LMFDB - Embedded newform 354.6.a.f.1.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("354.1");

S:= CuspForms(chi, 6);

N := Newforms(S);

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

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$56.7758722138$
Analytic rank:	$1$
Dimension:	$6$
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} - 2x^{5} - 6296x^{4} - 192180x^{3} - 1919598x^{2} - 7344954x - 8433643 $ x^6 - 2x^5 - 6296x^4 - 192180x^3 - 1919598x^2 - 7344954*x - 8433643
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{2}\cdot 3 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.6
Root			$93.6171$ 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)

$f(q)$	$=$	$q-4.00000 q^{2} -9.00000 q^{3} +16.0000 q^{4} +68.0049 q^{5} +36.0000 q^{6} -205.637 q^{7} -64.0000 q^{8} +81.0000 q^{9} +O(q^{10})$	\(q-4.00000 q^{2} -9.00000 q^{3} +16.0000 q^{4} +68.0049 q^{5} +36.0000 q^{6} -205.637 q^{7} -64.0000 q^{8} +81.0000 q^{9} -272.020 q^{10} +250.134 q^{11} -144.000 q^{12} +433.170 q^{13} +822.549 q^{14} -612.045 q^{15} +256.000 q^{16} +632.211 q^{17} -324.000 q^{18} -2720.73 q^{19} +1088.08 q^{20} +1850.74 q^{21} -1000.54 q^{22} -1106.12 q^{23} +576.000 q^{24} +1499.67 q^{25} -1732.68 q^{26} -729.000 q^{27} -3290.20 q^{28} +6647.26 q^{29} +2448.18 q^{30} -6542.87 q^{31} -1024.00 q^{32} -2251.21 q^{33} -2528.85 q^{34} -13984.4 q^{35} +1296.00 q^{36} +5391.52 q^{37} +10882.9 q^{38} -3898.53 q^{39} -4352.32 q^{40} +2883.94 q^{41} -7402.94 q^{42} -5809.69 q^{43} +4002.15 q^{44} +5508.40 q^{45} +4424.48 q^{46} +28068.4 q^{47} -2304.00 q^{48} +25479.7 q^{49} -5998.69 q^{50} -5689.90 q^{51} +6930.72 q^{52} +8592.49 q^{53} +2916.00 q^{54} +17010.4 q^{55} +13160.8 q^{56} +24486.6 q^{57} -26589.0 q^{58} -3481.00 q^{59} -9792.71 q^{60} -7037.67 q^{61} +26171.5 q^{62} -16656.6 q^{63} +4096.00 q^{64} +29457.7 q^{65} +9004.83 q^{66} +15760.5 q^{67} +10115.4 q^{68} +9955.07 q^{69} +55937.4 q^{70} -79586.3 q^{71} -5184.00 q^{72} -89540.3 q^{73} -21566.1 q^{74} -13497.1 q^{75} -43531.7 q^{76} -51436.9 q^{77} +15594.1 q^{78} -6146.10 q^{79} +17409.3 q^{80} +6561.00 q^{81} -11535.8 q^{82} +27961.3 q^{83} +29611.8 q^{84} +42993.5 q^{85} +23238.8 q^{86} -59825.3 q^{87} -16008.6 q^{88} -129719. q^{89} -22033.6 q^{90} -89075.9 q^{91} -17697.9 q^{92} +58885.8 q^{93} -112273. q^{94} -185023. q^{95} +9216.00 q^{96} -98201.9 q^{97} -101919. q^{98} +20260.9 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 24 q^{2} - 54 q^{3} + 96 q^{4} - 46 q^{5} + 216 q^{6} - 103 q^{7} - 384 q^{8} + 486 q^{9}+O(q^{10}) $ 6 * q - 24 * q^2 - 54 * q^3 + 96 * q^4 - 46 * q^5 + 216 * q^6 - 103 * q^7 - 384 * q^8 + 486 * q^9	\( 6 q - 24 q^{2} - 54 q^{3} + 96 q^{4} - 46 q^{5} + 216 q^{6} - 103 q^{7} - 384 q^{8} + 486 q^{9} + 184 q^{10} - 653 q^{11} - 864 q^{12} + 647 q^{13} + 412 q^{14} + 414 q^{15} + 1536 q^{16} + 621 q^{17} - 1944 q^{18} - 454 q^{19} - 736 q^{20} + 927 q^{21} + 2612 q^{22} - 3412 q^{23} + 3456 q^{24} + 3866 q^{25} - 2588 q^{26} - 4374 q^{27} - 1648 q^{28} + 1526 q^{29} - 1656 q^{30} + 5976 q^{31} - 6144 q^{32} + 5877 q^{33} - 2484 q^{34} + 8098 q^{35} + 7776 q^{36} + 37033 q^{37} + 1816 q^{38} - 5823 q^{39} + 2944 q^{40} + 13983 q^{41} - 3708 q^{42} + 11521 q^{43} - 10448 q^{44} - 3726 q^{45} + 13648 q^{46} + 12434 q^{47} - 13824 q^{48} + 54237 q^{49} - 15464 q^{50} - 5589 q^{51} + 10352 q^{52} + 21310 q^{53} + 17496 q^{54} + 57468 q^{55} + 6592 q^{56} + 4086 q^{57} - 6104 q^{58} - 20886 q^{59} + 6624 q^{60} - 23030 q^{61} - 23904 q^{62} - 8343 q^{63} + 24576 q^{64} - 37368 q^{65} - 23508 q^{66} + 24342 q^{67} + 9936 q^{68} + 30708 q^{69} - 32392 q^{70} - 184375 q^{71} - 31104 q^{72} - 24512 q^{73} - 148132 q^{74} - 34794 q^{75} - 7264 q^{76} - 46529 q^{77} + 23292 q^{78} - 17987 q^{79} - 11776 q^{80} + 39366 q^{81} - 55932 q^{82} - 46687 q^{83} + 14832 q^{84} - 29706 q^{85} - 46084 q^{86} - 13734 q^{87} + 41792 q^{88} - 178946 q^{89} + 14904 q^{90} - 340179 q^{91} - 54592 q^{92} - 53784 q^{93} - 49736 q^{94} - 532190 q^{95} + 55296 q^{96} - 214638 q^{97} - 216948 q^{98} - 52893 q^{99}+O(q^{100}) \) 6 * q - 24 * q^2 - 54 * q^3 + 96 * q^4 - 46 * q^5 + 216 * q^6 - 103 * q^7 - 384 * q^8 + 486 * q^9 + 184 * q^10 - 653 * q^11 - 864 * q^12 + 647 * q^13 + 412 * q^14 + 414 * q^15 + 1536 * q^16 + 621 * q^17 - 1944 * q^18 - 454 * q^19 - 736 * q^20 + 927 * q^21 + 2612 * q^22 - 3412 * q^23 + 3456 * q^24 + 3866 * q^25 - 2588 * q^26 - 4374 * q^27 - 1648 * q^28 + 1526 * q^29 - 1656 * q^30 + 5976 * q^31 - 6144 * q^32 + 5877 * q^33 - 2484 * q^34 + 8098 * q^35 + 7776 * q^36 + 37033 * q^37 + 1816 * q^38 - 5823 * q^39 + 2944 * q^40 + 13983 * q^41 - 3708 * q^42 + 11521 * q^43 - 10448 * q^44 - 3726 * q^45 + 13648 * q^46 + 12434 * q^47 - 13824 * q^48 + 54237 * q^49 - 15464 * q^50 - 5589 * q^51 + 10352 * q^52 + 21310 * q^53 + 17496 * q^54 + 57468 * q^55 + 6592 * q^56 + 4086 * q^57 - 6104 * q^58 - 20886 * q^59 + 6624 * q^60 - 23030 * q^61 - 23904 * q^62 - 8343 * q^63 + 24576 * q^64 - 37368 * q^65 - 23508 * q^66 + 24342 * q^67 + 9936 * q^68 + 30708 * q^69 - 32392 * q^70 - 184375 * q^71 - 31104 * q^72 - 24512 * q^73 - 148132 * q^74 - 34794 * q^75 - 7264 * q^76 - 46529 * q^77 + 23292 * q^78 - 17987 * q^79 - 11776 * q^80 + 39366 * q^81 - 55932 * q^82 - 46687 * q^83 + 14832 * q^84 - 29706 * q^85 - 46084 * q^86 - 13734 * q^87 + 41792 * q^88 - 178946 * q^89 + 14904 * q^90 - 340179 * q^91 - 54592 * q^92 - 53784 * q^93 - 49736 * q^94 - 532190 * q^95 + 55296 * q^96 - 214638 * q^97 - 216948 * q^98 - 52893 * 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
$5$	68.0049	1.21651	0.608255	−	0.793742i	$-0.291870\pi$
$5$	68.0049	1.21651	0.608255	+	0.793742i	$0.291870\pi$
$6$	36.0000	0.408248
$7$	−205.637	−1.58620	−0.793098	−	0.609094i	$-0.791533\pi$
$7$	−205.637	−1.58620	−0.793098	+	0.609094i	$0.791533\pi$
$8$	−64.0000	−0.353553
$9$	81.0000	0.333333
$10$	−272.020	−0.860202
$11$	250.134	0.623292	0.311646	−	0.950198i	$-0.399120\pi$
$11$	250.134	0.623292	0.311646	+	0.950198i	$0.399120\pi$
$12$	−144.000	−0.288675
$13$	433.170	0.710886	0.355443	−	0.934698i	$-0.384330\pi$
$13$	433.170	0.710886	0.355443	+	0.934698i	$0.384330\pi$
$14$	822.549	1.12161
$15$	−612.045	−0.702352
$16$	256.000	0.250000
$17$	632.211	0.530567	0.265283	−	0.964170i	$-0.414534\pi$
$17$	632.211	0.530567	0.265283	+	0.964170i	$0.414534\pi$
$18$	−324.000	−0.235702
$19$	−2720.73	−1.72903	−0.864514	−	0.502609i	$-0.832373\pi$
$19$	−2720.73	−1.72903	−0.864514	+	0.502609i	$0.832373\pi$
$20$	1088.08	0.608255
$21$	1850.74	0.915791
$22$	−1000.54	−0.440734
$23$	−1106.12	−0.435996	−0.217998	−	0.975949i	$-0.569953\pi$
$23$	−1106.12	−0.435996	−0.217998	+	0.975949i	$0.569953\pi$
$24$	576.000	0.204124
$25$	1499.67	0.479895
$26$	−1732.68	−0.502673
$27$	−729.000	−0.192450
$28$	−3290.20	−0.793098
$29$	6647.26	1.46773	0.733867	−	0.679293i	$-0.237714\pi$
$29$	6647.26	1.46773	0.733867	+	0.679293i	$0.237714\pi$
$30$	2448.18	0.496638
$31$	−6542.87	−1.22282	−0.611412	−	0.791313i	$-0.709398\pi$
$31$	−6542.87	−1.22282	−0.611412	+	0.791313i	$0.709398\pi$
$32$	−1024.00	−0.176777
$33$	−2251.21	−0.359858
$34$	−2528.85	−0.375167
$35$	−13984.4	−1.92962
$36$	1296.00	0.166667
$37$	5391.52	0.647451	0.323726	−	0.946151i	$-0.395065\pi$
$37$	5391.52	0.647451	0.323726	+	0.946151i	$0.395065\pi$
$38$	10882.9	1.22261
$39$	−3898.53	−0.410430
$40$	−4352.32	−0.430101
$41$	2883.94	0.267933	0.133967	−	0.990986i	$-0.457228\pi$
$41$	2883.94	0.267933	0.133967	+	0.990986i	$0.457228\pi$
$42$	−7402.94	−0.647562
$43$	−5809.69	−0.479161	−0.239581	−	0.970876i	$-0.577010\pi$
$43$	−5809.69	−0.479161	−0.239581	+	0.970876i	$0.577010\pi$
$44$	4002.15	0.311646
$45$	5508.40	0.405503
$46$	4424.48	0.308296
$47$	28068.4	1.85341	0.926707	−	0.375785i	$-0.122627\pi$
$47$	28068.4	1.85341	0.926707	+	0.375785i	$0.122627\pi$
$48$	−2304.00	−0.144338
$49$	25479.7	1.51602
$50$	−5998.69	−0.339337
$51$	−5689.90	−0.306323
$52$	6930.72	0.355443
$53$	8592.49	0.420174	0.210087	−	0.977683i	$-0.432625\pi$
$53$	8592.49	0.420174	0.210087	+	0.977683i	$0.432625\pi$
$54$	2916.00	0.136083
$55$	17010.4	0.758240
$56$	13160.8	0.560805
$57$	24486.6	0.998254
$58$	−26589.0	−1.03784
$59$	−3481.00	−0.130189
$59$	−3481.00	−0.130189
$60$	−9792.71	−0.351176
$61$	−7037.67	−0.242161	−0.121080	−	0.992643i	$-0.538636\pi$
$61$	−7037.67	−0.242161	−0.121080	+	0.992643i	$0.538636\pi$
$62$	26171.5	0.864667
$63$	−16656.6	−0.528732
$64$	4096.00	0.125000
$65$	29457.7	0.864800
$66$	9004.83	0.254458
$67$	15760.5	0.428925	0.214463	−	0.976732i	$-0.431200\pi$
$67$	15760.5	0.428925	0.214463	+	0.976732i	$0.431200\pi$
$68$	10115.4	0.265283
$69$	9955.07	0.251722
$70$	55937.4	1.36445
$71$	−79586.3	−1.87367	−0.936834	−	0.349775i	$-0.886258\pi$
$71$	−79586.3	−1.87367	−0.936834	+	0.349775i	$0.886258\pi$
$72$	−5184.00	−0.117851
$73$	−89540.3	−1.96658	−0.983290	−	0.182049i	$-0.941727\pi$
$73$	−89540.3	−1.96658	−0.983290	+	0.182049i	$0.941727\pi$
$74$	−21566.1	−0.457817
$75$	−13497.1	−0.277068
$76$	−43531.7	−0.864514
$77$	−51436.9	−0.988663
$78$	15594.1	0.290218
$79$	−6146.10	−0.110798	−0.0553990	−	0.998464i	$-0.517643\pi$
$79$	−6146.10	−0.110798	−0.0553990	+	0.998464i	$0.517643\pi$
$80$	17409.3	0.304127
$81$	6561.00	0.111111
$82$	−11535.8	−0.189458
$83$	27961.3	0.445515	0.222757	−	0.974874i	$-0.428494\pi$
$83$	27961.3	0.445515	0.222757	+	0.974874i	$0.428494\pi$
$84$	29611.8	0.457895
$85$	42993.5	0.645439
$86$	23238.8	0.338818
$87$	−59825.3	−0.847397
$88$	−16008.6	−0.220367
$89$	−129719.	−1.73591	−0.867955	−	0.496643i	$-0.834566\pi$
$89$	−129719.	−1.73591	−0.867955	+	0.496643i	$0.834566\pi$
$90$	−22033.6	−0.286734
$91$	−89075.9	−1.12760
$92$	−17697.9	−0.217998
$93$	58885.8	0.705998
$94$	−112273.	−1.31056
$95$	−185023.	−2.10338
$96$	9216.00	0.102062
$97$	−98201.9	−1.05972	−0.529859	−	0.848086i	$-0.677755\pi$
$97$	−98201.9	−1.05972	−0.529859	+	0.848086i	$0.677755\pi$
$98$	−101919.	−1.07199
$99$	20260.9	0.207764
$100$	23994.8	0.239948
$101$	26354.4	0.257069	0.128534	−	0.991705i	$-0.458973\pi$
$101$	26354.4	0.257069	0.128534	+	0.991705i	$0.458973\pi$
$102$	22759.6	0.216603
$103$	162933.	1.51326	0.756632	−	0.653840i	$-0.226843\pi$
$103$	162933.	1.51326	0.756632	+	0.653840i	$0.226843\pi$
$104$	−27722.9	−0.251336
$105$	125859.	1.11407
$106$	−34370.0	−0.297108
$107$	−194588.	−1.64307	−0.821535	−	0.570158i	$-0.806882\pi$
$107$	−194588.	−1.64307	−0.821535	+	0.570158i	$0.806882\pi$
$108$	−11664.0	−0.0962250
$109$	33164.6	0.267367	0.133684	−	0.991024i	$-0.457319\pi$
$109$	33164.6	0.267367	0.133684	+	0.991024i	$0.457319\pi$
$110$	−68041.5	−0.536157
$111$	−48523.7	−0.373806
$112$	−52643.1	−0.396549
$113$	−222178.	−1.63683	−0.818417	−	0.574625i	$-0.805148\pi$
$113$	−222178.	−1.63683	−0.818417	+	0.574625i	$0.805148\pi$
$114$	−97946.4	−0.705872
$115$	−75221.6	−0.530393
$116$	106356.	0.733867
$117$	35086.8	0.236962
$118$	13924.0	0.0920575
$119$	−130006.	−0.841583
$120$	39170.8	0.248319
$121$	−98483.9	−0.611507
$122$	28150.7	0.171234
$123$	−25955.5	−0.154691
$124$	−104686.	−0.611412
$125$	−110530.	−0.632712
$126$	66626.5	0.373870
$127$	123493.	0.679414	0.339707	−	0.940531i	$-0.389672\pi$
$127$	123493.	0.679414	0.339707	+	0.940531i	$0.389672\pi$
$128$	−16384.0	−0.0883883
$129$	52287.2	0.276644
$130$	−117831.	−0.611506
$131$	−181421.	−0.923656	−0.461828	−	0.886970i	$-0.652806\pi$
$131$	−181421.	−0.923656	−0.461828	+	0.886970i	$0.652806\pi$
$132$	−36019.3	−0.179929
$133$	559484.	2.74258
$134$	−63041.8	−0.303296
$135$	−49575.6	−0.234117
$136$	−40461.5	−0.187584
$137$	99522.2	0.453021	0.226511	−	0.974009i	$-0.427268\pi$
$137$	99522.2	0.453021	0.226511	+	0.974009i	$0.427268\pi$
$138$	−39820.3	−0.177995
$139$	−202233.	−0.887799	−0.443899	−	0.896077i	$-0.646405\pi$
$139$	−202233.	−0.887799	−0.443899	+	0.896077i	$0.646405\pi$
$140$	−223750.	−0.964811
$141$	−252615.	−1.07007
$142$	318345.	1.32488
$143$	108351.	0.443090
$144$	20736.0	0.0833333
$145$	452046.	1.78551
$146$	358161.	1.39058
$147$	−229317.	−0.875273
$148$	86264.3	0.323726
$149$	25033.1	0.0923737	0.0461868	−	0.998933i	$-0.485293\pi$
$149$	25033.1	0.0923737	0.0461868	+	0.998933i	$0.485293\pi$
$150$	53988.2	0.195916
$151$	414265.	1.47855	0.739274	−	0.673404i	$-0.235169\pi$
$151$	414265.	1.47855	0.739274	+	0.673404i	$0.235169\pi$
$152$	174127.	0.611304
$153$	51209.1	0.176856
$154$	205748.	0.699090
$155$	−444947.	−1.48758
$156$	−62376.5	−0.205215
$157$	−361520.	−1.17053	−0.585266	−	0.810842i	$-0.699010\pi$
$157$	−361520.	−1.17053	−0.585266	+	0.810842i	$0.699010\pi$
$158$	24584.4	0.0783460
$159$	−77332.4	−0.242588
$160$	−69637.1	−0.215051
$161$	227459.	0.691575
$162$	−26244.0	−0.0785674
$163$	−163015.	−0.480572	−0.240286	−	0.970702i	$-0.577241\pi$
$163$	−163015.	−0.480572	−0.240286	+	0.970702i	$0.577241\pi$
$164$	46143.1	0.133967
$165$	−153093.	−0.437770
$166$	−111845.	−0.315027
$167$	−63848.6	−0.177158	−0.0885789	−	0.996069i	$-0.528233\pi$
$167$	−63848.6	−0.177158	−0.0885789	+	0.996069i	$0.528233\pi$
$168$	−118447.	−0.323781
$169$	−183657.	−0.494641
$170$	−171974.	−0.456395
$171$	−220379.	−0.576342
$172$	−92955.0	−0.239581
$173$	−313576.	−0.796577	−0.398288	−	0.917260i	$-0.630396\pi$
$173$	−313576.	−0.796577	−0.398288	+	0.917260i	$0.630396\pi$
$174$	239301.	0.599200
$175$	−308389.	−0.761208
$176$	64034.4	0.155823
$177$	31329.0	0.0751646
$178$	518874.	1.22747
$179$	−78941.2	−0.184150	−0.0920749	−	0.995752i	$-0.529350\pi$
$179$	−78941.2	−0.184150	−0.0920749	+	0.995752i	$0.529350\pi$
$180$	88134.4	0.202752
$181$	−683941.	−1.55175	−0.775876	−	0.630886i	$-0.782692\pi$
$181$	−683941.	−1.55175	−0.775876	+	0.630886i	$0.782692\pi$
$182$	356304.	0.797337
$183$	63339.0	0.139812
$184$	70791.6	0.154148
$185$	366650.	0.787630
$186$	−235543.	−0.499216
$187$	158138.	0.330698
$188$	449094.	0.926707
$189$	149910.	0.305264
$190$	740093.	1.48731
$191$	−694445.	−1.37738	−0.688691	−	0.725055i	$-0.741814\pi$
$191$	−694445.	−1.37738	−0.688691	+	0.725055i	$0.741814\pi$
$192$	−36864.0	−0.0721688
$193$	387381.	0.748592	0.374296	−	0.927309i	$-0.377884\pi$
$193$	387381.	0.748592	0.374296	+	0.927309i	$0.377884\pi$
$194$	392808.	0.749334
$195$	−265119.	−0.499293
$196$	407675.	0.758009
$197$	−158087.	−0.290222	−0.145111	−	0.989415i	$-0.546354\pi$
$197$	−158087.	−0.290222	−0.145111	+	0.989415i	$0.546354\pi$
$198$	−81043.5	−0.146911
$199$	−668727.	−1.19706	−0.598531	−	0.801100i	$-0.704248\pi$
$199$	−668727.	−1.19706	−0.598531	+	0.801100i	$0.704248\pi$
$200$	−95979.0	−0.169669
$201$	−141844.	−0.247640
$202$	−105417.	−0.181775
$203$	−1.36692e6	−2.32811
$204$	−91038.4	−0.153161
$205$	196122.	0.325944
$206$	−651730.	−1.07004
$207$	−89595.7	−0.145332
$208$	110892.	0.177722
$209$	−680548.	−1.07769
$210$	−503437.	−0.787765
$211$	191246.	0.295724	0.147862	−	0.989008i	$-0.452761\pi$
$211$	191246.	0.295724	0.147862	+	0.989008i	$0.452761\pi$
$212$	137480.	0.210087
$213$	716277.	1.08176
$214$	778351.	1.16183
$215$	−395088.	−0.582904
$216$	46656.0	0.0680414
$217$	1.34546e6	1.93964
$218$	−132658.	−0.189057
$219$	805863.	1.13540
$220$	272166.	0.379120
$221$	273855.	0.377173
$222$	194095.	0.264321
$223$	−621887.	−0.837431	−0.418715	−	0.908117i	$-0.637520\pi$
$223$	−621887.	−0.837431	−0.418715	+	0.908117i	$0.637520\pi$
$224$	210573.	0.280402
$225$	121473.	0.159965
$226$	888711.	1.15742
$227$	−1.03669e6	−1.33531	−0.667655	−	0.744471i	$-0.732702\pi$
$227$	−1.03669e6	−1.33531	−0.667655	+	0.744471i	$0.732702\pi$
$228$	391786.	0.499127
$229$	−835750.	−1.05314	−0.526572	−	0.850131i	$-0.676523\pi$
$229$	−835750.	−1.05314	−0.526572	+	0.850131i	$0.676523\pi$
$230$	300886.	0.375045
$231$	462932.	0.570805
$232$	−425424.	−0.518922
$233$	1.63019e6	1.96720	0.983602	−	0.180355i	$-0.0577247\pi$
$233$	1.63019e6	1.96720	0.983602	+	0.180355i	$0.0577247\pi$
$234$	−140347.	−0.167558
$235$	1.90879e6	2.25469
$236$	−55696.0	−0.0650945
$237$	55314.9	0.0639693
$238$	520025.	0.595089
$239$	523873.	0.593241	0.296621	−	0.954995i	$-0.404140\pi$
$239$	523873.	0.593241	0.296621	+	0.954995i	$0.404140\pi$
$240$	−156683.	−0.175588
$241$	−889692.	−0.986727	−0.493363	−	0.869823i	$-0.664233\pi$
$241$	−889692.	−0.986727	−0.493363	+	0.869823i	$0.664233\pi$
$242$	393935.	0.432401
$243$	−59049.0	−0.0641500
$244$	−112603.	−0.121080
$245$	1.73275e6	1.84425
$246$	103822.	0.109383
$247$	−1.17854e6	−1.22914
$248$	418743.	0.432333
$249$	−251652.	−0.257218
$250$	442121.	0.447395
$251$	563002.	0.564060	0.282030	−	0.959406i	$-0.408992\pi$
$251$	563002.	0.564060	0.282030	+	0.959406i	$0.408992\pi$
$252$	−266506.	−0.264366
$253$	−276678.	−0.271753
$254$	−493973.	−0.480418
$255$	−386942.	−0.372645
$256$	65536.0	0.0625000
$257$	1.09850e6	1.03745	0.518726	−	0.854941i	$-0.326407\pi$
$257$	1.09850e6	1.03745	0.518726	+	0.854941i	$0.326407\pi$
$258$	−209149.	−0.195617
$259$	−1.10870e6	−1.02698
$260$	471323.	0.432400
$261$	538428.	0.489245
$262$	725685.	0.653123
$263$	1.92651e6	1.71745	0.858723	−	0.512441i	$-0.171259\pi$
$263$	1.92651e6	1.71745	0.858723	+	0.512441i	$0.171259\pi$
$264$	144077.	0.127229
$265$	584332.	0.511146
$266$	−2.23794e6	−1.93929
$267$	1.16747e6	1.00223
$268$	252167.	0.214463
$269$	−1.04576e6	−0.881152	−0.440576	−	0.897715i	$-0.645226\pi$
$269$	−1.04576e6	−0.881152	−0.440576	+	0.897715i	$0.645226\pi$
$270$	198302.	0.165546
$271$	2.14698e6	1.77585	0.887923	−	0.459992i	$-0.152148\pi$
$271$	2.14698e6	1.77585	0.887923	+	0.459992i	$0.152148\pi$
$272$	161846.	0.132642
$273$	801684.	0.651023
$274$	−398089.	−0.320334
$275$	375119.	0.299115
$276$	159281.	0.125861
$277$	−2.21851e6	−1.73725	−0.868626	−	0.495469i	$-0.834996\pi$
$277$	−2.21851e6	−1.73725	−0.868626	+	0.495469i	$0.834996\pi$
$278$	808931.	0.627769
$279$	−529972.	−0.407608
$280$	894999.	0.682224
$281$	−248679.	−0.187877	−0.0939385	−	0.995578i	$-0.529946\pi$
$281$	−248679.	−0.187877	−0.0939385	+	0.995578i	$0.529946\pi$
$282$	1.01046e6	0.756653
$283$	208199.	0.154530	0.0772650	−	0.997011i	$-0.475381\pi$
$283$	208199.	0.154530	0.0772650	+	0.997011i	$0.475381\pi$
$284$	−1.27338e6	−0.936834
$285$	1.66521e6	1.21439
$286$	−433403.	−0.313312
$287$	−593046.	−0.424995
$288$	−82944.0	−0.0589256
$289$	−1.02017e6	−0.718499
$290$	−1.80818e6	−1.26255
$291$	883817.	0.611829
$292$	−1.43264e6	−0.983290
$293$	550923.	0.374906	0.187453	−	0.982274i	$-0.439977\pi$
$293$	550923.	0.374906	0.187453	+	0.982274i	$0.439977\pi$
$294$	917269.	0.618911
$295$	−236725.	−0.158376
$296$	−345057.	−0.228909
$297$	−182348.	−0.119953
$298$	−100132.	−0.0653180
$299$	−479138.	−0.309944
$300$	−215953.	−0.138534
$301$	1.19469e6	0.760044
$302$	−1.65706e6	−1.04549
$303$	−237189.	−0.148419
$304$	−696508.	−0.432257
$305$	−478596.	−0.294591
$306$	−204836.	−0.125056
$307$	2.80648e6	1.69948	0.849741	−	0.527201i	$-0.176758\pi$
$307$	2.80648e6	1.69948	0.849741	+	0.527201i	$0.176758\pi$
$308$	−822991.	−0.494331
$309$	−1.46639e6	−0.873684
$310$	1.77979e6	1.05188
$311$	−1.26554e6	−0.741948	−0.370974	−	0.928643i	$-0.620976\pi$
$311$	−1.26554e6	−0.741948	−0.370974	+	0.928643i	$0.620976\pi$
$312$	249506.	0.145109
$313$	−253585.	−0.146306	−0.0731530	−	0.997321i	$-0.523306\pi$
$313$	−253585.	−0.146306	−0.0731530	+	0.997321i	$0.523306\pi$
$314$	1.44608e6	0.827691
$315$	−1.13273e6	−0.643207
$316$	−98337.6	−0.0553990
$317$	469931.	0.262655	0.131327	−	0.991339i	$-0.458076\pi$
$317$	469931.	0.262655	0.131327	+	0.991339i	$0.458076\pi$
$318$	309330.	0.171535
$319$	1.66271e6	0.914827
$320$	278548.	0.152064
$321$	1.75129e6	0.948627
$322$	−909838.	−0.489017
$323$	−1.72008e6	−0.917364
$324$	104976.	0.0555556
$325$	649613.	0.341151
$326$	652059.	0.339815
$327$	−298481.	−0.154365
$328$	−184572.	−0.0947288
$329$	−5.77190e6	−2.93988
$330$	612373.	0.309550
$331$	2.92902e6	1.46944	0.734721	−	0.678369i	$-0.237313\pi$
$331$	2.92902e6	1.46944	0.734721	+	0.678369i	$0.237313\pi$
$332$	447381.	0.222757
$333$	436713.	0.215817
$334$	255394.	0.125269
$335$	1.07179e6	0.521792
$336$	473788.	0.228948
$337$	743717.	0.356725	0.178362	−	0.983965i	$-0.442920\pi$
$337$	743717.	0.356725	0.178362	+	0.983965i	$0.442920\pi$
$338$	734626.	0.349764
$339$	1.99960e6	0.945026
$340$	687896.	0.322720
$341$	−1.63659e6	−0.762176
$342$	881517.	0.407536
$343$	−1.78343e6	−0.818504
$344$	371820.	0.169409
$345$	676994.	0.306223
$346$	1.25430e6	0.563265
$347$	1.85284e6	0.826065	0.413032	−	0.910716i	$-0.364470\pi$
$347$	1.85284e6	0.826065	0.413032	+	0.910716i	$0.364470\pi$
$348$	−957205.	−0.423698
$349$	−590164.	−0.259364	−0.129682	−	0.991556i	$-0.541396\pi$
$349$	−590164.	−0.259364	−0.129682	+	0.991556i	$0.541396\pi$
$350$	1.23355e6	0.538255
$351$	−315781.	−0.136810
$352$	−256137.	−0.110183
$353$	−504493.	−0.215486	−0.107743	−	0.994179i	$-0.534362\pi$
$353$	−504493.	−0.215486	−0.107743	+	0.994179i	$0.534362\pi$
$354$	−125316.	−0.0531494
$355$	−5.41226e6	−2.27933
$356$	−2.07550e6	−0.867955
$357$	1.17006e6	0.485888
$358$	315765.	0.130214
$359$	1.52383e6	0.624022	0.312011	−	0.950079i	$-0.398997\pi$
$359$	1.52383e6	0.624022	0.312011	+	0.950079i	$0.398997\pi$
$360$	−352538.	−0.143367
$361$	4.92629e6	1.98954
$362$	2.73576e6	1.09725
$363$	886355.	0.353054
$364$	−1.42522e6	−0.563802
$365$	−6.08918e6	−2.39236
$366$	−253356.	−0.0988618
$367$	636042.	0.246502	0.123251	−	0.992376i	$-0.460668\pi$
$367$	636042.	0.246502	0.123251	+	0.992376i	$0.460668\pi$
$368$	−283167.	−0.108999
$369$	233599.	0.0893111
$370$	−1.46660e6	−0.556939
$371$	−1.76694e6	−0.666479
$372$	942173.	0.352999
$373$	1.29816e6	0.483122	0.241561	−	0.970386i	$-0.422341\pi$
$373$	1.29816e6	0.483122	0.241561	+	0.970386i	$0.422341\pi$
$374$	−632551.	−0.233839
$375$	994773.	0.365297
$376$	−1.79637e6	−0.655281
$377$	2.87939e6	1.04339
$378$	−599638.	−0.215854
$379$	−3.96844e6	−1.41913	−0.709564	−	0.704641i	$-0.751108\pi$
$379$	−3.96844e6	−1.41913	−0.709564	+	0.704641i	$0.751108\pi$
$380$	−2.96037e6	−1.05169
$381$	−1.11144e6	−0.392260
$382$	2.77778e6	0.973956
$383$	4.37588e6	1.52429	0.762147	−	0.647405i	$-0.224146\pi$
$383$	4.37588e6	1.52429	0.762147	+	0.647405i	$0.224146\pi$
$384$	147456.	0.0510310
$385$	−3.49797e6	−1.20272
$386$	−1.54953e6	−0.529335
$387$	−470585.	−0.159720
$388$	−1.57123e6	−0.529859
$389$	−1.63957e6	−0.549357	−0.274679	−	0.961536i	$-0.588571\pi$
$389$	−1.63957e6	−0.549357	−0.274679	+	0.961536i	$0.588571\pi$
$390$	1.06048e6	0.353053
$391$	−699301.	−0.231325
$392$	−1.63070e6	−0.535993
$393$	1.63279e6	0.533273
$394$	632348.	0.205218
$395$	−417965.	−0.134787
$396$	324174.	0.103882
$397$	−429919.	−0.136902	−0.0684511	−	0.997654i	$-0.521806\pi$
$397$	−429919.	−0.136902	−0.0684511	+	0.997654i	$0.521806\pi$
$398$	2.67491e6	0.846450
$399$	−5.03536e6	−1.58343
$400$	383916.	0.119974
$401$	−4.75253e6	−1.47592	−0.737961	−	0.674843i	$-0.764211\pi$
$401$	−4.75253e6	−1.47592	−0.737961	+	0.674843i	$0.764211\pi$
$402$	567376.	0.175108
$403$	−2.83417e6	−0.869289
$404$	421670.	0.128534
$405$	446180.	0.135168
$406$	5.46769e6	1.64622
$407$	1.34860e6	0.403551
$408$	364154.	0.108301
$409$	1.53524e6	0.453803	0.226901	−	0.973918i	$-0.427140\pi$
$409$	1.53524e6	0.453803	0.226901	+	0.973918i	$0.427140\pi$
$410$	−784489.	−0.230477
$411$	−895699.	−0.261552
$412$	2.60692e6	0.756632
$413$	715823.	0.206505
$414$	358383.	0.102765
$415$	1.90151e6	0.541973
$416$	−443566.	−0.125668
$417$	1.82010e6	0.512571
$418$	2.72219e6	0.762041
$419$	−2.76198e6	−0.768574	−0.384287	−	0.923214i	$-0.625553\pi$
$419$	−2.76198e6	−0.768574	−0.384287	+	0.923214i	$0.625553\pi$
$420$	2.01375e6	0.557034
$421$	−5.32532e6	−1.46434	−0.732168	−	0.681124i	$-0.761491\pi$
$421$	−5.32532e6	−1.46434	−0.732168	+	0.681124i	$0.761491\pi$
$422$	−764986.	−0.209109
$423$	2.27354e6	0.617804
$424$	−549920.	−0.148554
$425$	948110.	0.254616
$426$	−2.86511e6	−0.764921
$427$	1.44721e6	0.384115
$428$	−3.11340e6	−0.821535
$429$	−975156.	−0.255818
$430$	1.58035e6	0.412176
$431$	−3.52117e6	−0.913048	−0.456524	−	0.889711i	$-0.650906\pi$
$431$	−3.52117e6	−0.913048	−0.456524	+	0.889711i	$0.650906\pi$
$432$	−186624.	−0.0481125
$433$	2.87949e6	0.738068	0.369034	−	0.929416i	$-0.379689\pi$
$433$	2.87949e6	0.738068	0.369034	+	0.929416i	$0.379689\pi$
$434$	−5.38183e6	−1.37153
$435$	−4.06842e6	−1.03087
$436$	530634.	0.133684
$437$	3.00945e6	0.753849
$438$	−3.22345e6	−0.802853
$439$	−4.72669e6	−1.17056	−0.585282	−	0.810830i	$-0.699016\pi$
$439$	−4.72669e6	−1.17056	−0.585282	+	0.810830i	$0.699016\pi$
$440$	−1.08866e6	−0.268078
$441$	2.06386e6	0.505339
$442$	−1.09542e6	−0.266701
$443$	−246981.	−0.0597935	−0.0298967	−	0.999553i	$-0.509518\pi$
$443$	−246981.	−0.0597935	−0.0298967	+	0.999553i	$0.509518\pi$
$444$	−776379.	−0.186903
$445$	−8.82151e6	−2.11175
$446$	2.48755e6	0.592153
$447$	−225297.	−0.0533320
$448$	−842290.	−0.198274
$449$	6.08559e6	1.42458	0.712289	−	0.701886i	$-0.247658\pi$
$449$	6.08559e6	1.42458	0.712289	+	0.701886i	$0.247658\pi$
$450$	−485894.	−0.113112
$451$	721373.	0.167001
$452$	−3.55484e6	−0.818417
$453$	−3.72838e6	−0.853641
$454$	4.14674e6	0.944207
$455$	−6.05761e6	−1.37174
$456$	−1.56714e6	−0.352936
$457$	−1.95396e6	−0.437649	−0.218825	−	0.975764i	$-0.570222\pi$
$457$	−1.95396e6	−0.437649	−0.218825	+	0.975764i	$0.570222\pi$
$458$	3.34300e6	0.744685
$459$	−460882.	−0.102108
$460$	−1.20355e6	−0.265197
$461$	1.84230e6	0.403746	0.201873	−	0.979412i	$-0.435297\pi$
$461$	1.84230e6	0.403746	0.201873	+	0.979412i	$0.435297\pi$
$462$	−1.85173e6	−0.403620
$463$	4.19131e6	0.908652	0.454326	−	0.890835i	$-0.349880\pi$
$463$	4.19131e6	0.908652	0.454326	+	0.890835i	$0.349880\pi$
$464$	1.70170e6	0.366934
$465$	4.00453e6	0.858853
$466$	−6.52077e6	−1.39102
$467$	−6.23608e6	−1.32318	−0.661590	−	0.749865i	$-0.730118\pi$
$467$	−6.23608e6	−1.32318	−0.661590	+	0.749865i	$0.730118\pi$
$468$	561389.	0.118481
$469$	−3.24094e6	−0.680360
$470$	−7.63515e6	−1.59431
$471$	3.25368e6	0.675807
$472$	222784.	0.0460287
$473$	−1.45320e6	−0.298657
$474$	−221260.	−0.0452331
$475$	−4.08021e6	−0.829752
$476$	−2.08010e6	−0.420791
$477$	695992.	0.140058
$478$	−2.09549e6	−0.419485
$479$	1.95255e6	0.388834	0.194417	−	0.980919i	$-0.437719\pi$
$479$	1.95255e6	0.388834	0.194417	+	0.980919i	$0.437719\pi$
$480$	626734.	0.124159
$481$	2.33545e6	0.460264
$482$	3.55877e6	0.697721
$483$	−2.04713e6	−0.399281
$484$	−1.57574e6	−0.305754
$485$	−6.67821e6	−1.28916
$486$	236196.	0.0453609
$487$	−67350.8	−0.0128683	−0.00643414	−	0.999979i	$-0.502048\pi$
$487$	−67350.8	−0.0128683	−0.00643414	+	0.999979i	$0.502048\pi$
$488$	450411.	0.0856168
$489$	1.46713e6	0.277458
$490$	−6.93098e6	−1.30408
$491$	3.16104e6	0.591734	0.295867	−	0.955229i	$-0.404392\pi$
$491$	3.16104e6	0.591734	0.295867	+	0.955229i	$0.404392\pi$
$492$	−415288.	−0.0773457
$493$	4.20247e6	0.778731
$494$	4.71416e6	0.869135
$495$	1.37784e6	0.252747
$496$	−1.67497e6	−0.305706
$497$	1.63659e7	2.97200
$498$	1.00661e6	0.181881
$499$	508501.	0.0914198	0.0457099	−	0.998955i	$-0.485445\pi$
$499$	508501.	0.0914198	0.0457099	+	0.998955i	$0.485445\pi$
$500$	−1.76848e6	−0.316356
$501$	574637.	0.102282
$502$	−2.25201e6	−0.398851
$503$	917585.	0.161706	0.0808530	−	0.996726i	$-0.474236\pi$
$503$	917585.	0.161706	0.0808530	+	0.996726i	$0.474236\pi$
$504$	1.06602e6	0.186935
$505$	1.79223e6	0.312726
$506$	1.10671e6	0.192158
$507$	1.65291e6	0.285581
$508$	1.97589e6	0.339707
$509$	3.46025e6	0.591988	0.295994	−	0.955190i	$-0.404349\pi$
$509$	3.46025e6	0.591988	0.295994	+	0.955190i	$0.404349\pi$
$510$	1.54777e6	0.263500
$511$	1.84128e7	3.11938
$512$	−262144.	−0.0441942
$513$	1.98341e6	0.332751
$514$	−4.39400e6	−0.733589
$515$	1.10802e7	1.84090
$516$	836595.	0.138322
$517$	7.02086e6	1.15522
$518$	4.43479e6	0.726188
$519$	2.82218e6	0.459904
$520$	−1.88529e6	−0.305753
$521$	−385404.	−0.0622045	−0.0311022	−	0.999516i	$-0.509902\pi$
$521$	−385404.	−0.0622045	−0.0311022	+	0.999516i	$0.509902\pi$
$522$	−2.15371e6	−0.345948
$523$	2.60043e6	0.415711	0.207855	−	0.978160i	$-0.433352\pi$
$523$	2.60043e6	0.415711	0.207855	+	0.978160i	$0.433352\pi$
$524$	−2.90274e6	−0.461828
$525$	2.77550e6	0.439484
$526$	−7.70606e6	−1.21442
$527$	−4.13647e6	−0.648790
$528$	−576309.	−0.0899644
$529$	−5.21284e6	−0.809908
$530$	−2.33733e6	−0.361435
$531$	−281961.	−0.0433963
$532$	8.95175e6	1.37129
$533$	1.24924e6	0.190470
$534$	−4.66987e6	−0.708682
$535$	−1.32329e7	−1.99881
$536$	−1.00867e6	−0.151648
$537$	710471.	0.106319
$538$	4.18303e6	0.623068
$539$	6.37335e6	0.944921
$540$	−793210.	−0.117059
$541$	5.10755e6	0.750274	0.375137	−	0.926969i	$-0.377596\pi$
$541$	5.10755e6	0.750274	0.375137	+	0.926969i	$0.377596\pi$
$542$	−8.58793e6	−1.25571
$543$	6.15547e6	0.895904
$544$	−647384.	−0.0937918
$545$	2.25536e6	0.325255
$546$	−3.20673e6	−0.460343
$547$	−5.90999e6	−0.844536	−0.422268	−	0.906471i	$-0.638766\pi$
$547$	−5.90999e6	−0.844536	−0.422268	+	0.906471i	$0.638766\pi$
$548$	1.59235e6	0.226511
$549$	−570051.	−0.0807203
$550$	−1.50048e6	−0.211506
$551$	−1.80854e7	−2.53775
$552$	−637125.	−0.0889973
$553$	1.26387e6	0.175747
$554$	8.87406e6	1.22842
$555$	−3.29985e6	−0.454739
$556$	−3.23572e6	−0.443899
$557$	3.82030e6	0.521746	0.260873	−	0.965373i	$-0.415990\pi$
$557$	3.82030e6	0.521746	0.260873	+	0.965373i	$0.415990\pi$
$558$	2.11989e6	0.288222
$559$	−2.51658e6	−0.340629
$560$	−3.57999e6	−0.482406
$561$	−1.42324e6	−0.190929
$562$	994717.	0.132849
$563$	−8.94271e6	−1.18904	−0.594522	−	0.804079i	$-0.702659\pi$
$563$	−8.94271e6	−1.18904	−0.594522	+	0.804079i	$0.702659\pi$
$564$	−4.04184e6	−0.535034
$565$	−1.51092e7	−1.99122
$566$	−832797.	−0.109269
$567$	−1.34919e6	−0.176244
$568$	5.09352e6	0.662441
$569$	−1.49040e7	−1.92984	−0.964921	−	0.262539i	$-0.915440\pi$
$569$	−1.49040e7	−1.92984	−0.964921	+	0.262539i	$0.915440\pi$
$570$	−6.66084e6	−0.858701
$571$	−9.99156e6	−1.28246	−0.641229	−	0.767350i	$-0.721575\pi$
$571$	−9.99156e6	−1.28246	−0.641229	+	0.767350i	$0.721575\pi$
$572$	1.73361e6	0.221545
$573$	6.25000e6	0.795232
$574$	2.37218e6	0.300517
$575$	−1.65882e6	−0.209232
$576$	331776.	0.0416667
$577$	6.97890e6	0.872665	0.436333	−	0.899785i	$-0.356277\pi$
$577$	6.97890e6	0.872665	0.436333	+	0.899785i	$0.356277\pi$
$578$	4.08066e6	0.508055
$579$	−3.48643e6	−0.432200
$580$	7.23274e6	0.892756
$581$	−5.74989e6	−0.706674
$582$	−3.53527e6	−0.432628
$583$	2.14928e6	0.261891
$584$	5.73058e6	0.695291
$585$	2.38607e6	0.288267
$586$	−2.20369e6	−0.265098
$587$	3.52066e6	0.421724	0.210862	−	0.977516i	$-0.432373\pi$
$587$	3.52066e6	0.421724	0.210862	+	0.977516i	$0.432373\pi$
$588$	−3.66908e6	−0.437636
$589$	1.78014e7	2.11430
$590$	946901.	0.111989
$591$	1.42278e6	0.167560
$592$	1.38023e6	0.161863
$593$	1.31152e7	1.53157	0.765787	−	0.643094i	$-0.222349\pi$
$593$	1.31152e7	1.53157	0.765787	+	0.643094i	$0.222349\pi$
$594$	729391.	0.0848193
$595$	−8.84107e6	−1.02379
$596$	400529.	0.0461868
$597$	6.01855e6	0.691124
$598$	1.91655e6	0.219163
$599$	6.27444e6	0.714510	0.357255	−	0.934007i	$-0.383713\pi$
$599$	6.27444e6	0.714510	0.357255	+	0.934007i	$0.383713\pi$
$600$	863811.	0.0979582
$601$	5.39175e6	0.608896	0.304448	−	0.952529i	$-0.401528\pi$
$601$	5.39175e6	0.608896	0.304448	+	0.952529i	$0.401528\pi$
$602$	−4.77875e6	−0.537432
$603$	1.27660e6	0.142975
$604$	6.62824e6	0.739274
$605$	−6.69739e6	−0.743904
$606$	948757.	0.104948
$607$	−6.57709e6	−0.724540	−0.362270	−	0.932073i	$-0.617998\pi$
$607$	−6.57709e6	−0.724540	−0.362270	+	0.932073i	$0.617998\pi$
$608$	2.78603e6	0.305652
$609$	1.23023e7	1.34414
$610$	1.91438e6	0.208307
$611$	1.21584e7	1.31757
$612$	819346.	0.0884278
$613$	−8.64696e6	−0.929421	−0.464710	−	0.885463i	$-0.653842\pi$
$613$	−8.64696e6	−0.929421	−0.464710	+	0.885463i	$0.653842\pi$
$614$	−1.12259e7	−1.20171
$615$	−1.76510e6	−0.188184
$616$	3.29196e6	0.349545
$617$	−8.53272e6	−0.902350	−0.451175	−	0.892436i	$-0.648995\pi$
$617$	−8.53272e6	−0.902350	−0.451175	+	0.892436i	$0.648995\pi$
$618$	5.86557e6	0.617788
$619$	−4.50849e6	−0.472938	−0.236469	−	0.971639i	$-0.575990\pi$
$619$	−4.50849e6	−0.472938	−0.236469	+	0.971639i	$0.575990\pi$
$620$	−7.11916e6	−0.743788
$621$	806361.	0.0839074
$622$	5.06214e6	0.524636
$623$	2.66750e7	2.75349
$624$	−998024.	−0.102608
$625$	−1.22031e7	−1.24960
$626$	1.01434e6	0.103454
$627$	6.12494e6	0.622204
$628$	−5.78432e6	−0.585266
$629$	3.40858e6	0.343516
$630$	4.53093e6	0.454816
$631$	1.70722e7	1.70693	0.853466	−	0.521148i	$-0.174496\pi$
$631$	1.70722e7	1.70693	0.853466	+	0.521148i	$0.174496\pi$
$632$	393350.	0.0391730
$633$	−1.72122e6	−0.170737
$634$	−1.87972e6	−0.185725
$635$	8.39816e6	0.826513
$636$	−1.23732e6	−0.121294
$637$	1.10370e7	1.07772
$638$	−6.65082e6	−0.646880
$639$	−6.44649e6	−0.624556
$640$	−1.11419e6	−0.107525
$641$	−7.97593e6	−0.766719	−0.383359	−	0.923599i	$-0.625233\pi$
$641$	−7.97593e6	−0.766719	−0.383359	+	0.923599i	$0.625233\pi$
$642$	−7.00516e6	−0.670780
$643$	−1.39923e7	−1.33463	−0.667316	−	0.744775i	$-0.732557\pi$
$643$	−1.39923e7	−1.33463	−0.667316	+	0.744775i	$0.732557\pi$
$644$	3.63935e6	0.345787
$645$	3.55579e6	0.336540
$646$	6.88031e6	0.648675
$647$	−1.32005e7	−1.23973	−0.619867	−	0.784707i	$-0.712813\pi$
$647$	−1.32005e7	−1.23973	−0.619867	+	0.784707i	$0.712813\pi$
$648$	−419904.	−0.0392837
$649$	−870717.	−0.0811457
$650$	−2.59845e6	−0.241230
$651$	−1.21091e7	−1.11985
$652$	−2.60824e6	−0.240286
$653$	−5.81782e6	−0.533922	−0.266961	−	0.963707i	$-0.586019\pi$
$653$	−5.81782e6	−0.533922	−0.266961	+	0.963707i	$0.586019\pi$
$654$	1.19393e6	0.109152
$655$	−1.23375e7	−1.12364
$656$	738289.	0.0669834
$657$	−7.25276e6	−0.655526
$658$	2.30876e7	2.07881
$659$	1.02065e7	0.915506	0.457753	−	0.889079i	$-0.348654\pi$
$659$	1.02065e7	0.915506	0.457753	+	0.889079i	$0.348654\pi$
$660$	−2.44949e6	−0.218885
$661$	8.52653e6	0.759047	0.379524	−	0.925182i	$-0.376088\pi$
$661$	8.52653e6	0.759047	0.379524	+	0.925182i	$0.376088\pi$
$662$	−1.17161e7	−1.03905
$663$	−2.46470e6	−0.217761
$664$	−1.78952e6	−0.157513
$665$	3.80477e7	3.33637
$666$	−1.74685e6	−0.152606
$667$	−7.35266e6	−0.639926
$668$	−1.02158e6	−0.0885789
$669$	5.59698e6	0.483491
$670$	−4.28716e6	−0.368963
$671$	−1.76036e6	−0.150937
$672$	−1.89515e6	−0.161890
$673$	−2.09490e6	−0.178289	−0.0891447	−	0.996019i	$-0.528413\pi$
$673$	−2.09490e6	−0.178289	−0.0891447	+	0.996019i	$0.528413\pi$
$674$	−2.97487e6	−0.252242
$675$	−1.09326e6	−0.0923559
$676$	−2.93851e6	−0.247320
$677$	−8.78347e6	−0.736537	−0.368268	−	0.929720i	$-0.620049\pi$
$677$	−8.78347e6	−0.736537	−0.368268	+	0.929720i	$0.620049\pi$
$678$	−7.99840e6	−0.668235
$679$	2.01940e7	1.68092
$680$	−2.75158e6	−0.228197
$681$	9.33017e6	0.770942
$682$	6.54638e6	0.538940
$683$	−427011.	−0.0350258	−0.0175129	−	0.999847i	$-0.505575\pi$
$683$	−427011.	−0.0350258	−0.0175129	+	0.999847i	$0.505575\pi$
$684$	−3.52607e6	−0.288171
$685$	6.76800e6	0.551104
$686$	7.13372e6	0.578770
$687$	7.52175e6	0.608033
$688$	−1.48728e6	−0.119790
$689$	3.72201e6	0.298696
$690$	−2.70798e6	−0.216532
$691$	1.01304e7	0.807104	0.403552	−	0.914957i	$-0.367775\pi$
$691$	1.01304e7	0.807104	0.403552	+	0.914957i	$0.367775\pi$
$692$	−5.01722e6	−0.398288
$693$	−4.16639e6	−0.329554
$694$	−7.41136e6	−0.584116
$695$	−1.37528e7	−1.08002
$696$	3.82882e6	0.299600
$697$	1.82326e6	0.142157
$698$	2.36066e6	0.183398
$699$	−1.46717e7	−1.13577
$700$	−4.93422e6	−0.380604
$701$	−6.76460e6	−0.519933	−0.259966	−	0.965618i	$-0.583711\pi$
$701$	−6.76460e6	−0.519933	−0.259966	+	0.965618i	$0.583711\pi$
$702$	1.26312e6	0.0967394
$703$	−1.46689e7	−1.11946
$704$	1.02455e6	0.0779115
$705$	−1.71791e7	−1.30175
$706$	2.01797e6	0.152371
$707$	−5.41944e6	−0.407761
$708$	501264.	0.0375823
$709$	1.89481e7	1.41563	0.707814	−	0.706399i	$-0.249682\pi$
$709$	1.89481e7	1.41563	0.707814	+	0.706399i	$0.249682\pi$
$710$	2.16491e7	1.61173
$711$	−497834.	−0.0369327
$712$	8.30199e6	0.613737
$713$	7.23719e6	0.533146
$714$	−4.68022e6	−0.343575
$715$	7.36838e6	0.539023
$716$	−1.26306e6	−0.0920749
$717$	−4.71486e6	−0.342508
$718$	−6.09531e6	−0.441250
$719$	1.79064e7	1.29177	0.645887	−	0.763433i	$-0.276488\pi$
$719$	1.79064e7	1.29177	0.645887	+	0.763433i	$0.276488\pi$
$720$	1.41015e6	0.101376
$721$	−3.35050e7	−2.40033
$722$	−1.97052e7	−1.40681
$723$	8.00723e6	0.569687
$724$	−1.09431e7	−0.775876
$725$	9.96871e6	0.704359
$726$	−3.54542e6	−0.249647
$727$	−2.04164e7	−1.43266	−0.716331	−	0.697761i	$-0.754180\pi$
$727$	−2.04164e7	−1.43266	−0.716331	+	0.697761i	$0.754180\pi$
$728$	5.70086e6	0.398669
$729$	531441.	0.0370370
$730$	2.43567e7	1.69166
$731$	−3.67295e6	−0.254227
$732$	1.01342e6	0.0699058
$733$	−1.75134e7	−1.20395	−0.601977	−	0.798513i	$-0.705620\pi$
$733$	−1.75134e7	−1.20395	−0.601977	+	0.798513i	$0.705620\pi$
$734$	−2.54417e6	−0.174303
$735$	−1.55947e7	−1.06478
$736$	1.13267e6	0.0770739
$737$	3.94223e6	0.267346
$738$	−934397.	−0.0631525
$739$	−1.87051e7	−1.25994	−0.629969	−	0.776620i	$-0.716933\pi$
$739$	−1.87051e7	−1.25994	−0.629969	+	0.776620i	$0.716933\pi$
$740$	5.86640e6	0.393815
$741$	1.06069e7	0.709645
$742$	7.06775e6	0.471272
$743$	4.41257e6	0.293237	0.146619	−	0.989193i	$-0.453161\pi$
$743$	4.41257e6	0.293237	0.146619	+	0.989193i	$0.453161\pi$
$744$	−3.76869e6	−0.249608
$745$	1.70237e6	0.112373
$746$	−5.19265e6	−0.341619
$747$	2.26487e6	0.148505
$748$	2.53020e6	0.165349
$749$	4.00145e7	2.60623
$750$	−3.97909e6	−0.258304
$751$	1.21184e7	0.784056	0.392028	−	0.919953i	$-0.371774\pi$
$751$	1.21184e7	0.784056	0.392028	+	0.919953i	$0.371774\pi$
$752$	7.18550e6	0.463353
$753$	−5.06701e6	−0.325660
$754$	−1.15176e7	−0.737790
$755$	2.81721e7	1.79867
$756$	2.39855e6	0.152632
$757$	1.84696e7	1.17144	0.585718	−	0.810515i	$-0.300812\pi$
$757$	1.84696e7	1.17144	0.585718	+	0.810515i	$0.300812\pi$
$758$	1.58738e7	1.00348
$759$	2.49010e6	0.156896
$760$	1.18415e7	0.743657
$761$	−1.61990e7	−1.01398	−0.506988	−	0.861953i	$-0.669241\pi$
$761$	−1.61990e7	−1.01398	−0.506988	+	0.861953i	$0.669241\pi$
$762$	4.44576e6	0.277369
$763$	−6.81988e6	−0.424097
$764$	−1.11111e7	−0.688691
$765$	3.48247e6	0.215146
$766$	−1.75035e7	−1.07784
$767$	−1.50787e6	−0.0925495
$768$	−589824.	−0.0360844
$769$	1.74721e7	1.06544	0.532721	−	0.846291i	$-0.321169\pi$
$769$	1.74721e7	1.06544	0.532721	+	0.846291i	$0.321169\pi$
$770$	1.39919e7	0.850450
$771$	−9.88651e6	−0.598973
$772$	6.19810e6	0.374296
$773$	1.70921e7	1.02884	0.514418	−	0.857540i	$-0.328008\pi$
$773$	1.70921e7	1.02884	0.514418	+	0.857540i	$0.328008\pi$
$774$	1.88234e6	0.112939
$775$	−9.81216e6	−0.586827
$776$	6.28492e6	0.374667
$777$	9.97828e6	0.592930
$778$	6.55826e6	0.388454
$779$	−7.84644e6	−0.463264
$780$	−4.24191e6	−0.249646
$781$	−1.99073e7	−1.16784
$782$	2.79720e6	0.163571
$783$	−4.84585e6	−0.282466
$784$	6.52280e6	0.379004
$785$	−2.45851e7	−1.42396
$786$	−6.53117e6	−0.377081
$787$	1.65600e7	0.953068	0.476534	−	0.879156i	$-0.341893\pi$
$787$	1.65600e7	0.953068	0.476534	+	0.879156i	$0.341893\pi$
$788$	−2.52939e6	−0.145111
$789$	−1.73386e7	−0.991567
$790$	1.67186e6	0.0953087
$791$	4.56880e7	2.59634
$792$	−1.29670e6	−0.0734556
$793$	−3.04851e6	−0.172149
$794$	1.71968e6	0.0968045
$795$	−5.25899e6	−0.295110
$796$	−1.06996e7	−0.598531
$797$	1.21738e7	0.678863	0.339431	−	0.940631i	$-0.389765\pi$
$797$	1.21738e7	0.678863	0.339431	+	0.940631i	$0.389765\pi$
$798$	2.01414e7	1.11965
$799$	1.77451e7	0.983359
$800$	−1.53566e6	−0.0848343
$801$	−1.05072e7	−0.578637
$802$	1.90101e7	1.04363
$803$	−2.23971e7	−1.22575
$804$	−2.26951e6	−0.123820
$805$	1.54684e7	0.841307
$806$	1.13367e7	0.614680
$807$	9.41183e6	0.508733
$808$	−1.68668e6	−0.0908875
$809$	−1.13317e7	−0.608729	−0.304365	−	0.952556i	$-0.598444\pi$
$809$	−1.13317e7	−0.608729	−0.304365	+	0.952556i	$0.598444\pi$
$810$	−1.78472e6	−0.0955780
$811$	4.95636e6	0.264612	0.132306	−	0.991209i	$-0.457762\pi$
$811$	4.95636e6	0.264612	0.132306	+	0.991209i	$0.457762\pi$
$812$	−2.18708e7	−1.16406
$813$	−1.93228e7	−1.02529
$814$	−5.39442e6	−0.285354
$815$	−1.10858e7	−0.584620
$816$	−1.45662e6	−0.0765807
$817$	1.58066e7	0.828483
$818$	−6.14095e6	−0.320887
$819$	−7.21515e6	−0.375868
$820$	3.13796e6	0.162972
$821$	1.95212e7	1.01076	0.505380	−	0.862897i	$-0.331352\pi$
$821$	1.95212e7	1.01076	0.505380	+	0.862897i	$0.331352\pi$
$822$	3.58280e6	0.184945
$823$	−2.68907e7	−1.38389	−0.691946	−	0.721949i	$-0.743246\pi$
$823$	−2.68907e7	−1.38389	−0.691946	+	0.721949i	$0.743246\pi$
$824$	−1.04277e7	−0.535020
$825$	−3.37608e6	−0.172694
$826$	−2.86329e6	−0.146021
$827$	3.60061e7	1.83068	0.915341	−	0.402680i	$-0.131921\pi$
$827$	3.60061e7	1.83068	0.915341	+	0.402680i	$0.131921\pi$
$828$	−1.43353e6	−0.0726660
$829$	7.72979e6	0.390644	0.195322	−	0.980739i	$-0.437425\pi$
$829$	7.72979e6	0.390644	0.195322	+	0.980739i	$0.437425\pi$
$830$	−7.60603e6	−0.383233
$831$	1.99666e7	1.00300
$832$	1.77427e6	0.0888608
$833$	1.61086e7	0.804348
$834$	−7.28038e6	−0.362442
$835$	−4.34202e6	−0.215514
$836$	−1.08888e7	−0.538844
$837$	4.76975e6	0.235333
$838$	1.10479e7	0.543464
$839$	−1.55781e7	−0.764028	−0.382014	−	0.924156i	$-0.624769\pi$
$839$	−1.55781e7	−0.764028	−0.382014	+	0.924156i	$0.624769\pi$
$840$	−8.05499e6	−0.393882
$841$	2.36749e7	1.15424
$842$	2.13013e7	1.03544
$843$	2.23811e6	0.108471
$844$	3.05994e6	0.147862
$845$	−1.24896e7	−0.601735
$846$	−9.09415e6	−0.436854
$847$	2.02520e7	0.969970
$848$	2.19968e6	0.105044
$849$	−1.87379e6	−0.0892180
$850$	−3.79244e6	−0.180041
$851$	−5.96367e6	−0.282286
$852$	1.14604e7	0.540881
$853$	9.00588e6	0.423793	0.211896	−	0.977292i	$-0.432036\pi$
$853$	9.00588e6	0.423793	0.211896	+	0.977292i	$0.432036\pi$
$854$	−5.78883e6	−0.271610
$855$	−1.49869e7	−0.701126
$856$	1.24536e7	0.580913
$857$	8.42480e6	0.391839	0.195919	−	0.980620i	$-0.437231\pi$
$857$	8.42480e6	0.391839	0.195919	+	0.980620i	$0.437231\pi$
$858$	3.90063e6	0.180891
$859$	−4.06216e6	−0.187834	−0.0939170	−	0.995580i	$-0.529939\pi$
$859$	−4.06216e6	−0.187834	−0.0939170	+	0.995580i	$0.529939\pi$
$860$	−6.32140e6	−0.291452
$861$	5.33742e6	0.245371
$862$	1.40847e7	0.645623
$863$	3.40064e6	0.155430	0.0777148	−	0.996976i	$-0.475238\pi$
$863$	3.40064e6	0.155430	0.0777148	+	0.996976i	$0.475238\pi$
$864$	746496.	0.0340207
$865$	−2.13247e7	−0.969043
$866$	−1.15180e7	−0.521893
$867$	9.18149e6	0.414826
$868$	2.15273e7	0.969819
$869$	−1.53735e6	−0.0690595
$870$	1.62737e7	0.728932
$871$	6.82696e6	0.304917
$872$	−2.12253e6	−0.0945287
$873$	−7.95435e6	−0.353240
$874$	−1.20378e7	−0.533052
$875$	2.27292e7	1.00361
$876$	1.28938e7	0.567702
$877$	−7.33990e6	−0.322249	−0.161124	−	0.986934i	$-0.551512\pi$
$877$	−7.33990e6	−0.322249	−0.161124	+	0.986934i	$0.551512\pi$
$878$	1.89067e7	0.827714
$879$	−4.95831e6	−0.216452
$880$	4.35465e6	0.189560
$881$	2.84797e7	1.23622	0.618110	−	0.786092i	$-0.287899\pi$
$881$	2.84797e7	1.23622	0.618110	+	0.786092i	$0.287899\pi$
$882$	−8.25542e6	−0.357329
$883$	−3.30834e7	−1.42793	−0.713967	−	0.700179i	$-0.753103\pi$
$883$	−3.30834e7	−1.42793	−0.713967	+	0.700179i	$0.753103\pi$
$884$	4.38168e6	0.188586
$885$	2.13053e6	0.0914384
$886$	987923.	0.0422804
$887$	−7.55484e6	−0.322416	−0.161208	−	0.986920i	$-0.551539\pi$
$887$	−7.55484e6	−0.322416	−0.161208	+	0.986920i	$0.551539\pi$
$888$	3.10552e6	0.132160
$889$	−2.53948e7	−1.07768
$890$	3.52860e7	1.49323
$891$	1.64113e6	0.0692546
$892$	−9.95019e6	−0.418715
$893$	−7.63665e7	−3.20460
$894$	901190.	0.0377114
$895$	−5.36839e6	−0.224020
$896$	3.36916e6	0.140201
$897$	4.31224e6	0.178946
$898$	−2.43423e7	−1.00733
$899$	−4.34921e7	−1.79478
$900$	1.94358e6	0.0799825
$901$	5.43227e6	0.222931
$902$	−2.88549e6	−0.118087
$903$	−1.07522e7	−0.438811
$904$	1.42194e7	0.578708
$905$	−4.65114e7	−1.88772
$906$	1.49135e7	0.603615
$907$	2.58616e7	1.04385	0.521925	−	0.852991i	$-0.325214\pi$
$907$	2.58616e7	1.04385	0.521925	+	0.852991i	$0.325214\pi$
$908$	−1.65870e7	−0.667655
$909$	2.13470e6	0.0856895
$910$	2.42304e7	0.969968
$911$	−2.28584e7	−0.912537	−0.456268	−	0.889842i	$-0.650814\pi$
$911$	−2.28584e7	−0.912537	−0.456268	+	0.889842i	$0.650814\pi$
$912$	6.26857e6	0.249564
$913$	6.99408e6	0.277686
$914$	7.81586e6	0.309465
$915$	4.30737e6	0.170082
$916$	−1.33720e7	−0.526572
$917$	3.73070e7	1.46510
$918$	1.84353e6	0.0722010
$919$	2.46539e7	0.962937	0.481468	−	0.876464i	$-0.340104\pi$
$919$	2.46539e7	0.962937	0.481468	+	0.876464i	$0.340104\pi$
$920$	4.81418e6	0.187522
$921$	−2.52583e7	−0.981196
$922$	−7.36921e6	−0.285492
$923$	−3.44744e7	−1.33196
$924$	7.40692e6	0.285402
$925$	8.08552e6	0.310709
$926$	−1.67653e7	−0.642514
$927$	1.31975e7	0.504422
$928$	−6.80679e6	−0.259461
$929$	2.50774e7	0.953332	0.476666	−	0.879085i	$-0.341845\pi$
$929$	2.50774e7	0.953332	0.476666	+	0.879085i	$0.341845\pi$
$930$	−1.60181e7	−0.607301
$931$	−6.93235e7	−2.62124
$932$	2.60831e7	0.983602
$933$	1.13898e7	0.428364
$934$	2.49443e7	0.935630
$935$	1.07541e7	0.402297
$936$	−2.24555e6	−0.0837788
$937$	−9.71072e6	−0.361329	−0.180664	−	0.983545i	$-0.557825\pi$
$937$	−9.71072e6	−0.361329	−0.180664	+	0.983545i	$0.557825\pi$
$938$	1.29638e7	0.481087
$939$	2.28226e6	0.0844698
$940$	3.05406e7	1.12735
$941$	1.67964e7	0.618363	0.309181	−	0.951003i	$-0.399945\pi$
$941$	1.67964e7	0.618363	0.309181	+	0.951003i	$0.399945\pi$
$942$	−1.30147e7	−0.477867
$943$	−3.18998e6	−0.116818
$944$	−891136.	−0.0325472
$945$	1.01946e7	0.371356
$946$	5.81281e6	0.211183
$947$	368100.	0.0133380	0.00666901	−	0.999978i	$-0.497877\pi$
$947$	368100.	0.0133380	0.00666901	+	0.999978i	$0.497877\pi$
$948$	885039.	0.0319846
$949$	−3.87862e7	−1.39801
$950$	1.63208e7	0.586723
$951$	−4.22938e6	−0.151644
$952$	8.32040e6	0.297544
$953$	−2.35141e7	−0.838681	−0.419340	−	0.907829i	$-0.637739\pi$
$953$	−2.35141e7	−0.838681	−0.419340	+	0.907829i	$0.637739\pi$
$954$	−2.78397e6	−0.0990360
$955$	−4.72257e7	−1.67560
$956$	8.38197e6	0.296621
$957$	−1.49644e7	−0.528175
$958$	−7.81021e6	−0.274947
$959$	−2.04655e7	−0.718580
$960$	−2.50693e6	−0.0877940
$961$	1.41800e7	0.495298
$962$	−9.34179e6	−0.325456
$963$	−1.57616e7	−0.547690
$964$	−1.42351e7	−0.493363
$965$	2.63438e7	0.910670
$966$	8.18854e6	0.282334
$967$	−3.07149e7	−1.05629	−0.528145	−	0.849154i	$-0.677112\pi$
$967$	−3.07149e7	−1.05629	−0.528145	+	0.849154i	$0.677112\pi$
$968$	6.30297e6	0.216200
$969$	1.54807e7	0.529641
$970$	2.67129e7	0.911572
$971$	−9.01981e6	−0.307008	−0.153504	−	0.988148i	$-0.549056\pi$
$971$	−9.01981e6	−0.307008	−0.153504	+	0.988148i	$0.549056\pi$
$972$	−944784.	−0.0320750
$973$	4.15866e7	1.40822
$974$	269403.	0.00909925
$975$	−5.84652e6	−0.196964
$976$	−1.80164e6	−0.0605402
$977$	4.54745e6	0.152416	0.0762082	−	0.997092i	$-0.475719\pi$
$977$	4.54745e6	0.152416	0.0762082	+	0.997092i	$0.475719\pi$
$978$	−5.86853e6	−0.196193
$979$	−3.24471e7	−1.08198
$980$	2.77239e7	0.922125
$981$	2.68633e6	0.0891225
$982$	−1.26442e7	−0.418419
$983$	3.33195e7	1.09980	0.549901	−	0.835230i	$-0.314665\pi$
$983$	3.33195e7	1.09980	0.549901	+	0.835230i	$0.314665\pi$
$984$	1.66115e6	0.0546917
$985$	−1.07507e7	−0.353058
$986$	−1.68099e7	−0.550646
$987$	5.19471e7	1.69734
$988$	−1.88566e7	−0.614571
$989$	6.42621e6	0.208912
$990$	−5.51136e6	−0.178719
$991$	−5.49283e7	−1.77669	−0.888346	−	0.459175i	$-0.848145\pi$
$991$	−5.49283e7	−1.77669	−0.888346	+	0.459175i	$0.848145\pi$
$992$	6.69990e6	0.216167
$993$	−2.63612e7	−0.848383
$994$	−6.54637e7	−2.10152
$995$	−4.54768e7	−1.45624
$996$	−4.02643e6	−0.128609
$997$	−1.96011e7	−0.624514	−0.312257	−	0.949998i	$-0.601085\pi$
$997$	−1.96011e7	−0.624514	−0.312257	+	0.949998i	$0.601085\pi$
$998$	−2.03400e6	−0.0646436
$999$	−3.93042e6	−0.124602

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	354.6.a.f.1.6	✓	6
3.2	odd	2		1062.6.a.i.1.1		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
354.6.a.f.1.6	✓	6	1.1	even	1	trivial
1062.6.a.i.1.1		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)

\(f(q)\)	\(=\)	\(q-4.00000 q^{2} -9.00000 q^{3} +16.0000 q^{4} +68.0049 q^{5} +36.0000 q^{6} -205.637 q^{7} -64.0000 q^{8} +81.0000 q^{9} +O(q^{10})\)	\(q-4.00000 q^{2} -9.00000 q^{3} +16.0000 q^{4} +68.0049 q^{5} +36.0000 q^{6} -205.637 q^{7} -64.0000 q^{8} +81.0000 q^{9} -272.020 q^{10} +250.134 q^{11} -144.000 q^{12} +433.170 q^{13} +822.549 q^{14} -612.045 q^{15} +256.000 q^{16} +632.211 q^{17} -324.000 q^{18} -2720.73 q^{19} +1088.08 q^{20} +1850.74 q^{21} -1000.54 q^{22} -1106.12 q^{23} +576.000 q^{24} +1499.67 q^{25} -1732.68 q^{26} -729.000 q^{27} -3290.20 q^{28} +6647.26 q^{29} +2448.18 q^{30} -6542.87 q^{31} -1024.00 q^{32} -2251.21 q^{33} -2528.85 q^{34} -13984.4 q^{35} +1296.00 q^{36} +5391.52 q^{37} +10882.9 q^{38} -3898.53 q^{39} -4352.32 q^{40} +2883.94 q^{41} -7402.94 q^{42} -5809.69 q^{43} +4002.15 q^{44} +5508.40 q^{45} +4424.48 q^{46} +28068.4 q^{47} -2304.00 q^{48} +25479.7 q^{49} -5998.69 q^{50} -5689.90 q^{51} +6930.72 q^{52} +8592.49 q^{53} +2916.00 q^{54} +17010.4 q^{55} +13160.8 q^{56} +24486.6 q^{57} -26589.0 q^{58} -3481.00 q^{59} -9792.71 q^{60} -7037.67 q^{61} +26171.5 q^{62} -16656.6 q^{63} +4096.00 q^{64} +29457.7 q^{65} +9004.83 q^{66} +15760.5 q^{67} +10115.4 q^{68} +9955.07 q^{69} +55937.4 q^{70} -79586.3 q^{71} -5184.00 q^{72} -89540.3 q^{73} -21566.1 q^{74} -13497.1 q^{75} -43531.7 q^{76} -51436.9 q^{77} +15594.1 q^{78} -6146.10 q^{79} +17409.3 q^{80} +6561.00 q^{81} -11535.8 q^{82} +27961.3 q^{83} +29611.8 q^{84} +42993.5 q^{85} +23238.8 q^{86} -59825.3 q^{87} -16008.6 q^{88} -129719. q^{89} -22033.6 q^{90} -89075.9 q^{91} -17697.9 q^{92} +58885.8 q^{93} -112273. q^{94} -185023. q^{95} +9216.00 q^{96} -98201.9 q^{97} -101919. q^{98} +20260.9 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 24 q^{2} - 54 q^{3} + 96 q^{4} - 46 q^{5} + 216 q^{6} - 103 q^{7} - 384 q^{8} + 486 q^{9}+O(q^{10}) \) 6 * q - 24 * q^2 - 54 * q^3 + 96 * q^4 - 46 * q^5 + 216 * q^6 - 103 * q^7 - 384 * q^8 + 486 * q^9	\( 6 q - 24 q^{2} - 54 q^{3} + 96 q^{4} - 46 q^{5} + 216 q^{6} - 103 q^{7} - 384 q^{8} + 486 q^{9} + 184 q^{10} - 653 q^{11} - 864 q^{12} + 647 q^{13} + 412 q^{14} + 414 q^{15} + 1536 q^{16} + 621 q^{17} - 1944 q^{18} - 454 q^{19} - 736 q^{20} + 927 q^{21} + 2612 q^{22} - 3412 q^{23} + 3456 q^{24} + 3866 q^{25} - 2588 q^{26} - 4374 q^{27} - 1648 q^{28} + 1526 q^{29} - 1656 q^{30} + 5976 q^{31} - 6144 q^{32} + 5877 q^{33} - 2484 q^{34} + 8098 q^{35} + 7776 q^{36} + 37033 q^{37} + 1816 q^{38} - 5823 q^{39} + 2944 q^{40} + 13983 q^{41} - 3708 q^{42} + 11521 q^{43} - 10448 q^{44} - 3726 q^{45} + 13648 q^{46} + 12434 q^{47} - 13824 q^{48} + 54237 q^{49} - 15464 q^{50} - 5589 q^{51} + 10352 q^{52} + 21310 q^{53} + 17496 q^{54} + 57468 q^{55} + 6592 q^{56} + 4086 q^{57} - 6104 q^{58} - 20886 q^{59} + 6624 q^{60} - 23030 q^{61} - 23904 q^{62} - 8343 q^{63} + 24576 q^{64} - 37368 q^{65} - 23508 q^{66} + 24342 q^{67} + 9936 q^{68} + 30708 q^{69} - 32392 q^{70} - 184375 q^{71} - 31104 q^{72} - 24512 q^{73} - 148132 q^{74} - 34794 q^{75} - 7264 q^{76} - 46529 q^{77} + 23292 q^{78} - 17987 q^{79} - 11776 q^{80} + 39366 q^{81} - 55932 q^{82} - 46687 q^{83} + 14832 q^{84} - 29706 q^{85} - 46084 q^{86} - 13734 q^{87} + 41792 q^{88} - 178946 q^{89} + 14904 q^{90} - 340179 q^{91} - 54592 q^{92} - 53784 q^{93} - 49736 q^{94} - 532190 q^{95} + 55296 q^{96} - 214638 q^{97} - 216948 q^{98} - 52893 q^{99}+O(q^{100}) \) 6 * q - 24 * q^2 - 54 * q^3 + 96 * q^4 - 46 * q^5 + 216 * q^6 - 103 * q^7 - 384 * q^8 + 486 * q^9 + 184 * q^10 - 653 * q^11 - 864 * q^12 + 647 * q^13 + 412 * q^14 + 414 * q^15 + 1536 * q^16 + 621 * q^17 - 1944 * q^18 - 454 * q^19 - 736 * q^20 + 927 * q^21 + 2612 * q^22 - 3412 * q^23 + 3456 * q^24 + 3866 * q^25 - 2588 * q^26 - 4374 * q^27 - 1648 * q^28 + 1526 * q^29 - 1656 * q^30 + 5976 * q^31 - 6144 * q^32 + 5877 * q^33 - 2484 * q^34 + 8098 * q^35 + 7776 * q^36 + 37033 * q^37 + 1816 * q^38 - 5823 * q^39 + 2944 * q^40 + 13983 * q^41 - 3708 * q^42 + 11521 * q^43 - 10448 * q^44 - 3726 * q^45 + 13648 * q^46 + 12434 * q^47 - 13824 * q^48 + 54237 * q^49 - 15464 * q^50 - 5589 * q^51 + 10352 * q^52 + 21310 * q^53 + 17496 * q^54 + 57468 * q^55 + 6592 * q^56 + 4086 * q^57 - 6104 * q^58 - 20886 * q^59 + 6624 * q^60 - 23030 * q^61 - 23904 * q^62 - 8343 * q^63 + 24576 * q^64 - 37368 * q^65 - 23508 * q^66 + 24342 * q^67 + 9936 * q^68 + 30708 * q^69 - 32392 * q^70 - 184375 * q^71 - 31104 * q^72 - 24512 * q^73 - 148132 * q^74 - 34794 * q^75 - 7264 * q^76 - 46529 * q^77 + 23292 * q^78 - 17987 * q^79 - 11776 * q^80 + 39366 * q^81 - 55932 * q^82 - 46687 * q^83 + 14832 * q^84 - 29706 * q^85 - 46084 * q^86 - 13734 * q^87 + 41792 * q^88 - 178946 * q^89 + 14904 * q^90 - 340179 * q^91 - 54592 * q^92 - 53784 * q^93 - 49736 * q^94 - 532190 * q^95 + 55296 * q^96 - 214638 * q^97 - 216948 * q^98 - 52893 * q^99

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