LMFDB - Embedded newform 48.6.k.a.11.19

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			11.19
Character	$\chi$	$=$	48.11
Dual form			48.6.k.a.35.19

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.486958 - 5.63586i) q^{2} +(-15.0887 + 3.91558i) q^{3} +(-31.5257 + 5.48885i) q^{4} +(7.73181 - 7.73181i) q^{5} +(29.4152 + 83.1309i) q^{6} -59.0766 q^{7} +(46.2861 + 175.002i) q^{8} +(212.337 - 118.162i) q^{9} +O(q^{10})$	\(q+(-0.486958 - 5.63586i) q^{2} +(-15.0887 + 3.91558i) q^{3} +(-31.5257 + 5.48885i) q^{4} +(7.73181 - 7.73181i) q^{5} +(29.4152 + 83.1309i) 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} +(454.190 - 206.261i) 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} +(-769.342 - 1139.16i) q^{18} +(-228.236 - 228.236i) q^{19} +(-201.312 + 286.190i) q^{20} +(891.388 - 231.319i) q^{21} +(2689.61 - 3198.35i) q^{22} +3517.58i q^{23} +(-1383.63 - 2459.31i) q^{24} +3005.44i q^{25} +(-623.408 - 524.246i) q^{26} +(-2741.21 + 2614.33i) q^{27} +(1862.43 - 324.263i) q^{28} +(1240.19 + 1240.19i) q^{29} +(870.185 + 415.320i) 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} +(-6045.49 + 4890.62i) 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} +(-1737.75 - 4911.09i) q^{42} +(10658.1 - 10658.1i) q^{43} +(-19335.2 - 13600.8i) q^{44} +(728.142 - 2555.35i) q^{45} +(19824.6 - 1712.91i) q^{46} -16301.4 q^{47} +(-13186.5 + 8995.51i) q^{48} -13317.0 q^{49} +(16938.2 - 1463.52i) q^{50} +(1350.50 + 5204.14i) q^{51} +(-2651.00 + 3768.72i) q^{52} +(7009.26 - 7009.26i) q^{53} +(16068.8 + 14176.0i) 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} +(1916.94 - 5106.48i) 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} +(-28059.3 + 58790.3i) q^{66} +(33437.0 + 33437.0i) q^{67} +(1893.12 + 10873.3i) q^{68} +(-13773.4 - 53075.7i) q^{69} +(2796.71 + 2351.86i) q^{70} +69731.9i q^{71} +(30506.7 + 31690.0i) q^{72} +12833.1i q^{73} +(-4735.63 + 5631.38i) q^{74} +(-11768.0 - 45348.1i) q^{75} +(8448.06 + 5942.55i) q^{76} +(-30859.6 - 30859.6i) q^{77} +(11459.1 + 5469.19i) 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} +(-26832.0 + 12185.2i) 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} +(-14756.2 - 2859.35i) q^{90} +(-6015.02 + 6015.02i) q^{91} +(-19307.5 - 110894. i) q^{92} +(-31186.7 - 120178. i) q^{93} +(7938.11 + 91872.5i) q^{94} -3529.36 q^{95} +(57118.7 + 69937.0i) q^{96} -37819.1 q^{97} +(6484.80 + 75052.4i) q^{98} +(172641. + 49193.7i) 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
$3$	−15.0887	+	3.91558i	−0.967939	+	0.251184i
$3$	−15.0887	+	3.91558i	−0.967939	+	0.251184i
$4$	−31.5257	+	5.48885i	−0.985179	+	0.171527i
$5$	7.73181	−	7.73181i	0.138311	−	0.138311i	−0.634561	−	0.772872i	$-0.718819\pi$
$5$	7.73181	−	7.73181i	0.138311	−	0.138311i	0.772872	+	0.634561i	$0.218819\pi$
$6$	29.4152	+	83.1309i	0.333575	+	0.942724i
$7$	−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	$0.122140\pi$
$11$	522.367	+	522.367i	1.30165	+	1.30165i	0.374368	+	0.927280i	$0.377860\pi$
$12$	454.190	−	206.261i	0.910509	−	0.413489i
$13$	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	$-0.953770\pi$
$17$		−	344.903i		−	0.289451i	0.989472	−	0.144726i	$-0.0462299\pi$
$18$	−769.342	−	1139.16i	−0.559678	−	0.828710i
$19$	−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
$21$	891.388	−	231.319i	0.441081	−	0.114462i
$22$	2689.61	−	3198.35i	1.18477	−	1.40887i
$23$			3517.58i			1.38651i	0.720690	+	0.693257i	$0.243825\pi$
$23$			3517.58i			1.38651i	−0.720690	+	0.693257i	$0.756175\pi$
$24$	−1383.63	−	2459.31i	−0.490333	−	0.871535i
$25$			3005.44i			0.961740i
$26$	−623.408	−	524.246i	−0.180858	−	0.152091i
$27$	−2741.21	+	2614.33i	−0.723656	+	0.690161i
$28$	1862.43	−	324.263i	0.448937	−	0.0781631i
$29$	1240.19	+	1240.19i	0.273837	+	0.273837i	0.830643	−	0.556806i	$-0.187973\pi$
$29$	1240.19	+	1240.19i	0.273837	+	0.273837i	−0.556806	+	0.830643i	$0.687973\pi$
$30$	870.185	+	415.320i	0.176526	+	0.0842519i
$31$			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
$36$	−6045.49	+	4890.62i	−0.777455	+	0.628938i
$37$	−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	$-0.370233\pi$
$41$	8535.03			0.792949			0.396475	+	0.918046i	$0.370233\pi$
$42$	−1737.75	−	4911.09i	−0.152007	−	0.429591i
$43$	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
$45$	728.142	−	2555.35i	0.0536024	−	0.188113i
$46$	19824.6	−	1712.91i	1.38137	−	0.119355i
$47$	−16301.4			−1.07642			−0.538209	−	0.842812i	$-0.680899\pi$
$47$	−16301.4			−1.07642			−0.538209	+	0.842812i	$0.680899\pi$
$48$	−13186.5	+	8995.51i	−0.826091	+	0.563537i
$49$	−13317.0			−0.792346
$50$	16938.2	−	1463.52i	0.958170	−	0.0827893i
$51$	1350.50	+	5204.14i	0.0727056	+	0.280171i
$52$	−2651.00	+	3768.72i	−0.135957	+	0.193280i
$53$	7009.26	−	7009.26i	0.342754	−	0.342754i	−0.514648	−	0.857402i	$-0.672077\pi$
$53$	7009.26	−	7009.26i	0.342754	−	0.342754i	0.857402	+	0.514648i	$0.172077\pi$
$54$	16068.8	+	14176.0i	0.749893	+	0.661559i
$55$	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	0.893726	−	0.448613i	$-0.148082\pi$
$59$	11901.5	+	11901.5i	0.445113	+	0.445113i	−0.448613	+	0.893726i	$0.648082\pi$
$60$	1916.94	−	5106.48i	0.0687433	−	0.183123i
$61$	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
$66$	−28059.3	+	58790.3i	−0.792897	+	1.66129i
$67$	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
$69$	−13773.4	−	53075.7i	−0.348271	−	1.34206i
$70$	2796.71	+	2351.86i	0.0682186	+	0.0573675i
$71$			69731.9i			1.64167i	0.571165	+	0.820835i	$0.306492\pi$
$71$			69731.9i			1.64167i	−0.571165	+	0.820835i	$0.693508\pi$
$72$	30506.7	+	31690.0i	0.693529	+	0.720429i
$73$			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
$75$	−11768.0	−	45348.1i	−0.241574	−	0.930906i
$76$	8448.06	+	5942.55i	0.167773	+	0.118016i
$77$	−30859.6	−	30859.6i	−0.593149	−	0.593149i
$78$	11459.1	+	5469.19i	0.213263	+	0.101786i
$79$		−	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	−0.941365	−	0.337390i	$-0.890456\pi$
$83$	−37906.5	+	37906.5i	−0.603975	+	0.603975i	0.337390	+	0.941365i	$0.390456\pi$
$84$	−26832.0	+	12185.2i	−0.414911	+	0.188423i
$85$	−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	$-0.333740\pi$
$89$	74561.1			0.997786			0.498893	+	0.866664i	$0.333740\pi$
$90$	−14756.2	−	2859.35i	−0.192029	−	0.0372101i
$91$	−6015.02	+	6015.02i	−0.0761436	+	0.0761436i
$92$	−19307.5	−	110894.i	−0.237824	−	1.36597i
$93$	−31186.7	−	120178.i	−0.373906	−	1.44085i
$94$	7938.11	+	91872.5i	0.0926611	+	1.07242i
$95$	−3529.36			−0.0401224
$96$	57118.7	+	69937.0i	0.632558	+	0.774513i
$97$	−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
$99$	172641.	+	49193.7i	1.77034	+	0.504454i
$100$	−16496.4	−	94748.7i	−0.164964	−	0.947487i
$101$	−50654.5	+	50654.5i	−0.494100	+	0.494100i	−0.909595	−	0.415496i	$-0.863608\pi$
$101$	−50654.5	+	50654.5i	−0.494100	+	0.494100i	0.415496	+	0.909595i	$0.363608\pi$
$102$	28672.1	−	10145.4i	0.272872	−	0.0965536i
$103$	−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	0.721852	−	0.692047i	$-0.243291\pi$
$107$	3529.73	+	3529.73i	0.0298045	+	0.0298045i	−0.692047	+	0.721852i	$0.743291\pi$
$108$	72068.9	−	97464.6i	0.594550	−	0.804058i
$109$	−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	$0.276973\pi$
$113$			207518.i			1.52883i	−0.644723	+	0.764416i	$0.723027\pi$
$114$	12259.9	−	25687.1i	0.0883534	−	0.185120i
$115$	27197.3	+	27197.3i	0.191770	+	0.191770i
$116$	−45905.1	−	32290.6i	−0.316749	−	0.222809i
$117$	9588.61	−	33650.4i	0.0647576	−	0.227261i
$118$	61279.5	−	72870.5i	0.405145	−	0.481778i
$119$			20375.7i			0.131900i
$120$	−29712.9	−	8316.95i	−0.188361	−	0.0527243i
$121$			384683.i			2.38858i
$122$	−156360.	−	131489.i	−0.951102	−	0.799816i
$123$	−128782.	+	33419.6i	−0.767527	+	0.199176i
$124$	−43717.5	−	251095.i	−0.255329	−	1.46651i
$125$	47399.4	+	47399.4i	0.271330	+	0.271330i
$126$	45450.1	+	67297.6i	0.255040	+	0.377636i
$127$		−	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	$-0.476944\pi$
$131$	210116.	−	210116.i	1.06975	−	1.06975i	0.997378	−	0.0723679i	$-0.0230556\pi$
$132$	344997.	+	129510.i	1.72338	+	0.646945i
$133$	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	$-0.434387\pi$
$137$	89927.1			0.409345			0.204672	+	0.978831i	$0.434387\pi$
$138$	−292420.	+	103470.i	−1.30710	+	0.462507i
$139$	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
$141$	245967.	−	63829.5i	1.04191	−	0.270379i
$142$	392999.	−	33956.5i	1.63558	−	0.141320i
$143$	106372.			0.434997
$144$	163745.	−	187363.i	0.658054	−	0.752971i
$145$	19177.8			0.0757494
$146$	72325.3	−	6249.17i	0.280807	−	0.0242628i
$147$	200935.	−	52143.6i	0.766942	−	0.199025i
$148$	34043.7	+	23947.1i	0.127756	+	0.0898667i
$149$	−282937.	+	282937.i	−1.04406	+	1.04406i	−0.0450722	+	0.998984i	$0.514352\pi$
$149$	−282937.	+	282937.i	−1.04406	+	1.04406i	−0.998984	+	0.0450722i	$0.985648\pi$
$150$	−249845.	+	88405.5i	−0.906655	+	0.320812i
$151$	−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
$156$	25243.4	−	67245.3i	0.0830494	−	0.221233i
$157$	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
$162$	−297964.	−	150978.i	−0.892024	−	0.451987i
$163$	−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
$165$	−121882.	+	31628.8i	−0.348520	+	0.0904425i
$166$	232095.	+	195177.i	0.653725	+	0.549741i
$167$		−	395731.i		−	1.09802i	−0.835817	−	0.549009i	$-0.815005\pi$
$167$		−	395731.i		−	1.09802i	0.835817	−	0.549009i	$-0.184995\pi$
$168$	81740.1	+	145288.i	0.223441	+	0.397151i
$169$			350560.i			0.944159i
$170$	−13730.7	+	16327.9i	−0.0364394	+	0.0433319i
$171$	−75431.6	−	21494.1i	−0.197271	−	0.0562119i
$172$	−277504.	+	394505.i	−0.715234	+	1.01679i
$173$	−316976.	−	316976.i	−0.805213	−	0.805213i	0.178692	−	0.983905i	$-0.442813\pi$
$173$	−316976.	−	316976.i	−0.805213	−	0.805213i	−0.983905	+	0.178692i	$0.942813\pi$
$174$	−66617.6	+	139578.i	−0.166808	+	0.349498i
$175$		−	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	−0.703899	−	0.710300i	$-0.748559\pi$
$179$	2743.97	−	2743.97i	0.00640098	−	0.00640098i	0.710300	+	0.703899i	$0.248559\pi$
$180$	−8929.26	+	84556.0i	−0.0205416	+	0.194520i
$181$	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
$186$	−662119.	+	234285.i	−1.40331	+	0.496550i
$187$	180166.	−	180166.i	0.376763	−	0.376763i
$188$	513914.	−	89476.1i	1.06046	−	0.184634i
$189$	161941.	−	154445.i	0.329764	−	0.314500i
$190$	1718.65	+	19890.9i	0.00345385	+	0.0399734i
$191$	−640181.			−1.26975			−0.634877	−	0.772613i	$-0.718949\pi$
$191$	−640181.			−1.26975			−0.634877	+	0.772613i	$0.718949\pi$
$192$	366340.	−	355969.i	0.717186	−	0.696882i
$193$	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
$195$	6164.93	+	23756.6i	0.0116103	+	0.0447401i
$196$	419827.	−	73094.8i	0.780603	−	0.135908i
$197$	205631.	−	205631.i	0.377506	−	0.377506i	−0.492696	−	0.870202i	$-0.663988\pi$
$197$	205631.	−	205631.i	0.377506	−	0.377506i	0.870202	+	0.492696i	$0.163988\pi$
$198$	193180.	−	996937.i	0.350186	−	1.80719i
$199$	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
$204$	−71140.1	−	156652.i	−0.119685	−	0.263548i
$205$	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
$210$	−51407.6	−	24535.7i	−0.0804413	−	0.0383928i
$211$	−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
$213$	−273041.	−	1.05216e6i	−0.412362	−	1.58904i
$214$	18174.2	−	21611.9i	0.0271282	−	0.0322595i
$215$		−	164813.i		−	0.243162i
$216$	−584391.	−	358709.i	−0.852254	−	0.523128i
$217$		−	470532.i		−	0.678328i
$218$	177158.	+	148978.i	0.252475	+	0.212316i
$219$	−50248.9	−	193634.i	−0.0707972	−	0.272817i
$220$	−254655.	+	44337.2i	−0.354728	+	0.0617606i
$221$	−35117.1	−	35117.1i	−0.0483658	−	0.0483658i
$222$	49404.4	−	103513.i	0.0672795	−	0.140965i
$223$		−	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	−0.877195	−	0.480134i	$-0.840588\pi$
$227$	−308263.	+	308263.i	−0.397061	+	0.397061i	0.480134	+	0.877195i	$0.340588\pi$
$228$	−150739.	−	56586.3i	−0.192038	−	0.0720898i
$229$	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	$-0.281927\pi$
$233$	1.04870e6			1.26550			0.632749	+	0.774357i	$0.281927\pi$
$234$	−194318.	−	37653.7i	−0.231992	−	0.0449539i
$235$	−126040.	+	126040.i	−0.148880	+	0.148880i
$236$	−440528.	−	309877.i	−0.514865	−	0.362168i
$237$	347952.	+	1.34083e6i	0.402391	+	1.55061i
$238$	114835.	−	9922.12i	0.131411	−	0.0113544i
$239$	482455.			0.546339			0.273170	−	0.961966i	$-0.411928\pi$
$239$	482455.			0.546339			0.273170	+	0.961966i	$0.411928\pi$
$240$	−32404.2	+	171507.i	−0.0363139	+	0.192201i
$241$	−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
$243$	−273145.	+	879022.i	−0.296741	+	0.954958i
$244$	−664913.	+	945254.i	−0.714974	+	1.01642i
$245$	−102964.	+	102964.i	−0.109590	+	0.109590i
$246$	251059.	+	709525.i	0.264508	+	0.747532i
$247$	−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	0.981777	−	0.190037i	$-0.0608607\pi$
$251$	790255.	+	790255.i	0.791740	+	0.791740i	−0.190037	+	0.981777i	$0.560861\pi$
$252$	357147.	−	288921.i	0.354280	−	0.286601i
$253$	−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	$-0.802019\pi$
$257$		−	1.23386e6i		−	1.16528i	0.812729	−	0.582642i	$-0.197981\pi$
$258$	1.19953e6	+	572508.i	1.12192	+	0.535466i
$259$	54335.0	+	54335.0i	0.0503304	+	0.0503304i
$260$	8642.00	+	49636.1i	0.00792831	+	0.0455370i
$261$	409880.	+	116794.i	0.372439	+	0.106126i
$262$	−1.28650e6	−	1.08187e6i	−1.15786	−	0.973688i
$263$		−	1.58117e6i		−	1.40958i	−0.709417	−	0.704789i	$-0.751042\pi$
$263$		−	1.58117e6i		−	1.40958i	0.709417	−	0.704789i	$-0.248958\pi$
$264$	561899.	−	2.00742e6i	0.496190	−	1.77267i
$265$		−	108389.i		−	0.0948132i
$266$	69424.7	−	82556.4i	0.0601603	−	0.0715396i
$267$	−1.12503e6	+	291950.i	−0.965796	+	0.250628i
$268$	−1.23766e6	−	870594.i	−1.05260	−	0.740421i
$269$	−571637.	−	571637.i	−0.481659	−	0.481659i	0.424002	−	0.905661i	$-0.360625\pi$
$269$	−571637.	−	571637.i	−0.481659	−	0.481659i	−0.905661	+	0.424002i	$0.860625\pi$
$270$	233847.	−	14635.1i	0.195219	−	0.0122176i
$271$			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
$276$	725540.	+	1.59765e6i	0.573309	+	1.26243i
$277$	−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	$-0.520207\pi$
$281$	−167945.			−0.126882			−0.0634410	+	0.997986i	$0.520207\pi$
$282$	−479509.	−	1.35515e6i	−0.359066	−	1.01476i
$283$	−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
$285$	53253.3	−	13819.5i	0.0388360	−	0.0100781i
$286$	−51798.6	−	599496.i	−0.0374458	−	0.433383i
$287$	−504221.			−0.361340
$288$	−1.13569e6	−	831604.i	−0.806823	−	0.590793i
$289$	1.30090e6			0.916218
$290$	−9338.79	−	108083.i	−0.00652072	−	0.0754682i
$291$	570640.	−	148084.i	0.395030	−	0.102512i
$292$	−70438.8	−	404572.i	−0.0483454	−	0.277676i
$293$	769288.	−	769288.i	0.523504	−	0.523504i	−0.395124	−	0.918628i	$-0.629298\pi$
$293$	769288.	−	769288.i	0.523504	−	0.523504i	0.918628	+	0.395124i	$0.129298\pi$
$294$	−391721.	−	1.10705e6i	−0.264307	−	0.746963i
$295$	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
$300$	619905.	+	1.36504e6i	0.397669	+	0.875673i
$301$	−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
$306$	−392900.	+	265349.i	−0.239871	+	0.161999i
$307$	−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
$309$	3.07515e6	−	798015.i	1.83219	−	0.475461i
$310$	317080.	−	377056.i	0.187398	−	0.222844i
$311$		−	443631.i		−	0.260089i	−0.991508	−	0.130044i	$-0.958488\pi$
$311$		−	443631.i		−	0.260089i	0.991508	−	0.130044i	$-0.0415119\pi$
$312$	−391277.	−	109523.i	−0.227561	−	0.0636968i
$313$		−	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
$315$	−43016.1	+	150962.i	−0.0244262	+	0.0857215i
$316$	487759.	+	2.80149e6i	0.274781	+	1.57823i
$317$	1.34057e6	+	1.34057e6i	0.749274	+	0.749274i	0.974343	−	0.225069i	$-0.0722607\pi$
$317$	1.34057e6	+	1.34057e6i	0.749274	+	0.749274i	−0.225069	+	0.974343i	$0.572261\pi$
$318$	788864.	+	376507.i	0.437456	+	0.208788i
$319$			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
$324$	−705795.	+	1.75280e6i	−0.373522	+	0.927621i
$325$	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
$330$	237607.	+	671505.i	0.120108	+	0.339441i
$331$	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
$333$	−303972.	−	86616.0i	−0.150218	−	0.0428043i
$334$	−2.23028e6	+	192705.i	−1.09394	+	0.0945205i
$335$	517057.			0.251725
$336$	779016.	−	531424.i	0.376442	−	0.256799i
$337$	−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
$339$	−812553.	−	3.13117e6i	−0.384019	−	1.47982i
$340$	98707.9	+	69433.3i	0.0463078	+	0.0325740i
$341$	−4.16053e6	+	4.16053e6i	−1.93759	+	1.93759i
$342$	−84405.4	+	435588.i	−0.0390216	+	0.201377i
$343$	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	$0.0251453\pi$
$347$	2.41298e6	+	2.41298e6i	1.07580	+	1.07580i	0.0789140	+	0.996881i	$0.474855\pi$
$348$	819083.	+	307478.i	0.362560	+	0.136103i
$349$	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	$0.0819435\pi$
$353$			1.19213e6i			0.509198i	−0.967047	+	0.254599i	$0.918056\pi$
$354$	−639296.	+	1.33946e6i	−0.271140	+	0.568098i
$355$	539154.	+	539154.i	0.227061	+	0.227061i
$356$	−2.35059e6	+	409255.i	−0.982998	+	0.171147i
$357$	−79782.7	−	307443.i	−0.0331313	−	0.127671i
$358$	−16800.8	−	14128.4i	−0.00692823	−	0.00582620i
$359$		−	2.80596e6i		−	1.14907i	−0.818481	−	0.574534i	$-0.805183\pi$
$359$		−	2.80596e6i		−	1.14907i	0.818481	−	0.574534i	$-0.194817\pi$
$360$	480894.	+	9148.78i	0.195566	+	0.00372055i
$361$		−	2.37192e6i		−	0.957924i
$362$	2.04077e6	−	2.42678e6i	0.818506	−	0.973327i
$363$	−1.50625e6	−	5.80435e6i	−0.599973	−	2.31200i
$364$	156612.	−	222643.i	0.0619545	−	0.0880758i
$365$	99222.9	+	99222.9i	0.0389834	+	0.0389834i
$366$	2.87413e6	+	1.37176e6i	1.12151	+	0.535272i
$367$		−	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
$372$	1.64282e6	+	3.61752e6i	0.615507	+	1.35536i
$373$	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
$378$	−949291.	−	837469.i	−0.341720	−	0.301467i
$379$	−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
$381$	533270.	+	2.05496e6i	0.188207	+	0.725254i
$382$	311741.	+	3.60797e6i	0.109304	+	1.26504i
$383$	−449214.			−0.156479			−0.0782396	−	0.996935i	$-0.524930\pi$
$383$	−449214.			−0.156479			−0.0782396	+	0.996935i	$0.524930\pi$
$384$	−2.18458e6	−	1.89130e6i	−0.756033	−	0.654534i
$385$	−477202.			−0.164078
$386$	−94778.5	−	1.09693e6i	−0.0323774	−	0.374723i
$387$	1.00372e6	−	3.52249e6i	0.340672	−	1.19556i
$388$	1.19228e6	−	207583.i	0.402066	−	0.0700025i
$389$	−1.95846e6	+	1.95846e6i	−0.656206	+	0.656206i	−0.954480	−	0.298274i	$-0.903589\pi$
$389$	−1.95846e6	+	1.95846e6i	−0.656206	+	0.656206i	0.298274	+	0.954480i	$0.403589\pi$
$390$	130887.	−	46313.1i	0.0435746	−	0.0154185i
$391$	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
$396$	−5.71266e6	−	603267.i	−1.83063	−	0.193318i
$397$	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	$0.0343915\pi$
$401$			694459.i			0.215668i	−0.994169	+	0.107834i	$0.965609\pi$
$402$	−1.79609e6	+	3.76320e6i	−0.554323	+	1.16143i
$403$	810951.	+	810951.i	0.248732	+	0.248732i
$404$	1.31889e6	−	1.87496e6i	0.402026	−	0.571528i
$405$	−147334.	−	628633.i	−0.0446339	−	0.190441i
$406$	−377240.	+	448595.i	−0.113580	+	0.135064i
$407$		−	960880.i		−	0.287530i
$408$	−848224.	+	477218.i	−0.252267	+	0.141928i
$409$			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
$411$	−1.35688e6	+	352116.i	−0.396221	+	0.102821i
$412$	6.42511e6	−	1.11866e6i	1.86482	−	0.324679i
$413$	−703099.	−	703099.i	−0.202834	−	0.202834i
$414$	4.00708e6	−	2.70622e6i	1.14902	−	0.776002i
$415$			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	−0.301510	−	0.953463i	$-0.597491\pi$
$419$	2.34289e6	−	2.34289e6i	0.651953	−	0.651953i	0.953463	+	0.301510i	$0.0974908\pi$
$420$	−113246.	+	301674.i	−0.0313257	+	0.0834477i
$421$	−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
$426$	−5.79688e6	+	2.05118e6i	−1.54764	+	0.547620i
$427$	−1.50866e6	+	1.50866e6i	−0.400425	+	0.400425i
$428$	−130652.	−	91903.2i	−0.0344751	−	0.0242505i
$429$	−1.60501e6	+	416507.i	−0.421051	+	0.109265i
$430$	−928862.	+	80257.0i	−0.242259	+	0.0209321i
$431$	−445928.			−0.115630			−0.0578152	−	0.998327i	$-0.518413\pi$
$431$	−445928.			−0.115630			−0.0578152	+	0.998327i	$0.518413\pi$
$432$	−1.73706e6	+	3.46822e6i	−0.447821	+	0.894123i
$433$	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
$435$	−289368.	+	75092.2i	−0.0733208	+	0.0190271i
$436$	753353.	−	1.07098e6i	0.189794	−	0.269815i
$437$	802838.	−	802838.i	0.201106	−	0.201106i
$438$	−1.06682e6	+	377487.i	−0.265710	+	0.0940193i
$439$	−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	0.915803	−	0.401627i	$-0.131555\pi$
$443$	2.12384e6	+	2.12384e6i	0.514176	+	0.514176i	−0.401627	+	0.915803i	$0.631555\pi$
$444$	−607441.	−	228029.i	−0.146234	−	0.0548951i
$445$	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	$0.108587\pi$
$449$			2.85835e6i			0.669114i	−0.942376	+	0.334557i	$0.891413\pi$
$450$	3.42367e6	−	2.31221e6i	0.797004	−	0.538265i
$451$	4.45841e6	+	4.45841e6i	1.03214	+	1.03214i
$452$	−1.13904e6	−	6.54216e6i	−0.262235	−	1.50617i
$453$	4.85502e6	−	1.25990e6i	1.11159	−	0.288463i
$454$	1.88744e6	+	1.58722e6i	0.429767	+	0.361407i
$455$			93014.0i			0.0210630i
$456$	−245509.	+	877096.i	−0.0552910	+	0.197531i
$457$		−	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
$459$	901690.	+	945451.i	0.199768	+	0.209463i
$460$	−1.00670e6	−	708133.i	−0.221822	−	0.156034i
$461$	−3.39546e6	−	3.39546e6i	−0.744126	−	0.744126i	0.229243	−	0.973369i	$-0.426375\pi$
$461$	−3.39546e6	−	3.39546e6i	−0.744126	−	0.744126i	−0.973369	+	0.229243i	$0.926375\pi$
$462$	1.65765e6	−	3.47313e6i	0.361316	−	0.757036i
$463$			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	−0.929612	−	0.368539i	$-0.879858\pi$
$467$	−2.64430e6	+	2.64430e6i	−0.561073	+	0.561073i	0.368539	+	0.929612i	$0.379858\pi$
$468$	−117586.	+	1.11348e6i	−0.0248165	+	0.235001i
$469$	−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
$474$	7.38730e6	−	2.61394e6i	1.51022	−	0.534379i
$475$	685949.	−	685949.i	0.139495	−	0.139495i
$476$	−111839.	−	642360.i	−0.0226244	−	0.129945i
$477$	660095.	−	2.31655e6i	0.132834	−	0.466171i
$478$	−234936.	−	2.71905e6i	−0.0470304	−	0.544311i
$479$	−2.93376e6			−0.584233			−0.292116	−	0.956383i	$-0.594359\pi$
$479$	−2.93376e6			−0.584233			−0.292116	+	0.956383i	$0.594359\pi$
$480$	982371.	+	99108.5i	0.194613	+	0.0196340i
$481$	−187290.			−0.0369107
$482$	134342.	+	1.55482e6i	0.0263386	+	0.304833i
$483$	813684.	+	3.13553e6i	0.158704	+	0.611566i
$484$	−2.11147e6	−	1.21274e7i	−0.409704	−	2.35318i
$485$	−292410.	+	292410.i	−0.0564467	+	0.0564467i
$486$	5.08705e6	+	1.11136e6i	0.976958	+	0.213434i
$487$	−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	0.951385	−	0.308003i	$-0.0996607\pi$
$491$	3.43695e6	+	3.43695e6i	0.643382	+	0.643382i	−0.308003	+	0.951385i	$0.599661\pi$
$492$	3.87652e6	−	1.76044e6i	0.721988	−	0.327876i
$493$	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
$498$	−4.26623e6	−	2.03618e6i	−0.770852	−	0.367910i
$499$	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
$501$	1.54952e6	+	5.97106e6i	0.275805	+	1.06281i
$502$	4.06894e6	−	4.83858e6i	0.720646	−	0.856957i
$503$			5.03844e6i			0.887925i	0.896045	+	0.443962i	$0.146428\pi$
$503$			5.03844e6i			0.887925i	−0.896045	+	0.443962i	$0.853572\pi$
$504$	−1.80223e6	−	1.87214e6i	−0.316035	−	0.328293i
$505$			783302.i			0.136679i
$506$	1.12505e7	+	9.46093e6i	1.95341	+	1.64270i
$507$	−1.37264e6	−	5.28948e6i	−0.237158	−	0.913888i
$508$	747537.	+	4.29355e6i	0.128521	+	0.738172i
$509$	−944873.	−	944873.i	−0.161651	−	0.161651i	0.621647	−	0.783298i	$-0.286464\pi$
$509$	−944873.	−	944873.i	−0.161651	−	0.161651i	−0.783298	+	0.621647i	$0.786464\pi$
$510$	143245.	−	300130.i	0.0243868	−	0.0510956i
$511$		−	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
$516$	2.64245e6	−	7.03915e6i	0.436901	−	1.16385i
$517$	−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	$-0.601210\pi$
$521$	−3.87395e6			−0.625259			−0.312630	+	0.949875i	$0.601210\pi$
$522$	458642.	−	2.36690e6i	0.0736712	−	0.380192i
$523$	−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
$525$	695215.	+	2.67901e6i	0.110083	+	0.424206i
$526$	−8.91124e6	+	769963.i	−1.40435	+	0.121340i
$527$	2.74708e6			0.430868
$528$	−1.15872e7	−	2.18925e6i	−1.80881	−	0.341752i
$529$	−5.93704e6			−0.922424
$530$	−610862.	+	52780.7i	−0.0944612	+	0.00816179i
$531$	3.93342e6	+	1.12082e6i	0.605388	+	0.172504i
$532$	−499083.	−	351066.i	−0.0764528	−	0.0537786i
$533$	869013.	−	869013.i	0.132498	−	0.132498i
$534$	2.19323e6	+	6.19833e6i	0.332836	+	0.940636i
$535$	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
$540$	−196355.	−	1.31080e6i	−0.0289773	−	0.193443i
$541$	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
$546$	−676967.	−	323101.i	−0.0971820	−	0.0463828i
$547$	−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
$549$	2.40497e6	−	8.44004e6i	0.340549	−	1.19513i
$550$	9.61245e6	+	8.08346e6i	1.35496	+	1.13944i
$551$		−	566111.i		−	0.0794370i
$552$	8.65082e6	−	4.86703e6i	1.20840	−	0.679855i
$553$			5.24976e6i			0.730006i
$554$	−4.17674e6	+	4.96678e6i	−0.578180	+	0.687544i
$555$	214598.	−	55689.2i	0.0295729	−	0.00767430i
$556$	−3.73245e6	+	5.30613e6i	−0.512044	+	0.727932i
$557$	−7.21675e6	−	7.21675e6i	−0.985606	−	0.985606i	0.0142917	−	0.999898i	$-0.495451\pi$
$557$	−7.21675e6	−	7.21675e6i	−0.985606	−	0.985606i	−0.999898	+	0.0142917i	$0.995451\pi$
$558$	9.07314e6	−	6.12763e6i	1.23359	−	0.833119i
$559$		−	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	−0.238341	−	0.971182i	$-0.576604\pi$
$563$	5.51164e6	−	5.51164e6i	0.732841	−	0.732841i	0.971182	+	0.238341i	$0.0766036\pi$
$564$	−7.40394e6	+	3.36235e6i	−0.980088	+	0.445087i
$565$	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	$-0.392338\pi$
$569$	5.12519e6			0.663635			0.331818	+	0.943344i	$0.392338\pi$
$570$	−103817.	−	293398.i	−0.0133838	−	0.0378243i
$571$	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
$573$	9.65949e6	−	2.50668e6i	1.22904	−	0.318942i
$574$	245534.	+	2.84172e6i	0.0311052	+	0.359999i
$575$	−1.05719e7			−1.33347
$576$	−4.13377e6	+	6.80554e6i	−0.519146	+	0.854685i
$577$	−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
$579$	−2.93677e6	+	762103.i	−0.364060	+	0.0944751i
$580$	−604595.	+	105264.i	−0.0746267	+	0.0129930i
$581$	2.23939e6	−	2.23939e6i	0.275226	−	0.275226i
$582$	−1.11246e6	−	3.14394e6i	−0.136137	−	0.384739i
$583$	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	0.666374	−	0.745617i	$-0.267845\pi$
$587$	−661538.	−	661538.i	−0.0792428	−	0.0792428i	−0.745617	+	0.666374i	$0.767845\pi$
$588$	−6.04842e6	+	2.74677e6i	−0.721438	+	0.327626i
$589$	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	$-0.677493\pi$
$593$		−	1.45321e7i		−	1.69704i	0.529160	−	0.848522i	$-0.322507\pi$
$594$	988755.	+	1.57989e7i	0.114980	+	1.83721i
$595$	157541.	+	157541.i	0.0182432	+	0.0182432i
$596$	7.36680e6	−	1.04728e7i	0.849499	−	1.20767i
$597$	−1.17435e7	+	3.04748e6i	−1.34853	+	0.349949i
$598$	1.84408e6	−	2.19289e6i	0.210876	−	0.250763i
$599$		−	1.13672e7i		−	1.29445i	−0.762297	−	0.647227i	$-0.775928\pi$
$599$		−	1.13672e7i		−	1.29445i	0.762297	−	0.647227i	$-0.224072\pi$
$600$	7.39130e6	−	4.15841e6i	0.838190	−	0.471573i
$601$		−	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
$603$	1.10509e7	+	3.14892e6i	1.23766	+	0.352669i
$604$	1.01439e7	−	1.76612e6i	1.13139	−	0.196983i
$605$	2.97429e6	+	2.97429e6i	0.330366	+	0.330366i
$606$	−5.70096e6	−	2.72094e6i	−0.630619	−	0.300980i
$607$			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
$612$	1.68679e6	+	2.08511e6i	0.182047	+	0.225035i
$613$	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	$-0.633895\pi$
$617$	−7.72279e6			−0.816698			−0.408349	+	0.912826i	$0.633895\pi$
$618$	−5.99497e6	−	1.69425e7i	−0.631416	−	1.78446i
$619$	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
$621$	−9.19610e6	−	9.64242e6i	−0.956918	−	1.00336i
$622$	−2.50024e6	+	216030.i	−0.259123	+	0.0223892i
$623$	−4.40482e6			−0.454682
$624$	−426718.	+	2.25851e6i	−0.0438712	+	0.232200i
$625$	−8.65903e6			−0.886684
$626$	−7.67922e6	+	663512.i	−0.783215	+	0.0676726i
$627$	933652.	+	3.59783e6i	0.0948454	+	0.365487i
$628$	−5.85124e6	+	8.31825e6i	−0.592037	+	0.841652i
$629$	−317221.	+	317221.i	−0.0319694	+	0.0319694i
$630$	871744.	+	168921.i	0.0875060	+	0.0169563i
$631$	−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
$636$	1.73780e6	−	4.62927e6i	0.170356	−	0.453805i
$637$	−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	$0.0870569\pi$
$641$			5.61954e6i			0.540201i	−0.962832	+	0.270100i	$0.912943\pi$
$642$	−189602.	+	397257.i	−0.0181554	+	0.0380395i
$643$	−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
$645$	645338.	+	2.48681e6i	0.0610784	+	0.235366i
$646$	481984.	+	405318.i	0.0454413	+	0.0382133i
$647$			1.15453e7i			1.08429i	0.840285	+	0.542145i	$0.182388\pi$
$647$			1.15453e7i			1.08429i	−0.840285	+	0.542145i	$0.817612\pi$
$648$	1.02222e7	+	3.12421e6i	0.956332	+	0.292283i
$649$			1.24339e7i			1.15876i
$650$	1.57559e6	−	1.87361e6i	0.146272	−	0.173939i
$651$	1.84240e6	+	7.09971e6i	0.170385	+	0.656580i
$652$	7.36388e6	+	5.17992e6i	0.678403	+	0.477204i
$653$	9.52579e6	+	9.52579e6i	0.874215	+	0.874215i	0.992929	−	0.118714i	$-0.0378771\pi$
$653$	9.52579e6	+	9.52579e6i	0.874215	+	0.874215i	−0.118714	+	0.992929i	$0.537877\pi$
$654$	−3.25641e6	−	1.55421e6i	−0.297711	−	0.142091i
$655$		−	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	−0.607075	−	0.794644i	$-0.707657\pi$
$659$	2.09110e6	−	2.09110e6i	0.187569	−	0.187569i	0.794644	+	0.607075i	$0.207657\pi$
$660$	3.66880e6	−	1.66611e6i	0.327842	−	0.148883i
$661$	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
$666$	−340134.	+	1.75532e6i	−0.0297142	+	0.153345i
$667$	−4.36246e6	+	4.36246e6i	−0.379680	+	0.379680i
$668$	2.17211e6	+	1.24757e7i	0.188339	+	1.08174i
$669$	4.03672e6	+	1.55555e7i	0.348709	+	1.34375i
$670$	−251785.	−	2.91406e6i	−0.0216692	−	0.250790i
$671$	2.66797e7			2.28757
$672$	−3.37438e6	−	4.13164e6i	−0.288251	−	0.352939i
$673$	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
$675$	−7.85719e6	−	8.23853e6i	−0.663755	−	0.695969i
$676$	−1.92417e6	−	1.10516e7i	−0.161948	−	0.930166i
$677$	3.32334e6	−	3.32334e6i	0.278679	−	0.278679i	−0.553903	−	0.832581i	$-0.686862\pi$
$677$	3.32334e6	−	3.32334e6i	0.278679	−	0.278679i	0.832581	+	0.553903i	$0.186862\pi$
$678$	−1.72512e7	+	6.10418e6i	−1.44127	+	0.509980i
$679$	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	0.796866	−	0.604156i	$-0.206490\pi$
$683$	2.34939e6	+	2.34939e6i	0.192710	+	0.192710i	−0.604156	+	0.796866i	$0.706490\pi$
$684$	2.49601e6	+	263583.i	0.203989	+	0.0215416i
$685$	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
$690$	−1.46092e6	+	3.06095e6i	−0.116817	+	0.244756i
$691$	−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
$693$	−1.01991e7	−	2.90620e6i	−0.806728	−	0.229875i
$694$	1.24242e7	−	1.47742e7i	0.979195	−	1.16441i
$695$		−	2.21675e6i		−	0.174082i
$696$	1.33404e6	−	4.76597e6i	0.104387	−	0.372930i
$697$		−	2.94376e6i		−	0.229520i
$698$	−1.49864e7	−	1.26026e7i	−1.16428	−	0.979087i
$699$	−1.58235e7	+	4.10626e6i	−1.22492	+	0.317873i
$700$	974552.	+	5.59743e6i	0.0751726	+	0.431761i
$701$	2.16826e6	+	2.16826e6i	0.166654	+	0.166654i	0.785507	−	0.618853i	$-0.212402\pi$
$701$	2.16826e6	+	2.16826e6i	0.166654	+	0.166654i	−0.618853	+	0.785507i	$0.712402\pi$
$702$	3.07944e6	−	192723.i	0.235846	−	0.0147602i
$703$			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
$708$	7.86034e6	+	2.95072e6i	0.589329	+	0.221230i
$709$	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
$714$	−1.69385e6	+	599356.i	−0.124345	+	0.0439986i
$715$	822447.	−	822447.i	0.0601649	−	0.0601649i
$716$	−71444.4	+	101567.i	−0.00520817	+	0.00740405i
$717$	−7.27961e6	+	1.88909e6i	−0.528823	+	0.137232i
$718$	−1.58140e7	+	1.36639e6i	−1.14480	+	0.0989150i
$719$	−505647.			−0.0364775			−0.0182388	−	0.999834i	$-0.505806\pi$
$719$	−505647.			−0.0364775			−0.0182388	+	0.999834i	$0.505806\pi$
$720$	−182614.	−	2.71470e6i	−0.0131281	−	0.195160i
$721$	1.20401e7			0.862567
$722$	−1.33678e7	+	1.15502e6i	−0.954369	+	0.0824609i
$723$	4.16265e6	−	1.08023e6i	0.296159	−	0.0768544i
$724$	−1.46707e7	−	1.03197e7i	−1.04017	−	0.731681i
$725$	−3.72731e6	+	3.72731e6i	−0.263360	+	0.263360i
$726$	−3.19790e7	+	1.13155e7i	−2.25177	+	0.796769i
$727$	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
$732$	6.33144e6	−	1.68662e7i	0.436742	−	1.16342i
$733$	−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
$738$	−6.56635e6	−	9.72275e6i	−0.443796	−	0.657125i
$739$	−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
$741$	701272.	−	181983.i	0.0469182	−	0.0121755i
$742$	2.53535e6	+	2.13207e6i	0.169055	+	0.142165i
$743$			1.06139e6i			0.0705344i	0.999378	+	0.0352672i	$0.0112282\pi$
$743$			1.06139e6i			0.0705344i	−0.999378	+	0.0352672i	$0.988772\pi$
$744$	1.95878e7	−	1.10203e7i	1.29734	−	0.729896i
$745$			4.37523e6i			0.288809i
$746$	1.19740e7	−	1.42389e7i	0.787756	−	0.936760i
$747$	−3.56984e6	+	1.25280e7i	−0.234071	+	0.821451i
$748$	−4.69096e6	+	6.66877e6i	−0.306555	+	0.435805i
$749$	−208525.	−	208525.i	−0.0135817	−	0.0135817i
$750$	−2.54609e6	+	5.33462e6i	−0.165280	+	0.346298i
$751$		−	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
$756$	−4.25759e6	+	5.75788e6i	−0.270931	+	0.366402i
$757$	−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	$-0.387747\pi$
$761$	1.10357e7			0.690775			0.345388	+	0.938460i	$0.387747\pi$
$762$	1.13218e7	−	4.00611e6i	0.706361	−	0.249940i
$763$	1.70933e6	−	1.70933e6i	0.106295	−	0.106295i
$764$	2.01822e7	−	3.51386e6i	1.25094	−	0.217797i
$765$	−881349.	−	251138.i	−0.0544496	−	0.0155153i
$766$	218749.	+	2.53171e6i	0.0134702	+	0.155898i
$767$	2.42355e6			0.148752
$768$	−9.59529e6	+	1.32330e7i	−0.587023	+	0.809570i
$769$	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
$771$	4.83126e6	+	1.86173e7i	0.292701	+	1.12793i
$772$	−6.13597e6	+	1.06832e6i	−0.370544	+	0.0645144i
$773$	3.14828e6	−	3.14828e6i	0.189507	−	0.189507i	−0.605976	−	0.795483i	$-0.707217\pi$
$773$	3.14828e6	−	3.14828e6i	0.189507	−	0.189507i	0.795483	+	0.605976i	$0.207217\pi$
$774$	−2.03410e7	−	3.94154e6i	−1.22045	−	0.236491i
$775$	−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
$780$	−324750.	−	715105.i	−0.0191123	−	0.0420856i
$781$	−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
$786$	2.36477e7	+	1.12865e7i	1.36532	+	0.651634i
$787$	−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
$789$	6.19119e6	+	2.38578e7i	0.354064	+	1.36439i
$790$	−3.53768e6	+	4.20684e6i	−0.201675	+	0.239822i
$791$		−	1.22595e7i		−	0.696675i
$792$	−618098.	+	3.24895e7i	−0.0350142	+	1.84048i
$793$		−	5.20028e6i		−	0.293659i
$794$	−4.53400e6	−	3.81281e6i	−0.255229	−	0.214631i
$795$	424404.	+	1.63544e6i	0.0238156	+	0.0917734i
$796$	−2.45364e7	+	4.27195e6i	−1.37255	+	0.238970i
$797$	1.69769e7	+	1.69769e7i	0.946700	+	0.946700i	0.998650	−	0.0519495i	$-0.0165435\pi$
$797$	1.69769e7	+	1.69769e7i	0.946700	+	0.946700i	−0.0519495	+	0.998650i	$0.516543\pi$
$798$	−724271.	+	1.51750e6i	−0.0402619	+	0.0843573i
$799$			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
$804$	2.20835e7	+	8.28998e6i	1.20483	+	0.452286i
$805$	−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	$-0.687609\pi$
$809$	−2.06948e7			−1.11171			−0.555854	+	0.831280i	$0.687609\pi$
$810$	−3.47114e6	+	1.13647e6i	−0.185891	+	0.0608619i
$811$	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
$813$	−7.49923e6	−	2.88983e7i	−0.397915	−	1.53337i
$814$	−5.41538e6	+	467908.i	−0.286463	+	0.0247514i
$815$	−3.07642e6			−0.162237
$816$	3.10258e6	+	4.54808e6i	0.163117	+	0.239113i
$817$	−4.86512e6			−0.254999
$818$	1.25813e7	−	1.08707e6i	0.657417	−	0.0568032i
$819$	−566463.	+	1.98795e6i	−0.0295095	+	0.103561i
$820$	−1.71821e6	+	2.44264e6i	−0.0892362	+	0.126860i
$821$	−4.84077e6	+	4.84077e6i	−0.250644	+	0.250644i	−0.821235	−	0.570591i	$-0.806714\pi$
$821$	−4.84077e6	+	4.84077e6i	−0.250644	+	0.250644i	0.570591	+	0.821235i	$0.306714\pi$
$822$	2.64522e6	+	7.47572e6i	0.136547	+	0.385899i
$823$	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	0.432034	−	0.901857i	$-0.357796\pi$
$827$	−9.24056e6	−	9.24056e6i	−0.469824	−	0.469824i	−0.901857	+	0.432034i	$0.857796\pi$
$828$	−1.72032e7	−	2.12655e7i	−0.872032	−	1.07795i
$829$	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
$834$	1.61337e7	+	7.70028e6i	0.803193	+	0.383346i
$835$	−3.05972e6	−	3.05972e6i	−0.151868	−	0.151868i
$836$	1.30879e6	+	7.51718e6i	0.0647672	+	0.371997i
$837$	−2.08225e7	−	2.18331e7i	−1.02735	−	1.07721i
$838$	−1.43451e7	−	1.20633e7i	−0.705655	−	0.593411i
$839$			3.25226e7i			1.59507i	0.603270	+	0.797537i	$0.293864\pi$
$839$			3.25226e7i			1.59507i	−0.603270	+	0.797537i	$0.706136\pi$
$840$	1.75534e6	+	491337.i	0.0858345	+	0.0240260i
$841$		−	1.74350e7i		−	0.850026i
$842$	−1.39169e7	+	1.65493e7i	−0.676493	+	0.804452i
$843$	2.53406e6	−	657600.i	0.122814	−	0.0318708i
$844$	3.41000e6	+	2.39867e6i	0.164778	+	0.115908i
$845$	2.71046e6	+	2.71046e6i	0.130587	+	0.130587i
$846$	1.25414e7	+	1.85699e7i	0.602447	+	0.892038i
$847$		−	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
$852$	1.43830e7	+	3.16715e7i	0.678813	+	1.49476i
$853$	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	$-0.611978\pi$
$857$	−1.48173e7			−0.689154			−0.344577	+	0.938758i	$0.611978\pi$
$858$	3.12895e6	+	8.84279e6i	0.145104	+	0.410082i
$859$	−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
$861$	7.60802e6	−	1.97431e6i	0.349755	−	0.0907629i
$862$	217148.	+	2.51319e6i	0.00995379	+	0.115201i
$863$	1.46553e7			0.669835			0.334917	−	0.942248i	$-0.391292\pi$
$863$	1.46553e7			0.669835			0.334917	+	0.942248i	$0.391292\pi$
$864$	2.03923e7	+	8.10093e6i	0.929354	+	0.369190i
$865$	−4.90159e6			−0.222739
$866$	−561635.	−	6.50014e6i	−0.0254484	−	0.294529i
$867$	−1.96288e7	+	5.09377e6i	−0.886843	+	0.230140i
$868$	2.58268e6	+	1.48339e7i	0.116351	+	0.668275i
$869$	4.64193e7	−	4.64193e7i	2.08521	−	2.08521i
$870$	564119.	+	1.59427e6i	0.0252681	+	0.0714107i
$871$	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
$876$	2.64696e6	+	5.82865e6i	0.116543	+	0.256630i
$877$	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	$-0.788465\pi$
$881$		−	2.84152e7i		−	1.23342i	0.787191	−	0.616709i	$-0.211535\pi$
$882$	1.02453e7	+	1.51701e7i	0.443458	+	0.656625i
$883$	−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
$885$	−2.77692e6	+	720623.i	−0.119180	+	0.0309278i
$886$	1.09354e7	−	1.30039e7i	0.468006	−	0.556529i
$887$			3.90345e7i			1.66586i	0.553375	+	0.832932i	$0.313339\pi$
$887$			3.90345e7i			1.66586i	−0.553375	+	0.832932i	$0.686661\pi$
$888$	−989342.	+	3.53449e6i	−0.0421031	+	0.150416i
$889$			8.04576e6i			0.341439i
$890$	−3.52976e6	−	2.96830e6i	−0.149372	−	0.125613i
$891$	4.24709e7	−	9.95397e6i	1.79224	−	0.420051i
$892$	5.65867e6	+	3.25011e7i	0.238123	+	1.36769i
$893$	3.72057e6	+	3.72057e6i	0.156128	+	0.156128i
$894$	−3.18434e7	−	1.51982e7i	−1.33253	−	0.635985i
$895$		−	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
$900$	−1.46985e7	−	1.81694e7i	−0.604875	−	0.747710i
$901$	−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
$906$	−9.46480e6	−	2.67487e7i	−0.383081	−	1.08263i
$907$	−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
$909$	−4.77037e6	+	1.67412e7i	−0.191488	+	0.672013i
$910$	524213.	−	45293.9i	0.0209848	−	0.00181316i
$911$	−1.80200e7			−0.719379			−0.359690	−	0.933072i	$-0.617117\pi$
$911$	−1.80200e7			−0.719379			−0.359690	+	0.933072i	$0.617117\pi$
$912$	5.06274e6	+	956542.i	0.201557	+	0.0380818i
$913$	−3.96022e7			−1.57233
$914$	−1.10758e6	+	95698.7i	−0.0438539	+	0.00378914i
$915$	1.54626e6	+	5.95852e6i	0.0610562	+	0.235280i
$916$	−5.10913e6	−	3.59387e6i	−0.201191	−	0.141522i
$917$	−1.24129e7	+	1.24129e7i	−0.487474	+	0.487474i
$918$	4.88934e6	−	5.54219e6i	0.191489	−	0.217057i
$919$	−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
$924$	−2.03813e7	−	7.65100e6i	−0.785329	−	0.294807i
$925$	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	$-0.955506\pi$
$929$		−	7.33000e6i		−	0.278654i	0.990246	−	0.139327i	$-0.0444939\pi$
$930$	−3.30793e6	+	6.93083e6i	−0.125415	+	0.262771i
$931$	3.03941e6	+	3.03941e6i	0.114925	+	0.114925i
$932$	−3.30610e7	+	5.75615e6i	−1.24674	+	0.217066i
$933$	1.73707e6	+	6.69381e6i	0.0653302	+	0.251750i
$934$	1.61906e7	+	1.36153e7i	0.607289	+	0.510691i
$935$		−	2.78602e6i		−	0.104221i
$936$	6.33270e6	+	120477.i	0.236265	+	0.00449483i
$937$			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
$939$	5.33523e6	+	2.05593e7i	0.197464	+	0.760929i
$940$	3.28168e6	−	4.66530e6i	0.121137	−	0.172211i
$941$	−2.54751e7	−	2.54751e7i	−0.937869	−	0.937869i	0.0603102	−	0.998180i	$-0.480791\pi$
$941$	−2.54751e7	−	2.54751e7i	−0.937869	−	0.937869i	−0.998180	+	0.0603102i	$0.980791\pi$
$942$	2.52924e7	+	1.20715e7i	0.928671	+	0.443234i
$943$			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	−0.465734	−	0.884925i	$-0.654209\pi$
$947$	1.15688e7	−	1.15688e7i	0.419191	−	0.419191i	0.884925	+	0.465734i	$0.154209\pi$
$948$	−1.83291e7	−	4.03609e7i	−0.662399	−	1.45861i
$949$	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	$-0.546935\pi$
$953$	−8.23821e6			−0.293833			−0.146916	+	0.989149i	$0.546935\pi$
$954$	−1.33772e7	−	2.59214e6i	−0.475875	−	0.0922119i
$955$	−4.94976e6	+	4.94976e6i	−0.175621	+	0.175621i
$956$	−1.52098e7	+	2.64813e6i	−0.538242	+	0.0937117i
$957$	−5.07328e6	−	1.95499e7i	−0.179064	−	0.690024i
$958$	1.42862e6	+	1.65343e7i	0.0502924	+	0.582064i
$959$	−5.31259e6			−0.186535
$960$	80187.9	−	5.58476e6i	0.00280822	−	0.195581i
$961$	−3.48085e7			−1.21584
$962$	91202.5	+	1.05554e6i	0.00317738	+	0.0367737i
$963$	1.16657e6	+	332411.i	0.0405364	+	0.0115508i
$964$	8.69730e6	−	1.51426e6i	0.301434	−	0.0524817i
$965$	1.50487e6	−	1.50487e6i	0.0520213	−	0.0520213i
$966$	1.72752e7	−	6.11268e6i	0.595634	−	0.210760i
$967$	−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	0.708744	−	0.705466i	$-0.249262\pi$
$971$	96290.7	+	96290.7i	0.00327745	+	0.00327745i	−0.705466	+	0.708744i	$0.749262\pi$
$972$	3.78627e6	−	2.92111e7i	0.128542	−	0.991704i
$973$	−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	$0.0209310\pi$
$977$			3.92097e6i			0.131419i	−0.997839	+	0.0657093i	$0.979069\pi$
$978$	1.06865e7	−	2.23905e7i	0.357263	−	0.748543i
$979$	3.89482e7	+	3.89482e7i	1.29877	+	1.29877i
$980$	2.68087e6	−	3.81118e6i	0.0891682	−	0.126763i
$981$	−2.72486e6	+	9.56265e6i	−0.0904006	+	0.317253i
$982$	1.76965e7	−	2.10438e7i	0.585610	−	0.696378i
$983$			9.05571e6i			0.298909i	0.988769	+	0.149454i	$0.0477517\pi$
$983$			9.05571e6i			0.298909i	−0.988769	+	0.149454i	$0.952248\pi$
$984$	−1.18093e7	−	2.09903e7i	−0.388809	−	0.691083i
$985$		−	3.17980e6i		−	0.104426i
$986$	−2.61900e6	−	2.20242e6i	−0.0857914	−	0.0721451i
$987$	−1.45309e7	+	3.77083e6i	−0.474788	+	0.123209i
$988$	1.46521e6	−	255104.i	0.0477538	−	0.00831427i
$989$	3.74908e7	+	3.74908e7i	1.21880	+	1.21880i
$990$	−6.21450e6	−	9.20176e6i	−0.201520	−	0.298389i
$991$			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
$996$	−9.39812e6	+	2.50354e7i	−0.300188	+	0.799662i
$997$	−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.11.19	✓	76
3.2	odd	2	inner	48.6.k.a.11.20	yes	76
4.3	odd	2		192.6.k.a.143.35		76
12.11	even	2		192.6.k.a.143.16		76
16.3	odd	4	inner	48.6.k.a.35.20	yes	76
16.13	even	4		192.6.k.a.47.16		76
48.29	odd	4		192.6.k.a.47.35		76
48.35	even	4	inner	48.6.k.a.35.19	yes	76

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

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

\(f(q)\)	\(=\)	\(q+(-0.486958 - 5.63586i) q^{2} +(-15.0887 + 3.91558i) q^{3} +(-31.5257 + 5.48885i) q^{4} +(7.73181 - 7.73181i) q^{5} +(29.4152 + 83.1309i) q^{6} -59.0766 q^{7} +(46.2861 + 175.002i) q^{8} +(212.337 - 118.162i) q^{9} +O(q^{10})\)	\(q+(-0.486958 - 5.63586i) q^{2} +(-15.0887 + 3.91558i) q^{3} +(-31.5257 + 5.48885i) q^{4} +(7.73181 - 7.73181i) q^{5} +(29.4152 + 83.1309i) 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} +(454.190 - 206.261i) 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} +(-769.342 - 1139.16i) q^{18} +(-228.236 - 228.236i) q^{19} +(-201.312 + 286.190i) q^{20} +(891.388 - 231.319i) q^{21} +(2689.61 - 3198.35i) q^{22} +3517.58i q^{23} +(-1383.63 - 2459.31i) q^{24} +3005.44i q^{25} +(-623.408 - 524.246i) q^{26} +(-2741.21 + 2614.33i) q^{27} +(1862.43 - 324.263i) q^{28} +(1240.19 + 1240.19i) q^{29} +(870.185 + 415.320i) 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} +(-6045.49 + 4890.62i) 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} +(-1737.75 - 4911.09i) q^{42} +(10658.1 - 10658.1i) q^{43} +(-19335.2 - 13600.8i) q^{44} +(728.142 - 2555.35i) q^{45} +(19824.6 - 1712.91i) q^{46} -16301.4 q^{47} +(-13186.5 + 8995.51i) q^{48} -13317.0 q^{49} +(16938.2 - 1463.52i) q^{50} +(1350.50 + 5204.14i) q^{51} +(-2651.00 + 3768.72i) q^{52} +(7009.26 - 7009.26i) q^{53} +(16068.8 + 14176.0i) 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} +(1916.94 - 5106.48i) 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} +(-28059.3 + 58790.3i) q^{66} +(33437.0 + 33437.0i) q^{67} +(1893.12 + 10873.3i) q^{68} +(-13773.4 - 53075.7i) q^{69} +(2796.71 + 2351.86i) q^{70} +69731.9i q^{71} +(30506.7 + 31690.0i) q^{72} +12833.1i q^{73} +(-4735.63 + 5631.38i) q^{74} +(-11768.0 - 45348.1i) q^{75} +(8448.06 + 5942.55i) q^{76} +(-30859.6 - 30859.6i) q^{77} +(11459.1 + 5469.19i) 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} +(-26832.0 + 12185.2i) 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} +(-14756.2 - 2859.35i) q^{90} +(-6015.02 + 6015.02i) q^{91} +(-19307.5 - 110894. i) q^{92} +(-31186.7 - 120178. i) q^{93} +(7938.11 + 91872.5i) q^{94} -3529.36 q^{95} +(57118.7 + 69937.0i) q^{96} -37819.1 q^{97} +(6484.80 + 75052.4i) q^{98} +(172641. + 49193.7i) 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

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more