LMFDB - Embedded newform 525.2.w.a.104.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [525,2,Mod(104,525)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(525, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([5, 1, 5]))

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

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

chi := DirichletCharacter("525.104");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 525 = 3 \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	525.w (of order $10$, degree $4$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$4.19214610612$
Analytic rank:	$0$
Dimension:	$304$
Relative dimension:	$76$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			104.5
Character	$\chi$	$=$	525.104
Dual form			525.2.w.a.419.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.780529 + 2.40222i) q^{2} +(-0.282161 + 1.70891i) q^{3} +(-3.54341 - 2.57444i) q^{4} +(-0.607661 - 2.15192i) q^{5} +(-3.88495 - 2.01167i) q^{6} +(1.54353 - 2.14884i) q^{7} +(4.86320 - 3.53332i) q^{8} +(-2.84077 - 0.964377i) q^{9} +O(q^{10})$	\(q+(-0.780529 + 2.40222i) q^{2} +(-0.282161 + 1.70891i) q^{3} +(-3.54341 - 2.57444i) q^{4} +(-0.607661 - 2.15192i) q^{5} +(-3.88495 - 2.01167i) q^{6} +(1.54353 - 2.14884i) q^{7} +(4.86320 - 3.53332i) q^{8} +(-2.84077 - 0.964377i) q^{9} +(5.64368 + 0.219898i) q^{10} +(0.141659 + 0.0460279i) q^{11} +(5.39930 - 5.32897i) q^{12} +(-0.431166 - 1.32699i) q^{13} +(3.95723 + 5.38513i) q^{14} +(3.84890 - 0.431253i) q^{15} +(1.98503 + 6.10928i) q^{16} +(2.60663 + 3.58771i) q^{17} +(4.53395 - 6.07144i) q^{18} +(1.72014 + 2.36757i) q^{19} +(-3.38678 + 9.18951i) q^{20} +(3.23666 + 3.24408i) q^{21} +(-0.221138 + 0.304371i) q^{22} +(2.50331 - 7.70441i) q^{23} +(4.66593 + 9.30775i) q^{24} +(-4.26150 + 2.61527i) q^{25} +3.52427 q^{26} +(2.44959 - 4.58252i) q^{27} +(-11.0014 + 3.64051i) q^{28} +(1.46476 - 2.01607i) q^{29} +(-1.96821 + 9.58251i) q^{30} +(5.16981 + 7.11564i) q^{31} -4.20273 q^{32} +(-0.118628 + 0.229096i) q^{33} +(-10.6530 + 3.46138i) q^{34} +(-5.56207 - 2.01578i) q^{35} +(7.58328 + 10.7306i) q^{36} +(6.79870 - 2.20903i) q^{37} +(-7.03005 + 2.28420i) q^{38} +(2.38937 - 0.362400i) q^{39} +(-10.5586 - 8.31814i) q^{40} +(-1.57199 - 4.83810i) q^{41} +(-10.3193 + 5.24308i) q^{42} -12.0930i q^{43} +(-0.383461 - 0.527789i) q^{44} +(-0.349035 + 6.69912i) q^{45} +(16.5538 + 12.0270i) q^{46} +(0.551230 - 0.758704i) q^{47} +(-11.0003 + 1.66844i) q^{48} +(-2.23504 - 6.63360i) q^{49} +(-2.95624 - 12.2784i) q^{50} +(-6.86658 + 3.44219i) q^{51} +(-1.88846 + 5.81208i) q^{52} +(-2.37035 - 1.72216i) q^{53} +(9.09625 + 9.46125i) q^{54} +(0.0129674 - 0.332809i) q^{55} +(-0.0860630 - 15.9040i) q^{56} +(-4.53133 + 2.27154i) q^{57} +(3.69975 + 5.09227i) q^{58} +(-3.34775 - 10.3033i) q^{59} +(-14.7485 - 8.38064i) q^{60} +(5.61365 + 1.82399i) q^{61} +(-21.1285 + 6.86507i) q^{62} +(-6.45710 + 4.61582i) q^{63} +(-0.689696 + 2.12267i) q^{64} +(-2.59357 + 1.73419i) q^{65} +(-0.457747 - 0.463788i) q^{66} +(2.31482 + 3.18607i) q^{67} -19.4233i q^{68} +(12.4598 + 6.45183i) q^{69} +(9.18370 - 11.7880i) q^{70} +(-2.55145 + 3.51178i) q^{71} +(-17.2227 + 5.34739i) q^{72} +(-0.515093 + 1.58529i) q^{73} +18.0562i q^{74} +(-3.26685 - 8.02046i) q^{75} -12.8177i q^{76} +(0.317562 - 0.233358i) q^{77} +(-0.994410 + 6.02267i) q^{78} +(-8.77942 - 6.37862i) q^{79} +(11.9404 - 7.98398i) q^{80} +(7.13995 + 5.47915i) q^{81} +12.8492 q^{82} +(4.15253 + 5.71546i) q^{83} +(-3.11715 - 19.8277i) q^{84} +(6.13652 - 7.78935i) q^{85} +(29.0500 + 9.43892i) q^{86} +(3.03199 + 3.07200i) q^{87} +(0.851549 - 0.276685i) q^{88} +(2.11719 - 6.51604i) q^{89} +(-15.8203 - 6.06731i) q^{90} +(-3.51701 - 1.12174i) q^{91} +(-28.7048 + 20.8552i) q^{92} +(-13.6187 + 6.82701i) q^{93} +(1.39232 + 1.91637i) q^{94} +(4.04956 - 5.14028i) q^{95} +(1.18585 - 7.18211i) q^{96} +(9.51528 + 6.91326i) q^{97} +(17.6799 - 0.191351i) q^{98} +(-0.358033 - 0.267368i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 304 q - 84 q^{4} - 6 q^{9}+O(q^{10}) $ 304 * q - 84 * q^4 - 6 * q^9	$ 304 q - 84 q^{4} - 6 q^{9} - 36 q^{15} - 60 q^{16} - 18 q^{21} - 40 q^{22} - 8 q^{25} + 60 q^{28} + 14 q^{30} + 28 q^{36} - 20 q^{37} - 2 q^{39} - 35 q^{42} - 24 q^{46} - 20 q^{49} - 52 q^{51} - 80 q^{58} + 4 q^{60} + 55 q^{63} - 76 q^{64} - 20 q^{67} + 6 q^{70} + 30 q^{72} - 40 q^{78} - 68 q^{79} - 10 q^{81} + 80 q^{84} - 88 q^{85} - 20 q^{88} - 82 q^{91} - 36 q^{99}+O(q^{100}) $ 304 * q - 84 * q^4 - 6 * q^9 - 36 * q^15 - 60 * q^16 - 18 * q^21 - 40 * q^22 - 8 * q^25 + 60 * q^28 + 14 * q^30 + 28 * q^36 - 20 * q^37 - 2 * q^39 - 35 * q^42 - 24 * q^46 - 20 * q^49 - 52 * q^51 - 80 * q^58 + 4 * q^60 + 55 * q^63 - 76 * q^64 - 20 * q^67 + 6 * q^70 + 30 * q^72 - 40 * q^78 - 68 * q^79 - 10 * q^81 + 80 * q^84 - 88 * q^85 - 20 * q^88 - 82 * q^91 - 36 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/525\mathbb{Z}\right)^\times$.

$n$	$127$	$176$	$451$
$\chi(n)$	$e\left(\frac{1}{10}\right)$	$-1$	$-1$

Coefficient data

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

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

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

$2$	−0.780529	+	2.40222i	−0.551917	+	1.69863i	0.152031	+	0.988376i	$0.451419\pi$
$2$	−0.780529	+	2.40222i	−0.551917	+	1.69863i	−0.703948	+	0.710251i	$0.748581\pi$
$3$	−0.282161	+	1.70891i	−0.162906	+	0.986642i
$3$	−0.282161	+	1.70891i	−0.162906	+	0.986642i
$4$	−3.54341	−	2.57444i	−1.77170	−	1.28722i
$5$	−0.607661	−	2.15192i	−0.271754	−	0.962367i
$5$	−0.607661	−	2.15192i	−0.271754	−	0.962367i
$6$	−3.88495	−	2.01167i	−1.58603	−	0.821261i
$7$	1.54353	−	2.14884i	0.583399	−	0.812186i
$7$	1.54353	−	2.14884i	0.583399	−	0.812186i
$8$	4.86320	−	3.53332i	1.71940	−	1.24922i
$9$	−2.84077	−	0.964377i	−0.946924	−	0.321459i
$10$	5.64368	+	0.219898i	1.78469	+	0.0695379i
$11$	0.141659	+	0.0460279i	0.0427119	+	0.0138779i	0.330295	−	0.943878i	$-0.392852\pi$
$11$	0.141659	+	0.0460279i	0.0427119	+	0.0138779i	−0.287583	+	0.957756i	$0.592852\pi$
$12$	5.39930	−	5.32897i	1.55864	−	1.53834i
$13$	−0.431166	−	1.32699i	−0.119584	−	0.368041i	0.873292	−	0.487198i	$-0.161981\pi$
$13$	−0.431166	−	1.32699i	−0.119584	−	0.368041i	−0.992875	+	0.119157i	$0.961981\pi$
$14$	3.95723	+	5.38513i	1.05761	+	1.43924i
$15$	3.84890	−	0.431253i	0.993781	−	0.111349i
$16$	1.98503	+	6.10928i	0.496256	+	1.52732i
$17$	2.60663	+	3.58771i	0.632199	+	0.870148i	0.998169	−	0.0604787i	$-0.0192627\pi$
$17$	2.60663	+	3.58771i	0.632199	+	0.870148i	−0.365970	+	0.930627i	$0.619263\pi$
$18$	4.53395	−	6.07144i	1.06866	−	1.43105i
$19$	1.72014	+	2.36757i	0.394628	+	0.543158i	0.959385	−	0.282098i	$-0.0910305\pi$
$19$	1.72014	+	2.36757i	0.394628	+	0.543158i	−0.564758	+	0.825257i	$0.691030\pi$
$20$	−3.38678	+	9.18951i	−0.757308	+	2.05484i
$21$	3.23666	+	3.24408i	0.706297	+	0.707915i
$22$	−0.221138	+	0.304371i	−0.0471469	+	0.0648921i
$23$	2.50331	−	7.70441i	0.521977	−	1.60648i	−0.248241	−	0.968698i	$-0.579852\pi$
$23$	2.50331	−	7.70441i	0.521977	−	1.60648i	0.770218	−	0.637781i	$-0.220148\pi$
$24$	4.66593	+	9.30775i	0.952430	+	1.89994i
$25$	−4.26150	+	2.61527i	−0.852299	+	0.523054i
$26$	3.52427			0.691165
$27$	2.44959	−	4.58252i	0.471424	−	0.881907i
$28$	−11.0014	+	3.64051i	−2.07907	+	0.687991i
$29$	1.46476	−	2.01607i	0.271999	−	0.374374i	−0.651064	−	0.759023i	$-0.725677\pi$
$29$	1.46476	−	2.01607i	0.271999	−	0.374374i	0.923063	+	0.384648i	$0.125677\pi$
$30$	−1.96821	+	9.58251i	−0.359345	+	1.74952i
$31$	5.16981	+	7.11564i	0.928526	+	1.27801i	0.960432	+	0.278515i	$0.0898423\pi$
$31$	5.16981	+	7.11564i	0.928526	+	1.27801i	−0.0319059	+	0.999491i	$0.510158\pi$
$32$	−4.20273			−0.742945
$33$	−0.118628	+	0.229096i	−0.0206506	+	0.0398806i
$34$	−10.6530	+	3.46138i	−1.82698	+	0.593621i
$35$	−5.56207	−	2.01578i	−0.940162	−	0.340729i
$36$	7.58328	+	10.7306i	1.26388	+	1.78843i
$37$	6.79870	−	2.20903i	1.11770	−	0.363162i	0.308810	−	0.951124i	$-0.400069\pi$
$37$	6.79870	−	2.20903i	1.11770	−	0.363162i	0.808889	+	0.587962i	$0.200069\pi$
$38$	−7.03005	+	2.28420i	−1.14042	+	0.370547i
$39$	2.38937	−	0.362400i	0.382606	−	0.0580304i
$40$	−10.5586	−	8.31814i	−1.66946	−	1.31521i
$41$	−1.57199	−	4.83810i	−0.245504	−	0.755584i	−0.995553	−	0.0942018i	$-0.969970\pi$
$41$	−1.57199	−	4.83810i	−0.245504	−	0.755584i	0.750049	−	0.661382i	$-0.230030\pi$
$42$	−10.3193	+	5.24308i	−1.59230	+	0.809025i
$43$		−	12.0930i		−	1.84416i	−0.386998	−	0.922081i	$-0.626488\pi$
$43$		−	12.0930i		−	1.84416i	0.386998	−	0.922081i	$-0.373512\pi$
$44$	−0.383461	−	0.527789i	−0.0578089	−	0.0795672i
$45$	−0.349035	+	6.69912i	−0.0520310	+	0.998645i
$46$	16.5538	+	12.0270i	2.44072	+	1.77329i
$47$	0.551230	−	0.758704i	0.0804052	−	0.110668i	−0.766920	−	0.641743i	$-0.778212\pi$
$47$	0.551230	−	0.758704i	0.0804052	−	0.110668i	0.847325	+	0.531075i	$0.178212\pi$
$48$	−11.0003	+	1.66844i	−1.58776	+	0.240818i
$49$	−2.23504	−	6.63360i	−0.319292	−	0.947656i
$50$	−2.95624	−	12.2784i	−0.418075	−	1.73642i
$51$	−6.86658	+	3.44219i	−0.961513	+	0.482002i
$52$	−1.88846	+	5.81208i	−0.261882	+	0.805991i
$53$	−2.37035	−	1.72216i	−0.325592	−	0.236557i	0.412966	−	0.910747i	$-0.364493\pi$
$53$	−2.37035	−	1.72216i	−0.325592	−	0.236557i	−0.738558	+	0.674190i	$0.764493\pi$
$54$	9.09625	+	9.46125i	1.23784	+	1.28751i
$55$	0.0129674	−	0.332809i	0.00174853	−	0.0448759i
$56$	−0.0860630	−	15.9040i	−0.0115006	−	2.12526i
$57$	−4.53133	+	2.27154i	−0.600190	+	0.300872i
$58$	3.69975	+	5.09227i	0.485802	+	0.668648i
$59$	−3.34775	−	10.3033i	−0.435839	−	1.34138i	−0.892224	−	0.451593i	$-0.850856\pi$
$59$	−3.34775	−	10.3033i	−0.435839	−	1.34138i	0.456384	−	0.889783i	$-0.349144\pi$
$60$	−14.7485	−	8.38064i	−1.90402	−	1.08194i
$61$	5.61365	+	1.82399i	0.718754	+	0.233537i	0.645483	−	0.763775i	$-0.276656\pi$
$61$	5.61365	+	1.82399i	0.718754	+	0.233537i	0.0732714	+	0.997312i	$0.476656\pi$
$62$	−21.1285	+	6.86507i	−2.68333	+	0.871865i
$63$	−6.45710	+	4.61582i	−0.813518	+	0.581539i
$64$	−0.689696	+	2.12267i	−0.0862120	+	0.265333i
$65$	−2.59357	+	1.73419i	−0.321693	+	0.215100i
$66$	−0.457747	−	0.463788i	−0.0563448	−	0.0570884i
$67$	2.31482	+	3.18607i	0.282800	+	0.389241i	0.926659	−	0.375903i	$-0.122668\pi$
$67$	2.31482	+	3.18607i	0.282800	+	0.389241i	−0.643859	+	0.765144i	$0.722668\pi$
$68$		−	19.4233i		−	2.35542i
$69$	12.4598	+	6.45183i	1.49999	+	0.776709i
$70$	9.18370	−	11.7880i	1.09766	−	1.40893i
$71$	−2.55145	+	3.51178i	−0.302802	+	0.416771i	−0.933120	−	0.359566i	$-0.882925\pi$
$71$	−2.55145	+	3.51178i	−0.302802	+	0.416771i	0.630318	+	0.776337i	$0.282925\pi$
$72$	−17.2227	+	5.34739i	−2.02971	+	0.630196i
$73$	−0.515093	+	1.58529i	−0.0602871	+	0.185545i	−0.976664	−	0.214771i	$-0.931099\pi$
$73$	−0.515093	+	1.58529i	−0.0602871	+	0.185545i	0.916377	+	0.400316i	$0.131099\pi$
$74$			18.0562i			2.09899i
$75$	−3.26685	−	8.02046i	−0.377223	−	0.926123i
$76$		−	12.8177i		−	1.47029i
$77$	0.317562	−	0.233358i	0.0361895	−	0.0265936i
$78$	−0.994410	+	6.02267i	−0.112595	+	0.681933i
$79$	−8.77942	−	6.37862i	−0.987762	−	0.717651i	−0.0283320	−	0.999599i	$-0.509020\pi$
$79$	−8.77942	−	6.37862i	−0.987762	−	0.717651i	−0.959430	+	0.281948i	$0.909020\pi$
$80$	11.9404	−	7.98398i	1.33498	−	0.892636i
$81$	7.13995	+	5.47915i	0.793328	+	0.608794i
$82$	12.8492			1.41895
$83$	4.15253	+	5.71546i	0.455799	+	0.627353i	0.973631	−	0.228129i	$-0.0732608\pi$
$83$	4.15253	+	5.71546i	0.455799	+	0.627353i	−0.517832	+	0.855482i	$0.673261\pi$
$84$	−3.11715	−	19.8277i	−0.340109	−	2.16338i
$85$	6.13652	−	7.78935i	0.665599	−	0.844874i
$86$	29.0500	+	9.43892i	3.13254	+	1.01782i
$87$	3.03199	+	3.07200i	0.325063	+	0.329353i
$88$	0.851549	−	0.276685i	0.0907754	−	0.0294947i
$89$	2.11719	−	6.51604i	0.224422	−	0.690699i	−0.773928	−	0.633273i	$-0.781711\pi$
$89$	2.11719	−	6.51604i	0.224422	−	0.690699i	0.998350	−	0.0574254i	$-0.0182891\pi$
$90$	−15.8203	−	6.06731i	−1.66761	−	0.639551i
$91$	−3.51701	−	1.12174i	−0.368683	−	0.117591i
$92$	−28.7048	+	20.8552i	−2.99268	+	2.17431i
$93$	−13.6187	+	6.82701i	−1.41220	+	0.707928i
$94$	1.39232	+	1.91637i	0.143607	+	0.197658i
$95$	4.04956	−	5.14028i	0.415476	−	0.527382i
$96$	1.18585	−	7.18211i	0.121030	−	0.733021i
$97$	9.51528	+	6.91326i	0.966131	+	0.701935i	0.954566	−	0.297998i	$-0.0963189\pi$
$97$	9.51528	+	6.91326i	0.966131	+	0.701935i	0.0115641	+	0.999933i	$0.496319\pi$
$98$	17.6799	−	0.191351i	1.78594	−	0.0193294i
$99$	−0.358033	−	0.267368i	−0.0359837	−	0.0268715i
$100$	21.8331	+	1.70398i	2.18331	+	0.170398i
$101$	4.92436			0.489992			0.244996	−	0.969524i	$-0.421213\pi$
$101$	4.92436			0.489992			0.244996	+	0.969524i	$0.421213\pi$
$102$	−2.90933	−	19.1818i	−0.288066	−	1.89928i
$103$	−3.42595	−	2.48910i	−0.337569	−	0.245258i	0.406067	−	0.913843i	$-0.366900\pi$
$103$	−3.42595	−	2.48910i	−0.337569	−	0.245258i	−0.743635	+	0.668585i	$0.766900\pi$
$104$	−6.78553	−	4.92998i	−0.665376	−	0.483424i
$105$	5.01419	−	8.93633i	0.489335	−	0.872096i
$106$	5.98713	−	4.34991i	0.581522	−	0.422500i
$107$	14.7698			1.42785			0.713927	−	0.700220i	$-0.246915\pi$
$107$	14.7698			1.42785			0.713927	+	0.700220i	$0.246915\pi$
$108$	−20.4773	+	9.93143i	−1.97043	+	0.955652i
$109$	5.52062	+	16.9907i	0.528779	+	1.62742i	0.756719	+	0.653740i	$0.226801\pi$
$109$	5.52062	+	16.9907i	0.528779	+	1.62742i	−0.227940	+	0.973675i	$0.573199\pi$
$110$	0.789359	+	0.290917i	0.0752624	+	0.0277379i
$111$	1.85672	+	12.2417i	0.176232	+	1.16193i
$112$	16.1918	+	5.16434i	1.52998	+	0.487984i
$113$	0.364948	+	1.12319i	0.0343314	+	0.105661i	0.966754	−	0.255709i	$-0.0823090\pi$
$113$	0.364948	+	1.12319i	0.0343314	+	0.105661i	−0.932422	+	0.361370i	$0.882309\pi$
$114$	−1.91990	−	12.6583i	−0.179815	−	1.18555i
$115$	−18.1004	−	0.705258i	−1.68787	−	0.0657656i
$116$	−10.3805	+	3.37282i	−0.963803	+	0.313159i
$117$	−0.0548773	+	4.18549i	−0.00507341	+	0.386948i
$118$	27.3638			2.51904
$119$	11.7328	−	0.0634910i	1.07555	−	0.00582021i
$120$	17.1942	−	15.6967i	1.56961	−	1.43290i
$121$	−8.88124	−	6.45260i	−0.807385	−	0.586600i
$122$	−8.76324	+	12.0616i	−0.793386	+	1.09200i
$123$	8.71145	−	1.32128i	0.785485	−	0.119136i
$124$		−	38.5230i		−	3.45946i
$125$	8.21739	+	7.58119i	0.734986	+	0.678082i
$126$	−6.04827	−	19.1142i	−0.538823	−	1.70283i
$127$	−14.0028	−	4.54979i	−1.24255	−	0.403729i	−0.387304	−	0.921952i	$-0.626594\pi$
$127$	−14.0028	−	4.54979i	−1.24255	−	0.403729i	−0.855245	+	0.518223i	$0.826594\pi$
$128$	−11.3610	−	8.25421i	−1.00418	−	0.729576i
$129$	20.6658	+	3.41216i	1.81953	+	0.300424i
$130$	−2.14156	−	7.58393i	−0.187827	−	0.665155i
$131$	−10.8788	+	7.90393i	−0.950488	+	0.690570i	−0.950922	−	0.309430i	$-0.899862\pi$
$131$	−10.8788	+	7.90393i	−0.950488	+	0.690570i	0.000434450		1.00000i	$0.499862\pi$
$132$	1.01014	−	0.506380i	0.0879217	−	0.0440747i
$133$	7.74262	−	0.0418984i	0.671371	−	0.00363305i
$134$	−9.46044	+	3.07388i	−0.817258	+	0.265543i
$135$	−11.3497	−	2.48670i	−0.976829	−	0.214021i
$136$	25.3531	+	8.23771i	2.17401	+	0.706378i
$137$	−4.55455	−	14.0175i	−0.389121	−	1.19759i	−0.933446	−	0.358718i	$-0.883214\pi$
$137$	−4.55455	−	14.0175i	−0.389121	−	1.19759i	0.544325	−	0.838875i	$-0.316786\pi$
$138$	−25.2240	+	24.8954i	−2.14721	+	2.11924i
$139$	−7.88011	−	2.56040i	−0.668382	−	0.217170i	−0.0448802	−	0.998992i	$-0.514291\pi$
$139$	−7.88011	−	2.56040i	−0.668382	−	0.217170i	−0.623502	+	0.781822i	$0.714291\pi$
$140$	14.5192	+	21.4619i	1.22710	+	1.81386i
$141$	1.14102	+	1.15608i	0.0960915	+	0.0973596i
$142$	−6.44458	−	8.87020i	−0.540817	−	0.744371i
$143$		−	0.207826i		−	0.0173793i
$144$	0.252647	−	19.2694i	0.0210540	−	1.60578i
$145$	−5.22849	−	1.92695i	−0.434202	−	0.160025i
$146$	−3.40618	−	2.47474i	−0.281898	−	0.204811i
$147$	11.9669	−	1.94775i	0.987012	−	0.160648i
$148$	−29.7776	−	9.67532i	−2.44770	−	0.795306i
$149$			7.01536i			0.574721i	0.957823	+	0.287360i	$0.0927778\pi$
$149$			7.01536i			0.574721i	−0.957823	+	0.287360i	$0.907222\pi$
$150$	21.8168	−	1.58749i	1.78133	−	0.129618i
$151$	−0.255234			−0.0207707			−0.0103853	−	0.999946i	$-0.503306\pi$
$151$	−0.255234			−0.0207707			−0.0103853	+	0.999946i	$0.503306\pi$
$152$	16.7308	+	5.43616i	1.35704	+	0.440931i
$153$	−3.94492	−	12.7056i	−0.318928	−	1.02719i
$154$	0.312712	+	0.944997i	0.0251990	+	0.0761500i
$155$	12.1708	−	15.4489i	0.977580	−	1.24089i
$156$	−9.39950	−	4.86716i	−0.752562	−	0.389684i
$157$	5.94125			0.474163			0.237082	−	0.971490i	$-0.423809\pi$
$157$	5.94125			0.474163			0.237082	+	0.971490i	$0.423809\pi$
$158$	22.1755	−	16.1114i	1.76418	−	1.28175i
$159$	3.61184	−	3.56479i	0.286438	−	0.282707i
$160$	2.55384	+	9.04394i	0.201899	+	0.714986i
$161$	−12.6916	−	17.2712i	−1.00024	−	1.36116i
$162$	−18.7351	+	12.8751i	−1.47197	+	1.01156i
$163$	4.75790	−	1.54594i	0.372668	−	0.121087i	−0.116694	−	0.993168i	$-0.537230\pi$
$163$	4.75790	−	1.54594i	0.372668	−	0.121087i	0.489362	+	0.872081i	$0.337230\pi$
$164$	−6.88516	+	21.1904i	−0.537641	+	1.65469i
$165$	0.565082	+	0.116066i	0.0439916	+	0.00903571i
$166$	−16.9710	+	5.51420i	−1.31720	+	0.427985i
$167$	−10.1199	−	13.9288i	−0.783098	−	1.07784i	−0.994933	−	0.100537i	$-0.967944\pi$
$167$	−10.1199	−	13.9288i	−0.783098	−	1.07784i	0.211835	−	0.977305i	$-0.432056\pi$
$168$	27.2029	+	4.34042i	2.09875	+	0.334870i
$169$	8.94222	−	6.49690i	0.687863	−	0.499762i
$170$	13.9220	+	20.8211i	1.06777	+	1.59690i
$171$	−2.60330	−	8.38459i	−0.199079	−	0.641186i
$172$	−31.1326	+	42.8503i	−2.37384	+	3.26731i
$173$	1.29617	+	0.421150i	0.0985457	+	0.0320194i	0.357875	−	0.933770i	$-0.383501\pi$
$173$	1.29617	+	0.421150i	0.0985457	+	0.0320194i	−0.259329	+	0.965789i	$0.583501\pi$
$174$	−9.74618	+	4.88572i	−0.738856	+	0.370385i
$175$	−0.957935	+	13.1940i	−0.0724131	+	0.997375i
$176$			0.956804i			0.0721218i
$177$	18.5521	−	2.81382i	1.39446	−	0.211500i
$178$	14.0004	+	10.1719i	1.04938	+	0.762417i
$179$	−4.19918	+	5.77967i	−0.313861	+	0.431993i	−0.936581	−	0.350452i	$-0.886028\pi$
$179$	−4.19918	+	5.77967i	−0.313861	+	0.431993i	0.622719	+	0.782445i	$0.286028\pi$
$180$	18.4832	−	22.8391i	1.37766	−	1.70233i
$181$	−5.40591	−	7.44059i	−0.401818	−	0.553055i	0.559381	−	0.828911i	$-0.311039\pi$
$181$	−5.40591	−	7.44059i	−0.401818	−	0.553055i	−0.961199	+	0.275856i	$0.911039\pi$
$182$	5.43980	−	7.57309i	0.403225	−	0.561355i
$183$	−4.70099	+	9.07859i	−0.347507	+	0.671109i
$184$	−15.0480	−	46.3130i	−1.10935	−	3.41424i
$185$	−8.88495	−	13.2879i	−0.653235	−	0.976945i
$186$	−5.77017	−	38.0439i	−0.423090	−	2.78951i
$187$	0.204118	+	0.628211i	0.0149266	+	0.0459393i
$188$	−3.90647	+	1.26929i	−0.284909	+	0.0925724i
$189$	−6.06610	−	12.3370i	−0.441244	−	0.897387i
$190$	9.18730	+	13.7401i	0.666517	+	0.996809i
$191$	−13.4758	+	4.37854i	−0.975072	+	0.316820i	−0.752862	−	0.658179i	$-0.771327\pi$
$191$	−13.4758	+	4.37854i	−0.975072	+	0.316820i	−0.222210	+	0.974999i	$0.571327\pi$
$192$	−3.43285	−	1.77756i	−0.247744	−	0.128285i
$193$		−	13.7543i		−	0.990057i	−0.868877	−	0.495028i	$-0.835158\pi$
$193$		−	13.7543i		−	0.990057i	0.868877	−	0.495028i	$-0.164842\pi$
$194$	−24.0341	+	17.4618i	−1.72555	+	1.25369i
$195$	−2.23178	−	4.92152i	−0.159821	−	0.352437i
$196$	−9.15811	+	29.2595i	−0.654150	+	2.08996i
$197$	11.1636	+	8.11080i	0.795370	+	0.577870i	0.909552	−	0.415589i	$-0.136425\pi$
$197$	11.1636	+	8.11080i	0.795370	+	0.577870i	−0.114182	+	0.993460i	$0.536425\pi$
$198$	0.921732	−	0.651387i	0.0655047	−	0.0462921i
$199$			13.1129i			0.929552i	0.885428	+	0.464776i	$0.153865\pi$
$199$			13.1129i			0.929552i	−0.885428	+	0.464776i	$0.846135\pi$
$200$	−11.4839	+	27.7758i	−0.812035	+	1.96405i
$201$	−6.09788	+	3.05684i	−0.430111	+	0.215613i
$202$	−3.84360	+	11.8294i	−0.270435	+	0.832313i
$203$	−2.07131	−	6.25939i	−0.145378	−	0.439323i
$204$	33.1928	+	5.48050i	2.32396	+	0.383712i
$205$	−9.45595	+	6.32272i	−0.660432	+	0.441598i
$206$	8.65341	−	6.28707i	0.602912	−	0.438041i
$207$	−14.5413	+	19.4723i	−1.01069	+	1.35342i
$208$	7.25109	−	5.26823i	0.502773	−	0.365286i
$209$	0.134700	+	0.414563i	0.00931738	+	0.0286759i
$210$	17.5533	+	19.0203i	1.21129	+	1.31252i
$211$	−2.77452	+	8.53908i	−0.191006	+	0.587855i	0.808994	+	0.587816i	$0.200012\pi$
$211$	−2.77452	+	8.53908i	−0.191006	+	0.587855i	−1.00000		3.82909e-5i	$0.999988\pi$
$212$	3.96552	+	12.2046i	0.272353	+	0.838217i
$213$	−5.28140	−	5.35110i	−0.361876	−	0.366651i
$214$	−11.5283	+	35.4804i	−0.788057	+	2.42539i
$215$	−26.0231	+	7.34843i	−1.77476	+	0.501159i
$216$	−4.27867	−	30.9409i	−0.291127	−	2.10526i
$217$	23.2701	−	0.125924i	1.57968	−	0.00854827i
$218$	−45.1245			−3.05621
$219$	−2.56379	−	1.32756i	−0.173245	−	0.0897080i
$220$	−0.902744	+	1.14589i	−0.0608630	+	0.0772561i
$221$	3.63698	−	5.00587i	0.244650	−	0.336731i
$222$	−30.8565	−	5.09475i	−2.07095	−	0.341937i
$223$	7.33067	−	22.5615i	0.490898	−	1.51083i	−0.332355	−	0.943154i	$-0.607843\pi$
$223$	7.33067	−	22.5615i	0.490898	−	1.51083i	0.823253	−	0.567674i	$-0.192157\pi$
$224$	−6.48704	+	9.03101i	−0.433433	+	0.603410i
$225$	14.6280	−	3.31970i	0.975203	−	0.221313i
$226$	−2.98301			−0.198427
$227$	2.87015	+	0.932568i	0.190499	+	0.0618967i	0.402713	−	0.915326i	$-0.368067\pi$
$227$	2.87015	+	0.932568i	0.190499	+	0.0618967i	−0.212214	+	0.977223i	$0.568067\pi$
$228$	21.9043	+	3.61664i	1.45065	+	0.239518i
$229$	−14.4628	+	19.9064i	−0.955730	+	1.31545i	−0.00679545	+	0.999977i	$0.502163\pi$
$229$	−14.4628	+	19.9064i	−0.955730	+	1.31545i	−0.948935	+	0.315473i	$0.897837\pi$
$230$	15.8221	−	42.9307i	1.04328	−	2.83077i
$231$	0.309185	+	0.608530i	0.0203429	+	0.0400384i
$232$		−	14.9800i		−	0.983485i
$233$	−2.85116	+	2.07149i	−0.186786	+	0.135708i	−0.677249	−	0.735754i	$-0.736828\pi$
$233$	−2.85116	+	2.07149i	−0.186786	+	0.135708i	0.490463	+	0.871462i	$0.336828\pi$
$234$	−10.0116	−	3.39872i	−0.654481	−	0.222181i
$235$	−1.96763	−	0.725168i	−0.128354	−	0.0473047i
$236$	−14.6628	+	45.1274i	−0.954465	+	2.93754i
$237$	13.3777	−	13.2035i	0.868976	−	0.857658i
$238$	−9.00529	+	28.2344i	−0.583726	+	1.83016i
$239$	5.99070	+	1.94650i	0.387506	+	0.125908i	0.496289	−	0.868157i	$-0.334695\pi$
$239$	5.99070	+	1.94650i	0.387506	+	0.125908i	−0.108783	+	0.994065i	$0.534695\pi$
$240$	10.2748	+	22.6580i	0.663236	+	1.46256i
$241$	−16.3263	+	5.30472i	−1.05167	+	0.341707i	−0.783322	−	0.621616i	$-0.786477\pi$
$241$	−16.3263	+	5.30472i	−1.05167	+	0.341707i	−0.268345	+	0.963323i	$0.586477\pi$
$242$	22.4326	−	16.2983i	1.44202	−	1.04769i
$243$	−11.3780	+	10.6556i	−0.729899	+	0.683555i
$244$	−15.1957	−	20.9151i	−0.972807	−	1.33895i
$245$	−12.9168	+	8.84060i	−0.825224	+	0.564805i
$246$	−3.62553	+	21.9581i	−0.231156	+	1.40000i
$247$	2.40008	−	3.30343i	0.152714	−	0.210192i
$248$	50.2836	+	16.3381i	3.19301	+	1.03747i
$249$	−10.9389	+	5.48363i	−0.693225	+	0.347511i
$250$	−24.6256	+	13.8227i	−1.55746	+	0.874222i
$251$	29.8968			1.88707			0.943533	−	0.331277i	$-0.107480\pi$
$251$	29.8968			1.88707			0.943533	+	0.331277i	$0.107480\pi$
$252$	34.7633	+	0.267656i	2.18988	+	0.0168608i
$253$	0.709235	−	0.976179i	0.0445893	−	0.0613718i
$254$	21.8592	−	30.0866i	1.37157	−	1.88780i
$255$	11.5798	+	12.6846i	0.725158	+	0.794342i
$256$	25.0847	−	18.2251i	1.56779	−	1.13907i
$257$		−	21.1410i		−	1.31874i	−0.751818	−	0.659371i	$-0.770823\pi$
$257$		−	21.1410i		−	1.31874i	0.751818	−	0.659371i	$-0.229177\pi$
$258$	−24.3271	+	46.9807i	−1.51454	+	2.92489i
$259$	5.74712	−	18.0190i	0.357109	−	1.11965i
$260$	13.6547	+	0.532035i	0.846826	+	0.0329954i
$261$	−6.10529	+	4.31461i	−0.377908	+	0.267067i
$262$	−10.4958	−	32.3026i	−0.648430	−	1.99566i
$263$	7.42063	+	22.8383i	0.457576	+	1.40827i	0.868085	+	0.496416i	$0.165351\pi$
$263$	7.42063	+	22.8383i	0.457576	+	1.40827i	−0.410509	+	0.911857i	$0.634649\pi$
$264$	0.232557	+	1.53329i	0.0143129	+	0.0943676i
$265$	−2.26558	+	6.14728i	−0.139173	+	0.377624i
$266$	−5.94269	+	18.6322i	−0.364370	+	1.14241i
$267$	10.5380	+	5.45667i	0.644913	+	0.333943i
$268$		−	17.2489i		−	1.05365i
$269$	12.4359	−	9.03523i	0.758232	−	0.550888i	−0.140136	−	0.990132i	$-0.544754\pi$
$269$	12.4359	−	9.03523i	0.758232	−	0.550888i	0.898367	+	0.439245i	$0.144754\pi$
$270$	14.8324	−	25.3236i	0.902671	−	1.54115i
$271$	−2.91826	+	4.01663i	−0.177271	+	0.243993i	−0.888402	−	0.459067i	$-0.848184\pi$
$271$	−2.91826	+	4.01663i	−0.177271	+	0.243993i	0.711130	+	0.703060i	$0.248184\pi$
$272$	−16.7441	+	23.0463i	−1.01526	+	1.39739i
$273$	2.90932	−	5.69376i	0.176080	−	0.344602i
$274$	37.2280			2.24903
$275$	−0.724056	+	0.174330i	−0.0436622	+	0.0105125i
$276$	−27.5404	−	54.9385i	−1.65774	−	3.30691i
$277$	8.76581	+	2.84818i	0.526686	+	0.171131i	0.560278	−	0.828305i	$-0.310694\pi$
$277$	8.76581	+	2.84818i	0.526686	+	0.171131i	−0.0335912	+	0.999436i	$0.510694\pi$
$278$	12.3013	−	16.9313i	0.737783	−	1.01547i
$279$	−7.82410	−	25.1995i	−0.468416	−	1.50866i
$280$	−34.1718	+	9.84945i	−2.04216	+	0.588617i
$281$	9.48616	+	13.0566i	0.565897	+	0.778890i	0.992061	−	0.125756i	$-0.0401356\pi$
$281$	9.48616	+	13.0566i	0.565897	+	0.778890i	−0.426165	+	0.904646i	$0.640136\pi$
$282$	−3.66777	+	1.83864i	−0.218412	+	0.109489i
$283$	−22.8631	+	16.6110i	−1.35907	+	0.987424i	−0.360570	+	0.932732i	$0.617418\pi$
$283$	−22.8631	+	16.6110i	−1.35907	+	0.987424i	−0.998503	+	0.0546921i	$0.982582\pi$
$284$	18.0817	−	5.87510i	1.07295	−	0.348623i
$285$	7.64167	+	8.37073i	0.452654	+	0.495839i
$286$	0.499245	+	0.162215i	0.0295210	+	0.00959195i
$287$	−12.8227	−	4.08978i	−0.756902	−	0.241412i
$288$	11.9390	+	4.05302i	0.703512	+	0.238826i
$289$	−0.823893	+	2.53568i	−0.0484643	+	0.149158i
$290$	8.70996	−	11.0559i	0.511466	−	0.649227i
$291$	−14.4990	+	14.3101i	−0.849946	+	0.838875i
$292$	5.90642	−	4.29127i	0.345647	−	0.251127i
$293$			14.9958i			0.876064i	0.898959	+	0.438032i	$0.144324\pi$
$293$			14.9958i			0.876064i	−0.898959	+	0.438032i	$0.855676\pi$
$294$	−4.66157	+	30.2674i	−0.271868	+	1.76523i
$295$	−20.1376	+	13.4650i	−1.17245	+	0.783962i
$296$	25.2582	−	34.7649i	1.46810	−	2.02067i
$297$	0.557931	−	0.536408i	0.0323745	−	0.0311255i
$298$	−16.8525	−	5.47569i	−0.976236	−	0.317198i
$299$	−11.3030			−0.653671
$300$	−9.07239	+	36.8300i	−0.523795	+	2.12638i
$301$	−25.9859	−	18.6658i	−1.49780	−	1.07588i
$302$	0.199218	−	0.613129i	0.0114637	−	0.0352816i
$303$	−1.38946	+	8.41530i	−0.0798224	+	0.483446i
$304$	−11.0496	+	15.2085i	−0.633740	+	0.872268i
$305$	0.513871	−	13.1885i	0.0294242	−	0.755170i
$306$	33.6009	+	0.440553i	1.92083	+	0.0251847i
$307$	−31.3309			−1.78815			−0.894075	−	0.447917i	$-0.852166\pi$
$307$	−31.3309			−1.78815			−0.894075	+	0.447917i	$0.852166\pi$
$308$	−1.72602	+	0.00934017i	−0.0983490	+	0.000532205i
$309$	5.22032	−	5.15232i	0.296974	−	0.293105i
$310$	27.6120	+	41.2952i	1.56826	+	2.34541i
$311$	−5.21775	+	16.0586i	−0.295872	+	0.910599i	0.687056	+	0.726605i	$0.258903\pi$
$311$	−5.21775	+	16.0586i	−0.295872	+	0.910599i	−0.982927	+	0.183994i	$0.941097\pi$
$312$	10.3395	−	10.2048i	0.585360	−	0.577735i
$313$	7.12583	+	21.9311i	0.402776	+	1.23962i	0.922738	+	0.385428i	$0.125946\pi$
$313$	7.12583	+	21.9311i	0.402776	+	1.23962i	−0.519962	+	0.854189i	$0.674054\pi$
$314$	−4.63732	+	14.2722i	−0.261699	+	0.805427i
$315$	13.8566	+	11.0903i	0.780731	+	0.624867i
$316$	14.6877	+	45.2041i	0.826248	+	2.54293i
$317$	9.07728	−	6.59503i	0.509831	−	0.370414i	−0.302929	−	0.953013i	$-0.597964\pi$
$317$	9.07728	−	6.59503i	0.509831	−	0.370414i	0.812759	+	0.582600i	$0.197964\pi$
$318$	5.74428	+	11.4589i	0.322123	+	0.642581i
$319$	0.300292	−	0.218175i	0.0168131	−	0.0122155i
$320$	4.98690	+	0.194308i	0.278776	+	0.0108621i
$321$	−4.16747	+	25.2404i	−0.232605	+	1.40878i
$322$	51.3954	−	17.0074i	2.86415	−	0.947785i
$323$	−4.01040	+	12.3427i	−0.223145	+	0.686769i
$324$	−11.1941	−	37.7962i	−0.621892	−	2.09979i
$325$	5.30786	+	4.52736i	0.294427	+	0.251133i
$326$			12.6362i			0.699853i
$327$	−30.5934	+	4.64014i	−1.69182	+	0.256600i
$328$	−24.7395	−	17.9743i	−1.36601	−	0.992463i
$329$	−0.779494	−	2.35559i	−0.0429749	−	0.129868i
$330$	−0.719879	+	1.26686i	−0.0396280	+	0.0697383i
$331$	−7.96564	+	5.78738i	−0.437831	+	0.318103i	−0.784773	−	0.619784i	$-0.787220\pi$
$331$	−7.96564	+	5.78738i	−0.437831	+	0.318103i	0.346941	+	0.937887i	$0.387220\pi$
$332$		−	30.9426i		−	1.69820i
$333$	−21.4439	−	0.281158i	−1.17512	−	0.0154074i
$334$	41.3589	−	13.4383i	2.26306	−	0.735312i
$335$	5.44955	−	6.91735i	0.297740	−	0.377935i
$336$	−13.3941	+	26.2132i	−0.730709	+	1.43005i
$337$	5.04670	−	1.63977i	0.274911	−	0.0893241i	−0.168317	−	0.985733i	$-0.553833\pi$
$337$	5.04670	−	1.63977i	0.274911	−	0.0893241i	0.443228	+	0.896409i	$0.353833\pi$
$338$	8.62733	+	26.5522i	0.469265	+	1.44425i
$339$	−2.02241	+	0.306743i	−0.109842	+	0.0166600i
$340$	−41.7974	+	11.8028i	−2.26678	+	0.640096i
$341$	0.404834	+	1.24595i	0.0219230	+	0.0674721i
$342$	22.1736	+	0.290726i	1.19901	+	0.0157206i
$343$	−17.7044	−	5.43639i	−0.955948	−	0.293537i
$344$	−42.7283	−	58.8105i	−2.30376	−	3.17085i
$345$	6.31245	−	30.7330i	0.339851	−	1.65461i
$346$	−2.02339	+	2.78496i	−0.108778	+	0.149720i
$347$	−10.5654	−	7.67622i	−0.567181	−	0.412081i	0.266899	−	0.963724i	$-0.414001\pi$
$347$	−10.5654	−	7.67622i	−0.567181	−	0.412081i	−0.834080	+	0.551644i	$0.814001\pi$
$348$	−2.83490	−	18.6910i	−0.151966	−	1.00194i
$349$		−	2.77928i		−	0.148771i	−0.997230	−	0.0743857i	$-0.976300\pi$
$349$		−	2.77928i		−	0.148771i	0.997230	−	0.0743857i	$-0.0236996\pi$
$350$	−30.9473	−	12.5995i	−1.65420	−	0.673471i
$351$	−7.13715	−	1.27476i	−0.380953	−	0.0680417i
$352$	−0.595357	−	0.193443i	−0.0317326	−	0.0103106i
$353$	−7.22549	+	9.94504i	−0.384574	+	0.529321i	−0.956789	−	0.290783i	$-0.906084\pi$
$353$	−7.22549	+	9.94504i	−0.384574	+	0.529321i	0.572215	+	0.820104i	$0.306084\pi$
$354$	−7.72100	+	46.7624i	−0.410367	+	2.48539i
$355$	9.10747	+	3.35655i	0.483374	+	0.178147i
$356$	−24.2772	+	17.6384i	−1.28669	+	0.934834i
$357$	−3.20204	+	20.0683i	−0.169470	+	1.06213i
$358$	−10.6065	−	14.5986i	−0.560570	−	0.771558i
$359$	23.4436	−	7.61729i	1.23731	−	0.402025i	0.383950	−	0.923354i	$-0.374563\pi$
$359$	23.4436	−	7.61729i	1.23731	−	0.402025i	0.853356	+	0.521329i	$0.174563\pi$
$360$	21.9727	+	33.8124i	1.15806	+	1.78207i
$361$	3.22481	−	9.92496i	0.169727	−	0.522366i
$362$	22.0934	−	7.17859i	1.16120	−	0.377298i
$363$	13.5329	−	13.3566i	0.710291	−	0.701040i
$364$	9.57436	+	13.0291i	0.501833	+	0.682911i
$365$	3.72442	+	0.145117i	0.194945	+	0.00759577i
$366$	−18.1395	−	18.3789i	−0.948168	−	0.960681i
$367$	17.8767	−	12.9882i	0.933159	−	0.677979i	−0.0136055	−	0.999907i	$-0.504331\pi$
$367$	17.8767	−	12.9882i	0.933159	−	0.677979i	0.946764	+	0.321928i	$0.104331\pi$
$368$	52.0375			2.71264
$369$	−0.200078	+	15.2599i	−0.0104156	+	0.794400i
$370$	38.8554	−	10.9720i	2.02000	−	0.570409i
$371$	−7.35935	+	2.43530i	−0.382078	+	0.126435i
$372$	65.8324	+	10.8697i	3.41325	+	0.563566i
$373$	16.6088	+	5.39652i	0.859970	+	0.279421i	0.705616	−	0.708595i	$-0.250670\pi$
$373$	16.6088	+	5.39652i	0.859970	+	0.279421i	0.154354	+	0.988016i	$0.450670\pi$
$374$	−1.66842			−0.0862720
$375$	−15.2742	+	11.9037i	−0.788758	+	0.614704i
$376$		−	5.63740i		−	0.290727i
$377$	−3.30686	−	1.07446i	−0.170312	−	0.0553377i
$378$	34.3711	−	4.94270i	1.76786	−	0.254225i
$379$	−14.6888	−	10.6720i	−0.754513	−	0.548186i	0.142709	−	0.989765i	$-0.454419\pi$
$379$	−14.6888	−	10.6720i	−0.754513	−	0.548186i	−0.897222	+	0.441579i	$0.854419\pi$
$380$	−27.5826	+	7.78879i	−1.41496	+	0.399557i
$381$	11.7263	−	22.6458i	0.600754	−	1.16018i
$382$		−	35.7894i		−	1.83114i
$383$	−1.29730	−	1.78558i	−0.0662890	−	0.0912389i	0.774585	−	0.632469i	$-0.217959\pi$
$383$	−1.29730	−	1.78558i	−0.0662890	−	0.0912389i	−0.840874	+	0.541231i	$0.817959\pi$
$384$	17.3114	−	17.0859i	0.883416	−	0.871910i
$385$	−0.695137	−	0.541564i	−0.0354275	−	0.0276007i
$386$	33.0409	+	10.7356i	1.68174	+	0.546430i
$387$	−11.6622	+	34.3534i	−0.592822	+	1.74628i
$388$	−15.9188	−	48.9930i	−0.808154	−	2.48724i
$389$	8.02721	+	2.60820i	0.406996	+	0.132241i	0.505358	−	0.862910i	$-0.331360\pi$
$389$	8.02721	+	2.60820i	0.406996	+	0.132241i	−0.0983624	+	0.995151i	$0.531360\pi$
$390$	13.5645	−	1.51985i	0.686867	−	0.0769606i
$391$	34.1664	−	11.1013i	1.72787	−	0.561418i
$392$	−34.3081	−	24.3634i	−1.73282	−	1.23054i
$393$	−10.4376	−	20.8212i	−0.526505	−	1.05029i
$394$	−28.1974	+	20.4866i	−1.42056	+	1.03210i
$395$	−8.39136	+	22.7686i	−0.422215	+	1.14561i
$396$	0.580337	+	1.86913i	0.0291630	+	0.0939272i
$397$	22.4113	+	16.2828i	1.12479	+	0.817208i	0.984928	−	0.172963i	$-0.0553340\pi$
$397$	22.4113	+	16.2828i	1.12479	+	0.817208i	0.139862	+	0.990171i	$0.455334\pi$
$398$	−31.5002	−	10.2350i	−1.57896	−	0.513036i
$399$	−2.11306	+	13.2433i	−0.105786	+	0.662994i
$400$	−24.4366	−	20.8433i	−1.22183	−	1.04217i
$401$			10.1998i			0.509355i	0.967026	+	0.254677i	$0.0819693\pi$
$401$			10.1998i			0.509355i	−0.967026	+	0.254677i	$0.918031\pi$
$402$	−2.58363	−	17.0344i	−0.128860	−	0.849599i
$403$	7.21335	−	9.92832i	0.359322	−	0.494565i
$404$	−17.4490	−	12.6774i	−0.868120	−	0.630726i
$405$	7.45200	−	18.6941i	0.370293	−	0.928915i
$406$	16.6532	−	0.0901169i	0.826483	−	0.00447243i
$407$	1.06478			0.0527790
$408$	−21.2312	+	41.0018i	−1.05110	+	2.02989i
$409$	−28.2418	+	9.17632i	−1.39647	+	0.453740i	−0.908047	−	0.418868i	$-0.862427\pi$
$409$	−28.2418	+	9.17632i	−1.39647	+	0.453740i	−0.488421	+	0.872608i	$0.662427\pi$
$410$	−7.80794	−	27.6504i	−0.385607	−	1.36555i
$411$	25.2397	−	3.82815i	1.24498	−	0.188829i
$412$	5.73151	+	17.6398i	0.282371	+	0.869049i
$413$	−27.3075	−	8.70966i	−1.34371	−	0.428574i
$414$	−35.4269	−	50.1301i	−1.74114	−	2.46376i
$415$	9.77588	−	12.4090i	0.479879	−	0.609132i
$416$	1.81208	+	5.57699i	0.0888443	+	0.273435i
$417$	6.59896	−	12.7440i	0.323153	−	0.624075i
$418$	−1.10101			−0.0538521
$419$	−11.3625	+	8.25536i	−0.555096	+	0.403301i	−0.829661	−	0.558268i	$-0.811466\pi$
$419$	−11.3625	+	8.25536i	−0.555096	+	0.403301i	0.274565	+	0.961569i	$0.411466\pi$
$420$	−40.7733	+	18.7563i	−1.98953	+	0.915215i
$421$	2.58759	+	1.88000i	0.126112	+	0.0916255i	0.649053	−	0.760743i	$-0.275165\pi$
$421$	2.58759	+	1.88000i	0.126112	+	0.0916255i	−0.522941	+	0.852369i	$0.675165\pi$
$422$	−18.3472	−	13.3300i	−0.893126	−	0.648894i
$423$	−2.29760	+	1.62371i	−0.111713	+	0.0789474i
$424$	−17.6124			−0.855334
$425$	−20.4910	−	8.47199i	−0.993958	−	0.410952i
$426$	16.9768	−	8.51040i	0.822529	−	0.412330i
$427$	12.5843	−	9.24748i	0.608996	−	0.447517i
$428$	−52.3355	−	38.0240i	−2.52973	−	1.83796i
$429$	0.355157	+	0.0586405i	0.0171472	+	0.00283119i
$430$	2.65922	−	68.2489i	0.128239	−	3.29125i
$431$	−22.2092	−	30.5683i	−1.06978	−	1.47242i	−0.870299	−	0.492523i	$-0.836075\pi$
$431$	−22.2092	−	30.5683i	−1.06978	−	1.47242i	−0.199480	−	0.979902i	$-0.563925\pi$
$432$	32.8584	+	5.86882i	1.58090	+	0.282364i
$433$	4.97978	−	3.61802i	0.239313	−	0.173871i	−0.461664	−	0.887055i	$-0.652747\pi$
$433$	4.97978	−	3.61802i	0.239313	−	0.173871i	0.700977	+	0.713184i	$0.252747\pi$
$434$	−17.8605	+	55.9983i	−0.857332	+	2.68800i
$435$	4.76827	−	8.39132i	0.228621	−	0.402333i
$436$	24.1797	−	74.4175i	1.15800	−	3.56395i
$437$	22.5468	−	7.32589i	1.07856	−	0.350445i
$438$	5.19020	−	5.12260i	0.247997	−	0.244767i
$439$	−14.6208	−	4.75060i	−0.697815	−	0.226734i	−0.0614365	−	0.998111i	$-0.519568\pi$
$439$	−14.6208	−	4.75060i	−0.697815	−	0.226734i	−0.636378	+	0.771377i	$0.719568\pi$
$440$	−1.11286	−	1.66433i	−0.0530533	−	0.0793439i
$441$	−0.0480459	+	20.9999i	−0.00228790	+	0.999997i
$442$	9.18644	+	12.6441i	0.436954	+	0.601416i
$443$	15.6187			0.742064			0.371032	−	0.928620i	$-0.379004\pi$
$443$	15.6187			0.742064			0.371032	+	0.928620i	$0.379004\pi$
$444$	24.9363	−	48.1573i	1.18343	−	2.28544i
$445$	−15.3085	−	0.596475i	−0.725693	−	0.0282756i
$446$	48.4759	+	35.2198i	2.29540	+	1.66771i
$447$	−11.9886	−	1.97946i	−0.567044	−	0.0936253i
$448$	3.49671	+	4.75844i	0.165204	+	0.224815i
$449$		−	16.9917i		−	0.801890i	−0.916102	−	0.400945i	$-0.868682\pi$
$449$		−	16.9917i		−	0.801890i	0.916102	−	0.400945i	$-0.131318\pi$
$450$	−3.44296	+	37.7309i	−0.162303	+	1.77865i
$451$		−	0.757718i		−	0.0356795i
$452$	1.59843	−	4.91947i	0.0751839	−	0.231392i
$453$	0.0720171	−	0.436173i	0.00338366	−	0.0204932i
$454$	−4.48047	+	6.16684i	−0.210279	+	0.289424i
$455$	−0.276746	+	8.24996i	−0.0129741	+	0.386764i
$456$	−14.0107	+	27.0576i	−0.656111	+	1.26709i
$457$			1.57647i			0.0737444i	0.999320	+	0.0368722i	$0.0117394\pi$
$457$			1.57647i			0.0737444i	−0.999320	+	0.0368722i	$0.988261\pi$
$458$	−36.5308	−	50.2804i	−1.70697	−	2.34945i
$459$	22.8259	−	3.15649i	1.06542	−	0.147332i
$460$	62.3215	+	49.0974i	2.90575	+	2.28918i
$461$	−9.94027	+	30.5930i	−0.462964	+	1.42486i	0.398560	+	0.917142i	$0.369510\pi$
$461$	−9.94027	+	30.5930i	−0.462964	+	1.42486i	−0.861525	+	0.507716i	$0.830490\pi$
$462$	−1.70315	+	0.267756i	−0.0792378	+	0.0124571i
$463$	16.7029	−	5.42711i	0.776251	−	0.252219i	0.106012	−	0.994365i	$-0.466192\pi$
$463$	16.7029	−	5.42711i	0.776251	−	0.252219i	0.670239	+	0.742146i	$0.266192\pi$
$464$	15.2243	+	4.94668i	0.706771	+	0.229644i
$465$	22.9667	+	25.1579i	1.06506	+	1.16667i
$466$	−2.75077	−	8.46599i	−0.127427	−	0.392179i
$467$	8.90654	+	12.2588i	0.412146	+	0.567270i	0.963740	−	0.266843i	$-0.0859804\pi$
$467$	8.90654	+	12.2588i	0.412146	+	0.567270i	−0.551595	+	0.834112i	$0.685980\pi$
$468$	10.9697	−	14.6896i	0.507076	−	0.679027i
$469$	10.4194	−	0.0563833i	0.481121	−	0.00260354i
$470$	3.27781	−	4.16067i	0.151194	−	0.191917i
$471$	−1.67639	+	10.1531i	−0.0772439	+	0.467829i
$472$	−52.6856	−	38.2783i	−2.42505	−	1.76190i
$473$	0.556614	−	1.71308i	0.0255932	−	0.0787677i
$474$	21.2760	+	42.4419i	0.977237	+	1.94942i
$475$	−13.5222	−	5.59076i	−0.620442	−	0.256522i
$476$	−41.7376	−	29.9804i	−1.91304	−	1.37415i
$477$	5.07280	+	7.17817i	0.232268	+	0.328666i
$478$	−9.35183	+	12.8717i	−0.427743	+	0.588737i
$479$	14.1406	+	10.2738i	0.646101	+	0.469420i	0.861941	−	0.507009i	$-0.169249\pi$
$479$	14.1406	+	10.2738i	0.646101	+	0.469420i	−0.215840	+	0.976429i	$0.569249\pi$
$480$	−16.1759	+	1.81244i	−0.738325	+	0.0827262i
$481$	−5.86273	−	8.06936i	−0.267317	−	0.367931i
$482$		−	43.3598i		−	1.97498i
$483$	33.0960	−	16.8156i	1.50592	−	0.765137i
$484$	14.8580	+	45.7284i	0.675366	+	2.07856i
$485$	9.09469	−	24.6770i	0.412969	−	1.12053i
$486$	−16.7162	−	35.6495i	−0.758260	−	1.61709i
$487$	8.05255	−	2.61643i	0.364896	−	0.118562i	−0.120830	−	0.992673i	$-0.538555\pi$
$487$	8.05255	−	2.61643i	0.364896	−	0.118562i	0.485726	+	0.874111i	$0.338555\pi$
$488$	33.7450	−	10.9644i	1.52757	−	0.496336i
$489$	1.29938	+	8.56705i	0.0587599	+	0.387415i
$490$	−11.1551	−	37.9294i	−0.503938	−	1.71347i
$491$	21.5879	−	7.01435i	0.974251	−	0.316553i	0.221720	−	0.975110i	$-0.428833\pi$
$491$	21.5879	−	7.01435i	0.974251	−	0.316553i	0.752531	+	0.658557i	$0.228833\pi$
$492$	−34.2698	−	17.7452i	−1.54500	−	0.800017i
$493$	11.0511			0.497719
$494$	6.06224	+	8.34395i	0.272753	+	0.375412i
$495$	−0.357790	+	0.932927i	−0.0160815	+	0.0419320i
$496$	−33.2092	+	45.7086i	−1.49114	+	2.05238i
$497$	3.60801	+	10.9032i	0.161841	+	0.489075i
$498$	−4.63475	−	30.5578i	−0.207688	−	1.36933i
$499$	28.5646			1.27873			0.639363	−	0.768905i	$-0.279198\pi$
$499$	28.5646			1.27873			0.639363	+	0.768905i	$0.279198\pi$
$500$	−9.60028	−	48.0184i	−0.429338	−	2.14745i
$501$	26.6585	−	13.3638i	1.19102	−	0.597051i
$502$	−23.3353	+	71.8186i	−1.04151	+	3.20542i
$503$	−25.5498	+	35.1663i	−1.13921	+	1.56799i	−0.369951	+	0.929051i	$0.620626\pi$
$503$	−25.5498	+	35.1663i	−1.13921	+	1.56799i	−0.769259	+	0.638937i	$0.779374\pi$
$504$	−15.0930	+	45.2627i	−0.672295	+	2.01616i
$505$	−2.99234	−	10.5968i	−0.133157	−	0.471552i
$506$	1.79142	+	2.46568i	0.0796383	+	0.109613i
$507$	8.57950	+	17.1146i	0.381029	+	0.760088i
$508$	37.9046	+	52.1712i	1.68174	+	2.31472i
$509$	−4.20960	−	12.9558i	−0.186587	−	0.574256i	0.813385	−	0.581726i	$-0.197622\pi$
$509$	−4.20960	−	12.9558i	−0.186587	−	0.574256i	−0.999972	+	0.00746969i	$0.997622\pi$
$510$	−39.5097	+	17.9166i	−1.74952	+	0.793362i
$511$	2.61148	+	3.55380i	0.115525	+	0.157211i
$512$	15.5224	+	47.7731i	0.686000	+	2.11129i
$513$	15.0631	−	2.08300i	0.665052	−	0.0919668i
$514$	50.7854	+	16.5012i	2.24005	+	0.727836i
$515$	−3.27452	+	8.88488i	−0.144292	+	0.391515i
$516$	−64.4431	−	65.2936i	−2.83695	−	2.87439i
$517$	0.113009	−	0.0821055i	0.00497011	−	0.00361100i
$518$	38.7999	+	27.8702i	1.70477	+	1.22455i
$519$	−1.08544	+	2.09620i	−0.0476453	+	0.0920131i
$520$	−6.48560	+	17.5977i	−0.284412	+	0.771708i
$521$	0.552607	+	0.401492i	0.0242101	+	0.0175897i	0.599825	−	0.800132i	$-0.295237\pi$
$521$	0.552607	+	0.401492i	0.0242101	+	0.0175897i	−0.575614	+	0.817721i	$0.695237\pi$
$522$	−5.59928	−	18.0339i	−0.245074	−	0.789324i
$523$	−3.41329	+	10.5050i	−0.149253	+	0.459353i	−0.997533	−	0.0701940i	$-0.977638\pi$
$523$	−3.41329	+	10.5050i	−0.149253	+	0.459353i	0.848280	+	0.529547i	$0.177638\pi$
$524$	58.8963			2.57290
$525$	−22.2772	−	5.35987i	−0.972255	−	0.233924i
$526$	−60.6548			−2.64467
$527$	−12.0531	+	37.0956i	−0.525041	+	1.61591i
$528$	−1.63509	−	0.269973i	−0.0711584	−	0.0117490i
$529$	−34.4839	−	25.0540i	−1.49930	−	1.08930i
$530$	−12.9988	−	10.2405i	−0.564631	−	0.444821i
$531$	−0.426090	+	32.4978i	−0.0184907	+	1.41028i
$532$	−27.5431	−	19.7844i	−1.19415	−	0.857764i
$533$	−5.74233	+	4.17205i	−0.248728	+	0.180711i
$534$	−21.3333	+	21.0554i	−0.923182	+	0.911158i
$535$	−8.97505	−	31.7835i	−0.388025	−	1.37412i
$536$	22.5148	+	7.31551i	0.972493	+	0.315982i
$537$	−8.69212	−	8.80683i	−0.375093	−	0.380043i
$538$	11.9980	+	36.9261i	0.517271	+	1.59200i
$539$	−0.0112840	−	1.04259i	−0.000486037	−	0.0449073i
$540$	33.8149	+	38.0305i	1.45516	+	1.63657i
$541$	1.44799	+	4.45644i	0.0622538	+	0.191597i	0.977346	−	0.211647i	$-0.0678826\pi$
$541$	1.44799	+	4.45644i	0.0622538	+	0.191597i	−0.915092	+	0.403244i	$0.867883\pi$
$542$	−7.37106	−	10.1454i	−0.316614	−	0.435782i
$543$	14.2407	−	7.13878i	0.611125	−	0.306354i
$544$	−10.9550	−	15.0782i	−0.469690	−	0.646472i
$545$	33.2079	−	22.2045i	1.42247	−	0.951136i
$546$	11.4069	+	11.4330i	0.488168	+	0.489286i
$547$	−4.26552	+	5.87098i	−0.182380	+	0.251025i	−0.890412	−	0.455156i	$-0.849584\pi$
$547$	−4.26552	+	5.87098i	−0.182380	+	0.251025i	0.708031	+	0.706181i	$0.249584\pi$
$548$	−19.9484	+	61.3950i	−0.852155	+	2.62266i
$549$	−14.1881	−	10.5952i	−0.605533	−	0.452192i
$550$	0.146368	−	1.87541i	0.00624116	−	0.0799679i
$551$	7.29278			0.310683
$552$	83.3909	−	12.6480i	3.54935	−	0.538336i
$553$	−27.2579	+	9.02000i	−1.15913	+	0.383569i
$554$	−13.6839	+	18.8343i	−0.581375	+	0.800194i
$555$	25.2148	−	11.4343i	1.07031	−	0.485359i
$556$	21.3308	+	29.3594i	0.904629	+	1.24512i
$557$	−31.3506			−1.32837			−0.664185	−	0.747569i	$-0.731221\pi$
$557$	−31.3506			−1.32837			−0.664185	+	0.747569i	$0.731221\pi$
$558$	66.6418	+	0.873764i	2.82117	+	0.0369894i
$559$	−16.0473	+	5.21408i	−0.678728	+	0.220532i
$560$	1.27410	−	37.9816i	0.0538406	−	1.60502i
$561$	−1.13115	+	0.171564i	−0.0477573	+	0.00724342i
$562$	−38.7690	+	12.5968i	−1.63537	+	0.531364i
$563$	37.0496	−	12.0382i	1.56146	−	0.507348i	0.604260	−	0.796787i	$-0.293469\pi$
$563$	37.0496	−	12.0382i	1.56146	−	0.507348i	0.957196	+	0.289439i	$0.0934688\pi$
$564$	−1.06685	−	7.03396i	−0.0449226	−	0.296183i
$565$	2.19525	−	1.46786i	0.0923551	−	0.0617532i
$566$	−22.0581	−	67.8877i	−0.927170	−	2.85353i
$567$	22.7945	−	6.88541i	0.957281	−	0.289160i
$568$			26.0936i			1.09486i
$569$	−0.0210466	−	0.0289682i	−0.000882320	−	0.00121441i	0.808576	−	0.588392i	$-0.200239\pi$
$569$	−0.0210466	−	0.0289682i	−0.000882320	−	0.00121441i	−0.809458	+	0.587178i	$0.800239\pi$
$570$	−26.0729	+	11.8234i	−1.09207	+	0.495227i
$571$	−14.3479	−	10.4243i	−0.600440	−	0.436245i	0.245595	−	0.969372i	$-0.421017\pi$
$571$	−14.3479	−	10.4243i	−0.600440	−	0.436245i	−0.846035	+	0.533128i	$0.821017\pi$
$572$	−0.535036	+	0.736414i	−0.0223710	+	0.0307910i
$573$	−3.68022	−	24.2644i	−0.153743	−	1.01366i
$574$	19.8331	−	27.6108i	0.827816	−	1.15245i
$575$	9.48125	+	39.3791i	0.395396	+	1.64222i
$576$	4.00632	−	5.36488i	0.166930	−	0.223537i
$577$	−4.56417	+	14.0471i	−0.190009	+	0.584787i	−0.999999	−	0.00165695i	$-0.999473\pi$
$577$	−4.56417	+	14.0471i	−0.190009	+	0.584787i	0.809990	+	0.586444i	$0.199473\pi$
$578$	−5.44819	−	3.95834i	−0.226615	−	0.164645i
$579$	23.5049	+	3.88093i	0.976831	+	0.161286i
$580$	13.5658	+	20.2884i	0.563291	+	0.842430i
$581$	18.6912	−	0.101145i	0.775440	−	0.00419622i
$582$	−23.0592	−	45.9993i	−0.955836	−	1.90673i
$583$	−0.256515	−	0.353062i	−0.0106238	−	0.0146223i
$584$	3.09635	+	9.52958i	0.128128	+	0.394337i
$585$	9.04017	−	2.42526i	0.373765	−	0.100272i
$586$	−36.0232	−	11.7047i	−1.48811	−	0.483515i
$587$	−10.0068	+	3.25140i	−0.413024	+	0.134200i	−0.508156	−	0.861265i	$-0.669673\pi$
$587$	−10.0068	+	3.25140i	−0.413024	+	0.134200i	0.0951319	+	0.995465i	$0.469673\pi$
$588$	−47.4179	−	23.9063i	−1.95548	−	0.985879i
$589$	−7.95397	+	24.4798i	−0.327738	+	1.00867i
$590$	−16.6279	−	58.8847i	−0.684561	−	2.42424i
$591$	−17.0106	+	16.7890i	−0.699721	+	0.690607i
$592$	26.9912	+	37.1502i	1.10933	+	1.52686i
$593$		−	8.25794i		−	0.339113i	−0.985520	−	0.169556i	$-0.945766\pi$
$593$		−	8.25794i		−	0.339113i	0.985520	−	0.169556i	$-0.0542335\pi$
$594$	0.853088	+	1.75896i	0.0350026	+	0.0721709i
$595$	−7.26620	−	25.2095i	−0.297885	−	1.03349i
$596$	18.0606	−	24.8583i	0.739791	−	1.01824i
$597$	−22.4089	−	3.69996i	−0.917135	−	0.151429i
$598$	8.82234	−	27.1524i	0.360772	−	1.11034i
$599$			46.0483i			1.88148i	0.339127	+	0.940741i	$0.389869\pi$
$599$			46.0483i			1.88148i	−0.339127	+	0.940741i	$0.610131\pi$
$600$	−44.2261	−	27.4623i	−1.80552	−	1.12114i
$601$		−	3.31965i		−	0.135411i	−0.997705	−	0.0677056i	$-0.978432\pi$
$601$		−	3.31965i		−	0.135411i	0.997705	−	0.0677056i	$-0.0215679\pi$
$602$	65.1222	−	47.8546i	2.65418	−	1.95041i
$603$	−3.50329	−	11.2833i	−0.142665	−	0.459490i
$604$	0.904399	+	0.657084i	0.0367995	+	0.0267364i
$605$	−8.48868	+	23.0327i	−0.345114	+	0.936412i
$606$	−19.1309	−	9.90618i	−0.777140	−	0.402411i
$607$	18.6894			0.758580			0.379290	−	0.925278i	$-0.376168\pi$
$607$	18.6894			0.758580			0.379290	+	0.925278i	$0.376168\pi$
$608$	−7.22930	−	9.95027i	−0.293187	−	0.403537i
$609$	11.2812	−	1.77354i	0.457137	−	0.0718675i
$610$	31.2806	+	11.5284i	1.26651	+	0.466772i
$611$	−1.24447	−	0.404351i	−0.0503457	−	0.0163583i
$612$	−18.7314	+	55.1772i	−0.757172	+	2.23041i
$613$	0.198295	−	0.0644298i	0.00800905	−	0.00260230i	−0.305010	−	0.952349i	$-0.598660\pi$
$613$	0.198295	−	0.0644298i	0.00800905	−	0.00260230i	0.313019	+	0.949747i	$0.398660\pi$
$614$	24.4547	−	75.2638i	0.986911	−	3.03740i
$615$	−8.13689	−	17.9434i	−0.328111	−	0.723549i
$616$	0.719837	−	2.25691i	0.0290031	−	0.0909337i
$617$	−20.5692	+	14.9444i	−0.828087	+	0.601640i	−0.919017	−	0.394217i	$-0.871016\pi$
$617$	−20.5692	+	14.9444i	−0.828087	+	0.601640i	0.0909306	+	0.995857i	$0.471016\pi$
$618$	8.30241	+	16.5619i	0.333972	+	0.666217i
$619$	1.44726	+	1.99199i	0.0581705	+	0.0800648i	0.837111	−	0.547033i	$-0.184243\pi$
$619$	1.44726	+	1.99199i	0.0581705	+	0.0800648i	−0.778941	+	0.627098i	$0.784243\pi$
$620$	−82.8982	+	23.4089i	−3.32927	+	0.940124i
$621$	−29.1735	−	30.3441i	−1.17069	−	1.21767i
$622$	−34.5037	−	25.0684i	−1.38347	−	1.00515i
$623$	−10.7340	−	14.6072i	−0.430049	−	0.585225i
$624$	6.95697	+	13.8780i	0.278502	+	0.555564i
$625$	11.3207	−	22.2899i	0.452828	−	0.891598i
$626$	−58.2452			−2.32795
$627$	−0.746460	+	0.113217i	−0.0298107	+	0.00452144i
$628$	−21.0523	−	15.2954i	−0.840077	−	0.610352i
$629$	25.6470	+	18.6336i	1.02261	+	0.742972i
$630$	−37.4568	+	24.6303i	−1.49232	+	0.981295i
$631$	−30.6902	+	22.2977i	−1.22176	+	0.887658i	−0.996245	−	0.0865820i	$-0.972406\pi$
$631$	−30.6902	+	22.2977i	−1.22176	+	0.887658i	−0.225512	+	0.974240i	$0.572406\pi$
$632$	−65.2337			−2.59486
$633$	−13.8097	−	7.15080i	−0.548886	−	0.284219i
$634$	8.75764	+	26.9532i	0.347810	+	1.07045i
$635$	−1.28181	+	32.8977i	−0.0508672	+	1.30550i
$636$	−21.9756	+	3.33307i	−0.871388	+	0.132165i
$637$	−7.83905	+	5.82606i	−0.310595	+	0.230837i
$638$	0.289718	+	0.891660i	0.0114700	+	0.0353012i
$639$	10.6348	−	7.51559i	0.420705	−	0.297312i
$640$	−10.8588	+	29.4636i	−0.429231	+	1.16465i
$641$	17.7088	−	5.75392i	0.699454	−	0.227266i	0.0623613	−	0.998054i	$-0.480137\pi$
$641$	17.7088	−	5.75392i	0.699454	−	0.227266i	0.637093	+	0.770787i	$0.280137\pi$
$642$	−57.3801	−	29.7120i	−2.26461	−	1.17264i
$643$	1.11839			0.0441051			0.0220525	−	0.999757i	$-0.492980\pi$
$643$	1.11839			0.0441051			0.0220525	+	0.999757i	$0.492980\pi$
$644$	0.507982	+	93.8726i	0.0200173	+	3.69910i
$645$	−5.21513	−	46.5446i	−0.205346	−	1.83269i
$646$	−26.5198	−	19.2677i	−1.04341	−	0.758079i
$647$	−15.6405	+	21.5274i	−0.614893	+	0.846328i	−0.996969	−	0.0778031i	$-0.975209\pi$
$647$	−15.6405	+	21.5274i	−0.614893	+	0.846328i	0.382075	+	0.924131i	$0.375209\pi$
$648$	54.0826	+	1.41843i	2.12456	+	0.0557214i
$649$		−	1.61365i		−	0.0633413i
$650$	−15.0186	+	9.21691i	−0.589080	+	0.361517i
$651$	−6.35073	+	39.8022i	−0.248905	+	1.55997i
$652$	−20.8391	−	6.77104i	−0.816122	−	0.265174i
$653$	10.0388	+	7.29361i	0.392848	+	0.285421i	0.766622	−	0.642099i	$-0.221936\pi$
$653$	10.0388	+	7.29361i	0.392848	+	0.285421i	−0.373773	+	0.927520i	$0.621936\pi$
$654$	12.7324	−	77.1138i	0.497874	−	3.01539i
$655$	23.6192	+	18.6074i	0.922880	+	0.727053i
$656$	26.4369	−	19.2075i	1.03219	−	0.749927i
$657$	2.99208	−	4.00671i	0.116732	−	0.156317i
$658$	6.26706	−	0.0339136i	0.244315	−	0.00132209i
$659$	−28.8945	+	9.38839i	−1.12557	+	0.365720i	−0.811891	−	0.583809i	$-0.801562\pi$
$659$	−28.8945	+	9.38839i	−1.12557	+	0.365720i	−0.313679	+	0.949529i	$0.601562\pi$
$660$	−1.70351	−	1.86604i	−0.0663091	−	0.0726354i
$661$	24.2139	+	7.86757i	0.941811	+	0.306013i	0.739384	−	0.673284i	$-0.235117\pi$
$661$	24.2139	+	7.86757i	0.941811	+	0.306013i	0.202428	+	0.979297i	$0.435117\pi$
$662$	−7.68515	−	23.6525i	−0.298692	−	0.919279i
$663$	7.52839	+	7.62774i	0.292378	+	0.296237i
$664$	40.3891	+	13.1232i	1.56740	+	0.509280i
$665$	−4.79505	−	16.6360i	−0.185944	−	0.645117i
$666$	17.4130	−	51.2935i	0.674739	−	1.98758i
$667$	−11.8659	−	16.3319i	−0.459448	−	0.632375i
$668$			75.4083i			2.91764i
$669$	36.4872	+	18.8934i	1.41068	+	0.730463i
$670$	12.3635	+	18.4902i	0.477643	+	0.714339i
$671$	0.711272	+	0.516769i	0.0274584	+	0.0199497i
$672$	−13.6028	−	13.6340i	−0.524740	−	0.525942i
$673$	27.8643	+	9.05366i	1.07409	+	0.348993i	0.792079	−	0.610419i	$-0.208999\pi$
$673$	27.8643	+	9.05366i	1.07409	+	0.348993i	0.282010	+	0.959411i	$0.408999\pi$
$674$			13.4032i			0.516271i
$675$	1.54561	+	25.9347i	0.0594907	+	0.998229i
$676$	−48.4118			−1.86199
$677$	0.220653	+	0.0716946i	0.00848039	+	0.00275545i	0.313254	−	0.949669i	$-0.398581\pi$
$677$	0.220653	+	0.0716946i	0.00848039	+	0.00275545i	−0.304774	+	0.952425i	$0.598581\pi$
$678$	0.841689	−	5.09771i	0.0323249	−	0.195776i
$679$	29.5426	−	9.77603i	1.13374	−	0.375170i
$680$	2.32081	−	59.5634i	0.0889989	−	2.28415i
$681$	−2.40352	+	4.64170i	−0.0921032	+	0.177870i
$682$	−3.30904			−0.126710
$683$	−22.7084	+	16.4987i	−0.868915	+	0.631303i	−0.930295	−	0.366811i	$-0.880450\pi$
$683$	−22.7084	+	16.4987i	−0.868915	+	0.631303i	0.0613809	+	0.998114i	$0.480450\pi$
$684$	−12.3611	+	36.4121i	−0.472637	+	1.39225i
$685$	−27.3968	+	18.3189i	−1.04678	+	0.699928i
$686$	26.8782	−	38.2866i	1.02621	−	1.46179i
$687$	−29.9374	−	30.3325i	−1.14218	−	1.15726i
$688$	73.8794	−	24.0049i	2.81663	−	0.915177i
$689$	−1.26328	+	3.88797i	−0.0481270	+	0.148120i
$690$	68.9005	+	39.1519i	2.62300	+	1.49049i
$691$	−0.0183011	+	0.00594640i	−0.000696208	+	0.000226212i	−0.309365	−	0.950943i	$-0.600117\pi$
$691$	−0.0183011	+	0.00594640i	−0.000696208	+	0.000226212i	0.308669	+	0.951170i	$0.400117\pi$
$692$	−3.50862	−	4.82920i	−0.133378	−	0.183579i
$693$	−1.12717	+	0.356668i	−0.0428175	+	0.0135487i
$694$	26.6866	−	19.3889i	1.01301	−	0.735994i
$695$	−0.721341	+	18.5132i	−0.0273620	+	0.702246i
$696$	25.5995	+	4.22677i	0.970347	+	0.160215i
$697$	13.2601	−	18.2510i	0.502262	−	0.691305i
$698$	6.67644	+	2.16931i	0.252707	+	0.0821095i
$699$	−2.73551	−	5.45689i	−0.103467	−	0.206398i
$700$	37.3615	−	44.2857i	1.41213	−	1.67384i
$701$			20.3707i			0.769392i	0.923043	+	0.384696i	$0.125694\pi$
$701$			20.3707i			0.769392i	−0.923043	+	0.384696i	$0.874306\pi$
$702$	8.63301	−	16.1500i	0.325832	−	0.609543i
$703$	16.9248	+	12.2966i	0.638329	+	0.463773i
$704$	−0.195404	+	0.268950i	−0.00736456	+	0.0101364i
$705$	1.79444	−	3.15789i	0.0675824	−	0.118933i
$706$	−18.2505	−	25.1196i	−0.686866	−	0.945390i
$707$	7.60088	−	10.5817i	0.285861	−	0.397964i
$708$	−72.9815	−	37.7906i	−2.74281	−	1.42026i
$709$	4.53884	+	13.9691i	0.170460	+	0.524621i	0.999397	−	0.0347207i	$-0.0110542\pi$
$709$	4.53884	+	13.9691i	0.170460	+	0.524621i	−0.828937	+	0.559341i	$0.811054\pi$
$710$	−15.1718	+	19.2583i	−0.569388	+	0.722750i
$711$	18.7889	+	26.5869i	0.704640	+	0.997086i
$712$	−12.7269	−	39.1695i	−0.476962	−	1.46794i
$713$	67.7634	−	22.0177i	2.53776	−	0.824568i
$714$	−45.7092	−	23.3559i	−1.71062	−	0.874073i
$715$	−0.447225	+	0.126288i	−0.0167253	+	0.00472290i
$716$	29.7588	−	9.66922i	1.11214	−	0.361356i
$717$	−5.01673	+	9.68836i	−0.187353	+	0.361818i
$718$			62.2622i			2.32361i
$719$	−11.0401	+	8.02111i	−0.411727	+	0.299137i	−0.774301	−	0.632818i	$-0.781898\pi$
$719$	−11.0401	+	8.02111i	−0.411727	+	0.299137i	0.362574	+	0.931955i	$0.381898\pi$
$720$	−41.6196	+	11.1656i	−1.55107	+	0.416116i
$721$	−10.6367	+	3.51983i	−0.396132	+	0.131085i
$722$	21.3249	+	15.4934i	0.793630	+	0.576606i
$723$	−4.45868	−	29.3970i	−0.165820	−	1.09328i
$724$			40.2822i			1.49708i
$725$	−0.969501	+	12.4222i	−0.0360064	+	0.461349i
$726$	21.5227	+	42.9342i	0.798783	+	1.59344i
$727$	6.12784	−	18.8596i	0.227269	−	0.699462i	−0.770784	−	0.637096i	$-0.780135\pi$
$727$	6.12784	−	18.8596i	0.227269	−	0.699462i	0.998053	−	0.0623661i	$-0.0198647\pi$
$728$	−21.0674	+	6.97147i	−0.780810	+	0.258380i
$729$	−14.9990	−	22.4506i	−0.555519	−	0.831504i
$730$	−3.25562	+	8.83362i	−0.120496	+	0.326947i
$731$	43.3861	−	31.5219i	1.60469	−	1.16588i
$732$	40.0298	−	20.0667i	1.47954	−	0.741688i
$733$	21.0726	−	15.3102i	0.778336	−	0.565494i	−0.126143	−	0.992012i	$-0.540260\pi$
$733$	21.0726	−	15.3102i	0.778336	−	0.565494i	0.904479	+	0.426518i	$0.140260\pi$
$734$	17.2473	+	53.0816i	0.636608	+	1.95928i
$735$	−11.4632	−	24.5682i	−0.422827	−	0.906211i
$736$	−10.5208	+	32.3796i	−0.387800	+	1.19353i
$737$	0.181267	+	0.557884i	0.00667707	+	0.0205499i
$738$	−36.5015	−	12.3914i	−1.34364	−	0.456135i
$739$	6.29184	−	19.3643i	0.231449	−	0.712327i	−0.766123	−	0.642693i	$-0.777817\pi$
$739$	6.29184	−	19.3643i	0.231449	−	0.712327i	0.997573	−	0.0696338i	$-0.0221831\pi$
$740$	−2.72582	+	69.9582i	−0.100203	+	2.57171i
$741$	4.96807	+	5.03363i	0.182506	+	0.184915i
$742$	−0.105953	−	19.5796i	−0.00388966	−	0.718790i
$743$	6.71469			0.246338			0.123169	−	0.992386i	$-0.460694\pi$
$743$	6.71469			0.246338			0.123169	+	0.992386i	$0.460694\pi$
$744$	−42.1085	+	81.3204i	−1.54377	+	2.98135i
$745$	15.0965	−	4.26296i	0.553092	−	0.156183i
$746$	−25.9273	+	35.6858i	−0.949264	+	1.30655i
$747$	−6.28451	−	20.2409i	−0.229938	−	0.740576i
$748$	0.894015	−	2.75150i	0.0326884	−	0.100605i
$749$	22.7977	−	31.7380i	0.833008	−	1.15968i
$750$	−16.6733	−	45.9833i	−0.608824	−	1.67907i
$751$	14.3500			0.523639			0.261820	−	0.965117i	$-0.415677\pi$
$751$	14.3500			0.523639			0.261820	+	0.965117i	$0.415677\pi$
$752$	5.72934	+	1.86158i	0.208928	+	0.0678847i
$753$	−8.43570	+	51.0910i	−0.307414	+	1.86186i
$754$	5.16220	−	7.10516i	0.187996	−	0.258755i
$755$	0.155096	+	0.549243i	0.00564451	+	0.0199890i
$756$	−10.2662	+	59.3319i	−0.373380	+	2.15788i
$757$			3.66894i			0.133350i	0.997775	+	0.0666750i	$0.0212391\pi$
$757$			3.66894i			0.133350i	−0.997775	+	0.0666750i	$0.978761\pi$
$758$	37.1016	−	26.9559i	1.34759	−	0.979083i
$759$	1.46809	+	1.48746i	0.0532882	+	0.0539914i
$760$	1.53153	−	39.3066i	0.0555543	−	1.42580i
$761$	−2.21793	+	6.82607i	−0.0803998	+	0.247445i	−0.983175	−	0.182669i	$-0.941526\pi$
$761$	−2.21793	+	6.82607i	−0.0803998	+	0.247445i	0.902775	+	0.430114i	$0.141526\pi$
$762$	45.2476	+	45.8448i	1.63915	+	1.66078i
$763$	45.0316	+	14.3627i	1.63025	+	0.519965i
$764$	59.0224	+	19.1775i	2.13536	+	0.693819i
$765$	−24.9443	+	16.2099i	−0.901863	+	0.586068i
$766$	5.30194	−	1.72271i	0.191567	−	0.0622439i
$767$	−12.2290	+	8.88487i	−0.441562	+	0.320814i
$768$	24.0672	+	48.0100i	0.868451	+	1.73241i
$769$	23.8988	+	32.8939i	0.861814	+	1.18619i	0.981134	+	0.193329i	$0.0619285\pi$
$769$	23.8988	+	32.8939i	0.861814	+	1.18619i	−0.119320	+	0.992856i	$0.538071\pi$
$770$	1.84353	−	1.24717i	0.0664363	−	0.0449448i
$771$	36.1282	+	5.96517i	1.30112	+	0.214830i
$772$	−35.4096	+	48.7371i	−1.27442	+	1.75409i
$773$	9.20835	+	2.99197i	0.331201	+	0.107614i	0.469897	−	0.882721i	$-0.344291\pi$
$773$	9.20835	+	2.99197i	0.331201	+	0.107614i	−0.138696	+	0.990335i	$0.544291\pi$
$774$	−73.4217	−	54.8290i	−2.63909	−	1.97079i
$775$	−40.6405	−	16.8028i	−1.45985	−	0.603574i
$776$	70.7014			2.53803
$777$	29.1713	+	14.9056i	1.04652	+	0.534735i
$778$	−12.5309	+	17.2474i	−0.449256	+	0.618348i
$779$	8.75049	−	12.0440i	0.313519	−	0.431522i
$780$	−4.76201	+	23.1845i	−0.170507	+	0.830139i
$781$	−0.523077	+	0.380038i	−0.0187172	+	0.0135988i
$782$			90.7401i			3.24486i
$783$	−5.65061	−	11.6508i	−0.201936	−	0.416367i
$784$	36.0899	−	26.8224i	1.28892	−	0.957941i
$785$	−3.61026	−	12.7851i	−0.128856	−	0.456319i
$786$	58.1638	−	8.82180i	2.07464	−	0.314663i
$787$	−3.46131	−	10.6528i	−0.123382	−	0.379732i	0.870220	−	0.492662i	$-0.163976\pi$
$787$	−3.46131	−	10.6528i	−0.123382	−	0.379732i	−0.993603	+	0.112930i	$0.963976\pi$
$788$	−18.6763	−	57.4797i	−0.665315	−	2.04763i
$789$	−41.1226	+	6.23713i	−1.46400	+	0.222048i
$790$	−48.1456	−	37.9295i	−1.71294	−	1.34947i
$791$	2.97687	+	0.949466i	0.105845	+	0.0337591i
$792$	−2.68588	−	0.0352155i	−0.0954387	−	0.00125133i
$793$		−	8.23571i		−	0.292459i
$794$	−56.6075	+	41.1277i	−2.00892	+	1.45957i
$795$	−9.86592	−	5.60619i	−0.349908	−	0.198831i
$796$	33.7584	−	46.4645i	1.19654	−	1.64689i
$797$	−9.44728	+	13.0031i	−0.334640	+	0.460592i	−0.942866	−	0.333171i	$-0.891881\pi$
$797$	−9.44728	+	13.0031i	−0.334640	+	0.460592i	0.608227	+	0.793763i	$0.291881\pi$
$798$	−30.1640	−	15.4128i	−1.06779	−	0.545608i
$799$	4.15886			0.147130
$800$	17.9099	−	10.9913i	0.633212	−	0.388601i
$801$	−12.2984	+	16.4688i	−0.434542	+	0.581897i
$802$	−24.5022	−	7.96126i	−0.865204	−	0.281122i
$803$	−0.145936	+	0.200863i	−0.00514995	+	0.00708830i
$804$	29.4769	+	4.86697i	1.03957	+	0.171645i
$805$	−29.4540	+	37.8063i	−1.03812	+	1.33250i
$806$	18.2198	+	25.0774i	0.641765	+	0.883314i
$807$	11.9315	+	23.8013i	0.420008	+	0.837846i
$808$	23.9481	−	17.3993i	0.842492	−	0.612106i
$809$	1.15994	−	0.376888i	0.0407814	−	0.0132507i	−0.288555	−	0.957463i	$-0.593175\pi$
$809$	1.15994	−	0.376888i	0.0407814	−	0.0132507i	0.329337	+	0.944213i	$0.393175\pi$
$810$	39.0908	+	32.4926i	1.37351	+	1.14167i
$811$	−9.28831	−	3.01795i	−0.326157	−	0.105975i	0.141362	−	0.989958i	$-0.454852\pi$
$811$	−9.28831	−	3.01795i	−0.326157	−	0.105975i	−0.467519	+	0.883983i	$0.654852\pi$
$812$	−8.77490	+	27.5120i	−0.307939	+	0.965484i
$813$	−6.04066	−	6.12038i	−0.211855	−	0.214651i
$814$	−0.831089	+	2.55783i	−0.0291296	+	0.0896518i
$815$	−6.21792	−	9.29921i	−0.217804	−	0.325737i
$816$	−34.6596	−	35.1170i	−1.21333	−	1.22934i
$817$	28.6310	−	20.8016i	1.00167	−	0.727757i
$818$		−	75.0055i		−	2.62251i
$819$	8.90924	+	6.57834i	0.311314	+	0.229866i
$820$	49.7837	+	1.93976i	1.73852	+	0.0677392i
$821$	−2.90849	+	4.00320i	−0.101507	+	0.139713i	−0.856749	−	0.515734i	$-0.827519\pi$
$821$	−2.90849	+	4.00320i	−0.101507	+	0.139713i	0.755242	+	0.655446i	$0.227519\pi$
$822$	−10.5043	+	63.6194i	−0.366379	+	2.21898i
$823$	−22.2277	−	7.22221i	−0.774809	−	0.251751i	−0.105186	−	0.994453i	$-0.533544\pi$
$823$	−22.2277	−	7.22221i	−0.774809	−	0.251751i	−0.669622	+	0.742702i	$0.733544\pi$
$824$	−25.4558			−0.886796
$825$	−0.0936143	−	1.28654i	−0.00325923	−	0.0447915i
$826$	42.2368	−	58.8005i	1.46961	−	2.04593i
$827$	−2.29210	+	7.05436i	−0.0797041	+	0.245304i	−0.982967	−	0.183784i	$-0.941165\pi$
$827$	−2.29210	+	7.05436i	−0.0797041	+	0.245304i	0.903262	+	0.429089i	$0.141165\pi$
$828$	101.656	−	31.5627i	3.53279	−	1.09688i
$829$	4.76329	−	6.55611i	0.165436	−	0.227703i	−0.718248	−	0.695787i	$-0.755056\pi$
$829$	4.76329	−	6.55611i	0.165436	−	0.227703i	0.883684	+	0.468084i	$0.155056\pi$
$830$	22.1787	+	33.1694i	0.769834	+	1.15133i
$831$	−7.34067	+	14.1764i	−0.254645	+	0.491773i
$832$	3.11413			0.107963
$833$	17.9735	−	25.3100i	0.622745	−	0.876939i
$834$	25.4632	+	25.7992i	0.881717	+	0.893354i
$835$	−23.8242	+	30.2411i	−0.824469	+	1.04654i
$836$	0.589971	−	1.81574i	0.0204046	−	0.0627988i
$837$	45.2715	−	6.26038i	1.56481	−	0.216390i
$838$	−10.9624	−	33.7389i	−0.378691	−	1.16549i
$839$	12.7229	−	39.1570i	0.439242	−	1.35185i	−0.449434	−	0.893313i	$-0.648374\pi$
$839$	12.7229	−	39.1570i	0.439242	−	1.35185i	0.888676	−	0.458535i	$-0.151626\pi$
$840$	−7.18990	−	61.1758i	−0.248075	−	2.11077i
$841$	7.04248	+	21.6745i	0.242844	+	0.747398i
$842$	−6.53586	+	4.74858i	−0.225241	+	0.163647i
$843$	−24.9892	+	12.5270i	−0.860673	+	0.431452i
$844$	31.8146	−	23.1146i	1.09510	−	0.795638i
$845$	−19.4146	−	15.2950i	−0.667884	−	0.526164i
$846$	−2.10717	−	6.78669i	−0.0724459	−	0.233331i
$847$	−27.5741	+	9.12461i	−0.947456	+	0.313525i
$848$	5.81595	−	17.8997i	0.199721	−	0.614677i
$849$	−21.9358	−	43.7581i	−0.752833	−	1.50178i
$850$	36.3454	−	42.6112i	1.24664	−	1.46155i
$851$		−	57.9098i		−	1.98512i
$852$	4.93809	+	32.5578i	0.169176	+	1.11541i
$853$	39.5938	+	28.7666i	1.35567	+	0.984949i	0.998707	+	0.0508286i	$0.0161862\pi$
$853$	39.5938	+	28.7666i	1.35567	+	0.984949i	0.356958	+	0.934120i	$0.383814\pi$
$854$	12.3921	+	37.4482i	0.424048	+	1.28145i
$855$	−16.4610	+	10.6971i	−0.562955	+	0.365832i
$856$	71.8286	−	52.1865i	2.45505	−	1.78370i
$857$			10.7355i			0.366718i	0.983046	+	0.183359i	$0.0586971\pi$
$857$			10.7355i			0.366718i	−0.983046	+	0.183359i	$0.941303\pi$
$858$	−0.418078	+	0.807396i	−0.0142730	+	0.0275641i
$859$	−49.6426	+	16.1299i	−1.69379	+	0.550344i	−0.987505	−	0.157588i	$-0.949628\pi$
$859$	−49.6426	+	16.1299i	−1.69379	+	0.550344i	−0.706280	+	0.707932i	$0.749628\pi$
$860$	111.128	+	40.9563i	3.78945	+	1.39660i
$861$	10.6071	−	20.7590i	0.361491	−	0.707463i
$862$	90.7668	−	29.4919i	3.09153	−	1.00450i
$863$	−6.09932	−	18.7718i	−0.207623	−	0.638998i	−0.999595	−	0.0284413i	$-0.990946\pi$
$863$	−6.09932	−	18.7718i	−0.207623	−	0.638998i	0.791972	−	0.610557i	$-0.209054\pi$
$864$	−10.2950	+	19.2591i	−0.350242	+	0.655208i
$865$	0.118650	−	3.04516i	0.00403424	−	0.103538i
$866$	4.80443	+	14.7865i	0.163261	+	0.502466i
$867$	−4.10079	−	2.12343i	−0.139270	−	0.0721155i
$868$	−82.7798	−	59.4613i	−2.80973	−	2.01825i
$869$	−0.950092	−	1.30769i	−0.0322297	−	0.0443603i
$870$	16.4360	+	18.0041i	0.557234	+	0.610397i
$871$	3.22982	−	4.44547i	0.109438	−	0.150629i
$872$	86.8815	+	63.1231i	2.94218	+	2.13762i
$873$	−20.3637	−	28.8153i	−0.689208	−	0.975250i
$874$			59.8804i			2.02549i
$875$	28.9746	−	5.95610i	0.979519	−	0.201353i
$876$	5.66684	+	11.3044i	0.191465	+	0.381940i
$877$	18.1443	+	5.89544i	0.612689	+	0.199075i	0.598892	−	0.800830i	$-0.295608\pi$
$877$	18.1443	+	5.89544i	0.612689	+	0.199075i	0.0137973	+	0.999905i	$0.495608\pi$
$878$	22.8240	−	31.4145i	0.770272	−	1.06019i
$879$	−25.6265	−	4.23123i	−0.864361	−	0.142716i
$880$	2.05896	−	0.581412i	0.0694076	−	0.0195994i
$881$	−39.5021	+	28.7000i	−1.33086	+	0.966926i	−0.331132	+	0.943584i	$0.607431\pi$
$881$	−39.5021	+	28.7000i	−1.33086	+	0.966926i	−0.999728	+	0.0233421i	$0.992569\pi$
$882$	−50.4090	−	16.5065i	−1.69736	−	0.555802i
$883$	−2.79172	−	3.84247i	−0.0939487	−	0.129309i	0.759455	−	0.650560i	$-0.225466\pi$
$883$	−2.79172	−	3.84247i	−0.0939487	−	0.129309i	−0.853404	+	0.521251i	$0.825466\pi$
$884$	−25.7746	+	8.37467i	−0.866893	+	0.281671i
$885$	−17.3285	−	38.2126i	−0.582490	−	1.28450i
$886$	−12.1908	+	37.5195i	−0.409558	+	1.26049i
$887$	−17.4978	+	5.68537i	−0.587518	+	0.190896i	−0.587666	−	0.809104i	$-0.699953\pi$
$887$	−17.4978	+	5.68537i	−0.587518	+	0.190896i	0.000147675		1.00000i	$0.499953\pi$
$888$	52.2834	+	52.9734i	1.75451	+	1.77767i
$889$	−31.3905	+	23.0671i	−1.05280	+	0.773646i
$890$	13.3816	−	36.3089i	0.448552	−	1.21708i
$891$	0.759248	+	1.10481i	0.0254358	+	0.0370125i
$892$	−84.0587	+	61.0722i	−2.81449	+	2.04485i
$893$	2.74448			0.0918405
$894$	14.1126	−	27.2544i	0.471996	−	0.911522i
$895$	14.9891	+	5.52421i	0.501029	+	0.184654i
$896$	−35.2730	+	11.6723i	−1.17839	+	0.389943i
$897$	3.18927	−	19.3159i	0.106487	−	0.644939i
$898$	40.8179	+	13.2626i	1.36211	+	0.442577i
$899$	21.9181			0.731011
$900$	−60.3795	−	25.8959i	−2.01265	−	0.863198i
$901$		−	12.9931i		−	0.432865i
$902$	1.82021	+	0.591421i	0.0606062	+	0.0196922i
$903$	39.2305	−	39.1409i	1.30551	−	1.30253i
$904$	5.74341	+	4.17283i	0.191023	+	0.138786i
$905$	−12.7266	+	16.1544i	−0.423046	+	0.536991i
$906$	0.991573	+	0.513447i	0.0329428	+	0.0170581i
$907$		−	20.2730i		−	0.673153i	−0.941656	−	0.336576i	$-0.890731\pi$
$907$		−	20.2730i		−	0.673153i	0.941656	−	0.336576i	$-0.109269\pi$
$908$	−7.76927	−	10.6935i	−0.257832	−	0.354876i
$909$	−13.9890	−	4.74894i	−0.463985	−	0.157512i
$910$	−19.6022	−	7.10414i	−0.649807	−	0.235500i
$911$	−44.7338	−	14.5349i	−1.48210	−	0.481563i	−0.547359	−	0.836898i	$-0.684367\pi$
$911$	−44.7338	−	14.5349i	−1.48210	−	0.481563i	−0.934739	+	0.355335i	$0.884367\pi$
$912$	−22.8723	−	23.1741i	−0.757376	−	0.767372i
$913$	0.325173	+	1.00078i	0.0107617	+	0.0331210i
$914$	−3.78704	−	1.23048i	−0.125264	−	0.0407008i
$915$	22.3930	+	4.59943i	0.740289	+	0.152053i
$916$	102.495	−	33.3028i	3.38654	−	1.10035i
$917$	0.192520	+	35.5768i	0.00635758	+	1.17485i
$918$	−10.2337	+	57.2967i	−0.337763	+	1.89107i
$919$	46.0338	−	33.4455i	1.51852	−	1.10327i	0.556298	−	0.830983i	$-0.312221\pi$
$919$	46.0338	−	33.4455i	1.51852	−	1.10327i	0.962217	−	0.272284i	$-0.0877789\pi$
$920$	−90.5177	+	60.5247i	−2.98428	+	1.99544i
$921$	8.84036	−	53.5418i	0.291300	−	1.76426i
$922$	−65.7325	−	47.7574i	−2.16478	−	1.57281i
$923$	5.76020	+	1.87160i	0.189599	+	0.0616045i
$924$	0.471053	−	2.95225i	0.0154965	−	0.0971219i
$925$	−23.1954	+	27.1942i	−0.762660	+	0.894140i
$926$			44.3602i			1.45777i
$927$	7.33190	+	10.3749i	0.240811	+	0.340755i
$928$	−6.15599	+	8.47300i	−0.202080	+	0.278140i
$929$	−33.2537	−	24.1602i	−1.09102	−	0.792671i	−0.111447	−	0.993770i	$-0.535548\pi$
$929$	−33.2537	−	24.1602i	−1.09102	−	0.792671i	−0.979571	+	0.201100i	$0.935548\pi$
$930$	−78.3610	+	35.5347i	−2.56956	+	1.16523i
$931$	11.8609	−	16.7023i	0.388726	−	0.547397i
$932$	15.4358			0.505615
$933$	−25.9705	−	13.4478i	−0.850236	−	0.440261i
$934$	−36.4002	+	11.8271i	−1.19105	+	0.386996i
$935$	1.22782	−	0.820984i	0.0401541	−	0.0268490i
$936$	14.5218	+	20.5487i	0.474659	+	0.671657i
$937$	−9.06587	−	27.9019i	−0.296169	−	0.911514i	−0.982826	−	0.184533i	$-0.940923\pi$
$937$	−9.06587	−	27.9019i	−0.296169	−	0.911514i	0.686657	−	0.726981i	$-0.259077\pi$
$938$	−7.99717	+	25.0736i	−0.261117	+	0.818683i
$939$	−39.4889	+	5.98935i	−1.28867	+	0.195455i
$940$	5.10521	+	7.63510i	0.166514	+	0.249030i
$941$	1.88778	+	5.80998i	0.0615397	+	0.189400i	0.977100	−	0.212781i	$-0.0682522\pi$
$941$	1.88778	+	5.80998i	0.0615397	+	0.189400i	−0.915560	+	0.402181i	$0.868252\pi$
$942$	−23.0815	−	11.9518i	−0.752035	−	0.389412i
$943$	−41.2099			−1.34198
$944$	56.3004	−	40.9047i	1.83242	−	1.33133i
$945$	−22.8621	+	20.5505i	−0.743706	+	0.668507i
$946$	3.68075	+	2.67422i	0.119672	+	0.0869465i
$947$	25.9898	+	18.8827i	0.844554	+	0.613604i	0.923639	−	0.383264i	$-0.125200\pi$
$947$	25.9898	+	18.8827i	0.844554	+	0.613604i	−0.0790853	+	0.996868i	$0.525200\pi$
$948$	−81.3942	+	12.3452i	−2.64356	+	0.400953i
$949$	2.32576			0.0754974
$950$	23.9847	−	28.1196i	0.778167	−	0.912321i
$951$	8.70908	+	17.3731i	0.282411	+	0.563363i
$952$	56.8347	−	41.7646i	1.84202	−	1.35360i
$953$	15.6937	+	11.4021i	0.508368	+	0.369351i	0.812204	−	0.583373i	$-0.198268\pi$
$953$	15.6937	+	11.4021i	0.508368	+	0.369351i	−0.303836	+	0.952724i	$0.598268\pi$
$954$	−21.2030	+	6.58323i	−0.686473	+	0.213140i
$955$	17.6110	+	26.3381i	0.569877	+	0.852280i
$956$	−16.2164	−	22.3199i	−0.524475	−	0.721877i
$957$	0.288112	+	0.574734i	0.00931333	+	0.0185785i
$958$	−35.7170	+	25.9499i	−1.15396	+	0.838404i
$959$	−37.1514	−	11.8493i	−1.19968	−	0.382635i
$960$	−1.73916	+	8.46736i	−0.0561313	+	0.273283i
$961$	−14.3258	+	44.0903i	−0.462123	+	1.42227i
$962$	23.9604	−	7.78521i	0.772515	−	0.251005i
$963$	−41.9577	−	14.2437i	−1.35207	−	0.458996i
$964$	71.5073	+	23.2341i	2.30309	+	0.748321i
$965$	−29.5981	+	8.35795i	−0.952798	+	0.269052i
$966$	14.5624	+	92.6291i	0.468538	+	2.98029i
$967$	−34.1747	−	47.0375i	−1.09899	−	1.51262i	−0.836722	−	0.547628i	$-0.815531\pi$
$967$	−34.1747	−	47.0375i	−1.09899	−	1.51262i	−0.262264	−	0.964996i	$-0.584469\pi$
$968$	−65.9903			−2.12101
$969$	−19.9611	−	10.3361i	−0.641243	−	0.332042i
$970$	52.1810	+	41.1086i	1.67543	+	1.31992i
$971$	7.96041	+	5.78358i	0.255462	+	0.185604i	0.708144	−	0.706068i	$-0.249533\pi$
$971$	7.96041	+	5.78358i	0.255462	+	0.185604i	−0.452682	+	0.891672i	$0.649533\pi$
$972$	67.7490	−	8.46506i	2.17305	−	0.271517i
$973$	−17.6651	+	12.9811i	−0.566316	+	0.416153i
$974$			21.3862i			0.685258i
$975$	−9.23453	+	7.79322i	−0.295742	+	0.249583i
$976$			37.9160i			1.21366i
$977$	−1.56454	+	4.81515i	−0.0500540	+	0.154050i	−0.972959	−	0.230977i	$-0.925808\pi$
$977$	−1.56454	+	4.81515i	−0.0500540	+	0.154050i	0.922905	+	0.385027i	$0.125808\pi$
$978$	−21.5941	−	3.56544i	−0.690505	−	0.114010i
$979$	0.599840	−	0.825608i	0.0191710	−	0.0263866i
$980$	68.5291	+	1.92763i	2.18908	+	0.0615759i
$981$	0.702646	−	53.5907i	0.0224337	−	1.71102i
$982$			57.3339i			1.82960i
$983$	−15.3289	−	21.0984i	−0.488916	−	0.672935i	0.491272	−	0.871006i	$-0.336532\pi$
$983$	−15.3289	−	21.0984i	−0.488916	−	0.672935i	−0.980188	+	0.198071i	$0.936532\pi$
$984$	37.6970	−	37.2060i	1.20174	−	1.18608i
$985$	10.6701	−	28.9517i	0.339978	−	0.922477i
$986$	−8.62574	+	26.5473i	−0.274700	+	0.845438i
$987$	4.24544	−	0.667434i	0.135134	−	0.0212447i
$988$	−17.0089	+	5.52654i	−0.541126	+	0.175823i
$989$	−93.1692	−	30.2725i	−2.96261	−	0.962610i
$990$	−1.96183	−	1.58767i	−0.0623511	−	0.0504594i
$991$	−2.04576	−	6.29620i	−0.0649857	−	0.200005i	0.913291	−	0.407307i	$-0.133532\pi$
$991$	−2.04576	−	6.29620i	−0.0649857	−	0.200005i	−0.978277	+	0.207301i	$0.933532\pi$
$992$	−21.7273	−	29.9051i	−0.689844	−	0.949489i
$993$	−7.64254	−	15.2456i	−0.242529	−	0.483804i
$994$	−29.0080	+	0.156974i	−0.920079	+	0.00497892i
$995$	28.2180	−	7.96822i	0.894570	−	0.252610i
$996$	52.8783	+	8.73080i	1.67551	+	0.276646i
$997$	2.04477	+	1.48561i	0.0647585	+	0.0470498i	0.619694	−	0.784844i	$-0.287257\pi$
$997$	2.04477	+	1.48561i	0.0647585	+	0.0470498i	−0.554935	+	0.831894i	$0.687257\pi$
$998$	−22.2955	+	68.6184i	−0.705751	+	2.17208i
$999$	6.53110	−	36.5664i	0.206635	−	1.15691i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	525.2.w.a.104.5	✓	304
3.2	odd	2	inner	525.2.w.a.104.72	yes	304
7.6	odd	2	inner	525.2.w.a.104.6	yes	304
21.20	even	2	inner	525.2.w.a.104.71	yes	304
25.19	even	10	inner	525.2.w.a.419.71	yes	304
75.44	odd	10	inner	525.2.w.a.419.6	yes	304
175.69	odd	10	inner	525.2.w.a.419.72	yes	304
525.419	even	10	inner	525.2.w.a.419.5	yes	304

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
525.2.w.a.104.5	✓	304	1.1	even	1	trivial
525.2.w.a.104.6	yes	304	7.6	odd	2	inner
525.2.w.a.104.71	yes	304	21.20	even	2	inner
525.2.w.a.104.72	yes	304	3.2	odd	2	inner
525.2.w.a.419.5	yes	304	525.419	even	10	inner
525.2.w.a.419.6	yes	304	75.44	odd	10	inner
525.2.w.a.419.71	yes	304	25.19	even	10	inner
525.2.w.a.419.72	yes	304	175.69	odd	10	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 525 = 3 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	525.w (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.780529 + 2.40222i) q^{2} +(-0.282161 + 1.70891i) q^{3} +(-3.54341 - 2.57444i) q^{4} +(-0.607661 - 2.15192i) q^{5} +(-3.88495 - 2.01167i) q^{6} +(1.54353 - 2.14884i) q^{7} +(4.86320 - 3.53332i) q^{8} +(-2.84077 - 0.964377i) q^{9} +O(q^{10})\)	\(q+(-0.780529 + 2.40222i) q^{2} +(-0.282161 + 1.70891i) q^{3} +(-3.54341 - 2.57444i) q^{4} +(-0.607661 - 2.15192i) q^{5} +(-3.88495 - 2.01167i) q^{6} +(1.54353 - 2.14884i) q^{7} +(4.86320 - 3.53332i) q^{8} +(-2.84077 - 0.964377i) q^{9} +(5.64368 + 0.219898i) q^{10} +(0.141659 + 0.0460279i) q^{11} +(5.39930 - 5.32897i) q^{12} +(-0.431166 - 1.32699i) q^{13} +(3.95723 + 5.38513i) q^{14} +(3.84890 - 0.431253i) q^{15} +(1.98503 + 6.10928i) q^{16} +(2.60663 + 3.58771i) q^{17} +(4.53395 - 6.07144i) q^{18} +(1.72014 + 2.36757i) q^{19} +(-3.38678 + 9.18951i) q^{20} +(3.23666 + 3.24408i) q^{21} +(-0.221138 + 0.304371i) q^{22} +(2.50331 - 7.70441i) q^{23} +(4.66593 + 9.30775i) q^{24} +(-4.26150 + 2.61527i) q^{25} +3.52427 q^{26} +(2.44959 - 4.58252i) q^{27} +(-11.0014 + 3.64051i) q^{28} +(1.46476 - 2.01607i) q^{29} +(-1.96821 + 9.58251i) q^{30} +(5.16981 + 7.11564i) q^{31} -4.20273 q^{32} +(-0.118628 + 0.229096i) q^{33} +(-10.6530 + 3.46138i) q^{34} +(-5.56207 - 2.01578i) q^{35} +(7.58328 + 10.7306i) q^{36} +(6.79870 - 2.20903i) q^{37} +(-7.03005 + 2.28420i) q^{38} +(2.38937 - 0.362400i) q^{39} +(-10.5586 - 8.31814i) q^{40} +(-1.57199 - 4.83810i) q^{41} +(-10.3193 + 5.24308i) q^{42} -12.0930i q^{43} +(-0.383461 - 0.527789i) q^{44} +(-0.349035 + 6.69912i) q^{45} +(16.5538 + 12.0270i) q^{46} +(0.551230 - 0.758704i) q^{47} +(-11.0003 + 1.66844i) q^{48} +(-2.23504 - 6.63360i) q^{49} +(-2.95624 - 12.2784i) q^{50} +(-6.86658 + 3.44219i) q^{51} +(-1.88846 + 5.81208i) q^{52} +(-2.37035 - 1.72216i) q^{53} +(9.09625 + 9.46125i) q^{54} +(0.0129674 - 0.332809i) q^{55} +(-0.0860630 - 15.9040i) q^{56} +(-4.53133 + 2.27154i) q^{57} +(3.69975 + 5.09227i) q^{58} +(-3.34775 - 10.3033i) q^{59} +(-14.7485 - 8.38064i) q^{60} +(5.61365 + 1.82399i) q^{61} +(-21.1285 + 6.86507i) q^{62} +(-6.45710 + 4.61582i) q^{63} +(-0.689696 + 2.12267i) q^{64} +(-2.59357 + 1.73419i) q^{65} +(-0.457747 - 0.463788i) q^{66} +(2.31482 + 3.18607i) q^{67} -19.4233i q^{68} +(12.4598 + 6.45183i) q^{69} +(9.18370 - 11.7880i) q^{70} +(-2.55145 + 3.51178i) q^{71} +(-17.2227 + 5.34739i) q^{72} +(-0.515093 + 1.58529i) q^{73} +18.0562i q^{74} +(-3.26685 - 8.02046i) q^{75} -12.8177i q^{76} +(0.317562 - 0.233358i) q^{77} +(-0.994410 + 6.02267i) q^{78} +(-8.77942 - 6.37862i) q^{79} +(11.9404 - 7.98398i) q^{80} +(7.13995 + 5.47915i) q^{81} +12.8492 q^{82} +(4.15253 + 5.71546i) q^{83} +(-3.11715 - 19.8277i) q^{84} +(6.13652 - 7.78935i) q^{85} +(29.0500 + 9.43892i) q^{86} +(3.03199 + 3.07200i) q^{87} +(0.851549 - 0.276685i) q^{88} +(2.11719 - 6.51604i) q^{89} +(-15.8203 - 6.06731i) q^{90} +(-3.51701 - 1.12174i) q^{91} +(-28.7048 + 20.8552i) q^{92} +(-13.6187 + 6.82701i) q^{93} +(1.39232 + 1.91637i) q^{94} +(4.04956 - 5.14028i) q^{95} +(1.18585 - 7.18211i) q^{96} +(9.51528 + 6.91326i) q^{97} +(17.6799 - 0.191351i) q^{98} +(-0.358033 - 0.267368i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 304 q - 84 q^{4} - 6 q^{9}+O(q^{10}) \) 304 * q - 84 * q^4 - 6 * q^9	\( 304 q - 84 q^{4} - 6 q^{9} - 36 q^{15} - 60 q^{16} - 18 q^{21} - 40 q^{22} - 8 q^{25} + 60 q^{28} + 14 q^{30} + 28 q^{36} - 20 q^{37} - 2 q^{39} - 35 q^{42} - 24 q^{46} - 20 q^{49} - 52 q^{51} - 80 q^{58} + 4 q^{60} + 55 q^{63} - 76 q^{64} - 20 q^{67} + 6 q^{70} + 30 q^{72} - 40 q^{78} - 68 q^{79} - 10 q^{81} + 80 q^{84} - 88 q^{85} - 20 q^{88} - 82 q^{91} - 36 q^{99}+O(q^{100}) \) 304 * q - 84 * q^4 - 6 * q^9 - 36 * q^15 - 60 * q^16 - 18 * q^21 - 40 * q^22 - 8 * q^25 + 60 * q^28 + 14 * q^30 + 28 * q^36 - 20 * q^37 - 2 * q^39 - 35 * q^42 - 24 * q^46 - 20 * q^49 - 52 * q^51 - 80 * q^58 + 4 * q^60 + 55 * q^63 - 76 * q^64 - 20 * q^67 + 6 * q^70 + 30 * q^72 - 40 * q^78 - 68 * q^79 - 10 * q^81 + 80 * q^84 - 88 * q^85 - 20 * q^88 - 82 * q^91 - 36 * q^99

Introduction

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