LMFDB - Embedded newform 475.2.u.c.99.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [475,2,Mod(24,475)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(475, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([9, 16]))

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

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

chi := DirichletCharacter("475.24");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 475 = 5^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	475.u (of order $18$, degree $6$, not 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:	$3.79289409601$
Analytic rank:	$0$
Dimension:	$36$
Relative dimension:	$6$ over $\Q(\zeta_{18})$
Twist minimal:	no (minimal twist has level 95)
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			99.5
Character	$\chi$	$=$	475.99
Dual form			475.2.u.c.24.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.575828 - 1.58207i) q^{2} +(-3.20261 + 0.564707i) q^{3} +(-0.639290 - 0.536428i) q^{4} +(-0.950745 + 5.39194i) q^{6} +(0.474919 + 0.274194i) q^{7} +(1.69930 - 0.981094i) q^{8} +(7.11876 - 2.59101i) q^{9} +O(q^{10})$	\(q+(0.575828 - 1.58207i) q^{2} +(-3.20261 + 0.564707i) q^{3} +(-0.639290 - 0.536428i) q^{4} +(-0.950745 + 5.39194i) q^{6} +(0.474919 + 0.274194i) q^{7} +(1.69930 - 0.981094i) q^{8} +(7.11876 - 2.59101i) q^{9} +(-0.165601 - 0.286829i) q^{11} +(2.35032 + 1.35696i) q^{12} +(-4.74830 - 0.837254i) q^{13} +(0.707267 - 0.593468i) q^{14} +(-0.863487 - 4.89708i) q^{16} +(1.80612 - 4.96227i) q^{17} -12.7544i q^{18} +(-4.30704 - 0.670409i) q^{19} +(-1.67582 - 0.609949i) q^{21} +(-0.549142 + 0.0968286i) q^{22} +(-0.713529 + 0.850350i) q^{23} +(-4.88818 + 4.10167i) q^{24} +(-4.05880 + 7.03005i) q^{26} +(-12.8865 + 7.44000i) q^{27} +(-0.156525 - 0.430050i) q^{28} +(-3.01199 + 1.09627i) q^{29} +(3.01060 - 5.21452i) q^{31} +(-4.38000 - 0.772312i) q^{32} +(0.692330 + 0.825087i) q^{33} +(-6.81067 - 5.71483i) q^{34} +(-5.94084 - 2.16229i) q^{36} -6.67261i q^{37} +(-3.54075 + 6.42801i) q^{38} +15.6798 q^{39} +(-1.37380 - 7.79121i) q^{41} +(-1.92997 + 2.30005i) q^{42} +(-1.05356 - 1.25559i) q^{43} +(-0.0479962 + 0.272200i) q^{44} +(0.934447 + 1.61851i) q^{46} +(1.57373 + 4.32380i) q^{47} +(5.53083 + 15.1958i) q^{48} +(-3.34963 - 5.80174i) q^{49} +(-2.98207 + 16.9122i) q^{51} +(2.58642 + 3.08237i) q^{52} +(4.32352 - 5.15257i) q^{53} +(4.35025 + 24.6715i) q^{54} +1.07604 q^{56} +(14.1723 - 0.285152i) q^{57} +5.39645i q^{58} +(-6.39331 - 2.32697i) q^{59} +(0.520640 + 0.436869i) q^{61} +(-6.51616 - 7.76566i) q^{62} +(4.09127 + 0.721402i) q^{63} +(1.22864 - 2.12807i) q^{64} +(1.70401 - 0.620209i) q^{66} +(2.65816 + 7.30324i) q^{67} +(-3.81654 + 2.20348i) q^{68} +(1.80496 - 3.12628i) q^{69} +(-0.832574 + 0.698612i) q^{71} +(9.55490 - 11.3871i) q^{72} +(13.7393 - 2.42261i) q^{73} +(-10.5566 - 3.84227i) q^{74} +(2.39382 + 2.73900i) q^{76} -0.181627i q^{77} +(9.02885 - 24.8065i) q^{78} +(0.243868 + 1.38304i) q^{79} +(19.6591 - 16.4960i) q^{81} +(-13.1173 - 2.31294i) q^{82} +(-0.740346 - 0.427439i) q^{83} +(0.744142 + 1.28889i) q^{84} +(-2.59310 + 0.943812i) q^{86} +(9.02715 - 5.21183i) q^{87} +(-0.562813 - 0.324940i) q^{88} +(-2.52694 + 14.3310i) q^{89} +(-2.02549 - 1.69959i) q^{91} +(0.912304 - 0.160864i) q^{92} +(-6.69712 + 18.4002i) q^{93} +7.74677 q^{94} +14.4636 q^{96} +(-2.40147 + 6.59799i) q^{97} +(-11.1076 + 1.95857i) q^{98} +(-1.92205 - 1.61279i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q + 6 q^{4} - 12 q^{6} + 42 q^{9}+O(q^{10}) $ 36 * q + 6 * q^4 - 12 * q^6 + 42 * q^9	$ 36 q + 6 q^{4} - 12 q^{6} + 42 q^{9} - 48 q^{14} + 42 q^{16} + 24 q^{19} + 6 q^{21} - 42 q^{24} - 42 q^{26} + 18 q^{29} + 60 q^{31} - 48 q^{34} - 42 q^{36} - 24 q^{39} - 12 q^{41} + 60 q^{44} + 42 q^{46} + 6 q^{49} + 54 q^{51} - 60 q^{54} - 144 q^{56} - 36 q^{59} + 12 q^{61} + 48 q^{64} - 66 q^{66} - 54 q^{69} + 48 q^{71} + 78 q^{74} + 54 q^{76} - 18 q^{79} + 30 q^{81} + 24 q^{84} - 66 q^{86} + 12 q^{89} - 12 q^{91} + 132 q^{94} - 36 q^{96} - 6 q^{99}+O(q^{100}) $ 36 * q + 6 * q^4 - 12 * q^6 + 42 * q^9 - 48 * q^14 + 42 * q^16 + 24 * q^19 + 6 * q^21 - 42 * q^24 - 42 * q^26 + 18 * q^29 + 60 * q^31 - 48 * q^34 - 42 * q^36 - 24 * q^39 - 12 * q^41 + 60 * q^44 + 42 * q^46 + 6 * q^49 + 54 * q^51 - 60 * q^54 - 144 * q^56 - 36 * q^59 + 12 * q^61 + 48 * q^64 - 66 * q^66 - 54 * q^69 + 48 * q^71 + 78 * q^74 + 54 * q^76 - 18 * q^79 + 30 * q^81 + 24 * q^84 - 66 * q^86 + 12 * q^89 - 12 * q^91 + 132 * q^94 - 36 * q^96 - 6 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/475\mathbb{Z}\right)^\times$.

$n$	$77$	$401$
$\chi(n)$	$-1$	$e\left(\frac{1}{9}\right)$

Coefficient data

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

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

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

$2$	0.575828	−	1.58207i	0.407172	−	1.11869i	−0.551499	−	0.834176i	$-0.685944\pi$
$2$	0.575828	−	1.58207i	0.407172	−	1.11869i	0.958670	−	0.284519i	$-0.0918339\pi$
$3$	−3.20261	+	0.564707i	−1.84903	+	0.326034i	−0.984341	−	0.176275i	$-0.943595\pi$
$3$	−3.20261	+	0.564707i	−1.84903	+	0.326034i	−0.864688	+	0.502309i	$0.832484\pi$
$4$	−0.639290	−	0.536428i	−0.319645	−	0.268214i
$5$		0			0
$5$		0			0
$6$	−0.950745	+	5.39194i	−0.388140	+	2.20125i
$7$	0.474919	+	0.274194i	0.179502	+	0.103636i	0.587059	−	0.809544i	$-0.300286\pi$
$7$	0.474919	+	0.274194i	0.179502	+	0.103636i	−0.407556	+	0.913180i	$0.633619\pi$
$8$	1.69930	−	0.981094i	0.600795	−	0.346869i
$9$	7.11876	−	2.59101i	2.37292	−	0.863672i
$10$		0			0
$11$	−0.165601	−	0.286829i	−0.0499306	−	0.0864823i	0.839980	−	0.542617i	$-0.182567\pi$
$11$	−0.165601	−	0.286829i	−0.0499306	−	0.0864823i	−0.889910	+	0.456135i	$0.849233\pi$
$12$	2.35032	+	1.35696i	0.678480	+	0.391720i
$13$	−4.74830	−	0.837254i	−1.31694	−	0.232212i	−0.529347	−	0.848406i	$-0.677563\pi$
$13$	−4.74830	−	0.837254i	−1.31694	−	0.232212i	−0.787595	+	0.616193i	$0.788674\pi$
$14$	0.707267	−	0.593468i	0.189025	−	0.158611i
$15$		0			0
$16$	−0.863487	−	4.89708i	−0.215872	−	1.22427i
$17$	1.80612	−	4.96227i	0.438048	−	1.20353i	−0.502711	−	0.864454i	$-0.667664\pi$
$17$	1.80612	−	4.96227i	0.438048	−	1.20353i	0.940760	−	0.339074i	$-0.110114\pi$
$18$		−	12.7544i		−	3.00623i
$19$	−4.30704	−	0.670409i	−0.988102	−	0.153802i
$19$	−4.30704	−	0.670409i	−0.988102	−	0.153802i
$20$		0			0
$21$	−1.67582	−	0.609949i	−0.365694	−	0.133102i
$22$	−0.549142	+	0.0968286i	−0.117078	+	0.0206439i
$23$	−0.713529	+	0.850350i	−0.148781	+	0.177310i	−0.835288	−	0.549813i	$-0.814699\pi$
$23$	−0.713529	+	0.850350i	−0.148781	+	0.177310i	0.686507	+	0.727124i	$0.259143\pi$
$24$	−4.88818	+	4.10167i	−0.997796	+	0.837250i
$25$		0			0
$26$	−4.05880	+	7.03005i	−0.795996	+	1.37871i
$27$	−12.8865	+	7.44000i	−2.48000	+	1.43183i
$28$	−0.156525	−	0.430050i	−0.0295805	−	0.0812717i
$29$	−3.01199	+	1.09627i	−0.559312	+	0.203573i	−0.606179	−	0.795328i	$-0.707298\pi$
$29$	−3.01199	+	1.09627i	−0.559312	+	0.203573i	0.0468671	+	0.998901i	$0.485076\pi$
$30$		0			0
$31$	3.01060	−	5.21452i	0.540720	−	0.936555i	−0.458142	−	0.888879i	$-0.651485\pi$
$31$	3.01060	−	5.21452i	0.540720	−	0.936555i	0.998863	−	0.0476765i	$-0.0151816\pi$
$32$	−4.38000	−	0.772312i	−0.774282	−	0.136527i
$33$	0.692330	+	0.825087i	0.120519	+	0.143629i
$34$	−6.81067	−	5.71483i	−1.16802	−	0.980085i
$35$		0			0
$36$	−5.94084	−	2.16229i	−0.990140	−	0.360382i
$37$		−	6.67261i		−	1.09697i	−0.836161	−	0.548485i	$-0.815205\pi$
$37$		−	6.67261i		−	1.09697i	0.836161	−	0.548485i	$-0.184795\pi$
$38$	−3.54075	+	6.42801i	−0.574385	+	1.04276i
$39$	15.6798			2.51077
$40$		0			0
$41$	−1.37380	−	7.79121i	−0.214552	−	1.21678i	−0.881683	−	0.471842i	$-0.843589\pi$
$41$	−1.37380	−	7.79121i	−0.214552	−	1.21678i	0.667131	−	0.744940i	$-0.267522\pi$
$42$	−1.92997	+	2.30005i	−0.297800	+	0.354905i
$43$	−1.05356	−	1.25559i	−0.160667	−	0.191475i	0.679705	−	0.733486i	$-0.262108\pi$
$43$	−1.05356	−	1.25559i	−0.160667	−	0.191475i	−0.840372	+	0.542010i	$0.817663\pi$
$44$	−0.0479962	+	0.272200i	−0.00723570	+	0.0410357i
$45$		0			0
$46$	0.934447	+	1.61851i	0.137777	+	0.238636i
$47$	1.57373	+	4.32380i	0.229553	+	0.630691i	0.999977	−	0.00684117i	$-0.00217763\pi$
$47$	1.57373	+	4.32380i	0.229553	+	0.630691i	−0.770424	+	0.637532i	$0.779955\pi$
$48$	5.53083	+	15.1958i	0.798306	+	2.19333i
$49$	−3.34963	−	5.80174i	−0.478519	−	0.828820i
$50$		0			0
$51$	−2.98207	+	16.9122i	−0.417574	+	2.36818i
$52$	2.58642	+	3.08237i	0.358671	+	0.427448i
$53$	4.32352	−	5.15257i	0.593881	−	0.707759i	−0.382466	−	0.923970i	$-0.624925\pi$
$53$	4.32352	−	5.15257i	0.593881	−	0.707759i	0.976347	+	0.216210i	$0.0693696\pi$
$54$	4.35025	+	24.6715i	0.591994	+	3.35736i
$55$		0			0
$56$	1.07604			0.143792
$57$	14.1723	−	0.285152i	1.87717	−	0.0377693i
$58$			5.39645i			0.708588i
$59$	−6.39331	−	2.32697i	−0.832338	−	0.302946i	−0.109520	−	0.993985i	$-0.534931\pi$
$59$	−6.39331	−	2.32697i	−0.832338	−	0.302946i	−0.722818	+	0.691038i	$0.757154\pi$
$60$		0			0
$61$	0.520640	+	0.436869i	0.0666612	+	0.0559354i	0.675509	−	0.737351i	$-0.263924\pi$
$61$	0.520640	+	0.436869i	0.0666612	+	0.0559354i	−0.608848	+	0.793287i	$0.708368\pi$
$62$	−6.51616	−	7.76566i	−0.827554	−	0.986240i
$63$	4.09127	+	0.721402i	0.515452	+	0.0908881i
$64$	1.22864	−	2.12807i	0.153580	−	0.266009i
$65$		0			0
$66$	1.70401	−	0.620209i	0.209749	−	0.0763425i
$67$	2.65816	+	7.30324i	0.324746	+	0.892232i	0.989418	+	0.145097i	$0.0463493\pi$
$67$	2.65816	+	7.30324i	0.324746	+	0.892232i	−0.664672	+	0.747136i	$0.731429\pi$
$68$	−3.81654	+	2.20348i	−0.462823	+	0.267211i
$69$	1.80496	−	3.12628i	0.217291	−	0.376360i
$70$		0			0
$71$	−0.832574	+	0.698612i	−0.0988083	+	0.0829101i	−0.690854	−	0.722995i	$-0.742765\pi$
$71$	−0.832574	+	0.698612i	−0.0988083	+	0.0829101i	0.592045	+	0.805905i	$0.298321\pi$
$72$	9.55490	−	11.3871i	1.12606	−	1.34198i
$73$	13.7393	−	2.42261i	1.60806	−	0.283545i	0.703761	−	0.710437i	$-0.251503\pi$
$73$	13.7393	−	2.42261i	1.60806	−	0.283545i	0.904302	+	0.426892i	$0.140392\pi$
$74$	−10.5566	−	3.84227i	−1.22717	−	0.446655i
$75$		0			0
$76$	2.39382	+	2.73900i	0.274590	+	0.314185i
$77$		−	0.181627i		−	0.0206984i
$78$	9.02885	−	24.8065i	1.02232	−	2.80879i
$79$	0.243868	+	1.38304i	0.0274373	+	0.155605i	0.995448	−	0.0953032i	$-0.0303821\pi$
$79$	0.243868	+	1.38304i	0.0274373	+	0.155605i	−0.968011	+	0.250908i	$0.919271\pi$
$80$		0			0
$81$	19.6591	−	16.4960i	2.18435	−	1.83289i
$82$	−13.1173	−	2.31294i	−1.44857	−	0.255422i
$83$	−0.740346	−	0.427439i	−0.0812636	−	0.0469176i	0.458818	−	0.888530i	$-0.348273\pi$
$83$	−0.740346	−	0.427439i	−0.0812636	−	0.0469176i	−0.540081	+	0.841613i	$0.681606\pi$
$84$	0.744142	+	1.28889i	0.0811925	+	0.140630i
$85$		0			0
$86$	−2.59310	+	0.943812i	−0.279621	+	0.101774i
$87$	9.02715	−	5.21183i	0.967812	−	0.558767i
$88$	−0.562813	−	0.324940i	−0.0599960	−	0.0346387i
$89$	−2.52694	+	14.3310i	−0.267855	+	1.51908i	0.492926	+	0.870071i	$0.335927\pi$
$89$	−2.52694	+	14.3310i	−0.267855	+	1.51908i	−0.760781	+	0.649009i	$0.775184\pi$
$90$		0			0
$91$	−2.02549	−	1.69959i	−0.212329	−	0.178165i
$92$	0.912304	−	0.160864i	0.0951142	−	0.0167712i
$93$	−6.69712	+	18.4002i	−0.694459	+	1.90801i
$94$	7.74677			0.799018
$95$		0			0
$96$	14.4636			1.47618
$97$	−2.40147	+	6.59799i	−0.243832	+	0.669924i	0.756049	+	0.654515i	$0.227127\pi$
$97$	−2.40147	+	6.59799i	−0.243832	+	0.669924i	−0.999881	+	0.0154088i	$0.995095\pi$
$98$	−11.1076	+	1.95857i	−1.12204	+	0.197845i
$99$	−1.92205	−	1.61279i	−0.193173	−	0.162092i
$100$		0			0
$101$	−1.25144	+	7.09728i	−0.124523	+	0.706206i	0.857067	+	0.515205i	$0.172284\pi$
$101$	−1.25144	+	7.09728i	−0.124523	+	0.706206i	−0.981590	+	0.191000i	$0.938827\pi$
$102$	25.0391	+	14.4563i	2.47924	+	1.43139i
$103$	−6.12729	+	3.53759i	−0.603739	+	0.348569i	−0.770511	−	0.637426i	$-0.779999\pi$
$103$	−6.12729	+	3.53759i	−0.603739	+	0.348569i	0.166772	+	0.985996i	$0.446666\pi$
$104$	−8.89023	+	3.23578i	−0.871759	+	0.317294i
$105$		0			0
$106$	−5.66214	−	9.80711i	−0.549956	−	0.952551i
$107$	5.63008	+	3.25053i	0.544281	+	0.314241i	0.746812	−	0.665035i	$-0.231583\pi$
$107$	5.63008	+	3.25053i	0.544281	+	0.314241i	−0.202531	+	0.979276i	$0.564917\pi$
$108$	12.2292	+	2.15634i	1.17676	+	0.207494i
$109$	13.5289	−	11.3521i	1.29583	−	1.08733i	0.304980	−	0.952359i	$-0.401350\pi$
$109$	13.5289	−	11.3521i	1.29583	−	1.08733i	0.990850	−	0.134971i	$-0.0430942\pi$
$110$		0			0
$111$	3.76807	+	21.3698i	0.357649	+	2.02833i
$112$	0.932665	−	2.56248i	0.0881286	−	0.242131i
$113$			4.86487i			0.457649i	0.973468	+	0.228824i	$0.0734882\pi$
$113$			4.86487i			0.457649i	−0.973468	+	0.228824i	$0.926512\pi$
$114$	7.70970	−	22.5859i	0.722079	−	2.11536i
$115$		0			0
$116$	2.51360	+	0.914877i	0.233382	+	0.0849442i
$117$	−35.9713	+	6.34272i	−3.32555	+	0.586384i
$118$	−7.36289	+	8.77475i	−0.677809	+	0.807781i
$119$	2.21839	−	1.86145i	0.203359	−	0.170639i
$120$		0			0
$121$	5.44515	−	9.43128i	0.495014	−	0.857389i
$122$	0.990958	−	0.572130i	0.0897171	−	0.0517982i
$123$	8.79950	+	24.1764i	0.793424	+	2.17992i
$124$	−4.72186	+	1.71862i	−0.424036	+	0.154336i
$125$		0			0
$126$	3.49718	−	6.05729i	0.311553	−	0.539626i
$127$	−2.92418	−	0.515613i	−0.259479	−	0.0457532i	0.0423950	−	0.999101i	$-0.486501\pi$
$127$	−2.92418	−	0.515613i	−0.259479	−	0.0457532i	−0.301874	+	0.953348i	$0.597612\pi$
$128$	−8.37696	−	9.98327i	−0.740426	−	0.882405i
$129$	4.08319	+	3.42620i	0.359505	+	0.301660i
$130$		0			0
$131$	7.51285	+	2.73445i	0.656400	+	0.238910i	0.648682	−	0.761060i	$-0.275321\pi$
$131$	7.51285	+	2.73445i	0.656400	+	0.238910i	0.00771895	+	0.999970i	$0.497543\pi$
$132$		−	0.898855i		−	0.0782353i
$133$	−1.86167	−	1.49936i	−0.161427	−	0.130011i
$134$	13.0849			1.13036
$135$		0			0
$136$	−1.79931	−	10.2044i	−0.154289	−	0.875019i
$137$	−0.591862	+	0.705354i	−0.0505662	+	0.0602625i	−0.790735	−	0.612159i	$-0.790301\pi$
$137$	−0.591862	+	0.705354i	−0.0505662	+	0.0602625i	0.740169	+	0.672421i	$0.234746\pi$
$138$	−3.90666	−	4.65577i	−0.332557	−	0.396326i
$139$	0.0173742	−	0.0985339i	0.00147366	−	0.00835754i	−0.984062	−	0.177825i	$-0.943094\pi$
$139$	0.0173742	−	0.0985339i	0.00147366	−	0.00835754i	0.985536	+	0.169468i	$0.0542049\pi$
$140$		0			0
$141$	−7.48174	−	12.9588i	−0.630076	−	1.09132i
$142$	0.625837	+	1.71947i	0.0525191	+	0.144295i
$143$	0.546174	+	1.50060i	0.0456734	+	0.125487i
$144$	−18.8353	−	32.6238i	−1.56961	−	2.71865i
$145$		0			0
$146$	4.07872	−	23.1316i	0.337557	−	1.91438i
$147$	14.0039	+	16.6892i	1.15502	+	1.37650i
$148$	−3.57937	+	4.26573i	−0.294223	+	0.350641i
$149$	3.00368	+	17.0347i	0.246071	+	1.39554i	0.817992	+	0.575229i	$0.195087\pi$
$149$	3.00368	+	17.0347i	0.246071	+	1.39554i	−0.571922	+	0.820308i	$0.693802\pi$
$150$		0			0
$151$	−19.2178			−1.56393			−0.781963	−	0.623325i	$-0.785781\pi$
$151$	−19.2178			−1.56393			−0.781963	+	0.623325i	$0.785781\pi$
$152$	−7.97670	+	3.08638i	−0.646996	+	0.250338i
$153$		−	40.0049i		−	3.23420i
$154$	−0.287348	−	0.104586i	−0.0231552	−	0.00842779i
$155$		0			0
$156$	−10.0239	−	8.41107i	−0.802556	−	0.673424i
$157$	−4.23125	−	5.04261i	−0.337690	−	0.402444i	0.570299	−	0.821437i	$-0.306827\pi$
$157$	−4.23125	−	5.04261i	−0.337690	−	0.402444i	−0.907989	+	0.418994i	$0.862383\pi$
$158$	2.32850	+	0.410578i	0.185246	+	0.0326638i
$159$	−10.9369	+	18.9432i	−0.867349	+	1.50229i
$160$		0			0
$161$	−0.572030	+	0.208202i	−0.0450822	+	0.0164086i
$162$	−14.7776	−	40.6010i	−1.16104	−	3.18992i
$163$	12.6377	−	7.29637i	0.989860	−	0.571496i	0.0846275	−	0.996413i	$-0.473030\pi$
$163$	12.6377	−	7.29637i	0.989860	−	0.571496i	0.905232	+	0.424917i	$0.139697\pi$
$164$	−3.30117	+	5.71779i	−0.257778	+	0.446484i
$165$		0			0
$166$	−1.10255	+	0.925151i	−0.0855746	+	0.0718057i
$167$	−2.25595	+	2.68854i	−0.174571	+	0.208045i	−0.846234	−	0.532811i	$-0.821136\pi$
$167$	−2.25595	+	2.68854i	−0.174571	+	0.208045i	0.671664	+	0.740856i	$0.265580\pi$
$168$	−3.44615	+	0.607648i	−0.265876	+	0.0468811i
$169$	9.62936	+	3.50480i	0.740720	+	0.269600i
$170$		0			0
$171$	−32.3978	+	6.38711i	−2.47752	+	0.488435i
$172$			1.36784i			0.104297i
$173$	−0.856059	+	2.35200i	−0.0650849	+	0.178819i	−0.967972	−	0.251059i	$-0.919221\pi$
$173$	−0.856059	+	2.35200i	−0.0650849	+	0.178819i	0.902887	+	0.429878i	$0.141443\pi$
$174$	−3.04741	−	17.2827i	−0.231024	−	1.31020i
$175$		0			0
$176$	−1.26163	+	1.05863i	−0.0950990	+	0.0797975i
$177$	21.7894	+	3.84205i	1.63779	+	0.288786i
$178$	21.2176	+	12.2500i	1.59032	+	0.918174i
$179$	−2.51029	−	4.34795i	−0.187628	−	0.324981i	0.756831	−	0.653610i	$-0.226747\pi$
$179$	−2.51029	−	4.34795i	−0.187628	−	0.324981i	−0.944459	+	0.328630i	$0.893413\pi$
$180$		0			0
$181$	5.09429	−	1.85417i	0.378656	−	0.137819i	−0.145678	−	0.989332i	$-0.546536\pi$
$181$	5.09429	−	1.85417i	0.378656	−	0.137819i	0.524334	+	0.851513i	$0.324314\pi$
$182$	−3.85520	+	2.22580i	−0.285766	+	0.164987i
$183$	−1.91411	−	1.10511i	−0.141495	−	0.0816923i
$184$	−0.378229	+	2.14504i	−0.0278834	+	0.158135i
$185$		0			0
$186$	25.2541	+	21.1907i	1.85172	+	1.55378i
$187$	−1.72242	+	0.303709i	−0.125956	+	0.0222094i
$188$	1.31333	−	3.60836i	0.0957847	−	0.263166i
$189$	−8.16003			−0.593555
$190$		0			0
$191$	5.98517			0.433071			0.216536	−	0.976275i	$-0.430524\pi$
$191$	5.98517			0.433071			0.216536	+	0.976275i	$0.430524\pi$
$192$	−2.73313	+	7.50921i	−0.197247	+	0.541931i
$193$	2.13565	−	0.376572i	0.153727	−	0.0271063i	−0.0962548	−	0.995357i	$-0.530686\pi$
$193$	2.13565	−	0.376572i	0.153727	−	0.0271063i	0.249982	+	0.968250i	$0.419575\pi$
$194$	9.05567	+	7.59861i	0.650159	+	0.545548i
$195$		0			0
$196$	−0.970827	+	5.50583i	−0.0693448	+	0.393274i
$197$	−14.3471	−	8.28327i	−1.02219	−	0.590159i	−0.107449	−	0.994211i	$-0.534268\pi$
$197$	−14.3471	−	8.28327i	−1.02219	−	0.590159i	−0.914736	+	0.404052i	$0.867602\pi$
$198$	−3.65833	+	2.11214i	−0.259986	+	0.150103i
$199$	13.1370	−	4.78149i	0.931259	−	0.338951i	0.168551	−	0.985693i	$-0.446091\pi$
$199$	13.1370	−	4.78149i	0.931259	−	0.338951i	0.762709	+	0.646742i	$0.223869\pi$
$200$		0			0
$201$	−12.6372	−	21.8884i	−0.891363	−	1.54389i
$202$	10.5078	+	6.06668i	0.739327	+	0.426850i
$203$	−1.73104	−	0.305229i	−0.121495	−	0.0214229i
$204$	10.9786	−	9.21211i	0.768654	−	0.644977i
$205$		0			0
$206$	2.06847	+	11.7309i	0.144117	+	0.817328i
$207$	−2.87617	+	7.90220i	−0.199907	+	0.549241i
$208$			23.9757i			1.66242i
$209$	0.520956	+	1.34640i	0.0360353	+	0.0931327i
$210$		0			0
$211$	16.9908	+	6.18415i	1.16970	+	0.425735i	0.852552	−	0.522643i	$-0.175054\pi$
$211$	16.9908	+	6.18415i	1.16970	+	0.425735i	0.317145	+	0.948377i	$0.397276\pi$
$212$	−5.52796	+	0.974729i	−0.379662	+	0.0669447i
$213$	2.27190	−	2.70755i	0.155668	−	0.185518i
$214$	8.38453	−	7.03546i	0.573155	−	0.480934i
$215$		0			0
$216$	−14.5987	+	25.2856i	−0.993314	+	1.72047i
$217$	2.85958	−	1.65098i	0.194121	−	0.112076i
$218$	−10.1695	−	27.9405i	−0.688766	−	1.89237i
$219$	−42.6336	+	15.5174i	−2.88091	+	1.04857i
$220$		0			0
$221$	−12.7307	+	22.0502i	−0.856358	+	1.48326i
$222$	35.9783	+	6.34395i	2.41471	+	0.425778i
$223$	−16.8838	−	20.1214i	−1.13062	−	1.34743i	−0.929915	−	0.367775i	$-0.880119\pi$
$223$	−16.8838	−	20.1214i	−1.13062	−	1.34743i	−0.200710	−	0.979651i	$-0.564325\pi$
$224$	−1.86838	−	1.56776i	−0.124836	−	0.104750i
$225$		0			0
$226$	7.69659	+	2.80133i	0.511969	+	0.186342i
$227$			6.97401i			0.462881i	0.972849	+	0.231441i	$0.0743439\pi$
$227$			6.97401i			0.462881i	−0.972849	+	0.231441i	$0.925656\pi$
$228$	−9.21321	−	7.42015i	−0.610159	−	0.491411i
$229$	−2.62489			−0.173458			−0.0867288	−	0.996232i	$-0.527641\pi$
$229$	−2.62489			−0.173458			−0.0867288	+	0.996232i	$0.527641\pi$
$230$		0			0
$231$	0.102566	+	0.581682i	0.00674837	+	0.0382719i
$232$	−4.04273	+	4.81794i	−0.265419	+	0.316313i
$233$	17.1358	+	20.4217i	1.12260	+	1.33787i	0.934600	+	0.355700i	$0.115757\pi$
$233$	17.1358	+	20.4217i	1.12260	+	1.33787i	0.188004	+	0.982168i	$0.439798\pi$
$234$	−10.6786	+	60.5616i	−0.698085	+	3.95904i
$235$		0			0
$236$	2.83892	+	4.91716i	0.184798	+	0.320080i
$237$	−1.56203	−	4.29164i	−0.101465	−	0.278772i
$238$	−1.66754	−	4.58153i	−0.108091	−	0.296976i
$239$	6.55369	+	11.3513i	0.423923	+	0.734256i	0.996319	−	0.0857211i	$-0.0273194\pi$
$239$	6.55369	+	11.3513i	0.423923	+	0.734256i	−0.572396	+	0.819977i	$0.693986\pi$
$240$		0			0
$241$	−2.63284	+	14.9316i	−0.169596	+	0.961828i	0.774602	+	0.632449i	$0.217950\pi$
$241$	−2.63284	+	14.9316i	−0.169596	+	0.961828i	−0.944198	+	0.329379i	$0.893161\pi$
$242$	−11.7855	−	14.0454i	−0.757601	−	0.902874i
$243$	−24.9511	+	29.7356i	−1.60062	+	1.90754i
$244$	−0.0984913	−	0.558572i	−0.00630526	−	0.0357589i
$245$		0			0
$246$	43.3159			2.76172
$247$	19.8898	+	6.78939i	1.26556	+	0.431998i
$248$		−	11.8147i		−	0.750237i
$249$	2.61242	+	0.950843i	0.165555	+	0.0602573i
$250$		0			0
$251$	14.5597	+	12.2170i	0.919001	+	0.771133i	0.973810	−	0.227364i	$-0.0730106\pi$
$251$	14.5597	+	12.2170i	0.919001	+	0.771133i	−0.0548090	+	0.998497i	$0.517455\pi$
$252$	−2.22853	−	2.65586i	−0.140384	−	0.167303i
$253$	0.362066	+	0.0638421i	0.0227629	+	0.00401372i
$254$	−2.49956	+	4.32937i	−0.156837	+	0.271649i
$255$		0			0
$256$	−15.9998	+	5.82344i	−0.999986	+	0.363965i
$257$	−7.46911	−	20.5212i	−0.465910	−	1.28008i	−0.920976	−	0.389620i	$-0.872606\pi$
$257$	−7.46911	−	20.5212i	−0.465910	−	1.28008i	0.455066	−	0.890458i	$-0.349616\pi$
$258$	7.77172	−	4.48701i	0.483846	−	0.279349i
$259$	1.82959	−	3.16895i	0.113685	−	0.196909i
$260$		0			0
$261$	−18.6011	+	15.6082i	−1.15138	+	0.966124i
$262$	8.65221	−	10.3113i	0.534535	−	0.637034i
$263$	−19.3231	+	3.40719i	−1.19152	+	0.210096i	−0.734028	−	0.679119i	$-0.762362\pi$
$263$	−19.3231	+	3.40719i	−1.19152	+	0.210096i	−0.457488	+	0.889216i	$0.651251\pi$
$264$	1.98597	+	0.722833i	0.122228	+	0.0444873i
$265$		0			0
$266$	−3.44409	+	2.08193i	−0.211171	+	0.127651i
$267$		−	47.3235i		−	2.89615i
$268$	2.21832	−	6.09480i	0.135506	−	0.372299i
$269$	0.293697	+	1.66564i	0.0179070	+	0.101556i	0.992451	−	0.122639i	$-0.0391359\pi$
$269$	0.293697	+	1.66564i	0.0179070	+	0.101556i	−0.974544	+	0.224195i	$0.928025\pi$
$270$		0			0
$271$	−6.08215	+	5.10353i	−0.369465	+	0.310018i	−0.808550	−	0.588428i	$-0.799747\pi$
$271$	−6.08215	+	5.10353i	−0.369465	+	0.310018i	0.439085	+	0.898445i	$0.355303\pi$
$272$	−25.8602	−	4.55985i	−1.56800	−	0.276481i
$273$	7.44662	+	4.29931i	0.450690	+	0.260206i
$274$	0.775111	+	1.34253i	0.0468262	+	0.0811053i
$275$		0			0
$276$	−2.83091	+	1.03037i	−0.170401	+	0.0620209i
$277$	−8.20468	+	4.73698i	−0.492972	+	0.284617i	−0.725806	−	0.687899i	$-0.758533\pi$
$277$	−8.20468	+	4.73698i	−0.492972	+	0.284617i	0.232835	+	0.972516i	$0.425200\pi$
$278$	−0.145883	−	0.0842258i	−0.00874950	−	0.00505153i
$279$	7.92086	−	44.9214i	0.474209	−	2.68937i
$280$		0			0
$281$	−9.62922	−	8.07988i	−0.574431	−	0.482005i	0.308682	−	0.951165i	$-0.400112\pi$
$281$	−9.62922	−	8.07988i	−0.574431	−	0.482005i	−0.883113	+	0.469160i	$0.844557\pi$
$282$	−24.8099	+	4.37465i	−1.47741	+	0.260507i
$283$	6.35609	−	17.4632i	0.377830	−	1.03808i	−0.594424	−	0.804152i	$-0.702620\pi$
$283$	6.35609	−	17.4632i	0.377830	−	1.03808i	0.972254	−	0.233928i	$-0.0751580\pi$
$284$	0.907012			0.0538212
$285$		0			0
$286$	2.68856			0.158978
$287$	1.48386	−	4.07688i	0.0875897	−	0.240651i
$288$	−33.1812	+	5.85074i	−1.95522	+	0.344758i
$289$	−8.33933	−	6.99753i	−0.490549	−	0.411619i
$290$		0			0
$291$	3.96505	−	22.4869i	0.232435	−	1.31821i
$292$	−10.0830	−	5.82139i	−0.590060	−	0.340671i
$293$	15.0386	−	8.68253i	0.878563	−	0.507239i	0.00837865	−	0.999965i	$-0.497333\pi$
$293$	15.0386	−	8.68253i	0.878563	−	0.507239i	0.870184	+	0.492726i	$0.164000\pi$
$294$	34.4673	−	12.5451i	2.01017	−	0.731643i
$295$		0			0
$296$	−6.54645	−	11.3388i	−0.380505	−	0.659054i
$297$	4.26802	+	2.46414i	0.247656	+	0.142984i
$298$	28.6798	+	5.05701i	1.66137	+	0.292945i
$299$	4.10001	−	3.44032i	0.237110	−	0.198959i
$300$		0			0
$301$	−0.156082	−	0.885183i	−0.00899639	−	0.0510211i
$302$	−11.0662	+	30.4040i	−0.636786	+	1.74956i
$303$		−	23.4365i		−	1.34639i
$304$	0.436022	+	21.6708i	0.0250076	+	1.24290i
$305$		0			0
$306$	−63.2907	−	23.0359i	−3.61809	−	1.31688i
$307$	24.6698	−	4.34996i	1.40798	−	0.248265i	0.582563	−	0.812786i	$-0.302050\pi$
$307$	24.6698	−	4.34996i	1.40798	−	0.248265i	0.825419	+	0.564521i	$0.190939\pi$
$308$	−0.0974301	+	0.116113i	−0.00555159	+	0.00661613i
$309$	17.6256	−	14.7897i	1.00269	−	0.841354i
$310$		0			0
$311$	2.79206	−	4.83598i	0.158323	−	0.274223i	−0.775941	−	0.630805i	$-0.782725\pi$
$311$	2.79206	−	4.83598i	0.158323	−	0.274223i	0.934264	+	0.356582i	$0.116058\pi$
$312$	26.6447	−	15.3833i	1.50846	−	0.870909i
$313$	−0.280835	−	0.771588i	−0.0158737	−	0.0436127i	0.931503	−	0.363734i	$-0.118498\pi$
$313$	−0.280835	−	0.771588i	−0.0158737	−	0.0436127i	−0.947376	+	0.320122i	$0.896276\pi$
$314$	−10.4142	+	3.79048i	−0.587710	+	0.213909i
$315$		0			0
$316$	0.586001	−	1.01498i	0.0329651	−	0.0570973i
$317$	33.0230	+	5.82285i	1.85476	+	0.327044i	0.985811	−	0.167860i	$-0.0536857\pi$
$317$	33.0230	+	5.82285i	1.85476	+	0.327044i	0.868948	+	0.494904i	$0.164797\pi$
$318$	23.6718	+	28.2109i	1.32745	+	1.58199i
$319$	0.813231	+	0.682382i	0.0455322	+	0.0382061i
$320$		0			0
$321$	−19.8666	−	7.23084i	−1.10884	−	0.403586i
$322$			1.02488i			0.0571144i
$323$	−11.1058	+	20.1618i	−0.617942	+	1.12184i
$324$	−21.4168			−1.18982
$325$		0			0
$326$	−4.26627	−	24.1952i	−0.236287	−	1.34005i
$327$	−36.9171	+	43.9961i	−2.04152	+	2.43299i
$328$	−9.97841	−	11.8918i	−0.550966	−	0.656615i
$329$	−0.438166	+	2.48496i	−0.0241569	+	0.137000i
$330$		0			0
$331$	−5.63364	−	9.75775i	−0.309653	−	0.536334i	0.668634	−	0.743592i	$-0.266879\pi$
$331$	−5.63364	−	9.75775i	−0.309653	−	0.536334i	−0.978286	+	0.207258i	$0.933546\pi$
$332$	0.244006	+	0.670400i	0.0133916	+	0.0367930i
$333$	−17.2888	−	47.5006i	−0.947421	−	2.60302i
$334$	2.95442	+	5.11721i	0.161659	+	0.280001i
$335$		0			0
$336$	−1.53992	+	8.73330i	−0.0840093	+	0.476441i
$337$	4.04684	+	4.82284i	0.220445	+	0.262717i	0.864921	−	0.501909i	$-0.167369\pi$
$337$	4.04684	+	4.82284i	0.220445	+	0.262717i	−0.644475	+	0.764625i	$0.722924\pi$
$338$	11.0897	−	13.2162i	0.603201	−	0.718866i
$339$	−2.74723	−	15.5803i	−0.149209	−	0.846206i
$340$		0			0
$341$	−1.99424			−0.107994
$342$	−8.55065	+	54.9335i	−0.462366	+	2.97046i
$343$		−	7.51253i		−	0.405638i
$344$	−3.02217	−	1.09998i	−0.162945	−	0.0593070i
$345$		0			0
$346$	3.22810	+	2.70870i	0.173544	+	0.145620i
$347$	−11.2851	−	13.4490i	−0.605814	−	0.721981i	0.372749	−	0.927932i	$-0.378415\pi$
$347$	−11.2851	−	13.4490i	−0.605814	−	0.721981i	−0.978562	+	0.205952i	$0.933971\pi$
$348$	−8.56674	−	1.51055i	−0.459225	−	0.0809738i
$349$	6.25844	−	10.8399i	0.335007	−	0.580248i	−0.648480	−	0.761232i	$-0.724595\pi$
$349$	6.25844	−	10.8399i	0.335007	−	0.580248i	0.983486	+	0.180984i	$0.0579281\pi$
$350$		0			0
$351$	67.4180	−	24.5381i	3.59850	−	1.30975i
$352$	0.503810	+	1.38421i	0.0268532	+	0.0737785i
$353$	−5.04735	+	2.91409i	−0.268643	+	0.155101i	−0.628271	−	0.777995i	$-0.716237\pi$
$353$	−5.04735	+	2.91409i	−0.268643	+	0.155101i	0.359628	+	0.933096i	$0.382904\pi$
$354$	18.6253	−	32.2600i	0.989924	−	1.71460i
$355$		0			0
$356$	9.30298	−	7.80613i	0.493057	−	0.413724i
$357$	−6.05346	+	7.21424i	−0.320383	+	0.381818i
$358$	−8.32426	+	1.46779i	−0.439951	+	0.0775752i
$359$	0.544588	+	0.198214i	0.0287423	+	0.0104613i	0.356351	−	0.934352i	$-0.384021\pi$
$359$	0.544588	+	0.198214i	0.0287423	+	0.0104613i	−0.327609	+	0.944813i	$0.606243\pi$
$360$		0			0
$361$	18.1011	+	5.77495i	0.952690	+	0.303945i
$362$		−	9.12723i		−	0.479717i
$363$	−12.1128	+	33.2797i	−0.635757	+	1.74673i
$364$	0.383168	+	2.17306i	0.0200835	+	0.113899i
$365$		0			0
$366$	−2.85057	+	2.39191i	−0.149002	+	0.125027i
$367$	−7.78614	−	1.37291i	−0.406433	−	0.0716651i	−0.0333057	−	0.999445i	$-0.510603\pi$
$367$	−7.78614	−	1.37291i	−0.406433	−	0.0716651i	−0.373127	+	0.927780i	$0.621715\pi$
$368$	4.78035	+	2.75994i	0.249193	+	0.143872i
$369$	−29.9669	−	51.9042i	−1.56001	−	2.70202i
$370$		0			0
$371$	3.46613	−	1.26157i	0.179952	−	0.0654973i
$372$	14.1518	−	8.17054i	0.733736	−	0.423623i
$373$	−7.19338	−	4.15310i	−0.372459	−	0.215039i	0.302073	−	0.953285i	$-0.402321\pi$
$373$	−7.19338	−	4.15310i	−0.372459	−	0.215039i	−0.674532	+	0.738245i	$0.735655\pi$
$374$	−0.511327	+	2.89988i	−0.0264401	+	0.149949i
$375$		0			0
$376$	6.91630	+	5.80347i	0.356681	+	0.299291i
$377$	15.2197	−	2.68364i	0.783853	−	0.138214i
$378$	−4.69877	+	12.9098i	−0.241679	+	0.664007i
$379$	−10.2928			−0.528707			−0.264354	−	0.964426i	$-0.585159\pi$
$379$	−10.2928			−0.528707			−0.264354	+	0.964426i	$0.585159\pi$
$380$		0			0
$381$	9.65620			0.494702
$382$	3.44642	−	9.46897i	0.176334	−	0.484475i
$383$	31.5418	−	5.56168i	1.61171	−	0.284188i	0.706042	−	0.708170i	$-0.250479\pi$
$383$	31.5418	−	5.56168i	1.61171	−	0.284188i	0.905671	+	0.423981i	$0.139368\pi$
$384$	32.4658	+	27.2420i	1.65676	+	1.39019i
$385$		0			0
$386$	0.634000	−	3.59559i	0.0322698	−	0.183011i
$387$	−10.7533	−	6.20842i	−0.546621	−	0.315592i
$388$	5.07458	−	2.92981i	0.257623	−	0.148739i
$389$	−28.7624	+	10.4686i	−1.45831	+	0.530781i	−0.944899	−	0.327362i	$-0.893840\pi$
$389$	−28.7624	+	10.4686i	−1.45831	+	0.530781i	−0.513411	+	0.858143i	$0.671618\pi$
$390$		0			0
$391$	2.93095	+	5.07656i	0.148225	+	0.256733i
$392$	−11.3841	−	6.57261i	−0.574984	−	0.331967i
$393$	−25.6049	−	4.51483i	−1.29160	−	0.227743i
$394$	−21.3662	+	17.9284i	−1.07641	+	0.903217i
$395$		0			0
$396$	0.363601	+	2.06208i	0.0182716	+	0.103624i
$397$	3.63241	−	9.97995i	0.182305	−	0.500880i	−0.814553	−	0.580090i	$-0.803018\pi$
$397$	3.63241	−	9.97995i	0.182305	−	0.500880i	0.996858	+	0.0792100i	$0.0252398\pi$
$398$		−	23.5371i		−	1.17981i
$399$	6.80890	+	3.75056i	0.340871	+	0.187763i
$400$		0			0
$401$	14.3159	+	5.21056i	0.714901	+	0.260203i	0.673760	−	0.738950i	$-0.264678\pi$
$401$	14.3159	+	5.21056i	0.714901	+	0.260203i	0.0411417	+	0.999153i	$0.486901\pi$
$402$	−41.9059	+	7.38913i	−2.09007	+	0.368536i
$403$	−18.6611	+	22.2395i	−0.929577	+	1.10783i
$404$	4.60721	−	3.86591i	0.229217	−	0.192336i
$405$		0			0
$406$	−1.47968	+	2.56287i	−0.0734351	+	0.127193i
$407$	−1.91390	+	1.10499i	−0.0948684	+	0.0547723i
$408$	11.5250	+	31.6646i	0.570571	+	1.56763i
$409$	−10.9607	+	3.98936i	−0.541971	+	0.197261i	−0.598476	−	0.801141i	$-0.704227\pi$
$409$	−10.9607	+	3.98936i	−0.541971	+	0.197261i	0.0565046	+	0.998402i	$0.482004\pi$
$410$		0			0
$411$	1.49719	−	2.59320i	0.0738508	−	0.127913i
$412$	5.81478	+	1.02530i	0.286473	+	0.0505130i
$413$	−2.39826	−	2.85813i	−0.118011	−	0.140640i
$414$	10.8457	+	9.10061i	0.533036	+	0.447271i
$415$		0			0
$416$	20.1509	+	7.33434i	0.987981	+	0.359595i
$417$			0.325377i			0.0159338i
$418$	2.43009	−	0.0488942i	0.118860	−	0.00239149i
$419$	−17.7028			−0.864840			−0.432420	−	0.901672i	$-0.642340\pi$
$419$	−17.7028			−0.864840			−0.432420	+	0.901672i	$0.642340\pi$
$420$		0			0
$421$	3.57756	+	20.2893i	0.174359	+	0.988841i	0.938881	+	0.344243i	$0.111864\pi$
$421$	3.57756	+	20.2893i	0.174359	+	0.988841i	−0.764521	+	0.644599i	$0.777025\pi$
$422$	19.5676	−	23.3197i	0.952534	−	1.13519i
$423$	22.4061	+	26.7025i	1.08942	+	1.29832i
$424$	2.29182	−	12.9976i	0.111301	−	0.631217i
$425$		0			0
$426$	−2.97531	−	5.15339i	−0.144154	−	0.249683i
$427$	0.127475	+	0.350234i	0.00616894	+	0.0169490i
$428$	−1.85558	−	5.09817i	−0.0896929	−	0.246429i
$429$	−2.59658	−	4.49742i	−0.125364	−	0.217137i
$430$		0			0
$431$	1.44676	−	8.20498i	0.0696879	−	0.395220i	−0.929934	−	0.367726i	$-0.880136\pi$
$431$	1.44676	−	8.20498i	0.0696879	−	0.395220i	0.999622	−	0.0274936i	$-0.00875258\pi$
$432$	47.5615	+	56.6816i	2.28831	+	2.72710i
$433$	18.1228	−	21.5979i	0.870926	−	1.03793i	−0.128008	−	0.991773i	$-0.540858\pi$
$433$	18.1228	−	21.5979i	0.870926	−	1.03793i	0.998934	−	0.0461560i	$-0.0146971\pi$
$434$	−0.965347	−	5.47475i	−0.0463381	−	0.262797i
$435$		0			0
$436$	−14.7384			−0.705843
$437$	3.64328	−	3.18413i	0.174282	−	0.152318i
$438$			76.3848i			3.64981i
$439$	28.5501	+	10.3914i	1.36262	+	0.495954i	0.916864	−	0.399199i	$-0.130712\pi$
$439$	28.5501	+	10.3914i	1.36262	+	0.495954i	0.445759	+	0.895153i	$0.352934\pi$
$440$		0			0
$441$	−38.8776	−	32.6222i	−1.85132	−	1.55344i
$442$	27.5543	+	32.8380i	1.31063	+	1.56194i
$443$	−24.1482	−	4.25799i	−1.14732	−	0.202303i	−0.432513	−	0.901628i	$-0.642373\pi$
$443$	−24.1482	−	4.25799i	−1.14732	−	0.202303i	−0.714804	+	0.699325i	$0.753484\pi$
$444$	9.05446	−	15.6828i	0.429705	−	0.744272i
$445$		0			0
$446$	−41.5556	+	15.1250i	−1.96772	+	0.716190i
$447$	−19.2392	−	52.8594i	−0.909984	−	2.50016i
$448$	1.16701	−	0.673774i	0.0551361	−	0.0318328i
$449$	12.3444	−	21.3812i	0.582570	−	1.00904i	−0.412604	−	0.910911i	$-0.635381\pi$
$449$	12.3444	−	21.3812i	0.582570	−	1.00904i	0.995174	−	0.0981300i	$-0.0312861\pi$
$450$		0			0
$451$	−2.00724	+	1.68428i	−0.0945174	+	0.0793095i
$452$	2.60965	−	3.11007i	0.122748	−	0.146285i
$453$	61.5473	−	10.8525i	2.89175	−	0.509893i
$454$	11.0334	+	4.01583i	0.517823	+	0.188472i
$455$		0			0
$456$	23.8034	−	14.3890i	1.11469	−	0.673825i
$457$			7.16480i			0.335155i	0.985859	+	0.167578i	$0.0535945\pi$
$457$			7.16480i			0.335155i	−0.985859	+	0.167578i	$0.946406\pi$
$458$	−1.51148	+	4.15277i	−0.0706270	+	0.194046i
$459$	13.6448	+	77.3837i	0.636886	+	3.61196i
$460$		0			0
$461$	16.6388	−	13.9616i	0.774947	−	0.650258i	−0.167024	−	0.985953i	$-0.553416\pi$
$461$	16.6388	−	13.9616i	0.774947	−	0.650258i	0.941971	+	0.335695i	$0.108971\pi$
$462$	0.979325	+	0.172681i	0.0455623	+	0.00803386i
$463$	−27.6508	−	15.9642i	−1.28504	−	0.741918i	−0.307274	−	0.951621i	$-0.599417\pi$
$463$	−27.6508	−	15.9642i	−1.28504	−	0.741918i	−0.977765	+	0.209703i	$0.932750\pi$
$464$	7.96934	+	13.8033i	0.369968	+	0.640803i
$465$		0			0
$466$	42.1759	−	15.3508i	1.95376	−	0.711110i
$467$	−16.9206	+	9.76911i	−0.782992	+	0.452061i	−0.837490	−	0.546453i	$-0.815978\pi$
$467$	−16.9206	+	9.76911i	−0.782992	+	0.452061i	0.0544977	+	0.998514i	$0.482644\pi$
$468$	26.3985	+	15.2412i	1.22027	+	0.704524i
$469$	−0.740097	+	4.19730i	−0.0341745	+	0.193813i
$470$		0			0
$471$	16.3986	+	13.7601i	0.755610	+	0.634032i
$472$	−13.1472	+	2.31820i	−0.605147	+	0.106704i
$473$	−0.185668	+	0.510119i	−0.00853703	+	0.0234553i
$474$	−7.68914			−0.353174
$475$		0			0
$476$	−2.41673			−0.110770
$477$	17.4277	−	47.8822i	0.797959	−	2.19237i
$478$	21.7324	−	3.83201i	0.994018	−	0.175272i
$479$	9.37543	+	7.86692i	0.428374	+	0.359449i	0.831338	−	0.555767i	$-0.187575\pi$
$479$	9.37543	+	7.86692i	0.428374	+	0.359449i	−0.402964	+	0.915216i	$0.632020\pi$
$480$		0			0
$481$	−5.58666	+	31.6835i	−0.254730	+	1.44464i
$482$	22.1068	+	12.7634i	1.00694	+	0.581356i
$483$	1.71442	−	0.989819i	0.0780086	−	0.0450383i
$484$	−8.54024	+	3.10839i	−0.388193	+	0.141291i
$485$		0			0
$486$	32.6764	+	56.5971i	1.48223	+	2.56730i
$487$	12.2125	+	7.05086i	0.553399	+	0.319505i	0.750492	−	0.660880i	$-0.229817\pi$
$487$	12.2125	+	7.05086i	0.553399	+	0.319505i	−0.197093	+	0.980385i	$0.563150\pi$
$488$	1.31334	+	0.231577i	0.0594519	+	0.0104830i
$489$	−36.3533	+	30.5040i	−1.64395	+	1.37944i
$490$		0			0
$491$	−3.45329	−	19.5846i	−0.155845	−	0.883839i	−0.958009	−	0.286737i	$-0.907430\pi$
$491$	−3.45329	−	19.5846i	−0.155845	−	0.883839i	0.802165	−	0.597103i	$-0.203682\pi$
$492$	7.34348	−	20.1761i	0.331070	−	0.909607i
$493$			16.9263i			0.762322i
$494$	22.1944	−	27.5576i	0.998573	−	1.23988i
$495$		0			0
$496$	−28.1355	−	10.2405i	−1.26332	−	0.459812i
$497$	−0.586961	+	0.103497i	−0.0263288	+	0.00464248i
$498$	3.00861	−	3.58552i	0.134819	−	0.160671i
$499$	5.69739	−	4.78068i	0.255050	−	0.214013i	−0.506293	−	0.862362i	$-0.668985\pi$
$499$	5.69739	−	4.78068i	0.255050	−	0.214013i	0.761343	+	0.648349i	$0.224540\pi$
$500$		0			0
$501$	5.70670	−	9.88429i	0.254956	−	0.441598i
$502$	27.7122	−	15.9996i	1.23685	−	0.714098i
$503$	−4.62141	−	12.6972i	−0.206059	−	0.566141i	0.793014	−	0.609204i	$-0.208511\pi$
$503$	−4.62141	−	12.6972i	−0.206059	−	0.566141i	−0.999072	+	0.0430624i	$0.986289\pi$
$504$	7.66008	−	2.78804i	0.341207	−	0.124189i
$505$		0			0
$506$	0.309491	−	0.536054i	0.0137585	−	0.0238305i
$507$	−32.8183	−	5.78675i	−1.45751	−	0.256999i
$508$	1.59281	+	1.89824i	0.0706696	+	0.0842208i
$509$	26.9446	+	22.6092i	1.19430	+	1.00214i	0.999774	+	0.0212383i	$0.00676087\pi$
$509$	26.9446	+	22.6092i	1.19430	+	1.00214i	0.194525	+	0.980898i	$0.437684\pi$
$510$		0			0
$511$	7.18932	+	2.61670i	0.318037	+	0.115756i
$512$			2.60163i			0.114977i
$513$	60.4903	−	23.4051i	2.67071	−	1.03336i
$514$	−36.7670			−1.62172
$515$		0			0
$516$	−0.772431	−	4.38068i	−0.0340044	−	0.192849i
$517$	0.979580	−	1.16742i	0.0430819	−	0.0513430i
$518$	−3.95998	−	4.71931i	−0.173991	−	0.207355i
$519$	1.41343	−	8.01597i	0.0620428	−	0.351862i
$520$		0			0
$521$	2.92797	+	5.07140i	0.128277	+	0.222182i	0.923009	−	0.384778i	$-0.125722\pi$
$521$	2.92797	+	5.07140i	0.128277	+	0.222182i	−0.794732	+	0.606960i	$0.792389\pi$
$522$	13.9823	+	38.4160i	0.611988	+	1.68142i
$523$	3.95014	+	10.8529i	0.172727	+	0.474565i	0.995605	−	0.0936543i	$-0.0298548\pi$
$523$	3.95014	+	10.8529i	0.172727	+	0.474565i	−0.822877	+	0.568219i	$0.807633\pi$
$524$	−3.33605	−	5.77821i	−0.145736	−	0.252422i
$525$		0			0
$526$	−5.73637	+	32.5326i	−0.250118	+	1.41849i
$527$	−20.4384	−	24.3575i	−0.890309	−	1.06103i
$528$	3.44270	−	4.10284i	0.149824	−	0.178553i
$529$	3.77994	+	21.4371i	0.164345	+	0.932047i
$530$		0			0
$531$	−51.5416			−2.23672
$532$	0.385851	+	1.95717i	0.0167287	+	0.0848543i
$533$			38.1452i			1.65225i
$534$	−74.8693	−	27.2502i	−3.23991	−	1.17923i
$535$		0			0
$536$	11.6822	+	9.80251i	0.504593	+	0.423404i
$537$	10.4948	+	12.5072i	0.452884	+	0.539726i
$538$	2.80428	+	0.494470i	0.120901	+	0.0213181i
$539$	−1.10941	+	1.92155i	−0.0477855	+	0.0827669i
$540$		0			0
$541$	−11.0424	+	4.01909i	−0.474748	+	0.172794i	−0.568302	−	0.822820i	$-0.692399\pi$
$541$	−11.0424	+	4.01909i	−0.474748	+	0.172794i	0.0935540	+	0.995614i	$0.470177\pi$
$542$	4.57189	+	12.5612i	0.196380	+	0.539548i
$543$	−15.2680	+	8.81497i	−0.655212	+	0.378287i
$544$	−11.7432	+	20.3399i	−0.503487	+	0.872064i
$545$		0			0
$546$	11.0898	−	9.30544i	0.474599	−	0.398236i
$547$	18.6150	−	22.1845i	0.795920	−	0.948541i	−0.203614	−	0.979051i	$-0.565269\pi$
$547$	18.6150	−	22.1845i	0.795920	−	0.948541i	0.999534	+	0.0305106i	$0.00971334\pi$
$548$	0.756743	−	0.133434i	0.0323265	−	0.00570003i
$549$	4.83825	+	1.76098i	0.206491	+	0.0751567i
$550$		0			0
$551$	13.7077	−	2.70242i	0.583967	−	0.115127i
$552$		−	7.08333i		−	0.301486i
$553$	−0.263405	+	0.723700i	−0.0112011	+	0.0307749i
$554$	2.76976	+	15.7081i	0.117676	+	0.667373i
$555$		0			0
$556$	−0.0639635	+	0.0536718i	−0.00271266	+	0.00227619i
$557$	−23.8476	−	4.20497i	−1.01045	−	0.178170i	−0.356171	−	0.934421i	$-0.615918\pi$
$557$	−23.8476	−	4.20497i	−1.01045	−	0.178170i	−0.654282	+	0.756250i	$0.727029\pi$
$558$	−66.5079	−	38.3984i	−2.81550	−	1.62553i
$559$	3.95139	+	6.84400i	0.167126	+	0.289470i
$560$		0			0
$561$	5.34474	−	1.94533i	0.225655	−	0.0821317i
$562$	−18.3277	+	10.5815i	−0.773109	+	0.446355i
$563$	39.3578	+	22.7232i	1.65873	+	0.957669i	0.973301	+	0.229531i	$0.0737194\pi$
$563$	39.3578	+	22.7232i	1.65873	+	0.957669i	0.685431	+	0.728138i	$0.259614\pi$
$564$	−2.16844	+	12.2978i	−0.0913076	+	0.517831i
$565$		0			0
$566$	−23.9681	−	20.1116i	−1.00745	−	0.845354i
$567$	13.8596	−	2.44382i	0.582048	−	0.102631i
$568$	−0.729392	+	2.00399i	−0.0306046	+	0.0840855i
$569$	−28.1695			−1.18093			−0.590463	−	0.807065i	$-0.701055\pi$
$569$	−28.1695			−1.18093			−0.590463	+	0.807065i	$0.701055\pi$
$570$		0			0
$571$	18.2742			0.764752			0.382376	−	0.924007i	$-0.375106\pi$
$571$	18.2742			0.764752			0.382376	+	0.924007i	$0.375106\pi$
$572$	0.455801	−	1.25230i	0.0190580	−	0.0523614i
$573$	−19.1682	+	3.37987i	−0.800762	+	0.141196i
$574$	−5.59547	−	4.69516i	−0.233551	−	0.195972i
$575$		0			0
$576$	3.23254	−	18.3327i	0.134689	−	0.763861i
$577$	17.4797	+	10.0919i	0.727689	+	0.420132i	0.817576	−	0.575820i	$-0.195317\pi$
$577$	17.4797	+	10.0919i	0.727689	+	0.420132i	−0.0898868	+	0.995952i	$0.528651\pi$
$578$	−15.8726	+	9.16406i	−0.660214	+	0.381175i
$579$	−6.62700	+	2.41203i	−0.275409	+	0.100241i
$580$		0			0
$581$	−0.234403	−	0.405998i	−0.00972467	−	0.0168436i
$582$	−33.2928	−	19.2216i	−1.38003	−	0.796761i
$583$	−2.19389	−	0.386841i	−0.0908614	−	0.0160213i
$584$	20.9704	−	17.5963i	0.867763	−	0.728140i
$585$		0			0
$586$	−5.07677	−	28.7918i	−0.209719	−	1.18938i
$587$	−6.32474	+	17.3771i	−0.261050	+	0.717229i	0.738047	+	0.674749i	$0.235748\pi$
$587$	−6.32474	+	17.3771i	−0.261050	+	0.717229i	−0.999097	+	0.0424803i	$0.986474\pi$
$588$		−	18.1813i		−	0.749783i
$589$	−16.4626	+	20.4408i	−0.678331	+	0.842248i
$590$		0			0
$591$	50.6257	+	18.4262i	2.08246	+	0.757954i
$592$	−32.6763	+	5.76170i	−1.34299	+	0.236805i
$593$	−3.28098	+	3.91012i	−0.134734	+	0.160569i	−0.829193	−	0.558963i	$-0.811199\pi$
$593$	−3.28098	+	3.91012i	−0.134734	+	0.160569i	0.694459	+	0.719532i	$0.255644\pi$
$594$	6.35610	−	5.33340i	0.260794	−	0.218832i
$595$		0			0
$596$	7.21767	−	12.5014i	0.295647	−	0.512076i
$597$	−39.3727	+	22.7318i	−1.61142	+	0.930352i
$598$	−3.08193	−	8.46754i	−0.126030	−	0.346264i
$599$	33.6127	−	12.2340i	1.37338	−	0.499869i	0.453215	−	0.891401i	$-0.350277\pi$
$599$	33.6127	−	12.2340i	1.37338	−	0.499869i	0.920164	+	0.391532i	$0.128055\pi$
$600$		0			0
$601$	−17.1676	+	29.7352i	−0.700281	+	1.21292i	0.268087	+	0.963395i	$0.413609\pi$
$601$	−17.1676	+	29.7352i	−0.700281	+	1.21292i	−0.968368	+	0.249528i	$0.919725\pi$
$602$	−1.49030	−	0.262780i	−0.0607401	−	0.0107101i
$603$	37.8456	+	45.1026i	1.54119	+	1.83672i
$604$	12.2858	+	10.3090i	0.499901	+	0.419467i
$605$		0			0
$606$	−37.0783	−	13.4954i	−1.50620	−	0.548213i
$607$		−	3.43239i		−	0.139316i	−0.997571	−	0.0696582i	$-0.977809\pi$
$607$		−	3.43239i		−	0.139316i	0.997571	−	0.0696582i	$-0.0221909\pi$
$608$	18.3470	+	6.26277i	0.744071	+	0.253989i
$609$	5.71622			0.231633
$610$		0			0
$611$	−3.85245	−	21.8483i	−0.155853	−	0.883888i
$612$	−21.4597	+	25.5747i	−0.867459	+	1.03380i
$613$	−18.0630	−	21.5266i	−0.729556	−	0.869451i	0.265966	−	0.963982i	$-0.414309\pi$
$613$	−18.0630	−	21.5266i	−0.729556	−	0.869451i	−0.995522	+	0.0945313i	$0.969865\pi$
$614$	7.32362	−	41.5343i	0.295557	−	1.67619i
$615$		0			0
$616$	−0.178194	−	0.308640i	−0.00717962	−	0.0124355i
$617$	4.07805	+	11.2044i	0.164176	+	0.451070i	0.994314	−	0.106488i	$-0.0339606\pi$
$617$	4.07805	+	11.2044i	0.164176	+	0.451070i	−0.830138	+	0.557558i	$0.811738\pi$
$618$	−13.2490	−	36.4013i	−0.532953	−	1.46428i
$619$	−13.9457	−	24.1547i	−0.560525	−	0.970858i	−0.997451	−	0.0713602i	$-0.977266\pi$
$619$	−13.9457	−	24.1547i	−0.560525	−	0.970858i	0.436926	−	0.899498i	$-0.356067\pi$
$620$		0			0
$621$	2.86825	−	16.2667i	0.115099	−	0.652759i
$622$	−6.04314	−	7.20193i	−0.242308	−	0.288771i
$623$	−5.12956	+	6.11318i	−0.205512	+	0.244919i
$624$	−13.5393	−	76.7850i	−0.542005	−	3.07386i
$625$		0			0
$626$	−1.38242			−0.0552527
$627$	−2.42874	−	4.01782i	−0.0969947	−	0.160456i
$628$			5.49345i			0.219212i
$629$	−33.1113	−	12.0515i	−1.32023	−	0.480526i
$630$		0			0
$631$	14.3666	+	12.0550i	0.571927	+	0.479904i	0.882285	−	0.470716i	$-0.156004\pi$
$631$	14.3666	+	12.0550i	0.571927	+	0.479904i	−0.310358	+	0.950620i	$0.600449\pi$
$632$	1.77130	+	2.11095i	0.0704586	+	0.0839692i
$633$	−57.9073	−	10.2106i	−2.30161	−	0.405835i
$634$	28.2278	−	48.8919i	1.12107	−	1.94175i
$635$		0			0
$636$	17.1535	−	6.24336i	0.680180	−	0.247565i
$637$	11.0475	+	30.3529i	0.437720	+	1.20263i
$638$	1.54786	−	0.893657i	0.0612803	−	0.0353802i
$639$	−4.11677	+	7.13046i	−0.162857	+	0.282077i
$640$		0			0
$641$	−16.7076	+	14.0193i	−0.659909	+	0.553729i	−0.910059	−	0.414478i	$-0.863964\pi$
$641$	−16.7076	+	14.0193i	−0.659909	+	0.553729i	0.250151	+	0.968207i	$0.419520\pi$
$642$	−22.8794	+	27.2667i	−0.902980	+	1.07613i
$643$	−46.7686	+	8.24656i	−1.84437	+	0.325213i	−0.983120	−	0.182964i	$-0.941431\pi$
$643$	−46.7686	+	8.24656i	−1.84437	+	0.325213i	−0.861253	+	0.508176i	$0.830320\pi$
$644$	0.477378	+	0.173751i	0.0188113	+	0.00684676i
$645$		0			0
$646$	25.5025	+	29.1799i	1.00338	+	1.14807i
$647$			35.0985i			1.37986i	0.723874	+	0.689932i	$0.242360\pi$
$647$			35.0985i			1.37986i	−0.723874	+	0.689932i	$0.757640\pi$
$648$	17.2227	−	47.3191i	0.676573	−	1.85887i
$649$	0.391294	+	2.21914i	0.0153596	+	0.0871087i
$650$		0			0
$651$	−8.22582	+	6.90228i	−0.322395	+	0.270522i
$652$	−11.9931	−	2.11471i	−0.469687	−	0.0828185i
$653$	40.2844	+	23.2582i	1.57645	+	0.910163i	0.995349	+	0.0963305i	$0.0307106\pi$
$653$	40.2844	+	23.2582i	1.57645	+	0.910163i	0.581099	+	0.813833i	$0.302623\pi$
$654$	48.3472	+	83.7397i	1.89052	+	3.27448i
$655$		0			0
$656$	−36.9679	+	13.4552i	−1.44335	+	0.525338i
$657$	91.5297	−	52.8447i	3.57091	−	2.06167i
$658$	3.67908	+	2.12412i	0.143426	+	0.0828068i
$659$	7.50737	−	42.5764i	0.292445	−	1.65854i	−0.384962	−	0.922932i	$-0.625785\pi$
$659$	7.50737	−	42.5764i	0.292445	−	1.65854i	0.677407	−	0.735608i	$-0.263103\pi$
$660$		0			0
$661$	−35.9309	−	30.1496i	−1.39755	−	1.17268i	−0.962174	−	0.272436i	$-0.912171\pi$
$661$	−35.9309	−	30.1496i	−1.39755	−	1.17268i	−0.435376	−	0.900249i	$-0.643385\pi$
$662$	−18.6815	+	3.29405i	−0.726076	+	0.128027i
$663$	28.3195	−	77.8073i	1.09984	−	3.02179i
$664$	−1.67743			−0.0650970
$665$		0			0
$666$	−85.1049			−3.29775
$667$	1.21692	−	3.34347i	0.0471194	−	0.129460i
$668$	2.88441	−	0.508600i	0.111601	−	0.0196783i
$669$	65.4350	+	54.9065i	2.52986	+	2.12281i
$670$		0			0
$671$	0.0390883	−	0.221681i	0.00150899	−	0.00855789i
$672$	6.86902	+	3.96583i	0.264978	+	0.152985i
$673$	−12.3944	+	7.15589i	−0.477768	+	0.275839i	−0.719486	−	0.694507i	$-0.755622\pi$
$673$	−12.3944	+	7.15589i	−0.477768	+	0.275839i	0.241718	+	0.970347i	$0.422289\pi$
$674$	9.96036	−	3.62528i	0.383659	−	0.139640i
$675$		0			0
$676$	−4.27588	−	7.40605i	−0.164457	−	0.284848i
$677$	23.9767	+	13.8430i	0.921501	+	0.532029i	0.884114	−	0.467272i	$-0.154763\pi$
$677$	23.9767	+	13.8430i	0.921501	+	0.532029i	0.0373874	+	0.999301i	$0.488096\pi$
$678$	−26.2311	−	4.62525i	−1.00740	−	0.177632i
$679$	−2.94963	+	2.47504i	−0.113197	+	0.0949832i
$680$		0			0
$681$	−3.93827	−	22.3350i	−0.150915	−	0.855881i
$682$	−1.14834	+	3.15503i	−0.0439721	+	0.120812i
$683$		−	20.0771i		−	0.768228i	−0.923286	−	0.384114i	$-0.874507\pi$
$683$		−	20.0771i		−	0.768228i	0.923286	−	0.384114i	$-0.125493\pi$
$684$	24.1378	+	13.2959i	0.922932	+	0.508380i
$685$		0			0
$686$	−11.8854	−	4.32592i	−0.453786	−	0.165164i
$687$	8.40651	−	1.48229i	0.320728	−	0.0565531i
$688$	−5.23897	+	6.24356i	−0.199734	+	0.238033i
$689$	−24.8434	+	20.8461i	−0.946457	+	0.794172i
$690$		0			0
$691$	14.3678	−	24.8857i	0.546577	−	0.946698i	−0.451929	−	0.892054i	$-0.649264\pi$
$691$	14.3678	−	24.8857i	0.546577	−	0.946698i	0.998506	−	0.0546446i	$-0.0174026\pi$
$692$	1.80895	−	1.04440i	0.0687659	−	0.0397020i
$693$	−0.470599	−	1.29296i	−0.0178766	−	0.0491155i
$694$	−27.7756	+	10.1095i	−1.05435	+	0.383751i
$695$		0			0
$696$	10.2266	−	17.7130i	0.387638	−	0.671408i
$697$	−41.1434	−	7.25468i	−1.55842	−	0.274791i
$698$	−13.5458	−	16.1432i	−0.512716	−	0.611031i
$699$	−66.4116	−	55.7260i	−2.51192	−	2.10775i
$700$		0			0
$701$	25.2861	+	9.20337i	0.955041	+	0.347607i	0.772089	−	0.635515i	$-0.219212\pi$
$701$	25.2861	+	9.20337i	0.955041	+	0.347607i	0.182953	+	0.983122i	$0.441434\pi$
$702$		−	120.790i		−	4.55892i
$703$	−4.47338	+	28.7391i	−0.168717	+	1.08392i
$704$	−0.813858			−0.0306734
$705$		0			0
$706$	1.70390	+	9.66329i	0.0641271	+	0.363683i
$707$	−2.54037	+	3.02749i	−0.0955404	+	0.113861i
$708$	−11.8687	−	14.1446i	−0.446054	−	0.531587i
$709$	1.74216	−	9.88027i	0.0654281	−	0.371061i	−0.934460	−	0.356069i	$-0.884117\pi$
$709$	1.74216	−	9.88027i	0.0654281	−	0.371061i	0.999888	−	0.0149918i	$-0.00477223\pi$
$710$		0			0
$711$	5.31952	+	9.21368i	0.199498	+	0.345540i
$712$	9.76599	+	26.8318i	0.365996	+	1.00557i
$713$	2.28602	+	6.28078i	0.0856120	+	0.235217i
$714$	7.92770	+	13.7312i	0.296687	+	0.513877i
$715$		0			0
$716$	−0.727558	+	4.12619i	−0.0271901	+	0.154203i
$717$	−27.3991	−	32.6530i	−1.02324	−	1.21945i
$718$	0.627178	−	0.747441i	0.0234061	−	0.0278943i
$719$	−4.57974	−	25.9730i	−0.170796	−	0.968630i	−0.942886	−	0.333117i	$-0.891900\pi$
$719$	−4.57974	−	25.9730i	−0.170796	−	0.968630i	0.772090	−	0.635513i	$-0.219211\pi$
$720$		0			0
$721$	−3.87995			−0.144497
$722$	19.5595	−	25.3119i	0.727930	−	0.942011i
$723$		−	49.3069i		−	1.83374i
$724$	−4.25136	−	1.54737i	−0.158001	−	0.0575075i
$725$		0			0
$726$	45.6760	+	38.3267i	1.69519	+	1.42244i
$727$	−31.1191	−	37.0863i	−1.15414	−	1.37546i	−0.914496	−	0.404595i	$-0.867412\pi$
$727$	−31.1191	−	37.0863i	−1.15414	−	1.37546i	−0.239648	−	0.970860i	$-0.577032\pi$
$728$	−5.10937	−	0.900920i	−0.189366	−	0.0333903i
$729$	24.6222	−	42.6469i	0.911932	−	1.57951i
$730$		0			0
$731$	−8.13342	+	2.96032i	−0.300826	+	0.109492i
$732$	0.630859	+	1.73327i	0.0233172	+	0.0640636i
$733$	30.6031	−	17.6687i	1.13035	−	0.652610i	0.186329	−	0.982487i	$-0.440341\pi$
$733$	30.6031	−	17.6687i	1.13035	−	0.652610i	0.944024	+	0.329878i	$0.107008\pi$
$734$	−6.65551	+	11.5277i	−0.245659	+	0.425495i
$735$		0			0
$736$	3.78199	−	3.17347i	0.139406	−	0.116976i
$737$	1.65459	−	1.97186i	0.0609475	−	0.0726344i
$738$	−99.3720	+	17.5220i	−3.65793	+	0.644992i
$739$	18.2924	+	6.65787i	0.672895	+	0.244914i	0.655794	−	0.754940i	$-0.272334\pi$
$739$	18.2924	+	6.65787i	0.672895	+	0.244914i	0.0171013	+	0.999854i	$0.494556\pi$
$740$		0			0
$741$	−67.5333	−	10.5119i	−2.48090	−	0.386163i
$742$		−	6.21011i		−	0.227980i
$743$	−9.78221	+	26.8764i	−0.358875	+	0.986000i	0.620546	+	0.784170i	$0.286911\pi$
$743$	−9.78221	+	26.8764i	−0.358875	+	0.986000i	−0.979421	+	0.201830i	$0.935311\pi$
$744$	6.67187	+	37.8380i	0.244602	+	1.38721i
$745$		0			0
$746$	−10.7127	+	8.98899i	−0.392218	+	0.329110i
$747$	−6.37785	−	1.12459i	−0.233353	−	0.0411465i
$748$	1.26404	+	0.729796i	0.0462180	+	0.0266840i
$749$	1.78255	+	3.08748i	0.0651331	+	0.112814i
$750$		0			0
$751$	−44.7071	+	16.2721i	−1.63139	+	0.593776i	−0.985503	−	0.169660i	$-0.945733\pi$
$751$	−44.7071	+	16.2721i	−1.63139	+	0.593776i	−0.645883	+	0.763436i	$0.723511\pi$
$752$	19.8151	−	11.4402i	0.722581	−	0.417182i
$753$	−53.5282	−	30.9045i	−1.95068	−	1.12622i
$754$	4.51820	−	25.6240i	0.164543	−	0.933170i
$755$		0			0
$756$	5.21663	+	4.37727i	0.189727	+	0.159200i
$757$	−11.6962	+	2.06236i	−0.425107	+	0.0749578i	−0.382109	−	0.924117i	$-0.624802\pi$
$757$	−11.6962	+	2.06236i	−0.425107	+	0.0749578i	−0.0429980	+	0.999075i	$0.513691\pi$
$758$	−5.92689	+	16.2840i	−0.215274	+	0.591462i
$759$	−1.19561			−0.0433979
$760$		0			0
$761$	28.1049			1.01880			0.509401	−	0.860530i	$-0.329867\pi$
$761$	28.1049			1.01880			0.509401	+	0.860530i	$0.329867\pi$
$762$	5.56031	−	15.2768i	0.201429	−	0.553421i
$763$	9.53778	−	1.68177i	0.345291	−	0.0608841i
$764$	−3.82626	−	3.21061i	−0.138429	−	0.116156i
$765$		0			0
$766$	9.36368	−	53.1041i	0.338324	−	1.91873i
$767$	28.4091	+	16.4020i	1.02579	+	0.592242i
$768$	47.9525	−	27.6854i	1.73034	−	0.999011i
$769$	52.0340	−	18.9388i	1.87639	−	0.682952i	0.918909	−	0.394471i	$-0.129072\pi$
$769$	52.0340	−	18.9388i	1.87639	−	0.682952i	0.957486	−	0.288481i	$-0.0931502\pi$
$770$		0			0
$771$	35.5091	+	61.5036i	1.27883	+	2.21500i
$772$	−1.56730	−	0.904883i	−0.0564085	−	0.0325674i
$773$	−17.6165	−	3.10626i	−0.633621	−	0.111725i	−0.152393	−	0.988320i	$-0.548698\pi$
$773$	−17.6165	−	3.10626i	−0.633621	−	0.111725i	−0.481228	+	0.876595i	$0.659809\pi$
$774$	−16.0142	+	13.4375i	−0.575619	+	0.483002i
$775$		0			0
$776$	2.39241	+	13.5681i	0.0858826	+	0.487065i
$777$	−4.06995	+	11.1821i	−0.146009	+	0.401155i
$778$			51.5323i			1.84752i
$779$	0.693708	+	34.4780i	0.0248547	+	1.23530i
$780$		0			0
$781$	0.338258	+	0.123116i	0.0121038	+	0.00440542i
$782$	9.71921	−	1.71376i	0.347558	−	0.0612839i
$783$	30.6576	−	36.5363i	1.09561	−	1.30570i
$784$	−25.5192	+	21.4131i	−0.911399	+	0.764755i
$785$		0			0
$786$	−21.8868	+	37.9091i	−0.780677	+	1.35217i
$787$	6.41114	−	3.70147i	0.228532	−	0.131943i	−0.381362	−	0.924426i	$-0.624545\pi$
$787$	6.41114	−	3.70147i	0.228532	−	0.131943i	0.609895	+	0.792482i	$0.291212\pi$
$788$	4.72855	+	12.9916i	0.168448	+	0.462806i
$789$	59.9605	−	21.8238i	2.13465	−	0.776949i
$790$		0			0
$791$	−1.33392	+	2.31042i	−0.0474288	+	0.0821491i
$792$	−4.84845	−	0.854913i	−0.172282	−	0.0303780i
$793$	−2.10639	−	2.51029i	−0.0748000	−	0.0891432i
$794$	−13.6974	−	11.4935i	−0.486102	−	0.407888i
$795$		0			0
$796$	−10.9633	−	3.99031i	−0.388584	−	0.141433i
$797$			45.6568i			1.61725i	0.588326	+	0.808624i	$0.299787\pi$
$797$			45.6568i			1.61725i	−0.588326	+	0.808624i	$0.700213\pi$
$798$	9.85441	−	8.61251i	0.348842	−	0.304880i
$799$	24.2982			0.859609
$800$		0			0
$801$	19.1431	+	108.566i	0.676389	+	3.83599i
$802$	16.4870	−	19.6484i	0.582175	−	0.693809i
$803$	−2.97012	−	3.53965i	−0.104813	−	0.124911i
$804$	−3.66266	+	20.7720i	−0.129172	+	0.732571i
$805$		0			0
$806$	24.4389	+	42.3294i	0.860823	+	1.49099i
$807$	−1.88119	−	5.16853i	−0.0662211	−	0.181941i
$808$	4.83652	+	13.2882i	0.170148	+	0.467478i
$809$	−9.67626	−	16.7598i	−0.340199	−	0.589242i	0.644270	−	0.764798i	$-0.277161\pi$
$809$	−9.67626	−	16.7598i	−0.340199	−	0.589242i	−0.984469	+	0.175556i	$0.943828\pi$
$810$		0			0
$811$	3.61818	−	20.5197i	0.127052	−	0.720546i	−0.853016	−	0.521884i	$-0.825229\pi$
$811$	3.61818	−	20.5197i	0.127052	−	0.720546i	0.980068	−	0.198662i	$-0.0636595\pi$
$812$	0.942904	+	1.12371i	0.0330894	+	0.0394345i
$813$	16.5968	−	19.7793i	0.582075	−	0.693689i
$814$	0.646099	+	3.66421i	0.0226458	+	0.128431i
$815$		0			0
$816$	85.3951			2.98943
$817$	3.69597	+	6.11417i	0.129306	+	0.213908i
$818$			19.6378i			0.686619i
$819$	−18.8226	−	6.85087i	−0.657715	−	0.239389i
$820$		0			0
$821$	−23.4739	−	19.6969i	−0.819244	−	0.687427i	0.133551	−	0.991042i	$-0.457362\pi$
$821$	−23.4739	−	19.6969i	−0.819244	−	0.687427i	−0.952795	+	0.303615i	$0.901806\pi$
$822$	−3.24052	−	3.86190i	−0.113026	−	0.134699i
$823$	−7.95277	−	1.40229i	−0.277216	−	0.0488807i	0.0333116	−	0.999445i	$-0.489395\pi$
$823$	−7.95277	−	1.40229i	−0.277216	−	0.0488807i	−0.310528	+	0.950564i	$0.600506\pi$
$824$	−6.94142	+	12.0229i	−0.241816	+	0.418837i
$825$		0			0
$826$	−5.90276	+	2.14843i	−0.205383	+	0.0747534i
$827$	12.4978	+	34.3375i	0.434593	+	1.19403i	0.942964	+	0.332895i	$0.108026\pi$
$827$	12.4978	+	34.3375i	0.434593	+	1.19403i	−0.508371	+	0.861138i	$0.669752\pi$
$828$	6.07767	−	3.50894i	0.211213	−	0.121944i
$829$	−21.3514	+	36.9817i	−0.741564	+	1.28443i	0.210218	+	0.977654i	$0.432582\pi$
$829$	−21.3514	+	36.9817i	−0.741564	+	1.28443i	−0.951783	+	0.306773i	$0.900751\pi$
$830$		0			0
$831$	23.6014	−	19.8039i	0.818724	−	0.686991i
$832$	−7.61570	+	9.07604i	−0.264027	+	0.314655i
$833$	−34.8396	+	6.14317i	−1.20712	+	0.212848i
$834$	0.514771	+	0.187361i	0.0178251	+	0.00648779i
$835$		0			0
$836$	0.389207	−	1.14020i	0.0134610	−	0.0394346i
$837$			89.5956i			3.09688i
$838$	−10.1938	+	28.0072i	−0.352138	+	0.967492i
$839$	−8.35614	−	47.3900i	−0.288486	−	1.63609i	−0.692561	−	0.721360i	$-0.743518\pi$
$839$	−8.35614	−	47.3900i	−0.288486	−	1.63609i	0.404075	−	0.914726i	$-0.367594\pi$
$840$		0			0
$841$	−14.3450	+	12.0369i	−0.494657	+	0.415066i
$842$	34.1593	+	6.02320i	1.17721	+	0.207573i
$843$	35.4014	+	20.4390i	1.21929	+	0.703958i
$844$	−7.54471	−	13.0678i	−0.259700	−	0.449813i
$845$		0			0
$846$	55.1473	−	20.0720i	1.89600	−	0.690089i
$847$	5.17201	−	2.98606i	0.177712	−	0.102602i
$848$	−28.9658	−	16.7234i	−0.994690	−	0.574285i
$849$	−10.4945	+	59.5172i	−0.360170	+	2.04263i
$850$		0			0
$851$	5.67405	+	4.76110i	0.194504	+	0.163208i
$852$	−2.90481	+	0.512196i	−0.0995170	+	0.0175475i
$853$	−11.0981	+	30.4917i	−0.379991	+	1.04402i	0.591368	+	0.806402i	$0.298588\pi$
$853$	−11.0981	+	30.4917i	−0.379991	+	1.04402i	−0.971359	+	0.237615i	$0.923634\pi$
$854$	0.627500			0.0214726
$855$		0			0
$856$	12.7563			0.436001
$857$	10.3213	−	28.3576i	0.352569	−	0.968677i	−0.628972	−	0.777428i	$-0.716524\pi$
$857$	10.3213	−	28.3576i	0.352569	−	0.968677i	0.981542	−	0.191249i	$-0.0612537\pi$
$858$	−8.61043	+	1.51825i	−0.293955	+	0.0518322i
$859$	−20.3519	−	17.0772i	−0.694396	−	0.582668i	0.225777	−	0.974179i	$-0.427508\pi$
$859$	−20.3519	−	17.0772i	−0.694396	−	0.582668i	−0.920173	+	0.391511i	$0.871952\pi$
$860$		0			0
$861$	−2.45000	+	13.8946i	−0.0834956	+	0.473527i
$862$	−12.1478	−	7.01353i	−0.413756	−	0.238882i
$863$	−10.0083	+	5.77830i	−0.340687	+	0.196696i	−0.660576	−	0.750759i	$-0.729688\pi$
$863$	−10.0083	+	5.77830i	−0.340687	+	0.196696i	0.319889	+	0.947455i	$0.396354\pi$
$864$	62.1887	−	22.6348i	2.11570	−	0.770052i
$865$		0			0
$866$	−23.7339	−	41.1083i	−0.806510	−	1.39692i
$867$	30.6592	+	17.7011i	1.04124	+	0.601161i
$868$	−2.71374	−	0.478505i	−0.0921102	−	0.0162415i
$869$	0.356312	−	0.298982i	0.0120871	−	0.0101423i
$870$		0			0
$871$	−6.50709	−	36.9035i	−0.220484	−	1.25043i
$872$	11.8522	−	32.5637i	0.401366	−	1.10275i
$873$			53.1917i			1.80027i
$874$	−2.93963	−	7.59744i	−0.0994346	−	0.256987i
$875$		0			0
$876$	35.5792	+	12.9498i	1.20211	+	0.437532i
$877$	−17.8905	+	3.15457i	−0.604118	+	0.106522i	−0.467338	−	0.884079i	$-0.654787\pi$
$877$	−17.8905	+	3.15457i	−0.604118	+	0.106522i	−0.136781	+	0.990601i	$0.543676\pi$
$878$	32.8799	−	39.1847i	1.10964	−	1.32242i
$879$	−43.2596	+	36.2992i	−1.45911	+	1.22434i
$880$		0			0
$881$	19.9306	−	34.5209i	0.671480	−	1.16304i	−0.306004	−	0.952030i	$-0.598992\pi$
$881$	19.9306	−	34.5209i	0.671480	−	1.16304i	0.977484	−	0.211008i	$-0.0676745\pi$
$882$	−73.9975	+	42.7225i	−2.49163	+	1.43854i
$883$	−9.01286	−	24.7626i	−0.303307	−	0.833329i	−0.993920	−	0.110104i	$-0.964882\pi$
$883$	−9.01286	−	24.7626i	−0.303307	−	0.833329i	0.690613	−	0.723224i	$-0.257341\pi$
$884$	19.9669	−	7.26737i	0.671561	−	0.244428i
$885$		0			0
$886$	−20.6417	+	35.7524i	−0.693470	+	1.20113i
$887$	55.1080	+	9.71703i	1.85035	+	0.326266i	0.984682	−	0.174360i	$-0.0557857\pi$
$887$	55.1080	+	9.71703i	1.85035	+	0.326266i	0.865664	+	0.500626i	$0.166897\pi$
$888$	27.3688	+	32.6169i	0.918438	+	1.09455i
$889$	−1.24737	−	1.04667i	−0.0418355	−	0.0351042i
$890$		0			0
$891$	−7.98710	−	2.90707i	−0.267578	−	0.0973903i
$892$			21.9203i			0.733947i
$893$	−3.87941	−	19.6778i	−0.129820	−	0.658492i
$894$	−94.7059			−3.16744
$895$		0			0
$896$	−1.24102	−	7.03816i	−0.0414595	−	0.235128i
$897$	−11.1880	+	13.3333i	−0.373555	+	0.445186i
$898$	−26.7183	−	31.8417i	−0.891603	−	1.06257i
$899$	−3.35136	+	19.0065i	−0.111774	+	0.633903i
$900$		0			0
$901$	−17.7597	−	30.7606i	−0.591660	−	1.02479i
$902$	1.50882	+	4.14546i	0.0502384	+	0.138029i
$903$	0.999738	+	2.74676i	0.0332692	+	0.0914064i
$904$	4.77290	+	8.26690i	0.158744	+	0.274953i
$905$		0			0
$906$	18.2713	−	103.622i	0.607022	−	3.44259i
$907$	−29.6403	−	35.3239i	−0.984188	−	1.17291i	−0.984938	−	0.172910i	$-0.944683\pi$
$907$	−29.6403	−	35.3239i	−0.984188	−	1.17291i	0.000749224	−	1.00000i	$-0.499762\pi$
$908$	3.74105	−	4.45841i	0.124151	−	0.147958i
$909$	9.48045	+	53.7663i	0.314447	+	1.78332i
$910$		0			0
$911$	1.40625			0.0465912			0.0232956	−	0.999729i	$-0.492584\pi$
$911$	1.40625			0.0465912			0.0232956	+	0.999729i	$0.492584\pi$
$912$	−13.6340	−	69.1568i	−0.451468	−	2.29001i
$913$			0.283137i			0.00937048i
$914$	11.3352	+	4.12569i	0.374936	+	0.136466i
$915$		0			0
$916$	1.67807	+	1.40807i	0.0554449	+	0.0465238i
$917$	2.81822	+	3.35862i	0.0930658	+	0.110912i
$918$	130.284	+	22.9725i	4.30000	+	0.758207i
$919$	23.5177	−	40.7338i	0.775777	−	1.34369i	−0.158579	−	0.987346i	$-0.550691\pi$
$919$	23.5177	−	40.7338i	0.775777	−	1.34369i	0.934357	−	0.356339i	$-0.115975\pi$
$920$		0			0
$921$	−76.5515	+	27.8625i	−2.52246	+	0.918099i
$922$	−12.5072	−	34.3633i	−0.411903	−	1.13170i
$923$	4.53823	−	2.62015i	0.149378	−	0.0862432i
$924$	0.246461	−	0.426883i	0.00810798	−	0.0140434i
$925$		0			0
$926$	−41.1786	+	34.5529i	−1.35321	+	1.13548i
$927$	−34.4527	+	41.0591i	−1.13158	+	1.34856i
$928$	14.0392	−	2.47548i	0.460858	−	0.0812617i
$929$	−0.927569	−	0.337607i	−0.0304325	−	0.0110765i	0.326759	−	0.945108i	$-0.394043\pi$
$929$	−0.927569	−	0.337607i	−0.0304325	−	0.0110765i	−0.357192	+	0.934031i	$0.616266\pi$
$930$		0			0
$931$	10.5375	+	27.2339i	0.345351	+	0.892555i
$932$		−	22.2475i		−	0.728741i
$933$	−6.21096	+	17.0645i	−0.203338	+	0.558666i
$934$	5.71210	+	32.3950i	0.186906	+	1.06000i
$935$		0			0
$936$	−54.9034	+	46.0694i	−1.79457	+	1.50583i
$937$	−10.4614	−	1.84463i	−0.341760	−	0.0602615i	0.000134284	−	1.00000i	$-0.499957\pi$
$937$	−10.4614	−	1.84463i	−0.341760	−	0.0602615i	−0.341894	+	0.939739i	$0.611068\pi$
$938$	6.21426	+	3.58781i	0.202903	+	0.117146i
$939$	1.33513	+	2.31251i	0.0435702	+	0.0754659i
$940$		0			0
$941$	9.88893	−	3.59928i	0.322370	−	0.117333i	−0.175766	−	0.984432i	$-0.556240\pi$
$941$	9.88893	−	3.59928i	0.322370	−	0.117333i	0.498136	+	0.867099i	$0.334018\pi$
$942$	31.2123	−	18.0204i	1.01695	−	0.587137i
$943$	7.60550	+	4.39104i	0.247669	+	0.142992i
$944$	−5.87483	+	33.3178i	−0.191210	+	1.08440i
$945$		0			0
$946$	0.700133	+	0.587481i	0.0227633	+	0.0191007i
$947$	−34.5779	+	6.09701i	−1.12363	+	0.198126i	−0.704434	−	0.709770i	$-0.748799\pi$
$947$	−34.5779	+	6.09701i	−1.12363	+	0.198126i	−0.419196	+	0.907896i	$0.637688\pi$
$948$	−1.30357	+	3.58152i	−0.0423378	+	0.116322i
$949$	−67.2667			−2.18357
$950$		0			0
$951$	−109.048			−3.53613
$952$	1.94346	−	5.33961i	0.0629879	−	0.173058i
$953$	20.7575	−	3.66011i	0.672402	−	0.118563i	0.172985	−	0.984924i	$-0.444659\pi$
$953$	20.7575	−	3.66011i	0.672402	−	0.118563i	0.499417	+	0.866362i	$0.333548\pi$
$954$	−65.7178	−	55.1437i	−2.12769	−	1.78534i
$955$		0			0
$956$	1.89946	−	10.7724i	0.0614329	−	0.348403i
$957$	−2.98981	−	1.72617i	−0.0966468	−	0.0557991i
$958$	17.8447	−	10.3026i	0.576535	−	0.332863i
$959$	−0.474491	+	0.172701i	−0.0153221	+	0.00557679i
$960$		0			0
$961$	−2.62747	−	4.55092i	−0.0847572	−	0.146804i
$962$	46.9087	+	27.0828i	1.51240	+	0.873183i
$963$	48.5014	+	8.55210i	1.56293	+	0.275587i
$964$	9.69287	−	8.13329i	0.312186	−	0.261956i
$965$		0			0
$966$	−0.578758	−	3.28230i	−0.0186212	−	0.105606i
$967$	16.2138	−	44.5471i	0.521401	−	1.43254i	−0.347560	−	0.937658i	$-0.612990\pi$
$967$	16.2138	−	44.5471i	0.521401	−	1.43254i	0.868961	−	0.494881i	$-0.164788\pi$
$968$		−	21.3688i		−	0.686820i
$969$	24.1820	−	70.8421i	0.776836	−	2.27578i
$970$		0			0
$971$	30.6348	+	11.1502i	0.983117	+	0.357825i	0.783051	−	0.621957i	$-0.213662\pi$
$971$	30.6348	+	11.1502i	0.983117	+	0.357825i	0.200066	+	0.979782i	$0.435884\pi$
$972$	31.9020	−	5.62519i	1.02326	−	0.180428i
$973$	0.0352688	−	0.0420317i	0.00113067	−	0.00134747i
$974$	18.1873	−	15.2609i	0.582757	−	0.488991i
$975$		0			0
$976$	1.68982	−	2.92685i	0.0540897	−	0.0936861i
$977$	−20.7772	+	11.9957i	−0.664721	+	0.383777i	−0.794073	−	0.607822i	$-0.792043\pi$
$977$	−20.7772	+	11.9957i	−0.664721	+	0.383777i	0.129353	+	0.991599i	$0.458710\pi$
$978$	27.3264	+	75.0787i	0.873802	+	2.40075i
$979$	4.52900	−	1.64842i	0.144748	−	0.0526838i
$980$		0			0
$981$	66.8953	−	115.866i	2.13580	−	3.69932i
$982$	−32.9727	−	5.81398i	−1.05220	−	0.185532i
$983$	−2.75592	−	3.28438i	−0.0879003	−	0.104756i	0.720302	−	0.693661i	$-0.244003\pi$
$983$	−2.75592	−	3.28438i	−0.0879003	−	0.104756i	−0.808202	+	0.588906i	$0.799559\pi$
$984$	38.6724	+	32.4500i	1.23283	+	1.03447i
$985$		0			0
$986$	26.7787	+	9.74663i	0.852806	+	0.310396i
$987$		−	8.20581i		−	0.261194i
$988$	−9.07333	−	15.0098i	−0.288661	−	0.477526i
$989$	1.81944			0.0578547
$990$		0			0
$991$	−7.94255	−	45.0444i	−0.252303	−	1.43088i	−0.802901	−	0.596113i	$-0.796711\pi$
$991$	−7.94255	−	45.0444i	−0.252303	−	1.43088i	0.550597	−	0.834771i	$-0.314400\pi$
$992$	−17.2137	+	20.5145i	−0.546535	+	0.651335i
$993$	23.5526	+	28.0689i	0.747420	+	0.890741i
$994$	−0.174248	+	0.988211i	−0.00552682	+	0.0313442i
$995$		0			0
$996$	−1.16004	−	2.00924i	−0.0367571	−	0.0636652i
$997$	−4.09478	−	11.2503i	−0.129683	−	0.356301i	0.857809	−	0.513968i	$-0.171825\pi$
$997$	−4.09478	−	11.2503i	−0.129683	−	0.356301i	−0.987492	+	0.157667i	$0.949603\pi$
$998$	−4.28267	−	11.7665i	−0.135566	−	0.372463i
$999$	49.6442	+	85.9863i	1.57067	+	2.72048i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	475.2.u.c.99.5		36
5.2	odd	4		475.2.l.b.251.3		18
5.3	odd	4		95.2.k.b.61.1	✓	18
5.4	even	2	inner	475.2.u.c.99.2		36
15.8	even	4		855.2.bs.b.631.3		18
19.5	even	9	inner	475.2.u.c.24.2		36
95.24	even	18	inner	475.2.u.c.24.5		36
95.28	odd	36		1805.2.a.t.1.7		9
95.43	odd	36		95.2.k.b.81.1	yes	18
95.47	odd	36		9025.2.a.ce.1.3		9
95.48	even	36		1805.2.a.u.1.3		9
95.62	odd	36		475.2.l.b.176.3		18
95.67	even	36		9025.2.a.cd.1.7		9
285.233	even	36		855.2.bs.b.271.3		18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
95.2.k.b.61.1	✓	18	5.3	odd	4
95.2.k.b.81.1	yes	18	95.43	odd	36
475.2.l.b.176.3		18	95.62	odd	36
475.2.l.b.251.3		18	5.2	odd	4
475.2.u.c.24.2		36	19.5	even	9	inner
475.2.u.c.24.5		36	95.24	even	18	inner
475.2.u.c.99.2		36	5.4	even	2	inner
475.2.u.c.99.5		36	1.1	even	1	trivial
855.2.bs.b.271.3		18	285.233	even	36
855.2.bs.b.631.3		18	15.8	even	4
1805.2.a.t.1.7		9	95.28	odd	36
1805.2.a.u.1.3		9	95.48	even	36
9025.2.a.cd.1.7		9	95.67	even	36
9025.2.a.ce.1.3		9	95.47	odd	36

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:	\( N \)	\(=\)	\( 475 = 5^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	475.u (of order \(18\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.575828 - 1.58207i) q^{2} +(-3.20261 + 0.564707i) q^{3} +(-0.639290 - 0.536428i) q^{4} +(-0.950745 + 5.39194i) q^{6} +(0.474919 + 0.274194i) q^{7} +(1.69930 - 0.981094i) q^{8} +(7.11876 - 2.59101i) q^{9} +O(q^{10})\)	\(q+(0.575828 - 1.58207i) q^{2} +(-3.20261 + 0.564707i) q^{3} +(-0.639290 - 0.536428i) q^{4} +(-0.950745 + 5.39194i) q^{6} +(0.474919 + 0.274194i) q^{7} +(1.69930 - 0.981094i) q^{8} +(7.11876 - 2.59101i) q^{9} +(-0.165601 - 0.286829i) q^{11} +(2.35032 + 1.35696i) q^{12} +(-4.74830 - 0.837254i) q^{13} +(0.707267 - 0.593468i) q^{14} +(-0.863487 - 4.89708i) q^{16} +(1.80612 - 4.96227i) q^{17} -12.7544i q^{18} +(-4.30704 - 0.670409i) q^{19} +(-1.67582 - 0.609949i) q^{21} +(-0.549142 + 0.0968286i) q^{22} +(-0.713529 + 0.850350i) q^{23} +(-4.88818 + 4.10167i) q^{24} +(-4.05880 + 7.03005i) q^{26} +(-12.8865 + 7.44000i) q^{27} +(-0.156525 - 0.430050i) q^{28} +(-3.01199 + 1.09627i) q^{29} +(3.01060 - 5.21452i) q^{31} +(-4.38000 - 0.772312i) q^{32} +(0.692330 + 0.825087i) q^{33} +(-6.81067 - 5.71483i) q^{34} +(-5.94084 - 2.16229i) q^{36} -6.67261i q^{37} +(-3.54075 + 6.42801i) q^{38} +15.6798 q^{39} +(-1.37380 - 7.79121i) q^{41} +(-1.92997 + 2.30005i) q^{42} +(-1.05356 - 1.25559i) q^{43} +(-0.0479962 + 0.272200i) q^{44} +(0.934447 + 1.61851i) q^{46} +(1.57373 + 4.32380i) q^{47} +(5.53083 + 15.1958i) q^{48} +(-3.34963 - 5.80174i) q^{49} +(-2.98207 + 16.9122i) q^{51} +(2.58642 + 3.08237i) q^{52} +(4.32352 - 5.15257i) q^{53} +(4.35025 + 24.6715i) q^{54} +1.07604 q^{56} +(14.1723 - 0.285152i) q^{57} +5.39645i q^{58} +(-6.39331 - 2.32697i) q^{59} +(0.520640 + 0.436869i) q^{61} +(-6.51616 - 7.76566i) q^{62} +(4.09127 + 0.721402i) q^{63} +(1.22864 - 2.12807i) q^{64} +(1.70401 - 0.620209i) q^{66} +(2.65816 + 7.30324i) q^{67} +(-3.81654 + 2.20348i) q^{68} +(1.80496 - 3.12628i) q^{69} +(-0.832574 + 0.698612i) q^{71} +(9.55490 - 11.3871i) q^{72} +(13.7393 - 2.42261i) q^{73} +(-10.5566 - 3.84227i) q^{74} +(2.39382 + 2.73900i) q^{76} -0.181627i q^{77} +(9.02885 - 24.8065i) q^{78} +(0.243868 + 1.38304i) q^{79} +(19.6591 - 16.4960i) q^{81} +(-13.1173 - 2.31294i) q^{82} +(-0.740346 - 0.427439i) q^{83} +(0.744142 + 1.28889i) q^{84} +(-2.59310 + 0.943812i) q^{86} +(9.02715 - 5.21183i) q^{87} +(-0.562813 - 0.324940i) q^{88} +(-2.52694 + 14.3310i) q^{89} +(-2.02549 - 1.69959i) q^{91} +(0.912304 - 0.160864i) q^{92} +(-6.69712 + 18.4002i) q^{93} +7.74677 q^{94} +14.4636 q^{96} +(-2.40147 + 6.59799i) q^{97} +(-11.1076 + 1.95857i) q^{98} +(-1.92205 - 1.61279i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q + 6 q^{4} - 12 q^{6} + 42 q^{9}+O(q^{10}) \) 36 * q + 6 * q^4 - 12 * q^6 + 42 * q^9	\( 36 q + 6 q^{4} - 12 q^{6} + 42 q^{9} - 48 q^{14} + 42 q^{16} + 24 q^{19} + 6 q^{21} - 42 q^{24} - 42 q^{26} + 18 q^{29} + 60 q^{31} - 48 q^{34} - 42 q^{36} - 24 q^{39} - 12 q^{41} + 60 q^{44} + 42 q^{46} + 6 q^{49} + 54 q^{51} - 60 q^{54} - 144 q^{56} - 36 q^{59} + 12 q^{61} + 48 q^{64} - 66 q^{66} - 54 q^{69} + 48 q^{71} + 78 q^{74} + 54 q^{76} - 18 q^{79} + 30 q^{81} + 24 q^{84} - 66 q^{86} + 12 q^{89} - 12 q^{91} + 132 q^{94} - 36 q^{96} - 6 q^{99}+O(q^{100}) \) 36 * q + 6 * q^4 - 12 * q^6 + 42 * q^9 - 48 * q^14 + 42 * q^16 + 24 * q^19 + 6 * q^21 - 42 * q^24 - 42 * q^26 + 18 * q^29 + 60 * q^31 - 48 * q^34 - 42 * q^36 - 24 * q^39 - 12 * q^41 + 60 * q^44 + 42 * q^46 + 6 * q^49 + 54 * q^51 - 60 * q^54 - 144 * q^56 - 36 * q^59 + 12 * q^61 + 48 * q^64 - 66 * q^66 - 54 * q^69 + 48 * q^71 + 78 * q^74 + 54 * q^76 - 18 * q^79 + 30 * q^81 + 24 * q^84 - 66 * q^86 + 12 * q^89 - 12 * q^91 + 132 * q^94 - 36 * q^96 - 6 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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