LMFDB - Embedded newform 483.3.b.a.323.6

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [483,3,Mod(323,483)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://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);

sage: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")

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:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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			323.6
Character	$\chi$	$=$	483.323
Dual form			483.3.b.a.323.83

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-3.53262i q^{2} +(-2.99242 + 0.213088i) q^{3} -8.47941 q^{4} -4.02890i q^{5} +(0.752759 + 10.5711i) q^{6} +2.64575 q^{7} +15.8240i q^{8} +(8.90919 - 1.27530i) q^{9} -14.2326 q^{10} +19.1190i q^{11} +(25.3740 - 1.80686i) q^{12} +11.8293 q^{13} -9.34643i q^{14} +(0.858512 + 12.0562i) q^{15} +21.9827 q^{16} +18.7454i q^{17} +(-4.50515 - 31.4728i) q^{18} +11.4507 q^{19} +34.1627i q^{20} +(-7.91721 + 0.563778i) q^{21} +67.5401 q^{22} -4.79583i q^{23} +(-3.37191 - 47.3522i) q^{24} +8.76793 q^{25} -41.7885i q^{26} +(-26.3883 + 5.71468i) q^{27} -22.4344 q^{28} +17.9980i q^{29} +(42.5899 - 3.03280i) q^{30} +6.53921 q^{31} -14.3604i q^{32} +(-4.07403 - 57.2121i) q^{33} +66.2205 q^{34} -10.6595i q^{35} +(-75.5446 + 10.8138i) q^{36} +8.26062 q^{37} -40.4510i q^{38} +(-35.3983 + 2.52068i) q^{39} +63.7536 q^{40} +13.1900i q^{41} +(1.99161 + 27.9685i) q^{42} -71.8906 q^{43} -162.118i q^{44} +(-5.13806 - 35.8943i) q^{45} -16.9419 q^{46} -17.3156i q^{47} +(-65.7816 + 4.68425i) q^{48} +7.00000 q^{49} -30.9738i q^{50} +(-3.99443 - 56.0943i) q^{51} -100.306 q^{52} -67.9200i q^{53} +(20.1878 + 93.2199i) q^{54} +77.0286 q^{55} +41.8665i q^{56} +(-34.2654 + 2.44001i) q^{57} +63.5801 q^{58} +99.5740i q^{59} +(-7.27967 - 102.229i) q^{60} +61.2454 q^{61} -23.1005i q^{62} +(23.5715 - 3.37412i) q^{63} +37.2010 q^{64} -47.6592i q^{65} +(-202.109 + 14.3920i) q^{66} +22.1740 q^{67} -158.950i q^{68} +(1.02193 + 14.3512i) q^{69} -37.6559 q^{70} -11.4688i q^{71} +(20.1804 + 140.979i) q^{72} +74.4034 q^{73} -29.1817i q^{74} +(-26.2373 + 1.86834i) q^{75} -97.0952 q^{76} +50.5841i q^{77} +(8.90462 + 125.049i) q^{78} -67.7335 q^{79} -88.5662i q^{80} +(77.7472 - 22.7238i) q^{81} +46.5953 q^{82} +36.0585i q^{83} +(67.1332 - 4.78050i) q^{84} +75.5236 q^{85} +253.962i q^{86} +(-3.83516 - 53.8576i) q^{87} -302.540 q^{88} +92.5832i q^{89} +(-126.801 + 18.1508i) q^{90} +31.2974 q^{91} +40.6658i q^{92} +(-19.5681 + 1.39343i) q^{93} -61.1695 q^{94} -46.1338i q^{95} +(3.06003 + 42.9724i) q^{96} +131.058 q^{97} -24.7283i q^{98} +(24.3824 + 170.335i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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}+ \cdots - 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

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 $

$2$		−	3.53262i		−	1.76631i	−0.469081	−	0.883155i	$-0.655415\pi$
$2$		−	3.53262i		−	1.76631i	0.469081	−	0.883155i	$-0.344585\pi$
$3$	−2.99242	+	0.213088i	−0.997474	+	0.0710294i
$3$	−2.99242	+	0.213088i	−0.997474	+	0.0710294i
$4$	−8.47941			−2.11985
$5$		−	4.02890i		−	0.805781i	−0.915248	−	0.402890i	$-0.868006\pi$
$5$		−	4.02890i		−	0.805781i	0.915248	−	0.402890i	$-0.131994\pi$
$6$	0.752759	+	10.5711i	0.125460	+	1.76185i
$7$	2.64575			0.377964
$7$	2.64575			0.377964
$8$			15.8240i			1.97801i
$9$	8.90919	−	1.27530i	0.989910	−	0.141700i
$10$	−14.2326			−1.42326
$11$			19.1190i			1.73809i	0.494733	+	0.869045i	$0.335266\pi$
$11$			19.1190i			1.73809i	−0.494733	+	0.869045i	$0.664734\pi$
$12$	25.3740	−	1.80686i	2.11450	−	0.150572i
$13$	11.8293			0.909947			0.454973	−	0.890505i	$-0.349649\pi$
$13$	11.8293			0.909947			0.454973	+	0.890505i	$0.349649\pi$
$14$		−	9.34643i		−	0.667602i
$15$	0.858512	+	12.0562i	0.0572341	+	0.803746i
$16$	21.9827			1.37392
$17$			18.7454i			1.10267i	0.834283	+	0.551336i	$0.185882\pi$
$17$			18.7454i			1.10267i	−0.834283	+	0.551336i	$0.814118\pi$
$18$	−4.50515	−	31.4728i	−0.250286	−	1.74849i
$19$	11.4507			0.602669			0.301334	−	0.953518i	$-0.402568\pi$
$19$	11.4507			0.602669			0.301334	+	0.953518i	$0.402568\pi$
$20$			34.1627i			1.70814i
$21$	−7.91721	+	0.563778i	−0.377010	+	0.0268466i
$22$	67.5401			3.07001
$23$		−	4.79583i		−	0.208514i
$23$		−	4.79583i		−	0.208514i
$24$	−3.37191	−	47.3522i	−0.140496	−	1.97301i
$25$	8.76793			0.350717
$26$		−	41.7885i		−	1.60725i
$27$	−26.3883	+	5.71468i	−0.977345	+	0.211655i
$28$	−22.4344			−0.801229
$29$			17.9980i			0.620620i	0.950635	+	0.310310i	$0.100433\pi$
$29$			17.9980i			0.620620i	−0.950635	+	0.310310i	$0.899567\pi$
$30$	42.5899	−	3.03280i	1.41966	−	0.101093i
$31$	6.53921			0.210942			0.105471	−	0.994422i	$-0.466365\pi$
$31$	6.53921			0.210942			0.105471	+	0.994422i	$0.466365\pi$
$32$		−	14.3604i		−	0.448762i
$33$	−4.07403	−	57.2121i	−0.123455	−	1.73370i
$34$	66.2205			1.94766
$35$		−	10.6595i		−	0.304557i
$36$	−75.5446	+	10.8138i	−2.09846	+	0.300383i
$37$	8.26062			0.223260			0.111630	−	0.993750i	$-0.464393\pi$
$37$	8.26062			0.223260			0.111630	+	0.993750i	$0.464393\pi$
$38$		−	40.4510i		−	1.06450i
$39$	−35.3983	+	2.52068i	−0.907649	+	0.0646329i
$40$	63.7536			1.59384
$41$			13.1900i			0.321707i	0.986978	+	0.160854i	$0.0514247\pi$
$41$			13.1900i			0.321707i	−0.986978	+	0.160854i	$0.948575\pi$
$42$	1.99161	+	27.9685i	0.0474194	+	0.665916i
$43$	−71.8906			−1.67187			−0.835937	−	0.548826i	$-0.815075\pi$
$43$	−71.8906			−1.67187			−0.835937	+	0.548826i	$0.815075\pi$
$44$		−	162.118i		−	3.68449i
$45$	−5.13806	−	35.8943i	−0.114179	−	0.797650i
$46$	−16.9419			−0.368301
$47$		−	17.3156i		−	0.368417i	−0.982887	−	0.184209i	$-0.941028\pi$
$47$		−	17.3156i		−	0.368417i	0.982887	−	0.184209i	$-0.0589722\pi$
$48$	−65.7816	+	4.68425i	−1.37045	+	0.0975886i
$49$	7.00000			0.142857
$50$		−	30.9738i		−	0.619475i
$51$	−3.99443	−	56.0943i	−0.0783221	−	1.09989i
$52$	−100.306			−1.92895
$53$		−	67.9200i		−	1.28151i	−0.767745	−	0.640755i	$-0.778621\pi$
$53$		−	67.9200i		−	1.28151i	0.767745	−	0.640755i	$-0.221379\pi$
$54$	20.1878	+	93.2199i	0.373848	+	1.72629i
$55$	77.0286			1.40052
$56$			41.8665i			0.747616i
$57$	−34.2654	+	2.44001i	−0.601147	+	0.0428072i
$58$	63.5801			1.09621
$59$			99.5740i			1.68769i	0.536584	+	0.843847i	$0.319715\pi$
$59$			99.5740i			1.68769i	−0.536584	+	0.843847i	$0.680285\pi$
$60$	−7.27967	−	102.229i	−0.121328	−	1.70382i
$61$	61.2454			1.00402			0.502011	−	0.864861i	$-0.332594\pi$
$61$	61.2454			1.00402			0.502011	+	0.864861i	$0.332594\pi$
$62$		−	23.1005i		−	0.372589i
$63$	23.5715	−	3.37412i	0.374151	−	0.0535575i
$64$	37.2010			0.581266
$65$		−	47.6592i		−	0.733218i
$66$	−202.109	+	14.3920i	−3.06225	+	0.218061i
$67$	22.1740			0.330955			0.165477	−	0.986214i	$-0.447084\pi$
$67$	22.1740			0.330955			0.165477	+	0.986214i	$0.447084\pi$
$68$		−	158.950i		−	2.33750i
$69$	1.02193	+	14.3512i	0.0148106	+	0.207988i
$70$	−37.6559			−0.537941
$71$		−	11.4688i		−	0.161532i	−0.996733	−	0.0807661i	$-0.974263\pi$
$71$		−	11.4688i		−	0.161532i	0.996733	−	0.0807661i	$-0.0257367\pi$
$72$	20.1804	+	140.979i	0.280283	+	1.95805i
$73$	74.4034			1.01922			0.509612	−	0.860404i	$-0.329789\pi$
$73$	74.4034			1.01922			0.509612	+	0.860404i	$0.329789\pi$
$74$		−	29.1817i		−	0.394347i
$75$	−26.2373	+	1.86834i	−0.349831	+	0.0249112i
$76$	−97.0952			−1.27757
$77$			50.5841i			0.656936i
$78$	8.90462	+	125.049i	0.114162	+	1.60319i
$79$	−67.7335			−0.857386			−0.428693	−	0.903450i	$-0.641026\pi$
$79$	−67.7335			−0.857386			−0.428693	+	0.903450i	$0.641026\pi$
$80$		−	88.5662i		−	1.10708i
$81$	77.7472	−	22.7238i	0.959842	−	0.280540i
$82$	46.5953			0.568235
$83$			36.0585i			0.434440i	0.976123	+	0.217220i	$0.0696988\pi$
$83$			36.0585i			0.434440i	−0.976123	+	0.217220i	$0.930301\pi$
$84$	67.1332	−	4.78050i	0.799205	−	0.0569107i
$85$	75.5236			0.888513
$86$			253.962i			2.95305i
$87$	−3.83516	−	53.8576i	−0.0440823	−	0.619053i
$88$	−302.540			−3.43795
$89$			92.5832i			1.04026i	0.854087	+	0.520130i	$0.174117\pi$
$89$			92.5832i			1.04026i	−0.854087	+	0.520130i	$0.825883\pi$
$90$	−126.801	+	18.1508i	−1.40890	+	0.201676i
$91$	31.2974			0.343928
$92$			40.6658i			0.442020i
$93$	−19.5681	+	1.39343i	−0.210409	+	0.0149831i
$94$	−61.1695			−0.650740
$95$		−	46.1338i		−	0.485619i
$96$	3.06003	+	42.9724i	0.0318753	+	0.447629i
$97$	131.058			1.35112			0.675558	−	0.737307i	$-0.263903\pi$
$97$	131.058			1.35112			0.675558	+	0.737307i	$0.263903\pi$
$98$		−	24.7283i		−	0.252330i
$99$	24.3824	+	170.335i	0.246287	+	1.72055i
$100$	−74.3468			−0.743468
$101$			81.8925i			0.810817i	0.914136	+	0.405408i	$0.132871\pi$
$101$			81.8925i			0.810817i	−0.914136	+	0.405408i	$0.867129\pi$
$102$	−198.160	+	14.1108i	−1.94274	+	0.138341i
$103$	110.294			1.07081			0.535407	−	0.844594i	$-0.320158\pi$
$103$	110.294			1.07081			0.535407	+	0.844594i	$0.320158\pi$
$104$			187.188i			1.79988i
$105$	2.27141	+	31.8977i	0.0216325	+	0.303787i
$106$	−239.936			−2.26354
$107$			208.721i			1.95066i	0.220747	+	0.975331i	$0.429151\pi$
$107$			208.721i			1.95066i	−0.220747	+	0.975331i	$0.570849\pi$
$108$	223.757	−	48.4571i	2.07183	−	0.448676i
$109$	141.688			1.29989			0.649944	−	0.759982i	$-0.274792\pi$
$109$	141.688			1.29989			0.649944	+	0.759982i	$0.274792\pi$
$110$		−	272.113i		−	2.47375i
$111$	−24.7193	+	1.76024i	−0.222696	+	0.0158580i
$112$	58.1608			0.519293
$113$		−	108.116i		−	0.956780i	−0.878147	−	0.478390i	$-0.841221\pi$
$113$		−	108.116i		−	0.956780i	0.878147	−	0.478390i	$-0.158779\pi$
$114$	8.61963	+	121.047i	0.0756108	+	1.06181i
$115$	−19.3219			−0.168017
$116$		−	152.612i		−	1.31562i
$117$	105.390	−	15.0859i	0.900765	−	0.128939i
$118$	351.757			2.98099
$119$			49.5958i			0.416771i
$120$	−190.778	+	13.5851i	−1.58981	+	0.113209i
$121$	−244.536			−2.02096
$122$		−	216.357i		−	1.77342i
$123$	−2.81063	−	39.4701i	−0.0228507	−	0.320895i
$124$	−55.4486			−0.447166
$125$		−	136.048i		−	1.08838i
$126$	−11.9195	−	83.2691i	−0.0945992	−	0.660866i
$127$	−240.921			−1.89702			−0.948509	−	0.316750i	$-0.897408\pi$
$127$	−240.921			−1.89702			−0.948509	+	0.316750i	$0.897408\pi$
$128$		−	188.859i		−	1.47546i
$129$	215.127	−	15.3190i	1.66765	−	0.118752i
$130$	−168.362			−1.29509
$131$		−	163.435i		−	1.24759i	−0.781587	−	0.623796i	$-0.785590\pi$
$131$		−	163.435i		−	1.24759i	0.781587	−	0.623796i	$-0.214410\pi$
$132$	34.5453	+	485.125i	0.261707	+	3.67519i
$133$	30.2957			0.227787
$134$		−	78.3322i		−	0.584569i
$135$	23.0239	+	106.316i	0.170547	+	0.787526i
$136$	−296.629			−2.18109
$137$		−	98.9892i		−	0.722549i	−0.932460	−	0.361274i	$-0.882342\pi$
$137$		−	98.9892i		−	0.722549i	0.932460	−	0.361274i	$-0.117658\pi$
$138$	50.6972	−	3.61011i	0.367371	−	0.0261602i
$139$	97.6190			0.702295			0.351147	−	0.936320i	$-0.385792\pi$
$139$	97.6190			0.702295			0.351147	+	0.936320i	$0.385792\pi$
$140$			90.3861i			0.645615i
$141$	3.68975	+	51.8157i	0.0261685	+	0.367487i
$142$	−40.5149			−0.285316
$143$			226.165i			1.58157i
$144$	195.848	−	28.0345i	1.36006	−	0.194684i
$145$	72.5122			0.500084
$146$		−	262.839i		−	1.80027i
$147$	−20.9470	+	1.49162i	−0.142496	+	0.0101471i
$148$	−70.0452			−0.473278
$149$			10.6067i			0.0711857i	0.999366	+	0.0355928i	$0.0113319\pi$
$149$			10.6067i			0.0711857i	−0.999366	+	0.0355928i	$0.988668\pi$
$150$	6.60014	+	92.6866i	0.0440009	+	0.617910i
$151$	98.0283			0.649194			0.324597	−	0.945852i	$-0.394771\pi$
$151$	98.0283			0.649194			0.324597	+	0.945852i	$0.394771\pi$
$152$			181.197i			1.19208i
$153$	23.9060	+	167.007i	0.156249	+	1.09155i
$154$	178.694			1.16035
$155$		−	26.3458i		−	0.169973i
$156$	300.157	−	21.3739i	1.92408	−	0.137012i
$157$	117.437			0.748006			0.374003	−	0.927427i	$-0.377985\pi$
$157$	117.437			0.748006			0.374003	+	0.927427i	$0.377985\pi$
$158$			239.277i			1.51441i
$159$	14.4729	+	203.245i	0.0910248	+	1.27827i
$160$	−57.8567			−0.361604
$161$		−	12.6886i		−	0.0788110i
$162$	−80.2744	−	274.651i	−0.495521	−	1.69538i
$163$	248.466			1.52433			0.762167	−	0.647381i	$-0.224136\pi$
$163$	248.466			1.52433			0.762167	+	0.647381i	$0.224136\pi$
$164$		−	111.843i		−	0.681972i
$165$	−230.502	+	16.4139i	−1.39698	+	0.0994780i
$166$	127.381			0.767355
$167$		−	54.8343i		−	0.328349i	−0.986431	−	0.164175i	$-0.947504\pi$
$167$		−	54.8343i		−	0.328349i	0.986431	−	0.164175i	$-0.0524961\pi$
$168$	−8.92125	−	125.282i	−0.0531027	−	0.745727i
$169$	−29.0674			−0.171996
$170$		−	266.796i		−	1.56939i
$171$	102.017	−	14.6031i	0.596588	−	0.0853981i
$172$	609.589			3.54412
$173$		−	21.4679i		−	0.124092i	−0.998073	−	0.0620459i	$-0.980237\pi$
$173$		−	21.4679i		−	0.124092i	0.998073	−	0.0620459i	$-0.0197625\pi$
$174$	−190.258	+	13.5482i	−1.09344	+	0.0778630i
$175$	23.1978			0.132559
$176$			420.287i			2.38800i
$177$	−21.2180	−	297.967i	−0.119876	−	1.68343i
$178$	327.061			1.83742
$179$			171.511i			0.958165i	0.877770	+	0.479082i	$0.159030\pi$
$179$			171.511i			0.958165i	−0.877770	+	0.479082i	$0.840970\pi$
$180$	43.5677	+	304.362i	0.242043	+	1.69090i
$181$	−80.5864			−0.445229			−0.222614	−	0.974907i	$-0.571459\pi$
$181$	−80.5864			−0.445229			−0.222614	+	0.974907i	$0.571459\pi$
$182$		−	110.562i		−	0.607483i
$183$	−183.272	+	13.0507i	−1.00149	+	0.0713151i
$184$	75.8894			0.412443
$185$		−	33.2813i		−	0.179899i
$186$	4.92245	+	69.1266i	0.0264648	+	0.371648i
$187$	−358.394			−1.91654
$188$			146.826i			0.780990i
$189$	−69.8169	+	15.1196i	−0.369402	+	0.0799979i
$190$	−162.973			−0.857754
$191$			153.269i			0.802457i	0.915978	+	0.401229i	$0.131417\pi$
$191$			153.269i			0.802457i	−0.915978	+	0.401229i	$0.868583\pi$
$192$	−111.321	+	7.92709i	−0.579798	+	0.0412869i
$193$	−214.106			−1.10936			−0.554678	−	0.832065i	$-0.687158\pi$
$193$	−214.106			−1.10936			−0.554678	+	0.832065i	$0.687158\pi$
$194$		−	462.979i		−	2.38649i
$195$	10.1556	+	142.616i	0.0520800	+	0.731366i
$196$	−59.3558			−0.302836
$197$			44.9020i			0.227929i	0.993485	+	0.113964i	$0.0363550\pi$
$197$			44.9020i			0.227929i	−0.993485	+	0.113964i	$0.963645\pi$
$198$	601.728	−	86.1339i	3.03903	−	0.435020i
$199$	258.244			1.29771			0.648853	−	0.760914i	$-0.275249\pi$
$199$	258.244			1.29771			0.648853	+	0.760914i	$0.275249\pi$
$200$			138.744i			0.693720i
$201$	−66.3539	+	4.72501i	−0.330119	+	0.0235075i
$202$	289.295			1.43215
$203$			47.6182i			0.234572i
$204$	33.8704	+	475.646i	0.166031	+	2.33160i
$205$	53.1413			0.259226
$206$		−	389.627i		−	1.89139i
$207$	−6.11612	−	42.7270i	−0.0295465	−	0.206410i
$208$	260.040			1.25019
$209$			218.926i			1.04749i
$210$	112.682	−	8.02402i	0.536583	−	0.0382096i
$211$	−329.655			−1.56235			−0.781173	−	0.624314i	$-0.785378\pi$
$211$	−329.655			−1.56235			−0.781173	+	0.624314i	$0.785378\pi$
$212$			575.922i			2.71661i
$213$	2.44386	+	34.3195i	0.0114735	+	0.161124i
$214$	737.332			3.44547
$215$			289.640i			1.34716i
$216$	−90.4293	−	417.570i	−0.418654	−	1.93319i
$217$	17.3011			0.0797286
$218$		−	500.530i		−	2.29601i
$219$	−222.646	+	15.8545i	−1.01665	+	0.0723948i
$220$	−653.157			−2.96889
$221$			221.746i			1.00337i
$222$	6.21826	+	87.3238i	0.0280102	+	0.393351i
$223$	291.706			1.30810			0.654050	−	0.756451i	$-0.273068\pi$
$223$	291.706			1.30810			0.654050	+	0.756451i	$0.273068\pi$
$224$		−	37.9940i		−	0.169616i
$225$	78.1151	−	11.1817i	0.347178	−	0.0496966i
$226$	−381.933			−1.68997
$227$		−	226.253i		−	0.996710i	−0.866973	−	0.498355i	$-0.833938\pi$
$227$		−	226.253i		−	0.996710i	0.866973	−	0.498355i	$-0.166062\pi$
$228$	290.550	−	20.6898i	1.27434	−	0.0907449i
$229$	−123.412			−0.538916			−0.269458	−	0.963012i	$-0.586844\pi$
$229$	−123.412			−0.538916			−0.269458	+	0.963012i	$0.586844\pi$
$230$			68.2571i			0.296770i
$231$	−10.7789	−	151.369i	−0.0466618	−	0.655277i
$232$	−284.801			−1.22759
$233$			82.4569i			0.353892i	0.984221	+	0.176946i	$0.0566219\pi$
$233$			82.4569i			0.353892i	−0.984221	+	0.176946i	$0.943378\pi$
$234$	−53.2928	−	372.301i	−0.227747	−	1.59103i
$235$	−69.7630			−0.296864
$236$		−	844.328i		−	3.57766i
$237$	202.687	−	14.4332i	0.855220	−	0.0608996i
$238$	175.203			0.736147
$239$		−	374.417i		−	1.56660i	−0.621644	−	0.783300i	$-0.713535\pi$
$239$		−	374.417i		−	1.56660i	0.621644	−	0.783300i	$-0.286465\pi$
$240$	18.8724	+	265.028i	0.0786350	+	1.10428i
$241$	−414.826			−1.72127			−0.860636	−	0.509221i	$-0.829933\pi$
$241$	−414.826			−1.72127			−0.860636	+	0.509221i	$0.829933\pi$
$242$			863.852i			3.56964i
$243$	−227.810	+	84.5661i	−0.937491	+	0.348009i
$244$	−519.325			−2.12838
$245$		−	28.2023i		−	0.115112i
$246$	−139.433	+	9.92890i	−0.566800	+	0.0403614i
$247$	135.454			0.548397
$248$			103.477i			0.417245i
$249$	−7.68363	−	107.902i	−0.0308580	−	0.433342i
$250$	−480.605			−1.92242
$251$			329.304i			1.31197i	0.754775	+	0.655984i	$0.227746\pi$
$251$			329.304i			1.31197i	−0.754775	+	0.655984i	$0.772254\pi$
$252$	−199.872	+	28.6106i	−0.793144	+	0.113534i
$253$	91.6915			0.362417
$254$			851.084i			3.35072i
$255$	−225.998	+	16.0932i	−0.886269	+	0.0631105i
$256$	−518.362			−2.02485
$257$			281.326i			1.09465i	0.836919	+	0.547327i	$0.184355\pi$
$257$			281.326i			1.09465i	−0.836919	+	0.547327i	$0.815645\pi$
$258$	−54.1163	−	759.962i	−0.209753	−	2.94559i
$259$	21.8556			0.0843844
$260$			404.121i			1.55431i
$261$	22.9528	+	160.347i	0.0879418	+	0.614358i
$262$	−577.352			−2.20364
$263$		−	23.3223i		−	0.0886778i	−0.999017	−	0.0443389i	$-0.985882\pi$
$263$		−	23.3223i		−	0.0886778i	0.999017	−	0.0443389i	$-0.0141181\pi$
$264$	905.327	−	64.4676i	3.42927	−	0.244195i
$265$	−273.643			−1.03262
$266$		−	107.023i		−	0.402343i
$267$	−19.7284	−	277.048i	−0.0738890	−	1.03763i
$268$	−188.022			−0.701575
$269$		−	372.758i		−	1.38572i	−0.721073	−	0.692859i	$-0.756351\pi$
$269$		−	372.758i		−	1.38572i	0.721073	−	0.692859i	$-0.243649\pi$
$270$	375.574	−	81.3346i	1.39101	−	0.301239i
$271$	306.651			1.13155			0.565776	−	0.824559i	$-0.308577\pi$
$271$	306.651			1.13155			0.565776	+	0.824559i	$0.308577\pi$
$272$			412.075i			1.51498i
$273$	−93.6551	+	6.66911i	−0.343059	+	0.0244290i
$274$	−349.691			−1.27625
$275$			167.634i			0.609578i
$276$	−8.66540	−	121.689i	−0.0313964	−	0.440903i
$277$	−394.189			−1.42307			−0.711533	−	0.702653i	$-0.751999\pi$
$277$	−394.189			−1.42307			−0.711533	+	0.702653i	$0.751999\pi$
$278$		−	344.851i		−	1.24047i
$279$	58.2590	−	8.33944i	0.208814	−	0.0298905i
$280$	168.676			0.602415
$281$		−	39.9000i		−	0.141993i	−0.997477	−	0.0709965i	$-0.977382\pi$
$281$		−	39.9000i		−	0.141993i	0.997477	−	0.0709965i	$-0.0226179\pi$
$282$	183.045	−	13.0345i	0.649096	−	0.0462216i
$283$	−63.2529			−0.223508			−0.111754	−	0.993736i	$-0.535647\pi$
$283$	−63.2529			−0.223508			−0.111754	+	0.993736i	$0.535647\pi$
$284$			97.2485i			0.342424i
$285$	9.83057	+	138.052i	0.0344932	+	0.484393i
$286$	798.953			2.79354
$287$			34.8975i			0.121594i
$288$	−18.3138	−	127.939i	−0.0635896	−	0.444234i
$289$	−62.3914			−0.215887
$290$		−	256.158i		−	0.883304i
$291$	−392.182	+	27.9270i	−1.34770	+	0.0959689i
$292$	−630.896			−2.16060
$293$			268.174i			0.915270i	0.889140	+	0.457635i	$0.151303\pi$
$293$			268.174i			0.915270i	−0.889140	+	0.457635i	$0.848697\pi$
$294$	5.26931	+	73.9977i	0.0179228	+	0.251693i
$295$	401.174			1.35991
$296$			130.716i			0.441610i
$297$	−109.259	−	504.518i	−0.367875	−	1.69871i
$298$	37.4693			0.125736
$299$		−	56.7314i		−	0.189737i
$300$	222.477	−	15.8424i	0.741590	−	0.0528081i
$301$	−190.205			−0.631909
$302$		−	346.297i		−	1.14668i
$303$	−17.4503	−	245.057i	−0.0575918	−	0.808769i
$304$	251.718			0.828019
$305$		−	246.752i		−	0.809022i
$306$	589.971	−	84.4510i	1.92801	−	0.275984i
$307$	360.148			1.17312			0.586560	−	0.809906i	$-0.300482\pi$
$307$	360.148			1.17312			0.586560	+	0.809906i	$0.300482\pi$
$308$		−	428.923i		−	1.39261i
$309$	−330.046	+	23.5023i	−1.06811	+	0.0760593i
$310$	−93.0699			−0.300225
$311$			549.283i			1.76618i	0.469201	+	0.883091i	$0.344542\pi$
$311$			549.283i			1.76618i	−0.469201	+	0.883091i	$0.655458\pi$
$312$	−39.8874	−	560.144i	−0.127844	−	1.79533i
$313$	−568.140			−1.81514			−0.907571	−	0.419898i	$-0.862066\pi$
$313$	−568.140			−1.81514			−0.907571	+	0.419898i	$0.862066\pi$
$314$		−	414.860i		−	1.32121i
$315$	−13.5940	−	94.9673i	−0.0431556	−	0.301484i
$316$	574.340			1.81753
$317$		−	414.543i		−	1.30771i	−0.756621	−	0.653854i	$-0.773151\pi$
$317$		−	414.543i		−	1.30771i	0.756621	−	0.653854i	$-0.226849\pi$
$318$	717.989	−	51.1274i	2.25783	−	0.160778i
$319$	−344.103			−1.07869
$320$		−	149.879i		−	0.468373i
$321$	−44.4759	−	624.581i	−0.138554	−	1.94574i
$322$	−44.8239			−0.139205
$323$			214.649i			0.664547i
$324$	−659.250	+	192.684i	−2.03472	+	0.594704i
$325$	103.719			0.319134
$326$		−	877.738i		−	2.69245i
$327$	−423.990	+	30.1920i	−1.29661	+	0.0923303i
$328$	−208.719			−0.636339
$329$		−	45.8128i		−	0.139249i
$330$	57.9840	+	814.277i	0.175709	+	2.46750i
$331$	−174.325			−0.526661			−0.263330	−	0.964706i	$-0.584821\pi$
$331$	−174.325			−0.526661			−0.263330	+	0.964706i	$0.584821\pi$
$332$		−	305.755i		−	0.920948i
$333$	73.5954	−	10.5348i	0.221007	−	0.0316359i
$334$	−193.709			−0.579967
$335$		−	89.3368i		−	0.266677i
$336$	−174.042	+	12.3934i	−0.517981	+	0.0368850i
$337$	577.749			1.71439			0.857194	−	0.514994i	$-0.172206\pi$
$337$	577.749			1.71439			0.857194	+	0.514994i	$0.172206\pi$
$338$			102.684i			0.303799i
$339$	23.0383	+	323.529i	0.0679595	+	0.954364i
$340$	−640.395			−1.88352
$341$			125.023i			0.366637i
$342$	−51.5871	−	360.386i	−0.150840	−	1.05376i
$343$	18.5203			0.0539949
$344$		−	1137.60i		−	3.30697i
$345$	57.8194	−	4.11728i	0.167593	−	0.0119341i
$346$	−75.8379			−0.219185
$347$			395.842i			1.14076i	0.821382	+	0.570378i	$0.193203\pi$
$347$			395.842i			1.14076i	−0.821382	+	0.570378i	$0.806797\pi$
$348$	32.5199	+	456.680i	0.0934479	+	1.31230i
$349$	−209.436			−0.600104			−0.300052	−	0.953923i	$-0.597004\pi$
$349$	−209.436			−0.600104			−0.300052	+	0.953923i	$0.597004\pi$
$350$		−	81.9488i		−	0.234140i
$351$	−312.155	+	67.6007i	−0.889332	+	0.192595i
$352$	274.556			0.779990
$353$		−	314.871i		−	0.891985i	−0.895037	−	0.445992i	$-0.852851\pi$
$353$		−	314.871i		−	0.891985i	0.895037	−	0.445992i	$-0.147149\pi$
$354$	−1052.61	+	74.9552i	−2.97346	+	0.211738i
$355$	−46.2067			−0.130160
$356$		−	785.050i		−	2.20520i
$357$	−10.5683	−	148.411i	−0.0296030	−	0.415718i
$358$	605.885			1.69242
$359$			276.829i			0.771110i	0.922685	+	0.385555i	$0.125990\pi$
$359$			276.829i			0.771110i	−0.922685	+	0.385555i	$0.874010\pi$
$360$	567.992	−	81.3049i	1.57776	−	0.225847i
$361$	−229.881			−0.636790
$362$			284.681i			0.786412i
$363$	731.755	−	52.1077i	2.01585	−	0.143547i
$364$	−265.384			−0.729076
$365$		−	299.764i		−	0.821272i
$366$	46.1030	+	647.431i	0.125965	+	1.76894i
$367$	425.352			1.15900			0.579499	−	0.814973i	$-0.303248\pi$
$367$	425.352			1.15900			0.579499	+	0.814973i	$0.303248\pi$
$368$		−	105.425i		−	0.286482i
$369$	16.8212	+	117.512i	0.0455859	+	0.318461i
$370$	−117.570			−0.317757
$371$		−	179.700i		−	0.484365i
$372$	165.926	−	11.8154i	0.446037	−	0.0317619i
$373$	647.292			1.73537			0.867683	−	0.497117i	$-0.165608\pi$
$373$	647.292			1.73537			0.867683	+	0.497117i	$0.165608\pi$
$374$			1266.07i			3.38521i
$375$	28.9902	+	407.112i	0.0773071	+	1.08563i
$376$	274.003			0.728732
$377$			212.904i			0.564732i
$378$	53.4118	+	246.637i	0.141301	+	0.652478i
$379$	345.064			0.910459			0.455229	−	0.890374i	$-0.349557\pi$
$379$	345.064			0.910459			0.455229	+	0.890374i	$0.349557\pi$
$380$			391.187i			1.02944i
$381$	720.938	−	51.3375i	1.89223	−	0.134744i
$382$	541.442			1.41739
$383$		−	252.439i		−	0.659110i	−0.944136	−	0.329555i	$-0.893101\pi$
$383$		−	252.439i		−	0.659110i	0.944136	−	0.329555i	$-0.106899\pi$
$384$	40.2435	+	565.145i	0.104801	+	1.47173i
$385$	203.799			0.529347
$386$			756.354i			1.95947i
$387$	−640.486	+	91.6820i	−1.65500	+	0.236904i
$388$	−1111.30			−2.86417
$389$			644.247i			1.65616i	0.560608	+	0.828081i	$0.310567\pi$
$389$			644.247i			1.65616i	−0.560608	+	0.828081i	$0.689433\pi$
$390$	503.810	−	35.8759i	1.29182	−	0.0919894i
$391$	89.9000			0.229923
$392$			110.768i			0.282572i
$393$	34.8260	+	489.065i	0.0886157	+	1.24444i
$394$	158.622			0.402593
$395$			272.892i			0.690865i
$396$	−206.749	−	1444.34i	−0.522092	−	3.64732i
$397$	459.670			1.15786			0.578930	−	0.815377i	$-0.303470\pi$
$397$	459.670			1.15786			0.578930	+	0.815377i	$0.303470\pi$
$398$		−	912.277i		−	2.29215i
$399$	−90.6576	+	6.45566i	−0.227212	+	0.0161796i
$400$	192.743			0.481857
$401$		−	353.486i		−	0.881510i	−0.897627	−	0.440755i	$-0.854711\pi$
$401$		−	353.486i		−	0.881510i	0.897627	−	0.440755i	$-0.145289\pi$
$402$	16.6917	+	234.403i	0.0415215	+	0.583092i
$403$	77.3543			0.191946
$404$		−	694.400i		−	1.71881i
$405$	−91.5519	−	313.236i	−0.226054	−	0.773423i
$406$	168.217			0.414328
$407$			157.935i			0.388046i
$408$	887.638	−	63.2080i	2.17558	−	0.154922i
$409$	−363.746			−0.889354			−0.444677	−	0.895691i	$-0.646681\pi$
$409$	−363.746			−0.889354			−0.444677	+	0.895691i	$0.646681\pi$
$410$		−	187.728i		−	0.457873i
$411$	21.0934	+	296.217i	0.0513222	+	0.720724i
$412$	−935.227			−2.26997
$413$			263.448i			0.637889i
$414$	−150.938	+	21.6059i	−0.364585	+	0.0521882i
$415$	145.276			0.350063
$416$		−	169.874i		−	0.408350i
$417$	−292.117	+	20.8014i	−0.700521	+	0.0498836i
$418$	773.383			1.85020
$419$			524.850i			1.25262i	0.779572	+	0.626312i	$0.215436\pi$
$419$			524.850i			1.25262i	−0.779572	+	0.626312i	$0.784564\pi$
$420$	−19.2602	−	270.473i	−0.0458576	−	0.643984i
$421$	577.561			1.37188			0.685939	−	0.727659i	$-0.259392\pi$
$421$	577.561			1.37188			0.685939	+	0.727659i	$0.259392\pi$
$422$			1164.55i			2.75959i
$423$	−22.0826	−	154.268i	−0.0522047	−	0.364700i
$424$	1074.77			2.53483
$425$			164.359i			0.386726i
$426$	121.238	−	8.63324i	0.284595	−	0.0202658i
$427$	162.040			0.379485
$428$		−	1769.83i		−	4.13511i
$429$	−48.1930	−	676.780i	−0.112338	−	1.57758i
$430$	1023.19			2.37951
$431$		−	658.087i		−	1.52688i	−0.645877	−	0.763441i	$-0.723508\pi$
$431$		−	658.087i		−	1.52688i	0.645877	−	0.763441i	$-0.276492\pi$
$432$	−580.086	+	125.624i	−1.34279	+	0.290796i
$433$	127.802			0.295154			0.147577	−	0.989051i	$-0.452853\pi$
$433$	127.802			0.295154			0.147577	+	0.989051i	$0.452853\pi$
$434$		−	61.1183i		−	0.140826i
$435$	−216.987	+	15.4515i	−0.498821	+	0.0355206i
$436$	−1201.43			−2.75557
$437$		−	54.9157i		−	0.125665i
$438$	56.0078	+	786.525i	0.127872	+	1.79572i
$439$	−625.152			−1.42404			−0.712018	−	0.702161i	$-0.752219\pi$
$439$	−625.152			−1.42404			−0.712018	+	0.702161i	$0.752219\pi$
$440$			1218.90i			2.77024i
$441$	62.3643	−	8.92709i	0.141416	−	0.0202428i
$442$	783.343			1.77227
$443$		−	23.0185i		−	0.0519604i	−0.999662	−	0.0259802i	$-0.991729\pi$
$443$		−	23.0185i		−	0.0519604i	0.999662	−	0.0259802i	$-0.00827069\pi$
$444$	209.605	−	14.9258i	0.472083	−	0.0336167i
$445$	373.009			0.838222
$446$		−	1030.49i		−	2.31051i
$447$	−2.26015	−	31.7396i	−0.00505627	−	0.0710059i
$448$	98.4246			0.219698
$449$			290.543i			0.647089i	0.946213	+	0.323545i	$0.104875\pi$
$449$			290.543i			0.647089i	−0.946213	+	0.323545i	$0.895125\pi$
$450$	−39.5008	−	275.951i	−0.0877796	−	0.613224i
$451$	−252.180			−0.559157
$452$			916.761i			2.02823i
$453$	−293.342	+	20.8887i	−0.647554	+	0.0461118i
$454$	−799.267			−1.76050
$455$		−	126.094i		−	0.277130i
$456$	−38.6108	−	542.217i	−0.0846728	−	1.18907i
$457$	415.313			0.908780			0.454390	−	0.890803i	$-0.349857\pi$
$457$	415.313			0.908780			0.454390	+	0.890803i	$0.349857\pi$
$458$			435.967i			0.951892i
$459$	−107.124	−	494.660i	−0.233386	−	1.07769i
$460$	163.839			0.356171
$461$		−	538.766i		−	1.16869i	−0.811505	−	0.584345i	$-0.801352\pi$
$461$		−	538.766i		−	1.16869i	0.811505	−	0.584345i	$-0.198648\pi$
$462$	−534.729	+	38.0776i	−1.15742	+	0.0824191i
$463$	−219.266			−0.473576			−0.236788	−	0.971561i	$-0.576095\pi$
$463$	−219.266			−0.473576			−0.236788	+	0.971561i	$0.576095\pi$
$464$			395.645i			0.852682i
$465$	5.61398	+	78.8379i	0.0120731	+	0.169544i
$466$	291.289			0.625084
$467$			615.648i			1.31830i	0.752009	+	0.659152i	$0.229085\pi$
$467$			615.648i			1.31830i	−0.752009	+	0.659152i	$0.770915\pi$
$468$	−893.641	+	127.920i	−1.90949	+	0.273332i
$469$	58.6668			0.125089
$470$			246.446i			0.524354i
$471$	−351.421	+	25.0244i	−0.746117	+	0.0531304i
$472$	−1575.66			−3.33827
$473$		−	1374.48i		−	2.90587i
$474$	−50.9870	−	716.017i	−0.107568	−	1.51058i
$475$	100.399			0.211366
$476$		−	420.543i		−	0.883493i
$477$	−86.6184	−	605.112i	−0.181590	−	1.26858i
$478$	−1322.67			−2.76710
$479$		−	862.042i		−	1.79967i	−0.436230	−	0.899835i	$-0.643687\pi$
$479$		−	862.042i		−	1.79967i	0.436230	−	0.899835i	$-0.356313\pi$
$480$	173.132	−	12.3286i	0.360691	−	0.0256845i
$481$	97.7175			0.203155
$482$			1465.42i			3.04030i
$483$	2.70378	+	37.9696i	0.00559790	+	0.0786120i
$484$	2073.52			4.28413
$485$		−	528.021i		−	1.08870i
$486$	298.740	+	804.768i	0.614691	+	1.65590i
$487$	−159.865			−0.328265			−0.164133	−	0.986438i	$-0.552482\pi$
$487$	−159.865			−0.328265			−0.164133	+	0.986438i	$0.552482\pi$
$488$			969.150i			1.98596i
$489$	−743.517	+	52.9452i	−1.52048	+	0.108272i
$490$	−99.6281			−0.203323
$491$			137.085i			0.279196i	0.990208	+	0.139598i	$0.0445811\pi$
$491$			137.085i			0.279196i	−0.990208	+	0.139598i	$0.955419\pi$
$492$	23.8325	+	334.683i	0.0484400	+	0.680250i
$493$	−337.380			−0.684341
$494$		−	478.508i		−	0.968639i
$495$	686.262	−	98.2345i	1.38639	−	0.198454i
$496$	143.749			0.289818
$497$		−	30.3436i		−	0.0610534i
$498$	−381.178	+	27.1434i	−0.765417	+	0.0545047i
$499$	−314.128			−0.629514			−0.314757	−	0.949172i	$-0.601923\pi$
$499$	−314.128			−0.629514			−0.314757	+	0.949172i	$0.601923\pi$
$500$			1153.60i			2.30721i
$501$	11.6845	+	164.088i	0.0233224	+	0.327520i
$502$	1163.31			2.31734
$503$		−	167.980i		−	0.333956i	−0.985961	−	0.166978i	$-0.946599\pi$
$503$		−	167.980i		−	0.333956i	0.985961	−	0.166978i	$-0.0534009\pi$
$504$	53.3923	+	372.996i	0.105937	+	0.740072i
$505$	329.937			0.653341
$506$		−	323.911i		−	0.640141i
$507$	86.9820	−	6.19392i	0.171562	−	0.0122168i
$508$	2042.87			4.02140
$509$			148.355i			0.291463i	0.989324	+	0.145732i	$0.0465536\pi$
$509$			148.355i			0.291463i	−0.989324	+	0.145732i	$0.953446\pi$
$510$	56.8511	+	798.367i	0.111473	+	1.56543i
$511$	196.853			0.385231
$512$			1075.74i			2.10106i
$513$	−302.165	+	65.4371i	−0.589015	+	0.127558i
$514$	993.819			1.93350
$515$		−	444.364i		−	0.862842i
$516$	−1824.15	+	129.896i	−3.53517	+	0.251737i
$517$	331.057			0.640343
$518$		−	77.2074i		−	0.149049i
$519$	4.57455	+	64.2410i	0.00881416	+	0.123778i
$520$	754.161			1.45031
$521$		−	328.954i		−	0.631389i	−0.948861	−	0.315694i	$-0.897763\pi$
$521$		−	328.954i		−	0.631389i	0.948861	−	0.315694i	$-0.102237\pi$
$522$	566.447	−	81.0836i	1.08515	−	0.155333i
$523$	−456.215			−0.872304			−0.436152	−	0.899873i	$-0.643659\pi$
$523$	−456.215			−0.872304			−0.436152	+	0.899873i	$0.643659\pi$
$524$			1385.83i			2.64471i
$525$	−69.4175	+	4.94316i	−0.132224	+	0.00941555i
$526$	−82.3887			−0.156633
$527$			122.580i			0.232600i
$528$	−89.5582	−	1257.68i	−0.169618	−	2.38196i
$529$	−23.0000			−0.0434783
$530$			966.678i			1.82392i
$531$	126.987	+	887.123i	0.239146	+	1.67066i
$532$	−256.890			−0.482876
$533$			156.029i			0.292737i
$534$	−978.705	+	69.6928i	−1.83278	+	0.130511i
$535$	840.917			1.57181
$536$			350.882i			0.654630i
$537$	−36.5470	−	513.235i	−0.0680578	−	0.955744i
$538$	−1316.81			−2.44761
$539$			133.833i			0.248299i
$540$	−195.229	−	901.496i	−0.361535	−	1.66944i
$541$	−533.598			−0.986318			−0.493159	−	0.869939i	$-0.664158\pi$
$541$	−533.598			−0.986318			−0.493159	+	0.869939i	$0.664158\pi$
$542$		−	1083.28i		−	1.99867i
$543$	241.148	−	17.1720i	0.444104	−	0.0316243i
$544$	269.192			0.494838
$545$		−	570.847i		−	1.04743i
$546$	23.5594	+	330.848i	0.0431491	+	0.605949i
$547$	102.870			0.188062			0.0940312	−	0.995569i	$-0.470025\pi$
$547$	102.870			0.188062			0.0940312	+	0.995569i	$0.470025\pi$
$548$			839.369i			1.53170i
$549$	545.647	−	78.1062i	0.993892	−	0.142270i
$550$	592.187			1.07670
$551$			206.090i			0.374029i
$552$	−227.093	+	16.1711i	−0.411401	+	0.0292955i
$553$	−179.206			−0.324061
$554$			1392.52i			2.51358i
$555$	7.09184	+	99.5916i	0.0127781	+	0.179444i
$556$	−827.751			−1.48876
$557$		−	164.664i		−	0.295627i	−0.989015	−	0.147814i	$-0.952776\pi$
$557$		−	164.664i		−	0.295627i	0.989015	−	0.147814i	$-0.0472236\pi$
$558$	−29.4601	−	205.807i	−0.0527959	−	0.368830i
$559$	−850.416			−1.52132
$560$		−	234.324i		−	0.418436i
$561$	1072.47	−	76.3695i	1.91170	−	0.136131i
$562$	−140.952			−0.250804
$563$		−	173.205i		−	0.307646i	−0.988098	−	0.153823i	$-0.950841\pi$
$563$		−	173.205i		−	0.307646i	0.988098	−	0.153823i	$-0.0491586\pi$
$564$	−31.2869	−	439.366i	−0.0554732	−	0.779018i
$565$	−435.590			−0.770955
$566$			223.448i			0.394785i
$567$	205.700	−	60.1214i	0.362786	−	0.106034i
$568$	181.483			0.319512
$569$		−	266.538i		−	0.468433i	−0.972185	−	0.234216i	$-0.924748\pi$
$569$		−	266.538i		−	0.468433i	0.972185	−	0.234216i	$-0.0752524\pi$
$570$	487.685	−	34.7277i	0.855588	−	0.0609257i
$571$	−888.444			−1.55594			−0.777972	−	0.628299i	$-0.783752\pi$
$571$	−888.444			−1.55594			−0.777972	+	0.628299i	$0.783752\pi$
$572$		−	1917.74i		−	3.35269i
$573$	−32.6599	−	458.647i	−0.0569980	−	0.800430i
$574$	123.280			0.214773
$575$		−	42.0495i		−	0.0731296i
$576$	331.431	−	47.4424i	0.575401	−	0.0823653i
$577$	679.272			1.17725			0.588624	−	0.808407i	$-0.299670\pi$
$577$	679.272			1.17725			0.588624	+	0.808407i	$0.299670\pi$
$578$			220.405i			0.381324i
$579$	640.694	−	45.6233i	1.10655	−	0.0787968i
$580$	−614.860			−1.06010
$581$			95.4018i			0.164203i
$582$	98.6553	+	1385.43i	0.169511	+	2.38046i
$583$	1298.56			2.22738
$584$			1177.36i			2.01603i
$585$	−60.7797	−	424.604i	−0.103897	−	0.725820i
$586$	947.358			1.61665
$587$			1113.75i			1.89736i	0.316235	+	0.948681i	$0.397581\pi$
$587$			1113.75i			1.89736i	−0.316235	+	0.948681i	$0.602419\pi$
$588$	177.618	−	12.6480i	0.302071	−	0.0215102i
$589$	74.8786			0.127128
$590$		−	1417.20i		−	2.40203i
$591$	−9.56808	−	134.366i	−0.0161896	−	0.227353i
$592$	181.591			0.306741
$593$		−	122.600i		−	0.206745i	−0.994643	−	0.103373i	$-0.967037\pi$
$593$		−	122.600i		−	0.206745i	0.994643	−	0.103373i	$-0.0329634\pi$
$594$	−1782.27	+	385.970i	−3.00045	+	0.649781i
$595$	199.817			0.335826
$596$		−	89.9382i		−	0.150903i
$597$	−772.774	+	55.0286i	−1.29443	+	0.0921752i
$598$	−200.410			−0.335135
$599$			234.009i			0.390667i	0.980737	+	0.195333i	$0.0625789\pi$
$599$			234.009i			0.390667i	−0.980737	+	0.195333i	$0.937421\pi$
$600$	−29.5647	−	415.181i	−0.0492745	−	0.691968i
$601$	277.580			0.461864			0.230932	−	0.972970i	$-0.425822\pi$
$601$	277.580			0.461864			0.230932	+	0.972970i	$0.425822\pi$
$602$			671.920i			1.11615i
$603$	197.552	−	28.2784i	0.327615	−	0.0468963i
$604$	−831.222			−1.37620
$605$			985.212i			1.62845i
$606$	−865.693	+	61.6453i	−1.42854	+	0.101725i
$607$	474.576			0.781839			0.390920	−	0.920425i	$-0.372157\pi$
$607$	474.576			0.781839			0.390920	+	0.920425i	$0.372157\pi$
$608$		−	164.437i		−	0.270455i
$609$	−10.1469	−	142.494i	−0.0166615	−	0.233980i
$610$	−871.681			−1.42898
$611$		−	204.832i		−	0.335240i
$612$	−202.709	−	1416.12i	−0.331224	−	2.31392i
$613$	590.654			0.963546			0.481773	−	0.876296i	$-0.339993\pi$
$613$	590.654			0.963546			0.481773	+	0.876296i	$0.339993\pi$
$614$		−	1272.27i		−	2.07209i
$615$	−159.021	+	11.3238i	−0.258571	+	0.0184126i
$616$	−800.445			−1.29942
$617$			153.245i			0.248372i	0.992259	+	0.124186i	$0.0396319\pi$
$617$			153.245i			0.248372i	−0.992259	+	0.124186i	$0.960368\pi$
$618$	83.0248	+	1165.93i	0.134344	+	1.88661i
$619$	243.059			0.392663			0.196332	−	0.980538i	$-0.437097\pi$
$619$	243.059			0.392663			0.196332	+	0.980538i	$0.437097\pi$
$620$			223.397i			0.360318i
$621$	27.4066	+	126.554i	0.0441330	+	0.203790i
$622$	1940.41			3.11963
$623$			244.952i			0.393181i
$624$	−778.151	+	55.4115i	−1.24704	+	0.0888005i
$625$	−328.925			−0.526281
$626$			2007.02i			3.20610i
$627$	−46.6505	−	655.119i	−0.0744028	−	1.04485i
$628$	−995.796			−1.58566
$629$			154.849i			0.246183i
$630$	−335.483	+	48.0225i	−0.532513	+	0.0762262i
$631$	−422.373			−0.669371			−0.334685	−	0.942330i	$-0.608630\pi$
$631$	−422.373			−0.669371			−0.334685	+	0.942330i	$0.608630\pi$
$632$		−	1071.82i		−	1.69591i
$633$	986.467	−	70.2456i	1.55840	−	0.110972i
$634$	−1464.42			−2.30982
$635$			970.649i			1.52858i
$636$	−122.722	−	1723.40i	−0.192959	−	2.70975i
$637$	82.8052			0.129992
$638$			1215.59i			1.90531i
$639$	−14.6261	−	102.178i	−0.0228891	−	0.159902i
$640$	−760.893			−1.18890
$641$		−	250.396i		−	0.390634i	−0.980740	−	0.195317i	$-0.937427\pi$
$641$		−	250.396i		−	0.390634i	0.980740	−	0.195317i	$-0.0625735\pi$
$642$	−2206.41	+	157.117i	−3.43677	+	0.244730i
$643$	−34.5634			−0.0537533			−0.0268767	−	0.999639i	$-0.508556\pi$
$643$	−34.5634			−0.0537533			−0.0268767	+	0.999639i	$0.508556\pi$
$644$			107.592i			0.167068i
$645$	−61.7189	−	866.726i	−0.0956882	−	1.34376i
$646$	758.272			1.17380
$647$		−	98.7339i		−	0.152603i	−0.997085	−	0.0763013i	$-0.975689\pi$
$647$		−	98.7339i		−	0.152603i	0.997085	−	0.0763013i	$-0.0243111\pi$
$648$	359.582	+	1230.28i	0.554910	+	1.89857i
$649$	−1903.75			−2.93337
$650$		−	366.398i		−	0.563689i
$651$	−51.7723	+	3.68666i	−0.0795273	+	0.00566307i
$652$	−2106.85			−3.23136
$653$			614.785i			0.941478i	0.882272	+	0.470739i	$0.156013\pi$
$653$			614.785i			0.941478i	−0.882272	+	0.470739i	$0.843987\pi$
$654$	106.657	+	1497.80i	0.163084	+	2.29021i
$655$	−658.462			−1.00529
$656$			289.952i			0.442000i
$657$	662.874	−	94.8865i	1.00894	−	0.144424i
$658$	−161.839			−0.245956
$659$		−	284.478i		−	0.431681i	−0.976429	−	0.215841i	$-0.930751\pi$
$659$		−	284.478i		−	0.431681i	0.976429	−	0.215841i	$-0.0692491\pi$
$660$	1954.52	−	139.180i	2.96140	−	0.210879i
$661$	−401.788			−0.607849			−0.303925	−	0.952696i	$-0.598297\pi$
$661$	−401.788			−0.607849			−0.303925	+	0.952696i	$0.598297\pi$
$662$			615.823i			0.930246i
$663$	−47.2513	−	663.557i	−0.0712690	−	1.00084i
$664$	−570.591			−0.859324
$665$		−	122.059i		−	0.183547i
$666$	−37.2153	−	259.985i	−0.0558789	−	0.390368i
$667$	86.3153			0.129408
$668$			464.963i			0.696052i
$669$	−872.909	+	62.1592i	−1.30480	+	0.0929135i
$670$	−315.593			−0.471034
$671$			1170.95i			1.74508i
$672$	8.09608	+	113.694i	0.0120477	+	0.169188i
$673$	−478.295			−0.710690			−0.355345	−	0.934735i	$-0.615637\pi$
$673$	−478.295			−0.710690			−0.355345	+	0.934735i	$0.615637\pi$
$674$		−	2040.97i		−	3.02814i
$675$	−231.371	+	50.1058i	−0.342771	+	0.0742309i
$676$	246.474			0.364607
$677$		−	170.727i		−	0.252182i	−0.992019	−	0.126091i	$-0.959757\pi$
$677$		−	170.727i		−	0.252182i	0.992019	−	0.126091i	$-0.0402431\pi$
$678$	1142.91	−	81.3854i	1.68570	−	0.120038i
$679$	346.748			0.510674
$680$			1195.09i			1.75748i
$681$	48.2118	+	677.045i	0.0707957	+	0.994193i
$682$	441.659			0.647594
$683$			291.715i			0.427108i	0.976931	+	0.213554i	$0.0685040\pi$
$683$			291.715i			0.427108i	−0.976931	+	0.213554i	$0.931496\pi$
$684$	−865.040	+	123.825i	−1.26468	+	0.181031i
$685$	−398.818			−0.582216
$686$		−	65.4250i		−	0.0953718i
$687$	369.300	−	26.2976i	0.537554	−	0.0382788i
$688$	−1580.35			−2.29702
$689$		−	803.447i		−	1.16611i
$690$	−14.5448	−	204.254i	−0.0210794	−	0.296020i
$691$	−916.615			−1.32651			−0.663253	−	0.748396i	$-0.730825\pi$
$691$	−916.615			−1.32651			−0.663253	+	0.748396i	$0.730825\pi$
$692$			182.035i			0.263056i
$693$	64.5099	+	450.663i	0.0930878	+	0.650308i
$694$	1398.36			2.01493
$695$		−	393.298i		−	0.565896i
$696$	852.245	−	60.6877i	1.22449	−	0.0871950i
$697$	−247.252			−0.354738
$698$			739.859i			1.05997i
$699$	−17.5706	−	246.746i	−0.0251367	−	0.352999i
$700$	−196.703			−0.281005
$701$			666.707i			0.951079i	0.879694	+	0.475540i	$0.157747\pi$
$701$			666.707i			0.951079i	−0.879694	+	0.475540i	$0.842253\pi$
$702$	238.808	+	1102.73i	0.340182	+	1.57084i
$703$	94.5900			0.134552
$704$			711.246i			1.01029i
$705$	208.760	−	14.8657i	0.296114	−	0.0210860i
$706$	−1112.32			−1.57552
$707$			216.667i			0.306460i
$708$	179.916	+	2526.59i	0.254119	+	3.56863i
$709$	−747.983			−1.05498			−0.527491	−	0.849560i	$-0.676867\pi$
$709$	−747.983			−1.05498			−0.527491	+	0.849560i	$0.676867\pi$
$710$			163.231i			0.229902i
$711$	−603.450	+	86.3805i	−0.848735	+	0.121492i
$712$	−1465.04			−2.05764
$713$		−	31.3609i		−	0.0439845i
$714$	−524.281	+	37.3337i	−0.734288	+	0.0522881i
$715$	911.195			1.27440
$716$		−	1454.32i		−	2.03117i
$717$	79.7838	+	1120.41i	0.111275	+	1.56264i
$718$	977.930			1.36202
$719$		−	754.324i		−	1.04913i	−0.851370	−	0.524565i	$-0.824228\pi$
$719$		−	754.324i		−	1.04913i	0.851370	−	0.524565i	$-0.175772\pi$
$720$	−112.948	−	789.053i	−0.156873	−	1.09591i
$721$	291.810			0.404730
$722$			812.083i			1.12477i
$723$	1241.34	−	88.3945i	1.71692	−	0.122261i
$724$	683.325			0.943818
$725$			157.805i			0.217662i
$726$	−184.077	−	2585.01i	−0.253549	−	3.56062i
$727$	−820.905			−1.12917			−0.564584	−	0.825376i	$-0.690963\pi$
$727$	−820.905			−1.12917			−0.564584	+	0.825376i	$0.690963\pi$
$728$			495.252i			0.680291i
$729$	663.685	−	301.601i	0.910405	−	0.413719i
$730$	−1058.95			−1.45062
$731$		−	1347.62i		−	1.84353i
$732$	1554.04	−	110.662i	2.12300	−	0.151177i
$733$	436.105			0.594959			0.297480	−	0.954728i	$-0.403854\pi$
$733$	436.105			0.594959			0.297480	+	0.954728i	$0.403854\pi$
$734$		−	1502.61i		−	2.04715i
$735$	6.00958	+	84.3933i	0.00817630	+	0.114821i
$736$	−68.8700			−0.0935734
$737$			423.944i			0.575229i
$738$	415.126	−	59.4229i	0.562501	−	0.0805189i
$739$	995.827			1.34753			0.673766	−	0.738944i	$-0.264675\pi$
$739$	995.827			1.34753			0.673766	+	0.738944i	$0.264675\pi$
$740$			282.205i			0.381359i
$741$	−405.336	+	28.8636i	−0.547012	+	0.0389523i
$742$	−634.810			−0.855539
$743$		−	1075.46i		−	1.44745i	−0.690086	−	0.723727i	$-0.742427\pi$
$743$		−	1075.46i		−	1.44745i	0.690086	−	0.723727i	$-0.257573\pi$
$744$	−22.0496	−	309.646i	−0.0296366	−	0.416191i
$745$	42.7332			0.0573600
$746$		−	2286.64i		−	3.06520i
$747$	45.9854	+	321.252i	0.0615600	+	0.430056i
$748$	3038.97			4.06279
$749$			552.224i			0.737281i
$750$	1438.17	−	102.411i	1.91756	−	0.136548i
$751$	931.379			1.24018			0.620092	−	0.784529i	$-0.287095\pi$
$751$	931.379			1.24018			0.620092	+	0.784529i	$0.287095\pi$
$752$		−	380.644i		−	0.506176i
$753$	−70.1707	−	985.417i	−0.0931882	−	1.30865i
$754$	752.108			0.997491
$755$		−	394.947i		−	0.523108i
$756$	592.006	−	128.205i	0.783076	−	0.169584i
$757$	615.024			0.812449			0.406224	−	0.913773i	$-0.366845\pi$
$757$	615.024			0.812449			0.406224	+	0.913773i	$0.366845\pi$
$758$		−	1218.98i		−	1.60815i
$759$	−274.380	+	19.5384i	−0.361501	+	0.0257422i
$760$	730.024			0.960557
$761$			848.152i			1.11452i	0.830337	+	0.557261i	$0.188148\pi$
$761$			848.152i			1.11452i	−0.830337	+	0.557261i	$0.811852\pi$
$762$	−181.356	−	2546.80i	−0.238000	−	3.34226i
$763$	374.871			0.491312
$764$		−	1299.63i		−	1.70109i
$765$	672.854	−	96.3152i	0.879547	−	0.125902i
$766$	−891.771			−1.16419
$767$			1177.89i			1.53571i
$768$	1551.16	−	110.457i	2.01974	−	0.143824i
$769$	1195.88			1.55511			0.777553	−	0.628818i	$-0.216461\pi$
$769$	1195.88			1.55511			0.777553	+	0.628818i	$0.216461\pi$
$770$		−	719.943i		−	0.934991i
$771$	−59.9473	−	841.847i	−0.0777526	−	1.09189i
$772$	1815.49			2.35167
$773$		−	776.877i		−	1.00502i	−0.864573	−	0.502508i	$-0.832411\pi$
$773$		−	776.877i		−	1.00502i	0.864573	−	0.502508i	$-0.167589\pi$
$774$	323.878	+	2262.60i	0.418446	+	2.92325i
$775$	57.3353			0.0739810
$776$			2073.87i			2.67252i
$777$	−65.4011	+	4.65716i	−0.0841713	+	0.00599377i
$778$	2275.88			2.92530
$779$			151.035i			0.193883i
$780$	−86.1135	−	1209.30i	−0.110402	−	1.55039i
$781$	219.272			0.280758
$782$		−	317.582i		−	0.406116i
$783$	−102.853	−	474.936i	−0.131357	−	0.606560i
$784$	153.879			0.196274
$785$		−	473.142i		−	0.602729i
$786$	1727.68	−	123.027i	2.19807	−	0.156523i
$787$	−308.118			−0.391509			−0.195755	−	0.980653i	$-0.562716\pi$
$787$	−308.118			−0.391509			−0.195755	+	0.980653i	$0.562716\pi$
$788$		−	380.742i		−	0.483176i
$789$	4.96970	+	69.7901i	0.00629873	+	0.0884539i
$790$	964.023			1.22028
$791$		−	286.048i		−	0.361629i
$792$	−2695.38	+	385.829i	−3.40326	+	0.487157i
$793$	724.491			0.913607
$794$		−	1623.84i		−	2.04514i
$795$	818.857	−	58.3101i	1.03001	−	0.0733461i
$796$	−2189.75			−2.75095
$797$		−	28.0427i		−	0.0351853i	−0.999845	−	0.0175926i	$-0.994400\pi$
$797$		−	28.0427i		−	0.0351853i	0.999845	−	0.0175926i	$-0.00560020\pi$
$798$	22.8054	+	320.259i	0.0285782	+	0.401327i
$799$	324.589			0.406244
$800$		−	125.911i		−	0.157389i
$801$	118.071	+	824.841i	0.147405	+	1.02976i
$802$	−1248.73			−1.55702
$803$			1422.52i			1.77150i
$804$	562.642	−	40.0653i	0.699803	−	0.0498324i
$805$	−51.1211			−0.0635044
$806$		−	273.263i		−	0.339037i
$807$	79.4303	+	1115.45i	0.0984266	+	1.38222i
$808$	−1295.87			−1.60380
$809$		−	450.754i		−	0.557174i	−0.960411	−	0.278587i	$-0.910134\pi$
$809$		−	450.754i		−	0.557174i	0.960411	−	0.278587i	$-0.0898661\pi$
$810$	−1106.54	+	323.418i	−1.36610	+	0.399281i
$811$	1087.32			1.34071			0.670357	−	0.742039i	$-0.266141\pi$
$811$	1087.32			1.34071			0.670357	+	0.742039i	$0.266141\pi$
$812$		−	403.774i		−	0.497259i
$813$	−917.628	+	65.3436i	−1.12869	+	0.0803734i
$814$	557.924			0.685410
$815$		−	1001.05i		−	1.22828i
$816$	−87.8084	−	1233.10i	−0.107608	−	1.51116i
$817$	−823.198			−1.00759
$818$			1284.98i			1.57087i
$819$	278.835	−	39.9136i	0.340457	−	0.0487345i
$820$	−450.607			−0.549520
$821$			1434.59i			1.74737i	0.486488	+	0.873687i	$0.338278\pi$
$821$			1434.59i			1.74737i	−0.486488	+	0.873687i	$0.661722\pi$
$822$	1046.42	−	74.5150i	1.27302	−	0.0906509i
$823$	−1511.84			−1.83699			−0.918493	−	0.395437i	$-0.870593\pi$
$823$	−1511.84			−1.83699			−0.918493	+	0.395437i	$0.870593\pi$
$824$			1745.30i			2.11808i
$825$	−35.7208	−	501.632i	−0.0432979	−	0.608038i
$826$	930.662			1.12671
$827$			724.732i			0.876339i	0.898892	+	0.438169i	$0.144373\pi$
$827$			724.732i			0.876339i	−0.898892	+	0.438169i	$0.855627\pi$
$828$	51.8611	+	362.299i	0.0626341	+	0.437559i
$829$	37.1153			0.0447712			0.0223856	−	0.999749i	$-0.492874\pi$
$829$	37.1153			0.0447712			0.0223856	+	0.999749i	$0.492874\pi$
$830$		−	513.206i		−	0.618320i
$831$	1179.58	−	83.9970i	1.41947	−	0.101079i
$832$	440.062			0.528921
$833$			131.218i			0.157525i
$834$	73.4836	+	1031.94i	0.0881098	+	1.23734i
$835$	−220.922			−0.264578
$836$		−	1856.36i		−	2.22053i
$837$	−172.559	+	37.3694i	−0.206163	+	0.0446469i
$838$	1854.09			2.21252
$839$		−	790.216i		−	0.941854i	−0.882172	−	0.470927i	$-0.843919\pi$
$839$		−	790.216i		−	0.941854i	0.882172	−	0.470927i	$-0.156081\pi$
$840$	−504.750	+	35.9429i	−0.600893	+	0.0427891i
$841$	517.072			0.614830
$842$		−	2040.30i		−	2.42316i
$843$	8.50222	+	119.398i	0.0100857	+	0.141634i
$844$	2795.28			3.31194
$845$			117.110i			0.138591i
$846$	−544.971	+	78.0094i	−0.644173	+	0.0922097i
$847$	−646.981			−0.763850
$848$		−	1493.07i		−	1.76069i
$849$	189.279	−	13.4784i	0.222944	−	0.0158757i
$850$	580.617			0.683078
$851$		−	39.6166i		−	0.0465530i
$852$	−20.7225	−	291.009i	−0.0243222	−	0.341559i
$853$	55.6054			0.0651881			0.0325940	−	0.999469i	$-0.489623\pi$
$853$	55.6054			0.0651881			0.0325940	+	0.999469i	$0.489623\pi$
$854$		−	572.426i		−	0.670288i
$855$	−58.8344	−	411.015i	−0.0688122	−	0.480719i
$856$	−3302.81			−3.85842
$857$			826.752i			0.964704i	0.875977	+	0.482352i	$0.160217\pi$
$857$			826.752i			0.964704i	−0.875977	+	0.482352i	$0.839783\pi$
$858$	−2390.81	+	170.247i	−2.78649	+	0.198424i
$859$	−781.754			−0.910074			−0.455037	−	0.890473i	$-0.650374\pi$
$859$	−781.754			−0.910074			−0.455037	+	0.890473i	$0.650374\pi$
$860$		−	2455.98i		−	2.85579i
$861$	−7.43624	−	104.428i	−0.00863674	−	0.121287i
$862$	−2324.77			−2.69695
$863$		−	740.925i		−	0.858545i	−0.903175	−	0.429273i	$-0.858770\pi$
$863$		−	740.925i		−	0.858545i	0.903175	−	0.429273i	$-0.141230\pi$
$864$	82.0650	+	378.946i	0.0949826	+	0.438595i
$865$	−86.4921			−0.0999909
$866$		−	451.475i		−	0.521333i
$867$	186.701	−	13.2949i	0.215342	−	0.0153343i
$868$	−146.703			−0.169013
$869$		−	1295.00i		−	1.49021i
$870$	54.5842	+	766.533i	0.0627405	+	0.881073i
$871$	262.303			0.301151
$872$			2242.08i			2.57119i
$873$	1167.62	−	167.139i	1.33748	−	0.191453i
$874$	−193.996			−0.221964
$875$		−	359.949i		−	0.411370i
$876$	1887.91	−	134.436i	2.15515	−	0.153466i
$877$	−1062.91			−1.21199			−0.605994	−	0.795469i	$-0.707225\pi$
$877$	−1062.91			−1.21199			−0.605994	+	0.795469i	$0.707225\pi$
$878$			2208.42i			2.51529i
$879$	−57.1447	−	802.491i	−0.0650111	−	0.912959i
$880$	1693.30			1.92420
$881$			928.056i			1.05341i	0.850047	+	0.526706i	$0.176573\pi$
$881$			928.056i			1.05341i	−0.850047	+	0.526706i	$0.823427\pi$
$882$	−31.5360	−	220.309i	−0.0357551	−	0.249784i
$883$	−876.728			−0.992897			−0.496449	−	0.868066i	$-0.665363\pi$
$883$	−876.728			−0.992897			−0.496449	+	0.868066i	$0.665363\pi$
$884$		−	1880.27i		−	2.12700i
$885$	−1200.48	+	85.4854i	−1.35648	+	0.0965937i
$886$	−81.3155			−0.0917782
$887$		−	758.845i		−	0.855518i	−0.903893	−	0.427759i	$-0.859303\pi$
$887$		−	758.845i		−	0.855518i	0.903893	−	0.427759i	$-0.140697\pi$
$888$	−27.8541	−	391.159i	−0.0313673	−	0.440494i
$889$	−637.418			−0.717006
$890$		−	1317.70i		−	1.48056i
$891$	434.455	+	1486.45i	0.487604	+	1.66829i
$892$	−2473.50			−2.77298
$893$		−	198.276i		−	0.222034i
$894$	−112.124	+	7.98426i	−0.125418	+	0.00893094i
$895$	691.003			0.772071
$896$		−	499.673i		−	0.557671i
$897$	12.0888	+	169.764i	0.0134769	+	0.189258i
$898$	1026.38			1.14296
$899$			117.693i			0.130915i
$900$	−662.370	+	94.8144i	−0.735966	+	0.105349i
$901$	1273.19			1.41309
$902$			890.855i			0.987644i
$903$	569.172	−	40.5303i	0.630313	−	0.0448841i
$904$	1710.83			1.89252
$905$			324.675i			0.358757i
$906$	73.7917	+	1036.27i	0.0814478	+	1.14378i
$907$	52.0217			0.0573558			0.0286779	−	0.999589i	$-0.490870\pi$
$907$	52.0217			0.0573558			0.0286779	+	0.999589i	$0.490870\pi$
$908$			1918.49i			2.11288i
$909$	104.437	+	729.595i	0.114893	+	0.802635i
$910$	−445.443			−0.489498
$911$			35.4574i			0.0389214i	0.999811	+	0.0194607i	$0.00619492\pi$
$911$			35.4574i			0.0389214i	−0.999811	+	0.0194607i	$0.993805\pi$
$912$	−753.246	+	53.6380i	−0.825927	+	0.0588136i
$913$	−689.402			−0.755095
$914$		−	1467.14i		−	1.60519i
$915$	52.5799	+	738.386i	0.0574643	+	0.806979i
$916$	1046.46			1.14242
$917$		−	432.407i		−	0.471546i
$918$	−1747.45	+	378.429i	−1.90354	+	0.412232i
$919$	−780.028			−0.848779			−0.424390	−	0.905480i	$-0.639511\pi$
$919$	−780.028			−0.848779			−0.424390	+	0.905480i	$0.639511\pi$
$920$		−	305.751i		−	0.332338i
$921$	−1077.71	+	76.7432i	−1.17016	+	0.0833260i
$922$	−1903.26			−2.06427
$923$		−	135.668i		−	0.146986i
$924$	91.3984	+	1283.52i	0.0989160	+	1.38909i
$925$	72.4285			0.0783011
$926$			774.582i			0.836482i
$927$	982.629	−	140.658i	1.06001	−	0.151734i
$928$	258.458			0.278511
$929$			771.790i			0.830775i	0.909644	+	0.415388i	$0.136354\pi$
$929$			771.790i			0.830775i	−0.909644	+	0.415388i	$0.863646\pi$
$930$	278.504	−	19.8321i	0.299467	−	0.0213248i
$931$	80.1550			0.0860956
$932$		−	699.186i		−	0.750199i
$933$	−117.046	−	1643.69i	−0.125451	−	1.76172i
$934$	2174.85			2.32853
$935$			1443.93i			1.54432i
$936$	238.720	+	1667.69i	0.255043	+	1.78172i
$937$	−628.263			−0.670505			−0.335252	−	0.942128i	$-0.608822\pi$
$937$	−628.263			−0.670505			−0.335252	+	0.942128i	$0.608822\pi$
$938$		−	207.248i		−	0.220946i
$939$	1700.11	−	121.064i	1.81056	−	0.128928i
$940$	591.549			0.629307
$941$		−	996.189i		−	1.05865i	−0.848419	−	0.529324i	$-0.822445\pi$
$941$		−	996.189i		−	1.05865i	0.848419	−	0.529324i	$-0.177555\pi$
$942$	88.4018	+	1241.44i	0.0938448	+	1.31787i
$943$	63.2570			0.0670806
$944$			2188.91i			2.31876i
$945$	60.9155	+	281.286i	0.0644608	+	0.297657i
$946$	−4855.50			−5.13266
$947$		−	316.695i		−	0.334419i	−0.985921	−	0.167210i	$-0.946524\pi$
$947$		−	316.695i		−	0.334419i	0.985921	−	0.167210i	$-0.0534756\pi$
$948$	−1718.67	+	122.385i	−1.81294	+	0.129098i
$949$	880.141			0.927440
$950$		−	354.671i		−	0.373338i
$951$	88.3343	+	1240.49i	0.0928856	+	1.30440i
$952$	−784.805			−0.824376
$953$		−	1527.18i		−	1.60250i	−0.598330	−	0.801250i	$-0.704169\pi$
$953$		−	1527.18i		−	1.60250i	0.598330	−	0.801250i	$-0.295831\pi$
$954$	−2137.63	+	305.990i	−2.24070	+	0.320744i
$955$	617.507			0.646605
$956$			3174.84i			3.32096i
$957$	1029.70	−	73.3243i	1.07597	−	0.0766190i
$958$	−3045.27			−3.17878
$959$		−	261.901i		−	0.273098i
$960$	31.9375	+	448.502i	0.0332682	+	0.467190i
$961$	−918.239			−0.955503
$962$		−	345.199i		−	0.358835i
$963$	266.182	+	1859.53i	0.276409	+	1.93098i
$964$	3517.48			3.64884
$965$			862.611i			0.893897i
$966$	134.132	−	9.55144i	0.138853	−	0.00988762i
$967$	889.228			0.919574			0.459787	−	0.888029i	$-0.347926\pi$
$967$	889.228			0.919574			0.459787	+	0.888029i	$0.347926\pi$
$968$		−	3869.55i		−	3.99746i
$969$	−45.7390	−	642.319i	−0.0472023	−	0.662868i
$970$	−1865.30			−1.92299
$971$		−	1854.15i		−	1.90953i	−0.297368	−	0.954763i	$-0.596109\pi$
$971$		−	1854.15i		−	1.90953i	0.297368	−	0.954763i	$-0.403891\pi$
$972$	1931.70	−	717.070i	1.98734	−	0.737727i
$973$	258.276			0.265443
$974$			564.743i			0.579818i
$975$	−310.370	+	22.1012i	−0.318328	+	0.0226679i
$976$	1346.34			1.37945
$977$		−	332.715i		−	0.340547i	−0.985397	−	0.170274i	$-0.945535\pi$
$977$		−	332.715i		−	0.340547i	0.985397	−	0.170274i	$-0.0544652\pi$
$978$	187.035	+	2626.56i	0.191243	+	2.68565i
$979$	−1770.10			−1.80807
$980$			239.139i			0.244019i
$981$	1262.32	−	180.694i	1.28677	−	0.184194i
$982$	484.271			0.493147
$983$			720.828i			0.733294i	0.930360	+	0.366647i	$0.119494\pi$
$983$			720.828i			0.733294i	−0.930360	+	0.366647i	$0.880506\pi$
$984$	624.576	−	44.4756i	0.634732	−	0.0451988i
$985$	180.906			0.183661
$986$			1191.84i			1.20876i
$987$	9.76217	+	137.091i	0.00989075	+	0.138897i
$988$	−1148.57			−1.16252
$989$			344.775i			0.348610i
$990$	−347.025	−	2424.30i	−0.350531	−	2.44879i
$991$	−535.689			−0.540554			−0.270277	−	0.962783i	$-0.587115\pi$
$991$	−535.689			−0.540554			−0.270277	+	0.962783i	$0.587115\pi$
$992$		−	93.9056i		−	0.0946629i
$993$	521.653	−	37.1465i	0.525330	−	0.0374084i
$994$	−107.192			−0.107839
$995$		−	1040.44i		−	1.04567i
$996$	65.1526	+	914.947i	0.0654143	+	0.918621i
$997$	−1327.41			−1.33140			−0.665702	−	0.746217i	$-0.731868\pi$
$997$	−1327.41			−1.33140			−0.665702	+	0.746217i	$0.731868\pi$
$998$			1109.69i			1.11192i
$999$	−217.984	+	47.2068i	−0.218202	+	0.0472540i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	483.3.b.a.323.6	✓	88
3.2	odd	2	inner	483.3.b.a.323.83	yes	88

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
483.3.b.a.323.6	✓	88	1.1	even	1	trivial
483.3.b.a.323.83	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 $\F_{q}$
Belyi maps

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-3.53262i q^{2} +(-2.99242 + 0.213088i) q^{3} -8.47941 q^{4} -4.02890i q^{5} +(0.752759 + 10.5711i) q^{6} +2.64575 q^{7} +15.8240i q^{8} +(8.90919 - 1.27530i) q^{9} -14.2326 q^{10} +19.1190i q^{11} +(25.3740 - 1.80686i) q^{12} +11.8293 q^{13} -9.34643i q^{14} +(0.858512 + 12.0562i) q^{15} +21.9827 q^{16} +18.7454i q^{17} +(-4.50515 - 31.4728i) q^{18} +11.4507 q^{19} +34.1627i q^{20} +(-7.91721 + 0.563778i) q^{21} +67.5401 q^{22} -4.79583i q^{23} +(-3.37191 - 47.3522i) q^{24} +8.76793 q^{25} -41.7885i q^{26} +(-26.3883 + 5.71468i) q^{27} -22.4344 q^{28} +17.9980i q^{29} +(42.5899 - 3.03280i) q^{30} +6.53921 q^{31} -14.3604i q^{32} +(-4.07403 - 57.2121i) q^{33} +66.2205 q^{34} -10.6595i q^{35} +(-75.5446 + 10.8138i) q^{36} +8.26062 q^{37} -40.4510i q^{38} +(-35.3983 + 2.52068i) q^{39} +63.7536 q^{40} +13.1900i q^{41} +(1.99161 + 27.9685i) q^{42} -71.8906 q^{43} -162.118i q^{44} +(-5.13806 - 35.8943i) q^{45} -16.9419 q^{46} -17.3156i q^{47} +(-65.7816 + 4.68425i) q^{48} +7.00000 q^{49} -30.9738i q^{50} +(-3.99443 - 56.0943i) q^{51} -100.306 q^{52} -67.9200i q^{53} +(20.1878 + 93.2199i) q^{54} +77.0286 q^{55} +41.8665i q^{56} +(-34.2654 + 2.44001i) q^{57} +63.5801 q^{58} +99.5740i q^{59} +(-7.27967 - 102.229i) q^{60} +61.2454 q^{61} -23.1005i q^{62} +(23.5715 - 3.37412i) q^{63} +37.2010 q^{64} -47.6592i q^{65} +(-202.109 + 14.3920i) q^{66} +22.1740 q^{67} -158.950i q^{68} +(1.02193 + 14.3512i) q^{69} -37.6559 q^{70} -11.4688i q^{71} +(20.1804 + 140.979i) q^{72} +74.4034 q^{73} -29.1817i q^{74} +(-26.2373 + 1.86834i) q^{75} -97.0952 q^{76} +50.5841i q^{77} +(8.90462 + 125.049i) q^{78} -67.7335 q^{79} -88.5662i q^{80} +(77.7472 - 22.7238i) q^{81} +46.5953 q^{82} +36.0585i q^{83} +(67.1332 - 4.78050i) q^{84} +75.5236 q^{85} +253.962i q^{86} +(-3.83516 - 53.8576i) q^{87} -302.540 q^{88} +92.5832i q^{89} +(-126.801 + 18.1508i) q^{90} +31.2974 q^{91} +40.6658i q^{92} +(-19.5681 + 1.39343i) q^{93} -61.1695 q^{94} -46.1338i q^{95} +(3.06003 + 42.9724i) q^{96} +131.058 q^{97} -24.7283i q^{98} +(24.3824 + 170.335i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 88 q + 8 q^{3} - 176 q^{4} - 22 q^{6} + 20 q^{9} - 16 q^{10} - 18 q^{12} + 64 q^{13} + 20 q^{15} + 272 q^{16} - 38 q^{18} - 48 q^{19} - 28 q^{21} + 208 q^{22} + 228 q^{24} - 568 q^{25} - 88 q^{27} - 8 q^{30}+ \cdots - 248 q^{99}+O(q^{100}) \) 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

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