LMFDB - Embedded newform 770.2.i.l.221.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [770,2,Mod(221,770)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(770, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 4, 0]))

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

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

chi := DirichletCharacter("770.221");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 770 = 2 \cdot 5 \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	770.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:	$6.14848095564$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{7} + 8x^{6} + 3x^{5} + 50x^{4} - 12x^{3} + 11x^{2} + 2x + 1 $ x^8 - x^7 + 8x^6 + 3x^5 + 50x^4 - 12x^3 + 11x^2 + 2x + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 3 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			221.4
Root			$1.52336 - 2.63854i$ of defining polynomial
Character	$\chi$	$=$	770.221
Dual form			770.2.i.l.331.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 - 0.866025i) q^{2} +(1.52336 - 2.63854i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(0.500000 + 0.866025i) q^{5} -3.04673 q^{6} +(2.18747 + 1.48827i) q^{7} +1.00000 q^{8} +(-3.14128 - 5.44086i) q^{9} +O(q^{10})$	\(q+(-0.500000 - 0.866025i) q^{2} +(1.52336 - 2.63854i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(0.500000 + 0.866025i) q^{5} -3.04673 q^{6} +(2.18747 + 1.48827i) q^{7} +1.00000 q^{8} +(-3.14128 - 5.44086i) q^{9} +(0.500000 - 0.866025i) q^{10} +(0.500000 - 0.866025i) q^{11} +(1.52336 + 2.63854i) q^{12} +0.517321 q^{13} +(0.195144 - 2.63854i) q^{14} +3.04673 q^{15} +(-0.500000 - 0.866025i) q^{16} +(0.664110 - 1.15027i) q^{17} +(-3.14128 + 5.44086i) q^{18} +(-1.78969 - 3.09984i) q^{19} -1.00000 q^{20} +(7.25919 - 3.50457i) q^{21} -1.00000 q^{22} +(-2.71851 - 4.70859i) q^{23} +(1.52336 - 2.63854i) q^{24} +(-0.500000 + 0.866025i) q^{25} +(-0.258661 - 0.448013i) q^{26} -10.0011 q^{27} +(-2.38262 + 1.15027i) q^{28} +0.281492 q^{29} +(-1.52336 - 2.63854i) q^{30} +(5.16464 - 8.94543i) q^{31} +(-0.500000 + 0.866025i) q^{32} +(-1.52336 - 2.63854i) q^{33} -1.32822 q^{34} +(-0.195144 + 2.63854i) q^{35} +6.28256 q^{36} +(2.57172 + 4.45435i) q^{37} +(-1.78969 + 3.09984i) q^{38} +(0.788069 - 1.36497i) q^{39} +(0.500000 + 0.866025i) q^{40} +2.65644 q^{41} +(-6.66464 - 4.53436i) q^{42} +2.56298 q^{43} +(0.500000 + 0.866025i) q^{44} +(3.14128 - 5.44086i) q^{45} +(-2.71851 + 4.70859i) q^{46} +(-2.37495 - 4.11353i) q^{47} -3.04673 q^{48} +(2.57009 + 6.51111i) q^{49} +1.00000 q^{50} +(-2.02336 - 3.50457i) q^{51} +(-0.258661 + 0.448013i) q^{52} +(0.921146 - 1.59547i) q^{53} +(5.00053 + 8.66118i) q^{54} +1.00000 q^{55} +(2.18747 + 1.48827i) q^{56} -10.9054 q^{57} +(-0.140746 - 0.243779i) q^{58} +(-3.11629 + 5.39757i) q^{59} +(-1.52336 + 2.63854i) q^{60} +(5.68801 + 9.85192i) q^{61} -10.3293 q^{62} +(1.22600 - 16.5768i) q^{63} +1.00000 q^{64} +(0.258661 + 0.448013i) q^{65} +(-1.52336 + 2.63854i) q^{66} +(-6.54673 + 11.3393i) q^{67} +(0.664110 + 1.15027i) q^{68} -16.5651 q^{69} +(2.38262 - 1.15027i) q^{70} -11.0792 q^{71} +(-3.14128 - 5.44086i) q^{72} +(-4.47717 + 7.75468i) q^{73} +(2.57172 - 4.45435i) q^{74} +(1.52336 + 2.63854i) q^{75} +3.57939 q^{76} +(2.38262 - 1.15027i) q^{77} -1.57614 q^{78} +(5.36746 + 9.29671i) q^{79} +(0.500000 - 0.866025i) q^{80} +(-5.81143 + 10.0657i) q^{81} +(-1.32822 - 2.30055i) q^{82} +13.2216 q^{83} +(-0.594550 + 8.03893i) q^{84} +1.32822 q^{85} +(-1.28149 - 2.21961i) q^{86} +(0.428814 - 0.742728i) q^{87} +(0.500000 - 0.866025i) q^{88} +(8.06458 + 13.9683i) q^{89} -6.28256 q^{90} +(1.13163 + 0.769914i) q^{91} +5.43702 q^{92} +(-15.7353 - 27.2543i) q^{93} +(-2.37495 + 4.11353i) q^{94} +(1.78969 - 3.09984i) q^{95} +(1.52336 + 2.63854i) q^{96} -15.3607 q^{97} +(4.35374 - 5.48132i) q^{98} -6.28256 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 4 q^{2} + q^{3} - 4 q^{4} + 4 q^{5} - 2 q^{6} + 3 q^{7} + 8 q^{8} - 3 q^{9}+O(q^{10}) $ 8 * q - 4 * q^2 + q^3 - 4 * q^4 + 4 * q^5 - 2 * q^6 + 3 * q^7 + 8 * q^8 - 3 * q^9	\( 8 q - 4 q^{2} + q^{3} - 4 q^{4} + 4 q^{5} - 2 q^{6} + 3 q^{7} + 8 q^{8} - 3 q^{9} + 4 q^{10} + 4 q^{11} + q^{12} - 2 q^{13} - 3 q^{14} + 2 q^{15} - 4 q^{16} + 2 q^{17} - 3 q^{18} - 10 q^{19} - 8 q^{20} + 25 q^{21} - 8 q^{22} - 6 q^{23} + q^{24} - 4 q^{25} + q^{26} - 20 q^{27} + 18 q^{29} - q^{30} + 8 q^{31} - 4 q^{32} - q^{33} - 4 q^{34} + 3 q^{35} + 6 q^{36} + 2 q^{37} - 10 q^{38} - 13 q^{39} + 4 q^{40} + 8 q^{41} - 20 q^{42} + 52 q^{43} + 4 q^{44} + 3 q^{45} - 6 q^{46} + 10 q^{47} - 2 q^{48} - 13 q^{49} + 8 q^{50} - 5 q^{51} + q^{52} - 14 q^{53} + 10 q^{54} + 8 q^{55} + 3 q^{56} + 18 q^{57} - 9 q^{58} + q^{59} - q^{60} + q^{61} - 16 q^{62} - 7 q^{63} + 8 q^{64} - q^{65} - q^{66} - 30 q^{67} + 2 q^{68} - 44 q^{69} + 36 q^{71} - 3 q^{72} - 17 q^{73} + 2 q^{74} + q^{75} + 20 q^{76} + 26 q^{78} + 15 q^{79} + 4 q^{80} - 16 q^{81} - 4 q^{82} + 4 q^{83} - 5 q^{84} + 4 q^{85} - 26 q^{86} - 8 q^{87} + 4 q^{88} + 6 q^{89} - 6 q^{90} + 3 q^{91} + 12 q^{92} - 29 q^{93} + 10 q^{94} + 10 q^{95} + q^{96} - 14 q^{97} + 2 q^{98} - 6 q^{99}+O(q^{100}) \) 8 * q - 4 * q^2 + q^3 - 4 * q^4 + 4 * q^5 - 2 * q^6 + 3 * q^7 + 8 * q^8 - 3 * q^9 + 4 * q^10 + 4 * q^11 + q^12 - 2 * q^13 - 3 * q^14 + 2 * q^15 - 4 * q^16 + 2 * q^17 - 3 * q^18 - 10 * q^19 - 8 * q^20 + 25 * q^21 - 8 * q^22 - 6 * q^23 + q^24 - 4 * q^25 + q^26 - 20 * q^27 + 18 * q^29 - q^30 + 8 * q^31 - 4 * q^32 - q^33 - 4 * q^34 + 3 * q^35 + 6 * q^36 + 2 * q^37 - 10 * q^38 - 13 * q^39 + 4 * q^40 + 8 * q^41 - 20 * q^42 + 52 * q^43 + 4 * q^44 + 3 * q^45 - 6 * q^46 + 10 * q^47 - 2 * q^48 - 13 * q^49 + 8 * q^50 - 5 * q^51 + q^52 - 14 * q^53 + 10 * q^54 + 8 * q^55 + 3 * q^56 + 18 * q^57 - 9 * q^58 + q^59 - q^60 + q^61 - 16 * q^62 - 7 * q^63 + 8 * q^64 - q^65 - q^66 - 30 * q^67 + 2 * q^68 - 44 * q^69 + 36 * q^71 - 3 * q^72 - 17 * q^73 + 2 * q^74 + q^75 + 20 * q^76 + 26 * q^78 + 15 * q^79 + 4 * q^80 - 16 * q^81 - 4 * q^82 + 4 * q^83 - 5 * q^84 + 4 * q^85 - 26 * q^86 - 8 * q^87 + 4 * q^88 + 6 * q^89 - 6 * q^90 + 3 * q^91 + 12 * q^92 - 29 * q^93 + 10 * q^94 + 10 * q^95 + q^96 - 14 * q^97 + 2 * q^98 - 6 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/770\mathbb{Z}\right)^\times$.

$n$	$211$	$617$	$661$
$\chi(n)$	$1$	$1$	$e\left(\frac{2}{3}\right)$

Coefficient data

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

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

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

$2$	−0.500000	−	0.866025i	−0.353553	−	0.612372i
$2$	−0.500000	−	0.866025i	−0.353553	−	0.612372i
$3$	1.52336	−	2.63854i	0.879515	−	1.52336i	0.0276409	−	0.999618i	$-0.491201\pi$
$3$	1.52336	−	2.63854i	0.879515	−	1.52336i	0.851874	−	0.523747i	$-0.175466\pi$
$4$	−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
$6$	−3.04673			−1.24382
$7$	2.18747	+	1.48827i	0.826788	+	0.562514i
$7$	2.18747	+	1.48827i	0.826788	+	0.562514i
$8$	1.00000			0.353553
$9$	−3.14128	−	5.44086i	−1.04709	−	1.81362i
$10$	0.500000	−	0.866025i	0.158114	−	0.273861i
$11$	0.500000	−	0.866025i	0.150756	−	0.261116i
$11$	0.500000	−	0.866025i	0.150756	−	0.261116i
$12$	1.52336	+	2.63854i	0.439757	+	0.761682i
$13$	0.517321			0.143479			0.0717395	−	0.997423i	$-0.477145\pi$
$13$	0.517321			0.143479			0.0717395	+	0.997423i	$0.477145\pi$
$14$	0.195144	−	2.63854i	0.0521544	−	0.705181i
$15$	3.04673			0.786662
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	0.664110	−	1.15027i	0.161070	−	0.278982i	−0.774182	−	0.632963i	$-0.781839\pi$
$17$	0.664110	−	1.15027i	0.161070	−	0.278982i	0.935253	+	0.353980i	$0.115172\pi$
$18$	−3.14128	+	5.44086i	−0.740407	+	1.28242i
$19$	−1.78969	−	3.09984i	−0.410584	−	0.711152i	0.584370	−	0.811488i	$-0.301342\pi$
$19$	−1.78969	−	3.09984i	−0.410584	−	0.711152i	−0.994954	+	0.100335i	$0.968008\pi$
$20$	−1.00000			−0.223607
$21$	7.25919	−	3.50457i	1.58409	−	0.764760i
$22$	−1.00000			−0.213201
$23$	−2.71851	−	4.70859i	−0.566848	−	0.981810i	−0.996875	−	0.0789938i	$-0.974829\pi$
$23$	−2.71851	−	4.70859i	−0.566848	−	0.981810i	0.430027	−	0.902816i	$-0.358504\pi$
$24$	1.52336	−	2.63854i	0.310955	−	0.538591i
$25$	−0.500000	+	0.866025i	−0.100000	+	0.173205i
$26$	−0.258661	−	0.448013i	−0.0507275	−	0.0878626i
$27$	−10.0011			−1.92471
$28$	−2.38262	+	1.15027i	−0.450273	+	0.217381i
$29$	0.281492			0.0522717			0.0261358	−	0.999658i	$-0.491680\pi$
$29$	0.281492			0.0522717			0.0261358	+	0.999658i	$0.491680\pi$
$30$	−1.52336	−	2.63854i	−0.278127	−	0.481730i
$31$	5.16464	−	8.94543i	0.927597	−	1.60665i	0.140268	−	0.990114i	$-0.455204\pi$
$31$	5.16464	−	8.94543i	0.927597	−	1.60665i	0.787330	−	0.616532i	$-0.211463\pi$
$32$	−0.500000	+	0.866025i	−0.0883883	+	0.153093i
$33$	−1.52336	−	2.63854i	−0.265184	−	0.459312i
$34$	−1.32822			−0.227788
$35$	−0.195144	+	2.63854i	−0.0329853	+	0.445995i
$36$	6.28256			1.04709
$37$	2.57172	+	4.45435i	0.422788	+	0.732290i	0.996211	−	0.0869692i	$-0.0277182\pi$
$37$	2.57172	+	4.45435i	0.422788	+	0.732290i	−0.573423	+	0.819259i	$0.694385\pi$
$38$	−1.78969	+	3.09984i	−0.290327	+	0.502861i
$39$	0.788069	−	1.36497i	0.126192	−	0.218571i
$40$	0.500000	+	0.866025i	0.0790569	+	0.136931i
$41$	2.65644			0.414866			0.207433	−	0.978249i	$-0.433489\pi$
$41$	2.65644			0.414866			0.207433	+	0.978249i	$0.433489\pi$
$42$	−6.66464	−	4.53436i	−1.02838	−	0.699667i
$43$	2.56298			0.390851			0.195426	−	0.980719i	$-0.437391\pi$
$43$	2.56298			0.390851			0.195426	+	0.980719i	$0.437391\pi$
$44$	0.500000	+	0.866025i	0.0753778	+	0.130558i
$45$	3.14128	−	5.44086i	0.468274	−	0.811075i
$46$	−2.71851	+	4.70859i	−0.400822	+	0.694244i
$47$	−2.37495	−	4.11353i	−0.346422	−	0.600021i	0.639189	−	0.769050i	$-0.279270\pi$
$47$	−2.37495	−	4.11353i	−0.346422	−	0.600021i	−0.985611	+	0.169029i	$0.945937\pi$
$48$	−3.04673			−0.439757
$49$	2.57009	+	6.51111i	0.367156	+	0.930159i
$50$	1.00000			0.141421
$51$	−2.02336	−	3.50457i	−0.283328	−	0.490738i
$52$	−0.258661	+	0.448013i	−0.0358698	+	0.0621283i
$53$	0.921146	−	1.59547i	0.126529	−	0.219155i	−0.795801	−	0.605559i	$-0.792950\pi$
$53$	0.921146	−	1.59547i	0.126529	−	0.219155i	0.922330	+	0.386404i	$0.126283\pi$
$54$	5.00053	+	8.66118i	0.680486	+	1.17864i
$55$	1.00000			0.134840
$56$	2.18747	+	1.48827i	0.292314	+	0.198879i
$57$	−10.9054			−1.44446
$58$	−0.140746	−	0.243779i	−0.0184808	−	0.0320097i
$59$	−3.11629	+	5.39757i	−0.405706	+	0.702704i	−0.994403	−	0.105650i	$-0.966308\pi$
$59$	−3.11629	+	5.39757i	−0.405706	+	0.702704i	0.588697	+	0.808354i	$0.299641\pi$
$60$	−1.52336	+	2.63854i	−0.196666	+	0.340635i
$61$	5.68801	+	9.85192i	0.728275	+	1.26141i	0.957612	+	0.288062i	$0.0930109\pi$
$61$	5.68801	+	9.85192i	0.728275	+	1.26141i	−0.229337	+	0.973347i	$0.573656\pi$
$62$	−10.3293			−1.31182
$63$	1.22600	−	16.5768i	0.154462	−	2.08848i
$64$	1.00000			0.125000
$65$	0.258661	+	0.448013i	0.0320829	+	0.0555692i
$66$	−1.52336	+	2.63854i	−0.187513	+	0.324782i
$67$	−6.54673	+	11.3393i	−0.799810	+	1.38531i	0.119929	+	0.992782i	$0.461733\pi$
$67$	−6.54673	+	11.3393i	−0.799810	+	1.38531i	−0.919739	+	0.392530i	$0.871600\pi$
$68$	0.664110	+	1.15027i	0.0805352	+	0.139491i
$69$	−16.5651			−1.99421
$70$	2.38262	−	1.15027i	0.284777	−	0.137484i
$71$	−11.0792			−1.31486			−0.657429	−	0.753517i	$-0.728356\pi$
$71$	−11.0792			−1.31486			−0.657429	+	0.753517i	$0.728356\pi$
$72$	−3.14128	−	5.44086i	−0.370203	−	0.641211i
$73$	−4.47717	+	7.75468i	−0.524013	+	0.907617i	0.475596	+	0.879664i	$0.342232\pi$
$73$	−4.47717	+	7.75468i	−0.524013	+	0.907617i	−0.999609	+	0.0279534i	$0.991101\pi$
$74$	2.57172	−	4.45435i	0.298956	−	0.517807i
$75$	1.52336	+	2.63854i	0.175903	+	0.304673i
$76$	3.57939			0.410584
$77$	2.38262	−	1.15027i	0.271525	−	0.131086i
$78$	−1.57614			−0.178462
$79$	5.36746	+	9.29671i	0.603886	+	1.04596i	0.992226	+	0.124445i	$0.0397151\pi$
$79$	5.36746	+	9.29671i	0.603886	+	1.04596i	−0.388340	+	0.921516i	$0.626952\pi$
$80$	0.500000	−	0.866025i	0.0559017	−	0.0968246i
$81$	−5.81143	+	10.0657i	−0.645715	+	1.11841i
$82$	−1.32822	−	2.30055i	−0.146677	−	0.254053i
$83$	13.2216			1.45125			0.725627	−	0.688088i	$-0.241550\pi$
$83$	13.2216			1.45125			0.725627	+	0.688088i	$0.241550\pi$
$84$	−0.594550	+	8.03893i	−0.0648707	+	0.877119i
$85$	1.32822			0.144066
$86$	−1.28149	−	2.21961i	−0.138187	−	0.239347i
$87$	0.428814	−	0.742728i	0.0459737	−	0.0796288i
$88$	0.500000	−	0.866025i	0.0533002	−	0.0923186i
$89$	8.06458	+	13.9683i	0.854844	+	1.48063i	0.876790	+	0.480874i	$0.159681\pi$
$89$	8.06458	+	13.9683i	0.854844	+	1.48063i	−0.0219454	+	0.999759i	$0.506986\pi$
$90$	−6.28256			−0.662240
$91$	1.13163	+	0.769914i	0.118627	+	0.0807090i
$92$	5.43702			0.566848
$93$	−15.7353	−	27.2543i	−1.63167	−	2.82614i
$94$	−2.37495	+	4.11353i	−0.244957	+	0.424279i
$95$	1.78969	−	3.09984i	0.183619	−	0.318037i
$96$	1.52336	+	2.63854i	0.155478	+	0.269295i
$97$	−15.3607			−1.55964			−0.779820	−	0.626003i	$-0.784690\pi$
$97$	−15.3607			−1.55964			−0.779820	+	0.626003i	$0.784690\pi$
$98$	4.35374	−	5.48132i	0.439795	−	0.553697i
$99$	−6.28256			−0.631421
$100$	−0.500000	−	0.866025i	−0.0500000	−	0.0866025i
$101$	−2.89029	+	5.00612i	−0.287594	+	0.498128i	−0.973235	−	0.229812i	$-0.926189\pi$
$101$	−2.89029	+	5.00612i	−0.287594	+	0.498128i	0.685641	+	0.727940i	$0.259522\pi$
$102$	−2.02336	+	3.50457i	−0.200343	+	0.347004i
$103$	−1.18910	−	2.05958i	−0.117166	−	0.202937i	0.801478	−	0.598025i	$-0.204047\pi$
$103$	−1.18910	−	2.05958i	−0.117166	−	0.202937i	−0.918643	+	0.395088i	$0.870714\pi$
$104$	0.517321			0.0507275
$105$	6.66464	+	4.53436i	0.650403	+	0.442508i
$106$	−1.84229			−0.178939
$107$	−1.67178	−	2.89561i	−0.161617	−	0.279929i	0.773832	−	0.633391i	$-0.218338\pi$
$107$	−1.67178	−	2.89561i	−0.161617	−	0.279929i	−0.935449	+	0.353462i	$0.885004\pi$
$108$	5.00053	−	8.66118i	0.481177	−	0.833422i
$109$	5.04122	−	8.73165i	0.482861	−	0.836340i	−0.516945	−	0.856019i	$-0.672931\pi$
$109$	5.04122	−	8.73165i	0.482861	−	0.836340i	0.999806	+	0.0196784i	$0.00626422\pi$
$110$	−0.500000	−	0.866025i	−0.0476731	−	0.0825723i
$111$	15.6707			1.48739
$112$	0.195144	−	2.63854i	0.0184394	−	0.249319i
$113$	−1.29790			−0.122096			−0.0610479	−	0.998135i	$-0.519444\pi$
$113$	−1.29790			−0.122096			−0.0610479	+	0.998135i	$0.519444\pi$
$114$	5.45271	+	9.44438i	0.510693	+	0.884547i
$115$	2.71851	−	4.70859i	0.253502	−	0.439079i
$116$	−0.140746	+	0.243779i	−0.0130679	+	0.0226343i
$117$	−1.62505	−	2.81467i	−0.150236	−	0.260216i
$118$	6.23258			0.573755
$119$	3.16464	−	1.52782i	0.290102	−	0.140055i
$120$	3.04673			0.278127
$121$	−0.500000	−	0.866025i	−0.0454545	−	0.0787296i
$122$	5.68801	−	9.85192i	0.514968	−	0.891951i
$123$	4.04673	−	7.00914i	0.364881	−	0.631993i
$124$	5.16464	+	8.94543i	0.463799	+	0.803323i
$125$	−1.00000			−0.0894427
$126$	−14.9689	+	7.22666i	−1.33354	+	0.643802i
$127$	15.8740			1.40859			0.704296	−	0.709906i	$-0.251263\pi$
$127$	15.8740			1.40859			0.704296	+	0.709906i	$0.251263\pi$
$128$	−0.500000	−	0.866025i	−0.0441942	−	0.0765466i
$129$	3.90436	−	6.76255i	0.343760	−	0.595409i
$130$	0.258661	−	0.448013i	0.0226860	−	0.0392934i
$131$	2.33589	+	4.04588i	0.204088	+	0.353490i	0.949842	−	0.312731i	$-0.101244\pi$
$131$	2.33589	+	4.04588i	0.204088	+	0.353490i	−0.745754	+	0.666221i	$0.767911\pi$
$132$	3.04673			0.265184
$133$	0.698495	−	9.44438i	0.0605672	−	0.818931i
$134$	13.0935			1.13110
$135$	−5.00053	−	8.66118i	−0.430377	−	0.745436i
$136$	0.664110	−	1.15027i	0.0569470	−	0.0986351i
$137$	−3.17836	+	5.50507i	−0.271545	+	0.470330i	−0.969258	−	0.246048i	$-0.920868\pi$
$137$	−3.17836	+	5.50507i	−0.271545	+	0.470330i	0.697712	+	0.716378i	$0.254201\pi$
$138$	8.28256	+	14.3458i	0.705058	+	1.22120i
$139$	15.9218			1.35047			0.675236	−	0.737602i	$-0.264042\pi$
$139$	15.9218			1.35047			0.675236	+	0.737602i	$0.264042\pi$
$140$	−2.18747	−	1.48827i	−0.184875	−	0.125782i
$141$	−14.4717			−1.21873
$142$	5.53959	+	9.59486i	0.464872	+	0.805183i
$143$	0.258661	−	0.448013i	0.0216303	−	0.0374647i
$144$	−3.14128	+	5.44086i	−0.261773	+	0.453405i
$145$	0.140746	+	0.243779i	0.0116883	+	0.0202447i
$146$	8.95434			0.741066
$147$	21.0951	+	3.13749i	1.73989	+	0.258776i
$148$	−5.14344			−0.422788
$149$	−9.64397	−	16.7038i	−0.790065	−	1.36843i	−0.925926	−	0.377705i	$-0.876713\pi$
$149$	−9.64397	−	16.7038i	−0.790065	−	1.36843i	0.135861	−	0.990728i	$-0.456620\pi$
$150$	1.52336	−	2.63854i	0.124382	−	0.215436i
$151$	−3.54015	+	6.13172i	−0.288094	+	0.498993i	−0.973355	−	0.229305i	$-0.926355\pi$
$151$	−3.54015	+	6.13172i	−0.288094	+	0.498993i	0.685261	+	0.728297i	$0.259688\pi$
$152$	−1.78969	−	3.09984i	−0.145163	−	0.251430i
$153$	−8.34463			−0.674623
$154$	−2.18747	−	1.48827i	−0.176272	−	0.119928i
$155$	10.3293			0.829668
$156$	0.788069	+	1.36497i	0.0630960	+	0.109285i
$157$	−9.63199	+	16.6831i	−0.768716	+	1.33146i	0.169543	+	0.985523i	$0.445771\pi$
$157$	−9.63199	+	16.6831i	−0.768716	+	1.33146i	−0.938259	+	0.345933i	$0.887563\pi$
$158$	5.36746	−	9.29671i	0.427012	−	0.739606i
$159$	−2.80648	−	4.86097i	−0.222568	−	0.385500i
$160$	−1.00000			−0.0790569
$161$	1.06100	−	14.3458i	0.0836185	−	1.13061i
$162$	11.6229			0.913179
$163$	2.17981	+	3.77554i	0.170736	+	0.295723i	0.938677	−	0.344797i	$-0.112052\pi$
$163$	2.17981	+	3.77554i	0.170736	+	0.295723i	−0.767942	+	0.640520i	$0.778719\pi$
$164$	−1.32822	+	2.30055i	−0.103717	+	0.179642i
$165$	1.52336	−	2.63854i	0.118594	−	0.205410i
$166$	−6.61078	−	11.4502i	−0.513096	−	0.888708i
$167$	1.42493			0.110264			0.0551322	−	0.998479i	$-0.482442\pi$
$167$	1.42493			0.110264			0.0551322	+	0.998479i	$0.482442\pi$
$168$	7.25919	−	3.50457i	0.560059	−	0.270383i
$169$	−12.7324			−0.979414
$170$	−0.664110	−	1.15027i	−0.0509349	−	0.0882219i
$171$	−11.2439	+	19.4749i	−0.859839	+	1.48929i
$172$	−1.28149	+	2.21961i	−0.0977128	+	0.169244i
$173$	−12.5076	−	21.6639i	−0.950939	−	1.64707i	−0.743400	−	0.668847i	$-0.766788\pi$
$173$	−12.5076	−	21.6639i	−0.950939	−	1.64707i	−0.207538	−	0.978227i	$-0.566545\pi$
$174$	−0.857629			−0.0650167
$175$	−2.38262	+	1.15027i	−0.180109	+	0.0869525i
$176$	−1.00000			−0.0753778
$177$	9.49449	+	16.4449i	0.713650	+	1.23608i
$178$	8.06458	−	13.9683i	0.604466	−	1.04697i
$179$	1.94253	−	3.36455i	0.145191	−	0.251479i	−0.784253	−	0.620441i	$-0.786954\pi$
$179$	1.94253	−	3.36455i	0.145191	−	0.251479i	0.929444	+	0.368962i	$0.120287\pi$
$180$	3.14128	+	5.44086i	0.234137	+	0.405537i
$181$	25.9108			1.92594			0.962968	−	0.269617i	$-0.0868971\pi$
$181$	25.9108			1.92594			0.962968	+	0.269617i	$0.0868971\pi$
$182$	0.100952	−	1.36497i	0.00748306	−	0.101179i
$183$	34.6596			2.56211
$184$	−2.71851	−	4.70859i	−0.200411	−	0.347122i
$185$	−2.57172	+	4.45435i	−0.189077	+	0.327490i
$186$	−15.7353	+	27.2543i	−1.15377	+	1.99838i
$187$	−0.664110	−	1.15027i	−0.0485646	−	0.0841163i
$188$	4.74990			0.346422
$189$	−21.8771	−	14.8843i	−1.59132	−	1.08267i
$190$	−3.57939			−0.259676
$191$	−5.75541	−	9.96866i	−0.416447	−	0.721307i	0.579132	−	0.815234i	$-0.303391\pi$
$191$	−5.75541	−	9.96866i	−0.416447	−	0.721307i	−0.995579	+	0.0939265i	$0.970058\pi$
$192$	1.52336	−	2.63854i	0.109939	−	0.190421i
$193$	0.797363	−	1.38107i	0.0573954	−	0.0994118i	−0.835900	−	0.548882i	$-0.815054\pi$
$193$	0.797363	−	1.38107i	0.0573954	−	0.0994118i	0.893295	+	0.449470i	$0.148387\pi$
$194$	7.68034	+	13.3027i	0.551416	+	0.955081i
$195$	1.57614			0.112870
$196$	−6.92384	−	1.02979i	−0.494560	−	0.0735565i
$197$	−3.39135			−0.241624			−0.120812	−	0.992675i	$-0.538550\pi$
$197$	−3.39135			−0.241624			−0.120812	+	0.992675i	$0.538550\pi$
$198$	3.14128	+	5.44086i	0.223241	+	0.386665i
$199$	−11.4049	+	19.7539i	−0.808471	+	1.40031i	0.105451	+	0.994424i	$0.466371\pi$
$199$	−11.4049	+	19.7539i	−0.808471	+	1.40031i	−0.913922	+	0.405889i	$0.866962\pi$
$200$	−0.500000	+	0.866025i	−0.0353553	+	0.0612372i
$201$	19.9461	+	34.5477i	1.40689	+	2.43681i
$202$	5.78057			0.406720
$203$	0.615756	+	0.418936i	0.0432176	+	0.0294036i
$204$	4.04673			0.283328
$205$	1.32822	+	2.30055i	0.0927670	+	0.160677i
$206$	−1.18910	+	2.05958i	−0.0828485	+	0.143498i
$207$	−17.0792	+	29.5820i	−1.18709	+	2.05609i
$208$	−0.258661	−	0.448013i	−0.0179349	−	0.0310641i
$209$	−3.57939			−0.247591
$210$	0.594550	−	8.03893i	0.0410279	−	0.554739i
$211$	7.76630			0.534654			0.267327	−	0.963606i	$-0.413860\pi$
$211$	7.76630			0.534654			0.267327	+	0.963606i	$0.413860\pi$
$212$	0.921146	+	1.59547i	0.0632645	+	0.109577i
$213$	−16.8776	+	29.2329i	−1.15644	+	2.00301i
$214$	−1.67178	+	2.89561i	−0.114280	+	0.197940i
$215$	1.28149	+	2.21961i	0.0873970	+	0.151376i
$216$	−10.0011			−0.680486
$217$	24.6108	−	11.8815i	1.67069	−	0.806569i
$218$	−10.0824			−0.682869
$219$	13.6407	+	23.6264i	0.921754	+	1.59653i
$220$	−0.500000	+	0.866025i	−0.0337100	+	0.0583874i
$221$	0.343558	−	0.595060i	0.0231102	−	0.0400281i
$222$	−7.83533	−	13.5712i	−0.525873	−	0.910839i
$223$	3.22156			0.215732			0.107866	−	0.994165i	$-0.465598\pi$
$223$	3.22156			0.215732			0.107866	+	0.994165i	$0.465598\pi$
$224$	−2.38262	+	1.15027i	−0.159195	+	0.0768558i
$225$	6.28256			0.418837
$226$	0.648948	+	1.12401i	0.0431674	+	0.0747681i
$227$	−7.48268	+	12.9604i	−0.496643	+	0.860211i	−0.999993	−	0.00387218i	$-0.998767\pi$
$227$	−7.48268	+	12.9604i	−0.496643	+	0.860211i	0.503350	+	0.864083i	$0.332101\pi$
$228$	5.45271	−	9.44438i	0.361115	−	0.625469i
$229$	2.82730	+	4.89703i	0.186834	+	0.323605i	0.944193	−	0.329393i	$-0.106844\pi$
$229$	2.82730	+	4.89703i	0.186834	+	0.323605i	−0.757359	+	0.652998i	$0.773511\pi$
$230$	−5.43702			−0.358506
$231$	0.594550	−	8.03893i	0.0391185	−	0.528923i
$232$	0.281492			0.0184808
$233$	12.0189	+	20.8174i	0.787386	+	1.36379i	0.927563	+	0.373666i	$0.121899\pi$
$233$	12.0189	+	20.8174i	0.787386	+	1.36379i	−0.140178	+	0.990126i	$0.544767\pi$
$234$	−1.62505	+	2.81467i	−0.106233	+	0.184001i
$235$	2.37495	−	4.11353i	0.154925	−	0.268337i
$236$	−3.11629	−	5.39757i	−0.202853	−	0.351352i
$237$	32.7064			2.12451
$238$	−2.90545	−	1.97675i	−0.188332	−	0.128134i
$239$	27.0824			1.75182			0.875909	−	0.482477i	$-0.160263\pi$
$239$	27.0824			1.75182			0.875909	+	0.482477i	$0.160263\pi$
$240$	−1.52336	−	2.63854i	−0.0983328	−	0.170317i
$241$	−7.61078	+	13.1823i	−0.490253	+	0.849144i	−0.999937	−	0.0112181i	$-0.996429\pi$
$241$	−7.61078	+	13.1823i	−0.490253	+	0.849144i	0.509684	+	0.860362i	$0.329762\pi$
$242$	−0.500000	+	0.866025i	−0.0321412	+	0.0556702i
$243$	2.70426	+	4.68392i	0.173479	+	0.300474i
$244$	−11.3760			−0.728275
$245$	−4.35374	+	5.48132i	−0.278151	+	0.350189i
$246$	−8.09346			−0.516020
$247$	−0.925846	−	1.60361i	−0.0589102	−	0.102035i
$248$	5.16464	−	8.94543i	0.327955	−	0.568035i
$249$	20.1413	−	34.8857i	1.27640	−	2.21079i
$250$	0.500000	+	0.866025i	0.0316228	+	0.0547723i
$251$	−16.9433			−1.06945			−0.534726	−	0.845025i	$-0.679585\pi$
$251$	−16.9433			−1.06945			−0.534726	+	0.845025i	$0.679585\pi$
$252$	13.7429	+	9.35016i	0.865724	+	0.589004i
$253$	−5.43702			−0.341822
$254$	−7.93702	−	13.7473i	−0.498013	−	0.862583i
$255$	2.02336	−	3.50457i	0.126708	−	0.219465i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−3.05422	−	5.29007i	−0.190517	−	0.329985i	0.754905	−	0.655835i	$-0.227683\pi$
$257$	−3.05422	−	5.29007i	−0.190517	−	0.329985i	−0.945422	+	0.325849i	$0.894350\pi$
$258$	−7.80872			−0.486149
$259$	−1.00371	+	13.5712i	−0.0623675	+	0.843273i
$260$	−0.517321			−0.0320829
$261$	−0.884244	−	1.53156i	−0.0547333	−	0.0948009i
$262$	2.33589	−	4.04588i	0.144312	−	0.249955i
$263$	7.50803	−	13.0043i	0.462965	−	0.801879i	−0.536142	−	0.844128i	$-0.680119\pi$
$263$	7.50803	−	13.0043i	0.462965	−	0.801879i	0.999107	+	0.0422491i	$0.0134523\pi$
$264$	−1.52336	−	2.63854i	−0.0937566	−	0.162391i
$265$	1.84229			0.113171
$266$	−8.52832	+	4.11727i	−0.522905	+	0.252446i
$267$	49.1412			3.00739
$268$	−6.54673	−	11.3393i	−0.399905	−	0.692656i
$269$	12.0824	−	20.9274i	0.736679	−	1.27597i	−0.217303	−	0.976104i	$-0.569726\pi$
$269$	12.0824	−	20.9274i	0.736679	−	1.27597i	0.953983	−	0.299862i	$-0.0969406\pi$
$270$	−5.00053	+	8.66118i	−0.304323	+	0.527103i
$271$	−9.16627	−	15.8764i	−0.556811	−	0.964425i	−0.997760	−	0.0668931i	$-0.978691\pi$
$271$	−9.16627	−	15.8764i	−0.556811	−	0.964425i	0.440949	−	0.897532i	$-0.354642\pi$
$272$	−1.32822			−0.0805352
$273$	3.75533	−	1.81299i	0.227283	−	0.109727i
$274$	6.35671			0.384023
$275$	0.500000	+	0.866025i	0.0301511	+	0.0522233i
$276$	8.28256	−	14.3458i	0.498551	−	0.863516i
$277$	−12.8826	+	22.3133i	−0.774040	+	1.34068i	0.161292	+	0.986907i	$0.448434\pi$
$277$	−12.8826	+	22.3133i	−0.774040	+	1.34068i	−0.935332	+	0.353770i	$0.884900\pi$
$278$	−7.96091	−	13.7887i	−0.477464	−	0.826992i
$279$	−64.8944			−3.88512
$280$	−0.195144	+	2.63854i	−0.0116621	+	0.157683i
$281$	−1.25010			−0.0745747			−0.0372874	−	0.999305i	$-0.511872\pi$
$281$	−1.25010			−0.0745747			−0.0372874	+	0.999305i	$0.511872\pi$
$282$	7.23583	+	12.5328i	0.430887	+	0.746319i
$283$	−4.64110	+	8.03863i	−0.275885	+	0.477847i	−0.970358	−	0.241672i	$-0.922304\pi$
$283$	−4.64110	+	8.03863i	−0.275885	+	0.477847i	0.694473	+	0.719519i	$0.255638\pi$
$284$	5.53959	−	9.59486i	0.328714	−	0.569350i
$285$	−5.45271	−	9.44438i	−0.322991	−	0.559436i
$286$	−0.517321			−0.0305898
$287$	5.81090	+	3.95351i	0.343007	+	0.233368i
$288$	6.28256			0.370203
$289$	7.61791	+	13.1946i	0.448113	+	0.776154i
$290$	0.140746	−	0.243779i	0.00826488	−	0.0143152i
$291$	−23.3999	+	40.5298i	−1.37173	+	2.37590i
$292$	−4.47717	−	7.75468i	−0.262006	−	0.453809i
$293$	−19.7845			−1.15583			−0.577913	−	0.816099i	$-0.696133\pi$
$293$	−19.7845			−1.15583			−0.577913	+	0.816099i	$0.696133\pi$
$294$	−7.83038	−	19.8376i	−0.456677	−	1.15695i
$295$	−6.23258			−0.362875
$296$	2.57172	+	4.45435i	0.149478	+	0.258904i
$297$	−5.00053	+	8.66118i	−0.290160	+	0.502573i
$298$	−9.64397	+	16.7038i	−0.558660	+	0.967628i
$299$	−1.40634	−	2.43586i	−0.0813308	−	0.140869i
$300$	−3.04673			−0.175903
$301$	5.60646	+	3.81442i	0.323151	+	0.219859i
$302$	7.08030			0.407426
$303$	8.80592	+	15.2523i	0.505887	+	0.876222i
$304$	−1.78969	+	3.09984i	−0.102646	+	0.177788i
$305$	−5.68801	+	9.85192i	−0.325694	+	0.564119i
$306$	4.17231	+	7.22666i	0.238515	+	0.413121i
$307$	−25.3150			−1.44480			−0.722402	−	0.691473i	$-0.756962\pi$
$307$	−25.3150			−1.44480			−0.722402	+	0.691473i	$0.756962\pi$
$308$	−0.195144	+	2.63854i	−0.0111193	+	0.150345i
$309$	−7.24573			−0.412195
$310$	−5.16464	−	8.94543i	−0.293332	−	0.508066i
$311$	−5.08472	+	8.80700i	−0.288328	+	0.499399i	−0.973411	−	0.229066i	$-0.926433\pi$
$311$	−5.08472	+	8.80700i	−0.288328	+	0.499399i	0.685083	+	0.728465i	$0.259766\pi$
$312$	0.788069	−	1.36497i	0.0446156	−	0.0772765i
$313$	−0.196594	−	0.340511i	−0.0111121	−	0.0192468i	0.860416	−	0.509593i	$-0.170204\pi$
$313$	−0.196594	−	0.340511i	−0.0111121	−	0.0192468i	−0.871528	+	0.490346i	$0.836871\pi$
$314$	19.2640			1.08713
$315$	14.9689	−	7.22666i	0.843404	−	0.407176i
$316$	−10.7349			−0.603886
$317$	−12.5243	−	21.6926i	−0.703432	−	1.21838i	−0.967254	−	0.253809i	$-0.918316\pi$
$317$	−12.5243	−	21.6926i	−0.703432	−	1.21838i	0.263822	−	0.964571i	$-0.415017\pi$
$318$	−2.80648	+	4.86097i	−0.157380	+	0.272590i
$319$	0.140746	−	0.243779i	0.00788025	−	0.0136490i
$320$	0.500000	+	0.866025i	0.0279508	+	0.0484123i
$321$	−10.1869			−0.568578
$322$	−12.9543	+	6.25405i	−0.721917	+	0.348525i
$323$	−4.75422			−0.264532
$324$	−5.81143	−	10.0657i	−0.322857	−	0.559205i
$325$	−0.258661	+	0.448013i	−0.0143479	+	0.0248513i
$326$	2.17981	−	3.77554i	0.120728	−	0.209108i
$327$	−15.3592	−	26.6030i	−0.849367	−	1.47115i
$328$	2.65644			0.146677
$329$	0.926913	−	12.5328i	0.0511024	−	0.690957i
$330$	−3.04673			−0.167717
$331$	−12.8391	−	22.2380i	−0.705702	−	1.22231i	−0.966438	−	0.256901i	$-0.917299\pi$
$331$	−12.8391	−	22.2380i	−0.705702	−	1.22231i	0.260736	−	0.965410i	$-0.416035\pi$
$332$	−6.61078	+	11.4502i	−0.362814	+	0.628412i
$333$	16.1570	−	27.9847i	0.885397	−	1.53355i
$334$	−0.712465	−	1.23403i	−0.0389843	−	0.0675229i
$335$	−13.0935			−0.715372
$336$	−6.66464	−	4.53436i	−0.363586	−	0.247370i
$337$	0.293579			0.0159922			0.00799612	−	0.999968i	$-0.497455\pi$
$337$	0.293579			0.0159922			0.00799612	+	0.999968i	$0.497455\pi$
$338$	6.36619	+	11.0266i	0.346275	+	0.599766i
$339$	−1.97717	+	3.42456i	−0.107385	+	0.185996i
$340$	−0.664110	+	1.15027i	−0.0360164	+	0.0623823i
$341$	−5.16464	−	8.94543i	−0.279681	−	0.484422i
$342$	22.4877			1.21600
$343$	−4.06829	+	18.0679i	−0.219667	+	0.975575i
$344$	2.56298			0.138187
$345$	−8.28256	−	14.3458i	−0.445918	−	0.772353i
$346$	−12.5076	+	21.6639i	−0.672415	+	1.16466i
$347$	16.6575	−	28.8517i	0.894222	−	1.54884i	0.0594573	−	0.998231i	$-0.481063\pi$
$347$	16.6575	−	28.8517i	0.894222	−	1.54884i	0.834765	−	0.550607i	$-0.185604\pi$
$348$	0.428814	+	0.742728i	0.0229869	+	0.0398144i
$349$	20.9172			1.11967			0.559835	−	0.828604i	$-0.310865\pi$
$349$	20.9172			1.11967			0.559835	+	0.828604i	$0.310865\pi$
$350$	2.18747	+	1.48827i	0.116925	+	0.0795515i
$351$	−5.17376			−0.276155
$352$	0.500000	+	0.866025i	0.0266501	+	0.0461593i
$353$	−2.81090	+	4.86862i	−0.149609	+	0.259131i	−0.931083	−	0.364807i	$-0.881135\pi$
$353$	−2.81090	+	4.86862i	−0.149609	+	0.259131i	0.781474	+	0.623938i	$0.214468\pi$
$354$	9.49449	−	16.4449i	0.504626	−	0.874039i
$355$	−5.53959	−	9.59486i	−0.294011	−	0.509242i
$356$	−16.1292			−0.854844
$357$	0.789694	−	10.6775i	0.0417950	−	0.565112i
$358$	−3.88505			−0.205331
$359$	10.6336	+	18.4180i	0.561220	+	0.972062i	0.997390	+	0.0721980i	$0.0230014\pi$
$359$	10.6336	+	18.4180i	0.561220	+	0.972062i	−0.436170	+	0.899864i	$0.643665\pi$
$360$	3.14128	−	5.44086i	0.165560	−	0.286758i
$361$	3.09399	−	5.35895i	0.162842	−	0.282050i
$362$	−12.9554	−	22.4394i	−0.680921	−	1.17939i
$363$	−3.04673			−0.159912
$364$	−1.23258	+	0.595060i	−0.0646047	+	0.0311896i
$365$	−8.95434			−0.468691
$366$	−17.3298	−	30.0161i	−0.905844	−	1.56897i
$367$	−10.8273	+	18.7534i	−0.565181	+	0.978922i	0.431852	+	0.901944i	$0.357860\pi$
$367$	−10.8273	+	18.7534i	−0.565181	+	0.978922i	−0.997033	+	0.0769772i	$0.975473\pi$
$368$	−2.71851	+	4.70859i	−0.141712	+	0.245452i
$369$	−8.34463	−	14.4533i	−0.434404	−	0.752410i
$370$	5.14344			0.267395
$371$	4.38948	−	2.11914i	0.227890	−	0.110020i
$372$	31.4705			1.63167
$373$	−7.05422	−	12.2183i	−0.365254	−	0.632638i	0.623563	−	0.781773i	$-0.285684\pi$
$373$	−7.05422	−	12.2183i	−0.365254	−	0.632638i	−0.988817	+	0.149135i	$0.952351\pi$
$374$	−0.664110	+	1.15027i	−0.0343403	+	0.0594792i
$375$	−1.52336	+	2.63854i	−0.0786662	+	0.136254i
$376$	−2.37495	−	4.11353i	−0.122479	−	0.212139i
$377$	0.145622			0.00749989
$378$	−1.95165	+	26.3883i	−0.100382	+	1.35727i
$379$	13.7674			0.707185			0.353592	−	0.935400i	$-0.384960\pi$
$379$	13.7674			0.707185			0.353592	+	0.935400i	$0.384960\pi$
$380$	1.78969	+	3.09984i	0.0918094	+	0.159018i
$381$	24.1819	−	41.8843i	1.23888	−	2.14580i
$382$	−5.75541	+	9.96866i	−0.294472	+	0.510041i
$383$	11.2205	+	19.4345i	0.573340	+	0.993055i	0.996220	+	0.0868687i	$0.0276860\pi$
$383$	11.2205	+	19.4345i	0.573340	+	0.993055i	−0.422879	+	0.906186i	$0.638981\pi$
$384$	−3.04673			−0.155478
$385$	2.18747	+	1.48827i	0.111484	+	0.0758494i
$386$	−1.59473			−0.0811694
$387$	−8.05105	−	13.9448i	−0.409258	−	0.708855i
$388$	7.68034	−	13.3027i	0.389910	−	0.675344i
$389$	8.82695	−	15.2887i	0.447544	−	0.775170i	−0.550681	−	0.834716i	$-0.685632\pi$
$389$	8.82695	−	15.2887i	0.447544	−	0.775170i	0.998226	+	0.0595461i	$0.0189653\pi$
$390$	−0.788069	−	1.36497i	−0.0399054	−	0.0691182i
$391$	−7.22156			−0.365210
$392$	2.57009	+	6.51111i	0.129809	+	0.328861i
$393$	14.2336			0.717992
$394$	1.69568	+	2.93700i	0.0854270	+	0.147964i
$395$	−5.36746	+	9.29671i	−0.270066	+	0.467768i
$396$	3.14128	−	5.44086i	0.157855	−	0.273413i
$397$	−19.2392	−	33.3232i	−0.965586	−	1.67244i	−0.708034	−	0.706179i	$-0.750417\pi$
$397$	−19.2392	−	33.3232i	−0.965586	−	1.67244i	−0.257552	−	0.966264i	$-0.582916\pi$
$398$	22.8098			1.14335
$399$	−23.8553	−	16.2302i	−1.19426	−	0.812528i
$400$	1.00000			0.0500000
$401$	−1.78952	−	3.09954i	−0.0893643	−	0.154784i	0.817878	−	0.575391i	$-0.195150\pi$
$401$	−1.78952	−	3.09954i	−0.0893643	−	0.154784i	−0.907243	+	0.420608i	$0.861817\pi$
$402$	19.9461	−	34.5477i	0.994822	−	1.72308i
$403$	2.67178	−	4.62766i	0.133091	−	0.230520i
$404$	−2.89029	−	5.00612i	−0.143797	−	0.249064i
$405$	−11.6229			−0.577545
$406$	0.0549313	−	0.742728i	0.00272620	−	0.0368610i
$407$	5.14344			0.254951
$408$	−2.02336	−	3.50457i	−0.100171	−	0.173502i
$409$	−19.7827	+	34.2647i	−0.978192	+	1.69428i	−0.309220	+	0.950990i	$0.600068\pi$
$409$	−19.7827	+	34.2647i	−0.978192	+	1.69428i	−0.668972	+	0.743288i	$0.733265\pi$
$410$	1.32822	−	2.30055i	0.0655962	−	0.113616i
$411$	9.68359	+	16.7725i	0.477656	+	0.827325i
$412$	2.37820			0.117166
$413$	−14.8499	+	7.16917i	−0.730714	+	0.352772i
$414$	34.1584			1.67879
$415$	6.61078	+	11.4502i	0.324510	+	0.562068i
$416$	−0.258661	+	0.448013i	−0.0126819	+	0.0219657i
$417$	24.2548	−	42.0105i	1.18776	−	2.05726i
$418$	1.78969	+	3.09984i	0.0875368	+	0.151618i
$419$	32.2846			1.57721			0.788604	−	0.614901i	$-0.210804\pi$
$419$	32.2846			1.57721			0.788604	+	0.614901i	$0.210804\pi$
$420$	−7.25919	+	3.50457i	−0.354212	+	0.171006i
$421$	35.8437			1.74691			0.873457	−	0.486902i	$-0.161873\pi$
$421$	35.8437			1.74691			0.873457	+	0.486902i	$0.161873\pi$
$422$	−3.88315	−	6.72582i	−0.189029	−	0.327408i
$423$	−14.9208	+	25.8435i	−0.725472	+	1.25655i
$424$	0.921146	−	1.59547i	0.0447348	−	0.0774829i
$425$	0.664110	+	1.15027i	0.0322141	+	0.0557964i
$426$	33.7553			1.63545
$427$	−2.21996	+	30.0161i	−0.107431	+	1.45258i
$428$	3.34356			0.161617
$429$	−0.788069	−	1.36497i	−0.0380483	−	0.0659016i
$430$	1.28149	−	2.21961i	0.0617990	−	0.107039i
$431$	1.02283	−	1.77160i	0.0492680	−	0.0853348i	−0.840340	−	0.542060i	$-0.817644\pi$
$431$	1.02283	−	1.77160i	0.0492680	−	0.0853348i	0.889608	+	0.456725i	$0.150978\pi$
$432$	5.00053	+	8.66118i	0.240588	+	0.416711i
$433$	−9.62180			−0.462394			−0.231197	−	0.972907i	$-0.574264\pi$
$433$	−9.62180			−0.462394			−0.231197	+	0.972907i	$0.574264\pi$
$434$	−22.5951	−	15.3728i	−1.08460	−	0.737917i
$435$	0.857629			0.0411202
$436$	5.04122	+	8.73165i	0.241431	+	0.418170i
$437$	−9.73060	+	16.8539i	−0.465477	+	0.806231i
$438$	13.6407	−	23.6264i	0.651779	−	1.12891i
$439$	1.93151	+	3.34547i	0.0921858	+	0.159670i	0.908431	−	0.418036i	$-0.137281\pi$
$439$	1.93151	+	3.34547i	0.0921858	+	0.159670i	−0.816245	+	0.577706i	$0.803948\pi$
$440$	1.00000			0.0476731
$441$	27.3527	−	34.4367i	1.30251	−	1.63984i
$442$	−0.687117			−0.0326828
$443$	−16.0021	−	27.7165i	−0.760284	−	1.31685i	−0.942704	−	0.333630i	$-0.891726\pi$
$443$	−16.0021	−	27.7165i	−0.760284	−	1.31685i	0.182420	−	0.983221i	$-0.441607\pi$
$444$	−7.83533	+	13.5712i	−0.371848	+	0.644060i
$445$	−8.06458	+	13.9683i	−0.382298	+	0.662159i
$446$	−1.61078	−	2.78995i	−0.0762726	−	0.132108i
$447$	−58.7651			−2.77950
$448$	2.18747	+	1.48827i	0.103348	+	0.0703142i
$449$	−14.7937			−0.698159			−0.349080	−	0.937093i	$-0.613506\pi$
$449$	−14.7937			−0.698159			−0.349080	+	0.937093i	$0.613506\pi$
$450$	−3.14128	−	5.44086i	−0.148081	−	0.256484i
$451$	1.32822	−	2.30055i	0.0625435	−	0.108328i
$452$	0.648948	−	1.12401i	0.0305239	−	0.0528690i
$453$	10.7859	+	18.6817i	0.506765	+	0.877743i
$454$	14.9654			0.702359
$455$	−0.100952	+	1.36497i	−0.00473270	+	0.0639910i
$456$	−10.9054			−0.510693
$457$	−10.3537	−	17.9332i	−0.484328	−	0.838880i	0.515510	−	0.856883i	$-0.327602\pi$
$457$	−10.3537	−	17.9332i	−0.484328	−	0.838880i	−0.999838	+	0.0180032i	$0.994269\pi$
$458$	2.82730	−	4.89703i	0.132111	−	0.228823i
$459$	−6.64181	+	11.5040i	−0.310013	+	0.536959i
$460$	2.71851	+	4.70859i	0.126751	+	0.219539i
$461$	−27.2847			−1.27077			−0.635387	−	0.772194i	$-0.719160\pi$
$461$	−27.2847			−1.27077			−0.635387	+	0.772194i	$0.719160\pi$
$462$	−7.25919	+	3.50457i	−0.337728	+	0.163047i
$463$	15.5305			0.721762			0.360881	−	0.932612i	$-0.382476\pi$
$463$	15.5305			0.721762			0.360881	+	0.932612i	$0.382476\pi$
$464$	−0.140746	−	0.243779i	−0.00653396	−	0.0113172i
$465$	15.7353	−	27.2543i	0.729706	−	1.26389i
$466$	12.0189	−	20.8174i	0.556766	−	0.964347i
$467$	−10.6141	−	18.3842i	−0.491163	−	0.850720i	0.508785	−	0.860894i	$-0.330095\pi$
$467$	−10.6141	−	18.3842i	−0.491163	−	0.850720i	−0.999948	+	0.0101738i	$0.996762\pi$
$468$	3.25010			0.150236
$469$	−31.1967	+	15.0611i	−1.44053	+	0.695455i
$470$	−4.74990			−0.219097
$471$	29.3461	+	50.8289i	1.35219	+	2.34207i
$472$	−3.11629	+	5.39757i	−0.143439	+	0.248443i
$473$	1.28149	−	2.21961i	0.0589231	−	0.102058i
$474$	−16.3532	−	28.3245i	−0.751127	−	1.30099i
$475$	3.57939			0.164234
$476$	−0.259194	+	3.50457i	−0.0118801	+	0.160632i
$477$	−11.5743			−0.529951
$478$	−13.5412	−	23.4541i	−0.619361	−	1.07276i
$479$	−13.8705	+	24.0244i	−0.633760	+	1.09770i	0.353017	+	0.935617i	$0.385156\pi$
$479$	−13.8705	+	24.0244i	−0.633760	+	1.09770i	−0.986776	+	0.162087i	$0.948178\pi$
$480$	−1.52336	+	2.63854i	−0.0695318	+	0.120433i
$481$	1.33040	+	2.30433i	0.0606612	+	0.105068i
$482$	15.2216			0.693323
$483$	−36.2358	−	24.6534i	−1.64879	−	1.12177i
$484$	1.00000			0.0454545
$485$	−7.68034	−	13.3027i	−0.348746	−	0.604046i
$486$	2.70426	−	4.68392i	0.122668	−	0.212467i
$487$	3.01209	−	5.21709i	0.136491	−	0.236409i	−0.789675	−	0.613525i	$-0.789751\pi$
$487$	3.01209	−	5.21709i	0.136491	−	0.236409i	0.926166	+	0.377116i	$0.123084\pi$
$488$	5.68801	+	9.85192i	0.257484	+	0.445975i
$489$	13.2826			0.600658
$490$	6.92384	+	1.02979i	0.312787	+	0.0465212i
$491$	2.87043			0.129541			0.0647704	−	0.997900i	$-0.479368\pi$
$491$	2.87043			0.129541			0.0647704	+	0.997900i	$0.479368\pi$
$492$	4.04673	+	7.00914i	0.182441	+	0.315996i
$493$	0.186942	−	0.323792i	0.00841942	−	0.0145829i
$494$	−0.925846	+	1.60361i	−0.0416558	+	0.0721500i
$495$	−3.14128	−	5.44086i	−0.141190	−	0.244548i
$496$	−10.3293			−0.463799
$497$	−24.2354	−	16.4888i	−1.08711	−	0.739626i
$498$	−40.2825			−1.80510
$499$	3.33254	+	5.77213i	0.149185	+	0.258396i	0.930926	−	0.365207i	$-0.119002\pi$
$499$	3.33254	+	5.77213i	0.149185	+	0.258396i	−0.781742	+	0.623603i	$0.785668\pi$
$500$	0.500000	−	0.866025i	0.0223607	−	0.0387298i
$501$	2.17069	−	3.75974i	0.0969792	−	0.167973i
$502$	8.47166	+	14.6733i	0.378109	+	0.654903i
$503$	22.2479			0.991983			0.495992	−	0.868327i	$-0.334805\pi$
$503$	22.2479			0.991983			0.495992	+	0.868327i	$0.334805\pi$
$504$	1.22600	−	16.5768i	0.0546105	−	0.738390i
$505$	−5.78057			−0.257232
$506$	2.71851	+	4.70859i	0.120852	+	0.209323i
$507$	−19.3961	+	33.5950i	−0.861409	+	1.49200i
$508$	−7.93702	+	13.7473i	−0.352148	+	0.609939i
$509$	16.5954	+	28.7441i	0.735580	+	1.27406i	0.954468	+	0.298312i	$0.0964236\pi$
$509$	16.5954	+	28.7441i	0.735580	+	1.27406i	−0.218888	+	0.975750i	$0.570243\pi$
$510$	−4.04673			−0.179192
$511$	−21.3348	+	10.2999i	−0.943795	+	0.455642i
$512$	1.00000			0.0441942
$513$	17.8988	+	31.0017i	0.790253	+	1.36876i
$514$	−3.05422	+	5.29007i	−0.134716	+	0.233335i
$515$	1.18910	−	2.05958i	0.0523980	−	0.0907560i
$516$	3.90436	+	6.76255i	0.171880	+	0.297705i
$517$	−4.74990			−0.208900
$518$	12.2549	−	5.91636i	0.538447	−	0.259950i
$519$	−76.2148			−3.34546
$520$	0.258661	+	0.448013i	0.0113430	+	0.0196467i
$521$	−6.70975	+	11.6216i	−0.293959	+	0.509153i	−0.974742	−	0.223333i	$-0.928306\pi$
$521$	−6.70975	+	11.6216i	−0.293959	+	0.509153i	0.680783	+	0.732485i	$0.261640\pi$
$522$	−0.884244	+	1.53156i	−0.0387023	+	0.0670344i
$523$	4.29683	+	7.44233i	0.187887	+	0.325430i	0.944546	−	0.328380i	$-0.106503\pi$
$523$	4.29683	+	7.44233i	0.187887	+	0.325430i	−0.756658	+	0.653810i	$0.773169\pi$
$524$	−4.67178			−0.204088
$525$	−0.594550	+	8.03893i	−0.0259483	+	0.350848i
$526$	−15.0161			−0.654731
$527$	−6.85979	−	11.8815i	−0.298817	−	0.517566i
$528$	−1.52336	+	2.63854i	−0.0662959	+	0.114828i
$529$	−3.28057	+	5.68212i	−0.142634	+	0.247049i
$530$	−0.921146	−	1.59547i	−0.0400120	−	0.0693028i
$531$	39.1565			1.69925
$532$	7.82982	+	5.32710i	0.339466	+	0.230959i
$533$	1.37423			0.0595247
$534$	−24.5706	−	42.5575i	−1.06327	−	1.84164i
$535$	1.67178	−	2.89561i	0.0722773	−	0.125188i
$536$	−6.54673	+	11.3393i	−0.282776	+	0.489782i
$537$	−5.91835	−	10.2509i	−0.255396	−	0.442358i
$538$	−24.1649			−1.04182
$539$	6.92384	+	1.02979i	0.298231	+	0.0443562i
$540$	10.0011			0.430377
$541$	−13.2897	−	23.0184i	−0.571367	−	0.989638i	−0.996426	−	0.0844716i	$-0.973080\pi$
$541$	−13.2897	−	23.0184i	−0.571367	−	0.989638i	0.425058	−	0.905166i	$-0.360254\pi$
$542$	−9.16627	+	15.8764i	−0.393725	+	0.681952i
$543$	39.4716	−	68.3668i	1.69389	−	2.93390i
$544$	0.664110	+	1.15027i	0.0284735	+	0.0493175i
$545$	10.0824			0.431884
$546$	−3.44776	−	2.34572i	−0.147551	−	0.100388i
$547$	7.17431			0.306752			0.153376	−	0.988168i	$-0.450986\pi$
$547$	7.17431			0.306752			0.153376	+	0.988168i	$0.450986\pi$
$548$	−3.17836	−	5.50507i	−0.135773	−	0.235165i
$549$	35.7352	−	61.8953i	1.52514	−	2.64163i
$550$	0.500000	−	0.866025i	0.0213201	−	0.0369274i
$551$	−0.503784	−	0.872579i	−0.0214619	−	0.0371731i
$552$	−16.5651			−0.705058
$553$	−2.09485	+	28.3245i	−0.0890821	+	1.20448i
$554$	25.7652			1.09466
$555$	7.83533	+	13.5712i	0.332591	+	0.576065i
$556$	−7.96091	+	13.7887i	−0.337618	+	0.584772i
$557$	−11.9900	+	20.7674i	−0.508035	+	0.879942i	0.491922	+	0.870639i	$0.336294\pi$
$557$	−11.9900	+	20.7674i	−0.508035	+	0.879942i	−0.999957	+	0.00930252i	$0.997039\pi$
$558$	32.4472	+	56.2002i	1.37360	+	2.37914i
$559$	1.32589			0.0560790
$560$	2.38262	−	1.15027i	0.100684	−	0.0486079i
$561$	−4.04673			−0.170853
$562$	0.625050	+	1.08262i	0.0263661	+	0.0456675i
$563$	2.40669	−	4.16851i	0.101430	−	0.175682i	−0.810844	−	0.585262i	$-0.800992\pi$
$563$	2.40669	−	4.16851i	0.101430	−	0.175682i	0.912274	+	0.409580i	$0.134325\pi$
$564$	7.23583	−	12.5328i	0.304683	−	0.527727i
$565$	−0.648948	−	1.12401i	−0.0273014	−	0.0472875i
$566$	9.28221			0.390160
$567$	−27.6929	+	13.3695i	−1.16299	+	0.561465i
$568$	−11.0792			−0.464872
$569$	20.6118	+	35.7008i	0.864094	+	1.49665i	0.867944	+	0.496661i	$0.165441\pi$
$569$	20.6118	+	35.7008i	0.864094	+	1.49665i	−0.00385087	+	0.999993i	$0.501226\pi$
$570$	−5.45271	+	9.44438i	−0.228389	+	0.395581i
$571$	−8.38155	+	14.5173i	−0.350757	+	0.607529i	−0.986382	−	0.164469i	$-0.947409\pi$
$571$	−8.38155	+	14.5173i	−0.350757	+	0.607529i	0.635625	+	0.771998i	$0.280742\pi$
$572$	0.258661	+	0.448013i	0.0108151	+	0.0187324i
$573$	−35.0704			−1.46508
$574$	0.518388	−	7.00914i	0.0216371	−	0.292556i
$575$	5.43702			0.226739
$576$	−3.14128	−	5.44086i	−0.130887	−	0.226702i
$577$	−1.71391	+	2.96859i	−0.0713512	+	0.123584i	−0.899494	−	0.436934i	$-0.856064\pi$
$577$	−1.71391	+	2.96859i	−0.0713512	+	0.123584i	0.828143	+	0.560518i	$0.189398\pi$
$578$	7.61791	−	13.1946i	0.316863	−	0.548824i
$579$	−2.42935	−	4.20775i	−0.100960	−	0.174868i
$580$	−0.281492			−0.0116883
$581$	28.9218	+	19.6773i	1.19988	+	0.816351i
$582$	46.7998			1.93992
$583$	−0.921146	−	1.59547i	−0.0381500	−	0.0660777i
$584$	−4.47717	+	7.75468i	−0.185267	+	0.320891i
$585$	1.62505	−	2.81467i	0.0671875	−	0.116372i
$586$	9.89227	+	17.1339i	0.408646	+	0.707796i
$587$	−34.6304			−1.42935			−0.714674	−	0.699457i	$-0.753425\pi$
$587$	−34.6304			−1.42935			−0.714674	+	0.699457i	$0.753425\pi$
$588$	−13.2647	+	16.7001i	−0.547026	+	0.688701i
$589$	−36.9725			−1.52343
$590$	3.11629	+	5.39757i	0.128296	+	0.222215i
$591$	−5.16627	+	8.94824i	−0.212512	+	0.368081i
$592$	2.57172	−	4.45435i	0.105697	−	0.183073i
$593$	5.09346	+	8.82213i	0.209163	+	0.362281i	0.951451	−	0.307800i	$-0.0995927\pi$
$593$	5.09346	+	8.82213i	0.209163	+	0.362281i	−0.742288	+	0.670081i	$0.766259\pi$
$594$	10.0011			0.410349
$595$	2.90545	+	1.97675i	0.119112	+	0.0810390i
$596$	19.2879			0.790065
$597$	34.7476	+	60.1846i	1.42213	+	2.46319i
$598$	−1.40634	+	2.43586i	−0.0575096	+	0.0996095i
$599$	−0.945602	+	1.63783i	−0.0386363	+	0.0669200i	−0.884697	−	0.466167i	$-0.845635\pi$
$599$	−0.945602	+	1.63783i	−0.0386363	+	0.0669200i	0.846061	+	0.533087i	$0.178968\pi$
$600$	1.52336	+	2.63854i	0.0621911	+	0.107718i
$601$	−10.5286			−0.429472			−0.214736	−	0.976672i	$-0.568889\pi$
$601$	−10.5286			−0.429472			−0.214736	+	0.976672i	$0.568889\pi$
$602$	0.500150	−	6.76255i	0.0203846	−	0.275621i
$603$	82.2604			3.34990
$604$	−3.54015	−	6.13172i	−0.144047	−	0.249496i
$605$	0.500000	−	0.866025i	0.0203279	−	0.0352089i
$606$	8.80592	−	15.2523i	0.357716	−	0.619583i
$607$	15.5983	+	27.0171i	0.633116	+	1.09659i	0.986911	+	0.161266i	$0.0515577\pi$
$607$	15.5983	+	27.0171i	0.633116	+	1.09659i	−0.353795	+	0.935323i	$0.615109\pi$
$608$	3.57939			0.145163
$609$	2.04340	−	0.986507i	0.0828029	−	0.0399753i
$610$	11.3760			0.460601
$611$	−1.22861	−	2.12802i	−0.0497043	−	0.0860904i
$612$	4.17231	−	7.22666i	0.168656	−	0.292120i
$613$	1.78057	−	3.08405i	0.0719167	−	0.124563i	−0.827825	−	0.560987i	$-0.810422\pi$
$613$	1.78057	−	3.08405i	0.0719167	−	0.124563i	0.899741	+	0.436424i	$0.143755\pi$
$614$	12.6575	+	21.9234i	0.510815	+	0.884758i
$615$	8.09346			0.326360
$616$	2.38262	−	1.15027i	0.0959984	−	0.0463458i
$617$	−36.9604			−1.48797			−0.743986	−	0.668196i	$-0.767067\pi$
$617$	−36.9604			−1.48797			−0.743986	+	0.668196i	$0.767067\pi$
$618$	3.62287	+	6.27499i	0.145733	+	0.252417i
$619$	14.7206	−	25.4969i	0.591673	−	1.02481i	−0.402335	−	0.915493i	$-0.631801\pi$
$619$	14.7206	−	25.4969i	0.591673	−	1.02481i	0.994007	−	0.109314i	$-0.0348655\pi$
$620$	−5.16464	+	8.94543i	−0.207417	+	0.359257i
$621$	27.1880	+	47.0910i	1.09102	+	1.88970i
$622$	10.1694			0.407758
$623$	−3.14751	+	42.5575i	−0.126102	+	1.70503i
$624$	−1.57614			−0.0630960
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$	−0.196594	+	0.340511i	−0.00785747	+	0.0136095i
$627$	−5.45271	+	9.44438i	−0.217760	+	0.377172i
$628$	−9.63199	−	16.6831i	−0.384358	−	0.665728i
$629$	6.83162			0.272395
$630$	−13.7429	−	9.35016i	−0.547532	−	0.372519i
$631$	22.5126			0.896213			0.448106	−	0.893980i	$-0.352099\pi$
$631$	22.5126			0.896213			0.448106	+	0.893980i	$0.352099\pi$
$632$	5.36746	+	9.29671i	0.213506	+	0.369803i
$633$	11.8309	−	20.4917i	0.470237	−	0.814474i
$634$	−12.5243	+	21.6926i	−0.497402	+	0.861525i
$635$	7.93702	+	13.7473i	0.314971	+	0.545546i
$636$	5.61296			0.222568
$637$	1.32956	+	3.36834i	0.0526792	+	0.133458i
$638$	−0.281492			−0.0111444
$639$	34.8028	+	60.2803i	1.37678	+	2.38465i
$640$	0.500000	−	0.866025i	0.0197642	−	0.0342327i
$641$	16.2583	−	28.1602i	0.642163	−	1.11226i	−0.342786	−	0.939414i	$-0.611370\pi$
$641$	16.2583	−	28.1602i	0.642163	−	1.11226i	0.984949	−	0.172846i	$-0.0552962\pi$
$642$	5.09346	+	8.82213i	0.201023	+	0.348182i
$643$	−3.97258			−0.156663			−0.0783315	−	0.996927i	$-0.524959\pi$
$643$	−3.97258			−0.156663			−0.0783315	+	0.996927i	$0.524959\pi$
$644$	11.8933	+	8.09176i	0.468663	+	0.318860i
$645$	7.80872			0.307468
$646$	2.37711	+	4.11727i	0.0935261	+	0.161992i
$647$	0.610779	−	1.05790i	0.0240122	−	0.0415904i	−0.853770	−	0.520651i	$-0.825689\pi$
$647$	0.610779	−	1.05790i	0.0240122	−	0.0415904i	0.877782	+	0.479061i	$0.159023\pi$
$648$	−5.81143	+	10.0657i	−0.228295	+	0.395418i
$649$	3.11629	+	5.39757i	0.122325	+	0.211873i
$650$	0.517321			0.0202910
$651$	6.14128	−	83.0364i	0.240696	−	3.25445i
$652$	−4.35961			−0.170736
$653$	−11.6998	−	20.2647i	−0.457849	−	0.793018i	0.540998	−	0.841024i	$-0.318047\pi$
$653$	−11.6998	−	20.2647i	−0.457849	−	0.793018i	−0.998847	+	0.0480058i	$0.984713\pi$
$654$	−15.3592	+	26.6030i	−0.600593	+	1.04026i
$655$	−2.33589	+	4.04588i	−0.0912708	+	0.158086i
$656$	−1.32822	−	2.30055i	−0.0518583	−	0.0898212i
$657$	56.2562			2.19476
$658$	−11.3172	+	5.46368i	−0.441190	+	0.212996i
$659$	−0.271538			−0.0105776			−0.00528882	−	0.999986i	$-0.501683\pi$
$659$	−0.271538			−0.0105776			−0.00528882	+	0.999986i	$0.501683\pi$
$660$	1.52336	+	2.63854i	0.0592969	+	0.102705i
$661$	16.8152	−	29.1248i	0.654036	−	1.13282i	−0.328098	−	0.944644i	$-0.606408\pi$
$661$	16.8152	−	29.1248i	0.654036	−	1.13282i	0.982135	−	0.188180i	$-0.0602589\pi$
$662$	−12.8391	+	22.2380i	−0.499006	+	0.864304i
$663$	−1.04673	−	1.81299i	−0.0406516	−	0.0704106i
$664$	13.2216			0.513096
$665$	8.52832	−	4.11727i	0.330714	−	0.159661i
$666$	−32.3140			−1.25214
$667$	−0.765237	−	1.32543i	−0.0296301	−	0.0513209i
$668$	−0.712465	+	1.23403i	−0.0275661	+	0.0477459i
$669$	4.90761	−	8.50023i	0.189739	−	0.328638i
$670$	6.54673	+	11.3393i	0.252922	+	0.438074i
$671$	11.3760			0.439166
$672$	−0.594550	+	8.03893i	−0.0229353	+	0.310109i
$673$	−44.1409			−1.70151			−0.850753	−	0.525565i	$-0.823854\pi$
$673$	−44.1409			−1.70151			−0.850753	+	0.525565i	$0.823854\pi$
$674$	−0.146789	−	0.254247i	−0.00565411	−	0.00979321i
$675$	5.00053	−	8.66118i	0.192471	−	0.333369i
$676$	6.36619	−	11.0266i	0.244853	−	0.424099i
$677$	−13.4249	−	23.2527i	−0.515962	−	0.893672i	−0.999828	−	0.0185304i	$-0.994101\pi$
$677$	−13.4249	−	23.2527i	−0.515962	−	0.893672i	0.483866	−	0.875142i	$-0.339232\pi$
$678$	3.95434			0.151865
$679$	−33.6011	−	22.8609i	−1.28949	−	0.877320i
$680$	1.32822			0.0509349
$681$	22.7977	+	39.4868i	0.873610	+	1.51314i
$682$	−5.16464	+	8.94543i	−0.197764	+	0.342538i
$683$	6.33271	−	10.9686i	0.242315	−	0.419701i	−0.719059	−	0.694949i	$-0.755427\pi$
$683$	6.33271	−	10.9686i	0.242315	−	0.419701i	0.961373	+	0.275248i	$0.0887601\pi$
$684$	−11.2439	−	19.4749i	−0.429920	−	0.744643i
$685$	−6.35671			−0.242877
$686$	17.6814	−	5.51070i	0.675079	−	0.210400i
$687$	17.2281			0.657291
$688$	−1.28149	−	2.21961i	−0.0488564	−	0.0846218i
$689$	0.476528	−	0.825371i	0.0181543	−	0.0314441i
$690$	−8.28256	+	14.3458i	−0.315312	+	0.546136i
$691$	−6.58505	−	11.4056i	−0.250507	−	0.433891i	0.713158	−	0.701003i	$-0.247264\pi$
$691$	−6.58505	−	11.4056i	−0.250507	−	0.433891i	−0.963666	+	0.267112i	$0.913931\pi$
$692$	25.0153			0.950939
$693$	−13.7429	−	9.35016i	−0.522051	−	0.355183i
$694$	−33.3150			−1.26462
$695$	7.96091	+	13.7887i	0.301975	+	0.523036i
$696$	0.428814	−	0.742728i	0.0162542	−	0.0281530i
$697$	1.76417	−	3.05563i	0.0668227	−	0.115740i
$698$	−10.4586	−	18.1148i	−0.395863	−	0.685655i
$699$	73.2368			2.77007
$700$	0.195144	−	2.63854i	0.00737574	−	0.0997276i
$701$	−24.5503			−0.927253			−0.463627	−	0.886031i	$-0.653452\pi$
$701$	−24.5503			−0.927253			−0.463627	+	0.886031i	$0.653452\pi$
$702$	2.58688	+	4.48061i	0.0976355	+	0.169110i
$703$	9.20518	−	15.9438i	0.347180	−	0.601333i
$704$	0.500000	−	0.866025i	0.0188445	−	0.0326396i
$705$	−7.23583	−	12.5328i	−0.272517	−	0.472013i
$706$	5.62180			0.211579
$707$	−13.7729	+	6.64924i	−0.517983	+	0.250070i
$708$	−18.9890			−0.713650
$709$	1.43992	+	2.49401i	0.0540772	+	0.0936645i	0.891797	−	0.452436i	$-0.149445\pi$
$709$	1.43992	+	2.49401i	0.0540772	+	0.0936645i	−0.837720	+	0.546101i	$0.816112\pi$
$710$	−5.53959	+	9.59486i	−0.207897	+	0.360089i
$711$	33.7214	−	58.4071i	1.26465	−	2.19044i
$712$	8.06458	+	13.9683i	0.302233	+	0.523483i
$713$	−56.1605			−2.10323
$714$	−9.64181	+	4.65484i	−0.360836	+	0.174203i
$715$	0.517321			0.0193467
$716$	1.94253	+	3.36455i	0.0725956	+	0.125739i
$717$	41.2564	−	71.4582i	1.54075	−	2.66866i
$718$	10.6336	−	18.4180i	0.396843	−	0.687352i
$719$	−6.29599	−	10.9050i	−0.234801	−	0.406687i	0.724414	−	0.689365i	$-0.242111\pi$
$719$	−6.29599	−	10.9050i	−0.234801	−	0.406687i	−0.959215	+	0.282678i	$0.908777\pi$
$720$	−6.28256			−0.234137
$721$	0.464091	−	6.27499i	0.0172836	−	0.233693i
$722$	−6.18798			−0.230293
$723$	23.1880	+	40.1628i	0.862370	+	1.49367i
$724$	−12.9554	+	22.4394i	−0.481484	+	0.833954i
$725$	−0.140746	+	0.243779i	−0.00522717	+	0.00905372i
$726$	1.52336	+	2.63854i	0.0565374	+	0.0979256i
$727$	4.93682			0.183096			0.0915482	−	0.995801i	$-0.470818\pi$
$727$	4.93682			0.183096			0.0915482	+	0.995801i	$0.470818\pi$
$728$	1.13163	+	0.769914i	0.0419409	+	0.0285349i
$729$	−18.3903			−0.681122
$730$	4.47717	+	7.75468i	0.165707	+	0.287014i
$731$	1.70210	−	2.94813i	0.0629546	−	0.109041i
$732$	−17.3298	+	30.0161i	−0.640529	+	1.10943i
$733$	17.2119	+	29.8119i	0.635735	+	1.10113i	0.986359	+	0.164609i	$0.0526364\pi$
$733$	17.2119	+	29.8119i	0.635735	+	1.10113i	−0.350623	+	0.936517i	$0.614030\pi$
$734$	21.6546			0.799286
$735$	7.83038	+	19.8376i	0.288828	+	0.731721i
$736$	5.43702			0.200411
$737$	6.54673	+	11.3393i	0.241152	+	0.417687i
$738$	−8.34463	+	14.4533i	−0.307170	+	0.532034i
$739$	−0.663019	+	1.14838i	−0.0243895	+	0.0422439i	−0.877963	−	0.478729i	$-0.841098\pi$
$739$	−0.663019	+	1.14838i	−0.0243895	+	0.0422439i	0.853573	+	0.520973i	$0.174431\pi$
$740$	−2.57172	−	4.45435i	−0.0945383	−	0.163745i
$741$	−5.64161			−0.207250
$742$	−4.02997	−	2.74183i	−0.147945	−	0.100656i
$743$	20.1227			0.738229			0.369115	−	0.929384i	$-0.379661\pi$
$743$	20.1227			0.738229			0.369115	+	0.929384i	$0.379661\pi$
$744$	−15.7353	−	27.2543i	−0.576883	−	0.999191i
$745$	9.64397	−	16.7038i	0.353328	−	0.611982i
$746$	−7.05422	+	12.2183i	−0.258273	+	0.447343i
$747$	−41.5326	−	71.9366i	−1.51960	−	2.63202i
$748$	1.32822			0.0485646
$749$	0.652474	−	8.82213i	0.0238409	−	0.322354i
$750$	3.04673			0.111251
$751$	−0.0109192	−	0.0189127i	−0.000398449	−	0.000690133i	0.865826	−	0.500345i	$-0.166793\pi$
$751$	−0.0109192	−	0.0189127i	−0.000398449	−	0.000690133i	−0.866225	+	0.499655i	$0.833460\pi$
$752$	−2.37495	+	4.11353i	−0.0866055	+	0.150005i
$753$	−25.8108	+	44.7057i	−0.940600	+	1.62917i
$754$	−0.0728108	−	0.126112i	−0.00265161	−	0.00459273i
$755$	−7.08030			−0.257679
$756$	23.8287	−	11.5040i	0.866643	−	0.418395i
$757$	19.4216			0.705891			0.352946	−	0.935644i	$-0.385180\pi$
$757$	19.4216			0.705891			0.352946	+	0.935644i	$0.385180\pi$
$758$	−6.88371	−	11.9229i	−0.250028	−	0.433061i
$759$	−8.28256	+	14.3458i	−0.300638	+	0.520720i
$760$	1.78969	−	3.09984i	0.0649190	−	0.112443i
$761$	11.9654	+	20.7246i	0.433744	+	0.751266i	0.997192	−	0.0748849i	$-0.0238589\pi$
$761$	11.9654	+	20.7246i	0.433744	+	0.751266i	−0.563448	+	0.826151i	$0.690526\pi$
$762$	−48.3639			−1.75204
$763$	24.0226	−	11.5976i	0.869677	−	0.419860i
$764$	11.5108			0.416447
$765$	−4.17231	−	7.22666i	−0.150850	−	0.261280i
$766$	11.2205	−	19.4345i	0.405413	−	0.702196i
$767$	−1.61212	+	2.79228i	−0.0582104	+	0.100823i
$768$	1.52336	+	2.63854i	0.0549697	+	0.0952103i
$769$	21.7153			0.783072			0.391536	−	0.920163i	$-0.371944\pi$
$769$	21.7153			0.783072			0.391536	+	0.920163i	$0.371944\pi$
$770$	0.195144	−	2.63854i	0.00703249	−	0.0950866i
$771$	−18.6108			−0.670251
$772$	0.797363	+	1.38107i	0.0286977	+	0.0497059i
$773$	−24.9674	+	43.2448i	−0.898015	+	1.55541i	−0.0679859	+	0.997686i	$0.521657\pi$
$773$	−24.9674	+	43.2448i	−0.898015	+	1.55541i	−0.830029	+	0.557721i	$0.811676\pi$
$774$	−8.05105	+	13.9448i	−0.289389	+	0.501236i
$775$	5.16464	+	8.94543i	0.185519	+	0.321329i
$776$	−15.3607			−0.551416
$777$	34.2792	+	23.3222i	1.22976	+	0.836679i
$778$	−17.6539			−0.632923
$779$	−4.75422	−	8.23455i	−0.170338	−	0.295033i
$780$	−0.788069	+	1.36497i	−0.0282174	+	0.0488739i
$781$	−5.53959	+	9.59486i	−0.198222	+	0.343331i
$782$	3.61078	+	6.25405i	0.129121	+	0.223644i
$783$	−2.81522			−0.100608
$784$	4.35374	−	5.48132i	0.155491	−	0.195762i
$785$	−19.2640			−0.687561
$786$	−7.11682	−	12.3267i	−0.253849	−	0.439679i
$787$	19.3347	−	33.4886i	0.689207	−	1.19374i	−0.282888	−	0.959153i	$-0.591293\pi$
$787$	19.3347	−	33.4886i	0.689207	−	1.19374i	0.972095	−	0.234588i	$-0.0753741\pi$
$788$	1.69568	−	2.93700i	0.0604060	−	0.104626i
$789$	−22.8749	−	39.6205i	−0.814369	−	1.41053i
$790$	10.7349			0.381931
$791$	−2.83912	−	1.93162i	−0.100947	−	0.0686806i
$792$	−6.28256			−0.223241
$793$	2.94253	+	5.09661i	0.104492	+	0.180986i
$794$	−19.2392	+	33.3232i	−0.682772	+	1.18260i
$795$	2.80648	−	4.86097i	0.0995356	−	0.172401i
$796$	−11.4049	−	19.7539i	−0.404236	−	0.700157i
$797$	−31.3996			−1.11223			−0.556115	−	0.831105i	$-0.687709\pi$
$797$	−31.3996			−1.11223			−0.556115	+	0.831105i	$0.687709\pi$
$798$	−2.12813	+	28.7745i	−0.0753348	+	1.01860i
$799$	−6.30892			−0.223193
$800$	−0.500000	−	0.866025i	−0.0176777	−	0.0306186i
$801$	50.6662	−	87.7565i	1.79020	−	3.10072i
$802$	−1.78952	+	3.09954i	−0.0631901	+	0.109448i
$803$	4.47717	+	7.75468i	0.157996	+	0.273657i
$804$	−39.8922			−1.40689
$805$	12.9543	−	6.25405i	0.456580	−	0.220426i
$806$	−5.34356			−0.188219
$807$	−36.8119	−	63.7601i	−1.29584	−	2.24446i
$808$	−2.89029	+	5.00612i	−0.101680	+	0.176115i
$809$	14.8587	−	25.7360i	0.522404	−	0.904830i	−0.477256	−	0.878764i	$-0.658369\pi$
$809$	14.8587	−	25.7360i	0.522404	−	0.904830i	0.999660	−	0.0260660i	$-0.00829800\pi$
$810$	5.81143	+	10.0657i	0.204193	+	0.353673i
$811$	49.6021			1.74177			0.870883	−	0.491491i	$-0.163548\pi$
$811$	49.6021			1.74177			0.870883	+	0.491491i	$0.163548\pi$
$812$	−0.670687	+	0.323792i	−0.0235365	+	0.0113629i
$813$	−55.8543			−1.95890
$814$	−2.57172	−	4.45435i	−0.0901387	−	0.156125i
$815$	−2.17981	+	3.77554i	−0.0763553	+	0.132251i
$816$	−2.02336	+	3.50457i	−0.0708319	+	0.122684i
$817$	−4.58696	−	7.94484i	−0.160477	−	0.277955i
$818$	39.5654			1.38337
$819$	0.634237	−	8.57553i	0.0221620	−	0.299653i
$820$	−2.65644			−0.0927670
$821$	−3.53571	−	6.12403i	−0.123397	−	0.213730i	0.797708	−	0.603044i	$-0.206046\pi$
$821$	−3.53571	−	6.12403i	−0.123397	−	0.213730i	−0.921105	+	0.389314i	$0.872712\pi$
$822$	9.68359	−	16.7725i	0.337754	−	0.585007i
$823$	−21.4891	+	37.2203i	−0.749064	+	1.29742i	0.199208	+	0.979957i	$0.436163\pi$
$823$	−21.4891	+	37.2203i	−0.749064	+	1.29742i	−0.948272	+	0.317460i	$0.897170\pi$
$824$	−1.18910	−	2.05958i	−0.0414243	−	0.0717489i
$825$	3.04673			0.106073
$826$	13.6336	+	9.27577i	0.474374	+	0.322745i
$827$	43.3864			1.50869			0.754347	−	0.656476i	$-0.227954\pi$
$827$	43.3864			1.50869			0.754347	+	0.656476i	$0.227954\pi$
$828$	−17.0792	−	29.5820i	−0.593543	−	1.02805i
$829$	27.6432	−	47.8795i	0.960089	−	1.66292i	0.237823	−	0.971309i	$-0.423566\pi$
$829$	27.6432	−	47.8795i	0.960089	−	1.66292i	0.722266	−	0.691615i	$-0.243100\pi$
$830$	6.61078	−	11.4502i	0.229464	−	0.397442i
$831$	39.2498	+	67.9826i	1.36156	+	2.35829i
$832$	0.517321			0.0179349
$833$	9.19639	+	1.36779i	0.318636	+	0.0473911i
$834$	−48.5095			−1.67975
$835$	0.712465	+	1.23403i	0.0246559	+	0.0427052i
$836$	1.78969	−	3.09984i	0.0618979	−	0.107210i
$837$	−51.6519	+	89.4638i	−1.78535	+	3.09232i
$838$	−16.1423	−	27.9593i	−0.557627	−	0.965839i
$839$	−23.1413			−0.798925			−0.399462	−	0.916750i	$-0.630803\pi$
$839$	−23.1413			−0.798925			−0.399462	+	0.916750i	$0.630803\pi$
$840$	6.66464	+	4.53436i	0.229952	+	0.156450i
$841$	−28.9208			−0.997268
$842$	−17.9218	−	31.0415i	−0.617627	−	1.06976i
$843$	−1.90436	+	3.29844i	−0.0655896	+	0.113604i
$844$	−3.88315	+	6.72582i	−0.133664	+	0.231512i
$845$	−6.36619	−	11.0266i	−0.219004	−	0.379325i
$846$	29.8415			1.02597
$847$	0.195144	−	2.63854i	0.00670522	−	0.0906615i
$848$	−1.84229			−0.0632645
$849$	14.1402	+	24.4915i	0.485290	+	0.840547i
$850$	0.664110	−	1.15027i	0.0227788	−	0.0394540i
$851$	13.9825	−	24.2184i	0.479313	−	0.830195i
$852$	−16.8776	−	29.2329i	−0.578218	−	1.00150i
$853$	−24.6972			−0.845616			−0.422808	−	0.906219i	$-0.638955\pi$
$853$	−24.6972			−0.845616			−0.422808	+	0.906219i	$0.638955\pi$
$854$	27.1047	−	13.0855i	0.927504	−	0.447777i
$855$	−22.4877			−0.769064
$856$	−1.67178	−	2.89561i	−0.0571402	−	0.0989698i
$857$	−6.75937	+	11.7076i	−0.230896	+	0.399923i	−0.958072	−	0.286528i	$-0.907499\pi$
$857$	−6.75937	+	11.7076i	−0.230896	+	0.399923i	0.727176	+	0.686451i	$0.240832\pi$
$858$	−0.788069	+	1.36497i	−0.0269042	+	0.0465995i
$859$	−18.0696	−	31.2974i	−0.616525	−	1.06785i	−0.990115	−	0.140259i	$-0.955206\pi$
$859$	−18.0696	−	31.2974i	−0.616525	−	1.06785i	0.373589	−	0.927594i	$-0.378127\pi$
$860$	−2.56298			−0.0873970
$861$	19.2836	−	9.30969i	0.657184	−	0.317273i
$862$	−2.04566			−0.0696755
$863$	−13.6532	−	23.6480i	−0.464760	−	0.804988i	0.534431	−	0.845212i	$-0.320526\pi$
$863$	−13.6532	−	23.6480i	−0.464760	−	0.804988i	−0.999191	+	0.0402243i	$0.987193\pi$
$864$	5.00053	−	8.66118i	0.170122	−	0.294659i
$865$	12.5076	−	21.6639i	0.425273	−	0.736594i
$866$	4.81090	+	8.33272i	0.163481	+	0.283157i
$867$	46.4194			1.57649
$868$	−2.01570	+	27.2543i	−0.0684172	+	0.925071i
$869$	10.7349			0.364157
$870$	−0.428814	−	0.742728i	−0.0145382	−	0.0251809i
$871$	−3.38676	+	5.86604i	−0.114756	+	0.198763i
$872$	5.04122	−	8.73165i	0.170717	−	0.295691i
$873$	48.2522	+	83.5752i	1.63309	+	2.82859i
$874$	19.4612			0.658285
$875$	−2.18747	−	1.48827i	−0.0739502	−	0.0503128i
$876$	−27.2814			−0.921754
$877$	−14.3795	−	24.9061i	−0.485563	−	0.841019i	0.514300	−	0.857611i	$-0.328052\pi$
$877$	−14.3795	−	24.9061i	−0.485563	−	0.841019i	−0.999862	+	0.0165913i	$0.994719\pi$
$878$	1.93151	−	3.34547i	0.0651852	−	0.112904i
$879$	−30.1391	+	52.2024i	−1.01657	+	1.76074i
$880$	−0.500000	−	0.866025i	−0.0168550	−	0.0291937i
$881$	25.7980			0.869157			0.434578	−	0.900634i	$-0.356897\pi$
$881$	25.7980			0.869157			0.434578	+	0.900634i	$0.356897\pi$
$882$	−43.4994	−	6.46972i	−1.46470	−	0.217847i
$883$	−31.9404			−1.07488			−0.537439	−	0.843302i	$-0.680608\pi$
$883$	−31.9404			−1.07488			−0.537439	+	0.843302i	$0.680608\pi$
$884$	0.343558	+	0.595060i	0.0115551	+	0.0200140i
$885$	−9.49449	+	16.4449i	−0.319154	+	0.552791i
$886$	−16.0021	+	27.7165i	−0.537602	+	0.931154i
$887$	−5.95751	−	10.3187i	−0.200034	−	0.346469i	0.748505	−	0.663129i	$-0.230772\pi$
$887$	−5.95751	−	10.3187i	−0.200034	−	0.346469i	−0.948539	+	0.316660i	$0.897439\pi$
$888$	15.6707			0.525873
$889$	34.7241	+	23.6249i	1.16461	+	0.792353i
$890$	16.1292			0.540651
$891$	5.81143	+	10.0657i	0.194690	+	0.337214i
$892$	−1.61078	+	2.78995i	−0.0539329	+	0.0934145i
$893$	−8.50087	+	14.7239i	−0.284471	+	0.492718i
$894$	29.3826	+	50.8921i	0.982700	+	1.70209i
$895$	3.88505			0.129863
$896$	0.195144	−	2.63854i	0.00651929	−	0.0881476i
$897$	−8.56948			−0.286127
$898$	7.39686	+	12.8117i	0.246837	+	0.427533i
$899$	1.45380	−	2.51806i	0.0484871	−	0.0839821i
$900$	−3.14128	+	5.44086i	−0.104709	+	0.181362i
$901$	−1.22348	−	2.11914i	−0.0407602	−	0.0705987i
$902$	−2.65644			−0.0884498
$903$	18.6052	−	8.98216i	0.619142	−	0.298907i
$904$	−1.29790			−0.0431674
$905$	12.9554	+	22.4394i	0.430652	+	0.745912i
$906$	10.7859	−	18.6817i	0.358337	−	0.620658i
$907$	15.2288	−	26.3771i	0.505665	−	0.875838i	−0.494313	−	0.869284i	$-0.664580\pi$
$907$	15.2288	−	26.3771i	0.505665	−	0.875838i	0.999979	−	0.00655433i	$-0.00208632\pi$
$908$	−7.48268	−	12.9604i	−0.248321	−	0.430105i
$909$	36.3168			1.20455
$910$	1.23258	−	0.595060i	0.0408596	−	0.0197261i
$911$	13.2127			0.437757			0.218879	−	0.975752i	$-0.429760\pi$
$911$	13.2127			0.437757			0.218879	+	0.975752i	$0.429760\pi$
$912$	5.45271	+	9.44438i	0.180557	+	0.312735i
$913$	6.61078	−	11.4502i	0.218785	−	0.378947i
$914$	−10.3537	+	17.9332i	−0.342471	+	0.593178i
$915$	17.3298	+	30.0161i	0.572906	+	0.992303i
$916$	−5.65461			−0.186834
$917$	−0.911668	+	12.3267i	−0.0301059	+	0.407063i
$918$	13.2836			0.438425
$919$	−8.30080	−	14.3774i	−0.273818	−	0.474267i	0.696018	−	0.718024i	$-0.254953\pi$
$919$	−8.30080	−	14.3774i	−0.273818	−	0.474267i	−0.969836	+	0.243757i	$0.921620\pi$
$920$	2.71851	−	4.70859i	0.0896266	−	0.155238i
$921$	−38.5640	+	66.7948i	−1.27073	+	2.20096i
$922$	13.6423	+	23.6292i	0.449287	+	0.778187i
$923$	−5.73150			−0.188655
$924$	6.66464	+	4.53436i	0.219251	+	0.149170i
$925$	−5.14344			−0.169115
$926$	−7.76524	−	13.4498i	−0.255182	−	0.441987i
$927$	−7.47059	+	12.9394i	−0.245366	+	0.424987i
$928$	−0.140746	+	0.243779i	−0.00462021	+	0.00800244i
$929$	21.1122	+	36.5674i	0.692669	+	1.19974i	0.970960	+	0.239241i	$0.0768986\pi$
$929$	21.1122	+	36.5674i	0.692669	+	1.19974i	−0.278291	+	0.960497i	$0.589768\pi$
$930$	−31.4705			−1.03196
$931$	15.5837	−	19.6198i	0.510736	−	0.643012i
$932$	−24.0378			−0.787386
$933$	15.4918	+	26.8325i	0.507178	+	0.878458i
$934$	−10.6141	+	18.3842i	−0.347305	+	0.601550i
$935$	0.664110	−	1.15027i	0.0217187	−	0.0376179i
$936$	−1.62505	−	2.81467i	−0.0531164	−	0.0920003i
$937$	57.6174			1.88228			0.941140	−	0.338018i	$-0.109756\pi$
$937$	57.6174			1.88228			0.941140	+	0.338018i	$0.109756\pi$
$938$	28.6416	+	19.4866i	0.935182	+	0.636261i
$939$	−1.19794			−0.0390932
$940$	2.37495	+	4.11353i	0.0774623	+	0.134169i
$941$	6.02535	−	10.4362i	0.196421	−	0.340211i	−0.750945	−	0.660365i	$-0.770401\pi$
$941$	6.02535	−	10.4362i	0.196421	−	0.340211i	0.947365	+	0.320155i	$0.103735\pi$
$942$	29.3461	−	50.8289i	0.956146	−	1.65609i
$943$	−7.22156	−	12.5081i	−0.235166	−	0.407320i
$944$	6.23258			0.202853
$945$	1.95165	−	26.3883i	0.0634870	−	0.858410i
$946$	−2.56298			−0.0833298
$947$	17.6407	+	30.5546i	0.573246	+	0.992892i	0.996230	+	0.0867544i	$0.0276496\pi$
$947$	17.6407	+	30.5546i	0.573246	+	0.992892i	−0.422983	+	0.906137i	$0.639017\pi$
$948$	−16.3532	+	28.3245i	−0.531127	+	0.919939i
$949$	−2.31613	+	4.01166i	−0.0751849	+	0.130224i
$950$	−1.78969	−	3.09984i	−0.0580653	−	0.100572i
$951$	−76.3160			−2.47472
$952$	3.16464	−	1.52782i	0.102567	−	0.0495168i
$953$	16.0167			0.518832			0.259416	−	0.965766i	$-0.416470\pi$
$953$	16.0167			0.518832			0.259416	+	0.965766i	$0.416470\pi$
$954$	5.78715	+	10.0236i	0.187366	+	0.324527i
$955$	5.75541	−	9.96866i	0.186241	−	0.322578i
$956$	−13.5412	+	23.4541i	−0.437954	+	0.758559i
$957$	−0.428814	−	0.742728i	−0.0138616	−	0.0240090i
$958$	27.7410			0.896271
$959$	−15.1456	+	7.31195i	−0.489078	+	0.236115i
$960$	3.04673			0.0983328
$961$	−37.8471	−	65.5531i	−1.22087	−	2.11462i
$962$	1.33040	−	2.30433i	0.0428940	−	0.0742945i
$963$	−10.5031	+	18.1918i	−0.338456	+	0.586223i
$964$	−7.61078	−	13.1823i	−0.245127	−	0.424572i
$965$	1.59473			0.0513360
$966$	−3.23258	+	43.7078i	−0.104007	+	1.40628i
$967$	7.74000			0.248902			0.124451	−	0.992226i	$-0.460283\pi$
$967$	7.74000			0.248902			0.124451	+	0.992226i	$0.460283\pi$
$968$	−0.500000	−	0.866025i	−0.0160706	−	0.0278351i
$969$	−7.24241	+	12.5442i	−0.232660	+	0.402978i
$970$	−7.68034	+	13.3027i	−0.246601	+	0.427125i
$971$	7.78375	+	13.4819i	0.249792	+	0.432653i	0.963468	−	0.267823i	$-0.0863043\pi$
$971$	7.78375	+	13.4819i	0.249792	+	0.432653i	−0.713676	+	0.700476i	$0.752971\pi$
$972$	−5.40853			−0.173479
$973$	34.8286	+	23.6960i	1.11655	+	0.759659i
$974$	−6.02417			−0.193027
$975$	0.788069	+	1.36497i	0.0252384	+	0.0437142i
$976$	5.68801	−	9.85192i	0.182069	−	0.315352i
$977$	−4.57939	+	7.93173i	−0.146508	+	0.253759i	−0.929934	−	0.367725i	$-0.880137\pi$
$977$	−4.57939	+	7.93173i	−0.146508	+	0.253759i	0.783427	+	0.621484i	$0.213470\pi$
$978$	−6.64128	−	11.5030i	−0.212365	−	0.367826i
$979$	16.1292			0.515490
$980$	−2.57009	−	6.51111i	−0.0820986	−	0.207990i
$981$	−63.3435			−2.02240
$982$	−1.43522	−	2.48587i	−0.0457996	−	0.0793272i
$983$	−7.09564	+	12.2900i	−0.226316	+	0.391991i	−0.956713	−	0.291032i	$-0.906001\pi$
$983$	−7.09564	+	12.2900i	−0.226316	+	0.391991i	0.730398	+	0.683022i	$0.239335\pi$
$984$	4.04673	−	7.00914i	0.129005	−	0.223443i
$985$	−1.69568	−	2.93700i	−0.0540288	−	0.0935806i
$986$	−0.373883			−0.0119069
$987$	−31.6564	−	21.5378i	−1.00763	−	0.685555i
$988$	1.85169			0.0589102
$989$	−6.96749	−	12.0680i	−0.221553	−	0.383742i
$990$	−3.14128	+	5.44086i	−0.0998364	+	0.172922i
$991$	21.7465	−	37.6661i	0.690801	−	1.19650i	−0.280775	−	0.959774i	$-0.590591\pi$
$991$	21.7465	−	37.6661i	0.690801	−	1.19650i	0.971576	−	0.236729i	$-0.0760753\pi$
$992$	5.16464	+	8.94543i	0.163978	+	0.284018i
$993$	−78.2346			−2.48270
$994$	−2.16203	+	29.2329i	−0.0685756	+	0.927212i
$995$	−22.8098			−0.723119
$996$	20.1413	+	34.8857i	0.638200	+	1.10539i
$997$	5.26722	−	9.12309i	0.166815	−	0.288931i	−0.770484	−	0.637460i	$-0.779985\pi$
$997$	5.26722	−	9.12309i	0.166815	−	0.288931i	0.937298	+	0.348528i	$0.113319\pi$
$998$	3.33254	−	5.77213i	0.105490	−	0.182713i
$999$	−25.7199	−	44.5482i	−0.813743	−	1.40944i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	770.2.i.l.221.4	✓	8
7.2	even	3	inner	770.2.i.l.331.4	yes	8
7.3	odd	6		5390.2.a.cf.1.4		4
7.4	even	3		5390.2.a.ce.1.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
770.2.i.l.221.4	✓	8	1.1	even	1	trivial
770.2.i.l.331.4	yes	8	7.2	even	3	inner
5390.2.a.ce.1.1		4	7.4	even	3
5390.2.a.cf.1.4		4	7.3	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:	\( N \)	\(=\)	\( 770 = 2 \cdot 5 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	770.i (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 - 0.866025i) q^{2} +(1.52336 - 2.63854i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(0.500000 + 0.866025i) q^{5} -3.04673 q^{6} +(2.18747 + 1.48827i) q^{7} +1.00000 q^{8} +(-3.14128 - 5.44086i) q^{9} +O(q^{10})\)	\(q+(-0.500000 - 0.866025i) q^{2} +(1.52336 - 2.63854i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(0.500000 + 0.866025i) q^{5} -3.04673 q^{6} +(2.18747 + 1.48827i) q^{7} +1.00000 q^{8} +(-3.14128 - 5.44086i) q^{9} +(0.500000 - 0.866025i) q^{10} +(0.500000 - 0.866025i) q^{11} +(1.52336 + 2.63854i) q^{12} +0.517321 q^{13} +(0.195144 - 2.63854i) q^{14} +3.04673 q^{15} +(-0.500000 - 0.866025i) q^{16} +(0.664110 - 1.15027i) q^{17} +(-3.14128 + 5.44086i) q^{18} +(-1.78969 - 3.09984i) q^{19} -1.00000 q^{20} +(7.25919 - 3.50457i) q^{21} -1.00000 q^{22} +(-2.71851 - 4.70859i) q^{23} +(1.52336 - 2.63854i) q^{24} +(-0.500000 + 0.866025i) q^{25} +(-0.258661 - 0.448013i) q^{26} -10.0011 q^{27} +(-2.38262 + 1.15027i) q^{28} +0.281492 q^{29} +(-1.52336 - 2.63854i) q^{30} +(5.16464 - 8.94543i) q^{31} +(-0.500000 + 0.866025i) q^{32} +(-1.52336 - 2.63854i) q^{33} -1.32822 q^{34} +(-0.195144 + 2.63854i) q^{35} +6.28256 q^{36} +(2.57172 + 4.45435i) q^{37} +(-1.78969 + 3.09984i) q^{38} +(0.788069 - 1.36497i) q^{39} +(0.500000 + 0.866025i) q^{40} +2.65644 q^{41} +(-6.66464 - 4.53436i) q^{42} +2.56298 q^{43} +(0.500000 + 0.866025i) q^{44} +(3.14128 - 5.44086i) q^{45} +(-2.71851 + 4.70859i) q^{46} +(-2.37495 - 4.11353i) q^{47} -3.04673 q^{48} +(2.57009 + 6.51111i) q^{49} +1.00000 q^{50} +(-2.02336 - 3.50457i) q^{51} +(-0.258661 + 0.448013i) q^{52} +(0.921146 - 1.59547i) q^{53} +(5.00053 + 8.66118i) q^{54} +1.00000 q^{55} +(2.18747 + 1.48827i) q^{56} -10.9054 q^{57} +(-0.140746 - 0.243779i) q^{58} +(-3.11629 + 5.39757i) q^{59} +(-1.52336 + 2.63854i) q^{60} +(5.68801 + 9.85192i) q^{61} -10.3293 q^{62} +(1.22600 - 16.5768i) q^{63} +1.00000 q^{64} +(0.258661 + 0.448013i) q^{65} +(-1.52336 + 2.63854i) q^{66} +(-6.54673 + 11.3393i) q^{67} +(0.664110 + 1.15027i) q^{68} -16.5651 q^{69} +(2.38262 - 1.15027i) q^{70} -11.0792 q^{71} +(-3.14128 - 5.44086i) q^{72} +(-4.47717 + 7.75468i) q^{73} +(2.57172 - 4.45435i) q^{74} +(1.52336 + 2.63854i) q^{75} +3.57939 q^{76} +(2.38262 - 1.15027i) q^{77} -1.57614 q^{78} +(5.36746 + 9.29671i) q^{79} +(0.500000 - 0.866025i) q^{80} +(-5.81143 + 10.0657i) q^{81} +(-1.32822 - 2.30055i) q^{82} +13.2216 q^{83} +(-0.594550 + 8.03893i) q^{84} +1.32822 q^{85} +(-1.28149 - 2.21961i) q^{86} +(0.428814 - 0.742728i) q^{87} +(0.500000 - 0.866025i) q^{88} +(8.06458 + 13.9683i) q^{89} -6.28256 q^{90} +(1.13163 + 0.769914i) q^{91} +5.43702 q^{92} +(-15.7353 - 27.2543i) q^{93} +(-2.37495 + 4.11353i) q^{94} +(1.78969 - 3.09984i) q^{95} +(1.52336 + 2.63854i) q^{96} -15.3607 q^{97} +(4.35374 - 5.48132i) q^{98} -6.28256 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 4 q^{2} + q^{3} - 4 q^{4} + 4 q^{5} - 2 q^{6} + 3 q^{7} + 8 q^{8} - 3 q^{9}+O(q^{10}) \) 8 * q - 4 * q^2 + q^3 - 4 * q^4 + 4 * q^5 - 2 * q^6 + 3 * q^7 + 8 * q^8 - 3 * q^9	\( 8 q - 4 q^{2} + q^{3} - 4 q^{4} + 4 q^{5} - 2 q^{6} + 3 q^{7} + 8 q^{8} - 3 q^{9} + 4 q^{10} + 4 q^{11} + q^{12} - 2 q^{13} - 3 q^{14} + 2 q^{15} - 4 q^{16} + 2 q^{17} - 3 q^{18} - 10 q^{19} - 8 q^{20} + 25 q^{21} - 8 q^{22} - 6 q^{23} + q^{24} - 4 q^{25} + q^{26} - 20 q^{27} + 18 q^{29} - q^{30} + 8 q^{31} - 4 q^{32} - q^{33} - 4 q^{34} + 3 q^{35} + 6 q^{36} + 2 q^{37} - 10 q^{38} - 13 q^{39} + 4 q^{40} + 8 q^{41} - 20 q^{42} + 52 q^{43} + 4 q^{44} + 3 q^{45} - 6 q^{46} + 10 q^{47} - 2 q^{48} - 13 q^{49} + 8 q^{50} - 5 q^{51} + q^{52} - 14 q^{53} + 10 q^{54} + 8 q^{55} + 3 q^{56} + 18 q^{57} - 9 q^{58} + q^{59} - q^{60} + q^{61} - 16 q^{62} - 7 q^{63} + 8 q^{64} - q^{65} - q^{66} - 30 q^{67} + 2 q^{68} - 44 q^{69} + 36 q^{71} - 3 q^{72} - 17 q^{73} + 2 q^{74} + q^{75} + 20 q^{76} + 26 q^{78} + 15 q^{79} + 4 q^{80} - 16 q^{81} - 4 q^{82} + 4 q^{83} - 5 q^{84} + 4 q^{85} - 26 q^{86} - 8 q^{87} + 4 q^{88} + 6 q^{89} - 6 q^{90} + 3 q^{91} + 12 q^{92} - 29 q^{93} + 10 q^{94} + 10 q^{95} + q^{96} - 14 q^{97} + 2 q^{98} - 6 q^{99}+O(q^{100}) \) 8 * q - 4 * q^2 + q^3 - 4 * q^4 + 4 * q^5 - 2 * q^6 + 3 * q^7 + 8 * q^8 - 3 * q^9 + 4 * q^10 + 4 * q^11 + q^12 - 2 * q^13 - 3 * q^14 + 2 * q^15 - 4 * q^16 + 2 * q^17 - 3 * q^18 - 10 * q^19 - 8 * q^20 + 25 * q^21 - 8 * q^22 - 6 * q^23 + q^24 - 4 * q^25 + q^26 - 20 * q^27 + 18 * q^29 - q^30 + 8 * q^31 - 4 * q^32 - q^33 - 4 * q^34 + 3 * q^35 + 6 * q^36 + 2 * q^37 - 10 * q^38 - 13 * q^39 + 4 * q^40 + 8 * q^41 - 20 * q^42 + 52 * q^43 + 4 * q^44 + 3 * q^45 - 6 * q^46 + 10 * q^47 - 2 * q^48 - 13 * q^49 + 8 * q^50 - 5 * q^51 + q^52 - 14 * q^53 + 10 * q^54 + 8 * q^55 + 3 * q^56 + 18 * q^57 - 9 * q^58 + q^59 - q^60 + q^61 - 16 * q^62 - 7 * q^63 + 8 * q^64 - q^65 - q^66 - 30 * q^67 + 2 * q^68 - 44 * q^69 + 36 * q^71 - 3 * q^72 - 17 * q^73 + 2 * q^74 + q^75 + 20 * q^76 + 26 * q^78 + 15 * q^79 + 4 * q^80 - 16 * q^81 - 4 * q^82 + 4 * q^83 - 5 * q^84 + 4 * q^85 - 26 * q^86 - 8 * q^87 + 4 * q^88 + 6 * q^89 - 6 * q^90 + 3 * q^91 + 12 * q^92 - 29 * q^93 + 10 * q^94 + 10 * q^95 + q^96 - 14 * q^97 + 2 * q^98 - 6 * q^99

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