LMFDB - Embedded newform 1050.3.e.c.701.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1050,3,Mod(701,1050)]

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, 0, 0]))

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

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

chi := DirichletCharacter("1050.701");

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.e (of order $2$, degree $1$, 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:	$16$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 4 x^{15} + 4 x^{14} - 4 x^{13} + 4 x^{12} - 364 x^{11} + 972 x^{10} + 1236 x^{9} + \cdots + 43046721 $ x^16 - 4x^15 + 4x^14 - 4x^13 + 4x^12 - 364x^11 + 972x^10 + 1236x^9 - 5274x^8 + 11124x^7 + 78732x^6 - 265356x^5 + 26244x^4 - 236196x^3 + 2125764x^2 - 19131876*x + 43046721
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{10}\cdot 3^{3} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			701.5
Root			$1.09006 - 2.79495i$ of defining polynomial
Character	$\chi$	$=$	1050.701
Dual form			1050.3.e.c.701.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.41421i q^{2} +(1.09006 + 2.79495i) q^{3} -2.00000 q^{4} +(3.95266 - 1.54158i) q^{6} +2.64575 q^{7} +2.82843i q^{8} +(-6.62354 + 6.09333i) q^{9} +O(q^{10})$	\(q-1.41421i q^{2} +(1.09006 + 2.79495i) q^{3} -2.00000 q^{4} +(3.95266 - 1.54158i) q^{6} +2.64575 q^{7} +2.82843i q^{8} +(-6.62354 + 6.09333i) q^{9} -3.30912i q^{11} +(-2.18012 - 5.58991i) q^{12} +13.2159 q^{13} -3.74166i q^{14} +4.00000 q^{16} -14.2264i q^{17} +(8.61727 + 9.36710i) q^{18} +7.45106 q^{19} +(2.88403 + 7.39475i) q^{21} -4.67981 q^{22} +7.07387i q^{23} +(-7.90533 + 3.08315i) q^{24} -18.6902i q^{26} +(-24.2506 - 11.8704i) q^{27} -5.29150 q^{28} +25.7409i q^{29} +41.5150 q^{31} -5.65685i q^{32} +(9.24885 - 3.60714i) q^{33} -20.1192 q^{34} +(13.2471 - 12.1867i) q^{36} +27.7055 q^{37} -10.5374i q^{38} +(14.4062 + 36.9380i) q^{39} -1.25580i q^{41} +(10.4578 - 4.07863i) q^{42} -2.12678 q^{43} +6.61825i q^{44} +10.0040 q^{46} +54.8353i q^{47} +(4.36024 + 11.1798i) q^{48} +7.00000 q^{49} +(39.7623 - 15.5077i) q^{51} -26.4319 q^{52} +62.3147i q^{53} +(-16.7873 + 34.2956i) q^{54} +7.48331i q^{56} +(8.12210 + 20.8254i) q^{57} +36.4032 q^{58} -21.7601i q^{59} +84.8047 q^{61} -58.7111i q^{62} +(-17.5242 + 16.1214i) q^{63} -8.00000 q^{64} +(-5.10127 - 13.0799i) q^{66} -54.7450 q^{67} +28.4529i q^{68} +(-19.7711 + 7.71093i) q^{69} +100.282i q^{71} +(-17.2345 - 18.7342i) q^{72} -63.2034 q^{73} -39.1815i q^{74} -14.9021 q^{76} -8.75512i q^{77} +(52.2382 - 20.3734i) q^{78} +116.942 q^{79} +(6.74263 - 80.7189i) q^{81} -1.77596 q^{82} -23.7433i q^{83} +(-5.76805 - 14.7895i) q^{84} +3.00772i q^{86} +(-71.9448 + 28.0592i) q^{87} +9.35962 q^{88} -3.26308i q^{89} +34.9661 q^{91} -14.1477i q^{92} +(45.2538 + 116.033i) q^{93} +77.5489 q^{94} +(15.8107 - 6.16631i) q^{96} -55.5754 q^{97} -9.89949i q^{98} +(20.1636 + 21.9181i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 4 q^{3} - 32 q^{4} - 8 q^{6} + 8 q^{9}+O(q^{10}) $ 16 * q + 4 * q^3 - 32 * q^4 - 8 * q^6 + 8 * q^9	$ 16 q + 4 q^{3} - 32 q^{4} - 8 q^{6} + 8 q^{9} - 8 q^{12} + 64 q^{16} + 16 q^{18} - 24 q^{19} + 28 q^{21} + 48 q^{22} + 16 q^{24} + 28 q^{27} + 24 q^{31} - 76 q^{33} - 128 q^{34} - 16 q^{36} + 80 q^{37} - 96 q^{39} - 192 q^{43} + 80 q^{46} + 16 q^{48} + 112 q^{49} + 144 q^{51} + 40 q^{54} + 72 q^{57} - 48 q^{58} - 56 q^{61} - 56 q^{63} - 128 q^{64} - 96 q^{66} - 240 q^{67} - 172 q^{69} - 32 q^{72} + 96 q^{73} + 48 q^{76} + 256 q^{78} + 128 q^{79} + 80 q^{81} + 64 q^{82} - 56 q^{84} - 180 q^{87} - 96 q^{88} - 224 q^{91} - 352 q^{93} - 208 q^{94} - 32 q^{96} - 264 q^{97} + 152 q^{99}+O(q^{100}) $ 16 * q + 4 * q^3 - 32 * q^4 - 8 * q^6 + 8 * q^9 - 8 * q^12 + 64 * q^16 + 16 * q^18 - 24 * q^19 + 28 * q^21 + 48 * q^22 + 16 * q^24 + 28 * q^27 + 24 * q^31 - 76 * q^33 - 128 * q^34 - 16 * q^36 + 80 * q^37 - 96 * q^39 - 192 * q^43 + 80 * q^46 + 16 * q^48 + 112 * q^49 + 144 * q^51 + 40 * q^54 + 72 * q^57 - 48 * q^58 - 56 * q^61 - 56 * q^63 - 128 * q^64 - 96 * q^66 - 240 * q^67 - 172 * q^69 - 32 * q^72 + 96 * q^73 + 48 * q^76 + 256 * q^78 + 128 * q^79 + 80 * q^81 + 64 * q^82 - 56 * q^84 - 180 * q^87 - 96 * q^88 - 224 * q^91 - 352 * q^93 - 208 * q^94 - 32 * q^96 - 264 * q^97 + 152 * 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 $

$2$		−	1.41421i		−	0.707107i
$2$		−	1.41421i		−	0.707107i
$3$	1.09006	+	2.79495i	0.363353	+	0.931652i
$3$	1.09006	+	2.79495i	0.363353	+	0.931652i
$4$	−2.00000			−0.500000
$5$		0			0
$5$		0			0
$6$	3.95266	−	1.54158i	0.658777	−	0.256929i
$7$	2.64575			0.377964
$7$	2.64575			0.377964
$8$			2.82843i			0.353553i
$9$	−6.62354	+	6.09333i	−0.735949	+	0.677037i
$10$		0			0
$11$		−	3.30912i		−	0.300830i	−0.988623	−	0.150415i	$-0.951939\pi$
$11$		−	3.30912i		−	0.300830i	0.988623	−	0.150415i	$-0.0480609\pi$
$12$	−2.18012	−	5.58991i	−0.181677	−	0.465826i
$13$	13.2159			1.01661			0.508306	−	0.861177i	$-0.330272\pi$
$13$	13.2159			1.01661			0.508306	+	0.861177i	$0.330272\pi$
$14$		−	3.74166i		−	0.267261i
$15$		0			0
$16$	4.00000			0.250000
$17$		−	14.2264i		−	0.836850i	−0.908251	−	0.418425i	$-0.862582\pi$
$17$		−	14.2264i		−	0.836850i	0.908251	−	0.418425i	$-0.137418\pi$
$18$	8.61727	+	9.36710i	0.478737	+	0.520395i
$19$	7.45106			0.392161			0.196081	−	0.980588i	$-0.437179\pi$
$19$	7.45106			0.392161			0.196081	+	0.980588i	$0.437179\pi$
$20$		0			0
$21$	2.88403	+	7.39475i	0.137335	+	0.352131i
$22$	−4.67981			−0.212719
$23$			7.07387i			0.307559i	0.988105	+	0.153780i	$0.0491446\pi$
$23$			7.07387i			0.307559i	−0.988105	+	0.153780i	$0.950855\pi$
$24$	−7.90533	+	3.08315i	−0.329389	+	0.128465i
$25$		0			0
$26$		−	18.6902i		−	0.718853i
$27$	−24.2506	−	11.8704i	−0.898172	−	0.439645i
$28$	−5.29150			−0.188982
$29$			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	$0.266467\pi$
$32$		−	5.65685i		−	0.176777i
$33$	9.24885	−	3.60714i	0.280268	−	0.109307i
$34$	−20.1192			−0.591742
$35$		0			0
$36$	13.2471	−	12.1867i	0.367975	−	0.338518i
$37$	27.7055			0.748797			0.374398	−	0.927268i	$-0.377849\pi$
$37$	27.7055			0.748797			0.374398	+	0.927268i	$0.377849\pi$
$38$		−	10.5374i		−	0.277300i
$39$	14.4062	+	36.9380i	0.369389	+	0.947127i
$40$		0			0
$41$		−	1.25580i		−	0.0306292i	−0.999883	−	0.0153146i	$-0.995125\pi$
$41$		−	1.25580i		−	0.0306292i	0.999883	−	0.0153146i	$-0.00487497\pi$
$42$	10.4578	−	4.07863i	0.248994	−	0.0971102i
$43$	−2.12678			−0.0494599			−0.0247300	−	0.999694i	$-0.507873\pi$
$43$	−2.12678			−0.0494599			−0.0247300	+	0.999694i	$0.507873\pi$
$44$			6.61825i			0.150415i
$45$		0			0
$46$	10.0040			0.217477
$47$			54.8353i			1.16671i	0.812218	+	0.583355i	$0.198260\pi$
$47$			54.8353i			1.16671i	−0.812218	+	0.583355i	$0.801740\pi$
$48$	4.36024	+	11.1798i	0.0908383	+	0.232913i
$49$	7.00000			0.142857
$50$		0			0
$51$	39.7623	−	15.5077i	0.779653	−	0.304072i
$52$	−26.4319			−0.508306
$53$			62.3147i			1.17575i	0.808952	+	0.587874i	$0.200035\pi$
$53$			62.3147i			1.17575i	−0.808952	+	0.587874i	$0.799965\pi$
$54$	−16.7873	+	34.2956i	−0.310876	+	0.635103i
$55$		0			0
$56$			7.48331i			0.133631i
$57$	8.12210	+	20.8254i	0.142493	+	0.365357i
$58$	36.4032			0.627641
$59$		−	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	$0.255351\pi$
$62$		−	58.7111i		−	0.946954i
$63$	−17.5242	+	16.1214i	−0.278163	+	0.255896i
$64$	−8.00000			−0.125000
$65$		0			0
$66$	−5.10127	−	13.0799i	−0.0772919	−	0.198180i
$67$	−54.7450			−0.817089			−0.408545	−	0.912738i	$-0.633964\pi$
$67$	−54.7450			−0.817089			−0.408545	+	0.912738i	$0.633964\pi$
$68$			28.4529i			0.418425i
$69$	−19.7711	+	7.71093i	−0.286538	+	0.111753i
$70$		0			0
$71$			100.282i			1.41243i	0.707999	+	0.706213i	$0.249598\pi$
$71$			100.282i			1.41243i	−0.707999	+	0.706213i	$0.750402\pi$
$72$	−17.2345	−	18.7342i	−0.239369	−	0.260197i
$73$	−63.2034			−0.865800			−0.432900	−	0.901442i	$-0.642510\pi$
$73$	−63.2034			−0.865800			−0.432900	+	0.901442i	$0.642510\pi$
$74$		−	39.1815i		−	0.529479i
$75$		0			0
$76$	−14.9021			−0.196081
$77$		−	8.75512i		−	0.113703i
$78$	52.2382	−	20.3734i	0.669720	−	0.261197i
$79$	116.942			1.48028			0.740138	−	0.672455i	$-0.234760\pi$
$79$	116.942			1.48028			0.740138	+	0.672455i	$0.234760\pi$
$80$		0			0
$81$	6.74263	−	80.7189i	0.0832423	−	0.996529i
$82$	−1.77596			−0.0216581
$83$		−	23.7433i		−	0.286064i	−0.989718	−	0.143032i	$-0.954315\pi$
$83$		−	23.7433i		−	0.286064i	0.989718	−	0.143032i	$-0.0456851\pi$
$84$	−5.76805	−	14.7895i	−0.0686673	−	0.176066i
$85$		0			0
$86$			3.00772i			0.0349734i
$87$	−71.9448	+	28.0592i	−0.826952	+	0.322519i
$88$	9.35962			0.106359
$89$		−	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
$92$		−	14.1477i		−	0.153780i
$93$	45.2538	+	116.033i	0.486600	+	1.24766i
$94$	77.5489			0.824988
$95$		0			0
$96$	15.8107	−	6.16631i	0.164694	−	0.0642323i
$97$	−55.5754			−0.572942			−0.286471	−	0.958089i	$-0.592482\pi$
$97$	−55.5754			−0.572942			−0.286471	+	0.958089i	$0.592482\pi$
$98$		−	9.89949i		−	0.101015i
$99$	20.1636	+	21.9181i	0.203673	+	0.221395i
$100$		0			0
$101$			124.810i			1.23574i	0.786280	+	0.617870i	$0.212004\pi$
$101$			124.810i			1.23574i	−0.786280	+	0.617870i	$0.787996\pi$
$102$	−21.9312	−	56.2324i	−0.215011	−	0.551298i
$103$	112.881			1.09593			0.547967	−	0.836500i	$-0.315402\pi$
$103$	112.881			1.09593			0.547967	+	0.836500i	$0.315402\pi$
$104$			37.3803i			0.359426i
$105$		0			0
$106$	88.1263			0.831380
$107$			84.6754i			0.791359i	0.918389	+	0.395680i	$0.129491\pi$
$107$			84.6754i			0.791359i	−0.918389	+	0.395680i	$0.870509\pi$
$108$	48.5013	+	23.7408i	0.449086	+	0.219822i
$109$	165.164			1.51527			0.757634	−	0.652680i	$-0.226355\pi$
$109$	165.164			1.51527			0.757634	+	0.652680i	$0.226355\pi$
$110$		0			0
$111$	30.2006	+	77.4356i	0.272078	+	0.697618i
$112$	10.5830			0.0944911
$113$		−	55.8626i		−	0.494359i	−0.968970	−	0.247179i	$-0.920496\pi$
$113$		−	55.8626i		−	0.494359i	0.968970	−	0.247179i	$-0.0795037\pi$
$114$	29.4515	−	11.4864i	0.258347	−	0.100758i
$115$		0			0
$116$		−	51.4819i		−	0.443809i
$117$	−87.5364	+	80.5291i	−0.748174	+	0.688283i
$118$	−30.7734			−0.260791
$119$		−	37.6396i		−	0.316300i
$120$		0			0
$121$	110.050			0.909502
$122$		−	119.932i		−	0.983049i
$123$	3.50989	−	1.36889i	0.0285357	−	0.0111292i
$124$	−83.0301			−0.669597
$125$		0			0
$126$	22.7992	+	24.7830i	0.180946	+	0.196691i
$127$	−166.400			−1.31023			−0.655117	−	0.755527i	$-0.727381\pi$
$127$	−166.400			−1.31023			−0.655117	+	0.755527i	$0.727381\pi$
$128$			11.3137i			0.0883883i
$129$	−2.31831	−	5.94424i	−0.0179714	−	0.0460794i
$130$		0			0
$131$			229.177i			1.74944i	0.484626	+	0.874721i	$0.338956\pi$
$131$			229.177i			1.74944i	−0.484626	+	0.874721i	$0.661044\pi$
$132$	−18.4977	+	7.21428i	−0.140134	+	0.0546537i
$133$	19.7137			0.148223
$134$			77.4211i			0.577769i
$135$		0			0
$136$	40.2385			0.295871
$137$			123.559i			0.901889i	0.892552	+	0.450945i	$0.148913\pi$
$137$			123.559i			0.901889i	−0.892552	+	0.450945i	$0.851087\pi$
$138$	10.9049	+	27.9606i	0.0790211	+	0.202613i
$139$	169.795			1.22155			0.610774	−	0.791805i	$-0.290859\pi$
$139$	169.795			1.22155			0.610774	+	0.791805i	$0.290859\pi$
$140$		0			0
$141$	−153.262	+	59.7738i	−1.08697	+	0.423927i
$142$	141.821			0.998736
$143$		−	43.7332i		−	0.305827i
$144$	−26.4942	+	24.3733i	−0.183987	+	0.169259i
$145$		0			0
$146$			89.3832i			0.612213i
$147$	7.63041	+	19.5647i	0.0519076	+	0.133093i
$148$	−55.4110			−0.374398
$149$		−	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	$0.373290\pi$
$152$			21.0748i			0.138650i
$153$	86.6865	+	94.2295i	0.566578	+	0.615879i
$154$	−12.3816			−0.0804001
$155$		0			0
$156$	−28.8123	−	73.8759i	−0.184694	−	0.473564i
$157$	−31.6151			−0.201370			−0.100685	−	0.994918i	$-0.532103\pi$
$157$	−31.6151			−0.201370			−0.100685	+	0.994918i	$0.532103\pi$
$158$		−	165.381i		−	1.04671i
$159$	−174.167	+	67.9267i	−1.09539	+	0.427212i
$160$		0			0
$161$			18.7157i			0.116247i
$162$	−114.154	−	9.53552i	−0.704653	−	0.0588612i
$163$	107.553			0.659833			0.329917	−	0.944010i	$-0.392979\pi$
$163$	107.553			0.659833			0.329917	+	0.944010i	$0.392979\pi$
$164$			2.51159i			0.0153146i
$165$		0			0
$166$	−33.5781			−0.202278
$167$		−	116.906i		−	0.700036i	−0.936743	−	0.350018i	$-0.886175\pi$
$167$		−	116.906i		−	0.700036i	0.936743	−	0.350018i	$-0.113825\pi$
$168$	−20.9155	+	8.15726i	−0.124497	+	0.0485551i
$169$	5.66117			0.0334980
$170$		0			0
$171$	−49.3524	+	45.4018i	−0.288611	+	0.265508i
$172$	4.25355			0.0247300
$173$		−	317.805i		−	1.83702i	−0.395392	−	0.918512i	$-0.629391\pi$
$173$		−	317.805i		−	1.83702i	0.395392	−	0.918512i	$-0.370609\pi$
$174$	39.6816	+	101.745i	0.228055	+	0.584743i
$175$		0			0
$176$		−	13.2365i		−	0.0752074i
$177$	60.8184	−	23.7198i	0.343607	−	0.134010i
$178$	−4.61469			−0.0259252
$179$		−	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	$0.530415\pi$
$182$		−	49.4495i		−	0.271701i
$183$	92.4421	+	237.025i	0.505148	+	1.29522i
$184$	−20.0079			−0.108739
$185$		0			0
$186$	164.095	−	63.9986i	0.882231	−	0.344079i
$187$	−47.0771			−0.251749
$188$		−	109.671i		−	0.583355i
$189$	−64.1612	−	31.4062i	−0.339477	−	0.166170i
$190$		0			0
$191$			80.5748i			0.421858i	0.977501	+	0.210929i	$0.0676489\pi$
$191$			80.5748i			0.421858i	−0.977501	+	0.210929i	$0.932351\pi$
$192$	−8.72047	−	22.3596i	−0.0454191	−	0.116456i
$193$	−102.042			−0.528717			−0.264359	−	0.964424i	$-0.585160\pi$
$193$	−102.042			−0.528717			−0.264359	+	0.964424i	$0.585160\pi$
$194$			78.5954i			0.405131i
$195$		0			0
$196$	−14.0000			−0.0714286
$197$		−	50.5512i		−	0.256605i	−0.991735	−	0.128303i	$-0.959047\pi$
$197$		−	50.5512i		−	0.256605i	0.991735	−	0.128303i	$-0.0409529\pi$
$198$	30.9969	−	28.5156i	0.156550	−	0.144018i
$199$	−10.1649			−0.0510800			−0.0255400	−	0.999674i	$-0.508131\pi$
$199$	−10.1649			−0.0510800			−0.0255400	+	0.999674i	$0.508131\pi$
$200$		0			0
$201$	−59.6752	−	153.010i	−0.296892	−	0.761242i
$202$	176.508			0.873801
$203$			68.1041i			0.335488i
$204$	−79.5246	+	31.0153i	−0.389826	+	0.152036i
$205$		0			0
$206$		−	159.638i		−	0.774943i
$207$	−43.1034	−	46.8541i	−0.208229	−	0.226348i
$208$	52.8638			0.254153
$209$		−	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	$0.757544\pi$
$212$		−	124.629i		−	0.587874i
$213$	−280.284	+	109.314i	−1.31589	+	0.513209i
$214$	119.749			0.559575
$215$		0			0
$216$	33.5746	−	68.5912i	0.155438	−	0.317552i
$217$	109.838			0.506168
$218$		−	233.577i		−	1.07146i
$219$	−68.8955	−	176.651i	−0.314591	−	0.806624i
$220$		0			0
$221$		−	188.016i		−	0.850751i
$222$	109.510	−	42.7101i	0.493290	−	0.192388i
$223$	103.856			0.465724			0.232862	−	0.972510i	$-0.425191\pi$
$223$	103.856			0.465724			0.232862	+	0.972510i	$0.425191\pi$
$224$		−	14.9666i		−	0.0668153i
$225$		0			0
$226$	−79.0016			−0.349565
$227$		−	392.738i		−	1.73012i	−0.501664	−	0.865062i	$-0.667279\pi$
$227$		−	392.738i		−	1.73012i	0.501664	−	0.865062i	$-0.332721\pi$
$228$	−16.2442	−	41.6508i	−0.0712465	−	0.182679i
$229$	−427.149			−1.86528			−0.932641	−	0.360806i	$-0.882502\pi$
$229$	−427.149			−1.86528			−0.932641	+	0.360806i	$0.882502\pi$
$230$		0			0
$231$	24.4702	−	9.54360i	0.105931	−	0.0413143i
$232$	−72.8064			−0.313821
$233$		−	57.7328i		−	0.247780i	−0.992296	−	0.123890i	$-0.960463\pi$
$233$		−	57.7328i		−	0.247780i	0.992296	−	0.123890i	$-0.0395370\pi$
$234$	113.885	+	123.795i	0.486690	+	0.529039i
$235$		0			0
$236$			43.5201i			0.184407i
$237$	127.473	+	326.847i	0.537863	+	1.37910i
$238$	−53.2305			−0.223658
$239$			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	$0.605785\pi$
$242$		−	155.634i		−	0.643115i
$243$	232.955	−	69.1430i	0.958664	−	0.284539i
$244$	−169.609			−0.695121
$245$		0			0
$246$	−1.93591	−	4.96374i	−0.00786953	−	0.0201778i
$247$	98.4728			0.398675
$248$			117.422i			0.473477i
$249$	66.3614	−	25.8816i	0.266512	−	0.103942i
$250$		0			0
$251$			150.522i			0.599688i	0.953988	+	0.299844i	$0.0969346\pi$
$251$			150.522i			0.599688i	−0.953988	+	0.299844i	$0.903065\pi$
$252$	35.0485	−	32.2429i	0.139081	−	0.127948i
$253$	23.4083			0.0925230
$254$			235.325i			0.926476i
$255$		0			0
$256$	16.0000			0.0625000
$257$			313.116i			1.21835i	0.793036	+	0.609175i	$0.208499\pi$
$257$			313.116i			1.21835i	−0.793036	+	0.609175i	$0.791501\pi$
$258$	−8.40643	+	3.27859i	−0.0325831	+	0.0127077i
$259$	73.3018			0.283019
$260$		0			0
$261$	−156.848	−	170.496i	−0.600951	−	0.653242i
$262$	324.105			1.23704
$263$		−	413.301i		−	1.57149i	−0.618552	−	0.785744i	$-0.712280\pi$
$263$		−	413.301i		−	1.57149i	0.618552	−	0.785744i	$-0.287720\pi$
$264$	10.2025	+	26.1597i	0.0386460	+	0.0990898i
$265$		0			0
$266$		−	27.8793i		−	0.104809i
$267$	9.12016	−	3.55695i	0.0341579	−	0.0133219i
$268$	109.490			0.408545
$269$		−	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	$0.328938\pi$
$272$		−	56.9058i		−	0.209212i
$273$	38.1151	+	97.7287i	0.139616	+	0.357980i
$274$	174.739			0.637732
$275$		0			0
$276$	39.5423	−	15.4219i	0.143269	−	0.0558763i
$277$	64.2751			0.232040			0.116020	−	0.993247i	$-0.462986\pi$
$277$	64.2751			0.232040			0.116020	+	0.993247i	$0.462986\pi$
$278$		−	240.127i		−	0.863764i
$279$	−274.977	+	252.965i	−0.985579	+	0.906684i
$280$		0			0
$281$		−	238.377i		−	0.848315i	−0.905588	−	0.424158i	$-0.860570\pi$
$281$		−	238.377i		−	0.848315i	0.905588	−	0.424158i	$-0.139430\pi$
$282$	84.5329	+	216.746i	0.299762	+	0.768601i
$283$	−295.213			−1.04315			−0.521577	−	0.853204i	$-0.674656\pi$
$283$	−295.213			−1.04315			−0.521577	+	0.853204i	$0.674656\pi$
$284$		−	200.564i		−	0.706213i
$285$		0			0
$286$	−61.8481			−0.216252
$287$		−	3.32252i		−	0.0115767i
$288$	34.4691	+	37.4684i	0.119684	+	0.130099i
$289$	86.6082			0.299682
$290$		0			0
$291$	−60.5804	−	155.331i	−0.208180	−	0.533782i
$292$	126.407			0.432900
$293$			358.351i			1.22304i	0.791228	+	0.611521i	$0.209442\pi$
$293$			358.351i			1.22304i	−0.791228	+	0.611521i	$0.790558\pi$
$294$	27.6686	−	10.7910i	0.0941110	−	0.0367042i
$295$		0			0
$296$			78.3629i			0.264740i
$297$	−39.2807	+	80.2484i	−0.132258	+	0.270197i
$298$	−336.288			−1.12848
$299$			93.4878i			0.312668i
$300$		0			0
$301$	−5.62692			−0.0186941
$302$		−	165.558i		−	0.548206i
$303$	−348.838	+	136.050i	−1.15128	+	0.449010i
$304$	29.8042			0.0980403
$305$		0			0
$306$	133.261	−	122.593i	0.435492	−	0.400631i
$307$	531.675			1.73184			0.865920	−	0.500182i	$-0.166733\pi$
$307$	531.675			1.73184			0.865920	+	0.500182i	$0.166733\pi$
$308$			17.5102i			0.0568514i
$309$	123.047	+	315.498i	0.398211	+	1.02103i
$310$		0			0
$311$			418.127i			1.34446i	0.740343	+	0.672229i	$0.234663\pi$
$311$			418.127i			1.34446i	−0.740343	+	0.672229i	$0.765337\pi$
$312$	−104.476	+	40.7468i	−0.334860	+	0.130599i
$313$	−306.865			−0.980399			−0.490199	−	0.871610i	$-0.663076\pi$
$313$	−306.865			−0.980399			−0.490199	+	0.871610i	$0.663076\pi$
$314$			44.7105i			0.142390i
$315$		0			0
$316$	−233.884			−0.740138
$317$		−	83.8149i		−	0.264400i	−0.991223	−	0.132200i	$-0.957796\pi$
$317$		−	83.8149i		−	0.264400i	0.991223	−	0.132200i	$-0.0422042\pi$
$318$	96.0628	+	246.309i	0.302084	+	0.774556i
$319$	85.1800			0.267022
$320$		0			0
$321$	−236.664	+	92.3012i	−0.737271	+	0.287543i
$322$	26.4680			0.0821987
$323$		−	106.002i		−	0.328180i
$324$	−13.4853	+	161.438i	−0.0416212	+	0.498265i
$325$		0			0
$326$		−	152.103i		−	0.466572i
$327$	180.039	+	461.626i	0.550577	+	1.41170i
$328$	3.55193			0.0108290
$329$			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	$0.429703\pi$
$332$			47.4866i			0.143032i
$333$	−183.508	+	168.819i	−0.551076	+	0.506963i
$334$	−165.330			−0.495000
$335$		0			0
$336$	11.5361	+	29.5790i	0.0343336	+	0.0880328i
$337$	−610.894			−1.81274			−0.906371	−	0.422483i	$-0.861159\pi$
$337$	−610.894			−1.81274			−0.906371	+	0.422483i	$0.861159\pi$
$338$		−	8.00610i		−	0.0236867i
$339$	156.133	−	60.8935i	0.460570	−	0.179627i
$340$		0			0
$341$		−	137.378i		−	0.402869i
$342$	64.2078	+	69.7949i	0.187742	+	0.204079i
$343$	18.5203			0.0539949
$344$		−	6.01543i		−	0.0174867i
$345$		0			0
$346$	−449.445			−1.29897
$347$			70.0988i			0.202014i	0.994886	+	0.101007i	$0.0322064\pi$
$347$			70.0988i			0.202014i	−0.994886	+	0.101007i	$0.967794\pi$
$348$	143.890	−	56.1183i	0.413476	−	0.161260i
$349$	−564.413			−1.61723			−0.808614	−	0.588340i	$-0.799782\pi$
$349$	−564.413			−1.61723			−0.808614	+	0.588340i	$0.799782\pi$
$350$		0			0
$351$	−320.495	−	156.879i	−0.913091	−	0.446948i
$352$	−18.7192			−0.0531796
$353$			1.65210i			0.00468018i	0.999997	+	0.00234009i	$0.000744874\pi$
$353$			1.65210i			0.00468018i	−0.999997	+	0.00234009i	$0.999255\pi$
$354$	−33.5448	−	86.0102i	−0.0947593	−	0.242967i
$355$		0			0
$356$			6.52616i			0.0183319i
$357$	105.201	−	41.0294i	0.294681	−	0.114928i
$358$	−459.964			−1.28482
$359$		−	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
$362$			48.8427i			0.134925i
$363$	119.961	+	307.584i	0.330470	+	0.847339i
$364$	−69.9322			−0.192121
$365$		0			0
$366$	335.204	−	130.733i	0.915859	−	0.357194i
$367$	−363.378			−0.990131			−0.495066	−	0.868856i	$-0.664856\pi$
$367$	−363.378			−0.990131			−0.495066	+	0.868856i	$0.664856\pi$
$368$			28.2955i			0.0768899i
$369$	7.65198	+	8.31782i	0.0207371	+	0.0225415i
$370$		0			0
$371$			164.869i			0.444391i
$372$	−90.5077	−	232.065i	−0.243300	−	0.623831i
$373$	−207.182			−0.555448			−0.277724	−	0.960661i	$-0.589580\pi$
$373$	−207.182			−0.555448			−0.277724	+	0.960661i	$0.589580\pi$
$374$			66.5771i			0.178014i
$375$		0			0
$376$	−155.098			−0.412494
$377$			340.191i			0.902363i
$378$	−44.4150	+	90.7376i	−0.117500	+	0.240046i
$379$	489.449			1.29142			0.645712	−	0.763581i	$-0.276561\pi$
$379$	489.449			1.29142			0.645712	+	0.763581i	$0.276561\pi$
$380$		0			0
$381$	−181.386	−	465.080i	−0.476078	−	1.22068i
$382$	113.950			0.298299
$383$		−	210.772i		−	0.550318i	−0.961399	−	0.275159i	$-0.911269\pi$
$383$		−	210.772i		−	0.550318i	0.961399	−	0.275159i	$-0.0887305\pi$
$384$	−31.6213	+	12.3326i	−0.0823471	+	0.0321162i
$385$		0			0
$386$			144.310i			0.373859i
$387$	14.0868	−	12.9592i	0.0364000	−	0.0334862i
$388$	111.151			0.286471
$389$		−	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
$392$			19.7990i			0.0505076i
$393$	−640.539	+	249.816i	−1.62987	+	0.635665i
$394$	−71.4902			−0.181447
$395$		0			0
$396$	−40.3272	−	43.8363i	−0.101836	−	0.110698i
$397$	−32.3623			−0.0815172			−0.0407586	−	0.999169i	$-0.512977\pi$
$397$	−32.3623			−0.0815172			−0.0407586	+	0.999169i	$0.512977\pi$
$398$			14.3754i			0.0361190i
$399$	21.4890	+	55.0988i	0.0538573	+	0.138092i
$400$		0			0
$401$		−	233.517i		−	0.582338i	−0.956672	−	0.291169i	$-0.905956\pi$
$401$		−	233.517i		−	0.582338i	0.956672	−	0.291169i	$-0.0940441\pi$
$402$	−216.388	+	84.3935i	−0.538280	+	0.209934i
$403$	548.660			1.36144
$404$		−	249.620i		−	0.617870i
$405$		0			0
$406$	96.3138			0.237226
$407$		−	91.6809i		−	0.225260i
$408$	43.8623	+	112.465i	0.107506	+	0.275649i
$409$	−30.2404			−0.0739375			−0.0369687	−	0.999316i	$-0.511770\pi$
$409$	−30.2404			−0.0739375			−0.0369687	+	0.999316i	$0.511770\pi$
$410$		0			0
$411$	−345.341	+	134.686i	−0.840246	+	0.327704i
$412$	−225.763			−0.547967
$413$		−	57.5717i		−	0.139399i
$414$	−66.2616	+	60.9574i	−0.160052	+	0.147240i
$415$		0			0
$416$		−	74.7607i		−	0.179713i
$417$	185.087	+	474.570i	0.443853	+	1.13806i
$418$	−34.8695			−0.0834200
$419$		−	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	$0.773425\pi$
$422$			431.882i			1.02342i
$423$	−334.130	−	363.204i	−0.789905	−	0.858639i
$424$	−176.253			−0.415690
$425$		0			0
$426$	154.593	+	396.382i	0.362894	+	0.930474i
$427$	224.372			0.525462
$428$		−	169.351i		−	0.395680i
$429$	122.232	−	47.6718i	0.284924	−	0.111123i
$430$		0			0
$431$		−	474.481i		−	1.10088i	−0.834874	−	0.550442i	$-0.814459\pi$
$431$		−	474.481i		−	1.10088i	0.834874	−	0.550442i	$-0.185541\pi$
$432$	−97.0025	−	47.4816i	−0.224543	−	0.109911i
$433$	−66.7488			−0.154154			−0.0770772	−	0.997025i	$-0.524559\pi$
$433$	−66.7488			−0.154154			−0.0770772	+	0.997025i	$0.524559\pi$
$434$		−	155.335i		−	0.357915i
$435$		0			0
$436$	−330.328			−0.757634
$437$			52.7078i			0.120613i
$438$	−249.822	+	97.4329i	−0.570370	+	0.222450i
$439$	−361.090			−0.822528			−0.411264	−	0.911516i	$-0.634913\pi$
$439$	−361.090			−0.822528			−0.411264	+	0.911516i	$0.634913\pi$
$440$		0			0
$441$	−46.3648	+	42.6533i	−0.105136	+	0.0967195i
$442$	−265.895			−0.601572
$443$		−	415.163i		−	0.937163i	−0.883420	−	0.468581i	$-0.844765\pi$
$443$		−	415.163i		−	0.937163i	0.883420	−	0.468581i	$-0.155235\pi$
$444$	−60.4012	−	154.871i	−0.136039	−	0.348809i
$445$		0			0
$446$		−	146.875i		−	0.329316i
$447$	664.616	−	259.207i	1.48684	−	0.579881i
$448$	−21.1660			−0.0472456
$449$			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
$452$			111.725i			0.247179i
$453$	127.610	+	327.198i	0.281701	+	0.722292i
$454$	−555.416			−1.22338
$455$		0			0
$456$	−58.9031	+	22.9728i	−0.129173	+	0.0503789i
$457$	666.562			1.45856			0.729280	−	0.684216i	$-0.239855\pi$
$457$	666.562			1.45856			0.729280	+	0.684216i	$0.239855\pi$
$458$			604.081i			1.31895i
$459$	−168.874	+	345.000i	−0.367917	+	0.751635i
$460$		0			0
$461$			246.725i			0.535196i	0.963531	+	0.267598i	$0.0862299\pi$
$461$			246.725i			0.535196i	−0.963531	+	0.267598i	$0.913770\pi$
$462$	−13.4967	−	34.6060i	−0.0292136	−	0.0749048i
$463$	−278.772			−0.602099			−0.301049	−	0.953609i	$-0.597337\pi$
$463$	−278.772			−0.602099			−0.301049	+	0.953609i	$0.597337\pi$
$464$			102.964i			0.221905i
$465$		0			0
$466$	−81.6465			−0.175207
$467$			263.485i			0.564208i	0.959384	+	0.282104i	$0.0910323\pi$
$467$			263.485i			0.564208i	−0.959384	+	0.282104i	$0.908968\pi$
$468$	175.073	−	161.058i	0.374087	−	0.344142i
$469$	−144.842			−0.308831
$470$		0			0
$471$	−34.4623	−	88.3628i	−0.0731685	−	0.187607i
$472$	61.5468			0.130396
$473$			7.03777i			0.0148790i
$474$	462.231	−	180.275i	0.975172	−	0.380326i
$475$		0			0
$476$			75.2793i			0.158150i
$477$	−379.704	−	412.744i	−0.796025	−	0.865291i
$478$	74.9123			0.156720
$479$			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
$482$			222.389i			0.461388i
$483$	−52.3095	+	20.4012i	−0.108301	+	0.0422385i
$484$	−220.099			−0.454751
$485$		0			0
$486$	−97.7830	−	329.449i	−0.201200	−	0.677878i
$487$	−752.251			−1.54466			−0.772332	−	0.635219i	$-0.780910\pi$
$487$	−752.251			−1.54466			−0.772332	+	0.635219i	$0.780910\pi$
$488$			239.864i			0.491524i
$489$	117.239	+	300.605i	0.239752	+	0.614735i
$490$		0			0
$491$		−	67.2107i		−	0.136885i	−0.997655	−	0.0684427i	$-0.978197\pi$
$491$		−	67.2107i		−	0.136885i	0.997655	−	0.0684427i	$-0.0218030\pi$
$492$	−7.01978	+	2.73778i	−0.0142679	+	0.00556460i
$493$	366.202			0.742804
$494$		−	139.262i		−	0.281906i
$495$		0			0
$496$	166.060			0.334799
$497$			265.322i			0.533847i
$498$	−36.6021	−	93.8492i	−0.0734982	−	0.188452i
$499$	−247.715			−0.496423			−0.248212	−	0.968706i	$-0.579843\pi$
$499$	−247.715			−0.496423			−0.248212	+	0.968706i	$0.579843\pi$
$500$		0			0
$501$	326.747	−	127.435i	0.652190	−	0.254360i
$502$	212.870			0.424043
$503$		−	142.465i		−	0.283231i	−0.989922	−	0.141616i	$-0.954770\pi$
$503$		−	142.465i		−	0.283231i	0.989922	−	0.141616i	$-0.0452297\pi$
$504$	−45.5983	−	49.5661i	−0.0904728	−	0.0983453i
$505$		0			0
$506$		−	33.1043i		−	0.0654236i
$507$	6.17101	+	15.8227i	0.0121716	+	0.0312085i
$508$	332.800			0.655117
$509$			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
$512$		−	22.6274i		−	0.0441942i
$513$	−180.693	−	88.4471i	−0.352228	−	0.172412i
$514$	442.813			0.861504
$515$		0			0
$516$	4.63662	+	11.8885i	0.00898571	+	0.0230397i
$517$	181.457			0.350981
$518$		−	103.664i		−	0.200124i
$519$	888.251	−	346.427i	1.71147	−	0.667489i
$520$		0			0
$521$			796.131i			1.52808i	0.645168	+	0.764041i	$0.276787\pi$
$521$			796.131i			1.52808i	−0.645168	+	0.764041i	$0.723213\pi$
$522$	−241.118	+	221.817i	−0.461912	+	0.424936i
$523$	382.162			0.730711			0.365355	−	0.930868i	$-0.380947\pi$
$523$	382.162			0.730711			0.365355	+	0.930868i	$0.380947\pi$
$524$		−	458.354i		−	0.874721i
$525$		0			0
$526$	−584.496			−1.11121
$527$		−	590.612i		−	1.12071i
$528$	36.9954	−	14.4286i	0.0700671	−	0.0273268i
$529$	478.960			0.905407
$530$		0			0
$531$	132.591	+	144.129i	0.249701	+	0.271429i
$532$	−39.4273			−0.0741115
$533$		−	16.5965i		−	0.0311380i
$534$	−5.03029	−	12.8979i	−0.00942001	−	0.0241533i
$535$		0			0
$536$		−	154.842i		−	0.288885i
$537$	909.042	−	354.535i	1.69282	−	0.660214i
$538$	−109.618			−0.203750
$539$		−	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	$0.242925\pi$
$542$		−	392.382i		−	0.723952i
$543$	−37.6474	−	96.5293i	−0.0693321	−	0.177770i
$544$	−80.4769			−0.147936
$545$		0			0
$546$	138.209	−	53.9029i	0.253130	−	0.0987233i
$547$	−836.992			−1.53015			−0.765075	−	0.643942i	$-0.777298\pi$
$547$	−836.992			−1.53015			−0.765075	+	0.643942i	$0.777298\pi$
$548$		−	247.118i		−	0.450945i
$549$	−561.708	+	516.743i	−1.02315	+	0.941244i
$550$		0			0
$551$			191.797i			0.348090i
$552$	−21.8098	−	55.9212i	−0.0395105	−	0.101307i
$553$	309.399			0.559492
$554$		−	90.8988i		−	0.164077i
$555$		0			0
$556$	−339.590			−0.610774
$557$			151.652i			0.272267i	0.990691	+	0.136133i	$0.0434675\pi$
$557$			151.652i			0.272267i	−0.990691	+	0.136133i	$0.956532\pi$
$558$	357.746	+	388.876i	0.641123	+	0.696910i
$559$	−28.1074			−0.0502815
$560$		0			0
$561$	−51.3168	−	131.578i	−0.0914738	−	0.234542i
$562$	−337.115			−0.599850
$563$		−	830.912i		−	1.47586i	−0.674875	−	0.737932i	$-0.735802\pi$
$563$		−	830.912i		−	1.47586i	0.674875	−	0.737932i	$-0.264198\pi$
$564$	306.525	−	119.548i	0.543483	−	0.211964i
$565$		0			0
$566$			417.494i			0.737621i
$567$	17.8393	−	213.562i	0.0314626	−	0.376653i
$568$	−283.641			−0.499368
$569$			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	$0.576973\pi$
$572$			87.4664i			0.152913i
$573$	−225.203	+	87.8313i	−0.393025	+	0.153283i
$574$	−4.69876			−0.00818599
$575$		0			0
$576$	52.9883	−	48.7466i	0.0919936	−	0.0846296i
$577$	−783.907			−1.35859			−0.679295	−	0.733865i	$-0.737714\pi$
$577$	−783.907			−1.35859			−0.679295	+	0.733865i	$0.737714\pi$
$578$		−	122.482i		−	0.211907i
$579$	−111.232	−	285.204i	−0.192111	−	0.492580i
$580$		0			0
$581$		−	62.8189i		−	0.108122i
$582$	−219.671	+	85.6736i	−0.377441	+	0.147206i
$583$	206.207			0.353700
$584$		−	178.766i		−	0.306107i
$585$		0			0
$586$	506.786			0.864822
$587$		−	552.525i		−	0.941269i	−0.882328	−	0.470634i	$-0.844025\pi$
$587$		−	552.525i		−	0.941269i	0.882328	−	0.470634i	$-0.155975\pi$
$588$	−15.2608	−	39.1294i	−0.0259538	−	0.0665465i
$589$	309.331			0.525180
$590$		0			0
$591$	141.288	−	55.1038i	0.239067	−	0.0932382i
$592$	110.822			0.187199
$593$			236.428i			0.398699i	0.979928	+	0.199349i	$0.0638829\pi$
$593$			236.428i			0.398699i	−0.979928	+	0.199349i	$0.936117\pi$
$594$	113.488	+	55.5512i	0.191058	+	0.0935206i
$595$		0			0
$596$			475.583i			0.797958i
$597$	−11.0804	−	28.4105i	−0.0185601	−	0.0475888i
$598$	132.212			0.221090
$599$			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	$0.138479\pi$
$602$			7.95767i			0.0132187i
$603$	362.606	−	333.579i	0.601336	−	0.553199i
$604$	−234.135			−0.387640
$605$		0			0
$606$	192.404	+	493.331i	0.317498	+	0.814078i
$607$	1077.37			1.77491			0.887456	−	0.460892i	$-0.152470\pi$
$607$	1077.37			1.77491			0.887456	+	0.460892i	$0.152470\pi$
$608$		−	42.1496i		−	0.0693249i
$609$	−190.348	+	74.2375i	−0.312558	+	0.121901i
$610$		0			0
$611$			724.701i			1.18609i
$612$	−173.373	−	188.459i	−0.283289	−	0.307939i
$613$	942.291			1.53718			0.768590	−	0.639742i	$-0.220959\pi$
$613$	942.291			1.53718			0.768590	+	0.639742i	$0.220959\pi$
$614$		−	751.902i		−	1.22460i
$615$		0			0
$616$	24.7632			0.0402000
$617$		−	863.672i		−	1.39979i	−0.714245	−	0.699896i	$-0.753230\pi$
$617$		−	863.672i		−	1.39979i	0.714245	−	0.699896i	$-0.246770\pi$
$618$	446.182	−	174.015i	0.721977	−	0.281578i
$619$	626.507			1.01213			0.506064	−	0.862496i	$-0.331100\pi$
$619$	626.507			1.01213			0.506064	+	0.862496i	$0.331100\pi$
$620$		0			0
$621$	83.9697	−	171.546i	0.135217	−	0.276241i
$622$	591.320			0.950676
$623$		−	8.63330i		−	0.0138576i
$624$	57.6246	+	147.752i	0.0923472	+	0.236782i
$625$		0			0
$626$			433.972i			0.693247i
$627$	68.9138	−	26.8770i	0.109910	−	0.0428661i
$628$	63.2302			0.100685
$629$		−	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	$0.338778\pi$
$632$			330.761i			0.523356i
$633$	−332.889	−	853.541i	−0.525891	−	1.34841i
$634$	−118.532			−0.186959
$635$		0			0
$636$	348.333	−	135.853i	0.547694	−	0.213606i
$637$	92.5116			0.145230
$638$		−	120.463i		−	0.188813i
$639$	−611.053	−	664.224i	−0.956264	−	1.03947i
$640$		0			0
$641$		−	804.983i		−	1.25582i	−0.778284	−	0.627912i	$-0.783910\pi$
$641$		−	804.983i		−	1.25582i	0.778284	−	0.627912i	$-0.216090\pi$
$642$	130.534	+	334.693i	0.203323	+	0.521329i
$643$	−71.5877			−0.111334			−0.0556670	−	0.998449i	$-0.517729\pi$
$643$	−71.5877			−0.111334			−0.0556670	+	0.998449i	$0.517729\pi$
$644$		−	37.4314i		−	0.0581233i
$645$		0			0
$646$	−149.910			−0.232058
$647$		−	579.969i		−	0.896397i	−0.893934	−	0.448199i	$-0.852066\pi$
$647$		−	579.969i		−	0.896397i	0.893934	−	0.448199i	$-0.147934\pi$
$648$	228.307	+	19.0710i	0.352326	+	0.0294306i
$649$	−72.0068			−0.110950
$650$		0			0
$651$	119.730	+	306.994i	0.183918	+	0.471572i
$652$	−215.106			−0.329917
$653$			1063.75i			1.62902i	0.580148	+	0.814511i	$0.302995\pi$
$653$			1063.75i			1.62902i	−0.580148	+	0.814511i	$0.697005\pi$
$654$	652.838	−	254.613i	0.998223	−	0.389317i
$655$		0			0
$656$		−	5.02318i		−	0.00765729i
$657$	418.631	−	385.119i	0.637185	−	0.586179i
$658$	205.175			0.311816
$659$		−	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	$0.478852\pi$
$662$		−	205.079i		−	0.309787i
$663$	525.496	−	204.948i	0.792603	−	0.309123i
$664$	67.1562			0.101139
$665$		0			0
$666$	238.746	+	259.520i	0.358477	+	0.389670i
$667$	−182.088			−0.272996
$668$			233.812i			0.350018i
$669$	113.210	+	290.274i	0.169222	+	0.433892i
$670$		0			0
$671$		−	280.629i		−	0.418226i
$672$	41.8311	−	16.3145i	0.0622486	−	0.0242775i
$673$	286.806			0.426160			0.213080	−	0.977035i	$-0.431650\pi$
$673$	286.806			0.426160			0.213080	+	0.977035i	$0.431650\pi$
$674$			863.935i			1.28180i
$675$		0			0
$676$	−11.3223			−0.0167490
$677$		−	739.076i		−	1.09169i	−0.837885	−	0.545847i	$-0.816208\pi$
$677$		−	739.076i		−	1.09169i	0.837885	−	0.545847i	$-0.183792\pi$
$678$	−86.1164	−	220.806i	−0.127015	−	0.325672i
$679$	−147.039			−0.216552
$680$		0			0
$681$	1097.69	−	428.108i	1.61187	−	0.628646i
$682$	−194.282			−0.284872
$683$		−	384.541i		−	0.563017i	−0.959559	−	0.281509i	$-0.909165\pi$
$683$		−	384.541i		−	0.563017i	0.959559	−	0.281509i	$-0.0908348\pi$
$684$	98.7048	−	90.8036i	0.144305	−	0.132754i
$685$		0			0
$686$		−	26.1916i		−	0.0381802i
$687$	−465.618	−	1193.86i	−0.677756	−	1.73779i
$688$	−8.50711			−0.0123650
$689$			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	$0.183729\pi$
$692$			635.611i			0.918512i
$693$	53.3479	+	57.9899i	0.0769810	+	0.0836795i
$694$	99.1347			0.142845
$695$		0			0
$696$	−79.3633	−	203.491i	−0.114028	−	0.292372i
$697$	−17.8655			−0.0256320
$698$			798.200i			1.14355i
$699$	161.360	−	62.9321i	0.230845	−	0.0900317i
$700$		0			0
$701$		−	1033.07i		−	1.47371i	−0.676049	−	0.736856i	$-0.736309\pi$
$701$		−	1033.07i		−	1.47371i	0.676049	−	0.736856i	$-0.263691\pi$
$702$	−221.860	+	453.248i	−0.316040	+	0.645653i
$703$	206.435			0.293649
$704$			26.4730i			0.0376037i
$705$		0			0
$706$	2.33643			0.00330939
$707$			330.216i			0.467066i
$708$	−121.637	+	47.4395i	−0.171803	+	0.0670050i
$709$	−978.655			−1.38033			−0.690166	−	0.723651i	$-0.742462\pi$
$709$	−978.655			−1.38033			−0.690166	+	0.723651i	$0.742462\pi$
$710$		0			0
$711$	−774.569	+	712.565i	−1.08941	+	1.00220i
$712$	9.22938			0.0129626
$713$			293.672i			0.411882i
$714$	−58.0244	−	148.777i	−0.0812666	−	0.208371i
$715$		0			0
$716$			650.488i			0.908502i
$717$	−148.052	+	57.7415i	−0.206488	+	0.0805321i
$718$	−560.235			−0.780271
$719$		−	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
$722$			432.016i			0.598361i
$723$	−171.415	−	439.515i	−0.237088	−	0.607904i
$724$	69.0740			0.0954060
$725$		0			0
$726$	434.989	−	169.650i	0.599159	−	0.233678i
$727$	416.273			0.572589			0.286295	−	0.958142i	$-0.407576\pi$
$727$	416.273			0.572589			0.286295	+	0.958142i	$0.407576\pi$
$728$			98.8991i			0.135850i
$729$	447.187	+	575.730i	0.613425	+	0.789753i
$730$		0			0
$731$			30.2565i			0.0413905i
$732$	−184.884	−	474.051i	−0.252574	−	0.647610i
$733$	−338.733			−0.462118			−0.231059	−	0.972940i	$-0.574219\pi$
$733$	−338.733			−0.462118			−0.231059	+	0.972940i	$0.574219\pi$
$734$			513.894i			0.700128i
$735$		0			0
$736$	40.0158			0.0543693
$737$			181.158i			0.245805i
$738$	11.7632	−	10.8215i	0.0159393	−	0.0146633i
$739$	324.854			0.439586			0.219793	−	0.975547i	$-0.429462\pi$
$739$	324.854			0.439586			0.219793	+	0.975547i	$0.429462\pi$
$740$		0			0
$741$	107.341	+	275.227i	0.144860	+	0.371426i
$742$	233.160			0.314232
$743$		−	857.635i		−	1.15429i	−0.816643	−	0.577143i	$-0.804167\pi$
$743$		−	857.635i		−	1.15429i	0.816643	−	0.577143i	$-0.195833\pi$
$744$	−328.190	+	127.997i	−0.441115	+	0.172039i
$745$		0			0
$746$			293.000i			0.392761i
$747$	144.676	+	157.265i	0.193676	+	0.210528i
$748$	94.1542			0.125875
$749$			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	$0.576305\pi$
$752$			219.341i			0.291677i
$753$	−420.701	+	164.077i	−0.558700	+	0.217898i
$754$	481.103			0.638067
$755$		0			0
$756$	128.322	+	62.8123i	0.169739	+	0.0830851i
$757$	−1356.47			−1.79191			−0.895954	−	0.444147i	$-0.853507\pi$
$757$	−1356.47			−1.79191			−0.895954	+	0.444147i	$0.853507\pi$
$758$		−	692.186i		−	0.913174i
$759$	25.5164	+	65.4252i	0.0336185	+	0.0861992i
$760$		0			0
$761$		−	106.889i		−	0.140459i	−0.997531	−	0.0702294i	$-0.977627\pi$
$761$		−	106.889i		−	0.140459i	0.997531	−	0.0702294i	$-0.0223731\pi$
$762$	−657.722	+	256.518i	−0.863153	+	0.336638i
$763$	436.983			0.572717
$764$		−	161.150i		−	0.210929i
$765$		0			0
$766$	−298.076			−0.389134
$767$		−	287.580i		−	0.374941i
$768$	17.4409	+	44.7193i	0.0227096	+	0.0582282i
$769$	500.283			0.650563			0.325282	−	0.945617i	$-0.394541\pi$
$769$	500.283			0.650563			0.325282	+	0.945617i	$0.394541\pi$
$770$		0			0
$771$	−875.145	+	341.315i	−1.13508	+	0.442691i
$772$	204.085			0.264359
$773$			1146.06i			1.48262i	0.671164	+	0.741309i	$0.265794\pi$
$773$			1146.06i			1.48262i	−0.671164	+	0.741309i	$0.734206\pi$
$774$	−18.3270	−	19.9217i	−0.0236783	−	0.0257387i
$775$		0			0
$776$		−	157.191i		−	0.202566i
$777$	79.9033	+	204.875i	0.102836	+	0.263675i
$778$	−465.246			−0.598003
$779$		−	9.35701i		−	0.0120116i
$780$		0			0
$781$	331.846			0.424899
$782$		−	142.321i		−	0.181996i
$783$	305.556	−	624.234i	0.390237	−	0.797234i
$784$	28.0000			0.0357143
$785$		0			0
$786$	353.294	+	905.859i	0.449483	+	1.15249i
$787$	−488.016			−0.620097			−0.310048	−	0.950721i	$-0.600345\pi$
$787$	−488.016			−0.620097			−0.310048	+	0.950721i	$0.600345\pi$
$788$			101.102i			0.128303i
$789$	1155.16	−	450.523i	1.46408	−	0.571005i
$790$		0			0
$791$		−	147.798i		−	0.186850i
$792$	−61.9938	+	57.0313i	−0.0782750	+	0.0720092i
$793$	1120.77			1.41333
$794$			45.7672i			0.0576413i
$795$		0			0
$796$	20.3299			0.0255400
$797$		−	197.490i		−	0.247792i	−0.992295	−	0.123896i	$-0.960461\pi$
$797$		−	197.490i		−	0.247792i	0.992295	−	0.123896i	$-0.0395389\pi$
$798$	77.9214	−	30.3901i	0.0976459	−	0.0380828i
$799$	780.112			0.976361
$800$		0			0
$801$	19.8830	+	21.6131i	0.0248228	+	0.0269827i
$802$	−330.243			−0.411775
$803$			209.148i			0.260458i
$804$	119.350	+	306.019i	0.148446	+	0.380621i
$805$		0			0
$806$		−	775.923i		−	0.962684i
$807$	216.641	−	84.4920i	0.268452	−	0.104699i
$808$	−353.015			−0.436900
$809$			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	$0.431905\pi$
$812$		−	136.208i		−	0.167744i
$813$	302.444	+	775.477i	0.372009	+	0.953846i
$814$	−129.656			−0.159283
$815$		0			0
$816$	159.049	−	62.0307i	0.194913	−	0.0760180i
$817$	−15.8467			−0.0193963
$818$			42.7664i			0.0522817i
$819$	−231.599	+	213.060i	−0.282783	+	0.260147i
$820$		0			0
$821$			616.490i			0.750901i	0.926842	+	0.375451i	$0.122512\pi$
$821$			616.490i			0.750901i	−0.926842	+	0.375451i	$0.877488\pi$
$822$	190.475	+	488.386i	0.231722	+	0.594144i
$823$	638.840			0.776234			0.388117	−	0.921610i	$-0.373126\pi$
$823$	638.840			0.776234			0.388117	+	0.921610i	$0.373126\pi$
$824$			319.276i			0.387471i
$825$		0			0
$826$	−81.4187			−0.0985699
$827$			1066.42i			1.28951i	0.764391	+	0.644753i	$0.223040\pi$
$827$			1066.42i			1.28951i	−0.764391	+	0.644753i	$0.776960\pi$
$828$	86.2068	+	93.7081i	0.104115	+	0.113174i
$829$	−625.285			−0.754265			−0.377132	−	0.926159i	$-0.623090\pi$
$829$	−625.285			−0.754265			−0.377132	+	0.926159i	$0.623090\pi$
$830$		0			0
$831$	70.0637	+	179.646i	0.0843125	+	0.216181i
$832$	−105.728			−0.127076
$833$		−	99.5851i		−	0.119550i
$834$	671.143	−	261.752i	0.804727	−	0.313851i
$835$		0			0
$836$			49.3130i			0.0589868i
$837$	−1006.77	−	492.801i	−1.20283	−	0.588770i
$838$	−976.713			−1.16553
$839$		−	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
$842$			901.629i			1.07082i
$843$	666.252	−	259.845i	0.790334	−	0.308238i
$844$	610.773			0.723665
$845$		0			0
$846$	−513.648	+	472.531i	−0.607149	+	0.558547i
$847$	291.164			0.343759
$848$			249.259i			0.293937i
$849$	−321.799	−	825.106i	−0.379033	−	0.971856i
$850$		0			0
$851$			195.985i			0.230299i
$852$	560.569	−	218.627i	0.657944	−	0.256605i
$853$	830.771			0.973940			0.486970	−	0.873419i	$-0.338102\pi$
$853$	830.771			0.973940			0.486970	+	0.873419i	$0.338102\pi$
$854$		−	317.310i		−	0.371558i
$855$		0			0
$856$	−239.498			−0.279788
$857$		−	292.550i		−	0.341365i	−0.985326	−	0.170683i	$-0.945403\pi$
$857$		−	292.550i		−	0.341365i	0.985326	−	0.170683i	$-0.0545973\pi$
$858$	−67.4181	−	172.863i	−0.0785758	−	0.201472i
$859$	−672.801			−0.783237			−0.391619	−	0.920128i	$-0.628085\pi$
$859$	−672.801			−0.783237			−0.391619	+	0.920128i	$0.628085\pi$
$860$		0			0
$861$	9.28630	−	3.62175i	0.0107855	−	0.00420644i
$862$	−671.017			−0.778442
$863$			699.281i			0.810291i	0.914252	+	0.405145i	$0.132779\pi$
$863$			699.281i			0.810291i	−0.914252	+	0.405145i	$0.867221\pi$
$864$	−67.1492	+	137.182i	−0.0777190	+	0.158776i
$865$		0			0
$866$			94.3971i			0.109004i
$867$	94.4080	+	242.066i	0.108890	+	0.279199i
$868$	−219.677			−0.253084
$869$		−	386.975i		−	0.445311i
$870$		0			0
$871$	−723.506			−0.830662
$872$			467.155i			0.535728i
$873$	368.106	−	338.639i	0.421656	−	0.387903i
$874$	74.5401			0.0852862
$875$		0			0
$876$	137.791	+	353.301i	0.157296	+	0.403312i
$877$	358.626			0.408924			0.204462	−	0.978874i	$-0.434456\pi$
$877$	358.626			0.408924			0.204462	+	0.978874i	$0.434456\pi$
$878$			510.658i			0.581615i
$879$	−1001.58	+	390.624i	−1.13945	+	0.444396i
$880$		0			0
$881$		−	1550.04i		−	1.75941i	−0.475522	−	0.879704i	$-0.657741\pi$
$881$		−	1550.04i		−	1.75941i	0.475522	−	0.879704i	$-0.342259\pi$
$882$	60.3209	+	65.5697i	0.0683910	+	0.0743421i
$883$	−1595.94			−1.80741			−0.903706	−	0.428154i	$-0.859164\pi$
$883$	−1595.94			−1.80741			−0.903706	+	0.428154i	$0.859164\pi$
$884$			376.032i			0.425375i
$885$		0			0
$886$	−587.129			−0.662674
$887$		−	134.533i		−	0.151671i	−0.997120	−	0.0758357i	$-0.975838\pi$
$887$		−	134.533i		−	0.151671i	0.997120	−	0.0758357i	$-0.0241624\pi$
$888$	−219.021	+	85.4202i	−0.246645	+	0.0961939i
$889$	−440.253			−0.495222
$890$		0			0
$891$	−267.109	−	22.3122i	−0.299785	−	0.0250418i
$892$	−207.713			−0.232862
$893$			408.581i			0.457538i
$894$	−366.574	−	939.909i	−0.410038	−	1.05135i
$895$		0			0
$896$			29.9333i			0.0334077i
$897$	−261.294	+	101.907i	−0.291298	+	0.113609i
$898$	761.841			0.848375
$899$			1068.64i			1.18869i
$900$		0			0
$901$	886.517			0.983925
$902$			5.87688i			0.00651539i
$903$	−6.13368	−	15.7270i	−0.00679256	−	0.0174164i
$904$	158.003			0.174782
$905$		0			0
$906$	462.728	−	180.468i	0.510737	−	0.199192i
$907$	−879.668			−0.969865			−0.484933	−	0.874551i	$-0.661156\pi$
$907$	−879.668			−0.969865			−0.484933	+	0.874551i	$0.661156\pi$
$908$			785.477i			0.865062i
$909$	−760.507	−	826.683i	−0.836642	−	0.909442i
$910$		0			0
$911$		−	1522.40i		−	1.67113i	−0.549391	−	0.835565i	$-0.685140\pi$
$911$		−	1522.40i		−	1.67113i	0.549391	−	0.835565i	$-0.314860\pi$
$912$	32.4884	+	83.3015i	0.0356232	+	0.0913394i
$913$	−78.5695			−0.0860564
$914$		−	942.661i		−	1.03136i
$915$		0			0
$916$	854.299			0.932641
$917$			606.345i			0.661227i
$918$	487.904	+	238.824i	0.531486	+	0.260156i
$919$	1178.73			1.28262			0.641309	−	0.767282i	$-0.278392\pi$
$919$	1178.73			1.28262			0.641309	+	0.767282i	$0.278392\pi$
$920$		0			0
$921$	579.557	+	1486.01i	0.629270	+	1.61347i
$922$	348.922			0.378441
$923$			1325.32i			1.43589i
$924$	−48.9403	+	19.0872i	−0.0529657	+	0.0206571i
$925$		0			0
$926$			394.243i			0.425748i
$927$	−747.674	+	687.823i	−0.806552	+	0.741988i
$928$	145.613			0.156910
$929$			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
$932$			115.466i			0.123890i
$933$	−1168.65	+	455.783i	−1.25257	+	0.488513i
$934$	372.624			0.398955
$935$		0			0
$936$	−227.771	−	247.590i	−0.243345	−	0.264519i
$937$	−1383.17			−1.47616			−0.738082	−	0.674711i	$-0.764268\pi$
$937$	−1383.17			−1.47616			−0.738082	+	0.674711i	$0.764268\pi$
$938$			204.837i			0.218376i
$939$	−334.501	−	857.673i	−0.356231	−	0.913390i
$940$		0			0
$941$		−	562.997i		−	0.598296i	−0.954207	−	0.299148i	$-0.903298\pi$
$941$		−	562.997i		−	0.598296i	0.954207	−	0.299148i	$-0.0967024\pi$
$942$	−124.964	+	48.7371i	−0.132658	+	0.0517379i
$943$	8.88333			0.00942029
$944$		−	87.0403i		−	0.0922037i
$945$		0			0
$946$	9.95291			0.0105210
$947$		−	722.442i		−	0.762874i	−0.924395	−	0.381437i	$-0.875429\pi$
$947$		−	722.442i		−	0.762874i	0.924395	−	0.381437i	$-0.124571\pi$
$948$	−254.947	−	653.694i	−0.268931	−	0.689551i
$949$	−835.293			−0.880182
$950$		0			0
$951$	234.259	−	91.3632i	0.246329	−	0.0960707i
$952$	106.461			0.111829
$953$			1567.96i			1.64529i	0.568557	+	0.822644i	$0.307502\pi$
$953$			1567.96i			1.64529i	−0.568557	+	0.822644i	$0.692498\pi$
$954$	−583.708	+	536.983i	−0.611853	+	0.562875i
$955$		0			0
$956$		−	105.942i		−	0.110818i
$957$	92.8512	+	238.074i	0.0970232	+	0.248771i
$958$	230.782			0.240899
$959$			326.906i			0.340882i
$960$		0			0
$961$	762.498			0.793443
$962$		−	517.820i		−	0.538274i
$963$	−515.955	−	560.851i	−0.535779	−	0.582400i
$964$	314.506			0.326251
$965$		0			0
$966$	28.8517	+	73.9768i	0.0298672	+	0.0765806i
$967$	1182.12			1.22246			0.611230	−	0.791453i	$-0.290675\pi$
$967$	1182.12			1.22246			0.611230	+	0.791453i	$0.290675\pi$
$968$			311.268i			0.321557i
$969$	296.271	−	115.549i	0.305749	−	0.119245i
$970$		0			0
$971$			1672.57i			1.72252i	0.508165	+	0.861260i	$0.330324\pi$
$971$			1672.57i			1.72252i	−0.508165	+	0.861260i	$0.669676\pi$
$972$	−465.911	+	138.286i	−0.479332	+	0.142270i
$973$	449.236			0.461702
$974$			1063.84i			1.09224i
$975$		0			0
$976$	339.219			0.347560
$977$			383.549i			0.392578i	0.980546	+	0.196289i	$0.0628891\pi$
$977$			383.549i			0.392578i	−0.980546	+	0.196289i	$0.937111\pi$
$978$	425.120	−	165.801i	0.434683	−	0.169531i
$979$	−10.7979			−0.0110296
$980$		0			0
$981$	−1093.97	+	1006.40i	−1.11516	+	1.02589i
$982$	−95.0503			−0.0967925
$983$		−	68.4583i		−	0.0696422i	−0.999394	−	0.0348211i	$-0.988914\pi$
$983$		−	68.4583i		−	0.0696422i	0.999394	−	0.0348211i	$-0.0110861\pi$
$984$	3.87181	+	9.92748i	0.00393477	+	0.0100889i
$985$		0			0
$986$		−	517.888i		−	0.525242i
$987$	−405.494	+	158.147i	−0.410835	+	0.160229i
$988$	−196.946			−0.199338
$989$		−	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	$0.614936\pi$
$992$		−	234.845i		−	0.236738i
$993$	158.072	+	405.304i	0.159187	+	0.408161i
$994$	375.222			0.377487
$995$		0			0
$996$	−132.723	+	51.7632i	−0.133256	+	0.0519711i
$997$	−1678.07			−1.68312			−0.841558	−	0.540166i	$-0.818361\pi$
$997$	−1678.07			−1.68312			−0.841558	+	0.540166i	$0.818361\pi$
$998$			350.322i			0.351024i
$999$	−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.e.c.701.5	yes	16
3.2	odd	2	inner	1050.3.e.c.701.13	yes	16
5.2	odd	4		1050.3.c.b.449.31		32
5.3	odd	4		1050.3.c.b.449.2		32
5.4	even	2		1050.3.e.b.701.12	yes	16
15.2	even	4		1050.3.c.b.449.1		32
15.8	even	4		1050.3.c.b.449.32		32
15.14	odd	2		1050.3.e.b.701.4	✓	16

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

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1050 = 2 \cdot 3 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	1050.e (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-1.41421i q^{2} +(1.09006 + 2.79495i) q^{3} -2.00000 q^{4} +(3.95266 - 1.54158i) q^{6} +2.64575 q^{7} +2.82843i q^{8} +(-6.62354 + 6.09333i) q^{9} +O(q^{10})\)	\(q-1.41421i q^{2} +(1.09006 + 2.79495i) q^{3} -2.00000 q^{4} +(3.95266 - 1.54158i) q^{6} +2.64575 q^{7} +2.82843i q^{8} +(-6.62354 + 6.09333i) q^{9} -3.30912i q^{11} +(-2.18012 - 5.58991i) q^{12} +13.2159 q^{13} -3.74166i q^{14} +4.00000 q^{16} -14.2264i q^{17} +(8.61727 + 9.36710i) q^{18} +7.45106 q^{19} +(2.88403 + 7.39475i) q^{21} -4.67981 q^{22} +7.07387i q^{23} +(-7.90533 + 3.08315i) q^{24} -18.6902i q^{26} +(-24.2506 - 11.8704i) q^{27} -5.29150 q^{28} +25.7409i q^{29} +41.5150 q^{31} -5.65685i q^{32} +(9.24885 - 3.60714i) q^{33} -20.1192 q^{34} +(13.2471 - 12.1867i) q^{36} +27.7055 q^{37} -10.5374i q^{38} +(14.4062 + 36.9380i) q^{39} -1.25580i q^{41} +(10.4578 - 4.07863i) q^{42} -2.12678 q^{43} +6.61825i q^{44} +10.0040 q^{46} +54.8353i q^{47} +(4.36024 + 11.1798i) q^{48} +7.00000 q^{49} +(39.7623 - 15.5077i) q^{51} -26.4319 q^{52} +62.3147i q^{53} +(-16.7873 + 34.2956i) q^{54} +7.48331i q^{56} +(8.12210 + 20.8254i) q^{57} +36.4032 q^{58} -21.7601i q^{59} +84.8047 q^{61} -58.7111i q^{62} +(-17.5242 + 16.1214i) q^{63} -8.00000 q^{64} +(-5.10127 - 13.0799i) q^{66} -54.7450 q^{67} +28.4529i q^{68} +(-19.7711 + 7.71093i) q^{69} +100.282i q^{71} +(-17.2345 - 18.7342i) q^{72} -63.2034 q^{73} -39.1815i q^{74} -14.9021 q^{76} -8.75512i q^{77} +(52.2382 - 20.3734i) q^{78} +116.942 q^{79} +(6.74263 - 80.7189i) q^{81} -1.77596 q^{82} -23.7433i q^{83} +(-5.76805 - 14.7895i) q^{84} +3.00772i q^{86} +(-71.9448 + 28.0592i) q^{87} +9.35962 q^{88} -3.26308i q^{89} +34.9661 q^{91} -14.1477i q^{92} +(45.2538 + 116.033i) q^{93} +77.5489 q^{94} +(15.8107 - 6.16631i) q^{96} -55.5754 q^{97} -9.89949i q^{98} +(20.1636 + 21.9181i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 4 q^{3} - 32 q^{4} - 8 q^{6} + 8 q^{9}+O(q^{10}) \) 16 * q + 4 * q^3 - 32 * q^4 - 8 * q^6 + 8 * q^9	\( 16 q + 4 q^{3} - 32 q^{4} - 8 q^{6} + 8 q^{9} - 8 q^{12} + 64 q^{16} + 16 q^{18} - 24 q^{19} + 28 q^{21} + 48 q^{22} + 16 q^{24} + 28 q^{27} + 24 q^{31} - 76 q^{33} - 128 q^{34} - 16 q^{36} + 80 q^{37} - 96 q^{39} - 192 q^{43} + 80 q^{46} + 16 q^{48} + 112 q^{49} + 144 q^{51} + 40 q^{54} + 72 q^{57} - 48 q^{58} - 56 q^{61} - 56 q^{63} - 128 q^{64} - 96 q^{66} - 240 q^{67} - 172 q^{69} - 32 q^{72} + 96 q^{73} + 48 q^{76} + 256 q^{78} + 128 q^{79} + 80 q^{81} + 64 q^{82} - 56 q^{84} - 180 q^{87} - 96 q^{88} - 224 q^{91} - 352 q^{93} - 208 q^{94} - 32 q^{96} - 264 q^{97} + 152 q^{99}+O(q^{100}) \) 16 * q + 4 * q^3 - 32 * q^4 - 8 * q^6 + 8 * q^9 - 8 * q^12 + 64 * q^16 + 16 * q^18 - 24 * q^19 + 28 * q^21 + 48 * q^22 + 16 * q^24 + 28 * q^27 + 24 * q^31 - 76 * q^33 - 128 * q^34 - 16 * q^36 + 80 * q^37 - 96 * q^39 - 192 * q^43 + 80 * q^46 + 16 * q^48 + 112 * q^49 + 144 * q^51 + 40 * q^54 + 72 * q^57 - 48 * q^58 - 56 * q^61 - 56 * q^63 - 128 * q^64 - 96 * q^66 - 240 * q^67 - 172 * q^69 - 32 * q^72 + 96 * q^73 + 48 * q^76 + 256 * q^78 + 128 * q^79 + 80 * q^81 + 64 * q^82 - 56 * q^84 - 180 * q^87 - 96 * q^88 - 224 * q^91 - 352 * q^93 - 208 * q^94 - 32 * q^96 - 264 * q^97 + 152 * q^99

Introduction

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