LMFDB - Embedded newform 48.6.k.a.11.20

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [48,6,Mod(11,48)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(48, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 1, 2]))

N = Newforms(chi, 6, names="a")

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

chi := DirichletCharacter("48.11");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 48 = 2^{4} \cdot 3 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	48.k (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$7.69842335102$
Analytic rank:	$0$
Dimension:	$76$
Relative dimension:	$38$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			11.20
Character	$\chi$	$=$	48.11
Dual form			48.6.k.a.35.20

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.486958 + 5.63586i) q^{2} +(3.91558 - 15.0887i) q^{3} +(-31.5257 + 5.48885i) q^{4} +(-7.73181 + 7.73181i) q^{5} +(86.9443 + 14.7201i) q^{6} -59.0766 q^{7} +(-46.2861 - 175.002i) q^{8} +(-212.337 - 118.162i) q^{9} +O(q^{10})$	\(q+(0.486958 + 5.63586i) q^{2} +(3.91558 - 15.0887i) q^{3} +(-31.5257 + 5.48885i) q^{4} +(-7.73181 + 7.73181i) q^{5} +(86.9443 + 14.7201i) q^{6} -59.0766 q^{7} +(-46.2861 - 175.002i) q^{8} +(-212.337 - 118.162i) q^{9} +(-47.3405 - 39.8103i) q^{10} +(-522.367 - 522.367i) q^{11} +(-40.6220 + 497.174i) q^{12} +(101.817 - 101.817i) q^{13} +(-28.7678 - 332.947i) q^{14} +(86.3884 + 146.937i) q^{15} +(963.745 - 346.080i) q^{16} +344.903i q^{17} +(562.544 - 1254.24i) q^{18} +(-228.236 - 228.236i) q^{19} +(201.312 - 286.190i) q^{20} +(-231.319 + 891.388i) q^{21} +(2689.61 - 3198.35i) q^{22} -3517.58i q^{23} +(-2821.78 + 13.1634i) q^{24} +3005.44i q^{25} +(623.408 + 524.246i) q^{26} +(-2614.33 + 2741.21i) q^{27} +(1862.43 - 324.263i) q^{28} +(-1240.19 - 1240.19i) q^{29} +(-786.050 + 558.425i) q^{30} +7964.77i q^{31} +(2419.76 + 5263.00i) q^{32} +(-9927.19 + 5836.46i) q^{33} +(-1943.83 + 167.954i) q^{34} +(456.769 - 456.769i) q^{35} +(7342.64 + 2559.65i) q^{36} +(-919.737 - 919.737i) q^{37} +(1175.16 - 1397.45i) q^{38} +(-1137.61 - 1934.96i) q^{39} +(1710.96 + 995.205i) q^{40} -8535.03 q^{41} +(-5136.38 - 869.612i) q^{42} +(10658.1 - 10658.1i) q^{43} +(19335.2 + 13600.8i) q^{44} +(2555.35 - 728.142i) q^{45} +(19824.6 - 1712.91i) q^{46} +16301.4 q^{47} +(-1448.28 - 15896.7i) q^{48} -13317.0 q^{49} +(-16938.2 + 1463.52i) q^{50} +(5204.14 + 1350.50i) q^{51} +(-2651.00 + 3768.72i) q^{52} +(-7009.26 + 7009.26i) q^{53} +(-16722.1 - 13399.1i) q^{54} +8077.68 q^{55} +(2734.43 + 10338.5i) q^{56} +(-4337.45 + 2550.10i) q^{57} +(6385.60 - 7593.44i) q^{58} +(-11901.5 - 11901.5i) q^{59} +(-3529.97 - 4158.14i) q^{60} +(25537.3 - 25537.3i) q^{61} +(-44888.3 + 3878.51i) q^{62} +(12544.1 + 6980.60i) q^{63} +(-28483.2 + 16200.3i) q^{64} +1574.46i q^{65} +(-37727.5 - 53106.1i) q^{66} +(33437.0 + 33437.0i) q^{67} +(-1893.12 - 10873.3i) q^{68} +(-53075.7 - 13773.4i) q^{69} +(2796.71 + 2351.86i) q^{70} -69731.9i q^{71} +(-10850.3 + 42628.5i) q^{72} +12833.1i q^{73} +(4735.63 - 5631.38i) q^{74} +(45348.1 + 11768.0i) q^{75} +(8448.06 + 5942.55i) q^{76} +(30859.6 + 30859.6i) q^{77} +(10351.2 - 7353.67i) q^{78} -88863.5i q^{79} +(-4775.67 + 10127.3i) q^{80} +(31124.6 + 50180.1i) q^{81} +(-4156.20 - 48102.2i) q^{82} +(37906.5 - 37906.5i) q^{83} +(2399.81 - 29371.3i) q^{84} +(-2666.73 - 2666.73i) q^{85} +(65257.6 + 54877.5i) q^{86} +(-23568.9 + 13856.8i) q^{87} +(-67236.7 + 115593. i) q^{88} -74561.1 q^{89} +(5348.05 + 14047.0i) q^{90} +(-6015.02 + 6015.02i) q^{91} +(19307.5 + 110894. i) q^{92} +(120178. + 31186.7i) q^{93} +(7938.11 + 91872.5i) q^{94} +3529.36 q^{95} +(88886.5 - 15903.3i) q^{96} -37819.1 q^{97} +(-6484.80 - 75052.4i) q^{98} +(49193.7 + 172641. i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 76 q - 2 q^{3} - 4 q^{4} - 116 q^{6} - 8 q^{7}+O(q^{10}) $ 76 * q - 2 * q^3 - 4 * q^4 - 116 * q^6 - 8 * q^7	$ 76 q - 2 q^{3} - 4 q^{4} - 116 q^{6} - 8 q^{7} - 104 q^{10} + 784 q^{12} - 4 q^{13} + 4560 q^{16} - 4076 q^{18} + 2356 q^{19} - 488 q^{21} + 2232 q^{22} + 2568 q^{24} - 3734 q^{27} - 12392 q^{28} + 628 q^{30} - 4 q^{33} + 26248 q^{34} - 30748 q^{36} - 4 q^{37} - 44908 q^{39} + 440 q^{40} + 11256 q^{42} + 652 q^{43} - 6252 q^{45} + 31320 q^{46} - 9168 q^{48} + 124844 q^{49} + 8664 q^{51} - 48448 q^{52} - 19480 q^{54} - 110056 q^{55} + 76088 q^{58} - 85408 q^{60} + 48076 q^{61} - 11080 q^{64} + 91492 q^{66} + 48924 q^{67} + 484 q^{69} + 86200 q^{70} - 16376 q^{72} - 69634 q^{75} + 30920 q^{76} + 13020 q^{78} - 4 q^{81} - 200768 q^{82} + 111760 q^{84} - 119904 q^{85} + 282180 q^{87} - 123616 q^{88} - 17680 q^{90} - 167288 q^{91} + 181660 q^{93} - 13200 q^{94} - 61688 q^{96} - 8 q^{97} - 287860 q^{99}+O(q^{100}) $ 76 * q - 2 * q^3 - 4 * q^4 - 116 * q^6 - 8 * q^7 - 104 * q^10 + 784 * q^12 - 4 * q^13 + 4560 * q^16 - 4076 * q^18 + 2356 * q^19 - 488 * q^21 + 2232 * q^22 + 2568 * q^24 - 3734 * q^27 - 12392 * q^28 + 628 * q^30 - 4 * q^33 + 26248 * q^34 - 30748 * q^36 - 4 * q^37 - 44908 * q^39 + 440 * q^40 + 11256 * q^42 + 652 * q^43 - 6252 * q^45 + 31320 * q^46 - 9168 * q^48 + 124844 * q^49 + 8664 * q^51 - 48448 * q^52 - 19480 * q^54 - 110056 * q^55 + 76088 * q^58 - 85408 * q^60 + 48076 * q^61 - 11080 * q^64 + 91492 * q^66 + 48924 * q^67 + 484 * q^69 + 86200 * q^70 - 16376 * q^72 - 69634 * q^75 + 30920 * q^76 + 13020 * q^78 - 4 * q^81 - 200768 * q^82 + 111760 * q^84 - 119904 * q^85 + 282180 * q^87 - 123616 * q^88 - 17680 * q^90 - 167288 * q^91 + 181660 * q^93 - 13200 * q^94 - 61688 * q^96 - 8 * q^97 - 287860 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/48\mathbb{Z}\right)^\times$.

$n$	$17$	$31$	$37$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{1}{4}\right)$

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 $

$2$	0.486958	+	5.63586i	0.0860828	+	0.996288i
$2$	0.486958	+	5.63586i	0.0860828	+	0.996288i
$3$	3.91558	−	15.0887i	0.251184	−	0.967939i
$3$	3.91558	−	15.0887i	0.251184	−	0.967939i
$4$	−31.5257	+	5.48885i	−0.985179	+	0.171527i
$5$	−7.73181	+	7.73181i	−0.138311	+	0.138311i	−0.772872	−	0.634561i	$-0.781181\pi$
$5$	−7.73181	+	7.73181i	−0.138311	+	0.138311i	0.634561	+	0.772872i	$0.281181\pi$
$6$	86.9443	+	14.7201i	0.985969	+	0.166929i
$7$	−59.0766			−0.455691			−0.227846	−	0.973697i	$-0.573168\pi$
$7$	−59.0766			−0.455691			−0.227846	+	0.973697i	$0.573168\pi$
$8$	−46.2861	−	175.002i	−0.255697	−	0.966757i
$9$	−212.337	−	118.162i	−0.873813	−	0.486262i
$10$	−47.3405	−	39.8103i	−0.149704	−	0.125891i
$11$	−522.367	−	522.367i	−1.30165	−	1.30165i	−0.927280	−	0.374368i	$-0.877860\pi$
$11$	−522.367	−	522.367i	−1.30165	−	1.30165i	−0.374368	−	0.927280i	$-0.622140\pi$
$12$	−40.6220	+	497.174i	−0.0814344	+	0.996679i
$13$	101.817	−	101.817i	0.167095	−	0.167095i	−0.618606	−	0.785701i	$-0.712302\pi$
$13$	101.817	−	101.817i	0.167095	−	0.167095i	0.785701	+	0.618606i	$0.212302\pi$
$14$	−28.7678	−	332.947i	−0.0392272	−	0.454000i
$15$	86.3884	+	146.937i	0.0991350	+	0.168618i
$16$	963.745	−	346.080i	0.941157	−	0.337969i
$17$			344.903i			0.289451i	0.989472	+	0.144726i	$0.0462299\pi$
$17$			344.903i			0.289451i	−0.989472	+	0.144726i	$0.953770\pi$
$18$	562.544	−	1254.24i	0.409237	−	0.912428i
$19$	−228.236	−	228.236i	−0.145044	−	0.145044i	0.630856	−	0.775900i	$-0.282704\pi$
$19$	−228.236	−	228.236i	−0.145044	−	0.145044i	−0.775900	+	0.630856i	$0.782704\pi$
$20$	201.312	−	286.190i	0.112537	−	0.159985i
$21$	−231.319	+	891.388i	−0.114462	+	0.441081i
$22$	2689.61	−	3198.35i	1.18477	−	1.40887i
$23$		−	3517.58i		−	1.38651i	−0.720690	−	0.693257i	$-0.756175\pi$
$23$		−	3517.58i		−	1.38651i	0.720690	−	0.693257i	$-0.243825\pi$
$24$	−2821.78	+	13.1634i	−0.999989	+	0.00466487i
$25$			3005.44i			0.961740i
$26$	623.408	+	524.246i	0.180858	+	0.152091i
$27$	−2614.33	+	2741.21i	−0.690161	+	0.723656i
$28$	1862.43	−	324.263i	0.448937	−	0.0781631i
$29$	−1240.19	−	1240.19i	−0.273837	−	0.273837i	0.556806	−	0.830643i	$-0.312027\pi$
$29$	−1240.19	−	1240.19i	−0.273837	−	0.273837i	−0.830643	+	0.556806i	$0.812027\pi$
$30$	−786.050	+	558.425i	−0.159458	+	0.113282i
$31$			7964.77i			1.48857i	0.667862	+	0.744285i	$0.267210\pi$
$31$			7964.77i			1.48857i	−0.667862	+	0.744285i	$0.732790\pi$
$32$	2419.76	+	5263.00i	0.417732	+	0.908570i
$33$	−9927.19	+	5836.46i	−1.58687	+	0.932963i
$34$	−1943.83	+	167.954i	−0.288377	+	0.0249168i
$35$	456.769	−	456.769i	0.0630270	−	0.0630270i
$36$	7342.64	+	2559.65i	0.944269	+	0.329174i
$37$	−919.737	−	919.737i	−0.110448	−	0.110448i	0.649723	−	0.760171i	$-0.274885\pi$
$37$	−919.737	−	919.737i	−0.110448	−	0.110448i	−0.760171	+	0.649723i	$0.774885\pi$
$38$	1175.16	−	1397.45i	0.132020	−	0.156991i
$39$	−1137.61	−	1934.96i	−0.119766	−	0.203709i
$40$	1710.96	+	995.205i	0.169079	+	0.0983473i
$41$	−8535.03			−0.792949			−0.396475	−	0.918046i	$-0.629767\pi$
$41$	−8535.03			−0.792949			−0.396475	+	0.918046i	$0.629767\pi$
$42$	−5136.38	−	869.612i	−0.449297	−	0.0760681i
$43$	10658.1	−	10658.1i	0.879041	−	0.879041i	−0.114395	−	0.993435i	$-0.536493\pi$
$43$	10658.1	−	10658.1i	0.879041	−	0.879041i	0.993435	+	0.114395i	$0.0364929\pi$
$44$	19335.2	+	13600.8i	1.50562	+	1.05909i
$45$	2555.35	−	728.142i	0.188113	−	0.0536024i
$46$	19824.6	−	1712.91i	1.38137	−	0.119355i
$47$	16301.4			1.07642			0.538209	−	0.842812i	$-0.319101\pi$
$47$	16301.4			1.07642			0.538209	+	0.842812i	$0.319101\pi$
$48$	−1448.28	−	15896.7i	−0.0907295	−	0.995876i
$49$	−13317.0			−0.792346
$50$	−16938.2	+	1463.52i	−0.958170	+	0.0827893i
$51$	5204.14	+	1350.50i	0.280171	+	0.0727056i
$52$	−2651.00	+	3768.72i	−0.135957	+	0.193280i
$53$	−7009.26	+	7009.26i	−0.342754	+	0.342754i	−0.857402	−	0.514648i	$-0.827923\pi$
$53$	−7009.26	+	7009.26i	−0.342754	+	0.342754i	0.514648	+	0.857402i	$0.327923\pi$
$54$	−16722.1	−	13399.1i	−0.780381	−	0.625304i
$55$	8077.68			0.360064
$56$	2734.43	+	10338.5i	0.116519	+	0.440543i
$57$	−4337.45	+	2550.10i	−0.176827	+	0.103961i
$58$	6385.60	−	7593.44i	0.249248	−	0.296394i
$59$	−11901.5	−	11901.5i	−0.445113	−	0.445113i	0.448613	−	0.893726i	$-0.351918\pi$
$59$	−11901.5	−	11901.5i	−0.445113	−	0.445113i	−0.893726	+	0.448613i	$0.851918\pi$
$60$	−3529.97	−	4158.14i	−0.126588	−	0.149115i
$61$	25537.3	−	25537.3i	0.878721	−	0.878721i	−0.114681	−	0.993402i	$-0.536585\pi$
$61$	25537.3	−	25537.3i	0.878721	−	0.878721i	0.993402	+	0.114681i	$0.0365847\pi$
$62$	−44888.3	+	3878.51i	−1.48304	+	0.128140i
$63$	12544.1	+	6980.60i	0.398189	+	0.221585i
$64$	−28483.2	+	16200.3i	−0.869238	+	0.494394i
$65$			1574.46i			0.0462221i
$66$	−37727.5	−	53106.1i	−1.06610	−	1.50067i
$67$	33437.0	+	33437.0i	0.909996	+	0.909996i	0.996271	−	0.0862749i	$-0.0274964\pi$
$67$	33437.0	+	33437.0i	0.909996	+	0.909996i	−0.0862749	+	0.996271i	$0.527496\pi$
$68$	−1893.12	−	10873.3i	−0.0496486	−	0.285161i
$69$	−53075.7	−	13773.4i	−1.34206	−	0.348271i
$70$	2796.71	+	2351.86i	0.0682186	+	0.0573675i
$71$		−	69731.9i		−	1.64167i	−0.571165	−	0.820835i	$-0.693508\pi$
$71$		−	69731.9i		−	1.64167i	0.571165	−	0.820835i	$-0.306492\pi$
$72$	−10850.3	+	42628.5i	−0.246666	+	0.969100i
$73$			12833.1i			0.281854i	0.990020	+	0.140927i	$0.0450082\pi$
$73$			12833.1i			0.281854i	−0.990020	+	0.140927i	$0.954992\pi$
$74$	4735.63	−	5631.38i	0.100531	−	0.119546i
$75$	45348.1	+	11768.0i	0.930906	+	0.241574i
$76$	8448.06	+	5942.55i	0.167773	+	0.118016i
$77$	30859.6	+	30859.6i	0.593149	+	0.593149i
$78$	10351.2	−	7353.67i	0.192643	−	0.136857i
$79$		−	88863.5i		−	1.60198i	−0.598681	−	0.800988i	$-0.704308\pi$
$79$		−	88863.5i		−	1.60198i	0.598681	−	0.800988i	$-0.295692\pi$
$80$	−4775.67	+	10127.3i	−0.0834275	+	0.176917i
$81$	31124.6	+	50180.1i	0.527098	+	0.849805i
$82$	−4156.20	−	48102.2i	−0.0682593	−	0.790006i
$83$	37906.5	−	37906.5i	0.603975	−	0.603975i	−0.337390	−	0.941365i	$-0.609544\pi$
$83$	37906.5	−	37906.5i	0.603975	−	0.603975i	0.941365	+	0.337390i	$0.109544\pi$
$84$	2399.81	−	29371.3i	0.0371089	−	0.454178i
$85$	−2666.73	−	2666.73i	−0.0400342	−	0.0400342i
$86$	65257.6	+	54877.5i	0.951448	+	0.800107i
$87$	−23568.9	+	13856.8i	−0.333842	+	0.196274i
$88$	−67236.7	+	115593.i	−0.925550	+	1.59121i
$89$	−74561.1			−0.997786			−0.498893	−	0.866664i	$-0.666260\pi$
$89$	−74561.1			−0.997786			−0.498893	+	0.866664i	$0.666260\pi$
$90$	5348.05	+	14047.0i	0.0695968	+	0.182801i
$91$	−6015.02	+	6015.02i	−0.0761436	+	0.0761436i
$92$	19307.5	+	110894.i	0.237824	+	1.36597i
$93$	120178.	+	31186.7i	1.44085	+	0.373906i
$94$	7938.11	+	91872.5i	0.0926611	+	1.07242i
$95$	3529.36			0.0401224
$96$	88886.5	−	15903.3i	0.984369	−	0.176120i
$97$	−37819.1			−0.408114			−0.204057	−	0.978959i	$-0.565413\pi$
$97$	−37819.1			−0.408114			−0.204057	+	0.978959i	$0.565413\pi$
$98$	−6484.80	−	75052.4i	−0.0682074	−	0.789404i
$99$	49193.7	+	172641.i	0.504454	+	1.77034i
$100$	−16496.4	−	94748.7i	−0.164964	−	0.947487i
$101$	50654.5	−	50654.5i	0.494100	−	0.494100i	−0.415496	−	0.909595i	$-0.636392\pi$
$101$	50654.5	−	50654.5i	0.494100	−	0.494100i	0.909595	+	0.415496i	$0.136392\pi$
$102$	−5077.00	+	29987.4i	−0.0483178	+	0.285390i
$103$	−203805.			−1.89288			−0.946438	−	0.322885i	$-0.895347\pi$
$103$	−203805.			−1.89288			−0.946438	+	0.322885i	$0.895347\pi$
$104$	−22530.9	−	13105.5i	−0.204266	−	0.118814i
$105$	−5103.53	−	8680.56i	−0.0451749	−	0.0768378i
$106$	−42916.4	−	36089.9i	−0.370987	−	0.311976i
$107$	−3529.73	−	3529.73i	−0.0298045	−	0.0298045i	0.692047	−	0.721852i	$-0.256709\pi$
$107$	−3529.73	−	3529.73i	−0.0298045	−	0.0298045i	−0.721852	+	0.692047i	$0.756709\pi$
$108$	67372.5	−	100768.i	0.555806	−	0.831312i
$109$	−28934.1	+	28934.1i	−0.233261	+	0.233261i	−0.814053	−	0.580791i	$-0.802743\pi$
$109$	−28934.1	+	28934.1i	−0.233261	+	0.233261i	0.580791	+	0.814053i	$0.302743\pi$
$110$	3933.49	+	45524.7i	0.0309954	+	0.358728i
$111$	−17478.9	+	10276.3i	−0.134650	+	0.0791644i
$112$	−56934.8	+	20445.3i	−0.428877	+	0.154009i
$113$		−	207518.i		−	1.52883i	−0.644723	−	0.764416i	$-0.723027\pi$
$113$		−	207518.i		−	1.52883i	0.644723	−	0.764416i	$-0.276973\pi$
$114$	−16484.2	−	23203.5i	−0.118797	−	0.167221i
$115$	27197.3	+	27197.3i	0.191770	+	0.191770i
$116$	45905.1	+	32290.6i	0.316749	+	0.222809i
$117$	−33650.4	+	9588.61i	−0.227261	+	0.0647576i
$118$	61279.5	−	72870.5i	0.405145	−	0.481778i
$119$		−	20375.7i		−	0.131900i
$120$	21715.7	−	21919.3i	0.137664	−	0.138955i
$121$			384683.i			2.38858i
$122$	156360.	+	131489.i	0.951102	+	0.799816i
$123$	−33419.6	+	128782.i	−0.199176	+	0.767527i
$124$	−43717.5	−	251095.i	−0.255329	−	1.46651i
$125$	−47399.4	−	47399.4i	−0.271330	−	0.271330i
$126$	−33233.2	+	74096.1i	−0.186486	+	0.415785i
$127$		−	136192.i		−	0.749277i	−0.927171	−	0.374638i	$-0.877767\pi$
$127$		−	136192.i		−	0.749277i	0.927171	−	0.374638i	$-0.122233\pi$
$128$	−105173.	−	152638.i	−0.567385	−	0.823453i
$129$	−119084.	−	202549.i	−0.630057	−	1.07166i
$130$	−8873.45	+	766.698i	−0.0460505	+	0.00397893i
$131$	−210116.	+	210116.i	−1.06975	+	1.06975i	−0.0723679	+	0.997378i	$0.523056\pi$
$131$	−210116.	+	210116.i	−1.06975	+	1.06975i	−0.997378	+	0.0723679i	$0.976944\pi$
$132$	280927.	−	238487.i	1.40332	−	1.19133i
$133$	13483.4	+	13483.4i	0.0660953	+	0.0660953i
$134$	−172163.	+	204728.i	−0.828283	+	0.984954i
$135$	−981.020	−	41408.0i	−0.00463280	−	0.195546i
$136$	60358.7	−	15964.2i	0.279829	−	0.0740118i
$137$	−89927.1			−0.409345			−0.204672	−	0.978831i	$-0.565613\pi$
$137$	−89927.1			−0.409345			−0.204672	+	0.978831i	$0.565613\pi$
$138$	51779.1	−	305834.i	0.231450	−	1.36706i
$139$	143352.	−	143352.i	0.629315	−	0.629315i	−0.318581	−	0.947896i	$-0.603206\pi$
$139$	143352.	−	143352.i	0.629315	−	0.629315i	0.947896	+	0.318581i	$0.103206\pi$
$140$	−11892.9	+	16907.1i	−0.0512821	+	0.0729038i
$141$	63829.5	−	245967.i	0.270379	−	1.04191i
$142$	392999.	−	33956.5i	1.63558	−	0.141320i
$143$	−106372.			−0.434997
$144$	−245532.	−	40392.3i	−0.986737	−	0.162328i
$145$	19177.8			0.0757494
$146$	−72325.3	+	6249.17i	−0.280807	+	0.0242628i
$147$	−52143.6	+	200935.i	−0.199025	+	0.766942i
$148$	34043.7	+	23947.1i	0.127756	+	0.0898667i
$149$	282937.	−	282937.i	1.04406	−	1.04406i	0.0450722	−	0.998984i	$-0.485648\pi$
$149$	282937.	−	282937.i	1.04406	−	1.04406i	0.998984	−	0.0450722i	$-0.0143518\pi$
$150$	−44240.3	+	261306.i	−0.160542	+	0.948246i
$151$	−321766.			−1.14841			−0.574205	−	0.818711i	$-0.694689\pi$
$151$	−321766.			−1.14841			−0.574205	+	0.818711i	$0.694689\pi$
$152$	−29377.5	+	50505.8i	−0.103135	+	0.177310i
$153$	40754.4	−	73235.6i	0.140749	−	0.252926i
$154$	−158893.	+	188948.i	−0.539888	+	0.642008i
$155$	−61582.2	−	61582.2i	−0.205885	−	0.205885i
$156$	46484.8	+	54756.9i	0.152933	+	0.180147i
$157$	224729.	−	224729.i	0.727628	−	0.727628i	−0.242518	−	0.970147i	$-0.577973\pi$
$157$	224729.	−	224729.i	0.727628	−	0.727628i	0.970147	+	0.242518i	$0.0779735\pi$
$158$	500822.	−	43272.8i	1.59603	−	0.137903i
$159$	78315.1	+	133206.i	0.245670	+	0.417859i
$160$	−59401.7	−	21983.4i	−0.183442	−	0.0678883i
$161$			207807.i			0.631822i
$162$	−267652.	+	199849.i	−0.801276	+	0.598295i
$163$	−198945.	−	198945.i	−0.586495	−	0.586495i	0.350185	−	0.936681i	$-0.386119\pi$
$163$	−198945.	−	198945.i	−0.586495	−	0.586495i	−0.936681	+	0.350185i	$0.886119\pi$
$164$	269073.	−	46847.5i	0.781197	−	0.136012i
$165$	31628.8	−	121882.i	0.0904425	−	0.348520i
$166$	232095.	+	195177.i	0.653725	+	0.549741i
$167$			395731.i			1.09802i	0.835817	+	0.549009i	$0.184995\pi$
$167$			395731.i			1.09802i	−0.835817	+	0.549009i	$0.815005\pi$
$168$	166701.	−	777.649i	0.455686	−	0.00212574i
$169$			350560.i			0.944159i
$170$	13730.7	−	16327.9i	0.0364394	−	0.0433319i
$171$	21494.1	+	75431.6i	0.0562119	+	0.197271i
$172$	−277504.	+	394505.i	−0.715234	+	1.01679i
$173$	316976.	+	316976.i	0.805213	+	0.805213i	0.983905	−	0.178692i	$-0.0571866\pi$
$173$	316976.	+	316976.i	0.805213	+	0.805213i	−0.178692	+	0.983905i	$0.557187\pi$
$174$	−89571.7	−	126083.i	−0.224284	−	0.315706i
$175$		−	177551.i		−	0.438256i
$176$	−684209.	−	322647.i	−1.66497	−	0.785139i
$177$	−226179.	+	132976.i	−0.542648	+	0.319037i
$178$	−36308.1	−	420216.i	−0.0858922	−	0.994082i
$179$	−2743.97	+	2743.97i	−0.00640098	+	0.00640098i	−0.710300	−	0.703899i	$-0.751441\pi$
$179$	−2743.97	+	2743.97i	−0.00640098	+	0.00640098i	0.703899	+	0.710300i	$0.251441\pi$
$180$	−76562.7	+	36981.1i	−0.176131	+	0.0850744i
$181$	396350.	+	396350.i	0.899254	+	0.899254i	0.995370	−	0.0961159i	$-0.0306419\pi$
$181$	396350.	+	396350.i	0.899254	+	0.899254i	−0.0961159	+	0.995370i	$0.530642\pi$
$182$	−36828.8	−	30970.7i	−0.0824156	−	0.0693063i
$183$	−285331.	−	485318.i	−0.629827	−	1.07127i
$184$	−615583.	+	162815.i	−1.34042	+	0.354528i
$185$	14222.5			0.0305524
$186$	−117242.	+	692492.i	−0.248486	+	1.46768i
$187$	180166.	−	180166.i	0.376763	−	0.376763i
$188$	−513914.	+	89476.1i	−1.06046	+	0.184634i
$189$	154445.	−	161941.i	0.314500	−	0.329764i
$190$	1718.65	+	19890.9i	0.00345385	+	0.0399734i
$191$	640181.			1.26975			0.634877	−	0.772613i	$-0.281051\pi$
$191$	640181.			1.26975			0.634877	+	0.772613i	$0.281051\pi$
$192$	132913.	+	493207.i	0.260204	+	0.965554i
$193$	194634.			0.376119			0.188059	−	0.982158i	$-0.439780\pi$
$193$	194634.			0.376119			0.188059	+	0.982158i	$0.439780\pi$
$194$	−18416.3	−	213143.i	−0.0351316	−	0.406599i
$195$	23756.6	+	6164.93i	0.0447401	+	0.0116103i
$196$	419827.	−	73094.8i	0.780603	−	0.135908i
$197$	−205631.	+	205631.i	−0.377506	+	0.377506i	−0.870202	−	0.492696i	$-0.836012\pi$
$197$	−205631.	+	205631.i	−0.377506	+	0.377506i	0.492696	+	0.870202i	$0.336012\pi$
$198$	−949026.	+	361318.i	−1.72034	+	0.654978i
$199$	778296.			1.39320			0.696598	−	0.717462i	$-0.254696\pi$
$199$	778296.			1.39320			0.696598	+	0.717462i	$0.254696\pi$
$200$	525957.	−	139110.i	0.929769	−	0.245914i
$201$	635444.	−	373595.i	1.10940	−	0.652244i
$202$	310148.	+	260815.i	0.534799	+	0.449732i
$203$	73266.1	+	73266.1i	0.124785	+	0.124785i
$204$	−171477.	−	14010.6i	−0.288490	−	0.0235713i
$205$	65991.3	−	65991.3i	0.109674	−	0.109674i
$206$	−99244.6	−	1.14862e6i	−0.162944	−	1.88585i
$207$	−415644.	+	746911.i	−0.674210	+	1.21155i
$208$	62888.9	−	133363.i	0.100790	−	0.213735i
$209$			238446.i			0.377593i
$210$	46437.2	−	32989.8i	0.0726637	−	0.0516217i
$211$	−92125.8	−	92125.8i	−0.142454	−	0.142454i	0.632283	−	0.774737i	$-0.282118\pi$
$211$	−92125.8	−	92125.8i	−0.142454	−	0.142454i	−0.774737	+	0.632283i	$0.782118\pi$
$212$	182499.	−	259445.i	0.278883	−	0.396465i
$213$	−1.05216e6	−	273041.i	−1.58904	−	0.412362i
$214$	18174.2	−	21611.9i	0.0271282	−	0.0322595i
$215$			164813.i			0.243162i
$216$	600723.	+	330632.i	0.876072	+	0.482181i
$217$		−	470532.i		−	0.678328i
$218$	−177158.	−	148978.i	−0.252475	−	0.212316i
$219$	193634.	+	50248.9i	0.272817	+	0.0707972i
$220$	−254655.	+	44337.2i	−0.354728	+	0.0617606i
$221$	35117.1	+	35117.1i	0.0483658	+	0.0483658i
$222$	−66427.4	−	93504.6i	−0.0904617	−	0.127336i
$223$		−	1.03094e6i		−	1.38826i	−0.719850	−	0.694130i	$-0.755789\pi$
$223$		−	1.03094e6i		−	1.38826i	0.719850	−	0.694130i	$-0.244211\pi$
$224$	−142951.	−	310920.i	−0.190357	−	0.414027i
$225$	355128.	−	638164.i	0.467658	−	0.840381i
$226$	1.16954e6	−	101053.i	1.52316	−	0.131606i
$227$	308263.	−	308263.i	0.397061	−	0.397061i	−0.480134	−	0.877195i	$-0.659412\pi$
$227$	308263.	−	308263.i	0.397061	−	0.397061i	0.877195	+	0.480134i	$0.159412\pi$
$228$	122744.	−	104202.i	0.156374	−	0.132751i
$229$	138030.	+	138030.i	0.173934	+	0.173934i	0.788705	−	0.614771i	$-0.210752\pi$
$229$	138030.	+	138030.i	0.173934	+	0.173934i	−0.614771	+	0.788705i	$0.710752\pi$
$230$	−140036.	+	166524.i	−0.174550	+	0.207566i
$231$	586465.	−	344798.i	0.723123	−	0.425143i
$232$	−159632.	+	274439.i	−0.194715	+	0.334754i
$233$	−1.04870e6			−1.26550			−0.632749	−	0.774357i	$-0.718073\pi$
$233$	−1.04870e6			−1.26550			−0.632749	+	0.774357i	$0.718073\pi$
$234$	−70426.4	−	184980.i	−0.0840806	−	0.220843i
$235$	−126040.	+	126040.i	−0.148880	+	0.148880i
$236$	440528.	+	309877.i	0.514865	+	0.362168i
$237$	−1.34083e6	−	347952.i	−1.55061	−	0.402391i
$238$	114835.	−	9922.12i	0.131411	−	0.0113544i
$239$	−482455.			−0.546339			−0.273170	−	0.961966i	$-0.588072\pi$
$239$	−482455.			−0.546339			−0.273170	+	0.961966i	$0.588072\pi$
$240$	134108.	+	111713.i	0.150289	+	0.125192i
$241$	−275879.			−0.305968			−0.152984	−	0.988229i	$-0.548888\pi$
$241$	−275879.			−0.305968			−0.152984	+	0.988229i	$0.548888\pi$
$242$	−2.16802e6	+	187324.i	−2.37971	+	0.205615i
$243$	879022.	−	273145.i	0.954958	−	0.296741i
$244$	−664913.	+	945254.i	−0.714974	+	1.01642i
$245$	102964.	−	102964.i	0.109590	−	0.109590i
$246$	−742073.	−	125636.i	−0.781823	−	0.132366i
$247$	−46476.7			−0.0484722
$248$	1.39385e6	−	368658.i	1.43909	−	0.380623i
$249$	−423534.	−	720386.i	−0.432902	−	0.736320i
$250$	244055.	−	290218.i	0.246966	−	0.293680i
$251$	−790255.	−	790255.i	−0.791740	−	0.791740i	0.190037	−	0.981777i	$-0.439139\pi$
$251$	−790255.	−	790255.i	−0.791740	−	0.791740i	−0.981777	+	0.190037i	$0.939139\pi$
$252$	−433778.	−	151216.i	−0.430295	−	0.150001i
$253$	−1.83747e6	+	1.83747e6i	−1.80475	+	1.80475i
$254$	767558.	−	66319.8i	0.746495	−	0.0644999i
$255$	−50679.2	+	29795.6i	−0.0488067	+	0.0286947i
$256$	809033.	−	667066.i	0.771554	−	0.636164i
$257$			1.23386e6i			1.16528i	0.812729	+	0.582642i	$0.197981\pi$
$257$			1.23386e6i			1.16528i	−0.812729	+	0.582642i	$0.802019\pi$
$258$	1.08355e6	−	769774.i	1.01344	−	0.719969i
$259$	54335.0	+	54335.0i	0.0503304	+	0.0503304i
$260$	−8642.00	−	49636.1i	−0.00792831	−	0.0455370i
$261$	116794.	+	409880.i	0.106126	+	0.372439i
$262$	−1.28650e6	−	1.08187e6i	−1.15786	−	0.973688i
$263$			1.58117e6i			1.40958i	0.709417	+	0.704789i	$0.248958\pi$
$263$			1.58117e6i			1.40958i	−0.709417	+	0.704789i	$0.751042\pi$
$264$	1.48088e6	+	1.46713e6i	1.30771	+	1.29556i
$265$		−	108389.i		−	0.0948132i
$266$	−69424.7	+	82556.4i	−0.0601603	+	0.0715396i
$267$	−291950.	+	1.12503e6i	−0.250628	+	0.965796i
$268$	−1.23766e6	−	870594.i	−1.05260	−	0.740421i
$269$	571637.	+	571637.i	0.481659	+	0.481659i	0.905661	−	0.424002i	$-0.139375\pi$
$269$	571637.	+	571637.i	0.481659	+	0.481659i	−0.424002	+	0.905661i	$0.639375\pi$
$270$	232892.	−	25692.8i	0.194422	−	0.0214488i
$271$			1.91523e6i			1.58416i	0.610421	+	0.792078i	$0.291000\pi$
$271$			1.91523e6i			1.58416i	−0.610421	+	0.792078i	$0.709000\pi$
$272$	119364.	+	332399.i	0.0978255	+	0.272419i
$273$	67206.4	+	114311.i	0.0545763	+	0.0928285i
$274$	−43790.7	−	506816.i	−0.0352376	−	0.407825i
$275$	1.56994e6	−	1.56994e6i	1.25185	−	1.25185i
$276$	1.74885e6	+	142891.i	1.38191	+	0.112910i
$277$	−811192.	−	811192.i	−0.635220	−	0.635220i	0.314153	−	0.949373i	$-0.398280\pi$
$277$	−811192.	−	811192.i	−0.635220	−	0.635220i	−0.949373	+	0.314153i	$0.898280\pi$
$278$	877720.	+	738107.i	0.681152	+	0.572805i
$279$	941132.	−	1.69121e6i	0.723836	−	1.30073i
$280$	−101077.	−	58793.4i	−0.0770477	−	0.0448160i
$281$	167945.			0.126882			0.0634410	−	0.997986i	$-0.479793\pi$
$281$	167945.			0.126882			0.0634410	+	0.997986i	$0.479793\pi$
$282$	1.41732e6	+	239958.i	1.06131	+	0.179685i
$283$	−886415.	+	886415.i	−0.657917	+	0.657917i	−0.954887	−	0.296970i	$-0.904024\pi$
$283$	−886415.	+	886415.i	−0.657917	+	0.657917i	0.296970	+	0.954887i	$0.404024\pi$
$284$	382748.	+	2.19835e6i	0.281590	+	1.61734i
$285$	13819.5	−	53253.3i	0.0100781	−	0.0388360i
$286$	−51798.6	−	599496.i	−0.0374458	−	0.433383i
$287$	504221.			0.361340
$288$	108082.	−	1.40345e6i	0.0767841	−	0.997048i
$289$	1.30090e6			0.916218
$290$	9338.79	+	108083.i	0.00652072	+	0.0754682i
$291$	−148084.	+	570640.i	−0.102512	+	0.395030i
$292$	−70438.8	−	404572.i	−0.0483454	−	0.277676i
$293$	−769288.	+	769288.i	−0.523504	+	0.523504i	−0.918628	−	0.395124i	$-0.870702\pi$
$293$	−769288.	+	769288.i	−0.523504	+	0.523504i	0.395124	+	0.918628i	$0.370702\pi$
$294$	−1.15783e6	−	196027.i	−0.781228	−	0.132265i
$295$	184040.			0.123128
$296$	−118385.	+	203527.i	−0.0785355	+	0.135018i
$297$	2.79755e6	−	66278.3i	1.84029	−	0.0435994i
$298$	1.73237e6	+	1.45681e6i	1.13006	+	0.950305i
$299$	−358150.	−	358150.i	−0.231679	−	0.231679i
$300$	−1.49423e6	−	122087.i	−0.958546	−	0.0783187i
$301$	−629645.	+	629645.i	−0.400571	+	0.400571i
$302$	−156686.	−	1.81342e6i	−0.0988585	−	1.14415i
$303$	−565968.	−	962651.i	−0.354148	−	0.602369i
$304$	−298949.	−	140973.i	−0.185530	−	0.0874889i
$305$			394900.i			0.243073i
$306$	432591.	+	194023.i	0.264103	+	0.118454i
$307$	−2.02513e6	−	2.02513e6i	−1.22633	−	1.22633i	−0.965342	−	0.260989i	$-0.915951\pi$
$307$	−2.02513e6	−	2.02513e6i	−1.22633	−	1.22633i	−0.260989	−	0.965342i	$-0.584049\pi$
$308$	−1.14226e6	−	803489.i	−0.686100	−	0.482618i
$309$	−798015.	+	3.07515e6i	−0.475461	+	1.83219i
$310$	317080.	−	377056.i	0.187398	−	0.222844i
$311$			443631.i			0.260089i	0.991508	+	0.130044i	$0.0415119\pi$
$311$			443631.i			0.260089i	−0.991508	+	0.130044i	$0.958488\pi$
$312$	−285966.	+	288646.i	−0.166313	+	0.167872i
$313$		−	1.36256e6i		−	0.786133i	−0.919510	−	0.393067i	$-0.871414\pi$
$313$		−	1.36256e6i		−	0.786133i	0.919510	−	0.393067i	$-0.128586\pi$
$314$	1.37597e6	+	1.15711e6i	0.787564	+	0.662291i
$315$	−150962.	+	43016.1i	−0.0857215	+	0.0244262i
$316$	487759.	+	2.80149e6i	0.274781	+	1.57823i
$317$	−1.34057e6	−	1.34057e6i	−0.749274	−	0.749274i	0.225069	−	0.974343i	$-0.427739\pi$
$317$	−1.34057e6	−	1.34057e6i	−0.749274	−	0.749274i	−0.974343	+	0.225069i	$0.927739\pi$
$318$	−712592.	+	506238.i	−0.395160	+	0.280729i
$319$			1.29567e6i			0.712880i
$320$	94969.1	−	345484.i	0.0518451	−	0.188605i
$321$	−67079.9	+	39438.0i	−0.0363354	+	0.0213625i
$322$	−1.17117e6	+	101193.i	−0.629477	+	0.0543891i
$323$	78719.3	−	78719.3i	0.0419832	−	0.0419832i
$324$	−1.25666e6	−	1.41113e6i	−0.665050	−	0.746799i
$325$	306005.	+	306005.i	0.160702	+	0.160702i
$326$	1.02435e6	−	1.21810e6i	0.533831	−	0.634806i
$327$	323283.	+	549870.i	0.167191	+	0.284375i
$328$	395053.	+	1.49364e6i	0.202755	+	0.766589i
$329$	−963033.			−0.490514
$330$	702309.	+	118904.i	0.355012	+	0.0601052i
$331$	1.44403e6	−	1.44403e6i	0.724446	−	0.724446i	−0.245062	−	0.969507i	$-0.578808\pi$
$331$	1.44403e6	−	1.44403e6i	0.724446	−	0.724446i	0.969507	+	0.245062i	$0.0788083\pi$
$332$	−986968.	+	1.40310e6i	−0.491426	+	0.698621i
$333$	86616.0	+	303972.i	0.0428043	+	0.150218i
$334$	−2.23028e6	+	192705.i	−1.09394	+	0.0945205i
$335$	−517057.			−0.251725
$336$	85559.3	+	939126.i	0.0413446	+	0.453812i
$337$	−861505.			−0.413222			−0.206611	−	0.978423i	$-0.566243\pi$
$337$	−861505.			−0.413222			−0.206611	+	0.978423i	$0.566243\pi$
$338$	−1.97570e6	+	170708.i	−0.940654	+	0.0812759i
$339$	−3.13117e6	−	812553.i	−1.47982	−	0.384019i
$340$	98707.9	+	69433.3i	0.0463078	+	0.0325740i
$341$	4.16053e6	−	4.16053e6i	1.93759	−	1.93759i
$342$	−414655.	+	157869.i	−0.191700	+	0.0729849i
$343$	1.77962e6			0.816756
$344$	−2.35851e6	−	1.37186e6i	−1.07459	−	0.625051i
$345$	516864.	−	303878.i	0.233791	−	0.137452i
$346$	−1.63208e6	+	1.94078e6i	−0.732909	+	0.871539i
$347$	−2.41298e6	−	2.41298e6i	−1.07580	−	1.07580i	−0.996881	−	0.0789140i	$-0.974855\pi$
$347$	−2.41298e6	−	2.41298e6i	−1.07580	−	1.07580i	−0.0789140	−	0.996881i	$-0.525145\pi$
$348$	666968.	−	566210.i	0.295228	−	0.250628i
$349$	2.44763e6	−	2.44763e6i	1.07568	−	1.07568i	0.0787853	−	0.996892i	$-0.474896\pi$
$349$	2.44763e6	−	2.44763e6i	1.07568	−	1.07568i	0.996892	−	0.0787853i	$-0.0251042\pi$
$350$	1.00065e6	−	86460.0i	0.436630	−	0.0377264i
$351$	12918.7	+	545285.i	0.00559693	+	0.236241i
$352$	1.48521e6	−	4.01322e6i	0.638899	−	1.72638i
$353$		−	1.19213e6i		−	0.509198i	−0.967047	−	0.254599i	$-0.918056\pi$
$353$		−	1.19213e6i		−	0.509198i	0.967047	−	0.254599i	$-0.0819435\pi$
$354$	−859575.	−	1.20996e6i	−0.364566	−	0.513170i
$355$	539154.	+	539154.i	0.227061	+	0.227061i
$356$	2.35059e6	−	409255.i	0.982998	−	0.171147i
$357$	−307443.	−	79782.7i	−0.127671	−	0.0331313i
$358$	−16800.8	−	14128.4i	−0.00692823	−	0.00582620i
$359$			2.80596e6i			1.14907i	0.818481	+	0.574534i	$0.194817\pi$
$359$			2.80596e6i			1.14907i	−0.818481	+	0.574534i	$0.805183\pi$
$360$	−245703.	−	413488.i	−0.0999205	−	0.168154i
$361$		−	2.37192e6i		−	0.957924i
$362$	−2.04077e6	+	2.42678e6i	−0.818506	+	0.973327i
$363$	5.80435e6	+	1.50625e6i	2.31200	+	0.599973i
$364$	156612.	−	222643.i	0.0619545	−	0.0880758i
$365$	−99222.9	−	99222.9i	−0.0389834	−	0.0389834i
$366$	2.59624e6	−	1.84442e6i	1.01308	−	0.719707i
$367$		−	1.25736e6i		−	0.487300i	−0.969863	−	0.243650i	$-0.921655\pi$
$367$		−	1.25736e6i		−	0.487300i	0.969863	−	0.243650i	$-0.0783448\pi$
$368$	−1.21737e6	−	3.39005e6i	−0.468599	−	1.30493i
$369$	1.81230e6	+	1.00851e6i	0.692889	+	0.385581i
$370$	6925.75	+	80155.8i	0.00263004	+	0.0304390i
$371$	414083.	−	414083.i	0.156190	−	0.156190i
$372$	−3.95988e6	−	323545.i	−1.48363	−	0.121221i
$373$	2.32554e6	+	2.32554e6i	0.865470	+	0.865470i	0.991967	−	0.126497i	$-0.0403733\pi$
$373$	2.32554e6	+	2.32554e6i	0.865470	+	0.865470i	−0.126497	+	0.991967i	$0.540373\pi$
$374$	1.10312e6	+	927656.i	0.407798	+	0.342932i
$375$	−900791.	+	529598.i	−0.330785	+	0.194477i
$376$	−754529.	−	2.85278e6i	−0.275237	−	1.04063i
$377$	−252545.			−0.0915136
$378$	987886.	+	791574.i	0.355613	+	0.284946i
$379$	−1.33888e6	+	1.33888e6i	−0.478787	+	0.478787i	−0.904744	−	0.425956i	$-0.859938\pi$
$379$	−1.33888e6	+	1.33888e6i	−0.478787	+	0.478787i	0.425956	+	0.904744i	$0.359938\pi$
$380$	−111266.	+	19372.1i	−0.0395277	+	0.00688205i
$381$	−2.05496e6	−	533270.i	−0.725254	−	0.188207i
$382$	311741.	+	3.60797e6i	0.109304	+	1.26504i
$383$	449214.			0.156479			0.0782396	−	0.996935i	$-0.475070\pi$
$383$	449214.			0.156479			0.0782396	+	0.996935i	$0.475070\pi$
$384$	−2.71492e6	+	989249.i	−0.939570	+	0.342356i
$385$	−477202.			−0.164078
$386$	94778.5	+	1.09693e6i	0.0323774	+	0.374723i
$387$	−3.52249e6	+	1.00372e6i	−1.19556	+	0.340672i
$388$	1.19228e6	−	207583.i	0.402066	−	0.0700025i
$389$	1.95846e6	−	1.95846e6i	0.656206	−	0.656206i	−0.298274	−	0.954480i	$-0.596411\pi$
$389$	1.95846e6	−	1.95846e6i	0.656206	−	0.656206i	0.954480	+	0.298274i	$0.0964111\pi$
$390$	−23176.2	+	136891.i	−0.00771580	+	0.0455735i
$391$	1.21323e6			0.401328
$392$	616390.	+	2.33049e6i	0.202600	+	0.766006i
$393$	2.34765e6	+	3.99310e6i	0.766746	+	1.30415i
$394$	−1.25904e6	−	1.05877e6i	−0.408601	−	0.343608i
$395$	687076.	+	687076.i	0.221571	+	0.221571i
$396$	−2.49847e6	−	5.17263e6i	−0.800638	−	1.65757i
$397$	740509.	−	740509.i	0.235806	−	0.235806i	−0.579305	−	0.815111i	$-0.696676\pi$
$397$	740509.	−	740509.i	0.235806	−	0.235806i	0.815111	+	0.579305i	$0.196676\pi$
$398$	378998.	+	4.38636e6i	0.119930	+	1.38802i
$399$	256242.	−	150651.i	0.0805783	−	0.0473741i
$400$	1.04012e6	+	2.89648e6i	0.325038	+	0.905149i
$401$		−	694459.i		−	0.215668i	−0.994169	−	0.107834i	$-0.965609\pi$
$401$		−	694459.i		−	0.215668i	0.994169	−	0.107834i	$-0.0343915\pi$
$402$	2.41496e6	+	3.39935e6i	0.745323	+	1.04913i
$403$	810951.	+	810951.i	0.248732	+	0.248732i
$404$	−1.31889e6	+	1.87496e6i	−0.402026	+	0.571528i
$405$	−628633.	−	147334.i	−0.190441	−	0.0446339i
$406$	−377240.	+	448595.i	−0.113580	+	0.135064i
$407$			960880.i			0.287530i
$408$	−4540.10	−	973242.i	−0.00135025	−	0.289448i
$409$			2.23236e6i			0.659867i	0.944004	+	0.329933i	$0.107026\pi$
$409$			2.23236e6i			0.659867i	−0.944004	+	0.329933i	$0.892974\pi$
$410$	404052.	+	339782.i	0.118707	+	0.0998254i
$411$	−352116.	+	1.35688e6i	−0.102821	+	0.396221i
$412$	6.42511e6	−	1.11866e6i	1.86482	−	0.324679i
$413$	703099.	+	703099.i	0.202834	+	0.202834i
$414$	−4.41188e6	−	1.97879e6i	−1.26510	−	0.567413i
$415$			586173.i			0.167073i
$416$	782238.	+	289491.i	0.221618	+	0.0820165i
$417$	−1.60169e6	−	2.72431e6i	−0.451064	−	0.767212i
$418$	−1.34385e6	+	116113.i	−0.376191	+	0.0325043i
$419$	−2.34289e6	+	2.34289e6i	−0.651953	+	0.651953i	−0.953463	−	0.301510i	$-0.902509\pi$
$419$	−2.34289e6	+	2.34289e6i	−0.651953	+	0.651953i	0.301510	+	0.953463i	$0.402509\pi$
$420$	208539.	+	245649.i	0.0576851	+	0.0679503i
$421$	−2.70290e6	−	2.70290e6i	−0.743231	−	0.743231i	0.229967	−	0.973198i	$-0.426138\pi$
$421$	−2.70290e6	−	2.70290e6i	−0.743231	−	0.743231i	−0.973198	+	0.229967i	$0.926138\pi$
$422$	474346.	−	564069.i	0.129662	−	0.154188i
$423$	−3.46139e6	−	1.92620e6i	−0.940588	−	0.523422i
$424$	1.55106e6	+	902201.i	0.419001	+	0.243719i
$425$	−1.03659e6			−0.278377
$426$	1.02646e6	−	6.06280e6i	0.274042	−	1.61864i
$427$	−1.50866e6	+	1.50866e6i	−0.400425	+	0.400425i
$428$	130652.	+	91903.2i	0.0344751	+	0.0242505i
$429$	−416507.	+	1.60501e6i	−0.109265	+	0.421051i
$430$	−928862.	+	80257.0i	−0.242259	+	0.0209321i
$431$	445928.			0.115630			0.0578152	−	0.998327i	$-0.481587\pi$
$431$	445928.			0.115630			0.0578152	+	0.998327i	$0.481587\pi$
$432$	−1.57087e6	+	3.54659e6i	−0.404976	+	0.914327i
$433$	1.15335e6			0.295626			0.147813	−	0.989015i	$-0.452777\pi$
$433$	1.15335e6			0.295626			0.147813	+	0.989015i	$0.452777\pi$
$434$	2.65185e6	−	229129.i	0.675810	−	0.0583924i
$435$	75092.2	−	289368.i	0.0190271	−	0.0733208i
$436$	753353.	−	1.07098e6i	0.189794	−	0.269815i
$437$	−802838.	+	802838.i	−0.201106	+	0.201106i
$438$	−188904.	+	1.11576e6i	−0.0470495	+	0.277899i
$439$	−3.66924e6			−0.908688			−0.454344	−	0.890826i	$-0.650126\pi$
$439$	−3.66924e6			−0.908688			−0.454344	+	0.890826i	$0.650126\pi$
$440$	−373884.	−	1.41361e6i	−0.0920673	−	0.348095i
$441$	2.82768e6	+	1.57355e6i	0.692362	+	0.385288i
$442$	−180814.	+	215015.i	−0.0440228	+	0.0523497i
$443$	−2.12384e6	−	2.12384e6i	−0.514176	−	0.514176i	0.401627	−	0.915803i	$-0.368445\pi$
$443$	−2.12384e6	−	2.12384e6i	−0.514176	−	0.514176i	−0.915803	+	0.401627i	$0.868445\pi$
$444$	494631.	−	419908.i	0.119076	−	0.101087i
$445$	576493.	−	576493.i	0.138005	−	0.138005i
$446$	5.81022e6	−	502024.i	1.38311	−	0.119505i
$447$	−3.16128e6	−	5.37700e6i	−0.748332	−	1.27283i
$448$	1.68269e6	−	957058.i	0.396104	−	0.225291i
$449$		−	2.85835e6i		−	0.669114i	−0.942376	−	0.334557i	$-0.891413\pi$
$449$		−	2.85835e6i		−	0.669114i	0.942376	−	0.334557i	$-0.108587\pi$
$450$	3.76953e6	+	1.69069e6i	0.877519	+	0.393580i
$451$	4.45841e6	+	4.45841e6i	1.03214	+	1.03214i
$452$	1.13904e6	+	6.54216e6i	0.262235	+	1.50617i
$453$	−1.25990e6	+	4.85502e6i	−0.288463	+	1.11159i
$454$	1.88744e6	+	1.58722e6i	0.429767	+	0.361407i
$455$		−	93014.0i		−	0.0210630i
$456$	647036.	+	641028.i	0.145719	+	0.144366i
$457$		−	196523.i		−	0.0440173i	−0.999758	−	0.0220087i	$-0.992994\pi$
$457$		−	196523.i		−	0.0440173i	0.999758	−	0.0220087i	$-0.00700614\pi$
$458$	−710703.	+	845132.i	−0.158316	+	0.188261i
$459$	−945451.	−	901690.i	−0.209463	−	0.199768i
$460$	−1.00670e6	−	708133.i	−0.221822	−	0.156034i
$461$	3.39546e6	+	3.39546e6i	0.744126	+	0.744126i	0.973369	−	0.229243i	$-0.0736252\pi$
$461$	3.39546e6	+	3.39546e6i	0.744126	+	0.744126i	−0.229243	+	0.973369i	$0.573625\pi$
$462$	2.22882e6	+	3.13733e6i	0.485813	+	0.683841i
$463$			2.38413e6i			0.516866i	0.966029	+	0.258433i	$0.0832061\pi$
$463$			2.38413e6i			0.516866i	−0.966029	+	0.258433i	$0.916794\pi$
$464$	−1.62443e6	−	766021.i	−0.350273	−	0.165175i
$465$	−1.17032e6	+	688064.i	−0.251000	+	0.147569i
$466$	−510673.	−	5.91032e6i	−0.108938	−	1.26080i
$467$	2.64430e6	−	2.64430e6i	0.561073	−	0.561073i	−0.368539	−	0.929612i	$-0.620142\pi$
$467$	2.64430e6	−	2.64430e6i	0.561073	−	0.561073i	0.929612	+	0.368539i	$0.120142\pi$
$468$	1.00822e6	−	486990.i	0.212786	−	0.102779i
$469$	−1.97534e6	−	1.97534e6i	−0.414677	−	0.414677i
$470$	−771717.	−	648965.i	−0.161144	−	0.135512i
$471$	−2.51092e6	−	4.27080e6i	−0.521531	−	0.887069i
$472$	−1.53191e6	+	2.63365e6i	−0.316502	+	0.544131i
$473$	−1.11349e7			−2.28840
$474$	1.30808e6	−	7.72618e6i	0.267416	−	1.57950i
$475$	685949.	−	685949.i	0.139495	−	0.139495i
$476$	111839.	+	642360.i	0.0226244	+	0.129945i
$477$	2.31655e6	−	660095.i	0.466171	−	0.132834i
$478$	−234936.	−	2.71905e6i	−0.0470304	−	0.544311i
$479$	2.93376e6			0.584233			0.292116	−	0.956383i	$-0.405641\pi$
$479$	2.93376e6			0.584233			0.292116	+	0.956383i	$0.405641\pi$
$480$	−564292.	+	810216.i	−0.111790	+	0.160508i
$481$	−187290.			−0.0369107
$482$	−134342.	−	1.55482e6i	−0.0263386	−	0.304833i
$483$	3.13553e6	+	813684.i	0.611566	+	0.158704i
$484$	−2.11147e6	−	1.21274e7i	−0.409704	−	2.35318i
$485$	292410.	−	292410.i	0.0564467	−	0.0564467i
$486$	1.96745e6	+	4.82103e6i	0.377845	+	0.925869i
$487$	−6.12618e6			−1.17049			−0.585245	−	0.810857i	$-0.699002\pi$
$487$	−6.12618e6			−1.17049			−0.585245	+	0.810857i	$0.699002\pi$
$488$	−5.65110e6	−	3.28705e6i	−1.07420	−	0.624823i
$489$	−3.78081e6	+	2.22284e6i	−0.715010	+	0.420373i
$490$	630431.	+	530152.i	0.118617	+	0.0997494i
$491$	−3.43695e6	−	3.43695e6i	−0.643382	−	0.643382i	0.308003	−	0.951385i	$-0.400339\pi$
$491$	−3.43695e6	−	3.43695e6i	−0.643382	−	0.643382i	−0.951385	+	0.308003i	$0.900339\pi$
$492$	346710.	−	4.24339e6i	0.0645733	−	0.790316i
$493$	427745.	−	427745.i	0.0792625	−	0.0792625i
$494$	−22632.2	−	261936.i	−0.00417263	−	0.0482923i
$495$	−1.71519e6	−	954473.i	−0.314629	−	0.175086i
$496$	2.75645e6	+	7.67601e6i	0.503090	+	1.40098i
$497$			4.11953e6i			0.748094i
$498$	3.85375e6	−	2.73777e6i	0.696321	−	0.494680i
$499$	6.27187e6	+	6.27187e6i	1.12758	+	1.12758i	0.990570	+	0.137005i	$0.0437477\pi$
$499$	6.27187e6	+	6.27187e6i	1.12758	+	1.12758i	0.137005	+	0.990570i	$0.456252\pi$
$500$	1.75447e6	+	1.23413e6i	0.313849	+	0.220768i
$501$	5.97106e6	+	1.54952e6i	1.06281	+	0.275805i
$502$	4.06894e6	−	4.83858e6i	0.720646	−	0.856957i
$503$		−	5.03844e6i		−	0.887925i	−0.896045	−	0.443962i	$-0.853572\pi$
$503$		−	5.03844e6i		−	0.887925i	0.896045	−	0.443962i	$-0.146428\pi$
$504$	640998.	−	2.51835e6i	0.112404	−	0.441610i
$505$			783302.i			0.136679i
$506$	−1.12505e7	−	9.46093e6i	−1.95341	−	1.64270i
$507$	5.28948e6	+	1.37264e6i	0.913888	+	0.237158i
$508$	747537.	+	4.29355e6i	0.128521	+	0.738172i
$509$	944873.	+	944873.i	0.161651	+	0.161651i	0.783298	−	0.621647i	$-0.213536\pi$
$509$	944873.	+	944873.i	0.161651	+	0.161651i	−0.621647	+	0.783298i	$0.713536\pi$
$510$	−192603.	−	271111.i	−0.0327896	−	0.0461554i
$511$		−	758134.i		−	0.128438i
$512$	4.15345e6	+	4.23476e6i	0.700220	+	0.713927i
$513$	1.22232e6	−	28958.8i	0.205066	−	0.00485833i
$514$	−6.95384e6	+	600837.i	−1.16096	+	0.100311i
$515$	1.57578e6	−	1.57578e6i	0.261805	−	0.261805i
$516$	4.86598e6	+	5.73188e6i	0.804537	+	0.947705i
$517$	−8.51532e6	−	8.51532e6i	−1.40112	−	1.40112i
$518$	−279765.	+	332683.i	−0.0458110	+	0.0544761i
$519$	6.02389e6	−	3.54160e6i	0.981654	−	0.577140i
$520$	275534.	−	72875.8i	0.0446855	−	0.0118188i
$521$	3.87395e6			0.625259			0.312630	−	0.949875i	$-0.398790\pi$
$521$	3.87395e6			0.625259			0.312630	+	0.949875i	$0.398790\pi$
$522$	−2.25315e6	+	857831.i	−0.361921	+	0.137792i
$523$	−823356.	+	823356.i	−0.131624	+	0.131624i	−0.769849	−	0.638226i	$-0.779669\pi$
$523$	−823356.	+	823356.i	−0.131624	+	0.131624i	0.638226	+	0.769849i	$0.279669\pi$
$524$	5.47076e6	−	7.77735e6i	0.870402	−	1.23738i
$525$	−2.67901e6	−	695215.i	−0.424206	−	0.110083i
$526$	−8.91124e6	+	769963.i	−1.40435	+	0.121340i
$527$	−2.74708e6			−0.430868
$528$	−7.54740e6	+	9.06046e6i	−1.17818	+	1.41438i
$529$	−5.93704e6			−0.922424
$530$	610862.	−	52780.7i	0.0944612	−	0.00816179i
$531$	1.12082e6	+	3.93342e6i	0.172504	+	0.605388i
$532$	−499083.	−	351066.i	−0.0764528	−	0.0537786i
$533$	−869013.	+	869013.i	−0.132498	+	0.132498i
$534$	−6.48267e6	−	1.09754e6i	−0.983786	−	0.166559i
$535$	54582.4			0.00824458
$536$	4.30386e6	−	7.39919e6i	0.647062	−	1.11243i
$537$	30658.6	+	52147.1i	0.00458793	+	0.00780358i
$538$	−2.94330e6	+	3.50002e6i	−0.438408	+	0.521333i
$539$	6.95633e6	+	6.95633e6i	1.03136	+	1.03136i
$540$	258210.	+	1.30003e6i	0.0381055	+	0.191854i
$541$	4.11836e6	−	4.11836e6i	0.604966	−	0.604966i	−0.336660	−	0.941626i	$-0.609297\pi$
$541$	4.11836e6	−	4.11836e6i	0.604966	−	0.604966i	0.941626	+	0.336660i	$0.109297\pi$
$542$	−1.07940e7	+	932637.i	−1.57827	+	0.136369i
$543$	7.53234e6	−	4.42846e6i	1.09630	−	0.644545i
$544$	−1.81523e6	+	834584.i	−0.262987	+	0.120913i
$545$		−	447425.i		−	0.0645252i
$546$	−611513.	+	434430.i	−0.0877858	+	0.0623646i
$547$	−1.53412e6	−	1.53412e6i	−0.219225	−	0.219225i	0.588947	−	0.808172i	$-0.299543\pi$
$547$	−1.53412e6	−	1.53412e6i	−0.219225	−	0.219225i	−0.808172	+	0.588947i	$0.799543\pi$
$548$	2.83502e6	−	493596.i	0.403278	−	0.0702135i
$549$	−8.44004e6	+	2.40497e6i	−1.19513	+	0.340549i
$550$	9.61245e6	+	8.08346e6i	1.35496	+	1.13944i
$551$			566111.i			0.0794370i
$552$	46303.3	+	9.92585e6i	0.00646791	+	1.38650i
$553$			5.24976e6i			0.730006i
$554$	4.17674e6	−	4.96678e6i	0.578180	−	0.687544i
$555$	55689.2	−	214598.i	0.00767430	−	0.0295729i
$556$	−3.73245e6	+	5.30613e6i	−0.512044	+	0.727932i
$557$	7.21675e6	+	7.21675e6i	0.985606	+	0.985606i	0.999898	−	0.0142917i	$-0.00454935\pi$
$557$	7.21675e6	+	7.21675e6i	0.985606	+	0.985606i	−0.0142917	+	0.999898i	$0.504549\pi$
$558$	9.98972e6	+	4.48053e6i	1.35821	+	0.609178i
$559$		−	2.17036e6i		−	0.293766i
$560$	282130.	−	598288.i	0.0380172	−	0.0806195i
$561$	−2.01301e6	−	3.42392e6i	−0.270047	−	0.459321i
$562$	81782.0	+	946511.i	0.0109224	+	0.126411i
$563$	−5.51164e6	+	5.51164e6i	−0.732841	+	0.732841i	−0.971182	−	0.238341i	$-0.923396\pi$
$563$	−5.51164e6	+	5.51164e6i	−0.732841	+	0.732841i	0.238341	+	0.971182i	$0.423396\pi$
$564$	−662196.	+	8.10464e6i	−0.0876574	+	1.07284i
$565$	1.60449e6	+	1.60449e6i	0.211454	+	0.211454i
$566$	−5.42735e6	−	4.56406e6i	−0.712110	−	0.598839i
$567$	−1.83874e6	−	2.96447e6i	−0.240194	−	0.387248i
$568$	−1.22032e7	+	3.22762e6i	−1.58710	+	0.419770i
$569$	−5.12519e6			−0.663635			−0.331818	−	0.943344i	$-0.607662\pi$
$569$	−5.12519e6			−0.663635			−0.331818	+	0.943344i	$0.607662\pi$
$570$	306857.	+	51952.4i	0.0395594	+	0.00669758i
$571$	4.97026e6	−	4.97026e6i	0.637953	−	0.637953i	−0.312097	−	0.950050i	$-0.601031\pi$
$571$	4.97026e6	−	4.97026e6i	0.637953	−	0.637953i	0.950050	+	0.312097i	$0.101031\pi$
$572$	3.35345e6	−	583859.i	0.428550	−	0.0746136i
$573$	2.50668e6	−	9.65949e6i	0.318942	−	1.22904i
$574$	245534.	+	2.84172e6i	0.0311052	+	0.359999i
$575$	1.05719e7			1.33347
$576$	7.96228e6	−	74288.4i	0.999956	−	0.00932964i
$577$	−2.31219e6			−0.289124			−0.144562	−	0.989496i	$-0.546177\pi$
$577$	−2.31219e6			−0.289124			−0.144562	+	0.989496i	$0.546177\pi$
$578$	633483.	+	7.33168e6i	0.0788707	+	0.912817i
$579$	762103.	−	2.93677e6i	0.0944751	−	0.364060i
$580$	−604595.	+	105264.i	−0.0746267	+	0.0129930i
$581$	−2.23939e6	+	2.23939e6i	−0.275226	+	0.275226i
$582$	−3.28816e6	−	556700.i	−0.402388	−	0.0681261i
$583$	7.32280e6			0.892290
$584$	2.24581e6	−	593993.i	0.272484	−	0.0720691i
$585$	186041.	−	334316.i	0.0224760	−	0.0403894i
$586$	−4.71021e6	−	3.96099e6i	−0.566626	−	0.476496i
$587$	661538.	+	661538.i	0.0792428	+	0.0792428i	0.745617	−	0.666374i	$-0.232155\pi$
$587$	661538.	+	661538.i	0.0792428	+	0.0792428i	−0.666374	+	0.745617i	$0.732155\pi$
$588$	540961.	−	6.62084e6i	0.0645242	−	0.789714i
$589$	1.81785e6	−	1.81785e6i	0.215908	−	0.215908i
$590$	89619.8	+	1.03722e6i	0.0105992	+	0.122671i
$591$	2.29754e6	+	3.90787e6i	0.270579	+	0.460226i
$592$	−1.20470e6	−	568089.i	−0.141277	−	0.0666212i
$593$			1.45321e7i			1.69704i	0.529160	+	0.848522i	$0.322507\pi$
$593$			1.45321e7i			1.69704i	−0.529160	+	0.848522i	$0.677493\pi$
$594$	1.73583e6	+	1.57343e7i	0.201855	+	1.82971i
$595$	157541.	+	157541.i	0.0182432	+	0.0182432i
$596$	−7.36680e6	+	1.04728e7i	−0.849499	+	1.20767i
$597$	3.04748e6	−	1.17435e7i	0.349949	−	1.34853i
$598$	1.84408e6	−	2.19289e6i	0.210876	−	0.250763i
$599$			1.13672e7i			1.29445i	0.762297	+	0.647227i	$0.224072\pi$
$599$			1.13672e7i			1.29445i	−0.762297	+	0.647227i	$0.775928\pi$
$600$	−39561.8	−	8.48069e6i	−0.00448639	−	0.961730i
$601$		−	1.01090e7i		−	1.14162i	−0.821083	−	0.570809i	$-0.806630\pi$
$601$		−	1.01090e7i		−	1.14162i	0.821083	−	0.570809i	$-0.193370\pi$
$602$	−3.85520e6	−	3.24198e6i	−0.433566	−	0.364602i
$603$	−3.14892e6	−	1.10509e7i	−0.352669	−	1.23766i
$604$	1.01439e7	−	1.76612e6i	1.13139	−	0.196983i
$605$	−2.97429e6	−	2.97429e6i	−0.330366	−	0.330366i
$606$	5.14976e6	−	3.65848e6i	0.569646	−	0.404687i
$607$			1.39697e6i			0.153892i	0.997035	+	0.0769461i	$0.0245169\pi$
$607$			1.39697e6i			0.153892i	−0.997035	+	0.0769461i	$0.975483\pi$
$608$	648929.	−	1.75348e6i	0.0711932	−	0.192372i
$609$	1.39237e6	−	818610.i	0.152129	−	0.0894404i
$610$	−2.22560e6	+	192300.i	−0.242171	+	0.0209244i
$611$	1.65977e6	−	1.65977e6i	0.179864	−	0.179864i
$612$	−882833.	+	2.53250e6i	−0.0952797	+	0.273320i
$613$	8.37199e6	+	8.37199e6i	0.899866	+	0.899866i	0.995424	−	0.0955580i	$-0.0304636\pi$
$613$	8.37199e6	+	8.37199e6i	0.899866	+	0.899866i	−0.0955580	+	0.995424i	$0.530464\pi$
$614$	1.04272e7	−	1.23995e7i	1.11621	−	1.32734i
$615$	−737327.	−	1.25411e6i	−0.0786090	−	0.133706i
$616$	3.97212e6	−	6.82886e6i	0.421765	−	0.725098i
$617$	7.72279e6			0.816698			0.408349	−	0.912826i	$-0.366105\pi$
$617$	7.72279e6			0.816698			0.408349	+	0.912826i	$0.366105\pi$
$618$	−1.77197e7	−	3.00003e6i	−1.86632	−	0.315976i
$619$	205983.	−	205983.i	0.0216076	−	0.0216076i	−0.696220	−	0.717828i	$-0.745136\pi$
$619$	205983.	−	205983.i	0.0216076	−	0.0216076i	0.717828	+	0.696220i	$0.245136\pi$
$620$	2.27944e6	+	1.60341e6i	0.238149	+	0.167519i
$621$	9.64242e6	+	9.19610e6i	1.00336	+	0.956918i
$622$	−2.50024e6	+	216030.i	−0.259123	+	0.0223892i
$623$	4.40482e6			0.454682
$624$	−1.76602e6	−	1.47110e6i	−0.181566	−	0.151245i
$625$	−8.65903e6			−0.886684
$626$	7.67922e6	−	663512.i	0.783215	−	0.0676726i
$627$	3.59783e6	+	933652.i	0.365487	+	0.0948454i
$628$	−5.85124e6	+	8.31825e6i	−0.592037	+	0.841652i
$629$	317221.	−	317221.i	0.0319694	−	0.0319694i
$630$	−315945.	−	829850.i	−0.0317146	−	0.0833006i
$631$	−5.98114e6			−0.598012			−0.299006	−	0.954251i	$-0.596655\pi$
$631$	−5.98114e6			−0.598012			−0.299006	+	0.954251i	$0.596655\pi$
$632$	−1.55513e7	+	4.11314e6i	−1.54872	+	0.409620i
$633$	−1.75078e6	+	1.02933e6i	−0.173669	+	0.102105i
$634$	6.90245e6	−	8.20805e6i	0.681993	−	0.810993i
$635$	1.05301e6	+	1.05301e6i	0.103633	+	0.103633i
$636$	−3.20009e6	−	3.76955e6i	−0.313703	−	0.369527i
$637$	−1.35590e6	+	1.35590e6i	−0.132397	+	0.132397i
$638$	−7.30219e6	+	630935.i	−0.710234	+	0.0613667i
$639$	−8.23965e6	+	1.48066e7i	−0.798283	+	1.43451i
$640$	1.99335e6	+	366996.i	0.192368	+	0.0354170i
$641$		−	5.61954e6i		−	0.540201i	−0.962832	−	0.270100i	$-0.912943\pi$
$641$		−	5.61954e6i		−	0.540201i	0.962832	−	0.270100i	$-0.0870569\pi$
$642$	−254932.	−	358848.i	−0.0244111	−	0.0343616i
$643$	−7.90927e6	−	7.90927e6i	−0.754412	−	0.754412i	0.220887	−	0.975299i	$-0.429105\pi$
$643$	−7.90927e6	−	7.90927e6i	−0.754412	−	0.754412i	−0.975299	+	0.220887i	$0.929105\pi$
$644$	−1.14062e6	−	6.55126e6i	−0.108374	−	0.622459i
$645$	2.48681e6	+	645338.i	0.235366	+	0.0610784i
$646$	481984.	+	405318.i	0.0454413	+	0.0382133i
$647$		−	1.15453e7i		−	1.08429i	−0.840285	−	0.542145i	$-0.817612\pi$
$647$		−	1.15453e7i		−	1.08429i	0.840285	−	0.542145i	$-0.182388\pi$
$648$	7.34097e6	−	7.76950e6i	0.686777	−	0.726868i
$649$			1.24339e7i			1.15876i
$650$	−1.57559e6	+	1.87361e6i	−0.146272	+	0.173939i
$651$	−7.09971e6	−	1.84240e6i	−0.656580	−	0.170385i
$652$	7.36388e6	+	5.17992e6i	0.678403	+	0.477204i
$653$	−9.52579e6	−	9.52579e6i	−0.874215	−	0.874215i	0.118714	−	0.992929i	$-0.462123\pi$
$653$	−9.52579e6	−	9.52579e6i	−0.874215	−	0.874215i	−0.992929	+	0.118714i	$0.962123\pi$
$654$	−2.94156e6	+	2.08974e6i	−0.268927	+	0.191050i
$655$		−	3.24915e6i		−	0.295915i
$656$	−8.22559e6	+	2.95381e6i	−0.746290	+	0.267992i
$657$	1.51638e6	−	2.72493e6i	0.137055	−	0.246287i
$658$	−468957.	−	5.42751e6i	−0.0422248	−	0.488693i
$659$	−2.09110e6	+	2.09110e6i	−0.187569	+	0.187569i	−0.794644	−	0.607075i	$-0.792343\pi$
$659$	−2.09110e6	+	2.09110e6i	−0.187569	+	0.187569i	0.607075	+	0.794644i	$0.292343\pi$
$660$	−328131.	+	4.01601e6i	−0.0293216	+	0.358868i
$661$	9.24120e6	+	9.24120e6i	0.822668	+	0.822668i	0.986490	−	0.163822i	$-0.0523821\pi$
$661$	9.24120e6	+	9.24120e6i	0.822668	+	0.822668i	−0.163822	+	0.986490i	$0.552382\pi$
$662$	8.84152e6	+	7.43516e6i	0.784119	+	0.659394i
$663$	667374.	−	392367.i	0.0589638	−	0.0346664i
$664$	−8.38825e6	−	4.87916e6i	−0.738331	−	0.429462i
$665$	−208502.			−0.0182834
$666$	−1.67096e6	+	636177.i	−0.145976	+	0.0555766i
$667$	−4.36246e6	+	4.36246e6i	−0.379680	+	0.379680i
$668$	−2.17211e6	−	1.24757e7i	−0.188339	−	1.08174i
$669$	−1.55555e7	−	4.03672e6i	−1.34375	−	0.348709i
$670$	−251785.	−	2.91406e6i	−0.0216692	−	0.250790i
$671$	−2.66797e7			−2.28757
$672$	−5.25111e6	+	939515.i	−0.448568	+	0.0802565i
$673$	1.40472e7			1.19551			0.597753	−	0.801681i	$-0.296060\pi$
$673$	1.40472e7			1.19551			0.597753	+	0.801681i	$0.296060\pi$
$674$	−419517.	−	4.85532e6i	−0.0355713	−	0.411688i
$675$	−8.23853e6	−	7.85719e6i	−0.695969	−	0.663755i
$676$	−1.92417e6	−	1.10516e7i	−0.161948	−	0.930166i
$677$	−3.32334e6	+	3.32334e6i	−0.278679	+	0.278679i	−0.832581	−	0.553903i	$-0.813138\pi$
$677$	−3.32334e6	+	3.32334e6i	−0.278679	+	0.278679i	0.553903	+	0.832581i	$0.313138\pi$
$678$	3.05468e6	−	1.80425e7i	0.255206	−	1.50738i
$679$	2.23422e6			0.185974
$680$	−343250.	+	590115.i	−0.0284667	+	0.0489400i
$681$	−3.44426e6	−	5.85832e6i	−0.284595	−	0.484066i
$682$	2.54742e7	+	2.14222e7i	2.09720	+	1.76361i
$683$	−2.34939e6	−	2.34939e6i	−0.192710	−	0.192710i	0.604156	−	0.796866i	$-0.293510\pi$
$683$	−2.34939e6	−	2.34939e6i	−0.192710	−	0.192710i	−0.796866	+	0.604156i	$0.793510\pi$
$684$	−1.09165e6	−	2.26006e6i	−0.0892160	−	0.184705i
$685$	695300.	−	695300.i	0.0566168	−	0.0566168i
$686$	866601.	+	1.00297e7i	0.0703087	+	0.813724i
$687$	2.62316e6	−	1.54222e6i	0.212047	−	0.124668i
$688$	6.58314e6	−	1.39603e7i	0.530227	−	1.12440i
$689$			1.42733e6i			0.114545i
$690$	1.96430e6	+	2.76500e6i	0.157067	+	0.221091i
$691$	−7.30645e6	−	7.30645e6i	−0.582118	−	0.582118i	0.353367	−	0.935485i	$-0.385037\pi$
$691$	−7.30645e6	−	7.30645e6i	−0.582118	−	0.582118i	−0.935485	+	0.353367i	$0.885037\pi$
$692$	−1.17327e7	−	8.25306e6i	−0.931395	−	0.655164i
$693$	−2.90620e6	−	1.01991e7i	−0.229875	−	0.806728i
$694$	1.24242e7	−	1.47742e7i	0.979195	−	1.16441i
$695$			2.21675e6i			0.174082i
$696$	3.51587e6	+	3.48322e6i	0.275112	+	0.272557i
$697$		−	2.94376e6i		−	0.229520i
$698$	1.49864e7	+	1.26026e7i	1.16428	+	0.979087i
$699$	−4.10626e6	+	1.58235e7i	−0.317873	+	1.22492i
$700$	974552.	+	5.59743e6i	0.0751726	+	0.431761i
$701$	−2.16826e6	−	2.16826e6i	−0.166654	−	0.166654i	0.618853	−	0.785507i	$-0.287598\pi$
$701$	−2.16826e6	−	2.16826e6i	−0.166654	−	0.166654i	−0.785507	+	0.618853i	$0.787598\pi$
$702$	−3.06686e6	+	338339.i	−0.234883	+	0.0259125i
$703$			419834.i			0.0320398i
$704$	2.33412e7	+	6.41618e6i	1.77497	+	0.487916i
$705$	1.40825e6	+	2.39529e6i	0.106711	+	0.181503i
$706$	6.71868e6	−	580518.i	0.507308	−	0.0438332i
$707$	−2.99250e6	+	2.99250e6i	−0.225157	+	0.225157i
$708$	6.40056e6	−	5.43364e6i	0.479883	−	0.407388i
$709$	1.78478e6	+	1.78478e6i	0.133342	+	0.133342i	0.770628	−	0.637285i	$-0.219943\pi$
$709$	1.78478e6	+	1.78478e6i	0.133342	+	0.133342i	−0.637285	+	0.770628i	$0.719943\pi$
$710$	−2.77605e6	+	3.30114e6i	−0.206672	+	0.245764i
$711$	−1.05003e7	+	1.88690e7i	−0.778980	+	1.39983i
$712$	3.45114e6	+	1.30483e7i	0.255131	+	0.964616i
$713$	2.80167e7			2.06392
$714$	299932.	−	1.77155e6i	0.0220180	−	0.130050i
$715$	822447.	−	822447.i	0.0601649	−	0.0601649i
$716$	71444.4	−	101567.i	0.00520817	−	0.00740405i
$717$	−1.88909e6	+	7.27961e6i	−0.137232	+	0.528823i
$718$	−1.58140e7	+	1.36639e6i	−1.14480	+	0.0989150i
$719$	505647.			0.0364775			0.0182388	−	0.999834i	$-0.494194\pi$
$719$	505647.			0.0364775			0.0182388	+	0.999834i	$0.494194\pi$
$720$	2.21071e6	−	1.58610e6i	0.158928	−	0.114025i
$721$	1.20401e7			0.862567
$722$	1.33678e7	−	1.15502e6i	0.954369	−	0.0824609i
$723$	−1.08023e6	+	4.16265e6i	−0.0768544	+	0.296159i
$724$	−1.46707e7	−	1.03197e7i	−1.04017	−	0.731681i
$725$	3.72731e6	−	3.72731e6i	0.263360	−	0.263360i
$726$	−5.66256e6	+	3.34460e7i	−0.398723	+	2.35506i
$727$	1.55989e7			1.09461			0.547303	−	0.836935i	$-0.315655\pi$
$727$	1.55989e7			1.09461			0.547303	+	0.836935i	$0.315655\pi$
$728$	1.33105e6	+	774227.i	0.0930820	+	0.0541427i
$729$	−679515.	−	1.43328e7i	−0.0473565	−	0.998878i
$730$	510889.	−	607523.i	0.0354829	−	0.0421945i
$731$	3.67602e6	+	3.67602e6i	0.254439	+	0.254439i
$732$	1.16591e7	+	1.37339e7i	0.804244	+	0.947360i
$733$	−1.52273e7	+	1.52273e7i	−1.04680	+	1.04680i	−0.0479484	+	0.998850i	$0.515268\pi$
$733$	−1.52273e7	+	1.52273e7i	−1.04680	+	1.04680i	−0.998850	+	0.0479484i	$0.984732\pi$
$734$	7.08633e6	−	612284.i	0.485491	−	0.0419482i
$735$	−1.15043e6	−	1.95676e6i	−0.0785492	−	0.133604i
$736$	1.85130e7	−	8.51171e6i	1.25975	−	0.579192i
$737$		−	3.49327e7i		−	2.36899i
$738$	−4.80133e6	+	1.07050e7i	−0.324504	+	0.723509i
$739$	−20165.7	−	20165.7i	−0.00135832	−	0.00135832i	0.706427	−	0.707786i	$-0.250306\pi$
$739$	−20165.7	−	20165.7i	−0.00135832	−	0.00135832i	−0.707786	+	0.706427i	$0.750306\pi$
$740$	−448374.	+	78065.1i	−0.0300996	+	0.00524056i
$741$	−181983.	+	701272.i	−0.0121755	+	0.0469182i
$742$	2.53535e6	+	2.13207e6i	0.169055	+	0.142165i
$743$		−	1.06139e6i		−	0.0705344i	−0.999378	−	0.0352672i	$-0.988772\pi$
$743$		−	1.06139e6i		−	0.0705344i	0.999378	−	0.0352672i	$-0.0112282\pi$
$744$	−104843.	−	2.24749e7i	−0.00694399	−	1.48855i
$745$			4.37523e6i			0.288809i
$746$	−1.19740e7	+	1.42389e7i	−0.787756	+	0.936760i
$747$	−1.25280e7	+	3.56984e6i	−0.821451	+	0.234071i
$748$	−4.69096e6	+	6.66877e6i	−0.306555	+	0.435805i
$749$	208525.	+	208525.i	0.0135817	+	0.0135817i
$750$	−3.42339e6	−	4.81883e6i	−0.222230	−	0.312816i
$751$		−	7.84071e6i		−	0.507289i	−0.967297	−	0.253645i	$-0.918371\pi$
$751$		−	7.84071e6i		−	0.507289i	0.967297	−	0.253645i	$-0.0816294\pi$
$752$	1.57104e7	−	5.64160e6i	1.01308	−	0.363796i
$753$	−1.50182e7	+	8.82960e6i	−0.965230	+	0.567484i
$754$	−122979.	−	1.42331e6i	−0.00787775	−	0.0911739i
$755$	2.48783e6	−	2.48783e6i	0.158838	−	0.158838i
$756$	−3.98014e6	+	5.95304e6i	−0.253276	+	0.378822i
$757$	−1.53326e6	−	1.53326e6i	−0.0972471	−	0.0972471i	0.656809	−	0.754057i	$-0.271906\pi$
$757$	−1.53326e6	−	1.53326e6i	−0.0972471	−	0.0972471i	−0.754057	+	0.656809i	$0.771906\pi$
$758$	−8.19769e6	−	6.89374e6i	−0.518225	−	0.435795i
$759$	2.05302e7	+	3.49197e7i	1.29357	+	2.20022i
$760$	−163360.	−	617643.i	−0.0102592	−	0.0387886i
$761$	−1.10357e7			−0.690775			−0.345388	−	0.938460i	$-0.612253\pi$
$761$	−1.10357e7			−0.690775			−0.345388	+	0.938460i	$0.612253\pi$
$762$	2.00476e6	−	1.18411e7i	0.125076	−	0.738763i
$763$	1.70933e6	−	1.70933e6i	0.106295	−	0.106295i
$764$	−2.01822e7	+	3.51386e6i	−1.25094	+	0.217797i
$765$	251138.	+	881349.i	0.0155153	+	0.0544496i
$766$	218749.	+	2.53171e6i	0.0134702	+	0.155898i
$767$	−2.42355e6			−0.148752
$768$	−6.89732e6	−	1.48192e7i	−0.421966	−	0.906612i
$769$	2.34150e7			1.42784			0.713919	−	0.700228i	$-0.246919\pi$
$769$	2.34150e7			1.42784			0.713919	+	0.700228i	$0.246919\pi$
$770$	−232377.	−	2.68944e6i	−0.0141243	−	0.163469i
$771$	1.86173e7	+	4.83126e6i	1.12793	+	0.292701i
$772$	−6.13597e6	+	1.06832e6i	−0.370544	+	0.0645144i
$773$	−3.14828e6	+	3.14828e6i	−0.189507	+	0.189507i	−0.795483	−	0.605976i	$-0.792783\pi$
$773$	−3.14828e6	+	3.14828e6i	−0.189507	+	0.189507i	0.605976	+	0.795483i	$0.292783\pi$
$774$	−7.37215e6	−	1.93635e7i	−0.442325	−	1.16180i
$775$	−2.39376e7			−1.43162
$776$	1.75050e6	+	6.61841e6i	0.104354	+	0.394547i
$777$	1.03260e6	−	607090.i	0.0613589	−	0.0360745i
$778$	1.19913e7	+	1.00839e7i	0.710258	+	0.597282i
$779$	1.94800e6	+	1.94800e6i	0.115013	+	0.115013i
$780$	−782782.	−	63957.8i	−0.0460685	−	0.00376406i
$781$	−3.64256e7	+	3.64256e7i	−2.13688	+	2.13688i
$782$	590790.	+	6.83757e6i	0.0345475	+	0.399838i
$783$	6.64187e6	−	157356.i	0.387156	−	0.00917233i
$784$	−1.28341e7	+	4.60873e6i	−0.745722	+	0.267788i
$785$			3.47512e6i			0.201278i
$786$	−2.13613e7	+	1.51755e7i	−1.23331	+	0.876165i
$787$	−1.91528e7	−	1.91528e7i	−1.10229	−	1.10229i	−0.994134	−	0.108156i	$-0.965506\pi$
$787$	−1.91528e7	−	1.91528e7i	−1.10229	−	1.10229i	−0.108156	−	0.994134i	$-0.534494\pi$
$788$	5.35400e6	−	7.61136e6i	0.307159	−	0.436663i
$789$	2.38578e7	+	6.19119e6i	1.36439	+	0.354064i
$790$	−3.53768e6	+	4.20684e6i	−0.201675	+	0.239822i
$791$			1.22595e7i			0.696675i
$792$	2.79355e7	−	1.65999e7i	1.58250	−	0.940355i
$793$		−	5.20028e6i		−	0.293659i
$794$	4.53400e6	+	3.81281e6i	0.255229	+	0.214631i
$795$	−1.63544e6	−	424404.i	−0.0917734	−	0.0238156i
$796$	−2.45364e7	+	4.27195e6i	−1.37255	+	0.238970i
$797$	−1.69769e7	−	1.69769e7i	−0.946700	−	0.946700i	0.0519495	−	0.998650i	$-0.483457\pi$
$797$	−1.69769e7	−	1.69769e7i	−0.946700	−	0.946700i	−0.998650	+	0.0519495i	$0.983457\pi$
$798$	973829.	+	1.37078e6i	0.0541347	+	0.0762011i
$799$			5.62242e6i			0.311570i
$800$	−1.58176e7	+	7.27244e6i	−0.873809	+	0.401750i
$801$	1.58320e7	+	8.81027e6i	0.871878	+	0.485186i
$802$	3.91387e6	−	338172.i	0.214867	−	0.0185653i
$803$	6.70357e6	−	6.70357e6i	0.366874	−	0.366874i
$804$	−1.79823e7	+	1.52657e7i	−0.981079	+	0.832869i
$805$	−1.60672e6	−	1.60672e6i	−0.0873879	−	0.0873879i
$806$	−4.17550e6	+	4.96530e6i	−0.226397	+	0.269221i
$807$	1.08635e7	−	6.38695e6i	0.587201	−	0.345231i
$808$	−1.12092e7	−	6.52002e6i	−0.604014	−	0.351334i
$809$	2.06948e7			1.11171			0.555854	−	0.831280i	$-0.312391\pi$
$809$	2.06948e7			1.11171			0.555854	+	0.831280i	$0.312391\pi$
$810$	524234.	−	3.61463e6i	0.0280746	−	0.193576i
$811$	7.59889e6	−	7.59889e6i	0.405693	−	0.405693i	−0.474540	−	0.880234i	$-0.657386\pi$
$811$	7.59889e6	−	7.59889e6i	0.405693	−	0.405693i	0.880234	+	0.474540i	$0.157386\pi$
$812$	−2.71192e6	−	1.90762e6i	−0.144340	−	0.101532i
$813$	2.88983e7	+	7.49923e6i	1.53337	+	0.397915i
$814$	−5.41538e6	+	467908.i	−0.286463	+	0.0247514i
$815$	3.07642e6			0.162237
$816$	5.48284e6	−	499515.i	0.288257	−	0.0262617i
$817$	−4.86512e6			−0.254999
$818$	−1.25813e7	+	1.08707e6i	−0.657417	+	0.0568032i
$819$	1.98795e6	−	566463.i	0.103561	−	0.0295095i
$820$	−1.71821e6	+	2.44264e6i	−0.0892362	+	0.126860i
$821$	4.84077e6	−	4.84077e6i	0.250644	−	0.250644i	−0.570591	−	0.821235i	$-0.693286\pi$
$821$	4.84077e6	−	4.84077e6i	0.250644	−	0.250644i	0.821235	+	0.570591i	$0.193286\pi$
$822$	−7.81865e6	−	1.32373e6i	−0.403601	−	0.0683315i
$823$	2.84839e7			1.46588			0.732942	−	0.680292i	$-0.238147\pi$
$823$	2.84839e7			1.46588			0.732942	+	0.680292i	$0.238147\pi$
$824$	9.43335e6	+	3.56663e7i	0.484003	+	1.82995i
$825$	−1.75411e7	−	2.98355e7i	−0.897268	−	1.52616i
$826$	−3.62018e6	+	4.30494e6i	−0.184621	+	0.219542i
$827$	9.24056e6	+	9.24056e6i	0.469824	+	0.469824i	0.901857	−	0.432034i	$-0.142204\pi$
$827$	9.24056e6	+	9.24056e6i	0.469824	+	0.469824i	−0.432034	+	0.901857i	$0.642204\pi$
$828$	9.00379e6	−	2.58283e7i	0.456404	−	1.30924i
$829$	2.73001e7	−	2.73001e7i	1.37968	−	1.37968i	0.534527	−	0.845151i	$-0.320490\pi$
$829$	2.73001e7	−	2.73001e7i	1.37968	−	1.37968i	0.845151	−	0.534527i	$-0.179510\pi$
$830$	−3.30358e6	+	285442.i	−0.166452	+	0.0143821i
$831$	−1.54161e7	+	9.06353e6i	−0.774412	+	0.455297i
$832$	−1.25061e6	+	4.54955e6i	−0.0626345	+	0.227856i
$833$		−	4.59306e6i		−	0.229345i
$834$	1.45738e7	−	1.03535e7i	0.725536	−	0.515434i
$835$	−3.05972e6	−	3.05972e6i	−0.151868	−	0.151868i
$836$	−1.30879e6	−	7.51718e6i	−0.0647672	−	0.371997i
$837$	−2.18331e7	−	2.08225e7i	−1.07721	−	1.02735i
$838$	−1.43451e7	−	1.20633e7i	−0.705655	−	0.593411i
$839$		−	3.25226e7i		−	1.59507i	−0.603270	−	0.797537i	$-0.706136\pi$
$839$		−	3.25226e7i		−	1.59507i	0.603270	−	0.797537i	$-0.293864\pi$
$840$	−1.28289e6	+	1.29492e6i	−0.0627323	+	0.0633204i
$841$		−	1.74350e7i		−	0.850026i
$842$	1.39169e7	−	1.65493e7i	0.676493	−	0.804452i
$843$	657600.	−	2.53406e6i	0.0318708	−	0.122814i
$844$	3.41000e6	+	2.39867e6i	0.164778	+	0.115908i
$845$	−2.71046e6	−	2.71046e6i	−0.130587	−	0.130587i
$846$	9.17026e6	−	2.04459e7i	0.440510	−	0.982154i
$847$		−	2.27257e7i		−	1.08845i
$848$	−4.32937e6	+	9.18090e6i	−0.206745	+	0.438425i
$849$	9.90400e6	+	1.68457e7i	0.471565	+	0.802082i
$850$	−504774.	−	5.84205e6i	−0.0239635	−	0.277343i
$851$	−3.23525e6	+	3.23525e6i	−0.153138	+	0.153138i
$852$	3.46689e7	+	2.83265e6i	1.63622	+	0.133688i
$853$	1.01270e7	+	1.01270e7i	0.476552	+	0.476552i	0.904027	−	0.427475i	$-0.140597\pi$
$853$	1.01270e7	+	1.01270e7i	0.476552	+	0.476552i	−0.427475	+	0.904027i	$0.640597\pi$
$854$	−9.23724e6	−	7.76793e6i	−0.433409	−	0.364469i
$855$	−749411.	−	417035.i	−0.0350594	−	0.0195100i
$856$	−454331.	+	781086.i	−0.0211928	+	0.0364346i
$857$	1.48173e7			0.689154			0.344577	−	0.938758i	$-0.388022\pi$
$857$	1.48173e7			0.689154			0.344577	+	0.938758i	$0.388022\pi$
$858$	−9.24843e6	−	1.56580e6i	−0.428894	−	0.0726137i
$859$	−3.92065e6	+	3.92065e6i	−0.181290	+	0.181290i	−0.791918	−	0.610628i	$-0.790917\pi$
$859$	−3.92065e6	+	3.92065e6i	−0.181290	+	0.181290i	0.610628	+	0.791918i	$0.290917\pi$
$860$	−904634.	−	5.19585e6i	−0.0417087	−	0.239558i
$861$	1.97431e6	−	7.60802e6i	0.0907629	−	0.349755i
$862$	217148.	+	2.51319e6i	0.00995379	+	0.115201i
$863$	−1.46553e7			−0.669835			−0.334917	−	0.942248i	$-0.608708\pi$
$863$	−1.46553e7			−0.669835			−0.334917	+	0.942248i	$0.608708\pi$
$864$	−2.07530e7	−	7.12613e6i	−0.945795	−	0.324765i
$865$	−4.90159e6			−0.222739
$866$	561635.	+	6.50014e6i	0.0254484	+	0.294529i
$867$	5.09377e6	−	1.96288e7i	0.230140	−	0.886843i
$868$	2.58268e6	+	1.48339e7i	0.116351	+	0.668275i
$869$	−4.64193e7	+	4.64193e7i	−2.08521	+	2.08521i
$870$	1.66740e6	+	282299.i	0.0746865	+	0.0126448i
$871$	6.80891e6			0.304111
$872$	6.40275e6	+	3.72426e6i	0.285151	+	0.165863i
$873$	8.03038e6	+	4.46877e6i	0.356616	+	0.198451i
$874$	−4.91563e6	−	4.13373e6i	−0.217671	−	0.183048i
$875$	2.80020e6	+	2.80020e6i	0.123643	+	0.123643i
$876$	−6.38027e6	−	521304.i	−0.280917	−	0.0229526i
$877$	4.24592e6	−	4.24592e6i	0.186412	−	0.186412i	−0.607731	−	0.794143i	$-0.707920\pi$
$877$	4.24592e6	−	4.24592e6i	0.186412	−	0.186412i	0.794143	+	0.607731i	$0.207920\pi$
$878$	−1.78677e6	−	2.06793e7i	−0.0782225	−	0.905315i
$879$	8.59534e6	+	1.46198e7i	0.375224	+	0.638216i
$880$	7.78483e6	−	2.79553e6i	0.338877	−	0.121691i
$881$			2.84152e7i			1.23342i	0.787191	+	0.616709i	$0.211535\pi$
$881$			2.84152e7i			1.23342i	−0.787191	+	0.616709i	$0.788465\pi$
$882$	−7.49137e6	+	1.67026e7i	−0.324257	+	0.722958i
$883$	−1.17605e6	−	1.17605e6i	−0.0507602	−	0.0507602i	0.681271	−	0.732031i	$-0.261428\pi$
$883$	−1.17605e6	−	1.17605e6i	−0.0507602	−	0.0507602i	−0.732031	+	0.681271i	$0.761428\pi$
$884$	−1.29985e6	−	914340.i	−0.0559450	−	0.0393529i
$885$	720623.	−	2.77692e6i	0.0309278	−	0.119180i
$886$	1.09354e7	−	1.30039e7i	0.468006	−	0.556529i
$887$		−	3.90345e7i		−	1.66586i	−0.553375	−	0.832932i	$-0.686661\pi$
$887$		−	3.90345e7i		−	1.66586i	0.553375	−	0.832932i	$-0.313339\pi$
$888$	2.60740e6	+	2.58319e6i	0.110962	+	0.109932i
$889$			8.04576e6i			0.341439i
$890$	3.52976e6	+	2.96830e6i	0.149372	+	0.125613i
$891$	9.95397e6	−	4.24709e7i	0.420051	−	1.79224i
$892$	5.65867e6	+	3.25011e7i	0.238123	+	1.36769i
$893$	−3.72057e6	−	3.72057e6i	−0.156128	−	0.156128i
$894$	2.87646e7	−	2.04349e7i	1.20369	−	0.855123i
$895$		−	42431.7i		−	0.00177065i
$896$	6.21324e6	+	9.01736e6i	0.258552	+	0.375240i
$897$	−6.80638e6	+	4.00165e6i	−0.282446	+	0.166057i
$898$	1.61093e7	−	1.39190e6i	0.666630	−	0.0575992i
$899$	9.87782e6	−	9.87782e6i	0.407626	−	0.407626i
$900$	−7.69288e6	+	2.20678e7i	−0.316580	+	0.908142i
$901$	−2.41752e6	−	2.41752e6i	−0.0992105	−	0.0992105i
$902$	−2.29559e7	+	2.72980e7i	−0.939460	+	1.11716i
$903$	7.03509e6	+	1.19659e7i	0.287111	+	0.488345i
$904$	−3.63160e7	+	9.60520e6i	−1.47801	+	0.390918i
$905$	−6.12901e6			−0.248753
$906$	−2.79757e7	−	4.73641e6i	−1.13230	−	0.191703i
$907$	−8.75411e6	+	8.75411e6i	−0.353341	+	0.353341i	−0.861351	−	0.508010i	$-0.830381\pi$
$907$	−8.75411e6	+	8.75411e6i	−0.353341	+	0.353341i	0.508010	+	0.861351i	$0.330381\pi$
$908$	−8.02622e6	+	1.14102e7i	−0.323070	+	0.459283i
$909$	−1.67412e7	+	4.77037e6i	−0.672013	+	0.191488i
$910$	524213.	−	45293.9i	0.0209848	−	0.00181316i
$911$	1.80200e7			0.719379			0.359690	−	0.933072i	$-0.382883\pi$
$911$	1.80200e7			0.719379			0.359690	+	0.933072i	$0.382883\pi$
$912$	−3.29766e6	+	3.95876e6i	−0.131286	+	0.157606i
$913$	−3.96022e7			−1.57233
$914$	1.10758e6	−	95698.7i	0.0438539	−	0.00378914i
$915$	5.95852e6	+	1.54626e6i	0.235280	+	0.0610562i
$916$	−5.10913e6	−	3.59387e6i	−0.201191	−	0.141522i
$917$	1.24129e7	−	1.24129e7i	0.487474	−	0.487474i
$918$	4.62140e6	−	5.76751e6i	0.180995	−	0.225882i
$919$	−1.28497e7			−0.501885			−0.250942	−	0.968002i	$-0.580740\pi$
$919$	−1.28497e7			−0.501885			−0.250942	+	0.968002i	$0.580740\pi$
$920$	3.50072e6	−	6.01843e6i	0.136360	−	0.234430i
$921$	−3.84861e7	+	2.26270e7i	−1.49505	+	0.878978i
$922$	−1.74829e7	+	2.07898e7i	−0.677307	+	0.805420i
$923$	−7.09991e6	−	7.09991e6i	−0.274314	−	0.274314i
$924$	−1.65962e7	+	1.40890e7i	−0.639482	+	0.542877i
$925$	2.76421e6	−	2.76421e6i	0.106223	−	0.106223i
$926$	−1.34366e7	+	1.16097e6i	−0.514947	+	0.0444933i
$927$	4.32753e7	+	2.40820e7i	1.65402	+	0.920435i
$928$	3.52615e6	−	9.52807e6i	0.134410	−	0.363191i
$929$			7.33000e6i			0.278654i	0.990246	+	0.139327i	$0.0444939\pi$
$929$			7.33000e6i			0.278654i	−0.990246	+	0.139327i	$0.955506\pi$
$930$	−4.44773e6	−	6.26071e6i	−0.168628	−	0.237365i
$931$	3.03941e6	+	3.03941e6i	0.114925	+	0.114925i
$932$	3.30610e7	−	5.75615e6i	1.24674	−	0.217066i
$933$	6.69381e6	+	1.73707e6i	0.251750	+	0.0653302i
$934$	1.61906e7	+	1.36153e7i	0.607289	+	0.510691i
$935$			2.78602e6i			0.104221i
$936$	3.23557e6	+	5.44506e6i	0.120715	+	0.203148i
$937$			1.20728e7i			0.449219i	0.974449	+	0.224609i	$0.0721106\pi$
$937$			1.20728e7i			0.449219i	−0.974449	+	0.224609i	$0.927889\pi$
$938$	1.01708e7	−	1.20947e7i	0.377441	−	0.448835i
$939$	−2.05593e7	−	5.33523e6i	−0.760929	−	0.197464i
$940$	3.28168e6	−	4.66530e6i	0.121137	−	0.172211i
$941$	2.54751e7	+	2.54751e7i	0.937869	+	0.937869i	0.998180	−	0.0603102i	$-0.0192090\pi$
$941$	2.54751e7	+	2.54751e7i	0.937869	+	0.937869i	−0.0603102	+	0.998180i	$0.519209\pi$
$942$	2.28469e7	−	1.62309e7i	0.838881	−	0.595957i
$943$			3.00227e7i			1.09944i
$944$	−1.55888e7	−	7.35112e6i	−0.569356	−	0.268487i
$945$	57955.3	+	2.44624e6i	0.00211112	+	0.0891087i
$946$	−5.42222e6	−	6.27546e7i	−0.196992	−	2.27991i
$947$	−1.15688e7	+	1.15688e7i	−0.419191	+	0.419191i	−0.884925	−	0.465734i	$-0.845791\pi$
$947$	−1.15688e7	+	1.15688e7i	−0.419191	+	0.419191i	0.465734	+	0.884925i	$0.345791\pi$
$948$	4.41806e7	+	3.60981e6i	1.59665	+	0.130456i
$949$	1.30663e6	+	1.30663e6i	0.0470962	+	0.0470962i
$950$	4.19994e6	+	3.53188e6i	0.150985	+	0.126969i
$951$	−2.54765e7	+	1.49783e7i	−0.913458	+	0.537046i
$952$	−3.56579e6	+	943113.i	−0.127516	+	0.0337265i
$953$	8.23821e6			0.293833			0.146916	−	0.989149i	$-0.453065\pi$
$953$	8.23821e6			0.293833			0.146916	+	0.989149i	$0.453065\pi$
$954$	4.84826e6	+	1.27343e7i	0.172471	+	0.453006i
$955$	−4.94976e6	+	4.94976e6i	−0.175621	+	0.175621i
$956$	1.52098e7	−	2.64813e6i	0.538242	−	0.0937117i
$957$	1.95499e7	+	5.07328e6i	0.690024	+	0.179064i
$958$	1.42862e6	+	1.65343e7i	0.0502924	+	0.582064i
$959$	5.31259e6			0.186535
$960$	−4.84104e6	−	2.78573e6i	−0.169536	−	0.0975575i
$961$	−3.48085e7			−1.21584
$962$	−91202.5	−	1.05554e6i	−0.00317738	−	0.0367737i
$963$	332411.	+	1.16657e6i	0.0115508	+	0.0405364i
$964$	8.69730e6	−	1.51426e6i	0.301434	−	0.0524817i
$965$	−1.50487e6	+	1.50487e6i	−0.0520213	+	0.0520213i
$966$	−3.05893e6	+	1.80676e7i	−0.105470	+	0.622957i
$967$	−162652.			−0.00559362			−0.00279681	−	0.999996i	$-0.500890\pi$
$967$	−162652.			−0.00559362			−0.00279681	+	0.999996i	$0.500890\pi$
$968$	6.73201e7	−	1.78055e7i	2.30917	−	0.610752i
$969$	−879539.	−	1.49600e6i	−0.0300916	−	0.0511827i
$970$	1.79037e6	+	1.50559e6i	0.0610962	+	0.0513780i
$971$	−96290.7	−	96290.7i	−0.00327745	−	0.00327745i	0.705466	−	0.708744i	$-0.250738\pi$
$971$	−96290.7	−	96290.7i	−0.00327745	−	0.00327745i	−0.708744	+	0.705466i	$0.750738\pi$
$972$	−2.62126e7	+	1.34359e7i	−0.889906	+	0.456144i
$973$	−8.46877e6	+	8.46877e6i	−0.286773	+	0.286773i
$974$	−2.98319e6	−	3.45263e7i	−0.100759	−	1.16614i
$975$	5.81540e6	−	3.41903e6i	0.195915	−	0.115184i
$976$	1.57735e7	−	3.34494e7i	0.530034	−	1.12399i
$977$		−	3.92097e6i		−	0.131419i	−0.997839	−	0.0657093i	$-0.979069\pi$
$977$		−	3.92097e6i		−	0.131419i	0.997839	−	0.0657093i	$-0.0209310\pi$
$978$	−1.43687e7	−	2.02257e7i	−0.480363	−	0.676169i
$979$	3.89482e7	+	3.89482e7i	1.29877	+	1.29877i
$980$	−2.68087e6	+	3.81118e6i	−0.0891682	+	0.126763i
$981$	9.56265e6	−	2.72486e6i	0.317253	−	0.0904006i
$982$	1.76965e7	−	2.10438e7i	0.585610	−	0.696378i
$983$		−	9.05571e6i		−	0.298909i	−0.988769	−	0.149454i	$-0.952248\pi$
$983$		−	9.05571e6i		−	0.298909i	0.988769	−	0.149454i	$-0.0477517\pi$
$984$	2.40840e7	−	112350.i	0.792941	−	0.00369901i
$985$		−	3.17980e6i		−	0.104426i
$986$	2.61900e6	+	2.20242e6i	0.0857914	+	0.0721451i
$987$	−3.77083e6	+	1.45309e7i	−0.123209	+	0.474788i
$988$	1.46521e6	−	255104.i	0.0477538	−	0.00831427i
$989$	−3.74908e7	−	3.74908e7i	−1.21880	−	1.21880i
$990$	4.54405e6	−	1.01313e7i	0.147352	−	0.328533i
$991$			2.01548e7i			0.651920i	0.945384	+	0.325960i	$0.105687\pi$
$991$			2.01548e7i			0.651920i	−0.945384	+	0.325960i	$0.894313\pi$
$992$	−4.19186e7	+	1.92729e7i	−1.35247	+	0.621823i
$993$	−1.61343e7	−	2.74427e7i	−0.519250	−	0.883189i
$994$	−2.32171e7	+	2.00604e6i	−0.745317	+	0.0643981i
$995$	−6.01764e6	+	6.01764e6i	−0.192694	+	0.192694i
$996$	1.73063e7	+	2.03860e7i	0.552785	+	0.651153i
$997$	−2.25108e7	−	2.25108e7i	−0.717222	−	0.717222i	0.250813	−	0.968035i	$-0.419302\pi$
$997$	−2.25108e7	−	2.25108e7i	−0.717222	−	0.717222i	−0.968035	+	0.250813i	$0.919302\pi$
$998$	−3.22932e7	+	3.84015e7i	−1.02632	+	1.22045i
$999$	4.92568e6	−	116697.i	0.156154	−	0.00369953i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	48.6.k.a.11.20	yes	76
3.2	odd	2	inner	48.6.k.a.11.19	✓	76
4.3	odd	2		192.6.k.a.143.16		76
12.11	even	2		192.6.k.a.143.35		76
16.3	odd	4	inner	48.6.k.a.35.19	yes	76
16.13	even	4		192.6.k.a.47.35		76
48.29	odd	4		192.6.k.a.47.16		76
48.35	even	4	inner	48.6.k.a.35.20	yes	76

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
48.6.k.a.11.19	✓	76	3.2	odd	2	inner
48.6.k.a.11.20	yes	76	1.1	even	1	trivial
48.6.k.a.35.19	yes	76	16.3	odd	4	inner
48.6.k.a.35.20	yes	76	48.35	even	4	inner
192.6.k.a.47.16		76	48.29	odd	4
192.6.k.a.47.35		76	16.13	even	4
192.6.k.a.143.16		76	4.3	odd	2
192.6.k.a.143.35		76	12.11	even	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 48 = 2^{4} \cdot 3 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	48.k (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.486958 + 5.63586i) q^{2} +(3.91558 - 15.0887i) q^{3} +(-31.5257 + 5.48885i) q^{4} +(-7.73181 + 7.73181i) q^{5} +(86.9443 + 14.7201i) q^{6} -59.0766 q^{7} +(-46.2861 - 175.002i) q^{8} +(-212.337 - 118.162i) q^{9} +O(q^{10})\)	\(q+(0.486958 + 5.63586i) q^{2} +(3.91558 - 15.0887i) q^{3} +(-31.5257 + 5.48885i) q^{4} +(-7.73181 + 7.73181i) q^{5} +(86.9443 + 14.7201i) q^{6} -59.0766 q^{7} +(-46.2861 - 175.002i) q^{8} +(-212.337 - 118.162i) q^{9} +(-47.3405 - 39.8103i) q^{10} +(-522.367 - 522.367i) q^{11} +(-40.6220 + 497.174i) q^{12} +(101.817 - 101.817i) q^{13} +(-28.7678 - 332.947i) q^{14} +(86.3884 + 146.937i) q^{15} +(963.745 - 346.080i) q^{16} +344.903i q^{17} +(562.544 - 1254.24i) q^{18} +(-228.236 - 228.236i) q^{19} +(201.312 - 286.190i) q^{20} +(-231.319 + 891.388i) q^{21} +(2689.61 - 3198.35i) q^{22} -3517.58i q^{23} +(-2821.78 + 13.1634i) q^{24} +3005.44i q^{25} +(623.408 + 524.246i) q^{26} +(-2614.33 + 2741.21i) q^{27} +(1862.43 - 324.263i) q^{28} +(-1240.19 - 1240.19i) q^{29} +(-786.050 + 558.425i) q^{30} +7964.77i q^{31} +(2419.76 + 5263.00i) q^{32} +(-9927.19 + 5836.46i) q^{33} +(-1943.83 + 167.954i) q^{34} +(456.769 - 456.769i) q^{35} +(7342.64 + 2559.65i) q^{36} +(-919.737 - 919.737i) q^{37} +(1175.16 - 1397.45i) q^{38} +(-1137.61 - 1934.96i) q^{39} +(1710.96 + 995.205i) q^{40} -8535.03 q^{41} +(-5136.38 - 869.612i) q^{42} +(10658.1 - 10658.1i) q^{43} +(19335.2 + 13600.8i) q^{44} +(2555.35 - 728.142i) q^{45} +(19824.6 - 1712.91i) q^{46} +16301.4 q^{47} +(-1448.28 - 15896.7i) q^{48} -13317.0 q^{49} +(-16938.2 + 1463.52i) q^{50} +(5204.14 + 1350.50i) q^{51} +(-2651.00 + 3768.72i) q^{52} +(-7009.26 + 7009.26i) q^{53} +(-16722.1 - 13399.1i) q^{54} +8077.68 q^{55} +(2734.43 + 10338.5i) q^{56} +(-4337.45 + 2550.10i) q^{57} +(6385.60 - 7593.44i) q^{58} +(-11901.5 - 11901.5i) q^{59} +(-3529.97 - 4158.14i) q^{60} +(25537.3 - 25537.3i) q^{61} +(-44888.3 + 3878.51i) q^{62} +(12544.1 + 6980.60i) q^{63} +(-28483.2 + 16200.3i) q^{64} +1574.46i q^{65} +(-37727.5 - 53106.1i) q^{66} +(33437.0 + 33437.0i) q^{67} +(-1893.12 - 10873.3i) q^{68} +(-53075.7 - 13773.4i) q^{69} +(2796.71 + 2351.86i) q^{70} -69731.9i q^{71} +(-10850.3 + 42628.5i) q^{72} +12833.1i q^{73} +(4735.63 - 5631.38i) q^{74} +(45348.1 + 11768.0i) q^{75} +(8448.06 + 5942.55i) q^{76} +(30859.6 + 30859.6i) q^{77} +(10351.2 - 7353.67i) q^{78} -88863.5i q^{79} +(-4775.67 + 10127.3i) q^{80} +(31124.6 + 50180.1i) q^{81} +(-4156.20 - 48102.2i) q^{82} +(37906.5 - 37906.5i) q^{83} +(2399.81 - 29371.3i) q^{84} +(-2666.73 - 2666.73i) q^{85} +(65257.6 + 54877.5i) q^{86} +(-23568.9 + 13856.8i) q^{87} +(-67236.7 + 115593. i) q^{88} -74561.1 q^{89} +(5348.05 + 14047.0i) q^{90} +(-6015.02 + 6015.02i) q^{91} +(19307.5 + 110894. i) q^{92} +(120178. + 31186.7i) q^{93} +(7938.11 + 91872.5i) q^{94} +3529.36 q^{95} +(88886.5 - 15903.3i) q^{96} -37819.1 q^{97} +(-6484.80 - 75052.4i) q^{98} +(49193.7 + 172641. i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 76 q - 2 q^{3} - 4 q^{4} - 116 q^{6} - 8 q^{7}+O(q^{10}) \) 76 * q - 2 * q^3 - 4 * q^4 - 116 * q^6 - 8 * q^7	\( 76 q - 2 q^{3} - 4 q^{4} - 116 q^{6} - 8 q^{7} - 104 q^{10} + 784 q^{12} - 4 q^{13} + 4560 q^{16} - 4076 q^{18} + 2356 q^{19} - 488 q^{21} + 2232 q^{22} + 2568 q^{24} - 3734 q^{27} - 12392 q^{28} + 628 q^{30} - 4 q^{33} + 26248 q^{34} - 30748 q^{36} - 4 q^{37} - 44908 q^{39} + 440 q^{40} + 11256 q^{42} + 652 q^{43} - 6252 q^{45} + 31320 q^{46} - 9168 q^{48} + 124844 q^{49} + 8664 q^{51} - 48448 q^{52} - 19480 q^{54} - 110056 q^{55} + 76088 q^{58} - 85408 q^{60} + 48076 q^{61} - 11080 q^{64} + 91492 q^{66} + 48924 q^{67} + 484 q^{69} + 86200 q^{70} - 16376 q^{72} - 69634 q^{75} + 30920 q^{76} + 13020 q^{78} - 4 q^{81} - 200768 q^{82} + 111760 q^{84} - 119904 q^{85} + 282180 q^{87} - 123616 q^{88} - 17680 q^{90} - 167288 q^{91} + 181660 q^{93} - 13200 q^{94} - 61688 q^{96} - 8 q^{97} - 287860 q^{99}+O(q^{100}) \) 76 * q - 2 * q^3 - 4 * q^4 - 116 * q^6 - 8 * q^7 - 104 * q^10 + 784 * q^12 - 4 * q^13 + 4560 * q^16 - 4076 * q^18 + 2356 * q^19 - 488 * q^21 + 2232 * q^22 + 2568 * q^24 - 3734 * q^27 - 12392 * q^28 + 628 * q^30 - 4 * q^33 + 26248 * q^34 - 30748 * q^36 - 4 * q^37 - 44908 * q^39 + 440 * q^40 + 11256 * q^42 + 652 * q^43 - 6252 * q^45 + 31320 * q^46 - 9168 * q^48 + 124844 * q^49 + 8664 * q^51 - 48448 * q^52 - 19480 * q^54 - 110056 * q^55 + 76088 * q^58 - 85408 * q^60 + 48076 * q^61 - 11080 * q^64 + 91492 * q^66 + 48924 * q^67 + 484 * q^69 + 86200 * q^70 - 16376 * q^72 - 69634 * q^75 + 30920 * q^76 + 13020 * q^78 - 4 * q^81 - 200768 * q^82 + 111760 * q^84 - 119904 * q^85 + 282180 * q^87 - 123616 * q^88 - 17680 * q^90 - 167288 * q^91 + 181660 * q^93 - 13200 * q^94 - 61688 * q^96 - 8 * q^97 - 287860 * q^99

Introduction

L-functions

Modular forms

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