LMFDB - Embedded newform 354.6.a.g.1.5

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:	$6$
Coefficient field:	$\mathbb{Q}[x]/(x^{6} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 358x^{4} - 404x^{3} + 26492x^{2} - 11664x - 353376 $ x^6 - 358x^4 - 404x^3 + 26492x^2 - 11664x - 353376
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{3}\cdot 3^{4} $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.5
Root			$-11.2438$ 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)

$f(q)$	$=$	$q-4.00000 q^{2} -9.00000 q^{3} +16.0000 q^{4} +62.9440 q^{5} +36.0000 q^{6} -185.768 q^{7} -64.0000 q^{8} +81.0000 q^{9} +O(q^{10})$	\(q-4.00000 q^{2} -9.00000 q^{3} +16.0000 q^{4} +62.9440 q^{5} +36.0000 q^{6} -185.768 q^{7} -64.0000 q^{8} +81.0000 q^{9} -251.776 q^{10} -393.752 q^{11} -144.000 q^{12} -456.145 q^{13} +743.073 q^{14} -566.496 q^{15} +256.000 q^{16} -860.763 q^{17} -324.000 q^{18} +1819.73 q^{19} +1007.10 q^{20} +1671.91 q^{21} +1575.01 q^{22} +738.863 q^{23} +576.000 q^{24} +836.947 q^{25} +1824.58 q^{26} -729.000 q^{27} -2972.29 q^{28} -6149.00 q^{29} +2265.98 q^{30} +8271.91 q^{31} -1024.00 q^{32} +3543.77 q^{33} +3443.05 q^{34} -11693.0 q^{35} +1296.00 q^{36} -3806.72 q^{37} -7278.90 q^{38} +4105.31 q^{39} -4028.42 q^{40} +10665.8 q^{41} -6687.65 q^{42} -14403.2 q^{43} -6300.03 q^{44} +5098.46 q^{45} -2955.45 q^{46} +4037.54 q^{47} -2304.00 q^{48} +17702.8 q^{49} -3347.79 q^{50} +7746.87 q^{51} -7298.32 q^{52} -28296.0 q^{53} +2916.00 q^{54} -24784.3 q^{55} +11889.2 q^{56} -16377.5 q^{57} +24596.0 q^{58} +3481.00 q^{59} -9063.94 q^{60} -13671.2 q^{61} -33087.6 q^{62} -15047.2 q^{63} +4096.00 q^{64} -28711.6 q^{65} -14175.1 q^{66} +21923.6 q^{67} -13772.2 q^{68} -6649.77 q^{69} +46772.0 q^{70} +57637.1 q^{71} -5184.00 q^{72} -30192.7 q^{73} +15226.9 q^{74} -7532.52 q^{75} +29115.6 q^{76} +73146.6 q^{77} -16421.2 q^{78} +54069.5 q^{79} +16113.7 q^{80} +6561.00 q^{81} -42663.1 q^{82} +45983.9 q^{83} +26750.6 q^{84} -54179.9 q^{85} +57613.0 q^{86} +55341.0 q^{87} +25200.1 q^{88} +52956.0 q^{89} -20393.9 q^{90} +84737.2 q^{91} +11821.8 q^{92} -74447.2 q^{93} -16150.2 q^{94} +114541. q^{95} +9216.00 q^{96} -70213.6 q^{97} -70811.3 q^{98} -31893.9 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 24 q^{2} - 54 q^{3} + 96 q^{4} + 4 q^{5} + 216 q^{6} - 54 q^{7} - 384 q^{8} + 486 q^{9}+O(q^{10}) $ 6 * q - 24 * q^2 - 54 * q^3 + 96 * q^4 + 4 * q^5 + 216 * q^6 - 54 * q^7 - 384 * q^8 + 486 * q^9	\( 6 q - 24 q^{2} - 54 q^{3} + 96 q^{4} + 4 q^{5} + 216 q^{6} - 54 q^{7} - 384 q^{8} + 486 q^{9} - 16 q^{10} + 436 q^{11} - 864 q^{12} - 536 q^{13} + 216 q^{14} - 36 q^{15} + 1536 q^{16} + 910 q^{17} - 1944 q^{18} + 1462 q^{19} + 64 q^{20} + 486 q^{21} - 1744 q^{22} + 1634 q^{23} + 3456 q^{24} - 1186 q^{25} + 2144 q^{26} - 4374 q^{27} - 864 q^{28} - 1598 q^{29} + 144 q^{30} - 5670 q^{31} - 6144 q^{32} - 3924 q^{33} - 3640 q^{34} - 7242 q^{35} + 7776 q^{36} - 20458 q^{37} - 5848 q^{38} + 4824 q^{39} - 256 q^{40} + 262 q^{41} - 1944 q^{42} - 34028 q^{43} + 6976 q^{44} + 324 q^{45} - 6536 q^{46} - 11194 q^{47} - 13824 q^{48} - 32652 q^{49} + 4744 q^{50} - 8190 q^{51} - 8576 q^{52} - 17164 q^{53} + 17496 q^{54} - 37040 q^{55} + 3456 q^{56} - 13158 q^{57} + 6392 q^{58} + 20886 q^{59} - 576 q^{60} - 43546 q^{61} + 22680 q^{62} - 4374 q^{63} + 24576 q^{64} + 65568 q^{65} + 15696 q^{66} - 52772 q^{67} + 14560 q^{68} - 14706 q^{69} + 28968 q^{70} + 84740 q^{71} - 31104 q^{72} - 36578 q^{73} + 81832 q^{74} + 10674 q^{75} + 23392 q^{76} + 90678 q^{77} - 19296 q^{78} + 85196 q^{79} + 1024 q^{80} + 39366 q^{81} - 1048 q^{82} + 217026 q^{83} + 7776 q^{84} + 26570 q^{85} + 136112 q^{86} + 14382 q^{87} - 27904 q^{88} + 333850 q^{89} - 1296 q^{90} + 214914 q^{91} + 26144 q^{92} + 51030 q^{93} + 44776 q^{94} + 458758 q^{95} + 55296 q^{96} + 173148 q^{97} + 130608 q^{98} + 35316 q^{99}+O(q^{100}) \) 6 * q - 24 * q^2 - 54 * q^3 + 96 * q^4 + 4 * q^5 + 216 * q^6 - 54 * q^7 - 384 * q^8 + 486 * q^9 - 16 * q^10 + 436 * q^11 - 864 * q^12 - 536 * q^13 + 216 * q^14 - 36 * q^15 + 1536 * q^16 + 910 * q^17 - 1944 * q^18 + 1462 * q^19 + 64 * q^20 + 486 * q^21 - 1744 * q^22 + 1634 * q^23 + 3456 * q^24 - 1186 * q^25 + 2144 * q^26 - 4374 * q^27 - 864 * q^28 - 1598 * q^29 + 144 * q^30 - 5670 * q^31 - 6144 * q^32 - 3924 * q^33 - 3640 * q^34 - 7242 * q^35 + 7776 * q^36 - 20458 * q^37 - 5848 * q^38 + 4824 * q^39 - 256 * q^40 + 262 * q^41 - 1944 * q^42 - 34028 * q^43 + 6976 * q^44 + 324 * q^45 - 6536 * q^46 - 11194 * q^47 - 13824 * q^48 - 32652 * q^49 + 4744 * q^50 - 8190 * q^51 - 8576 * q^52 - 17164 * q^53 + 17496 * q^54 - 37040 * q^55 + 3456 * q^56 - 13158 * q^57 + 6392 * q^58 + 20886 * q^59 - 576 * q^60 - 43546 * q^61 + 22680 * q^62 - 4374 * q^63 + 24576 * q^64 + 65568 * q^65 + 15696 * q^66 - 52772 * q^67 + 14560 * q^68 - 14706 * q^69 + 28968 * q^70 + 84740 * q^71 - 31104 * q^72 - 36578 * q^73 + 81832 * q^74 + 10674 * q^75 + 23392 * q^76 + 90678 * q^77 - 19296 * q^78 + 85196 * q^79 + 1024 * q^80 + 39366 * q^81 - 1048 * q^82 + 217026 * q^83 + 7776 * q^84 + 26570 * q^85 + 136112 * q^86 + 14382 * q^87 - 27904 * q^88 + 333850 * q^89 - 1296 * q^90 + 214914 * q^91 + 26144 * q^92 + 51030 * q^93 + 44776 * q^94 + 458758 * q^95 + 55296 * q^96 + 173148 * q^97 + 130608 * q^98 + 35316 * 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
$5$	62.9440	1.12598	0.562988	−	0.826465i	$-0.309652\pi$
$5$	62.9440	1.12598	0.562988	+	0.826465i	$0.309652\pi$
$6$	36.0000	0.408248
$7$	−185.768	−1.43293	−0.716467	−	0.697621i	$-0.754242\pi$
$7$	−185.768	−1.43293	−0.716467	+	0.697621i	$0.754242\pi$
$8$	−64.0000	−0.353553
$9$	81.0000	0.333333
$10$	−251.776	−0.796186
$11$	−393.752	−0.981163	−0.490581	−	0.871395i	$-0.663216\pi$
$11$	−393.752	−0.981163	−0.490581	+	0.871395i	$0.663216\pi$
$12$	−144.000	−0.288675
$13$	−456.145	−0.748591	−0.374295	−	0.927309i	$-0.622115\pi$
$13$	−456.145	−0.748591	−0.374295	+	0.927309i	$0.622115\pi$
$14$	743.073	1.01324
$15$	−566.496	−0.650083
$16$	256.000	0.250000
$17$	−860.763	−0.722373	−0.361186	−	0.932494i	$-0.617628\pi$
$17$	−860.763	−0.722373	−0.361186	+	0.932494i	$0.617628\pi$
$18$	−324.000	−0.235702
$19$	1819.73	1.15644	0.578219	−	0.815882i	$-0.303748\pi$
$19$	1819.73	1.15644	0.578219	+	0.815882i	$0.303748\pi$
$20$	1007.10	0.562988
$21$	1671.91	0.827305
$22$	1575.01	0.693787
$23$	738.863	0.291235	0.145618	−	0.989341i	$-0.453483\pi$
$23$	738.863	0.291235	0.145618	+	0.989341i	$0.453483\pi$
$24$	576.000	0.204124
$25$	836.947	0.267823
$26$	1824.58	0.529334
$27$	−729.000	−0.192450
$28$	−2972.29	−0.716467
$29$	−6149.00	−1.35772	−0.678859	−	0.734269i	$-0.737525\pi$
$29$	−6149.00	−1.35772	−0.678859	+	0.734269i	$0.737525\pi$
$30$	2265.98	0.459678
$31$	8271.91	1.54597	0.772986	−	0.634423i	$-0.218762\pi$
$31$	8271.91	1.54597	0.772986	+	0.634423i	$0.218762\pi$
$32$	−1024.00	−0.176777
$33$	3543.77	0.566475
$34$	3443.05	0.510795
$35$	−11693.0	−1.61345
$36$	1296.00	0.166667
$37$	−3806.72	−0.457138	−0.228569	−	0.973528i	$-0.573405\pi$
$37$	−3806.72	−0.457138	−0.228569	+	0.973528i	$0.573405\pi$
$38$	−7278.90	−0.817724
$39$	4105.31	0.432199
$40$	−4028.42	−0.398093
$41$	10665.8	0.990907	0.495454	−	0.868634i	$-0.335002\pi$
$41$	10665.8	0.990907	0.495454	+	0.868634i	$0.335002\pi$
$42$	−6687.65	−0.584993
$43$	−14403.2	−1.18793	−0.593963	−	0.804492i	$-0.702437\pi$
$43$	−14403.2	−1.18793	−0.593963	+	0.804492i	$0.702437\pi$
$44$	−6300.03	−0.490581
$45$	5098.46	0.375325
$46$	−2955.45	−0.205935
$47$	4037.54	0.266607	0.133304	−	0.991075i	$-0.457441\pi$
$47$	4037.54	0.266607	0.133304	+	0.991075i	$0.457441\pi$
$48$	−2304.00	−0.144338
$49$	17702.8	1.05330
$50$	−3347.79	−0.189379
$51$	7746.87	0.417062
$52$	−7298.32	−0.374295
$53$	−28296.0	−1.38368	−0.691839	−	0.722052i	$-0.743199\pi$
$53$	−28296.0	−1.38368	−0.691839	+	0.722052i	$0.743199\pi$
$54$	2916.00	0.136083
$55$	−24784.3	−1.10477
$56$	11889.2	0.506619
$57$	−16377.5	−0.667669
$58$	24596.0	0.960051
$59$	3481.00	0.130189
$59$	3481.00	0.130189
$60$	−9063.94	−0.325041
$61$	−13671.2	−0.470414	−0.235207	−	0.971945i	$-0.575577\pi$
$61$	−13671.2	−0.470414	−0.235207	+	0.971945i	$0.575577\pi$
$62$	−33087.6	−1.09317
$63$	−15047.2	−0.477645
$64$	4096.00	0.125000
$65$	−28711.6	−0.842896
$66$	−14175.1	−0.400558
$67$	21923.6	0.596658	0.298329	−	0.954463i	$-0.403571\pi$
$67$	21923.6	0.596658	0.298329	+	0.954463i	$0.403571\pi$
$68$	−13772.2	−0.361186
$69$	−6649.77	−0.168145
$70$	46772.0	1.14088
$71$	57637.1	1.35693	0.678463	−	0.734634i	$-0.262646\pi$
$71$	57637.1	1.35693	0.678463	+	0.734634i	$0.262646\pi$
$72$	−5184.00	−0.117851
$73$	−30192.7	−0.663124	−0.331562	−	0.943433i	$-0.607576\pi$
$73$	−30192.7	−0.663124	−0.331562	+	0.943433i	$0.607576\pi$
$74$	15226.9	0.323245
$75$	−7532.52	−0.154628
$76$	29115.6	0.578219
$77$	73146.6	1.40594
$78$	−16421.2	−0.305611
$79$	54069.5	0.974730	0.487365	−	0.873198i	$-0.337958\pi$
$79$	54069.5	0.974730	0.487365	+	0.873198i	$0.337958\pi$
$80$	16113.7	0.281494
$81$	6561.00	0.111111
$82$	−42663.1	−0.700677
$83$	45983.9	0.732673	0.366337	−	0.930482i	$-0.380612\pi$
$83$	45983.9	0.732673	0.366337	+	0.930482i	$0.380612\pi$
$84$	26750.6	0.413652
$85$	−54179.9	−0.813375
$86$	57613.0	0.839990
$87$	55341.0	0.783879
$88$	25200.1	0.346893
$89$	52956.0	0.708664	0.354332	−	0.935120i	$-0.384708\pi$
$89$	52956.0	0.708664	0.354332	+	0.935120i	$0.384708\pi$
$90$	−20393.9	−0.265395
$91$	84737.2	1.07268
$92$	11821.8	0.145618
$93$	−74447.2	−0.892567
$94$	−16150.2	−0.188520
$95$	114541.	1.30212
$96$	9216.00	0.102062
$97$	−70213.6	−0.757690	−0.378845	−	0.925460i	$-0.623679\pi$
$97$	−70213.6	−0.757690	−0.378845	+	0.925460i	$0.623679\pi$
$98$	−70811.3	−0.744796
$99$	−31893.9	−0.327054
$100$	13391.2	0.133912
$101$	18025.5	0.175826	0.0879132	−	0.996128i	$-0.471980\pi$
$101$	18025.5	0.175826	0.0879132	+	0.996128i	$0.471980\pi$
$102$	−30987.5	−0.294908
$103$	189420.	1.75927	0.879634	−	0.475651i	$-0.157787\pi$
$103$	189420.	1.75927	0.879634	+	0.475651i	$0.157787\pi$
$104$	29193.3	0.264667
$105$	105237.	0.931526
$106$	113184.	0.978408
$107$	162192.	1.36953	0.684764	−	0.728765i	$-0.259905\pi$
$107$	162192.	1.36953	0.684764	+	0.728765i	$0.259905\pi$
$108$	−11664.0	−0.0962250
$109$	−16426.1	−0.132425	−0.0662123	−	0.997806i	$-0.521091\pi$
$109$	−16426.1	−0.132425	−0.0662123	+	0.997806i	$0.521091\pi$
$110$	99137.3	0.781188
$111$	34260.5	0.263929
$112$	−47556.7	−0.358234
$113$	188269.	1.38702	0.693508	−	0.720449i	$-0.256064\pi$
$113$	188269.	1.38702	0.693508	+	0.720449i	$0.256064\pi$
$114$	65510.1	0.472113
$115$	46507.0	0.327924
$116$	−98384.0	−0.678859
$117$	−36947.8	−0.249530
$118$	−13924.0	−0.0920575
$119$	159902.	1.03511
$120$	36255.7	0.229839
$121$	−6010.35	−0.0373195
$122$	54684.6	0.332633
$123$	−95992.0	−0.572100
$124$	132351.	0.772986
$125$	−144019.	−0.824414
$126$	60188.9	0.337746
$127$	148223.	0.815469	0.407734	−	0.913101i	$-0.366319\pi$
$127$	148223.	0.815469	0.407734	+	0.913101i	$0.366319\pi$
$128$	−16384.0	−0.0883883
$129$	129629.	0.685849
$130$	114846.	0.596017
$131$	−4997.61	−0.0254439	−0.0127220	−	0.999919i	$-0.504050\pi$
$131$	−4997.61	−0.0254439	−0.0127220	+	0.999919i	$0.504050\pi$
$132$	56700.3	0.283237
$133$	−338047.	−1.65710
$134$	−87694.5	−0.421901
$135$	−45886.2	−0.216694
$136$	55088.9	0.255397
$137$	189646.	0.863261	0.431631	−	0.902050i	$-0.357938\pi$
$137$	189646.	0.863261	0.431631	+	0.902050i	$0.357938\pi$
$138$	26599.1	0.118896
$139$	−350725.	−1.53968	−0.769838	−	0.638239i	$-0.779663\pi$
$139$	−350725.	−1.53968	−0.769838	+	0.638239i	$0.779663\pi$
$140$	−187088.	−0.806725
$141$	−36337.9	−0.153926
$142$	−230548.	−0.959492
$143$	179608.	0.734490
$144$	20736.0	0.0833333
$145$	−387043.	−1.52876
$146$	120771.	0.468900
$147$	−159325.	−0.608123
$148$	−60907.6	−0.228569
$149$	486008.	1.79340	0.896702	−	0.442635i	$-0.145956\pi$
$149$	486008.	1.79340	0.896702	+	0.442635i	$0.145956\pi$
$150$	30130.1	0.109338
$151$	−80744.1	−0.288183	−0.144092	−	0.989564i	$-0.546026\pi$
$151$	−80744.1	−0.288183	−0.144092	+	0.989564i	$0.546026\pi$
$152$	−116462.	−0.408862
$153$	−69721.8	−0.240791
$154$	−292586.	−0.994151
$155$	520667.	1.74073
$156$	65684.9	0.216100
$157$	−461525.	−1.49433	−0.747165	−	0.664639i	$-0.768586\pi$
$157$	−461525.	−1.49433	−0.747165	+	0.664639i	$0.768586\pi$
$158$	−216278.	−0.689238
$159$	254664.	0.798867
$160$	−64454.7	−0.199046
$161$	−137257.	−0.417321
$162$	−26244.0	−0.0785674
$163$	545991.	1.60959	0.804797	−	0.593551i	$-0.202274\pi$
$163$	545991.	1.60959	0.804797	+	0.593551i	$0.202274\pi$
$164$	170652.	0.495454
$165$	223059.	0.637837
$166$	−183935.	−0.518078
$167$	−18120.8	−0.0502789	−0.0251394	−	0.999684i	$-0.508003\pi$
$167$	−18120.8	−0.0502789	−0.0251394	+	0.999684i	$0.508003\pi$
$168$	−107002.	−0.292496
$169$	−163225.	−0.439612
$170$	216720.	0.575143
$171$	147398.	0.385479
$172$	−230452.	−0.593963
$173$	−50761.0	−0.128948	−0.0644740	−	0.997919i	$-0.520537\pi$
$173$	−50761.0	−0.128948	−0.0644740	+	0.997919i	$0.520537\pi$
$174$	−221364.	−0.554286
$175$	−155478.	−0.383773
$176$	−100801.	−0.245291
$177$	−31329.0	−0.0751646
$178$	−211824.	−0.501101
$179$	694421.	1.61991	0.809954	−	0.586494i	$-0.199492\pi$
$179$	694421.	1.61991	0.809954	+	0.586494i	$0.199492\pi$
$180$	81575.4	0.187663
$181$	557838.	1.26564	0.632822	−	0.774297i	$-0.281897\pi$
$181$	557838.	1.26564	0.632822	+	0.774297i	$0.281897\pi$
$182$	−338949.	−0.758500
$183$	123040.	0.271594
$184$	−47287.2	−0.102967
$185$	−239610.	−0.514726
$186$	297789.	0.631140
$187$	338927.	0.708766
$188$	64600.6	0.133304
$189$	135425.	0.275768
$190$	−458163.	−0.920738
$191$	−151153.	−0.299801	−0.149900	−	0.988701i	$-0.547895\pi$
$191$	−151153.	−0.299801	−0.149900	+	0.988701i	$0.547895\pi$
$192$	−36864.0	−0.0721688
$193$	941172.	1.81876	0.909380	−	0.415966i	$-0.136556\pi$
$193$	941172.	1.81876	0.909380	+	0.415966i	$0.136556\pi$
$194$	280854.	0.535768
$195$	258404.	0.486646
$196$	283245.	0.526650
$197$	−180986.	−0.332260	−0.166130	−	0.986104i	$-0.553127\pi$
$197$	−180986.	−0.332260	−0.166130	+	0.986104i	$0.553127\pi$
$198$	127576.	0.231262
$199$	721133.	1.29087	0.645435	−	0.763815i	$-0.276676\pi$
$199$	721133.	1.29087	0.645435	+	0.763815i	$0.276676\pi$
$200$	−53564.6	−0.0946897
$201$	−197313.	−0.344480
$202$	−72102.0	−0.124328
$203$	1.14229e6	1.94552
$204$	123950.	0.208531
$205$	671347.	1.11574
$206$	−757679.	−1.24399
$207$	59847.9	0.0970785
$208$	−116773.	−0.187148
$209$	−716521.	−1.13465
$210$	−420948.	−0.658688
$211$	−713670.	−1.10355	−0.551774	−	0.833994i	$-0.686049\pi$
$211$	−713670.	−1.10355	−0.551774	+	0.833994i	$0.686049\pi$
$212$	−452736.	−0.691839
$213$	−518734.	−0.783422
$214$	−648769.	−0.968403
$215$	−906598.	−1.33758
$216$	46656.0	0.0680414
$217$	−1.53666e6	−2.21528
$218$	65704.4	0.0936383
$219$	271734.	0.382855
$220$	−396549.	−0.552383
$221$	392633.	0.540762
$222$	−137042.	−0.186626
$223$	−896839.	−1.20768	−0.603840	−	0.797105i	$-0.706364\pi$
$223$	−896839.	−1.20768	−0.603840	+	0.797105i	$0.706364\pi$
$224$	190227.	0.253309
$225$	67792.7	0.0892743
$226$	−753074.	−0.980769
$227$	−429143.	−0.552761	−0.276381	−	0.961048i	$-0.589135\pi$
$227$	−429143.	−0.552761	−0.276381	+	0.961048i	$0.589135\pi$
$228$	−262041.	−0.333835
$229$	1.22774e6	1.54710	0.773551	−	0.633734i	$-0.218479\pi$
$229$	1.22774e6	1.54710	0.773551	+	0.633734i	$0.218479\pi$
$230$	−186028.	−0.231877
$231$	−658319.	−0.811721
$232$	393536.	0.480026
$233$	297758.	0.359313	0.179657	−	0.983729i	$-0.442501\pi$
$233$	297758.	0.359313	0.179657	+	0.983729i	$0.442501\pi$
$234$	147791.	0.176445
$235$	254139.	0.300194
$236$	55696.0	0.0650945
$237$	−486625.	−0.562761
$238$	−639610.	−0.731935
$239$	840092.	0.951332	0.475666	−	0.879626i	$-0.342207\pi$
$239$	840092.	0.951332	0.475666	+	0.879626i	$0.342207\pi$
$240$	−145023.	−0.162521
$241$	342032.	0.379336	0.189668	−	0.981848i	$-0.439259\pi$
$241$	342032.	0.379336	0.189668	+	0.981848i	$0.439259\pi$
$242$	24041.4	0.0263889
$243$	−59049.0	−0.0641500
$244$	−218738.	−0.235207
$245$	1.11429e6	1.18599
$246$	383968.	0.404536
$247$	−830059.	−0.865698
$248$	−529402.	−0.546584
$249$	−413855.	−0.423009
$250$	576077.	0.582949
$251$	−1.40819e6	−1.41083	−0.705417	−	0.708792i	$-0.749240\pi$
$251$	−1.40819e6	−1.41083	−0.705417	+	0.708792i	$0.749240\pi$
$252$	−240756.	−0.238822
$253$	−290929.	−0.285749
$254$	−592894.	−0.576624
$255$	487619.	0.469602
$256$	65536.0	0.0625000
$257$	−239598.	−0.226282	−0.113141	−	0.993579i	$-0.536091\pi$
$257$	−239598.	−0.226282	−0.113141	+	0.993579i	$0.536091\pi$
$258$	−518517.	−0.484969
$259$	707168.	0.655048
$260$	−459386.	−0.421448
$261$	−498069.	−0.452573
$262$	19990.5	0.0179916
$263$	−591330.	−0.527157	−0.263579	−	0.964638i	$-0.584903\pi$
$263$	−591330.	−0.527157	−0.263579	+	0.964638i	$0.584903\pi$
$264$	−226801.	−0.200279
$265$	−1.78106e6	−1.55799
$266$	1.35219e6	1.17175
$267$	−476604.	−0.409147
$268$	350778.	0.298329
$269$	476101.	0.401161	0.200580	−	0.979677i	$-0.435717\pi$
$269$	476101.	0.401161	0.200580	+	0.979677i	$0.435717\pi$
$270$	183545.	0.153226
$271$	−163280.	−0.135055	−0.0675274	−	0.997717i	$-0.521511\pi$
$271$	−163280.	−0.135055	−0.0675274	+	0.997717i	$0.521511\pi$
$272$	−220355.	−0.180593
$273$	−762635.	−0.619313
$274$	−758584.	−0.610418
$275$	−329550.	−0.262778
$276$	−106396.	−0.0840724
$277$	−1.21877e6	−0.954384	−0.477192	−	0.878799i	$-0.658345\pi$
$277$	−1.21877e6	−0.954384	−0.477192	+	0.878799i	$0.658345\pi$
$278$	1.40290e6	1.08872
$279$	670025.	0.515324
$280$	748352.	0.570441
$281$	−268545.	−0.202886	−0.101443	−	0.994841i	$-0.532346\pi$
$281$	−268545.	−0.202886	−0.101443	+	0.994841i	$0.532346\pi$
$282$	145351.	0.108842
$283$	−874999.	−0.649444	−0.324722	−	0.945810i	$-0.605271\pi$
$283$	−874999.	−0.649444	−0.324722	+	0.945810i	$0.605271\pi$
$284$	922194.	0.678463
$285$	−1.03087e6	−0.751780
$286$	−718432.	−0.519363
$287$	−1.98136e6	−1.41990
$288$	−82944.0	−0.0589256
$289$	−678943.	−0.478177
$290$	1.54817e6	1.08100
$291$	631922.	0.437453
$292$	−483083.	−0.331562
$293$	2.15960e6	1.46962	0.734808	−	0.678275i	$-0.237272\pi$
$293$	2.15960e6	1.46962	0.734808	+	0.678275i	$0.237272\pi$
$294$	637302.	0.430008
$295$	219108.	0.146590
$296$	243630.	0.161623
$297$	287045.	0.188825
$298$	−1.94403e6	−1.26813
$299$	−337029.	−0.218016
$300$	−120520.	−0.0773139
$301$	2.67567e6	1.70222
$302$	322976.	0.203776
$303$	−162230.	−0.101513
$304$	465850.	0.289109
$305$	−860517.	−0.529675
$306$	278887.	0.170265
$307$	−348556.	−0.211070	−0.105535	−	0.994416i	$-0.533655\pi$
$307$	−348556.	−0.211070	−0.105535	+	0.994416i	$0.533655\pi$
$308$	1.17035e6	0.702971
$309$	−1.70478e6	−1.01571
$310$	−2.08267e6	−1.23088
$311$	1.23794e6	0.725770	0.362885	−	0.931834i	$-0.381792\pi$
$311$	1.23794e6	0.725770	0.362885	+	0.931834i	$0.381792\pi$
$312$	−262740.	−0.152805
$313$	217459.	0.125463	0.0627316	−	0.998030i	$-0.480019\pi$
$313$	217459.	0.125463	0.0627316	+	0.998030i	$0.480019\pi$
$314$	1.84610e6	1.05665
$315$	−947132.	−0.537817
$316$	865111.	0.487365
$317$	2.53310e6	1.41581	0.707905	−	0.706308i	$-0.249641\pi$
$317$	2.53310e6	1.41581	0.707905	+	0.706308i	$0.249641\pi$
$318$	−1.01866e6	−0.564884
$319$	2.42118e6	1.33214
$320$	257819.	0.140747
$321$	−1.45973e6	−0.790697
$322$	549029.	0.295091
$323$	−1.56635e6	−0.835379
$324$	104976.	0.0555556
$325$	−381769.	−0.200490
$326$	−2.18396e6	−1.13815
$327$	147835.	0.0764554
$328$	−682610.	−0.350339
$329$	−750047.	−0.382031
$330$	−892236.	−0.451019
$331$	422269.	0.211845	0.105923	−	0.994374i	$-0.466220\pi$
$331$	422269.	0.211845	0.105923	+	0.994374i	$0.466220\pi$
$332$	735742.	0.366337
$333$	−308345.	−0.152379
$334$	72483.1	0.0355525
$335$	1.37996e6	0.671823
$336$	428010.	0.206826
$337$	−1.69698e6	−0.813959	−0.406979	−	0.913437i	$-0.633418\pi$
$337$	−1.69698e6	−0.813959	−0.406979	+	0.913437i	$0.633418\pi$
$338$	652899.	0.310852
$339$	−1.69442e6	−0.800795
$340$	−866878.	−0.406687
$341$	−3.25708e6	−1.51685
$342$	−589591.	−0.272575
$343$	−166415.	−0.0763761
$344$	921808.	0.419995
$345$	−418563.	−0.189327
$346$	203044.	0.0911800
$347$	2.40421e6	1.07189	0.535943	−	0.844254i	$-0.319956\pi$
$347$	2.40421e6	1.07189	0.535943	+	0.844254i	$0.319956\pi$
$348$	885456.	0.391939
$349$	−722244.	−0.317410	−0.158705	−	0.987326i	$-0.550732\pi$
$349$	−722244.	−0.317410	−0.158705	+	0.987326i	$0.550732\pi$
$350$	621913.	0.271368
$351$	332530.	0.144066
$352$	403202.	0.173447
$353$	1.82340e6	0.778835	0.389418	−	0.921061i	$-0.372676\pi$
$353$	1.82340e6	0.778835	0.389418	+	0.921061i	$0.372676\pi$
$354$	125316.	0.0531494
$355$	3.62791e6	1.52787
$356$	847296.	0.354332
$357$	−1.43912e6	−0.597623
$358$	−2.77768e6	−1.14545
$359$	−4.18001e6	−1.71175	−0.855877	−	0.517180i	$-0.826982\pi$
$359$	−4.18001e6	−1.71175	−0.855877	+	0.517180i	$0.826982\pi$
$360$	−326302.	−0.132698
$361$	835303.	0.337347
$362$	−2.23135e6	−0.894945
$363$	54093.2	0.0215465
$364$	1.35580e6	0.536341
$365$	−1.90045e6	−0.746662
$366$	−492161.	−0.192046
$367$	516221.	0.200065	0.100032	−	0.994984i	$-0.468105\pi$
$367$	516221.	0.200065	0.100032	+	0.994984i	$0.468105\pi$
$368$	189149.	0.0728089
$369$	863928.	0.330302
$370$	958442.	0.363967
$371$	5.25649e6	1.98272
$372$	−1.19116e6	−0.446284
$373$	−1.57318e6	−0.585473	−0.292736	−	0.956193i	$-0.594566\pi$
$373$	−1.57318e6	−0.585473	−0.292736	+	0.956193i	$0.594566\pi$
$374$	−1.35571e6	−0.501173
$375$	1.29617e6	0.475976
$376$	−258403.	−0.0942600
$377$	2.80484e6	1.01638
$378$	−541700.	−0.194998
$379$	−1.99208e6	−0.712374	−0.356187	−	0.934415i	$-0.615923\pi$
$379$	−1.99208e6	−0.712374	−0.356187	+	0.934415i	$0.615923\pi$
$380$	1.83265e6	0.651060
$381$	−1.33401e6	−0.470811
$382$	604611.	0.211991
$383$	2.13569e6	0.743947	0.371973	−	0.928243i	$-0.378681\pi$
$383$	2.13569e6	0.743947	0.371973	+	0.928243i	$0.378681\pi$
$384$	147456.	0.0510310
$385$	4.60414e6	1.58306
$386$	−3.76469e6	−1.28606
$387$	−1.16666e6	−0.395975
$388$	−1.12342e6	−0.378845
$389$	4.60234e6	1.54207	0.771036	−	0.636792i	$-0.219739\pi$
$389$	4.60234e6	1.54207	0.771036	+	0.636792i	$0.219739\pi$
$390$	−1.03362e6	−0.344111
$391$	−635986.	−0.210381
$392$	−1.13298e6	−0.372398
$393$	44978.5	0.0146901
$394$	723942.	0.234943
$395$	3.40335e6	1.09752
$396$	−510303.	−0.163527
$397$	332462.	0.105868	0.0529341	−	0.998598i	$-0.483143\pi$
$397$	332462.	0.105868	0.0529341	+	0.998598i	$0.483143\pi$
$398$	−2.88453e6	−0.912783
$399$	3.04242e6	0.956726
$400$	214258.	0.0669558
$401$	957097.	0.297232	0.148616	−	0.988895i	$-0.452518\pi$
$401$	957097.	0.297232	0.148616	+	0.988895i	$0.452518\pi$
$402$	789250.	0.243584
$403$	−3.77319e6	−1.15730
$404$	288408.	0.0879132
$405$	412976.	0.125108
$406$	−4.56915e6	−1.37569
$407$	1.49891e6	0.448527
$408$	−495800.	−0.147454
$409$	6.44103e6	1.90391	0.951956	−	0.306236i	$-0.0990696\pi$
$409$	6.44103e6	1.90391	0.951956	+	0.306236i	$0.0990696\pi$
$410$	−2.68539e6	−0.788946
$411$	−1.70681e6	−0.498404
$412$	3.03071e6	0.879634
$413$	−646659.	−0.186552
$414$	−239392.	−0.0686449
$415$	2.89441e6	0.824973
$416$	467093.	0.132333
$417$	3.15652e6	0.888932
$418$	2.86608e6	0.802321
$419$	−3.34179e6	−0.929918	−0.464959	−	0.885332i	$-0.653931\pi$
$419$	−3.34179e6	−0.929918	−0.464959	+	0.885332i	$0.653931\pi$
$420$	1.68379e6	0.465763
$421$	−2.51868e6	−0.692576	−0.346288	−	0.938128i	$-0.612558\pi$
$421$	−2.51868e6	−0.692576	−0.346288	+	0.938128i	$0.612558\pi$
$422$	2.85468e6	0.780326
$423$	327041.	0.0888691
$424$	1.81094e6	0.489204
$425$	−720413.	−0.193468
$426$	2.07494e6	0.553963
$427$	2.53967e6	0.674073
$428$	2.59508e6	0.684764
$429$	−1.61647e6	−0.424058
$430$	3.62639e6	0.945809
$431$	2.92091e6	0.757400	0.378700	−	0.925520i	$-0.376371\pi$
$431$	2.92091e6	0.757400	0.378700	+	0.925520i	$0.376371\pi$
$432$	−186624.	−0.0481125
$433$	−6.19747e6	−1.58853	−0.794264	−	0.607573i	$-0.792143\pi$
$433$	−6.19747e6	−1.58853	−0.794264	+	0.607573i	$0.792143\pi$
$434$	6.14663e6	1.56644
$435$	3.48338e6	0.882629
$436$	−262818.	−0.0662123
$437$	1.34453e6	0.336795
$438$	−1.08694e6	−0.270719
$439$	−5.45081e6	−1.34989	−0.674947	−	0.737866i	$-0.735834\pi$
$439$	−5.45081e6	−1.34989	−0.674947	+	0.737866i	$0.735834\pi$
$440$	1.58620e6	0.390594
$441$	1.43393e6	0.351100
$442$	−1.57053e6	−0.382376
$443$	−1.46178e6	−0.353893	−0.176946	−	0.984221i	$-0.556622\pi$
$443$	−1.46178e6	−0.353893	−0.176946	+	0.984221i	$0.556622\pi$
$444$	548168.	0.131964
$445$	3.33326e6	0.797939
$446$	3.58735e6	0.853959
$447$	−4.37408e6	−1.03542
$448$	−760907.	−0.179117
$449$	−1.61835e6	−0.378840	−0.189420	−	0.981896i	$-0.560661\pi$
$449$	−1.61835e6	−0.378840	−0.189420	+	0.981896i	$0.560661\pi$
$450$	−271171.	−0.0631265
$451$	−4.19967e6	−0.972241
$452$	3.01230e6	0.693508
$453$	726697.	0.166383
$454$	1.71657e6	0.390861
$455$	5.33370e6	1.20781
$456$	1.04816e6	0.236057
$457$	8.51949e6	1.90820	0.954098	−	0.299495i	$-0.0968182\pi$
$457$	8.51949e6	1.90820	0.954098	+	0.299495i	$0.0968182\pi$
$458$	−4.91098e6	−1.09397
$459$	627497.	0.139021
$460$	744112.	0.163962
$461$	−3.26690e6	−0.715952	−0.357976	−	0.933731i	$-0.616533\pi$
$461$	−3.26690e6	−0.715952	−0.357976	+	0.933731i	$0.616533\pi$
$462$	2.63328e6	0.573973
$463$	−1.04366e6	−0.226260	−0.113130	−	0.993580i	$-0.536088\pi$
$463$	−1.04366e6	−0.226260	−0.113130	+	0.993580i	$0.536088\pi$
$464$	−1.57414e6	−0.339429
$465$	−4.68600e6	−1.00501
$466$	−1.19103e6	−0.254073
$467$	470458.	0.0998225	0.0499112	−	0.998754i	$-0.484106\pi$
$467$	470458.	0.0998225	0.0499112	+	0.998754i	$0.484106\pi$
$468$	−591164.	−0.124765
$469$	−4.07271e6	−0.854971
$470$	−1.01656e6	−0.212269
$471$	4.15373e6	0.862752
$472$	−222784.	−0.0460287
$473$	5.67131e6	1.16555
$474$	1.94650e6	0.397932
$475$	1.52301e6	0.309720
$476$	2.55844e6	0.517556
$477$	−2.29198e6	−0.461226
$478$	−3.36037e6	−0.672693
$479$	2.71229e6	0.540128	0.270064	−	0.962842i	$-0.412955\pi$
$479$	2.71229e6	0.540128	0.270064	+	0.962842i	$0.412955\pi$
$480$	580092.	0.114919
$481$	1.73642e6	0.342209
$482$	−1.36813e6	−0.268231
$483$	1.23532e6	0.240941
$484$	−96165.6	−0.0186598
$485$	−4.41952e6	−0.853142
$486$	236196.	0.0453609
$487$	−9.09483e6	−1.73769	−0.868845	−	0.495085i	$-0.835137\pi$
$487$	−9.09483e6	−1.73769	−0.868845	+	0.495085i	$0.835137\pi$
$488$	874954.	0.166317
$489$	−4.91391e6	−0.929299
$490$	−4.45715e6	−0.838623
$491$	−1.52066e6	−0.284662	−0.142331	−	0.989819i	$-0.545460\pi$
$491$	−1.52066e6	−0.284662	−0.142331	+	0.989819i	$0.545460\pi$
$492$	−1.53587e6	−0.286050
$493$	5.29283e6	0.980779
$494$	3.32024e6	0.612141
$495$	−2.00753e6	−0.368255
$496$	2.11761e6	0.386493
$497$	−1.07071e7	−1.94439
$498$	1.65542e6	0.299113
$499$	−2.83194e6	−0.509134	−0.254567	−	0.967055i	$-0.581933\pi$
$499$	−2.83194e6	−0.509134	−0.254567	+	0.967055i	$0.581933\pi$
$500$	−2.30431e6	−0.412207
$501$	163087.	0.0290285
$502$	5.63275e6	0.997611
$503$	−4.81664e6	−0.848837	−0.424419	−	0.905466i	$-0.639522\pi$
$503$	−4.81664e6	−0.848837	−0.424419	+	0.905466i	$0.639522\pi$
$504$	963022.	0.168873
$505$	1.13460e6	0.197976
$506$	1.16372e6	0.202055
$507$	1.46902e6	0.253810
$508$	2.37157e6	0.407734
$509$	1.80418e6	0.308664	0.154332	−	0.988019i	$-0.450677\pi$
$509$	1.80418e6	0.308664	0.154332	+	0.988019i	$0.450677\pi$
$510$	−1.95048e6	−0.332059
$511$	5.60885e6	0.950213
$512$	−262144.	−0.0441942
$513$	−1.32658e6	−0.222556
$514$	958392.	0.160006
$515$	1.19228e7	1.98089
$516$	2.07407e6	0.342925
$517$	−1.58979e6	−0.261585
$518$	−2.82867e6	−0.463189
$519$	456849.	0.0744482
$520$	1.83754e6	0.298009
$521$	4.47079e6	0.721589	0.360794	−	0.932645i	$-0.382506\pi$
$521$	4.47079e6	0.721589	0.360794	+	0.932645i	$0.382506\pi$
$522$	1.99228e6	0.320017
$523$	−2.25247e6	−0.360085	−0.180043	−	0.983659i	$-0.557624\pi$
$523$	−2.25247e6	−0.360085	−0.180043	+	0.983659i	$0.557624\pi$
$524$	−79961.8	−0.0127220
$525$	1.39930e6	0.221571
$526$	2.36532e6	0.372757
$527$	−7.12016e6	−1.11677
$528$	907205.	0.141619
$529$	−5.89042e6	−0.915182
$530$	7.12425e6	1.10166
$531$	281961.	0.0433963
$532$	−5.40876e6	−0.828549
$533$	−4.86514e6	−0.741784
$534$	1.90642e6	0.289311
$535$	1.02090e7	1.54206
$536$	−1.40311e6	−0.210950
$537$	−6.24979e6	−0.935254
$538$	−1.90440e6	−0.283664
$539$	−6.97052e6	−1.03346
$540$	−734179.	−0.108347
$541$	4.78508e6	0.702905	0.351452	−	0.936206i	$-0.385688\pi$
$541$	4.78508e6	0.702905	0.351452	+	0.936206i	$0.385688\pi$
$542$	653120.	0.0954981
$543$	−5.02054e6	−0.730720
$544$	881422.	0.127699
$545$	−1.03393e6	−0.149107
$546$	3.05054e6	0.437920
$547$	6.57173e6	0.939099	0.469549	−	0.882906i	$-0.344416\pi$
$547$	6.57173e6	0.939099	0.469549	+	0.882906i	$0.344416\pi$
$548$	3.03434e6	0.431631
$549$	−1.10736e6	−0.156805
$550$	1.31820e6	0.185812
$551$	−1.11895e7	−1.57011
$552$	425585.	0.0594482
$553$	−1.00444e7	−1.39672
$554$	4.87509e6	0.674851
$555$	2.15649e6	0.297177
$556$	−5.61160e6	−0.769838
$557$	−1.01664e7	−1.38845	−0.694223	−	0.719760i	$-0.744252\pi$
$557$	−1.01664e7	−1.38845	−0.694223	+	0.719760i	$0.744252\pi$
$558$	−2.68010e6	−0.364389
$559$	6.56997e6	0.889270
$560$	−2.99341e6	−0.403363
$561$	−3.05035e6	−0.409206
$562$	1.07418e6	0.143462
$563$	−1.00881e6	−0.134134	−0.0670670	−	0.997748i	$-0.521364\pi$
$563$	−1.00881e6	−0.134134	−0.0670670	+	0.997748i	$0.521364\pi$
$564$	−581406.	−0.0769629
$565$	1.18504e7	1.56175
$566$	3.50000e6	0.459226
$567$	−1.21883e6	−0.159215
$568$	−3.68878e6	−0.479746
$569$	−7.55296e6	−0.977995	−0.488998	−	0.872285i	$-0.662637\pi$
$569$	−7.55296e6	−0.977995	−0.488998	+	0.872285i	$0.662637\pi$
$570$	4.12347e6	0.531589
$571$	−2.06112e6	−0.264554	−0.132277	−	0.991213i	$-0.542229\pi$
$571$	−2.06112e6	−0.264554	−0.132277	+	0.991213i	$0.542229\pi$
$572$	2.87373e6	0.367245
$573$	1.36037e6	0.173090
$574$	7.92545e6	1.00402
$575$	618389.	0.0779996
$576$	331776.	0.0416667
$577$	−517348.	−0.0646909	−0.0323455	−	0.999477i	$-0.510298\pi$
$577$	−517348.	−0.0646909	−0.0323455	+	0.999477i	$0.510298\pi$
$578$	2.71577e6	0.338122
$579$	−8.47054e6	−1.05006
$580$	−6.19268e6	−0.764379
$581$	−8.54234e6	−1.04987
$582$	−2.52769e6	−0.309326
$583$	1.11416e7	1.35761
$584$	1.93233e6	0.234450
$585$	−2.32564e6	−0.280965
$586$	−8.63840e6	−1.03918
$587$	5.44786e6	0.652576	0.326288	−	0.945270i	$-0.394202\pi$
$587$	5.44786e6	0.652576	0.326288	+	0.945270i	$0.394202\pi$
$588$	−2.54921e6	−0.304062
$589$	1.50526e7	1.78782
$590$	−876432.	−0.103655
$591$	1.62887e6	0.191831
$592$	−974521.	−0.114284
$593$	8.90281e6	1.03966	0.519829	−	0.854270i	$-0.325996\pi$
$593$	8.90281e6	1.03966	0.519829	+	0.854270i	$0.325996\pi$
$594$	−1.14818e6	−0.133519
$595$	1.00649e7	1.16551
$596$	7.77613e6	0.896702
$597$	−6.49019e6	−0.745284
$598$	1.34811e6	0.154161
$599$	1.02769e7	1.17030	0.585148	−	0.810926i	$-0.301036\pi$
$599$	1.02769e7	1.17030	0.585148	+	0.810926i	$0.301036\pi$
$600$	482081.	0.0546692
$601$	−2.83405e6	−0.320052	−0.160026	−	0.987113i	$-0.551158\pi$
$601$	−2.83405e6	−0.320052	−0.160026	+	0.987113i	$0.551158\pi$
$602$	−1.07027e7	−1.20365
$603$	1.77581e6	0.198886
$604$	−1.29191e6	−0.144092
$605$	−378316.	−0.0420209
$606$	648918.	0.0717808
$607$	−1.99721e6	−0.220015	−0.110008	−	0.993931i	$-0.535087\pi$
$607$	−1.99721e6	−0.220015	−0.110008	+	0.993931i	$0.535087\pi$
$608$	−1.86340e6	−0.204431
$609$	−1.02806e7	−1.12325
$610$	3.44207e6	0.374537
$611$	−1.84170e6	−0.199580
$612$	−1.11555e6	−0.120395
$613$	−1.33213e7	−1.43184	−0.715920	−	0.698183i	$-0.753992\pi$
$613$	−1.33213e7	−1.43184	−0.715920	+	0.698183i	$0.753992\pi$
$614$	1.39422e6	0.149249
$615$	−6.04212e6	−0.644172
$616$	−4.68138e6	−0.497075
$617$	1.54747e7	1.63648	0.818240	−	0.574877i	$-0.194950\pi$
$617$	1.54747e7	1.63648	0.818240	+	0.574877i	$0.194950\pi$
$618$	6.81911e6	0.718218
$619$	−7.34230e6	−0.770204	−0.385102	−	0.922874i	$-0.625834\pi$
$619$	−7.34230e6	−0.770204	−0.385102	+	0.922874i	$0.625834\pi$
$620$	8.33068e6	0.870364
$621$	−538631.	−0.0560483
$622$	−4.95176e6	−0.513197
$623$	−9.83754e6	−1.01547
$624$	1.05096e6	0.108050
$625$	−1.16806e7	−1.19609
$626$	−869835.	−0.0887158
$627$	6.44869e6	0.655092
$628$	−7.38441e6	−0.747165
$629$	3.27669e6	0.330224
$630$	3.78853e6	0.380294
$631$	1.52768e7	1.52742	0.763712	−	0.645557i	$-0.223375\pi$
$631$	1.52768e7	1.52742	0.763712	+	0.645557i	$0.223375\pi$
$632$	−3.46044e6	−0.344619
$633$	6.42303e6	0.637134
$634$	−1.01324e7	−1.00113
$635$	9.32977e6	0.918199
$636$	4.07462e6	0.399434
$637$	−8.07505e6	−0.788491
$638$	−9.68472e6	−0.941967
$639$	4.66861e6	0.452309
$640$	−1.03127e6	−0.0995232
$641$	−7.95729e6	−0.764927	−0.382464	−	0.923971i	$-0.624924\pi$
$641$	−7.95729e6	−0.764927	−0.382464	+	0.923971i	$0.624924\pi$
$642$	5.83893e6	0.559108
$643$	−9.30487e6	−0.887530	−0.443765	−	0.896143i	$-0.646357\pi$
$643$	−9.30487e6	−0.887530	−0.443765	+	0.896143i	$0.646357\pi$
$644$	−2.19612e6	−0.208661
$645$	8.15938e6	0.772250
$646$	6.26541e6	0.590702
$647$	−1.31546e7	−1.23543	−0.617713	−	0.786403i	$-0.711941\pi$
$647$	−1.31546e7	−1.23543	−0.617713	+	0.786403i	$0.711941\pi$
$648$	−419904.	−0.0392837
$649$	−1.37065e6	−0.127737
$650$	1.52708e6	0.141768
$651$	1.38299e7	1.27899
$652$	8.73585e6	0.804797
$653$	−1.81805e7	−1.66849	−0.834243	−	0.551396i	$-0.814095\pi$
$653$	−1.81805e7	−1.66849	−0.834243	+	0.551396i	$0.814095\pi$
$654$	−591340.	−0.0540621
$655$	−314570.	−0.0286493
$656$	2.73044e6	0.247727
$657$	−2.44561e6	−0.221041
$658$	3.00019e6	0.270137
$659$	169147.	0.0151723	0.00758615	−	0.999971i	$-0.497585\pi$
$659$	169147.	0.0151723	0.00758615	+	0.999971i	$0.497585\pi$
$660$	3.56894e6	0.318919
$661$	−9.33289e6	−0.830831	−0.415415	−	0.909632i	$-0.636364\pi$
$661$	−9.33289e6	−0.830831	−0.415415	+	0.909632i	$0.636364\pi$
$662$	−1.68907e6	−0.149797
$663$	−3.53370e6	−0.312209
$664$	−2.94297e6	−0.259039
$665$	−2.12780e7	−1.86585
$666$	1.23338e6	0.107748
$667$	−4.54327e6	−0.395416
$668$	−289932.	−0.0251394
$669$	8.07155e6	0.697255
$670$	−5.51984e6	−0.475050
$671$	5.38304e6	0.461553
$672$	−1.71204e6	−0.146248
$673$	−1.13330e7	−0.964509	−0.482255	−	0.876031i	$-0.660182\pi$
$673$	−1.13330e7	−0.964509	−0.482255	+	0.876031i	$0.660182\pi$
$674$	6.78793e6	0.575556
$675$	−610134.	−0.0515426
$676$	−2.61159e6	−0.219806
$677$	1.62914e7	1.36611	0.683057	−	0.730365i	$-0.260650\pi$
$677$	1.62914e7	1.36611	0.683057	+	0.730365i	$0.260650\pi$
$678$	6.77767e6	0.566247
$679$	1.30434e7	1.08572
$680$	3.46751e6	0.287571
$681$	3.86229e6	0.319137
$682$	1.30283e7	1.07258
$683$	7.70885e6	0.632321	0.316161	−	0.948706i	$-0.397606\pi$
$683$	7.70885e6	0.632321	0.316161	+	0.948706i	$0.397606\pi$
$684$	2.35836e6	0.192740
$685$	1.19371e7	0.972012
$686$	665660.	0.0540060
$687$	−1.10497e7	−0.893220
$688$	−3.68723e6	−0.296981
$689$	1.29071e7	1.03581
$690$	1.67425e6	0.133875
$691$	1.69807e6	0.135288	0.0676442	−	0.997710i	$-0.478452\pi$
$691$	1.69807e6	0.135288	0.0676442	+	0.997710i	$0.478452\pi$
$692$	−812176.	−0.0644740
$693$	5.92487e6	0.468647
$694$	−9.61684e6	−0.757938
$695$	−2.20760e7	−1.73364
$696$	−3.54182e6	−0.277143
$697$	−9.18071e6	−0.715804
$698$	2.88897e6	0.224443
$699$	−2.67982e6	−0.207450
$700$	−2.48765e6	−0.191886
$701$	1.72294e7	1.32427	0.662134	−	0.749386i	$-0.269651\pi$
$701$	1.72294e7	1.32427	0.662134	+	0.749386i	$0.269651\pi$
$702$	−1.33012e6	−0.101870
$703$	−6.92719e6	−0.528651
$704$	−1.61281e6	−0.122645
$705$	−2.28725e6	−0.173317
$706$	−7.29361e6	−0.550720
$707$	−3.34857e6	−0.251948
$708$	−501264.	−0.0375823
$709$	2.10062e7	1.56939	0.784697	−	0.619880i	$-0.212819\pi$
$709$	2.10062e7	1.56939	0.784697	+	0.619880i	$0.212819\pi$
$710$	−1.45116e7	−1.08037
$711$	4.37963e6	0.324910
$712$	−3.38918e6	−0.250550
$713$	6.11181e6	0.450242
$714$	5.75649e6	0.422583
$715$	1.13052e7	0.827018
$716$	1.11107e7	0.809954
$717$	−7.56083e6	−0.549252
$718$	1.67200e7	1.21039
$719$	−1.38697e7	−1.00056	−0.500282	−	0.865862i	$-0.666770\pi$
$719$	−1.38697e7	−1.00056	−0.500282	+	0.865862i	$0.666770\pi$
$720$	1.30521e6	0.0938314
$721$	−3.51882e7	−2.52092
$722$	−3.34121e6	−0.238540
$723$	−3.07829e6	−0.219010
$724$	8.92540e6	0.632822
$725$	−5.14639e6	−0.363628
$726$	−216373.	−0.0152356
$727$	−2.40930e6	−0.169066	−0.0845328	−	0.996421i	$-0.526940\pi$
$727$	−2.40930e6	−0.169066	−0.0845328	+	0.996421i	$0.526940\pi$
$728$	−5.42318e6	−0.379250
$729$	531441.	0.0370370
$730$	7.60180e6	0.527970
$731$	1.23978e7	0.858125
$732$	1.96865e6	0.135797
$733$	7.08072e6	0.486763	0.243382	−	0.969931i	$-0.421743\pi$
$733$	7.08072e6	0.486763	0.243382	+	0.969931i	$0.421743\pi$
$734$	−2.06488e6	−0.141467
$735$	−1.00286e7	−0.684733
$736$	−756596.	−0.0514836
$737$	−8.63247e6	−0.585418
$738$	−3.45571e6	−0.233559
$739$	2.37610e7	1.60049	0.800245	−	0.599673i	$-0.204703\pi$
$739$	2.37610e7	1.60049	0.800245	+	0.599673i	$0.204703\pi$
$740$	−3.83377e6	−0.257363
$741$	7.47053e6	0.499811
$742$	−2.10260e7	−1.40199
$743$	−2.37902e7	−1.58098	−0.790491	−	0.612474i	$-0.790175\pi$
$743$	−2.37902e7	−1.58098	−0.790491	+	0.612474i	$0.790175\pi$
$744$	4.76462e6	0.315570
$745$	3.05913e7	2.01933
$746$	6.29272e6	0.413992
$747$	3.72469e6	0.244224
$748$	5.42284e6	0.354383
$749$	−3.01302e7	−1.96244
$750$	−5.18469e6	−0.336566
$751$	−1.86854e7	−1.20893	−0.604466	−	0.796631i	$-0.706613\pi$
$751$	−1.86854e7	−1.20893	−0.604466	+	0.796631i	$0.706613\pi$
$752$	1.03361e6	0.0666519
$753$	1.26737e7	0.814546
$754$	−1.12193e7	−0.718686
$755$	−5.08236e6	−0.324487
$756$	2.16680e6	0.137884
$757$	−1.21741e7	−0.772143	−0.386072	−	0.922469i	$-0.626168\pi$
$757$	−1.21741e7	−0.772143	−0.386072	+	0.922469i	$0.626168\pi$
$758$	7.96831e6	0.503725
$759$	2.61836e6	0.164978
$760$	−7.33061e6	−0.460369
$761$	4.35525e6	0.272616	0.136308	−	0.990667i	$-0.456476\pi$
$761$	4.35525e6	0.272616	0.136308	+	0.990667i	$0.456476\pi$
$762$	5.33604e6	0.332914
$763$	3.05145e6	0.189756
$764$	−2.41844e6	−0.149900
$765$	−4.38857e6	−0.271125
$766$	−8.54277e6	−0.526050
$767$	−1.58784e6	−0.0974582
$768$	−589824.	−0.0360844
$769$	2.04263e6	0.124559	0.0622793	−	0.998059i	$-0.480163\pi$
$769$	2.04263e6	0.124559	0.0622793	+	0.998059i	$0.480163\pi$
$770$	−1.84166e7	−1.11939
$771$	2.15638e6	0.130644
$772$	1.50587e7	0.909380
$773$	−2.20765e7	−1.32887	−0.664434	−	0.747347i	$-0.731327\pi$
$773$	−2.20765e7	−1.32887	−0.664434	+	0.747347i	$0.731327\pi$
$774$	4.66665e6	0.279997
$775$	6.92315e6	0.414047
$776$	4.49367e6	0.267884
$777$	−6.36451e6	−0.378192
$778$	−1.84094e7	−1.09041
$779$	1.94088e7	1.14592
$780$	4.13447e6	0.243323
$781$	−2.26947e7	−1.33137
$782$	2.54394e6	0.148762
$783$	4.48262e6	0.261293
$784$	4.53192e6	0.263325
$785$	−2.90503e7	−1.68258
$786$	−179914.	−0.0103874
$787$	−1.80554e7	−1.03913	−0.519565	−	0.854431i	$-0.673906\pi$
$787$	−1.80554e7	−1.03913	−0.519565	+	0.854431i	$0.673906\pi$
$788$	−2.89577e6	−0.166130
$789$	5.32197e6	0.304354
$790$	−1.36134e7	−0.776066
$791$	−3.49743e7	−1.98750
$792$	2.04121e6	0.115631
$793$	6.23603e6	0.352148
$794$	−1.32985e6	−0.0748601
$795$	1.60296e7	0.899506
$796$	1.15381e7	0.645435
$797$	2.72811e7	1.52130	0.760652	−	0.649159i	$-0.224879\pi$
$797$	2.72811e7	1.52130	0.760652	+	0.649159i	$0.224879\pi$
$798$	−1.21697e7	−0.676507
$799$	−3.47537e6	−0.192590
$800$	−857034.	−0.0473449
$801$	4.28944e6	0.236221
$802$	−3.82839e6	−0.210175
$803$	1.18884e7	0.650633
$804$	−3.15700e6	−0.172240
$805$	−8.63952e6	−0.469894
$806$	1.50928e7	0.818335
$807$	−4.28491e6	−0.231610
$808$	−1.15363e6	−0.0621640
$809$	1.97822e7	1.06268	0.531342	−	0.847158i	$-0.321688\pi$
$809$	1.97822e7	1.06268	0.531342	+	0.847158i	$0.321688\pi$
$810$	−1.65190e6	−0.0884651
$811$	1.35783e7	0.724923	0.362462	−	0.931999i	$-0.381936\pi$
$811$	1.35783e7	0.724923	0.362462	+	0.931999i	$0.381936\pi$
$812$	1.82766e7	0.972760
$813$	1.46952e6	0.0779739
$814$	−5.99562e6	−0.317156
$815$	3.43668e7	1.81236
$816$	1.98320e6	0.104266
$817$	−2.62100e7	−1.37376
$818$	−2.57641e7	−1.34627
$819$	6.86372e6	0.357561
$820$	1.07415e7	0.557869
$821$	−2.22493e7	−1.15202	−0.576008	−	0.817444i	$-0.695390\pi$
$821$	−2.22493e7	−1.15202	−0.576008	+	0.817444i	$0.695390\pi$
$822$	6.82725e6	0.352425
$823$	1.91811e7	0.987130	0.493565	−	0.869709i	$-0.335693\pi$
$823$	1.91811e7	0.987130	0.493565	+	0.869709i	$0.335693\pi$
$824$	−1.21229e7	−0.621995
$825$	2.96595e6	0.151715
$826$	2.58664e6	0.131912
$827$	9.98358e6	0.507601	0.253800	−	0.967257i	$-0.418319\pi$
$827$	9.98358e6	0.507601	0.253800	+	0.967257i	$0.418319\pi$
$828$	957566.	0.0485392
$829$	1.62374e7	0.820598	0.410299	−	0.911951i	$-0.365424\pi$
$829$	1.62374e7	0.820598	0.410299	+	0.911951i	$0.365424\pi$
$830$	−1.15776e7	−0.583344
$831$	1.09689e7	0.551014
$832$	−1.86837e6	−0.0935739
$833$	−1.52379e7	−0.760876
$834$	−1.26261e7	−0.628570
$835$	−1.14059e6	−0.0566129
$836$	−1.14643e7	−0.567326
$837$	−6.03022e6	−0.297522
$838$	1.33672e7	0.657551
$839$	−3.92113e7	−1.92312	−0.961561	−	0.274592i	$-0.911457\pi$
$839$	−3.92113e7	−1.92312	−0.961561	+	0.274592i	$0.911457\pi$
$840$	−6.73516e6	−0.329344
$841$	1.72990e7	0.843397
$842$	1.00747e7	0.489725
$843$	2.41691e6	0.117136
$844$	−1.14187e7	−0.551774
$845$	−1.02740e7	−0.494992
$846$	−1.30816e6	−0.0628400
$847$	1.11653e6	0.0534765
$848$	−7.24377e6	−0.345920
$849$	7.87499e6	0.374956
$850$	2.88165e6	0.136803
$851$	−2.81265e6	−0.133135
$852$	−8.29975e6	−0.391711
$853$	−2.18968e7	−1.03041	−0.515203	−	0.857068i	$-0.672284\pi$
$853$	−2.18968e7	−1.03041	−0.515203	+	0.857068i	$0.672284\pi$
$854$	−1.01587e7	−0.476641
$855$	9.27781e6	0.434040
$856$	−1.03803e7	−0.484201
$857$	−3.39370e7	−1.57842	−0.789209	−	0.614125i	$-0.789509\pi$
$857$	−3.39370e7	−1.57842	−0.789209	+	0.614125i	$0.789509\pi$
$858$	6.46589e6	0.299854
$859$	3.35859e7	1.55301	0.776504	−	0.630112i	$-0.216991\pi$
$859$	3.35859e7	1.55301	0.776504	+	0.630112i	$0.216991\pi$
$860$	−1.45056e7	−0.668788
$861$	1.78323e7	0.819782
$862$	−1.16836e7	−0.535563
$863$	3.49283e7	1.59643	0.798215	−	0.602373i	$-0.205778\pi$
$863$	3.49283e7	1.59643	0.798215	+	0.602373i	$0.205778\pi$
$864$	746496.	0.0340207
$865$	−3.19510e6	−0.145192
$866$	2.47899e7	1.12326
$867$	6.11049e6	0.276076
$868$	−2.45865e7	−1.10764
$869$	−2.12900e7	−0.956369
$870$	−1.39335e7	−0.624113
$871$	−1.00004e7	−0.446653
$872$	1.05127e6	0.0468192
$873$	−5.68730e6	−0.252563
$874$	−5.37811e6	−0.238150
$875$	2.67542e7	1.18133
$876$	4.34775e6	0.191427
$877$	1.79830e7	0.789521	0.394761	−	0.918784i	$-0.370828\pi$
$877$	1.79830e7	0.789521	0.394761	+	0.918784i	$0.370828\pi$
$878$	2.18032e7	0.954520
$879$	−1.94364e7	−0.848484
$880$	−6.34479e6	−0.276192
$881$	−1.53833e7	−0.667741	−0.333871	−	0.942619i	$-0.608355\pi$
$881$	−1.53833e7	−0.667741	−0.333871	+	0.942619i	$0.608355\pi$
$882$	−5.73571e6	−0.248265
$883$	3.27449e6	0.141332	0.0706661	−	0.997500i	$-0.477488\pi$
$883$	3.27449e6	0.141332	0.0706661	+	0.997500i	$0.477488\pi$
$884$	6.28213e6	0.270381
$885$	−1.97197e6	−0.0846336
$886$	5.84710e6	0.250240
$887$	−1.24073e7	−0.529502	−0.264751	−	0.964317i	$-0.585290\pi$
$887$	−1.24073e7	−0.529502	−0.264751	+	0.964317i	$0.585290\pi$
$888$	−2.19267e6	−0.0933129
$889$	−2.75352e7	−1.16851
$890$	−1.33330e7	−0.564228
$891$	−2.58341e6	−0.109018
$892$	−1.43494e7	−0.603840
$893$	7.34722e6	0.308315
$894$	1.74963e7	0.732154
$895$	4.37096e7	1.82398
$896$	3.04363e6	0.126655
$897$	3.03326e6	0.125872
$898$	6.47339e6	0.267881
$899$	−5.08640e7	−2.09899
$900$	1.08468e6	0.0446372
$901$	2.43562e7	0.999532
$902$	1.67987e7	0.687478
$903$	−2.40810e7	−0.982777
$904$	−1.20492e7	−0.490384
$905$	3.51125e7	1.42509
$906$	−2.90679e6	−0.117650
$907$	−2.01815e7	−0.814584	−0.407292	−	0.913298i	$-0.633527\pi$
$907$	−2.01815e7	−0.814584	−0.407292	+	0.913298i	$0.633527\pi$
$908$	−6.86629e6	−0.276381
$909$	1.46007e6	0.0586088
$910$	−2.13348e7	−0.854054
$911$	4.26847e7	1.70403	0.852013	−	0.523520i	$-0.175381\pi$
$911$	4.26847e7	1.70403	0.852013	+	0.523520i	$0.175381\pi$
$912$	−4.19265e6	−0.166917
$913$	−1.81062e7	−0.718872
$914$	−3.40779e7	−1.34930
$915$	7.74465e6	0.305808
$916$	1.96439e7	0.773551
$917$	928398.	0.0364595
$918$	−2.50999e6	−0.0983025
$919$	−2.38625e7	−0.932025	−0.466012	−	0.884778i	$-0.654310\pi$
$919$	−2.38625e7	−0.932025	−0.466012	+	0.884778i	$0.654310\pi$
$920$	−2.97645e6	−0.115939
$921$	3.13700e6	0.121861
$922$	1.30676e7	0.506255
$923$	−2.62909e7	−1.01578
$924$	−1.05331e7	−0.405860
$925$	−3.18603e6	−0.122432
$926$	4.17465e6	0.159990
$927$	1.53430e7	0.586423
$928$	6.29658e6	0.240013
$929$	1.01335e7	0.385231	0.192615	−	0.981274i	$-0.438303\pi$
$929$	1.01335e7	0.385231	0.192615	+	0.981274i	$0.438303\pi$
$930$	1.87440e7	0.710649
$931$	3.22143e7	1.21808
$932$	4.76412e6	0.179657
$933$	−1.11415e7	−0.419023
$934$	−1.88183e6	−0.0705851
$935$	2.13334e7	0.798053
$936$	2.36466e6	0.0882223
$937$	3.34388e6	0.124423	0.0622117	−	0.998063i	$-0.480185\pi$
$937$	3.34388e6	0.124423	0.0622117	+	0.998063i	$0.480185\pi$
$938$	1.62908e7	0.604556
$939$	−1.95713e6	−0.0724362
$940$	4.06622e6	0.150097
$941$	−4.32318e7	−1.59158	−0.795791	−	0.605572i	$-0.792944\pi$
$941$	−4.32318e7	−1.59158	−0.795791	+	0.605572i	$0.792944\pi$
$942$	−1.66149e7	−0.610058
$943$	7.88055e6	0.288587
$944$	891136.	0.0325472
$945$	8.52419e6	0.310509
$946$	−2.26852e7	−0.824167
$947$	2.93105e7	1.06206	0.531029	−	0.847354i	$-0.321805\pi$
$947$	2.93105e7	1.06206	0.531029	+	0.847354i	$0.321805\pi$
$948$	−7.78600e6	−0.281380
$949$	1.37723e7	0.496409
$950$	−6.09206e6	−0.219005
$951$	−2.27979e7	−0.817418
$952$	−1.02338e7	−0.365968
$953$	2.90317e7	1.03548	0.517739	−	0.855539i	$-0.326774\pi$
$953$	2.90317e7	1.03548	0.517739	+	0.855539i	$0.326774\pi$
$954$	9.16790e6	0.326136
$955$	−9.51416e6	−0.337569
$956$	1.34415e7	0.475666
$957$	−2.17906e7	−0.769113
$958$	−1.08491e7	−0.381928
$959$	−3.52302e7	−1.23700
$960$	−2.32037e6	−0.0812604
$961$	3.97954e7	1.39003
$962$	−6.94567e6	−0.241978
$963$	1.31376e7	0.456509
$964$	5.47252e6	0.189668
$965$	5.92411e7	2.04788
$966$	−4.94126e6	−0.170371
$967$	4.21862e7	1.45079	0.725395	−	0.688333i	$-0.241657\pi$
$967$	4.21862e7	1.45079	0.725395	+	0.688333i	$0.241657\pi$
$968$	384662.	0.0131945
$969$	1.40972e7	0.482306
$970$	1.76781e7	0.603262
$971$	3.42756e7	1.16664	0.583320	−	0.812242i	$-0.301753\pi$
$971$	3.42756e7	1.16664	0.583320	+	0.812242i	$0.301753\pi$
$972$	−944784.	−0.0320750
$973$	6.51535e7	2.20625
$974$	3.63793e7	1.22873
$975$	3.43592e6	0.115753
$976$	−3.49981e6	−0.117604
$977$	1.36171e7	0.456402	0.228201	−	0.973614i	$-0.426716\pi$
$977$	1.36171e7	0.456402	0.228201	+	0.973614i	$0.426716\pi$
$978$	1.96557e7	0.657114
$979$	−2.08515e7	−0.695314
$980$	1.78286e7	0.592996
$981$	−1.33052e6	−0.0441415
$982$	6.08265e6	0.201286
$983$	5.00625e7	1.65245	0.826225	−	0.563340i	$-0.190484\pi$
$983$	5.00625e7	1.65245	0.826225	+	0.563340i	$0.190484\pi$
$984$	6.14349e6	0.202268
$985$	−1.13920e7	−0.374117
$986$	−2.11713e7	−0.693515
$987$	6.75042e6	0.220566
$988$	−1.32809e7	−0.432849
$989$	−1.06420e7	−0.345966
$990$	8.03012e6	0.260396
$991$	6.06774e7	1.96265	0.981325	−	0.192358i	$-0.0616136\pi$
$991$	6.06774e7	1.96265	0.981325	+	0.192358i	$0.0616136\pi$
$992$	−8.47044e6	−0.273292
$993$	−3.80042e6	−0.122309
$994$	4.28286e7	1.37489
$995$	4.53910e7	1.45349
$996$	−6.62168e6	−0.211504
$997$	2.08606e7	0.664644	0.332322	−	0.943166i	$-0.392168\pi$
$997$	2.08606e7	0.664644	0.332322	+	0.943166i	$0.392168\pi$
$998$	1.13277e7	0.360012
$999$	2.77510e6	0.0879762

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	354.6.a.g.1.5	✓	6
3.2	odd	2		1062.6.a.h.1.2		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
354.6.a.g.1.5	✓	6	1.1	even	1	trivial
1062.6.a.h.1.2		6	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)

\(f(q)\)	\(=\)	\(q-4.00000 q^{2} -9.00000 q^{3} +16.0000 q^{4} +62.9440 q^{5} +36.0000 q^{6} -185.768 q^{7} -64.0000 q^{8} +81.0000 q^{9} +O(q^{10})\)	\(q-4.00000 q^{2} -9.00000 q^{3} +16.0000 q^{4} +62.9440 q^{5} +36.0000 q^{6} -185.768 q^{7} -64.0000 q^{8} +81.0000 q^{9} -251.776 q^{10} -393.752 q^{11} -144.000 q^{12} -456.145 q^{13} +743.073 q^{14} -566.496 q^{15} +256.000 q^{16} -860.763 q^{17} -324.000 q^{18} +1819.73 q^{19} +1007.10 q^{20} +1671.91 q^{21} +1575.01 q^{22} +738.863 q^{23} +576.000 q^{24} +836.947 q^{25} +1824.58 q^{26} -729.000 q^{27} -2972.29 q^{28} -6149.00 q^{29} +2265.98 q^{30} +8271.91 q^{31} -1024.00 q^{32} +3543.77 q^{33} +3443.05 q^{34} -11693.0 q^{35} +1296.00 q^{36} -3806.72 q^{37} -7278.90 q^{38} +4105.31 q^{39} -4028.42 q^{40} +10665.8 q^{41} -6687.65 q^{42} -14403.2 q^{43} -6300.03 q^{44} +5098.46 q^{45} -2955.45 q^{46} +4037.54 q^{47} -2304.00 q^{48} +17702.8 q^{49} -3347.79 q^{50} +7746.87 q^{51} -7298.32 q^{52} -28296.0 q^{53} +2916.00 q^{54} -24784.3 q^{55} +11889.2 q^{56} -16377.5 q^{57} +24596.0 q^{58} +3481.00 q^{59} -9063.94 q^{60} -13671.2 q^{61} -33087.6 q^{62} -15047.2 q^{63} +4096.00 q^{64} -28711.6 q^{65} -14175.1 q^{66} +21923.6 q^{67} -13772.2 q^{68} -6649.77 q^{69} +46772.0 q^{70} +57637.1 q^{71} -5184.00 q^{72} -30192.7 q^{73} +15226.9 q^{74} -7532.52 q^{75} +29115.6 q^{76} +73146.6 q^{77} -16421.2 q^{78} +54069.5 q^{79} +16113.7 q^{80} +6561.00 q^{81} -42663.1 q^{82} +45983.9 q^{83} +26750.6 q^{84} -54179.9 q^{85} +57613.0 q^{86} +55341.0 q^{87} +25200.1 q^{88} +52956.0 q^{89} -20393.9 q^{90} +84737.2 q^{91} +11821.8 q^{92} -74447.2 q^{93} -16150.2 q^{94} +114541. q^{95} +9216.00 q^{96} -70213.6 q^{97} -70811.3 q^{98} -31893.9 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 24 q^{2} - 54 q^{3} + 96 q^{4} + 4 q^{5} + 216 q^{6} - 54 q^{7} - 384 q^{8} + 486 q^{9}+O(q^{10}) \) 6 * q - 24 * q^2 - 54 * q^3 + 96 * q^4 + 4 * q^5 + 216 * q^6 - 54 * q^7 - 384 * q^8 + 486 * q^9	\( 6 q - 24 q^{2} - 54 q^{3} + 96 q^{4} + 4 q^{5} + 216 q^{6} - 54 q^{7} - 384 q^{8} + 486 q^{9} - 16 q^{10} + 436 q^{11} - 864 q^{12} - 536 q^{13} + 216 q^{14} - 36 q^{15} + 1536 q^{16} + 910 q^{17} - 1944 q^{18} + 1462 q^{19} + 64 q^{20} + 486 q^{21} - 1744 q^{22} + 1634 q^{23} + 3456 q^{24} - 1186 q^{25} + 2144 q^{26} - 4374 q^{27} - 864 q^{28} - 1598 q^{29} + 144 q^{30} - 5670 q^{31} - 6144 q^{32} - 3924 q^{33} - 3640 q^{34} - 7242 q^{35} + 7776 q^{36} - 20458 q^{37} - 5848 q^{38} + 4824 q^{39} - 256 q^{40} + 262 q^{41} - 1944 q^{42} - 34028 q^{43} + 6976 q^{44} + 324 q^{45} - 6536 q^{46} - 11194 q^{47} - 13824 q^{48} - 32652 q^{49} + 4744 q^{50} - 8190 q^{51} - 8576 q^{52} - 17164 q^{53} + 17496 q^{54} - 37040 q^{55} + 3456 q^{56} - 13158 q^{57} + 6392 q^{58} + 20886 q^{59} - 576 q^{60} - 43546 q^{61} + 22680 q^{62} - 4374 q^{63} + 24576 q^{64} + 65568 q^{65} + 15696 q^{66} - 52772 q^{67} + 14560 q^{68} - 14706 q^{69} + 28968 q^{70} + 84740 q^{71} - 31104 q^{72} - 36578 q^{73} + 81832 q^{74} + 10674 q^{75} + 23392 q^{76} + 90678 q^{77} - 19296 q^{78} + 85196 q^{79} + 1024 q^{80} + 39366 q^{81} - 1048 q^{82} + 217026 q^{83} + 7776 q^{84} + 26570 q^{85} + 136112 q^{86} + 14382 q^{87} - 27904 q^{88} + 333850 q^{89} - 1296 q^{90} + 214914 q^{91} + 26144 q^{92} + 51030 q^{93} + 44776 q^{94} + 458758 q^{95} + 55296 q^{96} + 173148 q^{97} + 130608 q^{98} + 35316 q^{99}+O(q^{100}) \) 6 * q - 24 * q^2 - 54 * q^3 + 96 * q^4 + 4 * q^5 + 216 * q^6 - 54 * q^7 - 384 * q^8 + 486 * q^9 - 16 * q^10 + 436 * q^11 - 864 * q^12 - 536 * q^13 + 216 * q^14 - 36 * q^15 + 1536 * q^16 + 910 * q^17 - 1944 * q^18 + 1462 * q^19 + 64 * q^20 + 486 * q^21 - 1744 * q^22 + 1634 * q^23 + 3456 * q^24 - 1186 * q^25 + 2144 * q^26 - 4374 * q^27 - 864 * q^28 - 1598 * q^29 + 144 * q^30 - 5670 * q^31 - 6144 * q^32 - 3924 * q^33 - 3640 * q^34 - 7242 * q^35 + 7776 * q^36 - 20458 * q^37 - 5848 * q^38 + 4824 * q^39 - 256 * q^40 + 262 * q^41 - 1944 * q^42 - 34028 * q^43 + 6976 * q^44 + 324 * q^45 - 6536 * q^46 - 11194 * q^47 - 13824 * q^48 - 32652 * q^49 + 4744 * q^50 - 8190 * q^51 - 8576 * q^52 - 17164 * q^53 + 17496 * q^54 - 37040 * q^55 + 3456 * q^56 - 13158 * q^57 + 6392 * q^58 + 20886 * q^59 - 576 * q^60 - 43546 * q^61 + 22680 * q^62 - 4374 * q^63 + 24576 * q^64 + 65568 * q^65 + 15696 * q^66 - 52772 * q^67 + 14560 * q^68 - 14706 * q^69 + 28968 * q^70 + 84740 * q^71 - 31104 * q^72 - 36578 * q^73 + 81832 * q^74 + 10674 * q^75 + 23392 * q^76 + 90678 * q^77 - 19296 * q^78 + 85196 * q^79 + 1024 * q^80 + 39366 * q^81 - 1048 * q^82 + 217026 * q^83 + 7776 * q^84 + 26570 * q^85 + 136112 * q^86 + 14382 * q^87 - 27904 * q^88 + 333850 * q^89 - 1296 * q^90 + 214914 * q^91 + 26144 * q^92 + 51030 * q^93 + 44776 * q^94 + 458758 * q^95 + 55296 * q^96 + 173148 * q^97 + 130608 * q^98 + 35316 * q^99

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