LMFDB - Embedded newform 338.6.a.m.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [338,6,Mod(1,338)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(338, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("338.1");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 338 = 2 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	338.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:	$54.2097310968$
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} - 1082x^{4} - 456x^{3} + 261469x^{2} + 235680x + 51012 $ x^6 - 1082x^4 - 456x^3 + 261469x^2 + 235680x + 51012
Coefficient ring:	$\Z[a_1, \ldots, a_{19}]$
Coefficient ring index:	$ 2^{3}\cdot 13 $
Twist minimal:	no (minimal twist has level 26)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$19.3520$ of defining polynomial
Character	$\chi$	$=$	338.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-4.00000 q^{2} -19.3520 q^{3} +16.0000 q^{4} -52.2356 q^{5} +77.4082 q^{6} -19.1214 q^{7} -64.0000 q^{8} +131.501 q^{9} +O(q^{10})$	\(q-4.00000 q^{2} -19.3520 q^{3} +16.0000 q^{4} -52.2356 q^{5} +77.4082 q^{6} -19.1214 q^{7} -64.0000 q^{8} +131.501 q^{9} +208.942 q^{10} +381.988 q^{11} -309.633 q^{12} +76.4855 q^{14} +1010.86 q^{15} +256.000 q^{16} -1057.42 q^{17} -526.006 q^{18} -2343.73 q^{19} -835.769 q^{20} +370.038 q^{21} -1527.95 q^{22} -2747.96 q^{23} +1238.53 q^{24} -396.447 q^{25} +2157.72 q^{27} -305.942 q^{28} -121.718 q^{29} -4043.46 q^{30} -5556.97 q^{31} -1024.00 q^{32} -7392.25 q^{33} +4229.66 q^{34} +998.816 q^{35} +2104.02 q^{36} +8146.46 q^{37} +9374.92 q^{38} +3343.08 q^{40} -13485.3 q^{41} -1480.15 q^{42} -22019.7 q^{43} +6111.81 q^{44} -6869.05 q^{45} +10991.8 q^{46} +3489.22 q^{47} -4954.12 q^{48} -16441.4 q^{49} +1585.79 q^{50} +20463.2 q^{51} -28937.9 q^{53} -8630.90 q^{54} -19953.4 q^{55} +1223.77 q^{56} +45355.9 q^{57} +486.873 q^{58} -34446.8 q^{59} +16173.8 q^{60} +5305.93 q^{61} +22227.9 q^{62} -2514.49 q^{63} +4096.00 q^{64} +29569.0 q^{66} +56900.3 q^{67} -16918.7 q^{68} +53178.6 q^{69} -3995.26 q^{70} -2393.52 q^{71} -8416.09 q^{72} +47969.6 q^{73} -32585.8 q^{74} +7672.05 q^{75} -37499.7 q^{76} -7304.14 q^{77} -79330.2 q^{79} -13372.3 q^{80} -73711.2 q^{81} +53941.1 q^{82} +22090.3 q^{83} +5920.60 q^{84} +55234.7 q^{85} +88078.6 q^{86} +2355.50 q^{87} -24447.2 q^{88} +124339. q^{89} +27476.2 q^{90} -43967.3 q^{92} +107539. q^{93} -13956.9 q^{94} +122426. q^{95} +19816.5 q^{96} +94093.5 q^{97} +65765.5 q^{98} +50232.0 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 24 q^{2} + 96 q^{4} + 92 q^{5} + 284 q^{7} - 384 q^{8} + 706 q^{9}+O(q^{10}) $ 6 * q - 24 * q^2 + 96 * q^4 + 92 * q^5 + 284 * q^7 - 384 * q^8 + 706 * q^9	\( 6 q - 24 q^{2} + 96 q^{4} + 92 q^{5} + 284 q^{7} - 384 q^{8} + 706 q^{9} - 368 q^{10} + 540 q^{11} - 1136 q^{14} + 2924 q^{15} + 1536 q^{16} - 1910 q^{17} - 2824 q^{18} + 3312 q^{19} + 1472 q^{20} + 5912 q^{21} - 2160 q^{22} + 5920 q^{23} + 2336 q^{25} - 1368 q^{27} + 4544 q^{28} - 7922 q^{29} - 11696 q^{30} + 1084 q^{31} - 6144 q^{32} - 792 q^{33} + 7640 q^{34} - 16864 q^{35} + 11296 q^{36} + 24052 q^{37} - 13248 q^{38} - 5888 q^{40} + 21760 q^{41} - 23648 q^{42} - 41920 q^{43} + 8640 q^{44} + 35252 q^{45} - 23680 q^{46} + 39564 q^{47} + 4682 q^{49} - 9344 q^{50} - 66632 q^{51} - 93906 q^{53} + 5472 q^{54} - 17472 q^{55} - 18176 q^{56} + 89616 q^{57} + 31688 q^{58} - 77860 q^{59} + 46784 q^{60} - 27934 q^{61} - 4336 q^{62} + 13400 q^{63} + 24576 q^{64} + 3168 q^{66} + 55096 q^{67} - 30560 q^{68} - 77348 q^{69} + 67456 q^{70} + 30384 q^{71} - 45184 q^{72} + 206488 q^{73} - 96208 q^{74} + 192080 q^{75} + 52992 q^{76} + 75972 q^{77} + 15232 q^{79} + 23552 q^{80} + 72310 q^{81} - 87040 q^{82} + 77096 q^{83} + 94592 q^{84} - 272948 q^{85} + 167680 q^{86} + 121936 q^{87} - 34560 q^{88} + 214224 q^{89} - 141008 q^{90} + 94720 q^{92} + 505168 q^{93} - 158256 q^{94} + 232560 q^{95} + 310272 q^{97} - 18728 q^{98} + 809784 q^{99}+O(q^{100}) \) 6 * q - 24 * q^2 + 96 * q^4 + 92 * q^5 + 284 * q^7 - 384 * q^8 + 706 * q^9 - 368 * q^10 + 540 * q^11 - 1136 * q^14 + 2924 * q^15 + 1536 * q^16 - 1910 * q^17 - 2824 * q^18 + 3312 * q^19 + 1472 * q^20 + 5912 * q^21 - 2160 * q^22 + 5920 * q^23 + 2336 * q^25 - 1368 * q^27 + 4544 * q^28 - 7922 * q^29 - 11696 * q^30 + 1084 * q^31 - 6144 * q^32 - 792 * q^33 + 7640 * q^34 - 16864 * q^35 + 11296 * q^36 + 24052 * q^37 - 13248 * q^38 - 5888 * q^40 + 21760 * q^41 - 23648 * q^42 - 41920 * q^43 + 8640 * q^44 + 35252 * q^45 - 23680 * q^46 + 39564 * q^47 + 4682 * q^49 - 9344 * q^50 - 66632 * q^51 - 93906 * q^53 + 5472 * q^54 - 17472 * q^55 - 18176 * q^56 + 89616 * q^57 + 31688 * q^58 - 77860 * q^59 + 46784 * q^60 - 27934 * q^61 - 4336 * q^62 + 13400 * q^63 + 24576 * q^64 + 3168 * q^66 + 55096 * q^67 - 30560 * q^68 - 77348 * q^69 + 67456 * q^70 + 30384 * q^71 - 45184 * q^72 + 206488 * q^73 - 96208 * q^74 + 192080 * q^75 + 52992 * q^76 + 75972 * q^77 + 15232 * q^79 + 23552 * q^80 + 72310 * q^81 - 87040 * q^82 + 77096 * q^83 + 94592 * q^84 - 272948 * q^85 + 167680 * q^86 + 121936 * q^87 - 34560 * q^88 + 214224 * q^89 - 141008 * q^90 + 94720 * q^92 + 505168 * q^93 - 158256 * q^94 + 232560 * q^95 + 310272 * q^97 - 18728 * q^98 + 809784 * 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
$3$	−19.3520	−1.24143	−0.620717	−	0.784035i	$-0.713158\pi$
$3$	−19.3520	−1.24143	−0.620717	+	0.784035i	$0.713158\pi$
$4$	16.0000	0.500000
$5$	−52.2356	−0.934418	−0.467209	−	0.884147i	$-0.654740\pi$
$5$	−52.2356	−0.934418	−0.467209	+	0.884147i	$0.654740\pi$
$6$	77.4082	0.877826
$7$	−19.1214	−0.147494	−0.0737469	−	0.997277i	$-0.523496\pi$
$7$	−19.1214	−0.147494	−0.0737469	+	0.997277i	$0.523496\pi$
$8$	−64.0000	−0.353553
$9$	131.501	0.541158
$10$	208.942	0.660733
$11$	381.988	0.951849	0.475924	−	0.879486i	$-0.342114\pi$
$11$	381.988	0.951849	0.475924	+	0.879486i	$0.342114\pi$
$12$	−309.633	−0.620717
$13$	0	0
$13$	0	0
$14$	76.4855	0.104294
$15$	1010.86	1.16002
$16$	256.000	0.250000
$17$	−1057.42	−0.887409	−0.443704	−	0.896173i	$-0.646336\pi$
$17$	−1057.42	−0.887409	−0.443704	+	0.896173i	$0.646336\pi$
$18$	−526.006	−0.382657
$19$	−2343.73	−1.48944	−0.744721	−	0.667376i	$-0.767417\pi$
$19$	−2343.73	−1.48944	−0.744721	+	0.667376i	$0.767417\pi$
$20$	−835.769	−0.467209
$21$	370.038	0.183104
$22$	−1527.95	−0.673059
$23$	−2747.96	−1.08315	−0.541577	−	0.840651i	$-0.682173\pi$
$23$	−2747.96	−1.08315	−0.541577	+	0.840651i	$0.682173\pi$
$24$	1238.53	0.438913
$25$	−396.447	−0.126863
$26$	0	0
$27$	2157.72	0.569622
$28$	−305.942	−0.0737469
$29$	−121.718	−0.0268757	−0.0134379	−	0.999910i	$-0.504278\pi$
$29$	−121.718	−0.0268757	−0.0134379	+	0.999910i	$0.504278\pi$
$30$	−4043.46	−0.820257
$31$	−5556.97	−1.03856	−0.519282	−	0.854603i	$-0.673801\pi$
$31$	−5556.97	−1.03856	−0.519282	+	0.854603i	$0.673801\pi$
$32$	−1024.00	−0.176777
$33$	−7392.25	−1.18166
$34$	4229.66	0.627493
$35$	998.816	0.137821
$36$	2104.02	0.270579
$37$	8146.46	0.978283	0.489142	−	0.872204i	$-0.337310\pi$
$37$	8146.46	0.978283	0.489142	+	0.872204i	$0.337310\pi$
$38$	9374.92	1.05319
$39$	0	0
$40$	3343.08	0.330367
$41$	−13485.3	−1.25285	−0.626426	−	0.779481i	$-0.715483\pi$
$41$	−13485.3	−1.25285	−0.626426	+	0.779481i	$0.715483\pi$
$42$	−1480.15	−0.129474
$43$	−22019.7	−1.81610	−0.908049	−	0.418863i	$-0.862429\pi$
$43$	−22019.7	−1.81610	−0.908049	+	0.418863i	$0.862429\pi$
$44$	6111.81	0.475924
$45$	−6869.05	−0.505668
$46$	10991.8	0.765906
$47$	3489.22	0.230401	0.115200	−	0.993342i	$-0.463249\pi$
$47$	3489.22	0.230401	0.115200	+	0.993342i	$0.463249\pi$
$48$	−4954.12	−0.310358
$49$	−16441.4	−0.978246
$50$	1585.79	0.0897056
$51$	20463.2	1.10166
$52$	0	0
$53$	−28937.9	−1.41507	−0.707534	−	0.706679i	$-0.750192\pi$
$53$	−28937.9	−1.41507	−0.707534	+	0.706679i	$0.750192\pi$
$54$	−8630.90	−0.402783
$55$	−19953.4	−0.889425
$56$	1223.77	0.0521470
$57$	45355.9	1.84904
$58$	486.873	0.0190040
$59$	−34446.8	−1.28830	−0.644152	−	0.764897i	$-0.722790\pi$
$59$	−34446.8	−1.28830	−0.644152	+	0.764897i	$0.722790\pi$
$60$	16173.8	0.580009
$61$	5305.93	0.182573	0.0912866	−	0.995825i	$-0.470902\pi$
$61$	5305.93	0.182573	0.0912866	+	0.995825i	$0.470902\pi$
$62$	22227.9	0.734376
$63$	−2514.49	−0.0798175
$64$	4096.00	0.125000
$65$	0	0
$66$	29569.0	0.835558
$67$	56900.3	1.54856	0.774279	−	0.632844i	$-0.218113\pi$
$67$	56900.3	1.54856	0.774279	+	0.632844i	$0.218113\pi$
$68$	−16918.7	−0.443704
$69$	53178.6	1.34466
$70$	−3995.26	−0.0974541
$71$	−2393.52	−0.0563496	−0.0281748	−	0.999603i	$-0.508969\pi$
$71$	−2393.52	−0.0563496	−0.0281748	+	0.999603i	$0.508969\pi$
$72$	−8416.09	−0.191328
$73$	47969.6	1.05356	0.526780	−	0.850002i	$-0.323399\pi$
$73$	47969.6	1.05356	0.526780	+	0.850002i	$0.323399\pi$
$74$	−32585.8	−0.691751
$75$	7672.05	0.157492
$76$	−37499.7	−0.744721
$77$	−7304.14	−0.140392
$78$	0	0
$79$	−79330.2	−1.43011	−0.715057	−	0.699066i	$-0.753599\pi$
$79$	−79330.2	−1.43011	−0.715057	+	0.699066i	$0.753599\pi$
$80$	−13372.3	−0.233605
$81$	−73711.2	−1.24831
$82$	53941.1	0.885901
$83$	22090.3	0.351971	0.175986	−	0.984393i	$-0.443689\pi$
$83$	22090.3	0.351971	0.175986	+	0.984393i	$0.443689\pi$
$84$	5920.60	0.0915520
$85$	55234.7	0.829211
$86$	88078.6	1.28418
$87$	2355.50	0.0333645
$88$	−24447.2	−0.336529
$89$	124339.	1.66392	0.831960	−	0.554835i	$-0.187219\pi$
$89$	124339.	1.66392	0.831960	+	0.554835i	$0.187219\pi$
$90$	27476.2	0.357561
$91$	0	0
$92$	−43967.3	−0.541577
$93$	107539.	1.28931
$94$	−13956.9	−0.162918
$95$	122426.	1.39176
$96$	19816.5	0.219457
$97$	94093.5	1.01538	0.507692	−	0.861539i	$-0.330499\pi$
$97$	94093.5	1.01538	0.507692	+	0.861539i	$0.330499\pi$
$98$	65765.5	0.691724
$99$	50232.0	0.515101
$100$	−6343.15	−0.0634315
$101$	−57335.4	−0.559267	−0.279634	−	0.960107i	$-0.590213\pi$
$101$	−57335.4	−0.559267	−0.279634	+	0.960107i	$0.590213\pi$
$102$	−81852.6	−0.778991
$103$	160258.	1.48842	0.744211	−	0.667945i	$-0.232826\pi$
$103$	160258.	1.48842	0.744211	+	0.667945i	$0.232826\pi$
$104$	0	0
$105$	−19329.1	−0.171096
$106$	115752.	1.00060
$107$	18055.2	0.152455	0.0762276	−	0.997090i	$-0.475712\pi$
$107$	18055.2	0.152455	0.0762276	+	0.997090i	$0.475712\pi$
$108$	34523.6	0.284811
$109$	25954.4	0.209240	0.104620	−	0.994512i	$-0.466637\pi$
$109$	25954.4	0.209240	0.104620	+	0.994512i	$0.466637\pi$
$110$	79813.4	0.628918
$111$	−157651.	−1.21447
$112$	−4895.07	−0.0368735
$113$	−109573.	−0.807246	−0.403623	−	0.914925i	$-0.632249\pi$
$113$	−109573.	−0.807246	−0.403623	+	0.914925i	$0.632249\pi$
$114$	−181424.	−1.30747
$115$	143541.	1.01212
$116$	−1947.49	−0.0134379
$117$	0	0
$118$	137787.	0.910969
$119$	20219.2	0.130887
$120$	−64695.3	−0.410128
$121$	−15136.2	−0.0939836
$122$	−21223.7	−0.129099
$123$	260968.	1.55533
$124$	−88911.5	−0.519282
$125$	183945.	1.05296
$126$	10058.0	0.0564395
$127$	−58353.4	−0.321038	−0.160519	−	0.987033i	$-0.551317\pi$
$127$	−58353.4	−0.321038	−0.160519	+	0.987033i	$0.551317\pi$
$128$	−16384.0	−0.0883883
$129$	426125.	2.25457
$130$	0	0
$131$	29397.6	0.149670	0.0748349	−	0.997196i	$-0.476157\pi$
$131$	29397.6	0.149670	0.0748349	+	0.997196i	$0.476157\pi$
$132$	−118276.	−0.590829
$133$	44815.3	0.219684
$134$	−227601.	−1.09500
$135$	−112710.	−0.532265
$136$	67674.6	0.313746
$137$	−229924.	−1.04660	−0.523302	−	0.852148i	$-0.675300\pi$
$137$	−229924.	−1.04660	−0.523302	+	0.852148i	$0.675300\pi$
$138$	−212714.	−0.950822
$139$	169311.	0.743273	0.371637	−	0.928378i	$-0.378797\pi$
$139$	169311.	0.743273	0.371637	+	0.928378i	$0.378797\pi$
$140$	15981.1	0.0689105
$141$	−67523.5	−0.286027
$142$	9574.07	0.0398452
$143$	0	0
$144$	33664.4	0.135290
$145$	6358.02	0.0251132
$146$	−191878.	−0.744979
$147$	318174.	1.21443
$148$	130343.	0.489142
$149$	−492678.	−1.81801	−0.909007	−	0.416780i	$-0.863158\pi$
$149$	−492678.	−1.81801	−0.909007	+	0.416780i	$0.863158\pi$
$150$	−30688.2	−0.111364
$151$	−36336.4	−0.129688	−0.0648440	−	0.997895i	$-0.520655\pi$
$151$	−36336.4	−0.129688	−0.0648440	+	0.997895i	$0.520655\pi$
$152$	149999.	0.526597
$153$	−139052.	−0.480229
$154$	29216.5	0.0992721
$155$	290271.	0.970453
$156$	0	0
$157$	368197.	1.19215	0.596075	−	0.802929i	$-0.296726\pi$
$157$	368197.	1.19215	0.596075	+	0.802929i	$0.296726\pi$
$158$	317321.	1.01124
$159$	560007.	1.75671
$160$	53489.2	0.165183
$161$	52544.7	0.159759
$162$	294845.	0.882686
$163$	−226017.	−0.666303	−0.333151	−	0.942873i	$-0.608112\pi$
$163$	−226017.	−0.666303	−0.333151	+	0.942873i	$0.608112\pi$
$164$	−215764.	−0.626426
$165$	386138.	1.10416
$166$	−88361.4	−0.248881
$167$	161239.	0.447382	0.223691	−	0.974660i	$-0.428189\pi$
$167$	161239.	0.447382	0.223691	+	0.974660i	$0.428189\pi$
$168$	−23682.4	−0.0647370
$169$	0	0
$170$	−220939.	−0.586340
$171$	−308204.	−0.806024
$172$	−352314.	−0.908049
$173$	−300682.	−0.763822	−0.381911	−	0.924199i	$-0.624734\pi$
$173$	−300682.	−0.763822	−0.381911	+	0.924199i	$0.624734\pi$
$174$	−9421.98	−0.0235922
$175$	7580.61	0.0187115
$176$	97788.9	0.237962
$177$	666616.	1.59935
$178$	−497356.	−1.17657
$179$	277007.	0.646186	0.323093	−	0.946367i	$-0.395277\pi$
$179$	277007.	0.646186	0.323093	+	0.946367i	$0.395277\pi$
$180$	−109905.	−0.252834
$181$	−585036.	−1.32735	−0.663676	−	0.748020i	$-0.731005\pi$
$181$	−585036.	−1.32735	−0.663676	+	0.748020i	$0.731005\pi$
$182$	0	0
$183$	−102681.	−0.226652
$184$	175869.	0.382953
$185$	−425535.	−0.914126
$186$	−430155.	−0.911679
$187$	−403920.	−0.844679
$188$	55827.5	0.115200
$189$	−41258.6	−0.0840157
$190$	−489704.	−0.984124
$191$	−648564.	−1.28638	−0.643190	−	0.765707i	$-0.722389\pi$
$191$	−648564.	−1.28638	−0.643190	+	0.765707i	$0.722389\pi$
$192$	−79266.0	−0.155179
$193$	658457.	1.27243	0.636215	−	0.771512i	$-0.280499\pi$
$193$	658457.	1.27243	0.636215	+	0.771512i	$0.280499\pi$
$194$	−376374.	−0.717985
$195$	0	0
$196$	−263062.	−0.489123
$197$	−639300.	−1.17365	−0.586826	−	0.809713i	$-0.699623\pi$
$197$	−639300.	−1.17365	−0.586826	+	0.809713i	$0.699623\pi$
$198$	−200928.	−0.364231
$199$	826294.	1.47911	0.739557	−	0.673093i	$-0.235035\pi$
$199$	826294.	1.47911	0.739557	+	0.673093i	$0.235035\pi$
$200$	25372.6	0.0448528
$201$	−1.10114e6	−1.92243
$202$	229342.	0.395462
$203$	2327.42	0.00396401
$204$	327411.	0.550830
$205$	704411.	1.17069
$206$	−641031.	−1.05247
$207$	−361360.	−0.586158
$208$	0	0
$209$	−895277.	−1.41772
$210$	77316.5	0.120983
$211$	448279.	0.693175	0.346587	−	0.938018i	$-0.387340\pi$
$211$	448279.	0.693175	0.346587	+	0.938018i	$0.387340\pi$
$212$	−463006.	−0.707534
$213$	46319.4	0.0699543
$214$	−72220.7	−0.107802
$215$	1.15021e6	1.69700
$216$	−138094.	−0.201392
$217$	106257.	0.153182
$218$	−103818.	−0.147955
$219$	−928310.	−1.30792
$220$	−319254.	−0.444712
$221$	0	0
$222$	630603.	0.858763
$223$	195080.	0.262695	0.131347	−	0.991336i	$-0.458070\pi$
$223$	195080.	0.262695	0.131347	+	0.991336i	$0.458070\pi$
$224$	19580.3	0.0260735
$225$	−52133.3	−0.0686529
$226$	438290.	0.570809
$227$	563534.	0.725864	0.362932	−	0.931816i	$-0.381776\pi$
$227$	563534.	0.725864	0.362932	+	0.931816i	$0.381776\pi$
$228$	725695.	0.924522
$229$	27368.8	0.0344879	0.0172440	−	0.999851i	$-0.494511\pi$
$229$	27368.8	0.0344879	0.0172440	+	0.999851i	$0.494511\pi$
$230$	−574164.	−0.715676
$231$	141350.	0.174287
$232$	7789.97	0.00950201
$233$	−489880.	−0.591153	−0.295577	−	0.955319i	$-0.595512\pi$
$233$	−489880.	−0.591153	−0.295577	+	0.955319i	$0.595512\pi$
$234$	0	0
$235$	−182261.	−0.215290
$236$	−551149.	−0.644152
$237$	1.53520e6	1.77539
$238$	−80877.0	−0.0925513
$239$	−97635.3	−0.110564	−0.0552818	−	0.998471i	$-0.517606\pi$
$239$	−97635.3	−0.110564	−0.0552818	+	0.998471i	$0.517606\pi$
$240$	258781.	0.290005
$241$	1.11350e6	1.23494	0.617470	−	0.786594i	$-0.288158\pi$
$241$	1.11350e6	1.23494	0.617470	+	0.786594i	$0.288158\pi$
$242$	60544.6	0.0664564
$243$	902136.	0.980068
$244$	84894.9	0.0912866
$245$	858824.	0.914090
$246$	−1.04387e6	−1.09979
$247$	0	0
$248$	355646.	0.367188
$249$	−427493.	−0.436949
$250$	−735779.	−0.744556
$251$	−1.21731e6	−1.21960	−0.609800	−	0.792555i	$-0.708750\pi$
$251$	−1.21731e6	−1.21960	−0.609800	+	0.792555i	$0.708750\pi$
$252$	−40231.8	−0.0399088
$253$	−1.04969e6	−1.03100
$254$	233414.	0.227008
$255$	−1.06890e6	−1.02941
$256$	65536.0	0.0625000
$257$	1.87353e6	1.76941	0.884704	−	0.466154i	$-0.154361\pi$
$257$	1.87353e6	1.76941	0.884704	+	0.466154i	$0.154361\pi$
$258$	−1.70450e6	−1.59422
$259$	−155772.	−0.144291
$260$	0	0
$261$	−16006.1	−0.0145440
$262$	−117591.	−0.105833
$263$	831123.	0.740927	0.370464	−	0.928847i	$-0.379199\pi$
$263$	831123.	0.740927	0.370464	+	0.928847i	$0.379199\pi$
$264$	473104.	0.417779
$265$	1.51159e6	1.32226
$266$	−179261.	−0.155340
$267$	−2.40621e6	−2.06565
$268$	910405.	0.774279
$269$	−810878.	−0.683242	−0.341621	−	0.939838i	$-0.610976\pi$
$269$	−810878.	−0.683242	−0.341621	+	0.939838i	$0.610976\pi$
$270$	450840.	0.376368
$271$	140436.	0.116160	0.0580799	−	0.998312i	$-0.481502\pi$
$271$	140436.	0.116160	0.0580799	+	0.998312i	$0.481502\pi$
$272$	−270699.	−0.221852
$273$	0	0
$274$	919694.	0.740060
$275$	−151438.	−0.120754
$276$	850857.	0.672332
$277$	−1.38608e6	−1.08540	−0.542698	−	0.839928i	$-0.682597\pi$
$277$	−1.38608e6	−1.08540	−0.542698	+	0.839928i	$0.682597\pi$
$278$	−677245.	−0.525574
$279$	−730749.	−0.562028
$280$	−63924.2	−0.0487271
$281$	−1.39045e6	−1.05049	−0.525243	−	0.850953i	$-0.676025\pi$
$281$	−1.39045e6	−1.05049	−0.525243	+	0.850953i	$0.676025\pi$
$282$	270094.	0.202252
$283$	912951.	0.677612	0.338806	−	0.940856i	$-0.389977\pi$
$283$	912951.	0.677612	0.338806	+	0.940856i	$0.389977\pi$
$284$	−38296.3	−0.0281748
$285$	−2.36919e6	−1.72778
$286$	0	0
$287$	257857.	0.184788
$288$	−134658.	−0.0956642
$289$	−301728.	−0.212506
$290$	−25432.1	−0.0177577
$291$	−1.82090e6	−1.26053
$292$	767513.	0.526780
$293$	68805.6	0.0468225	0.0234112	−	0.999726i	$-0.492547\pi$
$293$	68805.6	0.0468225	0.0234112	+	0.999726i	$0.492547\pi$
$294$	−1.27270e6	−0.858730
$295$	1.79935e6	1.20382
$296$	−521374.	−0.345875
$297$	824225.	0.542194
$298$	1.97071e6	1.28553
$299$	0	0
$300$	122753.	0.0787460
$301$	421046.	0.267863
$302$	145346.	0.0917033
$303$	1.10956e6	0.694294
$304$	−599995.	−0.372360
$305$	−277158.	−0.170600
$306$	556207.	0.339573
$307$	−2.66005e6	−1.61081	−0.805404	−	0.592726i	$-0.798052\pi$
$307$	−2.66005e6	−1.61081	−0.805404	+	0.592726i	$0.798052\pi$
$308$	−116866.	−0.0701959
$309$	−3.10132e6	−1.84778
$310$	−1.16108e6	−0.686214
$311$	2.21314e6	1.29750	0.648751	−	0.761000i	$-0.275291\pi$
$311$	2.21314e6	1.29750	0.648751	+	0.761000i	$0.275291\pi$
$312$	0	0
$313$	−635019.	−0.366375	−0.183188	−	0.983078i	$-0.558642\pi$
$313$	−635019.	−0.366375	−0.183188	+	0.983078i	$0.558642\pi$
$314$	−1.47279e6	−0.842978
$315$	131346.	0.0745830
$316$	−1.26928e6	−0.715057
$317$	−2.29568e6	−1.28311	−0.641554	−	0.767078i	$-0.721710\pi$
$317$	−2.29568e6	−1.28311	−0.641554	+	0.767078i	$0.721710\pi$
$318$	−2.24003e6	−1.24218
$319$	−46494.9	−0.0255817
$320$	−213957.	−0.116802
$321$	−349405.	−0.189263
$322$	−210179.	−0.112966
$323$	2.47830e6	1.32174
$324$	−1.17938e6	−0.624153
$325$	0	0
$326$	904067.	0.471147
$327$	−502272.	−0.259758
$328$	863057.	0.442950
$329$	−66718.7	−0.0339827
$330$	−1.54455e6	−0.780761
$331$	1.92131e6	0.963892	0.481946	−	0.876201i	$-0.339930\pi$
$331$	1.92131e6	0.963892	0.481946	+	0.876201i	$0.339930\pi$
$332$	353445.	0.175986
$333$	1.07127e6	0.529406
$334$	−644955.	−0.316347
$335$	−2.97222e6	−1.44700
$336$	94729.6	0.0457760
$337$	−574677.	−0.275644	−0.137822	−	0.990457i	$-0.544010\pi$
$337$	−574677.	−0.275644	−0.137822	+	0.990457i	$0.544010\pi$
$338$	0	0
$339$	2.12045e6	1.00214
$340$	883755.	0.414605
$341$	−2.12269e6	−0.988557
$342$	1.23282e6	0.569945
$343$	635755.	0.291779
$344$	1.40926e6	0.642088
$345$	−2.77781e6	−1.25648
$346$	1.20273e6	0.540104
$347$	2.63825e6	1.17623	0.588114	−	0.808778i	$-0.299871\pi$
$347$	2.63825e6	1.17623	0.588114	+	0.808778i	$0.299871\pi$
$348$	37687.9	0.0166822
$349$	−1.24694e6	−0.548004	−0.274002	−	0.961729i	$-0.588347\pi$
$349$	−1.24694e6	−0.548004	−0.274002	+	0.961729i	$0.588347\pi$
$350$	−30322.4	−0.0132310
$351$	0	0
$352$	−391156.	−0.168265
$353$	−1.50991e6	−0.644933	−0.322467	−	0.946581i	$-0.604512\pi$
$353$	−1.50991e6	−0.644933	−0.322467	+	0.946581i	$0.604512\pi$
$354$	−2.66646e6	−1.13091
$355$	125027.	0.0526540
$356$	1.98942e6	0.831960
$357$	−391284.	−0.162488
$358$	−1.10803e6	−0.456923
$359$	576783.	0.236198	0.118099	−	0.993002i	$-0.462320\pi$
$359$	576783.	0.236198	0.118099	+	0.993002i	$0.462320\pi$
$360$	439619.	0.178781
$361$	3.01697e6	1.21844
$362$	2.34014e6	0.938579
$363$	292915.	0.116674
$364$	0	0
$365$	−2.50572e6	−0.984465
$366$	410722.	0.160267
$367$	2.88039e6	1.11631	0.558157	−	0.829735i	$-0.311509\pi$
$367$	2.88039e6	1.11631	0.558157	+	0.829735i	$0.311509\pi$
$368$	−703477.	−0.270789
$369$	−1.77333e6	−0.677992
$370$	1.70214e6	0.646384
$371$	553332.	0.208714
$372$	1.72062e6	0.644655
$373$	−2.71423e6	−1.01012	−0.505061	−	0.863084i	$-0.668530\pi$
$373$	−2.71423e6	−1.01012	−0.505061	+	0.863084i	$0.668530\pi$
$374$	1.61568e6	0.597278
$375$	−3.55971e6	−1.30718
$376$	−223310.	−0.0814589
$377$	0	0
$378$	165035.	0.0594081
$379$	2.97459e6	1.06372	0.531861	−	0.846831i	$-0.321493\pi$
$379$	2.97459e6	1.06372	0.531861	+	0.846831i	$0.321493\pi$
$380$	1.95882e6	0.695881
$381$	1.12926e6	0.398548
$382$	2.59425e6	0.909608
$383$	4.05276e6	1.41174	0.705869	−	0.708342i	$-0.250557\pi$
$383$	4.05276e6	1.41174	0.705869	+	0.708342i	$0.250557\pi$
$384$	317064.	0.109728
$385$	381536.	0.131185
$386$	−2.63383e6	−0.899744
$387$	−2.89562e6	−0.982797
$388$	1.50550e6	0.507692
$389$	4.80279e6	1.60924	0.804618	−	0.593793i	$-0.202370\pi$
$389$	4.80279e6	1.60924	0.804618	+	0.593793i	$0.202370\pi$
$390$	0	0
$391$	2.90573e6	0.961201
$392$	1.05225e6	0.345862
$393$	−568904.	−0.185805
$394$	2.55720e6	0.829898
$395$	4.14385e6	1.33632
$396$	803712.	0.257551
$397$	4.61361e6	1.46915	0.734573	−	0.678530i	$-0.237383\pi$
$397$	4.61361e6	1.46915	0.734573	+	0.678530i	$0.237383\pi$
$398$	−3.30518e6	−1.04589
$399$	−867268.	−0.272723
$400$	−101490.	−0.0317157
$401$	−2.10739e6	−0.654461	−0.327230	−	0.944945i	$-0.606115\pi$
$401$	−2.10739e6	−0.654461	−0.327230	+	0.944945i	$0.606115\pi$
$402$	4.40455e6	1.35937
$403$	0	0
$404$	−917367.	−0.279634
$405$	3.85035e6	1.16644
$406$	−9309.68	−0.00280298
$407$	3.11185e6	0.931178
$408$	−1.30964e6	−0.389495
$409$	−2.17339e6	−0.642435	−0.321217	−	0.947006i	$-0.604092\pi$
$409$	−2.17339e6	−0.642435	−0.321217	+	0.947006i	$0.604092\pi$
$410$	−2.81764e6	−0.827802
$411$	4.44949e6	1.29929
$412$	2.56412e6	0.744211
$413$	658670.	0.190017
$414$	1.44544e6	0.414476
$415$	−1.15390e6	−0.328888
$416$	0	0
$417$	−3.27652e6	−0.922725
$418$	3.58111e6	1.00248
$419$	−1.84207e6	−0.512590	−0.256295	−	0.966599i	$-0.582502\pi$
$419$	−1.84207e6	−0.512590	−0.256295	+	0.966599i	$0.582502\pi$
$420$	−309266.	−0.0855478
$421$	2.27354e6	0.625170	0.312585	−	0.949890i	$-0.398805\pi$
$421$	2.27354e6	0.625170	0.312585	+	0.949890i	$0.398805\pi$
$422$	−1.79312e6	−0.490149
$423$	458838.	0.124683
$424$	1.85203e6	0.500302
$425$	419209.	0.112579
$426$	−185278.	−0.0494651
$427$	−101457.	−0.0269284
$428$	288883.	0.0762276
$429$	0	0
$430$	−4.60084e6	−1.19996
$431$	358055.	0.0928445	0.0464222	−	0.998922i	$-0.485218\pi$
$431$	358055.	0.0928445	0.0464222	+	0.998922i	$0.485218\pi$
$432$	552377.	0.142405
$433$	3.84975e6	0.986763	0.493382	−	0.869813i	$-0.335761\pi$
$433$	3.84975e6	0.986763	0.493382	+	0.869813i	$0.335761\pi$
$434$	−425027.	−0.108316
$435$	−123041.	−0.0311764
$436$	415271.	0.104620
$437$	6.44047e6	1.61330
$438$	3.71324e6	0.924842
$439$	5.07937e6	1.25791	0.628954	−	0.777443i	$-0.283483\pi$
$439$	5.07937e6	1.25791	0.628954	+	0.777443i	$0.283483\pi$
$440$	1.27701e6	0.314459
$441$	−2.16206e6	−0.529386
$442$	0	0
$443$	4.53588e6	1.09813	0.549063	−	0.835781i	$-0.314985\pi$
$443$	4.53588e6	1.09813	0.549063	+	0.835781i	$0.314985\pi$
$444$	−2.52241e6	−0.607237
$445$	−6.49492e6	−1.55480
$446$	−780321.	−0.185753
$447$	9.53432e6	2.25694
$448$	−78321.2	−0.0184367
$449$	−1.15562e6	−0.270520	−0.135260	−	0.990810i	$-0.543187\pi$
$449$	−1.15562e6	−0.270520	−0.135260	+	0.990810i	$0.543187\pi$
$450$	208533.	0.0485450
$451$	−5.15121e6	−1.19253
$452$	−1.75316e6	−0.403623
$453$	703184.	0.160999
$454$	−2.25414e6	−0.513264
$455$	0	0
$456$	−2.90278e6	−0.653736
$457$	−1.53521e6	−0.343857	−0.171928	−	0.985109i	$-0.555000\pi$
$457$	−1.53521e6	−0.343857	−0.171928	+	0.985109i	$0.555000\pi$
$458$	−109475.	−0.0243866
$459$	−2.28161e6	−0.505487
$460$	2.29666e6	0.506060
$461$	6.41152e6	1.40510	0.702552	−	0.711632i	$-0.252044\pi$
$461$	6.41152e6	1.40510	0.702552	+	0.711632i	$0.252044\pi$
$462$	−565400.	−0.123240
$463$	3.67970e6	0.797736	0.398868	−	0.917008i	$-0.369403\pi$
$463$	3.67970e6	0.797736	0.398868	+	0.917008i	$0.369403\pi$
$464$	−31159.9	−0.00671894
$465$	−5.61734e6	−1.20475
$466$	1.95952e6	0.418008
$467$	5.57471e6	1.18285	0.591425	−	0.806360i	$-0.298565\pi$
$467$	5.57471e6	1.18285	0.591425	+	0.806360i	$0.298565\pi$
$468$	0	0
$469$	−1.08801e6	−0.228403
$470$	729045.	0.152233
$471$	−7.12536e6	−1.47998
$472$	2.20459e6	0.455485
$473$	−8.41124e6	−1.72865
$474$	−6.14080e6	−1.25539
$475$	929164.	0.188955
$476$	323508.	0.0654437
$477$	−3.80538e6	−0.765776
$478$	390541.	0.0781803
$479$	−1.51593e6	−0.301884	−0.150942	−	0.988543i	$-0.548231\pi$
$479$	−1.51593e6	−0.301884	−0.150942	+	0.988543i	$0.548231\pi$
$480$	−1.03513e6	−0.205064
$481$	0	0
$482$	−4.45398e6	−0.873234
$483$	−1.01685e6	−0.198330
$484$	−242178.	−0.0469918
$485$	−4.91503e6	−0.948793
$486$	−3.60854e6	−0.693013
$487$	602882.	0.115189	0.0575943	−	0.998340i	$-0.481657\pi$
$487$	602882.	0.115189	0.0575943	+	0.998340i	$0.481657\pi$
$488$	−339579.	−0.0645493
$489$	4.37388e6	0.827171
$490$	−3.43530e6	−0.646359
$491$	−6.06738e6	−1.13579	−0.567895	−	0.823101i	$-0.692242\pi$
$491$	−6.06738e6	−1.13579	−0.567895	+	0.823101i	$0.692242\pi$
$492$	4.17548e6	0.777667
$493$	128707.	0.0238498
$494$	0	0
$495$	−2.62390e6	−0.481320
$496$	−1.42258e6	−0.259641
$497$	45767.3	0.00831122
$498$	1.70997e6	0.308970
$499$	−294588.	−0.0529618	−0.0264809	−	0.999649i	$-0.508430\pi$
$499$	−294588.	−0.0529618	−0.0264809	+	0.999649i	$0.508430\pi$
$500$	2.94312e6	0.526481
$501$	−3.12030e6	−0.555395
$502$	4.86924e6	0.862387
$503$	−4.49541e6	−0.792227	−0.396113	−	0.918202i	$-0.629641\pi$
$503$	−4.49541e6	−0.792227	−0.396113	+	0.918202i	$0.629641\pi$
$504$	160927.	0.0282198
$505$	2.99495e6	0.522590
$506$	4.19875e6	0.729027
$507$	0	0
$508$	−933654.	−0.160519
$509$	−953239.	−0.163082	−0.0815412	−	0.996670i	$-0.525984\pi$
$509$	−953239.	−0.163082	−0.0815412	+	0.996670i	$0.525984\pi$
$510$	4.27562e6	0.727903
$511$	−917245.	−0.155394
$512$	−262144.	−0.0441942
$513$	−5.05712e6	−0.848418
$514$	−7.49412e6	−1.25116
$515$	−8.37116e6	−1.39081
$516$	6.81800e6	1.12728
$517$	1.33284e6	0.219307
$518$	623086.	0.102029
$519$	5.81881e6	0.948235
$520$	0	0
$521$	3.66026e6	0.590769	0.295384	−	0.955378i	$-0.404552\pi$
$521$	3.66026e6	0.590769	0.295384	+	0.955378i	$0.404552\pi$
$522$	64024.5	0.0102842
$523$	−4.22181e6	−0.674908	−0.337454	−	0.941342i	$-0.609566\pi$
$523$	−4.22181e6	−0.674908	−0.337454	+	0.941342i	$0.609566\pi$
$524$	470362.	0.0748349
$525$	−146700.	−0.0232291
$526$	−3.32449e6	−0.523915
$527$	5.87602e6	0.921631
$528$	−1.89242e6	−0.295414
$529$	1.11493e6	0.173224
$530$	−6.04635e6	−0.934983
$531$	−4.52980e6	−0.697177
$532$	717045.	0.109842
$533$	0	0
$534$	9.62486e6	1.46063
$535$	−943122.	−0.142457
$536$	−3.64162e6	−0.547498
$537$	−5.36064e6	−0.802197
$538$	3.24351e6	0.483125
$539$	−6.28041e6	−0.931142
$540$	−1.80336e6	−0.266132
$541$	−1.03047e7	−1.51371	−0.756856	−	0.653582i	$-0.773266\pi$
$541$	−1.03047e7	−1.51371	−0.756856	+	0.653582i	$0.773266\pi$
$542$	−561744.	−0.0821373
$543$	1.13216e7	1.64782
$544$	1.08279e6	0.156873
$545$	−1.35574e6	−0.195518
$546$	0	0
$547$	−5.03080e6	−0.718901	−0.359450	−	0.933164i	$-0.617036\pi$
$547$	−5.03080e6	−0.718901	−0.359450	+	0.933164i	$0.617036\pi$
$548$	−3.67878e6	−0.523302
$549$	697737.	0.0988010
$550$	605752.	0.0853862
$551$	285275.	0.0400299
$552$	−3.40343e6	−0.475411
$553$	1.51690e6	0.210933
$554$	5.54431e6	0.767491
$555$	8.23497e6	1.13483
$556$	2.70898e6	0.371637
$557$	3.16081e6	0.431678	0.215839	−	0.976429i	$-0.430751\pi$
$557$	3.16081e6	0.431678	0.215839	+	0.976429i	$0.430751\pi$
$558$	2.92300e6	0.397414
$559$	0	0
$560$	255697.	0.0344552
$561$	7.81668e6	1.04861
$562$	5.56180e6	0.742805
$563$	−1.25890e7	−1.67387	−0.836933	−	0.547305i	$-0.815654\pi$
$563$	−1.25890e7	−1.67387	−0.836933	+	0.547305i	$0.815654\pi$
$564$	−1.08038e6	−0.143014
$565$	5.72359e6	0.754305
$566$	−3.65180e6	−0.479144
$567$	1.40946e6	0.184117
$568$	153185.	0.0199226
$569$	−1.10666e7	−1.43296	−0.716478	−	0.697609i	$-0.754247\pi$
$569$	−1.10666e7	−1.43296	−0.716478	+	0.697609i	$0.754247\pi$
$570$	9.47677e6	1.22172
$571$	−409116.	−0.0525117	−0.0262559	−	0.999655i	$-0.508358\pi$
$571$	−409116.	−0.0525117	−0.0262559	+	0.999655i	$0.508358\pi$
$572$	0	0
$573$	1.25510e7	1.59696
$574$	−1.03143e6	−0.130665
$575$	1.08942e6	0.137412
$576$	538630.	0.0676448
$577$	−1.63753e6	−0.204762	−0.102381	−	0.994745i	$-0.532646\pi$
$577$	−1.63753e6	−0.204762	−0.102381	+	0.994745i	$0.532646\pi$
$578$	1.20691e6	0.150264
$579$	−1.27425e7	−1.57964
$580$	101728.	0.0125566
$581$	−422398.	−0.0519136
$582$	7.28361e6	0.891331
$583$	−1.10539e7	−1.34693
$584$	−3.07005e6	−0.372489
$585$	0	0
$586$	−275222.	−0.0331085
$587$	−1.12561e7	−1.34832	−0.674161	−	0.738584i	$-0.735495\pi$
$587$	−1.12561e7	−1.34832	−0.674161	+	0.738584i	$0.735495\pi$
$588$	5.09079e6	0.607214
$589$	1.30240e7	1.54688
$590$	−7.19739e6	−0.851226
$591$	1.23718e7	1.45701
$592$	2.08549e6	0.244571
$593$	−7.47990e6	−0.873492	−0.436746	−	0.899585i	$-0.643869\pi$
$593$	−7.47990e6	−0.873492	−0.436746	+	0.899585i	$0.643869\pi$
$594$	−3.29690e6	−0.383389
$595$	−1.05616e6	−0.122303
$596$	−7.88285e6	−0.909007
$597$	−1.59905e7	−1.83622
$598$	0	0
$599$	7.02078e6	0.799499	0.399750	−	0.916624i	$-0.369097\pi$
$599$	7.02078e6	0.799499	0.399750	+	0.916624i	$0.369097\pi$
$600$	−491011.	−0.0556818
$601$	7.77451e6	0.877984	0.438992	−	0.898491i	$-0.355336\pi$
$601$	7.77451e6	0.877984	0.438992	+	0.898491i	$0.355336\pi$
$602$	−1.68418e6	−0.189408
$603$	7.48247e6	0.838015
$604$	−581383.	−0.0648440
$605$	790645.	0.0878200
$606$	−4.43823e6	−0.490940
$607$	1.46735e7	1.61644	0.808222	−	0.588878i	$-0.200430\pi$
$607$	1.46735e7	1.61644	0.808222	+	0.588878i	$0.200430\pi$
$608$	2.39998e6	0.263299
$609$	−45040.3	−0.00492106
$610$	1.10863e6	0.120632
$611$	0	0
$612$	−2.22483e6	−0.240114
$613$	1.35799e7	1.45964	0.729820	−	0.683639i	$-0.239604\pi$
$613$	1.35799e7	1.45964	0.729820	+	0.683639i	$0.239604\pi$
$614$	1.06402e7	1.13901
$615$	−1.36318e7	−1.45333
$616$	467465.	0.0496360
$617$	5.57160e6	0.589206	0.294603	−	0.955620i	$-0.404813\pi$
$617$	5.57160e6	0.589206	0.294603	+	0.955620i	$0.404813\pi$
$618$	1.24053e7	1.30658
$619$	−2.82758e6	−0.296611	−0.148306	−	0.988942i	$-0.547382\pi$
$619$	−2.82758e6	−0.296611	−0.148306	+	0.988942i	$0.547382\pi$
$620$	4.64434e6	0.485227
$621$	−5.92933e6	−0.616988
$622$	−8.85257e6	−0.917473
$623$	−2.37753e6	−0.245418
$624$	0	0
$625$	−8.36956e6	−0.857043
$626$	2.54008e6	0.259066
$627$	1.73254e7	1.76001
$628$	5.89115e6	0.596075
$629$	−8.61420e6	−0.868137
$630$	−525383.	−0.0527381
$631$	8.52815e6	0.852671	0.426336	−	0.904565i	$-0.359804\pi$
$631$	8.52815e6	0.852671	0.426336	+	0.904565i	$0.359804\pi$
$632$	5.07713e6	0.505622
$633$	−8.67512e6	−0.860531
$634$	9.18273e6	0.907295
$635$	3.04812e6	0.299984
$636$	8.96012e6	0.878357
$637$	0	0
$638$	185980.	0.0180890
$639$	−314751.	−0.0304940
$640$	855827.	0.0825917
$641$	1.73936e7	1.67203	0.836016	−	0.548704i	$-0.184879\pi$
$641$	1.73936e7	1.67203	0.836016	+	0.548704i	$0.184879\pi$
$642$	1.39762e6	0.133829
$643$	−3.04461e6	−0.290405	−0.145203	−	0.989402i	$-0.546383\pi$
$643$	−3.04461e6	−0.290405	−0.145203	+	0.989402i	$0.546383\pi$
$644$	840716.	0.0798793
$645$	−2.22589e7	−2.10671
$646$	−9.91319e6	−0.934614
$647$	−872410.	−0.0819332	−0.0409666	−	0.999161i	$-0.513044\pi$
$647$	−872410.	−0.0819332	−0.0409666	+	0.999161i	$0.513044\pi$
$648$	4.71752e6	0.441343
$649$	−1.31583e7	−1.22627
$650$	0	0
$651$	−2.05629e6	−0.190165
$652$	−3.61627e6	−0.333151
$653$	−1.96438e7	−1.80278	−0.901391	−	0.433005i	$-0.857453\pi$
$653$	−1.96438e7	−1.80278	−0.901391	+	0.433005i	$0.857453\pi$
$654$	2.00909e6	0.183677
$655$	−1.53560e6	−0.139854
$656$	−3.45223e6	−0.313213
$657$	6.30807e6	0.570142
$658$	266875.	0.0240294
$659$	−9.62362e6	−0.863227	−0.431613	−	0.902059i	$-0.642056\pi$
$659$	−9.62362e6	−0.863227	−0.431613	+	0.902059i	$0.642056\pi$
$660$	6.17821e6	0.552081
$661$	−1.59973e7	−1.42410	−0.712052	−	0.702126i	$-0.752234\pi$
$661$	−1.59973e7	−1.42410	−0.712052	+	0.702126i	$0.752234\pi$
$662$	−7.68526e6	−0.681575
$663$	0	0
$664$	−1.41378e6	−0.124441
$665$	−2.34095e6	−0.205276
$666$	−4.28509e6	−0.374347
$667$	334476.	0.0291106
$668$	2.57982e6	0.223691
$669$	−3.77520e6	−0.326118
$670$	1.18889e7	1.02318
$671$	2.02680e6	0.173782
$672$	−378919.	−0.0323685
$673$	5.09751e6	0.433831	0.216915	−	0.976190i	$-0.430400\pi$
$673$	5.09751e6	0.433831	0.216915	+	0.976190i	$0.430400\pi$
$674$	2.29871e6	0.194910
$675$	−855423.	−0.0722639
$676$	0	0
$677$	2.72355e6	0.228383	0.114191	−	0.993459i	$-0.463572\pi$
$677$	2.72355e6	0.228383	0.114191	+	0.993459i	$0.463572\pi$
$678$	−8.48181e6	−0.708622
$679$	−1.79920e6	−0.149763
$680$	−3.53502e6	−0.293170
$681$	−1.09055e7	−0.901113
$682$	8.49078e6	0.699015
$683$	1.23503e7	1.01304	0.506518	−	0.862230i	$-0.330932\pi$
$683$	1.23503e7	1.01304	0.506518	+	0.862230i	$0.330932\pi$
$684$	−4.93126e6	−0.403012
$685$	1.20102e7	0.977965
$686$	−2.54302e6	−0.206319
$687$	−529642.	−0.0428145
$688$	−5.63703e6	−0.454025
$689$	0	0
$690$	1.11113e7	0.888465
$691$	−6.72129e6	−0.535497	−0.267749	−	0.963489i	$-0.586280\pi$
$691$	−6.72129e6	−0.535497	−0.267749	+	0.963489i	$0.586280\pi$
$692$	−4.81091e6	−0.381911
$693$	−960505.	−0.0759742
$694$	−1.05530e7	−0.831719
$695$	−8.84406e6	−0.694528
$696$	−150752.	−0.0117961
$697$	1.42595e7	1.11179
$698$	4.98778e6	0.387497
$699$	9.48018e6	0.733878
$700$	121290.	0.00935575
$701$	−1.81950e7	−1.39848	−0.699241	−	0.714886i	$-0.746479\pi$
$701$	−1.81950e7	−1.39848	−0.699241	+	0.714886i	$0.746479\pi$
$702$	0	0
$703$	−1.90931e7	−1.45710
$704$	1.56462e6	0.118981
$705$	3.52713e6	0.267269
$706$	6.03964e6	0.456037
$707$	1.09633e6	0.0824885
$708$	1.06658e7	0.799673
$709$	1.74271e7	1.30199	0.650997	−	0.759080i	$-0.274351\pi$
$709$	1.74271e7	1.30199	0.650997	+	0.759080i	$0.274351\pi$
$710$	−500107.	−0.0372320
$711$	−1.04320e7	−0.773918
$712$	−7.95770e6	−0.588285
$713$	1.52703e7	1.12493
$714$	1.56513e6	0.114896
$715$	0	0
$716$	4.43211e6	0.323093
$717$	1.88944e6	0.137257
$718$	−2.30713e6	−0.167017
$719$	−4.60218e6	−0.332003	−0.166001	−	0.986126i	$-0.553086\pi$
$719$	−4.60218e6	−0.332003	−0.166001	+	0.986126i	$0.553086\pi$
$720$	−1.75848e6	−0.126417
$721$	−3.06435e6	−0.219533
$722$	−1.20679e7	−0.861564
$723$	−2.15484e7	−1.53310
$724$	−9.36057e6	−0.663676
$725$	48254.8	0.00340954
$726$	−1.17166e6	−0.0825013
$727$	−2.47173e7	−1.73446	−0.867231	−	0.497905i	$-0.834103\pi$
$727$	−2.47173e7	−1.73446	−0.867231	+	0.497905i	$0.834103\pi$
$728$	0	0
$729$	453661.	0.0316164
$730$	1.00229e7	0.696122
$731$	2.32839e7	1.61162
$732$	−1.64289e6	−0.113326
$733$	−6.19827e6	−0.426099	−0.213050	−	0.977041i	$-0.568340\pi$
$733$	−6.19827e6	−0.426099	−0.213050	+	0.977041i	$0.568340\pi$
$734$	−1.15216e7	−0.789353
$735$	−1.66200e7	−1.13478
$736$	2.81391e6	0.191476
$737$	2.17352e7	1.47399
$738$	7.09333e6	0.479413
$739$	−1.98238e7	−1.33529	−0.667644	−	0.744480i	$-0.732697\pi$
$739$	−1.98238e7	−1.33529	−0.667644	+	0.744480i	$0.732697\pi$
$740$	−6.80856e6	−0.457063
$741$	0	0
$742$	−2.21333e6	−0.147583
$743$	−1.81952e7	−1.20916	−0.604581	−	0.796543i	$-0.706660\pi$
$743$	−1.81952e7	−1.20916	−0.604581	+	0.796543i	$0.706660\pi$
$744$	−6.88247e6	−0.455840
$745$	2.57353e7	1.69879
$746$	1.08569e7	0.714264
$747$	2.90491e6	0.190472
$748$	−6.46272e6	−0.422339
$749$	−345240.	−0.0224862
$750$	1.42388e7	0.924317
$751$	1.52179e7	0.984592	0.492296	−	0.870428i	$-0.336158\pi$
$751$	1.52179e7	0.984592	0.492296	+	0.870428i	$0.336158\pi$
$752$	893240.	0.0576002
$753$	2.35575e7	1.51405
$754$	0	0
$755$	1.89805e6	0.121183
$756$	−660138.	−0.0420079
$757$	−3.35941e6	−0.213071	−0.106535	−	0.994309i	$-0.533976\pi$
$757$	−3.35941e6	−0.213071	−0.106535	+	0.994309i	$0.533976\pi$
$758$	−1.18983e7	−0.752165
$759$	2.03136e7	1.27992
$760$	−7.83526e6	−0.492062
$761$	−1.83089e7	−1.14605	−0.573023	−	0.819540i	$-0.694229\pi$
$761$	−1.83089e7	−1.14605	−0.573023	+	0.819540i	$0.694229\pi$
$762$	−4.51703e6	−0.281816
$763$	−496285.	−0.0308617
$764$	−1.03770e7	−0.643190
$765$	7.26345e6	0.448734
$766$	−1.62111e7	−0.998250
$767$	0	0
$768$	−1.26826e6	−0.0775896
$769$	1.74442e7	1.06374	0.531869	−	0.846826i	$-0.321490\pi$
$769$	1.74442e7	1.06374	0.531869	+	0.846826i	$0.321490\pi$
$770$	−1.52614e6	−0.0927616
$771$	−3.62566e7	−2.19660
$772$	1.05353e7	0.636215
$773$	−2.89508e7	−1.74265	−0.871327	−	0.490702i	$-0.836740\pi$
$773$	−2.89508e7	−1.74265	−0.871327	+	0.490702i	$0.836740\pi$
$774$	1.15825e7	0.694942
$775$	2.20304e6	0.131755
$776$	−6.02199e6	−0.358993
$777$	3.01450e6	0.179128
$778$	−1.92112e7	−1.13790
$779$	3.16058e7	1.86605
$780$	0	0
$781$	−914295.	−0.0536363
$782$	−1.16229e7	−0.679671
$783$	−262634.	−0.0153090
$784$	−4.20899e6	−0.244561
$785$	−1.92330e7	−1.11397
$786$	2.27562e6	0.131384
$787$	−5.63429e6	−0.324267	−0.162133	−	0.986769i	$-0.551837\pi$
$787$	−5.63429e6	−0.324267	−0.162133	+	0.986769i	$0.551837\pi$
$788$	−1.02288e7	−0.586826
$789$	−1.60839e7	−0.919813
$790$	−1.65754e7	−0.944924
$791$	2.09518e6	0.119064
$792$	−3.21485e6	−0.182116
$793$	0	0
$794$	−1.84544e7	−1.03884
$795$	−2.92523e7	−1.64150
$796$	1.32207e7	0.739557
$797$	−2.76037e7	−1.53929	−0.769646	−	0.638471i	$-0.779567\pi$
$797$	−2.76037e7	−1.53929	−0.769646	+	0.638471i	$0.779567\pi$
$798$	3.46907e6	0.192844
$799$	−3.68956e6	−0.204459
$800$	405961.	0.0224264
$801$	1.63508e7	0.900444
$802$	8.42955e6	0.462774
$803$	1.83238e7	1.00283
$804$	−1.76182e7	−0.961217
$805$	−2.74470e6	−0.149281
$806$	0	0
$807$	1.56921e7	0.848200
$808$	3.66947e6	0.197731
$809$	1.41851e7	0.762013	0.381007	−	0.924572i	$-0.375578\pi$
$809$	1.41851e7	0.762013	0.381007	+	0.924572i	$0.375578\pi$
$810$	−1.54014e7	−0.824797
$811$	2.59109e7	1.38334	0.691671	−	0.722212i	$-0.256875\pi$
$811$	2.59109e7	1.38334	0.691671	+	0.722212i	$0.256875\pi$
$812$	37238.7	0.00198200
$813$	−2.71772e6	−0.144205
$814$	−1.24474e7	−0.658442
$815$	1.18061e7	0.622605
$816$	5.23857e6	0.275415
$817$	5.16081e7	2.70497
$818$	8.69355e6	0.454270
$819$	0	0
$820$	1.12706e7	0.585344
$821$	−9.04298e6	−0.468224	−0.234112	−	0.972210i	$-0.575218\pi$
$821$	−9.04298e6	−0.468224	−0.234112	+	0.972210i	$0.575218\pi$
$822$	−1.77980e7	−0.918736
$823$	3.03689e7	1.56289	0.781446	−	0.623973i	$-0.214482\pi$
$823$	3.03689e7	1.56289	0.781446	+	0.623973i	$0.214482\pi$
$824$	−1.02565e7	−0.526237
$825$	2.93063e6	0.149909
$826$	−2.63468e6	−0.134362
$827$	2.58958e7	1.31664	0.658318	−	0.752740i	$-0.271268\pi$
$827$	2.58958e7	1.31664	0.658318	+	0.752740i	$0.271268\pi$
$828$	−5.78177e6	−0.293079
$829$	−1.38901e7	−0.701969	−0.350984	−	0.936381i	$-0.614153\pi$
$829$	−1.38901e7	−0.701969	−0.350984	+	0.936381i	$0.614153\pi$
$830$	4.61561e6	0.232559
$831$	2.68234e7	1.34745
$832$	0	0
$833$	1.73854e7	0.868103
$834$	1.31061e7	0.652465
$835$	−8.42239e6	−0.418041
$836$	−1.43244e7	−0.708862
$837$	−1.19904e7	−0.591589
$838$	7.36826e6	0.362456
$839$	−3.77438e6	−0.185115	−0.0925574	−	0.995707i	$-0.529504\pi$
$839$	−3.77438e6	−0.185115	−0.0925574	+	0.995707i	$0.529504\pi$
$840$	1.23706e6	0.0604914
$841$	−2.04963e7	−0.999278
$842$	−9.09417e6	−0.442062
$843$	2.69081e7	1.30411
$844$	7.17247e6	0.346587
$845$	0	0
$846$	−1.83535e6	−0.0881643
$847$	289424.	0.0138620
$848$	−7.40810e6	−0.353767
$849$	−1.76675e7	−0.841211
$850$	−1.67684e6	−0.0796056
$851$	−2.23861e7	−1.05963
$852$	741111.	0.0349771
$853$	2.15044e7	1.01194	0.505970	−	0.862551i	$-0.331134\pi$
$853$	2.15044e7	1.01194	0.505970	+	0.862551i	$0.331134\pi$
$854$	405827.	0.0190413
$855$	1.60992e7	0.753163
$856$	−1.15553e6	−0.0539011
$857$	−3.57752e6	−0.166391	−0.0831954	−	0.996533i	$-0.526513\pi$
$857$	−3.57752e6	−0.166391	−0.0831954	+	0.996533i	$0.526513\pi$
$858$	0	0
$859$	3.10648e7	1.43643	0.718217	−	0.695819i	$-0.244959\pi$
$859$	3.10648e7	1.43643	0.718217	+	0.695819i	$0.244959\pi$
$860$	1.84033e7	0.848498
$861$	−4.99006e6	−0.229402
$862$	−1.43222e6	−0.0656510
$863$	−2.54355e6	−0.116255	−0.0581277	−	0.998309i	$-0.518513\pi$
$863$	−2.54355e6	−0.116255	−0.0581277	+	0.998309i	$0.518513\pi$
$864$	−2.20951e6	−0.100696
$865$	1.57063e7	0.713729
$866$	−1.53990e7	−0.697747
$867$	5.83906e6	0.263812
$868$	1.70011e6	0.0765910
$869$	−3.03032e7	−1.36125
$870$	492163.	0.0220450
$871$	0	0
$872$	−1.66108e6	−0.0739777
$873$	1.23734e7	0.549484
$874$	−2.57619e7	−1.14077
$875$	−3.51728e6	−0.155305
$876$	−1.48530e7	−0.653962
$877$	4.32299e7	1.89795	0.948977	−	0.315345i	$-0.102120\pi$
$877$	4.32299e7	1.89795	0.948977	+	0.315345i	$0.102120\pi$
$878$	−2.03175e7	−0.889475
$879$	−1.33153e6	−0.0581270
$880$	−5.10806e6	−0.222356
$881$	−3.74303e6	−0.162474	−0.0812369	−	0.996695i	$-0.525887\pi$
$881$	−3.74303e6	−0.162474	−0.0812369	+	0.996695i	$0.525887\pi$
$882$	8.64826e6	0.374332
$883$	2.87001e7	1.23874	0.619371	−	0.785098i	$-0.287388\pi$
$883$	2.87001e7	1.23874	0.619371	+	0.785098i	$0.287388\pi$
$884$	0	0
$885$	−3.48210e7	−1.49446
$886$	−1.81435e7	−0.776492
$887$	1.08628e7	0.463590	0.231795	−	0.972765i	$-0.425540\pi$
$887$	1.08628e7	0.463590	0.231795	+	0.972765i	$0.425540\pi$
$888$	1.00896e7	0.429382
$889$	1.11580e6	0.0473512
$890$	2.59797e7	1.09941
$891$	−2.81568e7	−1.18820
$892$	3.12128e6	0.131347
$893$	−8.17779e6	−0.343168
$894$	−3.81373e7	−1.59590
$895$	−1.44696e7	−0.603808
$896$	313285.	0.0130367
$897$	0	0
$898$	4.62249e6	0.191287
$899$	676384.	0.0279122
$900$	−834133.	−0.0343265
$901$	3.05994e7	1.25574
$902$	2.06049e7	0.843244
$903$	−8.14810e6	−0.332535
$904$	7.01265e6	0.285405
$905$	3.05597e7	1.24030
$906$	−2.81274e6	−0.113844
$907$	−2.58463e7	−1.04323	−0.521615	−	0.853181i	$-0.674670\pi$
$907$	−2.58463e7	−1.04323	−0.521615	+	0.853181i	$0.674670\pi$
$908$	9.01654e6	0.362932
$909$	−7.53969e6	−0.302652
$910$	0	0
$911$	−4.52408e7	−1.80607	−0.903034	−	0.429569i	$-0.858666\pi$
$911$	−4.52408e7	−1.80607	−0.903034	+	0.429569i	$0.858666\pi$
$912$	1.16111e7	0.462261
$913$	8.43825e6	0.335023
$914$	6.14084e6	0.243143
$915$	5.36358e6	0.211788
$916$	437901.	0.0172440
$917$	−562123.	−0.0220754
$918$	9.12645e6	0.357433
$919$	−1.19556e7	−0.466963	−0.233481	−	0.972361i	$-0.575012\pi$
$919$	−1.19556e7	−0.466963	−0.233481	+	0.972361i	$0.575012\pi$
$920$	−9.18663e6	−0.357838
$921$	5.14774e7	1.99971
$922$	−2.56461e7	−0.993559
$923$	0	0
$924$	2.26160e6	0.0871436
$925$	−3.22964e6	−0.124108
$926$	−1.47188e7	−0.564085
$927$	2.10741e7	0.805472
$928$	124639.	0.00475101
$929$	−4.45911e7	−1.69515	−0.847576	−	0.530673i	$-0.821939\pi$
$929$	−4.45911e7	−1.69515	−0.847576	+	0.530673i	$0.821939\pi$
$930$	2.24694e7	0.851890
$931$	3.85341e7	1.45704
$932$	−7.83808e6	−0.295577
$933$	−4.28288e7	−1.61076
$934$	−2.22988e7	−0.836402
$935$	2.10990e7	0.789283
$936$	0	0
$937$	−4.58884e7	−1.70747	−0.853737	−	0.520705i	$-0.825669\pi$
$937$	−4.58884e7	−1.70747	−0.853737	+	0.520705i	$0.825669\pi$
$938$	4.35205e6	0.161505
$939$	1.22889e7	0.454830
$940$	−2.91618e6	−0.107645
$941$	−2.52187e7	−0.928430	−0.464215	−	0.885723i	$-0.653663\pi$
$941$	−2.52187e7	−0.928430	−0.464215	+	0.885723i	$0.653663\pi$
$942$	2.85014e7	1.04650
$943$	3.70570e7	1.35703
$944$	−8.81838e6	−0.322076
$945$	2.15517e6	0.0785058
$946$	3.36450e7	1.22234
$947$	−1.99538e7	−0.723022	−0.361511	−	0.932368i	$-0.617739\pi$
$947$	−1.99538e7	−0.723022	−0.361511	+	0.932368i	$0.617739\pi$
$948$	2.45632e7	0.887696
$949$	0	0
$950$	−3.71666e6	−0.133611
$951$	4.44261e7	1.59289
$952$	−1.29403e6	−0.0462757
$953$	4.03421e7	1.43889	0.719443	−	0.694552i	$-0.244397\pi$
$953$	4.03421e7	1.43889	0.719443	+	0.694552i	$0.244397\pi$
$954$	1.52215e7	0.541485
$955$	3.38781e7	1.20202
$956$	−1.56217e6	−0.0552818
$957$	899771.	0.0317579
$958$	6.06372e6	0.213464
$959$	4.39646e6	0.154368
$960$	4.14050e6	0.145002
$961$	2.25072e6	0.0786163
$962$	0	0
$963$	2.37428e6	0.0825024
$964$	1.78159e7	0.617470
$965$	−3.43949e7	−1.18898
$966$	4.06739e6	0.140240
$967$	3.93424e7	1.35299	0.676496	−	0.736447i	$-0.263498\pi$
$967$	3.93424e7	1.35299	0.676496	+	0.736447i	$0.263498\pi$
$968$	968714.	0.0332282
$969$	−4.79601e7	−1.64086
$970$	1.96601e7	0.670898
$971$	2.55227e7	0.868719	0.434359	−	0.900740i	$-0.356975\pi$
$971$	2.55227e7	0.868719	0.434359	+	0.900740i	$0.356975\pi$
$972$	1.44342e7	0.490034
$973$	−3.23746e6	−0.109628
$974$	−2.41153e6	−0.0814507
$975$	0	0
$976$	1.35832e6	0.0456433
$977$	1.53803e7	0.515500	0.257750	−	0.966212i	$-0.417019\pi$
$977$	1.53803e7	0.515500	0.257750	+	0.966212i	$0.417019\pi$
$978$	−1.74955e7	−0.584898
$979$	4.74960e7	1.58380
$980$	1.37412e7	0.457045
$981$	3.41305e6	0.113232
$982$	2.42695e7	0.803124
$983$	−1.23631e7	−0.408077	−0.204038	−	0.978963i	$-0.565407\pi$
$983$	−1.23631e7	−0.408077	−0.204038	+	0.978963i	$0.565407\pi$
$984$	−1.67019e7	−0.549894
$985$	3.33942e7	1.09668
$986$	−514827.	−0.0168643
$987$	1.29114e6	0.0421873
$988$	0	0
$989$	6.05091e7	1.96712
$990$	1.04956e7	0.340344
$991$	−2.73319e6	−0.0884068	−0.0442034	−	0.999023i	$-0.514075\pi$
$991$	−2.73319e6	−0.0884068	−0.0442034	+	0.999023i	$0.514075\pi$
$992$	5.69033e6	0.183594
$993$	−3.71814e7	−1.19661
$994$	−183069.	−0.00587692
$995$	−4.31619e7	−1.38211
$996$	−6.83989e6	−0.218475
$997$	8.43065e6	0.268611	0.134305	−	0.990940i	$-0.457120\pi$
$997$	8.43065e6	0.268611	0.134305	+	0.990940i	$0.457120\pi$
$998$	1.17835e6	0.0374497
$999$	1.75778e7	0.557251

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	338.6.a.m.1.2		6
13.5	odd	4		338.6.b.g.337.8		12
13.6	odd	12		26.6.e.a.23.6	yes	12
13.8	odd	4		338.6.b.g.337.2		12
13.11	odd	12		26.6.e.a.17.6	✓	12
13.12	even	2		338.6.a.o.1.2		6
39.11	even	12		234.6.l.c.199.3		12
39.32	even	12		234.6.l.c.127.1		12
52.11	even	12		208.6.w.c.17.2		12
52.19	even	12		208.6.w.c.49.2		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
26.6.e.a.17.6	✓	12	13.11	odd	12
26.6.e.a.23.6	yes	12	13.6	odd	12
208.6.w.c.17.2		12	52.11	even	12
208.6.w.c.49.2		12	52.19	even	12
234.6.l.c.127.1		12	39.32	even	12
234.6.l.c.199.3		12	39.11	even	12
338.6.a.m.1.2		6	1.1	even	1	trivial
338.6.a.o.1.2		6	13.12	even	2
338.6.b.g.337.2		12	13.8	odd	4
338.6.b.g.337.8		12	13.5	odd	4

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:	\( N \)	\(=\)	\( 338 = 2 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	338.a (trivial)

\(f(q)\)	\(=\)	\(q-4.00000 q^{2} -19.3520 q^{3} +16.0000 q^{4} -52.2356 q^{5} +77.4082 q^{6} -19.1214 q^{7} -64.0000 q^{8} +131.501 q^{9} +O(q^{10})\)	\(q-4.00000 q^{2} -19.3520 q^{3} +16.0000 q^{4} -52.2356 q^{5} +77.4082 q^{6} -19.1214 q^{7} -64.0000 q^{8} +131.501 q^{9} +208.942 q^{10} +381.988 q^{11} -309.633 q^{12} +76.4855 q^{14} +1010.86 q^{15} +256.000 q^{16} -1057.42 q^{17} -526.006 q^{18} -2343.73 q^{19} -835.769 q^{20} +370.038 q^{21} -1527.95 q^{22} -2747.96 q^{23} +1238.53 q^{24} -396.447 q^{25} +2157.72 q^{27} -305.942 q^{28} -121.718 q^{29} -4043.46 q^{30} -5556.97 q^{31} -1024.00 q^{32} -7392.25 q^{33} +4229.66 q^{34} +998.816 q^{35} +2104.02 q^{36} +8146.46 q^{37} +9374.92 q^{38} +3343.08 q^{40} -13485.3 q^{41} -1480.15 q^{42} -22019.7 q^{43} +6111.81 q^{44} -6869.05 q^{45} +10991.8 q^{46} +3489.22 q^{47} -4954.12 q^{48} -16441.4 q^{49} +1585.79 q^{50} +20463.2 q^{51} -28937.9 q^{53} -8630.90 q^{54} -19953.4 q^{55} +1223.77 q^{56} +45355.9 q^{57} +486.873 q^{58} -34446.8 q^{59} +16173.8 q^{60} +5305.93 q^{61} +22227.9 q^{62} -2514.49 q^{63} +4096.00 q^{64} +29569.0 q^{66} +56900.3 q^{67} -16918.7 q^{68} +53178.6 q^{69} -3995.26 q^{70} -2393.52 q^{71} -8416.09 q^{72} +47969.6 q^{73} -32585.8 q^{74} +7672.05 q^{75} -37499.7 q^{76} -7304.14 q^{77} -79330.2 q^{79} -13372.3 q^{80} -73711.2 q^{81} +53941.1 q^{82} +22090.3 q^{83} +5920.60 q^{84} +55234.7 q^{85} +88078.6 q^{86} +2355.50 q^{87} -24447.2 q^{88} +124339. q^{89} +27476.2 q^{90} -43967.3 q^{92} +107539. q^{93} -13956.9 q^{94} +122426. q^{95} +19816.5 q^{96} +94093.5 q^{97} +65765.5 q^{98} +50232.0 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 24 q^{2} + 96 q^{4} + 92 q^{5} + 284 q^{7} - 384 q^{8} + 706 q^{9}+O(q^{10}) \) 6 * q - 24 * q^2 + 96 * q^4 + 92 * q^5 + 284 * q^7 - 384 * q^8 + 706 * q^9	\( 6 q - 24 q^{2} + 96 q^{4} + 92 q^{5} + 284 q^{7} - 384 q^{8} + 706 q^{9} - 368 q^{10} + 540 q^{11} - 1136 q^{14} + 2924 q^{15} + 1536 q^{16} - 1910 q^{17} - 2824 q^{18} + 3312 q^{19} + 1472 q^{20} + 5912 q^{21} - 2160 q^{22} + 5920 q^{23} + 2336 q^{25} - 1368 q^{27} + 4544 q^{28} - 7922 q^{29} - 11696 q^{30} + 1084 q^{31} - 6144 q^{32} - 792 q^{33} + 7640 q^{34} - 16864 q^{35} + 11296 q^{36} + 24052 q^{37} - 13248 q^{38} - 5888 q^{40} + 21760 q^{41} - 23648 q^{42} - 41920 q^{43} + 8640 q^{44} + 35252 q^{45} - 23680 q^{46} + 39564 q^{47} + 4682 q^{49} - 9344 q^{50} - 66632 q^{51} - 93906 q^{53} + 5472 q^{54} - 17472 q^{55} - 18176 q^{56} + 89616 q^{57} + 31688 q^{58} - 77860 q^{59} + 46784 q^{60} - 27934 q^{61} - 4336 q^{62} + 13400 q^{63} + 24576 q^{64} + 3168 q^{66} + 55096 q^{67} - 30560 q^{68} - 77348 q^{69} + 67456 q^{70} + 30384 q^{71} - 45184 q^{72} + 206488 q^{73} - 96208 q^{74} + 192080 q^{75} + 52992 q^{76} + 75972 q^{77} + 15232 q^{79} + 23552 q^{80} + 72310 q^{81} - 87040 q^{82} + 77096 q^{83} + 94592 q^{84} - 272948 q^{85} + 167680 q^{86} + 121936 q^{87} - 34560 q^{88} + 214224 q^{89} - 141008 q^{90} + 94720 q^{92} + 505168 q^{93} - 158256 q^{94} + 232560 q^{95} + 310272 q^{97} - 18728 q^{98} + 809784 q^{99}+O(q^{100}) \) 6 * q - 24 * q^2 + 96 * q^4 + 92 * q^5 + 284 * q^7 - 384 * q^8 + 706 * q^9 - 368 * q^10 + 540 * q^11 - 1136 * q^14 + 2924 * q^15 + 1536 * q^16 - 1910 * q^17 - 2824 * q^18 + 3312 * q^19 + 1472 * q^20 + 5912 * q^21 - 2160 * q^22 + 5920 * q^23 + 2336 * q^25 - 1368 * q^27 + 4544 * q^28 - 7922 * q^29 - 11696 * q^30 + 1084 * q^31 - 6144 * q^32 - 792 * q^33 + 7640 * q^34 - 16864 * q^35 + 11296 * q^36 + 24052 * q^37 - 13248 * q^38 - 5888 * q^40 + 21760 * q^41 - 23648 * q^42 - 41920 * q^43 + 8640 * q^44 + 35252 * q^45 - 23680 * q^46 + 39564 * q^47 + 4682 * q^49 - 9344 * q^50 - 66632 * q^51 - 93906 * q^53 + 5472 * q^54 - 17472 * q^55 - 18176 * q^56 + 89616 * q^57 + 31688 * q^58 - 77860 * q^59 + 46784 * q^60 - 27934 * q^61 - 4336 * q^62 + 13400 * q^63 + 24576 * q^64 + 3168 * q^66 + 55096 * q^67 - 30560 * q^68 - 77348 * q^69 + 67456 * q^70 + 30384 * q^71 - 45184 * q^72 + 206488 * q^73 - 96208 * q^74 + 192080 * q^75 + 52992 * q^76 + 75972 * q^77 + 15232 * q^79 + 23552 * q^80 + 72310 * q^81 - 87040 * q^82 + 77096 * q^83 + 94592 * q^84 - 272948 * q^85 + 167680 * q^86 + 121936 * q^87 - 34560 * q^88 + 214224 * q^89 - 141008 * q^90 + 94720 * q^92 + 505168 * q^93 - 158256 * q^94 + 232560 * q^95 + 310272 * q^97 - 18728 * q^98 + 809784 * q^99

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