LMFDB - Embedded newform 133.2.i.c.12.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [133,2,Mod(12,133)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(133, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([5, 5]))

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

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

chi := DirichletCharacter("133.12");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 133 = 7 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	133.i (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:	$1.06201034688$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{6})$
Coefficient field:	$\Q(\sqrt{-3}, \sqrt{-7})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} - x^{2} - 2x + 4 $ x^4 - x^3 - x^2 - 2*x + 4
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			12.1
Root			$1.39564 - 0.228425i$ of defining polynomial
Character	$\chi$	$=$	133.12
Dual form			133.2.i.c.122.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.456850i q^{2} +(-0.895644 + 1.55130i) q^{3} +1.79129 q^{4} -1.27520i q^{5} +(0.708712 + 0.409175i) q^{6} +(0.500000 + 2.59808i) q^{7} -1.73205i q^{8} +(-0.104356 - 0.180750i) q^{9} +O(q^{10})$	\(q-0.456850i q^{2} +(-0.895644 + 1.55130i) q^{3} +1.79129 q^{4} -1.27520i q^{5} +(0.708712 + 0.409175i) q^{6} +(0.500000 + 2.59808i) q^{7} -1.73205i q^{8} +(-0.104356 - 0.180750i) q^{9} -0.582576 q^{10} +(1.50000 + 2.59808i) q^{11} +(-1.60436 + 2.77883i) q^{12} +(1.89564 - 3.28335i) q^{13} +(1.18693 - 0.228425i) q^{14} +(1.97822 + 1.14213i) q^{15} +2.79129 q^{16} +(-3.79129 - 2.18890i) q^{17} +(-0.0825757 + 0.0476751i) q^{18} +(-4.00000 + 1.73205i) q^{19} -2.28425i q^{20} +(-4.47822 - 1.55130i) q^{21} +(1.18693 - 0.685275i) q^{22} +(-3.79129 - 6.56670i) q^{23} +(2.68693 + 1.55130i) q^{24} +3.37386 q^{25} +(-1.50000 - 0.866025i) q^{26} -5.00000 q^{27} +(0.895644 + 4.65390i) q^{28} +(-3.08258 - 1.77973i) q^{29} +(0.521780 - 0.903750i) q^{30} -4.73930i q^{32} -5.37386 q^{33} +(-1.00000 + 1.73205i) q^{34} +(3.31307 - 0.637600i) q^{35} +(-0.186932 - 0.323775i) q^{36} +(-8.68693 - 5.01540i) q^{37} +(0.791288 + 1.82740i) q^{38} +(3.39564 + 5.88143i) q^{39} -2.20871 q^{40} +(2.68693 + 4.65390i) q^{41} +(-0.708712 + 2.04588i) q^{42} +(3.39564 + 5.88143i) q^{43} +(2.68693 + 4.65390i) q^{44} +(-0.230493 + 0.133075i) q^{45} +(-3.00000 + 1.73205i) q^{46} +(5.29129 - 3.05493i) q^{47} +(-2.50000 + 4.33013i) q^{48} +(-6.50000 + 2.59808i) q^{49} -1.54135i q^{50} +(6.79129 - 3.92095i) q^{51} +(3.39564 - 5.88143i) q^{52} +1.27520i q^{53} +2.28425i q^{54} +(3.31307 - 1.91280i) q^{55} +(4.50000 - 0.866025i) q^{56} +(0.895644 - 7.75650i) q^{57} +(-0.813068 + 1.40828i) q^{58} +(4.89564 - 8.47950i) q^{59} +(3.54356 + 2.04588i) q^{60} +(1.18693 - 0.685275i) q^{61} +(0.417424 - 0.361500i) q^{63} +3.41742 q^{64} +(-4.18693 - 2.41733i) q^{65} +2.45505i q^{66} -3.46410i q^{67} +(-6.79129 - 3.92095i) q^{68} +13.5826 q^{69} +(-0.291288 - 1.51358i) q^{70} +(-3.08258 + 1.77973i) q^{71} +(-0.313068 + 0.180750i) q^{72} +(5.37386 + 3.10260i) q^{73} +(-2.29129 + 3.96863i) q^{74} +(-3.02178 + 5.23388i) q^{75} +(-7.16515 + 3.10260i) q^{76} +(-6.00000 + 5.19615i) q^{77} +(2.68693 - 1.55130i) q^{78} +6.92820i q^{79} -3.55945i q^{80} +(4.79129 - 8.29875i) q^{81} +(2.12614 - 1.22753i) q^{82} +13.5903i q^{83} +(-8.02178 - 2.77883i) q^{84} +(-2.79129 + 4.83465i) q^{85} +(2.68693 - 1.55130i) q^{86} +(5.52178 - 3.18800i) q^{87} +(4.50000 - 2.59808i) q^{88} +(1.18693 + 2.05583i) q^{89} +(0.0607953 + 0.105301i) q^{90} +(9.47822 + 3.28335i) q^{91} +(-6.79129 - 11.7629i) q^{92} +(-1.39564 - 2.41733i) q^{94} +(2.20871 + 5.10080i) q^{95} +(7.35208 + 4.24473i) q^{96} +(1.00000 + 1.73205i) q^{97} +(1.18693 + 2.96953i) q^{98} +(0.313068 - 0.542250i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + q^{3} - 2 q^{4} + 12 q^{6} + 2 q^{7} - 5 q^{9}+O(q^{10}) $ 4 * q + q^3 - 2 * q^4 + 12 * q^6 + 2 * q^7 - 5 * q^9	$ 4 q + q^{3} - 2 q^{4} + 12 q^{6} + 2 q^{7} - 5 q^{9} + 16 q^{10} + 6 q^{11} - 11 q^{12} + 3 q^{13} - 9 q^{14} - 15 q^{15} + 2 q^{16} - 6 q^{17} + 18 q^{18} - 16 q^{19} + 5 q^{21} - 9 q^{22} - 6 q^{23} - 3 q^{24} - 14 q^{25} - 6 q^{26} - 20 q^{27} - q^{28} + 6 q^{29} + 25 q^{30} + 6 q^{33} - 4 q^{34} + 27 q^{35} + 13 q^{36} - 21 q^{37} - 6 q^{38} + 9 q^{39} - 18 q^{40} - 3 q^{41} - 12 q^{42} + 9 q^{43} - 3 q^{44} - 33 q^{45} - 12 q^{46} + 12 q^{47} - 10 q^{48} - 26 q^{49} + 18 q^{51} + 9 q^{52} + 27 q^{55} + 18 q^{56} - q^{57} - 17 q^{58} + 15 q^{59} + 60 q^{60} - 9 q^{61} + 20 q^{63} + 32 q^{64} - 3 q^{65} - 18 q^{68} + 36 q^{69} + 8 q^{70} + 6 q^{71} - 15 q^{72} - 6 q^{73} - 35 q^{75} + 8 q^{76} - 24 q^{77} - 3 q^{78} + 10 q^{81} + 36 q^{82} - 55 q^{84} - 2 q^{85} - 3 q^{86} + 45 q^{87} + 18 q^{88} - 9 q^{89} - 41 q^{90} + 15 q^{91} - 18 q^{92} - q^{94} + 18 q^{95} - 21 q^{96} + 4 q^{97} - 9 q^{98} + 15 q^{99}+O(q^{100}) $ 4 * q + q^3 - 2 * q^4 + 12 * q^6 + 2 * q^7 - 5 * q^9 + 16 * q^10 + 6 * q^11 - 11 * q^12 + 3 * q^13 - 9 * q^14 - 15 * q^15 + 2 * q^16 - 6 * q^17 + 18 * q^18 - 16 * q^19 + 5 * q^21 - 9 * q^22 - 6 * q^23 - 3 * q^24 - 14 * q^25 - 6 * q^26 - 20 * q^27 - q^28 + 6 * q^29 + 25 * q^30 + 6 * q^33 - 4 * q^34 + 27 * q^35 + 13 * q^36 - 21 * q^37 - 6 * q^38 + 9 * q^39 - 18 * q^40 - 3 * q^41 - 12 * q^42 + 9 * q^43 - 3 * q^44 - 33 * q^45 - 12 * q^46 + 12 * q^47 - 10 * q^48 - 26 * q^49 + 18 * q^51 + 9 * q^52 + 27 * q^55 + 18 * q^56 - q^57 - 17 * q^58 + 15 * q^59 + 60 * q^60 - 9 * q^61 + 20 * q^63 + 32 * q^64 - 3 * q^65 - 18 * q^68 + 36 * q^69 + 8 * q^70 + 6 * q^71 - 15 * q^72 - 6 * q^73 - 35 * q^75 + 8 * q^76 - 24 * q^77 - 3 * q^78 + 10 * q^81 + 36 * q^82 - 55 * q^84 - 2 * q^85 - 3 * q^86 + 45 * q^87 + 18 * q^88 - 9 * q^89 - 41 * q^90 + 15 * q^91 - 18 * q^92 - q^94 + 18 * q^95 - 21 * q^96 + 4 * q^97 - 9 * q^98 + 15 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/133\mathbb{Z}\right)^\times$.

$n$	$78$	$115$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{5}{6}\right)$

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 $

$2$		−	0.456850i		−	0.323042i	−0.986869	−	0.161521i	$-0.948360\pi$
$2$		−	0.456850i		−	0.323042i	0.986869	−	0.161521i	$-0.0516399\pi$
$3$	−0.895644	+	1.55130i	−0.517100	+	0.895644i	0.482703	+	0.875784i	$0.339655\pi$
$3$	−0.895644	+	1.55130i	−0.517100	+	0.895644i	−0.999803	+	0.0198595i	$0.993678\pi$
$4$	1.79129			0.895644
$5$		−	1.27520i		−	0.570287i	−0.958485	−	0.285144i	$-0.907959\pi$
$5$		−	1.27520i		−	0.570287i	0.958485	−	0.285144i	$-0.0920413\pi$
$6$	0.708712	+	0.409175i	0.289331	+	0.167045i
$7$	0.500000	+	2.59808i	0.188982	+	0.981981i
$7$	0.500000	+	2.59808i	0.188982	+	0.981981i
$8$		−	1.73205i		−	0.612372i
$9$	−0.104356	−	0.180750i	−0.0347854	−	0.0602500i
$10$	−0.582576			−0.184227
$11$	1.50000	+	2.59808i	0.452267	+	0.783349i	0.998526	−	0.0542666i	$-0.0172821\pi$
$11$	1.50000	+	2.59808i	0.452267	+	0.783349i	−0.546259	+	0.837616i	$0.683949\pi$
$12$	−1.60436	+	2.77883i	−0.463138	+	0.802178i
$13$	1.89564	−	3.28335i	0.525757	−	0.910638i	−0.473793	−	0.880636i	$-0.657115\pi$
$13$	1.89564	−	3.28335i	0.525757	−	0.910638i	0.999550	−	0.0300015i	$-0.00955122\pi$
$14$	1.18693	−	0.228425i	0.317221	−	0.0610492i
$15$	1.97822	+	1.14213i	0.510774	+	0.294896i
$16$	2.79129			0.697822
$17$	−3.79129	−	2.18890i	−0.919522	−	0.530886i	−0.0360397	−	0.999350i	$-0.511474\pi$
$17$	−3.79129	−	2.18890i	−0.919522	−	0.530886i	−0.883483	+	0.468464i	$0.844808\pi$
$18$	−0.0825757	+	0.0476751i	−0.0194633	+	0.0112371i
$19$	−4.00000	+	1.73205i	−0.917663	+	0.397360i
$19$	−4.00000	+	1.73205i	−0.917663	+	0.397360i
$20$		−	2.28425i		−	0.510774i
$21$	−4.47822	−	1.55130i	−0.977228	−	0.338522i
$22$	1.18693	−	0.685275i	0.253055	−	0.146101i
$23$	−3.79129	−	6.56670i	−0.790538	−	1.36925i	−0.925634	−	0.378420i	$-0.876468\pi$
$23$	−3.79129	−	6.56670i	−0.790538	−	1.36925i	0.135096	−	0.990833i	$-0.456866\pi$
$24$	2.68693	+	1.55130i	0.548468	+	0.316658i
$25$	3.37386			0.674773
$26$	−1.50000	−	0.866025i	−0.294174	−	0.169842i
$27$	−5.00000			−0.962250
$28$	0.895644	+	4.65390i	0.169261	+	0.879505i
$29$	−3.08258	−	1.77973i	−0.572420	−	0.330487i	0.185695	−	0.982607i	$-0.440546\pi$
$29$	−3.08258	−	1.77973i	−0.572420	−	0.330487i	−0.758115	+	0.652121i	$0.773880\pi$
$30$	0.521780	−	0.903750i	0.0952636	−	0.165001i
$31$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$31$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$32$		−	4.73930i		−	0.837798i
$33$	−5.37386			−0.935470
$34$	−1.00000	+	1.73205i	−0.171499	+	0.297044i
$35$	3.31307	−	0.637600i	0.560011	−	0.107774i
$36$	−0.186932	−	0.323775i	−0.0311553	−	0.0539626i
$37$	−8.68693	−	5.01540i	−1.42812	−	0.824527i	−0.431150	−	0.902280i	$-0.641892\pi$
$37$	−8.68693	−	5.01540i	−1.42812	−	0.824527i	−0.996973	+	0.0777531i	$0.975225\pi$
$38$	0.791288	+	1.82740i	0.128364	+	0.296444i
$39$	3.39564	+	5.88143i	0.543738	+	0.941782i
$40$	−2.20871			−0.349228
$41$	2.68693	+	4.65390i	0.419628	+	0.726817i	0.995902	−	0.0904393i	$-0.0288271\pi$
$41$	2.68693	+	4.65390i	0.419628	+	0.726817i	−0.576274	+	0.817257i	$0.695494\pi$
$42$	−0.708712	+	2.04588i	−0.109357	+	0.315685i
$43$	3.39564	+	5.88143i	0.517831	+	0.896909i	0.999785	+	0.0207131i	$0.00659367\pi$
$43$	3.39564	+	5.88143i	0.517831	+	0.896909i	−0.481955	+	0.876196i	$0.660073\pi$
$44$	2.68693	+	4.65390i	0.405070	+	0.701602i
$45$	−0.230493	+	0.133075i	−0.0343598	+	0.0198376i
$46$	−3.00000	+	1.73205i	−0.442326	+	0.255377i
$47$	5.29129	−	3.05493i	0.771814	−	0.445607i	−0.0617076	−	0.998094i	$-0.519655\pi$
$47$	5.29129	−	3.05493i	0.771814	−	0.445607i	0.833521	+	0.552487i	$0.186321\pi$
$48$	−2.50000	+	4.33013i	−0.360844	+	0.625000i
$49$	−6.50000	+	2.59808i	−0.928571	+	0.371154i
$50$		−	1.54135i		−	0.217980i
$51$	6.79129	−	3.92095i	0.950971	−	0.549043i
$52$	3.39564	−	5.88143i	0.470891	−	0.815607i
$53$			1.27520i			0.175162i	0.996157	+	0.0875811i	$0.0279137\pi$
$53$			1.27520i			0.175162i	−0.996157	+	0.0875811i	$0.972086\pi$
$54$			2.28425i			0.310847i
$55$	3.31307	−	1.91280i	0.446734	−	0.257922i
$56$	4.50000	−	0.866025i	0.601338	−	0.115728i
$57$	0.895644	−	7.75650i	0.118631	−	1.02737i
$58$	−0.813068	+	1.40828i	−0.106761	+	0.184916i
$59$	4.89564	−	8.47950i	0.637359	−	1.10394i	−0.348652	−	0.937252i	$-0.613360\pi$
$59$	4.89564	−	8.47950i	0.637359	−	1.10394i	0.986010	−	0.166685i	$-0.0533063\pi$
$60$	3.54356	+	2.04588i	0.457472	+	0.264121i
$61$	1.18693	−	0.685275i	0.151971	−	0.0877405i	−0.422086	−	0.906556i	$-0.638702\pi$
$61$	1.18693	−	0.685275i	0.151971	−	0.0877405i	0.574057	+	0.818815i	$0.305369\pi$
$62$		0			0
$63$	0.417424	−	0.361500i	0.0525905	−	0.0455447i
$64$	3.41742			0.427178
$65$	−4.18693	−	2.41733i	−0.519325	−	0.299832i
$66$			2.45505i			0.302196i
$67$		−	3.46410i		−	0.423207i	−0.977356	−	0.211604i	$-0.932131\pi$
$67$		−	3.46410i		−	0.423207i	0.977356	−	0.211604i	$-0.0678686\pi$
$68$	−6.79129	−	3.92095i	−0.823565	−	0.475485i
$69$	13.5826			1.63515
$70$	−0.291288	−	1.51358i	−0.0348156	−	0.180907i
$71$	−3.08258	+	1.77973i	−0.365834	+	0.211215i	−0.671637	−	0.740880i	$-0.734409\pi$
$71$	−3.08258	+	1.77973i	−0.365834	+	0.211215i	0.305803	+	0.952095i	$0.401075\pi$
$72$	−0.313068	+	0.180750i	−0.0368954	+	0.0213016i
$73$	5.37386	+	3.10260i	0.628963	+	0.363132i	0.780350	−	0.625342i	$-0.215041\pi$
$73$	5.37386	+	3.10260i	0.628963	+	0.363132i	−0.151387	+	0.988475i	$0.548374\pi$
$74$	−2.29129	+	3.96863i	−0.266357	+	0.461344i
$75$	−3.02178	+	5.23388i	−0.348925	+	0.604356i
$76$	−7.16515	+	3.10260i	−0.821899	+	0.355893i
$77$	−6.00000	+	5.19615i	−0.683763	+	0.592157i
$78$	2.68693	−	1.55130i	0.304235	−	0.175650i
$79$			6.92820i			0.779484i	0.920924	+	0.389742i	$0.127436\pi$
$79$			6.92820i			0.779484i	−0.920924	+	0.389742i	$0.872564\pi$
$80$		−	3.55945i		−	0.397959i
$81$	4.79129	−	8.29875i	0.532365	−	0.922084i
$82$	2.12614	−	1.22753i	0.234792	−	0.135558i
$83$			13.5903i			1.49172i	0.666100	+	0.745862i	$0.267962\pi$
$83$			13.5903i			1.49172i	−0.666100	+	0.745862i	$0.732038\pi$
$84$	−8.02178	−	2.77883i	−0.875248	−	0.303195i
$85$	−2.79129	+	4.83465i	−0.302758	+	0.524392i
$86$	2.68693	−	1.55130i	0.289739	−	0.167281i
$87$	5.52178	−	3.18800i	0.591997	−	0.341790i
$88$	4.50000	−	2.59808i	0.479702	−	0.276956i
$89$	1.18693	+	2.05583i	0.125815	+	0.217917i	0.922051	−	0.387068i	$-0.126512\pi$
$89$	1.18693	+	2.05583i	0.125815	+	0.217917i	−0.796237	+	0.604985i	$0.793179\pi$
$90$	0.0607953	+	0.105301i	0.00640839	+	0.0110997i
$91$	9.47822	+	3.28335i	0.993587	+	0.344189i
$92$	−6.79129	−	11.7629i	−0.708041	−	1.22636i
$93$		0			0
$94$	−1.39564	−	2.41733i	−0.143950	−	0.249328i
$95$	2.20871	+	5.10080i	0.226609	+	0.523331i
$96$	7.35208	+	4.24473i	0.750369	+	0.433226i
$97$	1.00000	+	1.73205i	0.101535	+	0.175863i	0.912317	−	0.409484i	$-0.134291\pi$
$97$	1.00000	+	1.73205i	0.101535	+	0.175863i	−0.810782	+	0.585348i	$0.800958\pi$
$98$	1.18693	+	2.96953i	0.119898	+	0.299967i
$99$	0.313068	−	0.542250i	0.0314645	−	0.0544982i
$100$	6.04356			0.604356
$101$			8.56490i			0.852240i	0.904667	+	0.426120i	$0.140120\pi$
$101$			8.56490i			0.852240i	−0.904667	+	0.426120i	$0.859880\pi$
$102$	−1.79129	−	3.10260i	−0.177364	−	0.307203i
$103$	−1.68693	+	2.92185i	−0.166218	+	0.287899i	−0.937087	−	0.349095i	$-0.886489\pi$
$103$	−1.68693	+	2.92185i	−0.166218	+	0.287899i	0.770869	+	0.636994i	$0.219822\pi$
$104$	−5.68693	−	3.28335i	−0.557650	−	0.321959i
$105$	−1.97822	+	5.71063i	−0.193054	+	0.557300i
$106$	0.582576			0.0565848
$107$	−8.20871	−	4.73930i	−0.793566	−	0.458166i	0.0476503	−	0.998864i	$-0.484827\pi$
$107$	−8.20871	−	4.73930i	−0.793566	−	0.458166i	−0.841216	+	0.540698i	$0.818160\pi$
$108$	−8.95644			−0.861834
$109$	−11.6869	−	6.74745i	−1.11941	−	0.646289i	−0.178156	−	0.984002i	$-0.557013\pi$
$109$	−11.6869	−	6.74745i	−1.11941	−	0.646289i	−0.941249	+	0.337713i	$0.890347\pi$
$110$	−0.873864	−	1.51358i	−0.0833196	−	0.144314i
$111$	15.5608	−	8.98403i	1.47697	−	0.852726i
$112$	1.39564	+	7.25198i	0.131876	+	0.685248i
$113$			13.2288i			1.24446i	0.782836	+	0.622228i	$0.213772\pi$
$113$			13.2288i			1.24446i	−0.782836	+	0.622228i	$0.786228\pi$
$114$	−3.54356	−	0.409175i	−0.331885	−	0.0383228i
$115$	−8.37386	+	4.83465i	−0.780867	+	0.450834i
$116$	−5.52178	−	3.18800i	−0.512684	−	0.295998i
$117$	−0.791288			−0.0731546
$118$	−3.87386	−	2.23658i	−0.356618	−	0.205894i
$119$	3.79129	−	10.9445i	0.347547	−	1.00328i
$120$	1.97822	−	3.42638i	0.180586	−	0.312784i
$121$	1.00000	−	1.73205i	0.0909091	−	0.157459i
$122$	−0.313068	−	0.542250i	−0.0283439	−	0.0490930i
$123$	−9.62614			−0.867959
$124$		0			0
$125$		−	10.6784i		−	0.955101i
$126$	−0.165151	−	0.190700i	−0.0147129	−	0.0169889i
$127$	10.1869	+	5.88143i	0.903944	+	0.521892i	0.878478	−	0.477783i	$-0.158560\pi$
$127$	10.1869	+	5.88143i	0.903944	+	0.521892i	0.0254663	+	0.999676i	$0.491893\pi$
$128$		−	11.0399i		−	0.975795i
$129$	−12.1652			−1.07108
$130$	−1.10436	+	1.91280i	−0.0968584	+	0.167764i
$131$		−	7.11890i		−	0.621981i	−0.950413	−	0.310991i	$-0.899339\pi$
$131$		−	7.11890i		−	0.621981i	0.950413	−	0.310991i	$-0.100661\pi$
$132$	−9.62614			−0.837848
$133$	−6.50000	−	9.52628i	−0.563621	−	0.826033i
$134$	−1.58258			−0.136714
$135$			6.37600i			0.548759i
$136$	−3.79129	+	6.56670i	−0.325100	+	0.563090i
$137$	−9.95644			−0.850636			−0.425318	−	0.905044i	$-0.639838\pi$
$137$	−9.95644			−0.850636			−0.425318	+	0.905044i	$0.639838\pi$
$138$		−	6.20520i		−	0.528222i
$139$	−9.24773	−	5.33918i	−0.784382	−	0.452863i	0.0535990	−	0.998563i	$-0.482931\pi$
$139$	−9.24773	−	5.33918i	−0.784382	−	0.452863i	−0.837981	+	0.545699i	$0.816264\pi$
$140$	5.93466	−	1.14213i	0.501570	−	0.0965272i
$141$			10.9445i			0.921694i
$142$	0.813068	+	1.40828i	0.0682312	+	0.118180i
$143$	11.3739			0.951130
$144$	−0.291288	−	0.504525i	−0.0242740	−	0.0420438i
$145$	−2.26951	+	3.93090i	−0.188472	+	0.326444i
$146$	1.41742	−	2.45505i	0.117307	−	0.203181i
$147$	1.79129	−	12.4104i	0.147743	−	1.02359i
$148$	−15.5608	−	8.98403i	−1.27909	−	0.738483i
$149$	11.2087			0.918253			0.459127	−	0.888371i	$-0.348162\pi$
$149$	11.2087			0.918253			0.459127	+	0.888371i	$0.348162\pi$
$150$	2.39110	+	1.38050i	0.195232	+	0.112717i
$151$	15.5608	−	8.98403i	1.26632	−	0.731110i	0.292030	−	0.956409i	$-0.405669\pi$
$151$	15.5608	−	8.98403i	1.26632	−	0.731110i	0.974290	+	0.225299i	$0.0723360\pi$
$152$	3.00000	+	6.92820i	0.243332	+	0.561951i
$153$			0.913701i			0.0738683i
$154$	2.37386	+	2.74110i	0.191291	+	0.220884i
$155$		0			0
$156$	6.08258	+	10.5353i	0.486996	+	0.843501i
$157$	−10.1869	−	5.88143i	−0.813006	−	0.469389i	0.0349929	−	0.999388i	$-0.488859\pi$
$157$	−10.1869	−	5.88143i	−0.813006	−	0.469389i	−0.847999	+	0.529999i	$0.822192\pi$
$158$	3.16515			0.251806
$159$	−1.97822	−	1.14213i	−0.156883	−	0.0905765i
$160$	−6.04356			−0.477785
$161$	15.1652	−	13.1334i	1.19518	−	1.03506i
$162$	−3.79129	−	2.18890i	−0.297872	−	0.171976i
$163$	3.00000	−	5.19615i	0.234978	−	0.406994i	−0.724288	−	0.689497i	$-0.757831\pi$
$163$	3.00000	−	5.19615i	0.234978	−	0.406994i	0.959266	+	0.282503i	$0.0911648\pi$
$164$	4.81307	+	8.33648i	0.375837	+	0.650970i
$165$			6.85275i			0.533486i
$166$	6.20871			0.481890
$167$	−9.56080	+	16.5598i	−0.739837	+	1.28143i	0.212732	+	0.977111i	$0.431764\pi$
$167$	−9.56080	+	16.5598i	−0.739837	+	1.28143i	−0.952569	+	0.304324i	$0.901569\pi$
$168$	−2.68693	+	7.75650i	−0.207301	+	0.598427i
$169$	−0.686932	−	1.18980i	−0.0528409	−	0.0915231i
$170$	2.20871	+	1.27520i	0.169400	+	0.0978034i
$171$	0.730493	+	0.542250i	0.0558622	+	0.0414669i
$172$	6.08258	+	10.5353i	0.463792	+	0.803311i
$173$	19.7477			1.50139			0.750696	−	0.660648i	$-0.229718\pi$
$173$	19.7477			1.50139			0.750696	+	0.660648i	$0.229718\pi$
$174$	−1.45644	−	2.52263i	−0.110412	−	0.191240i
$175$	1.68693	+	8.76555i	0.127520	+	0.662614i
$176$	4.18693	+	7.25198i	0.315602	+	0.546638i
$177$	8.76951	+	15.1892i	0.659157	+	1.14169i
$178$	0.939205	−	0.542250i	0.0703964	−	0.0406434i
$179$	−12.7913	+	7.38505i	−0.956066	+	0.551985i	−0.894960	−	0.446146i	$-0.852796\pi$
$179$	−12.7913	+	7.38505i	−0.956066	+	0.551985i	−0.0611058	+	0.998131i	$0.519463\pi$
$180$	−0.412878	+	0.238375i	−0.0307741	+	0.0177675i
$181$	5.87386	−	10.1738i	0.436601	−	0.756215i	−0.560824	−	0.827935i	$-0.689516\pi$
$181$	5.87386	−	10.1738i	0.436601	−	0.756215i	0.997425	+	0.0717202i	$0.0228489\pi$
$182$	1.50000	−	4.33013i	0.111187	−	0.320970i
$183$			2.45505i			0.181483i
$184$	−11.3739	+	6.56670i	−0.838492	+	0.484104i
$185$	−6.39564	+	11.0776i	−0.470217	+	0.814440i
$186$		0			0
$187$		−	13.1334i		−	0.960410i
$188$	9.47822	−	5.47225i	0.691270	−	0.399105i
$189$	−2.50000	−	12.9904i	−0.181848	−	0.944911i
$190$	2.33030	−	1.00905i	0.169058	−	0.0732042i
$191$	−10.2695	+	17.7873i	−0.743075	+	1.28704i	0.208013	+	0.978126i	$0.433300\pi$
$191$	−10.2695	+	17.7873i	−0.743075	+	1.28704i	−0.951089	+	0.308918i	$0.900033\pi$
$192$	−3.06080	+	5.30145i	−0.220894	+	0.382599i
$193$	21.2477	+	12.2674i	1.52944	+	0.883025i	0.999385	+	0.0350652i	$0.0111639\pi$
$193$	21.2477	+	12.2674i	1.52944	+	0.883025i	0.530060	+	0.847960i	$0.322169\pi$
$194$	0.791288	−	0.456850i	0.0568112	−	0.0327999i
$195$	7.50000	−	4.33013i	0.537086	−	0.310087i
$196$	−11.6434	+	4.65390i	−0.831669	+	0.332422i
$197$	−12.0000			−0.854965			−0.427482	−	0.904024i	$-0.640599\pi$
$197$	−12.0000			−0.854965			−0.427482	+	0.904024i	$0.640599\pi$
$198$	−0.247727	−	0.143025i	−0.0176052	−	0.0101644i
$199$		−	22.0797i		−	1.56519i	−0.622532	−	0.782595i	$-0.713896\pi$
$199$		−	22.0797i		−	1.56519i	0.622532	−	0.782595i	$-0.286104\pi$
$200$		−	5.84370i		−	0.413212i
$201$	5.37386	+	3.10260i	0.379043	+	0.218841i
$202$	3.91288			0.275309
$203$	3.08258	−	8.89863i	0.216354	−	0.624561i
$204$	12.1652	−	7.02355i	0.851731	−	0.491747i
$205$	5.93466	−	3.42638i	0.414495	−	0.239309i
$206$	1.33485	+	0.770675i	0.0930033	+	0.0536955i
$207$	−0.791288	+	1.37055i	−0.0549983	+	0.0952599i
$208$	5.29129	−	9.16478i	0.366885	−	0.635463i
$209$	−10.5000	−	7.79423i	−0.726300	−	0.539138i
$210$	2.60890	+	0.903750i	0.180031	+	0.0623647i
$211$	−12.2477	+	7.07123i	−0.843168	+	0.486803i	−0.858340	−	0.513081i	$-0.828504\pi$
$211$	−12.2477	+	7.07123i	−0.843168	+	0.486803i	0.0151716	+	0.999885i	$0.495171\pi$
$212$			2.28425i			0.156883i
$213$		−	6.37600i		−	0.436877i
$214$	−2.16515	+	3.75015i	−0.148007	+	0.256355i
$215$	7.50000	−	4.33013i	0.511496	−	0.295312i
$216$			8.66025i			0.589256i
$217$		0			0
$218$	−3.08258	+	5.33918i	−0.208778	+	0.361615i
$219$	−9.62614	+	5.55765i	−0.650474	+	0.375551i
$220$	5.93466	−	3.42638i	0.400115	−	0.231006i
$221$	−14.3739	+	8.29875i	−0.966891	+	0.558235i
$222$	−4.10436	−	7.10895i	−0.275466	−	0.477122i
$223$	6.79129	+	11.7629i	0.454778	+	0.787699i	0.998675	−	0.0514528i	$-0.0163852\pi$
$223$	6.79129	+	11.7629i	0.454778	+	0.787699i	−0.543897	+	0.839152i	$0.683052\pi$
$224$	12.3131	−	2.36965i	0.822701	−	0.158329i
$225$	−0.352083	−	0.609826i	−0.0234722	−	0.0406551i
$226$	6.04356			0.402012
$227$	13.2695	+	22.9835i	0.880728	+	1.52547i	0.850533	+	0.525922i	$0.176280\pi$
$227$	13.2695	+	22.9835i	0.880728	+	1.52547i	0.0301953	+	0.999544i	$0.490387\pi$
$228$	1.60436	−	13.8941i	0.106251	−	0.920161i
$229$	6.00000	+	3.46410i	0.396491	+	0.228914i	0.684969	−	0.728572i	$-0.259816\pi$
$229$	6.00000	+	3.46410i	0.396491	+	0.228914i	−0.288478	+	0.957487i	$0.593149\pi$
$230$	2.20871	+	3.82560i	0.145638	+	0.252253i
$231$	−2.68693	−	13.9617i	−0.176787	−	0.918613i
$232$	−3.08258	+	5.33918i	−0.202381	+	0.350534i
$233$	−13.4174			−0.879005			−0.439502	−	0.898241i	$-0.644845\pi$
$233$	−13.4174			−0.879005			−0.439502	+	0.898241i	$0.644845\pi$
$234$			0.361500i			0.0236320i
$235$	−3.89564	−	6.74745i	−0.254124	−	0.440155i
$236$	8.76951	−	15.1892i	0.570846	−	0.988735i
$237$	−10.7477	−	6.20520i	−0.698140	−	0.403071i
$238$	−5.00000	−	1.73205i	−0.324102	−	0.112272i
$239$	14.5390			0.940451			0.470225	−	0.882546i	$-0.344173\pi$
$239$	14.5390			0.940451			0.470225	+	0.882546i	$0.344173\pi$
$240$	5.52178	+	3.18800i	0.356429	+	0.205785i
$241$	7.37386			0.474992			0.237496	−	0.971388i	$-0.423673\pi$
$241$	7.37386			0.474992			0.237496	+	0.971388i	$0.423673\pi$
$242$	−0.791288	−	0.456850i	−0.0508659	−	0.0293674i
$243$	1.08258	+	1.87508i	0.0694473	+	0.120286i
$244$	2.12614	−	1.22753i	0.136112	−	0.0785843i
$245$	3.31307	+	8.28880i	0.211664	+	0.529552i
$246$			4.39770i			0.280387i
$247$	−1.89564	+	16.4168i	−0.120617	+	1.04457i
$248$		0			0
$249$	−21.0826	−	12.1720i	−1.33605	−	0.771371i
$250$	−4.87841			−0.308538
$251$	−8.29129	−	4.78698i	−0.523341	−	0.302151i	0.214959	−	0.976623i	$-0.431038\pi$
$251$	−8.29129	−	4.78698i	−0.523341	−	0.302151i	−0.738301	+	0.674472i	$0.764371\pi$
$252$	0.747727	−	0.647551i	0.0471024	−	0.0407919i
$253$	11.3739	−	19.7001i	0.715069	−	1.23854i
$254$	2.68693	−	4.65390i	0.168593	−	0.292012i
$255$	−5.00000	−	8.66025i	−0.313112	−	0.542326i
$256$	1.79129			0.111955
$257$	9.87386	+	17.1020i	0.615915	+	1.06680i	0.990223	+	0.139491i	$0.0445467\pi$
$257$	9.87386	+	17.1020i	0.615915	+	1.06680i	−0.374309	+	0.927304i	$0.622120\pi$
$258$			5.55765i			0.346004i
$259$	8.68693	−	25.0770i	0.539780	−	1.55821i
$260$	−7.50000	−	4.33013i	−0.465130	−	0.268543i
$261$			0.742901i			0.0459844i
$262$	−3.25227			−0.200926
$263$	−6.00000	+	10.3923i	−0.369976	+	0.640817i	−0.989561	−	0.144112i	$-0.953967\pi$
$263$	−6.00000	+	10.3923i	−0.369976	+	0.640817i	0.619586	+	0.784929i	$0.287301\pi$
$264$			9.30780i			0.572856i
$265$	1.62614			0.0998928
$266$	−4.35208	+	2.96953i	−0.266843	+	0.182073i
$267$	−4.25227			−0.260235
$268$		−	6.20520i		−	0.379043i
$269$	−3.79129	+	6.56670i	−0.231159	+	0.400379i	−0.958149	−	0.286269i	$-0.907585\pi$
$269$	−3.79129	+	6.56670i	−0.231159	+	0.400379i	0.726991	+	0.686647i	$0.240918\pi$
$270$	2.91288			0.177272
$271$			13.4949i			0.819757i	0.912140	+	0.409879i	$0.134429\pi$
$271$			13.4949i			0.819757i	−0.912140	+	0.409879i	$0.865571\pi$
$272$	−10.5826	−	6.10985i	−0.641663	−	0.370464i
$273$	−13.5826	+	11.7629i	−0.822055	+	0.711920i
$274$			4.54860i			0.274791i
$275$	5.06080	+	8.76555i	0.305177	+	0.528583i
$276$	24.3303			1.46451
$277$	−11.7695	−	20.3854i	−0.707161	−	1.22484i	−0.965906	−	0.258893i	$-0.916642\pi$
$277$	−11.7695	−	20.3854i	−0.707161	−	1.22484i	0.258745	−	0.965946i	$-0.416691\pi$
$278$	−2.43920	+	4.22483i	−0.146294	+	0.253388i
$279$		0			0
$280$	−1.10436	−	5.73840i	−0.0659979	−	0.342935i
$281$	1.02178	+	0.589925i	0.0609543	+	0.0351920i	0.530167	−	0.847893i	$-0.322129\pi$
$281$	1.02178	+	0.589925i	0.0609543	+	0.0351920i	−0.469213	+	0.883085i	$0.655462\pi$
$282$	5.00000			0.297746
$283$	−8.37386	−	4.83465i	−0.497775	−	0.287390i	0.230020	−	0.973186i	$-0.426121\pi$
$283$	−8.37386	−	4.83465i	−0.497775	−	0.287390i	−0.727794	+	0.685796i	$0.759454\pi$
$284$	−5.52178	+	3.18800i	−0.327657	+	0.189173i
$285$	−9.89110	−	1.14213i	−0.585898	−	0.0676537i
$286$		−	5.19615i		−	0.307255i
$287$	−10.7477	+	9.30780i	−0.634418	+	0.549422i
$288$	−0.856629	+	0.494575i	−0.0504773	+	0.0291431i
$289$	1.08258	+	1.87508i	0.0636809	+	0.110299i
$290$	1.79583	+	1.03683i	0.105455	+	0.0608845i
$291$	−3.58258			−0.210014
$292$	9.62614	+	5.55765i	0.563327	+	0.325237i
$293$	21.0000			1.22683			0.613417	−	0.789760i	$-0.289795\pi$
$293$	21.0000			1.22683			0.613417	+	0.789760i	$0.289795\pi$
$294$	−5.66970	−	0.818350i	−0.330663	−	0.0477272i
$295$	−10.8131	−	6.24293i	−0.629561	−	0.363477i
$296$	−8.68693	+	15.0462i	−0.504918	+	0.874543i
$297$	−7.50000	−	12.9904i	−0.435194	−	0.753778i
$298$		−	5.12070i		−	0.296634i
$299$	−28.7477			−1.66252
$300$	−5.41288	+	9.37538i	−0.312513	+	0.541288i
$301$	−13.5826	+	11.7629i	−0.782887	+	0.678000i
$302$	−4.10436	−	7.10895i	−0.236179	−	0.409074i
$303$	−13.2867	−	7.67110i	−0.763303	−	0.440693i
$304$	−11.1652	+	4.83465i	−0.640365	+	0.277286i
$305$	−0.873864	−	1.51358i	−0.0500373	−	0.0866671i
$306$	0.417424			0.0238626
$307$	−10.1044	−	17.5013i	−0.576686	−	0.998850i	−0.995856	−	0.0909419i	$-0.971012\pi$
$307$	−10.1044	−	17.5013i	−0.576686	−	0.998850i	0.419170	−	0.907908i	$-0.362321\pi$
$308$	−10.7477	+	9.30780i	−0.612409	+	0.530361i
$309$	−3.02178	−	5.23388i	−0.171903	−	0.297745i
$310$		0			0
$311$	20.7695	−	11.9913i	1.17773	−	0.679963i	0.222242	−	0.974991i	$-0.428662\pi$
$311$	20.7695	−	11.9913i	1.17773	−	0.679963i	0.955489	+	0.295028i	$0.0953291\pi$
$312$	10.1869	−	5.88143i	0.576721	−	0.332970i
$313$	−7.50000	+	4.33013i	−0.423925	+	0.244753i	−0.696755	−	0.717309i	$-0.745374\pi$
$313$	−7.50000	+	4.33013i	−0.423925	+	0.244753i	0.272830	+	0.962062i	$0.412040\pi$
$314$	−2.68693	+	4.65390i	−0.151632	+	0.262635i
$315$	−0.460985	−	0.532300i	−0.0259736	−	0.0299917i
$316$			12.4104i			0.698140i
$317$	12.7087	−	7.33738i	0.713792	−	0.412108i	−0.0986713	−	0.995120i	$-0.531459\pi$
$317$	12.7087	−	7.33738i	0.713792	−	0.412108i	0.812464	+	0.583012i	$0.198126\pi$
$318$	−0.521780	+	0.903750i	−0.0292600	+	0.0506798i
$319$		−	10.6784i		−	0.597873i
$320$		−	4.35790i		−	0.243614i
$321$	14.7042	−	8.48945i	0.820707	−	0.473835i
$322$	−6.00000	−	6.92820i	−0.334367	−	0.386094i
$323$	18.9564	+	2.18890i	1.05476	+	0.121794i
$324$	8.58258	−	14.8655i	0.476810	−	0.825859i
$325$	6.39564	−	11.0776i	0.354766	−	0.614474i
$326$	−2.37386	−	1.37055i	−0.131476	−	0.0759078i
$327$	20.9347	−	12.0866i	1.15769	−	0.668392i
$328$	8.06080	−	4.65390i	0.445083	−	0.256969i
$329$	10.5826	+	12.2197i	0.583436	+	0.673694i
$330$	3.13068			0.172338
$331$	1.81307	+	1.04678i	0.0996552	+	0.0575360i	0.548999	−	0.835823i	$-0.315009\pi$
$331$	1.81307	+	1.04678i	0.0996552	+	0.0575360i	−0.449344	+	0.893359i	$0.648342\pi$
$332$			24.3441i			1.33605i
$333$			2.09355i			0.114726i
$334$	7.56534	+	4.36785i	0.413957	+	0.238998i
$335$	−4.41742			−0.241350
$336$	−12.5000	−	4.33013i	−0.681931	−	0.236228i
$337$	−2.12614	+	1.22753i	−0.115818	+	0.0668676i	−0.556790	−	0.830653i	$-0.687967\pi$
$337$	−2.12614	+	1.22753i	−0.115818	+	0.0668676i	0.440972	+	0.897521i	$0.354634\pi$
$338$	−0.543561	+	0.313825i	−0.0295658	+	0.0170698i
$339$	−20.5218	−	11.8483i	−1.11459	−	0.643509i
$340$	−5.00000	+	8.66025i	−0.271163	+	0.469668i
$341$		0			0
$342$	0.247727	−	0.333726i	0.0133955	−	0.0180458i
$343$	−10.0000	−	15.5885i	−0.539949	−	0.841698i
$344$	10.1869	−	5.88143i	0.549243	−	0.317105i
$345$		−	17.3205i		−	0.932505i
$346$		−	9.02175i		−	0.485013i
$347$	−15.6434	+	27.0951i	−0.839780	+	1.45454i	0.0502981	+	0.998734i	$0.483983\pi$
$347$	−15.6434	+	27.0951i	−0.839780	+	1.45454i	−0.890078	+	0.455808i	$0.849350\pi$
$348$	9.89110	−	5.71063i	0.530219	−	0.306122i
$349$			32.1105i			1.71884i	0.511273	+	0.859418i	$0.329174\pi$
$349$			32.1105i			1.71884i	−0.511273	+	0.859418i	$0.670826\pi$
$350$	4.00455	−	0.770675i	0.214052	−	0.0411943i
$351$	−9.47822	+	16.4168i	−0.505910	+	0.876262i
$352$	12.3131	−	7.10895i	0.656289	−	0.378908i
$353$	−0.230493	+	0.133075i	−0.0122679	+	0.00708286i	−0.506121	−	0.862462i	$-0.668921\pi$
$353$	−0.230493	+	0.133075i	−0.0122679	+	0.00708286i	0.493854	+	0.869545i	$0.335588\pi$
$354$	6.93920	−	4.00635i	0.368815	−	0.212935i
$355$	2.26951	+	3.93090i	0.120453	+	0.208631i
$356$	2.12614	+	3.68258i	0.112685	+	0.195176i
$357$	13.5826	+	15.6838i	0.718866	+	0.830075i
$358$	3.37386	+	5.84370i	0.178314	+	0.308849i
$359$	−0.626136			−0.0330462			−0.0165231	−	0.999863i	$-0.505260\pi$
$359$	−0.626136			−0.0330462			−0.0165231	+	0.999863i	$0.505260\pi$
$360$	0.230493	+	0.399225i	0.0121480	+	0.0210410i
$361$	13.0000	−	13.8564i	0.684211	−	0.729285i
$362$	−4.64792	−	2.68348i	−0.244289	−	0.141040i
$363$	1.79129	+	3.10260i	0.0940182	+	0.162844i
$364$	16.9782	+	5.88143i	0.889901	+	0.308271i
$365$	3.95644	−	6.85275i	0.207089	−	0.358690i
$366$	1.12159			0.0586265
$367$			9.66930i			0.504734i	0.967632	+	0.252367i	$0.0812090\pi$
$367$			9.66930i			0.504734i	−0.967632	+	0.252367i	$0.918791\pi$
$368$	−10.5826	−	18.3296i	−0.551655	−	0.955494i
$369$	0.560795	−	0.971326i	0.0291938	−	0.0505652i
$370$	5.06080	+	2.92185i	0.263098	+	0.151900i
$371$	−3.31307	+	0.637600i	−0.172006	+	0.0331026i
$372$		0			0
$373$	−18.8085	−	10.8591i	−0.973868	−	0.562263i	−0.0734550	−	0.997299i	$-0.523403\pi$
$373$	−18.8085	−	10.8591i	−0.973868	−	0.562263i	−0.900413	+	0.435035i	$0.856736\pi$
$374$	−6.00000			−0.310253
$375$	16.5653	+	9.56400i	0.855431	+	0.493883i
$376$	−5.29129	−	9.16478i	−0.272877	−	0.472637i
$377$	−11.6869	+	6.74745i	−0.601908	+	0.347512i
$378$	−5.93466	+	1.14213i	−0.305246	+	0.0587446i
$379$			26.3423i			1.35311i	0.736392	+	0.676556i	$0.236528\pi$
$379$			26.3423i			1.35311i	−0.736392	+	0.676556i	$0.763472\pi$
$380$	3.95644	+	9.13701i	0.202961	+	0.468718i
$381$	−18.2477	+	10.5353i	−0.934859	+	0.539741i
$382$	8.12614	+	4.69163i	0.415769	+	0.240045i
$383$	−16.9129			−0.864208			−0.432104	−	0.901824i	$-0.642229\pi$
$383$	−16.9129			−0.864208			−0.432104	+	0.901824i	$0.642229\pi$
$384$	17.1261	+	9.88778i	0.873964	+	0.504584i
$385$	6.62614	+	7.65120i	0.337699	+	0.389941i
$386$	5.60436	−	9.70703i	0.285254	−	0.494075i
$387$	0.708712	−	1.22753i	0.0360259	−	0.0623986i
$388$	1.79129	+	3.10260i	0.0909389	+	0.157511i
$389$	33.9564			1.72166			0.860830	−	0.508893i	$-0.169945\pi$
$389$	33.9564			1.72166			0.860830	+	0.508893i	$0.169945\pi$
$390$	−1.97822	−	3.42638i	−0.100171	−	0.173501i
$391$			33.1950i			1.67874i
$392$	4.50000	+	11.2583i	0.227284	+	0.568632i
$393$	11.0436	+	6.37600i	0.557074	+	0.321627i
$394$			5.48220i			0.276189i
$395$	8.83485			0.444529
$396$	0.560795	−	0.971326i	0.0281810	−	0.0488110i
$397$		−	4.47315i		−	0.224501i	−0.993680	−	0.112251i	$-0.964194\pi$
$397$		−	4.47315i		−	0.224501i	0.993680	−	0.112251i	$-0.0358059\pi$
$398$	−10.0871			−0.505622
$399$	20.5998	−	1.55130i	1.03128	−	0.0776622i
$400$	9.41742			0.470871
$401$		−	4.20700i		−	0.210088i	−0.994468	−	0.105044i	$-0.966502\pi$
$401$		−	4.20700i		−	0.210088i	0.994468	−	0.105044i	$-0.0334983\pi$
$402$	1.41742	−	2.45505i	0.0706947	−	0.122447i
$403$		0			0
$404$			15.3422i			0.763303i
$405$	−10.5826	−	6.10985i	−0.525852	−	0.303601i
$406$	−4.06534	−	1.40828i	−0.201759	−	0.0698915i
$407$		−	30.0924i		−	1.49163i
$408$	−6.79129	−	11.7629i	−0.336219	−	0.582348i
$409$	−14.8348			−0.733536			−0.366768	−	0.930312i	$-0.619536\pi$
$409$	−14.8348			−0.733536			−0.366768	+	0.930312i	$0.619536\pi$
$410$	−1.56534	−	2.71125i	−0.0773067	−	0.133899i
$411$	8.91742	−	15.4454i	0.439864	−	0.761867i
$412$	−3.02178	+	5.23388i	−0.148872	+	0.257855i
$413$	24.4782	+	8.47950i	1.20449	+	0.417249i
$414$	0.626136	+	0.361500i	0.0307729	+	0.0177668i
$415$	17.3303			0.850711
$416$	−15.5608	−	8.98403i	−0.762931	−	0.440478i
$417$	16.5653	−	9.56400i	0.811208	−	0.468351i
$418$	−3.56080	+	4.79693i	−0.174164	+	0.234625i
$419$		−	38.7726i		−	1.89416i	−0.320992	−	0.947082i	$-0.604016\pi$
$419$		−	38.7726i		−	1.89416i	0.320992	−	0.947082i	$-0.395984\pi$
$420$	−3.54356	+	10.2294i	−0.172908	+	0.499143i
$421$	13.8131	−	7.97498i	0.673208	−	0.388677i	−0.124083	−	0.992272i	$-0.539599\pi$
$421$	13.8131	−	7.97498i	0.673208	−	0.388677i	0.797291	+	0.603595i	$0.206266\pi$
$422$	3.23049	+	5.59538i	0.157258	+	0.272379i
$423$	−1.10436	−	0.637600i	−0.0536956	−	0.0310012i
$424$	2.20871			0.107265
$425$	−12.7913	−	7.38505i	−0.620469	−	0.358228i
$426$	−2.91288			−0.141129
$427$	2.37386	+	2.74110i	0.114879	+	0.132651i
$428$	−14.7042	−	8.48945i	−0.710753	−	0.410353i
$429$	−10.1869	+	17.6443i	−0.491830	+	0.851874i
$430$	−1.97822	−	3.42638i	−0.0953982	−	0.165235i
$431$			18.1389i			0.873718i	0.899530	+	0.436859i	$0.143909\pi$
$431$			18.1389i			0.873718i	−0.899530	+	0.436859i	$0.856091\pi$
$432$	−13.9564			−0.671479
$433$	18.1869	−	31.5007i	0.874008	−	1.51383i	0.0161926	−	0.999869i	$-0.494846\pi$
$433$	18.1869	−	31.5007i	0.874008	−	1.51383i	0.857816	−	0.513958i	$-0.171821\pi$
$434$		0			0
$435$	−4.06534	−	7.04138i	−0.194918	−	0.337608i
$436$	−20.9347	−	12.0866i	−1.00259	−	0.578845i
$437$	26.5390	+	19.7001i	1.26953	+	0.942384i
$438$	2.53901	+	4.39770i	0.121319	+	0.210130i
$439$	−3.16515			−0.151064			−0.0755322	−	0.997143i	$-0.524066\pi$
$439$	−3.16515			−0.151064			−0.0755322	+	0.997143i	$0.524066\pi$
$440$	−3.31307	−	5.73840i	−0.157944	−	0.273568i
$441$	1.14792	+	0.903750i	0.0546627	+	0.0430357i
$442$	3.79129	+	6.56670i	0.180333	+	0.312346i
$443$	−10.6652	−	18.4726i	−0.506717	−	0.877659i	−0.999970	−	0.00777314i	$-0.997526\pi$
$443$	−10.6652	−	18.4726i	−0.506717	−	0.877659i	0.493253	−	0.869886i	$-0.335808\pi$
$444$	27.8739	−	16.0930i	1.32284	−	0.763739i
$445$	2.62159	−	1.51358i	0.124275	−	0.0717504i
$446$	5.37386	−	3.10260i	0.254460	−	0.146912i
$447$	−10.0390	+	17.3881i	−0.474829	+	0.822428i
$448$	1.70871	+	8.87873i	0.0807291	+	0.419481i
$449$			12.6766i			0.598244i	0.954215	+	0.299122i	$0.0966937\pi$
$449$			12.6766i			0.598244i	−0.954215	+	0.299122i	$0.903306\pi$
$450$	−0.278599	+	0.160849i	−0.0131333	+	0.00758251i
$451$	−8.06080	+	13.9617i	−0.379568	+	0.657431i
$452$			23.6965i			1.11459i
$453$			32.1860i			1.51223i
$454$	10.5000	−	6.06218i	0.492789	−	0.284512i
$455$	4.18693	−	12.0866i	0.196286	−	0.566630i
$456$	−13.4347	−	1.55130i	−0.629136	−	0.0726463i
$457$	19.0390	−	32.9765i	0.890608	−	1.54258i	0.0514591	−	0.998675i	$-0.483613\pi$
$457$	19.0390	−	32.9765i	0.890608	−	1.54258i	0.839148	−	0.543902i	$-0.183054\pi$
$458$	1.58258	−	2.74110i	0.0739489	−	0.128083i
$459$	18.9564	+	10.9445i	0.884811	+	0.510846i
$460$	−15.0000	+	8.66025i	−0.699379	+	0.403786i
$461$	4.66515	−	2.69343i	0.217278	−	0.125445i	−0.387411	−	0.921907i	$-0.626631\pi$
$461$	4.66515	−	2.69343i	0.217278	−	0.125445i	0.604689	+	0.796462i	$0.293297\pi$
$462$	−6.37841	+	1.22753i	−0.296750	+	0.0571097i
$463$	−19.0000			−0.883005			−0.441502	−	0.897260i	$-0.645554\pi$
$463$	−19.0000			−0.883005			−0.441502	+	0.897260i	$0.645554\pi$
$464$	−8.60436	−	4.96773i	−0.399447	−	0.230621i
$465$		0			0
$466$			6.12975i			0.283955i
$467$	−17.7695	−	10.2592i	−0.822275	−	0.474741i	0.0289255	−	0.999582i	$-0.490791\pi$
$467$	−17.7695	−	10.2592i	−0.822275	−	0.474741i	−0.851200	+	0.524841i	$0.824125\pi$
$468$	−1.41742			−0.0655205
$469$	9.00000	−	1.73205i	0.415581	−	0.0799787i
$470$	−3.08258	+	1.77973i	−0.142189	+	0.0820926i
$471$	18.2477	−	10.5353i	0.840811	−	0.485442i
$472$	−14.6869	−	8.47950i	−0.676021	−	0.390301i
$473$	−10.1869	+	17.6443i	−0.468396	+	0.811285i
$474$	−2.83485	+	4.91010i	−0.130209	+	0.225528i
$475$	−13.4955	+	5.84370i	−0.619214	+	0.268127i
$476$	6.79129	−	19.6048i	0.311278	−	0.898583i
$477$	0.230493	−	0.133075i	0.0105535	−	0.00609308i
$478$		−	6.64215i		−	0.303805i
$479$			0.190700i			0.00871332i	0.999991	+	0.00435666i	$0.00138677\pi$
$479$			0.190700i			0.00871332i	−0.999991	+	0.00435666i	$0.998613\pi$
$480$	5.41288	−	9.37538i	0.247063	−	0.427926i
$481$	−32.9347	+	19.0148i	−1.50169	+	0.867002i
$482$		−	3.36875i		−	0.153442i
$483$	6.79129	+	35.2886i	0.309014	+	1.60569i
$484$	1.79129	−	3.10260i	0.0814222	−	0.141027i
$485$	2.20871	−	1.27520i	0.100292	−	0.0579039i
$486$	0.856629	−	0.494575i	0.0388575	−	0.0224344i
$487$	8.68693	−	5.01540i	0.393642	−	0.227270i	−0.290095	−	0.956998i	$-0.593687\pi$
$487$	8.68693	−	5.01540i	0.393642	−	0.227270i	0.683737	+	0.729728i	$0.260353\pi$
$488$	−1.18693	−	2.05583i	−0.0537299	−	0.0930629i
$489$	5.37386	+	9.30780i	0.243015	+	0.420913i
$490$	3.78674	−	1.51358i	0.171068	−	0.0683764i
$491$	−19.0390	−	32.9765i	−0.859219	−	1.48821i	−0.872675	−	0.488301i	$-0.837617\pi$
$491$	−19.0390	−	32.9765i	−0.859219	−	1.48821i	0.0134566	−	0.999909i	$-0.495717\pi$
$492$	−17.2432			−0.777383
$493$	7.79129	+	13.4949i	0.350902	+	0.607780i
$494$	7.50000	+	0.866025i	0.337441	+	0.0389643i
$495$	−0.691478	−	0.399225i	−0.0310796	−	0.0179438i
$496$		0			0
$497$	−6.16515	−	7.11890i	−0.276545	−	0.319326i
$498$	−5.56080	+	9.63158i	−0.249185	+	0.431601i
$499$	−17.7477			−0.794497			−0.397249	−	0.917711i	$-0.630035\pi$
$499$	−17.7477			−0.794497			−0.397249	+	0.917711i	$0.630035\pi$
$500$		−	19.1280i		−	0.855431i
$501$	−17.1261	−	29.6633i	−0.765139	−	1.32526i
$502$	−2.18693	+	3.78788i	−0.0976075	+	0.169061i
$503$	10.4174	+	6.01450i	0.464490	+	0.268173i	0.713930	−	0.700217i	$-0.246913\pi$
$503$	10.4174	+	6.01450i	0.464490	+	0.268173i	−0.249440	+	0.968390i	$0.580247\pi$
$504$	−0.626136	−	0.723000i	−0.0278903	−	0.0322050i
$505$	10.9220			0.486021
$506$	−9.00000	−	5.19615i	−0.400099	−	0.230997i
$507$	2.46099			0.109296
$508$	18.2477	+	10.5353i	0.809612	+	0.467430i
$509$	−7.50000	−	12.9904i	−0.332432	−	0.575789i	0.650556	−	0.759458i	$-0.274536\pi$
$509$	−7.50000	−	12.9904i	−0.332432	−	0.575789i	−0.982988	+	0.183669i	$0.941202\pi$
$510$	−3.95644	+	2.28425i	−0.175194	+	0.101148i
$511$	−5.37386	+	15.5130i	−0.237726	+	0.686255i
$512$		−	22.8981i		−	1.01196i
$513$	20.0000	−	8.66025i	0.883022	−	0.382360i
$514$	7.81307	−	4.51088i	0.344620	−	0.198966i
$515$	3.72595	+	2.15118i	0.164185	+	0.0947922i
$516$	−21.7913			−0.959308
$517$	15.8739	+	9.16478i	0.698132	+	0.403067i
$518$	−11.4564	−	3.96863i	−0.503367	−	0.174371i
$519$	−17.6869	+	30.6347i	−0.776370	+	1.34471i
$520$	−4.18693	+	7.25198i	−0.183609	+	0.318020i
$521$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$521$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$522$	0.339394			0.0148549
$523$	−10.7477	−	18.6156i	−0.469965	−	0.814004i	0.529445	−	0.848344i	$-0.322400\pi$
$523$	−10.7477	−	18.6156i	−0.469965	−	0.814004i	−0.999410	+	0.0343406i	$0.989067\pi$
$524$		−	12.7520i		−	0.557074i
$525$	−15.1089	−	5.23388i	−0.659407	−	0.228425i
$526$	4.74773	+	2.74110i	0.207011	+	0.119518i
$527$		0			0
$528$	−15.0000			−0.652791
$529$	−17.2477	+	29.8739i	−0.749901	+	1.29887i
$530$		−	0.742901i		−	0.0322696i
$531$	−2.04356			−0.0886830
$532$	−11.6434	−	17.0643i	−0.504804	−	0.739832i
$533$	20.3739			0.882490
$534$			1.94265i			0.0840668i
$535$	−6.04356	+	10.4678i	−0.261286	+	0.452560i
$536$	−6.00000			−0.259161
$537$		−	26.4575i		−	1.14173i
$538$	3.00000	+	1.73205i	0.129339	+	0.0746740i
$539$	−16.5000	−	12.9904i	−0.710705	−	0.559535i
$540$			11.4213i			0.491493i
$541$	1.87386	+	3.24563i	0.0805637	+	0.139540i	0.903492	−	0.428605i	$-0.140995\pi$
$541$	1.87386	+	3.24563i	0.0805637	+	0.139540i	−0.822929	+	0.568145i	$0.807661\pi$
$542$	6.16515			0.264816
$543$	10.5218	+	18.2243i	0.451533	+	0.782078i
$544$	−10.3739	+	17.9681i	−0.444776	+	0.770374i
$545$	−8.60436	+	14.9032i	−0.368570	+	0.638382i
$546$	5.37386	+	6.20520i	0.229980	+	0.265558i
$547$	−10.4347	−	6.02445i	−0.446154	−	0.257587i	0.260051	−	0.965595i	$-0.416261\pi$
$547$	−10.4347	−	6.02445i	−0.446154	−	0.257587i	−0.706204	+	0.708008i	$0.749594\pi$
$548$	−17.8348			−0.761867
$549$	−0.247727	−	0.143025i	−0.0105727	−	0.00610417i
$550$	4.00455	−	2.31203i	0.170754	−	0.0985851i
$551$	15.4129	+	1.77973i	0.656611	+	0.0758189i
$552$		−	23.5257i		−	1.00132i
$553$	−18.0000	+	3.46410i	−0.765438	+	0.147309i
$554$	−9.31307	+	5.37690i	−0.395674	+	0.228443i
$555$	−11.4564	−	19.8431i	−0.486299	−	0.842294i
$556$	−16.5653	−	9.56400i	−0.702527	−	0.405604i
$557$	12.0000			0.508456			0.254228	−	0.967144i	$-0.418179\pi$
$557$	12.0000			0.508456			0.254228	+	0.967144i	$0.418179\pi$
$558$		0			0
$559$	25.7477			1.08901
$560$	9.24773	−	1.77973i	0.390788	−	0.0752071i
$561$	20.3739	+	11.7629i	0.860185	+	0.496628i
$562$	0.269507	−	0.466801i	0.0113685	−	0.0196908i
$563$	17.8521	+	30.9207i	0.752376	+	1.30315i	0.946668	+	0.322209i	$0.104425\pi$
$563$	17.8521	+	30.9207i	0.752376	+	1.30315i	−0.194293	+	0.980944i	$0.562241\pi$
$564$			19.6048i			0.825509i
$565$	16.8693			0.709698
$566$	−2.20871	+	3.82560i	−0.0928391	+	0.160802i
$567$	23.9564	+	8.29875i	1.00608	+	0.348515i
$568$	3.08258	+	5.33918i	0.129342	+	0.224027i
$569$	2.76951	+	1.59898i	0.116104	+	0.0670326i	0.556927	−	0.830561i	$-0.311980\pi$
$569$	2.76951	+	1.59898i	0.116104	+	0.0670326i	−0.440823	+	0.897594i	$0.645314\pi$
$570$	−0.521780	+	4.51875i	−0.0218550	+	0.189270i
$571$	−2.00000	−	3.46410i	−0.0836974	−	0.144968i	0.821138	−	0.570730i	$-0.193340\pi$
$571$	−2.00000	−	3.46410i	−0.0836974	−	0.144968i	−0.904835	+	0.425762i	$0.860006\pi$
$572$	20.3739			0.851874
$573$	−18.3956	−	31.8622i	−0.768489	−	1.33106i
$574$	4.25227	+	4.91010i	0.177486	+	0.204944i
$575$	−12.7913	−	22.1552i	−0.533434	−	0.923934i
$576$	−0.356629	−	0.617700i	−0.0148595	−	0.0257375i
$577$	26.3085	−	15.1892i	1.09524	−	0.632336i	0.160272	−	0.987073i	$-0.448763\pi$
$577$	26.3085	−	15.1892i	1.09524	−	0.632336i	0.934966	+	0.354737i	$0.115430\pi$
$578$	0.856629	−	0.494575i	0.0356311	−	0.0205716i
$579$	−38.0608	+	21.9744i	−1.58175	+	0.913225i
$580$	−4.06534	+	7.04138i	−0.168804	+	0.292377i
$581$	−35.3085	+	6.79513i	−1.46484	+	0.281909i
$582$			1.63670i			0.0678434i
$583$	−3.31307	+	1.91280i	−0.137213	+	0.0792201i
$584$	5.37386	−	9.30780i	0.222372	−	0.385160i
$585$			1.00905i			0.0417191i
$586$		−	9.59386i		−	0.396319i
$587$	−7.26951	+	4.19705i	−0.300045	+	0.173231i	−0.642463	−	0.766317i	$-0.722087\pi$
$587$	−7.26951	+	4.19705i	−0.300045	+	0.173231i	0.342418	+	0.939548i	$0.388754\pi$
$588$	3.20871	−	22.2306i	0.132325	−	0.916775i
$589$		0			0
$590$	−2.85208	+	4.93995i	−0.117418	+	0.203375i
$591$	10.7477	−	18.6156i	0.442102	−	0.765744i
$592$	−24.2477	−	13.9994i	−0.996575	−	0.575373i
$593$	14.8348	−	8.56490i	0.609194	−	0.351718i	−0.163456	−	0.986551i	$-0.552264\pi$
$593$	14.8348	−	8.56490i	0.609194	−	0.351718i	0.772650	+	0.634832i	$0.218931\pi$
$594$	−5.93466	+	3.42638i	−0.243502	+	0.140586i
$595$	−13.9564	−	4.83465i	−0.572158	−	0.198201i
$596$	20.0780			0.822428
$597$	34.2523	+	19.7756i	1.40185	+	0.809360i
$598$			13.1334i			0.537065i
$599$		−	36.2023i		−	1.47918i	−0.673055	−	0.739592i	$-0.735018\pi$
$599$		−	36.2023i		−	1.47918i	0.673055	−	0.739592i	$-0.264982\pi$
$600$	9.06534	+	5.23388i	0.370091	+	0.213672i
$601$	−20.4955			−0.836027			−0.418014	−	0.908441i	$-0.637274\pi$
$601$	−20.4955			−0.836027			−0.418014	+	0.908441i	$0.637274\pi$
$602$	5.37386	+	6.20520i	0.219022	+	0.252905i
$603$	−0.626136	+	0.361500i	−0.0254982	+	0.0147214i
$604$	27.8739	−	16.0930i	1.13417	−	0.654814i
$605$	−2.20871	−	1.27520i	−0.0897969	−	0.0518443i
$606$	−3.50455	+	6.07005i	−0.142362	+	0.246579i
$607$	−7.00000	+	12.1244i	−0.284121	+	0.492112i	−0.972396	−	0.233338i	$-0.925035\pi$
$607$	−7.00000	+	12.1244i	−0.284121	+	0.492112i	0.688274	+	0.725450i	$0.258368\pi$
$608$	8.20871	+	18.9572i	0.332907	+	0.768816i
$609$	11.0436	+	12.7520i	0.447508	+	0.516737i
$610$	−0.691478	+	0.399225i	−0.0279971	+	0.0161641i
$611$		−	23.1642i		−	0.937124i
$612$			1.63670i			0.0661597i
$613$	2.68693	−	4.65390i	0.108524	−	0.187969i	−0.806648	−	0.591032i	$-0.798721\pi$
$613$	2.68693	−	4.65390i	0.108524	−	0.187969i	0.915173	+	0.403062i	$0.132054\pi$
$614$	−7.99545	+	4.61618i	−0.322670	+	0.186294i
$615$			12.2753i			0.494986i
$616$	9.00000	+	10.3923i	0.362620	+	0.418718i
$617$	22.5826	−	39.1142i	0.909140	−	1.57468i	0.0938792	−	0.995584i	$-0.470073\pi$
$617$	22.5826	−	39.1142i	0.909140	−	1.57468i	0.815261	−	0.579094i	$-0.196593\pi$
$618$	−2.39110	+	1.38050i	−0.0961841	+	0.0555319i
$619$	7.50000	−	4.33013i	0.301450	−	0.174042i	−0.341644	−	0.939829i	$-0.610984\pi$
$619$	7.50000	−	4.33013i	0.301450	−	0.174042i	0.643094	+	0.765787i	$0.277650\pi$
$620$		0			0
$621$	18.9564	+	32.8335i	0.760696	+	1.31756i
$622$	−5.47822	−	9.48855i	−0.219657	−	0.380456i
$623$	−4.74773	+	4.11165i	−0.190214	+	0.164730i
$624$	9.47822	+	16.4168i	0.379432	+	0.657196i
$625$	3.25227			0.130091
$626$	1.97822	+	3.42638i	0.0790656	+	0.136946i
$627$	21.4955	−	9.30780i	0.858446	−	0.371718i
$628$	−18.2477	−	10.5353i	−0.728164	−	0.420405i
$629$	21.9564	+	38.0297i	0.875461	+	1.51634i
$630$	−0.243181	+	0.210601i	−0.00968857	+	0.00839055i
$631$	17.1434	−	29.6932i	0.682467	−	1.18207i	−0.291759	−	0.956492i	$-0.594240\pi$
$631$	17.1434	−	29.6932i	0.682467	−	1.18207i	0.974226	−	0.225575i	$-0.0724262\pi$
$632$	12.0000			0.477334
$633$		−	25.3332i		−	1.00690i
$634$	−3.35208	−	5.80598i	−0.133128	−	0.230585i
$635$	7.50000	−	12.9904i	0.297628	−	0.515508i
$636$	−3.54356	−	2.04588i	−0.140511	−	0.0811243i
$637$	−3.79129	+	26.2668i	−0.150216	+	1.04073i
$638$	−4.87841			−0.193138
$639$	0.643371	+	0.371450i	0.0254514	+	0.0146944i
$640$	−14.0780			−0.556483
$641$	6.16515	+	3.55945i	0.243509	+	0.140590i	0.616788	−	0.787129i	$-0.288433\pi$
$641$	6.16515	+	3.55945i	0.243509	+	0.140590i	−0.373280	+	0.927719i	$0.621767\pi$
$642$	−3.87841	−	6.71760i	−0.153069	−	0.265123i
$643$	9.24773	−	5.33918i	0.364695	−	0.210557i	−0.306443	−	0.951889i	$-0.599139\pi$
$643$	9.24773	−	5.33918i	0.364695	−	0.210557i	0.671138	+	0.741332i	$0.265806\pi$
$644$	27.1652	−	23.5257i	1.07046	−	0.927043i
$645$			15.5130i			0.610824i
$646$	1.00000	−	8.66025i	0.0393445	−	0.340733i
$647$	−5.76951	+	3.33103i	−0.226823	+	0.130956i	−0.609105	−	0.793089i	$-0.708471\pi$
$647$	−5.76951	+	3.33103i	−0.226823	+	0.130956i	0.382283	+	0.924045i	$0.375138\pi$
$648$	−14.3739	−	8.29875i	−0.564659	−	0.326006i
$649$	29.3739			1.15303
$650$	−5.06080	−	2.92185i	−0.198501	−	0.114604i
$651$		0			0
$652$	5.37386	−	9.30780i	0.210457	−	0.364522i
$653$	−7.50000	+	12.9904i	−0.293498	+	0.508353i	−0.974634	−	0.223803i	$-0.928153\pi$
$653$	−7.50000	+	12.9904i	−0.293498	+	0.508353i	0.681137	+	0.732156i	$0.261486\pi$
$654$	−5.52178	−	9.56400i	−0.215919	−	0.373982i
$655$	−9.07803			−0.354708
$656$	7.50000	+	12.9904i	0.292826	+	0.507189i
$657$		−	1.29510i		−	0.0505267i
$658$	5.58258	−	4.83465i	0.217631	−	0.188474i
$659$	−25.4174	−	14.6748i	−0.990122	−	0.571647i	−0.0848114	−	0.996397i	$-0.527029\pi$
$659$	−25.4174	−	14.6748i	−0.990122	−	0.571647i	−0.905311	+	0.424750i	$0.860362\pi$
$660$			12.2753i			0.477814i
$661$	−30.4955			−1.18614			−0.593068	−	0.805152i	$-0.702083\pi$
$661$	−30.4955			−1.18614			−0.593068	+	0.805152i	$0.702083\pi$
$662$	0.478220	−	0.828301i	0.0185865	−	0.0321928i
$663$		−	29.7309i		−	1.15465i
$664$	23.5390			0.913491
$665$	−12.1479	+	8.28880i	−0.471076	+	0.321426i
$666$	0.956439			0.0370613
$667$			26.9898i			1.04505i
$668$	−17.1261	+	29.6633i	−0.662630	+	1.14771i
$669$	−24.3303			−0.940664
$670$			2.01810i			0.0779661i
$671$	3.56080	+	2.05583i	0.137463	+	0.0793643i
$672$	−7.35208	+	21.2236i	−0.283613	+	0.818720i
$673$			11.6874i			0.450516i	0.974299	+	0.225258i	$0.0723226\pi$
$673$			11.6874i			0.450516i	−0.974299	+	0.225258i	$0.927677\pi$
$674$	0.560795	+	0.971326i	0.0216010	+	0.0374141i
$675$	−16.8693			−0.649300
$676$	−1.23049	−	2.13128i	−0.0473266	−	0.0819721i
$677$	−1.33485	+	2.31203i	−0.0513024	+	0.0888584i	−0.890536	−	0.454912i	$-0.849671\pi$
$677$	−1.33485	+	2.31203i	−0.0513024	+	0.0888584i	0.839234	+	0.543771i	$0.183004\pi$
$678$	−5.41288	+	9.37538i	−0.207880	+	0.360059i
$679$	−4.00000	+	3.46410i	−0.153506	+	0.132940i
$680$	8.37386	+	4.83465i	0.321123	+	0.185400i
$681$	−47.5390			−1.82170
$682$		0			0
$683$	30.2650	−	17.4735i	1.15806	−	0.668604i	0.207219	−	0.978295i	$-0.433559\pi$
$683$	30.2650	−	17.4735i	1.15806	−	0.668604i	0.950837	+	0.309690i	$0.100225\pi$
$684$	1.30852	+	0.971326i	0.0500326	+	0.0371396i
$685$			12.6965i			0.485107i
$686$	−7.12159	+	4.56850i	−0.271904	+	0.174426i
$687$	−10.7477	+	6.20520i	−0.410051	+	0.236743i
$688$	9.47822	+	16.4168i	0.361354	+	0.625883i
$689$	4.18693	+	2.41733i	0.159509	+	0.0920928i
$690$	−7.91288			−0.301238
$691$	37.5000	+	21.6506i	1.42657	+	0.823629i	0.996848	−	0.0793336i	$-0.0252792\pi$
$691$	37.5000	+	21.6506i	1.42657	+	0.823629i	0.429719	+	0.902963i	$0.358613\pi$
$692$	35.3739			1.34471
$693$	1.56534	+	0.542250i	0.0594624	+	0.0205984i
$694$	12.3784	+	7.14668i	0.469878	+	0.271284i
$695$	−6.80852	+	11.7927i	−0.258262	+	0.447323i
$696$	−5.52178	−	9.56400i	−0.209303	−	0.362523i
$697$		−	23.5257i		−	0.891100i
$698$	14.6697			0.555256
$699$	12.0172	−	20.8145i	0.454534	−	0.787275i
$700$	3.02178	+	15.7016i	0.114213	+	0.593466i
$701$	10.7477	+	18.6156i	0.405936	+	0.703102i	0.994430	−	0.105400i	$-0.0336122\pi$
$701$	10.7477	+	18.6156i	0.405936	+	0.703102i	−0.588494	+	0.808502i	$0.700279\pi$
$702$	7.50000	+	4.33013i	0.283069	+	0.163430i
$703$	43.4347	+	5.01540i	1.63817	+	0.189159i
$704$	5.12614	+	8.87873i	0.193199	+	0.334630i
$705$	13.9564			0.525630
$706$	0.0607953	+	0.105301i	0.00228806	+	0.00396304i
$707$	−22.2523	+	4.28245i	−0.836883	+	0.161058i
$708$	15.7087	+	27.2083i	0.590370	+	1.02255i
$709$	6.70871	+	11.6198i	0.251951	+	0.436392i	0.964063	−	0.265674i	$-0.0855945\pi$
$709$	6.70871	+	11.6198i	0.251951	+	0.436392i	−0.712112	+	0.702066i	$0.752261\pi$
$710$	1.79583	−	1.03683i	0.0673964	−	0.0389114i
$711$	1.25227	−	0.723000i	0.0469639	−	0.0271146i
$712$	3.56080	−	2.05583i	0.133446	−	0.0770453i
$713$		0			0
$714$	7.16515	−	6.20520i	0.268149	−	0.232224i
$715$		−	14.5040i		−	0.542417i
$716$	−22.9129	+	13.2288i	−0.856294	+	0.494382i
$717$	−13.0218	+	22.5544i	−0.486307	+	0.842309i
$718$			0.286051i			0.0106753i
$719$		−	31.3676i		−	1.16981i	−0.811100	−	0.584907i	$-0.801131\pi$
$719$		−	31.3676i		−	1.16981i	0.811100	−	0.584907i	$-0.198869\pi$
$720$	−0.643371	+	0.371450i	−0.0239770	+	0.0138431i
$721$	−8.43466	−	2.92185i	−0.314123	−	0.108815i
$722$	−6.33030	−	5.93905i	−0.235589	−	0.221029i
$723$	−6.60436	+	11.4391i	−0.245619	+	0.425424i
$724$	10.5218	−	18.2243i	0.391039	−	0.677299i
$725$	−10.4002	−	6.00455i	−0.386253	−	0.223003i
$726$	1.41742	−	0.818350i	0.0526055	−	0.0303718i
$727$	−39.2477	+	22.6597i	−1.45562	+	0.840401i	−0.998791	−	0.0491546i	$-0.984347\pi$
$727$	−39.2477	+	22.6597i	−1.45562	+	0.840401i	−0.456826	+	0.889556i	$0.651014\pi$
$728$	5.68693	−	16.4168i	0.210772	−	0.608446i
$729$	24.8693			0.921086
$730$	−3.13068	−	1.80750i	−0.115872	−	0.0668986i
$731$		−	29.7309i		−	1.09964i
$732$			4.39770i			0.162544i
$733$	24.8085	+	14.3232i	0.916324	+	0.529040i	0.882460	−	0.470387i	$-0.155886\pi$
$733$	24.8085	+	14.3232i	0.916324	+	0.529040i	0.0338633	+	0.999426i	$0.489219\pi$
$734$	4.41742			0.163050
$735$	−15.8258	−	2.28425i	−0.583742	−	0.0842559i
$736$	−31.1216	+	17.9681i	−1.14716	+	0.662311i
$737$	9.00000	−	5.19615i	0.331519	−	0.191403i
$738$	−0.443751	−	0.256199i	−0.0163347	−	0.00943083i
$739$	−12.8739	+	22.2982i	−0.473573	+	0.820252i	−0.999542	−	0.0302513i	$-0.990369\pi$
$739$	−12.8739	+	22.2982i	−0.473573	+	0.820252i	0.525970	+	0.850503i	$0.323703\pi$
$740$	−11.4564	+	19.8431i	−0.421147	+	0.729448i
$741$	−23.7695	−	17.6443i	−0.873195	−	0.648179i
$742$	0.291288	+	1.51358i	0.0106935	+	0.0555651i
$743$	28.8956	−	16.6829i	1.06008	−	0.612037i	0.134624	−	0.990897i	$-0.457017\pi$
$743$	28.8956	−	16.6829i	1.06008	−	0.612037i	0.925454	+	0.378860i	$0.123684\pi$
$744$		0			0
$745$		−	14.2934i		−	0.523668i
$746$	−4.96099	+	8.59268i	−0.181635	+	0.314600i
$747$	2.45644	−	1.41823i	0.0898764	−	0.0518902i
$748$		−	23.5257i		−	0.860185i
$749$	8.20871	−	23.6965i	0.299940	−	0.865852i
$750$	4.36932	−	7.56788i	0.159545	−	0.276340i
$751$	−7.81307	+	4.51088i	−0.285103	+	0.164604i	−0.635731	−	0.771910i	$-0.719301\pi$
$751$	−7.81307	+	4.51088i	−0.285103	+	0.164604i	0.350628	+	0.936515i	$0.385968\pi$
$752$	14.7695	−	8.52718i	0.538589	−	0.310954i
$753$	14.8521	−	8.57485i	0.541240	−	0.312485i
$754$	3.08258	+	5.33918i	0.112261	+	0.194441i
$755$	−11.4564	−	19.8431i	−0.416943	−	0.722166i
$756$	−4.47822	−	23.2695i	−0.162871	−	0.846304i
$757$	14.1216	+	24.4593i	0.513258	+	0.888989i	0.999882	+	0.0153772i	$0.00489491\pi$
$757$	14.1216	+	24.4593i	0.513258	+	0.888989i	−0.486624	+	0.873612i	$0.661772\pi$
$758$	12.0345			0.437112
$759$	20.3739	+	35.2886i	0.739524	+	1.28089i
$760$	8.83485	−	3.82560i	0.320474	−	0.138769i
$761$	−17.7695	−	10.2592i	−0.644144	−	0.371897i	0.142065	−	0.989857i	$-0.454626\pi$
$761$	−17.7695	−	10.2592i	−0.644144	−	0.371897i	−0.786209	+	0.617961i	$0.787959\pi$
$762$	4.81307	+	8.33648i	0.174359	+	0.301999i
$763$	11.6869	−	33.7373i	0.423095	−	1.22137i
$764$	−18.3956	+	31.8622i	−0.665531	+	1.15273i
$765$	1.16515			0.0421261
$766$			7.72665i			0.279175i
$767$	−18.5608	−	32.1482i	−0.670191	−	1.16081i
$768$	−1.60436	+	2.77883i	−0.0578922	+	0.100272i
$769$	−25.1869	−	14.5417i	−0.908264	−	0.524386i	−0.0283918	−	0.999597i	$-0.509039\pi$
$769$	−25.1869	−	14.5417i	−0.908264	−	0.524386i	−0.879872	+	0.475210i	$0.842372\pi$
$770$	3.49545	−	3.02715i	0.125967	−	0.109091i
$771$	−35.3739			−1.27396
$772$	38.0608	+	21.9744i	1.36984	+	0.790876i
$773$	−39.6606			−1.42649			−0.713246	−	0.700913i	$-0.752776\pi$
$773$	−39.6606			−1.42649			−0.713246	+	0.700913i	$0.752776\pi$
$774$	−0.560795	−	0.323775i	−0.0201574	−	0.0116379i
$775$		0			0
$776$	3.00000	−	1.73205i	0.107694	−	0.0621770i
$777$	31.1216	+	35.9361i	1.11648	+	1.28920i
$778$		−	15.5130i		−	0.556168i
$779$	−18.8085	−	13.9617i	−0.673885	−	0.500230i
$780$	13.4347	−	7.75650i	0.481038	−	0.277727i
$781$	−9.24773	−	5.33918i	−0.330910	−	0.191051i
$782$	15.1652			0.542305
$783$	15.4129	+	8.89863i	0.550811	+	0.318011i
$784$	−18.1434	+	7.25198i	−0.647978	+	0.258999i
$785$	−7.50000	+	12.9904i	−0.267686	+	0.463647i
$786$	2.91288	−	5.04525i	0.103899	−	0.179958i
$787$	12.7913	+	22.1552i	0.455960	+	0.789746i	0.998743	−	0.0501270i	$-0.0159626\pi$
$787$	12.7913	+	22.1552i	0.455960	+	0.789746i	−0.542783	+	0.839873i	$0.682629\pi$
$788$	−21.4955			−0.765744
$789$	−10.7477	−	18.6156i	−0.382629	−	0.662733i
$790$		−	4.03620i		−	0.143602i
$791$	−34.3693	+	6.61438i	−1.22203	+	0.235180i
$792$	−0.939205	−	0.542250i	−0.0333732	−	0.0192680i
$793$		−	5.19615i		−	0.184521i
$794$	−2.04356			−0.0725233
$795$	−1.45644	+	2.52263i	−0.0516546	+	0.0894684i
$796$		−	39.5511i		−	1.40185i
$797$	−48.4955			−1.71780			−0.858899	−	0.512146i	$-0.828851\pi$
$797$	−48.4955			−1.71780			−0.858899	+	0.512146i	$0.828851\pi$
$798$	−0.708712	−	9.41103i	−0.0250881	−	0.333147i
$799$	−26.7477			−0.946267
$800$		−	15.9898i		−	0.565323i
$801$	0.247727	−	0.429076i	0.00875301	−	0.0151607i
$802$	−1.92197			−0.0678671
$803$			18.6156i			0.656931i
$804$	9.62614	+	5.55765i	0.339488	+	0.196003i
$805$	−16.7477	−	19.3386i	−0.590280	−	0.681596i
$806$		0			0
$807$	−6.79129	−	11.7629i	−0.239065	−	0.414072i
$808$	14.8348			0.521888
$809$	−25.0390	−	43.3688i	−0.880325	−	1.52477i	−0.850980	−	0.525198i	$-0.823991\pi$
$809$	−25.0390	−	43.3688i	−0.880325	−	1.52477i	−0.0293449	−	0.999569i	$-0.509342\pi$
$810$	−2.79129	+	4.83465i	−0.0980759	+	0.169872i
$811$	7.56080	−	13.0957i	0.265495	−	0.459852i	−0.702198	−	0.711982i	$-0.747798\pi$
$811$	7.56080	−	13.0957i	0.265495	−	0.459852i	0.967693	+	0.252130i	$0.0811311\pi$
$812$	5.52178	−	15.9400i	0.193777	−	0.559385i
$813$	−20.9347	−	12.0866i	−0.734211	−	0.423897i
$814$	−13.7477			−0.481858
$815$	−6.62614	−	3.82560i	−0.232103	−	0.134005i
$816$	18.9564	−	10.9445i	0.663608	−	0.383134i
$817$	−23.7695	−	17.6443i	−0.831590	−	0.617295i
$818$			6.77730i			0.236963i
$819$	−0.395644	−	2.05583i	−0.0138249	−	0.0718364i
$820$	10.6307	−	6.13763i	0.371240	−	0.214335i
$821$	8.52178	+	14.7602i	0.297412	+	0.515133i	0.975543	−	0.219808i	$-0.0705431\pi$
$821$	8.52178	+	14.7602i	0.297412	+	0.515133i	−0.678131	+	0.734941i	$0.737210\pi$
$822$	−7.05625	−	4.07393i	−0.246115	−	0.142095i
$823$	−25.4174			−0.885996			−0.442998	−	0.896523i	$-0.646085\pi$
$823$	−25.4174			−0.885996			−0.442998	+	0.896523i	$0.646085\pi$
$824$	5.06080	+	2.92185i	0.176301	+	0.101788i
$825$	−18.1307			−0.631229
$826$	3.87386	−	11.1829i	0.134789	−	0.389102i
$827$	26.7042	+	15.4177i	0.928595	+	0.536124i	0.886367	−	0.462984i	$-0.153221\pi$
$827$	26.7042	+	15.4177i	0.928595	+	0.536124i	0.0422280	+	0.999108i	$0.486554\pi$
$828$	−1.41742	+	2.45505i	−0.0492589	+	0.0853189i
$829$	−7.12614	−	12.3428i	−0.247501	−	0.428684i	0.715331	−	0.698786i	$-0.246276\pi$
$829$	−7.12614	−	12.3428i	−0.247501	−	0.428684i	−0.962832	+	0.270102i	$0.912943\pi$
$830$		−	7.91735i		−	0.274815i
$831$	42.1652			1.46269
$832$	6.47822	−	11.2206i	0.224592	−	0.389005i
$833$	30.3303	+	4.37780i	1.05088	+	0.151682i
$834$	−4.36932	−	7.56788i	−0.151297	−	0.262054i
$835$	21.1170	+	12.1919i	0.730785	+	0.421919i
$836$	−18.8085	−	13.9617i	−0.650506	−	0.482876i
$837$		0			0
$838$	−17.7133			−0.611894
$839$	−11.9174	−	20.6416i	−0.411435	−	0.712627i	0.583612	−	0.812033i	$-0.301639\pi$
$839$	−11.9174	−	20.6416i	−0.411435	−	0.712627i	−0.995047	+	0.0994062i	$0.968306\pi$
$840$	9.89110	+	3.42638i	0.341275	+	0.118221i
$841$	−8.16515	−	14.1425i	−0.281557	−	0.487671i
$842$	−3.64337	−	6.31050i	−0.125559	−	0.217474i
$843$	−1.83030	+	1.05673i	−0.0630390	+	0.0363956i
$844$	−21.9392	+	12.6666i	−0.755179	+	0.436003i
$845$	−1.51723	+	0.875976i	−0.0521945	+	0.0301345i
$846$	−0.291288	+	0.504525i	−0.0100147	+	0.0173459i
$847$	5.00000	+	1.73205i	0.171802	+	0.0595140i
$848$			3.55945i			0.122232i
$849$	15.0000	−	8.66025i	0.514799	−	0.297219i
$850$	−3.37386	+	5.84370i	−0.115723	+	0.200437i
$851$			76.0593i			2.60728i
$852$		−	11.4213i		−	0.391286i
$853$	−0.873864	+	0.504525i	−0.0299205	+	0.0172746i	−0.514886	−	0.857259i	$-0.672166\pi$
$853$	−0.873864	+	0.504525i	−0.0299205	+	0.0172746i	0.484965	+	0.874533i	$0.338832\pi$
$854$	1.25227	−	1.08450i	0.0428519	−	0.0371108i
$855$	0.691478	−	0.931524i	0.0236480	−	0.0318575i
$856$	−8.20871	+	14.2179i	−0.280568	+	0.485958i
$857$	−6.56080	+	11.3636i	−0.224112	+	0.388174i	−0.956053	−	0.293195i	$-0.905282\pi$
$857$	−6.56080	+	11.3636i	−0.224112	+	0.388174i	0.731940	+	0.681369i	$0.238615\pi$
$858$	8.06080	+	4.65390i	0.275191	+	0.158882i
$859$	−5.68693	+	3.28335i	−0.194036	+	0.112027i	−0.593870	−	0.804561i	$-0.702401\pi$
$859$	−5.68693	+	3.28335i	−0.194036	+	0.112027i	0.399835	+	0.916587i	$0.369067\pi$
$860$	13.4347	−	7.75650i	0.458118	−	0.264495i
$861$	−4.81307	−	25.0094i	−0.164029	−	0.852319i
$862$	8.28674			0.282248
$863$	16.0390	+	9.26013i	0.545974	+	0.315218i	0.747497	−	0.664265i	$-0.231256\pi$
$863$	16.0390	+	9.26013i	0.545974	+	0.315218i	−0.201522	+	0.979484i	$0.564589\pi$
$864$			23.6965i			0.806172i
$865$		−	25.1823i		−	0.856224i
$866$	−14.3911	−	8.30870i	−0.489029	−	0.282341i
$867$	−3.87841			−0.131718
$868$		0			0
$869$	−18.0000	+	10.3923i	−0.610608	+	0.352535i
$870$	−3.21686	+	1.85725i	−0.109062	+	0.0629667i
$871$	−11.3739	−	6.56670i	−0.385389	−	0.222504i
$872$	−11.6869	+	20.2424i	−0.395769	+	0.685493i
$873$	0.208712	−	0.361500i	0.00706384	−	0.0122349i
$874$	9.00000	−	12.1244i	0.304430	−	0.410112i
$875$	27.7432	−	5.33918i	0.937891	−	0.180497i
$876$	−17.2432	+	9.95536i	−0.582593	+	0.336360i
$877$			42.8643i			1.44743i	0.690101	+	0.723713i	$0.257566\pi$
$877$			42.8643i			1.44743i	−0.690101	+	0.723713i	$0.742434\pi$
$878$			1.44600i			0.0488001i
$879$	−18.8085	+	32.5773i	−0.634396	+	1.09881i
$880$	9.24773	−	5.33918i	0.311741	−	0.179984i
$881$			13.5903i			0.457867i	0.973442	+	0.228934i	$0.0735239\pi$
$881$			13.5903i			0.457867i	−0.973442	+	0.228934i	$0.926476\pi$
$882$	0.412878	−	0.524426i	0.0139023	−	0.0176583i
$883$	−20.5000	+	35.5070i	−0.689880	+	1.19491i	0.281996	+	0.959415i	$0.409003\pi$
$883$	−20.5000	+	35.5070i	−0.689880	+	1.19491i	−0.971876	+	0.235492i	$0.924330\pi$
$884$	−25.7477	+	14.8655i	−0.865990	+	0.499979i
$885$	19.3693	−	11.1829i	0.651092	−	0.375908i
$886$	−8.43920	+	4.87238i	−0.283521	+	0.163691i
$887$	0.708712	+	1.22753i	0.0237962	+	0.0412163i	0.877678	−	0.479250i	$-0.159091\pi$
$887$	0.708712	+	1.22753i	0.0237962	+	0.0412163i	−0.853882	+	0.520467i	$0.825758\pi$
$888$	−15.5608	−	26.9521i	−0.522186	−	0.904453i
$889$	−10.1869	+	29.4071i	−0.341659	+	0.986284i
$890$	−0.691478	−	1.19767i	−0.0231784	−	0.0401461i
$891$	28.7477			0.963085
$892$	12.1652	+	21.0707i	0.407319	+	0.705498i
$893$	−15.8739	+	21.3845i	−0.531199	+	0.715605i
$894$	7.94375	+	4.58633i	0.265679	+	0.153390i
$895$	9.41742	+	16.3115i	0.314790	+	0.545232i
$896$	28.6824	−	5.51993i	0.958211	−	0.184408i
$897$	25.7477	−	44.5964i	0.859692	−	1.48903i
$898$	5.79129			0.193258
$899$		0			0
$900$	−0.630682	−	1.09237i	−0.0210227	−	0.0364125i
$901$	2.79129	−	4.83465i	0.0929913	−	0.161066i
$902$	6.37841	+	3.68258i	0.212378	+	0.122616i
$903$	−6.08258	−	31.6060i	−0.202415	−	1.05178i
$904$	22.9129			0.762071
$905$	−12.9737	−	7.49035i	−0.431260	−	0.248988i
$906$	14.7042			0.488513
$907$	34.9955	+	20.2046i	1.16200	+	0.670884i	0.951784	−	0.306770i	$-0.0992482\pi$
$907$	34.9955	+	20.2046i	1.16200	+	0.670884i	0.210221	+	0.977654i	$0.432582\pi$
$908$	23.7695	+	41.1700i	0.788819	+	1.36627i
$909$	1.54811	−	0.893800i	0.0513475	−	0.0296455i
$910$	−5.52178	−	1.91280i	−0.183045	−	0.0634087i
$911$		−	7.38505i		−	0.244678i	−0.992488	−	0.122339i	$-0.960961\pi$
$911$		−	7.38505i		−	0.244678i	0.992488	−	0.122339i	$-0.0390395\pi$
$912$	2.50000	−	21.6506i	0.0827833	−	0.716924i
$913$	−35.3085	+	20.3854i	−1.16854	+	0.674658i
$914$	−15.0653	−	8.69798i	−0.498317	−	0.287704i
$915$	3.13068			0.103497
$916$	10.7477	+	6.20520i	0.355115	+	0.205026i
$917$	18.4955	−	3.55945i	0.610774	−	0.117543i
$918$	5.00000	−	8.66025i	0.165025	−	0.285831i
$919$	−11.0000	+	19.0526i	−0.362857	+	0.628486i	−0.988430	−	0.151680i	$-0.951532\pi$
$919$	−11.0000	+	19.0526i	−0.362857	+	0.628486i	0.625573	+	0.780165i	$0.284865\pi$
$920$	8.37386	+	14.5040i	0.276078	+	0.478181i
$921$	36.1996			1.19282
$922$	−1.23049	−	2.13128i	−0.0405241	−	0.0701898i
$923$			13.4949i			0.444190i
$924$	−4.81307	−	25.0094i	−0.158338	−	0.822750i
$925$	−29.3085	−	16.9213i	−0.963658	−	0.556368i
$926$			8.68015i			0.285248i
$927$	0.704166			0.0231279
$928$	−8.43466	+	14.6093i	−0.276881	+	0.479572i
$929$			4.01630i			0.131771i	0.997827	+	0.0658853i	$0.0209871\pi$
$929$			4.01630i			0.131771i	−0.997827	+	0.0658853i	$0.979013\pi$
$930$		0			0
$931$	21.5000	−	21.6506i	0.704634	−	0.709571i
$932$	−24.0345			−0.787275
$933$			42.9597i			1.40644i
$934$	−4.68693	+	8.11800i	−0.153361	+	0.265629i
$935$	−16.7477			−0.547709
$936$			1.37055i			0.0447979i
$937$	9.93920	+	5.73840i	0.324700	+	0.187465i	0.653485	−	0.756939i	$-0.273306\pi$
$937$	9.93920	+	5.73840i	0.324700	+	0.187465i	−0.328786	+	0.944405i	$0.606639\pi$
$938$	−0.791288	−	4.11165i	−0.0258365	−	0.134250i
$939$		−	15.5130i		−	0.506248i
$940$	−6.97822	−	12.0866i	−0.227604	−	0.394222i
$941$	5.20871			0.169799			0.0848996	−	0.996390i	$-0.472943\pi$
$941$	5.20871			0.169799			0.0848996	+	0.996390i	$0.472943\pi$
$942$	−4.81307	−	8.33648i	−0.156818	−	0.271617i
$943$	20.3739	−	35.2886i	0.663464	−	1.14915i
$944$	13.6652	−	23.6687i	0.444763	−	0.770352i
$945$	−16.5653	+	3.18800i	−0.538871	+	0.103706i
$946$	8.06080	+	4.65390i	0.262079	+	0.151311i
$947$	35.8348			1.16448			0.582238	−	0.813018i	$-0.302177\pi$
$947$	35.8348			1.16448			0.582238	+	0.813018i	$0.302177\pi$
$948$	−19.2523	−	11.1153i	−0.625285	−	0.361008i
$949$	20.3739	−	11.7629i	0.661364	−	0.381838i
$950$	2.66970	+	6.16540i	0.0866164	+	0.200032i
$951$			26.2867i			0.852405i
$952$	−18.9564	−	6.56670i	−0.614382	−	0.212828i
$953$	−42.8911	+	24.7632i	−1.38938	+	0.802158i	−0.993245	−	0.116035i	$-0.962982\pi$
$953$	−42.8911	+	24.7632i	−1.38938	+	0.802158i	−0.396134	+	0.918193i	$0.629648\pi$
$954$	−0.0607953	−	0.105301i	−0.00196832	−	0.00340923i
$955$	22.6824	+	13.0957i	0.733985	+	0.423766i
$956$	26.0436			0.842309
$957$	16.5653	+	9.56400i	0.535481	+	0.309160i
$958$	0.0871215			0.00281477
$959$	−4.97822	−	25.8676i	−0.160755	−	0.835308i
$960$	6.76042	+	3.90313i	0.218191	+	0.125973i
$961$	15.5000	−	26.8468i	0.500000	−	0.866025i
$962$	8.68693	+	15.0462i	0.280078	+	0.485109i
$963$			1.97830i			0.0637498i
$964$	13.2087			0.425424
$965$	15.6434	−	27.0951i	0.503578	−	0.872223i
$966$	16.1216	−	3.10260i	0.518704	−	0.0998246i
$967$	−11.2087	−	19.4141i	−0.360448	−	0.624314i	0.627587	−	0.778547i	$-0.284043\pi$
$967$	−11.2087	−	19.4141i	−0.360448	−	0.624314i	−0.988035	+	0.154233i	$0.950709\pi$
$968$	−3.00000	−	1.73205i	−0.0964237	−	0.0556702i
$969$	−20.3739	+	27.4467i	−0.654503	+	0.881714i
$970$	−0.582576	−	1.00905i	−0.0187054	−	0.0323987i
$971$	−43.4519			−1.39444			−0.697219	−	0.716858i	$-0.745579\pi$
$971$	−43.4519			−1.39444			−0.697219	+	0.716858i	$0.745579\pi$
$972$	1.93920	+	3.35880i	0.0622000	+	0.107734i
$973$	9.24773	−	26.6959i	0.296469	−	0.855831i
$974$	−2.29129	−	3.96863i	−0.0734176	−	0.127163i
$975$	11.4564	+	19.8431i	0.366900	+	0.635489i
$976$	3.31307	−	1.91280i	0.106049	−	0.0612273i
$977$	16.4174	−	9.47860i	0.525240	−	0.303247i	−0.213836	−	0.976870i	$-0.568596\pi$
$977$	16.4174	−	9.47860i	0.525240	−	0.303247i	0.739076	+	0.673622i	$0.235262\pi$
$978$	4.25227	−	2.45505i	0.135973	−	0.0785039i
$979$	−3.56080	+	6.16748i	−0.113804	+	0.197113i
$980$	5.93466	+	14.8476i	0.189576	+	0.474290i
$981$			2.81655i			0.0899256i
$982$	−15.0653	+	8.69798i	−0.480754	+	0.277564i
$983$	29.1434	−	50.4778i	0.929529	−	1.60999i	0.145419	−	0.989370i	$-0.453547\pi$
$983$	29.1434	−	50.4778i	0.929529	−	1.60999i	0.784110	−	0.620622i	$-0.213120\pi$
$984$			16.6730i			0.531514i
$985$			15.3024i			0.487575i
$986$	6.16515	−	3.55945i	0.196338	−	0.113356i
$987$	−28.4347	+	5.47225i	−0.905085	+	0.174184i
$988$	−3.39564	+	29.4071i	−0.108030	+	0.935566i
$989$	25.7477	−	44.5964i	0.818730	−	1.41808i
$990$	−0.182386	+	0.315902i	−0.00579661	+	0.0100400i
$991$	30.3131	+	17.5013i	0.962926	+	0.555946i	0.897072	−	0.441883i	$-0.145690\pi$
$991$	30.3131	+	17.5013i	0.962926	+	0.555946i	0.0658539	+	0.997829i	$0.479023\pi$
$992$		0			0
$993$	−3.24773	+	1.87508i	−0.103064	+	0.0595037i
$994$	−3.25227	+	2.81655i	−0.103156	+	0.0893356i
$995$	−28.1561			−0.892607
$996$	−37.7650	−	21.8036i	−1.19663	−	0.690874i
$997$			5.48220i			0.173623i	0.996225	+	0.0868116i	$0.0276678\pi$
$997$			5.48220i			0.173623i	−0.996225	+	0.0868116i	$0.972332\pi$
$998$			8.10805i			0.256656i
$999$	43.4347	+	25.0770i	1.37421	+	0.793402i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	133.2.i.c.12.1	✓	4
7.2	even	3		931.2.p.f.734.1		4
7.3	odd	6		133.2.s.c.31.2	yes	4
7.4	even	3		931.2.s.c.31.2		4
7.5	odd	6		931.2.p.e.734.1		4
7.6	odd	2		931.2.i.d.411.1		4
19.8	odd	6		133.2.s.c.103.2	yes	4
133.27	even	6		931.2.s.c.901.2		4
133.46	odd	6		931.2.i.d.521.2		4
133.65	odd	6		931.2.p.e.293.1		4
133.103	even	6		931.2.p.f.293.1		4
133.122	even	6	inner	133.2.i.c.122.2	yes	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
133.2.i.c.12.1	✓	4	1.1	even	1	trivial
133.2.i.c.122.2	yes	4	133.122	even	6	inner
133.2.s.c.31.2	yes	4	7.3	odd	6
133.2.s.c.103.2	yes	4	19.8	odd	6
931.2.i.d.411.1		4	7.6	odd	2
931.2.i.d.521.2		4	133.46	odd	6
931.2.p.e.293.1		4	133.65	odd	6
931.2.p.e.734.1		4	7.5	odd	6
931.2.p.f.293.1		4	133.103	even	6
931.2.p.f.734.1		4	7.2	even	3
931.2.s.c.31.2		4	7.4	even	3
931.2.s.c.901.2		4	133.27	even	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:	\( N \)	\(=\)	\( 133 = 7 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	133.i (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-0.456850i q^{2} +(-0.895644 + 1.55130i) q^{3} +1.79129 q^{4} -1.27520i q^{5} +(0.708712 + 0.409175i) q^{6} +(0.500000 + 2.59808i) q^{7} -1.73205i q^{8} +(-0.104356 - 0.180750i) q^{9} +O(q^{10})\)	\(q-0.456850i q^{2} +(-0.895644 + 1.55130i) q^{3} +1.79129 q^{4} -1.27520i q^{5} +(0.708712 + 0.409175i) q^{6} +(0.500000 + 2.59808i) q^{7} -1.73205i q^{8} +(-0.104356 - 0.180750i) q^{9} -0.582576 q^{10} +(1.50000 + 2.59808i) q^{11} +(-1.60436 + 2.77883i) q^{12} +(1.89564 - 3.28335i) q^{13} +(1.18693 - 0.228425i) q^{14} +(1.97822 + 1.14213i) q^{15} +2.79129 q^{16} +(-3.79129 - 2.18890i) q^{17} +(-0.0825757 + 0.0476751i) q^{18} +(-4.00000 + 1.73205i) q^{19} -2.28425i q^{20} +(-4.47822 - 1.55130i) q^{21} +(1.18693 - 0.685275i) q^{22} +(-3.79129 - 6.56670i) q^{23} +(2.68693 + 1.55130i) q^{24} +3.37386 q^{25} +(-1.50000 - 0.866025i) q^{26} -5.00000 q^{27} +(0.895644 + 4.65390i) q^{28} +(-3.08258 - 1.77973i) q^{29} +(0.521780 - 0.903750i) q^{30} -4.73930i q^{32} -5.37386 q^{33} +(-1.00000 + 1.73205i) q^{34} +(3.31307 - 0.637600i) q^{35} +(-0.186932 - 0.323775i) q^{36} +(-8.68693 - 5.01540i) q^{37} +(0.791288 + 1.82740i) q^{38} +(3.39564 + 5.88143i) q^{39} -2.20871 q^{40} +(2.68693 + 4.65390i) q^{41} +(-0.708712 + 2.04588i) q^{42} +(3.39564 + 5.88143i) q^{43} +(2.68693 + 4.65390i) q^{44} +(-0.230493 + 0.133075i) q^{45} +(-3.00000 + 1.73205i) q^{46} +(5.29129 - 3.05493i) q^{47} +(-2.50000 + 4.33013i) q^{48} +(-6.50000 + 2.59808i) q^{49} -1.54135i q^{50} +(6.79129 - 3.92095i) q^{51} +(3.39564 - 5.88143i) q^{52} +1.27520i q^{53} +2.28425i q^{54} +(3.31307 - 1.91280i) q^{55} +(4.50000 - 0.866025i) q^{56} +(0.895644 - 7.75650i) q^{57} +(-0.813068 + 1.40828i) q^{58} +(4.89564 - 8.47950i) q^{59} +(3.54356 + 2.04588i) q^{60} +(1.18693 - 0.685275i) q^{61} +(0.417424 - 0.361500i) q^{63} +3.41742 q^{64} +(-4.18693 - 2.41733i) q^{65} +2.45505i q^{66} -3.46410i q^{67} +(-6.79129 - 3.92095i) q^{68} +13.5826 q^{69} +(-0.291288 - 1.51358i) q^{70} +(-3.08258 + 1.77973i) q^{71} +(-0.313068 + 0.180750i) q^{72} +(5.37386 + 3.10260i) q^{73} +(-2.29129 + 3.96863i) q^{74} +(-3.02178 + 5.23388i) q^{75} +(-7.16515 + 3.10260i) q^{76} +(-6.00000 + 5.19615i) q^{77} +(2.68693 - 1.55130i) q^{78} +6.92820i q^{79} -3.55945i q^{80} +(4.79129 - 8.29875i) q^{81} +(2.12614 - 1.22753i) q^{82} +13.5903i q^{83} +(-8.02178 - 2.77883i) q^{84} +(-2.79129 + 4.83465i) q^{85} +(2.68693 - 1.55130i) q^{86} +(5.52178 - 3.18800i) q^{87} +(4.50000 - 2.59808i) q^{88} +(1.18693 + 2.05583i) q^{89} +(0.0607953 + 0.105301i) q^{90} +(9.47822 + 3.28335i) q^{91} +(-6.79129 - 11.7629i) q^{92} +(-1.39564 - 2.41733i) q^{94} +(2.20871 + 5.10080i) q^{95} +(7.35208 + 4.24473i) q^{96} +(1.00000 + 1.73205i) q^{97} +(1.18693 + 2.96953i) q^{98} +(0.313068 - 0.542250i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + q^{3} - 2 q^{4} + 12 q^{6} + 2 q^{7} - 5 q^{9}+O(q^{10}) \) 4 * q + q^3 - 2 * q^4 + 12 * q^6 + 2 * q^7 - 5 * q^9	\( 4 q + q^{3} - 2 q^{4} + 12 q^{6} + 2 q^{7} - 5 q^{9} + 16 q^{10} + 6 q^{11} - 11 q^{12} + 3 q^{13} - 9 q^{14} - 15 q^{15} + 2 q^{16} - 6 q^{17} + 18 q^{18} - 16 q^{19} + 5 q^{21} - 9 q^{22} - 6 q^{23} - 3 q^{24} - 14 q^{25} - 6 q^{26} - 20 q^{27} - q^{28} + 6 q^{29} + 25 q^{30} + 6 q^{33} - 4 q^{34} + 27 q^{35} + 13 q^{36} - 21 q^{37} - 6 q^{38} + 9 q^{39} - 18 q^{40} - 3 q^{41} - 12 q^{42} + 9 q^{43} - 3 q^{44} - 33 q^{45} - 12 q^{46} + 12 q^{47} - 10 q^{48} - 26 q^{49} + 18 q^{51} + 9 q^{52} + 27 q^{55} + 18 q^{56} - q^{57} - 17 q^{58} + 15 q^{59} + 60 q^{60} - 9 q^{61} + 20 q^{63} + 32 q^{64} - 3 q^{65} - 18 q^{68} + 36 q^{69} + 8 q^{70} + 6 q^{71} - 15 q^{72} - 6 q^{73} - 35 q^{75} + 8 q^{76} - 24 q^{77} - 3 q^{78} + 10 q^{81} + 36 q^{82} - 55 q^{84} - 2 q^{85} - 3 q^{86} + 45 q^{87} + 18 q^{88} - 9 q^{89} - 41 q^{90} + 15 q^{91} - 18 q^{92} - q^{94} + 18 q^{95} - 21 q^{96} + 4 q^{97} - 9 q^{98} + 15 q^{99}+O(q^{100}) \) 4 * q + q^3 - 2 * q^4 + 12 * q^6 + 2 * q^7 - 5 * q^9 + 16 * q^10 + 6 * q^11 - 11 * q^12 + 3 * q^13 - 9 * q^14 - 15 * q^15 + 2 * q^16 - 6 * q^17 + 18 * q^18 - 16 * q^19 + 5 * q^21 - 9 * q^22 - 6 * q^23 - 3 * q^24 - 14 * q^25 - 6 * q^26 - 20 * q^27 - q^28 + 6 * q^29 + 25 * q^30 + 6 * q^33 - 4 * q^34 + 27 * q^35 + 13 * q^36 - 21 * q^37 - 6 * q^38 + 9 * q^39 - 18 * q^40 - 3 * q^41 - 12 * q^42 + 9 * q^43 - 3 * q^44 - 33 * q^45 - 12 * q^46 + 12 * q^47 - 10 * q^48 - 26 * q^49 + 18 * q^51 + 9 * q^52 + 27 * q^55 + 18 * q^56 - q^57 - 17 * q^58 + 15 * q^59 + 60 * q^60 - 9 * q^61 + 20 * q^63 + 32 * q^64 - 3 * q^65 - 18 * q^68 + 36 * q^69 + 8 * q^70 + 6 * q^71 - 15 * q^72 - 6 * q^73 - 35 * q^75 + 8 * q^76 - 24 * q^77 - 3 * q^78 + 10 * q^81 + 36 * q^82 - 55 * q^84 - 2 * q^85 - 3 * q^86 + 45 * q^87 + 18 * q^88 - 9 * q^89 - 41 * q^90 + 15 * q^91 - 18 * q^92 - q^94 + 18 * q^95 - 21 * q^96 + 4 * q^97 - 9 * q^98 + 15 * q^99

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