LMFDB - Embedded newform 273.2.t.d.4.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [273,2,Mod(4,273)]

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([0, 4, 1]))

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

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

chi := DirichletCharacter("273.4");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 273 = 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	273.t (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:	$20$
Relative dimension:	$10$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} + 33 x^{18} + 455 x^{16} + 3403 x^{14} + 15006 x^{12} + 39799 x^{10} + 62505 x^{8} + 55993 x^{6} + \cdots + 576 $ x^20 + 33x^18 + 455x^16 + 3403x^14 + 15006x^12 + 39799x^10 + 62505x^8 + 55993x^6 + 27166x^4 + 6435*x^2 + 576
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 3 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			4.3
Root			$-2.04830i$ of defining polynomial
Character	$\chi$	$=$	273.4
Dual form			273.2.t.d.205.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.04830i q^{2} +(0.500000 + 0.866025i) q^{3} -2.19554 q^{4} +(0.341406 - 0.197111i) q^{5} +(1.77388 - 1.02415i) q^{6} +(-0.908042 - 2.48505i) q^{7} +0.400534i q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q-2.04830i q^{2} +(0.500000 + 0.866025i) q^{3} -2.19554 q^{4} +(0.341406 - 0.197111i) q^{5} +(1.77388 - 1.02415i) q^{6} +(-0.908042 - 2.48505i) q^{7} +0.400534i q^{8} +(-0.500000 + 0.866025i) q^{9} +(-0.403742 - 0.699302i) q^{10} +(1.35713 - 0.783540i) q^{11} +(-1.09777 - 1.90140i) q^{12} +(1.46617 - 3.29398i) q^{13} +(-5.09013 + 1.85994i) q^{14} +(0.341406 + 0.197111i) q^{15} -3.57067 q^{16} +6.82735 q^{17} +(1.77388 + 1.02415i) q^{18} +(-6.75047 - 3.89739i) q^{19} +(-0.749571 + 0.432765i) q^{20} +(1.69809 - 2.02891i) q^{21} +(-1.60493 - 2.77982i) q^{22} +4.78346 q^{23} +(-0.346873 + 0.200267i) q^{24} +(-2.42229 + 4.19554i) q^{25} +(-6.74708 - 3.00317i) q^{26} -1.00000 q^{27} +(1.99365 + 5.45603i) q^{28} +(-3.94172 + 6.82725i) q^{29} +(0.403742 - 0.699302i) q^{30} +(5.14505 + 2.97049i) q^{31} +8.11489i q^{32} +(1.35713 + 0.783540i) q^{33} -13.9845i q^{34} +(-0.799840 - 0.669424i) q^{35} +(1.09777 - 1.90140i) q^{36} +1.17388i q^{37} +(-7.98303 + 13.8270i) q^{38} +(3.58576 - 0.377248i) q^{39} +(0.0789495 + 0.136745i) q^{40} +(6.17054 + 3.56256i) q^{41} +(-4.15582 - 3.47821i) q^{42} +(3.65167 + 6.32487i) q^{43} +(-2.97964 + 1.72030i) q^{44} +0.394221i q^{45} -9.79798i q^{46} +(-4.92450 + 2.84316i) q^{47} +(-1.78534 - 3.09229i) q^{48} +(-5.35092 + 4.51305i) q^{49} +(8.59373 + 4.96159i) q^{50} +(3.41367 + 5.91265i) q^{51} +(-3.21905 + 7.23209i) q^{52} +(-0.964998 + 1.67143i) q^{53} +2.04830i q^{54} +(0.308888 - 0.535010i) q^{55} +(0.995346 - 0.363702i) q^{56} -7.79477i q^{57} +(13.9843 + 8.07383i) q^{58} -11.4536i q^{59} +(-0.749571 - 0.432765i) q^{60} +(6.13376 - 10.6240i) q^{61} +(6.08447 - 10.5386i) q^{62} +(2.60613 + 0.456137i) q^{63} +9.48040 q^{64} +(-0.148719 - 1.41358i) q^{65} +(1.60493 - 2.77982i) q^{66} +(-2.41631 + 1.39506i) q^{67} -14.9897 q^{68} +(2.39173 + 4.14260i) q^{69} +(-1.37118 + 1.63831i) q^{70} +(7.66430 - 4.42499i) q^{71} +(-0.346873 - 0.200267i) q^{72} +(-2.23575 - 1.29081i) q^{73} +2.40446 q^{74} -4.84459 q^{75} +(14.8210 + 8.55689i) q^{76} +(-3.17947 - 2.66105i) q^{77} +(-0.772719 - 7.34472i) q^{78} +(1.55611 + 2.69526i) q^{79} +(-1.21905 + 0.703818i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(7.29720 - 12.6391i) q^{82} +3.01153i q^{83} +(-3.72824 + 4.45456i) q^{84} +(2.33089 - 1.34574i) q^{85} +(12.9552 - 7.47972i) q^{86} -7.88343 q^{87} +(0.313834 + 0.543577i) q^{88} +12.4945i q^{89} +0.807484 q^{90} +(-9.51705 - 0.652437i) q^{91} -10.5023 q^{92} +5.94099i q^{93} +(5.82365 + 10.0869i) q^{94} -3.07286 q^{95} +(-7.02770 + 4.05744i) q^{96} +(-9.58078 + 5.53147i) q^{97} +(9.24410 + 10.9603i) q^{98} +1.56708i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + 10 q^{3} - 26 q^{4} + 6 q^{5} + 3 q^{6} + 2 q^{7} - 10 q^{9}+O(q^{10}) $ 20 * q + 10 * q^3 - 26 * q^4 + 6 * q^5 + 3 * q^6 + 2 * q^7 - 10 * q^9	$ 20 q + 10 q^{3} - 26 q^{4} + 6 q^{5} + 3 q^{6} + 2 q^{7} - 10 q^{9} + 2 q^{10} - 12 q^{11} - 13 q^{12} + 8 q^{13} + 2 q^{14} + 6 q^{15} + 42 q^{16} + 16 q^{17} + 3 q^{18} - 9 q^{19} - 5 q^{21} - 9 q^{22} - 36 q^{23} + 3 q^{24} + 12 q^{25} - 16 q^{26} - 20 q^{27} - 2 q^{28} - 3 q^{29} - 2 q^{30} - 18 q^{31} - 12 q^{33} + 18 q^{35} + 13 q^{36} + 9 q^{38} + 7 q^{39} + 5 q^{40} + 21 q^{41} + 16 q^{42} + 16 q^{43} - 6 q^{44} + 21 q^{47} + 21 q^{48} - 24 q^{49} - 54 q^{50} + 8 q^{51} - 41 q^{52} - 26 q^{53} + 17 q^{55} - 6 q^{56} + 42 q^{58} + 4 q^{62} - 7 q^{63} - 46 q^{64} - 50 q^{65} + 9 q^{66} - 3 q^{67} + 6 q^{68} - 18 q^{69} + 15 q^{71} + 3 q^{72} - 9 q^{73} + 12 q^{74} + 24 q^{75} + 75 q^{76} + 20 q^{77} - 32 q^{78} + 3 q^{79} - 24 q^{80} - 10 q^{81} + 15 q^{82} + 41 q^{84} - 78 q^{85} + 3 q^{86} - 6 q^{87} - 22 q^{88} - 4 q^{90} + 4 q^{91} + 142 q^{92} + 36 q^{94} - 84 q^{95} - 24 q^{96} - 15 q^{97} + 81 q^{98}+O(q^{100}) $ 20 * q + 10 * q^3 - 26 * q^4 + 6 * q^5 + 3 * q^6 + 2 * q^7 - 10 * q^9 + 2 * q^10 - 12 * q^11 - 13 * q^12 + 8 * q^13 + 2 * q^14 + 6 * q^15 + 42 * q^16 + 16 * q^17 + 3 * q^18 - 9 * q^19 - 5 * q^21 - 9 * q^22 - 36 * q^23 + 3 * q^24 + 12 * q^25 - 16 * q^26 - 20 * q^27 - 2 * q^28 - 3 * q^29 - 2 * q^30 - 18 * q^31 - 12 * q^33 + 18 * q^35 + 13 * q^36 + 9 * q^38 + 7 * q^39 + 5 * q^40 + 21 * q^41 + 16 * q^42 + 16 * q^43 - 6 * q^44 + 21 * q^47 + 21 * q^48 - 24 * q^49 - 54 * q^50 + 8 * q^51 - 41 * q^52 - 26 * q^53 + 17 * q^55 - 6 * q^56 + 42 * q^58 + 4 * q^62 - 7 * q^63 - 46 * q^64 - 50 * q^65 + 9 * q^66 - 3 * q^67 + 6 * q^68 - 18 * q^69 + 15 * q^71 + 3 * q^72 - 9 * q^73 + 12 * q^74 + 24 * q^75 + 75 * q^76 + 20 * q^77 - 32 * q^78 + 3 * q^79 - 24 * q^80 - 10 * q^81 + 15 * q^82 + 41 * q^84 - 78 * q^85 + 3 * q^86 - 6 * q^87 - 22 * q^88 - 4 * q^90 + 4 * q^91 + 142 * q^92 + 36 * q^94 - 84 * q^95 - 24 * q^96 - 15 * q^97 + 81 * q^98

Display 100 coefficients 10 coefficients

Character values

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

$n$	$92$	$106$	$157$
$\chi(n)$	$1$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{2}{3}\right)$

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 $

$2$		−	2.04830i		−	1.44837i	−0.689606	−	0.724184i	$-0.742216\pi$
$2$		−	2.04830i		−	1.44837i	0.689606	−	0.724184i	$-0.257784\pi$
$3$	0.500000	+	0.866025i	0.288675	+	0.500000i
$3$	0.500000	+	0.866025i	0.288675	+	0.500000i
$4$	−2.19554			−1.09777
$5$	0.341406	−	0.197111i	0.152681	−	0.0881505i	−0.421713	−	0.906729i	$-0.638571\pi$
$5$	0.341406	−	0.197111i	0.152681	−	0.0881505i	0.574394	+	0.818579i	$0.305238\pi$
$6$	1.77388	−	1.02415i	0.724184	−	0.418108i
$7$	−0.908042	−	2.48505i	−0.343207	−	0.939260i
$7$	−0.908042	−	2.48505i	−0.343207	−	0.939260i
$8$			0.400534i			0.141610i
$9$	−0.500000	+	0.866025i	−0.166667	+	0.288675i
$10$	−0.403742	−	0.699302i	−0.127674	−	0.221139i
$11$	1.35713	−	0.783540i	0.409190	−	0.236246i	−0.281251	−	0.959634i	$-0.590749\pi$
$11$	1.35713	−	0.783540i	0.409190	−	0.236246i	0.690442	+	0.723388i	$0.257416\pi$
$12$	−1.09777	−	1.90140i	−0.316900	−	0.548886i
$13$	1.46617	−	3.29398i	0.406643	−	0.913587i
$13$	1.46617	−	3.29398i	0.406643	−	0.913587i
$14$	−5.09013	+	1.85994i	−1.36039	+	0.497091i
$15$	0.341406	+	0.197111i	0.0881505	+	0.0508937i
$16$	−3.57067			−0.892668
$17$	6.82735			1.65587			0.827937	−	0.560821i	$-0.189514\pi$
$17$	6.82735			1.65587			0.827937	+	0.560821i	$0.189514\pi$
$18$	1.77388	+	1.02415i	0.418108	+	0.241395i
$19$	−6.75047	−	3.89739i	−1.54866	−	0.894122i	−0.998244	−	0.0592342i	$-0.981134\pi$
$19$	−6.75047	−	3.89739i	−1.54866	−	0.894122i	−0.550420	−	0.834888i	$-0.685533\pi$
$20$	−0.749571	+	0.432765i	−0.167609	+	0.0967692i
$21$	1.69809	−	2.02891i	0.370554	−	0.442745i
$22$	−1.60493	−	2.77982i	−0.342172	−	0.592659i
$23$	4.78346			0.997421			0.498710	−	0.866769i	$-0.333807\pi$
$23$	4.78346			0.997421			0.498710	+	0.866769i	$0.333807\pi$
$24$	−0.346873	+	0.200267i	−0.0708051	+	0.0408793i
$25$	−2.42229	+	4.19554i	−0.484459	+	0.839108i
$26$	−6.74708	−	3.00317i	−1.32321	−	0.588970i
$27$	−1.00000			−0.192450
$28$	1.99365	+	5.45603i	0.376764	+	1.03109i
$29$	−3.94172	+	6.82725i	−0.731958	+	1.26779i	0.224087	+	0.974569i	$0.428060\pi$
$29$	−3.94172	+	6.82725i	−0.731958	+	1.26779i	−0.956045	+	0.293220i	$0.905273\pi$
$30$	0.403742	−	0.699302i	0.0737129	−	0.127674i
$31$	5.14505	+	2.97049i	0.924078	+	0.533517i	0.884934	−	0.465717i	$-0.154204\pi$
$31$	5.14505	+	2.97049i	0.924078	+	0.533517i	0.0391442	+	0.999234i	$0.487537\pi$
$32$			8.11489i			1.43452i
$33$	1.35713	+	0.783540i	0.236246	+	0.136397i
$34$		−	13.9845i		−	2.39832i
$35$	−0.799840	−	0.669424i	−0.135198	−	0.113153i
$36$	1.09777	−	1.90140i	0.182962	−	0.316900i
$37$			1.17388i			0.192984i	0.995334	+	0.0964922i	$0.0307623\pi$
$37$			1.17388i			0.192984i	−0.995334	+	0.0964922i	$0.969238\pi$
$38$	−7.98303	+	13.8270i	−1.29502	+	2.24304i
$39$	3.58576	−	0.377248i	0.574181	−	0.0604081i
$40$	0.0789495	+	0.136745i	0.0124830	+	0.0216212i
$41$	6.17054	+	3.56256i	0.963676	+	0.556378i	0.897302	−	0.441416i	$-0.145524\pi$
$41$	6.17054	+	3.56256i	0.963676	+	0.556378i	0.0663733	+	0.997795i	$0.478857\pi$
$42$	−4.15582	−	3.47821i	−0.641258	−	0.536699i
$43$	3.65167	+	6.32487i	0.556874	+	0.964534i	0.997755	+	0.0669682i	$0.0213326\pi$
$43$	3.65167	+	6.32487i	0.556874	+	0.964534i	−0.440881	+	0.897565i	$0.645334\pi$
$44$	−2.97964	+	1.72030i	−0.449198	+	0.259345i
$45$			0.394221i			0.0587670i
$46$		−	9.79798i		−	1.44463i
$47$	−4.92450	+	2.84316i	−0.718312	+	0.414717i	−0.814131	−	0.580681i	$-0.802786\pi$
$47$	−4.92450	+	2.84316i	−0.718312	+	0.414717i	0.0958193	+	0.995399i	$0.469453\pi$
$48$	−1.78534	−	3.09229i	−0.257691	−	0.446334i
$49$	−5.35092	+	4.51305i	−0.764417	+	0.644722i
$50$	8.59373	+	4.96159i	1.21534	+	0.701675i
$51$	3.41367	+	5.91265i	0.478010	+	0.827937i
$52$	−3.21905	+	7.23209i	−0.446402	+	1.00291i
$53$	−0.964998	+	1.67143i	−0.132553	+	0.229588i	−0.924660	−	0.380794i	$-0.875651\pi$
$53$	−0.964998	+	1.67143i	−0.132553	+	0.229588i	0.792107	+	0.610382i	$0.208984\pi$
$54$			2.04830i			0.278739i
$55$	0.308888	−	0.535010i	0.0416505	−	0.0721407i
$56$	0.995346	−	0.363702i	0.133009	−	0.0486017i
$57$		−	7.79477i		−	1.03244i
$58$	13.9843	+	8.07383i	1.83623	+	1.06015i
$59$		−	11.4536i		−	1.49113i	−0.666435	−	0.745563i	$-0.732181\pi$
$59$		−	11.4536i		−	1.49113i	0.666435	−	0.745563i	$-0.267819\pi$
$60$	−0.749571	−	0.432765i	−0.0967692	−	0.0558697i
$61$	6.13376	−	10.6240i	0.785348	−	1.36026i	−0.143443	−	0.989659i	$-0.545817\pi$
$61$	6.13376	−	10.6240i	0.785348	−	1.36026i	0.928791	−	0.370604i	$-0.120849\pi$
$62$	6.08447	−	10.5386i	0.772729	−	1.33841i
$63$	2.60613	+	0.456137i	0.328342	+	0.0574678i
$64$	9.48040			1.18505
$65$	−0.148719	−	1.41358i	−0.0184464	−	0.175333i
$66$	1.60493	−	2.77982i	0.197553	−	0.342172i
$67$	−2.41631	+	1.39506i	−0.295199	+	0.170433i	−0.640284	−	0.768138i	$-0.721183\pi$
$67$	−2.41631	+	1.39506i	−0.295199	+	0.170433i	0.345085	+	0.938571i	$0.387850\pi$
$68$	−14.9897			−1.81777
$69$	2.39173	+	4.14260i	0.287931	+	0.498710i
$70$	−1.37118	+	1.63831i	−0.163888	+	0.195816i
$71$	7.66430	−	4.42499i	0.909586	−	0.525150i	0.0292878	−	0.999571i	$-0.490676\pi$
$71$	7.66430	−	4.42499i	0.909586	−	0.525150i	0.880298	+	0.474422i	$0.157343\pi$
$72$	−0.346873	−	0.200267i	−0.0408793	−	0.0236017i
$73$	−2.23575	−	1.29081i	−0.261675	−	0.151078i	0.363423	−	0.931624i	$-0.381608\pi$
$73$	−2.23575	−	1.29081i	−0.261675	−	0.151078i	−0.625098	+	0.780546i	$0.714941\pi$
$74$	2.40446			0.279513
$75$	−4.84459			−0.559405
$76$	14.8210	+	8.55689i	1.70008	+	0.981542i
$77$	−3.17947	−	2.66105i	−0.362334	−	0.303255i
$78$	−0.772719	−	7.34472i	−0.0874932	−	0.831626i
$79$	1.55611	+	2.69526i	0.175076	+	0.303240i	0.940187	−	0.340657i	$-0.110650\pi$
$79$	1.55611	+	2.69526i	0.175076	+	0.303240i	−0.765112	+	0.643898i	$0.777316\pi$
$80$	−1.21905	+	0.703818i	−0.136294	+	0.0786892i
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	7.29720	−	12.6391i	0.805841	−	1.39576i
$83$			3.01153i			0.330559i	0.986247	+	0.165279i	$0.0528526\pi$
$83$			3.01153i			0.330559i	−0.986247	+	0.165279i	$0.947147\pi$
$84$	−3.72824	+	4.45456i	−0.406784	+	0.486033i
$85$	2.33089	−	1.34574i	0.252821	−	0.145966i
$86$	12.9552	−	7.47972i	1.39700	−	0.806559i
$87$	−7.88343			−0.845193
$88$	0.313834	+	0.543577i	0.0334549	+	0.0579455i
$89$			12.4945i			1.32441i	0.749322	+	0.662206i	$0.230380\pi$
$89$			12.4945i			1.32441i	−0.749322	+	0.662206i	$0.769620\pi$
$90$	0.807484			0.0851163
$91$	−9.51705	−	0.652437i	−0.997658	−	0.0683939i
$92$	−10.5023			−1.09494
$93$			5.94099i			0.616052i
$94$	5.82365	+	10.0869i	0.600664	+	1.04038i
$95$	−3.07286			−0.315269
$96$	−7.02770	+	4.05744i	−0.717262	+	0.414111i
$97$	−9.58078	+	5.53147i	−0.972781	+	0.561635i	−0.900083	−	0.435719i	$-0.856494\pi$
$97$	−9.58078	+	5.53147i	−0.972781	+	0.561635i	−0.0726979	+	0.997354i	$0.523161\pi$
$98$	9.24410	+	10.9603i	0.933795	+	1.10716i
$99$			1.56708i			0.157497i
$100$	5.31826	−	9.21149i	0.531826	−	0.921149i
$101$	2.63234	+	4.55935i	0.261928	+	0.453673i	0.966754	−	0.255707i	$-0.0823084\pi$
$101$	2.63234	+	4.55935i	0.261928	+	0.453673i	−0.704826	+	0.709380i	$0.748975\pi$
$102$	12.1109	−	6.99224i	1.19916	−	0.692334i
$103$	1.12396	+	1.94676i	0.110747	+	0.191820i	0.916072	−	0.401015i	$-0.131342\pi$
$103$	1.12396	+	1.94676i	0.110747	+	0.191820i	−0.805325	+	0.592834i	$0.798009\pi$
$104$	1.31935	+	0.587253i	0.129373	+	0.0575848i
$105$	0.179819	−	1.02739i	0.0175485	−	0.100263i
$106$	3.42359	+	1.97661i	0.332528	+	0.191985i
$107$	3.86277			0.373428			0.186714	−	0.982414i	$-0.440216\pi$
$107$	3.86277			0.373428			0.186714	+	0.982414i	$0.440216\pi$
$108$	2.19554			0.211266
$109$	8.85859	+	5.11451i	0.848499	+	0.489881i	0.860144	−	0.510051i	$-0.170373\pi$
$109$	8.85859	+	5.11451i	0.848499	+	0.489881i	−0.0116449	+	0.999932i	$0.503707\pi$
$110$	−1.09586	−	0.632696i	−0.104486	−	0.0603252i
$111$	−1.01661	+	0.586939i	−0.0964922	+	0.0557098i
$112$	3.24232	+	8.87329i	0.306370	+	0.838447i
$113$	−6.18490	−	10.7126i	−0.581826	−	1.00775i	−0.995263	−	0.0972197i	$-0.969005\pi$
$113$	−6.18490	−	10.7126i	−0.581826	−	1.00775i	0.413437	−	0.910533i	$-0.364328\pi$
$114$	−15.9661			−1.49536
$115$	1.63310	−	0.942871i	0.152287	−	0.0879232i
$116$	8.65421	−	14.9895i	0.803524	−	1.39174i
$117$	2.11959	+	2.91674i	0.195956	+	0.269652i
$118$	−23.4604			−2.15970
$119$	−6.19951	−	16.9663i	−0.568308	−	1.55530i
$120$	−0.0789495	+	0.136745i	−0.00720707	+	0.0124830i
$121$	−4.27213	+	7.39955i	−0.388375	+	0.672686i
$122$	−21.7611	−	12.5638i	−1.97016	−	1.13747i
$123$			7.12512i			0.642450i
$124$	−11.2962	−	6.52185i	−1.01443	−	0.585680i
$125$			3.88095i			0.347122i
$126$	0.934306	−	5.33815i	0.0832346	−	0.475561i
$127$	2.15693	−	3.73590i	0.191396	−	0.331508i	−0.754317	−	0.656510i	$-0.772032\pi$
$127$	2.15693	−	3.73590i	0.191396	−	0.331508i	0.945713	+	0.325002i	$0.105365\pi$
$128$		−	3.18896i		−	0.281867i
$129$	−3.65167	+	6.32487i	−0.321511	+	0.556874i
$130$	−2.89545	+	0.304622i	−0.253947	+	0.0267171i
$131$	−5.88647	−	10.1957i	−0.514303	−	0.890800i	−0.999862	−	0.0165956i	$-0.994717\pi$
$131$	−5.88647	−	10.1957i	−0.514303	−	0.890800i	0.485559	−	0.874204i	$-0.338616\pi$
$132$	−2.97964	−	1.72030i	−0.259345	−	0.149733i
$133$	−3.55548	+	20.3142i	−0.308299	+	1.76147i
$134$	2.85750	+	4.94933i	0.246850	+	0.427557i
$135$	−0.341406	+	0.197111i	−0.0293835	+	0.0169646i
$136$			2.73458i			0.234489i
$137$			7.62980i			0.651858i	0.945394	+	0.325929i	$0.105677\pi$
$137$			7.62980i			0.651858i	−0.945394	+	0.325929i	$0.894323\pi$
$138$	8.48530	−	4.89899i	0.722317	−	0.417030i
$139$	−1.70630	−	2.95540i	−0.144726	−	0.250673i	0.784544	−	0.620073i	$-0.212897\pi$
$139$	−1.70630	−	2.95540i	−0.144726	−	0.250673i	−0.929271	+	0.369399i	$0.879564\pi$
$140$	1.75608	+	1.46975i	0.148416	+	0.124217i
$141$	−4.92450	−	2.84316i	−0.414717	−	0.239437i
$142$	−9.06372	−	15.6988i	−0.760610	−	1.31742i
$143$	−0.591178	−	5.61918i	−0.0494368	−	0.469899i
$144$	1.78534	−	3.09229i	0.148778	−	0.257691i
$145$			3.10782i			0.258090i
$146$	−2.64397	+	4.57950i	−0.218817	+	0.379002i
$147$	−6.58388	−	2.37751i	−0.543029	−	0.196093i
$148$		−	2.57730i		−	0.211853i
$149$	7.40958	+	4.27792i	0.607016	+	0.350461i	0.771797	−	0.635869i	$-0.219358\pi$
$149$	7.40958	+	4.27792i	0.607016	+	0.350461i	−0.164781	+	0.986330i	$0.552692\pi$
$150$			9.92319i			0.810225i
$151$	−18.5011	−	10.6816i	−1.50560	−	0.869258i	−0.999979	−	0.00650133i	$-0.997931\pi$
$151$	−18.5011	−	10.6816i	−1.50560	−	0.869258i	−0.505620	−	0.862756i	$-0.668736\pi$
$152$	1.56104	−	2.70379i	0.126617	−	0.219307i
$153$	−3.41367	+	5.91265i	−0.275979	+	0.478010i
$154$	−5.45063	+	6.51251i	−0.439225	+	0.524793i
$155$	2.34206			0.188119
$156$	−7.87270	+	0.828266i	−0.630320	+	0.0663143i
$157$	1.41769	−	2.45552i	0.113144	−	0.195972i	−0.803892	−	0.594775i	$-0.797241\pi$
$157$	1.41769	−	2.45552i	0.113144	−	0.195972i	0.917036	+	0.398804i	$0.130574\pi$
$158$	5.52070	−	3.18738i	0.439204	−	0.253574i
$159$	−1.93000			−0.153059
$160$	1.59953	+	2.77047i	0.126454	+	0.219025i
$161$	−4.34358	−	11.8871i	−0.342322	−	0.936837i
$162$	−1.77388	+	1.02415i	−0.139369	+	0.0804649i
$163$	−8.99214	−	5.19162i	−0.704319	−	0.406639i	0.104635	−	0.994511i	$-0.466633\pi$
$163$	−8.99214	−	5.19162i	−0.704319	−	0.406639i	−0.808954	+	0.587872i	$0.799966\pi$
$164$	−13.5477	−	7.82176i	−1.05790	−	0.610777i
$165$	0.617776			0.0480938
$166$	6.16853			0.478771
$167$	5.99510	+	3.46127i	0.463915	+	0.267841i	0.713689	−	0.700463i	$-0.247023\pi$
$167$	5.99510	+	3.46127i	0.463915	+	0.267841i	−0.249774	+	0.968304i	$0.580356\pi$
$168$	0.812648	+	0.680144i	0.0626971	+	0.0524743i
$169$	−8.70067	−	9.65911i	−0.669282	−	0.743008i
$170$	−2.75649	−	4.77438i	−0.211413	−	0.366178i
$171$	6.75047	−	3.89739i	0.516221	−	0.298041i
$172$	−8.01739	−	13.8865i	−0.611320	−	1.05884i
$173$	4.99792	−	8.65666i	0.379985	−	0.658154i	−0.611074	−	0.791573i	$-0.709262\pi$
$173$	4.99792	−	8.65666i	0.379985	−	0.658154i	0.991060	+	0.133419i	$0.0425957\pi$
$174$			16.1477i			1.22415i
$175$	12.6257	+	2.20979i	0.954410	+	0.167045i
$176$	−4.84587	+	2.79777i	−0.365271	+	0.210890i
$177$	9.91907	−	5.72678i	0.745563	−	0.430451i
$178$	25.5925			1.91824
$179$	−10.7749	−	18.6626i	−0.805351	−	1.39491i	−0.916054	−	0.401055i	$-0.868643\pi$
$179$	−10.7749	−	18.6626i	−0.805351	−	1.39491i	0.110703	−	0.993854i	$-0.464690\pi$
$180$		−	0.865530i		−	0.0645128i
$181$	9.40672			0.699196			0.349598	−	0.936900i	$-0.386318\pi$
$181$	9.40672			0.699196			0.349598	+	0.936900i	$0.386318\pi$
$182$	−1.33639	+	19.4938i	−0.0990596	+	1.44498i
$183$	12.2675			0.906842
$184$			1.91594i			0.141245i
$185$	0.231384	+	0.400769i	0.0170117	+	0.0294651i
$186$	12.1689			0.892270
$187$	9.26560	−	5.34950i	0.677568	−	0.391194i
$188$	10.8120	−	6.24228i	0.788543	−	0.455265i
$189$	0.908042	+	2.48505i	0.0660503	+	0.180761i
$190$			6.29416i			0.456626i
$191$	−5.20842	+	9.02125i	−0.376868	+	0.652755i	−0.990605	−	0.136756i	$-0.956332\pi$
$191$	−5.20842	+	9.02125i	−0.376868	+	0.652755i	0.613737	+	0.789511i	$0.289666\pi$
$192$	4.74020	+	8.21027i	0.342095	+	0.592525i
$193$	−19.4289	+	11.2173i	−1.39852	+	0.807437i	−0.994238	−	0.107196i	$-0.965813\pi$
$193$	−19.4289	+	11.2173i	−1.39852	+	0.807437i	−0.404285	+	0.914633i	$0.632480\pi$
$194$	11.3301	+	19.6243i	0.813455	+	1.40895i
$195$	1.14984	−	0.835586i	0.0823417	−	0.0598376i
$196$	11.7482	−	9.90861i	0.839156	−	0.707758i
$197$	19.9893	+	11.5408i	1.42418	+	0.822248i	0.996652	−	0.0817559i	$-0.0260528\pi$
$197$	19.9893	+	11.5408i	1.42418	+	0.822248i	0.427524	+	0.904004i	$0.359386\pi$
$198$	3.20985			0.228114
$199$	−0.523796			−0.0371309			−0.0185655	−	0.999828i	$-0.505910\pi$
$199$	−0.523796			−0.0371309			−0.0185655	+	0.999828i	$0.505910\pi$
$200$	−1.68046	−	0.970211i	−0.118826	−	0.0686043i
$201$	−2.41631	−	1.39506i	−0.170433	−	0.0983996i
$202$	9.33894	−	5.39184i	0.657085	−	0.379368i
$203$	20.5453	+	3.59592i	1.44200	+	0.252384i
$204$	−7.49487	−	12.9815i	−0.524746	−	0.908886i
$205$	2.80887			0.196180
$206$	3.98754	−	2.30221i	0.277825	−	0.160403i
$207$	−2.39173	+	4.14260i	−0.166237	+	0.287931i
$208$	−5.23523	+	11.7617i	−0.362998	+	0.815530i
$209$	−12.2150			−0.844932
$210$	−2.10441	−	0.368323i	−0.145218	−	0.0254167i
$211$	−4.44244	+	7.69452i	−0.305830	+	0.529713i	−0.977446	−	0.211187i	$-0.932267\pi$
$211$	−4.44244	+	7.69452i	−0.305830	+	0.529713i	0.671616	+	0.740900i	$0.265601\pi$
$212$	2.11870	−	3.66969i	0.145513	−	0.252035i
$213$	7.66430	+	4.42499i	0.525150	+	0.303195i
$214$		−	7.91213i		−	0.540862i
$215$	2.49340	+	1.43956i	0.170048	+	0.0981774i
$216$		−	0.400534i		−	0.0272529i
$217$	2.70990	−	15.4830i	0.183960	−	1.05106i
$218$	10.4761	−	18.1451i	0.709529	−	1.22894i
$219$		−	2.58162i		−	0.174450i
$220$	−0.678178	+	1.17464i	−0.0457227	+	0.0791941i
$221$	10.0101	−	22.4892i	0.673351	−	1.51279i
$222$	1.20223	+	2.08232i	0.0806883	+	0.139756i
$223$	−0.701588	−	0.405062i	−0.0469818	−	0.0271249i	0.476325	−	0.879269i	$-0.341969\pi$
$223$	−0.701588	−	0.405062i	−0.0469818	−	0.0271249i	−0.523307	+	0.852144i	$0.675302\pi$
$224$	20.1659	−	7.36866i	1.34739	−	0.492339i
$225$	−2.42229	−	4.19554i	−0.161486	−	0.279703i
$226$	−21.9426	+	12.6685i	−1.45960	+	0.842699i
$227$		−	0.556650i		−	0.0369462i	−0.999829	−	0.0184731i	$-0.994119\pi$
$227$		−	0.556650i		−	0.0369462i	0.999829	−	0.0184731i	$-0.00588050\pi$
$228$			17.1138i			1.13339i
$229$	14.2673	−	8.23721i	0.942807	−	0.544330i	0.0519681	−	0.998649i	$-0.483451\pi$
$229$	14.2673	−	8.23721i	0.942807	−	0.544330i	0.890839	+	0.454319i	$0.150117\pi$
$230$	−1.93129	−	3.34508i	−0.127345	−	0.220568i
$231$	0.714803	−	4.08402i	0.0470306	−	0.268709i
$232$	−2.73455	−	1.57879i	−0.179532	−	0.103653i
$233$	3.31050	+	5.73395i	0.216878	+	0.375644i	0.953852	−	0.300278i	$-0.0970793\pi$
$233$	3.31050	+	5.73395i	0.216878	+	0.375644i	−0.736974	+	0.675921i	$0.763746\pi$
$234$	5.97436	−	4.34156i	0.390556	−	0.283816i
$235$	−1.12083	+	1.94134i	−0.0731151	+	0.126639i
$236$			25.1468i			1.63692i
$237$	−1.55611	+	2.69526i	−0.101080	+	0.175076i
$238$	−34.7521	+	12.6985i	−2.25264	+	0.823120i
$239$			6.07400i			0.392894i	0.980514	+	0.196447i	$0.0629404\pi$
$239$			6.07400i			0.392894i	−0.980514	+	0.196447i	$0.937060\pi$
$240$	−1.21905	−	0.703818i	−0.0786892	−	0.0454312i
$241$		−	20.6672i		−	1.33129i	−0.746269	−	0.665644i	$-0.768157\pi$
$241$		−	20.6672i		−	1.33129i	0.746269	−	0.665644i	$-0.231843\pi$
$242$	15.1565	+	8.75062i	0.974297	+	0.562511i
$243$	0.500000	−	0.866025i	0.0320750	−	0.0555556i
$244$	−13.4670	+	23.3254i	−0.862133	+	1.49326i
$245$	−0.937264	+	2.59550i	−0.0598796	+	0.165821i
$246$	14.5944			0.930505
$247$	−22.7353	+	16.5217i	−1.44661	+	1.05125i
$248$	−1.18978	+	2.06077i	−0.0755514	+	0.130859i
$249$	−2.60807	+	1.50577i	−0.165279	+	0.0954241i
$250$	7.94935			0.502761
$251$	−7.61211	−	13.1846i	−0.480472	−	0.832202i	0.519277	−	0.854606i	$-0.326201\pi$
$251$	−7.61211	−	13.1846i	−0.480472	−	0.832202i	−0.999749	+	0.0224037i	$0.992868\pi$
$252$	−5.72188	−	1.00147i	−0.360445	−	0.0630866i
$253$	6.49179	−	3.74803i	0.408135	−	0.235637i
$254$	−7.65226	−	4.41804i	−0.480146	−	0.277212i
$255$	2.33089	+	1.34574i	0.145966	+	0.0842736i
$256$	12.4289			0.776803
$257$	−1.70073			−0.106089			−0.0530444	−	0.998592i	$-0.516892\pi$
$257$	−1.70073			−0.106089			−0.0530444	+	0.998592i	$0.516892\pi$
$258$	12.9552	+	7.47972i	0.806559	+	0.465667i
$259$	2.91714	−	1.06593i	0.181262	−	0.0662337i
$260$	0.326520	+	3.10358i	0.0202499	+	0.192476i
$261$	−3.94172	−	6.82725i	−0.243986	−	0.422596i
$262$	−20.8838	+	12.0573i	−1.29021	+	0.744901i
$263$	−4.09154	−	7.08676i	−0.252295	−	0.436988i	0.711862	−	0.702319i	$-0.247852\pi$
$263$	−4.09154	−	7.08676i	−0.252295	−	0.436988i	−0.964157	+	0.265331i	$0.914519\pi$
$264$	−0.313834	+	0.543577i	−0.0193152	+	0.0334549i
$265$			0.760846i			0.0467384i
$266$	41.6097	+	7.28270i	2.55125	+	0.446531i
$267$	−10.8205	+	6.24724i	−0.662206	+	0.382325i
$268$	5.30511	−	3.06291i	0.324061	−	0.187097i
$269$	−11.6605			−0.710952			−0.355476	−	0.934685i	$-0.615681\pi$
$269$	−11.6605			−0.710952			−0.355476	+	0.934685i	$0.615681\pi$
$270$	0.403742	+	0.699302i	0.0245710	+	0.0425582i
$271$			5.64905i			0.343155i	0.985171	+	0.171578i	$0.0548864\pi$
$271$			5.64905i			0.343155i	−0.985171	+	0.171578i	$0.945114\pi$
$272$	−24.3782			−1.47815
$273$	−4.19350	−	8.56823i	−0.253802	−	0.518573i
$274$	15.6281			0.944131
$275$			7.59186i			0.457806i
$276$	−5.25115	−	9.09526i	−0.316082	−	0.547470i
$277$	−23.9714			−1.44030			−0.720152	−	0.693816i	$-0.755928\pi$
$277$	−23.9714			−1.44030			−0.720152	+	0.693816i	$0.755928\pi$
$278$	−6.05355	+	3.49502i	−0.363068	+	0.209617i
$279$	−5.14505	+	2.97049i	−0.308026	+	0.177839i
$280$	0.268127	−	0.320363i	0.0160237	−	0.0191454i
$281$			20.2883i			1.21030i	0.796113	+	0.605148i	$0.206886\pi$
$281$			20.2883i			1.21030i	−0.796113	+	0.605148i	$0.793114\pi$
$282$	−5.82365	+	10.0869i	−0.346793	+	0.600664i
$283$	1.05407	+	1.82570i	0.0626578	+	0.108527i	0.895653	−	0.444754i	$-0.146709\pi$
$283$	1.05407	+	1.82570i	0.0626578	+	0.108527i	−0.832995	+	0.553281i	$0.813376\pi$
$284$	−16.8273	+	9.71526i	−0.998518	+	0.576495i
$285$	−1.53643	−	2.66118i	−0.0910104	−	0.157635i
$286$	−11.5098	+	1.21091i	−0.680587	+	0.0716028i
$287$	3.25003	−	18.5690i	0.191843	−	1.09609i
$288$	−7.02770	−	4.05744i	−0.414111	−	0.239087i
$289$	29.6126			1.74192
$290$	6.36575			0.373810
$291$	−9.58078	−	5.53147i	−0.561635	−	0.324260i
$292$	4.90869	+	2.83404i	0.287260	+	0.165849i
$293$	−2.59210	+	1.49655i	−0.151432	+	0.0874294i	−0.573801	−	0.818994i	$-0.694532\pi$
$293$	−2.59210	+	1.49655i	−0.151432	+	0.0874294i	0.422369	+	0.906424i	$0.361199\pi$
$294$	−4.86985	+	13.4858i	−0.284016	+	0.786507i
$295$	−2.25762	−	3.91031i	−0.131444	−	0.227667i
$296$	−0.470178			−0.0273285
$297$	−1.35713	+	0.783540i	−0.0787487	+	0.0454656i
$298$	8.76248	−	15.1771i	0.507597	−	0.879183i
$299$	7.01339	−	15.7567i	0.405595	−	0.911231i
$300$	10.6365			0.614099
$301$	12.4017	−	14.8178i	0.714824	−	0.854084i
$302$	−21.8792	+	37.8959i	−1.25901	+	2.18066i
$303$	−2.63234	+	4.55935i	−0.151224	+	0.261928i
$304$	24.1037	+	13.9163i	1.38244	+	0.798154i
$305$		−	4.83612i		−	0.276915i
$306$	12.1109	+	6.99224i	0.692334	+	0.399719i
$307$		−	1.91377i		−	0.109225i	−0.998508	−	0.0546124i	$-0.982608\pi$
$307$		−	1.91377i		−	0.109225i	0.998508	−	0.0546124i	$-0.0173923\pi$
$308$	6.98066	+	5.84245i	0.397760	+	0.332904i
$309$	−1.12396	+	1.94676i	−0.0639398	+	0.110747i
$310$		−	4.79726i		−	0.272466i
$311$	−3.37549	+	5.84652i	−0.191406	+	0.331526i	−0.945717	−	0.324993i	$-0.894638\pi$
$311$	−3.37549	+	5.84652i	−0.191406	+	0.331526i	0.754310	+	0.656518i	$0.227971\pi$
$312$	0.151101	+	1.43622i	0.00855440	+	0.0813099i
$313$	5.51032	+	9.54416i	0.311462	+	0.539468i	0.978679	−	0.205396i	$-0.0658481\pi$
$313$	5.51032	+	9.54416i	0.311462	+	0.539468i	−0.667217	+	0.744863i	$0.732515\pi$
$314$	−5.02964	−	2.90386i	−0.283839	−	0.163875i
$315$	0.979658	−	0.357969i	0.0551975	−	0.0201693i
$316$	−3.41650	−	5.91756i	−0.192193	−	0.332889i
$317$	10.7991	−	6.23485i	0.606536	−	0.350184i	−0.165072	−	0.986281i	$-0.552786\pi$
$317$	10.7991	−	6.23485i	0.606536	−	0.350184i	0.771609	+	0.636098i	$0.219452\pi$
$318$			3.95322i			0.221685i
$319$			12.3540i			0.691690i
$320$	3.23666	−	1.86869i	0.180935	−	0.104463i
$321$	1.93139	+	3.34526i	0.107799	+	0.186714i
$322$	−24.3484	+	8.89697i	−1.35689	+	0.495809i
$323$	−46.0878	−	26.6088i	−2.56439	−	1.48055i
$324$	1.09777	+	1.90140i	0.0609873	+	0.105633i
$325$	10.2685	+	14.1304i	0.569596	+	0.783813i
$326$	−10.6340	+	18.4186i	−0.588963	+	1.02011i
$327$			10.2290i			0.565666i
$328$	−1.42693	+	2.47151i	−0.0787888	+	0.136466i
$329$	11.5370	+	9.65590i	0.636057	+	0.532347i
$330$		−	1.26539i		−	0.0696576i
$331$	−16.5449	−	9.55222i	−0.909392	−	0.525038i	−0.0291563	−	0.999575i	$-0.509282\pi$
$331$	−16.5449	−	9.55222i	−0.909392	−	0.525038i	−0.880235	+	0.474537i	$0.842615\pi$
$332$		−	6.61196i		−	0.362878i
$333$	−1.01661	−	0.586939i	−0.0557098	−	0.0321641i
$334$	7.08973	−	12.2798i	0.387933	−	0.671919i
$335$	−0.549961	+	0.952560i	−0.0300476	+	0.0520439i
$336$	−6.06334	+	7.24458i	−0.330782	+	0.395224i
$337$	35.4527			1.93123			0.965616	−	0.259972i	$-0.0837134\pi$
$337$	35.4527			1.93123			0.965616	+	0.259972i	$0.0837134\pi$
$338$	−19.7848	+	17.8216i	−1.07615	+	0.969367i
$339$	6.18490	−	10.7126i	0.335917	−	0.581826i
$340$	−5.11758	+	2.95464i	−0.277540	+	0.160238i
$341$	9.31001			0.504165
$342$	−7.98303	−	13.8270i	−0.431673	−	0.747679i
$343$	16.0740	+	9.19925i	0.867915	+	0.496713i
$344$	−2.53333	+	1.46262i	−0.136588	+	0.0788590i
$345$	1.63310	+	0.942871i	0.0879232	+	0.0507625i
$346$	−17.7315	−	10.2373i	−0.953249	−	0.550359i
$347$	18.0485			0.968896			0.484448	−	0.874820i	$-0.339021\pi$
$347$	18.0485			0.968896			0.484448	+	0.874820i	$0.339021\pi$
$348$	17.3084			0.927829
$349$	−12.1606	−	7.02095i	−0.650945	−	0.375823i	0.137873	−	0.990450i	$-0.455973\pi$
$349$	−12.1606	−	7.02095i	−0.650945	−	0.375823i	−0.788818	+	0.614627i	$0.789307\pi$
$350$	4.52633	−	25.8612i	0.241942	−	1.38234i
$351$	−1.46617	+	3.29398i	−0.0782586	+	0.175820i
$352$	6.35834	+	11.0130i	0.338901	+	0.586993i
$353$	−0.972671	+	0.561572i	−0.0517700	+	0.0298894i	−0.525662	−	0.850694i	$-0.676182\pi$
$353$	−0.972671	+	0.561572i	−0.0517700	+	0.0298894i	0.473892	+	0.880583i	$0.342849\pi$
$354$	−11.7302	−	20.3173i	−0.623452	−	1.07985i
$355$	1.74442	−	3.02143i	0.0925844	−	0.160361i
$356$		−	27.4322i		−	1.45390i
$357$	11.5935	−	13.8521i	0.613591	−	0.733130i
$358$	−38.2267	+	22.0702i	−2.02034	+	1.16645i
$359$	6.38193	−	3.68461i	0.336826	−	0.194466i	−0.322042	−	0.946725i	$-0.604369\pi$
$359$	6.38193	−	3.68461i	0.336826	−	0.194466i	0.658867	+	0.752259i	$0.271036\pi$
$360$	−0.157899			−0.00832201
$361$	20.8792	+	36.1639i	1.09891	+	1.90336i
$362$		−	19.2678i		−	1.01269i
$363$	−8.54426			−0.448457
$364$	20.8951	+	1.43245i	1.09520	+	0.0750810i
$365$	−1.01773			−0.0532705
$366$		−	25.1276i		−	1.31344i
$367$	−9.88689	−	17.1246i	−0.516091	−	0.893896i	−0.999825	−	0.0186814i	$-0.994053\pi$
$367$	−9.88689	−	17.1246i	−0.516091	−	0.893896i	0.483734	−	0.875215i	$-0.339280\pi$
$368$	−17.0802			−0.890366
$369$	−6.17054	+	3.56256i	−0.321225	+	0.185459i
$370$	0.820895	−	0.473944i	0.0426763	−	0.0246392i
$371$	5.02983	+	0.880342i	0.261136	+	0.0457051i
$372$		−	13.0437i		−	0.676285i
$373$	−4.65822	+	8.06828i	−0.241194	+	0.417760i	−0.961055	−	0.276359i	$-0.910872\pi$
$373$	−4.65822	+	8.06828i	−0.241194	+	0.417760i	0.719861	+	0.694118i	$0.244206\pi$
$374$	−10.9574	−	18.9788i	−0.566593	−	0.981368i
$375$	−3.36100	+	1.94047i	−0.173561	+	0.100206i
$376$	−1.13878	−	1.97243i	−0.0587282	−	0.101720i
$377$	16.7096	+	22.9939i	0.860590	+	1.18425i
$378$	5.09013	−	1.85994i	0.261808	−	0.0956652i
$379$	−10.8308	−	6.25315i	−0.556340	−	0.321203i	0.195335	−	0.980736i	$-0.437420\pi$
$379$	−10.8308	−	6.25315i	−0.556340	−	0.321203i	−0.751675	+	0.659534i	$0.770754\pi$
$380$	6.74661			0.346094
$381$	4.31385			0.221005
$382$	18.4782	+	10.6684i	0.945429	+	0.545844i
$383$	−30.1594	−	17.4126i	−1.54108	−	0.889740i	−0.998771	−	0.0495581i	$-0.984219\pi$
$383$	−30.1594	−	17.4126i	−1.54108	−	0.889740i	−0.542304	−	0.840182i	$-0.682448\pi$
$384$	2.76172	−	1.59448i	0.140933	−	0.0813679i
$385$	−1.61001	−	0.281790i	−0.0820536	−	0.0143614i
$386$	22.9764	+	39.7963i	1.16947	+	2.02558i
$387$	−7.30333			−0.371249
$388$	21.0350	−	12.1446i	1.06789	−	0.616547i
$389$	−7.22866	+	12.5204i	−0.366508	+	0.634810i	−0.989017	−	0.147802i	$-0.952780\pi$
$389$	−7.22866	+	12.5204i	−0.366508	+	0.634810i	0.622509	+	0.782613i	$0.286113\pi$
$390$	−1.71153	−	2.35522i	−0.0866669	−	0.119261i
$391$	32.6583			1.65160
$392$	−1.80763	−	2.14323i	−0.0912992	−	0.108249i
$393$	5.88647	−	10.1957i	0.296933	−	0.514303i
$394$	23.6391	−	40.9441i	1.19092	−	2.06273i
$395$	1.06253	+	0.613451i	0.0534616	+	0.0308660i
$396$		−	3.44059i		−	0.172896i
$397$	−3.30733	−	1.90949i	−0.165990	−	0.0958346i	0.414703	−	0.909957i	$-0.363885\pi$
$397$	−3.30733	−	1.90949i	−0.165990	−	0.0958346i	−0.580694	+	0.814122i	$0.697219\pi$
$398$			1.07289i			0.0537793i
$399$	−19.3704	+	7.07798i	−0.969732	+	0.354342i
$400$	8.64922	−	14.9809i	0.432461	−	0.749045i
$401$		−	12.6222i		−	0.630323i	−0.949038	−	0.315161i	$-0.897941\pi$
$401$		−	12.6222i		−	0.630323i	0.949038	−	0.315161i	$-0.102059\pi$
$402$	−2.85750	+	4.94933i	−0.142519	+	0.246850i
$403$	17.3283	−	12.5924i	0.863184	−	0.627274i
$404$	−5.77943	−	10.0103i	−0.287537	−	0.498029i
$405$	−0.341406	−	0.197111i	−0.0169646	−	0.00979450i
$406$	7.36554	−	42.0830i	0.365545	−	2.08854i
$407$	0.919781	+	1.59311i	0.0455918	+	0.0789674i
$408$	−2.36822	+	1.36729i	−0.117244	+	0.0676910i
$409$		−	31.5443i		−	1.55976i	−0.625927	−	0.779882i	$-0.715279\pi$
$409$		−	31.5443i		−	1.55976i	0.625927	−	0.779882i	$-0.284721\pi$
$410$		−	5.75342i		−	0.284141i
$411$	−6.60760	+	3.81490i	−0.325929	+	0.188175i
$412$	−2.46770	−	4.27419i	−0.121575	−	0.210574i
$413$	−28.4626	+	10.4003i	−1.40055	+	0.511766i
$414$	8.48530	+	4.89899i	0.417030	+	0.240772i
$415$	0.593605	+	1.02815i	0.0291389	+	0.0504701i
$416$	26.7303	+	11.8978i	1.31056	+	0.583340i
$417$	1.70630	−	2.95540i	0.0835578	−	0.144726i
$418$			25.0201i			1.22377i
$419$	5.19320	−	8.99489i	0.253705	−	0.439429i	−0.710838	−	0.703356i	$-0.751684\pi$
$419$	5.19320	−	8.99489i	0.253705	−	0.439429i	0.964543	+	0.263926i	$0.0850176\pi$
$420$	−0.394800	+	2.25569i	−0.0192643	+	0.110066i
$421$			0.368085i			0.0179394i	0.999960	+	0.00896969i	$0.00285518\pi$
$421$			0.368085i			0.0179394i	−0.999960	+	0.00896969i	$0.997145\pi$
$422$	15.7607	+	9.09945i	0.767220	+	0.442954i
$423$		−	5.68632i		−	0.276478i
$424$	−0.669463	−	0.386515i	−0.0325120	−	0.0187708i
$425$	−16.5378	+	28.6444i	−0.802203	+	1.38946i
$426$	9.06372	−	15.6988i	0.439138	−	0.760610i
$427$	−31.9708	−	5.59567i	−1.54718	−	0.270793i
$428$	−8.48089			−0.409939
$429$	4.57076	−	3.32156i	0.220678	−	0.160367i
$430$	2.94866	−	5.10723i	0.142197	−	0.246293i
$431$	−13.3306	+	7.69641i	−0.642111	+	0.370723i	−0.785427	−	0.618954i	$-0.787557\pi$
$431$	−13.3306	+	7.69641i	−0.642111	+	0.370723i	0.143316	+	0.989677i	$0.454223\pi$
$432$	3.57067			0.171794
$433$	9.13817	+	15.8278i	0.439152	+	0.760634i	0.997624	−	0.0688892i	$-0.0219455\pi$
$433$	9.13817	+	15.8278i	0.439152	+	0.760634i	−0.558472	+	0.829523i	$0.688612\pi$
$434$	−31.7139	−	5.55070i	−1.52232	−	0.266442i
$435$	−2.69145	+	1.55391i	−0.129045	+	0.0745042i
$436$	−19.4494	−	11.2291i	−0.931459	−	0.537778i
$437$	−32.2906	−	18.6430i	−1.54467	−	0.891816i
$438$	−5.28795			−0.252668
$439$	29.4344			1.40483			0.702414	−	0.711769i	$-0.252106\pi$
$439$	29.4344			1.40483			0.702414	+	0.711769i	$0.252106\pi$
$440$	0.214290	+	0.123720i	0.0102159	+	0.00589813i
$441$	−1.23296	−	6.89056i	−0.0587123	−	0.328122i
$442$	−46.0646	−	20.5037i	−2.19107	−	0.975260i
$443$	0.974301	+	1.68754i	0.0462904	+	0.0801773i	0.888242	−	0.459375i	$-0.151927\pi$
$443$	0.974301	+	1.68754i	0.0462904	+	0.0801773i	−0.841952	+	0.539553i	$0.818593\pi$
$444$	2.23201	−	1.28865i	0.105926	−	0.0611567i
$445$	2.46279	+	4.26568i	0.116748	+	0.202213i
$446$	−0.829689	+	1.43706i	−0.0392869	+	0.0680469i
$447$			8.55584i			0.404677i
$448$	−8.60860	−	23.5592i	−0.406718	−	1.11307i
$449$	−18.7184	+	10.8071i	−0.883376	+	0.510017i	−0.871770	−	0.489915i	$-0.837028\pi$
$449$	−18.7184	+	10.8071i	−0.883376	+	0.510017i	−0.0116058	+	0.999933i	$0.503694\pi$
$450$	−8.59373	+	4.96159i	−0.405112	+	0.233892i
$451$	11.1656			0.525769
$452$	13.5792	+	23.5199i	0.638713	+	1.10628i
$453$		−	21.3632i		−	1.00373i
$454$	−1.14019			−0.0535117
$455$	−3.37778	+	1.65317i	−0.158353	+	0.0775017i
$456$	3.12207			0.146204
$457$		−	19.1677i		−	0.896626i	−0.893877	−	0.448313i	$-0.852025\pi$
$457$		−	19.1677i		−	0.896626i	0.893877	−	0.448313i	$-0.147975\pi$
$458$	−16.8723	−	29.2237i	−0.788391	−	1.36553i
$459$	−6.82735			−0.318673
$460$	−3.58555	+	2.07012i	−0.167177	+	0.0965196i
$461$	6.88906	−	3.97740i	0.320856	−	0.185246i	−0.330918	−	0.943659i	$-0.607358\pi$
$461$	6.88906	−	3.97740i	0.320856	−	0.185246i	0.651774	+	0.758413i	$0.274025\pi$
$462$	−8.36531	−	1.46413i	−0.389190	−	0.0681176i
$463$			9.39286i			0.436523i	0.975890	+	0.218262i	$0.0700386\pi$
$463$			9.39286i			0.436523i	−0.975890	+	0.218262i	$0.929961\pi$
$464$	14.0746	−	24.3779i	0.653396	−	1.13172i
$465$	1.17103	+	2.02829i	0.0543053	+	0.0940596i
$466$	11.7449	−	6.78090i	0.544070	−	0.314119i
$467$	16.4836	+	28.5505i	0.762771	+	1.32116i	0.941417	+	0.337245i	$0.109495\pi$
$467$	16.4836	+	28.5505i	0.762771	+	1.32116i	−0.178645	+	0.983914i	$0.557171\pi$
$468$	−4.65365	−	6.40382i	−0.215115	−	0.296017i
$469$	5.66089	+	4.73787i	0.261395	+	0.218774i
$470$	3.97645	+	2.29581i	0.183420	+	0.105898i
$471$	2.83539			0.130648
$472$	4.58754			0.211159
$473$	9.91158	+	5.72245i	0.455735	+	0.263119i
$474$	5.52070	+	3.18738i	0.253574	+	0.146401i
$475$	32.7033	−	18.8812i	1.50053	−	0.866331i
$476$	13.6113	+	37.2502i	0.623873	+	1.70736i
$477$	−0.964998	−	1.67143i	−0.0441842	−	0.0765293i
$478$	12.4414			0.569056
$479$	−0.982107	+	0.567019i	−0.0448736	+	0.0259078i	−0.522269	−	0.852781i	$-0.674914\pi$
$479$	−0.982107	+	0.567019i	−0.0448736	+	0.0259078i	0.477395	+	0.878689i	$0.341581\pi$
$480$	−1.59953	+	2.77047i	−0.0730083	+	0.126454i
$481$	3.86674	+	1.72111i	0.176308	+	0.0784758i
$482$	−42.3326			−1.92820
$483$	8.12277	−	9.70522i	0.369599	−	0.441603i
$484$	9.37965	−	16.2460i	0.426348	−	0.738456i
$485$	−2.18062	+	3.77695i	−0.0990169	+	0.171502i
$486$	−1.77388	−	1.02415i	−0.0804649	−	0.0464565i
$487$			40.6679i			1.84284i	0.388569	+	0.921420i	$0.372970\pi$
$487$			40.6679i			1.84284i	−0.388569	+	0.921420i	$0.627030\pi$
$488$	4.25527	+	2.45678i	0.192627	+	0.111213i
$489$		−	10.3832i		−	0.469546i
$490$	5.31638	+	1.91980i	0.240170	+	0.0867277i
$491$	−14.7283	+	25.5102i	−0.664679	+	1.15126i	0.314693	+	0.949194i	$0.398098\pi$
$491$	−14.7283	+	25.5102i	−0.664679	+	1.15126i	−0.979372	+	0.202065i	$0.935235\pi$
$492$		−	15.6435i		−	0.705264i
$493$	−26.9115	+	46.6120i	−1.21203	+	2.09930i
$494$	33.8415	+	46.5688i	1.52260	+	2.09523i
$495$	0.308888	+	0.535010i	0.0138835	+	0.0240469i
$496$	−18.3713	−	10.6067i	−0.824895	−	0.476253i
$497$	−17.9558	−	15.0281i	−0.805428	−	0.674102i
$498$	3.08427	+	5.34211i	0.138209	+	0.239386i
$499$	−16.4691	+	9.50845i	−0.737259	+	0.425657i	−0.821072	−	0.570825i	$-0.806624\pi$
$499$	−16.4691	+	9.50845i	−0.737259	+	0.425657i	0.0838128	+	0.996482i	$0.473290\pi$
$500$		−	8.52079i		−	0.381061i
$501$			6.92254i			0.309276i
$502$	−27.0060	+	15.5919i	−1.20534	+	0.695901i
$503$	−4.49406	−	7.78393i	−0.200380	−	0.347068i	0.748271	−	0.663393i	$-0.230884\pi$
$503$	−4.49406	−	7.78393i	−0.200380	−	0.347068i	−0.948651	+	0.316325i	$0.897551\pi$
$504$	−0.182698	+	1.04385i	−0.00813802	+	0.0464966i
$505$	1.79739	+	1.03773i	0.0799830	+	0.0461782i
$506$	−7.67711	−	13.2971i	−0.341289	−	0.591130i
$507$	4.01470	−	12.3646i	0.178299	−	0.549129i
$508$	−4.73563	+	8.20234i	−0.210109	+	0.363920i
$509$			2.10006i			0.0930835i	0.998916	+	0.0465418i	$0.0148201\pi$
$509$			2.10006i			0.0930835i	−0.998916	+	0.0465418i	$0.985180\pi$
$510$	2.75649	−	4.77438i	0.122059	−	0.211413i
$511$	−1.17757	+	6.72806i	−0.0520928	+	0.297632i
$512$		−	31.8360i		−	1.40696i
$513$	6.75047	+	3.89739i	0.298041	+	0.172074i
$514$			3.48362i			0.153656i
$515$	0.767452	+	0.443089i	0.0338180	+	0.0195248i
$516$	8.01739	−	13.8865i	0.352946	−	0.611320i
$517$	−4.45546	+	7.71708i	−0.195951	+	0.339397i
$518$	−2.18335	−	5.97519i	−0.0959308	−	0.262535i
$519$	9.99585			0.438769
$520$	0.566188	−	0.0595671i	0.0248290	−	0.00261219i
$521$	−15.5547	+	26.9416i	−0.681464	+	1.18033i	0.293070	+	0.956091i	$0.405323\pi$
$521$	−15.5547	+	26.9416i	−0.681464	+	1.18033i	−0.974534	+	0.224240i	$0.928010\pi$
$522$	−13.9843	+	8.07383i	−0.612075	+	0.353382i
$523$	−43.2417			−1.89083			−0.945413	−	0.325875i	$-0.894341\pi$
$523$	−43.2417			−1.89083			−0.945413	+	0.325875i	$0.894341\pi$
$524$	12.9240	+	22.3850i	0.564588	+	0.977895i
$525$	4.39909	+	12.0390i	0.191992	+	0.525427i
$526$	−14.5158	+	8.38072i	−0.632920	+	0.365417i
$527$	35.1270	+	20.2806i	1.53016	+	0.883437i
$528$	−4.84587	−	2.79777i	−0.210890	−	0.121757i
$529$	−0.118486			−0.00515158
$530$	1.55844			0.0676944
$531$	9.91907	+	5.72678i	0.430451	+	0.248521i
$532$	7.80622	−	44.6008i	0.338442	−	1.93369i
$533$	20.7821	−	15.1023i	0.900172	−	0.654154i
$534$	12.7962	+	22.1637i	0.553747	+	0.959119i
$535$	1.31877	−	0.761393i	0.0570155	−	0.0329179i
$536$	−0.558767	−	0.967813i	−0.0241351	−	0.0418032i
$537$	10.7749	−	18.6626i	0.464970	−	0.805351i
$538$			23.8842i			1.02972i
$539$	−3.72574	+	10.3175i	−0.160479	+	0.444405i
$540$	0.749571	−	0.432765i	0.0322564	−	0.0186232i
$541$	−14.8267	+	8.56020i	−0.637450	+	0.368032i	−0.783631	−	0.621226i	$-0.786635\pi$
$541$	−14.8267	+	8.56020i	−0.637450	+	0.368032i	0.146182	+	0.989258i	$0.453302\pi$
$542$	11.5710			0.497015
$543$	4.70336	+	8.14646i	0.201841	+	0.349598i
$544$			55.4031i			2.37539i
$545$	4.03250			0.172733
$546$	−17.5503	+	8.58956i	−0.751085	+	0.367599i
$547$	−5.89728			−0.252149			−0.126075	−	0.992021i	$-0.540238\pi$
$547$	−5.89728			−0.252149			−0.126075	+	0.992021i	$0.540238\pi$
$548$		−	16.7516i		−	0.715592i
$549$	6.13376	+	10.6240i	0.261783	+	0.453421i
$550$	15.5504			0.663073
$551$	53.2169	−	30.7248i	2.26712	−	1.30892i
$552$	−1.65925	+	0.957970i	−0.0706225	+	0.0407739i
$553$	5.28483	−	6.31441i	0.224734	−	0.268516i
$554$			49.1008i			2.08609i
$555$	−0.231384	+	0.400769i	−0.00982170	+	0.0170117i
$556$	3.74625	+	6.48870i	0.158877	+	0.275182i
$557$	−32.4672	+	18.7450i	−1.37568	+	0.794249i	−0.991636	−	0.129066i	$-0.958802\pi$
$557$	−32.4672	+	18.7450i	−1.37568	+	0.794249i	−0.384044	+	0.923315i	$0.625469\pi$
$558$	6.08447	+	10.5386i	0.257576	+	0.446135i
$559$	26.1880	−	2.75517i	1.10763	−	0.116531i
$560$	2.85597	+	2.39030i	0.120687	+	0.101008i
$561$	9.26560	+	5.34950i	0.391194	+	0.225856i
$562$	41.5565			1.75296
$563$	37.4708			1.57920			0.789602	−	0.613619i	$-0.210287\pi$
$563$	37.4708			1.57920			0.789602	+	0.613619i	$0.210287\pi$
$564$	10.8120	+	6.24228i	0.455265	+	0.262848i
$565$	−4.22312	−	2.43822i	−0.177668	−	0.102577i
$566$	3.73958	−	2.15905i	0.157186	−	0.0907516i
$567$	−1.69809	+	2.02891i	−0.0713132	+	0.0852062i
$568$	1.77236	+	3.06981i	0.0743665	+	0.128807i
$569$	−43.6619			−1.83040			−0.915200	−	0.403000i	$-0.867967\pi$
$569$	−43.6619			−1.83040			−0.915200	+	0.403000i	$0.867967\pi$
$570$	−5.45090	+	3.14708i	−0.228313	+	0.131817i
$571$	5.02695	−	8.70694i	0.210371	−	0.364374i	−0.741459	−	0.670998i	$-0.765866\pi$
$571$	5.02695	−	8.70694i	0.210371	−	0.364374i	0.951831	+	0.306624i	$0.0991993\pi$
$572$	1.29796	+	12.3371i	0.0542704	+	0.515842i
$573$	−10.4168			−0.435170
$574$	−38.0350	−	6.65704i	−1.58755	−	0.277860i
$575$	−11.5870	+	20.0692i	−0.483209	+	0.836943i
$576$	−4.74020	+	8.21027i	−0.197508	+	0.342095i
$577$	−18.7295	−	10.8135i	−0.779719	−	0.450171i	0.0566114	−	0.998396i	$-0.481970\pi$
$577$	−18.7295	−	10.8135i	−0.779719	−	0.450171i	−0.836331	+	0.548225i	$0.815304\pi$
$578$		−	60.6557i		−	2.52294i
$579$	−19.4289	−	11.2173i	−0.807437	−	0.466174i
$580$		−	6.82335i		−	0.283324i
$581$	7.48381	−	2.73460i	0.310481	−	0.113450i
$582$	−11.3301	+	19.6243i	−0.469648	+	0.813455i
$583$			3.02446i			0.125260i
$584$	0.517014	−	0.895495i	0.0213942	−	0.0370558i
$585$	1.29856	+	0.577997i	0.0536888	+	0.0238972i
$586$	3.06539	+	5.30941i	0.126630	+	0.219330i
$587$	10.4783	+	6.04967i	0.432487	+	0.249697i	0.700406	−	0.713745i	$-0.253002\pi$
$587$	10.4783	+	6.04967i	0.432487	+	0.249697i	−0.267918	+	0.963442i	$0.586336\pi$
$588$	14.4552	+	5.21992i	0.596122	+	0.215266i
$589$	−23.1543	−	40.1045i	−0.954058	−	1.65248i
$590$	−8.00950	+	4.62428i	−0.329746	+	0.190379i
$591$			23.0816i			0.949451i
$592$		−	4.19154i		−	0.172271i
$593$	11.4586	−	6.61565i	0.470550	−	0.271672i	−0.245920	−	0.969290i	$-0.579090\pi$
$593$	11.4586	−	6.61565i	0.470550	−	0.271672i	0.716470	+	0.697618i	$0.245757\pi$
$594$	1.60493	+	2.77982i	0.0658510	+	0.114057i
$595$	−5.46078	−	4.57039i	−0.223870	−	0.187368i
$596$	−16.2681	−	9.39237i	−0.666366	−	0.384726i
$597$	−0.261898	−	0.453621i	−0.0107188	−	0.0185655i
$598$	−32.2744	−	14.3655i	−1.31980	−	0.587451i
$599$	3.64418	−	6.31190i	0.148897	−	0.257897i	−0.781923	−	0.623375i	$-0.785761\pi$
$599$	3.64418	−	6.31190i	0.148897	−	0.257897i	0.930820	+	0.365478i	$0.119094\pi$
$600$		−	1.94042i		−	0.0792174i
$601$	8.80780	−	15.2556i	0.359278	−	0.622287i	−0.628563	−	0.777759i	$-0.716356\pi$
$601$	8.80780	−	15.2556i	0.359278	−	0.622287i	0.987840	+	0.155472i	$0.0496897\pi$
$602$	−30.3514	−	25.4025i	−1.23703	−	1.03533i
$603$		−	2.79011i		−	0.113622i
$604$	40.6200	+	23.4520i	1.65280	+	0.954247i
$605$			3.36833i			0.136942i
$606$	9.33894	+	5.39184i	0.379368	+	0.219028i
$607$	−15.4983	+	26.8438i	−0.629055	+	1.08956i	0.358686	+	0.933458i	$0.383225\pi$
$607$	−15.4983	+	26.8438i	−0.629055	+	1.08956i	−0.987742	+	0.156097i	$0.950109\pi$
$608$	31.6269	−	54.7793i	1.28264	−	2.22160i
$609$	7.15849	+	19.5907i	0.290076	+	0.793855i
$610$	−9.90584			−0.401076
$611$	2.14515	+	20.3898i	0.0867837	+	0.824882i
$612$	7.49487	−	12.9815i	0.302962	−	0.524746i
$613$	33.5927	−	19.3947i	1.35679	−	0.783346i	0.367604	−	0.929982i	$-0.380178\pi$
$613$	33.5927	−	19.3947i	1.35679	−	0.783346i	0.989190	+	0.146636i	$0.0468447\pi$
$614$	−3.91999			−0.158198
$615$	1.40444	+	2.43256i	0.0566324	+	0.0980901i
$616$	1.06584	−	1.27348i	0.0429439	−	0.0513101i
$617$	−20.2564	+	11.6951i	−0.815493	+	0.470825i	−0.848860	−	0.528618i	$-0.822710\pi$
$617$	−20.2564	+	11.6951i	−0.815493	+	0.470825i	0.0333668	+	0.999443i	$0.489377\pi$
$618$	3.98754	+	2.30221i	0.160403	+	0.0926085i
$619$	−12.2074	−	7.04795i	−0.490657	−	0.283281i	0.234190	−	0.972191i	$-0.424756\pi$
$619$	−12.2074	−	7.04795i	−0.490657	−	0.283281i	−0.724847	+	0.688910i	$0.758090\pi$
$620$	−5.14211			−0.206512
$621$	−4.78346			−0.191954
$622$	11.9754	+	6.91402i	0.480171	+	0.277227i
$623$	31.0494	−	11.3455i	1.24397	−	0.454548i
$624$	−12.8036	+	1.34703i	−0.512554	+	0.0539244i
$625$	−11.3465	−	19.6527i	−0.453860	−	0.786108i
$626$	19.5493	−	11.2868i	0.781348	−	0.451112i
$627$	−6.10752	−	10.5785i	−0.243911	−	0.422466i
$628$	−3.11261	+	5.39119i	−0.124207	+	0.215132i
$629$			8.01447i			0.319558i
$630$	−0.733229	−	2.00664i	−0.0292126	−	0.0799463i
$631$	12.5153	−	7.22569i	0.498224	−	0.287650i	−0.229756	−	0.973248i	$-0.573793\pi$
$631$	12.5153	−	7.22569i	0.498224	−	0.287650i	0.727980	+	0.685598i	$0.240459\pi$
$632$	−1.07954	+	0.623274i	−0.0429419	+	0.0247925i
$633$	−8.88487			−0.353142
$634$	−12.7709	−	22.1198i	−0.507195	−	0.878488i
$635$		−	1.70061i		−	0.0674867i
$636$	4.23739			0.168024
$637$	7.02055	+	24.2428i	0.278164	+	0.960534i
$638$	25.3047			1.00182
$639$			8.84998i			0.350100i
$640$	−0.628577	−	1.08873i	−0.0248467	−	0.0430357i
$641$	−15.2485			−0.602279			−0.301140	−	0.953580i	$-0.597367\pi$
$641$	−15.2485			−0.602279			−0.301140	+	0.953580i	$0.597367\pi$
$642$	6.85210	−	3.95606i	0.270431	−	0.156133i
$643$	−23.1303	+	13.3543i	−0.912171	+	0.526642i	−0.881129	−	0.472876i	$-0.843216\pi$
$643$	−23.1303	+	13.3543i	−0.912171	+	0.526642i	−0.0310418	+	0.999518i	$0.509882\pi$
$644$	9.53653	+	26.0987i	0.375792	+	1.02843i
$645$			2.87913i			0.113366i
$646$	−54.5029	+	94.4018i	−2.14439	+	3.71419i
$647$	23.1345	+	40.0701i	0.909511	+	1.57532i	0.814745	+	0.579819i	$0.196877\pi$
$647$	23.1345	+	40.0701i	0.909511	+	1.57532i	0.0947659	+	0.995500i	$0.469790\pi$
$648$	0.346873	−	0.200267i	0.0136264	−	0.00786723i
$649$	−8.97432	−	15.5440i	−0.352273	−	0.610155i
$650$	28.9433	−	21.0331i	1.13525	−	0.824984i
$651$	14.7636	−	5.39467i	0.578633	−	0.211434i
$652$	19.7427	+	11.3984i	0.773182	+	0.446397i
$653$	29.4817			1.15371			0.576854	−	0.816848i	$-0.304280\pi$
$653$	29.4817			1.15371			0.576854	+	0.816848i	$0.304280\pi$
$654$	20.9521			0.819293
$655$	−4.01935	−	2.32057i	−0.157049	−	0.0906722i
$656$	−22.0330	−	12.7207i	−0.860243	−	0.496661i
$657$	2.23575	−	1.29081i	0.0872250	−	0.0503594i
$658$	19.7782	−	23.6313i	0.771035	−	0.921246i
$659$	−15.5729	−	26.9730i	−0.606633	−	1.05072i	−0.991791	−	0.127868i	$-0.959187\pi$
$659$	−15.5729	−	26.9730i	−0.606633	−	1.05072i	0.385158	−	0.922850i	$-0.374147\pi$
$660$	−1.35636			−0.0527960
$661$	18.2995	−	10.5652i	0.711767	−	0.410939i	−0.0999482	−	0.994993i	$-0.531868\pi$
$661$	18.2995	−	10.5652i	0.711767	−	0.410939i	0.811715	+	0.584054i	$0.198534\pi$
$662$	−19.5658	+	33.8890i	−0.760448	+	1.31713i
$663$	24.4812	−	2.57560i	0.950772	−	0.100028i
$664$	−1.20622			−0.0468105
$665$	2.79029	+	7.63621i	0.108203	+	0.296120i
$666$	−1.20223	+	2.08232i	−0.0465854	+	0.0806883i
$667$	−18.8551	+	32.6579i	−0.730071	+	1.26452i
$668$	−13.1625	−	7.59937i	−0.509272	−	0.294029i
$669$		−	0.810124i		−	0.0313212i
$670$	1.95113	+	1.12649i	0.0753787	+	0.0435199i
$671$		−	19.2242i		−	0.742142i
$672$	16.4644	+	13.7798i	0.635127	+	0.531569i
$673$	10.9573	−	18.9786i	0.422372	−	0.731570i	−0.573799	−	0.818996i	$-0.694531\pi$
$673$	10.9573	−	18.9786i	0.422372	−	0.731570i	0.996171	+	0.0874263i	$0.0278642\pi$
$674$		−	72.6179i		−	2.79714i
$675$	2.42229	−	4.19554i	0.0932342	−	0.161486i
$676$	19.1027	+	21.2070i	0.734719	+	0.815654i
$677$	7.94438	+	13.7601i	0.305327	+	0.528843i	0.977334	−	0.211702i	$-0.0679008\pi$
$677$	7.94438	+	13.7601i	0.305327	+	0.528843i	−0.672007	+	0.740545i	$0.734567\pi$
$678$	−21.9426	−	12.6685i	−0.842699	−	0.486532i
$679$	22.4457	+	18.7859i	0.861387	+	0.720936i
$680$	0.539015	+	0.933602i	0.0206703	+	0.0358020i
$681$	0.482073	−	0.278325i	0.0184731	−	0.0106654i
$682$		−	19.0697i		−	0.730217i
$683$		−	26.2637i		−	1.00495i	−0.864591	−	0.502476i	$-0.832422\pi$
$683$		−	26.2637i		−	1.00495i	0.864591	−	0.502476i	$-0.167578\pi$
$684$	−14.8210	+	8.55689i	−0.566694	+	0.327181i
$685$	1.50392	+	2.60486i	0.0574616	+	0.0995265i
$686$	18.8429	−	32.9244i	0.719423	−	1.25706i
$687$	14.2673	+	8.23721i	0.544330	+	0.314269i
$688$	−13.0389	−	22.5840i	−0.497104	−	0.861009i
$689$	4.09080	+	5.62929i	0.155847	+	0.214459i
$690$	1.93129	−	3.34508i	0.0735228	−	0.127345i
$691$		−	24.8257i		−	0.944416i	−0.881487	−	0.472208i	$-0.843457\pi$
$691$		−	24.8257i		−	0.944416i	0.881487	−	0.472208i	$-0.156543\pi$
$692$	−10.9732	+	19.0061i	−0.417137	+	0.722503i
$693$	3.89427	−	1.42297i	0.147931	−	0.0540543i
$694$		−	36.9688i		−	1.40332i
$695$	−1.16508	−	0.672659i	−0.0441940	−	0.0255154i
$696$		−	3.15758i		−	0.119688i
$697$	42.1284	+	24.3228i	1.59573	+	0.921293i
$698$	−14.3810	+	24.9087i	−0.544330	+	0.942808i
$699$	−3.31050	+	5.73395i	−0.125215	+	0.216878i
$700$	−27.7202	−	4.85170i	−1.04772	−	0.183377i
$701$	7.27739			0.274863			0.137432	−	0.990511i	$-0.456115\pi$
$701$	7.27739			0.274863			0.137432	+	0.990511i	$0.456115\pi$
$702$	6.74708	+	3.00317i	0.254652	+	0.113347i
$703$	4.57506	−	7.92423i	0.172552	−	0.298868i
$704$	12.8662	−	7.42828i	0.484911	−	0.279964i
$705$	−2.24167			−0.0844261
$706$	1.15027	+	1.99232i	0.0432909	+	0.0749821i
$707$	8.93993	−	10.6816i	0.336221	−	0.401722i
$708$	−21.7778	+	12.5734i	−0.818458	+	0.472537i
$709$	−17.3283	−	10.0045i	−0.650777	−	0.375726i	0.137977	−	0.990435i	$-0.455940\pi$
$709$	−17.3283	−	10.0045i	−0.650777	−	0.375726i	−0.788754	+	0.614709i	$0.789273\pi$
$710$	−6.18881	−	3.57311i	−0.232262	−	0.134096i
$711$	−3.11221			−0.116717
$712$	−5.00446			−0.187550
$713$	24.6111	+	14.2093i	0.921695	+	0.532141i
$714$	−28.3732	−	23.7469i	−1.06184	−	0.888707i
$715$	−1.30943	−	1.80189i	−0.0489699	−	0.0673869i
$716$	23.6567	+	40.9746i	0.884092	+	1.53129i
$717$	−5.26024	+	3.03700i	−0.196447	+	0.113419i
$718$	−7.54720	−	13.0721i	−0.281659	−	0.487848i
$719$	−11.7384	+	20.3315i	−0.437767	+	0.758235i	−0.997517	−	0.0704265i	$-0.977564\pi$
$719$	−11.7384	+	20.3315i	−0.437767	+	0.758235i	0.559750	+	0.828662i	$0.310897\pi$
$720$		−	1.40764i		−	0.0524595i
$721$	3.81718	−	4.56083i	0.142159	−	0.169854i
$722$	74.0747	−	42.7670i	2.75677	−	1.59162i
$723$	17.8983	−	10.3336i	0.665644	−	0.384310i
$724$	−20.6529			−0.767558
$725$	−19.0960	−	33.0752i	−0.709208	−	1.22838i
$726$			17.5012i			0.649532i
$727$	−19.2442			−0.713727			−0.356863	−	0.934157i	$-0.616154\pi$
$727$	−19.2442			−0.713727			−0.356863	+	0.934157i	$0.616154\pi$
$728$	0.261323	−	3.81190i	0.00968528	−	0.141279i
$729$	1.00000			0.0370370
$730$			2.08462i			0.0771553i
$731$	24.9312	+	43.1821i	0.922113	+	1.59715i
$732$	−26.9339			−0.995506
$733$	−22.6286	+	13.0646i	−0.835808	+	0.482554i	−0.855837	−	0.517246i	$-0.826957\pi$
$733$	−22.6286	+	13.0646i	−0.835808	+	0.482554i	0.0200293	+	0.999799i	$0.493624\pi$
$734$	−35.0763	+	20.2513i	−1.29469	+	0.747491i
$735$	−2.71640	+	0.486058i	−0.100196	+	0.0179285i
$736$			38.8173i			1.43082i
$737$	−2.18616	+	3.78655i	−0.0805284	+	0.139479i
$738$	7.29720	+	12.6391i	0.268614	+	0.465253i
$739$	16.1068	−	9.29927i	0.592498	−	0.342079i	−0.173586	−	0.984819i	$-0.555536\pi$
$739$	16.1068	−	9.29927i	0.592498	−	0.342079i	0.766085	+	0.642740i	$0.222202\pi$
$740$	−0.508013	−	0.879905i	−0.0186749	−	0.0323460i
$741$	−25.6759	−	11.4285i	−0.943226	−	0.419836i
$742$	1.80321	−	10.3026i	0.0661978	−	0.378221i
$743$	31.1212	+	17.9678i	1.14173	+	0.659176i	0.946858	−	0.321653i	$-0.104238\pi$
$743$	31.1212	+	17.9678i	1.14173	+	0.659176i	0.194869	+	0.980829i	$0.437572\pi$
$744$	−2.37957			−0.0872392
$745$	3.37289			0.123573
$746$	16.5263	+	9.54145i	0.605070	+	0.349337i
$747$	−2.60807	−	1.50577i	−0.0954241	−	0.0550931i
$748$	−20.3430	+	11.7451i	−0.743815	+	0.429442i
$749$	−3.50756	−	9.59917i	−0.128163	−	0.350746i
$750$	3.97468	+	6.88434i	0.145135	+	0.251381i
$751$	−0.208646			−0.00761359			−0.00380679	−	0.999993i	$-0.501212\pi$
$751$	−0.208646			−0.00761359			−0.00380679	+	0.999993i	$0.501212\pi$
$752$	17.5838	−	10.1520i	0.641214	−	0.370205i
$753$	7.61211	−	13.1846i	0.277401	−	0.480472i
$754$	47.0985	−	34.2264i	1.71522	−	1.24645i
$755$	−8.42184			−0.306502
$756$	−1.99365	−	5.45603i	−0.0725082	−	0.198434i
$757$	−16.7911	+	29.0830i	−0.610282	+	1.05704i	0.380910	+	0.924612i	$0.375611\pi$
$757$	−16.7911	+	29.0830i	−0.610282	+	1.05704i	−0.991193	+	0.132428i	$0.957723\pi$
$758$	−12.8083	+	22.1847i	−0.465220	+	0.805785i
$759$	6.49179	+	3.74803i	0.235637	+	0.136045i
$760$		−	1.23079i		−	0.0446453i
$761$	11.4557	+	6.61396i	0.415270	+	0.239756i	0.693051	−	0.720888i	$-0.256266\pi$
$761$	11.4557	+	6.61396i	0.415270	+	0.239756i	−0.277782	+	0.960644i	$0.589599\pi$
$762$		−	8.83607i		−	0.320097i
$763$	4.66583	−	26.6582i	0.168914	−	0.965092i
$764$	11.4353	−	19.8065i	0.413715	−	0.716576i
$765$			2.69148i			0.0973108i
$766$	−35.6662	+	61.7757i	−1.28867	+	2.23205i
$767$	−37.7278	−	16.7929i	−1.36227	−	0.606357i
$768$	6.21443	+	10.7637i	0.224244	+	0.388402i
$769$	3.35265	+	1.93565i	0.120900	+	0.0698014i	0.559230	−	0.829012i	$-0.311097\pi$
$769$	3.35265	+	1.93565i	0.120900	+	0.0698014i	−0.438331	+	0.898814i	$0.644430\pi$
$770$	−0.577192	+	3.29778i	−0.0208006	+	0.118844i
$771$	−0.850367	−	1.47288i	−0.0306252	−	0.0530444i
$772$	42.6570	−	24.6280i	1.53526	−	0.886382i
$773$		−	11.8313i		−	0.425544i	−0.977102	−	0.212772i	$-0.931751\pi$
$773$		−	11.8313i		−	0.425544i	0.977102	−	0.212772i	$-0.0682492\pi$
$774$			14.9594i			0.537706i
$775$	−24.9256	+	14.3908i	−0.895356	+	0.516934i
$776$	−2.21554	−	3.83743i	−0.0795332	−	0.137756i
$777$	2.38169	+	1.99335i	0.0854428	+	0.0715112i
$778$	25.6456	+	14.8065i	0.919439	+	0.530838i
$779$	−27.7693	−	48.0979i	−0.994940	−	1.72329i
$780$	−2.52452	+	1.83457i	−0.0903924	+	0.0656880i
$781$	6.93431	−	12.0106i	0.248129	−	0.429772i
$782$		−	66.8942i		−	2.39213i
$783$	3.94172	−	6.82725i	0.140865	−	0.243986i
$784$	19.1064	−	16.1146i	0.682371	−	0.575523i
$785$		−	1.11777i		−	0.0398949i
$786$	−20.8838	−	12.0573i	−0.744901	−	0.430069i
$787$			46.9994i			1.67535i	0.546171	+	0.837674i	$0.316085\pi$
$787$			46.9994i			1.67535i	−0.546171	+	0.837674i	$0.683915\pi$
$788$	−43.8873	−	25.3383i	−1.56342	−	0.902641i
$789$	4.09154	−	7.08676i	0.145663	−	0.252295i
$790$	1.25653	−	2.17638i	0.0447054	−	0.0774321i
$791$	−21.0051	+	25.0972i	−0.746854	+	0.892354i
$792$	−0.627669			−0.0223032
$793$	−26.0021	−	35.7811i	−0.923362	−	1.27063i
$794$	−3.91121	+	6.77442i	−0.138804	+	0.240415i
$795$	−0.658912	+	0.380423i	−0.0233692	+	0.0134922i
$796$	1.15002			0.0407613
$797$	25.8005	+	44.6879i	0.913902	+	1.58293i	0.808500	+	0.588496i	$0.200280\pi$
$797$	25.8005	+	44.6879i	0.913902	+	1.58293i	0.105402	+	0.994430i	$0.466387\pi$
$798$	14.4978	+	39.6764i	0.513218	+	1.40453i
$799$	−33.6212	+	19.4112i	−1.18943	+	0.686720i
$800$	−34.0463	−	19.6567i	−1.20372	−	0.694968i
$801$	−10.8205	−	6.24724i	−0.382325	−	0.220735i
$802$	−25.8541			−0.912940
$803$	−4.04561			−0.142767
$804$	5.30511	+	3.06291i	0.187097	+	0.108020i
$805$	−3.82600	−	3.20217i	−0.134849	−	0.112862i
$806$	−25.7931	−	35.4936i	−0.908525	−	1.25021i
$807$	−5.83024	−	10.0983i	−0.205234	−	0.355476i
$808$	−1.82618	+	1.05434i	−0.0642446	+	0.0370917i
$809$	−4.84238	−	8.38725i	−0.170249	−	0.294880i	0.768258	−	0.640141i	$-0.221124\pi$
$809$	−4.84238	−	8.38725i	−0.170249	−	0.294880i	−0.938507	+	0.345261i	$0.887791\pi$
$810$	−0.403742	+	0.699302i	−0.0141861	+	0.0245710i
$811$		−	3.81953i		−	0.134122i	−0.997749	−	0.0670609i	$-0.978638\pi$
$811$		−	3.81953i		−	0.134122i	0.997749	−	0.0670609i	$-0.0213622\pi$
$812$	−45.1081	−	7.89501i	−1.58298	−	0.277060i
$813$	−4.89222	+	2.82452i	−0.171578	+	0.0990604i
$814$	3.26316	−	1.88399i	0.114374	−	0.0660338i
$815$	−4.09329			−0.143382
$816$	−12.1891	−	21.1122i	−0.426704	−	0.739073i
$817$		−	56.9278i		−	1.99165i
$818$	−64.6122			−2.25911
$819$	5.32355	−	7.91579i	0.186020	−	0.276600i
$820$	−6.16701			−0.215361
$821$		−	15.8415i		−	0.552873i	−0.961032	−	0.276437i	$-0.910846\pi$
$821$		−	15.8415i		−	0.552873i	0.961032	−	0.276437i	$-0.0891536\pi$
$822$	7.81407	+	13.5344i	0.272547	+	0.472065i
$823$	28.4036			0.990088			0.495044	−	0.868868i	$-0.335152\pi$
$823$	28.4036			0.990088			0.495044	+	0.868868i	$0.335152\pi$
$824$	−0.779742	+	0.450184i	−0.0271636	+	0.0156829i
$825$	−6.57474	+	3.79593i	−0.228903	+	0.132157i
$826$	21.3030	+	58.3001i	0.741225	+	2.02852i
$827$		−	8.88006i		−	0.308790i	−0.988009	−	0.154395i	$-0.950657\pi$
$827$		−	8.88006i		−	0.308790i	0.988009	−	0.154395i	$-0.0493428\pi$
$828$	5.25115	−	9.09526i	0.182490	−	0.316082i
$829$	−26.6364	−	46.1356i	−0.925120	−	1.60235i	−0.791369	−	0.611339i	$-0.790631\pi$
$829$	−26.6364	−	46.1356i	−0.925120	−	1.60235i	−0.133751	−	0.991015i	$-0.542702\pi$
$830$	2.10597	−	1.21588i	0.0730993	−	0.0422039i
$831$	−11.9857	−	20.7599i	−0.415780	−	0.720152i
$832$	13.8999	−	31.2283i	0.481893	−	1.08265i
$833$	−36.5326	+	30.8122i	−1.26578	+	1.06758i
$834$	−6.05355	−	3.49502i	−0.209617	−	0.121023i
$835$	2.72901			0.0944414
$836$	26.8187			0.927542
$837$	−5.14505	−	2.97049i	−0.177839	−	0.102675i
$838$	−18.4243	−	10.6373i	−0.636456	−	0.367458i
$839$	13.0429	−	7.53032i	0.450291	−	0.259976i	−0.257662	−	0.966235i	$-0.582952\pi$
$839$	13.0429	−	7.53032i	0.450291	−	0.259976i	0.707953	+	0.706260i	$0.249619\pi$
$840$	0.411506	+	0.0720235i	0.0141983	+	0.00248505i
$841$	−16.5743	−	28.7075i	−0.571526	−	0.989913i
$842$	0.753950			0.0259828
$843$	−17.5702	+	10.1441i	−0.605148	+	0.349383i
$844$	9.75356	−	16.8937i	0.335732	−	0.581504i
$845$	−4.87437	−	1.58268i	−0.167683	−	0.0544458i
$846$	−11.6473			−0.400443
$847$	22.2675	+	3.89735i	0.765120	+	0.133915i
$848$	3.44569	−	5.96812i	0.118326	−	0.204946i
$849$	−1.05407	+	1.82570i	−0.0361755	+	0.0626578i
$850$	58.6724	+	33.8745i	2.01245	+	1.16189i
$851$			5.61520i			0.192487i
$852$	−16.8273	−	9.71526i	−0.576495	−	0.332839i
$853$		−	14.1733i		−	0.485283i	−0.970116	−	0.242642i	$-0.921986\pi$
$853$		−	14.1733i		−	0.485283i	0.970116	−	0.242642i	$-0.0780139\pi$
$854$	−11.4616	+	65.4859i	−0.392209	+	2.24088i
$855$	1.53643	−	2.66118i	0.0525449	−	0.0910104i
$856$			1.54717i			0.0528812i
$857$	16.5154	−	28.6055i	0.564156	−	0.977147i	−0.432972	−	0.901408i	$-0.642535\pi$
$857$	16.5154	−	28.6055i	0.564156	−	0.977147i	0.997128	−	0.0757394i	$-0.0241317\pi$
$858$	−6.80357	−	9.36230i	−0.232270	−	0.319624i
$859$	−0.596346	−	1.03290i	−0.0203471	−	0.0352421i	0.855673	−	0.517518i	$-0.173144\pi$
$859$	−0.596346	−	1.03290i	−0.0203471	−	0.0352421i	−0.876020	+	0.482275i	$0.839810\pi$
$860$	−5.47437	−	3.16063i	−0.186674	−	0.107776i
$861$	17.7063	−	6.46991i	0.603428	−	0.220494i
$862$	15.7646	+	27.3050i	0.536943	+	0.930013i
$863$	−4.99176	+	2.88199i	−0.169921	+	0.0981042i	−0.582549	−	0.812796i	$-0.697945\pi$
$863$	−4.99176	+	2.88199i	−0.169921	+	0.0981042i	0.412627	+	0.910900i	$0.364611\pi$
$864$		−	8.11489i		−	0.276074i
$865$		−	3.94058i		−	0.133984i
$866$	32.4201	−	18.7177i	1.10168	−	0.636055i
$867$	14.8063	+	25.6453i	0.502849	+	0.870960i
$868$	−5.94971	+	33.9937i	−0.201946	+	1.15382i
$869$	4.22368	+	2.43855i	0.143279	+	0.0827220i
$870$	3.18287	+	5.51290i	0.107910	+	0.186905i
$871$	1.05256	+	10.0047i	0.0356648	+	0.338995i
$872$	−2.04854	+	3.54817i	−0.0693722	+	0.120156i
$873$		−	11.0629i		−	0.374423i
$874$	−38.1865	+	66.1410i	−1.29168	+	2.23725i
$875$	9.64433	−	3.52406i	0.326038	−	0.119135i
$876$			5.66807i			0.191506i
$877$	4.34936	+	2.51110i	0.146867	+	0.0847940i	0.571633	−	0.820509i	$-0.306310\pi$
$877$	4.34936	+	2.51110i	0.146867	+	0.0847940i	−0.424766	+	0.905303i	$0.639643\pi$
$878$		−	60.2906i		−	2.03471i
$879$	−2.59210	−	1.49655i	−0.0874294	−	0.0504774i
$880$	−1.10294	+	1.91035i	−0.0371801	+	0.0643977i
$881$	−6.29570	+	10.9045i	−0.212108	+	0.367381i	−0.952374	−	0.304933i	$-0.901366\pi$
$881$	−6.29570	+	10.9045i	−0.212108	+	0.367381i	0.740266	+	0.672314i	$0.234699\pi$
$882$	−14.1140	+	2.52547i	−0.475242	+	0.0850371i
$883$	10.5722			0.355783			0.177891	−	0.984050i	$-0.443072\pi$
$883$	10.5722			0.355783			0.177891	+	0.984050i	$0.443072\pi$
$884$	−21.9776	+	49.3760i	−0.739186	+	1.66069i
$885$	2.25762	−	3.91031i	0.0758890	−	0.131444i
$886$	3.45659	−	1.99566i	0.116126	−	0.0670456i
$887$	8.95286			0.300608			0.150304	−	0.988640i	$-0.451975\pi$
$887$	8.95286			0.300608			0.150304	+	0.988640i	$0.451975\pi$
$888$	−0.235089	−	0.407186i	−0.00788907	−	0.0136643i
$889$	−11.2425	−	1.96771i	−0.377061	−	0.0659947i
$890$	8.73741	−	5.04455i	0.292879	−	0.169094i
$891$	−1.35713	−	0.783540i	−0.0454656	−	0.0262496i
$892$	1.54037	+	0.889331i	0.0515753	+	0.0297770i
$893$	44.3236			1.48323
$894$	17.5250			0.586122
$895$	−7.35720	−	4.24768i	−0.245924	−	0.141984i
$896$	−7.92471	+	2.89571i	−0.264746	+	0.0967387i
$897$	17.1524	−	1.80455i	0.572700	−	0.0602523i
$898$	22.1362	+	38.3409i	0.738693	+	1.27945i
$899$	−40.5606	+	23.4177i	−1.35277	+	0.781024i
$900$	5.31826	+	9.21149i	0.177275	+	0.307050i
$901$	−6.58838	+	11.4114i	−0.219491	+	0.380169i
$902$		−	22.8706i		−	0.761508i
$903$	19.0335	+	3.33132i	0.633394	+	0.110859i
$904$	4.29074	−	2.47726i	0.142708	−	0.0823925i
$905$	3.21151	−	1.85416i	0.106754	−	0.0616345i
$906$	−43.7584			−1.45377
$907$	18.1711	+	31.4733i	0.603363	+	1.04506i	0.992308	+	0.123794i	$0.0395063\pi$
$907$	18.1711	+	31.4733i	0.603363	+	1.04506i	−0.388945	+	0.921261i	$0.627160\pi$
$908$			1.22215i			0.0405585i
$909$	−5.26469			−0.174619
$910$	3.38619	+	6.91871i	0.112251	+	0.229353i
$911$	3.79484			0.125729			0.0628643	−	0.998022i	$-0.479976\pi$
$911$	3.79484			0.125729			0.0628643	+	0.998022i	$0.479976\pi$
$912$			27.8326i			0.921629i
$913$	2.35966	+	4.08705i	0.0780933	+	0.135262i
$914$	−39.2612			−1.29865
$915$	4.18820	−	2.41806i	0.138458	−	0.0799386i
$916$	−31.3244	+	18.0852i	−1.03499	+	0.597550i
$917$	−19.9916	+	23.8862i	−0.660179	+	0.788793i
$918$			13.9845i			0.461556i
$919$	1.68638	−	2.92090i	0.0556286	−	0.0963516i	−0.836870	−	0.547402i	$-0.815617\pi$
$919$	1.68638	−	2.92090i	0.0556286	−	0.0963516i	0.892499	+	0.451050i	$0.148950\pi$
$920$	0.377652	+	0.654112i	0.0124508	+	0.0215654i
$921$	1.65738	−	0.956886i	0.0546124	−	0.0315305i
$922$	−8.14693	−	14.1109i	−0.268305	−	0.464717i
$923$	−3.33864	−	31.7339i	−0.109893	−	1.04453i
$924$	−1.56938	+	8.96665i	−0.0516288	+	0.294981i
$925$	−4.92505	−	2.84348i	−0.161935	−	0.0934930i
$926$	19.2394			0.632247
$927$	−2.24792			−0.0738314
$928$	−55.4024	−	31.9866i	−1.81867	−	1.05001i
$929$	29.5925	+	17.0852i	0.970897	+	0.560548i	0.899510	−	0.436901i	$-0.143924\pi$
$929$	29.5925	+	17.0852i	0.970897	+	0.560548i	0.0713874	+	0.997449i	$0.477257\pi$
$930$	4.15455	−	2.39863i	0.136233	−	0.0786541i
$931$	53.7104	−	9.61063i	1.76029	−	0.314976i
$932$	−7.26834	−	12.5891i	−0.238083	−	0.412371i
$933$	−6.75098			−0.221017
$934$	58.4800	−	33.7635i	1.91353	−	1.10477i
$935$	2.10889	−	3.65270i	0.0689679	−	0.119456i
$936$	−1.16825	+	0.848967i	−0.0381855	+	0.0277493i
$937$	−12.8036			−0.418275			−0.209138	−	0.977886i	$-0.567066\pi$
$937$	−12.8036			−0.418275			−0.209138	+	0.977886i	$0.567066\pi$
$938$	9.70459	−	11.5952i	0.316866	−	0.378597i
$939$	−5.51032	+	9.54416i	−0.179823	+	0.311462i
$940$	2.46084	−	4.26230i	0.0802638	−	0.139021i
$941$	−42.7039	−	24.6551i	−1.39211	−	0.803733i	−0.398558	−	0.917143i	$-0.630489\pi$
$941$	−42.7039	−	24.6551i	−1.39211	−	0.803733i	−0.993548	+	0.113410i	$0.963823\pi$
$942$		−	5.80773i		−	0.189226i
$943$	29.5165	+	17.0414i	0.961190	+	0.554943i
$944$			40.8969i			1.33108i
$945$	0.799840	+	0.669424i	0.0260188	+	0.0217764i
$946$	11.7213	−	20.3019i	0.381093	−	0.660072i
$947$		−	17.6585i		−	0.573823i	−0.957957	−	0.286911i	$-0.907371\pi$
$947$		−	17.6585i		−	0.573823i	0.957957	−	0.286911i	$-0.0926286\pi$
$948$	3.41650	−	5.91756i	0.110963	−	0.192193i
$949$	−7.52992	+	5.47198i	−0.244431	+	0.177628i
$950$	−38.6745	−	66.9862i	−1.25477	−	2.17332i
$951$	10.7991	+	6.23485i	0.350184	+	0.202179i
$952$	6.79557	−	2.48312i	0.220246	−	0.0804783i
$953$	−21.5862	−	37.3884i	−0.699245	−	1.21113i	−0.968729	−	0.248123i	$-0.920186\pi$
$953$	−21.5862	−	37.3884i	−0.699245	−	1.21113i	0.269484	−	0.963005i	$-0.413147\pi$
$954$	−3.42359	+	1.97661i	−0.110843	+	0.0639951i
$955$			4.10654i			0.132884i
$956$		−	13.3357i		−	0.431309i
$957$	−10.6989	+	6.17699i	−0.345845	+	0.199674i
$958$	1.16143	+	2.01165i	0.0375240	+	0.0649935i
$959$	18.9604	−	6.92818i	0.612264	−	0.223723i
$960$	3.23666	+	1.86869i	0.104463	+	0.0603116i
$961$	2.14768	+	3.71989i	0.0692800	+	0.119996i
$962$	3.52535	−	7.92025i	0.113662	−	0.255359i
$963$	−1.93139	+	3.34526i	−0.0622380	+	0.107799i
$964$			45.3757i			1.46145i
$965$	−4.42209	+	7.65928i	−0.142352	+	0.246561i
$966$	−19.8792	−	16.6379i	−0.639604	−	0.535315i
$967$			7.19961i			0.231524i	0.993277	+	0.115762i	$0.0369310\pi$
$967$			7.19961i			0.231524i	−0.993277	+	0.115762i	$0.963069\pi$
$968$	−2.96377	−	1.71113i	−0.0952592	−	0.0549979i
$969$		−	53.2176i		−	1.70960i
$970$	7.73633	+	4.46657i	0.248399	+	0.143413i
$971$	9.31506	−	16.1342i	0.298934	−	0.517770i	−0.676958	−	0.736022i	$-0.736702\pi$
$971$	9.31506	−	16.1342i	0.298934	−	0.517770i	0.975892	+	0.218252i	$0.0700355\pi$
$972$	−1.09777	+	1.90140i	−0.0352111	+	0.0609873i
$973$	−5.79491	+	6.92386i	−0.185776	+	0.221969i
$974$	83.3002			2.66911
$975$	−7.10301	+	15.9580i	−0.227478	+	0.511065i
$976$	−21.9017	+	37.9348i	−0.701055	+	1.21426i
$977$	−9.83875	+	5.68040i	−0.314769	+	0.181732i	−0.649059	−	0.760738i	$-0.724837\pi$
$977$	−9.83875	+	5.68040i	−0.314769	+	0.181732i	0.334289	+	0.942471i	$0.391504\pi$
$978$	−21.2680			−0.680076
$979$	9.78992	+	16.9566i	0.312887	+	0.541937i
$980$	2.05780	−	5.69855i	0.0657341	−	0.182033i
$981$	−8.85859	+	5.11451i	−0.282833	+	0.163294i
$982$	52.2526	+	30.1680i	1.66745	+	0.962701i
$983$	−9.52228	−	5.49769i	−0.303714	−	0.175349i	0.340396	−	0.940282i	$-0.389439\pi$
$983$	−9.52228	−	5.49769i	−0.303714	−	0.175349i	−0.644110	+	0.764933i	$0.722772\pi$
$984$	−2.85385			−0.0909775
$985$	9.09926			0.289927
$986$	95.4755	+	55.1228i	3.04056	+	1.75547i
$987$	−2.59374	+	14.8193i	−0.0825596	+	0.471704i
$988$	49.9164	−	36.2741i	1.58805	−	1.15403i
$989$	17.4676	+	30.2548i	0.555437	+	0.962046i
$990$	1.09586	−	0.632696i	0.0348288	−	0.0201084i
$991$	−19.1780	−	33.2173i	−0.609210	−	1.05518i	−0.991371	−	0.131087i	$-0.958153\pi$
$991$	−19.1780	−	33.2173i	−0.609210	−	1.05518i	0.382161	−	0.924096i	$-0.375180\pi$
$992$	−24.1052	+	41.7515i	−0.765342	+	1.32561i
$993$		−	19.1044i		−	0.606261i
$994$	−30.7821	+	36.7789i	−0.976348	+	1.16656i
$995$	−0.178827	+	0.103246i	−0.00566920	+	0.00327311i
$996$	5.72612	−	3.30598i	0.181439	−	0.104754i
$997$	−25.5193			−0.808204			−0.404102	−	0.914714i	$-0.632416\pi$
$997$	−25.5193			−0.808204			−0.404102	+	0.914714i	$0.632416\pi$
$998$	19.4762	+	33.7337i	0.616508	+	1.06782i
$999$		−	1.17388i		−	0.0371399i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	273.2.t.d.4.3	✓	20
3.2	odd	2		819.2.bm.g.550.8		20
7.2	even	3		273.2.bl.d.121.3	yes	20
13.10	even	6		273.2.bl.d.88.3	yes	20
21.2	odd	6		819.2.do.g.667.8		20
39.23	odd	6		819.2.do.g.361.8		20
91.23	even	6	inner	273.2.t.d.205.8	yes	20
273.23	odd	6		819.2.bm.g.478.3		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
273.2.t.d.4.3	✓	20	1.1	even	1	trivial
273.2.t.d.205.8	yes	20	91.23	even	6	inner
273.2.bl.d.88.3	yes	20	13.10	even	6
273.2.bl.d.121.3	yes	20	7.2	even	3
819.2.bm.g.478.3		20	273.23	odd	6
819.2.bm.g.550.8		20	3.2	odd	2
819.2.do.g.361.8		20	39.23	odd	6
819.2.do.g.667.8		20	21.2	odd	6

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

\(f(q)\)	\(=\)	\(q-2.04830i q^{2} +(0.500000 + 0.866025i) q^{3} -2.19554 q^{4} +(0.341406 - 0.197111i) q^{5} +(1.77388 - 1.02415i) q^{6} +(-0.908042 - 2.48505i) q^{7} +0.400534i q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q-2.04830i q^{2} +(0.500000 + 0.866025i) q^{3} -2.19554 q^{4} +(0.341406 - 0.197111i) q^{5} +(1.77388 - 1.02415i) q^{6} +(-0.908042 - 2.48505i) q^{7} +0.400534i q^{8} +(-0.500000 + 0.866025i) q^{9} +(-0.403742 - 0.699302i) q^{10} +(1.35713 - 0.783540i) q^{11} +(-1.09777 - 1.90140i) q^{12} +(1.46617 - 3.29398i) q^{13} +(-5.09013 + 1.85994i) q^{14} +(0.341406 + 0.197111i) q^{15} -3.57067 q^{16} +6.82735 q^{17} +(1.77388 + 1.02415i) q^{18} +(-6.75047 - 3.89739i) q^{19} +(-0.749571 + 0.432765i) q^{20} +(1.69809 - 2.02891i) q^{21} +(-1.60493 - 2.77982i) q^{22} +4.78346 q^{23} +(-0.346873 + 0.200267i) q^{24} +(-2.42229 + 4.19554i) q^{25} +(-6.74708 - 3.00317i) q^{26} -1.00000 q^{27} +(1.99365 + 5.45603i) q^{28} +(-3.94172 + 6.82725i) q^{29} +(0.403742 - 0.699302i) q^{30} +(5.14505 + 2.97049i) q^{31} +8.11489i q^{32} +(1.35713 + 0.783540i) q^{33} -13.9845i q^{34} +(-0.799840 - 0.669424i) q^{35} +(1.09777 - 1.90140i) q^{36} +1.17388i q^{37} +(-7.98303 + 13.8270i) q^{38} +(3.58576 - 0.377248i) q^{39} +(0.0789495 + 0.136745i) q^{40} +(6.17054 + 3.56256i) q^{41} +(-4.15582 - 3.47821i) q^{42} +(3.65167 + 6.32487i) q^{43} +(-2.97964 + 1.72030i) q^{44} +0.394221i q^{45} -9.79798i q^{46} +(-4.92450 + 2.84316i) q^{47} +(-1.78534 - 3.09229i) q^{48} +(-5.35092 + 4.51305i) q^{49} +(8.59373 + 4.96159i) q^{50} +(3.41367 + 5.91265i) q^{51} +(-3.21905 + 7.23209i) q^{52} +(-0.964998 + 1.67143i) q^{53} +2.04830i q^{54} +(0.308888 - 0.535010i) q^{55} +(0.995346 - 0.363702i) q^{56} -7.79477i q^{57} +(13.9843 + 8.07383i) q^{58} -11.4536i q^{59} +(-0.749571 - 0.432765i) q^{60} +(6.13376 - 10.6240i) q^{61} +(6.08447 - 10.5386i) q^{62} +(2.60613 + 0.456137i) q^{63} +9.48040 q^{64} +(-0.148719 - 1.41358i) q^{65} +(1.60493 - 2.77982i) q^{66} +(-2.41631 + 1.39506i) q^{67} -14.9897 q^{68} +(2.39173 + 4.14260i) q^{69} +(-1.37118 + 1.63831i) q^{70} +(7.66430 - 4.42499i) q^{71} +(-0.346873 - 0.200267i) q^{72} +(-2.23575 - 1.29081i) q^{73} +2.40446 q^{74} -4.84459 q^{75} +(14.8210 + 8.55689i) q^{76} +(-3.17947 - 2.66105i) q^{77} +(-0.772719 - 7.34472i) q^{78} +(1.55611 + 2.69526i) q^{79} +(-1.21905 + 0.703818i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(7.29720 - 12.6391i) q^{82} +3.01153i q^{83} +(-3.72824 + 4.45456i) q^{84} +(2.33089 - 1.34574i) q^{85} +(12.9552 - 7.47972i) q^{86} -7.88343 q^{87} +(0.313834 + 0.543577i) q^{88} +12.4945i q^{89} +0.807484 q^{90} +(-9.51705 - 0.652437i) q^{91} -10.5023 q^{92} +5.94099i q^{93} +(5.82365 + 10.0869i) q^{94} -3.07286 q^{95} +(-7.02770 + 4.05744i) q^{96} +(-9.58078 + 5.53147i) q^{97} +(9.24410 + 10.9603i) q^{98} +1.56708i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 10 q^{3} - 26 q^{4} + 6 q^{5} + 3 q^{6} + 2 q^{7} - 10 q^{9}+O(q^{10}) \) 20 * q + 10 * q^3 - 26 * q^4 + 6 * q^5 + 3 * q^6 + 2 * q^7 - 10 * q^9	\( 20 q + 10 q^{3} - 26 q^{4} + 6 q^{5} + 3 q^{6} + 2 q^{7} - 10 q^{9} + 2 q^{10} - 12 q^{11} - 13 q^{12} + 8 q^{13} + 2 q^{14} + 6 q^{15} + 42 q^{16} + 16 q^{17} + 3 q^{18} - 9 q^{19} - 5 q^{21} - 9 q^{22} - 36 q^{23} + 3 q^{24} + 12 q^{25} - 16 q^{26} - 20 q^{27} - 2 q^{28} - 3 q^{29} - 2 q^{30} - 18 q^{31} - 12 q^{33} + 18 q^{35} + 13 q^{36} + 9 q^{38} + 7 q^{39} + 5 q^{40} + 21 q^{41} + 16 q^{42} + 16 q^{43} - 6 q^{44} + 21 q^{47} + 21 q^{48} - 24 q^{49} - 54 q^{50} + 8 q^{51} - 41 q^{52} - 26 q^{53} + 17 q^{55} - 6 q^{56} + 42 q^{58} + 4 q^{62} - 7 q^{63} - 46 q^{64} - 50 q^{65} + 9 q^{66} - 3 q^{67} + 6 q^{68} - 18 q^{69} + 15 q^{71} + 3 q^{72} - 9 q^{73} + 12 q^{74} + 24 q^{75} + 75 q^{76} + 20 q^{77} - 32 q^{78} + 3 q^{79} - 24 q^{80} - 10 q^{81} + 15 q^{82} + 41 q^{84} - 78 q^{85} + 3 q^{86} - 6 q^{87} - 22 q^{88} - 4 q^{90} + 4 q^{91} + 142 q^{92} + 36 q^{94} - 84 q^{95} - 24 q^{96} - 15 q^{97} + 81 q^{98}+O(q^{100}) \) 20 * q + 10 * q^3 - 26 * q^4 + 6 * q^5 + 3 * q^6 + 2 * q^7 - 10 * q^9 + 2 * q^10 - 12 * q^11 - 13 * q^12 + 8 * q^13 + 2 * q^14 + 6 * q^15 + 42 * q^16 + 16 * q^17 + 3 * q^18 - 9 * q^19 - 5 * q^21 - 9 * q^22 - 36 * q^23 + 3 * q^24 + 12 * q^25 - 16 * q^26 - 20 * q^27 - 2 * q^28 - 3 * q^29 - 2 * q^30 - 18 * q^31 - 12 * q^33 + 18 * q^35 + 13 * q^36 + 9 * q^38 + 7 * q^39 + 5 * q^40 + 21 * q^41 + 16 * q^42 + 16 * q^43 - 6 * q^44 + 21 * q^47 + 21 * q^48 - 24 * q^49 - 54 * q^50 + 8 * q^51 - 41 * q^52 - 26 * q^53 + 17 * q^55 - 6 * q^56 + 42 * q^58 + 4 * q^62 - 7 * q^63 - 46 * q^64 - 50 * q^65 + 9 * q^66 - 3 * q^67 + 6 * q^68 - 18 * q^69 + 15 * q^71 + 3 * q^72 - 9 * q^73 + 12 * q^74 + 24 * q^75 + 75 * q^76 + 20 * q^77 - 32 * q^78 + 3 * q^79 - 24 * q^80 - 10 * q^81 + 15 * q^82 + 41 * q^84 - 78 * q^85 + 3 * q^86 - 6 * q^87 - 22 * q^88 - 4 * q^90 + 4 * q^91 + 142 * q^92 + 36 * q^94 - 84 * q^95 - 24 * q^96 - 15 * q^97 + 81 * q^98

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