LMFDB - Embedded newform 273.2.k.d.22.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [273,2,Mod(22,273)]

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, 0, 4]))

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

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

chi := DirichletCharacter("273.22");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 273 = 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	273.k (of order $3$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$2.17991597518$
Analytic rank:	$0$
Dimension:	$6$
Relative dimension:	$3$ over $\Q(\zeta_{3})$
Coefficient field:	6.0.771147.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{5} + 5x^{4} + 6x^{3} + 15x^{2} + 4x + 1 $ x^6 - x^5 + 5x^4 + 6x^3 + 15x^2 + 4x + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			22.3
Root			$1.32555 - 2.29591i$ of defining polynomial
Character	$\chi$	$=$	273.22
Dual form			273.2.k.d.211.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.18860 - 2.05872i) q^{2} +(0.500000 - 0.866025i) q^{3} +(-1.82555 - 3.16194i) q^{4} -4.02830 q^{5} +(-1.18860 - 2.05872i) q^{6} +(0.500000 + 0.866025i) q^{7} -3.92498 q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(q+(1.18860 - 2.05872i) q^{2} +(0.500000 - 0.866025i) q^{3} +(-1.82555 - 3.16194i) q^{4} -4.02830 q^{5} +(-1.18860 - 2.05872i) q^{6} +(0.500000 + 0.866025i) q^{7} -3.92498 q^{8} +(-0.500000 - 0.866025i) q^{9} +(-4.78804 + 8.29313i) q^{10} +(1.63695 - 2.83527i) q^{11} -3.65109 q^{12} +(0.910836 - 3.48861i) q^{13} +2.37720 q^{14} +(-2.01415 + 3.48861i) q^{15} +(-1.01415 + 1.75656i) q^{16} +(0.188601 + 0.326667i) q^{17} -2.37720 q^{18} +(1.77389 + 3.07247i) q^{19} +(7.35384 + 12.7372i) q^{20} +1.00000 q^{21} +(-3.89135 - 6.74002i) q^{22} +(-0.948344 + 1.64258i) q^{23} +(-1.96249 + 3.39914i) q^{24} +11.2272 q^{25} +(-6.09944 - 6.02172i) q^{26} -1.00000 q^{27} +(1.82555 - 3.16194i) q^{28} +(4.33969 - 7.51657i) q^{29} +(4.78804 + 8.29313i) q^{30} +6.33048 q^{31} +(-1.51415 - 2.62258i) q^{32} +(-1.63695 - 2.83527i) q^{33} +0.896688 q^{34} +(-2.01415 - 3.48861i) q^{35} +(-1.82555 + 3.16194i) q^{36} +(-2.01415 + 3.48861i) q^{37} +8.43380 q^{38} +(-2.56580 - 2.53311i) q^{39} +15.8110 q^{40} +(-3.75441 + 6.50282i) q^{41} +(1.18860 - 2.05872i) q^{42} +(4.32555 + 7.49207i) q^{43} -11.9533 q^{44} +(2.01415 + 3.48861i) q^{45} +(2.25441 + 3.90475i) q^{46} -12.1239 q^{47} +(1.01415 + 1.75656i) q^{48} +(-0.500000 + 0.866025i) q^{49} +(13.3446 - 23.1136i) q^{50} +0.377203 q^{51} +(-12.6935 + 3.48861i) q^{52} +7.75441 q^{53} +(-1.18860 + 2.05872i) q^{54} +(-6.59410 + 11.4213i) q^{55} +(-1.96249 - 3.39914i) q^{56} +3.54778 q^{57} +(-10.3163 - 17.8684i) q^{58} +(1.05166 + 1.82152i) q^{59} +14.7077 q^{60} +(-3.87720 - 6.71551i) q^{61} +(7.52442 - 13.0327i) q^{62} +(0.500000 - 0.866025i) q^{63} -11.2555 q^{64} +(-3.66912 + 14.0531i) q^{65} -7.78270 q^{66} +(-2.79191 + 4.83574i) q^{67} +(0.688601 - 1.19269i) q^{68} +(0.948344 + 1.64258i) q^{69} -9.57608 q^{70} +(-1.99612 - 3.45739i) q^{71} +(1.96249 + 3.39914i) q^{72} +7.50106 q^{73} +(4.78804 + 8.29313i) q^{74} +(5.61359 - 9.72302i) q^{75} +(6.47664 - 11.2179i) q^{76} +3.27389 q^{77} +(-8.26468 + 2.27141i) q^{78} -1.16283 q^{79} +(4.08529 - 7.07593i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(8.92498 + 15.4585i) q^{82} +15.1805 q^{83} +(-1.82555 - 3.16194i) q^{84} +(-0.759742 - 1.31591i) q^{85} +20.5654 q^{86} +(-4.33969 - 7.51657i) q^{87} +(-6.42498 + 11.1284i) q^{88} +(-3.17939 + 5.50686i) q^{89} +9.57608 q^{90} +(3.47664 - 0.955496i) q^{91} +6.92498 q^{92} +(3.16524 - 5.48236i) q^{93} +(-14.4104 + 24.9596i) q^{94} +(-7.14576 - 12.3768i) q^{95} -3.02830 q^{96} +(-2.48585 - 4.30562i) q^{97} +(1.18860 + 2.05872i) q^{98} -3.27389 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 2 q^{2} + 3 q^{3} - 4 q^{4} - 2 q^{6} + 3 q^{7} - 6 q^{8} - 3 q^{9}+O(q^{10}) $ 6 * q + 2 * q^2 + 3 * q^3 - 4 * q^4 - 2 * q^6 + 3 * q^7 - 6 * q^8 - 3 * q^9	$ 6 q + 2 q^{2} + 3 q^{3} - 4 q^{4} - 2 q^{6} + 3 q^{7} - 6 q^{8} - 3 q^{9} - 13 q^{10} + 8 q^{11} - 8 q^{12} + 4 q^{14} + 6 q^{16} - 4 q^{17} - 4 q^{18} + 7 q^{19} + 13 q^{20} + 6 q^{21} - q^{22} - 9 q^{23} - 3 q^{24} + 22 q^{25} - 26 q^{26} - 6 q^{27} + 4 q^{28} + 7 q^{29} + 13 q^{30} - 14 q^{31} + 3 q^{32} - 8 q^{33} + 12 q^{34} - 4 q^{36} - 8 q^{38} + 26 q^{40} - 2 q^{41} + 2 q^{42} + 19 q^{43} - 30 q^{44} - 7 q^{46} - 34 q^{47} - 6 q^{48} - 3 q^{49} + 16 q^{50} - 8 q^{51} - 26 q^{52} + 26 q^{53} - 2 q^{54} - 3 q^{56} + 14 q^{57} - 22 q^{58} + 3 q^{59} + 26 q^{60} - 13 q^{61} + 17 q^{62} + 3 q^{63} + 2 q^{64} - 2 q^{66} - 5 q^{67} - q^{68} + 9 q^{69} - 26 q^{70} - 8 q^{71} + 3 q^{72} - 4 q^{73} + 13 q^{74} + 11 q^{75} + 18 q^{76} + 16 q^{77} - 13 q^{78} - 2 q^{79} + 26 q^{80} - 3 q^{81} + 36 q^{82} + 4 q^{83} - 4 q^{84} - 13 q^{85} + 34 q^{86} - 7 q^{87} - 21 q^{88} + 19 q^{89} + 26 q^{90} + 24 q^{92} - 7 q^{93} - 7 q^{94} + 6 q^{96} - 27 q^{97} + 2 q^{98} - 16 q^{99}+O(q^{100}) $ 6 * q + 2 * q^2 + 3 * q^3 - 4 * q^4 - 2 * q^6 + 3 * q^7 - 6 * q^8 - 3 * q^9 - 13 * q^10 + 8 * q^11 - 8 * q^12 + 4 * q^14 + 6 * q^16 - 4 * q^17 - 4 * q^18 + 7 * q^19 + 13 * q^20 + 6 * q^21 - q^22 - 9 * q^23 - 3 * q^24 + 22 * q^25 - 26 * q^26 - 6 * q^27 + 4 * q^28 + 7 * q^29 + 13 * q^30 - 14 * q^31 + 3 * q^32 - 8 * q^33 + 12 * q^34 - 4 * q^36 - 8 * q^38 + 26 * q^40 - 2 * q^41 + 2 * q^42 + 19 * q^43 - 30 * q^44 - 7 * q^46 - 34 * q^47 - 6 * q^48 - 3 * q^49 + 16 * q^50 - 8 * q^51 - 26 * q^52 + 26 * q^53 - 2 * q^54 - 3 * q^56 + 14 * q^57 - 22 * q^58 + 3 * q^59 + 26 * q^60 - 13 * q^61 + 17 * q^62 + 3 * q^63 + 2 * q^64 - 2 * q^66 - 5 * q^67 - q^68 + 9 * q^69 - 26 * q^70 - 8 * q^71 + 3 * q^72 - 4 * q^73 + 13 * q^74 + 11 * q^75 + 18 * q^76 + 16 * q^77 - 13 * q^78 - 2 * q^79 + 26 * q^80 - 3 * q^81 + 36 * q^82 + 4 * q^83 - 4 * q^84 - 13 * q^85 + 34 * q^86 - 7 * q^87 - 21 * q^88 + 19 * q^89 + 26 * q^90 + 24 * q^92 - 7 * q^93 - 7 * q^94 + 6 * q^96 - 27 * q^97 + 2 * q^98 - 16 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	1.18860	−	2.05872i	0.840468	−	1.45573i	−0.0490313	−	0.998797i	$-0.515613\pi$
$2$	1.18860	−	2.05872i	0.840468	−	1.45573i	0.889499	−	0.456936i	$-0.151053\pi$
$3$	0.500000	−	0.866025i	0.288675	−	0.500000i
$3$	0.500000	−	0.866025i	0.288675	−	0.500000i
$4$	−1.82555	−	3.16194i	−0.912773	−	1.58097i
$5$	−4.02830			−1.80151			−0.900754	−	0.434329i	$-0.856986\pi$
$5$	−4.02830			−1.80151			−0.900754	+	0.434329i	$0.856986\pi$
$6$	−1.18860	−	2.05872i	−0.485245	−	0.840468i
$7$	0.500000	+	0.866025i	0.188982	+	0.327327i
$7$	0.500000	+	0.866025i	0.188982	+	0.327327i
$8$	−3.92498			−1.38769
$9$	−0.500000	−	0.866025i	−0.166667	−	0.288675i
$10$	−4.78804	+	8.29313i	−1.51411	+	2.62252i
$11$	1.63695	−	2.83527i	0.493558	−	0.854867i	−0.506415	−	0.862290i	$-0.669030\pi$
$11$	1.63695	−	2.83527i	0.493558	−	0.854867i	0.999972	+	0.00742317i	$0.00236289\pi$
$12$	−3.65109			−1.05398
$13$	0.910836	−	3.48861i	0.252620	−	0.967565i
$13$	0.910836	−	3.48861i	0.252620	−	0.967565i
$14$	2.37720			0.635334
$15$	−2.01415	+	3.48861i	−0.520051	+	0.900754i
$16$	−1.01415	+	1.75656i	−0.253537	+	0.439139i
$17$	0.188601	+	0.326667i	0.0457426	+	0.0792284i	0.887990	−	0.459862i	$-0.152101\pi$
$17$	0.188601	+	0.326667i	0.0457426	+	0.0792284i	−0.842248	+	0.539091i	$0.818768\pi$
$18$	−2.37720			−0.560312
$19$	1.77389	+	3.07247i	0.406958	+	0.704873i	0.994547	−	0.104287i	$-0.0332561\pi$
$19$	1.77389	+	3.07247i	0.406958	+	0.704873i	−0.587589	+	0.809160i	$0.699923\pi$
$20$	7.35384	+	12.7372i	1.64437	+	2.84813i
$21$	1.00000			0.218218
$22$	−3.89135	−	6.74002i	−0.829639	−	1.43698i
$23$	−0.948344	+	1.64258i	−0.197743	+	0.342502i	−0.947796	−	0.318876i	$-0.896695\pi$
$23$	−0.948344	+	1.64258i	−0.197743	+	0.342502i	0.750053	+	0.661378i	$0.230028\pi$
$24$	−1.96249	+	3.39914i	−0.400592	+	0.693846i
$25$	11.2272			2.24543
$26$	−6.09944	−	6.02172i	−1.19620	−	1.18096i
$27$	−1.00000			−0.192450
$28$	1.82555	−	3.16194i	0.344996	−	0.597550i
$29$	4.33969	−	7.51657i	0.805861	−	1.39579i	−0.109847	−	0.993948i	$-0.535036\pi$
$29$	4.33969	−	7.51657i	0.805861	−	1.39579i	0.915708	−	0.401844i	$-0.131631\pi$
$30$	4.78804	+	8.29313i	0.874172	+	1.51411i
$31$	6.33048			1.13699			0.568494	−	0.822687i	$-0.307526\pi$
$31$	6.33048			1.13699			0.568494	+	0.822687i	$0.307526\pi$
$32$	−1.51415	−	2.62258i	−0.267666	−	0.463611i
$33$	−1.63695	−	2.83527i	−0.284956	−	0.493558i
$34$	0.896688			0.153781
$35$	−2.01415	−	3.48861i	−0.340453	−	0.589682i
$36$	−1.82555	+	3.16194i	−0.304258	+	0.526990i
$37$	−2.01415	+	3.48861i	−0.331124	+	0.573523i	−0.982733	−	0.185032i	$-0.940761\pi$
$37$	−2.01415	+	3.48861i	−0.331124	+	0.573523i	0.651609	+	0.758555i	$0.274094\pi$
$38$	8.43380			1.36814
$39$	−2.56580	−	2.53311i	−0.410858	−	0.405622i
$40$	15.8110			2.49994
$41$	−3.75441	+	6.50282i	−0.586340	+	1.01557i	0.408367	+	0.912818i	$0.366098\pi$
$41$	−3.75441	+	6.50282i	−0.586340	+	1.01557i	−0.994707	+	0.102752i	$0.967235\pi$
$42$	1.18860	−	2.05872i	0.183405	−	0.317667i
$43$	4.32555	+	7.49207i	0.659640	+	1.14253i	0.980709	+	0.195474i	$0.0626244\pi$
$43$	4.32555	+	7.49207i	0.659640	+	1.14253i	−0.321069	+	0.947056i	$0.604042\pi$
$44$	−11.9533			−1.80202
$45$	2.01415	+	3.48861i	0.300251	+	0.520051i
$46$	2.25441	+	3.90475i	0.332394	+	0.575723i
$47$	−12.1239			−1.76845			−0.884223	−	0.467064i	$-0.845312\pi$
$47$	−12.1239			−1.76845			−0.884223	+	0.467064i	$0.845312\pi$
$48$	1.01415	+	1.75656i	0.146380	+	0.253537i
$49$	−0.500000	+	0.866025i	−0.0714286	+	0.123718i
$50$	13.3446	−	23.1136i	1.88722	−	3.26875i
$51$	0.377203			0.0528190
$52$	−12.6935	+	3.48861i	−1.76028	+	0.483783i
$53$	7.75441			1.06515			0.532575	−	0.846383i	$-0.321225\pi$
$53$	7.75441			1.06515			0.532575	+	0.846383i	$0.321225\pi$
$54$	−1.18860	+	2.05872i	−0.161748	+	0.280156i
$55$	−6.59410	+	11.4213i	−0.889148	+	1.54005i
$56$	−1.96249	−	3.39914i	−0.262249	−	0.454229i
$57$	3.54778			0.469915
$58$	−10.3163	−	17.8684i	−1.35460	−	2.34624i
$59$	1.05166	+	1.82152i	0.136914	+	0.237142i	0.926327	−	0.376720i	$-0.122948\pi$
$59$	1.05166	+	1.82152i	0.136914	+	0.237142i	−0.789413	+	0.613862i	$0.789615\pi$
$60$	14.7077			1.89875
$61$	−3.87720	−	6.71551i	−0.496425	−	0.859833i	0.503567	−	0.863956i	$-0.332021\pi$
$61$	−3.87720	−	6.71551i	−0.496425	−	0.859833i	−0.999991	+	0.00412320i	$0.998688\pi$
$62$	7.52442	−	13.0327i	0.955602	−	1.65515i
$63$	0.500000	−	0.866025i	0.0629941	−	0.109109i
$64$	−11.2555			−1.40693
$65$	−3.66912	+	14.0531i	−0.455098	+	1.74308i
$66$	−7.78270			−0.957984
$67$	−2.79191	+	4.83574i	−0.341087	+	0.590779i	−0.984635	−	0.174626i	$-0.944128\pi$
$67$	−2.79191	+	4.83574i	−0.341087	+	0.590779i	0.643548	+	0.765406i	$0.277462\pi$
$68$	0.688601	−	1.19269i	0.0835052	−	0.144635i
$69$	0.948344	+	1.64258i	0.114167	+	0.197743i
$70$	−9.57608			−1.14456
$71$	−1.99612	−	3.45739i	−0.236896	−	0.410317i	0.722926	−	0.690926i	$-0.242797\pi$
$71$	−1.99612	−	3.45739i	−0.236896	−	0.410317i	−0.959822	+	0.280609i	$0.909464\pi$
$72$	1.96249	+	3.39914i	0.231282	+	0.400592i
$73$	7.50106			0.877933			0.438966	−	0.898503i	$-0.355345\pi$
$73$	7.50106			0.877933			0.438966	+	0.898503i	$0.355345\pi$
$74$	4.78804	+	8.29313i	0.556598	+	0.964056i
$75$	5.61359	−	9.72302i	0.648201	−	1.12272i
$76$	6.47664	−	11.2179i	0.742922	−	1.28678i
$77$	3.27389			0.373094
$78$	−8.26468	+	2.27141i	−0.935791	+	0.257186i
$79$	−1.16283			−0.130828			−0.0654142	−	0.997858i	$-0.520837\pi$
$79$	−1.16283			−0.130828			−0.0654142	+	0.997858i	$0.520837\pi$
$80$	4.08529	−	7.07593i	0.456749	−	0.791113i
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$	8.92498	+	15.4585i	0.985600	+	1.70711i
$83$	15.1805			1.66627			0.833135	−	0.553069i	$-0.186543\pi$
$83$	15.1805			1.66627			0.833135	+	0.553069i	$0.186543\pi$
$84$	−1.82555	−	3.16194i	−0.199183	−	0.344996i
$85$	−0.759742	−	1.31591i	−0.0824056	−	0.142731i
$86$	20.5654			2.21762
$87$	−4.33969	−	7.51657i	−0.465264	−	0.805861i
$88$	−6.42498	+	11.1284i	−0.684906	+	1.18629i
$89$	−3.17939	+	5.50686i	−0.337015	+	0.583726i	−0.983870	−	0.178886i	$-0.942751\pi$
$89$	−3.17939	+	5.50686i	−0.337015	+	0.583726i	0.646855	+	0.762613i	$0.276084\pi$
$90$	9.57608			1.00941
$91$	3.47664	−	0.955496i	0.364451	−	0.100163i
$92$	6.92498			0.721979
$93$	3.16524	−	5.48236i	0.328220	−	0.568494i
$94$	−14.4104	+	24.9596i	−1.48632	+	2.57439i
$95$	−7.14576	−	12.3768i	−0.733139	−	1.26983i
$96$	−3.02830			−0.309074
$97$	−2.48585	−	4.30562i	−0.252400	−	0.437170i	0.711786	−	0.702396i	$-0.247887\pi$
$97$	−2.48585	−	4.30562i	−0.252400	−	0.437170i	−0.964186	+	0.265227i	$0.914553\pi$
$98$	1.18860	+	2.05872i	0.120067	+	0.207962i
$99$	−3.27389			−0.329038
$100$	−20.4957	−	35.4996i	−2.04957	−	3.54996i
$101$	−2.94834	+	5.10668i	−0.293371	+	0.508134i	−0.974605	−	0.223932i	$-0.928111\pi$
$101$	−2.94834	+	5.10668i	−0.293371	+	0.508134i	0.681233	+	0.732066i	$0.261444\pi$
$102$	0.448344	−	0.776554i	0.0443927	−	0.0768903i
$103$	10.5654			1.04104			0.520520	−	0.853849i	$-0.325738\pi$
$103$	10.5654			1.04104			0.520520	+	0.853849i	$0.325738\pi$
$104$	−3.57502	+	13.6927i	−0.350559	+	1.34268i
$105$	−4.02830			−0.393121
$106$	9.21690	−	15.9641i	0.895224	−	1.55057i
$107$	6.20275	−	10.7435i	0.599642	−	1.03861i	−0.393231	−	0.919440i	$-0.628643\pi$
$107$	6.20275	−	10.7435i	0.599642	−	1.03861i	0.992874	−	0.119172i	$-0.0380239\pi$
$108$	1.82555	+	3.16194i	0.175663	+	0.304258i
$109$	−12.1316			−1.16200			−0.580999	−	0.813905i	$-0.697338\pi$
$109$	−12.1316			−1.16200			−0.580999	+	0.813905i	$0.697338\pi$
$110$	15.6755	+	27.1508i	1.49460	+	2.58873i
$111$	2.01415	+	3.48861i	0.191174	+	0.331124i
$112$	−2.02830			−0.191656
$113$	5.33582	+	9.24191i	0.501952	+	0.869406i	0.999997	+	0.00225510i	$0.000717821\pi$
$113$	5.33582	+	9.24191i	0.501952	+	0.869406i	−0.498046	+	0.867151i	$0.665949\pi$
$114$	4.21690	−	7.30388i	0.394949	−	0.684071i
$115$	3.82021	−	6.61680i	0.356236	−	0.617020i
$116$	−31.6893			−2.94227
$117$	−3.47664	+	0.955496i	−0.321415	+	0.0883357i
$118$	5.00000			0.460287
$119$	−0.188601	+	0.326667i	−0.0172891	+	0.0299455i
$120$	7.90550	−	13.6927i	0.721670	−	1.24997i
$121$	0.140820	+	0.243908i	0.0128018	+	0.0221734i
$122$	−18.4338			−1.66892
$123$	3.75441	+	6.50282i	0.338523	+	0.586340i
$124$	−11.5566	−	20.0166i	−1.03781	−	1.79754i
$125$	−25.0849			−2.24366
$126$	−1.18860	−	2.05872i	−0.105889	−	0.183405i
$127$	−3.66524	+	6.34838i	−0.325238	+	0.563328i	−0.981560	−	0.191152i	$-0.938778\pi$
$127$	−3.66524	+	6.34838i	−0.325238	+	0.563328i	0.656323	+	0.754480i	$0.272111\pi$
$128$	−10.3500	+	17.9267i	−0.914817	+	1.58451i
$129$	8.65109			0.761686
$130$	24.5703	+	24.2573i	2.15496	+	2.12750i
$131$	11.4239			0.998113			0.499056	−	0.866570i	$-0.333680\pi$
$131$	11.4239			0.998113			0.499056	+	0.866570i	$0.333680\pi$
$132$	−5.97664	+	10.3518i	−0.520200	+	0.901012i
$133$	−1.77389	+	3.07247i	−0.153816	+	0.266417i
$134$	6.63695	+	11.4955i	0.573345	+	0.993062i
$135$	4.02830			0.346701
$136$	−0.740258	−	1.28216i	−0.0634766	−	0.109945i
$137$	1.59556	+	2.76359i	0.136318	+	0.236110i	0.926100	−	0.377278i	$-0.123140\pi$
$137$	1.59556	+	2.76359i	0.136318	+	0.236110i	−0.789782	+	0.613387i	$0.789806\pi$
$138$	4.50881			0.383816
$139$	−2.68860	−	4.65679i	−0.228044	−	0.394984i	0.729184	−	0.684317i	$-0.239900\pi$
$139$	−2.68860	−	4.65679i	−0.228044	−	0.394984i	−0.957228	+	0.289333i	$0.906566\pi$
$140$	−7.35384	+	12.7372i	−0.621513	+	1.07649i
$141$	−6.06193	+	10.4996i	−0.510507	+	0.884223i
$142$	−9.49039			−0.796416
$143$	−8.40016	−	8.29313i	−0.702457	−	0.693506i
$144$	2.02830			0.169025
$145$	−17.4816	+	30.2790i	−1.45177	+	2.51453i
$146$	8.91577	−	15.4426i	0.737875	−	1.27804i
$147$	0.500000	+	0.866025i	0.0412393	+	0.0714286i
$148$	14.7077			1.20896
$149$	5.01415	+	8.68476i	0.410775	+	0.711483i	0.994975	−	0.100127i	$-0.0319248\pi$
$149$	5.01415	+	8.68476i	0.410775	+	0.711483i	−0.584200	+	0.811610i	$0.698592\pi$
$150$	−13.3446	−	23.1136i	−1.08958	−	1.88722i
$151$	−9.71544			−0.790631			−0.395315	−	0.918545i	$-0.629365\pi$
$151$	−9.71544			−0.790631			−0.395315	+	0.918545i	$0.629365\pi$
$152$	−6.96249	−	12.0594i	−0.564733	−	0.978146i
$153$	0.188601	−	0.326667i	0.0152475	−	0.0264095i
$154$	3.89135	−	6.74002i	0.313574	−	0.543126i
$155$	−25.5011			−2.04829
$156$	−3.32555	+	12.7372i	−0.266257	+	1.01979i
$157$	17.5761			1.40272			0.701362	−	0.712805i	$-0.252576\pi$
$157$	17.5761			1.40272			0.701362	+	0.712805i	$0.252576\pi$
$158$	−1.38214	+	2.39394i	−0.109957	+	0.190451i
$159$	3.87720	−	6.71551i	0.307482	−	0.532575i
$160$	6.09944	+	10.5645i	0.482203	+	0.835200i
$161$	−1.89669			−0.149480
$162$	1.18860	+	2.05872i	0.0933853	+	0.161748i
$163$	2.74559	+	4.75551i	0.215052	+	0.372480i	0.953289	−	0.302061i	$-0.0976747\pi$
$163$	2.74559	+	4.75551i	0.215052	+	0.372480i	−0.738237	+	0.674541i	$0.764341\pi$
$164$	27.4154			2.14078
$165$	6.59410	+	11.4213i	0.513350	+	0.889148i
$166$	18.0435	−	31.2523i	1.40045	−	2.42565i
$167$	−2.21836	+	3.84231i	−0.171662	+	0.297327i	−0.939001	−	0.343914i	$-0.888247\pi$
$167$	−2.21836	+	3.84231i	−0.171662	+	0.297327i	0.767339	+	0.641241i	$0.221580\pi$
$168$	−3.92498			−0.302819
$169$	−11.3408	−	6.35510i	−0.872366	−	0.488854i
$170$	−3.61212			−0.277037
$171$	1.77389	−	3.07247i	0.135653	−	0.234958i
$172$	15.7930	−	27.3542i	1.20420	−	2.08574i
$173$	−11.0800	−	19.1910i	−0.842393	−	1.45907i	−0.887866	−	0.460102i	$-0.847813\pi$
$173$	−11.0800	−	19.1910i	−0.842393	−	1.45907i	0.0454728	−	0.998966i	$-0.485521\pi$
$174$	−20.6327			−1.56416
$175$	5.61359	+	9.72302i	0.424347	+	0.734991i
$176$	3.32021	+	5.75077i	0.250270	+	0.433481i
$177$	2.10331			0.158095
$178$	7.55805	+	13.0909i	0.566500	+	0.981207i
$179$	0.970242	−	1.68051i	0.0725193	−	0.125607i	−0.827486	−	0.561487i	$-0.810229\pi$
$179$	0.970242	−	1.68051i	0.0725193	−	0.125607i	0.900005	+	0.435880i	$0.143563\pi$
$180$	7.35384	−	12.7372i	0.548123	−	0.949377i
$181$	−8.50106			−0.631879			−0.315939	−	0.948779i	$-0.602320\pi$
$181$	−8.50106			−0.631879			−0.315939	+	0.948779i	$0.602320\pi$
$182$	2.16524	−	8.29313i	0.160498	−	0.614727i
$183$	−7.75441			−0.573222
$184$	3.72223	−	6.44710i	0.274407	−	0.475286i
$185$	8.11359	−	14.0531i	0.596523	−	1.03321i
$186$	−7.52442	−	13.0327i	−0.551717	−	0.955602i
$187$	1.23492			0.0903064
$188$	22.1327	+	38.3349i	1.61419	+	2.79586i
$189$	−0.500000	−	0.866025i	−0.0363696	−	0.0629941i
$190$	−33.9738			−2.46472
$191$	−0.325547	−	0.563863i	−0.0235557	−	0.0407997i	0.854007	−	0.520261i	$-0.174165\pi$
$191$	−0.325547	−	0.563863i	−0.0235557	−	0.0407997i	−0.877563	+	0.479461i	$0.840832\pi$
$192$	−5.62773	+	9.74752i	−0.406147	+	0.703467i
$193$	−9.53217	+	16.5102i	−0.686141	+	1.18843i	0.286936	+	0.957950i	$0.407363\pi$
$193$	−9.53217	+	16.5102i	−0.686141	+	1.18843i	−0.973077	+	0.230481i	$0.925970\pi$
$194$	−11.8187			−0.848537
$195$	10.3358	+	10.2041i	0.740163	+	0.730732i
$196$	3.65109			0.260792
$197$	−12.3549	+	21.3993i	−0.880250	+	1.52464i	−0.0291881	+	0.999574i	$0.509292\pi$
$197$	−12.3549	+	21.3993i	−0.880250	+	1.52464i	−0.851062	+	0.525065i	$0.824041\pi$
$198$	−3.89135	+	6.74002i	−0.276546	+	0.478992i
$199$	−6.57220	−	11.3834i	−0.465891	−	0.806947i	0.533350	−	0.845895i	$-0.320933\pi$
$199$	−6.57220	−	11.3834i	−0.465891	−	0.806947i	−0.999241	+	0.0389475i	$0.987599\pi$
$200$	−44.0665			−3.11597
$201$	2.79191	+	4.83574i	0.196926	+	0.341087i
$202$	7.00881	+	12.1396i	0.493138	+	0.854141i
$203$	8.67939			0.609174
$204$	−0.688601	−	1.19269i	−0.0482117	−	0.0835052i
$205$	15.1239	−	26.1953i	1.05630	−	1.82956i
$206$	12.5581	−	21.7512i	0.874961	−	1.51548i
$207$	1.89669			0.131829
$208$	5.20421	+	5.13790i	0.360847	+	0.356249i
$209$	11.6150			0.803430
$210$	−4.78804	+	8.29313i	−0.330406	+	0.572280i
$211$	9.79831	−	16.9712i	0.674544	−	1.16834i	−0.302058	−	0.953289i	$-0.597674\pi$
$211$	9.79831	−	16.9712i	0.674544	−	1.16834i	0.976602	−	0.215054i	$-0.0689929\pi$
$212$	−14.1560	−	24.5190i	−0.972240	−	1.68397i
$213$	−3.99225			−0.273544
$214$	−14.7452	−	25.5394i	−1.00796	−	1.74584i
$215$	−17.4246	−	30.1803i	−1.18835	−	2.05828i
$216$	3.92498			0.267061
$217$	3.16524	+	5.48236i	0.214871	+	0.372167i
$218$	−14.4196	+	24.9756i	−0.976622	+	1.69156i
$219$	3.75053	−	6.49611i	0.253437	−	0.438966i
$220$	48.1514			3.24636
$221$	1.31140	−	0.360416i	0.0882142	−	0.0242442i
$222$	9.57608			0.642704
$223$	13.9338	−	24.1340i	0.933076	−	1.61613i	0.155046	−	0.987907i	$-0.450447\pi$
$223$	13.9338	−	24.1340i	0.933076	−	1.61613i	0.778029	−	0.628228i	$-0.216219\pi$
$224$	1.51415	−	2.62258i	0.101168	−	0.175229i
$225$	−5.61359	−	9.72302i	−0.374239	−	0.648201i
$226$	25.3687			1.68750
$227$	−6.01521	−	10.4186i	−0.399243	−	0.691510i	0.594389	−	0.804177i	$-0.297394\pi$
$227$	−6.01521	−	10.4186i	−0.399243	−	0.691510i	−0.993633	+	0.112667i	$0.964061\pi$
$228$	−6.47664	−	11.2179i	−0.428926	−	0.742922i
$229$	−9.19887			−0.607879			−0.303939	−	0.952691i	$-0.598302\pi$
$229$	−9.19887			−0.607879			−0.303939	+	0.952691i	$0.598302\pi$
$230$	−9.08141	−	15.7295i	−0.598811	−	1.03717i
$231$	1.63695	−	2.83527i	0.107703	−	0.186547i
$232$	−17.0332	+	29.5024i	−1.11829	+	1.93693i
$233$	−12.4522			−0.815772			−0.407886	−	0.913033i	$-0.633734\pi$
$233$	−12.4522			−0.815772			−0.407886	+	0.913033i	$0.633734\pi$
$234$	−2.16524	+	8.29313i	−0.141546	+	0.542139i
$235$	48.8385			3.18587
$236$	3.83969	−	6.65055i	0.249943	−	0.432914i
$237$	−0.581414	+	1.00704i	−0.0377669	+	0.0654142i
$238$	0.448344	+	0.776554i	0.0290618	+	0.0503365i
$239$	−3.24559			−0.209940			−0.104970	−	0.994475i	$-0.533475\pi$
$239$	−3.24559			−0.209940			−0.104970	+	0.994475i	$0.533475\pi$
$240$	−4.08529	−	7.07593i	−0.263704	−	0.456749i
$241$	−4.71302	−	8.16319i	−0.303592	−	0.525838i	0.673354	−	0.739320i	$-0.264853\pi$
$241$	−4.71302	−	8.16319i	−0.303592	−	0.525838i	−0.976947	+	0.213482i	$0.931519\pi$
$242$	0.669517			0.0430382
$243$	0.500000	+	0.866025i	0.0320750	+	0.0555556i
$244$	−14.1560	+	24.5190i	−0.906247	+	1.56967i
$245$	2.01415	−	3.48861i	0.128679	−	0.222879i
$246$	17.8500			1.13807
$247$	12.3344	−	3.38989i	0.784816	−	0.215694i
$248$	−24.8470			−1.57779
$249$	7.59023	−	13.1467i	0.481011	−	0.833135i
$250$	−29.8159	+	51.6427i	−1.88573	+	3.26617i
$251$	5.99466	+	10.3831i	0.378380	+	0.655373i	0.990827	−	0.135139i	$-0.0431480\pi$
$251$	5.99466	+	10.3831i	0.378380	+	0.655373i	−0.612447	+	0.790512i	$0.709815\pi$
$252$	−3.65109			−0.229997
$253$	3.10477	+	5.37763i	0.195195	+	0.338088i
$254$	8.71302	+	15.0914i	0.546704	+	0.946919i
$255$	−1.51948			−0.0951538
$256$	13.3485	+	23.1203i	0.834282	+	1.44502i
$257$	−7.29831	+	12.6410i	−0.455256	+	0.788527i	−0.998703	−	0.0509168i	$-0.983786\pi$
$257$	−7.29831	+	12.6410i	−0.455256	+	0.788527i	0.543447	+	0.839444i	$0.317119\pi$
$258$	10.2827	−	17.8102i	0.640173	−	1.10881i
$259$	−4.02830			−0.250306
$260$	51.1333	−	14.0531i	3.17115	−	0.871539i
$261$	−8.67939			−0.537241
$262$	13.5785	−	23.5186i	0.838882	−	1.45299i
$263$	−11.3266	+	19.6183i	−0.698429	+	1.20971i	0.270583	+	0.962697i	$0.412784\pi$
$263$	−11.3266	+	19.6183i	−0.698429	+	1.20971i	−0.969011	+	0.247017i	$0.920550\pi$
$264$	6.42498	+	11.1284i	0.395430	+	0.684906i
$265$	−31.2370			−1.91888
$266$	4.21690	+	7.30388i	0.258555	+	0.447830i
$267$	3.17939	+	5.50686i	0.194575	+	0.337015i
$268$	20.3871			1.24534
$269$	13.9947	+	24.2395i	0.853270	+	1.47791i	0.878241	+	0.478218i	$0.158717\pi$
$269$	13.9947	+	24.2395i	0.853270	+	1.47791i	−0.0249713	+	0.999688i	$0.507949\pi$
$270$	4.78804	−	8.29313i	0.291391	−	0.504704i
$271$	3.80365	−	6.58811i	0.231055	−	0.400199i	−0.727064	−	0.686570i	$-0.759116\pi$
$271$	3.80365	−	6.58811i	0.231055	−	0.400199i	0.958119	+	0.286371i	$0.0924489\pi$
$272$	−0.765079			−0.0463897
$273$	0.910836	−	3.48861i	0.0551263	−	0.211140i
$274$	7.58595			0.458284
$275$	18.3783	−	31.8321i	1.10825	−	1.91955i
$276$	3.46249	−	5.99721i	0.208418	−	0.360990i
$277$	3.44447	+	5.96599i	0.206958	+	0.358462i	0.950755	−	0.309944i	$-0.100310\pi$
$277$	3.44447	+	5.96599i	0.206958	+	0.358462i	−0.743797	+	0.668406i	$0.766977\pi$
$278$	−12.7827			−0.766656
$279$	−3.16524	−	5.48236i	−0.189498	−	0.328220i
$280$	7.90550	+	13.6927i	0.472444	+	0.818297i
$281$	10.8062			0.644642			0.322321	−	0.946630i	$-0.395537\pi$
$281$	10.8062			0.644642			0.322321	+	0.946630i	$0.395537\pi$
$282$	14.4104	+	24.9596i	0.858129	+	1.48632i
$283$	3.81246	−	6.60337i	0.226627	−	0.392530i	−0.730179	−	0.683256i	$-0.760563\pi$
$283$	3.81246	−	6.60337i	0.226627	−	0.392530i	0.956806	+	0.290726i	$0.0938968\pi$
$284$	−7.28804	+	12.6233i	−0.432466	+	0.749052i
$285$	−14.2915			−0.846556
$286$	−27.0577	+	7.43634i	−1.59995	+	0.439720i
$287$	−7.50881			−0.443231
$288$	−1.51415	+	2.62258i	−0.0892220	+	0.154537i
$289$	8.42886	−	14.5992i	0.495815	−	0.858777i
$290$	41.5573	+	71.9793i	2.44033	+	4.22677i
$291$	−4.97170			−0.291446
$292$	−13.6935	−	23.7179i	−0.801354	−	1.38799i
$293$	11.1458	+	19.3050i	0.651142	+	1.12781i	0.982846	+	0.184428i	$0.0590431\pi$
$293$	11.1458	+	19.3050i	0.651142	+	1.12781i	−0.331704	+	0.943384i	$0.607624\pi$
$294$	2.37720			0.138641
$295$	−4.23638	−	7.33763i	−0.246652	−	0.427213i
$296$	7.90550	−	13.6927i	0.459498	−	0.795874i
$297$	−1.63695	+	2.83527i	−0.0949852	+	0.164519i
$298$	23.8393			1.38097
$299$	4.86653	+	4.80452i	0.281439	+	0.277853i
$300$	−40.9914			−2.36664
$301$	−4.32555	+	7.49207i	−0.249320	+	0.431836i
$302$	−11.5478	+	20.0013i	−0.664500	+	1.15095i
$303$	2.94834	+	5.10668i	0.169378	+	0.293371i
$304$	−7.19595			−0.412716
$305$	15.6185	+	27.0521i	0.894314	+	1.54900i
$306$	−0.448344	−	0.776554i	−0.0256301	−	0.0443927i
$307$	−28.2448			−1.61202			−0.806008	−	0.591905i	$-0.798376\pi$
$307$	−28.2448			−1.61202			−0.806008	+	0.591905i	$0.798376\pi$
$308$	−5.97664	−	10.3518i	−0.340551	−	0.589851i
$309$	5.28270	−	9.14991i	0.300522	−	0.520520i
$310$	−30.3106	+	52.4995i	−1.72153	+	2.98177i
$311$	−2.66177			−0.150935			−0.0754675	−	0.997148i	$-0.524045\pi$
$311$	−2.66177			−0.150935			−0.0754675	+	0.997148i	$0.524045\pi$
$312$	10.0707	+	9.94242i	0.570143	+	0.562879i
$313$	−22.4826			−1.27079			−0.635397	−	0.772186i	$-0.719163\pi$
$313$	−22.4826			−1.27079			−0.635397	+	0.772186i	$0.719163\pi$
$314$	20.8910	−	36.1842i	1.17894	−	2.04199i
$315$	−2.01415	+	3.48861i	−0.113484	+	0.196561i
$316$	2.12280	+	3.67679i	0.119417	+	0.206836i
$317$	18.8315			1.05768			0.528842	−	0.848720i	$-0.322626\pi$
$317$	18.8315			1.05768			0.528842	+	0.848720i	$0.322626\pi$
$318$	−9.21690	−	15.9641i	−0.516858	−	0.895224i
$319$	−14.2077	−	24.6084i	−0.795478	−	1.37781i
$320$	45.3404			2.53460
$321$	−6.20275	−	10.7435i	−0.346204	−	0.599642i
$322$	−2.25441	+	3.90475i	−0.125633	+	0.217603i
$323$	−0.669117	+	1.15894i	−0.0372306	+	0.0644854i
$324$	3.65109			0.202839
$325$	10.2261	−	39.1672i	0.567242	−	2.17260i
$326$	13.0537			0.722976
$327$	−6.06580	+	10.5063i	−0.335440	+	0.580999i
$328$	14.7360	−	25.5235i	0.813659	−	1.40930i
$329$	−6.06193	−	10.4996i	−0.334205	−	0.578860i
$330$	31.3510			1.72582
$331$	8.91577	+	15.4426i	0.490055	+	0.848800i	0.999934	−	0.0114455i	$-0.00364329\pi$
$331$	8.91577	+	15.4426i	0.490055	+	0.848800i	−0.509879	+	0.860246i	$0.670310\pi$
$332$	−27.7126	−	47.9997i	−1.52093	−	2.63432i
$333$	4.02830			0.220749
$334$	5.27349	+	9.13395i	0.288553	+	0.499788i
$335$	11.2467	−	19.4798i	0.614470	−	1.06429i
$336$	−1.01415	+	1.75656i	−0.0553263	+	0.0958280i
$337$	7.57608			0.412695			0.206348	−	0.978479i	$-0.433842\pi$
$337$	7.57608			0.412695			0.206348	+	0.978479i	$0.433842\pi$
$338$	−26.5630	+	15.7937i	−1.44484	+	0.859066i
$339$	10.6716			0.579604
$340$	−2.77389	+	4.80452i	−0.150435	+	0.260562i
$341$	10.3627	−	17.9486i	0.561169	−	0.971974i
$342$	−4.21690	−	7.30388i	−0.228024	−	0.394949i
$343$	−1.00000			−0.0539949
$344$	−16.9777	−	29.4062i	−0.915376	−	1.58548i
$345$	−3.82021	−	6.61680i	−0.205673	−	0.356236i
$346$	−52.6786			−2.83202
$347$	−3.94407	−	6.83133i	−0.211729	−	0.366725i	0.740527	−	0.672027i	$-0.234576\pi$
$347$	−3.94407	−	6.83133i	−0.211729	−	0.366725i	−0.952256	+	0.305302i	$0.901243\pi$
$348$	−15.8446	+	27.4437i	−0.849361	+	1.47114i
$349$	5.86693	−	10.1618i	0.314050	−	0.543950i	−0.665185	−	0.746678i	$-0.731648\pi$
$349$	5.86693	−	10.1618i	0.314050	−	0.543950i	0.979235	+	0.202728i	$0.0649809\pi$
$350$	26.6893			1.42660
$351$	−0.910836	+	3.48861i	−0.0486168	+	0.186208i
$352$	−9.91431			−0.528435
$353$	6.26855	−	10.8575i	0.333641	−	0.577884i	−0.649581	−	0.760292i	$-0.725056\pi$
$353$	6.26855	−	10.8575i	0.333641	−	0.577884i	0.983223	+	0.182408i	$0.0583892\pi$
$354$	2.50000	−	4.33013i	0.132874	−	0.230144i
$355$	8.04098	+	13.9274i	0.426771	+	0.739189i
$356$	23.2165			1.23047
$357$	0.188601	+	0.326667i	0.00998185	+	0.0172891i
$358$	−2.30646	−	3.99491i	−0.121900	−	0.211138i
$359$	−5.01762			−0.264820			−0.132410	−	0.991195i	$-0.542272\pi$
$359$	−5.01762			−0.264820			−0.132410	+	0.991195i	$0.542272\pi$
$360$	−7.90550	−	13.6927i	−0.416656	−	0.721670i
$361$	3.20662	−	5.55404i	0.168770	−	0.292318i
$362$	−10.1044	+	17.5013i	−0.531074	+	0.919847i
$363$	0.281641			0.0147823
$364$	−9.36799	−	9.24862i	−0.491016	−	0.484760i
$365$	−30.2165			−1.58160
$366$	−9.21690	+	15.9641i	−0.481775	+	0.834459i
$367$	−11.8549	+	20.5333i	−0.618821	+	1.07183i	0.370880	+	0.928681i	$0.379056\pi$
$367$	−11.8549	+	20.5333i	−0.618821	+	1.07183i	−0.989701	+	0.143149i	$0.954277\pi$
$368$	−1.92352	−	3.33164i	−0.100271	−	0.173674i
$369$	7.50881			0.390893
$370$	−19.2876	−	33.4072i	−1.00272	−	1.73676i
$371$	3.87720	+	6.71551i	0.201294	+	0.348652i
$372$	−23.1132			−1.19836
$373$	4.97664	+	8.61979i	0.257681	+	0.446316i	0.965620	−	0.259957i	$-0.0837084\pi$
$373$	4.97664	+	8.61979i	0.257681	+	0.446316i	−0.707940	+	0.706273i	$0.750375\pi$
$374$	1.46783	−	2.54235i	0.0758996	−	0.131462i
$375$	−12.5424	+	21.7242i	−0.647689	+	1.12183i
$376$	47.5860			2.45406
$377$	−22.2696	−	21.9859i	−1.14694	−	1.13233i
$378$	−2.37720			−0.122270
$379$	13.9250	−	24.1188i	0.715278	−	1.23890i	−0.247574	−	0.968869i	$-0.579633\pi$
$379$	13.9250	−	24.1188i	0.715278	−	1.23890i	0.962852	−	0.270029i	$-0.0870334\pi$
$380$	−26.0898	+	45.1889i	−1.33838	+	2.31814i
$381$	3.66524	+	6.34838i	0.187776	+	0.325238i
$382$	−1.54778			−0.0791914
$383$	3.45222	+	5.97942i	0.176400	+	0.305534i	0.940645	−	0.339392i	$-0.110221\pi$
$383$	3.45222	+	5.97942i	0.176400	+	0.305534i	−0.764245	+	0.644926i	$0.776888\pi$
$384$	10.3500	+	17.9267i	0.528170	+	0.914817i
$385$	−13.1882			−0.672133
$386$	22.6599	+	39.2481i	1.15336	+	1.99768i
$387$	4.32555	−	7.49207i	0.219880	−	0.380843i
$388$	−9.07608	+	15.7202i	−0.460768	+	0.798074i
$389$	−28.3764			−1.43874			−0.719370	−	0.694627i	$-0.755570\pi$
$389$	−28.3764			−1.43874			−0.719370	+	0.694627i	$0.755570\pi$
$390$	33.2926	−	9.14991i	1.68584	−	0.463324i
$391$	−0.715436			−0.0361812
$392$	1.96249	−	3.39914i	0.0991208	−	0.171682i
$393$	5.71196	−	9.89341i	0.288130	−	0.499056i
$394$	29.3701	+	50.8705i	1.47964	+	2.56282i
$395$	4.68422			0.235689
$396$	5.97664	+	10.3518i	0.300337	+	0.520200i
$397$	2.38360	+	4.12852i	0.119630	+	0.207204i	0.919621	−	0.392807i	$-0.128496\pi$
$397$	2.38360	+	4.12852i	0.119630	+	0.207204i	−0.799991	+	0.600011i	$0.795163\pi$
$398$	−31.2469			−1.56627
$399$	1.77389	+	3.07247i	0.0888056	+	0.153816i
$400$	−11.3860	+	19.7212i	−0.569301	+	0.986058i
$401$	4.13307	−	7.15869i	0.206396	−	0.357488i	−0.744181	−	0.667978i	$-0.767160\pi$
$401$	4.13307	−	7.15869i	0.206396	−	0.357488i	0.950577	+	0.310490i	$0.100493\pi$
$402$	13.2739			0.662041
$403$	5.76603	−	22.0846i	0.287226	−	1.10011i
$404$	21.5294			1.07113
$405$	2.01415	−	3.48861i	0.100084	−	0.173350i
$406$	10.3163	−	17.8684i	0.511991	−	0.886795i
$407$	6.59410	+	11.4213i	0.326857	+	0.566134i
$408$	−1.48052			−0.0732964
$409$	−10.7169	−	18.5622i	−0.529916	−	0.917842i	−0.999391	−	0.0348962i	$-0.988890\pi$
$409$	−10.7169	−	18.5622i	−0.529916	−	0.917842i	0.469474	−	0.882946i	$-0.344443\pi$
$410$	−35.9525	−	62.2715i	−1.77557	−	3.07537i
$411$	3.19112			0.157407
$412$	−19.2876	−	33.4072i	−0.950234	−	1.64585i
$413$	−1.05166	+	1.82152i	−0.0517486	+	0.0896312i
$414$	2.25441	−	3.90475i	0.110798	−	0.191908i
$415$	−61.1514			−3.00180
$416$	−10.5283	+	2.89353i	−0.516192	+	0.141867i
$417$	−5.37720			−0.263323
$418$	13.8057	−	23.9121i	0.675257	−	1.16958i
$419$	1.14576	−	1.98451i	0.0559739	−	0.0969496i	−0.836681	−	0.547691i	$-0.815507\pi$
$419$	1.14576	−	1.98451i	0.0559739	−	0.0969496i	0.892655	+	0.450741i	$0.148840\pi$
$420$	7.35384	+	12.7372i	0.358831	+	0.621513i
$421$	7.61292			0.371031			0.185516	−	0.982641i	$-0.440604\pi$
$421$	7.61292			0.371031			0.185516	+	0.982641i	$0.440604\pi$
$422$	−23.2926	−	40.3439i	−1.13386	−	1.96391i
$423$	6.06193	+	10.4996i	0.294741	+	0.510507i
$424$	−30.4359			−1.47810
$425$	2.11746	+	3.66755i	0.102712	+	0.177902i
$426$	−4.74519	+	8.21892i	−0.229905	+	0.398208i
$427$	3.87720	−	6.71551i	0.187631	−	0.324986i
$428$	−45.2936			−2.18935
$429$	−11.3821	+	3.12819i	−0.549535	+	0.151030i
$430$	−82.8435			−3.99507
$431$	−10.4314	+	18.0677i	−0.502462	+	0.870290i	0.497534	+	0.867444i	$0.334239\pi$
$431$	−10.4314	+	18.0677i	−0.502462	+	0.870290i	−0.999996	+	0.00284520i	$0.999094\pi$
$432$	1.01415	−	1.75656i	0.0487932	−	0.0845123i
$433$	11.6882	+	20.2446i	0.561699	+	0.972891i	0.997348	+	0.0727749i	$0.0231855\pi$
$433$	11.6882	+	20.2446i	0.561699	+	0.972891i	−0.435649	+	0.900116i	$0.643481\pi$
$434$	15.0488			0.722368
$435$	17.4816	+	30.2790i	0.838177	+	1.45177i
$436$	22.1468	+	38.3594i	1.06064	+	1.83708i
$437$	−6.72903			−0.321893
$438$	−8.91577	−	15.4426i	−0.426012	−	0.737875i
$439$	−4.57754	+	7.92853i	−0.218474	+	0.378408i	−0.954342	−	0.298717i	$-0.903441\pi$
$439$	−4.57754	+	7.92853i	−0.218474	+	0.378408i	0.735868	+	0.677125i	$0.236775\pi$
$440$	25.8817	−	44.8285i	1.23386	−	2.13711i
$441$	1.00000			0.0476190
$442$	0.816735	−	3.12819i	0.0388481	−	0.148793i
$443$	11.2632			0.535132			0.267566	−	0.963540i	$-0.413781\pi$
$443$	11.2632			0.535132			0.267566	+	0.963540i	$0.413781\pi$
$444$	7.35384	−	12.7372i	0.348998	−	0.604482i
$445$	12.8075	−	22.1833i	0.607135	−	1.05159i
$446$	−33.1235	−	57.3715i	−1.56844	−	2.71662i
$447$	10.0283			0.474322
$448$	−5.62773	−	9.74752i	−0.265885	−	0.460527i
$449$	16.8924	+	29.2585i	0.797202	+	1.38079i	0.921431	+	0.388541i	$0.127021\pi$
$449$	16.8924	+	29.2585i	0.797202	+	1.38079i	−0.124229	+	0.992254i	$0.539646\pi$
$450$	−26.6893			−1.25814
$451$	12.2915	+	21.2895i	0.578785	+	1.00248i
$452$	19.4816	−	33.7431i	0.916336	−	1.58714i
$453$	−4.85772	+	8.41381i	−0.228236	+	0.395315i
$454$	−28.5987			−1.34221
$455$	−14.0049	+	3.84902i	−0.656562	+	0.180445i
$456$	−13.9250			−0.652097
$457$	−17.1472	+	29.6999i	−0.802113	+	1.38930i	0.116110	+	0.993236i	$0.462958\pi$
$457$	−17.1472	+	29.6999i	−0.802113	+	1.38930i	−0.918223	+	0.396064i	$0.870376\pi$
$458$	−10.9338	+	18.9379i	−0.510903	+	0.884909i
$459$	−0.188601	−	0.326667i	−0.00880316	−	0.0152475i
$460$	−27.8959			−1.30065
$461$	−9.66630	−	16.7425i	−0.450205	−	0.779777i	0.548194	−	0.836351i	$-0.315316\pi$
$461$	−9.66630	−	16.7425i	−0.450205	−	0.779777i	−0.998398	+	0.0565741i	$0.981982\pi$
$462$	−3.89135	−	6.74002i	−0.181042	−	0.313574i
$463$	6.29444			0.292527			0.146264	−	0.989246i	$-0.453275\pi$
$463$	6.29444			0.292527			0.146264	+	0.989246i	$0.453275\pi$
$464$	8.80219	+	15.2458i	0.408631	+	0.707770i
$465$	−12.7505	+	22.0846i	−0.591292	+	1.02415i
$466$	−14.8007	+	25.6356i	−0.685630	+	1.18755i
$467$	24.2293			1.12120			0.560599	−	0.828087i	$-0.310571\pi$
$467$	24.2293			1.12120			0.560599	+	0.828087i	$0.310571\pi$
$468$	9.36799	+	9.24862i	0.433036	+	0.427518i
$469$	−5.58383			−0.257837
$470$	58.0495	−	100.545i	2.67762	−	4.63778i
$471$	8.78804	−	15.2213i	0.404931	−	0.701362i
$472$	−4.12773	−	7.14944i	−0.189994	−	0.329080i
$473$	28.3227			1.30228
$474$	1.38214	+	2.39394i	0.0634838	+	0.109957i
$475$	19.9158	+	34.4951i	0.913798	+	1.58275i
$476$	1.37720			0.0631240
$477$	−3.87720	−	6.71551i	−0.177525	−	0.307482i
$478$	−3.85772	+	6.68176i	−0.176448	+	0.305617i
$479$	16.8149	−	29.1242i	0.768291	−	1.33072i	−0.170198	−	0.985410i	$-0.554441\pi$
$479$	16.8149	−	29.1242i	0.768291	−	1.33072i	0.938489	−	0.345309i	$-0.112226\pi$
$480$	12.1989			0.556800
$481$	10.3358	+	10.2041i	0.471273	+	0.465268i
$482$	−22.4076			−1.02064
$483$	−0.948344	+	1.64258i	−0.0431511	+	0.0747400i
$484$	0.514148	−	0.890531i	0.0233704	−	0.0404787i
$485$	10.0137	+	17.3443i	0.454701	+	0.787565i
$486$	2.37720			0.107832
$487$	3.96249	+	6.86324i	0.179558	+	0.311003i	0.941729	−	0.336372i	$-0.109200\pi$
$487$	3.96249	+	6.86324i	0.179558	+	0.311003i	−0.762171	+	0.647375i	$0.775867\pi$
$488$	15.2180	+	26.3583i	0.688885	+	1.19318i
$489$	5.49119			0.248320
$490$	−4.78804	−	8.29313i	−0.216302	−	0.374645i
$491$	−1.21584	+	2.10589i	−0.0548699	+	0.0950375i	−0.892156	−	0.451728i	$-0.850808\pi$
$491$	−1.21584	+	2.10589i	−0.0548699	+	0.0950375i	0.837286	+	0.546766i	$0.184141\pi$
$492$	13.7077	−	23.7424i	0.617990	−	1.07039i
$493$	3.27389			0.147449
$494$	7.68180	−	29.4222i	0.345621	−	1.32377i
$495$	13.1882			0.592766
$496$	−6.42005	+	11.1198i	−0.288269	+	0.499296i
$497$	1.99612	−	3.45739i	0.0895384	−	0.155085i
$498$	−18.0435	−	31.2523i	−0.808549	−	1.40045i
$499$	−18.5838			−0.831926			−0.415963	−	0.909381i	$-0.636555\pi$
$499$	−18.5838			−0.831926			−0.415963	+	0.909381i	$0.636555\pi$
$500$	45.7936	+	79.3169i	2.04795	+	3.54716i
$501$	2.21836	+	3.84231i	0.0991090	+	0.171662i
$502$	28.5011			1.27206
$503$	8.72717	+	15.1159i	0.389125	+	0.673985i	0.992332	−	0.123600i	$-0.0394440\pi$
$503$	8.72717	+	15.1159i	0.389125	+	0.673985i	−0.603207	+	0.797585i	$0.706111\pi$
$504$	−1.96249	+	3.39914i	−0.0874163	+	0.151410i
$505$	11.8768	−	20.5712i	0.528511	−	0.915408i
$506$	14.7614			0.656222
$507$	−11.1741	+	6.64383i	−0.496257	+	0.295063i
$508$	26.7643			1.18747
$509$	−1.38495	+	2.39881i	−0.0613870	+	0.106325i	−0.895086	−	0.445894i	$-0.852886\pi$
$509$	−1.38495	+	2.39881i	−0.0613870	+	0.106325i	0.833699	+	0.552220i	$0.186219\pi$
$510$	−1.80606	+	3.12819i	−0.0799738	+	0.138519i
$511$	3.75053	+	6.49611i	0.165914	+	0.287371i
$512$	22.0643			0.975115
$513$	−1.77389	−	3.07247i	−0.0783192	−	0.135653i
$514$	17.3496	+	30.0503i	0.765257	+	1.32546i
$515$	−42.5606			−1.87544
$516$	−15.7930	−	27.3542i	−0.695247	−	1.20420i
$517$	−19.8461	+	34.3744i	−0.872830	+	1.51179i
$518$	−4.78804	+	8.29313i	−0.210374	+	0.364379i
$519$	−22.1599			−0.972712
$520$	14.4012	−	55.1584i	0.631535	−	2.41885i
$521$	−26.2816			−1.15142			−0.575710	−	0.817654i	$-0.695274\pi$
$521$	−26.2816			−1.15142			−0.575710	+	0.817654i	$0.695274\pi$
$522$	−10.3163	+	17.8684i	−0.451534	+	0.782079i
$523$	−2.62521	+	4.54700i	−0.114792	+	0.198826i	−0.917697	−	0.397282i	$-0.869954\pi$
$523$	−2.62521	+	4.54700i	−0.114792	+	0.198826i	0.802904	+	0.596108i	$0.203287\pi$
$524$	−20.8549	−	36.1218i	−0.911051	−	1.57799i
$525$	11.2272			0.489994
$526$	26.9256	+	46.6366i	1.17401	+	2.03345i
$527$	1.19394	+	2.06796i	0.0520088	+	0.0900818i
$528$	6.64042			0.288987
$529$	9.70129	+	16.8031i	0.421795	+	0.730571i
$530$	−37.1284	+	64.3083i	−1.61275	+	2.79337i
$531$	1.05166	−	1.82152i	0.0456380	−	0.0790473i
$532$	12.9533			0.561596
$533$	19.2661	+	19.0206i	0.834509	+	0.823876i
$534$	15.1161			0.654138
$535$	−24.9865	+	43.2779i	−1.08026	+	1.87107i
$536$	10.9582	−	18.9802i	0.473323	−	0.819819i
$537$	−0.970242	−	1.68051i	−0.0418690	−	0.0725193i
$538$	66.5363			2.86858
$539$	1.63695	+	2.83527i	0.0705082	+	0.122124i
$540$	−7.35384	−	12.7372i	−0.316459	−	0.548123i
$541$	−0.111863			−0.00480937			−0.00240468	−	0.999997i	$-0.500765\pi$
$541$	−0.111863			−0.00480937			−0.00240468	+	0.999997i	$0.500765\pi$
$542$	−9.04204	−	15.6613i	−0.388389	−	0.672710i
$543$	−4.25053	+	7.36214i	−0.182408	+	0.315939i
$544$	0.571141	−	0.989245i	0.0244875	−	0.0424135i
$545$	48.8697			2.09335
$546$	−6.09944	−	6.02172i	−0.261032	−	0.257706i
$547$	−33.7515			−1.44311			−0.721555	−	0.692358i	$-0.756572\pi$
$547$	−33.7515			−1.44311			−0.721555	+	0.692358i	$0.756572\pi$
$548$	5.82555	−	10.0901i	0.248855	−	0.431030i
$549$	−3.87720	+	6.71551i	−0.165475	+	0.286611i
$550$	−43.6889	−	75.6713i	−1.86290	−	3.22664i
$551$	30.7926			1.31181
$552$	−3.72223	−	6.44710i	−0.158429	−	0.274407i
$553$	−0.581414	−	1.00704i	−0.0247242	−	0.0428236i
$554$	16.3764			0.695767
$555$	−8.11359	−	14.0531i	−0.344403	−	0.596523i
$556$	−9.81633	+	17.0024i	−0.416305	+	0.721062i
$557$	−14.5073	+	25.1275i	−0.614696	+	1.06468i	0.375742	+	0.926724i	$0.377388\pi$
$557$	−14.5073	+	25.1275i	−0.614696	+	1.06468i	−0.990438	+	0.137960i	$0.955945\pi$
$558$	−15.0488			−0.637068
$559$	30.0767	−	8.26609i	1.27211	−	0.349618i
$560$	8.17058			0.345270
$561$	0.617460	−	1.06947i	0.0260692	−	0.0451532i
$562$	12.8442	−	22.2469i	0.541801	−	0.938427i
$563$	−0.715836	−	1.23986i	−0.0301689	−	0.0522541i	0.850547	−	0.525899i	$-0.176271\pi$
$563$	−0.715836	−	1.23986i	−0.0301689	−	0.0522541i	−0.880716	+	0.473645i	$0.842938\pi$
$564$	44.2653			1.86391
$565$	−21.4943	−	37.2292i	−0.904270	−	1.56624i
$566$	−9.06299	−	15.6976i	−0.380946	−	0.659818i
$567$	−1.00000			−0.0419961
$568$	7.83476	+	13.5702i	0.328739	+	0.569393i
$569$	12.2505	−	21.2185i	0.513569	−	0.889528i	−0.486307	−	0.873788i	$-0.661656\pi$
$569$	12.2505	−	21.2185i	0.513569	−	0.889528i	0.999876	−	0.0157396i	$-0.00501028\pi$
$570$	−16.9869	+	29.4222i	−0.711503	+	1.23236i
$571$	−47.3735			−1.98252			−0.991259	−	0.131929i	$-0.957883\pi$
$571$	−47.3735			−1.98252			−0.991259	+	0.131929i	$0.957883\pi$
$572$	−10.8875	+	41.7003i	−0.455228	+	1.74358i
$573$	−0.651093			−0.0271998
$574$	−8.92498	+	15.4585i	−0.372522	+	0.645226i
$575$	−10.6472	+	18.4415i	−0.444020	+	0.769065i
$576$	5.62773	+	9.74752i	0.234489	+	0.406147i
$577$	27.4055			1.14091			0.570453	−	0.821330i	$-0.306768\pi$
$577$	27.4055			1.14091			0.570453	+	0.821330i	$0.306768\pi$
$578$	−20.0371	−	34.7053i	−0.833434	−	1.44355i
$579$	9.53217	+	16.5102i	0.396144	+	0.686141i
$580$	127.654			5.30053
$581$	7.59023	+	13.1467i	0.314896	+	0.545415i
$582$	−5.90937	+	10.2353i	−0.244951	+	0.424268i
$583$	12.6935	−	21.9859i	0.525713	−	0.910561i
$584$	−29.4415			−1.21830
$585$	14.0049	−	3.84902i	0.579033	−	0.159138i
$586$	52.9914			2.18906
$587$	−13.9479	+	24.1585i	−0.575693	+	0.997130i	0.420273	+	0.907398i	$0.361934\pi$
$587$	−13.9479	+	24.1585i	−0.575693	+	0.997130i	−0.995966	+	0.0897321i	$0.971399\pi$
$588$	1.82555	−	3.16194i	0.0752843	−	0.130396i
$589$	11.2296	+	19.4502i	0.462707	+	0.801432i
$590$	−20.1415			−0.829212
$591$	12.3549	+	21.3993i	0.508213	+	0.880250i
$592$	−4.08529	−	7.07593i	−0.167904	−	0.290819i
$593$	−16.6015			−0.681740			−0.340870	−	0.940110i	$-0.610722\pi$
$593$	−16.6015			−0.681740			−0.340870	+	0.940110i	$0.610722\pi$
$594$	3.89135	+	6.74002i	0.159664	+	0.276546i
$595$	0.759742	−	1.31591i	0.0311464	−	0.0539472i
$596$	18.3071	−	31.7089i	0.749889	−	1.29885i
$597$	−13.1444			−0.537965
$598$	15.6755	−	4.30815i	0.641019	−	0.176173i
$599$	11.7913			0.481778			0.240889	−	0.970553i	$-0.422561\pi$
$599$	11.7913			0.481778			0.240889	+	0.970553i	$0.422561\pi$
$600$	−22.0332	+	38.1627i	−0.899503	+	1.55798i
$601$	−6.91084	+	11.9699i	−0.281899	+	0.488263i	−0.971852	−	0.235590i	$-0.924298\pi$
$601$	−6.91084	+	11.9699i	−0.281899	+	0.488263i	0.689954	+	0.723854i	$0.257631\pi$
$602$	10.2827	+	17.8102i	0.419092	+	0.725888i
$603$	5.58383			0.227391
$604$	17.7360	+	30.7196i	0.721667	+	1.24996i
$605$	−0.567266	−	0.982533i	−0.0230626	−	0.0399457i
$606$	14.0176			0.569427
$607$	10.5474	+	18.2686i	0.428105	+	0.741500i	0.996705	−	0.0811147i	$-0.0258480\pi$
$607$	10.5474	+	18.2686i	0.428105	+	0.741500i	−0.568600	+	0.822614i	$0.692515\pi$
$608$	5.37187	−	9.30435i	0.217858	−	0.377341i
$609$	4.33969	−	7.51657i	0.175853	−	0.304587i
$610$	74.2568			3.00657
$611$	−11.0428	+	42.2954i	−0.446746	+	1.71109i
$612$	−1.37720			−0.0556701
$613$	−1.09691	+	1.89991i	−0.0443039	+	0.0767367i	−0.887327	−	0.461141i	$-0.847440\pi$
$613$	−1.09691	+	1.89991i	−0.0443039	+	0.0767367i	0.843023	+	0.537877i	$0.180774\pi$
$614$	−33.5718	+	58.1481i	−1.35485	+	2.34666i
$615$	−15.1239	−	26.1953i	−0.609853	−	1.05630i
$616$	−12.8500			−0.517740
$617$	3.17405	+	5.49762i	0.127783	+	0.221326i	0.922817	−	0.385238i	$-0.125881\pi$
$617$	3.17405	+	5.49762i	0.127783	+	0.221326i	−0.795035	+	0.606564i	$0.792547\pi$
$618$	−12.5581	−	21.7512i	−0.505159	−	0.874961i
$619$	−7.77203			−0.312384			−0.156192	−	0.987727i	$-0.549922\pi$
$619$	−7.77203			−0.312384			−0.156192	+	0.987727i	$0.549922\pi$
$620$	46.5534	+	80.6328i	1.86963	+	3.23829i
$621$	0.948344	−	1.64258i	0.0380557	−	0.0659145i
$622$	−3.16378	+	5.47983i	−0.126856	+	0.219721i
$623$	−6.35878			−0.254759
$624$	7.05166	−	1.93803i	0.282292	−	0.0775833i
$625$	44.9135			1.79654
$626$	−26.7229	+	46.2854i	−1.06806	+	1.84994i
$627$	5.80752	−	10.0589i	0.231930	−	0.401715i
$628$	−32.0860	−	55.5745i	−1.28037	−	2.21766i
$629$	−1.51948			−0.0605858
$630$	4.78804	+	8.29313i	0.190760	+	0.330406i
$631$	−17.1312	−	29.6721i	−0.681983	−	1.18123i	−0.974375	−	0.224930i	$-0.927785\pi$
$631$	−17.1312	−	29.6721i	−0.681983	−	1.18123i	0.292392	−	0.956298i	$-0.405549\pi$
$632$	4.56408			0.181549
$633$	−9.79831	−	16.9712i	−0.389448	−	0.674544i
$634$	22.3832	−	38.7688i	0.888950	−	1.53971i
$635$	14.7647	−	25.5732i	0.585918	−	1.01484i
$636$	−28.3121			−1.12265
$637$	2.56580	+	2.53311i	0.101661	+	0.100365i
$638$	−67.5491			−2.67429
$639$	−1.99612	+	3.45739i	−0.0789655	+	0.136772i
$640$	41.6927	−	72.2139i	1.64805	−	2.85451i
$641$	11.6093	+	20.1079i	0.458540	+	0.794215i	0.998884	−	0.0472294i	$-0.0150392\pi$
$641$	11.6093	+	20.1079i	0.458540	+	0.794215i	−0.540344	+	0.841444i	$0.681706\pi$
$642$	−29.4904			−1.16389
$643$	−10.0400	−	17.3898i	−0.395940	−	0.685788i	0.597281	−	0.802032i	$-0.296248\pi$
$643$	−10.0400	−	17.3898i	−0.395940	−	0.685788i	−0.993221	+	0.116244i	$0.962915\pi$
$644$	3.46249	+	5.99721i	0.136441	+	0.236323i
$645$	−34.8492			−1.37218
$646$	1.59063	+	2.75504i	0.0625823	+	0.108396i
$647$	8.26468	−	14.3148i	0.324918	−	0.562775i	−0.656578	−	0.754258i	$-0.727997\pi$
$647$	8.26468	−	14.3148i	0.324918	−	0.562775i	0.981496	+	0.191484i	$0.0613299\pi$
$648$	1.96249	−	3.39914i	0.0770940	−	0.133531i
$649$	6.88601			0.270300
$650$	−68.4794	−	67.6068i	−2.68598	−	2.65176i
$651$	6.33048			0.248111
$652$	10.0244	−	17.3628i	0.392587	−	0.679980i
$653$	0.463954	−	0.803591i	0.0181559	−	0.0314470i	−0.856805	−	0.515641i	$-0.827554\pi$
$653$	0.463954	−	0.803591i	0.0181559	−	0.0314470i	0.874961	+	0.484194i	$0.160887\pi$
$654$	14.4196	+	24.9756i	0.563853	+	0.976622i
$655$	−46.0189			−1.79811
$656$	−7.61505	−	13.1896i	−0.297318	−	0.514969i
$657$	−3.75053	−	6.49611i	−0.146322	−	0.253437i
$658$	−28.8209			−1.12355
$659$	−16.1284	−	27.9352i	−0.628273	−	1.08820i	−0.987898	−	0.155104i	$-0.950429\pi$
$659$	−16.1284	−	27.9352i	−0.628273	−	1.08820i	0.359625	−	0.933097i	$-0.382905\pi$
$660$	24.0757	−	41.7003i	0.937144	−	1.62318i
$661$	11.4285	−	19.7947i	0.444516	−	0.769923i	−0.553503	−	0.832847i	$-0.686709\pi$
$661$	11.4285	−	19.7947i	0.444516	−	0.769923i	0.998018	+	0.0629238i	$0.0200425\pi$
$662$	42.3892			1.64750
$663$	0.343570	−	1.31591i	0.0133431	−	0.0511058i
$664$	−59.5830			−2.31227
$665$	7.14576	−	12.3768i	0.277101	−	0.479952i
$666$	4.78804	−	8.29313i	0.185533	−	0.321352i
$667$	8.23105	+	14.2566i	0.318707	+	0.552017i
$668$	16.1989			0.626753
$669$	−13.9338	−	24.1340i	−0.538712	−	0.933076i
$670$	−26.7356	−	46.3074i	−1.03289	−	1.78901i
$671$	−25.3871			−0.980057
$672$	−1.51415	−	2.62258i	−0.0584095	−	0.101168i
$673$	−0.542845	+	0.940235i	−0.0209251	+	0.0362434i	−0.876298	−	0.481769i	$-0.839994\pi$
$673$	−0.542845	+	0.940235i	−0.0209251	+	0.0362434i	0.855373	+	0.518012i	$0.173328\pi$
$674$	9.00494	−	15.5970i	0.346857	−	0.600774i
$675$	−11.2272			−0.432134
$676$	0.608649	+	47.4603i	0.0234096	+	1.82540i
$677$	−8.60730			−0.330805			−0.165403	−	0.986226i	$-0.552892\pi$
$677$	−8.60730			−0.330805			−0.165403	+	0.986226i	$0.552892\pi$
$678$	12.6843	−	21.9699i	0.487139	−	0.843749i
$679$	2.48585	−	4.30562i	0.0953982	−	0.165235i
$680$	2.98198	+	5.16494i	0.114354	+	0.198066i
$681$	−12.0304			−0.461007
$682$	−24.6341	−	42.6676i	−0.943290	−	1.63383i
$683$	−16.7310	−	28.9790i	−0.640196	−	1.10885i	−0.985389	−	0.170320i	$-0.945520\pi$
$683$	−16.7310	−	28.9790i	−0.640196	−	1.10885i	0.345193	−	0.938532i	$-0.387813\pi$
$684$	−12.9533			−0.495281
$685$	−6.42740	−	11.1326i	−0.245578	−	0.425354i
$686$	−1.18860	+	2.05872i	−0.0453810	+	0.0786022i
$687$	−4.59944	+	7.96646i	−0.175479	+	0.303939i
$688$	−17.5470			−0.668972
$689$	7.06299	−	27.0521i	0.269079	−	1.03060i
$690$	−18.1628			−0.691447
$691$	2.34609	−	4.06355i	0.0892496	−	0.154585i	−0.817945	−	0.575297i	$-0.804886\pi$
$691$	2.34609	−	4.06355i	0.0892496	−	0.154585i	0.907194	+	0.420712i	$0.138220\pi$
$692$	−40.4539	+	70.0683i	−1.53783	+	2.66360i
$693$	−1.63695	−	2.83527i	−0.0621824	−	0.107703i
$694$	−18.7517			−0.711805
$695$	10.8305	+	18.7589i	0.410824	+	0.711567i
$696$	17.0332	+	29.5024i	0.645643	+	1.11829i
$697$	−2.83235			−0.107283
$698$	−13.9469	−	24.1567i	−0.527897	−	0.914345i
$699$	−6.22611	+	10.7839i	−0.235493	+	0.407886i
$700$	20.4957	−	35.4996i	0.774666	−	1.34176i
$701$	41.4535			1.56568			0.782839	−	0.622224i	$-0.213771\pi$
$701$	41.4535			1.56568			0.782839	+	0.622224i	$0.213771\pi$
$702$	6.09944	+	6.02172i	0.230208	+	0.227275i
$703$	−14.2915			−0.539015
$704$	−18.4246	+	31.9123i	−0.694403	+	1.20274i
$705$	24.4192	−	42.2954i	0.919682	−	1.59294i
$706$	−14.9016	−	25.8104i	−0.560830	−	0.971386i
$707$	−5.89669			−0.221768
$708$	−3.83969	−	6.65055i	−0.144305	−	0.249943i
$709$	−1.92111	−	3.32746i	−0.0721488	−	0.124965i	0.827694	−	0.561180i	$-0.189652\pi$
$709$	−1.92111	−	3.32746i	−0.0721488	−	0.124965i	−0.899843	+	0.436214i	$0.856319\pi$
$710$	38.2301			1.43475
$711$	0.581414	+	1.00704i	0.0218047	+	0.0377669i
$712$	12.4791	−	21.6144i	0.467672	−	0.810032i
$713$	−6.00347	+	10.3983i	−0.224832	+	0.389420i
$714$	0.896688			0.0335577
$715$	33.8383	+	33.4072i	1.26548	+	1.24936i
$716$	−7.08489			−0.264775
$717$	−1.62280	+	2.81077i	−0.0606045	+	0.104970i
$718$	−5.96395	+	10.3299i	−0.222573	+	0.385507i
$719$	−4.45609	−	7.71818i	−0.166184	−	0.287840i	0.770891	−	0.636967i	$-0.219811\pi$
$719$	−4.45609	−	7.71818i	−0.166184	−	0.287840i	−0.937075	+	0.349128i	$0.886478\pi$
$720$	−8.17058			−0.304499
$721$	5.28270	+	9.14991i	0.196738	+	0.340760i
$722$	−7.62280	−	13.2031i	−0.283691	−	0.491367i
$723$	−9.42605			−0.350558
$724$	15.5191	+	26.8798i	0.576762	+	0.998981i
$725$	48.7225	−	84.3898i	1.80951	−	3.13416i
$726$	0.334758	−	0.579819i	0.0124241	−	0.0215191i
$727$	29.6815			1.10083			0.550413	−	0.834892i	$-0.314470\pi$
$727$	29.6815			1.10083			0.550413	+	0.834892i	$0.314470\pi$
$728$	−13.6458	+	3.75031i	−0.505745	+	0.138996i
$729$	1.00000			0.0370370
$730$	−35.9154	+	62.2072i	−1.32929	+	2.30239i
$731$	−1.63161	+	2.82603i	−0.0603472	+	0.104524i
$732$	14.1560	+	24.5190i	0.523222	+	0.906247i
$733$	5.30299			0.195870			0.0979352	−	0.995193i	$-0.468776\pi$
$733$	5.30299			0.195870			0.0979352	+	0.995193i	$0.468776\pi$
$734$	28.1815	+	48.8118i	1.04020	+	1.80168i
$735$	−2.01415	−	3.48861i	−0.0742930	−	0.128679i
$736$	5.74373			0.211717
$737$	9.14042	+	15.8317i	0.336692	+	0.583167i
$738$	8.92498	−	15.4585i	0.328533	−	0.569036i
$739$	10.4572	−	18.1123i	0.384673	−	0.666273i	−0.607051	−	0.794663i	$-0.707648\pi$
$739$	10.4572	−	18.1123i	0.384673	−	0.666273i	0.991724	+	0.128390i	$0.0409810\pi$
$740$	−59.2469			−2.17796
$741$	3.23145	−	12.3768i	0.118710	−	0.454674i
$742$	18.4338			0.676726
$743$	0.159244	−	0.275818i	0.00584209	−	0.0101188i	−0.863090	−	0.505051i	$-0.831474\pi$
$743$	0.159244	−	0.275818i	0.00584209	−	0.0101188i	0.868932	+	0.494932i	$0.164807\pi$
$744$	−12.4235	+	21.5182i	−0.455468	+	0.788894i
$745$	−20.1985	−	34.9848i	−0.740015	−	1.28174i
$746$	23.6610			0.866290
$747$	−7.59023	−	13.1467i	−0.277712	−	0.481011i
$748$	−2.25441	−	3.90475i	−0.0824292	−	0.142772i
$749$	12.4055			0.453287
$750$	29.8159	+	51.6427i	1.08872	+	1.88573i
$751$	−19.7940	+	34.2843i	−0.722295	+	1.25105i	0.237783	+	0.971318i	$0.423579\pi$
$751$	−19.7940	+	34.2843i	−0.722295	+	1.25105i	−0.960078	+	0.279733i	$0.909754\pi$
$752$	12.2954	−	21.2962i	0.448367	−	0.776594i
$753$	11.9893			0.436915
$754$	−71.7324	+	19.7144i	−2.61234	+	0.717958i
$755$	39.1367			1.42433
$756$	−1.82555	+	3.16194i	−0.0663945	+	0.114999i
$757$	5.12667	−	8.87966i	0.186332	−	0.322737i	−0.757693	−	0.652612i	$-0.773673\pi$
$757$	5.12667	−	8.87966i	0.186332	−	0.322737i	0.944025	+	0.329875i	$0.107007\pi$
$758$	−33.1025	−	57.3352i	−1.20234	−	2.08251i
$759$	6.20955			0.225392
$760$	28.0470	+	48.5788i	1.01737	+	1.76214i
$761$	8.73920	+	15.1367i	0.316796	+	0.548706i	0.979818	−	0.199894i	$-0.0640597\pi$
$761$	8.73920	+	15.1367i	0.316796	+	0.548706i	−0.663022	+	0.748600i	$0.730726\pi$
$762$	17.4260			0.631279
$763$	−6.06580	−	10.5063i	−0.219597	−	0.380353i
$764$	−1.18860	+	2.05872i	−0.0430021	+	0.0744818i
$765$	−0.759742	+	1.31591i	−0.0274685	+	0.0475769i
$766$	16.4132			0.593035
$767$	7.31246	−	2.00971i	0.264038	−	0.0725663i
$768$	26.6970			0.963345
$769$	−18.0283	+	31.2259i	−0.650117	+	1.12604i	0.332977	+	0.942935i	$0.391947\pi$
$769$	−18.0283	+	31.2259i	−0.650117	+	1.12604i	−0.983094	+	0.183101i	$0.941387\pi$
$770$	−15.6755	+	27.1508i	−0.564906	+	0.978446i
$771$	7.29831	+	12.6410i	0.262842	+	0.455256i
$772$	69.6057			2.50516
$773$	5.35918	+	9.28237i	0.192756	+	0.333864i	0.946163	−	0.323691i	$-0.104924\pi$
$773$	5.35918	+	9.28237i	0.192756	+	0.333864i	−0.753406	+	0.657555i	$0.771591\pi$
$774$	−10.2827	−	17.8102i	−0.369604	−	0.640173i
$775$	71.0734			2.55303
$776$	9.75693	+	16.8995i	0.350253	+	0.606657i
$777$	−2.01415	+	3.48861i	−0.0722572	+	0.125153i
$778$	−33.7282	+	58.4190i	−1.20922	+	2.09442i
$779$	−26.6396			−0.954463
$780$	13.3963	−	51.3093i	0.479664	−	1.83717i
$781$	−13.0702			−0.467688
$782$	−0.850368	+	1.47288i	−0.0304091	+	0.0526701i
$783$	−4.33969	+	7.51657i	−0.155088	+	0.268620i
$784$	−1.01415	−	1.75656i	−0.0362196	−	0.0627341i
$785$	−70.8016			−2.52702
$786$	−13.5785	−	23.5186i	−0.484329	−	0.838882i
$787$	4.47905	+	7.75795i	0.159661	+	0.276541i	0.934746	−	0.355315i	$-0.115627\pi$
$787$	4.47905	+	7.75795i	0.159661	+	0.276541i	−0.775085	+	0.631856i	$0.782293\pi$
$788$	90.2178			3.21388
$789$	11.3266	+	19.6183i	0.403238	+	0.698429i
$790$	5.56767	−	9.64348i	0.198089	−	0.343100i
$791$	−5.33582	+	9.24191i	−0.189720	+	0.328605i
$792$	12.8500			0.456604
$793$	−26.9593	+	7.40931i	−0.957352	+	0.263112i
$794$	11.3326			0.402179
$795$	−15.6185	+	27.0521i	−0.553932	+	0.959438i
$796$	−23.9957	+	41.5618i	−0.850506	+	1.47312i
$797$	18.0343	+	31.2363i	0.638807	+	1.10645i	0.985695	+	0.168540i	$0.0539053\pi$
$797$	18.0343	+	31.2363i	0.638807	+	1.10645i	−0.346887	+	0.937907i	$0.612761\pi$
$798$	8.43380			0.298553
$799$	−2.28658	−	3.96047i	−0.0808933	−	0.140111i
$800$	−16.9996	−	29.4442i	−0.601027	−	1.04101i
$801$	6.35878			0.224676
$802$	−9.82515	−	17.0177i	−0.346938	−	0.600914i
$803$	12.2788	−	21.2676i	0.433310	−	0.750516i
$804$	10.1935	−	17.6557i	0.359498	−	0.622669i
$805$	7.64042			0.269289
$806$	−38.6124	−	38.1204i	−1.36006	−	1.34273i
$807$	27.9893			0.985271
$808$	11.5722	−	20.0436i	0.407109	−	0.705133i
$809$	−23.7647	+	41.1616i	−0.835522	+	1.44717i	0.0580834	+	0.998312i	$0.481501\pi$
$809$	−23.7647	+	41.1616i	−0.835522	+	1.44717i	−0.893605	+	0.448854i	$0.851832\pi$
$810$	−4.78804	−	8.29313i	−0.168235	−	0.291391i
$811$	−5.34678			−0.187751			−0.0938755	−	0.995584i	$-0.529926\pi$
$811$	−5.34678			−0.187751			−0.0938755	+	0.995584i	$0.529926\pi$
$812$	−15.8446	−	27.4437i	−0.556038	−	0.963085i
$813$	−3.80365	−	6.58811i	−0.133400	−	0.231055i
$814$	31.3510			1.09885
$815$	−11.0601	−	19.1566i	−0.387417	−	0.671026i
$816$	−0.382540	+	0.662578i	−0.0133916	+	0.0231949i
$817$	−15.3461	+	26.5802i	−0.536892	+	0.929924i
$818$	−50.9525			−1.78151
$819$	−2.56580	−	2.53311i	−0.0896565	−	0.0885140i
$820$	−110.437			−3.85664
$821$	10.9349	−	18.9397i	0.381629	−	0.661001i	−0.609666	−	0.792658i	$-0.708696\pi$
$821$	10.9349	−	18.9397i	0.381629	−	0.661001i	0.991295	+	0.131657i	$0.0420298\pi$
$822$	3.79298	−	6.56963i	0.132295	−	0.229142i
$823$	−11.4971	−	19.9135i	−0.400763	−	0.694142i	0.593055	−	0.805162i	$-0.297922\pi$
$823$	−11.4971	−	19.9135i	−0.400763	−	0.694142i	−0.993818	+	0.111020i	$0.964588\pi$
$824$	−41.4690			−1.44464
$825$	−18.3783	−	31.8321i	−0.639849	−	1.10825i
$826$	2.50000	+	4.33013i	0.0869861	+	0.150664i
$827$	21.3425			0.742151			0.371075	−	0.928603i	$-0.378989\pi$
$827$	21.3425			0.742151			0.371075	+	0.928603i	$0.378989\pi$
$828$	−3.46249	−	5.99721i	−0.120330	−	0.208418i
$829$	−13.7154	+	23.7558i	−0.476357	+	0.825074i	−0.999633	−	0.0270890i	$-0.991376\pi$
$829$	−13.7154	+	23.7558i	−0.476357	+	0.825074i	0.523276	+	0.852163i	$0.324710\pi$
$830$	−72.6846	+	125.893i	−2.52292	+	4.36982i
$831$	6.88894			0.238975
$832$	−10.2519	+	39.2659i	−0.355420	+	1.36130i
$833$	−0.377203			−0.0130693
$834$	−6.39135	+	11.0701i	−0.221314	+	0.383328i
$835$	8.93621	−	15.4780i	0.309250	−	0.535637i
$836$	−21.2038	−	36.7261i	−0.733349	−	1.27020i
$837$	−6.33048			−0.218814
$838$	−2.72370	−	4.71758i	−0.0940885	−	0.162966i
$839$	2.21584	+	3.83794i	0.0764992	+	0.132500i	0.901737	−	0.432285i	$-0.142292\pi$
$839$	2.21584	+	3.83794i	0.0764992	+	0.132500i	−0.825238	+	0.564785i	$0.808959\pi$
$840$	15.8110			0.545531
$841$	−23.1659	−	40.1245i	−0.798824	−	1.38360i
$842$	9.04873	−	15.6729i	0.311840	−	0.540123i
$843$	5.40309	−	9.35842i	0.186092	−	0.322321i
$844$	−71.5491			−2.46282
$845$	45.6839	+	25.6002i	1.57157	+	0.880674i
$846$	28.8209			0.990882
$847$	−0.140820	+	0.243908i	−0.00483864	+	0.00838078i
$848$	−7.86412	+	13.6210i	−0.270055	+	0.467749i
$849$	−3.81246	−	6.60337i	−0.130843	−	0.226627i
$850$	10.0673			0.345304
$851$	−3.82021	−	6.61680i	−0.130955	−	0.226821i
$852$	7.28804	+	12.6233i	0.249684	+	0.432466i
$853$	43.0040			1.47243			0.736215	−	0.676748i	$-0.236611\pi$
$853$	43.0040			1.47243			0.736215	+	0.676748i	$0.236611\pi$
$854$	−9.21690	−	15.9641i	−0.315396	−	0.546281i
$855$	−7.14576	+	12.3768i	−0.244380	+	0.423278i
$856$	−24.3457	+	42.1680i	−0.832119	+	1.44127i
$857$	0.866269			0.0295912			0.0147956	−	0.999891i	$-0.495290\pi$
$857$	0.866269			0.0295912			0.0147956	+	0.999891i	$0.495290\pi$
$858$	−7.08876	+	27.1508i	−0.242006	+	0.926913i
$859$	−15.3481			−0.523671			−0.261835	−	0.965113i	$-0.584328\pi$
$859$	−15.3481			−0.523671			−0.261835	+	0.965113i	$0.584328\pi$
$860$	−63.6188	+	110.191i	−2.16938	+	3.75748i
$861$	−3.75441	+	6.50282i	−0.127950	+	0.221616i
$862$	24.7975	+	42.9505i	0.844607	+	1.46290i
$863$	−37.0275			−1.26043			−0.630215	−	0.776420i	$-0.717033\pi$
$863$	−37.0275			−1.26043			−0.630215	+	0.776420i	$0.717033\pi$
$864$	1.51415	+	2.62258i	0.0515124	+	0.0892220i
$865$	44.6333	+	77.3072i	1.51758	+	2.62852i
$866$	55.5704			1.88836
$867$	−8.42886	−	14.5992i	−0.286259	−	0.495815i
$868$	11.5566	−	20.0166i	0.392256	−	0.679408i
$869$	−1.90349	+	3.29693i	−0.0645713	+	0.111841i
$870$	83.1145			2.81785
$871$	14.3270	+	14.1445i	0.485452	+	0.479266i
$872$	47.6164			1.61249
$873$	−2.48585	+	4.30562i	−0.0841333	+	0.145723i
$874$	−7.99814	+	13.8532i	−0.270541	+	0.468591i
$875$	−12.5424	−	21.7242i	−0.424012	−	0.734410i
$876$	−27.3871			−0.925324
$877$	−11.5103	−	19.9364i	−0.388674	−	0.673204i	0.603597	−	0.797289i	$-0.293734\pi$
$877$	−11.5103	−	19.9364i	−0.388674	−	0.673204i	−0.992271	+	0.124086i	$0.960400\pi$
$878$	10.8817	+	18.8477i	0.367241	+	0.636080i
$879$	22.2915			0.751874
$880$	−13.3748	−	23.1658i	−0.450864	−	0.780919i
$881$	−19.0084	+	32.9235i	−0.640410	+	1.10922i	0.344932	+	0.938628i	$0.387902\pi$
$881$	−19.0084	+	32.9235i	−0.640410	+	1.10922i	−0.985341	+	0.170594i	$0.945431\pi$
$882$	1.18860	−	2.05872i	0.0400223	−	0.0693206i
$883$	−6.95620			−0.234095			−0.117047	−	0.993126i	$-0.537343\pi$
$883$	−6.95620			−0.234095			−0.117047	+	0.993126i	$0.537343\pi$
$884$	−3.53363	−	3.48861i	−0.118849	−	0.117335i
$885$	−8.47277			−0.284809
$886$	13.3875	−	23.1878i	0.449761	−	0.779009i
$887$	12.9066	−	22.3548i	0.433360	−	0.750601i	−0.563800	−	0.825911i	$-0.690661\pi$
$887$	12.9066	−	22.3548i	0.433360	−	0.750601i	0.997160	+	0.0753098i	$0.0239946\pi$
$888$	−7.90550	−	13.6927i	−0.265291	−	0.459498i
$889$	−7.33048			−0.245857
$890$	−30.4461	−	52.7342i	−1.02055	−	1.76765i
$891$	1.63695	+	2.83527i	0.0548397	+	0.0949852i
$892$	−101.747			−3.40675
$893$	−21.5064	−	37.2502i	−0.719684	−	1.24653i
$894$	11.9196	−	20.6454i	0.398653	−	0.690487i
$895$	−3.90842	+	6.76959i	−0.130644	+	0.226282i
$896$	−20.6999			−0.691536
$897$	6.59410	−	1.81228i	0.220171	−	0.0605102i
$898$	80.3134			2.68009
$899$	27.4724	−	47.5835i	0.916255	−	1.58700i
$900$	−20.4957	+	35.4996i	−0.683191	+	1.18332i
$901$	1.46249	+	2.53311i	0.0487227	+	0.0843901i
$902$	58.4388			1.94580
$903$	4.32555	+	7.49207i	0.143945	+	0.249320i
$904$	−20.9430	−	36.2744i	−0.696554	−	1.20647i
$905$	34.2448			1.13834
$906$	11.5478	+	20.0013i	0.383649	+	0.664500i
$907$	1.29579	−	2.24437i	0.0430260	−	0.0745231i	−0.843710	−	0.536799i	$-0.819634\pi$
$907$	1.29579	−	2.24437i	0.0430260	−	0.0745231i	0.886736	+	0.462275i	$0.152967\pi$
$908$	−21.9621	+	38.0395i	−0.728838	+	1.26238i
$909$	5.89669			0.195581
$910$	−8.72223	+	33.4072i	−0.289139	+	1.10744i
$911$	36.7507			1.21760			0.608802	−	0.793322i	$-0.291650\pi$
$911$	36.7507			1.21760			0.608802	+	0.793322i	$0.291650\pi$
$912$	−3.59798	+	6.23188i	−0.119141	+	0.206358i
$913$	24.8496	−	43.0407i	0.822401	−	1.42444i
$914$	40.7624	+	70.6026i	1.34830	+	2.33533i
$915$	31.2370			1.03266
$916$	16.7930	+	29.0863i	0.554856	+	0.961038i
$917$	5.71196	+	9.89341i	0.188626	+	0.326709i
$918$	−0.896688			−0.0295951
$919$	1.58141	+	2.73909i	0.0521660	+	0.0903542i	0.890929	−	0.454142i	$-0.150054\pi$
$919$	1.58141	+	2.73909i	0.0521660	+	0.0903542i	−0.838763	+	0.544496i	$0.816721\pi$
$920$	−14.9943	+	25.9708i	−0.494346	+	0.856233i
$921$	−14.1224	+	24.4607i	−0.465349	+	0.806008i
$922$	−45.9575			−1.51353
$923$	−13.8796	+	3.81458i	−0.456853	+	0.125558i
$924$	−11.9533			−0.393234
$925$	−22.6132	+	39.1672i	−0.743517	+	1.28781i
$926$	7.48158	−	12.9585i	0.245860	−	0.425842i
$927$	−5.28270	−	9.14991i	−0.173507	−	0.300522i
$928$	−26.2838			−0.862807
$929$	−19.7964	−	34.2885i	−0.649500	−	1.12497i	−0.983242	−	0.182303i	$-0.941645\pi$
$929$	−19.7964	−	34.2885i	−0.649500	−	1.12497i	0.333742	−	0.942664i	$-0.391689\pi$
$930$	30.3106	+	52.4995i	0.993924	+	1.72153i
$931$	−3.54778			−0.116274
$932$	22.7321	+	39.3732i	0.744615	+	1.28971i
$933$	−1.33088	+	2.30516i	−0.0435712	+	0.0754675i
$934$	28.7990	−	49.8813i	0.942331	−	1.63217i
$935$	−4.97463			−0.162688
$936$	13.6458	−	3.75031i	0.446026	−	0.122583i
$937$	2.94553			0.0962263			0.0481131	−	0.998842i	$-0.484679\pi$
$937$	2.94553			0.0962263			0.0481131	+	0.998842i	$0.484679\pi$
$938$	−6.63695	+	11.4955i	−0.216704	+	0.375342i
$939$	−11.2413	+	19.4705i	−0.366847	+	0.635397i
$940$	−89.1570	−	154.424i	−2.90798	−	5.03677i
$941$	20.9893			0.684232			0.342116	−	0.939658i	$-0.388856\pi$
$941$	20.9893			0.684232			0.342116	+	0.939658i	$0.388856\pi$
$942$	−20.8910	−	36.1842i	−0.680664	−	1.17894i
$943$	−7.12094	−	12.3338i	−0.231890	−	0.401644i
$944$	−4.26614			−0.138851
$945$	2.01415	+	3.48861i	0.0655202	+	0.113484i
$946$	33.6644	−	58.3085i	1.09453	−	1.89577i
$947$	3.18367	−	5.51427i	0.103455	−	0.179190i	−0.809651	−	0.586912i	$-0.800343\pi$
$947$	3.18367	−	5.51427i	0.103455	−	0.179190i	0.913106	+	0.407722i	$0.133677\pi$
$948$	4.24559			0.137890
$949$	6.83224	−	26.1683i	0.221784	−	0.849457i
$950$	94.6877			3.07207
$951$	9.41577	−	16.3086i	0.305327	−	0.528842i
$952$	0.740258	−	1.28216i	0.0239919	−	0.0415552i
$953$	−30.2268	−	52.3543i	−0.979141	−	1.69592i	−0.665531	−	0.746370i	$-0.731795\pi$
$953$	−30.2268	−	52.3543i	−0.979141	−	1.69592i	−0.313610	−	0.949552i	$-0.601539\pi$
$954$	−18.4338			−0.596816
$955$	1.31140	+	2.27141i	0.0424359	+	0.0735011i
$956$	5.92498	+	10.2624i	0.191628	+	0.331909i
$957$	−28.4154			−0.918539
$958$	−39.9724	−	69.2342i	−1.29145	−	2.23685i
$959$	−1.59556	+	2.76359i	−0.0515234	+	0.0892411i
$960$	22.6702	−	39.2659i	0.731677	−	1.26730i
$961$	9.07502			0.292742
$962$	33.2926	−	9.14991i	1.07340	−	0.295005i
$963$	−12.4055			−0.399762
$964$	−17.2077	+	29.8046i	−0.554222	+	0.959941i
$965$	38.3984	−	66.5080i	1.23609	−	2.14097i
$966$	2.25441	+	3.90475i	0.0725343	+	0.125633i
$967$	48.1719			1.54910			0.774552	−	0.632510i	$-0.217975\pi$
$967$	48.1719			1.54910			0.774552	+	0.632510i	$0.217975\pi$
$968$	−0.552717	−	0.957335i	−0.0177650	−	0.0307699i
$969$	0.669117	+	1.15894i	0.0214951	+	0.0372306i
$970$	47.6094			1.52865
$971$	−8.98264	−	15.5584i	−0.288267	−	0.499292i	0.685130	−	0.728421i	$-0.259746\pi$
$971$	−8.98264	−	15.5584i	−0.288267	−	0.499292i	−0.973396	+	0.229129i	$0.926412\pi$
$972$	1.82555	−	3.16194i	0.0585544	−	0.101419i
$973$	2.68860	−	4.65679i	0.0861926	−	0.149290i
$974$	18.8393			0.603650
$975$	−28.8067	−	28.4397i	−0.922553	−	0.910798i
$976$	15.7282			0.503448
$977$	1.41336	−	2.44801i	0.0452174	−	0.0783188i	−0.842531	−	0.538648i	$-0.818935\pi$
$977$	1.41336	−	2.44801i	0.0452174	−	0.0783188i	0.887748	+	0.460329i	$0.152269\pi$
$978$	6.52683	−	11.3048i	0.208705	−	0.361488i
$979$	10.4090	+	18.0289i	0.332672	+	0.576205i
$980$	−14.7077			−0.469820
$981$	6.06580	+	10.5063i	0.193666	+	0.335440i
$982$	2.89029	+	5.00613i	0.0922328	+	0.159752i
$983$	−29.8873			−0.953258			−0.476629	−	0.879105i	$-0.658141\pi$
$983$	−29.8873			−0.953258			−0.476629	+	0.879105i	$0.658141\pi$
$984$	−14.7360	−	25.5235i	−0.469766	−	0.813659i
$985$	49.7692	−	86.2028i	1.58578	−	2.74665i
$986$	3.89135	−	6.74002i	0.123926	−	0.214646i
$987$	−12.1239			−0.385907
$988$	−33.2356	−	32.8121i	−1.05736	−	1.04389i
$989$	−16.4084			−0.521757
$990$	15.6755	−	27.1508i	0.498201	−	0.862909i
$991$	−18.4734	+	31.9969i	−0.586828	+	1.01642i	0.407817	+	0.913064i	$0.366290\pi$
$991$	−18.4734	+	31.9969i	−0.586828	+	1.01642i	−0.994645	+	0.103352i	$0.967043\pi$
$992$	−9.58529	−	16.6022i	−0.304333	−	0.527121i
$993$	17.8315			0.565867
$994$	−4.74519	−	8.21892i	−0.150508	−	0.260688i
$995$	26.4748	+	45.8557i	0.839307	+	1.45372i
$996$	−55.4252			−1.75622
$997$	−5.35878	−	9.28168i	−0.169714	−	0.293954i	0.768605	−	0.639724i	$-0.220951\pi$
$997$	−5.35878	−	9.28168i	−0.169714	−	0.293954i	−0.938319	+	0.345770i	$0.887618\pi$
$998$	−22.0888	+	38.2589i	−0.699208	+	1.21106i
$999$	2.01415	−	3.48861i	0.0637248	−	0.110375i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	273.2.k.d.22.3	✓	6
3.2	odd	2		819.2.o.d.568.1		6
13.3	even	3	inner	273.2.k.d.211.3	yes	6
13.4	even	6		3549.2.a.s.1.3		3
13.9	even	3		3549.2.a.h.1.1		3
39.29	odd	6		819.2.o.d.757.1		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
273.2.k.d.22.3	✓	6	1.1	even	1	trivial
273.2.k.d.211.3	yes	6	13.3	even	3	inner
819.2.o.d.568.1		6	3.2	odd	2
819.2.o.d.757.1		6	39.29	odd	6
3549.2.a.h.1.1		3	13.9	even	3
3549.2.a.s.1.3		3	13.4	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:	\( N \)	\(=\)	\( 273 = 3 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	273.k (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.18860 - 2.05872i) q^{2} +(0.500000 - 0.866025i) q^{3} +(-1.82555 - 3.16194i) q^{4} -4.02830 q^{5} +(-1.18860 - 2.05872i) q^{6} +(0.500000 + 0.866025i) q^{7} -3.92498 q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(q+(1.18860 - 2.05872i) q^{2} +(0.500000 - 0.866025i) q^{3} +(-1.82555 - 3.16194i) q^{4} -4.02830 q^{5} +(-1.18860 - 2.05872i) q^{6} +(0.500000 + 0.866025i) q^{7} -3.92498 q^{8} +(-0.500000 - 0.866025i) q^{9} +(-4.78804 + 8.29313i) q^{10} +(1.63695 - 2.83527i) q^{11} -3.65109 q^{12} +(0.910836 - 3.48861i) q^{13} +2.37720 q^{14} +(-2.01415 + 3.48861i) q^{15} +(-1.01415 + 1.75656i) q^{16} +(0.188601 + 0.326667i) q^{17} -2.37720 q^{18} +(1.77389 + 3.07247i) q^{19} +(7.35384 + 12.7372i) q^{20} +1.00000 q^{21} +(-3.89135 - 6.74002i) q^{22} +(-0.948344 + 1.64258i) q^{23} +(-1.96249 + 3.39914i) q^{24} +11.2272 q^{25} +(-6.09944 - 6.02172i) q^{26} -1.00000 q^{27} +(1.82555 - 3.16194i) q^{28} +(4.33969 - 7.51657i) q^{29} +(4.78804 + 8.29313i) q^{30} +6.33048 q^{31} +(-1.51415 - 2.62258i) q^{32} +(-1.63695 - 2.83527i) q^{33} +0.896688 q^{34} +(-2.01415 - 3.48861i) q^{35} +(-1.82555 + 3.16194i) q^{36} +(-2.01415 + 3.48861i) q^{37} +8.43380 q^{38} +(-2.56580 - 2.53311i) q^{39} +15.8110 q^{40} +(-3.75441 + 6.50282i) q^{41} +(1.18860 - 2.05872i) q^{42} +(4.32555 + 7.49207i) q^{43} -11.9533 q^{44} +(2.01415 + 3.48861i) q^{45} +(2.25441 + 3.90475i) q^{46} -12.1239 q^{47} +(1.01415 + 1.75656i) q^{48} +(-0.500000 + 0.866025i) q^{49} +(13.3446 - 23.1136i) q^{50} +0.377203 q^{51} +(-12.6935 + 3.48861i) q^{52} +7.75441 q^{53} +(-1.18860 + 2.05872i) q^{54} +(-6.59410 + 11.4213i) q^{55} +(-1.96249 - 3.39914i) q^{56} +3.54778 q^{57} +(-10.3163 - 17.8684i) q^{58} +(1.05166 + 1.82152i) q^{59} +14.7077 q^{60} +(-3.87720 - 6.71551i) q^{61} +(7.52442 - 13.0327i) q^{62} +(0.500000 - 0.866025i) q^{63} -11.2555 q^{64} +(-3.66912 + 14.0531i) q^{65} -7.78270 q^{66} +(-2.79191 + 4.83574i) q^{67} +(0.688601 - 1.19269i) q^{68} +(0.948344 + 1.64258i) q^{69} -9.57608 q^{70} +(-1.99612 - 3.45739i) q^{71} +(1.96249 + 3.39914i) q^{72} +7.50106 q^{73} +(4.78804 + 8.29313i) q^{74} +(5.61359 - 9.72302i) q^{75} +(6.47664 - 11.2179i) q^{76} +3.27389 q^{77} +(-8.26468 + 2.27141i) q^{78} -1.16283 q^{79} +(4.08529 - 7.07593i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(8.92498 + 15.4585i) q^{82} +15.1805 q^{83} +(-1.82555 - 3.16194i) q^{84} +(-0.759742 - 1.31591i) q^{85} +20.5654 q^{86} +(-4.33969 - 7.51657i) q^{87} +(-6.42498 + 11.1284i) q^{88} +(-3.17939 + 5.50686i) q^{89} +9.57608 q^{90} +(3.47664 - 0.955496i) q^{91} +6.92498 q^{92} +(3.16524 - 5.48236i) q^{93} +(-14.4104 + 24.9596i) q^{94} +(-7.14576 - 12.3768i) q^{95} -3.02830 q^{96} +(-2.48585 - 4.30562i) q^{97} +(1.18860 + 2.05872i) q^{98} -3.27389 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 2 q^{2} + 3 q^{3} - 4 q^{4} - 2 q^{6} + 3 q^{7} - 6 q^{8} - 3 q^{9}+O(q^{10}) \) 6 * q + 2 * q^2 + 3 * q^3 - 4 * q^4 - 2 * q^6 + 3 * q^7 - 6 * q^8 - 3 * q^9	\( 6 q + 2 q^{2} + 3 q^{3} - 4 q^{4} - 2 q^{6} + 3 q^{7} - 6 q^{8} - 3 q^{9} - 13 q^{10} + 8 q^{11} - 8 q^{12} + 4 q^{14} + 6 q^{16} - 4 q^{17} - 4 q^{18} + 7 q^{19} + 13 q^{20} + 6 q^{21} - q^{22} - 9 q^{23} - 3 q^{24} + 22 q^{25} - 26 q^{26} - 6 q^{27} + 4 q^{28} + 7 q^{29} + 13 q^{30} - 14 q^{31} + 3 q^{32} - 8 q^{33} + 12 q^{34} - 4 q^{36} - 8 q^{38} + 26 q^{40} - 2 q^{41} + 2 q^{42} + 19 q^{43} - 30 q^{44} - 7 q^{46} - 34 q^{47} - 6 q^{48} - 3 q^{49} + 16 q^{50} - 8 q^{51} - 26 q^{52} + 26 q^{53} - 2 q^{54} - 3 q^{56} + 14 q^{57} - 22 q^{58} + 3 q^{59} + 26 q^{60} - 13 q^{61} + 17 q^{62} + 3 q^{63} + 2 q^{64} - 2 q^{66} - 5 q^{67} - q^{68} + 9 q^{69} - 26 q^{70} - 8 q^{71} + 3 q^{72} - 4 q^{73} + 13 q^{74} + 11 q^{75} + 18 q^{76} + 16 q^{77} - 13 q^{78} - 2 q^{79} + 26 q^{80} - 3 q^{81} + 36 q^{82} + 4 q^{83} - 4 q^{84} - 13 q^{85} + 34 q^{86} - 7 q^{87} - 21 q^{88} + 19 q^{89} + 26 q^{90} + 24 q^{92} - 7 q^{93} - 7 q^{94} + 6 q^{96} - 27 q^{97} + 2 q^{98} - 16 q^{99}+O(q^{100}) \) 6 * q + 2 * q^2 + 3 * q^3 - 4 * q^4 - 2 * q^6 + 3 * q^7 - 6 * q^8 - 3 * q^9 - 13 * q^10 + 8 * q^11 - 8 * q^12 + 4 * q^14 + 6 * q^16 - 4 * q^17 - 4 * q^18 + 7 * q^19 + 13 * q^20 + 6 * q^21 - q^22 - 9 * q^23 - 3 * q^24 + 22 * q^25 - 26 * q^26 - 6 * q^27 + 4 * q^28 + 7 * q^29 + 13 * q^30 - 14 * q^31 + 3 * q^32 - 8 * q^33 + 12 * q^34 - 4 * q^36 - 8 * q^38 + 26 * q^40 - 2 * q^41 + 2 * q^42 + 19 * q^43 - 30 * q^44 - 7 * q^46 - 34 * q^47 - 6 * q^48 - 3 * q^49 + 16 * q^50 - 8 * q^51 - 26 * q^52 + 26 * q^53 - 2 * q^54 - 3 * q^56 + 14 * q^57 - 22 * q^58 + 3 * q^59 + 26 * q^60 - 13 * q^61 + 17 * q^62 + 3 * q^63 + 2 * q^64 - 2 * q^66 - 5 * q^67 - q^68 + 9 * q^69 - 26 * q^70 - 8 * q^71 + 3 * q^72 - 4 * q^73 + 13 * q^74 + 11 * q^75 + 18 * q^76 + 16 * q^77 - 13 * q^78 - 2 * q^79 + 26 * q^80 - 3 * q^81 + 36 * q^82 + 4 * q^83 - 4 * q^84 - 13 * q^85 + 34 * q^86 - 7 * q^87 - 21 * q^88 + 19 * q^89 + 26 * q^90 + 24 * q^92 - 7 * q^93 - 7 * q^94 + 6 * q^96 - 27 * q^97 + 2 * q^98 - 16 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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