LMFDB - Embedded newform 201.2.e.c.163.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [201,2,Mod(37,201)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(201, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 2]))

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

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

chi := DirichletCharacter("201.37");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 201 = 3 \cdot 67 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	201.e (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:	$1.60499308063$
Analytic rank:	$0$
Dimension:	$10$
Relative dimension:	$5$ over $\Q(\zeta_{3})$
Coefficient field:	10.0.3665654523963.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - 2x^{9} + 8x^{8} + 21x^{6} - 5x^{5} + 26x^{4} + 4x^{3} + 13x^{2} - 3x + 1 $ x^10 - 2x^9 + 8x^8 + 21x^6 - 5x^5 + 26x^4 + 4x^3 + 13x^2 - 3x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			163.4
Root			$0.133354 + 0.230976i$ of defining polynomial
Character	$\chi$	$=$	201.163
Dual form			201.2.e.c.37.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.538290 - 0.932346i) q^{2} +1.00000 q^{3} +(0.420487 + 0.728305i) q^{4} -0.343289 q^{5} +(0.538290 - 0.932346i) q^{6} +(-1.74135 - 3.01611i) q^{7} +3.05854 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+(0.538290 - 0.932346i) q^{2} +1.00000 q^{3} +(0.420487 + 0.728305i) q^{4} -0.343289 q^{5} +(0.538290 - 0.932346i) q^{6} +(-1.74135 - 3.01611i) q^{7} +3.05854 q^{8} +1.00000 q^{9} +(-0.184789 + 0.320064i) q^{10} +(1.62587 + 2.81608i) q^{11} +(0.420487 + 0.728305i) q^{12} +(2.55656 - 4.42810i) q^{13} -3.74942 q^{14} -0.343289 q^{15} +(0.805407 - 1.39501i) q^{16} +(-2.89298 + 5.01079i) q^{17} +(0.538290 - 0.932346i) q^{18} +(-1.78179 + 3.08616i) q^{19} +(-0.144349 - 0.250019i) q^{20} +(-1.74135 - 3.01611i) q^{21} +3.50075 q^{22} +(-2.90613 + 5.03356i) q^{23} +3.05854 q^{24} -4.88215 q^{25} +(-2.75235 - 4.76721i) q^{26} +1.00000 q^{27} +(1.46443 - 2.53647i) q^{28} +(-5.09820 - 8.83033i) q^{29} +(-0.184789 + 0.320064i) q^{30} +(-4.29870 - 7.44557i) q^{31} +(2.19145 + 3.79571i) q^{32} +(1.62587 + 2.81608i) q^{33} +(3.11453 + 5.39452i) q^{34} +(0.597787 + 1.03540i) q^{35} +(0.420487 + 0.728305i) q^{36} +(-5.46501 + 9.46567i) q^{37} +(1.91825 + 3.32250i) q^{38} +(2.55656 - 4.42810i) q^{39} -1.04996 q^{40} +(-1.08998 - 1.88790i) q^{41} -3.74942 q^{42} +6.88453 q^{43} +(-1.36731 + 2.36825i) q^{44} -0.343289 q^{45} +(3.12868 + 5.41903i) q^{46} +(3.30598 + 5.72613i) q^{47} +(0.805407 - 1.39501i) q^{48} +(-2.56463 + 4.44206i) q^{49} +(-2.62802 + 4.55186i) q^{50} +(-2.89298 + 5.01079i) q^{51} +4.30001 q^{52} +4.19796 q^{53} +(0.538290 - 0.932346i) q^{54} +(-0.558142 - 0.966730i) q^{55} +(-5.32600 - 9.22490i) q^{56} +(-1.78179 + 3.08616i) q^{57} -10.9772 q^{58} -4.93524 q^{59} +(-0.144349 - 0.250019i) q^{60} +(5.54693 - 9.60756i) q^{61} -9.25580 q^{62} +(-1.74135 - 3.01611i) q^{63} +7.94018 q^{64} +(-0.877640 + 1.52012i) q^{65} +3.50075 q^{66} +(8.16969 + 0.506056i) q^{67} -4.86585 q^{68} +(-2.90613 + 5.03356i) q^{69} +1.28713 q^{70} +(2.76671 + 4.79208i) q^{71} +3.05854 q^{72} +(1.87686 - 3.25081i) q^{73} +(5.88352 + 10.1906i) q^{74} -4.88215 q^{75} -2.99689 q^{76} +(5.66241 - 9.80759i) q^{77} +(-2.75235 - 4.76721i) q^{78} +(-0.758004 - 1.31290i) q^{79} +(-0.276487 + 0.478890i) q^{80} +1.00000 q^{81} -2.34691 q^{82} +(1.05201 - 1.82213i) q^{83} +(1.46443 - 2.53647i) q^{84} +(0.993129 - 1.72015i) q^{85} +(3.70588 - 6.41877i) q^{86} +(-5.09820 - 8.83033i) q^{87} +(4.97277 + 8.61309i) q^{88} +10.4923 q^{89} +(-0.184789 + 0.320064i) q^{90} -17.8075 q^{91} -4.88795 q^{92} +(-4.29870 - 7.44557i) q^{93} +7.11831 q^{94} +(0.611670 - 1.05944i) q^{95} +(2.19145 + 3.79571i) q^{96} +(1.66477 - 2.88347i) q^{97} +(2.76103 + 4.78224i) q^{98} +(1.62587 + 2.81608i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q + 10 q^{3} - 6 q^{4} + 6 q^{5} - q^{7} + 10 q^{9}+O(q^{10}) $ 10 * q + 10 * q^3 - 6 * q^4 + 6 * q^5 - q^7 + 10 * q^9	\( 10 q + 10 q^{3} - 6 q^{4} + 6 q^{5} - q^{7} + 10 q^{9} - 12 q^{10} + 6 q^{11} - 6 q^{12} - q^{13} - 6 q^{14} + 6 q^{15} - 24 q^{16} + 8 q^{17} - 5 q^{19} - 8 q^{20} - q^{21} + 22 q^{22} - 7 q^{23} - 8 q^{25} - 17 q^{26} + 10 q^{27} + 3 q^{28} - 12 q^{29} - 12 q^{30} - 12 q^{31} - 5 q^{32} + 6 q^{33} - 5 q^{35} - 6 q^{36} - 17 q^{37} + 30 q^{38} - q^{39} + 34 q^{40} + 13 q^{41} - 6 q^{42} - 4 q^{43} + 43 q^{44} + 6 q^{45} - 26 q^{46} - 25 q^{47} - 24 q^{48} + 16 q^{49} - 25 q^{50} + 8 q^{51} + 64 q^{52} - 12 q^{53} - 14 q^{55} - 11 q^{56} - 5 q^{57} + 4 q^{58} - 12 q^{59} - 8 q^{60} + 9 q^{61} + 46 q^{62} - q^{63} + 64 q^{64} - 14 q^{65} + 22 q^{66} + 2 q^{67} - 98 q^{68} - 7 q^{69} + 2 q^{70} + 29 q^{71} + 12 q^{73} + 15 q^{74} - 8 q^{75} - 6 q^{76} + 4 q^{77} - 17 q^{78} - q^{79} - 13 q^{80} + 10 q^{81} - 2 q^{82} - 6 q^{83} + 3 q^{84} + 9 q^{85} - 21 q^{86} - 12 q^{87} + 18 q^{88} - 4 q^{89} - 12 q^{90} - 40 q^{91} - 12 q^{93} + 30 q^{94} - 14 q^{95} - 5 q^{96} + 11 q^{97} + 12 q^{98} + 6 q^{99}+O(q^{100}) \) 10 * q + 10 * q^3 - 6 * q^4 + 6 * q^5 - q^7 + 10 * q^9 - 12 * q^10 + 6 * q^11 - 6 * q^12 - q^13 - 6 * q^14 + 6 * q^15 - 24 * q^16 + 8 * q^17 - 5 * q^19 - 8 * q^20 - q^21 + 22 * q^22 - 7 * q^23 - 8 * q^25 - 17 * q^26 + 10 * q^27 + 3 * q^28 - 12 * q^29 - 12 * q^30 - 12 * q^31 - 5 * q^32 + 6 * q^33 - 5 * q^35 - 6 * q^36 - 17 * q^37 + 30 * q^38 - q^39 + 34 * q^40 + 13 * q^41 - 6 * q^42 - 4 * q^43 + 43 * q^44 + 6 * q^45 - 26 * q^46 - 25 * q^47 - 24 * q^48 + 16 * q^49 - 25 * q^50 + 8 * q^51 + 64 * q^52 - 12 * q^53 - 14 * q^55 - 11 * q^56 - 5 * q^57 + 4 * q^58 - 12 * q^59 - 8 * q^60 + 9 * q^61 + 46 * q^62 - q^63 + 64 * q^64 - 14 * q^65 + 22 * q^66 + 2 * q^67 - 98 * q^68 - 7 * q^69 + 2 * q^70 + 29 * q^71 + 12 * q^73 + 15 * q^74 - 8 * q^75 - 6 * q^76 + 4 * q^77 - 17 * q^78 - q^79 - 13 * q^80 + 10 * q^81 - 2 * q^82 - 6 * q^83 + 3 * q^84 + 9 * q^85 - 21 * q^86 - 12 * q^87 + 18 * q^88 - 4 * q^89 - 12 * q^90 - 40 * q^91 - 12 * q^93 + 30 * q^94 - 14 * q^95 - 5 * q^96 + 11 * q^97 + 12 * q^98 + 6 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/201\mathbb{Z}\right)^\times$.

$n$	$68$	$136$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$

Coefficient data

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

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

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

$2$	0.538290	−	0.932346i	0.380629	−	0.659268i	−0.610524	−	0.791998i	$-0.709041\pi$
$2$	0.538290	−	0.932346i	0.380629	−	0.659268i	0.991152	+	0.132730i	$0.0423743\pi$
$3$	1.00000			0.577350
$3$	1.00000			0.577350
$4$	0.420487	+	0.728305i	0.210243	+	0.364152i
$5$	−0.343289			−0.153523			−0.0767617	−	0.997049i	$-0.524458\pi$
$5$	−0.343289			−0.153523			−0.0767617	+	0.997049i	$0.524458\pi$
$6$	0.538290	−	0.932346i	0.219756	−	0.380629i
$7$	−1.74135	−	3.01611i	−0.658170	−	1.13998i	−0.981089	−	0.193557i	$-0.937998\pi$
$7$	−1.74135	−	3.01611i	−0.658170	−	1.13998i	0.322919	−	0.946427i	$-0.395336\pi$
$8$	3.05854			1.08136
$9$	1.00000			0.333333
$10$	−0.184789	+	0.320064i	−0.0584354	+	0.101213i
$11$	1.62587	+	2.81608i	0.490217	+	0.849081i	0.999937	−	0.0112600i	$-0.00358424\pi$
$11$	1.62587	+	2.81608i	0.490217	+	0.849081i	−0.509720	+	0.860341i	$0.670251\pi$
$12$	0.420487	+	0.728305i	0.121384	+	0.210243i
$13$	2.55656	−	4.42810i	0.709064	−	1.22813i	−0.256141	−	0.966639i	$-0.582451\pi$
$13$	2.55656	−	4.42810i	0.709064	−	1.22813i	0.965205	−	0.261495i	$-0.0842154\pi$
$14$	−3.74942			−1.00207
$15$	−0.343289			−0.0886368
$16$	0.805407	−	1.39501i	0.201352	−	0.348752i
$17$	−2.89298	+	5.01079i	−0.701651	+	1.21530i	0.266235	+	0.963908i	$0.414220\pi$
$17$	−2.89298	+	5.01079i	−0.701651	+	1.21530i	−0.967886	+	0.251388i	$0.919113\pi$
$18$	0.538290	−	0.932346i	0.126876	−	0.219756i
$19$	−1.78179	+	3.08616i	−0.408772	+	0.708013i	−0.994752	−	0.102312i	$-0.967376\pi$
$19$	−1.78179	+	3.08616i	−0.408772	+	0.708013i	0.585981	+	0.810325i	$0.300709\pi$
$20$	−0.144349	−	0.250019i	−0.0322773	−	0.0559059i
$21$	−1.74135	−	3.01611i	−0.379995	−	0.658170i
$22$	3.50075			0.746363
$23$	−2.90613	+	5.03356i	−0.605969	+	1.04957i	0.385928	+	0.922529i	$0.373881\pi$
$23$	−2.90613	+	5.03356i	−0.605969	+	1.04957i	−0.991897	+	0.127041i	$0.959452\pi$
$24$	3.05854			0.624321
$25$	−4.88215			−0.976431
$26$	−2.75235	−	4.76721i	−0.539780	−	0.934926i
$27$	1.00000			0.192450
$28$	1.46443	−	2.53647i	0.276752	−	0.479348i
$29$	−5.09820	−	8.83033i	−0.946711	−	1.63975i	−0.752288	−	0.658834i	$-0.771050\pi$
$29$	−5.09820	−	8.83033i	−0.946711	−	1.63975i	−0.194423	−	0.980918i	$-0.562284\pi$
$30$	−0.184789	+	0.320064i	−0.0337377	+	0.0584354i
$31$	−4.29870	−	7.44557i	−0.772069	−	1.33726i	−0.936427	−	0.350863i	$-0.885888\pi$
$31$	−4.29870	−	7.44557i	−0.772069	−	1.33726i	0.164357	−	0.986401i	$-0.447445\pi$
$32$	2.19145	+	3.79571i	0.387398	+	0.670992i
$33$	1.62587	+	2.81608i	0.283027	+	0.490217i
$34$	3.11453	+	5.39452i	0.534137	+	0.925153i
$35$	0.597787	+	1.03540i	0.101045	+	0.175014i
$36$	0.420487	+	0.728305i	0.0700812	+	0.121384i
$37$	−5.46501	+	9.46567i	−0.898442	+	1.55615i	−0.0689551	+	0.997620i	$0.521967\pi$
$37$	−5.46501	+	9.46567i	−0.898442	+	1.55615i	−0.829487	+	0.558527i	$0.811367\pi$
$38$	1.91825	+	3.32250i	0.311181	+	0.538980i
$39$	2.55656	−	4.42810i	0.409378	−	0.709064i
$40$	−1.04996			−0.166014
$41$	−1.08998	−	1.88790i	−0.170226	−	0.294841i	0.768273	−	0.640123i	$-0.221117\pi$
$41$	−1.08998	−	1.88790i	−0.170226	−	0.294841i	−0.938499	+	0.345282i	$0.887783\pi$
$42$	−3.74942			−0.578547
$43$	6.88453			1.04988			0.524941	−	0.851139i	$-0.324087\pi$
$43$	6.88453			1.04988			0.524941	+	0.851139i	$0.324087\pi$
$44$	−1.36731	+	2.36825i	−0.206130	+	0.357027i
$45$	−0.343289			−0.0511745
$46$	3.12868	+	5.41903i	0.461299	+	0.798993i
$47$	3.30598	+	5.72613i	0.482227	+	0.835241i	0.999792	−	0.0204025i	$-0.00649476\pi$
$47$	3.30598	+	5.72613i	0.482227	+	0.835241i	−0.517565	+	0.855644i	$0.673161\pi$
$48$	0.805407	−	1.39501i	0.116251	−	0.201352i
$49$	−2.56463	+	4.44206i	−0.366375	+	0.634581i
$50$	−2.62802	+	4.55186i	−0.371658	+	0.643730i
$51$	−2.89298	+	5.01079i	−0.405099	+	0.701651i
$52$	4.30001			0.596304
$53$	4.19796			0.576634			0.288317	−	0.957535i	$-0.406904\pi$
$53$	4.19796			0.576634			0.288317	+	0.957535i	$0.406904\pi$
$54$	0.538290	−	0.932346i	0.0732520	−	0.126876i
$55$	−0.558142	−	0.966730i	−0.0752598	−	0.130354i
$56$	−5.32600	−	9.22490i	−0.711716	−	1.23273i
$57$	−1.78179	+	3.08616i	−0.236004	+	0.408772i
$58$	−10.9772			−1.44138
$59$	−4.93524			−0.642514			−0.321257	−	0.946992i	$-0.604105\pi$
$59$	−4.93524			−0.642514			−0.321257	+	0.946992i	$0.604105\pi$
$60$	−0.144349	−	0.250019i	−0.0186353	−	0.0322773i
$61$	5.54693	−	9.60756i	0.710211	−	1.23012i	−0.254567	−	0.967055i	$-0.581933\pi$
$61$	5.54693	−	9.60756i	0.710211	−	1.23012i	0.964778	−	0.263066i	$-0.0847338\pi$
$62$	−9.25580			−1.17549
$63$	−1.74135	−	3.01611i	−0.219390	−	0.379995i
$64$	7.94018			0.992522
$65$	−0.877640	+	1.52012i	−0.108858	+	0.188547i
$66$	3.50075			0.430913
$67$	8.16969	+	0.506056i	0.998087	+	0.0618246i
$67$	8.16969	+	0.506056i	0.998087	+	0.0618246i
$68$	−4.86585			−0.590071
$69$	−2.90613	+	5.03356i	−0.349857	+	0.605969i
$70$	1.28713			0.153842
$71$	2.76671	+	4.79208i	0.328348	+	0.568715i	0.982184	−	0.187921i	$-0.0601748\pi$
$71$	2.76671	+	4.79208i	0.328348	+	0.568715i	−0.653836	+	0.756636i	$0.726842\pi$
$72$	3.05854			0.360452
$73$	1.87686	−	3.25081i	0.219670	−	0.380479i	−0.735037	−	0.678027i	$-0.762835\pi$
$73$	1.87686	−	3.25081i	0.219670	−	0.380479i	0.954707	+	0.297548i	$0.0961687\pi$
$74$	5.88352	+	10.1906i	0.683945	+	1.18463i
$75$	−4.88215			−0.563742
$76$	−2.99689			−0.343766
$77$	5.66241	−	9.80759i	0.645292	−	1.11768i
$78$	−2.75235	−	4.76721i	−0.311642	−	0.539780i
$79$	−0.758004	−	1.31290i	−0.0852822	−	0.147713i	0.820229	−	0.572035i	$-0.193846\pi$
$79$	−0.758004	−	1.31290i	−0.0852822	−	0.147713i	−0.905511	+	0.424322i	$0.860512\pi$
$80$	−0.276487	+	0.478890i	−0.0309122	+	0.0535416i
$81$	1.00000			0.111111
$82$	−2.34691			−0.259172
$83$	1.05201	−	1.82213i	0.115473	−	0.200005i	−0.802496	−	0.596658i	$-0.796495\pi$
$83$	1.05201	−	1.82213i	0.115473	−	0.200005i	0.917969	+	0.396653i	$0.129828\pi$
$84$	1.46443	−	2.53647i	0.159783	−	0.276752i
$85$	0.993129	−	1.72015i	0.107720	−	0.186576i
$86$	3.70588	−	6.41877i	0.399615	−	0.692154i
$87$	−5.09820	−	8.83033i	−0.546584	−	0.946711i
$88$	4.97277	+	8.61309i	0.530099	+	0.918159i
$89$	10.4923			1.11218			0.556092	−	0.831120i	$-0.312300\pi$
$89$	10.4923			1.11218			0.556092	+	0.831120i	$0.312300\pi$
$90$	−0.184789	+	0.320064i	−0.0194785	+	0.0337377i
$91$	−17.8075			−1.86674
$92$	−4.88795			−0.509605
$93$	−4.29870	−	7.44557i	−0.445755	−	0.772069i
$94$	7.11831			0.734198
$95$	0.611670	−	1.05944i	0.0627560	−	0.108697i
$96$	2.19145	+	3.79571i	0.223664	+	0.387398i
$97$	1.66477	−	2.88347i	0.169032	−	0.292772i	−0.769048	−	0.639191i	$-0.779269\pi$
$97$	1.66477	−	2.88347i	0.169032	−	0.292772i	0.938080	+	0.346419i	$0.112603\pi$
$98$	2.76103	+	4.78224i	0.278906	+	0.483079i
$99$	1.62587	+	2.81608i	0.163406	+	0.283027i
$100$	−2.05288	−	3.55570i	−0.205288	−	0.355570i
$101$	−1.36420	−	2.36286i	−0.135743	−	0.235113i	0.790138	−	0.612929i	$-0.210009\pi$
$101$	−1.36420	−	2.36286i	−0.135743	−	0.235113i	−0.925881	+	0.377816i	$0.876675\pi$
$102$	3.11453	+	5.39452i	0.308384	+	0.534137i
$103$	1.07960	+	1.86993i	0.106377	+	0.184250i	0.914300	−	0.405038i	$-0.132742\pi$
$103$	1.07960	+	1.86993i	0.106377	+	0.184250i	−0.807923	+	0.589288i	$0.799408\pi$
$104$	7.81935	−	13.5435i	0.766750	−	1.32805i
$105$	0.597787	+	1.03540i	0.0583381	+	0.101045i
$106$	2.25972	−	3.91395i	0.219483	−	0.380156i
$107$	10.6008			1.02482			0.512408	−	0.858742i	$-0.328754\pi$
$107$	10.6008			1.02482			0.512408	+	0.858742i	$0.328754\pi$
$108$	0.420487	+	0.728305i	0.0404614	+	0.0700812i
$109$	−5.22306			−0.500278			−0.250139	−	0.968210i	$-0.580476\pi$
$109$	−5.22306			−0.500278			−0.250139	+	0.968210i	$0.580476\pi$
$110$	−1.20177			−0.114584
$111$	−5.46501	+	9.46567i	−0.518715	+	0.898442i
$112$	−5.61000			−0.530095
$113$	−3.34306	−	5.79034i	−0.314488	−	0.544710i	0.664840	−	0.746985i	$-0.268500\pi$
$113$	−3.34306	−	5.79034i	−0.314488	−	0.544710i	−0.979329	+	0.202276i	$0.935166\pi$
$114$	1.91825	+	3.32250i	0.179660	+	0.311181i
$115$	0.997641	−	1.72797i	0.0930305	−	0.161134i
$116$	4.28745	−	7.42608i	0.398080	−	0.689494i
$117$	2.55656	−	4.42810i	0.236355	−	0.409378i
$118$	−2.65659	+	4.60136i	−0.244559	+	0.423589i
$119$	20.1508			1.84722
$120$	−1.04996			−0.0958480
$121$	0.213123	−	0.369140i	0.0193748	−	0.0335582i
$122$	−5.97171	−	10.3433i	−0.540654	−	0.936439i
$123$	−1.08998	−	1.88790i	−0.0982803	−	0.170226i
$124$	3.61510	−	6.26153i	0.324645	−	0.562302i
$125$	3.39243			0.303428
$126$	−3.74942			−0.334025
$127$	0.249942	+	0.432913i	0.0221788	+	0.0384148i	0.876902	−	0.480670i	$-0.159606\pi$
$127$	0.249942	+	0.432913i	0.0221788	+	0.0384148i	−0.854723	+	0.519084i	$0.826273\pi$
$128$	−0.108782	+	0.188416i	−0.00961505	+	0.0166538i
$129$	6.88453			0.606149
$130$	0.944851	+	1.63653i	0.0828689	+	0.143533i
$131$	−5.57665			−0.487234			−0.243617	−	0.969872i	$-0.578334\pi$
$131$	−5.57665			−0.487234			−0.243617	+	0.969872i	$0.578334\pi$
$132$	−1.36731	+	2.36825i	−0.119009	+	0.206130i
$133$	12.4109			1.07616
$134$	4.86949	−	7.34458i	0.420660	−	0.634475i
$135$	−0.343289			−0.0295456
$136$	−8.84830	+	15.3257i	−0.758735	+	1.31417i
$137$	−19.0923			−1.63116			−0.815582	−	0.578641i	$-0.803583\pi$
$137$	−19.0923			−1.63116			−0.815582	+	0.578641i	$0.803583\pi$
$138$	3.12868	+	5.41903i	0.266331	+	0.461299i
$139$	−10.2632			−0.870515			−0.435258	−	0.900306i	$-0.643343\pi$
$139$	−10.2632			−0.870515			−0.435258	+	0.900306i	$0.643343\pi$
$140$	−0.502724	+	0.870743i	−0.0424879	+	0.0735912i
$141$	3.30598	+	5.72613i	0.278414	+	0.482227i
$142$	5.95717			0.499915
$143$	16.6265			1.39038
$144$	0.805407	−	1.39501i	0.0671173	−	0.116251i
$145$	1.75015	+	3.03136i	0.145342	+	0.251740i
$146$	−2.02059	−	3.49976i	−0.167225	−	0.289642i
$147$	−2.56463	+	4.44206i	−0.211527	+	0.366375i
$148$	−9.19186			−0.755566
$149$	−4.91471			−0.402628			−0.201314	−	0.979527i	$-0.564521\pi$
$149$	−4.91471			−0.402628			−0.201314	+	0.979527i	$0.564521\pi$
$150$	−2.62802	+	4.55186i	−0.214577	+	0.371658i
$151$	−9.74003	+	16.8702i	−0.792633	+	1.37288i	0.131699	+	0.991290i	$0.457957\pi$
$151$	−9.74003	+	16.8702i	−0.792633	+	1.37288i	−0.924332	+	0.381590i	$0.875377\pi$
$152$	−5.44969	+	9.43913i	−0.442028	+	0.765615i
$153$	−2.89298	+	5.01079i	−0.233884	+	0.405099i
$154$	−6.09605	−	10.5587i	−0.491233	−	0.850841i
$155$	1.47570	+	2.55598i	0.118531	+	0.205301i
$156$	4.30001			0.344276
$157$	2.31674	−	4.01272i	0.184896	−	0.320250i	−0.758645	−	0.651504i	$-0.774138\pi$
$157$	2.31674	−	4.01272i	0.184896	−	0.320250i	0.943542	+	0.331254i	$0.107472\pi$
$158$	−1.63211			−0.129843
$159$	4.19796			0.332920
$160$	−0.752301	−	1.30302i	−0.0594746	−	0.103013i
$161$	20.2424			1.59532
$162$	0.538290	−	0.932346i	0.0422921	−	0.0732520i
$163$	1.93006	+	3.34296i	0.151174	+	0.261841i	0.931659	−	0.363333i	$-0.118361\pi$
$163$	1.93006	+	3.34296i	0.151174	+	0.261841i	−0.780485	+	0.625174i	$0.785028\pi$
$164$	0.916646	−	1.58768i	0.0715780	−	0.123977i
$165$	−0.558142	−	0.966730i	−0.0434513	−	0.0752598i
$166$	−1.13257	−	1.96167i	−0.0879046	−	0.152255i
$167$	10.4684	+	18.1318i	0.810069	+	1.40308i	0.912815	+	0.408373i	$0.133904\pi$
$167$	10.4684	+	18.1318i	0.810069	+	1.40308i	−0.102747	+	0.994708i	$0.532763\pi$
$168$	−5.32600	−	9.22490i	−0.410910	−	0.711716i
$169$	−6.57205	−	11.3831i	−0.505542	−	0.875625i
$170$	−1.06918	−	1.85188i	−0.0820026	−	0.142033i
$171$	−1.78179	+	3.08616i	−0.136257	+	0.236004i
$172$	2.89486	+	5.01404i	0.220731	+	0.382317i
$173$	7.64393	−	13.2397i	0.581157	−	1.00659i	−0.414185	−	0.910193i	$-0.635933\pi$
$173$	7.64393	−	13.2397i	0.581157	−	1.00659i	0.995343	−	0.0964014i	$-0.0307332\pi$
$174$	−10.9772			−0.832182
$175$	8.50156	+	14.7251i	0.642657	+	1.11311i
$176$	5.23794			0.394824
$177$	−4.93524			−0.370956
$178$	5.64792	−	9.78249i	0.423330	−	0.733228i
$179$	−6.89292			−0.515201			−0.257600	−	0.966252i	$-0.582932\pi$
$179$	−6.89292			−0.515201			−0.257600	+	0.966252i	$0.582932\pi$
$180$	−0.144349	−	0.250019i	−0.0107591	−	0.0186353i
$181$	−5.93393	−	10.2779i	−0.441066	−	0.763949i	0.556703	−	0.830712i	$-0.312066\pi$
$181$	−5.93393	−	10.2779i	−0.441066	−	0.763949i	−0.997769	+	0.0667631i	$0.978733\pi$
$182$	−9.58563	+	16.6028i	−0.710534	+	1.23068i
$183$	5.54693	−	9.60756i	0.410041	−	0.710211i
$184$	−8.88850	+	15.3953i	−0.655269	+	1.13496i
$185$	1.87608	−	3.24946i	0.137932	−	0.238905i
$186$	−9.25580			−0.678668
$187$	−18.8144			−1.37585
$188$	−2.78024	+	4.81552i	−0.202770	+	0.351208i
$189$	−1.74135	−	3.01611i	−0.126665	−	0.219390i
$190$	−0.658512	−	1.14058i	−0.0477735	−	0.0827461i
$191$	4.51623	−	7.82235i	0.326783	−	0.566005i	−0.655088	−	0.755552i	$-0.727369\pi$
$191$	4.51623	−	7.82235i	0.326783	−	0.566005i	0.981872	+	0.189547i	$0.0607020\pi$
$192$	7.94018			0.573033
$193$	12.2171			0.879403			0.439702	−	0.898144i	$-0.355084\pi$
$193$	12.2171			0.879403			0.439702	+	0.898144i	$0.355084\pi$
$194$	−1.79226	−	3.10429i	−0.128677	−	0.222875i
$195$	−0.877640	+	1.52012i	−0.0628491	+	0.108858i
$196$	−4.31357			−0.308112
$197$	−3.82664	−	6.62793i	−0.272637	−	0.472221i	0.696899	−	0.717169i	$-0.254562\pi$
$197$	−3.82664	−	6.62793i	−0.272637	−	0.472221i	−0.969536	+	0.244948i	$0.921229\pi$
$198$	3.50075			0.248788
$199$	9.71520	−	16.8272i	0.688693	−	1.19285i	−0.283568	−	0.958952i	$-0.591518\pi$
$199$	9.71520	−	16.8272i	0.688693	−	1.19285i	0.972261	−	0.233899i	$-0.0751484\pi$
$200$	−14.9322			−1.05587
$201$	8.16969	+	0.506056i	0.576246	+	0.0356944i
$202$	−2.93733			−0.206670
$203$	−17.7555	+	30.7535i	−1.24619	+	2.15847i
$204$	−4.86585			−0.340677
$205$	0.374178	+	0.648096i	0.0261338	+	0.0452650i
$206$	2.32456			0.161960
$207$	−2.90613	+	5.03356i	−0.201990	+	0.349857i
$208$	−4.11815	−	7.13285i	−0.285542	−	0.494574i
$209$	−11.5878			−0.801547
$210$	1.28713			0.0888206
$211$	−10.0124	+	17.3420i	−0.689281	+	1.19387i	0.282790	+	0.959182i	$0.408740\pi$
$211$	−10.0124	+	17.3420i	−0.689281	+	1.19387i	−0.972071	+	0.234688i	$0.924593\pi$
$212$	1.76519	+	3.05739i	0.121233	+	0.209983i
$213$	2.76671	+	4.79208i	0.189572	+	0.328348i
$214$	5.70629	−	9.88359i	0.390074	−	0.675628i
$215$	−2.36338			−0.161181
$216$	3.05854			0.208107
$217$	−14.9711	+	25.9307i	−1.01631	+	1.76029i
$218$	−2.81152	+	4.86970i	−0.190420	+	0.329818i
$219$	1.87686	−	3.25081i	0.126826	−	0.219670i
$220$	0.469383	−	0.812994i	0.0316458	−	0.0548121i
$221$	14.7922	+	25.6208i	0.995031	+	1.72344i
$222$	5.88352	+	10.1906i	0.394876	+	0.683945i
$223$	14.6218			0.979151			0.489576	−	0.871961i	$-0.337152\pi$
$223$	14.6218			0.979151			0.489576	+	0.871961i	$0.337152\pi$
$224$	7.63219	−	13.2193i	0.509947	−	0.883254i
$225$	−4.88215			−0.325477
$226$	−7.19814			−0.478813
$227$	0.515824	+	0.893434i	0.0342365	+	0.0592993i	0.882636	−	0.470057i	$-0.155767\pi$
$227$	0.515824	+	0.893434i	0.0342365	+	0.0592993i	−0.848399	+	0.529357i	$0.822433\pi$
$228$	−2.99689			−0.198474
$229$	−2.64969	+	4.58939i	−0.175096	+	0.303276i	−0.940195	−	0.340638i	$-0.889357\pi$
$229$	−2.64969	+	4.58939i	−0.175096	+	0.303276i	0.765098	+	0.643913i	$0.222690\pi$
$230$	−1.07404	−	1.86029i	−0.0708202	−	0.122664i
$231$	5.66241	−	9.80759i	0.372560	−	0.645292i
$232$	−15.5930	−	27.0079i	−1.02373	−	1.77316i
$233$	−5.93846	−	10.2857i	−0.389042	−	0.673840i	0.603279	−	0.797530i	$-0.293860\pi$
$233$	−5.93846	−	10.2857i	−0.389042	−	0.673840i	−0.992321	+	0.123690i	$0.960527\pi$
$234$	−2.75235	−	4.76721i	−0.179927	−	0.311642i
$235$	−1.13491	−	1.96572i	−0.0740331	−	0.128229i
$236$	−2.07521	−	3.59436i	−0.135084	−	0.233973i
$237$	−0.758004	−	1.31290i	−0.0492377	−	0.0852822i
$238$	10.8470	−	18.7875i	0.703106	−	1.21782i
$239$	0.489214	+	0.847344i	0.0316446	+	0.0548101i	0.881414	−	0.472345i	$-0.156592\pi$
$239$	0.489214	+	0.847344i	0.0316446	+	0.0548101i	−0.849769	+	0.527155i	$0.823259\pi$
$240$	−0.276487	+	0.478890i	−0.0178472	+	0.0309122i
$241$	−9.10790			−0.586691			−0.293346	−	0.956006i	$-0.594769\pi$
$241$	−9.10790			−0.586691			−0.293346	+	0.956006i	$0.594769\pi$
$242$	−0.229444	−	0.397409i	−0.0147492	−	0.0255464i
$243$	1.00000			0.0641500
$244$	9.32964			0.597269
$245$	0.880408	−	1.52491i	0.0562472	−	0.0974230i
$246$	−2.34691			−0.149633
$247$	9.11055	+	15.7799i	0.579690	+	1.00405i
$248$	−13.1477	−	22.7726i	−0.834882	−	1.44606i
$249$	1.05201	−	1.82213i	0.0666683	−	0.115473i
$250$	1.82611	−	3.16292i	0.115494	−	0.200041i
$251$	−6.65387	+	11.5248i	−0.419989	+	0.727442i	−0.995938	−	0.0900439i	$-0.971299\pi$
$251$	−6.65387	+	11.5248i	−0.419989	+	0.727442i	0.575949	+	0.817485i	$0.304633\pi$
$252$	1.46443	−	2.53647i	0.0922506	−	0.159783i
$253$	−18.8999			−1.18823
$254$	0.538166			0.0337675
$255$	0.993129	−	1.72015i	0.0621921	−	0.107720i
$256$	8.05729	+	13.9556i	0.503581	+	0.872227i
$257$	−9.93977	−	17.2162i	−0.620026	−	1.07392i	−0.989480	−	0.144667i	$-0.953789\pi$
$257$	−9.93977	−	17.2162i	−0.620026	−	1.07392i	0.369455	−	0.929249i	$-0.379545\pi$
$258$	3.70588	−	6.41877i	0.230718	−	0.399615i
$259$	38.0660			2.36531
$260$	−1.47615			−0.0915467
$261$	−5.09820	−	8.83033i	−0.315570	−	0.546584i
$262$	−3.00186	+	5.19937i	−0.185455	+	0.321218i
$263$	2.77387			0.171044			0.0855221	−	0.996336i	$-0.472744\pi$
$263$	2.77387			0.171044			0.0855221	+	0.996336i	$0.472744\pi$
$264$	4.97277	+	8.61309i	0.306053	+	0.530099i
$265$	−1.44111			−0.0885268
$266$	6.68069	−	11.5713i	0.409619	−	0.709481i
$267$	10.4923			0.642120
$268$	3.06669	+	6.16282i	0.187328	+	0.376454i
$269$	−6.16204			−0.375706			−0.187853	−	0.982197i	$-0.560153\pi$
$269$	−6.16204			−0.375706			−0.187853	+	0.982197i	$0.560153\pi$
$270$	−0.184789	+	0.320064i	−0.0112459	+	0.0194785i
$271$	18.5823			1.12880			0.564398	−	0.825503i	$-0.309109\pi$
$271$	18.5823			1.12880			0.564398	+	0.825503i	$0.309109\pi$
$272$	4.66006	+	8.07146i	0.282558	+	0.489404i
$273$	−17.8075			−1.07776
$274$	−10.2772	+	17.8006i	−0.620868	+	1.07537i
$275$	−7.93772	−	13.7485i	−0.478663	−	0.829068i
$276$	−4.88795			−0.294220
$277$	24.5550			1.47537			0.737685	−	0.675146i	$-0.235919\pi$
$277$	24.5550			1.47537			0.737685	+	0.675146i	$0.235919\pi$
$278$	−5.52460	+	9.56888i	−0.331343	+	0.573903i
$279$	−4.29870	−	7.44557i	−0.257356	−	0.445755i
$280$	1.82836	+	3.16680i	0.109265	+	0.189253i
$281$	11.5331	−	19.9759i	0.688005	−	1.19166i	−0.284477	−	0.958683i	$-0.591820\pi$
$281$	11.5331	−	19.9759i	0.688005	−	1.19166i	0.972482	−	0.232977i	$-0.0748467\pi$
$282$	7.11831			0.423889
$283$	25.5746			1.52025			0.760127	−	0.649775i	$-0.225137\pi$
$283$	25.5746			1.52025			0.760127	+	0.649775i	$0.225137\pi$
$284$	−2.32673	+	4.03001i	−0.138066	+	0.239137i
$285$	0.611670	−	1.05944i	0.0362322	−	0.0627560i
$286$	8.94990	−	15.5017i	0.529218	−	0.916633i
$287$	−3.79609	+	6.57501i	−0.224076	+	0.388111i
$288$	2.19145	+	3.79571i	0.129133	+	0.223664i
$289$	−8.23870	−	14.2698i	−0.484629	−	0.839402i
$290$	3.76836			0.221286
$291$	1.66477	−	2.88347i	0.0975907	−	0.169032i
$292$	3.15678			0.184736
$293$	9.44665			0.551879			0.275940	−	0.961175i	$-0.411011\pi$
$293$	9.44665			0.551879			0.275940	+	0.961175i	$0.411011\pi$
$294$	2.76103	+	4.78224i	0.161026	+	0.278906i
$295$	1.69421			0.0986410
$296$	−16.7149	+	28.9511i	−0.971536	+	1.68275i
$297$	1.62587	+	2.81608i	0.0943423	+	0.163406i
$298$	−2.64554	+	4.58221i	−0.153252	+	0.265440i
$299$	14.8594	+	25.7372i	0.859342	+	1.48842i
$300$	−2.05288	−	3.55570i	−0.118523	−	0.205288i
$301$	−11.9884	−	20.7645i	−0.691001	−	1.19685i
$302$	10.4859	+	18.1622i	0.603398	+	1.04512i
$303$	−1.36420	−	2.36286i	−0.0783710	−	0.135743i
$304$	2.87014	+	4.97123i	0.164614	+	0.285120i
$305$	−1.90420	+	3.29817i	−0.109034	+	0.188853i
$306$	3.11453	+	5.39452i	0.178046	+	0.308384i
$307$	0.489214	−	0.847344i	0.0279209	−	0.0483605i	−0.851727	−	0.523985i	$-0.824445\pi$
$307$	0.489214	−	0.847344i	0.0279209	−	0.0483605i	0.879648	+	0.475625i	$0.157778\pi$
$308$	9.52389			0.542674
$309$	1.07960	+	1.86993i	0.0614165	+	0.106377i
$310$	3.17741			0.180465
$311$	−18.7178			−1.06139			−0.530696	−	0.847562i	$-0.678069\pi$
$311$	−18.7178			−1.06139			−0.530696	+	0.847562i	$0.678069\pi$
$312$	7.81935	−	13.5435i	0.442684	−	0.766750i
$313$	9.18556			0.519198			0.259599	−	0.965716i	$-0.416410\pi$
$313$	9.18556			0.519198			0.259599	+	0.965716i	$0.416410\pi$
$314$	−2.49416	−	4.32001i	−0.140754	−	0.243793i
$315$	0.597787	+	1.03540i	0.0336815	+	0.0583381i
$316$	0.637462	−	1.10412i	0.0358600	−	0.0621114i
$317$	−12.2411	+	21.2022i	−0.687528	+	1.19083i	0.285107	+	0.958496i	$0.407971\pi$
$317$	−12.2411	+	21.2022i	−0.687528	+	1.19083i	−0.972635	+	0.232338i	$0.925362\pi$
$318$	2.25972	−	3.91395i	0.126719	−	0.219483i
$319$	16.5780	−	28.7139i	0.928188	−	1.60767i
$320$	−2.72578			−0.152375
$321$	10.6008			0.591677
$322$	10.8963	−	18.8729i	0.607226	−	1.05175i
$323$	−10.3094	−	17.8564i	−0.573630	−	0.993557i
$324$	0.420487	+	0.728305i	0.0233604	+	0.0404614i
$325$	−12.4815	+	21.6187i	−0.692351	+	1.19919i
$326$	4.15573			0.230164
$327$	−5.22306			−0.288836
$328$	−3.33375	−	5.77422i	−0.184075	−	0.318828i
$329$	11.5138	−	19.9424i	0.634774	−	1.09946i
$330$	−1.20177			−0.0661552
$331$	−5.48861	−	9.50655i	−0.301681	−	0.522527i	0.674836	−	0.737968i	$-0.264214\pi$
$331$	−5.48861	−	9.50655i	−0.301681	−	0.522527i	−0.976517	+	0.215441i	$0.930881\pi$
$332$	1.76942			0.0971097
$333$	−5.46501	+	9.46567i	−0.299481	+	0.518715i
$334$	22.5401			1.23334
$335$	−2.80457	−	0.173723i	−0.153230	−	0.00949152i
$336$	−5.61000			−0.306050
$337$	−1.84882	+	3.20224i	−0.100711	+	0.174437i	−0.911978	−	0.410239i	$-0.865445\pi$
$337$	−1.84882	+	3.20224i	−0.100711	+	0.174437i	0.811267	+	0.584677i	$0.198779\pi$
$338$	−14.1507			−0.769695
$339$	−3.34306	−	5.79034i	−0.181570	−	0.314488i
$340$	1.67039			0.0905897
$341$	13.9782	−	24.2110i	0.756963	−	1.31110i
$342$	1.91825	+	3.32250i	0.103727	+	0.179660i
$343$	−6.51526			−0.351791
$344$	21.0566			1.13530
$345$	0.997641	−	1.72797i	0.0537112	−	0.0930305i
$346$	−8.22931	−	14.2536i	−0.442410	−	0.766277i
$347$	7.99087	+	13.8406i	0.428972	+	0.743002i	0.996782	−	0.0801580i	$-0.0255425\pi$
$347$	7.99087	+	13.8406i	0.428972	+	0.743002i	−0.567810	+	0.823160i	$0.692209\pi$
$348$	4.28745	−	7.42608i	0.229831	−	0.398080i
$349$	34.6373			1.85409			0.927045	−	0.374949i	$-0.122340\pi$
$349$	34.6373			1.85409			0.927045	+	0.374949i	$0.122340\pi$
$350$	18.3052			0.978455
$351$	2.55656	−	4.42810i	0.136459	−	0.236355i
$352$	−7.12601	+	12.3426i	−0.379818	+	0.657864i
$353$	7.76875	−	13.4559i	0.413489	−	0.716184i	−0.581780	−	0.813347i	$-0.697643\pi$
$353$	7.76875	−	13.4559i	0.413489	−	0.716184i	0.995269	+	0.0971626i	$0.0309767\pi$
$354$	−2.65659	+	4.60136i	−0.141196	+	0.244559i
$355$	−0.949780	−	1.64507i	−0.0504091	−	0.0873111i
$356$	4.41189	+	7.64162i	0.233830	+	0.405005i
$357$	20.1508			1.06649
$358$	−3.71039	+	6.42659i	−0.196100	+	0.339656i
$359$	−34.6365			−1.82805			−0.914023	−	0.405663i	$-0.867041\pi$
$359$	−34.6365			−1.82805			−0.914023	+	0.405663i	$0.867041\pi$
$360$	−1.04996			−0.0553379
$361$	3.15042	+	5.45668i	0.165811	+	0.287194i
$362$	−12.7767			−0.671529
$363$	0.213123	−	0.369140i	0.0111861	−	0.0193748i
$364$	−7.48784	−	12.9693i	−0.392469	−	0.679777i
$365$	−0.644305	+	1.11597i	−0.0337244	+	0.0584125i
$366$	−5.97171	−	10.3433i	−0.312146	−	0.540654i
$367$	−9.09658	−	15.7557i	−0.474837	−	0.822442i	0.524747	−	0.851258i	$-0.324160\pi$
$367$	−9.09658	−	15.7557i	−0.474837	−	0.822442i	−0.999585	+	0.0288155i	$0.990826\pi$
$368$	4.68123	+	8.10813i	0.244026	+	0.422666i
$369$	−1.08998	−	1.88790i	−0.0567422	−	0.0982803i
$370$	−2.01975	−	3.49831i	−0.105002	−	0.181868i
$371$	−7.31013	−	12.6615i	−0.379523	−	0.657353i
$372$	3.61510	−	6.26153i	0.187434	−	0.324645i
$373$	10.7838	+	18.6782i	0.558366	+	0.967118i	0.997633	+	0.0687618i	$0.0219048\pi$
$373$	10.7838	+	18.6782i	0.558366	+	0.967118i	−0.439267	+	0.898357i	$0.644762\pi$
$374$	−10.1276	+	17.5415i	−0.523686	+	0.907051i
$375$	3.39243			0.175185
$376$	10.1115	+	17.5136i	0.521459	+	0.903194i
$377$	−52.1355			−2.68511
$378$	−3.74942			−0.192849
$379$	−13.4539	+	23.3029i	−0.691081	+	1.19699i	0.280403	+	0.959882i	$0.409532\pi$
$379$	−13.4539	+	23.3029i	−0.691081	+	1.19699i	−0.971484	+	0.237105i	$0.923801\pi$
$380$	1.02880			0.0527762
$381$	0.249942	+	0.432913i	0.0128049	+	0.0221788i
$382$	−4.86209	−	8.42139i	−0.248766	−	0.430876i
$383$	−3.95724	+	6.85415i	−0.202206	+	0.350231i	−0.949239	−	0.314556i	$-0.898144\pi$
$383$	−3.95724	+	6.85415i	−0.202206	+	0.350231i	0.747033	+	0.664787i	$0.231478\pi$
$384$	−0.108782	+	0.188416i	−0.00555125	+	0.00961505i
$385$	−1.94384	+	3.36684i	−0.0990675	+	0.171590i
$386$	6.57632	−	11.3905i	0.334726	−	0.579763i
$387$	6.88453			0.349961
$388$	2.80006			0.142152
$389$	−13.3544	+	23.1306i	−0.677097	+	1.17277i	0.298754	+	0.954330i	$0.403429\pi$
$389$	−13.3544	+	23.1306i	−0.677097	+	1.17277i	−0.975851	+	0.218436i	$0.929904\pi$
$390$	0.944851	+	1.63653i	0.0478444	+	0.0828689i
$391$	−16.8147	−	29.1240i	−0.850358	−	1.47286i
$392$	−7.84401	+	13.5862i	−0.396182	+	0.686208i
$393$	−5.57665			−0.281305
$394$	−8.23937			−0.415093
$395$	0.260214	+	0.450705i	0.0130928	+	0.0226774i
$396$	−1.36731	+	2.36825i	−0.0687099	+	0.119009i
$397$	−38.8971			−1.95219			−0.976094	−	0.217349i	$-0.930259\pi$
$397$	−38.8971			−1.95219			−0.976094	+	0.217349i	$0.930259\pi$
$398$	−10.4592	−	18.1159i	−0.524272	−	0.908066i
$399$	12.4109			0.621324
$400$	−3.93212	+	6.81063i	−0.196606	+	0.340532i
$401$	32.0237			1.59919			0.799593	−	0.600543i	$-0.205049\pi$
$401$	32.0237			1.59919			0.799593	+	0.600543i	$0.205049\pi$
$402$	4.86949	−	7.34458i	0.242868	−	0.366314i
$403$	−43.9596			−2.18979
$404$	1.14725	−	1.98710i	0.0570780	−	0.0988620i
$405$	−0.343289			−0.0170582
$406$	19.1153	+	33.1086i	0.948674	+	1.64315i
$407$	−35.5415			−1.76172
$408$	−8.84830	+	15.3257i	−0.438056	+	0.758735i
$409$	−1.71772	−	2.97518i	−0.0849359	−	0.147113i	0.820428	−	0.571750i	$-0.193735\pi$
$409$	−1.71772	−	2.97518i	−0.0849359	−	0.147113i	−0.905364	+	0.424637i	$0.860402\pi$
$410$	0.805667			0.0397890
$411$	−19.0923			−0.941753
$412$	−0.907919	+	1.57256i	−0.0447300	+	0.0774746i
$413$	8.59400	+	14.8853i	0.422883	+	0.732455i
$414$	3.12868	+	5.41903i	0.153766	+	0.266331i
$415$	−0.361143	+	0.625518i	−0.0177278	+	0.0307055i
$416$	22.4104			1.09876
$417$	−10.2632			−0.502592
$418$	−6.23762	+	10.8039i	−0.305092	+	0.528435i
$419$	8.38259	−	14.5191i	0.409516	−	0.709303i	−0.585319	−	0.810803i	$-0.699031\pi$
$419$	8.38259	−	14.5191i	0.409516	−	0.709303i	0.994836	+	0.101500i	$0.0323641\pi$
$420$	−0.502724	+	0.870743i	−0.0245304	+	0.0424879i
$421$	−2.69702	+	4.67138i	−0.131445	+	0.227669i	−0.924234	−	0.381827i	$-0.875295\pi$
$421$	−2.69702	+	4.67138i	−0.131445	+	0.227669i	0.792789	+	0.609496i	$0.208628\pi$
$422$	10.7791	+	18.6700i	0.524720	+	0.908842i
$423$	3.30598	+	5.72613i	0.160742	+	0.278414i
$424$	12.8396			0.623547
$425$	14.1240	−	24.4635i	0.685114	−	1.18665i
$426$	5.95717			0.288626
$427$	−38.6366			−1.86976
$428$	4.45749	+	7.72059i	0.215461	+	0.373189i
$429$	16.6265			0.802736
$430$	−1.27219	+	2.20349i	−0.0613503	+	0.106262i
$431$	−0.483947	−	0.838221i	−0.0233109	−	0.0403757i	0.854135	−	0.520052i	$-0.174087\pi$
$431$	−0.483947	−	0.838221i	−0.0233109	−	0.0403757i	−0.877446	+	0.479676i	$0.840754\pi$
$432$	0.805407	−	1.39501i	0.0387502	−	0.0671173i
$433$	7.37386	+	12.7719i	0.354365	+	0.613778i	0.987009	−	0.160665i	$-0.0513637\pi$
$433$	7.37386	+	12.7719i	0.354365	+	0.613778i	−0.632644	+	0.774443i	$0.718030\pi$
$434$	16.1176	+	27.9165i	0.773670	+	1.34004i
$435$	1.75015	+	3.03136i	0.0839135	+	0.145342i
$436$	−2.19623	−	3.80398i	−0.105180	−	0.182178i
$437$	−10.3562	−	17.9375i	−0.495406	−	0.858069i
$438$	−2.02059	−	3.49976i	−0.0965475	−	0.167225i
$439$	−5.95169	+	10.3086i	−0.284058	+	0.492004i	−0.972380	−	0.233402i	$-0.925014\pi$
$439$	−5.95169	+	10.3086i	−0.284058	+	0.492004i	0.688322	+	0.725405i	$0.258348\pi$
$440$	−1.70710	−	2.95678i	−0.0813827	−	0.140959i
$441$	−2.56463	+	4.44206i	−0.122125	+	0.211527i
$442$	31.8500			1.51495
$443$	−1.14477	−	1.98280i	−0.0543897	−	0.0942057i	0.837549	−	0.546363i	$-0.183988\pi$
$443$	−1.14477	−	1.98280i	−0.0543897	−	0.0942057i	−0.891938	+	0.452157i	$0.850655\pi$
$444$	−9.19186			−0.436226
$445$	−3.60190			−0.170746
$446$	7.87080	−	13.6326i	0.372693	−	0.645523i
$447$	−4.91471			−0.232458
$448$	−13.8267	−	23.9485i	−0.653248	−	1.13146i
$449$	−2.47544	−	4.28759i	−0.116823	−	0.202344i	0.801684	−	0.597748i	$-0.203938\pi$
$449$	−2.47544	−	4.28759i	−0.116823	−	0.202344i	−0.918507	+	0.395404i	$0.870604\pi$
$450$	−2.62802	+	4.55186i	−0.123886	+	0.214577i
$451$	3.54433	−	6.13895i	0.166896	−	0.289072i
$452$	2.81142	−	4.86953i	0.132238	−	0.229043i
$453$	−9.74003	+	16.8702i	−0.457627	+	0.792633i
$454$	1.11065			0.0521255
$455$	6.11313			0.286588
$456$	−5.44969	+	9.43913i	−0.255205	+	0.442028i
$457$	−4.16515	−	7.21425i	−0.194837	−	0.337468i	0.752010	−	0.659152i	$-0.229085\pi$
$457$	−4.16515	−	7.21425i	−0.194837	−	0.337468i	−0.946847	+	0.321684i	$0.895751\pi$
$458$	2.85260	+	4.94085i	0.133293	+	0.230871i
$459$	−2.89298	+	5.01079i	−0.135033	+	0.233884i
$460$	1.67798			0.0782362
$461$	−31.1720			−1.45182			−0.725911	−	0.687788i	$-0.758582\pi$
$461$	−31.1720			−1.45182			−0.725911	+	0.687788i	$0.758582\pi$
$462$	−6.09605	−	10.5587i	−0.283614	−	0.491233i
$463$	6.45307	−	11.1770i	0.299899	−	0.519441i	−0.676213	−	0.736706i	$-0.736380\pi$
$463$	6.45307	−	11.1770i	0.299899	−	0.519441i	0.976113	+	0.217265i	$0.0697136\pi$
$464$	−16.4245			−0.762488
$465$	1.47570	+	2.55598i	0.0684338	+	0.118531i
$466$	−12.7865			−0.592322
$467$	−10.1508	+	17.5816i	−0.469721	+	0.813581i	−0.999401	−	0.0346170i	$-0.988979\pi$
$467$	−10.1508	+	17.5816i	−0.469721	+	0.813581i	0.529680	+	0.848198i	$0.322312\pi$
$468$	4.30001			0.198768
$469$	−12.7000	−	25.5219i	−0.586432	−	1.17849i
$470$	−2.44364			−0.112717
$471$	2.31674	−	4.01272i	0.106750	−	0.184896i
$472$	−15.0946			−0.694787
$473$	11.1933	+	19.3874i	0.514670	+	0.891434i
$474$	−1.63211			−0.0749651
$475$	8.69899	−	15.0671i	0.399137	−	0.691326i
$476$	8.47316	+	14.6759i	0.388367	+	0.672671i
$477$	4.19796			0.192211
$478$	1.05336			0.0481794
$479$	−5.34746	+	9.26207i	−0.244332	+	0.423195i	−0.961943	−	0.273248i	$-0.911902\pi$
$479$	−5.34746	+	9.26207i	−0.244332	+	0.423195i	0.717612	+	0.696443i	$0.245235\pi$
$480$	−0.752301	−	1.30302i	−0.0343377	−	0.0594746i
$481$	27.9433	+	48.3992i	1.27410	+	2.20681i
$482$	−4.90269	+	8.49172i	−0.223312	+	0.386787i
$483$	20.2424			0.921060
$484$	0.358462			0.0162937
$485$	−0.571498	+	0.989864i	−0.0259504	+	0.0449474i
$486$	0.538290	−	0.932346i	0.0244173	−	0.0422921i
$487$	7.93279	−	13.7400i	0.359469	−	0.622618i	−0.628403	−	0.777888i	$-0.716291\pi$
$487$	7.93279	−	13.7400i	0.359469	−	0.622618i	0.987872	+	0.155269i	$0.0496245\pi$
$488$	16.9655	−	29.3851i	0.767991	−	1.33020i
$489$	1.93006	+	3.34296i	0.0872802	+	0.151174i
$490$	−0.947830	−	1.64169i	−0.0428186	−	0.0741640i
$491$	8.06653			0.364037			0.182019	−	0.983295i	$-0.441737\pi$
$491$	8.06653			0.364037			0.182019	+	0.983295i	$0.441737\pi$
$492$	0.916646	−	1.58768i	0.0413256	−	0.0715780i
$493$	58.9960			2.65704
$494$	19.6165			0.882587
$495$	−0.558142	−	0.966730i	−0.0250866	−	0.0434513i
$496$	−13.8488			−0.621830
$497$	9.63564	−	16.6894i	0.432217	−	0.748622i
$498$	−1.13257	−	1.96167i	−0.0507518	−	0.0879046i
$499$	4.96639	−	8.60205i	0.222326	−	0.385081i	−0.733188	−	0.680026i	$-0.761968\pi$
$499$	4.96639	−	8.60205i	0.222326	−	0.385081i	0.955514	+	0.294946i	$0.0953016\pi$
$500$	1.42647	+	2.47073i	0.0637939	+	0.110494i
$501$	10.4684	+	18.1318i	0.467693	+	0.810069i
$502$	7.16343	+	12.4074i	0.319719	+	0.553770i
$503$	3.05075	+	5.28406i	0.136026	+	0.235605i	0.925989	−	0.377550i	$-0.123233\pi$
$503$	3.05075	+	5.28406i	0.136026	+	0.235605i	−0.789963	+	0.613155i	$0.789900\pi$
$504$	−5.32600	−	9.22490i	−0.237239	−	0.410910i
$505$	0.468313	+	0.811142i	0.0208397	+	0.0360954i
$506$	−10.1736	+	17.6212i	−0.452273	+	0.783360i
$507$	−6.57205	−	11.3831i	−0.291875	−	0.505542i
$508$	−0.210195	+	0.364068i	−0.00932589	+	0.0161529i
$509$	−25.2678			−1.11998			−0.559989	−	0.828500i	$-0.689195\pi$
$509$	−25.2678			−1.11998			−0.559989	+	0.828500i	$0.689195\pi$
$510$	−1.06918	−	1.85188i	−0.0473442	−	0.0820026i
$511$	−13.0731			−0.578320
$512$	16.9135			0.747479
$513$	−1.78179	+	3.08616i	−0.0786681	+	0.136257i
$514$	−21.4019			−0.943998
$515$	−0.370616	−	0.641926i	−0.0163313	−	0.0282866i
$516$	2.89486	+	5.01404i	0.127439	+	0.220731i
$517$	−10.7502	+	18.6198i	−0.472792	+	0.818899i
$518$	20.4906	−	35.4907i	0.900305	−	1.55937i
$519$	7.64393	−	13.2397i	0.335531	−	0.581157i
$520$	−2.68430	+	4.64934i	−0.117714	+	0.203887i
$521$	−4.07383			−0.178478			−0.0892389	−	0.996010i	$-0.528443\pi$
$521$	−4.07383			−0.178478			−0.0892389	+	0.996010i	$0.528443\pi$
$522$	−10.9772			−0.480461
$523$	−10.3091	+	17.8560i	−0.450788	+	0.780787i	−0.998435	−	0.0559221i	$-0.982190\pi$
$523$	−10.3091	+	17.8560i	−0.450788	+	0.780787i	0.547648	+	0.836709i	$0.315523\pi$
$524$	−2.34491	−	4.06150i	−0.102438	−	0.177427i
$525$	8.50156	+	14.7251i	0.371038	+	0.642657i
$526$	1.49315	−	2.58621i	0.0651043	−	0.112764i
$527$	49.7443			2.16689
$528$	5.23794			0.227952
$529$	−5.39115	−	9.33775i	−0.234398	−	0.405989i
$530$	−0.775737	+	1.34362i	−0.0336958	+	0.0583629i
$531$	−4.93524			−0.214171
$532$	5.21864	+	9.03895i	0.226257	+	0.391888i
$533$	−11.1464			−0.482805
$534$	5.64792	−	9.78249i	0.244409	−	0.423330i
$535$	−3.63913			−0.157333
$536$	24.9873	+	1.54779i	1.07929	+	0.0668544i
$537$	−6.89292			−0.297451
$538$	−3.31697	+	5.74516i	−0.143005	+	0.247691i
$539$	−16.6790			−0.718413
$540$	−0.144349	−	0.250019i	−0.00621177	−	0.0107591i
$541$	−6.82424			−0.293397			−0.146698	−	0.989181i	$-0.546865\pi$
$541$	−6.82424			−0.293397			−0.146698	+	0.989181i	$0.546865\pi$
$542$	10.0027	−	17.3251i	0.429652	−	0.744179i
$543$	−5.93393	−	10.2779i	−0.254650	−	0.441066i
$544$	−25.3593			−1.08727
$545$	1.79302			0.0768045
$546$	−9.58563	+	16.6028i	−0.410227	+	0.710534i
$547$	−6.56745	−	11.3752i	−0.280804	−	0.486367i	0.690779	−	0.723066i	$-0.257268\pi$
$547$	−6.56745	−	11.3752i	−0.280804	−	0.486367i	−0.971583	+	0.236699i	$0.923934\pi$
$548$	−8.02806	−	13.9050i	−0.342942	−	0.593992i
$549$	5.54693	−	9.60756i	0.236737	−	0.410041i
$550$	−17.0912			−0.728771
$551$	36.3358			1.54796
$552$	−8.88850	+	15.3953i	−0.378320	+	0.655269i
$553$	−2.63991	+	4.57245i	−0.112260	+	0.194441i
$554$	13.2177	−	22.8938i	0.561568	−	0.972664i
$555$	1.87608	−	3.24946i	0.0796350	−	0.137932i
$556$	−4.31555	−	7.47476i	−0.183020	−	0.317000i
$557$	5.39138	+	9.33815i	0.228440	+	0.395670i	0.957346	−	0.288944i	$-0.0933041\pi$
$557$	5.39138	+	9.33815i	0.228440	+	0.395670i	−0.728906	+	0.684614i	$0.759971\pi$
$558$	−9.25580			−0.391829
$559$	17.6008	−	30.4854i	0.744433	−	1.28940i
$560$	1.92585			0.0813820
$561$	−18.8144			−0.794345
$562$	−12.4163	−	21.5056i	−0.523749	−	0.907160i
$563$	−16.5207			−0.696264			−0.348132	−	0.937446i	$-0.613184\pi$
$563$	−16.5207			−0.696264			−0.348132	+	0.937446i	$0.613184\pi$
$564$	−2.78024	+	4.81552i	−0.117069	+	0.202770i
$565$	1.14763	+	1.98776i	0.0482813	+	0.0836257i
$566$	13.7666	−	23.8444i	0.578652	−	1.00225i
$567$	−1.74135	−	3.01611i	−0.0731300	−	0.126665i
$568$	8.46208	+	14.6568i	0.355061	+	0.614984i
$569$	15.7940	+	27.3561i	0.662120	+	1.14683i	0.980058	+	0.198714i	$0.0636765\pi$
$569$	15.7940	+	27.3561i	0.662120	+	1.14683i	−0.317937	+	0.948112i	$0.602990\pi$
$570$	−0.658512	−	1.14058i	−0.0275820	−	0.0477735i
$571$	3.40362	+	5.89523i	0.142437	+	0.246708i	0.928414	−	0.371548i	$-0.121173\pi$
$571$	3.40362	+	5.89523i	0.142437	+	0.246708i	−0.785977	+	0.618256i	$0.787840\pi$
$572$	6.99124	+	12.1092i	0.292318	+	0.506310i
$573$	4.51623	−	7.82235i	0.188668	−	0.326783i
$574$	4.08679	+	7.07853i	0.170579	+	0.295452i
$575$	14.1882	−	24.5746i	0.591687	−	1.02483i
$576$	7.94018			0.330841
$577$	−3.29747	−	5.71139i	−0.137276	−	0.237768i	0.789189	−	0.614151i	$-0.210501\pi$
$577$	−3.29747	−	5.71139i	−0.137276	−	0.237768i	−0.926464	+	0.376382i	$0.877168\pi$
$578$	−17.7392			−0.737855
$579$	12.2171			0.507724
$580$	−1.47183	+	2.54929i	−0.0611146	+	0.105854i
$581$	−7.32768			−0.304003
$582$	−1.79226	−	3.10429i	−0.0742917	−	0.128677i
$583$	6.82531	+	11.8218i	0.282676	+	0.489608i
$584$	5.74044	−	9.94274i	0.237541	−	0.411433i
$585$	−0.877640	+	1.52012i	−0.0362860	+	0.0628491i
$586$	5.08504	−	8.80755i	0.210061	−	0.363836i
$587$	9.61753	−	16.6581i	0.396958	−	0.687552i	−0.596391	−	0.802694i	$-0.703399\pi$
$587$	9.61753	−	16.6581i	0.396958	−	0.687552i	0.993349	+	0.115143i	$0.0367325\pi$
$588$	−4.31357			−0.177889
$589$	30.6376			1.26240
$590$	0.911979	−	1.57959i	0.0375456	−	0.0650309i
$591$	−3.82664	−	6.62793i	−0.157407	−	0.272637i
$592$	8.80311	+	15.2474i	0.361806	+	0.626666i
$593$	−3.73635	+	6.47154i	−0.153433	+	0.265754i	−0.932487	−	0.361202i	$-0.882366\pi$
$593$	−3.73635	+	6.47154i	−0.153433	+	0.265754i	0.779054	+	0.626957i	$0.215700\pi$
$594$	3.50075			0.143638
$595$	−6.91755			−0.283592
$596$	−2.06657	−	3.57941i	−0.0846500	−	0.146618i
$597$	9.71520	−	16.8272i	0.397617	−	0.688693i
$598$	31.9947			1.30836
$599$	−2.34541	−	4.06237i	−0.0958308	−	0.165984i	0.814124	−	0.580691i	$-0.197217\pi$
$599$	−2.34541	−	4.06237i	−0.0958308	−	0.165984i	−0.909955	+	0.414707i	$0.863884\pi$
$600$	−14.9322			−0.609606
$601$	−2.45628	+	4.25440i	−0.100194	+	0.173541i	−0.911764	−	0.410714i	$-0.865280\pi$
$601$	−2.45628	+	4.25440i	−0.100194	+	0.173541i	0.811571	+	0.584254i	$0.198613\pi$
$602$	−25.8130			−1.05206
$603$	8.16969	+	0.506056i	0.332696	+	0.0206082i
$604$	−16.3822			−0.666583
$605$	−0.0731627	+	0.126722i	−0.00297449	+	0.00515197i
$606$	−2.93733			−0.119321
$607$	1.32795	+	2.30007i	0.0538998	+	0.0933571i	0.891716	−	0.452595i	$-0.149502\pi$
$607$	1.32795	+	2.30007i	0.0538998	+	0.0933571i	−0.837817	+	0.545952i	$0.816168\pi$
$608$	−15.6189			−0.633429
$609$	−17.7555	+	30.7535i	−0.719490	+	1.24619i
$610$	2.05002	+	3.55074i	0.0830030	+	0.143765i
$611$	33.8078			1.36772
$612$	−4.86585			−0.196690
$613$	−2.74072	+	4.74706i	−0.110697	+	0.191732i	−0.916051	−	0.401061i	$-0.868642\pi$
$613$	−2.74072	+	4.74706i	−0.110697	+	0.191732i	0.805355	+	0.592793i	$0.201975\pi$
$614$	−0.526679	−	0.912234i	−0.0212550	−	0.0368148i
$615$	0.374178	+	0.648096i	0.0150883	+	0.0261338i
$616$	17.3187	−	29.9969i	0.697791	−	1.20861i
$617$	−21.0548			−0.847636			−0.423818	−	0.905747i	$-0.639310\pi$
$617$	−21.0548			−0.847636			−0.423818	+	0.905747i	$0.639310\pi$
$618$	2.32456			0.0935076
$619$	−4.28484	+	7.42156i	−0.172222	+	0.298298i	−0.939196	−	0.343380i	$-0.888428\pi$
$619$	−4.28484	+	7.42156i	−0.172222	+	0.298298i	0.766974	+	0.641678i	$0.221761\pi$
$620$	−1.24102	+	2.14951i	−0.0498407	+	0.0863265i
$621$	−2.90613	+	5.03356i	−0.116619	+	0.201990i
$622$	−10.0756	+	17.4515i	−0.403996	+	0.699742i
$623$	−18.2709	−	31.6461i	−0.732007	−	1.26787i
$624$	−4.11815	−	7.13285i	−0.164858	−	0.285542i
$625$	23.2462			0.929847
$626$	4.94450	−	8.56412i	0.197622	−	0.342291i
$627$	−11.5878			−0.462773
$628$	3.89664			0.155493
$629$	−31.6203	−	54.7680i	−1.26079	−	2.18374i
$630$	1.28713			0.0512806
$631$	−3.59219	+	6.22186i	−0.143003	+	0.247688i	−0.928626	−	0.371017i	$-0.879009\pi$
$631$	−3.59219	+	6.22186i	−0.143003	+	0.247688i	0.785623	+	0.618705i	$0.212343\pi$
$632$	−2.31838	−	4.01556i	−0.0922204	−	0.159730i
$633$	−10.0124	+	17.3420i	−0.397957	+	0.689281i
$634$	13.1785	+	22.8259i	0.523386	+	0.906531i
$635$	−0.0858024	−	0.148614i	−0.00340496	−	0.00589757i
$636$	1.76519	+	3.05739i	0.0699942	+	0.121233i
$637$	13.1133	+	22.7128i	0.519567	+	0.899916i
$638$	−17.8475	−	30.9128i	−0.706590	−	1.22385i
$639$	2.76671	+	4.79208i	0.109449	+	0.189572i
$640$	0.0373436	−	0.0646810i	0.00147614	−	0.00255674i
$641$	23.1021	+	40.0140i	0.912477	+	1.58046i	0.810554	+	0.585664i	$0.199166\pi$
$641$	23.1021	+	40.0140i	0.912477	+	1.58046i	0.101923	+	0.994792i	$0.467501\pi$
$642$	5.70629	−	9.88359i	0.225209	−	0.390074i
$643$	11.1017			0.437808			0.218904	−	0.975746i	$-0.429752\pi$
$643$	11.1017			0.437808			0.218904	+	0.975746i	$0.429752\pi$
$644$	8.51166	+	14.7426i	0.335406	+	0.580941i
$645$	−2.36338			−0.0930582
$646$	−22.1978			−0.873361
$647$	21.2070	−	36.7317i	0.833735	−	1.44407i	−0.0613210	−	0.998118i	$-0.519531\pi$
$647$	21.2070	−	36.7317i	0.833735	−	1.44407i	0.895056	−	0.445953i	$-0.147135\pi$
$648$	3.05854			0.120151
$649$	−8.02404	−	13.8980i	−0.314971	−	0.545546i
$650$	13.4374	+	23.2742i	0.527058	+	0.912891i
$651$	−14.9711	+	25.9307i	−0.586764	+	1.01631i
$652$	−1.62313	+	2.81134i	−0.0635666	+	0.110101i
$653$	−23.0014	+	39.8395i	−0.900113	+	1.55904i	−0.0727668	+	0.997349i	$0.523183\pi$
$653$	−23.0014	+	39.8395i	−0.900113	+	1.55904i	−0.827346	+	0.561692i	$0.810150\pi$
$654$	−2.81152	+	4.86970i	−0.109939	+	0.190420i
$655$	1.91440			0.0748018
$656$	−3.51152			−0.137102
$657$	1.87686	−	3.25081i	0.0732232	−	0.126826i
$658$	−12.3955	−	21.4696i	−0.483227	−	0.836973i
$659$	−7.33225	−	12.6998i	−0.285624	−	0.494715i	0.687136	−	0.726528i	$-0.258867\pi$
$659$	−7.33225	−	12.6998i	−0.285624	−	0.494715i	−0.972760	+	0.231813i	$0.925534\pi$
$660$	0.469383	−	0.812994i	0.0182707	−	0.0316458i
$661$	−25.5192			−0.992582			−0.496291	−	0.868156i	$-0.665305\pi$
$661$	−25.5192			−0.992582			−0.496291	+	0.868156i	$0.665305\pi$
$662$	−11.8179			−0.459314
$663$	14.7922	+	25.6208i	0.574481	+	0.995031i
$664$	3.21761	−	5.57306i	0.124867	−	0.216277i
$665$	−4.26054			−0.165217
$666$	5.88352	+	10.1906i	0.227982	+	0.394876i
$667$	59.2640			2.29471
$668$	−8.80365	+	15.2484i	−0.340623	+	0.589977i
$669$	14.6218			0.565313
$670$	−1.67164	+	2.52131i	−0.0645811	+	0.0974068i
$671$	36.0742			1.39263
$672$	7.63219	−	13.2193i	0.294418	−	0.509947i
$673$	−0.732979			−0.0282543			−0.0141271	−	0.999900i	$-0.504497\pi$
$673$	−0.732979			−0.0282543			−0.0141271	+	0.999900i	$0.504497\pi$
$674$	1.99040	+	3.44747i	0.0766673	+	0.132792i
$675$	−4.88215			−0.187914
$676$	5.52692	−	9.57291i	0.212574	−	0.368189i
$677$	−16.7758	−	29.0565i	−0.644745	−	1.11673i	−0.984360	−	0.176167i	$-0.943630\pi$
$677$	−16.7758	−	29.0565i	−0.644745	−	1.11673i	0.339615	−	0.940564i	$-0.389703\pi$
$678$	−7.19814			−0.276443
$679$	−11.5958			−0.445007
$680$	3.03752	−	5.26114i	0.116484	−	0.201756i
$681$	0.515824	+	0.893434i	0.0197664	+	0.0342365i
$682$	−15.0487	−	26.0651i	−0.576244	−	0.998083i
$683$	−11.0494	+	19.1380i	−0.422792	+	0.732297i	−0.996211	−	0.0869651i	$-0.972283\pi$
$683$	−11.0494	+	19.1380i	−0.422792	+	0.732297i	0.573420	+	0.819262i	$0.305616\pi$
$684$	−2.99689			−0.114589
$685$	6.55417			0.250422
$686$	−3.50710	+	6.07448i	−0.133902	+	0.231925i
$687$	−2.64969	+	4.58939i	−0.101092	+	0.175096i
$688$	5.54485	−	9.60397i	0.211396	−	0.366148i
$689$	10.7323	−	18.5890i	0.408870	−	0.708183i
$690$	−1.07404	−	1.86029i	−0.0408881	−	0.0708202i
$691$	2.39641	+	4.15071i	0.0911638	+	0.157900i	0.908001	−	0.418968i	$-0.137608\pi$
$691$	2.39641	+	4.15071i	0.0911638	+	0.157900i	−0.816837	+	0.576868i	$0.804275\pi$
$692$	12.8567			0.488738
$693$	5.66241	−	9.80759i	0.215097	−	0.372560i
$694$	17.2056			0.653117
$695$	3.52325			0.133645
$696$	−15.5930	−	27.0079i	−0.591052	−	1.02373i
$697$	12.6132			0.477758
$698$	18.6449	−	32.2939i	0.705720	−	1.22234i
$699$	−5.93846	−	10.2857i	−0.224613	−	0.389042i
$700$	−7.14959	+	12.3834i	−0.270229	+	0.468050i
$701$	−16.6173	−	28.7820i	−0.627627	−	1.08708i	−0.988027	−	0.154283i	$-0.950693\pi$
$701$	−16.6173	−	28.7820i	−0.627627	−	1.08708i	0.360400	−	0.932798i	$-0.382640\pi$
$702$	−2.75235	−	4.76721i	−0.103881	−	0.179927i
$703$	−19.4750	−	33.7318i	−0.734515	−	1.27222i
$704$	12.9097	+	22.3602i	0.486551	+	0.842731i
$705$	−1.13491	−	1.96572i	−0.0427431	−	0.0740331i
$706$	−8.36369	−	14.4863i	−0.314772	−	0.545200i
$707$	−4.75110	+	8.22914i	−0.178683	+	0.309489i
$708$	−2.07521	−	3.59436i	−0.0779910	−	0.135084i
$709$	−5.31674	+	9.20887i	−0.199675	+	0.345846i	−0.948423	−	0.317008i	$-0.897322\pi$
$709$	−5.31674	+	9.20887i	−0.199675	+	0.345846i	0.748748	+	0.662854i	$0.230655\pi$
$710$	−2.04503			−0.0767486
$711$	−0.758004	−	1.31290i	−0.0284274	−	0.0492377i
$712$	32.0912			1.20267
$713$	49.9703			1.87140
$714$	10.8470	−	18.7875i	0.405939	−	0.703106i
$715$	−5.70770			−0.213456
$716$	−2.89838	−	5.02015i	−0.108318	−	0.187612i
$717$	0.489214	+	0.847344i	0.0182700	+	0.0316446i
$718$	−18.6445	+	32.2932i	−0.695807	+	1.20517i
$719$	−4.32778	+	7.49594i	−0.161399	+	0.279551i	−0.935371	−	0.353669i	$-0.884934\pi$
$719$	−4.32778	+	7.49594i	−0.161399	+	0.279551i	0.773972	+	0.633220i	$0.218267\pi$
$720$	−0.276487	+	0.478890i	−0.0103041	+	0.0178472i
$721$	3.75995	−	6.51242i	0.140028	−	0.242535i
$722$	6.78336			0.252450
$723$	−9.10790			−0.338726
$724$	4.99028	−	8.64343i	0.185462	−	0.321230i
$725$	24.8902	+	43.1110i	0.924398	+	1.60110i
$726$	−0.229444	−	0.397409i	−0.00851547	−	0.0147492i
$727$	22.4287	−	38.8476i	0.831834	−	1.44078i	−0.0647480	−	0.997902i	$-0.520624\pi$
$727$	22.4287	−	38.8476i	0.831834	−	1.44078i	0.896582	−	0.442877i	$-0.146042\pi$
$728$	−54.4650			−2.01861
$729$	1.00000			0.0370370
$730$	0.693646	+	1.20143i	0.0256730	+	0.0444669i
$731$	−19.9168	+	34.4970i	−0.736651	+	1.27592i
$732$	9.32964			0.344833
$733$	23.0814	+	39.9781i	0.852530	+	1.47663i	0.878918	+	0.476973i	$0.158266\pi$
$733$	23.0814	+	39.9781i	0.852530	+	1.47663i	−0.0263879	+	0.999652i	$0.508400\pi$
$734$	−19.5864			−0.722947
$735$	0.880408	−	1.52491i	0.0324743	−	0.0562472i
$736$	−25.4745			−0.939004
$737$	11.8577	+	23.8293i	0.436785	+	0.877764i
$738$	−2.34691			−0.0863908
$739$	−22.5613	+	39.0774i	−0.829932	+	1.43748i	0.0681597	+	0.997674i	$0.478287\pi$
$739$	−22.5613	+	39.0774i	−0.829932	+	1.43748i	−0.898091	+	0.439809i	$0.855046\pi$
$740$	3.15546			0.115997
$741$	9.11055	+	15.7799i	0.334684	+	0.579690i
$742$	−15.7399			−0.577829
$743$	−22.8919	+	39.6500i	−0.839824	+	1.45462i	0.0502182	+	0.998738i	$0.484008\pi$
$743$	−22.8919	+	39.6500i	−0.839824	+	1.45462i	−0.890042	+	0.455879i	$0.849325\pi$
$744$	−13.1477	−	22.7726i	−0.482019	−	0.834882i
$745$	1.68716			0.0618129
$746$	23.2193			0.850121
$747$	1.05201	−	1.82213i	0.0384910	−	0.0666683i
$748$	−7.91121	−	13.7026i	−0.289263	−	0.501017i
$749$	−18.4597	−	31.9731i	−0.674503	−	1.16827i
$750$	1.82611	−	3.16292i	0.0666803	−	0.115494i
$751$	16.9859			0.619825			0.309912	−	0.950765i	$-0.399700\pi$
$751$	16.9859			0.619825			0.309912	+	0.950765i	$0.399700\pi$
$752$	10.6506			0.388389
$753$	−6.65387	+	11.5248i	−0.242481	+	0.419989i
$754$	−28.0640	+	48.6083i	−1.02203	+	1.77021i
$755$	3.34365	−	5.79136i	0.121688	−	0.210769i
$756$	1.46443	−	2.53647i	0.0532609	−	0.0922506i
$757$	−19.3633	−	33.5382i	−0.703771	−	1.21897i	−0.967133	−	0.254271i	$-0.918165\pi$
$757$	−19.3633	−	33.5382i	−0.703771	−	1.21897i	0.263362	−	0.964697i	$-0.415169\pi$
$758$	14.4842	+	25.0874i	0.526091	+	0.911216i
$759$	−18.8999			−0.686022
$760$	1.87082	−	3.24035i	0.0678617	−	0.117540i
$761$	−11.6991			−0.424091			−0.212046	−	0.977260i	$-0.568013\pi$
$761$	−11.6991			−0.424091			−0.212046	+	0.977260i	$0.568013\pi$
$762$	0.538166			0.0194957
$763$	9.09520	+	15.7533i	0.329268	+	0.570309i
$764$	7.59607			0.274816
$765$	0.993129	−	1.72015i	0.0359066	−	0.0621921i
$766$	4.26029	+	7.37904i	0.153931	+	0.266616i
$767$	−12.6173	+	21.8538i	−0.455583	+	0.789093i
$768$	8.05729	+	13.9556i	0.290742	+	0.503581i
$769$	−6.73194	−	11.6601i	−0.242760	−	0.420473i	0.718739	−	0.695280i	$-0.244719\pi$
$769$	−6.73194	−	11.6601i	−0.242760	−	0.420473i	−0.961499	+	0.274807i	$0.911386\pi$
$770$	2.09270	+	3.62467i	0.0754159	+	0.130624i
$771$	−9.93977	−	17.2162i	−0.357972	−	0.620026i
$772$	5.13711	+	8.89774i	0.184889	+	0.320237i
$773$	10.3156	+	17.8672i	0.371028	+	0.642639i	0.989724	−	0.142991i	$-0.0456721\pi$
$773$	10.3156	+	17.8672i	0.371028	+	0.642639i	−0.618696	+	0.785630i	$0.712339\pi$
$774$	3.70588	−	6.41877i	0.133205	−	0.230718i
$775$	20.9869	+	36.3504i	0.753872	+	1.30574i
$776$	5.09177	−	8.81921i	0.182784	−	0.316591i
$777$	38.0660			1.36561
$778$	14.3771	+	24.9019i	0.515445	+	0.892777i
$779$	7.76849			0.278335
$780$	−1.47615			−0.0528545
$781$	−8.99659	+	15.5826i	−0.321923	+	0.557588i
$782$	−36.2049			−1.29468
$783$	−5.09820	−	8.83033i	−0.182195	−	0.315570i
$784$	4.13114	+	7.15534i	0.147541	+	0.255548i
$785$	−0.795312	+	1.37752i	−0.0283859	+	0.0491659i
$786$	−3.00186	+	5.19937i	−0.107073	+	0.185455i
$787$	0.684812	−	1.18613i	0.0244109	−	0.0422809i	−0.853562	−	0.520991i	$-0.825562\pi$
$787$	0.684812	−	1.18613i	0.0244109	−	0.0422809i	0.877973	+	0.478711i	$0.158896\pi$
$788$	3.21810	−	5.57392i	0.114640	−	0.198563i
$789$	2.77387			0.0987524
$790$	0.560284			0.0199340
$791$	−11.6429	+	20.1661i	−0.413973	+	0.717023i
$792$	4.97277	+	8.61309i	0.176700	+	0.306053i
$793$	−28.3622	−	49.1247i	−1.00717	−	1.74447i
$794$	−20.9379	+	36.2655i	−0.743059	+	1.28702i
$795$	−1.44111			−0.0511110
$796$	16.3405			0.579173
$797$	17.5722	+	30.4360i	0.622440	+	1.07810i	0.989030	+	0.147715i	$0.0471918\pi$
$797$	17.5722	+	30.4360i	0.622440	+	1.07810i	−0.366590	+	0.930383i	$0.619475\pi$
$798$	6.68069	−	11.5713i	0.236494	−	0.409619i
$799$	−38.2566			−1.35342
$800$	−10.6990	−	18.5312i	−0.378267	−	0.655177i
$801$	10.4923			0.370728
$802$	17.2380	−	29.8571i	0.608696	−	1.05429i
$803$	12.2061			0.430743
$804$	3.06669	+	6.16282i	0.108154	+	0.217346i
$805$	−6.94899			−0.244920
$806$	−23.6630	+	40.9856i	−0.833495	+	1.44366i
$807$	−6.16204			−0.216914
$808$	−4.17244	−	7.22689i	−0.146786	−	0.254241i
$809$	−1.41533			−0.0497604			−0.0248802	−	0.999690i	$-0.507920\pi$
$809$	−1.41533			−0.0497604			−0.0248802	+	0.999690i	$0.507920\pi$
$810$	−0.184789	+	0.320064i	−0.00649283	+	0.0112459i
$811$	−12.9317	−	22.3984i	−0.454095	−	0.786516i	0.544541	−	0.838735i	$-0.316704\pi$
$811$	−12.9317	−	22.3984i	−0.454095	−	0.786516i	−0.998636	+	0.0522187i	$0.983371\pi$
$812$	−29.8639			−1.04802
$813$	18.5823			0.651710
$814$	−19.1316	+	33.1369i	−0.670563	+	1.16145i
$815$	−0.662567	−	1.14760i	−0.0232087	−	0.0401987i
$816$	4.66006	+	8.07146i	0.163135	+	0.282558i
$817$	−12.2668	+	21.2468i	−0.429162	+	0.743330i
$818$	−3.69854			−0.129316
$819$	−17.8075			−0.622246
$820$	−0.314674	+	0.545032i	−0.0109889	+	0.0190333i
$821$	7.99568	−	13.8489i	0.279051	−	0.483331i	−0.692098	−	0.721804i	$-0.743313\pi$
$821$	7.99568	−	13.8489i	0.279051	−	0.483331i	0.971149	+	0.238473i	$0.0766468\pi$
$822$	−10.2772	+	17.8006i	−0.358458	+	0.620868i
$823$	7.70041	−	13.3375i	0.268419	−	0.464916i	−0.700034	−	0.714109i	$-0.746832\pi$
$823$	7.70041	−	13.3375i	0.268419	−	0.464916i	0.968454	+	0.249193i	$0.0801654\pi$
$824$	3.30201	+	5.71925i	0.115031	+	0.199239i
$825$	−7.93772	−	13.7485i	−0.276356	−	0.478663i
$826$	18.5043			0.643846
$827$	−1.34933	+	2.33711i	−0.0469208	+	0.0812692i	−0.888532	−	0.458815i	$-0.848274\pi$
$827$	−1.34933	+	2.33711i	−0.0469208	+	0.0812692i	0.841611	+	0.540084i	$0.181608\pi$
$828$	−4.88795			−0.169868
$829$	49.4219			1.71649			0.858247	−	0.513237i	$-0.171554\pi$
$829$	49.4219			1.71649			0.858247	+	0.513237i	$0.171554\pi$
$830$	0.388799	+	0.673420i	0.0134954	+	0.0233748i
$831$	24.5550			0.851805
$832$	20.2996	−	35.1599i	0.703761	−	1.21895i
$833$	−14.8388	−	25.7016i	−0.514135	−	0.890509i
$834$	−5.52460	+	9.56888i	−0.191301	+	0.331343i
$835$	−3.59368	−	6.22444i	−0.124365	−	0.215406i
$836$	−4.87253	−	8.43947i	−0.168520	−	0.291885i
$837$	−4.29870	−	7.44557i	−0.148585	−	0.257356i
$838$	−9.02454	−	15.6310i	−0.311747	−	0.539962i
$839$	−10.0726	−	17.4463i	−0.347745	−	0.602312i	0.638103	−	0.769951i	$-0.279719\pi$
$839$	−10.0726	−	17.4463i	−0.347745	−	0.602312i	−0.985849	+	0.167639i	$0.946386\pi$
$840$	1.82836	+	3.16680i	0.0630843	+	0.109265i
$841$	−37.4832	+	64.9228i	−1.29252	+	2.23872i
$842$	2.90356	+	5.02912i	0.100063	+	0.173315i
$843$	11.5331	−	19.9759i	0.397220	−	0.688005i
$844$	−16.8403			−0.579667
$845$	2.25611	+	3.90770i	0.0776126	+	0.134429i
$846$	7.11831			0.244733
$847$	−1.48449			−0.0510077
$848$	3.38107	−	5.85618i	0.116106	−	0.201102i
$849$	25.5746			0.877719
$850$	−15.2056	−	26.3369i	−0.521548	−	0.903348i
$851$	−31.7640	−	55.0169i	−1.08886	−	1.88595i
$852$	−2.32673	+	4.03001i	−0.0797124	+	0.138066i
$853$	−13.7870	+	23.8799i	−0.472059	+	0.817631i	−0.999489	−	0.0319679i	$-0.989823\pi$
$853$	−13.7870	+	23.8799i	−0.472059	+	0.817631i	0.527429	+	0.849599i	$0.323156\pi$
$854$	−20.7977	+	36.0227i	−0.711684	+	1.23267i
$855$	0.611670	−	1.05944i	0.0209187	−	0.0362322i
$856$	32.4229			1.10819
$857$	−38.4987			−1.31509			−0.657546	−	0.753414i	$-0.728405\pi$
$857$	−38.4987			−1.31509			−0.657546	+	0.753414i	$0.728405\pi$
$858$	8.94990	−	15.5017i	0.305544	−	0.529218i
$859$	−9.08702	−	15.7392i	−0.310045	−	0.537014i	0.668327	−	0.743868i	$-0.267011\pi$
$859$	−9.08702	−	15.7392i	−0.310045	−	0.537014i	−0.978372	+	0.206854i	$0.933678\pi$
$860$	−0.993772	−	1.72126i	−0.0338874	−	0.0586946i
$861$	−3.79609	+	6.57501i	−0.129370	+	0.224076i
$862$	−1.04202			−0.0354912
$863$	29.7060			1.01120			0.505602	−	0.862767i	$-0.331270\pi$
$863$	29.7060			1.01120			0.505602	+	0.862767i	$0.331270\pi$
$864$	2.19145	+	3.79571i	0.0745547	+	0.129133i
$865$	−2.62408	+	4.54503i	−0.0892213	+	0.154536i
$866$	15.8771			0.539526
$867$	−8.23870	−	14.2698i	−0.279801	−	0.484629i
$868$	−25.1806			−0.854687
$869$	2.46483	−	4.26920i	0.0836135	−	0.144823i
$870$	3.76836			0.127760
$871$	23.1272	−	34.8825i	0.783636	−	1.18195i
$872$	−15.9749			−0.540979
$873$	1.66477	−	2.88347i	0.0563440	−	0.0975907i
$874$	−22.2987			−0.754263
$875$	−5.90743	−	10.2320i	−0.199707	−	0.345904i
$876$	3.15678			0.106658
$877$	5.01186	−	8.68079i	0.169238	−	0.293130i	−0.768914	−	0.639352i	$-0.779203\pi$
$877$	5.01186	−	8.68079i	0.169238	−	0.293130i	0.938152	+	0.346223i	$0.112536\pi$
$878$	6.40747	+	11.0981i	0.216242	+	0.374542i
$879$	9.44665			0.318628
$880$	−1.79813			−0.0606148
$881$	17.0824	−	29.5876i	0.575520	−	0.996831i	−0.420464	−	0.907309i	$-0.638133\pi$
$881$	17.0824	−	29.5876i	0.575520	−	0.996831i	0.995985	−	0.0895216i	$-0.0285338\pi$
$882$	2.76103	+	4.78224i	0.0929686	+	0.161026i
$883$	−6.83206	−	11.8335i	−0.229917	−	0.398228i	0.727866	−	0.685719i	$-0.240512\pi$
$883$	−6.83206	−	11.8335i	−0.229917	−	0.398228i	−0.957783	+	0.287491i	$0.907179\pi$
$884$	−12.4399	+	21.5465i	−0.418397	+	0.724686i
$885$	1.69421			0.0569504
$886$	−2.46487			−0.0828091
$887$	28.5700	−	49.4847i	0.959287	−	1.66153i	0.235050	−	0.971983i	$-0.424475\pi$
$887$	28.5700	−	49.4847i	0.959287	−	1.66153i	0.724237	−	0.689551i	$-0.242192\pi$
$888$	−16.7149	+	28.9511i	−0.560916	+	0.971536i
$889$	0.870476	−	1.50771i	0.0291948	−	0.0505669i
$890$	−1.93887	+	3.35822i	−0.0649910	+	0.112568i
$891$	1.62587	+	2.81608i	0.0544685	+	0.0943423i
$892$	6.14830	+	10.6492i	0.205860	+	0.356560i
$893$	−23.5623			−0.788483
$894$	−2.64554	+	4.58221i	−0.0884801	+	0.153252i
$895$	2.36626			0.0790954
$896$	0.757711			0.0253133
$897$	14.8594	+	25.7372i	0.496141	+	0.859342i
$898$	−5.33002			−0.177865
$899$	−43.8312	+	75.9179i	−1.46185	+	2.53200i
$900$	−2.05288	−	3.55570i	−0.0684294	−	0.118523i
$901$	−12.1446	+	21.0351i	−0.404596	+	0.700780i
$902$	−3.81575	−	6.60908i	−0.127051	−	0.220058i
$903$	−11.9884	−	20.7645i	−0.398949	−	0.691001i
$904$	−10.2249	−	17.7100i	−0.340074	−	0.589025i
$905$	2.03705	+	3.52828i	0.0677140	+	0.117284i
$906$	10.4859	+	18.1622i	0.348372	+	0.603398i
$907$	−21.7634	−	37.6952i	−0.722640	−	1.25165i	−0.959938	−	0.280213i	$-0.909595\pi$
$907$	−21.7634	−	37.6952i	−0.722640	−	1.25165i	0.237297	−	0.971437i	$-0.423738\pi$
$908$	−0.433795	+	0.751355i	−0.0143960	+	0.0249346i
$909$	−1.36420	−	2.36286i	−0.0452475	−	0.0783710i
$910$	3.29064	−	5.69955i	0.109084	−	0.188938i
$911$	35.8017			1.18616			0.593081	−	0.805143i	$-0.297911\pi$
$911$	35.8017			1.18616			0.593081	+	0.805143i	$0.297911\pi$
$912$	2.87014	+	4.97123i	0.0950399	+	0.164614i
$913$	6.84170			0.226427
$914$	−8.96823			−0.296643
$915$	−1.90420	+	3.29817i	−0.0629508	+	0.109034i
$916$	−4.45664			−0.147251
$917$	9.71092	+	16.8198i	0.320683	+	0.555439i
$918$	3.11453	+	5.39452i	0.102795	+	0.178046i
$919$	10.6899	−	18.5154i	0.352627	−	0.610768i	−0.634082	−	0.773266i	$-0.718622\pi$
$919$	10.6899	−	18.5154i	0.352627	−	0.610768i	0.986709	+	0.162498i	$0.0519552\pi$
$920$	3.05132	−	5.28505i	0.100599	−	0.174243i
$921$	0.489214	−	0.847344i	0.0161202	−	0.0279209i
$922$	−16.7796	+	29.0631i	−0.552605	+	0.957141i
$923$	28.2931			0.931278
$924$	9.52389			0.313313
$925$	26.6810	−	46.2128i	0.877266	−	1.51947i
$926$	−6.94725	−	12.0330i	−0.228301	−	0.395428i
$927$	1.07960	+	1.86993i	0.0354589	+	0.0614165i
$928$	22.3449	−	38.7025i	0.733507	−	1.27047i
$929$	−9.56408			−0.313787			−0.156894	−	0.987615i	$-0.550148\pi$
$929$	−9.56408			−0.313787			−0.156894	+	0.987615i	$0.550148\pi$
$930$	3.17741			0.104191
$931$	−9.13928	−	15.8297i	−0.299528	−	0.518797i
$932$	4.99409	−	8.65002i	0.163587	−	0.283341i
$933$	−18.7178			−0.612795
$934$	10.9281	+	18.9280i	0.357579	+	0.619344i
$935$	6.45878			0.211225
$936$	7.81935	−	13.5435i	0.255583	−	0.442684i
$937$	29.5922			0.966735			0.483367	−	0.875418i	$-0.339414\pi$
$937$	29.5922			0.966735			0.483367	+	0.875418i	$0.339414\pi$
$938$	−30.6316	−	1.89741i	−1.00016	−	0.0619528i
$939$	9.18556			0.299759
$940$	0.954427	−	1.65312i	0.0311300	−	0.0539187i
$941$	4.71313			0.153644			0.0768218	−	0.997045i	$-0.475523\pi$
$941$	4.71313			0.153644			0.0768218	+	0.997045i	$0.475523\pi$
$942$	−2.49416	−	4.32001i	−0.0812642	−	0.140754i
$943$	12.6705			0.412608
$944$	−3.97488	+	6.88470i	−0.129371	+	0.224078i
$945$	0.597787	+	1.03540i	0.0194460	+	0.0336815i
$946$	24.1010			0.783592
$947$	−27.2589			−0.885794			−0.442897	−	0.896572i	$-0.646049\pi$
$947$	−27.2589			−0.885794			−0.442897	+	0.896572i	$0.646049\pi$
$948$	0.637462	−	1.10412i	0.0207038	−	0.0358600i
$949$	−9.59662	−	16.6218i	−0.311519	−	0.539568i
$950$	−9.36517	−	16.2209i	−0.303846	−	0.526277i
$951$	−12.2411	+	21.2022i	−0.396945	+	0.687528i
$952$	61.6321			1.99751
$953$	54.9702			1.78066			0.890329	−	0.455318i	$-0.150474\pi$
$953$	54.9702			1.78066			0.890329	+	0.455318i	$0.150474\pi$
$954$	2.25972	−	3.91395i	0.0731611	−	0.126719i
$955$	−1.55037	+	2.68532i	−0.0501689	+	0.0868951i
$956$	−0.411416	+	0.712594i	−0.0133062	+	0.0230469i
$957$	16.5780	−	28.7139i	0.535889	−	0.928188i
$958$	5.75697	+	9.97137i	0.185999	+	0.322160i
$959$	33.2464	+	57.5845i	1.07358	+	1.85950i
$960$	−2.72578			−0.0879740
$961$	−21.4577	+	37.1658i	−0.692182	+	1.19890i
$962$	60.1664			1.93984
$963$	10.6008			0.341605
$964$	−3.82975	−	6.63333i	−0.123348	−	0.213645i
$965$	−4.19398			−0.135009
$966$	10.8963	−	18.8729i	0.350582	−	0.607226i
$967$	−2.80736	−	4.86249i	−0.0902786	−	0.156367i	0.817350	−	0.576142i	$-0.195442\pi$
$967$	−2.80736	−	4.86249i	−0.0902786	−	0.156367i	−0.907628	+	0.419775i	$0.862109\pi$
$968$	0.651845	−	1.12903i	0.0209511	−	0.0362883i
$969$	−10.3094	−	17.8564i	−0.331186	−	0.573630i
$970$	0.615264	+	1.06567i	0.0197549	+	0.0342165i
$971$	−16.5875	−	28.7304i	−0.532318	−	0.922002i	−0.999288	−	0.0377289i	$-0.987988\pi$
$971$	−16.5875	−	28.7304i	−0.532318	−	0.922002i	0.466970	−	0.884273i	$-0.345346\pi$
$972$	0.420487	+	0.728305i	0.0134871	+	0.0233604i
$973$	17.8719	+	30.9551i	0.572947	+	0.992373i
$974$	−8.54029	−	14.7922i	−0.273648	−	0.473973i
$975$	−12.4815	+	21.6187i	−0.399729	+	0.692351i
$976$	−8.93507	−	15.4760i	−0.286005	−	0.495375i
$977$	−6.88674	+	11.9282i	−0.220326	+	0.381616i	−0.954907	−	0.296905i	$-0.904046\pi$
$977$	−6.88674	+	11.9282i	−0.220326	+	0.381616i	0.734581	+	0.678521i	$0.237379\pi$
$978$	4.15573			0.132885
$979$	17.0591	+	29.5473i	0.545212	+	0.944335i
$980$	1.48080			0.0473024
$981$	−5.22306			−0.166759
$982$	4.34213	−	7.52080i	0.138563	−	0.239998i
$983$	−22.5825			−0.720269			−0.360134	−	0.932900i	$-0.617269\pi$
$983$	−22.5825			−0.720269			−0.360134	+	0.932900i	$0.617269\pi$
$984$	−3.33375	−	5.77422i	−0.106276	−	0.184075i
$985$	1.31364	+	2.27530i	0.0418561	+	0.0724969i
$986$	31.7570	−	55.0047i	1.01135	−	1.75171i
$987$	11.5138	−	19.9424i	0.366487	−	0.634774i
$988$	−7.66173	+	13.2705i	−0.243752	+	0.422191i
$989$	−20.0073	+	34.6537i	−0.636196	+	1.10192i
$990$	−1.20177			−0.0381947
$991$	9.43357			0.299667			0.149834	−	0.988711i	$-0.452126\pi$
$991$	9.43357			0.299667			0.149834	+	0.988711i	$0.452126\pi$
$992$	18.8408	−	32.6332i	0.598196	−	1.03611i
$993$	−5.48861	−	9.50655i	−0.174176	−	0.301681i
$994$	−10.3735	−	17.9675i	−0.329029	−	0.569894i
$995$	−3.33512	+	5.77660i	−0.105730	+	0.183131i
$996$	1.76942			0.0560663
$997$	−19.7167			−0.624435			−0.312217	−	0.950011i	$-0.601072\pi$
$997$	−19.7167			−0.624435			−0.312217	+	0.950011i	$0.601072\pi$
$998$	−5.34672	−	9.26080i	−0.169248	−	0.293145i
$999$	−5.46501	+	9.46567i	−0.172905	+	0.299481i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	201.2.e.c.163.4	yes	10
3.2	odd	2		603.2.g.f.163.2		10
67.37	even	3	inner	201.2.e.c.37.4	✓	10
201.104	odd	6		603.2.g.f.37.2		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
201.2.e.c.37.4	✓	10	67.37	even	3	inner
201.2.e.c.163.4	yes	10	1.1	even	1	trivial
603.2.g.f.37.2		10	201.104	odd	6
603.2.g.f.163.2		10	3.2	odd	2

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:	\( N \)	\(=\)	\( 201 = 3 \cdot 67 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	201.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.538290 - 0.932346i) q^{2} +1.00000 q^{3} +(0.420487 + 0.728305i) q^{4} -0.343289 q^{5} +(0.538290 - 0.932346i) q^{6} +(-1.74135 - 3.01611i) q^{7} +3.05854 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+(0.538290 - 0.932346i) q^{2} +1.00000 q^{3} +(0.420487 + 0.728305i) q^{4} -0.343289 q^{5} +(0.538290 - 0.932346i) q^{6} +(-1.74135 - 3.01611i) q^{7} +3.05854 q^{8} +1.00000 q^{9} +(-0.184789 + 0.320064i) q^{10} +(1.62587 + 2.81608i) q^{11} +(0.420487 + 0.728305i) q^{12} +(2.55656 - 4.42810i) q^{13} -3.74942 q^{14} -0.343289 q^{15} +(0.805407 - 1.39501i) q^{16} +(-2.89298 + 5.01079i) q^{17} +(0.538290 - 0.932346i) q^{18} +(-1.78179 + 3.08616i) q^{19} +(-0.144349 - 0.250019i) q^{20} +(-1.74135 - 3.01611i) q^{21} +3.50075 q^{22} +(-2.90613 + 5.03356i) q^{23} +3.05854 q^{24} -4.88215 q^{25} +(-2.75235 - 4.76721i) q^{26} +1.00000 q^{27} +(1.46443 - 2.53647i) q^{28} +(-5.09820 - 8.83033i) q^{29} +(-0.184789 + 0.320064i) q^{30} +(-4.29870 - 7.44557i) q^{31} +(2.19145 + 3.79571i) q^{32} +(1.62587 + 2.81608i) q^{33} +(3.11453 + 5.39452i) q^{34} +(0.597787 + 1.03540i) q^{35} +(0.420487 + 0.728305i) q^{36} +(-5.46501 + 9.46567i) q^{37} +(1.91825 + 3.32250i) q^{38} +(2.55656 - 4.42810i) q^{39} -1.04996 q^{40} +(-1.08998 - 1.88790i) q^{41} -3.74942 q^{42} +6.88453 q^{43} +(-1.36731 + 2.36825i) q^{44} -0.343289 q^{45} +(3.12868 + 5.41903i) q^{46} +(3.30598 + 5.72613i) q^{47} +(0.805407 - 1.39501i) q^{48} +(-2.56463 + 4.44206i) q^{49} +(-2.62802 + 4.55186i) q^{50} +(-2.89298 + 5.01079i) q^{51} +4.30001 q^{52} +4.19796 q^{53} +(0.538290 - 0.932346i) q^{54} +(-0.558142 - 0.966730i) q^{55} +(-5.32600 - 9.22490i) q^{56} +(-1.78179 + 3.08616i) q^{57} -10.9772 q^{58} -4.93524 q^{59} +(-0.144349 - 0.250019i) q^{60} +(5.54693 - 9.60756i) q^{61} -9.25580 q^{62} +(-1.74135 - 3.01611i) q^{63} +7.94018 q^{64} +(-0.877640 + 1.52012i) q^{65} +3.50075 q^{66} +(8.16969 + 0.506056i) q^{67} -4.86585 q^{68} +(-2.90613 + 5.03356i) q^{69} +1.28713 q^{70} +(2.76671 + 4.79208i) q^{71} +3.05854 q^{72} +(1.87686 - 3.25081i) q^{73} +(5.88352 + 10.1906i) q^{74} -4.88215 q^{75} -2.99689 q^{76} +(5.66241 - 9.80759i) q^{77} +(-2.75235 - 4.76721i) q^{78} +(-0.758004 - 1.31290i) q^{79} +(-0.276487 + 0.478890i) q^{80} +1.00000 q^{81} -2.34691 q^{82} +(1.05201 - 1.82213i) q^{83} +(1.46443 - 2.53647i) q^{84} +(0.993129 - 1.72015i) q^{85} +(3.70588 - 6.41877i) q^{86} +(-5.09820 - 8.83033i) q^{87} +(4.97277 + 8.61309i) q^{88} +10.4923 q^{89} +(-0.184789 + 0.320064i) q^{90} -17.8075 q^{91} -4.88795 q^{92} +(-4.29870 - 7.44557i) q^{93} +7.11831 q^{94} +(0.611670 - 1.05944i) q^{95} +(2.19145 + 3.79571i) q^{96} +(1.66477 - 2.88347i) q^{97} +(2.76103 + 4.78224i) q^{98} +(1.62587 + 2.81608i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + 10 q^{3} - 6 q^{4} + 6 q^{5} - q^{7} + 10 q^{9}+O(q^{10}) \) 10 * q + 10 * q^3 - 6 * q^4 + 6 * q^5 - q^7 + 10 * q^9	\( 10 q + 10 q^{3} - 6 q^{4} + 6 q^{5} - q^{7} + 10 q^{9} - 12 q^{10} + 6 q^{11} - 6 q^{12} - q^{13} - 6 q^{14} + 6 q^{15} - 24 q^{16} + 8 q^{17} - 5 q^{19} - 8 q^{20} - q^{21} + 22 q^{22} - 7 q^{23} - 8 q^{25} - 17 q^{26} + 10 q^{27} + 3 q^{28} - 12 q^{29} - 12 q^{30} - 12 q^{31} - 5 q^{32} + 6 q^{33} - 5 q^{35} - 6 q^{36} - 17 q^{37} + 30 q^{38} - q^{39} + 34 q^{40} + 13 q^{41} - 6 q^{42} - 4 q^{43} + 43 q^{44} + 6 q^{45} - 26 q^{46} - 25 q^{47} - 24 q^{48} + 16 q^{49} - 25 q^{50} + 8 q^{51} + 64 q^{52} - 12 q^{53} - 14 q^{55} - 11 q^{56} - 5 q^{57} + 4 q^{58} - 12 q^{59} - 8 q^{60} + 9 q^{61} + 46 q^{62} - q^{63} + 64 q^{64} - 14 q^{65} + 22 q^{66} + 2 q^{67} - 98 q^{68} - 7 q^{69} + 2 q^{70} + 29 q^{71} + 12 q^{73} + 15 q^{74} - 8 q^{75} - 6 q^{76} + 4 q^{77} - 17 q^{78} - q^{79} - 13 q^{80} + 10 q^{81} - 2 q^{82} - 6 q^{83} + 3 q^{84} + 9 q^{85} - 21 q^{86} - 12 q^{87} + 18 q^{88} - 4 q^{89} - 12 q^{90} - 40 q^{91} - 12 q^{93} + 30 q^{94} - 14 q^{95} - 5 q^{96} + 11 q^{97} + 12 q^{98} + 6 q^{99}+O(q^{100}) \) 10 * q + 10 * q^3 - 6 * q^4 + 6 * q^5 - q^7 + 10 * q^9 - 12 * q^10 + 6 * q^11 - 6 * q^12 - q^13 - 6 * q^14 + 6 * q^15 - 24 * q^16 + 8 * q^17 - 5 * q^19 - 8 * q^20 - q^21 + 22 * q^22 - 7 * q^23 - 8 * q^25 - 17 * q^26 + 10 * q^27 + 3 * q^28 - 12 * q^29 - 12 * q^30 - 12 * q^31 - 5 * q^32 + 6 * q^33 - 5 * q^35 - 6 * q^36 - 17 * q^37 + 30 * q^38 - q^39 + 34 * q^40 + 13 * q^41 - 6 * q^42 - 4 * q^43 + 43 * q^44 + 6 * q^45 - 26 * q^46 - 25 * q^47 - 24 * q^48 + 16 * q^49 - 25 * q^50 + 8 * q^51 + 64 * q^52 - 12 * q^53 - 14 * q^55 - 11 * q^56 - 5 * q^57 + 4 * q^58 - 12 * q^59 - 8 * q^60 + 9 * q^61 + 46 * q^62 - q^63 + 64 * q^64 - 14 * q^65 + 22 * q^66 + 2 * q^67 - 98 * q^68 - 7 * q^69 + 2 * q^70 + 29 * q^71 + 12 * q^73 + 15 * q^74 - 8 * q^75 - 6 * q^76 + 4 * q^77 - 17 * q^78 - q^79 - 13 * q^80 + 10 * q^81 - 2 * q^82 - 6 * q^83 + 3 * q^84 + 9 * q^85 - 21 * q^86 - 12 * q^87 + 18 * q^88 - 4 * q^89 - 12 * q^90 - 40 * q^91 - 12 * q^93 + 30 * q^94 - 14 * q^95 - 5 * q^96 + 11 * q^97 + 12 * q^98 + 6 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

Groups

Database

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