LMFDB - Embedded newform 138.6.a.h.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [138,6,Mod(1,138)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(138, 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("138.1");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 138 = 2 \cdot 3 \cdot 23 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	138.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:	$22.1329671342$
Analytic rank:	$0$
Dimension:	$3$
Coefficient field:	$\mathbb{Q}[x]/(x^{3} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - x^{2} - 1025x - 1873 $ x^3 - x^2 - 1025*x - 1873
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$33.3840$ of defining polynomial
Character	$\chi$	$=$	138.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-4.00000 q^{2} +9.00000 q^{3} +16.0000 q^{4} +64.7679 q^{5} -36.0000 q^{6} -91.1204 q^{7} -64.0000 q^{8} +81.0000 q^{9} +O(q^{10})$	\(q-4.00000 q^{2} +9.00000 q^{3} +16.0000 q^{4} +64.7679 q^{5} -36.0000 q^{6} -91.1204 q^{7} -64.0000 q^{8} +81.0000 q^{9} -259.072 q^{10} +642.496 q^{11} +144.000 q^{12} +597.072 q^{13} +364.482 q^{14} +582.911 q^{15} +256.000 q^{16} -847.166 q^{17} -324.000 q^{18} -1415.34 q^{19} +1036.29 q^{20} -820.084 q^{21} -2569.98 q^{22} -529.000 q^{23} -576.000 q^{24} +1069.88 q^{25} -2388.29 q^{26} +729.000 q^{27} -1457.93 q^{28} +3212.23 q^{29} -2331.65 q^{30} +7261.92 q^{31} -1024.00 q^{32} +5782.46 q^{33} +3388.67 q^{34} -5901.68 q^{35} +1296.00 q^{36} +7167.54 q^{37} +5661.37 q^{38} +5373.65 q^{39} -4145.15 q^{40} -10415.4 q^{41} +3280.33 q^{42} +23218.9 q^{43} +10279.9 q^{44} +5246.20 q^{45} +2116.00 q^{46} +9899.93 q^{47} +2304.00 q^{48} -8504.07 q^{49} -4279.53 q^{50} -7624.50 q^{51} +9553.15 q^{52} +9796.05 q^{53} -2916.00 q^{54} +41613.1 q^{55} +5831.71 q^{56} -12738.1 q^{57} -12848.9 q^{58} -4356.53 q^{59} +9326.58 q^{60} -2981.75 q^{61} -29047.7 q^{62} -7380.75 q^{63} +4096.00 q^{64} +38671.1 q^{65} -23129.9 q^{66} +58230.1 q^{67} -13554.7 q^{68} -4761.00 q^{69} +23606.7 q^{70} -29085.1 q^{71} -5184.00 q^{72} +36092.3 q^{73} -28670.2 q^{74} +9628.95 q^{75} -22645.5 q^{76} -58544.5 q^{77} -21494.6 q^{78} +56070.4 q^{79} +16580.6 q^{80} +6561.00 q^{81} +41661.6 q^{82} -4173.11 q^{83} -13121.3 q^{84} -54869.2 q^{85} -92875.7 q^{86} +28910.1 q^{87} -41119.7 q^{88} -15386.9 q^{89} -20984.8 q^{90} -54405.4 q^{91} -8464.00 q^{92} +65357.3 q^{93} -39599.7 q^{94} -91668.7 q^{95} -9216.00 q^{96} -116455. q^{97} +34016.3 q^{98} +52042.2 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q - 12 q^{2} + 27 q^{3} + 48 q^{4} - 4 q^{5} - 108 q^{6} - 34 q^{7} - 192 q^{8} + 243 q^{9}+O(q^{10}) $ 3 * q - 12 * q^2 + 27 * q^3 + 48 * q^4 - 4 * q^5 - 108 * q^6 - 34 * q^7 - 192 * q^8 + 243 * q^9	\( 3 q - 12 q^{2} + 27 q^{3} + 48 q^{4} - 4 q^{5} - 108 q^{6} - 34 q^{7} - 192 q^{8} + 243 q^{9} + 16 q^{10} + 300 q^{11} + 432 q^{12} + 998 q^{13} + 136 q^{14} - 36 q^{15} + 768 q^{16} + 392 q^{17} - 972 q^{18} + 2298 q^{19} - 64 q^{20} - 306 q^{21} - 1200 q^{22} - 1587 q^{23} - 1728 q^{24} - 1167 q^{25} - 3992 q^{26} + 2187 q^{27} - 544 q^{28} - 3834 q^{29} + 144 q^{30} + 11460 q^{31} - 3072 q^{32} + 2700 q^{33} - 1568 q^{34} + 5120 q^{35} + 3888 q^{36} + 28286 q^{37} - 9192 q^{38} + 8982 q^{39} + 256 q^{40} + 11998 q^{41} + 1224 q^{42} + 33666 q^{43} + 4800 q^{44} - 324 q^{45} + 6348 q^{46} + 31384 q^{47} + 6912 q^{48} + 61799 q^{49} + 4668 q^{50} + 3528 q^{51} + 15968 q^{52} + 24144 q^{53} - 8748 q^{54} + 51944 q^{55} + 2176 q^{56} + 20682 q^{57} + 15336 q^{58} - 14532 q^{59} - 576 q^{60} + 41222 q^{61} - 45840 q^{62} - 2754 q^{63} + 12288 q^{64} + 31480 q^{65} - 10800 q^{66} + 20030 q^{67} + 6272 q^{68} - 14283 q^{69} - 20480 q^{70} - 47928 q^{71} - 15552 q^{72} + 71894 q^{73} - 113144 q^{74} - 10503 q^{75} + 36768 q^{76} - 79712 q^{77} - 35928 q^{78} + 10922 q^{79} - 1024 q^{80} + 19683 q^{81} - 47992 q^{82} - 59068 q^{83} - 4896 q^{84} - 136840 q^{85} - 134664 q^{86} - 34506 q^{87} - 19200 q^{88} - 130140 q^{89} + 1296 q^{90} + 8988 q^{91} - 25392 q^{92} + 103140 q^{93} - 125536 q^{94} - 273752 q^{95} - 27648 q^{96} + 23658 q^{97} - 247196 q^{98} + 24300 q^{99}+O(q^{100}) \) 3 * q - 12 * q^2 + 27 * q^3 + 48 * q^4 - 4 * q^5 - 108 * q^6 - 34 * q^7 - 192 * q^8 + 243 * q^9 + 16 * q^10 + 300 * q^11 + 432 * q^12 + 998 * q^13 + 136 * q^14 - 36 * q^15 + 768 * q^16 + 392 * q^17 - 972 * q^18 + 2298 * q^19 - 64 * q^20 - 306 * q^21 - 1200 * q^22 - 1587 * q^23 - 1728 * q^24 - 1167 * q^25 - 3992 * q^26 + 2187 * q^27 - 544 * q^28 - 3834 * q^29 + 144 * q^30 + 11460 * q^31 - 3072 * q^32 + 2700 * q^33 - 1568 * q^34 + 5120 * q^35 + 3888 * q^36 + 28286 * q^37 - 9192 * q^38 + 8982 * q^39 + 256 * q^40 + 11998 * q^41 + 1224 * q^42 + 33666 * q^43 + 4800 * q^44 - 324 * q^45 + 6348 * q^46 + 31384 * q^47 + 6912 * q^48 + 61799 * q^49 + 4668 * q^50 + 3528 * q^51 + 15968 * q^52 + 24144 * q^53 - 8748 * q^54 + 51944 * q^55 + 2176 * q^56 + 20682 * q^57 + 15336 * q^58 - 14532 * q^59 - 576 * q^60 + 41222 * q^61 - 45840 * q^62 - 2754 * q^63 + 12288 * q^64 + 31480 * q^65 - 10800 * q^66 + 20030 * q^67 + 6272 * q^68 - 14283 * q^69 - 20480 * q^70 - 47928 * q^71 - 15552 * q^72 + 71894 * q^73 - 113144 * q^74 - 10503 * q^75 + 36768 * q^76 - 79712 * q^77 - 35928 * q^78 + 10922 * q^79 - 1024 * q^80 + 19683 * q^81 - 47992 * q^82 - 59068 * q^83 - 4896 * q^84 - 136840 * q^85 - 134664 * q^86 - 34506 * q^87 - 19200 * q^88 - 130140 * q^89 + 1296 * q^90 + 8988 * q^91 - 25392 * q^92 + 103140 * q^93 - 125536 * q^94 - 273752 * q^95 - 27648 * q^96 + 23658 * q^97 - 247196 * q^98 + 24300 * 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
$5$	64.7679	1.15860	0.579302	−	0.815113i	$-0.303325\pi$
$5$	64.7679	1.15860	0.579302	+	0.815113i	$0.303325\pi$
$6$	−36.0000	−0.408248
$7$	−91.1204	−0.702863	−0.351431	−	0.936214i	$-0.614305\pi$
$7$	−91.1204	−0.702863	−0.351431	+	0.936214i	$0.614305\pi$
$8$	−64.0000	−0.353553
$9$	81.0000	0.333333
$10$	−259.072	−0.819257
$11$	642.496	1.60099	0.800495	−	0.599339i	$-0.204570\pi$
$11$	642.496	1.60099	0.800495	+	0.599339i	$0.204570\pi$
$12$	144.000	0.288675
$13$	597.072	0.979869	0.489935	−	0.871759i	$-0.337021\pi$
$13$	597.072	0.979869	0.489935	+	0.871759i	$0.337021\pi$
$14$	364.482	0.496999
$15$	582.911	0.668920
$16$	256.000	0.250000
$17$	−847.166	−0.710962	−0.355481	−	0.934684i	$-0.615683\pi$
$17$	−847.166	−0.710962	−0.355481	+	0.934684i	$0.615683\pi$
$18$	−324.000	−0.235702
$19$	−1415.34	−0.899450	−0.449725	−	0.893167i	$-0.648478\pi$
$19$	−1415.34	−0.899450	−0.449725	+	0.893167i	$0.648478\pi$
$20$	1036.29	0.579302
$21$	−820.084	−0.405798
$22$	−2569.98	−1.13207
$23$	−529.000	−0.208514
$23$	−529.000	−0.208514
$24$	−576.000	−0.204124
$25$	1069.88	0.342363
$26$	−2388.29	−0.692872
$27$	729.000	0.192450
$28$	−1457.93	−0.351431
$29$	3212.23	0.709270	0.354635	−	0.935005i	$-0.384605\pi$
$29$	3212.23	0.709270	0.354635	+	0.935005i	$0.384605\pi$
$30$	−2331.65	−0.472998
$31$	7261.92	1.35721	0.678605	−	0.734503i	$-0.262585\pi$
$31$	7261.92	1.35721	0.678605	+	0.734503i	$0.262585\pi$
$32$	−1024.00	−0.176777
$33$	5782.46	0.924332
$34$	3388.67	0.502726
$35$	−5901.68	−0.814340
$36$	1296.00	0.166667
$37$	7167.54	0.860728	0.430364	−	0.902656i	$-0.358385\pi$
$37$	7167.54	0.860728	0.430364	+	0.902656i	$0.358385\pi$
$38$	5661.37	0.636007
$39$	5373.65	0.565728
$40$	−4145.15	−0.409628
$41$	−10415.4	−0.967645	−0.483823	−	0.875166i	$-0.660752\pi$
$41$	−10415.4	−0.967645	−0.483823	+	0.875166i	$0.660752\pi$
$42$	3280.33	0.286943
$43$	23218.9	1.91501	0.957505	−	0.288418i	$-0.0931294\pi$
$43$	23218.9	1.91501	0.957505	+	0.288418i	$0.0931294\pi$
$44$	10279.9	0.800495
$45$	5246.20	0.386201
$46$	2116.00	0.147442
$47$	9899.93	0.653714	0.326857	−	0.945074i	$-0.394010\pi$
$47$	9899.93	0.653714	0.326857	+	0.945074i	$0.394010\pi$
$48$	2304.00	0.144338
$49$	−8504.07	−0.505984
$50$	−4279.53	−0.242087
$51$	−7624.50	−0.410474
$52$	9553.15	0.489935
$53$	9796.05	0.479028	0.239514	−	0.970893i	$-0.423012\pi$
$53$	9796.05	0.479028	0.239514	+	0.970893i	$0.423012\pi$
$54$	−2916.00	−0.136083
$55$	41613.1	1.85491
$56$	5831.71	0.248500
$57$	−12738.1	−0.519298
$58$	−12848.9	−0.501530
$59$	−4356.53	−0.162934	−0.0814668	−	0.996676i	$-0.525960\pi$
$59$	−4356.53	−0.162934	−0.0814668	+	0.996676i	$0.525960\pi$
$60$	9326.58	0.334460
$61$	−2981.75	−0.102600	−0.0512999	−	0.998683i	$-0.516336\pi$
$61$	−2981.75	−0.102600	−0.0512999	+	0.998683i	$0.516336\pi$
$62$	−29047.7	−0.959693
$63$	−7380.75	−0.234288
$64$	4096.00	0.125000
$65$	38671.1	1.13528
$66$	−23129.9	−0.653601
$67$	58230.1	1.58475	0.792374	−	0.610035i	$-0.208845\pi$
$67$	58230.1	1.58475	0.792374	+	0.610035i	$0.208845\pi$
$68$	−13554.7	−0.355481
$69$	−4761.00	−0.120386
$70$	23606.7	0.575825
$71$	−29085.1	−0.684738	−0.342369	−	0.939566i	$-0.611229\pi$
$71$	−29085.1	−0.684738	−0.342369	+	0.939566i	$0.611229\pi$
$72$	−5184.00	−0.117851
$73$	36092.3	0.792697	0.396349	−	0.918100i	$-0.370277\pi$
$73$	36092.3	0.792697	0.396349	+	0.918100i	$0.370277\pi$
$74$	−28670.2	−0.608626
$75$	9628.95	0.197663
$76$	−22645.5	−0.449725
$77$	−58544.5	−1.12528
$78$	−21494.6	−0.400030
$79$	56070.4	1.01080	0.505401	−	0.862885i	$-0.331345\pi$
$79$	56070.4	1.01080	0.505401	+	0.862885i	$0.331345\pi$
$80$	16580.6	0.289651
$81$	6561.00	0.111111
$82$	41661.6	0.684228
$83$	−4173.11	−0.0664913	−0.0332457	−	0.999447i	$-0.510584\pi$
$83$	−4173.11	−0.0664913	−0.0332457	+	0.999447i	$0.510584\pi$
$84$	−13121.3	−0.202899
$85$	−54869.2	−0.823723
$86$	−92875.7	−1.35412
$87$	28910.1	0.409497
$88$	−41119.7	−0.566035
$89$	−15386.9	−0.205909	−0.102954	−	0.994686i	$-0.532830\pi$
$89$	−15386.9	−0.205909	−0.102954	+	0.994686i	$0.532830\pi$
$90$	−20984.8	−0.273086
$91$	−54405.4	−0.688714
$92$	−8464.00	−0.104257
$93$	65357.3	0.783586
$94$	−39599.7	−0.462245
$95$	−91668.7	−1.04211
$96$	−9216.00	−0.102062
$97$	−116455.	−1.25669	−0.628345	−	0.777935i	$-0.716267\pi$
$97$	−116455.	−1.25669	−0.628345	+	0.777935i	$0.716267\pi$
$98$	34016.3	0.357785
$99$	52042.2	0.533663
$100$	17118.1	0.171181
$101$	−340.371	−0.00332008	−0.00166004	−	0.999999i	$-0.500528\pi$
$101$	−340.371	−0.00332008	−0.00166004	+	0.999999i	$0.500528\pi$
$102$	30498.0	0.290249
$103$	−114382.	−1.06234	−0.531170	−	0.847265i	$-0.678247\pi$
$103$	−114382.	−1.06234	−0.531170	+	0.847265i	$0.678247\pi$
$104$	−38212.6	−0.346436
$105$	−53115.1	−0.470159
$106$	−39184.2	−0.338724
$107$	−210235.	−1.77519	−0.887595	−	0.460624i	$-0.847625\pi$
$107$	−210235.	−1.77519	−0.887595	+	0.460624i	$0.847625\pi$
$108$	11664.0	0.0962250
$109$	−136604.	−1.10128	−0.550640	−	0.834743i	$-0.685616\pi$
$109$	−136604.	−1.10128	−0.550640	+	0.834743i	$0.685616\pi$
$110$	−166452.	−1.31162
$111$	64507.8	0.496941
$112$	−23326.8	−0.175716
$113$	172475.	1.27066	0.635330	−	0.772241i	$-0.280864\pi$
$113$	172475.	1.27066	0.635330	+	0.772241i	$0.280864\pi$
$114$	50952.3	0.367199
$115$	−34262.2	−0.241586
$116$	51395.7	0.354635
$117$	48362.8	0.326623
$118$	17426.1	0.115211
$119$	77194.1	0.499709
$120$	−37306.3	−0.236499
$121$	251750.	1.56317
$122$	11927.0	0.0725490
$123$	−93738.6	−0.558670
$124$	116191.	0.678605
$125$	−133106.	−0.761941
$126$	29523.0	0.165666
$127$	291436.	1.60337	0.801684	−	0.597748i	$-0.203938\pi$
$127$	291436.	1.60337	0.801684	+	0.597748i	$0.203938\pi$
$128$	−16384.0	−0.0883883
$129$	208970.	1.10563
$130$	−154684.	−0.802764
$131$	−172218.	−0.876802	−0.438401	−	0.898780i	$-0.644455\pi$
$131$	−172218.	−0.876802	−0.438401	+	0.898780i	$0.644455\pi$
$132$	92519.4	0.462166
$133$	128966.	0.632190
$134$	−232920.	−1.12059
$135$	47215.8	0.222973
$136$	54218.6	0.251363
$137$	39849.0	0.181391	0.0906956	−	0.995879i	$-0.471091\pi$
$137$	39849.0	0.181391	0.0906956	+	0.995879i	$0.471091\pi$
$138$	19044.0	0.0851257
$139$	−242196.	−1.06324	−0.531619	−	0.846984i	$-0.678416\pi$
$139$	−242196.	−1.06324	−0.531619	+	0.846984i	$0.678416\pi$
$140$	−94426.9	−0.407170
$141$	89099.4	0.377422
$142$	116340.	0.484183
$143$	383616.	1.56876
$144$	20736.0	0.0833333
$145$	208049.	0.821763
$146$	−144369.	−0.560522
$147$	−76536.6	−0.292130
$148$	114681.	0.430364
$149$	−353404.	−1.30408	−0.652042	−	0.758183i	$-0.726087\pi$
$149$	−353404.	−1.30408	−0.652042	+	0.758183i	$0.726087\pi$
$150$	−38515.8	−0.139769
$151$	−366057.	−1.30649	−0.653246	−	0.757146i	$-0.726593\pi$
$151$	−366057.	−1.30649	−0.653246	+	0.757146i	$0.726593\pi$
$152$	90581.8	0.318004
$153$	−68620.5	−0.236987
$154$	234178.	0.795691
$155$	470340.	1.57247
$156$	85978.3	0.282864
$157$	41721.2	0.135085	0.0675427	−	0.997716i	$-0.478484\pi$
$157$	41721.2	0.135085	0.0675427	+	0.997716i	$0.478484\pi$
$158$	−224282.	−0.714745
$159$	88164.5	0.276567
$160$	−66322.3	−0.204814
$161$	48202.7	0.146557
$162$	−26244.0	−0.0785674
$163$	427382.	1.25993	0.629966	−	0.776623i	$-0.283069\pi$
$163$	427382.	1.25993	0.629966	+	0.776623i	$0.283069\pi$
$164$	−166646.	−0.483823
$165$	374518.	1.07093
$166$	16692.4	0.0470165
$167$	−448886.	−1.24550	−0.622751	−	0.782420i	$-0.713985\pi$
$167$	−448886.	−1.24550	−0.622751	+	0.782420i	$0.713985\pi$
$168$	52485.4	0.143471
$169$	−14798.4	−0.0398564
$170$	219477.	0.582460
$171$	−114643.	−0.299817
$172$	371503.	0.957505
$173$	−485205.	−1.23257	−0.616283	−	0.787525i	$-0.711362\pi$
$173$	−485205.	−1.23257	−0.616283	+	0.787525i	$0.711362\pi$
$174$	−115640.	−0.289558
$175$	−97488.2	−0.240634
$176$	164479.	0.400247
$177$	−39208.8	−0.0940697
$178$	61547.4	0.145600
$179$	−19129.9	−0.0446252	−0.0223126	−	0.999751i	$-0.507103\pi$
$179$	−19129.9	−0.0446252	−0.0223126	+	0.999751i	$0.507103\pi$
$180$	83939.2	0.193101
$181$	−332236.	−0.753790	−0.376895	−	0.926256i	$-0.623008\pi$
$181$	−332236.	−0.753790	−0.376895	+	0.926256i	$0.623008\pi$
$182$	217622.	0.486994
$183$	−26835.7	−0.0592360
$184$	33856.0	0.0737210
$185$	464227.	0.997242
$186$	−261429.	−0.554079
$187$	−544301.	−1.13824
$188$	158399.	0.326857
$189$	−66426.8	−0.135266
$190$	366675.	0.736881
$191$	468920.	0.930070	0.465035	−	0.885292i	$-0.346042\pi$
$191$	468920.	0.930070	0.465035	+	0.885292i	$0.346042\pi$
$192$	36864.0	0.0721688
$193$	154139.	0.297864	0.148932	−	0.988847i	$-0.452416\pi$
$193$	154139.	0.297864	0.148932	+	0.988847i	$0.452416\pi$
$194$	465819.	0.888613
$195$	348040.	0.655454
$196$	−136065.	−0.252992
$197$	−205747.	−0.377718	−0.188859	−	0.982004i	$-0.560479\pi$
$197$	−205747.	−0.377718	−0.188859	+	0.982004i	$0.560479\pi$
$198$	−208169.	−0.377357
$199$	−1.07026e6	−1.91582	−0.957910	−	0.287068i	$-0.907319\pi$
$199$	−1.07026e6	−1.91582	−0.957910	+	0.287068i	$0.907319\pi$
$200$	−68472.5	−0.121043
$201$	524071.	0.914955
$202$	1361.48	0.00234765
$203$	−292700.	−0.498519
$204$	−121992.	−0.205237
$205$	−674583.	−1.12112
$206$	457527.	0.751187
$207$	−42849.0	−0.0695048
$208$	152850.	0.244967
$209$	−909351.	−1.44001
$210$	212460.	0.332453
$211$	872488.	1.34913	0.674565	−	0.738216i	$-0.264331\pi$
$211$	872488.	1.34913	0.674565	+	0.738216i	$0.264331\pi$
$212$	156737.	0.239514
$213$	−261766.	−0.395334
$214$	840939.	1.25525
$215$	1.50384e6	2.21874
$216$	−46656.0	−0.0680414
$217$	−661709.	−0.953933
$218$	546416.	0.778722
$219$	324831.	0.457664
$220$	665810.	0.927456
$221$	−505819.	−0.696650
$222$	−258031.	−0.351391
$223$	1.34295e6	1.80842	0.904210	−	0.427088i	$-0.140461\pi$
$223$	1.34295e6	1.80842	0.904210	+	0.427088i	$0.140461\pi$
$224$	93307.3	0.124250
$225$	86660.5	0.114121
$226$	−689899.	−0.898492
$227$	−1.34791e6	−1.73618	−0.868090	−	0.496407i	$-0.834652\pi$
$227$	−1.34791e6	−1.73618	−0.868090	+	0.496407i	$0.834652\pi$
$228$	−203809.	−0.259649
$229$	−248094.	−0.312627	−0.156314	−	0.987707i	$-0.549961\pi$
$229$	−248094.	−0.312627	−0.156314	+	0.987707i	$0.549961\pi$
$230$	137049.	0.170827
$231$	−526900.	−0.649679
$232$	−205583.	−0.250765
$233$	−484670.	−0.584866	−0.292433	−	0.956286i	$-0.594465\pi$
$233$	−484670.	−0.584866	−0.292433	+	0.956286i	$0.594465\pi$
$234$	−193451.	−0.230957
$235$	641198.	0.757395
$236$	−69704.5	−0.0814668
$237$	504634.	0.583587
$238$	−308777.	−0.353347
$239$	889692.	1.00750	0.503750	−	0.863849i	$-0.331953\pi$
$239$	889692.	1.00750	0.503750	+	0.863849i	$0.331953\pi$
$240$	149225.	0.167230
$241$	−897939.	−0.995873	−0.497937	−	0.867213i	$-0.665909\pi$
$241$	−897939.	−0.995873	−0.497937	+	0.867213i	$0.665909\pi$
$242$	−1.00700e6	−1.10533
$243$	59049.0	0.0641500
$244$	−47708.0	−0.0512999
$245$	−550791.	−0.586235
$246$	374954.	0.395039
$247$	−845060.	−0.881344
$248$	−464763.	−0.479846
$249$	−37558.0	−0.0383888
$250$	532423.	0.538774
$251$	1.55905e6	1.56198	0.780992	−	0.624541i	$-0.214714\pi$
$251$	1.55905e6	1.56198	0.780992	+	0.624541i	$0.214714\pi$
$252$	−118092.	−0.117144
$253$	−339880.	−0.333829
$254$	−1.16574e6	−1.13375
$255$	−493823.	−0.475577
$256$	65536.0	0.0625000
$257$	−941940.	−0.889591	−0.444795	−	0.895632i	$-0.646724\pi$
$257$	−941940.	−0.889591	−0.444795	+	0.895632i	$0.646724\pi$
$258$	−835881.	−0.781799
$259$	−653109.	−0.604973
$260$	618737.	0.567640
$261$	260191.	0.236423
$262$	688874.	0.619992
$263$	1.13147e6	1.00868	0.504339	−	0.863506i	$-0.331736\pi$
$263$	1.13147e6	1.00868	0.504339	+	0.863506i	$0.331736\pi$
$264$	−370078.	−0.326801
$265$	634470.	0.555004
$266$	−515866.	−0.447026
$267$	−138482.	−0.118882
$268$	931681.	0.792374
$269$	994630.	0.838071	0.419036	−	0.907970i	$-0.362368\pi$
$269$	994630.	0.838071	0.419036	+	0.907970i	$0.362368\pi$
$270$	−188863.	−0.157666
$271$	−1.03444e6	−0.855625	−0.427813	−	0.903867i	$-0.640716\pi$
$271$	−1.03444e6	−0.855625	−0.427813	+	0.903867i	$0.640716\pi$
$272$	−216875.	−0.177740
$273$	−489649.	−0.397629
$274$	−159396.	−0.128263
$275$	687396.	0.548119
$276$	−76176.0	−0.0601929
$277$	−993217.	−0.777759	−0.388879	−	0.921289i	$-0.627138\pi$
$277$	−993217.	−0.777759	−0.388879	+	0.921289i	$0.627138\pi$
$278$	968785.	0.751823
$279$	588216.	0.452404
$280$	377707.	0.287912
$281$	1.74862e6	1.32109	0.660543	−	0.750789i	$-0.270326\pi$
$281$	1.74862e6	1.32109	0.660543	+	0.750789i	$0.270326\pi$
$282$	−356398.	−0.266878
$283$	406623.	0.301805	0.150902	−	0.988549i	$-0.451782\pi$
$283$	406623.	0.301805	0.150902	+	0.988549i	$0.451782\pi$
$284$	−465361.	−0.342369
$285$	−825018.	−0.601660
$286$	−1.53446e6	−1.10928
$287$	949055.	0.680122
$288$	−82944.0	−0.0589256
$289$	−702166.	−0.494533
$290$	−832198.	−0.581074
$291$	−1.04809e6	−0.725550
$292$	577477.	0.396349
$293$	−1.67185e6	−1.13770	−0.568851	−	0.822440i	$-0.692612\pi$
$293$	−1.67185e6	−1.13770	−0.568851	+	0.822440i	$0.692612\pi$
$294$	306147.	0.206567
$295$	−282163.	−0.188775
$296$	−458722.	−0.304313
$297$	468379.	0.308111
$298$	1.41362e6	0.922126
$299$	−315851.	−0.204317
$300$	154063.	0.0988316
$301$	−2.11572e6	−1.34599
$302$	1.46423e6	0.923829
$303$	−3063.34	−0.00191685
$304$	−362327.	−0.224863
$305$	−193122.	−0.118872
$306$	274482.	0.167575
$307$	−20962.2	−0.0126938	−0.00634688	−	0.999980i	$-0.502020\pi$
$307$	−20962.2	−0.0126938	−0.00634688	+	0.999980i	$0.502020\pi$
$308$	−936712.	−0.562638
$309$	−1.02943e6	−0.613342
$310$	−1.88136e6	−1.11190
$311$	−452612.	−0.265354	−0.132677	−	0.991159i	$-0.542357\pi$
$311$	−452612.	−0.265354	−0.132677	+	0.991159i	$0.542357\pi$
$312$	−343913.	−0.200015
$313$	−511910.	−0.295347	−0.147674	−	0.989036i	$-0.547178\pi$
$313$	−511910.	−0.295347	−0.147674	+	0.989036i	$0.547178\pi$
$314$	−166885.	−0.0955197
$315$	−478036.	−0.271447
$316$	897126.	0.505401
$317$	−2.29859e6	−1.28473	−0.642367	−	0.766397i	$-0.722047\pi$
$317$	−2.29859e6	−1.28473	−0.642367	+	0.766397i	$0.722047\pi$
$318$	−352658.	−0.195563
$319$	2.06384e6	1.13553
$320$	265289.	0.144825
$321$	−1.89211e6	−1.02491
$322$	−192811.	−0.103631
$323$	1.19903e6	0.639475
$324$	104976.	0.0555556
$325$	638797.	0.335471
$326$	−1.70953e6	−0.890906
$327$	−1.22944e6	−0.635824
$328$	666585.	0.342114
$329$	−902086.	−0.459471
$330$	−1.49807e6	−0.757265
$331$	−1.34111e6	−0.672812	−0.336406	−	0.941717i	$-0.609211\pi$
$331$	−1.34111e6	−0.672812	−0.336406	+	0.941717i	$0.609211\pi$
$332$	−66769.8	−0.0332457
$333$	580571.	0.286909
$334$	1.79554e6	0.880703
$335$	3.77144e6	1.83610
$336$	−209941.	−0.101450
$337$	−154408.	−0.0740620	−0.0370310	−	0.999314i	$-0.511790\pi$
$337$	−154408.	−0.0740620	−0.0370310	+	0.999314i	$0.511790\pi$
$338$	59193.7	0.0281828
$339$	1.55227e6	0.733616
$340$	−877907.	−0.411862
$341$	4.66575e6	2.17288
$342$	458571.	0.212002
$343$	2.30636e6	1.05850
$344$	−1.48601e6	−0.677058
$345$	−308360.	−0.139480
$346$	1.94082e6	0.871556
$347$	−1.14040e6	−0.508431	−0.254215	−	0.967148i	$-0.581817\pi$
$347$	−1.14040e6	−0.508431	−0.254215	+	0.967148i	$0.581817\pi$
$348$	462561.	0.204749
$349$	2.74115e6	1.20467	0.602336	−	0.798243i	$-0.294237\pi$
$349$	2.74115e6	1.20467	0.602336	+	0.798243i	$0.294237\pi$
$350$	389953.	0.170154
$351$	435265.	0.188576
$352$	−657916.	−0.283018
$353$	−1.21911e6	−0.520723	−0.260361	−	0.965511i	$-0.583842\pi$
$353$	−1.21911e6	−0.520723	−0.260361	+	0.965511i	$0.583842\pi$
$354$	156835.	0.0665174
$355$	−1.88378e6	−0.793340
$356$	−246190.	−0.102954
$357$	694747.	0.288507
$358$	76519.6	0.0315548
$359$	250131.	0.102431	0.0512155	−	0.998688i	$-0.483690\pi$
$359$	250131.	0.102431	0.0512155	+	0.998688i	$0.483690\pi$
$360$	−335757.	−0.136543
$361$	−472908.	−0.190989
$362$	1.32894e6	0.533010
$363$	2.26575e6	0.902496
$364$	−870487.	−0.344357
$365$	2.33762e6	0.918422
$366$	107343.	0.0418862
$367$	2.30403e6	0.892940	0.446470	−	0.894799i	$-0.352681\pi$
$367$	2.30403e6	0.892940	0.446470	+	0.894799i	$0.352681\pi$
$368$	−135424.	−0.0521286
$369$	−843647.	−0.322548
$370$	−1.85691e6	−0.705157
$371$	−892620.	−0.336691
$372$	1.04572e6	0.391793
$373$	−2.90923e6	−1.08269	−0.541347	−	0.840800i	$-0.682085\pi$
$373$	−2.90923e6	−1.08269	−0.541347	+	0.840800i	$0.682085\pi$
$374$	2.17720e6	0.804859
$375$	−1.19795e6	−0.439907
$376$	−633596.	−0.231123
$377$	1.91793e6	0.694992
$378$	265707.	0.0956475
$379$	478085.	0.170965	0.0854825	−	0.996340i	$-0.472757\pi$
$379$	478085.	0.170965	0.0854825	+	0.996340i	$0.472757\pi$
$380$	−1.46670e6	−0.521053
$381$	2.62292e6	0.925705
$382$	−1.87568e6	−0.657659
$383$	2.97658e6	1.03686	0.518431	−	0.855120i	$-0.326516\pi$
$383$	2.97658e6	1.03686	0.518431	+	0.855120i	$0.326516\pi$
$384$	−147456.	−0.0510310
$385$	−3.79180e6	−1.30375
$386$	−616554.	−0.210622
$387$	1.88073e6	0.638336
$388$	−1.86328e6	−0.628345
$389$	2.16865e6	0.726634	0.363317	−	0.931666i	$-0.381644\pi$
$389$	2.16865e6	0.726634	0.363317	+	0.931666i	$0.381644\pi$
$390$	−1.39216e6	−0.463476
$391$	448151.	0.148246
$392$	544261.	0.178892
$393$	−1.54997e6	−0.506222
$394$	822988.	0.267087
$395$	3.63156e6	1.17112
$396$	832675.	0.266832
$397$	−1.03445e6	−0.329407	−0.164703	−	0.986343i	$-0.552667\pi$
$397$	−1.03445e6	−0.329407	−0.164703	+	0.986343i	$0.552667\pi$
$398$	4.28102e6	1.35469
$399$	1.16070e6	0.364995
$400$	273890.	0.0855907
$401$	3.75892e6	1.16735	0.583677	−	0.811986i	$-0.301614\pi$
$401$	3.75892e6	1.16735	0.583677	+	0.811986i	$0.301614\pi$
$402$	−2.09628e6	−0.646971
$403$	4.33589e6	1.32989
$404$	−5445.94	−0.00166004
$405$	424942.	0.128734
$406$	1.17080e6	0.352507
$407$	4.60511e6	1.37802
$408$	487968.	0.145125
$409$	−5.06193e6	−1.49626	−0.748131	−	0.663551i	$-0.769049\pi$
$409$	−5.06193e6	−1.49626	−0.748131	+	0.663551i	$0.769049\pi$
$410$	2.69833e6	0.792750
$411$	358641.	0.104726
$412$	−1.83011e6	−0.531170
$413$	396969.	0.114520
$414$	171396.	0.0491473
$415$	−270284.	−0.0770371
$416$	−611401.	−0.173218
$417$	−2.17977e6	−0.613861
$418$	3.63740e6	1.01824
$419$	717508.	0.199660	0.0998301	−	0.995004i	$-0.468170\pi$
$419$	717508.	0.199660	0.0998301	+	0.995004i	$0.468170\pi$
$420$	−849842.	−0.235080
$421$	−2.29027e6	−0.629770	−0.314885	−	0.949130i	$-0.601966\pi$
$421$	−2.29027e6	−0.629770	−0.314885	+	0.949130i	$0.601966\pi$
$422$	−3.48995e6	−0.953978
$423$	801895.	0.217905
$424$	−626947.	−0.169362
$425$	−906369.	−0.243407
$426$	1.04706e6	0.279543
$427$	271698.	0.0721136
$428$	−3.36375e6	−0.887595
$429$	3.45254e6	0.905724
$430$	−6.01536e6	−1.56888
$431$	−4.38974e6	−1.13827	−0.569135	−	0.822244i	$-0.692722\pi$
$431$	−4.38974e6	−1.13827	−0.569135	+	0.822244i	$0.692722\pi$
$432$	186624.	0.0481125
$433$	4.31759e6	1.10668	0.553339	−	0.832956i	$-0.313353\pi$
$433$	4.31759e6	1.10668	0.553339	+	0.832956i	$0.313353\pi$
$434$	2.64684e6	0.674532
$435$	1.87244e6	0.474445
$436$	−2.18567e6	−0.550640
$437$	748716.	0.187548
$438$	−1.29932e6	−0.323617
$439$	5.67489e6	1.40539	0.702694	−	0.711492i	$-0.251980\pi$
$439$	5.67489e6	1.40539	0.702694	+	0.711492i	$0.251980\pi$
$440$	−2.66324e6	−0.655811
$441$	−688830.	−0.168661
$442$	2.02328e6	0.492606
$443$	−6.52521e6	−1.57974	−0.789869	−	0.613276i	$-0.789851\pi$
$443$	−6.52521e6	−1.57974	−0.789869	+	0.613276i	$0.789851\pi$
$444$	1.03213e6	0.248471
$445$	−996575.	−0.238567
$446$	−5.37182e6	−1.27875
$447$	−3.18063e6	−0.752913
$448$	−373229.	−0.0878579
$449$	−2.65518e6	−0.621553	−0.310777	−	0.950483i	$-0.600589\pi$
$449$	−2.65518e6	−0.621553	−0.310777	+	0.950483i	$0.600589\pi$
$450$	−346642.	−0.0806957
$451$	−6.69185e6	−1.54919
$452$	2.75960e6	0.635330
$453$	−3.29451e6	−0.754303
$454$	5.39162e6	1.22766
$455$	−3.52373e6	−0.797946
$456$	815237.	0.183600
$457$	6.80045e6	1.52317	0.761583	−	0.648067i	$-0.224422\pi$
$457$	6.80045e6	1.52317	0.761583	+	0.648067i	$0.224422\pi$
$458$	992375.	0.221061
$459$	−617584.	−0.136825
$460$	−548196.	−0.120793
$461$	−4.89587e6	−1.07294	−0.536472	−	0.843918i	$-0.680243\pi$
$461$	−4.89587e6	−1.07294	−0.536472	+	0.843918i	$0.680243\pi$
$462$	2.10760e6	0.459392
$463$	5.32386e6	1.15418	0.577091	−	0.816680i	$-0.304188\pi$
$463$	5.32386e6	1.15418	0.577091	+	0.816680i	$0.304188\pi$
$464$	822331.	0.177317
$465$	4.23306e6	0.907866
$466$	1.93868e6	0.413563
$467$	3.26412e6	0.692587	0.346293	−	0.938126i	$-0.387440\pi$
$467$	3.26412e6	0.692587	0.346293	+	0.938126i	$0.387440\pi$
$468$	773805.	0.163312
$469$	−5.30595e6	−1.11386
$470$	−2.56479e6	−0.535559
$471$	375491.	0.0779915
$472$	278818.	0.0576057
$473$	1.49181e7	3.06591
$474$	−2.01853e6	−0.412658
$475$	−1.51425e6	−0.307938
$476$	1.23511e6	0.249854
$477$	793480.	0.159676
$478$	−3.55877e6	−0.712410
$479$	−4.16002e6	−0.828431	−0.414215	−	0.910179i	$-0.635944\pi$
$479$	−4.16002e6	−0.828431	−0.414215	+	0.910179i	$0.635944\pi$
$480$	−596901.	−0.118250
$481$	4.27953e6	0.843400
$482$	3.59176e6	0.704189
$483$	433824.	0.0846147
$484$	4.02800e6	0.781584
$485$	−7.54253e6	−1.45600
$486$	−236196.	−0.0453609
$487$	−4.66023e6	−0.890399	−0.445200	−	0.895431i	$-0.646867\pi$
$487$	−4.66023e6	−0.890399	−0.445200	+	0.895431i	$0.646867\pi$
$488$	190832.	0.0362745
$489$	3.84644e6	0.727422
$490$	2.20316e6	0.414531
$491$	−9.57303e6	−1.79203	−0.896016	−	0.444022i	$-0.853551\pi$
$491$	−9.57303e6	−1.79203	−0.896016	+	0.444022i	$0.853551\pi$
$492$	−1.49982e6	−0.279335
$493$	−2.72129e6	−0.504264
$494$	3.38024e6	0.623204
$495$	3.37066e6	0.618304
$496$	1.85905e6	0.339303
$497$	2.65024e6	0.481277
$498$	150232.	0.0271450
$499$	6.08673e6	1.09429	0.547145	−	0.837038i	$-0.315715\pi$
$499$	6.08673e6	1.09429	0.547145	+	0.837038i	$0.315715\pi$
$500$	−2.12969e6	−0.380971
$501$	−4.03997e6	−0.719091
$502$	−6.23621e6	−1.10449
$503$	−1.04347e7	−1.83892	−0.919458	−	0.393189i	$-0.871372\pi$
$503$	−1.04347e7	−1.83892	−0.919458	+	0.393189i	$0.871372\pi$
$504$	472368.	0.0828332
$505$	−22045.1	−0.00384666
$506$	1.35952e6	0.236053
$507$	−133186.	−0.0230111
$508$	4.66297e6	0.801684
$509$	−7.33426e6	−1.25476	−0.627382	−	0.778712i	$-0.715873\pi$
$509$	−7.33426e6	−1.25476	−0.627382	+	0.778712i	$0.715873\pi$
$510$	1.97529e6	0.336284
$511$	−3.28875e6	−0.557158
$512$	−262144.	−0.0441942
$513$	−1.03178e6	−0.173099
$514$	3.76776e6	0.629036
$515$	−7.40826e6	−1.23083
$516$	3.34352e6	0.552815
$517$	6.36067e6	1.04659
$518$	2.61244e6	0.427781
$519$	−4.36685e6	−0.711623
$520$	−2.47495e6	−0.401382
$521$	−8.69631e6	−1.40359	−0.701796	−	0.712378i	$-0.747618\pi$
$521$	−8.69631e6	−1.40359	−0.701796	+	0.712378i	$0.747618\pi$
$522$	−1.04076e6	−0.167177
$523$	−848755.	−0.135684	−0.0678419	−	0.997696i	$-0.521611\pi$
$523$	−848755.	−0.135684	−0.0678419	+	0.997696i	$0.521611\pi$
$524$	−2.75549e6	−0.438401
$525$	−877394.	−0.138930
$526$	−4.52587e6	−0.713244
$527$	−6.15205e6	−0.964925
$528$	1.48031e6	0.231083
$529$	279841.	0.0434783
$530$	−2.53788e6	−0.392447
$531$	−352879.	−0.0543112
$532$	2.06346e6	0.316095
$533$	−6.21874e6	−0.948166
$534$	553927.	0.0840619
$535$	−1.36165e7	−2.05674
$536$	−3.72672e6	−0.560293
$537$	−172169.	−0.0257644
$538$	−3.97852e6	−0.592606
$539$	−5.46383e6	−0.810075
$540$	755453.	0.111487
$541$	−3.49531e6	−0.513443	−0.256721	−	0.966485i	$-0.582642\pi$
$541$	−3.49531e6	−0.513443	−0.256721	+	0.966485i	$0.582642\pi$
$542$	4.13777e6	0.605018
$543$	−2.99012e6	−0.435201
$544$	867498.	0.125682
$545$	−8.84756e6	−1.27595
$546$	1.95860e6	0.281166
$547$	4.41628e6	0.631086	0.315543	−	0.948911i	$-0.397813\pi$
$547$	4.41628e6	0.631086	0.315543	+	0.948911i	$0.397813\pi$
$548$	637584.	0.0906956
$549$	−241522.	−0.0341999
$550$	−2.74958e6	−0.387579
$551$	−4.54640e6	−0.637953
$552$	304704.	0.0425628
$553$	−5.10916e6	−0.710455
$554$	3.97287e6	0.549958
$555$	4.17804e6	0.575758
$556$	−3.87514e6	−0.531619
$557$	−2.52341e6	−0.344627	−0.172313	−	0.985042i	$-0.555124\pi$
$557$	−2.52341e6	−0.344627	−0.172313	+	0.985042i	$0.555124\pi$
$558$	−2.35286e6	−0.319898
$559$	1.38634e7	1.87646
$560$	−1.51083e6	−0.203585
$561$	−4.89871e6	−0.657165
$562$	−6.99450e6	−0.934148
$563$	1.32274e7	1.75874	0.879372	−	0.476136i	$-0.157963\pi$
$563$	1.32274e7	1.75874	0.879372	+	0.476136i	$0.157963\pi$
$564$	1.42559e6	0.188711
$565$	1.11708e7	1.47219
$566$	−1.62649e6	−0.213408
$567$	−597841.	−0.0780959
$568$	1.86144e6	0.242091
$569$	−6.92728e6	−0.896979	−0.448489	−	0.893788i	$-0.648038\pi$
$569$	−6.92728e6	−0.896979	−0.448489	+	0.893788i	$0.648038\pi$
$570$	3.30007e6	0.425438
$571$	8.78305e6	1.12734	0.563671	−	0.826000i	$-0.309389\pi$
$571$	8.78305e6	1.12734	0.563671	+	0.826000i	$0.309389\pi$
$572$	6.13786e6	0.784380
$573$	4.22028e6	0.536976
$574$	−3.79622e6	−0.480919
$575$	−565968.	−0.0713875
$576$	331776.	0.0416667
$577$	3.64088e6	0.455267	0.227634	−	0.973747i	$-0.426901\pi$
$577$	3.64088e6	0.455267	0.227634	+	0.973747i	$0.426901\pi$
$578$	2.80867e6	0.349688
$579$	1.38725e6	0.171972
$580$	3.32879e6	0.410881
$581$	380256.	0.0467343
$582$	4.19237e6	0.513041
$583$	6.29392e6	0.766920
$584$	−2.30991e6	−0.280261
$585$	3.13236e6	0.378427
$586$	6.68741e6	0.804477
$587$	−2.49805e6	−0.299231	−0.149615	−	0.988744i	$-0.547804\pi$
$587$	−2.49805e6	−0.299231	−0.149615	+	0.988744i	$0.547804\pi$
$588$	−1.22459e6	−0.146065
$589$	−1.02781e7	−1.22074
$590$	1.12865e6	0.133484
$591$	−1.85172e6	−0.218076
$592$	1.83489e6	0.215182
$593$	1.62002e7	1.89183	0.945917	−	0.324410i	$-0.105166\pi$
$593$	1.62002e7	1.89183	0.945917	+	0.324410i	$0.105166\pi$
$594$	−1.87352e6	−0.217867
$595$	4.99970e6	0.578964
$596$	−5.65446e6	−0.652042
$597$	−9.63230e6	−1.10610
$598$	1.26340e6	0.144474
$599$	−3.58952e6	−0.408761	−0.204381	−	0.978891i	$-0.565518\pi$
$599$	−3.58952e6	−0.408761	−0.204381	+	0.978891i	$0.565518\pi$
$600$	−616253.	−0.0698845
$601$	−520693.	−0.0588025	−0.0294012	−	0.999568i	$-0.509360\pi$
$601$	−520693.	−0.0588025	−0.0294012	+	0.999568i	$0.509360\pi$
$602$	8.46287e6	0.951758
$603$	4.71664e6	0.528249
$604$	−5.85691e6	−0.653246
$605$	1.63053e7	1.81109
$606$	12253.4	0.00135542
$607$	1.75753e7	1.93612	0.968059	−	0.250723i	$-0.0806685\pi$
$607$	1.75753e7	1.93612	0.968059	+	0.250723i	$0.0806685\pi$
$608$	1.44931e6	0.159002
$609$	−2.63430e6	−0.287820
$610$	772486.	0.0840555
$611$	5.91097e6	0.640554
$612$	−1.09793e6	−0.118494
$613$	−2.95142e6	−0.317234	−0.158617	−	0.987340i	$-0.550703\pi$
$613$	−2.95142e6	−0.317234	−0.158617	+	0.987340i	$0.550703\pi$
$614$	83848.7	0.00897585
$615$	−6.07125e6	−0.647277
$616$	3.74685e6	0.397845
$617$	−9.09331e6	−0.961633	−0.480816	−	0.876821i	$-0.659660\pi$
$617$	−9.09331e6	−0.961633	−0.480816	+	0.876821i	$0.659660\pi$
$618$	4.11774e6	0.433698
$619$	1.20302e7	1.26197	0.630983	−	0.775796i	$-0.282652\pi$
$619$	1.20302e7	1.26197	0.630983	+	0.775796i	$0.282652\pi$
$620$	7.52543e6	0.786235
$621$	−385641.	−0.0401286
$622$	1.81045e6	0.187634
$623$	1.40206e6	0.144726
$624$	1.37565e6	0.141432
$625$	−1.19644e7	−1.22515
$626$	2.04764e6	0.208842
$627$	−8.18416e6	−0.831391
$628$	667540.	0.0675427
$629$	−6.07210e6	−0.611945
$630$	1.91214e6	0.191942
$631$	−1.59449e7	−1.59422	−0.797110	−	0.603834i	$-0.793639\pi$
$631$	−1.59449e7	−1.59422	−0.797110	+	0.603834i	$0.793639\pi$
$632$	−3.58851e6	−0.357372
$633$	7.85240e6	0.778920
$634$	9.19435e6	0.908444
$635$	1.88757e7	1.85767
$636$	1.41063e6	0.138284
$637$	−5.07754e6	−0.495798
$638$	−8.25538e6	−0.802944
$639$	−2.35589e6	−0.228246
$640$	−1.06116e6	−0.102407
$641$	1.34900e7	1.29678	0.648392	−	0.761307i	$-0.275442\pi$
$641$	1.34900e7	1.29678	0.648392	+	0.761307i	$0.275442\pi$
$642$	7.56845e6	0.724718
$643$	1.35668e7	1.29405	0.647024	−	0.762470i	$-0.276013\pi$
$643$	1.35668e7	1.29405	0.647024	+	0.762470i	$0.276013\pi$
$644$	771243.	0.0732785
$645$	1.35346e7	1.28099
$646$	−4.79612e6	−0.452177
$647$	−129098.	−0.0121244	−0.00606219	−	0.999982i	$-0.501930\pi$
$647$	−129098.	−0.0121244	−0.00606219	+	0.999982i	$0.501930\pi$
$648$	−419904.	−0.0392837
$649$	−2.79905e6	−0.260855
$650$	−2.55519e6	−0.237214
$651$	−5.95538e6	−0.550753
$652$	6.83811e6	0.629966
$653$	−1.32353e6	−0.121465	−0.0607326	−	0.998154i	$-0.519344\pi$
$653$	−1.32353e6	−0.121465	−0.0607326	+	0.998154i	$0.519344\pi$
$654$	4.91775e6	0.449595
$655$	−1.11542e7	−1.01587
$656$	−2.66634e6	−0.241911
$657$	2.92348e6	0.264232
$658$	3.60834e6	0.324895
$659$	−2.76516e6	−0.248031	−0.124016	−	0.992280i	$-0.539577\pi$
$659$	−2.76516e6	−0.248031	−0.124016	+	0.992280i	$0.539577\pi$
$660$	5.99229e6	0.535467
$661$	1.80965e7	1.61099	0.805493	−	0.592605i	$-0.201901\pi$
$661$	1.80965e7	1.61099	0.805493	+	0.592605i	$0.201901\pi$
$662$	5.36443e6	0.475750
$663$	−4.55237e6	−0.402211
$664$	267079.	0.0235082
$665$	8.35289e6	0.732458
$666$	−2.32228e6	−0.202875
$667$	−1.69927e6	−0.147893
$668$	−7.18217e6	−0.622751
$669$	1.20866e7	1.04409
$670$	−1.50858e7	−1.29832
$671$	−1.91576e6	−0.164261
$672$	839766.	0.0717356
$673$	−1.42177e7	−1.21001	−0.605007	−	0.796220i	$-0.706830\pi$
$673$	−1.42177e7	−1.21001	−0.605007	+	0.796220i	$0.706830\pi$
$674$	617632.	0.0523697
$675$	779945.	0.0658877
$676$	−236775.	−0.0199282
$677$	−2.24474e7	−1.88233	−0.941163	−	0.337953i	$-0.890265\pi$
$677$	−2.24474e7	−1.88233	−0.941163	+	0.337953i	$0.890265\pi$
$678$	−6.20909e6	−0.518745
$679$	1.06114e7	0.883280
$680$	3.51163e6	0.291230
$681$	−1.21311e7	−1.00238
$682$	−1.86630e7	−1.53646
$683$	1.65590e7	1.35826	0.679129	−	0.734019i	$-0.262358\pi$
$683$	1.65590e7	1.35826	0.679129	+	0.734019i	$0.262358\pi$
$684$	−1.83428e6	−0.149908
$685$	2.58094e6	0.210160
$686$	−9.22542e6	−0.748473
$687$	−2.23284e6	−0.180496
$688$	5.94404e6	0.478752
$689$	5.84894e6	0.469385
$690$	1.23344e6	0.0986269
$691$	7.16950e6	0.571207	0.285603	−	0.958348i	$-0.407806\pi$
$691$	7.16950e6	0.571207	0.285603	+	0.958348i	$0.407806\pi$
$692$	−7.76329e6	−0.616283
$693$	−4.74210e6	−0.375092
$694$	4.56158e6	0.359515
$695$	−1.56865e7	−1.23187
$696$	−1.85024e6	−0.144779
$697$	8.82357e6	0.687959
$698$	−1.09646e7	−0.851831
$699$	−4.36203e6	−0.337673
$700$	−1.55981e6	−0.120317
$701$	3.10925e6	0.238979	0.119490	−	0.992835i	$-0.461874\pi$
$701$	3.10925e6	0.238979	0.119490	+	0.992835i	$0.461874\pi$
$702$	−1.74106e6	−0.133343
$703$	−1.01445e7	−0.774182
$704$	2.63166e6	0.200124
$705$	5.77078e6	0.437282
$706$	4.87645e6	0.368207
$707$	31014.7	0.00233356
$708$	−627340.	−0.0470349
$709$	−5.68310e6	−0.424590	−0.212295	−	0.977206i	$-0.568094\pi$
$709$	−5.68310e6	−0.424590	−0.212295	+	0.977206i	$0.568094\pi$
$710$	7.53512e6	0.560976
$711$	4.54170e6	0.336934
$712$	984759.	0.0727998
$713$	−3.84156e6	−0.282998
$714$	−2.77899e6	−0.204005
$715$	2.48460e7	1.81757
$716$	−306078.	−0.0223126
$717$	8.00723e6	0.581681
$718$	−1.00052e6	−0.0724297
$719$	−5.19955e6	−0.375097	−0.187548	−	0.982255i	$-0.560054\pi$
$719$	−5.19955e6	−0.375097	−0.187548	+	0.982255i	$0.560054\pi$
$720$	1.34303e6	0.0965503
$721$	1.04225e7	0.746679
$722$	1.89163e6	0.135050
$723$	−8.08145e6	−0.574968
$724$	−5.31578e6	−0.376895
$725$	3.43671e6	0.242828
$726$	−9.06300e6	−0.638161
$727$	−1.17844e7	−0.826935	−0.413468	−	0.910519i	$-0.635682\pi$
$727$	−1.17844e7	−0.826935	−0.413468	+	0.910519i	$0.635682\pi$
$728$	3.48195e6	0.243497
$729$	531441.	0.0370370
$730$	−9.35049e6	−0.649423
$731$	−1.96703e7	−1.36150
$732$	−429372.	−0.0296180
$733$	1.47263e7	1.01236	0.506178	−	0.862429i	$-0.331058\pi$
$733$	1.47263e7	1.01236	0.506178	+	0.862429i	$0.331058\pi$
$734$	−9.21611e6	−0.631404
$735$	−4.95712e6	−0.338463
$736$	541696.	0.0368605
$737$	3.74126e7	2.53717
$738$	3.37459e6	0.228076
$739$	−1.58677e7	−1.06882	−0.534408	−	0.845227i	$-0.679465\pi$
$739$	−1.58677e7	−1.06882	−0.534408	+	0.845227i	$0.679465\pi$
$740$	7.42762e6	0.498621
$741$	−7.60554e6	−0.508844
$742$	3.57048e6	0.238077
$743$	−3.31284e6	−0.220155	−0.110078	−	0.993923i	$-0.535110\pi$
$743$	−3.31284e6	−0.220155	−0.110078	+	0.993923i	$0.535110\pi$
$744$	−4.18287e6	−0.277039
$745$	−2.28892e7	−1.51092
$746$	1.16369e7	0.765580
$747$	−338022.	−0.0221638
$748$	−8.70881e6	−0.569121
$749$	1.91567e7	1.24772
$750$	4.79180e6	0.311061
$751$	−8.51168e6	−0.550701	−0.275350	−	0.961344i	$-0.588794\pi$
$751$	−8.51168e6	−0.550701	−0.275350	+	0.961344i	$0.588794\pi$
$752$	2.53438e6	0.163428
$753$	1.40315e7	0.901812
$754$	−7.67172e6	−0.491433
$755$	−2.37088e7	−1.51371
$756$	−1.06283e6	−0.0676330
$757$	2.57355e7	1.63228	0.816138	−	0.577857i	$-0.196111\pi$
$757$	2.57355e7	1.63228	0.816138	+	0.577857i	$0.196111\pi$
$758$	−1.91234e6	−0.120891
$759$	−3.05892e6	−0.192737
$760$	5.86680e6	0.368440
$761$	−2.07163e7	−1.29673	−0.648367	−	0.761328i	$-0.724548\pi$
$761$	−2.07163e7	−1.29673	−0.648367	+	0.761328i	$0.724548\pi$
$762$	−1.04917e7	−0.654572
$763$	1.24474e7	0.774048
$764$	7.50273e6	0.465035
$765$	−4.44440e6	−0.274574
$766$	−1.19063e7	−0.733172
$767$	−2.60116e6	−0.159654
$768$	589824.	0.0360844
$769$	1.43872e7	0.877327	0.438664	−	0.898651i	$-0.355452\pi$
$769$	1.43872e7	0.877327	0.438664	+	0.898651i	$0.355452\pi$
$770$	1.51672e7	0.921890
$771$	−8.47746e6	−0.513605
$772$	2.46622e6	0.148932
$773$	6.30053e6	0.379253	0.189626	−	0.981856i	$-0.439272\pi$
$773$	6.30053e6	0.379253	0.189626	+	0.981856i	$0.439272\pi$
$774$	−7.52293e6	−0.451372
$775$	7.76941e6	0.464658
$776$	7.45310e6	0.444307
$777$	−5.87798e6	−0.349282
$778$	−8.67461e6	−0.513808
$779$	1.47413e7	0.870349
$780$	5.56864e6	0.327727
$781$	−1.86870e7	−1.09626
$782$	−1.79260e6	−0.104826
$783$	2.34172e6	0.136499
$784$	−2.17704e6	−0.126496
$785$	2.70220e6	0.156510
$786$	6.19986e6	0.357953
$787$	1.09535e7	0.630401	0.315200	−	0.949025i	$-0.397928\pi$
$787$	1.09535e7	0.630401	0.315200	+	0.949025i	$0.397928\pi$
$788$	−3.29195e6	−0.188859
$789$	1.01832e7	0.582361
$790$	−1.45263e7	−0.828106
$791$	−1.57160e7	−0.893100
$792$	−3.33070e6	−0.188678
$793$	−1.78032e6	−0.100534
$794$	4.13779e6	0.232926
$795$	5.71023e6	0.320432
$796$	−1.71241e7	−0.957910
$797$	−9.15446e6	−0.510490	−0.255245	−	0.966876i	$-0.582156\pi$
$797$	−9.15446e6	−0.510490	−0.255245	+	0.966876i	$0.582156\pi$
$798$	−4.64279e6	−0.258091
$799$	−8.38689e6	−0.464766
$800$	−1.09556e6	−0.0605217
$801$	−1.24634e6	−0.0686363
$802$	−1.50357e7	−0.825444
$803$	2.31892e7	1.26910
$804$	8.38513e6	0.457477
$805$	3.12199e6	0.169802
$806$	−1.73435e7	−0.940373
$807$	8.95167e6	0.483861
$808$	21783.7	0.00117383
$809$	2.45254e7	1.31748	0.658742	−	0.752369i	$-0.271089\pi$
$809$	2.45254e7	1.31748	0.658742	+	0.752369i	$0.271089\pi$
$810$	−1.69977e6	−0.0910285
$811$	−2.09679e7	−1.11944	−0.559722	−	0.828681i	$-0.689092\pi$
$811$	−2.09679e7	−1.11944	−0.559722	+	0.828681i	$0.689092\pi$
$812$	−4.68319e6	−0.249260
$813$	−9.30999e6	−0.493995
$814$	−1.84205e7	−0.974405
$815$	2.76806e7	1.45976
$816$	−1.95187e6	−0.102619
$817$	−3.28627e7	−1.72246
$818$	2.02477e7	1.05802
$819$	−4.40684e6	−0.229571
$820$	−1.07933e7	−0.560559
$821$	−1.64389e7	−0.851168	−0.425584	−	0.904919i	$-0.639931\pi$
$821$	−1.64389e7	−0.851168	−0.425584	+	0.904919i	$0.639931\pi$
$822$	−1.43456e6	−0.0740526
$823$	2.37976e7	1.22471	0.612355	−	0.790583i	$-0.290222\pi$
$823$	2.37976e7	1.22471	0.612355	+	0.790583i	$0.290222\pi$
$824$	7.32043e6	0.375594
$825$	6.18656e6	0.316457
$826$	−1.58787e6	−0.0809778
$827$	2.35363e7	1.19667	0.598336	−	0.801245i	$-0.295829\pi$
$827$	2.35363e7	1.19667	0.598336	+	0.801245i	$0.295829\pi$
$828$	−685584.	−0.0347524
$829$	2.74777e7	1.38865	0.694327	−	0.719660i	$-0.255702\pi$
$829$	2.74777e7	1.38865	0.694327	+	0.719660i	$0.255702\pi$
$830$	1.08114e6	0.0544734
$831$	−8.93895e6	−0.449039
$832$	2.44561e6	0.122484
$833$	7.20436e6	0.359735
$834$	8.71906e6	0.434065
$835$	−2.90734e7	−1.44304
$836$	−1.45496e7	−0.720005
$837$	5.29394e6	0.261195
$838$	−2.87003e6	−0.141181
$839$	−1.84758e7	−0.906146	−0.453073	−	0.891473i	$-0.649672\pi$
$839$	−1.84758e7	−0.906146	−0.453073	+	0.891473i	$0.649672\pi$
$840$	3.39937e6	0.166226
$841$	−1.01927e7	−0.496936
$842$	9.16110e6	0.445315
$843$	1.57376e7	0.762729
$844$	1.39598e7	0.674565
$845$	−958462.	−0.0461778
$846$	−3.20758e6	−0.154082
$847$	−2.29396e7	−1.09869
$848$	2.50779e6	0.119757
$849$	3.65961e6	0.174247
$850$	3.62548e6	0.172115
$851$	−3.79163e6	−0.179474
$852$	−4.18825e6	−0.197667
$853$	−3.81544e7	−1.79544	−0.897722	−	0.440562i	$-0.854779\pi$
$853$	−3.81544e7	−1.79544	−0.897722	+	0.440562i	$0.854779\pi$
$854$	−1.08679e6	−0.0509920
$855$	−7.42517e6	−0.347369
$856$	1.34550e7	0.627625
$857$	2.41619e7	1.12377	0.561887	−	0.827214i	$-0.310076\pi$
$857$	2.41619e7	1.12377	0.561887	+	0.827214i	$0.310076\pi$
$858$	−1.38102e7	−0.640444
$859$	−3.85348e7	−1.78185	−0.890924	−	0.454153i	$-0.849942\pi$
$859$	−3.85348e7	−1.78185	−0.890924	+	0.454153i	$0.849942\pi$
$860$	2.40615e7	1.10937
$861$	8.54150e6	0.392669
$862$	1.75589e7	0.804878
$863$	−3.70206e7	−1.69207	−0.846033	−	0.533131i	$-0.821015\pi$
$863$	−3.70206e7	−1.69207	−0.846033	+	0.533131i	$0.821015\pi$
$864$	−746496.	−0.0340207
$865$	−3.14257e7	−1.42806
$866$	−1.72704e7	−0.782540
$867$	−6.31950e6	−0.285519
$868$	−1.05873e7	−0.476966
$869$	3.60250e7	1.61828
$870$	−7.48978e6	−0.335483
$871$	3.47675e7	1.55285
$872$	8.74266e6	0.389361
$873$	−9.43284e6	−0.418896
$874$	−2.99486e6	−0.132617
$875$	1.21286e7	0.535540
$876$	5.19729e6	0.228832
$877$	1.25283e7	0.550040	0.275020	−	0.961439i	$-0.411316\pi$
$877$	1.25283e7	0.550040	0.275020	+	0.961439i	$0.411316\pi$
$878$	−2.26996e7	−0.993760
$879$	−1.50467e7	−0.656853
$880$	1.06530e7	0.463728
$881$	1.04601e7	0.454042	0.227021	−	0.973890i	$-0.427101\pi$
$881$	1.04601e7	0.454042	0.227021	+	0.973890i	$0.427101\pi$
$882$	2.75532e6	0.119262
$883$	−1.53521e7	−0.662624	−0.331312	−	0.943521i	$-0.607491\pi$
$883$	−1.53521e7	−0.662624	−0.331312	+	0.943521i	$0.607491\pi$
$884$	−8.09310e6	−0.348325
$885$	−2.53947e6	−0.108990
$886$	2.61008e7	1.11704
$887$	8.97466e6	0.383009	0.191504	−	0.981492i	$-0.438663\pi$
$887$	8.97466e6	0.383009	0.191504	+	0.981492i	$0.438663\pi$
$888$	−4.12850e6	−0.175695
$889$	−2.65557e7	−1.12695
$890$	3.98630e6	0.168692
$891$	4.21542e6	0.177888
$892$	2.14873e7	0.904210
$893$	−1.40118e7	−0.587983
$894$	1.27225e7	0.532390
$895$	−1.23900e6	−0.0517029
$896$	1.49292e6	0.0621249
$897$	−2.84266e6	−0.117962
$898$	1.06207e7	0.439505
$899$	2.33270e7	0.962629
$900$	1.38657e6	0.0570604
$901$	−8.29888e6	−0.340571
$902$	2.67674e7	1.09544
$903$	−1.90415e7	−0.777107
$904$	−1.10384e7	−0.449246
$905$	−2.15182e7	−0.873344
$906$	1.31781e7	0.533373
$907$	−1.43938e6	−0.0580974	−0.0290487	−	0.999578i	$-0.509248\pi$
$907$	−1.43938e6	−0.0580974	−0.0290487	+	0.999578i	$0.509248\pi$
$908$	−2.15665e7	−0.868090
$909$	−27570.0	−0.00110669
$910$	1.40949e7	0.564233
$911$	−3.87755e7	−1.54797	−0.773984	−	0.633205i	$-0.781739\pi$
$911$	−3.87755e7	−1.54797	−0.773984	+	0.633205i	$0.781739\pi$
$912$	−3.26095e6	−0.129824
$913$	−2.68121e6	−0.106452
$914$	−2.72018e7	−1.07704
$915$	−1.73809e6	−0.0686311
$916$	−3.96950e6	−0.156314
$917$	1.56926e7	0.616271
$918$	2.47034e6	0.0967497
$919$	1.77509e7	0.693318	0.346659	−	0.937991i	$-0.387316\pi$
$919$	1.77509e7	0.693318	0.346659	+	0.937991i	$0.387316\pi$
$920$	2.19278e6	0.0854134
$921$	−188660.	−0.00732875
$922$	1.95835e7	0.758686
$923$	−1.73659e7	−0.670953
$924$	−8.43041e6	−0.324839
$925$	7.66843e6	0.294681
$926$	−2.12955e7	−0.816130
$927$	−9.26491e6	−0.354113
$928$	−3.28932e6	−0.125382
$929$	6.50796e6	0.247403	0.123702	−	0.992319i	$-0.460523\pi$
$929$	6.50796e6	0.247403	0.123702	+	0.992319i	$0.460523\pi$
$930$	−1.69322e7	−0.641958
$931$	1.20362e7	0.455107
$932$	−7.75473e6	−0.292433
$933$	−4.07351e6	−0.153202
$934$	−1.30565e7	−0.489733
$935$	−3.52532e7	−1.31877
$936$	−3.09522e6	−0.115479
$937$	4.81229e7	1.79062	0.895309	−	0.445446i	$-0.146955\pi$
$937$	4.81229e7	1.79062	0.895309	+	0.445446i	$0.146955\pi$
$938$	2.12238e7	0.787618
$939$	−4.60719e6	−0.170519
$940$	1.02592e7	0.378698
$941$	8.47762e6	0.312105	0.156052	−	0.987749i	$-0.450123\pi$
$941$	8.47762e6	0.312105	0.156052	+	0.987749i	$0.450123\pi$
$942$	−1.50196e6	−0.0551483
$943$	5.50974e6	0.201768
$944$	−1.11527e6	−0.0407334
$945$	−4.30232e6	−0.156720
$946$	−5.96722e7	−2.16793
$947$	3.98014e7	1.44219	0.721097	−	0.692834i	$-0.243638\pi$
$947$	3.98014e7	1.44219	0.721097	+	0.692834i	$0.243638\pi$
$948$	8.07414e6	0.291793
$949$	2.15497e7	0.776740
$950$	6.05700e6	0.217745
$951$	−2.06873e7	−0.741741
$952$	−4.94043e6	−0.176674
$953$	3.97637e7	1.41825	0.709127	−	0.705081i	$-0.249089\pi$
$953$	3.97637e7	1.41825	0.709127	+	0.705081i	$0.249089\pi$
$954$	−3.17392e6	−0.112908
$955$	3.03710e7	1.07758
$956$	1.42351e7	0.503750
$957$	1.85746e7	0.655601
$958$	1.66401e7	0.585789
$959$	−3.63106e6	−0.127493
$960$	2.38760e6	0.0836150
$961$	2.41063e7	0.842021
$962$	−1.71181e7	−0.596374
$963$	−1.70290e7	−0.591730
$964$	−1.43670e7	−0.497937
$965$	9.98324e6	0.345106
$966$	−1.73530e6	−0.0598317
$967$	1.00587e7	0.345920	0.172960	−	0.984929i	$-0.444667\pi$
$967$	1.00587e7	0.345920	0.172960	+	0.984929i	$0.444667\pi$
$968$	−1.61120e7	−0.552664
$969$	1.07913e7	0.369201
$970$	3.01701e7	1.02955
$971$	3.28538e7	1.11825	0.559123	−	0.829085i	$-0.311138\pi$
$971$	3.28538e7	1.11825	0.559123	+	0.829085i	$0.311138\pi$
$972$	944784.	0.0320750
$973$	2.20690e7	0.747310
$974$	1.86409e7	0.629607
$975$	5.74917e6	0.193684
$976$	−763328.	−0.0256499
$977$	4.91311e7	1.64672	0.823361	−	0.567518i	$-0.192096\pi$
$977$	4.91311e7	1.64672	0.823361	+	0.567518i	$0.192096\pi$
$978$	−1.53857e7	−0.514365
$979$	−9.88599e6	−0.329658
$980$	−8.81266e6	−0.293117
$981$	−1.10649e7	−0.367093
$982$	3.82921e7	1.26716
$983$	5.25434e6	0.173434	0.0867169	−	0.996233i	$-0.472362\pi$
$983$	5.25434e6	0.173434	0.0867169	+	0.996233i	$0.472362\pi$
$984$	5.99927e6	0.197520
$985$	−1.33258e7	−0.437626
$986$	1.08852e7	0.356568
$987$	−8.11877e6	−0.265276
$988$	−1.35210e7	−0.440672
$989$	−1.22828e7	−0.399307
$990$	−1.34827e7	−0.437207
$991$	−4.01080e7	−1.29732	−0.648660	−	0.761079i	$-0.724670\pi$
$991$	−4.01080e7	−1.29732	−0.648660	+	0.761079i	$0.724670\pi$
$992$	−7.43621e6	−0.239923
$993$	−1.20700e7	−0.388448
$994$	−1.06010e7	−0.340314
$995$	−6.93182e7	−2.21968
$996$	−600928.	−0.0191944
$997$	−4.13198e7	−1.31650	−0.658250	−	0.752800i	$-0.728703\pi$
$997$	−4.13198e7	−1.31650	−0.658250	+	0.752800i	$0.728703\pi$
$998$	−2.43469e7	−0.773780
$999$	5.22514e6	0.165647

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	138.6.a.h.1.3	✓	3
3.2	odd	2		414.6.a.m.1.1		3
4.3	odd	2		1104.6.a.j.1.3		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
138.6.a.h.1.3	✓	3	1.1	even	1	trivial
414.6.a.m.1.1		3	3.2	odd	2
1104.6.a.j.1.3		3	4.3	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:	\( N \)	\(=\)	\( 138 = 2 \cdot 3 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	138.a (trivial)

\(f(q)\)	\(=\)	\(q-4.00000 q^{2} +9.00000 q^{3} +16.0000 q^{4} +64.7679 q^{5} -36.0000 q^{6} -91.1204 q^{7} -64.0000 q^{8} +81.0000 q^{9} +O(q^{10})\)	\(q-4.00000 q^{2} +9.00000 q^{3} +16.0000 q^{4} +64.7679 q^{5} -36.0000 q^{6} -91.1204 q^{7} -64.0000 q^{8} +81.0000 q^{9} -259.072 q^{10} +642.496 q^{11} +144.000 q^{12} +597.072 q^{13} +364.482 q^{14} +582.911 q^{15} +256.000 q^{16} -847.166 q^{17} -324.000 q^{18} -1415.34 q^{19} +1036.29 q^{20} -820.084 q^{21} -2569.98 q^{22} -529.000 q^{23} -576.000 q^{24} +1069.88 q^{25} -2388.29 q^{26} +729.000 q^{27} -1457.93 q^{28} +3212.23 q^{29} -2331.65 q^{30} +7261.92 q^{31} -1024.00 q^{32} +5782.46 q^{33} +3388.67 q^{34} -5901.68 q^{35} +1296.00 q^{36} +7167.54 q^{37} +5661.37 q^{38} +5373.65 q^{39} -4145.15 q^{40} -10415.4 q^{41} +3280.33 q^{42} +23218.9 q^{43} +10279.9 q^{44} +5246.20 q^{45} +2116.00 q^{46} +9899.93 q^{47} +2304.00 q^{48} -8504.07 q^{49} -4279.53 q^{50} -7624.50 q^{51} +9553.15 q^{52} +9796.05 q^{53} -2916.00 q^{54} +41613.1 q^{55} +5831.71 q^{56} -12738.1 q^{57} -12848.9 q^{58} -4356.53 q^{59} +9326.58 q^{60} -2981.75 q^{61} -29047.7 q^{62} -7380.75 q^{63} +4096.00 q^{64} +38671.1 q^{65} -23129.9 q^{66} +58230.1 q^{67} -13554.7 q^{68} -4761.00 q^{69} +23606.7 q^{70} -29085.1 q^{71} -5184.00 q^{72} +36092.3 q^{73} -28670.2 q^{74} +9628.95 q^{75} -22645.5 q^{76} -58544.5 q^{77} -21494.6 q^{78} +56070.4 q^{79} +16580.6 q^{80} +6561.00 q^{81} +41661.6 q^{82} -4173.11 q^{83} -13121.3 q^{84} -54869.2 q^{85} -92875.7 q^{86} +28910.1 q^{87} -41119.7 q^{88} -15386.9 q^{89} -20984.8 q^{90} -54405.4 q^{91} -8464.00 q^{92} +65357.3 q^{93} -39599.7 q^{94} -91668.7 q^{95} -9216.00 q^{96} -116455. q^{97} +34016.3 q^{98} +52042.2 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q - 12 q^{2} + 27 q^{3} + 48 q^{4} - 4 q^{5} - 108 q^{6} - 34 q^{7} - 192 q^{8} + 243 q^{9}+O(q^{10}) \) 3 * q - 12 * q^2 + 27 * q^3 + 48 * q^4 - 4 * q^5 - 108 * q^6 - 34 * q^7 - 192 * q^8 + 243 * q^9	\( 3 q - 12 q^{2} + 27 q^{3} + 48 q^{4} - 4 q^{5} - 108 q^{6} - 34 q^{7} - 192 q^{8} + 243 q^{9} + 16 q^{10} + 300 q^{11} + 432 q^{12} + 998 q^{13} + 136 q^{14} - 36 q^{15} + 768 q^{16} + 392 q^{17} - 972 q^{18} + 2298 q^{19} - 64 q^{20} - 306 q^{21} - 1200 q^{22} - 1587 q^{23} - 1728 q^{24} - 1167 q^{25} - 3992 q^{26} + 2187 q^{27} - 544 q^{28} - 3834 q^{29} + 144 q^{30} + 11460 q^{31} - 3072 q^{32} + 2700 q^{33} - 1568 q^{34} + 5120 q^{35} + 3888 q^{36} + 28286 q^{37} - 9192 q^{38} + 8982 q^{39} + 256 q^{40} + 11998 q^{41} + 1224 q^{42} + 33666 q^{43} + 4800 q^{44} - 324 q^{45} + 6348 q^{46} + 31384 q^{47} + 6912 q^{48} + 61799 q^{49} + 4668 q^{50} + 3528 q^{51} + 15968 q^{52} + 24144 q^{53} - 8748 q^{54} + 51944 q^{55} + 2176 q^{56} + 20682 q^{57} + 15336 q^{58} - 14532 q^{59} - 576 q^{60} + 41222 q^{61} - 45840 q^{62} - 2754 q^{63} + 12288 q^{64} + 31480 q^{65} - 10800 q^{66} + 20030 q^{67} + 6272 q^{68} - 14283 q^{69} - 20480 q^{70} - 47928 q^{71} - 15552 q^{72} + 71894 q^{73} - 113144 q^{74} - 10503 q^{75} + 36768 q^{76} - 79712 q^{77} - 35928 q^{78} + 10922 q^{79} - 1024 q^{80} + 19683 q^{81} - 47992 q^{82} - 59068 q^{83} - 4896 q^{84} - 136840 q^{85} - 134664 q^{86} - 34506 q^{87} - 19200 q^{88} - 130140 q^{89} + 1296 q^{90} + 8988 q^{91} - 25392 q^{92} + 103140 q^{93} - 125536 q^{94} - 273752 q^{95} - 27648 q^{96} + 23658 q^{97} - 247196 q^{98} + 24300 q^{99}+O(q^{100}) \) 3 * q - 12 * q^2 + 27 * q^3 + 48 * q^4 - 4 * q^5 - 108 * q^6 - 34 * q^7 - 192 * q^8 + 243 * q^9 + 16 * q^10 + 300 * q^11 + 432 * q^12 + 998 * q^13 + 136 * q^14 - 36 * q^15 + 768 * q^16 + 392 * q^17 - 972 * q^18 + 2298 * q^19 - 64 * q^20 - 306 * q^21 - 1200 * q^22 - 1587 * q^23 - 1728 * q^24 - 1167 * q^25 - 3992 * q^26 + 2187 * q^27 - 544 * q^28 - 3834 * q^29 + 144 * q^30 + 11460 * q^31 - 3072 * q^32 + 2700 * q^33 - 1568 * q^34 + 5120 * q^35 + 3888 * q^36 + 28286 * q^37 - 9192 * q^38 + 8982 * q^39 + 256 * q^40 + 11998 * q^41 + 1224 * q^42 + 33666 * q^43 + 4800 * q^44 - 324 * q^45 + 6348 * q^46 + 31384 * q^47 + 6912 * q^48 + 61799 * q^49 + 4668 * q^50 + 3528 * q^51 + 15968 * q^52 + 24144 * q^53 - 8748 * q^54 + 51944 * q^55 + 2176 * q^56 + 20682 * q^57 + 15336 * q^58 - 14532 * q^59 - 576 * q^60 + 41222 * q^61 - 45840 * q^62 - 2754 * q^63 + 12288 * q^64 + 31480 * q^65 - 10800 * q^66 + 20030 * q^67 + 6272 * q^68 - 14283 * q^69 - 20480 * q^70 - 47928 * q^71 - 15552 * q^72 + 71894 * q^73 - 113144 * q^74 - 10503 * q^75 + 36768 * q^76 - 79712 * q^77 - 35928 * q^78 + 10922 * q^79 - 1024 * q^80 + 19683 * q^81 - 47992 * q^82 - 59068 * q^83 - 4896 * q^84 - 136840 * q^85 - 134664 * q^86 - 34506 * q^87 - 19200 * q^88 - 130140 * q^89 + 1296 * q^90 + 8988 * q^91 - 25392 * q^92 + 103140 * q^93 - 125536 * q^94 - 273752 * q^95 - 27648 * q^96 + 23658 * q^97 - 247196 * q^98 + 24300 * q^99

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