LMFDB - Embedded newform 354.6.a.i.1.3

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:	$0$
Dimension:	$8$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 17732 x^{6} - 152272 x^{5} + 93277609 x^{4} + 1554240404 x^{3} - 156444406614 x^{2} + \cdots + 6279664243680 $ x^8 - 17732x^6 - 152272x^5 + 93277609x^4 + 1554240404x^3 - 156444406614x^2 - 3720609623076x + 6279664243680
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{3} $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$65.0121$ 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)

$f(q)$	$=$	$q+4.00000 q^{2} +9.00000 q^{3} +16.0000 q^{4} -53.0121 q^{5} +36.0000 q^{6} -109.285 q^{7} +64.0000 q^{8} +81.0000 q^{9} +O(q^{10})$	\(q+4.00000 q^{2} +9.00000 q^{3} +16.0000 q^{4} -53.0121 q^{5} +36.0000 q^{6} -109.285 q^{7} +64.0000 q^{8} +81.0000 q^{9} -212.049 q^{10} +76.7585 q^{11} +144.000 q^{12} +550.484 q^{13} -437.140 q^{14} -477.109 q^{15} +256.000 q^{16} -1737.37 q^{17} +324.000 q^{18} +2701.90 q^{19} -848.194 q^{20} -983.566 q^{21} +307.034 q^{22} +4043.57 q^{23} +576.000 q^{24} -314.714 q^{25} +2201.94 q^{26} +729.000 q^{27} -1748.56 q^{28} -7127.37 q^{29} -1908.44 q^{30} +6674.76 q^{31} +1024.00 q^{32} +690.827 q^{33} -6949.48 q^{34} +5793.44 q^{35} +1296.00 q^{36} +4949.07 q^{37} +10807.6 q^{38} +4954.36 q^{39} -3392.78 q^{40} +13387.1 q^{41} -3934.26 q^{42} +11966.2 q^{43} +1228.14 q^{44} -4293.98 q^{45} +16174.3 q^{46} +24474.9 q^{47} +2304.00 q^{48} -4863.77 q^{49} -1258.86 q^{50} -15636.3 q^{51} +8807.75 q^{52} +15347.7 q^{53} +2916.00 q^{54} -4069.13 q^{55} -6994.25 q^{56} +24317.1 q^{57} -28509.5 q^{58} +3481.00 q^{59} -7633.75 q^{60} -11862.1 q^{61} +26699.0 q^{62} -8852.09 q^{63} +4096.00 q^{64} -29182.4 q^{65} +2763.31 q^{66} +58353.3 q^{67} -27797.9 q^{68} +36392.1 q^{69} +23173.7 q^{70} -7889.72 q^{71} +5184.00 q^{72} +10009.8 q^{73} +19796.3 q^{74} -2832.43 q^{75} +43230.4 q^{76} -8388.56 q^{77} +19817.4 q^{78} -45561.0 q^{79} -13571.1 q^{80} +6561.00 q^{81} +53548.3 q^{82} -73640.9 q^{83} -15737.1 q^{84} +92101.7 q^{85} +47864.7 q^{86} -64146.4 q^{87} +4912.55 q^{88} -14421.5 q^{89} -17175.9 q^{90} -60159.8 q^{91} +64697.1 q^{92} +60072.8 q^{93} +97899.4 q^{94} -143234. q^{95} +9216.00 q^{96} +58163.6 q^{97} -19455.1 q^{98} +6217.44 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 32 q^{2} + 72 q^{3} + 128 q^{4} + 96 q^{5} + 288 q^{6} + 181 q^{7} + 512 q^{8} + 648 q^{9}+O(q^{10}) $ 8 * q + 32 * q^2 + 72 * q^3 + 128 * q^4 + 96 * q^5 + 288 * q^6 + 181 * q^7 + 512 * q^8 + 648 * q^9	\( 8 q + 32 q^{2} + 72 q^{3} + 128 q^{4} + 96 q^{5} + 288 q^{6} + 181 q^{7} + 512 q^{8} + 648 q^{9} + 384 q^{10} + 897 q^{11} + 1152 q^{12} + 1743 q^{13} + 724 q^{14} + 864 q^{15} + 2048 q^{16} + 1861 q^{17} + 2592 q^{18} + 3154 q^{19} + 1536 q^{20} + 1629 q^{21} + 3588 q^{22} + 3808 q^{23} + 4608 q^{24} + 11616 q^{25} + 6972 q^{26} + 5832 q^{27} + 2896 q^{28} + 328 q^{29} + 3456 q^{30} + 570 q^{31} + 8192 q^{32} + 8073 q^{33} + 7444 q^{34} + 36086 q^{35} + 10368 q^{36} + 12777 q^{37} + 12616 q^{38} + 15687 q^{39} + 6144 q^{40} + 20167 q^{41} + 6516 q^{42} + 24579 q^{43} + 14352 q^{44} + 7776 q^{45} + 15232 q^{46} + 20490 q^{47} + 18432 q^{48} + 59391 q^{49} + 46464 q^{50} + 16749 q^{51} + 27888 q^{52} + 13404 q^{53} + 23328 q^{54} - 34588 q^{55} + 11584 q^{56} + 28386 q^{57} + 1312 q^{58} + 27848 q^{59} + 13824 q^{60} + 94944 q^{61} + 2280 q^{62} + 14661 q^{63} + 32768 q^{64} + 54560 q^{65} + 32292 q^{66} + 28838 q^{67} + 29776 q^{68} + 34272 q^{69} + 144344 q^{70} + 14983 q^{71} + 41472 q^{72} + 69384 q^{73} + 51108 q^{74} + 104544 q^{75} + 50464 q^{76} - 22359 q^{77} + 62748 q^{78} - 49199 q^{79} + 24576 q^{80} + 52488 q^{81} + 80668 q^{82} + 3995 q^{83} + 26064 q^{84} - 142290 q^{85} + 98316 q^{86} + 2952 q^{87} + 57408 q^{88} + 28722 q^{89} + 31104 q^{90} + 20815 q^{91} + 60928 q^{92} + 5130 q^{93} + 81960 q^{94} + 208010 q^{95} + 73728 q^{96} + 204150 q^{97} + 237564 q^{98} + 72657 q^{99}+O(q^{100}) \) 8 * q + 32 * q^2 + 72 * q^3 + 128 * q^4 + 96 * q^5 + 288 * q^6 + 181 * q^7 + 512 * q^8 + 648 * q^9 + 384 * q^10 + 897 * q^11 + 1152 * q^12 + 1743 * q^13 + 724 * q^14 + 864 * q^15 + 2048 * q^16 + 1861 * q^17 + 2592 * q^18 + 3154 * q^19 + 1536 * q^20 + 1629 * q^21 + 3588 * q^22 + 3808 * q^23 + 4608 * q^24 + 11616 * q^25 + 6972 * q^26 + 5832 * q^27 + 2896 * q^28 + 328 * q^29 + 3456 * q^30 + 570 * q^31 + 8192 * q^32 + 8073 * q^33 + 7444 * q^34 + 36086 * q^35 + 10368 * q^36 + 12777 * q^37 + 12616 * q^38 + 15687 * q^39 + 6144 * q^40 + 20167 * q^41 + 6516 * q^42 + 24579 * q^43 + 14352 * q^44 + 7776 * q^45 + 15232 * q^46 + 20490 * q^47 + 18432 * q^48 + 59391 * q^49 + 46464 * q^50 + 16749 * q^51 + 27888 * q^52 + 13404 * q^53 + 23328 * q^54 - 34588 * q^55 + 11584 * q^56 + 28386 * q^57 + 1312 * q^58 + 27848 * q^59 + 13824 * q^60 + 94944 * q^61 + 2280 * q^62 + 14661 * q^63 + 32768 * q^64 + 54560 * q^65 + 32292 * q^66 + 28838 * q^67 + 29776 * q^68 + 34272 * q^69 + 144344 * q^70 + 14983 * q^71 + 41472 * q^72 + 69384 * q^73 + 51108 * q^74 + 104544 * q^75 + 50464 * q^76 - 22359 * q^77 + 62748 * q^78 - 49199 * q^79 + 24576 * q^80 + 52488 * q^81 + 80668 * q^82 + 3995 * q^83 + 26064 * q^84 - 142290 * q^85 + 98316 * q^86 + 2952 * q^87 + 57408 * q^88 + 28722 * q^89 + 31104 * q^90 + 20815 * q^91 + 60928 * q^92 + 5130 * q^93 + 81960 * q^94 + 208010 * q^95 + 73728 * q^96 + 204150 * q^97 + 237564 * q^98 + 72657 * 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
$5$	−53.0121	−0.948310	−0.474155	−	0.880441i	$-0.657246\pi$
$5$	−53.0121	−0.948310	−0.474155	+	0.880441i	$0.657246\pi$
$6$	36.0000	0.408248
$7$	−109.285	−0.842977	−0.421489	−	0.906834i	$-0.638492\pi$
$7$	−109.285	−0.842977	−0.421489	+	0.906834i	$0.638492\pi$
$8$	64.0000	0.353553
$9$	81.0000	0.333333
$10$	−212.049	−0.670556
$11$	76.7585	0.191269	0.0956346	−	0.995417i	$-0.469512\pi$
$11$	76.7585	0.191269	0.0956346	+	0.995417i	$0.469512\pi$
$12$	144.000	0.288675
$13$	550.484	0.903414	0.451707	−	0.892166i	$-0.350815\pi$
$13$	550.484	0.903414	0.451707	+	0.892166i	$0.350815\pi$
$14$	−437.140	−0.596075
$15$	−477.109	−0.547507
$16$	256.000	0.250000
$17$	−1737.37	−1.45804	−0.729021	−	0.684491i	$-0.760025\pi$
$17$	−1737.37	−1.45804	−0.729021	+	0.684491i	$0.760025\pi$
$18$	324.000	0.235702
$19$	2701.90	1.71706	0.858530	−	0.512763i	$-0.171378\pi$
$19$	2701.90	1.71706	0.858530	+	0.512763i	$0.171378\pi$
$20$	−848.194	−0.474155
$21$	−983.566	−0.486693
$22$	307.034	0.135248
$23$	4043.57	1.59384	0.796921	−	0.604084i	$-0.206461\pi$
$23$	4043.57	1.59384	0.796921	+	0.604084i	$0.206461\pi$
$24$	576.000	0.204124
$25$	−314.714	−0.100709
$26$	2201.94	0.638810
$27$	729.000	0.192450
$28$	−1748.56	−0.421489
$29$	−7127.37	−1.57375	−0.786873	−	0.617115i	$-0.788301\pi$
$29$	−7127.37	−1.57375	−0.786873	+	0.617115i	$0.788301\pi$
$30$	−1908.44	−0.387146
$31$	6674.76	1.24747	0.623737	−	0.781634i	$-0.285614\pi$
$31$	6674.76	1.24747	0.623737	+	0.781634i	$0.285614\pi$
$32$	1024.00	0.176777
$33$	690.827	0.110429
$34$	−6949.48	−1.03099
$35$	5793.44	0.799404
$36$	1296.00	0.166667
$37$	4949.07	0.594318	0.297159	−	0.954828i	$-0.403961\pi$
$37$	4949.07	0.594318	0.297159	+	0.954828i	$0.403961\pi$
$38$	10807.6	1.21414
$39$	4954.36	0.521586
$40$	−3392.78	−0.335278
$41$	13387.1	1.24373	0.621864	−	0.783125i	$-0.286376\pi$
$41$	13387.1	1.24373	0.621864	+	0.783125i	$0.286376\pi$
$42$	−3934.26	−0.344144
$43$	11966.2	0.986925	0.493462	−	0.869767i	$-0.335731\pi$
$43$	11966.2	0.986925	0.493462	+	0.869767i	$0.335731\pi$
$44$	1228.14	0.0956346
$45$	−4293.98	−0.316103
$46$	16174.3	1.12702
$47$	24474.9	1.61613	0.808064	−	0.589095i	$-0.200516\pi$
$47$	24474.9	1.61613	0.808064	+	0.589095i	$0.200516\pi$
$48$	2304.00	0.144338
$49$	−4863.77	−0.289389
$50$	−1258.86	−0.0712117
$51$	−15636.3	−0.841801
$52$	8807.75	0.451707
$53$	15347.7	0.750505	0.375253	−	0.926923i	$-0.377556\pi$
$53$	15347.7	0.750505	0.375253	+	0.926923i	$0.377556\pi$
$54$	2916.00	0.136083
$55$	−4069.13	−0.181382
$56$	−6994.25	−0.298037
$57$	24317.1	0.991345
$58$	−28509.5	−1.11281
$59$	3481.00	0.130189
$59$	3481.00	0.130189
$60$	−7633.75	−0.273753
$61$	−11862.1	−0.408166	−0.204083	−	0.978954i	$-0.565421\pi$
$61$	−11862.1	−0.408166	−0.204083	+	0.978954i	$0.565421\pi$
$62$	26699.0	0.882097
$63$	−8852.09	−0.280992
$64$	4096.00	0.125000
$65$	−29182.4	−0.856716
$66$	2763.31	0.0780853
$67$	58353.3	1.58810	0.794051	−	0.607852i	$-0.207969\pi$
$67$	58353.3	1.58810	0.794051	+	0.607852i	$0.207969\pi$
$68$	−27797.9	−0.729021
$69$	36392.1	0.920205
$70$	23173.7	0.565264
$71$	−7889.72	−0.185745	−0.0928723	−	0.995678i	$-0.529605\pi$
$71$	−7889.72	−0.185745	−0.0928723	+	0.995678i	$0.529605\pi$
$72$	5184.00	0.117851
$73$	10009.8	0.219846	0.109923	−	0.993940i	$-0.464940\pi$
$73$	10009.8	0.219846	0.109923	+	0.993940i	$0.464940\pi$
$74$	19796.3	0.420246
$75$	−2832.43	−0.0581441
$76$	43230.4	0.858530
$77$	−8388.56	−0.161236
$78$	19817.4	0.368817
$79$	−45561.0	−0.821345	−0.410672	−	0.911783i	$-0.634706\pi$
$79$	−45561.0	−0.821345	−0.410672	+	0.911783i	$0.634706\pi$
$80$	−13571.1	−0.237077
$81$	6561.00	0.111111
$82$	53548.3	0.879449
$83$	−73640.9	−1.17334	−0.586670	−	0.809826i	$-0.699561\pi$
$83$	−73640.9	−1.17334	−0.586670	+	0.809826i	$0.699561\pi$
$84$	−15737.1	−0.243347
$85$	92101.7	1.38268
$86$	47864.7	0.697861
$87$	−64146.4	−0.908602
$88$	4912.55	0.0676239
$89$	−14421.5	−0.192990	−0.0964948	−	0.995333i	$-0.530763\pi$
$89$	−14421.5	−0.192990	−0.0964948	+	0.995333i	$0.530763\pi$
$90$	−17175.9	−0.223519
$91$	−60159.8	−0.761557
$92$	64697.1	0.796921
$93$	60072.8	0.720229
$94$	97899.4	1.14277
$95$	−143234.	−1.62830
$96$	9216.00	0.102062
$97$	58163.6	0.627656	0.313828	−	0.949480i	$-0.398388\pi$
$97$	58163.6	0.627656	0.313828	+	0.949480i	$0.398388\pi$
$98$	−19455.1	−0.204629
$99$	6217.44	0.0637564
$100$	−5035.43	−0.0503543
$101$	−160277.	−1.56339	−0.781697	−	0.623659i	$-0.785646\pi$
$101$	−160277.	−1.56339	−0.781697	+	0.623659i	$0.785646\pi$
$102$	−62545.4	−0.595243
$103$	−25448.6	−0.236358	−0.118179	−	0.992992i	$-0.537706\pi$
$103$	−25448.6	−0.236358	−0.118179	+	0.992992i	$0.537706\pi$
$104$	35231.0	0.319405
$105$	52140.9	0.461536
$106$	61390.8	0.530687
$107$	198473.	1.67588	0.837939	−	0.545764i	$-0.183761\pi$
$107$	198473.	1.67588	0.837939	+	0.545764i	$0.183761\pi$
$108$	11664.0	0.0962250
$109$	130154.	1.04928	0.524641	−	0.851324i	$-0.324200\pi$
$109$	130154.	1.04928	0.524641	+	0.851324i	$0.324200\pi$
$110$	−16276.5	−0.128257
$111$	44541.6	0.343130
$112$	−27977.0	−0.210744
$113$	−126612.	−0.932781	−0.466390	−	0.884579i	$-0.654446\pi$
$113$	−126612.	−0.932781	−0.466390	+	0.884579i	$0.654446\pi$
$114$	97268.5	0.700987
$115$	−214358.	−1.51146
$116$	−114038.	−0.786873
$117$	44589.2	0.301138
$118$	13924.0	0.0920575
$119$	189869.	1.22910
$120$	−30535.0	−0.193573
$121$	−155159.	−0.963416
$122$	−47448.4	−0.288617
$123$	120484.	0.718067
$124$	106796.	0.623737
$125$	182347.	1.04381
$126$	−35408.4	−0.198692
$127$	104825.	0.576708	0.288354	−	0.957524i	$-0.406892\pi$
$127$	104825.	0.576708	0.288354	+	0.957524i	$0.406892\pi$
$128$	16384.0	0.0883883
$129$	107696.	0.569801
$130$	−116729.	−0.605790
$131$	271952.	1.38457	0.692284	−	0.721625i	$-0.256604\pi$
$131$	271952.	1.38457	0.692284	+	0.721625i	$0.256604\pi$
$132$	11053.2	0.0552146
$133$	−295278.	−1.44744
$134$	233413.	1.12296
$135$	−38645.8	−0.182502
$136$	−111192.	−0.515496
$137$	93066.8	0.423637	0.211818	−	0.977309i	$-0.432061\pi$
$137$	93066.8	0.423637	0.211818	+	0.977309i	$0.432061\pi$
$138$	145568.	0.650683
$139$	−179026.	−0.785922	−0.392961	−	0.919555i	$-0.628549\pi$
$139$	−179026.	−0.785922	−0.392961	+	0.919555i	$0.628549\pi$
$140$	92695.0	0.399702
$141$	220274.	0.933072
$142$	−31558.9	−0.131341
$143$	42254.4	0.172795
$144$	20736.0	0.0833333
$145$	377837.	1.49240
$146$	40039.3	0.155455
$147$	−43773.9	−0.167079
$148$	79185.1	0.297159
$149$	−37188.3	−0.137227	−0.0686137	−	0.997643i	$-0.521858\pi$
$149$	−37188.3	−0.137227	−0.0686137	+	0.997643i	$0.521858\pi$
$150$	−11329.7	−0.0411141
$151$	24241.7	0.0865208	0.0432604	−	0.999064i	$-0.486225\pi$
$151$	24241.7	0.0865208	0.0432604	+	0.999064i	$0.486225\pi$
$152$	172922.	0.607072
$153$	−140727.	−0.486014
$154$	−33554.3	−0.114011
$155$	−353843.	−1.18299
$156$	79269.8	0.260793
$157$	−204922.	−0.663498	−0.331749	−	0.943368i	$-0.607639\pi$
$157$	−204922.	−0.663498	−0.331749	+	0.943368i	$0.607639\pi$
$158$	−182244.	−0.580778
$159$	138129.	0.433304
$160$	−54284.4	−0.167639
$161$	−441902.	−1.34357
$162$	26244.0	0.0785674
$163$	460811.	1.35848	0.679241	−	0.733915i	$-0.262309\pi$
$163$	460811.	1.35848	0.679241	+	0.733915i	$0.262309\pi$
$164$	214193.	0.621864
$165$	−36622.2	−0.104721
$166$	−294563.	−0.829676
$167$	−237616.	−0.659301	−0.329651	−	0.944103i	$-0.606931\pi$
$167$	−237616.	−0.659301	−0.329651	+	0.944103i	$0.606931\pi$
$168$	−62948.2	−0.172072
$169$	−68259.8	−0.183844
$170$	368407.	0.977700
$171$	218854.	0.572353
$172$	191459.	0.493462
$173$	−452786.	−1.15021	−0.575105	−	0.818079i	$-0.695039\pi$
$173$	−452786.	−1.15021	−0.575105	+	0.818079i	$0.695039\pi$
$174$	−256585.	−0.642479
$175$	34393.6	0.0848951
$176$	19650.2	0.0478173
$177$	31329.0	0.0751646
$178$	−57685.8	−0.136464
$179$	116264.	0.271214	0.135607	−	0.990763i	$-0.456702\pi$
$179$	116264.	0.271214	0.135607	+	0.990763i	$0.456702\pi$
$180$	−68703.7	−0.158052
$181$	−629709.	−1.42871	−0.714354	−	0.699784i	$-0.753279\pi$
$181$	−629709.	−1.42871	−0.714354	+	0.699784i	$0.753279\pi$
$182$	−240639.	−0.538502
$183$	−106759.	−0.235655
$184$	258788.	0.563508
$185$	−262361.	−0.563598
$186$	240291.	0.509279
$187$	−133358.	−0.278879
$188$	391598.	0.808064
$189$	−79668.8	−0.162231
$190$	−572934.	−1.15139
$191$	898666.	1.78244	0.891220	−	0.453572i	$-0.149850\pi$
$191$	898666.	1.78244	0.891220	+	0.453572i	$0.149850\pi$
$192$	36864.0	0.0721688
$193$	733424.	1.41730	0.708650	−	0.705560i	$-0.249304\pi$
$193$	733424.	1.41730	0.708650	+	0.705560i	$0.249304\pi$
$194$	232654.	0.443820
$195$	−262641.	−0.494625
$196$	−77820.3	−0.144695
$197$	−327919.	−0.602007	−0.301003	−	0.953623i	$-0.597322\pi$
$197$	−327919.	−0.602007	−0.301003	+	0.953623i	$0.597322\pi$
$198$	24869.8	0.0450826
$199$	939227.	1.68127	0.840636	−	0.541601i	$-0.182182\pi$
$199$	939227.	1.68127	0.840636	+	0.541601i	$0.182182\pi$
$200$	−20141.7	−0.0356059
$201$	525179.	0.916891
$202$	−641109.	−1.10549
$203$	778916.	1.32663
$204$	−250181.	−0.420901
$205$	−709677.	−1.17944
$206$	−101794.	−0.167130
$207$	327529.	0.531281
$208$	140924.	0.225853
$209$	207394.	0.328421
$210$	208564.	0.326355
$211$	−1.10092e6	−1.70236	−0.851179	−	0.524876i	$-0.824112\pi$
$211$	−1.10092e6	−1.70236	−0.851179	+	0.524876i	$0.824112\pi$
$212$	245563.	0.375253
$213$	−71007.5	−0.107240
$214$	793893.	1.18502
$215$	−634352.	−0.935910
$216$	46656.0	0.0680414
$217$	−729452.	−1.05159
$218$	520617.	0.741954
$219$	90088.4	0.126928
$220$	−65106.1	−0.0906912
$221$	−956396.	−1.31722
$222$	178166.	0.242629
$223$	−615256.	−0.828503	−0.414251	−	0.910162i	$-0.635957\pi$
$223$	−615256.	−0.828503	−0.414251	+	0.910162i	$0.635957\pi$
$224$	−111908.	−0.149019
$225$	−25491.9	−0.0335695
$226$	−506449.	−0.659575
$227$	−347677.	−0.447828	−0.223914	−	0.974609i	$-0.571884\pi$
$227$	−347677.	−0.447828	−0.223914	+	0.974609i	$0.571884\pi$
$228$	389074.	0.495673
$229$	408468.	0.514719	0.257359	−	0.966316i	$-0.417148\pi$
$229$	408468.	0.514719	0.257359	+	0.966316i	$0.417148\pi$
$230$	−857433.	−1.06876
$231$	−75497.1	−0.0930894
$232$	−456152.	−0.556403
$233$	−1.40007e6	−1.68950	−0.844752	−	0.535157i	$-0.820252\pi$
$233$	−1.40007e6	−1.68950	−0.844752	+	0.535157i	$0.820252\pi$
$234$	178357.	0.212937
$235$	−1.29746e6	−1.53259
$236$	55696.0	0.0650945
$237$	−410049.	−0.474203
$238$	759475.	0.869103
$239$	−211234.	−0.239204	−0.119602	−	0.992822i	$-0.538162\pi$
$239$	−211234.	−0.239204	−0.119602	+	0.992822i	$0.538162\pi$
$240$	−122140.	−0.136877
$241$	895804.	0.993505	0.496753	−	0.867892i	$-0.334526\pi$
$241$	895804.	0.993505	0.496753	+	0.867892i	$0.334526\pi$
$242$	−620637.	−0.681238
$243$	59049.0	0.0641500
$244$	−189793.	−0.204083
$245$	257839.	0.274431
$246$	481934.	0.507750
$247$	1.48735e6	1.55122
$248$	427185.	0.441049
$249$	−662768.	−0.677428
$250$	729386.	0.738087
$251$	−831527.	−0.833091	−0.416545	−	0.909115i	$-0.636759\pi$
$251$	−831527.	−0.833091	−0.416545	+	0.909115i	$0.636759\pi$
$252$	−141633.	−0.140496
$253$	310378.	0.304853
$254$	419300.	0.407794
$255$	828916.	0.798288
$256$	65536.0	0.0625000
$257$	1.41009e6	1.33173	0.665863	−	0.746074i	$-0.268063\pi$
$257$	1.41009e6	1.33173	0.665863	+	0.746074i	$0.268063\pi$
$258$	430782.	0.402910
$259$	−540859.	−0.500997
$260$	−466918.	−0.428358
$261$	−577317.	−0.524582
$262$	1.08781e6	0.979038
$263$	−1.85304e6	−1.65195	−0.825973	−	0.563709i	$-0.809374\pi$
$263$	−1.85304e6	−1.65195	−0.825973	+	0.563709i	$0.809374\pi$
$264$	44212.9	0.0390426
$265$	−813615.	−0.711712
$266$	−1.18111e6	−1.02350
$267$	−129793.	−0.111423
$268$	933652.	0.794051
$269$	−1.21301e6	−1.02207	−0.511037	−	0.859559i	$-0.670738\pi$
$269$	−1.21301e6	−1.02207	−0.511037	+	0.859559i	$0.670738\pi$
$270$	−154583.	−0.129049
$271$	343550.	0.284163	0.142081	−	0.989855i	$-0.454621\pi$
$271$	343550.	0.284163	0.142081	+	0.989855i	$0.454621\pi$
$272$	−444767.	−0.364511
$273$	−541438.	−0.439685
$274$	372267.	0.299556
$275$	−24157.0	−0.0192624
$276$	582274.	0.460103
$277$	1.55015e6	1.21388	0.606938	−	0.794749i	$-0.292397\pi$
$277$	1.55015e6	1.21388	0.606938	+	0.794749i	$0.292397\pi$
$278$	−716105.	−0.555731
$279$	540656.	0.415825
$280$	370780.	0.282632
$281$	−710641.	−0.536889	−0.268444	−	0.963295i	$-0.586510\pi$
$281$	−710641.	−0.536889	−0.268444	+	0.963295i	$0.586510\pi$
$282$	881095.	0.659781
$283$	−531910.	−0.394795	−0.197398	−	0.980323i	$-0.563249\pi$
$283$	−531910.	−0.394795	−0.197398	+	0.980323i	$0.563249\pi$
$284$	−126236.	−0.0928723
$285$	−1.28910e6	−0.940102
$286$	169018.	0.122185
$287$	−1.46301e6	−1.04843
$288$	82944.0	0.0589256
$289$	1.59860e6	1.12589
$290$	1.51135e6	1.05528
$291$	523472.	0.362377
$292$	160157.	0.109923
$293$	−2.57125e6	−1.74974	−0.874872	−	0.484354i	$-0.839055\pi$
$293$	−2.57125e6	−1.74974	−0.874872	+	0.484354i	$0.839055\pi$
$294$	−175096.	−0.118143
$295$	−184535.	−0.123459
$296$	316740.	0.210123
$297$	55957.0	0.0368098
$298$	−148753.	−0.0970344
$299$	2.22592e6	1.43990
$300$	−45318.9	−0.0290721
$301$	−1.30772e6	−0.831955
$302$	96966.8	0.0611794
$303$	−1.44250e6	−0.902626
$304$	691687.	0.429265
$305$	628834.	0.387068
$306$	−562908.	−0.343664
$307$	1.69347e6	1.02549	0.512746	−	0.858540i	$-0.328628\pi$
$307$	1.69347e6	1.02549	0.512746	+	0.858540i	$0.328628\pi$
$308$	−134217.	−0.0806178
$309$	−229037.	−0.136461
$310$	−1.41537e6	−0.836501
$311$	2.36779e6	1.38817	0.694084	−	0.719894i	$-0.255810\pi$
$311$	2.36779e6	1.38817	0.694084	+	0.719894i	$0.255810\pi$
$312$	317079.	0.184409
$313$	−378996.	−0.218662	−0.109331	−	0.994005i	$-0.534871\pi$
$313$	−378996.	−0.218662	−0.109331	+	0.994005i	$0.534871\pi$
$314$	−819688.	−0.469164
$315$	469268.	0.266468
$316$	−728976.	−0.410672
$317$	469888.	0.262631	0.131316	−	0.991341i	$-0.458080\pi$
$317$	469888.	0.262631	0.131316	+	0.991341i	$0.458080\pi$
$318$	552517.	0.306393
$319$	−547087.	−0.301009
$320$	−217138.	−0.118539
$321$	1.78626e6	0.967569
$322$	−1.76761e6	−0.950049
$323$	−4.69420e6	−2.50355
$324$	104976.	0.0555556
$325$	−173245.	−0.0909815
$326$	1.84324e6	0.960592
$327$	1.17139e6	0.605803
$328$	856772.	0.439725
$329$	−2.67474e6	−1.36236
$330$	−146489.	−0.0740491
$331$	−3.07624e6	−1.54330	−0.771649	−	0.636049i	$-0.780568\pi$
$331$	−3.07624e6	−1.54330	−0.771649	+	0.636049i	$0.780568\pi$
$332$	−1.17825e6	−0.586670
$333$	400874.	0.198106
$334$	−950463.	−0.466196
$335$	−3.09343e6	−1.50601
$336$	−251793.	−0.121673
$337$	2.40591e6	1.15400	0.576999	−	0.816745i	$-0.304224\pi$
$337$	2.40591e6	1.15400	0.576999	+	0.816745i	$0.304224\pi$
$338$	−273039.	−0.129997
$339$	−1.13951e6	−0.538541
$340$	1.47363e6	0.691338
$341$	512345.	0.238603
$342$	875416.	0.404715
$343$	2.36829e6	1.08693
$344$	765835.	0.348931
$345$	−1.92922e6	−0.872639
$346$	−1.81114e6	−0.813322
$347$	−763409.	−0.340356	−0.170178	−	0.985413i	$-0.554434\pi$
$347$	−763409.	−0.340356	−0.170178	+	0.985413i	$0.554434\pi$
$348$	−1.02634e6	−0.454301
$349$	1.25610e6	0.552026	0.276013	−	0.961154i	$-0.410987\pi$
$349$	1.25610e6	0.552026	0.276013	+	0.961154i	$0.410987\pi$
$350$	137574.	0.0600299
$351$	401303.	0.173862
$352$	78600.7	0.0338119
$353$	−3.14971e6	−1.34534	−0.672672	−	0.739941i	$-0.734854\pi$
$353$	−3.14971e6	−1.34534	−0.672672	+	0.739941i	$0.734854\pi$
$354$	125316.	0.0531494
$355$	418251.	0.176143
$356$	−230743.	−0.0964948
$357$	1.70882e6	0.709619
$358$	465055.	0.191777
$359$	−3.93017e6	−1.60944	−0.804721	−	0.593653i	$-0.797685\pi$
$359$	−3.93017e6	−1.60944	−0.804721	+	0.593653i	$0.797685\pi$
$360$	−274815.	−0.111759
$361$	4.82417e6	1.94830
$362$	−2.51884e6	−1.01025
$363$	−1.39643e6	−0.556229
$364$	−962556.	−0.380779
$365$	−530642.	−0.208483
$366$	−427035.	−0.166633
$367$	−4.17245e6	−1.61706	−0.808529	−	0.588456i	$-0.799736\pi$
$367$	−4.17245e6	−1.61706	−0.808529	+	0.588456i	$0.799736\pi$
$368$	1.03515e6	0.398460
$369$	1.08435e6	0.414576
$370$	−1.04944e6	−0.398524
$371$	−1.67728e6	−0.632659
$372$	961166.	0.360115
$373$	−5.07040e6	−1.88699	−0.943496	−	0.331383i	$-0.892485\pi$
$373$	−5.07040e6	−1.88699	−0.943496	+	0.331383i	$0.892485\pi$
$374$	−533432.	−0.197197
$375$	1.64112e6	0.602646
$376$	1.56639e6	0.571387
$377$	−3.92351e6	−1.42174
$378$	−318675.	−0.114715
$379$	3.84139e6	1.37369	0.686847	−	0.726802i	$-0.258994\pi$
$379$	3.84139e6	1.37369	0.686847	+	0.726802i	$0.258994\pi$
$380$	−2.29174e6	−0.814152
$381$	943426.	0.332963
$382$	3.59466e6	1.26038
$383$	5.04629e6	1.75782	0.878911	−	0.476985i	$-0.158271\pi$
$383$	5.04629e6	1.75782	0.878911	+	0.476985i	$0.158271\pi$
$384$	147456.	0.0510310
$385$	444696.	0.152901
$386$	2.93370e6	1.00218
$387$	969260.	0.328975
$388$	930617.	0.313828
$389$	−4.49301e6	−1.50544	−0.752720	−	0.658340i	$-0.771259\pi$
$389$	−4.49301e6	−1.50544	−0.752720	+	0.658340i	$0.771259\pi$
$390$	−1.05056e6	−0.349753
$391$	−7.02518e6	−2.32389
$392$	−311281.	−0.102315
$393$	2.44757e6	0.799381
$394$	−1.31168e6	−0.425683
$395$	2.41528e6	0.778889
$396$	99479.0	0.0318782
$397$	1.90605e6	0.606958	0.303479	−	0.952838i	$-0.401852\pi$
$397$	1.90605e6	0.606958	0.303479	+	0.952838i	$0.401852\pi$
$398$	3.75691e6	1.18884
$399$	−2.65750e6	−0.835681
$400$	−80566.9	−0.0251771
$401$	2.66813e6	0.828602	0.414301	−	0.910140i	$-0.364026\pi$
$401$	2.66813e6	0.828602	0.414301	+	0.910140i	$0.364026\pi$
$402$	2.10072e6	0.648340
$403$	3.67435e6	1.12699
$404$	−2.56444e6	−0.781697
$405$	−347813.	−0.105368
$406$	3.11566e6	0.938070
$407$	379883.	0.113675
$408$	−1.00073e6	−0.297622
$409$	3.67914e6	1.08752	0.543761	−	0.839240i	$-0.317000\pi$
$409$	3.67914e6	1.08752	0.543761	+	0.839240i	$0.317000\pi$
$410$	−2.83871e6	−0.833990
$411$	837602.	0.244587
$412$	−407177.	−0.118179
$413$	−380421.	−0.109746
$414$	1.31012e6	0.375672
$415$	3.90386e6	1.11269
$416$	563696.	0.159703
$417$	−1.61124e6	−0.453752
$418$	829576.	0.232228
$419$	5.51869e6	1.53568	0.767840	−	0.640642i	$-0.221332\pi$
$419$	5.51869e6	1.53568	0.767840	+	0.640642i	$0.221332\pi$
$420$	834255.	0.230768
$421$	3.64439e6	1.00212	0.501060	−	0.865412i	$-0.332943\pi$
$421$	3.64439e6	1.00212	0.501060	+	0.865412i	$0.332943\pi$
$422$	−4.40369e6	−1.20375
$423$	1.98246e6	0.538709
$424$	982253.	0.265344
$425$	546776.	0.146837
$426$	−284030.	−0.0758299
$427$	1.29635e6	0.344074
$428$	3.17557e6	0.837939
$429$	380289.	0.0997633
$430$	−2.53741e6	−0.661789
$431$	1.56571e6	0.405992	0.202996	−	0.979180i	$-0.434932\pi$
$431$	1.56571e6	0.405992	0.202996	+	0.979180i	$0.434932\pi$
$432$	186624.	0.0481125
$433$	3.43798e6	0.881219	0.440610	−	0.897699i	$-0.354762\pi$
$433$	3.43798e6	0.881219	0.440610	+	0.897699i	$0.354762\pi$
$434$	−2.91781e6	−0.743588
$435$	3.40054e6	0.861637
$436$	2.08247e6	0.524641
$437$	1.09253e7	2.73672
$438$	360354.	0.0897519
$439$	7.33536e6	1.81660	0.908301	−	0.418316i	$-0.137380\pi$
$439$	7.33536e6	1.81660	0.908301	+	0.418316i	$0.137380\pi$
$440$	−260424.	−0.0641284
$441$	−393965.	−0.0964631
$442$	−3.82558e6	−0.931412
$443$	−1.90472e6	−0.461128	−0.230564	−	0.973057i	$-0.574057\pi$
$443$	−1.90472e6	−0.461128	−0.230564	+	0.973057i	$0.574057\pi$
$444$	712666.	0.171565
$445$	764512.	0.183014
$446$	−2.46103e6	−0.585840
$447$	−334695.	−0.0792282
$448$	−447632.	−0.105372
$449$	1.87234e6	0.438296	0.219148	−	0.975692i	$-0.429672\pi$
$449$	1.87234e6	0.438296	0.219148	+	0.975692i	$0.429672\pi$
$450$	−101967.	−0.0237372
$451$	1.02757e6	0.237887
$452$	−2.02580e6	−0.466390
$453$	218175.	0.0499528
$454$	−1.39071e6	−0.316662
$455$	3.18920e6	0.722192
$456$	1.55630e6	0.350493
$457$	−1.18734e6	−0.265940	−0.132970	−	0.991120i	$-0.542451\pi$
$457$	−1.18734e6	−0.265940	−0.132970	+	0.991120i	$0.542451\pi$
$458$	1.63387e6	0.363961
$459$	−1.26654e6	−0.280600
$460$	−3.42973e6	−0.755728
$461$	−1.69795e6	−0.372111	−0.186055	−	0.982539i	$-0.559570\pi$
$461$	−1.69795e6	−0.372111	−0.186055	+	0.982539i	$0.559570\pi$
$462$	−301988.	−0.0658241
$463$	−5.97142e6	−1.29457	−0.647284	−	0.762249i	$-0.724095\pi$
$463$	−5.97142e6	−1.29457	−0.647284	+	0.762249i	$0.724095\pi$
$464$	−1.82461e6	−0.393436
$465$	−3.18459e6	−0.683001
$466$	−5.60027e6	−1.19466
$467$	6.91889e6	1.46806	0.734030	−	0.679117i	$-0.237637\pi$
$467$	6.91889e6	1.46806	0.734030	+	0.679117i	$0.237637\pi$
$468$	713428.	0.150569
$469$	−6.37714e6	−1.33873
$470$	−5.18986e6	−1.08370
$471$	−1.84430e6	−0.383071
$472$	222784.	0.0460287
$473$	918506.	0.188768
$474$	−1.64020e6	−0.335313
$475$	−850327.	−0.172923
$476$	3.03790e6	0.614548
$477$	1.24316e6	0.250168
$478$	−844935.	−0.169143
$479$	434865.	0.0865996	0.0432998	−	0.999062i	$-0.486213\pi$
$479$	434865.	0.0865996	0.0432998	+	0.999062i	$0.486213\pi$
$480$	−488560.	−0.0967865
$481$	2.72438e6	0.536915
$482$	3.58321e6	0.702514
$483$	−3.97712e6	−0.775712
$484$	−2.48255e6	−0.481708
$485$	−3.08337e6	−0.595212
$486$	236196.	0.0453609
$487$	3.70729e6	0.708328	0.354164	−	0.935183i	$-0.384766\pi$
$487$	3.70729e6	0.708328	0.354164	+	0.935183i	$0.384766\pi$
$488$	−759174.	−0.144308
$489$	4.14730e6	0.784320
$490$	1.03135e6	0.194052
$491$	−741253.	−0.138759	−0.0693797	−	0.997590i	$-0.522102\pi$
$491$	−741253.	−0.138759	−0.0693797	+	0.997590i	$0.522102\pi$
$492$	1.92774e6	0.359034
$493$	1.23829e7	2.29459
$494$	5.94942e6	1.09688
$495$	−329600.	−0.0604608
$496$	1.70874e6	0.311868
$497$	862229.	0.156578
$498$	−2.65107e6	−0.479014
$499$	6.60252e6	1.18702	0.593510	−	0.804826i	$-0.297742\pi$
$499$	6.60252e6	1.18702	0.593510	+	0.804826i	$0.297742\pi$
$500$	2.91755e6	0.521906
$501$	−2.13854e6	−0.380648
$502$	−3.32611e6	−0.589084
$503$	−5.47833e6	−0.965446	−0.482723	−	0.875773i	$-0.660352\pi$
$503$	−5.47833e6	−0.965446	−0.482723	+	0.875773i	$0.660352\pi$
$504$	−566534.	−0.0993458
$505$	8.49664e6	1.48258
$506$	1.24151e6	0.215563
$507$	−614338.	−0.106142
$508$	1.67720e6	0.288354
$509$	1.04014e6	0.177950	0.0889750	−	0.996034i	$-0.471641\pi$
$509$	1.04014e6	0.177950	0.0889750	+	0.996034i	$0.471641\pi$
$510$	3.31566e6	0.564475
$511$	−1.09393e6	−0.185326
$512$	262144.	0.0441942
$513$	1.96969e6	0.330448
$514$	5.64037e6	0.941673
$515$	1.34908e6	0.224141
$516$	1.72313e6	0.284901
$517$	1.87865e6	0.309115
$518$	−2.16344e6	−0.354258
$519$	−4.07507e6	−0.664074
$520$	−1.86767e6	−0.302895
$521$	8.98682e6	1.45048	0.725240	−	0.688496i	$-0.241729\pi$
$521$	8.98682e6	1.45048	0.725240	+	0.688496i	$0.241729\pi$
$522$	−2.30927e6	−0.370935
$523$	−2.54102e6	−0.406212	−0.203106	−	0.979157i	$-0.565104\pi$
$523$	−2.54102e6	−0.406212	−0.203106	+	0.979157i	$0.565104\pi$
$524$	4.35124e6	0.692284
$525$	309542.	0.0490142
$526$	−7.41217e6	−1.16810
$527$	−1.15965e7	−1.81887
$528$	176852.	0.0276073
$529$	9.91411e6	1.54033
$530$	−3.25446e6	−0.503256
$531$	281961.	0.0433963
$532$	−4.72444e6	−0.723721
$533$	7.36937e6	1.12360
$534$	−519172.	−0.0787877
$535$	−1.05215e7	−1.58925
$536$	3.73461e6	0.561478
$537$	1.04637e6	0.156585
$538$	−4.85202e6	−0.722715
$539$	−373336.	−0.0553513
$540$	−618333.	−0.0912511
$541$	1.74795e6	0.256765	0.128383	−	0.991725i	$-0.459021\pi$
$541$	1.74795e6	0.256765	0.128383	+	0.991725i	$0.459021\pi$
$542$	1.37420e6	0.200933
$543$	−5.66738e6	−0.824865
$544$	−1.77907e6	−0.257748
$545$	−6.89976e6	−0.995044
$546$	−2.16575e6	−0.310904
$547$	−8.05210e6	−1.15064	−0.575322	−	0.817927i	$-0.695123\pi$
$547$	−8.05210e6	−1.15064	−0.575322	+	0.817927i	$0.695123\pi$
$548$	1.48907e6	0.211818
$549$	−960829.	−0.136055
$550$	−96628.0	−0.0136206
$551$	−1.92575e7	−2.70222
$552$	2.32910e6	0.325342
$553$	4.97914e6	0.692375
$554$	6.20060e6	0.858340
$555$	−2.36125e6	−0.325393
$556$	−2.86442e6	−0.392961
$557$	−1.21602e7	−1.66074	−0.830372	−	0.557209i	$-0.811872\pi$
$557$	−1.21602e7	−1.66074	−0.830372	+	0.557209i	$0.811872\pi$
$558$	2.16262e6	0.294032
$559$	6.58719e6	0.891602
$560$	1.48312e6	0.199851
$561$	−1.20022e6	−0.161011
$562$	−2.84256e6	−0.379638
$563$	−4.71212e6	−0.626535	−0.313268	−	0.949665i	$-0.601424\pi$
$563$	−4.71212e6	−0.626535	−0.313268	+	0.949665i	$0.601424\pi$
$564$	3.52438e6	0.466536
$565$	6.71198e6	0.884565
$566$	−2.12764e6	−0.279162
$567$	−717020.	−0.0936641
$568$	−504942.	−0.0656706
$569$	3.57479e6	0.462882	0.231441	−	0.972849i	$-0.425656\pi$
$569$	3.57479e6	0.462882	0.231441	+	0.972849i	$0.425656\pi$
$570$	−5.15641e6	−0.664753
$571$	1.40109e7	1.79836	0.899181	−	0.437577i	$-0.144163\pi$
$571$	1.40109e7	1.79836	0.899181	+	0.437577i	$0.144163\pi$
$572$	676070.	0.0863976
$573$	8.08799e6	1.02909
$574$	−5.85203e6	−0.741355
$575$	−1.27257e6	−0.160514
$576$	331776.	0.0416667
$577$	−2.47519e6	−0.309506	−0.154753	−	0.987953i	$-0.549458\pi$
$577$	−2.47519e6	−0.309506	−0.154753	+	0.987953i	$0.549458\pi$
$578$	6.39440e6	0.796123
$579$	6.60082e6	0.818279
$580$	6.04540e6	0.746199
$581$	8.04785e6	0.989098
$582$	2.09389e6	0.256239
$583$	1.17807e6	0.143549
$584$	640629.	0.0777275
$585$	−2.36377e6	−0.285572
$586$	−1.02850e7	−1.23726
$587$	1.49097e7	1.78597	0.892986	−	0.450084i	$-0.148606\pi$
$587$	1.49097e7	1.78597	0.892986	+	0.450084i	$0.148606\pi$
$588$	−700383.	−0.0835395
$589$	1.80345e7	2.14199
$590$	−738141.	−0.0872990
$591$	−2.95127e6	−0.347569
$592$	1.26696e6	0.148580
$593$	297158.	0.0347017	0.0173508	−	0.999849i	$-0.494477\pi$
$593$	297158.	0.0347017	0.0173508	+	0.999849i	$0.494477\pi$
$594$	223828.	0.0260284
$595$	−1.00653e7	−1.16556
$596$	−595013.	−0.0686137
$597$	8.45304e6	0.970682
$598$	8.90369e6	1.01816
$599$	−4.55146e6	−0.518303	−0.259151	−	0.965837i	$-0.583443\pi$
$599$	−4.55146e6	−0.518303	−0.259151	+	0.965837i	$0.583443\pi$
$600$	−181275.	−0.0205571
$601$	−2.18973e6	−0.247289	−0.123645	−	0.992327i	$-0.539458\pi$
$601$	−2.18973e6	−0.247289	−0.123645	+	0.992327i	$0.539458\pi$
$602$	−5.23090e6	−0.588281
$603$	4.72661e6	0.529367
$604$	387867.	0.0432604
$605$	8.22532e6	0.913617
$606$	−5.76998e6	−0.638253
$607$	9.25951e6	1.02004	0.510019	−	0.860163i	$-0.329638\pi$
$607$	9.25951e6	1.02004	0.510019	+	0.860163i	$0.329638\pi$
$608$	2.76675e6	0.303536
$609$	7.01024e6	0.765931
$610$	2.51534e6	0.273698
$611$	1.34730e7	1.46003
$612$	−2.25163e6	−0.243007
$613$	−6.98532e6	−0.750819	−0.375409	−	0.926859i	$-0.622498\pi$
$613$	−6.98532e6	−0.750819	−0.375409	+	0.926859i	$0.622498\pi$
$614$	6.77389e6	0.725133
$615$	−6.38709e6	−0.680950
$616$	−536868.	−0.0570054
$617$	−9.47142e6	−1.00162	−0.500809	−	0.865558i	$-0.666964\pi$
$617$	−9.47142e6	−1.00162	−0.500809	+	0.865558i	$0.666964\pi$
$618$	−916148.	−0.0964927
$619$	−1.02442e6	−0.107461	−0.0537305	−	0.998555i	$-0.517111\pi$
$619$	−1.02442e6	−0.107461	−0.0537305	+	0.998555i	$0.517111\pi$
$620$	−5.66149e6	−0.591496
$621$	2.94776e6	0.306735
$622$	9.47115e6	0.981583
$623$	1.57605e6	0.162686
$624$	1.26832e6	0.130397
$625$	−8.68310e6	−0.889149
$626$	−1.51598e6	−0.154618
$627$	1.86655e6	0.189614
$628$	−3.27875e6	−0.331749
$629$	−8.59837e6	−0.866541
$630$	1.87707e6	0.188421
$631$	6.44578e6	0.644469	0.322235	−	0.946660i	$-0.395566\pi$
$631$	6.44578e6	0.644469	0.322235	+	0.946660i	$0.395566\pi$
$632$	−2.91590e6	−0.290389
$633$	−9.90831e6	−0.982857
$634$	1.87955e6	0.185708
$635$	−5.55700e6	−0.546898
$636$	2.21007e6	0.216652
$637$	−2.67743e6	−0.261438
$638$	−2.18835e6	−0.212845
$639$	−639068.	−0.0619148
$640$	−868551.	−0.0838195
$641$	373191.	0.0358745	0.0179372	−	0.999839i	$-0.494290\pi$
$641$	373191.	0.0358745	0.0179372	+	0.999839i	$0.494290\pi$
$642$	7.14503e6	0.684174
$643$	5.76190e6	0.549590	0.274795	−	0.961503i	$-0.411390\pi$
$643$	5.76190e6	0.549590	0.274795	+	0.961503i	$0.411390\pi$
$644$	−7.07043e6	−0.671786
$645$	−5.70917e6	−0.540348
$646$	−1.87768e7	−1.77027
$647$	−1.71169e7	−1.60755	−0.803774	−	0.594935i	$-0.797178\pi$
$647$	−1.71169e7	−1.60755	−0.803774	+	0.594935i	$0.797178\pi$
$648$	419904.	0.0392837
$649$	267196.	0.0249011
$650$	−692981.	−0.0643337
$651$	−6.56507e6	−0.607137
$652$	7.37298e6	0.679241
$653$	−638316.	−0.0585805	−0.0292902	−	0.999571i	$-0.509325\pi$
$653$	−638316.	−0.0585805	−0.0292902	+	0.999571i	$0.509325\pi$
$654$	4.68555e6	0.428368
$655$	−1.44168e7	−1.31300
$656$	3.42709e6	0.310932
$657$	810796.	0.0732821
$658$	−1.06990e7	−0.963333
$659$	8.50102e6	0.762531	0.381266	−	0.924466i	$-0.375488\pi$
$659$	8.50102e6	0.762531	0.381266	+	0.924466i	$0.375488\pi$
$660$	−585955.	−0.0523606
$661$	3.12176e6	0.277905	0.138952	−	0.990299i	$-0.455627\pi$
$661$	3.12176e6	0.277905	0.138952	+	0.990299i	$0.455627\pi$
$662$	−1.23049e7	−1.09128
$663$	−8.60756e6	−0.760495
$664$	−4.71301e6	−0.414838
$665$	1.56533e7	1.37262
$666$	1.60350e6	0.140082
$667$	−2.88200e7	−2.50830
$668$	−3.80185e6	−0.329651
$669$	−5.53731e6	−0.478336
$670$	−1.23737e7	−1.06491
$671$	−910516.	−0.0780695
$672$	−1.00717e6	−0.0860360
$673$	−1.05991e7	−0.902048	−0.451024	−	0.892512i	$-0.648941\pi$
$673$	−1.05991e7	−0.902048	−0.451024	+	0.892512i	$0.648941\pi$
$674$	9.62365e6	0.816000
$675$	−229427.	−0.0193814
$676$	−1.09216e6	−0.0919218
$677$	−1.84160e7	−1.54427	−0.772134	−	0.635460i	$-0.780811\pi$
$677$	−1.84160e7	−1.54427	−0.772134	+	0.635460i	$0.780811\pi$
$678$	−4.55804e6	−0.380806
$679$	−6.35641e6	−0.529100
$680$	5.89451e6	0.488850
$681$	−3.12909e6	−0.258554
$682$	2.04938e6	0.168718
$683$	−8.44466e6	−0.692676	−0.346338	−	0.938110i	$-0.612575\pi$
$683$	−8.44466e6	−0.692676	−0.346338	+	0.938110i	$0.612575\pi$
$684$	3.50166e6	0.286177
$685$	−4.93367e6	−0.401739
$686$	9.47317e6	0.768573
$687$	3.67622e6	0.297173
$688$	3.06334e6	0.246731
$689$	8.44867e6	0.678017
$690$	−7.71689e6	−0.617049
$691$	−2.35215e6	−0.187400	−0.0937000	−	0.995600i	$-0.529869\pi$
$691$	−2.35215e6	−0.187400	−0.0937000	+	0.995600i	$0.529869\pi$
$692$	−7.24457e6	−0.575105
$693$	−679474.	−0.0537452
$694$	−3.05364e6	−0.240668
$695$	9.49056e6	0.745298
$696$	−4.10537e6	−0.321239
$697$	−2.32583e7	−1.81341
$698$	5.02438e6	0.390341
$699$	−1.26006e7	−0.975436
$700$	550297.	0.0424475
$701$	857928.	0.0659411	0.0329705	−	0.999456i	$-0.489503\pi$
$701$	857928.	0.0659411	0.0329705	+	0.999456i	$0.489503\pi$
$702$	1.60521e6	0.122939
$703$	1.33719e7	1.02048
$704$	314403.	0.0239086
$705$	−1.16772e7	−0.884841
$706$	−1.25988e7	−0.951302
$707$	1.75159e7	1.31791
$708$	501264.	0.0375823
$709$	−8.82979e6	−0.659682	−0.329841	−	0.944037i	$-0.606995\pi$
$709$	−8.82979e6	−0.659682	−0.329841	+	0.944037i	$0.606995\pi$
$710$	1.67300e6	0.124552
$711$	−3.69044e6	−0.273782
$712$	−922973.	−0.0682321
$713$	2.69899e7	1.98828
$714$	6.83527e6	0.501777
$715$	−2.23999e6	−0.163863
$716$	1.86022e6	0.135607
$717$	−1.90110e6	−0.138105
$718$	−1.57207e7	−1.13805
$719$	−1.00870e7	−0.727679	−0.363839	−	0.931462i	$-0.618534\pi$
$719$	−1.00870e7	−0.727679	−0.363839	+	0.931462i	$0.618534\pi$
$720$	−1.09926e6	−0.0790258
$721$	2.78115e6	0.199244
$722$	1.92967e7	1.37765
$723$	8.06223e6	0.573601
$724$	−1.00753e7	−0.714354
$725$	2.24309e6	0.158490
$726$	−5.58573e6	−0.393313
$727$	8.18479e6	0.574343	0.287172	−	0.957879i	$-0.407285\pi$
$727$	8.18479e6	0.574343	0.287172	+	0.957879i	$0.407285\pi$
$728$	−3.85022e6	−0.269251
$729$	531441.	0.0370370
$730$	−2.12257e6	−0.147419
$731$	−2.07897e7	−1.43898
$732$	−1.70814e6	−0.117827
$733$	1.34613e6	0.0925396	0.0462698	−	0.998929i	$-0.485267\pi$
$733$	1.34613e6	0.0925396	0.0462698	+	0.998929i	$0.485267\pi$
$734$	−1.66898e7	−1.14343
$735$	2.32055e6	0.158443
$736$	4.14061e6	0.281754
$737$	4.47911e6	0.303755
$738$	4.33741e6	0.293150
$739$	−1.61485e7	−1.08773	−0.543865	−	0.839173i	$-0.683040\pi$
$739$	−1.61485e7	−1.08773	−0.543865	+	0.839173i	$0.683040\pi$
$740$	−4.19777e6	−0.281799
$741$	1.33862e7	0.895595
$742$	−6.70910e6	−0.447357
$743$	5.32262e6	0.353715	0.176857	−	0.984236i	$-0.443407\pi$
$743$	5.32262e6	0.353715	0.176857	+	0.984236i	$0.443407\pi$
$744$	3.84466e6	0.254640
$745$	1.97143e6	0.130134
$746$	−2.02816e7	−1.33431
$747$	−5.96491e6	−0.391113
$748$	−2.13373e6	−0.139439
$749$	−2.16902e7	−1.41273
$750$	6.56448e6	0.426135
$751$	−1.83357e7	−1.18631	−0.593155	−	0.805089i	$-0.702118\pi$
$751$	−1.83357e7	−1.18631	−0.593155	+	0.805089i	$0.702118\pi$
$752$	6.26556e6	0.404032
$753$	−7.48375e6	−0.480985
$754$	−1.56940e7	−1.00532
$755$	−1.28510e6	−0.0820485
$756$	−1.27470e6	−0.0811155
$757$	−3.00076e6	−0.190323	−0.0951616	−	0.995462i	$-0.530337\pi$
$757$	−3.00076e6	−0.190323	−0.0951616	+	0.995462i	$0.530337\pi$
$758$	1.53655e7	0.971348
$759$	2.79341e6	0.176007
$760$	−9.16695e6	−0.575693
$761$	−9.38288e6	−0.587320	−0.293660	−	0.955910i	$-0.594873\pi$
$761$	−9.38288e6	−0.587320	−0.293660	+	0.955910i	$0.594873\pi$
$762$	3.77370e6	0.235440
$763$	−1.42239e7	−0.884521
$764$	1.43787e7	0.891220
$765$	7.46024e6	0.460892
$766$	2.01851e7	1.24297
$767$	1.91624e6	0.117614
$768$	589824.	0.0360844
$769$	1.21025e7	0.738002	0.369001	−	0.929429i	$-0.379700\pi$
$769$	1.21025e7	0.738002	0.369001	+	0.929429i	$0.379700\pi$
$770$	1.77878e6	0.108117
$771$	1.26908e7	0.768872
$772$	1.17348e7	0.708650
$773$	−9.74978e6	−0.586876	−0.293438	−	0.955978i	$-0.594799\pi$
$773$	−9.74978e6	−0.586876	−0.293438	+	0.955978i	$0.594799\pi$
$774$	3.87704e6	0.232620
$775$	−2.10064e6	−0.125631
$776$	3.72247e6	0.221910
$777$	−4.86773e6	−0.289251
$778$	−1.79721e7	−1.06451
$779$	3.61705e7	2.13556
$780$	−4.20226e6	−0.247313
$781$	−605604.	−0.0355272
$782$	−2.81007e7	−1.64324
$783$	−5.19586e6	−0.302867
$784$	−1.24512e6	−0.0723473
$785$	1.08634e7	0.629202
$786$	9.79028e6	0.565248
$787$	2.75847e7	1.58756	0.793782	−	0.608202i	$-0.208109\pi$
$787$	2.75847e7	1.58756	0.793782	+	0.608202i	$0.208109\pi$
$788$	−5.24671e6	−0.301003
$789$	−1.66774e7	−0.953752
$790$	9.66114e6	0.550758
$791$	1.38368e7	0.786313
$792$	397916.	0.0225413
$793$	−6.52990e6	−0.368743
$794$	7.62421e6	0.429184
$795$	−7.32253e6	−0.410907
$796$	1.50276e7	0.840636
$797$	−1.25819e7	−0.701616	−0.350808	−	0.936447i	$-0.614093\pi$
$797$	−1.25819e7	−0.701616	−0.350808	+	0.936447i	$0.614093\pi$
$798$	−1.06300e7	−0.590916
$799$	−4.25219e7	−2.35638
$800$	−322268.	−0.0178029
$801$	−1.16814e6	−0.0643299
$802$	1.06725e7	0.585910
$803$	768340.	0.0420498
$804$	8.40287e6	0.458445
$805$	2.34262e7	1.27412
$806$	1.46974e7	0.796899
$807$	−1.09170e7	−0.590094
$808$	−1.02577e7	−0.552743
$809$	−6.71199e6	−0.360562	−0.180281	−	0.983615i	$-0.557701\pi$
$809$	−6.71199e6	−0.360562	−0.180281	+	0.983615i	$0.557701\pi$
$810$	−1.39125e6	−0.0745063
$811$	−1.35568e7	−0.723776	−0.361888	−	0.932222i	$-0.617868\pi$
$811$	−1.35568e7	−0.723776	−0.361888	+	0.932222i	$0.617868\pi$
$812$	1.24627e7	0.663316
$813$	3.09195e6	0.164062
$814$	1.51953e6	0.0803802
$815$	−2.44286e7	−1.28826
$816$	−4.00290e6	−0.210450
$817$	3.23314e7	1.69461
$818$	1.47166e7	0.768994
$819$	−4.87294e6	−0.253852
$820$	−1.13548e7	−0.589720
$821$	−2.72631e7	−1.41162	−0.705809	−	0.708403i	$-0.749416\pi$
$821$	−2.72631e7	−1.41162	−0.705809	+	0.708403i	$0.749416\pi$
$822$	3.35041e6	0.172949
$823$	−1.10798e7	−0.570208	−0.285104	−	0.958497i	$-0.592028\pi$
$823$	−1.10798e7	−0.570208	−0.285104	+	0.958497i	$0.592028\pi$
$824$	−1.62871e6	−0.0835652
$825$	−217413.	−0.0111212
$826$	−1.52169e6	−0.0776023
$827$	1.91684e7	0.974590	0.487295	−	0.873237i	$-0.337984\pi$
$827$	1.91684e7	0.974590	0.487295	+	0.873237i	$0.337984\pi$
$828$	5.24047e6	0.265640
$829$	−1.62455e7	−0.821006	−0.410503	−	0.911859i	$-0.634647\pi$
$829$	−1.62455e7	−0.821006	−0.410503	+	0.911859i	$0.634647\pi$
$830$	1.56154e7	0.786790
$831$	1.39514e7	0.700832
$832$	2.25478e6	0.112927
$833$	8.45017e6	0.421942
$834$	−6.44494e6	−0.320851
$835$	1.25965e7	0.625222
$836$	3.31830e6	0.164210
$837$	4.86590e6	0.240076
$838$	2.20748e7	1.08589
$839$	3.53050e7	1.73153	0.865766	−	0.500448i	$-0.166831\pi$
$839$	3.53050e7	1.73153	0.865766	+	0.500448i	$0.166831\pi$
$840$	3.33702e6	0.163178
$841$	3.02883e7	1.47668
$842$	1.45776e7	0.708606
$843$	−6.39577e6	−0.309973
$844$	−1.76148e7	−0.851179
$845$	3.61860e6	0.174341
$846$	7.92986e6	0.380925
$847$	1.69566e7	0.812138
$848$	3.92901e6	0.187626
$849$	−4.78719e6	−0.227935
$850$	2.18710e6	0.103830
$851$	2.00119e7	0.947249
$852$	−1.13612e6	−0.0536198
$853$	−2.56765e7	−1.20827	−0.604134	−	0.796882i	$-0.706481\pi$
$853$	−2.56765e7	−1.20827	−0.604134	+	0.796882i	$0.706481\pi$
$854$	5.18540e6	0.243297
$855$	−1.16019e7	−0.542768
$856$	1.27023e7	0.592512
$857$	3.77287e7	1.75477	0.877384	−	0.479789i	$-0.159287\pi$
$857$	3.77287e7	1.75477	0.877384	+	0.479789i	$0.159287\pi$
$858$	1.52116e6	0.0705433
$859$	−1.84391e7	−0.852624	−0.426312	−	0.904576i	$-0.640187\pi$
$859$	−1.84391e7	−0.852624	−0.426312	+	0.904576i	$0.640187\pi$
$860$	−1.01496e7	−0.467955
$861$	−1.31671e7	−0.605314
$862$	6.26282e6	0.287079
$863$	−6.63586e6	−0.303298	−0.151649	−	0.988434i	$-0.548458\pi$
$863$	−6.63586e6	−0.303298	−0.151649	+	0.988434i	$0.548458\pi$
$864$	746496.	0.0340207
$865$	2.40031e7	1.09076
$866$	1.37519e7	0.623116
$867$	1.43874e7	0.650032
$868$	−1.16712e7	−0.525796
$869$	−3.49719e6	−0.157098
$870$	1.36021e7	0.609269
$871$	3.21226e7	1.43471
$872$	8.32987e6	0.370977
$873$	4.71125e6	0.209219
$874$	4.37013e7	1.93516
$875$	−1.99278e7	−0.879910
$876$	1.44142e6	0.0634642
$877$	−1.16427e7	−0.511157	−0.255579	−	0.966788i	$-0.582266\pi$
$877$	−1.16427e7	−0.511157	−0.255579	+	0.966788i	$0.582266\pi$
$878$	2.93414e7	1.28453
$879$	−2.31412e7	−1.01022
$880$	−1.04170e6	−0.0453456
$881$	2.04553e7	0.887903	0.443951	−	0.896051i	$-0.353576\pi$
$881$	2.04553e7	0.887903	0.443951	+	0.896051i	$0.353576\pi$
$882$	−1.57586e6	−0.0682097
$883$	2.29035e6	0.0988554	0.0494277	−	0.998778i	$-0.484260\pi$
$883$	2.29035e6	0.0988554	0.0494277	+	0.998778i	$0.484260\pi$
$884$	−1.53023e7	−0.658608
$885$	−1.66082e6	−0.0712793
$886$	−7.61888e6	−0.326067
$887$	1.38836e7	0.592506	0.296253	−	0.955109i	$-0.404263\pi$
$887$	1.38836e7	0.592506	0.296253	+	0.955109i	$0.404263\pi$
$888$	2.85066e6	0.121315
$889$	−1.14558e7	−0.486152
$890$	3.05805e6	0.129410
$891$	503613.	0.0212521
$892$	−9.84410e6	−0.414251
$893$	6.61287e7	2.77499
$894$	−1.33878e6	−0.0560228
$895$	−6.16339e6	−0.257195
$896$	−1.79053e6	−0.0745094
$897$	2.00333e7	0.831326
$898$	7.48934e6	0.309922
$899$	−4.75735e7	−1.96321
$900$	−407870.	−0.0167848
$901$	−2.66647e7	−1.09427
$902$	4.11028e6	0.168211
$903$	−1.17695e7	−0.480330
$904$	−8.10318e6	−0.329788
$905$	3.33822e7	1.35486
$906$	872701.	0.0353220
$907$	−8.62631e6	−0.348182	−0.174091	−	0.984730i	$-0.555699\pi$
$907$	−8.62631e6	−0.348182	−0.174091	+	0.984730i	$0.555699\pi$
$908$	−5.56284e6	−0.223914
$909$	−1.29825e7	−0.521131
$910$	1.27568e7	0.510667
$911$	−3.18120e7	−1.26998	−0.634988	−	0.772522i	$-0.718995\pi$
$911$	−3.18120e7	−1.26998	−0.634988	+	0.772522i	$0.718995\pi$
$912$	6.22518e6	0.247836
$913$	−5.65256e6	−0.224424
$914$	−4.74935e6	−0.188048
$915$	5.65951e6	0.223474
$916$	6.53550e6	0.257359
$917$	−2.97203e7	−1.16716
$918$	−5.06617e6	−0.198414
$919$	1.72582e7	0.674072	0.337036	−	0.941492i	$-0.390576\pi$
$919$	1.72582e7	0.674072	0.337036	+	0.941492i	$0.390576\pi$
$920$	−1.37189e7	−0.534380
$921$	1.52413e7	0.592068
$922$	−6.79179e6	−0.263122
$923$	−4.34317e6	−0.167804
$924$	−1.20795e6	−0.0465447
$925$	−1.55754e6	−0.0598530
$926$	−2.38857e7	−0.915398
$927$	−2.06133e6	−0.0787860
$928$	−7.29843e6	−0.278202
$929$	−2.95430e7	−1.12309	−0.561547	−	0.827445i	$-0.689793\pi$
$929$	−2.95430e7	−1.12309	−0.561547	+	0.827445i	$0.689793\pi$
$930$	−1.27384e7	−0.482954
$931$	−1.31414e7	−0.496899
$932$	−2.24011e7	−0.844752
$933$	2.13101e7	0.801459
$934$	2.76755e7	1.03808
$935$	7.06959e6	0.264463
$936$	2.85371e6	0.106468
$937$	4.03991e7	1.50322	0.751611	−	0.659607i	$-0.229277\pi$
$937$	4.03991e7	1.50322	0.751611	+	0.659607i	$0.229277\pi$
$938$	−2.55086e7	−0.946627
$939$	−3.41096e6	−0.126245
$940$	−2.07594e7	−0.766295
$941$	4.33474e7	1.59584	0.797919	−	0.602764i	$-0.205934\pi$
$941$	4.33474e7	1.59584	0.797919	+	0.602764i	$0.205934\pi$
$942$	−7.37719e6	−0.270872
$943$	5.41315e7	1.98231
$944$	891136.	0.0325472
$945$	4.22341e6	0.153845
$946$	3.67402e6	0.133479
$947$	3.13806e7	1.13707	0.568535	−	0.822659i	$-0.307511\pi$
$947$	3.13806e7	1.13707	0.568535	+	0.822659i	$0.307511\pi$
$948$	−6.56078e6	−0.237102
$949$	5.51025e6	0.198612
$950$	−3.40131e6	−0.122275
$951$	4.22899e6	0.151630
$952$	1.21516e7	0.434551
$953$	−7.23171e6	−0.257934	−0.128967	−	0.991649i	$-0.541166\pi$
$953$	−7.23171e6	−0.257934	−0.128967	+	0.991649i	$0.541166\pi$
$954$	4.97266e6	0.176896
$955$	−4.76402e7	−1.69030
$956$	−3.37974e6	−0.119602
$957$	−4.92378e6	−0.173788
$958$	1.73946e6	0.0612352
$959$	−1.01708e7	−0.357116
$960$	−1.95424e6	−0.0684384
$961$	1.59233e7	0.556191
$962$	1.08975e7	0.379656
$963$	1.60763e7	0.558626
$964$	1.43329e7	0.496753
$965$	−3.88804e7	−1.34404
$966$	−1.59085e7	−0.548511
$967$	−3.99252e7	−1.37303	−0.686517	−	0.727114i	$-0.740861\pi$
$967$	−3.99252e7	−1.37303	−0.686517	+	0.727114i	$0.740861\pi$
$968$	−9.93018e6	−0.340619
$969$	−4.22478e7	−1.44542
$970$	−1.23335e7	−0.420879
$971$	−4.80997e7	−1.63717	−0.818586	−	0.574384i	$-0.805241\pi$
$971$	−4.80997e7	−1.63717	−0.818586	+	0.574384i	$0.805241\pi$
$972$	944784.	0.0320750
$973$	1.95649e7	0.662514
$974$	1.48292e7	0.500863
$975$	−1.55921e6	−0.0525282
$976$	−3.03669e6	−0.102041
$977$	1.47229e7	0.493465	0.246733	−	0.969084i	$-0.420643\pi$
$977$	1.47229e7	0.493465	0.246733	+	0.969084i	$0.420643\pi$
$978$	1.65892e7	0.554598
$979$	−1.10697e6	−0.0369130
$980$	4.12542e6	0.137215
$981$	1.05425e7	0.349761
$982$	−2.96501e6	−0.0981177
$983$	69935.6	0.00230842	0.00115421	−	0.999999i	$-0.499633\pi$
$983$	69935.6	0.00230842	0.00115421	+	0.999999i	$0.499633\pi$
$984$	7.71095e6	0.253875
$985$	1.73837e7	0.570889
$986$	4.95316e7	1.62252
$987$	−2.40726e7	−0.786558
$988$	2.37977e7	0.775608
$989$	4.83860e7	1.57300
$990$	−1.31840e6	−0.0427522
$991$	−1.15094e7	−0.372278	−0.186139	−	0.982523i	$-0.559598\pi$
$991$	−1.15094e7	−0.372278	−0.186139	+	0.982523i	$0.559598\pi$
$992$	6.83496e6	0.220524
$993$	−2.76861e7	−0.891023
$994$	3.44892e6	0.110718
$995$	−4.97904e7	−1.59437
$996$	−1.06043e7	−0.338714
$997$	5.17946e7	1.65024	0.825118	−	0.564960i	$-0.191108\pi$
$997$	5.17946e7	1.65024	0.825118	+	0.564960i	$0.191108\pi$
$998$	2.64101e7	0.839351
$999$	3.60787e6	0.114377

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	354.6.a.i.1.3	✓	8
3.2	odd	2		1062.6.a.k.1.6		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
354.6.a.i.1.3	✓	8	1.1	even	1	trivial
1062.6.a.k.1.6		8	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)

\(f(q)\)	\(=\)	\(q+4.00000 q^{2} +9.00000 q^{3} +16.0000 q^{4} -53.0121 q^{5} +36.0000 q^{6} -109.285 q^{7} +64.0000 q^{8} +81.0000 q^{9} +O(q^{10})\)	\(q+4.00000 q^{2} +9.00000 q^{3} +16.0000 q^{4} -53.0121 q^{5} +36.0000 q^{6} -109.285 q^{7} +64.0000 q^{8} +81.0000 q^{9} -212.049 q^{10} +76.7585 q^{11} +144.000 q^{12} +550.484 q^{13} -437.140 q^{14} -477.109 q^{15} +256.000 q^{16} -1737.37 q^{17} +324.000 q^{18} +2701.90 q^{19} -848.194 q^{20} -983.566 q^{21} +307.034 q^{22} +4043.57 q^{23} +576.000 q^{24} -314.714 q^{25} +2201.94 q^{26} +729.000 q^{27} -1748.56 q^{28} -7127.37 q^{29} -1908.44 q^{30} +6674.76 q^{31} +1024.00 q^{32} +690.827 q^{33} -6949.48 q^{34} +5793.44 q^{35} +1296.00 q^{36} +4949.07 q^{37} +10807.6 q^{38} +4954.36 q^{39} -3392.78 q^{40} +13387.1 q^{41} -3934.26 q^{42} +11966.2 q^{43} +1228.14 q^{44} -4293.98 q^{45} +16174.3 q^{46} +24474.9 q^{47} +2304.00 q^{48} -4863.77 q^{49} -1258.86 q^{50} -15636.3 q^{51} +8807.75 q^{52} +15347.7 q^{53} +2916.00 q^{54} -4069.13 q^{55} -6994.25 q^{56} +24317.1 q^{57} -28509.5 q^{58} +3481.00 q^{59} -7633.75 q^{60} -11862.1 q^{61} +26699.0 q^{62} -8852.09 q^{63} +4096.00 q^{64} -29182.4 q^{65} +2763.31 q^{66} +58353.3 q^{67} -27797.9 q^{68} +36392.1 q^{69} +23173.7 q^{70} -7889.72 q^{71} +5184.00 q^{72} +10009.8 q^{73} +19796.3 q^{74} -2832.43 q^{75} +43230.4 q^{76} -8388.56 q^{77} +19817.4 q^{78} -45561.0 q^{79} -13571.1 q^{80} +6561.00 q^{81} +53548.3 q^{82} -73640.9 q^{83} -15737.1 q^{84} +92101.7 q^{85} +47864.7 q^{86} -64146.4 q^{87} +4912.55 q^{88} -14421.5 q^{89} -17175.9 q^{90} -60159.8 q^{91} +64697.1 q^{92} +60072.8 q^{93} +97899.4 q^{94} -143234. q^{95} +9216.00 q^{96} +58163.6 q^{97} -19455.1 q^{98} +6217.44 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 32 q^{2} + 72 q^{3} + 128 q^{4} + 96 q^{5} + 288 q^{6} + 181 q^{7} + 512 q^{8} + 648 q^{9}+O(q^{10}) \) 8 * q + 32 * q^2 + 72 * q^3 + 128 * q^4 + 96 * q^5 + 288 * q^6 + 181 * q^7 + 512 * q^8 + 648 * q^9	\( 8 q + 32 q^{2} + 72 q^{3} + 128 q^{4} + 96 q^{5} + 288 q^{6} + 181 q^{7} + 512 q^{8} + 648 q^{9} + 384 q^{10} + 897 q^{11} + 1152 q^{12} + 1743 q^{13} + 724 q^{14} + 864 q^{15} + 2048 q^{16} + 1861 q^{17} + 2592 q^{18} + 3154 q^{19} + 1536 q^{20} + 1629 q^{21} + 3588 q^{22} + 3808 q^{23} + 4608 q^{24} + 11616 q^{25} + 6972 q^{26} + 5832 q^{27} + 2896 q^{28} + 328 q^{29} + 3456 q^{30} + 570 q^{31} + 8192 q^{32} + 8073 q^{33} + 7444 q^{34} + 36086 q^{35} + 10368 q^{36} + 12777 q^{37} + 12616 q^{38} + 15687 q^{39} + 6144 q^{40} + 20167 q^{41} + 6516 q^{42} + 24579 q^{43} + 14352 q^{44} + 7776 q^{45} + 15232 q^{46} + 20490 q^{47} + 18432 q^{48} + 59391 q^{49} + 46464 q^{50} + 16749 q^{51} + 27888 q^{52} + 13404 q^{53} + 23328 q^{54} - 34588 q^{55} + 11584 q^{56} + 28386 q^{57} + 1312 q^{58} + 27848 q^{59} + 13824 q^{60} + 94944 q^{61} + 2280 q^{62} + 14661 q^{63} + 32768 q^{64} + 54560 q^{65} + 32292 q^{66} + 28838 q^{67} + 29776 q^{68} + 34272 q^{69} + 144344 q^{70} + 14983 q^{71} + 41472 q^{72} + 69384 q^{73} + 51108 q^{74} + 104544 q^{75} + 50464 q^{76} - 22359 q^{77} + 62748 q^{78} - 49199 q^{79} + 24576 q^{80} + 52488 q^{81} + 80668 q^{82} + 3995 q^{83} + 26064 q^{84} - 142290 q^{85} + 98316 q^{86} + 2952 q^{87} + 57408 q^{88} + 28722 q^{89} + 31104 q^{90} + 20815 q^{91} + 60928 q^{92} + 5130 q^{93} + 81960 q^{94} + 208010 q^{95} + 73728 q^{96} + 204150 q^{97} + 237564 q^{98} + 72657 q^{99}+O(q^{100}) \) 8 * q + 32 * q^2 + 72 * q^3 + 128 * q^4 + 96 * q^5 + 288 * q^6 + 181 * q^7 + 512 * q^8 + 648 * q^9 + 384 * q^10 + 897 * q^11 + 1152 * q^12 + 1743 * q^13 + 724 * q^14 + 864 * q^15 + 2048 * q^16 + 1861 * q^17 + 2592 * q^18 + 3154 * q^19 + 1536 * q^20 + 1629 * q^21 + 3588 * q^22 + 3808 * q^23 + 4608 * q^24 + 11616 * q^25 + 6972 * q^26 + 5832 * q^27 + 2896 * q^28 + 328 * q^29 + 3456 * q^30 + 570 * q^31 + 8192 * q^32 + 8073 * q^33 + 7444 * q^34 + 36086 * q^35 + 10368 * q^36 + 12777 * q^37 + 12616 * q^38 + 15687 * q^39 + 6144 * q^40 + 20167 * q^41 + 6516 * q^42 + 24579 * q^43 + 14352 * q^44 + 7776 * q^45 + 15232 * q^46 + 20490 * q^47 + 18432 * q^48 + 59391 * q^49 + 46464 * q^50 + 16749 * q^51 + 27888 * q^52 + 13404 * q^53 + 23328 * q^54 - 34588 * q^55 + 11584 * q^56 + 28386 * q^57 + 1312 * q^58 + 27848 * q^59 + 13824 * q^60 + 94944 * q^61 + 2280 * q^62 + 14661 * q^63 + 32768 * q^64 + 54560 * q^65 + 32292 * q^66 + 28838 * q^67 + 29776 * q^68 + 34272 * q^69 + 144344 * q^70 + 14983 * q^71 + 41472 * q^72 + 69384 * q^73 + 51108 * q^74 + 104544 * q^75 + 50464 * q^76 - 22359 * q^77 + 62748 * q^78 - 49199 * q^79 + 24576 * q^80 + 52488 * q^81 + 80668 * q^82 + 3995 * q^83 + 26064 * q^84 - 142290 * q^85 + 98316 * q^86 + 2952 * q^87 + 57408 * q^88 + 28722 * q^89 + 31104 * q^90 + 20815 * q^91 + 60928 * q^92 + 5130 * q^93 + 81960 * q^94 + 208010 * q^95 + 73728 * q^96 + 204150 * q^97 + 237564 * q^98 + 72657 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more