LMFDB - Embedded newform 403.2.v.a.36.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [403,2,Mod(36,403)]

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([5, 4]))

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

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

chi := DirichletCharacter("403.36");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 403 = 13 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	403.v (of order $6$, 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:	$70$
Relative dimension:	$35$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			36.6
Character	$\chi$	$=$	403.36
Dual form			403.2.v.a.56.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.88902 + 1.09062i) q^{2} -0.144762 q^{3} +(1.37892 - 2.38836i) q^{4} +(-1.56313 + 0.902471i) q^{5} +(0.273457 - 0.157881i) q^{6} +(2.20942 - 1.27561i) q^{7} +1.65304i q^{8} -2.97904 q^{9} +O(q^{10})$	\(q+(-1.88902 + 1.09062i) q^{2} -0.144762 q^{3} +(1.37892 - 2.38836i) q^{4} +(-1.56313 + 0.902471i) q^{5} +(0.273457 - 0.157881i) q^{6} +(2.20942 - 1.27561i) q^{7} +1.65304i q^{8} -2.97904 q^{9} +(1.96851 - 3.40956i) q^{10} +(1.68417 + 0.972354i) q^{11} +(-0.199615 + 0.345743i) q^{12} +(3.38576 + 1.23960i) q^{13} +(-2.78242 + 4.81929i) q^{14} +(0.226281 - 0.130643i) q^{15} +(0.954997 + 1.65410i) q^{16} +(-1.86710 - 3.23392i) q^{17} +(5.62746 - 3.24902i) q^{18} +(2.14106 - 1.23614i) q^{19} +4.97774i q^{20} +(-0.319840 + 0.184660i) q^{21} -4.24189 q^{22} +(2.71631 + 4.70478i) q^{23} -0.239297i q^{24} +(-0.871093 + 1.50878i) q^{25} +(-7.74770 + 1.35096i) q^{26} +0.865537 q^{27} -7.03586i q^{28} +(4.87686 + 8.44698i) q^{29} +(-0.284965 + 0.493574i) q^{30} +(3.89883 - 3.97481i) q^{31} +(-6.47116 - 3.73612i) q^{32} +(-0.243803 - 0.140760i) q^{33} +(7.05398 + 4.07262i) q^{34} +(-2.30240 + 3.98788i) q^{35} +(-4.10787 + 7.11503i) q^{36} +6.17379i q^{37} +(-2.69633 + 4.67019i) q^{38} +(-0.490129 - 0.179447i) q^{39} +(-1.49182 - 2.58391i) q^{40} +(-9.38852 - 5.42047i) q^{41} +(0.402788 - 0.697650i) q^{42} +(3.54099 + 6.13318i) q^{43} +(4.64467 - 2.68160i) q^{44} +(4.65662 - 2.68850i) q^{45} +(-10.2623 - 5.92494i) q^{46} +9.10729i q^{47} +(-0.138247 - 0.239451i) q^{48} +(-0.245639 + 0.425459i) q^{49} -3.80014i q^{50} +(0.270285 + 0.468148i) q^{51} +(7.62932 - 6.37710i) q^{52} +(3.99233 + 6.91492i) q^{53} +(-1.63501 + 0.943975i) q^{54} -3.51009 q^{55} +(2.10863 + 3.65226i) q^{56} +(-0.309944 + 0.178946i) q^{57} +(-18.4249 - 10.6376i) q^{58} +(3.89999 - 2.25166i) q^{59} -0.720587i q^{60} +(-0.124616 + 0.215841i) q^{61} +(-3.02994 + 11.7606i) q^{62} +(-6.58196 + 3.80010i) q^{63} +12.4788 q^{64} +(-6.41107 + 1.11789i) q^{65} +0.614064 q^{66} +(-4.55298 - 2.62866i) q^{67} -10.2984 q^{68} +(-0.393217 - 0.681072i) q^{69} -10.0442i q^{70} +6.28972i q^{71} -4.92448i q^{72} +(0.291183 - 0.168115i) q^{73} +(-6.73328 - 11.6624i) q^{74} +(0.126101 - 0.218413i) q^{75} -6.81817i q^{76} +4.96138 q^{77} +(1.12157 - 0.195568i) q^{78} +(5.01397 - 8.68445i) q^{79} +(-2.98556 - 1.72371i) q^{80} +8.81184 q^{81} +23.6468 q^{82} +(13.8506 - 7.99664i) q^{83} +1.01852i q^{84} +(5.83703 + 3.37001i) q^{85} +(-13.3780 - 7.72378i) q^{86} +(-0.705983 - 1.22280i) q^{87} +(-1.60734 + 2.78399i) q^{88} +(14.2527 - 8.22881i) q^{89} +(-5.86428 + 10.1572i) q^{90} +(9.06182 - 1.58010i) q^{91} +14.9823 q^{92} +(-0.564402 + 0.575400i) q^{93} +(-9.93263 - 17.2038i) q^{94} +(-2.23117 + 3.86449i) q^{95} +(0.936776 + 0.540848i) q^{96} +(3.15104 + 1.81925i) q^{97} -1.07160i q^{98} +(-5.01721 - 2.89669i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 70 q - 6 q^{2} + 4 q^{3} + 30 q^{4} + 6 q^{6} - 12 q^{7} + 58 q^{9}+O(q^{10}) $ 70 * q - 6 * q^2 + 4 * q^3 + 30 * q^4 + 6 * q^6 - 12 * q^7 + 58 * q^9	$ 70 q - 6 q^{2} + 4 q^{3} + 30 q^{4} + 6 q^{6} - 12 q^{7} + 58 q^{9} - q^{10} - 6 q^{11} + 13 q^{12} - 14 q^{13} - 14 q^{14} - 15 q^{15} - 28 q^{16} + 6 q^{17} + 12 q^{19} + 9 q^{21} - 8 q^{22} + 10 q^{23} + 19 q^{25} + 34 q^{27} - 18 q^{29} - 31 q^{30} + 2 q^{31} + 36 q^{32} - 12 q^{33} - 9 q^{34} - 12 q^{35} + 8 q^{36} - 21 q^{38} - 30 q^{39} + 5 q^{40} + 18 q^{41} - 49 q^{42} + 19 q^{43} - 42 q^{44} - 63 q^{45} - 6 q^{46} - 27 q^{48} + 9 q^{49} - 7 q^{51} - 43 q^{52} - 22 q^{53} + 18 q^{54} + 30 q^{55} + 25 q^{56} - 15 q^{57} - 12 q^{58} + 33 q^{59} - 13 q^{61} - 17 q^{62} - 6 q^{63} - 38 q^{64} + 9 q^{65} - 52 q^{66} + 30 q^{67} + 88 q^{68} - 16 q^{69} + 9 q^{73} - 19 q^{74} + 25 q^{75} + 34 q^{77} + 14 q^{78} + 6 q^{79} + 6 q^{80} + 22 q^{81} - 78 q^{82} + 54 q^{83} - 33 q^{85} + 24 q^{86} - 14 q^{87} + 16 q^{88} - 6 q^{89} - 11 q^{90} - 70 q^{91} - 6 q^{92} + 7 q^{93} - 43 q^{94} + 25 q^{95} - 36 q^{96} - 75 q^{97} - 93 q^{99}+O(q^{100}) $ 70 * q - 6 * q^2 + 4 * q^3 + 30 * q^4 + 6 * q^6 - 12 * q^7 + 58 * q^9 - q^10 - 6 * q^11 + 13 * q^12 - 14 * q^13 - 14 * q^14 - 15 * q^15 - 28 * q^16 + 6 * q^17 + 12 * q^19 + 9 * q^21 - 8 * q^22 + 10 * q^23 + 19 * q^25 + 34 * q^27 - 18 * q^29 - 31 * q^30 + 2 * q^31 + 36 * q^32 - 12 * q^33 - 9 * q^34 - 12 * q^35 + 8 * q^36 - 21 * q^38 - 30 * q^39 + 5 * q^40 + 18 * q^41 - 49 * q^42 + 19 * q^43 - 42 * q^44 - 63 * q^45 - 6 * q^46 - 27 * q^48 + 9 * q^49 - 7 * q^51 - 43 * q^52 - 22 * q^53 + 18 * q^54 + 30 * q^55 + 25 * q^56 - 15 * q^57 - 12 * q^58 + 33 * q^59 - 13 * q^61 - 17 * q^62 - 6 * q^63 - 38 * q^64 + 9 * q^65 - 52 * q^66 + 30 * q^67 + 88 * q^68 - 16 * q^69 + 9 * q^73 - 19 * q^74 + 25 * q^75 + 34 * q^77 + 14 * q^78 + 6 * q^79 + 6 * q^80 + 22 * q^81 - 78 * q^82 + 54 * q^83 - 33 * q^85 + 24 * q^86 - 14 * q^87 + 16 * q^88 - 6 * q^89 - 11 * q^90 - 70 * q^91 - 6 * q^92 + 7 * q^93 - 43 * q^94 + 25 * q^95 - 36 * q^96 - 75 * q^97 - 93 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$249$	$313$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{2}{3}\right)$

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 $

$2$	−1.88902	+	1.09062i	−1.33574	+	0.771187i	−0.986172	−	0.165725i	$-0.947004\pi$
$2$	−1.88902	+	1.09062i	−1.33574	+	0.771187i	−0.349564	+	0.936913i	$0.613670\pi$
$3$	−0.144762			−0.0835782			−0.0417891	−	0.999126i	$-0.513306\pi$
$3$	−0.144762			−0.0835782			−0.0417891	+	0.999126i	$0.513306\pi$
$4$	1.37892	−	2.38836i	0.689460	−	1.19418i
$5$	−1.56313	+	0.902471i	−0.699051	+	0.403597i	−0.806994	−	0.590560i	$-0.798907\pi$
$5$	−1.56313	+	0.902471i	−0.699051	+	0.403597i	0.107943	+	0.994157i	$0.465574\pi$
$6$	0.273457	−	0.157881i	0.111638	−	0.0644545i
$7$	2.20942	−	1.27561i	0.835083	−	0.482135i	−0.0205071	−	0.999790i	$-0.506528\pi$
$7$	2.20942	−	1.27561i	0.835083	−	0.482135i	0.855590	+	0.517654i	$0.173195\pi$
$8$			1.65304i			0.584438i
$9$	−2.97904			−0.993015
$10$	1.96851	−	3.40956i	0.622498	−	1.07820i
$11$	1.68417	+	0.972354i	0.507796	+	0.293176i	0.731927	−	0.681383i	$-0.238621\pi$
$11$	1.68417	+	0.972354i	0.507796	+	0.293176i	−0.224131	+	0.974559i	$0.571955\pi$
$12$	−0.199615	+	0.345743i	−0.0576239	+	0.0998075i
$13$	3.38576	+	1.23960i	0.939041	+	0.343804i
$13$	3.38576	+	1.23960i	0.939041	+	0.343804i
$14$	−2.78242	+	4.81929i	−0.743633	+	1.28801i
$15$	0.226281	−	0.130643i	0.0584254	−	0.0337319i
$16$	0.954997	+	1.65410i	0.238749	+	0.413526i
$17$	−1.86710	−	3.23392i	−0.452839	−	0.784341i	0.545722	−	0.837966i	$-0.316256\pi$
$17$	−1.86710	−	3.23392i	−0.452839	−	0.784341i	−0.998561	+	0.0536258i	$0.982922\pi$
$18$	5.62746	−	3.24902i	1.32641	−	0.765800i
$19$	2.14106	−	1.23614i	0.491193	−	0.283591i	−0.233876	−	0.972266i	$-0.575141\pi$
$19$	2.14106	−	1.23614i	0.491193	−	0.283591i	0.725069	+	0.688676i	$0.241808\pi$
$20$			4.97774i			1.11306i
$21$	−0.319840	+	0.184660i	−0.0697947	+	0.0402960i
$22$	−4.24189			−0.904374
$23$	2.71631	+	4.70478i	0.566389	+	0.981015i	0.996919	+	0.0784383i	$0.0249933\pi$
$23$	2.71631	+	4.70478i	0.566389	+	0.981015i	−0.430530	+	0.902576i	$0.641673\pi$
$24$		−	0.239297i		−	0.0488463i
$25$	−0.871093	+	1.50878i	−0.174219	+	0.301756i
$26$	−7.74770	+	1.35096i	−1.51945	+	0.264945i
$27$	0.865537			0.166573
$28$		−	7.03586i		−	1.32965i
$29$	4.87686	+	8.44698i	0.905611	+	1.56856i	0.820095	+	0.572227i	$0.193921\pi$
$29$	4.87686	+	8.44698i	0.905611	+	1.56856i	0.0855159	+	0.996337i	$0.472746\pi$
$30$	−0.284965	+	0.493574i	−0.0520273	+	0.0901139i
$31$	3.89883	−	3.97481i	0.700251	−	0.713897i
$31$	3.89883	−	3.97481i	0.700251	−	0.713897i
$32$	−6.47116	−	3.73612i	−1.14395	−	0.660460i
$33$	−0.243803	−	0.140760i	−0.0424407	−	0.0245031i
$34$	7.05398	+	4.07262i	1.20975	+	0.698448i
$35$	−2.30240	+	3.98788i	−0.389177	+	0.674074i
$36$	−4.10787	+	7.11503i	−0.684644	+	1.18584i
$37$			6.17379i			1.01496i	0.861662	+	0.507482i	$0.169424\pi$
$37$			6.17379i			1.01496i	−0.861662	+	0.507482i	$0.830576\pi$
$38$	−2.69633	+	4.67019i	−0.437403	+	0.757604i
$39$	−0.490129	−	0.179447i	−0.0784834	−	0.0287346i
$40$	−1.49182	−	2.58391i	−0.235877	−	0.408552i
$41$	−9.38852	−	5.42047i	−1.46624	−	0.846535i	−0.466953	−	0.884282i	$-0.654648\pi$
$41$	−9.38852	−	5.42047i	−1.46624	−	0.846535i	−0.999287	+	0.0377474i	$0.987982\pi$
$42$	0.402788	−	0.697650i	0.0621516	−	0.107650i
$43$	3.54099	+	6.13318i	0.539996	+	0.935301i	0.998903	+	0.0468170i	$0.0149078\pi$
$43$	3.54099	+	6.13318i	0.539996	+	0.935301i	−0.458907	+	0.888484i	$0.651759\pi$
$44$	4.64467	−	2.68160i	0.700210	−	0.404266i
$45$	4.65662	−	2.68850i	0.694168	−	0.400778i
$46$	−10.2623	−	5.92494i	−1.51309	−	0.873584i
$47$			9.10729i			1.32843i	0.747539	+	0.664217i	$0.231235\pi$
$47$			9.10729i			1.32843i	−0.747539	+	0.664217i	$0.768765\pi$
$48$	−0.138247	−	0.239451i	−0.0199542	−	0.0345618i
$49$	−0.245639	+	0.425459i	−0.0350913	+	0.0607798i
$50$		−	3.80014i		−	0.537421i
$51$	0.270285	+	0.468148i	0.0378475	+	0.0655538i
$52$	7.62932	−	6.37710i	1.05800	−	0.884345i
$53$	3.99233	+	6.91492i	0.548389	+	0.949838i	0.998385	+	0.0568072i	$0.0180920\pi$
$53$	3.99233	+	6.91492i	0.548389	+	0.949838i	−0.449996	+	0.893031i	$0.648575\pi$
$54$	−1.63501	+	0.943975i	−0.222497	+	0.128459i
$55$	−3.51009			−0.473300
$56$	2.10863	+	3.65226i	0.281778	+	0.488054i
$57$	−0.309944	+	0.178946i	−0.0410531	+	0.0237020i
$58$	−18.4249	−	10.6376i	−2.41931	−	1.39679i
$59$	3.89999	−	2.25166i	0.507736	−	0.293141i	−0.224167	−	0.974551i	$-0.571966\pi$
$59$	3.89999	−	2.25166i	0.507736	−	0.293141i	0.731902	+	0.681409i	$0.238633\pi$
$60$		−	0.720587i		−	0.0930273i
$61$	−0.124616	+	0.215841i	−0.0159554	+	0.0276356i	−0.873893	−	0.486119i	$-0.838412\pi$
$61$	−0.124616	+	0.215841i	−0.0159554	+	0.0276356i	0.857937	+	0.513754i	$0.171746\pi$
$62$	−3.02994	+	11.7606i	−0.384802	+	1.49360i
$63$	−6.58196	+	3.80010i	−0.829249	+	0.478767i
$64$	12.4788			1.55985
$65$	−6.41107	+	1.11789i	−0.795196	+	0.138658i
$66$	0.614064			0.0755860
$67$	−4.55298	−	2.62866i	−0.556235	−	0.321142i	0.195398	−	0.980724i	$-0.437400\pi$
$67$	−4.55298	−	2.62866i	−0.556235	−	0.321142i	−0.751633	+	0.659582i	$0.770733\pi$
$68$	−10.2984			−1.24886
$69$	−0.393217	−	0.681072i	−0.0473378	−	0.0819915i
$70$		−	10.0442i		−	1.20051i
$71$			6.28972i			0.746453i	0.927740	+	0.373226i	$0.121749\pi$
$71$			6.28972i			0.746453i	−0.927740	+	0.373226i	$0.878251\pi$
$72$		−	4.92448i		−	0.580355i
$73$	0.291183	−	0.168115i	0.0340804	−	0.0196763i	−0.482863	−	0.875696i	$-0.660403\pi$
$73$	0.291183	−	0.168115i	0.0340804	−	0.0196763i	0.516943	+	0.856020i	$0.327070\pi$
$74$	−6.73328	−	11.6624i	−0.782728	−	1.35572i
$75$	0.126101	−	0.218413i	0.0145609	−	0.0252202i
$76$		−	6.81817i		−	0.782098i
$77$	4.96138			0.565402
$78$	1.12157	−	0.195568i	0.126993	−	0.0221437i
$79$	5.01397	−	8.68445i	0.564115	−	0.977077i	−0.433016	−	0.901386i	$-0.642551\pi$
$79$	5.01397	−	8.68445i	0.564115	−	0.977077i	0.997131	−	0.0756903i	$-0.0241160\pi$
$80$	−2.98556	−	1.72371i	−0.333796	−	0.192717i
$81$	8.81184			0.979093
$82$	23.6468			2.61135
$83$	13.8506	−	7.99664i	1.52030	−	0.877745i	0.520586	−	0.853809i	$-0.325714\pi$
$83$	13.8506	−	7.99664i	1.52030	−	0.877745i	0.999713	−	0.0239361i	$-0.00761981\pi$
$84$			1.01852i			0.111130i
$85$	5.83703	+	3.37001i	0.633115	+	0.365529i
$86$	−13.3780	−	7.72378i	−1.44259	−	0.832877i
$87$	−0.705983	−	1.22280i	−0.0756894	−	0.131098i
$88$	−1.60734	+	2.78399i	−0.171343	+	0.296775i
$89$	14.2527	−	8.22881i	1.51078	−	0.872252i	0.510863	−	0.859662i	$-0.329326\pi$
$89$	14.2527	−	8.22881i	1.51078	−	0.872252i	0.999921	−	0.0125896i	$-0.00400751\pi$
$90$	−5.86428	+	10.1572i	−0.618150	+	1.07067i
$91$	9.06182	−	1.58010i	0.949937	−	0.165640i
$92$	14.9823			1.56201
$93$	−0.564402	+	0.575400i	−0.0585258	+	0.0596662i
$94$	−9.93263	−	17.2038i	−1.02447	−	1.77444i
$95$	−2.23117	+	3.86449i	−0.228913	+	0.396488i
$96$	0.936776	+	0.540848i	0.0956093	+	0.0552001i
$97$	3.15104	+	1.81925i	0.319940	+	0.184717i	0.651366	−	0.758764i	$-0.274196\pi$
$97$	3.15104	+	1.81925i	0.319940	+	0.184717i	−0.331426	+	0.943481i	$0.607530\pi$
$98$		−	1.07160i		−	0.108248i
$99$	−5.01721	−	2.89669i	−0.504248	−	0.291128i
$100$	2.40234	+	4.16097i	0.240234	+	0.416097i
$101$	−8.22357	−	14.2436i	−0.818276	−	1.41730i	−0.906951	−	0.421235i	$-0.861597\pi$
$101$	−8.22357	−	14.2436i	−0.818276	−	1.41730i	0.0886752	−	0.996061i	$-0.471737\pi$
$102$	−1.02115	−	0.589559i	−0.101109	−	0.0583750i
$103$	7.14555	+	12.3764i	0.704072	+	1.21949i	0.967026	+	0.254679i	$0.0819700\pi$
$103$	7.14555	+	12.3764i	0.704072	+	1.21949i	−0.262954	+	0.964808i	$0.584697\pi$
$104$	−2.04911	+	5.59680i	−0.200932	+	0.548811i
$105$	0.333300	−	0.577292i	0.0325267	−	0.0563379i
$106$	−15.0832	−	8.70827i	−1.46501	−	0.845822i
$107$	1.96582			0.190043			0.0950217	−	0.995475i	$-0.469708\pi$
$107$	1.96582			0.190043			0.0950217	+	0.995475i	$0.469708\pi$
$108$	1.19351	−	2.06721i	0.114845	−	0.198918i
$109$		−	6.94579i		−	0.665286i	−0.943053	−	0.332643i	$-0.892060\pi$
$109$		−	6.94579i		−	0.665286i	0.943053	−	0.332643i	$-0.107940\pi$
$110$	6.63061	−	3.82818i	0.632204	−	0.365003i
$111$		−	0.893728i		−	0.0848289i
$112$	4.21998	+	2.43641i	0.398751	+	0.230219i
$113$	5.64094			0.530655			0.265327	−	0.964158i	$-0.414520\pi$
$113$	5.64094			0.530655			0.265327	+	0.964158i	$0.414520\pi$
$114$	0.390326	−	0.676064i	0.0365574	−	0.0633192i
$115$	−8.49185	−	4.90277i	−0.791869	−	0.457186i
$116$	26.8992			2.49753
$117$	−10.0863	−	3.69283i	−0.932482	−	0.341403i
$118$	−4.91143	+	8.50685i	−0.452134	+	0.783119i
$119$	−8.25044	−	4.76339i	−0.756316	−	0.436659i
$120$	0.215958	+	0.374051i	0.0197142	+	0.0341460i
$121$	−3.60905	−	6.25106i	−0.328096	−	0.568279i
$122$		−	0.543636i		−	0.0492185i
$123$	1.35910	+	0.784676i	0.122546	+	0.0707519i
$124$	−4.11709	−	14.7928i	−0.369726	−	1.32843i
$125$		−	12.1693i		−	1.08845i
$126$	8.28895	−	14.3569i	0.738439	−	1.27901i
$127$	−10.2799			−0.912194			−0.456097	−	0.889930i	$-0.650753\pi$
$127$	−10.2799			−0.912194			−0.456097	+	0.889930i	$0.650753\pi$
$128$	−10.6304	+	6.13747i	−0.939604	+	0.542481i
$129$	−0.512600	−	0.887850i	−0.0451320	−	0.0781708i
$130$	10.8914	−	9.10379i	0.955241	−	0.798455i
$131$	−5.96807	+	10.3370i	−0.521433	+	0.903148i	0.478256	+	0.878220i	$0.341269\pi$
$131$	−5.96807	+	10.3370i	−0.521433	+	0.903148i	−0.999689	+	0.0249279i	$0.992064\pi$
$132$	−0.672370	+	0.388193i	−0.0585223	+	0.0337879i
$133$	3.15367	−	5.46232i	0.273458	−	0.473643i
$134$	11.4675			0.990644
$135$	−1.35294	+	0.781122i	−0.116443	+	0.0672283i
$136$	5.34580	−	3.08640i	0.458398	−	0.264656i
$137$			18.5763i			1.58708i	0.608519	+	0.793540i	$0.291764\pi$
$137$			18.5763i			1.58708i	−0.608519	+	0.793540i	$0.708236\pi$
$138$	1.48559	+	0.857704i	0.126462	+	0.0730126i
$139$	−6.22829	+	10.7877i	−0.528276	+	0.915002i	0.471180	+	0.882037i	$0.343828\pi$
$139$	−6.22829	+	10.7877i	−0.528276	+	0.915002i	−0.999457	+	0.0329645i	$0.989505\pi$
$140$	6.34966	+	10.9979i	0.536644	+	0.929495i
$141$		−	1.31839i		−	0.111028i
$142$	−6.85972	−	11.8814i	−0.575655	−	0.997064i
$143$	4.49686	+	5.37986i	0.376046	+	0.449887i
$144$	−2.84498	−	4.92765i	−0.237082	−	0.410637i
$145$	−15.2463	−	8.80245i	−1.26614	−	0.731004i
$146$	−0.366700	+	0.635142i	−0.0303483	+	0.0525648i
$147$	0.0355591	−	0.0615902i	0.00293287	−	0.00507987i
$148$	14.7452	+	8.51316i	1.21205	+	0.699778i
$149$	14.9976	−	8.65889i	1.22865	−	0.709364i	0.261906	−	0.965093i	$-0.415649\pi$
$149$	14.9976	−	8.65889i	1.22865	−	0.709364i	0.966748	+	0.255729i	$0.0823156\pi$
$150$			0.550115i			0.0449167i
$151$		−	12.3975i		−	1.00889i	−0.863443	−	0.504447i	$-0.831696\pi$
$151$		−	12.3975i		−	1.00889i	0.863443	−	0.504447i	$-0.168304\pi$
$152$	2.04339	+	3.53926i	0.165741	+	0.287072i
$153$	5.56219	+	9.63399i	0.449676	+	0.778862i
$154$	−9.37213	+	5.41100i	−0.755227	+	0.436031i
$155$	−2.50722	+	9.73170i	−0.201384	+	0.781669i
$156$	−1.10443	+	0.923161i	−0.0884254	+	0.0739120i
$157$	−0.100633			−0.00803136			−0.00401568	−	0.999992i	$-0.501278\pi$
$157$	−0.100633			−0.00803136			−0.00401568	+	0.999992i	$0.501278\pi$
$158$			21.8734i			1.74016i
$159$	−0.577937	−	1.00102i	−0.0458334	−	0.0793858i
$160$	13.4870			1.06624
$161$	12.0029	+	6.92989i	0.945963	+	0.546152i
$162$	−16.6457	+	9.61040i	−1.30781	+	0.755064i
$163$	−16.8539	−	9.73060i	−1.32010	−	0.762159i	−0.336354	−	0.941736i	$-0.609194\pi$
$163$	−16.8539	−	9.73060i	−1.32010	−	0.762159i	−0.983744	+	0.179576i	$0.942527\pi$
$164$	−25.8921	+	14.9488i	−2.02183	+	1.16730i
$165$	0.508126			0.0395576
$166$	−17.4427	+	30.2116i	−1.35381	+	2.34487i
$167$			2.43477i			0.188408i	0.995553	+	0.0942041i	$0.0300306\pi$
$167$			2.43477i			0.188408i	−0.995553	+	0.0942041i	$0.969969\pi$
$168$	−0.305249	−	0.528708i	−0.0235505	−	0.0407907i
$169$	9.92677	+	8.39401i	0.763597	+	0.645693i
$170$	−14.7017			−1.12757
$171$	−6.37832	+	3.68252i	−0.487762	+	0.281610i
$172$	19.5310			1.48922
$173$	−5.99131			−0.455511			−0.227755	−	0.973718i	$-0.573139\pi$
$173$	−5.99131			−0.455511			−0.227755	+	0.973718i	$0.573139\pi$
$174$	2.66723	+	1.53992i	0.202202	+	0.116741i
$175$			4.44470i			0.335988i
$176$			3.71438i			0.279982i
$177$	−0.564570	+	0.325954i	−0.0424357	+	0.0245002i
$178$	−17.9491	+	31.0887i	−1.34534	+	2.33020i
$179$	−15.1841			−1.13491			−0.567457	−	0.823403i	$-0.692073\pi$
$179$	−15.1841			−1.13491			−0.567457	+	0.823403i	$0.692073\pi$
$180$		−	14.8289i		−	1.10528i
$181$	5.22717	+	9.05372i	0.388532	+	0.672957i	0.992252	−	0.124239i	$-0.0396489\pi$
$181$	5.22717	+	9.05372i	0.388532	+	0.672957i	−0.603720	+	0.797196i	$0.706316\pi$
$182$	−15.3946	+	12.8679i	−1.14113	+	0.953831i
$183$	0.0180396	−	0.0312455i	0.00133353	−	0.00230973i
$184$	−7.77719	+	4.49016i	−0.573342	+	0.331019i
$185$	−5.57166	−	9.65040i	−0.409637	−	0.709512i
$186$	0.438619	−	1.70249i	0.0321611	−	0.124833i
$187$		−	7.26195i		−	0.531046i
$188$	21.7515	+	12.5582i	1.58639	+	0.915903i
$189$	1.91234	−	1.10409i	0.139102	−	0.0803105i
$190$		−	9.73345i		−	0.706138i
$191$	−11.0446			−0.799157			−0.399579	−	0.916699i	$-0.630844\pi$
$191$	−11.0446			−0.799157			−0.399579	+	0.916699i	$0.630844\pi$
$192$	−1.80646			−0.130370
$193$			14.2144i			1.02317i	0.859232	+	0.511587i	$0.170942\pi$
$193$			14.2144i			1.02317i	−0.859232	+	0.511587i	$0.829058\pi$
$194$	−7.93648			−0.569806
$195$	0.928078	−	0.161828i	0.0664611	−	0.0115888i
$196$	0.677433	+	1.17335i	0.0483881	+	0.0838106i
$197$	1.90237	+	1.09833i	0.135538	+	0.0782531i	0.566236	−	0.824243i	$-0.308399\pi$
$197$	1.90237	+	1.09833i	0.135538	+	0.0782531i	−0.430698	+	0.902496i	$0.641732\pi$
$198$	12.6368			0.898057
$199$	−3.96506			−0.281076			−0.140538	−	0.990075i	$-0.544883\pi$
$199$	−3.96506			−0.281076			−0.140538	+	0.990075i	$0.544883\pi$
$200$	−2.49407	−	1.43995i	−0.176357	−	0.101820i
$201$	0.659097	+	0.380530i	0.0464891	+	0.0268405i
$202$	31.0689	+	17.9377i	2.18600	+	1.26209i
$203$	21.5501	+	12.4420i	1.51252	+	0.873254i
$204$	1.49081			0.104377
$205$	19.5672			1.36664
$206$	−26.9961	−	15.5862i	−1.88091	−	1.08594i
$207$	−8.09200	−	14.0157i	−0.562433	−	0.974162i
$208$	1.18296	+	6.78422i	0.0820235	+	0.470401i
$209$	4.80788			0.332568
$210$			1.45402i			0.100337i
$211$	−14.0336			−0.966116			−0.483058	−	0.875588i	$-0.660474\pi$
$211$	−14.0336			−0.966116			−0.483058	+	0.875588i	$0.660474\pi$
$212$	22.0204			1.51237
$213$		−	0.910511i		−	0.0623872i
$214$	−3.71347	+	2.14398i	−0.253848	+	0.146559i
$215$	−11.0700	−	6.39129i	−0.754970	−	0.435882i
$216$			1.43077i			0.0973513i
$217$	3.54386	−	13.7554i	0.240573	−	0.933778i
$218$	7.57524	+	13.1207i	0.513060	+	0.888646i
$219$	−0.0421522	+	0.0243366i	−0.00284838	+	0.00164451i
$220$	−4.84013	+	8.38335i	−0.326321	+	0.565205i
$221$	−2.31279	−	13.2637i	−0.155575	−	0.892216i
$222$	0.974721	+	1.68827i	0.0654190	+	0.113309i
$223$			1.71753i			0.115015i	0.998345	+	0.0575073i	$0.0183152\pi$
$223$			1.71753i			0.115015i	−0.998345	+	0.0575073i	$0.981685\pi$
$224$	−19.0634			−1.27372
$225$	2.59503	−	4.49472i	0.173002	−	0.299648i
$226$	−10.6558	+	6.15214i	−0.708814	+	0.409234i
$227$		−	23.1116i		−	1.53397i	−0.641666	−	0.766984i	$-0.721756\pi$
$227$		−	23.1116i		−	1.53397i	0.641666	−	0.766984i	$-0.278244\pi$
$228$			0.987010i			0.0653664i
$229$	−1.63191	−	0.942182i	−0.107839	−	0.0622612i	0.445110	−	0.895476i	$-0.353165\pi$
$229$	−1.63191	−	0.942182i	−0.107839	−	0.0622612i	−0.552950	+	0.833215i	$0.686498\pi$
$230$	21.3883			1.41030
$231$	−0.718218			−0.0472553
$232$	−13.9632	+	8.06165i	−0.916728	+	0.529273i
$233$	17.6256			1.15469			0.577345	−	0.816500i	$-0.304089\pi$
$233$	17.6256			1.15469			0.577345	+	0.816500i	$0.304089\pi$
$234$	23.0807	−	4.02457i	1.50883	−	0.263095i
$235$	−8.21906	−	14.2358i	−0.536153	−	0.928643i
$236$		−	12.4194i		−	0.808437i
$237$	−0.725831	+	1.25718i	−0.0471478	+	0.0816623i
$238$	20.7803			1.34699
$239$	−14.8170	+	8.55461i	−0.958433	+	0.553352i	−0.895690	−	0.444678i	$-0.853318\pi$
$239$	−14.8170	+	8.55461i	−0.958433	+	0.553352i	−0.0627426	+	0.998030i	$0.519985\pi$
$240$	0.432195	+	0.249528i	0.0278981	+	0.0161070i
$241$	4.72999	−	2.73086i	0.304685	−	0.175910i	−0.339861	−	0.940476i	$-0.610380\pi$
$241$	4.72999	−	2.73086i	0.304685	−	0.175910i	0.644546	+	0.764566i	$0.277047\pi$
$242$	13.6351	+	7.87224i	0.876499	+	0.506047i
$243$	−3.87223			−0.248404
$244$	0.343671	+	0.595255i	0.0220013	+	0.0381073i
$245$		−	0.886727i		−	0.0566509i
$246$	−3.42315			−0.218252
$247$	8.78145	−	1.53122i	0.558750	−	0.0974290i
$248$	6.57051	+	6.44492i	0.417228	+	0.409253i
$249$	−2.00504	+	1.15761i	−0.127064	+	0.0733604i
$250$	13.2721	+	22.9879i	0.839400	+	1.45388i
$251$	−6.12667	−	10.6117i	−0.386712	−	0.669805i	0.605293	−	0.796003i	$-0.293056\pi$
$251$	−6.12667	−	10.6117i	−0.386712	−	0.669805i	−0.992005	+	0.126198i	$0.959723\pi$
$252$			20.9601i			1.32036i
$253$			10.5649i			0.664206i
$254$	19.4189	−	11.2115i	1.21845	−	0.703473i
$255$	−0.844979	−	0.487849i	−0.0529147	−	0.0305503i
$256$	0.908500	−	1.57357i	0.0567812	−	0.0983480i
$257$	0.182380	−	0.315892i	0.0113766	−	0.0197048i	−0.860281	−	0.509820i	$-0.829712\pi$
$257$	0.182380	−	0.315892i	0.0113766	−	0.0197048i	0.871658	+	0.490115i	$0.163045\pi$
$258$	1.93662	+	1.11811i	0.120569	+	0.0696104i
$259$	7.87534	+	13.6405i	0.489350	+	0.847579i
$260$	−6.17043	+	16.8534i	−0.382674	+	1.04521i
$261$	−14.5284	−	25.1639i	−0.899285	−	1.55761i
$262$		−	26.0357i		−	1.60849i
$263$	−3.59707	−	6.23031i	−0.221805	−	0.384177i	0.733551	−	0.679634i	$-0.237861\pi$
$263$	−3.59707	−	6.23031i	−0.221805	−	0.384177i	−0.955356	+	0.295457i	$0.904528\pi$
$264$	0.232681	−	0.403016i	0.0143205	−	0.0248039i
$265$	−12.4810	−	7.20593i	−0.766704	−	0.442657i
$266$			13.7579i			0.843550i
$267$	−2.06325	+	1.19122i	−0.126269	+	0.0729013i
$268$	−12.5564	+	7.24944i	−0.767004	+	0.442830i
$269$	12.1785			0.742538			0.371269	−	0.928525i	$-0.378923\pi$
$269$	12.1785			0.742538			0.371269	+	0.928525i	$0.378923\pi$
$270$	1.70382	−	2.95110i	0.103691	−	0.179598i
$271$	2.92260	−	1.68736i	0.177535	−	0.102500i	−0.408599	−	0.912714i	$-0.633982\pi$
$271$	2.92260	−	1.68736i	0.177535	−	0.102500i	0.586134	+	0.810214i	$0.300649\pi$
$272$	3.56616	−	6.17677i	0.216230	−	0.374522i
$273$	−1.31181	+	0.228739i	−0.0793941	+	0.0138439i
$274$	−20.2597	−	35.0909i	−1.22394	−	2.11992i
$275$	−2.93413	+	1.69402i	−0.176935	+	0.102153i
$276$	−2.16886			−0.130550
$277$	5.77142	−	9.99640i	0.346771	−	0.600625i	−0.638903	−	0.769288i	$-0.720611\pi$
$277$	5.77142	−	9.99640i	0.346771	−	0.600625i	0.985674	+	0.168662i	$0.0539447\pi$
$278$		−	27.1709i		−	1.62960i
$279$	−11.6148	+	11.8411i	−0.695360	+	0.708910i
$280$	−6.59211	−	3.80596i	−0.393954	−	0.227450i
$281$		−	2.34103i		−	0.139654i	−0.997559	−	0.0698271i	$-0.977755\pi$
$281$		−	2.34103i		−	0.139654i	0.997559	−	0.0698271i	$-0.0222447\pi$
$282$	1.43786	+	2.49045i	0.0856236	+	0.148304i
$283$	4.39693	+	7.61570i	0.261370	+	0.452707i	0.966606	−	0.256266i	$-0.0824923\pi$
$283$	4.39693	+	7.61570i	0.261370	+	0.452707i	−0.705236	+	0.708973i	$0.749159\pi$
$284$	15.0221	+	8.67303i	0.891399	+	0.514650i
$285$	0.322987	−	0.559431i	0.0191321	−	0.0331378i
$286$	−14.3620	−	5.25827i	−0.849245	−	0.310928i
$287$	−27.6576			−1.63258
$288$	19.2779	+	11.1301i	1.13596	+	0.655846i
$289$	1.52785	−	2.64631i	0.0898732	−	0.155665i
$290$	38.4007			2.25496
$291$	−0.456150	−	0.263358i	−0.0267400	−	0.0154383i
$292$		−	0.927267i		−	0.0542642i
$293$	−10.1336	+	5.85065i	−0.592013	+	0.341799i	−0.765893	−	0.642968i	$-0.777703\pi$
$293$	−10.1336	+	5.85065i	−0.592013	+	0.341799i	0.173880	+	0.984767i	$0.444369\pi$
$294$			0.155126i			0.00904716i
$295$	−4.06412	+	7.03926i	−0.236622	+	0.409841i
$296$	−10.2055			−0.593183
$297$	1.45771	+	0.841609i	0.0845849	+	0.0488351i
$298$	−18.8872	+	32.7136i	−1.09411	+	1.89505i
$299$	3.36470	+	19.2964i	0.194586	+	1.11594i
$300$	−0.347767	−	0.602349i	−0.0200783	−	0.0347767i
$301$	15.6471	+	9.03385i	0.901883	+	0.520703i
$302$	13.5210	+	23.4191i	0.778046	+	1.34762i
$303$	1.19046	+	2.06194i	0.0683901	+	0.118455i
$304$	4.08942	+	2.36103i	0.234544	+	0.135414i
$305$		−	0.449848i		−	0.0257582i
$306$	−21.0141	−	12.1325i	−1.20130	−	0.693569i
$307$	1.70910	+	0.986747i	0.0975432	+	0.0563166i	0.547978	−	0.836493i	$-0.315398\pi$
$307$	1.70910	+	0.986747i	0.0975432	+	0.0563166i	−0.450435	+	0.892809i	$0.648731\pi$
$308$	6.84135	−	11.8496i	0.389822	−	0.675192i
$309$	−1.03440	−	1.79164i	−0.0588451	−	0.101923i
$310$	−5.87746	−	21.1178i	−0.333817	−	1.19941i
$311$	−16.7773			−0.951355			−0.475677	−	0.879620i	$-0.657797\pi$
$311$	−16.7773			−0.951355			−0.475677	+	0.879620i	$0.657797\pi$
$312$	0.296633	−	0.810202i	0.0167936	−	0.0458687i
$313$	3.42282	−	5.92850i	0.193469	−	0.335099i	−0.752928	−	0.658103i	$-0.771359\pi$
$313$	3.42282	−	5.92850i	0.193469	−	0.335099i	0.946398	+	0.323004i	$0.104693\pi$
$314$	0.190097	−	0.109752i	0.0107278	−	0.00619369i
$315$	6.85895	−	11.8801i	0.386458	−	0.669365i
$316$	−13.8277	−	23.9503i	−0.777870	−	1.34731i
$317$	−20.1304	−	11.6223i	−1.13063	−	0.652772i	−0.186540	−	0.982447i	$-0.559727\pi$
$317$	−20.1304	−	11.6223i	−1.13063	−	0.652772i	−0.944094	+	0.329675i	$0.893061\pi$
$318$	2.18346	+	1.26062i	0.122443	+	0.0706923i
$319$			18.9682i			1.06201i
$320$	−19.5060	+	11.2618i	−1.09042	+	0.629553i
$321$	−0.284576			−0.0158835
$322$	−30.2316			−1.68474
$323$	−7.99517	−	4.61601i	−0.444863	−	0.256842i
$324$	12.1508	−	21.0458i	0.675046	−	1.16921i
$325$	−4.81960	+	4.02855i	−0.267343	+	0.223464i
$326$	42.4497			2.35107
$327$			1.00548i			0.0556034i
$328$	8.96024	−	15.5196i	0.494747	−	0.856926i
$329$	11.6174	+	20.1218i	0.640485	+	1.10935i
$330$	−0.959858	+	0.554174i	−0.0528385	+	0.0305063i
$331$		−	0.241070i		−	0.0132504i	−0.999978	−	0.00662520i	$-0.997891\pi$
$331$		−	0.241070i		−	0.0132504i	0.999978	−	0.00662520i	$-0.00210888\pi$
$332$		−	44.1069i		−	2.42068i
$333$		−	18.3920i		−	1.00787i
$334$	−2.65542	−	4.59932i	−0.145298	−	0.251664i
$335$	9.48917			0.518449
$336$	−0.610892	−	0.352699i	−0.0333269	−	0.0192413i
$337$	−18.5926			−1.01280			−0.506402	−	0.862298i	$-0.669025\pi$
$337$	−18.5926			−1.01280			−0.506402	+	0.862298i	$0.669025\pi$
$338$	−27.9065	−	5.03004i	−1.51791	−	0.273598i
$339$	−0.816592			−0.0443512
$340$	16.0976	−	9.29396i	0.873016	−	0.504036i
$341$	10.4312	−	2.90319i	0.564882	−	0.157217i
$342$	8.03250	−	13.9127i	0.434348	−	0.752312i
$343$			19.1119i			1.03195i
$344$	−10.1384	+	5.85340i	−0.546625	+	0.315594i
$345$	1.22930	+	0.709734i	0.0661830	+	0.0382108i
$346$	11.3177	−	6.53426i	0.608442	−	0.351284i
$347$	7.99765	+	13.8523i	0.429336	+	0.743632i	0.996814	−	0.0797562i	$-0.0254142\pi$
$347$	7.99765	+	13.8523i	0.429336	+	0.743632i	−0.567478	+	0.823389i	$0.692081\pi$
$348$	−3.89398			−0.208739
$349$	8.96805	−	5.17771i	0.480049	−	0.277156i	−0.240388	−	0.970677i	$-0.577275\pi$
$349$	8.96805	−	5.17771i	0.480049	−	0.277156i	0.720437	+	0.693521i	$0.243941\pi$
$350$	−4.84750	−	8.39611i	−0.259110	−	0.448791i
$351$	2.93050	+	1.07292i	0.156419	+	0.0572684i
$352$	−7.26568	−	12.5845i	−0.387262	−	0.670757i
$353$		−	11.7034i		−	0.622911i	−0.950261	−	0.311456i	$-0.899184\pi$
$353$		−	11.7034i		−	0.622911i	0.950261	−	0.311456i	$-0.100816\pi$
$354$	0.710987	−	1.23147i	0.0377886	−	0.0654517i
$355$	−5.67629	−	9.83162i	−0.301266	−	0.521808i
$356$		−	45.3875i		−	2.40553i
$357$	1.19435	+	0.689557i	0.0632116	+	0.0364952i
$358$	28.6830	−	16.5602i	1.51595	−	0.875232i
$359$	27.6725	−	15.9767i	1.46050	−	0.843220i	0.461466	−	0.887158i	$-0.347324\pi$
$359$	27.6725	−	15.9767i	1.46050	−	0.843220i	0.999034	+	0.0439378i	$0.0139904\pi$
$360$	4.44420	+	7.69757i	0.234230	+	0.405698i
$361$	−6.44390	+	11.1612i	−0.339153	+	0.587430i
$362$	−19.7484	−	11.4017i	−1.03795	−	0.599262i
$363$	0.522453	+	0.904915i	0.0274217	+	0.0474957i
$364$	8.72168	−	23.8217i	0.457140	−	1.24860i
$365$	−0.303437	+	0.525568i	−0.0158826	+	0.0275095i
$366$			0.0786977i			0.00411359i
$367$	−1.50123	+	2.60021i	−0.0783637	+	0.135730i	−0.902544	−	0.430597i	$-0.858303\pi$
$367$	−1.50123	+	2.60021i	−0.0783637	+	0.135730i	0.824180	+	0.566327i	$0.191636\pi$
$368$	−5.18813	+	8.98610i	−0.270450	+	0.468433i
$369$	27.9688	+	16.1478i	1.45600	+	0.840621i
$370$	21.0499	+	12.1532i	1.09433	+	0.631813i
$371$	17.6415	+	10.1853i	0.915900	+	0.528795i
$372$	0.595998	+	2.14143i	0.0309010	+	0.111028i
$373$	9.52291	−	16.4942i	0.493078	−	0.854036i	−0.506891	−	0.862010i	$-0.669205\pi$
$373$	9.52291	−	16.4942i	0.493078	−	0.854036i	0.999968	+	0.00797484i	$0.00253850\pi$
$374$	7.92005	+	13.7179i	0.409536	+	0.709338i
$375$			1.76164i			0.0909708i
$376$	−15.0547			−0.776387
$377$	6.04100	+	34.6448i	0.311127	+	1.78430i
$378$	−2.40829	+	4.17128i	−0.123869	+	0.214547i
$379$			15.6708i			0.804954i	0.915430	+	0.402477i	$0.131851\pi$
$379$			15.6708i			0.804954i	−0.915430	+	0.402477i	$0.868149\pi$
$380$	6.15320	+	10.6577i	0.315652	+	0.546726i
$381$	1.48814			0.0762396
$382$	20.8634	−	12.0455i	1.06746	−	0.616300i
$383$			32.3139i			1.65116i	0.564282	+	0.825582i	$0.309153\pi$
$383$			32.3139i			1.65116i	−0.564282	+	0.825582i	$0.690847\pi$
$384$	1.53888	−	0.888471i	0.0785305	−	0.0453396i
$385$	−7.75526	+	4.47750i	−0.395245	+	0.228195i
$386$	−15.5025	−	26.8512i	−0.789058	−	1.36669i
$387$	−10.5488	−	18.2710i	−0.536224	−	0.928768i
$388$	8.69006	−	5.01721i	0.441171	−	0.254710i
$389$	18.5330	−	32.1000i	0.939658	−	1.62754i	0.173550	−	0.984825i	$-0.444476\pi$
$389$	18.5330	−	32.1000i	0.939658	−	1.62754i	0.766109	−	0.642711i	$-0.222190\pi$
$390$	−1.57666	+	1.31788i	−0.0798373	+	0.0667335i
$391$	10.1433	−	17.5686i	0.512966	−	0.888484i
$392$	−0.703300	−	0.406051i	−0.0355220	−	0.0205087i
$393$	0.863948	−	1.49640i	0.0435804	−	0.0754835i
$394$	−4.79148			−0.241391
$395$			18.0998i			0.910702i
$396$	−13.8367	+	7.98860i	−0.695319	+	0.401442i
$397$	14.3527	−	8.28653i	0.720341	−	0.415889i	−0.0945374	−	0.995521i	$-0.530137\pi$
$397$	14.3527	−	8.28653i	0.720341	−	0.415889i	0.814878	+	0.579632i	$0.196804\pi$
$398$	7.49006	−	4.32439i	0.375443	−	0.216762i
$399$	−0.456531	+	0.790735i	−0.0228551	+	0.0395863i
$400$	−3.32757			−0.166378
$401$	8.84906	−	5.10901i	0.441901	−	0.255132i	−0.262503	−	0.964931i	$-0.584548\pi$
$401$	8.84906	−	5.10901i	0.441901	−	0.255132i	0.704404	+	0.709800i	$0.251214\pi$
$402$	−1.66006			−0.0827963
$403$	18.1277	−	8.62474i	0.903005	−	0.429629i
$404$	−45.3586			−2.25668
$405$	−13.7740	+	7.95242i	−0.684436	+	0.395159i
$406$	−54.2780			−2.69377
$407$	−6.00311	+	10.3977i	−0.297563	+	0.515394i
$408$	−0.773867	+	0.446792i	−0.0383121	+	0.0221195i
$409$	−31.1229	+	17.9688i	−1.53893	+	0.888502i	−0.540029	+	0.841647i	$0.681587\pi$
$409$	−31.1229	+	17.9688i	−1.53893	+	0.888502i	−0.998902	+	0.0468552i	$0.985080\pi$
$410$	−36.9628	+	21.3405i	−1.82546	+	1.05393i
$411$		−	2.68914i		−	0.132645i
$412$	39.4126			1.94172
$413$	5.74448	−	9.94974i	0.282668	−	0.489595i
$414$	30.5718	+	17.6506i	1.50252	+	0.867482i
$415$	−14.4335	+	24.9995i	−0.708511	+	1.22718i
$416$	−17.2785	−	20.6713i	−0.847147	−	1.01349i
$417$	0.901618	−	1.56165i	0.0441524	−	0.0764742i
$418$	−9.08215	+	5.24358i	−0.444223	+	0.256472i
$419$	−7.12989	−	12.3493i	−0.348318	−	0.603304i	0.637633	−	0.770340i	$-0.279914\pi$
$419$	−7.12989	−	12.3493i	−0.348318	−	0.603304i	−0.985951	+	0.167036i	$0.946580\pi$
$420$	−0.919187	−	1.59208i	−0.0448518	−	0.0776855i
$421$	−13.5428	+	7.81892i	−0.660034	+	0.381071i	−0.792290	−	0.610145i	$-0.791111\pi$
$421$	−13.5428	+	7.81892i	−0.660034	+	0.381071i	0.132256	+	0.991216i	$0.457778\pi$
$422$	26.5098	−	15.3054i	1.29048	−	0.745056i
$423$		−	27.1310i		−	1.31916i
$424$	−11.4306	+	6.59948i	−0.555121	+	0.320499i
$425$	6.50569			0.315572
$426$	0.993025	+	1.71997i	0.0481122	+	0.0833328i
$427$			0.635844i			0.0307707i
$428$	2.71072	−	4.69510i	0.131027	−	0.226946i
$429$	−0.650973	−	0.778798i	−0.0314293	−	0.0376007i
$430$	27.8820			1.34459
$431$		−	31.7843i		−	1.53099i	−0.643440	−	0.765497i	$-0.722493\pi$
$431$		−	31.7843i		−	1.53099i	0.643440	−	0.765497i	$-0.277507\pi$
$432$	0.826585	+	1.43169i	0.0397691	+	0.0688821i
$433$	−17.0916	+	29.6035i	−0.821368	+	1.42265i	0.0832953	+	0.996525i	$0.473456\pi$
$433$	−17.0916	+	29.6035i	−0.821368	+	1.42265i	−0.904664	+	0.426127i	$0.859878\pi$
$434$	8.30758	+	29.8492i	0.398776	+	1.43281i
$435$	2.20708	+	1.27426i	0.105821	+	0.0610960i
$436$	−16.5890	−	9.57769i	−0.794471	−	0.458688i
$437$	11.6316	+	6.71548i	0.556413	+	0.321245i
$438$	0.0530841	−	0.0919443i	0.00253646	−	0.00439327i
$439$	8.62972	−	14.9471i	0.411874	−	0.713387i	−0.583221	−	0.812314i	$-0.698208\pi$
$439$	8.62972	−	14.9471i	0.411874	−	0.713387i	0.995095	+	0.0989269i	$0.0315410\pi$
$440$		−	5.80231i		−	0.276614i
$441$	0.731769	−	1.26746i	0.0348461	−	0.0603553i
$442$	18.8347	+	22.5330i	0.895873	+	1.07179i
$443$	−12.0506	−	20.8723i	−0.572543	−	0.991674i	−0.996304	−	0.0858995i	$-0.972624\pi$
$443$	−12.0506	−	20.8723i	−0.572543	−	0.991674i	0.423761	−	0.905774i	$-0.360710\pi$
$444$	−2.13455	−	1.23238i	−0.101301	−	0.0584862i
$445$	−14.8525	+	25.7253i	−0.704077	+	1.21950i
$446$	−1.87318	−	3.24445i	−0.0886978	−	0.153629i
$447$	−2.17108	+	1.25348i	−0.102689	+	0.0592874i
$448$	27.5710	−	15.9181i	1.30261	−	0.752061i
$449$	−26.9848	−	15.5797i	−1.27349	−	0.735250i	−0.297847	−	0.954614i	$-0.596268\pi$
$449$	−26.9848	−	15.5797i	−1.27349	−	0.735250i	−0.975643	+	0.219364i	$0.929602\pi$
$450$			11.3208i			0.533667i
$451$	−10.5412	−	18.2579i	−0.496367	−	0.859733i
$452$	7.77840	−	13.4726i	0.365865	−	0.633697i
$453$			1.79468i			0.0843215i
$454$	25.2060	+	43.6581i	1.18298	+	2.04898i
$455$	−12.7388	+	10.6479i	−0.597203	+	0.499183i
$456$	−0.295805	−	0.512349i	−0.0138523	−	0.0239930i
$457$	−25.8142	+	14.9038i	−1.20754	+	0.697172i	−0.962221	−	0.272271i	$-0.912225\pi$
$457$	−25.8142	+	14.9038i	−1.20754	+	0.697172i	−0.245317	+	0.969443i	$0.578892\pi$
$458$	4.11027			0.192060
$459$	−1.61605	−	2.79908i	−0.0754306	−	0.130650i
$460$	−23.4192	+	13.5211i	−1.09192	+	0.630423i
$461$	8.22549	+	4.74899i	0.383099	+	0.221182i	0.679166	−	0.733985i	$-0.262342\pi$
$461$	8.22549	+	4.74899i	0.383099	+	0.221182i	−0.296067	+	0.955167i	$0.595675\pi$
$462$	1.35673	−	0.783306i	0.0631206	−	0.0364427i
$463$		−	6.74496i		−	0.313465i	−0.987641	−	0.156732i	$-0.949904\pi$
$463$		−	6.74496i		−	0.313465i	0.987641	−	0.156732i	$-0.0500960\pi$
$464$	−9.31478	+	16.1337i	−0.432428	+	0.748987i
$465$	0.362949	−	1.40878i	0.0168314	−	0.0653305i
$466$	−33.2950	+	19.2229i	−1.54236	+	0.890483i
$467$	7.67226			0.355030			0.177515	−	0.984118i	$-0.443194\pi$
$467$	7.67226			0.355030			0.177515	+	0.984118i	$0.443194\pi$
$468$	−22.7281	+	18.9977i	−1.05061	+	0.878168i
$469$	−13.4126			−0.619336
$470$	31.0519	+	17.9278i	1.43232	+	0.826948i
$471$	0.0145678			0.000671247
$472$	3.72208	+	6.44684i	0.171323	+	0.296740i
$473$			13.7724i			0.633256i
$474$		−	3.16643i		−	0.145439i
$475$			4.30718i			0.197627i
$476$	−22.7534	+	13.1367i	−1.04290	+	0.602119i
$477$	−11.8933	−	20.5999i	−0.544558	−	0.943203i
$478$	18.6597	−	32.3196i	0.853476	−	1.47826i
$479$			14.7863i			0.675601i	0.941218	+	0.337801i	$0.109683\pi$
$479$			14.7863i			0.675601i	−0.941218	+	0.337801i	$0.890317\pi$
$480$	−1.95240			−0.0891144
$481$	−7.65305	+	20.9030i	−0.348949	+	0.953094i
$482$	−5.95668	+	10.3173i	−0.271319	+	0.469939i
$483$	−1.73757	−	1.00318i	−0.0790620	−	0.0456464i
$484$	−19.9064			−0.904836
$485$	−6.56729			−0.298205
$486$	7.31470	−	4.22314i	0.331802	−	0.191566i
$487$		−	7.34133i		−	0.332667i	−0.986070	−	0.166334i	$-0.946807\pi$
$487$		−	7.34133i		−	0.332667i	0.986070	−	0.166334i	$-0.0531929\pi$
$488$	−0.356793	−	0.205995i	−0.0161513	−	0.00932495i
$489$	2.43980	+	1.40862i	0.110331	+	0.0636999i
$490$	0.967086	+	1.67504i	0.0436885	+	0.0756707i
$491$	20.7481	−	35.9368i	0.936350	−	1.62180i	0.164140	−	0.986437i	$-0.447515\pi$
$491$	20.7481	−	35.9368i	0.936350	−	1.62180i	0.772210	−	0.635368i	$-0.219152\pi$
$492$	3.74818	−	2.16401i	0.168981	−	0.0975612i
$493$	18.2112	−	31.5428i	0.820192	−	1.42061i
$494$	−14.9183	+	12.4698i	−0.671207	+	0.561041i
$495$	10.4567			0.469994
$496$	10.2981	+	2.65314i	0.462399	+	0.119130i
$497$	8.02323	+	13.8966i	0.359891	+	0.623350i
$498$	2.52503	−	4.37348i	0.113149	−	0.195980i
$499$	−2.57595	−	1.48723i	−0.115315	−	0.0665774i	0.441233	−	0.897393i	$-0.354541\pi$
$499$	−2.57595	−	1.48723i	−0.115315	−	0.0665774i	−0.556548	+	0.830815i	$0.687875\pi$
$500$	−29.0646	−	16.7804i	−1.29981	−	0.750444i
$501$		−	0.352462i		−	0.0157468i
$502$	23.1468	+	13.3638i	1.03309	+	0.596455i
$503$	8.30859	+	14.3909i	0.370462	+	0.641659i	0.989637	−	0.143595i	$-0.0458661\pi$
$503$	8.30859	+	14.3909i	0.370462	+	0.641659i	−0.619175	+	0.785253i	$0.712533\pi$
$504$	−6.28171	−	10.8802i	−0.279810	−	0.484645i
$505$	25.7089	+	14.8431i	1.14403	+	0.660508i
$506$	−11.5223	−	19.9572i	−0.512228	−	0.887204i
$507$	−1.43702	−	1.21513i	−0.0638201	−	0.0539659i
$508$	−14.1752	+	24.5521i	−0.628922	+	1.08932i
$509$	−6.12075	−	3.53381i	−0.271297	−	0.156634i	0.358180	−	0.933653i	$-0.383397\pi$
$509$	−6.12075	−	3.53381i	−0.271297	−	0.156634i	−0.629477	+	0.777019i	$0.716731\pi$
$510$	2.12824			0.0942400
$511$	0.428897	−	0.742872i	0.0189733	−	0.0328627i
$512$		−	20.5865i		−	0.909805i
$513$	1.85317	−	1.06993i	0.0818194	−	0.0472384i
$514$			0.795634i			0.0350939i
$515$	−22.3388	−	12.8973i	−0.984364	−	0.568323i
$516$	−2.82734			−0.124467
$517$	−8.85552	+	15.3382i	−0.389465	+	0.674573i
$518$	−29.7533	−	17.1781i	−1.30729	−	0.754761i
$519$	0.867312			0.0380708
$520$	−1.84792	−	10.5978i	−0.0810368	−	0.464742i
$521$	1.02615	−	1.77734i	0.0449563	−	0.0778666i	−0.842672	−	0.538428i	$-0.819018\pi$
$521$	1.02615	−	1.77734i	0.0449563	−	0.0778666i	0.887628	+	0.460561i	$0.152352\pi$
$522$	54.8887	+	31.6900i	2.40241	+	1.38703i
$523$	3.02324	+	5.23640i	0.132197	+	0.228972i	0.924523	−	0.381126i	$-0.124464\pi$
$523$	3.02324	+	5.23640i	0.132197	+	0.228972i	−0.792326	+	0.610098i	$0.791130\pi$
$524$	16.4590	+	28.5078i	0.719014	+	1.24537i
$525$		−	0.643423i		−	0.0280813i
$526$	13.5898	+	7.84610i	0.592545	+	0.342106i
$527$	−20.1337	−	5.18713i	−0.877039	−	0.225955i
$528$		−	0.537701i		−	0.0234004i
$529$	−3.25664	+	5.64067i	−0.141593	+	0.245246i
$530$	31.4358			1.36548
$531$	−11.6182	+	6.70780i	−0.504189	+	0.291094i
$532$	−8.69733	−	15.0642i	−0.377077	−	0.653116i
$533$	−25.0681	−	29.9905i	−1.08582	−	1.29903i
$534$	2.59834	−	4.50045i	0.112441	−	0.194754i
$535$	−3.07283	+	1.77410i	−0.132850	+	0.0767010i
$536$	4.34528	−	7.52625i	0.187688	−	0.325085i
$537$	2.19808			0.0948542
$538$	−23.0054	+	13.2822i	−0.991834	+	0.572636i
$539$	−0.827394	+	0.477696i	−0.0356384	+	0.0205758i
$540$			4.30842i			0.185405i
$541$	−6.82338	−	3.93948i	−0.293360	−	0.169371i	0.346096	−	0.938199i	$-0.387507\pi$
$541$	−6.82338	−	3.93948i	−0.293360	−	0.169371i	−0.639456	+	0.768828i	$0.720840\pi$
$542$	−3.68056	+	6.37492i	−0.158094	+	0.273826i
$543$	−0.756694	−	1.31063i	−0.0324728	−	0.0562446i
$544$			27.9029i			1.19633i
$545$	6.26837	+	10.8571i	0.268508	+	0.465069i
$546$	2.22855	−	1.86278i	0.0953733	−	0.0797195i
$547$	19.2082	+	33.2695i	0.821281	+	1.42250i	0.904729	+	0.425989i	$0.140074\pi$
$547$	19.2082	+	33.2695i	0.821281	+	1.42250i	−0.0834473	+	0.996512i	$0.526593\pi$
$548$	44.3669	+	25.6152i	1.89526	+	1.09423i
$549$	0.371236	−	0.642999i	0.0158440	−	0.0274425i
$550$	3.69508	−	6.40007i	0.157559	−	0.272900i
$551$	20.8833	+	12.0570i	0.889660	+	0.513646i
$552$	1.12584	−	0.650004i	0.0479189	−	0.0276660i
$553$		−	25.5835i		−	1.08792i
$554$			25.1778i			1.06970i
$555$	0.806564	+	1.39701i	0.0342367	+	0.0592997i
$556$	17.1766	+	29.7508i	0.728451	+	1.26171i
$557$	−3.40611	+	1.96652i	−0.144321	+	0.0833240i	−0.570422	−	0.821352i	$-0.693220\pi$
$557$	−3.40611	+	1.96652i	−0.144321	+	0.0833240i	0.426101	+	0.904676i	$0.359887\pi$
$558$	9.02632	−	35.0355i	0.382114	−	1.48317i
$559$	4.38625	+	25.1549i	0.185518	+	1.06394i
$560$	−8.79515			−0.371663
$561$			1.05125i			0.0443839i
$562$	2.55318	+	4.42224i	0.107700	+	0.186541i
$563$	−28.7728			−1.21263			−0.606314	−	0.795226i	$-0.707352\pi$
$563$	−28.7728			−1.21263			−0.606314	+	0.795226i	$0.707352\pi$
$564$	−3.14878	−	1.81795i	−0.132588	−	0.0765496i
$565$	−8.81749	+	5.09078i	−0.370954	+	0.214171i
$566$	−16.6117	−	9.59079i	−0.698243	−	0.403131i
$567$	19.4691	−	11.2405i	0.817623	−	0.472055i
$568$	−10.3972			−0.436255
$569$	6.96294	−	12.0602i	0.291902	−	0.505589i	−0.682358	−	0.731018i	$-0.739045\pi$
$569$	6.96294	−	12.0602i	0.291902	−	0.505589i	0.974259	+	0.225430i	$0.0723786\pi$
$570$			1.40903i			0.0590178i
$571$	12.7133	+	22.0200i	0.532033	+	0.921509i	0.999301	+	0.0373925i	$0.0119052\pi$
$571$	12.7133	+	22.0200i	0.532033	+	0.921509i	−0.467267	+	0.884116i	$0.654761\pi$
$572$	19.0499	−	3.32171i	0.796514	−	0.138888i
$573$	1.59883			0.0667922
$574$	52.2456	−	30.1640i	2.18069	−	1.25902i
$575$	−9.46463			−0.394702
$576$	−37.1750			−1.54896
$577$	−32.7655	−	18.9172i	−1.36405	−	0.787533i	−0.373887	−	0.927474i	$-0.621975\pi$
$577$	−32.7655	−	18.9172i	−1.36405	−	0.787533i	−0.990160	+	0.139941i	$0.955309\pi$
$578$			6.66522i			0.277237i
$579$		−	2.05770i		−	0.0855150i
$580$	−42.0469	+	24.2758i	−1.74590	+	1.00800i
$581$	20.4012	−	35.3359i	0.846384	−	1.46598i
$582$	1.14890			0.0476234
$583$			15.5278i			0.643098i
$584$	0.277900	+	0.481337i	0.0114996	+	0.0199179i
$585$	19.0989	−	3.33026i	0.789641	−	0.137689i
$586$	12.7617	−	22.1039i	0.527182	−	0.913106i
$587$	−1.56719	+	0.904815i	−0.0646847	+	0.0373457i	−0.531994	−	0.846748i	$-0.678557\pi$
$587$	−1.56719	+	0.904815i	−0.0646847	+	0.0373457i	0.467309	+	0.884094i	$0.345224\pi$
$588$	−0.0980664	−	0.169856i	−0.00404419	−	0.00700474i
$589$	3.43421	−	13.3298i	0.141504	−	0.549246i
$590$		−	17.7297i		−	0.729920i
$591$	−0.275390	−	0.158997i	−0.0113281	−	0.00654025i
$592$	−10.2121	+	5.89595i	−0.419714	+	0.242322i
$593$			1.51685i			0.0622897i	0.999515	+	0.0311449i	$0.00991532\pi$
$593$			1.51685i			0.0622897i	−0.999515	+	0.0311449i	$0.990085\pi$
$594$	−3.67151			−0.150644
$595$	17.1953			0.704938
$596$		−	47.7597i		−	1.95631i
$597$	0.573989			0.0234918
$598$	−27.4011	−	32.7816i	−1.12051	−	1.34054i
$599$	13.3807	+	23.1761i	0.546721	+	0.946949i	0.998496	+	0.0548170i	$0.0174575\pi$
$599$	13.3807	+	23.1761i	0.546721	+	0.946949i	−0.451775	+	0.892132i	$0.649209\pi$
$600$	0.361046	+	0.208450i	0.0147396	+	0.00850993i
$601$	15.3585			0.626488			0.313244	−	0.949673i	$-0.398584\pi$
$601$	15.3585			0.626488			0.313244	+	0.949673i	$0.398584\pi$
$602$	−39.4101			−1.60624
$603$	13.5635	+	7.83090i	0.552349	+	0.318899i
$604$	−29.6097	−	17.0952i	−1.20480	−	0.695592i
$605$	11.2828	+	6.51413i	0.458711	+	0.264837i
$606$	−4.49759	−	2.59669i	−0.182702	−	0.105483i
$607$	36.4938			1.48124			0.740618	−	0.671926i	$-0.234533\pi$
$607$	36.4938			1.48124			0.740618	+	0.671926i	$0.234533\pi$
$608$	−18.4735			−0.749201
$609$	−3.11963	−	1.80112i	−0.126414	−	0.0729850i
$610$	0.490615	+	0.849771i	0.0198644	+	0.0344062i
$611$	−11.2894	+	30.8351i	−0.456722	+	1.24746i
$612$	30.6792			1.24014
$613$		−	17.1255i		−	0.691694i	−0.938291	−	0.345847i	$-0.887592\pi$
$613$		−	17.1255i		−	0.691694i	0.938291	−	0.345847i	$-0.112408\pi$
$614$	−4.30468			−0.173723
$615$	−2.83259			−0.114221
$616$			8.20136i			0.330442i
$617$	−0.636961	+	0.367750i	−0.0256431	+	0.0148050i	−0.512767	−	0.858528i	$-0.671379\pi$
$617$	−0.636961	+	0.367750i	−0.0256431	+	0.0148050i	0.487124	+	0.873333i	$0.338046\pi$
$618$	3.90800	+	2.25629i	0.157203	+	0.0907612i
$619$		−	0.196601i		−	0.00790205i	−0.999992	−	0.00395103i	$-0.998742\pi$
$619$		−	0.196601i		−	0.00790205i	0.999992	−	0.00395103i	$-0.00125765\pi$
$620$	19.7856	+	19.4074i	0.794607	+	0.779419i
$621$	2.35106	+	4.07216i	0.0943449	+	0.163410i
$622$	31.6926	−	18.2977i	1.27076	−	0.733673i
$623$	20.9935	−	36.3618i	0.841086	−	1.45680i
$624$	−0.171247	−	0.982095i	−0.00685538	−	0.0393153i
$625$	6.62693	+	11.4782i	0.265077	+	0.459127i
$626$			14.9320i			0.596804i
$627$	−0.695997			−0.0277954
$628$	−0.138764	+	0.240347i	−0.00553731	+	0.00959090i
$629$	19.9655	−	11.5271i	0.796078	−	0.459616i
$630$			29.9222i			1.19213i
$631$			8.85644i			0.352569i	0.984339	+	0.176285i	$0.0564079\pi$
$631$			8.85644i			0.352569i	−0.984339	+	0.176285i	$0.943592\pi$
$632$	14.3557	+	8.28829i	0.571040	+	0.329690i
$633$	2.03153			0.0807462
$634$	50.7021			2.01364
$635$	16.0688	−	9.27731i	0.637670	−	0.368159i
$636$	−3.18772			−0.126401
$637$	−1.35907	+	1.13601i	−0.0538485	+	0.0450103i
$638$	−20.6871	−	35.8312i	−0.819011	−	1.41857i
$639$		−	18.7374i		−	0.741239i
$640$	11.0778	−	19.1873i	0.437887	−	0.758443i
$641$	−4.64282			−0.183380			−0.0916902	−	0.995788i	$-0.529227\pi$
$641$	−4.64282			−0.183380			−0.0916902	+	0.995788i	$0.529227\pi$
$642$	0.537569	−	0.310366i	0.0212162	−	0.0122492i
$643$	−26.7849	−	15.4643i	−1.05629	−	0.609852i	−0.131889	−	0.991264i	$-0.542104\pi$
$643$	−26.7849	−	15.4643i	−1.05629	−	0.609852i	−0.924405	+	0.381413i	$0.875438\pi$
$644$	33.1022	−	19.1115i	1.30441	−	0.753100i
$645$	1.60252	+	0.925214i	0.0630991	+	0.0364303i
$646$	20.1373			0.792293
$647$	−11.9370	−	20.6755i	−0.469293	−	0.812839i	0.530091	−	0.847941i	$-0.322158\pi$
$647$	−11.9370	−	20.6755i	−0.469293	−	0.812839i	−0.999384	+	0.0351016i	$0.988825\pi$
$648$			14.5663i			0.572219i
$649$	8.75765			0.343768
$650$	4.71067	−	12.8664i	0.184768	−	0.504661i
$651$	−0.513015	+	1.99126i	−0.0201067	+	0.0780436i
$652$	−46.4803	+	26.8354i	−1.82031	+	1.05096i
$653$	1.73299	+	3.00162i	0.0678171	+	0.117463i	0.897940	−	0.440118i	$-0.145063\pi$
$653$	1.73299	+	3.00162i	0.0678171	+	0.117463i	−0.830123	+	0.557580i	$0.811730\pi$
$654$	−1.09661	−	1.89938i	−0.0428807	−	0.0742715i
$655$		−	21.5440i		−	0.841795i
$656$		−	20.7061i		−	0.808438i
$657$	−0.867447	+	0.500821i	−0.0338423	+	0.0195389i
$658$	−43.8907	−	25.3403i	−1.71104	−	0.987868i
$659$	−9.62296	+	16.6675i	−0.374857	+	0.649272i	−0.990306	−	0.138905i	$-0.955642\pi$
$659$	−9.62296	+	16.6675i	−0.374857	+	0.649272i	0.615448	+	0.788177i	$0.288975\pi$
$660$	0.700666	−	1.21359i	0.0272734	−	0.0472389i
$661$	25.8318	+	14.9140i	1.00474	+	0.580087i	0.909647	−	0.415382i	$-0.136352\pi$
$661$	25.8318	+	14.9140i	1.00474	+	0.580087i	0.0950926	+	0.995468i	$0.469685\pi$
$662$	0.262916	+	0.455385i	0.0102185	+	0.0176990i
$663$	0.334804	+	1.92008i	0.0130027	+	0.0745699i
$664$	13.2188	+	22.8956i	0.512987	+	0.888520i
$665$			11.3844i			0.441468i
$666$	20.0587	+	34.7428i	0.777260	+	1.34625i
$667$	−26.4941	+	45.8892i	−1.02586	+	1.77684i
$668$	5.81511	+	3.35736i	0.224993	+	0.129900i
$669$		−	0.248633i		−	0.00961272i
$670$	−17.9252	+	10.3491i	−0.692510	+	0.399821i
$671$	−0.419748	+	0.242341i	−0.0162042	+	0.00935549i
$672$	2.75964			0.106456
$673$	20.5841	−	35.6526i	0.793457	−	1.37431i	−0.130357	−	0.991467i	$-0.541612\pi$
$673$	20.5841	−	35.6526i	0.793457	−	1.37431i	0.923814	−	0.382841i	$-0.125054\pi$
$674$	35.1217	−	20.2775i	1.35284	−	0.781061i
$675$	−0.753964	+	1.30590i	−0.0290201	+	0.0502642i
$676$	33.7361	−	12.1340i	1.29754	−	0.466693i
$677$	−12.0689	−	20.9040i	−0.463846	−	0.803404i	0.535303	−	0.844660i	$-0.320197\pi$
$677$	−12.0689	−	20.9040i	−0.463846	−	0.803404i	−0.999149	+	0.0412560i	$0.986864\pi$
$678$	1.54255	−	0.890594i	0.0592415	−	0.0342031i
$679$	9.28263			0.356235
$680$	−5.57076	+	9.64885i	−0.213629	+	0.370016i
$681$			3.34567i			0.128206i
$682$	−16.5384	+	16.8607i	−0.633289	+	0.645630i
$683$	25.8064	+	14.8994i	0.987456	+	0.570108i	0.904513	−	0.426446i	$-0.140235\pi$
$683$	25.8064	+	14.8994i	0.987456	+	0.570108i	0.0829429	+	0.996554i	$0.473568\pi$
$684$			20.3116i			0.776635i
$685$	−16.7646	−	29.0371i	−0.640541	−	1.10945i
$686$	−20.8439	−	36.1027i	−0.795823	−	1.37841i
$687$	0.236238	+	0.136392i	0.00901304	+	0.00520368i
$688$	−6.76328	+	11.7143i	−0.257848	+	0.446605i
$689$	4.94532	+	28.3612i	0.188402	+	1.08048i
$690$	−3.09621			−0.117871
$691$	−10.8978	−	6.29187i	−0.414573	−	0.239354i	0.278180	−	0.960529i	$-0.410269\pi$
$691$	−10.8978	−	6.29187i	−0.414573	−	0.239354i	−0.692753	+	0.721175i	$0.743602\pi$
$692$	−8.26154	+	14.3094i	−0.314057	+	0.543962i
$693$	−14.7802			−0.561452
$694$	−30.2154	−	17.4449i	−1.14696	−	0.662198i
$695$		−	22.4834i		−	0.852843i
$696$	2.02134	−	1.16702i	0.0766185	−	0.0442357i
$697$			40.4823i			1.53338i
$698$	−11.2939	+	19.5615i	−0.427479	+	0.740415i
$699$	−2.55151			−0.0965070
$700$	10.6155	+	6.12889i	0.401230	+	0.231650i
$701$	−19.6713	+	34.0717i	−0.742974	+	1.28687i	0.208162	+	0.978094i	$0.433252\pi$
$701$	−19.6713	+	34.0717i	−0.742974	+	1.28687i	−0.951135	+	0.308774i	$0.900081\pi$
$702$	−6.70592	+	1.16931i	−0.253099	+	0.0441326i
$703$	7.63168	+	13.2185i	0.287834	+	0.498544i
$704$	21.0165	+	12.1339i	0.792087	+	0.457312i
$705$	1.18981	+	2.06080i	0.0448107	+	0.0776144i
$706$	12.7640	+	22.1080i	0.480381	+	0.832045i
$707$	−36.3387	−	20.9801i	−1.36666	−	0.789040i
$708$			1.79786i			0.0675678i
$709$	−12.6445	−	7.30028i	−0.474872	−	0.274168i	0.243405	−	0.969925i	$-0.421736\pi$
$709$	−12.6445	−	7.30028i	−0.474872	−	0.274168i	−0.718277	+	0.695757i	$0.755069\pi$
$710$	21.4452	+	12.3814i	0.804824	+	0.464665i
$711$	−14.9368	+	25.8713i	−0.560175	+	0.970251i
$712$	13.6025	+	23.5603i	0.509777	+	0.882959i
$713$	29.2910	+	7.54636i	1.09696	+	0.282613i
$714$	−3.00819			−0.112579
$715$	−11.8843	−	4.35112i	−0.444448	−	0.162722i
$716$	−20.9377	+	36.2652i	−0.782478	+	1.35529i
$717$	2.14494	−	1.23838i	0.0801042	−	0.0462482i
$718$	−34.8492	+	60.3606i	−1.30056	+	2.25264i
$719$	−2.08162	−	3.60547i	−0.0776313	−	0.134461i	0.824596	−	0.565722i	$-0.191402\pi$
$719$	−2.08162	−	3.60547i	−0.0776313	−	0.134461i	−0.902227	+	0.431260i	$0.858069\pi$
$720$	8.89411	+	5.13502i	0.331464	+	0.191371i
$721$	31.5750	+	18.2299i	1.17592	+	0.678915i
$722$		−	28.1115i		−	1.04620i
$723$	−0.684721	+	0.395324i	−0.0254651	+	0.0147023i
$724$	28.8314			1.07151
$725$	−16.9928			−0.631097
$726$	−1.97384	−	1.13960i	−0.0732562	−	0.0422945i
$727$	−14.8458	+	25.7136i	−0.550599	+	0.953666i	0.447632	+	0.894218i	$0.352267\pi$
$727$	−14.8458	+	25.7136i	−0.550599	+	0.953666i	−0.998231	+	0.0594478i	$0.981066\pi$
$728$	2.61197	+	14.9796i	0.0968062	+	0.555179i
$729$	−25.8750			−0.958332
$730$		−	1.32374i		−	0.0489939i
$731$	13.2228	−	22.9026i	0.489063	−	0.847082i
$732$	−0.0497504	−	0.0861701i	−0.00183883	−	0.00318494i
$733$	43.2916	−	24.9944i	1.59901	−	0.923189i	0.607333	−	0.794448i	$-0.292240\pi$
$733$	43.2916	−	24.9944i	1.59901	−	0.923189i	0.991678	−	0.128742i	$-0.0410938\pi$
$734$		−	6.54912i		−	0.241732i
$735$			0.128364i			0.00473478i
$736$		−	40.5938i		−	1.49631i
$737$	−5.11199	−	8.85422i	−0.188302	−	0.326149i
$738$	−70.4447			−2.59311
$739$	−14.9823	−	8.65004i	−0.551133	−	0.318197i	0.198446	−	0.980112i	$-0.436411\pi$
$739$	−14.9823	−	8.65004i	−0.551133	−	0.318197i	−0.749579	+	0.661915i	$0.769744\pi$
$740$	−30.7315			−1.12971
$741$	−1.27122	+	0.221662i	−0.0466994	+	0.00814294i
$742$	−44.4334			−1.63120
$743$	8.34061	−	4.81546i	0.305987	−	0.176662i	−0.339142	−	0.940735i	$-0.610137\pi$
$743$	8.34061	−	4.81546i	0.305987	−	0.176662i	0.645130	+	0.764073i	$0.276803\pi$
$744$	−0.951159	−	0.932979i	−0.0348712	−	0.0342047i
$745$	−15.6288	+	27.0699i	−0.572595	+	0.991763i
$746$			41.5437i			1.52102i
$747$	−41.2615	+	23.8223i	−1.50968	+	0.871614i
$748$	−17.3441	−	10.0136i	−0.634165	−	0.366135i
$749$	4.34334	−	2.50763i	0.158702	−	0.0916266i
$750$	−1.92129	−	3.32777i	−0.0701556	−	0.121513i
$751$	27.2614			0.994782			0.497391	−	0.867527i	$-0.334291\pi$
$751$	27.2614			0.994782			0.497391	+	0.867527i	$0.334291\pi$
$752$	−15.0644	+	8.69744i	−0.549342	+	0.317163i
$753$	0.886908	+	1.53617i	0.0323207	+	0.0559812i
$754$	−49.1960	−	58.8562i	−1.79161	−	2.14342i
$755$	11.1884	+	19.3788i	0.407187	+	0.705268i
$756$		−	6.08980i		−	0.221484i
$757$	1.29014	−	2.23459i	0.0468910	−	0.0812177i	−0.841627	−	0.540059i	$-0.818402\pi$
$757$	1.29014	−	2.23459i	0.0468910	−	0.0812177i	0.888518	+	0.458841i	$0.151735\pi$
$758$	−17.0909	−	29.6024i	−0.620770	−	1.07521i
$759$		−	1.52939i		−	0.0555132i
$760$	−6.38816	−	3.68820i	−0.231723	−	0.133785i
$761$	0.447280	−	0.258237i	0.0162139	−	0.00936108i	−0.491871	−	0.870668i	$-0.663687\pi$
$761$	0.447280	−	0.258237i	0.0162139	−	0.00936108i	0.508085	+	0.861307i	$0.330354\pi$
$762$	−2.81111	+	1.62300i	−0.101836	+	0.0587950i
$763$	−8.86012	−	15.3462i	−0.320758	−	0.555569i
$764$	−15.2296	+	26.3784i	−0.550987	+	0.954338i
$765$	−17.3888	−	10.0394i	−0.628693	−	0.362976i
$766$	−35.2423	−	61.0415i	−1.27336	−	2.20552i
$767$	15.9956	−	2.78914i	0.577568	−	0.100710i
$768$	−0.131516	+	0.227792i	−0.00474567	+	0.00821975i
$769$		−	42.3666i		−	1.52778i	−0.645347	−	0.763890i	$-0.723287\pi$
$769$		−	42.3666i		−	1.52778i	0.645347	−	0.763890i	$-0.276713\pi$
$770$	9.76654	−	16.9161i	0.351962	−	0.609615i
$771$	−0.0264017	+	0.0457291i	−0.000950834	+	0.00164689i
$772$	33.9491	+	19.6005i	1.22185	+	0.705437i
$773$	11.4379	+	6.60365i	0.411391	+	0.237517i	0.691387	−	0.722484i	$-0.257000\pi$
$773$	11.4379	+	6.60365i	0.411391	+	0.237517i	−0.279996	+	0.960001i	$0.590333\pi$
$774$	39.8536	+	23.0095i	1.43251	+	0.827059i
$775$	2.60086	+	9.34490i	0.0934255	+	0.335679i
$776$	−3.00730	+	5.20879i	−0.107956	+	0.186985i
$777$	−1.14005	−	1.97462i	−0.0408990	−	0.0708392i
$778$			80.8500i			2.89861i
$779$	−26.8019			−0.960277
$780$	0.893242	−	2.43973i	0.0319832	−	0.0873565i
$781$	−6.11584	+	10.5929i	−0.218842	+	0.379045i
$782$			44.2499i			1.58237i
$783$	4.22111	+	7.31117i	0.150850	+	0.261280i
$784$	−0.938337			−0.0335121
$785$	0.157301	−	0.0908181i	0.00561433	−	0.00324144i
$786$			3.76897i			0.134435i
$787$	43.5543	−	25.1461i	1.55254	−	0.896361i	0.554608	−	0.832111i	$-0.312868\pi$
$787$	43.5543	−	25.1461i	1.55254	−	0.896361i	0.997934	−	0.0642492i	$-0.0204653\pi$
$788$	5.24644	−	3.02903i	0.186897	−	0.107905i
$789$	0.520718	+	0.901910i	0.0185381	+	0.0321089i
$790$	−19.7401	−	34.1909i	−0.702322	−	1.21646i
$791$	12.4632	−	7.19563i	0.443140	−	0.255847i
$792$	4.78834	−	8.29364i	0.170146	−	0.294702i
$793$	−0.689476	+	0.576312i	−0.0244840	+	0.0204654i
$794$	−18.0750	+	31.3068i	−0.641457	+	1.11104i
$795$	1.80678	+	1.04314i	0.0640797	+	0.0369965i
$796$	−5.46750	+	9.46999i	−0.193790	+	0.335655i
$797$	40.0509			1.41868			0.709338	−	0.704868i	$-0.248994\pi$
$797$	40.0509			1.41868			0.709338	+	0.704868i	$0.248994\pi$
$798$		−	1.99161i		−	0.0705024i
$799$	29.4522	−	17.0043i	1.04195	−	0.601567i
$800$	11.2740	−	6.50903i	0.398595	−	0.230129i
$801$	−42.4594	+	24.5140i	−1.50023	+	0.866159i
$802$	−11.1440	+	19.3020i	−0.393509	+	0.681577i
$803$	0.653868			0.0230745
$804$	1.81769	−	1.04944i	0.0641048	−	0.0370109i
$805$	−25.0161			−0.881702
$806$	−24.8372	+	36.0628i	−0.874852	+	1.27026i
$807$	−1.76298			−0.0620600
$808$	23.5453	−	13.5939i	0.828321	−	0.478231i
$809$	19.4878			0.685155			0.342578	−	0.939490i	$-0.388700\pi$
$809$	19.4878			0.685155			0.342578	+	0.939490i	$0.388700\pi$
$810$	17.3462	−	30.0445i	0.609483	−	1.05566i
$811$	2.19727	−	1.26860i	0.0771567	−	0.0445465i	−0.460925	−	0.887439i	$-0.652482\pi$
$811$	2.19727	−	1.26860i	0.0771567	−	0.0445465i	0.538082	+	0.842892i	$0.319149\pi$
$812$	59.4317	−	34.3129i	2.08565	−	1.20415i
$813$	−0.423081	+	0.244266i	−0.0148381	+	0.00856678i
$814$		−	26.1885i		−	0.917908i
$815$	35.1263			1.23042
$816$	−0.516243	+	0.894160i	−0.0180721	+	0.0313019i
$817$	15.1630	+	8.75435i	0.530485	+	0.306276i
$818$	39.1945	−	67.8868i	1.37040	−	2.37361i
$819$	−26.9956	+	4.70720i	−0.943302	+	0.164483i
$820$	26.9817	−	46.7336i	0.942241	−	1.63201i
$821$	−13.4111	+	7.74290i	−0.468050	+	0.270229i	−0.715423	−	0.698691i	$-0.753766\pi$
$821$	−13.4111	+	7.74290i	−0.468050	+	0.270229i	0.247373	+	0.968920i	$0.420433\pi$
$822$	2.93284	+	5.07982i	0.102294	+	0.177179i
$823$	−15.4150	−	26.6995i	−0.537332	−	0.930687i	−0.999047	−	0.0436579i	$-0.986099\pi$
$823$	−15.4150	−	26.6995i	−0.537332	−	0.930687i	0.461714	−	0.887029i	$-0.347235\pi$
$824$	−20.4588	+	11.8119i	−0.712715	+	0.411486i
$825$	0.424750	−	0.245230i	0.0147879	−	0.00853781i
$826$			25.0603i			0.871959i
$827$	6.77853	−	3.91359i	0.235713	−	0.136089i	−0.377492	−	0.926013i	$-0.623213\pi$
$827$	6.77853	−	3.91359i	0.235713	−	0.136089i	0.613205	+	0.789924i	$0.289880\pi$
$828$	−44.6329			−1.55110
$829$	−9.03289	−	15.6454i	−0.313725	−	0.543388i	0.665441	−	0.746451i	$-0.268244\pi$
$829$	−9.03289	−	15.6454i	−0.313725	−	0.543388i	−0.979166	+	0.203063i	$0.934910\pi$
$830$		−	62.9659i		−	2.18558i
$831$	−0.835481	+	1.44710i	−0.0289825	+	0.0501992i
$832$	42.2504	+	15.4688i	1.46477	+	0.536285i
$833$	1.83453			0.0635628
$834$			3.93330i			0.136199i
$835$	−2.19731	−	3.80585i	−0.0760411	−	0.131707i
$836$	6.62968	−	11.4829i	0.229292	−	0.397146i
$837$	3.37458	−	3.44034i	0.116643	−	0.118916i
$838$	26.9369	+	15.5520i	0.930521	+	0.537237i
$839$	−14.9884	−	8.65357i	−0.517458	−	0.298754i	0.218436	−	0.975851i	$-0.429904\pi$
$839$	−14.9884	−	8.65357i	−0.517458	−	0.298754i	−0.735894	+	0.677097i	$0.763238\pi$
$840$	0.954286	+	0.550957i	0.0329260	+	0.0190098i
$841$	−33.0676	+	57.2748i	−1.14026	+	1.97499i
$842$	17.0550	−	29.5401i	0.587754	−	1.01802i
$843$			0.338892i			0.0116720i
$844$	−19.3513	+	33.5174i	−0.666098	+	1.15372i
$845$	−23.0921	−	4.16227i	−0.794393	−	0.143186i
$846$	29.5897	+	51.2509i	1.01732	+	1.76204i
$847$	−15.9478	−	9.20749i	−0.547974	−	0.316373i
$848$	−7.62533	+	13.2075i	−0.261855	+	0.453546i
$849$	−0.636507	−	1.10246i	−0.0218449	−	0.0378364i
$850$	−12.2893	+	7.09526i	−0.421521	+	0.243365i
$851$	−29.0463	+	16.7699i	−0.995695	+	0.574865i
$852$	−2.17463	−	1.25552i	−0.0745016	−	0.0430135i
$853$		−	38.9670i		−	1.33421i	−0.744966	−	0.667103i	$-0.767534\pi$
$853$		−	38.9670i		−	1.33421i	0.744966	−	0.667103i	$-0.232466\pi$
$854$	−0.693467	−	1.20112i	−0.0237300	−	0.0411015i
$855$	6.64674	−	11.5125i	0.227314	−	0.393719i
$856$			3.24959i			0.111069i
$857$	−10.2459	−	17.7465i	−0.349994	−	0.606207i	0.636254	−	0.771480i	$-0.280483\pi$
$857$	−10.2459	−	17.7465i	−0.349994	−	0.606207i	−0.986248	+	0.165272i	$0.947150\pi$
$858$	2.07907	+	0.761196i	0.0709784	+	0.0259868i
$859$	15.6460	+	27.0997i	0.533836	+	0.924630i	0.999219	+	0.0395210i	$0.0125832\pi$
$859$	15.6460	+	27.0997i	0.533836	+	0.924630i	−0.465383	+	0.885109i	$0.654083\pi$
$860$	−30.5294	+	17.6261i	−1.04104	+	0.601047i
$861$	4.00376			0.136448
$862$	34.6647	+	60.0410i	1.18068	+	2.04500i
$863$	−35.9638	+	20.7637i	−1.22422	+	0.706804i	−0.965815	−	0.259232i	$-0.916530\pi$
$863$	−35.9638	+	20.7637i	−1.22422	+	0.706804i	−0.258406	+	0.966036i	$0.583197\pi$
$864$	−5.60103	−	3.23375i	−0.190551	−	0.110015i
$865$	9.36516	−	5.40698i	0.318425	−	0.183843i
$866$		−	74.5619i		−	2.53372i
$867$	−0.221174	+	0.383084i	−0.00751145	+	0.0130102i
$868$	−27.9662	−	27.4316i	−0.949234	−	0.931091i
$869$	16.8887	−	9.75071i	0.572911	−	0.330770i
$870$	−5.55895			−0.188466
$871$	−12.1568	−	14.5439i	−0.411917	−	0.492802i
$872$	11.4817			0.388818
$873$	−9.38708	−	5.41964i	−0.317705	−	0.183427i
$874$	−29.2963			−0.990961
$875$	−15.5232	−	26.8870i	−0.524781	−	0.908947i
$876$			0.134233i			0.00453531i
$877$			7.22204i			0.243871i	0.992538	+	0.121935i	$0.0389101\pi$
$877$			7.22204i			0.243871i	−0.992538	+	0.121935i	$0.961090\pi$
$878$			37.6471i			1.27053i
$879$	1.46696	−	0.846951i	0.0494794	−	0.0285669i
$880$	−3.35212	−	5.80605i	−0.113000	−	0.195722i
$881$	17.9172	−	31.0335i	0.603645	−	1.04554i	−0.388619	−	0.921399i	$-0.627048\pi$
$881$	17.9172	−	31.0335i	0.603645	−	1.04554i	0.992264	−	0.124145i	$-0.0396190\pi$
$882$			3.19234i			0.107492i
$883$	38.1246			1.28299			0.641497	−	0.767125i	$-0.278314\pi$
$883$	38.1246			1.28299			0.641497	+	0.767125i	$0.278314\pi$
$884$	−34.8678	−	12.7659i	−1.17273	−	0.429363i
$885$	0.588329	−	1.01902i	0.0197765	−	0.0342538i
$886$	45.5277	+	26.2854i	1.52953	+	0.883076i
$887$	−26.4556			−0.888294			−0.444147	−	0.895954i	$-0.646493\pi$
$887$	−26.4556			−0.888294			−0.444147	+	0.895954i	$0.646493\pi$
$888$	1.47737			0.0495772
$889$	−22.7126	+	13.1131i	−0.761758	+	0.439801i
$890$		−	64.7940i		−	2.17190i
$891$	14.8406	+	8.56823i	0.497179	+	0.287046i
$892$	4.10209	+	2.36834i	0.137348	+	0.0792980i
$893$	11.2579	+	19.4993i	0.376732	+	0.652518i
$894$	2.73414	−	4.73567i	0.0914434	−	0.158385i
$895$	23.7347	−	13.7032i	0.793363	−	0.458048i
$896$	−15.6580	+	27.1205i	−0.523098	+	0.906032i
$897$	−0.487080	−	2.79338i	−0.0162631	−	0.0932683i
$898$	67.9662			2.26806
$899$	52.5892	+	13.5488i	1.75395	+	0.451876i
$900$	−7.15667	−	12.3957i	−0.238556	−	0.413190i
$901$	14.9082	−	25.8218i	0.496664	−	0.860248i
$902$	39.8251	+	22.9930i	1.32603	+	0.765584i
$903$	−2.26510	−	1.30776i	−0.0753778	−	0.0435194i
$904$			9.32469i			0.310135i
$905$	−16.3414	−	9.43473i	−0.543207	−	0.313621i
$906$	−1.95732	−	3.39018i	−0.0650277	−	0.112631i
$907$	11.2053	+	19.4081i	0.372066	+	0.644437i	0.989883	−	0.141885i	$-0.0453163\pi$
$907$	11.2053	+	19.4081i	0.372066	+	0.644437i	−0.617818	+	0.786322i	$0.711983\pi$
$908$	−55.1988	−	31.8690i	−1.83183	−	1.05761i
$909$	24.4984	+	42.4325i	0.812560	+	1.40740i
$910$	12.4508	−	34.0073i	0.412741	−	1.12733i
$911$	17.3066	−	29.9759i	0.573393	−	0.993146i	−0.422821	−	0.906213i	$-0.638960\pi$
$911$	17.3066	−	29.9759i	0.573393	−	0.993146i	0.996214	−	0.0869326i	$-0.0277065\pi$
$912$	−0.591991	−	0.341786i	−0.0196028	−	0.0113177i
$913$	31.1023			1.02934
$914$	32.5090	−	56.3072i	1.07530	−	1.86248i
$915$			0.0651208i			0.00215283i
$916$	−4.50054	+	2.59839i	−0.148702	+	0.0858532i
$917$			30.4517i			1.00560i
$918$	6.10548	+	3.52500i	0.201511	+	0.116342i
$919$	−12.5428			−0.413747			−0.206874	−	0.978368i	$-0.566329\pi$
$919$	−12.5428			−0.413747			−0.206874	+	0.978368i	$0.566329\pi$
$920$	8.10448	−	14.0374i	0.267197	−	0.462798i
$921$	−0.247412	−	0.142843i	−0.00815249	−	0.00470684i
$922$	−20.7174			−0.682292
$923$	−7.79676	+	21.2955i	−0.256634	+	0.700950i
$924$	−0.990366	+	1.71536i	−0.0325806	+	0.0564313i
$925$	−9.31488	−	5.37795i	−0.306271	−	0.176826i
$926$	7.35621	+	12.7413i	0.241740	+	0.418706i
$927$	−21.2869	−	36.8700i	−0.699153	−	1.21097i
$928$		−	72.8823i		−	2.39248i
$929$	0.332401	+	0.191912i	0.0109057	+	0.00629643i	0.505443	−	0.862860i	$-0.331329\pi$
$929$	0.332401	+	0.191912i	0.0109057	+	0.00629643i	−0.494537	+	0.869156i	$0.664662\pi$
$930$	0.850831	+	3.05705i	0.0278999	+	0.100244i
$931$			1.21458i			0.0398062i
$932$	24.3043	−	42.0962i	0.796113	−	1.37891i
$933$	2.42872			0.0795126
$934$	−14.4930	+	8.36754i	−0.474226	+	0.273794i
$935$	6.55369	+	11.3513i	0.214329	+	0.371228i
$936$	6.10440	−	16.6731i	0.199529	−	0.544977i
$937$	27.3748	−	47.4146i	0.894297	−	1.54897i	0.0596245	−	0.998221i	$-0.481010\pi$
$937$	27.3748	−	47.4146i	0.894297	−	1.54897i	0.834672	−	0.550747i	$-0.185657\pi$
$938$	25.3366	−	14.6281i	0.827270	−	0.477624i
$939$	−0.495494	+	0.858220i	−0.0161698	+	0.0280070i
$940$	−45.3337			−1.47862
$941$	−13.7895	+	7.96137i	−0.449525	+	0.259533i	−0.707629	−	0.706584i	$-0.750235\pi$
$941$	−13.7895	+	7.96137i	−0.449525	+	0.259533i	0.258105	+	0.966117i	$0.416902\pi$
$942$	−0.0275187	+	0.0158880i	−0.000896609	+	0.000517657i
$943$		−	58.8946i		−	1.91787i
$944$	7.44896	+	4.30066i	0.242443	+	0.139975i
$945$	−1.99281	+	3.45165i	−0.0648262	+	0.112282i
$946$	−15.0205	−	26.0163i	−0.488359	−	0.845862i
$947$		−	20.4305i		−	0.663902i	−0.943297	−	0.331951i	$-0.892293\pi$
$947$		−	20.4305i		−	0.663902i	0.943297	−	0.331951i	$-0.107707\pi$
$948$	2.00173	+	3.46709i	0.0650130	+	0.112606i
$949$	1.19427	−	0.208244i	0.0387677	−	0.00675990i
$950$	−4.69752	−	8.13634i	−0.152408	−	0.263978i
$951$	2.91411	+	1.68246i	0.0944965	+	0.0545576i
$952$	7.87408	−	13.6383i	0.255200	−	0.442020i
$953$	0.274065	−	0.474694i	0.00887782	−	0.0153768i	−0.861552	−	0.507669i	$-0.830507\pi$
$953$	0.274065	−	0.474694i	0.00887782	−	0.0153768i	0.870430	+	0.492292i	$0.163841\pi$
$954$	44.9334	+	25.9423i	1.45477	+	0.839913i
$955$	17.2640	−	9.96740i	0.558651	−	0.322538i
$956$			47.1845i			1.52606i
$957$		−	2.74586i		−	0.0887612i
$958$	−16.1262	−	27.9315i	−0.521015	−	0.902425i
$959$	23.6961	+	41.0428i	0.765187	+	1.32534i
$960$	2.82372	−	1.63028i	0.0911352	−	0.0526169i
$961$	−0.598198	−	30.9942i	−0.0192967	−	0.999814i
$962$	−8.34055	−	47.8326i	−0.268910	−	1.54219i
$963$	−5.85628			−0.188716
$964$		−	15.0625i		−	0.485132i
$965$	−12.8281	−	22.2188i	−0.412950	−	0.715250i
$966$	4.37638			0.140808
$967$	−45.4147	−	26.2202i	−1.46044	−	0.843185i	−0.461407	−	0.887189i	$-0.652655\pi$
$967$	−45.4147	−	26.2202i	−1.46044	−	0.843185i	−0.999031	+	0.0440040i	$0.985989\pi$
$968$	10.3333	−	5.96591i	0.332123	−	0.191752i
$969$	1.15740	+	0.668222i	0.0371809	+	0.0214664i
$970$	12.4057	−	7.16244i	0.398324	−	0.229972i
$971$	13.1532			0.422107			0.211054	−	0.977474i	$-0.432311\pi$
$971$	13.1532			0.422107			0.211054	+	0.977474i	$0.432311\pi$
$972$	−5.33949	+	9.24828i	−0.171264	+	0.296639i
$973$			31.7795i			1.01880i
$974$	8.00663	+	13.8679i	0.256549	+	0.444356i
$975$	0.697694	−	0.583180i	0.0223441	−	0.0186767i
$976$	−0.476031			−0.0152374
$977$	−5.97299	+	3.44851i	−0.191093	+	0.110328i	−0.592494	−	0.805575i	$-0.701857\pi$
$977$	−5.97299	+	3.44851i	−0.191093	+	0.110328i	0.401401	+	0.915902i	$0.368523\pi$
$978$	−6.14509			−0.196498
$979$	32.0053			1.02289
$980$	−2.11782	−	1.22273i	−0.0676514	−	0.0390586i
$981$			20.6918i			0.660639i
$982$			90.5136i			2.88840i
$983$	38.6445	−	22.3114i	1.23257	−	0.711624i	0.265004	−	0.964247i	$-0.414627\pi$
$983$	38.6445	−	22.3114i	1.23257	−	0.711624i	0.967565	+	0.252624i	$0.0812935\pi$
$984$	−1.29710	+	2.24664i	−0.0413501	+	0.0716204i
$985$	−3.96486			−0.126331
$986$			79.4464i			2.53009i
$987$	−1.68175	−	2.91287i	−0.0535306	−	0.0927178i
$988$	8.45183	−	23.0847i	0.268889	−	0.734422i
$989$	−19.2368	+	33.3192i	−0.611696	+	1.05949i
$990$	−19.7529	+	11.4043i	−0.627787	+	0.362453i
$991$	−17.9204	−	31.0391i	−0.569261	−	0.985990i	−0.996639	−	0.0819165i	$-0.973896\pi$
$991$	−17.9204	−	31.0391i	−0.569261	−	0.985990i	0.427378	−	0.904073i	$-0.359437\pi$
$992$	−40.0803	+	11.1551i	−1.27255	+	0.354174i
$993$			0.0348977i			0.00110744i
$994$	−30.3120	−	17.5007i	−0.961439	−	0.555087i
$995$	6.19788	−	3.57835i	0.196486	−	0.113441i
$996$			6.38500i			0.202316i
$997$	16.5921			0.525478			0.262739	−	0.964867i	$-0.415374\pi$
$997$	16.5921			0.525478			0.262739	+	0.964867i	$0.415374\pi$
$998$	6.48802			0.205375
$999$			5.34364i			0.169065i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	403.2.v.a.36.6	yes	70
13.4	even	6		403.2.s.a.160.6	✓	70
31.25	even	3		403.2.s.a.335.6	yes	70
403.56	even	6	inner	403.2.v.a.56.6	yes	70

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
403.2.s.a.160.6	✓	70	13.4	even	6
403.2.s.a.335.6	yes	70	31.25	even	3
403.2.v.a.36.6	yes	70	1.1	even	1	trivial
403.2.v.a.56.6	yes	70	403.56	even	6	inner

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.v (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.88902 + 1.09062i) q^{2} -0.144762 q^{3} +(1.37892 - 2.38836i) q^{4} +(-1.56313 + 0.902471i) q^{5} +(0.273457 - 0.157881i) q^{6} +(2.20942 - 1.27561i) q^{7} +1.65304i q^{8} -2.97904 q^{9} +O(q^{10})\)	\(q+(-1.88902 + 1.09062i) q^{2} -0.144762 q^{3} +(1.37892 - 2.38836i) q^{4} +(-1.56313 + 0.902471i) q^{5} +(0.273457 - 0.157881i) q^{6} +(2.20942 - 1.27561i) q^{7} +1.65304i q^{8} -2.97904 q^{9} +(1.96851 - 3.40956i) q^{10} +(1.68417 + 0.972354i) q^{11} +(-0.199615 + 0.345743i) q^{12} +(3.38576 + 1.23960i) q^{13} +(-2.78242 + 4.81929i) q^{14} +(0.226281 - 0.130643i) q^{15} +(0.954997 + 1.65410i) q^{16} +(-1.86710 - 3.23392i) q^{17} +(5.62746 - 3.24902i) q^{18} +(2.14106 - 1.23614i) q^{19} +4.97774i q^{20} +(-0.319840 + 0.184660i) q^{21} -4.24189 q^{22} +(2.71631 + 4.70478i) q^{23} -0.239297i q^{24} +(-0.871093 + 1.50878i) q^{25} +(-7.74770 + 1.35096i) q^{26} +0.865537 q^{27} -7.03586i q^{28} +(4.87686 + 8.44698i) q^{29} +(-0.284965 + 0.493574i) q^{30} +(3.89883 - 3.97481i) q^{31} +(-6.47116 - 3.73612i) q^{32} +(-0.243803 - 0.140760i) q^{33} +(7.05398 + 4.07262i) q^{34} +(-2.30240 + 3.98788i) q^{35} +(-4.10787 + 7.11503i) q^{36} +6.17379i q^{37} +(-2.69633 + 4.67019i) q^{38} +(-0.490129 - 0.179447i) q^{39} +(-1.49182 - 2.58391i) q^{40} +(-9.38852 - 5.42047i) q^{41} +(0.402788 - 0.697650i) q^{42} +(3.54099 + 6.13318i) q^{43} +(4.64467 - 2.68160i) q^{44} +(4.65662 - 2.68850i) q^{45} +(-10.2623 - 5.92494i) q^{46} +9.10729i q^{47} +(-0.138247 - 0.239451i) q^{48} +(-0.245639 + 0.425459i) q^{49} -3.80014i q^{50} +(0.270285 + 0.468148i) q^{51} +(7.62932 - 6.37710i) q^{52} +(3.99233 + 6.91492i) q^{53} +(-1.63501 + 0.943975i) q^{54} -3.51009 q^{55} +(2.10863 + 3.65226i) q^{56} +(-0.309944 + 0.178946i) q^{57} +(-18.4249 - 10.6376i) q^{58} +(3.89999 - 2.25166i) q^{59} -0.720587i q^{60} +(-0.124616 + 0.215841i) q^{61} +(-3.02994 + 11.7606i) q^{62} +(-6.58196 + 3.80010i) q^{63} +12.4788 q^{64} +(-6.41107 + 1.11789i) q^{65} +0.614064 q^{66} +(-4.55298 - 2.62866i) q^{67} -10.2984 q^{68} +(-0.393217 - 0.681072i) q^{69} -10.0442i q^{70} +6.28972i q^{71} -4.92448i q^{72} +(0.291183 - 0.168115i) q^{73} +(-6.73328 - 11.6624i) q^{74} +(0.126101 - 0.218413i) q^{75} -6.81817i q^{76} +4.96138 q^{77} +(1.12157 - 0.195568i) q^{78} +(5.01397 - 8.68445i) q^{79} +(-2.98556 - 1.72371i) q^{80} +8.81184 q^{81} +23.6468 q^{82} +(13.8506 - 7.99664i) q^{83} +1.01852i q^{84} +(5.83703 + 3.37001i) q^{85} +(-13.3780 - 7.72378i) q^{86} +(-0.705983 - 1.22280i) q^{87} +(-1.60734 + 2.78399i) q^{88} +(14.2527 - 8.22881i) q^{89} +(-5.86428 + 10.1572i) q^{90} +(9.06182 - 1.58010i) q^{91} +14.9823 q^{92} +(-0.564402 + 0.575400i) q^{93} +(-9.93263 - 17.2038i) q^{94} +(-2.23117 + 3.86449i) q^{95} +(0.936776 + 0.540848i) q^{96} +(3.15104 + 1.81925i) q^{97} -1.07160i q^{98} +(-5.01721 - 2.89669i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 70 q - 6 q^{2} + 4 q^{3} + 30 q^{4} + 6 q^{6} - 12 q^{7} + 58 q^{9}+O(q^{10}) \) 70 * q - 6 * q^2 + 4 * q^3 + 30 * q^4 + 6 * q^6 - 12 * q^7 + 58 * q^9	\( 70 q - 6 q^{2} + 4 q^{3} + 30 q^{4} + 6 q^{6} - 12 q^{7} + 58 q^{9} - q^{10} - 6 q^{11} + 13 q^{12} - 14 q^{13} - 14 q^{14} - 15 q^{15} - 28 q^{16} + 6 q^{17} + 12 q^{19} + 9 q^{21} - 8 q^{22} + 10 q^{23} + 19 q^{25} + 34 q^{27} - 18 q^{29} - 31 q^{30} + 2 q^{31} + 36 q^{32} - 12 q^{33} - 9 q^{34} - 12 q^{35} + 8 q^{36} - 21 q^{38} - 30 q^{39} + 5 q^{40} + 18 q^{41} - 49 q^{42} + 19 q^{43} - 42 q^{44} - 63 q^{45} - 6 q^{46} - 27 q^{48} + 9 q^{49} - 7 q^{51} - 43 q^{52} - 22 q^{53} + 18 q^{54} + 30 q^{55} + 25 q^{56} - 15 q^{57} - 12 q^{58} + 33 q^{59} - 13 q^{61} - 17 q^{62} - 6 q^{63} - 38 q^{64} + 9 q^{65} - 52 q^{66} + 30 q^{67} + 88 q^{68} - 16 q^{69} + 9 q^{73} - 19 q^{74} + 25 q^{75} + 34 q^{77} + 14 q^{78} + 6 q^{79} + 6 q^{80} + 22 q^{81} - 78 q^{82} + 54 q^{83} - 33 q^{85} + 24 q^{86} - 14 q^{87} + 16 q^{88} - 6 q^{89} - 11 q^{90} - 70 q^{91} - 6 q^{92} + 7 q^{93} - 43 q^{94} + 25 q^{95} - 36 q^{96} - 75 q^{97} - 93 q^{99}+O(q^{100}) \) 70 * q - 6 * q^2 + 4 * q^3 + 30 * q^4 + 6 * q^6 - 12 * q^7 + 58 * q^9 - q^10 - 6 * q^11 + 13 * q^12 - 14 * q^13 - 14 * q^14 - 15 * q^15 - 28 * q^16 + 6 * q^17 + 12 * q^19 + 9 * q^21 - 8 * q^22 + 10 * q^23 + 19 * q^25 + 34 * q^27 - 18 * q^29 - 31 * q^30 + 2 * q^31 + 36 * q^32 - 12 * q^33 - 9 * q^34 - 12 * q^35 + 8 * q^36 - 21 * q^38 - 30 * q^39 + 5 * q^40 + 18 * q^41 - 49 * q^42 + 19 * q^43 - 42 * q^44 - 63 * q^45 - 6 * q^46 - 27 * q^48 + 9 * q^49 - 7 * q^51 - 43 * q^52 - 22 * q^53 + 18 * q^54 + 30 * q^55 + 25 * q^56 - 15 * q^57 - 12 * q^58 + 33 * q^59 - 13 * q^61 - 17 * q^62 - 6 * q^63 - 38 * q^64 + 9 * q^65 - 52 * q^66 + 30 * q^67 + 88 * q^68 - 16 * q^69 + 9 * q^73 - 19 * q^74 + 25 * q^75 + 34 * q^77 + 14 * q^78 + 6 * q^79 + 6 * q^80 + 22 * q^81 - 78 * q^82 + 54 * q^83 - 33 * q^85 + 24 * q^86 - 14 * q^87 + 16 * q^88 - 6 * q^89 - 11 * q^90 - 70 * q^91 - 6 * q^92 + 7 * q^93 - 43 * q^94 + 25 * q^95 - 36 * q^96 - 75 * q^97 - 93 * q^99

Introduction

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