LMFDB - Embedded newform 403.2.h.a.222.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [403,2,Mod(118,403)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(403, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 2]))

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

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

chi := DirichletCharacter("403.118");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 403 = 13 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	403.h (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:	$3.21797120146$
Analytic rank:	$0$
Dimension:	$30$
Relative dimension:	$15$ over $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			222.3
Character	$\chi$	$=$	403.222
Dual form			403.2.h.a.118.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.19969 q^{2} +(-0.332345 + 0.575638i) q^{3} +2.83864 q^{4} +(2.12692 + 3.68393i) q^{5} +(0.731057 - 1.26623i) q^{6} +(-0.0876538 + 0.151821i) q^{7} -1.84476 q^{8} +(1.27909 + 2.21546i) q^{9} +O(q^{10})$	\(q-2.19969 q^{2} +(-0.332345 + 0.575638i) q^{3} +2.83864 q^{4} +(2.12692 + 3.68393i) q^{5} +(0.731057 - 1.26623i) q^{6} +(-0.0876538 + 0.151821i) q^{7} -1.84476 q^{8} +(1.27909 + 2.21546i) q^{9} +(-4.67856 - 8.10350i) q^{10} +(1.99067 + 3.44793i) q^{11} +(-0.943409 + 1.63403i) q^{12} +(0.500000 + 0.866025i) q^{13} +(0.192811 - 0.333959i) q^{14} -2.82748 q^{15} -1.61939 q^{16} +(3.45009 - 5.97573i) q^{17} +(-2.81361 - 4.87332i) q^{18} +(2.57950 - 4.46782i) q^{19} +(6.03756 + 10.4574i) q^{20} +(-0.0582626 - 0.100914i) q^{21} +(-4.37885 - 7.58439i) q^{22} -1.72269 q^{23} +(0.613097 - 1.06191i) q^{24} +(-6.54754 + 11.3407i) q^{25} +(-1.09985 - 1.90499i) q^{26} -3.69447 q^{27} +(-0.248818 + 0.430965i) q^{28} +0.527159 q^{29} +6.21958 q^{30} +(1.99051 - 5.19980i) q^{31} +7.25167 q^{32} -2.64635 q^{33} +(-7.58913 + 13.1448i) q^{34} -0.745729 q^{35} +(3.63089 + 6.28889i) q^{36} +(-4.16942 + 7.22166i) q^{37} +(-5.67410 + 9.82783i) q^{38} -0.664690 q^{39} +(-3.92365 - 6.79596i) q^{40} +(1.40188 + 2.42813i) q^{41} +(0.128160 + 0.221979i) q^{42} +(-0.102590 + 0.177692i) q^{43} +(5.65079 + 9.78746i) q^{44} +(-5.44105 + 9.42417i) q^{45} +3.78938 q^{46} +4.16016 q^{47} +(0.538195 - 0.932181i) q^{48} +(3.48463 + 6.03556i) q^{49} +(14.4026 - 24.9460i) q^{50} +(2.29324 + 3.97201i) q^{51} +(1.41932 + 2.45834i) q^{52} +(-3.90677 - 6.76673i) q^{53} +8.12670 q^{54} +(-8.46796 + 14.6669i) q^{55} +(0.161700 - 0.280073i) q^{56} +(1.71457 + 2.96972i) q^{57} -1.15959 q^{58} +(1.56112 - 2.70394i) q^{59} -8.02621 q^{60} -10.0722 q^{61} +(-4.37850 + 11.4380i) q^{62} -0.448469 q^{63} -12.7127 q^{64} +(-2.12692 + 3.68393i) q^{65} +5.82116 q^{66} +(-7.96137 - 13.7895i) q^{67} +(9.79357 - 16.9630i) q^{68} +(0.572527 - 0.991645i) q^{69} +1.64037 q^{70} +(4.54762 + 7.87671i) q^{71} +(-2.35962 - 4.08698i) q^{72} +(-4.77745 - 8.27478i) q^{73} +(9.17145 - 15.8854i) q^{74} +(-4.35208 - 7.53803i) q^{75} +(7.32228 - 12.6826i) q^{76} -0.697957 q^{77} +1.46211 q^{78} +(-1.03909 + 1.79975i) q^{79} +(-3.44430 - 5.96570i) q^{80} +(-2.60944 + 4.51968i) q^{81} +(-3.08370 - 5.34113i) q^{82} +(-5.42715 - 9.40010i) q^{83} +(-0.165387 - 0.286458i) q^{84} +29.3522 q^{85} +(0.225667 - 0.390867i) q^{86} +(-0.175199 + 0.303453i) q^{87} +(-3.67230 - 6.36061i) q^{88} +12.3602 q^{89} +(11.9686 - 20.7303i) q^{90} -0.175308 q^{91} -4.89010 q^{92} +(2.33167 + 2.87394i) q^{93} -9.15107 q^{94} +21.9455 q^{95} +(-2.41006 + 4.17434i) q^{96} +10.8244 q^{97} +(-7.66512 - 13.2764i) q^{98} +(-5.09250 + 8.82046i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 30 q - 6 q^{2} - 2 q^{3} + 22 q^{4} + 7 q^{5} + 6 q^{7} - 24 q^{8} - 13 q^{9}+O(q^{10}) $ 30 * q - 6 * q^2 - 2 * q^3 + 22 * q^4 + 7 * q^5 + 6 * q^7 - 24 * q^8 - 13 * q^9	\( 30 q - 6 q^{2} - 2 q^{3} + 22 q^{4} + 7 q^{5} + 6 q^{7} - 24 q^{8} - 13 q^{9} - 3 q^{10} - 3 q^{11} + 12 q^{12} + 15 q^{13} + 3 q^{14} + 4 q^{15} + 22 q^{16} + 4 q^{17} - 6 q^{18} + 5 q^{19} + 10 q^{20} - 15 q^{21} + 2 q^{22} - 6 q^{23} - 6 q^{24} - 20 q^{25} - 3 q^{26} + 4 q^{27} + 13 q^{28} + 26 q^{29} + 28 q^{30} + 19 q^{31} - 74 q^{32} + 2 q^{33} - 21 q^{34} - 30 q^{35} + 37 q^{36} - 4 q^{37} - 4 q^{38} - 4 q^{39} - 17 q^{40} + 7 q^{41} + 44 q^{42} + 15 q^{43} - 70 q^{44} + 15 q^{45} - 58 q^{46} - 24 q^{47} + 31 q^{48} - 29 q^{49} + 2 q^{50} + 25 q^{51} + 11 q^{52} + 4 q^{53} + 34 q^{54} + 13 q^{55} - 41 q^{56} + 8 q^{57} - 46 q^{58} + 27 q^{59} + 78 q^{60} + 8 q^{61} + 20 q^{62} - 112 q^{63} + 60 q^{64} - 7 q^{65} + 60 q^{66} + 29 q^{67} + 41 q^{68} - 23 q^{69} - 112 q^{70} + 29 q^{71} + 14 q^{72} - 10 q^{73} + 25 q^{74} - 18 q^{75} + 24 q^{76} - 72 q^{77} + 9 q^{79} - 11 q^{81} - 38 q^{82} - 13 q^{83} - 62 q^{84} + 108 q^{85} - 38 q^{86} - 18 q^{87} + 32 q^{88} + 6 q^{89} + 7 q^{90} + 12 q^{91} + 2 q^{92} + 37 q^{93} - 154 q^{94} - 28 q^{95} - 105 q^{96} - 84 q^{97} + 50 q^{98} + 10 q^{99}+O(q^{100}) \) 30 * q - 6 * q^2 - 2 * q^3 + 22 * q^4 + 7 * q^5 + 6 * q^7 - 24 * q^8 - 13 * q^9 - 3 * q^10 - 3 * q^11 + 12 * q^12 + 15 * q^13 + 3 * q^14 + 4 * q^15 + 22 * q^16 + 4 * q^17 - 6 * q^18 + 5 * q^19 + 10 * q^20 - 15 * q^21 + 2 * q^22 - 6 * q^23 - 6 * q^24 - 20 * q^25 - 3 * q^26 + 4 * q^27 + 13 * q^28 + 26 * q^29 + 28 * q^30 + 19 * q^31 - 74 * q^32 + 2 * q^33 - 21 * q^34 - 30 * q^35 + 37 * q^36 - 4 * q^37 - 4 * q^38 - 4 * q^39 - 17 * q^40 + 7 * q^41 + 44 * q^42 + 15 * q^43 - 70 * q^44 + 15 * q^45 - 58 * q^46 - 24 * q^47 + 31 * q^48 - 29 * q^49 + 2 * q^50 + 25 * q^51 + 11 * q^52 + 4 * q^53 + 34 * q^54 + 13 * q^55 - 41 * q^56 + 8 * q^57 - 46 * q^58 + 27 * q^59 + 78 * q^60 + 8 * q^61 + 20 * q^62 - 112 * q^63 + 60 * q^64 - 7 * q^65 + 60 * q^66 + 29 * q^67 + 41 * q^68 - 23 * q^69 - 112 * q^70 + 29 * q^71 + 14 * q^72 - 10 * q^73 + 25 * q^74 - 18 * q^75 + 24 * q^76 - 72 * q^77 + 9 * q^79 - 11 * q^81 - 38 * q^82 - 13 * q^83 - 62 * q^84 + 108 * q^85 - 38 * q^86 - 18 * q^87 + 32 * q^88 + 6 * q^89 + 7 * q^90 + 12 * q^91 + 2 * q^92 + 37 * q^93 - 154 * q^94 - 28 * q^95 - 105 * q^96 - 84 * q^97 + 50 * q^98 + 10 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/403\mathbb{Z}\right)^\times$.

$n$	$249$	$313$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$

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 $

$2$	−2.19969			−1.55542			−0.777709	−	0.628625i	$-0.783618\pi$
$2$	−2.19969			−1.55542			−0.777709	+	0.628625i	$0.783618\pi$
$3$	−0.332345	+	0.575638i	−0.191879	+	0.332345i	−0.945873	−	0.324537i	$-0.894792\pi$
$3$	−0.332345	+	0.575638i	−0.191879	+	0.332345i	0.753994	+	0.656882i	$0.228125\pi$
$4$	2.83864			1.41932
$5$	2.12692	+	3.68393i	0.951185	+	1.64750i	0.742865	+	0.669441i	$0.233466\pi$
$5$	2.12692	+	3.68393i	0.951185	+	1.64750i	0.208320	+	0.978061i	$0.433200\pi$
$6$	0.731057	−	1.26623i	0.298453	−	0.516935i
$7$	−0.0876538	+	0.151821i	−0.0331300	+	0.0573829i	−0.882115	−	0.471034i	$-0.843881\pi$
$7$	−0.0876538	+	0.151821i	−0.0331300	+	0.0573829i	0.848985	+	0.528417i	$0.177214\pi$
$8$	−1.84476			−0.652221
$9$	1.27909	+	2.21546i	0.426365	+	0.738485i
$10$	−4.67856	−	8.10350i	−1.47949	−	2.56255i
$11$	1.99067	+	3.44793i	0.600208	+	1.03959i	0.992789	+	0.119874i	$0.0382490\pi$
$11$	1.99067	+	3.44793i	0.600208	+	1.03959i	−0.392581	+	0.919718i	$0.628418\pi$
$12$	−0.943409	+	1.63403i	−0.272339	+	0.471705i
$13$	0.500000	+	0.866025i	0.138675	+	0.240192i
$13$	0.500000	+	0.866025i	0.138675	+	0.240192i
$14$	0.192811	−	0.333959i	0.0515310	−	0.0892543i
$15$	−2.82748			−0.730052
$16$	−1.61939			−0.404847
$17$	3.45009	−	5.97573i	0.836769	−	1.44933i	−0.0558125	−	0.998441i	$-0.517775\pi$
$17$	3.45009	−	5.97573i	0.836769	−	1.44933i	0.892582	−	0.450886i	$-0.148892\pi$
$18$	−2.81361	−	4.87332i	−0.663175	−	1.14865i
$19$	2.57950	−	4.46782i	0.591777	−	1.02499i	−0.402216	−	0.915545i	$-0.631760\pi$
$19$	2.57950	−	4.46782i	0.591777	−	1.02499i	0.993993	−	0.109443i	$-0.0349069\pi$
$20$	6.03756	+	10.4574i	1.35004	+	2.33834i
$21$	−0.0582626	−	0.100914i	−0.0127139	−	0.0220212i
$22$	−4.37885	−	7.58439i	−0.933574	−	1.61700i
$23$	−1.72269			−0.359205			−0.179603	−	0.983739i	$-0.557481\pi$
$23$	−1.72269			−0.359205			−0.179603	+	0.983739i	$0.557481\pi$
$24$	0.613097	−	1.06191i	0.125148	−	0.216762i
$25$	−6.54754	+	11.3407i	−1.30951	+	2.26813i
$26$	−1.09985	−	1.90499i	−0.215698	−	0.373599i
$27$	−3.69447			−0.711001
$28$	−0.248818	+	0.430965i	−0.0470222	+	0.0814448i
$29$	0.527159			0.0978910			0.0489455	−	0.998801i	$-0.484414\pi$
$29$	0.527159			0.0978910			0.0489455	+	0.998801i	$0.484414\pi$
$30$	6.21958			1.13554
$31$	1.99051	−	5.19980i	0.357505	−	0.933911i
$31$	1.99051	−	5.19980i	0.357505	−	0.933911i
$32$	7.25167			1.28193
$33$	−2.64635			−0.460671
$34$	−7.58913	+	13.1448i	−1.30153	+	2.25431i
$35$	−0.745729			−0.126051
$36$	3.63089	+	6.28889i	0.605149	+	1.04815i
$37$	−4.16942	+	7.22166i	−0.685449	+	1.18723i	0.287846	+	0.957677i	$0.407061\pi$
$37$	−4.16942	+	7.22166i	−0.685449	+	1.18723i	−0.973295	+	0.229556i	$0.926273\pi$
$38$	−5.67410	+	9.82783i	−0.920461	+	1.59428i
$39$	−0.664690			−0.106436
$40$	−3.92365	−	6.79596i	−0.620383	−	1.07454i
$41$	1.40188	+	2.42813i	0.218937	+	0.379209i	0.954483	−	0.298265i	$-0.0964079\pi$
$41$	1.40188	+	2.42813i	0.218937	+	0.379209i	−0.735546	+	0.677474i	$0.763075\pi$
$42$	0.128160	+	0.221979i	0.0197755	+	0.0342521i
$43$	−0.102590	+	0.177692i	−0.0156449	+	0.0270977i	−0.873742	−	0.486390i	$-0.838313\pi$
$43$	−0.102590	+	0.177692i	−0.0156449	+	0.0270977i	0.858097	+	0.513488i	$0.171647\pi$
$44$	5.65079	+	9.78746i	0.851889	+	1.47552i
$45$	−5.44105	+	9.42417i	−0.811103	+	1.40487i
$46$	3.78938			0.558714
$47$	4.16016			0.606822			0.303411	−	0.952860i	$-0.401875\pi$
$47$	4.16016			0.606822			0.303411	+	0.952860i	$0.401875\pi$
$48$	0.538195	−	0.932181i	0.0776818	−	0.134549i
$49$	3.48463	+	6.03556i	0.497805	+	0.862223i
$50$	14.4026	−	24.9460i	2.03683	−	3.52789i
$51$	2.29324	+	3.97201i	0.321118	+	0.556192i
$52$	1.41932	+	2.45834i	0.196825	+	0.340910i
$53$	−3.90677	−	6.76673i	−0.536636	−	0.929481i	−0.999082	−	0.0428337i	$-0.986361\pi$
$53$	−3.90677	−	6.76673i	−0.536636	−	0.929481i	0.462446	−	0.886647i	$-0.346972\pi$
$54$	8.12670			1.10590
$55$	−8.46796	+	14.6669i	−1.14182	+	1.97769i
$56$	0.161700	−	0.280073i	0.0216081	−	0.0374263i
$57$	1.71457	+	2.96972i	0.227100	+	0.393349i
$58$	−1.15959			−0.152261
$59$	1.56112	−	2.70394i	0.203241	−	0.352023i	−0.746330	−	0.665576i	$-0.768186\pi$
$59$	1.56112	−	2.70394i	0.203241	−	0.352023i	0.949571	+	0.313553i	$0.101519\pi$
$60$	−8.02621			−1.03618
$61$	−10.0722			−1.28961			−0.644805	−	0.764347i	$-0.723061\pi$
$61$	−10.0722			−1.28961			−0.644805	+	0.764347i	$0.723061\pi$
$62$	−4.37850	+	11.4380i	−0.556070	+	1.45262i
$63$	−0.448469			−0.0565018
$64$	−12.7127			−1.58908
$65$	−2.12692	+	3.68393i	−0.263811	+	0.456935i
$66$	5.82116			0.716535
$67$	−7.96137	−	13.7895i	−0.972637	−	1.68466i	−0.687524	−	0.726162i	$-0.741302\pi$
$67$	−7.96137	−	13.7895i	−0.972637	−	1.68466i	−0.285113	−	0.958494i	$-0.592031\pi$
$68$	9.79357	−	16.9630i	1.18765	−	2.05706i
$69$	0.572527	−	0.991645i	0.0689241	−	0.119380i
$70$	1.64037			0.196062
$71$	4.54762	+	7.87671i	0.539703	+	0.934793i	0.998920	+	0.0464691i	$0.0147969\pi$
$71$	4.54762	+	7.87671i	0.539703	+	0.934793i	−0.459216	+	0.888324i	$0.651870\pi$
$72$	−2.35962	−	4.08698i	−0.278084	−	0.481655i
$73$	−4.77745	−	8.27478i	−0.559158	−	0.968490i	−0.997567	−	0.0697145i	$-0.977791\pi$
$73$	−4.77745	−	8.27478i	−0.559158	−	0.968490i	0.438409	−	0.898776i	$-0.355542\pi$
$74$	9.17145	−	15.8854i	1.06616	−	1.84664i
$75$	−4.35208	−	7.53803i	−0.502535	−	0.870417i
$76$	7.32228	−	12.6826i	0.839923	−	1.45479i
$77$	−0.697957			−0.0795396
$78$	1.46211			0.165552
$79$	−1.03909	+	1.79975i	−0.116906	+	0.202488i	−0.918540	−	0.395328i	$-0.870631\pi$
$79$	−1.03909	+	1.79975i	−0.116906	+	0.202488i	0.801634	+	0.597815i	$0.203964\pi$
$80$	−3.44430	−	5.96570i	−0.385084	−	0.666985i
$81$	−2.60944	+	4.51968i	−0.289938	+	0.502187i
$82$	−3.08370	−	5.34113i	−0.340538	−	0.589829i
$83$	−5.42715	−	9.40010i	−0.595707	−	1.03180i	−0.993447	−	0.114297i	$-0.963539\pi$
$83$	−5.42715	−	9.40010i	−0.595707	−	1.03180i	0.397739	−	0.917498i	$-0.369795\pi$
$84$	−0.165387	−	0.286458i	−0.0180452	−	0.0312552i
$85$	29.3522			3.18369
$86$	0.225667	−	0.390867i	0.0243343	−	0.0421482i
$87$	−0.175199	+	0.303453i	−0.0187833	+	0.0325336i
$88$	−3.67230	−	6.36061i	−0.391469	−	0.678043i
$89$	12.3602			1.31018			0.655088	−	0.755552i	$-0.272631\pi$
$89$	12.3602			1.31018			0.655088	+	0.755552i	$0.272631\pi$
$90$	11.9686	−	20.7303i	1.26160	−	2.18516i
$91$	−0.175308			−0.0183772
$92$	−4.89010			−0.509828
$93$	2.33167	+	2.87394i	0.241783	+	0.298014i
$94$	−9.15107			−0.943861
$95$	21.9455			2.25156
$96$	−2.41006	+	4.17434i	−0.245975	+	0.426042i
$97$	10.8244			1.09905			0.549526	−	0.835477i	$-0.314809\pi$
$97$	10.8244			1.09905			0.549526	+	0.835477i	$0.314809\pi$
$98$	−7.66512	−	13.2764i	−0.774294	−	1.34112i
$99$	−5.09250	+	8.82046i	−0.511815	+	0.886490i
$100$	−18.5861	+	32.1921i	−1.85861	+	3.21921i
$101$	−7.87298			−0.783391			−0.391696	−	0.920095i	$-0.628111\pi$
$101$	−7.87298			−0.783391			−0.391696	+	0.920095i	$0.628111\pi$
$102$	−5.04442	−	8.73719i	−0.499472	−	0.865111i
$103$	−6.60127	−	11.4337i	−0.650443	−	1.12660i	−0.983016	−	0.183522i	$-0.941250\pi$
$103$	−6.60127	−	11.4337i	−0.650443	−	1.12660i	0.332573	−	0.943077i	$-0.392083\pi$
$104$	−0.922380	−	1.59761i	−0.0904468	−	0.156658i
$105$	0.247839	−	0.429270i	0.0241866	−	0.0418925i
$106$	8.59369	+	14.8847i	0.834693	+	1.44573i
$107$	2.82645	−	4.89555i	0.273243	−	0.473271i	−0.696447	−	0.717608i	$-0.745237\pi$
$107$	2.82645	−	4.89555i	0.273243	−	0.473271i	0.969690	+	0.244337i	$0.0785703\pi$
$108$	−10.4873			−1.00914
$109$	7.91332			0.757958			0.378979	−	0.925405i	$-0.376275\pi$
$109$	7.91332			0.757958			0.378979	+	0.925405i	$0.376275\pi$
$110$	18.6269	−	32.2627i	1.77600	−	3.07613i
$111$	−2.77138	−	4.80016i	−0.263047	−	0.455611i
$112$	0.141945	−	0.245856i	0.0134126	−	0.0232313i
$113$	3.07859	+	5.33228i	0.289610	+	0.501619i	0.973717	−	0.227763i	$-0.0731411\pi$
$113$	3.07859	+	5.33228i	0.289610	+	0.501619i	−0.684107	+	0.729382i	$0.739808\pi$
$114$	−3.77152	−	6.53246i	−0.353235	−	0.611821i
$115$	−3.66401	−	6.34625i	−0.341671	−	0.591791i
$116$	1.49642			0.138939
$117$	−1.27909	+	2.21546i	−0.118252	+	0.204819i
$118$	−3.43399	+	5.94784i	−0.316124	+	0.547543i
$119$	0.604826	+	1.04759i	0.0554443	+	0.0960324i
$120$	5.21602			0.476155
$121$	−2.42550	+	4.20109i	−0.220500	+	0.381918i
$122$	22.1557			2.00588
$123$	−1.86363			−0.168038
$124$	5.65034	−	14.7604i	0.507415	−	1.32552i
$125$	−34.4351			−3.07997
$126$	0.986495			0.0878839
$127$	2.85794	−	4.95010i	0.253601	−	0.439251i	−0.710913	−	0.703280i	$-0.751718\pi$
$127$	2.85794	−	4.95010i	0.253601	−	0.439251i	0.964515	+	0.264029i	$0.0850515\pi$
$128$	13.4606			1.18976
$129$	−0.0681907	−	0.118110i	−0.00600386	−	0.0103990i
$130$	4.67856	−	8.10350i	0.410337	−	0.710724i
$131$	−5.11558	+	8.86045i	−0.446950	+	0.774141i	−0.998186	−	0.0602089i	$-0.980823\pi$
$131$	−5.11558	+	8.86045i	−0.446950	+	0.774141i	0.551235	+	0.834350i	$0.314157\pi$
$132$	−7.51205			−0.653840
$133$	0.452205	+	0.783243i	0.0392112	+	0.0679157i
$134$	17.5126	+	30.3327i	1.51286	+	2.62034i
$135$	−7.85783	−	13.6102i	−0.676294	−	1.17138i
$136$	−6.36458	+	11.0238i	−0.545759	+	0.945281i
$137$	0.698375	+	1.20962i	0.0596662	+	0.103345i	0.894316	−	0.447437i	$-0.147663\pi$
$137$	0.698375	+	1.20962i	0.0596662	+	0.103345i	−0.834649	+	0.550782i	$0.814330\pi$
$138$	−1.25938	+	2.18131i	−0.107206	+	0.185686i
$139$	−10.5807			−0.897444			−0.448722	−	0.893671i	$-0.648121\pi$
$139$	−10.5807			−0.897444			−0.448722	+	0.893671i	$0.648121\pi$
$140$	−2.11686			−0.178907
$141$	−1.38261	+	2.39475i	−0.116437	+	0.201674i
$142$	−10.0034	−	17.3263i	−0.839464	−	1.45399i
$143$	−1.99067	+	3.44793i	−0.166468	+	0.288331i
$144$	−2.07135	−	3.58768i	−0.172612	−	0.298973i
$145$	1.12122	+	1.94202i	0.0931125	+	0.161276i
$146$	10.5089	+	18.2020i	0.869724	+	1.50641i
$147$	−4.63240			−0.382074
$148$	−11.8355	+	20.4997i	−0.972873	+	1.68507i
$149$	1.37587	−	2.38307i	0.112715	−	0.195229i	−0.804149	−	0.594428i	$-0.797379\pi$
$149$	1.37587	−	2.38307i	0.112715	−	0.195229i	0.916864	+	0.399199i	$0.130712\pi$
$150$	9.57324	+	16.5813i	0.781652	+	1.35386i
$151$	2.61468			0.212780			0.106390	−	0.994324i	$-0.466071\pi$
$151$	2.61468			0.212780			0.106390	+	0.994324i	$0.466071\pi$
$152$	−4.75855	+	8.24206i	−0.385970	+	0.668519i
$153$	17.6519			1.42707
$154$	1.53529			0.123717
$155$	23.3893	−	3.72665i	1.87867	−	0.299332i
$156$	−1.88682			−0.151066
$157$	0.959902			0.0766085			0.0383043	−	0.999266i	$-0.487804\pi$
$157$	0.959902			0.0766085			0.0383043	+	0.999266i	$0.487804\pi$
$158$	2.28567	−	3.95889i	0.181838	−	0.314953i
$159$	5.19358			0.411878
$160$	15.4237	+	26.7146i	1.21935	+	2.11198i
$161$	0.151000	−	0.261540i	0.0119005	−	0.0206122i
$162$	5.73997	−	9.94191i	0.450974	−	0.781111i
$163$	−6.63116			−0.519393			−0.259696	−	0.965690i	$-0.583622\pi$
$163$	−6.63116			−0.519393			−0.259696	+	0.965690i	$0.583622\pi$
$164$	3.97944	+	6.89258i	0.310742	+	0.538220i
$165$	−5.62857	−	9.74896i	−0.438183	−	0.758956i
$166$	11.9381	+	20.6773i	0.926573	+	1.60487i
$167$	−5.10281	+	8.83832i	−0.394867	+	0.683930i	−0.993084	−	0.117404i	$-0.962543\pi$
$167$	−5.10281	+	8.83832i	−0.394867	+	0.683930i	0.598217	+	0.801334i	$0.295876\pi$
$168$	0.107480	+	0.186162i	0.00829230	+	0.0143627i
$169$	−0.500000	+	0.866025i	−0.0384615	+	0.0666173i
$170$	−64.5658			−4.95197
$171$	13.1977			1.00925
$172$	−0.291217	+	0.504403i	−0.0222051	+	0.0384604i
$173$	−9.61039	−	16.6457i	−0.730664	−	1.26555i	−0.956600	−	0.291406i	$-0.905877\pi$
$173$	−9.61039	−	16.6457i	−0.730664	−	1.26555i	0.225935	−	0.974142i	$-0.427456\pi$
$174$	0.385383	−	0.667503i	0.0292158	−	0.0506033i
$175$	−1.14783	−	1.98810i	−0.0867680	−	0.150287i
$176$	−3.22366	−	5.58354i	−0.242992	−	0.420875i
$177$	1.03766	+	1.79728i	0.0779955	+	0.135092i
$178$	−27.1886			−2.03787
$179$	1.78743	−	3.09591i	0.133599	−	0.231399i	−0.791463	−	0.611217i	$-0.790680\pi$
$179$	1.78743	−	3.09591i	0.133599	−	0.231399i	0.925061	+	0.379818i	$0.124013\pi$
$180$	−15.4452	+	26.7519i	−1.15122	+	1.99397i
$181$	−0.954786	−	1.65374i	−0.0709687	−	0.122921i	0.828357	−	0.560200i	$-0.189276\pi$
$181$	−0.954786	−	1.65374i	−0.0709687	−	0.122921i	−0.899326	+	0.437279i	$0.855942\pi$
$182$	0.385623			0.0285842
$183$	3.34744	−	5.79793i	0.247450	−	0.428596i
$184$	3.17794			0.234281
$185$	−35.4721			−2.60796
$186$	−5.12895	−	6.32178i	−0.376073	−	0.463535i
$187$	27.4719			2.00894
$188$	11.8092			0.861276
$189$	0.323834	−	0.560898i	0.0235555	−	0.0407993i
$190$	−48.2733			−3.50211
$191$	9.75182	+	16.8906i	0.705617	+	1.22216i	0.966469	+	0.256785i	$0.0826632\pi$
$191$	9.75182	+	16.8906i	0.705617	+	1.22216i	−0.260852	+	0.965379i	$0.584003\pi$
$192$	4.22499	−	7.31790i	0.304913	−	0.528124i
$193$	−5.76575	+	9.98657i	−0.415028	+	0.718849i	−0.995431	−	0.0954798i	$-0.969561\pi$
$193$	−5.76575	+	9.98657i	−0.415028	+	0.718849i	0.580404	+	0.814329i	$0.302895\pi$
$194$	−23.8103			−1.70948
$195$	−1.41374	−	2.44867i	−0.101240	−	0.175353i
$196$	9.89164	+	17.1328i	0.706545	+	1.22377i
$197$	8.19239	+	14.1896i	0.583684	+	1.01097i	0.995038	+	0.0994941i	$0.0317224\pi$
$197$	8.19239	+	14.1896i	0.583684	+	1.01097i	−0.411355	+	0.911475i	$0.634944\pi$
$198$	11.2019	−	19.4023i	0.796086	−	1.37886i
$199$	−4.26588	−	7.38872i	−0.302400	−	0.523773i	0.674279	−	0.738477i	$-0.264455\pi$
$199$	−4.26588	−	7.38872i	−0.302400	−	0.523773i	−0.976679	+	0.214704i	$0.931121\pi$
$200$	12.0786	−	20.9208i	0.854088	−	1.47932i
$201$	10.5837			0.746516
$202$	17.3181			1.21850
$203$	−0.0462075	+	0.0800337i	−0.00324313	+	0.00561727i
$204$	6.50969	+	11.2751i	0.455770	+	0.789416i
$205$	−5.96335	+	10.3288i	−0.416499	+	0.721397i
$206$	14.5208	+	25.1507i	1.01171	+	1.75233i
$207$	−2.20348	−	3.81654i	−0.153152	−	0.265268i
$208$	−0.809693	−	1.40243i	−0.0561421	−	0.0972410i
$209$	20.5397			1.42076
$210$	−0.545170	+	0.944262i	−0.0376203	+	0.0651603i
$211$	7.53879	−	13.0576i	0.518992	−	0.898920i	−0.480765	−	0.876850i	$-0.659641\pi$
$211$	7.53879	−	13.0576i	0.518992	−	0.898920i	0.999756	−	0.0220704i	$-0.00702578\pi$
$212$	−11.0899	−	19.2083i	−0.761660	−	1.31923i
$213$	−6.04552			−0.414232
$214$	−6.21732	+	10.7687i	−0.425007	+	0.736134i
$215$	−0.872803			−0.0595247
$216$	6.81541			0.463730
$217$	0.614962	+	0.757982i	0.0417463	+	0.0514552i
$218$	−17.4069			−1.17894
$219$	6.35104			0.429164
$220$	−24.0375	+	41.6342i	−1.62061	+	2.80698i
$221$	6.90018			0.464156
$222$	6.09617	+	10.5589i	0.409148	+	0.708666i
$223$	14.0863	−	24.3981i	0.943286	−	1.63382i	0.184140	−	0.982900i	$-0.441050\pi$
$223$	14.0863	−	24.3981i	0.943286	−	1.63382i	0.759146	−	0.650920i	$-0.225617\pi$
$224$	−0.635636	+	1.10095i	−0.0424702	+	0.0735606i
$225$	−33.4997			−2.23331
$226$	−6.77196	−	11.7294i	−0.450464	−	0.780227i
$227$	13.6625	+	23.6642i	0.906814	+	1.57065i	0.818463	+	0.574559i	$0.194826\pi$
$227$	13.6625	+	23.6642i	0.906814	+	1.57065i	0.0883512	+	0.996089i	$0.471840\pi$
$228$	4.86704	+	8.42997i	0.322328	+	0.558288i
$229$	1.65194	−	2.86124i	0.109163	−	0.189076i	−0.806268	−	0.591550i	$-0.798516\pi$
$229$	1.65194	−	2.86124i	0.109163	−	0.189076i	0.915432	+	0.402474i	$0.131850\pi$
$230$	8.05969	+	13.9598i	0.531441	+	0.920482i
$231$	0.231963	−	0.401771i	0.0152620	−	0.0264346i
$232$	−0.972482			−0.0638466
$233$	7.08821			0.464364			0.232182	−	0.972672i	$-0.425413\pi$
$233$	7.08821			0.464364			0.232182	+	0.972672i	$0.425413\pi$
$234$	2.81361	−	4.87332i	0.183932	−	0.318579i
$235$	8.84831	+	15.3257i	0.577200	+	0.999740i
$236$	4.43147	−	7.67553i	0.288464	−	0.499635i
$237$	−0.690670	−	1.19628i	−0.0448638	−	0.0777064i
$238$	−1.33043	−	2.30438i	−0.0862391	−	0.149370i
$239$	2.08498	+	3.61129i	0.134866	+	0.233595i	0.925546	−	0.378634i	$-0.123606\pi$
$239$	2.08498	+	3.61129i	0.134866	+	0.233595i	−0.790680	+	0.612229i	$0.790273\pi$
$240$	4.57878			0.295559
$241$	2.84548	−	4.92852i	0.183294	−	0.317474i	−0.759707	−	0.650266i	$-0.774657\pi$
$241$	2.84548	−	4.92852i	0.183294	−	0.317474i	0.943000	+	0.332792i	$0.107991\pi$
$242$	5.33536	−	9.24111i	0.342970	−	0.594041i
$243$	−7.27618	−	12.6027i	−0.466767	−	0.808464i
$244$	−28.5913			−1.83037
$245$	−14.8230	+	25.6743i	−0.947009	+	1.64027i
$246$	4.09941			0.261369
$247$	5.15900			0.328259
$248$	−3.67201	+	9.59238i	−0.233173	+	0.609116i
$249$	7.21475			0.457216
$250$	75.7466			4.79063
$251$	14.1278	−	24.4701i	0.891741	−	1.54454i	0.0539535	−	0.998543i	$-0.482818\pi$
$251$	14.1278	−	24.4701i	0.891741	−	1.54454i	0.837787	−	0.545997i	$-0.183849\pi$
$252$	−1.27305			−0.0801943
$253$	−3.42930	−	5.93971i	−0.215598	−	0.373427i
$254$	−6.28660	+	10.8887i	−0.394456	+	0.683218i
$255$	−9.75505	+	16.8962i	−0.610885	+	1.05808i
$256$	−4.18387			−0.261492
$257$	7.07011	+	12.2458i	0.441021	+	0.763871i	0.997766	−	0.0668128i	$-0.0212830\pi$
$257$	7.07011	+	12.2458i	0.441021	+	0.763871i	−0.556744	+	0.830684i	$0.687950\pi$
$258$	0.149999	+	0.259805i	0.00933851	+	0.0161748i
$259$	−0.730931	−	1.26601i	−0.0454179	−	0.0786661i
$260$	−6.03756	+	10.4574i	−0.374433	+	0.648538i
$261$	0.674286	+	1.16790i	0.0417373	+	0.0722910i
$262$	11.2527	−	19.4903i	0.695194	−	1.20411i
$263$	−7.57554			−0.467128			−0.233564	−	0.972341i	$-0.575039\pi$
$263$	−7.57554			−0.467128			−0.233564	+	0.972341i	$0.575039\pi$
$264$	4.88188			0.300459
$265$	16.6187	−	28.7845i	1.02088	−	1.76822i
$266$	−0.994712	−	1.72289i	−0.0609897	−	0.105637i
$267$	−4.10785	+	7.11500i	−0.251396	+	0.435431i
$268$	−22.5995	−	39.1435i	−1.38048	−	2.39107i
$269$	−8.33135	−	14.4303i	−0.507971	−	0.879832i	−0.999957	−	0.00922889i	$-0.997062\pi$
$269$	−8.33135	−	14.4303i	−0.507971	−	0.879832i	0.491986	−	0.870603i	$-0.336271\pi$
$270$	17.2848	+	29.9382i	1.05192	+	1.82198i
$271$	1.41460			0.0859306			0.0429653	−	0.999077i	$-0.486320\pi$
$271$	1.41460			0.0859306			0.0429653	+	0.999077i	$0.486320\pi$
$272$	−5.58702	+	9.67701i	−0.338763	+	0.586755i
$273$	0.0582626	−	0.100914i	0.00352621	−	0.00610758i
$274$	−1.53621	−	2.66079i	−0.0928059	−	0.160745i
$275$	−52.1358			−3.14391
$276$	1.62520	−	2.81493i	0.0978255	−	0.169439i
$277$	−23.1279			−1.38962			−0.694809	−	0.719194i	$-0.744511\pi$
$277$	−23.1279			−1.38962			−0.694809	+	0.719194i	$0.744511\pi$
$278$	23.2743			1.39590
$279$	14.0660	−	2.24115i	0.842107	−	0.134174i
$280$	1.37569			0.0822132
$281$	25.4511			1.51829			0.759143	−	0.650924i	$-0.225618\pi$
$281$	25.4511			1.51829			0.759143	+	0.650924i	$0.225618\pi$
$282$	3.04131	−	5.26771i	0.181108	−	0.313687i
$283$	26.8673			1.59709			0.798547	−	0.601932i	$-0.205602\pi$
$283$	26.8673			1.59709			0.798547	+	0.601932i	$0.205602\pi$
$284$	12.9091	+	22.3592i	0.766013	+	1.32677i
$285$	−7.29348	+	12.6327i	−0.432028	+	0.748295i
$286$	4.37885	−	7.58439i	0.258927	−	0.448475i
$287$	−0.491520			−0.0290135
$288$	9.27556	+	16.0657i	0.546568	+	0.946683i
$289$	−15.3062	−	26.5111i	−0.900366	−	1.55948i
$290$	−2.46635	−	4.27184i	−0.144829	−	0.250851i
$291$	−3.59743	+	6.23094i	−0.210885	+	0.365264i
$292$	−13.5615	−	23.4892i	−0.793625	−	1.37460i
$293$	−3.36946	+	5.83608i	−0.196846	+	0.340948i	−0.947504	−	0.319743i	$-0.896403\pi$
$293$	−3.36946	+	5.83608i	−0.196846	+	0.340948i	0.750658	+	0.660691i	$0.229737\pi$
$294$	10.1899			0.594285
$295$	13.2815			0.773279
$296$	7.69159	−	13.3222i	0.447064	−	0.774338i
$297$	−7.35446	−	12.7383i	−0.426749	−	0.739151i
$298$	−3.02648	+	5.24202i	−0.175319	+	0.303662i
$299$	−0.861344	−	1.49189i	−0.0498128	−	0.0862783i
$300$	−12.3540	−	21.3978i	−0.713260	−	1.23540i
$301$	−0.0179848	−	0.0311507i	−0.00103663	−	0.00179549i
$302$	−5.75150			−0.330961
$303$	2.61655	−	4.53199i	0.150317	−	0.260356i
$304$	−4.17720	+	7.23513i	−0.239579	+	0.414963i
$305$	−21.4227	−	37.1051i	−1.22666	−	2.12463i
$306$	−38.8288			−2.21970
$307$	−3.15191	+	5.45926i	−0.179889	+	0.311577i	−0.941842	−	0.336055i	$-0.890907\pi$
$307$	−3.15191	+	5.45926i	−0.179889	+	0.311577i	0.761953	+	0.647632i	$0.224240\pi$
$308$	−1.98125			−0.112892
$309$	8.77560			0.499226
$310$	−51.4493	+	8.19749i	−2.92212	+	0.465586i
$311$	3.68406			0.208904			0.104452	−	0.994530i	$-0.466691\pi$
$311$	3.68406			0.208904			0.104452	+	0.994530i	$0.466691\pi$
$312$	1.22619			0.0694195
$313$	−1.75059	+	3.03211i	−0.0989491	+	0.171385i	−0.911250	−	0.411854i	$-0.864881\pi$
$313$	−1.75059	+	3.03211i	−0.0989491	+	0.171385i	0.812301	+	0.583239i	$0.198215\pi$
$314$	−2.11149			−0.119158
$315$	−0.953857	−	1.65213i	−0.0537437	−	0.0930869i
$316$	−2.94959	+	5.10885i	−0.165928	+	0.287395i
$317$	−8.03891	+	13.9238i	−0.451510	+	0.782039i	−0.998480	−	0.0551134i	$-0.982448\pi$
$317$	−8.03891	+	13.9238i	−0.451510	+	0.782039i	0.546970	+	0.837152i	$0.315781\pi$
$318$	−11.4243			−0.640642
$319$	1.04940	+	1.81761i	0.0587550	+	0.101767i
$320$	−27.0388	−	46.8325i	−1.51151	−	2.61802i
$321$	1.87871	+	3.25402i	0.104859	+	0.181622i
$322$	−0.332154	+	0.575307i	−0.0185102	+	0.0320606i
$323$	−17.7990	−	30.8287i	−0.990362	−	1.71536i
$324$	−7.40728	+	12.8298i	−0.411515	+	0.712765i
$325$	−13.0951			−0.726384
$326$	14.5865			0.807872
$327$	−2.62995	+	4.55521i	−0.145437	+	0.251904i
$328$	−2.58613	−	4.47931i	−0.142795	−	0.247328i
$329$	−0.364654	+	0.631599i	−0.0201040	+	0.0348212i
$330$	12.3811	+	21.4447i	0.681558	+	1.18049i
$331$	−6.87814	−	11.9133i	−0.378057	−	0.654814i	0.612723	−	0.790298i	$-0.290074\pi$
$331$	−6.87814	−	11.9133i	−0.378057	−	0.654814i	−0.990779	+	0.135484i	$0.956741\pi$
$332$	−15.4058	−	26.6835i	−0.845500	−	1.46445i
$333$	−21.3323			−1.16900
$334$	11.2246	−	19.4416i	0.614183	−	1.06380i
$335$	33.8663	−	58.6582i	1.85032	−	3.20484i
$336$	0.0943496	+	0.163418i	0.00514719	+	0.00891520i
$337$	30.1022			1.63977			0.819887	−	0.572526i	$-0.194036\pi$
$337$	30.1022			1.63977			0.819887	+	0.572526i	$0.194036\pi$
$338$	1.09985	−	1.90499i	0.0598237	−	0.103618i
$339$	−4.09262			−0.222281
$340$	83.3204			4.51868
$341$	21.8910	−	3.48792i	1.18546	−	0.188882i
$342$	−29.0308			−1.56981
$343$	−2.44892			−0.132229
$344$	0.189254	−	0.327798i	0.0102039	−	0.0176737i
$345$	4.87086			0.262238
$346$	21.1399	+	36.6154i	1.13649	+	1.96845i
$347$	0.366543	−	0.634871i	0.0196771	−	0.0340817i	−0.856019	−	0.516944i	$-0.827070\pi$
$347$	0.366543	−	0.634871i	0.0196771	−	0.0340817i	0.875696	+	0.482862i	$0.160403\pi$
$348$	−0.497327	+	0.861396i	−0.0266595	+	0.0461757i
$349$	4.39134			0.235063			0.117532	−	0.993069i	$-0.462502\pi$
$349$	4.39134			0.235063			0.117532	+	0.993069i	$0.462502\pi$
$350$	2.52488	+	4.37322i	0.134960	+	0.233758i
$351$	−1.84724	−	3.19951i	−0.0985982	−	0.170777i
$352$	14.4357	+	25.0033i	0.769423	+	1.33268i
$353$	−17.7697	+	30.7780i	−0.945785	+	1.63815i	−0.191613	+	0.981471i	$0.561372\pi$
$353$	−17.7697	+	30.7780i	−0.945785	+	1.63815i	−0.754172	+	0.656677i	$0.771961\pi$
$354$	−2.28254	−	3.95347i	−0.121315	−	0.210125i
$355$	−19.3448	+	33.5062i	−1.02672	+	1.77832i
$356$	35.0862			1.85956
$357$	−0.804044			−0.0425545
$358$	−3.93179	+	6.81005i	−0.207801	+	0.359923i
$359$	3.26882	+	5.66177i	0.172522	+	0.298817i	0.939301	−	0.343095i	$-0.111475\pi$
$359$	3.26882	+	5.66177i	0.172522	+	0.298817i	−0.766779	+	0.641911i	$0.778142\pi$
$360$	10.0374	−	17.3853i	0.529019	−	0.916287i
$361$	−3.80761	−	6.59498i	−0.200401	−	0.347104i
$362$	2.10024	+	3.63771i	0.110386	+	0.191194i
$363$	−1.61221	−	2.79243i	−0.0846190	−	0.146564i
$364$	−0.497636			−0.0260832
$365$	20.3225	−	35.1995i	1.06373	−	1.84243i
$366$	−7.36333	+	12.7537i	−0.384888	+	0.666645i
$367$	16.5992	+	28.7507i	0.866472	+	1.50077i	0.865578	+	0.500774i	$0.166951\pi$
$367$	16.5992	+	28.7507i	0.866472	+	1.50077i	0.000894480		1.00000i	$0.499715\pi$
$368$	2.78970			0.145423
$369$	−3.58627	+	6.21160i	−0.186694	+	0.323363i
$370$	78.0276			4.05646
$371$	1.36977			0.0711150
$372$	6.61878	+	8.15809i	0.343168	+	0.422977i
$373$	−8.70439			−0.450696			−0.225348	−	0.974278i	$-0.572352\pi$
$373$	−8.70439			−0.450696			−0.225348	+	0.974278i	$0.572352\pi$
$374$	−60.4297			−3.12475
$375$	11.4443	−	19.8222i	0.590983	−	1.02361i
$376$	−7.67450			−0.395782
$377$	0.263580	+	0.456533i	0.0135750	+	0.0235127i
$378$	−0.712336	+	1.23380i	−0.0366386	+	0.0634599i
$379$	1.11846	−	1.93722i	0.0574513	−	0.0995085i	−0.835869	−	0.548928i	$-0.815036\pi$
$379$	1.11846	−	1.93722i	0.0574513	−	0.0995085i	0.893321	+	0.449420i	$0.148369\pi$
$380$	62.2955			3.19569
$381$	1.89965	+	3.29028i	0.0973219	+	0.168566i
$382$	−21.4510	−	37.1542i	−1.09753	−	1.90097i
$383$	1.85479	+	3.21260i	0.0947755	+	0.164156i	0.909515	−	0.415671i	$-0.136453\pi$
$383$	1.85479	+	3.21260i	0.0947755	+	0.164156i	−0.814739	+	0.579827i	$0.803120\pi$
$384$	−4.47357	+	7.74845i	−0.228291	+	0.395411i
$385$	−1.48450	−	2.57122i	−0.0756569	−	0.131042i
$386$	12.6829	−	21.9674i	0.645541	−	1.11811i
$387$	−0.524890			−0.0266817
$388$	30.7266			1.55991
$389$	15.2247	−	26.3700i	0.771925	−	1.33701i	−0.164582	−	0.986363i	$-0.552628\pi$
$389$	15.2247	−	26.3700i	0.771925	−	1.33701i	0.936507	−	0.350649i	$-0.114039\pi$
$390$	3.10979	+	5.38632i	0.157470	+	0.272747i
$391$	−5.94342	+	10.2943i	−0.300572	+	0.520606i
$392$	−6.42831	−	11.1342i	−0.324679	−	0.562360i
$393$	−3.40028	−	5.88945i	−0.171521	−	0.297084i
$394$	−18.0207	−	31.2128i	−0.907871	−	1.57248i
$395$	−8.84019			−0.444798
$396$	−14.4558	+	25.0382i	−0.726431	+	1.25821i
$397$	−0.0708522	+	0.122720i	−0.00355597	+	0.00615912i	−0.867798	−	0.496917i	$-0.834465\pi$
$397$	−0.0708522	+	0.122720i	−0.00355597	+	0.00615912i	0.864242	+	0.503076i	$0.167799\pi$
$398$	9.38362	+	16.2529i	0.470359	+	0.814685i
$399$	−0.601153			−0.0300953
$400$	10.6030	−	18.3649i	0.530150	−	0.918246i
$401$	−10.2005			−0.509388			−0.254694	−	0.967022i	$-0.581975\pi$
$401$	−10.2005			−0.509388			−0.254694	+	0.967022i	$0.581975\pi$
$402$	−23.2809			−1.16114
$403$	5.49841	−	0.876070i	0.273895	−	0.0436401i
$404$	−22.3486			−1.11188
$405$	−22.2002			−1.10314
$406$	0.101642	−	0.176050i	0.00504442	−	0.00873719i
$407$	−33.1997			−1.64565
$408$	−4.23048	−	7.32740i	−0.209440	−	0.362760i
$409$	−1.97707	+	3.42438i	−0.0977597	+	0.169325i	−0.910757	−	0.412943i	$-0.864501\pi$
$409$	−1.97707	+	3.42438i	−0.0977597	+	0.169325i	0.812997	+	0.582267i	$0.197834\pi$
$410$	13.1175	−	22.7203i	0.647829	−	1.12207i
$411$	−0.928406			−0.0457949
$412$	−18.7387	−	32.4563i	−0.923188	−	1.59901i
$413$	0.273676	+	0.474021i	0.0134667	+	0.0233251i
$414$	4.84697	+	8.39521i	0.238216	+	0.412602i
$415$	23.0862	−	39.9864i	1.13326	−	1.96286i
$416$	3.62584	+	6.28013i	0.177771	+	0.307909i
$417$	3.51645	−	6.09066i	0.172201	−	0.298261i
$418$	−45.1810			−2.20987
$419$	−40.6189			−1.98437			−0.992183	−	0.124794i	$-0.960173\pi$
$419$	−40.6189			−1.98437			−0.992183	+	0.124794i	$0.960173\pi$
$420$	0.703527	−	1.21855i	0.0343286	−	0.0594589i
$421$	−5.10322	−	8.83903i	−0.248716	−	0.430788i	0.714454	−	0.699682i	$-0.246675\pi$
$421$	−5.10322	−	8.83903i	−0.248716	−	0.430788i	−0.963170	+	0.268894i	$0.913342\pi$
$422$	−16.5830	+	28.7226i	−0.807249	+	1.39820i
$423$	5.32123	+	9.21665i	0.258727	+	0.448129i
$424$	7.20705	+	12.4830i	0.350005	+	0.606227i
$425$	45.1792	+	78.2526i	2.19151	+	3.79581i
$426$	13.2983			0.644303
$427$	0.882864	−	1.52917i	0.0427248	−	0.0740015i
$428$	8.02328	−	13.8967i	0.387820	−	0.671724i
$429$	−1.32318	−	2.29181i	−0.0638835	−	0.110650i
$430$	1.91990			0.0925857
$431$	−6.84249	+	11.8515i	−0.329591	+	0.570868i	−0.982431	−	0.186628i	$-0.940244\pi$
$431$	−6.84249	+	11.8515i	−0.329591	+	0.570868i	0.652840	+	0.757496i	$0.273577\pi$
$432$	5.98278			0.287846
$433$	34.9188			1.67809			0.839045	−	0.544062i	$-0.183115\pi$
$433$	34.9188			1.67809			0.839045	+	0.544062i	$0.183115\pi$
$434$	−1.35273	−	1.66733i	−0.0649329	−	0.0800342i
$435$	−1.49053			−0.0714655
$436$	22.4631			1.07579
$437$	−4.44367	+	7.69666i	−0.212569	+	0.368181i
$438$	−13.9703			−0.667529
$439$	−5.95008	−	10.3058i	−0.283982	−	0.491871i	0.688380	−	0.725350i	$-0.258322\pi$
$439$	−5.95008	−	10.3058i	−0.283982	−	0.491871i	−0.972362	+	0.233480i	$0.924989\pi$
$440$	15.6213	−	27.0570i	0.744718	−	1.28989i
$441$	−8.91434	+	15.4401i	−0.424493	+	0.735243i
$442$	−15.1783			−0.721956
$443$	11.4799	+	19.8838i	0.545428	+	0.944710i	0.998580	+	0.0532762i	$0.0169664\pi$
$443$	11.4799	+	19.8838i	0.545428	+	0.944710i	−0.453151	+	0.891434i	$0.649700\pi$
$444$	−7.86695	−	13.6260i	−0.373349	−	0.646659i
$445$	26.2891	+	45.5340i	1.24622	+	2.15852i
$446$	−30.9855	+	53.6684i	−1.46720	+	2.54127i
$447$	0.914525	+	1.58400i	0.0432555	+	0.0749208i
$448$	1.11431	−	1.93005i	0.0526463	−	0.0911861i
$449$	−3.44611			−0.162632			−0.0813161	−	0.996688i	$-0.525912\pi$
$449$	−3.44611			−0.162632			−0.0813161	+	0.996688i	$0.525912\pi$
$450$	73.6889			3.47373
$451$	−5.58134	+	9.66717i	−0.262815	+	0.455209i
$452$	8.73904	+	15.1365i	0.411050	+	0.711959i
$453$	−0.868977	+	1.50511i	−0.0408281	+	0.0707163i
$454$	−30.0534	−	52.0540i	−1.41047	−	2.44301i
$455$	−0.372864	−	0.645820i	−0.0174801	−	0.0302765i
$456$	−3.16296	−	5.47841i	−0.148119	−	0.256550i
$457$	−1.13720			−0.0531961			−0.0265980	−	0.999646i	$-0.508467\pi$
$457$	−1.13720			−0.0531961			−0.0265980	+	0.999646i	$0.508467\pi$
$458$	−3.63376	+	6.29386i	−0.169794	+	0.294093i
$459$	−12.7463	+	22.0772i	−0.594944	+	1.03047i
$460$	−10.4008	−	18.0148i	−0.484941	−	0.839942i
$461$	24.6611			1.14858			0.574291	−	0.818651i	$-0.305278\pi$
$461$	24.6611			1.14858			0.574291	+	0.818651i	$0.305278\pi$
$462$	−0.510246	+	0.883773i	−0.0237388	+	0.0411168i
$463$	−12.3351			−0.573260			−0.286630	−	0.958041i	$-0.592535\pi$
$463$	−12.3351			−0.573260			−0.286630	+	0.958041i	$0.592535\pi$
$464$	−0.853674			−0.0396308
$465$	−5.62811	+	14.7023i	−0.260998	+	0.681804i
$466$	−15.5919			−0.722280
$467$	15.3487			0.710251			0.355125	−	0.934819i	$-0.384438\pi$
$467$	15.3487			0.710251			0.355125	+	0.934819i	$0.384438\pi$
$468$	−3.63089	+	6.28889i	−0.167838	+	0.290704i
$469$	2.79138			0.128894
$470$	−19.4636	−	33.7119i	−0.897787	−	1.55501i
$471$	−0.319019	+	0.552557i	−0.0146996	+	0.0254605i
$472$	−2.87989	+	4.98812i	−0.132558	+	0.229597i
$473$	−0.816892			−0.0375607
$474$	1.51926	+	2.63144i	0.0697819	+	0.120866i
$475$	33.7787	+	58.5065i	1.54987	+	2.68446i
$476$	1.71689	+	2.97374i	0.0786934	+	0.136301i
$477$	9.99425	−	17.3105i	0.457605	−	0.792596i
$478$	−4.58631	−	7.94373i	−0.209773	−	0.363338i
$479$	7.11391	−	12.3216i	0.325043	−	0.562990i	−0.656478	−	0.754345i	$-0.727955\pi$
$479$	7.11391	−	12.3216i	0.325043	−	0.562990i	0.981521	+	0.191354i	$0.0612880\pi$
$480$	−20.5039			−0.935873
$481$	−8.33885			−0.380219
$482$	−6.25918	+	10.8412i	−0.285098	+	0.493804i
$483$	0.100368	+	0.173843i	0.00456691	+	0.00791012i
$484$	−6.88514	+	11.9254i	−0.312961	+	0.542064i
$485$	23.0226	+	39.8763i	1.04540	+	1.81069i
$486$	16.0053	+	27.7221i	0.726017	+	1.25750i
$487$	−2.32414	−	4.02553i	−0.105317	−	0.182414i	0.808551	−	0.588426i	$-0.200252\pi$
$487$	−2.32414	−	4.02553i	−0.105317	−	0.182414i	−0.913868	+	0.406012i	$0.866919\pi$
$488$	18.5807			0.841111
$489$	2.20383	−	3.81715i	0.0996608	−	0.172618i
$490$	32.6061	−	56.4755i	1.47299	−	2.55130i
$491$	0.714985	+	1.23839i	0.0322668	+	0.0558878i	0.881708	−	0.471796i	$-0.156394\pi$
$491$	0.714985	+	1.23839i	0.0322668	+	0.0558878i	−0.849441	+	0.527684i	$0.823061\pi$
$492$	−5.29018			−0.238500
$493$	1.81875	−	3.15016i	0.0819122	−	0.141876i
$494$	−11.3482			−0.510580
$495$	−43.3252			−1.94732
$496$	−3.22340	+	8.42048i	−0.144735	+	0.378091i
$497$	−1.59446			−0.0715215
$498$	−15.8702			−0.711162
$499$	−10.3469	+	17.9213i	−0.463190	+	0.802269i	−0.999118	−	0.0419951i	$-0.986629\pi$
$499$	−10.3469	+	17.9213i	−0.463190	+	0.802269i	0.535928	+	0.844264i	$0.319962\pi$
$500$	−97.7490			−4.37147
$501$	−3.39179	−	5.87475i	−0.151534	−	0.262464i
$502$	−31.0769	+	53.8267i	−1.38703	+	2.40240i
$503$	−13.9315	+	24.1300i	−0.621173	+	1.07590i	0.368095	+	0.929788i	$0.380010\pi$
$503$	−13.9315	+	24.1300i	−0.621173	+	1.07590i	−0.989268	+	0.146115i	$0.953323\pi$
$504$	0.827318			0.0368517
$505$	−16.7452	−	29.0035i	−0.745150	−	1.29064i
$506$	7.54339	+	13.0655i	0.335345	+	0.580834i
$507$	−0.332345	−	0.575638i	−0.0147600	−	0.0255650i
$508$	8.11269	−	14.0516i	0.359942	−	0.623438i
$509$	−6.27520	−	10.8690i	−0.278143	−	0.481758i	0.692780	−	0.721149i	$-0.256386\pi$
$509$	−6.27520	−	10.8690i	−0.278143	−	0.481758i	−0.970923	+	0.239391i	$0.923052\pi$
$510$	21.4581	−	37.1665i	0.950181	−	1.64576i
$511$	1.67505			0.0740996
$512$	−17.7180			−0.783033
$513$	−9.52988	+	16.5062i	−0.420755	+	0.728768i
$514$	−15.5521	−	26.9370i	−0.685972	−	1.18814i
$515$	28.0807	−	48.6372i	1.23738	−	2.14321i
$516$	−0.193569	−	0.335272i	−0.00852141	−	0.0147595i
$517$	8.28149	+	14.3440i	0.364220	+	0.630847i
$518$	1.60782	+	2.78483i	0.0706437	+	0.122359i
$519$	12.7759			0.560798
$520$	3.92365	−	6.79596i	0.172063	−	0.298022i
$521$	−3.73936	+	6.47676i	−0.163824	+	0.283752i	−0.936237	−	0.351369i	$-0.885716\pi$
$521$	−3.73936	+	6.47676i	−0.163824	+	0.283752i	0.772413	+	0.635121i	$0.219050\pi$
$522$	−1.48322	−	2.56901i	−0.0649188	−	0.112443i
$523$	6.87275			0.300525			0.150262	−	0.988646i	$-0.451988\pi$
$523$	6.87275			0.300525			0.150262	+	0.988646i	$0.451988\pi$
$524$	−14.5213	+	25.1517i	−0.634367	+	1.09876i
$525$	1.52591			0.0665960
$526$	16.6639			0.726578
$527$	−24.2051	−	29.8345i	−1.05439	−	1.29961i
$528$	4.28547			0.186501
$529$	−20.0323			−0.870972
$530$	−36.5561	+	63.3170i	−1.58790	+	2.75032i
$531$	7.98728			0.346619
$532$	1.28365	+	2.22335i	0.0556533	+	0.0963943i
$533$	−1.40188	+	2.42813i	−0.0607221	+	0.105174i
$534$	9.03599	−	15.6508i	0.391026	−	0.677276i
$535$	24.0465			1.03962
$536$	14.6868	+	25.4383i	0.634374	+	1.09877i
$537$	1.18808	+	2.05782i	0.0512696	+	0.0888016i
$538$	18.3264	+	31.7422i	0.790107	+	1.36851i
$539$	−13.8735	+	24.0296i	−0.597573	+	1.03503i
$540$	−22.3056	−	38.6344i	−0.959879	−	1.66256i
$541$	−2.67977	+	4.64150i	−0.115212	+	0.199554i	−0.917865	−	0.396894i	$-0.870088\pi$
$541$	−2.67977	+	4.64150i	−0.115212	+	0.199554i	0.802652	+	0.596447i	$0.203422\pi$
$542$	−3.11168			−0.133658
$543$	1.26927			0.0544697
$544$	25.0189	−	43.3340i	1.07268	−	1.85793i
$545$	16.8310	+	29.1521i	0.720959	+	1.24874i
$546$	−0.128160	+	0.221979i	−0.00548473	+	0.00949983i
$547$	1.77141	+	3.06817i	0.0757399	+	0.131185i	0.901408	−	0.432971i	$-0.142535\pi$
$547$	1.77141	+	3.06817i	0.0757399	+	0.131185i	−0.825668	+	0.564156i	$0.809201\pi$
$548$	1.98244	+	3.43369i	0.0846856	+	0.146680i
$549$	−12.8833	−	22.3145i	−0.549844	−	0.952358i
$550$	114.683			4.89009
$551$	1.35981	−	2.35525i	0.0579297	−	0.100337i
$552$	−1.05617	+	1.82935i	−0.0449538	+	0.0778622i
$553$	−0.182159	−	0.315509i	−0.00774621	−	0.0134168i
$554$	50.8742			2.16144
$555$	11.7890	−	20.4191i	0.500414	−	0.866742i
$556$	−30.0349			−1.27376
$557$	27.0832			1.14755			0.573775	−	0.819013i	$-0.305478\pi$
$557$	27.0832			1.14755			0.573775	+	0.819013i	$0.305478\pi$
$558$	−30.9408	+	4.92984i	−1.30983	+	0.208697i
$559$	−0.205181			−0.00867821
$560$	1.20762			0.0510314
$561$	−9.13015	+	15.8139i	−0.385475	+	0.667662i
$562$	−55.9846			−2.36157
$563$	−19.6526	−	34.0393i	−0.828257	−	1.43458i	−0.899404	−	0.437118i	$-0.855999\pi$
$563$	−19.6526	−	34.0393i	−0.828257	−	1.43458i	0.0711470	−	0.997466i	$-0.477334\pi$
$564$	−3.92473	+	6.79784i	−0.165261	+	0.286241i
$565$	−13.0958	+	22.6826i	−0.550945	+	0.954265i
$566$	−59.0997			−2.48415
$567$	−0.457455	−	0.792335i	−0.0192113	−	0.0332749i
$568$	−8.38927	−	14.5306i	−0.352006	−	0.609692i
$569$	−0.0719497	−	0.124621i	−0.00301629	−	0.00522437i	0.864513	−	0.502610i	$-0.167627\pi$
$569$	−0.0719497	−	0.124621i	−0.00301629	−	0.00522437i	−0.867530	+	0.497386i	$0.834293\pi$
$570$	16.0434	−	27.7880i	0.671984	−	1.16391i
$571$	−3.86922	−	6.70169i	−0.161922	−	0.280457i	0.773636	−	0.633630i	$-0.218436\pi$
$571$	−3.86922	−	6.70169i	−0.161922	−	0.280457i	−0.935558	+	0.353173i	$0.885103\pi$
$572$	−5.65079	+	9.78746i	−0.236272	+	0.409234i
$573$	−12.9639			−0.541573
$574$	1.08119			0.0451281
$575$	11.2794	−	19.5364i	0.470382	−	0.814725i
$576$	−16.2607	−	28.1643i	−0.677529	−	1.17351i
$577$	3.39968	−	5.88842i	0.141530	−	0.245138i	−0.786543	−	0.617536i	$-0.788131\pi$
$577$	3.39968	−	5.88842i	0.141530	−	0.245138i	0.928073	+	0.372398i	$0.121464\pi$
$578$	33.6690	+	58.3163i	1.40044	+	2.42564i
$579$	−3.83244	−	6.63798i	−0.159271	−	0.275865i
$580$	3.18275	+	5.51269i	0.132157	+	0.228902i
$581$	1.90284			0.0789431
$582$	7.91325	−	13.7061i	0.328015	−	0.568138i
$583$	15.5542	−	26.9406i	0.644187	−	1.11576i
$584$	8.81324	+	15.2650i	0.364695	+	0.631670i
$585$	−10.8821			−0.449919
$586$	7.41178	−	12.8376i	0.306178	−	0.530316i
$587$	13.7975			0.569483			0.284742	−	0.958604i	$-0.408092\pi$
$587$	13.7975			0.569483			0.284742	+	0.958604i	$0.408092\pi$
$588$	−13.1497			−0.542286
$589$	−18.0973	−	22.3061i	−0.745684	−	0.919106i
$590$	−29.2152			−1.20277
$591$	−10.8908			−0.447988
$592$	6.75191	−	11.6946i	0.277502	−	0.480647i
$593$	4.59830			0.188829			0.0944147	−	0.995533i	$-0.469902\pi$
$593$	4.59830			0.188829			0.0944147	+	0.995533i	$0.469902\pi$
$594$	16.1775	+	28.0203i	0.663773	+	1.14969i
$595$	−2.57283	+	4.45627i	−0.105476	+	0.182689i
$596$	3.90560	−	6.76469i	0.159979	−	0.277093i
$597$	5.67098			0.232098
$598$	1.89469	+	3.28170i	0.0774797	+	0.134199i
$599$	−0.227400	−	0.393868i	−0.00929130	−	0.0160930i	0.861342	−	0.508025i	$-0.169624\pi$
$599$	−0.227400	−	0.393868i	−0.00929130	−	0.0160930i	−0.870634	+	0.491932i	$0.836291\pi$
$600$	8.02855	+	13.9059i	0.327764	+	0.567704i
$601$	12.6698	−	21.9448i	0.516813	−	0.895146i	−0.482996	−	0.875622i	$-0.660452\pi$
$601$	12.6698	−	21.9448i	0.516813	−	0.895146i	0.999809	−	0.0195239i	$-0.00621506\pi$
$602$	0.0395611	+	0.0685219i	0.00161239	+	0.00279274i
$603$	20.3667	−	35.2761i	0.829395	−	1.43656i
$604$	7.42216			0.302003
$605$	−20.6354			−0.838947
$606$	−5.75560	+	9.96899i	−0.233805	+	0.404962i
$607$	−19.5865	−	33.9249i	−0.794993	−	1.37697i	−0.922844	−	0.385174i	$-0.874141\pi$
$607$	−19.5865	−	33.9249i	−0.794993	−	1.37697i	0.127851	−	0.991793i	$-0.459192\pi$
$608$	18.7057	−	32.3992i	0.758615	−	1.31396i
$609$	−0.0307137	−	0.0531976i	−0.00124458	−	0.00215568i
$610$	47.1233	+	81.6199i	1.90797	+	3.30469i
$611$	2.08008	+	3.60280i	0.0841510	+	0.145754i
$612$	50.1076			2.02548
$613$	−10.8560	+	18.8032i	−0.438470	+	0.759452i	−0.997572	−	0.0696466i	$-0.977813\pi$
$613$	−10.8560	+	18.8032i	−0.438470	+	0.759452i	0.559102	+	0.829099i	$0.311146\pi$
$614$	6.93323	−	12.0087i	0.279802	−	0.484632i
$615$	−3.96378	−	6.86547i	−0.159835	−	0.276843i
$616$	1.28756			0.0518774
$617$	2.91051	−	5.04115i	0.117173	−	0.202949i	−0.801473	−	0.598030i	$-0.795950\pi$
$617$	2.91051	−	5.04115i	0.117173	−	0.202949i	0.918646	+	0.395081i	$0.129284\pi$
$618$	−19.3036			−0.776505
$619$	−30.8019			−1.23803			−0.619016	−	0.785378i	$-0.712468\pi$
$619$	−30.8019			−1.23803			−0.619016	+	0.785378i	$0.712468\pi$
$620$	66.3939	−	10.5786i	2.66644	−	0.424848i
$621$	6.36442			0.255395
$622$	−8.10380			−0.324933
$623$	−1.08342	+	1.87653i	−0.0434062	+	0.0751817i
$624$	1.07639			0.0430901
$625$	−40.5028	−	70.1530i	−1.62011	−	2.80612i
$626$	3.85075	−	6.66970i	0.153907	−	0.266575i
$627$	−6.82626	+	11.8234i	−0.272614	+	0.472182i
$628$	2.72482			0.108732
$629$	28.7698	+	49.8307i	1.14713	+	1.98688i
$630$	2.09819	+	3.63417i	0.0835939	+	0.144789i
$631$	18.4479	+	31.9528i	0.734401	+	1.27202i	0.954986	+	0.296652i	$0.0958702\pi$
$631$	18.4479	+	31.9528i	0.734401	+	1.27202i	−0.220585	+	0.975368i	$0.570797\pi$
$632$	1.91686	−	3.32010i	0.0762487	−	0.132067i
$633$	5.01096	+	8.67924i	0.199168	+	0.344969i
$634$	17.6831	−	30.6281i	0.702287	−	1.21640i
$635$	24.3144			0.964888
$636$	14.7427			0.584588
$637$	−3.48463	+	6.03556i	−0.138066	+	0.239138i
$638$	−2.30835	−	3.99818i	−0.0913885	−	0.158290i
$639$	−11.6337	+	20.1501i	−0.460221	+	0.797126i
$640$	28.6296	+	49.5879i	1.13168	+	1.96013i
$641$	5.30220	+	9.18367i	0.209424	+	0.362733i	0.951533	−	0.307546i	$-0.0995077\pi$
$641$	5.30220	+	9.18367i	0.209424	+	0.362733i	−0.742109	+	0.670279i	$0.766174\pi$
$642$	−4.13259	−	7.15785i	−0.163100	−	0.282498i
$643$	25.9773			1.02444			0.512222	−	0.858853i	$-0.328822\pi$
$643$	25.9773			1.02444			0.512222	+	0.858853i	$0.328822\pi$
$644$	0.428635	−	0.742418i	0.0168906	−	0.0292554i
$645$	0.290072	−	0.502419i	0.0114216	−	0.0197827i
$646$	39.1523	+	67.8138i	1.54043	+	2.66810i
$647$	2.02425			0.0795816			0.0397908	−	0.999208i	$-0.487331\pi$
$647$	2.02425			0.0795816			0.0397908	+	0.999208i	$0.487331\pi$
$648$	4.81379	−	8.33773i	0.189104	−	0.327537i
$649$	12.4307			0.487947
$650$	28.8051			1.12983
$651$	−0.640703	+	0.102084i	−0.0251111	+	0.00400099i
$652$	−18.8235			−0.737186
$653$	−19.5868			−0.766490			−0.383245	−	0.923647i	$-0.625193\pi$
$653$	−19.5868			−0.766490			−0.383245	+	0.923647i	$0.625193\pi$
$654$	5.78508	−	10.0201i	0.226215	−	0.391815i
$655$	−43.5216			−1.70053
$656$	−2.27018	−	3.93207i	−0.0886358	−	0.153522i
$657$	12.2216	−	21.1684i	0.476810	−	0.825860i
$658$	0.802126	−	1.38932i	0.0312701	−	0.0541614i
$659$	23.1213			0.900677			0.450338	−	0.892858i	$-0.351303\pi$
$659$	23.1213			0.900677			0.450338	+	0.892858i	$0.351303\pi$
$660$	−15.9775	−	27.6738i	−0.621923	−	1.07720i
$661$	13.8772	+	24.0360i	0.539759	+	0.934891i	0.998917	+	0.0465356i	$0.0148181\pi$
$661$	13.8772	+	24.0360i	0.539759	+	0.934891i	−0.459157	+	0.888355i	$0.651849\pi$
$662$	15.1298	+	26.2056i	0.588036	+	1.01851i
$663$	−2.29324	+	3.97201i	−0.0890620	+	0.154260i
$664$	10.0118	+	17.3409i	0.388533	+	0.672958i
$665$	−1.92360	+	3.33178i	−0.0745942	+	0.129201i
$666$	46.9246			1.81829
$667$	−0.908131			−0.0351630
$668$	−14.4851	+	25.0889i	−0.560444	+	0.970717i
$669$	9.36300	+	16.2172i	0.361995	+	0.626993i
$670$	−74.4955	+	129.030i	−2.87801	+	4.98486i
$671$	−20.0503	−	34.7282i	−0.774035	−	1.34067i
$672$	−0.422501	−	0.731793i	−0.0162983	−	0.0282295i
$673$	−16.9157	−	29.2988i	−0.652052	−	1.12939i	−0.982624	−	0.185606i	$-0.940575\pi$
$673$	−16.9157	−	29.2988i	−0.652052	−	1.12939i	0.330572	−	0.943781i	$-0.392758\pi$
$674$	−66.2156			−2.55053
$675$	24.1897	−	41.8978i	0.931062	−	1.61265i
$676$	−1.41932	+	2.45834i	−0.0545893	+	0.0945515i
$677$	−14.4187	−	24.9739i	−0.554154	−	0.959823i	−0.997969	−	0.0637046i	$-0.979708\pi$
$677$	−14.4187	−	24.9739i	−0.554154	−	0.959823i	0.443815	−	0.896119i	$-0.353625\pi$
$678$	9.00251			0.345739
$679$	−0.948799	+	1.64337i	−0.0364116	+	0.0630667i
$680$	−54.1477			−2.07647
$681$	−18.1627			−0.695996
$682$	−48.1534	+	7.67236i	−1.84389	+	0.293790i
$683$	−42.8269			−1.63873			−0.819364	−	0.573274i	$-0.805673\pi$
$683$	−42.8269			−1.63873			−0.819364	+	0.573274i	$0.805673\pi$
$684$	37.4635			1.43245
$685$	−2.97077	+	5.14553i	−0.113507	+	0.196600i
$686$	5.38686			0.205671
$687$	1.09803	+	1.90184i	0.0418924	+	0.0725597i
$688$	0.166133	−	0.287751i	0.00633377	−	0.0109704i
$689$	3.90677	−	6.76673i	0.148836	−	0.257792i
$690$	−10.7144			−0.407890
$691$	−1.67539	−	2.90186i	−0.0637348	−	0.110392i	0.832397	−	0.554179i	$-0.186968\pi$
$691$	−1.67539	−	2.90186i	−0.0637348	−	0.110392i	−0.896132	+	0.443787i	$0.853635\pi$
$692$	−27.2805	−	47.2512i	−1.03705	−	1.79622i
$693$	−0.892753	−	1.54629i	−0.0339129	−	0.0587388i
$694$	−0.806282	+	1.39652i	−0.0306060	+	0.0530112i
$695$	−22.5043	−	38.9786i	−0.853636	−	1.47854i
$696$	0.323200	−	0.559798i	0.0122508	−	0.0212191i
$697$	19.3464			0.732798
$698$	−9.65960			−0.365621
$699$	−2.35573	+	4.08025i	−0.0891020	+	0.154329i
$700$	−3.25829	−	5.64352i	−0.123152	−	0.213305i
$701$	13.5036	−	23.3889i	0.510024	−	0.883388i	−0.489908	−	0.871774i	$-0.662970\pi$
$701$	13.5036	−	23.3889i	0.510024	−	0.883388i	0.999933	−	0.0116141i	$-0.00369697\pi$
$702$	4.06335	+	7.03793i	0.153361	+	0.265629i
$703$	21.5100	+	37.2565i	0.811267	+	1.40515i
$704$	−25.3067	−	43.8324i	−0.953781	−	1.65200i
$705$	−11.7628			−0.443011
$706$	39.0878	−	67.7021i	1.47109	−	2.54800i
$707$	0.690097	−	1.19528i	0.0259538	−	0.0449532i
$708$	2.94555	+	5.10185i	0.110701	+	0.191739i
$709$	−4.96873			−0.186604			−0.0933022	−	0.995638i	$-0.529742\pi$
$709$	−4.96873			−0.186604			−0.0933022	+	0.995638i	$0.529742\pi$
$710$	42.5526	−	73.7033i	1.59697	−	2.76604i
$711$	−5.31635			−0.199379
$712$	−22.8016			−0.854525
$713$	−3.42902	+	8.95763i	−0.128418	+	0.335466i
$714$	1.76865			0.0661900
$715$	−16.9359			−0.633367
$716$	5.07387	−	8.78820i	0.189619	−	0.328430i
$717$	−2.77173			−0.103512
$718$	−7.19040	−	12.4541i	−0.268343	−	0.464785i
$719$	−8.54357	+	14.7979i	−0.318621	+	0.551868i	−0.980201	−	0.198007i	$-0.936553\pi$
$719$	−8.54357	+	14.7979i	−0.318621	+	0.551868i	0.661579	+	0.749875i	$0.269887\pi$
$720$	8.81116	−	15.2614i	0.328372	−	0.568758i
$721$	2.31450			0.0861967
$722$	8.37558	+	14.5069i	0.311707	+	0.539892i
$723$	1.89136	+	3.27594i	0.0703405	+	0.121833i
$724$	−2.71030	−	4.69437i	−0.100727	−	0.174465i
$725$	−3.45160	+	5.97834i	−0.128189	+	0.222030i
$726$	3.54636	+	6.14248i	0.131618	+	0.227969i
$727$	−24.3612	+	42.1948i	−0.903506	+	1.56492i	−0.0805962	+	0.996747i	$0.525682\pi$
$727$	−24.3612	+	42.1948i	−0.903506	+	1.56492i	−0.822910	+	0.568172i	$0.807651\pi$
$728$	0.323400			0.0119860
$729$	−5.98384			−0.221624
$730$	−44.7031	+	77.4281i	−1.65454	+	2.86574i
$731$	0.707891	+	1.22610i	0.0261823	+	0.0453491i
$732$	9.50219	−	16.4583i	0.351211	−	0.608315i
$733$	15.8156	+	27.3933i	0.584161	+	1.01180i	0.994979	+	0.100079i	$0.0319096\pi$
$733$	15.8156	+	27.3933i	0.584161	+	1.01180i	−0.410819	+	0.911717i	$0.634757\pi$
$734$	−36.5132	−	63.2427i	−1.34773	−	2.33433i
$735$	−9.85273	−	17.0654i	−0.363423	−	0.629468i
$736$	−12.4924			−0.460475
$737$	31.6969	−	54.9006i	1.16757	−	2.02229i
$738$	7.88868	−	13.6636i	0.290386	−	0.502964i
$739$	−18.1810	−	31.4904i	−0.668799	−	1.15839i	−0.978240	−	0.207475i	$-0.933475\pi$
$739$	−18.1810	−	31.4904i	−0.668799	−	1.15839i	0.309442	−	0.950918i	$-0.399858\pi$
$740$	−100.693			−3.70153
$741$	−1.71457	+	2.96972i	−0.0629862	+	0.109095i
$742$	−3.01308			−0.110614
$743$	−38.7446			−1.42140			−0.710701	−	0.703494i	$-0.751622\pi$
$743$	−38.7446			−1.42140			−0.710701	+	0.703494i	$0.751622\pi$
$744$	−4.30137	−	5.30173i	−0.157696	−	0.194371i
$745$	11.7054			0.428853
$746$	19.1470			0.701021
$747$	13.8837	−	24.0472i	0.507977	−	0.879842i
$748$	77.9829			2.85134
$749$	0.495498	+	0.858227i	0.0181051	+	0.0313589i
$750$	−25.1740	+	43.6026i	−0.919225	+	1.59214i
$751$	−20.4793	+	35.4712i	−0.747301	+	1.29436i	0.201811	+	0.979425i	$0.435317\pi$
$751$	−20.4793	+	35.4712i	−0.747301	+	1.29436i	−0.949112	+	0.314939i	$0.898016\pi$
$752$	−6.73691			−0.245670
$753$	9.39063	+	16.2650i	0.342214	+	0.592731i
$754$	−0.579794	−	1.00423i	−0.0211149	−	0.0365720i
$755$	5.56121	+	9.63230i	0.202393	+	0.350555i
$756$	0.919251	−	1.59219i	0.0334328	−	0.0579073i
$757$	19.9417	+	34.5400i	0.724793	+	1.25538i	0.959059	+	0.283206i	$0.0913979\pi$
$757$	19.9417	+	34.5400i	0.724793	+	1.25538i	−0.234266	+	0.972172i	$0.575269\pi$
$758$	−2.46026	+	4.26130i	−0.0893607	+	0.154777i
$759$	4.55884			0.165475
$760$	−40.4842			−1.46851
$761$	22.7054	−	39.3269i	0.823070	−	1.42560i	−0.0803161	−	0.996769i	$-0.525593\pi$
$761$	22.7054	−	39.3269i	0.823070	−	1.42560i	0.903386	−	0.428829i	$-0.141074\pi$
$762$	−4.17864	−	7.23761i	−0.151376	−	0.262191i
$763$	−0.693632	+	1.20141i	−0.0251112	+	0.0434938i
$764$	27.6819	+	47.9465i	1.00150	+	1.73464i
$765$	37.5442	+	65.0284i	1.35741	+	2.35111i
$766$	−4.07997	−	7.06672i	−0.147415	−	0.255331i
$767$	3.12224			0.112738
$768$	1.39049	−	2.40839i	0.0501749	−	0.0869054i
$769$	−4.56701	+	7.91030i	−0.164691	+	0.285253i	−0.936545	−	0.350546i	$-0.885996\pi$
$769$	−4.56701	+	7.91030i	−0.164691	+	0.285253i	0.771855	+	0.635799i	$0.219329\pi$
$770$	3.26543	+	5.65590i	0.117678	+	0.203824i
$771$	−9.39886			−0.338492
$772$	−16.3669	+	28.3483i	−0.589058	+	1.02028i
$773$	−1.56450			−0.0562713			−0.0281356	−	0.999604i	$-0.508957\pi$
$773$	−1.56450			−0.0562713			−0.0281356	+	0.999604i	$0.508957\pi$
$774$	1.15460			0.0415011
$775$	45.9363	+	56.6195i	1.65008	+	2.03383i
$776$	−19.9684			−0.716824
$777$	0.971686			0.0348590
$778$	−33.4897	+	58.0059i	−1.20066	+	2.07961i
$779$	14.4646			0.518247
$780$	−4.01310	−	6.95090i	−0.143692	−	0.248882i
$781$	−18.1056	+	31.3598i	−0.647869	+	1.12214i
$782$	13.0737	−	22.6443i	0.467515	−	0.809759i
$783$	−1.94757			−0.0696007
$784$	−5.64297	−	9.77391i	−0.201535	−	0.349068i
$785$	2.04163	+	3.53621i	0.0728689	+	0.126213i
$786$	7.47956	+	12.9550i	0.266787	+	0.462089i
$787$	−22.7750	+	39.4474i	−0.811841	+	1.40615i	0.0997340	+	0.995014i	$0.468201\pi$
$787$	−22.7750	+	39.4474i	−0.811841	+	1.40615i	−0.911574	+	0.411135i	$0.865133\pi$
$788$	23.2553	+	40.2793i	0.828435	+	1.43489i
$789$	2.51769	−	4.36077i	0.0896322	−	0.155248i
$790$	19.4457			0.691846
$791$	−1.07940			−0.0383791
$792$	9.39443	−	16.2716i	0.333817	−	0.578187i
$793$	−5.03609	−	8.72276i	−0.178837	−	0.309754i
$794$	0.155853	−	0.269945i	0.00553101	−	0.00958000i
$795$	11.0463	+	19.1328i	0.391772	+	0.678570i
$796$	−12.1093	−	20.9740i	−0.429203	−	0.743402i
$797$	0.452334	+	0.783465i	0.0160225	+	0.0277517i	0.873925	−	0.486060i	$-0.161566\pi$
$797$	0.452334	+	0.783465i	0.0160225	+	0.0277517i	−0.857903	+	0.513812i	$0.828233\pi$
$798$	1.32235			0.0468107
$799$	14.3529	−	24.8600i	0.507770	−	0.879483i
$800$	−47.4806	+	82.2388i	−1.67869	+	2.90758i
$801$	15.8098	+	27.3834i	0.558613	+	0.967546i
$802$	22.4379			0.792311
$803$	19.0206	−	32.9447i	0.671223	−	1.16259i
$804$	30.0433			1.05955
$805$	1.28466			0.0452782
$806$	−12.0948	+	1.92708i	−0.426021	+	0.0678786i
$807$	11.0755			0.389877
$808$	14.5238			0.510944
$809$	−4.43018	+	7.67329i	−0.155757	+	0.269779i	−0.933334	−	0.359008i	$-0.883115\pi$
$809$	−4.43018	+	7.67329i	−0.155757	+	0.269779i	0.777578	+	0.628787i	$0.216448\pi$
$810$	48.8337			1.71584
$811$	−2.99032	−	5.17939i	−0.105004	−	0.181873i	0.808736	−	0.588172i	$-0.200152\pi$
$811$	−2.99032	−	5.17939i	−0.105004	−	0.181873i	−0.913740	+	0.406299i	$0.866819\pi$
$812$	−0.131167	+	0.227187i	−0.00460305	+	0.00797271i
$813$	−0.470134	+	0.814296i	−0.0164883	+	0.0285586i
$814$	73.0292			2.55967
$815$	−14.1039	−	24.4287i	−0.494039	−	0.855700i
$816$	−3.71364	−	6.43221i	−0.130003	−	0.225172i
$817$	0.529263	+	0.916710i	0.0185166	+	0.0320716i
$818$	4.34894	−	7.53258i	0.152057	−	0.263371i
$819$	−0.224235	−	0.388386i	−0.00783540	−	0.0135713i
$820$	−16.9278	+	29.3199i	−0.591146	+	1.02389i
$821$	23.7722			0.829655			0.414828	−	0.909900i	$-0.363842\pi$
$821$	23.7722			0.829655			0.414828	+	0.909900i	$0.363842\pi$
$822$	2.04221			0.0712302
$823$	5.00491	−	8.66875i	0.174460	−	0.302174i	−0.765514	−	0.643419i	$-0.777515\pi$
$823$	5.00491	−	8.66875i	0.174460	−	0.302174i	0.939974	+	0.341245i	$0.110849\pi$
$824$	12.1778	+	21.0925i	0.424232	+	0.734792i
$825$	17.3271	−	30.0114i	0.603252	−	1.04486i
$826$	−0.602004	−	1.04270i	−0.0209464	−	0.0362802i
$827$	−3.97554	−	6.88584i	−0.138243	−	0.239444i	0.788589	−	0.614921i	$-0.210812\pi$
$827$	−3.97554	−	6.88584i	−0.138243	−	0.239444i	−0.926832	+	0.375477i	$0.877479\pi$
$828$	−6.25489	−	10.8338i	−0.217373	−	0.376500i
$829$	−34.3018			−1.19135			−0.595676	−	0.803225i	$-0.703116\pi$
$829$	−34.3018			−1.19135			−0.595676	+	0.803225i	$0.703116\pi$
$830$	−50.7825	+	87.9578i	−1.76269	+	3.05306i
$831$	7.68643	−	13.3133i	0.266639	−	0.461833i
$832$	−6.35633	−	11.0095i	−0.220366	−	0.381686i
$833$	48.0892			1.66619
$834$	−7.73510	+	13.3976i	−0.267845	+	0.463920i
$835$	−43.4130			−1.50237
$836$	58.3048			2.01651
$837$	−7.35387	+	19.2105i	−0.254187	+	0.664012i
$838$	89.3492			3.08652
$839$	28.5060			0.984135			0.492067	−	0.870557i	$-0.336241\pi$
$839$	28.5060			0.984135			0.492067	+	0.870557i	$0.336241\pi$
$840$	−0.457204	+	0.791900i	−0.0157750	+	0.0273231i
$841$	−28.7221			−0.990417
$842$	11.2255	+	19.4431i	0.386856	+	0.670055i
$843$	−8.45855	+	14.6506i	−0.291328	+	0.504595i
$844$	21.3999	−	37.0658i	0.736616	−	1.27586i
$845$	−4.25383			−0.146336
$846$	−11.7051	−	20.2738i	−0.402429	−	0.697027i
$847$	−0.425209	−	0.736483i	−0.0146103	−	0.0253059i
$848$	6.32657	+	10.9579i	0.217255	+	0.376297i
$849$	−8.92921	+	15.4658i	−0.306450	+	0.530786i
$850$	−99.3802	−	172.132i	−3.40871	−	5.90407i
$851$	7.18262	−	12.4407i	0.246217	−	0.426460i
$852$	−17.1611			−0.587929
$853$	−10.0497			−0.344096			−0.172048	−	0.985089i	$-0.555038\pi$
$853$	−10.0497			−0.344096			−0.172048	+	0.985089i	$0.555038\pi$
$854$	−1.94203	+	3.36369i	−0.0664549	+	0.115103i
$855$	28.0703	+	48.6193i	0.959985	+	1.66274i
$856$	−5.21412	+	9.03112i	−0.178215	+	0.308677i
$857$	−20.3192	−	35.1940i	−0.694092	−	1.20220i	−0.970486	−	0.241159i	$-0.922473\pi$
$857$	−20.3192	−	35.1940i	−0.694092	−	1.20220i	0.276393	−	0.961045i	$-0.410861\pi$
$858$	2.91058	+	5.04127i	0.0993655	+	0.172106i
$859$	8.70467	+	15.0769i	0.297000	+	0.514418i	0.975448	−	0.220230i	$-0.0706807\pi$
$859$	8.70467	+	15.0769i	0.297000	+	0.514418i	−0.678449	+	0.734648i	$0.737347\pi$
$860$	−2.47758			−0.0844847
$861$	0.163354	−	0.282938i	0.00556709	−	0.00964249i
$862$	15.0514	−	26.0697i	0.512651	−	0.887938i
$863$	−1.56768	−	2.71530i	−0.0533644	−	0.0924298i	0.838109	−	0.545502i	$-0.183661\pi$
$863$	−1.56768	−	2.71530i	−0.0533644	−	0.0924298i	−0.891474	+	0.453073i	$0.850328\pi$
$864$	−26.7911			−0.911451
$865$	40.8810	−	70.8079i	1.38999	−	2.40754i
$866$	−76.8106			−2.61013
$867$	20.3478			0.691047
$868$	1.74566	+	2.15164i	0.0592515	+	0.0730315i
$869$	−8.27389			−0.280672
$870$	3.27871			0.111159
$871$	7.96137	−	13.7895i	0.269761	−	0.467240i
$872$	−14.5982			−0.494356
$873$	13.8454	+	23.9810i	0.468596	+	0.811633i
$874$	9.77470	−	16.9303i	0.330634	−	0.572675i
$875$	3.01836	−	5.22796i	0.102039	−	0.176737i
$876$	18.0284			0.609122
$877$	12.7197	+	22.0312i	0.429514	+	0.743940i	0.996830	−	0.0795601i	$-0.0253516\pi$
$877$	12.7197	+	22.0312i	0.429514	+	0.743940i	−0.567316	+	0.823500i	$0.692018\pi$
$878$	13.0883	+	22.6697i	0.441710	+	0.765064i
$879$	−2.23965	−	3.87919i	−0.0755415	−	0.130842i
$880$	13.7129	−	23.7514i	0.462261	−	0.800660i
$881$	−1.82465	−	3.16039i	−0.0614742	−	0.106476i	0.833650	−	0.552293i	$-0.186247\pi$
$881$	−1.82465	−	3.16039i	−0.0614742	−	0.106476i	−0.895125	+	0.445816i	$0.852914\pi$
$882$	19.6088	−	33.9635i	0.660263	−	1.14361i
$883$	18.0576			0.607685			0.303843	−	0.952722i	$-0.401730\pi$
$883$	18.0576			0.607685			0.303843	+	0.952722i	$0.401730\pi$
$884$	19.5871			0.658787
$885$	−4.41404	+	7.64534i	−0.148376	+	0.256995i
$886$	−25.2523	−	43.7383i	−0.848369	−	1.46942i
$887$	−20.2254	+	35.0314i	−0.679102	+	1.17624i	0.296149	+	0.955142i	$0.404297\pi$
$887$	−20.2254	+	35.0314i	−0.679102	+	1.17624i	−0.975252	+	0.221098i	$0.929036\pi$
$888$	5.11252	+	8.85515i	0.171565	+	0.297159i
$889$	0.501019	+	0.867790i	0.0168036	+	0.0291048i
$890$	−57.8278	−	100.161i	−1.93839	−	3.35740i
$891$	−20.7781			−0.696093
$892$	39.9859	−	69.2576i	1.33883	−	2.31892i
$893$	10.7311	−	18.5869i	0.359103	−	0.621985i
$894$	−2.01167	−	3.48432i	−0.0672804	−	0.116533i
$895$	15.2068			0.508308
$896$	−1.17987	+	2.04360i	−0.0394168	+	0.0682719i
$897$	1.14505			0.0382322
$898$	7.58039			0.252961
$899$	1.04931	−	2.74112i	0.0349966	−	0.0914215i
$900$	−95.0936			−3.16979
$901$	−53.9148			−1.79616
$902$	12.2772	−	21.2648i	0.408787	−	0.708040i
$903$	0.0239087			0.000795632
$904$	−5.67927	−	9.83678i	−0.188890	−	0.327166i
$905$	4.06150	−	7.03472i	0.135009	−	0.233842i
$906$	1.91148	−	3.31078i	0.0635047	−	0.109993i
$907$	−16.7974			−0.557749			−0.278875	−	0.960327i	$-0.589961\pi$
$907$	−16.7974			−0.557749			−0.278875	+	0.960327i	$0.589961\pi$
$908$	38.7831	+	67.1743i	1.28706	+	2.22926i
$909$	−10.0703	−	17.4422i	−0.334010	−	0.578523i
$910$	0.820187	+	1.42060i	0.0271889	+	0.0470926i
$911$	−18.0784	+	31.3127i	−0.598965	+	1.03744i	0.394010	+	0.919106i	$0.371088\pi$
$911$	−18.0784	+	31.3127i	−0.598965	+	1.03744i	−0.992974	+	0.118331i	$0.962246\pi$
$912$	−2.77655	−	4.80912i	−0.0919406	−	0.159246i
$913$	21.6073	−	37.4249i	0.715097	−	1.23858i
$914$	2.50150			0.0827421
$915$	28.4789			0.941482
$916$	4.68927	−	8.12206i	0.154938	−	0.268360i
$917$	−0.896800	−	1.55330i	−0.0296149	−	0.0512946i
$918$	28.0378	−	48.5629i	0.925386	−	1.60282i
$919$	−9.88007	−	17.1128i	−0.325913	−	0.564499i	0.655783	−	0.754949i	$-0.272338\pi$
$919$	−9.88007	−	17.1128i	−0.325913	−	0.564499i	−0.981697	+	0.190450i	$0.939005\pi$
$920$	6.75922	+	11.7073i	0.222845	+	0.385979i
$921$	−2.09504	−	3.62872i	−0.0690340	−	0.119570i
$922$	−54.2468			−1.78652
$923$	−4.54762	+	7.87671i	−0.149687	+	0.259265i
$924$	0.658460	−	1.14049i	0.0216617	−	0.0375192i
$925$	−54.5989	−	94.5681i	−1.79520	−	3.10938i
$926$	27.1334			0.891658
$927$	16.8873	−	29.2496i	0.554651	−	0.960684i
$928$	3.82278			0.125489
$929$	14.8897			0.488514			0.244257	−	0.969711i	$-0.421456\pi$
$929$	14.8897			0.488514			0.244257	+	0.969711i	$0.421456\pi$
$930$	12.3801	−	32.3406i	0.405960	−	1.06049i
$931$	35.9544			1.17836
$932$	20.1209			0.659082
$933$	−1.22438	+	2.12069i	−0.0400844	+	0.0694282i
$934$	−33.7623			−1.10474
$935$	58.4304	+	101.204i	1.91088	+	3.30974i
$936$	2.35962	−	4.08698i	0.0771266	−	0.133587i
$937$	18.1329	−	31.4072i	0.592377	−	1.02603i	−0.401534	−	0.915844i	$-0.631523\pi$
$937$	18.1329	−	31.4072i	0.592377	−	1.02603i	0.993911	−	0.110183i	$-0.0351438\pi$
$938$	−6.14017			−0.200484
$939$	−1.16360	−	2.01541i	−0.0379726	−	0.0657705i
$940$	25.1172	+	43.5043i	0.819233	+	1.41895i
$941$	−22.4542	−	38.8918i	−0.731987	−	1.26784i	−0.956033	−	0.293259i	$-0.905260\pi$
$941$	−22.4542	−	38.8918i	−0.731987	−	1.26784i	0.224046	−	0.974578i	$-0.428073\pi$
$942$	0.701743	−	1.21545i	0.0228640	−	0.0396016i
$943$	−2.41500	−	4.18290i	−0.0786432	−	0.136214i
$944$	−2.52806	+	4.37873i	−0.0822813	+	0.142515i
$945$	2.75507			0.0896225
$946$	1.79691			0.0584226
$947$	−14.9366	+	25.8709i	−0.485373	+	0.840690i	−0.999859	−	0.0168085i	$-0.994649\pi$
$947$	−14.9366	+	25.8709i	−0.485373	+	0.840690i	0.514486	+	0.857499i	$0.327983\pi$
$948$	−1.96057	−	3.39580i	−0.0636762	−	0.110290i
$949$	4.77745	−	8.27478i	0.155083	−	0.268611i
$950$	−74.3028	−	128.696i	−2.41070	−	4.17546i
$951$	−5.34339	−	9.25502i	−0.173271	−	0.300114i
$952$	−1.11576	−	1.93255i	−0.0361620	−	0.0626344i
$953$	−12.0590			−0.390630			−0.195315	−	0.980741i	$-0.562573\pi$
$953$	−12.0590			−0.390630			−0.195315	+	0.980741i	$0.562573\pi$
$954$	−21.9843	+	38.0779i	−0.711767	+	1.23282i
$955$	−41.4826	+	71.8499i	−1.34234	+	2.32501i
$956$	5.91852	+	10.2512i	0.191418	+	0.331547i
$957$	−1.39505			−0.0450955
$958$	−15.6484	+	27.1038i	−0.505577	+	0.875685i
$959$	−0.244861			−0.00790697
$960$	35.9448			1.16011
$961$	−23.0758	−	20.7005i	−0.744380	−	0.667757i
$962$	18.3429			0.591399
$963$	14.4612			0.466005
$964$	8.07731	−	13.9903i	0.260153	−	0.450597i
$965$	−49.0531			−1.57907
$966$	−0.220779	−	0.382401i	−0.00710345	−	0.0123035i
$967$	12.1515	−	21.0470i	0.390765	−	0.676825i	−0.601786	−	0.798658i	$-0.705544\pi$
$967$	12.1515	−	21.0470i	0.390765	−	0.676825i	0.992551	+	0.121833i	$0.0388772\pi$
$968$	4.47447	−	7.75001i	0.143815	−	0.249095i
$969$	23.6616			0.760121
$970$	−50.6426	−	87.7155i	−1.62604	−	2.81638i
$971$	−15.6976	−	27.1890i	−0.503759	−	0.872536i	−0.999991	−	0.00434589i	$-0.998617\pi$
$971$	−15.6976	−	27.1890i	−0.503759	−	0.872536i	0.496232	−	0.868190i	$-0.334717\pi$
$972$	−20.6545	−	35.7746i	−0.662493	−	1.14747i
$973$	0.927439	−	1.60637i	0.0297323	−	0.0514979i
$974$	5.11239	+	8.85492i	0.163812	+	0.283730i
$975$	4.35208	−	7.53803i	0.139378	−	0.241410i
$976$	16.3107			0.522094
$977$	35.9974			1.15166			0.575829	−	0.817570i	$-0.304679\pi$
$977$	35.9974			1.15166			0.575829	+	0.817570i	$0.304679\pi$
$978$	−4.84776	+	8.39656i	−0.155014	+	0.268492i
$979$	24.6050	+	42.6171i	0.786379	+	1.36205i
$980$	−42.0773	+	72.8801i	−1.34411	+	2.32807i
$981$	10.1219	+	17.5316i	0.323166	+	0.559741i
$982$	−1.57275	−	2.72408i	−0.0501884	−	0.0869288i
$983$	9.12884	+	15.8116i	0.291165	+	0.504312i	0.974085	−	0.226180i	$-0.0726239\pi$
$983$	9.12884	+	15.8116i	0.291165	+	0.504312i	−0.682921	+	0.730493i	$0.739291\pi$
$984$	3.43795			0.109598
$985$	−34.8490	+	60.3603i	−1.11038	+	1.92324i
$986$	−4.00068	+	6.92938i	−0.127408	+	0.220676i
$987$	−0.242382	−	0.419817i	−0.00771509	−	0.0133629i
$988$	14.6446			0.465905
$989$	0.176731	−	0.306107i	0.00561972	−	0.00973364i
$990$	95.3022			3.02890
$991$	−49.0253			−1.55734			−0.778670	−	0.627433i	$-0.784105\pi$
$991$	−49.0253			−1.55734			−0.778670	+	0.627433i	$0.784105\pi$
$992$	14.4345	−	37.7072i	0.458296	−	1.19721i
$993$	9.14367			0.290165
$994$	3.50733			0.111246
$995$	18.1463	−	31.4304i	0.575278	−	0.996410i
$996$	20.4801			0.648937
$997$	19.4289	+	33.6519i	0.615320	+	1.06577i	0.990328	+	0.138744i	$0.0443067\pi$
$997$	19.4289	+	33.6519i	0.615320	+	1.06577i	−0.375008	+	0.927022i	$0.622360\pi$
$998$	22.7600	−	39.4214i	0.720454	−	1.24786i
$999$	15.4038	−	26.6802i	0.487355	−	0.844124i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	403.2.h.a.222.3	yes	30
31.25	even	3	inner	403.2.h.a.118.3	✓	30

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
403.2.h.a.118.3	✓	30	31.25	even	3	inner
403.2.h.a.222.3	yes	30	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 403 = 13 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	403.h (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-2.19969 q^{2} +(-0.332345 + 0.575638i) q^{3} +2.83864 q^{4} +(2.12692 + 3.68393i) q^{5} +(0.731057 - 1.26623i) q^{6} +(-0.0876538 + 0.151821i) q^{7} -1.84476 q^{8} +(1.27909 + 2.21546i) q^{9} +O(q^{10})\)	\(q-2.19969 q^{2} +(-0.332345 + 0.575638i) q^{3} +2.83864 q^{4} +(2.12692 + 3.68393i) q^{5} +(0.731057 - 1.26623i) q^{6} +(-0.0876538 + 0.151821i) q^{7} -1.84476 q^{8} +(1.27909 + 2.21546i) q^{9} +(-4.67856 - 8.10350i) q^{10} +(1.99067 + 3.44793i) q^{11} +(-0.943409 + 1.63403i) q^{12} +(0.500000 + 0.866025i) q^{13} +(0.192811 - 0.333959i) q^{14} -2.82748 q^{15} -1.61939 q^{16} +(3.45009 - 5.97573i) q^{17} +(-2.81361 - 4.87332i) q^{18} +(2.57950 - 4.46782i) q^{19} +(6.03756 + 10.4574i) q^{20} +(-0.0582626 - 0.100914i) q^{21} +(-4.37885 - 7.58439i) q^{22} -1.72269 q^{23} +(0.613097 - 1.06191i) q^{24} +(-6.54754 + 11.3407i) q^{25} +(-1.09985 - 1.90499i) q^{26} -3.69447 q^{27} +(-0.248818 + 0.430965i) q^{28} +0.527159 q^{29} +6.21958 q^{30} +(1.99051 - 5.19980i) q^{31} +7.25167 q^{32} -2.64635 q^{33} +(-7.58913 + 13.1448i) q^{34} -0.745729 q^{35} +(3.63089 + 6.28889i) q^{36} +(-4.16942 + 7.22166i) q^{37} +(-5.67410 + 9.82783i) q^{38} -0.664690 q^{39} +(-3.92365 - 6.79596i) q^{40} +(1.40188 + 2.42813i) q^{41} +(0.128160 + 0.221979i) q^{42} +(-0.102590 + 0.177692i) q^{43} +(5.65079 + 9.78746i) q^{44} +(-5.44105 + 9.42417i) q^{45} +3.78938 q^{46} +4.16016 q^{47} +(0.538195 - 0.932181i) q^{48} +(3.48463 + 6.03556i) q^{49} +(14.4026 - 24.9460i) q^{50} +(2.29324 + 3.97201i) q^{51} +(1.41932 + 2.45834i) q^{52} +(-3.90677 - 6.76673i) q^{53} +8.12670 q^{54} +(-8.46796 + 14.6669i) q^{55} +(0.161700 - 0.280073i) q^{56} +(1.71457 + 2.96972i) q^{57} -1.15959 q^{58} +(1.56112 - 2.70394i) q^{59} -8.02621 q^{60} -10.0722 q^{61} +(-4.37850 + 11.4380i) q^{62} -0.448469 q^{63} -12.7127 q^{64} +(-2.12692 + 3.68393i) q^{65} +5.82116 q^{66} +(-7.96137 - 13.7895i) q^{67} +(9.79357 - 16.9630i) q^{68} +(0.572527 - 0.991645i) q^{69} +1.64037 q^{70} +(4.54762 + 7.87671i) q^{71} +(-2.35962 - 4.08698i) q^{72} +(-4.77745 - 8.27478i) q^{73} +(9.17145 - 15.8854i) q^{74} +(-4.35208 - 7.53803i) q^{75} +(7.32228 - 12.6826i) q^{76} -0.697957 q^{77} +1.46211 q^{78} +(-1.03909 + 1.79975i) q^{79} +(-3.44430 - 5.96570i) q^{80} +(-2.60944 + 4.51968i) q^{81} +(-3.08370 - 5.34113i) q^{82} +(-5.42715 - 9.40010i) q^{83} +(-0.165387 - 0.286458i) q^{84} +29.3522 q^{85} +(0.225667 - 0.390867i) q^{86} +(-0.175199 + 0.303453i) q^{87} +(-3.67230 - 6.36061i) q^{88} +12.3602 q^{89} +(11.9686 - 20.7303i) q^{90} -0.175308 q^{91} -4.89010 q^{92} +(2.33167 + 2.87394i) q^{93} -9.15107 q^{94} +21.9455 q^{95} +(-2.41006 + 4.17434i) q^{96} +10.8244 q^{97} +(-7.66512 - 13.2764i) q^{98} +(-5.09250 + 8.82046i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 30 q - 6 q^{2} - 2 q^{3} + 22 q^{4} + 7 q^{5} + 6 q^{7} - 24 q^{8} - 13 q^{9}+O(q^{10}) \) 30 * q - 6 * q^2 - 2 * q^3 + 22 * q^4 + 7 * q^5 + 6 * q^7 - 24 * q^8 - 13 * q^9	\( 30 q - 6 q^{2} - 2 q^{3} + 22 q^{4} + 7 q^{5} + 6 q^{7} - 24 q^{8} - 13 q^{9} - 3 q^{10} - 3 q^{11} + 12 q^{12} + 15 q^{13} + 3 q^{14} + 4 q^{15} + 22 q^{16} + 4 q^{17} - 6 q^{18} + 5 q^{19} + 10 q^{20} - 15 q^{21} + 2 q^{22} - 6 q^{23} - 6 q^{24} - 20 q^{25} - 3 q^{26} + 4 q^{27} + 13 q^{28} + 26 q^{29} + 28 q^{30} + 19 q^{31} - 74 q^{32} + 2 q^{33} - 21 q^{34} - 30 q^{35} + 37 q^{36} - 4 q^{37} - 4 q^{38} - 4 q^{39} - 17 q^{40} + 7 q^{41} + 44 q^{42} + 15 q^{43} - 70 q^{44} + 15 q^{45} - 58 q^{46} - 24 q^{47} + 31 q^{48} - 29 q^{49} + 2 q^{50} + 25 q^{51} + 11 q^{52} + 4 q^{53} + 34 q^{54} + 13 q^{55} - 41 q^{56} + 8 q^{57} - 46 q^{58} + 27 q^{59} + 78 q^{60} + 8 q^{61} + 20 q^{62} - 112 q^{63} + 60 q^{64} - 7 q^{65} + 60 q^{66} + 29 q^{67} + 41 q^{68} - 23 q^{69} - 112 q^{70} + 29 q^{71} + 14 q^{72} - 10 q^{73} + 25 q^{74} - 18 q^{75} + 24 q^{76} - 72 q^{77} + 9 q^{79} - 11 q^{81} - 38 q^{82} - 13 q^{83} - 62 q^{84} + 108 q^{85} - 38 q^{86} - 18 q^{87} + 32 q^{88} + 6 q^{89} + 7 q^{90} + 12 q^{91} + 2 q^{92} + 37 q^{93} - 154 q^{94} - 28 q^{95} - 105 q^{96} - 84 q^{97} + 50 q^{98} + 10 q^{99}+O(q^{100}) \) 30 * q - 6 * q^2 - 2 * q^3 + 22 * q^4 + 7 * q^5 + 6 * q^7 - 24 * q^8 - 13 * q^9 - 3 * q^10 - 3 * q^11 + 12 * q^12 + 15 * q^13 + 3 * q^14 + 4 * q^15 + 22 * q^16 + 4 * q^17 - 6 * q^18 + 5 * q^19 + 10 * q^20 - 15 * q^21 + 2 * q^22 - 6 * q^23 - 6 * q^24 - 20 * q^25 - 3 * q^26 + 4 * q^27 + 13 * q^28 + 26 * q^29 + 28 * q^30 + 19 * q^31 - 74 * q^32 + 2 * q^33 - 21 * q^34 - 30 * q^35 + 37 * q^36 - 4 * q^37 - 4 * q^38 - 4 * q^39 - 17 * q^40 + 7 * q^41 + 44 * q^42 + 15 * q^43 - 70 * q^44 + 15 * q^45 - 58 * q^46 - 24 * q^47 + 31 * q^48 - 29 * q^49 + 2 * q^50 + 25 * q^51 + 11 * q^52 + 4 * q^53 + 34 * q^54 + 13 * q^55 - 41 * q^56 + 8 * q^57 - 46 * q^58 + 27 * q^59 + 78 * q^60 + 8 * q^61 + 20 * q^62 - 112 * q^63 + 60 * q^64 - 7 * q^65 + 60 * q^66 + 29 * q^67 + 41 * q^68 - 23 * q^69 - 112 * q^70 + 29 * q^71 + 14 * q^72 - 10 * q^73 + 25 * q^74 - 18 * q^75 + 24 * q^76 - 72 * q^77 + 9 * q^79 - 11 * q^81 - 38 * q^82 - 13 * q^83 - 62 * q^84 + 108 * q^85 - 38 * q^86 - 18 * q^87 + 32 * q^88 + 6 * q^89 + 7 * q^90 + 12 * q^91 + 2 * q^92 + 37 * q^93 - 154 * q^94 - 28 * q^95 - 105 * q^96 - 84 * q^97 + 50 * q^98 + 10 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more