LMFDB - Embedded newform 403.2.h.b.222.7

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:	$34$
Relative dimension:	$17$ over $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			222.7
Character	$\chi$	$=$	403.222
Dual form			403.2.h.b.118.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.708536 q^{2} +(-0.837990 + 1.45144i) q^{3} -1.49798 q^{4} +(1.10081 + 1.90665i) q^{5} +(0.593746 - 1.02840i) q^{6} +(1.50089 - 2.59962i) q^{7} +2.47844 q^{8} +(0.0955444 + 0.165488i) q^{9} +O(q^{10})$	\(q-0.708536 q^{2} +(-0.837990 + 1.45144i) q^{3} -1.49798 q^{4} +(1.10081 + 1.90665i) q^{5} +(0.593746 - 1.02840i) q^{6} +(1.50089 - 2.59962i) q^{7} +2.47844 q^{8} +(0.0955444 + 0.165488i) q^{9} +(-0.779961 - 1.35093i) q^{10} +(2.27605 + 3.94223i) q^{11} +(1.25529 - 2.17423i) q^{12} +(-0.500000 - 0.866025i) q^{13} +(-1.06343 + 1.84192i) q^{14} -3.68986 q^{15} +1.23989 q^{16} +(-3.32635 + 5.76141i) q^{17} +(-0.0676966 - 0.117254i) q^{18} +(0.733221 - 1.26998i) q^{19} +(-1.64898 - 2.85612i) q^{20} +(2.51546 + 4.35691i) q^{21} +(-1.61266 - 2.79321i) q^{22} -6.58855 q^{23} +(-2.07691 + 3.59732i) q^{24} +(0.0764505 - 0.132416i) q^{25} +(0.354268 + 0.613610i) q^{26} -5.34820 q^{27} +(-2.24830 + 3.89416i) q^{28} -5.25374 q^{29} +2.61440 q^{30} +(-0.0357722 + 5.56765i) q^{31} -5.83539 q^{32} -7.62922 q^{33} +(2.35684 - 4.08216i) q^{34} +6.60875 q^{35} +(-0.143123 - 0.247897i) q^{36} +(1.42159 - 2.46227i) q^{37} +(-0.519514 + 0.899824i) q^{38} +1.67598 q^{39} +(2.72829 + 4.72553i) q^{40} +(3.27262 + 5.66835i) q^{41} +(-1.78229 - 3.08702i) q^{42} +(1.10219 - 1.90904i) q^{43} +(-3.40947 - 5.90537i) q^{44} +(-0.210352 + 0.364340i) q^{45} +4.66822 q^{46} +10.4132 q^{47} +(-1.03901 + 1.79962i) q^{48} +(-1.00533 - 1.74129i) q^{49} +(-0.0541679 + 0.0938216i) q^{50} +(-5.57490 - 9.65601i) q^{51} +(0.748988 + 1.29729i) q^{52} +(5.14880 + 8.91797i) q^{53} +3.78939 q^{54} +(-5.01097 + 8.67926i) q^{55} +(3.71987 - 6.44300i) q^{56} +(1.22886 + 2.12846i) q^{57} +3.72247 q^{58} +(2.65403 - 4.59691i) q^{59} +5.52732 q^{60} -11.2874 q^{61} +(0.0253459 - 3.94488i) q^{62} +0.573606 q^{63} +1.65481 q^{64} +(1.10081 - 1.90665i) q^{65} +5.40558 q^{66} +(-0.702967 - 1.21757i) q^{67} +(4.98279 - 8.63045i) q^{68} +(5.52114 - 9.56289i) q^{69} -4.68254 q^{70} +(4.94784 + 8.56991i) q^{71} +(0.236801 + 0.410152i) q^{72} +(1.60143 + 2.77376i) q^{73} +(-1.00725 + 1.74460i) q^{74} +(0.128130 + 0.221927i) q^{75} +(-1.09835 + 1.90239i) q^{76} +13.6644 q^{77} -1.18749 q^{78} +(1.38059 - 2.39126i) q^{79} +(1.36488 + 2.36403i) q^{80} +(4.19511 - 7.26614i) q^{81} +(-2.31877 - 4.01623i) q^{82} +(-7.35669 - 12.7422i) q^{83} +(-3.76810 - 6.52654i) q^{84} -14.6467 q^{85} +(-0.780939 + 1.35263i) q^{86} +(4.40259 - 7.62550i) q^{87} +(5.64105 + 9.77059i) q^{88} -8.89431 q^{89} +(0.149042 - 0.258148i) q^{90} -3.00178 q^{91} +9.86949 q^{92} +(-8.05114 - 4.71756i) q^{93} -7.37811 q^{94} +3.22854 q^{95} +(4.89000 - 8.46973i) q^{96} -0.237685 q^{97} +(0.712316 + 1.23377i) q^{98} +(-0.434927 + 0.753316i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 34 q + 6 q^{2} - 2 q^{3} + 34 q^{4} - 5 q^{5} - 2 q^{7} + 36 q^{8} - 23 q^{9}+O(q^{10}) $ 34 * q + 6 * q^2 - 2 * q^3 + 34 * q^4 - 5 * q^5 - 2 * q^7 + 36 * q^8 - 23 * q^9	\( 34 q + 6 q^{2} - 2 q^{3} + 34 q^{4} - 5 q^{5} - 2 q^{7} + 36 q^{8} - 23 q^{9} - 7 q^{10} - 5 q^{11} - 28 q^{12} - 17 q^{13} - 7 q^{14} + 8 q^{15} + 18 q^{16} - 8 q^{17} + 6 q^{18} + 3 q^{19} - 8 q^{20} + 13 q^{21} + 12 q^{22} - 14 q^{23} - 6 q^{24} - 26 q^{25} - 3 q^{26} + 28 q^{27} - 7 q^{28} - 18 q^{29} - 60 q^{30} - 9 q^{31} + 58 q^{32} - 14 q^{33} - 15 q^{34} + 50 q^{35} - 49 q^{36} - 6 q^{37} + 2 q^{38} + 4 q^{39} - 29 q^{40} - 5 q^{41} + 8 q^{42} - q^{43} - 22 q^{44} + 13 q^{45} + 34 q^{46} + 16 q^{47} - 49 q^{48} + 3 q^{49} - 35 q^{51} - 17 q^{52} + 30 q^{53} - 2 q^{54} + 21 q^{55} - 7 q^{56} + 34 q^{58} - 9 q^{59} - 38 q^{60} - 28 q^{61} - 62 q^{62} + 88 q^{63} + 56 q^{64} - 5 q^{65} + 140 q^{66} - 31 q^{67} - 39 q^{68} + 5 q^{69} + 56 q^{70} + q^{71} - 32 q^{72} - 10 q^{73} - 39 q^{74} - 2 q^{75} - 16 q^{76} + 76 q^{77} - 23 q^{79} - 22 q^{80} - 29 q^{81} - 10 q^{82} + 3 q^{83} + 52 q^{84} - 32 q^{85} + 4 q^{86} + 18 q^{87} - 10 q^{88} + 26 q^{89} + 35 q^{90} + 4 q^{91} - 94 q^{92} - 41 q^{93} + 70 q^{94} + 28 q^{95} - 23 q^{96} + 32 q^{97} - 38 q^{98} - 70 q^{99}+O(q^{100}) \) 34 * q + 6 * q^2 - 2 * q^3 + 34 * q^4 - 5 * q^5 - 2 * q^7 + 36 * q^8 - 23 * q^9 - 7 * q^10 - 5 * q^11 - 28 * q^12 - 17 * q^13 - 7 * q^14 + 8 * q^15 + 18 * q^16 - 8 * q^17 + 6 * q^18 + 3 * q^19 - 8 * q^20 + 13 * q^21 + 12 * q^22 - 14 * q^23 - 6 * q^24 - 26 * q^25 - 3 * q^26 + 28 * q^27 - 7 * q^28 - 18 * q^29 - 60 * q^30 - 9 * q^31 + 58 * q^32 - 14 * q^33 - 15 * q^34 + 50 * q^35 - 49 * q^36 - 6 * q^37 + 2 * q^38 + 4 * q^39 - 29 * q^40 - 5 * q^41 + 8 * q^42 - q^43 - 22 * q^44 + 13 * q^45 + 34 * q^46 + 16 * q^47 - 49 * q^48 + 3 * q^49 - 35 * q^51 - 17 * q^52 + 30 * q^53 - 2 * q^54 + 21 * q^55 - 7 * q^56 + 34 * q^58 - 9 * q^59 - 38 * q^60 - 28 * q^61 - 62 * q^62 + 88 * q^63 + 56 * q^64 - 5 * q^65 + 140 * q^66 - 31 * q^67 - 39 * q^68 + 5 * q^69 + 56 * q^70 + q^71 - 32 * q^72 - 10 * q^73 - 39 * q^74 - 2 * q^75 - 16 * q^76 + 76 * q^77 - 23 * q^79 - 22 * q^80 - 29 * q^81 - 10 * q^82 + 3 * q^83 + 52 * q^84 - 32 * q^85 + 4 * q^86 + 18 * q^87 - 10 * q^88 + 26 * q^89 + 35 * q^90 + 4 * q^91 - 94 * q^92 - 41 * q^93 + 70 * q^94 + 28 * q^95 - 23 * q^96 + 32 * q^97 - 38 * q^98 - 70 * 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 $

$2$	−0.708536			−0.501011			−0.250505	−	0.968115i	$-0.580597\pi$
$2$	−0.708536			−0.501011			−0.250505	+	0.968115i	$0.580597\pi$
$3$	−0.837990	+	1.45144i	−0.483814	+	0.837990i	−0.999827	−	0.0185903i	$-0.994082\pi$
$3$	−0.837990	+	1.45144i	−0.483814	+	0.837990i	0.516013	+	0.856581i	$0.327416\pi$
$4$	−1.49798			−0.748988
$5$	1.10081	+	1.90665i	0.492296	+	0.852681i	0.999961	−	0.00887355i	$-0.00282458\pi$
$5$	1.10081	+	1.90665i	0.492296	+	0.852681i	−0.507665	+	0.861555i	$0.669491\pi$
$6$	0.593746	−	1.02840i	0.242396	−	0.419842i
$7$	1.50089	−	2.59962i	0.567283	−	0.982562i	−0.429551	−	0.903043i	$-0.641328\pi$
$7$	1.50089	−	2.59962i	0.567283	−	0.982562i	0.996833	−	0.0795196i	$-0.0253386\pi$
$8$	2.47844			0.876262
$9$	0.0955444	+	0.165488i	0.0318481	+	0.0551626i
$10$	−0.779961	−	1.35093i	−0.246645	−	0.427202i
$11$	2.27605	+	3.94223i	0.686254	+	1.18863i	0.973041	+	0.230633i	$0.0740795\pi$
$11$	2.27605	+	3.94223i	0.686254	+	1.18863i	−0.286787	+	0.957994i	$0.592587\pi$
$12$	1.25529	−	2.17423i	0.362371	−	0.627645i
$13$	−0.500000	−	0.866025i	−0.138675	−	0.240192i
$13$	−0.500000	−	0.866025i	−0.138675	−	0.240192i
$14$	−1.06343	+	1.84192i	−0.284215	+	0.492274i
$15$	−3.68986			−0.952718
$16$	1.23989			0.309972
$17$	−3.32635	+	5.76141i	−0.806758	+	1.39735i	0.108339	+	0.994114i	$0.465447\pi$
$17$	−3.32635	+	5.76141i	−0.806758	+	1.39735i	−0.915098	+	0.403232i	$0.867887\pi$
$18$	−0.0676966	−	0.117254i	−0.0159563	−	0.0276370i
$19$	0.733221	−	1.26998i	0.168212	−	0.291353i	−0.769579	−	0.638552i	$-0.779534\pi$
$19$	0.733221	−	1.26998i	0.168212	−	0.291353i	0.937791	+	0.347199i	$0.112867\pi$
$20$	−1.64898	−	2.85612i	−0.368724	−	0.638648i
$21$	2.51546	+	4.35691i	0.548919	+	0.950755i
$22$	−1.61266	−	2.79321i	−0.343821	−	0.595515i
$23$	−6.58855			−1.37381			−0.686903	−	0.726749i	$-0.741030\pi$
$23$	−6.58855			−1.37381			−0.686903	+	0.726749i	$0.741030\pi$
$24$	−2.07691	+	3.59732i	−0.423948	+	0.734299i
$25$	0.0764505	−	0.132416i	0.0152901	−	0.0264832i
$26$	0.354268	+	0.613610i	0.0694777	+	0.120339i
$27$	−5.34820			−1.02926
$28$	−2.24830	+	3.89416i	−0.424888	+	0.735928i
$29$	−5.25374			−0.975596			−0.487798	−	0.872957i	$-0.662200\pi$
$29$	−5.25374			−0.975596			−0.487798	+	0.872957i	$0.662200\pi$
$30$	2.61440			0.477322
$31$	−0.0357722	+	5.56765i	−0.00642487	+	0.999979i
$31$	−0.0357722	+	5.56765i	−0.00642487	+	0.999979i
$32$	−5.83539			−1.03156
$33$	−7.62922			−1.32808
$34$	2.35684	−	4.08216i	0.404194	−	0.700085i
$35$	6.60875			1.11708
$36$	−0.143123	−	0.247897i	−0.0238539	−	0.0413161i
$37$	1.42159	−	2.46227i	0.233708	−	0.404794i	−0.725188	−	0.688550i	$-0.758247\pi$
$37$	1.42159	−	2.46227i	0.233708	−	0.404794i	0.958896	+	0.283756i	$0.0915807\pi$
$38$	−0.519514	+	0.899824i	−0.0842762	+	0.145971i
$39$	1.67598			0.268372
$40$	2.72829	+	4.72553i	0.431380	+	0.747172i
$41$	3.27262	+	5.66835i	0.511098	+	0.885248i	0.999917	+	0.0128627i	$0.00409443\pi$
$41$	3.27262	+	5.66835i	0.511098	+	0.885248i	−0.488819	+	0.872385i	$0.662572\pi$
$42$	−1.78229	−	3.08702i	−0.275014	−	0.476338i
$43$	1.10219	−	1.90904i	0.168082	−	0.291126i	−0.769664	−	0.638450i	$-0.779576\pi$
$43$	1.10219	−	1.90904i	0.168082	−	0.291126i	0.937745	+	0.347323i	$0.112909\pi$
$44$	−3.40947	−	5.90537i	−0.513996	−	0.890268i
$45$	−0.210352	+	0.364340i	−0.0313574	+	0.0543126i
$46$	4.66822			0.688292
$47$	10.4132			1.51892			0.759459	−	0.650555i	$-0.225464\pi$
$47$	10.4132			1.51892			0.759459	+	0.650555i	$0.225464\pi$
$48$	−1.03901	+	1.79962i	−0.149969	+	0.259753i
$49$	−1.00533	−	1.74129i	−0.143619	−	0.248756i
$50$	−0.0541679	+	0.0938216i	−0.00766050	+	0.0132684i
$51$	−5.57490	−	9.65601i	−0.780642	−	1.35211i
$52$	0.748988	+	1.29729i	0.103866	+	0.179901i
$53$	5.14880	+	8.91797i	0.707241	+	1.22498i	0.965877	+	0.259003i	$0.0833939\pi$
$53$	5.14880	+	8.91797i	0.707241	+	1.22498i	−0.258635	+	0.965975i	$0.583273\pi$
$54$	3.78939			0.515671
$55$	−5.01097	+	8.67926i	−0.675680	+	1.17031i
$56$	3.71987	−	6.44300i	0.497088	−	0.860982i
$57$	1.22886	+	2.12846i	0.162767	+	0.281921i
$58$	3.72247			0.488784
$59$	2.65403	−	4.59691i	0.345525	−	0.598467i	−0.639924	−	0.768438i	$-0.721034\pi$
$59$	2.65403	−	4.59691i	0.345525	−	0.598467i	0.985449	+	0.169971i	$0.0543675\pi$
$60$	5.52732			0.713575
$61$	−11.2874			−1.44520			−0.722602	−	0.691265i	$-0.757054\pi$
$61$	−11.2874			−1.44520			−0.722602	+	0.691265i	$0.757054\pi$
$62$	0.0253459	−	3.94488i	0.00321893	−	0.501000i
$63$	0.573606			0.0722676
$64$	1.65481			0.206851
$65$	1.10081	−	1.90665i	0.136538	−	0.236491i
$66$	5.40558			0.665381
$67$	−0.702967	−	1.21757i	−0.0858811	−	0.148750i	0.819885	−	0.572528i	$-0.194037\pi$
$67$	−0.702967	−	1.21757i	−0.0858811	−	0.148750i	−0.905766	+	0.423777i	$0.860704\pi$
$68$	4.98279	−	8.63045i	0.604252	−	1.04660i
$69$	5.52114	−	9.56289i	0.664667	−	1.15124i
$70$	−4.68254			−0.559670
$71$	4.94784	+	8.56991i	0.587201	+	1.01706i	0.994597	+	0.103810i	$0.0331034\pi$
$71$	4.94784	+	8.56991i	0.587201	+	1.01706i	−0.407396	+	0.913251i	$0.633563\pi$
$72$	0.236801	+	0.410152i	0.0279073	+	0.0483369i
$73$	1.60143	+	2.77376i	0.187433	+	0.324644i	0.944394	−	0.328817i	$-0.106650\pi$
$73$	1.60143	+	2.77376i	0.187433	+	0.324644i	−0.756960	+	0.653461i	$0.773316\pi$
$74$	−1.00725	+	1.74460i	−0.117090	+	0.202806i
$75$	0.128130	+	0.221927i	0.0147951	+	0.0256259i
$76$	−1.09835	+	1.90239i	−0.125989	+	0.218220i
$77$	13.6644			1.55720
$78$	−1.18749			−0.134457
$79$	1.38059	−	2.39126i	0.155329	−	0.269038i	−0.777850	−	0.628450i	$-0.783690\pi$
$79$	1.38059	−	2.39126i	0.155329	−	0.269038i	0.933179	+	0.359413i	$0.117023\pi$
$80$	1.36488	+	2.36403i	0.152598	+	0.264307i
$81$	4.19511	−	7.26614i	0.466123	−	0.807349i
$82$	−2.31877	−	4.01623i	−0.256066	−	0.443519i
$83$	−7.35669	−	12.7422i	−0.807501	−	1.39863i	−0.914589	−	0.404384i	$-0.867486\pi$
$83$	−7.35669	−	12.7422i	−0.807501	−	1.39863i	0.107088	−	0.994250i	$-0.465847\pi$
$84$	−3.76810	−	6.52654i	−0.411134	−	0.712104i
$85$	−14.6467			−1.58865
$86$	−0.780939	+	1.35263i	−0.0842108	+	0.145857i
$87$	4.40259	−	7.62550i	0.472007	−	0.817540i
$88$	5.64105	+	9.77059i	0.601338	+	1.04155i
$89$	−8.89431			−0.942795			−0.471398	−	0.881921i	$-0.656250\pi$
$89$	−8.89431			−0.942795			−0.471398	+	0.881921i	$0.656250\pi$
$90$	0.149042	−	0.258148i	0.0157104	−	0.0272112i
$91$	−3.00178			−0.314672
$92$	9.86949			1.02897
$93$	−8.05114	−	4.71756i	−0.834865	−	0.489188i
$94$	−7.37811			−0.760994
$95$	3.22854			0.331241
$96$	4.89000	−	8.46973i	0.499084	−	0.864438i
$97$	−0.237685			−0.0241332			−0.0120666	−	0.999927i	$-0.503841\pi$
$97$	−0.237685			−0.0241332			−0.0120666	+	0.999927i	$0.503841\pi$
$98$	0.712316	+	1.23377i	0.0719547	+	0.124629i
$99$	−0.434927	+	0.753316i	−0.0437118	+	0.0757111i
$100$	−0.114521	+	0.198356i	−0.0114521	+	0.0198356i
$101$	−1.53942			−0.153178			−0.0765891	−	0.997063i	$-0.524403\pi$
$101$	−1.53942			−0.153178			−0.0765891	+	0.997063i	$0.524403\pi$
$102$	3.95002	+	6.84163i	0.391110	+	0.677422i
$103$	4.60051	+	7.96832i	0.453302	+	0.785142i	0.998589	−	0.0531076i	$-0.0169126\pi$
$103$	4.60051	+	7.96832i	0.453302	+	0.785142i	−0.545287	+	0.838249i	$0.683579\pi$
$104$	−1.23922	−	2.14639i	−0.121516	−	0.210471i
$105$	−5.53807	+	9.59222i	−0.540460	+	0.936105i
$106$	−3.64811	−	6.31871i	−0.354335	−	0.613727i
$107$	−1.12869	+	1.95495i	−0.109115	+	0.188992i	−0.915412	−	0.402519i	$-0.868135\pi$
$107$	−1.12869	+	1.95495i	−0.109115	+	0.188992i	0.806297	+	0.591511i	$0.201468\pi$
$108$	8.01148			0.770905
$109$	−1.89458			−0.181467			−0.0907337	−	0.995875i	$-0.528921\pi$
$109$	−1.89458			−0.181467			−0.0907337	+	0.995875i	$0.528921\pi$
$110$	3.55046	−	6.14957i	0.338523	−	0.586339i
$111$	2.38256	+	4.12671i	0.226142	+	0.391690i
$112$	1.86093	−	3.22323i	0.175842	−	0.304567i
$113$	0.0197680	+	0.0342392i	0.00185962	+	0.00322095i	0.866954	−	0.498389i	$-0.166075\pi$
$113$	0.0197680	+	0.0342392i	0.00185962	+	0.00322095i	−0.865094	+	0.501610i	$0.832741\pi$
$114$	−0.870695	−	1.50809i	−0.0815480	−	0.141245i
$115$	−7.25271	−	12.5621i	−0.676319	−	1.17142i
$116$	7.86999			0.730710
$117$	0.0955444	−	0.165488i	0.00883308	−	0.0152993i
$118$	−1.88048	+	3.25708i	−0.173112	+	0.299838i
$119$	9.98496	+	17.2945i	0.915320	+	1.58538i
$120$	−9.14511			−0.834830
$121$	−4.86078	+	8.41912i	−0.441889	+	0.765375i
$122$	7.99753			0.724062
$123$	−10.9697			−0.989105
$124$	0.0535859	−	8.34021i	0.00481215	−	0.748973i
$125$	11.3447			1.01470
$126$	−0.406421			−0.0362068
$127$	7.73043	−	13.3895i	0.685965	−	1.18813i	−0.287168	−	0.957880i	$-0.592714\pi$
$127$	7.73043	−	13.3895i	0.685965	−	1.18813i	0.973133	−	0.230246i	$-0.0739530\pi$
$128$	10.4983			0.927926
$129$	1.84724	+	3.19952i	0.162641	+	0.281702i
$130$	−0.779961	+	1.35093i	−0.0684071	+	0.118485i
$131$	7.47146	−	12.9409i	0.652785	−	1.13066i	−0.329660	−	0.944100i	$-0.606934\pi$
$131$	7.47146	−	12.9409i	0.652785	−	1.13066i	0.982444	−	0.186556i	$-0.0597326\pi$
$132$	11.4284			0.994714
$133$	−2.20097	−	3.81219i	−0.190848	−	0.330558i
$134$	0.498078	+	0.862696i	0.0430273	+	0.0745255i
$135$	−5.88734	−	10.1972i	−0.506701	−	0.877632i
$136$	−8.24417	+	14.2793i	−0.706931	+	1.22444i
$137$	−3.50354	−	6.06831i	−0.299328	−	0.518451i	0.676654	−	0.736301i	$-0.263429\pi$
$137$	−3.50354	−	6.06831i	−0.299328	−	0.518451i	−0.975982	+	0.217850i	$0.930096\pi$
$138$	−3.91193	+	6.77565i	−0.333005	+	0.576782i
$139$	17.0630			1.44727			0.723634	−	0.690184i	$-0.242471\pi$
$139$	17.0630			1.44727			0.723634	+	0.690184i	$0.242471\pi$
$140$	−9.89976			−0.836682
$141$	−8.72614	+	15.1141i	−0.734874	+	1.27284i
$142$	−3.50572	−	6.07209i	−0.294194	−	0.509559i
$143$	2.27605	−	3.94223i	0.190333	−	0.329666i
$144$	0.118464	+	0.205186i	0.00987202	+	0.0170988i
$145$	−5.78336	−	10.0171i	−0.480282	−	0.831872i
$146$	−1.13467	−	1.96531i	−0.0939061	−	0.162650i
$147$	3.36984			0.277940
$148$	−2.12951	+	3.68842i	−0.175045	+	0.303186i
$149$	−6.64847	+	11.5155i	−0.544664	+	0.943385i	0.453964	+	0.891020i	$0.350009\pi$
$149$	−6.64847	+	11.5155i	−0.544664	+	0.943385i	−0.998628	+	0.0523652i	$0.983324\pi$
$150$	−0.0907844	−	0.157243i	−0.00741252	−	0.0128389i
$151$	23.5398			1.91564			0.957821	−	0.287366i	$-0.0927797\pi$
$151$	23.5398			1.91564			0.957821	+	0.287366i	$0.0927797\pi$
$152$	1.81725	−	3.14756i	0.147398	−	0.255301i
$153$	−1.27126			−0.102775
$154$	−9.68170			−0.780174
$155$	−10.6550	+	6.06070i	−0.855826	+	0.486807i
$156$	−2.51058			−0.201007
$157$	−8.94058			−0.713536			−0.356768	−	0.934193i	$-0.616121\pi$
$157$	−8.94058			−0.713536			−0.356768	+	0.934193i	$0.616121\pi$
$158$	−0.978201	+	1.69429i	−0.0778215	+	0.134791i
$159$	−17.2586			−1.36869
$160$	−6.42363	−	11.1261i	−0.507833	−	0.879592i
$161$	−9.88867	+	17.1277i	−0.779337	+	1.34985i
$162$	−2.97239	+	5.14832i	−0.233533	+	0.404491i
$163$	−11.2462			−0.880869			−0.440435	−	0.897785i	$-0.645176\pi$
$163$	−11.2462			−0.880869			−0.440435	+	0.897785i	$0.645176\pi$
$164$	−4.90231	−	8.49106i	−0.382806	−	0.663040i
$165$	−8.39830	−	14.5463i	−0.653807	−	1.13243i
$166$	5.21248	+	9.02828i	0.404567	+	0.700730i
$167$	7.43910	−	12.8849i	0.575655	−	0.997064i	−0.420315	−	0.907378i	$-0.638080\pi$
$167$	7.43910	−	12.8849i	0.575655	−	0.997064i	0.995970	−	0.0896855i	$-0.0285862\pi$
$168$	6.23442	+	10.7983i	0.480996	+	0.833110i
$169$	−0.500000	+	0.866025i	−0.0384615	+	0.0666173i
$170$	10.3777			0.795933
$171$	0.280221			0.0214290
$172$	−1.65105	+	2.85970i	−0.125891	+	0.218050i
$173$	7.74038	+	13.4067i	0.588490	+	1.01930i	0.994430	+	0.105395i	$0.0336108\pi$
$173$	7.74038	+	13.4067i	0.588490	+	1.01930i	−0.405940	+	0.913900i	$0.633056\pi$
$174$	−3.11939	+	5.40294i	−0.236480	+	0.409596i
$175$	−0.229487	−	0.397484i	−0.0173476	−	0.0300470i
$176$	2.82204	+	4.88792i	0.212719	+	0.368441i
$177$	4.44810	+	7.70434i	0.334340	+	0.579094i
$178$	6.30194			0.472350
$179$	12.0976	−	20.9537i	0.904220	−	1.56615i	0.0822581	−	0.996611i	$-0.473787\pi$
$179$	12.0976	−	20.9537i	0.904220	−	1.56615i	0.821961	−	0.569543i	$-0.192880\pi$
$180$	0.315102	−	0.545773i	0.0234863	−	0.0406795i
$181$	11.5612	+	20.0246i	0.859338	+	1.48842i	0.872562	+	0.488504i	$0.162457\pi$
$181$	11.5612	+	20.0246i	0.859338	+	1.48842i	−0.0132241	+	0.999913i	$0.504209\pi$
$182$	2.12687			0.157654
$183$	9.45873	−	16.3830i	0.699210	−	1.21107i
$184$	−16.3293			−1.20381
$185$	6.25958			0.460214
$186$	5.70452	+	3.34256i	0.418276	+	0.245088i
$187$	−30.2837			−2.21456
$188$	−15.5987			−1.13765
$189$	−8.02706	+	13.9033i	−0.583883	+	1.01131i
$190$	−2.28754			−0.165955
$191$	4.80502	+	8.32254i	0.347679	+	0.602198i	0.985837	−	0.167708i	$-0.0536366\pi$
$191$	4.80502	+	8.32254i	0.347679	+	0.602198i	−0.638158	+	0.769906i	$0.720303\pi$
$192$	−1.38671	+	2.40186i	−0.100078	+	0.173339i
$193$	6.14684	−	10.6466i	0.442459	−	0.766362i	−0.555412	−	0.831575i	$-0.687439\pi$
$193$	6.14684	−	10.6466i	0.442459	−	0.766362i	0.997871	+	0.0652132i	$0.0207728\pi$
$194$	0.168408			0.0120910
$195$	1.84493	+	3.19551i	0.132118	+	0.228835i
$196$	1.50597	+	2.60841i	0.107569	+	0.186315i
$197$	−9.33800	−	16.1739i	−0.665305	−	1.15234i	−0.979203	−	0.202885i	$-0.934968\pi$
$197$	−9.33800	−	16.1739i	−0.665305	−	1.15234i	0.313898	−	0.949457i	$-0.398365\pi$
$198$	0.308162	−	0.533751i	0.0219001	−	0.0379321i
$199$	11.4585	+	19.8466i	0.812269	+	1.40689i	0.911273	+	0.411804i	$0.135101\pi$
$199$	11.4585	+	19.8466i	0.812269	+	1.40689i	−0.0990039	+	0.995087i	$0.531566\pi$
$200$	0.189478	−	0.328186i	0.0133981	−	0.0232062i
$201$	2.35632			0.166202
$202$	1.09074			0.0767439
$203$	−7.88529	+	13.6577i	−0.553439	+	0.958584i
$204$	8.35107	+	14.4645i	0.584692	+	1.01272i
$205$	−7.20505	+	12.4795i	−0.503223	+	0.871607i
$206$	−3.25963	−	5.64584i	−0.227109	−	0.393364i
$207$	−0.629499	−	1.09032i	−0.0437532	−	0.0757827i
$208$	−0.619944	−	1.07377i	−0.0429854	−	0.0744528i
$209$	6.67538			0.461746
$210$	3.92392	−	6.79643i	0.270776	−	0.468998i
$211$	4.77153	−	8.26453i	0.328485	−	0.568953i	−0.653726	−	0.756731i	$-0.726795\pi$
$211$	4.77153	−	8.26453i	0.328485	−	0.568953i	0.982212	+	0.187778i	$0.0601285\pi$
$212$	−7.71277	−	13.3589i	−0.529716	−	0.917494i
$213$	−16.5850			−1.13638
$214$	0.799718	−	1.38515i	0.0546676	−	0.0946871i
$215$	4.85318			0.330984
$216$	−13.2552			−0.901903
$217$	14.4201	+	8.44942i	0.978897	+	0.573584i
$218$	1.34238			0.0909171
$219$	−5.36794			−0.362732
$220$	7.50632	−	13.0013i	0.506076	−	0.876550i
$221$	6.65270			0.447509
$222$	−1.68813	−	2.92392i	−0.113300	−	0.196241i
$223$	3.59963	−	6.23474i	0.241049	−	0.417509i	−0.719964	−	0.694011i	$-0.755842\pi$
$223$	3.59963	−	6.23474i	0.241049	−	0.417509i	0.961013	+	0.276502i	$0.0891752\pi$
$224$	−8.75827	+	15.1698i	−0.585187	+	1.01357i
$225$	0.0292177			0.00194784
$226$	−0.0140063	−	0.0242597i	−0.000931687	−	0.00161373i
$227$	10.7319	+	18.5882i	0.712300	+	1.23374i	0.963992	+	0.265933i	$0.0856799\pi$
$227$	10.7319	+	18.5882i	0.712300	+	1.23374i	−0.251691	+	0.967808i	$0.580987\pi$
$228$	−1.84081	−	3.18838i	−0.121911	−	0.211155i
$229$	−1.82376	+	3.15885i	−0.120518	+	0.208743i	−0.919972	−	0.391984i	$-0.871789\pi$
$229$	−1.82376	+	3.15885i	−0.120518	+	0.208743i	0.799454	+	0.600727i	$0.205122\pi$
$230$	5.13881	+	8.90068i	0.338843	+	0.586893i
$231$	−11.4506	+	19.8330i	−0.753395	+	1.30492i
$232$	−13.0211			−0.854877
$233$	5.29283			0.346745			0.173372	−	0.984856i	$-0.444534\pi$
$233$	5.29283			0.346745			0.173372	+	0.984856i	$0.444534\pi$
$234$	−0.0676966	+	0.117254i	−0.00442547	+	0.00766514i
$235$	11.4629	+	19.8543i	0.747756	+	1.29515i
$236$	−3.97567	+	6.88607i	−0.258794	+	0.448245i
$237$	2.31385	+	4.00770i	0.150301	+	0.260328i
$238$	−7.07470	−	12.2537i	−0.458585	−	0.794293i
$239$	3.22644	+	5.58836i	0.208701	+	0.361481i	0.951306	−	0.308249i	$-0.0997431\pi$
$239$	3.22644	+	5.58836i	0.208701	+	0.361481i	−0.742605	+	0.669730i	$0.766410\pi$
$240$	−4.57501			−0.295316
$241$	−10.0872	+	17.4715i	−0.649771	+	1.12544i	0.333407	+	0.942783i	$0.391802\pi$
$241$	−10.0872	+	17.4715i	−0.649771	+	1.12544i	−0.983177	+	0.182653i	$0.941531\pi$
$242$	3.44404	−	5.96525i	0.221391	−	0.383461i
$243$	−0.991382	−	1.71712i	−0.0635972	−	0.110154i
$244$	16.9083			1.08244
$245$	2.21336	−	3.83365i	0.141406	−	0.244923i
$246$	7.77244			0.495552
$247$	−1.46644			−0.0933075
$248$	−0.0886593	+	13.7991i	−0.00562987	+	0.876244i
$249$	24.6593			1.56272
$250$	−8.03812			−0.508376
$251$	−7.91399	+	13.7074i	−0.499526	+	0.865205i	−1.00000		0.000546839i	$-0.999826\pi$
$251$	−7.91399	+	13.7074i	−0.499526	+	0.865205i	0.500474	+	0.865752i	$0.333159\pi$
$252$	−0.859248			−0.0541276
$253$	−14.9958	−	25.9736i	−0.942781	−	1.63294i
$254$	−5.47729	+	9.48694i	−0.343676	+	0.595264i
$255$	12.2738	−	21.2588i	0.768613	−	1.33128i
$256$	−10.7480			−0.671752
$257$	−2.79388	−	4.83914i	−0.174277	−	0.301857i	0.765634	−	0.643277i	$-0.222426\pi$
$257$	−2.79388	−	4.83914i	−0.174277	−	0.301857i	−0.939911	+	0.341420i	$0.889092\pi$
$258$	−1.30884	−	2.26698i	−0.0814848	−	0.141136i
$259$	−4.26730	−	7.39117i	−0.265157	−	0.459265i
$260$	−1.64898	+	2.85612i	−0.102266	+	0.177129i
$261$	−0.501966	−	0.869430i	−0.0310709	−	0.0538164i
$262$	−5.29380	+	9.16913i	−0.327052	+	0.566471i
$263$	23.6267			1.45689			0.728443	−	0.685106i	$-0.240244\pi$
$263$	23.6267			1.45689			0.728443	+	0.685106i	$0.240244\pi$
$264$	−18.9086			−1.16374
$265$	−11.3357	+	19.6339i	−0.696344	+	1.20610i
$266$	1.55946	+	2.70107i	0.0956169	+	0.165613i
$267$	7.45335	−	12.9096i	0.456137	−	0.790053i
$268$	1.05303	+	1.82390i	0.0643239	+	0.111412i
$269$	−7.72534	−	13.3807i	−0.471023	−	0.815835i	0.528428	−	0.848978i	$-0.322782\pi$
$269$	−7.72534	−	13.3807i	−0.471023	−	0.815835i	−0.999451	+	0.0331431i	$0.989448\pi$
$270$	4.17139	+	7.22506i	0.253863	+	0.439703i
$271$	−4.92814			−0.299363			−0.149682	−	0.988734i	$-0.547825\pi$
$271$	−4.92814			−0.299363			−0.149682	+	0.988734i	$0.547825\pi$
$272$	−4.12430	+	7.14349i	−0.250072	+	0.433138i
$273$	2.51546	−	4.35691i	0.152243	−	0.263692i
$274$	2.48239	+	4.29962i	0.149966	+	0.259749i
$275$	0.696020			0.0419716
$276$	−8.27054	+	14.3250i	−0.497828	+	0.862263i
$277$	−3.75504			−0.225618			−0.112809	−	0.993617i	$-0.535985\pi$
$277$	−3.75504			−0.225618			−0.112809	+	0.993617i	$0.535985\pi$
$278$	−12.0898			−0.725096
$279$	−0.924796	+	0.526038i	−0.0553661	+	0.0314931i
$280$	16.3794			0.978857
$281$	−2.61081			−0.155748			−0.0778740	−	0.996963i	$-0.524813\pi$
$281$	−2.61081			−0.155748			−0.0778740	+	0.996963i	$0.524813\pi$
$282$	6.18278	−	10.7089i	0.368179	−	0.637706i
$283$	5.71029			0.339441			0.169721	−	0.985492i	$-0.445713\pi$
$283$	5.71029			0.339441			0.169721	+	0.985492i	$0.445713\pi$
$284$	−7.41175	−	12.8375i	−0.439807	−	0.761767i
$285$	−2.70548	+	4.68604i	−0.160259	+	0.277577i
$286$	−1.61266	+	2.79321i	−0.0953587	+	0.165166i
$287$	19.6474			1.15975
$288$	−0.557539	−	0.965686i	−0.0328533	−	0.0569036i
$289$	−13.6292	−	23.6065i	−0.801718	−	1.38862i
$290$	4.09772	+	7.09745i	0.240626	+	0.416777i
$291$	0.199178	−	0.344986i	0.0116760	−	0.0202234i
$292$	−2.39891	−	4.15503i	−0.140385	−	0.243155i
$293$	12.7659	−	22.1112i	0.745791	−	1.29175i	−0.204034	−	0.978964i	$-0.565405\pi$
$293$	12.7659	−	22.1112i	0.745791	−	1.29175i	0.949824	−	0.312784i	$-0.101261\pi$
$294$	−2.38765			−0.139251
$295$	11.6863			0.680402
$296$	3.52333	−	6.10258i	0.204789	−	0.354706i
$297$	−12.1728	−	21.0838i	−0.706335	−	1.22341i
$298$	4.71068	−	8.15913i	0.272882	−	0.472646i
$299$	3.29427	+	5.70585i	0.190513	+	0.329978i
$300$	−0.191935	−	0.332441i	−0.0110814	−	0.0191935i
$301$	−3.30852	−	5.73053i	−0.190700	−	0.330302i
$302$	−16.6788			−0.959757
$303$	1.29002	−	2.23438i	0.0741097	−	0.128362i
$304$	0.909112	−	1.57463i	0.0521411	−	0.0903111i
$305$	−12.4252	−	21.5211i	−0.711467	−	1.23230i
$306$	0.900731			0.0514914
$307$	−3.15551	+	5.46551i	−0.180095	+	0.311933i	−0.941913	−	0.335858i	$-0.890974\pi$
$307$	−3.15551	+	5.46551i	−0.180095	+	0.311933i	0.761818	+	0.647791i	$0.224307\pi$
$308$	−20.4689			−1.16632
$309$	−15.4207			−0.877255
$310$	7.54942	−	4.29422i	0.428778	−	0.243896i
$311$	−0.633190			−0.0359049			−0.0179524	−	0.999839i	$-0.505715\pi$
$311$	−0.633190			−0.0359049			−0.0179524	+	0.999839i	$0.505715\pi$
$312$	4.15382			0.235164
$313$	16.7812	−	29.0659i	0.948530	−	1.64290i	0.200005	−	0.979795i	$-0.435904\pi$
$313$	16.7812	−	29.0659i	0.948530	−	1.64290i	0.748525	−	0.663107i	$-0.230762\pi$
$314$	6.33472			0.357489
$315$	0.631429	+	1.09367i	0.0355770	+	0.0616212i
$316$	−2.06810	+	3.58205i	−0.116340	+	0.201506i
$317$	13.2042	−	22.8704i	0.741623	−	1.28453i	−0.210132	−	0.977673i	$-0.567389\pi$
$317$	13.2042	−	22.8704i	0.741623	−	1.28453i	0.951756	−	0.306857i	$-0.0992772\pi$
$318$	12.2283			0.685730
$319$	−11.9578	−	20.7115i	−0.669507	−	1.15962i
$320$	1.82163	+	3.15515i	0.101832	+	0.176378i
$321$	−1.89166	−	3.27646i	−0.105582	−	0.182874i
$322$	7.00648	−	12.1356i	0.390456	−	0.676290i
$323$	4.87790	+	8.44877i	0.271414	+	0.470102i
$324$	−6.28418	+	10.8845i	−0.349121	+	0.604695i
$325$	−0.152901			−0.00848142
$326$	7.96833			0.441325
$327$	1.58764	−	2.74987i	0.0877965	−	0.152068i
$328$	8.11101	+	14.0487i	0.447856	+	0.775709i
$329$	15.6290	−	27.0703i	0.861656	−	1.49243i
$330$	5.95050	+	10.3066i	0.327564	+	0.567358i
$331$	−15.2280	−	26.3757i	−0.837008	−	1.44974i	−0.892385	−	0.451275i	$-0.850969\pi$
$331$	−15.2280	−	26.3757i	−0.837008	−	1.44974i	0.0553768	−	0.998466i	$-0.482364\pi$
$332$	11.0201	+	19.0875i	0.604809	+	1.04756i
$333$	0.543300			0.0297726
$334$	−5.27087	+	9.12942i	−0.288409	+	0.499540i
$335$	1.54766	−	2.68063i	0.0845578	−	0.146458i
$336$	3.11889	+	5.40207i	0.170149	+	0.294707i
$337$	−18.8044			−1.02434			−0.512171	−	0.858883i	$-0.671159\pi$
$337$	−18.8044			−1.02434			−0.512171	+	0.858883i	$0.671159\pi$
$338$	0.354268	−	0.613610i	0.0192696	−	0.0333760i
$339$	−0.0662615			−0.00359883
$340$	21.9404			1.18988
$341$	−22.0304	+	12.5312i	−1.19301	+	0.678603i
$342$	−0.198546			−0.0107362
$343$	14.9769			0.808675
$344$	2.73171	−	4.73146i	0.147284	−	0.255103i
$345$	24.3108			1.30885
$346$	−5.48434	−	9.49915i	−0.294840	−	0.510678i
$347$	0.737302	−	1.27704i	0.0395804	−	0.0685553i	−0.845557	−	0.533886i	$-0.820731\pi$
$347$	0.737302	−	1.27704i	0.0395804	−	0.0685553i	0.885137	+	0.465331i	$0.154065\pi$
$348$	−6.59497	+	11.4228i	−0.353528	+	0.612328i
$349$	33.4211			1.78899			0.894496	−	0.447076i	$-0.147535\pi$
$349$	33.4211			1.78899			0.894496	+	0.447076i	$0.147535\pi$
$350$	0.162600	+	0.281632i	0.00869134	+	0.0150538i
$351$	2.67410	+	4.63168i	0.142733	+	0.247221i
$352$	−13.2816	−	23.0044i	−0.707913	−	1.22614i
$353$	−3.84514	+	6.65998i	−0.204656	+	0.354475i	−0.950023	−	0.312179i	$-0.898941\pi$
$353$	−3.84514	+	6.65998i	−0.204656	+	0.354475i	0.745367	+	0.666654i	$0.232274\pi$
$354$	−3.15164	−	5.45880i	−0.167508	−	0.290132i
$355$	−10.8932	+	18.8676i	−0.578153	+	1.00139i
$356$	13.3235			0.706142
$357$	−33.4692			−1.77138
$358$	−8.57161	+	14.8465i	−0.453024	+	0.784660i
$359$	−3.86535	−	6.69498i	−0.204005	−	0.353348i	0.745810	−	0.666159i	$-0.232063\pi$
$359$	−3.86535	−	6.69498i	−0.204005	−	0.353348i	−0.949815	+	0.312811i	$0.898729\pi$
$360$	−0.521345	+	0.902996i	−0.0274773	+	0.0475920i
$361$	8.42477	+	14.5921i	0.443409	+	0.768007i
$362$	−8.19153	−	14.1881i	−0.430537	−	0.745713i
$363$	−8.14658	−	14.1103i	−0.427584	−	0.740598i
$364$	4.49659			0.235685
$365$	−3.52573	+	6.10675i	−0.184545	+	0.319642i
$366$	−6.70185	+	11.6079i	−0.350311	+	0.606757i
$367$	−8.56551	−	14.8359i	−0.447116	−	0.774428i	0.551081	−	0.834452i	$-0.314216\pi$
$367$	−8.56551	−	14.8359i	−0.447116	−	0.774428i	−0.998197	+	0.0600242i	$0.980882\pi$
$368$	−8.16905			−0.425841
$369$	−0.625362	+	1.08316i	−0.0325550	+	0.0563870i
$370$	−4.43514			−0.230572
$371$	30.9111			1.60482
$372$	12.0604	+	7.06679i	0.625304	+	0.366396i
$373$	14.1241			0.731318			0.365659	−	0.930749i	$-0.380844\pi$
$373$	14.1241			0.731318			0.365659	+	0.930749i	$0.380844\pi$
$374$	21.4571			1.10952
$375$	−9.50674	+	16.4662i	−0.490926	+	0.850309i
$376$	25.8085			1.33097
$377$	2.62687	+	4.54988i	0.135291	+	0.234331i
$378$	5.68746	−	9.85097i	0.292531	−	0.506679i
$379$	−3.04615	+	5.27609i	−0.156470	+	0.271014i	−0.933593	−	0.358334i	$-0.883345\pi$
$379$	−3.04615	+	5.27609i	−0.156470	+	0.271014i	0.777123	+	0.629349i	$0.216678\pi$
$380$	−4.83627			−0.248096
$381$	12.9561	+	22.4405i	0.663759	+	1.14966i
$382$	−3.40453	−	5.89682i	−0.174191	−	0.301707i
$383$	−7.22779	−	12.5189i	−0.369323	−	0.639686i	0.620137	−	0.784494i	$-0.287077\pi$
$383$	−7.22779	−	12.5189i	−0.369323	−	0.639686i	−0.989460	+	0.144807i	$0.953744\pi$
$384$	−8.79746	+	15.2377i	−0.448944	+	0.777593i
$385$	15.0418	+	26.0532i	0.766603	+	1.32779i
$386$	−4.35526	+	7.54353i	−0.221677	+	0.383956i
$387$	0.421231			0.0214124
$388$	0.356046			0.0180755
$389$	−7.04822	+	12.2079i	−0.357359	+	0.618964i	−0.987519	−	0.157502i	$-0.949656\pi$
$389$	−7.04822	+	12.2079i	−0.357359	+	0.618964i	0.630160	+	0.776466i	$0.282989\pi$
$390$	−1.30720	−	2.26414i	−0.0661926	−	0.114649i
$391$	21.9158	−	37.9593i	1.10833	−	1.91968i
$392$	−2.49166	−	4.31569i	−0.125848	−	0.217975i
$393$	12.5220	+	21.6888i	0.631653	+	1.09405i
$394$	6.61631	+	11.4598i	0.333325	+	0.577336i
$395$	6.07907			0.305871
$396$	0.651511	−	1.12845i	0.0327396	−	0.0567067i
$397$	−11.1760	+	19.3574i	−0.560907	+	0.971519i	0.436511	+	0.899699i	$0.356214\pi$
$397$	−11.1760	+	19.3574i	−0.560907	+	0.971519i	−0.997418	+	0.0718201i	$0.977119\pi$
$398$	−8.11873	−	14.0621i	−0.406955	−	0.704867i
$399$	7.37756			0.369340
$400$	0.0947900	−	0.164181i	0.00473950	−	0.00820906i
$401$	9.80738			0.489757			0.244878	−	0.969554i	$-0.421252\pi$
$401$	9.80738			0.489757			0.244878	+	0.969554i	$0.421252\pi$
$402$	−1.66954			−0.0832689
$403$	4.83961	−	2.75285i	0.241078	−	0.137129i
$404$	2.30602			0.114729
$405$	18.4720			0.917882
$406$	5.58701	−	9.67698i	0.277279	−	0.480261i
$407$	12.9424			0.641532
$408$	−13.8171	−	23.9319i	−0.684047	−	1.18480i
$409$	4.92478	−	8.52998i	0.243515	−	0.421780i	−0.718198	−	0.695839i	$-0.755033\pi$
$409$	4.92478	−	8.52998i	0.243515	−	0.421780i	0.961713	+	0.274058i	$0.0883662\pi$
$410$	5.10504	−	8.84219i	0.252120	−	0.436684i
$411$	11.7437			0.579276
$412$	−6.89146	−	11.9364i	−0.339518	−	0.588062i
$413$	−7.96681	−	13.7989i	−0.392021	−	0.679000i
$414$	0.446022	+	0.772534i	0.0219208	+	0.0379680i
$415$	16.1966	−	28.0533i	0.795059	−	1.37708i
$416$	2.91770	+	5.05360i	0.143052	+	0.247773i
$417$	−14.2987	+	24.7660i	−0.700208	+	1.21280i
$418$	−4.72975			−0.231340
$419$	−32.3603			−1.58091			−0.790453	−	0.612523i	$-0.790155\pi$
$419$	−32.3603			−1.58091			−0.790453	+	0.612523i	$0.790155\pi$
$420$	8.29590	−	14.3689i	0.404798	−	0.701132i
$421$	−3.96754	−	6.87199i	−0.193366	−	0.334920i	0.752998	−	0.658023i	$-0.228607\pi$
$421$	−3.96754	−	6.87199i	−0.193366	−	0.334920i	−0.946364	+	0.323103i	$0.895274\pi$
$422$	−3.38080	+	5.85572i	−0.164575	+	0.285052i
$423$	0.994920	+	1.72325i	0.0483747	+	0.0837874i
$424$	12.7610	+	22.1027i	0.619729	+	1.07340i
$425$	0.508602	+	0.880925i	0.0246708	+	0.0427311i
$426$	11.7511			0.569340
$427$	−16.9411	+	29.3429i	−0.819839	+	1.42000i
$428$	1.69075	−	2.92847i	0.0817256	−	0.141553i
$429$	3.81461	+	6.60710i	0.184171	+	0.318994i
$430$	−3.43865			−0.165827
$431$	−8.67563	+	15.0266i	−0.417891	+	0.723808i	−0.995727	−	0.0923449i	$-0.970564\pi$
$431$	−8.67563	+	15.0266i	−0.417891	+	0.723808i	0.577837	+	0.816153i	$0.303897\pi$
$432$	−6.63117			−0.319042
$433$	29.1336			1.40007			0.700035	−	0.714109i	$-0.253168\pi$
$433$	29.1336			1.40007			0.700035	+	0.714109i	$0.253168\pi$
$434$	−10.2171	−	5.98672i	−0.490438	−	0.287372i
$435$	19.3856			0.929468
$436$	2.83803			0.135917
$437$	−4.83086	+	8.36730i	−0.231091	+	0.400262i
$438$	3.80338			0.181732
$439$	2.46278	+	4.26565i	0.117542	+	0.203588i	0.918793	−	0.394740i	$-0.129165\pi$
$439$	2.46278	+	4.26565i	0.117542	+	0.203588i	−0.801251	+	0.598328i	$0.795832\pi$
$440$	−12.4194	+	21.5111i	−0.592072	+	1.02550i
$441$	0.192108	−	0.332741i	0.00914800	−	0.0158448i
$442$	−4.71368			−0.224207
$443$	−13.3047	−	23.0444i	−0.632126	−	1.09487i	−0.987116	−	0.160004i	$-0.948849\pi$
$443$	−13.3047	−	23.0444i	−0.632126	−	1.09487i	0.354991	−	0.934870i	$-0.384484\pi$
$444$	−3.56901	−	6.18172i	−0.169378	−	0.293371i
$445$	−9.79091	−	16.9584i	−0.464134	−	0.803903i
$446$	−2.55047	+	4.41754i	−0.120768	+	0.209177i
$447$	−11.1427	−	19.2997i	−0.527032	−	0.912846i
$448$	2.48369	−	4.30187i	0.117343	−	0.203244i
$449$	−11.2816			−0.532410			−0.266205	−	0.963916i	$-0.585770\pi$
$449$	−11.2816			−0.532410			−0.266205	+	0.963916i	$0.585770\pi$
$450$	−0.0207018			−0.000975891
$451$	−14.8973	+	25.8029i	−0.701486	+	1.21501i
$452$	−0.0296120	−	0.0512895i	−0.00139283	−	0.00241245i
$453$	−19.7261	+	34.1666i	−0.926814	+	1.60529i
$454$	−7.60393	−	13.1704i	−0.356870	−	0.618117i
$455$	−3.30438	−	5.72335i	−0.154912	−	0.268315i
$456$	3.04567	+	5.27526i	0.142627	+	0.247036i
$457$	−13.1608			−0.615636			−0.307818	−	0.951445i	$-0.599599\pi$
$457$	−13.1608			−0.615636			−0.307818	+	0.951445i	$0.599599\pi$
$458$	1.29220	−	2.23816i	0.0603807	−	0.104582i
$459$	17.7900	−	30.8132i	0.830366	−	1.43824i
$460$	10.8644	+	18.8177i	0.506555	+	0.877379i
$461$	21.7849			1.01462			0.507312	−	0.861762i	$-0.330639\pi$
$461$	21.7849			1.01462			0.507312	+	0.861762i	$0.330639\pi$
$462$	8.11317	−	14.0524i	0.377459	−	0.653778i
$463$	2.26043			0.105051			0.0525255	−	0.998620i	$-0.483273\pi$
$463$	2.26043			0.105051			0.0525255	+	0.998620i	$0.483273\pi$
$464$	−6.51405			−0.302407
$465$	0.131994	−	20.5438i	0.00612109	−	0.952698i
$466$	−3.75016			−0.173723
$467$	−28.5324			−1.32032			−0.660162	−	0.751123i	$-0.729512\pi$
$467$	−28.5324			−1.32032			−0.660162	+	0.751123i	$0.729512\pi$
$468$	−0.143123	+	0.247897i	−0.00661588	+	0.0114590i
$469$	−4.22030			−0.194875
$470$	−8.12187	−	14.0675i	−0.374634	−	0.648885i
$471$	7.49212	−	12.9767i	0.345219	−	0.597936i
$472$	6.57786	−	11.3932i	0.302771	−	0.524414i
$473$	10.0345			0.461388
$474$	−1.63945	−	2.83960i	−0.0753022	−	0.130427i
$475$	−0.112110	−	0.194181i	−0.00514397	−	0.00890962i
$476$	−14.9572	−	25.9067i	−0.685564	−	1.18743i
$477$	−0.983877	+	1.70412i	−0.0450486	+	0.0780265i
$478$	−2.28605	−	3.95955i	−0.104561	−	0.181106i
$479$	−10.6784	+	18.4956i	−0.487910	+	0.845085i	−0.999903	−	0.0139041i	$-0.995574\pi$
$479$	−10.6784	+	18.4956i	−0.487910	+	0.845085i	0.511993	+	0.858990i	$0.328907\pi$
$480$	21.5318			0.982787
$481$	−2.84318			−0.129638
$482$	7.14711	−	12.3792i	0.325542	−	0.563856i
$483$	−16.5732	−	28.7057i	−0.754108	−	1.30615i
$484$	7.28134	−	12.6116i	0.330970	−	0.573257i
$485$	−0.261645	−	0.453182i	−0.0118807	−	0.0205780i
$486$	0.702430	+	1.21664i	0.0318629	+	0.0551881i
$487$	13.6938	+	23.7184i	0.620527	+	1.07478i	0.989388	+	0.145300i	$0.0464146\pi$
$487$	13.6938	+	23.7184i	0.620527	+	1.07478i	−0.368861	+	0.929485i	$0.620252\pi$
$488$	−27.9752			−1.26638
$489$	9.42419	−	16.3232i	0.426177	−	0.738160i
$490$	−1.56824	+	2.71628i	−0.0708460	+	0.122709i
$491$	−7.68619	−	13.3129i	−0.346873	−	0.600802i	0.638819	−	0.769357i	$-0.279423\pi$
$491$	−7.68619	−	13.3129i	−0.346873	−	0.600802i	−0.985692	+	0.168555i	$0.946090\pi$
$492$	16.4324			0.740828
$493$	17.4758	−	30.2690i	0.787070	−	1.36325i
$494$	1.03903			0.0467480
$495$	−1.91508			−0.0860765
$496$	−0.0443535	+	6.90326i	−0.00199153	+	0.309965i
$497$	29.7046			1.33244
$498$	−17.4720			−0.782940
$499$	−5.33948	+	9.24826i	−0.239028	+	0.414009i	−0.960436	−	0.278502i	$-0.910162\pi$
$499$	−5.33948	+	9.24826i	−0.239028	+	0.414009i	0.721408	+	0.692511i	$0.243495\pi$
$500$	−16.9941			−0.759999
$501$	12.4678	+	21.5948i	0.557020	+	0.964787i
$502$	5.60734	−	9.71221i	0.250268	−	0.433477i
$503$	−12.9423	+	22.4167i	−0.577067	+	0.999510i	0.418746	+	0.908103i	$0.362470\pi$
$503$	−12.9423	+	22.4167i	−0.577067	+	0.999510i	−0.995814	+	0.0914068i	$0.970864\pi$
$504$	1.42165			0.0633253
$505$	−1.69460	−	2.93514i	−0.0754089	−	0.130612i
$506$	10.6251	+	18.4032i	0.472343	+	0.818122i
$507$	−0.837990	−	1.45144i	−0.0372165	−	0.0644608i
$508$	−11.5800	+	20.0572i	−0.513780	+	0.889893i
$509$	11.3121	+	19.5932i	0.501402	+	0.868454i	0.999999	+	0.00161980i	$0.000515599\pi$
$509$	11.3121	+	19.5932i	0.501402	+	0.868454i	−0.498597	+	0.866834i	$0.666151\pi$
$510$	−8.69641	+	15.0626i	−0.385083	+	0.666984i
$511$	9.61428			0.425311
$512$	−13.3812			−0.591371
$513$	−3.92142	+	6.79209i	−0.173135	+	0.299878i
$514$	1.97956	+	3.42870i	0.0873148	+	0.151234i
$515$	−10.1285	+	17.5432i	−0.446317	+	0.773044i
$516$	−2.76713	−	4.79281i	−0.121816	−	0.210992i
$517$	23.7009	+	41.0511i	1.04236	+	1.80543i
$518$	3.02353	+	5.23691i	0.132846	+	0.230097i
$519$	−25.9455			−1.13888
$520$	2.72829	−	4.72553i	0.119643	−	0.207228i
$521$	−17.8719	+	30.9550i	−0.782982	+	1.35616i	0.147216	+	0.989104i	$0.452969\pi$
$521$	−17.8719	+	30.9550i	−0.782982	+	1.35616i	−0.930198	+	0.367059i	$0.880365\pi$
$522$	0.355661	+	0.616023i	0.0155669	+	0.0269626i
$523$	23.6932			1.03603			0.518017	−	0.855371i	$-0.326671\pi$
$523$	23.6932			1.03603			0.518017	+	0.855371i	$0.326671\pi$
$524$	−11.1921	+	19.3852i	−0.488928	+	0.846848i
$525$	0.769233			0.0335721
$526$	−16.7404			−0.729916
$527$	−31.9585	−	18.7260i	−1.39213	−	0.815719i
$528$	−9.45938			−0.411667
$529$	20.4089			0.887345
$530$	8.03172	−	13.9113i	0.348876	−	0.604270i
$531$	1.01431			0.0440173
$532$	3.29700	+	5.71057i	0.142943	+	0.247584i
$533$	3.27262	−	5.66835i	0.141753	−	0.245524i
$534$	−5.28096	+	9.14690i	−0.228530	+	0.395825i
$535$	−4.96988			−0.214867
$536$	−1.74226	−	3.01769i	−0.0752543	−	0.130344i
$537$	20.2754	+	35.1180i	0.874948	+	1.51545i
$538$	5.47369	+	9.48070i	0.235987	+	0.408742i
$539$	4.57638	−	7.92652i	0.197118	−	0.341419i
$540$	8.81909	+	15.2751i	0.379513	+	0.657336i
$541$	7.58455	−	13.1368i	0.326085	−	0.564796i	−0.655646	−	0.755068i	$-0.727604\pi$
$541$	7.58455	−	13.1368i	0.326085	−	0.564796i	0.981731	+	0.190272i	$0.0609370\pi$
$542$	3.49177			0.149984
$543$	−38.7527			−1.66304
$544$	19.4105	−	33.6201i	0.832220	−	1.44145i
$545$	−2.08556	−	3.61230i	−0.0893356	−	0.154734i
$546$	−1.78229	+	3.08702i	−0.0762752	+	0.132112i
$547$	−16.1377	−	27.9513i	−0.689999	−	1.19511i	−0.971838	−	0.235651i	$-0.924278\pi$
$547$	−16.1377	−	27.9513i	−0.689999	−	1.19511i	0.281839	−	0.959462i	$-0.409056\pi$
$548$	5.24823	+	9.09019i	0.224193	+	0.388314i
$549$	−1.07845	−	1.86793i	−0.0460270	−	0.0797211i
$550$	−0.493155			−0.0210282
$551$	−3.85216	+	6.67213i	−0.164107	+	0.284242i
$552$	13.6838	−	23.7011i	0.582422	−	1.00878i
$553$	−4.14424	−	7.17803i	−0.176231	−	0.305241i
$554$	2.66058			0.113037
$555$	−5.24547	+	9.08542i	−0.222658	+	0.385654i
$556$	−25.5600			−1.08399
$557$	−12.1909			−0.516545			−0.258272	−	0.966072i	$-0.583153\pi$
$557$	−12.1909			−0.516545			−0.258272	+	0.966072i	$0.583153\pi$
$558$	0.655251	−	0.372717i	0.0277390	−	0.0157784i
$559$	−2.20437			−0.0932351
$560$	8.19411			0.346264
$561$	25.3775	−	43.9550i	1.07144	−	1.85578i
$562$	1.84985			0.0780314
$563$	−20.2610	−	35.0931i	−0.853900	−	1.47900i	−0.877662	−	0.479280i	$-0.840898\pi$
$563$	−20.2610	−	35.0931i	−0.853900	−	1.47900i	0.0237625	−	0.999718i	$-0.492435\pi$
$564$	13.0716	−	22.6406i	0.550412	−	0.953341i
$565$	−0.0435214	+	0.0753814i	−0.00183096	+	0.00317132i
$566$	−4.04595			−0.170064
$567$	−12.5928	−	21.8113i	−0.528847	−	0.915990i
$568$	12.2629	+	21.2400i	0.514542	+	0.891212i
$569$	−5.47465	−	9.48236i	−0.229509	−	0.397521i	0.728154	−	0.685414i	$-0.240379\pi$
$569$	−5.47465	−	9.48236i	−0.229509	−	0.397521i	−0.957663	+	0.287893i	$0.907045\pi$
$570$	1.91693	−	3.32023i	0.0802915	−	0.139069i
$571$	0.339152	+	0.587428i	0.0141931	+	0.0245831i	0.873035	−	0.487658i	$-0.162149\pi$
$571$	0.339152	+	0.587428i	0.0141931	+	0.0245831i	−0.858842	+	0.512241i	$0.828815\pi$
$572$	−3.40947	+	5.90537i	−0.142557	+	0.246916i
$573$	−16.1062			−0.672848
$574$	−13.9209			−0.581046
$575$	−0.503698	+	0.872430i	−0.0210056	+	0.0363828i
$576$	0.158108	+	0.273851i	0.00658782	+	0.0114104i
$577$	−10.4228	+	18.0527i	−0.433905	+	0.751546i	−0.997206	−	0.0747064i	$-0.976198\pi$
$577$	−10.4228	+	18.0527i	−0.433905	+	0.751546i	0.563300	+	0.826252i	$0.309531\pi$
$578$	9.65678	+	16.7260i	0.401669	+	0.695711i
$579$	10.3020	+	17.8436i	0.428136	+	0.741553i
$580$	8.66333	+	15.0053i	0.359725	+	0.623062i
$581$	−44.1663			−1.83233
$582$	−0.141124	+	0.244435i	−0.00584980	+	0.0101321i
$583$	−23.4378	+	40.5955i	−0.970695	+	1.68129i
$584$	3.96906	+	6.87461i	0.164241	+	0.284473i
$585$	0.420704			0.0173939
$586$	−9.04509	+	15.6666i	−0.373649	+	0.647179i
$587$	30.2850			1.24999			0.624997	−	0.780627i	$-0.285100\pi$
$587$	30.2850			1.24999			0.624997	+	0.780627i	$0.285100\pi$
$588$	−5.04794			−0.208174
$589$	7.04455	+	4.12775i	0.290266	+	0.170081i
$590$	−8.28016			−0.340889
$591$	31.3006			1.28754
$592$	1.76261	−	3.05293i	0.0724429	−	0.125475i
$593$	11.9210			0.489538			0.244769	−	0.969581i	$-0.421288\pi$
$593$	11.9210			0.489538			0.244769	+	0.969581i	$0.421288\pi$
$594$	8.62484	+	14.9387i	0.353882	+	0.612941i
$595$	−21.9830	+	38.0757i	−0.901216	+	1.56095i
$596$	9.95925	−	17.2499i	0.407947	−	0.706584i
$597$	−38.4083			−1.57195
$598$	−2.33411	−	4.04280i	−0.0954489	−	0.165322i
$599$	−10.1985	−	17.6644i	−0.416700	−	0.721746i	0.578905	−	0.815395i	$-0.303480\pi$
$599$	−10.1985	−	17.6644i	−0.416700	−	0.721746i	−0.995605	+	0.0936490i	$0.970147\pi$
$600$	0.317562	+	0.550033i	0.0129644	+	0.0224550i
$601$	−6.17320	+	10.6923i	−0.251810	+	0.436148i	−0.964024	−	0.265815i	$-0.914359\pi$
$601$	−6.17320	+	10.6923i	−0.251810	+	0.436148i	0.712214	+	0.701962i	$0.247692\pi$
$602$	2.34421	+	4.06028i	0.0955427	+	0.165485i
$603$	0.134329	−	0.232665i	0.00547030	−	0.00947485i
$604$	−35.2621			−1.43479
$605$	−21.4031			−0.870161
$606$	−0.914026	+	1.58314i	−0.0371298	+	0.0643106i
$607$	−11.0019	−	19.0559i	−0.446554	−	0.773454i	0.551605	−	0.834105i	$-0.314016\pi$
$607$	−11.0019	−	19.0559i	−0.446554	−	0.773454i	−0.998159	+	0.0606513i	$0.980682\pi$
$608$	−4.27863	+	7.41081i	−0.173521	+	0.300548i
$609$	−13.2156	−	22.8901i	−0.535523	−	0.927552i
$610$	8.80373	+	15.2485i	0.356453	+	0.617394i
$611$	−5.20659	−	9.01807i	−0.210636	−	0.364832i
$612$	1.90431			0.0769772
$613$	1.48933	−	2.57960i	0.0601535	−	0.104189i	−0.834380	−	0.551189i	$-0.814174\pi$
$613$	1.48933	−	2.57960i	0.0601535	−	0.104189i	0.894534	+	0.447000i	$0.147508\pi$
$614$	2.23580	−	3.87251i	0.0902294	−	0.156282i
$615$	−12.0755	−	20.9154i	−0.486932	−	0.843391i
$616$	33.8664			1.36451
$617$	−1.05071	+	1.81988i	−0.0422999	+	0.0732655i	−0.886400	−	0.462920i	$-0.846802\pi$
$617$	−1.05071	+	1.81988i	−0.0422999	+	0.0732655i	0.844100	+	0.536185i	$0.180135\pi$
$618$	10.9261			0.439514
$619$	−21.4350			−0.861545			−0.430772	−	0.902461i	$-0.641759\pi$
$619$	−21.4350			−0.861545			−0.430772	+	0.902461i	$0.641759\pi$
$620$	15.9609	−	9.07879i	0.641004	−	0.364613i
$621$	35.2369			1.41401
$622$	0.448638			0.0179887
$623$	−13.3494	+	23.1218i	−0.534831	+	0.926355i
$624$	2.07803			0.0831877
$625$	12.1061	+	20.9683i	0.484242	+	0.838732i
$626$	−11.8901	+	20.5942i	−0.475223	+	0.823111i
$627$	−5.59391	+	9.68893i	−0.223399	+	0.386939i
$628$	13.3928			0.534430
$629$	9.45741	+	16.3807i	0.377092	+	0.653142i
$630$	−0.447390	−	0.774903i	−0.0178245	−	0.0308729i
$631$	−5.14507	−	8.91152i	−0.204822	−	0.354762i	0.745254	−	0.666781i	$-0.232328\pi$
$631$	−5.14507	−	8.91152i	−0.204822	−	0.354762i	−0.950076	+	0.312019i	$0.898995\pi$
$632$	3.42172	−	5.92660i	0.136109	−	0.235747i
$633$	7.99699	+	13.8512i	0.317852	+	0.550535i
$634$	−9.35567	+	16.2045i	−0.371561	+	0.643563i
$635$	34.0388			1.35079
$636$	25.8529			1.02514
$637$	−1.00533	+	1.74129i	−0.0398328	+	0.0689924i
$638$	8.47251	+	14.6748i	0.335430	+	0.580982i
$639$	−0.945477	+	1.63761i	−0.0374025	+	0.0647830i
$640$	11.5566	+	20.0166i	0.456814	+	0.791225i
$641$	13.3138	+	23.0602i	0.525863	+	0.910822i	0.999546	+	0.0301265i	$0.00959101\pi$
$641$	13.3138	+	23.0602i	0.525863	+	0.910822i	−0.473683	+	0.880696i	$0.657076\pi$
$642$	1.34031	+	2.32149i	0.0528979	+	0.0916218i
$643$	3.88725			0.153298			0.0766491	−	0.997058i	$-0.475578\pi$
$643$	3.88725			0.153298			0.0766491	+	0.997058i	$0.475578\pi$
$644$	14.8130	−	25.6569i	0.583714	−	1.01102i
$645$	−4.06692	+	7.04411i	−0.160135	+	0.277361i
$646$	−3.45617	−	5.98626i	−0.135981	−	0.235526i
$647$	−17.8590			−0.702108			−0.351054	−	0.936355i	$-0.614177\pi$
$647$	−17.8590			−0.702108			−0.351054	+	0.936355i	$0.614177\pi$
$648$	10.3973	−	18.0087i	0.408446	−	0.707449i
$649$	24.1628			0.948472
$650$	0.108336			0.00424928
$651$	−24.3477	+	13.8493i	−0.954262	+	0.542799i
$652$	16.8465			0.659761
$653$	−7.33076			−0.286875			−0.143437	−	0.989659i	$-0.545816\pi$
$653$	−7.33076			−0.286875			−0.143437	+	0.989659i	$0.545816\pi$
$654$	−1.12490	+	1.94838i	−0.0439870	+	0.0761877i
$655$	32.8985			1.28545
$656$	4.05769	+	7.02812i	0.158426	+	0.274402i
$657$	−0.306016	+	0.530035i	−0.0119388	+	0.0206786i
$658$	−11.0737	+	19.1802i	−0.431699	+	0.747724i
$659$	9.43041			0.367357			0.183678	−	0.982986i	$-0.441200\pi$
$659$	9.43041			0.367357			0.183678	+	0.982986i	$0.441200\pi$
$660$	12.5805	+	21.7900i	0.489693	+	0.848174i
$661$	9.99018	+	17.3035i	0.388573	+	0.673028i	0.992258	−	0.124195i	$-0.0396348\pi$
$661$	9.99018	+	17.3035i	0.388573	+	0.673028i	−0.603685	+	0.797223i	$0.706301\pi$
$662$	10.7896	+	18.6881i	0.419350	+	0.726336i
$663$	−5.57490	+	9.65601i	−0.216511	+	0.375008i
$664$	−18.2331	−	31.5807i	−0.707583	−	1.22557i
$665$	4.84568	−	8.39296i	0.187907	−	0.325465i
$666$	−0.384947			−0.0149164
$667$	34.6145			1.34028
$668$	−11.1436	+	19.3013i	−0.431159	+	0.746789i
$669$	6.03291	+	10.4493i	0.233246	+	0.403993i
$670$	−1.09657	+	1.89932i	−0.0423643	+	0.0733772i
$671$	−25.6907	−	44.4975i	−0.991777	−	1.71781i
$672$	−14.6787	−	25.4242i	−0.566243	−	0.980761i
$673$	−4.98470	−	8.63375i	−0.192146	−	0.332806i	0.753815	−	0.657086i	$-0.228211\pi$
$673$	−4.98470	−	8.63375i	−0.192146	−	0.332806i	−0.945961	+	0.324280i	$0.894878\pi$
$674$	13.3236			0.513207
$675$	−0.408873	+	0.708189i	−0.0157375	+	0.0272582i
$676$	0.748988	−	1.29729i	0.0288072	−	0.0498956i
$677$	10.6494	+	18.4454i	0.409291	+	0.708913i	0.994810	−	0.101746i	$-0.0324428\pi$
$677$	10.6494	+	18.4454i	0.409291	+	0.708913i	−0.585520	+	0.810658i	$0.699109\pi$
$678$	0.0469487			0.00180305
$679$	−0.356738	+	0.617889i	−0.0136904	+	0.0237124i
$680$	−36.3009			−1.39208
$681$	−35.9729			−1.37848
$682$	15.6093	−	8.87882i	0.597711	−	0.339987i
$683$	41.9401			1.60479			0.802397	−	0.596791i	$-0.203558\pi$
$683$	41.9401			1.60479			0.802397	+	0.596791i	$0.203558\pi$
$684$	−0.419764			−0.0160501
$685$	7.71344	−	13.3601i	0.294716	−	0.510462i
$686$	−10.6116			−0.405155
$687$	−3.05659	−	5.29418i	−0.116616	−	0.201985i
$688$	1.36659	−	2.36700i	0.0521007	−	0.0902410i
$689$	5.14880	−	8.91797i	0.196153	−	0.339748i
$690$	−17.2251			−0.655748
$691$	15.9514	+	27.6287i	0.606821	+	1.05104i	0.991761	+	0.128103i	$0.0408887\pi$
$691$	15.9514	+	27.6287i	0.606821	+	1.05104i	−0.384940	+	0.922941i	$0.625778\pi$
$692$	−11.5949	−	20.0830i	−0.440772	−	0.763440i
$693$	1.30555	+	2.26129i	0.0495939	+	0.0858992i
$694$	−0.522405	+	0.904832i	−0.0198302	+	0.0343470i
$695$	18.7831	+	32.5333i	0.712483	+	1.23406i
$696$	10.9116	−	18.8994i	0.413602	−	0.716379i
$697$	−43.5436			−1.64933
$698$	−23.6801			−0.896304
$699$	−4.43534	+	7.68224i	−0.167760	+	0.290569i
$700$	0.343767	+	0.595422i	0.0129932	+	0.0225048i
$701$	10.3529	−	17.9318i	0.391025	−	0.677274i	−0.601560	−	0.798827i	$-0.705454\pi$
$701$	10.3529	−	17.9318i	0.391025	−	0.677274i	0.992585	+	0.121553i	$0.0387874\pi$
$702$	−1.89470	−	3.28171i	−0.0715107	−	0.123860i
$703$	−2.08468	−	3.61077i	−0.0786252	−	0.136183i
$704$	3.76643	+	6.52364i	0.141952	+	0.245869i
$705$	−38.4232			−1.44710
$706$	2.72442	−	4.71884i	0.102535	−	0.177596i
$707$	−2.31050	+	4.00190i	−0.0868953	+	0.150507i
$708$	−6.66315	−	11.5409i	−0.250417	−	0.433734i
$709$	−32.6314			−1.22550			−0.612750	−	0.790277i	$-0.709937\pi$
$709$	−32.6314			−1.22550			−0.612750	+	0.790277i	$0.709937\pi$
$710$	7.71825	−	13.3684i	0.289661	−	0.501707i
$711$	0.527632			0.0197878
$712$	−22.0440			−0.826135
$713$	0.235687	−	36.6827i	0.00882653	−	1.37378i
$714$	23.7141			0.887479
$715$	10.0219			0.374800
$716$	−18.1220	+	31.3882i	−0.677250	+	1.17303i
$717$	−10.8149			−0.403890
$718$	2.73874	+	4.74364i	0.102209	+	0.177031i
$719$	11.1779	−	19.3607i	0.416865	−	0.722032i	−0.578757	−	0.815500i	$-0.696462\pi$
$719$	11.1779	−	19.3607i	0.416865	−	0.722032i	0.995622	+	0.0934680i	$0.0297953\pi$
$720$	−0.260812	+	0.451740i	−0.00971991	+	0.0168354i
$721$	27.6194			1.02860
$722$	−5.96926	−	10.3391i	−0.222153	−	0.384780i
$723$	−16.9059	−	29.2818i	−0.628736	−	1.08900i
$724$	−17.3184	−	29.9964i	−0.643634	−	1.11481i
$725$	−0.401651	+	0.695681i	−0.0149170	+	0.0258369i
$726$	5.77214	+	9.99765i	0.214224	+	0.371047i
$727$	−6.59099	+	11.4159i	−0.244446	+	0.423393i	−0.961976	−	0.273135i	$-0.911939\pi$
$727$	−6.59099	+	11.4159i	−0.244446	+	0.423393i	0.717530	+	0.696528i	$0.245273\pi$
$728$	−7.43973			−0.275735
$729$	28.4937			1.05532
$730$	2.49811	−	4.32685i	0.0924591	−	0.160144i
$731$	7.33252	+	12.7003i	0.271203	+	0.469737i
$732$	−14.1690	+	24.5414i	−0.523700	+	0.907075i
$733$	−20.3344	−	35.2202i	−0.751068	−	1.30089i	−0.947305	−	0.320332i	$-0.896206\pi$
$733$	−20.3344	−	35.2202i	−0.751068	−	1.30089i	0.196237	−	0.980556i	$-0.437128\pi$
$734$	6.06897	+	10.5118i	0.224010	+	0.387996i
$735$	3.70954	+	6.42512i	0.136829	+	0.236994i
$736$	38.4467			1.41717
$737$	3.19997	−	5.54252i	0.117873	−	0.204161i
$738$	0.443091	−	0.767457i	0.0163104	−	0.0282505i
$739$	−5.42295	−	9.39283i	−0.199486	−	0.345521i	0.748876	−	0.662711i	$-0.230594\pi$
$739$	−5.42295	−	9.39283i	−0.199486	−	0.345521i	−0.948362	+	0.317190i	$0.897261\pi$
$740$	−9.37671			−0.344695
$741$	1.22886	−	2.12846i	0.0451435	−	0.0781908i
$742$	−21.9016			−0.804033
$743$	−41.7334			−1.53105			−0.765525	−	0.643406i	$-0.777521\pi$
$743$	−41.7334			−1.53105			−0.765525	+	0.643406i	$0.777521\pi$
$744$	−19.9543	−	11.6922i	−0.731560	−	0.428657i
$745$	−29.2747			−1.07254
$746$	−10.0074			−0.366398
$747$	1.40578	−	2.43488i	0.0514348	−	0.0890877i
$748$	45.3643			1.65868
$749$	3.38808	+	5.86832i	0.123798	+	0.214424i
$750$	6.73587	−	11.6669i	0.245959	−	0.426014i
$751$	21.8011	−	37.7606i	0.795533	−	1.37790i	−0.126967	−	0.991907i	$-0.540524\pi$
$751$	21.8011	−	37.7606i	0.795533	−	1.37790i	0.922500	−	0.385996i	$-0.126142\pi$
$752$	12.9112			0.470822
$753$	−13.2637	−	22.9734i	−0.483356	−	0.837197i
$754$	−1.86123	−	3.22375i	−0.0677821	−	0.117402i
$755$	25.9128	+	44.8822i	0.943062	+	1.63343i
$756$	12.0243	−	20.8268i	0.437321	−	0.757463i
$757$	15.1269	+	26.2005i	0.549796	+	0.952275i	0.998288	+	0.0584879i	$0.0186279\pi$
$757$	15.1269	+	26.2005i	0.549796	+	0.952275i	−0.448492	+	0.893787i	$0.648039\pi$
$758$	2.15831	−	3.73830i	0.0783932	−	0.135781i
$759$	50.2655			1.82452
$760$	8.00175			0.290254
$761$	4.08758	−	7.07989i	0.148175	−	0.256646i	−0.782378	−	0.622804i	$-0.785994\pi$
$761$	4.08758	−	7.07989i	0.148175	−	0.256646i	0.930553	+	0.366158i	$0.119327\pi$
$762$	−9.17983	−	15.8999i	−0.332550	−	0.575994i
$763$	−2.84355	+	4.92517i	−0.102943	+	0.178303i
$764$	−7.19781	−	12.4670i	−0.260407	−	0.451039i
$765$	−1.39941	−	2.42384i	−0.0505957	−	0.0876343i
$766$	5.12115	+	8.87010i	0.185035	+	0.320490i
$767$	−5.30806			−0.191663
$768$	9.00675	−	15.6001i	0.325003	−	0.562922i
$769$	−3.07833	+	5.33182i	−0.111007	+	0.192270i	−0.916177	−	0.400775i	$-0.868741\pi$
$769$	−3.07833	+	5.33182i	−0.111007	+	0.192270i	0.805169	+	0.593045i	$0.202074\pi$
$770$	−10.6577	−	18.4596i	−0.384076	−	0.665239i
$771$	9.36497			0.337271
$772$	−9.20783	+	15.9484i	−0.331397	+	0.573996i
$773$	50.9783			1.83356			0.916781	−	0.399391i	$-0.130778\pi$
$773$	50.9783			1.83356			0.916781	+	0.399391i	$0.130778\pi$
$774$	−0.298457			−0.0107278
$775$	0.734512	+	0.430386i	0.0263844	+	0.0154599i
$776$	−0.589088			−0.0211470
$777$	14.3038			0.513146
$778$	4.99392	−	8.64972i	0.179041	−	0.310108i
$779$	9.59823			0.343892
$780$	−2.76366	−	4.78680i	−0.0989550	−	0.171395i
$781$	−22.5230	+	39.0111i	−0.805938	+	1.39593i
$782$	−15.5281	+	26.8955i	−0.555285	+	0.961782i
$783$	28.0981			1.00414
$784$	−1.24650	−	2.15900i	−0.0445179	−	0.0771073i
$785$	−9.84185	−	17.0466i	−0.351271	−	0.608418i
$786$	−8.87231	−	15.3673i	−0.316465	−	0.548133i
$787$	6.44000	−	11.1544i	0.229561	−	0.397612i	−0.728117	−	0.685453i	$-0.759604\pi$
$787$	6.44000	−	11.1544i	0.229561	−	0.397612i	0.957678	+	0.287841i	$0.0929375\pi$
$788$	13.9881	+	24.2281i	0.498306	+	0.863091i
$789$	−19.7990	+	34.2928i	−0.704862	+	1.22086i
$790$	−4.30724			−0.153245
$791$	0.118678			0.00421971
$792$	−1.07794	+	1.86705i	−0.0383030	+	0.0663427i
$793$	5.64370	+	9.77517i	0.200414	+	0.347127i
$794$	7.91859	−	13.7154i	0.281020	−	0.486741i
$795$	−18.9983	−	32.9061i	−0.673802	−	1.16706i
$796$	−17.1645	−	29.7298i	−0.608380	−	1.05374i
$797$	20.3336	+	35.2188i	0.720253	+	1.24751i	0.960898	+	0.276902i	$0.0893076\pi$
$797$	20.3336	+	35.2188i	0.720253	+	1.24751i	−0.240645	+	0.970613i	$0.577359\pi$
$798$	−5.22726			−0.185043
$799$	−34.6379	+	59.9945i	−1.22540	+	2.12245i
$800$	−0.446119	+	0.772700i	−0.0157727	+	0.0273191i
$801$	−0.849801	−	1.47190i	−0.0300263	−	0.0520070i
$802$	−6.94888			−0.245373
$803$	−7.28987	+	12.6264i	−0.257254	+	0.445577i
$804$	−3.52971			−0.124483
$805$	−43.5421			−1.53466
$806$	−3.42904	+	1.95049i	−0.120783	+	0.0687031i
$807$	25.8951			0.911549
$808$	−3.81537			−0.134224
$809$	12.1468	−	21.0388i	0.427058	−	0.739685i	−0.569553	−	0.821955i	$-0.692884\pi$
$809$	12.1468	−	21.0388i	0.427058	−	0.739685i	0.996610	+	0.0822695i	$0.0262168\pi$
$810$	−13.0881			−0.459869
$811$	−6.37683	−	11.0450i	−0.223921	−	0.387842i	0.732074	−	0.681225i	$-0.238552\pi$
$811$	−6.37683	−	11.0450i	−0.223921	−	0.387842i	−0.955995	+	0.293383i	$0.905219\pi$
$812$	11.8120	−	20.4589i	0.414519	−	0.717968i
$813$	4.12974	−	7.15291i	0.144836	−	0.250864i
$814$	−9.17017			−0.321414
$815$	−12.3799	−	21.4426i	−0.433648	−	0.751100i
$816$	−6.91224	−	11.9724i	−0.241977	−	0.419116i
$817$	−1.61629	−	2.79950i	−0.0565470	−	0.0979422i
$818$	−3.48939	+	6.04380i	−0.122004	+	0.211316i
$819$	−0.286803	−	0.496757i	−0.0100217	−	0.0173581i
$820$	10.7930	−	18.6940i	0.376908	−	0.652824i
$821$	−29.8428			−1.04152			−0.520761	−	0.853702i	$-0.674352\pi$
$821$	−29.8428			−1.04152			−0.520761	+	0.853702i	$0.674352\pi$
$822$	−8.32086			−0.290223
$823$	−0.115726	+	0.200443i	−0.00403394	+	0.00698700i	−0.868035	−	0.496502i	$-0.834617\pi$
$823$	−0.115726	+	0.200443i	−0.00403394	+	0.00698700i	0.864001	+	0.503489i	$0.167951\pi$
$824$	11.4021	+	19.7490i	0.397211	+	0.687990i
$825$	−0.583258	+	1.01023i	−0.0203064	+	0.0351718i
$826$	5.64477	+	9.77703i	0.196407	+	0.340186i
$827$	−4.96229	−	8.59494i	−0.172556	−	0.298875i	0.766757	−	0.641938i	$-0.221869\pi$
$827$	−4.96229	−	8.59494i	−0.172556	−	0.298875i	−0.939313	+	0.343062i	$0.888536\pi$
$828$	0.942974	+	1.63328i	0.0327706	+	0.0567604i
$829$	44.7872			1.55552			0.777762	−	0.628559i	$-0.216355\pi$
$829$	44.7872			1.55552			0.777762	+	0.628559i	$0.216355\pi$
$830$	−11.4759	+	19.8768i	−0.398333	+	0.689933i
$831$	3.14668	−	5.45022i	0.109157	−	0.189066i
$832$	−0.827405	−	1.43311i	−0.0286851	−	0.0496841i
$833$	13.3764			0.463464
$834$	10.1311	−	17.5476i	0.350812	−	0.607624i
$835$	32.7560			1.13357
$836$	−9.99957			−0.345842
$837$	0.191317	−	29.7769i	0.00661288	−	1.02924i
$838$	22.9285			0.792051
$839$	−46.2945			−1.59826			−0.799132	−	0.601156i	$-0.794707\pi$
$839$	−46.2945			−1.59826			−0.799132	+	0.601156i	$0.794707\pi$
$840$	−13.7258	+	23.7738i	−0.473585	+	0.820273i
$841$	−1.39817			−0.0482129
$842$	2.81115	+	4.86905i	0.0968785	+	0.167799i
$843$	2.18784	−	3.78944i	0.0753531	−	0.130515i
$844$	−7.14764	+	12.3801i	−0.246032	+	0.426140i
$845$	−2.20161			−0.0757378
$846$	−0.704937	−	1.22099i	−0.0242362	−	0.0419784i
$847$	14.5910	+	25.2723i	0.501352	+	0.868368i
$848$	6.38393	+	11.0573i	0.219225	+	0.379709i
$849$	−4.78517	+	8.28815i	−0.164227	+	0.284449i
$850$	−0.360363	−	0.624167i	−0.0123603	−	0.0214088i
$851$	−9.36621	+	16.2228i	−0.321070	+	0.556109i
$852$	24.8439			0.851138
$853$	−5.18402			−0.177497			−0.0887487	−	0.996054i	$-0.528287\pi$
$853$	−5.18402			−0.177497			−0.0887487	+	0.996054i	$0.528287\pi$
$854$	12.0034	−	20.7905i	0.410748	−	0.711436i
$855$	0.308469	+	0.534283i	0.0105494	+	0.0182721i
$856$	−2.79740	+	4.84523i	−0.0956130	+	0.165607i
$857$	5.16537	+	8.94669i	0.176446	+	0.305613i	0.940661	−	0.339349i	$-0.110207\pi$
$857$	5.16537	+	8.94669i	0.176446	+	0.305613i	−0.764215	+	0.644962i	$0.776873\pi$
$858$	−2.70279	−	4.68137i	−0.0922717	−	0.159819i
$859$	−20.7186	−	35.8857i	−0.706910	−	1.22440i	−0.965998	−	0.258551i	$-0.916755\pi$
$859$	−20.7186	−	35.8857i	−0.706910	−	1.22440i	0.259087	−	0.965854i	$-0.416578\pi$
$860$	−7.26995			−0.247903
$861$	−16.4643	+	28.5170i	−0.561102	+	0.971858i
$862$	6.14700	−	10.6469i	0.209368	−	0.362635i
$863$	22.2027	+	38.4563i	0.755790	+	1.30907i	0.944981	+	0.327126i	$0.106080\pi$
$863$	22.2027	+	38.4563i	0.755790	+	1.30907i	−0.189191	+	0.981940i	$0.560586\pi$
$864$	31.2089			1.06175
$865$	−17.0413	+	29.5164i	−0.579422	+	1.00359i
$866$	−20.6422			−0.701450
$867$	45.6846			1.55153
$868$	−21.6009	−	12.6570i	−0.733183	−	0.429608i
$869$	12.5692			0.426381
$870$	−13.7354			−0.465673
$871$	−0.702967	+	1.21757i	−0.0238191	+	0.0412559i
$872$	−4.69560			−0.159013
$873$	−0.0227095	−	0.0393339i	−0.000768598	−	0.00133125i
$874$	3.42284	−	5.92853i	0.115779	−	0.200536i
$875$	17.0271	−	29.4918i	0.575622	−	0.997006i
$876$	8.04104			0.271682
$877$	−2.56932	−	4.45020i	−0.0867599	−	0.150272i	0.819380	−	0.573251i	$-0.194318\pi$
$877$	−2.56932	−	4.45020i	−0.0867599	−	0.150272i	−0.906140	+	0.422978i	$0.860985\pi$
$878$	−1.74497	−	3.02237i	−0.0588897	−	0.102000i
$879$	21.3954	+	37.0579i	0.721648	+	1.24993i
$880$	−6.21304	+	10.7613i	−0.209442	+	0.362764i
$881$	−13.9441	−	24.1519i	−0.469788	−	0.813698i	0.529615	−	0.848238i	$-0.322336\pi$
$881$	−13.9441	−	24.1519i	−0.469788	−	0.813698i	−0.999403	+	0.0345407i	$0.989003\pi$
$882$	−0.136116	+	0.235759i	−0.00458325	+	0.00793842i
$883$	−58.1813			−1.95796			−0.978979	−	0.203961i	$-0.934619\pi$
$883$	−58.1813			−1.95796			−0.978979	+	0.203961i	$0.934619\pi$
$884$	−9.96559			−0.335179
$885$	−9.79300	+	16.9620i	−0.329188	+	0.570170i
$886$	9.42686	+	16.3278i	0.316702	+	0.548543i
$887$	17.5532	−	30.4031i	0.589379	−	1.02083i	−0.404935	−	0.914346i	$-0.632706\pi$
$887$	17.5532	−	30.4031i	0.589379	−	1.02083i	0.994314	−	0.106489i	$-0.0339610\pi$
$888$	5.90503	+	10.2278i	0.198160	+	0.343223i
$889$	−23.2050	−	40.1923i	−0.778272	−	1.34801i
$890$	6.93722	+	12.0156i	0.232536	+	0.402764i
$891$	38.1931			1.27952
$892$	−5.39216	+	9.33950i	−0.180543	+	0.312709i
$893$	7.63516	−	13.2245i	0.255501	−	0.442541i
$894$	7.89501	+	13.6746i	0.264048	+	0.457345i
$895$	53.2686			1.78057
$896$	15.7568	−	27.2915i	0.526396	−	0.911745i
$897$	−11.0423			−0.368691
$898$	7.99340			0.266743
$899$	0.187938	−	29.2510i	0.00626808	−	0.975576i
$900$	−0.0437674			−0.00145891
$901$	−68.5068			−2.28229
$902$	10.5553	−	18.2823i	0.351452	−	0.608733i
$903$	11.0900			0.369053
$904$	0.0489938	+	0.0848598i	0.00162951	+	0.00282239i
$905$	−25.4533	+	44.0864i	−0.846096	+	1.46548i
$906$	13.9767	−	24.2083i	0.464344	−	0.804267i
$907$	−26.7591			−0.888520			−0.444260	−	0.895898i	$-0.646533\pi$
$907$	−26.7591			−0.888520			−0.444260	+	0.895898i	$0.646533\pi$
$908$	−16.0761	−	27.8446i	−0.533505	−	0.924057i
$909$	−0.147083	−	0.254755i	−0.00487844	−	0.00844970i
$910$	2.34127	+	4.05520i	0.0776123	+	0.134428i
$911$	−14.9825	+	25.9504i	−0.496392	+	0.859776i	−0.999991	−	0.00416106i	$-0.998675\pi$
$911$	−14.9825	+	25.9504i	−0.496392	+	0.859776i	0.503599	+	0.863937i	$0.332009\pi$
$912$	1.52365	+	2.63905i	0.0504532	+	0.0873875i
$913$	33.4883	−	58.0035i	1.10830	−	1.91964i
$914$	9.32490			0.308440
$915$	41.6489			1.37687
$916$	2.73196	−	4.73189i	0.0902664	−	0.156346i
$917$	−22.4277	−	38.8459i	−0.740627	−	1.28280i
$918$	−12.6049	+	21.8322i	−0.416022	+	0.720571i
$919$	15.3970	+	26.6684i	0.507900	+	0.879709i	0.999958	+	0.00914683i	$0.00291157\pi$
$919$	15.3970	+	26.6684i	0.507900	+	0.879709i	−0.492058	+	0.870563i	$0.663755\pi$
$920$	−17.9754	−	31.1344i	−0.592633	−	1.02647i
$921$	−5.28858	−	9.16009i	−0.174265	−	0.301835i
$922$	−15.4354			−0.508338
$923$	4.94784	−	8.56991i	0.162860	−	0.282082i
$924$	17.1528	−	29.7094i	0.564284	−	0.977369i
$925$	−0.217363	−	0.376483i	−0.00714684	−	0.0123787i
$926$	−1.60160			−0.0526317
$927$	−0.879106	+	1.52266i	−0.0288736	+	0.0500106i
$928$	30.6576			1.00639
$929$	31.5727			1.03587			0.517933	−	0.855421i	$-0.326702\pi$
$929$	31.5727			1.03587			0.517933	+	0.855421i	$0.326702\pi$
$930$	−0.0935228	+	14.5561i	−0.00306673	+	0.477312i
$931$	−2.94853			−0.0966341
$932$	−7.92854			−0.259708
$933$	0.530607	−	0.919038i	0.0173713	−	0.0300880i
$934$	20.2163			0.661496
$935$	−33.3365	−	57.7405i	−1.09022	−	1.88832i
$936$	0.236801	−	0.410152i	0.00774009	−	0.0134062i
$937$	22.4359	−	38.8602i	0.732950	−	1.26951i	−0.222667	−	0.974894i	$-0.571476\pi$
$937$	22.4359	−	38.8602i	0.732950	−	1.26951i	0.955617	−	0.294612i	$-0.0951903\pi$
$938$	2.99024			0.0976347
$939$	28.1250	+	48.7139i	0.917824	+	1.58972i
$940$	−17.1711	−	29.7413i	−0.560061	−	0.970054i
$941$	11.6769	+	20.2249i	0.380655	+	0.659314i	0.991156	−	0.132701i	$-0.0423651\pi$
$941$	11.6769	+	20.2249i	0.380655	+	0.659314i	−0.610501	+	0.792016i	$0.709032\pi$
$942$	−5.30844	+	9.19448i	−0.172958	+	0.299572i
$943$	−21.5618	−	37.3462i	−0.702150	−	1.21616i
$944$	3.29070	−	5.69965i	0.107103	−	0.185508i
$945$	−35.3449			−1.14977
$946$	−7.10982			−0.231160
$947$	−2.25913	+	3.91293i	−0.0734119	+	0.127153i	−0.900395	−	0.435074i	$-0.856722\pi$
$947$	−2.25913	+	3.91293i	−0.0734119	+	0.127153i	0.826983	+	0.562227i	$0.190055\pi$
$948$	−3.46609	−	6.00345i	−0.112573	−	0.194983i
$949$	1.60143	−	2.77376i	0.0519847	−	0.0900401i
$950$	0.0794342	+	0.137584i	0.00257718	+	0.00446381i
$951$	22.1300	+	38.3303i	0.717616	+	1.24295i
$952$	24.7472	+	42.8633i	0.802060	+	1.38921i
$953$	29.9709			0.970853			0.485426	−	0.874277i	$-0.338664\pi$
$953$	29.9709			0.970853			0.485426	+	0.874277i	$0.338664\pi$
$954$	0.697112	−	1.20743i	0.0225698	−	0.0390921i
$955$	−10.5788	+	18.3230i	−0.342322	+	0.592918i
$956$	−4.83313	−	8.37123i	−0.156315	−	0.270745i
$957$	40.0820			1.29567
$958$	7.56606	−	13.1048i	0.244448	−	0.423397i
$959$	−21.0337			−0.679214
$960$	−6.10602			−0.197071
$961$	−30.9974	−	0.398334i	−0.999917	−	0.0128495i
$962$	2.01450			0.0649499
$963$	−0.431360			−0.0139004
$964$	15.1103	−	26.1719i	0.486671	−	0.842939i
$965$	27.0659			0.871283
$966$	11.7427	+	20.3390i	0.377816	+	0.654397i
$967$	−3.41313	+	5.91171i	−0.109759	+	0.190108i	−0.915673	−	0.401925i	$-0.868341\pi$
$967$	−3.41313	+	5.91171i	−0.109759	+	0.190108i	0.805914	+	0.592033i	$0.201675\pi$
$968$	−12.0472	+	20.8663i	−0.387211	+	0.670669i
$969$	−16.3505			−0.525255
$970$	0.185385	+	0.321096i	0.00595235	+	0.0103098i
$971$	−0.279857	−	0.484726i	−0.00898103	−	0.0155556i	0.861500	−	0.507758i	$-0.169525\pi$
$971$	−0.279857	−	0.484726i	−0.00898103	−	0.0155556i	−0.870481	+	0.492202i	$0.836192\pi$
$972$	1.48507	+	2.57221i	0.0476336	+	0.0825038i
$973$	25.6097	−	44.3573i	0.821010	−	1.42203i
$974$	−9.70258	−	16.8054i	−0.310891	−	0.538478i
$975$	0.128130	−	0.221927i	0.00410343	−	0.00710735i
$976$	−13.9951			−0.447972
$977$	−5.83835			−0.186785			−0.0933927	−	0.995629i	$-0.529771\pi$
$977$	−5.83835			−0.186785			−0.0933927	+	0.995629i	$0.529771\pi$
$978$	−6.67738	+	11.5656i	−0.213519	+	0.369826i
$979$	−20.2439	−	35.0634i	−0.646997	−	1.12063i
$980$	−3.31556	+	5.74271i	−0.105912	+	0.183444i
$981$	−0.181016	−	0.313529i	−0.00577940	−	0.0100102i
$982$	5.44594	+	9.43265i	0.173787	+	0.301008i
$983$	29.5444	+	51.1723i	0.942319	+	1.63214i	0.761033	+	0.648713i	$0.224692\pi$
$983$	29.5444	+	51.1723i	0.942319	+	1.63214i	0.181285	+	0.983431i	$0.441974\pi$
$984$	−27.1878			−0.866715
$985$	20.5587	−	35.6086i	0.655053	−	1.13459i
$986$	−12.3822	+	21.4466i	−0.394330	+	0.683000i
$987$	26.1939	+	45.3692i	0.833762	+	1.44412i
$988$	2.19670			0.0698862
$989$	−7.26181	+	12.5778i	−0.230912	+	0.399952i
$990$	1.35690			0.0431253
$991$	−0.176071			−0.00559307			−0.00279653	−	0.999996i	$-0.500890\pi$
$991$	−0.176071			−0.00559307			−0.00279653	+	0.999996i	$0.500890\pi$
$992$	0.208745	−	32.4894i	0.00662765	−	1.03154i
$993$	51.0438			1.61982
$994$	−21.0468			−0.667564
$995$	−25.2271	+	43.6946i	−0.799753	+	1.38521i
$996$	−36.9391			−1.17046
$997$	−2.09091	−	3.62156i	−0.0662197	−	0.114696i	0.831015	−	0.556250i	$-0.187760\pi$
$997$	−2.09091	−	3.62156i	−0.0662197	−	0.114696i	−0.897234	+	0.441555i	$0.854427\pi$
$998$	3.78322	−	6.55272i	0.119756	−	0.207423i
$999$	−7.60295	+	13.1687i	−0.240547	+	0.416639i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	403.2.h.b.222.7	yes	34
31.25	even	3	inner	403.2.h.b.118.7	✓	34

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
403.2.h.b.118.7	✓	34	31.25	even	3	inner
403.2.h.b.222.7	yes	34	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)

\(f(q)\)	\(=\)	\(q-0.708536 q^{2} +(-0.837990 + 1.45144i) q^{3} -1.49798 q^{4} +(1.10081 + 1.90665i) q^{5} +(0.593746 - 1.02840i) q^{6} +(1.50089 - 2.59962i) q^{7} +2.47844 q^{8} +(0.0955444 + 0.165488i) q^{9} +O(q^{10})\)	\(q-0.708536 q^{2} +(-0.837990 + 1.45144i) q^{3} -1.49798 q^{4} +(1.10081 + 1.90665i) q^{5} +(0.593746 - 1.02840i) q^{6} +(1.50089 - 2.59962i) q^{7} +2.47844 q^{8} +(0.0955444 + 0.165488i) q^{9} +(-0.779961 - 1.35093i) q^{10} +(2.27605 + 3.94223i) q^{11} +(1.25529 - 2.17423i) q^{12} +(-0.500000 - 0.866025i) q^{13} +(-1.06343 + 1.84192i) q^{14} -3.68986 q^{15} +1.23989 q^{16} +(-3.32635 + 5.76141i) q^{17} +(-0.0676966 - 0.117254i) q^{18} +(0.733221 - 1.26998i) q^{19} +(-1.64898 - 2.85612i) q^{20} +(2.51546 + 4.35691i) q^{21} +(-1.61266 - 2.79321i) q^{22} -6.58855 q^{23} +(-2.07691 + 3.59732i) q^{24} +(0.0764505 - 0.132416i) q^{25} +(0.354268 + 0.613610i) q^{26} -5.34820 q^{27} +(-2.24830 + 3.89416i) q^{28} -5.25374 q^{29} +2.61440 q^{30} +(-0.0357722 + 5.56765i) q^{31} -5.83539 q^{32} -7.62922 q^{33} +(2.35684 - 4.08216i) q^{34} +6.60875 q^{35} +(-0.143123 - 0.247897i) q^{36} +(1.42159 - 2.46227i) q^{37} +(-0.519514 + 0.899824i) q^{38} +1.67598 q^{39} +(2.72829 + 4.72553i) q^{40} +(3.27262 + 5.66835i) q^{41} +(-1.78229 - 3.08702i) q^{42} +(1.10219 - 1.90904i) q^{43} +(-3.40947 - 5.90537i) q^{44} +(-0.210352 + 0.364340i) q^{45} +4.66822 q^{46} +10.4132 q^{47} +(-1.03901 + 1.79962i) q^{48} +(-1.00533 - 1.74129i) q^{49} +(-0.0541679 + 0.0938216i) q^{50} +(-5.57490 - 9.65601i) q^{51} +(0.748988 + 1.29729i) q^{52} +(5.14880 + 8.91797i) q^{53} +3.78939 q^{54} +(-5.01097 + 8.67926i) q^{55} +(3.71987 - 6.44300i) q^{56} +(1.22886 + 2.12846i) q^{57} +3.72247 q^{58} +(2.65403 - 4.59691i) q^{59} +5.52732 q^{60} -11.2874 q^{61} +(0.0253459 - 3.94488i) q^{62} +0.573606 q^{63} +1.65481 q^{64} +(1.10081 - 1.90665i) q^{65} +5.40558 q^{66} +(-0.702967 - 1.21757i) q^{67} +(4.98279 - 8.63045i) q^{68} +(5.52114 - 9.56289i) q^{69} -4.68254 q^{70} +(4.94784 + 8.56991i) q^{71} +(0.236801 + 0.410152i) q^{72} +(1.60143 + 2.77376i) q^{73} +(-1.00725 + 1.74460i) q^{74} +(0.128130 + 0.221927i) q^{75} +(-1.09835 + 1.90239i) q^{76} +13.6644 q^{77} -1.18749 q^{78} +(1.38059 - 2.39126i) q^{79} +(1.36488 + 2.36403i) q^{80} +(4.19511 - 7.26614i) q^{81} +(-2.31877 - 4.01623i) q^{82} +(-7.35669 - 12.7422i) q^{83} +(-3.76810 - 6.52654i) q^{84} -14.6467 q^{85} +(-0.780939 + 1.35263i) q^{86} +(4.40259 - 7.62550i) q^{87} +(5.64105 + 9.77059i) q^{88} -8.89431 q^{89} +(0.149042 - 0.258148i) q^{90} -3.00178 q^{91} +9.86949 q^{92} +(-8.05114 - 4.71756i) q^{93} -7.37811 q^{94} +3.22854 q^{95} +(4.89000 - 8.46973i) q^{96} -0.237685 q^{97} +(0.712316 + 1.23377i) q^{98} +(-0.434927 + 0.753316i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 34 q + 6 q^{2} - 2 q^{3} + 34 q^{4} - 5 q^{5} - 2 q^{7} + 36 q^{8} - 23 q^{9}+O(q^{10}) \) 34 * q + 6 * q^2 - 2 * q^3 + 34 * q^4 - 5 * q^5 - 2 * q^7 + 36 * q^8 - 23 * q^9	\( 34 q + 6 q^{2} - 2 q^{3} + 34 q^{4} - 5 q^{5} - 2 q^{7} + 36 q^{8} - 23 q^{9} - 7 q^{10} - 5 q^{11} - 28 q^{12} - 17 q^{13} - 7 q^{14} + 8 q^{15} + 18 q^{16} - 8 q^{17} + 6 q^{18} + 3 q^{19} - 8 q^{20} + 13 q^{21} + 12 q^{22} - 14 q^{23} - 6 q^{24} - 26 q^{25} - 3 q^{26} + 28 q^{27} - 7 q^{28} - 18 q^{29} - 60 q^{30} - 9 q^{31} + 58 q^{32} - 14 q^{33} - 15 q^{34} + 50 q^{35} - 49 q^{36} - 6 q^{37} + 2 q^{38} + 4 q^{39} - 29 q^{40} - 5 q^{41} + 8 q^{42} - q^{43} - 22 q^{44} + 13 q^{45} + 34 q^{46} + 16 q^{47} - 49 q^{48} + 3 q^{49} - 35 q^{51} - 17 q^{52} + 30 q^{53} - 2 q^{54} + 21 q^{55} - 7 q^{56} + 34 q^{58} - 9 q^{59} - 38 q^{60} - 28 q^{61} - 62 q^{62} + 88 q^{63} + 56 q^{64} - 5 q^{65} + 140 q^{66} - 31 q^{67} - 39 q^{68} + 5 q^{69} + 56 q^{70} + q^{71} - 32 q^{72} - 10 q^{73} - 39 q^{74} - 2 q^{75} - 16 q^{76} + 76 q^{77} - 23 q^{79} - 22 q^{80} - 29 q^{81} - 10 q^{82} + 3 q^{83} + 52 q^{84} - 32 q^{85} + 4 q^{86} + 18 q^{87} - 10 q^{88} + 26 q^{89} + 35 q^{90} + 4 q^{91} - 94 q^{92} - 41 q^{93} + 70 q^{94} + 28 q^{95} - 23 q^{96} + 32 q^{97} - 38 q^{98} - 70 q^{99}+O(q^{100}) \) 34 * q + 6 * q^2 - 2 * q^3 + 34 * q^4 - 5 * q^5 - 2 * q^7 + 36 * q^8 - 23 * q^9 - 7 * q^10 - 5 * q^11 - 28 * q^12 - 17 * q^13 - 7 * q^14 + 8 * q^15 + 18 * q^16 - 8 * q^17 + 6 * q^18 + 3 * q^19 - 8 * q^20 + 13 * q^21 + 12 * q^22 - 14 * q^23 - 6 * q^24 - 26 * q^25 - 3 * q^26 + 28 * q^27 - 7 * q^28 - 18 * q^29 - 60 * q^30 - 9 * q^31 + 58 * q^32 - 14 * q^33 - 15 * q^34 + 50 * q^35 - 49 * q^36 - 6 * q^37 + 2 * q^38 + 4 * q^39 - 29 * q^40 - 5 * q^41 + 8 * q^42 - q^43 - 22 * q^44 + 13 * q^45 + 34 * q^46 + 16 * q^47 - 49 * q^48 + 3 * q^49 - 35 * q^51 - 17 * q^52 + 30 * q^53 - 2 * q^54 + 21 * q^55 - 7 * q^56 + 34 * q^58 - 9 * q^59 - 38 * q^60 - 28 * q^61 - 62 * q^62 + 88 * q^63 + 56 * q^64 - 5 * q^65 + 140 * q^66 - 31 * q^67 - 39 * q^68 + 5 * q^69 + 56 * q^70 + q^71 - 32 * q^72 - 10 * q^73 - 39 * q^74 - 2 * q^75 - 16 * q^76 + 76 * q^77 - 23 * q^79 - 22 * q^80 - 29 * q^81 - 10 * q^82 + 3 * q^83 + 52 * q^84 - 32 * q^85 + 4 * q^86 + 18 * q^87 - 10 * q^88 + 26 * q^89 + 35 * q^90 + 4 * q^91 - 94 * q^92 - 41 * q^93 + 70 * q^94 + 28 * q^95 - 23 * q^96 + 32 * q^97 - 38 * q^98 - 70 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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