LMFDB - Embedded newform 354.6.a.g.1.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("354.1");

S:= CuspForms(chi, 6);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

Self dual:	yes
Analytic conductor:	$56.7758722138$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	$\mathbb{Q}[x]/(x^{6} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 358x^{4} - 404x^{3} + 26492x^{2} - 11664x - 353376 $ x^6 - 358x^4 - 404x^3 + 26492x^2 - 11664x - 353376
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{3}\cdot 3^{4} $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Root			$6.78105$ 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)

$f(q)$	$=$	$q-4.00000 q^{2} -9.00000 q^{3} +16.0000 q^{4} -14.2062 q^{5} +36.0000 q^{6} +60.7262 q^{7} -64.0000 q^{8} +81.0000 q^{9} +O(q^{10})$	\(q-4.00000 q^{2} -9.00000 q^{3} +16.0000 q^{4} -14.2062 q^{5} +36.0000 q^{6} +60.7262 q^{7} -64.0000 q^{8} +81.0000 q^{9} +56.8247 q^{10} +675.451 q^{11} -144.000 q^{12} +758.340 q^{13} -242.905 q^{14} +127.856 q^{15} +256.000 q^{16} -102.382 q^{17} -324.000 q^{18} -984.536 q^{19} -227.299 q^{20} -546.536 q^{21} -2701.80 q^{22} +77.2619 q^{23} +576.000 q^{24} -2923.18 q^{25} -3033.36 q^{26} -729.000 q^{27} +971.619 q^{28} +4967.22 q^{29} -511.422 q^{30} +8007.84 q^{31} -1024.00 q^{32} -6079.06 q^{33} +409.527 q^{34} -862.687 q^{35} +1296.00 q^{36} -1336.97 q^{37} +3938.15 q^{38} -6825.06 q^{39} +909.195 q^{40} +8983.78 q^{41} +2186.14 q^{42} -19843.1 q^{43} +10807.2 q^{44} -1150.70 q^{45} -309.048 q^{46} -19513.7 q^{47} -2304.00 q^{48} -13119.3 q^{49} +11692.7 q^{50} +921.436 q^{51} +12133.4 q^{52} +4070.85 q^{53} +2916.00 q^{54} -9595.57 q^{55} -3886.47 q^{56} +8860.83 q^{57} -19868.9 q^{58} +3481.00 q^{59} +2045.69 q^{60} +7976.13 q^{61} -32031.3 q^{62} +4918.82 q^{63} +4096.00 q^{64} -10773.1 q^{65} +24316.2 q^{66} +32500.8 q^{67} -1638.11 q^{68} -695.357 q^{69} +3450.75 q^{70} -12511.7 q^{71} -5184.00 q^{72} -59240.9 q^{73} +5347.87 q^{74} +26308.7 q^{75} -15752.6 q^{76} +41017.5 q^{77} +27300.2 q^{78} +33329.1 q^{79} -3636.78 q^{80} +6561.00 q^{81} -35935.1 q^{82} +114298. q^{83} -8744.57 q^{84} +1454.45 q^{85} +79372.5 q^{86} -44704.9 q^{87} -43228.9 q^{88} +144266. q^{89} +4602.80 q^{90} +46051.1 q^{91} +1236.19 q^{92} -72070.5 q^{93} +78054.9 q^{94} +13986.5 q^{95} +9216.00 q^{96} +168603. q^{97} +52477.3 q^{98} +54711.5 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 24 q^{2} - 54 q^{3} + 96 q^{4} + 4 q^{5} + 216 q^{6} - 54 q^{7} - 384 q^{8} + 486 q^{9}+O(q^{10}) $ 6 * q - 24 * q^2 - 54 * q^3 + 96 * q^4 + 4 * q^5 + 216 * q^6 - 54 * q^7 - 384 * q^8 + 486 * q^9	\( 6 q - 24 q^{2} - 54 q^{3} + 96 q^{4} + 4 q^{5} + 216 q^{6} - 54 q^{7} - 384 q^{8} + 486 q^{9} - 16 q^{10} + 436 q^{11} - 864 q^{12} - 536 q^{13} + 216 q^{14} - 36 q^{15} + 1536 q^{16} + 910 q^{17} - 1944 q^{18} + 1462 q^{19} + 64 q^{20} + 486 q^{21} - 1744 q^{22} + 1634 q^{23} + 3456 q^{24} - 1186 q^{25} + 2144 q^{26} - 4374 q^{27} - 864 q^{28} - 1598 q^{29} + 144 q^{30} - 5670 q^{31} - 6144 q^{32} - 3924 q^{33} - 3640 q^{34} - 7242 q^{35} + 7776 q^{36} - 20458 q^{37} - 5848 q^{38} + 4824 q^{39} - 256 q^{40} + 262 q^{41} - 1944 q^{42} - 34028 q^{43} + 6976 q^{44} + 324 q^{45} - 6536 q^{46} - 11194 q^{47} - 13824 q^{48} - 32652 q^{49} + 4744 q^{50} - 8190 q^{51} - 8576 q^{52} - 17164 q^{53} + 17496 q^{54} - 37040 q^{55} + 3456 q^{56} - 13158 q^{57} + 6392 q^{58} + 20886 q^{59} - 576 q^{60} - 43546 q^{61} + 22680 q^{62} - 4374 q^{63} + 24576 q^{64} + 65568 q^{65} + 15696 q^{66} - 52772 q^{67} + 14560 q^{68} - 14706 q^{69} + 28968 q^{70} + 84740 q^{71} - 31104 q^{72} - 36578 q^{73} + 81832 q^{74} + 10674 q^{75} + 23392 q^{76} + 90678 q^{77} - 19296 q^{78} + 85196 q^{79} + 1024 q^{80} + 39366 q^{81} - 1048 q^{82} + 217026 q^{83} + 7776 q^{84} + 26570 q^{85} + 136112 q^{86} + 14382 q^{87} - 27904 q^{88} + 333850 q^{89} - 1296 q^{90} + 214914 q^{91} + 26144 q^{92} + 51030 q^{93} + 44776 q^{94} + 458758 q^{95} + 55296 q^{96} + 173148 q^{97} + 130608 q^{98} + 35316 q^{99}+O(q^{100}) \) 6 * q - 24 * q^2 - 54 * q^3 + 96 * q^4 + 4 * q^5 + 216 * q^6 - 54 * q^7 - 384 * q^8 + 486 * q^9 - 16 * q^10 + 436 * q^11 - 864 * q^12 - 536 * q^13 + 216 * q^14 - 36 * q^15 + 1536 * q^16 + 910 * q^17 - 1944 * q^18 + 1462 * q^19 + 64 * q^20 + 486 * q^21 - 1744 * q^22 + 1634 * q^23 + 3456 * q^24 - 1186 * q^25 + 2144 * q^26 - 4374 * q^27 - 864 * q^28 - 1598 * q^29 + 144 * q^30 - 5670 * q^31 - 6144 * q^32 - 3924 * q^33 - 3640 * q^34 - 7242 * q^35 + 7776 * q^36 - 20458 * q^37 - 5848 * q^38 + 4824 * q^39 - 256 * q^40 + 262 * q^41 - 1944 * q^42 - 34028 * q^43 + 6976 * q^44 + 324 * q^45 - 6536 * q^46 - 11194 * q^47 - 13824 * q^48 - 32652 * q^49 + 4744 * q^50 - 8190 * q^51 - 8576 * q^52 - 17164 * q^53 + 17496 * q^54 - 37040 * q^55 + 3456 * q^56 - 13158 * q^57 + 6392 * q^58 + 20886 * q^59 - 576 * q^60 - 43546 * q^61 + 22680 * q^62 - 4374 * q^63 + 24576 * q^64 + 65568 * q^65 + 15696 * q^66 - 52772 * q^67 + 14560 * q^68 - 14706 * q^69 + 28968 * q^70 + 84740 * q^71 - 31104 * q^72 - 36578 * q^73 + 81832 * q^74 + 10674 * q^75 + 23392 * q^76 + 90678 * q^77 - 19296 * q^78 + 85196 * q^79 + 1024 * q^80 + 39366 * q^81 - 1048 * q^82 + 217026 * q^83 + 7776 * q^84 + 26570 * q^85 + 136112 * q^86 + 14382 * q^87 - 27904 * q^88 + 333850 * q^89 - 1296 * q^90 + 214914 * q^91 + 26144 * q^92 + 51030 * q^93 + 44776 * q^94 + 458758 * q^95 + 55296 * q^96 + 173148 * q^97 + 130608 * q^98 + 35316 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	−4.00000	−0.707107
$2$	−4.00000	−0.707107
$3$	−9.00000	−0.577350
$3$	−9.00000	−0.577350
$4$	16.0000	0.500000
$5$	−14.2062	−0.254128	−0.127064	−	0.991895i	$-0.540555\pi$
$5$	−14.2062	−0.254128	−0.127064	+	0.991895i	$0.540555\pi$
$6$	36.0000	0.408248
$7$	60.7262	0.468415	0.234207	−	0.972187i	$-0.424750\pi$
$7$	60.7262	0.468415	0.234207	+	0.972187i	$0.424750\pi$
$8$	−64.0000	−0.353553
$9$	81.0000	0.333333
$10$	56.8247	0.179695
$11$	675.451	1.68311	0.841554	−	0.540173i	$-0.181641\pi$
$11$	675.451	1.68311	0.841554	+	0.540173i	$0.181641\pi$
$12$	−144.000	−0.288675
$13$	758.340	1.24453	0.622265	−	0.782806i	$-0.286212\pi$
$13$	758.340	1.24453	0.622265	+	0.782806i	$0.286212\pi$
$14$	−242.905	−0.331219
$15$	127.856	0.146721
$16$	256.000	0.250000
$17$	−102.382	−0.0859212	−0.0429606	−	0.999077i	$-0.513679\pi$
$17$	−102.382	−0.0859212	−0.0429606	+	0.999077i	$0.513679\pi$
$18$	−324.000	−0.235702
$19$	−984.536	−0.625673	−0.312837	−	0.949807i	$-0.601279\pi$
$19$	−984.536	−0.625673	−0.312837	+	0.949807i	$0.601279\pi$
$20$	−227.299	−0.127064
$21$	−546.536	−0.270440
$22$	−2701.80	−1.19014
$23$	77.2619	0.0304541	0.0152270	−	0.999884i	$-0.495153\pi$
$23$	77.2619	0.0304541	0.0152270	+	0.999884i	$0.495153\pi$
$24$	576.000	0.204124
$25$	−2923.18	−0.935419
$26$	−3033.36	−0.880016
$27$	−729.000	−0.192450
$28$	971.619	0.234207
$29$	4967.22	1.09678	0.548388	−	0.836224i	$-0.315242\pi$
$29$	4967.22	1.09678	0.548388	+	0.836224i	$0.315242\pi$
$30$	−511.422	−0.103747
$31$	8007.84	1.49662	0.748309	−	0.663350i	$-0.230866\pi$
$31$	8007.84	1.49662	0.748309	+	0.663350i	$0.230866\pi$
$32$	−1024.00	−0.176777
$33$	−6079.06	−0.971743
$34$	409.527	0.0607555
$35$	−862.687	−0.119037
$36$	1296.00	0.166667
$37$	−1336.97	−0.160552	−0.0802762	−	0.996773i	$-0.525580\pi$
$37$	−1336.97	−0.160552	−0.0802762	+	0.996773i	$0.525580\pi$
$38$	3938.15	0.442418
$39$	−6825.06	−0.718530
$40$	909.195	0.0898477
$41$	8983.78	0.834640	0.417320	−	0.908760i	$-0.362969\pi$
$41$	8983.78	0.834640	0.417320	+	0.908760i	$0.362969\pi$
$42$	2186.14	0.191230
$43$	−19843.1	−1.63659	−0.818293	−	0.574801i	$-0.805079\pi$
$43$	−19843.1	−1.63659	−0.818293	+	0.574801i	$0.805079\pi$
$44$	10807.2	0.841554
$45$	−1150.70	−0.0847093
$46$	−309.048	−0.0215343
$47$	−19513.7	−1.28853	−0.644266	−	0.764801i	$-0.722837\pi$
$47$	−19513.7	−1.28853	−0.644266	+	0.764801i	$0.722837\pi$
$48$	−2304.00	−0.144338
$49$	−13119.3	−0.780587
$50$	11692.7	0.661441
$51$	921.436	0.0496066
$52$	12133.4	0.622265
$53$	4070.85	0.199065	0.0995325	−	0.995034i	$-0.468265\pi$
$53$	4070.85	0.199065	0.0995325	+	0.995034i	$0.468265\pi$
$54$	2916.00	0.136083
$55$	−9595.57	−0.427725
$56$	−3886.47	−0.165610
$57$	8860.83	0.361233
$58$	−19868.9	−0.775538
$59$	3481.00	0.130189
$59$	3481.00	0.130189
$60$	2045.69	0.0733604
$61$	7976.13	0.274453	0.137226	−	0.990540i	$-0.456181\pi$
$61$	7976.13	0.274453	0.137226	+	0.990540i	$0.456181\pi$
$62$	−32031.3	−1.05827
$63$	4918.82	0.156138
$64$	4096.00	0.125000
$65$	−10773.1	−0.316270
$66$	24316.2	0.687126
$67$	32500.8	0.884519	0.442260	−	0.896887i	$-0.354177\pi$
$67$	32500.8	0.884519	0.442260	+	0.896887i	$0.354177\pi$
$68$	−1638.11	−0.0429606
$69$	−695.357	−0.0175827
$70$	3450.75	0.0841721
$71$	−12511.7	−0.294558	−0.147279	−	0.989095i	$-0.547051\pi$
$71$	−12511.7	−0.294558	−0.147279	+	0.989095i	$0.547051\pi$
$72$	−5184.00	−0.117851
$73$	−59240.9	−1.30111	−0.650556	−	0.759458i	$-0.725464\pi$
$73$	−59240.9	−1.30111	−0.650556	+	0.759458i	$0.725464\pi$
$74$	5347.87	0.113528
$75$	26308.7	0.540064
$76$	−15752.6	−0.312837
$77$	41017.5	0.788393
$78$	27300.2	0.508078
$79$	33329.1	0.600835	0.300418	−	0.953808i	$-0.402874\pi$
$79$	33329.1	0.600835	0.300418	+	0.953808i	$0.402874\pi$
$80$	−3636.78	−0.0635319
$81$	6561.00	0.111111
$82$	−35935.1	−0.590180
$83$	114298.	1.82114	0.910570	−	0.413354i	$-0.135643\pi$
$83$	114298.	1.82114	0.910570	+	0.413354i	$0.135643\pi$
$84$	−8744.57	−0.135220
$85$	1454.45	0.0218350
$86$	79372.5	1.15724
$87$	−44704.9	−0.633224
$88$	−43228.9	−0.595069
$89$	144266.	1.93058	0.965291	−	0.261175i	$-0.0841101\pi$
$89$	144266.	1.93058	0.965291	+	0.261175i	$0.0841101\pi$
$90$	4602.80	0.0598985
$91$	46051.1	0.582957
$92$	1236.19	0.0152270
$93$	−72070.5	−0.864073
$94$	78054.9	0.911130
$95$	13986.5	0.159001
$96$	9216.00	0.102062
$97$	168603.	1.81943	0.909714	−	0.415235i	$-0.136301\pi$
$97$	168603.	1.81943	0.909714	+	0.415235i	$0.136301\pi$
$98$	52477.3	0.551959
$99$	54711.5	0.561036
$100$	−46771.0	−0.467710
$101$	−66071.8	−0.644485	−0.322243	−	0.946657i	$-0.604437\pi$
$101$	−66071.8	−0.644485	−0.322243	+	0.946657i	$0.604437\pi$
$102$	−3685.74	−0.0350772
$103$	−173587.	−1.61222	−0.806109	−	0.591767i	$-0.798431\pi$
$103$	−173587.	−1.61222	−0.806109	+	0.591767i	$0.798431\pi$
$104$	−48533.8	−0.440008
$105$	7764.18	0.0687262
$106$	−16283.4	−0.140760
$107$	117019.	0.988089	0.494044	−	0.869437i	$-0.335518\pi$
$107$	117019.	0.988089	0.494044	+	0.869437i	$0.335518\pi$
$108$	−11664.0	−0.0962250
$109$	−47152.0	−0.380132	−0.190066	−	0.981771i	$-0.560870\pi$
$109$	−47152.0	−0.380132	−0.190066	+	0.981771i	$0.560870\pi$
$110$	38382.3	0.302447
$111$	12032.7	0.0926950
$112$	15545.9	0.117104
$113$	202162.	1.48937	0.744687	−	0.667414i	$-0.232599\pi$
$113$	202162.	1.48937	0.744687	+	0.667414i	$0.232599\pi$
$114$	−35443.3	−0.255430
$115$	−1097.60	−0.00773923
$116$	79475.5	0.548388
$117$	61425.6	0.414844
$118$	−13924.0	−0.0920575
$119$	−6217.25	−0.0402468
$120$	−8182.76	−0.0518736
$121$	295183.	1.83285
$122$	−31904.5	−0.194067
$123$	−80854.0	−0.481880
$124$	128125.	0.748309
$125$	85921.6	0.491844
$126$	−19675.3	−0.110406
$127$	169874.	0.934584	0.467292	−	0.884103i	$-0.345230\pi$
$127$	169874.	0.934584	0.467292	+	0.884103i	$0.345230\pi$
$128$	−16384.0	−0.0883883
$129$	178588.	0.944884
$130$	43092.5	0.223637
$131$	−221952.	−1.13001	−0.565003	−	0.825089i	$-0.691125\pi$
$131$	−221952.	−1.13001	−0.565003	+	0.825089i	$0.691125\pi$
$132$	−97264.9	−0.485871
$133$	−59787.1	−0.293075
$134$	−130003.	−0.625450
$135$	10356.3	0.0489069
$136$	6552.43	0.0303777
$137$	−372422.	−1.69525	−0.847626	−	0.530595i	$-0.821969\pi$
$137$	−372422.	−1.69525	−0.847626	+	0.530595i	$0.821969\pi$
$138$	2781.43	0.0124328
$139$	104704.	0.459648	0.229824	−	0.973232i	$-0.426185\pi$
$139$	104704.	0.459648	0.229824	+	0.973232i	$0.426185\pi$
$140$	−13803.0	−0.0595186
$141$	175623.	0.743935
$142$	50046.8	0.208284
$143$	512222.	2.09468
$144$	20736.0	0.0833333
$145$	−70565.1	−0.278721
$146$	236964.	0.920025
$147$	118074.	0.450672
$148$	−21391.5	−0.0802762
$149$	493793.	1.82213	0.911066	−	0.412261i	$-0.135261\pi$
$149$	493793.	1.82213	0.911066	+	0.412261i	$0.135261\pi$
$150$	−105235.	−0.381883
$151$	−357533.	−1.27607	−0.638034	−	0.770008i	$-0.720252\pi$
$151$	−357533.	−1.27607	−0.638034	+	0.770008i	$0.720252\pi$
$152$	63010.3	0.221209
$153$	−8292.92	−0.0286404
$154$	−164070.	−0.557478
$155$	−113761.	−0.380332
$156$	−109201.	−0.359265
$157$	394830.	1.27838	0.639192	−	0.769047i	$-0.279269\pi$
$157$	394830.	1.27838	0.639192	+	0.769047i	$0.279269\pi$
$158$	−133316.	−0.424855
$159$	−36637.6	−0.114930
$160$	14547.1	0.0449239
$161$	4691.82	0.0142652
$162$	−26244.0	−0.0785674
$163$	548794.	1.61786	0.808929	−	0.587906i	$-0.200048\pi$
$163$	548794.	1.61786	0.808929	+	0.587906i	$0.200048\pi$
$164$	143740.	0.417320
$165$	86360.2	0.246947
$166$	−457192.	−1.28774
$167$	652920.	1.81163	0.905813	−	0.423677i	$-0.139261\pi$
$167$	652920.	1.81163	0.905813	+	0.423677i	$0.139261\pi$
$168$	34978.3	0.0956148
$169$	203787.	0.548857
$170$	−5817.81	−0.0154396
$171$	−79747.4	−0.208558
$172$	−317490.	−0.818293
$173$	−705077.	−1.79111	−0.895553	−	0.444954i	$-0.853220\pi$
$173$	−705077.	−1.79111	−0.895553	+	0.444954i	$0.853220\pi$
$174$	178820.	0.447757
$175$	−177514.	−0.438164
$176$	172915.	0.420777
$177$	−31329.0	−0.0751646
$178$	−577063.	−1.36513
$179$	307521.	0.717368	0.358684	−	0.933459i	$-0.383226\pi$
$179$	307521.	0.717368	0.358684	+	0.933459i	$0.383226\pi$
$180$	−18411.2	−0.0423546
$181$	−426695.	−0.968103	−0.484052	−	0.875039i	$-0.660835\pi$
$181$	−426695.	−0.968103	−0.484052	+	0.875039i	$0.660835\pi$
$182$	−184204.	−0.412213
$183$	−71785.2	−0.158455
$184$	−4944.76	−0.0107671
$185$	18993.2	0.0408008
$186$	288282.	0.610992
$187$	−69153.8	−0.144615
$188$	−312220.	−0.644266
$189$	−44269.4	−0.0901465
$190$	−55946.0	−0.112431
$191$	120908.	0.239813	0.119906	−	0.992785i	$-0.461741\pi$
$191$	120908.	0.239813	0.119906	+	0.992785i	$0.461741\pi$
$192$	−36864.0	−0.0721688
$193$	−371583.	−0.718063	−0.359031	−	0.933325i	$-0.616893\pi$
$193$	−371583.	−0.718063	−0.359031	+	0.933325i	$0.616893\pi$
$194$	−674410.	−1.28653
$195$	96958.0	0.182598
$196$	−209909.	−0.390294
$197$	273915.	0.502863	0.251432	−	0.967875i	$-0.419099\pi$
$197$	273915.	0.502863	0.251432	+	0.967875i	$0.419099\pi$
$198$	−218846.	−0.396712
$199$	−944880.	−1.69139	−0.845695	−	0.533667i	$-0.820814\pi$
$199$	−944880.	−1.69139	−0.845695	+	0.533667i	$0.820814\pi$
$200$	187084.	0.330721
$201$	−292507.	−0.510678
$202$	264287.	0.455720
$203$	301640.	0.513746
$204$	14743.0	0.0248033
$205$	−127625.	−0.212105
$206$	694347.	1.14001
$207$	6258.21	0.0101514
$208$	194135.	0.311133
$209$	−665006.	−1.05308
$210$	−31056.7	−0.0485968
$211$	−96540.0	−0.149280	−0.0746399	−	0.997211i	$-0.523781\pi$
$211$	−96540.0	−0.149280	−0.0746399	+	0.997211i	$0.523781\pi$
$212$	65133.5	0.0995325
$213$	112605.	0.170063
$214$	−468075.	−0.698684
$215$	281895.	0.415902
$216$	46656.0	0.0680414
$217$	486285.	0.701038
$218$	188608.	0.268794
$219$	533168.	0.751197
$220$	−153529.	−0.213862
$221$	−77640.2	−0.106932
$222$	−48130.9	−0.0655452
$223$	−1.19124e6	−1.60412	−0.802059	−	0.597245i	$-0.796262\pi$
$223$	−1.19124e6	−1.60412	−0.802059	+	0.597245i	$0.796262\pi$
$224$	−62183.6	−0.0828049
$225$	−236778.	−0.311806
$226$	−808649.	−1.05315
$227$	1.04626e6	1.34764	0.673822	−	0.738894i	$-0.264652\pi$
$227$	1.04626e6	1.34764	0.673822	+	0.738894i	$0.264652\pi$
$228$	141773.	0.180616
$229$	−119410.	−0.150471	−0.0752353	−	0.997166i	$-0.523971\pi$
$229$	−119410.	−0.150471	−0.0752353	+	0.997166i	$0.523971\pi$
$230$	4390.38	0.00547246
$231$	−369158.	−0.455179
$232$	−317902.	−0.387769
$233$	−419739.	−0.506512	−0.253256	−	0.967399i	$-0.581501\pi$
$233$	−419739.	−0.506512	−0.253256	+	0.967399i	$0.581501\pi$
$234$	−245702.	−0.293339
$235$	277215.	0.327452
$236$	55696.0	0.0650945
$237$	−299961.	−0.346892
$238$	24869.0	0.0284588
$239$	518364.	0.587003	0.293501	−	0.955959i	$-0.405179\pi$
$239$	518364.	0.587003	0.293501	+	0.955959i	$0.405179\pi$
$240$	32731.0	0.0366802
$241$	830571.	0.921158	0.460579	−	0.887619i	$-0.347642\pi$
$241$	830571.	0.921158	0.460579	+	0.887619i	$0.347642\pi$
$242$	−1.18073e6	−1.29602
$243$	−59049.0	−0.0641500
$244$	127618.	0.137226
$245$	186376.	0.198369
$246$	323416.	0.340740
$247$	−746613.	−0.778670
$248$	−512501.	−0.529134
$249$	−1.02868e6	−1.05144
$250$	−343686.	−0.347786
$251$	1.72879e6	1.73204	0.866020	−	0.500009i	$-0.166670\pi$
$251$	1.72879e6	1.73204	0.866020	+	0.500009i	$0.166670\pi$
$252$	78701.1	0.0780692
$253$	52186.6	0.0512575
$254$	−679497.	−0.660851
$255$	−13090.1	−0.0126064
$256$	65536.0	0.0625000
$257$	39663.2	0.0374589	0.0187294	−	0.999825i	$-0.494038\pi$
$257$	39663.2	0.0374589	0.0187294	+	0.999825i	$0.494038\pi$
$258$	−714353.	−0.668134
$259$	−81189.0	−0.0752051
$260$	−172370.	−0.158135
$261$	402344.	0.365592
$262$	887808.	0.799035
$263$	626354.	0.558381	0.279191	−	0.960236i	$-0.409934\pi$
$263$	626354.	0.558381	0.279191	+	0.960236i	$0.409934\pi$
$264$	389060.	0.343563
$265$	−57831.1	−0.0505879
$266$	239148.	0.207235
$267$	−1.29839e6	−1.11462
$268$	520013.	0.442260
$269$	−127502.	−0.107433	−0.0537165	−	0.998556i	$-0.517107\pi$
$269$	−127502.	−0.107433	−0.0537165	+	0.998556i	$0.517107\pi$
$270$	−41425.2	−0.0345824
$271$	1.02686e6	0.849351	0.424676	−	0.905346i	$-0.360388\pi$
$271$	1.02686e6	0.849351	0.424676	+	0.905346i	$0.360388\pi$
$272$	−26209.7	−0.0214803
$273$	−414460.	−0.336570
$274$	1.48969e6	1.19872
$275$	−1.97447e6	−1.57441
$276$	−11125.7	−0.00879134
$277$	1.13094e6	0.885603	0.442801	−	0.896620i	$-0.353985\pi$
$277$	1.13094e6	0.885603	0.442801	+	0.896620i	$0.353985\pi$
$278$	−418815.	−0.325020
$279$	648635.	0.498873
$280$	55211.9	0.0420860
$281$	330372.	0.249596	0.124798	−	0.992182i	$-0.460172\pi$
$281$	330372.	0.249596	0.124798	+	0.992182i	$0.460172\pi$
$282$	−702494.	−0.526041
$283$	−1.06761e6	−0.792400	−0.396200	−	0.918164i	$-0.629671\pi$
$283$	−1.06761e6	−0.792400	−0.396200	+	0.918164i	$0.629671\pi$
$284$	−200187.	−0.147279
$285$	−125878.	−0.0917993
$286$	−2.04889e6	−1.48116
$287$	545550.	0.390958
$288$	−82944.0	−0.0589256
$289$	−1.40937e6	−0.992618
$290$	282261.	0.197086
$291$	−1.51742e6	−1.05045
$292$	−947855.	−0.650556
$293$	−378875.	−0.257826	−0.128913	−	0.991656i	$-0.541149\pi$
$293$	−378875.	−0.257826	−0.128913	+	0.991656i	$0.541149\pi$
$294$	−472296.	−0.318673
$295$	−49451.7	−0.0330846
$296$	85566.0	0.0567638
$297$	−492404.	−0.323914
$298$	−1.97517e6	−1.28844
$299$	58590.8	0.0379011
$300$	420939.	0.270032
$301$	−1.20500e6	−0.766602
$302$	1.43013e6	0.902317
$303$	594647.	0.372094
$304$	−252041.	−0.156418
$305$	−113310.	−0.0697461
$306$	33171.7	0.0202518
$307$	−267279.	−0.161852	−0.0809261	−	0.996720i	$-0.525788\pi$
$307$	−267279.	−0.161852	−0.0809261	+	0.996720i	$0.525788\pi$
$308$	656281.	0.394197
$309$	1.56228e6	0.930815
$310$	455043.	0.268935
$311$	1.51807e6	0.890000	0.445000	−	0.895530i	$-0.353204\pi$
$311$	1.51807e6	0.890000	0.445000	+	0.895530i	$0.353204\pi$
$312$	436804.	0.254039
$313$	−1.00045e6	−0.577213	−0.288607	−	0.957448i	$-0.593192\pi$
$313$	−1.00045e6	−0.577213	−0.288607	+	0.957448i	$0.593192\pi$
$314$	−1.57932e6	−0.903953
$315$	−69877.6	−0.0396791
$316$	533265.	0.300418
$317$	−1.79591e6	−1.00378	−0.501888	−	0.864933i	$-0.667361\pi$
$317$	−1.79591e6	−1.00378	−0.501888	+	0.864933i	$0.667361\pi$
$318$	146550.	0.0812680
$319$	3.35511e6	1.84599
$320$	−58188.5	−0.0317660
$321$	−1.05317e6	−0.570473
$322$	−18767.3	−0.0100870
$323$	100799.	0.0537586
$324$	104976.	0.0555556
$325$	−2.21677e6	−1.16416
$326$	−2.19518e6	−1.14400
$327$	424368.	0.219469
$328$	−574962.	−0.295090
$329$	−1.18499e6	−0.603568
$330$	−345441.	−0.174618
$331$	3.27490e6	1.64296	0.821481	−	0.570236i	$-0.193148\pi$
$331$	3.27490e6	1.64296	0.821481	+	0.570236i	$0.193148\pi$
$332$	1.82877e6	0.910570
$333$	−108294.	−0.0535175
$334$	−2.61168e6	−1.28101
$335$	−461712.	−0.224781
$336$	−139913.	−0.0676099
$337$	−2.67548e6	−1.28330	−0.641649	−	0.766999i	$-0.721749\pi$
$337$	−2.67548e6	−1.28330	−0.641649	+	0.766999i	$0.721749\pi$
$338$	−815147.	−0.388101
$339$	−1.81946e6	−0.859891
$340$	23271.2	0.0109175
$341$	5.40890e6	2.51897
$342$	318990.	0.147473
$343$	−1.81731e6	−0.834054
$344$	1.26996e6	0.578621
$345$	9878.36	0.00446825
$346$	2.82031e6	1.26650
$347$	−200835.	−0.0895396	−0.0447698	−	0.998997i	$-0.514255\pi$
$347$	−200835.	−0.0895396	−0.0447698	+	0.998997i	$0.514255\pi$
$348$	−715279.	−0.316612
$349$	671754.	0.295221	0.147610	−	0.989046i	$-0.452842\pi$
$349$	671754.	0.295221	0.147610	+	0.989046i	$0.452842\pi$
$350$	710055.	0.309829
$351$	−552830.	−0.239510
$352$	−691662.	−0.297534
$353$	−2.29041e6	−0.978310	−0.489155	−	0.872197i	$-0.662695\pi$
$353$	−2.29041e6	−0.978310	−0.489155	+	0.872197i	$0.662695\pi$
$354$	125316.	0.0531494
$355$	177743.	0.0748553
$356$	2.30825e6	0.965291
$357$	55955.3	0.0232365
$358$	−1.23008e6	−0.507256
$359$	1.04304e6	0.427135	0.213567	−	0.976928i	$-0.431492\pi$
$359$	1.04304e6	0.427135	0.213567	+	0.976928i	$0.431492\pi$
$360$	73644.8	0.0299492
$361$	−1.50679e6	−0.608533
$362$	1.70678e6	0.684552
$363$	−2.65665e6	−1.05820
$364$	736818.	0.291478
$365$	841587.	0.330649
$366$	287141.	0.112045
$367$	−3.31985e6	−1.28663	−0.643314	−	0.765602i	$-0.722441\pi$
$367$	−3.31985e6	−1.28663	−0.643314	+	0.765602i	$0.722441\pi$
$368$	19779.0	0.00761352
$369$	727686.	0.278213
$370$	−75972.8	−0.0288505
$371$	247207.	0.0932450
$372$	−1.15313e6	−0.432036
$373$	2.58608e6	0.962432	0.481216	−	0.876602i	$-0.340195\pi$
$373$	2.58608e6	0.962432	0.481216	+	0.876602i	$0.340195\pi$
$374$	276615.	0.102258
$375$	−773294.	−0.283966
$376$	1.24888e6	0.455565
$377$	3.76684e6	1.36497
$378$	177078.	0.0637432
$379$	1.04792e6	0.374739	0.187370	−	0.982289i	$-0.440004\pi$
$379$	1.04792e6	0.374739	0.187370	+	0.982289i	$0.440004\pi$
$380$	223784.	0.0795005
$381$	−1.52887e6	−0.539582
$382$	−483633.	−0.169573
$383$	4.07716e6	1.42024	0.710118	−	0.704083i	$-0.248642\pi$
$383$	4.07716e6	1.42024	0.710118	+	0.704083i	$0.248642\pi$
$384$	147456.	0.0510310
$385$	−582702.	−0.200353
$386$	1.48633e6	0.507747
$387$	−1.60729e6	−0.545529
$388$	2.69764e6	0.909714
$389$	−3.11484e6	−1.04367	−0.521833	−	0.853048i	$-0.674752\pi$
$389$	−3.11484e6	−1.04367	−0.521833	+	0.853048i	$0.674752\pi$
$390$	−387832.	−0.129117
$391$	−7910.21	−0.00261665
$392$	839637.	0.275979
$393$	1.99757e6	0.652410
$394$	−1.09566e6	−0.355578
$395$	−473478.	−0.152689
$396$	875384.	0.280518
$397$	659120.	0.209888	0.104944	−	0.994478i	$-0.466534\pi$
$397$	659120.	0.209888	0.104944	+	0.994478i	$0.466534\pi$
$398$	3.77952e6	1.19599
$399$	538084.	0.169207
$400$	−748335.	−0.233855
$401$	1.96358e6	0.609801	0.304900	−	0.952384i	$-0.401377\pi$
$401$	1.96358e6	0.609801	0.304900	+	0.952384i	$0.401377\pi$
$402$	1.17003e6	0.361104
$403$	6.07266e6	1.86259
$404$	−1.05715e6	−0.322243
$405$	−93206.7	−0.0282364
$406$	−1.20656e6	−0.363274
$407$	−903056.	−0.270227
$408$	−58971.9	−0.0175386
$409$	1.91571e6	0.566267	0.283133	−	0.959081i	$-0.408626\pi$
$409$	1.91571e6	0.566267	0.283133	+	0.959081i	$0.408626\pi$
$410$	510500.	0.149981
$411$	3.35180e6	0.978754
$412$	−2.77739e6	−0.806109
$413$	211388.	0.0609824
$414$	−25032.9	−0.00717810
$415$	−1.62374e6	−0.462802
$416$	−776540.	−0.220004
$417$	−942335.	−0.265378
$418$	2.66002e6	0.744637
$419$	4.63185e6	1.28890	0.644450	−	0.764647i	$-0.277086\pi$
$419$	4.63185e6	1.28890	0.644450	+	0.764647i	$0.277086\pi$
$420$	124227.	0.0343631
$421$	−507841.	−0.139644	−0.0698221	−	0.997559i	$-0.522243\pi$
$421$	−507841.	−0.139644	−0.0698221	+	0.997559i	$0.522243\pi$
$422$	386160.	0.105557
$423$	−1.58061e6	−0.429511
$424$	−260534.	−0.0703801
$425$	299281.	0.0803723
$426$	−450421.	−0.120253
$427$	484360.	0.128558
$428$	1.87230e6	0.494044
$429$	−4.60999e6	−1.20936
$430$	−1.12758e6	−0.294087
$431$	−972161.	−0.252084	−0.126042	−	0.992025i	$-0.540227\pi$
$431$	−972161.	−0.252084	−0.126042	+	0.992025i	$0.540227\pi$
$432$	−186624.	−0.0481125
$433$	5.13587e6	1.31642	0.658210	−	0.752834i	$-0.271314\pi$
$433$	5.13587e6	1.31642	0.658210	+	0.752834i	$0.271314\pi$
$434$	−1.94514e6	−0.495709
$435$	635086.	0.160920
$436$	−754432.	−0.190066
$437$	−76067.1	−0.0190543
$438$	−2.13267e6	−0.531177
$439$	6.29775e6	1.55964	0.779819	−	0.626005i	$-0.215311\pi$
$439$	6.29775e6	1.55964	0.779819	+	0.626005i	$0.215311\pi$
$440$	614117.	0.151223
$441$	−1.06267e6	−0.260196
$442$	310561.	0.0756120
$443$	−6.75000e6	−1.63416	−0.817080	−	0.576524i	$-0.804409\pi$
$443$	−6.75000e6	−1.63416	−0.817080	+	0.576524i	$0.804409\pi$
$444$	192523.	0.0463475
$445$	−2.04947e6	−0.490615
$446$	4.76495e6	1.13428
$447$	−4.44414e6	−1.05201
$448$	248734.	0.0585519
$449$	6.32915e6	1.48160	0.740798	−	0.671728i	$-0.234448\pi$
$449$	6.32915e6	1.48160	0.740798	+	0.671728i	$0.234448\pi$
$450$	947112.	0.220480
$451$	6.06810e6	1.40479
$452$	3.23460e6	0.744687
$453$	3.21780e6	0.736739
$454$	−4.18504e6	−0.952928
$455$	−654210.	−0.148146
$456$	−567093.	−0.127715
$457$	−282797.	−0.0633409	−0.0316705	−	0.999498i	$-0.510083\pi$
$457$	−282797.	−0.0633409	−0.0316705	+	0.999498i	$0.510083\pi$
$458$	477640.	0.106399
$459$	74636.3	0.0165355
$460$	−17561.5	−0.00386962
$461$	2.19134e6	0.480238	0.240119	−	0.970743i	$-0.422814\pi$
$461$	2.19134e6	0.480238	0.240119	+	0.970743i	$0.422814\pi$
$462$	1.47663e6	0.321860
$463$	6.36020e6	1.37885	0.689427	−	0.724355i	$-0.257862\pi$
$463$	6.36020e6	1.37885	0.689427	+	0.724355i	$0.257862\pi$
$464$	1.27161e6	0.274194
$465$	1.02385e6	0.219585
$466$	1.67896e6	0.358158
$467$	−3.58046e6	−0.759707	−0.379853	−	0.925047i	$-0.624026\pi$
$467$	−3.58046e6	−0.759707	−0.379853	+	0.925047i	$0.624026\pi$
$468$	982809.	0.207422
$469$	1.97365e6	0.414322
$470$	−1.10886e6	−0.231544
$471$	−3.55347e6	−0.738075
$472$	−222784.	−0.0460287
$473$	−1.34031e7	−2.75455
$474$	1.19985e6	0.245290
$475$	2.87798e6	0.585267
$476$	−99476.0	−0.0201234
$477$	329738.	0.0663550
$478$	−2.07346e6	−0.415074
$479$	9.10022e6	1.81223	0.906115	−	0.423032i	$-0.139034\pi$
$479$	9.10022e6	1.81223	0.906115	+	0.423032i	$0.139034\pi$
$480$	−130924.	−0.0259368
$481$	−1.01388e6	−0.199812
$482$	−3.32229e6	−0.651357
$483$	−42226.4	−0.00823599
$484$	4.72293e6	0.916427
$485$	−2.39520e6	−0.462367
$486$	236196.	0.0453609
$487$	6.43143e6	1.22881	0.614406	−	0.788990i	$-0.289396\pi$
$487$	6.43143e6	1.22881	0.614406	+	0.788990i	$0.289396\pi$
$488$	−510472.	−0.0970337
$489$	−4.93915e6	−0.934071
$490$	−745502.	−0.140268
$491$	−225470.	−0.0422071	−0.0211035	−	0.999777i	$-0.506718\pi$
$491$	−225470.	−0.0422071	−0.0211035	+	0.999777i	$0.506718\pi$
$492$	−1.29366e6	−0.240940
$493$	−508552.	−0.0942363
$494$	2.98645e6	0.550603
$495$	−777241.	−0.142575
$496$	2.05001e6	0.374154
$497$	−759788.	−0.137975
$498$	4.11473e6	0.743478
$499$	3.89416e6	0.700103	0.350051	−	0.936730i	$-0.386164\pi$
$499$	3.89416e6	0.700103	0.350051	+	0.936730i	$0.386164\pi$
$500$	1.37475e6	0.245922
$501$	−5.87628e6	−1.04594
$502$	−6.91516e6	−1.22474
$503$	−2.58494e6	−0.455543	−0.227772	−	0.973715i	$-0.573144\pi$
$503$	−2.58494e6	−0.455543	−0.227772	+	0.973715i	$0.573144\pi$
$504$	−314804.	−0.0552032
$505$	938628.	0.163782
$506$	−208746.	−0.0362446
$507$	−1.83408e6	−0.316883
$508$	2.71799e6	0.467292
$509$	−2.26785e6	−0.387990	−0.193995	−	0.981003i	$-0.562145\pi$
$509$	−2.26785e6	−0.387990	−0.193995	+	0.981003i	$0.562145\pi$
$510$	52360.3	0.00891409
$511$	−3.59747e6	−0.609460
$512$	−262144.	−0.0441942
$513$	717727.	0.120411
$514$	−158653.	−0.0264874
$515$	2.46601e6	0.409709
$516$	2.85741e6	0.472442
$517$	−1.31806e7	−2.16874
$518$	324756.	0.0531781
$519$	6.34570e6	1.03410
$520$	689479.	0.111818
$521$	−1.09899e6	−0.177378	−0.0886888	−	0.996059i	$-0.528268\pi$
$521$	−1.09899e6	−0.177378	−0.0886888	+	0.996059i	$0.528268\pi$
$522$	−1.60938e6	−0.258513
$523$	−249313.	−0.0398558	−0.0199279	−	0.999801i	$-0.506344\pi$
$523$	−249313.	−0.0398558	−0.0199279	+	0.999801i	$0.506344\pi$
$524$	−3.55123e6	−0.565003
$525$	1.59762e6	0.252974
$526$	−2.50542e6	−0.394835
$527$	−819856.	−0.128591
$528$	−1.55624e6	−0.242936
$529$	−6.43037e6	−0.999073
$530$	231325.	0.0357711
$531$	281961.	0.0433963
$532$	−956594.	−0.146537
$533$	6.81276e6	1.03874
$534$	5.19357e6	0.788157
$535$	−1.66239e6	−0.251101
$536$	−2.08005e6	−0.312725
$537$	−2.76769e6	−0.414172
$538$	510010.	0.0759666
$539$	−8.86146e6	−1.31381
$540$	165701.	0.0244535
$541$	2.51858e6	0.369966	0.184983	−	0.982742i	$-0.440777\pi$
$541$	2.51858e6	0.369966	0.184983	+	0.982742i	$0.440777\pi$
$542$	−4.10743e6	−0.600582
$543$	3.84026e6	0.558935
$544$	104839.	0.0151889
$545$	669850.	0.0966020
$546$	1.65784e6	0.237991
$547$	5.32569e6	0.761040	0.380520	−	0.924773i	$-0.375745\pi$
$547$	5.32569e6	0.761040	0.380520	+	0.924773i	$0.375745\pi$
$548$	−5.95876e6	−0.847626
$549$	646067.	0.0914843
$550$	7.89787e6	1.11328
$551$	−4.89040e6	−0.686224
$552$	44502.8	0.00621642
$553$	2.02395e6	0.281440
$554$	−4.52375e6	−0.626216
$555$	−170939.	−0.0235564
$556$	1.67526e6	0.229824
$557$	−8.54774e6	−1.16738	−0.583691	−	0.811976i	$-0.698392\pi$
$557$	−8.54774e6	−1.16738	−0.583691	+	0.811976i	$0.698392\pi$
$558$	−2.59454e6	−0.352756
$559$	−1.50478e7	−2.03678
$560$	−220848.	−0.0297593
$561$	622385.	0.0834933
$562$	−1.32149e6	−0.176491
$563$	7.09651e6	0.943569	0.471785	−	0.881714i	$-0.343610\pi$
$563$	7.09651e6	0.943569	0.471785	+	0.881714i	$0.343610\pi$
$564$	2.80998e6	0.371967
$565$	−2.87195e6	−0.378491
$566$	4.27042e6	0.560312
$567$	398424.	0.0520461
$568$	800749.	0.104142
$569$	7.28012e6	0.942667	0.471333	−	0.881955i	$-0.343773\pi$
$569$	7.28012e6	0.942667	0.471333	+	0.881955i	$0.343773\pi$
$570$	503514.	0.0649119
$571$	−9.20342e6	−1.18130	−0.590648	−	0.806929i	$-0.701128\pi$
$571$	−9.20342e6	−1.18130	−0.590648	+	0.806929i	$0.701128\pi$
$572$	8.19554e6	1.04734
$573$	−1.08817e6	−0.138456
$574$	−2.18220e6	−0.276449
$575$	−225851.	−0.0284873
$576$	331776.	0.0416667
$577$	6.86485e6	0.858404	0.429202	−	0.903209i	$-0.358795\pi$
$577$	6.86485e6	0.858404	0.429202	+	0.903209i	$0.358795\pi$
$578$	5.63750e6	0.701887
$579$	3.34425e6	0.414574
$580$	−1.12904e6	−0.139361
$581$	6.94088e6	0.853050
$582$	6.06969e6	0.742778
$583$	2.74966e6	0.335048
$584$	3.79142e6	0.460012
$585$	−872622.	−0.105423
$586$	1.51550e6	0.182311
$587$	6.47613e6	0.775748	0.387874	−	0.921712i	$-0.373210\pi$
$587$	6.47613e6	0.775748	0.387874	+	0.921712i	$0.373210\pi$
$588$	1.88918e6	0.225336
$589$	−7.88400e6	−0.936394
$590$	197807.	0.0233944
$591$	−2.46523e6	−0.290328
$592$	−342264.	−0.0401381
$593$	−3.76506e6	−0.439678	−0.219839	−	0.975536i	$-0.570553\pi$
$593$	−3.76506e6	−0.439678	−0.219839	+	0.975536i	$0.570553\pi$
$594$	1.96961e6	0.229042
$595$	88323.4	0.0102278
$596$	7.90070e6	0.911066
$597$	8.50392e6	0.976524
$598$	−234363.	−0.0268001
$599$	−2.48233e6	−0.282678	−0.141339	−	0.989961i	$-0.545141\pi$
$599$	−2.48233e6	−0.282678	−0.141339	+	0.989961i	$0.545141\pi$
$600$	−1.68375e6	−0.190942
$601$	4.96681e6	0.560908	0.280454	−	0.959868i	$-0.409515\pi$
$601$	4.96681e6	0.560908	0.280454	+	0.959868i	$0.409515\pi$
$602$	4.81999e6	0.542069
$603$	2.63257e6	0.294840
$604$	−5.72053e6	−0.638034
$605$	−4.19342e6	−0.465779
$606$	−2.37859e6	−0.263110
$607$	1.61639e6	0.178063	0.0890316	−	0.996029i	$-0.471623\pi$
$607$	1.61639e6	0.178063	0.0890316	+	0.996029i	$0.471623\pi$
$608$	1.00817e6	0.110604
$609$	−2.71476e6	−0.296612
$610$	453241.	0.0493179
$611$	−1.47980e7	−1.60362
$612$	−132687.	−0.0143202
$613$	−6.95923e6	−0.748014	−0.374007	−	0.927426i	$-0.622016\pi$
$613$	−6.95923e6	−0.748014	−0.374007	+	0.927426i	$0.622016\pi$
$614$	1.06912e6	0.114447
$615$	1.14863e6	0.122459
$616$	−2.62512e6	−0.278739
$617$	−1.21309e7	−1.28287	−0.641433	−	0.767179i	$-0.721660\pi$
$617$	−1.21309e7	−1.28287	−0.641433	+	0.767179i	$0.721660\pi$
$618$	−6.24913e6	−0.658185
$619$	−1.47287e7	−1.54503	−0.772515	−	0.634996i	$-0.781002\pi$
$619$	−1.47287e7	−1.54503	−0.772515	+	0.634996i	$0.781002\pi$
$620$	−1.82017e6	−0.190166
$621$	−56323.9	−0.00586089
$622$	−6.07227e6	−0.629325
$623$	8.76071e6	0.904314
$624$	−1.74722e6	−0.179633
$625$	7.91434e6	0.810428
$626$	4.00182e6	0.408151
$627$	5.98505e6	0.607994
$628$	6.31728e6	0.639192
$629$	136881.	0.0137949
$630$	279510.	0.0280574
$631$	9.22299e6	0.922144	0.461072	−	0.887363i	$-0.347465\pi$
$631$	9.22299e6	0.922144	0.461072	+	0.887363i	$0.347465\pi$
$632$	−2.13306e6	−0.212427
$633$	868860.	0.0861868
$634$	7.18364e6	0.709777
$635$	−2.41326e6	−0.237504
$636$	−586202.	−0.0574651
$637$	−9.94892e6	−0.971465
$638$	−1.34204e7	−1.30531
$639$	−1.01345e6	−0.0981859
$640$	232754.	0.0224619
$641$	2.55155e6	0.245278	0.122639	−	0.992451i	$-0.460864\pi$
$641$	2.55155e6	0.245278	0.122639	+	0.992451i	$0.460864\pi$
$642$	4.21267e6	0.403386
$643$	−1.79226e7	−1.70952	−0.854760	−	0.519024i	$-0.826296\pi$
$643$	−1.79226e7	−1.70952	−0.854760	+	0.519024i	$0.826296\pi$
$644$	75069.1	0.00713258
$645$	−2.53705e6	−0.240121
$646$	−403194.	−0.0380131
$647$	−168551.	−0.0158296	−0.00791481	−	0.999969i	$-0.502519\pi$
$647$	−168551.	−0.0158296	−0.00791481	+	0.999969i	$0.502519\pi$
$648$	−419904.	−0.0392837
$649$	2.35124e6	0.219122
$650$	8.86707e6	0.823184
$651$	−4.37657e6	−0.404745
$652$	8.78071e6	0.808929
$653$	−1.58633e7	−1.45583	−0.727916	−	0.685666i	$-0.759511\pi$
$653$	−1.58633e7	−1.45583	−0.727916	+	0.685666i	$0.759511\pi$
$654$	−1.69747e6	−0.155188
$655$	3.15309e6	0.287166
$656$	2.29985e6	0.208660
$657$	−4.79851e6	−0.433704
$658$	4.73997e6	0.426787
$659$	154714.	0.0138776	0.00693881	−	0.999976i	$-0.497791\pi$
$659$	154714.	0.0138776	0.00693881	+	0.999976i	$0.497791\pi$
$660$	1.38176e6	0.123473
$661$	7.43247e6	0.661652	0.330826	−	0.943692i	$-0.392673\pi$
$661$	7.43247e6	0.661652	0.330826	+	0.943692i	$0.392673\pi$
$662$	−1.30996e7	−1.16175
$663$	698762.	0.0617370
$664$	−7.31507e6	−0.643870
$665$	849346.	0.0744785
$666$	433178.	0.0378426
$667$	383776.	0.0334013
$668$	1.04467e7	0.905813
$669$	1.07211e7	0.926138
$670$	1.84685e6	0.158944
$671$	5.38748e6	0.461934
$672$	559652.	0.0478074
$673$	2.02011e7	1.71924	0.859622	−	0.510930i	$-0.170699\pi$
$673$	2.02011e7	1.71924	0.859622	+	0.510930i	$0.170699\pi$
$674$	1.07019e7	0.907428
$675$	2.13100e6	0.180021
$676$	3.26059e6	0.274429
$677$	−1.19325e7	−1.00060	−0.500300	−	0.865852i	$-0.666777\pi$
$677$	−1.19325e7	−1.00060	−0.500300	+	0.865852i	$0.666777\pi$
$678$	7.27784e6	0.608034
$679$	1.02386e7	0.852247
$680$	−93085.0	−0.00771982
$681$	−9.41634e6	−0.778062
$682$	−2.16356e7	−1.78118
$683$	−1.21038e7	−0.992819	−0.496409	−	0.868089i	$-0.665348\pi$
$683$	−1.21038e7	−0.992819	−0.496409	+	0.868089i	$0.665348\pi$
$684$	−1.27596e6	−0.104279
$685$	5.29069e6	0.430810
$686$	7.26925e6	0.589765
$687$	1.07469e6	0.0868743
$688$	−5.07984e6	−0.409147
$689$	3.08709e6	0.247743
$690$	−39513.5	−0.00315953
$691$	2.21688e7	1.76623	0.883115	−	0.469157i	$-0.155442\pi$
$691$	2.21688e7	1.76623	0.883115	+	0.469157i	$0.155442\pi$
$692$	−1.12812e7	−0.895553
$693$	3.32242e6	0.262798
$694$	803339.	0.0633141
$695$	−1.48744e6	−0.116809
$696$	2.86112e6	0.223879
$697$	−919775.	−0.0717133
$698$	−2.68702e6	−0.208753
$699$	3.77765e6	0.292435
$700$	−2.84022e6	−0.219082
$701$	−1.79518e7	−1.37979	−0.689895	−	0.723909i	$-0.742343\pi$
$701$	−1.79518e7	−1.37979	−0.689895	+	0.723909i	$0.742343\pi$
$702$	2.21132e6	0.169359
$703$	1.31629e6	0.100453
$704$	2.76665e6	0.210389
$705$	−2.49494e6	−0.189054
$706$	9.16164e6	0.691769
$707$	−4.01229e6	−0.301887
$708$	−501264.	−0.0375823
$709$	−2.43916e7	−1.82232	−0.911159	−	0.412055i	$-0.864811\pi$
$709$	−2.43916e7	−1.82232	−0.911159	+	0.412055i	$0.864811\pi$
$710$	−710974.	−0.0529307
$711$	2.69965e6	0.200278
$712$	−9.23301e6	−0.682564
$713$	618701.	0.0455781
$714$	−223821.	−0.0164307
$715$	−7.27671e6	−0.532316
$716$	4.92033e6	0.358684
$717$	−4.66528e6	−0.338906
$718$	−4.17216e6	−0.302030
$719$	5.07880e6	0.366386	0.183193	−	0.983077i	$-0.441357\pi$
$719$	5.07880e6	0.366386	0.183193	+	0.983077i	$0.441357\pi$
$720$	−294579.	−0.0211773
$721$	−1.05413e7	−0.755187
$722$	6.02715e6	0.430298
$723$	−7.47514e6	−0.531831
$724$	−6.82713e6	−0.484052
$725$	−1.45201e7	−1.02595
$726$	1.06266e7	0.748259
$727$	2.58783e7	1.81594	0.907968	−	0.419040i	$-0.137633\pi$
$727$	2.58783e7	1.81594	0.907968	+	0.419040i	$0.137633\pi$
$728$	−2.94727e6	−0.206106
$729$	531441.	0.0370370
$730$	−3.36635e6	−0.233804
$731$	2.03157e6	0.140617
$732$	−1.14856e6	−0.0792277
$733$	2.25369e7	1.54930	0.774648	−	0.632393i	$-0.217927\pi$
$733$	2.25369e7	1.54930	0.774648	+	0.632393i	$0.217927\pi$
$734$	1.32794e7	0.909784
$735$	−1.67738e6	−0.114528
$736$	−79116.2	−0.00538357
$737$	2.19527e7	1.48874
$738$	−2.91074e6	−0.196727
$739$	5.84673e6	0.393823	0.196912	−	0.980421i	$-0.436909\pi$
$739$	5.84673e6	0.393823	0.196912	+	0.980421i	$0.436909\pi$
$740$	303891.	0.0204004
$741$	6.71952e6	0.449565
$742$	−988827.	−0.0659342
$743$	−2.31068e7	−1.53556	−0.767782	−	0.640711i	$-0.778640\pi$
$743$	−2.31068e7	−1.53556	−0.767782	+	0.640711i	$0.778640\pi$
$744$	4.61251e6	0.305496
$745$	−7.01492e6	−0.463054
$746$	−1.03443e7	−0.680542
$747$	9.25814e6	0.607047
$748$	−1.10646e6	−0.0723073
$749$	7.10610e6	0.462836
$750$	3.09318e6	0.200794
$751$	−1.97362e7	−1.27692	−0.638459	−	0.769655i	$-0.720428\pi$
$751$	−1.97362e7	−1.27692	−0.638459	+	0.769655i	$0.720428\pi$
$752$	−4.99551e6	−0.322133
$753$	−1.55591e7	−0.999994
$754$	−1.50674e7	−0.965181
$755$	5.07918e6	0.324284
$756$	−708310.	−0.0450733
$757$	1.04314e7	0.661611	0.330805	−	0.943699i	$-0.392680\pi$
$757$	1.04314e7	0.661611	0.330805	+	0.943699i	$0.392680\pi$
$758$	−4.19167e6	−0.264981
$759$	−469679.	−0.0295936
$760$	−895136.	−0.0562153
$761$	−2.27052e6	−0.142123	−0.0710614	−	0.997472i	$-0.522639\pi$
$761$	−2.27052e6	−0.142123	−0.0710614	+	0.997472i	$0.522639\pi$
$762$	6.11547e6	0.381542
$763$	−2.86336e6	−0.178059
$764$	1.93453e6	0.119906
$765$	117811.	0.00727832
$766$	−1.63086e7	−1.00426
$767$	2.63978e6	0.162024
$768$	−589824.	−0.0360844
$769$	1.43619e6	0.0875783	0.0437892	−	0.999041i	$-0.486057\pi$
$769$	1.43619e6	0.0875783	0.0437892	+	0.999041i	$0.486057\pi$
$770$	2.33081e6	0.141671
$771$	−356968.	−0.0216269
$772$	−5.94533e6	−0.359031
$773$	−1.24365e7	−0.748601	−0.374301	−	0.927307i	$-0.622117\pi$
$773$	−1.24365e7	−0.748601	−0.374301	+	0.927307i	$0.622117\pi$
$774$	6.42917e6	0.385747
$775$	−2.34084e7	−1.39996
$776$	−1.07906e7	−0.643265
$777$	730701.	0.0434197
$778$	1.24593e7	0.737983
$779$	−8.84485e6	−0.522212
$780$	1.55133e6	0.0912992
$781$	−8.45104e6	−0.495773
$782$	31640.8	0.00185025
$783$	−3.62110e6	−0.211075
$784$	−3.35855e6	−0.195147
$785$	−5.60902e6	−0.324873
$786$	−7.99028e6	−0.461323
$787$	7.62883e6	0.439057	0.219528	−	0.975606i	$-0.429548\pi$
$787$	7.62883e6	0.439057	0.219528	+	0.975606i	$0.429548\pi$
$788$	4.38264e6	0.251432
$789$	−5.63719e6	−0.322381
$790$	1.89391e6	0.107967
$791$	1.22765e7	0.697645
$792$	−3.50154e6	−0.198356
$793$	6.04862e6	0.341565
$794$	−2.63648e6	−0.148413
$795$	520480.	0.0292070
$796$	−1.51181e7	−0.845695
$797$	−1.14344e7	−0.637626	−0.318813	−	0.947818i	$-0.603284\pi$
$797$	−1.14344e7	−0.637626	−0.318813	+	0.947818i	$0.603284\pi$
$798$	−2.15234e6	−0.119647
$799$	1.99785e6	0.110712
$800$	2.99334e6	0.165360
$801$	1.16855e7	0.643528
$802$	−7.85432e6	−0.431194
$803$	−4.00143e7	−2.18991
$804$	−4.68012e6	−0.255339
$805$	−66652.8	−0.00362517
$806$	−2.42907e7	−1.31705
$807$	1.14752e6	0.0620265
$808$	4.22860e6	0.227860
$809$	−1.94374e7	−1.04416	−0.522079	−	0.852897i	$-0.674843\pi$
$809$	−1.94374e7	−1.04416	−0.522079	+	0.852897i	$0.674843\pi$
$810$	372827.	0.0199662
$811$	9.97001e6	0.532284	0.266142	−	0.963934i	$-0.414251\pi$
$811$	9.97001e6	0.532284	0.266142	+	0.963934i	$0.414251\pi$
$812$	4.82624e6	0.256873
$813$	−9.24172e6	−0.490373
$814$	3.61223e6	0.191079
$815$	−7.79626e6	−0.411143
$816$	235888.	0.0124017
$817$	1.95363e7	1.02397
$818$	−7.66283e6	−0.400411
$819$	3.73014e6	0.194319
$820$	−2.04200e6	−0.106053
$821$	1.26528e7	0.655132	0.327566	−	0.944828i	$-0.393772\pi$
$821$	1.26528e7	0.655132	0.327566	+	0.944828i	$0.393772\pi$
$822$	−1.34072e7	−0.692084
$823$	3.63579e6	0.187111	0.0935556	−	0.995614i	$-0.470177\pi$
$823$	3.63579e6	0.187111	0.0935556	+	0.995614i	$0.470177\pi$
$824$	1.11096e7	0.570005
$825$	1.77702e7	0.908987
$826$	−845551.	−0.0431211
$827$	−2.73581e7	−1.39099	−0.695493	−	0.718533i	$-0.744814\pi$
$827$	−2.73581e7	−1.39099	−0.695493	+	0.718533i	$0.744814\pi$
$828$	100131.	0.00507568
$829$	−3.20389e7	−1.61917	−0.809583	−	0.587006i	$-0.800307\pi$
$829$	−3.20389e7	−1.61917	−0.809583	+	0.587006i	$0.800307\pi$
$830$	6.49495e6	0.327251
$831$	−1.01784e7	−0.511303
$832$	3.10616e6	0.155566
$833$	1.34318e6	0.0670690
$834$	3.76934e6	0.187651
$835$	−9.27549e6	−0.460385
$836$	−1.06401e7	−0.526538
$837$	−5.83771e6	−0.288024
$838$	−1.85274e7	−0.911390
$839$	2.66829e7	1.30866	0.654331	−	0.756208i	$-0.272950\pi$
$839$	2.66829e7	1.30866	0.654331	+	0.756208i	$0.272950\pi$
$840$	−496907.	−0.0242984
$841$	4.16208e6	0.202918
$842$	2.03137e6	0.0987433
$843$	−2.97335e6	−0.144104
$844$	−1.54464e6	−0.0746399
$845$	−2.89503e6	−0.139480
$846$	6.32245e6	0.303710
$847$	1.79253e7	0.858536
$848$	1.04214e6	0.0497663
$849$	9.60845e6	0.457492
$850$	−1.19712e6	−0.0568318
$851$	−103297.	−0.00488948
$852$	1.80169e6	0.0850315
$853$	−8.78108e6	−0.413214	−0.206607	−	0.978424i	$-0.566242\pi$
$853$	−8.78108e6	−0.413214	−0.206607	+	0.978424i	$0.566242\pi$
$854$	−1.93744e6	−0.0909041
$855$	1.13291e6	0.0530003
$856$	−7.48920e6	−0.349342
$857$	−2.82327e7	−1.31311	−0.656554	−	0.754279i	$-0.727987\pi$
$857$	−2.82327e7	−1.31311	−0.656554	+	0.754279i	$0.727987\pi$
$858$	1.84400e7	0.855150
$859$	7.79828e6	0.360592	0.180296	−	0.983612i	$-0.442294\pi$
$859$	7.79828e6	0.360592	0.180296	+	0.983612i	$0.442294\pi$
$860$	4.51032e6	0.207951
$861$	−4.90995e6	−0.225720
$862$	3.88864e6	0.178250
$863$	3.61364e7	1.65165	0.825825	−	0.563926i	$-0.190710\pi$
$863$	3.61364e7	1.65165	0.825825	+	0.563926i	$0.190710\pi$
$864$	746496.	0.0340207
$865$	1.00165e7	0.455170
$866$	−2.05435e7	−0.930850
$867$	1.26844e7	0.573088
$868$	7.78056e6	0.350519
$869$	2.25121e7	1.01127
$870$	−2.54034e6	−0.113787
$871$	2.46467e7	1.10081
$872$	3.01773e6	0.134397
$873$	1.36568e7	0.606476
$874$	304269.	0.0134734
$875$	5.21769e6	0.230387
$876$	8.53069e6	0.375599
$877$	1.27409e7	0.559372	0.279686	−	0.960092i	$-0.409770\pi$
$877$	1.27409e7	0.559372	0.279686	+	0.960092i	$0.409770\pi$
$878$	−2.51910e7	−1.10283
$879$	3.40988e6	0.148856
$880$	−2.45647e6	−0.106931
$881$	1.86041e6	0.0807547	0.0403774	−	0.999185i	$-0.487144\pi$
$881$	1.86041e6	0.0807547	0.0403774	+	0.999185i	$0.487144\pi$
$882$	4.25066e6	0.183986
$883$	−9.81276e6	−0.423535	−0.211767	−	0.977320i	$-0.567922\pi$
$883$	−9.81276e6	−0.423535	−0.211767	+	0.977320i	$0.567922\pi$
$884$	−1.24224e6	−0.0534658
$885$	445065.	0.0191014
$886$	2.70000e7	1.15553
$887$	2.85145e7	1.21690	0.608452	−	0.793591i	$-0.291791\pi$
$887$	2.85145e7	1.21690	0.608452	+	0.793591i	$0.291791\pi$
$888$	−770094.	−0.0327726
$889$	1.03158e7	0.437773
$890$	8.19786e6	0.346917
$891$	4.43163e6	0.187012
$892$	−1.90598e7	−0.802059
$893$	1.92120e7	0.806201
$894$	1.77766e7	0.743882
$895$	−4.36869e6	−0.182303
$896$	−994938.	−0.0414024
$897$	−527317.	−0.0218822
$898$	−2.53166e7	−1.04765
$899$	3.97766e7	1.64145
$900$	−3.78845e6	−0.155903
$901$	−416780.	−0.0171039
$902$	−2.42724e7	−0.993336
$903$	1.08450e7	0.442598
$904$	−1.29384e7	−0.526573
$905$	6.06171e6	0.246022
$906$	−1.28712e7	−0.520953
$907$	−1.49273e7	−0.602507	−0.301254	−	0.953544i	$-0.597405\pi$
$907$	−1.49273e7	−0.602507	−0.301254	+	0.953544i	$0.597405\pi$
$908$	1.67402e7	0.673822
$909$	−5.35182e6	−0.214828
$910$	2.61684e6	0.104755
$911$	1.85935e7	0.742277	0.371138	−	0.928578i	$-0.378968\pi$
$911$	1.85935e7	0.742277	0.371138	+	0.928578i	$0.378968\pi$
$912$	2.26837e6	0.0903082
$913$	7.72027e7	3.06518
$914$	1.13119e6	0.0447888
$915$	1.01979e6	0.0402679
$916$	−1.91056e6	−0.0752353
$917$	−1.34783e7	−0.529312
$918$	−298545.	−0.0116924
$919$	1.58584e7	0.619400	0.309700	−	0.950834i	$-0.399771\pi$
$919$	1.58584e7	0.619400	0.309700	+	0.950834i	$0.399771\pi$
$920$	70246.1	0.00273623
$921$	2.40551e6	0.0934455
$922$	−8.76534e6	−0.339580
$923$	−9.48813e6	−0.366586
$924$	−5.90653e6	−0.227589
$925$	3.90820e6	0.150184
$926$	−2.54408e7	−0.974997
$927$	−1.40605e7	−0.537406
$928$	−5.08643e6	−0.193884
$929$	4.00351e6	0.152196	0.0760978	−	0.997100i	$-0.475754\pi$
$929$	4.00351e6	0.152196	0.0760978	+	0.997100i	$0.475754\pi$
$930$	−4.09539e6	−0.155270
$931$	1.29165e7	0.488393
$932$	−6.71583e6	−0.253256
$933$	−1.36626e7	−0.513842
$934$	1.43218e7	0.537194
$935$	982412.	0.0367506
$936$	−3.93124e6	−0.146669
$937$	−2.34958e7	−0.874262	−0.437131	−	0.899398i	$-0.644005\pi$
$937$	−2.34958e7	−0.874262	−0.437131	+	0.899398i	$0.644005\pi$
$938$	−7.89460e6	−0.292970
$939$	9.00408e6	0.333254
$940$	4.43545e6	0.163726
$941$	−4.24139e7	−1.56147	−0.780736	−	0.624862i	$-0.785155\pi$
$941$	−4.24139e7	−1.56147	−0.780736	+	0.624862i	$0.785155\pi$
$942$	1.42139e7	0.521898
$943$	694104.	0.0254182
$944$	891136.	0.0325472
$945$	628898.	0.0229087
$946$	5.36122e7	1.94776
$947$	−1.43678e7	−0.520613	−0.260306	−	0.965526i	$-0.583824\pi$
$947$	−1.43678e7	−0.520613	−0.260306	+	0.965526i	$0.583824\pi$
$948$	−4.79938e6	−0.173446
$949$	−4.49248e7	−1.61927
$950$	−1.15119e7	−0.413846
$951$	1.61632e7	0.579530
$952$	397904.	0.0142294
$953$	−5.33886e7	−1.90422	−0.952108	−	0.305761i	$-0.901089\pi$
$953$	−5.33886e7	−1.90422	−0.952108	+	0.305761i	$0.901089\pi$
$954$	−1.31895e6	−0.0469201
$955$	−1.71764e6	−0.0609431
$956$	8.29383e6	0.293501
$957$	−3.01960e7	−1.06578
$958$	−3.64009e7	−1.28144
$959$	−2.26158e7	−0.794081
$960$	523696.	0.0183401
$961$	3.54963e7	1.23986
$962$	4.05551e6	0.141289
$963$	9.47852e6	0.329363
$964$	1.32891e7	0.460579
$965$	5.27877e6	0.182480
$966$	168905.	0.00582373
$967$	4.39478e7	1.51137	0.755685	−	0.654935i	$-0.227304\pi$
$967$	4.39478e7	1.51137	0.755685	+	0.654935i	$0.227304\pi$
$968$	−1.88917e7	−0.648011
$969$	−907187.	−0.0310375
$970$	9.58079e6	0.326943
$971$	−2.71730e7	−0.924887	−0.462444	−	0.886649i	$-0.653027\pi$
$971$	−2.71730e7	−0.924887	−0.462444	+	0.886649i	$0.653027\pi$
$972$	−944784.	−0.0320750
$973$	6.35826e6	0.215306
$974$	−2.57257e7	−0.868901
$975$	1.99509e7	0.672127
$976$	2.04189e6	0.0686132
$977$	−1.90049e7	−0.636986	−0.318493	−	0.947925i	$-0.603177\pi$
$977$	−1.90049e7	−0.636986	−0.318493	+	0.947925i	$0.603177\pi$
$978$	1.97566e7	0.660488
$979$	9.74445e7	3.24938
$980$	2.98201e6	0.0991845
$981$	−3.81931e6	−0.126711
$982$	901880.	0.0298449
$983$	1.85064e7	0.610856	0.305428	−	0.952215i	$-0.401201\pi$
$983$	1.85064e7	0.610856	0.305428	+	0.952215i	$0.401201\pi$
$984$	5.17466e6	0.170370
$985$	−3.89128e6	−0.127792
$986$	2.03421e6	0.0666351
$987$	1.06649e7	0.348470
$988$	−1.19458e7	−0.389335
$989$	−1.53312e6	−0.0498408
$990$	3.10897e6	0.100816
$991$	−3.81597e7	−1.23430	−0.617151	−	0.786845i	$-0.711713\pi$
$991$	−3.81597e7	−1.23430	−0.617151	+	0.786845i	$0.711713\pi$
$992$	−8.20002e6	−0.264567
$993$	−2.94741e7	−0.948565
$994$	3.03915e6	0.0975633
$995$	1.34231e7	0.429829
$996$	−1.64589e7	−0.525718
$997$	3.66596e7	1.16802	0.584009	−	0.811747i	$-0.301483\pi$
$997$	3.66596e7	1.16802	0.584009	+	0.811747i	$0.301483\pi$
$998$	−1.55766e7	−0.495048
$999$	974650.	0.0308983

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	354.6.a.g.1.4	✓	6
3.2	odd	2		1062.6.a.h.1.3		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
354.6.a.g.1.4	✓	6	1.1	even	1	trivial
1062.6.a.h.1.3		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)

\(f(q)\)	\(=\)	\(q-4.00000 q^{2} -9.00000 q^{3} +16.0000 q^{4} -14.2062 q^{5} +36.0000 q^{6} +60.7262 q^{7} -64.0000 q^{8} +81.0000 q^{9} +O(q^{10})\)	\(q-4.00000 q^{2} -9.00000 q^{3} +16.0000 q^{4} -14.2062 q^{5} +36.0000 q^{6} +60.7262 q^{7} -64.0000 q^{8} +81.0000 q^{9} +56.8247 q^{10} +675.451 q^{11} -144.000 q^{12} +758.340 q^{13} -242.905 q^{14} +127.856 q^{15} +256.000 q^{16} -102.382 q^{17} -324.000 q^{18} -984.536 q^{19} -227.299 q^{20} -546.536 q^{21} -2701.80 q^{22} +77.2619 q^{23} +576.000 q^{24} -2923.18 q^{25} -3033.36 q^{26} -729.000 q^{27} +971.619 q^{28} +4967.22 q^{29} -511.422 q^{30} +8007.84 q^{31} -1024.00 q^{32} -6079.06 q^{33} +409.527 q^{34} -862.687 q^{35} +1296.00 q^{36} -1336.97 q^{37} +3938.15 q^{38} -6825.06 q^{39} +909.195 q^{40} +8983.78 q^{41} +2186.14 q^{42} -19843.1 q^{43} +10807.2 q^{44} -1150.70 q^{45} -309.048 q^{46} -19513.7 q^{47} -2304.00 q^{48} -13119.3 q^{49} +11692.7 q^{50} +921.436 q^{51} +12133.4 q^{52} +4070.85 q^{53} +2916.00 q^{54} -9595.57 q^{55} -3886.47 q^{56} +8860.83 q^{57} -19868.9 q^{58} +3481.00 q^{59} +2045.69 q^{60} +7976.13 q^{61} -32031.3 q^{62} +4918.82 q^{63} +4096.00 q^{64} -10773.1 q^{65} +24316.2 q^{66} +32500.8 q^{67} -1638.11 q^{68} -695.357 q^{69} +3450.75 q^{70} -12511.7 q^{71} -5184.00 q^{72} -59240.9 q^{73} +5347.87 q^{74} +26308.7 q^{75} -15752.6 q^{76} +41017.5 q^{77} +27300.2 q^{78} +33329.1 q^{79} -3636.78 q^{80} +6561.00 q^{81} -35935.1 q^{82} +114298. q^{83} -8744.57 q^{84} +1454.45 q^{85} +79372.5 q^{86} -44704.9 q^{87} -43228.9 q^{88} +144266. q^{89} +4602.80 q^{90} +46051.1 q^{91} +1236.19 q^{92} -72070.5 q^{93} +78054.9 q^{94} +13986.5 q^{95} +9216.00 q^{96} +168603. q^{97} +52477.3 q^{98} +54711.5 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 24 q^{2} - 54 q^{3} + 96 q^{4} + 4 q^{5} + 216 q^{6} - 54 q^{7} - 384 q^{8} + 486 q^{9}+O(q^{10}) \) 6 * q - 24 * q^2 - 54 * q^3 + 96 * q^4 + 4 * q^5 + 216 * q^6 - 54 * q^7 - 384 * q^8 + 486 * q^9	\( 6 q - 24 q^{2} - 54 q^{3} + 96 q^{4} + 4 q^{5} + 216 q^{6} - 54 q^{7} - 384 q^{8} + 486 q^{9} - 16 q^{10} + 436 q^{11} - 864 q^{12} - 536 q^{13} + 216 q^{14} - 36 q^{15} + 1536 q^{16} + 910 q^{17} - 1944 q^{18} + 1462 q^{19} + 64 q^{20} + 486 q^{21} - 1744 q^{22} + 1634 q^{23} + 3456 q^{24} - 1186 q^{25} + 2144 q^{26} - 4374 q^{27} - 864 q^{28} - 1598 q^{29} + 144 q^{30} - 5670 q^{31} - 6144 q^{32} - 3924 q^{33} - 3640 q^{34} - 7242 q^{35} + 7776 q^{36} - 20458 q^{37} - 5848 q^{38} + 4824 q^{39} - 256 q^{40} + 262 q^{41} - 1944 q^{42} - 34028 q^{43} + 6976 q^{44} + 324 q^{45} - 6536 q^{46} - 11194 q^{47} - 13824 q^{48} - 32652 q^{49} + 4744 q^{50} - 8190 q^{51} - 8576 q^{52} - 17164 q^{53} + 17496 q^{54} - 37040 q^{55} + 3456 q^{56} - 13158 q^{57} + 6392 q^{58} + 20886 q^{59} - 576 q^{60} - 43546 q^{61} + 22680 q^{62} - 4374 q^{63} + 24576 q^{64} + 65568 q^{65} + 15696 q^{66} - 52772 q^{67} + 14560 q^{68} - 14706 q^{69} + 28968 q^{70} + 84740 q^{71} - 31104 q^{72} - 36578 q^{73} + 81832 q^{74} + 10674 q^{75} + 23392 q^{76} + 90678 q^{77} - 19296 q^{78} + 85196 q^{79} + 1024 q^{80} + 39366 q^{81} - 1048 q^{82} + 217026 q^{83} + 7776 q^{84} + 26570 q^{85} + 136112 q^{86} + 14382 q^{87} - 27904 q^{88} + 333850 q^{89} - 1296 q^{90} + 214914 q^{91} + 26144 q^{92} + 51030 q^{93} + 44776 q^{94} + 458758 q^{95} + 55296 q^{96} + 173148 q^{97} + 130608 q^{98} + 35316 q^{99}+O(q^{100}) \) 6 * q - 24 * q^2 - 54 * q^3 + 96 * q^4 + 4 * q^5 + 216 * q^6 - 54 * q^7 - 384 * q^8 + 486 * q^9 - 16 * q^10 + 436 * q^11 - 864 * q^12 - 536 * q^13 + 216 * q^14 - 36 * q^15 + 1536 * q^16 + 910 * q^17 - 1944 * q^18 + 1462 * q^19 + 64 * q^20 + 486 * q^21 - 1744 * q^22 + 1634 * q^23 + 3456 * q^24 - 1186 * q^25 + 2144 * q^26 - 4374 * q^27 - 864 * q^28 - 1598 * q^29 + 144 * q^30 - 5670 * q^31 - 6144 * q^32 - 3924 * q^33 - 3640 * q^34 - 7242 * q^35 + 7776 * q^36 - 20458 * q^37 - 5848 * q^38 + 4824 * q^39 - 256 * q^40 + 262 * q^41 - 1944 * q^42 - 34028 * q^43 + 6976 * q^44 + 324 * q^45 - 6536 * q^46 - 11194 * q^47 - 13824 * q^48 - 32652 * q^49 + 4744 * q^50 - 8190 * q^51 - 8576 * q^52 - 17164 * q^53 + 17496 * q^54 - 37040 * q^55 + 3456 * q^56 - 13158 * q^57 + 6392 * q^58 + 20886 * q^59 - 576 * q^60 - 43546 * q^61 + 22680 * q^62 - 4374 * q^63 + 24576 * q^64 + 65568 * q^65 + 15696 * q^66 - 52772 * q^67 + 14560 * q^68 - 14706 * q^69 + 28968 * q^70 + 84740 * q^71 - 31104 * q^72 - 36578 * q^73 + 81832 * q^74 + 10674 * q^75 + 23392 * q^76 + 90678 * q^77 - 19296 * q^78 + 85196 * q^79 + 1024 * q^80 + 39366 * q^81 - 1048 * q^82 + 217026 * q^83 + 7776 * q^84 + 26570 * q^85 + 136112 * q^86 + 14382 * q^87 - 27904 * q^88 + 333850 * q^89 - 1296 * q^90 + 214914 * q^91 + 26144 * q^92 + 51030 * q^93 + 44776 * q^94 + 458758 * q^95 + 55296 * q^96 + 173148 * q^97 + 130608 * q^98 + 35316 * q^99

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