LMFDB - Embedded newform 273.2.bf.b.185.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [273,2,Mod(152,273)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(273, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 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("273.152");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 273 = 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	273.bf (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:	$2.17991597518$
Analytic rank:	$0$
Dimension:	$64$
Relative dimension:	$32$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			185.11
Character	$\chi$	$=$	273.185
Dual form			273.2.bf.b.152.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.913280 - 0.527282i) q^{2} +(-1.53174 + 0.808559i) q^{3} +(-0.443947 - 0.768938i) q^{4} +(-0.000964697 - 0.00167090i) q^{5} +(1.82525 + 0.0692194i) q^{6} +(1.27194 + 2.31995i) q^{7} +3.04547i q^{8} +(1.69246 - 2.47701i) q^{9} +0.00203467i q^{10} -2.49689i q^{11} +(1.30174 + 0.818857i) q^{12} +(-0.922193 - 3.48562i) q^{13} +(0.0616352 - 2.78943i) q^{14} +(0.00282869 + 0.00177938i) q^{15} +(0.717929 - 1.24349i) q^{16} +(-2.08762 - 3.61586i) q^{17} +(-2.85178 + 1.36979i) q^{18} -5.36837i q^{19} +(-0.000856548 + 0.00148358i) q^{20} +(-3.82410 - 2.52513i) q^{21} +(-1.31657 + 2.28036i) q^{22} +(4.21813 + 2.43534i) q^{23} +(-2.46244 - 4.66487i) q^{24} +(2.50000 - 4.33012i) q^{25} +(-0.995686 + 3.66960i) q^{26} +(-0.589610 + 5.16259i) q^{27} +(1.21923 - 2.00798i) q^{28} +(7.57023 - 4.37067i) q^{29} +(-0.00164515 - 0.00311659i) q^{30} +(-6.57778 - 3.79768i) q^{31} +(3.96357 - 2.28837i) q^{32} +(2.01888 + 3.82459i) q^{33} +4.40306i q^{34} +(0.00264938 - 0.00436333i) q^{35} +(-2.65603 - 0.201741i) q^{36} +(-1.82786 + 3.16594i) q^{37} +(-2.83065 + 4.90282i) q^{38} +(4.23089 + 4.59342i) q^{39} +(0.00508869 - 0.00293796i) q^{40} +(1.83038 + 3.17031i) q^{41} +(2.16101 + 4.32253i) q^{42} +(1.32938 - 2.30256i) q^{43} +(-1.91995 + 1.10849i) q^{44} +(-0.00577156 - 0.000438383i) q^{45} +(-2.56822 - 4.44829i) q^{46} +(1.79190 + 3.10366i) q^{47} +(-0.0942468 + 2.48519i) q^{48} +(-3.76435 + 5.90167i) q^{49} +(-4.56640 + 2.63641i) q^{50} +(6.12133 + 3.85060i) q^{51} +(-2.27082 + 2.25654i) q^{52} +(-12.3735 - 7.14382i) q^{53} +(3.26062 - 4.40400i) q^{54} +(-0.00417206 + 0.00240874i) q^{55} +(-7.06534 + 3.87365i) q^{56} +(4.34064 + 8.22295i) q^{57} -9.21832 q^{58} +(2.61565 + 4.53044i) q^{59} +(0.000112444 - 0.00296504i) q^{60} -7.57921i q^{61} +(4.00490 + 6.93670i) q^{62} +(7.89925 + 0.775837i) q^{63} -7.69818 q^{64} +(-0.00493450 + 0.00490346i) q^{65} +(0.172833 - 4.55744i) q^{66} +14.2543 q^{67} +(-1.85358 + 3.21050i) q^{68} +(-8.43019 - 0.319701i) q^{69} +(-0.00472034 + 0.00258797i) q^{70} +(-1.24050 - 0.716205i) q^{71} +(7.54365 + 5.15435i) q^{72} +(1.61067 + 0.929921i) q^{73} +(3.33869 - 1.92759i) q^{74} +(-0.328189 + 8.65403i) q^{75} +(-4.12794 + 2.38327i) q^{76} +(5.79266 - 3.17589i) q^{77} +(-1.44196 - 6.42596i) q^{78} +(3.64483 + 6.31302i) q^{79} -0.00277034 q^{80} +(-3.27113 - 8.38449i) q^{81} -3.86050i q^{82} +10.4089 q^{83} +(-0.243974 + 4.06152i) q^{84} +(-0.00402784 + 0.00697642i) q^{85} +(-2.42820 + 1.40192i) q^{86} +(-8.06169 + 12.8157i) q^{87} +7.60420 q^{88} +(2.70190 - 4.67983i) q^{89} +(0.00503989 + 0.00344361i) q^{90} +(6.91350 - 6.57294i) q^{91} -4.32464i q^{92} +(13.1461 + 0.498544i) q^{93} -3.77934i q^{94} +(-0.00897003 + 0.00517885i) q^{95} +(-4.22088 + 6.70997i) q^{96} +(-2.07015 - 1.19520i) q^{97} +(6.54975 - 3.40500i) q^{98} +(-6.18481 - 4.22589i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 64 q + 32 q^{4} - 12 q^{6} - 4 q^{7} + 8 q^{9} + 6 q^{12} - 12 q^{13} - 9 q^{15} - 16 q^{16} + 2 q^{18} + 10 q^{21} + 10 q^{22} - 24 q^{25} - 50 q^{28} - 16 q^{30} - 24 q^{31} - 33 q^{39} + 90 q^{40} - 48 q^{42}+ \cdots + 22 q^{99}+O(q^{100}) $ 64 * q + 32 * q^4 - 12 * q^6 - 4 * q^7 + 8 * q^9 + 6 * q^12 - 12 * q^13 - 9 * q^15 - 16 * q^16 + 2 * q^18 + 10 * q^21 + 10 * q^22 - 24 * q^25 - 50 * q^28 - 16 * q^30 - 24 * q^31 - 33 * q^39 + 90 * q^40 - 48 * q^42 - 20 * q^43 - 3 * q^45 + 6 * q^48 - 10 * q^51 + 30 * q^52 - 27 * q^54 + 18 * q^55 + 4 * q^57 - 60 * q^58 + 55 * q^60 - 74 * q^63 - 84 * q^64 + 75 * q^66 - 88 * q^67 - 33 * q^69 + 20 * q^70 - 34 * q^72 + 84 * q^73 + 33 * q^75 + 18 * q^76 - 71 * q^78 + 20 * q^79 - 32 * q^81 - 6 * q^84 - 2 * q^85 + 3 * q^87 + 92 * q^88 - 76 * q^91 + 28 * q^93 + 30 * q^96 + 24 * q^97 + 22 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/273\mathbb{Z}\right)^\times$.

$n$	$92$	$106$	$157$
$\chi(n)$	$-1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{6}\right)$

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 $

$2$	−0.913280	−	0.527282i	−0.645786	−	0.372845i	0.141054	−	0.990002i	$-0.454951\pi$
$2$	−0.913280	−	0.527282i	−0.645786	−	0.372845i	−0.786840	+	0.617157i	$0.788284\pi$
$3$	−1.53174	+	0.808559i	−0.884351	+	0.466822i
$3$	−1.53174	+	0.808559i	−0.884351	+	0.466822i
$4$	−0.443947	−	0.768938i	−0.221973	−	0.384469i
$5$	−0.000964697	−	0.00167090i	−0.000431425	−	0.000747251i	0.865810	−	0.500374i	$-0.166804\pi$
$5$	−0.000964697	−	0.00167090i	−0.000431425	−	0.000747251i	−0.866241	+	0.499626i	$0.833471\pi$
$6$	1.82525	+	0.0692194i	0.745154	+	0.0282587i
$7$	1.27194	+	2.31995i	0.480747	+	0.876859i
$7$	1.27194	+	2.31995i	0.480747	+	0.876859i
$8$			3.04547i			1.07674i
$9$	1.69246	−	2.47701i	0.564155	−	0.825669i
$10$			0.00203467i			0.000643419i
$11$		−	2.49689i		−	0.752840i	−0.926449	−	0.376420i	$-0.877155\pi$
$11$		−	2.49689i		−	0.752840i	0.926449	−	0.376420i	$-0.122845\pi$
$12$	1.30174	+	0.818857i	0.375781	+	0.236384i
$13$	−0.922193	−	3.48562i	−0.255770	−	0.966738i
$13$	−0.922193	−	3.48562i	−0.255770	−	0.966738i
$14$	0.0616352	−	2.78943i	0.0164727	−	0.745508i
$15$	0.00282869	+	0.00177938i	0.000730365	+	0.000459433i
$16$	0.717929	−	1.24349i	0.179482	−	0.310873i
$17$	−2.08762	−	3.61586i	−0.506322	−	0.876975i	−0.999973	−	0.00731523i	$-0.997671\pi$
$17$	−2.08762	−	3.61586i	−0.506322	−	0.876975i	0.493651	−	0.869660i	$-0.335662\pi$
$18$	−2.85178	+	1.36979i	−0.672170	+	0.322864i
$19$		−	5.36837i		−	1.23159i	−0.787907	−	0.615794i	$-0.788835\pi$
$19$		−	5.36837i		−	1.23159i	0.787907	−	0.615794i	$-0.211165\pi$
$20$	−0.000856548		0.00148358i	−0.000191530		0.000331740i
$21$	−3.82410	−	2.52513i	−0.834486	−	0.551029i
$22$	−1.31657	+	2.28036i	−0.280693	+	0.486174i
$23$	4.21813	+	2.43534i	0.879540	+	0.507803i	0.870507	−	0.492156i	$-0.163791\pi$
$23$	4.21813	+	2.43534i	0.879540	+	0.507803i	0.00903348	+	0.999959i	$0.497125\pi$
$24$	−2.46244	−	4.66487i	−0.502644	−	0.952213i
$25$	2.50000	−	4.33012i	0.500000	−	0.866025i
$26$	−0.995686	+	3.66960i	−0.195270	+	0.719669i
$27$	−0.589610	+	5.16259i	−0.113470	+	0.993541i
$28$	1.21923	−	2.00798i	0.230412	−	0.379472i
$29$	7.57023	−	4.37067i	1.40576	−	0.811614i	0.410781	−	0.911734i	$-0.365256\pi$
$29$	7.57023	−	4.37067i	1.40576	−	0.811614i	0.994975	+	0.100120i	$0.0319227\pi$
$30$	−0.00164515	−	0.00311659i	−0.000300362	−	0.000569009i
$31$	−6.57778	−	3.79768i	−1.18140	−	0.682084i	−0.225065	−	0.974344i	$-0.572260\pi$
$31$	−6.57778	−	3.79768i	−1.18140	−	0.682084i	−0.956339	+	0.292260i	$0.905593\pi$
$32$	3.96357	−	2.28837i	0.700667	−	0.404530i
$33$	2.01888	+	3.82459i	0.351442	+	0.665775i
$34$			4.40306i			0.755118i
$35$	0.00264938	−	0.00436333i	0.000447827	−	0.000737538i
$36$	−2.65603	−	0.201741i	−0.442672	−	0.0336235i
$37$	−1.82786	+	3.16594i	−0.300498	+	0.520478i	−0.976249	−	0.216652i	$-0.930486\pi$
$37$	−1.82786	+	3.16594i	−0.300498	+	0.520478i	0.675751	+	0.737130i	$0.263820\pi$
$38$	−2.83065	+	4.90282i	−0.459191	+	0.795343i
$39$	4.23089	+	4.59342i	0.677485	+	0.735536i
$40$	0.00508869	−	0.00293796i	0.000804592	−	0.000464531i
$41$	1.83038	+	3.17031i	0.285857	+	0.495119i	0.972817	−	0.231577i	$-0.0743884\pi$
$41$	1.83038	+	3.17031i	0.285857	+	0.495119i	−0.686960	+	0.726696i	$0.741055\pi$
$42$	2.16101	+	4.32253i	0.333452	+	0.666981i
$43$	1.32938	−	2.30256i	0.202729	−	0.351137i	−0.746678	−	0.665186i	$-0.768352\pi$
$43$	1.32938	−	2.30256i	0.202729	−	0.351137i	0.949407	+	0.314049i	$0.101686\pi$
$44$	−1.91995	+	1.10849i	−0.289444	+	0.167110i
$45$	−0.00577156		0.000438383i	−0.000860373		6.53503e-5i
$46$	−2.56822	−	4.44829i	−0.378663	−	0.655864i
$47$	1.79190	+	3.10366i	0.261375	+	0.452715i	0.966608	−	0.256261i	$-0.0824907\pi$
$47$	1.79190	+	3.10366i	0.261375	+	0.452715i	−0.705232	+	0.708976i	$0.749157\pi$
$48$	−0.0942468	+	2.48519i	−0.0136033	+	0.358707i
$49$	−3.76435	+	5.90167i	−0.537765	+	0.843095i
$50$	−4.56640	+	2.63641i	−0.645786	+	0.372845i
$51$	6.12133	+	3.85060i	0.857158	+	0.539192i
$52$	−2.27082	+	2.25654i	−0.314907	+	0.312926i
$53$	−12.3735	−	7.14382i	−1.69962	−	0.981279i	−0.946108	−	0.323850i	$-0.895023\pi$
$53$	−12.3735	−	7.14382i	−1.69962	−	0.981279i	−0.753516	−	0.657429i	$-0.771644\pi$
$54$	3.26062	−	4.40400i	0.443715	−	0.599309i
$55$	−0.00417206	+	0.00240874i	−0.000562561	+	0.000324795i
$56$	−7.06534	+	3.87365i	−0.944146	+	0.517638i
$57$	4.34064	+	8.22295i	0.574932	+	1.08916i
$58$	−9.21832			−1.21042
$59$	2.61565	+	4.53044i	0.340529	+	0.589813i	0.984531	−	0.175211i	$-0.0560607\pi$
$59$	2.61565	+	4.53044i	0.340529	+	0.589813i	−0.644002	+	0.765023i	$0.722727\pi$
$60$	0.000112444	−	0.00296504i	1.45165e−5	−	0.000382785i
$61$		−	7.57921i		−	0.970418i	−0.874398	−	0.485209i	$-0.838744\pi$
$61$		−	7.57921i		−	0.970418i	0.874398	−	0.485209i	$-0.161256\pi$
$62$	4.00490	+	6.93670i	0.508623	+	0.880961i
$63$	7.89925	+	0.775837i	0.995211	+	0.0977463i
$64$	−7.69818			−0.962273
$65$	−0.00493450	+	0.00490346i	−0.000612050	+	0.000608200i
$66$	0.172833	−	4.55744i	0.0212743	−	0.560982i
$67$	14.2543			1.74143			0.870717	−	0.491784i	$-0.163655\pi$
$67$	14.2543			1.74143			0.870717	+	0.491784i	$0.163655\pi$
$68$	−1.85358	+	3.21050i	−0.224780	+	0.389330i
$69$	−8.43019	−	0.319701i	−1.01488	−	0.0384875i
$70$	−0.00472034	+	0.00258797i	−0.000564188	+	0.000309322i
$71$	−1.24050	−	0.716205i	−0.147221	−	0.0849979i	0.424580	−	0.905390i	$-0.360422\pi$
$71$	−1.24050	−	0.716205i	−0.147221	−	0.0849979i	−0.571801	+	0.820392i	$0.693755\pi$
$72$	7.54365	+	5.15435i	0.889028	+	0.607446i
$73$	1.61067	+	0.929921i	0.188515	+	0.108839i	0.591287	−	0.806461i	$-0.298620\pi$
$73$	1.61067	+	0.929921i	0.188515	+	0.108839i	−0.402772	+	0.915300i	$0.631953\pi$
$74$	3.33869	−	1.92759i	0.388115	−	0.224078i
$75$	−0.328189	+	8.65403i	−0.0378960	+	0.999281i
$76$	−4.12794	+	2.38327i	−0.473508	+	0.273380i
$77$	5.79266	−	3.17589i	0.660135	−	0.361926i
$78$	−1.44196	−	6.42596i	−0.163270	−	0.727596i
$79$	3.64483	+	6.31302i	0.410075	+	0.710271i	0.994898	−	0.100891i	$-0.0321692\pi$
$79$	3.64483	+	6.31302i	0.410075	+	0.710271i	−0.584823	+	0.811161i	$0.698836\pi$
$80$	−0.00277034			−0.000309733
$81$	−3.27113	−	8.38449i	−0.363459	−	0.931610i
$82$		−	3.86050i		−	0.426321i
$83$	10.4089			1.14253			0.571263	−	0.820767i	$-0.306454\pi$
$83$	10.4089			1.14253			0.571263	+	0.820767i	$0.306454\pi$
$84$	−0.243974	+	4.06152i	−0.0266197	+	0.443148i
$85$	−0.00402784	+	0.00697642i	−0.000436880	+	0.000756699i
$86$	−2.42820	+	1.40192i	−0.261839	+	0.151173i
$87$	−8.06169	+	12.8157i	−0.864303	+	1.37399i
$88$	7.60420			0.810611
$89$	2.70190	−	4.67983i	0.286401	−	0.496061i	−0.686547	−	0.727085i	$-0.740874\pi$
$89$	2.70190	−	4.67983i	0.286401	−	0.496061i	0.972948	+	0.231025i	$0.0742078\pi$
$90$	0.00503989	+	0.00344361i	0.000531251	+	0.000362988i
$91$	6.91350	−	6.57294i	0.724732	−	0.689031i
$92$		−	4.32464i		−	0.450875i
$93$	13.1461	+	0.498544i	1.36319	+	0.0516966i
$94$		−	3.77934i		−	0.389809i
$95$	−0.00897003	+	0.00517885i	−0.000920305	+	0.000531339i
$96$	−4.22088	+	6.70997i	−0.430792	+	0.684833i
$97$	−2.07015	−	1.19520i	−0.210192	−	0.121354i	0.391209	−	0.920302i	$-0.372057\pi$
$97$	−2.07015	−	1.19520i	−0.210192	−	0.121354i	−0.601401	+	0.798948i	$0.705390\pi$
$98$	6.54975	−	3.40500i	0.661625	−	0.343956i
$99$	−6.18481	−	4.22589i	−0.621597	−	0.424718i
$100$	−4.43946			−0.443946
$101$	−18.0599			−1.79703			−0.898514	−	0.438946i	$-0.855352\pi$
$101$	−18.0599			−1.79703			−0.898514	+	0.438946i	$0.855352\pi$
$102$	−3.56013	−	6.74434i	−0.352506	−	0.667790i
$103$	−8.45144	+	4.87944i	−0.832745	+	0.480786i	−0.854792	−	0.518971i	$-0.826315\pi$
$103$	−8.45144	+	4.87944i	−0.832745	+	0.480786i	0.0220466	+	0.999757i	$0.492982\pi$
$104$	10.6154	−	2.80851i	1.04092	−	0.275397i
$105$	−0.000530155		0.00882568i	−5.17378e−5		0.000861298i
$106$	7.53362	+	13.0486i	0.731730	+	1.26739i
$107$	−4.73086	−	2.73136i	−0.457349	−	0.264051i	0.253580	−	0.967314i	$-0.418392\pi$
$107$	−4.73086	−	2.73136i	−0.457349	−	0.264051i	−0.710929	+	0.703264i	$0.751725\pi$
$108$	4.23147	−	1.83854i	0.407173	−	0.176914i
$109$	−3.68535	+	6.38321i	−0.352993	+	0.611401i	−0.986772	−	0.162113i	$-0.948169\pi$
$109$	−3.68535	+	6.38321i	−0.352993	+	0.611401i	0.633780	+	0.773514i	$0.281503\pi$
$110$	0.00508035			0.000484392
$111$	0.239954	−	6.32734i	0.0227754	−	0.600564i
$112$	3.79800	+	0.0839203i	0.358877	+	0.00792972i
$113$	−0.390686	−	0.225562i	−0.0367526	−	0.0212191i	0.481511	−	0.876440i	$-0.340088\pi$
$113$	−0.390686	−	0.225562i	−0.0367526	−	0.0212191i	−0.518264	+	0.855221i	$0.673421\pi$
$114$	0.371595	−	9.79860i	0.0348031	−	0.917723i
$115$		−	0.00939745i		−	0.000876316i
$116$	−6.72156	−	3.88069i	−0.624081	−	0.360313i
$117$	−10.1947	−	3.61501i	−0.942499	−	0.334208i
$118$		−	5.51674i		−	0.507857i
$119$	5.73330	−	9.44232i	0.525571	−	0.865576i
$120$	−0.00541904	+	0.00861469i	−0.000494689	+	0.000786410i
$121$	4.76555			0.433231
$122$	−3.99638	+	6.92194i	−0.361815	+	0.626683i
$123$	−5.36705	−	3.37612i	−0.483930	−	0.304415i
$124$			6.74388i			0.605618i
$125$	−0.0192939			−0.00172570
$126$	−6.80514	−	4.87369i	−0.606250	−	0.434183i
$127$	−4.71924	−	8.17397i	−0.418765	−	0.725322i	0.577051	−	0.816708i	$-0.304204\pi$
$127$	−4.71924	−	8.17397i	−0.418765	−	0.725322i	−0.995816	+	0.0913863i	$0.970870\pi$
$128$	−0.896545	−	0.517620i	−0.0792441	−	0.0457516i
$129$	−0.174516	+	4.60181i	−0.0153653	+	0.405167i
$130$	0.00709209	−	0.00187636i	0.000622017	−	0.000164568i
$131$	−3.11100	−	5.38841i	−0.271809	−	0.470788i	0.697516	−	0.716569i	$-0.254289\pi$
$131$	−3.11100	−	5.38841i	−0.271809	−	0.470788i	−0.969325	+	0.245782i	$0.920955\pi$
$132$	2.04460	−	3.25031i	0.177959	−	0.282903i
$133$	12.4544	−	6.82823i	1.07993	−	0.592082i
$134$	−13.0181	−	7.51602i	−1.12459	−	0.649285i
$135$	0.00919499	−	0.00399515i	0.000791379	−	0.000343848i
$136$	11.0120	−	6.35778i	0.944271	−	0.545175i
$137$	−5.33148	+	3.07813i	−0.455499	+	0.262983i	−0.710150	−	0.704051i	$-0.751373\pi$
$137$	−5.33148	+	3.07813i	−0.455499	+	0.262983i	0.254651	+	0.967033i	$0.418040\pi$
$138$	7.53055	+	4.73707i	0.641043	+	0.403246i
$139$	10.6666	+	6.15838i	0.904731	+	0.522347i	0.878732	−	0.477315i	$-0.158390\pi$
$139$	10.6666	+	6.15838i	0.904731	+	0.522347i	0.0259992	+	0.999662i	$0.491723\pi$
$140$	−0.00453132		0.000100124i	−0.000382966		8.46200e-6i
$141$	−5.25421	−	3.30515i	−0.442485	−	0.278343i
$142$	0.755285	+	1.30819i	0.0633821	+	0.109781i
$143$	−8.70321	+	2.30261i	−0.727799	+	0.192554i
$144$	−1.86506	−	3.88288i	−0.155422	−	0.323573i
$145$	−0.0146060	−	0.00843275i	−0.00121296	−	0.000700302i
$146$	−0.980661	−	1.69856i	−0.0811601	−	0.140573i
$147$	0.994169	−	12.0835i	0.0819977	−	0.996633i
$148$	3.24589			0.266810
$149$		−	7.16171i		−	0.586710i	−0.956004	−	0.293355i	$-0.905228\pi$
$149$		−	7.16171i		−	0.586710i	0.956004	−	0.293355i	$-0.0947718\pi$
$150$	4.86284	−	7.73050i	0.397050	−	0.631193i
$151$	−8.14880	+	14.1141i	−0.663140	+	1.14859i	0.316646	+	0.948544i	$0.397443\pi$
$151$	−8.14880	+	14.1141i	−0.663140	+	1.14859i	−0.979786	+	0.200049i	$0.935890\pi$
$152$	16.3492			1.32610
$153$	−12.4897	−	0.948668i	−1.00974	−	0.0766953i
$154$	−6.96491	−	0.153896i	−0.561248	−	0.0124013i
$155$			0.0146545i			0.00117707i
$156$	1.65377	−	5.29253i	0.132407	−	0.423742i
$157$	4.07713	+	2.35393i	0.325391	+	0.187864i	0.653793	−	0.756674i	$-0.273177\pi$
$157$	4.07713	+	2.35393i	0.325391	+	0.187864i	−0.328402	+	0.944538i	$0.606510\pi$
$158$		−	7.68741i		−	0.611577i
$159$	24.7291	+	0.937811i	1.96115	+	0.0743732i
$160$	−0.00764728	−	0.00441516i	−0.000604571	−	0.000349049i
$161$	−0.284672	+	12.8834i	−0.0224353	+	1.01536i
$162$	−1.43354	+	9.38220i	−0.112629	+	0.737135i
$163$	−4.20632			−0.329464			−0.164732	−	0.986338i	$-0.552676\pi$
$163$	−4.20632			−0.329464			−0.164732	+	0.986338i	$0.552676\pi$
$164$	1.62518	−	2.81490i	0.126905	−	0.219806i
$165$	0.00444291	−	0.00706293i	0.000345880	−	0.000549848i
$166$	−9.50624	−	5.48843i	−0.737828	−	0.425985i
$167$	7.24993	+	12.5573i	0.561017	+	0.971709i	0.997408	+	0.0719525i	$0.0229230\pi$
$167$	7.24993	+	12.5573i	0.561017	+	0.971709i	−0.436391	+	0.899757i	$0.643744\pi$
$168$	7.69021	−	11.6462i	0.593312	−	0.898522i
$169$	−11.2991	+	6.42883i	−0.869163	+	0.494526i
$170$	0.00735708	−	0.00424761i	0.000564263	−	0.000325777i
$171$	−13.2975	−	9.08577i	−1.01688	−	0.694806i
$172$	−2.36070			−0.180002
$173$	−15.6967			−1.19340			−0.596700	−	0.802465i	$-0.703522\pi$
$173$	−15.6967			−1.19340			−0.596700	+	0.802465i	$0.703522\pi$
$174$	14.1201	−	7.45356i	1.07044	−	0.565053i
$175$	13.2255	+	0.292230i	0.999755	+	0.0220905i
$176$	−3.10486	−	1.79259i	−0.234037	−	0.135122i
$177$	−7.66963	−	4.82455i	−0.576484	−	0.362636i
$178$	−4.93518	+	2.84933i	−0.369907	+	0.213566i
$179$		−	6.46461i		−	0.483188i	−0.970377	−	0.241594i	$-0.922330\pi$
$179$		−	6.46461i		−	0.483188i	0.970377	−	0.241594i	$-0.0776702\pi$
$180$	0.00222517	+	0.00463259i	0.000165855	+	0.000345293i
$181$			0.939369i			0.0698227i	0.999390	+	0.0349114i	$0.0111149\pi$
$181$			0.939369i			0.0698227i	−0.999390	+	0.0349114i	$0.988885\pi$
$182$	−9.77976	+	2.35756i	−0.724924	+	0.174754i
$183$	6.12824	+	11.6094i	0.453012	+	0.858190i
$184$	−7.41675	+	12.8462i	−0.546770	+	0.947033i
$185$	0.00705331			0.000518570
$186$	−11.7432	−	7.38702i	−0.861054	−	0.541643i
$187$	−9.02840	+	5.21255i	−0.660222	+	0.381179i
$188$	1.59101	−	2.75572i	0.116037	−	0.200981i
$189$	−12.7269	+	5.19863i	−0.925747	+	0.378144i
$190$	0.0109229			0.000792428
$191$		−	5.37944i		−	0.389243i	−0.980878	−	0.194621i	$-0.937652\pi$
$191$		−	5.37944i		−	0.389243i	0.980878	−	0.194621i	$-0.0623478\pi$
$192$	11.7916	−	6.22443i	0.850987	−	0.449210i
$193$	21.1426			1.52188			0.760938	−	0.648825i	$-0.224739\pi$
$193$	21.1426			1.52188			0.760938	+	0.648825i	$0.224739\pi$
$194$	1.26042	+	2.18311i	0.0904928	+	0.156738i
$195$	0.00359364	−	0.0115007i	0.000257346	−	0.000823581i
$196$	6.20919	+	0.274530i	0.443513	+	0.0196093i
$197$	22.4348	−	12.9527i	1.59841	−	0.922843i	0.606616	−	0.794995i	$-0.292526\pi$
$197$	22.4348	−	12.9527i	1.59841	−	0.922843i	0.991794	−	0.127848i	$-0.0408069\pi$
$198$	3.42022	+	7.12057i	0.243065	+	0.506037i
$199$	2.39732	−	1.38409i	0.169941	−	0.0981157i	−0.412617	−	0.910905i	$-0.635385\pi$
$199$	2.39732	−	1.38409i	0.169941	−	0.0981157i	0.582558	+	0.812789i	$0.302052\pi$
$200$	13.1873	+	7.61367i	0.932480	+	0.538368i
$201$	−21.8338	+	11.5254i	−1.54004	+	0.812940i
$202$	16.4937	+	9.52267i	1.16050	+	0.670012i
$203$	19.7686	+	12.0033i	1.38748	+	0.842470i
$204$	0.243331	−	6.41639i	0.0170365	−	0.449237i
$205$	0.00353152	−	0.00611677i	0.000246652	−	0.000427214i
$206$	10.2914			0.717034
$207$	13.1714	−	6.32661i	0.915474	−	0.439730i
$208$	−4.99641	−	1.35569i	−0.346438	−	0.0940003i
$209$	−13.4042			−0.927189
$210$	0.00513781	−	0.00778078i	0.000354542	−	0.000536925i
$211$	−3.90647	−	6.76621i	−0.268933	−	0.465805i	0.699654	−	0.714482i	$-0.253338\pi$
$211$	−3.90647	−	6.76621i	−0.268933	−	0.465805i	−0.968586	+	0.248677i	$0.920004\pi$
$212$			12.6859i			0.871271i
$213$	2.47923	+	0.0940204i	0.169874	+	0.00644217i
$214$	2.88040	+	4.98900i	0.196900	+	0.341041i
$215$	−0.00512981			−0.000349850
$216$	−15.7225	−	1.79564i	−1.06978	−	0.122178i
$217$	0.443919	−	20.0906i	0.0301352	−	1.36384i
$218$	6.73151	−	3.88644i	0.455916	−	0.263223i
$219$	−3.21903	−	0.122076i	−0.217522	−	0.00824914i
$220$	0.00370435	+	0.00213870i	0.000249747	+	0.000144191i
$221$	−10.6783	+	10.6112i	−0.718303	+	0.713785i
$222$	−3.55544	+	5.65211i	−0.238625	+	0.379345i
$223$	−6.48830	+	3.74602i	−0.434489	+	0.250852i	−0.701257	−	0.712909i	$-0.747377\pi$
$223$	−6.48830	+	3.74602i	−0.434489	+	0.250852i	0.266768	+	0.963761i	$0.414044\pi$
$224$	10.3503	+	6.28463i	0.691559	+	0.419909i
$225$	−6.49459	−	13.5211i	−0.432973	−	0.901406i
$226$	0.237870	+	0.412003i	0.0158229	+	0.0274061i
$227$	4.27068	+	7.39703i	0.283455	+	0.490958i	0.972233	−	0.234014i	$-0.0751861\pi$
$227$	4.27068	+	7.39703i	0.283455	+	0.490958i	−0.688779	+	0.724972i	$0.741853\pi$
$228$	4.39593	−	6.98824i	0.291127	−	0.462808i
$229$	8.92049	−	5.15025i	0.589482	−	0.340338i	−0.175410	−	0.984495i	$-0.556125\pi$
$229$	8.92049	−	5.15025i	0.589482	−	0.340338i	0.764893	+	0.644158i	$0.222792\pi$
$230$	−0.00495511	+	0.00858250i	−0.000326730	+	0.000565913i
$231$	−6.30497	+	9.54835i	−0.414837	+	0.628235i
$232$	13.3108	+	23.0549i	0.873894	+	1.51363i
$233$	1.09700	−	0.633351i	0.0718666	−	0.0414922i	−0.463636	−	0.886026i	$-0.653456\pi$
$233$	1.09700	−	0.633351i	0.0718666	−	0.0414922i	0.535503	+	0.844534i	$0.320122\pi$
$234$	7.40447	+	8.67700i	0.484046	+	0.567233i
$235$	0.00345727	−	0.00598818i	0.000225528	−	0.000390626i
$236$	2.32242	−	4.02255i	0.151177	−	0.261845i
$237$	−10.6874	−	6.72286i	−0.694220	−	0.436697i
$238$	−10.2149	+	5.60041i	−0.662132	+	0.363021i
$239$			18.8399i			1.21865i	0.792921	+	0.609325i	$0.208559\pi$
$239$			18.8399i			1.21865i	−0.792921	+	0.609325i	$0.791441\pi$
$240$	0.00424344	−	0.00223998i	0.000273913	−	0.000144590i
$241$	−1.05943	+	0.611661i	−0.0682438	+	0.0394006i	−0.533734	−	0.845653i	$-0.679212\pi$
$241$	−1.05943	+	0.611661i	−0.0682438	+	0.0394006i	0.465490	+	0.885053i	$0.345878\pi$
$242$	−4.35228	−	2.51279i	−0.279775	−	0.161528i
$243$	11.7899	+	10.1980i	0.756322	+	0.654200i
$244$	−5.82794	+	3.36476i	−0.373096	+	0.215407i
$245$	0.0134926		0.000596553i	0.000862009		3.81124e-5i
$246$	3.12145	+	5.91329i	0.199016	+	0.377018i
$247$	−18.7121	+	4.95067i	−1.19062	+	0.315004i
$248$	11.5657	−	20.0324i	0.734425	−	1.27206i
$249$	−15.9438	+	8.41622i	−1.01039	+	0.533356i
$250$	0.0176208	+	0.0101733i	0.00111443	+	0.000643419i
$251$	4.42278	−	7.66048i	0.279163	−	0.483525i	−0.692014	−	0.721884i	$-0.743276\pi$
$251$	4.42278	−	7.66048i	0.279163	−	0.483525i	0.971177	+	0.238359i	$0.0766096\pi$
$252$	−2.91027	−	6.41846i	−0.183330	−	0.404325i
$253$	6.08077	−	10.5322i	0.382294	−	0.662153i
$254$			9.95349i			0.624538i
$255$	0.000528758	−	0.0139428i	3.31121e−5	−	0.000873133i
$256$	8.24404	+	14.2791i	0.515253	+	0.892444i
$257$	−5.47193	+	9.47765i	−0.341329	+	0.591200i	−0.984680	−	0.174372i	$-0.944210\pi$
$257$	−5.47193	+	9.47765i	−0.341329	+	0.591200i	0.643350	+	0.765572i	$0.277544\pi$
$258$	2.58584	−	4.11072i	0.160987	−	0.255922i
$259$	−9.66976	−	0.213662i	−0.600849	−	0.0132763i
$260$	0.00596112	+	0.00161745i	0.000369693	+	0.000100310i
$261$	1.98615	−	26.1487i	0.122940	−	1.61857i
$262$			6.56150i			0.405371i
$263$			12.7145i			0.784011i	0.919963	+	0.392005i	$0.128219\pi$
$263$			12.7145i			0.784011i	−0.919963	+	0.392005i	$0.871781\pi$
$264$	−11.6477	+	6.14845i	−0.716865	+	0.378411i
$265$			0.0275665i			0.00169339i
$266$	−14.9747	−	0.330880i	−0.918159	−	0.0202876i
$267$	−0.354694	+	9.35293i	−0.0217069	+	0.572390i
$268$	−6.32813	−	10.9606i	−0.386552	−	0.669528i
$269$	11.5793	+	20.0560i	0.706003	+	1.22283i	0.966328	+	0.257313i	$0.0828370\pi$
$269$	11.5793	+	20.0560i	0.706003	+	1.22283i	−0.260325	+	0.965521i	$0.583830\pi$
$270$	−0.0105042	−	0.00119966i	−0.000639264	−	7.30091e-5i
$271$	−22.8158	−	13.1727i	−1.38596	−	0.800185i	−0.393104	−	0.919494i	$-0.628599\pi$
$271$	−22.8158	−	13.1727i	−1.38596	−	0.800185i	−0.992857	+	0.119309i	$0.961932\pi$
$272$	−5.99505			−0.363503
$273$	−5.27509	+	15.6580i	−0.319263	+	0.947666i
$274$	6.49218			0.392207
$275$	−10.8118	−	6.24222i	−0.651978	−	0.376420i
$276$	3.49673	+	6.62423i	0.210478	+	0.398732i
$277$	2.20225	+	3.81442i	0.132321	+	0.229186i	0.924571	−	0.381010i	$-0.124424\pi$
$277$	2.20225	+	3.81442i	0.132321	+	0.229186i	−0.792250	+	0.610196i	$0.791090\pi$
$278$	−6.49441	−	11.2486i	−0.389509	−	0.674649i
$279$	−20.5395	+	9.86577i	−1.22967	+	0.590648i
$280$	0.0132884	+	0.00806862i	0.000794134	+	0.000482192i
$281$			13.2912i			0.792885i	0.918060	+	0.396442i	$0.129755\pi$
$281$			13.2912i			0.792885i	−0.918060	+	0.396442i	$0.870245\pi$
$282$	3.05582	+	5.78898i	0.181972	+	0.344729i
$283$			16.3786i			0.973605i	0.873512	+	0.486803i	$0.161837\pi$
$283$			16.3786i			0.973605i	−0.873512	+	0.486803i	$0.838163\pi$
$284$			1.27183i			0.0754691i
$285$	0.00955236	−	0.0151855i	0.000565833	−	0.000899509i
$286$	9.16259	+	2.48612i	0.541796	+	0.147007i
$287$	−5.02684	+	8.27882i	−0.296725	+	0.488683i
$288$	1.03989	−	13.6908i	0.0612763	−	0.806736i
$289$	−0.216300	+	0.374642i	−0.0127235	+	0.0220378i
$290$	0.00889288	+	0.0154029i	0.000522208	+	0.000904491i
$291$	4.13733	+	0.156901i	0.242534	+	0.00919771i
$292$		−	1.65134i		−	0.0966374i
$293$	−9.96323	+	17.2568i	−0.582058	+	1.00815i	0.413177	+	0.910651i	$0.364419\pi$
$293$	−9.96323	+	17.2568i	−0.582058	+	1.00815i	−0.995235	+	0.0975037i	$0.968914\pi$
$294$	−7.27938	+	10.5114i	−0.424542	+	0.613039i
$295$	0.00504662	−	0.00874100i	0.000293825	−	0.000508920i
$296$	−9.64179	−	5.56669i	−0.560417	−	0.323557i
$297$	12.8904	+	1.47219i	0.747978	+	0.0854252i
$298$	−3.77624	+	6.54065i	−0.218752	+	0.378889i
$299$	4.59874	−	16.9486i	0.265952	−	0.980166i
$300$	6.80011	−	3.58957i	0.392605	−	0.207244i
$301$	7.03272	+	0.155395i	0.405359	+	0.00895679i
$302$	14.8843	−	8.59344i	0.856494	−	0.494497i
$303$	27.6631	−	14.6025i	1.58920	−	0.838892i
$304$	−6.67551	−	3.85411i	−0.382867	−	0.221048i
$305$	−0.0126641	+	0.00731164i	−0.000725146	+	0.000418663i
$306$	10.9064	+	7.45201i	0.623478	+	0.426003i
$307$		−	4.93316i		−	0.281551i	−0.990042	−	0.140775i	$-0.955040\pi$
$307$		−	4.93316i		−	0.281551i	0.990042	−	0.140775i	$-0.0449595\pi$
$308$	−5.01369	−	3.04428i	−0.285682	−	0.173464i
$309$	9.00010	−	14.3075i	0.511998	−	0.813927i
$310$	0.00772703	−	0.0133836i	0.000438866	−	0.000760138i
$311$	6.69213	−	11.5911i	0.379476	−	0.657272i	−0.611510	−	0.791237i	$-0.709438\pi$
$311$	6.69213	−	11.5911i	0.379476	−	0.657272i	0.990986	+	0.133965i	$0.0427710\pi$
$312$	−13.9891	+	12.8851i	−0.791979	+	0.729473i
$313$	23.9599	−	13.8332i	1.35429	−	0.781901i	0.365445	−	0.930833i	$-0.380917\pi$
$313$	23.9599	−	13.8332i	1.35429	−	0.781901i	0.988847	+	0.148932i	$0.0475835\pi$
$314$	−2.48238	−	4.29960i	−0.140089	−	0.242641i
$315$	−0.00632403	−	0.0139473i	−0.000356319	−	0.000785843i
$316$	3.23622	−	5.60529i	0.182051	−	0.315322i
$317$	12.8384	−	7.41223i	0.721075	−	0.416313i	−0.0940735	−	0.995565i	$-0.529989\pi$
$317$	12.8384	−	7.41223i	0.721075	−	0.416313i	0.815148	+	0.579253i	$0.196656\pi$
$318$	−22.0901	−	13.8957i	−1.23875	−	0.779233i
$319$	−10.9131	−	18.9020i	−0.611016	−	1.05831i
$320$	0.00742641	+	0.0128629i	0.000415149	+	0.000719059i
$321$	9.45492	+	0.358562i	0.527722	+	0.0200130i
$322$	7.05320	−	11.6161i	0.393059	−	0.647339i
$323$	−19.4113	+	11.2071i	−1.08007	+	0.623580i
$324$	−4.99495	+	6.23757i	−0.277497	+	0.346531i
$325$	−17.3987	−	4.72084i	−0.965104	−	0.261865i
$326$	3.84155	+	2.21792i	0.212764	+	0.122839i
$327$	0.483797	−	12.7573i	0.0267541	−	0.705478i
$328$	−9.65508	+	5.57436i	−0.533113	+	0.307793i
$329$	−4.92115	+	8.10477i	−0.271312	+	0.446831i
$330$	−0.00778178	+	0.00410776i	−0.000428373	+	0.000226125i
$331$	5.80880			0.319280			0.159640	−	0.987175i	$-0.448967\pi$
$331$	5.80880			0.319280			0.159640	+	0.987175i	$0.448967\pi$
$332$	−4.62100	−	8.00380i	−0.253610	−	0.439266i
$333$	4.74848	+	9.88586i	0.260215	+	0.541742i
$334$		−	15.2910i		−	0.836689i
$335$	−0.0137510	−	0.0238175i	−0.000751299	−	0.00130129i
$336$	−5.88541	+	2.94236i	−0.321075	+	0.160519i
$337$	−9.55520			−0.520505			−0.260252	−	0.965541i	$-0.583806\pi$
$337$	−9.55520			−0.520505			−0.260252	+	0.965541i	$0.583806\pi$
$338$	13.7091	+	0.0865022i	0.745675	+	0.00470510i
$339$	0.780810	+	0.0296109i	0.0424078	+	0.00160824i
$340$	0.00715258			0.000387903
$341$	−9.48239	+	16.4240i	−0.513500	+	0.889409i
$342$	7.35356	+	15.3094i	0.397635	+	0.827837i
$343$	−18.4796	−	1.22657i	−0.997804	−	0.0662285i
$344$	7.01238	+	4.04860i	0.378082	+	0.218286i
$345$	0.00759839	+	0.0143945i	0.000409084	+	0.000774972i
$346$	14.3355	+	8.27660i	0.770681	+	0.444953i
$347$	25.2168	−	14.5589i	1.35371	−	0.781563i	0.364941	−	0.931031i	$-0.381089\pi$
$347$	25.2168	−	14.5589i	1.35371	−	0.781563i	0.988767	+	0.149467i	$0.0477558\pi$
$348$	13.4335	+	0.509441i	0.720109	+	0.0273089i
$349$	27.1567	−	15.6790i	1.45367	−	0.839275i	0.454980	−	0.890501i	$-0.349646\pi$
$349$	27.1567	−	15.6790i	1.45367	−	0.839275i	0.998687	+	0.0512262i	$0.0163129\pi$
$350$	−11.9245	−	7.24047i	−0.637392	−	0.387019i
$351$	18.5386	−	2.70575i	0.989516	−	0.144422i
$352$	−5.71380	−	9.89659i	−0.304547	−	0.527490i
$353$	−1.59546			−0.0849177			−0.0424588	−	0.999098i	$-0.513519\pi$
$353$	−1.59546			−0.0849177			−0.0424588	+	0.999098i	$0.513519\pi$
$354$	4.46061	+	8.45022i	0.237079	+	0.449124i
$355$			0.00276368i			0.000146681i
$356$	−4.79800			−0.254293
$357$	−1.14726	+	19.0989i	−0.0607196	+	1.01082i
$358$	−3.40868	+	5.90400i	−0.180154	+	0.312036i
$359$	11.1728	−	6.45064i	0.589680	−	0.340452i	−0.175291	−	0.984517i	$-0.556087\pi$
$359$	11.1728	−	6.45064i	0.589680	−	0.340452i	0.764971	+	0.644065i	$0.222753\pi$
$360$	0.00133508	−	0.0175771i	7.03651e−5	−	0.000926395i
$361$	−9.81939			−0.516810
$362$	0.495312	−	0.857906i	0.0260330	−	0.0450906i
$363$	−7.29958	+	3.85323i	−0.383129	+	0.202242i
$364$	−8.12341	−	2.39802i	−0.425782	−	0.125691i
$365$		−	0.00358837i		−	0.000187824i
$366$	0.524628	−	13.8339i	0.0274228	−	0.723111i
$367$			13.0999i			0.683807i	0.939735	+	0.341903i	$0.111072\pi$
$367$			13.0999i			0.683807i	−0.939735	+	0.341903i	$0.888928\pi$
$368$	6.05663	−	3.49680i	0.315724	−	0.182283i
$369$	10.9507	+	0.831772i	0.570072	+	0.0433003i
$370$	−0.00644165	−	0.00371909i	−0.000334885	−	0.000193346i
$371$	0.835056	−	37.7923i	0.0433540	−	1.96208i
$372$	−5.45282	−	10.3299i	−0.282716	−	0.535579i
$373$	6.13740			0.317783			0.158891	−	0.987296i	$-0.449208\pi$
$373$	6.13740			0.317783			0.158891	+	0.987296i	$0.449208\pi$
$374$	10.9939			0.568483
$375$	0.0295533	−	0.0156003i	0.00152613	−	0.000805595i
$376$	−9.45210	+	5.45717i	−0.487455	+	0.281432i
$377$	−22.2157	−	22.3564i	−1.14417	−	1.15141i
$378$	14.3644	+	1.96288i	0.738824	+	0.100959i
$379$	6.45103	+	11.1735i	0.331367	+	0.573945i	0.982780	−	0.184779i	$-0.0591568\pi$
$379$	6.45103	+	11.1735i	0.331367	+	0.573945i	−0.651413	+	0.758723i	$0.725823\pi$
$380$	0.00796443	+	0.00459826i	0.000408567	+	0.000235886i
$381$	13.8378	+	8.70462i	0.708932	+	0.445951i
$382$	−2.83648	+	4.91293i	−0.145127	+	0.251368i
$383$	9.23976			0.472130			0.236065	−	0.971737i	$-0.424142\pi$
$383$	9.23976			0.472130			0.236065	+	0.971737i	$0.424142\pi$
$384$	1.79180	+	0.0679510i	0.0914375	+	0.00346761i
$385$	−0.0108948	−	0.00661521i	−0.000555248	−	0.000337143i
$386$	−19.3091	−	11.1481i	−0.982806	−	0.567423i
$387$	−3.45352	−	7.18989i	−0.175553	−	0.365483i
$388$			2.12242i			0.107750i
$389$	11.3864	+	6.57391i	0.577311	+	0.333311i	0.760064	−	0.649848i	$-0.225168\pi$
$389$	11.3864	+	6.57391i	0.577311	+	0.333311i	−0.182753	+	0.983159i	$0.558501\pi$
$390$	−0.00934610	+	0.00860847i	−0.000473258	+	0.000435907i
$391$		−	20.3362i		−	1.02845i
$392$	−17.9733	−	11.4642i	−0.907791	−	0.579031i
$393$	9.12210	+	5.73823i	0.460149	+	0.289455i
$394$	−27.3189			−1.37631
$395$	0.00703230	−	0.0121803i	0.000353834	−	0.000612858i
$396$	−0.503725	+	6.63181i	−0.0253131	+	0.333261i
$397$		−	18.5599i		−	0.931495i	−0.884918	−	0.465747i	$-0.845786\pi$
$397$		−	18.5599i		−	0.931495i	0.884918	−	0.465747i	$-0.154214\pi$
$398$	−2.91923			−0.146328
$399$	−13.5558	+	20.5292i	−0.678640	+	1.02774i
$400$	−3.58964	−	6.21745i	−0.179482	−	0.310872i
$401$	−10.6982	−	6.17658i	−0.534240	−	0.308444i	0.208501	−	0.978022i	$-0.433142\pi$
$401$	−10.6982	−	6.17658i	−0.534240	−	0.308444i	−0.742741	+	0.669578i	$0.766475\pi$
$402$	26.0176	+	0.986671i	1.29764	+	0.0492107i
$403$	−7.17130	+	26.4299i	−0.357228	+	1.31656i
$404$	8.01763	+	13.8869i	0.398892	+	0.690901i
$405$	−0.0108540	+	0.0135542i	−0.000539341	+	0.000673515i
$406$	−11.7251	−	21.3861i	−0.581908	−	1.06137i
$407$	7.90501	+	4.56396i	0.391837	+	0.226227i
$408$	−11.7269	+	18.6423i	−0.580568	+	0.922933i
$409$	4.99900	−	2.88618i	0.247185	−	0.142712i	−0.371290	−	0.928517i	$-0.621084\pi$
$409$	4.99900	−	2.88618i	0.247185	−	0.142712i	0.618475	+	0.785805i	$0.287751\pi$
$410$	−0.00645053	+	0.00372422i	−0.000318569	+	0.000183926i
$411$	5.67760	−	9.02572i	0.280055	−	0.445206i
$412$	7.50398	+	4.33242i	0.369694	+	0.213443i
$413$	−7.18346	+	11.8306i	−0.353475	+	0.582146i
$414$	−15.3651	−	1.16707i	−0.755152	−	0.0573582i
$415$	−0.0100414	−	0.0173923i	−0.000492915	−	0.000853753i
$416$	−11.6316	−	11.7052i	−0.570284	−	0.573894i
$417$	−21.3179	−	0.808446i	−1.04394	−	0.0395898i
$418$	12.2418	+	7.06781i	0.598766	+	0.345698i
$419$	−17.6169	−	30.5134i	−0.860644	−	1.49068i	−0.871309	−	0.490736i	$-0.836728\pi$
$419$	−17.6169	−	30.5134i	−0.860644	−	1.49068i	0.0106648	−	0.999943i	$-0.496605\pi$
$420$	0.00702177	−	0.00351048i	0.000342627	−	0.000171294i
$421$	27.0300			1.31736			0.658682	−	0.752421i	$-0.271114\pi$
$421$	27.0300			1.31736			0.658682	+	0.752421i	$0.271114\pi$
$422$			8.23926i			0.401081i
$423$	10.7205	+	0.814285i	0.521249	+	0.0395919i
$424$	21.7563	−	37.6830i	1.05658	−	1.83005i
$425$	−20.8762			−1.01264
$426$	−2.21465	−	1.39312i	−0.107300	−	0.0674968i
$427$	17.5834	−	9.64027i	0.850920	−	0.466526i
$428$			4.85032i			0.234449i
$429$	11.4693	−	10.5641i	0.553742	−	0.510038i
$430$	0.00468495	+	0.00270486i	0.000225928	+	0.000130440i
$431$			31.3272i			1.50898i	0.656312	+	0.754490i	$0.272116\pi$
$431$			31.3272i			1.50898i	−0.656312	+	0.754490i	$0.727884\pi$
$432$	5.99633	+	4.43955i	0.288499	+	0.213598i
$433$	−3.41909	−	1.97401i	−0.164311	−	0.0948649i	0.415590	−	0.909552i	$-0.363575\pi$
$433$	−3.41909	−	1.97401i	−0.164311	−	0.0948649i	−0.579900	+	0.814687i	$0.696909\pi$
$434$	−10.9988	+	18.1142i	−0.527960	+	0.869511i
$435$	0.0291909	+	0.00110702i	0.00139960	+	5.30774e-5i
$436$	6.54440			0.313420
$437$	13.0738	−	22.6445i	0.625404	−	1.08323i
$438$	2.87550	+	1.80883i	0.137397	+	0.0864290i
$439$	26.7313	+	15.4333i	1.27582	+	0.736593i	0.976076	−	0.217429i	$-0.0697669\pi$
$439$	26.7313	+	15.4333i	1.27582	+	0.736593i	0.299739	+	0.954021i	$0.403100\pi$
$440$	−0.00733575	−	0.0127059i	−0.000349718	−	0.000605729i
$441$	8.24744	+	19.3127i	0.392735	+	0.919652i
$442$	15.3474	−	4.06047i	0.730001	−	0.193137i
$443$	−16.2769	+	9.39748i	−0.773340	+	0.446488i	−0.834065	−	0.551667i	$-0.813992\pi$
$443$	−16.2769	+	9.39748i	−0.773340	+	0.446488i	0.0607250	+	0.998155i	$0.480659\pi$
$444$	−4.97186	+	2.62449i	−0.235954	+	0.124553i
$445$	−0.0104261			−0.000494242
$446$	7.90084			0.374116
$447$	5.79067	+	10.9699i	0.273889	+	0.518858i
$448$	−9.79160	−	17.8594i	−0.462610	−	0.843778i
$449$	−4.95835	−	2.86270i	−0.233999	−	0.135099i	0.378417	−	0.925635i	$-0.376469\pi$
$449$	−4.95835	−	2.86270i	−0.233999	−	0.135099i	−0.612415	+	0.790536i	$0.709802\pi$
$450$	−1.19805	+	15.7730i	−0.0564768	+	0.743547i
$451$	7.91591	−	4.57025i	0.372745	−	0.215205i
$452$			0.400551i			0.0188403i
$453$	1.06974	−	28.2080i	0.0502608	−	1.32533i
$454$		−	9.00741i		−	0.422739i
$455$	−0.0176522	−	0.00521091i	−0.000827547	−	0.000244291i
$456$	−25.0428	+	13.2193i	−1.17273	+	0.619051i
$457$	−16.9493	+	29.3570i	−0.792854	+	1.37326i	0.131339	+	0.991337i	$0.458072\pi$
$457$	−16.9493	+	29.3570i	−0.792854	+	1.37326i	−0.924193	+	0.381926i	$0.875261\pi$
$458$	−10.8625			−0.507573
$459$	19.8981	−	8.64557i	0.928764	−	0.403541i
$460$	−0.00722605	+	0.00417196i	−0.000336917	+	0.000194519i
$461$	9.37925	−	16.2453i	0.436835	−	0.756621i	−0.560608	−	0.828081i	$-0.689433\pi$
$461$	9.37925	−	16.2453i	0.436835	−	0.756621i	0.997443	+	0.0714602i	$0.0227659\pi$
$462$	10.7929	−	5.39581i	0.502130	−	0.251036i
$463$	−20.1902			−0.938317			−0.469158	−	0.883114i	$-0.655443\pi$
$463$	−20.1902			−0.938317			−0.469158	+	0.883114i	$0.655443\pi$
$464$		−	12.5513i		−	0.582681i
$465$	−0.0118490	−	0.0224468i	−0.000549484	−	0.00104095i
$466$	−1.33582			−0.0618806
$467$	−3.57259	−	6.18791i	−0.165320	−	0.286342i	0.771449	−	0.636291i	$-0.219532\pi$
$467$	−3.57259	−	6.18791i	−0.165320	−	0.286342i	−0.936769	+	0.349949i	$0.886199\pi$
$468$	1.74618	+	9.44396i	0.0807172	+	0.436547i
$469$	18.1305	+	33.0692i	0.837190	+	1.52699i
$470$	−0.00631492	+	0.00364592i	−0.000291285	+	0.000168174i
$471$	−8.14841	−	0.309015i	−0.375459	−	0.0142386i
$472$	−13.7973	+	7.96588i	−0.635073	+	0.366659i
$473$	−5.74924	−	3.31932i	−0.264350	−	0.152623i
$474$	6.21572	+	11.7751i	0.285498	+	0.540849i
$475$	−23.2457	−	13.4209i	−1.06659	−	0.615794i
$476$	−9.80584	−	0.216669i	−0.449450	−	0.00993102i
$477$	−38.6369	+	18.5585i	−1.76906	+	0.849735i
$478$	9.93393	−	17.2061i	0.454367	−	0.786987i
$479$	9.23925			0.422152			0.211076	−	0.977470i	$-0.432303\pi$
$479$	9.23925			0.422152			0.211076	+	0.977470i	$0.432303\pi$
$480$	0.0152836		0.000579604i	0.000697597		2.64552e-5i
$481$	12.7209	+	3.45161i	0.580024	+	0.157380i
$482$	1.29007			0.0587612
$483$	−9.98099	−	19.9643i	−0.454151	−	0.908406i
$484$	−2.11565	−	3.66441i	−0.0961658	−	0.166564i
$485$			0.00461203i			0.000209422i
$486$	−5.39026	−	15.5302i	−0.244507	−	0.704464i
$487$	−0.650774	−	1.12717i	−0.0294894	−	0.0510771i	0.850904	−	0.525321i	$-0.176055\pi$
$487$	−0.650774	−	1.12717i	−0.0294894	−	0.0510771i	−0.880393	+	0.474244i	$0.842721\pi$
$488$	23.0822			1.04488
$489$	6.44299	−	3.40106i	0.291362	−	0.153801i
$490$	−0.0120079	−	0.00765922i	−0.000542464	−	0.000346008i
$491$	−11.4486	+	6.60986i	−0.516668	+	0.298299i	−0.735570	−	0.677448i	$-0.763086\pi$
$491$	−11.4486	+	6.60986i	−0.516668	+	0.298299i	0.218902	+	0.975747i	$0.429752\pi$
$492$	−0.213347	+	5.62575i	−0.00961842	+	0.253628i
$493$	−31.6075	−	18.2486i	−1.42353	−	0.821876i
$494$	19.6998	+	5.34521i	0.886335	+	0.240492i
$495$	−0.00109459	+	0.0144109i	−4.91984e−5	+	0.000647723i
$496$	−9.44476	+	5.45294i	−0.424082	+	0.244844i
$497$	0.0837188	−	3.78888i	0.00375530	−	0.169954i
$498$	18.9988	+	0.720498i	0.851358	+	0.0322863i
$499$	3.18217	+	5.51168i	0.142454	+	0.246737i	0.928420	−	0.371532i	$-0.121168\pi$
$499$	3.18217	+	5.51168i	0.142454	+	0.246737i	−0.785966	+	0.618269i	$0.787834\pi$
$500$	0.00856547	+	0.0148358i	0.000383060	+	0.000663479i
$501$	−21.2583	−	13.3725i	−0.949751	−	0.597438i
$502$	−8.07847	+	4.66411i	−0.360560	+	0.208169i
$503$	−17.7261	+	30.7026i	−0.790370	+	1.36896i	0.135369	+	0.990795i	$0.456778\pi$
$503$	−17.7261	+	30.7026i	−0.790370	+	1.36896i	−0.925738	+	0.378165i	$0.876555\pi$
$504$	−2.36279	+	24.0569i	−0.105247	+	1.07158i
$505$	0.0174223	+	0.0301764i	0.000775283	+	0.00134283i
$506$	−11.1069	+	6.41256i	−0.493761	+	0.285073i
$507$	12.1092	−	18.9833i	0.537790	−	0.843079i
$508$	−4.19018	+	7.25761i	−0.185909	+	0.322004i
$509$	7.82495	−	13.5532i	0.346835	−	0.600736i	−0.638850	−	0.769331i	$-0.720590\pi$
$509$	7.82495	−	13.5532i	0.346835	−	0.600736i	0.985685	+	0.168595i	$0.0539231\pi$
$510$	−0.00783470	+	0.0124549i	−0.000346926	+	0.000551512i
$511$	−0.108700	+	4.91948i	−0.00480862	+	0.217625i
$512$		−	15.3173i		−	0.676934i
$513$	27.7147	+	3.16524i	1.22363	+	0.139749i
$514$	9.99480	−	5.77050i	0.440852	−	0.254526i
$515$	0.0163062	+	0.00941436i	0.000718535	+	0.000414846i
$516$	3.61599	−	1.90877i	0.159185	−	0.0840288i
$517$	7.74949	−	4.47417i	0.340822	−	0.196774i
$518$	8.71853	+	5.29382i	0.383070	+	0.232597i
$519$	24.0433	−	12.6917i	1.05538	−	0.557105i
$520$	−0.0149334	−	0.0150279i	−0.000654871	−	0.000659016i
$521$	19.1120	−	33.1029i	0.837310	−	1.45026i	−0.0548261	−	0.998496i	$-0.517460\pi$
$521$	19.1120	−	33.1029i	0.837310	−	1.45026i	0.892136	−	0.451767i	$-0.149206\pi$
$522$	−15.6017	+	22.8338i	−0.682867	+	0.999410i
$523$	−26.5888	−	15.3510i	−1.16265	−	0.671254i	−0.210709	−	0.977549i	$-0.567577\pi$
$523$	−26.5888	−	15.3510i	−1.16265	−	0.671254i	−0.951937	+	0.306295i	$0.900911\pi$
$524$	−2.76224	+	4.78434i	−0.120669	+	0.209005i
$525$	−20.4944	+	10.2460i	−0.894447	+	0.447172i
$526$	6.70414	−	11.6119i	0.292314	−	0.506303i
$527$			31.7125i			1.38142i
$528$	6.20525	+	0.235324i	0.270049	+	0.0102411i
$529$	0.361731	+	0.626536i	0.0157274	+	0.0272407i
$530$	0.0145353	−	0.0251759i	0.000631374	−	0.00109357i
$531$	15.6488	+	1.18862i	0.679101	+	0.0515817i
$532$	−10.7796	−	6.54526i	−0.467353	−	0.283773i
$533$	9.36253	−	9.30364i	0.405536	−	0.402985i
$534$	5.25557	−	8.35482i	0.227431	−	0.361548i
$535$			0.0105397i			0.000455673i
$536$			43.4109i			1.87507i
$537$	5.22702	+	9.90212i	0.225563	+	0.427308i
$538$		−	24.4223i		−	1.05292i
$539$	14.7358	+	9.39917i	0.634716	+	0.404851i
$540$	−0.00715411	−	0.00529674i	−0.000307864	−	0.000227936i
$541$	4.56917	+	7.91403i	0.196444	+	0.340251i	0.947373	−	0.320132i	$-0.103727\pi$
$541$	4.56917	+	7.91403i	0.196444	+	0.340251i	−0.750929	+	0.660383i	$0.770394\pi$
$542$	13.8915	+	24.0607i	0.596690	+	1.03350i
$543$	−0.759535	−	1.43887i	−0.0325948	−	0.0617478i
$544$	−16.5488	−	9.55448i	−0.709525	−	0.409645i
$545$	0.0142210			0.000609160
$546$	13.0738	−	11.5187i	0.559508	−	0.492954i
$547$	−35.4176			−1.51435			−0.757173	−	0.653214i	$-0.773420\pi$
$547$	−35.4176			−1.51435			−0.757173	+	0.653214i	$0.773420\pi$
$548$	4.73379	+	2.73305i	0.202217	+	0.116750i
$549$	−18.7738	−	12.8275i	−0.801244	−	0.547466i
$550$	6.58282	+	11.4018i	0.280692	+	0.486174i
$551$	−23.4634	−	40.6398i	−0.999574	−	1.73131i
$552$	0.973639	−	25.6739i	0.0414408	−	1.09275i
$553$	−10.0099	+	16.4856i	−0.425665	+	0.701038i
$554$		−	4.64484i		−	0.197340i
$555$	−0.0108039	+	0.00570302i	−0.000458598	+	0.000242080i
$556$		−	10.9360i		−	0.463788i
$557$			4.53358i			0.192094i	0.995377	+	0.0960470i	$0.0306199\pi$
$557$			4.53358i			0.192094i	−0.995377	+	0.0960470i	$0.969380\pi$
$558$	23.9604	+	1.81993i	1.01432	+	0.0770439i
$559$	−9.25180	−	2.51032i	−0.391310	−	0.106175i
$560$	−0.00352369	−	0.00642705i	−0.000148903	−	0.000271592i
$561$	9.61452	−	15.2843i	0.405925	−	0.645303i
$562$	7.00820	−	12.1386i	0.295623	−	0.512034i
$563$	6.06622	+	10.5070i	0.255661	+	0.442817i	0.965075	−	0.261975i	$-0.0843737\pi$
$563$	6.06622	+	10.5070i	0.255661	+	0.442817i	−0.709414	+	0.704792i	$0.751040\pi$
$564$	−0.208862	+	5.50747i	−0.00879466	+	0.231906i
$565$		0	0.000870398i		0	3.66179e-5i
$566$	8.63613	−	14.9582i	0.363004	−	0.628741i
$567$	15.2909	−	18.2534i	0.642159	−	0.766571i
$568$	2.18118	−	3.77792i	0.0915204	−	0.158518i
$569$	31.4844	+	18.1775i	1.31990	+	0.762042i	0.983712	−	0.179754i	$-0.0575303\pi$
$569$	31.4844	+	18.1775i	1.31990	+	0.762042i	0.336184	+	0.941796i	$0.390864\pi$
$570$	−0.0167310	+	0.00883178i	−0.000700784	+	0.000369923i
$571$	7.04698	−	12.2057i	0.294907	−	0.510794i	−0.680056	−	0.733160i	$-0.738045\pi$
$571$	7.04698	−	12.2057i	0.294907	−	0.510794i	0.974963	+	0.222366i	$0.0713780\pi$
$572$	5.63433	+	5.66999i	0.235583	+	0.237074i
$573$	4.34960	+	8.23991i	0.181707	+	0.344227i
$574$	8.95618	−	4.91032i	0.373824	−	0.204953i
$575$	21.0906	−	12.1767i	0.879540	−	0.507802i
$576$	−13.0289	+	19.0684i	−0.542871	+	0.794519i
$577$	11.4758	+	6.62558i	0.477745	+	0.275826i	0.719476	−	0.694517i	$-0.244382\pi$
$577$	11.4758	+	6.62558i	0.477745	+	0.275826i	−0.241731	+	0.970343i	$0.577715\pi$
$578$	0.395085	−	0.228102i	0.0164334	−	0.00948780i
$579$	−32.3849	+	17.0950i	−1.34587	+	0.710445i
$580$			0.0149748i			0.000621793i
$581$	13.2395	+	24.1482i	0.549266	+	1.00183i
$582$	−3.69581	−	2.32483i	−0.153196	−	0.0963675i
$583$	−17.8373	+	30.8951i	−0.738746	+	1.27955i
$584$	−2.83205	+	4.90525i	−0.117191	+	0.202981i
$585$	0.00379445	+	0.0205217i	0.000156881	+	0.000848469i
$586$	18.1984	−	10.5069i	0.751771	−	0.434035i
$587$	15.6011	+	27.0220i	0.643928	+	1.11532i	0.984548	+	0.175115i	$0.0560296\pi$
$587$	15.6011	+	27.0220i	0.643928	+	1.11532i	−0.340620	+	0.940201i	$0.610637\pi$
$588$	−9.73284	+	4.59999i	−0.401376	+	0.189700i
$589$	−20.3874	+	35.3120i	−0.840047	+	1.45500i
$590$	−0.00921795	+	0.00532198i	−0.000379497	+	0.000219103i
$591$	−23.8912	+	37.9800i	−0.982753	+	1.56229i
$592$	2.62455	+	4.54585i	0.107868	+	0.186833i
$593$	5.48292	+	9.49670i	0.225157	+	0.389983i	0.956366	−	0.292170i	$-0.0943773\pi$
$593$	5.48292	+	9.49670i	0.225157	+	0.389983i	−0.731210	+	0.682153i	$0.761044\pi$
$594$	−10.9963	−	8.14141i	−0.451184	−	0.334046i
$595$	−0.0213081		0.000470823i	−0.000873547		1.93018e-5i
$596$	−5.50691	+	3.17942i	−0.225572	+	0.130234i
$597$	−2.55295	+	4.05845i	−0.104485	+	0.166101i
$598$	−13.1367	+	13.0540i	−0.537198	+	0.533819i
$599$	−12.1466	−	7.01285i	−0.496297	−	0.286537i	0.230886	−	0.972981i	$-0.425838\pi$
$599$	−12.1466	−	7.01285i	−0.496297	−	0.286537i	−0.727183	+	0.686444i	$0.759171\pi$
$600$	−26.3556	−	0.999491i	−1.07596	−	0.0408040i
$601$	3.15684	−	1.82260i	0.128770	−	0.0743455i	−0.434231	−	0.900801i	$-0.642980\pi$
$601$	3.15684	−	1.82260i	0.128770	−	0.0743455i	0.563001	+	0.826456i	$0.309647\pi$
$602$	−6.34091	−	3.85015i	−0.258436	−	0.156920i
$603$	24.1248	−	35.3079i	0.982439	−	1.43785i
$604$	14.4705			0.588798
$605$	−0.00459731	−	0.00796277i	−0.000186907	−	0.000323733i
$606$	−32.9638	−	1.25010i	−1.33906	−	0.0507817i
$607$		−	17.2352i		−	0.699557i	−0.936833	−	0.349778i	$-0.886257\pi$
$607$		−	17.2352i		−	0.699557i	0.936833	−	0.349778i	$-0.113743\pi$
$608$	−12.2848	−	21.2779i	−0.498214	−	0.862933i
$609$	−39.9858	−	2.40193i	−1.62031	−	0.0973311i
$610$	0.0154212			0.000624386
$611$	9.16570	−	9.10805i	0.370805	−	0.368472i
$612$	4.81531	+	10.0250i	0.194647	+	0.405236i
$613$	−30.5124			−1.23239			−0.616193	−	0.787596i	$-0.711326\pi$
$613$	−30.5124			−1.23239			−0.616193	+	0.787596i	$0.711326\pi$
$614$	−2.60117	+	4.50536i	−0.104975	+	0.181821i
$615$	−0.000463603		0.0122248i	−1.86943e−5		0.000492950i
$616$	9.67207	+	17.6414i	0.389699	+	0.710791i
$617$	5.82452	+	3.36279i	0.234486	+	0.135381i	0.612640	−	0.790362i	$-0.290108\pi$
$617$	5.82452	+	3.36279i	0.234486	+	0.135381i	−0.378154	+	0.925743i	$0.623441\pi$
$618$	−15.7637	+	8.32118i	−0.634110	+	0.334727i
$619$	8.43263	+	4.86858i	0.338936	+	0.195685i	0.659801	−	0.751440i	$-0.270640\pi$
$619$	8.43263	+	4.86858i	0.338936	+	0.195685i	−0.320865	+	0.947125i	$0.603974\pi$
$620$	0.0112684	−	0.00650580i	0.000452549	−	0.000261279i
$621$	−15.0597	+	20.3406i	−0.604325	+	0.816239i
$622$	−12.2236	+	7.05729i	−0.490121	+	0.282971i
$623$	14.2936	+	0.315831i	0.572662	+	0.0126535i
$624$	8.74936	−	1.96332i	0.350255	−	0.0785957i
$625$	−12.5000	−	21.6506i	−0.499999	−	0.866023i
$626$	−29.1761			−1.16611
$627$	20.5318	−	10.8381i	0.819961	−	0.432832i
$628$		−	4.18009i		−	0.166804i
$629$	15.2635			0.608595
$630$	−0.00157857	+	0.0160724i	−6.28918e−5	+	0.000640338i
$631$	−1.16211	+	2.01284i	−0.0462630	+	0.0801299i	−0.888230	−	0.459400i	$-0.848065\pi$
$631$	−1.16211	+	2.01284i	−0.0462630	+	0.0801299i	0.841967	+	0.539530i	$0.181398\pi$
$632$	−19.2261	+	11.1002i	−0.764774	+	0.441543i
$633$	11.4546	+	7.20547i	0.455279	+	0.286392i
$634$	−15.6334			−0.620880
$635$	−0.00910527	+	0.0157708i	−0.000361332	+	0.000625845i
$636$	−10.2573	−	19.4315i	−0.406728	−	0.770510i
$637$	24.0424	+	7.67863i	0.952596	+	0.304239i
$638$			23.0171i			0.911256i
$639$	−3.87355	+	1.86059i	−0.153235	+	0.0736036i
$640$			0.00199739i			7.89536e-5i
$641$	9.55907	−	5.51893i	0.377561	−	0.217985i	−0.299196	−	0.954192i	$-0.596718\pi$
$641$	9.55907	−	5.51893i	0.377561	−	0.217985i	0.676756	+	0.736207i	$0.263385\pi$
$642$	−8.44592	−	5.31288i	−0.333334	−	0.209683i
$643$	2.75926	+	1.59306i	0.108815	+	0.0628241i	0.553420	−	0.832903i	$-0.313323\pi$
$643$	2.75926	+	1.59306i	0.108815	+	0.0628241i	−0.444605	+	0.895727i	$0.646656\pi$
$644$	10.0330	−	5.50067i	0.395354	−	0.216757i
$645$	0.00785754	−	0.00414775i	0.000309390	−	0.000163318i
$646$	23.6372			0.929995
$647$	39.9534			1.57073			0.785365	−	0.619033i	$-0.212475\pi$
$647$	39.9534			1.57073			0.785365	+	0.619033i	$0.212475\pi$
$648$	25.5347	−	9.96213i	1.00310	−	0.391350i
$649$	11.3120	−	6.53099i	0.444035	−	0.256364i
$650$	13.4006	+	13.4854i	0.525616	+	0.528943i
$651$	15.5644	+	31.1325i	0.610018	+	1.22018i
$652$	1.86738	+	3.23440i	0.0731323	+	0.126669i
$653$	−13.7639	−	7.94656i	−0.538621	−	0.310973i	0.205899	−	0.978573i	$-0.433988\pi$
$653$	−13.7639	−	7.94656i	−0.538621	−	0.310973i	−0.744520	+	0.667600i	$0.767322\pi$
$654$	−7.16852	+	11.3958i	−0.280311	+	0.445613i
$655$	−0.00600235	+	0.0103964i	−0.000234531	+	0.000406220i
$656$	5.25633			0.205225
$657$	5.02942	−	2.41578i	0.196216	−	0.0942487i
$658$	8.76789	−	4.80709i	0.341808	−	0.187400i
$659$	−43.5079	−	25.1193i	−1.69483	−	0.978510i	−0.950514	−	0.310681i	$-0.899443\pi$
$659$	−43.5079	−	25.1193i	−1.69483	−	0.978510i	−0.744315	−	0.667829i	$-0.767224\pi$
$660$	−0.00740337		0.000280760i	−0.000288176		1.09286e-5i
$661$			50.3595i			1.95876i	0.202032	+	0.979379i	$0.435246\pi$
$661$			50.3595i			1.95876i	−0.202032	+	0.979379i	$0.564754\pi$
$662$	−5.30506	−	3.06288i	−0.206187	−	0.119042i
$663$	7.77669	−	24.8876i	0.302022	−	0.966556i
$664$			31.7000i			1.23020i
$665$	−0.0234240	−	0.0142229i	−0.000908343	−	0.000551539i
$666$	0.875949	−	11.5323i	0.0339423	−	0.446869i
$667$	42.5763			1.64856
$668$	6.43717	−	11.1495i	0.249062	−	0.431387i
$669$	6.90952	−	10.9841i	0.267137	−	0.424670i
$670$			0.0290027i			0.00112047i
$671$	−18.9244			−0.730570
$672$	−20.9355	−	1.25759i	−0.807604	−	0.0485124i
$673$	18.1511	+	31.4387i	0.699674	+	1.21187i	0.968579	+	0.248704i	$0.0800048\pi$
$673$	18.1511	+	31.4387i	0.699674	+	1.21187i	−0.268905	+	0.963167i	$0.586662\pi$
$674$	8.72657	+	5.03829i	0.336135	+	0.194068i
$675$	20.8806	+	15.4596i	0.803696	+	0.595039i
$676$	9.95958	+	5.83427i	0.383061	+	0.224395i
$677$	18.7369	+	32.4533i	0.720119	+	1.24728i	0.960952	+	0.276716i	$0.0892460\pi$
$677$	18.7369	+	32.4533i	0.720119	+	1.24728i	−0.240833	+	0.970567i	$0.577421\pi$
$678$	−0.697485	−	0.438750i	−0.0267867	−	0.0168501i
$679$	0.139710	−	6.32287i	0.00536157	−	0.242650i
$680$	−0.0212465	−	0.0122667i	−0.000814765	−	0.000470405i
$681$	−12.5225	−	7.87724i	−0.479864	−	0.301857i
$682$	17.3202	−	9.99980i	0.663223	−	0.382912i
$683$	−32.7411	+	18.9031i	−1.25281	+	0.723307i	−0.971666	−	0.236359i	$-0.924046\pi$
$683$	−32.7411	+	18.9031i	−1.25281	+	0.723307i	−0.281140	+	0.959667i	$0.590712\pi$
$684$	−1.08302	+	14.2585i	−0.0414103	+	0.545189i
$685$	0.0102865	+	0.00593893i	0.000393028	+	0.000226915i
$686$	16.2303	+	10.8642i	0.619676	+	0.414796i
$687$	−9.49960	+	15.1016i	−0.362432	+	0.576162i
$688$	−1.90881	−	3.30615i	−0.0727726	−	0.126046i
$689$	−13.4899	+	49.7172i	−0.513925	+	1.89407i
$690$	0.000650486	−	0.0171527i	2.47636e−5	−	0.000652991i
$691$	11.2268	+	6.48179i	0.427087	+	0.246579i	0.698105	−	0.715995i	$-0.254027\pi$
$691$	11.2268	+	6.48179i	0.427087	+	0.246579i	−0.271018	+	0.962574i	$0.587360\pi$
$692$	6.96851	+	12.0698i	0.264903	+	0.458825i
$693$	1.93718	−	19.7235i	0.0735874	−	0.749235i
$694$	−30.7066			−1.16561
$695$		−	0.0237639i		−	0.000901415i
$696$	−39.0299	−	24.5516i	−1.47942	−	0.930627i
$697$	7.64226	−	13.2368i	0.289471	−	0.501379i
$698$	−33.0689			−1.25168
$699$	−1.16821	+	1.85712i	−0.0441858	+	0.0702425i
$700$	−5.64672	−	10.2993i	−0.213426	−	0.389279i
$701$			34.9085i			1.31848i	0.751934	+	0.659238i	$0.229121\pi$
$701$			34.9085i			1.31848i	−0.751934	+	0.659238i	$0.770879\pi$
$702$	−18.3576	−	7.30396i	−0.692863	−	0.275670i
$703$	16.9960	+	9.81262i	0.641014	+	0.370090i
$704$			19.2215i			0.724438i
$705$	−0.000453857		0.0119677i	−1.70932e−5		0.000450731i
$706$	1.45710	+	0.841257i	0.0548387	+	0.0316611i
$707$	−22.9711	−	41.8981i	−0.863915	−	1.57574i
$708$	−0.304877	+	8.03931i	−0.0114580	+	0.302136i
$709$	36.5640			1.37319			0.686595	−	0.727040i	$-0.259105\pi$
$709$	36.5640			1.37319			0.686595	+	0.727040i	$0.259105\pi$
$710$	0.00145724	−	0.00252402i	5.46893e−5	−	9.47247e-5i
$711$	21.8061	+	1.65630i	0.817794	+	0.0621162i
$712$	14.2523	+	8.22855i	0.534126	+	0.308378i
$713$	−18.4973	−	32.0382i	−0.692729	−	1.19984i
$714$	11.1183	−	16.8377i	0.416092	−	0.630136i
$715$	0.0122434	+	0.0123209i	0.000457877	+	0.000460776i
$716$	−4.97089	+	2.86994i	−0.185771	+	0.107255i
$717$	−15.2331	−	28.8578i	−0.568892	−	1.07771i
$718$	−13.6052			−0.507743
$719$	39.6806			1.47984			0.739919	−	0.672696i	$-0.234864\pi$
$719$	39.6806			1.47984			0.739919	+	0.672696i	$0.234864\pi$
$720$	−0.00468869	+	0.00686214i	−0.000174737	+	0.000255737i
$721$	−22.0698	−	13.4006i	−0.821921	−	0.499064i
$722$	8.96785	+	5.17759i	0.333749	+	0.192690i
$723$	1.12821	−	1.79352i	0.0419584	−	0.0667017i
$724$	0.722316	−	0.417030i	0.0268447	−	0.0154988i
$725$		−	43.7067i		−	1.62323i
$726$	8.69830	+	0.329868i	0.322824	+	0.0122426i
$727$			15.6289i			0.579644i	0.957081	+	0.289822i	$0.0935961\pi$
$727$			15.6289i			0.579644i	−0.957081	+	0.289822i	$0.906404\pi$
$728$	20.0177	+	21.0549i	0.741905	+	0.780345i
$729$	−26.3047	−	6.08783i	−0.974249	−	0.225475i
$730$	−0.00189208	+	0.00327718i	−7.00291e−5	+	0.000121294i
$731$	−11.1010			−0.410585
$732$	6.20629	−	9.86618i	0.229391	−	0.364665i
$733$	−25.0179	+	14.4441i	−0.924055	+	0.533504i	−0.884927	−	0.465730i	$-0.845792\pi$
$733$	−25.0179	+	14.4441i	−0.924055	+	0.533504i	−0.0391289	+	0.999234i	$0.512458\pi$
$734$	6.90732	−	11.9638i	0.254954	−	0.441593i
$735$	−0.0211495	+	0.00999578i	−0.000780110	+	0.000368700i
$736$	22.2918			0.821686
$737$		−	35.5913i		−	1.31102i
$738$	−9.56250	−	6.53376i	−0.352000	−	0.240511i
$739$	15.1318			0.556634			0.278317	−	0.960489i	$-0.410223\pi$
$739$	15.1318			0.556634			0.278317	+	0.960489i	$0.410223\pi$
$740$	−0.00313130	−	0.00542356i	−0.000115109	−	0.000199374i
$741$	24.6592	−	22.7130i	0.905878	−	0.834383i
$742$	−20.6899	+	34.0746i	−0.759549	+	1.25092i
$743$	−30.5018	+	17.6102i	−1.11900	+	0.646056i	−0.941146	−	0.338001i	$-0.890249\pi$
$743$	−30.5018	+	17.6102i	−1.11900	+	0.646056i	−0.177856	+	0.984057i	$0.556916\pi$
$744$	−1.51830	+	40.0361i	−0.0556636	+	1.46779i
$745$	−0.0119665	+	0.00690888i	−0.000438420	+	0.000253122i
$746$	−5.60517	−	3.23614i	−0.205220	−	0.118484i
$747$	17.6167	−	25.7829i	0.644561	−	0.943348i
$748$	8.01626	+	4.62819i	0.293103	+	0.169223i
$749$	0.319275	−	14.4495i	0.0116660	−	0.527973i
$750$	−0.0352162	−	0.00133551i	−0.00128591	−	4.87661e-5i
$751$	−0.826755	+	1.43198i	−0.0301687	+	0.0522538i	−0.880716	−	0.473646i	$-0.842938\pi$
$751$	−0.826755	+	1.43198i	−0.0301687	+	0.0522538i	0.850547	+	0.525899i	$0.176271\pi$
$752$	5.14582			0.187649
$753$	−0.580604	+	15.3100i	−0.0211584	+	0.557926i
$754$	8.50107	+	32.1316i	0.309591	+	1.17016i
$755$	0.0314445			0.00114438
$756$	9.64749	+	7.47830i	0.350876	+	0.271983i
$757$	−7.44232	−	12.8905i	−0.270496	−	0.468513i	0.698493	−	0.715617i	$-0.253854\pi$
$757$	−7.44232	−	12.8905i	−0.270496	−	0.468513i	−0.968989	+	0.247104i	$0.920521\pi$
$758$		−	13.6061i		−	0.494194i
$759$	−0.798257	+	21.0493i	−0.0289749	+	0.764040i
$760$	−0.0157720	−	0.0273180i	−0.000572112	−	0.000990926i
$761$	−8.40012			−0.304504			−0.152252	−	0.988342i	$-0.548653\pi$
$761$	−8.40012			−0.304504			−0.152252	+	0.988342i	$0.548653\pi$
$762$	−8.04799	−	15.2462i	−0.291548	−	0.552311i
$763$	−19.4963	−	0.430789i	−0.705813	−	0.0155956i
$764$	−4.13646	+	2.38818i	−0.149652	+	0.0864015i
$765$	0.0104637	+	0.0217843i	0.000378315	+	0.000787614i
$766$	−8.43849	−	4.87196i	−0.304895	−	0.176031i
$767$	13.3793	−	13.2951i	0.483097	−	0.480058i
$768$	−24.1732	−	15.2061i	−0.872277	−	0.548703i
$769$	40.4429	−	23.3497i	1.45841	−	0.842013i	0.459476	−	0.888190i	$-0.348037\pi$
$769$	40.4429	−	23.3497i	1.45841	−	0.842013i	0.998933	+	0.0461769i	$0.0147038\pi$
$770$	0.00646188	+	0.0117862i	0.000232870	+	0.000424744i
$771$	0.718332	−	18.9417i	0.0258701	−	0.682168i
$772$	−9.38617	−	16.2573i	−0.337816	−	0.585114i
$773$	−17.3505	−	30.0520i	−0.624055	−	1.08089i	−0.988723	−	0.149757i	$-0.952151\pi$
$773$	−17.3505	−	30.0520i	−0.624055	−	1.08089i	0.364668	−	0.931138i	$-0.381182\pi$
$774$	−0.637070	+	8.38737i	−0.0228990	+	0.301478i
$775$	−32.8889	+	18.9884i	−1.18140	+	0.682084i
$776$	3.63995	−	6.30458i	0.130667	−	0.226321i
$777$	14.9843	−	7.49129i	0.537560	−	0.268749i
$778$	−6.93262	−	12.0076i	−0.248546	−	0.430495i
$779$	17.0194	−	9.82614i	0.609783	−	0.352058i
$780$	−0.0104387	+	0.00234240i	−0.000373765	+	8.38714e-5i
$781$	−1.78829	+	3.09740i	−0.0639899	+	0.110834i
$782$	−10.7229	+	18.5727i	−0.383451	+	0.664157i
$783$	18.1005	+	41.6590i	0.646860	+	1.48877i
$784$	4.63612	+	8.91791i	0.165576	+	0.318497i
$785$		−	0.00908333i		−	0.000324198i
$786$	−5.30537	−	10.0505i	−0.189236	−	0.358491i
$787$	19.9645	−	11.5265i	0.711657	−	0.410875i	−0.100017	−	0.994986i	$-0.531890\pi$
$787$	19.9645	−	11.5265i	0.711657	−	0.410875i	0.811674	+	0.584111i	$0.198557\pi$
$788$	−19.9197	−	11.5006i	−0.709609	−	0.409693i
$789$	−10.2804	−	19.4754i	−0.365993	−	0.693341i
$790$	−0.0128449	+	0.00741602i	−0.000457002	+	0.000263850i
$791$	0.0263665	−	1.19327i	0.000937484	−	0.0424279i
$792$	12.8698	−	18.8357i	0.457310	−	0.669296i
$793$	−26.4182	+	6.98949i	−0.938140	+	0.248204i
$794$	−9.78631	+	16.9504i	−0.347303	+	0.601547i
$795$	−0.0222891	−	0.0422247i	−0.000790514	−	0.00149756i
$796$	−2.12856	−	1.22893i	−0.0754449	−	0.0435581i
$797$	18.0616	−	31.2836i	0.639774	−	1.10812i	−0.345708	−	0.938342i	$-0.612361\pi$
$797$	18.0616	−	31.2836i	0.639774	−	1.10812i	0.985482	−	0.169779i	$-0.0543054\pi$
$798$	23.2049	−	11.6011i	0.821446	−	0.410675i
$799$	7.48159	−	12.9585i	0.264680	−	0.458439i
$800$		−	22.8837i		−	0.809059i
$801$	−7.01910	−	14.6131i	−0.248008	−	0.516327i
$802$	6.51361	+	11.2819i	0.230003	+	0.398378i
$803$	2.32191	−	4.02166i	0.0819384	−	0.141921i
$804$	18.5554	+	11.6722i	0.654398	+	0.411647i
$805$	0.0218016	−	0.0119530i	0.000768406	−	0.000421286i
$806$	20.4854	−	20.3566i	0.721568	−	0.717029i
$807$	−33.9530	−	21.3580i	−1.19520	−	0.751837i
$808$		−	55.0009i		−	1.93492i
$809$		−	29.7538i		−	1.04609i	−0.852306	−	0.523044i	$-0.824796\pi$
$809$		−	29.7538i		−	1.04609i	0.852306	−	0.523044i	$-0.175204\pi$
$810$	0.0170597	−	0.00665567i	0.000599416	−	0.000233857i
$811$		−	17.0021i		−	0.597025i	−0.954406	−	0.298512i	$-0.903510\pi$
$811$		−	17.0021i		−	0.597025i	0.954406	−	0.298512i	$-0.0964904\pi$
$812$	0.453623	−	20.5297i	0.0159190	−	0.720451i
$813$	45.5988	+	1.72926i	1.59922	+	0.0606477i
$814$	−4.81299	−	8.33634i	−0.168695	−	0.292189i
$815$	0.00405782	+	0.00702835i	0.000142139	+	0.000246192i
$816$	9.18287	−	4.84735i	0.321465	−	0.169691i
$817$	−12.3610	−	7.13662i	−0.432456	−	0.249679i
$818$	−6.08732			−0.212838
$819$	−4.58036	−	28.2493i	−0.160051	−	0.987109i
$820$	−0.00627123			−0.000219001
$821$	25.3845	+	14.6558i	0.885926	+	0.511490i	0.872608	−	0.488422i	$-0.162427\pi$
$821$	25.3845	+	14.6558i	0.885926	+	0.511490i	0.0133184	+	0.999911i	$0.495760\pi$
$822$	−9.94434	+	5.24931i	−0.346849	+	0.183091i
$823$	1.08892	+	1.88607i	0.0379575	+	0.0657443i	0.884380	−	0.466768i	$-0.154582\pi$
$823$	1.08892	+	1.88607i	0.0379575	+	0.0657443i	−0.846423	+	0.532512i	$0.821248\pi$
$824$	−14.8602	−	25.7386i	−0.517679	−	0.896647i
$825$	21.6081	+	0.819452i	0.752299	+	0.0285297i
$826$	12.7986	−	7.01695i	0.445319	−	0.244151i
$827$			15.2048i			0.528724i	0.964424	+	0.264362i	$0.0851613\pi$
$827$			15.2048i			0.528724i	−0.964424	+	0.264362i	$0.914839\pi$
$828$	−10.7122	−	7.31930i	−0.372273	−	0.254363i
$829$		−	3.97612i		−	0.138097i	−0.997613	−	0.0690483i	$-0.978004\pi$
$829$		−	3.97612i		−	0.138097i	0.997613	−	0.0690483i	$-0.0219962\pi$
$830$			0.0211787i			0.000735123i
$831$	−6.45746	−	4.06205i	−0.224007	−	0.140911i
$832$	7.09921	+	26.8329i	0.246121	+	0.930265i
$833$	29.1981	+	1.29095i	1.01166	+	0.0447288i
$834$	19.0430	+	11.9789i	0.659404	+	0.414796i
$835$	0.0139880	−	0.0242279i	0.000484074	−	0.000838440i
$836$	5.95076	+	10.3070i	0.205811	+	0.356476i
$837$	23.4842	−	31.7193i	0.811733	−	1.09638i
$838$			37.1564i			1.28355i
$839$	−17.0612	+	29.5509i	−0.589019	+	1.02021i	0.405342	+	0.914165i	$0.367152\pi$
$839$	−17.0612	+	29.5509i	−0.589019	+	1.02021i	−0.994361	+	0.106046i	$0.966181\pi$
$840$	−0.0268784	−	0.00161457i	−0.000927391	−	5.57080e-5i
$841$	23.7056	−	41.0593i	0.817434	−	1.41584i
$842$	−24.6860	−	14.2525i	−0.850736	−	0.491172i
$843$	−10.7467	−	20.3586i	−0.370136	−	0.701188i
$844$	−3.46853	+	6.00767i	−0.119392	+	0.206793i
$845$	0.0216422	+	0.0126779i	0.000744514	+	0.000436132i
$846$	−9.36146	−	6.39640i	−0.321854	−	0.219913i
$847$	6.06147	+	11.0558i	0.208275	+	0.379883i
$848$	−17.7665	+	10.2575i	−0.610105	+	0.352244i
$849$	−13.2430	−	25.0877i	−0.454500	−	0.861009i
$850$	19.0658	+	11.0076i	0.653951	+	0.377559i
$851$	−15.4203	+	8.90290i	−0.528600	+	0.305187i
$852$	−1.02835	−	1.94811i	−0.0352306	−	0.0667412i
$853$			56.0005i			1.91742i	0.284387	+	0.958710i	$0.408210\pi$
$853$			56.0005i			1.91742i	−0.284387	+	0.958710i	$0.591790\pi$
$854$	−21.1417	−	0.467146i	−0.723454	−	0.0159854i
$855$	−0.00235340	+	0.0309838i	−8.04847e−5	+	0.00105962i
$856$	8.31828	−	14.4077i	0.284313	−	0.492445i
$857$	7.20743	−	12.4836i	0.246201	−	0.426433i	−0.716268	−	0.697826i	$-0.754151\pi$
$857$	7.20743	−	12.4836i	0.246201	−	0.426433i	0.962469	+	0.271393i	$0.0874843\pi$
$858$	−16.0449	+	3.60041i	−0.547764	+	0.122916i
$859$	2.32454	−	1.34207i	0.0793121	−	0.0457909i	−0.459819	−	0.888012i	$-0.652086\pi$
$859$	2.32454	−	1.34207i	0.0793121	−	0.0457909i	0.539132	+	0.842222i	$0.318753\pi$
$860$	0.00227736	+	0.00394451i	7.76574e−5	+	0.000134507i
$861$	1.00590	−	16.7455i	0.0342808	−	0.570685i
$862$	16.5183	−	28.6105i	0.562615	−	0.974479i
$863$	25.8619	−	14.9314i	0.880349	−	0.508270i	0.00957560	−	0.999954i	$-0.496952\pi$
$863$	25.8619	−	14.9314i	0.880349	−	0.508270i	0.870773	+	0.491684i	$0.163619\pi$
$864$	9.47695	+	21.8115i	0.322412	+	0.742043i
$865$	0.0151426	+	0.0262277i	0.000514863	+	0.000891769i
$866$	2.08172	+	3.60565i	0.0707398	+	0.122525i
$867$	0.0283949	−	0.748746i	0.000964343	−	0.0254288i
$868$	−15.6455	+	8.57779i	−0.531042	+	0.291149i
$869$	15.7629	−	9.10072i	0.534720	−	0.308721i
$870$	−0.0260758	−	0.0164029i	−0.000884051	−	0.000556109i
$871$	−13.1452	−	49.6850i	−0.445407	−	1.68351i
$872$	−19.4399	−	11.2236i	−0.658318	−	0.380080i
$873$	−6.46418	+	3.10494i	−0.218779	+	0.105086i
$874$	−23.8800	+	13.7872i	−0.807755	+	0.466357i
$875$	−0.0245407	−	0.0447610i	−0.000829626	−	0.00151320i
$876$	1.33521	+	2.52943i	0.0451125	+	0.0854614i
$877$	−11.5406			−0.389700			−0.194850	−	0.980833i	$-0.562422\pi$
$877$	−11.5406			−0.389700			−0.194850	+	0.980833i	$0.562422\pi$
$878$	−16.2754	−	28.1899i	−0.549270	−	0.951363i
$879$	1.30793	−	34.4889i	0.0441154	−	1.16328i
$880$			0.00691722i			0.000233180i
$881$	3.76362	+	6.51878i	0.126800	+	0.219623i	0.922435	−	0.386153i	$-0.126196\pi$
$881$	3.76362	+	6.51878i	0.126800	+	0.219623i	−0.795635	+	0.605776i	$0.792863\pi$
$882$	2.65102	−	21.9866i	0.0892644	−	0.740328i
$883$	−38.2310			−1.28658			−0.643289	−	0.765624i	$-0.722430\pi$
$883$	−38.2310			−1.28658			−0.643289	+	0.765624i	$0.722430\pi$
$884$	12.8999	+	3.50019i	0.433872	+	0.117724i
$885$	−0.000662499		0.0174694i	−2.22696e−5		0.000587229i
$886$	19.8205			0.665883
$887$	−14.3116	+	24.7885i	−0.480537	+	0.832315i	−0.999751	−	0.0223297i	$-0.992892\pi$
$887$	−14.3116	+	24.7885i	−0.480537	+	0.832315i	0.519213	+	0.854645i	$0.326225\pi$
$888$	19.2697	+	0.730771i	0.646649	+	0.0245231i
$889$	12.9606	−	21.3452i	0.434686	−	0.715894i
$890$	0.00952190	+	0.00549747i	0.000319175	+	0.000184276i
$891$	−20.9351	+	8.16765i	−0.701354	+	0.273627i
$892$	5.76092	+	3.32607i	0.192890	+	0.111365i
$893$	16.6616	−	9.61957i	0.557558	−	0.321906i
$894$	0.495729	−	13.0719i	0.0165797	−	0.437190i
$895$	−0.0108017	+	0.00623639i	−0.000361063	+	0.000208460i
$896$	0.0605058	−	2.73832i	0.00202136	−	0.0914809i
$897$	6.65991	+	29.6793i	0.222368	+	0.990963i
$898$	3.01891	+	5.22890i	0.100742	+	0.174491i
$899$	−66.3938			−2.21436
$900$	−7.51363	+	10.9966i	−0.250454	+	0.366553i
$901$			59.6543i			1.98737i
$902$	−9.63925			−0.320952
$903$	−10.8980	+	5.44835i	−0.362661	+	0.181310i
$904$	0.686944	−	1.18982i	0.0228474	−	0.0395729i
$905$	0.00156959		0.000906206i	5.21751e−5		3.01233e-5i
$906$	−15.8506	+	25.1977i	−0.526599	+	0.837139i
$907$	−29.7990			−0.989460			−0.494730	−	0.869047i	$-0.664733\pi$
$907$	−29.7990			−0.989460			−0.494730	+	0.869047i	$0.664733\pi$
$908$	3.79191	−	6.56777i	0.125839	−	0.217959i
$909$	−30.5657	+	44.7345i	−1.01380	+	1.48375i
$910$	0.0133738	+	0.0140667i	0.000443336	+	0.000466306i
$911$			28.3029i			0.937717i	0.883273	+	0.468859i	$0.155335\pi$
$911$			28.3029i			0.937717i	−0.883273	+	0.468859i	$0.844665\pi$
$912$	13.3414	+	0.505951i	0.441779	+	0.0167537i
$913$		−	25.9899i		−	0.860139i
$914$	30.9589	−	17.8741i	1.02403	−	0.591223i
$915$	0.0134863	−	0.0214392i	0.000445842	−	0.000708759i
$916$	−7.92044	−	4.57287i	−0.261699	−	0.151092i
$917$	8.54386	−	14.0711i	0.282143	−	0.464669i
$918$	−22.7312	−	2.59609i	−0.750241	−	0.0856836i
$919$	−49.0844			−1.61915			−0.809573	−	0.587020i	$-0.800301\pi$
$919$	−49.0844			−1.61915			−0.809573	+	0.587020i	$0.800301\pi$
$920$	0.0286196			0.000943562
$921$	3.98876	+	7.55633i	0.131434	+	0.248990i
$922$	−17.1318	+	9.89103i	−0.564205	+	0.325744i
$923$	−1.35244	+	4.98441i	−0.0445160	+	0.164064i
$924$	10.1412	+	0.609175i	0.333620	+	0.0200404i
$925$	9.13928	+	15.8297i	0.300498	+	0.520477i
$926$	18.4393	+	10.6459i	0.605952	+	0.349847i
$927$	−2.21735	+	29.1926i	−0.0728272	+	0.958809i
$928$	20.0034	−	34.6469i	0.656644	−	1.13734i
$929$	−20.7889			−0.682061			−0.341031	−	0.940052i	$-0.610776\pi$
$929$	−20.7889			−0.682061			−0.341031	+	0.940052i	$0.610776\pi$
$930$	−0.00101437	+	0.0267480i	−3.32626e−5	+	0.000877102i
$931$	31.6823	+	20.2084i	1.03835	+	0.662305i
$932$	−0.974015	−	0.562348i	−0.0319049	−	0.0184203i
$933$	−0.878515	+	23.1656i	−0.0287613	+	0.758407i
$934$			7.53505i			0.246554i
$935$	0.0174193	+	0.0100571i	0.000569673	+	0.000328901i
$936$	11.0094	−	31.0476i	0.359854	−	1.01482i
$937$			10.5891i			0.345930i	0.984928	+	0.172965i	$0.0553347\pi$
$937$			10.5891i			0.345930i	−0.984928	+	0.172965i	$0.944665\pi$
$938$	0.878564	−	39.7613i	0.0286861	−	1.29825i
$939$	−25.5153	+	40.5619i	−0.832662	+	1.32369i
$940$	−0.00613938			−0.000200245
$941$	−21.4748	+	37.1955i	−0.700059	+	1.21254i	0.268386	+	0.963311i	$0.413510\pi$
$941$	−21.4748	+	37.1955i	−0.700059	+	1.21254i	−0.968445	+	0.249227i	$0.919824\pi$
$942$	7.27884	+	4.57873i	0.237157	+	0.149183i
$943$			17.8303i			0.580636i
$944$	7.51141			0.244475
$945$	0.0209640	+	0.0162503i	0.000681959	+	0.000528624i
$946$	3.50044	+	6.06294i	0.113809	+	0.197123i
$947$	−42.4865	−	24.5296i	−1.38063	−	0.797104i	−0.388392	−	0.921494i	$-0.626969\pi$
$947$	−42.4865	−	24.5296i	−1.38063	−	0.797104i	−0.992233	+	0.124390i	$0.960303\pi$
$948$	−0.424837	+	11.2025i	−0.0137981	+	0.363841i
$949$	1.75600	−	6.47175i	0.0570023	−	0.210082i
$950$	14.1532	+	24.5141i	0.459191	+	0.795342i
$951$	−13.6718	+	21.7342i	−0.443339	+	0.704780i
$952$	28.7563	+	17.4606i	0.931997	+	0.565902i
$953$	28.5078	+	16.4590i	0.923458	+	0.533159i	0.884737	−	0.466091i	$-0.154338\pi$
$953$	28.5078	+	16.4590i	0.923458	+	0.533159i	0.0387215	+	0.999250i	$0.487671\pi$
$954$	45.0719	+	3.42347i	1.45926	+	0.110839i
$955$	−0.00898853	+	0.00518953i	−0.000290862	+	0.000167929i
$956$	14.4867	−	8.36390i	0.468533	−	0.270508i
$957$	31.9994	+	20.1291i	1.03439	+	0.650683i
$958$	−8.43802	−	4.87169i	−0.272620	−	0.157397i
$959$	−13.9224	−	8.45359i	−0.449579	−	0.272981i
$960$	−0.0217758	−	0.0136980i	−0.000702810	−	0.000442100i
$961$	13.3448	+	23.1139i	0.430478	+	0.745609i
$962$	−9.79778	−	9.85980i	−0.315893	−	0.317893i
$963$	−14.7724	+	7.09564i	−0.476034	+	0.228654i
$964$	0.940660	+	0.543090i	0.0302966	+	0.0174918i
$965$	−0.0203962	−	0.0353272i	−0.000656576	−	0.00113722i
$966$	−1.41138	+	23.4958i	−0.0454104	+	0.755964i
$967$	27.5780			0.886848			0.443424	−	0.896312i	$-0.353764\pi$
$967$	27.5780			0.886848			0.443424	+	0.896312i	$0.353764\pi$
$968$			14.5133i			0.466476i
$969$	20.6714	−	32.8616i	0.664063	−	1.05567i
$970$	0.00243184	−	0.00421207i	7.80818e−5	−	0.000135242i
$971$	34.5747			1.10956			0.554778	−	0.831998i	$-0.312803\pi$
$971$	34.5747			1.10956			0.554778	+	0.831998i	$0.312803\pi$
$972$	2.60753	−	13.5930i	0.0836365	−	0.435997i
$973$	−0.719866	+	32.5791i	−0.0230779	+	1.04444i
$974$			1.37257i			0.0439798i
$975$	30.4673	−	6.83674i	0.975735	−	0.218951i
$976$	−9.42467	−	5.44133i	−0.301676	−	0.174173i
$977$			57.8801i			1.85175i	0.377833	+	0.925874i	$0.376669\pi$
$977$			57.8801i			1.85175i	−0.377833	+	0.925874i	$0.623331\pi$
$978$	−7.67757	−	0.291159i	−0.245502	−	0.00931024i
$979$	−11.6850	−	6.74634i	−0.373454	−	0.215614i
$980$	−0.00553127	−	0.0106398i	−0.000176690	−	0.000339876i
$981$	9.57395	+	19.9320i	0.305673	+	0.636380i
$982$	13.9410			0.444876
$983$	1.73371	−	3.00288i	0.0552969	−	0.0957770i	−0.837052	−	0.547123i	$-0.815723\pi$
$983$	1.73371	−	3.00288i	0.0552969	−	0.0957770i	0.892349	+	0.451347i	$0.149056\pi$
$984$	10.2819	−	16.3452i	0.327774	−	0.521065i
$985$	−0.0432855	−	0.0249909i	−0.00137919	−	0.000796276i
$986$	19.2443	+	33.3322i	0.612864	+	1.06151i
$987$	0.984748	−	16.3935i	0.0313449	−	0.521810i
$988$	12.1139	+	12.1906i	0.385396	+	0.387835i
$989$	11.2150	−	6.47499i	0.356617	−	0.205893i
$990$	0.00859830	−	0.0125841i	0.000273272	−	0.000399947i
$991$	8.95038			0.284318			0.142159	−	0.989844i	$-0.454596\pi$
$991$	8.95038			0.284318			0.142159	+	0.989844i	$0.454596\pi$
$992$	−34.7620			−1.10369
$993$	−8.89757	+	4.69676i	−0.282356	+	0.149047i
$994$	−2.07427	+	3.41616i	−0.0657918	+	0.108354i
$995$	−0.00462537	−	0.00267046i	−0.000146634	−	8.46592e-5i
$996$	13.5497	+	8.52341i	0.429339	+	0.270075i
$997$	2.82101	−	1.62871i	0.0893424	−	0.0515818i	−0.454663	−	0.890663i	$-0.650240\pi$
$997$	2.82101	−	1.62871i	0.0893424	−	0.0515818i	0.544006	+	0.839082i	$0.316907\pi$
$998$		−	6.71161i		−	0.212452i
$999$	−15.2667	−	11.3032i	−0.483019	−	0.357616i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	273.2.bf.b.185.11	yes	64
3.2	odd	2	inner	273.2.bf.b.185.22	yes	64
7.5	odd	6		273.2.r.b.68.22	yes	64
13.9	even	3		273.2.r.b.269.22	yes	64
21.5	even	6		273.2.r.b.68.11	✓	64
39.35	odd	6		273.2.r.b.269.11	yes	64
91.61	odd	6	inner	273.2.bf.b.152.22	yes	64
273.152	even	6	inner	273.2.bf.b.152.11	yes	64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
273.2.r.b.68.11	✓	64	21.5	even	6
273.2.r.b.68.22	yes	64	7.5	odd	6
273.2.r.b.269.11	yes	64	39.35	odd	6
273.2.r.b.269.22	yes	64	13.9	even	3
273.2.bf.b.152.11	yes	64	273.152	even	6	inner
273.2.bf.b.152.22	yes	64	91.61	odd	6	inner
273.2.bf.b.185.11	yes	64	1.1	even	1	trivial
273.2.bf.b.185.22	yes	64	3.2	odd	2	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:	\( N \)	\(=\)	\( 273 = 3 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	273.bf (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.913280 - 0.527282i) q^{2} +(-1.53174 + 0.808559i) q^{3} +(-0.443947 - 0.768938i) q^{4} +(-0.000964697 - 0.00167090i) q^{5} +(1.82525 + 0.0692194i) q^{6} +(1.27194 + 2.31995i) q^{7} +3.04547i q^{8} +(1.69246 - 2.47701i) q^{9} +0.00203467i q^{10} -2.49689i q^{11} +(1.30174 + 0.818857i) q^{12} +(-0.922193 - 3.48562i) q^{13} +(0.0616352 - 2.78943i) q^{14} +(0.00282869 + 0.00177938i) q^{15} +(0.717929 - 1.24349i) q^{16} +(-2.08762 - 3.61586i) q^{17} +(-2.85178 + 1.36979i) q^{18} -5.36837i q^{19} +(-0.000856548 + 0.00148358i) q^{20} +(-3.82410 - 2.52513i) q^{21} +(-1.31657 + 2.28036i) q^{22} +(4.21813 + 2.43534i) q^{23} +(-2.46244 - 4.66487i) q^{24} +(2.50000 - 4.33012i) q^{25} +(-0.995686 + 3.66960i) q^{26} +(-0.589610 + 5.16259i) q^{27} +(1.21923 - 2.00798i) q^{28} +(7.57023 - 4.37067i) q^{29} +(-0.00164515 - 0.00311659i) q^{30} +(-6.57778 - 3.79768i) q^{31} +(3.96357 - 2.28837i) q^{32} +(2.01888 + 3.82459i) q^{33} +4.40306i q^{34} +(0.00264938 - 0.00436333i) q^{35} +(-2.65603 - 0.201741i) q^{36} +(-1.82786 + 3.16594i) q^{37} +(-2.83065 + 4.90282i) q^{38} +(4.23089 + 4.59342i) q^{39} +(0.00508869 - 0.00293796i) q^{40} +(1.83038 + 3.17031i) q^{41} +(2.16101 + 4.32253i) q^{42} +(1.32938 - 2.30256i) q^{43} +(-1.91995 + 1.10849i) q^{44} +(-0.00577156 - 0.000438383i) q^{45} +(-2.56822 - 4.44829i) q^{46} +(1.79190 + 3.10366i) q^{47} +(-0.0942468 + 2.48519i) q^{48} +(-3.76435 + 5.90167i) q^{49} +(-4.56640 + 2.63641i) q^{50} +(6.12133 + 3.85060i) q^{51} +(-2.27082 + 2.25654i) q^{52} +(-12.3735 - 7.14382i) q^{53} +(3.26062 - 4.40400i) q^{54} +(-0.00417206 + 0.00240874i) q^{55} +(-7.06534 + 3.87365i) q^{56} +(4.34064 + 8.22295i) q^{57} -9.21832 q^{58} +(2.61565 + 4.53044i) q^{59} +(0.000112444 - 0.00296504i) q^{60} -7.57921i q^{61} +(4.00490 + 6.93670i) q^{62} +(7.89925 + 0.775837i) q^{63} -7.69818 q^{64} +(-0.00493450 + 0.00490346i) q^{65} +(0.172833 - 4.55744i) q^{66} +14.2543 q^{67} +(-1.85358 + 3.21050i) q^{68} +(-8.43019 - 0.319701i) q^{69} +(-0.00472034 + 0.00258797i) q^{70} +(-1.24050 - 0.716205i) q^{71} +(7.54365 + 5.15435i) q^{72} +(1.61067 + 0.929921i) q^{73} +(3.33869 - 1.92759i) q^{74} +(-0.328189 + 8.65403i) q^{75} +(-4.12794 + 2.38327i) q^{76} +(5.79266 - 3.17589i) q^{77} +(-1.44196 - 6.42596i) q^{78} +(3.64483 + 6.31302i) q^{79} -0.00277034 q^{80} +(-3.27113 - 8.38449i) q^{81} -3.86050i q^{82} +10.4089 q^{83} +(-0.243974 + 4.06152i) q^{84} +(-0.00402784 + 0.00697642i) q^{85} +(-2.42820 + 1.40192i) q^{86} +(-8.06169 + 12.8157i) q^{87} +7.60420 q^{88} +(2.70190 - 4.67983i) q^{89} +(0.00503989 + 0.00344361i) q^{90} +(6.91350 - 6.57294i) q^{91} -4.32464i q^{92} +(13.1461 + 0.498544i) q^{93} -3.77934i q^{94} +(-0.00897003 + 0.00517885i) q^{95} +(-4.22088 + 6.70997i) q^{96} +(-2.07015 - 1.19520i) q^{97} +(6.54975 - 3.40500i) q^{98} +(-6.18481 - 4.22589i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q + 32 q^{4} - 12 q^{6} - 4 q^{7} + 8 q^{9} + 6 q^{12} - 12 q^{13} - 9 q^{15} - 16 q^{16} + 2 q^{18} + 10 q^{21} + 10 q^{22} - 24 q^{25} - 50 q^{28} - 16 q^{30} - 24 q^{31} - 33 q^{39} + 90 q^{40} - 48 q^{42}+ \cdots + 22 q^{99}+O(q^{100}) \) 64 * q + 32 * q^4 - 12 * q^6 - 4 * q^7 + 8 * q^9 + 6 * q^12 - 12 * q^13 - 9 * q^15 - 16 * q^16 + 2 * q^18 + 10 * q^21 + 10 * q^22 - 24 * q^25 - 50 * q^28 - 16 * q^30 - 24 * q^31 - 33 * q^39 + 90 * q^40 - 48 * q^42 - 20 * q^43 - 3 * q^45 + 6 * q^48 - 10 * q^51 + 30 * q^52 - 27 * q^54 + 18 * q^55 + 4 * q^57 - 60 * q^58 + 55 * q^60 - 74 * q^63 - 84 * q^64 + 75 * q^66 - 88 * q^67 - 33 * q^69 + 20 * q^70 - 34 * q^72 + 84 * q^73 + 33 * q^75 + 18 * q^76 - 71 * q^78 + 20 * q^79 - 32 * q^81 - 6 * q^84 - 2 * q^85 + 3 * q^87 + 92 * q^88 - 76 * q^91 + 28 * q^93 + 30 * q^96 + 24 * q^97 + 22 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more