LMFDB - Embedded newform 483.3.b.a.323.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [483,3,Mod(323,483)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(483, 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("483.323");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 483 = 3 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	483.b (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:	$13.1607967686$
Analytic rank:	$0$
Dimension:	$88$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			323.2
Character	$\chi$	$=$	483.323
Dual form			483.3.b.a.323.87

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-3.81832i q^{2} +(-0.852935 - 2.87620i) q^{3} -10.5796 q^{4} -8.03455i q^{5} +(-10.9822 + 3.25678i) q^{6} +2.64575 q^{7} +25.1228i q^{8} +(-7.54500 + 4.90642i) q^{9} +O(q^{10})$	\(q-3.81832i q^{2} +(-0.852935 - 2.87620i) q^{3} -10.5796 q^{4} -8.03455i q^{5} +(-10.9822 + 3.25678i) q^{6} +2.64575 q^{7} +25.1228i q^{8} +(-7.54500 + 4.90642i) q^{9} -30.6785 q^{10} -10.7629i q^{11} +(9.02367 + 30.4289i) q^{12} -11.1345 q^{13} -10.1023i q^{14} +(-23.1089 + 6.85295i) q^{15} +53.6087 q^{16} -3.24515i q^{17} +(18.7343 + 28.8092i) q^{18} +29.6813 q^{19} +85.0019i q^{20} +(-2.25665 - 7.60970i) q^{21} -41.0963 q^{22} +4.79583i q^{23} +(72.2582 - 21.4281i) q^{24} -39.5539 q^{25} +42.5150i q^{26} +(20.5472 + 17.5161i) q^{27} -27.9909 q^{28} -19.2560i q^{29} +(26.1667 + 88.2372i) q^{30} -10.5205 q^{31} -104.204i q^{32} +(-30.9563 + 9.18009i) q^{33} -12.3910 q^{34} -21.2574i q^{35} +(79.8228 - 51.9077i) q^{36} -58.1187 q^{37} -113.333i q^{38} +(9.49698 + 32.0249i) q^{39} +201.850 q^{40} -31.5647i q^{41} +(-29.0562 + 8.61662i) q^{42} +64.5269 q^{43} +113.867i q^{44} +(39.4208 + 60.6207i) q^{45} +18.3120 q^{46} -81.0506i q^{47} +(-45.7247 - 154.189i) q^{48} +7.00000 q^{49} +151.030i q^{50} +(-9.33367 + 2.76790i) q^{51} +117.798 q^{52} +10.5227i q^{53} +(66.8819 - 78.4558i) q^{54} -86.4753 q^{55} +66.4687i q^{56} +(-25.3162 - 85.3693i) q^{57} -73.5257 q^{58} -38.6771i q^{59} +(244.482 - 72.5011i) q^{60} +68.4630 q^{61} +40.1705i q^{62} +(-19.9622 + 12.9812i) q^{63} -183.449 q^{64} +89.4604i q^{65} +(35.0525 + 118.201i) q^{66} +25.5535 q^{67} +34.3322i q^{68} +(13.7938 - 4.09053i) q^{69} -81.1676 q^{70} +0.0320263i q^{71} +(-123.263 - 189.552i) q^{72} -18.4715 q^{73} +221.916i q^{74} +(33.7369 + 113.765i) q^{75} -314.015 q^{76} -28.4761i q^{77} +(122.281 - 36.2625i) q^{78} -144.679 q^{79} -430.722i q^{80} +(32.8542 - 74.0378i) q^{81} -120.524 q^{82} +118.138i q^{83} +(23.8744 + 80.5072i) q^{84} -26.0733 q^{85} -246.384i q^{86} +(-55.3842 + 16.4242i) q^{87} +270.395 q^{88} +153.161i q^{89} +(231.469 - 150.521i) q^{90} -29.4590 q^{91} -50.7378i q^{92} +(8.97327 + 30.2589i) q^{93} -309.477 q^{94} -238.476i q^{95} +(-299.711 + 88.8791i) q^{96} +153.521 q^{97} -26.7282i q^{98} +(52.8074 + 81.2064i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 88 q + 8 q^{3} - 176 q^{4} - 22 q^{6} + 20 q^{9}+O(q^{10}) $ 88 * q + 8 * q^3 - 176 * q^4 - 22 * q^6 + 20 * q^9	$ 88 q + 8 q^{3} - 176 q^{4} - 22 q^{6} + 20 q^{9} - 16 q^{10} - 18 q^{12} + 64 q^{13} + 20 q^{15} + 272 q^{16} - 38 q^{18} - 48 q^{19} - 28 q^{21} + 208 q^{22} + 228 q^{24} - 568 q^{25} - 88 q^{27} - 8 q^{30} + 8 q^{31} - 160 q^{33} - 32 q^{34} - 138 q^{36} - 136 q^{37} + 76 q^{39} - 48 q^{40} - 140 q^{42} + 424 q^{43} + 172 q^{45} + 334 q^{48} + 616 q^{49} + 288 q^{51} - 140 q^{52} - 240 q^{55} - 252 q^{57} - 380 q^{58} - 364 q^{60} + 312 q^{61} - 252 q^{64} + 44 q^{66} - 224 q^{67} + 168 q^{70} - 592 q^{72} + 216 q^{73} - 284 q^{75} + 328 q^{76} + 470 q^{78} - 8 q^{79} + 380 q^{81} - 548 q^{82} + 224 q^{84} - 712 q^{85} + 56 q^{87} - 896 q^{88} + 1136 q^{90} + 168 q^{91} - 236 q^{93} - 252 q^{94} - 546 q^{96} + 480 q^{97} - 248 q^{99}+O(q^{100}) $ 88 * q + 8 * q^3 - 176 * q^4 - 22 * q^6 + 20 * q^9 - 16 * q^10 - 18 * q^12 + 64 * q^13 + 20 * q^15 + 272 * q^16 - 38 * q^18 - 48 * q^19 - 28 * q^21 + 208 * q^22 + 228 * q^24 - 568 * q^25 - 88 * q^27 - 8 * q^30 + 8 * q^31 - 160 * q^33 - 32 * q^34 - 138 * q^36 - 136 * q^37 + 76 * q^39 - 48 * q^40 - 140 * q^42 + 424 * q^43 + 172 * q^45 + 334 * q^48 + 616 * q^49 + 288 * q^51 - 140 * q^52 - 240 * q^55 - 252 * q^57 - 380 * q^58 - 364 * q^60 + 312 * q^61 - 252 * q^64 + 44 * q^66 - 224 * q^67 + 168 * q^70 - 592 * q^72 + 216 * q^73 - 284 * q^75 + 328 * q^76 + 470 * q^78 - 8 * q^79 + 380 * q^81 - 548 * q^82 + 224 * q^84 - 712 * q^85 + 56 * q^87 - 896 * q^88 + 1136 * q^90 + 168 * q^91 - 236 * q^93 - 252 * q^94 - 546 * q^96 + 480 * q^97 - 248 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/483\mathbb{Z}\right)^\times$.

$n$	$323$	$346$	$442$
$\chi(n)$	$-1$	$1$	$1$

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 $

$2$		−	3.81832i		−	1.90916i	−0.297956	−	0.954580i	$-0.596305\pi$
$2$		−	3.81832i		−	1.90916i	0.297956	−	0.954580i	$-0.403695\pi$
$3$	−0.852935	−	2.87620i	−0.284312	−	0.958732i
$3$	−0.852935	−	2.87620i	−0.284312	−	0.958732i
$4$	−10.5796			−2.64489
$5$		−	8.03455i		−	1.60691i	−0.595366	−	0.803455i	$-0.702993\pi$
$5$		−	8.03455i		−	1.60691i	0.595366	−	0.803455i	$-0.297007\pi$
$6$	−10.9822	+	3.25678i	−1.83037	+	0.542796i
$7$	2.64575			0.377964
$7$	2.64575			0.377964
$8$			25.1228i			3.14035i
$9$	−7.54500	+	4.90642i	−0.838334	+	0.545157i
$10$	−30.6785			−3.06785
$11$		−	10.7629i		−	0.978449i	−0.872158	−	0.489224i	$-0.837280\pi$
$11$		−	10.7629i		−	0.978449i	0.872158	−	0.489224i	$-0.162720\pi$
$12$	9.02367	+	30.4289i	0.751972	+	2.53574i
$13$	−11.1345			−0.856498			−0.428249	−	0.903661i	$-0.640869\pi$
$13$	−11.1345			−0.856498			−0.428249	+	0.903661i	$0.640869\pi$
$14$		−	10.1023i		−	0.721594i
$15$	−23.1089	+	6.85295i	−1.54060	+	0.456863i
$16$	53.6087			3.35055
$17$		−	3.24515i		−	0.190891i	−0.995435	−	0.0954455i	$-0.969572\pi$
$17$		−	3.24515i		−	0.190891i	0.995435	−	0.0954455i	$-0.0304275\pi$
$18$	18.7343	+	28.8092i	1.04079	+	1.60051i
$19$	29.6813			1.56218			0.781088	−	0.624421i	$-0.214665\pi$
$19$	29.6813			1.56218			0.781088	+	0.624421i	$0.214665\pi$
$20$			85.0019i			4.25010i
$21$	−2.25665	−	7.60970i	−0.107460	−	0.362367i
$22$	−41.0963			−1.86801
$23$			4.79583i			0.208514i
$23$			4.79583i			0.208514i
$24$	72.2582	−	21.4281i	3.01076	−	0.892839i
$25$	−39.5539			−1.58216
$26$			42.5150i			1.63519i
$27$	20.5472	+	17.5161i	0.761008	+	0.648743i
$28$	−27.9909			−0.999674
$29$		−	19.2560i		−	0.664002i	−0.943279	−	0.332001i	$-0.892276\pi$
$29$		−	19.2560i		−	0.664002i	0.943279	−	0.332001i	$-0.107724\pi$
$30$	26.1667	+	88.2372i	0.872224	+	2.94124i
$31$	−10.5205			−0.339370			−0.169685	−	0.985498i	$-0.554275\pi$
$31$	−10.5205			−0.339370			−0.169685	+	0.985498i	$0.554275\pi$
$32$		−	104.204i		−	3.25637i
$33$	−30.9563	+	9.18009i	−0.938070	+	0.278184i
$34$	−12.3910			−0.364441
$35$		−	21.2574i		−	0.607355i
$36$	79.8228	−	51.9077i	2.21730	−	1.44188i
$37$	−58.1187			−1.57078			−0.785388	−	0.619004i	$-0.787536\pi$
$37$	−58.1187			−1.57078			−0.785388	+	0.619004i	$0.787536\pi$
$38$		−	113.333i		−	2.98244i
$39$	9.49698	+	32.0249i	0.243512	+	0.821152i
$40$	201.850			5.04626
$41$		−	31.5647i		−	0.769870i	−0.922944	−	0.384935i	$-0.874224\pi$
$41$		−	31.5647i		−	0.769870i	0.922944	−	0.384935i	$-0.125776\pi$
$42$	−29.0562	+	8.61662i	−0.691815	+	0.205158i
$43$	64.5269			1.50063			0.750313	−	0.661083i	$-0.229903\pi$
$43$	64.5269			1.50063			0.750313	+	0.661083i	$0.229903\pi$
$44$			113.867i			2.58789i
$45$	39.4208	+	60.6207i	0.876018	+	1.34713i
$46$	18.3120			0.398087
$47$		−	81.0506i		−	1.72448i	−0.506499	−	0.862240i	$-0.669061\pi$
$47$		−	81.0506i		−	1.72448i	0.506499	−	0.862240i	$-0.330939\pi$
$48$	−45.7247	−	154.189i	−0.952599	−	3.21227i
$49$	7.00000			0.142857
$50$			151.030i			3.02059i
$51$	−9.33367	+	2.76790i	−0.183013	+	0.0542725i
$52$	117.798			2.26534
$53$			10.5227i			0.198541i	0.995060	+	0.0992706i	$0.0316509\pi$
$53$			10.5227i			0.198541i	−0.995060	+	0.0992706i	$0.968349\pi$
$54$	66.8819	−	78.4558i	1.23855	−	1.45288i
$55$	−86.4753			−1.57228
$56$			66.4687i			1.18694i
$57$	−25.3162	−	85.3693i	−0.444145	−	1.49771i
$58$	−73.5257			−1.26768
$59$		−	38.6771i		−	0.655544i	−0.944757	−	0.327772i	$-0.893702\pi$
$59$		−	38.6771i		−	0.655544i	0.944757	−	0.327772i	$-0.106298\pi$
$60$	244.482	−	72.5011i	4.07470	−	1.20835i
$61$	68.4630			1.12234			0.561172	−	0.827699i	$-0.310350\pi$
$61$	68.4630			1.12234			0.561172	+	0.827699i	$0.310350\pi$
$62$			40.1705i			0.647911i
$63$	−19.9622	+	12.9812i	−0.316860	+	0.206050i
$64$	−183.449			−2.86638
$65$			89.4604i			1.37631i
$66$	35.0525	+	118.201i	0.531098	+	1.79093i
$67$	25.5535			0.381395			0.190698	−	0.981649i	$-0.438925\pi$
$67$	25.5535			0.381395			0.190698	+	0.981649i	$0.438925\pi$
$68$			34.3322i			0.504885i
$69$	13.7938	−	4.09053i	0.199909	−	0.0592831i
$70$	−81.1676			−1.15954
$71$			0.0320263i			0.000451074i	1.00000		0.000225537i	$7.17907e-5\pi$
$71$			0.0320263i			0.000451074i	−1.00000		0.000225537i	$0.999928\pi$
$72$	−123.263	−	189.552i	−1.71199	−	2.63266i
$73$	−18.4715			−0.253034			−0.126517	−	0.991964i	$-0.540380\pi$
$73$	−18.4715			−0.253034			−0.126517	+	0.991964i	$0.540380\pi$
$74$			221.916i			2.99886i
$75$	33.7369	+	113.765i	0.449826	+	1.51686i
$76$	−314.015			−4.13178
$77$		−	28.4761i		−	0.369819i
$78$	122.281	−	36.2625i	1.56771	−	0.464904i
$79$	−144.679			−1.83137			−0.915687	−	0.401891i	$-0.868353\pi$
$79$	−144.679			−1.83137			−0.915687	+	0.401891i	$0.868353\pi$
$80$		−	430.722i		−	5.38402i
$81$	32.8542	−	74.0378i	0.405607	−	0.914048i
$82$	−120.524			−1.46981
$83$			118.138i			1.42335i	0.702508	+	0.711676i	$0.252064\pi$
$83$			118.138i			1.42335i	−0.702508	+	0.711676i	$0.747936\pi$
$84$	23.8744	+	80.5072i	0.284219	+	0.958419i
$85$	−26.0733			−0.306744
$86$		−	246.384i		−	2.86493i
$87$	−55.3842	+	16.4242i	−0.636600	+	0.188783i
$88$	270.395			3.07268
$89$			153.161i			1.72091i	0.509527	+	0.860454i	$0.329820\pi$
$89$			153.161i			1.72091i	−0.509527	+	0.860454i	$0.670180\pi$
$90$	231.469	−	150.521i	2.57188	−	1.67246i
$91$	−29.4590			−0.323726
$92$		−	50.7378i		−	0.551497i
$93$	8.97327	+	30.2589i	0.0964868	+	0.325365i
$94$	−309.477			−3.29231
$95$		−	238.476i		−	2.51027i
$96$	−299.711	+	88.8791i	−3.12199	+	0.925824i
$97$	153.521			1.58269			0.791345	−	0.611370i	$-0.209381\pi$
$97$	153.521			1.58269			0.791345	+	0.611370i	$0.209381\pi$
$98$		−	26.7282i		−	0.272737i
$99$	52.8074	+	81.2064i	0.533409	+	0.820267i
$100$	418.463			4.18463
$101$			65.5926i			0.649431i	0.945812	+	0.324716i	$0.105269\pi$
$101$			65.5926i			0.649431i	−0.945812	+	0.324716i	$0.894731\pi$
$102$	10.5687	+	35.6389i	0.103615	+	0.349401i
$103$	20.7703			0.201654			0.100827	−	0.994904i	$-0.467851\pi$
$103$	20.7703			0.201654			0.100827	+	0.994904i	$0.467851\pi$
$104$		−	279.729i		−	2.68971i
$105$	−61.1405	+	18.1312i	−0.582290	+	0.172678i
$106$	40.1790			0.379047
$107$			80.7358i			0.754540i	0.926103	+	0.377270i	$0.123137\pi$
$107$			80.7358i			0.754540i	−0.926103	+	0.377270i	$0.876863\pi$
$108$	−217.380	−	185.312i	−2.01278	−	1.71585i
$109$	32.8861			0.301707			0.150854	−	0.988556i	$-0.451798\pi$
$109$	32.8861			0.301707			0.150854	+	0.988556i	$0.451798\pi$
$110$			330.190i			3.00173i
$111$	49.5714	+	167.161i	0.446590	+	1.50595i
$112$	141.835			1.26639
$113$			48.3251i			0.427656i	0.976871	+	0.213828i	$0.0685932\pi$
$113$			48.3251i			0.427656i	−0.976871	+	0.213828i	$0.931407\pi$
$114$	−325.967	+	96.6655i	−2.85936	+	0.847943i
$115$	38.5323			0.335064
$116$			203.720i			1.75621i
$117$	84.0096	−	54.6304i	0.718031	−	0.466926i
$118$	−147.682			−1.25154
$119$		−	8.58585i		−	0.0721500i
$120$	−172.165	−	580.562i	−1.43471	−	4.83801i
$121$	5.15916			0.0426377
$122$		−	261.414i		−	2.14274i
$123$	−90.7862	+	26.9226i	−0.738099	+	0.218883i
$124$	111.302			0.897595
$125$			116.934i			0.935474i
$126$	49.5662	+	76.2220i	0.393382	+	0.604937i
$127$	−35.8390			−0.282196			−0.141098	−	0.989996i	$-0.545063\pi$
$127$	−35.8390			−0.282196			−0.141098	+	0.989996i	$0.545063\pi$
$128$			283.650i			2.21601i
$129$	−55.0372	−	185.592i	−0.426645	−	1.43870i
$130$	341.588			2.62760
$131$			115.117i			0.878753i	0.898303	+	0.439376i	$0.144801\pi$
$131$			115.117i			0.878753i	−0.898303	+	0.439376i	$0.855199\pi$
$132$	327.504	−	97.1212i	2.48109	−	0.735767i
$133$	78.5294			0.590447
$134$		−	97.5713i		−	0.728144i
$135$	140.734	−	165.088i	1.04247	−	1.22287i
$136$	81.5272			0.599465
$137$		−	184.024i		−	1.34324i	−0.740896	−	0.671620i	$-0.765599\pi$
$137$		−	184.024i		−	1.34324i	0.740896	−	0.671620i	$-0.234401\pi$
$138$	−15.6190	−	52.6689i	−0.113181	−	0.381659i
$139$	−240.242			−1.72836			−0.864180	−	0.503182i	$-0.832163\pi$
$139$	−240.242			−1.72836			−0.864180	+	0.503182i	$0.832163\pi$
$140$			224.894i			1.60639i
$141$	−233.117	+	69.1309i	−1.65331	+	0.490290i
$142$	0.122286			0.000861172
$143$			119.840i			0.838040i
$144$	−404.478	+	263.027i	−2.80888	+	1.82657i
$145$	−154.714			−1.06699
$146$			70.5300i			0.483082i
$147$	−5.97054	−	20.1334i	−0.0406159	−	0.136962i
$148$	614.870			4.15452
$149$		−	62.9249i		−	0.422315i	−0.977452	−	0.211157i	$-0.932277\pi$
$149$		−	62.9249i		−	0.422315i	0.977452	−	0.211157i	$-0.0677232\pi$
$150$	434.390	−	128.818i	2.89594	−	0.858789i
$151$	−147.552			−0.977169			−0.488584	−	0.872517i	$-0.662487\pi$
$151$	−147.552			−0.977169			−0.488584	+	0.872517i	$0.662487\pi$
$152$			745.679i			4.90578i
$153$	15.9220	+	24.4846i	0.104066	+	0.160030i
$154$	−108.731			−0.706043
$155$			84.5272i			0.545337i
$156$	−100.474	−	338.809i	−0.644063	−	2.17186i
$157$	−228.432			−1.45498			−0.727489	−	0.686119i	$-0.759313\pi$
$157$	−228.432			−1.45498			−0.727489	+	0.686119i	$0.759313\pi$
$158$			552.429i			3.49639i
$159$	30.2653	−	8.97517i	0.190348	−	0.0564476i
$160$	−837.231			−5.23269
$161$			12.6886i			0.0788110i
$162$	−282.700	−	125.448i	−1.74506	−	0.774368i
$163$	129.165			0.792421			0.396211	−	0.918160i	$-0.370325\pi$
$163$	129.165			0.792421			0.396211	+	0.918160i	$0.370325\pi$
$164$			333.940i			2.03622i
$165$	73.7578	+	248.720i	0.447017	+	1.50739i
$166$	451.089			2.71741
$167$			165.277i			0.989683i	0.868983	+	0.494841i	$0.164774\pi$
$167$			165.277i			0.989683i	−0.868983	+	0.494841i	$0.835226\pi$
$168$	191.177	−	56.6935i	1.13796	−	0.337461i
$169$	−45.0235			−0.266411
$170$			99.5560i			0.585624i
$171$	−223.946	+	145.629i	−1.30962	+	0.851631i
$172$	−682.666			−3.96899
$173$			152.977i			0.884261i	0.896951	+	0.442131i	$0.145777\pi$
$173$			152.977i			0.884261i	−0.896951	+	0.442131i	$0.854223\pi$
$174$	62.7126	+	211.474i	0.360417	+	1.21537i
$175$	−104.650			−0.597999
$176$		−	576.987i		−	3.27834i
$177$	−111.243	+	32.9891i	−0.628491	+	0.186379i
$178$	584.817			3.28549
$179$		−	275.769i		−	1.54061i	−0.637677	−	0.770304i	$-0.720104\pi$
$179$		−	275.769i		−	1.54061i	0.637677	−	0.770304i	$-0.279896\pi$
$180$	−417.055	−	641.340i	−2.31697	−	3.56300i
$181$	−68.5052			−0.378482			−0.189241	−	0.981931i	$-0.560603\pi$
$181$	−68.5052			−0.378482			−0.189241	+	0.981931i	$0.560603\pi$
$182$			112.484i			0.618044i
$183$	−58.3945	−	196.913i	−0.319096	−	1.07603i
$184$	−120.485			−0.654809
$185$			466.957i			2.52409i
$186$	115.538	−	34.2628i	0.621173	−	0.184209i
$187$	−34.9273			−0.186777
$188$			857.479i			4.56106i
$189$	54.3628	+	46.3431i	0.287634	+	0.245202i
$190$	−910.578			−4.79251
$191$		−	225.515i		−	1.18071i	−0.807145	−	0.590354i	$-0.798988\pi$
$191$		−	225.515i		−	1.18071i	0.807145	−	0.590354i	$-0.201012\pi$
$192$	156.470	+	527.634i	0.814946	+	2.74809i
$193$	164.665			0.853188			0.426594	−	0.904443i	$-0.359713\pi$
$193$	164.665			0.853188			0.426594	+	0.904443i	$0.359713\pi$
$194$		−	586.192i		−	3.02161i
$195$	257.306	−	76.3039i	1.31952	−	0.391302i
$196$	−74.0569			−0.377841
$197$		−	133.981i		−	0.680109i	−0.940406	−	0.340054i	$-0.889555\pi$
$197$		−	133.981i		−	0.680109i	0.940406	−	0.340054i	$-0.110445\pi$
$198$	310.072	−	201.636i	1.56602	−	1.01836i
$199$	29.4083			0.147780			0.0738902	−	0.997266i	$-0.476459\pi$
$199$	29.4083			0.147780			0.0738902	+	0.997266i	$0.476459\pi$
$200$		−	993.707i		−	4.96853i
$201$	−21.7954	−	73.4968i	−0.108435	−	0.365656i
$202$	250.453			1.23987
$203$		−	50.9467i		−	0.250969i
$204$	98.7461	−	29.2831i	0.484049	−	0.143545i
$205$	−253.608			−1.23711
$206$		−	79.3077i		−	0.384989i
$207$	−23.5303	−	36.1846i	−0.113673	−	0.174805i
$208$	−596.905			−2.86974
$209$		−	319.458i		−	1.52851i
$210$	69.2306	+	233.454i	0.329670	+	1.11168i
$211$	287.595			1.36301			0.681504	−	0.731814i	$-0.261326\pi$
$211$	287.595			1.36301			0.681504	+	0.731814i	$0.261326\pi$
$212$		−	111.325i		−	0.525119i
$213$	0.0921138	−	0.0273163i	0.000432459	−	0.000128246i
$214$	308.275			1.44054
$215$		−	518.444i		−	2.41137i
$216$	−440.053	+	516.204i	−2.03728	+	2.38983i
$217$	−27.8345			−0.128270
$218$		−	125.569i		−	0.576007i
$219$	15.7550	+	53.1276i	0.0719405	+	0.242592i
$220$	914.870			4.15850
$221$			36.1330i			0.163498i
$222$	638.273	−	189.280i	2.87510	−	0.852611i
$223$	256.268			1.14918			0.574592	−	0.818440i	$-0.305161\pi$
$223$	256.268			1.14918			0.574592	+	0.818440i	$0.305161\pi$
$224$		−	275.697i		−	1.23079i
$225$	298.435	−	194.068i	1.32638	−	0.862525i
$226$	184.521			0.816463
$227$			54.6752i			0.240860i	0.992722	+	0.120430i	$0.0384273\pi$
$227$			54.6752i			0.240860i	−0.992722	+	0.120430i	$0.961573\pi$
$228$	267.835	+	903.169i	1.17471	+	3.96127i
$229$	45.6936			0.199535			0.0997677	−	0.995011i	$-0.468190\pi$
$229$	45.6936			0.199535			0.0997677	+	0.995011i	$0.468190\pi$
$230$		−	147.129i		−	0.639690i
$231$	−81.9027	+	24.2882i	−0.354557	+	0.105144i
$232$	483.766			2.08520
$233$		−	209.558i		−	0.899389i	−0.893182	−	0.449695i	$-0.851533\pi$
$233$		−	209.558i		−	0.899389i	0.893182	−	0.449695i	$-0.148467\pi$
$234$	−208.596	−	320.776i	−0.891436	−	1.37084i
$235$	−651.205			−2.77108
$236$			409.187i			1.73384i
$237$	123.401	+	416.124i	0.520681	+	1.75580i
$238$	−32.7835			−0.137746
$239$			234.078i			0.979406i	0.871889	+	0.489703i	$0.162895\pi$
$239$			234.078i			0.979406i	−0.871889	+	0.489703i	$0.837105\pi$
$240$	−1238.84	+	367.378i	−5.16183	+	1.53074i
$241$	−113.026			−0.468990			−0.234495	−	0.972117i	$-0.575344\pi$
$241$	−113.026			−0.468990			−0.234495	+	0.972117i	$0.575344\pi$
$242$		−	19.6993i		−	0.0814021i
$243$	−240.970	−	31.3456i	−0.991645	−	0.128994i
$244$	−724.308			−2.96848
$245$		−	56.2418i		−	0.229558i
$246$	102.799	+	346.651i	0.417883	+	1.40915i
$247$	−330.486			−1.33800
$248$		−	264.304i		−	1.06574i
$249$	339.789	−	100.764i	1.36461	−	0.404676i
$250$	446.492			1.78597
$251$		−	255.970i		−	1.01980i	−0.860234	−	0.509900i	$-0.829682\pi$
$251$		−	255.970i		−	1.01980i	0.860234	−	0.509900i	$-0.170318\pi$
$252$	211.191	−	137.335i	0.838060	−	0.544979i
$253$	51.6172			0.204021
$254$			136.845i			0.538758i
$255$	22.2388	+	74.9918i	0.0872110	+	0.294086i
$256$	349.270			1.36434
$257$		−	207.023i		−	0.805537i	−0.915302	−	0.402768i	$-0.868048\pi$
$257$		−	207.023i		−	0.805537i	0.915302	−	0.402768i	$-0.131952\pi$
$258$	−708.649	+	210.150i	−2.74670	+	0.814534i
$259$	−153.768			−0.593697
$260$		−	946.451i		−	3.64020i
$261$	94.4782	+	145.287i	0.361985	+	0.556655i
$262$	439.552			1.67768
$263$			81.4458i			0.309680i	0.987940	+	0.154840i	$0.0494862\pi$
$263$			81.4458i			0.309680i	−0.987940	+	0.154840i	$0.950514\pi$
$264$	−230.630	−	777.710i	−0.873597	−	2.94587i
$265$	84.5450			0.319038
$266$		−	299.850i		−	1.12726i
$267$	440.521	−	130.636i	1.64989	−	0.489274i
$268$	−270.344			−1.00875
$269$		−	168.553i		−	0.626592i	−0.949656	−	0.313296i	$-0.898567\pi$
$269$		−	168.553i		−	0.626592i	0.949656	−	0.313296i	$-0.101433\pi$
$270$	−630.357	−	537.366i	−2.33465	−	1.99024i
$271$	−460.201			−1.69816			−0.849079	−	0.528266i	$-0.822842\pi$
$271$	−460.201			−1.69816			−0.849079	+	0.528266i	$0.822842\pi$
$272$		−	173.968i		−	0.639589i
$273$	25.1267	+	84.7300i	0.0920390	+	0.310366i
$274$	−702.662			−2.56446
$275$			425.717i			1.54806i
$276$	−145.932	+	43.2760i	−0.528738	+	0.156797i
$277$	183.241			0.661519			0.330760	−	0.943715i	$-0.392695\pi$
$277$	183.241			0.661519			0.330760	+	0.943715i	$0.392695\pi$
$278$			917.321i			3.29972i
$279$	79.3769	−	51.6178i	0.284505	−	0.185010i
$280$	534.046			1.90731
$281$			50.9677i			0.181380i	0.995879	+	0.0906898i	$0.0289072\pi$
$281$			50.9677i			0.181380i	−0.995879	+	0.0906898i	$0.971093\pi$
$282$	263.964	+	890.116i	0.936041	+	3.15644i
$283$	100.235			0.354186			0.177093	−	0.984194i	$-0.443331\pi$
$283$	100.235			0.354186			0.177093	+	0.984194i	$0.443331\pi$
$284$		−	0.338824i		−	0.00119304i
$285$	−685.904	+	203.405i	−2.40668	+	0.713700i
$286$	457.586			1.59995
$287$		−	83.5123i		−	0.290984i
$288$	511.267	+	786.218i	1.77523	+	2.72993i
$289$	278.469			0.963561
$290$			590.746i			2.03705i
$291$	−130.943	−	441.556i	−0.449977	−	1.51738i
$292$	195.420			0.669246
$293$			248.494i			0.848103i	0.905638	+	0.424052i	$0.139393\pi$
$293$			248.494i			0.848103i	−0.905638	+	0.424052i	$0.860607\pi$
$294$	−76.8756	+	22.7974i	−0.261482	+	0.0775423i
$295$	−310.753			−1.05340
$296$		−	1460.11i		−	4.93279i
$297$	188.524	−	221.148i	0.634762	−	0.744607i
$298$	−240.267			−0.806266
$299$		−	53.3991i		−	0.178592i
$300$	−356.922	−	1203.58i	−1.18974	−	4.01194i
$301$	170.722			0.567183
$302$			563.402i			1.86557i
$303$	188.657	−	55.9462i	0.622630	−	0.184641i
$304$	1591.18			5.23414
$305$		−	550.070i		−	1.80351i
$306$	93.4901	−	60.7954i	0.305523	−	0.198678i
$307$	177.307			0.577546			0.288773	−	0.957398i	$-0.406753\pi$
$307$	177.307			0.577546			0.288773	+	0.957398i	$0.406753\pi$
$308$			301.264i			0.978130i
$309$	−17.7157	−	59.7395i	−0.0573325	−	0.193332i
$310$	322.752			1.04113
$311$		−	232.386i		−	0.747223i	−0.927585	−	0.373611i	$-0.878119\pi$
$311$		−	232.386i		−	0.747223i	0.927585	−	0.373611i	$-0.121881\pi$
$312$	−804.557	+	238.591i	−2.57871	+	0.764715i
$313$	−16.8161			−0.0537254			−0.0268627	−	0.999639i	$-0.508552\pi$
$313$	−16.8161			−0.0537254			−0.0268627	+	0.999639i	$0.508552\pi$
$314$			872.224i			2.77778i
$315$	104.298	+	160.387i	0.331104	+	0.509166i
$316$	1530.63			4.84378
$317$		−	432.103i		−	1.36310i	−0.731772	−	0.681550i	$-0.761306\pi$
$317$		−	432.103i		−	1.36310i	0.731772	−	0.681550i	$-0.238694\pi$
$318$	−34.2700	−	115.563i	−0.107767	−	0.363404i
$319$	−207.252			−0.649692
$320$			1473.93i			4.60602i
$321$	232.212	−	68.8624i	0.723401	−	0.214524i
$322$	48.4490			0.150463
$323$		−	96.3203i		−	0.298205i
$324$	−347.582	+	783.287i	−1.07279	+	2.41755i
$325$	440.412			1.35511
$326$		−	493.192i		−	1.51286i
$327$	−28.0497	−	94.5868i	−0.0857788	−	0.289256i
$328$	792.994			2.41767
$329$		−	214.440i		−	0.651792i
$330$	949.692	−	281.631i	2.87785	−	0.853427i
$331$	−631.270			−1.90716			−0.953580	−	0.301139i	$-0.902633\pi$
$331$	−631.270			−1.90716			−0.953580	+	0.301139i	$0.902633\pi$
$332$		−	1249.85i		−	3.76461i
$333$	438.506	−	285.154i	1.31683	−	0.856319i
$334$	631.080			1.88946
$335$		−	205.311i		−	0.612867i
$336$	−120.976	−	407.946i	−0.360049	−	1.21413i
$337$	−463.251			−1.37463			−0.687317	−	0.726358i	$-0.741211\pi$
$337$	−463.251			−1.37463			−0.687317	+	0.726358i	$0.741211\pi$
$338$			171.914i			0.508621i
$339$	138.992	−	41.2182i	0.410007	−	0.121588i
$340$	275.844			0.811305
$341$			113.231i			0.332056i
$342$	556.058	+	855.096i	1.62590	+	2.50028i
$343$	18.5203			0.0539949
$344$			1621.10i			4.71249i
$345$	−32.8656	−	110.827i	−0.0952625	−	0.321236i
$346$	584.115			1.68819
$347$		−	105.940i		−	0.305304i	−0.988280	−	0.152652i	$-0.951219\pi$
$347$		−	105.940i		−	0.305304i	0.988280	−	0.152652i	$-0.0487813\pi$
$348$	585.940	−	173.760i	1.68373	−	0.499311i
$349$	−294.414			−0.843593			−0.421796	−	0.906691i	$-0.638600\pi$
$349$	−294.414			−0.843593			−0.421796	+	0.906691i	$0.638600\pi$
$350$			399.587i			1.14168i
$351$	−228.782	−	195.032i	−0.651802	−	0.555647i
$352$	−1121.54			−3.18619
$353$		−	195.964i		−	0.555139i	−0.960706	−	0.277570i	$-0.910471\pi$
$353$		−	195.964i		−	0.555139i	0.960706	−	0.277570i	$-0.0895289\pi$
$354$	125.963	+	424.761i	0.355827	+	1.19989i
$355$	0.257317			0.000724835
$356$		−	1620.37i		−	4.55161i
$357$	−24.6946	+	7.32317i	−0.0691725	+	0.0205131i
$358$	−1052.97			−2.94127
$359$		−	682.261i		−	1.90045i	−0.311565	−	0.950225i	$-0.600853\pi$
$359$		−	682.261i		−	1.90045i	0.311565	−	0.950225i	$-0.399147\pi$
$360$	−1522.96	+	990.362i	−4.23045	+	2.75101i
$361$	519.982			1.44039
$362$			261.575i			0.722582i
$363$	−4.40043	−	14.8388i	−0.0121224	−	0.0408781i
$364$	311.664			0.856219
$365$			148.410i			0.406603i
$366$	−751.877	+	222.969i	−2.05431	+	0.609204i
$367$	150.739			0.410732			0.205366	−	0.978685i	$-0.434161\pi$
$367$	150.739			0.410732			0.205366	+	0.978685i	$0.434161\pi$
$368$			257.098i			0.698637i
$369$	154.869	+	238.156i	0.419700	+	0.645408i
$370$	1782.99			4.81890
$371$			27.8404i			0.0750415i
$372$	−94.9332	−	320.126i	−0.255197	−	0.860553i
$373$	439.464			1.17819			0.589093	−	0.808065i	$-0.299485\pi$
$373$	439.464			1.17819			0.589093	+	0.808065i	$0.299485\pi$
$374$			133.364i			0.356587i
$375$	336.326	−	99.7373i	0.896869	−	0.265966i
$376$	2036.22			5.41548
$377$			214.406i			0.568716i
$378$	176.953	−	207.574i	0.468129	−	0.549139i
$379$	−575.965			−1.51970			−0.759848	−	0.650100i	$-0.774727\pi$
$379$	−575.965			−1.51970			−0.759848	+	0.650100i	$0.774727\pi$
$380$			2522.97i			6.63940i
$381$	30.5683	+	103.080i	0.0802317	+	0.270551i
$382$	−861.088			−2.25416
$383$		−	230.035i		−	0.600614i	−0.953843	−	0.300307i	$-0.902911\pi$
$383$		−	230.035i		−	0.600614i	0.953843	−	0.300307i	$-0.0970892\pi$
$384$	815.832	−	241.935i	2.12456	−	0.630038i
$385$	−228.792			−0.594265
$386$		−	628.744i		−	1.62887i
$387$	−486.856	+	316.596i	−1.25803	+	0.818077i
$388$	−1624.18			−4.18604
$389$		−	301.450i		−	0.774935i	−0.921883	−	0.387467i	$-0.873350\pi$
$389$		−	301.450i		−	0.774935i	0.921883	−	0.387467i	$-0.126650\pi$
$390$	−291.353	−	982.475i	−0.747058	−	2.51917i
$391$	15.5632			0.0398035
$392$			175.860i			0.448622i
$393$	331.098	−	98.1870i	0.842488	−	0.249840i
$394$	−511.584			−1.29844
$395$			1162.43i			2.94285i
$396$	−558.679	−	859.128i	−1.41081	−	2.16951i
$397$	−366.113			−0.922198			−0.461099	−	0.887349i	$-0.652545\pi$
$397$	−366.113			−0.922198			−0.461099	+	0.887349i	$0.652545\pi$
$398$		−	112.290i		−	0.282136i
$399$	−66.9805	−	225.866i	−0.167871	−	0.566080i
$400$	−2120.44			−5.30109
$401$			111.901i			0.279054i	0.990218	+	0.139527i	$0.0445583\pi$
$401$			111.901i			0.279054i	−0.990218	+	0.139527i	$0.955442\pi$
$402$	−280.634	+	83.2219i	−0.698095	+	0.207020i
$403$	117.140			0.290670
$404$		−	693.940i		−	1.71767i
$405$	−594.861	−	263.968i	−1.46879	−	0.651774i
$406$	−194.531			−0.479140
$407$			625.528i			1.53692i
$408$	−69.5374	−	234.488i	−0.170435	−	0.574726i
$409$	−489.884			−1.19776			−0.598880	−	0.800839i	$-0.704387\pi$
$409$	−489.884			−1.19776			−0.598880	+	0.800839i	$0.704387\pi$
$410$			968.356i			2.36184i
$411$	−529.289	+	156.960i	−1.28781	+	0.381899i
$412$	−219.741			−0.533351
$413$		−	102.330i		−	0.247773i
$414$	−138.164	+	89.8463i	−0.333730	+	0.217020i
$415$	949.187			2.28720
$416$			1160.26i			2.78907i
$417$	204.911	+	690.984i	0.491393	+	1.65703i
$418$	−1219.79			−2.91817
$419$			200.686i			0.478964i	0.970901	+	0.239482i	$0.0769777\pi$
$419$			200.686i			0.478964i	−0.970901	+	0.239482i	$0.923022\pi$
$420$	646.839	−	191.820i	1.54009	−	0.456714i
$421$	541.671			1.28663			0.643315	−	0.765601i	$-0.277558\pi$
$421$	541.671			1.28663			0.643315	+	0.765601i	$0.277558\pi$
$422$		−	1098.13i		−	2.60220i
$423$	397.668	+	611.527i	0.940113	+	1.44569i
$424$	−264.360			−0.623490
$425$			128.358i			0.302019i
$426$	−0.104302	−	0.351720i	−0.000244841	−	0.000825633i
$427$	181.136			0.424207
$428$		−	854.148i		−	1.99567i
$429$	344.682	−	102.215i	0.803455	−	0.238264i
$430$	−1979.59			−4.60369
$431$			383.933i			0.890797i	0.895333	+	0.445398i	$0.146938\pi$
$431$			383.933i			0.890797i	−0.895333	+	0.445398i	$0.853062\pi$
$432$	1101.51	+	939.013i	2.54979	+	2.17364i
$433$	370.615			0.855925			0.427962	−	0.903797i	$-0.359232\pi$
$433$	370.615			0.855925			0.427962	+	0.903797i	$0.359232\pi$
$434$			106.281i			0.244887i
$435$	131.961	+	444.987i	0.303358	+	1.02296i
$436$	−347.920			−0.797982
$437$			142.347i			0.325736i
$438$	202.858	−	60.1575i	0.463146	−	0.137346i
$439$	−70.3834			−0.160327			−0.0801633	−	0.996782i	$-0.525544\pi$
$439$	−70.3834			−0.160327			−0.0801633	+	0.996782i	$0.525544\pi$
$440$		−	2172.50i		−	4.93751i
$441$	−52.8150	+	34.3449i	−0.119762	+	0.0778796i
$442$	137.967			0.312143
$443$		−	452.722i		−	1.02195i	−0.859597	−	0.510973i	$-0.829285\pi$
$443$		−	452.722i		−	1.02195i	0.859597	−	0.510973i	$-0.170715\pi$
$444$	−524.444	−	1768.49i	−1.18118	−	3.98308i
$445$	1230.58			2.76534
$446$		−	978.513i		−	2.19398i
$447$	−180.984	+	53.6708i	−0.404886	+	0.120069i
$448$	−485.359			−1.08339
$449$			56.5910i			0.126038i	0.998012	+	0.0630190i	$0.0200729\pi$
$449$			56.5910i			0.126038i	−0.998012	+	0.0630190i	$0.979927\pi$
$450$	−741.014	−	1139.52i	−1.64670	−	2.53226i
$451$	−339.729			−0.753279
$452$		−	511.258i		−	1.13110i
$453$	125.853	+	424.390i	0.277820	+	0.936843i
$454$	208.767			0.459840
$455$			236.690i			0.520198i
$456$	2144.72	−	636.016i	4.70333	−	1.39477i
$457$	192.705			0.421675			0.210837	−	0.977521i	$-0.432381\pi$
$457$	192.705			0.421675			0.210837	+	0.977521i	$0.432381\pi$
$458$		−	174.473i		−	0.380945i
$459$	56.8421	−	66.6787i	0.123839	−	0.145269i
$460$	−407.655			−0.886206
$461$			263.418i			0.571406i	0.958318	+	0.285703i	$0.0922271\pi$
$461$			263.418i			0.571406i	−0.958318	+	0.285703i	$0.907773\pi$
$462$	92.7402	+	312.731i	0.200736	+	0.676906i
$463$	−208.445			−0.450204			−0.225102	−	0.974335i	$-0.572272\pi$
$463$	−208.445			−0.450204			−0.225102	+	0.974335i	$0.572272\pi$
$464$		−	1032.29i		−	2.22477i
$465$	243.117	−	72.0962i	0.522832	−	0.155046i
$466$	−800.158			−1.71708
$467$		−	685.237i		−	1.46732i	−0.679518	−	0.733659i	$-0.737811\pi$
$467$		−	685.237i		−	1.46732i	0.679518	−	0.733659i	$-0.262189\pi$
$468$	−888.785	+	577.965i	−1.89911	+	1.23497i
$469$	67.6081			0.144154
$470$			2486.51i			5.29044i
$471$	194.837	+	657.014i	0.413667	+	1.39493i
$472$	971.678			2.05864
$473$		−	694.499i		−	1.46829i
$474$	1588.89	−	471.186i	3.35210	−	0.994063i
$475$	−1174.01			−2.47161
$476$			90.8344i			0.190829i
$477$	−51.6287	−	79.3937i	−0.108236	−	0.166444i
$478$	893.784			1.86984
$479$		−	113.671i		−	0.237309i	−0.992936	−	0.118655i	$-0.962142\pi$
$479$		−	113.671i		−	0.237309i	0.992936	−	0.118655i	$-0.0378581\pi$
$480$	714.103	+	2408.04i	1.48772	+	5.01675i
$481$	647.121			1.34537
$482$			431.571i			0.895376i
$483$	36.4948	−	10.8225i	0.0755587	−	0.0224069i
$484$	−54.5816			−0.112772
$485$		−	1233.47i		−	2.54324i
$486$	−119.687	+	920.099i	−0.246270	+	1.89321i
$487$	−467.524			−0.960008			−0.480004	−	0.877266i	$-0.659365\pi$
$487$	−467.524			−0.960008			−0.480004	+	0.877266i	$0.659365\pi$
$488$			1719.99i			3.52456i
$489$	−110.169	−	371.503i	−0.225295	−	0.759720i
$490$	−214.749			−0.438264
$491$			624.968i			1.27285i	0.771340	+	0.636424i	$0.219587\pi$
$491$			624.968i			1.27285i	−0.771340	+	0.636424i	$0.780413\pi$
$492$	960.478	−	284.829i	1.95219	−	0.578921i
$493$	−62.4887			−0.126752
$494$			1261.90i			2.55446i
$495$	652.457	−	424.284i	1.31809	−	0.857139i
$496$	−563.989			−1.13707
$497$			0.0847335i			0.000170490i
$498$	−384.750	−	1297.42i	−0.772590	−	2.60526i
$499$	−967.520			−1.93892			−0.969459	−	0.245255i	$-0.921128\pi$
$499$	−967.520			−1.93892			−0.969459	+	0.245255i	$0.921128\pi$
$500$		−	1237.11i		−	2.47422i
$501$	475.369	−	140.971i	0.948840	−	0.281378i
$502$	−977.374			−1.94696
$503$			440.525i			0.875795i	0.899025	+	0.437898i	$0.144277\pi$
$503$			440.525i			0.875795i	−0.899025	+	0.437898i	$0.855723\pi$
$504$	−326.123	−	501.507i	−0.647070	−	0.995053i
$505$	527.006			1.04358
$506$		−	197.091i		−	0.389508i
$507$	38.4021	+	129.496i	0.0757438	+	0.255417i
$508$	379.160			0.746378
$509$			580.895i			1.14125i	0.821212	+	0.570623i	$0.193298\pi$
$509$			580.895i			1.14125i	−0.821212	+	0.570623i	$0.806702\pi$
$510$	286.343	−	84.9148i	0.561456	−	0.166500i
$511$	−48.8709			−0.0956378
$512$		−	199.025i		−	0.388721i
$513$	609.869	+	519.900i	1.18883	+	1.01345i
$514$	−790.479			−1.53790
$515$		−	166.880i		−	0.324039i
$516$	582.269	+	1963.48i	1.12843	+	3.80519i
$517$	−872.343			−1.68732
$518$			587.133i			1.13346i
$519$	439.992	−	130.480i	0.847769	−	0.251406i
$520$	−2247.50			−4.32211
$521$		−	176.446i		−	0.338668i	−0.985559	−	0.169334i	$-0.945838\pi$
$521$		−	176.446i		−	0.338668i	0.985559	−	0.169334i	$-0.0541616\pi$
$522$	554.752	−	360.748i	1.06274	−	0.691088i
$523$	−276.966			−0.529571			−0.264785	−	0.964307i	$-0.585301\pi$
$523$	−276.966			−0.529571			−0.264785	+	0.964307i	$0.585301\pi$
$524$		−	1217.88i		−	2.32420i
$525$	89.2595	+	300.994i	0.170018	+	0.573321i
$526$	310.986			0.591228
$527$			34.1404i			0.0647826i
$528$	−1659.53	+	492.133i	−3.14305	+	0.932069i
$529$	−23.0000			−0.0434783
$530$		−	322.820i		−	0.609094i
$531$	189.766	+	291.819i	0.357375	+	0.549565i
$532$	−830.806			−1.56167
$533$			351.456i			0.659393i
$534$	−498.811	−	1682.05i	−0.934103	−	3.14990i
$535$	648.675			1.21248
$536$			641.975i			1.19771i
$537$	−793.165	+	235.213i	−1.47703	+	0.438013i
$538$	−643.590			−1.19626
$539$		−	75.3406i		−	0.139778i
$540$	−1488.90	+	1746.55i	−2.75722	+	3.23436i
$541$	60.3100			0.111479			0.0557394	−	0.998445i	$-0.482248\pi$
$541$	60.3100			0.111479			0.0557394	+	0.998445i	$0.482248\pi$
$542$			1757.19i			3.24205i
$543$	58.4305	+	197.034i	0.107607	+	0.362863i
$544$	−338.157			−0.621611
$545$		−	264.225i		−	0.484816i
$546$	323.526	−	95.9415i	0.592539	−	0.175717i
$547$	44.7960			0.0818939			0.0409469	−	0.999161i	$-0.486963\pi$
$547$	44.7960			0.0818939			0.0409469	+	0.999161i	$0.486963\pi$
$548$			1946.89i			3.55272i
$549$	−516.554	+	335.908i	−0.940900	+	0.611855i
$550$	1625.52			2.95549
$551$		−	571.545i		−	1.03729i
$552$	102.766	+	346.538i	0.186170	+	0.627786i
$553$	−382.784			−0.692195
$554$		−	699.672i		−	1.26295i
$555$	1343.06	−	398.284i	2.41993	−	0.717629i
$556$	2541.65			4.57132
$557$		−	448.787i		−	0.805721i	−0.915261	−	0.402860i	$-0.868016\pi$
$557$		−	448.787i		−	0.805721i	0.915261	−	0.402860i	$-0.131984\pi$
$558$	−197.093	−	303.086i	−0.353213	−	0.543166i
$559$	−718.473			−1.28528
$560$		−	1139.58i		−	2.03497i
$561$	29.7907	+	100.458i	0.0531029	+	0.179069i
$562$	194.611			0.346283
$563$			101.553i			0.180378i	0.995925	+	0.0901891i	$0.0287472\pi$
$563$			101.553i			0.180378i	−0.995925	+	0.0901891i	$0.971253\pi$
$564$	2466.28	−	731.374i	4.37283	−	1.29676i
$565$	388.270			0.687204
$566$		−	382.728i		−	0.676198i
$567$	86.9240	−	195.886i	0.153305	−	0.345477i
$568$	−0.804590			−0.00141653
$569$		−	323.100i		−	0.567838i	−0.958848	−	0.283919i	$-0.908365\pi$
$569$		−	323.100i		−	0.567838i	0.958848	−	0.283919i	$-0.0916347\pi$
$570$	776.663	+	2619.00i	1.36257	+	4.59474i
$571$	496.515			0.869553			0.434776	−	0.900538i	$-0.356827\pi$
$571$	496.515			0.869553			0.434776	+	0.900538i	$0.356827\pi$
$572$		−	1267.85i		−	2.21652i
$573$	−648.625	+	192.350i	−1.13198	+	0.335689i
$574$	−318.877			−0.555534
$575$		−	189.694i		−	0.329903i
$576$	1384.12	−	900.075i	2.40299	−	1.56263i
$577$	1076.83			1.86625			0.933127	−	0.359548i	$-0.117069\pi$
$577$	1076.83			1.86625			0.933127	+	0.359548i	$0.117069\pi$
$578$		−	1063.28i		−	1.83959i
$579$	−140.449	−	473.609i	−0.242571	−	0.817978i
$580$	1636.80			2.82207
$581$			312.564i			0.537976i
$582$	−1686.00	+	499.983i	−2.89691	+	0.859078i
$583$	113.255			0.194262
$584$		−	464.056i		−	0.794616i
$585$	−438.930	−	674.979i	−0.750308	−	1.15381i
$586$	948.830			1.61916
$587$			162.606i			0.277012i	0.990362	+	0.138506i	$0.0442300\pi$
$587$			162.606i			0.277012i	−0.990362	+	0.138506i	$0.955770\pi$
$588$	63.1657	+	213.002i	0.107425	+	0.362248i
$589$	−312.261			−0.530155
$590$			1186.55i			2.01111i
$591$	−385.357	+	114.277i	−0.652042	+	0.193363i
$592$	−3115.67			−5.26295
$593$		−	1045.71i		−	1.76343i	−0.471784	−	0.881714i	$-0.656390\pi$
$593$		−	1045.71i		−	1.76343i	0.471784	−	0.881714i	$-0.343610\pi$
$594$	−844.415	−	719.845i	−1.42157	−	1.21186i
$595$	−68.9834			−0.115938
$596$			665.717i			1.11697i
$597$	−25.0834	−	84.5840i	−0.0420157	−	0.141682i
$598$	−203.895			−0.340961
$599$			47.4017i			0.0791347i	0.999217	+	0.0395673i	$0.0125980\pi$
$599$			47.4017i			0.0791347i	−0.999217	+	0.0395673i	$0.987402\pi$
$600$	−2858.09	+	847.567i	−4.76349	+	1.41261i
$601$	797.136			1.32635			0.663175	−	0.748465i	$-0.269209\pi$
$601$	797.136			1.32635			0.663175	+	0.748465i	$0.269209\pi$
$602$		−	651.871i		−	1.08284i
$603$	−192.801	+	125.376i	−0.319736	+	0.207920i
$604$	1561.04			2.58450
$605$		−	41.4515i		−	0.0685149i
$606$	−213.620	−	720.353i	−0.352509	−	1.18870i
$607$	391.605			0.645149			0.322574	−	0.946544i	$-0.395452\pi$
$607$	391.605			0.645149			0.322574	+	0.946544i	$0.395452\pi$
$608$		−	3092.91i		−	5.08702i
$609$	−146.533	+	43.4542i	−0.240612	+	0.0713534i
$610$	−2100.34			−3.44318
$611$			902.456i			1.47701i
$612$	−168.448	−	259.036i	−0.275242	−	0.423262i
$613$	−47.1721			−0.0769528			−0.0384764	−	0.999260i	$-0.512250\pi$
$613$	−47.1721			−0.0769528			−0.0384764	+	0.999260i	$0.512250\pi$
$614$		−	677.013i		−	1.10263i
$615$	216.311	+	729.426i	0.351725	+	1.18606i
$616$	715.399			1.16136
$617$		−	148.886i		−	0.241306i	−0.992695	−	0.120653i	$-0.961501\pi$
$617$		−	148.886i		−	0.241306i	0.992695	−	0.120653i	$-0.0384989\pi$
$618$	−228.105	+	67.6443i	−0.369101	+	0.109457i
$619$	122.878			0.198510			0.0992549	−	0.995062i	$-0.468354\pi$
$619$	122.878			0.198510			0.0992549	+	0.995062i	$0.468354\pi$
$620$		−	894.260i		−	1.44235i
$621$	−84.0041	+	98.5410i	−0.135272	+	0.158681i
$622$	−887.325			−1.42657
$623$			405.226i			0.650442i
$624$	509.121	+	1716.82i	0.815899	+	2.75131i
$625$	−49.3345			−0.0789352
$626$			64.2091i			0.102570i
$627$	−918.825	+	272.477i	−1.46543	+	0.434573i
$628$	2416.70			3.84825
$629$			188.604i			0.299847i
$630$	612.410	−	398.242i	0.972079	−	0.632130i
$631$	−491.938			−0.779617			−0.389809	−	0.920896i	$-0.627459\pi$
$631$	−491.938			−0.779617			−0.389809	+	0.920896i	$0.627459\pi$
$632$		−	3634.73i		−	5.75116i
$633$	−245.300	−	827.179i	−0.387519	−	1.30676i
$634$	−1649.91			−2.60237
$635$			287.950i			0.453464i
$636$	−320.193	+	94.9532i	−0.503449	+	0.149298i
$637$	−77.9413			−0.122357
$638$			791.353i			1.24036i
$639$	−0.157134	−	0.241638i	−0.000245906	−	0.000378151i
$640$	2279.00			3.56093
$641$			219.296i			0.342116i	0.985261	+	0.171058i	$0.0547185\pi$
$641$			219.296i			0.342116i	−0.985261	+	0.171058i	$0.945282\pi$
$642$	−262.938	−	886.659i	−0.409561	−	1.38109i
$643$	101.633			0.158061			0.0790305	−	0.996872i	$-0.474818\pi$
$643$	101.633			0.158061			0.0790305	+	0.996872i	$0.474818\pi$
$644$		−	134.239i		−	0.208446i
$645$	−1491.15	+	442.199i	−2.31186	+	0.685580i
$646$	−367.781			−0.569321
$647$			664.051i			1.02635i	0.858283	+	0.513177i	$0.171532\pi$
$647$			664.051i			1.02635i	−0.858283	+	0.513177i	$0.828468\pi$
$648$	1860.04	+	825.390i	2.87043	+	1.27375i
$649$	−416.279			−0.641417
$650$		−	1681.63i		−	2.58713i
$651$	23.7410	+	80.0576i	0.0364686	+	0.122976i
$652$	−1366.50			−2.09587
$653$			159.122i			0.243678i	0.992550	+	0.121839i	$0.0388791\pi$
$653$			159.122i			0.243678i	−0.992550	+	0.121839i	$0.961121\pi$
$654$	−361.162	+	107.103i	−0.552236	+	0.163765i
$655$	924.910			1.41208
$656$		−	1692.14i		−	2.57949i
$657$	139.367	−	90.6287i	0.212127	−	0.137943i
$658$	−818.799			−1.24438
$659$		−	565.243i		−	0.857729i	−0.903369	−	0.428865i	$-0.858914\pi$
$659$		−	565.243i		−	0.857729i	0.903369	−	0.428865i	$-0.141086\pi$
$660$	−780.325	−	2631.35i	−1.18231	−	3.98689i
$661$	637.665			0.964697			0.482349	−	0.875979i	$-0.339784\pi$
$661$	637.665			0.964697			0.482349	+	0.875979i	$0.339784\pi$
$662$			2410.39i			3.64107i
$663$	103.926	−	30.8191i	0.156750	−	0.0464843i
$664$	−2967.97			−4.46983
$665$		−	630.948i		−	0.948795i
$666$	−1088.81	−	1674.35i	−1.63485	−	2.51405i
$667$	92.3488			0.138454
$668$		−	1748.56i		−	2.61760i
$669$	−218.580	−	737.077i	−0.326726	−	1.10176i
$670$	−783.941			−1.17006
$671$		−	736.864i		−	1.09816i
$672$	−792.960	+	235.152i	−1.18000	+	0.349929i
$673$	883.968			1.31347			0.656737	−	0.754120i	$-0.271936\pi$
$673$	883.968			1.31347			0.656737	+	0.754120i	$0.271936\pi$
$674$			1768.84i			2.62439i
$675$	−812.723	−	692.829i	−1.20403	−	1.02641i
$676$	476.328			0.704628
$677$			403.341i			0.595776i	0.954601	+	0.297888i	$0.0962823\pi$
$677$			403.341i			0.595776i	−0.954601	+	0.297888i	$0.903718\pi$
$678$	−157.384	−	530.718i	−0.232130	−	0.782769i
$679$	406.178			0.598201
$680$		−	655.034i		−	0.963286i
$681$	157.257	−	46.6344i	0.230920	−	0.0684793i
$682$	432.352			0.633948
$683$		−	23.2612i		−	0.0340573i	−0.999855	−	0.0170287i	$-0.994579\pi$
$683$		−	23.2612i		−	0.0340573i	0.999855	−	0.0170287i	$-0.00542066\pi$
$684$	2369.25	−	1540.69i	3.46381	−	2.25247i
$685$	−1478.55			−2.15846
$686$		−	70.7162i		−	0.103085i
$687$	−38.9737	−	131.424i	−0.0567302	−	0.191301i
$688$	3459.20			5.02791
$689$		−	117.165i		−	0.170050i
$690$	−423.171	+	125.491i	−0.613291	+	0.181871i
$691$	−262.680			−0.380145			−0.190073	−	0.981770i	$-0.560872\pi$
$691$	−262.680			−0.380145			−0.190073	+	0.981770i	$0.560872\pi$
$692$		−	1618.43i		−	2.33877i
$693$	139.715	+	214.852i	0.201609	+	0.310032i
$694$	−404.514			−0.582873
$695$			1930.24i			2.77732i
$696$	−412.621	−	1391.41i	−0.592846	−	1.99915i
$697$	−102.432			−0.146961
$698$			1124.17i			1.61055i
$699$	−602.729	+	178.739i	−0.862273	+	0.255707i
$700$	1107.15			1.58164
$701$			523.480i			0.746762i	0.927678	+	0.373381i	$0.121802\pi$
$701$			523.480i			0.746762i	−0.927678	+	0.373381i	$0.878198\pi$
$702$	−744.694	+	873.564i	−1.06082	+	1.24439i
$703$	−1725.04			−2.45383
$704$			1974.45i			2.80461i
$705$	555.435	+	1872.99i	0.787851	+	2.65673i
$706$	−748.253			−1.05985
$707$			173.542i			0.245462i
$708$	1176.90	−	349.010i	1.66229	−	0.492951i
$709$	−181.361			−0.255798			−0.127899	−	0.991787i	$-0.540823\pi$
$709$	−181.361			−0.255798			−0.127899	+	0.991787i	$0.540823\pi$
$710$		−	0.982516i		−	0.00138383i
$711$	1091.60	−	709.853i	1.53530	−	0.998387i
$712$	−3847.83			−5.40426
$713$		−	50.4544i		−	0.0707635i
$714$	27.9622	+	94.2918i	0.0391627	+	0.132061i
$715$	962.857			1.34665
$716$			2917.51i			4.07474i
$717$	673.254	−	199.653i	0.938988	−	0.278456i
$718$	−2605.09			−3.62826
$719$		−	295.049i		−	0.410360i	−0.978724	−	0.205180i	$-0.934222\pi$
$719$		−	295.049i		−	0.410360i	0.978724	−	0.205180i	$-0.0657779\pi$
$720$	2113.30	+	3249.80i	2.93514	+	4.51361i
$721$	54.9531			0.0762179
$722$		−	1985.46i		−	2.74994i
$723$	96.4042	+	325.086i	0.133339	+	0.449635i
$724$	724.755			1.00104
$725$			761.652i			1.05056i
$726$	−56.6591	+	16.8022i	−0.0780428	+	0.0231436i
$727$	1334.41			1.83551			0.917753	−	0.397151i	$-0.130001\pi$
$727$	1334.41			1.83551			0.917753	+	0.397151i	$0.130001\pi$
$728$		−	740.094i		−	1.01661i
$729$	115.376	+	719.812i	0.158266	+	0.987397i
$730$	566.676			0.776269
$731$		−	209.399i		−	0.286456i
$732$	617.788	+	2083.25i	0.843973	+	2.84597i
$733$	835.725			1.14014			0.570071	−	0.821595i	$-0.306916\pi$
$733$	835.725			1.14014			0.570071	+	0.821595i	$0.306916\pi$
$734$		−	575.568i		−	0.784153i
$735$	−161.762	+	47.9706i	−0.220085	+	0.0652661i
$736$	499.744			0.679000
$737$		−	275.030i		−	0.373176i
$738$	909.354	−	591.341i	1.23219	−	0.801275i
$739$	−554.694			−0.750600			−0.375300	−	0.926903i	$-0.622460\pi$
$739$	−554.694			−0.750600			−0.375300	+	0.926903i	$0.622460\pi$
$740$		−	4940.20i		−	6.67594i
$741$	281.883	+	950.543i	0.380409	+	1.28278i
$742$	106.304			0.143266
$743$		−	671.207i		−	0.903375i	−0.892176	−	0.451687i	$-0.850822\pi$
$743$		−	671.207i		−	0.903375i	0.892176	−	0.451687i	$-0.149178\pi$
$744$	−760.189	+	225.434i	−1.02176	+	0.303003i
$745$	−505.573			−0.678621
$746$		−	1678.01i		−	2.24935i
$747$	−579.635	−	891.353i	−0.775951	−	1.19324i
$748$	369.515			0.494004
$749$			213.607i			0.285189i
$750$	−380.829	−	1284.20i	−0.507772	−	1.71227i
$751$	262.036			0.348916			0.174458	−	0.984665i	$-0.444183\pi$
$751$	262.036			0.348916			0.174458	+	0.984665i	$0.444183\pi$
$752$		−	4345.02i		−	5.77795i
$753$	−736.219	+	218.326i	−0.977715	+	0.289941i
$754$	818.670			1.08577
$755$			1185.52i			1.57022i
$756$	−575.134	−	490.290i	−0.760759	−	0.648531i
$757$	1082.91			1.43052			0.715262	−	0.698856i	$-0.246307\pi$
$757$	1082.91			1.43052			0.715262	+	0.698856i	$0.246307\pi$
$758$			2199.22i			2.90134i
$759$	−44.0261	−	148.461i	−0.0580055	−	0.195601i
$760$	5991.19			7.88315
$761$			90.8649i			0.119402i	0.998216	+	0.0597010i	$0.0190147\pi$
$761$			90.8649i			0.119402i	−0.998216	+	0.0597010i	$0.980985\pi$
$762$	393.592	−	116.719i	0.516524	−	0.153175i
$763$	87.0084			0.114035
$764$			2385.85i			3.12284i
$765$	196.723	−	127.926i	0.257154	−	0.167224i
$766$	−878.348			−1.14667
$767$			430.649i			0.561472i
$768$	−297.904	−	1004.57i	−0.387896	−	1.30803i
$769$	−449.022			−0.583904			−0.291952	−	0.956433i	$-0.594305\pi$
$769$	−449.022			−0.583904			−0.291952	+	0.956433i	$0.594305\pi$
$770$			873.601i			1.13455i
$771$	−595.439	+	176.577i	−0.772294	+	0.229023i
$772$	−1742.08			−2.25659
$773$			1207.20i			1.56171i	0.624710	+	0.780857i	$0.285217\pi$
$773$			1207.20i			1.56171i	−0.624710	+	0.780857i	$0.714783\pi$
$774$	1208.86	+	1858.97i	1.56184	+	2.40177i
$775$	416.126			0.536936
$776$			3856.88i			4.97021i
$777$	131.154	+	442.266i	0.168795	+	0.569196i
$778$	−1151.03			−1.47947
$779$		−	936.882i		−	1.20267i
$780$	−2722.18	+	807.261i	−3.48997	+	1.03495i
$781$	0.344697			0.000441353
$782$		−	59.4251i		−	0.0759912i
$783$	337.290	−	395.658i	0.430766	−	0.505310i
$784$	375.261			0.478649
$785$			1835.34i			2.33802i
$786$	−374.909	−	1264.24i	−0.476984	−	1.60844i
$787$	352.431			0.447816			0.223908	−	0.974610i	$-0.428119\pi$
$787$	352.431			0.447816			0.223908	+	0.974610i	$0.428119\pi$
$788$			1417.46i			1.79881i
$789$	234.254	−	69.4680i	0.296900	−	0.0880456i
$790$	4438.52			5.61837
$791$			127.856i			0.161639i
$792$	−2040.13	+	1326.67i	−2.57593	+	1.67509i
$793$	−762.300			−0.961286
$794$			1397.93i			1.76062i
$795$	−72.1114	−	243.168i	−0.0907061	−	0.305872i
$796$	−311.127			−0.390863
$797$			468.856i			0.588276i	0.955763	+	0.294138i	$0.0950324\pi$
$797$			468.856i			0.588276i	−0.955763	+	0.294138i	$0.904968\pi$
$798$	−862.428	+	255.753i	−1.08074	+	0.320492i
$799$	−263.021			−0.329188
$800$			4121.67i			5.15209i
$801$	−751.471	−	1155.60i	−0.938166	−	1.44270i
$802$	427.273			0.532759
$803$			198.807i			0.247581i
$804$	230.586	+	777.563i	0.286799	+	0.967118i
$805$	101.947			0.126642
$806$		−	447.277i		−	0.554934i
$807$	−484.792	+	143.765i	−0.600734	+	0.178147i
$808$	−1647.87			−2.03944
$809$			578.145i			0.714641i	0.933982	+	0.357320i	$0.116310\pi$
$809$			578.145i			0.714641i	−0.933982	+	0.357320i	$0.883690\pi$
$810$	−1007.92	+	2271.37i	−1.24434	+	2.80416i
$811$	−829.513			−1.02283			−0.511414	−	0.859335i	$-0.670878\pi$
$811$	−829.513			−1.02283			−0.511414	+	0.859335i	$0.670878\pi$
$812$			538.993i			0.663785i
$813$	392.521	+	1323.63i	0.482806	+	1.62808i
$814$	2388.46			2.93423
$815$		−	1037.78i		−	1.27335i
$816$	−500.366	+	148.383i	−0.613194	+	0.181842i
$817$	1915.24			2.34424
$818$			1870.53i			2.28672i
$819$	222.269	−	144.538i	0.271390	−	0.176481i
$820$	2683.06			3.27202
$821$			1031.30i			1.25615i	0.778152	+	0.628076i	$0.216157\pi$
$821$			1031.30i			1.25615i	−0.778152	+	0.628076i	$0.783843\pi$
$822$	599.325	+	2020.99i	0.729105	+	2.45863i
$823$	−657.840			−0.799320			−0.399660	−	0.916664i	$-0.630872\pi$
$823$	−657.840			−0.799320			−0.399660	+	0.916664i	$0.630872\pi$
$824$			521.809i			0.633264i
$825$	1224.44	−	363.109i	1.48417	−	0.440132i
$826$	−390.729			−0.473037
$827$			296.371i			0.358368i	0.983816	+	0.179184i	$0.0573458\pi$
$827$			296.371i			0.358368i	−0.983816	+	0.179184i	$0.942654\pi$
$828$	248.940	+	382.817i	0.300653	+	0.462339i
$829$	694.490			0.837744			0.418872	−	0.908045i	$-0.362426\pi$
$829$	694.490			0.837744			0.418872	+	0.908045i	$0.362426\pi$
$830$		−	3624.30i		−	4.36662i
$831$	−156.293	−	527.037i	−0.188078	−	0.634220i
$832$	2042.60			2.45505
$833$		−	22.7160i		−	0.0272701i
$834$	2638.39	−	782.415i	3.16354	−	0.938148i
$835$	1327.93			1.59033
$836$			3379.73i			4.04274i
$837$	−216.166	−	184.277i	−0.258263	−	0.220164i
$838$	766.283			0.914419
$839$			220.004i			0.262221i	0.991368	+	0.131111i	$0.0418543\pi$
$839$			220.004i			0.262221i	−0.991368	+	0.131111i	$0.958146\pi$
$840$	−455.507	−	1536.02i	−0.542270	−	1.82860i
$841$	470.205			0.559102
$842$		−	2068.27i		−	2.45638i
$843$	146.593	−	43.4721i	0.173894	−	0.0515683i
$844$	−3042.62			−3.60500
$845$			361.743i			0.428099i
$846$	2335.00	−	1518.42i	2.76005	−	1.79483i
$847$	13.6499			0.0161155
$848$			564.108i			0.665221i
$849$	−85.4937	−	288.295i	−0.100699	−	0.339570i
$850$	490.113			0.576603
$851$		−	278.727i		−	0.327529i
$852$	−0.974523	+	0.288994i	−0.00114381	+	0.000339195i
$853$	660.080			0.773834			0.386917	−	0.922115i	$-0.373540\pi$
$853$	660.080			0.773834			0.386917	+	0.922115i	$0.373540\pi$
$854$		−	691.636i		−	0.809878i
$855$	1170.06	+	1799.30i	1.36849	+	2.10445i
$856$	−2028.31			−2.36952
$857$			116.469i			0.135903i	0.997689	+	0.0679517i	$0.0216464\pi$
$857$			116.469i			0.135903i	−0.997689	+	0.0679517i	$0.978354\pi$
$858$	−390.291	−	1316.11i	−0.454885	−	1.53392i
$859$	1471.11			1.71259			0.856293	−	0.516491i	$-0.172762\pi$
$859$	1471.11			1.71259			0.856293	+	0.516491i	$0.172762\pi$
$860$			5484.91i			6.37780i
$861$	−240.198	+	71.2306i	−0.278975	+	0.0827300i
$862$	1465.98			1.70067
$863$		−	1397.87i		−	1.61978i	−0.586581	−	0.809891i	$-0.699526\pi$
$863$		−	1397.87i		−	1.61978i	0.586581	−	0.809891i	$-0.300474\pi$
$864$	1825.24	−	2141.10i	2.11255	−	2.47812i
$865$	1229.10			1.42093
$866$		−	1415.13i		−	1.63410i
$867$	−237.516	−	800.931i	−0.273952	−	0.923796i
$868$	294.477			0.339259
$869$			1557.17i			1.79191i
$870$	1699.10	−	503.868i	1.95299	−	0.579158i
$871$	−284.524			−0.326664
$872$			826.191i			0.947467i
$873$	−1158.32	+	753.238i	−1.32682	+	0.862815i
$874$	543.525			0.621882
$875$			309.379i			0.353576i
$876$	−166.681	−	562.066i	−0.190275	−	0.641628i
$877$	−1456.74			−1.66105			−0.830523	−	0.556984i	$-0.811958\pi$
$877$	−1456.74			−1.66105			−0.830523	+	0.556984i	$0.811958\pi$
$878$			268.746i			0.306089i
$879$	714.718	−	211.949i	0.813104	−	0.241126i
$880$	−4635.83			−5.26799
$881$		−	1386.92i		−	1.57426i	−0.616786	−	0.787131i	$-0.711566\pi$
$881$		−	1386.92i		−	1.57426i	0.616786	−	0.787131i	$-0.288434\pi$
$882$	131.140	+	201.665i	0.148685	+	0.228645i
$883$	596.537			0.675580			0.337790	−	0.941222i	$-0.390321\pi$
$883$	596.537			0.675580			0.337790	+	0.941222i	$0.390321\pi$
$884$		−	382.271i		−	0.432433i
$885$	265.052	+	893.787i	0.299494	+	1.00993i
$886$	−1728.64			−1.95106
$887$		−	84.9721i		−	0.0957972i	−0.998852	−	0.0478986i	$-0.984748\pi$
$887$		−	84.9721i		−	0.0957972i	0.998852	−	0.0478986i	$-0.0152524\pi$
$888$	−4199.55	+	1245.37i	−4.72922	+	1.40245i
$889$	−94.8210			−0.106660
$890$		−	4698.74i		−	5.27948i
$891$	−796.865	−	353.607i	−0.894349	−	0.396866i
$892$	−2711.20			−3.03946
$893$		−	2405.69i		−	2.69394i
$894$	204.932	+	691.055i	0.229231	+	0.772993i
$895$	−2215.68			−2.47562
$896$			750.466i			0.837574i
$897$	−153.586	+	45.5459i	−0.171222	+	0.0507758i
$898$	216.083			0.240626
$899$			202.583i			0.225342i
$900$	−3157.30	+	2053.15i	−3.50812	+	2.28128i
$901$	34.1476			0.0378997
$902$			1297.19i			1.43813i
$903$	−145.615	−	491.030i	−0.161257	−	0.543777i
$904$	−1214.06			−1.34299
$905$			550.408i			0.608186i
$906$	1620.46	−	480.545i	1.78858	−	0.530403i
$907$	−882.149			−0.972601			−0.486300	−	0.873792i	$-0.661654\pi$
$907$	−882.149			−0.972601			−0.486300	+	0.873792i	$0.661654\pi$
$908$		−	578.439i		−	0.637047i
$909$	−321.824	−	494.896i	−0.354042	−	0.544440i
$910$	903.758			0.993141
$911$		−	1196.08i		−	1.31293i	−0.754357	−	0.656464i	$-0.772051\pi$
$911$		−	1196.08i		−	1.31293i	0.754357	−	0.656464i	$-0.227949\pi$
$912$	−1357.17	−	4576.54i	−1.48813	−	5.01814i
$913$	1271.51			1.39268
$914$		−	735.810i		−	0.805044i
$915$	−1582.11	+	469.173i	−1.72908	+	0.512758i
$916$	−483.418			−0.527749
$917$			304.570i			0.332137i
$918$	−254.600	−	217.041i	−0.277342	−	0.236429i
$919$	1033.89			1.12501			0.562506	−	0.826793i	$-0.309837\pi$
$919$	1033.89			1.12501			0.562506	+	0.826793i	$0.309837\pi$
$920$			968.041i			1.05222i
$921$	−151.231	−	509.969i	−0.164203	−	0.553712i
$922$	1005.81			1.09091
$923$		−	0.356596i		−	0.000386344i
$924$	866.494	−	256.959i	0.937764	−	0.278094i
$925$	2298.82			2.48521
$926$			795.908i			0.859512i
$927$	−156.712	+	101.908i	−0.169053	+	0.109933i
$928$	−2006.55			−2.16224
$929$		−	1189.13i		−	1.28001i	−0.768371	−	0.640005i	$-0.778932\pi$
$929$		−	1189.13i		−	1.28001i	0.768371	−	0.640005i	$-0.221068\pi$
$930$	−275.286	−	928.297i	−0.296007	−	0.998169i
$931$	207.769			0.223168
$932$			2217.03i			2.37878i
$933$	−668.389	+	198.210i	−0.716386	+	0.212444i
$934$	−2616.45			−2.80134
$935$			280.625i			0.300134i
$936$	1372.47	+	2110.56i	1.46631	+	2.25487i
$937$	−65.9846			−0.0704212			−0.0352106	−	0.999380i	$-0.511210\pi$
$937$	−65.9846			−0.0704212			−0.0352106	+	0.999380i	$0.511210\pi$
$938$		−	258.149i		−	0.275212i
$939$	14.3430	+	48.3663i	0.0152748	+	0.0515083i
$940$	6889.46			7.32921
$941$			482.472i			0.512723i	0.966581	+	0.256361i	$0.0825237\pi$
$941$			482.472i			0.512723i	−0.966581	+	0.256361i	$0.917476\pi$
$942$	2508.69	−	743.950i	2.66315	−	0.789756i
$943$	151.379			0.160529
$944$		−	2073.43i		−	2.19643i
$945$	372.346	−	436.780i	0.394017	−	0.462202i
$946$	−2651.82			−2.80319
$947$		−	588.553i		−	0.621492i	−0.950493	−	0.310746i	$-0.899421\pi$
$947$		−	588.553i		−	0.621492i	0.950493	−	0.310746i	$-0.100579\pi$
$948$	−1305.53	−	4402.41i	−1.37714	−	4.64389i
$949$	205.670			0.216723
$950$			4482.76i			4.71869i
$951$	−1242.81	+	368.555i	−1.30685	+	0.387545i
$952$	215.701			0.226576
$953$		−	974.710i		−	1.02278i	−0.859349	−	0.511390i	$-0.829131\pi$
$953$		−	974.710i		−	1.02278i	0.859349	−	0.511390i	$-0.170869\pi$
$954$	−303.150	+	197.135i	−0.317768	+	0.206640i
$955$	−1811.91			−1.89729
$956$		−	2476.44i		−	2.59042i
$957$	176.772	+	596.096i	0.184715	+	0.622880i
$958$	−434.033			−0.453061
$959$		−	486.881i		−	0.507697i
$960$	4239.30	−	1257.16i	4.41594	−	1.30954i
$961$	−850.320			−0.884828
$962$		−	2470.91i		−	2.56852i
$963$	−396.123	−	609.152i	−0.411343	−	0.632556i
$964$	1195.77			1.24042
$965$		−	1323.01i		−	1.37100i
$966$	−41.3239	−	139.349i	−0.0427783	−	0.144253i
$967$	640.433			0.662288			0.331144	−	0.943580i	$-0.392565\pi$
$967$	640.433			0.662288			0.331144	+	0.943580i	$0.392565\pi$
$968$			129.613i			0.133897i
$969$	−277.036	+	82.1549i	−0.285899	+	0.0847832i
$970$	−4709.79			−4.85545
$971$		−	548.993i		−	0.565389i	−0.959210	−	0.282695i	$-0.908772\pi$
$971$		−	548.993i		−	0.565389i	0.959210	−	0.282695i	$-0.0912283\pi$
$972$	2549.35	+	331.622i	2.62279	+	0.341175i
$973$	−635.621			−0.653259
$974$			1785.15i			1.83281i
$975$	−375.643	−	1266.71i	−0.385275	−	1.29919i
$976$	3670.22			3.76047
$977$			320.761i			0.328312i	0.986434	+	0.164156i	$0.0524900\pi$
$977$			320.761i			0.328312i	−0.986434	+	0.164156i	$0.947510\pi$
$978$	−1418.52	+	420.661i	−1.45043	+	0.430123i
$979$	1648.46			1.68382
$980$			595.013i			0.607156i
$981$	−248.126	+	161.353i	−0.252931	+	0.164478i
$982$	2386.33			2.43007
$983$		−	661.814i		−	0.673260i	−0.941637	−	0.336630i	$-0.890713\pi$
$983$		−	661.814i		−	0.673260i	0.941637	−	0.336630i	$-0.109287\pi$
$984$	−676.372	−	2280.81i	−0.687370	−	2.31789i
$985$	−1076.48			−1.09287
$986$			238.602i			0.241989i
$987$	−616.771	+	182.903i	−0.624894	+	0.185312i
$988$	3496.39			3.53886
$989$			309.460i			0.312902i
$990$	−1620.05	−	2491.29i	−1.63641	−	2.51645i
$991$	−1251.36			−1.26273			−0.631364	−	0.775487i	$-0.717505\pi$
$991$	−1251.36			−1.26273			−0.631364	+	0.775487i	$0.717505\pi$
$992$			1096.27i			1.10511i
$993$	538.432	+	1815.66i	0.542228	+	1.82846i
$994$	0.323540			0.000325493
$995$		−	236.282i		−	0.237470i
$996$	−3594.81	+	1066.04i	−3.60925	+	1.07032i
$997$	1186.99			1.19056			0.595280	−	0.803518i	$-0.297041\pi$
$997$	1186.99			1.19056			0.595280	+	0.803518i	$0.297041\pi$
$998$			3694.30i			3.70170i
$999$	−1194.18	−	1018.01i	−1.19537	−	1.01903i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	483.3.b.a.323.2	✓	88
3.2	odd	2	inner	483.3.b.a.323.87	yes	88

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
483.3.b.a.323.2	✓	88	1.1	even	1	trivial
483.3.b.a.323.87	yes	88	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:	\( N \)	\(=\)	\( 483 = 3 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	483.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-3.81832i q^{2} +(-0.852935 - 2.87620i) q^{3} -10.5796 q^{4} -8.03455i q^{5} +(-10.9822 + 3.25678i) q^{6} +2.64575 q^{7} +25.1228i q^{8} +(-7.54500 + 4.90642i) q^{9} +O(q^{10})\)	\(q-3.81832i q^{2} +(-0.852935 - 2.87620i) q^{3} -10.5796 q^{4} -8.03455i q^{5} +(-10.9822 + 3.25678i) q^{6} +2.64575 q^{7} +25.1228i q^{8} +(-7.54500 + 4.90642i) q^{9} -30.6785 q^{10} -10.7629i q^{11} +(9.02367 + 30.4289i) q^{12} -11.1345 q^{13} -10.1023i q^{14} +(-23.1089 + 6.85295i) q^{15} +53.6087 q^{16} -3.24515i q^{17} +(18.7343 + 28.8092i) q^{18} +29.6813 q^{19} +85.0019i q^{20} +(-2.25665 - 7.60970i) q^{21} -41.0963 q^{22} +4.79583i q^{23} +(72.2582 - 21.4281i) q^{24} -39.5539 q^{25} +42.5150i q^{26} +(20.5472 + 17.5161i) q^{27} -27.9909 q^{28} -19.2560i q^{29} +(26.1667 + 88.2372i) q^{30} -10.5205 q^{31} -104.204i q^{32} +(-30.9563 + 9.18009i) q^{33} -12.3910 q^{34} -21.2574i q^{35} +(79.8228 - 51.9077i) q^{36} -58.1187 q^{37} -113.333i q^{38} +(9.49698 + 32.0249i) q^{39} +201.850 q^{40} -31.5647i q^{41} +(-29.0562 + 8.61662i) q^{42} +64.5269 q^{43} +113.867i q^{44} +(39.4208 + 60.6207i) q^{45} +18.3120 q^{46} -81.0506i q^{47} +(-45.7247 - 154.189i) q^{48} +7.00000 q^{49} +151.030i q^{50} +(-9.33367 + 2.76790i) q^{51} +117.798 q^{52} +10.5227i q^{53} +(66.8819 - 78.4558i) q^{54} -86.4753 q^{55} +66.4687i q^{56} +(-25.3162 - 85.3693i) q^{57} -73.5257 q^{58} -38.6771i q^{59} +(244.482 - 72.5011i) q^{60} +68.4630 q^{61} +40.1705i q^{62} +(-19.9622 + 12.9812i) q^{63} -183.449 q^{64} +89.4604i q^{65} +(35.0525 + 118.201i) q^{66} +25.5535 q^{67} +34.3322i q^{68} +(13.7938 - 4.09053i) q^{69} -81.1676 q^{70} +0.0320263i q^{71} +(-123.263 - 189.552i) q^{72} -18.4715 q^{73} +221.916i q^{74} +(33.7369 + 113.765i) q^{75} -314.015 q^{76} -28.4761i q^{77} +(122.281 - 36.2625i) q^{78} -144.679 q^{79} -430.722i q^{80} +(32.8542 - 74.0378i) q^{81} -120.524 q^{82} +118.138i q^{83} +(23.8744 + 80.5072i) q^{84} -26.0733 q^{85} -246.384i q^{86} +(-55.3842 + 16.4242i) q^{87} +270.395 q^{88} +153.161i q^{89} +(231.469 - 150.521i) q^{90} -29.4590 q^{91} -50.7378i q^{92} +(8.97327 + 30.2589i) q^{93} -309.477 q^{94} -238.476i q^{95} +(-299.711 + 88.8791i) q^{96} +153.521 q^{97} -26.7282i q^{98} +(52.8074 + 81.2064i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 88 q + 8 q^{3} - 176 q^{4} - 22 q^{6} + 20 q^{9}+O(q^{10}) \) 88 * q + 8 * q^3 - 176 * q^4 - 22 * q^6 + 20 * q^9	\( 88 q + 8 q^{3} - 176 q^{4} - 22 q^{6} + 20 q^{9} - 16 q^{10} - 18 q^{12} + 64 q^{13} + 20 q^{15} + 272 q^{16} - 38 q^{18} - 48 q^{19} - 28 q^{21} + 208 q^{22} + 228 q^{24} - 568 q^{25} - 88 q^{27} - 8 q^{30} + 8 q^{31} - 160 q^{33} - 32 q^{34} - 138 q^{36} - 136 q^{37} + 76 q^{39} - 48 q^{40} - 140 q^{42} + 424 q^{43} + 172 q^{45} + 334 q^{48} + 616 q^{49} + 288 q^{51} - 140 q^{52} - 240 q^{55} - 252 q^{57} - 380 q^{58} - 364 q^{60} + 312 q^{61} - 252 q^{64} + 44 q^{66} - 224 q^{67} + 168 q^{70} - 592 q^{72} + 216 q^{73} - 284 q^{75} + 328 q^{76} + 470 q^{78} - 8 q^{79} + 380 q^{81} - 548 q^{82} + 224 q^{84} - 712 q^{85} + 56 q^{87} - 896 q^{88} + 1136 q^{90} + 168 q^{91} - 236 q^{93} - 252 q^{94} - 546 q^{96} + 480 q^{97} - 248 q^{99}+O(q^{100}) \) 88 * q + 8 * q^3 - 176 * q^4 - 22 * q^6 + 20 * q^9 - 16 * q^10 - 18 * q^12 + 64 * q^13 + 20 * q^15 + 272 * q^16 - 38 * q^18 - 48 * q^19 - 28 * q^21 + 208 * q^22 + 228 * q^24 - 568 * q^25 - 88 * q^27 - 8 * q^30 + 8 * q^31 - 160 * q^33 - 32 * q^34 - 138 * q^36 - 136 * q^37 + 76 * q^39 - 48 * q^40 - 140 * q^42 + 424 * q^43 + 172 * q^45 + 334 * q^48 + 616 * q^49 + 288 * q^51 - 140 * q^52 - 240 * q^55 - 252 * q^57 - 380 * q^58 - 364 * q^60 + 312 * q^61 - 252 * q^64 + 44 * q^66 - 224 * q^67 + 168 * q^70 - 592 * q^72 + 216 * q^73 - 284 * q^75 + 328 * q^76 + 470 * q^78 - 8 * q^79 + 380 * q^81 - 548 * q^82 + 224 * q^84 - 712 * q^85 + 56 * q^87 - 896 * q^88 + 1136 * q^90 + 168 * q^91 - 236 * q^93 - 252 * q^94 - 546 * q^96 + 480 * q^97 - 248 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more