LMFDB - Embedded newform 48.6.j.a.13.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [48,6,Mod(13,48)]

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([0, 3, 0]))

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

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

chi := DirichletCharacter("48.13");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 48 = 2^{4} \cdot 3 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	48.j (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:	$40$
Relative dimension:	$20$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			13.3
Character	$\chi$	$=$	48.13
Dual form			48.6.j.a.37.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-5.12822 - 2.38775i) q^{2} +(-6.36396 - 6.36396i) q^{3} +(20.5973 + 24.4898i) q^{4} +(12.6306 - 12.6306i) q^{5} +(17.4402 + 47.8313i) q^{6} -213.506i q^{7} +(-47.1519 - 174.770i) q^{8} +81.0000i q^{9} +O(q^{10})$	\(q+(-5.12822 - 2.38775i) q^{2} +(-6.36396 - 6.36396i) q^{3} +(20.5973 + 24.4898i) q^{4} +(12.6306 - 12.6306i) q^{5} +(17.4402 + 47.8313i) q^{6} -213.506i q^{7} +(-47.1519 - 174.770i) q^{8} +81.0000i q^{9} +(-94.9313 + 34.6138i) q^{10} +(-416.817 + 416.817i) q^{11} +(24.7719 - 286.933i) q^{12} +(377.778 + 377.778i) q^{13} +(-509.800 + 1094.91i) q^{14} -160.761 q^{15} +(-175.503 + 1008.85i) q^{16} -2258.17 q^{17} +(193.408 - 415.386i) q^{18} +(-758.876 - 758.876i) q^{19} +(569.478 + 49.1651i) q^{20} +(-1358.75 + 1358.75i) q^{21} +(3132.78 - 1142.27i) q^{22} -218.598i q^{23} +(-812.160 + 1412.30i) q^{24} +2805.94i q^{25} +(-1035.29 - 2839.37i) q^{26} +(515.481 - 515.481i) q^{27} +(5228.73 - 4397.65i) q^{28} +(-2265.72 - 2265.72i) q^{29} +(824.420 + 383.858i) q^{30} -5253.31 q^{31} +(3308.90 - 4754.54i) q^{32} +5305.21 q^{33} +(11580.4 + 5391.95i) q^{34} +(-2696.72 - 2696.72i) q^{35} +(-1983.68 + 1668.38i) q^{36} +(722.521 - 722.521i) q^{37} +(2079.68 + 5703.69i) q^{38} -4808.33i q^{39} +(-2803.01 - 1611.90i) q^{40} +7896.08i q^{41} +(10212.3 - 3723.60i) q^{42} +(16319.5 - 16319.5i) q^{43} +(-18793.1 - 1622.47i) q^{44} +(1023.08 + 1023.08i) q^{45} +(-521.958 + 1121.02i) q^{46} -8068.09 q^{47} +(7537.17 - 5303.38i) q^{48} -28778.0 q^{49} +(6699.87 - 14389.5i) q^{50} +(14370.9 + 14370.9i) q^{51} +(-1470.51 + 17032.9i) q^{52} +(-11962.6 + 11962.6i) q^{53} +(-3874.34 + 1412.66i) q^{54} +10529.3i q^{55} +(-37314.6 + 10067.2i) q^{56} +9658.91i q^{57} +(6209.14 + 17029.1i) q^{58} +(13211.9 - 13211.9i) q^{59} +(-3311.25 - 3937.02i) q^{60} +(15391.3 + 15391.3i) q^{61} +(26940.1 + 12543.6i) q^{62} +17294.0 q^{63} +(-28321.4 + 16481.5i) q^{64} +9543.13 q^{65} +(-27206.3 - 12667.5i) q^{66} +(-39484.4 - 39484.4i) q^{67} +(-46512.2 - 55302.2i) q^{68} +(-1391.15 + 1391.15i) q^{69} +(7390.27 + 20268.4i) q^{70} -38475.8i q^{71} +(14156.4 - 3819.30i) q^{72} -18530.6i q^{73} +(-5430.45 + 1980.05i) q^{74} +(17856.9 - 17856.9i) q^{75} +(2953.95 - 34215.5i) q^{76} +(88993.1 + 88993.1i) q^{77} +(-11481.1 + 24658.2i) q^{78} +1727.63 q^{79} +(10525.7 + 14959.1i) q^{80} -6561.00 q^{81} +(18853.9 - 40492.8i) q^{82} +(33102.2 + 33102.2i) q^{83} +(-61262.0 - 5288.96i) q^{84} +(-28522.1 + 28522.1i) q^{85} +(-122657. + 44723.0i) q^{86} +28837.9i q^{87} +(92500.9 + 53193.6i) q^{88} -71812.1i q^{89} +(-2803.72 - 7689.44i) q^{90} +(80658.0 - 80658.0i) q^{91} +(5353.43 - 4502.53i) q^{92} +(33431.9 + 33431.9i) q^{93} +(41375.0 + 19264.6i) q^{94} -19170.1 q^{95} +(-51315.4 + 9200.01i) q^{96} -77367.6 q^{97} +(147580. + 68714.6i) q^{98} +(-33762.2 - 33762.2i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q + 44 q^{4} - 492 q^{8}+O(q^{10}) $ 40 * q + 44 * q^4 - 492 * q^8	\( 40 q + 44 q^{4} - 492 q^{8} + 968 q^{10} + 1208 q^{11} - 792 q^{12} + 324 q^{14} - 1800 q^{15} - 384 q^{16} - 324 q^{18} + 2360 q^{19} - 7600 q^{20} - 1024 q^{22} + 5220 q^{24} - 12980 q^{26} + 10472 q^{28} - 8144 q^{29} - 1368 q^{30} + 23064 q^{31} + 44160 q^{32} + 4864 q^{34} - 4776 q^{35} - 1620 q^{36} + 21296 q^{37} - 72088 q^{38} - 90864 q^{40} - 14220 q^{42} + 31416 q^{43} + 43768 q^{44} + 90664 q^{46} + 44784 q^{48} - 96040 q^{49} + 106212 q^{50} + 10440 q^{51} - 116432 q^{52} - 49456 q^{53} - 14580 q^{54} - 158592 q^{56} - 111472 q^{58} + 28960 q^{59} + 49464 q^{60} + 48080 q^{61} + 191100 q^{62} + 31752 q^{63} + 369032 q^{64} - 55376 q^{65} + 63720 q^{66} + 101488 q^{67} - 122336 q^{68} - 22320 q^{69} - 460192 q^{70} - 28836 q^{72} - 94996 q^{74} - 96624 q^{75} + 211304 q^{76} - 14896 q^{77} + 200124 q^{78} - 71960 q^{79} + 623368 q^{80} - 262440 q^{81} + 33880 q^{82} - 126440 q^{83} - 116856 q^{84} + 132400 q^{85} - 581168 q^{86} - 466400 q^{88} - 46008 q^{90} + 429496 q^{91} - 12752 q^{92} + 524120 q^{94} - 76848 q^{95} + 51840 q^{96} + 477736 q^{98} + 97848 q^{99}+O(q^{100}) \) 40 * q + 44 * q^4 - 492 * q^8 + 968 * q^10 + 1208 * q^11 - 792 * q^12 + 324 * q^14 - 1800 * q^15 - 384 * q^16 - 324 * q^18 + 2360 * q^19 - 7600 * q^20 - 1024 * q^22 + 5220 * q^24 - 12980 * q^26 + 10472 * q^28 - 8144 * q^29 - 1368 * q^30 + 23064 * q^31 + 44160 * q^32 + 4864 * q^34 - 4776 * q^35 - 1620 * q^36 + 21296 * q^37 - 72088 * q^38 - 90864 * q^40 - 14220 * q^42 + 31416 * q^43 + 43768 * q^44 + 90664 * q^46 + 44784 * q^48 - 96040 * q^49 + 106212 * q^50 + 10440 * q^51 - 116432 * q^52 - 49456 * q^53 - 14580 * q^54 - 158592 * q^56 - 111472 * q^58 + 28960 * q^59 + 49464 * q^60 + 48080 * q^61 + 191100 * q^62 + 31752 * q^63 + 369032 * q^64 - 55376 * q^65 + 63720 * q^66 + 101488 * q^67 - 122336 * q^68 - 22320 * q^69 - 460192 * q^70 - 28836 * q^72 - 94996 * q^74 - 96624 * q^75 + 211304 * q^76 - 14896 * q^77 + 200124 * q^78 - 71960 * q^79 + 623368 * q^80 - 262440 * q^81 + 33880 * q^82 - 126440 * q^83 - 116856 * q^84 + 132400 * q^85 - 581168 * q^86 - 466400 * q^88 - 46008 * q^90 + 429496 * q^91 - 12752 * q^92 + 524120 * q^94 - 76848 * q^95 + 51840 * q^96 + 477736 * q^98 + 97848 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$17$	$31$	$37$
$\chi(n)$	$1$	$1$	$e\left(\frac{3}{4}\right)$

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 $

$2$	−5.12822	−	2.38775i	−0.906550	−	0.422099i
$2$	−5.12822	−	2.38775i	−0.906550	−	0.422099i
$3$	−6.36396	−	6.36396i	−0.408248	−	0.408248i
$3$	−6.36396	−	6.36396i	−0.408248	−	0.408248i
$4$	20.5973	+	24.4898i	0.643665	+	0.765307i
$5$	12.6306	−	12.6306i	0.225943	−	0.225943i	−0.585052	−	0.810996i	$-0.698926\pi$
$5$	12.6306	−	12.6306i	0.225943	−	0.225943i	0.810996	+	0.585052i	$0.198926\pi$
$6$	17.4402	+	47.8313i	0.197776	+	0.542419i
$7$		−	213.506i		−	1.64689i	−0.567393	−	0.823447i	$-0.692048\pi$
$7$		−	213.506i		−	1.64689i	0.567393	−	0.823447i	$-0.307952\pi$
$8$	−47.1519	−	174.770i	−0.260480	−	0.965479i
$9$			81.0000i			0.333333i
$10$	−94.9313	+	34.6138i	−0.300199	+	0.109458i
$11$	−416.817	+	416.817i	−1.03864	+	1.03864i	−0.0394133	+	0.999223i	$0.512549\pi$
$11$	−416.817	+	416.817i	−1.03864	+	1.03864i	−0.999223	+	0.0394133i	$0.987451\pi$
$12$	24.7719	−	286.933i	0.0496600	−	0.575211i
$13$	377.778	+	377.778i	0.619980	+	0.619980i	0.945526	−	0.325546i	$-0.105548\pi$
$13$	377.778	+	377.778i	0.619980	+	0.619980i	−0.325546	+	0.945526i	$0.605548\pi$
$14$	−509.800	+	1094.91i	−0.695152	+	1.49299i
$15$	−160.761			−0.184482
$16$	−175.503	+	1008.85i	−0.171390	+	0.985203i
$17$	−2258.17			−1.89511			−0.947556	−	0.319591i	$-0.896454\pi$
$17$	−2258.17			−1.89511			−0.947556	+	0.319591i	$0.896454\pi$
$18$	193.408	−	415.386i	0.140700	−	0.302183i
$19$	−758.876	−	758.876i	−0.482266	−	0.482266i	0.423589	−	0.905855i	$-0.360770\pi$
$19$	−758.876	−	758.876i	−0.482266	−	0.482266i	−0.905855	+	0.423589i	$0.860770\pi$
$20$	569.478	+	49.1651i	0.318348	+	0.0274841i
$21$	−1358.75	+	1358.75i	−0.672342	+	0.672342i
$22$	3132.78	−	1142.27i	1.37998	−	0.503169i
$23$		−	218.598i		−	0.0861642i	−0.999072	−	0.0430821i	$-0.986282\pi$
$23$		−	218.598i		−	0.0861642i	0.999072	−	0.0430821i	$-0.0137177\pi$
$24$	−812.160	+	1412.30i	−0.287815	+	0.500496i
$25$			2805.94i			0.897899i
$26$	−1035.29	−	2839.37i	−0.300350	−	0.823736i
$27$	515.481	−	515.481i	0.136083	−	0.136083i
$28$	5228.73	−	4397.65i	1.26038	−	1.06005i
$29$	−2265.72	−	2265.72i	−0.500278	−	0.500278i	0.411246	−	0.911524i	$-0.365094\pi$
$29$	−2265.72	−	2265.72i	−0.500278	−	0.500278i	−0.911524	+	0.411246i	$0.865094\pi$
$30$	824.420	+	383.858i	0.167242	+	0.0778696i
$31$	−5253.31			−0.981813			−0.490906	−	0.871212i	$-0.663334\pi$
$31$	−5253.31			−0.981813			−0.490906	+	0.871212i	$0.663334\pi$
$32$	3308.90	−	4754.54i	0.571226	−	0.820793i
$33$	5305.21			0.848043
$34$	11580.4	+	5391.95i	1.71801	+	0.799924i
$35$	−2696.72	−	2696.72i	−0.372105	−	0.372105i
$36$	−1983.68	+	1668.38i	−0.255102	+	0.214555i
$37$	722.521	−	722.521i	0.0867653	−	0.0867653i	−0.662392	−	0.749157i	$-0.730459\pi$
$37$	722.521	−	722.521i	0.0867653	−	0.0867653i	0.749157	+	0.662392i	$0.230459\pi$
$38$	2079.68	+	5703.69i	0.233634	+	0.640762i
$39$		−	4808.33i		−	0.506212i
$40$	−2803.01	−	1611.90i	−0.276997	−	0.159290i
$41$			7896.08i			0.733587i	0.930302	+	0.366794i	$0.119544\pi$
$41$			7896.08i			0.733587i	−0.930302	+	0.366794i	$0.880456\pi$
$42$	10212.3	−	3723.60i	0.893306	−	0.325717i
$43$	16319.5	−	16319.5i	1.34597	−	1.34597i	0.455978	−	0.889991i	$-0.349289\pi$
$43$	16319.5	−	16319.5i	1.34597	−	1.34597i	0.889991	−	0.455978i	$-0.150711\pi$
$44$	−18793.1	−	1622.47i	−1.46341	−	0.126341i
$45$	1023.08	+	1023.08i	0.0753144	+	0.0753144i
$46$	−521.958	+	1121.02i	−0.0363698	+	0.0781121i
$47$	−8068.09			−0.532753			−0.266377	−	0.963869i	$-0.585827\pi$
$47$	−8068.09			−0.532753			−0.266377	+	0.963869i	$0.585827\pi$
$48$	7537.17	−	5303.38i	0.472177	−	0.332238i
$49$	−28778.0			−1.71226
$50$	6699.87	−	14389.5i	0.379002	−	0.813991i
$51$	14370.9	+	14370.9i	0.773676	+	0.773676i
$52$	−1470.51	+	17032.9i	−0.0754154	+	0.873535i
$53$	−11962.6	+	11962.6i	−0.584973	+	0.584973i	−0.936266	−	0.351293i	$-0.885742\pi$
$53$	−11962.6	+	11962.6i	−0.584973	+	0.584973i	0.351293	+	0.936266i	$0.385742\pi$
$54$	−3874.34	+	1412.66i	−0.180806	+	0.0659255i
$55$			10529.3i			0.469346i
$56$	−37314.6	+	10067.2i	−1.59004	+	0.428983i
$57$			9658.91i			0.393768i
$58$	6209.14	+	17029.1i	0.242360	+	0.664693i
$59$	13211.9	−	13211.9i	0.494122	−	0.494122i	−0.415480	−	0.909602i	$-0.636386\pi$
$59$	13211.9	−	13211.9i	0.494122	−	0.494122i	0.909602	+	0.415480i	$0.136386\pi$
$60$	−3311.25	−	3937.02i	−0.118745	−	0.141185i
$61$	15391.3	+	15391.3i	0.529602	+	0.529602i	0.920454	−	0.390851i	$-0.127819\pi$
$61$	15391.3	+	15391.3i	0.529602	+	0.529602i	−0.390851	+	0.920454i	$0.627819\pi$
$62$	26940.1	+	12543.6i	0.890062	+	0.414422i
$63$	17294.0			0.548965
$64$	−28321.4	+	16481.5i	−0.864301	+	0.502976i
$65$	9543.13			0.280161
$66$	−27206.3	−	12667.5i	−0.768793	−	0.357958i
$67$	−39484.4	−	39484.4i	−1.07458	−	1.07458i	−0.996985	−	0.0775955i	$-0.975276\pi$
$67$	−39484.4	−	39484.4i	−1.07458	−	1.07458i	−0.0775955	−	0.996985i	$-0.524724\pi$
$68$	−46512.2	−	55302.2i	−1.21982	−	1.45034i
$69$	−1391.15	+	1391.15i	−0.0351764	+	0.0351764i
$70$	7390.27	+	20268.4i	0.180267	+	0.494396i
$71$		−	38475.8i		−	0.905819i	−0.891556	−	0.452910i	$-0.850386\pi$
$71$		−	38475.8i		−	0.905819i	0.891556	−	0.452910i	$-0.149614\pi$
$72$	14156.4	−	3819.30i	0.321826	−	0.0868266i
$73$		−	18530.6i		−	0.406989i	−0.979076	−	0.203495i	$-0.934770\pi$
$73$		−	18530.6i		−	0.406989i	0.979076	−	0.203495i	$-0.0652299\pi$
$74$	−5430.45	+	1980.05i	−0.115281	+	0.0420336i
$75$	17856.9	−	17856.9i	0.366566	−	0.366566i
$76$	2953.95	−	34215.5i	0.0586636	−	0.679499i
$77$	88993.1	+	88993.1i	1.71052	+	1.71052i
$78$	−11481.1	+	24658.2i	−0.213671	+	0.458906i
$79$	1727.63			0.0311446			0.0155723	−	0.999879i	$-0.495043\pi$
$79$	1727.63			0.0311446			0.0155723	+	0.999879i	$0.495043\pi$
$80$	10525.7	+	14959.1i	0.183876	+	0.261324i
$81$	−6561.00			−0.111111
$82$	18853.9	−	40492.8i	0.309646	−	0.665033i
$83$	33102.2	+	33102.2i	0.527427	+	0.527427i	0.919804	−	0.392377i	$-0.128347\pi$
$83$	33102.2	+	33102.2i	0.527427	+	0.527427i	−0.392377	+	0.919804i	$0.628347\pi$
$84$	−61262.0	−	5288.96i	−0.947311	−	0.0817848i
$85$	−28522.1	+	28522.1i	−0.428188	+	0.428188i
$86$	−122657.	+	44723.0i	−1.78832	+	0.652056i
$87$			28837.9i			0.408475i
$88$	92500.9	+	53193.6i	1.27333	+	0.732238i
$89$		−	71812.1i		−	0.960998i	−0.876995	−	0.480499i	$-0.840456\pi$
$89$		−	71812.1i		−	0.960998i	0.876995	−	0.480499i	$-0.159544\pi$
$90$	−2803.72	−	7689.44i	−0.0364862	−	0.100066i
$91$	80658.0	−	80658.0i	1.02104	−	1.02104i
$92$	5353.43	−	4502.53i	0.0659420	−	0.0554609i
$93$	33431.9	+	33431.9i	0.400823	+	0.400823i
$94$	41375.0	+	19264.6i	0.482967	+	0.224874i
$95$	−19170.1			−0.217929
$96$	−51315.4	+	9200.01i	−0.568289	+	0.101885i
$97$	−77367.6			−0.834891			−0.417446	−	0.908702i	$-0.637075\pi$
$97$	−77367.6			−0.834891			−0.417446	+	0.908702i	$0.637075\pi$
$98$	147580.	+	68714.6i	1.55225	+	0.722743i
$99$	−33762.2	−	33762.2i	−0.346212	−	0.346212i
$100$	−68716.9	+	57794.7i	−0.687169	+	0.577947i
$101$	76819.1	−	76819.1i	0.749317	−	0.749317i	−0.225034	−	0.974351i	$-0.572249\pi$
$101$	76819.1	−	76819.1i	0.749317	−	0.749317i	0.974351	+	0.225034i	$0.0722492\pi$
$102$	−39383.1	−	108011.i	−0.374808	−	1.02794i
$103$		−	23384.0i		−	0.217183i	−0.994086	−	0.108591i	$-0.965366\pi$
$103$		−	23384.0i		−	0.217183i	0.994086	−	0.108591i	$-0.0346340\pi$
$104$	48211.5	−	83837.3i	0.437086	−	0.760071i
$105$			34323.6i			0.303822i
$106$	89910.5	−	32783.1i	0.777224	−	0.283391i
$107$	−4831.19	+	4831.19i	−0.0407938	+	0.0407938i	−0.727209	−	0.686416i	$-0.759183\pi$
$107$	−4831.19	+	4831.19i	−0.0407938	+	0.0407938i	0.686416	+	0.727209i	$0.259183\pi$
$108$	23241.5	+	2006.53i	0.191737	+	0.0165533i
$109$	−73757.2	−	73757.2i	−0.594618	−	0.594618i	0.344257	−	0.938875i	$-0.388131\pi$
$109$	−73757.2	−	73757.2i	−0.594618	−	0.594618i	−0.938875	+	0.344257i	$0.888131\pi$
$110$	25141.3	−	53996.6i	0.198110	−	0.425485i
$111$	−9196.19			−0.0708436
$112$	215396.	+	37471.0i	1.62253	+	0.282261i
$113$	−18699.2			−0.137761			−0.0688807	−	0.997625i	$-0.521943\pi$
$113$	−18699.2			−0.137761			−0.0688807	+	0.997625i	$0.521943\pi$
$114$	23063.1	−	49533.0i	0.166209	−	0.356971i
$115$	−2761.03	−	2761.03i	−0.0194682	−	0.0194682i
$116$	8819.39	−	102155.i	0.0608546	−	0.704878i
$117$	−30600.0	+	30600.0i	−0.206660	+	0.206660i
$118$	−99300.0	+	36206.7i	−0.656515	+	0.239378i
$119$			482134.i			3.12105i
$120$	7580.20	+	28096.3i	0.0480538	+	0.178113i
$121$		−	186421.i		−	1.15753i
$122$	−42179.3	−	115680.i	−0.256567	−	0.703656i
$123$	50250.3	−	50250.3i	0.299486	−	0.299486i
$124$	−108204.	−	128653.i	−0.631959	−	0.751388i
$125$	74911.3	+	74911.3i	0.428817	+	0.428817i
$126$	−88687.5	−	41293.8i	−0.497664	−	0.231717i
$127$	−324158.			−1.78339			−0.891697	−	0.452632i	$-0.850485\pi$
$127$	−324158.			−1.78339			−0.891697	+	0.452632i	$0.850485\pi$
$128$	184592.	−	16896.3i	0.995837	−	0.0911522i
$129$	−207713.			−1.09898
$130$	−48939.3	−	22786.6i	−0.253980	−	0.118255i
$131$	−84000.1	−	84000.1i	−0.427663	−	0.427663i	0.460169	−	0.887832i	$-0.347789\pi$
$131$	−84000.1	−	84000.1i	−0.427663	−	0.427663i	−0.887832	+	0.460169i	$0.847789\pi$
$132$	109273.	+	129924.i	0.545856	+	0.649013i
$133$	−162025.	+	162025.i	−0.794241	+	0.794241i
$134$	108206.	+	296764.i	0.520582	+	1.42774i
$135$		−	13021.7i		−	0.0614940i
$136$	106477.	+	394662.i	0.493638	+	1.82969i
$137$		−	217868.i		−	0.991726i	−0.868401	−	0.495863i	$-0.834852\pi$
$137$		−	217868.i		−	0.991726i	0.868401	−	0.495863i	$-0.165148\pi$
$138$	10455.8	−	3812.40i	0.0467370	−	0.0170412i
$139$	−120923.	+	120923.i	−0.530852	+	0.530852i	−0.920826	−	0.389974i	$-0.872484\pi$
$139$	−120923.	+	120923.i	−0.530852	+	0.530852i	0.389974	+	0.920826i	$0.372484\pi$
$140$	10497.1	−	121587.i	0.0452634	−	0.524285i
$141$	51345.0	+	51345.0i	0.217496	+	0.217496i
$142$	−91870.6	+	197312.i	−0.382345	+	0.821170i
$143$	−314928.			−1.28787
$144$	−81716.7	−	14215.7i	−0.328401	−	0.0571299i
$145$	−57234.8			−0.226069
$146$	−44246.5	+	95029.1i	−0.171790	+	0.368956i
$147$	183142.	+	183142.i	0.699028	+	0.699028i
$148$	32576.4	+	2812.44i	0.122250	+	0.0105543i
$149$	347991.	−	347991.i	1.28411	−	1.28411i	0.345805	−	0.938307i	$-0.387606\pi$
$149$	347991.	−	347991.i	1.28411	−	1.28411i	0.938307	−	0.345805i	$-0.112394\pi$
$150$	−134212.	+	48936.2i	−0.487037	+	0.177583i
$151$			198497.i			0.708453i	0.935160	+	0.354226i	$0.115256\pi$
$151$			198497.i			0.708453i	−0.935160	+	0.354226i	$0.884744\pi$
$152$	−96846.6	+	168411.i	−0.339997	+	0.591238i
$153$		−	182912.i		−	0.631704i
$154$	−243883.	−	668869.i	−0.828666	−	2.27269i
$155$	−66352.5	+	66352.5i	−0.221834	+	0.221834i
$156$	117755.	−	99038.5i	0.387408	−	0.325831i
$157$	56261.9	+	56261.9i	0.182165	+	0.182165i	0.792299	−	0.610134i	$-0.208884\pi$
$157$	56261.9	+	56261.9i	0.182165	+	0.182165i	−0.610134	+	0.792299i	$0.708884\pi$
$158$	−8859.66	−	4125.15i	−0.0282341	−	0.0131461i
$159$	152259.			0.477628
$160$	−18259.3	−	101846.i	−0.0563878	−	0.314517i
$161$	−46672.1			−0.141903
$162$	33646.3	+	15666.0i	0.100728	+	0.0468999i
$163$	181309.	+	181309.i	0.534502	+	0.534502i	0.921909	−	0.387407i	$-0.126629\pi$
$163$	181309.	+	181309.i	0.534502	+	0.534502i	−0.387407	+	0.921909i	$0.626629\pi$
$164$	−193374.	+	162638.i	−0.561419	+	0.472185i
$165$	67008.1	−	67008.1i	0.191610	−	0.191610i
$166$	−90715.7	−	248796.i	−0.255513	−	0.700765i
$167$		−	266344.i		−	0.739013i	−0.929228	−	0.369507i	$-0.879527\pi$
$167$		−	266344.i		−	0.739013i	0.929228	−	0.369507i	$-0.120473\pi$
$168$	301536.	+	173401.i	0.824264	+	0.474001i
$169$		−	85861.0i		−	0.231249i
$170$	214371.	−	78163.9i	0.568911	−	0.207436i
$171$	61468.9	−	61468.9i	0.160755	−	0.160755i
$172$	735798.	+	63524.1i	1.89643	+	0.163726i
$173$	212693.	+	212693.i	0.540303	+	0.540303i	0.923618	−	0.383315i	$-0.125218\pi$
$173$	212693.	+	212693.i	0.540303	+	0.540303i	−0.383315	+	0.923618i	$0.625218\pi$
$174$	68857.7	−	147887.i	0.172417	−	0.370303i
$175$	599085.			1.47875
$176$	−347352.	−	493657.i	−0.845256	−	1.20128i
$177$	−168160.			−0.403449
$178$	−171469.	+	368268.i	−0.405636	+	0.871193i
$179$	18674.7	+	18674.7i	0.0435633	+	0.0435633i	0.728553	−	0.684990i	$-0.240193\pi$
$179$	18674.7	+	18674.7i	0.0435633	+	0.0435633i	−0.684990	+	0.728553i	$0.740193\pi$
$180$	−3982.37	+	46127.7i	−0.00916137	+	0.106116i
$181$	164622.	−	164622.i	0.373502	−	0.373502i	−0.495249	−	0.868751i	$-0.664923\pi$
$181$	164622.	−	164622.i	0.373502	−	0.373502i	0.868751	+	0.495249i	$0.164923\pi$
$182$	−606223.	+	221041.i	−1.35661	+	0.494645i
$183$		−	195899.i		−	0.432419i
$184$	−38204.5	+	10307.3i	−0.0831897	+	0.0224440i
$185$		−	18251.8i		−	0.0392081i
$186$	−91619.0	−	251273.i	−0.194179	−	0.532553i
$187$	941244.	−	941244.i	1.96833	−	1.96833i
$188$	−166181.	−	197586.i	−0.342915	−	0.407720i
$189$	−110058.	−	110058.i	−0.224114	−	0.224114i
$190$	98308.6	+	45773.5i	0.197564	+	0.0919877i
$191$	−929181.			−1.84297			−0.921483	−	0.388420i	$-0.873021\pi$
$191$	−929181.			−1.84297			−0.921483	+	0.388420i	$0.873021\pi$
$192$	285124.	+	75348.7i	0.558188	+	0.147510i
$193$	771455.			1.49079			0.745397	−	0.666621i	$-0.232260\pi$
$193$	771455.			1.49079			0.745397	+	0.666621i	$0.232260\pi$
$194$	396758.	+	184735.i	0.756870	+	0.352406i
$195$	−60732.1	−	60732.1i	−0.114375	−	0.114375i
$196$	−592749.	−	704768.i	−1.10212	−	1.31041i
$197$	77950.9	−	77950.9i	0.143105	−	0.143105i	−0.631925	−	0.775030i	$-0.717735\pi$
$197$	77950.9	−	77950.9i	0.143105	−	0.143105i	0.775030	+	0.631925i	$0.217735\pi$
$198$	92524.2	+	253755.i	0.167723	+	0.459994i
$199$			1.04073e6i			1.86296i	0.363786	+	0.931482i	$0.381484\pi$
$199$			1.04073e6i			1.86296i	−0.363786	+	0.931482i	$0.618516\pi$
$200$	490395.	−	132305.i	0.866903	−	0.233885i
$201$			502555.i			0.877391i
$202$	−577370.	+	210520.i	−0.995579	+	0.363008i
$203$	−483746.	+	483746.i	−0.823905	+	0.823905i
$204$	−55939.3	+	647943.i	−0.0941112	+	1.09009i
$205$	99732.3	+	99732.3i	0.165749	+	0.165749i
$206$	−55835.2	+	119918.i	−0.0916726	+	0.196887i
$207$	17706.4			0.0287214
$208$	−447422.	+	314819.i	−0.717065	+	0.504549i
$209$	632624.			1.00180
$210$	81956.2	−	176019.i	0.128243	−	0.275430i
$211$	−475900.	−	475900.i	−0.735885	−	0.735885i	0.235894	−	0.971779i	$-0.424198\pi$
$211$	−475900.	−	475900.i	−0.735885	−	0.735885i	−0.971779	+	0.235894i	$0.924198\pi$
$212$	−539359.	−	46564.8i	−0.824211	−	0.0711571i
$213$	−244858.	+	244858.i	−0.369799	+	0.369799i
$214$	36311.1	−	13239.7i	0.0542007	−	0.0197626i
$215$		−	412250.i		−	0.608225i
$216$	−114397.	−	65784.9i	−0.166832	−	0.0959383i
$217$			1.12162e6i			1.61694i
$218$	202129.	+	554357.i	0.288063	+	0.790038i
$219$	−117928.	+	117928.i	−0.166153	+	0.166153i
$220$	−257861.	+	216875.i	−0.359194	+	0.302102i
$221$	−853087.	−	853087.i	−1.17493	−	1.17493i
$222$	47160.1	+	21958.2i	0.0642232	+	0.0299030i
$223$	1.05418e6			1.41956			0.709781	−	0.704423i	$-0.248794\pi$
$223$	1.05418e6			1.41956			0.709781	+	0.704423i	$0.248794\pi$
$224$	−1.01512e6	−	706471.i	−1.35176	−	0.940750i
$225$	−227281.			−0.299300
$226$	95893.8	+	44649.1i	0.124888	+	0.0581489i
$227$	330999.	+	330999.i	0.426346	+	0.426346i	0.887382	−	0.461036i	$-0.152522\pi$
$227$	330999.	+	330999.i	0.426346	+	0.426346i	−0.461036	+	0.887382i	$0.652522\pi$
$228$	−236545.	+	198947.i	−0.301354	+	0.253455i
$229$	−492611.	+	492611.i	−0.620748	+	0.620748i	−0.945723	−	0.324975i	$-0.894644\pi$
$229$	−492611.	+	492611.i	−0.620748	+	0.620748i	0.324975	+	0.945723i	$0.394644\pi$
$230$	7566.51	+	20751.8i	0.00943140	+	0.0258664i
$231$		−	1.13270e6i		−	1.39664i
$232$	−289148.	+	502814.i	−0.352696	+	0.613320i
$233$		−	532533.i		−	0.642624i	−0.946973	−	0.321312i	$-0.895876\pi$
$233$		−	532533.i		−	0.642624i	0.946973	−	0.321312i	$-0.104124\pi$
$234$	229989.	−	83858.4i	0.274579	−	0.100117i
$235$	−101905.	+	101905.i	−0.120372	+	0.120372i
$236$	595685.	+	51427.6i	0.696204	+	0.0601058i
$237$	−10994.6	−	10994.6i	−0.0127147	−	0.0127147i
$238$	1.15122e6	−	2.47249e6i	1.31739	−	2.82939i
$239$	735676.			0.833090			0.416545	−	0.909115i	$-0.363241\pi$
$239$	735676.			0.833090			0.416545	+	0.909115i	$0.363241\pi$
$240$	28214.1	−	162184.i	0.0316183	−	0.181752i
$241$	−978367.			−1.08507			−0.542537	−	0.840032i	$-0.682536\pi$
$241$	−978367.			−1.08507			−0.542537	+	0.840032i	$0.682536\pi$
$242$	−445128.	+	956010.i	−0.488592	+	1.04936i
$243$	41753.9	+	41753.9i	0.0453609	+	0.0453609i
$244$	−59911.0	+	693948.i	−0.0644217	+	0.746195i
$245$	−363483.	+	363483.i	−0.386874	+	0.386874i
$246$	−377680.	+	137709.i	−0.397911	+	0.145086i
$247$		−	573373.i		−	0.597991i
$248$	247703.	+	918123.i	0.255742	+	0.947920i
$249$		−	421323.i		−	0.430642i
$250$	−205292.	−	563031.i	−0.207741	−	0.569748i
$251$	−821882.	+	821882.i	−0.823427	+	0.823427i	−0.986598	−	0.163171i	$-0.947828\pi$
$251$	−821882.	+	821882.i	−0.823427	+	0.823427i	0.163171	+	0.986598i	$0.447828\pi$
$252$	356210.	+	423527.i	0.353350	+	0.420127i
$253$	91115.3	+	91115.3i	0.0894932	+	0.0894932i
$254$	1.66235e6	+	774009.i	1.61674	+	0.752769i
$255$	363027.			0.349614
$256$	−986973.	−	354112.i	−0.941251	−	0.337707i
$257$	−609538.			−0.575662			−0.287831	−	0.957681i	$-0.592934\pi$
$257$	−609538.			−0.575662			−0.287831	+	0.957681i	$0.592934\pi$
$258$	1.06520e6	+	495967.i	0.996280	+	0.463878i
$259$	−154263.	−	154263.i	−0.142893	−	0.142893i
$260$	196563.	+	233709.i	0.180330	+	0.214409i
$261$	183523.	−	183523.i	0.166759	−	0.166759i
$262$	230200.	+	631343.i	0.207182	+	0.568214i
$263$		−	1.17966e6i		−	1.05164i	−0.850595	−	0.525821i	$-0.823758\pi$
$263$		−	1.17966e6i		−	1.05164i	0.850595	−	0.525821i	$-0.176242\pi$
$264$	−250151.	−	927194.i	−0.220898	−	0.818768i
$265$			302190.i			0.264341i
$266$	1.21777e6	−	444024.i	1.05527	−	0.384771i
$267$	−457009.	+	457009.i	−0.392326	+	0.392326i
$268$	153694.	−	1.78024e6i	0.130714	−	1.51405i
$269$	1.16117e6	+	1.16117e6i	0.978401	+	0.978401i	0.999772	−	0.0213711i	$-0.00680314\pi$
$269$	1.16117e6	+	1.16117e6i	0.978401	+	0.978401i	−0.0213711	+	0.999772i	$0.506803\pi$
$270$	−31092.5	+	66778.0i	−0.0259565	+	0.0557473i
$271$	−915264.			−0.757047			−0.378524	−	0.925592i	$-0.623568\pi$
$271$	−915264.			−0.757047			−0.378524	+	0.925592i	$0.623568\pi$
$272$	396316.	−	2.27815e6i	0.324803	−	1.86707i
$273$	−1.02661e6			−0.833678
$274$	−520214.	+	1.11727e6i	−0.418606	+	0.899049i
$275$	−1.16956e6	−	1.16956e6i	−0.932591	−	0.932591i
$276$	−62722.9	−	5415.09i	−0.0495625	−	0.00427891i
$277$	−1.48010e6	+	1.48010e6i	−1.15902	+	1.15902i	−0.174332	+	0.984687i	$0.555777\pi$
$277$	−1.48010e6	+	1.48010e6i	−1.15902	+	1.15902i	−0.984687	+	0.174332i	$0.944223\pi$
$278$	908857.	−	331387.i	0.705316	−	0.257172i
$279$		−	425518.i		−	0.327271i
$280$	−344151.	+	598461.i	−0.262334	+	0.456185i
$281$			1.73789e6i			1.31297i	0.754339	+	0.656486i	$0.227958\pi$
$281$			1.73789e6i			1.31297i	−0.754339	+	0.656486i	$0.772042\pi$
$282$	−140709.	−	385908.i	−0.105366	−	0.288975i
$283$	−515036.	+	515036.i	−0.382271	+	0.382271i	−0.871920	−	0.489649i	$-0.837125\pi$
$283$	−515036.	+	515036.i	−0.382271	+	0.382271i	0.489649	+	0.871920i	$0.337125\pi$
$284$	942265.	−	792497.i	0.693230	−	0.583044i
$285$	121998.	+	121998.i	0.0889693	+	0.0889693i
$286$	1.61502e6	+	751970.i	1.16752	+	0.543608i
$287$	1.68586e6			1.20814
$288$	385118.	+	268021.i	0.273598	+	0.190409i
$289$	3.67948e6			2.59145
$290$	293513.	+	136663.i	0.204943	+	0.0954233i
$291$	492364.	+	492364.i	0.340843	+	0.340843i
$292$	453812.	−	381681.i	0.311472	−	0.261965i
$293$	800711.	−	800711.i	0.544887	−	0.544887i	−0.380070	−	0.924958i	$-0.624100\pi$
$293$	800711.	−	800711.i	0.544887	−	0.544887i	0.924958	+	0.380070i	$0.124100\pi$
$294$	−501895.	−	1.37649e6i	−0.338645	−	0.928762i
$295$		−	333748.i		−	0.223287i
$296$	−160344.	−	92207.1i	−0.106371	−	0.0611695i
$297$			429722.i			0.282681i
$298$	−2.61549e6	+	953659.i	−1.70613	+	0.622089i
$299$	82581.5	−	82581.5i	0.0534201	−	0.0534201i
$300$	805115.	+	69508.4i	0.516481	+	0.0445897i
$301$	−3.48431e6	−	3.48431e6i	−2.21667	−	2.21667i
$302$	473961.	−	1.01793e6i	0.299037	−	0.642248i
$303$	−977747.			−0.611815
$304$	898775.	−	632405.i	0.557785	−	0.392475i
$305$	388802.			0.239320
$306$	−436748.	+	938013.i	−0.266641	+	0.572671i
$307$	−846214.	−	846214.i	−0.512430	−	0.512430i	0.402840	−	0.915270i	$-0.368023\pi$
$307$	−846214.	−	846214.i	−0.512430	−	0.512430i	−0.915270	+	0.402840i	$0.868023\pi$
$308$	−346408.	+	4.01244e6i	−0.208071	+	2.41008i
$309$	−148815.	+	148815.i	−0.0886646	+	0.0886646i
$310$	498703.	−	181837.i	0.294739	−	0.107468i
$311$		−	1.32240e6i		−	0.775283i	−0.921810	−	0.387642i	$-0.873290\pi$
$311$		−	1.32240e6i		−	0.775283i	0.921810	−	0.387642i	$-0.126710\pi$
$312$	−840353.	+	226722.i	−0.488737	+	0.131858i
$313$		−	70206.7i		−	0.0405058i	−0.999795	−	0.0202529i	$-0.993553\pi$
$313$		−	70206.7i		−	0.0405058i	0.999795	−	0.0202529i	$-0.00644715\pi$
$314$	−154184.	−	422863.i	−0.0882501	−	0.242033i
$315$	218434.	−	218434.i	0.124035	−	0.124035i
$316$	35584.5	+	42309.3i	0.0200467	+	0.0238352i
$317$	−32380.8	−	32380.8i	−0.0180984	−	0.0180984i	0.698000	−	0.716098i	$-0.254074\pi$
$317$	−32380.8	−	32380.8i	−0.0180984	−	0.0180984i	−0.716098	+	0.698000i	$0.754074\pi$
$318$	−780818.	−	363557.i	−0.432994	−	0.201606i
$319$	1.88878e6			1.03921
$320$	−149545.	+	565888.i	−0.0816390	+	0.308927i
$321$	61491.0			0.0333080
$322$	239345.	+	111441.i	0.128642	+	0.0598972i
$323$	1.71367e6	+	1.71367e6i	0.913947	+	0.913947i
$324$	−135139.	−	160678.i	−0.0715184	−	0.0850341i
$325$	−1.06002e6	+	1.06002e6i	−0.556680	+	0.556680i
$326$	−496871.	−	1.36271e6i	−0.258940	−	0.710166i
$327$			938776.i			0.485504i
$328$	1.38000e6	−	372315.i	0.708263	−	0.191085i
$329$			1.72259e6i			0.877389i
$330$	−503631.	+	183634.i	−0.254582	+	0.0928255i
$331$	896229.	−	896229.i	0.449623	−	0.449623i	−0.445606	−	0.895229i	$-0.647012\pi$
$331$	896229.	−	896229.i	0.449623	−	0.449623i	0.895229	+	0.445606i	$0.147012\pi$
$332$	−128852.	+	1.49248e6i	−0.0641571	+	0.743130i
$333$	58524.2	+	58524.2i	0.0289218	+	0.0289218i
$334$	−635964.	+	1.36587e6i	−0.311937	+	0.669952i
$335$	−997425.			−0.485588
$336$	−1.13230e6	−	1.60923e6i	−0.547161	−	0.777626i
$337$	3.42998e6			1.64519			0.822595	−	0.568627i	$-0.192525\pi$
$337$	3.42998e6			1.64519			0.822595	+	0.568627i	$0.192525\pi$
$338$	−205015.	+	440314.i	−0.0976097	+	0.209638i
$339$	119001.	+	119001.i	0.0562409	+	0.0562409i
$340$	−1.28598e6	−	111023.i	−0.603304	−	0.0520854i
$341$	2.18967e6	−	2.18967e6i	1.01975	−	1.01975i
$342$	−461999.	+	168454.i	−0.213587	+	0.0778781i
$343$			2.55588e6i			1.17302i
$344$	−3.62166e6	−	2.08267e6i	−1.65010	−	0.948908i
$345$			35142.1i			0.0158957i
$346$	−582878.	−	1.59859e6i	−0.261750	−	0.717872i
$347$	−834902.	+	834902.i	−0.372231	+	0.372231i	−0.868289	−	0.496059i	$-0.834780\pi$
$347$	−834902.	+	834902.i	−0.372231	+	0.372231i	0.496059	+	0.868289i	$0.334780\pi$
$348$	−706235.	+	593983.i	−0.312609	+	0.262921i
$349$	−1.13588e6	−	1.13588e6i	−0.499192	−	0.499192i	0.411994	−	0.911186i	$-0.364832\pi$
$349$	−1.13588e6	−	1.13588e6i	−0.499192	−	0.499192i	−0.911186	+	0.411994i	$0.864832\pi$
$350$	−3.07224e6	−	1.43047e6i	−1.34056	−	0.624177i
$351$	389474.			0.168737
$352$	602568.	+	3.36098e6i	0.259209	+	1.44580i
$353$	−3.07447e6			−1.31321			−0.656605	−	0.754235i	$-0.728008\pi$
$353$	−3.07447e6			−1.31321			−0.656605	+	0.754235i	$0.728008\pi$
$354$	862360.	+	401523.i	0.365747	+	0.170295i
$355$	−485972.	−	485972.i	−0.204664	−	0.204664i
$356$	1.75867e6	−	1.47913e6i	0.735459	−	0.618561i
$357$	3.06828e6	−	3.06828e6i	1.27416	−	1.27416i
$358$	−51177.4	−	140358.i	−0.0211043	−	0.0578803i
$359$			101127.i			0.0414123i	0.999786	+	0.0207062i	$0.00659144\pi$
$359$			101127.i			0.0414123i	−0.999786	+	0.0207062i	$0.993409\pi$
$360$	130564.	−	227044.i	0.0530966	−	0.0923324i
$361$		−	1.32431e6i		−	0.534839i
$362$	−1.23730e6	+	451143.i	−0.496252	+	0.180943i
$363$	−1.18638e6	+	1.18638e6i	−0.472560	+	0.472560i
$364$	3.63664e6	+	313964.i	1.43862	+	0.124201i
$365$	−234053.	−	234053.i	−0.0919564	−	0.0919564i
$366$	−467758.	+	1.00461e6i	−0.182523	+	0.392009i
$367$	−3.89710e6			−1.51035			−0.755173	−	0.655525i	$-0.772447\pi$
$367$	−3.89710e6			−1.51035			−0.755173	+	0.655525i	$0.772447\pi$
$368$	220532.	+	38364.6i	0.0848892	+	0.0147677i
$369$	−639582.			−0.244529
$370$	−43580.7	+	93599.1i	−0.0165497	+	0.0355441i
$371$	2.55409e6	+	2.55409e6i	0.963389	+	0.963389i
$372$	−130135.	+	1.50735e6i	−0.0487568	+	0.564749i
$373$	1.34820e6	−	1.34820e6i	0.501743	−	0.501743i	−0.410236	−	0.911979i	$-0.634554\pi$
$373$	1.34820e6	−	1.34820e6i	0.501743	−	0.501743i	0.911979	+	0.410236i	$0.134554\pi$
$374$	−7.07436e6	+	2.57945e6i	−2.61522	+	0.953560i
$375$		−	953466.i		−	0.350128i
$376$	380426.	+	1.41006e6i	0.138771	+	0.514362i
$377$		−	1.71188e6i		−	0.620325i
$378$	301612.	+	827196.i	0.108572	+	0.297769i
$379$	−2.10804e6	+	2.10804e6i	−0.753842	+	0.753842i	−0.975194	−	0.221352i	$-0.928953\pi$
$379$	−2.10804e6	+	2.10804e6i	−0.753842	+	0.753842i	0.221352	+	0.975194i	$0.428953\pi$
$380$	−394853.	−	469473.i	−0.140274	−	0.166783i
$381$	2.06293e6	+	2.06293e6i	0.728068	+	0.728068i
$382$	4.76505e6	+	2.21865e6i	1.67074	+	0.777913i
$383$	3.42898e6			1.19445			0.597225	−	0.802073i	$-0.296270\pi$
$383$	3.42898e6			1.19445			0.597225	+	0.802073i	$0.296270\pi$
$384$	−1.28226e6	−	1.06721e6i	−0.443761	−	0.369336i
$385$	2.24807e6			0.772963
$386$	−3.95619e6	−	1.84204e6i	−1.35148	−	0.629262i
$387$	1.32188e6	+	1.32188e6i	0.448656	+	0.448656i
$388$	−1.59356e6	−	1.89472e6i	−0.537390	−	0.638948i
$389$	−3.49620e6	+	3.49620e6i	−1.17145	+	1.17145i	−0.189580	+	0.981865i	$0.560713\pi$
$389$	−3.49620e6	+	3.49620e6i	−1.17145	+	1.17145i	−0.981865	+	0.189580i	$0.939287\pi$
$390$	166434.	+	456461.i	0.0554092	+	0.151964i
$391$			493632.i			0.163291i
$392$	1.35694e6	+	5.02954e6i	0.446009	+	1.65315i
$393$			1.06915e6i			0.349185i
$394$	−585877.	+	213622.i	−0.190137	+	0.0693275i
$395$	21821.0	−	21821.0i	0.00703691	−	0.00703691i
$396$	131420.	−	1.52224e6i	0.0421138	−	0.487803i
$397$	232390.	+	232390.i	0.0740016	+	0.0740016i	0.743139	−	0.669137i	$-0.233336\pi$
$397$	232390.	+	232390.i	0.0740016	+	0.0740016i	−0.669137	+	0.743139i	$0.733336\pi$
$398$	2.48500e6	−	5.33708e6i	0.786355	−	1.68887i
$399$	2.06224e6			0.648495
$400$	−2.83076e6	−	492450.i	−0.884613	−	0.153891i
$401$	740282.			0.229898			0.114949	−	0.993371i	$-0.463329\pi$
$401$	740282.			0.229898			0.114949	+	0.993371i	$0.463329\pi$
$402$	1.19998e6	−	2.57721e6i	0.370346	−	0.795399i
$403$	−1.98458e6	−	1.98458e6i	−0.608705	−	0.608705i
$404$	3.46355e6	+	299021.i	1.05577	+	0.0911482i
$405$	−82869.4	+	82869.4i	−0.0251048	+	0.0251048i
$406$	3.63582e6	−	1.32569e6i	1.09468	−	0.399142i
$407$			602318.i			0.180235i
$408$	1.83400e6	−	3.18923e6i	0.545441	−	0.948495i
$409$		−	1.78885e6i		−	0.528767i	−0.964418	−	0.264384i	$-0.914831\pi$
$409$		−	1.78885e6i		−	0.528767i	0.964418	−	0.264384i	$-0.0851685\pi$
$410$	−273313.	−	749585.i	−0.0802973	−	0.220222i
$411$	−1.38650e6	+	1.38650e6i	−0.404870	+	0.404870i
$412$	572670.	−	481647.i	0.166212	−	0.139793i
$413$	−2.82082e6	−	2.82082e6i	−0.813767	−	0.813767i
$414$	−90802.5	−	42278.6i	−0.0260374	−	0.0121233i
$415$	836203.			0.238337
$416$	3.04619e6	−	546131.i	0.863025	−	0.154726i
$417$	1.53910e6			0.433439
$418$	−3.24424e6	−	1.51055e6i	−0.908180	−	0.422858i
$419$	668440.	+	668440.i	0.186006	+	0.186006i	0.793967	−	0.607961i	$-0.208012\pi$
$419$	668440.	+	668440.i	0.186006	+	0.186006i	−0.607961	+	0.793967i	$0.708012\pi$
$420$	−840579.	+	706973.i	−0.232517	+	0.195560i
$421$	3.50469e6	−	3.50469e6i	0.963705	−	0.963705i	−0.0356589	−	0.999364i	$-0.511353\pi$
$421$	3.50469e6	−	3.50469e6i	0.963705	−	0.963705i	0.999364	+	0.0356589i	$0.0113530\pi$
$422$	1.30419e6	+	3.57685e6i	0.356500	+	0.977732i
$423$		−	653515.i		−	0.177584i
$424$	2.65477e6	+	1.52665e6i	0.717153	+	0.412406i
$425$		−	6.33628e6i		−	1.70162i
$426$	1.84035e6	−	671027.i	0.491333	−	0.179150i
$427$	3.28614e6	−	3.28614e6i	0.872199	−	0.872199i
$428$	−217824.	−	18805.6i	−0.0574774	−	0.00496223i
$429$	2.00419e6	+	2.00419e6i	0.525770	+	0.525770i
$430$	−984350.	+	2.11411e6i	−0.256731	+	0.551386i
$431$	−1.70105e6			−0.441087			−0.220544	−	0.975377i	$-0.570783\pi$
$431$	−1.70105e6			−0.441087			−0.220544	+	0.975377i	$0.570783\pi$
$432$	429573.	+	610510.i	0.110746	+	0.157392i
$433$	−5.58590e6			−1.43177			−0.715885	−	0.698218i	$-0.753977\pi$
$433$	−5.58590e6			−1.43177			−0.715885	+	0.698218i	$0.753977\pi$
$434$	2.67814e6	−	5.75189e6i	0.682509	−	1.46584i
$435$	364240.	+	364240.i	0.0922922	+	0.0922922i
$436$	287102.	−	3.32550e6i	0.0723303	−	0.837801i
$437$	−165889.	+	165889.i	−0.0415540	+	0.0415540i
$438$	886345.	−	323179.i	0.220758	−	0.0804928i
$439$			7.43169e6i			1.84046i	0.391378	+	0.920230i	$0.371999\pi$
$439$			7.43169e6i			1.84046i	−0.391378	+	0.920230i	$0.628001\pi$
$440$	1.84021e6	−	496476.i	0.453144	−	0.122255i
$441$		−	2.33102e6i		−	0.570754i
$442$	2.33786e6	+	6.41178e6i	0.569197	+	1.56107i
$443$	3.67896e6	−	3.67896e6i	0.890669	−	0.890669i	−0.103917	−	0.994586i	$-0.533138\pi$
$443$	3.67896e6	−	3.67896e6i	0.890669	−	0.890669i	0.994586	+	0.103917i	$0.0331376\pi$
$444$	−189417.	−	225213.i	−0.0455996	−	0.0542171i
$445$	−907030.	−	907030.i	−0.217131	−	0.217131i
$446$	−5.40609e6	−	2.51713e6i	−1.28690	−	0.599195i
$447$	−4.42921e6			−1.04847
$448$	3.51891e6	+	6.04680e6i	0.828348	+	1.42341i
$449$	−4.31863e6			−1.01095			−0.505476	−	0.862841i	$-0.668683\pi$
$449$	−4.31863e6			−1.01095			−0.505476	+	0.862841i	$0.668683\pi$
$450$	1.16555e6	+	542690.i	0.271330	+	0.126334i
$451$	−3.29122e6	−	3.29122e6i	−0.761930	−	0.761930i
$452$	−385153.	−	457941.i	−0.0886722	−	0.105430i
$453$	1.26322e6	−	1.26322e6i	0.289225	−	0.289225i
$454$	−907093.	−	2.48778e6i	−0.206544	−	0.566464i
$455$		−	2.03752e6i		−	0.461395i
$456$	1.68809e6	−	455436.i	0.380175	−	0.102569i
$457$		−	2.08389e6i		−	0.466751i	−0.972387	−	0.233375i	$-0.925023\pi$
$457$		−	2.08389e6i		−	0.466751i	0.972387	−	0.233375i	$-0.0749771\pi$
$458$	3.70245e6	−	1.34998e6i	0.824755	−	0.300722i
$459$	−1.16404e6	+	1.16404e6i	−0.257892	+	0.257892i
$460$	10747.4	−	124487.i	0.00236814	−	0.0274302i
$461$	6.40698e6	+	6.40698e6i	1.40411	+	1.40411i	0.786429	+	0.617681i	$0.211928\pi$
$461$	6.40698e6	+	6.40698e6i	1.40411	+	1.40411i	0.617681	+	0.786429i	$0.288072\pi$
$462$	−2.70460e6	+	5.80872e6i	−0.589519	+	1.26612i
$463$	−3.80770e6			−0.825488			−0.412744	−	0.910847i	$-0.635430\pi$
$463$	−3.80770e6			−0.825488			−0.412744	+	0.910847i	$0.635430\pi$
$464$	2.68341e6	−	1.88813e6i	0.578618	−	0.407133i
$465$	844529.			0.181127
$466$	−1.27156e6	+	2.73095e6i	−0.271251	+	0.582571i
$467$	−1.98709e6	−	1.98709e6i	−0.421624	−	0.421624i	0.464139	−	0.885762i	$-0.346364\pi$
$467$	−1.98709e6	−	1.98709e6i	−0.421624	−	0.421624i	−0.885762	+	0.464139i	$0.846364\pi$
$468$	−1.37967e6	−	119111.i	−0.291178	−	0.0251385i
$469$	−8.43018e6	+	8.43018e6i	−1.76972	+	1.76972i
$470$	765914.	−	279267.i	0.159932	−	0.0583144i
$471$		−	716097.i		−	0.148737i
$472$	−2.93201e6	−	1.68608e6i	−0.605773	−	0.348356i
$473$			1.36045e7i			2.79594i
$474$	30130.3	+	82634.8i	0.00615966	+	0.0168934i
$475$	2.12936e6	−	2.12936e6i	0.433026	−	0.433026i
$476$	−1.18074e7	+	9.93066e6i	−2.38856	+	2.00891i
$477$	−968970.	−	968970.i	−0.194991	−	0.194991i
$478$	−3.77271e6	−	1.75661e6i	−0.755238	−	0.351646i
$479$	−5.29674e6			−1.05480			−0.527400	−	0.849617i	$-0.676833\pi$
$479$	−5.29674e6			−1.05480			−0.527400	+	0.849617i	$0.676833\pi$
$480$	−531943.	+	764346.i	−0.105381	+	0.151421i
$481$	545905.			0.107586
$482$	5.01728e6	+	2.33610e6i	0.983673	+	0.458008i
$483$	297019.	+	297019.i	0.0579318	+	0.0579318i
$484$	4.56543e6	−	3.83978e6i	0.885866	−	0.745062i
$485$	−977200.	+	977200.i	−0.188638	+	0.188638i
$486$	−114425.	−	313821.i	−0.0219752	−	0.0602687i
$487$			6.57579e6i			1.25639i	0.778055	+	0.628197i	$0.216207\pi$
$487$			6.57579e6i			1.25639i	−0.778055	+	0.628197i	$0.783793\pi$
$488$	1.96421e6	−	3.41567e6i	0.373370	−	0.649271i
$489$		−	2.30768e6i		−	0.436419i
$490$	2.73193e6	−	996115.i	0.514019	−	0.187422i
$491$	−1.73881e6	+	1.73881e6i	−0.325497	+	0.325497i	−0.850871	−	0.525374i	$-0.823925\pi$
$491$	−1.73881e6	+	1.73881e6i	−0.325497	+	0.325497i	0.525374	+	0.850871i	$0.323925\pi$
$492$	2.26564e6	+	195601.i	0.421967	+	0.0364299i
$493$	5.11638e6	+	5.11638e6i	0.948082	+	0.948082i
$494$	−1.36907e6	+	2.94038e6i	−0.252411	+	0.542109i
$495$	−852873.			−0.156449
$496$	921972.	−	5.29979e6i	0.168273	−	0.967285i
$497$	−8.21482e6			−1.49179
$498$	−1.00601e6	+	2.16064e6i	−0.181774	+	0.390399i
$499$	−1.24229e6	−	1.24229e6i	−0.223343	−	0.223343i	0.586561	−	0.809905i	$-0.300481\pi$
$499$	−1.24229e6	−	1.24229e6i	−0.223343	−	0.223343i	−0.809905	+	0.586561i	$0.800481\pi$
$500$	−291595.	+	3.37754e6i	−0.0521621	+	0.604192i
$501$	−1.69500e6	+	1.69500e6i	−0.301701	+	0.301701i
$502$	6.17724e6	−	2.25234e6i	1.09405	−	0.398910i
$503$		−	5.60295e6i		−	0.987408i	−0.869630	−	0.493704i	$-0.835643\pi$
$503$		−	5.60295e6i		−	0.987408i	0.869630	−	0.493704i	$-0.164357\pi$
$504$	−815445.	−	3.02248e6i	−0.142994	−	0.530014i
$505$		−	1.94054e6i		−	0.338606i
$506$	−249699.	−	684820.i	−0.0433551	−	0.118905i
$507$	−546416.	+	546416.i	−0.0944068	+	0.0944068i
$508$	−6.67678e6	−	7.93857e6i	−1.14791	−	1.36484i
$509$	92100.4	+	92100.4i	0.0157568	+	0.0157568i	0.714941	−	0.699185i	$-0.246453\pi$
$509$	92100.4	+	92100.4i	0.0157568	+	0.0157568i	−0.699185	+	0.714941i	$0.746453\pi$
$510$	−1.86168e6	−	866818.i	−0.316942	−	0.147571i
$511$	−3.95641e6			−0.670268
$512$	4.21589e6	+	4.17261e6i	0.710745	+	0.703449i
$513$	−782372.			−0.131256
$514$	3.12584e6	+	1.45542e6i	0.521867	+	0.242986i
$515$	−295354.	−	295354.i	−0.0490710	−	0.0490710i
$516$	−4.27833e6	−	5.08686e6i	−0.707375	−	0.841057i
$517$	3.36292e6	−	3.36292e6i	0.553337	−	0.553337i
$518$	422753.	+	1.15944e6i	0.0692248	+	0.189855i
$519$		−	2.70713e6i		−	0.441155i
$520$	−449976.	−	1.66786e6i	−0.0729762	−	0.270489i
$521$		−	5.65637e6i		−	0.912943i	−0.889738	−	0.456472i	$-0.849113\pi$
$521$		−	5.65637e6i		−	0.912943i	0.889738	−	0.456472i	$-0.150887\pi$
$522$	−1.37936e6	+	502940.i	−0.221564	+	0.0807867i
$523$	3.45835e6	−	3.45835e6i	0.552859	−	0.552859i	−0.374406	−	0.927265i	$-0.622153\pi$
$523$	3.45835e6	−	3.45835e6i	0.552859	−	0.552859i	0.927265	+	0.374406i	$0.122153\pi$
$524$	326973.	−	3.78732e6i	0.0520216	−	0.602565i
$525$	−3.81255e6	−	3.81255e6i	−0.603695	−	0.603695i
$526$	−2.81674e6	+	6.04956e6i	−0.443896	+	0.953365i
$527$	1.18629e7			1.86064
$528$	−931081.	+	5.35215e6i	−0.145346	+	0.835495i
$529$	6.38856e6			0.992576
$530$	721554.	−	1.54970e6i	0.111578	−	0.239639i
$531$	1.07016e6	+	1.07016e6i	0.164707	+	0.164707i
$532$	−7.30523e6	−	630687.i	−1.11906	−	0.0966128i
$533$	−2.98296e6	+	2.98296e6i	−0.454810	+	0.454810i
$534$	3.43487e6	−	1.25242e6i	0.521263	−	0.190063i
$535$			122042.i			0.0184342i
$536$	−5.03895e6	+	8.76248e6i	−0.757579	+	1.31739i
$537$		−	237690.i		−	0.0355693i
$538$	−3.18216e6	−	8.72735e6i	−0.473987	−	1.29995i
$539$	1.19951e7	−	1.19951e7i	1.77842	−	1.77842i
$540$	318899.	−	268211.i	0.0470618	−	0.0395815i
$541$	3.83860e6	+	3.83860e6i	0.563871	+	0.563871i	0.930405	−	0.366534i	$-0.119456\pi$
$541$	3.83860e6	+	3.83860e6i	0.563871	+	0.563871i	−0.366534	+	0.930405i	$0.619456\pi$
$542$	4.69368e6	+	2.18542e6i	0.686301	+	0.319549i
$543$	−2.09530e6			−0.304963
$544$	−7.47206e6	+	1.07366e7i	−1.08254	+	1.55549i
$545$	−1.86320e6			−0.268700
$546$	5.26467e6	+	2.45128e6i	0.755770	+	0.351894i
$547$	1.01026e6	+	1.01026e6i	0.144366	+	0.144366i	0.775596	−	0.631230i	$-0.217450\pi$
$547$	1.01026e6	+	1.01026e6i	0.144366	+	0.144366i	−0.631230	+	0.775596i	$0.717450\pi$
$548$	5.33554e6	−	4.48749e6i	0.758975	−	0.638339i
$549$	−1.24669e6	+	1.24669e6i	−0.176534	+	0.176534i
$550$	3.20515e6	+	8.79039e6i	0.451795	+	1.23909i
$551$			3.43880e6i			0.482534i
$552$	308727.	+	177536.i	0.0431248	+	0.0247993i
$553$		−	368860.i		−	0.0512919i
$554$	1.11244e7	−	4.05616e6i	1.53993	−	0.561488i
$555$	−116153.	+	116153.i	−0.0160066	+	0.0160066i
$556$	−5.45209e6	−	470698.i	−0.747956	−	0.0645737i
$557$	3.61545e6	+	3.61545e6i	0.493769	+	0.493769i	0.909492	−	0.415722i	$-0.136471\pi$
$557$	3.61545e6	+	3.61545e6i	0.493769	+	0.493769i	−0.415722	+	0.909492i	$0.636471\pi$
$558$	−1.01603e6	+	2.18215e6i	−0.138141	+	0.296687i
$559$	1.23303e7			1.66895
$560$	3.19386e6	−	2.24730e6i	0.430374	−	0.302824i
$561$	−1.19801e7			−1.60714
$562$	4.14964e6	−	8.91226e6i	0.554203	−	1.19027i
$563$	2.71462e6	+	2.71462e6i	0.360942	+	0.360942i	0.864160	−	0.503218i	$-0.167851\pi$
$563$	2.71462e6	+	2.71462e6i	0.360942	+	0.360942i	−0.503218	+	0.864160i	$0.667851\pi$
$564$	−199862.	+	2.31500e6i	−0.0264565	+	0.306445i
$565$	−236183.	+	236183.i	−0.0311263	+	0.0311263i
$566$	3.87100e6	−	1.41144e6i	0.507904	−	0.185192i
$567$			1.40082e6i			0.182988i
$568$	−6.72443e6	+	1.81420e6i	−0.874550	+	0.235948i
$569$		−	1.49148e6i		−	0.193124i	−0.995327	−	0.0965619i	$-0.969215\pi$
$569$		−	1.49148e6i		−	0.193124i	0.995327	−	0.0965619i	$-0.0307846\pi$
$570$	−334332.	−	916933.i	−0.0431013	−	0.118209i
$571$	4.63869e6	−	4.63869e6i	0.595394	−	0.595394i	−0.343689	−	0.939083i	$-0.611677\pi$
$571$	4.63869e6	−	4.63869e6i	0.595394	−	0.595394i	0.939083	+	0.343689i	$0.111677\pi$
$572$	−6.48667e6	−	7.71254e6i	−0.828956	−	0.985615i
$573$	5.91327e6	+	5.91327e6i	0.752387	+	0.752387i
$574$	−8.64548e6	−	4.02542e6i	−1.09524	−	0.509955i
$575$	613372.			0.0773667
$576$	−1.33500e6	−	2.29403e6i	−0.167659	−	0.288100i
$577$	4.21405e6			0.526939			0.263469	−	0.964668i	$-0.415133\pi$
$577$	4.21405e6			0.526939			0.263469	+	0.964668i	$0.415133\pi$
$578$	−1.88692e7	−	8.78569e6i	−2.34928	−	1.09385i
$579$	−4.90951e6	−	4.90951e6i	−0.608614	−	0.608614i
$580$	−1.17888e6	−	1.40167e6i	−0.145513	−	0.173012i
$581$	7.06754e6	−	7.06754e6i	0.868616	−	0.868616i
$582$	−1.34931e6	−	3.70060e6i	−0.165122	−	0.452860i
$583$		−	9.97242e6i		−	1.21515i
$584$	−3.23860e6	+	873753.i	−0.392940	+	0.106012i
$585$			772993.i			0.0933869i
$586$	−6.01812e6	+	2.19432e6i	−0.723964	+	0.263971i
$587$	−2.61374e6	+	2.61374e6i	−0.313089	+	0.313089i	−0.846105	−	0.533016i	$-0.821058\pi$
$587$	−2.61374e6	+	2.61374e6i	−0.313089	+	0.313089i	0.533016	+	0.846105i	$0.321058\pi$
$588$	−712886.	+	8.25734e6i	−0.0850309	+	0.984911i
$589$	3.98661e6	+	3.98661e6i	0.473495	+	0.473495i
$590$	−796907.	+	1.71153e6i	−0.0942492	+	0.202421i
$591$	−992153.			−0.116845
$592$	602109.	+	855719.i	0.0706108	+	0.100352i
$593$	4.08412e6			0.476937			0.238469	−	0.971150i	$-0.423355\pi$
$593$	4.08412e6			0.476937			0.238469	+	0.971150i	$0.423355\pi$
$594$	1.02607e6	−	2.20371e6i	0.119319	−	0.256264i
$595$	6.08965e6	+	6.08965e6i	0.705180	+	0.705180i
$596$	1.56899e7	+	1.35457e6i	1.80928	+	0.156201i
$597$	6.62315e6	−	6.62315e6i	0.760552	−	0.760552i
$598$	−620680.	+	226312.i	−0.0709765	+	0.0258794i
$599$			6.97060e6i			0.793785i	0.917865	+	0.396893i	$0.129911\pi$
$599$			6.97060e6i			0.793785i	−0.917865	+	0.396893i	$0.870089\pi$
$600$	−3.96284e6	−	2.27887e6i	−0.449395	−	0.258429i
$601$			1.11077e7i			1.25440i	0.778857	+	0.627202i	$0.215800\pi$
$601$			1.11077e7i			1.25440i	−0.778857	+	0.627202i	$0.784200\pi$
$602$	9.54865e6	+	2.61880e7i	1.07387	+	2.94517i
$603$	3.19824e6	−	3.19824e6i	0.358193	−	0.358193i
$604$	−4.86115e6	+	4.08849e6i	−0.542184	+	0.456006i
$605$	−2.35462e6	−	2.35462e6i	−0.261536	−	0.261536i
$606$	5.01410e6	+	2.33462e6i	0.554641	+	0.258246i
$607$	−4.72283e6			−0.520272			−0.260136	−	0.965572i	$-0.583767\pi$
$607$	−4.72283e6			−0.520272			−0.260136	+	0.965572i	$0.583767\pi$
$608$	−6.11914e6	+	1.09706e6i	−0.671323	+	0.120357i
$609$	6.15708e6			0.672715
$610$	−1.99386e6	−	928363.i	−0.216956	−	0.101017i
$611$	−3.04795e6	−	3.04795e6i	−0.330297	−	0.330297i
$612$	4.47948e6	−	3.76749e6i	0.483447	−	0.406606i
$613$	289319.	−	289319.i	0.0310975	−	0.0310975i	−0.691387	−	0.722485i	$-0.743000\pi$
$613$	289319.	−	289319.i	0.0310975	−	0.0310975i	0.722485	+	0.691387i	$0.243000\pi$
$614$	2.31902e6	+	6.36012e6i	0.248247	+	0.680839i
$615$		−	1.26938e6i		−	0.135334i
$616$	1.13572e7	−	1.97495e7i	1.20592	−	2.09703i
$617$		−	9.19988e6i		−	0.972902i	−0.873708	−	0.486451i	$-0.838291\pi$
$617$		−	9.19988e6i		−	0.972902i	0.873708	−	0.486451i	$-0.161709\pi$
$618$	1.11849e6	−	407823.i	0.117804	−	0.0429537i
$619$	−9.28135e6	+	9.28135e6i	−0.973609	+	0.973609i	−0.999661	−	0.0260518i	$-0.991707\pi$
$619$	−9.28135e6	+	9.28135e6i	−0.973609	+	0.973609i	0.0260518	+	0.999661i	$0.491707\pi$
$620$	−2.99164e6	−	258279.i	−0.312558	−	0.0269842i
$621$	−112683.	−	112683.i	−0.0117255	−	0.0117255i
$622$	−3.15755e6	+	6.78153e6i	−0.327246	+	0.702833i
$623$	−1.53323e7			−1.58266
$624$	4.85087e6	+	843876.i	0.498722	+	0.0867595i
$625$	−6.87620e6			−0.704123
$626$	−167636.	+	360035.i	−0.0170975	+	0.0367206i
$627$	−4.02600e6	−	4.02600e6i	−0.408982	−	0.408982i
$628$	−219001.	+	2.53669e6i	−0.0221589	+	0.256666i
$629$	−1.63158e6	+	1.63158e6i	−0.164430	+	0.164430i
$630$	−1.64174e6	+	598612.i	−0.164799	+	0.0600888i
$631$		−	7.04706e6i		−	0.704587i	−0.935890	−	0.352293i	$-0.885402\pi$
$631$		−	7.04706e6i		−	0.704587i	0.935890	−	0.352293i	$-0.114598\pi$
$632$	−81460.9	−	301938.i	−0.00811253	−	0.0300695i
$633$			6.05722e6i			0.600847i
$634$	88738.6	+	243373.i	0.00876778	+	0.0240464i
$635$	−4.09431e6	+	4.09431e6i	−0.402946	+	0.402946i
$636$	3.13612e6	+	3.72880e6i	0.307433	+	0.365532i
$637$	−1.08717e7	−	1.08717e7i	−1.06157	−	1.06157i
$638$	−9.68608e6	−	4.50994e6i	−0.942099	−	0.438651i
$639$	3.11654e6			0.301940
$640$	2.11810e6	−	2.54492e6i	0.204407	−	0.245598i
$641$	7.30962e6			0.702667			0.351334	−	0.936250i	$-0.385728\pi$
$641$	7.30962e6			0.702667			0.351334	+	0.936250i	$0.385728\pi$
$642$	−315339.	−	146825.i	−0.0301954	−	0.0140593i
$643$	7.63199e6	+	7.63199e6i	0.727964	+	0.727964i	0.970214	−	0.242250i	$-0.0778853\pi$
$643$	7.63199e6	+	7.63199e6i	0.727964	+	0.727964i	−0.242250	+	0.970214i	$0.577885\pi$
$644$	−961318.	−	1.14299e6i	−0.0913382	−	0.108600i
$645$	−2.62354e6	+	2.62354e6i	−0.248307	+	0.248307i
$646$	−4.69626e6	−	1.28799e7i	−0.442763	−	1.21432i
$647$		−	3.42010e6i		−	0.321202i	−0.987019	−	0.160601i	$-0.948657\pi$
$647$		−	3.42010e6i		−	0.321202i	0.987019	−	0.160601i	$-0.0513432\pi$
$648$	309363.	+	1.14667e6i	0.0289422	+	0.107275i
$649$			1.10139e7i			1.02643i
$650$	7.96708e6	−	2.90495e6i	0.739632	−	0.269684i
$651$	7.13791e6	−	7.13791e6i	0.660114	−	0.660114i
$652$	−705750.	+	8.17469e6i	−0.0650177	+	0.753099i
$653$	−5.79994e6	−	5.79994e6i	−0.532280	−	0.532280i	0.388970	−	0.921250i	$-0.372831\pi$
$653$	−5.79994e6	−	5.79994e6i	−0.532280	−	0.532280i	−0.921250	+	0.388970i	$0.872831\pi$
$654$	2.24156e6	−	4.81425e6i	0.204930	−	0.440133i
$655$	−2.12195e6			−0.193255
$656$	−7.96594e6	−	1.38579e6i	−0.722733	−	0.125729i
$657$	1.50098e6			0.135663
$658$	4.11311e6	−	8.83382e6i	0.370345	−	0.795396i
$659$	2.77175e6	+	2.77175e6i	0.248622	+	0.248622i	0.820405	−	0.571783i	$-0.193748\pi$
$659$	2.77175e6	+	2.77175e6i	0.248622	+	0.248622i	−0.571783	+	0.820405i	$0.693748\pi$
$660$	3.02120e6	+	260831.i	0.269973	+	0.0233077i
$661$	−6.38359e6	+	6.38359e6i	−0.568278	+	0.568278i	−0.931646	−	0.363368i	$-0.881627\pi$
$661$	−6.38359e6	+	6.38359e6i	−0.568278	+	0.568278i	0.363368	+	0.931646i	$0.381627\pi$
$662$	−6.73603e6	+	2.45609e6i	−0.597391	+	0.217821i
$663$			1.08580e7i			0.959328i
$664$	4.22446e6	−	7.34613e6i	0.371836	−	0.646604i
$665$			4.09294e6i			0.358907i
$666$	−160384.	−	439866.i	−0.0140112	−	0.0384269i
$667$	−495282.	+	495282.i	−0.0431060	+	0.0431060i
$668$	6.52273e6	−	5.48597e6i	0.565572	−	0.475677i
$669$	−6.70878e6	−	6.70878e6i	−0.579534	−	0.579534i
$670$	5.11502e6	+	2.38160e6i	0.440210	+	0.204966i
$671$	−1.28307e7			−1.10013
$672$	1.96426e6	+	1.09562e7i	0.167794	+	0.935913i
$673$	4.87715e6			0.415076			0.207538	−	0.978227i	$-0.433455\pi$
$673$	4.87715e6			0.415076			0.207538	+	0.978227i	$0.433455\pi$
$674$	−1.75897e7	−	8.18993e6i	−1.49145	−	0.694433i
$675$	1.44641e6	+	1.44641e6i	0.122189	+	0.122189i
$676$	2.10272e6	−	1.76850e6i	0.176976	−	0.148847i
$677$	−3.49376e6	+	3.49376e6i	−0.292969	+	0.292969i	−0.838252	−	0.545283i	$-0.816422\pi$
$677$	−3.49376e6	+	3.49376e6i	−0.292969	+	0.292969i	0.545283	+	0.838252i	$0.316422\pi$
$678$	−326119.	−	894409.i	−0.0272459	−	0.0747243i
$679$			1.65185e7i			1.37498i
$680$	6.32969e6	+	3.63995e6i	0.524940	+	0.301872i
$681$		−	4.21293e6i		−	0.348110i
$682$	−1.64575e7	+	6.00072e6i	−1.35488	+	0.494017i
$683$	−3.14846e6	+	3.14846e6i	−0.258253	+	0.258253i	−0.824343	−	0.566090i	$-0.808455\pi$
$683$	−3.14846e6	+	3.14846e6i	−0.258253	+	0.258253i	0.566090	+	0.824343i	$0.308455\pi$
$684$	2.77146e6	+	239270.i	0.226500	+	0.0195545i
$685$	−2.75180e6	−	2.75180e6i	−0.224074	−	0.224074i
$686$	6.10281e6	−	1.31071e7i	0.495130	−	1.06340i
$687$	6.26991e6			0.506838
$688$	1.35998e7	+	1.93280e7i	1.09537	+	1.55674i
$689$	−9.03841e6			−0.725344
$690$	83910.6	−	180217.i	0.00670956	−	0.0144103i
$691$	−509310.	−	509310.i	−0.0405776	−	0.0405776i	0.686527	−	0.727104i	$-0.259134\pi$
$691$	−509310.	−	509310.i	−0.0405776	−	0.0405776i	−0.727104	+	0.686527i	$0.759134\pi$
$692$	−827913.	+	9.58970e6i	−0.0657233	+	0.761272i
$693$	−7.20844e6	+	7.20844e6i	−0.570175	+	0.570175i
$694$	6.27510e6	−	2.28802e6i	0.494564	−	0.180328i
$695$			3.05467e6i			0.239885i
$696$	5.04001e6	−	1.35976e6i	0.394374	−	0.106399i
$697$		−	1.78307e7i		−	1.39023i
$698$	3.11284e6	+	8.53722e6i	0.241834	+	0.663251i
$699$	−3.38902e6	+	3.38902e6i	−0.262350	+	0.262350i
$700$	1.23395e7	+	1.46715e7i	0.951817	+	1.13169i
$701$	−1.29319e6	−	1.29319e6i	−0.0993957	−	0.0993957i	0.655660	−	0.755056i	$-0.272390\pi$
$701$	−1.29319e6	−	1.29319e6i	−0.0993957	−	0.0993957i	−0.755056	+	0.655660i	$0.772390\pi$
$702$	−1.99731e6	−	929968.i	−0.152969	−	0.0712238i
$703$	−1.09661e6			−0.0836879
$704$	4.93507e6	−	1.86746e7i	0.375285	−	1.42010i
$705$	1.29704e6			0.0982833
$706$	1.57666e7	+	7.34108e6i	1.19049	+	0.554304i
$707$	−1.64014e7	−	1.64014e7i	−1.23405	−	1.23405i
$708$	−3.46363e6	−	4.11820e6i	−0.259686	−	0.308762i
$709$	1.19401e7	−	1.19401e7i	0.892056	−	0.892056i	−0.102660	−	0.994717i	$-0.532735\pi$
$709$	1.19401e7	−	1.19401e7i	0.892056	−	0.892056i	0.994717	+	0.102660i	$0.0327354\pi$
$710$	1.33179e6	+	3.65256e6i	0.0991496	+	0.271926i
$711$			139938.i			0.0103815i
$712$	−1.25506e7	+	3.38607e6i	−0.927824	+	0.250320i
$713$			1.14836e6i			0.0845971i
$714$	−2.30611e7	+	8.40854e6i	−1.69291	+	0.617270i
$715$	−3.97774e6	+	3.97774e6i	−0.290985	+	0.290985i
$716$	−72691.8	+	841988.i	−0.00529911	+	0.0613795i
$717$	−4.68182e6	−	4.68182e6i	−0.340108	−	0.340108i
$718$	241465.	−	518600.i	0.0174801	−	0.0375423i
$719$	8.95548e6			0.646050			0.323025	−	0.946390i	$-0.395300\pi$
$719$	8.95548e6			0.646050			0.323025	+	0.946390i	$0.395300\pi$
$720$	−1.21169e6	+	852578.i	−0.0871081	+	0.0612919i
$721$	−4.99263e6			−0.357677
$722$	−3.16213e6	+	6.79138e6i	−0.225755	+	0.484858i
$723$	6.22629e6	+	6.22629e6i	0.442979	+	0.442979i
$724$	7.42235e6	+	640798.i	0.526254	+	0.0454334i
$725$	6.35746e6	−	6.35746e6i	0.449199	−	0.449199i
$726$	8.91679e6	−	3.25124e6i	0.627866	−	0.228932i
$727$		−	2.37950e7i		−	1.66974i	−0.550447	−	0.834870i	$-0.685543\pi$
$727$		−	2.37950e7i		−	1.66974i	0.550447	−	0.834870i	$-0.314457\pi$
$728$	−1.78998e7	−	1.02935e7i	−1.25176	−	0.719835i
$729$		−	531441.i		−	0.0370370i
$730$	641415.	+	1.75914e6i	0.0445484	+	0.122178i
$731$	−3.68522e7	+	3.68522e7i	−2.55076	+	2.55076i
$732$	4.79753e6	−	4.03499e6i	0.330933	−	0.278333i
$733$	−3.47762e6	−	3.47762e6i	−0.239069	−	0.239069i	0.577396	−	0.816464i	$-0.304069\pi$
$733$	−3.47762e6	−	3.47762e6i	−0.239069	−	0.239069i	−0.816464	+	0.577396i	$0.804069\pi$
$734$	1.99852e7	+	9.30531e6i	1.36920	+	0.637515i
$735$	4.62639e6			0.315881
$736$	−1.03933e6	−	723318.i	−0.0707229	−	0.0492192i
$737$	3.29156e7			2.23220
$738$	3.27992e6	+	1.52716e6i	0.221678	+	0.103215i
$739$	642515.	+	642515.i	0.0432785	+	0.0432785i	0.728415	−	0.685136i	$-0.240257\pi$
$739$	642515.	+	642515.i	0.0432785	+	0.0432785i	−0.685136	+	0.728415i	$0.740257\pi$
$740$	446982.	−	375937.i	0.0300062	−	0.0252369i
$741$	−3.64892e6	+	3.64892e6i	−0.244129	+	0.244129i
$742$	−6.99941e6	−	1.91965e7i	−0.466715	−	1.28001i
$743$			830390.i			0.0551836i	0.999619	+	0.0275918i	$0.00878386\pi$
$743$			830390.i			0.0551836i	−0.999619	+	0.0275918i	$0.991216\pi$
$744$	4.26652e6	−	7.41927e6i	0.282580	−	0.491393i
$745$		−	8.79068e6i		−	0.580272i
$746$	−1.01330e7	+	3.69469e6i	−0.666640	+	0.243070i
$747$	−2.68128e6	+	2.68128e6i	−0.175809	+	0.175809i
$748$	4.24380e7	+	3.66382e6i	2.77332	+	0.239431i
$749$	1.03149e6	+	1.03149e6i	0.0671832	+	0.0671832i
$750$	−2.27664e6	+	4.88958e6i	−0.147789	+	0.317409i
$751$	2.18689e7			1.41490			0.707451	−	0.706763i	$-0.249845\pi$
$751$	2.18689e7			1.41490			0.707451	+	0.706763i	$0.249845\pi$
$752$	1.41597e6	−	8.13948e6i	0.0913084	−	0.524870i
$753$	1.04609e7			0.672326
$754$	−4.08754e6	+	8.77888e6i	−0.261838	+	0.562355i
$755$	2.50713e6	+	2.50713e6i	0.160070	+	0.160070i
$756$	428406.	−	4.96222e6i	0.0272616	−	0.315770i
$757$	8.02083e6	−	8.02083e6i	0.508721	−	0.508721i	−0.405413	−	0.914134i	$-0.632872\pi$
$757$	8.02083e6	−	8.02083e6i	0.508721	−	0.508721i	0.914134	+	0.405413i	$0.132872\pi$
$758$	1.58440e7	−	5.77702e6i	1.00159	−	0.365200i
$759$		−	1.15971e6i		−	0.0730709i
$760$	903907.	+	3.35037e6i	0.0567662	+	0.210406i
$761$		−	1.38178e6i		−	0.0864925i	−0.999064	−	0.0432463i	$-0.986230\pi$
$761$		−	1.38178e6i		−	0.0864925i	0.999064	−	0.0432463i	$-0.0137700\pi$
$762$	−5.65340e6	−	1.55049e7i	−0.352713	−	0.967346i
$763$	−1.57476e7	+	1.57476e7i	−0.979273	+	0.979273i
$764$	−1.91386e7	−	2.27555e7i	−1.18625	−	1.41043i
$765$	−2.31029e6	−	2.31029e6i	−0.142729	−	0.142729i
$766$	−1.75846e7	−	8.18755e6i	−1.08283	−	0.504176i
$767$	9.98230e6			0.612692
$768$	4.02751e6	+	8.53461e6i	0.246396	+	0.522133i
$769$	−2.75922e7			−1.68256			−0.841279	−	0.540601i	$-0.818197\pi$
$769$	−2.75922e7			−1.68256			−0.841279	+	0.540601i	$0.818197\pi$
$770$	−1.15286e7	−	5.36784e6i	−0.700729	−	0.326267i
$771$	3.87907e6	+	3.87907e6i	0.235013	+	0.235013i
$772$	1.58899e7	+	1.88928e7i	0.959572	+	1.14091i
$773$	1.90003e7	−	1.90003e7i	1.14370	−	1.14370i	0.155934	−	0.987767i	$-0.450161\pi$
$773$	1.90003e7	−	1.90003e7i	1.14370	−	1.14370i	0.987767	−	0.155934i	$-0.0498389\pi$
$774$	−3.62257e6	−	9.93519e6i	−0.217352	−	0.596107i
$775$		−	1.47404e7i		−	0.881569i
$776$	3.64803e6	+	1.35216e7i	0.217472	+	0.806070i
$777$			1.96345e6i			0.116672i
$778$	2.62773e7	−	9.58123e6i	1.55644	−	0.567508i
$779$	5.99214e6	−	5.99214e6i	0.353784	−	0.353784i
$780$	236402.	−	2.73823e6i	0.0139128	−	0.161151i
$781$	1.60373e7	+	1.60373e7i	0.940817	+	0.940817i
$782$	1.17867e6	−	2.53145e6i	0.0689248	−	0.148031i
$783$	−2.33587e6			−0.136158
$784$	5.05062e6	−	2.90326e7i	0.293464	−	1.68693i
$785$	1.42124e6			0.0823179
$786$	2.55286e6	−	5.48282e6i	0.147391	−	0.316554i
$787$	−418691.	−	418691.i	−0.0240966	−	0.0240966i	0.694956	−	0.719052i	$-0.255424\pi$
$787$	−418691.	−	418691.i	−0.0240966	−	0.0240966i	−0.719052	+	0.694956i	$0.755424\pi$
$788$	3.51458e6	+	303427.i	0.201631	+	0.0174076i
$789$	−7.50731e6	+	7.50731e6i	−0.429331	+	0.429331i
$790$	−164006.	+	59799.8i	−0.00934958	+	0.00340904i
$791$			3.99240e6i			0.226878i
$792$	−4.30868e6	+	7.49258e6i	−0.244079	+	0.424442i
$793$			1.16290e7i			0.656686i
$794$	−636858.	−	1.74664e6i	−0.0358502	−	0.0983222i
$795$	1.92312e6	−	1.92312e6i	0.107917	−	0.107917i
$796$	−2.54873e7	+	2.14362e7i	−1.42574	+	1.19913i
$797$	−1.82471e7	−	1.82471e7i	−1.01753	−	1.01753i	−0.999844	−	0.0176910i	$-0.994368\pi$
$797$	−1.82471e7	−	1.82471e7i	−1.01753	−	1.01753i	−0.0176910	−	0.999844i	$-0.505632\pi$
$798$	−1.05756e7	−	4.92411e6i	−0.587893	−	0.273729i
$799$	1.82191e7			1.00963
$800$	1.33409e7	+	9.28455e6i	0.736989	+	0.512904i
$801$	5.81678e6			0.320333
$802$	−3.79633e6	−	1.76761e6i	−0.208414	−	0.0970398i
$803$	7.72387e6	+	7.72387e6i	0.422714	+	0.422714i
$804$	−1.23075e7	+	1.03513e7i	−0.671474	+	0.564746i
$805$	−589497.	+	589497.i	−0.0320621	+	0.0320621i
$806$	5.43869e6	+	1.49161e7i	0.294888	+	0.808755i
$807$		−	1.47793e7i		−	0.798861i
$808$	−1.70479e7	−	9.80354e6i	−0.918632	−	0.528268i
$809$		−	9.32306e6i		−	0.500827i	−0.968139	−	0.250413i	$-0.919433\pi$
$809$		−	9.32306e6i		−	0.500827i	0.968139	−	0.250413i	$-0.0805665\pi$
$810$	622844.	−	227101.i	0.0333555	−	0.0121621i
$811$	1.75779e6	−	1.75779e6i	0.0938456	−	0.0938456i	−0.658625	−	0.752471i	$-0.728862\pi$
$811$	1.75779e6	−	1.75779e6i	0.0938456	−	0.0938456i	0.752471	+	0.658625i	$0.228862\pi$
$812$	−2.18107e7	−	1.88300e6i	−1.16086	−	0.100221i
$813$	5.82470e6	+	5.82470e6i	0.309063	+	0.309063i
$814$	1.43818e6	−	3.08882e6i	0.0760770	−	0.163392i
$815$	4.58008e6			0.241534
$816$	−1.70202e7	+	1.19759e7i	−0.894828	+	0.629628i
$817$	−2.47689e7			−1.29823
$818$	−4.27132e6	+	9.17359e6i	−0.223192	+	0.479354i
$819$	6.53330e6	+	6.53330e6i	0.340347	+	0.340347i
$820$	−388211.	+	4.49664e6i	−0.0201620	+	0.233536i
$821$	−1.55087e7	+	1.55087e7i	−0.803004	+	0.803004i	−0.983564	−	0.180560i	$-0.942209\pi$
$821$	−1.55087e7	+	1.55087e7i	−0.803004	+	0.803004i	0.180560	+	0.983564i	$0.442209\pi$
$822$	1.04209e7	−	3.79967e6i	0.537930	−	0.196140i
$823$		−	6.22629e6i		−	0.320428i	−0.987082	−	0.160214i	$-0.948782\pi$
$823$		−	6.22629e6i		−	0.320428i	0.987082	−	0.160214i	$-0.0512184\pi$
$824$	−4.08683e6	+	1.10260e6i	−0.209686	+	0.0565717i
$825$			1.48861e7i			0.761457i
$826$	7.73037e6	+	2.12012e7i	0.394230	+	1.08121i
$827$	9.78407e6	−	9.78407e6i	0.497457	−	0.497457i	−0.413188	−	0.910646i	$-0.635585\pi$
$827$	9.78407e6	−	9.78407e6i	0.497457	−	0.497457i	0.910646	+	0.413188i	$0.135585\pi$
$828$	364705.	+	433628.i	0.0184870	+	0.0219807i
$829$	−1.87040e7	−	1.87040e7i	−0.945252	−	0.945252i	0.0533250	−	0.998577i	$-0.483018\pi$
$829$	−1.87040e7	−	1.87040e7i	−0.945252	−	0.945252i	−0.998577	+	0.0533250i	$0.983018\pi$
$830$	−4.28823e6	−	1.99664e6i	−0.216064	−	0.100602i
$831$	1.88386e7			0.946335
$832$	−1.69255e7	−	4.47285e6i	−0.847684	−	0.224015i
$833$	6.49856e7			3.24493
$834$	−7.89287e6	−	3.67500e6i	−0.392934	−	0.182954i
$835$	−3.36409e6	−	3.36409e6i	−0.166975	−	0.166975i
$836$	1.30303e7	+	1.54929e7i	0.644823	+	0.766683i
$837$	−2.70798e6	+	2.70798e6i	−0.133608	+	0.133608i
$838$	−1.83184e6	−	5.02397e6i	−0.0901109	−	0.247137i
$839$			3.83928e7i			1.88298i	0.337046	+	0.941488i	$0.390572\pi$
$839$			3.83928e7i			1.88298i	−0.337046	+	0.941488i	$0.609428\pi$
$840$	5.99875e6	−	1.61842e6i	0.293334	−	0.0791395i
$841$		−	1.02442e7i		−	0.499444i
$842$	−2.63411e7	+	9.60449e6i	−1.28043	+	0.466868i
$843$	1.10598e7	−	1.10598e7i	0.536018	−	0.536018i
$844$	1.85246e6	−	2.14570e7i	0.0895142	−	1.03684i
$845$	−1.08448e6	−	1.08448e6i	−0.0522490	−	0.0522490i
$846$	−1.56043e6	+	3.35137e6i	−0.0749582	+	0.160989i
$847$	−3.98022e7			−1.90633
$848$	−9.96897e6	−	1.41679e7i	−0.476059	−	0.676576i
$849$	6.55534e6			0.312123
$850$	−1.51295e7	+	3.24939e7i	−0.718251	+	1.54260i
$851$	−157942.	−	157942.i	−0.00747606	−	0.00747606i
$852$	−1.10400e7	−	953119.i	−0.521037	−	0.0449830i
$853$	−1.38466e7	+	1.38466e7i	−0.651585	+	0.651585i	−0.953375	−	0.301789i	$-0.902416\pi$
$853$	−1.38466e7	+	1.38466e7i	−0.651585	+	0.651585i	0.301789	+	0.953375i	$0.402416\pi$
$854$	−2.46985e7	+	9.00556e6i	−1.15885	+	0.422538i
$855$		−	1.55278e6i		−	0.0726431i
$856$	1.07215e6	+	616549.i	0.0500116	+	0.0287596i
$857$			3.40265e7i			1.58258i	0.611442	+	0.791290i	$0.290590\pi$
$857$			3.40265e7i			1.58258i	−0.611442	+	0.791290i	$0.709410\pi$
$858$	−5.49242e6	−	1.50634e7i	−0.254710	−	0.698564i
$859$	−1.27124e7	+	1.27124e7i	−0.587822	+	0.587822i	−0.937041	−	0.349219i	$-0.886447\pi$
$859$	−1.27124e7	+	1.27124e7i	−0.587822	+	0.587822i	0.349219	+	0.937041i	$0.386447\pi$
$860$	1.00959e7	−	8.49123e6i	0.465479	−	0.391494i
$861$	−1.07288e7	−	1.07288e7i	−0.493221	−	0.493221i
$862$	8.72337e6	+	4.06169e6i	0.399868	+	0.186182i
$863$	9.58438e6			0.438063			0.219032	−	0.975718i	$-0.429710\pi$
$863$	9.58438e6			0.438063			0.219032	+	0.975718i	$0.429710\pi$
$864$	−745201.	−	4.15655e6i	−0.0339617	−	0.189430i
$865$	5.37287e6			0.244155
$866$	2.86457e7	+	1.33377e7i	1.29797	+	0.604348i
$867$	−2.34161e7	−	2.34161e7i	−1.05795	−	1.05795i
$868$	−2.74682e7	+	2.31022e7i	−1.23746	+	1.04077i
$869$	−720105.	+	720105.i	−0.0323479	+	0.0323479i
$870$	−998190.	−	2.73762e6i	−0.0447111	−	0.122624i
$871$		−	2.98327e7i		−	1.33244i
$872$	−9.41279e6	+	1.63684e7i	−0.419206	+	0.728977i
$873$		−	6.26678e6i		−	0.278297i
$874$	1.24681e6	−	454613.i	0.0552107	−	0.0201309i
$875$	1.59940e7	−	1.59940e7i	0.706217	−	0.706217i
$876$	−5.31704e6	−	459039.i	−0.234104	−	0.0202111i
$877$	1.17965e7	+	1.17965e7i	0.517910	+	0.517910i	0.916938	−	0.399029i	$-0.130653\pi$
$877$	1.17965e7	+	1.17965e7i	0.517910	+	0.517910i	−0.399029	+	0.916938i	$0.630653\pi$
$878$	1.77450e7	−	3.81114e7i	0.776856	−	1.66847i
$879$	−1.01914e7			−0.444899
$880$	−1.06225e7	−	1.84792e6i	−0.462401	−	0.0804410i
$881$	3.06310e6			0.132960			0.0664800	−	0.997788i	$-0.478823\pi$
$881$	3.06310e6			0.132960			0.0664800	+	0.997788i	$0.478823\pi$
$882$	−5.56589e6	+	1.19540e7i	−0.240914	+	0.517417i
$883$	−9.27704e6	−	9.27704e6i	−0.400413	−	0.400413i	0.477966	−	0.878378i	$-0.341374\pi$
$883$	−9.27704e6	−	9.27704e6i	−0.400413	−	0.400413i	−0.878378	+	0.477966i	$0.841374\pi$
$884$	3.32067e6	−	3.84632e7i	0.142921	−	1.65545i
$885$	−2.12396e6	+	2.12396e6i	−0.0911566	+	0.0911566i
$886$	−2.76510e7	+	1.00821e7i	−1.18339	+	0.431486i
$887$		−	2.28423e7i		−	0.974832i	−0.873170	−	0.487416i	$-0.837939\pi$
$887$		−	2.28423e7i		−	0.974832i	0.873170	−	0.487416i	$-0.162061\pi$
$888$	433618.	+	1.60722e6i	0.0184533	+	0.0683980i
$889$			6.92098e7i			2.93706i
$890$	2.48569e6	+	6.81721e6i	0.105189	+	0.288491i
$891$	2.73474e6	−	2.73474e6i	0.115404	−	0.115404i
$892$	2.17133e7	+	2.58168e7i	0.913723	+	1.08640i
$893$	6.12268e6	+	6.12268e6i	0.256929	+	0.256929i
$894$	2.27139e7	+	1.05758e7i	0.950492	+	0.442559i
$895$	471745.			0.0196857
$896$	−3.60747e6	−	3.94116e7i	−0.150118	−	1.64004i
$897$	−1.05109e6			−0.0436173
$898$	2.21469e7	+	1.03118e7i	0.916478	+	0.426721i
$899$	1.19025e7	+	1.19025e7i	0.491179	+	0.491179i
$900$	−4.68137e6	−	5.56607e6i	−0.192649	−	0.229056i
$901$	2.70136e7	−	2.70136e7i	1.10859	−	1.10859i
$902$	9.01948e6	+	2.47367e7i	0.369118	+	1.01234i
$903$			4.43481e7i			1.80990i
$904$	881703.	+	3.26807e6i	0.0358840	+	0.133006i
$905$		−	4.15856e6i		−	0.168780i
$906$	−9.49436e6	+	3.46183e6i	−0.384278	+	0.140115i
$907$	2.55965e7	−	2.55965e7i	1.03315	−	1.03315i	0.0337177	−	0.999431i	$-0.489265\pi$
$907$	2.55965e7	−	2.55965e7i	1.03315	−	1.03315i	0.999431	−	0.0337177i	$-0.0107347\pi$
$908$	−1.28843e6	+	1.49238e7i	−0.0518614	+	0.600710i
$909$	6.22235e6	+	6.22235e6i	0.249772	+	0.249772i
$910$	−4.86509e6	+	1.04488e7i	−0.194754	+	0.418278i
$911$	−4.10116e6			−0.163723			−0.0818617	−	0.996644i	$-0.526087\pi$
$911$	−4.10116e6			−0.163723			−0.0818617	+	0.996644i	$0.526087\pi$
$912$	−9.74437e6	−	1.69517e6i	−0.387942	−	0.0674879i
$913$	−2.75951e7			−1.09561
$914$	−4.97582e6	+	1.06867e7i	−0.197015	+	0.423133i
$915$	−2.47432e6	−	2.47432e6i	−0.0977020	−	0.0977020i
$916$	−2.22104e7	−	1.91750e6i	−0.874616	−	0.0755088i
$917$	−1.79346e7	+	1.79346e7i	−0.704316	+	0.704316i
$918$	8.74892e6	−	3.19003e6i	0.342648	−	0.124936i
$919$		−	4.21448e7i		−	1.64610i	−0.567970	−	0.823049i	$-0.692271\pi$
$919$		−	4.21448e7i		−	1.64610i	0.567970	−	0.823049i	$-0.307729\pi$
$920$	−352358.	+	612733.i	−0.0137251	+	0.0238672i
$921$			1.07705e7i			0.418397i
$922$	−1.75581e7	−	4.81547e7i	−0.680223	−	1.86557i
$923$	1.45353e7	−	1.45353e7i	0.561590	−	0.561590i
$924$	2.77395e7	−	2.33305e7i	1.06886	−	0.898967i
$925$	2.02735e6	+	2.02735e6i	0.0779065	+	0.0779065i
$926$	1.95267e7	+	9.09185e6i	0.748346	+	0.348437i
$927$	1.89410e6			0.0723943
$928$	−1.82695e7	+	3.27542e6i	−0.696396	+	0.124852i
$929$	−2.46296e7			−0.936305			−0.468153	−	0.883648i	$-0.655080\pi$
$929$	−2.46296e7			−0.936305			−0.468153	+	0.883648i	$0.655080\pi$
$930$	−4.33093e6	−	2.01653e6i	−0.164200	−	0.0764533i
$931$	2.18389e7	+	2.18389e7i	0.825765	+	0.825765i
$932$	1.30416e7	−	1.09687e7i	0.491805	−	0.413635i
$933$	−8.41567e6	+	8.41567e6i	−0.316508	+	0.316508i
$934$	5.44556e6	+	1.49349e7i	0.204256	+	0.560190i
$935$		−	2.37770e7i		−	0.889462i
$936$	6.79082e6	+	3.90513e6i	0.253357	+	0.145695i
$937$		−	4.32292e7i		−	1.60853i	−0.594272	−	0.804264i	$-0.702560\pi$
$937$		−	4.32292e7i		−	1.60853i	0.594272	−	0.804264i	$-0.297440\pi$
$938$	6.33610e7	−	2.31027e7i	2.35134	−	0.857343i
$939$	−446793.	+	446793.i	−0.0165364	+	0.0165364i
$940$	−4.59460e6	−	396668.i	−0.169601	−	0.0146422i
$941$	2.45195e7	+	2.45195e7i	0.902687	+	0.902687i	0.995668	−	0.0929805i	$-0.0296394\pi$
$941$	2.45195e7	+	2.45195e7i	0.902687	+	0.902687i	−0.0929805	+	0.995668i	$0.529639\pi$
$942$	−1.70986e6	+	3.67230e6i	−0.0627818	+	0.134838i
$943$	1.72607e6			0.0632089
$944$	1.10100e7	+	1.56475e7i	0.402123	+	0.571498i
$945$	−2.78021e6			−0.101274
$946$	3.24841e7	−	6.97667e7i	1.18016	−	2.53466i
$947$	−2.62905e7	−	2.62905e7i	−0.952629	−	0.952629i	0.0462987	−	0.998928i	$-0.485257\pi$
$947$	−2.62905e7	−	2.62905e7i	−0.952629	−	0.952629i	−0.998928	+	0.0462987i	$0.985257\pi$
$948$	42796.7	−	495713.i	0.00154664	−	0.0179147i
$949$	7.00046e6	−	7.00046e6i	0.252325	−	0.252325i
$950$	−1.60042e7	+	5.83544e6i	−0.575340	+	0.209780i
$951$			412140.i			0.0147773i
$952$	8.42628e7	−	2.27335e7i	3.01331	−	0.812970i
$953$		−	3.59328e7i		−	1.28162i	−0.767700	−	0.640809i	$-0.778599\pi$
$953$		−	3.59328e7i		−	1.28162i	0.767700	−	0.640809i	$-0.221401\pi$
$954$	2.65543e6	+	7.28275e6i	0.0944636	+	0.259075i
$955$	−1.17361e7	+	1.17361e7i	−0.416405	+	0.416405i
$956$	1.51529e7	+	1.80166e7i	0.536231	+	0.637570i
$957$	−1.20201e7	−	1.20201e7i	−0.424257	−	0.424257i
$958$	2.71629e7	+	1.26473e7i	0.956229	+	0.445230i
$959$	−4.65162e7			−1.63327
$960$	4.55299e6	−	2.64959e6i	0.159448	−	0.0927899i
$961$	−1.03190e6			−0.0360436
$962$	−2.79952e6	−	1.30348e6i	−0.0975317	−	0.0454117i
$963$	−391326.	−	391326.i	−0.0135979	−	0.0135979i
$964$	−2.01517e7	−	2.39600e7i	−0.698424	−	0.830415i
$965$	9.74395e6	−	9.74395e6i	0.336835	−	0.336835i
$966$	−813972.	−	2.23239e6i	−0.0280651	−	0.0769710i
$967$			1.02535e7i			0.352617i	0.984335	+	0.176309i	$0.0564157\pi$
$967$			1.02535e7i			0.352617i	−0.984335	+	0.176309i	$0.943584\pi$
$968$	−3.25810e7	+	8.79012e6i	−1.11757	+	0.301513i
$969$		−	2.18115e7i		−	0.746235i
$970$	7.34461e6	−	2.67799e6i	0.250634	−	0.0913859i
$971$	−1.44922e7	+	1.44922e7i	−0.493270	+	0.493270i	−0.909335	−	0.416065i	$-0.863409\pi$
$971$	−1.44922e7	+	1.44922e7i	−0.493270	+	0.493270i	0.416065	+	0.909335i	$0.363409\pi$
$972$	−162529.	+	1.88257e6i	−0.00551778	+	0.0639123i
$973$	2.58179e7	+	2.58179e7i	0.874257	+	0.874257i
$974$	1.57013e7	−	3.37221e7i	0.530322	−	1.13898i
$975$	1.34919e7			0.454527
$976$	−1.82287e7	+	1.28262e7i	−0.612534	+	0.430998i
$977$	−5.23927e7			−1.75604			−0.878020	−	0.478623i	$-0.841136\pi$
$977$	−5.23927e7			−1.75604			−0.878020	+	0.478623i	$0.841136\pi$
$978$	−5.51017e6	+	1.18343e7i	−0.184212	+	0.395636i
$979$	2.99325e7	+	2.99325e7i	0.998127	+	0.998127i
$980$	−1.63884e7	−	1.41487e6i	−0.545095	−	0.0470600i
$981$	5.97433e6	−	5.97433e6i	0.198206	−	0.198206i
$982$	1.30688e7	−	4.76515e6i	0.432472	−	0.157688i
$983$			7.30511e6i			0.241125i	0.992706	+	0.120563i	$0.0384699\pi$
$983$			7.30511e6i			0.241125i	−0.992706	+	0.120563i	$0.961530\pi$
$984$	−1.11517e7	−	6.41287e6i	−0.367157	−	0.211137i
$985$		−	1.96914e6i		−	0.0646673i
$986$	−1.40213e7	−	3.84546e7i	−0.459299	−	1.25967i
$987$	1.09625e7	−	1.09625e7i	0.358192	−	0.358192i
$988$	1.40418e7	−	1.18099e7i	0.457647	−	0.384906i
$989$	−3.56741e6	−	3.56741e6i	−0.115974	−	0.115974i
$990$	4.37372e6	+	2.03645e6i	0.141828	+	0.0660367i
$991$	1.44937e7			0.468809			0.234404	−	0.972139i	$-0.424686\pi$
$991$	1.44937e7			0.468809			0.234404	+	0.972139i	$0.424686\pi$
$992$	−1.73827e7	+	2.49771e7i	−0.560837	+	0.805865i
$993$	−1.14071e7			−0.367116
$994$	4.21274e7	+	1.96150e7i	1.35238	+	0.629682i
$995$	1.31450e7	+	1.31450e7i	0.420924	+	0.420924i
$996$	1.03181e7	−	8.67811e6i	0.329574	−	0.277189i
$997$	−3.04660e7	+	3.04660e7i	−0.970683	+	0.970683i	−0.999582	−	0.0288998i	$-0.990800\pi$
$997$	−3.04660e7	+	3.04660e7i	−0.970683	+	0.970683i	0.0288998	+	0.999582i	$0.490800\pi$
$998$	3.40447e6	+	9.33705e6i	0.108199	+	0.296745i
$999$		−	744891.i		−	0.0236145i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	48.6.j.a.13.3	✓	40
3.2	odd	2		144.6.k.c.109.18		40
4.3	odd	2		192.6.j.a.145.18		40
8.3	odd	2		384.6.j.b.289.3		40
8.5	even	2		384.6.j.a.289.18		40
12.11	even	2		576.6.k.c.145.10		40
16.3	odd	4		384.6.j.b.97.3		40
16.5	even	4	inner	48.6.j.a.37.3	yes	40
16.11	odd	4		192.6.j.a.49.18		40
16.13	even	4		384.6.j.a.97.18		40
48.5	odd	4		144.6.k.c.37.18		40
48.11	even	4		576.6.k.c.433.10		40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
48.6.j.a.13.3	✓	40	1.1	even	1	trivial
48.6.j.a.37.3	yes	40	16.5	even	4	inner
144.6.k.c.37.18		40	48.5	odd	4
144.6.k.c.109.18		40	3.2	odd	2
192.6.j.a.49.18		40	16.11	odd	4
192.6.j.a.145.18		40	4.3	odd	2
384.6.j.a.97.18		40	16.13	even	4
384.6.j.a.289.18		40	8.5	even	2
384.6.j.b.97.3		40	16.3	odd	4
384.6.j.b.289.3		40	8.3	odd	2
576.6.k.c.145.10		40	12.11	even	2
576.6.k.c.433.10		40	48.11	even	4

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.j (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-5.12822 - 2.38775i) q^{2} +(-6.36396 - 6.36396i) q^{3} +(20.5973 + 24.4898i) q^{4} +(12.6306 - 12.6306i) q^{5} +(17.4402 + 47.8313i) q^{6} -213.506i q^{7} +(-47.1519 - 174.770i) q^{8} +81.0000i q^{9} +O(q^{10})\)	\(q+(-5.12822 - 2.38775i) q^{2} +(-6.36396 - 6.36396i) q^{3} +(20.5973 + 24.4898i) q^{4} +(12.6306 - 12.6306i) q^{5} +(17.4402 + 47.8313i) q^{6} -213.506i q^{7} +(-47.1519 - 174.770i) q^{8} +81.0000i q^{9} +(-94.9313 + 34.6138i) q^{10} +(-416.817 + 416.817i) q^{11} +(24.7719 - 286.933i) q^{12} +(377.778 + 377.778i) q^{13} +(-509.800 + 1094.91i) q^{14} -160.761 q^{15} +(-175.503 + 1008.85i) q^{16} -2258.17 q^{17} +(193.408 - 415.386i) q^{18} +(-758.876 - 758.876i) q^{19} +(569.478 + 49.1651i) q^{20} +(-1358.75 + 1358.75i) q^{21} +(3132.78 - 1142.27i) q^{22} -218.598i q^{23} +(-812.160 + 1412.30i) q^{24} +2805.94i q^{25} +(-1035.29 - 2839.37i) q^{26} +(515.481 - 515.481i) q^{27} +(5228.73 - 4397.65i) q^{28} +(-2265.72 - 2265.72i) q^{29} +(824.420 + 383.858i) q^{30} -5253.31 q^{31} +(3308.90 - 4754.54i) q^{32} +5305.21 q^{33} +(11580.4 + 5391.95i) q^{34} +(-2696.72 - 2696.72i) q^{35} +(-1983.68 + 1668.38i) q^{36} +(722.521 - 722.521i) q^{37} +(2079.68 + 5703.69i) q^{38} -4808.33i q^{39} +(-2803.01 - 1611.90i) q^{40} +7896.08i q^{41} +(10212.3 - 3723.60i) q^{42} +(16319.5 - 16319.5i) q^{43} +(-18793.1 - 1622.47i) q^{44} +(1023.08 + 1023.08i) q^{45} +(-521.958 + 1121.02i) q^{46} -8068.09 q^{47} +(7537.17 - 5303.38i) q^{48} -28778.0 q^{49} +(6699.87 - 14389.5i) q^{50} +(14370.9 + 14370.9i) q^{51} +(-1470.51 + 17032.9i) q^{52} +(-11962.6 + 11962.6i) q^{53} +(-3874.34 + 1412.66i) q^{54} +10529.3i q^{55} +(-37314.6 + 10067.2i) q^{56} +9658.91i q^{57} +(6209.14 + 17029.1i) q^{58} +(13211.9 - 13211.9i) q^{59} +(-3311.25 - 3937.02i) q^{60} +(15391.3 + 15391.3i) q^{61} +(26940.1 + 12543.6i) q^{62} +17294.0 q^{63} +(-28321.4 + 16481.5i) q^{64} +9543.13 q^{65} +(-27206.3 - 12667.5i) q^{66} +(-39484.4 - 39484.4i) q^{67} +(-46512.2 - 55302.2i) q^{68} +(-1391.15 + 1391.15i) q^{69} +(7390.27 + 20268.4i) q^{70} -38475.8i q^{71} +(14156.4 - 3819.30i) q^{72} -18530.6i q^{73} +(-5430.45 + 1980.05i) q^{74} +(17856.9 - 17856.9i) q^{75} +(2953.95 - 34215.5i) q^{76} +(88993.1 + 88993.1i) q^{77} +(-11481.1 + 24658.2i) q^{78} +1727.63 q^{79} +(10525.7 + 14959.1i) q^{80} -6561.00 q^{81} +(18853.9 - 40492.8i) q^{82} +(33102.2 + 33102.2i) q^{83} +(-61262.0 - 5288.96i) q^{84} +(-28522.1 + 28522.1i) q^{85} +(-122657. + 44723.0i) q^{86} +28837.9i q^{87} +(92500.9 + 53193.6i) q^{88} -71812.1i q^{89} +(-2803.72 - 7689.44i) q^{90} +(80658.0 - 80658.0i) q^{91} +(5353.43 - 4502.53i) q^{92} +(33431.9 + 33431.9i) q^{93} +(41375.0 + 19264.6i) q^{94} -19170.1 q^{95} +(-51315.4 + 9200.01i) q^{96} -77367.6 q^{97} +(147580. + 68714.6i) q^{98} +(-33762.2 - 33762.2i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q + 44 q^{4} - 492 q^{8}+O(q^{10}) \) 40 * q + 44 * q^4 - 492 * q^8	\( 40 q + 44 q^{4} - 492 q^{8} + 968 q^{10} + 1208 q^{11} - 792 q^{12} + 324 q^{14} - 1800 q^{15} - 384 q^{16} - 324 q^{18} + 2360 q^{19} - 7600 q^{20} - 1024 q^{22} + 5220 q^{24} - 12980 q^{26} + 10472 q^{28} - 8144 q^{29} - 1368 q^{30} + 23064 q^{31} + 44160 q^{32} + 4864 q^{34} - 4776 q^{35} - 1620 q^{36} + 21296 q^{37} - 72088 q^{38} - 90864 q^{40} - 14220 q^{42} + 31416 q^{43} + 43768 q^{44} + 90664 q^{46} + 44784 q^{48} - 96040 q^{49} + 106212 q^{50} + 10440 q^{51} - 116432 q^{52} - 49456 q^{53} - 14580 q^{54} - 158592 q^{56} - 111472 q^{58} + 28960 q^{59} + 49464 q^{60} + 48080 q^{61} + 191100 q^{62} + 31752 q^{63} + 369032 q^{64} - 55376 q^{65} + 63720 q^{66} + 101488 q^{67} - 122336 q^{68} - 22320 q^{69} - 460192 q^{70} - 28836 q^{72} - 94996 q^{74} - 96624 q^{75} + 211304 q^{76} - 14896 q^{77} + 200124 q^{78} - 71960 q^{79} + 623368 q^{80} - 262440 q^{81} + 33880 q^{82} - 126440 q^{83} - 116856 q^{84} + 132400 q^{85} - 581168 q^{86} - 466400 q^{88} - 46008 q^{90} + 429496 q^{91} - 12752 q^{92} + 524120 q^{94} - 76848 q^{95} + 51840 q^{96} + 477736 q^{98} + 97848 q^{99}+O(q^{100}) \) 40 * q + 44 * q^4 - 492 * q^8 + 968 * q^10 + 1208 * q^11 - 792 * q^12 + 324 * q^14 - 1800 * q^15 - 384 * q^16 - 324 * q^18 + 2360 * q^19 - 7600 * q^20 - 1024 * q^22 + 5220 * q^24 - 12980 * q^26 + 10472 * q^28 - 8144 * q^29 - 1368 * q^30 + 23064 * q^31 + 44160 * q^32 + 4864 * q^34 - 4776 * q^35 - 1620 * q^36 + 21296 * q^37 - 72088 * q^38 - 90864 * q^40 - 14220 * q^42 + 31416 * q^43 + 43768 * q^44 + 90664 * q^46 + 44784 * q^48 - 96040 * q^49 + 106212 * q^50 + 10440 * q^51 - 116432 * q^52 - 49456 * q^53 - 14580 * q^54 - 158592 * q^56 - 111472 * q^58 + 28960 * q^59 + 49464 * q^60 + 48080 * q^61 + 191100 * q^62 + 31752 * q^63 + 369032 * q^64 - 55376 * q^65 + 63720 * q^66 + 101488 * q^67 - 122336 * q^68 - 22320 * q^69 - 460192 * q^70 - 28836 * q^72 - 94996 * q^74 - 96624 * q^75 + 211304 * q^76 - 14896 * q^77 + 200124 * q^78 - 71960 * q^79 + 623368 * q^80 - 262440 * q^81 + 33880 * q^82 - 126440 * q^83 - 116856 * q^84 + 132400 * q^85 - 581168 * q^86 - 466400 * q^88 - 46008 * q^90 + 429496 * q^91 - 12752 * q^92 + 524120 * q^94 - 76848 * q^95 + 51840 * q^96 + 477736 * q^98 + 97848 * q^99

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