LMFDB - Embedded newform 375.2.l.a.293.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [375,2,Mod(32,375)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(375, base_ring=CyclotomicField(20))

chi = DirichletCharacter(H, H._module([10, 1]))

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

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

chi := DirichletCharacter("375.32");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 375 = 3 \cdot 5^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	375.l (of order $20$, degree $8$, 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:	$2.99439007580$
Analytic rank:	$0$
Dimension:	$64$
Relative dimension:	$8$ over $\Q(\zeta_{20})$
Twist minimal:	no (minimal twist has level 75)
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			293.8
Character	$\chi$	$=$	375.293
Dual form			375.2.l.a.32.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.329364 + 2.07952i) q^{2} +(0.266688 - 1.71140i) q^{3} +(-2.31381 + 0.751802i) q^{4} +(3.64672 - 0.00908913i) q^{6} +(1.98257 - 1.98257i) q^{7} +(-0.413771 - 0.812071i) q^{8} +(-2.85776 - 0.912817i) q^{9} +O(q^{10})$	\(q+(0.329364 + 2.07952i) q^{2} +(0.266688 - 1.71140i) q^{3} +(-2.31381 + 0.751802i) q^{4} +(3.64672 - 0.00908913i) q^{6} +(1.98257 - 1.98257i) q^{7} +(-0.413771 - 0.812071i) q^{8} +(-2.85776 - 0.912817i) q^{9} +(0.542989 - 0.747360i) q^{11} +(0.669567 + 4.16034i) q^{12} +(5.01590 + 0.794440i) q^{13} +(4.77577 + 3.46980i) q^{14} +(-2.38405 + 1.73211i) q^{16} +(4.67502 - 2.38204i) q^{17} +(0.956980 - 6.24341i) q^{18} +(0.201787 + 0.0655644i) q^{19} +(-2.86423 - 3.92169i) q^{21} +(1.73299 + 0.883003i) q^{22} +(0.202701 - 0.0321047i) q^{23} +(-1.50012 + 0.491557i) q^{24} +10.6923i q^{26} +(-2.32432 + 4.64731i) q^{27} +(-3.09678 + 6.07778i) q^{28} +(0.160641 + 0.494401i) q^{29} +(-2.03788 + 6.27196i) q^{31} +(-5.67611 - 5.67611i) q^{32} +(-1.13422 - 1.12858i) q^{33} +(6.49329 + 8.93724i) q^{34} +(7.29856 - 0.0363822i) q^{36} +(0.370134 - 2.33693i) q^{37} +(-0.0698814 + 0.441214i) q^{38} +(2.69728 - 8.37232i) q^{39} +(-4.36217 - 6.00401i) q^{41} +(7.21185 - 7.24789i) q^{42} +(-0.516864 - 0.516864i) q^{43} +(-0.694506 + 2.13747i) q^{44} +(0.133525 + 0.410946i) q^{46} +(-4.17408 + 8.19208i) q^{47} +(2.32854 + 4.54199i) q^{48} -0.861150i q^{49} +(-2.82985 - 8.63608i) q^{51} +(-12.2031 + 1.93278i) q^{52} +(-10.4035 - 5.30087i) q^{53} +(-10.4297 - 3.30281i) q^{54} +(-2.43031 - 0.789657i) q^{56} +(0.166021 - 0.327852i) q^{57} +(-0.975208 + 0.496893i) q^{58} +(-0.0415323 + 0.0301750i) q^{59} +(-3.17882 - 2.30955i) q^{61} +(-13.7139 - 2.17206i) q^{62} +(-7.47542 + 3.85597i) q^{63} +(6.46985 - 8.90499i) q^{64} +(1.97334 - 2.73035i) q^{66} +(2.08186 + 4.08589i) q^{67} +(-9.02628 + 9.02628i) q^{68} +(-0.000885961 - 0.355463i) q^{69} +(-3.13172 + 1.01756i) q^{71} +(0.441184 + 2.69840i) q^{72} +(-1.78126 - 11.2465i) q^{73} +4.98160 q^{74} -0.516187 q^{76} +(-0.405180 - 2.55821i) q^{77} +(18.2988 + 2.85151i) q^{78} +(-3.90882 + 1.27005i) q^{79} +(7.33353 + 5.21722i) q^{81} +(11.0487 - 11.0487i) q^{82} +(7.11778 + 13.9694i) q^{83} +(9.57562 + 6.92070i) q^{84} +(0.904592 - 1.24506i) q^{86} +(0.888957 - 0.143069i) q^{87} +(-0.831583 - 0.131710i) q^{88} +(-6.24638 - 4.53826i) q^{89} +(11.5194 - 8.36933i) q^{91} +(-0.444875 + 0.226675i) q^{92} +(10.1903 + 5.16028i) q^{93} +(-18.4104 - 5.98190i) q^{94} +(-11.2278 + 8.20033i) q^{96} +(7.86930 + 4.00961i) q^{97} +(1.79078 - 0.283631i) q^{98} +(-2.23393 + 1.64012i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 64 q + 20 q^{4} - 6 q^{6} - 20 q^{7} + 10 q^{9}+O(q^{10}) $ 64 * q + 20 * q^4 - 6 * q^6 - 20 * q^7 + 10 * q^9	$ 64 q + 20 q^{4} - 6 q^{6} - 20 q^{7} + 10 q^{9} - 40 q^{12} - 8 q^{16} - 10 q^{18} - 6 q^{21} + 30 q^{27} + 80 q^{28} - 12 q^{31} + 50 q^{33} - 20 q^{34} - 22 q^{36} + 120 q^{37} - 30 q^{39} - 60 q^{42} - 20 q^{43} - 12 q^{46} - 100 q^{48} - 16 q^{51} - 100 q^{52} - 120 q^{54} + 70 q^{57} - 120 q^{58} - 12 q^{61} + 70 q^{63} + 100 q^{64} - 30 q^{66} + 60 q^{67} + 80 q^{69} + 40 q^{72} + 80 q^{73} - 64 q^{76} - 70 q^{78} + 60 q^{79} + 14 q^{81} - 60 q^{82} + 130 q^{84} - 100 q^{87} - 60 q^{88} - 12 q^{91} - 20 q^{93} - 260 q^{94} + 42 q^{96}+O(q^{100}) $ 64 * q + 20 * q^4 - 6 * q^6 - 20 * q^7 + 10 * q^9 - 40 * q^12 - 8 * q^16 - 10 * q^18 - 6 * q^21 + 30 * q^27 + 80 * q^28 - 12 * q^31 + 50 * q^33 - 20 * q^34 - 22 * q^36 + 120 * q^37 - 30 * q^39 - 60 * q^42 - 20 * q^43 - 12 * q^46 - 100 * q^48 - 16 * q^51 - 100 * q^52 - 120 * q^54 + 70 * q^57 - 120 * q^58 - 12 * q^61 + 70 * q^63 + 100 * q^64 - 30 * q^66 + 60 * q^67 + 80 * q^69 + 40 * q^72 + 80 * q^73 - 64 * q^76 - 70 * q^78 + 60 * q^79 + 14 * q^81 - 60 * q^82 + 130 * q^84 - 100 * q^87 - 60 * q^88 - 12 * q^91 - 20 * q^93 - 260 * q^94 + 42 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/375\mathbb{Z}\right)^\times$.

$n$	$127$	$251$
$\chi(n)$	$e\left(\frac{19}{20}\right)$	$-1$

Coefficient data

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

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

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

$2$	0.329364	+	2.07952i	0.232895	+	1.47044i	0.775976	+	0.630762i	$0.217258\pi$
$2$	0.329364	+	2.07952i	0.232895	+	1.47044i	−0.543081	+	0.839680i	$0.682742\pi$
$3$	0.266688	−	1.71140i	0.153972	−	0.988075i
$3$	0.266688	−	1.71140i	0.153972	−	0.988075i
$4$	−2.31381	+	0.751802i	−1.15690	+	0.375901i
$5$		0			0
$5$		0			0
$6$	3.64672	−	0.00908913i	1.48877	−	0.00371062i
$7$	1.98257	−	1.98257i	0.749340	−	0.749340i	−0.225015	−	0.974355i	$-0.572243\pi$
$7$	1.98257	−	1.98257i	0.749340	−	0.749340i	0.974355	+	0.225015i	$0.0722431\pi$
$8$	−0.413771	−	0.812071i	−0.146290	−	0.287110i
$9$	−2.85776	−	0.912817i	−0.952585	−	0.304272i
$10$		0			0
$11$	0.542989	−	0.747360i	0.163717	−	0.225338i	−0.719274	−	0.694726i	$-0.755526\pi$
$11$	0.542989	−	0.747360i	0.163717	−	0.225338i	0.882992	+	0.469388i	$0.155526\pi$
$12$	0.669567	+	4.16034i	0.193287	+	1.20099i
$13$	5.01590	+	0.794440i	1.39116	+	0.220338i	0.806641	−	0.591042i	$-0.201283\pi$
$13$	5.01590	+	0.794440i	1.39116	+	0.220338i	0.584519	+	0.811380i	$0.301283\pi$
$14$	4.77577	+	3.46980i	1.27638	+	0.927344i
$15$		0			0
$16$	−2.38405	+	1.73211i	−0.596012	+	0.433028i
$17$	4.67502	−	2.38204i	1.13386	−	0.577730i	0.216695	−	0.976239i	$-0.430472\pi$
$17$	4.67502	−	2.38204i	1.13386	−	0.577730i	0.917164	+	0.398509i	$0.130472\pi$
$18$	0.956980	−	6.24341i	0.225562	−	1.47159i
$19$	0.201787	+	0.0655644i	0.0462930	+	0.0150415i	0.332072	−	0.943254i	$-0.392252\pi$
$19$	0.201787	+	0.0655644i	0.0462930	+	0.0150415i	−0.285779	+	0.958296i	$0.592252\pi$
$20$		0			0
$21$	−2.86423	−	3.92169i	−0.625027	−	0.855782i
$22$	1.73299	+	0.883003i	0.369475	+	0.188257i
$23$	0.202701	−	0.0321047i	0.0422660	−	0.00669428i	−0.135266	−	0.990809i	$-0.543189\pi$
$23$	0.202701	−	0.0321047i	0.0422660	−	0.00669428i	0.177532	+	0.984115i	$0.443189\pi$
$24$	−1.50012	+	0.491557i	−0.306211	+	0.100339i
$25$		0			0
$26$			10.6923i			2.09694i
$27$	−2.32432	+	4.64731i	−0.447316	+	0.894376i
$28$	−3.09678	+	6.07778i	−0.585237	+	1.14859i
$29$	0.160641	+	0.494401i	0.0298302	+	0.0918080i	0.964863	−	0.262753i	$-0.0846304\pi$
$29$	0.160641	+	0.494401i	0.0298302	+	0.0918080i	−0.935033	+	0.354561i	$0.884630\pi$
$30$		0			0
$31$	−2.03788	+	6.27196i	−0.366015	+	1.12648i	0.583329	+	0.812236i	$0.301750\pi$
$31$	−2.03788	+	6.27196i	−0.366015	+	1.12648i	−0.949343	+	0.314241i	$0.898250\pi$
$32$	−5.67611	−	5.67611i	−1.00340	−	1.00340i
$33$	−1.13422	−	1.12858i	−0.197443	−	0.196461i
$34$	6.49329	+	8.93724i	1.11359	+	1.53272i
$35$		0			0
$36$	7.29856	−	0.0363822i	1.21643	−	0.00606371i
$37$	0.370134	−	2.33693i	0.0608496	−	0.384189i	−0.938403	−	0.345542i	$-0.887695\pi$
$37$	0.370134	−	2.33693i	0.0608496	−	0.384189i	0.999253	−	0.0386473i	$-0.0123049\pi$
$38$	−0.0698814	+	0.441214i	−0.0113363	+	0.0715743i
$39$	2.69728	−	8.37232i	0.431911	−	1.34064i
$40$		0			0
$41$	−4.36217	−	6.00401i	−0.681256	−	0.937668i	0.318692	−	0.947858i	$-0.396756\pi$
$41$	−4.36217	−	6.00401i	−0.681256	−	0.937668i	−0.999948	+	0.0101899i	$0.996756\pi$
$42$	7.21185	−	7.24789i	1.11281	−	1.11837i
$43$	−0.516864	−	0.516864i	−0.0788210	−	0.0788210i	0.666597	−	0.745418i	$-0.267750\pi$
$43$	−0.516864	−	0.516864i	−0.0788210	−	0.0788210i	−0.745418	+	0.666597i	$0.767750\pi$
$44$	−0.694506	+	2.13747i	−0.104701	+	0.322236i
$45$		0			0
$46$	0.133525	+	0.410946i	0.0196871	+	0.0605907i
$47$	−4.17408	+	8.19208i	−0.608851	+	1.19494i	0.356576	+	0.934266i	$0.383944\pi$
$47$	−4.17408	+	8.19208i	−0.608851	+	1.19494i	−0.965427	+	0.260672i	$0.916056\pi$
$48$	2.32854	+	4.54199i	0.336095	+	0.655580i
$49$		−	0.861150i		−	0.123021i
$50$		0			0
$51$	−2.82985	−	8.63608i	−0.396258	−	1.20929i
$52$	−12.2031	+	1.93278i	−1.69226	+	0.268028i
$53$	−10.4035	−	5.30087i	−1.42904	−	0.728130i	−0.443291	−	0.896378i	$-0.646189\pi$
$53$	−10.4035	−	5.30087i	−1.42904	−	0.728130i	−0.985745	+	0.168248i	$0.946189\pi$
$54$	−10.4297	−	3.30281i	−1.41931	−	0.449456i
$55$		0			0
$56$	−2.43031	−	0.789657i	−0.324764	−	0.105522i
$57$	0.166021	−	0.327852i	0.0219900	−	0.0434250i
$58$	−0.975208	+	0.496893i	−0.128051	+	0.0652453i
$59$	−0.0415323	+	0.0301750i	−0.00540705	+	0.00392845i	−0.590485	−	0.807048i	$-0.701064\pi$
$59$	−0.0415323	+	0.0301750i	−0.00540705	+	0.00392845i	0.585078	+	0.810977i	$0.301064\pi$
$60$		0			0
$61$	−3.17882	−	2.30955i	−0.407006	−	0.295707i	0.365382	−	0.930857i	$-0.380938\pi$
$61$	−3.17882	−	2.30955i	−0.407006	−	0.295707i	−0.772389	+	0.635150i	$0.780938\pi$
$62$	−13.7139	−	2.17206i	−1.74166	−	0.275852i
$63$	−7.47542	+	3.85597i	−0.941814	+	0.485807i
$64$	6.46985	−	8.90499i	0.808731	−	1.11312i
$65$		0			0
$66$	1.97334	−	2.73035i	0.242901	−	0.336083i
$67$	2.08186	+	4.08589i	0.254340	+	0.499170i	0.982506	−	0.186230i	$-0.0596271\pi$
$67$	2.08186	+	4.08589i	0.254340	+	0.499170i	−0.728166	+	0.685401i	$0.759627\pi$
$68$	−9.02628	+	9.02628i	−1.09460	+	1.09460i
$69$	−0.000885961	−	0.355463i	−0.000106657	−	0.0427928i
$70$		0			0
$71$	−3.13172	+	1.01756i	−0.371667	+	0.120762i	−0.488894	−	0.872343i	$-0.662600\pi$
$71$	−3.13172	+	1.01756i	−0.371667	+	0.120762i	0.117227	+	0.993105i	$0.462600\pi$
$72$	0.441184	+	2.69840i	0.0519940	+	0.318009i
$73$	−1.78126	−	11.2465i	−0.208481	−	1.31630i	−0.840697	−	0.541505i	$-0.817855\pi$
$73$	−1.78126	−	11.2465i	−0.208481	−	1.31630i	0.632216	−	0.774792i	$-0.282145\pi$
$74$	4.98160			0.579100
$75$		0			0
$76$	−0.516187			−0.0592107
$77$	−0.405180	−	2.55821i	−0.0461745	−	0.291535i
$78$	18.2988	+	2.85151i	2.07193	+	0.322870i
$79$	−3.90882	+	1.27005i	−0.439776	+	0.142892i	−0.520532	−	0.853842i	$-0.674267\pi$
$79$	−3.90882	+	1.27005i	−0.439776	+	0.142892i	0.0807561	+	0.996734i	$0.474267\pi$
$80$		0			0
$81$	7.33353	+	5.21722i	0.814837	+	0.579691i
$82$	11.0487	−	11.0487i	1.22013	−	1.22013i
$83$	7.11778	+	13.9694i	0.781278	+	1.53335i	0.844628	+	0.535354i	$0.179822\pi$
$83$	7.11778	+	13.9694i	0.781278	+	1.53335i	−0.0633496	+	0.997991i	$0.520178\pi$
$84$	9.57562	+	6.92070i	1.04479	+	0.755110i
$85$		0			0
$86$	0.904592	−	1.24506i	0.0975447	−	0.134259i
$87$	0.888957	−	0.143069i	0.0953062	−	0.0153386i
$88$	−0.831583	−	0.131710i	−0.0886470	−	0.0140403i
$89$	−6.24638	−	4.53826i	−0.662115	−	0.481054i	0.205262	−	0.978707i	$-0.434195\pi$
$89$	−6.24638	−	4.53826i	−0.662115	−	0.481054i	−0.867376	+	0.497653i	$0.834195\pi$
$90$		0			0
$91$	11.5194	−	8.36933i	1.20756	−	0.877344i
$92$	−0.444875	+	0.226675i	−0.0463814	+	0.0236325i
$93$	10.1903	+	5.16028i	1.05669	+	0.535096i
$94$	−18.4104	−	5.98190i	−1.89889	−	0.616986i
$95$		0			0
$96$	−11.2278	+	8.20033i	−1.14593	+	0.836942i
$97$	7.86930	+	4.00961i	0.799006	+	0.407114i	0.805301	−	0.592866i	$-0.202004\pi$
$97$	7.86930	+	4.00961i	0.799006	+	0.407114i	−0.00629464	+	0.999980i	$0.502004\pi$
$98$	1.79078	−	0.283631i	0.180896	−	0.0286511i
$99$	−2.23393	+	1.64012i	−0.224519	+	0.164839i
$100$		0			0
$101$			5.72257i			0.569417i	0.958614	+	0.284709i	$0.0918969\pi$
$101$			5.72257i			0.569417i	−0.958614	+	0.284709i	$0.908103\pi$
$102$	17.0268	−	8.72913i	1.68591	−	0.864313i
$103$	1.03168	−	2.02479i	0.101655	−	0.199508i	−0.834578	−	0.550891i	$-0.814288\pi$
$103$	1.03168	−	2.02479i	0.101655	−	0.199508i	0.936232	+	0.351382i	$0.114288\pi$
$104$	−1.43029	−	4.40198i	−0.140252	−	0.431650i
$105$		0			0
$106$	7.59671	−	23.3803i	0.737858	−	2.27089i
$107$	0.338061	+	0.338061i	0.0326816	+	0.0326816i	0.723259	−	0.690577i	$-0.242643\pi$
$107$	0.338061	+	0.338061i	0.0326816	+	0.0326816i	−0.690577	+	0.723259i	$0.742643\pi$
$108$	1.88417	−	12.5004i	0.181304	−	1.20285i
$109$	2.94311	+	4.05085i	0.281899	+	0.388001i	0.926362	−	0.376635i	$-0.122919\pi$
$109$	2.94311	+	4.05085i	0.281899	+	0.388001i	−0.644463	+	0.764636i	$0.722919\pi$
$110$		0			0
$111$	−3.90071	−	1.25668i	−0.370239	−	0.119278i
$112$	−1.29251	+	8.16057i	−0.122131	+	0.771102i
$113$	0.906443	−	5.72305i	0.0852710	−	0.538380i	−0.907662	−	0.419702i	$-0.862135\pi$
$113$	0.906443	−	5.72305i	0.0852710	−	0.538380i	0.992933	−	0.118678i	$-0.0378655\pi$
$114$	0.736455	+	0.237261i	0.0689753	+	0.0222215i
$115$		0			0
$116$	−0.743383	−	1.02318i	−0.0690214	−	0.0949998i
$117$	−13.6090	−	6.84891i	−1.25816	−	0.633182i
$118$	−0.0764287	−	0.0764287i	−0.00703583	−	0.00703583i
$119$	4.54599	−	13.9911i	0.416730	−	1.28256i
$120$		0			0
$121$	3.13548	+	9.65000i	0.285043	+	0.877273i
$122$	3.75576	−	7.37110i	0.340031	−	0.667348i
$123$	−11.4386	+	5.86420i	−1.03138	+	0.528757i
$124$		−	16.0442i		−	1.44081i
$125$		0			0
$126$	−10.4807	−	14.2753i	−0.933695	−	1.27174i
$127$	−12.8459	+	2.03459i	−1.13989	+	0.180541i	−0.697707	−	0.716383i	$-0.745796\pi$
$127$	−12.8459	+	2.03459i	−1.13989	+	0.180541i	−0.442184	+	0.896924i	$0.645796\pi$
$128$	6.34440	+	3.23263i	0.560771	+	0.285727i
$129$	−1.02240	+	0.746718i	−0.0900173	+	0.0657448i
$130$		0			0
$131$	−19.2637	−	6.25917i	−1.68308	−	0.546866i	−0.697575	−	0.716512i	$-0.745738\pi$
$131$	−19.2637	−	6.25917i	−1.68308	−	0.546866i	−0.985505	+	0.169646i	$0.945738\pi$
$132$	3.47284	+	1.75861i	0.302272	+	0.153068i
$133$	0.530041	−	0.270070i	0.0459604	−	0.0234180i
$134$	−7.81099	+	5.67502i	−0.674767	+	0.490247i
$135$		0			0
$136$	−3.86878	−	2.81083i	−0.331745	−	0.241027i
$137$	11.0507	+	1.75026i	0.944123	+	0.149534i	0.609472	−	0.792808i	$-0.291381\pi$
$137$	11.0507	+	1.75026i	0.944123	+	0.149534i	0.334651	+	0.942342i	$0.391381\pi$
$138$	0.738901	−	0.118919i	0.0628995	−	0.0101231i
$139$	−2.00883	+	2.76492i	−0.170387	+	0.234517i	−0.885668	−	0.464320i	$-0.846299\pi$
$139$	−2.00883	+	2.76492i	−0.170387	+	0.234517i	0.715281	+	0.698837i	$0.246299\pi$
$140$		0			0
$141$	12.9067	+	9.32823i	1.08694	+	0.785578i
$142$	−3.14751	−	6.17734i	−0.264133	−	0.518391i
$143$	3.31731	−	3.31731i	0.277408	−	0.277408i
$144$	8.39413	−	2.77376i	0.699511	−	0.231146i
$145$		0			0
$146$	22.8005	−	7.40834i	1.88699	−	0.613119i
$147$	−1.47377	−	0.229658i	−0.121554	−	0.0189419i
$148$	0.900492	+	5.68548i	0.0740199	+	0.467344i
$149$	4.86008			0.398153			0.199077	−	0.979984i	$-0.436206\pi$
$149$	4.86008			0.398153			0.199077	+	0.979984i	$0.436206\pi$
$150$		0			0
$151$	8.48112			0.690184			0.345092	−	0.938569i	$-0.387848\pi$
$151$	8.48112			0.690184			0.345092	+	0.938569i	$0.387848\pi$
$152$	−0.0302504	−	0.190994i	−0.00245363	−	0.0154916i
$153$	−15.5344	+	2.53986i	−1.25588	+	0.205335i
$154$	5.18639	−	1.68516i	0.417931	−	0.135794i
$155$		0			0
$156$	0.0533371	+	21.3998i	0.00427038	+	1.71335i
$157$	−10.9610	+	10.9610i	−0.874786	+	0.874786i	−0.992989	−	0.118204i	$-0.962286\pi$
$157$	−10.9610	+	10.9610i	−0.874786	+	0.874786i	0.118204	+	0.992989i	$0.462286\pi$
$158$	−3.92852	−	7.71015i	−0.312536	−	0.613387i
$159$	−11.8464	+	16.3909i	−0.939479	+	1.29988i
$160$		0			0
$161$	0.338219	−	0.465518i	0.0266554	−	0.0366879i
$162$	−8.43390	+	16.9686i	−0.662630	+	1.33318i
$163$	−17.6369	−	2.79341i	−1.38143	−	0.218797i	−0.578895	−	0.815402i	$-0.696516\pi$
$163$	−17.6369	−	2.79341i	−1.38143	−	0.218797i	−0.802535	+	0.596605i	$0.796516\pi$
$164$	14.6070	+	10.6126i	1.14062	+	0.828708i
$165$		0			0
$166$	−26.7054	+	19.4026i	−2.07274	+	1.50593i
$167$	−8.21094	+	4.18368i	−0.635381	+	0.323743i	−0.741843	−	0.670574i	$-0.766048\pi$
$167$	−8.21094	+	4.18368i	−0.635381	+	0.323743i	0.106461	+	0.994317i	$0.466048\pi$
$168$	−1.99955	+	3.94864i	−0.154269	+	0.304644i
$169$	12.1644	+	3.95244i	0.935721	+	0.304034i
$170$		0			0
$171$	−0.516808	−	0.371561i	−0.0395213	−	0.0284140i
$172$	1.58450	+	0.807345i	0.120817	+	0.0615595i
$173$	12.4375	−	1.96990i	0.945602	−	0.149769i	0.335454	−	0.942056i	$-0.391110\pi$
$173$	12.4375	−	1.96990i	0.945602	−	0.149769i	0.610148	+	0.792288i	$0.291110\pi$
$174$	0.590305	+	1.80148i	0.0447509	+	0.136570i
$175$		0			0
$176$			2.72226i			0.205198i
$177$	0.0405652	+	0.0791256i	0.00304907	+	0.00594744i
$178$	7.38007	−	14.4842i	0.553160	−	1.08564i
$179$	3.09902	+	9.53780i	0.231631	+	0.712888i	0.997550	+	0.0699512i	$0.0222844\pi$
$179$	3.09902	+	9.53780i	0.231631	+	0.712888i	−0.765919	+	0.642937i	$0.777716\pi$
$180$		0			0
$181$	−1.02409	+	3.15183i	−0.0761202	+	0.234274i	−0.981875	−	0.189527i	$-0.939304\pi$
$181$	−1.02409	+	3.15183i	−0.0761202	+	0.234274i	0.905755	+	0.423801i	$0.139304\pi$
$182$	21.1982	+	21.1982i	1.57132	+	1.57132i
$183$	−4.80031	+	4.82429i	−0.354849	+	0.356622i
$184$	−0.109943	−	0.151324i	−0.00810510	−	0.0111557i
$185$		0			0
$186$	−7.37458	+	22.8906i	−0.540731	+	1.67842i
$187$	0.758242	−	4.78735i	0.0554481	−	0.350086i
$188$	3.49919	−	22.0930i	0.255204	−	1.61130i
$189$	4.60549	+	13.8217i	0.335000	+	1.00538i
$190$		0			0
$191$	5.50332	+	7.57467i	0.398206	+	0.548084i	0.960293	−	0.278995i	$-0.0900011\pi$
$191$	5.50332	+	7.57467i	0.398206	+	0.548084i	−0.562086	+	0.827079i	$0.690001\pi$
$192$	−13.5145	−	13.4473i	−0.975327	−	0.970478i
$193$	1.55757	+	1.55757i	0.112116	+	0.112116i	0.760939	−	0.648823i	$-0.224738\pi$
$193$	1.55757	+	1.55757i	0.112116	+	0.112116i	−0.648823	+	0.760939i	$0.724738\pi$
$194$	−5.74620	+	17.6850i	−0.412553	+	1.26971i
$195$		0			0
$196$	0.647414	+	1.99254i	0.0462439	+	0.142324i
$197$	7.01627	−	13.7702i	0.499889	−	0.981087i	−0.493870	−	0.869536i	$-0.664418\pi$
$197$	7.01627	−	13.7702i	0.499889	−	0.981087i	0.993759	−	0.111551i	$-0.0355819\pi$
$198$	−4.14645	−	4.10531i	−0.294675	−	0.291752i
$199$			6.87281i			0.487200i	0.969876	+	0.243600i	$0.0783285\pi$
$199$			6.87281i			0.487200i	−0.969876	+	0.243600i	$0.921672\pi$
$200$		0			0
$201$	7.54778	−	2.47324i	0.532379	−	0.174449i
$202$	−11.9002	+	1.88481i	−0.837295	+	0.132615i
$203$	1.29866	+	0.661703i	0.0911484	+	0.0464424i
$204$	13.0403	+	17.8547i	0.913007	+	1.25008i
$205$		0			0
$206$	4.55039	+	1.47851i	0.317041	+	0.103013i
$207$	−0.608575	−	0.0932815i	−0.0422989	−	0.00648351i
$208$	−13.3342	+	6.79412i	−0.924561	+	0.471088i
$209$	0.158568	−	0.115207i	0.0109684	−	0.00796900i
$210$		0			0
$211$	−3.79498	−	2.75721i	−0.261257	−	0.189814i	0.449444	−	0.893309i	$-0.351622\pi$
$211$	−3.79498	−	2.75721i	−0.261257	−	0.189814i	−0.710701	+	0.703494i	$0.751622\pi$
$212$	28.0570	+	4.44379i	1.92696	+	0.305201i
$213$	0.906254	+	5.63099i	0.0620955	+	0.385829i
$214$	−0.591659	+	0.814349i	−0.0404450	+	0.0556677i
$215$		0			0
$216$	4.73569	−	0.0354104i	0.322223	−	0.00240937i
$217$	8.39434	+	16.4748i	0.569845	+	1.11838i
$218$	−7.45447	+	7.45447i	−0.504880	+	0.504880i
$219$	−19.7222	+	0.0491558i	−1.33270	+	0.00332164i
$220$		0			0
$221$	25.3418	−	8.23406i	1.70468	−	0.553883i
$222$	1.32853	−	8.52550i	0.0891653	−	0.572194i
$223$	2.60889	+	16.4719i	0.174704	+	1.10304i	0.906715	+	0.421745i	$0.138582\pi$
$223$	2.60889	+	16.4719i	0.174704	+	1.10304i	−0.732010	+	0.681293i	$0.761418\pi$
$224$	−22.5065			−1.50378
$225$		0			0
$226$	12.1998			0.811516
$227$	−3.41634	−	21.5699i	−0.226750	−	1.43164i	−0.793909	−	0.608036i	$-0.791958\pi$
$227$	−3.41634	−	21.5699i	−0.226750	−	1.43164i	0.567159	−	0.823608i	$-0.308042\pi$
$228$	−0.137661	+	0.883400i	−0.00911681	+	0.0585046i
$229$	−14.7727	+	4.79995i	−0.976209	+	0.317190i	−0.753320	−	0.657654i	$-0.771549\pi$
$229$	−14.7727	+	4.79995i	−0.976209	+	0.317190i	−0.222889	+	0.974844i	$0.571549\pi$
$230$		0			0
$231$	−4.48616	+	0.0111814i	−0.295168	+	0.000735680i
$232$	0.335020	−	0.335020i	0.0219952	−	0.0219952i
$233$	−2.53536	−	4.97593i	−0.166097	−	0.325984i	0.792923	−	0.609322i	$-0.208558\pi$
$233$	−2.53536	−	4.97593i	−0.166097	−	0.325984i	−0.959020	+	0.283338i	$0.908558\pi$
$234$	9.76013	−	30.5560i	0.638040	−	1.99751i
$235$		0			0
$236$	0.0734122	−	0.101043i	0.00477873	−	0.00657735i
$237$	1.13113	+	7.02824i	0.0734747	+	0.456533i
$238$	30.5921	+	4.84531i	1.98299	+	0.314075i
$239$	−14.9846	−	10.8869i	−0.969271	−	0.704217i	−0.0139860	−	0.999902i	$-0.504452\pi$
$239$	−14.9846	−	10.8869i	−0.969271	−	0.704217i	−0.955285	+	0.295685i	$0.904452\pi$
$240$		0			0
$241$	−10.4630	+	7.60183i	−0.673982	+	0.489677i	−0.871356	−	0.490651i	$-0.836759\pi$
$241$	−10.4630	+	7.60183i	−0.673982	+	0.489677i	0.197373	+	0.980328i	$0.436759\pi$
$242$	−19.0347	+	9.69864i	−1.22359	+	0.623453i
$243$	10.8845	−	11.1592i	0.698240	−	0.715864i
$244$	9.09151	+	2.95401i	0.582024	+	0.189111i
$245$		0			0
$246$	−15.9622	−	21.8553i	−1.01771	−	1.39344i
$247$	0.960054	+	0.489172i	0.0610868	+	0.0311253i
$248$	5.93649	−	0.940248i	0.376968	−	0.0597058i
$249$	25.8055	−	8.45587i	1.63536	−	0.535869i
$250$		0			0
$251$			4.70685i			0.297094i	0.988905	+	0.148547i	$0.0474596\pi$
$251$			4.70685i			0.297094i	−0.988905	+	0.148547i	$0.952540\pi$
$252$	14.3978	−	14.5420i	0.906973	−	0.916061i
$253$	0.0860706	−	0.168923i	0.00541121	−	0.0106201i
$254$	−8.46195	−	26.0432i	−0.530950	−	1.63410i
$255$		0			0
$256$	2.17010	−	6.67887i	0.135631	−	0.417429i
$257$	11.3472	+	11.3472i	0.707820	+	0.707820i	0.966076	−	0.258256i	$-0.0831479\pi$
$257$	11.3472	+	11.3472i	0.707820	+	0.707820i	−0.258256	+	0.966076i	$0.583148\pi$
$258$	−1.88956	−	1.88016i	−0.117639	−	0.117054i
$259$	−3.89931	−	5.36694i	−0.242291	−	0.333485i
$260$		0			0
$261$	−0.00777395	−	1.55951i	−0.000481195	−	0.0965314i
$262$	6.67129	−	42.1209i	0.412154	−	2.60223i
$263$	−1.11866	+	7.06296i	−0.0689797	+	0.435521i	0.928894	+	0.370345i	$0.120761\pi$
$263$	−1.11866	+	7.06296i	−0.0689797	+	0.435521i	−0.997874	+	0.0651753i	$0.979239\pi$
$264$	−0.447181	+	1.38804i	−0.0275221	+	0.0854281i
$265$		0			0
$266$	0.736191	+	1.01328i	0.0451388	+	0.0621282i
$267$	−9.43259	+	9.47973i	−0.577265	+	0.580150i
$268$	−7.88881	−	7.88881i	−0.481886	−	0.481886i
$269$	0.354740	−	1.09178i	0.0216289	−	0.0665668i	−0.939660	−	0.342111i	$-0.888858\pi$
$269$	0.354740	−	1.09178i	0.0216289	−	0.0665668i	0.961288	+	0.275544i	$0.0888581\pi$
$270$		0			0
$271$	−2.97307	−	9.15016i	−0.180601	−	0.555832i	0.819244	−	0.573445i	$-0.194393\pi$
$271$	−2.97307	−	9.15016i	−0.180601	−	0.555832i	−0.999845	+	0.0176127i	$0.994393\pi$
$272$	−7.01952	+	13.7766i	−0.425621	+	0.835328i
$273$	−11.2512	−	21.9462i	−0.680951	−	1.32825i
$274$			23.5566i			1.42310i
$275$		0			0
$276$	0.269288	+	0.821808i	0.0162092	+	0.0494670i
$277$	22.6764	−	3.59160i	1.36250	−	0.215798i	0.567980	−	0.823042i	$-0.307725\pi$
$277$	22.6764	−	3.59160i	1.36250	−	0.215798i	0.794515	+	0.607244i	$0.207725\pi$
$278$	−6.41134	−	3.26674i	−0.384527	−	0.195926i
$279$	11.5489	−	16.0635i	0.691416	−	0.961697i
$280$		0			0
$281$	−8.86944	−	2.88186i	−0.529107	−	0.171917i	0.0322675	−	0.999479i	$-0.489727\pi$
$281$	−8.86944	−	2.88186i	−0.529107	−	0.171917i	−0.561374	+	0.827562i	$0.689727\pi$
$282$	−15.1472	+	29.9122i	−0.902004	+	1.78124i
$283$	29.6409	−	15.1028i	1.76197	−	0.897769i	0.813087	−	0.582143i	$-0.197786\pi$
$283$	29.6409	−	15.1028i	1.76197	−	0.897769i	0.948884	−	0.315626i	$-0.102214\pi$
$284$	6.48121	−	4.70887i	0.384589	−	0.279420i
$285$		0			0
$286$	7.99102	+	5.80581i	0.472519	+	0.343305i
$287$	−20.5516	−	3.25506i	−1.21313	−	0.192140i
$288$	11.0397	+	21.4022i	0.650520	+	1.26114i
$289$	6.18935	−	8.51891i	0.364080	−	0.501112i
$290$		0			0
$291$	8.96068	−	12.3982i	0.525284	−	0.726794i
$292$	12.5766	+	24.6830i	0.735990	+	1.44446i
$293$	19.5495	−	19.5495i	1.14209	−	1.14209i	0.154025	−	0.988067i	$-0.450776\pi$
$293$	19.5495	−	19.5495i	1.14209	−	1.14209i	0.988067	−	0.154025i	$-0.0492235\pi$
$294$	−0.00782710	−	3.14037i	−0.000456486	−	0.183150i
$295$		0			0
$296$	−2.05090	+	0.666379i	−0.119206	+	0.0387325i
$297$	2.21114	+	4.26055i	0.128303	+	0.247222i
$298$	1.60073	+	10.1066i	0.0927280	+	0.585462i
$299$	1.04223			0.0602738
$300$		0			0
$301$	−2.04944			−0.118127
$302$	2.79337	+	17.6367i	0.160741	+	1.01488i
$303$	9.79359	+	1.52614i	0.562627	+	0.0876745i
$304$	−0.594634	+	0.193208i	−0.0341046	+	0.0110813i
$305$		0			0
$306$	−10.3982	−	31.4676i	−0.594423	−	1.79888i
$307$	16.9428	−	16.9428i	0.966975	−	0.966975i	−0.0324970	−	0.999472i	$-0.510346\pi$
$307$	16.9428	−	16.9428i	0.966975	−	0.966975i	0.999472	+	0.0324970i	$0.0103459\pi$
$308$	2.86077	+	5.61458i	0.163008	+	0.319921i
$309$	−3.19008	−	2.30560i	−0.181477	−	0.131161i
$310$		0			0
$311$	−1.70402	+	2.34539i	−0.0966263	+	0.132995i	−0.854593	−	0.519299i	$-0.826193\pi$
$311$	−1.70402	+	2.34539i	−0.0966263	+	0.132995i	0.757966	+	0.652294i	$0.226193\pi$
$312$	−7.91498	+	1.27384i	−0.448097	+	0.0721170i
$313$	−13.4521	−	2.13060i	−0.760357	−	0.120429i	−0.235797	−	0.971802i	$-0.575770\pi$
$313$	−13.4521	−	2.13060i	−0.760357	−	0.120429i	−0.524560	+	0.851374i	$0.675770\pi$
$314$	−26.4038	−	19.1835i	−1.49006	−	1.08259i
$315$		0			0
$316$	8.08943	−	5.87731i	0.455066	−	0.330625i
$317$	26.9459	−	13.7296i	1.51343	−	0.771132i	0.517037	−	0.855963i	$-0.327035\pi$
$317$	26.9459	−	13.7296i	1.51343	−	0.771132i	0.996395	+	0.0848304i	$0.0270348\pi$
$318$	−37.9870	−	19.2362i	−2.13020	−	1.07871i
$319$	0.456722	+	0.148398i	0.0255715	+	0.00830869i
$320$		0			0
$321$	0.668712	−	0.488399i	0.0373239	−	0.0272598i
$322$	1.07945	+	0.550007i	0.0601554	+	0.0306507i
$323$	1.09953	−	0.174149i	0.0611797	−	0.00968991i
$324$	−20.8907	−	6.55828i	−1.16059	−	0.364349i
$325$		0			0
$326$		−	37.5964i		−	2.08227i
$327$	7.71750	−	3.95652i	0.426779	−	0.218796i
$328$	−3.07074	+	6.02667i	−0.169553	+	0.332767i
$329$	7.96597	+	24.5167i	0.439178	+	1.35165i
$330$		0			0
$331$	−2.97741	+	9.16351i	−0.163653	+	0.503672i	−0.998935	−	0.0461504i	$-0.985305\pi$
$331$	−2.97741	+	9.16351i	−0.163653	+	0.503672i	0.835282	+	0.549823i	$0.185305\pi$
$332$	−26.9714	−	26.9714i	−1.48025	−	1.48025i
$333$	−3.19094	+	6.34051i	−0.174863	+	0.347458i
$334$	−11.4044	−	15.6969i	−0.624023	−	0.858894i
$335$		0			0
$336$	13.6213	+	4.38832i	0.743102	+	0.239402i
$337$	1.23274	−	7.78320i	0.0671515	−	0.423978i	−0.931095	−	0.364778i	$-0.881145\pi$
$337$	1.23274	−	7.78320i	0.0671515	−	0.423978i	0.998246	−	0.0592003i	$-0.0188551\pi$
$338$	−4.21268	+	26.5978i	−0.229140	+	1.44673i
$339$	−9.55268	−	3.07755i	−0.518830	−	0.167150i
$340$		0			0
$341$	3.58087	+	4.92864i	0.193915	+	0.266901i
$342$	0.602451	−	1.19709i	0.0325768	−	0.0647313i
$343$	12.1707	+	12.1707i	0.657155	+	0.657155i
$344$	−0.205867	+	0.633593i	−0.0110996	+	0.0341611i
$345$		0			0
$346$	8.19289	+	25.2151i	0.440452	+	1.35557i
$347$	1.48744	−	2.91927i	0.0798502	−	0.156715i	−0.847629	−	0.530589i	$-0.821971\pi$
$347$	1.48744	−	2.91927i	0.0798502	−	0.156715i	0.927479	+	0.373874i	$0.121971\pi$
$348$	−1.94932	+	0.999354i	−0.104494	+	0.0535710i
$349$			10.1798i			0.544913i	0.962168	+	0.272457i	$0.0878361\pi$
$349$			10.1798i			0.544913i	−0.962168	+	0.272457i	$0.912164\pi$
$350$		0			0
$351$	−15.3506	+	21.4639i	−0.819353	+	1.14566i
$352$	−7.32417	+	1.16003i	−0.390379	+	0.0618300i
$353$	1.64473	+	0.838034i	0.0875404	+	0.0446041i	0.497213	−	0.867629i	$-0.334357\pi$
$353$	1.64473	+	0.838034i	0.0875404	+	0.0446041i	−0.409672	+	0.912233i	$0.634357\pi$
$354$	−0.151182	+	0.110417i	−0.00803526	+	0.00586861i
$355$		0			0
$356$	17.8648	+	5.80462i	0.946832	+	0.307644i
$357$	−22.7320	−	11.5112i	−1.20310	−	0.609240i
$358$	−18.8133	+	9.58587i	−0.994315	+	0.506629i
$359$	21.6017	−	15.6946i	1.14009	−	0.828327i	0.152962	−	0.988232i	$-0.451119\pi$
$359$	21.6017	−	15.6946i	1.14009	−	0.828327i	0.987132	+	0.159905i	$0.0511187\pi$
$360$		0			0
$361$	−15.3349	−	11.1415i	−0.807100	−	0.586393i
$362$	−6.89160	−	1.09152i	−0.362214	−	0.0573691i
$363$	17.3512	−	2.79250i	0.910701	−	0.146568i
$364$	−20.3616	+	28.0253i	−1.06724	+	1.46893i
$365$		0			0
$366$	−11.6133	−	8.39338i	−0.607035	−	0.438729i
$367$	−13.9058	−	27.2917i	−0.725877	−	1.42461i	−0.898206	−	0.439575i	$-0.855129\pi$
$367$	−13.9058	−	27.2917i	−0.725877	−	1.42461i	0.172328	−	0.985040i	$-0.444871\pi$
$368$	−0.427640	+	0.427640i	−0.0222923	+	0.0222923i
$369$	6.98544	+	21.1398i	0.363648	+	1.10050i
$370$		0			0
$371$	−31.1350	+	10.1164i	−1.61645	+	0.525217i
$372$	−27.4580	−	4.27879i	−1.42363	−	0.221845i
$373$	0.292978	+	1.84979i	0.0151698	+	0.0957785i	0.994112	−	0.108361i	$-0.0345603\pi$
$373$	0.292978	+	1.84979i	0.0151698	+	0.0957785i	−0.978942	+	0.204140i	$0.934560\pi$
$374$	10.2051			0.527694
$375$		0			0
$376$	8.37966			0.432148
$377$	0.412985	+	2.60749i	0.0212698	+	0.134292i
$378$	−27.2257	+	14.1296i	−1.40034	+	0.726748i
$379$	22.0932	−	7.17851i	1.13485	−	0.368735i	0.319433	−	0.947609i	$-0.396508\pi$
$379$	22.0932	−	7.17851i	1.13485	−	0.368735i	0.815417	+	0.578874i	$0.196508\pi$
$380$		0			0
$381$	0.0561467	+	22.5271i	0.00287648	+	1.15410i
$382$	−13.9391	+	13.9391i	−0.713186	+	0.713186i
$383$	15.0503	+	29.5378i	0.769032	+	1.50931i	0.858212	+	0.513295i	$0.171575\pi$
$383$	15.0503	+	29.5378i	0.769032	+	1.50931i	−0.0891798	+	0.996016i	$0.528425\pi$
$384$	7.22429	−	9.99567i	0.368663	−	0.510090i
$385$		0			0
$386$	−2.72599	+	3.75201i	−0.138749	+	0.190972i
$387$	1.00527	+	1.94887i	0.0511007	+	0.0990668i
$388$	−21.2225	−	3.36131i	−1.07741	−	0.170645i
$389$	24.6907	+	17.9388i	1.25187	+	0.909534i	0.998329	−	0.0577917i	$-0.0184059\pi$
$389$	24.6907	+	17.9388i	1.25187	+	0.909534i	0.253537	+	0.967326i	$0.418406\pi$
$390$		0			0
$391$	0.871156	−	0.632932i	0.0440563	−	0.0320087i
$392$	−0.699315	+	0.356319i	−0.0353207	+	0.0179968i
$393$	−15.8493	+	31.2986i	−0.799492	+	1.57881i
$394$	30.9463	+	10.0551i	1.55905	+	0.506567i
$395$		0			0
$396$	3.93585	−	5.47441i	0.197784	−	0.275099i
$397$	−31.3810	−	15.9894i	−1.57497	−	0.802487i	−0.575090	−	0.818090i	$-0.695033\pi$
$397$	−31.3810	−	15.9894i	−1.57497	−	0.802487i	−0.999878	+	0.0156032i	$0.995033\pi$
$398$	−14.2921	+	2.26365i	−0.716400	+	0.113467i
$399$	−0.320841	−	0.979135i	−0.0160621	−	0.0490181i
$400$		0			0
$401$		−	1.91078i		−	0.0954199i	−0.998861	−	0.0477099i	$-0.984808\pi$
$401$		−	1.91078i		−	0.0954199i	0.998861	−	0.0477099i	$-0.0151923\pi$
$402$	7.62911	+	14.8812i	0.380505	+	0.742205i
$403$	−15.2045	+	29.8405i	−0.757391	+	1.48646i
$404$	−4.30224	−	13.2409i	−0.214045	−	0.658761i
$405$		0			0
$406$	−0.948291	+	2.91854i	−0.0470629	+	0.144845i
$407$	−1.54555	−	1.54555i	−0.0766102	−	0.0766102i
$408$	−5.84220	+	5.87139i	−0.289232	+	0.290677i
$409$	−21.1310	−	29.0844i	−1.04486	−	1.43813i	−0.893179	−	0.449701i	$-0.851531\pi$
$409$	−21.1310	−	29.0844i	−1.04486	−	1.43813i	−0.151683	−	0.988429i	$-0.548469\pi$
$410$		0			0
$411$	5.94246	−	18.4453i	0.293120	−	0.909841i
$412$	−0.864873	+	5.46060i	−0.0426093	+	0.269024i
$413$	−0.0225167	+	0.142165i	−0.00110797	+	0.00699546i
$414$	−0.00646171	−	1.29627i	−0.000317575	−	0.0637081i
$415$		0			0
$416$	−23.9615	−	32.9801i	−1.17481	−	1.61698i
$417$	4.19614	+	4.17528i	0.205486	+	0.204464i
$418$	0.291801	+	0.291801i	0.0142724	+	0.0142724i
$419$	6.87568	−	21.1612i	0.335899	−	1.03379i	−0.630378	−	0.776288i	$-0.717100\pi$
$419$	6.87568	−	21.1612i	0.335899	−	1.03379i	0.966277	−	0.257503i	$-0.0828998\pi$
$420$		0			0
$421$	5.74528	+	17.6821i	0.280008	+	0.861775i	0.987851	+	0.155405i	$0.0496684\pi$
$421$	5.74528	+	17.6821i	0.280008	+	0.861775i	−0.707843	+	0.706370i	$0.750332\pi$
$422$	4.48375	−	8.79986i	0.218266	−	0.428371i
$423$	19.4064	−	19.6008i	0.943569	−	0.953024i
$424$			10.6418i			0.516809i
$425$		0			0
$426$	−11.4113	+	3.73922i	−0.552878	+	0.181166i
$427$	−10.8811	+	1.72339i	−0.526572	+	0.0834007i
$428$	−1.03636	−	0.528053i	−0.0500945	−	0.0255244i
$429$	−4.79255	−	6.56192i	−0.231386	−	0.316813i
$430$		0			0
$431$	14.0978	+	4.58064i	0.679065	+	0.220642i	0.628186	−	0.778063i	$-0.283798\pi$
$431$	14.0978	+	4.58064i	0.679065	+	0.220642i	0.0508791	+	0.998705i	$0.483798\pi$
$432$	−2.50838	−	15.1054i	−0.120685	−	0.726760i
$433$	7.60685	−	3.87588i	0.365562	−	0.186263i	−0.261554	−	0.965189i	$-0.584235\pi$
$433$	7.60685	−	3.87588i	0.365562	−	0.186263i	0.627116	+	0.778926i	$0.284235\pi$
$434$	−31.4949	+	22.8824i	−1.51181	+	1.09839i
$435$		0			0
$436$	−9.85524	−	7.16025i	−0.471980	−	0.342914i
$437$	0.0430072	+	0.00681168i	0.00205731	+	0.000325847i
$438$	−6.59799	−	40.9965i	−0.315264	−	1.95889i
$439$	4.12954	−	5.68383i	0.197092	−	0.271274i	−0.699020	−	0.715103i	$-0.746380\pi$
$439$	4.12954	−	5.68383i	0.197092	−	0.271274i	0.896112	+	0.443828i	$0.146380\pi$
$440$		0			0
$441$	−0.786073	+	2.46096i	−0.0374320	+	0.117188i
$442$	25.4696	+	49.9868i	1.21146	+	2.37763i
$443$	−4.70856	+	4.70856i	−0.223711	+	0.223711i	−0.810059	−	0.586348i	$-0.800565\pi$
$443$	−4.70856	+	4.70856i	−0.223711	+	0.223711i	0.586348	+	0.810059i	$0.300565\pi$
$444$	9.97026	−	0.0248500i	0.473168	−	0.00117933i
$445$		0			0
$446$	−33.3943	+	10.8505i	−1.58127	+	0.513785i
$447$	1.29612	−	8.31752i	0.0613046	−	0.393405i
$448$	−4.82782	−	30.4817i	−0.228093	−	1.44012i
$449$	−27.1755			−1.28249			−0.641245	−	0.767336i	$-0.721582\pi$
$449$	−27.1755			−1.28249			−0.641245	+	0.767336i	$0.721582\pi$
$450$		0			0
$451$	−6.85577			−0.322825
$452$	2.20527	+	13.9235i	0.103727	+	0.654907i
$453$	2.26181	−	14.5146i	0.106269	−	0.681954i
$454$	43.7298	−	14.2087i	2.05234	−	0.666846i
$455$		0			0
$456$	−0.334933		0.000834792i	−0.0156847		3.90927e-5i
$457$	2.13051	−	2.13051i	0.0996610	−	0.0996610i	−0.655518	−	0.755179i	$-0.727550\pi$
$457$	2.13051	−	2.13051i	0.0996610	−	0.0996610i	0.755179	+	0.655518i	$0.227550\pi$
$458$	−14.8472	−	29.1392i	−0.693764	−	1.36159i
$459$	0.203855	+	27.2629i	0.00951512	+	1.27252i
$460$		0			0
$461$	19.4302	−	26.7433i	0.904953	−	1.24556i	−0.0639082	−	0.997956i	$-0.520356\pi$
$461$	19.4302	−	26.7433i	0.904953	−	1.24556i	0.968861	−	0.247605i	$-0.0796435\pi$
$462$	−1.50083	−	9.32538i	−0.0698249	−	0.433856i
$463$	−14.4917	−	2.29527i	−0.673488	−	0.106670i	−0.189683	−	0.981845i	$-0.560746\pi$
$463$	−14.4917	−	2.29527i	−0.673488	−	0.106670i	−0.483806	+	0.875175i	$0.660746\pi$
$464$	−1.23933	−	0.900429i	−0.0575346	−	0.0418014i
$465$		0			0
$466$	9.51249	−	6.91123i	0.440658	−	0.320156i
$467$	−0.0405649	+	0.0206689i	−0.00187712	+	0.000956441i	−0.454929	−	0.890528i	$-0.650335\pi$
$467$	−0.0405649	+	0.0206689i	−0.00187712	+	0.000956441i	0.453052	+	0.891484i	$0.350335\pi$
$468$	36.6377	+	5.61578i	1.69358	+	0.259589i
$469$	12.2280	+	3.97311i	0.564636	+	0.183461i
$470$		0			0
$471$	15.8355	+	21.6818i	0.729661	+	0.999047i
$472$	0.0416891	+	0.0212417i	0.00191890	+	0.000977726i
$473$	−0.666935	+	0.105632i	−0.0306657	+	0.00485697i
$474$	−14.2428	+	4.66705i	−0.654194	+	0.214365i
$475$		0			0
$476$			35.7904i			1.64045i
$477$	24.8920	+	24.6451i	1.13973	+	1.12842i
$478$	17.7042	−	34.7465i	0.809772	−	1.58927i
$479$	1.78148	+	5.48284i	0.0813980	+	0.250517i	0.983471	−	0.181067i	$-0.0579549\pi$
$479$	1.78148	+	5.48284i	0.0813980	+	0.250517i	−0.902073	+	0.431584i	$0.857955\pi$
$480$		0			0
$481$	3.71311	−	11.4278i	0.169303	−	0.521061i
$482$	−19.2543	−	19.2543i	−0.877009	−	0.877009i
$483$	−0.706487	−	0.702974i	−0.0321463	−	0.0319864i
$484$	−14.5098	−	19.9710i	−0.659536	−	0.907773i
$485$		0			0
$486$	26.7907	+	18.9591i	1.21525	+	0.860001i
$487$	−1.30341	+	8.22938i	−0.0590629	+	0.372909i	0.940398	+	0.340076i	$0.110453\pi$
$487$	−1.30341	+	8.22938i	−0.0590629	+	0.372909i	−0.999461	+	0.0328326i	$0.989547\pi$
$488$	−0.560214	+	3.53705i	−0.0253597	+	0.160115i
$489$	−9.48419	+	29.4388i	−0.428890	+	1.33127i
$490$		0			0
$491$	1.38128	+	1.90117i	0.0623362	+	0.0857985i	0.839047	−	0.544059i	$-0.183113\pi$
$491$	1.38128	+	1.90117i	0.0623362	+	0.0857985i	−0.776711	+	0.629858i	$0.783113\pi$
$492$	22.0580	−	22.1682i	0.994449	−	0.999419i
$493$	1.92868	+	1.92868i	0.0868635	+	0.0868635i
$494$	−0.701036	+	2.15757i	−0.0315411	+	0.0970735i
$495$		0			0
$496$	−6.00533	−	18.4825i	−0.269647	−	0.829889i
$497$	−4.19148	+	8.22624i	−0.188013	+	0.368997i
$498$	26.0835	+	50.8779i	1.16883	+	2.27989i
$499$		−	14.4704i		−	0.647786i	−0.946094	−	0.323893i	$-0.895008\pi$
$499$		−	14.4704i		−	0.647786i	0.946094	−	0.323893i	$-0.104992\pi$
$500$		0			0
$501$	4.97018	+	15.1679i	0.222051	+	0.677652i
$502$	−9.78798	+	1.55026i	−0.436859	+	0.0691917i
$503$	7.10512	+	3.62024i	0.316802	+	0.161419i	0.605160	−	0.796104i	$-0.293109\pi$
$503$	7.10512	+	3.62024i	0.316802	+	0.161419i	−0.288358	+	0.957523i	$0.593109\pi$
$504$	6.22443	+	4.47508i	0.277258	+	0.199336i
$505$		0			0
$506$	0.379627	+	0.123348i	0.0168765	+	0.00548351i
$507$	10.0083	−	19.7640i	0.444484	−	0.877750i
$508$	28.1934	−	14.3652i	1.25088	−	0.637355i
$509$	31.5666	−	22.9345i	1.39917	−	1.01655i	0.404377	−	0.914592i	$-0.367488\pi$
$509$	31.5666	−	22.9345i	1.39917	−	1.01655i	0.994788	−	0.101961i	$-0.0325115\pi$
$510$		0			0
$511$	−25.8283	−	18.7654i	−1.14258	−	0.830131i
$512$	28.6692	+	4.54076i	1.26701	+	0.200675i
$513$	−0.773715	+	0.785373i	−0.0341604	+	0.0346751i
$514$	−19.8594	+	27.3341i	−0.875961	+	1.20566i
$515$		0			0
$516$	1.80425	−	2.49640i	0.0794279	−	0.109898i
$517$	3.85596	+	7.56775i	0.169585	+	0.332829i
$518$	9.87637	−	9.87637i	0.433943	−	0.433943i
$519$	−0.0543614	−	21.8108i	−0.00238620	−	0.957386i
$520$		0			0
$521$	−19.4591	+	6.32266i	−0.852521	+	0.277001i	−0.702501	−	0.711682i	$-0.747934\pi$
$521$	−19.4591	+	6.32266i	−0.852521	+	0.277001i	−0.150019	+	0.988683i	$0.547934\pi$
$522$	3.24048	−	0.529813i	0.141832	−	0.0231893i
$523$	−1.61103	−	10.1716i	−0.0704454	−	0.444775i	−0.997549	−	0.0699699i	$-0.977710\pi$
$523$	−1.61103	−	10.1716i	−0.0704454	−	0.444775i	0.927104	−	0.374805i	$-0.122290\pi$
$524$	49.2782			2.15273
$525$		0			0
$526$	−15.0560			−0.656473
$527$	5.41293	+	34.1759i	0.235791	+	1.48872i
$528$	4.65887	+	0.725994i	0.202751	+	0.0315949i
$529$	−21.8342	+	7.09438i	−0.949315	+	0.308451i
$530$		0			0
$531$	0.146233	−	0.0483213i	0.00634599	−	0.00209697i
$532$	−1.02338	+	1.02338i	−0.0443690	+	0.0443690i
$533$	−17.1104	−	33.5810i	−0.741132	−	1.45455i
$534$	−22.8200	−	16.4930i	−0.987519	−	0.713721i
$535$		0			0
$536$	2.45662	−	3.38124i	0.106110	−	0.146047i
$537$	17.1494	−	2.76003i	0.740052	−	0.119104i
$538$	2.38721	+	0.378097i	0.102920	+	0.0163009i
$539$	−0.643590	−	0.467595i	−0.0277214	−	0.0201408i
$540$		0			0
$541$	25.8243	−	18.7625i	1.11028	−	0.806662i	0.127568	−	0.991830i	$-0.459283\pi$
$541$	25.8243	−	18.7625i	1.11028	−	0.806662i	0.982707	+	0.185167i	$0.0592827\pi$
$542$	18.0487	−	9.19628i	0.775259	−	0.395014i
$543$	5.12092	+	2.59318i	0.219760	+	0.111284i
$544$	−40.0567	−	13.0152i	−1.71742	−	0.558022i
$545$		0			0
$546$	41.9319	−	30.6253i	1.79452	−	1.31064i
$547$	27.7417	+	14.1351i	1.18615	+	0.604373i	0.931882	−	0.362761i	$-0.118166\pi$
$547$	27.7417	+	14.1351i	1.18615	+	0.604373i	0.254267	+	0.967134i	$0.418166\pi$
$548$	−26.8850	+	4.25817i	−1.14847	+	0.181900i
$549$	6.97610	+	9.50181i	0.297733	+	0.405527i
$550$		0			0
$551$			0.110296i			0.00469876i
$552$	−0.288295	+	0.147800i	−0.0122706	+	0.00629078i
$553$	−5.23153	+	10.2675i	−0.222467	+	0.436617i
$554$	14.9376	+	45.9732i	0.634637	+	1.95321i
$555$		0			0
$556$	2.56938	−	7.90774i	0.108966	−	0.335363i
$557$	−13.9418	−	13.9418i	−0.590734	−	0.590734i	0.347096	−	0.937830i	$-0.387168\pi$
$557$	−13.9418	−	13.9418i	−0.590734	−	0.590734i	−0.937830	+	0.347096i	$0.887168\pi$
$558$	37.2082	+	18.7255i	1.57515	+	0.792713i
$559$	−2.18192	−	3.00315i	−0.0922854	−	0.127020i
$560$		0			0
$561$	−7.99084	−	2.57438i	−0.337373	−	0.108690i
$562$	3.07161	−	19.3934i	0.129568	−	0.818060i
$563$	0.662743	−	4.18439i	0.0279313	−	0.176351i	−0.969779	−	0.243985i	$-0.921545\pi$
$563$	0.662743	−	4.18439i	0.0279313	−	0.176351i	0.997710	+	0.0676342i	$0.0215451\pi$
$564$	−36.8767	−	11.8804i	−1.55279	−	0.500256i
$565$		0			0
$566$	41.1692	+	56.6646i	1.73047	+	2.38179i
$567$	24.8827	−	4.19574i	1.04498	−	0.176204i
$568$	2.12215	+	2.12215i	0.0890433	+	0.0890433i
$569$	−11.0678	+	34.0631i	−0.463985	+	1.42800i	0.396270	+	0.918134i	$0.370304\pi$
$569$	−11.0678	+	34.0631i	−0.463985	+	1.42800i	−0.860255	+	0.509864i	$0.829696\pi$
$570$		0			0
$571$	−7.59320	−	23.3695i	−0.317766	−	0.977982i	−0.974601	−	0.223948i	$-0.928105\pi$
$571$	−7.59320	−	23.3695i	−0.317766	−	0.977982i	0.656835	−	0.754034i	$-0.271895\pi$
$572$	−5.18166	+	10.1696i	−0.216656	+	0.425212i
$573$	14.4309	−	7.39829i	0.602861	−	0.309068i
$574$		−	43.8096i		−	1.82858i
$575$		0			0
$576$	−26.6179	+	19.5425i	−1.10908	+	0.814270i
$577$	−27.6840	+	4.38472i	−1.15250	+	0.182538i	−0.703300	−	0.710893i	$-0.748291\pi$
$577$	−27.6840	+	4.38472i	−1.15250	+	0.182538i	−0.449200	+	0.893431i	$0.648291\pi$
$578$	19.7538	+	10.0651i	0.821649	+	0.418651i
$579$	3.08101	−	2.25024i	0.128042	−	0.0935166i
$580$		0			0
$581$	41.8069	+	13.5839i	1.73444	+	0.563554i
$582$	28.7336	+	14.5504i	1.19105	+	0.603133i
$583$	−9.61066	+	4.89688i	−0.398033	+	0.202808i
$584$	−8.39588	+	6.09997i	−0.347424	+	0.252418i
$585$		0			0
$586$	47.0924	+	34.2146i	1.94537	+	1.41339i
$587$	−36.2186	−	5.73646i	−1.49490	−	0.236769i	−0.645191	−	0.764021i	$-0.723222\pi$
$587$	−36.2186	−	5.73646i	−1.49490	−	0.236769i	−0.849709	+	0.527252i	$0.823222\pi$
$588$	3.58268	−	0.576598i	0.147747	−	0.0237785i
$589$	−0.822435	+	1.13198i	−0.0338878	+	0.0466426i
$590$		0			0
$591$	−21.6951	−	15.6800i	−0.892419	−	0.644988i
$592$	3.16541	+	6.21248i	0.130098	+	0.255331i
$593$	−18.0099	+	18.0099i	−0.739577	+	0.739577i	−0.972496	−	0.232919i	$-0.925172\pi$
$593$	−18.0099	+	18.0099i	−0.739577	+	0.739577i	0.232919	+	0.972496i	$0.425172\pi$
$594$	−8.13162	+	6.00138i	−0.333645	+	0.246239i
$595$		0			0
$596$	−11.2453	+	3.65382i	−0.460625	+	0.149666i
$597$	11.7621	+	1.83289i	0.481391	+	0.0750154i
$598$	0.343273	+	2.16734i	0.0140375	+	0.0886292i
$599$	−16.9050			−0.690719			−0.345360	−	0.938470i	$-0.612243\pi$
$599$	−16.9050			−0.690719			−0.345360	+	0.938470i	$0.612243\pi$
$600$		0			0
$601$	23.5312			0.959857			0.479929	−	0.877308i	$-0.340663\pi$
$601$	23.5312			0.959857			0.479929	+	0.877308i	$0.340663\pi$
$602$	−0.675009	−	4.26184i	−0.0275113	−	0.173700i
$603$	−2.21979	−	13.5768i	−0.0903968	−	0.552891i
$604$	−19.6237	+	6.37613i	−0.798477	+	0.259441i
$605$		0			0
$606$	0.0520132	+	20.8686i	0.00211289	+	0.847730i
$607$	−17.3958	+	17.3958i	−0.706072	+	0.706072i	−0.965707	−	0.259635i	$-0.916398\pi$
$607$	−17.3958	+	17.3958i	−0.706072	+	0.706072i	0.259635	+	0.965707i	$0.416398\pi$
$608$	−0.773212	−	1.51751i	−0.0313579	−	0.0615433i
$609$	1.47877	−	2.04606i	0.0599229	−	0.0829106i
$610$		0			0
$611$	−27.4449	+	37.7746i	−1.11030	+	1.52820i
$612$	34.0342	−	17.5556i	1.37575	−	0.709641i
$613$	26.8108	+	4.24641i	1.08288	+	0.171511i	0.672273	−	0.740303i	$-0.265318\pi$
$613$	26.8108	+	4.24641i	1.08288	+	0.171511i	0.410604	+	0.911814i	$0.365318\pi$
$614$	40.8132	+	29.6525i	1.64708	+	1.19668i
$615$		0			0
$616$	−1.90979	+	1.38755i	−0.0769478	+	0.0559058i
$617$	8.56494	−	4.36406i	0.344812	−	0.175690i	−0.273005	−	0.962013i	$-0.588017\pi$
$617$	8.56494	−	4.36406i	0.344812	−	0.175690i	0.617816	+	0.786322i	$0.288017\pi$
$618$	3.74385	−	7.39322i	0.150600	−	0.297399i
$619$	−34.6660	−	11.2637i	−1.39334	−	0.452725i	−0.486311	−	0.873786i	$-0.661658\pi$
$619$	−34.6660	−	11.2637i	−1.39334	−	0.452725i	−0.907032	+	0.421061i	$0.861658\pi$
$620$		0			0
$621$	−0.321941	+	1.01664i	−0.0129191	+	0.0407962i
$622$	−5.43852	−	2.77106i	−0.218065	−	0.111110i
$623$	−21.3813	+	3.38646i	−0.856622	+	0.135676i
$624$	8.07136	+	24.6320i	0.323113	+	0.986071i
$625$		0			0
$626$		−	28.6756i		−	1.14611i
$627$	−0.154876	−	0.302097i	−0.00618514	−	0.0120646i
$628$	17.1212	−	33.6023i	0.683210	−	1.34088i
$629$	−3.83629	−	11.8069i	−0.152963	−	0.470771i
$630$		0			0
$631$	−3.21512	+	9.89511i	−0.127992	+	0.393918i	−0.994434	−	0.105359i	$-0.966401\pi$
$631$	−3.21512	+	9.89511i	−0.127992	+	0.393918i	0.866443	+	0.499277i	$0.166401\pi$
$632$	2.64873	+	2.64873i	0.105361	+	0.105361i
$633$	−5.73076	+	5.75940i	−0.227777	+	0.228916i
$634$	37.4260	+	51.5125i	1.48638	+	2.04582i
$635$		0			0
$636$	15.0875	−	46.8315i	0.598260	−	1.85699i
$637$	0.684132	−	4.31944i	0.0271063	−	0.171143i
$638$	−0.158169	+	0.998639i	−0.00626197	+	0.0395365i
$639$	9.87855	−	0.0492431i	0.390789	−	0.00194803i
$640$		0			0
$641$	−4.96036	−	6.82734i	−0.195922	−	0.269664i	0.699741	−	0.714397i	$-0.253299\pi$
$641$	−4.96036	−	6.82734i	−0.195922	−	0.269664i	−0.895663	+	0.444733i	$0.853299\pi$
$642$	1.23589	+	1.22974i	0.0487765	+	0.0485340i
$643$	−32.9970	−	32.9970i	−1.30127	−	1.30127i	−0.927534	−	0.373739i	$-0.878076\pi$
$643$	−32.9970	−	32.9970i	−1.30127	−	1.30127i	−0.373739	−	0.927534i	$-0.621924\pi$
$644$	−0.432596	+	1.33139i	−0.0170467	+	0.0524642i
$645$		0			0
$646$	0.724293	+	2.22914i	0.0284969	+	0.0877045i
$647$	−14.1573	+	27.7853i	−0.556582	+	1.09235i	0.425686	+	0.904871i	$0.360033\pi$
$647$	−14.1573	+	27.7853i	−0.556582	+	1.09235i	−0.982268	+	0.187482i	$0.939967\pi$
$648$	1.20235	−	8.11408i	0.0472327	−	0.318751i
$649$			0.0474243i			0.00186157i
$650$		0			0
$651$	30.4336	−	9.97242i	1.19279	−	0.390850i
$652$	42.9085	−	6.79605i	1.68043	−	0.266154i
$653$	17.6616	+	8.99906i	0.691153	+	0.352160i	0.764030	−	0.645181i	$-0.223218\pi$
$653$	17.6616	+	8.99906i	0.691153	+	0.352160i	−0.0728766	+	0.997341i	$0.523218\pi$
$654$	10.7695	+	14.7456i	0.421122	+	0.576597i
$655$		0			0
$656$	20.7992	+	6.75808i	0.812074	+	0.263859i
$657$	−5.17554	+	33.7656i	−0.201917	+	1.31732i
$658$	−48.3594	+	24.6403i	−1.88524	+	0.960580i
$659$	−25.0740	+	18.2173i	−0.976745	+	0.709647i	−0.956979	−	0.290158i	$-0.906292\pi$
$659$	−25.0740	+	18.2173i	−0.976745	+	0.709647i	−0.0197663	+	0.999805i	$0.506292\pi$
$660$		0			0
$661$	4.14459	+	3.01122i	0.161206	+	0.117123i	0.665464	−	0.746430i	$-0.268234\pi$
$661$	4.14459	+	3.01122i	0.161206	+	0.117123i	−0.504258	+	0.863553i	$0.668234\pi$
$662$	−20.0364	−	3.17345i	−0.778735	−	0.123339i
$663$	−7.33338	−	45.5658i	−0.284805	−	1.76963i
$664$	8.39904	−	11.5603i	0.325946	−	0.448626i
$665$		0			0
$666$	−14.2362	−	4.54729i	−0.551642	−	0.176204i
$667$	0.0484346	+	0.0950582i	0.00187539	+	0.00368067i
$668$	15.8532	−	15.8532i	0.613380	−	0.613380i
$669$	28.8857	−	0.0719950i	1.11678	−	0.00278349i
$670$		0			0
$671$	−3.45213	+	1.12167i	−0.133268	+	0.0433014i
$672$	−6.00222	+	38.5176i	−0.231541	+	1.48585i
$673$	2.89759	+	18.2947i	0.111694	+	0.705208i	0.978451	+	0.206478i	$0.0662002\pi$
$673$	2.89759	+	18.2947i	0.111694	+	0.705208i	−0.866757	+	0.498730i	$0.833800\pi$
$674$	16.5913			0.639075
$675$		0			0
$676$	−31.1175			−1.19683
$677$	−3.57266	−	22.5569i	−0.137308	−	0.866931i	−0.956143	−	0.292901i	$-0.905379\pi$
$677$	−3.57266	−	22.5569i	−0.137308	−	0.866931i	0.818834	−	0.574030i	$-0.194621\pi$
$678$	3.25353	−	20.8786i	0.124951	−	0.801838i
$679$	23.5507	−	7.65210i	0.903795	−	0.293661i
$680$		0			0
$681$	−37.8257	+	0.0942773i	−1.44949	+	0.00361271i
$682$	−9.06980	+	9.06980i	−0.347300	+	0.347300i
$683$	−16.9964	−	33.3574i	−0.650351	−	1.27639i	−0.946949	−	0.321383i	$-0.895852\pi$
$683$	−16.9964	−	33.3574i	−0.650351	−	1.27639i	0.296598	−	0.955002i	$-0.404148\pi$
$684$	1.47514	+	0.471184i	0.0564032	+	0.0180162i
$685$		0			0
$686$	−21.3006	+	29.3178i	−0.813261	+	1.11936i
$687$	4.27491	+	26.5621i	0.163098	+	1.01341i
$688$	2.12750	+	0.336962i	0.0811100	+	0.0128466i
$689$	−47.9719	−	34.8536i	−1.82758	−	1.32782i
$690$		0			0
$691$	−27.2396	+	19.7907i	−1.03624	+	0.752875i	−0.969549	−	0.244899i	$-0.921245\pi$
$691$	−27.2396	+	19.7907i	−1.03624	+	0.752875i	−0.0666945	+	0.997773i	$0.521245\pi$
$692$	−27.2969	+	13.9085i	−1.03767	+	0.528721i
$693$	−1.17727	+	7.68058i	−0.0447207	+	0.291761i
$694$	6.56060	+	2.13167i	0.249037	+	0.0809170i
$695$		0			0
$696$	−0.484007	−	0.662698i	−0.0183462	−	0.0251195i
$697$	−34.6950	−	17.6780i	−1.31417	−	0.669602i
$698$	−21.1691	+	3.35286i	−0.801263	+	0.126908i
$699$	−9.19194	+	3.01199i	−0.347671	+	0.113924i
$700$		0			0
$701$		−	41.4824i		−	1.56677i	−0.621538	−	0.783384i	$-0.713492\pi$
$701$		−	41.4824i		−	1.56677i	0.621538	−	0.783384i	$-0.286508\pi$
$702$	−49.6906	−	24.8524i	−1.87545	−	0.937992i
$703$	0.227908	−	0.447294i	0.00859570	−	0.0168700i
$704$	−3.14218	−	9.67062i	−0.118425	−	0.364475i
$705$		0			0
$706$	−1.20099	+	3.69628i	−0.0452000	+	0.139111i
$707$	11.3454	+	11.3454i	0.426687	+	0.426687i
$708$	−0.153347	−	0.152584i	−0.00576313	−	0.00573447i
$709$	12.5345	+	17.2522i	0.470742	+	0.647921i	0.976693	−	0.214641i	$-0.0688582\pi$
$709$	12.5345	+	17.2522i	0.470742	+	0.647921i	−0.505951	+	0.862562i	$0.668858\pi$
$710$		0			0
$711$	12.3298	−	0.0614621i	0.462402	−	0.00230501i
$712$	−1.10082	+	6.95030i	−0.0412550	+	0.260474i
$713$	−0.211722	+	1.33676i	−0.00792903	+	0.0500620i
$714$	16.4508	−	51.0630i	0.615655	−	1.91098i
$715$		0			0
$716$	−14.3411	−	19.7388i	−0.535951	−	0.737673i
$717$	−22.6281	+	22.7411i	−0.845060	+	0.849283i
$718$	39.7520	+	39.7520i	1.48353	+	1.48353i
$719$	−8.68648	+	26.7342i	−0.323951	+	0.997019i	0.647961	+	0.761674i	$0.275622\pi$
$719$	−8.68648	+	26.7342i	−0.323951	+	0.997019i	−0.971912	+	0.235345i	$0.924378\pi$
$720$		0			0
$721$	−1.96890	−	6.05966i	−0.0733258	−	0.225674i
$722$	18.1181	−	35.5588i	0.674287	−	1.32336i
$723$	10.2194	+	19.9337i	0.380063	+	0.741342i
$724$		−	8.06265i		−	0.299646i
$725$		0			0
$726$	11.5219	+	35.1624i	0.427618	+	1.30500i
$727$	17.7949	−	2.81844i	0.659977	−	0.104530i	0.182543	−	0.983198i	$-0.441567\pi$
$727$	17.7949	−	2.81844i	0.659977	−	0.104530i	0.477434	+	0.878668i	$0.341567\pi$
$728$	−11.5629	−	5.89158i	−0.428549	−	0.218356i
$729$	−16.1951	−	21.6037i	−0.599817	−	0.800137i
$730$		0			0
$731$	−3.64754	−	1.18516i	−0.134909	−	0.0438347i
$732$	7.48007	−	14.7714i	0.276472	−	0.545966i
$733$	−20.2674	+	10.3267i	−0.748592	+	0.381427i	−0.786286	−	0.617863i	$-0.787999\pi$
$733$	−20.2674	+	10.3267i	−0.748592	+	0.381427i	0.0376939	+	0.999289i	$0.487999\pi$
$734$	52.1735	−	37.9063i	1.92576	−	1.39915i
$735$		0			0
$736$	−1.33278	−	0.968323i	−0.0491270	−	0.0356929i
$737$	4.18406	+	0.662690i	0.154122	+	0.0244105i
$738$	−41.6600	+	21.4891i	−1.53352	+	0.791023i
$739$	17.5716	−	24.1852i	0.646382	−	0.889669i	−0.352554	−	0.935792i	$-0.614687\pi$
$739$	17.5716	−	24.1852i	0.646382	−	0.889669i	0.998936	+	0.0461231i	$0.0146866\pi$
$740$		0			0
$741$	1.09320	−	1.51258i	0.0401598	−	0.0555659i
$742$	−31.2920	−	61.4140i	−1.14876	−	2.25458i
$743$	−35.7229	+	35.7229i	−1.31055	+	1.31055i	−0.389537	+	0.921011i	$0.627365\pi$
$743$	−35.7229	+	35.7229i	−1.31055	+	1.31055i	−0.921011	+	0.389537i	$0.872635\pi$
$744$	−0.0259471	−	10.4104i	−0.000951268	−	0.381665i
$745$		0			0
$746$	−3.75018	+	1.21851i	−0.137304	+	0.0446127i
$747$	−7.58935	−	46.4185i	−0.277680	−	1.69836i
$748$	1.84471	+	11.6471i	0.0674494	+	0.425859i
$749$	1.34046			0.0489792
$750$		0			0
$751$	43.1672			1.57520			0.787598	−	0.616190i	$-0.211325\pi$
$751$	43.1672			1.57520			0.787598	+	0.616190i	$0.211325\pi$
$752$	−4.23842	−	26.7603i	−0.154559	−	0.975848i
$753$	8.05528	+	1.25526i	0.293551	+	0.0457442i
$754$	−5.28629	+	1.71762i	−0.192515	+	0.0625521i
$755$		0			0
$756$	−21.0474	−	28.5184i	−0.765488	−	1.03721i
$757$	12.8580	−	12.8580i	0.467331	−	0.467331i	−0.433718	−	0.901049i	$-0.642798\pi$
$757$	12.8580	−	12.8580i	0.467331	−	0.467331i	0.901049	+	0.433718i	$0.142798\pi$
$758$	22.2045	+	43.5789i	0.806505	+	1.58286i
$759$	−0.266140	−	0.192351i	−0.00966028	−	0.00698189i
$760$		0			0
$761$	8.40118	−	11.5632i	0.304543	−	0.419167i	−0.629127	−	0.777303i	$-0.716587\pi$
$761$	8.40118	−	11.5632i	0.304543	−	0.419167i	0.933670	+	0.358136i	$0.116587\pi$
$762$	−46.8270	+	7.53635i	−1.69636	+	0.273013i
$763$	13.8660	+	2.19616i	0.501983	+	0.0795063i
$764$	−18.4283	−	13.3889i	−0.666712	−	0.484395i
$765$		0			0
$766$	−56.4674	+	41.0260i	−2.04025	+	1.48233i
$767$	−0.232294	+	0.118360i	−0.00838765	+	0.00427372i
$768$	−10.8515	−	5.49507i	−0.391568	−	0.198286i
$769$	27.6008	+	8.96803i	0.995309	+	0.323395i	0.760989	−	0.648764i	$-0.224714\pi$
$769$	27.6008	+	8.96803i	0.995309	+	0.323395i	0.234319	+	0.972160i	$0.424714\pi$
$770$		0			0
$771$	22.4458	−	16.3934i	0.808364	−	0.590395i
$772$	−4.77491	−	2.43294i	−0.171853	−	0.0875633i
$773$	8.96649	−	1.42015i	0.322502	−	0.0510793i	0.00691550	−	0.999976i	$-0.497799\pi$
$773$	8.96649	−	1.42015i	0.322502	−	0.0510793i	0.315587	+	0.948897i	$0.397799\pi$
$774$	−3.72162	+	2.73236i	−0.133771	+	0.0982128i
$775$		0			0
$776$		−	8.04949i		−	0.288960i
$777$	−10.2249	+	5.24197i	−0.366815	+	0.188055i
$778$	−29.1719	+	57.2531i	−1.04586	+	2.05262i
$779$	−0.486577	−	1.49753i	−0.0174334	−	0.0536546i
$780$		0			0
$781$	−0.940009	+	2.89305i	−0.0336362	+	0.103522i
$782$	1.60312	+	1.60312i	0.0573275	+	0.0573275i
$783$	−2.67102	−	0.402599i	−0.0954544	−	0.0143877i
$784$	1.49161	+	2.05303i	0.0532718	+	0.0733223i
$785$		0			0
$786$	−70.3063	−	22.6503i	−2.50774	−	0.807911i
$787$	−5.37304	+	33.9240i	−0.191528	+	1.20926i	0.685229	+	0.728328i	$0.259702\pi$
$787$	−5.37304	+	33.9240i	−0.191528	+	1.20926i	−0.876757	+	0.480934i	$0.840298\pi$
$788$	−5.88184	+	37.1365i	−0.209532	+	1.32293i
$789$	11.7892	+	3.79808i	0.419706	+	0.135215i
$790$		0			0
$791$	−9.54926	−	13.1434i	−0.339533	−	0.467327i
$792$	2.25623	+	1.13548i	0.0801718	+	0.0403474i
$793$	−14.1098	−	14.1098i	−0.501055	−	0.501055i
$794$	22.9146	−	70.5238i	0.813208	−	2.50280i
$795$		0			0
$796$	−5.16699	−	15.9024i	−0.183139	−	0.563644i
$797$	6.21933	−	12.2061i	0.220300	−	0.432363i	−0.754233	−	0.656607i	$-0.771991\pi$
$797$	6.21933	−	12.2061i	0.220300	−	0.432363i	0.974533	+	0.224244i	$0.0719911\pi$
$798$	1.93046	−	0.989686i	0.0683375	−	0.0350345i
$799$			48.2410i			1.70664i
$800$		0			0
$801$	13.7080	+	18.6710i	0.484349	+	0.659708i
$802$	3.97351	−	0.629342i	0.140309	−	0.0222228i
$803$	−9.37236	−	4.77546i	−0.330743	−	0.168522i
$804$	−15.6047	+	11.3970i	−0.550336	+	0.401942i
$805$		0			0
$806$	−67.0618	−	21.7897i	−2.36215	−	0.767509i
$807$	−1.77386	−	0.898264i	−0.0624428	−	0.0316204i
$808$	4.64714	−	2.36783i	0.163486	−	0.0833001i
$809$	−15.4929	+	11.2563i	−0.544702	+	0.395749i	−0.825828	−	0.563922i	$-0.809292\pi$
$809$	−15.4929	+	11.2563i	−0.544702	+	0.395749i	0.281126	+	0.959671i	$0.409292\pi$
$810$		0			0
$811$	24.0863	+	17.4997i	0.845785	+	0.614499i	0.923981	−	0.382439i	$-0.124916\pi$
$811$	24.0863	+	17.4997i	0.845785	+	0.614499i	−0.0781955	+	0.996938i	$0.524916\pi$
$812$	−3.50233	−	0.554715i	−0.122908	−	0.0194667i
$813$	−16.4524	+	2.64786i	−0.577012	+	0.0928645i
$814$	2.70496	−	3.72305i	0.0948087	−	0.130493i
$815$		0			0
$816$	21.7052	+	15.6872i	0.759833	+	0.549163i
$817$	−0.0704083	−	0.138184i	−0.00246327	−	0.00483445i
$818$	53.5217	−	53.5217i	1.87134	−	1.87134i
$819$	−40.5593	+	13.4024i	−1.41726	+	0.468318i
$820$		0			0
$821$	−12.5951	+	4.09240i	−0.439572	+	0.142826i	−0.520438	−	0.853899i	$-0.674231\pi$
$821$	−12.5951	+	4.09240i	−0.439572	+	0.142826i	0.0808659	+	0.996725i	$0.474231\pi$
$822$	40.3146	+	6.28225i	1.40613	+	0.219119i
$823$	0.267813	+	1.69091i	0.00933539	+	0.0589413i	0.991916	−	0.126894i	$-0.0405009\pi$
$823$	0.267813	+	1.69091i	0.00933539	+	0.0589413i	−0.982581	+	0.185835i	$0.940501\pi$
$824$	−2.07115			−0.0721520
$825$		0			0
$826$	−0.303050			−0.0105445
$827$	−4.13831	−	26.1282i	−0.143903	−	0.908568i	−0.948966	−	0.315379i	$-0.897868\pi$
$827$	−4.13831	−	26.1282i	−0.143903	−	0.908568i	0.805063	−	0.593189i	$-0.202132\pi$
$828$	1.47826	−	0.241692i	0.0513729	−	0.00839939i
$829$	−17.9708	+	5.83907i	−0.624152	+	0.202799i	−0.603983	−	0.796997i	$-0.706421\pi$
$829$	−17.9708	+	5.83907i	−0.624152	+	0.202799i	−0.0201694	+	0.999797i	$0.506421\pi$
$830$		0			0
$831$	−0.0991138	−	39.7662i	−0.00343822	−	1.37947i
$832$	39.5266	−	39.5266i	1.37034	−	1.37034i
$833$	−2.05130	−	4.02590i	−0.0710732	−	0.139489i
$834$	−7.30052	+	10.1011i	−0.252796	+	0.349774i
$835$		0			0
$836$	−0.280284	+	0.385778i	−0.00969382	+	0.0133424i
$837$	−24.4111	−	24.0487i	−0.843770	−	0.831246i
$838$	46.2697	+	7.32840i	1.59836	+	0.253155i
$839$	42.3961	+	30.8026i	1.46368	+	1.06342i	0.982386	+	0.186863i	$0.0598322\pi$
$839$	42.3961	+	30.8026i	1.46368	+	1.06342i	0.481292	+	0.876561i	$0.340168\pi$
$840$		0			0
$841$	23.2429	−	16.8869i	0.801478	−	0.582308i
$842$	−34.8781	+	17.7713i	−1.20198	+	0.612439i
$843$	−7.29737	+	14.4106i	−0.251335	+	0.496327i
$844$	10.8537	+	3.52659i	0.373601	+	0.121390i
$845$		0			0
$846$	47.1520	+	33.9001i	1.62112	+	1.16551i
$847$	25.3481	+	12.9155i	0.870970	+	0.443782i
$848$	33.9842	−	5.38258i	1.16702	−	0.184838i
$849$	−17.9420	−	54.7551i	−0.615768	−	1.87919i
$850$		0			0
$851$		−	0.485581i		−	0.0166455i
$852$	−6.33029	−	12.3477i	−0.216872	−	0.423026i
$853$	−5.07914	+	9.96838i	−0.173906	+	0.341311i	−0.961464	−	0.274930i	$-0.911345\pi$
$853$	−5.07914	+	9.96838i	−0.173906	+	0.341311i	0.787558	+	0.616241i	$0.211345\pi$
$854$	−7.16765	−	22.0598i	−0.245272	−	0.754870i
$855$		0			0
$856$	0.134650	−	0.414409i	0.00460223	−	0.0141642i
$857$	37.2269	+	37.2269i	1.27165	+	1.27165i	0.945224	+	0.326423i	$0.105843\pi$
$857$	37.2269	+	37.2269i	1.27165	+	1.27165i	0.326423	+	0.945224i	$0.394157\pi$
$858$	12.0672	−	12.1275i	0.411966	−	0.414025i
$859$	24.6352	+	33.9074i	0.840542	+	1.15691i	0.985868	+	0.167523i	$0.0535769\pi$
$859$	24.6352	+	33.9074i	0.840542	+	1.15691i	−0.145326	+	0.989384i	$0.546423\pi$
$860$		0			0
$861$	−11.0516	+	34.3039i	−0.376636	+	1.16907i
$862$	−4.88224	+	30.8253i	−0.166290	+	1.04991i
$863$	−1.61464	+	10.1944i	−0.0549630	+	0.347023i	0.944847	+	0.327513i	$0.106211\pi$
$863$	−1.61464	+	10.1944i	−0.0549630	+	0.347023i	−0.999810	+	0.0195098i	$0.993789\pi$
$864$	39.5718	−	13.1856i	1.34626	−	0.448582i
$865$		0			0
$866$	10.5654	+	14.5420i	0.359027	+	0.494158i
$867$	−12.9286	−	12.8643i	−0.439079	−	0.436895i
$868$	−31.8087	−	31.8087i	−1.07966	−	1.07966i
$869$	−1.17326	+	3.61092i	−0.0398001	+	0.122492i
$870$		0			0
$871$	7.19642	+	22.1483i	0.243841	+	0.750467i
$872$	2.07180	−	4.06614i	0.0701601	−	0.137697i
$873$	−18.8285	−	18.6417i	−0.637248	−	0.630926i
$874$			0.0916779i			0.00310105i
$875$		0			0
$876$	45.5964	−	14.9409i	1.54056	−	0.504807i
$877$	33.6506	−	5.32972i	1.13630	−	0.179972i	0.440187	−	0.897906i	$-0.354912\pi$
$877$	33.6506	−	5.32972i	1.13630	−	0.179972i	0.696111	+	0.717934i	$0.254912\pi$
$878$	13.1797	+	6.71542i	0.444795	+	0.226634i
$879$	−28.2433	−	38.6705i	−0.952622	−	1.30432i
$880$		0			0
$881$	−28.3863	−	9.22328i	−0.956360	−	0.310740i	−0.211063	−	0.977472i	$-0.567692\pi$
$881$	−28.3863	−	9.22328i	−0.956360	−	0.310740i	−0.745297	+	0.666732i	$0.767692\pi$
$882$	−5.37651	−	0.824104i	−0.181037	−	0.0277490i
$883$	50.1305	−	25.5428i	1.68703	−	0.859583i	0.697272	−	0.716806i	$-0.254397\pi$
$883$	50.1305	−	25.5428i	1.68703	−	0.859583i	0.989755	−	0.142777i	$-0.0456032\pi$
$884$	−52.4458	+	38.1041i	−1.76394	+	1.28158i
$885$		0			0
$886$	−11.3424	−	8.24072i	−0.381055	−	0.276852i
$887$	37.6688	+	5.96616i	1.26480	+	0.200324i	0.752562	−	0.658522i	$-0.228818\pi$
$887$	37.6688	+	5.96616i	1.26480	+	0.200324i	0.512234	+	0.858846i	$0.328818\pi$
$888$	0.593488	+	3.68763i	0.0199162	+	0.123749i
$889$	−21.4342	+	29.5016i	−0.718879	+	0.989452i
$890$		0			0
$891$	7.88117	−	2.64790i	0.264029	−	0.0887080i
$892$	−18.4201	−	36.1514i	−0.616749	−	1.21044i
$893$	−1.37938	+	1.37938i	−0.0461592	+	0.0461592i
$894$	17.7234	−	0.0441739i	0.592758	−	0.00147740i
$895$		0			0
$896$	18.9871	−	6.16928i	0.634315	−	0.206101i
$897$	0.277951	−	1.78367i	0.00928050	−	0.0595551i
$898$	−8.95061	−	56.5119i	−0.298686	−	1.88583i
$899$	−3.42823			−0.114338
$900$		0			0
$901$	−61.2636			−2.04099
$902$	−2.25804	−	14.2567i	−0.0751845	−	0.474696i
$903$	−0.546559	+	3.50740i	−0.0181884	+	0.116719i
$904$	−5.02259	+	1.63194i	−0.167049	+	0.0542774i
$905$		0			0
$906$	30.9283	−	0.0770860i	1.02752	−	0.00256101i
$907$	−9.39707	+	9.39707i	−0.312024	+	0.312024i	−0.845693	−	0.533669i	$-0.820813\pi$
$907$	−9.39707	+	9.39707i	−0.312024	+	0.312024i	0.533669	+	0.845693i	$0.320813\pi$
$908$	24.1210	+	47.3402i	0.800485	+	1.57104i
$909$	5.22366	−	16.3537i	0.173258	−	0.542418i
$910$		0			0
$911$	16.0441	−	22.0828i	0.531566	−	0.731637i	−0.455802	−	0.890081i	$-0.650648\pi$
$911$	16.0441	−	22.0828i	0.531566	−	0.731637i	0.987368	+	0.158444i	$0.0506476\pi$
$912$	0.172074	+	1.06918i	0.00569795	+	0.0354041i
$913$	14.3051	+	2.26570i	0.473429	+	0.0749838i
$914$	5.13214	+	3.72872i	0.169756	+	0.123335i
$915$		0			0
$916$	30.5727	−	22.2123i	1.01015	−	0.733916i
$917$	−50.6009	+	25.7824i	−1.67099	+	0.851411i
$918$	−56.6267	+	9.40333i	−1.86896	+	0.310356i
$919$	−34.4230	−	11.1847i	−1.13551	−	0.368949i	−0.319842	−	0.947471i	$-0.603630\pi$
$919$	−34.4230	−	11.1847i	−1.13551	−	0.368949i	−0.815667	+	0.578521i	$0.803630\pi$
$920$		0			0
$921$	−24.4774	−	33.5142i	−0.806557	−	1.10433i
$922$	62.0129	+	31.5971i	2.04228	+	1.04060i
$923$	−16.5168	+	2.61600i	−0.543657	+	0.0861068i
$924$	10.3717	−	3.39858i	0.341204	−	0.111805i
$925$		0			0
$926$		−	30.8918i		−	1.01517i
$927$	−4.79656	+	4.84462i	−0.157540	+	0.159118i
$928$	1.89446	−	3.71809i	0.0621887	−	0.122052i
$929$	−13.7579	−	42.3425i	−0.451383	−	1.38921i	−0.875330	−	0.483526i	$-0.839356\pi$
$929$	−13.7579	−	42.3425i	−0.451383	−	1.38921i	0.423948	−	0.905687i	$-0.360644\pi$
$930$		0			0
$931$	0.0564608	−	0.173769i	0.00185043	−	0.00569503i
$932$	9.60726	+	9.60726i	0.314696	+	0.314696i
$933$	3.55944	+	3.54174i	0.116531	+	0.115951i
$934$	−0.0563419	−	0.0775480i	−0.00184356	−	0.00253745i
$935$		0			0
$936$	0.0692166	+	13.8854i	0.00226242	+	0.453858i
$937$	−3.02798	+	19.1179i	−0.0989196	+	0.624554i	0.887563	+	0.460687i	$0.152397\pi$
$937$	−3.02798	+	19.1179i	−0.0989196	+	0.624554i	−0.986482	+	0.163867i	$0.947603\pi$
$938$	−4.23471	+	26.7369i	−0.138268	+	0.872992i
$939$	−7.23381	+	22.4536i	−0.236066	+	0.732747i
$940$		0			0
$941$	21.8140	+	30.0244i	0.711116	+	0.978767i	0.999772	+	0.0213346i	$0.00679152\pi$
$941$	21.8140	+	30.0244i	0.711116	+	0.978767i	−0.288656	+	0.957433i	$0.593208\pi$
$942$	−39.8722	+	40.0714i	−1.29911	+	1.30560i
$943$	−1.07697	−	1.07697i	−0.0350710	−	0.0350710i
$944$	0.0467486	−	0.143877i	0.00152154	−	0.00468281i
$945$		0			0
$946$	−0.439328	−	1.35211i	−0.0142838	−	0.0439610i
$947$	−19.2923	+	37.8632i	−0.626915	+	1.23039i	0.331080	+	0.943603i	$0.392587\pi$
$947$	−19.2923	+	37.8632i	−0.626915	+	1.23039i	−0.957994	+	0.286787i	$0.907413\pi$
$948$	−7.90106	−	15.4116i	−0.256615	−	0.500546i
$949$		−	57.8262i		−	1.87712i
$950$		0			0
$951$	−16.3107	−	49.7766i	−0.528910	−	1.61412i
$952$	−13.2428	+	2.09745i	−0.429201	+	0.0679787i
$953$	−5.22226	−	2.66087i	−0.169166	−	0.0861942i	0.367357	−	0.930080i	$-0.380263\pi$
$953$	−5.22226	−	2.66087i	−0.169166	−	0.0861942i	−0.536523	+	0.843886i	$0.680263\pi$
$954$	−43.0514	+	59.8807i	−1.39384	+	1.93871i
$955$		0			0
$956$	42.8562	+	13.9248i	1.38607	+	0.450361i
$957$	0.375770	−	0.742056i	0.0121469	−	0.0239873i
$958$	−10.8149	+	5.51047i	−0.349414	+	0.178035i
$959$	25.3787	−	18.4387i	0.819522	−	0.595417i
$960$		0			0
$961$	−10.1050	−	7.34170i	−0.325967	−	0.236829i
$962$	24.9872	+	3.95759i	0.805620	+	0.127598i
$963$	−0.657507	−	1.27468i	−0.0211879	−	0.0410761i
$964$	18.4944	−	25.4553i	0.595663	−	0.819860i
$965$		0			0
$966$	1.22916	−	1.70069i	0.0395475	−	0.0547187i
$967$	−25.0823	−	49.2268i	−0.806593	−	1.58303i	−0.812440	−	0.583045i	$-0.801861\pi$
$967$	−25.0823	−	49.2268i	−0.806593	−	1.58303i	0.00584637	−	0.999983i	$-0.498139\pi$
$968$	6.53912	−	6.53912i	0.210175	−	0.210175i
$969$	−0.00480582	−	1.92818i	−0.000154385	−	0.0619421i
$970$		0			0
$971$	50.9146	−	16.5432i	1.63393	−	0.530895i	0.658758	−	0.752355i	$-0.271082\pi$
$971$	50.9146	−	16.5432i	1.63393	−	0.530895i	0.975169	+	0.221460i	$0.0710823\pi$
$972$	−16.7951	+	34.0033i	−0.538703	+	1.09065i
$973$	1.49900	+	9.46429i	0.0480556	+	0.303411i
$974$	−17.5424			−0.562096
$975$		0			0
$976$	11.5789			0.370631
$977$	2.80780	+	17.7277i	0.0898294	+	0.567161i	0.991017	+	0.133732i	$0.0426962\pi$
$977$	2.80780	+	17.7277i	0.0898294	+	0.567161i	−0.901188	+	0.433428i	$0.857304\pi$
$978$	−64.3423	−	10.0265i	−2.05744	−	0.320612i
$979$	−6.78343	+	2.20407i	−0.216799	+	0.0704424i
$980$		0			0
$981$	−4.71302	−	14.2629i	−0.150475	−	0.455378i
$982$	−3.49857	+	3.49857i	−0.111644	+	0.111644i
$983$	−8.86036	−	17.3894i	−0.282602	−	0.554637i	0.705450	−	0.708760i	$-0.250745\pi$
$983$	−8.86036	−	17.3894i	−0.282602	−	0.554637i	−0.988052	+	0.154123i	$0.950745\pi$
$984$	9.49509	+	6.86250i	0.302693	+	0.218768i
$985$		0			0
$986$	−3.37550	+	4.64597i	−0.107498	+	0.147958i
$987$	44.0823	−	7.09462i	1.40316	−	0.225824i
$988$	−2.58914	−	0.410080i	−0.0823716	−	0.0130464i
$989$	−0.121362	−	0.0881750i	−0.00385910	−	0.00280380i
$990$		0			0
$991$	12.9781	−	9.42911i	0.412262	−	0.299526i	−0.362255	−	0.932079i	$-0.617993\pi$
$991$	12.9781	−	9.42911i	0.412262	−	0.299526i	0.774517	+	0.632553i	$0.217993\pi$
$992$	47.1676	−	24.0331i	1.49757	−	0.763051i
$993$	14.8884	+	7.53932i	0.472468	+	0.239253i
$994$	−18.4871	−	6.00684i	−0.586376	−	0.190525i
$995$		0			0
$996$	−53.3518	+	38.9659i	−1.69052	+	1.23468i
$997$	10.7494	+	5.47711i	0.340438	+	0.173462i	0.615848	−	0.787865i	$-0.288814\pi$
$997$	10.7494	+	5.47711i	0.340438	+	0.173462i	−0.275410	+	0.961327i	$0.588814\pi$
$998$	30.0915	−	4.76603i	0.952531	−	0.150866i
$999$	10.0001	+	7.15190i	0.316391	+	0.226276i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	375.2.l.a.293.8		64
3.2	odd	2	inner	375.2.l.a.293.1		64
5.2	odd	4		75.2.l.a.62.1	yes	64
5.3	odd	4		375.2.l.c.332.8		64
5.4	even	2		375.2.l.b.293.1		64
15.2	even	4		75.2.l.a.62.8	yes	64
15.8	even	4		375.2.l.c.332.1		64
15.14	odd	2		375.2.l.b.293.8		64
25.2	odd	20	inner	375.2.l.a.32.1		64
25.11	even	5		75.2.l.a.23.8	yes	64
25.14	even	10		375.2.l.c.218.1		64
25.23	odd	20		375.2.l.b.32.8		64
75.2	even	20	inner	375.2.l.a.32.8		64
75.11	odd	10		75.2.l.a.23.1	✓	64
75.14	odd	10		375.2.l.c.218.8		64
75.23	even	20		375.2.l.b.32.1		64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
75.2.l.a.23.1	✓	64	75.11	odd	10
75.2.l.a.23.8	yes	64	25.11	even	5
75.2.l.a.62.1	yes	64	5.2	odd	4
75.2.l.a.62.8	yes	64	15.2	even	4
375.2.l.a.32.1		64	25.2	odd	20	inner
375.2.l.a.32.8		64	75.2	even	20	inner
375.2.l.a.293.1		64	3.2	odd	2	inner
375.2.l.a.293.8		64	1.1	even	1	trivial
375.2.l.b.32.1		64	75.23	even	20
375.2.l.b.32.8		64	25.23	odd	20
375.2.l.b.293.1		64	5.4	even	2
375.2.l.b.293.8		64	15.14	odd	2
375.2.l.c.218.1		64	25.14	even	10
375.2.l.c.218.8		64	75.14	odd	10
375.2.l.c.332.1		64	15.8	even	4
375.2.l.c.332.8		64	5.3	odd	4

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:	\( N \)	\(=\)	\( 375 = 3 \cdot 5^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	375.l (of order \(20\), degree \(8\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.329364 + 2.07952i) q^{2} +(0.266688 - 1.71140i) q^{3} +(-2.31381 + 0.751802i) q^{4} +(3.64672 - 0.00908913i) q^{6} +(1.98257 - 1.98257i) q^{7} +(-0.413771 - 0.812071i) q^{8} +(-2.85776 - 0.912817i) q^{9} +O(q^{10})\)	\(q+(0.329364 + 2.07952i) q^{2} +(0.266688 - 1.71140i) q^{3} +(-2.31381 + 0.751802i) q^{4} +(3.64672 - 0.00908913i) q^{6} +(1.98257 - 1.98257i) q^{7} +(-0.413771 - 0.812071i) q^{8} +(-2.85776 - 0.912817i) q^{9} +(0.542989 - 0.747360i) q^{11} +(0.669567 + 4.16034i) q^{12} +(5.01590 + 0.794440i) q^{13} +(4.77577 + 3.46980i) q^{14} +(-2.38405 + 1.73211i) q^{16} +(4.67502 - 2.38204i) q^{17} +(0.956980 - 6.24341i) q^{18} +(0.201787 + 0.0655644i) q^{19} +(-2.86423 - 3.92169i) q^{21} +(1.73299 + 0.883003i) q^{22} +(0.202701 - 0.0321047i) q^{23} +(-1.50012 + 0.491557i) q^{24} +10.6923i q^{26} +(-2.32432 + 4.64731i) q^{27} +(-3.09678 + 6.07778i) q^{28} +(0.160641 + 0.494401i) q^{29} +(-2.03788 + 6.27196i) q^{31} +(-5.67611 - 5.67611i) q^{32} +(-1.13422 - 1.12858i) q^{33} +(6.49329 + 8.93724i) q^{34} +(7.29856 - 0.0363822i) q^{36} +(0.370134 - 2.33693i) q^{37} +(-0.0698814 + 0.441214i) q^{38} +(2.69728 - 8.37232i) q^{39} +(-4.36217 - 6.00401i) q^{41} +(7.21185 - 7.24789i) q^{42} +(-0.516864 - 0.516864i) q^{43} +(-0.694506 + 2.13747i) q^{44} +(0.133525 + 0.410946i) q^{46} +(-4.17408 + 8.19208i) q^{47} +(2.32854 + 4.54199i) q^{48} -0.861150i q^{49} +(-2.82985 - 8.63608i) q^{51} +(-12.2031 + 1.93278i) q^{52} +(-10.4035 - 5.30087i) q^{53} +(-10.4297 - 3.30281i) q^{54} +(-2.43031 - 0.789657i) q^{56} +(0.166021 - 0.327852i) q^{57} +(-0.975208 + 0.496893i) q^{58} +(-0.0415323 + 0.0301750i) q^{59} +(-3.17882 - 2.30955i) q^{61} +(-13.7139 - 2.17206i) q^{62} +(-7.47542 + 3.85597i) q^{63} +(6.46985 - 8.90499i) q^{64} +(1.97334 - 2.73035i) q^{66} +(2.08186 + 4.08589i) q^{67} +(-9.02628 + 9.02628i) q^{68} +(-0.000885961 - 0.355463i) q^{69} +(-3.13172 + 1.01756i) q^{71} +(0.441184 + 2.69840i) q^{72} +(-1.78126 - 11.2465i) q^{73} +4.98160 q^{74} -0.516187 q^{76} +(-0.405180 - 2.55821i) q^{77} +(18.2988 + 2.85151i) q^{78} +(-3.90882 + 1.27005i) q^{79} +(7.33353 + 5.21722i) q^{81} +(11.0487 - 11.0487i) q^{82} +(7.11778 + 13.9694i) q^{83} +(9.57562 + 6.92070i) q^{84} +(0.904592 - 1.24506i) q^{86} +(0.888957 - 0.143069i) q^{87} +(-0.831583 - 0.131710i) q^{88} +(-6.24638 - 4.53826i) q^{89} +(11.5194 - 8.36933i) q^{91} +(-0.444875 + 0.226675i) q^{92} +(10.1903 + 5.16028i) q^{93} +(-18.4104 - 5.98190i) q^{94} +(-11.2278 + 8.20033i) q^{96} +(7.86930 + 4.00961i) q^{97} +(1.79078 - 0.283631i) q^{98} +(-2.23393 + 1.64012i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q + 20 q^{4} - 6 q^{6} - 20 q^{7} + 10 q^{9}+O(q^{10}) \) 64 * q + 20 * q^4 - 6 * q^6 - 20 * q^7 + 10 * q^9	\( 64 q + 20 q^{4} - 6 q^{6} - 20 q^{7} + 10 q^{9} - 40 q^{12} - 8 q^{16} - 10 q^{18} - 6 q^{21} + 30 q^{27} + 80 q^{28} - 12 q^{31} + 50 q^{33} - 20 q^{34} - 22 q^{36} + 120 q^{37} - 30 q^{39} - 60 q^{42} - 20 q^{43} - 12 q^{46} - 100 q^{48} - 16 q^{51} - 100 q^{52} - 120 q^{54} + 70 q^{57} - 120 q^{58} - 12 q^{61} + 70 q^{63} + 100 q^{64} - 30 q^{66} + 60 q^{67} + 80 q^{69} + 40 q^{72} + 80 q^{73} - 64 q^{76} - 70 q^{78} + 60 q^{79} + 14 q^{81} - 60 q^{82} + 130 q^{84} - 100 q^{87} - 60 q^{88} - 12 q^{91} - 20 q^{93} - 260 q^{94} + 42 q^{96}+O(q^{100}) \) 64 * q + 20 * q^4 - 6 * q^6 - 20 * q^7 + 10 * q^9 - 40 * q^12 - 8 * q^16 - 10 * q^18 - 6 * q^21 + 30 * q^27 + 80 * q^28 - 12 * q^31 + 50 * q^33 - 20 * q^34 - 22 * q^36 + 120 * q^37 - 30 * q^39 - 60 * q^42 - 20 * q^43 - 12 * q^46 - 100 * q^48 - 16 * q^51 - 100 * q^52 - 120 * q^54 + 70 * q^57 - 120 * q^58 - 12 * q^61 + 70 * q^63 + 100 * q^64 - 30 * q^66 + 60 * q^67 + 80 * q^69 + 40 * q^72 + 80 * q^73 - 64 * q^76 - 70 * q^78 + 60 * q^79 + 14 * q^81 - 60 * q^82 + 130 * q^84 - 100 * q^87 - 60 * q^88 - 12 * q^91 - 20 * q^93 - 260 * q^94 + 42 * q^96

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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