LMFDB - Embedded newform 585.2.bt.b.571.27

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			571.27
Character	$\chi$	$=$	585.571
Dual form			585.2.bt.b.376.27

$q$-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 $\left(\mathbb{Z}/585\mathbb{Z}\right)^\times$.

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

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	−0.517176	−	0.855879i	$-0.673017\pi$
$2$	−0.0488628	+	0.0282110i	−0.0345512	+	0.0199482i	0.482625	+	0.875827i	$0.339683\pi$
$3$	−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	−0.977600	−	0.210473i	$-0.932500\pi$
$7$	−3.39747	+	1.96153i	−1.28412	+	0.741390i	−0.306525	+	0.951863i	$0.599166\pi$
$8$		−	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	−0.762718	−	0.646731i	$-0.776136\pi$
$11$	−1.93688	+	1.11826i	−0.583991	+	0.337168i	0.178727	+	0.983899i	$0.442802\pi$
$12$	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	$-0.754936\pi$
$19$		−	6.06808i		−	1.39211i	0.717987	−	0.696056i	$-0.245064\pi$
$20$	−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	−0.966342	−	0.257262i	$-0.917180\pi$
$23$	−1.24872	+	2.16284i	−0.260376	+	0.450984i	0.705966	+	0.708246i	$0.250513\pi$
$24$	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	0.575644	−	0.817700i	$-0.304751\pi$
$29$	−2.26353	−	3.92055i	−0.420327	−	0.728028i	−0.995971	+	0.0896720i	$0.971418\pi$
$30$	0.0870494	−	0.0444151i	0.0158930	−	0.00810905i
$31$	1.13390	+	0.654658i	0.203655	+	0.117580i	0.598359	−	0.801228i	$-0.295820\pi$
$31$	1.13390	+	0.654658i	0.203655	+	0.117580i	−0.394704	+	0.918808i	$0.629153\pi$
$32$	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	$-0.751763\pi$
$37$		−	8.55454i		−	1.40636i	0.711013	−	0.703179i	$-0.248237\pi$
$38$	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	−0.997865	−	0.0653099i	$-0.979196\pi$
$41$	−9.94634	−	5.74252i	−1.55336	−	0.896831i	−0.555493	−	0.831522i	$-0.687470\pi$
$42$	−0.0198512	+	0.382870i	−0.00306311	+	0.0590781i
$43$	4.04825	+	7.01177i	0.617352	+	1.06929i	0.989967	+	0.141299i	$0.0451279\pi$
$43$	4.04825	+	7.01177i	0.617352	+	1.06929i	−0.372615	+	0.927986i	$0.621539\pi$
$44$		−	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	−0.423373	−	0.905956i	$-0.639154\pi$
$47$	1.02507	−	0.591824i	0.149522	−	0.0863264i	0.572894	+	0.819629i	$0.305821\pi$
$48$	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	0.230297	−	0.973120i	$-0.426030\pi$
$59$	−3.81984	−	2.20539i	−0.497301	−	0.287117i	−0.727598	+	0.686003i	$0.759363\pi$
$60$	1.88206	−	2.90167i	0.242973	−	0.374603i
$61$	−1.24259	−	2.15224i	−0.159098	−	0.275566i	0.775446	−	0.631414i	$-0.217525\pi$
$61$	−1.24259	−	2.15224i	−0.159098	−	0.275566i	−0.934544	+	0.355849i	$0.884192\pi$
$62$	−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	−0.335480	−	0.942048i	$-0.608898\pi$
$67$	−10.7969	−	6.23362i	−1.31906	−	0.761558i	−0.983577	+	0.180490i	$0.942232\pi$
$68$	−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	$0.409078\pi$
$71$			16.1695i			1.91896i	−0.281771	+	0.959482i	$0.590922\pi$
$72$	−0.547763	−	0.397040i	−0.0645545	−	0.0467916i
$73$			2.60190i			0.304530i	0.988340	+	0.152265i	$0.0486566\pi$
$73$			2.60190i			0.304530i	−0.988340	+	0.152265i	$0.951343\pi$
$74$	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	0.733909	−	0.679248i	$-0.237694\pi$
$79$	−1.96689	−	3.40675i	−0.221292	−	0.383289i	−0.955201	+	0.295959i	$0.904361\pi$
$80$		−	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	−0.930146	−	0.367189i	$-0.880320\pi$
$83$	−9.81398	+	5.66610i	−1.07722	+	0.621936i	−0.147078	+	0.989125i	$0.546987\pi$
$84$	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	$0.118153\pi$
$89$			6.84387i			0.725449i	−0.931896	+	0.362725i	$0.881847\pi$
$90$	−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	−0.0452095	−	0.998978i	$-0.514396\pi$
$97$	7.85275	−	4.53379i	0.797326	−	0.460336i	0.842535	+	0.538641i	$0.181062\pi$
$98$			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	0.919540	+	0.392996i	$0.128561\pi$
$101$	8.04105	+	13.9275i	0.800115	+	1.38584i	−0.119425	+	0.992843i	$0.538105\pi$
$102$	0.297949	−	0.459362i	0.0295014	−	0.0454836i
$103$	−2.49430	+	4.32026i	−0.245771	+	0.425688i	−0.962348	−	0.271820i	$-0.912374\pi$
$103$	−2.49430	+	4.32026i	−0.245771	+	0.425688i	0.716577	+	0.697508i	$0.245708\pi$
$104$	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	$-0.950045\pi$
$109$		−	3.26351i		−	0.312587i	0.987711	−	0.156294i	$-0.0499546\pi$
$110$	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	0.309712	+	0.950831i	$0.399768\pi$
$113$	−7.10718	+	12.3100i	−0.668588	+	1.15803i	−0.978299	+	0.207197i	$0.933566\pi$
$114$	−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	−0.585481	−	0.810686i	$-0.699094\pi$
$131$	4.68504	−	8.11473i	0.409334	−	0.708988i	0.994815	+	0.101698i	$0.0324277\pi$
$132$	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	−0.356100	−	0.934448i	$-0.615894\pi$
$137$	3.22002	−	1.85908i	0.275105	−	0.158832i	0.631205	+	0.775616i	$0.282561\pi$
$138$	0.110924	+	0.217400i	0.00944246	+	0.0185063i
$139$	7.25279	−	12.5622i	0.615173	−	1.06551i	−0.375181	−	0.926952i	$-0.622419\pi$
$139$	7.25279	−	12.5622i	0.615173	−	1.06551i	0.990354	−	0.138560i	$-0.0442473\pi$
$140$	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	0.806366	−	0.591417i	$-0.201431\pi$
$149$	8.51245	+	4.91467i	0.697367	+	0.402625i	−0.108999	+	0.994042i	$0.534764\pi$
$150$	0.0975946	+	0.00506013i	0.00796856	+	0.000413158i
$151$	−7.20109	+	4.15755i	−0.586016	+	0.338336i	−0.763521	−	0.645783i	$-0.776531\pi$
$151$	−7.20109	+	4.15755i	−0.586016	+	0.338336i	0.177505	+	0.984120i	$0.443198\pi$
$152$	−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	−0.997238	−	0.0742665i	$-0.976338\pi$
$157$	−5.44180	+	9.42547i	−0.434303	+	0.752234i	0.562936	+	0.826501i	$0.309672\pi$
$158$	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	$-0.909679\pi$
$163$		−	7.14857i		−	0.559920i	0.960012	−	0.279960i	$-0.0903211\pi$
$164$	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	−0.195877	−	0.980629i	$-0.562755\pi$
$167$	−14.7716	−	8.52841i	−1.14306	−	0.659948i	−0.947188	+	0.320680i	$0.896089\pi$
$168$	−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	−0.994593	−	0.103848i	$-0.966884\pi$
$173$	−7.72383	−	13.3781i	−0.587232	−	1.01711i	0.407362	−	0.913267i	$-0.366449\pi$
$174$	−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	0.768987	−	0.639264i	$-0.220761\pi$
$191$	−2.33736	−	4.04843i	−0.169125	−	0.292934i	−0.938113	+	0.346330i	$0.887428\pi$
$192$	−12.2249	+	6.23750i	−0.882257	+	0.450153i
$193$	−9.77243	−	5.64211i	−0.703435	−	0.406128i	0.105191	−	0.994452i	$-0.466455\pi$
$193$	−9.77243	−	5.64211i	−0.703435	−	0.406128i	−0.808625	+	0.588324i	$0.799788\pi$
$194$	−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	$0.195631\pi$
$197$			16.1866i			1.15325i	−0.817009	+	0.576625i	$0.804369\pi$
$198$	−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	−0.107079	−	0.994251i	$-0.534150\pi$
$211$	11.7297	−	20.3165i	0.807507	−	1.39864i	0.914586	−	0.404392i	$-0.132517\pi$
$212$	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	−0.999436	−	0.0335730i	$-0.989311\pi$
$223$	−21.9530	+	12.6746i	−1.47008	+	0.848751i	−0.470643	+	0.882324i	$0.655978\pi$
$224$	−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	−0.931251	−	0.364378i	$-0.881282\pi$
$227$	−16.2917	+	9.40600i	−1.08132	+	0.624298i	−0.150065	+	0.988676i	$0.547948\pi$
$228$	−20.9588	−	1.08668i	−1.38803	−	0.0719674i
$229$	0.913257	+	0.527269i	0.0603497	+	0.0348429i	0.529871	−	0.848078i	$-0.322240\pi$
$229$	0.913257	+	0.527269i	0.0603497	+	0.0348429i	−0.469522	+	0.882921i	$0.655574\pi$
$230$	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	0.745701	−	0.666280i	$-0.232115\pi$
$239$	8.37195	+	4.83355i	0.541537	+	0.312656i	−0.204165	+	0.978937i	$0.565448\pi$
$240$	3.13375	+	6.14187i	0.202283	+	0.396456i
$241$	−19.7643	+	11.4109i	−1.27313	+	0.735041i	−0.975575	−	0.219664i	$-0.929504\pi$
$241$	−19.7643	+	11.4109i	−1.27313	+	0.735041i	−0.297553	+	0.954705i	$0.596170\pi$
$242$		−	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	−0.977830	−	0.209402i	$-0.932848\pi$
$257$	−4.93068	+	8.54019i	−0.307567	+	0.532722i	0.670262	+	0.742124i	$0.266182\pi$
$258$	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	0.962491	−	0.271315i	$-0.0874586\pi$
$263$	3.99398	+	6.91778i	0.246279	+	0.426568i	−0.716211	+	0.697884i	$0.754125\pi$
$264$	−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	$0.0600033\pi$
$271$			6.16970i			0.374783i	−0.982285	+	0.187391i	$0.939997\pi$
$272$	−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	0.525672	−	0.850688i	$-0.323814\pi$
$277$	−7.88696	−	13.6606i	−0.473881	−	0.820786i	−0.999553	+	0.0299012i	$0.990481\pi$
$278$			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	0.394764	−	0.918783i	$-0.370826\pi$
$281$	23.2643	−	13.4317i	1.38783	−	0.801267i	0.993071	+	0.117516i	$0.0374931\pi$
$282$	0.00598941	−	0.115518i	0.000356664	−	0.00687897i
$283$	9.52837	−	16.5036i	0.566403	−	0.981039i	−0.430515	−	0.902584i	$-0.641668\pi$
$283$	9.52837	−	16.5036i	0.566403	−	0.981039i	0.996918	−	0.0784550i	$-0.0249987\pi$
$284$	−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	0.875885	−	0.482519i	$-0.160278\pi$
$293$	15.3363	+	8.85439i	0.895954	+	0.517279i	0.0200686	+	0.999799i	$0.493612\pi$
$294$	−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	$0.222009\pi$
$307$			22.5071i			1.28455i	−0.766476	+	0.642274i	$0.777991\pi$
$308$	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	−0.792715	−	0.609592i	$-0.791333\pi$
$311$	2.32016	−	4.01864i	0.131564	−	0.227876i	0.924280	+	0.381716i	$0.124667\pi$
$312$	−1.39971	−	0.155247i	−0.0792432	−	0.00878915i
$313$	−16.2853	−	28.2070i	−0.920500	−	1.59435i	−0.798643	−	0.601805i	$-0.794449\pi$
$313$	−16.2853	−	28.2070i	−0.920500	−	1.59435i	−0.121856	−	0.992548i	$-0.538885\pi$
$314$		−	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	0.209147	−	0.977884i	$-0.432931\pi$
$317$	20.6638	−	11.9302i	1.16059	−	0.670069i	0.951446	+	0.307815i	$0.0995978\pi$
$318$	−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	0.326525	−	0.945189i	$-0.394122\pi$
$331$	23.8032	−	13.7428i	1.30834	−	0.755373i	0.981820	+	0.189815i	$0.0607889\pi$
$332$		−	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	−0.940191	−	0.340649i	$-0.889353\pi$
$337$	−3.21413	+	5.56704i	−0.175085	+	0.303256i	0.765106	+	0.643905i	$0.222687\pi$
$338$	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	−0.336043	−	0.941847i	$-0.609089\pi$
$347$	12.0642	−	20.8959i	0.647642	−	1.12175i	0.983685	−	0.179902i	$-0.0575780\pi$
$348$	−13.9467	+	7.11602i	−0.747624	+	0.381459i
$349$	12.2509	−	7.07307i	0.655776	−	0.378613i	−0.134889	−	0.990861i	$-0.543068\pi$
$349$	12.2509	−	7.07307i	0.655776	−	0.378613i	0.790666	+	0.612248i	$0.209735\pi$
$350$	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	−0.761248	−	0.648461i	$-0.775413\pi$
$353$	−10.9026	+	6.29463i	−0.580288	+	0.335029i	0.180960	+	0.983490i	$0.442080\pi$
$354$	−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	$0.0503334\pi$
$359$			5.96722i			0.314938i	−0.987524	+	0.157469i	$0.949667\pi$
$360$	−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	0.864717	−	0.502259i	$-0.167497\pi$
$367$	−0.0500029	−	0.0866076i	−0.00261013	−	0.00452088i	−0.867328	+	0.497738i	$0.834164\pi$
$368$	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	0.454146	+	0.890927i	$0.349944\pi$
$373$	−10.5159	+	18.2141i	−0.544492	+	0.943088i	−0.998639	+	0.0521612i	$0.983389\pi$
$374$	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	$0.0626664\pi$
$379$			7.61597i			0.391206i	−0.980683	+	0.195603i	$0.937334\pi$
$380$	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	0.283071	−	0.959099i	$-0.408647\pi$
$383$	−7.94552	−	4.58735i	−0.405997	−	0.234403i	−0.689068	+	0.724696i	$0.741980\pi$
$384$	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	0.942141	+	0.335217i	$0.108810\pi$
$389$	15.0167	+	26.0097i	0.761377	+	1.31874i	−0.180764	+	0.983527i	$0.557857\pi$
$390$	−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	$-0.891979\pi$
$397$		−	13.2652i		−	0.665763i	0.942969	−	0.332882i	$-0.108021\pi$
$398$	−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	0.952765	−	0.303708i	$-0.0982246\pi$
$401$	23.3517	+	13.4821i	1.16613	+	0.673265i	0.213364	+	0.976973i	$0.431558\pi$
$402$	−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	−0.176781	−	0.984250i	$-0.556568\pi$
$409$	−22.6012	−	13.0488i	−1.11756	−	0.645222i	−0.940776	+	0.339028i	$0.889902\pi$
$410$	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	−0.971271	−	0.237975i	$-0.923517\pi$
$419$	−5.72212	+	9.91100i	−0.279544	+	0.484184i	0.691728	+	0.722158i	$0.256850\pi$
$420$	−0.702551	+	13.5501i	−0.0342810	+	0.661175i
$421$	−8.24733	+	4.76160i	−0.401950	+	0.232066i	−0.687325	−	0.726350i	$-0.741215\pi$
$421$	−8.24733	+	4.76160i	−0.401950	+	0.232066i	0.285375	+	0.958416i	$0.407882\pi$
$422$			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	$0.189191\pi$
$431$			23.2510i			1.11996i	−0.828506	+	0.559980i	$0.810809\pi$
$432$	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	0.978784	+	0.204896i	$0.0656858\pi$
$439$	13.9718	+	24.1999i	0.666837	+	1.15500i	−0.311946	+	0.950100i	$0.600981\pi$
$440$			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	0.661977	−	0.749524i	$-0.269718\pi$
$443$	−6.69562	−	11.5972i	−0.318119	−	0.550998i	−0.980095	+	0.198527i	$0.936384\pi$
$444$	−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	$0.0239651\pi$
$449$			3.18766i			0.150435i	−0.997167	+	0.0752175i	$0.976035\pi$
$450$	−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	−0.716458	−	0.697630i	$-0.754238\pi$
$457$	−10.0586	+	5.80733i	−0.470521	+	0.271656i	0.245937	+	0.969286i	$0.420904\pi$
$458$	−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	−0.782971	−	0.622058i	$-0.786297\pi$
$461$	−13.6499	+	7.88076i	−0.635738	+	0.367043i	0.147233	+	0.989102i	$0.452963\pi$
$462$	−0.389698	−	0.763772i	−0.0181304	−	0.0355339i
$463$	23.6139	+	13.6335i	1.09743	+	0.633603i	0.935546	−	0.353206i	$-0.114909\pi$
$463$	23.6139	+	13.6335i	1.09743	+	0.633603i	0.161887	+	0.986809i	$0.448242\pi$
$464$	−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	0.162076	−	0.986778i	$-0.448181\pi$
$479$	24.0241	−	13.8703i	1.09769	−	0.633751i	0.935613	+	0.353027i	$0.114848\pi$
$480$	−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	$-0.839037\pi$
$487$		−	21.3797i		−	0.968805i	0.874845	−	0.484402i	$-0.160963\pi$
$488$	−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	−0.739598	−	0.673049i	$-0.764984\pi$
$491$	4.72150	−	8.17788i	0.213078	−	0.369063i	0.952676	+	0.303986i	$0.0983177\pi$
$492$	−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	0.654560	−	0.756010i	$-0.272854\pi$
$499$	7.30721	+	4.21882i	0.327116	+	0.188860i	−0.327444	+	0.944871i	$0.606187\pi$
$500$	−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	0.824359	−	0.566068i	$-0.191536\pi$
$509$	16.8375	+	9.72113i	0.746309	+	0.430882i	−0.0780498	+	0.996949i	$0.524869\pi$
$510$	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	$0.386786\pi$
$541$			43.6073i			1.87483i	−0.348220	+	0.937413i	$0.613214\pi$
$542$	−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	0.733957	−	0.679196i	$-0.237671\pi$
$547$	−5.17395	−	8.96155i	−0.221222	−	0.383168i	−0.955179	+	0.296028i	$0.904338\pi$
$548$			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	$0.00384436\pi$
$557$			0.570061i			0.0241543i	−0.999927	+	0.0120771i	$0.996156\pi$
$558$	−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	0.444865	+	0.895598i	$0.353252\pi$
$563$	−13.1256	+	22.7342i	−0.553178	+	0.958132i	−0.998043	+	0.0625346i	$0.980082\pi$
$564$	−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	0.996477	+	0.0838621i	$0.0267255\pi$
$569$	13.6173	+	23.5858i	0.570865	+	0.988768i	−0.425612	+	0.904906i	$0.639941\pi$
$570$	−0.269514	−	0.528223i	−0.0112887	−	0.0221248i
$571$	16.6581	−	28.8527i	0.697120	−	1.20745i	−0.272340	−	0.962201i	$-0.587798\pi$
$571$	16.6581	−	28.8527i	0.697120	−	1.20745i	0.969461	−	0.245247i	$-0.0788691\pi$
$572$	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	$0.195320\pi$
$577$			27.6637i			1.15166i	−0.817571	+	0.575828i	$0.804680\pi$
$578$	−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	−0.657581	−	0.753384i	$-0.728420\pi$
$587$	−8.09027	+	4.67092i	−0.333921	+	0.192789i	0.323660	+	0.946174i	$0.395087\pi$
$588$	−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	$0.382724\pi$
$593$			45.4348i			1.86578i	−0.360156	+	0.932892i	$0.617276\pi$
$594$	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	0.120752	+	0.992683i	$0.461469\pi$
$599$	−19.5627	+	33.8837i	−0.799312	+	1.38445i	−0.920065	+	0.391767i	$0.871864\pi$
$600$	−0.212549	+	0.327696i	−0.00867726	+	0.0133781i
$601$	−0.777604	−	1.34685i	−0.0317191	−	0.0549392i	0.849730	−	0.527218i	$-0.176765\pi$
$601$	−0.777604	−	1.34685i	−0.0317191	−	0.0549392i	−0.881449	+	0.472279i	$0.843432\pi$
$602$	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	−0.849062	−	0.528294i	$-0.822832\pi$
$607$	0.812671	−	1.40759i	0.0329853	−	0.0571322i	0.882047	+	0.471162i	$0.156165\pi$
$608$	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	$-0.862668\pi$
$613$		−	20.7073i		−	0.836361i	0.908364	−	0.418181i	$-0.137332\pi$
$614$	−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	0.982624	+	0.185608i	$0.0594256\pi$
$617$	40.6045	+	23.4430i	1.63468	+	0.943781i	0.652054	+	0.758173i	$0.273908\pi$
$618$	0.221569	+	0.434255i	0.00891282	+	0.0174683i
$619$	2.68056	−	1.54762i	0.107741	−	0.0622041i	−0.445161	−	0.895450i	$-0.646854\pi$
$619$	2.68056	−	1.54762i	0.107741	−	0.0622041i	0.552902	+	0.833246i	$0.313520\pi$
$620$	−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	$-0.933679\pi$
$631$		−	10.3920i		−	0.413697i	0.978373	−	0.206849i	$-0.0663208\pi$
$632$	−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	0.775387	−	0.631486i	$-0.217555\pi$
$641$	−4.03035	−	6.98077i	−0.159189	−	0.275724i	−0.934577	+	0.355762i	$0.884221\pi$
$642$	0.158924	−	0.245021i	0.00627225	−	0.00967022i
$643$	−29.5621	−	17.0677i	−1.16581	−	0.673083i	−0.213123	−	0.977025i	$-0.568364\pi$
$643$	−29.5621	−	17.0677i	−1.16581	−	0.673083i	−0.952690	+	0.303942i	$0.901697\pi$
$644$	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	−0.768954	−	0.639304i	$-0.779223\pi$
$653$	4.32310	−	7.48783i	0.169176	−	0.293021i	0.938130	+	0.346282i	$0.112556\pi$
$654$	−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	0.561954	−	0.827169i	$-0.310050\pi$
$659$	−11.1764	−	19.3582i	−0.435372	−	0.754087i	−0.997326	+	0.0730819i	$0.976717\pi$
$660$	−0.400520	+	7.72481i	−0.0155902	+	0.300688i
$661$	16.8969	+	9.75541i	0.657212	+	0.379441i	0.791214	−	0.611540i	$-0.209449\pi$
$661$	16.8969	+	9.75541i	0.657212	+	0.379441i	−0.134002	+	0.990981i	$0.542783\pi$
$662$	−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	0.854804	+	0.518950i	$0.173677\pi$
$673$	22.7468	+	39.3987i	0.876826	+	1.51871i	0.0220221	+	0.999757i	$0.492990\pi$
$674$		−	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	0.911920	−	0.410368i	$-0.134600\pi$
$677$	2.61677	+	4.53238i	0.100571	+	0.174193i	−0.811349	+	0.584562i	$0.801267\pi$
$678$	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	$0.262497\pi$
$683$			38.3817i			1.46863i	−0.678807	+	0.734317i	$0.737503\pi$
$684$	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	−0.455454	−	0.890259i	$-0.650523\pi$
$691$	2.30815	−	1.33261i	0.0878063	−	0.0506950i	0.543260	+	0.839564i	$0.317190\pi$
$692$	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	−0.879733	−	0.475468i	$-0.842279\pi$
$709$	−24.1729	+	13.9562i	−0.907832	+	0.524137i	−0.0280989	+	0.999605i	$0.508945\pi$
$710$		−	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	0.689236	−	0.724537i	$-0.257946\pi$
$727$	−7.62646	−	13.2094i	−0.282850	−	0.489910i	−0.972085	+	0.234627i	$0.924613\pi$
$728$	−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	0.153848	−	0.988095i	$-0.450833\pi$
$733$	−16.9197	−	9.76859i	−0.624943	−	0.360811i	−0.778791	+	0.627284i	$0.784167\pi$
$734$	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	$0.0338374\pi$
$739$			5.76873i			0.212206i	−0.994355	+	0.106103i	$0.966163\pi$
$740$	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	0.520583	−	0.853811i	$-0.325715\pi$
$743$	1.12991	+	0.652354i	0.0414524	+	0.0239325i	−0.479131	+	0.877744i	$0.659048\pi$
$744$	−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	−0.939985	−	0.341216i	$-0.889161\pi$
$751$	−4.78180	+	8.28232i	−0.174490	+	0.302226i	0.765494	+	0.643443i	$0.222494\pi$
$752$	−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	−0.397918	−	0.917421i	$-0.630267\pi$
$761$	−38.3831	−	22.1605i	−1.39139	−	0.803317i	−0.993469	+	0.114104i	$0.963600\pi$
$762$	−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	−0.313640	−	0.949542i	$-0.601548\pi$
$769$	−35.8501	−	20.6981i	−1.29279	−	0.746391i	−0.979147	+	0.203151i	$0.934882\pi$
$770$	−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	$-0.925435\pi$
$773$		−	12.9069i		−	0.464231i	0.972688	−	0.232115i	$-0.0745647\pi$
$774$	−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	0.798328	−	0.602223i	$-0.205718\pi$
$787$	18.9628	+	10.9482i	0.675950	+	0.390260i	−0.122377	+	0.992484i	$0.539052\pi$
$788$	−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	0.485332	+	0.874330i	$0.338699\pi$
$797$	−14.5257	+	25.1592i	−0.514526	+	0.891185i	−0.999858	+	0.0168549i	$0.994635\pi$
$798$	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	$-0.981615\pi$
$811$		−	3.28781i		−	0.115451i	0.998333	−	0.0577253i	$-0.0183848\pi$
$812$	−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	−0.918761	−	0.394814i	$-0.870809\pi$
$821$	−29.6910	+	17.1421i	−1.03622	+	0.598263i	−0.117461	+	0.993077i	$0.537476\pi$
$822$	0.0188144	−	0.362872i	0.000656226	−	0.0126566i
$823$	2.90511	−	5.03180i	0.101266	−	0.175397i	−0.810941	−	0.585128i	$-0.801044\pi$
$823$	2.90511	−	5.03180i	0.101266	−	0.175397i	0.912206	+	0.409731i	$0.134377\pi$
$824$	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	$-0.614111\pi$
$827$		−	53.8589i		−	1.87286i	0.350860	−	0.936428i	$-0.385889\pi$
$828$	−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	−0.756181	−	0.654363i	$-0.772937\pi$
$839$	−16.4401	+	9.49171i	−0.567576	+	0.327690i	0.188605	+	0.982053i	$0.439604\pi$
$840$	−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	0.0748515	−	0.997195i	$-0.476152\pi$
$853$	28.5015	−	16.4554i	0.975873	−	0.563421i	0.901022	+	0.433774i	$0.142818\pi$
$854$	−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	0.758840	−	0.651277i	$-0.225766\pi$
$857$	−5.40414	−	9.36025i	−0.184602	−	0.319740i	−0.943442	+	0.331537i	$0.892433\pi$
$858$	−0.634873	−	0.466856i	−0.0216742	−	0.0159382i
$859$	−16.8254	+	29.1424i	−0.574074	+	0.994325i	0.422068	+	0.906564i	$0.361304\pi$
$859$	−16.8254	+	29.1424i	−0.574074	+	0.994325i	−0.996142	+	0.0877609i	$0.972029\pi$
$860$	−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	$0.140216\pi$
$863$			25.0522i			0.852787i	−0.904538	+	0.426394i	$0.859784\pi$
$864$	−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	−0.120030	−	0.992770i	$-0.538299\pi$
$877$	−30.7931	−	17.7784i	−1.03981	−	0.600334i	−0.919779	+	0.392436i	$0.871632\pi$
$878$	−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	−0.990406	−	0.138191i	$-0.955871\pi$
$887$	−11.1841	+	19.3715i	−0.375526	+	0.650430i	0.614880	+	0.788621i	$0.289205\pi$
$888$	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	−0.767271	−	0.641323i	$-0.778386\pi$
$907$	−28.2805	−	48.9832i	−0.939037	−	1.62646i	−0.171766	−	0.985138i	$-0.554947\pi$
$908$		−	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	0.985292	+	0.170881i	$0.0546614\pi$
$911$	19.3361	+	33.4911i	0.640633	+	1.10961i	−0.344659	+	0.938728i	$0.612005\pi$
$912$	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	−0.797831	−	0.602881i	$-0.794020\pi$
$929$	−20.5626	+	11.8718i	−0.674637	+	0.389502i	0.123194	+	0.992383i	$0.460686\pi$
$930$	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	0.487942	−	0.872876i	$-0.337748\pi$
$941$	−0.736837	−	0.425413i	−0.0240202	−	0.0138681i	−0.511962	+	0.859008i	$0.671081\pi$
$942$	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	−0.303065	−	0.952970i	$-0.598010\pi$
$947$	11.4077	−	6.58621i	0.370699	−	0.214023i	0.673764	+	0.738947i	$0.264677\pi$
$948$	−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	0.799038	−	0.601281i	$-0.205343\pi$
$967$	21.0783	+	12.1696i	0.677832	+	0.391347i	−0.121206	+	0.992627i	$0.538676\pi$
$968$	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	0.288818	−	0.957384i	$-0.406738\pi$
$977$	−12.3744	−	7.14435i	−0.395891	−	0.228568i	−0.684710	+	0.728816i	$0.740071\pi$
$978$	−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	−0.985831	−	0.167744i	$-0.946352\pi$
$983$	−41.8082	+	24.1380i	−1.33347	+	0.769882i	−0.347644	+	0.937626i	$0.613018\pi$
$984$	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	0.935992	−	0.352020i	$-0.114505\pi$
$997$	5.15112	+	8.92200i	0.163138	+	0.282563i	−0.772855	+	0.634583i	$0.781172\pi$
$998$	−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.571.27	yes	108
9.7	even	3	inner	585.2.bt.b.376.28	yes	108
13.12	even	2	inner	585.2.bt.b.571.28	yes	108
117.25	even	6	inner	585.2.bt.b.376.27	✓	108

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
585.2.bt.b.376.27	✓	108	117.25	even	6	inner
585.2.bt.b.376.28	yes	108	9.7	even	3	inner
585.2.bt.b.571.27	yes	108	1.1	even	1	trivial
585.2.bt.b.571.28	yes	108	13.12	even	2	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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