LMFDB - Embedded newform 585.2.bt.b.376.27

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [585,2,Mod(376,585)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(585, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([4, 0, 3]))

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

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

chi := DirichletCharacter("585.376");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 585 = 3^{2} \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	585.bt (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$4.67124851824$
Analytic rank:	$0$
Dimension:	$108$
Relative dimension:	$54$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			376.27
Character	$\chi$	$=$	585.376
Dual form			585.2.bt.b.571.27

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.0488628 - 0.0282110i) q^{2} +(-1.54283 - 0.787195i) q^{3} +(-0.998408 - 1.72929i) q^{4} +(0.866025 - 0.500000i) q^{5} +(0.0531795 + 0.0819893i) q^{6} +(-3.39747 - 1.96153i) q^{7} +0.225508i q^{8} +(1.76065 + 2.42902i) q^{9} +O(q^{10})$	\(q+(-0.0488628 - 0.0282110i) q^{2} +(-1.54283 - 0.787195i) q^{3} +(-0.998408 - 1.72929i) q^{4} +(0.866025 - 0.500000i) q^{5} +(0.0531795 + 0.0819893i) q^{6} +(-3.39747 - 1.96153i) q^{7} +0.225508i q^{8} +(1.76065 + 2.42902i) q^{9} -0.0564219 q^{10} +(-1.93688 - 1.11826i) q^{11} +(0.179082 + 3.45395i) q^{12} +(-1.98274 - 3.01144i) q^{13} +(0.110673 + 0.191692i) q^{14} +(-1.72973 + 0.0896838i) q^{15} +(-1.99045 + 3.44757i) q^{16} +5.60271 q^{17} +(-0.0175053 - 0.168358i) q^{18} +6.06808i q^{19} +(-1.72929 - 0.998408i) q^{20} +(3.69761 + 5.70079i) q^{21} +(0.0630943 + 0.109282i) q^{22} +(-1.24872 - 2.16284i) q^{23} +(0.177519 - 0.347921i) q^{24} +(0.500000 - 0.866025i) q^{25} +(0.0119265 + 0.203082i) q^{26} +(-0.804269 - 5.13353i) q^{27} +7.83364i q^{28} +(-2.26353 + 3.92055i) q^{29} +(0.0870494 + 0.0444151i) q^{30} +(1.13390 - 0.654658i) q^{31} +(0.585110 - 0.337813i) q^{32} +(2.10799 + 3.24998i) q^{33} +(-0.273764 - 0.158058i) q^{34} -3.92306 q^{35} +(2.44264 - 5.46983i) q^{36} +8.55454i q^{37} +(0.171186 - 0.296503i) q^{38} +(0.688433 + 6.20694i) q^{39} +(0.112754 + 0.195296i) q^{40} +(-9.94634 + 5.74252i) q^{41} +(-0.0198512 - 0.382870i) q^{42} +(4.04825 - 7.01177i) q^{43} +4.46591i q^{44} +(2.73927 + 1.22327i) q^{45} +0.140910i q^{46} +(1.02507 + 0.591824i) q^{47} +(5.78484 - 3.75214i) q^{48} +(4.19522 + 7.26633i) q^{49} +(-0.0488628 + 0.0282110i) q^{50} +(-8.64402 - 4.41042i) q^{51} +(-3.22808 + 6.43538i) q^{52} -4.19836 q^{53} +(-0.105523 + 0.273528i) q^{54} -2.23652 q^{55} +(0.442341 - 0.766158i) q^{56} +(4.77676 - 9.36201i) q^{57} +(0.221205 - 0.127713i) q^{58} +(-3.81984 + 2.20539i) q^{59} +(1.88206 + 2.90167i) q^{60} +(-1.24259 + 2.15224i) q^{61} -0.0738742 q^{62} +(-1.21716 - 11.7061i) q^{63} +7.92370 q^{64} +(-3.22282 - 1.61661i) q^{65} +(-0.0113171 - 0.218272i) q^{66} +(-10.7969 + 6.23362i) q^{67} +(-5.59379 - 9.68873i) q^{68} +(0.223979 + 4.31988i) q^{69} +(0.191692 + 0.110673i) q^{70} -16.1695i q^{71} +(-0.547763 + 0.397040i) q^{72} -2.60190i q^{73} +(0.241332 - 0.417999i) q^{74} +(-1.45315 + 0.942532i) q^{75} +(10.4935 - 6.05842i) q^{76} +(4.38700 + 7.59851i) q^{77} +(0.141465 - 0.322710i) q^{78} +(-1.96689 + 3.40675i) q^{79} +3.98091i q^{80} +(-2.80024 + 8.55328i) q^{81} +0.648008 q^{82} +(-9.81398 - 5.66610i) q^{83} +(6.16660 - 12.0860i) q^{84} +(4.85209 - 2.80135i) q^{85} +(-0.395618 + 0.228410i) q^{86} +(6.57849 - 4.26690i) q^{87} +(0.252176 - 0.436782i) q^{88} -6.84387i q^{89} +(-0.0993391 - 0.137050i) q^{90} +(0.829258 + 14.1205i) q^{91} +(-2.49346 + 4.31880i) q^{92} +(-2.26476 + 0.117424i) q^{93} +(-0.0333918 - 0.0578364i) q^{94} +(3.03404 + 5.25511i) q^{95} +(-1.16865 + 0.0605928i) q^{96} +(7.85275 + 4.53379i) q^{97} -0.473405i q^{98} +(-0.693895 - 6.67357i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 108 q - 6 q^{3} + 52 q^{4} - 14 q^{9}+O(q^{10}) $ 108 * q - 6 * q^3 + 52 * q^4 - 14 * q^9	$ 108 q - 6 q^{3} + 52 q^{4} - 14 q^{9} - 8 q^{10} - 36 q^{12} - 4 q^{13} - 8 q^{14} - 64 q^{16} + 36 q^{17} + 24 q^{22} - 22 q^{23} + 54 q^{25} + 40 q^{26} + 48 q^{27} - 16 q^{29} + 20 q^{30} - 40 q^{35} - 76 q^{36} - 12 q^{38} + 26 q^{39} - 52 q^{42} - 6 q^{43} - 68 q^{48} + 58 q^{49} + 34 q^{51} + 22 q^{52} - 116 q^{53} + 24 q^{55} + 40 q^{56} + 18 q^{61} + 152 q^{62} - 216 q^{64} + 2 q^{65} - 72 q^{66} - 134 q^{69} + 32 q^{74} + 40 q^{77} - 34 q^{78} + 18 q^{79} + 34 q^{81} + 88 q^{82} + 60 q^{87} + 8 q^{90} + 16 q^{91} + 176 q^{92} - 76 q^{94} - 56 q^{95}+O(q^{100}) $ 108 * q - 6 * q^3 + 52 * q^4 - 14 * q^9 - 8 * q^10 - 36 * q^12 - 4 * q^13 - 8 * q^14 - 64 * q^16 + 36 * q^17 + 24 * q^22 - 22 * q^23 + 54 * q^25 + 40 * q^26 + 48 * q^27 - 16 * q^29 + 20 * q^30 - 40 * q^35 - 76 * q^36 - 12 * q^38 + 26 * q^39 - 52 * q^42 - 6 * q^43 - 68 * q^48 + 58 * q^49 + 34 * q^51 + 22 * q^52 - 116 * q^53 + 24 * q^55 + 40 * q^56 + 18 * q^61 + 152 * q^62 - 216 * q^64 + 2 * q^65 - 72 * q^66 - 134 * q^69 + 32 * q^74 + 40 * q^77 - 34 * q^78 + 18 * q^79 + 34 * q^81 + 88 * q^82 + 60 * q^87 + 8 * q^90 + 16 * q^91 + 176 * q^92 - 76 * q^94 - 56 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/585\mathbb{Z}\right)^\times$.

$n$	$326$	$352$	$496$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$	$-1$

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 $

$2$	−0.0488628	−	0.0282110i	−0.0345512	−	0.0199482i	0.482625	−	0.875827i	$-0.339683\pi$
$2$	−0.0488628	−	0.0282110i	−0.0345512	−	0.0199482i	−0.517176	+	0.855879i	$0.673017\pi$
$3$	−1.54283	−	0.787195i	−0.890753	−	0.454487i
$3$	−1.54283	−	0.787195i	−0.890753	−	0.454487i
$4$	−0.998408	−	1.72929i	−0.499204	−	0.864647i
$5$	0.866025	−	0.500000i	0.387298	−	0.223607i
$5$	0.866025	−	0.500000i	0.387298	−	0.223607i
$6$	0.0531795	+	0.0819893i	0.0217104	+	0.0334720i
$7$	−3.39747	−	1.96153i	−1.28412	−	0.741390i	−0.306525	−	0.951863i	$-0.599166\pi$
$7$	−3.39747	−	1.96153i	−1.28412	−	0.741390i	−0.977600	+	0.210473i	$0.932500\pi$
$8$			0.225508i			0.0797291i
$9$	1.76065	+	2.42902i	0.586882	+	0.809672i
$10$	−0.0564219			−0.0178422
$11$	−1.93688	−	1.11826i	−0.583991	−	0.337168i	0.178727	−	0.983899i	$-0.442802\pi$
$11$	−1.93688	−	1.11826i	−0.583991	−	0.337168i	−0.762718	+	0.646731i	$0.776136\pi$
$12$	0.179082	+	3.45395i	0.0516965	+	0.997069i
$13$	−1.98274	−	3.01144i	−0.549912	−	0.835223i
$13$	−1.98274	−	3.01144i	−0.549912	−	0.835223i
$14$	0.110673	+	0.191692i	0.0295787	+	0.0512318i
$15$	−1.72973	+	0.0896838i	−0.446614	+	0.0231563i
$16$	−1.99045	+	3.44757i	−0.497614	+	0.861892i
$17$	5.60271			1.35886			0.679428	−	0.733742i	$-0.262228\pi$
$17$	5.60271			1.35886			0.679428	+	0.733742i	$0.262228\pi$
$18$	−0.0175053	−	0.168358i	−0.00412604	−	0.0396824i
$19$			6.06808i			1.39211i	0.717987	+	0.696056i	$0.245064\pi$
$19$			6.06808i			1.39211i	−0.717987	+	0.696056i	$0.754936\pi$
$20$	−1.72929	−	0.998408i	−0.386682	−	0.223251i
$21$	3.69761	+	5.70079i	0.806886	+	1.24401i
$22$	0.0630943	+	0.109282i	0.0134517	+	0.0232991i
$23$	−1.24872	−	2.16284i	−0.260376	−	0.450984i	0.705966	−	0.708246i	$-0.250513\pi$
$23$	−1.24872	−	2.16284i	−0.260376	−	0.450984i	−0.966342	+	0.257262i	$0.917180\pi$
$24$	0.177519	−	0.347921i	0.0362359	−	0.0710190i
$25$	0.500000	−	0.866025i	0.100000	−	0.173205i
$26$	0.0119265	+	0.203082i	0.00233898	+	0.0398277i
$27$	−0.804269	−	5.13353i	−0.154782	−	0.987949i
$28$			7.83364i			1.48042i
$29$	−2.26353	+	3.92055i	−0.420327	+	0.728028i	−0.995971	−	0.0896720i	$-0.971418\pi$
$29$	−2.26353	+	3.92055i	−0.420327	+	0.728028i	0.575644	+	0.817700i	$0.304751\pi$
$30$	0.0870494	+	0.0444151i	0.0158930	+	0.00810905i
$31$	1.13390	−	0.654658i	0.203655	−	0.117580i	−0.394704	−	0.918808i	$-0.629153\pi$
$31$	1.13390	−	0.654658i	0.203655	−	0.117580i	0.598359	+	0.801228i	$0.295820\pi$
$32$	0.585110	−	0.337813i	0.103434	−	0.0597175i
$33$	2.10799	+	3.24998i	0.366954	+	0.565750i
$34$	−0.273764	−	0.158058i	−0.0469502	−	0.0271067i
$35$	−3.92306			−0.663119
$36$	2.44264	−	5.46983i	0.407106	−	0.911638i
$37$			8.55454i			1.40636i	0.711013	+	0.703179i	$0.248237\pi$
$37$			8.55454i			1.40636i	−0.711013	+	0.703179i	$0.751763\pi$
$38$	0.171186	−	0.296503i	0.0277701	−	0.0480992i
$39$	0.688433	+	6.20694i	0.110238	+	0.993905i
$40$	0.112754	+	0.195296i	0.0178280	+	0.0308790i
$41$	−9.94634	+	5.74252i	−1.55336	+	0.896831i	−0.555493	+	0.831522i	$0.687470\pi$
$41$	−9.94634	+	5.74252i	−1.55336	+	0.896831i	−0.997865	+	0.0653099i	$0.979196\pi$
$42$	−0.0198512	−	0.382870i	−0.00306311	−	0.0590781i
$43$	4.04825	−	7.01177i	0.617352	−	1.06929i	−0.372615	−	0.927986i	$-0.621539\pi$
$43$	4.04825	−	7.01177i	0.617352	−	1.06929i	0.989967	−	0.141299i	$-0.0451279\pi$
$44$			4.46591i			0.673262i
$45$	2.73927	+	1.22327i	0.408347	+	0.182354i
$46$			0.140910i			0.0207761i
$47$	1.02507	+	0.591824i	0.149522	+	0.0863264i	0.572894	−	0.819629i	$-0.305821\pi$
$47$	1.02507	+	0.591824i	0.149522	+	0.0863264i	−0.423373	+	0.905956i	$0.639154\pi$
$48$	5.78484	−	3.75214i	0.834970	−	0.541574i
$49$	4.19522	+	7.26633i	0.599317	+	1.03805i
$50$	−0.0488628	+	0.0282110i	−0.00691025	+	0.00398963i
$51$	−8.64402	−	4.41042i	−1.21041	−	0.617583i
$52$	−3.22808	+	6.43538i	−0.447654	+	0.892426i
$53$	−4.19836			−0.576689			−0.288345	−	0.957527i	$-0.593105\pi$
$53$	−4.19836			−0.576689			−0.288345	+	0.957527i	$0.593105\pi$
$54$	−0.105523	+	0.273528i	−0.0143599	+	0.0372225i
$55$	−2.23652			−0.301572
$56$	0.442341	−	0.766158i	0.0591104	−	0.102382i
$57$	4.77676	−	9.36201i	0.632698	−	1.24003i
$58$	0.221205	−	0.127713i	0.0290457	−	0.0167695i
$59$	−3.81984	+	2.20539i	−0.497301	+	0.287117i	−0.727598	−	0.686003i	$-0.759363\pi$
$59$	−3.81984	+	2.20539i	−0.497301	+	0.287117i	0.230297	+	0.973120i	$0.426030\pi$
$60$	1.88206	+	2.90167i	0.242973	+	0.374603i
$61$	−1.24259	+	2.15224i	−0.159098	+	0.275566i	−0.934544	−	0.355849i	$-0.884192\pi$
$61$	−1.24259	+	2.15224i	−0.159098	+	0.275566i	0.775446	+	0.631414i	$0.217525\pi$
$62$	−0.0738742			−0.00938203
$63$	−1.21716	−	11.7061i	−0.153348	−	1.47483i
$64$	7.92370			0.990462
$65$	−3.22282	−	1.61661i	−0.399741	−	0.200516i
$66$	−0.0113171	−	0.218272i	−0.00139303	−	0.0268674i
$67$	−10.7969	+	6.23362i	−1.31906	+	0.761558i	−0.983577	−	0.180490i	$-0.942232\pi$
$67$	−10.7969	+	6.23362i	−1.31906	+	0.761558i	−0.335480	+	0.942048i	$0.608898\pi$
$68$	−5.59379	−	9.68873i	−0.678347	−	1.17493i
$69$	0.223979	+	4.31988i	0.0269640	+	0.520053i
$70$	0.191692	+	0.110673i	0.0229116	+	0.0132280i
$71$		−	16.1695i		−	1.91896i	−0.281771	−	0.959482i	$-0.590922\pi$
$71$		−	16.1695i		−	1.91896i	0.281771	−	0.959482i	$-0.409078\pi$
$72$	−0.547763	+	0.397040i	−0.0645545	+	0.0467916i
$73$		−	2.60190i		−	0.304530i	−0.988340	−	0.152265i	$-0.951343\pi$
$73$		−	2.60190i		−	0.304530i	0.988340	−	0.152265i	$-0.0486566\pi$
$74$	0.241332	−	0.417999i	0.0280542	−	0.0485914i
$75$	−1.45315	+	0.942532i	−0.167795	+	0.108834i
$76$	10.4935	−	6.05842i	1.20369	−	0.694948i
$77$	4.38700	+	7.59851i	0.499945	+	0.865930i
$78$	0.141465	−	0.322710i	0.0160177	−	0.0365397i
$79$	−1.96689	+	3.40675i	−0.221292	+	0.383289i	−0.955201	−	0.295959i	$-0.904361\pi$
$79$	−1.96689	+	3.40675i	−0.221292	+	0.383289i	0.733909	+	0.679248i	$0.237694\pi$
$80$			3.98091i			0.445079i
$81$	−2.80024	+	8.55328i	−0.311138	+	0.950365i
$82$	0.648008			0.0715606
$83$	−9.81398	−	5.66610i	−1.07722	−	0.621936i	−0.147078	−	0.989125i	$-0.546987\pi$
$83$	−9.81398	−	5.66610i	−1.07722	−	0.621936i	−0.930146	+	0.367189i	$0.880320\pi$
$84$	6.16660	−	12.0860i	0.672832	−	1.31869i
$85$	4.85209	−	2.80135i	0.526283	−	0.303849i
$86$	−0.395618	+	0.228410i	−0.0426606	+	0.0246301i
$87$	6.57849	−	4.26690i	0.705288	−	0.457460i
$88$	0.252176	−	0.436782i	0.0268821	−	0.0465611i
$89$		−	6.84387i		−	0.725449i	−0.931896	−	0.362725i	$-0.881847\pi$
$89$		−	6.84387i		−	0.725449i	0.931896	−	0.362725i	$-0.118153\pi$
$90$	−0.0993391	−	0.137050i	−0.0104713	−	0.0144463i
$91$	0.829258	+	14.1205i	0.0869299	+	1.48023i
$92$	−2.49346	+	4.31880i	−0.259961	+	0.450266i
$93$	−2.26476	+	0.117424i	−0.234845	+	0.0121764i
$94$	−0.0333918	−	0.0578364i	−0.00344411	−	0.00596536i
$95$	3.03404	+	5.25511i	0.311286	+	0.539163i
$96$	−1.16865	+	0.0605928i	−0.119275	+	0.00618422i
$97$	7.85275	+	4.53379i	0.797326	+	0.460336i	0.842535	−	0.538641i	$-0.181062\pi$
$97$	7.85275	+	4.53379i	0.797326	+	0.460336i	−0.0452095	+	0.998978i	$0.514396\pi$
$98$		−	0.473405i		−	0.0478211i
$99$	−0.693895	−	6.67357i	−0.0697391	−	0.670719i
$100$	−1.99682			−0.199682
$101$	8.04105	−	13.9275i	0.800115	−	1.38584i	−0.119425	−	0.992843i	$-0.538105\pi$
$101$	8.04105	−	13.9275i	0.800115	−	1.38584i	0.919540	−	0.392996i	$-0.128561\pi$
$102$	0.297949	+	0.459362i	0.0295014	+	0.0454836i
$103$	−2.49430	−	4.32026i	−0.245771	−	0.425688i	0.716577	−	0.697508i	$-0.245708\pi$
$103$	−2.49430	−	4.32026i	−0.245771	−	0.425688i	−0.962348	+	0.271820i	$0.912374\pi$
$104$	0.679104	−	0.447123i	0.0665916	−	0.0438440i
$105$	6.05262	+	3.08822i	0.590675	+	0.301379i
$106$	0.205144	+	0.118440i	0.0199253	+	0.0115039i
$107$	2.98845			0.288905			0.144452	−	0.989512i	$-0.453858\pi$
$107$	2.98845			0.288905			0.144452	+	0.989512i	$0.453858\pi$
$108$	−8.07440	+	6.51618i	−0.776959	+	0.627020i
$109$			3.26351i			0.312587i	0.987711	+	0.156294i	$0.0499546\pi$
$109$			3.26351i			0.312587i	−0.987711	+	0.156294i	$0.950045\pi$
$110$	0.109282	+	0.0630943i	0.0104197	+	0.00601580i
$111$	6.73409	−	13.1982i	0.639172	−	1.25272i
$112$	13.5250	−	7.80868i	1.27800	−	0.737851i
$113$	−7.10718	−	12.3100i	−0.668588	−	1.15803i	−0.978299	−	0.207197i	$-0.933566\pi$
$113$	−7.10718	−	12.3100i	−0.668588	−	1.15803i	0.309712	−	0.950831i	$-0.399768\pi$
$114$	−0.497517	+	0.322697i	−0.0465968	+	0.0302234i
$115$	−2.16284	−	1.24872i	−0.201686	−	0.116444i
$116$	9.03972			0.839317
$117$	3.82394	−	10.1182i	0.353523	−	0.935426i
$118$	0.248864			0.0229098
$119$	−19.0351	−	10.9899i	−1.74494	−	1.00744i
$120$	−0.0202244	−	0.390068i	−0.00184623	−	0.0356081i
$121$	−2.99900	−	5.19442i	−0.272636	−	0.472220i
$122$	0.121433	−	0.0701095i	0.0109941	−	0.00634742i
$123$	19.8660	−	1.03002i	1.79126	−	0.0928740i
$124$	−2.26419	−	1.30723i	−0.203331	−	0.117393i
$125$		−	1.00000i		−	0.0894427i
$126$	−0.270766	+	0.606330i	−0.0241218	+	0.0540161i
$127$	−13.7243			−1.21784			−0.608918	−	0.793233i	$-0.708396\pi$
$127$	−13.7243			−1.21784			−0.608918	+	0.793233i	$0.708396\pi$
$128$	−1.55739	−	0.899162i	−0.137655	−	0.0794754i
$129$	−11.7654	+	7.63121i	−1.03588	+	0.671890i
$130$	0.111870	+	0.169911i	0.00981163	+	0.0149022i
$131$	4.68504	+	8.11473i	0.409334	+	0.708988i	0.994815	−	0.101698i	$-0.0324277\pi$
$131$	4.68504	+	8.11473i	0.409334	+	0.708988i	−0.585481	+	0.810686i	$0.699094\pi$
$132$	3.51555	−	6.89014i	0.305989	−	0.599710i
$133$	11.9027	−	20.6161i	1.03210	−	1.78765i
$134$	0.703425			0.0607667
$135$	−3.26328	−	4.04363i	−0.280859	−	0.348021i
$136$			1.26346i			0.108340i
$137$	3.22002	+	1.85908i	0.275105	+	0.158832i	0.631205	−	0.775616i	$-0.282561\pi$
$137$	3.22002	+	1.85908i	0.275105	+	0.158832i	−0.356100	+	0.934448i	$0.615894\pi$
$138$	0.110924	−	0.217400i	0.00944246	−	0.0185063i
$139$	7.25279	+	12.5622i	0.615173	+	1.06551i	0.990354	+	0.138560i	$0.0442473\pi$
$139$	7.25279	+	12.5622i	0.615173	+	1.06551i	−0.375181	+	0.926952i	$0.622419\pi$
$140$	3.91682	+	6.78413i	0.331032	+	0.573364i
$141$	−1.11563	−	1.72001i	−0.0939526	−	0.144851i
$142$	−0.456156	+	0.790086i	−0.0382798	+	0.0663025i
$143$	0.472755	+	8.05000i	0.0395338	+	0.673175i
$144$	−11.8787	+	1.23511i	−0.989891	+	0.102925i
$145$			4.52707i			0.375952i
$146$	−0.0734021	+	0.127136i	−0.00607480	+	0.0105219i
$147$	−0.752486	−	14.5132i	−0.0620640	−	1.19703i
$148$	14.7933	−	8.54092i	1.21600	−	0.702059i
$149$	8.51245	−	4.91467i	0.697367	−	0.402625i	−0.108999	−	0.994042i	$-0.534764\pi$
$149$	8.51245	−	4.91467i	0.697367	−	0.402625i	0.806366	+	0.591417i	$0.201431\pi$
$150$	0.0975946	−	0.00506013i	0.00796856	−	0.000413158i
$151$	−7.20109	−	4.15755i	−0.586016	−	0.338336i	0.177505	−	0.984120i	$-0.443198\pi$
$151$	−7.20109	−	4.15755i	−0.586016	−	0.338336i	−0.763521	+	0.645783i	$0.776531\pi$
$152$	−1.36840			−0.110992
$153$	9.86439	+	13.6091i	0.797489	+	1.10023i
$154$		−	0.495046i		−	0.0398919i
$155$	0.654658	−	1.13390i	0.0525834	−	0.0910772i
$156$	10.0463	−	7.38756i	0.804346	−	0.591478i
$157$	−5.44180	−	9.42547i	−0.434303	−	0.752234i	0.562936	−	0.826501i	$-0.309672\pi$
$157$	−5.44180	−	9.42547i	−0.434303	−	0.752234i	−0.997238	+	0.0742665i	$0.976338\pi$
$158$	0.192215	−	0.110976i	0.0152918	−	0.00882874i
$159$	6.47736	+	3.30493i	0.513688	+	0.262098i
$160$	0.337813	−	0.585110i	0.0267065	−	0.0462570i
$161$			9.79760i			0.772159i
$162$	0.378124	−	0.338940i	0.0297082	−	0.0266296i
$163$			7.14857i			0.559920i	0.960012	+	0.279960i	$0.0903211\pi$
$163$			7.14857i			0.559920i	−0.960012	+	0.279960i	$0.909679\pi$
$164$	19.8610	+	11.4668i	1.55089	+	0.895404i
$165$	3.45056	+	1.76057i	0.268626	+	0.137061i
$166$	0.319692	+	0.553724i	0.0248129	+	0.0429773i
$167$	−14.7716	+	8.52841i	−1.14306	+	0.659948i	−0.947188	−	0.320680i	$-0.896089\pi$
$167$	−14.7716	+	8.52841i	−1.14306	+	0.659948i	−0.195877	+	0.980629i	$0.562755\pi$
$168$	−1.28557	+	0.833842i	−0.0991841	+	0.0643323i
$169$	−5.13752	+	11.9418i	−0.395194	+	0.918598i
$170$	−0.316116			−0.0242450
$171$	−14.7395	+	10.6837i	−1.12715	+	0.817006i
$172$	−16.1672			−1.23274
$173$	−7.72383	+	13.3781i	−0.587232	+	1.01711i	0.407362	+	0.913267i	$0.366449\pi$
$173$	−7.72383	+	13.3781i	−0.587232	+	1.01711i	−0.994593	+	0.103848i	$0.966884\pi$
$174$	−0.441817	+	0.0229075i	−0.0334941	+	0.00173662i
$175$	−3.39747	+	1.96153i	−0.256825	+	0.148278i
$176$	7.71054	−	4.45168i	0.581204	−	0.335558i
$177$	7.62944	−	0.395575i	0.573464	−	0.0297332i
$178$	−0.193072	+	0.334411i	−0.0144714	+	0.0250652i
$179$	−8.60028			−0.642815			−0.321407	−	0.946941i	$-0.604156\pi$
$179$	−8.60028			−0.642815			−0.321407	+	0.946941i	$0.604156\pi$
$180$	−0.619526	−	5.95833i	−0.0461768	−	0.444108i
$181$	−5.06617			−0.376565			−0.188283	−	0.982115i	$-0.560292\pi$
$181$	−5.06617			−0.376565			−0.188283	+	0.982115i	$0.560292\pi$
$182$	0.357833	−	0.713361i	0.0265243	−	0.0528778i
$183$	3.61134	−	2.34237i	0.266958	−	0.173153i
$184$	0.487739	−	0.281596i	0.0359566	−	0.0207595i
$185$	4.27727	+	7.40845i	0.314471	+	0.544680i
$186$	0.113975	+	0.0581534i	0.00835707	+	0.00426401i
$187$	−10.8518	−	6.26527i	−0.793560	−	0.458162i
$188$		−	2.36353i		−	0.172378i
$189$	−7.33711	+	19.0186i	−0.533696	+	1.38340i
$190$		−	0.342373i		−	0.0248383i
$191$	−2.33736	+	4.04843i	−0.169125	+	0.292934i	−0.938113	−	0.346330i	$-0.887428\pi$
$191$	−2.33736	+	4.04843i	−0.169125	+	0.292934i	0.768987	+	0.639264i	$0.220761\pi$
$192$	−12.2249	−	6.23750i	−0.882257	−	0.450153i
$193$	−9.77243	+	5.64211i	−0.703435	+	0.406128i	−0.808625	−	0.588324i	$-0.799788\pi$
$193$	−9.77243	+	5.64211i	−0.703435	+	0.406128i	0.105191	+	0.994452i	$0.466455\pi$
$194$	−0.255805	−	0.443067i	−0.0183657	−	0.0318104i
$195$	3.69967	+	5.03115i	0.264939	+	0.360288i
$196$	8.37708	−	14.5095i	0.598363	−	1.03640i
$197$		−	16.1866i		−	1.15325i	−0.817009	−	0.576625i	$-0.804369\pi$
$197$		−	16.1866i		−	1.15325i	0.817009	−	0.576625i	$-0.195631\pi$
$198$	−0.154362	+	0.345665i	−0.0109700	+	0.0245653i
$199$	2.33078			0.165224			0.0826121	−	0.996582i	$-0.473674\pi$
$199$	2.33078			0.165224			0.0826121	+	0.996582i	$0.473674\pi$
$200$	0.195296	+	0.112754i	0.0138095	+	0.00797291i
$201$	21.5649	−	1.11811i	1.52107	−	0.0788653i
$202$	−0.785817	+	0.453692i	−0.0552899	+	0.0319216i
$203$	15.3806	−	8.87998i	1.07951	−	0.623253i
$204$	1.00334	+	19.3515i	0.0702482	+	1.35487i
$205$	−5.74252	+	9.94634i	−0.401075	+	0.694683i
$206$			0.281467i			0.0196107i
$207$	3.05503	−	6.84116i	0.212339	−	0.475493i
$208$	14.3287	−	0.841486i	0.993516	−	0.0583465i
$209$	6.78568	−	11.7531i	0.469375	−	0.812981i
$210$	−0.208627	−	0.321649i	−0.0143966	−	0.0221959i
$211$	11.7297	+	20.3165i	0.807507	+	1.39864i	0.914586	+	0.404392i	$0.132517\pi$
$211$	11.7297	+	20.3165i	0.807507	+	1.39864i	−0.107079	+	0.994251i	$0.534150\pi$
$212$	4.19168	+	7.26020i	0.287886	+	0.498633i
$213$	−12.7285	+	24.9467i	−0.872145	+	1.70932i
$214$	−0.146024	−	0.0843072i	−0.00998201	−	0.00576312i
$215$		−	8.09650i		−	0.552176i
$216$	1.15765	−	0.181369i	0.0787683	−	0.0123406i
$217$	−5.13653			−0.348691
$218$	0.0920667	−	0.159464i	0.00623554	−	0.0108003i
$219$	−2.04820	+	4.01429i	−0.138405	+	0.271261i
$220$	2.23296	+	3.86759i	0.150546	+	0.260753i
$221$	−11.1087	−	16.8722i	−0.747251	−	1.13495i
$222$	−0.701380	+	0.454926i	−0.0470736	+	0.0305326i
$223$	−21.9530	−	12.6746i	−1.47008	−	0.848751i	−0.470643	−	0.882324i	$-0.655978\pi$
$223$	−21.9530	−	12.6746i	−1.47008	−	0.848751i	−0.999436	+	0.0335730i	$0.989311\pi$
$224$	−2.65053			−0.177096
$225$	2.98391	−	0.310257i	0.198928	−	0.0206838i
$226$			0.802002i			0.0533484i
$227$	−16.2917	−	9.40600i	−1.08132	−	0.624298i	−0.150065	−	0.988676i	$-0.547948\pi$
$227$	−16.2917	−	9.40600i	−1.08132	−	0.624298i	−0.931251	+	0.364378i	$0.881282\pi$
$228$	−20.9588	+	1.08668i	−1.38803	+	0.0719674i
$229$	0.913257	−	0.527269i	0.0603497	−	0.0348429i	−0.469522	−	0.882921i	$-0.655574\pi$
$229$	0.913257	−	0.527269i	0.0603497	−	0.0348429i	0.529871	+	0.848078i	$0.322240\pi$
$230$	0.0704551	+	0.122032i	0.00464567	+	0.00804654i
$231$	−0.786885	−	15.1766i	−0.0517733	−	0.998549i
$232$	−0.884116	−	0.510445i	−0.0580451	−	0.0335123i
$233$	0.222496			0.0145762			0.00728811	−	0.999973i	$-0.497680\pi$
$233$	0.222496			0.0145762			0.00728811	+	0.999973i	$0.497680\pi$
$234$	−0.472292	+	0.386526i	−0.0308747	+	0.0252680i
$235$	1.18365			0.0772127
$236$	7.62752	+	4.40375i	0.496510	+	0.286660i
$237$	5.71635	−	3.70771i	0.371317	−	0.240842i
$238$	0.620071	+	1.07399i	0.0401932	+	0.0696167i
$239$	8.37195	−	4.83355i	0.541537	−	0.312656i	−0.204165	−	0.978937i	$-0.565448\pi$
$239$	8.37195	−	4.83355i	0.541537	−	0.312656i	0.745701	+	0.666280i	$0.232115\pi$
$240$	3.13375	−	6.14187i	0.202283	−	0.396456i
$241$	−19.7643	−	11.4109i	−1.27313	−	0.735041i	−0.297553	−	0.954705i	$-0.596170\pi$
$241$	−19.7643	−	11.4109i	−1.27313	−	0.735041i	−0.975575	+	0.219664i	$0.929504\pi$
$242$			0.338418i			0.0217544i
$243$	11.0534	−	10.9919i	0.709076	−	0.705132i
$244$	4.96246			0.317689
$245$	7.26633	+	4.19522i	0.464229	+	0.268023i
$246$	−0.999767	−	0.510109i	−0.0637428	−	0.0325234i
$247$	18.2736	−	12.0314i	1.16272	−	0.765539i
$248$	0.147631	+	0.255704i	0.00937456	+	0.0162372i
$249$	10.6810	+	16.4674i	0.676879	+	1.04358i
$250$	−0.0282110	+	0.0488628i	−0.00178422	+	0.00309036i
$251$	−23.5586			−1.48701			−0.743503	−	0.668732i	$-0.766837\pi$
$251$	−23.5586			−1.48701			−0.743503	+	0.668732i	$0.766837\pi$
$252$	−19.0280	+	13.7923i	−1.19865	+	0.868832i
$253$			5.58556i			0.351161i
$254$	0.670609	+	0.387176i	0.0420777	+	0.0242936i
$255$	−9.69116	+	0.502472i	−0.606884	+	0.0314660i
$256$	−7.87297	−	13.6364i	−0.492060	−	0.852274i
$257$	−4.93068	−	8.54019i	−0.307567	−	0.532722i	0.670262	−	0.742124i	$-0.266182\pi$
$257$	−4.93068	−	8.54019i	−0.307567	−	0.532722i	−0.977830	+	0.209402i	$0.932848\pi$
$258$	0.790174	−	0.0409693i	0.0491941	−	0.00255064i
$259$	16.7800	−	29.0638i	1.04266	−	1.80594i
$260$	0.422088	+	7.18724i	0.0261768	+	0.445734i
$261$	−13.5084	+	1.40455i	−0.836147	+	0.0869397i
$262$		−	0.528678i		−	0.0326619i
$263$	3.99398	−	6.91778i	0.246279	−	0.426568i	−0.716211	−	0.697884i	$-0.754125\pi$
$263$	3.99398	−	6.91778i	0.246279	−	0.426568i	0.962491	+	0.271315i	$0.0874586\pi$
$264$	−0.732898	+	0.475368i	−0.0451067	+	0.0292569i
$265$	−3.63589	+	2.09918i	−0.223351	+	0.128952i
$266$	−1.16320	+	0.671575i	−0.0713205	+	0.0411769i
$267$	−5.38747	+	10.5589i	−0.329708	+	0.646196i
$268$	21.5595	+	12.4474i	1.31696	+	0.760345i
$269$	−16.6199			−1.01333			−0.506666	−	0.862143i	$-0.669122\pi$
$269$	−16.6199			−1.01333			−0.506666	+	0.862143i	$0.669122\pi$
$270$	0.0453784	+	0.289644i	0.00276164	+	0.0176272i
$271$		−	6.16970i		−	0.374783i	−0.982285	−	0.187391i	$-0.939997\pi$
$271$		−	6.16970i		−	0.374783i	0.982285	−	0.187391i	$-0.0600033\pi$
$272$	−11.1519	+	19.3157i	−0.676185	+	1.17119i
$273$	9.83617	−	22.4383i	0.595312	−	1.35803i
$274$	−0.104893	−	0.181680i	−0.00633681	−	0.0109757i
$275$	−1.93688	+	1.11826i	−0.116798	+	0.0674335i
$276$	7.24672	−	4.70033i	0.436202	−	0.282927i
$277$	−7.88696	+	13.6606i	−0.473881	+	0.820786i	−0.999553	−	0.0299012i	$-0.990481\pi$
$277$	−7.88696	+	13.6606i	−0.473881	+	0.820786i	0.525672	+	0.850688i	$0.323814\pi$
$278$		−	0.818432i		−	0.0490863i
$279$	3.58658	+	1.60164i	0.214723	+	0.0958879i
$280$		−	0.884683i		−	0.0528699i
$281$	23.2643	+	13.4317i	1.38783	+	0.801267i	0.993071	−	0.117516i	$-0.0374931\pi$
$281$	23.2643	+	13.4317i	1.38783	+	0.801267i	0.394764	+	0.918783i	$0.370826\pi$
$282$	0.00598941	+	0.115518i	0.000356664	+	0.00687897i
$283$	9.52837	+	16.5036i	0.566403	+	0.981039i	0.996918	+	0.0784550i	$0.0249987\pi$
$283$	9.52837	+	16.5036i	0.566403	+	0.981039i	−0.430515	+	0.902584i	$0.641668\pi$
$284$	−27.9618	+	16.1437i	−1.65923	+	0.957954i
$285$	−0.544208	−	10.4961i	−0.0322361	−	0.621736i
$286$	0.203998	−	0.406683i	0.0120627	−	0.0240477i
$287$	45.0566			2.65961
$288$	1.85073	+	0.826472i	0.109055	+	0.0487003i
$289$	14.3903			0.846490
$290$	0.127713	−	0.221205i	0.00749956	−	0.0129896i
$291$	−8.54648	−	13.1765i	−0.501003	−	0.772420i
$292$	−4.49945	+	2.59776i	−0.263310	+	0.152022i
$293$	15.3363	−	8.85439i	0.895954	−	0.517279i	0.0200686	−	0.999799i	$-0.493612\pi$
$293$	15.3363	−	8.85439i	0.895954	−	0.517279i	0.875885	+	0.482519i	$0.160278\pi$
$294$	−0.372662	+	0.730383i	−0.0217341	+	0.0425968i
$295$	−2.20539	+	3.81984i	−0.128403	+	0.222400i
$296$	−1.92912			−0.112128
$297$	−4.18284	+	10.8424i	−0.242713	+	0.629141i
$298$	−0.554590			−0.0321265
$299$	−4.03739	+	8.04878i	−0.233488	+	0.465473i
$300$	3.08075	+	1.57188i	0.177867	+	0.0907528i
$301$	−27.5076	+	15.8815i	−1.58551	+	0.915397i
$302$	0.234577	+	0.406299i	0.0134984	+	0.0233799i
$303$	−23.3697	+	15.1579i	−1.34255	+	0.870799i
$304$	−20.9201	−	12.0782i	−1.19985	−	0.692734i
$305$			2.48519i			0.142301i
$306$	−0.0980771	−	0.943262i	−0.00560669	−	0.0539227i
$307$		−	22.5071i		−	1.28455i	−0.766476	−	0.642274i	$-0.777991\pi$
$307$		−	22.5071i		−	1.28455i	0.766476	−	0.642274i	$-0.222009\pi$
$308$	8.76003	−	15.1728i	0.499149	−	0.864552i
$309$	0.447397	+	8.62892i	0.0254515	+	0.490882i
$310$	−0.0639769	+	0.0369371i	−0.00363364	+	0.00209789i
$311$	2.32016	+	4.01864i	0.131564	+	0.227876i	0.924280	−	0.381716i	$-0.124667\pi$
$311$	2.32016	+	4.01864i	0.131564	+	0.227876i	−0.792715	+	0.609592i	$0.791333\pi$
$312$	−1.39971	+	0.155247i	−0.0792432	+	0.00878915i
$313$	−16.2853	+	28.2070i	−0.920500	+	1.59435i	−0.121856	+	0.992548i	$0.538885\pi$
$313$	−16.2853	+	28.2070i	−0.920500	+	1.59435i	−0.798643	+	0.601805i	$0.794449\pi$
$314$			0.614073i			0.0346542i
$315$	−6.90713	−	9.52919i	−0.389173	−	0.536909i
$316$	7.85502			0.441880
$317$	20.6638	+	11.9302i	1.16059	+	0.670069i	0.951446	−	0.307815i	$-0.0995978\pi$
$317$	20.6638	+	11.9302i	1.16059	+	0.670069i	0.209147	+	0.977884i	$0.432931\pi$
$318$	−0.223267	−	0.344221i	−0.0125202	−	0.0193029i
$319$	8.76838	−	5.06243i	0.490935	−	0.283442i
$320$	6.86212	−	3.96185i	0.383604	−	0.221474i
$321$	−4.61068	−	2.35250i	−0.257343	−	0.131304i
$322$	0.276400	−	0.478739i	0.0154032	−	0.0266791i
$323$			33.9977i			1.89168i
$324$	17.5869	−	3.69723i	0.977051	−	0.205401i
$325$	−3.59935	+	0.211380i	−0.199656	+	0.0117253i
$326$	0.201668	−	0.349299i	0.0111694	−	0.0193459i
$327$	2.56902	−	5.03503i	0.142067	−	0.278438i
$328$	−1.29499	−	2.24298i	−0.0715036	−	0.123848i
$329$	−2.32176	−	4.02141i	−0.128003	−	0.221708i
$330$	−0.118937	−	0.183370i	−0.00654725	−	0.0100942i
$331$	23.8032	+	13.7428i	1.30834	+	0.755373i	0.981820	−	0.189815i	$-0.0607889\pi$
$331$	23.8032	+	13.7428i	1.30834	+	0.755373i	0.326525	+	0.945189i	$0.394122\pi$
$332$			22.6283i			1.24189i
$333$	−20.7791	+	15.0615i	−1.13869	+	0.825366i
$334$	0.962379			0.0526590
$335$	−6.23362	+	10.7969i	−0.340579	+	0.589900i
$336$	−27.0138	+	1.40062i	−1.47372	+	0.0764103i
$337$	−3.21413	−	5.56704i	−0.175085	−	0.303256i	0.765106	−	0.643905i	$-0.222687\pi$
$337$	−3.21413	−	5.56704i	−0.175085	−	0.303256i	−0.940191	+	0.340649i	$0.889353\pi$
$338$	0.587923	−	0.438574i	0.0319788	−	0.0238553i
$339$	1.27480	+	24.5870i	0.0692375	+	1.33538i
$340$	−9.68873	−	5.59379i	−0.525445	−	0.303366i
$341$	−2.92831			−0.158577
$342$	1.02161	−	0.106223i	0.0552424	−	0.00574391i
$343$		−	5.45478i		−	0.294530i
$344$	1.58121	+	0.912913i	0.0852532	+	0.0492210i
$345$	2.35391	+	3.62914i	0.126730	+	0.195386i
$346$	0.754816	−	0.435793i	0.0405792	−	0.0234284i
$347$	12.0642	+	20.8959i	0.647642	+	1.12175i	0.983685	+	0.179902i	$0.0575780\pi$
$347$	12.0642	+	20.8959i	0.647642	+	1.12175i	−0.336043	+	0.941847i	$0.609089\pi$
$348$	−13.9467	−	7.11602i	−0.747624	−	0.381459i
$349$	12.2509	+	7.07307i	0.655776	+	0.378613i	0.790666	−	0.612248i	$-0.209735\pi$
$349$	12.2509	+	7.07307i	0.655776	+	0.378613i	−0.134889	+	0.990861i	$0.543068\pi$
$350$	0.221347			0.0118315
$351$	−13.8647	+	12.6004i	−0.740041	+	0.672562i
$352$	−1.51105			−0.0805392
$353$	−10.9026	−	6.29463i	−0.580288	−	0.335029i	0.180960	−	0.983490i	$-0.442080\pi$
$353$	−10.9026	−	6.29463i	−0.580288	−	0.335029i	−0.761248	+	0.648461i	$0.775413\pi$
$354$	−0.383955	−	0.195905i	−0.0204070	−	0.0104122i
$355$	−8.08474	−	14.0032i	−0.429093	−	0.743211i
$356$	−11.8351	+	6.83298i	−0.627257	+	0.362147i
$357$	20.7167	+	31.9398i	1.09644	+	1.69044i
$358$	0.420234	+	0.242622i	0.0222100	+	0.0128230i
$359$		−	5.96722i		−	0.314938i	−0.987524	−	0.157469i	$-0.949667\pi$
$359$		−	5.96722i		−	0.314938i	0.987524	−	0.157469i	$-0.0503334\pi$
$360$	−0.275856	+	0.617728i	−0.0145389	+	0.0325571i
$361$	−17.8216			−0.937977
$362$	0.247547	+	0.142921i	0.0130108	+	0.00751178i
$363$	0.537923	+	10.3749i	0.0282336	+	0.544541i
$364$	23.5905	−	15.5320i	1.23648	−	0.814100i
$365$	−1.30095	−	2.25331i	−0.0680949	−	0.117944i
$366$	−0.242541	+	0.0125754i	−0.0126778	+	0.000657326i
$367$	−0.0500029	+	0.0866076i	−0.00261013	+	0.00452088i	−0.867328	−	0.497738i	$-0.834164\pi$
$367$	−0.0500029	+	0.0866076i	−0.00261013	+	0.00452088i	0.864717	+	0.502259i	$0.167497\pi$
$368$	9.94207			0.518266
$369$	−31.4607	−	14.0493i	−1.63778	−	0.731376i
$370$		−	0.482663i		−	0.0250925i
$371$	14.2638	+	8.23522i	0.740541	+	0.427551i
$372$	2.46422	+	3.79920i	0.127764	+	0.196979i
$373$	−10.5159	−	18.2141i	−0.544492	−	0.943088i	−0.998639	−	0.0521612i	$-0.983389\pi$
$373$	−10.5159	−	18.2141i	−0.544492	−	0.943088i	0.454146	−	0.890927i	$-0.349944\pi$
$374$	0.353499	+	0.612278i	0.0182790	+	0.0316601i
$375$	−0.787195	+	1.54283i	−0.0406506	+	0.0796714i
$376$	−0.133461	+	0.231161i	−0.00688273	+	0.0119212i
$377$	16.2945	−	0.956932i	0.839209	−	0.0492845i
$378$	0.895046	−	0.722318i	0.0460362	−	0.0371520i
$379$		−	7.61597i		−	0.391206i	−0.980683	−	0.195603i	$-0.937334\pi$
$379$		−	7.61597i		−	0.391206i	0.980683	−	0.195603i	$-0.0626664\pi$
$380$	6.05842	−	10.4935i	0.310790	−	0.538305i
$381$	21.1743	+	10.8037i	1.08479	+	0.553491i
$382$	0.228420	−	0.131878i	0.0116870	−	0.00674749i
$383$	−7.94552	+	4.58735i	−0.405997	+	0.234403i	−0.689068	−	0.724696i	$-0.741980\pi$
$383$	−7.94552	+	4.58735i	−0.405997	+	0.234403i	0.283071	+	0.959099i	$0.408647\pi$
$384$	1.69498	+	2.61323i	0.0864965	+	0.133356i
$385$	7.59851	+	4.38700i	0.387256	+	0.223582i
$386$	0.636678			0.0324061
$387$	24.1592	−	2.51199i	1.22808	−	0.127692i
$388$		−	18.1063i		−	0.919207i
$389$	15.0167	−	26.0097i	0.761377	−	1.31874i	−0.180764	−	0.983527i	$-0.557857\pi$
$389$	15.0167	−	26.0097i	0.761377	−	1.31874i	0.942141	−	0.335217i	$-0.108810\pi$
$390$	−0.0388427	−	0.350207i	−0.00196688	−	0.0177334i
$391$	−6.99620	−	12.1178i	−0.353813	−	0.612822i
$392$	−1.63862	+	0.946056i	−0.0827626	+	0.0477830i
$393$	−0.840345	−	16.2077i	−0.0423898	−	0.817570i
$394$	−0.456641	+	0.790925i	−0.0230052	+	0.0398462i
$395$			3.93377i			0.197930i
$396$	−10.8478	+	7.86290i	−0.545121	+	0.395125i
$397$			13.2652i			0.665763i	0.942969	+	0.332882i	$0.108021\pi$
$397$			13.2652i			0.665763i	−0.942969	+	0.332882i	$0.891979\pi$
$398$	−0.113888	−	0.0657534i	−0.00570870	−	0.00329592i
$399$	−34.5928	+	22.4374i	−1.73181	+	1.12328i
$400$	1.99045	+	3.44757i	0.0995227	+	0.172378i
$401$	23.3517	−	13.4821i	1.16613	−	0.673265i	0.213364	−	0.976973i	$-0.431558\pi$
$401$	23.3517	−	13.4821i	1.16613	−	0.673265i	0.952765	+	0.303708i	$0.0982246\pi$
$402$	−1.08527	−	0.553733i	−0.0541281	−	0.0276177i
$403$	−4.21969	−	2.11666i	−0.210198	−	0.105438i
$404$	−32.1130			−1.59768
$405$	1.85156	+	8.80748i	0.0920048	+	0.437647i
$406$	−1.00205			−0.0497310
$407$	9.56618	−	16.5691i	0.474178	−	0.821300i
$408$	0.994587	−	1.94930i	0.0492394	−	0.0965046i
$409$	−22.6012	+	13.0488i	−1.11756	+	0.645222i	−0.940776	−	0.339028i	$-0.889902\pi$
$409$	−22.6012	+	13.0488i	−1.11756	+	0.645222i	−0.176781	+	0.984250i	$0.556568\pi$
$410$	0.561192	−	0.324004i	0.0277153	−	0.0160014i
$411$	−3.50448	−	5.40303i	−0.172863	−	0.266512i
$412$	−4.98066	+	8.62676i	−0.245380	+	0.425010i
$413$	17.3038			0.851462
$414$	−0.342273	+	0.248093i	−0.0168218	+	0.0121931i
$415$	−11.3322			−0.556276
$416$	−2.17742	−	1.09223i	−0.106757	−	0.0535509i
$417$	−1.30091	−	25.0907i	−0.0637061	−	1.22870i
$418$	−0.663135	+	0.382861i	−0.0324350	+	0.0187263i
$419$	−5.72212	−	9.91100i	−0.279544	−	0.484184i	0.691728	−	0.722158i	$-0.256850\pi$
$419$	−5.72212	−	9.91100i	−0.279544	−	0.484184i	−0.971271	+	0.237975i	$0.923517\pi$
$420$	−0.702551	−	13.5501i	−0.0342810	−	0.661175i
$421$	−8.24733	−	4.76160i	−0.401950	−	0.232066i	0.285375	−	0.958416i	$-0.407882\pi$
$421$	−8.24733	−	4.76160i	−0.401950	−	0.232066i	−0.687325	+	0.726350i	$0.741215\pi$
$422$		−	1.32363i		−	0.0644331i
$423$	0.367235	+	3.53190i	0.0178556	+	0.171727i
$424$		−	0.946765i		−	0.0459789i
$425$	2.80135	−	4.85209i	0.135886	−	0.235361i
$426$	1.32572	−	0.859884i	0.0642315	−	0.0416615i
$427$	8.44336	−	4.87478i	0.408603	−	0.235907i
$428$	−2.98370	−	5.16791i	−0.144222	−	0.249801i
$429$	5.60754	−	12.7919i	0.270735	−	0.617601i
$430$	−0.228410	+	0.395618i	−0.0110149	+	0.0190784i
$431$		−	23.2510i		−	1.11996i	−0.828506	−	0.559980i	$-0.810809\pi$
$431$		−	23.2510i		−	1.11996i	0.828506	−	0.559980i	$-0.189191\pi$
$432$	19.2991	+	7.44529i	0.928527	+	0.358212i
$433$	20.5579			0.987950			0.493975	−	0.869476i	$-0.335543\pi$
$433$	20.5579			0.987950			0.493975	+	0.869476i	$0.335543\pi$
$434$	0.250986	+	0.144907i	0.0120477	+	0.00695574i
$435$	3.56368	−	6.98449i	0.170866	−	0.334881i
$436$	5.64356	−	3.25831i	0.270278	−	0.156045i
$437$	13.1243	−	7.57732i	0.627820	−	0.362472i
$438$	0.213328	−	0.138368i	0.0101932	−	0.00661147i
$439$	13.9718	−	24.1999i	0.666837	−	1.15500i	−0.311946	−	0.950100i	$-0.600981\pi$
$439$	13.9718	−	24.1999i	0.666837	−	1.15500i	0.978784	−	0.204896i	$-0.0656858\pi$
$440$		−	0.504353i		−	0.0240441i
$441$	−10.2637	+	22.9837i	−0.488750	+	1.09446i
$442$	0.0668206	+	1.13781i	0.00317833	+	0.0541201i
$443$	−6.69562	+	11.5972i	−0.318119	+	0.550998i	−0.980095	−	0.198527i	$-0.936384\pi$
$443$	−6.69562	+	11.5972i	−0.318119	+	0.550998i	0.661977	+	0.749524i	$0.269718\pi$
$444$	−29.5469	+	1.53196i	−1.40224	+	0.0727038i
$445$	−3.42194	−	5.92697i	−0.162215	−	0.280965i
$446$	0.715123	+	1.23863i	0.0338620	+	0.0586508i
$447$	−17.0021	+	0.881532i	−0.804170	+	0.0416950i
$448$	−26.9206	−	15.5426i	−1.27188	−	0.734318i
$449$		−	3.18766i		−	0.150435i	−0.997167	−	0.0752175i	$-0.976035\pi$
$449$		−	3.18766i		−	0.150435i	0.997167	−	0.0752175i	$-0.0239651\pi$
$450$	−0.154555	−	0.0690190i	−0.00728580	−	0.00325359i
$451$	25.6865			1.20953
$452$	−14.1917	+	24.5808i	−0.667523	+	1.15618i
$453$	7.83725	+	12.0830i	0.368226	+	0.567711i
$454$	0.530705	+	0.919207i	0.0249072	+	0.0431405i
$455$	7.77840	+	11.8141i	0.364657	+	0.553852i
$456$	2.11121	+	1.07720i	0.0988664	+	0.0504444i
$457$	−10.0586	−	5.80733i	−0.470521	−	0.271656i	0.245937	−	0.969286i	$-0.420904\pi$
$457$	−10.0586	−	5.80733i	−0.470521	−	0.271656i	−0.716458	+	0.697630i	$0.754238\pi$
$458$	−0.0594991			−0.00278021
$459$	−4.50608	−	28.7617i	−0.210326	−	1.34248i
$460$			4.98692i			0.232516i
$461$	−13.6499	−	7.88076i	−0.635738	−	0.367043i	0.147233	−	0.989102i	$-0.452963\pi$
$461$	−13.6499	−	7.88076i	−0.635738	−	0.367043i	−0.782971	+	0.622058i	$0.786297\pi$
$462$	−0.389698	+	0.763772i	−0.0181304	+	0.0355339i
$463$	23.6139	−	13.6335i	1.09743	−	0.633603i	0.161887	−	0.986809i	$-0.448242\pi$
$463$	23.6139	−	13.6335i	1.09743	−	0.633603i	0.935546	+	0.353206i	$0.114909\pi$
$464$	−9.01092	−	15.6074i	−0.418321	−	0.724554i
$465$	−1.90263	+	1.23407i	−0.0882323	+	0.0572288i
$466$	−0.0108718	−	0.00627684i	−0.000503626	−	0.000290769i
$467$	−15.6111			−0.722398			−0.361199	−	0.932489i	$-0.617632\pi$
$467$	−15.6111			−0.722398			−0.361199	+	0.932489i	$0.617632\pi$
$468$	−21.3152	+	3.48936i	−0.985293	+	0.161296i
$469$	48.9098			2.25844
$470$	−0.0578364	−	0.0333918i	−0.00266779	−	0.00154025i
$471$	0.976082	+	18.8256i	0.0449755	+	0.867440i
$472$	−0.497333	−	0.861405i	−0.0228916	−	0.0396494i
$473$	−15.6819	+	9.05397i	−0.721056	+	0.416302i
$474$	−0.383915	+	0.0199054i	−0.0176338	+	0.000914286i
$475$	5.25511	+	3.03404i	0.241121	+	0.139211i
$476$			43.8896i			2.01168i
$477$	−7.39183	−	10.1979i	−0.338449	−	0.466929i
$478$	−0.545436			−0.0249477
$479$	24.0241	+	13.8703i	1.09769	+	0.633751i	0.935613	−	0.353027i	$-0.114848\pi$
$479$	24.0241	+	13.8703i	1.09769	+	0.633751i	0.162076	+	0.986778i	$0.448181\pi$
$480$	−0.981784	+	0.636800i	−0.0448121	+	0.0290658i
$481$	25.7615	−	16.9614i	1.17462	−	0.773372i
$482$	0.643825	+	1.11514i	0.0293254	+	0.0507931i
$483$	7.71263	−	15.1160i	0.350937	−	0.687803i
$484$	−5.98845	+	10.3723i	−0.272202	+	0.471468i
$485$	9.06757			0.411737
$486$	−0.850193	+	0.225269i	−0.0385655	+	0.0102184i
$487$			21.3797i			0.968805i	0.874845	+	0.484402i	$0.160963\pi$
$487$			21.3797i			0.968805i	−0.874845	+	0.484402i	$0.839037\pi$
$488$	−0.485347	−	0.280215i	−0.0219706	−	0.0126847i
$489$	5.62732	−	11.0290i	0.254476	−	0.498750i
$490$	−0.236702	−	0.409980i	−0.0106931	−	0.0185210i
$491$	4.72150	+	8.17788i	0.213078	+	0.369063i	0.952676	−	0.303986i	$-0.0983177\pi$
$491$	4.72150	+	8.17788i	0.213078	+	0.369063i	−0.739598	+	0.673049i	$0.764984\pi$
$492$	−21.6156	−	33.3258i	−0.974506	−	1.50244i
$493$	−12.6819	+	21.9657i	−0.571165	+	0.989286i
$494$	−1.23232	+	0.0723708i	−0.0554446	+	0.00325612i
$495$	−3.93772	−	5.43253i	−0.176987	−	0.244174i
$496$			5.21227i			0.234038i
$497$	−31.7169	+	54.9354i	−1.42270	+	2.46419i
$498$	−0.0573425	−	1.10596i	−0.00256958	−	0.0495593i
$499$	7.30721	−	4.21882i	0.327116	−	0.188860i	−0.327444	−	0.944871i	$-0.606187\pi$
$499$	7.30721	−	4.21882i	0.327116	−	0.188860i	0.654560	+	0.756010i	$0.272854\pi$
$500$	−1.72929	+	0.998408i	−0.0773364	+	0.0446502i
$501$	29.5037	−	1.52972i	1.31813	−	0.0683429i
$502$	1.15114	+	0.664611i	0.0513779	+	0.0296631i
$503$	1.89645			0.0845587			0.0422794	−	0.999106i	$-0.486538\pi$
$503$	1.89645			0.0845587			0.0422794	+	0.999106i	$0.486538\pi$
$504$	2.63982	−	0.274479i	0.117587	−	0.0122263i
$505$		−	16.0821i		−	0.715644i
$506$	0.157574	−	0.272926i	0.00700501	−	0.0121330i
$507$	17.3268	−	14.3799i	0.769511	−	0.638633i
$508$	13.7025	+	23.7334i	0.607949	+	1.05300i
$509$	16.8375	−	9.72113i	0.746309	−	0.430882i	−0.0780498	−	0.996949i	$-0.524869\pi$
$509$	16.8375	−	9.72113i	0.746309	−	0.430882i	0.824359	+	0.566068i	$0.191536\pi$
$510$	0.487712	+	0.248845i	0.0215963	+	0.0110190i
$511$	−5.10371	+	8.83989i	−0.225775	+	0.391054i
$512$			4.48506i			0.198214i
$513$	31.1507	−	4.88036i	1.37534	−	0.215473i
$514$			0.556397i			0.0245416i
$515$	−4.32026	−	2.49430i	−0.190373	−	0.109912i
$516$	24.9433	+	12.7268i	1.09807	+	0.560264i
$517$	−1.32362	−	2.29258i	−0.0582129	−	0.100828i
$518$	−1.63984	+	0.946760i	−0.0720503	+	0.0415982i
$519$	22.4477	−	14.5599i	0.985344	−	0.639109i
$520$	0.364560	−	0.726772i	0.0159870	−	0.0318710i
$521$	−27.8647			−1.22078			−0.610388	−	0.792102i	$-0.708987\pi$
$521$	−27.8647			−1.22078			−0.610388	+	0.792102i	$0.708987\pi$
$522$	0.699681	+	0.312454i	0.0306242	+	0.0136757i
$523$	3.41624			0.149382			0.0746908	−	0.997207i	$-0.476203\pi$
$523$	3.41624			0.149382			0.0746908	+	0.997207i	$0.476203\pi$
$524$	9.35517	−	16.2036i	0.408683	−	0.707859i
$525$	6.78583	−	0.351835i	0.296158	−	0.0153554i
$526$	−0.390314	+	0.225348i	−0.0170185	+	0.00982564i
$527$	6.35292	−	3.66786i	0.276737	−	0.159774i
$528$	−15.4004	+	0.798488i	−0.670216	+	0.0347497i
$529$	8.38141	−	14.5170i	0.364409	−	0.631175i
$530$	0.236880			0.0102894
$531$	−12.0823	−	5.39555i	−0.524328	−	0.234147i
$532$	−47.5351			−2.06091
$533$	37.0142	+	18.5669i	1.60326	+	0.804221i
$534$	0.561124	−	0.363954i	0.0242822	−	0.0157498i
$535$	2.58808	−	1.49423i	0.111892	−	0.0646011i
$536$	−1.40573	−	2.43480i	−0.0607183	−	0.105167i
$537$	13.2688	+	6.77010i	0.572589	+	0.292151i
$538$	0.812094	+	0.468862i	0.0350118	+	0.0202141i
$539$		−	18.7654i		−	0.808281i
$540$	−3.73454	+	9.68037i	−0.160709	+	0.416577i
$541$		−	43.6073i		−	1.87483i	−0.348220	−	0.937413i	$-0.613214\pi$
$541$		−	43.6073i		−	1.87483i	0.348220	−	0.937413i	$-0.386786\pi$
$542$	−0.174053	+	0.301469i	−0.00747623	+	0.0129492i
$543$	7.81623	+	3.98806i	0.335427	+	0.171144i
$544$	3.27820	−	1.89267i	0.140552	−	0.0811475i
$545$	1.63175	+	2.82628i	0.0698966	+	0.121065i
$546$	−1.11363	+	0.818910i	−0.0476589	+	0.0350461i
$547$	−5.17395	+	8.96155i	−0.221222	+	0.383168i	−0.955179	−	0.296028i	$-0.904338\pi$
$547$	−5.17395	+	8.96155i	−0.221222	+	0.383168i	0.733957	+	0.679196i	$0.237671\pi$
$548$		−	7.42448i		−	0.317158i
$549$	−7.41559	+	0.771047i	−0.316490	+	0.0329075i
$550$	0.126189			0.00538070
$551$	−23.7902	−	13.7353i	−1.01350	−	0.585143i
$552$	−0.974169	+	0.0505092i	−0.0414634	+	0.00214981i
$553$	13.3649	−	7.71622i	0.568333	−	0.328127i
$554$	0.770758	−	0.444997i	0.0327464	−	0.0189061i
$555$	−0.767203	−	14.7970i	−0.0325660	−	0.628098i
$556$	14.4825	−	25.0844i	0.614194	−	1.06382i
$557$		−	0.570061i		−	0.0241543i	−0.999927	−	0.0120771i	$-0.996156\pi$
$557$		−	0.570061i		−	0.0241543i	0.999927	−	0.0120771i	$-0.00384436\pi$
$558$	−0.130066	−	0.179442i	−0.00550615	−	0.00759637i
$559$	−29.1421	+	1.71144i	−1.23258	+	0.0723862i
$560$	7.80868	−	13.5250i	0.329977	−	0.571537i
$561$	11.8104	+	18.2087i	0.498637	+	0.768772i
$562$	−0.757841	−	1.31262i	−0.0319676	−	0.0553695i
$563$	−13.1256	−	22.7342i	−0.553178	−	0.958132i	−0.998043	−	0.0625346i	$-0.980082\pi$
$563$	−13.1256	−	22.7342i	−0.553178	−	0.958132i	0.444865	−	0.895598i	$-0.353252\pi$
$564$	−1.86056	+	3.64652i	−0.0783436	+	0.153546i
$565$	−12.3100	−	7.10718i	−0.517886	−	0.299001i
$566$		−	1.07522i		−	0.0451948i
$567$	26.2913	−	23.5668i	1.10413	−	0.989712i
$568$	3.64635			0.152997
$569$	13.6173	−	23.5858i	0.570865	−	0.988768i	−0.425612	−	0.904906i	$-0.639941\pi$
$569$	13.6173	−	23.5858i	0.570865	−	0.988768i	0.996477	−	0.0838621i	$-0.0267255\pi$
$570$	−0.269514	+	0.528223i	−0.0112887	+	0.0221248i
$571$	16.6581	+	28.8527i	0.697120	+	1.20745i	0.969461	+	0.245247i	$0.0788691\pi$
$571$	16.6581	+	28.8527i	0.697120	+	1.20745i	−0.272340	+	0.962201i	$0.587798\pi$
$572$	13.4488	−	8.85472i	0.562323	−	0.370235i
$573$	6.79305	−	4.40608i	0.283784	−	0.184066i
$574$	−2.20159	−	1.27109i	−0.0918927	−	0.0530543i
$575$	−2.49744			−0.104150
$576$	13.9508	+	19.2468i	0.581285	+	0.801950i
$577$		−	27.6637i		−	1.15166i	−0.817571	−	0.575828i	$-0.804680\pi$
$577$		−	27.6637i		−	1.15166i	0.817571	−	0.575828i	$-0.195320\pi$
$578$	−0.703152	−	0.405965i	−0.0292473	−	0.0168859i
$579$	19.5186	−	1.01201i	0.811167	−	0.0420578i
$580$	7.82863	−	4.51986i	0.325066	−	0.187677i
$581$	22.2285	+	38.5009i	0.922193	+	1.59729i
$582$	0.0458831	+	0.884945i	0.00190192	+	0.0366822i
$583$	8.13172	+	4.69485i	0.336782	+	0.194441i
$584$	0.586750			0.0242799
$585$	−1.74746	−	10.6746i	−0.0722487	−	0.441339i
$586$	−0.999164			−0.0412751
$587$	−8.09027	−	4.67092i	−0.333921	−	0.192789i	0.323660	−	0.946174i	$-0.395087\pi$
$587$	−8.09027	−	4.67092i	−0.333921	−	0.192789i	−0.657581	+	0.753384i	$0.728420\pi$
$588$	−24.3462	+	15.7913i	−1.00402	+	0.651224i
$589$	3.97252	+	6.88060i	0.163685	+	0.283510i
$590$	0.215523	−	0.124432i	0.00887293	−	0.00512279i
$591$	−12.7421	+	24.9732i	−0.524138	+	1.02726i
$592$	−29.4924	−	17.0274i	−1.21213	−	0.699823i
$593$		−	45.4348i		−	1.86578i	−0.360156	−	0.932892i	$-0.617276\pi$
$593$		−	45.4348i		−	1.86578i	0.360156	−	0.932892i	$-0.382724\pi$
$594$	0.510260	−	0.411789i	0.0209362	−	0.0168959i
$595$	−21.9798			−0.901083
$596$	−16.9978	−	9.81369i	−0.696257	−	0.401984i
$597$	−3.59599	−	1.83478i	−0.147174	−	0.0750924i
$598$	0.424342	−	0.279388i	0.0173526	−	0.0114250i
$599$	−19.5627	−	33.8837i	−0.799312	−	1.38445i	−0.920065	−	0.391767i	$-0.871864\pi$
$599$	−19.5627	−	33.8837i	−0.799312	−	1.38445i	0.120752	−	0.992683i	$-0.461469\pi$
$600$	−0.212549	−	0.327696i	−0.00867726	−	0.0133781i
$601$	−0.777604	+	1.34685i	−0.0317191	+	0.0549392i	−0.881449	−	0.472279i	$-0.843432\pi$
$601$	−0.777604	+	1.34685i	−0.0317191	+	0.0549392i	0.849730	+	0.527218i	$0.176765\pi$
$602$	1.79213			0.0730419
$603$	−34.1512	−	15.2507i	−1.39074	−	0.621058i
$604$			16.6037i			0.675596i
$605$	−5.19442	−	2.99900i	−0.211183	−	0.121927i
$606$	1.56953	−	0.0813776i	0.0637576	−	0.00330574i
$607$	0.812671	+	1.40759i	0.0329853	+	0.0571322i	0.882047	−	0.471162i	$-0.156165\pi$
$607$	0.812671	+	1.40759i	0.0329853	+	0.0571322i	−0.849062	+	0.528294i	$0.822832\pi$
$608$	2.04988	+	3.55049i	0.0831335	+	0.143991i
$609$	−30.7199	+	1.59278i	−1.24483	+	0.0645428i
$610$	0.0701095	−	0.121433i	0.00283865	−	0.00491669i
$611$	−0.250200	−	4.26036i	−0.0101220	−	0.172356i
$612$	13.6854	−	30.6458i	0.553199	−	1.23878i
$613$			20.7073i			0.836361i	0.908364	+	0.418181i	$0.137332\pi$
$613$			20.7073i			0.836361i	−0.908364	+	0.418181i	$0.862668\pi$
$614$	−0.634946	+	1.09976i	−0.0256244	+	0.0443827i
$615$	16.6894	−	10.8250i	0.672983	−	0.436507i
$616$	−1.71352	+	0.989304i	−0.0690399	+	0.0398602i
$617$	40.6045	−	23.4430i	1.63468	−	0.943781i	0.652054	−	0.758173i	$-0.273908\pi$
$617$	40.6045	−	23.4430i	1.63468	−	0.943781i	0.982624	−	0.185608i	$-0.0594256\pi$
$618$	0.221569	−	0.434255i	0.00891282	−	0.0174683i
$619$	2.68056	+	1.54762i	0.107741	+	0.0622041i	0.552902	−	0.833246i	$-0.313520\pi$
$619$	2.68056	+	1.54762i	0.107741	+	0.0622041i	−0.445161	+	0.895450i	$0.646854\pi$
$620$	−2.61447			−0.104999
$621$	−10.0987	+	8.14984i	−0.405248	+	0.327042i
$622$		−	0.261816i		−	0.0104979i
$623$	−13.4245	+	23.2519i	−0.537840	+	0.931567i
$624$	−22.7691	−	9.98120i	−0.911495	−	0.399568i
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$	1.59149	−	0.918848i	0.0636088	−	0.0367246i
$627$	−19.7212	+	12.7914i	−0.787587	+	0.510841i
$628$	−10.8663	+	18.8209i	−0.433611	+	0.751037i
$629$			47.9286i			1.91104i
$630$	0.0686744	+	0.660480i	0.00273605	+	0.0263142i
$631$			10.3920i			0.413697i	0.978373	+	0.206849i	$0.0663208\pi$
$631$			10.3920i			0.413697i	−0.978373	+	0.206849i	$0.933679\pi$
$632$	−0.768249	−	0.443549i	−0.0305593	−	0.0176434i
$633$	−2.10393	−	40.5784i	−0.0836237	−	1.61285i
$634$	−0.673127	−	1.16589i	−0.0267333	−	0.0463034i
$635$	−11.8856	+	6.86216i	−0.471666	+	0.272316i
$636$	−0.751851	−	14.5009i	−0.0298128	−	0.574999i
$637$	13.5641	−	27.0409i	0.537429	−	1.07140i
$638$	−0.571264			−0.0226165
$639$	39.2759	−	28.4687i	1.55373	−	1.12621i
$640$	−1.79832			−0.0710850
$641$	−4.03035	+	6.98077i	−0.159189	+	0.275724i	−0.934577	−	0.355762i	$-0.884221\pi$
$641$	−4.03035	+	6.98077i	−0.159189	+	0.275724i	0.775387	+	0.631486i	$0.217555\pi$
$642$	0.158924	+	0.245021i	0.00627225	+	0.00967022i
$643$	−29.5621	+	17.0677i	−1.16581	+	0.673083i	−0.952690	−	0.303942i	$-0.901697\pi$
$643$	−29.5621	+	17.0677i	−1.16581	+	0.673083i	−0.213123	+	0.977025i	$0.568364\pi$
$644$	16.9429	−	9.78201i	0.667645	−	0.385465i
$645$	−6.37352	+	12.4915i	−0.250957	+	0.491853i
$646$	0.959107	−	1.66122i	0.0377356	−	0.0653599i
$647$	13.8990			0.546425			0.273212	−	0.961954i	$-0.411914\pi$
$647$	13.8990			0.546425			0.273212	+	0.961954i	$0.411914\pi$
$648$	−1.92883	−	0.631477i	−0.0757718	−	0.0248068i
$649$	9.86477			0.387226
$650$	0.181838	+	0.0912125i	0.00713226	+	0.00357765i
$651$	7.92480	+	4.04346i	0.310597	+	0.158476i
$652$	12.3620	−	7.13720i	0.484133	−	0.279514i
$653$	4.32310	+	7.48783i	0.169176	+	0.293021i	0.938130	−	0.346282i	$-0.112556\pi$
$653$	4.32310	+	7.48783i	0.169176	+	0.293021i	−0.768954	+	0.639304i	$0.779223\pi$
$654$	−0.267573	+	0.173552i	−0.0104629	+	0.00678640i
$655$	8.11473	+	4.68504i	0.317069	+	0.183060i
$656$		−	45.7209i		−	1.78510i
$657$	6.32006	−	4.58103i	0.246569	−	0.178723i
$658$			0.261997i			0.0102137i
$659$	−11.1764	+	19.3582i	−0.435372	+	0.754087i	−0.997326	−	0.0730819i	$-0.976717\pi$
$659$	−11.1764	+	19.3582i	−0.435372	+	0.754087i	0.561954	+	0.827169i	$0.310050\pi$
$660$	−0.400520	−	7.72481i	−0.0155902	−	0.300688i
$661$	16.8969	−	9.75541i	0.657212	−	0.379441i	−0.134002	−	0.990981i	$-0.542783\pi$
$661$	16.8969	−	9.75541i	0.657212	−	0.379441i	0.791214	+	0.611540i	$0.209449\pi$
$662$	−0.775396	−	1.34303i	−0.0301366	−	0.0521982i
$663$	3.85709	+	34.7757i	0.149797	+	1.35057i
$664$	1.27775	−	2.21313i	0.0495864	−	0.0858862i
$665$		−	23.8055i		−	0.923136i
$666$	1.44023	−	0.149750i	0.0558076	−	0.00580268i
$667$	11.3061			0.437772
$668$	29.4963	+	17.0297i	1.14124	+	0.658898i
$669$	23.8923	+	36.8359i	0.923731	+	1.42416i
$670$	0.609184	−	0.351713i	0.0235348	−	0.0135878i
$671$	4.81351	−	2.77908i	0.185824	−	0.107285i
$672$	4.08931	+	2.08648i	0.157749	+	0.0804878i
$673$	22.7468	−	39.3987i	0.876826	−	1.51871i	0.0220221	−	0.999757i	$-0.492990\pi$
$673$	22.7468	−	39.3987i	0.876826	−	1.51871i	0.854804	−	0.518950i	$-0.173677\pi$
$674$			0.362695i			0.0139705i
$675$	−4.84790	−	1.87025i	−0.186596	−	0.0719859i
$676$	25.7802	−	3.03848i	0.991545	−	0.116865i
$677$	2.61677	−	4.53238i	0.100571	−	0.174193i	−0.811349	−	0.584562i	$-0.801267\pi$
$677$	2.61677	−	4.53238i	0.100571	−	0.174193i	0.911920	+	0.410368i	$0.134600\pi$
$678$	0.631332	−	1.23735i	0.0242462	−	0.0475202i
$679$	−17.7863	−	30.8068i	−0.682577	−	1.18226i
$680$	0.631728	+	1.09418i	0.0242257	+	0.0419601i
$681$	17.7309	+	27.3366i	0.679450	+	1.04754i
$682$	0.143085	+	0.0826104i	0.00547902	+	0.00316332i
$683$		−	38.3817i		−	1.46863i	−0.678807	−	0.734317i	$-0.737503\pi$
$683$		−	38.3817i		−	1.46863i	0.678807	−	0.734317i	$-0.262497\pi$
$684$	33.1913	+	14.8221i	1.26910	+	0.566738i
$685$	3.71816			0.142064
$686$	−0.153885	+	0.266536i	−0.00587534	+	0.0101764i
$687$	−1.82406	+	0.0945750i	−0.0695924	+	0.00360826i
$688$	16.1157	+	27.9132i	0.614406	+	1.06418i
$689$	8.32424	+	12.6431i	0.317128	+	0.481664i
$690$	−0.0126374	−	0.243736i	−0.000481096	−	0.00927888i
$691$	2.30815	+	1.33261i	0.0878063	+	0.0506950i	0.543260	−	0.839564i	$-0.317190\pi$
$691$	2.30815	+	1.33261i	0.0878063	+	0.0506950i	−0.455454	+	0.890259i	$0.650523\pi$
$692$	30.8461			1.17259
$693$	−10.7329	+	24.0344i	−0.407711	+	0.912991i
$694$		−	1.36137i		−	0.0516771i
$695$	12.5622	+	7.25279i	0.476511	+	0.275114i
$696$	0.962221	+	1.48350i	0.0364729	+	0.0562320i
$697$	−55.7264	+	32.1737i	−2.11079	+	1.21866i
$698$	−0.399076	−	0.691220i	−0.0151053	−	0.0261631i
$699$	−0.343274	−	0.175148i	−0.0129838	−	0.00662471i
$700$	6.78413	+	3.91682i	0.256416	+	0.148042i
$701$	−17.4343			−0.658483			−0.329241	−	0.944246i	$-0.606793\pi$
$701$	−17.4343			−0.658483			−0.329241	+	0.944246i	$0.606793\pi$
$702$	1.03294	−	0.224558i	0.0389857	−	0.00847538i
$703$	−51.9096			−1.95781
$704$	−15.3473	−	8.86074i	−0.578421	−	0.333952i
$705$	−1.82617	−	0.931762i	−0.0687774	−	0.0350922i
$706$	0.355155	+	0.615147i	0.0133664	+	0.0231514i
$707$	−54.6385	+	31.5456i	−2.05489	+	1.18639i
$708$	−8.30136	−	12.7986i	−0.311984	−	0.481001i
$709$	−24.1729	−	13.9562i	−0.907832	−	0.524137i	−0.0280989	−	0.999605i	$-0.508945\pi$
$709$	−24.1729	−	13.9562i	−0.907832	−	0.524137i	−0.879733	+	0.475468i	$0.842279\pi$
$710$			0.912313i			0.0342385i
$711$	−11.7380	+	1.22048i	−0.440211	+	0.0457716i
$712$	1.54335			0.0578395
$713$	−2.83185	−	1.63497i	−0.106053	−	0.0612300i
$714$	−0.111221	−	2.14511i	−0.00416233	−	0.0802786i
$715$	4.43442	+	6.73513i	0.165838	+	0.251880i
$716$	8.58659	+	14.8724i	0.320896	+	0.555808i
$717$	−16.7214	+	0.866982i	−0.624474	+	0.0323780i
$718$	−0.168341	+	0.291575i	−0.00628243	+	0.0108815i
$719$	20.1921			0.753040			0.376520	−	0.926408i	$-0.377121\pi$
$719$	20.1921			0.753040			0.376520	+	0.926408i	$0.377121\pi$
$720$	−9.66970	+	7.00898i	−0.360368	+	0.261209i
$721$			19.5706i			0.728848i
$722$	0.870812	+	0.502763i	0.0324083	+	0.0187109i
$723$	21.5103	+	33.1634i	0.799976	+	1.23336i
$724$	5.05810	+	8.76089i	0.187983	+	0.325596i
$725$	2.26353	+	3.92055i	0.0840655	+	0.145606i
$726$	0.266401	−	0.522122i	0.00988708	−	0.0193778i
$727$	−7.62646	+	13.2094i	−0.282850	+	0.489910i	−0.972085	−	0.234627i	$-0.924613\pi$
$727$	−7.62646	+	13.2094i	−0.282850	+	0.489910i	0.689236	+	0.724537i	$0.257946\pi$
$728$	−3.18428	+	0.187004i	−0.118017	+	0.00693085i
$729$	−25.7063	+	8.25748i	−0.952085	+	0.305833i
$730$			0.146804i			0.00543347i
$731$	22.6812	−	39.2849i	0.838893	−	1.45300i
$732$	−7.65624	−	3.90643i	−0.282983	−	0.144386i
$733$	−16.9197	+	9.76859i	−0.624943	+	0.360811i	−0.778791	−	0.627284i	$-0.784167\pi$
$733$	−16.9197	+	9.76859i	−0.624943	+	0.360811i	0.153848	+	0.988095i	$0.450833\pi$
$734$	0.00488657	−	0.00282126i	0.000180367	−	0.000104135i
$735$	−7.90826	−	12.1925i	−0.291700	−	0.449728i
$736$	−1.46127	−	0.843667i	−0.0538633	−	0.0310980i
$737$	27.8832			1.02709
$738$	1.14091	+	1.57402i	0.0419976	+	0.0579406i
$739$		−	5.76873i		−	0.212206i	−0.994355	−	0.106103i	$-0.966163\pi$
$739$		−	5.76873i		−	0.212206i	0.994355	−	0.106103i	$-0.0338374\pi$
$740$	8.54092	−	14.7933i	0.313970	−	0.543813i
$741$	−37.6642	+	4.17747i	−1.38363	+	0.153463i
$742$	−0.464647	−	0.804792i	−0.0170577	−	0.0295449i
$743$	1.12991	−	0.652354i	0.0414524	−	0.0239325i	−0.479131	−	0.877744i	$-0.659048\pi$
$743$	1.12991	−	0.652354i	0.0414524	−	0.0239325i	0.520583	+	0.853811i	$0.325715\pi$
$744$	−0.0264802	−	0.510722i	−0.000970810	−	0.0187240i
$745$	4.91467	−	8.51245i	0.180060	−	0.311872i
$746$			1.18665i			0.0434465i
$747$	−3.51590	−	33.8143i	−0.128640	−	1.23720i
$748$			25.0212i			0.914866i
$749$	−10.1532	−	5.86195i	−0.370990	−	0.214191i
$750$	0.0819893	−	0.0531795i	0.00299383	−	0.00194184i
$751$	−4.78180	−	8.28232i	−0.174490	−	0.302226i	0.765494	−	0.643443i	$-0.222494\pi$
$751$	−4.78180	−	8.28232i	−0.174490	−	0.302226i	−0.939985	+	0.341216i	$0.889161\pi$
$752$	−4.08071	+	2.35600i	−0.148808	+	0.0859144i
$753$	36.3469	+	18.5452i	1.32456	+	0.675826i
$754$	−0.823191	−	0.412925i	−0.0299788	−	0.0150378i
$755$	−8.31510			−0.302617
$756$	40.2142	−	6.30035i	1.46258	−	0.229142i
$757$	−26.1510			−0.950474			−0.475237	−	0.879858i	$-0.657638\pi$
$757$	−26.1510			−0.950474			−0.475237	+	0.879858i	$0.657638\pi$
$758$	−0.214854	+	0.372138i	−0.00780384	+	0.0135166i
$759$	4.39692	−	8.61756i	0.159598	−	0.312798i
$760$	−1.18507	+	0.684200i	−0.0429870	+	0.0248186i
$761$	−38.3831	+	22.1605i	−1.39139	+	0.803317i	−0.993469	−	0.114104i	$-0.963600\pi$
$761$	−38.3831	+	22.1605i	−1.39139	+	0.803317i	−0.397918	+	0.917421i	$0.630267\pi$
$762$	−0.729852	−	1.12525i	−0.0264397	−	0.0407634i
$763$	6.40147	−	11.0877i	0.231749	−	0.401401i
$764$	9.33456			0.337713
$765$	15.3473	+	6.85360i	0.554885	+	0.247793i
$766$	0.517654			0.0187036
$767$	14.2151	+	7.13052i	0.513278	+	0.257468i
$768$	1.41215	+	27.2362i	0.0509567	+	0.982801i
$769$	−35.8501	+	20.6981i	−1.29279	+	0.746391i	−0.979147	−	0.203151i	$-0.934882\pi$
$769$	−35.8501	+	20.6981i	−1.29279	+	0.746391i	−0.313640	+	0.949542i	$0.601548\pi$
$770$	−0.247523	−	0.428722i	−0.00892011	−	0.0154501i
$771$	0.884404	+	17.0575i	0.0318510	+	0.614310i
$772$	19.5137	+	11.2663i	0.702315	+	0.405482i
$773$			12.9069i			0.464231i	0.972688	+	0.232115i	$0.0745647\pi$
$773$			12.9069i			0.464231i	−0.972688	+	0.232115i	$0.925435\pi$
$774$	−1.25135	−	0.558812i	−0.0449790	−	0.0200861i
$775$		−	1.30932i		−	0.0470320i
$776$	−1.02241	+	1.77086i	−0.0367022	+	0.0635701i
$777$	−48.7676	+	31.6314i	−1.74953	+	1.13477i
$778$	−1.46752	+	0.847271i	−0.0526130	+	0.0303762i
$779$	−34.8461	−	60.3552i	−1.24849	−	2.16245i
$780$	5.00655	−	11.4210i	0.179263	−	0.408936i
$781$	−18.0816	+	31.3183i	−0.647012	+	1.12066i
$782$			0.789478i			0.0282317i
$783$	21.9468	+	8.46674i	0.784314	+	0.302577i
$784$	−33.4016			−1.19291
$785$	−9.42547	−	5.44180i	−0.336409	−	0.194226i
$786$	−0.416173	+	0.815661i	−0.0148444	+	0.0290937i
$787$	18.9628	−	10.9482i	0.675950	−	0.390260i	−0.122377	−	0.992484i	$-0.539052\pi$
$787$	18.9628	−	10.9482i	0.675950	−	0.390260i	0.798328	+	0.602223i	$0.205718\pi$
$788$	−27.9915	+	16.1609i	−0.997155	+	0.575708i
$789$	−11.6077	+	7.52891i	−0.413244	+	0.268036i
$790$	0.110976	−	0.192215i	0.00394833	−	0.00683871i
$791$			55.7639i			1.98274i
$792$	1.50494	−	0.156479i	0.0534759	−	0.00556024i
$793$	8.94506	−	0.525320i	0.317648	−	0.0186546i
$794$	0.374225	−	0.648177i	0.0132808	−	0.0230029i
$795$	7.26202	−	0.376525i	0.257557	−	0.0133540i
$796$	−2.32707	−	4.03060i	−0.0824806	−	0.142861i
$797$	−14.5257	−	25.1592i	−0.514526	−	0.891185i	−0.999858	−	0.0168549i	$-0.994635\pi$
$797$	−14.5257	−	25.1592i	−0.514526	−	0.891185i	0.485332	−	0.874330i	$-0.338699\pi$
$798$	2.32328	−	0.120459i	0.0822433	−	0.00426419i
$799$	5.74316	+	3.31582i	0.203178	+	0.117305i
$800$		−	0.675627i		−	0.0238870i
$801$	16.6239	−	12.0496i	0.587376	−	0.425753i
$802$	−1.52137			−0.0537216
$803$	−2.90960	+	5.03957i	−0.102677	+	0.177843i
$804$	−23.4641	−	36.1757i	−0.827516	−	1.27582i
$805$	4.89880	+	8.48497i	0.172660	+	0.299056i
$806$	0.146473	+	0.222467i	0.00515929	+	0.00783608i
$807$	25.6416	+	13.0831i	0.902628	+	0.460546i
$808$	3.14077	+	1.81332i	0.110492	+	0.0637925i
$809$	25.8648			0.909358			0.454679	−	0.890655i	$-0.349754\pi$
$809$	25.8648			0.909358			0.454679	+	0.890655i	$0.349754\pi$
$810$	0.157995	−	0.482593i	0.00555138	−	0.0169566i
$811$			3.28781i			0.115451i	0.998333	+	0.0577253i	$0.0183848\pi$
$811$			3.28781i			0.115451i	−0.998333	+	0.0577253i	$0.981615\pi$
$812$	−30.7122	−	17.7317i	−1.07779	−	0.622261i
$813$	−4.85676	+	9.51880i	−0.170334	+	0.333839i
$814$	−0.934861	+	0.539742i	−0.0327669	+	0.0189180i
$815$	3.57429	+	6.19085i	0.125202	+	0.216856i
$816$	32.4108	−	21.0221i	1.13460	−	0.735921i
$817$	42.5480	+	24.5651i	1.48857	+	0.859424i
$818$	1.47248			0.0514840
$819$	−32.8389	+	26.8755i	−1.14748	+	0.939105i
$820$	22.9335			0.800874
$821$	−29.6910	−	17.1421i	−1.03622	−	0.598263i	−0.117461	−	0.993077i	$-0.537476\pi$
$821$	−29.6910	−	17.1421i	−1.03622	−	0.598263i	−0.918761	+	0.394814i	$0.870809\pi$
$822$	0.0188144	+	0.362872i	0.000656226	+	0.0126566i
$823$	2.90511	+	5.03180i	0.101266	+	0.175397i	0.912206	−	0.409731i	$-0.134377\pi$
$823$	2.90511	+	5.03180i	0.101266	+	0.175397i	−0.810941	+	0.585128i	$0.801044\pi$
$824$	0.974253	−	0.562485i	0.0339397	−	0.0195951i
$825$	3.86856	−	0.200579i	0.134686	−	0.00698327i
$826$	−0.845510	−	0.488155i	−0.0294191	−	0.0169851i
$827$			53.8589i			1.87286i	0.350860	+	0.936428i	$0.385889\pi$
$827$			53.8589i			1.87286i	−0.350860	+	0.936428i	$0.614111\pi$
$828$	−14.8805	+	1.54723i	−0.517135	+	0.0537699i
$829$	20.8733			0.724959			0.362479	−	0.931992i	$-0.381930\pi$
$829$	20.8733			0.724959			0.362479	+	0.931992i	$0.381930\pi$
$830$	0.553724	+	0.319692i	0.0192200	+	0.0110967i
$831$	22.9218	−	14.8674i	0.795148	−	0.515745i
$832$	−15.7106	−	23.8617i	−0.544667	−	0.827257i
$833$	23.5046	+	40.7111i	0.814386	+	1.41056i
$834$	−0.644266	+	1.26270i	−0.0223091	+	0.0437238i
$835$	−8.52841	+	14.7716i	−0.295138	+	0.511194i
$836$	−27.0995			−0.937256
$837$	−4.27267	−	5.29440i	−0.147685	−	0.183001i
$838$			0.645706i			0.0223055i
$839$	−16.4401	−	9.49171i	−0.567576	−	0.327690i	0.188605	−	0.982053i	$-0.439604\pi$
$839$	−16.4401	−	9.49171i	−0.567576	−	0.327690i	−0.756181	+	0.654363i	$0.772937\pi$
$840$	−0.696418	+	1.36492i	−0.0240287	+	0.0470940i
$841$	4.25284	+	7.36614i	0.146650	+	0.254005i
$842$	0.268659	+	0.465330i	0.00925859	+	0.0160363i
$843$	−25.3196	−	39.0364i	−0.872053	−	1.34448i
$844$	23.4221	−	40.5682i	0.806221	−	1.39642i
$845$	1.52166	+	12.9106i	0.0523468	+	0.444139i
$846$	0.0816942	−	0.182939i	0.00280871	−	0.00628956i
$847$			23.5305i			0.808518i
$848$	8.35665	−	14.4741i	0.286969	−	0.497044i
$849$	−1.70908	−	32.9630i	−0.0586555	−	1.13129i
$850$	−0.273764	+	0.158058i	−0.00939003	+	0.00542134i
$851$	18.5021	−	10.6822i	0.634244	−	0.366181i
$852$	55.8485	−	2.89566i	1.91334	−	0.0992038i
$853$	28.5015	+	16.4554i	0.975873	+	0.563421i	0.901022	−	0.433774i	$-0.142818\pi$
$853$	28.5015	+	16.4554i	0.975873	+	0.563421i	0.0748515	+	0.997195i	$0.476152\pi$
$854$	−0.550089			−0.0188236
$855$	−7.42288	+	16.6221i	−0.253857	+	0.568465i
$856$			0.673920i			0.0230341i
$857$	−5.40414	+	9.36025i	−0.184602	+	0.319740i	−0.943442	−	0.331537i	$-0.892433\pi$
$857$	−5.40414	+	9.36025i	−0.184602	+	0.319740i	0.758840	+	0.651277i	$0.225766\pi$
$858$	−0.634873	+	0.466856i	−0.0216742	+	0.0159382i
$859$	−16.8254	−	29.1424i	−0.574074	−	0.994325i	−0.996142	−	0.0877609i	$-0.972029\pi$
$859$	−16.8254	−	29.1424i	−0.574074	−	0.994325i	0.422068	−	0.906564i	$-0.361304\pi$
$860$	−14.0012	+	8.08361i	−0.477438	+	0.275649i
$861$	−69.5146	−	35.4683i	−2.36905	−	1.20876i
$862$	−0.655933	+	1.13611i	−0.0223412	+	0.0386960i
$863$		−	25.0522i		−	0.852787i	−0.904538	−	0.426394i	$-0.859784\pi$
$863$		−	25.0522i		−	0.852787i	0.904538	−	0.426394i	$-0.140216\pi$
$864$	−2.20476	−	2.73199i	−0.0750075	−	0.0929441i
$865$			15.4477i			0.525236i
$866$	−1.00452	−	0.579958i	−0.0341349	−	0.0197078i
$867$	−22.2018	−	11.3280i	−0.754014	−	0.384719i
$868$	5.12836	+	8.88258i	0.174068	+	0.301494i
$869$	7.61925	−	4.39897i	0.258465	−	0.149225i
$870$	−0.371171	+	0.240747i	−0.0125839	+	0.00816209i
$871$	40.1796	+	20.1547i	1.36143	+	0.682916i
$872$	−0.735947			−0.0249223
$873$	2.81328	+	27.0568i	0.0952150	+	0.915736i
$874$	−0.855054			−0.0289226
$875$	−1.96153	+	3.39747i	−0.0663119	+	0.114856i
$876$	8.98683	−	0.465954i	0.303637	−	0.0157431i
$877$	−30.7931	+	17.7784i	−1.03981	+	0.600334i	−0.919779	−	0.392436i	$-0.871632\pi$
$877$	−30.7931	+	17.7784i	−1.03981	+	0.600334i	−0.120030	+	0.992770i	$0.538299\pi$
$878$	−1.36540	+	0.788316i	−0.0460801	+	0.0266044i
$879$	−30.6314	+	1.58819i	−1.03317	+	0.0535684i
$880$	4.45168	−	7.71054i	0.150066	−	0.259922i
$881$	−33.1329			−1.11628			−0.558138	−	0.829748i	$-0.688484\pi$
$881$	−33.1329			−1.11628			−0.558138	+	0.829748i	$0.688484\pi$
$882$	1.14991	−	0.833499i	0.0387194	−	0.0280654i
$883$	6.09535			0.205125			0.102562	−	0.994727i	$-0.467296\pi$
$883$	6.09535			0.205125			0.102562	+	0.994727i	$0.467296\pi$
$884$	−18.0860	+	36.0555i	−0.608298	+	1.21268i
$885$	6.40950	−	4.15730i	0.215453	−	0.139746i
$886$	0.654334	−	0.377780i	0.0219828	−	0.0126918i
$887$	−11.1841	−	19.3715i	−0.375526	−	0.650430i	0.614880	−	0.788621i	$-0.289205\pi$
$887$	−11.1841	−	19.3715i	−0.375526	−	0.650430i	−0.990406	+	0.138191i	$0.955871\pi$
$888$	2.97630	+	1.51859i	0.0998781	+	0.0509606i
$889$	46.6280	+	26.9207i	1.56385	+	0.902891i
$890$			0.386145i			0.0129436i
$891$	14.9885	−	13.4353i	0.502134	−	0.450099i
$892$			50.6175i			1.69480i
$893$	−3.59123	+	6.22020i	−0.120176	+	0.208151i
$894$	0.855638	+	0.436571i	0.0286168	+	0.0146011i
$895$	−7.44806	+	4.30014i	−0.248961	+	0.143738i
$896$	3.52747	+	6.10976i	0.117845	+	0.204113i
$897$	12.5650	−	9.23969i	0.419532	−	0.308504i
$898$	−0.0899270	+	0.155758i	−0.00300090	+	0.00519771i
$899$			5.92736i			0.197689i
$900$	−3.51569	−	4.85030i	−0.117190	−	0.161677i
$901$	−23.5222			−0.783638
$902$	−1.25511	−	0.724641i	−0.0417907	−	0.0241279i
$903$	54.9415	−	2.84863i	1.82834	−	0.0947966i
$904$	2.77601	−	1.60273i	0.0923286	−	0.0533059i
$905$	−4.38743	+	2.53308i	−0.145843	+	0.0842025i
$906$	−0.0420755	−	0.811508i	−0.00139786	−	0.0269606i
$907$	−28.2805	+	48.9832i	−0.939037	+	1.62646i	−0.171766	+	0.985138i	$0.554947\pi$
$907$	−28.2805	+	48.9832i	−0.939037	+	1.62646i	−0.767271	+	0.641323i	$0.778386\pi$
$908$			37.5641i			1.24661i
$909$	47.9876	−	4.98959i	1.59165	−	0.165494i
$910$	−0.0467884	−	0.796705i	−0.00155102	−	0.0264105i
$911$	19.3361	−	33.4911i	0.640633	−	1.10961i	−0.344659	−	0.938728i	$-0.612005\pi$
$911$	19.3361	−	33.4911i	0.640633	−	1.10961i	0.985292	−	0.170881i	$-0.0546614\pi$
$912$	22.7682	+	35.1029i	0.753932	+	1.16237i
$913$	12.6723	+	21.9491i	0.419393	+	0.726410i
$914$	0.327661	+	0.567525i	0.0108381	+	0.0187721i
$915$	1.95633	−	3.83422i	0.0646742	−	0.126755i
$916$	−1.82361	−	1.05286i	−0.0602536	−	0.0347875i
$917$		−	36.7595i		−	1.21390i
$918$	−0.591215	+	1.53250i	−0.0195130	+	0.0505800i
$919$	14.0369			0.463035			0.231518	−	0.972831i	$-0.425631\pi$
$919$	14.0369			0.463035			0.231518	+	0.972831i	$0.425631\pi$
$920$	0.281596	−	0.487739i	0.00928395	−	0.0160803i
$921$	−17.7175	+	34.7246i	−0.583810	+	1.14421i
$922$	0.444647	+	0.770152i	0.0146437	+	0.0253636i
$923$	−48.6934	+	32.0598i	−1.60276	+	1.05526i
$924$	−25.4592	+	16.5132i	−0.837547	+	0.543245i
$925$	7.40845	+	4.27727i	0.243588	+	0.140636i
$926$	−1.53846			−0.0505569
$927$	6.10239	−	13.6651i	0.200429	−	0.448822i
$928$			3.05861i			0.100404i
$929$	−20.5626	−	11.8718i	−0.674637	−	0.389502i	0.123194	−	0.992383i	$-0.460686\pi$
$929$	−20.5626	−	11.8718i	−0.674637	−	0.389502i	−0.797831	+	0.602881i	$0.794020\pi$
$930$	0.127782	−	0.00662531i	0.00419014	−	0.000217253i
$931$	−44.0927	+	25.4569i	−1.44508	+	0.834317i
$932$	−0.222142	−	0.384762i	−0.00727651	−	0.0126033i
$933$	−0.416162	−	8.02650i	−0.0136245	−	0.262776i
$934$	0.762805	+	0.440405i	0.0249597	+	0.0144105i
$935$	−12.5305			−0.409793
$936$	2.28173	+	0.862328i	0.0745807	+	0.0281861i
$937$	32.8701			1.07382			0.536910	−	0.843640i	$-0.319592\pi$
$937$	32.8701			1.07382			0.536910	+	0.843640i	$0.319592\pi$
$938$	−2.38987	−	1.37979i	−0.0780320	−	0.0450518i
$939$	47.3298	−	30.6988i	1.54455	−	1.00182i
$940$	−1.18176	−	2.04687i	−0.0385449	−	0.0667617i
$941$	−0.736837	+	0.425413i	−0.0240202	+	0.0138681i	−0.511962	−	0.859008i	$-0.671081\pi$
$941$	−0.736837	+	0.425413i	−0.0240202	+	0.0138681i	0.487942	+	0.872876i	$0.337748\pi$
$942$	0.483395	−	0.947410i	0.0157499	−	0.0308683i
$943$	24.8403	+	14.3416i	0.808913	+	0.467026i
$944$		−	17.5589i		−	0.571493i
$945$	3.15520	+	20.1392i	0.102639	+	0.655128i
$946$	1.02169			0.0332179
$947$	11.4077	+	6.58621i	0.370699	+	0.214023i	0.673764	−	0.738947i	$-0.264677\pi$
$947$	11.4077	+	6.58621i	0.370699	+	0.214023i	−0.303065	+	0.952970i	$0.598010\pi$
$948$	−12.1190	−	6.18344i	−0.393606	−	0.200829i
$949$	−7.83546	+	5.15888i	−0.254350	+	0.167464i
$950$	−0.171186	−	0.296503i	−0.00555402	−	0.00961984i
$951$	−22.4893	−	34.6728i	−0.729265	−	1.12434i
$952$	2.47831	−	4.29256i	0.0803225	−	0.139123i
$953$	−19.8134			−0.641820			−0.320910	−	0.947110i	$-0.603989\pi$
$953$	−19.8134			−0.641820			−0.320910	+	0.947110i	$0.603989\pi$
$954$	0.0734936	+	0.706828i	0.00237944	+	0.0228844i
$955$			4.67472i			0.151270i
$956$	−16.7173	−	9.65171i	−0.540675	−	0.312159i
$957$	−17.5132	+	0.908035i	−0.566123	+	0.0293526i
$958$	−0.782590	−	1.35549i	−0.0252843	−	0.0437938i
$959$	−7.29329	−	12.6323i	−0.235513	−	0.407920i
$960$	−13.7058	+	0.710627i	−0.442354	+	0.0229354i
$961$	−14.6428	+	25.3622i	−0.472350	+	0.818134i
$962$	−1.73727	+	0.102026i	−0.0560120	+	0.00328943i
$963$	5.26161	+	7.25900i	0.169553	+	0.233918i
$964$			45.5710i			1.46774i
$965$	−5.64211	+	9.77243i	−0.181626	+	0.314586i
$966$	−0.803299	+	0.521031i	−0.0258457	+	0.0167639i
$967$	21.0783	−	12.1696i	0.677832	−	0.391347i	−0.121206	−	0.992627i	$-0.538676\pi$
$967$	21.0783	−	12.1696i	0.677832	−	0.391347i	0.799038	+	0.601281i	$0.205343\pi$
$968$	1.17138	−	0.676298i	0.0376497	−	0.0217370i
$969$	26.7628	−	52.4526i	0.859745	−	1.68502i
$970$	−0.443067	−	0.255805i	−0.0142260	−	0.00821340i
$971$	−0.853040			−0.0273754			−0.0136877	−	0.999906i	$-0.504357\pi$
$971$	−0.853040			−0.0273754			−0.0136877	+	0.999906i	$0.504357\pi$
$972$	−30.0441	−	8.14015i	−0.963664	−	0.261096i
$973$		−	56.9063i		−	1.82433i
$974$	0.603141	−	1.04467i	0.0193259	−	0.0334734i
$975$	5.71958	+	2.50727i	0.183173	+	0.0802968i
$976$	−4.94665	−	8.56786i	−0.158339	−	0.274250i
$977$	−12.3744	+	7.14435i	−0.395891	+	0.228568i	−0.684710	−	0.728816i	$-0.740071\pi$
$977$	−12.3744	+	7.14435i	−0.395891	+	0.228568i	0.288818	+	0.957384i	$0.406738\pi$
$978$	−0.586107	+	0.380157i	−0.0187416	+	0.0121561i
$979$	−7.65322	+	13.2558i	−0.244598	+	0.423656i
$980$		−	16.7542i		−	0.535192i
$981$	−7.92711	+	5.74588i	−0.253093	+	0.183452i
$982$		−	0.532792i		−	0.0170021i
$983$	−41.8082	−	24.1380i	−1.33347	−	0.769882i	−0.347644	−	0.937626i	$-0.613018\pi$
$983$	−41.8082	−	24.1380i	−1.33347	−	0.769882i	−0.985831	+	0.167744i	$0.946352\pi$
$984$	0.232278	+	4.47994i	0.00740476	+	0.142815i
$985$	−8.09332	−	14.0180i	−0.257875	−	0.446652i
$986$	1.23935	−	0.715538i	0.0394689	−	0.0227874i
$987$	0.416449	+	8.03203i	0.0132557	+	0.255662i
$988$	−39.0504	−	19.5883i	−1.24236	−	0.623185i
$989$	−20.2205			−0.642974
$990$	0.0391509	+	0.376536i	0.00124430	+	0.0119671i
$991$	42.7913			1.35931			0.679655	−	0.733532i	$-0.262129\pi$
$991$	42.7913			1.35931			0.679655	+	0.733532i	$0.262129\pi$
$992$	0.442305	−	0.766094i	0.0140432	−	0.0243235i
$993$	−25.9061	−	39.9406i	−0.822105	−	1.26748i
$994$	3.09956	−	1.78953i	0.0983120	−	0.0567605i
$995$	2.01851	−	1.16539i	0.0639911	−	0.0369453i
$996$	17.8129	−	34.9117i	0.564424	−	1.10622i
$997$	5.15112	−	8.92200i	0.163138	−	0.282563i	−0.772855	−	0.634583i	$-0.781172\pi$
$997$	5.15112	−	8.92200i	0.163138	−	0.282563i	0.935992	+	0.352020i	$0.114505\pi$
$998$	−0.476068			−0.0150697
$999$	43.9150	−	6.88015i	1.38941	−	0.217678i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	585.2.bt.b.376.27	✓	108
9.4	even	3	inner	585.2.bt.b.571.28	yes	108
13.12	even	2	inner	585.2.bt.b.376.28	yes	108
117.103	even	6	inner	585.2.bt.b.571.27	yes	108

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
585.2.bt.b.376.27	✓	108	1.1	even	1	trivial
585.2.bt.b.376.28	yes	108	13.12	even	2	inner
585.2.bt.b.571.27	yes	108	117.103	even	6	inner
585.2.bt.b.571.28	yes	108	9.4	even	3	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 585 = 3^{2} \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	585.bt (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.0488628 - 0.0282110i) q^{2} +(-1.54283 - 0.787195i) q^{3} +(-0.998408 - 1.72929i) q^{4} +(0.866025 - 0.500000i) q^{5} +(0.0531795 + 0.0819893i) q^{6} +(-3.39747 - 1.96153i) q^{7} +0.225508i q^{8} +(1.76065 + 2.42902i) q^{9} +O(q^{10})\)	\(q+(-0.0488628 - 0.0282110i) q^{2} +(-1.54283 - 0.787195i) q^{3} +(-0.998408 - 1.72929i) q^{4} +(0.866025 - 0.500000i) q^{5} +(0.0531795 + 0.0819893i) q^{6} +(-3.39747 - 1.96153i) q^{7} +0.225508i q^{8} +(1.76065 + 2.42902i) q^{9} -0.0564219 q^{10} +(-1.93688 - 1.11826i) q^{11} +(0.179082 + 3.45395i) q^{12} +(-1.98274 - 3.01144i) q^{13} +(0.110673 + 0.191692i) q^{14} +(-1.72973 + 0.0896838i) q^{15} +(-1.99045 + 3.44757i) q^{16} +5.60271 q^{17} +(-0.0175053 - 0.168358i) q^{18} +6.06808i q^{19} +(-1.72929 - 0.998408i) q^{20} +(3.69761 + 5.70079i) q^{21} +(0.0630943 + 0.109282i) q^{22} +(-1.24872 - 2.16284i) q^{23} +(0.177519 - 0.347921i) q^{24} +(0.500000 - 0.866025i) q^{25} +(0.0119265 + 0.203082i) q^{26} +(-0.804269 - 5.13353i) q^{27} +7.83364i q^{28} +(-2.26353 + 3.92055i) q^{29} +(0.0870494 + 0.0444151i) q^{30} +(1.13390 - 0.654658i) q^{31} +(0.585110 - 0.337813i) q^{32} +(2.10799 + 3.24998i) q^{33} +(-0.273764 - 0.158058i) q^{34} -3.92306 q^{35} +(2.44264 - 5.46983i) q^{36} +8.55454i q^{37} +(0.171186 - 0.296503i) q^{38} +(0.688433 + 6.20694i) q^{39} +(0.112754 + 0.195296i) q^{40} +(-9.94634 + 5.74252i) q^{41} +(-0.0198512 - 0.382870i) q^{42} +(4.04825 - 7.01177i) q^{43} +4.46591i q^{44} +(2.73927 + 1.22327i) q^{45} +0.140910i q^{46} +(1.02507 + 0.591824i) q^{47} +(5.78484 - 3.75214i) q^{48} +(4.19522 + 7.26633i) q^{49} +(-0.0488628 + 0.0282110i) q^{50} +(-8.64402 - 4.41042i) q^{51} +(-3.22808 + 6.43538i) q^{52} -4.19836 q^{53} +(-0.105523 + 0.273528i) q^{54} -2.23652 q^{55} +(0.442341 - 0.766158i) q^{56} +(4.77676 - 9.36201i) q^{57} +(0.221205 - 0.127713i) q^{58} +(-3.81984 + 2.20539i) q^{59} +(1.88206 + 2.90167i) q^{60} +(-1.24259 + 2.15224i) q^{61} -0.0738742 q^{62} +(-1.21716 - 11.7061i) q^{63} +7.92370 q^{64} +(-3.22282 - 1.61661i) q^{65} +(-0.0113171 - 0.218272i) q^{66} +(-10.7969 + 6.23362i) q^{67} +(-5.59379 - 9.68873i) q^{68} +(0.223979 + 4.31988i) q^{69} +(0.191692 + 0.110673i) q^{70} -16.1695i q^{71} +(-0.547763 + 0.397040i) q^{72} -2.60190i q^{73} +(0.241332 - 0.417999i) q^{74} +(-1.45315 + 0.942532i) q^{75} +(10.4935 - 6.05842i) q^{76} +(4.38700 + 7.59851i) q^{77} +(0.141465 - 0.322710i) q^{78} +(-1.96689 + 3.40675i) q^{79} +3.98091i q^{80} +(-2.80024 + 8.55328i) q^{81} +0.648008 q^{82} +(-9.81398 - 5.66610i) q^{83} +(6.16660 - 12.0860i) q^{84} +(4.85209 - 2.80135i) q^{85} +(-0.395618 + 0.228410i) q^{86} +(6.57849 - 4.26690i) q^{87} +(0.252176 - 0.436782i) q^{88} -6.84387i q^{89} +(-0.0993391 - 0.137050i) q^{90} +(0.829258 + 14.1205i) q^{91} +(-2.49346 + 4.31880i) q^{92} +(-2.26476 + 0.117424i) q^{93} +(-0.0333918 - 0.0578364i) q^{94} +(3.03404 + 5.25511i) q^{95} +(-1.16865 + 0.0605928i) q^{96} +(7.85275 + 4.53379i) q^{97} -0.473405i q^{98} +(-0.693895 - 6.67357i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 108 q - 6 q^{3} + 52 q^{4} - 14 q^{9}+O(q^{10}) \) 108 * q - 6 * q^3 + 52 * q^4 - 14 * q^9	\( 108 q - 6 q^{3} + 52 q^{4} - 14 q^{9} - 8 q^{10} - 36 q^{12} - 4 q^{13} - 8 q^{14} - 64 q^{16} + 36 q^{17} + 24 q^{22} - 22 q^{23} + 54 q^{25} + 40 q^{26} + 48 q^{27} - 16 q^{29} + 20 q^{30} - 40 q^{35} - 76 q^{36} - 12 q^{38} + 26 q^{39} - 52 q^{42} - 6 q^{43} - 68 q^{48} + 58 q^{49} + 34 q^{51} + 22 q^{52} - 116 q^{53} + 24 q^{55} + 40 q^{56} + 18 q^{61} + 152 q^{62} - 216 q^{64} + 2 q^{65} - 72 q^{66} - 134 q^{69} + 32 q^{74} + 40 q^{77} - 34 q^{78} + 18 q^{79} + 34 q^{81} + 88 q^{82} + 60 q^{87} + 8 q^{90} + 16 q^{91} + 176 q^{92} - 76 q^{94} - 56 q^{95}+O(q^{100}) \) 108 * q - 6 * q^3 + 52 * q^4 - 14 * q^9 - 8 * q^10 - 36 * q^12 - 4 * q^13 - 8 * q^14 - 64 * q^16 + 36 * q^17 + 24 * q^22 - 22 * q^23 + 54 * q^25 + 40 * q^26 + 48 * q^27 - 16 * q^29 + 20 * q^30 - 40 * q^35 - 76 * q^36 - 12 * q^38 + 26 * q^39 - 52 * q^42 - 6 * q^43 - 68 * q^48 + 58 * q^49 + 34 * q^51 + 22 * q^52 - 116 * q^53 + 24 * q^55 + 40 * q^56 + 18 * q^61 + 152 * q^62 - 216 * q^64 + 2 * q^65 - 72 * q^66 - 134 * q^69 + 32 * q^74 + 40 * q^77 - 34 * q^78 + 18 * q^79 + 34 * q^81 + 88 * q^82 + 60 * q^87 + 8 * q^90 + 16 * q^91 + 176 * q^92 - 76 * q^94 - 56 * q^95

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