LMFDB - Embedded newform 770.2.i.m.331.1

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			331.1
Root			$1.26598 - 2.19274i$ of defining polynomial
Character	$\chi$	$=$	770.331
Dual form			770.2.i.m.221.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 + 0.866025i) q^{2} +(-1.26598 - 2.19274i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-0.500000 + 0.866025i) q^{5} +2.53196 q^{6} +(2.22551 + 1.43078i) q^{7} +1.00000 q^{8} +(-1.70541 + 2.95386i) q^{9} +O(q^{10})$	\(q+(-0.500000 + 0.866025i) q^{2} +(-1.26598 - 2.19274i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-0.500000 + 0.866025i) q^{5} +2.53196 q^{6} +(2.22551 + 1.43078i) q^{7} +1.00000 q^{8} +(-1.70541 + 2.95386i) q^{9} +(-0.500000 - 0.866025i) q^{10} +(-0.500000 - 0.866025i) q^{11} +(-1.26598 + 2.19274i) q^{12} -2.66350 q^{13} +(-2.35184 + 1.21195i) q^{14} +2.53196 q^{15} +(-0.500000 + 0.866025i) q^{16} +(0.959525 + 1.66195i) q^{17} +(-1.70541 - 2.95386i) q^{18} +(-2.47139 + 4.28058i) q^{19} +1.00000 q^{20} +(0.319883 - 6.69130i) q^{21} +1.00000 q^{22} +(-2.08586 + 3.61282i) q^{23} +(-1.26598 - 2.19274i) q^{24} +(-0.500000 - 0.866025i) q^{25} +(1.33175 - 2.30666i) q^{26} +1.04019 q^{27} +(0.126338 - 2.64273i) q^{28} +6.95636 q^{29} +(-1.26598 + 2.19274i) q^{30} +(1.47139 + 2.54852i) q^{31} +(-0.500000 - 0.866025i) q^{32} +(-1.26598 + 2.19274i) q^{33} -1.91905 q^{34} +(-2.35184 + 1.21195i) q^{35} +3.41082 q^{36} +(2.74416 - 4.75303i) q^{37} +(-2.47139 - 4.28058i) q^{38} +(3.37194 + 5.84037i) q^{39} +(-0.500000 + 0.866025i) q^{40} +12.5626 q^{41} +(5.63489 + 3.62267i) q^{42} -0.171726 q^{43} +(-0.500000 + 0.866025i) q^{44} +(-1.70541 - 2.95386i) q^{45} +(-2.08586 - 3.61282i) q^{46} +(-4.94278 + 8.56115i) q^{47} +2.53196 q^{48} +(2.90575 + 6.36841i) q^{49} +1.00000 q^{50} +(2.42948 - 4.20798i) q^{51} +(1.33175 + 2.30666i) q^{52} +(5.09442 + 8.82379i) q^{53} +(-0.520094 + 0.900829i) q^{54} +1.00000 q^{55} +(2.22551 + 1.43078i) q^{56} +12.5149 q^{57} +(-3.47818 + 6.02439i) q^{58} +(4.78276 + 8.28398i) q^{59} +(-1.26598 - 2.19274i) q^{60} +(-1.07387 + 1.86000i) q^{61} -2.94278 q^{62} +(-8.02172 + 4.13376i) q^{63} +1.00000 q^{64} +(1.33175 - 2.30666i) q^{65} +(-1.26598 - 2.19274i) q^{66} +(-3.03196 - 5.25151i) q^{67} +(0.959525 - 1.66195i) q^{68} +10.5626 q^{69} +(0.126338 - 2.64273i) q^{70} +15.2862 q^{71} +(-1.70541 + 2.95386i) q^{72} +(2.40939 + 4.17318i) q^{73} +(2.74416 + 4.75303i) q^{74} +(-1.26598 + 2.19274i) q^{75} +4.94278 q^{76} +(0.126338 - 2.64273i) q^{77} -6.74387 q^{78} +(3.14299 - 5.44383i) q^{79} +(-0.500000 - 0.866025i) q^{80} +(3.79938 + 6.58072i) q^{81} +(-6.28132 + 10.8796i) q^{82} -10.7303 q^{83} +(-5.95477 + 3.06862i) q^{84} -1.91905 q^{85} +(0.0858629 - 0.148719i) q^{86} +(-8.80662 - 15.2535i) q^{87} +(-0.500000 - 0.866025i) q^{88} +(-6.04874 + 10.4767i) q^{89} +3.41082 q^{90} +(-5.92763 - 3.81088i) q^{91} +4.17173 q^{92} +(3.72551 - 6.45276i) q^{93} +(-4.94278 - 8.56115i) q^{94} +(-2.47139 - 4.28058i) q^{95} +(-1.26598 + 2.19274i) q^{96} -11.9697 q^{97} +(-6.96808 - 0.667755i) q^{98} +3.41082 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 $\left(\mathbb{Z}/770\mathbb{Z}\right)^\times$.

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

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
$3$	−1.26598	−	2.19274i	−0.730914	−	1.26598i	−0.956493	−	0.291755i	$-0.905761\pi$
$3$	−1.26598	−	2.19274i	−0.730914	−	1.26598i	0.225579	−	0.974225i	$-0.427573\pi$
$4$	−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
$6$	2.53196			1.03367
$7$	2.22551	+	1.43078i	0.841162	+	0.540783i
$7$	2.22551	+	1.43078i	0.841162	+	0.540783i
$8$	1.00000			0.353553
$9$	−1.70541	+	2.95386i	−0.568470	+	0.984620i
$10$	−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
$12$	−1.26598	+	2.19274i	−0.365457	+	0.632990i
$13$	−2.66350			−0.738722			−0.369361	−	0.929286i	$-0.620423\pi$
$13$	−2.66350			−0.738722			−0.369361	+	0.929286i	$0.620423\pi$
$14$	−2.35184	+	1.21195i	−0.628557	+	0.323909i
$15$	2.53196			0.653749
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	0.959525	+	1.66195i	0.232719	+	0.403081i	0.958607	−	0.284731i	$-0.0919044\pi$
$17$	0.959525	+	1.66195i	0.232719	+	0.403081i	−0.725888	+	0.687813i	$0.758571\pi$
$18$	−1.70541	−	2.95386i	−0.401969	−	0.696231i
$19$	−2.47139	+	4.28058i	−0.566976	+	0.982031i	0.429887	+	0.902883i	$0.358553\pi$
$19$	−2.47139	+	4.28058i	−0.566976	+	0.982031i	−0.996863	+	0.0791486i	$0.974780\pi$
$20$	1.00000			0.223607
$21$	0.319883	−	6.69130i	0.0698041	−	1.46016i
$22$	1.00000			0.213201
$23$	−2.08586	+	3.61282i	−0.434932	+	0.753325i	−0.997290	−	0.0735689i	$-0.976561\pi$
$23$	−2.08586	+	3.61282i	−0.434932	+	0.753325i	0.562358	+	0.826894i	$0.309894\pi$
$24$	−1.26598	−	2.19274i	−0.258417	−	0.447592i
$25$	−0.500000	−	0.866025i	−0.100000	−	0.173205i
$26$	1.33175	−	2.30666i	0.261178	−	0.452373i
$27$	1.04019			0.200184
$28$	0.126338	−	2.64273i	0.0238756	−	0.499430i
$29$	6.95636			1.29176			0.645882	−	0.763437i	$-0.276490\pi$
$29$	6.95636			1.29176			0.645882	+	0.763437i	$0.276490\pi$
$30$	−1.26598	+	2.19274i	−0.231135	+	0.400338i
$31$	1.47139	+	2.54852i	0.264270	+	0.457729i	0.967372	−	0.253360i	$-0.0815358\pi$
$31$	1.47139	+	2.54852i	0.264270	+	0.457729i	−0.703102	+	0.711089i	$0.748202\pi$
$32$	−0.500000	−	0.866025i	−0.0883883	−	0.153093i
$33$	−1.26598	+	2.19274i	−0.220379	+	0.381707i
$34$	−1.91905			−0.329114
$35$	−2.35184	+	1.21195i	−0.397534	+	0.204858i
$36$	3.41082			0.568470
$37$	2.74416	−	4.75303i	0.451137	−	0.781393i	−0.547320	−	0.836924i	$-0.684352\pi$
$37$	2.74416	−	4.75303i	0.451137	−	0.781393i	0.998457	+	0.0555309i	$0.0176851\pi$
$38$	−2.47139	−	4.28058i	−0.400913	−	0.694401i
$39$	3.37194	+	5.84037i	0.539942	+	0.935207i
$40$	−0.500000	+	0.866025i	−0.0790569	+	0.136931i
$41$	12.5626			1.96196			0.980978	−	0.194120i	$-0.0621853\pi$
$41$	12.5626			1.96196			0.980978	+	0.194120i	$0.0621853\pi$
$42$	5.63489	+	3.62267i	0.869482	+	0.558991i
$43$	−0.171726			−0.0261879			−0.0130940	−	0.999914i	$-0.504168\pi$
$43$	−0.171726			−0.0261879			−0.0130940	+	0.999914i	$0.504168\pi$
$44$	−0.500000	+	0.866025i	−0.0753778	+	0.130558i
$45$	−1.70541	−	2.95386i	−0.254228	−	0.440335i
$46$	−2.08586	−	3.61282i	−0.307544	−	0.532681i
$47$	−4.94278	+	8.56115i	−0.720979	+	1.24877i	0.239629	+	0.970865i	$0.422974\pi$
$47$	−4.94278	+	8.56115i	−0.720979	+	1.24877i	−0.960608	+	0.277908i	$0.910359\pi$
$48$	2.53196			0.365457
$49$	2.90575	+	6.36841i	0.415107	+	0.909773i
$50$	1.00000			0.141421
$51$	2.42948	−	4.20798i	0.340195	−	0.589235i
$52$	1.33175	+	2.30666i	0.184680	+	0.319876i
$53$	5.09442	+	8.82379i	0.699772	+	1.21204i	0.968545	+	0.248837i	$0.0800483\pi$
$53$	5.09442	+	8.82379i	0.699772	+	1.21204i	−0.268774	+	0.963203i	$0.586618\pi$
$54$	−0.520094	+	0.900829i	−0.0707758	+	0.122587i
$55$	1.00000			0.134840
$56$	2.22551	+	1.43078i	0.297396	+	0.191196i
$57$	12.5149			1.65764
$58$	−3.47818	+	6.02439i	−0.456708	+	0.791041i
$59$	4.78276	+	8.28398i	0.622662	+	1.07848i	0.988988	+	0.147996i	$0.0472823\pi$
$59$	4.78276	+	8.28398i	0.622662	+	1.07848i	−0.366326	+	0.930487i	$0.619384\pi$
$60$	−1.26598	−	2.19274i	−0.163437	−	0.283082i
$61$	−1.07387	+	1.86000i	−0.137495	+	0.238149i	−0.926548	−	0.376177i	$-0.877239\pi$
$61$	−1.07387	+	1.86000i	−0.137495	+	0.238149i	0.789053	+	0.614326i	$0.210572\pi$
$62$	−2.94278			−0.373734
$63$	−8.02172	+	4.13376i	−1.01064	+	0.520805i
$64$	1.00000			0.125000
$65$	1.33175	−	2.30666i	0.165183	−	0.286106i
$66$	−1.26598	−	2.19274i	−0.155831	−	0.269908i
$67$	−3.03196	−	5.25151i	−0.370413	−	0.641574i	0.619216	−	0.785221i	$-0.287450\pi$
$67$	−3.03196	−	5.25151i	−0.370413	−	0.641574i	−0.989629	+	0.143647i	$0.954117\pi$
$68$	0.959525	−	1.66195i	0.116359	−	0.201541i
$69$	10.5626			1.27159
$70$	0.126338	−	2.64273i	0.0151003	−	0.315867i
$71$	15.2862			1.81414			0.907071	−	0.420977i	$-0.138313\pi$
$71$	15.2862			1.81414			0.907071	+	0.420977i	$0.138313\pi$
$72$	−1.70541	+	2.95386i	−0.200985	+	0.348116i
$73$	2.40939	+	4.17318i	0.281997	+	0.488434i	0.971877	−	0.235491i	$-0.0756698\pi$
$73$	2.40939	+	4.17318i	0.281997	+	0.488434i	−0.689879	+	0.723924i	$0.742336\pi$
$74$	2.74416	+	4.75303i	0.319002	+	0.552528i
$75$	−1.26598	+	2.19274i	−0.146183	+	0.253196i
$76$	4.94278			0.566976
$77$	0.126338	−	2.64273i	0.0143976	−	0.301167i
$78$	−6.74387			−0.763593
$79$	3.14299	−	5.44383i	0.353614	−	0.612478i	−0.633265	−	0.773935i	$-0.718286\pi$
$79$	3.14299	−	5.44383i	0.353614	−	0.612478i	0.986880	+	0.161457i	$0.0516192\pi$
$80$	−0.500000	−	0.866025i	−0.0559017	−	0.0968246i
$81$	3.79938	+	6.58072i	0.422153	+	0.731191i
$82$	−6.28132	+	10.8796i	−0.693656	+	1.20145i
$83$	−10.7303			−1.17780			−0.588901	−	0.808205i	$-0.700439\pi$
$83$	−10.7303			−1.17780			−0.588901	+	0.808205i	$0.700439\pi$
$84$	−5.95477	+	3.06862i	−0.649719	+	0.334814i
$85$	−1.91905			−0.208150
$86$	0.0858629	−	0.148719i	0.00925884	−	0.0160368i
$87$	−8.80662	−	15.2535i	−0.944168	−	1.63535i
$88$	−0.500000	−	0.866025i	−0.0533002	−	0.0923186i
$89$	−6.04874	+	10.4767i	−0.641165	+	1.11053i	0.344008	+	0.938967i	$0.388215\pi$
$89$	−6.04874	+	10.4767i	−0.641165	+	1.11053i	−0.985173	+	0.171564i	$0.945118\pi$
$90$	3.41082			0.359532
$91$	−5.92763	−	3.81088i	−0.621384	−	0.399488i
$92$	4.17173			0.434932
$93$	3.72551	−	6.45276i	0.386317	−	0.669120i
$94$	−4.94278	−	8.56115i	−0.509809	−	0.883015i
$95$	−2.47139	−	4.28058i	−0.253559	−	0.439178i
$96$	−1.26598	+	2.19274i	−0.129209	+	0.223796i
$97$	−11.9697			−1.21534			−0.607669	−	0.794190i	$-0.707895\pi$
$97$	−11.9697			−1.21534			−0.607669	+	0.794190i	$0.707895\pi$
$98$	−6.96808	−	0.667755i	−0.703882	−	0.0674535i
$99$	3.41082			0.342801
$100$	−0.500000	+	0.866025i	−0.0500000	+	0.0866025i
$101$	−1.63154	−	2.82591i	−0.162344	−	0.281188i	0.773365	−	0.633961i	$-0.218572\pi$
$101$	−1.63154	−	2.82591i	−0.162344	−	0.281188i	−0.935709	+	0.352773i	$0.885239\pi$
$102$	2.42948	+	4.20798i	0.240554	+	0.416652i
$103$	5.77597	−	10.0043i	0.569123	−	0.985750i	−0.427530	−	0.904001i	$-0.640616\pi$
$103$	5.77597	−	10.0043i	0.569123	−	0.985750i	0.996653	−	0.0817491i	$-0.0260506\pi$
$104$	−2.66350			−0.261178
$105$	5.63489	+	3.62267i	0.549909	+	0.353537i
$106$	−10.1888			−0.989627
$107$	−2.21740	+	3.84065i	−0.214364	+	0.371290i	−0.953076	−	0.302732i	$-0.902101\pi$
$107$	−2.21740	+	3.84065i	−0.214364	+	0.371290i	0.738711	+	0.674022i	$0.235435\pi$
$108$	−0.520094	−	0.900829i	−0.0500460	−	0.0866823i
$109$	−7.41430	−	12.8419i	−0.710161	−	1.23003i	−0.964796	−	0.262998i	$-0.915289\pi$
$109$	−7.41430	−	12.8419i	−0.710161	−	1.23003i	0.254635	−	0.967037i	$-0.418045\pi$
$110$	−0.500000	+	0.866025i	−0.0476731	+	0.0825723i
$111$	−13.8962			−1.31897
$112$	−2.35184	+	1.21195i	−0.222228	+	0.114519i
$113$	2.08413			0.196058			0.0980291	−	0.995184i	$-0.468746\pi$
$113$	2.08413			0.196058			0.0980291	+	0.995184i	$0.468746\pi$
$114$	−6.25747	+	10.8382i	−0.586065	+	1.01509i
$115$	−2.08586	−	3.61282i	−0.194508	−	0.336897i
$116$	−3.47818	−	6.02439i	−0.322941	−	0.559350i
$117$	4.54236	−	7.86760i	0.419941	−	0.727360i
$118$	−9.56552			−0.880577
$119$	−0.242449	+	5.07154i	−0.0222253	+	0.464907i
$120$	2.53196			0.231135
$121$	−0.500000	+	0.866025i	−0.0454545	+	0.0787296i
$122$	−1.07387	−	1.86000i	−0.0972239	−	0.168397i
$123$	−15.9041	−	27.5466i	−1.43402	−	2.48380i
$124$	1.47139	−	2.54852i	0.132135	−	0.228864i
$125$	1.00000			0.0894427
$126$	0.430917	−	9.01389i	0.0383891	−	0.803022i
$127$	−2.25645			−0.200227			−0.100114	−	0.994976i	$-0.531921\pi$
$127$	−2.25645			−0.200227			−0.100114	+	0.994976i	$0.531921\pi$
$128$	−0.500000	+	0.866025i	−0.0441942	+	0.0765466i
$129$	0.217402	+	0.376551i	0.0191411	+	0.0331534i
$130$	1.33175	+	2.30666i	0.116802	+	0.202307i
$131$	5.02345	−	8.70086i	0.438900	−	0.760198i	−0.558704	−	0.829367i	$-0.688701\pi$
$131$	5.02345	−	8.70086i	0.438900	−	0.760198i	0.997605	+	0.0691689i	$0.0220347\pi$
$132$	2.53196			0.220379
$133$	−11.6247	+	5.99043i	−1.00799	+	0.519436i
$134$	6.06392			0.523843
$135$	−0.520094	+	0.900829i	−0.0447625	+	0.0775310i
$136$	0.959525	+	1.66195i	0.0822786	+	0.142511i
$137$	3.48990	+	6.04468i	0.298162	+	0.516432i	0.975715	−	0.219042i	$-0.0702931\pi$
$137$	3.48990	+	6.04468i	0.298162	+	0.516432i	−0.677554	+	0.735473i	$0.736960\pi$
$138$	−5.28132	+	9.14752i	−0.449576	+	0.778688i
$139$	−0.239400			−0.0203056			−0.0101528	−	0.999948i	$-0.503232\pi$
$139$	−0.239400			−0.0203056			−0.0101528	+	0.999948i	$0.503232\pi$
$140$	2.22551	+	1.43078i	0.188090	+	0.120923i
$141$	25.0299			2.10789
$142$	−7.64312	+	13.2383i	−0.641396	+	1.11093i
$143$	1.33175	+	2.30666i	0.111366	+	0.192892i
$144$	−1.70541	−	2.95386i	−0.142118	−	0.246155i
$145$	−3.47818	+	6.02439i	−0.288847	+	0.500298i
$146$	−4.81877			−0.398804
$147$	10.2857	−	14.4338i	0.848347	−	1.19048i
$148$	−5.48832			−0.451137
$149$	−3.10596	+	5.37967i	−0.254450	+	0.440720i	−0.964746	−	0.263183i	$-0.915228\pi$
$149$	−3.10596	+	5.37967i	−0.254450	+	0.440720i	0.710296	+	0.703903i	$0.248561\pi$
$150$	−1.26598	−	2.19274i	−0.103367	−	0.179037i
$151$	2.71596	+	4.70419i	0.221022	+	0.382821i	0.955119	−	0.296224i	$-0.0957274\pi$
$151$	2.71596	+	4.70419i	0.221022	+	0.382821i	−0.734097	+	0.679045i	$0.762394\pi$
$152$	−2.47139	+	4.28058i	−0.200456	+	0.347201i
$153$	−6.54554			−0.529175
$154$	2.22551	+	1.43078i	0.179336	+	0.115295i
$155$	−2.94278			−0.236370
$156$	3.37194	−	5.84037i	0.269971	−	0.467603i
$157$	3.56880	+	6.18134i	0.284821	+	0.493324i	0.972566	−	0.232628i	$-0.0747325\pi$
$157$	3.56880	+	6.18134i	0.284821	+	0.493324i	−0.687745	+	0.725953i	$0.741399\pi$
$158$	3.14299	+	5.44383i	0.250043	+	0.433087i
$159$	12.8989	−	22.3415i	1.02295	−	1.77179i
$160$	1.00000			0.0790569
$161$	−9.81124	+	5.05594i	−0.773234	+	0.398464i
$162$	−7.59876			−0.597015
$163$	1.60739	−	2.78409i	0.125901	−	0.218067i	−0.796184	−	0.605055i	$-0.793151\pi$
$163$	1.60739	−	2.78409i	0.125901	−	0.218067i	0.922085	+	0.386988i	$0.126485\pi$
$164$	−6.28132	−	10.8796i	−0.490489	−	0.849552i
$165$	−1.26598	−	2.19274i	−0.0985564	−	0.170705i
$166$	5.36515	−	9.29271i	0.416416	−	0.721254i
$167$	−20.1012			−1.55548			−0.777740	−	0.628586i	$-0.783634\pi$
$167$	−20.1012			−1.55548			−0.777740	+	0.628586i	$0.783634\pi$
$168$	0.319883	−	6.69130i	0.0246795	−	0.516245i
$169$	−5.90577			−0.454290
$170$	0.959525	−	1.66195i	0.0735922	−	0.127465i
$171$	−8.42948	−	14.6003i	−0.644618	−	1.11651i
$172$	0.0858629	+	0.148719i	0.00654699	+	0.0113397i
$173$	−4.62461	+	8.01006i	−0.351603	+	0.608994i	−0.986530	−	0.163578i	$-0.947697\pi$
$173$	−4.62461	+	8.01006i	−0.351603	+	0.608994i	0.634928	+	0.772572i	$0.281030\pi$
$174$	17.6132			1.33526
$175$	0.126338	−	2.64273i	0.00955025	−	0.199772i
$176$	1.00000			0.0753778
$177$	12.1098	−	20.9747i	0.910225	−	1.57656i
$178$	−6.04874	−	10.4767i	−0.453372	−	0.785264i
$179$	5.67495	+	9.82931i	0.424166	+	0.734677i	0.996342	−	0.0854537i	$-0.0272340\pi$
$179$	5.67495	+	9.82931i	0.424166	+	0.734677i	−0.572176	+	0.820131i	$0.693901\pi$
$180$	−1.70541	+	2.95386i	−0.127114	+	0.220168i
$181$	4.32037			0.321131			0.160565	−	0.987025i	$-0.448668\pi$
$181$	4.32037			0.321131			0.160565	+	0.987025i	$0.448668\pi$
$182$	6.26413	−	3.22804i	0.464328	−	0.239278i
$183$	5.43801			0.401989
$184$	−2.08586	+	3.61282i	−0.153772	+	0.266341i
$185$	2.74416	+	4.75303i	0.201755	+	0.349449i
$186$	3.72551	+	6.45276i	0.273167	+	0.473140i
$187$	0.959525	−	1.66195i	0.0701674	−	0.121534i
$188$	9.88557			0.720979
$189$	2.31494	+	1.48828i	0.168387	+	0.108256i
$190$	4.94278			0.358587
$191$	−9.63145	+	16.6822i	−0.696907	+	1.20708i	0.272626	+	0.962120i	$0.412108\pi$
$191$	−9.63145	+	16.6822i	−0.696907	+	1.20708i	−0.969533	+	0.244959i	$0.921225\pi$
$192$	−1.26598	−	2.19274i	−0.0913642	−	0.158248i
$193$	7.87905	+	13.6469i	0.567147	+	0.982327i	0.996846	+	0.0793549i	$0.0252860\pi$
$193$	7.87905	+	13.6469i	0.567147	+	0.982327i	−0.429700	+	0.902972i	$0.641381\pi$
$194$	5.98485	−	10.3661i	0.429687	−	0.744240i
$195$	−6.74387			−0.482939
$196$	4.06233	−	5.70065i	0.290167	−	0.407190i
$197$	15.7806			1.12432			0.562162	−	0.827027i	$-0.309970\pi$
$197$	15.7806			1.12432			0.562162	+	0.827027i	$0.309970\pi$
$198$	−1.70541	+	2.95386i	−0.121198	+	0.209922i
$199$	−5.93914	−	10.2869i	−0.421015	−	0.729219i	0.575024	−	0.818136i	$-0.304993\pi$
$199$	−5.93914	−	10.2869i	−0.421015	−	0.729219i	−0.996039	+	0.0889175i	$0.971659\pi$
$200$	−0.500000	−	0.866025i	−0.0353553	−	0.0612372i
$201$	−7.67680	+	13.2966i	−0.541480	+	0.937871i
$202$	3.26308			0.229589
$203$	15.4814	+	9.95301i	1.08658	+	0.698565i
$204$	−4.85896			−0.340195
$205$	−6.28132	+	10.8796i	−0.438707	+	0.759862i
$206$	5.77597	+	10.0043i	0.402431	+	0.697031i
$207$	−7.11451	−	12.3227i	−0.494493	−	0.856486i
$208$	1.33175	−	2.30666i	0.0923402	−	0.159938i
$209$	4.94278			0.341899
$210$	−5.95477	+	3.06862i	−0.410918	+	0.211755i
$211$	−2.85551			−0.196581			−0.0982906	−	0.995158i	$-0.531337\pi$
$211$	−2.85551			−0.196581			−0.0982906	+	0.995158i	$0.531337\pi$
$212$	5.09442	−	8.82379i	0.349886	−	0.606020i
$213$	−19.3521	−	33.5188i	−1.32598	−	2.29667i
$214$	−2.21740	−	3.84065i	−0.151578	−	0.262542i
$215$	0.0858629	−	0.148719i	0.00585580	−	0.0101425i
$216$	1.04019			0.0707758
$217$	−0.371785	+	7.77699i	−0.0252384	+	0.527937i
$218$	14.8286			1.00432
$219$	6.10047	−	10.5663i	0.412231	−	0.714006i
$220$	−0.500000	−	0.866025i	−0.0337100	−	0.0583874i
$221$	−2.55569	−	4.42659i	−0.171915	−	0.297765i
$222$	6.94811	−	12.0345i	0.466326	−	0.807701i
$223$	−20.7876			−1.39204			−0.696020	−	0.718023i	$-0.745047\pi$
$223$	−20.7876			−1.39204			−0.696020	+	0.718023i	$0.745047\pi$
$224$	0.126338	−	2.64273i	0.00844131	−	0.176575i
$225$	3.41082			0.227388
$226$	−1.04206	+	1.80491i	−0.0693171	+	0.120061i
$227$	10.9495	+	18.9651i	0.726743	+	1.25876i	0.958253	+	0.285923i	$0.0923002\pi$
$227$	10.9495	+	18.9651i	0.726743	+	1.25876i	−0.231510	+	0.972833i	$0.574366\pi$
$228$	−6.25747	−	10.8382i	−0.414411	−	0.717781i
$229$	10.1041	−	17.5008i	0.667698	−	1.15649i	−0.310848	−	0.950460i	$-0.600613\pi$
$229$	10.1041	−	17.5008i	0.667698	−	1.15649i	0.978546	−	0.206028i	$-0.0660537\pi$
$230$	4.17173			0.275075
$231$	−5.95477	+	3.06862i	−0.391795	+	0.201900i
$232$	6.95636			0.456708
$233$	4.55205	−	7.88439i	0.298215	−	0.516523i	−0.677513	−	0.735511i	$-0.736942\pi$
$233$	4.55205	−	7.88439i	0.298215	−	0.516523i	0.975728	+	0.218988i	$0.0702754\pi$
$234$	4.54236	+	7.86760i	0.296943	+	0.514321i
$235$	−4.94278	−	8.56115i	−0.322432	−	0.558468i
$236$	4.78276	−	8.28398i	0.311331	−	0.539241i
$237$	−15.9159			−1.03385
$238$	−4.27086	−	2.74574i	−0.276838	−	0.177980i
$239$	−22.7573			−1.47205			−0.736023	−	0.676956i	$-0.763299\pi$
$239$	−22.7573			−1.47205			−0.736023	+	0.676956i	$0.763299\pi$
$240$	−1.26598	+	2.19274i	−0.0817187	+	0.141541i
$241$	9.39092	+	16.2655i	0.604922	+	1.04776i	0.992064	+	0.125736i	$0.0401291\pi$
$241$	9.39092	+	16.2655i	0.604922	+	1.04776i	−0.387142	+	0.922020i	$0.626538\pi$
$242$	−0.500000	−	0.866025i	−0.0321412	−	0.0556702i
$243$	11.1802	−	19.3646i	0.717207	−	1.24224i
$244$	2.14775			0.137495
$245$	−6.96808	−	0.667755i	−0.445174	−	0.0426613i
$246$	31.8081			2.02801
$247$	6.58255	−	11.4013i	0.418838	−	0.725448i
$248$	1.47139	+	2.54852i	0.0934335	+	0.161831i
$249$	13.5843	+	23.5288i	0.860873	+	1.49107i
$250$	−0.500000	+	0.866025i	−0.0316228	+	0.0547723i
$251$	−20.4384			−1.29006			−0.645030	−	0.764157i	$-0.723155\pi$
$251$	−20.4384			−1.29006			−0.645030	+	0.764157i	$0.723155\pi$
$252$	7.59080	+	4.88013i	0.478176	+	0.307419i
$253$	4.17173			0.262274
$254$	1.12822	−	1.95414i	0.0707911	−	0.122614i
$255$	2.42948	+	4.20798i	0.152140	+	0.263514i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	12.0756	−	20.9156i	0.753257	−	1.30468i	−0.192980	−	0.981203i	$-0.561815\pi$
$257$	12.0756	−	20.9156i	0.753257	−	1.30468i	0.946236	−	0.323476i	$-0.104852\pi$
$258$	−0.434803			−0.0270697
$259$	12.9077	−	6.65160i	0.802044	−	0.413310i
$260$	−2.66350			−0.165183
$261$	−11.8635	+	20.5481i	−0.734330	+	1.27190i
$262$	5.02345	+	8.70086i	0.310350	+	0.537541i
$263$	−5.70341	−	9.87860i	−0.351687	−	0.609140i	0.634858	−	0.772629i	$-0.281059\pi$
$263$	−5.70341	−	9.87860i	−0.351687	−	0.609140i	−0.986545	+	0.163489i	$0.947725\pi$
$264$	−1.26598	+	2.19274i	−0.0779157	+	0.134954i
$265$	−10.1888			−0.625895
$266$	0.624461	−	13.0625i	0.0382882	−	0.800911i
$267$	30.6303			1.87455
$268$	−3.03196	+	5.25151i	−0.185206	+	0.320787i
$269$	−6.47008	−	11.2065i	−0.394488	−	0.683273i	0.598548	−	0.801087i	$-0.295745\pi$
$269$	−6.47008	−	11.2065i	−0.394488	−	0.683273i	−0.993036	+	0.117814i	$0.962411\pi$
$270$	−0.520094	−	0.900829i	−0.0316519	−	0.0548227i
$271$	−7.30139	+	12.6464i	−0.443528	+	0.768213i	−0.997948	−	0.0640241i	$-0.979607\pi$
$271$	−7.30139	+	12.6464i	−0.443528	+	0.768213i	0.554421	+	0.832237i	$0.312940\pi$
$272$	−1.91905			−0.116359
$273$	−0.852007	+	17.8223i	−0.0515658	+	1.07865i
$274$	−6.97979			−0.421665
$275$	−0.500000	+	0.866025i	−0.0301511	+	0.0522233i
$276$	−5.28132	−	9.14752i	−0.317898	−	0.550616i
$277$	−9.88744	−	17.1256i	−0.594079	−	1.02897i	−0.993676	−	0.112284i	$-0.964183\pi$
$277$	−9.88744	−	17.1256i	−0.594079	−	1.02897i	0.399597	−	0.916691i	$-0.369150\pi$
$278$	0.119700	−	0.207326i	0.00717912	−	0.0124346i
$279$	−10.0373			−0.600918
$280$	−2.35184	+	1.21195i	−0.140550	+	0.0724281i
$281$	30.2233			1.80297			0.901485	−	0.432811i	$-0.142478\pi$
$281$	30.2233			1.80297			0.901485	+	0.432811i	$0.142478\pi$
$282$	−12.5149	+	21.6765i	−0.745253	+	1.29082i
$283$	−6.07720	−	10.5260i	−0.361252	−	0.625707i	0.626915	−	0.779087i	$-0.284317\pi$
$283$	−6.07720	−	10.5260i	−0.361252	−	0.625707i	−0.988167	+	0.153381i	$0.950984\pi$
$284$	−7.64312	−	13.2383i	−0.453536	−	0.785547i
$285$	−6.25747	+	10.8382i	−0.370660	+	0.642002i
$286$	−2.66350			−0.157496
$287$	27.9582	+	17.9744i	1.65032	+	1.06099i
$288$	3.41082			0.200985
$289$	6.65862	−	11.5331i	0.391684	−	0.678416i
$290$	−3.47818	−	6.02439i	−0.204246	−	0.353764i
$291$	15.1534	+	26.2465i	0.888308	+	1.53859i
$292$	2.40939	−	4.17318i	0.140999	−	0.244217i
$293$	−13.0027			−0.759626			−0.379813	−	0.925063i	$-0.624012\pi$
$293$	−13.0027			−0.759626			−0.379813	+	0.925063i	$0.624012\pi$
$294$	7.35723	+	16.1246i	0.429083	+	0.940403i
$295$	−9.56552			−0.556926
$296$	2.74416	−	4.75303i	0.159501	−	0.276264i
$297$	−0.520094	−	0.900829i	−0.0301789	−	0.0522714i
$298$	−3.10596	−	5.37967i	−0.179923	−	0.311636i
$299$	5.55569	−	9.62274i	0.321294	−	0.556498i
$300$	2.53196			0.146183
$301$	−0.382177	−	0.245702i	−0.0220283	−	0.0141620i
$302$	−5.43193			−0.312572
$303$	−4.13099	+	7.15509i	−0.237319	+	0.411049i
$304$	−2.47139	−	4.28058i	−0.141744	−	0.245508i
$305$	−1.07387	−	1.86000i	−0.0614898	−	0.106503i
$306$	3.27277	−	5.66860i	0.187092	−	0.324052i
$307$	−18.4615			−1.05365			−0.526826	−	0.849973i	$-0.676618\pi$
$307$	−18.4615			−1.05365			−0.526826	+	0.849973i	$0.676618\pi$
$308$	−2.35184	+	1.21195i	−0.134009	+	0.0690575i
$309$	−29.2491			−1.66392
$310$	1.47139	−	2.54852i	0.0835694	−	0.144746i
$311$	2.66034	+	4.60784i	0.150854	+	0.261286i	0.931542	−	0.363635i	$-0.118464\pi$
$311$	2.66034	+	4.60784i	0.150854	+	0.261286i	−0.780688	+	0.624921i	$0.785131\pi$
$312$	3.37194	+	5.84037i	0.190898	+	0.330646i
$313$	−3.22707	+	5.58944i	−0.182405	+	0.315934i	−0.942699	−	0.333645i	$-0.891721\pi$
$313$	−3.22707	+	5.58944i	−0.182405	+	0.315934i	0.760294	+	0.649579i	$0.225055\pi$
$314$	−7.13759			−0.402798
$315$	0.430917	−	9.01389i	0.0242794	−	0.507875i
$316$	−6.28599			−0.353614
$317$	2.83163	−	4.90452i	0.159040	−	0.275465i	−0.775483	−	0.631369i	$-0.782493\pi$
$317$	2.83163	−	4.90452i	0.159040	−	0.275465i	0.934523	+	0.355903i	$0.115827\pi$
$318$	12.8989	+	22.3415i	0.723332	+	1.25285i
$319$	−3.47818	−	6.02439i	−0.194741	−	0.337301i
$320$	−0.500000	+	0.866025i	−0.0279508	+	0.0484123i
$321$	11.2287			0.626727
$322$	0.527047	−	11.0248i	0.0293712	−	0.614386i
$323$	−9.48545			−0.527784
$324$	3.79938	−	6.58072i	0.211077	−	0.365595i
$325$	1.33175	+	2.30666i	0.0738722	+	0.127950i
$326$	1.60739	+	2.78409i	0.0890253	+	0.154196i
$327$	−18.7727	+	32.5153i	−1.03813	+	1.79810i
$328$	12.5626			0.693656
$329$	−23.2493	+	11.9809i	−1.28178	+	0.660526i
$330$	2.53196			0.139380
$331$	−14.9918	+	25.9666i	−0.824024	+	1.42725i	0.0786394	+	0.996903i	$0.474942\pi$
$331$	−14.9918	+	25.9666i	−0.824024	+	1.42725i	−0.902663	+	0.430348i	$0.858391\pi$
$332$	5.36515	+	9.29271i	0.294451	+	0.510004i
$333$	9.35985	+	16.2117i	0.512917	+	0.888397i
$334$	10.0506	−	17.4082i	0.549945	−	0.952533i
$335$	6.06392			0.331307
$336$	5.63489	+	3.62267i	0.307408	+	0.197633i
$337$	27.7116			1.50955			0.754773	−	0.655986i	$-0.227747\pi$
$337$	27.7116			1.50955			0.754773	+	0.655986i	$0.227747\pi$
$338$	2.95289	−	5.11455i	0.160616	−	0.278195i
$339$	−2.63846	−	4.56995i	−0.143302	−	0.248206i
$340$	0.959525	+	1.66195i	0.0520375	+	0.0901317i
$341$	1.47139	−	2.54852i	0.0796803	−	0.138010i
$342$	16.8590			0.911628
$343$	−2.64503	+	18.3304i	−0.142818	+	0.989749i
$344$	−0.171726			−0.00925884
$345$	−5.28132	+	9.14752i	−0.284337	+	0.492486i
$346$	−4.62461	−	8.01006i	−0.248621	−	0.430624i
$347$	−15.2880	−	26.4796i	−0.820704	−	1.42150i	−0.905159	−	0.425074i	$-0.860248\pi$
$347$	−15.2880	−	26.4796i	−0.820704	−	1.42150i	0.0844543	−	0.996427i	$-0.473085\pi$
$348$	−8.80662	+	15.2535i	−0.472084	+	0.817674i
$349$	−1.71721			−0.0919201			−0.0459601	−	0.998943i	$-0.514635\pi$
$349$	−1.71721			−0.0919201			−0.0459601	+	0.998943i	$0.514635\pi$
$350$	2.22551	+	1.43078i	0.118958	+	0.0764783i
$351$	−2.77054			−0.147880
$352$	−0.500000	+	0.866025i	−0.0266501	+	0.0461593i
$353$	13.9899	+	24.2313i	0.744608	+	1.28970i	0.950378	+	0.311099i	$0.100697\pi$
$353$	13.9899	+	24.2313i	0.744608	+	1.28970i	−0.205769	+	0.978601i	$0.565970\pi$
$354$	12.1098	+	20.9747i	0.643626	+	1.11479i
$355$	−7.64312	+	13.2383i	−0.405655	+	0.702614i
$356$	12.0975			0.641165
$357$	11.4275	−	5.88884i	0.604808	−	0.311670i
$358$	−11.3499			−0.599861
$359$	5.35203	−	9.26999i	0.282469	−	0.489251i	−0.689523	−	0.724264i	$-0.742180\pi$
$359$	5.35203	−	9.26999i	0.282469	−	0.489251i	0.971992	+	0.235012i	$0.0755131\pi$
$360$	−1.70541	−	2.95386i	−0.0898831	−	0.155682i
$361$	−2.71555	−	4.70348i	−0.142924	−	0.247551i
$362$	−2.16018	+	3.74155i	−0.113537	+	0.196651i
$363$	2.53196			0.132893
$364$	−0.336501	+	7.03892i	−0.0176375	+	0.368939i
$365$	−4.81877			−0.252226
$366$	−2.71900	+	4.70945i	−0.142125	+	0.246167i
$367$	9.65196	+	16.7177i	0.503828	+	0.872656i	0.999990	+	0.00442596i	$0.00140883\pi$
$367$	9.65196	+	16.7177i	0.503828	+	0.872656i	−0.496162	+	0.868230i	$0.665258\pi$
$368$	−2.08586	−	3.61282i	−0.108733	−	0.188331i
$369$	−21.4245	+	37.1083i	−1.11531	+	1.93178i
$370$	−5.48832			−0.285324
$371$	−1.28724	+	26.9264i	−0.0668300	+	1.39795i
$372$	−7.45101			−0.386317
$373$	−12.1632	+	21.0673i	−0.629788	+	1.09082i	0.357806	+	0.933796i	$0.383525\pi$
$373$	−12.1632	+	21.0673i	−0.629788	+	1.09082i	−0.987594	+	0.157028i	$0.949809\pi$
$374$	0.959525	+	1.66195i	0.0496159	+	0.0859372i
$375$	−1.26598	−	2.19274i	−0.0653749	−	0.113233i
$376$	−4.94278	+	8.56115i	−0.254905	+	0.441508i
$377$	−18.5283			−0.954254
$378$	−2.44636	+	1.26066i	−0.125827	+	0.0648413i
$379$	−1.22957			−0.0631590			−0.0315795	−	0.999501i	$-0.510054\pi$
$379$	−1.22957			−0.0631590			−0.0315795	+	0.999501i	$0.510054\pi$
$380$	−2.47139	+	4.28058i	−0.126780	+	0.219589i
$381$	2.85662	+	4.94781i	0.146349	+	0.253484i
$382$	−9.63145	−	16.6822i	−0.492788	−	0.853534i
$383$	7.72251	−	13.3758i	0.394602	−	0.683470i	−0.598449	−	0.801161i	$-0.704216\pi$
$383$	7.72251	−	13.3758i	0.394602	−	0.683470i	0.993050	+	0.117691i	$0.0375493\pi$
$384$	2.53196			0.129209
$385$	2.22551	+	1.43078i	0.113422	+	0.0729192i
$386$	−15.7581			−0.802066
$387$	0.292863	−	0.507254i	0.0148871	−	0.0257852i
$388$	5.98485	+	10.3661i	0.303835	+	0.526257i
$389$	6.02691	+	10.4389i	0.305577	+	0.529274i	0.977390	−	0.211447i	$-0.0678175\pi$
$389$	6.02691	+	10.4389i	0.305577	+	0.529274i	−0.671813	+	0.740721i	$0.734484\pi$
$390$	3.37194	−	5.84037i	0.170745	−	0.295738i
$391$	−8.00575			−0.404868
$392$	2.90575	+	6.36841i	0.146762	+	0.321653i
$393$	−25.4383			−1.28319
$394$	−7.89032	+	13.6664i	−0.397508	+	0.688505i
$395$	3.14299	+	5.44383i	0.158141	+	0.273909i
$396$	−1.70541	−	2.95386i	−0.0857001	−	0.148437i
$397$	3.33531	−	5.77693i	0.167394	−	0.289936i	−0.770109	−	0.637913i	$-0.779798\pi$
$397$	3.33531	−	5.77693i	0.167394	−	0.289936i	0.937503	+	0.347977i	$0.113131\pi$
$398$	11.8783			0.595405
$399$	27.8520	+	17.9061i	1.39435	+	0.896426i
$400$	1.00000			0.0500000
$401$	8.37379	−	14.5038i	0.418167	−	0.724286i	−0.577588	−	0.816328i	$-0.696006\pi$
$401$	8.37379	−	14.5038i	0.418167	−	0.724286i	0.995755	+	0.0920420i	$0.0293394\pi$
$402$	−7.67680	−	13.2966i	−0.382884	−	0.663175i
$403$	−3.91905	−	6.78799i	−0.195222	−	0.338134i
$404$	−1.63154	+	2.82591i	−0.0811721	+	0.140594i
$405$	−7.59876			−0.377585
$406$	−16.3603	+	8.43080i	−0.811947	+	0.418413i
$407$	−5.48832			−0.272046
$408$	2.42948	−	4.20798i	0.120277	−	0.208326i
$409$	−6.79995	−	11.7779i	−0.336236	−	0.582378i	0.647486	−	0.762078i	$-0.275821\pi$
$409$	−6.79995	−	11.7779i	−0.336236	−	0.582378i	−0.983721	+	0.179700i	$0.942487\pi$
$410$	−6.28132	−	10.8796i	−0.310212	−	0.537304i
$411$	8.83628	−	15.3049i	0.435861	−	0.754934i
$412$	−11.5519			−0.569123
$413$	−1.20849	+	25.2791i	−0.0594658	+	1.24390i
$414$	14.2290			0.699318
$415$	5.36515	−	9.29271i	0.263365	−	0.456161i
$416$	1.33175	+	2.30666i	0.0652944	+	0.113093i
$417$	0.303075	+	0.524942i	0.0148417	+	0.0257065i
$418$	−2.47139	+	4.28058i	−0.120880	+	0.209370i
$419$	30.5459			1.49227			0.746133	−	0.665797i	$-0.231908\pi$
$419$	30.5459			1.49227			0.746133	+	0.665797i	$0.231908\pi$
$420$	0.319883	−	6.69130i	0.0156087	−	0.326502i
$421$	−8.93265			−0.435351			−0.217675	−	0.976021i	$-0.569847\pi$
$421$	−8.93265			−0.435351			−0.217675	+	0.976021i	$0.569847\pi$
$422$	1.42775	−	2.47294i	0.0695020	−	0.120381i
$423$	−16.8590	−	29.2006i	−0.819711	−	1.41978i
$424$	5.09442	+	8.82379i	0.247407	+	0.428521i
$425$	0.959525	−	1.66195i	0.0465438	−	0.0806162i
$426$	38.7041			1.87522
$427$	−5.05116	+	2.60297i	−0.244443	+	0.125967i
$428$	4.43480			0.214364
$429$	3.37194	−	5.84037i	0.162799	−	0.281976i
$430$	0.0858629	+	0.148719i	0.00414068	+	0.00717187i
$431$	1.22707	+	2.12534i	0.0591057	+	0.102374i	0.894064	−	0.447939i	$-0.147842\pi$
$431$	1.22707	+	2.12534i	0.0591057	+	0.102374i	−0.834959	+	0.550313i	$0.814508\pi$
$432$	−0.520094	+	0.900829i	−0.0250230	+	0.0433411i
$433$	11.8109			0.567598			0.283799	−	0.958884i	$-0.408405\pi$
$433$	11.8109			0.567598			0.283799	+	0.958884i	$0.408405\pi$
$434$	−6.54918	−	4.21047i	−0.314371	−	0.202109i
$435$	17.6132			0.844490
$436$	−7.41430	+	12.8419i	−0.355080	+	0.615017i
$437$	−10.3100	−	17.8574i	−0.493193	−	0.854235i
$438$	6.10047	+	10.5663i	0.291492	+	0.504878i
$439$	12.8331	−	22.2276i	0.612491	−	1.06086i	−0.378329	−	0.925671i	$-0.623501\pi$
$439$	12.8331	−	22.2276i	0.612491	−	1.06086i	0.990819	−	0.135193i	$-0.0431656\pi$
$440$	1.00000			0.0476731
$441$	−23.7669	−	2.27759i	−1.13176	−	0.108457i
$442$	5.11139			0.243124
$443$	−3.43194	+	5.94430i	−0.163057	+	0.282422i	−0.935963	−	0.352097i	$-0.885469\pi$
$443$	−3.43194	+	5.94430i	−0.163057	+	0.282422i	0.772907	+	0.634519i	$0.218802\pi$
$444$	6.94811	+	12.0345i	0.329743	+	0.571131i
$445$	−6.04874	−	10.4767i	−0.286738	−	0.496644i
$446$	10.3938	−	18.0026i	0.492160	−	0.852447i
$447$	15.7283			0.743924
$448$	2.22551	+	1.43078i	0.105145	+	0.0675979i
$449$	−39.0097			−1.84098			−0.920490	−	0.390767i	$-0.872210\pi$
$449$	−39.0097			−1.84098			−0.920490	+	0.390767i	$0.872210\pi$
$450$	−1.70541	+	2.95386i	−0.0803939	+	0.139246i
$451$	−6.28132	−	10.8796i	−0.295776	−	0.512299i
$452$	−1.04206	−	1.80491i	−0.0490146	−	0.0848957i
$453$	6.87671	−	11.9108i	0.323096	−	0.559619i
$454$	−21.8990			−1.02777
$455$	6.26413	−	3.22804i	0.293667	−	0.151333i
$456$	12.5149			0.586065
$457$	−7.60963	+	13.1803i	−0.355964	+	0.616547i	−0.987282	−	0.158976i	$-0.949181\pi$
$457$	−7.60963	+	13.1803i	−0.355964	+	0.616547i	0.631319	+	0.775523i	$0.282514\pi$
$458$	10.1041	+	17.5008i	0.472134	+	0.817760i
$459$	0.998086	+	1.72873i	0.0465866	+	0.0806904i
$460$	−2.08586	+	3.61282i	−0.0972539	+	0.168449i
$461$	3.02783			0.141020			0.0705102	−	0.997511i	$-0.477537\pi$
$461$	3.02783			0.141020			0.0705102	+	0.997511i	$0.477537\pi$
$462$	0.319883	−	6.69130i	0.0148823	−	0.311307i
$463$	−8.36604			−0.388803			−0.194401	−	0.980922i	$-0.562276\pi$
$463$	−8.36604			−0.388803			−0.194401	+	0.980922i	$0.562276\pi$
$464$	−3.47818	+	6.02439i	−0.161471	+	0.279675i
$465$	3.72551	+	6.45276i	0.172766	+	0.299240i
$466$	4.55205	+	7.88439i	0.210870	+	0.365237i
$467$	18.9847	−	32.8825i	0.878508	−	1.52162i	0.0255299	−	0.999674i	$-0.491873\pi$
$467$	18.9847	−	32.8825i	0.878508	−	1.52162i	0.852978	−	0.521947i	$-0.174794\pi$
$468$	−9.08472			−0.419941
$469$	0.766104	−	16.0253i	0.0353754	−	0.739981i
$470$	9.88557			0.455987
$471$	9.03605	−	15.6509i	0.416359	−	0.721155i
$472$	4.78276	+	8.28398i	0.220144	+	0.381301i
$473$	0.0858629	+	0.148719i	0.00394798	+	0.00683811i
$474$	7.95794	−	13.7835i	0.365520	−	0.633099i
$475$	4.94278			0.226790
$476$	4.51330	−	2.32580i	0.206867	−	0.106603i
$477$	−34.7523			−1.59120
$478$	11.3786	−	19.7084i	0.520447	−	0.901440i
$479$	−17.5301	−	30.3630i	−0.800970	−	1.38732i	−0.918978	−	0.394308i	$-0.870984\pi$
$479$	−17.5301	−	30.3630i	−0.800970	−	1.38732i	0.118008	−	0.993013i	$-0.462349\pi$
$480$	−1.26598	−	2.19274i	−0.0577838	−	0.100085i
$481$	−7.30907	+	12.6597i	−0.333265	+	0.577232i
$482$	−18.7818			−0.855489
$483$	23.5072	+	15.1128i	1.06962	+	0.687656i
$484$	1.00000			0.0454545
$485$	5.98485	−	10.3661i	0.271758	−	0.470699i
$486$	11.1802	+	19.3646i	0.507142	+	0.878396i
$487$	−2.04682	−	3.54519i	−0.0927501	−	0.160648i	0.815917	−	0.578169i	$-0.196232\pi$
$487$	−2.04682	−	3.54519i	−0.0927501	−	0.160648i	−0.908667	+	0.417521i	$0.862899\pi$
$488$	−1.07387	+	1.86000i	−0.0486119	+	0.0841983i
$489$	−8.13972			−0.368091
$490$	4.06233	−	5.70065i	0.183517	−	0.257529i
$491$	11.4608			0.517219			0.258610	−	0.965982i	$-0.416736\pi$
$491$	11.4608			0.517219			0.258610	+	0.965982i	$0.416736\pi$
$492$	−15.9041	+	27.5466i	−0.717010	+	1.24190i
$493$	6.67480	+	11.5611i	0.300618	+	0.520686i
$494$	6.58255	+	11.4013i	0.296163	+	0.512969i
$495$	−1.70541	+	2.95386i	−0.0766525	+	0.132766i
$496$	−2.94278			−0.132135
$497$	34.0196	+	21.8712i	1.52599	+	0.981058i
$498$	−27.1687			−1.21746
$499$	−8.79797	+	15.2385i	−0.393851	+	0.682170i	−0.992954	−	0.118502i	$-0.962191\pi$
$499$	−8.79797	+	15.2385i	−0.393851	+	0.682170i	0.599103	+	0.800672i	$0.295524\pi$
$500$	−0.500000	−	0.866025i	−0.0223607	−	0.0387298i
$501$	25.4478	+	44.0768i	1.13692	+	1.96921i
$502$	10.2192	−	17.7002i	0.456105	−	0.789997i
$503$	40.0104			1.78397			0.891987	−	0.452061i	$-0.149311\pi$
$503$	40.0104			1.78397			0.891987	+	0.452061i	$0.149311\pi$
$504$	−8.02172	+	4.13376i	−0.357316	+	0.184132i
$505$	3.26308			0.145205
$506$	−2.08586	+	3.61282i	−0.0927279	+	0.160609i
$507$	7.47659	+	12.9498i	0.332047	+	0.575122i
$508$	1.12822	+	1.95414i	0.0500569	+	0.0867010i
$509$	8.91766	−	15.4458i	0.395268	−	0.684625i	−0.597867	−	0.801595i	$-0.703985\pi$
$509$	8.91766	−	15.4458i	0.395268	−	0.684625i	0.993135	+	0.116970i	$0.0373182\pi$
$510$	−4.85896			−0.215158
$511$	−0.608794	+	12.7347i	−0.0269315	+	0.563351i
$512$	1.00000			0.0441942
$513$	−2.57071	+	4.45260i	−0.113500	+	0.196587i
$514$	12.0756	+	20.9156i	0.532633	+	0.922547i
$515$	5.77597	+	10.0043i	0.254520	+	0.440841i
$516$	0.217402	−	0.376551i	0.00957057	−	0.0165767i
$517$	9.88557			0.434767
$518$	−0.693384	+	14.5042i	−0.0304655	+	0.637277i
$519$	23.4187			1.02797
$520$	1.33175	−	2.30666i	0.0584011	−	0.101154i
$521$	−12.1533	−	21.0501i	−0.532444	−	0.922220i	−0.999282	−	0.0378773i	$-0.987940\pi$
$521$	−12.1533	−	21.0501i	−0.532444	−	0.922220i	0.466838	−	0.884343i	$-0.345393\pi$
$522$	−11.8635	−	20.5481i	−0.519250	−	0.899367i
$523$	7.76761	−	13.4539i	0.339654	−	0.588298i	−0.644714	−	0.764424i	$-0.723023\pi$
$523$	7.76761	−	13.4539i	0.339654	−	0.588298i	0.984368	+	0.176127i	$0.0563568\pi$
$524$	−10.0469			−0.438900
$525$	−5.95477	+	3.06862i	−0.259888	+	0.133926i
$526$	11.4068			0.497361
$527$	−2.82367	+	4.89075i	−0.123001	+	0.213044i
$528$	−1.26598	−	2.19274i	−0.0550947	−	0.0954268i
$529$	2.79835	+	4.84689i	0.121667	+	0.210734i
$530$	5.09442	−	8.82379i	0.221287	−	0.383281i
$531$	−32.6263			−1.41586
$532$	11.0002	+	7.07203i	0.476919	+	0.306611i
$533$	−33.4606			−1.44934
$534$	−15.3152	+	26.5267i	−0.662752	+	1.14792i
$535$	−2.21740	−	3.84065i	−0.0958666	−	0.166046i
$536$	−3.03196	−	5.25151i	−0.130961	−	0.226831i
$537$	14.3688	−	24.8874i	0.620058	−	1.07397i
$538$	12.9402			0.557890
$539$	4.06233	−	5.70065i	0.174977	−	0.245545i
$540$	1.04019			0.0447625
$541$	16.2796	−	28.1972i	0.699916	−	1.21229i	−0.268579	−	0.963258i	$-0.586554\pi$
$541$	16.2796	−	28.1972i	0.699916	−	1.21229i	0.968495	−	0.249033i	$-0.0801127\pi$
$542$	−7.30139	−	12.6464i	−0.313621	−	0.543208i
$543$	−5.46950	−	9.47346i	−0.234719	−	0.406545i
$544$	0.959525	−	1.66195i	0.0411393	−	0.0712553i
$545$	14.8286			0.635187
$546$	−15.0085	−	9.64899i	−0.642306	−	0.412939i
$547$	−20.7303			−0.886363			−0.443182	−	0.896432i	$-0.646150\pi$
$547$	−20.7303			−0.886363			−0.443182	+	0.896432i	$0.646150\pi$
$548$	3.48990	−	6.04468i	0.149081	−	0.258216i
$549$	−3.66279	−	6.34414i	−0.156324	−	0.270761i
$550$	−0.500000	−	0.866025i	−0.0213201	−	0.0369274i
$551$	−17.1919	+	29.7772i	−0.732399	+	1.26855i
$552$	10.5626			0.449576
$553$	14.7837	−	7.61833i	0.628665	−	0.323964i
$554$	19.7749			0.840154
$555$	6.94811	−	12.0345i	0.294931	−	0.510835i
$556$	0.119700	+	0.207326i	0.00507641	+	0.00879259i
$557$	3.63977	+	6.30426i	0.154222	+	0.267120i	0.932775	−	0.360458i	$-0.117380\pi$
$557$	3.63977	+	6.30426i	0.154222	+	0.267120i	−0.778554	+	0.627578i	$0.784046\pi$
$558$	5.01866	−	8.69257i	0.212457	−	0.367986i
$559$	0.457392			0.0193456
$560$	0.126338	−	2.64273i	0.00533875	−	0.111676i
$561$	−4.85896			−0.205145
$562$	−15.1116	+	26.1741i	−0.637446	+	1.10409i
$563$	−3.56748	−	6.17906i	−0.150351	−	0.260416i	0.781005	−	0.624524i	$-0.214707\pi$
$563$	−3.56748	−	6.17906i	−0.150351	−	0.260416i	−0.931357	+	0.364108i	$0.881374\pi$
$564$	−12.5149	−	21.6765i	−0.526974	−	0.912745i
$565$	−1.04206	+	1.80491i	−0.0438400	+	0.0759330i
$566$	12.1544			0.510887
$567$	−0.960012	+	20.0815i	−0.0403167	+	0.843343i
$568$	15.2862			0.641396
$569$	20.9732	−	36.3267i	0.879243	−	1.52289i	0.0270702	−	0.999634i	$-0.491382\pi$
$569$	20.9732	−	36.3267i	0.879243	−	1.52289i	0.852173	−	0.523260i	$-0.175284\pi$
$570$	−6.25747	−	10.8382i	−0.262096	−	0.453964i
$571$	4.86587	+	8.42794i	0.203630	+	0.352698i	0.949696	−	0.313175i	$-0.101393\pi$
$571$	4.86587	+	8.42794i	0.203630	+	0.352698i	−0.746065	+	0.665873i	$0.768059\pi$
$572$	1.33175	−	2.30666i	0.0556832	−	0.0964462i
$573$	48.7729			2.03752
$574$	−29.5454	+	15.2254i	−1.23320	+	0.635494i
$575$	4.17173			0.173973
$576$	−1.70541	+	2.95386i	−0.0710588	+	0.123077i
$577$	16.8603	+	29.2028i	0.701902	+	1.21573i	0.967798	+	0.251728i	$0.0809988\pi$
$577$	16.8603	+	29.2028i	0.701902	+	1.21573i	−0.265896	+	0.964002i	$0.585668\pi$
$578$	6.65862	+	11.5331i	0.276962	+	0.479713i
$579$	19.9494	−	34.5535i	0.829071	−	1.43599i
$580$	6.95636			0.288847
$581$	−23.8803	−	15.3527i	−0.990723	−	0.636936i
$582$	−30.3068			−1.25626
$583$	5.09442	−	8.82379i	0.210989	−	0.365444i
$584$	2.40939	+	4.17318i	0.0997011	+	0.172687i
$585$	4.54236	+	7.86760i	0.187804	+	0.325285i
$586$	6.50135	−	11.2607i	0.268568	−	0.465174i
$587$	6.39398			0.263908			0.131954	−	0.991256i	$-0.457875\pi$
$587$	6.39398			0.263908			0.131954	+	0.991256i	$0.457875\pi$
$588$	−17.6429	−	1.69073i	−0.727581	−	0.0697245i
$589$	−14.5455			−0.599339
$590$	4.78276	−	8.28398i	0.196903	−	0.341046i
$591$	−19.9780	−	34.6029i	−0.821784	−	1.42337i
$592$	2.74416	+	4.75303i	0.112784	+	0.195348i
$593$	−9.77776	+	16.9356i	−0.401525	+	0.695461i	−0.993910	−	0.110194i	$-0.964853\pi$
$593$	−9.77776	+	16.9356i	−0.401525	+	0.695461i	0.592386	+	0.805655i	$0.298186\pi$
$594$	1.04019			0.0426794
$595$	−4.27086	−	2.74574i	−0.175088	−	0.112564i
$596$	6.21191			0.254450
$597$	−15.0377	+	26.0460i	−0.615451	+	1.06599i
$598$	5.55569	+	9.62274i	0.227189	+	0.393503i
$599$	12.5857	+	21.7991i	0.514238	+	0.890687i	0.999864	+	0.0165197i	$0.00525862\pi$
$599$	12.5857	+	21.7991i	0.514238	+	0.890687i	−0.485625	+	0.874167i	$0.661408\pi$
$600$	−1.26598	+	2.19274i	−0.0516834	+	0.0895183i
$601$	−35.9661			−1.46709			−0.733544	−	0.679642i	$-0.762135\pi$
$601$	−35.9661			−1.46709			−0.733544	+	0.679642i	$0.762135\pi$
$602$	0.403872	−	0.208124i	0.0164606	−	0.00848250i
$603$	20.6830			0.842275
$604$	2.71596	−	4.70419i	0.110511	−	0.191411i
$605$	−0.500000	−	0.866025i	−0.0203279	−	0.0352089i
$606$	−4.13099	−	7.15509i	−0.167810	−	0.290656i
$607$	−7.74637	+	13.4171i	−0.314416	+	0.544584i	−0.979313	−	0.202351i	$-0.935142\pi$
$607$	−7.74637	+	13.4171i	−0.314416	+	0.544584i	0.664898	+	0.746935i	$0.268475\pi$
$608$	4.94278			0.200456
$609$	2.22522	−	46.5471i	0.0901705	−	1.88618i
$610$	2.14775			0.0869597
$611$	13.1651	−	22.8026i	0.532603	−	0.922495i
$612$	3.27277	+	5.66860i	0.132294	+	0.229140i
$613$	−18.9602	−	32.8400i	−0.765795	−	1.32640i	−0.939825	−	0.341655i	$-0.889012\pi$
$613$	−18.9602	−	32.8400i	−0.765795	−	1.32640i	0.174030	−	0.984740i	$-0.444321\pi$
$614$	9.23073	−	15.9881i	0.372522	−	0.645227i
$615$	31.8081			1.28263
$616$	0.126338	−	2.64273i	0.00509030	−	0.106479i
$617$	43.5467			1.75312			0.876561	−	0.481290i	$-0.159832\pi$
$617$	43.5467			1.75312			0.876561	+	0.481290i	$0.159832\pi$
$618$	14.6245	−	25.3304i	0.588285	−	1.01894i
$619$	16.1009	+	27.8876i	0.647151	+	1.12090i	0.983800	+	0.179268i	$0.0573730\pi$
$619$	16.1009	+	27.8876i	0.647151	+	1.12090i	−0.336649	+	0.941630i	$0.609294\pi$
$620$	1.47139	+	2.54852i	0.0590925	+	0.102351i
$621$	−2.16969	+	3.75801i	−0.0870666	+	0.150804i
$622$	−5.32067			−0.213340
$623$	−28.4514	+	14.6616i	−1.13988	+	0.587404i
$624$	−6.74387			−0.269971
$625$	−0.500000	+	0.866025i	−0.0200000	+	0.0346410i
$626$	−3.22707	−	5.58944i	−0.128979	−	0.223399i
$627$	−6.25747	−	10.8382i	−0.249899	−	0.432838i
$628$	3.56880	−	6.18134i	0.142410	−	0.246662i
$629$	10.5324			0.419953
$630$	7.59080	+	4.88013i	0.302425	+	0.194429i
$631$	−10.2949			−0.409834			−0.204917	−	0.978779i	$-0.565692\pi$
$631$	−10.2949			−0.409834			−0.204917	+	0.978779i	$0.565692\pi$
$632$	3.14299	−	5.44383i	0.125022	−	0.216544i
$633$	3.61502	+	6.26139i	0.143684	+	0.248868i
$634$	2.83163	+	4.90452i	0.112458	+	0.194783i
$635$	1.12822	−	1.95414i	0.0447722	−	0.0775478i
$636$	−25.7977			−1.02295
$637$	−7.73945	−	16.9623i	−0.306648	−	0.672069i
$638$	6.95636			0.275405
$639$	−26.0693	+	45.1534i	−1.03129	+	1.78624i
$640$	−0.500000	−	0.866025i	−0.0197642	−	0.0342327i
$641$	−14.1851	−	24.5693i	−0.560278	−	0.970430i	−0.997472	−	0.0710626i	$-0.977361\pi$
$641$	−14.1851	−	24.5693i	−0.560278	−	0.970430i	0.437194	−	0.899367i	$-0.355972\pi$
$642$	−5.61437	+	9.72438i	−0.221582	+	0.383791i
$643$	38.2932			1.51014			0.755068	−	0.655647i	$-0.227604\pi$
$643$	38.2932			1.51014			0.755068	+	0.655647i	$0.227604\pi$
$644$	9.28420	+	5.96882i	0.365849	+	0.235204i
$645$	−0.434803			−0.0171204
$646$	4.74272	−	8.21464i	0.186600	−	0.323201i
$647$	−12.5302	−	21.7030i	−0.492615	−	0.853234i	0.507349	−	0.861741i	$-0.330625\pi$
$647$	−12.5302	−	21.7030i	−0.492615	−	0.853234i	−0.999964	+	0.00850686i	$0.997292\pi$
$648$	3.79938	+	6.58072i	0.149254	+	0.258515i
$649$	4.78276	−	8.28398i	0.187740	−	0.325175i
$650$	−2.66350			−0.104471
$651$	17.5236	−	9.03029i	0.686804	−	0.353925i
$652$	−3.21479			−0.125901
$653$	12.1009	−	20.9594i	0.473544	−	0.820203i	−0.525997	−	0.850486i	$-0.676308\pi$
$653$	12.1009	−	20.9594i	0.473544	−	0.820203i	0.999541	+	0.0302835i	$0.00964101\pi$
$654$	−18.7727	−	32.5153i	−0.734071	−	1.27145i
$655$	5.02345	+	8.70086i	0.196282	+	0.339971i
$656$	−6.28132	+	10.8796i	−0.245244	+	0.424776i
$657$	−16.4360			−0.641228
$658$	1.24892	−	26.1249i	0.0486881	−	1.01846i
$659$	−29.2062			−1.13771			−0.568857	−	0.822437i	$-0.692614\pi$
$659$	−29.2062			−1.13771			−0.568857	+	0.822437i	$0.692614\pi$
$660$	−1.26598	+	2.19274i	−0.0492782	+	0.0853524i
$661$	−15.3282	−	26.5492i	−0.596198	−	1.03265i	−0.993377	−	0.114904i	$-0.963344\pi$
$661$	−15.3282	−	26.5492i	−0.596198	−	1.03265i	0.397178	−	0.917742i	$-0.369990\pi$
$662$	−14.9918	−	25.9666i	−0.582673	−	1.00922i
$663$	−6.47091	+	11.2080i	−0.251310	+	0.435281i
$664$	−10.7303			−0.416416
$665$	0.624461	−	13.0625i	0.0242156	−	0.506540i
$666$	−18.7197			−0.725373
$667$	−14.5100	+	25.1321i	−0.561830	+	0.973118i
$668$	10.0506	+	17.4082i	0.388870	+	0.673543i
$669$	26.3167	+	45.5818i	1.01746	+	1.76229i
$670$	−3.03196	+	5.25151i	−0.117135	+	0.202884i
$671$	2.14775			0.0829128
$672$	−5.95477	+	3.06862i	−0.229710	+	0.118375i
$673$	5.89074			0.227071			0.113536	−	0.993534i	$-0.463782\pi$
$673$	5.89074			0.227071			0.113536	+	0.993534i	$0.463782\pi$
$674$	−13.8558	+	23.9989i	−0.533705	+	0.924405i
$675$	−0.520094	−	0.900829i	−0.0200184	−	0.0346729i
$676$	2.95289	+	5.11455i	0.113573	+	0.196713i
$677$	−21.4381	+	37.1318i	−0.823931	+	1.42709i	0.0788018	+	0.996890i	$0.474891\pi$
$677$	−21.4381	+	37.1318i	−0.823931	+	1.42709i	−0.902733	+	0.430201i	$0.858443\pi$
$678$	5.27693			0.202659
$679$	−26.6386	−	17.1260i	−1.02230	−	0.657235i
$680$	−1.91905			−0.0735922
$681$	27.7237	−	48.0188i	1.06237	−	1.84008i
$682$	1.47139	+	2.54852i	0.0563425	+	0.0975881i
$683$	17.4344	+	30.1973i	0.667110	+	1.15547i	0.978709	+	0.205254i	$0.0658022\pi$
$683$	17.4344	+	30.1973i	0.667110	+	1.15547i	−0.311599	+	0.950214i	$0.600864\pi$
$684$	−8.42948	+	14.6003i	−0.322309	+	0.558256i
$685$	−6.97979			−0.266684
$686$	−14.5521	−	11.4559i	−0.555601	−	0.437387i
$687$	−51.1664			−1.95212
$688$	0.0858629	−	0.148719i	0.00327349	−	0.00566986i
$689$	−13.5690	−	23.5021i	−0.516937	−	0.895360i
$690$	−5.28132	−	9.14752i	−0.201056	−	0.348240i
$691$	24.2671	−	42.0318i	0.923163	−	1.59897i	0.128675	−	0.991687i	$-0.458928\pi$
$691$	24.2671	−	42.0318i	0.923163	−	1.59897i	0.794489	−	0.607279i	$-0.207739\pi$
$692$	9.24923			0.351603
$693$	7.59080	+	4.88013i	0.288351	+	0.185381i
$694$	30.5761			1.16065
$695$	0.119700	−	0.207326i	0.00454048	−	0.00786433i
$696$	−8.80662	−	15.2535i	−0.333814	−	0.578183i
$697$	12.0542	+	20.8784i	0.456584	+	0.790827i
$698$	0.858605	−	1.48715i	0.0324987	−	0.0562893i
$699$	−23.0512			−0.871878
$700$	−2.35184	+	1.21195i	−0.0888913	+	0.0458076i
$701$	38.7007			1.46171			0.730853	−	0.682535i	$-0.239123\pi$
$701$	38.7007			1.46171			0.730853	+	0.682535i	$0.239123\pi$
$702$	1.38527	−	2.39936i	0.0522836	−	0.0905579i
$703$	13.5638	+	23.4932i	0.511568	+	0.886062i
$704$	−0.500000	−	0.866025i	−0.0188445	−	0.0326396i
$705$	−12.5149	+	21.6765i	−0.471340	+	0.816384i
$706$	−27.9798			−1.05304
$707$	0.412251	−	8.62344i	0.0155043	−	0.324318i
$708$	−24.2195			−0.910225
$709$	17.6245	−	30.5266i	0.661903	−	1.14645i	−0.318212	−	0.948020i	$-0.603082\pi$
$709$	17.6245	−	30.5266i	0.661903	−	1.14645i	0.980115	−	0.198430i	$-0.0635843\pi$
$710$	−7.64312	−	13.2383i	−0.286841	−	0.496823i
$711$	10.7202	+	18.5679i	0.402039	+	0.696352i
$712$	−6.04874	+	10.4767i	−0.226686	+	0.392632i
$713$	−12.2765			−0.459758
$714$	−0.613871	+	12.8409i	−0.0229735	+	0.480560i
$715$	−2.66350			−0.0996092
$716$	5.67495	−	9.82931i	0.212083	−	0.367339i
$717$	28.8103	+	49.9008i	1.07594	+	1.86358i
$718$	5.35203	+	9.26999i	0.199736	+	0.345953i
$719$	2.98337	−	5.16735i	0.111261	−	0.192710i	−0.805018	−	0.593250i	$-0.797844\pi$
$719$	2.98337	−	5.16735i	0.111261	−	0.192710i	0.916279	+	0.400541i	$0.131178\pi$
$720$	3.41082			0.127114
$721$	27.1684	−	14.0004i	1.01180	−	0.521403i
$722$	5.43111			0.202125
$723$	23.7774	−	41.1837i	0.884292	−	1.53164i
$724$	−2.16018	−	3.74155i	−0.0802826	−	0.139054i
$725$	−3.47818	−	6.02439i	−0.129176	−	0.223740i
$726$	−1.26598	+	2.19274i	−0.0469849	+	0.0813803i
$727$	39.9371			1.48119			0.740593	−	0.671954i	$-0.234545\pi$
$727$	39.9371			1.48119			0.740593	+	0.671954i	$0.234545\pi$
$728$	−5.92763	−	3.81088i	−0.219693	−	0.141240i
$729$	−33.8191			−1.25256
$730$	2.40939	−	4.17318i	0.0891754	−	0.154456i
$731$	−0.164775	−	0.285399i	−0.00609443	−	0.0105559i
$732$	−2.71900	−	4.70945i	−0.100497	−	0.174066i
$733$	−11.9516	+	20.7008i	−0.441443	+	0.764601i	−0.997797	−	0.0663440i	$-0.978867\pi$
$733$	−11.9516	+	20.7008i	−0.441443	+	0.764601i	0.556354	+	0.830945i	$0.312200\pi$
$734$	−19.3039			−0.712521
$735$	7.35723	+	16.1246i	0.271376	+	0.594763i
$736$	4.17173			0.153772
$737$	−3.03196	+	5.25151i	−0.111684	+	0.193442i
$738$	−21.4245	−	37.1083i	−0.788646	−	1.36597i
$739$	−15.7832	−	27.3373i	−0.580594	−	1.00562i	−0.995409	−	0.0957130i	$-0.969487\pi$
$739$	−15.7832	−	27.3373i	−0.580594	−	1.00562i	0.414815	−	0.909906i	$-0.363846\pi$
$740$	2.74416	−	4.75303i	0.100877	−	0.174725i
$741$	−33.3335			−1.22454
$742$	−22.6753	−	14.5780i	−0.832436	−	0.535174i
$743$	0.461089			0.0169157			0.00845786	−	0.999964i	$-0.497308\pi$
$743$	0.461089			0.0169157			0.00845786	+	0.999964i	$0.497308\pi$
$744$	3.72551	−	6.45276i	0.136584	−	0.236570i
$745$	−3.10596	−	5.37967i	−0.113793	−	0.197096i
$746$	−12.1632	−	21.0673i	−0.445327	−	0.771329i
$747$	18.2996	−	31.6958i	0.669546	−	1.15969i
$748$	−1.91905			−0.0701674
$749$	−10.4300	+	5.37478i	−0.381102	+	0.196390i
$750$	2.53196			0.0924541
$751$	−20.8122	+	36.0477i	−0.759446	+	1.31540i	0.183687	+	0.982985i	$0.441197\pi$
$751$	−20.8122	+	36.0477i	−0.759446	+	1.31540i	−0.943133	+	0.332415i	$0.892137\pi$
$752$	−4.94278	−	8.56115i	−0.180245	−	0.312193i
$753$	25.8746	+	44.8161i	0.942922	+	1.63319i
$754$	9.26413	−	16.0459i	0.337380	−	0.584359i
$755$	−5.43193			−0.197688
$756$	0.131415	−	2.74894i	0.00477952	−	0.0999779i
$757$	−21.2368			−0.771866			−0.385933	−	0.922527i	$-0.626120\pi$
$757$	−21.2368			−0.771866			−0.385933	+	0.922527i	$0.626120\pi$
$758$	0.614787	−	1.06484i	0.0223301	−	0.0386768i
$759$	−5.28132	−	9.14752i	−0.191700	−	0.332034i
$760$	−2.47139	−	4.28058i	−0.0896468	−	0.155273i
$761$	−16.0639	+	27.8235i	−0.582317	+	1.00860i	0.412887	+	0.910782i	$0.364520\pi$
$761$	−16.0639	+	27.8235i	−0.582317	+	1.00860i	−0.995204	+	0.0978200i	$0.968813\pi$
$762$	−5.71324			−0.206969
$763$	1.87342	−	39.1880i	0.0678222	−	1.41870i
$764$	19.2629			0.696907
$765$	3.27277	−	5.66860i	0.118327	−	0.204949i
$766$	7.72251	+	13.3758i	0.279026	+	0.483286i
$767$	−12.7389	−	22.0644i	−0.459974	−	0.796699i
$768$	−1.26598	+	2.19274i	−0.0456821	+	0.0791238i
$769$	−7.08472			−0.255482			−0.127741	−	0.991808i	$-0.540773\pi$
$769$	−7.08472			−0.255482			−0.127741	+	0.991808i	$0.540773\pi$
$770$	−2.35184	+	1.21195i	−0.0847545	+	0.0436758i
$771$	−61.1500			−2.20226
$772$	7.87905	−	13.6469i	0.283573	−	0.491163i
$773$	2.92539	+	5.06692i	0.105219	+	0.182245i	0.913828	−	0.406102i	$-0.133112\pi$
$773$	2.92539	+	5.06692i	0.105219	+	0.182245i	−0.808609	+	0.588347i	$0.799779\pi$
$774$	0.292863	+	0.507254i	0.0105268	+	0.0182329i
$775$	1.47139	−	2.54852i	0.0528539	−	0.0915457i
$776$	−11.9697			−0.429687
$777$	−30.9261	−	19.8824i	−1.10947	−	0.713277i
$778$	−12.0538			−0.432150
$779$	−31.0472	+	53.7754i	−1.11238	+	1.92670i
$780$	3.37194	+	5.84037i	0.120735	+	0.209119i
$781$	−7.64312	−	13.2383i	−0.273492	−	0.473702i
$782$	4.00287	−	6.93318i	0.143143	−	0.247930i
$783$	7.23592			0.258591
$784$	−6.96808	−	0.667755i	−0.248860	−	0.0238484i
$785$	−7.13759			−0.254752
$786$	12.7192	−	22.0302i	0.453678	−	0.785793i
$787$	0.159534	+	0.276320i	0.00568676	+	0.00984976i	0.868855	−	0.495067i	$-0.164857\pi$
$787$	0.159534	+	0.276320i	0.00568676	+	0.00984976i	−0.863168	+	0.504917i	$0.831523\pi$
$788$	−7.89032	−	13.6664i	−0.281081	−	0.486846i
$789$	−14.4408	+	25.0122i	−0.514106	+	0.890459i
$790$	−6.28599			−0.223645
$791$	4.63824	+	2.98193i	0.164917	+	0.106025i
$792$	3.41082			0.121198
$793$	2.86026	−	4.95411i	0.101571	−	0.175926i
$794$	3.33531	+	5.77693i	0.118366	+	0.205015i
$795$	12.8989	+	22.3415i	0.457475	+	0.792371i
$796$	−5.93914	+	10.2869i	−0.210507	+	0.364609i
$797$	−18.1255			−0.642037			−0.321018	−	0.947073i	$-0.604025\pi$
$797$	−18.1255			−0.642037			−0.321018	+	0.947073i	$0.604025\pi$
$798$	−29.4332	+	15.1675i	−1.04192	+	0.536925i
$799$	−18.9709			−0.671142
$800$	−0.500000	+	0.866025i	−0.0176777	+	0.0306186i
$801$	−20.6312	−	35.7343i	−0.728967	−	1.26261i
$802$	8.37379	+	14.5038i	0.295689	+	0.512148i
$803$	2.40939	−	4.17318i	0.0850254	−	0.147268i
$804$	15.3536			0.541480
$805$	0.527047	−	11.0248i	0.0185760	−	0.388572i
$806$	7.83810			0.276085
$807$	−16.3820	+	28.3744i	−0.576673	+	0.998827i
$808$	−1.63154	−	2.82591i	−0.0573973	−	0.0994151i
$809$	−3.61407	−	6.25975i	−0.127064	−	0.220081i	0.795474	−	0.605988i	$-0.207222\pi$
$809$	−3.61407	−	6.25975i	−0.127064	−	0.220081i	−0.922538	+	0.385907i	$0.873889\pi$
$810$	3.79938	−	6.58072i	0.133497	−	0.231223i
$811$	19.0304			0.668249			0.334125	−	0.942529i	$-0.391559\pi$
$811$	19.0304			0.668249			0.334125	+	0.942529i	$0.391559\pi$
$812$	0.878853	−	18.3838i	0.0308417	−	0.645145i
$813$	36.9736			1.29672
$814$	2.74416	−	4.75303i	0.0961828	−	0.166593i
$815$	1.60739	+	2.78409i	0.0563046	+	0.0975224i
$816$	2.42948	+	4.20798i	0.0850488	+	0.147309i
$817$	0.424402	−	0.735086i	0.0148479	−	0.0257174i
$818$	13.5999			0.475509
$819$	21.3658	−	11.0103i	0.746583	−	0.384730i
$820$	12.5626			0.438707
$821$	−21.4139	+	37.0899i	−0.747350	+	1.29445i	0.201739	+	0.979439i	$0.435341\pi$
$821$	−21.4139	+	37.0899i	−0.747350	+	1.29445i	−0.949089	+	0.315008i	$0.897993\pi$
$822$	8.83628	+	15.3049i	0.308201	+	0.533819i
$823$	−13.1001	−	22.6900i	−0.456641	−	0.790925i	0.542140	−	0.840288i	$-0.317614\pi$
$823$	−13.1001	−	22.6900i	−0.456641	−	0.790925i	−0.998781	+	0.0493633i	$0.984281\pi$
$824$	5.77597	−	10.0043i	0.201215	−	0.348515i
$825$	2.53196			0.0881515
$826$	−21.2881	−	13.6861i	−0.740708	−	0.476202i
$827$	−7.35138			−0.255633			−0.127816	−	0.991798i	$-0.540797\pi$
$827$	−7.35138			−0.255633			−0.127816	+	0.991798i	$0.540797\pi$
$828$	−7.11451	+	12.3227i	−0.247246	+	0.428243i
$829$	12.4175	+	21.5077i	0.431276	+	0.746992i	0.996983	−	0.0776142i	$-0.0247302\pi$
$829$	12.4175	+	21.5077i	0.431276	+	0.746992i	−0.565708	+	0.824606i	$0.691397\pi$
$830$	5.36515	+	9.29271i	0.186227	+	0.322555i
$831$	−25.0346	+	43.3612i	−0.868441	+	1.50418i
$832$	−2.66350			−0.0923402
$833$	−7.79582	+	10.9398i	−0.270109	+	0.379043i
$834$	−0.606151			−0.0209893
$835$	10.0506	−	17.4082i	0.347816	−	0.602435i
$836$	−2.47139	−	4.28058i	−0.0854749	−	0.148047i
$837$	1.53052	+	2.65094i	0.0529026	+	0.0916300i
$838$	−15.2730	+	26.4535i	−0.527596	+	0.913822i
$839$	−12.0972			−0.417642			−0.208821	−	0.977954i	$-0.566963\pi$
$839$	−12.0972			−0.417642			−0.208821	+	0.977954i	$0.566963\pi$
$840$	5.63489	+	3.62267i	0.194422	+	0.124994i
$841$	19.3910			0.668654
$842$	4.46632	−	7.73590i	0.153920	−	0.266597i
$843$	−38.2621	−	66.2718i	−1.31782	−	2.28252i
$844$	1.42775	+	2.47294i	0.0491453	+	0.0851222i
$845$	2.95289	−	5.11455i	0.101582	−	0.175946i
$846$	33.7179			1.15925
$847$	−2.35184	+	1.21195i	−0.0808103	+	0.0416433i
$848$	−10.1888			−0.349886
$849$	−15.3872	+	26.6514i	−0.528088	+	0.914675i
$850$	0.959525	+	1.66195i	0.0329114	+	0.0570043i
$851$	11.4479	+	19.8283i	0.392429	+	0.679706i
$852$	−19.3521	+	33.5188i	−0.662991	+	1.14833i
$853$	50.6530			1.73433			0.867163	−	0.498025i	$-0.165941\pi$
$853$	50.6530			1.73433			0.867163	+	0.498025i	$0.165941\pi$
$854$	0.271342	−	5.67592i	0.00928513	−	0.194226i
$855$	16.8590			0.576564
$856$	−2.21740	+	3.84065i	−0.0757892	+	0.131271i
$857$	−18.3127	−	31.7186i	−0.625551	−	1.08349i	−0.988434	−	0.151652i	$-0.951541\pi$
$857$	−18.3127	−	31.7186i	−0.625551	−	1.08349i	0.362883	−	0.931835i	$-0.381793\pi$
$858$	3.37194	+	5.84037i	0.115116	+	0.199387i
$859$	−1.80649	+	3.12894i	−0.0616367	+	0.106758i	−0.895197	−	0.445670i	$-0.852965\pi$
$859$	−1.80649	+	3.12894i	−0.0616367	+	0.106758i	0.833560	+	0.552428i	$0.186299\pi$
$860$	−0.171726			−0.00585580
$861$	4.01857	−	84.0604i	0.136953	−	2.86477i
$862$	−2.45413			−0.0835881
$863$	−13.0697	+	22.6374i	−0.444899	+	0.770587i	−0.998045	−	0.0624967i	$-0.980094\pi$
$863$	−13.0697	+	22.6374i	−0.444899	+	0.770587i	0.553146	+	0.833084i	$0.313427\pi$
$864$	−0.520094	−	0.900829i	−0.0176939	−	0.0306468i
$865$	−4.62461	−	8.01006i	−0.157242	−	0.272350i
$866$	−5.90547	+	10.2286i	−0.200676	+	0.347581i
$867$	−33.7187			−1.14515
$868$	6.92096	−	3.56652i	0.234913	−	0.121056i
$869$	−6.28599			−0.213238
$870$	−8.80662	+	15.2535i	−0.298572	+	0.517142i
$871$	8.07562	+	13.9874i	0.273632	+	0.473945i
$872$	−7.41430	−	12.8419i	−0.251080	−	0.434883i
$873$	20.4133	−	35.3568i	0.690884	−	1.19665i
$874$	20.6199			0.697480
$875$	2.22551	+	1.43078i	0.0752358	+	0.0483691i
$876$	−12.2009			−0.412231
$877$	14.5779	−	25.2496i	0.492259	−	0.852618i	−0.507701	−	0.861533i	$-0.669505\pi$
$877$	14.5779	−	25.2496i	0.492259	−	0.852618i	0.999960	+	0.00891545i	$0.00283791\pi$
$878$	12.8331	+	22.2276i	0.433096	+	0.750145i
$879$	16.4612	+	28.5116i	0.555221	+	0.961671i
$880$	−0.500000	+	0.866025i	−0.0168550	+	0.0291937i
$881$	45.4344			1.53072			0.765361	−	0.643601i	$-0.222560\pi$
$881$	45.4344			1.53072			0.765361	+	0.643601i	$0.222560\pi$
$882$	13.8559	−	19.4439i	0.466552	−	0.654711i
$883$	49.9297			1.68027			0.840134	−	0.542379i	$-0.182476\pi$
$883$	49.9297			1.68027			0.840134	+	0.542379i	$0.182476\pi$
$884$	−2.55569	+	4.42659i	−0.0859573	+	0.148882i
$885$	12.1098	+	20.9747i	0.407065	+	0.705057i
$886$	−3.43194	−	5.94430i	−0.115298	−	0.199703i
$887$	17.4176	−	30.1682i	0.584826	−	1.01295i	−0.410071	−	0.912054i	$-0.634496\pi$
$887$	17.4176	−	30.1682i	0.584826	−	1.01295i	0.994897	−	0.100895i	$-0.0321706\pi$
$888$	−13.8962			−0.466326
$889$	−5.02174	−	3.22848i	−0.168424	−	0.108280i
$890$	12.0975			0.405508
$891$	3.79938	−	6.58072i	0.127284	−	0.220462i
$892$	10.3938	+	18.0026i	0.348010	+	0.602771i
$893$	−24.4311	−	42.3159i	−0.817556	−	1.41605i
$894$	−7.86416	+	13.6211i	−0.263017	+	0.455558i
$895$	−11.3499			−0.379386
$896$	−2.35184	+	1.21195i	−0.0785696	+	0.0404886i
$897$	−28.1336			−0.939353
$898$	19.5048	−	33.7834i	0.650885	−	1.12737i
$899$	10.2355	+	17.7285i	0.341374	+	0.591277i
$900$	−1.70541	−	2.95386i	−0.0568470	−	0.0984620i
$901$	−9.77644	+	16.9333i	−0.325700	+	0.564130i
$902$	12.5626			0.418290
$903$	−0.0549321	+	1.14907i	−0.00182803	+	0.0382386i
$904$	2.08413			0.0693171
$905$	−2.16018	+	3.74155i	−0.0718070	+	0.124373i
$906$	6.87671	+	11.9108i	0.228463	+	0.395710i
$907$	−19.0691	−	33.0286i	−0.633178	−	1.09670i	−0.986898	−	0.161345i	$-0.948417\pi$
$907$	−19.0691	−	33.0286i	−0.633178	−	1.09670i	0.353720	−	0.935351i	$-0.384917\pi$
$908$	10.9495	−	18.9651i	0.363371	−	0.629378i
$909$	11.1298			0.369151
$910$	−0.336501	+	7.03892i	−0.0111549	+	0.233338i
$911$	2.99048			0.0990789			0.0495395	−	0.998772i	$-0.484225\pi$
$911$	2.99048			0.0990789			0.0495395	+	0.998772i	$0.484225\pi$
$912$	−6.25747	+	10.8382i	−0.207205	+	0.358890i
$913$	5.36515	+	9.29271i	0.177560	+	0.307544i
$914$	−7.60963	−	13.1803i	−0.251704	−	0.435965i
$915$	−2.71900	+	4.70945i	−0.0898875	+	0.155690i
$916$	−20.2082			−0.667698
$917$	23.6287	−	12.1764i	0.780289	−	0.402099i
$918$	−1.99617			−0.0658835
$919$	7.12839	−	12.3467i	0.235144	−	0.407281i	−0.724171	−	0.689621i	$-0.757777\pi$
$919$	7.12839	−	12.3467i	0.235144	−	0.407281i	0.959314	+	0.282340i	$0.0911105\pi$
$920$	−2.08586	−	3.61282i	−0.0687689	−	0.119111i
$921$	23.3719	+	40.4812i	0.770129	+	1.33390i
$922$	−1.51392	+	2.62218i	−0.0498582	+	0.0863570i
$923$	−40.7149			−1.34015
$924$	5.63489	+	3.62267i	0.185374	+	0.119177i
$925$	−5.48832			−0.180455
$926$	4.18302	−	7.24520i	0.137463	−	0.238092i
$927$	19.7008	+	34.1228i	0.647060	+	1.12074i
$928$	−3.47818	−	6.02439i	−0.114177	−	0.197760i
$929$	−13.8720	+	24.0270i	−0.455125	+	0.788299i	−0.998695	−	0.0510643i	$-0.983739\pi$
$929$	−13.8720	+	24.0270i	−0.455125	+	0.788299i	0.543571	+	0.839363i	$0.317072\pi$
$930$	−7.45101			−0.244328
$931$	−34.4417	−	3.30057i	−1.12878	−	0.108172i
$932$	−9.10411			−0.298215
$933$	6.73587	−	11.6669i	0.220522	−	0.381956i
$934$	18.9847	+	32.8825i	0.621199	+	1.07595i
$935$	0.959525	+	1.66195i	0.0313798	+	0.0543514i
$936$	4.54236	−	7.86760i	0.148472	−	0.257161i
$937$	−5.97284			−0.195124			−0.0975621	−	0.995229i	$-0.531104\pi$
$937$	−5.97284			−0.195124			−0.0975621	+	0.995229i	$0.531104\pi$
$938$	13.4953	+	8.67613i	0.440637	+	0.283286i
$939$	16.3416			0.533288
$940$	−4.94278	+	8.56115i	−0.161216	+	0.279234i
$941$	18.8778	+	32.6974i	0.615400	+	1.06590i	0.990314	+	0.138844i	$0.0443387\pi$
$941$	18.8778	+	32.6974i	0.615400	+	1.06590i	−0.374915	+	0.927059i	$0.622328\pi$
$942$	9.03605	+	15.6509i	0.294410	+	0.509934i
$943$	−26.2040	+	45.3866i	−0.853318	+	1.47799i
$944$	−9.56552			−0.311331
$945$	−2.44636	+	1.26066i	−0.0795800	+	0.0410093i
$946$	−0.171726			−0.00558329
$947$	8.15367	−	14.1226i	0.264959	−	0.458922i	−0.702594	−	0.711591i	$-0.747975\pi$
$947$	8.15367	−	14.1226i	0.264959	−	0.458922i	0.967553	+	0.252669i	$0.0813083\pi$
$948$	7.95794	+	13.7835i	0.258462	+	0.447669i
$949$	−6.41740	−	11.1153i	−0.208317	−	0.360816i
$950$	−2.47139	+	4.28058i	−0.0801825	+	0.138880i
$951$	−14.3391			−0.464978
$952$	−0.242449	+	5.07154i	−0.00785781	+	0.164369i
$953$	−5.26593			−0.170580			−0.0852900	−	0.996356i	$-0.527182\pi$
$953$	−5.26593			−0.170580			−0.0852900	+	0.996356i	$0.527182\pi$
$954$	17.3761	−	30.0964i	0.562574	−	0.974406i
$955$	−9.63145	−	16.6822i	−0.311666	−	0.539822i
$956$	11.3786	+	19.7084i	0.368012	+	0.637415i
$957$	−8.80662	+	15.2535i	−0.284677	+	0.493076i
$958$	35.0602			1.13274
$959$	−0.881813	+	18.4457i	−0.0284752	+	0.595644i
$960$	2.53196			0.0817187
$961$	11.1700	−	19.3470i	0.360323	−	0.624098i
$962$	−7.30907	−	12.6597i	−0.235654	−	0.408165i
$963$	−7.56316	−	13.0998i	−0.243720	−	0.422135i
$964$	9.39092	−	16.2655i	0.302461	−	0.523878i
$965$	−15.7581			−0.507271
$966$	−24.8417	+	12.8014i	−0.799268	+	0.411880i
$967$	23.3373			0.750476			0.375238	−	0.926928i	$-0.377561\pi$
$967$	23.3373			0.750476			0.375238	+	0.926928i	$0.377561\pi$
$968$	−0.500000	+	0.866025i	−0.0160706	+	0.0278351i
$969$	12.0084	+	20.7991i	0.385765	+	0.668165i
$970$	5.98485	+	10.3661i	0.192162	+	0.332834i
$971$	−6.04959	+	10.4782i	−0.194141	+	0.336261i	−0.946618	−	0.322356i	$-0.895525\pi$
$971$	−6.04959	+	10.4782i	−0.194141	+	0.336261i	0.752478	+	0.658618i	$0.228858\pi$
$972$	−22.3603			−0.717207
$973$	−0.532785	−	0.342528i	−0.0170803	−	0.0109809i
$974$	4.09363			0.131168
$975$	3.37194	−	5.84037i	0.107988	−	0.187041i
$976$	−1.07387	−	1.86000i	−0.0343738	−	0.0595372i
$977$	20.5662	+	35.6216i	0.657969	+	1.13964i	0.981140	+	0.193296i	$0.0619178\pi$
$977$	20.5662	+	35.6216i	0.657969	+	1.13964i	−0.323171	+	0.946341i	$0.604749\pi$
$978$	4.06986	−	7.04920i	0.130140	−	0.225409i
$979$	12.0975			0.386637
$980$	2.90575	+	6.36841i	0.0928206	+	0.203431i
$981$	50.5777			1.61482
$982$	−5.73041	+	9.92536i	−0.182865	+	0.316731i
$983$	−4.69847	−	8.13799i	−0.149858	−	0.259562i	0.781317	−	0.624135i	$-0.214548\pi$
$983$	−4.69847	−	8.13799i	−0.149858	−	0.259562i	−0.931175	+	0.364573i	$0.881215\pi$
$984$	−15.9041	−	27.5466i	−0.507003	−	0.878155i
$985$	−7.89032	+	13.6664i	−0.251406	+	0.435449i
$986$	−13.3496			−0.425138
$987$	55.7041	+	35.8122i	1.77308	+	1.13991i
$988$	−13.1651			−0.418838
$989$	0.358197	−	0.620415i	0.0113900	−	0.0197280i
$990$	−1.70541	−	2.95386i	−0.0542015	−	0.0938798i
$991$	3.77592	+	6.54008i	0.119946	+	0.207753i	0.919746	−	0.392514i	$-0.128395\pi$
$991$	3.77592	+	6.54008i	0.119946	+	0.207753i	−0.799800	+	0.600267i	$0.795061\pi$
$992$	1.47139	−	2.54852i	0.0467167	−	0.0809157i
$993$	75.9173			2.40916
$994$	−35.9508	+	18.5262i	−1.14029	+	0.587616i
$995$	11.8783			0.376567
$996$	13.5843	−	23.5288i	0.430436	−	0.745537i
$997$	8.51486	+	14.7482i	0.269668	+	0.467079i	0.968776	−	0.247937i	$-0.0797527\pi$
$997$	8.51486	+	14.7482i	0.269668	+	0.467079i	−0.699108	+	0.715016i	$0.746419\pi$
$998$	−8.79797	−	15.2385i	−0.278495	−	0.482367i
$999$	2.85444	−	4.94404i	0.0903105	−	0.156422i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	770.2.i.m.331.1	yes	10
7.2	even	3		5390.2.a.ci.1.5		5
7.4	even	3	inner	770.2.i.m.221.1	✓	10
7.5	odd	6		5390.2.a.ch.1.1		5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
770.2.i.m.221.1	✓	10	7.4	even	3	inner
770.2.i.m.331.1	yes	10	1.1	even	1	trivial
5390.2.a.ch.1.1		5	7.5	odd	6
5390.2.a.ci.1.5		5	7.2	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)

\(f(q)\)	\(=\)	\(q+(-0.500000 + 0.866025i) q^{2} +(-1.26598 - 2.19274i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-0.500000 + 0.866025i) q^{5} +2.53196 q^{6} +(2.22551 + 1.43078i) q^{7} +1.00000 q^{8} +(-1.70541 + 2.95386i) q^{9} +O(q^{10})\)	\(q+(-0.500000 + 0.866025i) q^{2} +(-1.26598 - 2.19274i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-0.500000 + 0.866025i) q^{5} +2.53196 q^{6} +(2.22551 + 1.43078i) q^{7} +1.00000 q^{8} +(-1.70541 + 2.95386i) q^{9} +(-0.500000 - 0.866025i) q^{10} +(-0.500000 - 0.866025i) q^{11} +(-1.26598 + 2.19274i) q^{12} -2.66350 q^{13} +(-2.35184 + 1.21195i) q^{14} +2.53196 q^{15} +(-0.500000 + 0.866025i) q^{16} +(0.959525 + 1.66195i) q^{17} +(-1.70541 - 2.95386i) q^{18} +(-2.47139 + 4.28058i) q^{19} +1.00000 q^{20} +(0.319883 - 6.69130i) q^{21} +1.00000 q^{22} +(-2.08586 + 3.61282i) q^{23} +(-1.26598 - 2.19274i) q^{24} +(-0.500000 - 0.866025i) q^{25} +(1.33175 - 2.30666i) q^{26} +1.04019 q^{27} +(0.126338 - 2.64273i) q^{28} +6.95636 q^{29} +(-1.26598 + 2.19274i) q^{30} +(1.47139 + 2.54852i) q^{31} +(-0.500000 - 0.866025i) q^{32} +(-1.26598 + 2.19274i) q^{33} -1.91905 q^{34} +(-2.35184 + 1.21195i) q^{35} +3.41082 q^{36} +(2.74416 - 4.75303i) q^{37} +(-2.47139 - 4.28058i) q^{38} +(3.37194 + 5.84037i) q^{39} +(-0.500000 + 0.866025i) q^{40} +12.5626 q^{41} +(5.63489 + 3.62267i) q^{42} -0.171726 q^{43} +(-0.500000 + 0.866025i) q^{44} +(-1.70541 - 2.95386i) q^{45} +(-2.08586 - 3.61282i) q^{46} +(-4.94278 + 8.56115i) q^{47} +2.53196 q^{48} +(2.90575 + 6.36841i) q^{49} +1.00000 q^{50} +(2.42948 - 4.20798i) q^{51} +(1.33175 + 2.30666i) q^{52} +(5.09442 + 8.82379i) q^{53} +(-0.520094 + 0.900829i) q^{54} +1.00000 q^{55} +(2.22551 + 1.43078i) q^{56} +12.5149 q^{57} +(-3.47818 + 6.02439i) q^{58} +(4.78276 + 8.28398i) q^{59} +(-1.26598 - 2.19274i) q^{60} +(-1.07387 + 1.86000i) q^{61} -2.94278 q^{62} +(-8.02172 + 4.13376i) q^{63} +1.00000 q^{64} +(1.33175 - 2.30666i) q^{65} +(-1.26598 - 2.19274i) q^{66} +(-3.03196 - 5.25151i) q^{67} +(0.959525 - 1.66195i) q^{68} +10.5626 q^{69} +(0.126338 - 2.64273i) q^{70} +15.2862 q^{71} +(-1.70541 + 2.95386i) q^{72} +(2.40939 + 4.17318i) q^{73} +(2.74416 + 4.75303i) q^{74} +(-1.26598 + 2.19274i) q^{75} +4.94278 q^{76} +(0.126338 - 2.64273i) q^{77} -6.74387 q^{78} +(3.14299 - 5.44383i) q^{79} +(-0.500000 - 0.866025i) q^{80} +(3.79938 + 6.58072i) q^{81} +(-6.28132 + 10.8796i) q^{82} -10.7303 q^{83} +(-5.95477 + 3.06862i) q^{84} -1.91905 q^{85} +(0.0858629 - 0.148719i) q^{86} +(-8.80662 - 15.2535i) q^{87} +(-0.500000 - 0.866025i) q^{88} +(-6.04874 + 10.4767i) q^{89} +3.41082 q^{90} +(-5.92763 - 3.81088i) q^{91} +4.17173 q^{92} +(3.72551 - 6.45276i) q^{93} +(-4.94278 - 8.56115i) q^{94} +(-2.47139 - 4.28058i) q^{95} +(-1.26598 + 2.19274i) q^{96} -11.9697 q^{97} +(-6.96808 - 0.667755i) q^{98} +3.41082 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

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