LMFDB - Embedded newform 200.6.f.d.149.18

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [200,6,Mod(149,200)] 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("200.149"); S:= CuspForms(chi, 6); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(200, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 1, 1])) N = Newforms(chi, 6, names="a")

Level:	$ N $	$=$	$ 200 = 2^{3} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	200.f (of order $2$, degree $1$, not minimal)

Newform invariants

comment:select newform

sage:traces = [40,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

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

Self dual:	no
Analytic conductor:	$32.0767639626$
Analytic rank:	$0$
Dimension:	$40$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			149.18
Character	$\chi$	$=$	200.149
Dual form			200.6.f.d.149.17

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.74979 + 5.37943i) q^{2} -25.2673 q^{3} +(-25.8765 - 18.8258i) q^{4} +(44.2124 - 135.923i) q^{6} -185.199i q^{7} +(146.550 - 106.259i) q^{8} +395.434 q^{9} +574.919i q^{11} +(653.827 + 475.675i) q^{12} -65.8691 q^{13} +(996.264 + 324.060i) q^{14} +(315.182 + 974.288i) q^{16} -1966.88i q^{17} +(-691.927 + 2127.21i) q^{18} +611.668i q^{19} +4679.47i q^{21} +(-3092.74 - 1005.99i) q^{22} +2976.41i q^{23} +(-3702.92 + 2684.88i) q^{24} +(115.257 - 354.338i) q^{26} -3851.59 q^{27} +(-3486.51 + 4792.29i) q^{28} -4474.76i q^{29} +7724.41 q^{31} +(-5792.61 - 9.30513i) q^{32} -14526.6i q^{33} +(10580.7 + 3441.64i) q^{34} +(-10232.4 - 7444.34i) q^{36} +7287.23 q^{37} +(-3290.42 - 1070.29i) q^{38} +1664.33 q^{39} -6220.02 q^{41} +(-25172.8 - 8188.09i) q^{42} +14399.5 q^{43} +(10823.3 - 14876.9i) q^{44} +(-16011.4 - 5208.11i) q^{46} -5910.00i q^{47} +(-7963.77 - 24617.6i) q^{48} -17491.6 q^{49} +49697.7i q^{51} +(1704.46 + 1240.04i) q^{52} -20628.0 q^{53} +(6739.48 - 20719.3i) q^{54} +(-19679.1 - 27140.9i) q^{56} -15455.2i q^{57} +(24071.6 + 7829.90i) q^{58} -12426.8i q^{59} -19832.6i q^{61} +(-13516.1 + 41552.9i) q^{62} -73233.9i q^{63} +(10185.9 - 31144.6i) q^{64} +(78144.9 + 25418.6i) q^{66} -56232.3 q^{67} +(-37028.1 + 50896.0i) q^{68} -75205.8i q^{69} -55797.8 q^{71} +(57950.9 - 42018.5i) q^{72} +3795.29i q^{73} +(-12751.1 + 39201.1i) q^{74} +(11515.1 - 15827.8i) q^{76} +106474. q^{77} +(-2912.23 + 8953.14i) q^{78} +74070.3 q^{79} +1228.55 q^{81} +(10883.7 - 33460.1i) q^{82} -117441. q^{83} +(88094.5 - 121088. i) q^{84} +(-25196.1 + 77461.0i) q^{86} +113065. i q^{87} +(61090.5 + 84254.5i) q^{88} +28115.4 q^{89} +12198.9i q^{91} +(56033.3 - 77019.0i) q^{92} -195175. q^{93} +(31792.4 + 10341.3i) q^{94} +(146363. + 235.115i) q^{96} -38940.1i q^{97} +(30606.7 - 94094.9i) q^{98} +227343. i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q - 2 q^{4} + 66 q^{6} + 3240 q^{9} + 848 q^{14} - 110 q^{16} - 18918 q^{24} + 18344 q^{26} + 14320 q^{31} + 19182 q^{34} + 29656 q^{36} - 44904 q^{39} - 11608 q^{41} + 23186 q^{44} - 75224 q^{46} - 125304 q^{49}+ \cdots + 115582 q^{96}+O(q^{100}) $ 40 * q - 2 * q^4 + 66 * q^6 + 3240 * q^9 + 848 * q^14 - 110 * q^16 - 18918 * q^24 + 18344 * q^26 + 14320 * q^31 + 19182 * q^34 + 29656 * q^36 - 44904 * q^39 - 11608 * q^41 + 23186 * q^44 - 75224 * q^46 - 125304 * q^49 - 177894 * q^54 - 73816 * q^56 - 230354 * q^64 + 262878 * q^66 - 15448 * q^71 - 4224 * q^74 + 111902 * q^76 + 15560 * q^79 + 193968 * q^81 + 195112 * q^84 - 131972 * q^86 + 6320 * q^89 + 117080 * q^94 + 115582 * q^96

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/200\mathbb{Z}\right)^\times$.

$n$	$101$	$151$	$177$
$\chi(n)$	$-1$	$1$	$-1$

Coefficient data

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

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

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

$2$	−1.74979	+	5.37943i	−0.309323	+	0.950957i
$2$	−1.74979	+	5.37943i	−0.309323	+	0.950957i
$3$	−25.2673			−1.62089			−0.810447	−	0.585811i	$-0.800776\pi$
$3$	−25.2673			−1.62089			−0.810447	+	0.585811i	$0.800776\pi$
$4$	−25.8765	−	18.8258i	−0.808639	−	0.588305i
$5$		0			0
$5$		0			0
$6$	44.2124	−	135.923i	0.501379	−	1.54140i
$7$		−	185.199i		−	1.42854i	−0.699869	−	0.714271i	$-0.746758\pi$
$7$		−	185.199i		−	1.42854i	0.699869	−	0.714271i	$-0.253242\pi$
$8$	146.550	−	106.259i	0.809583	−	0.587005i
$9$	395.434			1.62730
$10$		0			0
$11$			574.919i			1.43260i	0.697792	+	0.716300i	$0.254166\pi$
$11$			574.919i			1.43260i	−0.697792	+	0.716300i	$0.745834\pi$
$12$	653.827	+	475.675i	1.31072	+	0.953580i
$13$	−65.8691			−0.108099			−0.0540497	−	0.998538i	$-0.517213\pi$
$13$	−65.8691			−0.108099			−0.0540497	+	0.998538i	$0.517213\pi$
$14$	996.264	+	324.060i	1.35848	+	0.441880i
$15$		0			0
$16$	315.182	+	974.288i	0.307795	+	0.951453i
$17$		−	1966.88i		−	1.65065i	−0.564655	−	0.825327i	$-0.690991\pi$
$17$		−	1966.88i		−	1.65065i	0.564655	−	0.825327i	$-0.309009\pi$
$18$	−691.927	+	2127.21i	−0.503361	+	1.54749i
$19$			611.668i			0.388715i	0.980931	+	0.194358i	$0.0622622\pi$
$19$			611.668i			0.388715i	−0.980931	+	0.194358i	$0.937738\pi$
$20$		0			0
$21$			4679.47i			2.31552i
$22$	−3092.74	−	1005.99i	−1.36234	−	0.443136i
$23$			2976.41i			1.17320i	0.809875	+	0.586602i	$0.199535\pi$
$23$			2976.41i			1.17320i	−0.809875	+	0.586602i	$0.800465\pi$
$24$	−3702.92	+	2684.88i	−1.31225	+	0.951474i
$25$		0			0
$26$	115.257	−	354.338i	0.0334376	−	0.102798i
$27$	−3851.59			−1.01679
$28$	−3486.51	+	4792.29i	−0.840419	+	1.15518i
$29$		−	4474.76i		−	0.988041i	−0.869450	−	0.494020i	$-0.835527\pi$
$29$		−	4474.76i		−	0.988041i	0.869450	−	0.494020i	$-0.164473\pi$
$30$		0			0
$31$	7724.41			1.44365			0.721824	−	0.692077i	$-0.243304\pi$
$31$	7724.41			1.44365			0.721824	+	0.692077i	$0.243304\pi$
$32$	−5792.61	−	9.30513i	−0.999999	−	0.00160638i
$33$		−	14526.6i		−	2.32209i
$34$	10580.7	+	3441.64i	1.56970	+	0.510585i
$35$		0			0
$36$	−10232.4	−	7444.34i	−1.31590	−	0.957349i
$37$	7287.23			0.875101			0.437551	−	0.899194i	$-0.355846\pi$
$37$	7287.23			0.875101			0.437551	+	0.899194i	$0.355846\pi$
$38$	−3290.42	−	1070.29i	−0.369652	−	0.120238i
$39$	1664.33			0.175218
$40$		0			0
$41$	−6220.02			−0.577873			−0.288936	−	0.957348i	$-0.593302\pi$
$41$	−6220.02			−0.577873			−0.288936	+	0.957348i	$0.593302\pi$
$42$	−25172.8	−	8188.09i	−2.20196	−	0.716242i
$43$	14399.5			1.18762			0.593808	−	0.804607i	$-0.297624\pi$
$43$	14399.5			1.18762			0.593808	+	0.804607i	$0.297624\pi$
$44$	10823.3	−	14876.9i	0.842806	−	1.15846i
$45$		0			0
$46$	−16011.4	−	5208.11i	−1.11567	−	0.362899i
$47$		−	5910.00i		−	0.390250i	−0.980778	−	0.195125i	$-0.937489\pi$
$47$		−	5910.00i		−	0.390250i	0.980778	−	0.195125i	$-0.0625113\pi$
$48$	−7963.77	−	24617.6i	−0.498903	−	1.54221i
$49$	−17491.6			−1.04073
$50$		0			0
$51$			49697.7i			2.67554i
$52$	1704.46	+	1240.04i	0.0874134	+	0.0635954i
$53$	−20628.0			−1.00871			−0.504357	−	0.863495i	$-0.668271\pi$
$53$	−20628.0			−1.00871			−0.504357	+	0.863495i	$0.668271\pi$
$54$	6739.48	−	20719.3i	0.314515	−	0.966921i
$55$		0			0
$56$	−19679.1	−	27140.9i	−0.838562	−	1.15652i
$57$		−	15455.2i		−	0.630067i
$58$	24071.6	+	7829.90i	0.939584	+	0.305623i
$59$		−	12426.8i		−	0.464761i	−0.972625	−	0.232381i	$-0.925348\pi$
$59$		−	12426.8i		−	0.464761i	0.972625	−	0.232381i	$-0.0746515\pi$
$60$		0			0
$61$		−	19832.6i		−	0.682425i	−0.939986	−	0.341212i	$-0.889162\pi$
$61$		−	19832.6i		−	0.682425i	0.939986	−	0.341212i	$-0.110838\pi$
$62$	−13516.1	+	41552.9i	−0.446553	+	1.37285i
$63$		−	73233.9i		−	2.32467i
$64$	10185.9	−	31144.6i	0.310850	−	0.950459i
$65$		0			0
$66$	78144.9	+	25418.6i	2.20821	+	0.718276i
$67$	−56232.3			−1.53038			−0.765189	−	0.643806i	$-0.777354\pi$
$67$	−56232.3			−1.53038			−0.765189	+	0.643806i	$0.777354\pi$
$68$	−37028.1	+	50896.0i	−0.971088	+	1.33478i
$69$		−	75205.8i		−	1.90164i
$70$		0			0
$71$	−55797.8			−1.31363			−0.656813	−	0.754054i	$-0.728096\pi$
$71$	−55797.8			−1.31363			−0.656813	+	0.754054i	$0.728096\pi$
$72$	57950.9	−	42018.5i	1.31743	−	0.955234i
$73$			3795.29i			0.0833562i	0.999131	+	0.0416781i	$0.0132704\pi$
$73$			3795.29i			0.0833562i	−0.999131	+	0.0416781i	$0.986730\pi$
$74$	−12751.1	+	39201.1i	−0.270689	+	0.832184i
$75$		0			0
$76$	11515.1	−	15827.8i	0.228683	−	0.314330i
$77$	106474.			2.04653
$78$	−2912.23	+	8953.14i	−0.0541988	+	0.166625i
$79$	74070.3			1.33529			0.667647	−	0.744478i	$-0.267302\pi$
$79$	74070.3			1.33529			0.667647	+	0.744478i	$0.267302\pi$
$80$		0			0
$81$	1228.55			0.0208055
$82$	10883.7	−	33460.1i	0.178749	−	0.549532i
$83$	−117441.			−1.87122			−0.935611	−	0.353032i	$-0.885151\pi$
$83$	−117441.			−1.87122			−0.935611	+	0.353032i	$0.885151\pi$
$84$	88094.5	−	121088.i	1.36223	−	1.87242i
$85$		0			0
$86$	−25196.1	+	77461.0i	−0.367356	+	1.12937i
$87$			113065.i			1.60151i
$88$	61090.5	+	84254.5i	0.840944	+	1.15981i
$89$	28115.4			0.376244			0.188122	−	0.982146i	$-0.439760\pi$
$89$	28115.4			0.376244			0.188122	+	0.982146i	$0.439760\pi$
$90$		0			0
$91$			12198.9i			0.154425i
$92$	56033.3	−	77019.0i	0.690202	−	0.948699i
$93$	−195175.			−2.34000
$94$	31792.4	+	10341.3i	0.371111	+	0.120713i
$95$		0			0
$96$	146363.	+	235.115i	1.62089	+	0.00260377i
$97$		−	38940.1i		−	0.420211i	−0.977679	−	0.210105i	$-0.932619\pi$
$97$		−	38940.1i		−	0.420211i	0.977679	−	0.210105i	$-0.0673807\pi$
$98$	30606.7	−	94094.9i	0.321922	−	0.989693i
$99$			227343.i			2.33127i
$100$		0			0
$101$		−	137534.i		−	1.34155i	−0.741662	−	0.670773i	$-0.765962\pi$
$101$		−	137534.i		−	1.34155i	0.741662	−	0.670773i	$-0.234038\pi$
$102$	−267345.	−	86960.7i	−2.54432	−	0.827604i
$103$			32564.0i			0.302443i	0.988500	+	0.151222i	$0.0483207\pi$
$103$			32564.0i			0.302443i	−0.988500	+	0.151222i	$0.951679\pi$
$104$	−9653.12	+	6999.20i	−0.0875154	+	0.0634549i
$105$		0			0
$106$	36094.8	−	110967.i	0.312018	−	0.959245i
$107$	−154623.			−1.30561			−0.652807	−	0.757524i	$-0.726409\pi$
$107$	−154623.			−1.30561			−0.652807	+	0.757524i	$0.726409\pi$
$108$	99665.4	+	72509.0i	0.822214	+	0.598181i
$109$			98459.1i			0.793761i	0.917870	+	0.396880i	$0.129907\pi$
$109$			98459.1i			0.793761i	−0.917870	+	0.396880i	$0.870093\pi$
$110$		0			0
$111$	−184128.			−1.41845
$112$	180437.	−	58371.3i	1.35919	−	0.439698i
$113$		−	132338.i		−	0.974960i	−0.873134	−	0.487480i	$-0.837916\pi$
$113$		−	132338.i		−	0.974960i	0.873134	−	0.487480i	$-0.162084\pi$
$114$	83139.9	+	27043.3i	0.599166	+	0.194894i
$115$		0			0
$116$	−84240.8	+	115791.i	−0.581269	+	0.798968i
$117$	−26046.9			−0.175910
$118$	66849.2	+	21744.4i	0.441968	+	0.143761i
$119$	−364264.			−2.35803
$120$		0			0
$121$	−169481.			−1.05234
$122$	106688.	+	34702.9i	0.648957	+	0.211089i
$123$	157163.			0.936671
$124$	−199880.	−	145418.i	−1.16739	−	0.849305i
$125$		0			0
$126$	393956.	+	128144.i	2.21066	+	0.719072i
$127$			324744.i			1.78662i	0.449444	+	0.893309i	$0.351622\pi$
$127$			324744.i			1.78662i	−0.449444	+	0.893309i	$0.648378\pi$
$128$	149717.	+	109291.i	0.807693	+	0.589603i
$129$	−363835.			−1.92500
$130$		0			0
$131$			177689.i			0.904651i	0.891853	+	0.452326i	$0.149406\pi$
$131$			177689.i			0.904651i	−0.891853	+	0.452326i	$0.850594\pi$
$132$	−273475.	+	375898.i	−1.36610	+	1.87774i
$133$	113280.			0.555296
$134$	98394.8	−	302497.i	0.473380	−	1.45532i
$135$		0			0
$136$	−209000.	−	288247.i	−0.968943	−	1.33634i
$137$		−	19760.3i		−	0.0899480i	−0.998988	−	0.0449740i	$-0.985680\pi$
$137$		−	19760.3i		−	0.0899480i	0.998988	−	0.0449740i	$-0.0143205\pi$
$138$	404564.	+	131595.i	1.80838	+	0.588221i
$139$			55428.9i			0.243332i	0.992571	+	0.121666i	$0.0388237\pi$
$139$			55428.9i			0.243332i	−0.992571	+	0.121666i	$0.961176\pi$
$140$		0			0
$141$			149330.i			0.632555i
$142$	97634.6	−	300160.i	0.406334	−	1.24920i
$143$		−	37869.4i		−	0.154863i
$144$	124633.	+	385266.i	0.500874	+	1.54830i
$145$		0			0
$146$	−20416.5	−	6640.97i	−0.0792682	−	0.0257840i
$147$	441965.			1.68692
$148$	−188568.	−	137188.i	−0.707641	−	0.514827i
$149$			311409.i			1.14912i	0.818462	+	0.574560i	$0.194827\pi$
$149$			311409.i			1.14912i	−0.818462	+	0.574560i	$0.805173\pi$
$150$		0			0
$151$	−191117.			−0.682114			−0.341057	−	0.940043i	$-0.610785\pi$
$151$	−191117.			−0.682114			−0.341057	+	0.940043i	$0.610785\pi$
$152$	64995.4	+	89640.0i	0.228178	+	0.314697i
$153$		−	777772.i		−	2.68611i
$154$	−186308.	+	572771.i	−0.633038	+	1.94616i
$155$		0			0
$156$	−43067.0	−	31332.3i	−0.141688	−	0.103081i
$157$	−30356.8			−0.0982895			−0.0491448	−	0.998792i	$-0.515650\pi$
$157$	−30356.8			−0.0982895			−0.0491448	+	0.998792i	$0.515650\pi$
$158$	−129608.	+	398456.i	−0.413036	+	1.26981i
$159$	521214.			1.63502
$160$		0			0
$161$	551229.			1.67597
$162$	−2149.70	+	6608.87i	−0.00643562	+	0.0197852i
$163$	79111.8			0.233224			0.116612	−	0.993178i	$-0.462797\pi$
$163$	79111.8			0.233224			0.116612	+	0.993178i	$0.462797\pi$
$164$	160952.	+	117097.i	0.467290	+	0.339965i
$165$		0			0
$166$	205498.	−	631767.i	0.578811	−	1.77945i
$167$		−	533772.i		−	1.48103i	−0.672038	−	0.740516i	$-0.734581\pi$
$167$		−	533772.i		−	1.48103i	0.672038	−	0.740516i	$-0.265419\pi$
$168$	497237.	+	685777.i	1.35922	+	1.87460i
$169$	−366954.			−0.988315
$170$		0			0
$171$			241874.i			0.632556i
$172$	−372608.	−	271081.i	−0.960352	−	0.698680i
$173$	−355303.			−0.902575			−0.451288	−	0.892379i	$-0.649035\pi$
$173$	−355303.			−0.902575			−0.451288	+	0.892379i	$0.649035\pi$
$174$	−608224.	−	197840.i	−1.52297	−	0.495383i
$175$		0			0
$176$	−560137.	+	181204.i	−1.36305	+	0.440947i
$177$			313992.i			0.753329i
$178$	−49196.2	+	151245.i	−0.116381	+	0.357792i
$179$		−	610019.i		−	1.42302i	−0.702677	−	0.711509i	$-0.748012\pi$
$179$		−	610019.i		−	1.42302i	0.702677	−	0.711509i	$-0.251988\pi$
$180$		0			0
$181$			405423.i			0.919840i	0.887960	+	0.459920i	$0.152122\pi$
$181$			405423.i			0.919840i	−0.887960	+	0.459920i	$0.847878\pi$
$182$	−65622.9	−	21345.5i	−0.146851	−	0.0477670i
$183$			501115.i			1.10614i
$184$	316272.	+	436194.i	0.688677	+	0.949807i
$185$		0			0
$186$	341515.	−	1.04993e6i	0.723815	−	2.22524i
$187$	1.13080e6			2.36473
$188$	−111260.	+	152930.i	−0.229586	+	0.315572i
$189$			713309.i			1.45252i
$190$		0			0
$191$	−237405.			−0.470876			−0.235438	−	0.971889i	$-0.575653\pi$
$191$	−237405.			−0.470876			−0.235438	+	0.971889i	$0.575653\pi$
$192$	−257370.	+	786939.i	−0.503855	+	1.54059i
$193$			363225.i			0.701911i	0.936392	+	0.350956i	$0.114143\pi$
$193$			363225.i			0.701911i	−0.936392	+	0.350956i	$0.885857\pi$
$194$	209475.	+	68137.0i	0.399603	+	0.129981i
$195$		0			0
$196$	452621.	+	329293.i	0.841578	+	0.612269i
$197$	−162663.			−0.298623			−0.149311	−	0.988790i	$-0.547706\pi$
$197$	−162663.			−0.298623			−0.149311	+	0.988790i	$0.547706\pi$
$198$	−1.22297e6	−	397802.i	−2.21694	−	0.721115i
$199$	−306808.			−0.549205			−0.274602	−	0.961558i	$-0.588546\pi$
$199$	−306808.			−0.549205			−0.274602	+	0.961558i	$0.588546\pi$
$200$		0			0
$201$	1.42083e6			2.48058
$202$	739852.	+	240655.i	1.27575	+	0.414971i
$203$	−828721.			−1.41146
$204$	935597.	−	1.28600e6i	1.57403	−	2.16354i
$205$		0			0
$206$	−175175.	−	56980.2i	−0.287611	−	0.0935525i
$207$			1.17698e6i			1.90916i
$208$	−20760.7	−	64175.4i	−0.0332724	−	0.102851i
$209$	−351659.			−0.556874
$210$		0			0
$211$		−	916430.i		−	1.41708i	−0.705673	−	0.708538i	$-0.749355\pi$
$211$		−	916430.i		−	1.41708i	0.705673	−	0.708538i	$-0.250645\pi$
$212$	533781.	+	388339.i	0.815686	+	0.593432i
$213$	1.40986e6			2.12925
$214$	270558.	−	831784.i	0.403856	−	1.24158i
$215$		0			0
$216$	−564451.	+	409267.i	−0.823174	+	0.596860i
$217$		−	1.43055e6i		−	2.06231i
$218$	−529654.	−	172283.i	−0.754833	−	0.245528i
$219$		−	95896.6i		−	0.135112i
$220$		0			0
$221$			129557.i			0.178435i
$222$	322186.	−	990505.i	0.438758	−	1.34888i
$223$		−	122070.i		−	0.164379i	−0.996617	−	0.0821897i	$-0.973809\pi$
$223$		−	122070.i		−	0.164379i	0.996617	−	0.0821897i	$-0.0261913\pi$
$224$	−1723.30	+	1.07278e6i	−0.00229478	+	1.42854i
$225$		0			0
$226$	711900.	+	231563.i	0.927145	+	0.301577i
$227$	91677.1			0.118085			0.0590427	−	0.998255i	$-0.481195\pi$
$227$	91677.1			0.118085			0.0590427	+	0.998255i	$0.481195\pi$
$228$	−290955.	+	399925.i	−0.370671	+	0.509496i
$229$		−	1.04406e6i		−	1.31564i	−0.753174	−	0.657821i	$-0.771478\pi$
$229$		−	1.04406e6i		−	1.31564i	0.753174	−	0.657821i	$-0.228522\pi$
$230$		0			0
$231$	−2.69031e6			−3.31721
$232$	−475485.	−	655777.i	−0.579985	−	0.799901i
$233$		−	706266.i		−	0.852272i	−0.904659	−	0.426136i	$-0.859874\pi$
$233$		−	706266.i		−	0.852272i	0.904659	−	0.426136i	$-0.140126\pi$
$234$	45576.6	−	140117.i	0.0544130	−	0.167283i
$235$		0			0
$236$	−233944.	+	321562.i	−0.273421	+	0.375824i
$237$	−1.87155e6			−2.16437
$238$	637387.	−	1.95953e6i	0.729392	−	2.24239i
$239$	−244587.			−0.276974			−0.138487	−	0.990364i	$-0.544224\pi$
$239$	−244587.			−0.276974			−0.138487	+	0.990364i	$0.544224\pi$
$240$		0			0
$241$	602450.			0.668156			0.334078	−	0.942545i	$-0.391575\pi$
$241$	602450.			0.668156			0.334078	+	0.942545i	$0.391575\pi$
$242$	296557.	−	911711.i	0.325514	−	1.00073i
$243$	904893.			0.983064
$244$	−373363.	+	513197.i	−0.401474	+	0.551835i
$245$		0			0
$246$	−275002.	+	845446.i	−0.289733	+	0.890734i
$247$		−	40290.0i		−	0.0420199i
$248$	1.13201e6	−	820791.i	1.16875	−	0.847429i
$249$	2.96742e6			3.03306
$250$		0			0
$251$			416637.i			0.417421i	0.977977	+	0.208710i	$0.0669266\pi$
$251$			416637.i			0.417421i	−0.977977	+	0.208710i	$0.933073\pi$
$252$	−1.37868e6	+	1.89503e6i	−1.36761	+	1.87982i
$253$	−1.71120e6			−1.68073
$254$	−1.74694e6	−	568234.i	−1.69900	−	0.552641i
$255$		0			0
$256$	−849897.	+	614155.i	−0.810525	+	0.585704i
$257$		−	2065.15i		−	0.00195038i	−1.00000		0.000975191i	$-0.999690\pi$
$257$		−	2065.15i		−	0.00195038i	1.00000		0.000975191i	$-0.000310413\pi$
$258$	636636.	−	1.95723e6i	0.595446	−	1.83059i
$259$		−	1.34959e6i		−	1.25012i
$260$		0			0
$261$		−	1.76947e6i		−	1.60784i
$262$	−955863.	−	310918.i	−0.860285	−	0.279829i
$263$			1.69358e6i			1.50979i	0.655844	+	0.754897i	$0.272313\pi$
$263$			1.69358e6i			1.50979i	−0.655844	+	0.754897i	$0.727687\pi$
$264$	−1.54359e6	−	2.12888e6i	−1.36308	−	1.87993i
$265$		0			0
$266$	−198217.	+	609382.i	−0.171766	+	0.528063i
$267$	−710400.			−0.609852
$268$	1.45509e6	+	1.05861e6i	1.23752	+	0.900329i
$269$			404802.i			0.341085i	0.985350	+	0.170542i	$0.0545520\pi$
$269$			404802.i			0.341085i	−0.985350	+	0.170542i	$0.945448\pi$
$270$		0			0
$271$	826006.			0.683219			0.341609	−	0.939842i	$-0.389028\pi$
$271$	826006.			0.683219			0.341609	+	0.939842i	$0.389028\pi$
$272$	1.91631e6	−	619925.i	1.57052	−	0.508062i
$273$		−	308232.i		−	0.250306i
$274$	106299.	+	34576.4i	0.0855367	+	0.0278229i
$275$		0			0
$276$	−1.41581e6	+	1.94606e6i	−1.11875	+	1.53774i
$277$	−1.86599e6			−1.46120			−0.730602	−	0.682804i	$-0.760760\pi$
$277$	−1.86599e6			−1.46120			−0.730602	+	0.682804i	$0.760760\pi$
$278$	−298176.	−	96989.1i	−0.231398	−	0.0752681i
$279$	3.05449e6			2.34925
$280$		0			0
$281$	−687132.			−0.519128			−0.259564	−	0.965726i	$-0.583579\pi$
$281$	−687132.			−0.519128			−0.259564	+	0.965726i	$0.583579\pi$
$282$	−803307.	−	261296.i	−0.601532	−	0.195663i
$283$	341635.			0.253569			0.126784	−	0.991930i	$-0.459534\pi$
$283$	341635.			0.253569			0.126784	+	0.991930i	$0.459534\pi$
$284$	1.44385e6	+	1.05044e6i	1.06225	+	0.772812i
$285$		0			0
$286$	203716.	+	66263.6i	0.147268	+	0.0479027i
$287$			1.15194e6i			0.825516i
$288$	−2.29060e6	−	3679.56i	−1.62730	−	0.00261406i
$289$	−2.44877e6			−1.72466
$290$		0			0
$291$			983908.i			0.681118i
$292$	71449.3	−	98208.7i	0.0490389	−	0.0674051i
$293$	−1.13497e6			−0.772355			−0.386178	−	0.922424i	$-0.626205\pi$
$293$	−1.13497e6			−0.772355			−0.386178	+	0.922424i	$0.626205\pi$
$294$	−773347.	+	2.37752e6i	−0.521802	+	1.60419i
$295$		0			0
$296$	1.06795e6	−	774336.i	0.708467	−	0.513689i
$297$		−	2.21435e6i		−	1.45665i
$298$	−1.67520e6	−	544901.i	−1.09276	−	0.355449i
$299$		−	196054.i		−	0.126823i
$300$		0			0
$301$		−	2.66677e6i		−	1.69656i
$302$	334415.	−	1.02810e6i	0.210993	−	0.648661i
$303$			3.47510e6i			2.17451i
$304$	−595940.	+	192786.i	−0.369844	+	0.119644i
$305$		0			0
$306$	4.18397e6	+	1.36094e6i	2.55438	+	0.830874i
$307$	−3.14641e6			−1.90533			−0.952663	−	0.304030i	$-0.901668\pi$
$307$	−3.14641e6			−1.90533			−0.952663	+	0.304030i	$0.901668\pi$
$308$	−2.75518e6	−	2.00446e6i	−1.65490	−	1.20398i
$309$		−	822802.i		−	0.490229i
$310$		0			0
$311$	−837157.			−0.490802			−0.245401	−	0.969422i	$-0.578920\pi$
$311$	−837157.			−0.490802			−0.245401	+	0.969422i	$0.578920\pi$
$312$	243908.	−	176851.i	0.141853	−	0.102854i
$313$			529258.i			0.305356i	0.988276	+	0.152678i	$0.0487898\pi$
$313$			529258.i			0.305356i	−0.988276	+	0.152678i	$0.951210\pi$
$314$	53118.1	−	163302.i	0.0304032	−	0.0934691i
$315$		0			0
$316$	−1.91668e6	−	1.39443e6i	−1.07977	−	0.785560i
$317$	2.04482e6			1.14290			0.571448	−	0.820638i	$-0.306382\pi$
$317$	2.04482e6			1.14290			0.571448	+	0.820638i	$0.306382\pi$
$318$	−912016.	+	2.80383e6i	−0.505749	+	1.55483i
$319$	2.57263e6			1.41547
$320$		0			0
$321$	3.90690e6			2.11626
$322$	−964536.	+	2.96529e6i	−0.518416	+	1.59378i
$323$	1.20308e6			0.641635
$324$	−31790.4	−	23128.3i	−0.0168242	−	0.0122400i
$325$		0			0
$326$	−138429.	+	425576.i	−0.0721413	+	0.221786i
$327$		−	2.48779e6i		−	1.28660i
$328$	−911545.	+	660935.i	−0.467836	+	0.339214i
$329$	−1.09453e6			−0.557489
$330$		0			0
$331$		−	535804.i		−	0.268804i	−0.990927	−	0.134402i	$-0.957089\pi$
$331$		−	535804.i		−	0.268804i	0.990927	−	0.134402i	$-0.0429114\pi$
$332$	3.03896e6	+	2.21092e6i	1.51314	+	1.10085i
$333$	2.88162e6			1.42405
$334$	2.87139e6	+	933990.i	1.40840	+	0.458117i
$335$		0			0
$336$	−4.55915e6	+	1.47488e6i	−2.20311	+	0.712704i
$337$		−	795512.i		−	0.381568i	−0.981632	−	0.190784i	$-0.938897\pi$
$337$		−	795512.i		−	0.381568i	0.981632	−	0.190784i	$-0.0611030\pi$
$338$	642094.	−	1.97400e6i	0.305708	−	0.939845i
$339$			3.34381e6i			1.58031i
$340$		0			0
$341$			4.44091e6i			2.06817i
$342$	−1.30114e6	−	423230.i	−0.601534	−	0.195664i
$343$			126790.i			0.0581902i
$344$	2.11025e6	−	1.53008e6i	0.961473	−	0.697136i
$345$		0			0
$346$	621706.	−	1.91132e6i	0.279187	−	0.858310i
$347$	−1.16949e6			−0.521401			−0.260700	−	0.965420i	$-0.583953\pi$
$347$	−1.16949e6			−0.521401			−0.260700	+	0.965420i	$0.583953\pi$
$348$	2.12853e6	−	2.92572e6i	0.942176	−	1.29504i
$349$		−	1.63512e6i		−	0.718596i	−0.933223	−	0.359298i	$-0.883016\pi$
$349$		−	1.63512e6i		−	0.718596i	0.933223	−	0.359298i	$-0.116984\pi$
$350$		0			0
$351$	253700.			0.109914
$352$	5349.70	−	3.33028e6i	0.00230130	−	1.43260i
$353$			2.34590e6i			1.00201i	0.865444	+	0.501006i	$0.167037\pi$
$353$			2.34590e6i			1.00201i	−0.865444	+	0.501006i	$0.832963\pi$
$354$	−1.68909e6	−	549420.i	−0.716384	−	0.233022i
$355$		0			0
$356$	−727528.	−	529294.i	−0.304246	−	0.221346i
$357$	9.20396e6			3.82212
$358$	3.28155e6	+	1.06741e6i	1.35323	+	0.440172i
$359$	−462114.			−0.189240			−0.0946200	−	0.995513i	$-0.530164\pi$
$359$	−462114.			−0.189240			−0.0946200	+	0.995513i	$0.530164\pi$
$360$		0			0
$361$	2.10196e6			0.848900
$362$	−2.18094e6	−	709407.i	−0.874728	−	0.284527i
$363$	4.28232e6			1.70574
$364$	229653.	−	315664.i	0.0908487	−	0.124874i
$365$		0			0
$366$	−2.69571e6	−	876847.i	−1.05189	−	0.342154i
$367$			3.73676e6i			1.44820i	0.689693	+	0.724102i	$0.257746\pi$
$367$			3.73676e6i			1.44820i	−0.689693	+	0.724102i	$0.742254\pi$
$368$	−2.89988e6	+	938111.i	−1.11625	+	0.361106i
$369$	−2.45961e6			−0.940372
$370$		0			0
$371$			3.82029e6i			1.44099i
$372$	5.05043e6	+	3.67431e6i	1.89222	+	1.37663i
$373$	214685.			0.0798970			0.0399485	−	0.999202i	$-0.487281\pi$
$373$	214685.			0.0798970			0.0399485	+	0.999202i	$0.487281\pi$
$374$	−1.97866e6	+	6.08305e6i	−0.731464	+	2.24876i
$375$		0			0
$376$	−627993.	−	866112.i	−0.229079	−	0.315940i
$377$			294748.i			0.106807i
$378$	−3.83719e6	−	1.24814e6i	−1.38129	−	0.449298i
$379$		−	2.28648e6i		−	0.817652i	−0.912612	−	0.408826i	$-0.865938\pi$
$379$		−	2.28648e6i		−	0.817652i	0.912612	−	0.408826i	$-0.134062\pi$
$380$		0			0
$381$		−	8.20538e6i		−	2.89592i
$382$	415410.	−	1.27710e6i	0.145653	−	0.447783i
$383$		−	1.69175e6i		−	0.589302i	−0.955605	−	0.294651i	$-0.904797\pi$
$383$		−	1.69175e6i		−	0.589302i	0.955605	−	0.294651i	$-0.0952034\pi$
$384$	−3.78294e6	−	2.76149e6i	−1.30919	−	0.955685i
$385$		0			0
$386$	−1.95394e6	−	635568.i	−0.667487	−	0.217117i
$387$	5.69404e6			1.93261
$388$	−733076.	+	1.00763e6i	−0.247212	+	0.339799i
$389$		−	2.43317e6i		−	0.815266i	−0.913146	−	0.407633i	$-0.866354\pi$
$389$		−	2.43317e6i		−	0.815266i	0.913146	−	0.407633i	$-0.133646\pi$
$390$		0			0
$391$	5.85426e6			1.93656
$392$	−2.56340e6	+	1.85865e6i	−0.842561	+	0.610916i
$393$		−	4.48970e6i		−	1.46634i
$394$	284626.	−	875033.i	0.0923708	−	0.283978i
$395$		0			0
$396$	4.27990e6	−	5.88282e6i	1.37150	−	1.88516i
$397$	−3.05521e6			−0.972893			−0.486446	−	0.873710i	$-0.661707\pi$
$397$	−3.05521e6			−0.972893			−0.486446	+	0.873710i	$0.661707\pi$
$398$	536851.	−	1.65045e6i	0.169881	−	0.522270i
$399$	−2.86228e6			−0.900077
$400$		0			0
$401$	−131858.			−0.0409493			−0.0204746	−	0.999790i	$-0.506518\pi$
$401$	−131858.			−0.0409493			−0.0204746	+	0.999790i	$0.506518\pi$
$402$	−2.48617e6	+	7.64327e6i	−0.767300	+	2.35893i
$403$	−508800.			−0.156057
$404$	−2.58918e6	+	3.55888e6i	−0.789238	+	1.08483i
$405$		0			0
$406$	1.45009e6	−	4.45804e6i	0.436596	−	1.34224i
$407$			4.18957e6i			1.25367i
$408$	5.28085e6	+	7.28321e6i	1.57055	+	2.16607i
$409$	2.64156e6			0.780821			0.390411	−	0.920641i	$-0.372333\pi$
$409$	2.64156e6			0.780821			0.390411	+	0.920641i	$0.372333\pi$
$410$		0			0
$411$			499288.i			0.145796i
$412$	613041.	−	842640.i	0.177929	−	0.244568i
$413$	−2.30143e6			−0.663931
$414$	−6.33145e6	−	2.05946e6i	−1.81553	−	0.590545i
$415$		0			0
$416$	381554.	+	612.920i	0.108099	+	0.000173648i
$417$		−	1.40054e6i		−	0.394416i
$418$	615331.	−	1.89173e6i	0.172254	−	0.529563i
$419$			1.36333e6i			0.379372i	0.981845	+	0.189686i	$0.0607470\pi$
$419$			1.36333e6i			0.379372i	−0.981845	+	0.189686i	$0.939253\pi$
$420$		0			0
$421$			3.78864e6i			1.04178i	0.853623	+	0.520892i	$0.174401\pi$
$421$			3.78864e6i			1.04178i	−0.853623	+	0.520892i	$0.825599\pi$
$422$	4.92987e6	+	1.60356e6i	1.34758	+	0.438334i
$423$		−	2.33702e6i		−	0.635054i
$424$	−3.02304e6	+	2.19192e6i	−0.816638	+	0.592121i
$425$		0			0
$426$	−2.46696e6	+	7.58423e6i	−0.658625	+	2.02482i
$427$	−3.67297e6			−0.974873
$428$	4.00110e6	+	2.91090e6i	1.05577	+	0.768100i
$429$			956855.i			0.251017i
$430$		0			0
$431$	−6.99954e6			−1.81500			−0.907499	−	0.420054i	$-0.862011\pi$
$431$	−6.99954e6			−1.81500			−0.907499	+	0.420054i	$0.862011\pi$
$432$	−1.21395e6	−	3.75255e6i	−0.312962	−	0.967425i
$433$			1.07862e6i			0.276470i	0.990399	+	0.138235i	$0.0441430\pi$
$433$			1.07862e6i			0.276470i	−0.990399	+	0.138235i	$0.955857\pi$
$434$	7.69555e6	+	2.50317e6i	1.96117	+	0.637920i
$435$		0			0
$436$	1.85357e6	−	2.54777e6i	0.466974	−	0.641866i
$437$	−1.82058e6			−0.456043
$438$	515869.	+	167799.i	0.128485	+	0.0417931i
$439$	−6.18225e6			−1.53104			−0.765518	−	0.643415i	$-0.777517\pi$
$439$	−6.18225e6			−1.53104			−0.765518	+	0.643415i	$0.777517\pi$
$440$		0			0
$441$	−6.91678e6			−1.69359
$442$	−696941.	−	226697.i	−0.169684	−	0.0551939i
$443$	1.96693e6			0.476189			0.238094	−	0.971242i	$-0.423477\pi$
$443$	1.96693e6			0.476189			0.238094	+	0.971242i	$0.423477\pi$
$444$	4.76459e6	+	3.46636e6i	1.14701	+	0.834480i
$445$		0			0
$446$	656667.	+	213597.i	0.156318	+	0.0508462i
$447$		−	7.86845e6i		−	1.86260i
$448$	−5.76795e6	−	1.88642e6i	−1.35777	−	0.444062i
$449$	3.64999e6			0.854430			0.427215	−	0.904150i	$-0.359495\pi$
$449$	3.64999e6			0.854430			0.427215	+	0.904150i	$0.359495\pi$
$450$		0			0
$451$		−	3.57601e6i		−	0.827860i
$452$	−2.49135e6	+	3.42443e6i	−0.573574	+	0.788391i
$453$	4.82900e6			1.10564
$454$	−160416.	+	493170.i	−0.0365265	+	0.112294i
$455$		0			0
$456$	−1.64225e6	−	2.26496e6i	−0.369852	−	0.510091i
$457$		−	512099.i		−	0.114700i	−0.998354	−	0.0573500i	$-0.981735\pi$
$457$		−	512099.i		−	0.114700i	0.998354	−	0.0573500i	$-0.0182651\pi$
$458$	5.61646e6	+	1.82689e6i	1.25112	+	0.406958i
$459$			7.57562e6i			1.67836i
$460$		0			0
$461$		−	1.17026e6i		−	0.256466i	−0.991744	−	0.128233i	$-0.959069\pi$
$461$		−	1.17026e6i		−	0.256466i	0.991744	−	0.128233i	$-0.0409306\pi$
$462$	4.70749e6	−	1.44723e7i	1.02609	−	3.15453i
$463$		−	2.99324e6i		−	0.648918i	−0.945900	−	0.324459i	$-0.894818\pi$
$463$		−	2.99324e6i		−	0.648918i	0.945900	−	0.324459i	$-0.105182\pi$
$464$	4.35970e6	−	1.41036e6i	0.940074	−	0.304114i
$465$		0			0
$466$	3.79930e6	+	1.23582e6i	0.810474	+	0.263627i
$467$	−814584.			−0.172840			−0.0864198	−	0.996259i	$-0.527543\pi$
$467$	−814584.			−0.172840			−0.0864198	+	0.996259i	$0.527543\pi$
$468$	674000.	+	490352.i	0.142248	+	0.103489i
$469$			1.04141e7i			2.18621i
$470$		0			0
$471$	767033.			0.159317
$472$	−1.32047e6	−	1.82115e6i	−0.272817	−	0.376263i
$473$			8.27854e6i			1.70138i
$474$	3.27483e6	−	1.00679e7i	0.669488	−	2.05822i
$475$		0			0
$476$	9.42587e6	+	6.85755e6i	1.90680	+	1.38724i
$477$	−8.15703e6			−1.64148
$478$	427977.	−	1.31574e6i	0.0856742	−	0.263390i
$479$	−3.00391e6			−0.598202			−0.299101	−	0.954222i	$-0.596687\pi$
$479$	−3.00391e6			−0.598202			−0.299101	+	0.954222i	$0.596687\pi$
$480$		0			0
$481$	−480003.			−0.0945979
$482$	−1.05416e6	+	3.24083e6i	−0.206676	+	0.635388i
$483$	−1.39280e7			−2.71658
$484$	4.38557e6	+	3.19061e6i	0.850966	+	0.619099i
$485$		0			0
$486$	−1.58338e6	+	4.86781e6i	−0.304084	+	0.934852i
$487$			7.07824e6i			1.35239i	0.736722	+	0.676196i	$0.236373\pi$
$487$			7.07824e6i			1.35239i	−0.736722	+	0.676196i	$0.763627\pi$
$488$	−2.10740e6	−	2.90647e6i	−0.400587	−	0.552479i
$489$	−1.99894e6			−0.378031
$490$		0			0
$491$		−	1.91785e6i		−	0.359014i	−0.983757	−	0.179507i	$-0.942550\pi$
$491$		−	1.91785e6i		−	0.359014i	0.983757	−	0.179507i	$-0.0574502\pi$
$492$	−4.06682e6	−	2.95871e6i	−0.757429	−	0.551048i
$493$	−8.80133e6			−1.63091
$494$	216737.	+	70499.1i	0.0399591	+	0.0129977i
$495$		0			0
$496$	2.43459e6	+	7.52580e6i	0.444347	+	1.37356i
$497$			1.03337e7i			1.87657i
$498$	−5.19236e6	+	1.59630e7i	−0.938192	+	2.88431i
$499$		−	2.99398e6i		−	0.538267i	−0.963103	−	0.269133i	$-0.913263\pi$
$499$		−	2.99398e6i		−	0.538267i	0.963103	−	0.269133i	$-0.0867372\pi$
$500$		0			0
$501$			1.34870e7i			2.40060i
$502$	−2.24127e6	−	729029.i	−0.396949	−	0.129118i
$503$			3.15402e6i			0.555832i	0.960605	+	0.277916i	$0.0896437\pi$
$503$			3.15402e6i			0.555832i	−0.960605	+	0.277916i	$0.910356\pi$
$504$	−7.78178e6	−	1.07324e7i	−1.36459	−	1.88201i
$505$		0			0
$506$	2.99424e6	−	9.20526e6i	0.519889	−	1.59831i
$507$	9.27193e6			1.60195
$508$	6.11355e6	−	8.40322e6i	1.05108	−	1.44473i
$509$			4.01915e6i			0.687606i	0.939042	+	0.343803i	$0.111715\pi$
$509$			4.01915e6i			0.687606i	−0.939042	+	0.343803i	$0.888285\pi$
$510$		0			0
$511$	702884.			0.119078
$512$	−1.81666e6	−	5.64660e6i	−0.306266	−	0.951946i
$513$		−	2.35589e6i		−	0.395241i
$514$	11109.3	+	3613.59i	0.00185473	+	0.000603297i
$515$		0			0
$516$	9.41477e6	+	6.84948e6i	1.55663	+	1.13249i
$517$	3.39777e6			0.559073
$518$	7.26001e6	+	2.36150e6i	1.18881	+	0.386690i
$519$	8.97752e6			1.46298
$520$		0			0
$521$	−2.01168e6			−0.324687			−0.162344	−	0.986734i	$-0.551905\pi$
$521$	−2.01168e6			−0.324687			−0.162344	+	0.986734i	$0.551905\pi$
$522$	9.51875e6	+	3.09621e6i	1.52899	+	0.497341i
$523$	−1.04130e7			−1.66464			−0.832320	−	0.554295i	$-0.812988\pi$
$523$	−1.04130e7			−1.66464			−0.832320	+	0.554295i	$0.812988\pi$
$524$	3.34512e6	−	4.59795e6i	0.532211	−	0.731536i
$525$		0			0
$526$	−9.11052e6	−	2.96342e6i	−1.43575	−	0.467013i
$527$		−	1.51930e7i		−	2.38296i
$528$	1.41531e7	−	4.57853e6i	2.20936	−	0.714728i
$529$	−2.42270e6			−0.376409
$530$		0			0
$531$		−	4.91399e6i		−	0.756306i
$532$	−2.93129e6	−	2.13259e6i	−0.449034	−	0.326684i
$533$	409707.			0.0624676
$534$	1.24305e6	−	3.82154e6i	0.188641	−	0.579943i
$535$		0			0
$536$	−8.24085e6	+	5.97520e6i	−1.23897	+	0.898339i
$537$			1.54135e7i			2.30656i
$538$	−2.17760e6	−	708320.i	−0.324357	−	0.105505i
$539$		−	1.00563e7i		−	1.49096i
$540$		0			0
$541$		−	4.03497e6i		−	0.592717i	−0.955077	−	0.296358i	$-0.904228\pi$
$541$		−	4.03497e6i		−	0.592717i	0.955077	−	0.296358i	$-0.0957723\pi$
$542$	−1.44534e6	+	4.44344e6i	−0.211335	+	0.649712i
$543$		−	1.02439e7i		−	1.49096i
$544$	−18302.1	+	1.13934e7i	−0.00265157	+	1.65065i
$545$		0			0
$546$	1.65811e6	+	539342.i	0.238030	+	0.0774253i
$547$	−3.72273e6			−0.531978			−0.265989	−	0.963976i	$-0.585698\pi$
$547$	−3.72273e6			−0.531978			−0.265989	+	0.963976i	$0.585698\pi$
$548$	−372002.	+	511326.i	−0.0529168	+	0.0727354i
$549$		−	7.84248e6i		−	1.11051i
$550$		0			0
$551$	2.73707e6			0.384066
$552$	−7.99132e6	−	1.10214e7i	−1.11627	−	1.53954i
$553$		−	1.37177e7i		−	1.90752i
$554$	3.26510e6	−	1.00380e7i	0.451983	−	1.38954i
$555$		0			0
$556$	1.04349e6	−	1.43430e6i	0.143153	−	0.196768i
$557$	−1.07331e7			−1.46584			−0.732919	−	0.680316i	$-0.761843\pi$
$557$	−1.07331e7			−1.46584			−0.732919	+	0.680316i	$0.761843\pi$
$558$	−5.34473e6	+	1.64314e7i	−0.726675	+	2.23403i
$559$	−948480.			−0.128380
$560$		0			0
$561$	−2.85722e7			−3.83298
$562$	1.20234e6	−	3.69637e6i	0.160578	−	0.493668i
$563$	1.10773e7			1.47287			0.736433	−	0.676511i	$-0.236509\pi$
$563$	1.10773e7			1.47287			0.736433	+	0.676511i	$0.236509\pi$
$564$	2.81124e6	−	3.86412e6i	0.372135	−	0.511508i
$565$		0			0
$566$	−597790.	+	1.83780e6i	−0.0784346	+	0.241133i
$567$		−	227525.i		−	0.0297216i
$568$	−8.17718e6	+	5.92904e6i	−1.06349	+	0.771105i
$569$	−6.94176e6			−0.898854			−0.449427	−	0.893317i	$-0.648372\pi$
$569$	−6.94176e6			−0.898854			−0.449427	+	0.893317i	$0.648372\pi$
$570$		0			0
$571$		−	1.13064e7i		−	1.45122i	−0.688107	−	0.725609i	$-0.741558\pi$
$571$		−	1.13064e7i		−	1.45122i	0.688107	−	0.725609i	$-0.258442\pi$
$572$	−712920.	+	979925.i	−0.0911068	+	0.125228i
$573$	5.99858e6			0.763241
$574$	−6.19678e6	−	2.01566e6i	−0.785030	−	0.255351i
$575$		0			0
$576$	4.02786e6	−	1.23156e7i	0.505846	−	1.54668i
$577$		−	1.47805e6i		−	0.184820i	−0.995721	−	0.0924101i	$-0.970543\pi$
$577$		−	1.47805e6i		−	0.184820i	0.995721	−	0.0924101i	$-0.0294571\pi$
$578$	4.28484e6	−	1.31730e7i	0.533476	−	1.64008i
$579$		−	9.17769e6i		−	1.13772i
$580$		0			0
$581$			2.17500e7i			2.67312i
$582$	−5.29286e6	−	1.72164e6i	−0.647714	−	0.210685i
$583$		−	1.18595e7i		−	1.44509i
$584$	403285.	+	556201.i	0.0489305	+	0.0674838i
$585$		0			0
$586$	1.98597e6	−	6.10551e6i	0.238907	−	0.734477i
$587$	−967824.			−0.115931			−0.0579657	−	0.998319i	$-0.518461\pi$
$587$	−967824.			−0.115931			−0.0579657	+	0.998319i	$0.518461\pi$
$588$	−1.14365e7	−	8.32033e6i	−1.36411	−	0.992424i
$589$			4.72477e6i			0.561168i
$590$		0			0
$591$	4.11005e6			0.484036
$592$	2.29680e6	+	7.09986e6i	0.269351	+	0.832618i
$593$		−	1.26252e7i		−	1.47435i	−0.675699	−	0.737177i	$-0.736158\pi$
$593$		−	1.26252e7i		−	1.47435i	0.675699	−	0.737177i	$-0.263842\pi$
$594$	1.19119e7	+	3.87465e6i	1.38521	+	0.450575i
$595$		0			0
$596$	5.86251e6	−	8.05816e6i	0.676033	−	0.929224i
$597$	7.75220e6			0.890204
$598$	1.05466e6	+	343053.i	0.120603	+	0.0392291i
$599$	−4.49357e6			−0.511710			−0.255855	−	0.966715i	$-0.582357\pi$
$599$	−4.49357e6			−0.511710			−0.255855	+	0.966715i	$0.582357\pi$
$600$		0			0
$601$	6.32166e6			0.713913			0.356956	−	0.934121i	$-0.383814\pi$
$601$	6.32166e6			0.713913			0.356956	+	0.934121i	$0.383814\pi$
$602$	1.43457e7	+	4.66629e6i	1.61335	+	0.524784i
$603$	−2.22361e7			−2.49038
$604$	4.94543e6	+	3.59792e6i	0.551584	+	0.401291i
$605$		0			0
$606$	−1.86940e7	−	6.08070e6i	−2.06786	−	0.672624i
$607$		−	1.12652e7i		−	1.24099i	−0.784212	−	0.620493i	$-0.786933\pi$
$607$		−	1.12652e7i		−	1.24099i	0.784212	−	0.620493i	$-0.213067\pi$
$608$	5691.65	−	3.54315e6i	0.000624423	−	0.388715i
$609$	2.09395e7			2.28783
$610$		0			0
$611$			389286.i			0.0421858i
$612$	−1.46422e7	+	2.01260e7i	−1.58025	+	2.17209i
$613$	−2.50596e6			−0.269354			−0.134677	−	0.990890i	$-0.543000\pi$
$613$	−2.50596e6			−0.269354			−0.134677	+	0.990890i	$0.543000\pi$
$614$	5.50556e6	−	1.69259e7i	0.589360	−	1.81188i
$615$		0			0
$616$	1.56038e7	−	1.13139e7i	1.65684	−	1.20132i
$617$		−	8.68891e6i		−	0.918867i	−0.888212	−	0.459433i	$-0.848053\pi$
$617$		−	8.68891e6i		−	0.918867i	0.888212	−	0.459433i	$-0.151947\pi$
$618$	4.42620e6	+	1.43973e6i	0.466187	+	0.151639i
$619$			3.52743e6i			0.370026i	0.982736	+	0.185013i	$0.0592327\pi$
$619$			3.52743e6i			0.370026i	−0.982736	+	0.185013i	$0.940767\pi$
$620$		0			0
$621$		−	1.14639e7i		−	1.19290i
$622$	1.46485e6	−	4.50343e6i	0.151816	−	0.466732i
$623$		−	5.20695e6i		−	0.537481i
$624$	524566.	+	1.62154e6i	0.0539310	+	0.166711i
$625$		0			0
$626$	−2.84711e6	−	926092.i	−0.290381	−	0.0944536i
$627$	8.88547e6			0.902634
$628$	785527.	+	571490.i	0.0794807	+	0.0578242i
$629$		−	1.43331e7i		−	1.44449i
$630$		0			0
$631$	1.36732e7			1.36709			0.683544	−	0.729909i	$-0.260438\pi$
$631$	1.36732e7			1.36709			0.683544	+	0.729909i	$0.260438\pi$
$632$	1.08550e7	−	7.87066e6i	1.08103	−	0.783824i
$633$			2.31557e7i			2.29693i
$634$	−3.57801e6	+	1.10000e7i	−0.353524	+	1.08685i
$635$		0			0
$636$	−1.34872e7	−	9.81225e6i	−1.32214	−	0.961891i
$637$	1.15216e6			0.112503
$638$	−4.50156e6	+	1.38392e7i	−0.437836	+	1.34605i
$639$	−2.20644e7			−2.13766
$640$		0			0
$641$	3.09731e6			0.297742			0.148871	−	0.988857i	$-0.452436\pi$
$641$	3.09731e6			0.297742			0.148871	+	0.988857i	$0.452436\pi$
$642$	−6.83627e6	+	2.10169e7i	−0.654608	+	2.01248i
$643$	1.56372e7			1.49152			0.745762	−	0.666212i	$-0.232086\pi$
$643$	1.56372e7			1.49152			0.745762	+	0.666212i	$0.232086\pi$
$644$	−1.42638e7	−	1.03773e7i	−1.35526	−	0.985983i
$645$		0			0
$646$	−2.10514e6	+	6.47187e6i	−0.198472	+	0.610167i
$647$		−	2.67797e6i		−	0.251504i	−0.992062	−	0.125752i	$-0.959866\pi$
$647$		−	2.67797e6i		−	0.251504i	0.992062	−	0.125752i	$-0.0401343\pi$
$648$	180044.	−	130544.i	0.0168438	−	0.0122130i
$649$	7.14442e6			0.665817
$650$		0			0
$651$			3.61461e7i			3.34279i
$652$	−2.04713e6	−	1.48934e6i	−0.188594	−	0.137207i
$653$	−1.36294e7			−1.25082			−0.625409	−	0.780297i	$-0.715068\pi$
$653$	−1.36294e7			−1.25082			−0.625409	+	0.780297i	$0.715068\pi$
$654$	1.33829e7	+	4.35312e6i	1.22350	+	0.397975i
$655$		0			0
$656$	−1.96044e6	−	6.06009e6i	−0.177866	−	0.549819i
$657$			1.50079e6i			0.135646i
$658$	1.91519e6	−	5.88792e6i	0.172444	−	0.530148i
$659$			9.26345e6i			0.830920i	0.909611	+	0.415460i	$0.136379\pi$
$659$			9.26345e6i			0.830920i	−0.909611	+	0.415460i	$0.863621\pi$
$660$		0			0
$661$			5.35606e6i			0.476806i	0.971166	+	0.238403i	$0.0766239\pi$
$661$			5.35606e6i			0.476806i	−0.971166	+	0.238403i	$0.923376\pi$
$662$	2.88232e6	+	937546.i	0.255621	+	0.0831472i
$663$		−	3.27354e6i		−	0.289224i
$664$	−1.72110e7	+	1.24792e7i	−1.51491	+	1.09842i
$665$		0			0
$666$	−5.04224e6	+	1.55015e7i	−0.440492	+	1.35421i
$667$	1.33187e7			1.15917
$668$	−1.00487e7	+	1.38121e7i	−0.871299	+	1.19762i
$669$			3.08438e6i			0.266442i
$670$		0			0
$671$	1.14021e7			0.977642
$672$	43543.0	−	2.71063e7i	0.00371959	−	2.31551i
$673$			1.80861e7i			1.53924i	0.638501	+	0.769621i	$0.279555\pi$
$673$			1.80861e7i			1.53924i	−0.638501	+	0.769621i	$0.720445\pi$
$674$	4.27940e6	+	1.39198e6i	0.362855	+	0.118028i
$675$		0			0
$676$	9.49547e6	+	6.90819e6i	0.799190	+	0.581430i
$677$	1.52433e7			1.27822			0.639111	−	0.769114i	$-0.279302\pi$
$677$	1.52433e7			1.27822			0.639111	+	0.769114i	$0.279302\pi$
$678$	−1.79878e7	−	5.85097e6i	−1.50281	−	0.488825i
$679$	−7.21166e6			−0.600289
$680$		0			0
$681$	−2.31643e6			−0.191404
$682$	−2.38896e7	−	7.77068e6i	−1.96674	−	0.639732i
$683$	2.13600e7			1.75206			0.876031	−	0.482256i	$-0.160182\pi$
$683$	2.13600e7			1.75206			0.876031	+	0.482256i	$0.160182\pi$
$684$	4.55347e6	−	6.25885e6i	0.372136	−	0.511510i
$685$		0			0
$686$	−682057.	−	221856.i	−0.0553364	−	0.0179995i
$687$			2.63806e7i			2.13252i
$688$	4.53845e6	+	1.40292e7i	0.365541	+	1.12996i
$689$	1.35875e6			0.109041
$690$		0			0
$691$		−	5.43768e6i		−	0.433230i	−0.976257	−	0.216615i	$-0.930498\pi$
$691$		−	5.43768e6i		−	0.433230i	0.976257	−	0.216615i	$-0.0695016\pi$
$692$	9.19397e6	+	6.68884e6i	0.729858	+	0.530989i
$693$	4.21036e7			3.33032
$694$	2.04636e6	−	6.29117e6i	0.161281	−	0.495830i
$695$		0			0
$696$	1.20142e7	+	1.65697e7i	0.940095	+	1.29656i
$697$			1.22340e7i			0.953868i
$698$	8.79599e6	+	2.86111e6i	0.683354	+	0.222278i
$699$			1.78454e7i			1.38144i
$700$		0			0
$701$		−	8.82961e6i		−	0.678651i	−0.940669	−	0.339326i	$-0.889801\pi$
$701$		−	8.82961e6i		−	0.678651i	0.940669	−	0.339326i	$-0.110199\pi$
$702$	−443923.	+	1.36476e6i	−0.0339989	+	0.104524i
$703$			4.45737e6i			0.340165i
$704$	1.79057e7	+	5.85608e6i	1.36163	+	0.445323i
$705$		0			0
$706$	−1.26196e7	−	4.10484e6i	−0.952871	−	0.309945i
$707$	−2.54711e7			−1.91646
$708$	5.91113e6	−	8.12499e6i	0.443187	−	0.609171i
$709$		−	1.19737e7i		−	0.894566i	−0.894393	−	0.447283i	$-0.852392\pi$
$709$		−	1.19737e7i		−	0.894566i	0.894393	−	0.447283i	$-0.147608\pi$
$710$		0			0
$711$	2.92899e7			2.17292
$712$	4.12032e6	−	2.98753e6i	0.304601	−	0.220857i
$713$			2.29911e7i			1.69369i
$714$	−1.61050e7	+	4.95120e7i	−1.18227	+	3.63467i
$715$		0			0
$716$	−1.14841e7	+	1.57851e7i	−0.837169	+	1.15071i
$717$	6.18004e6			0.448945
$718$	808603.	−	2.48591e6i	0.0585362	−	0.179959i
$719$	6.87706e6			0.496113			0.248056	−	0.968746i	$-0.420208\pi$
$719$	6.87706e6			0.496113			0.248056	+	0.968746i	$0.420208\pi$
$720$		0			0
$721$	6.03081e6			0.432053
$722$	−3.67800e6	+	1.13073e7i	−0.262584	+	0.807268i
$723$	−1.52222e7			−1.08301
$724$	7.63240e6	−	1.04909e7i	0.541146	−	0.743819i
$725$		0			0
$726$	−7.49317e6	+	2.30364e7i	−0.527623	+	1.62208i
$727$		−	2.24438e7i		−	1.57493i	−0.616360	−	0.787464i	$-0.711394\pi$
$727$		−	2.24438e7i		−	1.57493i	0.616360	−	0.787464i	$-0.288606\pi$
$728$	1.29624e6	+	1.78775e6i	0.0906480	+	0.125019i
$729$	−2.31627e7			−1.61425
$730$		0			0
$731$		−	2.83221e7i		−	1.96034i
$732$	9.43387e6	−	1.29671e7i	0.650747	−	0.894467i
$733$	−2.81360e7			−1.93420			−0.967101	−	0.254393i	$-0.918124\pi$
$733$	−2.81360e7			−1.93420			−0.967101	+	0.254393i	$0.918124\pi$
$734$	−2.01016e7	−	6.53855e6i	−1.37718	−	0.447962i
$735$		0			0
$736$	27695.9	−	1.72412e7i	0.00188461	−	1.17320i
$737$		−	3.23290e7i		−	2.19242i
$738$	4.30380e6	−	1.32313e7i	0.290878	−	0.894254i
$739$			1.34928e7i			0.908845i	0.890786	+	0.454422i	$0.150154\pi$
$739$			1.34928e7i			0.908845i	−0.890786	+	0.454422i	$0.849846\pi$
$740$		0			0
$741$			1.01802e6i			0.0681098i
$742$	−2.05510e7	−	6.68471e6i	−1.37032	−	0.445731i
$743$			3.12986e6i			0.207995i	0.994578	+	0.103997i	$0.0331634\pi$
$743$			3.12986e6i			0.207995i	−0.994578	+	0.103997i	$0.966837\pi$
$744$	−2.86029e7	+	2.07391e7i	−1.89443	+	1.37359i
$745$		0			0
$746$	−375655.	+	1.15488e6i	−0.0247139	+	0.0759786i
$747$	−4.64403e7			−3.04504
$748$	−2.92611e7	−	2.12881e7i	−1.91221	−	1.39118i
$749$			2.86360e7i			1.86513i
$750$		0			0
$751$	−2.80509e7			−1.81487			−0.907437	−	0.420188i	$-0.861964\pi$
$751$	−2.80509e7			−1.81487			−0.907437	+	0.420188i	$0.861964\pi$
$752$	5.75804e6	−	1.86272e6i	0.371305	−	0.120117i
$753$		−	1.05273e7i		−	0.676595i
$754$	−1.58558e6	−	515748.i	−0.101568	−	0.0330377i
$755$		0			0
$756$	1.34286e7	−	1.84579e7i	0.854527	−	1.17457i
$757$	2.74473e7			1.74084			0.870421	−	0.492308i	$-0.163847\pi$
$757$	2.74473e7			1.74084			0.870421	+	0.492308i	$0.163847\pi$
$758$	1.22999e7	+	4.00086e6i	0.777552	+	0.252918i
$759$	4.32373e7			2.72429
$760$		0			0
$761$	−2.29174e7			−1.43451			−0.717255	−	0.696810i	$-0.754602\pi$
$761$	−2.29174e7			−1.43451			−0.717255	+	0.696810i	$0.754602\pi$
$762$	4.41403e7	+	1.43577e7i	2.75389	+	0.895773i
$763$	1.82345e7			1.13392
$764$	6.14320e6	+	4.46933e6i	0.380769	+	0.277019i
$765$		0			0
$766$	9.10062e6	+	2.96020e6i	0.560401	+	0.182284i
$767$			818543.i			0.0502404i
$768$	2.14746e7	−	1.55180e7i	1.31378	−	0.949365i
$769$	1.75616e7			1.07090			0.535448	−	0.844568i	$-0.320143\pi$
$769$	1.75616e7			1.07090			0.535448	+	0.844568i	$0.320143\pi$
$770$		0			0
$771$			52180.8i			0.00316136i
$772$	6.83798e6	−	9.39897e6i	0.412938	−	0.567593i
$773$	3.23291e7			1.94601			0.973005	−	0.230785i	$-0.0741295\pi$
$773$	3.23291e7			1.94601			0.973005	+	0.230785i	$0.0741295\pi$
$774$	−9.96340e6	+	3.06307e7i	−0.597799	+	1.83783i
$775$		0			0
$776$	−4.13774e6	−	5.70667e6i	−0.246666	−	0.340196i
$777$			3.41004e7i			2.02631i
$778$	1.30891e7	+	4.25755e6i	0.775283	+	0.252180i
$779$		−	3.80459e6i		−	0.224628i
$780$		0			0
$781$		−	3.20792e7i		−	1.88190i
$782$	−1.02437e7	+	3.14926e7i	−0.599020	+	1.84158i
$783$			1.72349e7i			1.00463i
$784$	−5.51304e6	−	1.70419e7i	−0.320332	−	0.990209i
$785$		0			0
$786$	2.41520e7	+	7.85605e6i	1.39443	+	0.453573i
$787$	−1.69534e7			−0.975707			−0.487853	−	0.872926i	$-0.662220\pi$
$787$	−1.69534e7			−0.975707			−0.487853	+	0.872926i	$0.662220\pi$
$788$	4.20914e6	+	3.06225e6i	0.241478	+	0.175681i
$789$		−	4.27922e7i		−	2.44722i
$790$		0			0
$791$	−2.45088e7			−1.39277
$792$	2.41573e7	+	3.33171e7i	1.36847	+	1.88736i
$793$			1.30635e6i			0.0737697i
$794$	5.34598e6	−	1.64353e7i	0.300938	−	0.925179i
$795$		0			0
$796$	7.93911e6	+	5.77590e6i	0.444109	+	0.323100i
$797$	−1.44730e7			−0.807073			−0.403537	−	0.914963i	$-0.632219\pi$
$797$	−1.44730e7			−0.807073			−0.403537	+	0.914963i	$0.632219\pi$
$798$	5.00839e6	−	1.53974e7i	0.278414	−	0.855935i
$799$	−1.16243e7			−0.644168
$800$		0			0
$801$	1.11178e7			0.612262
$802$	230725.	−	709322.i	0.0126665	−	0.0389410i
$803$	−2.18199e6			−0.119416
$804$	−3.67662e7	−	2.67483e7i	−2.00589	−	1.45934i
$805$		0			0
$806$	890294.	−	2.73705e6i	0.0482721	−	0.148404i
$807$		−	1.02282e7i		−	0.552863i
$808$	−1.46142e7	−	2.01556e7i	−0.787495	−	1.08609i
$809$	−2.41458e7			−1.29709			−0.648544	−	0.761177i	$-0.724622\pi$
$809$	−2.41458e7			−1.29709			−0.648544	+	0.761177i	$0.724622\pi$
$810$		0			0
$811$		−	1.55615e7i		−	0.830803i	−0.909638	−	0.415402i	$-0.863641\pi$
$811$		−	1.55615e7i		−	0.830803i	0.909638	−	0.415402i	$-0.136359\pi$
$812$	2.14443e7	+	1.56013e7i	1.14136	+	0.830368i
$813$	−2.08709e7			−1.10743
$814$	−2.25375e7	−	7.33088e6i	−1.19219	−	0.387789i
$815$		0			0
$816$	−4.84199e7	+	1.56638e7i	−2.54565	+	0.823516i
$817$			8.80770e6i			0.461644i
$818$	−4.62217e6	+	1.42101e7i	−0.241526	+	0.742527i
$819$			4.82385e6i			0.251295i
$820$		0			0
$821$		−	1.97285e7i		−	1.02150i	−0.859730	−	0.510749i	$-0.829368\pi$
$821$		−	1.97285e7i		−	1.02150i	0.859730	−	0.510749i	$-0.170632\pi$
$822$	−2.68588e6	−	873650.i	−0.138646	−	0.0450980i
$823$			2.08659e7i			1.07384i	0.843634	+	0.536919i	$0.180412\pi$
$823$			2.08659e7i			1.07384i	−0.843634	+	0.536919i	$0.819588\pi$
$824$	3.46022e6	+	4.77225e6i	0.177536	+	0.244853i
$825$		0			0
$826$	4.02703e6	−	1.23804e7i	0.205369	−	0.631370i
$827$	4.63684e6			0.235753			0.117877	−	0.993028i	$-0.462391\pi$
$827$	4.63684e6			0.235753			0.117877	+	0.993028i	$0.462391\pi$
$828$	2.21575e7	−	3.04559e7i	1.12317	−	1.54382i
$829$			3.84848e6i			0.194493i	0.995260	+	0.0972464i	$0.0310035\pi$
$829$			3.84848e6i			0.194493i	−0.995260	+	0.0972464i	$0.968997\pi$
$830$		0			0
$831$	4.71485e7			2.36846
$832$	−670937.	+	2.05147e6i	−0.0336027	+	0.102744i
$833$			3.44040e7i			1.71789i
$834$	7.53408e6	+	2.45065e6i	0.375073	+	0.122002i
$835$		0			0
$836$	9.09970e6	+	6.62026e6i	0.450310	+	0.327612i
$837$	−2.97512e7			−1.46788
$838$	−7.33393e6	−	2.38554e6i	−0.360767	−	0.117348i
$839$	−369751.			−0.0181344			−0.00906722	−	0.999959i	$-0.502886\pi$
$839$	−369751.			−0.0181344			−0.00906722	+	0.999959i	$0.502886\pi$
$840$		0			0
$841$	487665.			0.0237756
$842$	−2.03807e7	−	6.62933e6i	−0.990692	−	0.322247i
$843$	1.73619e7			0.841451
$844$	−1.72525e7	+	2.37140e7i	−0.833673	+	1.14590i
$845$		0			0
$846$	1.25718e7	+	4.08929e6i	0.603909	+	0.196437i
$847$			3.13877e7i			1.50332i
$848$	−6.50158e6	−	2.00977e7i	−0.310477	−	0.959745i
$849$	−8.63217e6			−0.411009
$850$		0			0
$851$			2.16898e7i			1.02667i
$852$	−3.64821e7	−	2.65416e7i	−1.72179	−	1.25265i
$853$	−2.12932e7			−1.00200			−0.501000	−	0.865447i	$-0.667034\pi$
$853$	−2.12932e7			−1.00200			−0.501000	+	0.865447i	$0.667034\pi$
$854$	6.42694e6	−	1.97585e7i	0.301550	−	0.927062i
$855$		0			0
$856$	−2.26600e7	+	1.64301e7i	−1.05700	+	0.766403i
$857$		−	3.65134e7i		−	1.69824i	−0.528198	−	0.849121i	$-0.677132\pi$
$857$		−	3.65134e7i		−	1.69824i	0.528198	−	0.849121i	$-0.322868\pi$
$858$	−5.14733e6	−	1.67430e6i	−0.238706	−	0.0776452i
$859$		−	2.21742e7i		−	1.02533i	−0.858588	−	0.512666i	$-0.828658\pi$
$859$		−	2.21742e7i		−	1.02533i	0.858588	−	0.512666i	$-0.171342\pi$
$860$		0			0
$861$		−	2.91064e7i		−	1.33807i
$862$	1.22477e7	−	3.76535e7i	0.561420	−	1.72599i
$863$		−	1.76878e7i		−	0.808439i	−0.914662	−	0.404220i	$-0.867543\pi$
$863$		−	1.76878e7i		−	0.808439i	0.914662	−	0.404220i	$-0.132457\pi$
$864$	2.23107e7	+	35839.5i	1.01679	+	0.00163334i
$865$		0			0
$866$	−5.80235e6	−	1.88736e6i	−0.262911	−	0.0855185i
$867$	6.18737e7			2.79549
$868$	−2.69312e7	+	3.70176e7i	−1.21327	+	1.66767i
$869$			4.25845e7i			1.91294i
$870$		0			0
$871$	3.70397e6			0.165433
$872$	1.04622e7	+	1.44292e7i	0.465942	+	0.642615i
$873$		−	1.53982e7i		−	0.683809i
$874$	3.18563e6	−	9.79366e6i	0.141064	−	0.433677i
$875$		0			0
$876$	−1.80533e6	+	2.48146e6i	−0.0794869	+	0.109257i
$877$	8.63639e6			0.379169			0.189585	−	0.981864i	$-0.439286\pi$
$877$	8.63639e6			0.379169			0.189585	+	0.981864i	$0.439286\pi$
$878$	1.08177e7	−	3.32569e7i	0.473584	−	1.45595i
$879$	2.86777e7			1.25191
$880$		0			0
$881$	−1.47043e7			−0.638269			−0.319135	−	0.947709i	$-0.603392\pi$
$881$	−1.47043e7			−0.638269			−0.319135	+	0.947709i	$0.603392\pi$
$882$	1.21029e7	−	3.72083e7i	0.523864	−	1.61053i
$883$	1.00513e7			0.433832			0.216916	−	0.976190i	$-0.430400\pi$
$883$	1.00513e7			0.433832			0.216916	+	0.976190i	$0.430400\pi$
$884$	2.43900e6	−	3.35247e6i	0.104974	−	0.144289i
$885$		0			0
$886$	−3.44172e6	+	1.05809e7i	−0.147296	+	0.452835i
$887$		−	7.52032e6i		−	0.320943i	−0.987041	−	0.160471i	$-0.948699\pi$
$887$		−	7.52032e6i		−	0.320943i	0.987041	−	0.160471i	$-0.0513014\pi$
$888$	−2.69840e7	+	1.95654e7i	−1.14835	+	0.832636i
$889$	6.01422e7			2.55226
$890$		0			0
$891$			706315.i			0.0298060i
$892$	−2.29806e6	+	3.15874e6i	−0.0967052	+	0.132924i
$893$	3.61496e6			0.151696
$894$	4.23278e7	+	1.37682e7i	1.77126	+	0.576145i
$895$		0			0
$896$	2.02406e7	−	2.77274e7i	0.842273	−	1.15382i
$897$			4.95374e6i			0.205566i
$898$	−6.38673e6	+	1.96349e7i	−0.264294	+	0.812526i
$899$		−	3.45649e7i		−	1.42638i
$900$		0			0
$901$			4.05729e7i			1.66504i
$902$	1.92369e7	+	6.25727e6i	0.787260	+	0.256076i
$903$			6.73819e7i			2.74994i
$904$	−1.40621e7	−	1.93941e7i	−0.572307	−	0.789311i
$905$		0			0
$906$	−8.44975e6	+	2.59773e7i	−0.341998	+	1.05141i
$907$	1.20026e7			0.484457			0.242229	−	0.970219i	$-0.422122\pi$
$907$	1.20026e7			0.484457			0.242229	+	0.970219i	$0.422122\pi$
$908$	−2.37228e6	−	1.72589e6i	−0.0954885	−	0.0694702i
$909$		−	5.43855e7i		−	2.18310i
$910$		0			0
$911$	−1.14643e7			−0.457671			−0.228836	−	0.973465i	$-0.573492\pi$
$911$	−1.14643e7			−0.457671			−0.228836	+	0.973465i	$0.573492\pi$
$912$	1.50578e7	−	4.87118e6i	0.599479	−	0.193931i
$913$		−	6.75192e7i		−	2.68071i
$914$	2.75480e6	+	896067.i	0.109075	+	0.0354793i
$915$		0			0
$916$	−1.96553e7	+	2.70166e7i	−0.773999	+	1.06388i
$917$	3.29077e7			1.29233
$918$	−4.07525e7	−	1.32558e7i	−1.59605	−	0.519156i
$919$	−1.71829e7			−0.671133			−0.335567	−	0.942016i	$-0.608928\pi$
$919$	−1.71829e7			−0.671133			−0.335567	+	0.942016i	$0.608928\pi$
$920$		0			0
$921$	7.95011e7			3.08833
$922$	6.29533e6	+	2.04771e6i	0.243889	+	0.0793308i
$923$	3.67535e6			0.142002
$924$	6.96158e7	+	5.06472e7i	2.68243	+	1.95153i
$925$		0			0
$926$	1.61019e7	+	5.23755e6i	0.617093	+	0.200725i
$927$			1.28769e7i			0.492166i
$928$	−41638.2	+	2.59206e7i	−0.00158717	+	0.988039i
$929$	1.26147e7			0.479554			0.239777	−	0.970828i	$-0.422926\pi$
$929$	1.26147e7			0.479554			0.239777	+	0.970828i	$0.422926\pi$
$930$		0			0
$931$		−	1.06991e7i		−	0.404549i
$932$	−1.32960e7	+	1.82756e7i	−0.501396	+	0.689181i
$933$	2.11527e7			0.795538
$934$	1.42535e6	−	4.38199e6i	0.0534632	−	0.164363i
$935$		0			0
$936$	−3.81717e6	+	2.76772e6i	−0.142414	+	0.103260i
$937$		−	1.36188e7i		−	0.506747i	−0.967368	−	0.253374i	$-0.918460\pi$
$937$		−	1.36188e7i		−	0.506747i	0.967368	−	0.253374i	$-0.0815402\pi$
$938$	−5.60222e7	−	1.82226e7i	−2.07899	−	0.676244i
$939$		−	1.33729e7i		−	0.494950i
$940$		0			0
$941$			4.59567e7i			1.69190i	0.533261	+	0.845951i	$0.320966\pi$
$941$			4.59567e7i			1.69190i	−0.533261	+	0.845951i	$0.679034\pi$
$942$	−1.34215e6	+	4.12620e6i	−0.0492803	+	0.151504i
$943$		−	1.85134e7i		−	0.677963i
$944$	1.21073e7	−	3.91670e6i	0.442198	−	0.143051i
$945$		0			0
$946$	−4.45338e7	−	1.44857e7i	−1.61794	−	0.526275i
$947$	−5.53327e6			−0.200497			−0.100248	−	0.994962i	$-0.531964\pi$
$947$	−5.53327e6			−0.200497			−0.100248	+	0.994962i	$0.531964\pi$
$948$	4.84292e7	+	3.52334e7i	1.75019	+	1.27331i
$949$		−	249992.i		−	0.00901076i
$950$		0			0
$951$	−5.16670e7			−1.85252
$952$	−5.33830e7	+	3.87065e7i	−1.90902	+	1.38418i
$953$		−	2.16609e6i		−	0.0772581i	−0.999254	−	0.0386290i	$-0.987701\pi$
$953$		−	2.16609e6i		−	0.0772581i	0.999254	−	0.0386290i	$-0.0122991\pi$
$954$	1.42731e7	−	4.38801e7i	0.507747	−	1.56098i
$955$		0			0
$956$	6.32904e6	+	4.60454e6i	0.223972	+	0.162945i
$957$	−6.50032e7			−2.29432
$958$	5.25621e6	−	1.61593e7i	0.185037	−	0.568864i
$959$	−3.65958e6			−0.128495
$960$		0			0
$961$	3.10374e7			1.08412
$962$	839906.	−	2.58214e6i	0.0292613	−	0.0899586i
$963$	−6.11432e7			−2.12463
$964$	−1.55893e7	−	1.13416e7i	−0.540297	−	0.393080i
$965$		0			0
$966$	2.43712e7	−	7.49248e7i	0.840298	−	2.58335i
$967$		−	2.88706e7i		−	0.992865i	−0.868075	−	0.496433i	$-0.834643\pi$
$967$		−	2.88706e7i		−	0.992865i	0.868075	−	0.496433i	$-0.165357\pi$
$968$	−2.48375e7	+	1.80089e7i	−0.851960	+	0.617731i
$969$	−3.03985e7			−1.04002
$970$		0			0
$971$			1.96724e7i			0.669592i	0.942291	+	0.334796i	$0.108667\pi$
$971$			1.96724e7i			0.669592i	−0.942291	+	0.334796i	$0.891333\pi$
$972$	−2.34154e7	−	1.70353e7i	−0.794944	−	0.578341i
$973$	1.02654e7			0.347610
$974$	−3.80768e7	−	1.23854e7i	−1.28607	−	0.418325i
$975$		0			0
$976$	1.93226e7	−	6.25087e6i	0.649295	−	0.210047i
$977$		−	3.27929e7i		−	1.09912i	−0.835455	−	0.549558i	$-0.814796\pi$
$977$		−	3.27929e7i		−	1.09912i	0.835455	−	0.549558i	$-0.185204\pi$
$978$	3.49773e6	−	1.07531e7i	0.116933	−	0.359491i
$979$			1.61641e7i			0.539008i
$980$		0			0
$981$			3.89341e7i			1.29169i
$982$	1.03169e7	+	3.35584e6i	0.341407	+	0.111051i
$983$			1.63310e7i			0.539048i	0.962994	+	0.269524i	$0.0868664\pi$
$983$			1.63310e7i			0.539048i	−0.962994	+	0.269524i	$0.913134\pi$
$984$	2.30322e7	−	1.67000e7i	0.758313	−	0.549831i
$985$		0			0
$986$	1.54005e7	−	4.73461e7i	0.504478	−	1.55093i
$987$	2.76557e7			0.903631
$988$	−758489.	+	1.04256e6i	−0.0247205	+	0.0339789i
$989$			4.28588e7i			1.39332i
$990$		0			0
$991$	−8.71507e6			−0.281895			−0.140947	−	0.990017i	$-0.545015\pi$
$991$	−8.71507e6			−0.281895			−0.140947	+	0.990017i	$0.545015\pi$
$992$	−4.47445e7	−	71876.6i	−1.44365	−	0.00231904i
$993$			1.35383e7i			0.435703i
$994$	−5.55894e7	−	1.80818e7i	−1.78454	−	0.580465i
$995$		0			0
$996$	−7.67862e7	−	5.58639e7i	−2.45265	−	1.78436i
$997$	−5.34960e7			−1.70445			−0.852224	−	0.523177i	$-0.824746\pi$
$997$	−5.34960e7			−1.70445			−0.852224	+	0.523177i	$0.824746\pi$
$998$	1.61059e7	+	5.23884e6i	0.511869	+	0.166498i
$999$	−2.80674e7			−0.889792

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	200.6.f.d.149.18		40
4.3	odd	2		800.6.f.d.49.37		40
5.2	odd	4		200.6.d.d.101.1	yes	20
5.3	odd	4		200.6.d.c.101.20	yes	20
5.4	even	2	inner	200.6.f.d.149.23		40
8.3	odd	2		800.6.f.d.49.3		40
8.5	even	2	inner	200.6.f.d.149.24		40
20.3	even	4		800.6.d.d.401.19		20
20.7	even	4		800.6.d.b.401.2		20
20.19	odd	2		800.6.f.d.49.4		40
40.3	even	4		800.6.d.d.401.2		20
40.13	odd	4		200.6.d.c.101.19	✓	20
40.19	odd	2		800.6.f.d.49.38		40
40.27	even	4		800.6.d.b.401.19		20
40.29	even	2	inner	200.6.f.d.149.17		40
40.37	odd	4		200.6.d.d.101.2	yes	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
200.6.d.c.101.19	✓	20	40.13	odd	4
200.6.d.c.101.20	yes	20	5.3	odd	4
200.6.d.d.101.1	yes	20	5.2	odd	4
200.6.d.d.101.2	yes	20	40.37	odd	4
200.6.f.d.149.17		40	40.29	even	2	inner
200.6.f.d.149.18		40	1.1	even	1	trivial
200.6.f.d.149.23		40	5.4	even	2	inner
200.6.f.d.149.24		40	8.5	even	2	inner
800.6.d.b.401.2		20	20.7	even	4
800.6.d.b.401.19		20	40.27	even	4
800.6.d.d.401.2		20	40.3	even	4
800.6.d.d.401.19		20	20.3	even	4
800.6.f.d.49.3		40	8.3	odd	2
800.6.f.d.49.4		40	20.19	odd	2
800.6.f.d.49.37		40	4.3	odd	2
800.6.f.d.49.38		40	40.19	odd	2

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:	\( N \)	\(=\)	\( 200 = 2^{3} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	200.f (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.74979 + 5.37943i) q^{2} -25.2673 q^{3} +(-25.8765 - 18.8258i) q^{4} +(44.2124 - 135.923i) q^{6} -185.199i q^{7} +(146.550 - 106.259i) q^{8} +395.434 q^{9} +574.919i q^{11} +(653.827 + 475.675i) q^{12} -65.8691 q^{13} +(996.264 + 324.060i) q^{14} +(315.182 + 974.288i) q^{16} -1966.88i q^{17} +(-691.927 + 2127.21i) q^{18} +611.668i q^{19} +4679.47i q^{21} +(-3092.74 - 1005.99i) q^{22} +2976.41i q^{23} +(-3702.92 + 2684.88i) q^{24} +(115.257 - 354.338i) q^{26} -3851.59 q^{27} +(-3486.51 + 4792.29i) q^{28} -4474.76i q^{29} +7724.41 q^{31} +(-5792.61 - 9.30513i) q^{32} -14526.6i q^{33} +(10580.7 + 3441.64i) q^{34} +(-10232.4 - 7444.34i) q^{36} +7287.23 q^{37} +(-3290.42 - 1070.29i) q^{38} +1664.33 q^{39} -6220.02 q^{41} +(-25172.8 - 8188.09i) q^{42} +14399.5 q^{43} +(10823.3 - 14876.9i) q^{44} +(-16011.4 - 5208.11i) q^{46} -5910.00i q^{47} +(-7963.77 - 24617.6i) q^{48} -17491.6 q^{49} +49697.7i q^{51} +(1704.46 + 1240.04i) q^{52} -20628.0 q^{53} +(6739.48 - 20719.3i) q^{54} +(-19679.1 - 27140.9i) q^{56} -15455.2i q^{57} +(24071.6 + 7829.90i) q^{58} -12426.8i q^{59} -19832.6i q^{61} +(-13516.1 + 41552.9i) q^{62} -73233.9i q^{63} +(10185.9 - 31144.6i) q^{64} +(78144.9 + 25418.6i) q^{66} -56232.3 q^{67} +(-37028.1 + 50896.0i) q^{68} -75205.8i q^{69} -55797.8 q^{71} +(57950.9 - 42018.5i) q^{72} +3795.29i q^{73} +(-12751.1 + 39201.1i) q^{74} +(11515.1 - 15827.8i) q^{76} +106474. q^{77} +(-2912.23 + 8953.14i) q^{78} +74070.3 q^{79} +1228.55 q^{81} +(10883.7 - 33460.1i) q^{82} -117441. q^{83} +(88094.5 - 121088. i) q^{84} +(-25196.1 + 77461.0i) q^{86} +113065. i q^{87} +(61090.5 + 84254.5i) q^{88} +28115.4 q^{89} +12198.9i q^{91} +(56033.3 - 77019.0i) q^{92} -195175. q^{93} +(31792.4 + 10341.3i) q^{94} +(146363. + 235.115i) q^{96} -38940.1i q^{97} +(30606.7 - 94094.9i) q^{98} +227343. i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q - 2 q^{4} + 66 q^{6} + 3240 q^{9} + 848 q^{14} - 110 q^{16} - 18918 q^{24} + 18344 q^{26} + 14320 q^{31} + 19182 q^{34} + 29656 q^{36} - 44904 q^{39} - 11608 q^{41} + 23186 q^{44} - 75224 q^{46} - 125304 q^{49}+ \cdots + 115582 q^{96}+O(q^{100}) \) 40 * q - 2 * q^4 + 66 * q^6 + 3240 * q^9 + 848 * q^14 - 110 * q^16 - 18918 * q^24 + 18344 * q^26 + 14320 * q^31 + 19182 * q^34 + 29656 * q^36 - 44904 * q^39 - 11608 * q^41 + 23186 * q^44 - 75224 * q^46 - 125304 * q^49 - 177894 * q^54 - 73816 * q^56 - 230354 * q^64 + 262878 * q^66 - 15448 * q^71 - 4224 * q^74 + 111902 * q^76 + 15560 * q^79 + 193968 * q^81 + 195112 * q^84 - 131972 * q^86 + 6320 * q^89 + 117080 * q^94 + 115582 * q^96

Introduction

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