LMFDB - Embedded newform 1014.6.a.t.1.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1014,6,Mod(1,1014)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1014, 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("1014.1");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 1014 = 2 \cdot 3 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	1014.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:	$162.629193290$
Analytic rank:	$1$
Dimension:	$4$
Coefficient field:	$\mathbb{Q}[x]/(x^{4} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} - 2192x^{2} - 12432x + 55224 $ x^4 - x^3 - 2192x^2 - 12432x + 55224
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{5}\cdot 3 $
Twist minimal:	no (minimal twist has level 78)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Root			$-42.7585$ of defining polynomial
Character	$\chi$	$=$	1014.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-4.00000 q^{2} +9.00000 q^{3} +16.0000 q^{4} +83.5169 q^{5} -36.0000 q^{6} +187.367 q^{7} -64.0000 q^{8} +81.0000 q^{9} +O(q^{10})$	\(q-4.00000 q^{2} +9.00000 q^{3} +16.0000 q^{4} +83.5169 q^{5} -36.0000 q^{6} +187.367 q^{7} -64.0000 q^{8} +81.0000 q^{9} -334.068 q^{10} -786.334 q^{11} +144.000 q^{12} -749.468 q^{14} +751.652 q^{15} +256.000 q^{16} -923.787 q^{17} -324.000 q^{18} +434.886 q^{19} +1336.27 q^{20} +1686.30 q^{21} +3145.33 q^{22} -3790.69 q^{23} -576.000 q^{24} +3850.08 q^{25} +729.000 q^{27} +2997.87 q^{28} -3735.14 q^{29} -3006.61 q^{30} +2690.43 q^{31} -1024.00 q^{32} -7077.00 q^{33} +3695.15 q^{34} +15648.3 q^{35} +1296.00 q^{36} -1734.37 q^{37} -1739.54 q^{38} -5345.08 q^{40} -12144.6 q^{41} -6745.21 q^{42} -1808.26 q^{43} -12581.3 q^{44} +6764.87 q^{45} +15162.8 q^{46} -5647.45 q^{47} +2304.00 q^{48} +18299.4 q^{49} -15400.3 q^{50} -8314.09 q^{51} -30508.2 q^{53} -2916.00 q^{54} -65672.2 q^{55} -11991.5 q^{56} +3913.97 q^{57} +14940.6 q^{58} -38919.0 q^{59} +12026.4 q^{60} +9010.71 q^{61} -10761.7 q^{62} +15176.7 q^{63} +4096.00 q^{64} +28308.0 q^{66} -28172.0 q^{67} -14780.6 q^{68} -34116.2 q^{69} -62593.3 q^{70} -80313.2 q^{71} -5184.00 q^{72} -5864.17 q^{73} +6937.48 q^{74} +34650.7 q^{75} +6958.18 q^{76} -147333. q^{77} -17250.7 q^{79} +21380.3 q^{80} +6561.00 q^{81} +48578.5 q^{82} +74769.4 q^{83} +26980.8 q^{84} -77151.9 q^{85} +7233.02 q^{86} -33616.3 q^{87} +50325.4 q^{88} +45780.6 q^{89} -27059.5 q^{90} -60651.0 q^{92} +24213.9 q^{93} +22589.8 q^{94} +36320.4 q^{95} -9216.00 q^{96} -77912.8 q^{97} -73197.5 q^{98} -63693.0 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 16 q^{2} + 36 q^{3} + 64 q^{4} - 10 q^{5} - 144 q^{6} + 72 q^{7} - 256 q^{8} + 324 q^{9}+O(q^{10}) $ 4 * q - 16 * q^2 + 36 * q^3 + 64 * q^4 - 10 * q^5 - 144 * q^6 + 72 * q^7 - 256 * q^8 + 324 * q^9	\( 4 q - 16 q^{2} + 36 q^{3} + 64 q^{4} - 10 q^{5} - 144 q^{6} + 72 q^{7} - 256 q^{8} + 324 q^{9} + 40 q^{10} - 702 q^{11} + 576 q^{12} - 288 q^{14} - 90 q^{15} + 1024 q^{16} - 300 q^{17} - 1296 q^{18} - 1800 q^{19} - 160 q^{20} + 648 q^{21} + 2808 q^{22} + 828 q^{23} - 2304 q^{24} + 5064 q^{25} + 2916 q^{27} + 1152 q^{28} - 1680 q^{29} + 360 q^{30} + 972 q^{31} - 4096 q^{32} - 6318 q^{33} + 1200 q^{34} + 13572 q^{35} + 5184 q^{36} - 9204 q^{37} + 7200 q^{38} + 640 q^{40} - 20054 q^{41} - 2592 q^{42} - 8472 q^{43} - 11232 q^{44} - 810 q^{45} - 3312 q^{46} + 8034 q^{47} + 9216 q^{48} + 29740 q^{49} - 20256 q^{50} - 2700 q^{51} + 4788 q^{53} - 11664 q^{54} + 2712 q^{55} - 4608 q^{56} - 16200 q^{57} + 6720 q^{58} - 96658 q^{59} - 1440 q^{60} + 29172 q^{61} - 3888 q^{62} + 5832 q^{63} + 16384 q^{64} + 25272 q^{66} - 22452 q^{67} - 4800 q^{68} + 7452 q^{69} - 54288 q^{70} - 30030 q^{71} - 20736 q^{72} + 105132 q^{73} + 36816 q^{74} + 45576 q^{75} - 28800 q^{76} - 121980 q^{77} + 77984 q^{79} - 2560 q^{80} + 26244 q^{81} + 80216 q^{82} - 181390 q^{83} + 10368 q^{84} - 277044 q^{85} + 33888 q^{86} - 15120 q^{87} + 44928 q^{88} - 1386 q^{89} + 3240 q^{90} + 13248 q^{92} + 8748 q^{93} - 32136 q^{94} + 184116 q^{95} - 36864 q^{96} + 55188 q^{97} - 118960 q^{98} - 56862 q^{99}+O(q^{100}) \) 4 * q - 16 * q^2 + 36 * q^3 + 64 * q^4 - 10 * q^5 - 144 * q^6 + 72 * q^7 - 256 * q^8 + 324 * q^9 + 40 * q^10 - 702 * q^11 + 576 * q^12 - 288 * q^14 - 90 * q^15 + 1024 * q^16 - 300 * q^17 - 1296 * q^18 - 1800 * q^19 - 160 * q^20 + 648 * q^21 + 2808 * q^22 + 828 * q^23 - 2304 * q^24 + 5064 * q^25 + 2916 * q^27 + 1152 * q^28 - 1680 * q^29 + 360 * q^30 + 972 * q^31 - 4096 * q^32 - 6318 * q^33 + 1200 * q^34 + 13572 * q^35 + 5184 * q^36 - 9204 * q^37 + 7200 * q^38 + 640 * q^40 - 20054 * q^41 - 2592 * q^42 - 8472 * q^43 - 11232 * q^44 - 810 * q^45 - 3312 * q^46 + 8034 * q^47 + 9216 * q^48 + 29740 * q^49 - 20256 * q^50 - 2700 * q^51 + 4788 * q^53 - 11664 * q^54 + 2712 * q^55 - 4608 * q^56 - 16200 * q^57 + 6720 * q^58 - 96658 * q^59 - 1440 * q^60 + 29172 * q^61 - 3888 * q^62 + 5832 * q^63 + 16384 * q^64 + 25272 * q^66 - 22452 * q^67 - 4800 * q^68 + 7452 * q^69 - 54288 * q^70 - 30030 * q^71 - 20736 * q^72 + 105132 * q^73 + 36816 * q^74 + 45576 * q^75 - 28800 * q^76 - 121980 * q^77 + 77984 * q^79 - 2560 * q^80 + 26244 * q^81 + 80216 * q^82 - 181390 * q^83 + 10368 * q^84 - 277044 * q^85 + 33888 * q^86 - 15120 * q^87 + 44928 * q^88 - 1386 * q^89 + 3240 * q^90 + 13248 * q^92 + 8748 * q^93 - 32136 * q^94 + 184116 * q^95 - 36864 * q^96 + 55188 * q^97 - 118960 * q^98 - 56862 * 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
$5$	83.5169	1.49400	0.746998	−	0.664826i	$-0.231494\pi$
$5$	83.5169	1.49400	0.746998	+	0.664826i	$0.231494\pi$
$6$	−36.0000	−0.408248
$7$	187.367	1.44527	0.722633	−	0.691232i	$-0.242932\pi$
$7$	187.367	1.44527	0.722633	+	0.691232i	$0.242932\pi$
$8$	−64.0000	−0.353553
$9$	81.0000	0.333333
$10$	−334.068	−1.05642
$11$	−786.334	−1.95941	−0.979705	−	0.200447i	$-0.935761\pi$
$11$	−786.334	−1.95941	−0.979705	+	0.200447i	$0.935761\pi$
$12$	144.000	0.288675
$13$	0	0
$13$	0	0
$14$	−749.468	−1.02196
$15$	751.652	0.862559
$16$	256.000	0.250000
$17$	−923.787	−0.775264	−0.387632	−	0.921814i	$-0.626707\pi$
$17$	−923.787	−0.775264	−0.387632	+	0.921814i	$0.626707\pi$
$18$	−324.000	−0.235702
$19$	434.886	0.276370	0.138185	−	0.990406i	$-0.455873\pi$
$19$	434.886	0.276370	0.138185	+	0.990406i	$0.455873\pi$
$20$	1336.27	0.746998
$21$	1686.30	0.834425
$22$	3145.33	1.38551
$23$	−3790.69	−1.49416	−0.747082	−	0.664732i	$-0.768546\pi$
$23$	−3790.69	−1.49416	−0.747082	+	0.664732i	$0.768546\pi$
$24$	−576.000	−0.204124
$25$	3850.08	1.23203
$26$	0	0
$27$	729.000	0.192450
$28$	2997.87	0.722633
$29$	−3735.14	−0.824731	−0.412365	−	0.911019i	$-0.635297\pi$
$29$	−3735.14	−0.824731	−0.412365	+	0.911019i	$0.635297\pi$
$30$	−3006.61	−0.609921
$31$	2690.43	0.502826	0.251413	−	0.967880i	$-0.419105\pi$
$31$	2690.43	0.502826	0.251413	+	0.967880i	$0.419105\pi$
$32$	−1024.00	−0.176777
$33$	−7077.00	−1.13127
$34$	3695.15	0.548195
$35$	15648.3	2.15922
$36$	1296.00	0.166667
$37$	−1734.37	−0.208275	−0.104138	−	0.994563i	$-0.533208\pi$
$37$	−1734.37	−0.208275	−0.104138	+	0.994563i	$0.533208\pi$
$38$	−1739.54	−0.195423
$39$	0	0
$40$	−5345.08	−0.528208
$41$	−12144.6	−1.12830	−0.564150	−	0.825672i	$-0.690796\pi$
$41$	−12144.6	−1.12830	−0.564150	+	0.825672i	$0.690796\pi$
$42$	−6745.21	−0.590027
$43$	−1808.26	−0.149138	−0.0745690	−	0.997216i	$-0.523758\pi$
$43$	−1808.26	−0.149138	−0.0745690	+	0.997216i	$0.523758\pi$
$44$	−12581.3	−0.979705
$45$	6764.87	0.497999
$46$	15162.8	1.05653
$47$	−5647.45	−0.372913	−0.186457	−	0.982463i	$-0.559700\pi$
$47$	−5647.45	−0.372913	−0.186457	+	0.982463i	$0.559700\pi$
$48$	2304.00	0.144338
$49$	18299.4	1.08879
$50$	−15400.3	−0.871174
$51$	−8314.09	−0.447599
$52$	0	0
$53$	−30508.2	−1.49186	−0.745929	−	0.666026i	$-0.767994\pi$
$53$	−30508.2	−1.49186	−0.745929	+	0.666026i	$0.767994\pi$
$54$	−2916.00	−0.136083
$55$	−65672.2	−2.92735
$56$	−11991.5	−0.510979
$57$	3913.97	0.159563
$58$	14940.6	0.583173
$59$	−38919.0	−1.45556	−0.727782	−	0.685808i	$-0.759449\pi$
$59$	−38919.0	−1.45556	−0.727782	+	0.685808i	$0.759449\pi$
$60$	12026.4	0.431280
$61$	9010.71	0.310052	0.155026	−	0.987910i	$-0.450454\pi$
$61$	9010.71	0.310052	0.155026	+	0.987910i	$0.450454\pi$
$62$	−10761.7	−0.355551
$63$	15176.7	0.481755
$64$	4096.00	0.125000
$65$	0	0
$66$	28308.0	0.799925
$67$	−28172.0	−0.766709	−0.383355	−	0.923601i	$-0.625231\pi$
$67$	−28172.0	−0.766709	−0.383355	+	0.923601i	$0.625231\pi$
$68$	−14780.6	−0.387632
$69$	−34116.2	−0.862656
$70$	−62593.3	−1.52680
$71$	−80313.2	−1.89078	−0.945390	−	0.325941i	$-0.894319\pi$
$71$	−80313.2	−1.89078	−0.945390	+	0.325941i	$0.894319\pi$
$72$	−5184.00	−0.117851
$73$	−5864.17	−0.128795	−0.0643975	−	0.997924i	$-0.520513\pi$
$73$	−5864.17	−0.128795	−0.0643975	+	0.997924i	$0.520513\pi$
$74$	6937.48	0.147273
$75$	34650.7	0.711310
$76$	6958.18	0.138185
$77$	−147333.	−2.83187
$78$	0	0
$79$	−17250.7	−0.310985	−0.155492	−	0.987837i	$-0.549696\pi$
$79$	−17250.7	−0.310985	−0.155492	+	0.987837i	$0.549696\pi$
$80$	21380.3	0.373499
$81$	6561.00	0.111111
$82$	48578.5	0.797829
$83$	74769.4	1.19132	0.595661	−	0.803236i	$-0.296890\pi$
$83$	74769.4	1.19132	0.595661	+	0.803236i	$0.296890\pi$
$84$	26980.8	0.417212
$85$	−77151.9	−1.15824
$86$	7233.02	0.105457
$87$	−33616.3	−0.476158
$88$	50325.4	0.692756
$89$	45780.6	0.612641	0.306320	−	0.951928i	$-0.400902\pi$
$89$	45780.6	0.612641	0.306320	+	0.951928i	$0.400902\pi$
$90$	−27059.5	−0.352138
$91$	0	0
$92$	−60651.0	−0.747082
$93$	24213.9	0.290307
$94$	22589.8	0.263690
$95$	36320.4	0.412896
$96$	−9216.00	−0.102062
$97$	−77912.8	−0.840774	−0.420387	−	0.907345i	$-0.638106\pi$
$97$	−77912.8	−0.840774	−0.420387	+	0.907345i	$0.638106\pi$
$98$	−73197.5	−0.769894
$99$	−63693.0	−0.653136
$100$	61601.3	0.616013
$101$	−17140.1	−0.167190	−0.0835949	−	0.996500i	$-0.526640\pi$
$101$	−17140.1	−0.167190	−0.0835949	+	0.996500i	$0.526640\pi$
$102$	33256.3	0.316500
$103$	102916.	0.955848	0.477924	−	0.878401i	$-0.341390\pi$
$103$	102916.	0.955848	0.477924	+	0.878401i	$0.341390\pi$
$104$	0	0
$105$	140835.	1.24663
$106$	122033.	1.05490
$107$	133735.	1.12924	0.564619	−	0.825352i	$-0.309023\pi$
$107$	133735.	1.12924	0.564619	+	0.825352i	$0.309023\pi$
$108$	11664.0	0.0962250
$109$	−237067.	−1.91120	−0.955598	−	0.294674i	$-0.904789\pi$
$109$	−237067.	−1.91120	−0.955598	+	0.294674i	$0.904789\pi$
$110$	262689.	2.06995
$111$	−15609.3	−0.120248
$112$	47965.9	0.361317
$113$	138273.	1.01869	0.509343	−	0.860564i	$-0.329889\pi$
$113$	138273.	1.01869	0.509343	+	0.860564i	$0.329889\pi$
$114$	−15655.9	−0.112828
$115$	−316587.	−2.23228
$116$	−59762.3	−0.412365
$117$	0	0
$118$	155676.	1.02924
$119$	−173087.	−1.12046
$120$	−48105.8	−0.304961
$121$	457270.	2.83928
$122$	−36042.8	−0.219240
$123$	−109302.	−0.651425
$124$	43046.9	0.251413
$125$	60556.4	0.346645
$126$	−60706.9	−0.340653
$127$	−283497.	−1.55969	−0.779847	−	0.625970i	$-0.784703\pi$
$127$	−283497.	−1.55969	−0.779847	+	0.625970i	$0.784703\pi$
$128$	−16384.0	−0.0883883
$129$	−16274.3	−0.0861049
$130$	0	0
$131$	101624.	0.517391	0.258695	−	0.965959i	$-0.416707\pi$
$131$	101624.	0.517391	0.258695	+	0.965959i	$0.416707\pi$
$132$	−113232.	−0.565633
$133$	81483.3	0.399429
$134$	112688.	0.542145
$135$	60883.8	0.287520
$136$	59122.4	0.274097
$137$	136816.	0.622781	0.311390	−	0.950282i	$-0.399205\pi$
$137$	136816.	0.622781	0.311390	+	0.950282i	$0.399205\pi$
$138$	136465.	0.609990
$139$	122457.	0.537585	0.268793	−	0.963198i	$-0.413375\pi$
$139$	122457.	0.537585	0.268793	+	0.963198i	$0.413375\pi$
$140$	250373.	1.07961
$141$	−50827.1	−0.215302
$142$	321253.	1.33698
$143$	0	0
$144$	20736.0	0.0833333
$145$	−311948.	−1.23214
$146$	23456.7	0.0910718
$147$	164694.	0.628616
$148$	−27749.9	−0.104138
$149$	−247858.	−0.914613	−0.457307	−	0.889309i	$-0.651186\pi$
$149$	−247858.	−0.914613	−0.457307	+	0.889309i	$0.651186\pi$
$150$	−138603.	−0.502972
$151$	−324290.	−1.15742	−0.578711	−	0.815533i	$-0.696444\pi$
$151$	−324290.	−1.15742	−0.578711	+	0.815533i	$0.696444\pi$
$152$	−27832.7	−0.0977117
$153$	−74826.8	−0.258421
$154$	589332.	2.00243
$155$	224696.	0.751220
$156$	0	0
$157$	407075.	1.31803	0.659014	−	0.752130i	$-0.270974\pi$
$157$	407075.	1.31803	0.659014	+	0.752130i	$0.270974\pi$
$158$	69002.8	0.219900
$159$	−274574.	−0.861324
$160$	−85521.3	−0.264104
$161$	−710250.	−2.15947
$162$	−26244.0	−0.0785674
$163$	192942.	0.568799	0.284399	−	0.958706i	$-0.408206\pi$
$163$	192942.	0.568799	0.284399	+	0.958706i	$0.408206\pi$
$164$	−194314.	−0.564150
$165$	−591050.	−1.69011
$166$	−299078.	−0.842391
$167$	358847.	0.995675	0.497838	−	0.867270i	$-0.334128\pi$
$167$	358847.	0.995675	0.497838	+	0.867270i	$0.334128\pi$
$168$	−107923.	−0.295014
$169$	0	0
$170$	308608.	0.819001
$171$	35225.8	0.0921235
$172$	−28932.1	−0.0745690
$173$	−575252.	−1.46131	−0.730656	−	0.682746i	$-0.760786\pi$
$173$	−575252.	−1.46131	−0.730656	+	0.682746i	$0.760786\pi$
$174$	134465.	0.336695
$175$	721378.	1.78060
$176$	−201301.	−0.489852
$177$	−350271.	−0.840371
$178$	−183122.	−0.433203
$179$	730150.	1.70326	0.851628	−	0.524147i	$-0.175616\pi$
$179$	730150.	1.70326	0.851628	+	0.524147i	$0.175616\pi$
$180$	108238.	0.248999
$181$	−18004.4	−0.0408490	−0.0204245	−	0.999791i	$-0.506502\pi$
$181$	−18004.4	−0.0408490	−0.0204245	+	0.999791i	$0.506502\pi$
$182$	0	0
$183$	81096.4	0.179009
$184$	242604.	0.528267
$185$	−144849.	−0.311162
$186$	−96855.5	−0.205278
$187$	726405.	1.51906
$188$	−90359.3	−0.186457
$189$	136591.	0.278142
$190$	−145281.	−0.291962
$191$	718887.	1.42586	0.712930	−	0.701235i	$-0.247368\pi$
$191$	718887.	1.42586	0.712930	+	0.701235i	$0.247368\pi$
$192$	36864.0	0.0721688
$193$	−163524.	−0.316001	−0.158000	−	0.987439i	$-0.550505\pi$
$193$	−163524.	−0.316001	−0.158000	+	0.987439i	$0.550505\pi$
$194$	311651.	0.594517
$195$	0	0
$196$	292790.	0.544397
$197$	41747.3	0.0766412	0.0383206	−	0.999265i	$-0.487799\pi$
$197$	41747.3	0.0766412	0.0383206	+	0.999265i	$0.487799\pi$
$198$	254772.	0.461837
$199$	−159023.	−0.284661	−0.142331	−	0.989819i	$-0.545460\pi$
$199$	−159023.	−0.284661	−0.142331	+	0.989819i	$0.545460\pi$
$200$	−246405.	−0.435587
$201$	−253548.	−0.442660
$202$	68560.4	0.118221
$203$	−699842.	−1.19196
$204$	−133025.	−0.223800
$205$	−1.01428e6	−1.68568
$206$	−411663.	−0.675886
$207$	−307046.	−0.498055
$208$	0	0
$209$	−341966.	−0.541523
$210$	−563339.	−0.881499
$211$	−323039.	−0.499516	−0.249758	−	0.968308i	$-0.580351\pi$
$211$	−323039.	−0.499516	−0.249758	+	0.968308i	$0.580351\pi$
$212$	−488132.	−0.745929
$213$	−722819.	−1.09164
$214$	−534940.	−0.798492
$215$	−151020.	−0.222812
$216$	−46656.0	−0.0680414
$217$	504098.	0.726717
$218$	948269.	1.35142
$219$	−52777.5	−0.0743598
$220$	−1.05075e6	−1.46368
$221$	0	0
$222$	62437.3	0.0850280
$223$	−1.20727e6	−1.62570	−0.812852	−	0.582470i	$-0.802086\pi$
$223$	−1.20727e6	−1.62570	−0.812852	+	0.582470i	$0.802086\pi$
$224$	−191864.	−0.255489
$225$	311856.	0.410675
$226$	−553090.	−0.720319
$227$	885255.	1.14026	0.570130	−	0.821555i	$-0.306893\pi$
$227$	885255.	1.14026	0.570130	+	0.821555i	$0.306893\pi$
$228$	62623.6	0.0797813
$229$	473761.	0.596995	0.298498	−	0.954410i	$-0.403515\pi$
$229$	473761.	0.596995	0.298498	+	0.954410i	$0.403515\pi$
$230$	1.26635e6	1.57846
$231$	−1.32600e6	−1.63498
$232$	239049.	0.291586
$233$	−169230.	−0.204215	−0.102107	−	0.994773i	$-0.532559\pi$
$233$	−169230.	−0.204215	−0.102107	+	0.994773i	$0.532559\pi$
$234$	0	0
$235$	−471658.	−0.557131
$236$	−622704.	−0.727782
$237$	−155256.	−0.179547
$238$	692349.	0.792287
$239$	1.46535e6	1.65939	0.829694	−	0.558219i	$-0.188515\pi$
$239$	1.46535e6	1.65939	0.829694	+	0.558219i	$0.188515\pi$
$240$	192423.	0.215640
$241$	−34983.5	−0.0387990	−0.0193995	−	0.999812i	$-0.506175\pi$
$241$	−34983.5	−0.0387990	−0.0193995	+	0.999812i	$0.506175\pi$
$242$	−1.82908e6	−2.00768
$243$	59049.0	0.0641500
$244$	144171.	0.155026
$245$	1.52831e6	1.62666
$246$	437207.	0.460627
$247$	0	0
$248$	−172188.	−0.177776
$249$	672925.	0.687810
$250$	−242226.	−0.245115
$251$	629330.	0.630513	0.315256	−	0.949007i	$-0.397909\pi$
$251$	629330.	0.630513	0.315256	+	0.949007i	$0.397909\pi$
$252$	242828.	0.240878
$253$	2.98075e6	2.92768
$254$	1.13399e6	1.10287
$255$	−694367.	−0.668711
$256$	65536.0	0.0625000
$257$	829748.	0.783634	0.391817	−	0.920043i	$-0.371847\pi$
$257$	829748.	0.783634	0.391817	+	0.920043i	$0.371847\pi$
$258$	65097.2	0.0608854
$259$	−324964.	−0.301013
$260$	0	0
$261$	−302546.	−0.274910
$262$	−406497.	−0.365850
$263$	−209606.	−0.186859	−0.0934294	−	0.995626i	$-0.529783\pi$
$263$	−209606.	−0.186859	−0.0934294	+	0.995626i	$0.529783\pi$
$264$	452928.	0.399963
$265$	−2.54795e6	−2.22883
$266$	−325933.	−0.282439
$267$	412025.	0.353708
$268$	−450752.	−0.383355
$269$	1.68780e6	1.42213	0.711066	−	0.703125i	$-0.248213\pi$
$269$	1.68780e6	1.42213	0.711066	+	0.703125i	$0.248213\pi$
$270$	−243535.	−0.203307
$271$	1.42123e6	1.17555	0.587774	−	0.809025i	$-0.300004\pi$
$271$	1.42123e6	1.17555	0.587774	+	0.809025i	$0.300004\pi$
$272$	−236490.	−0.193816
$273$	0	0
$274$	−547264.	−0.440372
$275$	−3.02745e6	−2.41404
$276$	−545859.	−0.431328
$277$	428628.	0.335646	0.167823	−	0.985817i	$-0.446326\pi$
$277$	428628.	0.335646	0.167823	+	0.985817i	$0.446326\pi$
$278$	−489829.	−0.380130
$279$	217925.	0.167609
$280$	−1.00149e6	−0.763401
$281$	−243338.	−0.183842	−0.0919208	−	0.995766i	$-0.529301\pi$
$281$	−243338.	−0.183842	−0.0919208	+	0.995766i	$0.529301\pi$
$282$	203308.	0.152241
$283$	1.53845e6	1.14187	0.570937	−	0.820994i	$-0.306580\pi$
$283$	1.53845e6	1.14187	0.570937	+	0.820994i	$0.306580\pi$
$284$	−1.28501e6	−0.945390
$285$	326883.	0.238386
$286$	0	0
$287$	−2.27550e6	−1.63070
$288$	−82944.0	−0.0589256
$289$	−566474.	−0.398965
$290$	1.24779e6	0.871258
$291$	−701215.	−0.485421
$292$	−93826.7	−0.0643975
$293$	−1.02136e6	−0.695038	−0.347519	−	0.937673i	$-0.612976\pi$
$293$	−1.02136e6	−0.695038	−0.347519	+	0.937673i	$0.612976\pi$
$294$	−658777.	−0.444499
$295$	−3.25040e6	−2.17461
$296$	111000.	0.0736364
$297$	−573237.	−0.377088
$298$	991432.	0.646729
$299$	0	0
$300$	554411.	0.355655
$301$	−338807.	−0.215544
$302$	1.29716e6	0.818420
$303$	−154261.	−0.0965271
$304$	111331.	0.0690926
$305$	752547.	0.463217
$306$	299307.	0.182732
$307$	−535631.	−0.324354	−0.162177	−	0.986762i	$-0.551852\pi$
$307$	−535631.	−0.324354	−0.162177	+	0.986762i	$0.551852\pi$
$308$	−2.35733e6	−1.41593
$309$	926241.	0.551859
$310$	−898786.	−0.531193
$311$	−2.97584e6	−1.74465	−0.872325	−	0.488926i	$-0.837389\pi$
$311$	−2.97584e6	−1.74465	−0.872325	+	0.488926i	$0.837389\pi$
$312$	0	0
$313$	16412.0	0.00946893	0.00473447	−	0.999989i	$-0.498493\pi$
$313$	16412.0	0.00946893	0.00473447	+	0.999989i	$0.498493\pi$
$314$	−1.62830e6	−0.931987
$315$	1.26751e6	0.719741
$316$	−276011.	−0.155492
$317$	−2.98387e6	−1.66775	−0.833876	−	0.551951i	$-0.813884\pi$
$317$	−2.98387e6	−1.66775	−0.833876	+	0.551951i	$0.813884\pi$
$318$	1.09830e6	0.609048
$319$	2.93707e6	1.61598
$320$	342085.	0.186750
$321$	1.20361e6	0.651966
$322$	2.84100e6	1.52697
$323$	−401742.	−0.214260
$324$	104976.	0.0555556
$325$	0	0
$326$	−771770.	−0.402202
$327$	−2.13360e6	−1.10343
$328$	777257.	0.398915
$329$	−1.05815e6	−0.538959
$330$	2.36420e6	1.19509
$331$	848266.	0.425561	0.212781	−	0.977100i	$-0.431748\pi$
$331$	848266.	0.425561	0.212781	+	0.977100i	$0.431748\pi$
$332$	1.19631e6	0.595661
$333$	−140484.	−0.0694251
$334$	−1.43539e6	−0.704049
$335$	−2.35284e6	−1.14546
$336$	431693.	0.208606
$337$	−403049.	−0.193323	−0.0966615	−	0.995317i	$-0.530816\pi$
$337$	−403049.	−0.193323	−0.0966615	+	0.995317i	$0.530816\pi$
$338$	0	0
$339$	1.24445e6	0.588138
$340$	−1.23443e6	−0.579121
$341$	−2.11558e6	−0.985241
$342$	−140903.	−0.0651411
$343$	279621.	0.128332
$344$	115728.	0.0527283
$345$	−2.84928e6	−1.28881
$346$	2.30101e6	1.03330
$347$	−455097.	−0.202899	−0.101450	−	0.994841i	$-0.532348\pi$
$347$	−455097.	−0.202899	−0.101450	+	0.994841i	$0.532348\pi$
$348$	−537860.	−0.238079
$349$	2.55559e6	1.12312	0.561562	−	0.827435i	$-0.310201\pi$
$349$	2.55559e6	1.12312	0.561562	+	0.827435i	$0.310201\pi$
$350$	−2.88551e6	−1.25908
$351$	0	0
$352$	805206.	0.346378
$353$	492691.	0.210445	0.105222	−	0.994449i	$-0.466445\pi$
$353$	492691.	0.210445	0.105222	+	0.994449i	$0.466445\pi$
$354$	1.40108e6	0.594232
$355$	−6.70751e6	−2.82482
$356$	732489.	0.306320
$357$	−1.55779e6	−0.646900
$358$	−2.92060e6	−1.20438
$359$	−2.17485e6	−0.890623	−0.445311	−	0.895376i	$-0.646907\pi$
$359$	−2.17485e6	−0.890623	−0.445311	+	0.895376i	$0.646907\pi$
$360$	−432952.	−0.176069
$361$	−2.28697e6	−0.923619
$362$	72017.4	0.0288846
$363$	4.11543e6	1.63926
$364$	0	0
$365$	−489757.	−0.192419
$366$	−324386.	−0.126578
$367$	741107.	0.287221	0.143610	−	0.989634i	$-0.454129\pi$
$367$	741107.	0.287221	0.143610	+	0.989634i	$0.454129\pi$
$368$	−970416.	−0.373541
$369$	−983716.	−0.376100
$370$	579397.	0.220025
$371$	−5.71623e6	−2.15613
$372$	387422.	0.145153
$373$	−3.42043e6	−1.27294	−0.636471	−	0.771300i	$-0.719607\pi$
$373$	−3.42043e6	−1.27294	−0.636471	+	0.771300i	$0.719607\pi$
$374$	−2.90562e6	−1.07414
$375$	545008.	0.200136
$376$	361437.	0.131845
$377$	0	0
$378$	−546362.	−0.196676
$379$	−2.40039e6	−0.858387	−0.429193	−	0.903213i	$-0.641202\pi$
$379$	−2.40039e6	−0.858387	−0.429193	+	0.903213i	$0.641202\pi$
$380$	581126.	0.206448
$381$	−2.55148e6	−0.900490
$382$	−2.87555e6	−1.00824
$383$	−70722.4	−0.0246354	−0.0123177	−	0.999924i	$-0.503921\pi$
$383$	−70722.4	−0.0246354	−0.0123177	+	0.999924i	$0.503921\pi$
$384$	−147456.	−0.0510310
$385$	−1.23048e7	−4.23080
$386$	654096.	0.223446
$387$	−146469.	−0.0497127
$388$	−1.24660e6	−0.420387
$389$	3.95890e6	1.32648	0.663240	−	0.748406i	$-0.269181\pi$
$389$	3.95890e6	1.32648	0.663240	+	0.748406i	$0.269181\pi$
$390$	0	0
$391$	3.50179e6	1.15837
$392$	−1.17116e6	−0.384947
$393$	914617.	0.298716
$394$	−166989.	−0.0541935
$395$	−1.44073e6	−0.464610
$396$	−1.01909e6	−0.326568
$397$	559732.	0.178240	0.0891198	−	0.996021i	$-0.471595\pi$
$397$	559732.	0.178240	0.0891198	+	0.996021i	$0.471595\pi$
$398$	636094.	0.201286
$399$	733349.	0.230610
$400$	985620.	0.308006
$401$	−731268.	−0.227099	−0.113550	−	0.993532i	$-0.536222\pi$
$401$	−731268.	−0.227099	−0.113550	+	0.993532i	$0.536222\pi$
$402$	1.01419e6	0.313008
$403$	0	0
$404$	−274242.	−0.0835949
$405$	547955.	0.166000
$406$	2.79937e6	0.842840
$407$	1.36379e6	0.408096
$408$	532102.	0.158250
$409$	4.10605e6	1.21371	0.606856	−	0.794812i	$-0.292431\pi$
$409$	4.10605e6	1.21371	0.606856	+	0.794812i	$0.292431\pi$
$410$	4.05713e6	1.19195
$411$	1.23134e6	0.359563
$412$	1.64665e6	0.477924
$413$	−7.29213e6	−2.10368
$414$	1.22818e6	0.352178
$415$	6.24451e6	1.77983
$416$	0	0
$417$	1.10211e6	0.310375
$418$	1.36786e6	0.382914
$419$	−2.16620e6	−0.602787	−0.301393	−	0.953500i	$-0.597452\pi$
$419$	−2.16620e6	−0.602787	−0.301393	+	0.953500i	$0.597452\pi$
$420$	2.25336e6	0.623314
$421$	−5.73337e6	−1.57654	−0.788270	−	0.615330i	$-0.789023\pi$
$421$	−5.73337e6	−1.57654	−0.788270	+	0.615330i	$0.789023\pi$
$422$	1.29216e6	0.353211
$423$	−457444.	−0.124304
$424$	1.95253e6	0.527451
$425$	−3.55665e6	−0.955145
$426$	2.89128e6	0.771908
$427$	1.68831e6	0.448108
$428$	2.13976e6	0.564619
$429$	0	0
$430$	604080.	0.157552
$431$	−943230.	−0.244582	−0.122291	−	0.992494i	$-0.539024\pi$
$431$	−943230.	−0.244582	−0.122291	+	0.992494i	$0.539024\pi$
$432$	186624.	0.0481125
$433$	−907853.	−0.232700	−0.116350	−	0.993208i	$-0.537119\pi$
$433$	−907853.	−0.232700	−0.116350	+	0.993208i	$0.537119\pi$
$434$	−2.01639e6	−0.513867
$435$	−2.80753e6	−0.711379
$436$	−3.79307e6	−0.955598
$437$	−1.64852e6	−0.412943
$438$	211110.	0.0525803
$439$	801162.	0.198408	0.0992039	−	0.995067i	$-0.468370\pi$
$439$	801162.	0.198408	0.0992039	+	0.995067i	$0.468370\pi$
$440$	4.20302e6	1.03497
$441$	1.48225e6	0.362932
$442$	0	0
$443$	−5.98329e6	−1.44854	−0.724270	−	0.689516i	$-0.757823\pi$
$443$	−5.98329e6	−1.44854	−0.724270	+	0.689516i	$0.757823\pi$
$444$	−249749.	−0.0601239
$445$	3.82345e6	0.915283
$446$	4.82907e6	1.14955
$447$	−2.23072e6	−0.528052
$448$	767455.	0.180658
$449$	674540.	0.157904	0.0789518	−	0.996878i	$-0.474843\pi$
$449$	674540.	0.157904	0.0789518	+	0.996878i	$0.474843\pi$
$450$	−1.24743e6	−0.290391
$451$	9.54974e6	2.21080
$452$	2.21236e6	0.509343
$453$	−2.91861e6	−0.668237
$454$	−3.54102e6	−0.806286
$455$	0	0
$456$	−250494.	−0.0564139
$457$	2.44421e6	0.547455	0.273728	−	0.961807i	$-0.411743\pi$
$457$	2.44421e6	0.547455	0.273728	+	0.961807i	$0.411743\pi$
$458$	−1.89504e6	−0.422139
$459$	−673441.	−0.149200
$460$	−5.06539e6	−1.11614
$461$	858805.	0.188210	0.0941049	−	0.995562i	$-0.470001\pi$
$461$	858805.	0.188210	0.0941049	+	0.995562i	$0.470001\pi$
$462$	5.30399e6	1.15611
$463$	7.81981e6	1.69529	0.847645	−	0.530564i	$-0.178020\pi$
$463$	7.81981e6	1.69529	0.847645	+	0.530564i	$0.178020\pi$
$464$	−956196.	−0.206183
$465$	2.02227e6	0.433717
$466$	676919.	0.144402
$467$	6.27959e6	1.33241	0.666207	−	0.745767i	$-0.267917\pi$
$467$	6.27959e6	1.33241	0.666207	+	0.745767i	$0.267917\pi$
$468$	0	0
$469$	−5.27850e6	−1.10810
$470$	1.88663e6	0.393951
$471$	3.66367e6	0.760964
$472$	2.49082e6	0.514620
$473$	1.42189e6	0.292223
$474$	621026.	0.126959
$475$	1.67435e6	0.340495
$476$	−2.76940e6	−0.560232
$477$	−2.47117e6	−0.497286
$478$	−5.86142e6	−1.17336
$479$	2.29110e6	0.456252	0.228126	−	0.973632i	$-0.426740\pi$
$479$	2.29110e6	0.456252	0.228126	+	0.973632i	$0.426740\pi$
$480$	−769692.	−0.152480
$481$	0	0
$482$	139934.	0.0274350
$483$	−6.39225e6	−1.24677
$484$	7.31631e6	1.41964
$485$	−6.50704e6	−1.25611
$486$	−236196.	−0.0453609
$487$	−4.05799e6	−0.775333	−0.387666	−	0.921800i	$-0.626719\pi$
$487$	−4.05799e6	−0.775333	−0.387666	+	0.921800i	$0.626719\pi$
$488$	−576686.	−0.109620
$489$	1.73648e6	0.328396
$490$	−6.11323e6	−1.15022
$491$	609711.	0.114135	0.0570677	−	0.998370i	$-0.481825\pi$
$491$	609711.	0.114135	0.0570677	+	0.998370i	$0.481825\pi$
$492$	−1.74883e6	−0.325712
$493$	3.45048e6	0.639384
$494$	0	0
$495$	−5.31945e6	−0.975783
$496$	688750.	0.125706
$497$	−1.50480e7	−2.73268
$498$	−2.69170e6	−0.486355
$499$	9.43555e6	1.69635	0.848176	−	0.529715i	$-0.177701\pi$
$499$	9.43555e6	1.69635	0.848176	+	0.529715i	$0.177701\pi$
$500$	968903.	0.173323
$501$	3.22962e6	0.574853
$502$	−2.51732e6	−0.445840
$503$	−4.48965e6	−0.791211	−0.395606	−	0.918421i	$-0.629465\pi$
$503$	−4.48965e6	−0.791211	−0.395606	+	0.918421i	$0.629465\pi$
$504$	−971310.	−0.170326
$505$	−1.43149e6	−0.249781
$506$	−1.19230e7	−2.07018
$507$	0	0
$508$	−4.53596e6	−0.779847
$509$	−4.48242e6	−0.766863	−0.383432	−	0.923569i	$-0.625258\pi$
$509$	−4.48242e6	−0.766863	−0.383432	+	0.923569i	$0.625258\pi$
$510$	2.77747e6	0.472850
$511$	−1.09875e6	−0.186143
$512$	−262144.	−0.0441942
$513$	317032.	0.0531875
$514$	−3.31899e6	−0.554113
$515$	8.59521e6	1.42803
$516$	−260389.	−0.0430525
$517$	4.44078e6	0.730690
$518$	1.29985e6	0.212848
$519$	−5.17727e6	−0.843689
$520$	0	0
$521$	7.38286e6	1.19160	0.595799	−	0.803133i	$-0.296835\pi$
$521$	7.38286e6	1.19160	0.595799	+	0.803133i	$0.296835\pi$
$522$	1.21019e6	0.194391
$523$	2.71336e6	0.433764	0.216882	−	0.976198i	$-0.430411\pi$
$523$	2.71336e6	0.433764	0.216882	+	0.976198i	$0.430411\pi$
$524$	1.62599e6	0.258695
$525$	6.49240e6	1.02803
$526$	838422.	0.132129
$527$	−2.48539e6	−0.389823
$528$	−1.81171e6	−0.282816
$529$	7.93297e6	1.23253
$530$	1.01918e7	1.57602
$531$	−3.15244e6	−0.485188
$532$	1.30373e6	0.199714
$533$	0	0
$534$	−1.64810e6	−0.250110
$535$	1.11691e7	1.68708
$536$	1.80301e6	0.271073
$537$	6.57135e6	0.983375
$538$	−6.75119e6	−1.00560
$539$	−1.43894e7	−2.13339
$540$	974142.	0.143760
$541$	−4.37688e6	−0.642942	−0.321471	−	0.946920i	$-0.604177\pi$
$541$	−4.37688e6	−0.642942	−0.321471	+	0.946920i	$0.604177\pi$
$542$	−5.68491e6	−0.831238
$543$	−162039.	−0.0235842
$544$	945958.	0.137049
$545$	−1.97991e7	−2.85532
$546$	0	0
$547$	2.72786e6	0.389811	0.194905	−	0.980822i	$-0.437560\pi$
$547$	2.72786e6	0.389811	0.194905	+	0.980822i	$0.437560\pi$
$548$	2.18905e6	0.311390
$549$	729868.	0.103351
$550$	1.21098e7	1.70699
$551$	−1.62436e6	−0.227931
$552$	2.18344e6	0.304995
$553$	−3.23221e6	−0.449456
$554$	−1.71451e6	−0.237338
$555$	−1.30364e6	−0.179650
$556$	1.95932e6	0.268793
$557$	−1.11073e7	−1.51694	−0.758472	−	0.651706i	$-0.774054\pi$
$557$	−1.11073e7	−1.51694	−0.758472	+	0.651706i	$0.774054\pi$
$558$	−871699.	−0.118517
$559$	0	0
$560$	4.00597e6	0.539806
$561$	6.53765e6	0.877030
$562$	973351.	0.129996
$563$	−1.20957e7	−1.60827	−0.804137	−	0.594444i	$-0.797372\pi$
$563$	−1.20957e7	−1.60827	−0.804137	+	0.594444i	$0.797372\pi$
$564$	−813233.	−0.107651
$565$	1.15481e7	1.52191
$566$	−6.15381e6	−0.807427
$567$	1.22931e6	0.160585
$568$	5.14004e6	0.668492
$569$	1.25640e7	1.62685	0.813426	−	0.581669i	$-0.197600\pi$
$569$	1.25640e7	1.62685	0.813426	+	0.581669i	$0.197600\pi$
$570$	−1.30753e6	−0.168564
$571$	−1.01907e7	−1.30802	−0.654009	−	0.756487i	$-0.726914\pi$
$571$	−1.01907e7	−1.30802	−0.654009	+	0.756487i	$0.726914\pi$
$572$	0	0
$573$	6.46998e6	0.823221
$574$	9.10201e6	1.15308
$575$	−1.45944e7	−1.84085
$576$	331776.	0.0416667
$577$	396134.	0.0495340	0.0247670	−	0.999693i	$-0.492116\pi$
$577$	396134.	0.0495340	0.0247670	+	0.999693i	$0.492116\pi$
$578$	2.26590e6	0.282111
$579$	−1.47172e6	−0.182443
$580$	−4.99116e6	−0.616072
$581$	1.40093e7	1.72178
$582$	2.80486e6	0.343245
$583$	2.39896e7	2.92316
$584$	375307.	0.0455359
$585$	0	0
$586$	4.08543e6	0.491466
$587$	−4.04427e6	−0.484446	−0.242223	−	0.970221i	$-0.577876\pi$
$587$	−4.04427e6	−0.484446	−0.242223	+	0.970221i	$0.577876\pi$
$588$	2.63511e6	0.314308
$589$	1.17003e6	0.138966
$590$	1.30016e7	1.53768
$591$	375725.	0.0442488
$592$	−443999.	−0.0520688
$593$	−3.61298e6	−0.421918	−0.210959	−	0.977495i	$-0.567659\pi$
$593$	−3.61298e6	−0.421918	−0.210959	+	0.977495i	$0.567659\pi$
$594$	2.29295e6	0.266642
$595$	−1.44557e7	−1.67397
$596$	−3.96573e6	−0.457307
$597$	−1.43121e6	−0.164349
$598$	0	0
$599$	1.13849e7	1.29647	0.648235	−	0.761441i	$-0.275508\pi$
$599$	1.13849e7	1.29647	0.648235	+	0.761441i	$0.275508\pi$
$600$	−2.21765e6	−0.251486
$601$	−1.38080e7	−1.55935	−0.779677	−	0.626181i	$-0.784617\pi$
$601$	−1.38080e7	−1.55935	−0.779677	+	0.626181i	$0.784617\pi$
$602$	1.35523e6	0.152413
$603$	−2.28193e6	−0.255570
$604$	−5.18864e6	−0.578711
$605$	3.81898e7	4.24188
$606$	617043.	0.0682550
$607$	−4.80008e6	−0.528782	−0.264391	−	0.964416i	$-0.585171\pi$
$607$	−4.80008e6	−0.528782	−0.264391	+	0.964416i	$0.585171\pi$
$608$	−445323.	−0.0488558
$609$	−6.29858e6	−0.688176
$610$	−3.01019e6	−0.327544
$611$	0	0
$612$	−1.19723e6	−0.129211
$613$	−8.26464e6	−0.888327	−0.444163	−	0.895946i	$-0.646499\pi$
$613$	−8.26464e6	−0.888327	−0.444163	+	0.895946i	$0.646499\pi$
$614$	2.14252e6	0.229353
$615$	−9.12855e6	−0.973226
$616$	9.42931e6	1.00122
$617$	−6.25819e6	−0.661814	−0.330907	−	0.943663i	$-0.607355\pi$
$617$	−6.25819e6	−0.661814	−0.330907	+	0.943663i	$0.607355\pi$
$618$	−3.70497e6	−0.390223
$619$	1.49773e7	1.57111	0.785556	−	0.618791i	$-0.212377\pi$
$619$	1.49773e7	1.57111	0.785556	+	0.618791i	$0.212377\pi$
$620$	3.59514e6	0.375610
$621$	−2.76341e6	−0.287552
$622$	1.19034e7	1.23365
$623$	8.57776e6	0.885429
$624$	0	0
$625$	−6.97401e6	−0.714139
$626$	−65648.0	−0.00669554
$627$	−3.07769e6	−0.312648
$628$	6.51319e6	0.659014
$629$	1.60219e6	0.161468
$630$	−5.07005e6	−0.508934
$631$	−9.45858e6	−0.945698	−0.472849	−	0.881143i	$-0.656774\pi$
$631$	−9.45858e6	−0.945698	−0.472849	+	0.881143i	$0.656774\pi$
$632$	1.10405e6	0.109950
$633$	−2.90735e6	−0.288396
$634$	1.19355e7	1.17928
$635$	−2.36768e7	−2.33018
$636$	−4.39318e6	−0.430662
$637$	0	0
$638$	−1.17483e7	−1.14267
$639$	−6.50537e6	−0.630260
$640$	−1.36834e6	−0.132052
$641$	8.37531e6	0.805111	0.402556	−	0.915395i	$-0.368122\pi$
$641$	8.37531e6	0.805111	0.402556	+	0.915395i	$0.368122\pi$
$642$	−4.81446e6	−0.461009
$643$	627456.	0.0598489	0.0299244	−	0.999552i	$-0.490473\pi$
$643$	627456.	0.0598489	0.0299244	+	0.999552i	$0.490473\pi$
$644$	−1.13640e7	−1.07973
$645$	−1.35918e6	−0.128640
$646$	1.60697e6	0.151505
$647$	−9.06494e6	−0.851343	−0.425671	−	0.904878i	$-0.639962\pi$
$647$	−9.06494e6	−0.851343	−0.425671	+	0.904878i	$0.639962\pi$
$648$	−419904.	−0.0392837
$649$	3.06033e7	2.85205
$650$	0	0
$651$	4.53688e6	0.419570
$652$	3.08708e6	0.284399
$653$	4.92251e6	0.451756	0.225878	−	0.974156i	$-0.427475\pi$
$653$	4.92251e6	0.451756	0.225878	+	0.974156i	$0.427475\pi$
$654$	8.53442e6	0.780242
$655$	8.48734e6	0.772980
$656$	−3.10903e6	−0.282075
$657$	−474997.	−0.0429317
$658$	4.23258e6	0.381102
$659$	1.00268e7	0.899389	0.449694	−	0.893182i	$-0.351533\pi$
$659$	1.00268e7	0.899389	0.449694	+	0.893182i	$0.351533\pi$
$660$	−9.45679e6	−0.845053
$661$	97629.5	0.00869116	0.00434558	−	0.999991i	$-0.498617\pi$
$661$	97629.5	0.00869116	0.00434558	+	0.999991i	$0.498617\pi$
$662$	−3.39306e6	−0.300917
$663$	0	0
$664$	−4.78524e6	−0.421196
$665$	6.80523e6	0.596745
$666$	561936.	0.0490909
$667$	1.41588e7	1.23228
$668$	5.74155e6	0.497838
$669$	−1.08654e7	−0.938601
$670$	9.41136e6	0.809963
$671$	−7.08543e6	−0.607519
$672$	−1.72677e6	−0.147507
$673$	−7.82943e6	−0.666334	−0.333167	−	0.942868i	$-0.608117\pi$
$673$	−7.82943e6	−0.666334	−0.333167	+	0.942868i	$0.608117\pi$
$674$	1.61220e6	0.136700
$675$	2.80671e6	0.237103
$676$	0	0
$677$	−6.24465e6	−0.523644	−0.261822	−	0.965116i	$-0.584323\pi$
$677$	−6.24465e6	−0.523644	−0.261822	+	0.965116i	$0.584323\pi$
$678$	−4.97781e6	−0.415876
$679$	−1.45983e7	−1.21514
$680$	4.93772e6	0.409500
$681$	7.96730e6	0.658329
$682$	8.46230e6	0.696671
$683$	−1.22265e7	−1.00288	−0.501441	−	0.865192i	$-0.667197\pi$
$683$	−1.22265e7	−1.00288	−0.501441	+	0.865192i	$0.667197\pi$
$684$	563612.	0.0460617
$685$	1.14264e7	0.930432
$686$	−1.11848e6	−0.0907444
$687$	4.26385e6	0.344675
$688$	−462913.	−0.0372845
$689$	0	0
$690$	1.13971e7	0.911323
$691$	1.33096e7	1.06040	0.530198	−	0.847874i	$-0.322117\pi$
$691$	1.33096e7	1.06040	0.530198	+	0.847874i	$0.322117\pi$
$692$	−9.20403e6	−0.730656
$693$	−1.19340e7	−0.943956
$694$	1.82039e6	0.143471
$695$	1.02273e7	0.803150
$696$	2.15144e6	0.168347
$697$	1.12191e7	0.874731
$698$	−1.02224e7	−0.794169
$699$	−1.52307e6	−0.117903
$700$	1.15420e7	0.890302
$701$	8.08924e6	0.621745	0.310873	−	0.950452i	$-0.399379\pi$
$701$	8.08924e6	0.621745	0.310873	+	0.950452i	$0.399379\pi$
$702$	0	0
$703$	−754254.	−0.0575611
$704$	−3.22082e6	−0.244926
$705$	−4.24492e6	−0.321660
$706$	−1.97076e6	−0.148807
$707$	−3.21149e6	−0.241634
$708$	−5.60433e6	−0.420185
$709$	−1.44669e7	−1.08084	−0.540418	−	0.841397i	$-0.681734\pi$
$709$	−1.44669e7	−1.08084	−0.540418	+	0.841397i	$0.681734\pi$
$710$	2.68301e7	1.99745
$711$	−1.39731e6	−0.103662
$712$	−2.92996e6	−0.216601
$713$	−1.01986e7	−0.751304
$714$	6.23114e6	0.457427
$715$	0	0
$716$	1.16824e7	0.851628
$717$	1.31882e7	0.958048
$718$	8.69941e6	0.629765
$719$	−1.10888e7	−0.799950	−0.399975	−	0.916526i	$-0.630981\pi$
$719$	−1.10888e7	−0.799950	−0.399975	+	0.916526i	$0.630981\pi$
$720$	1.73181e6	0.124500
$721$	1.92830e7	1.38145
$722$	9.14789e6	0.653098
$723$	−314851.	−0.0224006
$724$	−288070.	−0.0204245
$725$	−1.43806e7	−1.01609
$726$	−1.64617e7	−1.15913
$727$	1.58622e7	1.11308	0.556542	−	0.830819i	$-0.312128\pi$
$727$	1.58622e7	1.11308	0.556542	+	0.830819i	$0.312128\pi$
$728$	0	0
$729$	531441.	0.0370370
$730$	1.95903e6	0.136061
$731$	1.67044e6	0.115621
$732$	1.29754e6	0.0895043
$733$	−1.25058e7	−0.859711	−0.429856	−	0.902898i	$-0.641436\pi$
$733$	−1.25058e7	−0.859711	−0.429856	+	0.902898i	$0.641436\pi$
$734$	−2.96443e6	−0.203096
$735$	1.37548e7	0.939150
$736$	3.88166e6	0.264133
$737$	2.21526e7	1.50230
$738$	3.93486e6	0.265943
$739$	−1.10338e7	−0.743217	−0.371609	−	0.928389i	$-0.621194\pi$
$739$	−1.10338e7	−0.743217	−0.371609	+	0.928389i	$0.621194\pi$
$740$	−2.31759e6	−0.155581
$741$	0	0
$742$	2.28649e7	1.52461
$743$	2.80392e7	1.86335	0.931674	−	0.363296i	$-0.118349\pi$
$743$	2.80392e7	1.86335	0.931674	+	0.363296i	$0.118349\pi$
$744$	−1.54969e6	−0.102639
$745$	−2.07003e7	−1.36643
$746$	1.36817e7	0.900107
$747$	6.05632e6	0.397107
$748$	1.16225e7	0.759530
$749$	2.50575e7	1.63205
$750$	−2.18003e6	−0.141517
$751$	−3.13111e6	−0.202581	−0.101291	−	0.994857i	$-0.532297\pi$
$751$	−3.13111e6	−0.202581	−0.101291	+	0.994857i	$0.532297\pi$
$752$	−1.44575e6	−0.0932284
$753$	5.66397e6	0.364027
$754$	0	0
$755$	−2.70837e7	−1.72918
$756$	2.18545e6	0.139071
$757$	−4.09411e6	−0.259669	−0.129834	−	0.991536i	$-0.541445\pi$
$757$	−4.09411e6	−0.259669	−0.129834	+	0.991536i	$0.541445\pi$
$758$	9.60154e6	0.606971
$759$	2.68267e7	1.69030
$760$	−2.32450e6	−0.145981
$761$	7.05171e6	0.441400	0.220700	−	0.975342i	$-0.429166\pi$
$761$	7.05171e6	0.441400	0.220700	+	0.975342i	$0.429166\pi$
$762$	1.02059e7	0.636743
$763$	−4.44185e7	−2.76219
$764$	1.15022e7	0.712930
$765$	−6.24930e6	−0.386081
$766$	282890.	0.0174199
$767$	0	0
$768$	589824.	0.0360844
$769$	1.49719e7	0.912977	0.456488	−	0.889729i	$-0.349107\pi$
$769$	1.49719e7	0.912977	0.456488	+	0.889729i	$0.349107\pi$
$770$	4.92192e7	2.99163
$771$	7.46773e6	0.452431
$772$	−2.61638e6	−0.158000
$773$	−2.67527e7	−1.61035	−0.805173	−	0.593040i	$-0.797928\pi$
$773$	−2.67527e7	−1.61035	−0.805173	+	0.593040i	$0.797928\pi$
$774$	585875.	0.0351522
$775$	1.03584e7	0.619494
$776$	4.98642e6	0.297259
$777$	−2.92467e6	−0.173790
$778$	−1.58356e7	−0.937963
$779$	−5.28153e6	−0.311829
$780$	0	0
$781$	6.31530e7	3.70481
$782$	−1.40072e7	−0.819093
$783$	−2.72292e6	−0.158719
$784$	4.68464e6	0.272199
$785$	3.39976e7	1.96913
$786$	−3.65847e6	−0.211224
$787$	−1.16234e7	−0.668956	−0.334478	−	0.942404i	$-0.608560\pi$
$787$	−1.16234e7	−0.668956	−0.334478	+	0.942404i	$0.608560\pi$
$788$	667956.	0.0383206
$789$	−1.88645e6	−0.107883
$790$	5.76291e6	0.328529
$791$	2.59077e7	1.47227
$792$	4.07635e6	0.230919
$793$	0	0
$794$	−2.23893e6	−0.126034
$795$	−2.29316e7	−1.28682
$796$	−2.54437e6	−0.142331
$797$	2.45692e7	1.37008	0.685040	−	0.728505i	$-0.259785\pi$
$797$	2.45692e7	1.37008	0.685040	+	0.728505i	$0.259785\pi$
$798$	−2.93340e6	−0.163066
$799$	5.21705e6	0.289106
$800$	−3.94248e6	−0.217793
$801$	3.70822e6	0.204214
$802$	2.92507e6	0.160583
$803$	4.61119e6	0.252362
$804$	−4.05677e6	−0.221330
$805$	−5.93179e7	−3.22623
$806$	0	0
$807$	1.51902e7	0.821068
$808$	1.09697e6	0.0591105
$809$	2.45251e7	1.31747	0.658734	−	0.752376i	$-0.271092\pi$
$809$	2.45251e7	1.31747	0.658734	+	0.752376i	$0.271092\pi$
$810$	−2.19182e6	−0.117379
$811$	−6.07437e6	−0.324302	−0.162151	−	0.986766i	$-0.551843\pi$
$811$	−6.07437e6	−0.324302	−0.162151	+	0.986766i	$0.551843\pi$
$812$	−1.11975e7	−0.595978
$813$	1.27910e7	0.678703
$814$	−5.45518e6	−0.288568
$815$	1.61140e7	0.849783
$816$	−2.12841e6	−0.111900
$817$	−786385.	−0.0412174
$818$	−1.64242e7	−0.858224
$819$	0	0
$820$	−1.62285e7	−0.842839
$821$	−7.25192e6	−0.375487	−0.187744	−	0.982218i	$-0.560117\pi$
$821$	−7.25192e6	−0.375487	−0.187744	+	0.982218i	$0.560117\pi$
$822$	−4.92537e6	−0.254249
$823$	−3.62080e7	−1.86340	−0.931699	−	0.363233i	$-0.881673\pi$
$823$	−3.62080e7	−1.86340	−0.931699	+	0.363233i	$0.881673\pi$
$824$	−6.58661e6	−0.337943
$825$	−2.72470e7	−1.39375
$826$	2.91685e7	1.48753
$827$	−1.58515e7	−0.805946	−0.402973	−	0.915212i	$-0.632023\pi$
$827$	−1.58515e7	−0.805946	−0.402973	+	0.915212i	$0.632023\pi$
$828$	−4.91273e6	−0.249027
$829$	8.06150e6	0.407408	0.203704	−	0.979033i	$-0.434702\pi$
$829$	8.06150e6	0.407408	0.203704	+	0.979033i	$0.434702\pi$
$830$	−2.49781e7	−1.25853
$831$	3.85765e6	0.193785
$832$	0	0
$833$	−1.69047e7	−0.844104
$834$	−4.40846e6	−0.219468
$835$	2.99698e7	1.48754
$836$	−5.47145e6	−0.270761
$837$	1.96132e6	0.0967688
$838$	8.66480e6	0.426235
$839$	−1.60489e7	−0.787118	−0.393559	−	0.919299i	$-0.628756\pi$
$839$	−1.60489e7	−0.787118	−0.393559	+	0.919299i	$0.628756\pi$
$840$	−9.01343e6	−0.440749
$841$	−6.55987e6	−0.319820
$842$	2.29335e7	1.11478
$843$	−2.19004e6	−0.106141
$844$	−5.16863e6	−0.249758
$845$	0	0
$846$	1.82977e6	0.0878965
$847$	8.56772e7	4.10352
$848$	−7.81010e6	−0.372964
$849$	1.38461e7	0.659262
$850$	1.42266e7	0.675390
$851$	6.57446e6	0.311197
$852$	−1.15651e7	−0.545821
$853$	1.48875e7	0.700566	0.350283	−	0.936644i	$-0.386085\pi$
$853$	1.48875e7	0.700566	0.350283	+	0.936644i	$0.386085\pi$
$854$	−6.75324e6	−0.316860
$855$	2.94195e6	0.137632
$856$	−8.55904e6	−0.399246
$857$	1.30374e7	0.606369	0.303185	−	0.952932i	$-0.401950\pi$
$857$	1.30374e7	0.606369	0.303185	+	0.952932i	$0.401950\pi$
$858$	0	0
$859$	−1.33964e7	−0.619448	−0.309724	−	0.950826i	$-0.600237\pi$
$859$	−1.33964e7	−0.619448	−0.309724	+	0.950826i	$0.600237\pi$
$860$	−2.41632e6	−0.111406
$861$	−2.04795e7	−0.941482
$862$	3.77292e6	0.172946
$863$	2.38224e7	1.08882	0.544412	−	0.838818i	$-0.316753\pi$
$863$	2.38224e7	1.08882	0.544412	+	0.838818i	$0.316753\pi$
$864$	−746496.	−0.0340207
$865$	−4.80433e7	−2.18319
$866$	3.63141e6	0.164544
$867$	−5.09826e6	−0.230343
$868$	8.06556e6	0.363359
$869$	1.35648e7	0.609347
$870$	1.12301e7	0.503021
$871$	0	0
$872$	1.51723e7	0.675710
$873$	−6.31093e6	−0.280258
$874$	6.59407e6	0.291995
$875$	1.13463e7	0.500995
$876$	−844440.	−0.0371799
$877$	−2.72239e7	−1.19523	−0.597616	−	0.801783i	$-0.703885\pi$
$877$	−2.72239e7	−1.19523	−0.597616	+	0.801783i	$0.703885\pi$
$878$	−3.20465e6	−0.140296
$879$	−9.19221e6	−0.401280
$880$	−1.68121e7	−0.731838
$881$	−1.21240e7	−0.526268	−0.263134	−	0.964759i	$-0.584756\pi$
$881$	−1.21240e7	−0.526268	−0.263134	+	0.964759i	$0.584756\pi$
$882$	−5.92900e6	−0.256631
$883$	5.51350e6	0.237972	0.118986	−	0.992896i	$-0.462036\pi$
$883$	5.51350e6	0.237972	0.118986	+	0.992896i	$0.462036\pi$
$884$	0	0
$885$	−2.92536e7	−1.25551
$886$	2.39332e7	1.02427
$887$	2.79700e7	1.19367	0.596835	−	0.802364i	$-0.296425\pi$
$887$	2.79700e7	1.19367	0.596835	+	0.802364i	$0.296425\pi$
$888$	998998.	0.0425140
$889$	−5.31180e7	−2.25417
$890$	−1.52938e7	−0.647203
$891$	−5.15914e6	−0.217712
$892$	−1.93163e7	−0.812852
$893$	−2.45600e6	−0.103062
$894$	8.92289e6	0.373389
$895$	6.09799e7	2.54466
$896$	−3.06982e6	−0.127745
$897$	0	0
$898$	−2.69816e6	−0.111655
$899$	−1.00491e7	−0.414696
$900$	4.98970e6	0.205338
$901$	2.81831e7	1.15658
$902$	−3.81989e7	−1.56327
$903$	−3.04927e6	−0.124445
$904$	−8.84944e6	−0.360160
$905$	−1.50367e6	−0.0610282
$906$	1.16744e7	0.472515
$907$	−5.29278e6	−0.213632	−0.106816	−	0.994279i	$-0.534066\pi$
$907$	−5.29278e6	−0.213632	−0.106816	+	0.994279i	$0.534066\pi$
$908$	1.41641e7	0.570130
$909$	−1.38835e6	−0.0557299
$910$	0	0
$911$	−2.21671e7	−0.884939	−0.442469	−	0.896784i	$-0.645897\pi$
$911$	−2.21671e7	−0.884939	−0.442469	+	0.896784i	$0.645897\pi$
$912$	1.00198e6	0.0398906
$913$	−5.87937e7	−2.33429
$914$	−9.77685e6	−0.387109
$915$	6.77292e6	0.267438
$916$	7.58018e6	0.298498
$917$	1.90410e7	0.747767
$918$	2.69376e6	0.105500
$919$	2.94503e7	1.15027	0.575136	−	0.818058i	$-0.304949\pi$
$919$	2.94503e7	1.15027	0.575136	+	0.818058i	$0.304949\pi$
$920$	2.02615e7	0.789229
$921$	−4.82068e6	−0.187266
$922$	−3.43522e6	−0.133084
$923$	0	0
$924$	−2.12159e7	−0.817490
$925$	−6.67747e6	−0.256600
$926$	−3.12793e7	−1.19875
$927$	8.33617e6	0.318616
$928$	3.82478e6	0.145793
$929$	−3.97704e7	−1.51189	−0.755945	−	0.654635i	$-0.772822\pi$
$929$	−3.97704e7	−1.51189	−0.755945	+	0.654635i	$0.772822\pi$
$930$	−8.08907e6	−0.306684
$931$	7.95814e6	0.300911
$932$	−2.70768e6	−0.102107
$933$	−2.67825e7	−1.00727
$934$	−2.51184e7	−0.942159
$935$	6.06671e7	2.26947
$936$	0	0
$937$	−4.09277e7	−1.52289	−0.761445	−	0.648229i	$-0.775510\pi$
$937$	−4.09277e7	−1.52289	−0.761445	+	0.648229i	$0.775510\pi$
$938$	2.11140e7	0.783544
$939$	147708.	0.00546689
$940$	−7.54653e6	−0.278566
$941$	3.05137e7	1.12337	0.561683	−	0.827353i	$-0.310154\pi$
$941$	3.05137e7	1.12337	0.561683	+	0.827353i	$0.310154\pi$
$942$	−1.46547e7	−0.538083
$943$	4.60365e7	1.68587
$944$	−9.96326e6	−0.363891
$945$	1.14076e7	0.415543
$946$	−5.68757e6	−0.206633
$947$	−3.50278e7	−1.26922	−0.634611	−	0.772831i	$-0.718840\pi$
$947$	−3.50278e7	−1.26922	−0.634611	+	0.772831i	$0.718840\pi$
$948$	−2.48410e6	−0.0897736
$949$	0	0
$950$	−6.69738e6	−0.240767
$951$	−2.68548e7	−0.962878
$952$	1.10776e7	0.396144
$953$	−3.97551e7	−1.41795	−0.708974	−	0.705234i	$-0.750842\pi$
$953$	−3.97551e7	−1.41795	−0.708974	+	0.705234i	$0.750842\pi$
$954$	9.88466e6	0.351634
$955$	6.00392e7	2.13023
$956$	2.34457e7	0.829694
$957$	2.64336e7	0.932989
$958$	−9.16439e6	−0.322619
$959$	2.56348e7	0.900084
$960$	3.07877e6	0.107820
$961$	−2.13907e7	−0.747166
$962$	0	0
$963$	1.08325e7	0.376413
$964$	−559735.	−0.0193995
$965$	−1.36570e7	−0.472104
$966$	2.55690e7	0.881598
$967$	−1.45550e7	−0.500547	−0.250274	−	0.968175i	$-0.580521\pi$
$967$	−1.45550e7	−0.500547	−0.250274	+	0.968175i	$0.580521\pi$
$968$	−2.92653e7	−1.00384
$969$	−3.61568e6	−0.123703
$970$	2.60281e7	0.888206
$971$	−1.10708e7	−0.376818	−0.188409	−	0.982091i	$-0.560333\pi$
$971$	−1.10708e7	−0.376818	−0.188409	+	0.982091i	$0.560333\pi$
$972$	944784.	0.0320750
$973$	2.29444e7	0.776954
$974$	1.62319e7	0.548243
$975$	0	0
$976$	2.30674e6	0.0775130
$977$	1.10774e7	0.371280	0.185640	−	0.982618i	$-0.440564\pi$
$977$	1.10774e7	0.371280	0.185640	+	0.982618i	$0.440564\pi$
$978$	−6.94593e6	−0.232211
$979$	−3.59988e7	−1.20041
$980$	2.44529e7	0.813328
$981$	−1.92024e7	−0.637065
$982$	−2.43885e6	−0.0807060
$983$	3.48354e7	1.14984	0.574919	−	0.818210i	$-0.305033\pi$
$983$	3.48354e7	1.14984	0.574919	+	0.818210i	$0.305033\pi$
$984$	6.99531e6	0.230313
$985$	3.48660e6	0.114502
$986$	−1.38019e7	−0.452113
$987$	−9.52331e6	−0.311168
$988$	0	0
$989$	6.85453e6	0.222837
$990$	2.12778e7	0.689983
$991$	1.08055e7	0.349512	0.174756	−	0.984612i	$-0.444086\pi$
$991$	1.08055e7	0.349512	0.174756	+	0.984612i	$0.444086\pi$
$992$	−2.75500e6	−0.0888879
$993$	7.63439e6	0.245698
$994$	6.01922e7	1.93230
$995$	−1.32811e7	−0.425283
$996$	1.07668e7	0.343905
$997$	−2.76495e6	−0.0880945	−0.0440473	−	0.999029i	$-0.514025\pi$
$997$	−2.76495e6	−0.0880945	−0.0440473	+	0.999029i	$0.514025\pi$
$998$	−3.77422e7	−1.19950
$999$	−1.26436e6	−0.0400826

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1014.6.a.t.1.4		4
13.5	odd	4		78.6.b.b.25.5	yes	8
13.8	odd	4		78.6.b.b.25.4	✓	8
13.12	even	2		1014.6.a.u.1.1		4
39.5	even	4		234.6.b.d.181.4		8
39.8	even	4		234.6.b.d.181.5		8
52.31	even	4		624.6.c.f.337.2		8
52.47	even	4		624.6.c.f.337.7		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
78.6.b.b.25.4	✓	8	13.8	odd	4
78.6.b.b.25.5	yes	8	13.5	odd	4
234.6.b.d.181.4		8	39.5	even	4
234.6.b.d.181.5		8	39.8	even	4
624.6.c.f.337.2		8	52.31	even	4
624.6.c.f.337.7		8	52.47	even	4
1014.6.a.t.1.4		4	1.1	even	1	trivial
1014.6.a.u.1.1		4	13.12	even	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:	\( N \)	\(=\)	\( 1014 = 2 \cdot 3 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	1014.a (trivial)

\(f(q)\)	\(=\)	\(q-4.00000 q^{2} +9.00000 q^{3} +16.0000 q^{4} +83.5169 q^{5} -36.0000 q^{6} +187.367 q^{7} -64.0000 q^{8} +81.0000 q^{9} +O(q^{10})\)	\(q-4.00000 q^{2} +9.00000 q^{3} +16.0000 q^{4} +83.5169 q^{5} -36.0000 q^{6} +187.367 q^{7} -64.0000 q^{8} +81.0000 q^{9} -334.068 q^{10} -786.334 q^{11} +144.000 q^{12} -749.468 q^{14} +751.652 q^{15} +256.000 q^{16} -923.787 q^{17} -324.000 q^{18} +434.886 q^{19} +1336.27 q^{20} +1686.30 q^{21} +3145.33 q^{22} -3790.69 q^{23} -576.000 q^{24} +3850.08 q^{25} +729.000 q^{27} +2997.87 q^{28} -3735.14 q^{29} -3006.61 q^{30} +2690.43 q^{31} -1024.00 q^{32} -7077.00 q^{33} +3695.15 q^{34} +15648.3 q^{35} +1296.00 q^{36} -1734.37 q^{37} -1739.54 q^{38} -5345.08 q^{40} -12144.6 q^{41} -6745.21 q^{42} -1808.26 q^{43} -12581.3 q^{44} +6764.87 q^{45} +15162.8 q^{46} -5647.45 q^{47} +2304.00 q^{48} +18299.4 q^{49} -15400.3 q^{50} -8314.09 q^{51} -30508.2 q^{53} -2916.00 q^{54} -65672.2 q^{55} -11991.5 q^{56} +3913.97 q^{57} +14940.6 q^{58} -38919.0 q^{59} +12026.4 q^{60} +9010.71 q^{61} -10761.7 q^{62} +15176.7 q^{63} +4096.00 q^{64} +28308.0 q^{66} -28172.0 q^{67} -14780.6 q^{68} -34116.2 q^{69} -62593.3 q^{70} -80313.2 q^{71} -5184.00 q^{72} -5864.17 q^{73} +6937.48 q^{74} +34650.7 q^{75} +6958.18 q^{76} -147333. q^{77} -17250.7 q^{79} +21380.3 q^{80} +6561.00 q^{81} +48578.5 q^{82} +74769.4 q^{83} +26980.8 q^{84} -77151.9 q^{85} +7233.02 q^{86} -33616.3 q^{87} +50325.4 q^{88} +45780.6 q^{89} -27059.5 q^{90} -60651.0 q^{92} +24213.9 q^{93} +22589.8 q^{94} +36320.4 q^{95} -9216.00 q^{96} -77912.8 q^{97} -73197.5 q^{98} -63693.0 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 16 q^{2} + 36 q^{3} + 64 q^{4} - 10 q^{5} - 144 q^{6} + 72 q^{7} - 256 q^{8} + 324 q^{9}+O(q^{10}) \) 4 * q - 16 * q^2 + 36 * q^3 + 64 * q^4 - 10 * q^5 - 144 * q^6 + 72 * q^7 - 256 * q^8 + 324 * q^9	\( 4 q - 16 q^{2} + 36 q^{3} + 64 q^{4} - 10 q^{5} - 144 q^{6} + 72 q^{7} - 256 q^{8} + 324 q^{9} + 40 q^{10} - 702 q^{11} + 576 q^{12} - 288 q^{14} - 90 q^{15} + 1024 q^{16} - 300 q^{17} - 1296 q^{18} - 1800 q^{19} - 160 q^{20} + 648 q^{21} + 2808 q^{22} + 828 q^{23} - 2304 q^{24} + 5064 q^{25} + 2916 q^{27} + 1152 q^{28} - 1680 q^{29} + 360 q^{30} + 972 q^{31} - 4096 q^{32} - 6318 q^{33} + 1200 q^{34} + 13572 q^{35} + 5184 q^{36} - 9204 q^{37} + 7200 q^{38} + 640 q^{40} - 20054 q^{41} - 2592 q^{42} - 8472 q^{43} - 11232 q^{44} - 810 q^{45} - 3312 q^{46} + 8034 q^{47} + 9216 q^{48} + 29740 q^{49} - 20256 q^{50} - 2700 q^{51} + 4788 q^{53} - 11664 q^{54} + 2712 q^{55} - 4608 q^{56} - 16200 q^{57} + 6720 q^{58} - 96658 q^{59} - 1440 q^{60} + 29172 q^{61} - 3888 q^{62} + 5832 q^{63} + 16384 q^{64} + 25272 q^{66} - 22452 q^{67} - 4800 q^{68} + 7452 q^{69} - 54288 q^{70} - 30030 q^{71} - 20736 q^{72} + 105132 q^{73} + 36816 q^{74} + 45576 q^{75} - 28800 q^{76} - 121980 q^{77} + 77984 q^{79} - 2560 q^{80} + 26244 q^{81} + 80216 q^{82} - 181390 q^{83} + 10368 q^{84} - 277044 q^{85} + 33888 q^{86} - 15120 q^{87} + 44928 q^{88} - 1386 q^{89} + 3240 q^{90} + 13248 q^{92} + 8748 q^{93} - 32136 q^{94} + 184116 q^{95} - 36864 q^{96} + 55188 q^{97} - 118960 q^{98} - 56862 q^{99}+O(q^{100}) \) 4 * q - 16 * q^2 + 36 * q^3 + 64 * q^4 - 10 * q^5 - 144 * q^6 + 72 * q^7 - 256 * q^8 + 324 * q^9 + 40 * q^10 - 702 * q^11 + 576 * q^12 - 288 * q^14 - 90 * q^15 + 1024 * q^16 - 300 * q^17 - 1296 * q^18 - 1800 * q^19 - 160 * q^20 + 648 * q^21 + 2808 * q^22 + 828 * q^23 - 2304 * q^24 + 5064 * q^25 + 2916 * q^27 + 1152 * q^28 - 1680 * q^29 + 360 * q^30 + 972 * q^31 - 4096 * q^32 - 6318 * q^33 + 1200 * q^34 + 13572 * q^35 + 5184 * q^36 - 9204 * q^37 + 7200 * q^38 + 640 * q^40 - 20054 * q^41 - 2592 * q^42 - 8472 * q^43 - 11232 * q^44 - 810 * q^45 - 3312 * q^46 + 8034 * q^47 + 9216 * q^48 + 29740 * q^49 - 20256 * q^50 - 2700 * q^51 + 4788 * q^53 - 11664 * q^54 + 2712 * q^55 - 4608 * q^56 - 16200 * q^57 + 6720 * q^58 - 96658 * q^59 - 1440 * q^60 + 29172 * q^61 - 3888 * q^62 + 5832 * q^63 + 16384 * q^64 + 25272 * q^66 - 22452 * q^67 - 4800 * q^68 + 7452 * q^69 - 54288 * q^70 - 30030 * q^71 - 20736 * q^72 + 105132 * q^73 + 36816 * q^74 + 45576 * q^75 - 28800 * q^76 - 121980 * q^77 + 77984 * q^79 - 2560 * q^80 + 26244 * q^81 + 80216 * q^82 - 181390 * q^83 + 10368 * q^84 - 277044 * q^85 + 33888 * q^86 - 15120 * q^87 + 44928 * q^88 - 1386 * q^89 + 3240 * q^90 + 13248 * q^92 + 8748 * q^93 - 32136 * q^94 + 184116 * q^95 - 36864 * q^96 + 55188 * q^97 - 118960 * q^98 - 56862 * q^99

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