LMFDB - Embedded newform 770.2.i.m.221.5

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:	$10$
Relative dimension:	$5$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} + 12x^{8} - 6x^{7} + 113x^{6} - 43x^{5} + 381x^{4} - 75x^{3} + 982x^{2} - 217x + 49 $ x^10 + 12x^8 - 6x^7 + 113x^6 - 43x^5 + 381x^4 - 75x^3 + 982x^2 - 217x + 49
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			221.5
Root			$-1.53759 - 2.66319i$ of defining polynomial
Character	$\chi$	$=$	770.221
Dual form			770.2.i.m.331.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 - 0.866025i) q^{2} +(1.53759 - 2.66319i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-0.500000 - 0.866025i) q^{5} -3.07519 q^{6} +(-2.08672 + 1.62653i) q^{7} +1.00000 q^{8} +(-3.22839 - 5.59173i) q^{9} +O(q^{10})$	\(q+(-0.500000 - 0.866025i) q^{2} +(1.53759 - 2.66319i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-0.500000 - 0.866025i) q^{5} -3.07519 q^{6} +(-2.08672 + 1.62653i) q^{7} +1.00000 q^{8} +(-3.22839 - 5.59173i) q^{9} +(-0.500000 + 0.866025i) q^{10} +(-0.500000 + 0.866025i) q^{11} +(1.53759 + 2.66319i) q^{12} -4.72627 q^{13} +(2.45197 + 0.993893i) q^{14} -3.07519 q^{15} +(-0.500000 - 0.866025i) q^{16} +(-0.549130 + 0.951122i) q^{17} +(-3.22839 + 5.59173i) q^{18} +(-1.19079 - 2.06251i) q^{19} +1.00000 q^{20} +(1.12321 + 8.05828i) q^{21} +1.00000 q^{22} +(-0.0856193 - 0.148297i) q^{23} +(1.53759 - 2.66319i) q^{24} +(-0.500000 + 0.866025i) q^{25} +(2.36314 + 4.09307i) q^{26} -10.6302 q^{27} +(-0.365250 - 2.62042i) q^{28} -3.63445 q^{29} +(1.53759 + 2.66319i) q^{30} +(0.190793 - 0.330463i) q^{31} +(-0.500000 + 0.866025i) q^{32} +(1.53759 + 2.66319i) q^{33} +1.09826 q^{34} +(2.45197 + 0.993893i) q^{35} +6.45677 q^{36} +(-5.35482 - 9.27482i) q^{37} +(-1.19079 + 2.06251i) q^{38} +(-7.26708 + 12.5870i) q^{39} +(-0.500000 - 0.866025i) q^{40} +1.47341 q^{41} +(6.41706 - 5.00187i) q^{42} +3.82876 q^{43} +(-0.500000 - 0.866025i) q^{44} +(-3.22839 + 5.59173i) q^{45} +(-0.0856193 + 0.148297i) q^{46} +(-2.38159 - 4.12503i) q^{47} -3.07519 q^{48} +(1.70883 - 6.78822i) q^{49} +1.00000 q^{50} +(1.68868 + 2.92488i) q^{51} +(2.36314 - 4.09307i) q^{52} +(4.36793 - 7.56548i) q^{53} +(5.31511 + 9.20604i) q^{54} +1.00000 q^{55} +(-2.08672 + 1.62653i) q^{56} -7.32382 q^{57} +(1.81722 + 3.14752i) q^{58} +(-2.81031 + 4.86760i) q^{59} +(1.53759 - 2.66319i) q^{60} +(5.07307 + 8.78682i) q^{61} -0.381586 q^{62} +(15.8318 + 6.41734i) q^{63} +1.00000 q^{64} +(2.36314 + 4.09307i) q^{65} +(1.53759 - 2.66319i) q^{66} +(2.57519 - 4.46035i) q^{67} +(-0.549130 - 0.951122i) q^{68} -0.526591 q^{69} +(-0.365250 - 2.62042i) q^{70} +4.72406 q^{71} +(-3.22839 - 5.59173i) q^{72} +(7.50379 - 12.9969i) q^{73} +(-5.35482 + 9.27482i) q^{74} +(1.53759 + 2.66319i) q^{75} +2.38159 q^{76} +(-0.365250 - 2.62042i) q^{77} +14.5342 q^{78} +(-6.05674 - 10.4906i) q^{79} +(-0.500000 + 0.866025i) q^{80} +(-6.65980 + 11.5351i) q^{81} +(-0.736705 - 1.27601i) q^{82} +2.51813 q^{83} +(-7.54028 - 3.05641i) q^{84} +1.09826 q^{85} +(-1.91438 - 3.31580i) q^{86} +(-5.58830 + 9.67923i) q^{87} +(-0.500000 + 0.866025i) q^{88} +(4.34790 + 7.53079i) q^{89} +6.45677 q^{90} +(9.86242 - 7.68740i) q^{91} +0.171239 q^{92} +(-0.586724 - 1.01624i) q^{93} +(-2.38159 + 4.12503i) q^{94} +(-1.19079 + 2.06251i) q^{95} +(1.53759 + 2.66319i) q^{96} +14.4880 q^{97} +(-6.73318 + 1.91422i) q^{98} +6.45677 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q - 5 q^{2} - 5 q^{4} - 5 q^{5} + 10 q^{8} - 9 q^{9}+O(q^{10}) $ 10 * q - 5 * q^2 - 5 * q^4 - 5 * q^5 + 10 * q^8 - 9 * q^9	$ 10 q - 5 q^{2} - 5 q^{4} - 5 q^{5} + 10 q^{8} - 9 q^{9} - 5 q^{10} - 5 q^{11} - 2 q^{13} + 3 q^{14} - 5 q^{16} - 9 q^{18} - 4 q^{19} + 10 q^{20} + 2 q^{21} + 10 q^{22} - 7 q^{23} - 5 q^{25} + q^{26} - 18 q^{27} - 3 q^{28} + 8 q^{29} - 6 q^{31} - 5 q^{32} + 3 q^{35} + 18 q^{36} - 16 q^{37} - 4 q^{38} - 7 q^{39} - 5 q^{40} - 2 q^{41} + 11 q^{42} + 26 q^{43} - 5 q^{44} - 9 q^{45} - 7 q^{46} - 8 q^{47} + 14 q^{49} + 10 q^{50} - 13 q^{51} + q^{52} - 4 q^{53} + 9 q^{54} + 10 q^{55} + 30 q^{57} - 4 q^{58} - 9 q^{59} - 2 q^{61} + 12 q^{62} + 25 q^{63} + 10 q^{64} + q^{65} - 5 q^{67} - 22 q^{69} - 3 q^{70} + 56 q^{71} - 9 q^{72} + q^{73} - 16 q^{74} + 8 q^{76} - 3 q^{77} + 14 q^{78} - 23 q^{79} - 5 q^{80} + 7 q^{81} + q^{82} - 46 q^{83} - 13 q^{84} - 13 q^{86} - 15 q^{87} - 5 q^{88} + 9 q^{89} + 18 q^{90} + 29 q^{91} + 14 q^{92} + 15 q^{93} - 8 q^{94} - 4 q^{95} - 26 q^{97} - 19 q^{98} + 18 q^{99}+O(q^{100}) $ 10 * q - 5 * q^2 - 5 * q^4 - 5 * q^5 + 10 * q^8 - 9 * q^9 - 5 * q^10 - 5 * q^11 - 2 * q^13 + 3 * q^14 - 5 * q^16 - 9 * q^18 - 4 * q^19 + 10 * q^20 + 2 * q^21 + 10 * q^22 - 7 * q^23 - 5 * q^25 + q^26 - 18 * q^27 - 3 * q^28 + 8 * q^29 - 6 * q^31 - 5 * q^32 + 3 * q^35 + 18 * q^36 - 16 * q^37 - 4 * q^38 - 7 * q^39 - 5 * q^40 - 2 * q^41 + 11 * q^42 + 26 * q^43 - 5 * q^44 - 9 * q^45 - 7 * q^46 - 8 * q^47 + 14 * q^49 + 10 * q^50 - 13 * q^51 + q^52 - 4 * q^53 + 9 * q^54 + 10 * q^55 + 30 * q^57 - 4 * q^58 - 9 * q^59 - 2 * q^61 + 12 * q^62 + 25 * q^63 + 10 * q^64 + q^65 - 5 * q^67 - 22 * q^69 - 3 * q^70 + 56 * q^71 - 9 * q^72 + q^73 - 16 * q^74 + 8 * q^76 - 3 * q^77 + 14 * q^78 - 23 * q^79 - 5 * q^80 + 7 * q^81 + q^82 - 46 * q^83 - 13 * q^84 - 13 * q^86 - 15 * q^87 - 5 * q^88 + 9 * q^89 + 18 * q^90 + 29 * q^91 + 14 * q^92 + 15 * q^93 - 8 * q^94 - 4 * q^95 - 26 * q^97 - 19 * q^98 + 18 * 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
$3$	1.53759	−	2.66319i	0.887730	−	1.53759i	0.0451774	−	0.998979i	$-0.485615\pi$
$3$	1.53759	−	2.66319i	0.887730	−	1.53759i	0.842552	−	0.538614i	$-0.181052\pi$
$4$	−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
$6$	−3.07519			−1.25544
$7$	−2.08672	+	1.62653i	−0.788707	+	0.614769i
$7$	−2.08672	+	1.62653i	−0.788707	+	0.614769i
$8$	1.00000			0.353553
$9$	−3.22839	−	5.59173i	−1.07613	−	1.86391i
$10$	−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
$12$	1.53759	+	2.66319i	0.443865	+	0.768797i
$13$	−4.72627			−1.31083			−0.655416	−	0.755268i	$-0.727507\pi$
$13$	−4.72627			−1.31083			−0.655416	+	0.755268i	$0.727507\pi$
$14$	2.45197	+	0.993893i	0.655318	+	0.265629i
$15$	−3.07519			−0.794010
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	−0.549130	+	0.951122i	−0.133184	+	0.230681i	−0.924902	−	0.380205i	$-0.875853\pi$
$17$	−0.549130	+	0.951122i	−0.133184	+	0.230681i	0.791718	+	0.610886i	$0.209187\pi$
$18$	−3.22839	+	5.59173i	−0.760938	+	1.31798i
$19$	−1.19079	−	2.06251i	−0.273187	−	0.473173i	0.696489	−	0.717567i	$-0.254744\pi$
$19$	−1.19079	−	2.06251i	−0.273187	−	0.473173i	−0.969676	+	0.244394i	$0.921411\pi$
$20$	1.00000			0.223607
$21$	1.12321	+	8.05828i	0.245105	+	1.75846i
$22$	1.00000			0.213201
$23$	−0.0856193	−	0.148297i	−0.0178529	−	0.0309221i	0.856961	−	0.515381i	$-0.172350\pi$
$23$	−0.0856193	−	0.148297i	−0.0178529	−	0.0309221i	−0.874814	+	0.484459i	$0.839016\pi$
$24$	1.53759	−	2.66319i	0.313860	−	0.543621i
$25$	−0.500000	+	0.866025i	−0.100000	+	0.173205i
$26$	2.36314	+	4.09307i	0.463449	+	0.802717i
$27$	−10.6302			−2.04579
$28$	−0.365250	−	2.62042i	−0.0690258	−	0.495213i
$29$	−3.63445			−0.674900			−0.337450	−	0.941343i	$-0.609564\pi$
$29$	−3.63445			−0.674900			−0.337450	+	0.941343i	$0.609564\pi$
$30$	1.53759	+	2.66319i	0.280725	+	0.486230i
$31$	0.190793	−	0.330463i	0.0342674	−	0.0593529i	−0.848383	−	0.529383i	$-0.822424\pi$
$31$	0.190793	−	0.330463i	0.0342674	−	0.0593529i	0.882650	+	0.470030i	$0.155757\pi$
$32$	−0.500000	+	0.866025i	−0.0883883	+	0.153093i
$33$	1.53759	+	2.66319i	0.267661	+	0.463602i
$34$	1.09826			0.188350
$35$	2.45197	+	0.993893i	0.414459	+	0.167999i
$36$	6.45677			1.07613
$37$	−5.35482	−	9.27482i	−0.880327	−	1.52477i	−0.850978	−	0.525201i	$-0.823990\pi$
$37$	−5.35482	−	9.27482i	−0.880327	−	1.52477i	−0.0293484	−	0.999569i	$-0.509343\pi$
$38$	−1.19079	+	2.06251i	−0.193172	+	0.334584i
$39$	−7.26708	+	12.5870i	−1.16366	+	2.01553i
$40$	−0.500000	−	0.866025i	−0.0790569	−	0.136931i
$41$	1.47341			0.230108			0.115054	−	0.993359i	$-0.463296\pi$
$41$	1.47341			0.230108			0.115054	+	0.993359i	$0.463296\pi$
$42$	6.41706	−	5.00187i	0.990175	−	0.771805i
$43$	3.82876			0.583881			0.291940	−	0.956437i	$-0.405699\pi$
$43$	3.82876			0.583881			0.291940	+	0.956437i	$0.405699\pi$
$44$	−0.500000	−	0.866025i	−0.0753778	−	0.130558i
$45$	−3.22839	+	5.59173i	−0.481259	+	0.833566i
$46$	−0.0856193	+	0.148297i	−0.0126239	+	0.0218652i
$47$	−2.38159	−	4.12503i	−0.347390	−	0.601697i	0.638395	−	0.769709i	$-0.279599\pi$
$47$	−2.38159	−	4.12503i	−0.347390	−	0.601697i	−0.985785	+	0.168012i	$0.946265\pi$
$48$	−3.07519			−0.443865
$49$	1.70883	−	6.78822i	0.244119	−	0.969745i
$50$	1.00000			0.141421
$51$	1.68868	+	2.92488i	0.236462	+	0.409565i
$52$	2.36314	−	4.09307i	0.327708	−	0.567607i
$53$	4.36793	−	7.56548i	0.599982	−	1.03920i	−0.392841	−	0.919606i	$-0.628508\pi$
$53$	4.36793	−	7.56548i	0.599982	−	1.03920i	0.992823	−	0.119593i	$-0.0381589\pi$
$54$	5.31511	+	9.20604i	0.723295	+	1.25278i
$55$	1.00000			0.134840
$56$	−2.08672	+	1.62653i	−0.278850	+	0.217354i
$57$	−7.32382			−0.970064
$58$	1.81722	+	3.14752i	0.238613	+	0.413290i
$59$	−2.81031	+	4.86760i	−0.365871	+	0.633708i	−0.988916	−	0.148479i	$-0.952562\pi$
$59$	−2.81031	+	4.86760i	−0.365871	+	0.633708i	0.623044	+	0.782187i	$0.285896\pi$
$60$	1.53759	−	2.66319i	0.198502	−	0.343816i
$61$	5.07307	+	8.78682i	0.649540	+	1.12504i	0.983233	+	0.182355i	$0.0583720\pi$
$61$	5.07307	+	8.78682i	0.649540	+	1.12504i	−0.333692	+	0.942682i	$0.608295\pi$
$62$	−0.381586			−0.0484614
$63$	15.8318	+	6.41734i	1.99462	+	0.808509i
$64$	1.00000			0.125000
$65$	2.36314	+	4.09307i	0.293111	+	0.507683i
$66$	1.53759	−	2.66319i	0.189265	−	0.327816i
$67$	2.57519	−	4.46035i	0.314609	−	0.544919i	−0.664745	−	0.747070i	$-0.731460\pi$
$67$	2.57519	−	4.46035i	0.314609	−	0.544919i	0.979354	+	0.202151i	$0.0647932\pi$
$68$	−0.549130	−	0.951122i	−0.0665918	−	0.115340i
$69$	−0.526591			−0.0633941
$70$	−0.365250	−	2.62042i	−0.0436558	−	0.313200i
$71$	4.72406			0.560643			0.280322	−	0.959906i	$-0.409559\pi$
$71$	4.72406			0.560643			0.280322	+	0.959906i	$0.409559\pi$
$72$	−3.22839	−	5.59173i	−0.380469	−	0.658992i
$73$	7.50379	−	12.9969i	0.878252	−	1.52118i	0.0249943	−	0.999688i	$-0.492043\pi$
$73$	7.50379	−	12.9969i	0.878252	−	1.52118i	0.853258	−	0.521490i	$-0.174623\pi$
$74$	−5.35482	+	9.27482i	−0.622485	+	1.07818i
$75$	1.53759	+	2.66319i	0.177546	+	0.307519i
$76$	2.38159			0.273187
$77$	−0.365250	−	2.62042i	−0.0416241	−	0.298624i
$78$	14.5342			1.64567
$79$	−6.05674	−	10.4906i	−0.681436	−	1.18028i	−0.974543	−	0.224202i	$-0.928022\pi$
$79$	−6.05674	−	10.4906i	−0.681436	−	1.18028i	0.293107	−	0.956080i	$-0.405311\pi$
$80$	−0.500000	+	0.866025i	−0.0559017	+	0.0968246i
$81$	−6.65980	+	11.5351i	−0.739977	+	1.28168i
$82$	−0.736705	−	1.27601i	−0.0813554	−	0.140912i
$83$	2.51813			0.276401			0.138201	−	0.990404i	$-0.455868\pi$
$83$	2.51813			0.276401			0.138201	+	0.990404i	$0.455868\pi$
$84$	−7.54028	−	3.05641i	−0.822712	−	0.333481i
$85$	1.09826			0.119123
$86$	−1.91438	−	3.31580i	−0.206433	−	0.357552i
$87$	−5.58830	+	9.67923i	−0.599129	+	1.03772i
$88$	−0.500000	+	0.866025i	−0.0533002	+	0.0923186i
$89$	4.34790	+	7.53079i	0.460877	+	0.798262i	0.999005	−	0.0446008i	$-0.0142016\pi$
$89$	4.34790	+	7.53079i	0.460877	+	0.798262i	−0.538128	+	0.842863i	$0.680868\pi$
$90$	6.45677			0.680604
$91$	9.86242	−	7.68740i	1.03386	−	0.805858i
$92$	0.171239			0.0178529
$93$	−0.586724	−	1.01624i	−0.0608404	−	0.105379i
$94$	−2.38159	+	4.12503i	−0.245642	+	0.425464i
$95$	−1.19079	+	2.06251i	−0.122173	+	0.211609i
$96$	1.53759	+	2.66319i	0.156930	+	0.271811i
$97$	14.4880			1.47104			0.735518	−	0.677505i	$-0.236939\pi$
$97$	14.4880			1.47104			0.735518	+	0.677505i	$0.236939\pi$
$98$	−6.73318	+	1.91422i	−0.680154	+	0.193365i
$99$	6.45677			0.648930
$100$	−0.500000	−	0.866025i	−0.0500000	−	0.0866025i
$101$	−9.30146	+	16.1106i	−0.925530	+	1.60306i	−0.134823	+	0.990870i	$0.543046\pi$
$101$	−9.30146	+	16.1106i	−0.925530	+	1.60306i	−0.790707	+	0.612195i	$0.790287\pi$
$102$	1.68868	−	2.92488i	0.167204	−	0.289606i
$103$	2.19771	+	3.80654i	0.216546	+	0.375069i	0.953750	−	0.300602i	$-0.0971874\pi$
$103$	2.19771	+	3.80654i	0.216546	+	0.375069i	−0.737203	+	0.675671i	$0.763854\pi$
$104$	−4.72627			−0.463449
$105$	6.41706	−	5.00187i	0.626241	−	0.488132i
$106$	−8.73587			−0.848503
$107$	−7.88708	−	13.6608i	−0.762473	−	1.32064i	−0.941573	−	0.336810i	$-0.890652\pi$
$107$	−7.88708	−	13.6608i	−0.762473	−	1.32064i	0.179100	−	0.983831i	$-0.442681\pi$
$108$	5.31511	−	9.20604i	0.511447	−	0.885852i
$109$	−7.49115	+	12.9750i	−0.717522	+	1.24278i	0.244457	+	0.969660i	$0.421390\pi$
$109$	−7.49115	+	12.9750i	−0.717522	+	1.24278i	−0.961979	+	0.273124i	$0.911943\pi$
$110$	−0.500000	−	0.866025i	−0.0476731	−	0.0825723i
$111$	−32.9341			−3.12597
$112$	2.45197	+	0.993893i	0.231690	+	0.0939141i
$113$	−19.2512			−1.81100			−0.905500	−	0.424347i	$-0.860504\pi$
$113$	−19.2512			−1.81100			−0.905500	+	0.424347i	$0.860504\pi$
$114$	3.66191	+	6.34261i	0.342969	+	0.594040i
$115$	−0.0856193	+	0.148297i	−0.00798404	+	0.0138288i
$116$	1.81722	−	3.14752i	0.168725	−	0.292240i
$117$	15.2582	+	26.4280i	1.41062	+	2.44327i
$118$	5.62062			0.517420
$119$	−0.401140	−	2.87790i	−0.0367724	−	0.263817i
$120$	−3.07519			−0.280725
$121$	−0.500000	−	0.866025i	−0.0454545	−	0.0787296i
$122$	5.07307	−	8.78682i	0.459294	−	0.795521i
$123$	2.26550	−	3.92397i	0.204274	−	0.353812i
$124$	0.190793	+	0.330463i	0.0171337	+	0.0296765i
$125$	1.00000			0.0894427
$126$	−2.35834	−	16.9194i	−0.210097	−	1.50730i
$127$	−19.6877			−1.74700			−0.873500	−	0.486823i	$-0.838156\pi$
$127$	−19.6877			−1.74700			−0.873500	+	0.486823i	$0.838156\pi$
$128$	−0.500000	−	0.866025i	−0.0441942	−	0.0765466i
$129$	5.88708	−	10.1967i	0.518328	−	0.897771i
$130$	2.36314	−	4.09307i	0.207261	−	0.358986i
$131$	−7.69950	−	13.3359i	−0.672709	−	1.16517i	−0.977133	−	0.212629i	$-0.931797\pi$
$131$	−7.69950	−	13.3359i	−0.672709	−	1.16517i	0.304424	−	0.952537i	$-0.401536\pi$
$132$	−3.07519			−0.267661
$133$	5.83959	+	2.36704i	0.506356	+	0.205249i
$134$	−5.15037			−0.444924
$135$	5.31511	+	9.20604i	0.457452	+	0.792330i
$136$	−0.549130	+	0.951122i	−0.0470875	+	0.0815580i
$137$	8.55041	−	14.8097i	0.730511	−	1.26528i	−0.226154	−	0.974091i	$-0.572615\pi$
$137$	8.55041	−	14.8097i	0.730511	−	1.26528i	0.956665	−	0.291190i	$-0.0940513\pi$
$138$	0.263295	+	0.456041i	0.0224132	+	0.0388208i
$139$	12.9699			1.10009			0.550046	−	0.835135i	$-0.314610\pi$
$139$	12.9699			1.10009			0.550046	+	0.835135i	$0.314610\pi$
$140$	−2.08672	+	1.62653i	−0.176360	+	0.137466i
$141$	−14.6476			−1.23355
$142$	−2.36203	−	4.09116i	−0.198217	−	0.343322i
$143$	2.36314	−	4.09307i	0.197615	−	0.342280i
$144$	−3.22839	+	5.59173i	−0.269032	+	0.465977i
$145$	1.81722	+	3.14752i	0.150912	+	0.261388i
$146$	−15.0076			−1.24204
$147$	−15.4508	−	14.9885i	−1.27436	−	1.23623i
$148$	10.7096			0.880327
$149$	4.72949	+	8.19172i	0.387455	+	0.671092i	0.992106	−	0.125398i	$-0.0400209\pi$
$149$	4.72949	+	8.19172i	0.387455	+	0.671092i	−0.604651	+	0.796490i	$0.706688\pi$
$150$	1.53759	−	2.66319i	0.125544	−	0.217449i
$151$	10.4341	−	18.0724i	0.849115	−	1.47071i	−0.0328850	−	0.999459i	$-0.510469\pi$
$151$	10.4341	−	18.0724i	0.849115	−	1.47071i	0.881999	−	0.471250i	$-0.156197\pi$
$152$	−1.19079	−	2.06251i	−0.0965861	−	0.167292i
$153$	7.09122			0.573291
$154$	−2.08672	+	1.62653i	−0.168153	+	0.131069i
$155$	−0.381586			−0.0306497
$156$	−7.26708	−	12.5870i	−0.581832	−	1.00776i
$157$	−6.82101	+	11.8143i	−0.544376	+	0.942887i	0.454270	+	0.890864i	$0.349900\pi$
$157$	−6.82101	+	11.8143i	−0.544376	+	0.942887i	−0.998646	+	0.0520229i	$0.983433\pi$
$158$	−6.05674	+	10.4906i	−0.481848	+	0.834585i
$159$	−13.4322	−	23.2653i	−1.06524	−	1.84506i
$160$	1.00000			0.0790569
$161$	0.419873	+	0.170193i	0.0330906	+	0.0134131i
$162$	13.3196			1.04649
$163$	−8.27651	−	14.3353i	−0.648266	−	1.12283i	−0.983537	−	0.180708i	$-0.942161\pi$
$163$	−8.27651	−	14.3353i	−0.648266	−	1.12283i	0.335271	−	0.942122i	$-0.391172\pi$
$164$	−0.736705	+	1.27601i	−0.0575270	+	0.0996396i
$165$	1.53759	−	2.66319i	0.119701	−	0.207329i
$166$	−1.25907	−	2.18077i	−0.0977225	−	0.169260i
$167$	−1.31344			−0.101637			−0.0508185	−	0.998708i	$-0.516183\pi$
$167$	−1.31344			−0.101637			−0.0508185	+	0.998708i	$0.516183\pi$
$168$	1.12321	+	8.05828i	0.0866577	+	0.621709i
$169$	9.33765			0.718280
$170$	−0.549130	−	0.951122i	−0.0421164	−	0.0729477i
$171$	−7.68868	+	13.3172i	−0.587968	+	1.01839i
$172$	−1.91438	+	3.31580i	−0.145970	+	0.252828i
$173$	6.99758	+	12.1202i	0.532016	+	0.921480i	0.999301	+	0.0373728i	$0.0118989\pi$
$173$	6.99758	+	12.1202i	0.532016	+	0.921480i	−0.467285	+	0.884107i	$0.654768\pi$
$174$	11.1766			0.847296
$175$	−0.365250	−	2.62042i	−0.0276103	−	0.198085i
$176$	1.00000			0.0753778
$177$	8.64223	+	14.9688i	0.649590	+	1.12512i
$178$	4.34790	−	7.53079i	0.325889	−	0.564457i
$179$	−9.13192	+	15.8170i	−0.682552	+	1.18221i	0.291647	+	0.956526i	$0.405797\pi$
$179$	−9.13192	+	15.8170i	−0.682552	+	1.18221i	−0.974199	+	0.225689i	$0.927537\pi$
$180$	−3.22839	−	5.59173i	−0.240630	−	0.416783i
$181$	10.5373			0.783233			0.391617	−	0.920128i	$-0.371916\pi$
$181$	10.5373			0.783233			0.391617	+	0.920128i	$0.371916\pi$
$182$	−11.5887	−	4.69741i	−0.859011	−	0.348195i
$183$	31.2013			2.30647
$184$	−0.0856193	−	0.148297i	−0.00631194	−	0.0109326i
$185$	−5.35482	+	9.27482i	−0.393694	+	0.681898i
$186$	−0.586724	+	1.01624i	−0.0430207	+	0.0745140i
$187$	−0.549130	−	0.951122i	−0.0401564	−	0.0695529i
$188$	4.76317			0.347390
$189$	22.1823	−	17.2903i	1.61353	−	1.25769i
$190$	2.38159			0.172778
$191$	−7.54069	−	13.0609i	−0.545625	−	0.945050i	−0.998567	−	0.0535104i	$-0.982959\pi$
$191$	−7.54069	−	13.0609i	−0.545625	−	0.945050i	0.452942	−	0.891540i	$-0.350374\pi$
$192$	1.53759	−	2.66319i	0.110966	−	0.192199i
$193$	0.562247	−	0.973841i	0.0404714	−	0.0700986i	−0.845080	−	0.534640i	$-0.820447\pi$
$193$	0.562247	−	0.973841i	0.0404714	−	0.0700986i	0.885552	+	0.464541i	$0.153781\pi$
$194$	−7.24401	−	12.5470i	−0.520090	−	0.900822i
$195$	14.5342			1.04081
$196$	5.02435	+	4.87400i	0.358882	+	0.348143i
$197$	−0.652473			−0.0464867			−0.0232434	−	0.999730i	$-0.507399\pi$
$197$	−0.652473			−0.0464867			−0.0232434	+	0.999730i	$0.507399\pi$
$198$	−3.22839	−	5.59173i	−0.229431	−	0.397387i
$199$	2.91337	−	5.04611i	0.206523	−	0.357709i	−0.744094	−	0.668075i	$-0.767118\pi$
$199$	2.91337	−	5.04611i	0.206523	−	0.357709i	0.950617	+	0.310366i	$0.100452\pi$
$200$	−0.500000	+	0.866025i	−0.0353553	+	0.0612372i
$201$	−7.91918	−	13.7164i	−0.558576	−	0.967482i
$202$	18.6029			1.30890
$203$	7.58409	−	5.91152i	0.532299	−	0.414907i
$204$	−3.37736			−0.236462
$205$	−0.736705	−	1.27601i	−0.0514537	−	0.0891204i
$206$	2.19771	−	3.80654i	0.153121	−	0.265214i
$207$	−0.552824	+	0.957520i	−0.0384240	+	0.0665522i
$208$	2.36314	+	4.09307i	0.163854	+	0.283803i
$209$	2.38159			0.164738
$210$	−7.54028	−	3.05641i	−0.520329	−	0.210912i
$211$	20.8873			1.43794			0.718971	−	0.695040i	$-0.244613\pi$
$211$	20.8873			1.43794			0.718971	+	0.695040i	$0.244613\pi$
$212$	4.36793	+	7.56548i	0.299991	+	0.519600i
$213$	7.26369	−	12.5811i	0.497700	−	0.862041i
$214$	−7.88708	+	13.6608i	−0.539150	+	0.933834i
$215$	−1.91438	−	3.31580i	−0.130560	−	0.226136i
$216$	−10.6302			−0.723295
$217$	0.139374	+	0.999914i	0.00946134	+	0.0678786i
$218$	14.9823			1.01473
$219$	−23.0755	−	39.9680i	−1.55930	−	2.70079i
$220$	−0.500000	+	0.866025i	−0.0337100	+	0.0583874i
$221$	2.59534	−	4.49526i	0.174581	−	0.302384i
$222$	16.4671	+	28.5218i	1.10520	+	1.91426i
$223$	1.58372			0.106054			0.0530270	−	0.998593i	$-0.483113\pi$
$223$	1.58372			0.106054			0.0530270	+	0.998593i	$0.483113\pi$
$224$	−0.365250	−	2.62042i	−0.0244043	−	0.175084i
$225$	6.45677			0.430451
$226$	9.62560	+	16.6720i	0.640285	+	1.10901i
$227$	−5.38720	+	9.33091i	−0.357561	+	0.619314i	−0.987553	−	0.157288i	$-0.949725\pi$
$227$	−5.38720	+	9.33091i	−0.357561	+	0.619314i	0.629992	+	0.776602i	$0.283058\pi$
$228$	3.66191	−	6.34261i	0.242516	−	0.420050i
$229$	−12.7806	−	22.1366i	−0.844565	−	1.46283i	−0.885998	−	0.463689i	$-0.846526\pi$
$229$	−12.7806	−	22.1366i	−0.844565	−	1.46283i	0.0414328	−	0.999141i	$-0.486808\pi$
$230$	0.171239			0.0112911
$231$	−7.54028	−	3.05641i	−0.496114	−	0.201097i
$232$	−3.63445			−0.238613
$233$	−6.89030	−	11.9343i	−0.451398	−	0.781845i	0.547075	−	0.837084i	$-0.315741\pi$
$233$	−6.89030	−	11.9343i	−0.451398	−	0.781845i	−0.998473	+	0.0552389i	$0.982408\pi$
$234$	15.2582	−	26.4280i	0.997462	−	1.72765i
$235$	−2.38159	+	4.12503i	−0.155358	+	0.269087i
$236$	−2.81031	−	4.86760i	−0.182936	−	0.316854i
$237$	−37.2512			−2.41972
$238$	−2.29177	+	1.78635i	−0.148553	+	0.115792i
$239$	26.0717			1.68644			0.843220	−	0.537568i	$-0.180657\pi$
$239$	26.0717			1.68644			0.843220	+	0.537568i	$0.180657\pi$
$240$	1.53759	+	2.66319i	0.0992512	+	0.171908i
$241$	2.30217	−	3.98748i	0.148296	−	0.256856i	−0.782302	−	0.622899i	$-0.785955\pi$
$241$	2.30217	−	3.98748i	0.148296	−	0.256856i	0.930598	+	0.366044i	$0.119288\pi$
$242$	−0.500000	+	0.866025i	−0.0321412	+	0.0556702i
$243$	4.53479	+	7.85448i	0.290907	+	0.503865i
$244$	−10.1461			−0.649540
$245$	−6.73318	+	1.91422i	−0.430167	+	0.122295i
$246$	−4.53101			−0.288887
$247$	5.62801	+	9.74800i	0.358102	+	0.620250i
$248$	0.190793	−	0.330463i	0.0121154	−	0.0209844i
$249$	3.87187	−	6.70627i	0.245369	−	0.424992i
$250$	−0.500000	−	0.866025i	−0.0316228	−	0.0547723i
$251$	−14.2619			−0.900201			−0.450100	−	0.892978i	$-0.648612\pi$
$251$	−14.2619			−0.900201			−0.450100	+	0.892978i	$0.648612\pi$
$252$	−13.4735	+	10.5021i	−0.848751	+	0.661570i
$253$	0.171239			0.0107657
$254$	9.84385	+	17.0500i	0.617658	+	1.06982i
$255$	1.68868	−	2.92488i	0.105749	−	0.183163i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−8.17103	−	14.1526i	−0.509695	−	0.882818i	−0.999937	−	0.0112312i	$-0.996425\pi$
$257$	−8.17103	−	14.1526i	−0.509695	−	0.882818i	0.490242	−	0.871586i	$-0.336908\pi$
$258$	−11.7742			−0.733027
$259$	26.2597	+	10.6442i	1.63170	+	0.661400i
$260$	−4.72627			−0.293111
$261$	11.7334	+	20.3228i	0.726279	+	1.25795i
$262$	−7.69950	+	13.3359i	−0.475677	+	0.823897i
$263$	−2.30499	+	3.99237i	−0.142132	+	0.246180i	−0.928299	−	0.371834i	$-0.878729\pi$
$263$	−2.30499	+	3.99237i	−0.142132	+	0.246180i	0.786167	+	0.618014i	$0.212062\pi$
$264$	1.53759	+	2.66319i	0.0946323	+	0.163908i
$265$	−8.73587			−0.536640
$266$	−0.869875	−	6.24075i	−0.0533354	−	0.382645i
$267$	26.7412			1.63654
$268$	2.57519	+	4.46035i	0.157305	+	0.272459i
$269$	−11.1566	+	19.3238i	−0.680229	+	1.17819i	0.294682	+	0.955595i	$0.404786\pi$
$269$	−11.1566	+	19.3238i	−0.680229	+	1.17819i	−0.974911	+	0.222595i	$0.928547\pi$
$270$	5.31511	−	9.20604i	0.323467	−	0.560262i
$271$	−9.96807	−	17.2652i	−0.605517	−	1.04879i	−0.991970	−	0.126477i	$-0.959633\pi$
$271$	−9.96807	−	17.2652i	−0.605517	−	1.04879i	0.386452	−	0.922309i	$-0.373700\pi$
$272$	1.09826			0.0665918
$273$	−5.30861	−	38.0856i	−0.321292	−	2.30505i
$274$	−17.1008			−1.03310
$275$	−0.500000	−	0.866025i	−0.0301511	−	0.0522233i
$276$	0.263295	−	0.456041i	0.0158485	−	0.0274504i
$277$	−5.76780	+	9.99012i	−0.346553	+	0.600248i	−0.985635	−	0.168891i	$-0.945981\pi$
$277$	−5.76780	+	9.99012i	−0.346553	+	0.600248i	0.639081	+	0.769139i	$0.279315\pi$
$278$	−6.48494	−	11.2323i	−0.388941	−	0.673666i
$279$	−2.46381			−0.147505
$280$	2.45197	+	0.993893i	0.146533	+	0.0593965i
$281$	25.2937			1.50890			0.754448	−	0.656360i	$-0.227905\pi$
$281$	25.2937			1.50890			0.754448	+	0.656360i	$0.227905\pi$
$282$	7.32382	+	12.6852i	0.436127	+	0.755394i
$283$	−7.08901	+	12.2785i	−0.421398	+	0.729883i	−0.996076	−	0.0884965i	$-0.971794\pi$
$283$	−7.08901	+	12.2785i	−0.421398	+	0.729883i	0.574678	+	0.818379i	$0.305127\pi$
$284$	−2.36203	+	4.09116i	−0.140161	+	0.242766i
$285$	3.66191	+	6.34261i	0.216913	+	0.375704i
$286$	−4.72627			−0.279470
$287$	−3.07460	+	2.39654i	−0.181488	+	0.141463i
$288$	6.45677			0.380469
$289$	7.89691	+	13.6779i	0.464524	+	0.804580i
$290$	1.81722	−	3.14752i	0.106711	−	0.184829i
$291$	22.2767	−	38.5843i	1.30588	−	2.26185i
$292$	7.50379	+	12.9969i	0.439126	+	0.760589i
$293$	10.6156			0.620168			0.310084	−	0.950709i	$-0.399643\pi$
$293$	10.6156			0.620168			0.310084	+	0.950709i	$0.399643\pi$
$294$	−5.25498	+	20.8750i	−0.306476	+	1.21746i
$295$	5.62062			0.327245
$296$	−5.35482	−	9.27482i	−0.311242	−	0.539088i
$297$	5.31511	−	9.20604i	0.308414	−	0.534189i
$298$	4.72949	−	8.19172i	0.273972	−	0.474533i
$299$	0.404660	+	0.700892i	0.0234021	+	0.0405336i
$300$	−3.07519			−0.177546
$301$	−7.98957	+	6.22758i	−0.460511	+	0.358952i
$302$	−20.8682			−1.20083
$303$	28.6037	+	49.5431i	1.64324	+	2.84618i
$304$	−1.19079	+	2.06251i	−0.0682967	+	0.118293i
$305$	5.07307	−	8.78682i	0.290483	−	0.503132i
$306$	−3.54561	−	6.14118i	−0.202689	−	0.351068i
$307$	1.93299			0.110321			0.0551607	−	0.998477i	$-0.482433\pi$
$307$	1.93299			0.110321			0.0551607	+	0.998477i	$0.482433\pi$
$308$	2.45197	+	0.993893i	0.139714	+	0.0566323i
$309$	13.5167			0.768939
$310$	0.190793	+	0.330463i	0.0108363	+	0.0187690i
$311$	−4.35905	+	7.55009i	−0.247179	+	0.428126i	−0.962742	−	0.270422i	$-0.912837\pi$
$311$	−4.35905	+	7.55009i	−0.247179	+	0.428126i	0.715563	+	0.698548i	$0.246170\pi$
$312$	−7.26708	+	12.5870i	−0.411418	+	0.712596i
$313$	−0.785028	−	1.35971i	−0.0443724	−	0.0768553i	0.842986	−	0.537935i	$-0.180795\pi$
$313$	−0.785028	−	1.35971i	−0.0443724	−	0.0768553i	−0.887359	+	0.461080i	$0.847462\pi$
$314$	13.6420			0.769864
$315$	−2.35834	−	16.9194i	−0.132877	−	0.953303i
$316$	12.1135			0.681436
$317$	−0.0556323	−	0.0963579i	−0.00312462	−	0.00541200i	0.864459	−	0.502704i	$-0.167661\pi$
$317$	−0.0556323	−	0.0963579i	−0.00312462	−	0.00541200i	−0.867583	+	0.497292i	$0.834328\pi$
$318$	−13.4322	+	23.2653i	−0.753241	+	1.30465i
$319$	1.81722	−	3.14752i	0.101745	−	0.176228i
$320$	−0.500000	−	0.866025i	−0.0279508	−	0.0484123i
$321$	−48.5085			−2.70748
$322$	−0.0625449	−	0.448717i	−0.00348549	−	0.0250060i
$323$	2.61560			0.145536
$324$	−6.65980	−	11.5351i	−0.369989	−	0.640839i
$325$	2.36314	−	4.09307i	0.131083	−	0.227043i
$326$	−8.27651	+	14.3353i	−0.458393	+	0.793961i
$327$	23.0367	+	39.9007i	1.27393	+	2.20651i
$328$	1.47341			0.0813554
$329$	11.6792	+	4.73408i	0.643894	+	0.260998i
$330$	−3.07519			−0.169283
$331$	4.17526	+	7.23176i	0.229493	+	0.397494i	0.957658	−	0.287908i	$-0.0929598\pi$
$331$	4.17526	+	7.23176i	0.229493	+	0.397494i	−0.728165	+	0.685402i	$0.759627\pi$
$332$	−1.25907	+	2.18077i	−0.0691003	+	0.119685i
$333$	−34.5748	+	59.8854i	−1.89469	+	3.28170i
$334$	0.656720	+	1.13747i	0.0359341	+	0.0622397i
$335$	−5.15037			−0.281395
$336$	6.41706	−	5.00187i	0.350080	−	0.272874i
$337$	6.58408			0.358658			0.179329	−	0.983789i	$-0.442607\pi$
$337$	6.58408			0.358658			0.179329	+	0.983789i	$0.442607\pi$
$338$	−4.66882	−	8.08664i	−0.253950	−	0.439855i
$339$	−29.6005	+	51.2696i	−1.60768	+	2.78458i
$340$	−0.549130	+	0.951122i	−0.0297808	+	0.0515818i
$341$	0.190793	+	0.330463i	0.0103320	+	0.0178956i
$342$	15.3774			0.831512
$343$	7.47535	+	16.9446i	0.403631	+	0.914922i
$344$	3.82876			0.206433
$345$	0.263295	+	0.456041i	0.0141753	+	0.0245524i
$346$	6.99758	−	12.1202i	0.376192	−	0.651584i
$347$	4.03208	−	6.98377i	0.216454	−	0.374909i	−0.737268	−	0.675601i	$-0.763884\pi$
$347$	4.03208	−	6.98377i	0.216454	−	0.374909i	0.953721	+	0.300692i	$0.0972177\pi$
$348$	−5.58830	−	9.67923i	−0.299565	−	0.518861i
$349$	−12.1730			−0.651604			−0.325802	−	0.945438i	$-0.605634\pi$
$349$	−12.1730			−0.651604			−0.325802	+	0.945438i	$0.605634\pi$
$350$	−2.08672	+	1.62653i	−0.111540	+	0.0869414i
$351$	50.2413			2.68168
$352$	−0.500000	−	0.866025i	−0.0266501	−	0.0461593i
$353$	−6.17988	+	10.7039i	−0.328922	+	0.569710i	−0.982298	−	0.187324i	$-0.940019\pi$
$353$	−6.17988	+	10.7039i	−0.328922	+	0.569710i	0.653376	+	0.757033i	$0.273352\pi$
$354$	8.64223	−	14.9688i	0.459329	−	0.795582i
$355$	−2.36203	−	4.09116i	−0.125364	−	0.217136i
$356$	−8.69581			−0.460877
$357$	−8.28119	−	3.35673i	−0.438287	−	0.177657i
$358$	18.2638			0.965274
$359$	−15.4217	−	26.7111i	−0.813925	−	1.40976i	−0.910097	−	0.414395i	$-0.863993\pi$
$359$	−15.4217	−	26.7111i	−0.813925	−	1.40976i	0.0961715	−	0.995365i	$-0.469340\pi$
$360$	−3.22839	+	5.59173i	−0.170151	+	0.294710i
$361$	6.66402	−	11.5424i	0.350738	−	0.607496i
$362$	−5.26866	−	9.12559i	−0.276915	−	0.479631i
$363$	−3.07519			−0.161405
$364$	1.72627	+	12.3848i	0.0904812	+	0.649140i
$365$	−15.0076			−0.785532
$366$	−15.6006	−	27.0211i	−0.815459	−	1.41242i
$367$	18.8237	−	32.6036i	0.982589	−	1.70189i	0.330393	−	0.943843i	$-0.392819\pi$
$367$	18.8237	−	32.6036i	0.982589	−	1.70189i	0.652196	−	0.758051i	$-0.273848\pi$
$368$	−0.0856193	+	0.148297i	−0.00446322	+	0.00773052i
$369$	−4.75673	−	8.23891i	−0.247626	−	0.428900i
$370$	10.7096			0.556767
$371$	3.19078	+	22.8916i	0.165657	+	1.18847i
$372$	1.17345			0.0608404
$373$	−9.25140	−	16.0239i	−0.479019	−	0.829686i	0.520691	−	0.853745i	$-0.325674\pi$
$373$	−9.25140	−	16.0239i	−0.479019	−	0.829686i	−0.999711	+	0.0240594i	$0.992341\pi$
$374$	−0.549130	+	0.951122i	−0.0283949	+	0.0491813i
$375$	1.53759	−	2.66319i	0.0794010	−	0.137527i
$376$	−2.38159	−	4.12503i	−0.122821	−	0.212732i
$377$	17.1774			0.884681
$378$	−26.0650	−	10.5653i	−1.34064	−	0.543421i
$379$	1.94460			0.0998875			0.0499438	−	0.998752i	$-0.484096\pi$
$379$	1.94460			0.0998875			0.0499438	+	0.998752i	$0.484096\pi$
$380$	−1.19079	−	2.06251i	−0.0610864	−	0.105805i
$381$	−30.2717	+	52.4321i	−1.55086	+	2.68618i
$382$	−7.54069	+	13.0609i	−0.385815	+	0.668251i
$383$	3.58854	+	6.21553i	0.183366	+	0.317599i	0.943025	−	0.332723i	$-0.107967\pi$
$383$	3.58854	+	6.21553i	0.183366	+	0.317599i	−0.759659	+	0.650322i	$0.774634\pi$
$384$	−3.07519			−0.156930
$385$	−2.08672	+	1.62653i	−0.106349	+	0.0828954i
$386$	−1.12449			−0.0572353
$387$	−12.3607	−	21.4094i	−0.628331	−	1.08830i
$388$	−7.24401	+	12.5470i	−0.367759	+	0.636977i
$389$	−17.8696	+	30.9511i	−0.906025	+	1.56928i	−0.0864894	+	0.996253i	$0.527565\pi$
$389$	−17.8696	+	30.9511i	−0.906025	+	1.56928i	−0.819535	+	0.573028i	$0.805768\pi$
$390$	−7.26708	−	12.5870i	−0.367983	−	0.637365i
$391$	0.188065			0.00951084
$392$	1.70883	−	6.78822i	0.0863090	−	0.342857i
$393$	−47.3548			−2.38873
$394$	0.326236	+	0.565058i	0.0164355	+	0.0284672i
$395$	−6.05674	+	10.4906i	−0.304747	+	0.527838i
$396$	−3.22839	+	5.59173i	−0.162233	+	0.280995i
$397$	11.1583	+	19.3267i	0.560018	+	0.969980i	0.997494	+	0.0707497i	$0.0225391\pi$
$397$	11.1583	+	19.3267i	0.560018	+	0.969980i	−0.437476	+	0.899230i	$0.644128\pi$
$398$	−5.82674			−0.292068
$399$	15.2828	−	11.9124i	0.765096	−	0.596365i
$400$	1.00000			0.0500000
$401$	12.7840	+	22.1426i	0.638403	+	1.10575i	0.985783	+	0.168023i	$0.0537382\pi$
$401$	12.7840	+	22.1426i	0.638403	+	1.10575i	−0.347380	+	0.937725i	$0.612929\pi$
$402$	−7.91918	+	13.7164i	−0.394973	+	0.684113i
$403$	−0.901739	+	1.56186i	−0.0449188	+	0.0778017i
$404$	−9.30146	−	16.1106i	−0.462765	−	0.801532i
$405$	13.3196			0.661856
$406$	−8.91157	−	3.61225i	−0.442274	−	0.179273i
$407$	10.7096			0.530857
$408$	1.68868	+	2.92488i	0.0836020	+	0.144803i
$409$	−11.5151	+	19.9447i	−0.569384	+	0.986203i	0.427242	+	0.904137i	$0.359485\pi$
$409$	−11.5151	+	19.9447i	−0.569384	+	0.986203i	−0.996627	+	0.0820658i	$0.973848\pi$
$410$	−0.736705	+	1.27601i	−0.0363832	+	0.0630176i
$411$	−26.2941	−	45.5427i	−1.29699	−	2.24646i
$412$	−4.39541			−0.216546
$413$	−2.05293	−	14.7284i	−0.101018	−	0.724736i
$414$	1.10565			0.0543397
$415$	−1.25907	−	2.18077i	−0.0618052	−	0.107050i
$416$	2.36314	−	4.09307i	0.115862	−	0.200679i
$417$	19.9424	−	34.5413i	0.976584	−	1.69149i
$418$	−1.19079	−	2.06251i	−0.0582436	−	0.100881i
$419$	−15.0306			−0.734295			−0.367148	−	0.930163i	$-0.619666\pi$
$419$	−15.0306			−0.734295			−0.367148	+	0.930163i	$0.619666\pi$
$420$	1.12321	+	8.05828i	0.0548072	+	0.393204i
$421$	−14.2947			−0.696679			−0.348339	−	0.937368i	$-0.613254\pi$
$421$	−14.2947			−0.696679			−0.348339	+	0.937368i	$0.613254\pi$
$422$	−10.4437	−	18.0889i	−0.508389	−	0.880556i
$423$	−15.3774	+	26.6344i	−0.747673	+	1.29501i
$424$	4.36793	−	7.56548i	0.212126	−	0.367412i
$425$	−0.549130	−	0.951122i	−0.0266367	−	0.0461362i
$426$	−14.5274			−0.703854
$427$	−24.8781	−	10.0842i	−1.20393	−	0.488008i
$428$	15.7742			0.762473
$429$	−7.26708	−	12.5870i	−0.350858	−	0.607704i
$430$	−1.91438	+	3.31580i	−0.0923196	+	0.159902i
$431$	−1.21497	+	2.10439i	−0.0585231	+	0.101365i	−0.893803	−	0.448461i	$-0.851972\pi$
$431$	−1.21497	+	2.10439i	−0.0585231	+	0.101365i	0.835280	+	0.549826i	$0.185306\pi$
$432$	5.31511	+	9.20604i	0.255723	+	0.442926i
$433$	21.8355			1.04935			0.524675	−	0.851303i	$-0.324187\pi$
$433$	21.8355			1.04935			0.524675	+	0.851303i	$0.324187\pi$
$434$	0.796264	−	0.620659i	0.0382219	−	0.0297926i
$435$	11.1766			0.535877
$436$	−7.49115	−	12.9750i	−0.358761	−	0.621392i
$437$	−0.203910	+	0.353182i	−0.00975433	+	0.0168950i
$438$	−23.0755	+	39.9680i	−1.10259	+	1.90975i
$439$	2.05535	+	3.55997i	0.0980965	+	0.169908i	0.910897	−	0.412634i	$-0.135391\pi$
$439$	2.05535	+	3.55997i	0.0980965	+	0.169908i	−0.812800	+	0.582542i	$0.802058\pi$
$440$	1.00000			0.0476731
$441$	−43.4746	+	12.3597i	−2.07022	+	0.588555i
$442$	−5.19068			−0.246895
$443$	18.5035	+	32.0490i	0.879126	+	1.52269i	0.852301	+	0.523052i	$0.175207\pi$
$443$	18.5035	+	32.0490i	0.879126	+	1.52269i	0.0268255	+	0.999640i	$0.491460\pi$
$444$	16.4671	−	28.5218i	0.781492	−	1.35358i
$445$	4.34790	−	7.53079i	0.206110	−	0.356994i
$446$	−0.791862	−	1.37154i	−0.0374957	−	0.0649445i
$447$	29.0881			1.37582
$448$	−2.08672	+	1.62653i	−0.0985884	+	0.0768461i
$449$	−9.45318			−0.446123			−0.223061	−	0.974804i	$-0.571605\pi$
$449$	−9.45318			−0.446123			−0.223061	+	0.974804i	$0.571605\pi$
$450$	−3.22839	−	5.59173i	−0.152188	−	0.263597i
$451$	−0.736705	+	1.27601i	−0.0346901	+	0.0600850i
$452$	9.62560	−	16.6720i	0.452750	−	0.784186i
$453$	−32.0868	−	55.5759i	−1.50757	−	2.61119i
$454$	10.7744			0.505668
$455$	−11.5887	−	4.69741i	−0.543286	−	0.220218i
$456$	−7.32382			−0.342969
$457$	−0.223464	−	0.387051i	−0.0104532	−	0.0181055i	0.860751	−	0.509025i	$-0.169994\pi$
$457$	−0.223464	−	0.387051i	−0.0104532	−	0.0181055i	−0.871205	+	0.490920i	$0.836661\pi$
$458$	−12.7806	+	22.1366i	−0.597198	+	1.03438i
$459$	5.83738	−	10.1106i	0.272465	−	0.471924i
$460$	−0.0856193	−	0.148297i	−0.00399202	−	0.00691438i
$461$	40.4192			1.88251			0.941255	−	0.337696i	$-0.109648\pi$
$461$	40.4192			1.88251			0.941255	+	0.337696i	$0.109648\pi$
$462$	1.12321	+	8.05828i	0.0522566	+	0.374905i
$463$	29.5274			1.37226			0.686128	−	0.727480i	$-0.259309\pi$
$463$	29.5274			1.37226			0.686128	+	0.727480i	$0.259309\pi$
$464$	1.81722	+	3.14752i	0.0843625	+	0.146120i
$465$	−0.586724	+	1.01624i	−0.0272087	+	0.0471268i
$466$	−6.89030	+	11.9343i	−0.319187	+	0.552848i
$467$	−9.34659	−	16.1888i	−0.432509	−	0.749127i	0.564580	−	0.825378i	$-0.309038\pi$
$467$	−9.34659	−	16.1888i	−0.432509	−	0.749127i	−0.997089	+	0.0762513i	$0.975705\pi$
$468$	−30.5165			−1.41062
$469$	1.88117	+	13.4961i	0.0868646	+	0.623193i
$470$	4.76317			0.219709
$471$	20.9759	+	36.3313i	0.966518	+	1.67406i
$472$	−2.81031	+	4.86760i	−0.129355	+	0.224050i
$473$	−1.91438	+	3.31580i	−0.0880233	+	0.152461i
$474$	18.6256	+	32.2605i	0.855502	+	1.48177i
$475$	2.38159			0.109275
$476$	2.69291	+	1.09155i	0.123429	+	0.0500313i
$477$	−56.4055			−2.58263
$478$	−13.0359	−	22.5788i	−0.596247	−	1.03273i
$479$	−10.9202	+	18.9143i	−0.498956	+	0.864217i	−0.999999	−	0.00120489i	$-0.999616\pi$
$479$	−10.9202	+	18.9143i	−0.498956	+	0.864217i	0.501043	+	0.865422i	$0.332950\pi$
$480$	1.53759	−	2.66319i	0.0701812	−	0.121557i
$481$	25.3083	+	43.8353i	1.15396	+	1.99872i
$482$	−4.60434			−0.209722
$483$	1.09885	−	0.856513i	0.0499994	−	0.0389727i
$484$	1.00000			0.0454545
$485$	−7.24401	−	12.5470i	−0.328934	−	0.569730i
$486$	4.53479	−	7.85448i	0.205702	−	0.356286i
$487$	11.7150	−	20.2910i	0.530857	−	0.919472i	−0.468494	−	0.883467i	$-0.655203\pi$
$487$	11.7150	−	20.2910i	0.530857	−	0.919472i	0.999352	−	0.0360055i	$-0.0114634\pi$
$488$	5.07307	+	8.78682i	0.229647	+	0.397761i
$489$	−50.9036			−2.30194
$490$	5.02435	+	4.87400i	0.226977	+	0.220185i
$491$	−23.6077			−1.06540			−0.532700	−	0.846304i	$-0.678823\pi$
$491$	−23.6077			−1.06540			−0.532700	+	0.846304i	$0.678823\pi$
$492$	2.26550	+	3.92397i	0.102137	+	0.176906i
$493$	1.99579	−	3.45680i	0.0898857	−	0.155687i
$494$	5.62801	−	9.74800i	0.253216	−	0.438583i
$495$	−3.22839	−	5.59173i	−0.145105	−	0.251330i
$496$	−0.381586			−0.0171337
$497$	−9.85781	+	7.68381i	−0.442183	+	0.344666i
$498$	−7.74373			−0.347005
$499$	13.6593	+	23.6585i	0.611472	+	1.05910i	0.990992	+	0.133918i	$0.0427558\pi$
$499$	13.6593	+	23.6585i	0.611472	+	1.05910i	−0.379520	+	0.925183i	$0.623911\pi$
$500$	−0.500000	+	0.866025i	−0.0223607	+	0.0387298i
$501$	−2.01954	+	3.49794i	−0.0902262	+	0.156276i
$502$	7.13093	+	12.3511i	0.318269	+	0.551258i
$503$	−2.96508			−0.132207			−0.0661033	−	0.997813i	$-0.521057\pi$
$503$	−2.96508			−0.132207			−0.0661033	+	0.997813i	$0.521057\pi$
$504$	15.8318	+	6.41734i	0.705206	+	0.285851i
$505$	18.6029			0.827819
$506$	−0.0856193	−	0.148297i	−0.00380624	−	0.00659261i
$507$	14.3575	−	24.8679i	0.637639	−	1.10442i
$508$	9.84385	−	17.0500i	0.436750	−	0.756474i
$509$	21.4950	+	37.2305i	0.952751	+	1.65021i	0.739433	+	0.673231i	$0.235094\pi$
$509$	21.4950	+	37.2305i	0.952751	+	1.65021i	0.213319	+	0.976983i	$0.431573\pi$
$510$	−3.37736			−0.149552
$511$	5.48152	+	39.3261i	0.242488	+	1.73969i
$512$	1.00000			0.0441942
$513$	12.6584	+	21.9250i	0.558882	+	0.968011i
$514$	−8.17103	+	14.1526i	−0.360409	+	0.624246i
$515$	2.19771	−	3.80654i	0.0968425	−	0.167736i
$516$	5.88708	+	10.1967i	0.259164	+	0.448885i
$517$	4.76317			0.209484
$518$	−3.91170	−	28.0637i	−0.171870	−	1.23305i
$519$	43.0378			1.88915
$520$	2.36314	+	4.09307i	0.103630	+	0.179493i
$521$	4.03038	−	6.98082i	0.176574	−	0.305835i	−0.764131	−	0.645061i	$-0.776832\pi$
$521$	4.03038	−	6.98082i	0.176574	−	0.305835i	0.940705	+	0.339226i	$0.110165\pi$
$522$	11.7334	−	20.3228i	0.513557	−	0.889507i
$523$	−13.0543	−	22.6107i	−0.570826	−	0.988699i	−0.996481	−	0.0838138i	$-0.973290\pi$
$523$	−13.0543	−	22.6107i	−0.570826	−	0.988699i	0.425656	−	0.904885i	$-0.360043\pi$
$524$	15.3990			0.672709
$525$	−7.54028	−	3.05641i	−0.329085	−	0.133393i
$526$	4.60999			0.201005
$527$	0.209540	+	0.362935i	0.00912772	+	0.0158097i
$528$	1.53759	−	2.66319i	0.0669152	−	0.115900i
$529$	11.4853	−	19.8932i	0.499363	−	0.864921i
$530$	4.36793	+	7.56548i	0.189731	+	0.328624i
$531$	36.2911			1.57490
$532$	−4.96971	+	3.87371i	−0.215464	+	0.167947i
$533$	−6.96373			−0.301633
$534$	−13.3706	−	23.1586i	−0.578603	−	1.00217i
$535$	−7.88708	+	13.6608i	−0.340988	+	0.590609i
$536$	2.57519	−	4.46035i	0.111231	−	0.192658i
$537$	28.0824	+	48.6401i	1.21184	+	2.09897i
$538$	22.3132			0.961988
$539$	5.02435	+	4.87400i	0.216414	+	0.209938i
$540$	−10.6302			−0.457452
$541$	−6.23763	−	10.8039i	−0.268177	−	0.464496i	0.700214	−	0.713933i	$-0.253088\pi$
$541$	−6.23763	−	10.8039i	−0.268177	−	0.464496i	−0.968391	+	0.249437i	$0.919754\pi$
$542$	−9.96807	+	17.2652i	−0.428165	+	0.741604i
$543$	16.2021	−	28.0629i	0.695300	−	1.20429i
$544$	−0.549130	−	0.951122i	−0.0235438	−	0.0407790i
$545$	14.9823			0.641771
$546$	−30.3288	+	23.6402i	−1.29795	+	1.01171i
$547$	−7.48187			−0.319902			−0.159951	−	0.987125i	$-0.551134\pi$
$547$	−7.48187			−0.319902			−0.159951	+	0.987125i	$0.551134\pi$
$548$	8.55041	+	14.8097i	0.365255	+	0.632641i
$549$	32.7557	−	56.7345i	1.39798	−	2.42137i
$550$	−0.500000	+	0.866025i	−0.0213201	+	0.0369274i
$551$	4.32788	+	7.49610i	0.184374	+	0.319345i
$552$	−0.526591			−0.0224132
$553$	29.7019	+	12.0395i	1.26305	+	0.511972i
$554$	11.5356			0.490100
$555$	16.4671	+	28.5218i	0.698988	+	1.21068i
$556$	−6.48494	+	11.2323i	−0.275023	+	0.476354i
$557$	5.24643	−	9.08707i	0.222298	−	0.385032i	−0.733207	−	0.680005i	$-0.761977\pi$
$557$	5.24643	−	9.08707i	0.222298	−	0.385032i	0.955505	+	0.294974i	$0.0953108\pi$
$558$	1.23191	+	2.13372i	0.0521508	+	0.0903278i
$559$	−18.0958			−0.765369
$560$	−0.365250	−	2.62042i	−0.0154346	−	0.110733i
$561$	−3.37736			−0.142592
$562$	−12.6469	−	21.9050i	−0.533475	−	0.924007i
$563$	0.855228	−	1.48130i	0.0360436	−	0.0624293i	−0.847441	−	0.530890i	$-0.821858\pi$
$563$	0.855228	−	1.48130i	0.0360436	−	0.0624293i	0.883484	+	0.468460i	$0.155191\pi$
$564$	7.32382	−	12.6852i	0.308388	−	0.534145i
$565$	9.62560	+	16.6720i	0.404952	+	0.701397i
$566$	14.1780			0.595947
$567$	−4.86498	−	34.9029i	−0.204310	−	1.46578i
$568$	4.72406			0.198217
$569$	5.09265	+	8.82072i	0.213495	+	0.369784i	0.952806	−	0.303580i	$-0.0981820\pi$
$569$	5.09265	+	8.82072i	0.213495	+	0.369784i	−0.739311	+	0.673364i	$0.764849\pi$
$570$	3.66191	−	6.34261i	0.153381	−	0.265663i
$571$	14.4719	−	25.0661i	0.605631	−	1.04898i	−0.386320	−	0.922365i	$-0.626254\pi$
$571$	14.4719	−	25.0661i	0.605631	−	1.04898i	0.991951	−	0.126619i	$-0.0404126\pi$
$572$	2.36314	+	4.09307i	0.0988077	+	0.171140i
$573$	−46.3780			−1.93747
$574$	3.61276	+	1.46441i	0.150794	+	0.0611234i
$575$	0.171239			0.00714114
$576$	−3.22839	−	5.59173i	−0.134516	−	0.232989i
$577$	−9.97672	+	17.2802i	−0.415336	+	0.719383i	−0.995464	−	0.0951422i	$-0.969669\pi$
$577$	−9.97672	+	17.2802i	−0.415336	+	0.719383i	0.580127	+	0.814526i	$0.303003\pi$
$578$	7.89691	−	13.6779i	0.328468	−	0.568924i
$579$	−1.72902	−	2.99474i	−0.0718554	−	0.124457i
$580$	−3.63445			−0.150912
$581$	−5.25465	+	4.09581i	−0.218000	+	0.169923i
$582$	−44.5534			−1.84680
$583$	4.36793	+	7.56548i	0.180901	+	0.313330i
$584$	7.50379	−	12.9969i	0.310509	−	0.537817i
$585$	15.2582	−	26.4280i	0.630850	−	1.09266i
$586$	−5.30779	−	9.19336i	−0.219263	−	0.379774i
$587$	31.1386			1.28523			0.642614	−	0.766190i	$-0.277850\pi$
$587$	31.1386			1.28523			0.642614	+	0.766190i	$0.277850\pi$
$588$	20.7058	−	5.88657i	0.853893	−	0.242758i
$589$	−0.908779			−0.0374456
$590$	−2.81031	−	4.86760i	−0.115699	−	0.200396i
$591$	−1.00324	+	1.73766i	−0.0412677	+	0.0714777i
$592$	−5.35482	+	9.27482i	−0.220082	+	0.381193i
$593$	2.55844	+	4.43135i	0.105063	+	0.181974i	0.913764	−	0.406246i	$-0.133162\pi$
$593$	2.55844	+	4.43135i	0.105063	+	0.181974i	−0.808701	+	0.588220i	$0.799829\pi$
$594$	−10.6302			−0.436163
$595$	−2.29177	+	1.78635i	−0.0939533	+	0.0732332i
$596$	−9.45898			−0.387455
$597$	−8.95916	−	15.5177i	−0.366674	−	0.635098i
$598$	0.404660	−	0.700892i	0.0165478	−	0.0286616i
$599$	20.7133	−	35.8765i	0.846324	−	1.46588i	−0.0381430	−	0.999272i	$-0.512144\pi$
$599$	20.7133	−	35.8765i	0.846324	−	1.46588i	0.884467	−	0.466603i	$-0.154522\pi$
$600$	1.53759	+	2.66319i	0.0627720	+	0.108724i
$601$	15.8653			0.647158			0.323579	−	0.946201i	$-0.395114\pi$
$601$	15.8653			0.647158			0.323579	+	0.946201i	$0.395114\pi$
$602$	9.38802	+	3.80538i	0.382627	+	0.155096i
$603$	−33.2548			−1.35424
$604$	10.4341	+	18.0724i	0.424557	+	0.735355i
$605$	−0.500000	+	0.866025i	−0.0203279	+	0.0352089i
$606$	28.6037	−	49.5431i	1.16195	−	2.01255i
$607$	−16.1916	−	28.0447i	−0.657198	−	1.13830i	−0.981338	−	0.192291i	$-0.938408\pi$
$607$	−16.1916	−	28.0447i	−0.657198	−	1.13830i	0.324140	−	0.946009i	$-0.394925\pi$
$608$	2.38159			0.0965861
$609$	−4.08226	−	29.2874i	−0.165421	−	1.18678i
$610$	−10.1461			−0.410805
$611$	11.2560	+	19.4960i	0.455370	+	0.788724i
$612$	−3.54561	+	6.14118i	−0.143323	+	0.248242i
$613$	1.30920	−	2.26761i	0.0528782	−	0.0915878i	−0.838375	−	0.545094i	$-0.816494\pi$
$613$	1.30920	−	2.26761i	0.0528782	−	0.0915878i	0.891253	+	0.453507i	$0.149827\pi$
$614$	−0.966493	−	1.67401i	−0.0390045	−	0.0675577i
$615$	−4.53101			−0.182708
$616$	−0.365250	−	2.62042i	−0.0147164	−	0.105580i
$617$	17.3690			0.699250			0.349625	−	0.936890i	$-0.386309\pi$
$617$	17.3690			0.699250			0.349625	+	0.936890i	$0.386309\pi$
$618$	−6.75835	−	11.7058i	−0.271861	−	0.470877i
$619$	17.5689	−	30.4302i	0.706152	−	1.22309i	−0.260122	−	0.965576i	$-0.583763\pi$
$619$	17.5689	−	30.4302i	0.706152	−	1.22309i	0.966274	−	0.257515i	$-0.0829038\pi$
$620$	0.190793	−	0.330463i	0.00766243	−	0.0132717i
$621$	0.910152	+	1.57643i	0.0365231	+	0.0632599i
$622$	8.71809			0.349564
$623$	−21.3219	−	8.64271i	−0.854244	−	0.346263i
$624$	14.5342			0.581832
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$	−0.785028	+	1.35971i	−0.0313760	+	0.0543449i
$627$	3.66191	−	6.34261i	0.146243	−	0.253300i
$628$	−6.82101	−	11.8143i	−0.272188	−	0.471444i
$629$	11.7620			0.468981
$630$	−13.4735	+	10.5021i	−0.536797	+	0.418414i
$631$	40.6510			1.61829			0.809145	−	0.587609i	$-0.199931\pi$
$631$	40.6510			1.61829			0.809145	+	0.587609i	$0.199931\pi$
$632$	−6.05674	−	10.4906i	−0.240924	−	0.417293i
$633$	32.1162	−	55.6269i	1.27650	−	2.21097i
$634$	−0.0556323	+	0.0963579i	−0.00220944	+	0.00382686i
$635$	9.84385	+	17.0500i	0.390641	+	0.676611i
$636$	26.8644			1.06524
$637$	−8.07640	+	32.0830i	−0.319999	+	1.27117i
$638$	−3.63445			−0.143889
$639$	−15.2511	−	26.4157i	−0.603324	−	1.04499i
$640$	−0.500000	+	0.866025i	−0.0197642	+	0.0342327i
$641$	3.31986	−	5.75016i	0.131127	−	0.227118i	−0.792985	−	0.609242i	$-0.791474\pi$
$641$	3.31986	−	5.75016i	0.131127	−	0.227118i	0.924111	+	0.382124i	$0.124807\pi$
$642$	24.2542	+	42.0096i	0.957238	+	1.65799i
$643$	21.7928			0.859425			0.429712	−	0.902966i	$-0.358615\pi$
$643$	21.7928			0.859425			0.429712	+	0.902966i	$0.358615\pi$
$644$	−0.357328	+	0.278524i	−0.0140807	+	0.0109754i
$645$	−11.7742			−0.463607
$646$	−1.30780	−	2.26518i	−0.0514548	−	0.0891222i
$647$	−3.99696	+	6.92293i	−0.157137	+	0.272168i	−0.933835	−	0.357704i	$-0.883560\pi$
$647$	−3.99696	+	6.92293i	−0.157137	+	0.272168i	0.776698	+	0.629873i	$0.216893\pi$
$648$	−6.65980	+	11.5351i	−0.261621	+	0.453142i
$649$	−2.81031	−	4.86760i	−0.110314	−	0.191070i
$650$	−4.72627			−0.185380
$651$	2.87726	+	1.16628i	0.112769	+	0.0457102i
$652$	16.5530			0.648266
$653$	8.22704	+	14.2497i	0.321949	+	0.557632i	0.980890	−	0.194562i	$-0.0623287\pi$
$653$	8.22704	+	14.2497i	0.321949	+	0.557632i	−0.658941	+	0.752195i	$0.728995\pi$
$654$	23.0367	−	39.9007i	0.900805	−	1.56024i
$655$	−7.69950	+	13.3359i	−0.300844	+	0.521078i
$656$	−0.736705	−	1.27601i	−0.0287635	−	0.0498198i
$657$	−96.9005			−3.78045
$658$	−1.73975	−	12.4815i	−0.0678225	−	0.486580i
$659$	−10.0451			−0.391301			−0.195650	−	0.980674i	$-0.562682\pi$
$659$	−10.0451			−0.391301			−0.195650	+	0.980674i	$0.562682\pi$
$660$	1.53759	+	2.66319i	0.0598507	+	0.103665i
$661$	15.6623	−	27.1279i	0.609193	−	1.05515i	−0.382181	−	0.924088i	$-0.624827\pi$
$661$	15.6623	−	27.1279i	0.609193	−	1.05515i	0.991374	−	0.131066i	$-0.0418398\pi$
$662$	4.17526	−	7.23176i	0.162276	−	0.281070i
$663$	−7.98115	−	13.8238i	−0.309962	−	0.536871i
$664$	2.51813			0.0977225
$665$	−0.869875	−	6.24075i	−0.0337323	−	0.242006i
$666$	69.1497			2.67950
$667$	0.311179	+	0.538978i	0.0120489	+	0.0208693i
$668$	0.656720	−	1.13747i	0.0254092	−	0.0440101i
$669$	2.43512	−	4.21776i	0.0941473	−	0.163068i
$670$	2.57519	+	4.46035i	0.0994881	+	0.172319i
$671$	−10.1461			−0.391688
$672$	−7.54028	−	3.05641i	−0.290873	−	0.117903i
$673$	−33.7836			−1.30226			−0.651131	−	0.758965i	$-0.725705\pi$
$673$	−33.7836			−1.30226			−0.651131	+	0.758965i	$0.725705\pi$
$674$	−3.29204	−	5.70198i	−0.126805	−	0.219632i
$675$	5.31511	−	9.20604i	0.204579	−	0.354341i
$676$	−4.66882	+	8.08664i	−0.179570	+	0.311025i
$677$	3.25930	+	5.64527i	0.125265	+	0.216965i	0.921837	−	0.387579i	$-0.126689\pi$
$677$	3.25930	+	5.64527i	0.125265	+	0.216965i	−0.796571	+	0.604544i	$0.793355\pi$
$678$	59.2010			2.27360
$679$	−30.2325	+	23.5651i	−1.16022	+	0.904347i
$680$	1.09826			0.0421164
$681$	16.5666	+	28.6943i	0.634835	+	1.09957i
$682$	0.190793	−	0.330463i	0.00730584	−	0.0126541i
$683$	5.83403	−	10.1048i	0.223233	−	0.386651i	−0.732555	−	0.680708i	$-0.761672\pi$
$683$	5.83403	−	10.1048i	0.223233	−	0.386651i	0.955788	+	0.294057i	$0.0950055\pi$
$684$	−7.68868	−	13.3172i	−0.293984	−	0.509195i
$685$	−17.1008			−0.653389
$686$	10.9368	−	14.9461i	0.417568	−	0.570646i
$687$	−78.6054			−2.99898
$688$	−1.91438	−	3.31580i	−0.0729851	−	0.126414i
$689$	−20.6440	+	35.7565i	−0.786475	+	1.36222i
$690$	0.263295	−	0.456041i	0.0100235	−	0.0173612i
$691$	−9.36673	−	16.2237i	−0.356327	−	0.617177i	0.631017	−	0.775769i	$-0.282638\pi$
$691$	−9.36673	−	16.2237i	−0.356327	−	0.617177i	−0.987344	+	0.158592i	$0.949305\pi$
$692$	−13.9952			−0.532016
$693$	−13.4735	+	10.5021i	−0.511816	+	0.398942i
$694$	−8.06417			−0.306112
$695$	−6.48494	−	11.2323i	−0.245988	−	0.426064i
$696$	−5.58830	+	9.67923i	−0.211824	+	0.366890i
$697$	−0.809094	+	1.40139i	−0.0306466	+	0.0530815i
$698$	6.08649	+	10.5421i	0.230377	+	0.399025i
$699$	−42.3779			−1.60288
$700$	2.45197	+	0.993893i	0.0926759	+	0.0375656i
$701$	1.98454			0.0749550			0.0374775	−	0.999297i	$-0.488068\pi$
$701$	1.98454			0.0749550			0.0374775	+	0.999297i	$0.488068\pi$
$702$	−25.1207	−	43.5102i	−0.948118	−	1.64219i
$703$	−12.7530	+	22.0888i	−0.480987	+	0.833094i
$704$	−0.500000	+	0.866025i	−0.0188445	+	0.0326396i
$705$	7.32382	+	12.6852i	0.275831	+	0.477753i
$706$	12.3598			0.465166
$707$	−6.79472	−	48.7474i	−0.255542	−	1.83334i
$708$	−17.2845			−0.649590
$709$	−3.75835	−	6.50966i	−0.141148	−	0.244475i	0.786781	−	0.617232i	$-0.211746\pi$
$709$	−3.75835	−	6.50966i	−0.141148	−	0.244475i	−0.927929	+	0.372757i	$0.878413\pi$
$710$	−2.36203	+	4.09116i	−0.0886455	+	0.153538i
$711$	−39.1070	+	67.7353i	−1.46663	+	2.54027i
$712$	4.34790	+	7.53079i	0.162945	+	0.282228i
$713$	−0.0653422			−0.00244709
$714$	1.23358	+	8.85009i	0.0461656	+	0.331206i
$715$	−4.72627			−0.176753
$716$	−9.13192	−	15.8170i	−0.341276	−	0.591107i
$717$	40.0877	−	69.4340i	1.49710	−	2.59306i
$718$	−15.4217	+	26.7111i	−0.575532	+	0.996851i
$719$	−2.35499	−	4.07896i	−0.0878264	−	0.152120i	0.818766	−	0.574128i	$-0.194659\pi$
$719$	−2.35499	−	4.07896i	−0.0878264	−	0.152120i	−0.906592	+	0.422008i	$0.861325\pi$
$720$	6.45677			0.240630
$721$	−10.7774	−	4.36857i	−0.401373	−	0.162694i
$722$	−13.3280			−0.496019
$723$	−7.07960	−	12.2622i	−0.263293	−	0.456037i
$724$	−5.26866	+	9.12559i	−0.195808	+	0.339150i
$725$	1.81722	−	3.14752i	0.0674900	−	0.116896i
$726$	1.53759	+	2.66319i	0.0570654	+	0.0988402i
$727$	33.8856			1.25675			0.628375	−	0.777911i	$-0.283721\pi$
$727$	33.8856			1.25675			0.628375	+	0.777911i	$0.283721\pi$
$728$	9.86242	−	7.68740i	0.365526	−	0.284914i
$729$	−12.0682			−0.446969
$730$	7.50379	+	12.9969i	0.277728	+	0.481038i
$731$	−2.10249	+	3.64162i	−0.0777634	+	0.134690i
$732$	−15.6006	+	27.0211i	−0.576616	+	0.998729i
$733$	−4.45496	−	7.71622i	−0.164548	−	0.285005i	0.771947	−	0.635687i	$-0.219283\pi$
$733$	−4.45496	−	7.71622i	−0.164548	−	0.285005i	−0.936495	+	0.350682i	$0.885950\pi$
$734$	−37.6474			−1.38959
$735$	−5.25498	+	20.8750i	−0.193833	+	0.769987i
$736$	0.171239			0.00631194
$737$	2.57519	+	4.46035i	0.0948582	+	0.164299i
$738$	−4.75673	+	8.23891i	−0.175098	+	0.303278i
$739$	−11.2413	+	19.4706i	−0.413519	+	0.716236i	−0.995272	−	0.0971298i	$-0.969034\pi$
$739$	−11.2413	+	19.4706i	−0.413519	+	0.716236i	0.581753	+	0.813366i	$0.302367\pi$
$740$	−5.35482	−	9.27482i	−0.196847	−	0.340949i
$741$	34.6144			1.27159
$742$	18.2293	−	14.2091i	0.669220	−	0.521633i
$743$	12.0064			0.440473			0.220237	−	0.975446i	$-0.429317\pi$
$743$	12.0064			0.440473			0.220237	+	0.975446i	$0.429317\pi$
$744$	−0.586724	−	1.01624i	−0.0215103	−	0.0372570i
$745$	4.72949	−	8.19172i	0.173275	−	0.300121i
$746$	−9.25140	+	16.0239i	−0.338718	+	0.586676i
$747$	−8.12951	−	14.0807i	−0.297443	−	0.515187i
$748$	1.09826			0.0401564
$749$	38.6778	+	15.6778i	1.41326	+	0.572855i
$750$	−3.07519			−0.112290
$751$	0.342409	+	0.593070i	0.0124947	+	0.0216414i	0.872205	−	0.489140i	$-0.162689\pi$
$751$	0.342409	+	0.593070i	0.0124947	+	0.0216414i	−0.859710	+	0.510782i	$0.829356\pi$
$752$	−2.38159	+	4.12503i	−0.0868475	+	0.150424i
$753$	−21.9289	+	37.9820i	−0.799135	+	1.38414i
$754$	−8.58870	−	14.8761i	−0.312782	−	0.541754i
$755$	−20.8682			−0.759471
$756$	3.88269	+	27.8556i	0.141212	+	1.01310i
$757$	−8.27768			−0.300857			−0.150429	−	0.988621i	$-0.548065\pi$
$757$	−8.27768			−0.300857			−0.150429	+	0.988621i	$0.548065\pi$
$758$	−0.972301	−	1.68407i	−0.0353156	−	0.0611684i
$759$	0.263295	−	0.456041i	0.00955702	−	0.0165532i
$760$	−1.19079	+	2.06251i	−0.0431946	+	0.0748152i
$761$	−4.84963	−	8.39980i	−0.175799	−	0.304493i	0.764639	−	0.644459i	$-0.222917\pi$
$761$	−4.84963	−	8.39980i	−0.175799	−	0.304493i	−0.940437	+	0.339967i	$0.889584\pi$
$762$	60.5434			2.19325
$763$	−5.47229	−	39.2599i	−0.198110	−	1.42130i
$764$	15.0814			0.545625
$765$	−3.54561	−	6.14118i	−0.128192	−	0.222035i
$766$	3.58854	−	6.21553i	0.129659	−	0.224576i
$767$	13.2823	−	23.0056i	0.479596	−	0.830685i
$768$	1.53759	+	2.66319i	0.0554831	+	0.0960996i
$769$	−28.5165			−1.02833			−0.514165	−	0.857691i	$-0.671898\pi$
$769$	−28.5165			−1.02833			−0.514165	+	0.857691i	$0.671898\pi$
$770$	2.45197	+	0.993893i	0.0883630	+	0.0358174i
$771$	−50.2549			−1.80989
$772$	0.562247	+	0.973841i	0.0202357	+	0.0350493i
$773$	−15.3624	+	26.6084i	−0.552547	+	0.957039i	0.445543	+	0.895261i	$0.353011\pi$
$773$	−15.3624	+	26.6084i	−0.552547	+	0.957039i	−0.998090	+	0.0617788i	$0.980323\pi$
$774$	−12.3607	+	21.4094i	−0.444297	+	0.769545i
$775$	0.190793	+	0.330463i	0.00685348	+	0.0118706i
$776$	14.4880			0.520090
$777$	68.7244	−	53.5682i	2.46547	−	1.92175i
$778$	35.7392			1.28131
$779$	−1.75453	−	3.03893i	−0.0628624	−	0.108881i
$780$	−7.26708	+	12.5870i	−0.260203	+	0.450685i
$781$	−2.36203	+	4.09116i	−0.0845201	+	0.146393i
$782$	−0.0940323	−	0.162869i	−0.00336259	−	0.00582418i
$783$	38.6350			1.38070
$784$	−6.73318	+	1.91422i	−0.240471	+	0.0683649i
$785$	13.6420			0.486905
$786$	23.6774	+	41.0105i	0.844545	+	1.46280i
$787$	−11.4060	+	19.7558i	−0.406581	+	0.704219i	−0.994504	−	0.104698i	$-0.966612\pi$
$787$	−11.4060	+	19.7558i	−0.406581	+	0.704219i	0.587923	+	0.808917i	$0.299946\pi$
$788$	0.326236	−	0.565058i	0.0116217	−	0.0201293i
$789$	7.08828	+	12.2773i	0.252350	+	0.437082i
$790$	12.1135			0.430978
$791$	40.1719	−	31.3125i	1.42835	−	1.11335i
$792$	6.45677			0.229431
$793$	−23.9767	−	41.5289i	−0.851438	−	1.47473i
$794$	11.1583	−	19.3267i	0.395993	−	0.685879i
$795$	−13.4322	+	23.2653i	−0.476391	+	0.825134i
$796$	2.91337	+	5.04611i	0.103262	+	0.178854i
$797$	−15.4684			−0.547917			−0.273959	−	0.961741i	$-0.588333\pi$
$797$	−15.4684			−0.547917			−0.273959	+	0.961741i	$0.588333\pi$
$798$	−17.9578	−	7.27910i	−0.635700	−	0.257677i
$799$	5.23121			0.185067
$800$	−0.500000	−	0.866025i	−0.0176777	−	0.0306186i
$801$	28.0734	−	48.6246i	0.991926	−	1.71807i
$802$	12.7840	−	22.1426i	0.451419	−	0.781881i
$803$	7.50379	+	12.9969i	0.264803	+	0.458652i
$804$	15.8384			0.558576
$805$	−0.0625449	−	0.448717i	−0.00220442	−	0.0158152i
$806$	1.80348			0.0635248
$807$	34.3086	+	59.4242i	1.20772	+	2.09183i
$808$	−9.30146	+	16.1106i	−0.327224	+	0.566769i
$809$	5.99882	−	10.3903i	0.210907	−	0.365302i	−0.741092	−	0.671404i	$-0.765692\pi$
$809$	5.99882	−	10.3903i	0.210907	−	0.365302i	0.951999	+	0.306102i	$0.0990249\pi$
$810$	−6.65980	−	11.5351i	−0.234001	−	0.405302i
$811$	5.71106			0.200542			0.100271	−	0.994960i	$-0.468029\pi$
$811$	5.71106			0.200542			0.100271	+	0.994960i	$0.468029\pi$
$812$	1.32748	+	9.52378i	0.0465855	+	0.334219i
$813$	−61.3074			−2.15014
$814$	−5.35482	−	9.27482i	−0.187686	−	0.325082i
$815$	−8.27651	+	14.3353i	−0.289913	+	0.502145i
$816$	1.68868	−	2.92488i	0.0591156	−	0.102391i
$817$	−4.55926	−	7.89687i	−0.159508	−	0.276277i
$818$	23.0302			0.805231
$819$	−74.8256	−	30.3301i	−2.61462	−	1.05982i
$820$	1.47341			0.0514537
$821$	6.79079	+	11.7620i	0.237000	+	0.410496i	0.959852	−	0.280507i	$-0.0905025\pi$
$821$	6.79079	+	11.7620i	0.237000	+	0.410496i	−0.722852	+	0.691003i	$0.757169\pi$
$822$	−26.2941	+	45.5427i	−0.917112	+	1.58848i
$823$	−17.7443	+	30.7340i	−0.618527	+	1.07132i	0.371228	+	0.928542i	$0.378937\pi$
$823$	−17.7443	+	30.7340i	−0.618527	+	1.07132i	−0.989755	+	0.142778i	$0.954396\pi$
$824$	2.19771	+	3.80654i	0.0765607	+	0.132607i
$825$	−3.07519			−0.107064
$826$	−11.7287	+	9.14208i	−0.408093	+	0.318094i
$827$	−26.6071			−0.925219			−0.462610	−	0.886562i	$-0.653087\pi$
$827$	−26.6071			−0.925219			−0.462610	+	0.886562i	$0.653087\pi$
$828$	−0.552824	−	0.957520i	−0.0192120	−	0.0332761i
$829$	13.3720	−	23.1610i	0.464428	−	0.804414i	−0.534747	−	0.845012i	$-0.679593\pi$
$829$	13.3720	−	23.1610i	0.464428	−	0.804414i	0.999176	+	0.0405986i	$0.0129265\pi$
$830$	−1.25907	+	2.18077i	−0.0437028	+	0.0756955i
$831$	17.7370	+	30.7215i	0.615291	+	1.06572i
$832$	−4.72627			−0.163854
$833$	5.51805	+	5.35292i	0.191189	+	0.185468i
$834$	−39.8848			−1.38110
$835$	0.656720	+	1.13747i	0.0227267	+	0.0393638i
$836$	−1.19079	+	2.06251i	−0.0411844	+	0.0713335i
$837$	−2.02817	+	3.51289i	−0.0701038	+	0.121423i
$838$	7.51532	+	13.0169i	0.259612	+	0.449662i
$839$	−50.3362			−1.73780			−0.868899	−	0.494989i	$-0.835172\pi$
$839$	−50.3362			−1.73780			−0.868899	+	0.494989i	$0.835172\pi$
$840$	6.41706	−	5.00187i	0.221410	−	0.172581i
$841$	−15.7908			−0.544510
$842$	7.14733	+	12.3795i	0.246313	+	0.426627i
$843$	38.8914	−	67.3620i	1.33949	−	2.32007i
$844$	−10.4437	+	18.0889i	−0.359485	+	0.622647i
$845$	−4.66882	−	8.08664i	−0.160612	−	0.278189i
$846$	30.7547			1.05737
$847$	2.45197	+	0.993893i	0.0842508	+	0.0341506i
$848$	−8.73587			−0.299991
$849$	21.8000	+	37.7588i	0.748175	+	1.29588i
$850$	−0.549130	+	0.951122i	−0.0188350	+	0.0326232i
$851$	−0.916952	+	1.58821i	−0.0314327	+	0.0544430i
$852$	7.26369	+	12.5811i	0.248850	+	0.431021i
$853$	−17.1803			−0.588243			−0.294122	−	0.955768i	$-0.595027\pi$
$853$	−17.1803			−0.588243			−0.294122	+	0.955768i	$0.595027\pi$
$854$	3.70588	+	26.5871i	0.126813	+	0.909793i
$855$	15.3774			0.525895
$856$	−7.88708	−	13.6608i	−0.269575	−	0.466917i
$857$	25.0392	−	43.3691i	0.855322	−	1.48146i	−0.0210235	−	0.999779i	$-0.506692\pi$
$857$	25.0392	−	43.3691i	0.855322	−	1.48146i	0.876346	−	0.481683i	$-0.159974\pi$
$858$	−7.26708	+	12.5870i	−0.248094	+	0.429712i
$859$	5.33046	+	9.23264i	0.181873	+	0.315013i	0.942518	−	0.334154i	$-0.108451\pi$
$859$	5.33046	+	9.23264i	0.181873	+	0.315013i	−0.760645	+	0.649168i	$0.775117\pi$
$860$	3.82876			0.130560
$861$	1.65495	+	11.8731i	0.0564006	+	0.404635i
$862$	2.42994			0.0827642
$863$	−19.3492	−	33.5138i	−0.658655	−	1.14082i	−0.980964	−	0.194189i	$-0.937792\pi$
$863$	−19.3492	−	33.5138i	−0.658655	−	1.14082i	0.322309	−	0.946635i	$-0.395541\pi$
$864$	5.31511	−	9.20604i	0.180824	−	0.313196i
$865$	6.99758	−	12.1202i	0.237925	−	0.412098i
$866$	−10.9178	−	18.9101i	−0.371001	−	0.642593i
$867$	48.5690			1.64949
$868$	−0.935638	−	0.379256i	−0.0317576	−	0.0128728i
$869$	12.1135			0.410921
$870$	−5.58830	−	9.67923i	−0.189461	−	0.328156i
$871$	−12.1710	+	21.0808i	−0.412400	+	0.714297i
$872$	−7.49115	+	12.9750i	−0.253682	+	0.439391i
$873$	−46.7729	−	81.0131i	−1.58302	−	2.74188i
$874$	0.407819			0.0137947
$875$	−2.08672	+	1.62653i	−0.0705441	+	0.0549866i
$876$	46.1511			1.55930
$877$	−11.3755	−	19.7030i	−0.384125	−	0.665323i	0.607523	−	0.794302i	$-0.292163\pi$
$877$	−11.3755	−	19.7030i	−0.384125	−	0.665323i	−0.991647	+	0.128979i	$0.958830\pi$
$878$	2.05535	−	3.55997i	0.0693647	−	0.120143i
$879$	16.3224	−	28.2713i	0.550542	−	0.953567i
$880$	−0.500000	−	0.866025i	−0.0168550	−	0.0291937i
$881$	−9.36150			−0.315397			−0.157699	−	0.987487i	$-0.550407\pi$
$881$	−9.36150			−0.315397			−0.157699	+	0.987487i	$0.550407\pi$
$882$	32.4411	+	31.4703i	1.09235	+	1.05966i
$883$	−55.0953			−1.85411			−0.927053	−	0.374930i	$-0.877667\pi$
$883$	−55.0953			−1.85411			−0.927053	+	0.374930i	$0.877667\pi$
$884$	2.59534	+	4.49526i	0.0872907	+	0.151192i
$885$	8.64223	−	14.9688i	0.290505	−	0.503170i
$886$	18.5035	−	32.0490i	0.621636	−	1.07671i
$887$	16.4488	+	28.4901i	0.552295	+	0.956603i	0.998108	+	0.0614773i	$0.0195812\pi$
$887$	16.4488	+	28.4901i	0.552295	+	0.956603i	−0.445813	+	0.895126i	$0.647085\pi$
$888$	−32.9341			−1.10520
$889$	41.0828	−	32.0225i	1.37787	−	1.07400i
$890$	−8.69581			−0.291484
$891$	−6.65980	−	11.5351i	−0.223112	−	0.386441i
$892$	−0.791862	+	1.37154i	−0.0265135	+	0.0459227i
$893$	−5.67195	+	9.82411i	−0.189805	+	0.328751i
$894$	−14.5441	−	25.1911i	−0.486426	−	0.842515i
$895$	18.2638			0.610493
$896$	2.45197	+	0.993893i	0.0819147	+	0.0332036i
$897$	2.48881			0.0830990
$898$	4.72659	+	8.18669i	0.157728	+	0.273193i
$899$	−0.693427	+	1.20105i	−0.0231271	+	0.0400573i
$900$	−3.22839	+	5.59173i	−0.107613	+	0.186391i
$901$	4.79713	+	8.30888i	0.159816	+	0.276809i
$902$	1.47341			0.0490592
$903$	4.30051	+	30.8532i	0.143112	+	1.02673i
$904$	−19.2512			−0.640285
$905$	−5.26866	−	9.12559i	−0.175136	−	0.303345i
$906$	−32.0868	+	55.5759i	−1.06601	+	1.84639i
$907$	7.79091	−	13.4943i	0.258693	−	0.448069i	−0.707199	−	0.707015i	$-0.750042\pi$
$907$	7.79091	−	13.4943i	0.258693	−	0.448069i	0.965892	+	0.258945i	$0.0833749\pi$
$908$	−5.38720	−	9.33091i	−0.178781	−	0.309657i
$909$	120.115			3.98396
$910$	1.72627	+	12.3848i	0.0572254	+	0.410552i
$911$	−7.23014			−0.239545			−0.119773	−	0.992801i	$-0.538217\pi$
$911$	−7.23014			−0.239545			−0.119773	+	0.992801i	$0.538217\pi$
$912$	3.66191	+	6.34261i	0.121258	+	0.210025i
$913$	−1.25907	+	2.18077i	−0.0416690	+	0.0721729i
$914$	−0.223464	+	0.387051i	−0.00739153	+	0.0128025i
$915$	−15.6006	−	27.0211i	−0.515741	−	0.893290i
$916$	25.5612			0.844565
$917$	37.7580	+	15.3050i	1.24688	+	0.505415i
$918$	−11.6748			−0.385324
$919$	−27.7186	−	48.0101i	−0.914353	−	1.58371i	−0.807845	−	0.589394i	$-0.799366\pi$
$919$	−27.7186	−	48.0101i	−0.914353	−	1.58371i	−0.106508	−	0.994312i	$-0.533967\pi$
$920$	−0.0856193	+	0.148297i	−0.00282279	+	0.00488921i
$921$	2.97215	−	5.14791i	0.0979355	−	0.169629i
$922$	−20.2096	−	35.0041i	−0.665568	−	1.15280i
$923$	−22.3272			−0.734909
$924$	6.41706	−	5.00187i	0.211106	−	0.164549i
$925$	10.7096			0.352131
$926$	−14.7637	−	25.5715i	−0.485166	−	0.840332i
$927$	14.1901	−	24.5779i	0.466064	−	0.807246i
$928$	1.81722	−	3.14752i	0.0596533	−	0.103323i
$929$	2.60909	+	4.51907i	0.0856013	+	0.148266i	0.905647	−	0.424032i	$-0.139386\pi$
$929$	2.60909	+	4.51907i	0.0856013	+	0.148266i	−0.820046	+	0.572298i	$0.806052\pi$
$930$	1.17345			0.0384789
$931$	−16.0357	+	4.55887i	−0.525547	+	0.149411i
$932$	13.7806			0.451398
$933$	13.4049	+	23.2179i	0.438856	+	0.760121i
$934$	−9.34659	+	16.1888i	−0.305830	+	0.529713i
$935$	−0.549130	+	0.951122i	−0.0179585	+	0.0311050i
$936$	15.2582	+	26.4280i	0.498731	+	0.863827i
$937$	−22.0321			−0.719756			−0.359878	−	0.932999i	$-0.617182\pi$
$937$	−22.0321			−0.719756			−0.359878	+	0.932999i	$0.617182\pi$
$938$	10.7474	−	8.37721i	0.350915	−	0.273526i
$939$	−4.82822			−0.157563
$940$	−2.38159	−	4.12503i	−0.0776788	−	0.134544i
$941$	25.2323	−	43.7037i	0.822550	−	1.42470i	−0.0812272	−	0.996696i	$-0.525884\pi$
$941$	25.2323	−	43.7037i	0.822550	−	1.42470i	0.903777	−	0.428003i	$-0.140783\pi$
$942$	20.9759	−	36.3313i	0.683431	−	1.18374i
$943$	−0.126152	−	0.218502i	−0.00410808	−	0.00711541i
$944$	5.62062			0.182936
$945$	−26.0650	−	10.5653i	−0.847895	−	0.343689i
$946$	3.82876			0.124484
$947$	9.06774	+	15.7058i	0.294662	+	0.510369i	0.974906	−	0.222616i	$-0.0714596\pi$
$947$	9.06774	+	15.7058i	0.294662	+	0.510369i	−0.680244	+	0.732986i	$0.738126\pi$
$948$	18.6256	−	32.2605i	0.604931	−	1.04777i
$949$	−35.4649	+	61.4271i	−1.15124	+	1.99401i
$950$	−1.19079	−	2.06251i	−0.0386344	−	0.0669168i
$951$	−0.342159			−0.0110953
$952$	−0.401140	−	2.87790i	−0.0130010	−	0.0932734i
$953$	22.2677			0.721322			0.360661	−	0.932697i	$-0.382551\pi$
$953$	22.2677			0.721322			0.360661	+	0.932697i	$0.382551\pi$
$954$	28.2028	+	48.8486i	0.913098	+	1.58153i
$955$	−7.54069	+	13.0609i	−0.244011	+	0.422639i
$956$	−13.0359	+	22.5788i	−0.421610	+	0.730250i
$957$	−5.58830	−	9.67923i	−0.180644	−	0.312885i
$958$	21.8404			0.705631
$959$	6.24608	+	44.8113i	0.201696	+	1.44703i
$960$	−3.07519			−0.0992512
$961$	15.4272	+	26.7207i	0.497651	+	0.861958i
$962$	25.3083	−	43.8353i	0.815973	−	1.41331i
$963$	−50.9251	+	88.2048i	−1.64104	+	2.84236i
$964$	2.30217	+	3.98748i	0.0741479	+	0.128428i
$965$	−1.12449			−0.0361988
$966$	−1.29119	−	0.523375i	−0.0415433	−	0.0168393i
$967$	−3.82853			−0.123117			−0.0615587	−	0.998103i	$-0.519607\pi$
$967$	−3.82853			−0.123117			−0.0615587	+	0.998103i	$0.519607\pi$
$968$	−0.500000	−	0.866025i	−0.0160706	−	0.0278351i
$969$	4.02173	−	6.96585i	0.129197	−	0.223775i
$970$	−7.24401	+	12.5470i	−0.232591	+	0.402860i
$971$	−15.8019	−	27.3696i	−0.507106	−	0.878333i	−0.999966	−	0.00822441i	$-0.997382\pi$
$971$	−15.8019	−	27.3696i	−0.507106	−	0.878333i	0.492861	−	0.870108i	$-0.335951\pi$
$972$	−9.06957			−0.290907
$973$	−27.0646	+	21.0958i	−0.867650	+	0.676302i
$974$	−23.4300			−0.750746
$975$	−7.26708	−	12.5870i	−0.232733	−	0.403105i
$976$	5.07307	−	8.78682i	0.162385	−	0.281259i
$977$	3.64512	−	6.31354i	0.116618	−	0.201988i	−0.801808	−	0.597582i	$-0.796128\pi$
$977$	3.64512	−	6.31354i	0.116618	−	0.201988i	0.918425	+	0.395594i	$0.129461\pi$
$978$	25.4518	+	44.0838i	0.813859	+	1.40964i
$979$	−8.69581			−0.277919
$980$	1.70883	−	6.78822i	0.0545866	−	0.216842i
$981$	96.7373			3.08858
$982$	11.8038	+	20.4449i	0.376676	+	0.652421i
$983$	−20.3641	+	35.2717i	−0.649514	+	1.12499i	0.333725	+	0.942671i	$0.391694\pi$
$983$	−20.3641	+	35.2717i	−0.649514	+	1.12499i	−0.983239	+	0.182321i	$0.941639\pi$
$984$	2.26550	−	3.92397i	0.0722216	−	0.125092i
$985$	0.326236	+	0.565058i	0.0103948	+	0.0180042i
$986$	−3.99157			−0.127118
$987$	30.5656	−	23.8248i	0.972913	−	0.758350i
$988$	−11.2560			−0.358102
$989$	−0.327816	−	0.567794i	−0.0104239	−	0.0180548i
$990$	−3.22839	+	5.59173i	−0.102605	+	0.177717i
$991$	−13.3486	+	23.1204i	−0.424032	+	0.734445i	−0.996329	−	0.0856014i	$-0.972719\pi$
$991$	−13.3486	+	23.1204i	−0.424032	+	0.734445i	0.572298	+	0.820046i	$0.306052\pi$
$992$	0.190793	+	0.330463i	0.00605768	+	0.0104922i
$993$	25.6794			0.814911
$994$	11.5833	+	4.69521i	0.367399	+	0.148923i
$995$	−5.82674			−0.184720
$996$	3.87187	+	6.70627i	0.122685	+	0.212496i
$997$	0.360183	−	0.623856i	0.0114071	−	0.0197577i	−0.860265	−	0.509846i	$-0.829702\pi$
$997$	0.360183	−	0.623856i	0.0114071	−	0.0197577i	0.871673	+	0.490089i	$0.163036\pi$
$998$	13.6593	−	23.6585i	0.432376	−	0.748898i
$999$	56.9229	+	98.5933i	1.80096	+	3.11935i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	770.2.i.m.221.5	✓	10
7.2	even	3	inner	770.2.i.m.331.5	yes	10
7.3	odd	6		5390.2.a.ch.1.5		5
7.4	even	3		5390.2.a.ci.1.1		5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
770.2.i.m.221.5	✓	10	1.1	even	1	trivial
770.2.i.m.331.5	yes	10	7.2	even	3	inner
5390.2.a.ch.1.5		5	7.3	odd	6
5390.2.a.ci.1.1		5	7.4	even	3

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)

\(f(q)\)	\(=\)	\(q+(-0.500000 - 0.866025i) q^{2} +(1.53759 - 2.66319i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-0.500000 - 0.866025i) q^{5} -3.07519 q^{6} +(-2.08672 + 1.62653i) q^{7} +1.00000 q^{8} +(-3.22839 - 5.59173i) q^{9} +O(q^{10})\)	\(q+(-0.500000 - 0.866025i) q^{2} +(1.53759 - 2.66319i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-0.500000 - 0.866025i) q^{5} -3.07519 q^{6} +(-2.08672 + 1.62653i) q^{7} +1.00000 q^{8} +(-3.22839 - 5.59173i) q^{9} +(-0.500000 + 0.866025i) q^{10} +(-0.500000 + 0.866025i) q^{11} +(1.53759 + 2.66319i) q^{12} -4.72627 q^{13} +(2.45197 + 0.993893i) q^{14} -3.07519 q^{15} +(-0.500000 - 0.866025i) q^{16} +(-0.549130 + 0.951122i) q^{17} +(-3.22839 + 5.59173i) q^{18} +(-1.19079 - 2.06251i) q^{19} +1.00000 q^{20} +(1.12321 + 8.05828i) q^{21} +1.00000 q^{22} +(-0.0856193 - 0.148297i) q^{23} +(1.53759 - 2.66319i) q^{24} +(-0.500000 + 0.866025i) q^{25} +(2.36314 + 4.09307i) q^{26} -10.6302 q^{27} +(-0.365250 - 2.62042i) q^{28} -3.63445 q^{29} +(1.53759 + 2.66319i) q^{30} +(0.190793 - 0.330463i) q^{31} +(-0.500000 + 0.866025i) q^{32} +(1.53759 + 2.66319i) q^{33} +1.09826 q^{34} +(2.45197 + 0.993893i) q^{35} +6.45677 q^{36} +(-5.35482 - 9.27482i) q^{37} +(-1.19079 + 2.06251i) q^{38} +(-7.26708 + 12.5870i) q^{39} +(-0.500000 - 0.866025i) q^{40} +1.47341 q^{41} +(6.41706 - 5.00187i) q^{42} +3.82876 q^{43} +(-0.500000 - 0.866025i) q^{44} +(-3.22839 + 5.59173i) q^{45} +(-0.0856193 + 0.148297i) q^{46} +(-2.38159 - 4.12503i) q^{47} -3.07519 q^{48} +(1.70883 - 6.78822i) q^{49} +1.00000 q^{50} +(1.68868 + 2.92488i) q^{51} +(2.36314 - 4.09307i) q^{52} +(4.36793 - 7.56548i) q^{53} +(5.31511 + 9.20604i) q^{54} +1.00000 q^{55} +(-2.08672 + 1.62653i) q^{56} -7.32382 q^{57} +(1.81722 + 3.14752i) q^{58} +(-2.81031 + 4.86760i) q^{59} +(1.53759 - 2.66319i) q^{60} +(5.07307 + 8.78682i) q^{61} -0.381586 q^{62} +(15.8318 + 6.41734i) q^{63} +1.00000 q^{64} +(2.36314 + 4.09307i) q^{65} +(1.53759 - 2.66319i) q^{66} +(2.57519 - 4.46035i) q^{67} +(-0.549130 - 0.951122i) q^{68} -0.526591 q^{69} +(-0.365250 - 2.62042i) q^{70} +4.72406 q^{71} +(-3.22839 - 5.59173i) q^{72} +(7.50379 - 12.9969i) q^{73} +(-5.35482 + 9.27482i) q^{74} +(1.53759 + 2.66319i) q^{75} +2.38159 q^{76} +(-0.365250 - 2.62042i) q^{77} +14.5342 q^{78} +(-6.05674 - 10.4906i) q^{79} +(-0.500000 + 0.866025i) q^{80} +(-6.65980 + 11.5351i) q^{81} +(-0.736705 - 1.27601i) q^{82} +2.51813 q^{83} +(-7.54028 - 3.05641i) q^{84} +1.09826 q^{85} +(-1.91438 - 3.31580i) q^{86} +(-5.58830 + 9.67923i) q^{87} +(-0.500000 + 0.866025i) q^{88} +(4.34790 + 7.53079i) q^{89} +6.45677 q^{90} +(9.86242 - 7.68740i) q^{91} +0.171239 q^{92} +(-0.586724 - 1.01624i) q^{93} +(-2.38159 + 4.12503i) q^{94} +(-1.19079 + 2.06251i) q^{95} +(1.53759 + 2.66319i) q^{96} +14.4880 q^{97} +(-6.73318 + 1.91422i) q^{98} +6.45677 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - 5 q^{2} - 5 q^{4} - 5 q^{5} + 10 q^{8} - 9 q^{9}+O(q^{10}) \) 10 * q - 5 * q^2 - 5 * q^4 - 5 * q^5 + 10 * q^8 - 9 * q^9	\( 10 q - 5 q^{2} - 5 q^{4} - 5 q^{5} + 10 q^{8} - 9 q^{9} - 5 q^{10} - 5 q^{11} - 2 q^{13} + 3 q^{14} - 5 q^{16} - 9 q^{18} - 4 q^{19} + 10 q^{20} + 2 q^{21} + 10 q^{22} - 7 q^{23} - 5 q^{25} + q^{26} - 18 q^{27} - 3 q^{28} + 8 q^{29} - 6 q^{31} - 5 q^{32} + 3 q^{35} + 18 q^{36} - 16 q^{37} - 4 q^{38} - 7 q^{39} - 5 q^{40} - 2 q^{41} + 11 q^{42} + 26 q^{43} - 5 q^{44} - 9 q^{45} - 7 q^{46} - 8 q^{47} + 14 q^{49} + 10 q^{50} - 13 q^{51} + q^{52} - 4 q^{53} + 9 q^{54} + 10 q^{55} + 30 q^{57} - 4 q^{58} - 9 q^{59} - 2 q^{61} + 12 q^{62} + 25 q^{63} + 10 q^{64} + q^{65} - 5 q^{67} - 22 q^{69} - 3 q^{70} + 56 q^{71} - 9 q^{72} + q^{73} - 16 q^{74} + 8 q^{76} - 3 q^{77} + 14 q^{78} - 23 q^{79} - 5 q^{80} + 7 q^{81} + q^{82} - 46 q^{83} - 13 q^{84} - 13 q^{86} - 15 q^{87} - 5 q^{88} + 9 q^{89} + 18 q^{90} + 29 q^{91} + 14 q^{92} + 15 q^{93} - 8 q^{94} - 4 q^{95} - 26 q^{97} - 19 q^{98} + 18 q^{99}+O(q^{100}) \) 10 * q - 5 * q^2 - 5 * q^4 - 5 * q^5 + 10 * q^8 - 9 * q^9 - 5 * q^10 - 5 * q^11 - 2 * q^13 + 3 * q^14 - 5 * q^16 - 9 * q^18 - 4 * q^19 + 10 * q^20 + 2 * q^21 + 10 * q^22 - 7 * q^23 - 5 * q^25 + q^26 - 18 * q^27 - 3 * q^28 + 8 * q^29 - 6 * q^31 - 5 * q^32 + 3 * q^35 + 18 * q^36 - 16 * q^37 - 4 * q^38 - 7 * q^39 - 5 * q^40 - 2 * q^41 + 11 * q^42 + 26 * q^43 - 5 * q^44 - 9 * q^45 - 7 * q^46 - 8 * q^47 + 14 * q^49 + 10 * q^50 - 13 * q^51 + q^52 - 4 * q^53 + 9 * q^54 + 10 * q^55 + 30 * q^57 - 4 * q^58 - 9 * q^59 - 2 * q^61 + 12 * q^62 + 25 * q^63 + 10 * q^64 + q^65 - 5 * q^67 - 22 * q^69 - 3 * q^70 + 56 * q^71 - 9 * q^72 + q^73 - 16 * q^74 + 8 * q^76 - 3 * q^77 + 14 * q^78 - 23 * q^79 - 5 * q^80 + 7 * q^81 + q^82 - 46 * q^83 - 13 * q^84 - 13 * q^86 - 15 * q^87 - 5 * q^88 + 9 * q^89 + 18 * q^90 + 29 * q^91 + 14 * q^92 + 15 * q^93 - 8 * q^94 - 4 * q^95 - 26 * q^97 - 19 * q^98 + 18 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more