
$281$	0.107657	+	0.186467i	0.00642225	+	0.0111237i	−0.862796	+	0.505552i	$0.831289\pi$
$282$	−4.07177	+	7.05251i	−0.242470	+	0.419971i
$283$	14.2153	−	24.6216i	0.845013	−	1.46360i	−0.0405976	−	0.999176i	$-0.512926\pi$
$283$	14.2153	−	24.6216i	0.845013	−	1.46360i	0.885610	−	0.464429i	$-0.153741\pi$
$284$	−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	−0.993634	−	0.112654i	$-0.964065\pi$
$307$	−6.99553	+	12.1166i	−0.399256	+	0.691531i	0.594378	+	0.804185i	$0.297398\pi$
$308$	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	−0.848293	−	0.529528i	$-0.822369\pi$
$313$	−15.6171	−	27.0496i	−0.882731	−	1.52893i	−0.0344382	−	0.999407i	$-0.510964\pi$
$314$	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	−0.996388	−	0.0849162i	$-0.972938\pi$
$317$	−10.1794	−	17.6313i	−0.571734	−	0.990272i	0.424654	−	0.905355i	$-0.360396\pi$
$318$	−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	−0.680349	−	0.732888i	$-0.738172\pi$
$337$	5.40676	−	9.36479i	0.294525	−	0.510132i	0.974874	+	0.222756i	$0.0715052\pi$
$338$	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	−0.716534	−	0.697552i	$-0.754273\pi$
$347$	4.57932	−	7.93161i	0.245831	−	0.425791i	0.962365	+	0.271761i	$0.0876059\pi$
$348$	−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	−0.711142	−	0.703049i	$-0.751822\pi$
$359$	4.79911	−	8.31229i	0.253287	−	0.438706i	0.964429	+	0.264343i	$0.0851549\pi$
$360$	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	0.847624	−	0.530598i	$-0.178033\pi$
$367$	−0.683901	−	1.18455i	−0.0356993	−	0.0618330i	−0.883323	+	0.468765i	$0.844699\pi$
$368$	−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	0.485212	+	0.874396i	$0.338742\pi$
$383$	−10.0718	+	17.4448i	−0.514643	+	0.891389i	−0.999856	+	0.0169922i	$0.994591\pi$
$384$	−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	0.999625	+	0.0273819i	$0.00871701\pi$
$389$	10.3255	+	17.8844i	0.523526	+	0.906773i	−0.476099	+	0.879392i	$0.657950\pi$
$390$	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	0.288766	+	0.957400i	$0.406755\pi$
$397$	−13.6435	+	23.6313i	−0.684750	+	1.18602i	−0.973515	+	0.228622i	$0.926578\pi$
$398$	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	0.0195060	+	0.999810i	$0.493791\pi$
$401$	−17.1435	+	29.6935i	−0.856108	+	1.48282i	−0.875614	+	0.483012i	$0.839543\pi$
$402$	−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	0.999881	+	0.0153958i	$0.00490083\pi$
$409$	10.3803	+	17.9792i	0.513274	+	0.889016i	−0.486608	+	0.873621i	$0.661766\pi$
$410$	−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	−0.791880	−	0.610677i	$-0.790897\pi$
$421$	2.72733	−	4.72388i	0.132922	−	0.230228i	0.924802	+	0.380449i	$0.124231\pi$
$422$	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	0.707729	+	0.706484i	$0.249720\pi$
$431$	20.0484	+	34.7249i	0.965698	+	1.67264i	0.257969	+	0.966153i	$0.416947\pi$
$432$	−0.500000	+	0.866025i	−0.0240563	+	0.0416667i
$433$	−5.60766	−	9.71275i	−0.269487	−	0.466765i	0.699243	−	0.714884i	$-0.253521\pi$
$433$	−5.60766	−	9.71275i	−0.269487	−	0.466765i	−0.968729	+	0.248120i	$0.920187\pi$
$434$	−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	−0.984991	−	0.172605i	$-0.944782\pi$
$439$	−7.18698	+	12.4482i	−0.343016	+	0.594121i	0.641976	+	0.766725i	$0.278115\pi$
$440$	−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	0.932910	−	0.360109i	$-0.117261\pi$
$443$	3.25377	+	5.63570i	0.154591	+	0.267760i	−0.778319	+	0.627869i	$0.783927\pi$
$444$	−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	−0.854787	−	0.518979i	$-0.826312\pi$
$461$	0.473560	−	0.820230i	0.0220559	−	0.0382019i	0.876843	+	0.480777i	$0.159645\pi$
$462$	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	−0.968079	−	0.250646i	$-0.919357\pi$
$479$	−15.3444	−	26.5773i	−0.701105	−	1.21435i	0.266974	−	0.963704i	$-0.413976\pi$
$480$	−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	−0.633992	−	0.773340i	$-0.718585\pi$
$491$	7.81610	−	13.5379i	0.352736	−	0.610956i	0.986728	+	0.162384i	$0.0519182\pi$
$492$	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	−0.868315	−	0.496014i	$-0.834797\pi$
$499$	−0.102684	+	0.177854i	−0.00459676	+	0.00796183i	0.863718	+	0.503976i	$0.168130\pi$
$500$	−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	0.822693	−	0.568485i	$-0.192470\pi$
$503$	−1.81610	−	3.14558i	−0.0809759	−	0.140254i	−0.903669	+	0.428231i	$0.859137\pi$
$504$	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	0.733095	−	0.680126i	$-0.238075\pi$
$509$	−5.01889	−	8.69298i	−0.222458	−	0.385309i	−0.955554	+	0.294816i	$0.904742\pi$
$510$	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	−0.995409	−	0.0957084i	$-0.969488\pi$
$523$	−13.2776	−	22.9975i	−0.580591	−	1.00561i	0.414819	−	0.909904i	$-0.363845\pi$
$524$	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	0.983935	+	0.178526i	$0.0571328\pi$
$541$	15.0390	+	26.0482i	0.646575	+	1.11990i	−0.337360	+	0.941376i	$0.609534\pi$
$542$	−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	0.927317	−	0.374277i	$-0.122109\pi$
$547$	3.26322	+	5.65206i	0.139525	+	0.241665i	−0.787792	+	0.615942i	$0.788776\pi$
$548$	−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	0.985403	+	0.170238i	$0.0544537\pi$
$557$	15.1077	+	26.1672i	0.640132	+	1.10874i	−0.345271	+	0.938503i	$0.612213\pi$
$558$	−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	−0.982703	−	0.185187i	$-0.940711\pi$
$587$	−8.01889	+	13.8891i	−0.330975	+	0.573266i	0.651728	+	0.758453i	$0.274044\pi$
$588$	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	−0.993554	−	0.113360i	$-0.963839\pi$
$593$	−14.4880	−	25.0939i	−0.594950	−	1.03048i	0.398604	−	0.917123i	$-0.369495\pi$
$594$	−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	−0.754874	−	0.655869i	$-0.772302\pi$
$599$	−23.1391	−	40.0780i	−0.945437	−	1.63754i	−0.190562	−	0.981675i	$-0.561031\pi$
$600$	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	0.498589	+	0.866838i	$0.333852\pi$
$613$	−12.4143	+	21.5022i	−0.501409	+	0.868466i	−0.999999	+	0.00162804i	$0.999482\pi$
$614$	−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	0.961156	−	0.276005i	$-0.0890106\pi$
$617$	6.00000	+	10.3923i	0.241551	+	0.418378i	−0.719605	+	0.694383i	$0.755677\pi$
$618$	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	0.972184	−	0.234220i	$-0.0752534\pi$
$631$	7.11520	+	12.3239i	0.283252	+	0.490607i	−0.688932	+	0.724826i	$0.741920\pi$
$632$	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	0.479848	+	0.877352i	$0.340692\pi$
$641$	−13.1624	+	22.7980i	−0.519885	+	0.900467i	−0.999733	+	0.0231153i	$0.992642\pi$
$642$	5.39732	+	9.34843i	0.213015	+	0.368953i
$643$	−8.25875	+	14.3046i	−0.325693	+	0.564117i	−0.981652	−	0.190679i	$-0.938931\pi$
$643$	−8.25875	+	14.3046i	−0.325693	+	0.564117i	0.655959	+	0.754796i	$0.272264\pi$
$644$	−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	−0.999984	−	0.00559311i	$-0.998220\pi$
$659$	−12.9596	−	22.4468i	−0.504836	−	0.874402i	0.495148	−	0.868808i	$-0.335114\pi$
$660$	−0.236780	+	0.410115i	−0.00921665	+	0.0159637i
$661$	14.8135	+	25.6578i	0.576179	+	0.997972i	0.995912	+	0.0903242i	$0.0287903\pi$
$661$	14.8135	+	25.6578i	0.576179	+	0.997972i	−0.419733	+	0.907648i	$0.637876\pi$
$662$	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	−0.353886	−	0.935289i	$-0.615140\pi$
$701$	16.7606	−	29.0303i	0.633041	−	1.09646i	0.986927	−	0.161170i	$-0.0515268\pi$
$702$	−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	0.929589	+	0.368597i	$0.120162\pi$
$709$	20.8758	+	36.1580i	0.784009	+	1.35794i	−0.145580	+	0.989346i	$0.546505\pi$
$710$	−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	−0.917038	−	0.398799i	$-0.869427\pi$
$719$	−3.03399	+	5.25502i	−0.113149	+	0.195979i	0.803890	+	0.594779i	$0.202760\pi$
$720$	−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	−0.684112	−	0.729377i	$-0.739810\pi$
$727$	7.80855	−	13.5248i	0.289603	−	0.501607i	0.973715	+	0.227770i	$0.0731433\pi$
$728$	−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	−0.450404	−	0.892825i	$-0.648720\pi$
$739$	14.8973	−	25.8029i	0.548007	−	0.949175i	0.998411	−	0.0563507i	$-0.0179465\pi$
$740$	−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	−0.424962	−	0.905211i	$-0.639712\pi$
$743$	15.5767	−	26.9797i	0.571455	−	0.989790i	0.996417	−	0.0845782i	$-0.0269543\pi$
$744$	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	−0.999575	−	0.0291367i	$-0.990724\pi$
$751$	−14.3879	−	24.9205i	−0.525021	−	0.909363i	0.474555	−	0.880226i	$-0.342609\pi$
$752$	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	−0.587361	−	0.809325i	$-0.699833\pi$
$757$	11.2040	−	19.4058i	0.407215	−	0.705317i	0.994577	+	0.104007i	$0.0331666\pi$
$758$	−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	0.956288	+	0.292425i	$0.0944622\pi$
$769$	20.2821	+	35.1296i	0.731392	+	1.26681i	−0.224897	+	0.974383i	$0.572205\pi$
$770$	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	0.704252	−	0.709951i	$-0.251283\pi$
$773$	−7.30408	−	12.6510i	−0.262709	−	0.455026i	−0.966961	+	0.254924i	$0.917949\pi$
$774$	−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	0.628540	−	0.777777i	$-0.283653\pi$
$811$	−10.2323	−	17.7229i	−0.359305	−	0.622334i	−0.987845	+	0.155443i	$0.950320\pi$
$812$	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	0.997780	+	0.0665894i	$0.0212118\pi$
$821$	15.9471	+	27.6212i	0.556558	+	0.963987i	−0.441222	+	0.897398i	$0.645455\pi$
$822$	−4.66998	+	8.08865i	−0.162884	+	0.282124i
$823$	8.01699	+	13.8858i	0.279455	+	0.484030i	0.971249	−	0.238064i	$-0.0765129\pi$
$823$	8.01699	+	13.8858i	0.279455	+	0.484030i	−0.691795	+	0.722094i	$0.743180\pi$
$824$	−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	−0.976072	−	0.217446i	$-0.930228\pi$
$827$	−19.4502	−	33.6887i	−0.676350	−	1.17147i	0.299723	−	0.954026i	$-0.403106\pi$
$828$	−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	−0.866612	−	0.498983i	$-0.833707\pi$
$839$	−0.0339879	+	0.0588688i	−0.00117339	+	0.00203238i	0.865438	+	0.501016i	$0.167040\pi$
$840$	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	−0.887140	−	0.461501i	$-0.847311\pi$
$853$	−1.28211	+	2.22068i	−0.0438987	+	0.0760347i	0.843241	+	0.537535i	$0.180645\pi$
$854$	−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	−0.983808	−	0.179225i	$-0.942641\pi$
$857$	−9.85646	+	17.0719i	−0.336690	+	0.583165i	0.647118	+	0.762390i	$0.275974\pi$
$858$	0.124650	−	0.215901i	0.00425550	−	0.00737074i
$859$	−5.75377	−	9.96583i	−0.196316	−	0.340030i	0.751015	−	0.660285i	$-0.229565\pi$
$859$	−5.75377	−	9.96583i	−0.196316	−	0.340030i	−0.947331	+	0.320255i	$0.896231\pi$
$860$	−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	−0.293556	−	0.955942i	$-0.594839\pi$
$877$	20.1700	−	34.9354i	0.681092	−	1.17969i	0.974648	−	0.223744i	$-0.0718279\pi$
$878$	−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	−0.929676	−	0.368378i	$-0.879913\pi$
$883$	−23.2927	−	40.3442i	−0.783863	−	1.35769i	0.145813	−	0.989312i	$-0.453420\pi$
$884$	−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	0.631937	−	0.775020i	$-0.282260\pi$
$887$	−10.5793	−	18.3239i	−0.355219	−	0.615257i	−0.987155	+	0.159763i	$0.948927\pi$
$888$	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	−0.888071	−	0.459706i	$-0.847955\pi$
$907$	−1.38290	+	2.39525i	−0.0459184	+	0.0795329i	0.842153	+	0.539239i	$0.181288\pi$
$908$	−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	−0.308384	−	0.951262i	$-0.599788\pi$
$929$	20.4098	−	35.3509i	0.669625	−	1.15982i	0.978009	−	0.208563i	$-0.0668785\pi$
$930$	−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	0.519568	−	0.854429i	$-0.326093\pi$
$937$	−14.6983	−	25.4582i	−0.480173	−	0.831684i	−0.999741	+	0.0227447i	$0.992760\pi$
$938$	−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	−0.754054	−	0.656812i	$-0.771905\pi$
$941$	−29.0144	−	50.2544i	−0.945843	−	1.63825i	−0.191789	−	0.981436i	$-0.561429\pi$
$942$	−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	−0.516576	−	0.856241i	$-0.672794\pi$
$947$	14.8709	−	25.7571i	0.483239	−	0.836994i	0.999815	+	0.0192475i	$0.00612705\pi$
$948$	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	−0.319872	−	0.947461i	$-0.603640\pi$
$953$	20.3928	−	35.3214i	0.660589	−	1.14417i	0.980461	−	0.196713i	$-0.0630267\pi$
$954$	−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	0.426151	+	0.904652i	$0.359869\pi$
$967$	−17.7368	+	30.7210i	−0.570376	+	0.987921i	−0.996527	+	0.0832687i	$0.973464\pi$
$968$	−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	−0.600706	−	0.799470i	$-0.705114\pi$
$971$	12.2153	−	21.1575i	0.392008	−	0.678978i	0.992714	+	0.120492i	$0.0384472\pi$
$972$	−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	−0.409157	−	0.912464i	$-0.634177\pi$
$983$	18.3614	−	31.8029i	0.585639	−	1.01436i	0.994795	−	0.101892i	$-0.0324896\pi$
$984$	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	0.458862	+	0.888507i	$0.348257\pi$
$991$	−17.0005	+	29.4457i	−0.540039	+	0.935374i	−0.998901	+	0.0468671i	$0.985076\pi$
$992$	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	0.969544	−	0.244917i	$-0.0787608\pi$
$997$	8.60955	+	14.9122i	0.272667	+	0.472274i	−0.696877	+	0.717191i	$0.745428\pi$
$998$	−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.391.1	yes	6
3.2	odd	2		1710.2.l.q.1531.1		6
19.7	even	3	inner	570.2.i.j.121.1	✓	6
57.26	odd	6		1710.2.l.q.1261.1		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
570.2.i.j.121.1	✓	6	19.7	even	3	inner
570.2.i.j.391.1	yes	6	1.1	even	1	trivial
1710.2.l.q.1261.1		6	57.26	odd	6
1710.2.l.q.1531.1		6	3.2	odd	2

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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