LMFDB - Embedded newform 338.10.a.e.1.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [338,10,Mod(1,338)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(338, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0])) N = Newforms(chi, 10, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("338.1"); S:= CuspForms(chi, 10); N := Newforms(S);

Level:	$ N $	$=$	$ 338 = 2 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 10 $
Character orbit:	$[\chi]$	$=$	338.a (trivial)

Newform invariants

comment:select newform

sage:traces = [3,-48,156,768,1272] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)

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

Self dual:	yes
Analytic conductor:	$174.082112623$
Analytic rank:	$1$
Dimension:	$3$
Coefficient field:	3.3.2119705.1
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - x^{2} - 376x + 1820 $ x^3 - x^2 - 376*x + 1820
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2\cdot 3^{3} $
Twist minimal:	no (minimal twist has level 26)
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$5.12938$ 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)

$f(q)$	$=$	\(q-16.0000 q^{2} +249.022 q^{3} +256.000 q^{4} +716.175 q^{5} -3984.35 q^{6} -6927.79 q^{7} -4096.00 q^{8} +42328.8 q^{9} -11458.8 q^{10} +64797.9 q^{11} +63749.5 q^{12} +110845. q^{14} +178343. q^{15} +65536.0 q^{16} -52936.2 q^{17} -677261. q^{18} -811860. q^{19} +183341. q^{20} -1.72517e6 q^{21} -1.03677e6 q^{22} -1.17347e6 q^{23} -1.01999e6 q^{24} -1.44022e6 q^{25} +5.63929e6 q^{27} -1.77351e6 q^{28} -3.27842e6 q^{29} -2.85349e6 q^{30} -7.47282e6 q^{31} -1.04858e6 q^{32} +1.61361e7 q^{33} +846979. q^{34} -4.96151e6 q^{35} +1.08362e7 q^{36} +1.26693e6 q^{37} +1.29898e7 q^{38} -2.93345e6 q^{40} +2.30350e7 q^{41} +2.76027e7 q^{42} -2.89799e7 q^{43} +1.65883e7 q^{44} +3.03148e7 q^{45} +1.87755e7 q^{46} -9.91630e6 q^{47} +1.63199e7 q^{48} +7.64069e6 q^{49} +2.30435e7 q^{50} -1.31823e7 q^{51} -1.08085e8 q^{53} -9.02286e7 q^{54} +4.64066e7 q^{55} +2.83762e7 q^{56} -2.02171e8 q^{57} +5.24548e7 q^{58} -8.73536e7 q^{59} +4.56558e7 q^{60} +1.08586e8 q^{61} +1.19565e8 q^{62} -2.93245e8 q^{63} +1.67772e7 q^{64} -2.58177e8 q^{66} +2.48447e8 q^{67} -1.35517e7 q^{68} -2.92220e8 q^{69} +7.93842e7 q^{70} -2.90630e8 q^{71} -1.73379e8 q^{72} +3.58455e8 q^{73} -2.02709e7 q^{74} -3.58646e8 q^{75} -2.07836e8 q^{76} -4.48906e8 q^{77} +4.06821e8 q^{79} +4.69352e7 q^{80} +5.71148e8 q^{81} -3.68561e8 q^{82} -4.70848e8 q^{83} -4.41644e8 q^{84} -3.79116e7 q^{85} +4.63678e8 q^{86} -8.16398e8 q^{87} -2.65412e8 q^{88} -3.65116e8 q^{89} -4.85037e8 q^{90} -3.00409e8 q^{92} -1.86089e9 q^{93} +1.58661e8 q^{94} -5.81433e8 q^{95} -2.61118e8 q^{96} -8.96766e8 q^{97} -1.22251e8 q^{98} +2.74282e9 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q - 48 q^{2} + 156 q^{3} + 768 q^{4} + 1272 q^{5} - 2496 q^{6} - 17058 q^{7} - 12288 q^{8} + 42273 q^{9} - 20352 q^{10} - 73974 q^{11} + 39936 q^{12} + 272928 q^{14} - 393756 q^{15} + 196608 q^{16} + 374976 q^{17}+ \cdots + 2480087466 q^{99}+O(q^{100}) $ 3 * q - 48 * q^2 + 156 * q^3 + 768 * q^4 + 1272 * q^5 - 2496 * q^6 - 17058 * q^7 - 12288 * q^8 + 42273 * q^9 - 20352 * q^10 - 73974 * q^11 + 39936 * q^12 + 272928 * q^14 - 393756 * q^15 + 196608 * q^16 + 374976 * q^17 - 676368 * q^18 - 418338 * q^19 + 325632 * q^20 + 284694 * q^21 + 1183584 * q^22 + 1026168 * q^23 - 638976 * q^24 + 3337287 * q^25 + 4218588 * q^27 - 4366848 * q^28 - 3075834 * q^29 + 6300096 * q^30 - 9286482 * q^31 - 3145728 * q^32 + 25456452 * q^33 - 5999616 * q^34 - 31802592 * q^35 + 10821888 * q^36 + 17647776 * q^37 + 6693408 * q^38 - 5210112 * q^40 + 47257110 * q^41 - 4555104 * q^42 - 60023760 * q^43 - 18937344 * q^44 + 81112122 * q^45 - 16418688 * q^46 + 40824726 * q^47 + 10223616 * q^48 + 45921177 * q^49 - 53396592 * q^50 - 27559188 * q^51 + 8072046 * q^53 - 67497408 * q^54 - 36910236 * q^55 + 69869568 * q^56 - 245224476 * q^57 + 49213344 * q^58 - 138035310 * q^59 - 100801536 * q^60 + 264203886 * q^61 + 148583712 * q^62 - 436094838 * q^63 + 50331648 * q^64 - 407303232 * q^66 - 203167074 * q^67 + 95993856 * q^68 - 397637544 * q^69 + 508841472 * q^70 - 123067110 * q^71 - 173150208 * q^72 + 433013250 * q^73 - 282364416 * q^74 - 884469216 * q^75 - 107094528 * q^76 + 380043264 * q^77 + 406418748 * q^79 + 83361792 * q^80 + 100121427 * q^81 - 756113760 * q^82 - 105365610 * q^83 + 72881664 * q^84 - 5268186 * q^85 + 960380160 * q^86 - 12753768 * q^87 + 302997504 * q^88 - 1365375798 * q^89 - 1297793952 * q^90 + 262699008 * q^92 + 95909856 * q^93 - 653195616 * q^94 - 85600692 * q^95 - 163577856 * q^96 - 669691662 * q^97 - 734738832 * q^98 + 2480087466 * q^99

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 $

$2$	−16.0000	−0.707107
$2$	−16.0000	−0.707107
$3$	249.022	1.77497	0.887486	−	0.460835i	$-0.152450\pi$
$3$	249.022	1.77497	0.887486	+	0.460835i	$0.152450\pi$
$4$	256.000	0.500000
$5$	716.175	0.512453	0.256227	−	0.966617i	$-0.417521\pi$
$5$	716.175	0.512453	0.256227	+	0.966617i	$0.417521\pi$
$6$	−3984.35	−1.25509
$7$	−6927.79	−1.09057	−0.545285	−	0.838251i	$-0.683579\pi$
$7$	−6927.79	−1.09057	−0.545285	+	0.838251i	$0.683579\pi$
$8$	−4096.00	−0.353553
$9$	42328.8	2.15052
$10$	−11458.8	−0.362359
$11$	64797.9	1.33442	0.667212	−	0.744868i	$-0.267488\pi$
$11$	64797.9	1.33442	0.667212	+	0.744868i	$0.267488\pi$
$12$	63749.5	0.887486
$13$	0	0
$13$	0	0
$14$	110845.	0.771150
$15$	178343.	0.909590
$16$	65536.0	0.250000
$17$	−52936.2	−0.153721	−0.0768604	−	0.997042i	$-0.524490\pi$
$17$	−52936.2	−0.153721	−0.0768604	+	0.997042i	$0.524490\pi$
$18$	−677261.	−1.52065
$19$	−811860.	−1.42919	−0.714595	−	0.699539i	$-0.753389\pi$
$19$	−811860.	−1.42919	−0.714595	+	0.699539i	$0.753389\pi$
$20$	183341.	0.256227
$21$	−1.72517e6	−1.93573
$22$	−1.03677e6	−0.943580
$23$	−1.17347e6	−0.874374	−0.437187	−	0.899371i	$-0.644025\pi$
$23$	−1.17347e6	−0.874374	−0.437187	+	0.899371i	$0.644025\pi$
$24$	−1.01999e6	−0.627547
$25$	−1.44022e6	−0.737392
$26$	0	0
$27$	5.63929e6	2.04215
$28$	−1.77351e6	−0.545285
$29$	−3.27842e6	−0.860744	−0.430372	−	0.902652i	$-0.641618\pi$
$29$	−3.27842e6	−0.860744	−0.430372	+	0.902652i	$0.641618\pi$
$30$	−2.85349e6	−0.643177
$31$	−7.47282e6	−1.45331	−0.726653	−	0.687005i	$-0.758925\pi$
$31$	−7.47282e6	−1.45331	−0.726653	+	0.687005i	$0.758925\pi$
$32$	−1.04858e6	−0.176777
$33$	1.61361e7	2.36856
$34$	846979.	0.108697
$35$	−4.96151e6	−0.558866
$36$	1.08362e7	1.07526
$37$	1.26693e6	0.111134	0.0555668	−	0.998455i	$-0.482303\pi$
$37$	1.26693e6	0.111134	0.0555668	+	0.998455i	$0.482303\pi$
$38$	1.29898e7	1.01059
$39$	0	0
$40$	−2.93345e6	−0.181180
$41$	2.30350e7	1.27310	0.636548	−	0.771237i	$-0.280362\pi$
$41$	2.30350e7	1.27310	0.636548	+	0.771237i	$0.280362\pi$
$42$	2.76027e7	1.36877
$43$	−2.89799e7	−1.29267	−0.646336	−	0.763053i	$-0.723699\pi$
$43$	−2.89799e7	−1.29267	−0.646336	+	0.763053i	$0.723699\pi$
$44$	1.65883e7	0.667212
$45$	3.03148e7	1.10204
$46$	1.87755e7	0.618276
$47$	−9.91630e6	−0.296421	−0.148211	−	0.988956i	$-0.547351\pi$
$47$	−9.91630e6	−0.296421	−0.148211	+	0.988956i	$0.547351\pi$
$48$	1.63199e7	0.443743
$49$	7.64069e6	0.189343
$50$	2.30435e7	0.521415
$51$	−1.31823e7	−0.272850
$52$	0	0
$53$	−1.08085e8	−1.88158	−0.940791	−	0.338986i	$-0.889916\pi$
$53$	−1.08085e8	−1.88158	−0.940791	+	0.338986i	$0.889916\pi$
$54$	−9.02286e7	−1.44402
$55$	4.64066e7	0.683829
$56$	2.83762e7	0.385575
$57$	−2.02171e8	−2.53677
$58$	5.24548e7	0.608638
$59$	−8.73536e7	−0.938527	−0.469263	−	0.883058i	$-0.655480\pi$
$59$	−8.73536e7	−0.938527	−0.469263	+	0.883058i	$0.655480\pi$
$60$	4.56558e7	0.454795
$61$	1.08586e8	1.00413	0.502065	−	0.864830i	$-0.332574\pi$
$61$	1.08586e8	1.00413	0.502065	+	0.864830i	$0.332574\pi$
$62$	1.19565e8	1.02764
$63$	−2.93245e8	−2.34530
$64$	1.67772e7	0.125000
$65$	0	0
$66$	−2.58177e8	−1.67483
$67$	2.48447e8	1.50625	0.753124	−	0.657878i	$-0.228546\pi$
$67$	2.48447e8	1.50625	0.753124	+	0.657878i	$0.228546\pi$
$68$	−1.35517e7	−0.0768604
$69$	−2.92220e8	−1.55199
$70$	7.93842e7	0.395178
$71$	−2.90630e8	−1.35731	−0.678653	−	0.734459i	$-0.737436\pi$
$71$	−2.90630e8	−1.35731	−0.678653	+	0.734459i	$0.737436\pi$
$72$	−1.73379e8	−0.760325
$73$	3.58455e8	1.47734	0.738672	−	0.674065i	$-0.235453\pi$
$73$	3.58455e8	1.47734	0.738672	+	0.674065i	$0.235453\pi$
$74$	−2.02709e7	−0.0785834
$75$	−3.58646e8	−1.30885
$76$	−2.07836e8	−0.714595
$77$	−4.48906e8	−1.45528
$78$	0	0
$79$	4.06821e8	1.17512	0.587559	−	0.809181i	$-0.300089\pi$
$79$	4.06821e8	1.17512	0.587559	+	0.809181i	$0.300089\pi$
$80$	4.69352e7	0.128113
$81$	5.71148e8	1.47423
$82$	−3.68561e8	−0.900215
$83$	−4.70848e8	−1.08900	−0.544502	−	0.838759i	$-0.683281\pi$
$83$	−4.70848e8	−1.08900	−0.544502	+	0.838759i	$0.683281\pi$
$84$	−4.41644e8	−0.967866
$85$	−3.79116e7	−0.0787747
$86$	4.63678e8	0.914057
$87$	−8.16398e8	−1.52780
$88$	−2.65412e8	−0.471790
$89$	−3.65116e8	−0.616845	−0.308422	−	0.951249i	$-0.599801\pi$
$89$	−3.65116e8	−0.616845	−0.308422	+	0.951249i	$0.599801\pi$
$90$	−4.85037e8	−0.779262
$91$	0	0
$92$	−3.00409e8	−0.437187
$93$	−1.86089e9	−2.57958
$94$	1.58661e8	0.209601
$95$	−5.81433e8	−0.732392
$96$	−2.61118e8	−0.313774
$97$	−8.96766e8	−1.02850	−0.514252	−	0.857639i	$-0.671931\pi$
$97$	−8.96766e8	−1.02850	−0.514252	+	0.857639i	$0.671931\pi$
$98$	−1.22251e8	−0.133886
$99$	2.74282e9	2.86971
$100$	−3.68696e8	−0.368696
$101$	−1.62603e8	−0.155482	−0.0777412	−	0.996974i	$-0.524771\pi$
$101$	−1.62603e8	−0.155482	−0.0777412	+	0.996974i	$0.524771\pi$
$102$	2.10916e8	0.192934
$103$	−2.32078e8	−0.203173	−0.101586	−	0.994827i	$-0.532392\pi$
$103$	−2.32078e8	−0.203173	−0.101586	+	0.994827i	$0.532392\pi$
$104$	0	0
$105$	−1.23552e9	−0.991971
$106$	1.72936e9	1.33048
$107$	1.84672e9	1.36199	0.680994	−	0.732289i	$-0.261548\pi$
$107$	1.84672e9	1.36199	0.680994	+	0.732289i	$0.261548\pi$
$108$	1.44366e9	1.02107
$109$	−1.10794e9	−0.751791	−0.375896	−	0.926662i	$-0.622665\pi$
$109$	−1.10794e9	−0.751791	−0.375896	+	0.926662i	$0.622665\pi$
$110$	−7.42506e8	−0.483540
$111$	3.15494e8	0.197259
$112$	−4.54020e8	−0.272643
$113$	2.55084e9	1.47174	0.735868	−	0.677125i	$-0.236774\pi$
$113$	2.55084e9	1.47174	0.735868	+	0.677125i	$0.236774\pi$
$114$	3.23473e9	1.79377
$115$	−8.40411e8	−0.448076
$116$	−8.39276e8	−0.430372
$117$	0	0
$118$	1.39766e9	0.663638
$119$	3.66731e8	0.167643
$120$	−7.30493e8	−0.321589
$121$	1.84082e9	0.780686
$122$	−1.73738e9	−0.710027
$123$	5.73622e9	2.25971
$124$	−1.91304e9	−0.726653
$125$	−2.43023e9	−0.890332
$126$	4.69192e9	1.65838
$127$	−1.39169e9	−0.474706	−0.237353	−	0.971423i	$-0.576280\pi$
$127$	−1.39169e9	−0.474706	−0.237353	+	0.971423i	$0.576280\pi$
$128$	−2.68435e8	−0.0883883
$129$	−7.21661e9	−2.29446
$130$	0	0
$131$	−4.17723e8	−0.123927	−0.0619637	−	0.998078i	$-0.519736\pi$
$131$	−4.17723e8	−0.123927	−0.0619637	+	0.998078i	$0.519736\pi$
$132$	4.13084e9	1.18428
$133$	5.62439e9	1.55863
$134$	−3.97515e9	−1.06508
$135$	4.03872e9	1.04651
$136$	2.16827e8	0.0543485
$137$	3.17262e9	0.769441	0.384721	−	0.923033i	$-0.374298\pi$
$137$	3.17262e9	0.769441	0.384721	+	0.923033i	$0.374298\pi$
$138$	4.67552e9	1.09742
$139$	7.49108e8	0.170207	0.0851036	−	0.996372i	$-0.472878\pi$
$139$	7.49108e8	0.170207	0.0851036	+	0.996372i	$0.472878\pi$
$140$	−1.27015e9	−0.279433
$141$	−2.46937e9	−0.526139
$142$	4.65008e9	0.959761
$143$	0	0
$144$	2.77406e9	0.537631
$145$	−2.34792e9	−0.441091
$146$	−5.73527e9	−1.04464
$147$	1.90270e9	0.336079
$148$	3.24335e8	0.0555668
$149$	3.94098e9	0.655038	0.327519	−	0.944845i	$-0.393787\pi$
$149$	3.94098e9	0.655038	0.327519	+	0.944845i	$0.393787\pi$
$150$	5.73833e9	0.925497
$151$	−8.63414e9	−1.35152	−0.675760	−	0.737121i	$-0.736185\pi$
$151$	−8.63414e9	−1.35152	−0.675760	+	0.737121i	$0.736185\pi$
$152$	3.32538e9	0.505295
$153$	−2.24072e9	−0.330580
$154$	7.18250e9	1.02904
$155$	−5.35185e9	−0.744751
$156$	0	0
$157$	1.08229e10	1.42166	0.710829	−	0.703365i	$-0.248320\pi$
$157$	1.08229e10	1.42166	0.710829	+	0.703365i	$0.248320\pi$
$158$	−6.50914e9	−0.830934
$159$	−2.69155e10	−3.33976
$160$	−7.50964e8	−0.0905898
$161$	8.12956e9	0.953566
$162$	−9.13837e9	−1.04244
$163$	5.62787e8	0.0624453	0.0312226	−	0.999512i	$-0.490060\pi$
$163$	5.62787e8	0.0624453	0.0312226	+	0.999512i	$0.490060\pi$
$164$	5.89697e9	0.636548
$165$	1.15563e10	1.21378
$166$	7.53358e9	0.770043
$167$	−7.18451e9	−0.714781	−0.357390	−	0.933955i	$-0.616333\pi$
$167$	−7.18451e9	−0.714781	−0.357390	+	0.933955i	$0.616333\pi$
$168$	7.06630e9	0.684384
$169$	0	0
$170$	6.06585e8	0.0557021
$171$	−3.43650e10	−3.07351
$172$	−7.41884e9	−0.646336
$173$	−7.72366e9	−0.655565	−0.327783	−	0.944753i	$-0.606301\pi$
$173$	−7.72366e9	−0.655565	−0.327783	+	0.944753i	$0.606301\pi$
$174$	1.30624e10	1.08031
$175$	9.97753e9	0.804178
$176$	4.24659e9	0.333606
$177$	−2.17529e10	−1.66586
$178$	5.84186e9	0.436175
$179$	−2.20856e10	−1.60794	−0.803972	−	0.594667i	$-0.797284\pi$
$179$	−2.20856e10	−1.60794	−0.803972	+	0.594667i	$0.797284\pi$
$180$	7.76059e9	0.551022
$181$	−8.63359e8	−0.0597913	−0.0298956	−	0.999553i	$-0.509517\pi$
$181$	−8.63359e8	−0.0597913	−0.0298956	+	0.999553i	$0.509517\pi$
$182$	0	0
$183$	2.70403e10	1.78230
$184$	4.80654e9	0.309138
$185$	9.07345e8	0.0569508
$186$	2.97743e10	1.82404
$187$	−3.43015e9	−0.205129
$188$	−2.53857e9	−0.148211
$189$	−3.90678e10	−2.22711
$190$	9.30293e9	0.517880
$191$	−6.46347e9	−0.351411	−0.175706	−	0.984443i	$-0.556221\pi$
$191$	−6.46347e9	−0.351411	−0.175706	+	0.984443i	$0.556221\pi$
$192$	4.17789e9	0.221871
$193$	3.91408e9	0.203059	0.101529	−	0.994833i	$-0.467626\pi$
$193$	3.91408e9	0.203059	0.101529	+	0.994833i	$0.467626\pi$
$194$	1.43483e10	0.727263
$195$	0	0
$196$	1.95602e9	0.0946717
$197$	1.33095e10	0.629600	0.314800	−	0.949158i	$-0.398062\pi$
$197$	1.33095e10	0.629600	0.314800	+	0.949158i	$0.398062\pi$
$198$	−4.38850e10	−2.02919
$199$	4.22698e10	1.91069	0.955347	−	0.295488i	$-0.0954821\pi$
$199$	4.22698e10	1.91069	0.955347	+	0.295488i	$0.0954821\pi$
$200$	5.89914e9	0.260707
$201$	6.18686e10	2.67355
$202$	2.60164e9	0.109943
$203$	2.27122e10	0.938702
$204$	−3.37466e9	−0.136425
$205$	1.64971e10	0.652402
$206$	3.71324e9	0.143665
$207$	−4.96716e10	−1.88036
$208$	0	0
$209$	−5.26068e10	−1.90714
$210$	1.97684e10	0.701430
$211$	−4.36607e10	−1.51642	−0.758211	−	0.652010i	$-0.773926\pi$
$211$	−4.36607e10	−1.51642	−0.758211	+	0.652010i	$0.773926\pi$
$212$	−2.76697e10	−0.940791
$213$	−7.23732e10	−2.40918
$214$	−2.95475e10	−0.963071
$215$	−2.07546e10	−0.662434
$216$	−2.30985e10	−0.722009
$217$	5.17702e10	1.58493
$218$	1.77271e10	0.531597
$219$	8.92630e10	2.62224
$220$	1.18801e10	0.341915
$221$	0	0
$222$	−5.04790e9	−0.139483
$223$	−3.96069e10	−1.07250	−0.536252	−	0.844058i	$-0.680160\pi$
$223$	−3.96069e10	−1.07250	−0.536252	+	0.844058i	$0.680160\pi$
$224$	7.26432e9	0.192787
$225$	−6.09627e10	−1.58578
$226$	−4.08134e10	−1.04067
$227$	5.88274e9	0.147049	0.0735247	−	0.997293i	$-0.476575\pi$
$227$	5.88274e9	0.147049	0.0735247	+	0.997293i	$0.476575\pi$
$228$	−5.17557e10	−1.26839
$229$	−2.02060e10	−0.485536	−0.242768	−	0.970084i	$-0.578055\pi$
$229$	−2.02060e10	−0.485536	−0.242768	+	0.970084i	$0.578055\pi$
$230$	1.34466e10	0.316837
$231$	−1.11787e11	−2.58309
$232$	1.34284e10	0.304319
$233$	5.28051e10	1.17375	0.586873	−	0.809679i	$-0.300359\pi$
$233$	5.28051e10	1.17375	0.586873	+	0.809679i	$0.300359\pi$
$234$	0	0
$235$	−7.10181e9	−0.151902
$236$	−2.23625e10	−0.469263
$237$	1.01307e11	2.08580
$238$	−5.86769e9	−0.118542
$239$	1.98291e10	0.393109	0.196555	−	0.980493i	$-0.437025\pi$
$239$	1.98291e10	0.393109	0.196555	+	0.980493i	$0.437025\pi$
$240$	1.16879e10	0.227397
$241$	9.13883e10	1.74507	0.872537	−	0.488548i	$-0.162473\pi$
$241$	9.13883e10	1.74507	0.872537	+	0.488548i	$0.162473\pi$
$242$	−2.94531e10	−0.552029
$243$	3.12301e10	0.574572
$244$	2.77980e10	0.502065
$245$	5.47207e9	0.0970296
$246$	−9.17795e10	−1.59786
$247$	0	0
$248$	3.06087e10	0.513821
$249$	−1.17251e11	−1.93295
$250$	3.88836e10	0.629560
$251$	−4.66320e9	−0.0741570	−0.0370785	−	0.999312i	$-0.511805\pi$
$251$	−4.66320e9	−0.0741570	−0.0370785	+	0.999312i	$0.511805\pi$
$252$	−7.50707e10	−1.17265
$253$	−7.60384e10	−1.16679
$254$	2.22670e10	0.335668
$255$	−9.44080e9	−0.139823
$256$	4.29497e9	0.0625000
$257$	−1.20163e11	−1.71819	−0.859094	−	0.511817i	$-0.828972\pi$
$257$	−1.20163e11	−1.71819	−0.859094	+	0.511817i	$0.828972\pi$
$258$	1.15466e11	1.62243
$259$	−8.77704e9	−0.121199
$260$	0	0
$261$	−1.38772e11	−1.85105
$262$	6.68356e9	0.0876299
$263$	−4.25793e9	−0.0548779	−0.0274389	−	0.999623i	$-0.508735\pi$
$263$	−4.25793e9	−0.0548779	−0.0274389	+	0.999623i	$0.508735\pi$
$264$	−6.60934e10	−0.837414
$265$	−7.74076e10	−0.964223
$266$	−8.99903e10	−1.10212
$267$	−9.09218e10	−1.09488
$268$	6.36023e10	0.753124
$269$	1.29999e11	1.51375	0.756874	−	0.653561i	$-0.226726\pi$
$269$	1.29999e11	1.51375	0.756874	+	0.653561i	$0.226726\pi$
$270$	−6.46195e10	−0.739991
$271$	−9.56827e10	−1.07763	−0.538817	−	0.842423i	$-0.681129\pi$
$271$	−9.56827e10	−1.07763	−0.538817	+	0.842423i	$0.681129\pi$
$272$	−3.46923e9	−0.0384302
$273$	0	0
$274$	−5.07619e10	−0.544077
$275$	−9.33231e10	−0.983993
$276$	−7.48083e10	−0.775995
$277$	−7.37939e10	−0.753115	−0.376558	−	0.926393i	$-0.622892\pi$
$277$	−7.37939e10	−0.753115	−0.376558	+	0.926393i	$0.622892\pi$
$278$	−1.19857e10	−0.120355
$279$	−3.16316e11	−3.12537
$280$	2.03223e10	0.197589
$281$	−4.75391e9	−0.0454854	−0.0227427	−	0.999741i	$-0.507240\pi$
$281$	−4.75391e9	−0.0454854	−0.0227427	+	0.999741i	$0.507240\pi$
$282$	3.95100e10	0.372037
$283$	1.13785e11	1.05450	0.527251	−	0.849710i	$-0.323223\pi$
$283$	1.13785e11	1.05450	0.527251	+	0.849710i	$0.323223\pi$
$284$	−7.44013e10	−0.678653
$285$	−1.44790e11	−1.29998
$286$	0	0
$287$	−1.59582e11	−1.38840
$288$	−4.43849e10	−0.380163
$289$	−1.15786e11	−0.976370
$290$	3.75668e10	0.311898
$291$	−2.23314e11	−1.82557
$292$	9.17644e10	0.738672
$293$	−6.88493e10	−0.545752	−0.272876	−	0.962049i	$-0.587975\pi$
$293$	−6.88493e10	−0.545752	−0.272876	+	0.962049i	$0.587975\pi$
$294$	−3.04432e10	−0.237644
$295$	−6.25604e10	−0.480951
$296$	−5.18935e9	−0.0392917
$297$	3.65414e11	2.72509
$298$	−6.30558e10	−0.463182
$299$	0	0
$300$	−9.18133e10	−0.654425
$301$	2.00766e11	1.40975
$302$	1.38146e11	0.955669
$303$	−4.04916e10	−0.275977
$304$	−5.32060e10	−0.357297
$305$	7.77666e10	0.514569
$306$	3.58516e10	0.233756
$307$	1.19876e11	0.770209	0.385105	−	0.922873i	$-0.374165\pi$
$307$	1.19876e11	0.770209	0.385105	+	0.922873i	$0.374165\pi$
$308$	−1.14920e11	−0.727641
$309$	−5.77924e10	−0.360626
$310$	8.56296e10	0.526619
$311$	−1.92486e11	−1.16675	−0.583375	−	0.812203i	$-0.698268\pi$
$311$	−1.92486e11	−1.16675	−0.583375	+	0.812203i	$0.698268\pi$
$312$	0	0
$313$	−8.85346e10	−0.521391	−0.260695	−	0.965421i	$-0.583952\pi$
$313$	−8.85346e10	−0.521391	−0.260695	+	0.965421i	$0.583952\pi$
$314$	−1.73166e11	−1.00526
$315$	−2.10015e11	−1.20186
$316$	1.04146e11	0.587559
$317$	−9.22613e10	−0.513160	−0.256580	−	0.966523i	$-0.582596\pi$
$317$	−9.22613e10	−0.513160	−0.256580	+	0.966523i	$0.582596\pi$
$318$	4.30647e11	2.36156
$319$	−2.12435e11	−1.14860
$320$	1.20154e10	0.0640566
$321$	4.59873e11	2.41749
$322$	−1.30073e11	−0.674273
$323$	4.29767e10	0.219696
$324$	1.46214e11	0.737116
$325$	0	0
$326$	−9.00458e9	−0.0441555
$327$	−2.75901e11	−1.33441
$328$	−9.43515e10	−0.450108
$329$	6.86981e10	0.323268
$330$	−1.84900e11	−0.858271
$331$	−1.73234e11	−0.793246	−0.396623	−	0.917981i	$-0.629818\pi$
$331$	−1.73234e11	−0.793246	−0.396623	+	0.917981i	$0.629818\pi$
$332$	−1.20537e11	−0.544502
$333$	5.36277e10	0.238996
$334$	1.14952e11	0.505426
$335$	1.77931e11	0.771881
$336$	−1.13061e11	−0.483933
$337$	5.97509e10	0.252354	0.126177	−	0.992008i	$-0.459729\pi$
$337$	5.97509e10	0.252354	0.126177	+	0.992008i	$0.459729\pi$
$338$	0	0
$339$	6.35214e11	2.61229
$340$	−9.70536e9	−0.0393873
$341$	−4.84223e11	−1.93933
$342$	5.49840e11	2.17330
$343$	2.26628e11	0.884078
$344$	1.18702e11	0.457028
$345$	−2.09280e11	−0.795321
$346$	1.23579e11	0.463555
$347$	−1.05729e11	−0.391481	−0.195740	−	0.980656i	$-0.562711\pi$
$347$	−1.05729e11	−0.391481	−0.195740	+	0.980656i	$0.562711\pi$
$348$	−2.08998e11	−0.763898
$349$	3.04810e11	1.09980	0.549901	−	0.835230i	$-0.314665\pi$
$349$	3.04810e11	1.09980	0.549901	+	0.835230i	$0.314665\pi$
$350$	−1.59641e11	−0.568639
$351$	0	0
$352$	−6.79455e10	−0.235895
$353$	−1.32310e11	−0.453530	−0.226765	−	0.973950i	$-0.572815\pi$
$353$	−1.32310e11	−0.453530	−0.226765	+	0.973950i	$0.572815\pi$
$354$	3.48047e11	1.17794
$355$	−2.08142e11	−0.695556
$356$	−9.34697e10	−0.308422
$357$	9.13239e10	0.297562
$358$	3.53370e11	1.13699
$359$	−3.72672e11	−1.18414	−0.592069	−	0.805887i	$-0.701689\pi$
$359$	−3.72672e11	−1.18414	−0.592069	+	0.805887i	$0.701689\pi$
$360$	−1.24169e11	−0.389631
$361$	3.36428e11	1.04258
$362$	1.38137e10	0.0422788
$363$	4.58403e11	1.38570
$364$	0	0
$365$	2.56716e11	0.757069
$366$	−4.32645e11	−1.26028
$367$	−4.80734e11	−1.38327	−0.691635	−	0.722247i	$-0.743109\pi$
$367$	−4.80734e11	−1.38327	−0.691635	+	0.722247i	$0.743109\pi$
$368$	−7.69046e10	−0.218593
$369$	9.75045e11	2.73783
$370$	−1.45175e10	−0.0402703
$371$	7.48789e11	2.05200
$372$	−4.76389e11	−1.28979
$373$	−6.45327e10	−0.172620	−0.0863098	−	0.996268i	$-0.527507\pi$
$373$	−6.45327e10	−0.172620	−0.0863098	+	0.996268i	$0.527507\pi$
$374$	5.48824e10	0.145048
$375$	−6.05179e11	−1.58031
$376$	4.06172e10	0.104801
$377$	0	0
$378$	6.25085e11	1.57480
$379$	4.64545e11	1.15652	0.578258	−	0.815854i	$-0.303733\pi$
$379$	4.64545e11	1.15652	0.578258	+	0.815854i	$0.303733\pi$
$380$	−1.48847e11	−0.366196
$381$	−3.46560e11	−0.842591
$382$	1.03416e11	0.248485
$383$	3.32737e11	0.790145	0.395073	−	0.918650i	$-0.370719\pi$
$383$	3.32737e11	0.790145	0.395073	+	0.918650i	$0.370719\pi$
$384$	−6.68462e10	−0.156887
$385$	−3.21495e11	−0.745764
$386$	−6.26253e10	−0.143584
$387$	−1.22668e12	−2.77992
$388$	−2.29572e11	−0.514252
$389$	5.73386e11	1.26962	0.634810	−	0.772668i	$-0.281078\pi$
$389$	5.73386e11	1.26962	0.634810	+	0.772668i	$0.281078\pi$
$390$	0	0
$391$	6.21191e10	0.134409
$392$	−3.12963e10	−0.0669430
$393$	−1.04022e11	−0.219968
$394$	−2.12953e11	−0.445195
$395$	2.91355e11	0.602193
$396$	7.02161e11	1.43486
$397$	−5.39945e11	−1.09092	−0.545459	−	0.838137i	$-0.683645\pi$
$397$	−5.39945e11	−1.09092	−0.545459	+	0.838137i	$0.683645\pi$
$398$	−6.76316e11	−1.35106
$399$	1.40060e12	2.76653
$400$	−9.43862e10	−0.184348
$401$	3.41860e11	0.660236	0.330118	−	0.943940i	$-0.392912\pi$
$401$	3.41860e11	0.660236	0.330118	+	0.943940i	$0.392912\pi$
$402$	−9.89898e11	−1.89048
$403$	0	0
$404$	−4.16263e10	−0.0777412
$405$	4.09042e11	0.755475
$406$	−3.63396e11	−0.663762
$407$	8.20945e10	0.148299
$408$	5.39945e10	0.0964670
$409$	−4.81409e11	−0.850666	−0.425333	−	0.905037i	$-0.639843\pi$
$409$	−4.81409e11	−0.850666	−0.425333	+	0.905037i	$0.639843\pi$
$410$	−2.63954e11	−0.461318
$411$	7.90051e11	1.36574
$412$	−5.94119e10	−0.101586
$413$	6.05167e11	1.02353
$414$	7.94746e11	1.32962
$415$	−3.37210e11	−0.558064
$416$	0	0
$417$	1.86544e11	0.302113
$418$	8.41708e11	1.34855
$419$	4.42064e11	0.700683	0.350342	−	0.936622i	$-0.386065\pi$
$419$	4.42064e11	0.700683	0.350342	+	0.936622i	$0.386065\pi$
$420$	−3.16294e11	−0.495986
$421$	4.81550e11	0.747088	0.373544	−	0.927613i	$-0.378143\pi$
$421$	4.81550e11	0.747088	0.373544	+	0.927613i	$0.378143\pi$
$422$	6.98572e11	1.07227
$423$	−4.19745e11	−0.637461
$424$	4.42715e11	0.665240
$425$	7.62397e10	0.113352
$426$	1.15797e12	1.70355
$427$	−7.52262e11	−1.09507
$428$	4.72760e11	0.680994
$429$	0	0
$430$	3.32074e11	0.468411
$431$	1.16295e11	0.162335	0.0811676	−	0.996700i	$-0.474135\pi$
$431$	1.16295e11	0.162335	0.0811676	+	0.996700i	$0.474135\pi$
$432$	3.69577e11	0.510537
$433$	8.57306e11	1.17203	0.586017	−	0.810298i	$-0.300695\pi$
$433$	8.57306e11	1.17203	0.586017	+	0.810298i	$0.300695\pi$
$434$	−8.28323e11	−1.12072
$435$	−5.84684e11	−0.782924
$436$	−2.83633e11	−0.375896
$437$	9.52694e11	1.24965
$438$	−1.42821e12	−1.85421
$439$	1.03627e12	1.33163	0.665814	−	0.746118i	$-0.268084\pi$
$439$	1.03627e12	1.33163	0.665814	+	0.746118i	$0.268084\pi$
$440$	−1.90081e11	−0.241770
$441$	3.23421e11	0.407188
$442$	0	0
$443$	−1.13736e12	−1.40307	−0.701535	−	0.712635i	$-0.747502\pi$
$443$	−1.13736e12	−1.40307	−0.701535	+	0.712635i	$0.747502\pi$
$444$	8.07663e10	0.0986296
$445$	−2.61487e11	−0.316104
$446$	6.33710e11	0.758375
$447$	9.81391e11	1.16267
$448$	−1.16229e11	−0.136321
$449$	4.47904e11	0.520088	0.260044	−	0.965597i	$-0.416263\pi$
$449$	4.47904e11	0.520088	0.260044	+	0.965597i	$0.416263\pi$
$450$	9.75403e11	1.12132
$451$	1.49262e12	1.69885
$452$	6.53015e11	0.735868
$453$	−2.15009e12	−2.39891
$454$	−9.41238e10	−0.103980
$455$	0	0
$456$	8.28091e11	0.896884
$457$	−1.48228e12	−1.58968	−0.794838	−	0.606822i	$-0.792444\pi$
$457$	−1.48228e12	−1.58968	−0.794838	+	0.606822i	$0.792444\pi$
$458$	3.23297e11	0.343326
$459$	−2.98522e11	−0.313921
$460$	−2.15145e11	−0.224038
$461$	−1.10053e11	−0.113487	−0.0567435	−	0.998389i	$-0.518072\pi$
$461$	−1.10053e11	−0.113487	−0.0567435	+	0.998389i	$0.518072\pi$
$462$	1.78860e12	1.82652
$463$	1.90086e11	0.192236	0.0961181	−	0.995370i	$-0.469357\pi$
$463$	1.90086e11	0.192236	0.0961181	+	0.995370i	$0.469357\pi$
$464$	−2.14855e11	−0.215186
$465$	−1.33273e12	−1.32191
$466$	−8.44882e11	−0.829964
$467$	−8.85267e11	−0.861288	−0.430644	−	0.902522i	$-0.641714\pi$
$467$	−8.85267e11	−0.861288	−0.430644	+	0.902522i	$0.641714\pi$
$468$	0	0
$469$	−1.72119e12	−1.64267
$470$	1.13629e11	0.107411
$471$	2.69514e12	2.52340
$472$	3.57800e11	0.331819
$473$	−1.87783e12	−1.72497
$474$	−1.62092e12	−1.47488
$475$	1.16926e12	1.05387
$476$	9.38831e10	0.0838216
$477$	−4.57510e12	−4.04639
$478$	−3.17266e11	−0.277970
$479$	−9.62538e10	−0.0835426	−0.0417713	−	0.999127i	$-0.513300\pi$
$479$	−9.62538e10	−0.0835426	−0.0417713	+	0.999127i	$0.513300\pi$
$480$	−1.87006e11	−0.160794
$481$	0	0
$482$	−1.46221e12	−1.23395
$483$	2.02444e12	1.69255
$484$	4.71249e11	0.390343
$485$	−6.42241e11	−0.527060
$486$	−4.99681e11	−0.406284
$487$	1.05656e12	0.851163	0.425581	−	0.904920i	$-0.360070\pi$
$487$	1.05656e12	0.851163	0.425581	+	0.904920i	$0.360070\pi$
$488$	−4.44769e11	−0.355014
$489$	1.40146e11	0.110839
$490$	−8.75531e10	−0.0686103
$491$	−3.08706e11	−0.239706	−0.119853	−	0.992792i	$-0.538242\pi$
$491$	−3.08706e11	−0.239706	−0.119853	+	0.992792i	$0.538242\pi$
$492$	1.46847e12	1.12986
$493$	1.73547e11	0.132314
$494$	0	0
$495$	1.96434e12	1.47059
$496$	−4.89739e11	−0.363327
$497$	2.01342e12	1.48024
$498$	1.87602e12	1.36680
$499$	2.72504e11	0.196752	0.0983762	−	0.995149i	$-0.468635\pi$
$499$	2.72504e11	0.196752	0.0983762	+	0.995149i	$0.468635\pi$
$500$	−6.22138e11	−0.445166
$501$	−1.78910e12	−1.26872
$502$	7.46112e10	0.0524369
$503$	−1.67621e12	−1.16754	−0.583769	−	0.811920i	$-0.698423\pi$
$503$	−1.67621e12	−1.16754	−0.583769	+	0.811920i	$0.698423\pi$
$504$	1.20113e12	0.829188
$505$	−1.16452e11	−0.0796774
$506$	1.21662e12	0.825042
$507$	0	0
$508$	−3.56272e11	−0.237353
$509$	1.08327e11	0.0715331	0.0357666	−	0.999360i	$-0.488613\pi$
$509$	1.08327e11	0.0715331	0.0357666	+	0.999360i	$0.488613\pi$
$510$	1.51053e11	0.0988696
$511$	−2.48330e12	−1.61115
$512$	−6.87195e10	−0.0441942
$513$	−4.57831e12	−2.91862
$514$	1.92260e12	1.21494
$515$	−1.66208e11	−0.104117
$516$	−1.84745e12	−1.14723
$517$	−6.42555e11	−0.395552
$518$	1.40433e11	0.0857007
$519$	−1.92336e12	−1.16361
$520$	0	0
$521$	−6.57658e11	−0.391048	−0.195524	−	0.980699i	$-0.562641\pi$
$521$	−6.57658e11	−0.391048	−0.195524	+	0.980699i	$0.562641\pi$
$522$	2.22035e12	1.30889
$523$	2.28923e11	0.133793	0.0668964	−	0.997760i	$-0.478690\pi$
$523$	2.28923e11	0.133793	0.0668964	+	0.997760i	$0.478690\pi$
$524$	−1.06937e11	−0.0619637
$525$	2.48462e12	1.42739
$526$	6.81268e10	0.0388045
$527$	3.95583e11	0.223403
$528$	1.05749e12	0.592141
$529$	−4.24118e11	−0.235470
$530$	1.23852e12	0.681808
$531$	−3.69757e12	−2.01832
$532$	1.43984e12	0.779316
$533$	0	0
$534$	1.45475e12	0.774199
$535$	1.32257e12	0.697955
$536$	−1.01764e12	−0.532539
$537$	−5.49980e12	−2.85405
$538$	−2.07998e12	−1.07038
$539$	4.95101e11	0.252664
$540$	1.03391e12	0.523253
$541$	−1.87557e12	−0.941336	−0.470668	−	0.882310i	$-0.655987\pi$
$541$	−1.87557e12	−0.941336	−0.470668	+	0.882310i	$0.655987\pi$
$542$	1.53092e12	0.762003
$543$	−2.14995e11	−0.106128
$544$	5.55076e10	0.0271742
$545$	−7.93479e11	−0.385258
$546$	0	0
$547$	−2.73493e12	−1.30618	−0.653089	−	0.757281i	$-0.726527\pi$
$547$	−2.73493e12	−1.30618	−0.653089	+	0.757281i	$0.726527\pi$
$548$	8.12191e11	0.384721
$549$	4.59632e12	2.15941
$550$	1.49317e12	0.695788
$551$	2.66162e12	1.23017
$552$	1.19693e12	0.548711
$553$	−2.81837e12	−1.28155
$554$	1.18070e12	0.532533
$555$	2.25949e11	0.101086
$556$	1.91772e11	0.0851036
$557$	2.61842e12	1.15263	0.576316	−	0.817227i	$-0.304490\pi$
$557$	2.61842e12	1.15263	0.576316	+	0.817227i	$0.304490\pi$
$558$	5.06105e12	2.20997
$559$	0	0
$560$	−3.25158e11	−0.139717
$561$	−8.54182e11	−0.364097
$562$	7.60625e10	0.0321630
$563$	−3.12388e11	−0.131041	−0.0655203	−	0.997851i	$-0.520871\pi$
$563$	−3.12388e11	−0.131041	−0.0655203	+	0.997851i	$0.520871\pi$
$564$	−6.32160e11	−0.263070
$565$	1.82685e12	0.754196
$566$	−1.82056e12	−0.745645
$567$	−3.95679e12	−1.60775
$568$	1.19042e12	0.479880
$569$	−1.39773e12	−0.559006	−0.279503	−	0.960145i	$-0.590170\pi$
$569$	−1.39773e12	−0.559006	−0.279503	+	0.960145i	$0.590170\pi$
$570$	2.31663e12	0.919222
$571$	2.54454e12	1.00172	0.500861	−	0.865527i	$-0.333017\pi$
$571$	2.54454e12	1.00172	0.500861	+	0.865527i	$0.333017\pi$
$572$	0	0
$573$	−1.60954e12	−0.623745
$574$	2.55331e12	0.981748
$575$	1.69005e12	0.644756
$576$	7.10159e11	0.268816
$577$	−1.47191e12	−0.552828	−0.276414	−	0.961039i	$-0.589146\pi$
$577$	−1.47191e12	−0.552828	−0.276414	+	0.961039i	$0.589146\pi$
$578$	1.85257e12	0.690398
$579$	9.74691e11	0.360424
$580$	−6.01068e11	−0.220545
$581$	3.26194e12	1.18764
$582$	3.57303e12	1.29087
$583$	−7.00367e12	−2.51083
$584$	−1.46823e12	−0.522320
$585$	0	0
$586$	1.10159e12	0.385905
$587$	2.93835e12	1.02149	0.510743	−	0.859733i	$-0.329370\pi$
$587$	2.93835e12	1.02149	0.510743	+	0.859733i	$0.329370\pi$
$588$	4.87091e11	0.168040
$589$	6.06688e12	2.07705
$590$	1.00097e12	0.340084
$591$	3.31436e12	1.11752
$592$	8.30297e10	0.0277834
$593$	−2.96605e12	−0.984991	−0.492495	−	0.870315i	$-0.663915\pi$
$593$	−2.96605e12	−0.984991	−0.492495	+	0.870315i	$0.663915\pi$
$594$	−5.84662e12	−1.92693
$595$	2.62643e11	0.0859093
$596$	1.00889e12	0.327519
$597$	1.05261e13	3.39143
$598$	0	0
$599$	5.13235e11	0.162890	0.0814452	−	0.996678i	$-0.474046\pi$
$599$	5.13235e11	0.162890	0.0814452	+	0.996678i	$0.474046\pi$
$600$	1.46901e12	0.462748
$601$	−1.16242e12	−0.363436	−0.181718	−	0.983351i	$-0.558166\pi$
$601$	−1.16242e12	−0.363436	−0.181718	+	0.983351i	$0.558166\pi$
$602$	−3.21226e12	−0.996843
$603$	1.05164e13	3.23922
$604$	−2.21034e12	−0.675760
$605$	1.31835e12	0.400065
$606$	6.47865e11	0.195145
$607$	−1.30452e12	−0.390034	−0.195017	−	0.980800i	$-0.562476\pi$
$607$	−1.30452e12	−0.390034	−0.195017	+	0.980800i	$0.562476\pi$
$608$	8.51296e11	0.252647
$609$	5.65584e12	1.66617
$610$	−1.24427e12	−0.363856
$611$	0	0
$612$	−5.73625e11	−0.165290
$613$	−1.51535e12	−0.433453	−0.216727	−	0.976232i	$-0.569538\pi$
$613$	−1.51535e12	−0.433453	−0.216727	+	0.976232i	$0.569538\pi$
$614$	−1.91801e12	−0.544620
$615$	4.10814e12	1.15800
$616$	1.83872e12	0.514520
$617$	−4.34398e12	−1.20672	−0.603358	−	0.797471i	$-0.706171\pi$
$617$	−4.34398e12	−1.20672	−0.603358	+	0.797471i	$0.706171\pi$
$618$	9.24678e11	0.255001
$619$	3.76078e12	1.02960	0.514802	−	0.857309i	$-0.327865\pi$
$619$	3.76078e12	1.02960	0.514802	+	0.857309i	$0.327865\pi$
$620$	−1.37007e12	−0.372376
$621$	−6.61754e12	−1.78560
$622$	3.07978e12	0.825016
$623$	2.52945e12	0.672713
$624$	0	0
$625$	1.07246e12	0.281139
$626$	1.41655e12	0.368679
$627$	−1.31002e13	−3.38513
$628$	2.77066e12	0.710829
$629$	−6.70665e10	−0.0170835
$630$	3.36024e12	0.849840
$631$	−4.80012e12	−1.20537	−0.602684	−	0.797980i	$-0.705902\pi$
$631$	−4.80012e12	−1.20537	−0.602684	+	0.797980i	$0.705902\pi$
$632$	−1.66634e12	−0.415467
$633$	−1.08725e13	−2.69160
$634$	1.47618e12	0.362859
$635$	−9.96692e11	−0.243265
$636$	−6.89036e12	−1.66988
$637$	0	0
$638$	3.39896e12	0.812181
$639$	−1.23020e13	−2.91892
$640$	−1.92247e11	−0.0452949
$641$	−2.46922e12	−0.577695	−0.288848	−	0.957375i	$-0.593272\pi$
$641$	−2.46922e12	−0.577695	−0.288848	+	0.957375i	$0.593272\pi$
$642$	−7.35796e12	−1.70942
$643$	5.12941e12	1.18336	0.591682	−	0.806171i	$-0.298464\pi$
$643$	5.12941e12	1.18336	0.591682	+	0.806171i	$0.298464\pi$
$644$	2.08117e12	0.476783
$645$	−5.16836e12	−1.17580
$646$	−6.87628e11	−0.155349
$647$	1.17603e12	0.263846	0.131923	−	0.991260i	$-0.457885\pi$
$647$	1.17603e12	0.263846	0.131923	+	0.991260i	$0.457885\pi$
$648$	−2.33942e12	−0.521220
$649$	−5.66033e12	−1.25239
$650$	0	0
$651$	1.28919e13	2.81321
$652$	1.44073e11	0.0312226
$653$	−3.83054e12	−0.824424	−0.412212	−	0.911088i	$-0.635244\pi$
$653$	−3.83054e12	−0.824424	−0.412212	+	0.911088i	$0.635244\pi$
$654$	4.41442e12	0.943569
$655$	−2.99162e11	−0.0635070
$656$	1.50962e12	0.318274
$657$	1.51730e13	3.17706
$658$	−1.09917e12	−0.228585
$659$	7.92312e12	1.63649	0.818243	−	0.574873i	$-0.194949\pi$
$659$	7.92312e12	1.63649	0.818243	+	0.574873i	$0.194949\pi$
$660$	2.95840e12	0.606889
$661$	−8.08129e11	−0.164655	−0.0823273	−	0.996605i	$-0.526235\pi$
$661$	−8.08129e11	−0.164655	−0.0823273	+	0.996605i	$0.526235\pi$
$662$	2.77175e12	0.560910
$663$	0	0
$664$	1.92860e12	0.385021
$665$	4.02805e12	0.798725
$666$	−8.58043e11	−0.168995
$667$	3.84713e12	0.752612
$668$	−1.83923e12	−0.357390
$669$	−9.86297e12	−1.90366
$670$	−2.84690e12	−0.545803
$671$	7.03615e12	1.33993
$672$	1.80897e12	0.342192
$673$	−2.18500e12	−0.410568	−0.205284	−	0.978702i	$-0.565812\pi$
$673$	−2.18500e12	−0.410568	−0.205284	+	0.978702i	$0.565812\pi$
$674$	−9.56014e11	−0.178441
$675$	−8.12181e12	−1.50586
$676$	0	0
$677$	−5.92825e12	−1.08462	−0.542310	−	0.840179i	$-0.682450\pi$
$677$	−5.92825e12	−1.08462	−0.542310	+	0.840179i	$0.682450\pi$
$678$	−1.01634e13	−1.84717
$679$	6.21261e12	1.12166
$680$	1.55286e11	0.0278510
$681$	1.46493e12	0.261009
$682$	7.74757e12	1.37131
$683$	−9.91825e12	−1.74398	−0.871990	−	0.489523i	$-0.837171\pi$
$683$	−9.91825e12	−1.74398	−0.871990	+	0.489523i	$0.837171\pi$
$684$	−8.79745e12	−1.53675
$685$	2.27215e12	0.394303
$686$	−3.62605e12	−0.625137
$687$	−5.03174e12	−0.861813
$688$	−1.89922e12	−0.323168
$689$	0	0
$690$	3.34849e12	0.562377
$691$	7.28392e12	1.21539	0.607693	−	0.794172i	$-0.292095\pi$
$691$	7.28392e12	1.21539	0.607693	+	0.794172i	$0.292095\pi$
$692$	−1.97726e12	−0.327783
$693$	−1.90017e13	−3.12962
$694$	1.69166e12	0.276819
$695$	5.36493e11	0.0872232
$696$	3.34397e12	0.540157
$697$	−1.21939e12	−0.195701
$698$	−4.87696e12	−0.777678
$699$	1.31496e13	2.08337
$700$	2.55425e12	0.402089
$701$	7.97899e12	1.24801	0.624003	−	0.781422i	$-0.285505\pi$
$701$	7.97899e12	1.24801	0.624003	+	0.781422i	$0.285505\pi$
$702$	0	0
$703$	−1.02857e12	−0.158831
$704$	1.08713e12	0.166803
$705$	−1.76850e12	−0.269622
$706$	2.11696e12	0.320694
$707$	1.12648e12	0.169564
$708$	−5.56875e12	−0.832929
$709$	−3.06000e12	−0.454793	−0.227396	−	0.973802i	$-0.573021\pi$
$709$	−3.06000e12	−0.454793	−0.227396	+	0.973802i	$0.573021\pi$
$710$	3.33027e12	0.491832
$711$	1.72202e13	2.52712
$712$	1.49552e12	0.218088
$713$	8.76914e12	1.27073
$714$	−1.46118e12	−0.210408
$715$	0	0
$716$	−5.65392e12	−0.803972
$717$	4.93788e12	0.697758
$718$	5.96276e12	0.837312
$719$	1.05167e13	1.46758	0.733789	−	0.679377i	$-0.237750\pi$
$719$	1.05167e13	1.46758	0.733789	+	0.679377i	$0.237750\pi$
$720$	1.98671e12	0.275511
$721$	1.60779e12	0.221574
$722$	−5.38285e12	−0.737216
$723$	2.27577e13	3.09746
$724$	−2.21020e11	−0.0298956
$725$	4.72164e12	0.634705
$726$	−7.33445e12	−0.979835
$727$	−8.09614e12	−1.07491	−0.537456	−	0.843292i	$-0.680615\pi$
$727$	−8.09614e12	−1.07491	−0.537456	+	0.843292i	$0.680615\pi$
$728$	0	0
$729$	−3.46495e12	−0.454384
$730$	−4.10746e12	−0.535329
$731$	1.53408e12	0.198710
$732$	6.92231e12	0.891151
$733$	−3.20844e12	−0.410512	−0.205256	−	0.978708i	$-0.565803\pi$
$733$	−3.20844e12	−0.410512	−0.205256	+	0.978708i	$0.565803\pi$
$734$	7.69174e12	0.978120
$735$	1.36266e12	0.172225
$736$	1.23047e12	0.154569
$737$	1.60988e13	2.00997
$738$	−1.56007e13	−1.93594
$739$	7.62960e12	0.941026	0.470513	−	0.882393i	$-0.344069\pi$
$739$	7.62960e12	0.941026	0.470513	+	0.882393i	$0.344069\pi$
$740$	2.32280e11	0.0284754
$741$	0	0
$742$	−1.19806e13	−1.45098
$743$	1.41259e12	0.170046	0.0850229	−	0.996379i	$-0.472904\pi$
$743$	1.41259e12	0.170046	0.0850229	+	0.996379i	$0.472904\pi$
$744$	7.62223e12	0.912018
$745$	2.82243e12	0.335676
$746$	1.03252e12	0.122060
$747$	−1.99304e13	−2.34193
$748$	−8.78119e11	−0.102564
$749$	−1.27937e13	−1.48534
$750$	9.68287e12	1.11745
$751$	−1.49642e13	−1.71662	−0.858311	−	0.513130i	$-0.828486\pi$
$751$	−1.49642e13	−1.71662	−0.858311	+	0.513130i	$0.828486\pi$
$752$	−6.49875e11	−0.0741053
$753$	−1.16124e12	−0.131627
$754$	0	0
$755$	−6.18355e12	−0.692591
$756$	−1.00014e13	−1.11355
$757$	−1.41035e12	−0.156097	−0.0780487	−	0.996950i	$-0.524869\pi$
$757$	−1.41035e12	−0.156097	−0.0780487	+	0.996950i	$0.524869\pi$
$758$	−7.43272e12	−0.817780
$759$	−1.89352e13	−2.07101
$760$	2.38155e12	0.258940
$761$	−9.06064e12	−0.979327	−0.489664	−	0.871911i	$-0.662880\pi$
$761$	−9.06064e12	−0.979327	−0.489664	+	0.871911i	$0.662880\pi$
$762$	5.54497e12	0.595801
$763$	7.67558e12	0.819881
$764$	−1.65465e12	−0.175706
$765$	−1.60475e12	−0.169407
$766$	−5.32380e12	−0.558717
$767$	0	0
$768$	1.06954e12	0.110936
$769$	6.70677e12	0.691584	0.345792	−	0.938311i	$-0.387610\pi$
$769$	6.70677e12	0.691584	0.345792	+	0.938311i	$0.387610\pi$
$770$	5.14393e12	0.527335
$771$	−2.99231e13	−3.04974
$772$	1.00201e12	0.101529
$773$	1.17340e13	1.18206	0.591029	−	0.806650i	$-0.298722\pi$
$773$	1.17340e13	1.18206	0.591029	+	0.806650i	$0.298722\pi$
$774$	1.96269e13	1.96570
$775$	1.07625e13	1.07166
$776$	3.67315e12	0.363631
$777$	−2.18567e12	−0.215125
$778$	−9.17417e12	−0.897757
$779$	−1.87012e13	−1.81950
$780$	0	0
$781$	−1.88322e13	−1.81122
$782$	−9.93905e11	−0.0950418
$783$	−1.84880e13	−1.75777
$784$	5.00740e11	0.0473359
$785$	7.75109e12	0.728533
$786$	1.66435e12	0.155541
$787$	−1.08434e12	−0.100758	−0.0503790	−	0.998730i	$-0.516043\pi$
$787$	−1.08434e12	−0.100758	−0.0503790	+	0.998730i	$0.516043\pi$
$788$	3.40724e12	0.314800
$789$	−1.06032e12	−0.0974067
$790$	−4.66168e12	−0.425815
$791$	−1.76717e13	−1.60503
$792$	−1.12346e13	−1.01460
$793$	0	0
$794$	8.63912e12	0.771396
$795$	−1.92762e13	−1.71147
$796$	1.08211e13	0.955347
$797$	4.17303e12	0.366344	0.183172	−	0.983081i	$-0.441363\pi$
$797$	4.17303e12	0.366344	0.183172	+	0.983081i	$0.441363\pi$
$798$	−2.24095e13	−1.95623
$799$	5.24931e11	0.0455661
$800$	1.51018e12	0.130354
$801$	−1.54549e13	−1.32654
$802$	−5.46976e12	−0.466857
$803$	2.32271e13	1.97140
$804$	1.58384e13	1.33677
$805$	5.82219e12	0.488658
$806$	0	0
$807$	3.23725e13	2.68686
$808$	6.66020e11	0.0549713
$809$	2.03832e13	1.67303	0.836515	−	0.547944i	$-0.184589\pi$
$809$	2.03832e13	1.67303	0.836515	+	0.547944i	$0.184589\pi$
$810$	−6.54467e12	−0.534201
$811$	−3.12648e12	−0.253782	−0.126891	−	0.991917i	$-0.540500\pi$
$811$	−3.12648e12	−0.253782	−0.126891	+	0.991917i	$0.540500\pi$
$812$	5.81433e12	0.469351
$813$	−2.38271e13	−1.91277
$814$	−1.31351e12	−0.104863
$815$	4.03054e11	0.0320003
$816$	−8.63912e11	−0.0682125
$817$	2.35276e13	1.84747
$818$	7.70254e12	0.601512
$819$	0	0
$820$	4.22326e12	0.326201
$821$	−1.57719e12	−0.121155	−0.0605773	−	0.998164i	$-0.519294\pi$
$821$	−1.57719e12	−0.121155	−0.0605773	+	0.998164i	$0.519294\pi$
$822$	−1.26408e13	−0.965722
$823$	2.74085e12	0.208250	0.104125	−	0.994564i	$-0.466796\pi$
$823$	2.74085e12	0.208250	0.104125	+	0.994564i	$0.466796\pi$
$824$	9.50590e11	0.0718325
$825$	−2.32395e13	−1.74656
$826$	−9.68268e12	−0.723744
$827$	1.51185e13	1.12391	0.561957	−	0.827166i	$-0.310048\pi$
$827$	1.51185e13	1.12391	0.561957	+	0.827166i	$0.310048\pi$
$828$	−1.27159e13	−0.940181
$829$	−1.10159e13	−0.810070	−0.405035	−	0.914301i	$-0.632741\pi$
$829$	−1.10159e13	−0.810070	−0.405035	+	0.914301i	$0.632741\pi$
$830$	5.39536e12	0.394611
$831$	−1.83763e13	−1.33676
$832$	0	0
$833$	−4.04469e11	−0.0291060
$834$	−2.98471e12	−0.213626
$835$	−5.14536e12	−0.366292
$836$	−1.34673e13	−0.953572
$837$	−4.21414e13	−2.96787
$838$	−7.07302e12	−0.495458
$839$	1.56657e13	1.09149	0.545747	−	0.837950i	$-0.316246\pi$
$839$	1.56657e13	1.09149	0.545747	+	0.837950i	$0.316246\pi$
$840$	5.06070e12	0.350715
$841$	−3.75909e12	−0.259120
$842$	−7.70479e12	−0.528271
$843$	−1.18383e12	−0.0807353
$844$	−1.11771e13	−0.758211
$845$	0	0
$846$	6.71592e12	0.450753
$847$	−1.27528e13	−0.851393
$848$	−7.08345e12	−0.470396
$849$	2.83350e13	1.87171
$850$	−1.21983e12	−0.0801523
$851$	−1.48671e12	−0.0971724
$852$	−1.85275e13	−1.20459
$853$	9.67583e12	0.625774	0.312887	−	0.949790i	$-0.398704\pi$
$853$	9.67583e12	0.625774	0.312887	+	0.949790i	$0.398704\pi$
$854$	1.20362e13	0.774334
$855$	−2.46114e13	−1.57503
$856$	−7.56416e12	−0.481536
$857$	1.90306e13	1.20514	0.602571	−	0.798065i	$-0.294143\pi$
$857$	1.90306e13	1.20514	0.602571	+	0.798065i	$0.294143\pi$
$858$	0	0
$859$	−1.52060e13	−0.952895	−0.476447	−	0.879203i	$-0.658076\pi$
$859$	−1.52060e13	−0.952895	−0.476447	+	0.879203i	$0.658076\pi$
$860$	−5.31319e12	−0.331217
$861$	−3.97393e13	−2.46437
$862$	−1.86072e12	−0.114788
$863$	9.61352e12	0.589975	0.294988	−	0.955501i	$-0.404685\pi$
$863$	9.61352e12	0.589975	0.294988	+	0.955501i	$0.404685\pi$
$864$	−5.91322e12	−0.361004
$865$	−5.53149e12	−0.335946
$866$	−1.37169e13	−0.828754
$867$	−2.88331e13	−1.73303
$868$	1.32532e13	0.792466
$869$	2.63611e13	1.56811
$870$	9.35494e12	0.553611
$871$	0	0
$872$	4.53813e12	0.265798
$873$	−3.79590e13	−2.21183
$874$	−1.52431e13	−0.883633
$875$	1.68361e13	0.970969
$876$	2.28513e13	1.31112
$877$	1.61211e13	0.920227	0.460114	−	0.887860i	$-0.347809\pi$
$877$	1.61211e13	0.920227	0.460114	+	0.887860i	$0.347809\pi$
$878$	−1.65803e13	−0.941603
$879$	−1.71450e13	−0.968694
$880$	3.04130e12	0.170957
$881$	1.55403e13	0.869099	0.434549	−	0.900648i	$-0.356908\pi$
$881$	1.55403e13	0.869099	0.434549	+	0.900648i	$0.356908\pi$
$882$	−5.17474e12	−0.287925
$883$	1.81773e13	1.00625	0.503124	−	0.864214i	$-0.332184\pi$
$883$	1.81773e13	1.00625	0.503124	+	0.864214i	$0.332184\pi$
$884$	0	0
$885$	−1.55789e13	−0.853674
$886$	1.81977e13	0.992121
$887$	2.45772e13	1.33314	0.666572	−	0.745441i	$-0.267761\pi$
$887$	2.45772e13	1.33314	0.666572	+	0.745441i	$0.267761\pi$
$888$	−1.29226e12	−0.0697416
$889$	9.64132e12	0.517701
$890$	4.18379e12	0.223519
$891$	3.70092e13	1.96725
$892$	−1.01394e13	−0.536252
$893$	8.05064e12	0.423642
$894$	−1.57022e13	−0.822135
$895$	−1.58172e13	−0.823996
$896$	1.85966e12	0.0963937
$897$	0	0
$898$	−7.16647e12	−0.367758
$899$	2.44991e13	1.25092
$900$	−1.56065e13	−0.792890
$901$	5.72160e12	0.289238
$902$	−2.38819e13	−1.20127
$903$	4.99952e13	2.50227
$904$	−1.04482e13	−0.520337
$905$	−6.18316e11	−0.0306402
$906$	3.44014e13	1.69629
$907$	2.50906e13	1.23106	0.615529	−	0.788115i	$-0.288943\pi$
$907$	2.50906e13	1.23106	0.615529	+	0.788115i	$0.288943\pi$
$908$	1.50598e12	0.0735247
$909$	−6.88277e12	−0.334369
$910$	0	0
$911$	−1.70571e13	−0.820490	−0.410245	−	0.911975i	$-0.634557\pi$
$911$	−1.70571e13	−0.820490	−0.410245	+	0.911975i	$0.634557\pi$
$912$	−1.32495e13	−0.634193
$913$	−3.05100e13	−1.45319
$914$	2.37165e13	1.12407
$915$	1.93656e13	0.913346
$916$	−5.17275e12	−0.242768
$917$	2.89390e12	0.135151
$918$	4.77636e12	0.221975
$919$	3.78241e13	1.74924	0.874620	−	0.484809i	$-0.161111\pi$
$919$	3.78241e13	1.74924	0.874620	+	0.484809i	$0.161111\pi$
$920$	3.44232e12	0.158419
$921$	2.98517e13	1.36710
$922$	1.76084e12	0.0802474
$923$	0	0
$924$	−2.86176e13	−1.29154
$925$	−1.82466e12	−0.0819491
$926$	−3.04137e12	−0.135932
$927$	−9.82356e12	−0.436928
$928$	3.43767e12	0.152159
$929$	2.88455e13	1.27059	0.635297	−	0.772268i	$-0.280878\pi$
$929$	2.88455e13	1.27059	0.635297	+	0.772268i	$0.280878\pi$
$930$	2.13236e13	0.934733
$931$	−6.20317e12	−0.270608
$932$	1.35181e13	0.586873
$933$	−4.79332e13	−2.07095
$934$	1.41643e13	0.609022
$935$	−2.45659e12	−0.105119
$936$	0	0
$937$	6.13062e12	0.259822	0.129911	−	0.991526i	$-0.458531\pi$
$937$	6.13062e12	0.259822	0.129911	+	0.991526i	$0.458531\pi$
$938$	2.75390e13	1.16154
$939$	−2.20470e13	−0.925454
$940$	−1.81806e12	−0.0759510
$941$	6.77593e12	0.281719	0.140859	−	0.990030i	$-0.455013\pi$
$941$	6.77593e12	0.281719	0.140859	+	0.990030i	$0.455013\pi$
$942$	−4.31222e13	−1.78432
$943$	−2.70309e13	−1.11316
$944$	−5.72480e12	−0.234632
$945$	−2.79794e13	−1.14129
$946$	3.00453e13	1.21974
$947$	2.51244e13	1.01513	0.507565	−	0.861614i	$-0.330546\pi$
$947$	2.51244e13	1.01513	0.507565	+	0.861614i	$0.330546\pi$
$948$	2.59347e13	1.04290
$949$	0	0
$950$	−1.87081e13	−0.745200
$951$	−2.29751e13	−0.910844
$952$	−1.50213e12	−0.0592708
$953$	6.21828e12	0.244204	0.122102	−	0.992518i	$-0.461037\pi$
$953$	6.21828e12	0.244204	0.122102	+	0.992518i	$0.461037\pi$
$954$	7.32016e13	2.86123
$955$	−4.62898e12	−0.180082
$956$	5.07626e12	0.196555
$957$	−5.29009e13	−2.03873
$958$	1.54006e12	0.0590735
$959$	−2.19793e13	−0.839130
$960$	2.99210e12	0.113699
$961$	2.94035e13	1.11210
$962$	0	0
$963$	7.81693e13	2.92899
$964$	2.33954e13	0.872537
$965$	2.80317e12	0.104058
$966$	−3.23910e13	−1.19682
$967$	−9.31427e12	−0.342554	−0.171277	−	0.985223i	$-0.554789\pi$
$967$	−9.31427e12	−0.342554	−0.171277	+	0.985223i	$0.554789\pi$
$968$	−7.53999e12	−0.276014
$969$	1.07021e13	0.389954
$970$	1.02759e13	0.372688
$971$	2.14377e13	0.773912	0.386956	−	0.922098i	$-0.373527\pi$
$971$	2.14377e13	0.773912	0.386956	+	0.922098i	$0.373527\pi$
$972$	7.99489e12	0.287286
$973$	−5.18967e12	−0.185623
$974$	−1.69049e13	−0.601863
$975$	0	0
$976$	7.11630e12	0.251032
$977$	1.22818e13	0.431258	0.215629	−	0.976475i	$-0.430820\pi$
$977$	1.22818e13	0.431258	0.215629	+	0.976475i	$0.430820\pi$
$978$	−2.24234e12	−0.0783747
$979$	−2.36587e13	−0.823132
$980$	1.40085e12	0.0485148
$981$	−4.68978e13	−1.61675
$982$	4.93930e12	0.169498
$983$	−5.75537e13	−1.96599	−0.982997	−	0.183622i	$-0.941218\pi$
$983$	−5.75537e13	−1.96599	−0.982997	+	0.183622i	$0.941218\pi$
$984$	−2.34956e13	−0.798929
$985$	9.53196e12	0.322641
$986$	−2.77675e12	−0.0935602
$987$	1.71073e13	0.573792
$988$	0	0
$989$	3.40070e13	1.13028
$990$	−3.14294e13	−1.03987
$991$	3.89816e13	1.28389	0.641945	−	0.766751i	$-0.278128\pi$
$991$	3.89816e13	1.28389	0.641945	+	0.766751i	$0.278128\pi$
$992$	7.83582e12	0.256911
$993$	−4.31391e13	−1.40799
$994$	−3.22148e13	−1.04669
$995$	3.02725e13	0.979141
$996$	−3.00164e13	−0.966476
$997$	−3.28468e13	−1.05285	−0.526423	−	0.850223i	$-0.676467\pi$
$997$	−3.28468e13	−1.05285	−0.526423	+	0.850223i	$0.676467\pi$
$998$	−4.36006e12	−0.139125
$999$	7.14460e12	0.226952

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	338.10.a.e.1.3		3
13.12	even	2		26.10.a.e.1.3	✓	3
39.38	odd	2		234.10.a.k.1.2		3
52.51	odd	2		208.10.a.d.1.1		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
26.10.a.e.1.3	✓	3	13.12	even	2
208.10.a.d.1.1		3	52.51	odd	2
234.10.a.k.1.2		3	39.38	odd	2
338.10.a.e.1.3		3	1.1	even	1	trivial

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 338 = 2 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	338.a (trivial)

\(f(q)\)	\(=\)	\(q-16.0000 q^{2} +249.022 q^{3} +256.000 q^{4} +716.175 q^{5} -3984.35 q^{6} -6927.79 q^{7} -4096.00 q^{8} +42328.8 q^{9} -11458.8 q^{10} +64797.9 q^{11} +63749.5 q^{12} +110845. q^{14} +178343. q^{15} +65536.0 q^{16} -52936.2 q^{17} -677261. q^{18} -811860. q^{19} +183341. q^{20} -1.72517e6 q^{21} -1.03677e6 q^{22} -1.17347e6 q^{23} -1.01999e6 q^{24} -1.44022e6 q^{25} +5.63929e6 q^{27} -1.77351e6 q^{28} -3.27842e6 q^{29} -2.85349e6 q^{30} -7.47282e6 q^{31} -1.04858e6 q^{32} +1.61361e7 q^{33} +846979. q^{34} -4.96151e6 q^{35} +1.08362e7 q^{36} +1.26693e6 q^{37} +1.29898e7 q^{38} -2.93345e6 q^{40} +2.30350e7 q^{41} +2.76027e7 q^{42} -2.89799e7 q^{43} +1.65883e7 q^{44} +3.03148e7 q^{45} +1.87755e7 q^{46} -9.91630e6 q^{47} +1.63199e7 q^{48} +7.64069e6 q^{49} +2.30435e7 q^{50} -1.31823e7 q^{51} -1.08085e8 q^{53} -9.02286e7 q^{54} +4.64066e7 q^{55} +2.83762e7 q^{56} -2.02171e8 q^{57} +5.24548e7 q^{58} -8.73536e7 q^{59} +4.56558e7 q^{60} +1.08586e8 q^{61} +1.19565e8 q^{62} -2.93245e8 q^{63} +1.67772e7 q^{64} -2.58177e8 q^{66} +2.48447e8 q^{67} -1.35517e7 q^{68} -2.92220e8 q^{69} +7.93842e7 q^{70} -2.90630e8 q^{71} -1.73379e8 q^{72} +3.58455e8 q^{73} -2.02709e7 q^{74} -3.58646e8 q^{75} -2.07836e8 q^{76} -4.48906e8 q^{77} +4.06821e8 q^{79} +4.69352e7 q^{80} +5.71148e8 q^{81} -3.68561e8 q^{82} -4.70848e8 q^{83} -4.41644e8 q^{84} -3.79116e7 q^{85} +4.63678e8 q^{86} -8.16398e8 q^{87} -2.65412e8 q^{88} -3.65116e8 q^{89} -4.85037e8 q^{90} -3.00409e8 q^{92} -1.86089e9 q^{93} +1.58661e8 q^{94} -5.81433e8 q^{95} -2.61118e8 q^{96} -8.96766e8 q^{97} -1.22251e8 q^{98} +2.74282e9 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q - 48 q^{2} + 156 q^{3} + 768 q^{4} + 1272 q^{5} - 2496 q^{6} - 17058 q^{7} - 12288 q^{8} + 42273 q^{9} - 20352 q^{10} - 73974 q^{11} + 39936 q^{12} + 272928 q^{14} - 393756 q^{15} + 196608 q^{16} + 374976 q^{17}+ \cdots + 2480087466 q^{99}+O(q^{100}) \) 3 * q - 48 * q^2 + 156 * q^3 + 768 * q^4 + 1272 * q^5 - 2496 * q^6 - 17058 * q^7 - 12288 * q^8 + 42273 * q^9 - 20352 * q^10 - 73974 * q^11 + 39936 * q^12 + 272928 * q^14 - 393756 * q^15 + 196608 * q^16 + 374976 * q^17 - 676368 * q^18 - 418338 * q^19 + 325632 * q^20 + 284694 * q^21 + 1183584 * q^22 + 1026168 * q^23 - 638976 * q^24 + 3337287 * q^25 + 4218588 * q^27 - 4366848 * q^28 - 3075834 * q^29 + 6300096 * q^30 - 9286482 * q^31 - 3145728 * q^32 + 25456452 * q^33 - 5999616 * q^34 - 31802592 * q^35 + 10821888 * q^36 + 17647776 * q^37 + 6693408 * q^38 - 5210112 * q^40 + 47257110 * q^41 - 4555104 * q^42 - 60023760 * q^43 - 18937344 * q^44 + 81112122 * q^45 - 16418688 * q^46 + 40824726 * q^47 + 10223616 * q^48 + 45921177 * q^49 - 53396592 * q^50 - 27559188 * q^51 + 8072046 * q^53 - 67497408 * q^54 - 36910236 * q^55 + 69869568 * q^56 - 245224476 * q^57 + 49213344 * q^58 - 138035310 * q^59 - 100801536 * q^60 + 264203886 * q^61 + 148583712 * q^62 - 436094838 * q^63 + 50331648 * q^64 - 407303232 * q^66 - 203167074 * q^67 + 95993856 * q^68 - 397637544 * q^69 + 508841472 * q^70 - 123067110 * q^71 - 173150208 * q^72 + 433013250 * q^73 - 282364416 * q^74 - 884469216 * q^75 - 107094528 * q^76 + 380043264 * q^77 + 406418748 * q^79 + 83361792 * q^80 + 100121427 * q^81 - 756113760 * q^82 - 105365610 * q^83 + 72881664 * q^84 - 5268186 * q^85 + 960380160 * q^86 - 12753768 * q^87 + 302997504 * q^88 - 1365375798 * q^89 - 1297793952 * q^90 + 262699008 * q^92 + 95909856 * q^93 - 653195616 * q^94 - 85600692 * q^95 - 163577856 * q^96 - 669691662 * q^97 - 734738832 * q^98 + 2480087466 * q^99

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