LMFDB - Embedded newform 1050.3.c.b.449.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1050,3,Mod(449,1050)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1050, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 1, 0]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("1050.449");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 1050 = 2 \cdot 3 \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	1050.c (of order $2$, degree $1$, 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:	$28.6104277578$
Analytic rank:	$0$
Dimension:	$32$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			449.1
Character	$\chi$	$=$	1050.449
Dual form			1050.3.c.b.449.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.41421 q^{2} +(-2.79495 - 1.09006i) q^{3} +2.00000 q^{4} +(3.95266 + 1.54158i) q^{6} +2.64575i q^{7} -2.82843 q^{8} +(6.62354 + 6.09333i) q^{9} +O(q^{10})$	\(q-1.41421 q^{2} +(-2.79495 - 1.09006i) q^{3} +2.00000 q^{4} +(3.95266 + 1.54158i) q^{6} +2.64575i q^{7} -2.82843 q^{8} +(6.62354 + 6.09333i) q^{9} +3.30912i q^{11} +(-5.58991 - 2.18012i) q^{12} -13.2159i q^{13} -3.74166i q^{14} +4.00000 q^{16} -14.2264 q^{17} +(-9.36710 - 8.61727i) q^{18} -7.45106 q^{19} +(2.88403 - 7.39475i) q^{21} -4.67981i q^{22} -7.07387 q^{23} +(7.90533 + 3.08315i) q^{24} +18.6902i q^{26} +(-11.8704 - 24.2506i) q^{27} +5.29150i q^{28} +25.7409i q^{29} +41.5150 q^{31} -5.65685 q^{32} +(3.60714 - 9.24885i) q^{33} +20.1192 q^{34} +(13.2471 + 12.1867i) q^{36} +27.7055i q^{37} +10.5374 q^{38} +(-14.4062 + 36.9380i) q^{39} +1.25580i q^{41} +(-4.07863 + 10.4578i) q^{42} +2.12678i q^{43} +6.61825i q^{44} +10.0040 q^{46} +54.8353 q^{47} +(-11.1798 - 4.36024i) q^{48} -7.00000 q^{49} +(39.7623 + 15.5077i) q^{51} -26.4319i q^{52} -62.3147 q^{53} +(16.7873 + 34.2956i) q^{54} -7.48331i q^{56} +(20.8254 + 8.12210i) q^{57} -36.4032i q^{58} -21.7601i q^{59} +84.8047 q^{61} -58.7111 q^{62} +(-16.1214 + 17.5242i) q^{63} +8.00000 q^{64} +(-5.10127 + 13.0799i) q^{66} -54.7450i q^{67} -28.4529 q^{68} +(19.7711 + 7.71093i) q^{69} -100.282i q^{71} +(-18.7342 - 17.2345i) q^{72} +63.2034i q^{73} -39.1815i q^{74} -14.9021 q^{76} -8.75512 q^{77} +(20.3734 - 52.2382i) q^{78} -116.942 q^{79} +(6.74263 + 80.7189i) q^{81} -1.77596i q^{82} +23.7433 q^{83} +(5.76805 - 14.7895i) q^{84} -3.00772i q^{86} +(28.0592 - 71.9448i) q^{87} -9.35962i q^{88} -3.26308i q^{89} +34.9661 q^{91} -14.1477 q^{92} +(-116.033 - 45.2538i) q^{93} -77.5489 q^{94} +(15.8107 + 6.16631i) q^{96} -55.5754i q^{97} +9.89949 q^{98} +(-20.1636 + 21.9181i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 64 q^{4} - 16 q^{6} - 16 q^{9}+O(q^{10}) $ 32 * q + 64 * q^4 - 16 * q^6 - 16 * q^9	$ 32 q + 64 q^{4} - 16 q^{6} - 16 q^{9} + 128 q^{16} + 48 q^{19} + 56 q^{21} - 32 q^{24} + 48 q^{31} + 256 q^{34} - 32 q^{36} + 192 q^{39} + 160 q^{46} - 224 q^{49} + 288 q^{51} - 80 q^{54} - 112 q^{61} + 256 q^{64} - 192 q^{66} + 344 q^{69} + 96 q^{76} - 256 q^{79} + 160 q^{81} + 112 q^{84} - 448 q^{91} + 416 q^{94} - 64 q^{96} - 304 q^{99}+O(q^{100}) $ 32 * q + 64 * q^4 - 16 * q^6 - 16 * q^9 + 128 * q^16 + 48 * q^19 + 56 * q^21 - 32 * q^24 + 48 * q^31 + 256 * q^34 - 32 * q^36 + 192 * q^39 + 160 * q^46 - 224 * q^49 + 288 * q^51 - 80 * q^54 - 112 * q^61 + 256 * q^64 - 192 * q^66 + 344 * q^69 + 96 * q^76 - 256 * q^79 + 160 * q^81 + 112 * q^84 - 448 * q^91 + 416 * q^94 - 64 * q^96 - 304 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1050\mathbb{Z}\right)^\times$.

$n$	$127$	$451$	$701$
$\chi(n)$	$-1$	$1$	$-1$

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 $

$2$	−1.41421			−0.707107
$2$	−1.41421			−0.707107
$3$	−2.79495	−	1.09006i	−0.931652	−	0.363353i
$3$	−2.79495	−	1.09006i	−0.931652	−	0.363353i
$4$	2.00000			0.500000
$5$		0			0
$5$		0			0
$6$	3.95266	+	1.54158i	0.658777	+	0.256929i
$7$			2.64575i			0.377964i
$7$			2.64575i			0.377964i
$8$	−2.82843			−0.353553
$9$	6.62354	+	6.09333i	0.735949	+	0.677037i
$10$		0			0
$11$			3.30912i			0.300830i	0.988623	+	0.150415i	$0.0480609\pi$
$11$			3.30912i			0.300830i	−0.988623	+	0.150415i	$0.951939\pi$
$12$	−5.58991	−	2.18012i	−0.465826	−	0.181677i
$13$		−	13.2159i		−	1.01661i	−0.861177	−	0.508306i	$-0.830272\pi$
$13$		−	13.2159i		−	1.01661i	0.861177	−	0.508306i	$-0.169728\pi$
$14$		−	3.74166i		−	0.267261i
$15$		0			0
$16$	4.00000			0.250000
$17$	−14.2264			−0.836850			−0.418425	−	0.908251i	$-0.637418\pi$
$17$	−14.2264			−0.836850			−0.418425	+	0.908251i	$0.637418\pi$
$18$	−9.36710	−	8.61727i	−0.520395	−	0.478737i
$19$	−7.45106			−0.392161			−0.196081	−	0.980588i	$-0.562821\pi$
$19$	−7.45106			−0.392161			−0.196081	+	0.980588i	$0.562821\pi$
$20$		0			0
$21$	2.88403	−	7.39475i	0.137335	−	0.352131i
$22$		−	4.67981i		−	0.212719i
$23$	−7.07387			−0.307559			−0.153780	−	0.988105i	$-0.549145\pi$
$23$	−7.07387			−0.307559			−0.153780	+	0.988105i	$0.549145\pi$
$24$	7.90533	+	3.08315i	0.329389	+	0.128465i
$25$		0			0
$26$			18.6902i			0.718853i
$27$	−11.8704	−	24.2506i	−0.439645	−	0.898172i
$28$			5.29150i			0.188982i
$29$			25.7409i			0.887619i	0.896121	+	0.443809i	$0.146373\pi$
$29$			25.7409i			0.887619i	−0.896121	+	0.443809i	$0.853627\pi$
$30$		0			0
$31$	41.5150			1.33919			0.669597	−	0.742724i	$-0.266467\pi$
$31$	41.5150			1.33919			0.669597	+	0.742724i	$0.266467\pi$
$32$	−5.65685			−0.176777
$33$	3.60714	−	9.24885i	0.109307	−	0.280268i
$34$	20.1192			0.591742
$35$		0			0
$36$	13.2471	+	12.1867i	0.367975	+	0.338518i
$37$			27.7055i			0.748797i	0.927268	+	0.374398i	$0.122151\pi$
$37$			27.7055i			0.748797i	−0.927268	+	0.374398i	$0.877849\pi$
$38$	10.5374			0.277300
$39$	−14.4062	+	36.9380i	−0.369389	+	0.947127i
$40$		0			0
$41$			1.25580i			0.0306292i	0.999883	+	0.0153146i	$0.00487497\pi$
$41$			1.25580i			0.0306292i	−0.999883	+	0.0153146i	$0.995125\pi$
$42$	−4.07863	+	10.4578i	−0.0971102	+	0.248994i
$43$			2.12678i			0.0494599i	0.999694	+	0.0247300i	$0.00787259\pi$
$43$			2.12678i			0.0494599i	−0.999694	+	0.0247300i	$0.992127\pi$
$44$			6.61825i			0.150415i
$45$		0			0
$46$	10.0040			0.217477
$47$	54.8353			1.16671			0.583355	−	0.812218i	$-0.301740\pi$
$47$	54.8353			1.16671			0.583355	+	0.812218i	$0.301740\pi$
$48$	−11.1798	−	4.36024i	−0.232913	−	0.0908383i
$49$	−7.00000			−0.142857
$50$		0			0
$51$	39.7623	+	15.5077i	0.779653	+	0.304072i
$52$		−	26.4319i		−	0.508306i
$53$	−62.3147			−1.17575			−0.587874	−	0.808952i	$-0.700035\pi$
$53$	−62.3147			−1.17575			−0.587874	+	0.808952i	$0.700035\pi$
$54$	16.7873	+	34.2956i	0.310876	+	0.635103i
$55$		0			0
$56$		−	7.48331i		−	0.133631i
$57$	20.8254	+	8.12210i	0.365357	+	0.142493i
$58$		−	36.4032i		−	0.627641i
$59$		−	21.7601i		−	0.368815i	−0.982850	−	0.184407i	$-0.940963\pi$
$59$		−	21.7601i		−	0.368815i	0.982850	−	0.184407i	$-0.0590366\pi$
$60$		0			0
$61$	84.8047			1.39024			0.695121	−	0.718893i	$-0.255351\pi$
$61$	84.8047			1.39024			0.695121	+	0.718893i	$0.255351\pi$
$62$	−58.7111			−0.946954
$63$	−16.1214	+	17.5242i	−0.255896	+	0.278163i
$64$	8.00000			0.125000
$65$		0			0
$66$	−5.10127	+	13.0799i	−0.0772919	+	0.198180i
$67$		−	54.7450i		−	0.817089i	−0.912738	−	0.408545i	$-0.866036\pi$
$67$		−	54.7450i		−	0.817089i	0.912738	−	0.408545i	$-0.133964\pi$
$68$	−28.4529			−0.418425
$69$	19.7711	+	7.71093i	0.286538	+	0.111753i
$70$		0			0
$71$		−	100.282i		−	1.41243i	−0.707999	−	0.706213i	$-0.750402\pi$
$71$		−	100.282i		−	1.41243i	0.707999	−	0.706213i	$-0.249598\pi$
$72$	−18.7342	−	17.2345i	−0.260197	−	0.239369i
$73$			63.2034i			0.865800i	0.901442	+	0.432900i	$0.142510\pi$
$73$			63.2034i			0.865800i	−0.901442	+	0.432900i	$0.857490\pi$
$74$		−	39.1815i		−	0.529479i
$75$		0			0
$76$	−14.9021			−0.196081
$77$	−8.75512			−0.113703
$78$	20.3734	−	52.2382i	0.261197	−	0.669720i
$79$	−116.942			−1.48028			−0.740138	−	0.672455i	$-0.765240\pi$
$79$	−116.942			−1.48028			−0.740138	+	0.672455i	$0.765240\pi$
$80$		0			0
$81$	6.74263	+	80.7189i	0.0832423	+	0.996529i
$82$		−	1.77596i		−	0.0216581i
$83$	23.7433			0.286064			0.143032	−	0.989718i	$-0.454315\pi$
$83$	23.7433			0.286064			0.143032	+	0.989718i	$0.454315\pi$
$84$	5.76805	−	14.7895i	0.0686673	−	0.176066i
$85$		0			0
$86$		−	3.00772i		−	0.0349734i
$87$	28.0592	−	71.9448i	0.322519	−	0.826952i
$88$		−	9.35962i		−	0.106359i
$89$		−	3.26308i		−	0.0366638i	−0.999832	−	0.0183319i	$-0.994164\pi$
$89$		−	3.26308i		−	0.0366638i	0.999832	−	0.0183319i	$-0.00583555\pi$
$90$		0			0
$91$	34.9661			0.384243
$92$	−14.1477			−0.153780
$93$	−116.033	−	45.2538i	−1.24766	−	0.486600i
$94$	−77.5489			−0.824988
$95$		0			0
$96$	15.8107	+	6.16631i	0.164694	+	0.0642323i
$97$		−	55.5754i		−	0.572942i	−0.958089	−	0.286471i	$-0.907518\pi$
$97$		−	55.5754i		−	0.572942i	0.958089	−	0.286471i	$-0.0924822\pi$
$98$	9.89949			0.101015
$99$	−20.1636	+	21.9181i	−0.203673	+	0.221395i
$100$		0			0
$101$		−	124.810i		−	1.23574i	−0.786280	−	0.617870i	$-0.787996\pi$
$101$		−	124.810i		−	1.23574i	0.786280	−	0.617870i	$-0.212004\pi$
$102$	−56.2324	−	21.9312i	−0.551298	−	0.215011i
$103$		−	112.881i		−	1.09593i	−0.836500	−	0.547967i	$-0.815402\pi$
$103$		−	112.881i		−	1.09593i	0.836500	−	0.547967i	$-0.184598\pi$
$104$			37.3803i			0.359426i
$105$		0			0
$106$	88.1263			0.831380
$107$	84.6754			0.791359			0.395680	−	0.918389i	$-0.370509\pi$
$107$	84.6754			0.791359			0.395680	+	0.918389i	$0.370509\pi$
$108$	−23.7408	−	48.5013i	−0.219822	−	0.449086i
$109$	−165.164			−1.51527			−0.757634	−	0.652680i	$-0.773645\pi$
$109$	−165.164			−1.51527			−0.757634	+	0.652680i	$0.773645\pi$
$110$		0			0
$111$	30.2006	−	77.4356i	0.272078	−	0.697618i
$112$			10.5830i			0.0944911i
$113$	55.8626			0.494359			0.247179	−	0.968970i	$-0.420496\pi$
$113$	55.8626			0.494359			0.247179	+	0.968970i	$0.420496\pi$
$114$	−29.4515	−	11.4864i	−0.258347	−	0.100758i
$115$		0			0
$116$			51.4819i			0.443809i
$117$	80.5291	−	87.5364i	0.688283	−	0.748174i
$118$			30.7734i			0.260791i
$119$		−	37.6396i		−	0.316300i
$120$		0			0
$121$	110.050			0.909502
$122$	−119.932			−0.983049
$123$	1.36889	−	3.50989i	0.0111292	−	0.0285357i
$124$	83.0301			0.669597
$125$		0			0
$126$	22.7992	−	24.7830i	0.180946	−	0.196691i
$127$		−	166.400i		−	1.31023i	−0.755527	−	0.655117i	$-0.772619\pi$
$127$		−	166.400i		−	1.31023i	0.755527	−	0.655117i	$-0.227381\pi$
$128$	−11.3137			−0.0883883
$129$	2.31831	−	5.94424i	0.0179714	−	0.0460794i
$130$		0			0
$131$		−	229.177i		−	1.74944i	−0.484626	−	0.874721i	$-0.661044\pi$
$131$		−	229.177i		−	1.74944i	0.484626	−	0.874721i	$-0.338956\pi$
$132$	7.21428	−	18.4977i	0.0546537	−	0.140134i
$133$		−	19.7137i		−	0.148223i
$134$			77.4211i			0.577769i
$135$		0			0
$136$	40.2385			0.295871
$137$	123.559			0.901889			0.450945	−	0.892552i	$-0.351087\pi$
$137$	123.559			0.901889			0.450945	+	0.892552i	$0.351087\pi$
$138$	−27.9606	−	10.9049i	−0.202613	−	0.0790211i
$139$	−169.795			−1.22155			−0.610774	−	0.791805i	$-0.709141\pi$
$139$	−169.795			−1.22155			−0.610774	+	0.791805i	$0.709141\pi$
$140$		0			0
$141$	−153.262	−	59.7738i	−1.08697	−	0.423927i
$142$			141.821i			0.998736i
$143$	43.7332			0.305827
$144$	26.4942	+	24.3733i	0.183987	+	0.169259i
$145$		0			0
$146$		−	89.3832i		−	0.612213i
$147$	19.5647	+	7.63041i	0.133093	+	0.0519076i
$148$			55.4110i			0.374398i
$149$		−	237.791i		−	1.59592i	−0.602713	−	0.797958i	$-0.705914\pi$
$149$		−	237.791i		−	1.59592i	0.602713	−	0.797958i	$-0.294086\pi$
$150$		0			0
$151$	117.067			0.775281			0.387640	−	0.921811i	$-0.373290\pi$
$151$	117.067			0.775281			0.387640	+	0.921811i	$0.373290\pi$
$152$	21.0748			0.138650
$153$	−94.2295	−	86.6865i	−0.615879	−	0.566578i
$154$	12.3816			0.0804001
$155$		0			0
$156$	−28.8123	+	73.8759i	−0.184694	+	0.473564i
$157$		−	31.6151i		−	0.201370i	−0.994918	−	0.100685i	$-0.967897\pi$
$157$		−	31.6151i		−	0.201370i	0.994918	−	0.100685i	$-0.0321035\pi$
$158$	165.381			1.04671
$159$	174.167	+	67.9267i	1.09539	+	0.427212i
$160$		0			0
$161$		−	18.7157i		−	0.116247i
$162$	−9.53552	−	114.154i	−0.0588612	−	0.704653i
$163$		−	107.553i		−	0.659833i	−0.944010	−	0.329917i	$-0.892979\pi$
$163$		−	107.553i		−	0.659833i	0.944010	−	0.329917i	$-0.107021\pi$
$164$			2.51159i			0.0153146i
$165$		0			0
$166$	−33.5781			−0.202278
$167$	−116.906			−0.700036			−0.350018	−	0.936743i	$-0.613825\pi$
$167$	−116.906			−0.700036			−0.350018	+	0.936743i	$0.613825\pi$
$168$	−8.15726	+	20.9155i	−0.0485551	+	0.124497i
$169$	−5.66117			−0.0334980
$170$		0			0
$171$	−49.3524	−	45.4018i	−0.288611	−	0.265508i
$172$			4.25355i			0.0247300i
$173$	317.805			1.83702			0.918512	−	0.395392i	$-0.129391\pi$
$173$	317.805			1.83702			0.918512	+	0.395392i	$0.129391\pi$
$174$	−39.6816	+	101.745i	−0.228055	+	0.584743i
$175$		0			0
$176$			13.2365i			0.0752074i
$177$	−23.7198	+	60.8184i	−0.134010	+	0.343607i
$178$			4.61469i			0.0259252i
$179$		−	325.244i		−	1.81700i	−0.417880	−	0.908502i	$-0.637227\pi$
$179$		−	325.244i		−	1.81700i	0.417880	−	0.908502i	$-0.362773\pi$
$180$		0			0
$181$	−34.5370			−0.190812			−0.0954060	−	0.995438i	$-0.530415\pi$
$181$	−34.5370			−0.190812			−0.0954060	+	0.995438i	$0.530415\pi$
$182$	−49.4495			−0.271701
$183$	−237.025	−	92.4421i	−1.29522	−	0.505148i
$184$	20.0079			0.108739
$185$		0			0
$186$	164.095	+	63.9986i	0.882231	+	0.344079i
$187$		−	47.0771i		−	0.251749i
$188$	109.671			0.583355
$189$	64.1612	−	31.4062i	0.339477	−	0.166170i
$190$		0			0
$191$		−	80.5748i		−	0.421858i	−0.977501	−	0.210929i	$-0.932351\pi$
$191$		−	80.5748i		−	0.421858i	0.977501	−	0.210929i	$-0.0676489\pi$
$192$	−22.3596	−	8.72047i	−0.116456	−	0.0454191i
$193$			102.042i			0.528717i	0.964424	+	0.264359i	$0.0851602\pi$
$193$			102.042i			0.528717i	−0.964424	+	0.264359i	$0.914840\pi$
$194$			78.5954i			0.405131i
$195$		0			0
$196$	−14.0000			−0.0714286
$197$	−50.5512			−0.256605			−0.128303	−	0.991735i	$-0.540953\pi$
$197$	−50.5512			−0.256605			−0.128303	+	0.991735i	$0.540953\pi$
$198$	28.5156	−	30.9969i	0.144018	−	0.156550i
$199$	10.1649			0.0510800			0.0255400	−	0.999674i	$-0.491869\pi$
$199$	10.1649			0.0510800			0.0255400	+	0.999674i	$0.491869\pi$
$200$		0			0
$201$	−59.6752	+	153.010i	−0.296892	+	0.761242i
$202$			176.508i			0.873801i
$203$	−68.1041			−0.335488
$204$	79.5246	+	31.0153i	0.389826	+	0.152036i
$205$		0			0
$206$			159.638i			0.774943i
$207$	−46.8541	−	43.1034i	−0.226348	−	0.208229i
$208$		−	52.8638i		−	0.254153i
$209$		−	24.6565i		−	0.117974i
$210$		0			0
$211$	−305.386			−1.44733			−0.723665	−	0.690152i	$-0.757544\pi$
$211$	−305.386			−1.44733			−0.723665	+	0.690152i	$0.757544\pi$
$212$	−124.629			−0.587874
$213$	−109.314	+	280.284i	−0.513209	+	1.31589i
$214$	−119.749			−0.559575
$215$		0			0
$216$	33.5746	+	68.5912i	0.155438	+	0.317552i
$217$			109.838i			0.506168i
$218$	233.577			1.07146
$219$	68.8955	−	176.651i	0.314591	−	0.806624i
$220$		0			0
$221$			188.016i			0.850751i
$222$	−42.7101	+	109.510i	−0.192388	+	0.493290i
$223$		−	103.856i		−	0.465724i	−0.972510	−	0.232862i	$-0.925191\pi$
$223$		−	103.856i		−	0.465724i	0.972510	−	0.232862i	$-0.0748090\pi$
$224$		−	14.9666i		−	0.0668153i
$225$		0			0
$226$	−79.0016			−0.349565
$227$	−392.738			−1.73012			−0.865062	−	0.501664i	$-0.832721\pi$
$227$	−392.738			−1.73012			−0.865062	+	0.501664i	$0.832721\pi$
$228$	41.6508	+	16.2442i	0.182679	+	0.0712465i
$229$	427.149			1.86528			0.932641	−	0.360806i	$-0.117498\pi$
$229$	427.149			1.86528			0.932641	+	0.360806i	$0.117498\pi$
$230$		0			0
$231$	24.4702	+	9.54360i	0.105931	+	0.0413143i
$232$		−	72.8064i		−	0.313821i
$233$	57.7328			0.247780			0.123890	−	0.992296i	$-0.460463\pi$
$233$	57.7328			0.247780			0.123890	+	0.992296i	$0.460463\pi$
$234$	−113.885	+	123.795i	−0.486690	+	0.529039i
$235$		0			0
$236$		−	43.5201i		−	0.184407i
$237$	326.847	+	127.473i	1.37910	+	0.537863i
$238$			53.2305i			0.223658i
$239$			52.9710i			0.221636i	0.993841	+	0.110818i	$0.0353471\pi$
$239$			52.9710i			0.221636i	−0.993841	+	0.110818i	$0.964653\pi$
$240$		0			0
$241$	−157.253			−0.652502			−0.326251	−	0.945283i	$-0.605785\pi$
$241$	−157.253			−0.652502			−0.326251	+	0.945283i	$0.605785\pi$
$242$	−155.634			−0.643115
$243$	69.1430	−	232.955i	0.284539	−	0.958664i
$244$	169.609			0.695121
$245$		0			0
$246$	−1.93591	+	4.96374i	−0.00786953	+	0.0201778i
$247$			98.4728i			0.398675i
$248$	−117.422			−0.473477
$249$	−66.3614	−	25.8816i	−0.266512	−	0.103942i
$250$		0			0
$251$		−	150.522i		−	0.599688i	−0.953988	−	0.299844i	$-0.903065\pi$
$251$		−	150.522i		−	0.599688i	0.953988	−	0.299844i	$-0.0969346\pi$
$252$	−32.2429	+	35.0485i	−0.127948	+	0.139081i
$253$		−	23.4083i		−	0.0925230i
$254$			235.325i			0.926476i
$255$		0			0
$256$	16.0000			0.0625000
$257$	313.116			1.21835			0.609175	−	0.793036i	$-0.291501\pi$
$257$	313.116			1.21835			0.609175	+	0.793036i	$0.291501\pi$
$258$	−3.27859	+	8.40643i	−0.0127077	+	0.0325831i
$259$	−73.3018			−0.283019
$260$		0			0
$261$	−156.848	+	170.496i	−0.600951	+	0.653242i
$262$			324.105i			1.23704i
$263$	413.301			1.57149			0.785744	−	0.618552i	$-0.212280\pi$
$263$	413.301			1.57149			0.785744	+	0.618552i	$0.212280\pi$
$264$	−10.2025	+	26.1597i	−0.0386460	+	0.0990898i
$265$		0			0
$266$			27.8793i			0.104809i
$267$	−3.55695	+	9.12016i	−0.0133219	+	0.0341579i
$268$		−	109.490i		−	0.408545i
$269$		−	77.5114i		−	0.288147i	−0.989567	−	0.144073i	$-0.953980\pi$
$269$		−	77.5114i		−	0.288147i	0.989567	−	0.144073i	$-0.0460201\pi$
$270$		0			0
$271$	277.456			1.02382			0.511912	−	0.859038i	$-0.328938\pi$
$271$	277.456			1.02382			0.511912	+	0.859038i	$0.328938\pi$
$272$	−56.9058			−0.209212
$273$	−97.7287	−	38.1151i	−0.357980	−	0.139616i
$274$	−174.739			−0.637732
$275$		0			0
$276$	39.5423	+	15.4219i	0.143269	+	0.0558763i
$277$			64.2751i			0.232040i	0.993247	+	0.116020i	$0.0370137\pi$
$277$			64.2751i			0.232040i	−0.993247	+	0.116020i	$0.962986\pi$
$278$	240.127			0.863764
$279$	274.977	+	252.965i	0.985579	+	0.906684i
$280$		0			0
$281$			238.377i			0.848315i	0.905588	+	0.424158i	$0.139430\pi$
$281$			238.377i			0.848315i	−0.905588	+	0.424158i	$0.860570\pi$
$282$	216.746	+	84.5329i	0.768601	+	0.299762i
$283$			295.213i			1.04315i	0.853204	+	0.521577i	$0.174656\pi$
$283$			295.213i			1.04315i	−0.853204	+	0.521577i	$0.825344\pi$
$284$		−	200.564i		−	0.706213i
$285$		0			0
$286$	−61.8481			−0.216252
$287$	−3.32252			−0.0115767
$288$	−37.4684	−	34.4691i	−0.130099	−	0.119684i
$289$	−86.6082			−0.299682
$290$		0			0
$291$	−60.5804	+	155.331i	−0.208180	+	0.533782i
$292$			126.407i			0.432900i
$293$	−358.351			−1.22304			−0.611521	−	0.791228i	$-0.709442\pi$
$293$	−358.351			−1.22304			−0.611521	+	0.791228i	$0.709442\pi$
$294$	−27.6686	−	10.7910i	−0.0941110	−	0.0367042i
$295$		0			0
$296$		−	78.3629i		−	0.264740i
$297$	80.2484	−	39.2807i	0.270197	−	0.132258i
$298$			336.288i			1.12848i
$299$			93.4878i			0.312668i
$300$		0			0
$301$	−5.62692			−0.0186941
$302$	−165.558			−0.548206
$303$	−136.050	+	348.838i	−0.449010	+	1.15128i
$304$	−29.8042			−0.0980403
$305$		0			0
$306$	133.261	+	122.593i	0.435492	+	0.400631i
$307$			531.675i			1.73184i	0.500182	+	0.865920i	$0.333267\pi$
$307$			531.675i			1.73184i	−0.500182	+	0.865920i	$0.666733\pi$
$308$	−17.5102			−0.0568514
$309$	−123.047	+	315.498i	−0.398211	+	1.02103i
$310$		0			0
$311$		−	418.127i		−	1.34446i	−0.740343	−	0.672229i	$-0.765337\pi$
$311$		−	418.127i		−	1.34446i	0.740343	−	0.672229i	$-0.234663\pi$
$312$	40.7468	−	104.476i	0.130599	−	0.334860i
$313$			306.865i			0.980399i	0.871610	+	0.490199i	$0.163076\pi$
$313$			306.865i			0.980399i	−0.871610	+	0.490199i	$0.836924\pi$
$314$			44.7105i			0.142390i
$315$		0			0
$316$	−233.884			−0.740138
$317$	−83.8149			−0.264400			−0.132200	−	0.991223i	$-0.542204\pi$
$317$	−83.8149			−0.264400			−0.132200	+	0.991223i	$0.542204\pi$
$318$	−246.309	−	96.0628i	−0.774556	−	0.302084i
$319$	−85.1800			−0.267022
$320$		0			0
$321$	−236.664	−	92.3012i	−0.737271	−	0.287543i
$322$			26.4680i			0.0821987i
$323$	106.002			0.328180
$324$	13.4853	+	161.438i	0.0416212	+	0.498265i
$325$		0			0
$326$			152.103i			0.466572i
$327$	461.626	+	180.039i	1.41170	+	0.550577i
$328$		−	3.55193i		−	0.0108290i
$329$			145.081i			0.440975i
$330$		0			0
$331$	145.013			0.438105			0.219052	−	0.975713i	$-0.429703\pi$
$331$	145.013			0.438105			0.219052	+	0.975713i	$0.429703\pi$
$332$	47.4866			0.143032
$333$	−168.819	+	183.508i	−0.506963	+	0.551076i
$334$	165.330			0.495000
$335$		0			0
$336$	11.5361	−	29.5790i	0.0343336	−	0.0880328i
$337$		−	610.894i		−	1.81274i	−0.422483	−	0.906371i	$-0.638841\pi$
$337$		−	610.894i		−	1.81274i	0.422483	−	0.906371i	$-0.361159\pi$
$338$	8.00610			0.0236867
$339$	−156.133	−	60.8935i	−0.460570	−	0.179627i
$340$		0			0
$341$			137.378i			0.402869i
$342$	69.7949	+	64.2078i	0.204079	+	0.187742i
$343$		−	18.5203i		−	0.0539949i
$344$		−	6.01543i		−	0.0174867i
$345$		0			0
$346$	−449.445			−1.29897
$347$	70.0988			0.202014			0.101007	−	0.994886i	$-0.467794\pi$
$347$	70.0988			0.202014			0.101007	+	0.994886i	$0.467794\pi$
$348$	56.1183	−	143.890i	0.161260	−	0.413476i
$349$	564.413			1.61723			0.808614	−	0.588340i	$-0.200218\pi$
$349$	564.413			1.61723			0.808614	+	0.588340i	$0.200218\pi$
$350$		0			0
$351$	−320.495	+	156.879i	−0.913091	+	0.446948i
$352$		−	18.7192i		−	0.0531796i
$353$	−1.65210			−0.00468018			−0.00234009	−	0.999997i	$-0.500745\pi$
$353$	−1.65210			−0.00468018			−0.00234009	+	0.999997i	$0.500745\pi$
$354$	33.5448	−	86.0102i	0.0947593	−	0.242967i
$355$		0			0
$356$		−	6.52616i		−	0.0183319i
$357$	−41.0294	+	105.201i	−0.114928	+	0.294681i
$358$			459.964i			1.28482i
$359$		−	396.146i		−	1.10347i	−0.834020	−	0.551735i	$-0.813966\pi$
$359$		−	396.146i		−	1.10347i	0.834020	−	0.551735i	$-0.186034\pi$
$360$		0			0
$361$	−305.482			−0.846210
$362$	48.8427			0.134925
$363$	−307.584	−	119.961i	−0.847339	−	0.330470i
$364$	69.9322			0.192121
$365$		0			0
$366$	335.204	+	130.733i	0.915859	+	0.357194i
$367$		−	363.378i		−	0.990131i	−0.868856	−	0.495066i	$-0.835144\pi$
$367$		−	363.378i		−	0.990131i	0.868856	−	0.495066i	$-0.164856\pi$
$368$	−28.2955			−0.0768899
$369$	−7.65198	+	8.31782i	−0.0207371	+	0.0225415i
$370$		0			0
$371$		−	164.869i		−	0.444391i
$372$	−232.065	−	90.5077i	−0.623831	−	0.243300i
$373$			207.182i			0.555448i	0.960661	+	0.277724i	$0.0895800\pi$
$373$			207.182i			0.555448i	−0.960661	+	0.277724i	$0.910420\pi$
$374$			66.5771i			0.178014i
$375$		0			0
$376$	−155.098			−0.412494
$377$	340.191			0.902363
$378$	−90.7376	+	44.4150i	−0.240046	+	0.117500i
$379$	−489.449			−1.29142			−0.645712	−	0.763581i	$-0.723439\pi$
$379$	−489.449			−1.29142			−0.645712	+	0.763581i	$0.723439\pi$
$380$		0			0
$381$	−181.386	+	465.080i	−0.476078	+	1.22068i
$382$			113.950i			0.298299i
$383$	210.772			0.550318			0.275159	−	0.961399i	$-0.411269\pi$
$383$	210.772			0.550318			0.275159	+	0.961399i	$0.411269\pi$
$384$	31.6213	+	12.3326i	0.0823471	+	0.0321162i
$385$		0			0
$386$		−	144.310i		−	0.373859i
$387$	−12.9592	+	14.0868i	−0.0334862	+	0.0364000i
$388$		−	111.151i		−	0.286471i
$389$		−	328.979i		−	0.845704i	−0.906199	−	0.422852i	$-0.861029\pi$
$389$		−	328.979i		−	0.845704i	0.906199	−	0.422852i	$-0.138971\pi$
$390$		0			0
$391$	100.636			0.257381
$392$	19.7990			0.0505076
$393$	−249.816	+	640.539i	−0.635665	+	1.62987i
$394$	71.4902			0.181447
$395$		0			0
$396$	−40.3272	+	43.8363i	−0.101836	+	0.110698i
$397$		−	32.3623i		−	0.0815172i	−0.999169	−	0.0407586i	$-0.987023\pi$
$397$		−	32.3623i		−	0.0815172i	0.999169	−	0.0407586i	$-0.0129775\pi$
$398$	−14.3754			−0.0361190
$399$	−21.4890	+	55.0988i	−0.0538573	+	0.138092i
$400$		0			0
$401$			233.517i			0.582338i	0.956672	+	0.291169i	$0.0940441\pi$
$401$			233.517i			0.582338i	−0.956672	+	0.291169i	$0.905956\pi$
$402$	84.3935	−	216.388i	0.209934	−	0.538280i
$403$		−	548.660i		−	1.36144i
$404$		−	249.620i		−	0.617870i
$405$		0			0
$406$	96.3138			0.237226
$407$	−91.6809			−0.225260
$408$	−112.465	−	43.8623i	−0.275649	−	0.107506i
$409$	30.2404			0.0739375			0.0369687	−	0.999316i	$-0.488230\pi$
$409$	30.2404			0.0739375			0.0369687	+	0.999316i	$0.488230\pi$
$410$		0			0
$411$	−345.341	−	134.686i	−0.840246	−	0.327704i
$412$		−	225.763i		−	0.547967i
$413$	57.5717			0.139399
$414$	66.2616	+	60.9574i	0.160052	+	0.147240i
$415$		0			0
$416$			74.7607i			0.179713i
$417$	474.570	+	185.087i	1.13806	+	0.443853i
$418$			34.8695i			0.0834200i
$419$		−	690.640i		−	1.64831i	−0.566367	−	0.824153i	$-0.691652\pi$
$419$		−	690.640i		−	1.64831i	0.566367	−	0.824153i	$-0.308348\pi$
$420$		0			0
$421$	−637.548			−1.51437			−0.757183	−	0.653203i	$-0.773425\pi$
$421$	−637.548			−1.51437			−0.757183	+	0.653203i	$0.773425\pi$
$422$	431.882			1.02342
$423$	363.204	+	334.130i	0.858639	+	0.789905i
$424$	176.253			0.415690
$425$		0			0
$426$	154.593	−	396.382i	0.362894	−	0.930474i
$427$			224.372i			0.525462i
$428$	169.351			0.395680
$429$	−122.232	−	47.6718i	−0.284924	−	0.111123i
$430$		0			0
$431$			474.481i			1.10088i	0.834874	+	0.550442i	$0.185541\pi$
$431$			474.481i			1.10088i	−0.834874	+	0.550442i	$0.814459\pi$
$432$	−47.4816	−	97.0025i	−0.109911	−	0.224543i
$433$			66.7488i			0.154154i	0.997025	+	0.0770772i	$0.0245588\pi$
$433$			66.7488i			0.154154i	−0.997025	+	0.0770772i	$0.975441\pi$
$434$		−	155.335i		−	0.357915i
$435$		0			0
$436$	−330.328			−0.757634
$437$	52.7078			0.120613
$438$	−97.4329	+	249.822i	−0.222450	+	0.570370i
$439$	361.090			0.822528			0.411264	−	0.911516i	$-0.365087\pi$
$439$	361.090			0.822528			0.411264	+	0.911516i	$0.365087\pi$
$440$		0			0
$441$	−46.3648	−	42.6533i	−0.105136	−	0.0967195i
$442$		−	265.895i		−	0.601572i
$443$	415.163			0.937163			0.468581	−	0.883420i	$-0.344765\pi$
$443$	415.163			0.937163			0.468581	+	0.883420i	$0.344765\pi$
$444$	60.4012	−	154.871i	0.136039	−	0.348809i
$445$		0			0
$446$			146.875i			0.329316i
$447$	−259.207	+	664.616i	−0.579881	+	1.48684i
$448$			21.1660i			0.0472456i
$449$			538.703i			1.19978i	0.800081	+	0.599892i	$0.204790\pi$
$449$			538.703i			1.19978i	−0.800081	+	0.599892i	$0.795210\pi$
$450$		0			0
$451$	−4.15559			−0.00921416
$452$	111.725			0.247179
$453$	−327.198	−	127.610i	−0.722292	−	0.281701i
$454$	555.416			1.22338
$455$		0			0
$456$	−58.9031	−	22.9728i	−0.129173	−	0.0503789i
$457$			666.562i			1.45856i	0.684216	+	0.729280i	$0.260145\pi$
$457$			666.562i			1.45856i	−0.684216	+	0.729280i	$0.739855\pi$
$458$	−604.081			−1.31895
$459$	168.874	+	345.000i	0.367917	+	0.751635i
$460$		0			0
$461$		−	246.725i		−	0.535196i	−0.963531	−	0.267598i	$-0.913770\pi$
$461$		−	246.725i		−	0.535196i	0.963531	−	0.267598i	$-0.0862299\pi$
$462$	−34.6060	−	13.4967i	−0.0749048	−	0.0292136i
$463$			278.772i			0.602099i	0.953609	+	0.301049i	$0.0973369\pi$
$463$			278.772i			0.602099i	−0.953609	+	0.301049i	$0.902663\pi$
$464$			102.964i			0.221905i
$465$		0			0
$466$	−81.6465			−0.175207
$467$	263.485			0.564208			0.282104	−	0.959384i	$-0.408968\pi$
$467$	263.485			0.564208			0.282104	+	0.959384i	$0.408968\pi$
$468$	161.058	−	175.073i	0.344142	−	0.374087i
$469$	144.842			0.308831
$470$		0			0
$471$	−34.4623	+	88.3628i	−0.0731685	+	0.187607i
$472$			61.5468i			0.130396i
$473$	−7.03777			−0.0148790
$474$	−462.231	−	180.275i	−0.975172	−	0.380326i
$475$		0			0
$476$		−	75.2793i		−	0.158150i
$477$	−412.744	−	379.704i	−0.865291	−	0.796025i
$478$		−	74.9123i		−	0.156720i
$479$			163.187i			0.340683i	0.985385	+	0.170342i	$0.0544871\pi$
$479$			163.187i			0.340683i	−0.985385	+	0.170342i	$0.945513\pi$
$480$		0			0
$481$	366.154			0.761235
$482$	222.389			0.461388
$483$	−20.4012	+	52.3095i	−0.0422385	+	0.108301i
$484$	220.099			0.454751
$485$		0			0
$486$	−97.7830	+	329.449i	−0.201200	+	0.677878i
$487$		−	752.251i		−	1.54466i	−0.635219	−	0.772332i	$-0.719090\pi$
$487$		−	752.251i		−	1.54466i	0.635219	−	0.772332i	$-0.280910\pi$
$488$	−239.864			−0.491524
$489$	−117.239	+	300.605i	−0.239752	+	0.614735i
$490$		0			0
$491$			67.2107i			0.136885i	0.997655	+	0.0684427i	$0.0218030\pi$
$491$			67.2107i			0.136885i	−0.997655	+	0.0684427i	$0.978197\pi$
$492$	2.73778	−	7.01978i	0.00556460	−	0.0142679i
$493$		−	366.202i		−	0.742804i
$494$		−	139.262i		−	0.281906i
$495$		0			0
$496$	166.060			0.334799
$497$	265.322			0.533847
$498$	93.8492	+	36.6021i	0.188452	+	0.0734982i
$499$	247.715			0.496423			0.248212	−	0.968706i	$-0.420157\pi$
$499$	247.715			0.496423			0.248212	+	0.968706i	$0.420157\pi$
$500$		0			0
$501$	326.747	+	127.435i	0.652190	+	0.254360i
$502$			212.870i			0.424043i
$503$	142.465			0.283231			0.141616	−	0.989922i	$-0.454770\pi$
$503$	142.465			0.283231			0.141616	+	0.989922i	$0.454770\pi$
$504$	45.5983	−	49.5661i	0.0904728	−	0.0983453i
$505$		0			0
$506$			33.1043i			0.0654236i
$507$	15.8227	+	6.17101i	0.0312085	+	0.0121716i
$508$		−	332.800i		−	0.655117i
$509$			541.364i			1.06358i	0.846875	+	0.531792i	$0.178481\pi$
$509$			541.364i			1.06358i	−0.846875	+	0.531792i	$0.821519\pi$
$510$		0			0
$511$	−167.221			−0.327242
$512$	−22.6274			−0.0441942
$513$	88.4471	+	180.693i	0.172412	+	0.352228i
$514$	−442.813			−0.861504
$515$		0			0
$516$	4.63662	−	11.8885i	0.00898571	−	0.0230397i
$517$			181.457i			0.350981i
$518$	103.664			0.200124
$519$	−888.251	−	346.427i	−1.71147	−	0.667489i
$520$		0			0
$521$		−	796.131i		−	1.52808i	−0.645168	−	0.764041i	$-0.723213\pi$
$521$		−	796.131i		−	1.52808i	0.645168	−	0.764041i	$-0.276787\pi$
$522$	221.817	−	241.118i	0.424936	−	0.461912i
$523$		−	382.162i		−	0.730711i	−0.930868	−	0.365355i	$-0.880947\pi$
$523$		−	382.162i		−	0.730711i	0.930868	−	0.365355i	$-0.119053\pi$
$524$		−	458.354i		−	0.874721i
$525$		0			0
$526$	−584.496			−1.11121
$527$	−590.612			−1.12071
$528$	14.4286	−	36.9954i	0.0273268	−	0.0700671i
$529$	−478.960			−0.905407
$530$		0			0
$531$	132.591	−	144.129i	0.249701	−	0.271429i
$532$		−	39.4273i		−	0.0741115i
$533$	16.5965			0.0311380
$534$	5.03029	−	12.8979i	0.00942001	−	0.0241533i
$535$		0			0
$536$			154.842i			0.288885i
$537$	−354.535	+	909.042i	−0.660214	+	1.69282i
$538$			109.618i			0.203750i
$539$		−	23.1639i		−	0.0429756i
$540$		0			0
$541$	781.905			1.44530			0.722648	−	0.691217i	$-0.242925\pi$
$541$	781.905			1.44530			0.722648	+	0.691217i	$0.242925\pi$
$542$	−392.382			−0.723952
$543$	96.5293	+	37.6474i	0.177770	+	0.0693321i
$544$	80.4769			0.147936
$545$		0			0
$546$	138.209	+	53.9029i	0.253130	+	0.0987233i
$547$		−	836.992i		−	1.53015i	−0.643942	−	0.765075i	$-0.722702\pi$
$547$		−	836.992i		−	1.53015i	0.643942	−	0.765075i	$-0.277298\pi$
$548$	247.118			0.450945
$549$	561.708	+	516.743i	1.02315	+	0.941244i
$550$		0			0
$551$		−	191.797i		−	0.348090i
$552$	−55.9212	−	21.8098i	−0.101307	−	0.0395105i
$553$		−	309.399i		−	0.559492i
$554$		−	90.8988i		−	0.164077i
$555$		0			0
$556$	−339.590			−0.610774
$557$	151.652			0.272267			0.136133	−	0.990691i	$-0.456532\pi$
$557$	151.652			0.272267			0.136133	+	0.990691i	$0.456532\pi$
$558$	−388.876	−	357.746i	−0.696910	−	0.641123i
$559$	28.1074			0.0502815
$560$		0			0
$561$	−51.3168	+	131.578i	−0.0914738	+	0.234542i
$562$		−	337.115i		−	0.599850i
$563$	830.912			1.47586			0.737932	−	0.674875i	$-0.235802\pi$
$563$	830.912			1.47586			0.737932	+	0.674875i	$0.235802\pi$
$564$	−306.525	−	119.548i	−0.543483	−	0.211964i
$565$		0			0
$566$		−	417.494i		−	0.737621i
$567$	−213.562	+	17.8393i	−0.376653	+	0.0314626i
$568$			283.641i			0.499368i
$569$			76.3013i			0.134097i	0.997750	+	0.0670486i	$0.0213583\pi$
$569$			76.3013i			0.134097i	−0.997750	+	0.0670486i	$0.978642\pi$
$570$		0			0
$571$	−273.471			−0.478933			−0.239467	−	0.970905i	$-0.576973\pi$
$571$	−273.471			−0.478933			−0.239467	+	0.970905i	$0.576973\pi$
$572$	87.4664			0.152913
$573$	−87.8313	+	225.203i	−0.153283	+	0.393025i
$574$	4.69876			0.00818599
$575$		0			0
$576$	52.9883	+	48.7466i	0.0919936	+	0.0846296i
$577$		−	783.907i		−	1.35859i	−0.733865	−	0.679295i	$-0.762286\pi$
$577$		−	783.907i		−	1.35859i	0.733865	−	0.679295i	$-0.237714\pi$
$578$	122.482			0.211907
$579$	111.232	−	285.204i	0.192111	−	0.492580i
$580$		0			0
$581$			62.8189i			0.108122i
$582$	85.6736	−	219.671i	0.147206	−	0.377441i
$583$		−	206.207i		−	0.353700i
$584$		−	178.766i		−	0.306107i
$585$		0			0
$586$	506.786			0.864822
$587$	−552.525			−0.941269			−0.470634	−	0.882328i	$-0.655975\pi$
$587$	−552.525			−0.941269			−0.470634	+	0.882328i	$0.655975\pi$
$588$	39.1294	+	15.2608i	0.0665465	+	0.0259538i
$589$	−309.331			−0.525180
$590$		0			0
$591$	141.288	+	55.1038i	0.239067	+	0.0932382i
$592$			110.822i			0.187199i
$593$	−236.428			−0.398699			−0.199349	−	0.979928i	$-0.563883\pi$
$593$	−236.428			−0.398699			−0.199349	+	0.979928i	$0.563883\pi$
$594$	−113.488	+	55.5512i	−0.191058	+	0.0935206i
$595$		0			0
$596$		−	475.583i		−	0.797958i
$597$	−28.4105	−	11.0804i	−0.0475888	−	0.0185601i
$598$		−	132.212i		−	0.221090i
$599$			1179.57i			1.96923i	0.174727	+	0.984617i	$0.444096\pi$
$599$			1179.57i			1.96923i	−0.174727	+	0.984617i	$0.555904\pi$
$600$		0			0
$601$	1090.04			1.81370			0.906851	−	0.421451i	$-0.138479\pi$
$601$	1090.04			1.81370			0.906851	+	0.421451i	$0.138479\pi$
$602$	7.95767			0.0132187
$603$	333.579	−	362.606i	0.553199	−	0.601336i
$604$	234.135			0.387640
$605$		0			0
$606$	192.404	−	493.331i	0.317498	−	0.814078i
$607$			1077.37i			1.77491i	0.460892	+	0.887456i	$0.347530\pi$
$607$			1077.37i			1.77491i	−0.460892	+	0.887456i	$0.652470\pi$
$608$	42.1496			0.0693249
$609$	190.348	+	74.2375i	0.312558	+	0.121901i
$610$		0			0
$611$		−	724.701i		−	1.18609i
$612$	−188.459	−	173.373i	−0.307939	−	0.283289i
$613$		−	942.291i		−	1.53718i	−0.639742	−	0.768590i	$-0.720959\pi$
$613$		−	942.291i		−	1.53718i	0.639742	−	0.768590i	$-0.279041\pi$
$614$		−	751.902i		−	1.22460i
$615$		0			0
$616$	24.7632			0.0402000
$617$	−863.672			−1.39979			−0.699896	−	0.714245i	$-0.746770\pi$
$617$	−863.672			−1.39979			−0.699896	+	0.714245i	$0.746770\pi$
$618$	174.015	−	446.182i	0.281578	−	0.721977i
$619$	−626.507			−1.01213			−0.506064	−	0.862496i	$-0.668900\pi$
$619$	−626.507			−1.01213			−0.506064	+	0.862496i	$0.668900\pi$
$620$		0			0
$621$	83.9697	+	171.546i	0.135217	+	0.276241i
$622$			591.320i			0.950676i
$623$	8.63330			0.0138576
$624$	−57.6246	+	147.752i	−0.0923472	+	0.236782i
$625$		0			0
$626$		−	433.972i		−	0.693247i
$627$	−26.8770	+	68.9138i	−0.0428661	+	0.109910i
$628$		−	63.2302i		−	0.100685i
$629$		−	394.151i		−	0.626630i
$630$		0			0
$631$	612.214			0.970228			0.485114	−	0.874451i	$-0.338778\pi$
$631$	612.214			0.970228			0.485114	+	0.874451i	$0.338778\pi$
$632$	330.761			0.523356
$633$	853.541	+	332.889i	1.34841	+	0.525891i
$634$	118.532			0.186959
$635$		0			0
$636$	348.333	+	135.853i	0.547694	+	0.213606i
$637$			92.5116i			0.145230i
$638$	120.463			0.188813
$639$	611.053	−	664.224i	0.956264	−	1.03947i
$640$		0			0
$641$			804.983i			1.25582i	0.778284	+	0.627912i	$0.216090\pi$
$641$			804.983i			1.25582i	−0.778284	+	0.627912i	$0.783910\pi$
$642$	334.693	+	130.534i	0.521329	+	0.203323i
$643$			71.5877i			0.111334i	0.998449	+	0.0556670i	$0.0177285\pi$
$643$			71.5877i			0.111334i	−0.998449	+	0.0556670i	$0.982271\pi$
$644$		−	37.4314i		−	0.0581233i
$645$		0			0
$646$	−149.910			−0.232058
$647$	−579.969			−0.896397			−0.448199	−	0.893934i	$-0.647934\pi$
$647$	−579.969			−0.896397			−0.448199	+	0.893934i	$0.647934\pi$
$648$	−19.0710	−	228.307i	−0.0294306	−	0.352326i
$649$	72.0068			0.110950
$650$		0			0
$651$	119.730	−	306.994i	0.183918	−	0.471572i
$652$		−	215.106i		−	0.329917i
$653$	−1063.75			−1.62902			−0.814511	−	0.580148i	$-0.802995\pi$
$653$	−1063.75			−1.62902			−0.814511	+	0.580148i	$0.802995\pi$
$654$	−652.838	−	254.613i	−0.998223	−	0.389317i
$655$		0			0
$656$			5.02318i			0.00765729i
$657$	−385.119	+	418.631i	−0.586179	+	0.637185i
$658$		−	205.175i		−	0.311816i
$659$		−	227.741i		−	0.345586i	−0.984958	−	0.172793i	$-0.944721\pi$
$659$		−	227.741i		−	0.345586i	0.984958	−	0.172793i	$-0.0552792\pi$
$660$		0			0
$661$	87.7668			0.132779			0.0663894	−	0.997794i	$-0.478852\pi$
$661$	87.7668			0.132779			0.0663894	+	0.997794i	$0.478852\pi$
$662$	−205.079			−0.309787
$663$	204.948	−	525.496i	0.309123	−	0.792603i
$664$	−67.1562			−0.101139
$665$		0			0
$666$	238.746	−	259.520i	0.358477	−	0.389670i
$667$		−	182.088i		−	0.272996i
$668$	−233.812			−0.350018
$669$	−113.210	+	290.274i	−0.169222	+	0.433892i
$670$		0			0
$671$			280.629i			0.418226i
$672$	−16.3145	+	41.8311i	−0.0242775	+	0.0622486i
$673$		−	286.806i		−	0.426160i	−0.977035	−	0.213080i	$-0.931650\pi$
$673$		−	286.806i		−	0.426160i	0.977035	−	0.213080i	$-0.0683495\pi$
$674$			863.935i			1.28180i
$675$		0			0
$676$	−11.3223			−0.0167490
$677$	−739.076			−1.09169			−0.545847	−	0.837885i	$-0.683792\pi$
$677$	−739.076			−1.09169			−0.545847	+	0.837885i	$0.683792\pi$
$678$	220.806	+	86.1164i	0.325672	+	0.127015i
$679$	147.039			0.216552
$680$		0			0
$681$	1097.69	+	428.108i	1.61187	+	0.628646i
$682$		−	194.282i		−	0.284872i
$683$	384.541			0.563017			0.281509	−	0.959559i	$-0.409165\pi$
$683$	384.541			0.563017			0.281509	+	0.959559i	$0.409165\pi$
$684$	−98.7048	−	90.8036i	−0.144305	−	0.132754i
$685$		0			0
$686$			26.1916i			0.0381802i
$687$	−1193.86	−	465.618i	−1.73779	−	0.677756i
$688$			8.50711i			0.0123650i
$689$			823.547i			1.19528i
$690$		0			0
$691$	1158.11			1.67599			0.837994	−	0.545680i	$-0.183729\pi$
$691$	1158.11			1.67599			0.837994	+	0.545680i	$0.183729\pi$
$692$	635.611			0.918512
$693$	−57.9899	−	53.3479i	−0.0836795	−	0.0769810i
$694$	−99.1347			−0.142845
$695$		0			0
$696$	−79.3633	+	203.491i	−0.114028	+	0.292372i
$697$		−	17.8655i		−	0.0256320i
$698$	−798.200			−1.14355
$699$	−161.360	−	62.9321i	−0.230845	−	0.0900317i
$700$		0			0
$701$			1033.07i			1.47371i	0.676049	+	0.736856i	$0.263691\pi$
$701$			1033.07i			1.47371i	−0.676049	+	0.736856i	$0.736309\pi$
$702$	453.248	−	221.860i	0.645653	−	0.316040i
$703$		−	206.435i		−	0.293649i
$704$			26.4730i			0.0376037i
$705$		0			0
$706$	2.33643			0.00330939
$707$	330.216			0.467066
$708$	−47.4395	+	121.637i	−0.0670050	+	0.171803i
$709$	978.655			1.38033			0.690166	−	0.723651i	$-0.257538\pi$
$709$	978.655			1.38033			0.690166	+	0.723651i	$0.257538\pi$
$710$		0			0
$711$	−774.569	−	712.565i	−1.08941	−	1.00220i
$712$			9.22938i			0.0129626i
$713$	−293.672			−0.411882
$714$	58.0244	−	148.777i	0.0812666	−	0.208371i
$715$		0			0
$716$		−	650.488i		−	0.908502i
$717$	57.7415	−	148.052i	0.0805321	−	0.206488i
$718$			560.235i			0.780271i
$719$		−	1081.91i		−	1.50474i	−0.658739	−	0.752372i	$-0.728910\pi$
$719$		−	1081.91i		−	1.50474i	0.658739	−	0.752372i	$-0.271090\pi$
$720$		0			0
$721$	298.656			0.414224
$722$	432.016			0.598361
$723$	439.515	+	171.415i	0.607904	+	0.237088i
$724$	−69.0740			−0.0954060
$725$		0			0
$726$	434.989	+	169.650i	0.599159	+	0.233678i
$727$			416.273i			0.572589i	0.958142	+	0.286295i	$0.0924237\pi$
$727$			416.273i			0.572589i	−0.958142	+	0.286295i	$0.907576\pi$
$728$	−98.8991			−0.135850
$729$	−447.187	+	575.730i	−0.613425	+	0.789753i
$730$		0			0
$731$		−	30.2565i		−	0.0413905i
$732$	−474.051	−	184.884i	−0.647610	−	0.252574i
$733$			338.733i			0.462118i	0.972940	+	0.231059i	$0.0742191\pi$
$733$			338.733i			0.462118i	−0.972940	+	0.231059i	$0.925781\pi$
$734$			513.894i			0.700128i
$735$		0			0
$736$	40.0158			0.0543693
$737$	181.158			0.245805
$738$	10.8215	−	11.7632i	0.0146633	−	0.0159393i
$739$	−324.854			−0.439586			−0.219793	−	0.975547i	$-0.570538\pi$
$739$	−324.854			−0.439586			−0.219793	+	0.975547i	$0.570538\pi$
$740$		0			0
$741$	107.341	−	275.227i	0.144860	−	0.371426i
$742$			233.160i			0.314232i
$743$	857.635			1.15429			0.577143	−	0.816643i	$-0.304167\pi$
$743$	857.635			1.15429			0.577143	+	0.816643i	$0.304167\pi$
$744$	328.190	+	127.997i	0.441115	+	0.172039i
$745$		0			0
$746$		−	293.000i		−	0.392761i
$747$	157.265	+	144.676i	0.210528	+	0.193676i
$748$		−	94.1542i		−	0.125875i
$749$			224.030i			0.299106i
$750$		0			0
$751$	−356.621			−0.474861			−0.237431	−	0.971404i	$-0.576305\pi$
$751$	−356.621			−0.474861			−0.237431	+	0.971404i	$0.576305\pi$
$752$	219.341			0.291677
$753$	−164.077	+	420.701i	−0.217898	+	0.558700i
$754$	−481.103			−0.638067
$755$		0			0
$756$	128.322	−	62.8123i	0.169739	−	0.0830851i
$757$		−	1356.47i		−	1.79191i	−0.444147	−	0.895954i	$-0.646493\pi$
$757$		−	1356.47i		−	1.79191i	0.444147	−	0.895954i	$-0.353507\pi$
$758$	692.186			0.913174
$759$	−25.5164	+	65.4252i	−0.0336185	+	0.0861992i
$760$		0			0
$761$			106.889i			0.140459i	0.997531	+	0.0702294i	$0.0223731\pi$
$761$			106.889i			0.140459i	−0.997531	+	0.0702294i	$0.977627\pi$
$762$	256.518	−	657.722i	0.336638	−	0.863153i
$763$		−	436.983i		−	0.572717i
$764$		−	161.150i		−	0.210929i
$765$		0			0
$766$	−298.076			−0.389134
$767$	−287.580			−0.374941
$768$	−44.7193	−	17.4409i	−0.0582282	−	0.0227096i
$769$	−500.283			−0.650563			−0.325282	−	0.945617i	$-0.605459\pi$
$769$	−500.283			−0.650563			−0.325282	+	0.945617i	$0.605459\pi$
$770$		0			0
$771$	−875.145	−	341.315i	−1.13508	−	0.442691i
$772$			204.085i			0.264359i
$773$	−1146.06			−1.48262			−0.741309	−	0.671164i	$-0.765794\pi$
$773$	−1146.06			−1.48262			−0.741309	+	0.671164i	$0.765794\pi$
$774$	18.3270	−	19.9217i	0.0236783	−	0.0257387i
$775$		0			0
$776$			157.191i			0.202566i
$777$	204.875	+	79.9033i	0.263675	+	0.102836i
$778$			465.246i			0.598003i
$779$		−	9.35701i		−	0.0120116i
$780$		0			0
$781$	331.846			0.424899
$782$	−142.321			−0.181996
$783$	624.234	−	305.556i	0.797234	−	0.390237i
$784$	−28.0000			−0.0357143
$785$		0			0
$786$	353.294	−	905.859i	0.449483	−	1.15249i
$787$		−	488.016i		−	0.620097i	−0.950721	−	0.310048i	$-0.899655\pi$
$787$		−	488.016i		−	0.620097i	0.950721	−	0.310048i	$-0.100345\pi$
$788$	−101.102			−0.128303
$789$	−1155.16	−	450.523i	−1.46408	−	0.571005i
$790$		0			0
$791$			147.798i			0.186850i
$792$	57.0313	−	61.9938i	0.0720092	−	0.0782750i
$793$		−	1120.77i		−	1.41333i
$794$			45.7672i			0.0576413i
$795$		0			0
$796$	20.3299			0.0255400
$797$	−197.490			−0.247792			−0.123896	−	0.992295i	$-0.539539\pi$
$797$	−197.490			−0.247792			−0.123896	+	0.992295i	$0.539539\pi$
$798$	30.3901	−	77.9214i	0.0380828	−	0.0976459i
$799$	−780.112			−0.976361
$800$		0			0
$801$	19.8830	−	21.6131i	0.0248228	−	0.0269827i
$802$		−	330.243i		−	0.411775i
$803$	−209.148			−0.260458
$804$	−119.350	+	306.019i	−0.148446	+	0.380621i
$805$		0			0
$806$			775.923i			0.962684i
$807$	−84.4920	+	216.641i	−0.104699	+	0.268452i
$808$			353.015i			0.436900i
$809$			982.627i			1.21462i	0.794465	+	0.607310i	$0.207751\pi$
$809$			982.627i			1.21462i	−0.794465	+	0.607310i	$0.792249\pi$
$810$		0			0
$811$	344.348			0.424597			0.212298	−	0.977205i	$-0.431905\pi$
$811$	344.348			0.424597			0.212298	+	0.977205i	$0.431905\pi$
$812$	−136.208			−0.167744
$813$	−775.477	−	302.444i	−0.953846	−	0.372009i
$814$	129.656			0.159283
$815$		0			0
$816$	159.049	+	62.0307i	0.194913	+	0.0760180i
$817$		−	15.8467i		−	0.0193963i
$818$	−42.7664			−0.0522817
$819$	231.599	+	213.060i	0.282783	+	0.260147i
$820$		0			0
$821$		−	616.490i		−	0.750901i	−0.926842	−	0.375451i	$-0.877488\pi$
$821$		−	616.490i		−	0.750901i	0.926842	−	0.375451i	$-0.122512\pi$
$822$	488.386	+	190.475i	0.594144	+	0.231722i
$823$		−	638.840i		−	0.776234i	−0.921610	−	0.388117i	$-0.873126\pi$
$823$		−	638.840i		−	0.776234i	0.921610	−	0.388117i	$-0.126874\pi$
$824$			319.276i			0.387471i
$825$		0			0
$826$	−81.4187			−0.0985699
$827$	1066.42			1.28951			0.644753	−	0.764391i	$-0.276960\pi$
$827$	1066.42			1.28951			0.644753	+	0.764391i	$0.276960\pi$
$828$	−93.7081	−	86.2068i	−0.113174	−	0.104115i
$829$	625.285			0.754265			0.377132	−	0.926159i	$-0.376910\pi$
$829$	625.285			0.754265			0.377132	+	0.926159i	$0.376910\pi$
$830$		0			0
$831$	70.0637	−	179.646i	0.0843125	−	0.216181i
$832$		−	105.728i		−	0.127076i
$833$	99.5851			0.119550
$834$	−671.143	−	261.752i	−0.804727	−	0.313851i
$835$		0			0
$836$		−	49.3130i		−	0.0589868i
$837$	−492.801	−	1006.77i	−0.588770	−	1.20283i
$838$			976.713i			1.16553i
$839$		−	387.376i		−	0.461712i	−0.972988	−	0.230856i	$-0.925847\pi$
$839$		−	387.376i		−	0.461712i	0.972988	−	0.230856i	$-0.0741526\pi$
$840$		0			0
$841$	178.404			0.212133
$842$	901.629			1.07082
$843$	259.845	−	666.252i	0.308238	−	0.790334i
$844$	−610.773			−0.723665
$845$		0			0
$846$	−513.648	−	472.531i	−0.607149	−	0.558547i
$847$			291.164i			0.343759i
$848$	−249.259			−0.293937
$849$	321.799	−	825.106i	0.379033	−	0.971856i
$850$		0			0
$851$		−	195.985i		−	0.230299i
$852$	−218.627	+	560.569i	−0.256605	+	0.657944i
$853$		−	830.771i		−	0.973940i	−0.873419	−	0.486970i	$-0.838102\pi$
$853$		−	830.771i		−	0.973940i	0.873419	−	0.486970i	$-0.161898\pi$
$854$		−	317.310i		−	0.371558i
$855$		0			0
$856$	−239.498			−0.279788
$857$	−292.550			−0.341365			−0.170683	−	0.985326i	$-0.554597\pi$
$857$	−292.550			−0.341365			−0.170683	+	0.985326i	$0.554597\pi$
$858$	172.863	+	67.4181i	0.201472	+	0.0785758i
$859$	672.801			0.783237			0.391619	−	0.920128i	$-0.371915\pi$
$859$	672.801			0.783237			0.391619	+	0.920128i	$0.371915\pi$
$860$		0			0
$861$	9.28630	+	3.62175i	0.0107855	+	0.00420644i
$862$		−	671.017i		−	0.778442i
$863$	−699.281			−0.810291			−0.405145	−	0.914252i	$-0.632779\pi$
$863$	−699.281			−0.810291			−0.405145	+	0.914252i	$0.632779\pi$
$864$	67.1492	+	137.182i	0.0777190	+	0.158776i
$865$		0			0
$866$		−	94.3971i		−	0.109004i
$867$	242.066	+	94.4080i	0.279199	+	0.108890i
$868$			219.677i			0.253084i
$869$		−	386.975i		−	0.445311i
$870$		0			0
$871$	−723.506			−0.830662
$872$	467.155			0.535728
$873$	338.639	−	368.106i	0.387903	−	0.421656i
$874$	−74.5401			−0.0852862
$875$		0			0
$876$	137.791	−	353.301i	0.157296	−	0.403312i
$877$			358.626i			0.408924i	0.978874	+	0.204462i	$0.0655445\pi$
$877$			358.626i			0.408924i	−0.978874	+	0.204462i	$0.934456\pi$
$878$	−510.658			−0.581615
$879$	1001.58	+	390.624i	1.13945	+	0.444396i
$880$		0			0
$881$			1550.04i			1.75941i	0.475522	+	0.879704i	$0.342259\pi$
$881$			1550.04i			1.75941i	−0.475522	+	0.879704i	$0.657741\pi$
$882$	65.5697	+	60.3209i	0.0743421	+	0.0683910i
$883$			1595.94i			1.80741i	0.428154	+	0.903706i	$0.359164\pi$
$883$			1595.94i			1.80741i	−0.428154	+	0.903706i	$0.640836\pi$
$884$			376.032i			0.425375i
$885$		0			0
$886$	−587.129			−0.662674
$887$	−134.533			−0.151671			−0.0758357	−	0.997120i	$-0.524162\pi$
$887$	−134.533			−0.151671			−0.0758357	+	0.997120i	$0.524162\pi$
$888$	−85.4202	+	219.021i	−0.0961939	+	0.246645i
$889$	440.253			0.495222
$890$		0			0
$891$	−267.109	+	22.3122i	−0.299785	+	0.0250418i
$892$		−	207.713i		−	0.232862i
$893$	−408.581			−0.457538
$894$	366.574	−	939.909i	0.410038	−	1.05135i
$895$		0			0
$896$		−	29.9333i		−	0.0334077i
$897$	101.907	−	261.294i	0.113609	−	0.291298i
$898$		−	761.841i		−	0.848375i
$899$			1068.64i			1.18869i
$900$		0			0
$901$	886.517			0.983925
$902$	5.87688			0.00651539
$903$	15.7270	+	6.13368i	0.0174164	+	0.00679256i
$904$	−158.003			−0.174782
$905$		0			0
$906$	462.728	+	180.468i	0.510737	+	0.199192i
$907$		−	879.668i		−	0.969865i	−0.874551	−	0.484933i	$-0.838844\pi$
$907$		−	879.668i		−	0.969865i	0.874551	−	0.484933i	$-0.161156\pi$
$908$	−785.477			−0.865062
$909$	760.507	−	826.683i	0.836642	−	0.909442i
$910$		0			0
$911$			1522.40i			1.67113i	0.549391	+	0.835565i	$0.314860\pi$
$911$			1522.40i			1.67113i	−0.549391	+	0.835565i	$0.685140\pi$
$912$	83.3015	+	32.4884i	0.0913394	+	0.0356232i
$913$			78.5695i			0.0860564i
$914$		−	942.661i		−	1.03136i
$915$		0			0
$916$	854.299			0.932641
$917$	606.345			0.661227
$918$	−238.824	−	487.904i	−0.260156	−	0.531486i
$919$	−1178.73			−1.28262			−0.641309	−	0.767282i	$-0.721608\pi$
$919$	−1178.73			−1.28262			−0.641309	+	0.767282i	$0.721608\pi$
$920$		0			0
$921$	579.557	−	1486.01i	0.629270	−	1.61347i
$922$			348.922i			0.378441i
$923$	−1325.32			−1.43589
$924$	48.9403	+	19.0872i	0.0529657	+	0.0206571i
$925$		0			0
$926$		−	394.243i		−	0.425748i
$927$	687.823	−	747.674i	0.741988	−	0.806552i
$928$		−	145.613i		−	0.156910i
$929$			534.346i			0.575184i	0.957753	+	0.287592i	$0.0928547\pi$
$929$			534.346i			0.575184i	−0.957753	+	0.287592i	$0.907145\pi$
$930$		0			0
$931$	52.1574			0.0560230
$932$	115.466			0.123890
$933$	−455.783	+	1168.65i	−0.488513	+	1.25257i
$934$	−372.624			−0.398955
$935$		0			0
$936$	−227.771	+	247.590i	−0.243345	+	0.264519i
$937$		−	1383.17i		−	1.47616i	−0.674711	−	0.738082i	$-0.735732\pi$
$937$		−	1383.17i		−	1.47616i	0.674711	−	0.738082i	$-0.264268\pi$
$938$	−204.837			−0.218376
$939$	334.501	−	857.673i	0.356231	−	0.913390i
$940$		0			0
$941$			562.997i			0.598296i	0.954207	+	0.299148i	$0.0967024\pi$
$941$			562.997i			0.598296i	−0.954207	+	0.299148i	$0.903298\pi$
$942$	48.7371	−	124.964i	0.0517379	−	0.132658i
$943$		−	8.88333i		−	0.00942029i
$944$		−	87.0403i		−	0.0922037i
$945$		0			0
$946$	9.95291			0.0105210
$947$	−722.442			−0.762874			−0.381437	−	0.924395i	$-0.624571\pi$
$947$	−722.442			−0.762874			−0.381437	+	0.924395i	$0.624571\pi$
$948$	653.694	+	254.947i	0.689551	+	0.268931i
$949$	835.293			0.880182
$950$		0			0
$951$	234.259	+	91.3632i	0.246329	+	0.0960707i
$952$			106.461i			0.111829i
$953$	−1567.96			−1.64529			−0.822644	−	0.568557i	$-0.807502\pi$
$953$	−1567.96			−1.64529			−0.822644	+	0.568557i	$0.807502\pi$
$954$	583.708	+	536.983i	0.611853	+	0.562875i
$955$		0			0
$956$			105.942i			0.110818i
$957$	238.074	+	92.8512i	0.248771	+	0.0970232i
$958$		−	230.782i		−	0.240899i
$959$			326.906i			0.340882i
$960$		0			0
$961$	762.498			0.793443
$962$	−517.820			−0.538274
$963$	560.851	+	515.955i	0.582400	+	0.535779i
$964$	−314.506			−0.326251
$965$		0			0
$966$	28.8517	−	73.9768i	0.0298672	−	0.0765806i
$967$			1182.12i			1.22246i	0.791453	+	0.611230i	$0.209325\pi$
$967$			1182.12i			1.22246i	−0.791453	+	0.611230i	$0.790675\pi$
$968$	−311.268			−0.321557
$969$	−296.271	−	115.549i	−0.305749	−	0.119245i
$970$		0			0
$971$		−	1672.57i		−	1.72252i	−0.508165	−	0.861260i	$-0.669676\pi$
$971$		−	1672.57i		−	1.72252i	0.508165	−	0.861260i	$-0.330324\pi$
$972$	138.286	−	465.911i	0.142270	−	0.479332i
$973$		−	449.236i		−	0.461702i
$974$			1063.84i			1.09224i
$975$		0			0
$976$	339.219			0.347560
$977$	383.549			0.392578			0.196289	−	0.980546i	$-0.437111\pi$
$977$	383.549			0.392578			0.196289	+	0.980546i	$0.437111\pi$
$978$	165.801	−	425.120i	0.169531	−	0.434683i
$979$	10.7979			0.0110296
$980$		0			0
$981$	−1093.97	−	1006.40i	−1.11516	−	1.02589i
$982$		−	95.0503i		−	0.0967925i
$983$	68.4583			0.0696422			0.0348211	−	0.999394i	$-0.488914\pi$
$983$	68.4583			0.0696422			0.0348211	+	0.999394i	$0.488914\pi$
$984$	−3.87181	+	9.92748i	−0.00393477	+	0.0100889i
$985$		0			0
$986$			517.888i			0.525242i
$987$	158.147	−	405.494i	0.160229	−	0.410835i
$988$			196.946i			0.199338i
$989$		−	15.0445i		−	0.0152119i
$990$		0			0
$991$	−700.214			−0.706573			−0.353287	−	0.935515i	$-0.614936\pi$
$991$	−700.214			−0.706573			−0.353287	+	0.935515i	$0.614936\pi$
$992$	−234.845			−0.236738
$993$	−405.304	−	158.072i	−0.408161	−	0.159187i
$994$	−375.222			−0.377487
$995$		0			0
$996$	−132.723	−	51.7632i	−0.133256	−	0.0519711i
$997$		−	1678.07i		−	1.68312i	−0.540166	−	0.841558i	$-0.681639\pi$
$997$		−	1678.07i		−	1.68312i	0.540166	−	0.841558i	$-0.318361\pi$
$998$	−350.322			−0.351024
$999$	671.875	−	328.875i	0.672548	−	0.329205i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1050.3.c.b.449.1		32
3.2	odd	2	inner	1050.3.c.b.449.31		32
5.2	odd	4		1050.3.e.b.701.4	✓	16
5.3	odd	4		1050.3.e.c.701.13	yes	16
5.4	even	2	inner	1050.3.c.b.449.32		32
15.2	even	4		1050.3.e.b.701.12	yes	16
15.8	even	4		1050.3.e.c.701.5	yes	16
15.14	odd	2	inner	1050.3.c.b.449.2		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1050.3.c.b.449.1		32	1.1	even	1	trivial
1050.3.c.b.449.2		32	15.14	odd	2	inner
1050.3.c.b.449.31		32	3.2	odd	2	inner
1050.3.c.b.449.32		32	5.4	even	2	inner
1050.3.e.b.701.4	✓	16	5.2	odd	4
1050.3.e.b.701.12	yes	16	15.2	even	4
1050.3.e.c.701.5	yes	16	15.8	even	4
1050.3.e.c.701.13	yes	16	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:	\( N \)	\(=\)	\( 1050 = 2 \cdot 3 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	1050.c (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q-1.41421 q^{2} +(-2.79495 - 1.09006i) q^{3} +2.00000 q^{4} +(3.95266 + 1.54158i) q^{6} +2.64575i q^{7} -2.82843 q^{8} +(6.62354 + 6.09333i) q^{9} +O(q^{10})\)	\(q-1.41421 q^{2} +(-2.79495 - 1.09006i) q^{3} +2.00000 q^{4} +(3.95266 + 1.54158i) q^{6} +2.64575i q^{7} -2.82843 q^{8} +(6.62354 + 6.09333i) q^{9} +3.30912i q^{11} +(-5.58991 - 2.18012i) q^{12} -13.2159i q^{13} -3.74166i q^{14} +4.00000 q^{16} -14.2264 q^{17} +(-9.36710 - 8.61727i) q^{18} -7.45106 q^{19} +(2.88403 - 7.39475i) q^{21} -4.67981i q^{22} -7.07387 q^{23} +(7.90533 + 3.08315i) q^{24} +18.6902i q^{26} +(-11.8704 - 24.2506i) q^{27} +5.29150i q^{28} +25.7409i q^{29} +41.5150 q^{31} -5.65685 q^{32} +(3.60714 - 9.24885i) q^{33} +20.1192 q^{34} +(13.2471 + 12.1867i) q^{36} +27.7055i q^{37} +10.5374 q^{38} +(-14.4062 + 36.9380i) q^{39} +1.25580i q^{41} +(-4.07863 + 10.4578i) q^{42} +2.12678i q^{43} +6.61825i q^{44} +10.0040 q^{46} +54.8353 q^{47} +(-11.1798 - 4.36024i) q^{48} -7.00000 q^{49} +(39.7623 + 15.5077i) q^{51} -26.4319i q^{52} -62.3147 q^{53} +(16.7873 + 34.2956i) q^{54} -7.48331i q^{56} +(20.8254 + 8.12210i) q^{57} -36.4032i q^{58} -21.7601i q^{59} +84.8047 q^{61} -58.7111 q^{62} +(-16.1214 + 17.5242i) q^{63} +8.00000 q^{64} +(-5.10127 + 13.0799i) q^{66} -54.7450i q^{67} -28.4529 q^{68} +(19.7711 + 7.71093i) q^{69} -100.282i q^{71} +(-18.7342 - 17.2345i) q^{72} +63.2034i q^{73} -39.1815i q^{74} -14.9021 q^{76} -8.75512 q^{77} +(20.3734 - 52.2382i) q^{78} -116.942 q^{79} +(6.74263 + 80.7189i) q^{81} -1.77596i q^{82} +23.7433 q^{83} +(5.76805 - 14.7895i) q^{84} -3.00772i q^{86} +(28.0592 - 71.9448i) q^{87} -9.35962i q^{88} -3.26308i q^{89} +34.9661 q^{91} -14.1477 q^{92} +(-116.033 - 45.2538i) q^{93} -77.5489 q^{94} +(15.8107 + 6.16631i) q^{96} -55.5754i q^{97} +9.89949 q^{98} +(-20.1636 + 21.9181i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 64 q^{4} - 16 q^{6} - 16 q^{9}+O(q^{10}) \) 32 * q + 64 * q^4 - 16 * q^6 - 16 * q^9	\( 32 q + 64 q^{4} - 16 q^{6} - 16 q^{9} + 128 q^{16} + 48 q^{19} + 56 q^{21} - 32 q^{24} + 48 q^{31} + 256 q^{34} - 32 q^{36} + 192 q^{39} + 160 q^{46} - 224 q^{49} + 288 q^{51} - 80 q^{54} - 112 q^{61} + 256 q^{64} - 192 q^{66} + 344 q^{69} + 96 q^{76} - 256 q^{79} + 160 q^{81} + 112 q^{84} - 448 q^{91} + 416 q^{94} - 64 q^{96} - 304 q^{99}+O(q^{100}) \) 32 * q + 64 * q^4 - 16 * q^6 - 16 * q^9 + 128 * q^16 + 48 * q^19 + 56 * q^21 - 32 * q^24 + 48 * q^31 + 256 * q^34 - 32 * q^36 + 192 * q^39 + 160 * q^46 - 224 * q^49 + 288 * q^51 - 80 * q^54 - 112 * q^61 + 256 * q^64 - 192 * q^66 + 344 * q^69 + 96 * q^76 - 256 * q^79 + 160 * q^81 + 112 * q^84 - 448 * q^91 + 416 * q^94 - 64 * q^96 - 304 * q^99

Introduction

L-functions

Modular forms

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Database

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