LMFDB - Embedded newform 354.6.a.b.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [354,6,Mod(1,354)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(354, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0]))

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

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

chi := DirichletCharacter("354.1");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 354 = 2 \cdot 3 \cdot 59 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	354.a (trivial)

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:	yes
Analytic conductor:	$56.7758722138$
Analytic rank:	$1$
Dimension:	$4$
Coefficient field:	4.4.32832.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - 2x^{3} - 9x^{2} + 10x + 1 $ x^4 - 2x^3 - 9x^2 + 10*x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{2}\cdot 3^{4} $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$3.68575$ of defining polynomial
Character	$\chi$	$=$	354.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+4.00000 q^{2} +9.00000 q^{3} +16.0000 q^{4} -84.5867 q^{5} +36.0000 q^{6} +83.0564 q^{7} +64.0000 q^{8} +81.0000 q^{9} +O(q^{10})$	\(q+4.00000 q^{2} +9.00000 q^{3} +16.0000 q^{4} -84.5867 q^{5} +36.0000 q^{6} +83.0564 q^{7} +64.0000 q^{8} +81.0000 q^{9} -338.347 q^{10} +426.903 q^{11} +144.000 q^{12} -689.405 q^{13} +332.226 q^{14} -761.281 q^{15} +256.000 q^{16} -1685.77 q^{17} +324.000 q^{18} -1966.54 q^{19} -1353.39 q^{20} +747.508 q^{21} +1707.61 q^{22} +330.319 q^{23} +576.000 q^{24} +4029.91 q^{25} -2757.62 q^{26} +729.000 q^{27} +1328.90 q^{28} +550.776 q^{29} -3045.12 q^{30} +5532.16 q^{31} +1024.00 q^{32} +3842.12 q^{33} -6743.06 q^{34} -7025.47 q^{35} +1296.00 q^{36} -9360.44 q^{37} -7866.15 q^{38} -6204.64 q^{39} -5413.55 q^{40} -7312.65 q^{41} +2990.03 q^{42} +1045.71 q^{43} +6830.44 q^{44} -6851.52 q^{45} +1321.28 q^{46} -5062.95 q^{47} +2304.00 q^{48} -9908.63 q^{49} +16119.7 q^{50} -15171.9 q^{51} -11030.5 q^{52} -9945.71 q^{53} +2916.00 q^{54} -36110.3 q^{55} +5315.61 q^{56} -17698.8 q^{57} +2203.10 q^{58} -3481.00 q^{59} -12180.5 q^{60} -39266.0 q^{61} +22128.6 q^{62} +6727.57 q^{63} +4096.00 q^{64} +58314.5 q^{65} +15368.5 q^{66} -72602.9 q^{67} -26972.3 q^{68} +2972.87 q^{69} -28101.9 q^{70} +2116.78 q^{71} +5184.00 q^{72} -6382.13 q^{73} -37441.7 q^{74} +36269.2 q^{75} -31464.6 q^{76} +35457.0 q^{77} -24818.6 q^{78} -73458.2 q^{79} -21654.2 q^{80} +6561.00 q^{81} -29250.6 q^{82} -64990.7 q^{83} +11960.1 q^{84} +142593. q^{85} +4182.85 q^{86} +4956.98 q^{87} +27321.8 q^{88} +84420.1 q^{89} -27406.1 q^{90} -57259.5 q^{91} +5285.10 q^{92} +49789.4 q^{93} -20251.8 q^{94} +166343. q^{95} +9216.00 q^{96} -56734.0 q^{97} -39634.5 q^{98} +34579.1 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 16 q^{2} + 36 q^{3} + 64 q^{4} - 104 q^{5} + 144 q^{6} - 162 q^{7} + 256 q^{8} + 324 q^{9}+O(q^{10}) $ 4 * q + 16 * q^2 + 36 * q^3 + 64 * q^4 - 104 * q^5 + 144 * q^6 - 162 * q^7 + 256 * q^8 + 324 * q^9	\( 4 q + 16 q^{2} + 36 q^{3} + 64 q^{4} - 104 q^{5} + 144 q^{6} - 162 q^{7} + 256 q^{8} + 324 q^{9} - 416 q^{10} - 676 q^{11} + 576 q^{12} - 792 q^{13} - 648 q^{14} - 936 q^{15} + 1024 q^{16} - 2474 q^{17} + 1296 q^{18} - 4538 q^{19} - 1664 q^{20} - 1458 q^{21} - 2704 q^{22} - 1238 q^{23} + 2304 q^{24} - 832 q^{25} - 3168 q^{26} + 2916 q^{27} - 2592 q^{28} - 4958 q^{29} - 3744 q^{30} - 7138 q^{31} + 4096 q^{32} - 6084 q^{33} - 9896 q^{34} - 13554 q^{35} + 5184 q^{36} - 13570 q^{37} - 18152 q^{38} - 7128 q^{39} - 6656 q^{40} - 13826 q^{41} - 5832 q^{42} - 1236 q^{43} - 10816 q^{44} - 8424 q^{45} - 4952 q^{46} - 12410 q^{47} + 9216 q^{48} - 24622 q^{49} - 3328 q^{50} - 22266 q^{51} - 12672 q^{52} - 50904 q^{53} + 11664 q^{54} - 20872 q^{55} - 10368 q^{56} - 40842 q^{57} - 19832 q^{58} - 13924 q^{59} - 14976 q^{60} - 70622 q^{61} - 28552 q^{62} - 13122 q^{63} + 16384 q^{64} + 17460 q^{65} - 24336 q^{66} - 50012 q^{67} - 39584 q^{68} - 11142 q^{69} - 54216 q^{70} + 21192 q^{71} + 20736 q^{72} - 13358 q^{73} - 54280 q^{74} - 7488 q^{75} - 72608 q^{76} + 98658 q^{77} - 28512 q^{78} + 6464 q^{79} - 26624 q^{80} + 26244 q^{81} - 55304 q^{82} + 51506 q^{83} - 23328 q^{84} + 61786 q^{85} - 4944 q^{86} - 44622 q^{87} - 43264 q^{88} + 90738 q^{89} - 33696 q^{90} + 48870 q^{91} - 19808 q^{92} - 64242 q^{93} - 49640 q^{94} + 171394 q^{95} + 36864 q^{96} - 266068 q^{97} - 98488 q^{98} - 54756 q^{99}+O(q^{100}) \) 4 * q + 16 * q^2 + 36 * q^3 + 64 * q^4 - 104 * q^5 + 144 * q^6 - 162 * q^7 + 256 * q^8 + 324 * q^9 - 416 * q^10 - 676 * q^11 + 576 * q^12 - 792 * q^13 - 648 * q^14 - 936 * q^15 + 1024 * q^16 - 2474 * q^17 + 1296 * q^18 - 4538 * q^19 - 1664 * q^20 - 1458 * q^21 - 2704 * q^22 - 1238 * q^23 + 2304 * q^24 - 832 * q^25 - 3168 * q^26 + 2916 * q^27 - 2592 * q^28 - 4958 * q^29 - 3744 * q^30 - 7138 * q^31 + 4096 * q^32 - 6084 * q^33 - 9896 * q^34 - 13554 * q^35 + 5184 * q^36 - 13570 * q^37 - 18152 * q^38 - 7128 * q^39 - 6656 * q^40 - 13826 * q^41 - 5832 * q^42 - 1236 * q^43 - 10816 * q^44 - 8424 * q^45 - 4952 * q^46 - 12410 * q^47 + 9216 * q^48 - 24622 * q^49 - 3328 * q^50 - 22266 * q^51 - 12672 * q^52 - 50904 * q^53 + 11664 * q^54 - 20872 * q^55 - 10368 * q^56 - 40842 * q^57 - 19832 * q^58 - 13924 * q^59 - 14976 * q^60 - 70622 * q^61 - 28552 * q^62 - 13122 * q^63 + 16384 * q^64 + 17460 * q^65 - 24336 * q^66 - 50012 * q^67 - 39584 * q^68 - 11142 * q^69 - 54216 * q^70 + 21192 * q^71 + 20736 * q^72 - 13358 * q^73 - 54280 * q^74 - 7488 * q^75 - 72608 * q^76 + 98658 * q^77 - 28512 * q^78 + 6464 * q^79 - 26624 * q^80 + 26244 * q^81 - 55304 * q^82 + 51506 * q^83 - 23328 * q^84 + 61786 * q^85 - 4944 * q^86 - 44622 * q^87 - 43264 * q^88 + 90738 * q^89 - 33696 * q^90 + 48870 * q^91 - 19808 * q^92 - 64242 * q^93 - 49640 * q^94 + 171394 * q^95 + 36864 * q^96 - 266068 * q^97 - 98488 * q^98 - 54756 * q^99

Display 100 coefficients 10 coefficients

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 $

$2$	4.00000	0.707107
$2$	4.00000	0.707107
$3$	9.00000	0.577350
$3$	9.00000	0.577350
$4$	16.0000	0.500000
$5$	−84.5867	−1.51313	−0.756567	−	0.653917i	$-0.773125\pi$
$5$	−84.5867	−1.51313	−0.756567	+	0.653917i	$0.773125\pi$
$6$	36.0000	0.408248
$7$	83.0564	0.640661	0.320330	−	0.947306i	$-0.396206\pi$
$7$	83.0564	0.640661	0.320330	+	0.947306i	$0.396206\pi$
$8$	64.0000	0.353553
$9$	81.0000	0.333333
$10$	−338.347	−1.06995
$11$	426.903	1.06377	0.531884	−	0.846817i	$-0.321484\pi$
$11$	426.903	1.06377	0.531884	+	0.846817i	$0.321484\pi$
$12$	144.000	0.288675
$13$	−689.405	−1.13140	−0.565699	−	0.824612i	$-0.691394\pi$
$13$	−689.405	−1.13140	−0.565699	+	0.824612i	$0.691394\pi$
$14$	332.226	0.453016
$15$	−761.281	−0.873608
$16$	256.000	0.250000
$17$	−1685.77	−1.41473	−0.707367	−	0.706846i	$-0.750117\pi$
$17$	−1685.77	−1.41473	−0.707367	+	0.706846i	$0.750117\pi$
$18$	324.000	0.235702
$19$	−1966.54	−1.24974	−0.624868	−	0.780730i	$-0.714847\pi$
$19$	−1966.54	−1.24974	−0.624868	+	0.780730i	$0.714847\pi$
$20$	−1353.39	−0.756567
$21$	747.508	0.369886
$22$	1707.61	0.752198
$23$	330.319	0.130201	0.0651004	−	0.997879i	$-0.479263\pi$
$23$	330.319	0.130201	0.0651004	+	0.997879i	$0.479263\pi$
$24$	576.000	0.204124
$25$	4029.91	1.28957
$26$	−2757.62	−0.800020
$27$	729.000	0.192450
$28$	1328.90	0.320330
$29$	550.776	0.121613	0.0608064	−	0.998150i	$-0.480633\pi$
$29$	550.776	0.121613	0.0608064	+	0.998150i	$0.480633\pi$
$30$	−3045.12	−0.617734
$31$	5532.16	1.03393	0.516964	−	0.856007i	$-0.327062\pi$
$31$	5532.16	1.03393	0.516964	+	0.856007i	$0.327062\pi$
$32$	1024.00	0.176777
$33$	3842.12	0.614167
$34$	−6743.06	−1.00037
$35$	−7025.47	−0.969405
$36$	1296.00	0.166667
$37$	−9360.44	−1.12407	−0.562033	−	0.827115i	$-0.689981\pi$
$37$	−9360.44	−1.12407	−0.562033	+	0.827115i	$0.689981\pi$
$38$	−7866.15	−0.883697
$39$	−6204.64	−0.653213
$40$	−5413.55	−0.534973
$41$	−7312.65	−0.679383	−0.339692	−	0.940537i	$-0.610323\pi$
$41$	−7312.65	−0.679383	−0.339692	+	0.940537i	$0.610323\pi$
$42$	2990.03	0.261549
$43$	1045.71	0.0862464	0.0431232	−	0.999070i	$-0.486269\pi$
$43$	1045.71	0.0862464	0.0431232	+	0.999070i	$0.486269\pi$
$44$	6830.44	0.531884
$45$	−6851.52	−0.504378
$46$	1321.28	0.0920659
$47$	−5062.95	−0.334318	−0.167159	−	0.985930i	$-0.553459\pi$
$47$	−5062.95	−0.334318	−0.167159	+	0.985930i	$0.553459\pi$
$48$	2304.00	0.144338
$49$	−9908.63	−0.589554
$50$	16119.7	0.911865
$51$	−15171.9	−0.816797
$52$	−11030.5	−0.565699
$53$	−9945.71	−0.486347	−0.243173	−	0.969983i	$-0.578188\pi$
$53$	−9945.71	−0.486347	−0.243173	+	0.969983i	$0.578188\pi$
$54$	2916.00	0.136083
$55$	−36110.3	−1.60962
$56$	5315.61	0.226508
$57$	−17698.8	−0.721535
$58$	2203.10	0.0859933
$59$	−3481.00	−0.130189
$59$	−3481.00	−0.130189
$60$	−12180.5	−0.436804
$61$	−39266.0	−1.35111	−0.675557	−	0.737308i	$-0.736097\pi$
$61$	−39266.0	−1.35111	−0.675557	+	0.737308i	$0.736097\pi$
$62$	22128.6	0.731098
$63$	6727.57	0.213554
$64$	4096.00	0.125000
$65$	58314.5	1.71196
$66$	15368.5	0.434282
$67$	−72602.9	−1.97591	−0.987954	−	0.154745i	$-0.950545\pi$
$67$	−72602.9	−1.97591	−0.987954	+	0.154745i	$0.950545\pi$
$68$	−26972.3	−0.707367
$69$	2972.87	0.0751715
$70$	−28101.9	−0.685473
$71$	2116.78	0.0498344	0.0249172	−	0.999690i	$-0.492068\pi$
$71$	2116.78	0.0498344	0.0249172	+	0.999690i	$0.492068\pi$
$72$	5184.00	0.117851
$73$	−6382.13	−0.140171	−0.0700855	−	0.997541i	$-0.522327\pi$
$73$	−6382.13	−0.140171	−0.0700855	+	0.997541i	$0.522327\pi$
$74$	−37441.7	−0.794835
$75$	36269.2	0.744535
$76$	−31464.6	−0.624868
$77$	35457.0	0.681515
$78$	−24818.6	−0.461892
$79$	−73458.2	−1.32426	−0.662129	−	0.749390i	$-0.730347\pi$
$79$	−73458.2	−1.32426	−0.662129	+	0.749390i	$0.730347\pi$
$80$	−21654.2	−0.378283
$81$	6561.00	0.111111
$82$	−29250.6	−0.480397
$83$	−64990.7	−1.03551	−0.517757	−	0.855528i	$-0.673233\pi$
$83$	−64990.7	−1.03551	−0.517757	+	0.855528i	$0.673233\pi$
$84$	11960.1	0.184943
$85$	142593.	2.14068
$86$	4182.85	0.0609854
$87$	4956.98	0.0702132
$88$	27321.8	0.376099
$89$	84420.1	1.12972	0.564860	−	0.825187i	$-0.308930\pi$
$89$	84420.1	1.12972	0.564860	+	0.825187i	$0.308930\pi$
$90$	−27406.1	−0.356649
$91$	−57259.5	−0.724843
$92$	5285.10	0.0651004
$93$	49789.4	0.596939
$94$	−20251.8	−0.236398
$95$	166343.	1.89102
$96$	9216.00	0.102062
$97$	−56734.0	−0.612229	−0.306114	−	0.951995i	$-0.599029\pi$
$97$	−56734.0	−0.612229	−0.306114	+	0.951995i	$0.599029\pi$
$98$	−39634.5	−0.416877
$99$	34579.1	0.354589
$100$	64478.6	0.644786
$101$	35772.4	0.348935	0.174468	−	0.984663i	$-0.444180\pi$
$101$	35772.4	0.348935	0.174468	+	0.984663i	$0.444180\pi$
$102$	−60687.6	−0.577563
$103$	124371.	1.15512	0.577559	−	0.816349i	$-0.304005\pi$
$103$	124371.	1.15512	0.577559	+	0.816349i	$0.304005\pi$
$104$	−44121.9	−0.400010
$105$	−63229.3	−0.559686
$106$	−39782.8	−0.343899
$107$	−160376.	−1.35419	−0.677095	−	0.735896i	$-0.736761\pi$
$107$	−160376.	−1.35419	−0.677095	+	0.735896i	$0.736761\pi$
$108$	11664.0	0.0962250
$109$	51999.9	0.419214	0.209607	−	0.977786i	$-0.432781\pi$
$109$	51999.9	0.419214	0.209607	+	0.977786i	$0.432781\pi$
$110$	−144441.	−1.13818
$111$	−84243.9	−0.648980
$112$	21262.4	0.160165
$113$	242787.	1.78866	0.894332	−	0.447405i	$-0.147652\pi$
$113$	242787.	1.78866	0.894332	+	0.447405i	$0.147652\pi$
$114$	−70795.4	−0.510203
$115$	−27940.6	−0.197011
$116$	8812.41	0.0608064
$117$	−55841.8	−0.377133
$118$	−13924.0	−0.0920575
$119$	−140014.	−0.906365
$120$	−48722.0	−0.308867
$121$	21194.8	0.131603
$122$	−157064.	−0.955381
$123$	−65813.8	−0.392242
$124$	88514.5	0.516964
$125$	−76543.7	−0.438162
$126$	26910.3	0.151005
$127$	−4307.74	−0.0236995	−0.0118498	−	0.999930i	$-0.503772\pi$
$127$	−4307.74	−0.0236995	−0.0118498	+	0.999930i	$0.503772\pi$
$128$	16384.0	0.0883883
$129$	9411.41	0.0497944
$130$	233258.	1.21054
$131$	−24120.2	−0.122801	−0.0614006	−	0.998113i	$-0.519557\pi$
$131$	−24120.2	−0.122801	−0.0614006	+	0.998113i	$0.519557\pi$
$132$	61474.0	0.307083
$133$	−163334.	−0.800657
$134$	−290412.	−1.39718
$135$	−61663.7	−0.291203
$136$	−107889.	−0.500184
$137$	135699.	0.617698	0.308849	−	0.951111i	$-0.400056\pi$
$137$	135699.	0.617698	0.308849	+	0.951111i	$0.400056\pi$
$138$	11891.5	0.0531543
$139$	152530.	0.669604	0.334802	−	0.942289i	$-0.391331\pi$
$139$	152530.	0.669604	0.334802	+	0.942289i	$0.391331\pi$
$140$	−112408.	−0.484703
$141$	−45566.6	−0.193018
$142$	8467.10	0.0352382
$143$	−294309.	−1.20355
$144$	20736.0	0.0833333
$145$	−46588.3	−0.184017
$146$	−25528.5	−0.0991159
$147$	−89177.6	−0.340379
$148$	−149767.	−0.562033
$149$	−67789.8	−0.250149	−0.125074	−	0.992147i	$-0.539917\pi$
$149$	−67789.8	−0.250149	−0.125074	+	0.992147i	$0.539917\pi$
$150$	145077.	0.526466
$151$	−185468.	−0.661951	−0.330975	−	0.943639i	$-0.607378\pi$
$151$	−185468.	−0.661951	−0.330975	+	0.943639i	$0.607378\pi$
$152$	−125858.	−0.441848
$153$	−136547.	−0.471578
$154$	141828.	0.481904
$155$	−467947.	−1.56447
$156$	−99274.3	−0.326607
$157$	158238.	0.512343	0.256172	−	0.966631i	$-0.417539\pi$
$157$	158238.	0.512343	0.256172	+	0.966631i	$0.417539\pi$
$158$	−293833.	−0.936392
$159$	−89511.4	−0.280792
$160$	−86616.8	−0.267487
$161$	27435.1	0.0834146
$162$	26244.0	0.0785674
$163$	654115.	1.92835	0.964174	−	0.265272i	$-0.0854618\pi$
$163$	654115.	1.92835	0.964174	+	0.265272i	$0.0854618\pi$
$164$	−117002.	−0.339692
$165$	−324993.	−0.929316
$166$	−259963.	−0.732219
$167$	343990.	0.954455	0.477227	−	0.878780i	$-0.341642\pi$
$167$	343990.	0.954455	0.477227	+	0.878780i	$0.341642\pi$
$168$	47840.5	0.130774
$169$	103986.	0.280063
$170$	570374.	1.51369
$171$	−159290.	−0.416579
$172$	16731.4	0.0431232
$173$	342377.	0.869739	0.434869	−	0.900494i	$-0.356795\pi$
$173$	342377.	0.869739	0.434869	+	0.900494i	$0.356795\pi$
$174$	19827.9	0.0496483
$175$	334710.	0.826179
$176$	109287.	0.265942
$177$	−31329.0	−0.0751646
$178$	337680.	0.798833
$179$	548493.	1.27950	0.639748	−	0.768585i	$-0.279039\pi$
$179$	548493.	1.27950	0.639748	+	0.768585i	$0.279039\pi$
$180$	−109624.	−0.252189
$181$	−718144.	−1.62935	−0.814676	−	0.579916i	$-0.803085\pi$
$181$	−718144.	−1.62935	−0.814676	+	0.579916i	$0.803085\pi$
$182$	−229038.	−0.512541
$183$	−353394.	−0.780066
$184$	21140.4	0.0460329
$185$	791769.	1.70086
$186$	199158.	0.422099
$187$	−719658.	−1.50495
$188$	−81007.2	−0.167159
$189$	60548.1	0.123295
$190$	665372.	1.33715
$191$	−184411.	−0.365765	−0.182883	−	0.983135i	$-0.558543\pi$
$191$	−184411.	−0.365765	−0.182883	+	0.983135i	$0.558543\pi$
$192$	36864.0	0.0721688
$193$	559684.	1.08156	0.540779	−	0.841165i	$-0.318130\pi$
$193$	559684.	1.08156	0.540779	+	0.841165i	$0.318130\pi$
$194$	−226936.	−0.432911
$195$	524830.	0.988399
$196$	−158538.	−0.294777
$197$	902197.	1.65629	0.828144	−	0.560515i	$-0.189397\pi$
$197$	902197.	1.65629	0.828144	+	0.560515i	$0.189397\pi$
$198$	138316.	0.250733
$199$	480123.	0.859449	0.429724	−	0.902960i	$-0.358611\pi$
$199$	480123.	0.859449	0.429724	+	0.902960i	$0.358611\pi$
$200$	257915.	0.455933
$201$	−653426.	−1.14079
$202$	143090.	0.246735
$203$	45745.5	0.0779126
$204$	−242750.	−0.408399
$205$	618553.	1.02800
$206$	497484.	0.816792
$207$	26755.8	0.0434003
$208$	−176488.	−0.282850
$209$	−839520.	−1.32943
$210$	−252917.	−0.395758
$211$	−565301.	−0.874125	−0.437062	−	0.899431i	$-0.643981\pi$
$211$	−565301.	−0.874125	−0.437062	+	0.899431i	$0.643981\pi$
$212$	−159131.	−0.243173
$213$	19051.0	0.0287719
$214$	−641503.	−0.957557
$215$	−88453.3	−0.130502
$216$	46656.0	0.0680414
$217$	459481.	0.662397
$218$	208000.	0.296429
$219$	−57439.1	−0.0809278
$220$	−577765.	−0.804812
$221$	1.16217e6	1.60063
$222$	−336976.	−0.458898
$223$	−541358.	−0.728992	−0.364496	−	0.931205i	$-0.618759\pi$
$223$	−541358.	−0.728992	−0.364496	+	0.931205i	$0.618759\pi$
$224$	85049.8	0.113254
$225$	326423.	0.429858
$226$	971146.	1.26478
$227$	−184928.	−0.238198	−0.119099	−	0.992882i	$-0.538001\pi$
$227$	−184928.	−0.238198	−0.119099	+	0.992882i	$0.538001\pi$
$228$	−283181.	−0.360768
$229$	−53106.1	−0.0669200	−0.0334600	−	0.999440i	$-0.510653\pi$
$229$	−53106.1	−0.0669200	−0.0334600	+	0.999440i	$0.510653\pi$
$230$	−111762.	−0.139308
$231$	319113.	0.393473
$232$	35249.6	0.0429967
$233$	70291.2	0.0848226	0.0424113	−	0.999100i	$-0.486496\pi$
$233$	70291.2	0.0848226	0.0424113	+	0.999100i	$0.486496\pi$
$234$	−223367.	−0.266673
$235$	428258.	0.505867
$236$	−55696.0	−0.0650945
$237$	−661124.	−0.764561
$238$	−560055.	−0.640897
$239$	−828232.	−0.937901	−0.468951	−	0.883224i	$-0.655368\pi$
$239$	−828232.	−0.937901	−0.468951	+	0.883224i	$0.655368\pi$
$240$	−194888.	−0.218402
$241$	172216.	0.190998	0.0954992	−	0.995430i	$-0.469555\pi$
$241$	172216.	0.190998	0.0954992	+	0.995430i	$0.469555\pi$
$242$	84779.1	0.0930573
$243$	59049.0	0.0641500
$244$	−628256.	−0.675557
$245$	838138.	0.892073
$246$	−263255.	−0.277357
$247$	1.35574e6	1.41395
$248$	354058.	0.365549
$249$	−584917.	−0.597855
$250$	−306175.	−0.309827
$251$	−1.23041e6	−1.23272	−0.616362	−	0.787463i	$-0.711394\pi$
$251$	−1.23041e6	−1.23272	−0.616362	+	0.787463i	$0.711394\pi$
$252$	107641.	0.106777
$253$	141014.	0.138503
$254$	−17230.9	−0.0167581
$255$	1.28334e6	1.23592
$256$	65536.0	0.0625000
$257$	−789715.	−0.745827	−0.372913	−	0.927866i	$-0.621641\pi$
$257$	−789715.	−0.745827	−0.372913	+	0.927866i	$0.621641\pi$
$258$	37645.6	0.0352099
$259$	−777445.	−0.720145
$260$	933032.	0.855979
$261$	44612.8	0.0405376
$262$	−96480.8	−0.0868336
$263$	1.70833e6	1.52294	0.761471	−	0.648199i	$-0.224477\pi$
$263$	1.70833e6	1.52294	0.761471	+	0.648199i	$0.224477\pi$
$264$	245896.	0.217141
$265$	841275.	0.735908
$266$	−653335.	−0.566150
$267$	759781.	0.652244
$268$	−1.16165e6	−0.987954
$269$	1.21227e6	1.02145	0.510725	−	0.859744i	$-0.329377\pi$
$269$	1.21227e6	1.02145	0.510725	+	0.859744i	$0.329377\pi$
$270$	−246655.	−0.205911
$271$	−1.62703e6	−1.34578	−0.672889	−	0.739744i	$-0.734947\pi$
$271$	−1.62703e6	−1.34578	−0.672889	+	0.739744i	$0.734947\pi$
$272$	−431556.	−0.353684
$273$	−515335.	−0.418488
$274$	542797.	0.436779
$275$	1.72038e6	1.37181
$276$	47565.9	0.0375857
$277$	642861.	0.503405	0.251702	−	0.967805i	$-0.419010\pi$
$277$	642861.	0.503405	0.251702	+	0.967805i	$0.419010\pi$
$278$	610120.	0.473481
$279$	448105.	0.344643
$280$	−449630.	−0.342737
$281$	−363676.	−0.274757	−0.137379	−	0.990519i	$-0.543868\pi$
$281$	−363676.	−0.274757	−0.137379	+	0.990519i	$0.543868\pi$
$282$	−182266.	−0.136485
$283$	−2.06628e6	−1.53364	−0.766820	−	0.641862i	$-0.778162\pi$
$283$	−2.06628e6	−1.53364	−0.766820	+	0.641862i	$0.778162\pi$
$284$	33868.4	0.0249172
$285$	1.49709e6	1.09178
$286$	−1.17723e6	−0.851036
$287$	−607362.	−0.435254
$288$	82944.0	0.0589256
$289$	1.42195e6	1.00147
$290$	−186353.	−0.130119
$291$	−510606.	−0.353471
$292$	−102114.	−0.0700855
$293$	1.83646e6	1.24972	0.624860	−	0.780737i	$-0.285156\pi$
$293$	1.83646e6	1.24972	0.624860	+	0.780737i	$0.285156\pi$
$294$	−356711.	−0.240684
$295$	294446.	0.196993
$296$	−599068.	−0.397417
$297$	311212.	0.204722
$298$	−271159.	−0.176882
$299$	−227723.	−0.147309
$300$	580308.	0.372268
$301$	86853.1	0.0552547
$302$	−741870.	−0.468070
$303$	321952.	0.201458
$304$	−503434.	−0.312434
$305$	3.32138e6	2.04441
$306$	−546188.	−0.333456
$307$	2.65588e6	1.60828	0.804142	−	0.594437i	$-0.202625\pi$
$307$	2.65588e6	1.60828	0.804142	+	0.594437i	$0.202625\pi$
$308$	567312.	0.340757
$309$	1.11934e6	0.666908
$310$	−1.87179e6	−1.10625
$311$	−881290.	−0.516675	−0.258338	−	0.966055i	$-0.583175\pi$
$311$	−881290.	−0.516675	−0.258338	+	0.966055i	$0.583175\pi$
$312$	−397097.	−0.230946
$313$	−239340.	−0.138088	−0.0690439	−	0.997614i	$-0.521995\pi$
$313$	−239340.	−0.138088	−0.0690439	+	0.997614i	$0.521995\pi$
$314$	632951.	0.362281
$315$	−569063.	−0.323135
$316$	−1.17533e6	−0.662129
$317$	−35531.2	−0.0198592	−0.00992959	−	0.999951i	$-0.503161\pi$
$317$	−35531.2	−0.0198592	−0.00992959	+	0.999951i	$0.503161\pi$
$318$	−358046.	−0.198550
$319$	235127.	0.129368
$320$	−346467.	−0.189142
$321$	−1.44338e6	−0.781842
$322$	109740.	0.0589830
$323$	3.31512e6	1.76804
$324$	104976.	0.0555556
$325$	−2.77824e6	−1.45902
$326$	2.61646e6	1.36355
$327$	467999.	0.242034
$328$	−468009.	−0.240198
$329$	−420511.	−0.214184
$330$	−1.29997e6	−0.657126
$331$	−1.90903e6	−0.957729	−0.478865	−	0.877889i	$-0.658952\pi$
$331$	−1.90903e6	−0.957729	−0.478865	+	0.877889i	$0.658952\pi$
$332$	−1.03985e6	−0.517757
$333$	−758195.	−0.374689
$334$	1.37596e6	0.674901
$335$	6.14124e6	2.98981
$336$	191362.	0.0924714
$337$	951535.	0.456404	0.228202	−	0.973614i	$-0.426715\pi$
$337$	951535.	0.456404	0.228202	+	0.973614i	$0.426715\pi$
$338$	415942.	0.198035
$339$	2.18508e6	1.03269
$340$	2.28149e6	1.07034
$341$	2.36169e6	1.09986
$342$	−637158.	−0.294566
$343$	−2.21890e6	−1.01836
$344$	66925.6	0.0304927
$345$	−251465.	−0.113744
$346$	1.36951e6	0.614998
$347$	1.30931e6	0.583740	0.291870	−	0.956458i	$-0.405722\pi$
$347$	1.30931e6	0.583740	0.291870	+	0.956458i	$0.405722\pi$
$348$	79311.7	0.0351066
$349$	−1.61456e6	−0.709563	−0.354782	−	0.934949i	$-0.615445\pi$
$349$	−1.61456e6	−0.709563	−0.354782	+	0.934949i	$0.615445\pi$
$350$	1.33884e6	0.584197
$351$	−502576.	−0.217738
$352$	437148.	0.188049
$353$	−3.61799e6	−1.54536	−0.772682	−	0.634794i	$-0.781085\pi$
$353$	−3.61799e6	−1.54536	−0.772682	+	0.634794i	$0.781085\pi$
$354$	−125316.	−0.0531494
$355$	−179051.	−0.0754061
$356$	1.35072e6	0.564860
$357$	−1.26012e6	−0.523290
$358$	2.19397e6	0.904740
$359$	2.56480e6	1.05031	0.525155	−	0.851006i	$-0.324007\pi$
$359$	2.56480e6	1.05031	0.525155	+	0.851006i	$0.324007\pi$
$360$	−438498.	−0.178324
$361$	1.39117e6	0.561840
$362$	−2.87258e6	−1.15213
$363$	190753.	0.0759810
$364$	−916152.	−0.362422
$365$	539843.	0.212097
$366$	−1.41357e6	−0.551590
$367$	641408.	0.248582	0.124291	−	0.992246i	$-0.460334\pi$
$367$	641408.	0.248582	0.124291	+	0.992246i	$0.460334\pi$
$368$	84561.6	0.0325502
$369$	−592324.	−0.226461
$370$	3.16707e6	1.20269
$371$	−826055.	−0.311583
$372$	796631.	0.298469
$373$	4.72696e6	1.75918	0.879589	−	0.475735i	$-0.157818\pi$
$373$	4.72696e6	1.75918	0.879589	+	0.475735i	$0.157818\pi$
$374$	−2.87863e6	−1.06416
$375$	−688894.	−0.252973
$376$	−324029.	−0.118199
$377$	−379707.	−0.137593
$378$	242193.	0.0871829
$379$	−3.73591e6	−1.33597	−0.667987	−	0.744173i	$-0.732844\pi$
$379$	−3.73591e6	−1.33597	−0.667987	+	0.744173i	$0.732844\pi$
$380$	2.66149e6	0.945509
$381$	−38769.6	−0.0136829
$382$	−737643.	−0.258635
$383$	−2.25023e6	−0.783844	−0.391922	−	0.919998i	$-0.628190\pi$
$383$	−2.25023e6	−0.783844	−0.391922	+	0.919998i	$0.628190\pi$
$384$	147456.	0.0510310
$385$	−2.99919e6	−1.03122
$386$	2.23874e6	0.764776
$387$	84702.7	0.0287488
$388$	−907744.	−0.306114
$389$	1.42342e6	0.476933	0.238467	−	0.971151i	$-0.423355\pi$
$389$	1.42342e6	0.476933	0.238467	+	0.971151i	$0.423355\pi$
$390$	2.09932e6	0.698904
$391$	−556840.	−0.184200
$392$	−634152.	−0.208439
$393$	−217082.	−0.0708993
$394$	3.60879e6	1.17117
$395$	6.21359e6	2.00378
$396$	553266.	0.177295
$397$	−3.86077e6	−1.22941	−0.614706	−	0.788757i	$-0.710725\pi$
$397$	−3.86077e6	−1.22941	−0.614706	+	0.788757i	$0.710725\pi$
$398$	1.92049e6	0.607722
$399$	−1.47000e6	−0.462260
$400$	1.03166e6	0.322393
$401$	−1.76635e6	−0.548549	−0.274274	−	0.961651i	$-0.588438\pi$
$401$	−1.76635e6	−0.548549	−0.274274	+	0.961651i	$0.588438\pi$
$402$	−2.61370e6	−0.806661
$403$	−3.81389e6	−1.16979
$404$	572359.	0.174468
$405$	−554974.	−0.168126
$406$	182982.	0.0550925
$407$	−3.99599e6	−1.19575
$408$	−971001.	−0.288781
$409$	−6.36346e6	−1.88098	−0.940492	−	0.339815i	$-0.889636\pi$
$409$	−6.36346e6	−1.88098	−0.940492	+	0.339815i	$0.889636\pi$
$410$	2.47421e6	0.726904
$411$	1.22129e6	0.356628
$412$	1.98994e6	0.577559
$413$	−289119.	−0.0834069
$414$	107023.	0.0306886
$415$	5.49735e6	1.56687
$416$	−705950.	−0.200005
$417$	1.37277e6	0.386596
$418$	−3.35808e6	−0.940049
$419$	−5.93403e6	−1.65126	−0.825628	−	0.564214i	$-0.809179\pi$
$419$	−5.93403e6	−1.65126	−0.825628	+	0.564214i	$0.809179\pi$
$420$	−1.01167e6	−0.279843
$421$	−6.31604e6	−1.73676	−0.868380	−	0.495900i	$-0.834838\pi$
$421$	−6.31604e6	−1.73676	−0.868380	+	0.495900i	$0.834838\pi$
$422$	−2.26120e6	−0.618099
$423$	−410099.	−0.111439
$424$	−636525.	−0.171950
$425$	−6.79349e6	−1.82440
$426$	76203.9	0.0203448
$427$	−3.26129e6	−0.865605
$428$	−2.56601e6	−0.677095
$429$	−2.64878e6	−0.694868
$430$	−353813.	−0.0922790
$431$	2.76241e6	0.716301	0.358150	−	0.933664i	$-0.383408\pi$
$431$	2.76241e6	0.716301	0.358150	+	0.933664i	$0.383408\pi$
$432$	186624.	0.0481125
$433$	−6.44275e6	−1.65140	−0.825699	−	0.564111i	$-0.809219\pi$
$433$	−6.44275e6	−1.65140	−0.825699	+	0.564111i	$0.809219\pi$
$434$	1.83793e6	0.468386
$435$	−419295.	−0.106242
$436$	831998.	0.209607
$437$	−649584.	−0.162717
$438$	−229757.	−0.0572246
$439$	5.57995e6	1.38187	0.690937	−	0.722915i	$-0.257198\pi$
$439$	5.57995e6	1.38187	0.690937	+	0.722915i	$0.257198\pi$
$440$	−2.31106e6	−0.569088
$441$	−802599.	−0.196518
$442$	4.64870e6	1.13182
$443$	−6.99188e6	−1.69272	−0.846359	−	0.532612i	$-0.821210\pi$
$443$	−6.99188e6	−1.69272	−0.846359	+	0.532612i	$0.821210\pi$
$444$	−1.34790e6	−0.324490
$445$	−7.14082e6	−1.70942
$446$	−2.16543e6	−0.515475
$447$	−610108.	−0.144423
$448$	340199.	0.0800826
$449$	5.16727e6	1.20961	0.604805	−	0.796374i	$-0.293251\pi$
$449$	5.16727e6	1.20961	0.604805	+	0.796374i	$0.293251\pi$
$450$	1.30569e6	0.303955
$451$	−3.12179e6	−0.722706
$452$	3.88459e6	0.894332
$453$	−1.66921e6	−0.382177
$454$	−739711.	−0.168431
$455$	4.84339e6	1.09678
$456$	−1.13273e6	−0.255101
$457$	2.05988e6	0.461372	0.230686	−	0.973028i	$-0.425903\pi$
$457$	2.05988e6	0.461372	0.230686	+	0.973028i	$0.425903\pi$
$458$	−212425.	−0.0473196
$459$	−1.22892e6	−0.272266
$460$	−447049.	−0.0985056
$461$	2.72445e6	0.597072	0.298536	−	0.954398i	$-0.403502\pi$
$461$	2.72445e6	0.597072	0.298536	+	0.954398i	$0.403502\pi$
$462$	1.27645e6	0.278227
$463$	5.55137e6	1.20350	0.601752	−	0.798683i	$-0.294470\pi$
$463$	5.55137e6	1.20350	0.601752	+	0.798683i	$0.294470\pi$
$464$	140999.	0.0304032
$465$	−4.21152e6	−0.903248
$466$	281165.	0.0599786
$467$	−1.72469e6	−0.365947	−0.182973	−	0.983118i	$-0.558572\pi$
$467$	−1.72469e6	−0.365947	−0.182973	+	0.983118i	$0.558572\pi$
$468$	−893468.	−0.188566
$469$	−6.03014e6	−1.26589
$470$	1.71303e6	0.357702
$471$	1.42414e6	0.295801
$472$	−222784.	−0.0460287
$473$	446417.	0.0917462
$474$	−2.64449e6	−0.540626
$475$	−7.92498e6	−1.61163
$476$	−2.24022e6	−0.453183
$477$	−805602.	−0.162116
$478$	−3.31293e6	−0.663196
$479$	3.93769e6	0.784156	0.392078	−	0.919932i	$-0.371756\pi$
$479$	3.93769e6	0.784156	0.392078	+	0.919932i	$0.371756\pi$
$480$	−779551.	−0.154434
$481$	6.45313e6	1.27177
$482$	688862.	0.135056
$483$	246916.	0.0481594
$484$	339117.	0.0658015
$485$	4.79894e6	0.926384
$486$	236196.	0.0453609
$487$	5.70852e6	1.09069	0.545345	−	0.838212i	$-0.316399\pi$
$487$	5.70852e6	1.09069	0.545345	+	0.838212i	$0.316399\pi$
$488$	−2.51302e6	−0.477691
$489$	5.88704e6	1.11333
$490$	3.35255e6	0.630791
$491$	2.02649e6	0.379351	0.189675	−	0.981847i	$-0.439256\pi$
$491$	2.02649e6	0.379351	0.189675	+	0.981847i	$0.439256\pi$
$492$	−1.05302e6	−0.196121
$493$	−928479.	−0.172050
$494$	5.42296e6	0.999814
$495$	−2.92493e6	−0.536541
$496$	1.41623e6	0.258482
$497$	175812.	0.0319269
$498$	−2.33967e6	−0.422747
$499$	8.48663e6	1.52575	0.762876	−	0.646545i	$-0.223787\pi$
$499$	8.48663e6	1.52575	0.762876	+	0.646545i	$0.223787\pi$
$500$	−1.22470e6	−0.219081
$501$	3.09591e6	0.551055
$502$	−4.92164e6	−0.871667
$503$	3.88342e6	0.684375	0.342187	−	0.939632i	$-0.388832\pi$
$503$	3.88342e6	0.684375	0.342187	+	0.939632i	$0.388832\pi$
$504$	430565.	0.0755026
$505$	−3.02587e6	−0.527986
$506$	564056.	0.0979368
$507$	935871.	0.161695
$508$	−68923.8	−0.0118498
$509$	−5.81830e6	−0.995410	−0.497705	−	0.867346i	$-0.665824\pi$
$509$	−5.81830e6	−0.995410	−0.497705	+	0.867346i	$0.665824\pi$
$510$	5.13336e6	0.873930
$511$	−530077.	−0.0898021
$512$	262144.	0.0441942
$513$	−1.43361e6	−0.240512
$514$	−3.15886e6	−0.527379
$515$	−1.05201e7	−1.74785
$516$	150583.	0.0248972
$517$	−2.16139e6	−0.355636
$518$	−3.10978e6	−0.509220
$519$	3.08139e6	0.502144
$520$	3.73213e6	0.605268
$521$	735274.	0.118674	0.0593369	−	0.998238i	$-0.481101\pi$
$521$	735274.	0.118674	0.0593369	+	0.998238i	$0.481101\pi$
$522$	178451.	0.0286644
$523$	−1.02363e7	−1.63639	−0.818197	−	0.574938i	$-0.805026\pi$
$523$	−1.02363e7	−1.63639	−0.818197	+	0.574938i	$0.805026\pi$
$524$	−385923.	−0.0614006
$525$	3.01239e6	0.476995
$526$	6.83334e6	1.07688
$527$	−9.32592e6	−1.46273
$528$	983583.	0.153542
$529$	−6.32723e6	−0.983048
$530$	3.36510e6	0.520365
$531$	−281961.	−0.0433963
$532$	−2.61334e6	−0.400329
$533$	5.04137e6	0.768654
$534$	3.03912e6	0.461206
$535$	1.35657e7	2.04907
$536$	−4.64659e6	−0.698589
$537$	4.93644e6	0.738717
$538$	4.84906e6	0.722274
$539$	−4.23002e6	−0.627148
$540$	−986620.	−0.145601
$541$	−5.41666e6	−0.795681	−0.397840	−	0.917455i	$-0.630240\pi$
$541$	−5.41666e6	−0.795681	−0.397840	+	0.917455i	$0.630240\pi$
$542$	−6.50813e6	−0.951608
$543$	−6.46330e6	−0.940707
$544$	−1.72622e6	−0.250092
$545$	−4.39850e6	−0.634327
$546$	−2.06134e6	−0.295916
$547$	91634.7	0.0130946	0.00654729	−	0.999979i	$-0.497916\pi$
$547$	91634.7	0.0130946	0.00654729	+	0.999979i	$0.497916\pi$
$548$	2.17119e6	0.308849
$549$	−3.18054e6	−0.450371
$550$	6.88152e6	0.970014
$551$	−1.08312e6	−0.151984
$552$	190264.	0.0265771
$553$	−6.10118e6	−0.848400
$554$	2.57144e6	0.355961
$555$	7.12592e6	0.981993
$556$	2.44048e6	0.334802
$557$	−1.08598e7	−1.48315	−0.741574	−	0.670871i	$-0.765921\pi$
$557$	−1.08598e7	−1.48315	−0.741574	+	0.670871i	$0.765921\pi$
$558$	1.79242e6	0.243699
$559$	−720919.	−0.0975791
$560$	−1.79852e6	−0.242351
$561$	−6.47692e6	−0.868883
$562$	−1.45471e6	−0.194283
$563$	1.26642e6	0.168387	0.0841933	−	0.996449i	$-0.473169\pi$
$563$	1.26642e6	0.168387	0.0841933	+	0.996449i	$0.473169\pi$
$564$	−729065.	−0.0965092
$565$	−2.05365e7	−2.70649
$566$	−8.26513e6	−1.08445
$567$	544933.	0.0711845
$568$	135474.	0.0176191
$569$	8.54113e6	1.10595	0.552974	−	0.833198i	$-0.313493\pi$
$569$	8.54113e6	1.10595	0.552974	+	0.833198i	$0.313493\pi$
$570$	5.98835e6	0.772005
$571$	−978262.	−0.125564	−0.0627820	−	0.998027i	$-0.519997\pi$
$571$	−978262.	−0.125564	−0.0627820	+	0.998027i	$0.519997\pi$
$572$	−4.70894e6	−0.601773
$573$	−1.65970e6	−0.211175
$574$	−2.42945e6	−0.307771
$575$	1.33116e6	0.167903
$576$	331776.	0.0416667
$577$	−4.44848e6	−0.556252	−0.278126	−	0.960545i	$-0.589713\pi$
$577$	−4.44848e6	−0.556252	−0.278126	+	0.960545i	$0.589713\pi$
$578$	5.68780e6	0.708149
$579$	5.03715e6	0.624437
$580$	−745413.	−0.0920083
$581$	−5.39790e6	−0.663414
$582$	−2.04242e6	−0.249941
$583$	−4.24585e6	−0.517360
$584$	−408456.	−0.0495579
$585$	4.72347e6	0.570652
$586$	7.34585e6	0.883686
$587$	1.15561e7	1.38426	0.692128	−	0.721775i	$-0.256673\pi$
$587$	1.15561e7	1.38426	0.692128	+	0.721775i	$0.256673\pi$
$588$	−1.42684e6	−0.170189
$589$	−1.08792e7	−1.29214
$590$	1.17779e6	0.139295
$591$	8.11978e6	0.956259
$592$	−2.39627e6	−0.281016
$593$	−9.06120e6	−1.05815	−0.529077	−	0.848574i	$-0.677462\pi$
$593$	−9.06120e6	−1.05815	−0.529077	+	0.848574i	$0.677462\pi$
$594$	1.24485e6	0.144761
$595$	1.18433e7	1.37145
$596$	−1.08464e6	−0.125074
$597$	4.32111e6	0.496203
$598$	−910893.	−0.104163
$599$	−4.71057e6	−0.536421	−0.268211	−	0.963360i	$-0.586432\pi$
$599$	−4.71057e6	−0.536421	−0.268211	+	0.963360i	$0.586432\pi$
$600$	2.32123e6	0.263233
$601$	1.51830e7	1.71463	0.857316	−	0.514790i	$-0.172130\pi$
$601$	1.51830e7	1.71463	0.857316	+	0.514790i	$0.172130\pi$
$602$	347412.	0.0390710
$603$	−5.88083e6	−0.658636
$604$	−2.96748e6	−0.330975
$605$	−1.79280e6	−0.199133
$606$	1.28781e6	0.142452
$607$	1.08612e6	0.119648	0.0598241	−	0.998209i	$-0.480946\pi$
$607$	1.08612e6	0.119648	0.0598241	+	0.998209i	$0.480946\pi$
$608$	−2.01373e6	−0.220924
$609$	411709.	0.0449829
$610$	1.32855e7	1.44562
$611$	3.49042e6	0.378246
$612$	−2.18475e6	−0.235789
$613$	1.69412e7	1.82093	0.910465	−	0.413585i	$-0.135724\pi$
$613$	1.69412e7	1.82093	0.910465	+	0.413585i	$0.135724\pi$
$614$	1.06235e7	1.13723
$615$	5.56697e6	0.593515
$616$	2.26925e6	0.240952
$617$	−5.17957e6	−0.547748	−0.273874	−	0.961766i	$-0.588305\pi$
$617$	−5.17957e6	−0.547748	−0.273874	+	0.961766i	$0.588305\pi$
$618$	4.47736e6	0.471575
$619$	−1.26846e7	−1.33061	−0.665304	−	0.746573i	$-0.731698\pi$
$619$	−1.26846e7	−1.33061	−0.665304	+	0.746573i	$0.731698\pi$
$620$	−7.48715e6	−0.782235
$621$	240802.	0.0250572
$622$	−3.52516e6	−0.365345
$623$	7.01163e6	0.723767
$624$	−1.58839e6	−0.163303
$625$	−6.11890e6	−0.626575
$626$	−957361.	−0.0976428
$627$	−7.55568e6	−0.767546
$628$	2.53180e6	0.256172
$629$	1.57795e7	1.59025
$630$	−2.27625e6	−0.228491
$631$	−5.81202e6	−0.581104	−0.290552	−	0.956859i	$-0.593839\pi$
$631$	−5.81202e6	−0.581104	−0.290552	+	0.956859i	$0.593839\pi$
$632$	−4.70132e6	−0.468196
$633$	−5.08771e6	−0.504676
$634$	−142125.	−0.0140426
$635$	364377.	0.0358605
$636$	−1.43218e6	−0.140396
$637$	6.83105e6	0.667020
$638$	940510.	0.0914769
$639$	171459.	0.0166115
$640$	−1.38587e6	−0.133743
$641$	7.73784e6	0.743832	0.371916	−	0.928266i	$-0.378701\pi$
$641$	7.73784e6	0.743832	0.371916	+	0.928266i	$0.378701\pi$
$642$	−5.77353e6	−0.552846
$643$	−1.77268e7	−1.69084	−0.845419	−	0.534104i	$-0.820649\pi$
$643$	−1.77268e7	−1.69084	−0.845419	+	0.534104i	$0.820649\pi$
$644$	438962.	0.0417073
$645$	−796080.	−0.0753455
$646$	1.32605e7	1.25020
$647$	1.23884e7	1.16347	0.581735	−	0.813379i	$-0.302374\pi$
$647$	1.23884e7	1.16347	0.581735	+	0.813379i	$0.302374\pi$
$648$	419904.	0.0392837
$649$	−1.48605e6	−0.138491
$650$	−1.11130e7	−1.03168
$651$	4.13533e6	0.382435
$652$	1.04658e7	0.964174
$653$	1.48310e7	1.36109	0.680547	−	0.732705i	$-0.261742\pi$
$653$	1.48310e7	1.36109	0.680547	+	0.732705i	$0.261742\pi$
$654$	1.87200e6	0.171144
$655$	2.04025e6	0.185815
$656$	−1.87204e6	−0.169846
$657$	−516952.	−0.0467237
$658$	−1.68204e6	−0.151451
$659$	−1.47278e7	−1.32106	−0.660531	−	0.750799i	$-0.729669\pi$
$659$	−1.47278e7	−1.32106	−0.660531	+	0.750799i	$0.729669\pi$
$660$	−5.19988e6	−0.464658
$661$	2.61686e6	0.232958	0.116479	−	0.993193i	$-0.462839\pi$
$661$	2.61686e6	0.232958	0.116479	+	0.993193i	$0.462839\pi$
$662$	−7.63612e6	−0.677217
$663$	1.04596e7	0.924124
$664$	−4.15941e6	−0.366110
$665$	1.38159e7	1.21150
$666$	−3.03278e6	−0.264945
$667$	181932.	0.0158341
$668$	5.50385e6	0.477227
$669$	−4.87223e6	−0.420884
$670$	2.45650e7	2.11412
$671$	−1.67627e7	−1.43727
$672$	765448.	0.0653872
$673$	−1.00253e7	−0.853218	−0.426609	−	0.904436i	$-0.640292\pi$
$673$	−1.00253e7	−0.853218	−0.426609	+	0.904436i	$0.640292\pi$
$674$	3.80614e6	0.322727
$675$	2.93781e6	0.248178
$676$	1.66377e6	0.140032
$677$	2.78401e6	0.233453	0.116726	−	0.993164i	$-0.462760\pi$
$677$	2.78401e6	0.233453	0.116726	+	0.993164i	$0.462760\pi$
$678$	8.74032e6	0.730219
$679$	−4.71212e6	−0.392231
$680$	9.12598e6	0.756845
$681$	−1.66435e6	−0.137523
$682$	9.44677e6	0.777718
$683$	1.81676e7	1.49021	0.745104	−	0.666948i	$-0.232400\pi$
$683$	1.81676e7	1.49021	0.745104	+	0.666948i	$0.232400\pi$
$684$	−2.54863e6	−0.208289
$685$	−1.14784e7	−0.934660
$686$	−8.87562e6	−0.720093
$687$	−477955.	−0.0386363
$688$	267702.	0.0215616
$689$	6.85662e6	0.550252
$690$	−1.00586e6	−0.0804295
$691$	1.14502e7	0.912257	0.456128	−	0.889914i	$-0.349236\pi$
$691$	1.14502e7	0.912257	0.456128	+	0.889914i	$0.349236\pi$
$692$	5.47803e6	0.434869
$693$	2.87202e6	0.227172
$694$	5.23725e6	0.412767
$695$	−1.29020e7	−1.01320
$696$	317247.	0.0248241
$697$	1.23274e7	0.961147
$698$	−6.45825e6	−0.501737
$699$	632621.	0.0489723
$700$	5.35537e6	0.413089
$701$	5.89455e6	0.453060	0.226530	−	0.974004i	$-0.427262\pi$
$701$	5.89455e6	0.453060	0.226530	+	0.974004i	$0.427262\pi$
$702$	−2.01030e6	−0.153964
$703$	1.84077e7	1.40479
$704$	1.74859e6	0.132971
$705$	3.85433e6	0.292062
$706$	−1.44720e7	−1.09274
$707$	2.97113e6	0.223549
$708$	−501264.	−0.0375823
$709$	654216.	0.0488771	0.0244386	−	0.999701i	$-0.492220\pi$
$709$	654216.	0.0488771	0.0244386	+	0.999701i	$0.492220\pi$
$710$	−716205.	−0.0533201
$711$	−5.95011e6	−0.441419
$712$	5.40289e6	0.399416
$713$	1.82738e6	0.134618
$714$	−5.04049e6	−0.370022
$715$	2.48946e7	1.82113
$716$	8.77589e6	0.639748
$717$	−7.45408e6	−0.541497
$718$	1.02592e7	0.742682
$719$	2.01964e6	0.145698	0.0728488	−	0.997343i	$-0.476791\pi$
$719$	2.01964e6	0.145698	0.0728488	+	0.997343i	$0.476791\pi$
$720$	−1.75399e6	−0.126094
$721$	1.03298e7	0.740039
$722$	5.56469e6	0.397281
$723$	1.54994e6	0.110273
$724$	−1.14903e7	−0.814676
$725$	2.21958e6	0.156829
$726$	763012.	0.0537267
$727$	1.90948e7	1.33992	0.669962	−	0.742395i	$-0.266310\pi$
$727$	1.90948e7	1.33992	0.669962	+	0.742395i	$0.266310\pi$
$728$	−3.66461e6	−0.256271
$729$	531441.	0.0370370
$730$	2.15937e6	0.149976
$731$	−1.76283e6	−0.122016
$732$	−5.65430e6	−0.390033
$733$	1.83531e7	1.26168	0.630839	−	0.775914i	$-0.282711\pi$
$733$	1.83531e7	1.26168	0.630839	+	0.775914i	$0.282711\pi$
$734$	2.56563e6	0.175774
$735$	7.54324e6	0.515039
$736$	338246.	0.0230165
$737$	−3.09944e7	−2.10191
$738$	−2.36930e6	−0.160132
$739$	5.10847e6	0.344096	0.172048	−	0.985089i	$-0.444962\pi$
$739$	5.10847e6	0.344096	0.172048	+	0.985089i	$0.444962\pi$
$740$	1.26683e7	0.850431
$741$	1.22017e7	0.816344
$742$	−3.30422e6	−0.220323
$743$	−7.75700e6	−0.515492	−0.257746	−	0.966213i	$-0.582980\pi$
$743$	−7.75700e6	−0.515492	−0.257746	+	0.966213i	$0.582980\pi$
$744$	3.18652e6	0.211050
$745$	5.73411e6	0.378509
$746$	1.89078e7	1.24393
$747$	−5.26425e6	−0.345172
$748$	−1.15145e7	−0.752475
$749$	−1.33202e7	−0.867576
$750$	−2.75557e6	−0.178879
$751$	−9.66566e6	−0.625362	−0.312681	−	0.949858i	$-0.601227\pi$
$751$	−9.66566e6	−0.625362	−0.312681	+	0.949858i	$0.601227\pi$
$752$	−1.29612e6	−0.0835794
$753$	−1.10737e7	−0.711713
$754$	−1.51883e6	−0.0972927
$755$	1.56881e7	1.00162
$756$	968770.	0.0616476
$757$	−1.62997e7	−1.03381	−0.516904	−	0.856044i	$-0.672915\pi$
$757$	−1.62997e7	−1.03381	−0.516904	+	0.856044i	$0.672915\pi$
$758$	−1.49436e7	−0.944677
$759$	1.26913e6	0.0799650
$760$	1.06460e7	0.668576
$761$	9.20630e6	0.576267	0.288133	−	0.957590i	$-0.406965\pi$
$761$	9.20630e6	0.576267	0.288133	+	0.957590i	$0.406965\pi$
$762$	−155078.	−0.00967529
$763$	4.31893e6	0.268574
$764$	−2.95057e6	−0.182883
$765$	1.15501e7	0.713561
$766$	−9.00092e6	−0.554262
$767$	2.39982e6	0.147296
$768$	589824.	0.0360844
$769$	2.94310e7	1.79469	0.897345	−	0.441331i	$-0.145493\pi$
$769$	2.94310e7	1.79469	0.897345	+	0.441331i	$0.145493\pi$
$770$	−1.19968e7	−0.729185
$771$	−7.10744e6	−0.430603
$772$	8.95494e6	0.540779
$773$	−1.38549e7	−0.833976	−0.416988	−	0.908912i	$-0.636914\pi$
$773$	−1.38549e7	−0.833976	−0.416988	+	0.908912i	$0.636914\pi$
$774$	338811.	0.0203285
$775$	2.22941e7	1.33333
$776$	−3.63097e6	−0.216456
$777$	−6.99700e6	−0.415776
$778$	5.69366e6	0.337243
$779$	1.43806e7	0.849050
$780$	8.39728e6	0.494200
$781$	903657.	0.0530122
$782$	−2.22736e6	−0.130249
$783$	401515.	0.0234044
$784$	−2.53661e6	−0.147388
$785$	−1.33848e7	−0.775244
$786$	−868327.	−0.0501334
$787$	2.44180e7	1.40531	0.702657	−	0.711529i	$-0.251997\pi$
$787$	2.44180e7	1.40531	0.702657	+	0.711529i	$0.251997\pi$
$788$	1.44352e7	0.828144
$789$	1.53750e7	0.879271
$790$	2.48544e7	1.41689
$791$	2.01650e7	1.14593
$792$	2.21306e6	0.125366
$793$	2.70701e7	1.52865
$794$	−1.54431e7	−0.869325
$795$	7.57148e6	0.424876
$796$	7.68197e6	0.429724
$797$	−1.82529e7	−1.01785	−0.508926	−	0.860810i	$-0.669957\pi$
$797$	−1.82529e7	−1.01785	−0.508926	+	0.860810i	$0.669957\pi$
$798$	−5.88001e6	−0.326867
$799$	8.53495e6	0.472971
$800$	4.12663e6	0.227966
$801$	6.83803e6	0.376573
$802$	−7.06539e6	−0.387883
$803$	−2.72455e6	−0.149109
$804$	−1.04548e7	−0.570396
$805$	−2.32065e6	−0.126217
$806$	−1.52556e7	−0.827163
$807$	1.09104e7	0.589734
$808$	2.28944e6	0.123367
$809$	−612373.	−0.0328962	−0.0164481	−	0.999865i	$-0.505236\pi$
$809$	−612373.	−0.0328962	−0.0164481	+	0.999865i	$0.505236\pi$
$810$	−2.21989e6	−0.118883
$811$	−2.49830e7	−1.33381	−0.666903	−	0.745144i	$-0.732381\pi$
$811$	−2.49830e7	−1.33381	−0.666903	+	0.745144i	$0.732381\pi$
$812$	731927.	0.0389563
$813$	−1.46433e7	−0.776985
$814$	−1.59840e7	−0.845520
$815$	−5.53295e7	−2.91785
$816$	−3.88400e6	−0.204199
$817$	−2.05643e6	−0.107785
$818$	−2.54539e7	−1.33006
$819$	−4.63802e6	−0.241614
$820$	9.89684e6	0.513999
$821$	−1.89324e7	−0.980274	−0.490137	−	0.871646i	$-0.663053\pi$
$821$	−1.89324e7	−0.980274	−0.490137	+	0.871646i	$0.663053\pi$
$822$	4.88518e6	0.252174
$823$	2.13907e7	1.10084	0.550421	−	0.834887i	$-0.314467\pi$
$823$	2.13907e7	1.10084	0.550421	+	0.834887i	$0.314467\pi$
$824$	7.95975e6	0.408396
$825$	1.54834e7	0.792013
$826$	−1.15648e6	−0.0589776
$827$	−4.91183e6	−0.249735	−0.124867	−	0.992173i	$-0.539851\pi$
$827$	−4.91183e6	−0.249735	−0.124867	+	0.992173i	$0.539851\pi$
$828$	428093.	0.0217001
$829$	−1.60441e7	−0.810827	−0.405413	−	0.914133i	$-0.632872\pi$
$829$	−1.60441e7	−0.810827	−0.405413	+	0.914133i	$0.632872\pi$
$830$	2.19894e7	1.10795
$831$	5.78575e6	0.290641
$832$	−2.82380e6	−0.141425
$833$	1.67036e7	0.834062
$834$	5.49108e6	0.273365
$835$	−2.90970e7	−1.44422
$836$	−1.34323e7	−0.664715
$837$	4.03294e6	0.198980
$838$	−2.37361e7	−1.16761
$839$	−1.91588e7	−0.939646	−0.469823	−	0.882761i	$-0.655682\pi$
$839$	−1.91588e7	−0.939646	−0.469823	+	0.882761i	$0.655682\pi$
$840$	−4.04667e6	−0.197879
$841$	−2.02078e7	−0.985210
$842$	−2.52642e7	−1.22807
$843$	−3.27309e6	−0.158631
$844$	−9.04481e6	−0.437062
$845$	−8.79580e6	−0.423773
$846$	−1.64040e6	−0.0787994
$847$	1.76036e6	0.0843128
$848$	−2.54610e6	−0.121587
$849$	−1.85965e7	−0.885448
$850$	−2.71740e7	−1.29005
$851$	−3.09193e6	−0.146354
$852$	304816.	0.0143859
$853$	−7.89213e6	−0.371383	−0.185691	−	0.982608i	$-0.559452\pi$
$853$	−7.89213e6	−0.371383	−0.185691	+	0.982608i	$0.559452\pi$
$854$	−1.30452e7	−0.612075
$855$	1.34738e7	0.630339
$856$	−1.02641e7	−0.478778
$857$	−9.70470e6	−0.451367	−0.225684	−	0.974201i	$-0.572462\pi$
$857$	−9.70470e6	−0.451367	−0.225684	+	0.974201i	$0.572462\pi$
$858$	−1.05951e7	−0.491346
$859$	−2.18223e7	−1.00906	−0.504531	−	0.863394i	$-0.668335\pi$
$859$	−2.18223e7	−1.00906	−0.504531	+	0.863394i	$0.668335\pi$
$860$	−1.41525e6	−0.0652511
$861$	−5.46626e6	−0.251294
$862$	1.10496e7	0.506501
$863$	−1.25291e7	−0.572653	−0.286326	−	0.958132i	$-0.592434\pi$
$863$	−1.25291e7	−0.572653	−0.286326	+	0.958132i	$0.592434\pi$
$864$	746496.	0.0340207
$865$	−2.89605e7	−1.31603
$866$	−2.57710e7	−1.16771
$867$	1.27975e7	0.578201
$868$	7.35170e6	0.331199
$869$	−3.13595e7	−1.40870
$870$	−1.67718e6	−0.0751244
$871$	5.00528e7	2.23554
$872$	3.32799e6	0.148215
$873$	−4.59545e6	−0.204076
$874$	−2.59834e6	−0.115058
$875$	−6.35745e6	−0.280713
$876$	−919026.	−0.0404639
$877$	−1.37306e7	−0.602824	−0.301412	−	0.953494i	$-0.597458\pi$
$877$	−1.37306e7	−0.602824	−0.301412	+	0.953494i	$0.597458\pi$
$878$	2.23198e7	0.977133
$879$	1.65282e7	0.721526
$880$	−9.24423e6	−0.402406
$881$	−4.07060e7	−1.76693	−0.883463	−	0.468501i	$-0.844794\pi$
$881$	−4.07060e7	−1.76693	−0.883463	+	0.468501i	$0.844794\pi$
$882$	−3.21040e6	−0.138959
$883$	−2.43048e7	−1.04904	−0.524518	−	0.851400i	$-0.675754\pi$
$883$	−2.43048e7	−1.04904	−0.524518	+	0.851400i	$0.675754\pi$
$884$	1.85948e7	0.800314
$885$	2.65002e6	0.113734
$886$	−2.79675e7	−1.19693
$887$	4.23815e7	1.80870	0.904351	−	0.426789i	$-0.140355\pi$
$887$	4.23815e7	1.80870	0.904351	+	0.426789i	$0.140355\pi$
$888$	−5.39161e6	−0.229449
$889$	−357785.	−0.0151834
$890$	−2.85633e7	−1.20874
$891$	2.80091e6	0.118196
$892$	−8.66173e6	−0.364496
$893$	9.95649e6	0.417809
$894$	−2.44043e6	−0.102123
$895$	−4.63953e7	−1.93605
$896$	1.36080e6	0.0566270
$897$	−2.04951e6	−0.0850489
$898$	2.06691e7	0.855323
$899$	3.04698e6	0.125739
$900$	5.22277e6	0.214929
$901$	1.67661e7	0.688052
$902$	−1.24871e7	−0.511031
$903$	781678.	0.0319013
$904$	1.55383e7	0.632388
$905$	6.07455e7	2.46543
$906$	−6.67683e6	−0.270240
$907$	8.46090e6	0.341506	0.170753	−	0.985314i	$-0.445380\pi$
$907$	8.46090e6	0.341506	0.170753	+	0.985314i	$0.445380\pi$
$908$	−2.95884e6	−0.119099
$909$	2.89757e6	0.116312
$910$	1.93736e7	0.775544
$911$	−3.26892e7	−1.30499	−0.652497	−	0.757792i	$-0.726278\pi$
$911$	−3.26892e7	−1.30499	−0.652497	+	0.757792i	$0.726278\pi$
$912$	−4.53090e6	−0.180384
$913$	−2.77447e7	−1.10155
$914$	8.23951e6	0.326239
$915$	2.98924e7	1.18034
$916$	−849698.	−0.0334600
$917$	−2.00334e6	−0.0786739
$918$	−4.91569e6	−0.192521
$919$	1.94127e7	0.758224	0.379112	−	0.925351i	$-0.376229\pi$
$919$	1.94127e7	0.758224	0.379112	+	0.925351i	$0.376229\pi$
$920$	−1.78820e6	−0.0696540
$921$	2.39029e7	0.928544
$922$	1.08978e7	0.422193
$923$	−1.45932e6	−0.0563826
$924$	5.10581e6	0.196736
$925$	−3.77218e7	−1.44956
$926$	2.22055e7	0.851006
$927$	1.00741e7	0.385039
$928$	563994.	0.0214983
$929$	−2.93231e7	−1.11473	−0.557366	−	0.830267i	$-0.688188\pi$
$929$	−2.93231e7	−1.11473	−0.557366	+	0.830267i	$0.688188\pi$
$930$	−1.68461e7	−0.638693
$931$	1.94857e7	0.736786
$932$	1.12466e6	0.0424113
$933$	−7.93161e6	−0.298303
$934$	−6.89874e6	−0.258763
$935$	6.08735e7	2.27719
$936$	−3.57387e6	−0.133337
$937$	−1.87668e7	−0.698297	−0.349149	−	0.937067i	$-0.613529\pi$
$937$	−1.87668e7	−0.698297	−0.349149	+	0.937067i	$0.613529\pi$
$938$	−2.41206e7	−0.895118
$939$	−2.15406e6	−0.0797250
$940$	6.85214e6	0.252933
$941$	3.41601e7	1.25761	0.628803	−	0.777565i	$-0.283545\pi$
$941$	3.41601e7	1.25761	0.628803	+	0.777565i	$0.283545\pi$
$942$	5.69656e6	0.209163
$943$	−2.41550e6	−0.0884563
$944$	−891136.	−0.0325472
$945$	−5.12157e6	−0.186562
$946$	1.78567e6	0.0648743
$947$	3.54709e7	1.28528	0.642640	−	0.766168i	$-0.277839\pi$
$947$	3.54709e7	1.28528	0.642640	+	0.766168i	$0.277839\pi$
$948$	−1.05780e7	−0.382280
$949$	4.39987e6	0.158589
$950$	−3.16999e7	−1.13959
$951$	−319780.	−0.0114657
$952$	−8.96088e6	−0.320448
$953$	−2.16839e7	−0.773402	−0.386701	−	0.922205i	$-0.626385\pi$
$953$	−2.16839e7	−0.773402	−0.386701	+	0.922205i	$0.626385\pi$
$954$	−3.22241e6	−0.114633
$955$	1.55987e7	0.553452
$956$	−1.32517e7	−0.468951
$957$	2.11615e6	0.0746906
$958$	1.57507e7	0.554482
$959$	1.12707e7	0.395735
$960$	−3.11821e6	−0.109201
$961$	1.97562e6	0.0690072
$962$	2.58125e7	0.899275
$963$	−1.29904e7	−0.451397
$964$	2.75545e6	0.0954992
$965$	−4.73418e7	−1.63654
$966$	987664.	0.0340539
$967$	−1.71354e7	−0.589287	−0.294644	−	0.955607i	$-0.595201\pi$
$967$	−1.71354e7	−0.589287	−0.294644	+	0.955607i	$0.595201\pi$
$968$	1.35647e6	0.0465287
$969$	2.98361e7	1.02078
$970$	1.91958e7	0.655052
$971$	6.63195e6	0.225732	0.112866	−	0.993610i	$-0.463997\pi$
$971$	6.63195e6	0.225732	0.112866	+	0.993610i	$0.463997\pi$
$972$	944784.	0.0320750
$973$	1.26686e7	0.428989
$974$	2.28341e7	0.771234
$975$	−2.50042e7	−0.842366
$976$	−1.00521e7	−0.337778
$977$	387628.	0.0129921	0.00649603	−	0.999979i	$-0.497932\pi$
$977$	387628.	0.0129921	0.00649603	+	0.999979i	$0.497932\pi$
$978$	2.35481e7	0.787244
$979$	3.60391e7	1.20176
$980$	1.34102e7	0.446037
$981$	4.21199e6	0.139738
$982$	8.10596e6	0.268241
$983$	−2.29393e7	−0.757175	−0.378587	−	0.925566i	$-0.623590\pi$
$983$	−2.29393e7	−0.757175	−0.378587	+	0.925566i	$0.623590\pi$
$984$	−4.21208e6	−0.138679
$985$	−7.63139e7	−2.50619
$986$	−3.71391e6	−0.121658
$987$	−3.78460e6	−0.123659
$988$	2.16918e7	0.706975
$989$	345418.	0.0112293
$990$	−1.16997e7	−0.379392
$991$	1.92555e7	0.622831	0.311415	−	0.950274i	$-0.399197\pi$
$991$	1.92555e7	0.622831	0.311415	+	0.950274i	$0.399197\pi$
$992$	5.66493e6	0.182774
$993$	−1.71813e7	−0.552945
$994$	703248.	0.0225758
$995$	−4.06120e7	−1.30046
$996$	−9.35867e6	−0.298927
$997$	−1.09492e7	−0.348854	−0.174427	−	0.984670i	$-0.555807\pi$
$997$	−1.09492e7	−0.348854	−0.174427	+	0.984670i	$0.555807\pi$
$998$	3.39465e7	1.07887
$999$	−6.82376e6	−0.216327

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	354.6.a.b.1.1	✓	4
3.2	odd	2		1062.6.a.b.1.4		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
354.6.a.b.1.1	✓	4	1.1	even	1	trivial
1062.6.a.b.1.4		4	3.2	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:	\( N \)	\(=\)	\( 354 = 2 \cdot 3 \cdot 59 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	354.a (trivial)

\(f(q)\)	\(=\)	\(q+4.00000 q^{2} +9.00000 q^{3} +16.0000 q^{4} -84.5867 q^{5} +36.0000 q^{6} +83.0564 q^{7} +64.0000 q^{8} +81.0000 q^{9} +O(q^{10})\)	\(q+4.00000 q^{2} +9.00000 q^{3} +16.0000 q^{4} -84.5867 q^{5} +36.0000 q^{6} +83.0564 q^{7} +64.0000 q^{8} +81.0000 q^{9} -338.347 q^{10} +426.903 q^{11} +144.000 q^{12} -689.405 q^{13} +332.226 q^{14} -761.281 q^{15} +256.000 q^{16} -1685.77 q^{17} +324.000 q^{18} -1966.54 q^{19} -1353.39 q^{20} +747.508 q^{21} +1707.61 q^{22} +330.319 q^{23} +576.000 q^{24} +4029.91 q^{25} -2757.62 q^{26} +729.000 q^{27} +1328.90 q^{28} +550.776 q^{29} -3045.12 q^{30} +5532.16 q^{31} +1024.00 q^{32} +3842.12 q^{33} -6743.06 q^{34} -7025.47 q^{35} +1296.00 q^{36} -9360.44 q^{37} -7866.15 q^{38} -6204.64 q^{39} -5413.55 q^{40} -7312.65 q^{41} +2990.03 q^{42} +1045.71 q^{43} +6830.44 q^{44} -6851.52 q^{45} +1321.28 q^{46} -5062.95 q^{47} +2304.00 q^{48} -9908.63 q^{49} +16119.7 q^{50} -15171.9 q^{51} -11030.5 q^{52} -9945.71 q^{53} +2916.00 q^{54} -36110.3 q^{55} +5315.61 q^{56} -17698.8 q^{57} +2203.10 q^{58} -3481.00 q^{59} -12180.5 q^{60} -39266.0 q^{61} +22128.6 q^{62} +6727.57 q^{63} +4096.00 q^{64} +58314.5 q^{65} +15368.5 q^{66} -72602.9 q^{67} -26972.3 q^{68} +2972.87 q^{69} -28101.9 q^{70} +2116.78 q^{71} +5184.00 q^{72} -6382.13 q^{73} -37441.7 q^{74} +36269.2 q^{75} -31464.6 q^{76} +35457.0 q^{77} -24818.6 q^{78} -73458.2 q^{79} -21654.2 q^{80} +6561.00 q^{81} -29250.6 q^{82} -64990.7 q^{83} +11960.1 q^{84} +142593. q^{85} +4182.85 q^{86} +4956.98 q^{87} +27321.8 q^{88} +84420.1 q^{89} -27406.1 q^{90} -57259.5 q^{91} +5285.10 q^{92} +49789.4 q^{93} -20251.8 q^{94} +166343. q^{95} +9216.00 q^{96} -56734.0 q^{97} -39634.5 q^{98} +34579.1 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 16 q^{2} + 36 q^{3} + 64 q^{4} - 104 q^{5} + 144 q^{6} - 162 q^{7} + 256 q^{8} + 324 q^{9}+O(q^{10}) \) 4 * q + 16 * q^2 + 36 * q^3 + 64 * q^4 - 104 * q^5 + 144 * q^6 - 162 * q^7 + 256 * q^8 + 324 * q^9	\( 4 q + 16 q^{2} + 36 q^{3} + 64 q^{4} - 104 q^{5} + 144 q^{6} - 162 q^{7} + 256 q^{8} + 324 q^{9} - 416 q^{10} - 676 q^{11} + 576 q^{12} - 792 q^{13} - 648 q^{14} - 936 q^{15} + 1024 q^{16} - 2474 q^{17} + 1296 q^{18} - 4538 q^{19} - 1664 q^{20} - 1458 q^{21} - 2704 q^{22} - 1238 q^{23} + 2304 q^{24} - 832 q^{25} - 3168 q^{26} + 2916 q^{27} - 2592 q^{28} - 4958 q^{29} - 3744 q^{30} - 7138 q^{31} + 4096 q^{32} - 6084 q^{33} - 9896 q^{34} - 13554 q^{35} + 5184 q^{36} - 13570 q^{37} - 18152 q^{38} - 7128 q^{39} - 6656 q^{40} - 13826 q^{41} - 5832 q^{42} - 1236 q^{43} - 10816 q^{44} - 8424 q^{45} - 4952 q^{46} - 12410 q^{47} + 9216 q^{48} - 24622 q^{49} - 3328 q^{50} - 22266 q^{51} - 12672 q^{52} - 50904 q^{53} + 11664 q^{54} - 20872 q^{55} - 10368 q^{56} - 40842 q^{57} - 19832 q^{58} - 13924 q^{59} - 14976 q^{60} - 70622 q^{61} - 28552 q^{62} - 13122 q^{63} + 16384 q^{64} + 17460 q^{65} - 24336 q^{66} - 50012 q^{67} - 39584 q^{68} - 11142 q^{69} - 54216 q^{70} + 21192 q^{71} + 20736 q^{72} - 13358 q^{73} - 54280 q^{74} - 7488 q^{75} - 72608 q^{76} + 98658 q^{77} - 28512 q^{78} + 6464 q^{79} - 26624 q^{80} + 26244 q^{81} - 55304 q^{82} + 51506 q^{83} - 23328 q^{84} + 61786 q^{85} - 4944 q^{86} - 44622 q^{87} - 43264 q^{88} + 90738 q^{89} - 33696 q^{90} + 48870 q^{91} - 19808 q^{92} - 64242 q^{93} - 49640 q^{94} + 171394 q^{95} + 36864 q^{96} - 266068 q^{97} - 98488 q^{98} - 54756 q^{99}+O(q^{100}) \) 4 * q + 16 * q^2 + 36 * q^3 + 64 * q^4 - 104 * q^5 + 144 * q^6 - 162 * q^7 + 256 * q^8 + 324 * q^9 - 416 * q^10 - 676 * q^11 + 576 * q^12 - 792 * q^13 - 648 * q^14 - 936 * q^15 + 1024 * q^16 - 2474 * q^17 + 1296 * q^18 - 4538 * q^19 - 1664 * q^20 - 1458 * q^21 - 2704 * q^22 - 1238 * q^23 + 2304 * q^24 - 832 * q^25 - 3168 * q^26 + 2916 * q^27 - 2592 * q^28 - 4958 * q^29 - 3744 * q^30 - 7138 * q^31 + 4096 * q^32 - 6084 * q^33 - 9896 * q^34 - 13554 * q^35 + 5184 * q^36 - 13570 * q^37 - 18152 * q^38 - 7128 * q^39 - 6656 * q^40 - 13826 * q^41 - 5832 * q^42 - 1236 * q^43 - 10816 * q^44 - 8424 * q^45 - 4952 * q^46 - 12410 * q^47 + 9216 * q^48 - 24622 * q^49 - 3328 * q^50 - 22266 * q^51 - 12672 * q^52 - 50904 * q^53 + 11664 * q^54 - 20872 * q^55 - 10368 * q^56 - 40842 * q^57 - 19832 * q^58 - 13924 * q^59 - 14976 * q^60 - 70622 * q^61 - 28552 * q^62 - 13122 * q^63 + 16384 * q^64 + 17460 * q^65 - 24336 * q^66 - 50012 * q^67 - 39584 * q^68 - 11142 * q^69 - 54216 * q^70 + 21192 * q^71 + 20736 * q^72 - 13358 * q^73 - 54280 * q^74 - 7488 * q^75 - 72608 * q^76 + 98658 * q^77 - 28512 * q^78 + 6464 * q^79 - 26624 * q^80 + 26244 * q^81 - 55304 * q^82 + 51506 * q^83 - 23328 * q^84 + 61786 * q^85 - 4944 * q^86 - 44622 * q^87 - 43264 * q^88 + 90738 * q^89 - 33696 * q^90 + 48870 * q^91 - 19808 * q^92 - 64242 * q^93 - 49640 * q^94 + 171394 * q^95 + 36864 * q^96 - 266068 * q^97 - 98488 * q^98 - 54756 * q^99

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