LMFDB - Embedded newform 338.10.a.i.1.4

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 = [5,80,81,1280,914] 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:	$0$
Dimension:	$5$
Coefficient field:	$\mathbb{Q}[x]/(x^{5} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{5} - x^{4} - 55443x^{3} - 74771x^{2} + 273667790x + 7141148352 $ x^5 - x^4 - 55443x^3 - 74771x^2 + 273667790*x + 7141148352
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{4}\cdot 3 $
Twist minimal:	no (minimal twist has level 26)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Root			$85.2901$ 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)

$f(q)$	$=$	\(q+16.0000 q^{2} +101.290 q^{3} +256.000 q^{4} -496.759 q^{5} +1620.64 q^{6} -4702.56 q^{7} +4096.00 q^{8} -9423.31 q^{9} -7948.14 q^{10} -77003.3 q^{11} +25930.3 q^{12} -75241.0 q^{14} -50316.8 q^{15} +65536.0 q^{16} +66918.1 q^{17} -150773. q^{18} +998917. q^{19} -127170. q^{20} -476323. q^{21} -1.23205e6 q^{22} +118136. q^{23} +414884. q^{24} -1.70636e6 q^{25} -2.94818e6 q^{27} -1.20386e6 q^{28} +926412. q^{29} -805068. q^{30} -1.69046e6 q^{31} +1.04858e6 q^{32} -7.79967e6 q^{33} +1.07069e6 q^{34} +2.33604e6 q^{35} -2.41237e6 q^{36} -2.46364e6 q^{37} +1.59827e7 q^{38} -2.03472e6 q^{40} +2.99902e7 q^{41} -7.62117e6 q^{42} +9.51190e6 q^{43} -1.97128e7 q^{44} +4.68111e6 q^{45} +1.89018e6 q^{46} +6.47000e7 q^{47} +6.63815e6 q^{48} -1.82395e7 q^{49} -2.73017e7 q^{50} +6.77814e6 q^{51} +4.73931e7 q^{53} -4.71709e7 q^{54} +3.82521e7 q^{55} -1.92617e7 q^{56} +1.01180e8 q^{57} +1.48226e7 q^{58} +6.57744e7 q^{59} -1.28811e7 q^{60} -7.54398e7 q^{61} -2.70474e7 q^{62} +4.43137e7 q^{63} +1.67772e7 q^{64} -1.24795e8 q^{66} -5.34676e7 q^{67} +1.71310e7 q^{68} +1.19660e7 q^{69} +3.73766e7 q^{70} +2.65576e8 q^{71} -3.85979e7 q^{72} -2.19898e7 q^{73} -3.94183e7 q^{74} -1.72837e8 q^{75} +2.55723e8 q^{76} +3.62113e8 q^{77} -2.38980e7 q^{79} -3.25556e7 q^{80} -1.13143e8 q^{81} +4.79842e8 q^{82} +3.61556e8 q^{83} -1.21939e8 q^{84} -3.32421e7 q^{85} +1.52190e8 q^{86} +9.38364e7 q^{87} -3.15405e8 q^{88} +6.70531e8 q^{89} +7.48978e7 q^{90} +3.02428e7 q^{92} -1.71227e8 q^{93} +1.03520e9 q^{94} -4.96221e8 q^{95} +1.06210e8 q^{96} -1.22647e9 q^{97} -2.91832e8 q^{98} +7.25626e8 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 5 q + 80 q^{2} + 81 q^{3} + 1280 q^{4} + 914 q^{5} + 1296 q^{6} + 3323 q^{7} + 20480 q^{8} + 13784 q^{9} + 14624 q^{10} + 53337 q^{11} + 20736 q^{12} + 53168 q^{14} + 65996 q^{15} + 327680 q^{16} + 173255 q^{17}+ \cdots + 970554586 q^{99}+O(q^{100}) $ 5 * q + 80 * q^2 + 81 * q^3 + 1280 * q^4 + 914 * q^5 + 1296 * q^6 + 3323 * q^7 + 20480 * q^8 + 13784 * q^9 + 14624 * q^10 + 53337 * q^11 + 20736 * q^12 + 53168 * q^14 + 65996 * q^15 + 327680 * q^16 + 173255 * q^17 + 220544 * q^18 - 32351 * q^19 + 233984 * q^20 + 1198763 * q^21 + 853392 * q^22 + 695969 * q^23 + 331776 * q^24 - 245227 * q^25 + 2545821 * q^27 + 850688 * q^28 + 3162725 * q^29 + 1055936 * q^30 - 2956286 * q^31 + 5242880 * q^32 + 329501 * q^33 + 2772080 * q^34 + 19935514 * q^35 + 3528704 * q^36 + 5891731 * q^37 - 517616 * q^38 + 3743744 * q^40 - 1800323 * q^41 + 19180208 * q^42 + 29311717 * q^43 + 13654272 * q^44 + 50968384 * q^45 + 11135504 * q^46 - 19266174 * q^47 + 5308416 * q^48 - 64680864 * q^49 - 3923632 * q^50 + 133318747 * q^51 - 145385254 * q^53 + 40733136 * q^54 + 61117082 * q^55 + 13611008 * q^56 + 235331279 * q^57 + 50603600 * q^58 + 12606999 * q^59 + 16894976 * q^60 + 33553237 * q^61 - 47300576 * q^62 - 107603502 * q^63 + 83886080 * q^64 + 5272016 * q^66 + 50917531 * q^67 + 44353280 * q^68 + 1842303 * q^69 + 318968224 * q^70 + 395345149 * q^71 + 56459264 * q^72 + 75481772 * q^73 + 94267696 * q^74 - 150047035 * q^75 - 8281856 * q^76 + 850958589 * q^77 - 244279556 * q^79 + 59899904 * q^80 + 561233537 * q^81 - 28805168 * q^82 + 1085718192 * q^83 + 306883328 * q^84 - 605879602 * q^85 + 468987472 * q^86 - 493630617 * q^87 + 218468352 * q^88 + 1420841923 * q^89 + 815494144 * q^90 + 178168064 * q^92 - 1050116916 * q^93 - 308258784 * q^94 + 432108524 * q^95 + 84934656 * q^96 + 1806622227 * q^97 - 1034893824 * q^98 + 970554586 * 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
$3$	101.290	0.721974	0.360987	−	0.932571i	$-0.382440\pi$
$3$	101.290	0.721974	0.360987	+	0.932571i	$0.382440\pi$
$4$	256.000	0.500000
$5$	−496.759	−0.355452	−0.177726	−	0.984080i	$-0.556874\pi$
$5$	−496.759	−0.355452	−0.177726	+	0.984080i	$0.556874\pi$
$6$	1620.64	0.510513
$7$	−4702.56	−0.740275	−0.370138	−	0.928977i	$-0.620689\pi$
$7$	−4702.56	−0.740275	−0.370138	+	0.928977i	$0.620689\pi$
$8$	4096.00	0.353553
$9$	−9423.31	−0.478754
$10$	−7948.14	−0.251342
$11$	−77003.3	−1.58578	−0.792888	−	0.609367i	$-0.791424\pi$
$11$	−77003.3	−1.58578	−0.792888	+	0.609367i	$0.791424\pi$
$12$	25930.3	0.360987
$13$	0	0
$13$	0	0
$14$	−75241.0	−0.523454
$15$	−50316.8	−0.256627
$16$	65536.0	0.250000
$17$	66918.1	0.194323	0.0971613	−	0.995269i	$-0.469024\pi$
$17$	66918.1	0.194323	0.0971613	+	0.995269i	$0.469024\pi$
$18$	−150773.	−0.338530
$19$	998917.	1.75848	0.879241	−	0.476376i	$-0.158050\pi$
$19$	998917.	1.75848	0.879241	+	0.476376i	$0.158050\pi$
$20$	−127170.	−0.177726
$21$	−476323.	−0.534459
$22$	−1.23205e6	−1.12131
$23$	118136.	0.0880253	0.0440126	−	0.999031i	$-0.485986\pi$
$23$	118136.	0.0880253	0.0440126	+	0.999031i	$0.485986\pi$
$24$	414884.	0.255256
$25$	−1.70636e6	−0.873654
$26$	0	0
$27$	−2.94818e6	−1.06762
$28$	−1.20386e6	−0.370138
$29$	926412.	0.243228	0.121614	−	0.992577i	$-0.461193\pi$
$29$	926412.	0.243228	0.121614	+	0.992577i	$0.461193\pi$
$30$	−805068.	−0.181463
$31$	−1.69046e6	−0.328759	−0.164380	−	0.986397i	$-0.552562\pi$
$31$	−1.69046e6	−0.328759	−0.164380	+	0.986397i	$0.552562\pi$
$32$	1.04858e6	0.176777
$33$	−7.79967e6	−1.14489
$34$	1.07069e6	0.137407
$35$	2.33604e6	0.263132
$36$	−2.41237e6	−0.239377
$37$	−2.46364e6	−0.216107	−0.108054	−	0.994145i	$-0.534462\pi$
$37$	−2.46364e6	−0.216107	−0.108054	+	0.994145i	$0.534462\pi$
$38$	1.59827e7	1.24344
$39$	0	0
$40$	−2.03472e6	−0.125671
$41$	2.99902e7	1.65749	0.828746	−	0.559625i	$-0.189055\pi$
$41$	2.99902e7	1.65749	0.828746	+	0.559625i	$0.189055\pi$
$42$	−7.62117e6	−0.377920
$43$	9.51190e6	0.424287	0.212143	−	0.977239i	$-0.431956\pi$
$43$	9.51190e6	0.424287	0.212143	+	0.977239i	$0.431956\pi$
$44$	−1.97128e7	−0.792888
$45$	4.68111e6	0.170174
$46$	1.89018e6	0.0622433
$47$	6.47000e7	1.93403	0.967017	−	0.254713i	$-0.0819811\pi$
$47$	6.47000e7	1.93403	0.967017	+	0.254713i	$0.0819811\pi$
$48$	6.63815e6	0.180493
$49$	−1.82395e7	−0.451992
$50$	−2.73017e7	−0.617767
$51$	6.77814e6	0.140296
$52$	0	0
$53$	4.73931e7	0.825038	0.412519	−	0.910949i	$-0.364649\pi$
$53$	4.73931e7	0.825038	0.412519	+	0.910949i	$0.364649\pi$
$54$	−4.71709e7	−0.754922
$55$	3.82521e7	0.563667
$56$	−1.92617e7	−0.261727
$57$	1.01180e8	1.26958
$58$	1.48226e7	0.171988
$59$	6.57744e7	0.706681	0.353340	−	0.935495i	$-0.385046\pi$
$59$	6.57744e7	0.706681	0.353340	+	0.935495i	$0.385046\pi$
$60$	−1.28811e7	−0.128313
$61$	−7.54398e7	−0.697615	−0.348808	−	0.937194i	$-0.613413\pi$
$61$	−7.54398e7	−0.697615	−0.348808	+	0.937194i	$0.613413\pi$
$62$	−2.70474e7	−0.232468
$63$	4.43137e7	0.354410
$64$	1.67772e7	0.125000
$65$	0	0
$66$	−1.24795e8	−0.809559
$67$	−5.34676e7	−0.324156	−0.162078	−	0.986778i	$-0.551820\pi$
$67$	−5.34676e7	−0.324156	−0.162078	+	0.986778i	$0.551820\pi$
$68$	1.71310e7	0.0971613
$69$	1.19660e7	0.0635519
$70$	3.73766e7	0.186062
$71$	2.65576e8	1.24030	0.620150	−	0.784483i	$-0.287072\pi$
$71$	2.65576e8	1.24030	0.620150	+	0.784483i	$0.287072\pi$
$72$	−3.85979e7	−0.169265
$73$	−2.19898e7	−0.0906293	−0.0453147	−	0.998973i	$-0.514429\pi$
$73$	−2.19898e7	−0.0906293	−0.0453147	+	0.998973i	$0.514429\pi$
$74$	−3.94183e7	−0.152811
$75$	−1.72837e8	−0.630755
$76$	2.55723e8	0.879241
$77$	3.62113e8	1.17391
$78$	0	0
$79$	−2.38980e7	−0.0690302	−0.0345151	−	0.999404i	$-0.510989\pi$
$79$	−2.38980e7	−0.0690302	−0.0345151	+	0.999404i	$0.510989\pi$
$80$	−3.25556e7	−0.0888629
$81$	−1.13143e8	−0.292041
$82$	4.79842e8	1.17202
$83$	3.61556e8	0.836226	0.418113	−	0.908395i	$-0.362692\pi$
$83$	3.61556e8	0.836226	0.418113	+	0.908395i	$0.362692\pi$
$84$	−1.21939e8	−0.267230
$85$	−3.32421e7	−0.0690723
$86$	1.52190e8	0.300016
$87$	9.38364e7	0.175604
$88$	−3.15405e8	−0.560657
$89$	6.70531e8	1.13283	0.566414	−	0.824121i	$-0.308330\pi$
$89$	6.70531e8	1.13283	0.566414	+	0.824121i	$0.308330\pi$
$90$	7.48978e7	0.120331
$91$	0	0
$92$	3.02428e7	0.0440126
$93$	−1.71227e8	−0.237355
$94$	1.03520e9	1.36757
$95$	−4.96221e8	−0.625056
$96$	1.06210e8	0.127628
$97$	−1.22647e9	−1.40665	−0.703324	−	0.710869i	$-0.748302\pi$
$97$	−1.22647e9	−1.40665	−0.703324	+	0.710869i	$0.748302\pi$
$98$	−2.91832e8	−0.319607
$99$	7.25626e8	0.759197
$100$	−4.36827e8	−0.436827
$101$	8.40879e8	0.804058	0.402029	−	0.915627i	$-0.368305\pi$
$101$	8.40879e8	0.804058	0.402029	+	0.915627i	$0.368305\pi$
$102$	1.08450e8	0.0992041
$103$	1.42090e9	1.24393	0.621967	−	0.783043i	$-0.286334\pi$
$103$	1.42090e9	1.24393	0.621967	+	0.783043i	$0.286334\pi$
$104$	0	0
$105$	2.36618e8	0.189974
$106$	7.58290e8	0.583390
$107$	4.04662e8	0.298446	0.149223	−	0.988804i	$-0.452323\pi$
$107$	4.04662e8	0.298446	0.149223	+	0.988804i	$0.452323\pi$
$108$	−7.54735e8	−0.533811
$109$	9.19763e8	0.624103	0.312052	−	0.950065i	$-0.398984\pi$
$109$	9.19763e8	0.624103	0.312052	+	0.950065i	$0.398984\pi$
$110$	6.12033e8	0.398573
$111$	−2.49543e8	−0.156024
$112$	−3.08187e8	−0.185069
$113$	−2.53394e9	−1.46198	−0.730992	−	0.682386i	$-0.760942\pi$
$113$	−2.53394e9	−1.46198	−0.730992	+	0.682386i	$0.760942\pi$
$114$	1.61889e9	0.897728
$115$	−5.86851e7	−0.0312887
$116$	2.37161e8	0.121614
$117$	0	0
$118$	1.05239e9	0.499699
$119$	−3.14686e8	−0.143852
$120$	−2.06097e8	−0.0907313
$121$	3.57156e9	1.51469
$122$	−1.20704e9	−0.493289
$123$	3.03771e9	1.19667
$124$	−4.32758e8	−0.164380
$125$	1.81788e9	0.665993
$126$	7.09019e8	0.250605
$127$	3.61563e9	1.23330	0.616648	−	0.787239i	$-0.288490\pi$
$127$	3.61563e9	1.23330	0.616648	+	0.787239i	$0.288490\pi$
$128$	2.68435e8	0.0883883
$129$	9.63462e8	0.306324
$130$	0	0
$131$	−3.45874e9	−1.02612	−0.513059	−	0.858353i	$-0.671488\pi$
$131$	−3.45874e9	−1.02612	−0.513059	+	0.858353i	$0.671488\pi$
$132$	−1.99672e9	−0.572445
$133$	−4.69747e9	−1.30176
$134$	−8.55482e8	−0.229213
$135$	1.46454e9	0.379488
$136$	2.74096e8	0.0687034
$137$	−2.90188e9	−0.703781	−0.351890	−	0.936041i	$-0.614461\pi$
$137$	−2.90188e9	−0.703781	−0.351890	+	0.936041i	$0.614461\pi$
$138$	1.91456e8	0.0449380
$139$	−5.78382e8	−0.131416	−0.0657080	−	0.997839i	$-0.520931\pi$
$139$	−5.78382e8	−0.131416	−0.0657080	+	0.997839i	$0.520931\pi$
$140$	5.98026e8	0.131566
$141$	6.55347e9	1.39632
$142$	4.24922e9	0.877025
$143$	0	0
$144$	−6.17566e8	−0.119688
$145$	−4.60203e8	−0.0864557
$146$	−3.51837e8	−0.0640846
$147$	−1.84748e9	−0.326327
$148$	−6.30692e8	−0.108054
$149$	−1.47865e9	−0.245769	−0.122884	−	0.992421i	$-0.539214\pi$
$149$	−1.47865e9	−0.245769	−0.122884	+	0.992421i	$0.539214\pi$
$150$	−2.76539e9	−0.446011
$151$	−1.09605e10	−1.71568	−0.857840	−	0.513918i	$-0.828194\pi$
$151$	−1.09605e10	−1.71568	−0.857840	+	0.513918i	$0.828194\pi$
$152$	4.09156e9	0.621718
$153$	−6.30590e8	−0.0930327
$154$	5.79380e9	0.830081
$155$	8.39752e8	0.116858
$156$	0	0
$157$	4.74736e9	0.623597	0.311798	−	0.950148i	$-0.399069\pi$
$157$	4.74736e9	0.623597	0.311798	+	0.950148i	$0.399069\pi$
$158$	−3.82368e8	−0.0488117
$159$	4.80046e9	0.595656
$160$	−5.20889e8	−0.0628356
$161$	−5.55542e8	−0.0651629
$162$	−1.81028e9	−0.206504
$163$	7.22749e9	0.801943	0.400971	−	0.916091i	$-0.368673\pi$
$163$	7.22749e9	0.801943	0.400971	+	0.916091i	$0.368673\pi$
$164$	7.67748e9	0.828746
$165$	3.87456e9	0.406953
$166$	5.78489e9	0.591301
$167$	−1.60515e10	−1.59695	−0.798475	−	0.602028i	$-0.794360\pi$
$167$	−1.60515e10	−1.59695	−0.798475	+	0.602028i	$0.794360\pi$
$168$	−1.95102e9	−0.188960
$169$	0	0
$170$	−5.31874e8	−0.0488415
$171$	−9.41310e9	−0.841880
$172$	2.43505e9	0.212143
$173$	−1.32848e10	−1.12758	−0.563791	−	0.825917i	$-0.690658\pi$
$173$	−1.32848e10	−1.12758	−0.563791	+	0.825917i	$0.690658\pi$
$174$	1.50138e9	0.124171
$175$	8.02424e9	0.646745
$176$	−5.04649e9	−0.396444
$177$	6.66230e9	0.510205
$178$	1.07285e10	0.801030
$179$	2.15712e10	1.57049	0.785245	−	0.619185i	$-0.212537\pi$
$179$	2.15712e10	1.57049	0.785245	+	0.619185i	$0.212537\pi$
$180$	1.19836e9	0.0850869
$181$	1.69038e10	1.17066	0.585331	−	0.810795i	$-0.300965\pi$
$181$	1.69038e10	1.17066	0.585331	+	0.810795i	$0.300965\pi$
$182$	0	0
$183$	−7.64130e9	−0.503660
$184$	4.83885e8	0.0311216
$185$	1.22384e9	0.0768157
$186$	−2.73963e9	−0.167836
$187$	−5.15291e9	−0.308152
$188$	1.65632e10	0.967017
$189$	1.38640e10	0.790334
$190$	−7.93953e9	−0.441981
$191$	6.59988e9	0.358827	0.179414	−	0.983774i	$-0.442580\pi$
$191$	6.59988e9	0.358827	0.179414	+	0.983774i	$0.442580\pi$
$192$	1.69937e9	0.0902467
$193$	3.53743e10	1.83519	0.917593	−	0.397522i	$-0.130130\pi$
$193$	3.53743e10	1.83519	0.917593	+	0.397522i	$0.130130\pi$
$194$	−1.96236e10	−0.994651
$195$	0	0
$196$	−4.66932e9	−0.225996
$197$	2.31046e10	1.09295	0.546476	−	0.837475i	$-0.315969\pi$
$197$	2.31046e10	1.09295	0.546476	+	0.837475i	$0.315969\pi$
$198$	1.16100e10	0.536833
$199$	−3.00516e10	−1.35841	−0.679203	−	0.733951i	$-0.737674\pi$
$199$	−3.00516e10	−1.35841	−0.679203	+	0.733951i	$0.737674\pi$
$200$	−6.98923e9	−0.308883
$201$	−5.41574e9	−0.234032
$202$	1.34541e10	0.568555
$203$	−4.35651e9	−0.180056
$204$	1.73520e9	0.0701479
$205$	−1.48979e10	−0.589158
$206$	2.27345e10	0.879594
$207$	−1.11323e9	−0.0421424
$208$	0	0
$209$	−7.69199e10	−2.78856
$210$	3.78588e9	0.134332
$211$	−4.28559e10	−1.48847	−0.744234	−	0.667918i	$-0.767185\pi$
$211$	−4.28559e10	−1.48847	−0.744234	+	0.667918i	$0.767185\pi$
$212$	1.21326e10	0.412519
$213$	2.69003e10	0.895465
$214$	6.47460e9	0.211033
$215$	−4.72512e9	−0.150813
$216$	−1.20758e10	−0.377461
$217$	7.94950e9	0.243372
$218$	1.47162e10	0.441308
$219$	−2.22735e9	−0.0654320
$220$	9.79253e9	0.281834
$221$	0	0
$222$	−3.99268e9	−0.110326
$223$	3.17732e10	0.860378	0.430189	−	0.902739i	$-0.358447\pi$
$223$	3.17732e10	0.860378	0.430189	+	0.902739i	$0.358447\pi$
$224$	−4.93099e9	−0.130863
$225$	1.60795e10	0.418265
$226$	−4.05430e10	−1.03378
$227$	−7.11270e9	−0.177794	−0.0888972	−	0.996041i	$-0.528334\pi$
$227$	−7.11270e9	−0.177794	−0.0888972	+	0.996041i	$0.528334\pi$
$228$	2.59022e10	0.634789
$229$	3.39605e10	0.816046	0.408023	−	0.912972i	$-0.366218\pi$
$229$	3.39605e10	0.816046	0.408023	+	0.912972i	$0.366218\pi$
$230$	−9.38962e8	−0.0221245
$231$	3.66784e10	0.847533
$232$	3.79458e9	0.0859940
$233$	2.07087e10	0.460311	0.230155	−	0.973154i	$-0.426077\pi$
$233$	2.07087e10	0.460311	0.230155	+	0.973154i	$0.426077\pi$
$234$	0	0
$235$	−3.21403e10	−0.687455
$236$	1.68383e10	0.353340
$237$	−2.42063e9	−0.0498380
$238$	−5.03498e9	−0.101719
$239$	−5.76591e10	−1.14308	−0.571541	−	0.820574i	$-0.693654\pi$
$239$	−5.76591e10	−1.14308	−0.571541	+	0.820574i	$0.693654\pi$
$240$	−3.29756e9	−0.0641567
$241$	9.93359e10	1.89684	0.948418	−	0.317024i	$-0.102683\pi$
$241$	9.93359e10	1.89684	0.948418	+	0.317024i	$0.102683\pi$
$242$	5.71449e10	1.07105
$243$	4.65688e10	0.856776
$244$	−1.93126e10	−0.348808
$245$	9.06064e9	0.160661
$246$	4.86033e10	0.846170
$247$	0	0
$248$	−6.92413e9	−0.116234
$249$	3.66220e10	0.603733
$250$	2.90861e10	0.470928
$251$	−7.09479e10	−1.12826	−0.564129	−	0.825687i	$-0.690788\pi$
$251$	−7.09479e10	−1.12826	−0.564129	+	0.825687i	$0.690788\pi$
$252$	1.13443e10	0.177205
$253$	−9.09686e9	−0.139588
$254$	5.78501e10	0.872072
$255$	−3.36710e9	−0.0498684
$256$	4.29497e9	0.0625000
$257$	3.64522e10	0.521225	0.260612	−	0.965444i	$-0.416076\pi$
$257$	3.64522e10	0.521225	0.260612	+	0.965444i	$0.416076\pi$
$258$	1.54154e10	0.216604
$259$	1.15854e10	0.159979
$260$	0	0
$261$	−8.72987e9	−0.116446
$262$	−5.53399e10	−0.725575
$263$	9.72635e10	1.25357	0.626785	−	0.779192i	$-0.284370\pi$
$263$	9.72635e10	1.25357	0.626785	+	0.779192i	$0.284370\pi$
$264$	−3.19475e10	−0.404780
$265$	−2.35430e10	−0.293261
$266$	−7.51595e10	−0.920484
$267$	6.79182e10	0.817872
$268$	−1.36877e10	−0.162078
$269$	−7.28970e10	−0.848837	−0.424418	−	0.905466i	$-0.639521\pi$
$269$	−7.28970e10	−0.848837	−0.424418	+	0.905466i	$0.639521\pi$
$270$	2.34326e10	0.268338
$271$	1.47255e11	1.65847	0.829235	−	0.558900i	$-0.188776\pi$
$271$	1.47255e11	1.65847	0.829235	+	0.558900i	$0.188776\pi$
$272$	4.38554e9	0.0485806
$273$	0	0
$274$	−4.64301e10	−0.497648
$275$	1.31395e11	1.38542
$276$	3.06330e9	0.0317760
$277$	−7.41672e10	−0.756926	−0.378463	−	0.925617i	$-0.623547\pi$
$277$	−7.41672e10	−0.756926	−0.378463	+	0.925617i	$0.623547\pi$
$278$	−9.25411e9	−0.0929252
$279$	1.59297e10	0.157395
$280$	9.56841e9	0.0930312
$281$	1.17698e11	1.12614	0.563068	−	0.826410i	$-0.309621\pi$
$281$	1.17698e11	1.12614	0.563068	+	0.826410i	$0.309621\pi$
$282$	1.04856e11	0.987348
$283$	−2.40423e10	−0.222811	−0.111406	−	0.993775i	$-0.535535\pi$
$283$	−2.40423e10	−0.222811	−0.111406	+	0.993775i	$0.535535\pi$
$284$	6.79876e10	0.620150
$285$	−5.02623e10	−0.451274
$286$	0	0
$287$	−1.41031e11	−1.22700
$288$	−9.88106e9	−0.0846325
$289$	−1.14110e11	−0.962239
$290$	−7.36325e9	−0.0611334
$291$	−1.24230e11	−1.01556
$292$	−5.62939e9	−0.0453147
$293$	1.54985e11	1.22853	0.614264	−	0.789101i	$-0.289453\pi$
$293$	1.54985e11	1.22853	0.614264	+	0.789101i	$0.289453\pi$
$294$	−2.95597e10	−0.230748
$295$	−3.26740e10	−0.251191
$296$	−1.00911e10	−0.0764055
$297$	2.27020e11	1.69301
$298$	−2.36584e10	−0.173785
$299$	0	0
$300$	−4.42463e10	−0.315378
$301$	−4.47303e10	−0.314089
$302$	−1.75369e11	−1.21317
$303$	8.51727e10	0.580509
$304$	6.54650e10	0.439621
$305$	3.74754e10	0.247969
$306$	−1.00894e10	−0.0657840
$307$	9.17019e10	0.589191	0.294595	−	0.955622i	$-0.404815\pi$
$307$	9.17019e10	0.589191	0.294595	+	0.955622i	$0.404815\pi$
$308$	9.27008e10	0.586956
$309$	1.43924e11	0.898088
$310$	1.34360e10	0.0826310
$311$	1.15680e11	0.701190	0.350595	−	0.936527i	$-0.385979\pi$
$311$	1.15680e11	0.701190	0.350595	+	0.936527i	$0.385979\pi$
$312$	0	0
$313$	−1.79916e11	−1.05954	−0.529772	−	0.848140i	$-0.677723\pi$
$313$	−1.79916e11	−1.05954	−0.529772	+	0.848140i	$0.677723\pi$
$314$	7.59578e10	0.440950
$315$	−2.20132e10	−0.125975
$316$	−6.11788e9	−0.0345151
$317$	−2.85448e11	−1.58767	−0.793836	−	0.608133i	$-0.791919\pi$
$317$	−2.85448e11	−1.58767	−0.793836	+	0.608133i	$0.791919\pi$
$318$	7.68073e10	0.421192
$319$	−7.13367e10	−0.385705
$320$	−8.33423e9	−0.0444315
$321$	4.09883e10	0.215470
$322$	−8.88867e9	−0.0460771
$323$	6.68456e10	0.341713
$324$	−2.89645e10	−0.146020
$325$	0	0
$326$	1.15640e11	0.567059
$327$	9.31629e10	0.450586
$328$	1.22840e11	0.586012
$329$	−3.04256e11	−1.43172
$330$	6.19929e10	0.287759
$331$	−5.37068e10	−0.245925	−0.122963	−	0.992411i	$-0.539240\pi$
$331$	−5.37068e10	−0.245925	−0.122963	+	0.992411i	$0.539240\pi$
$332$	9.25582e10	0.418113
$333$	2.32157e10	0.103462
$334$	−2.56824e11	−1.12921
$335$	2.65605e10	0.115222
$336$	−3.12163e10	−0.133615
$337$	−1.31238e11	−0.554276	−0.277138	−	0.960830i	$-0.589386\pi$
$337$	−1.31238e11	−0.554276	−0.277138	+	0.960830i	$0.589386\pi$
$338$	0	0
$339$	−2.56663e11	−1.05551
$340$	−8.50999e9	−0.0345361
$341$	1.30171e11	0.521338
$342$	−1.50610e11	−0.595299
$343$	2.75538e11	1.07487
$344$	3.89608e10	0.150008
$345$	−5.94422e9	−0.0225896
$346$	−2.12557e11	−0.797321
$347$	1.86715e11	0.691346	0.345673	−	0.938355i	$-0.387651\pi$
$347$	1.86715e11	0.691346	0.345673	+	0.938355i	$0.387651\pi$
$348$	2.40221e10	0.0878020
$349$	−4.23843e11	−1.52929	−0.764646	−	0.644450i	$-0.777086\pi$
$349$	−4.23843e11	−1.52929	−0.764646	+	0.644450i	$0.777086\pi$
$350$	1.28388e11	0.457317
$351$	0	0
$352$	−8.07438e10	−0.280328
$353$	−1.80107e11	−0.617370	−0.308685	−	0.951164i	$-0.599889\pi$
$353$	−1.80107e11	−0.617370	−0.308685	+	0.951164i	$0.599889\pi$
$354$	1.06597e11	0.360769
$355$	−1.31927e11	−0.440867
$356$	1.71656e11	0.566414
$357$	−3.18746e10	−0.103858
$358$	3.45139e11	1.11050
$359$	1.96595e11	0.624666	0.312333	−	0.949973i	$-0.398889\pi$
$359$	1.96595e11	0.624666	0.312333	+	0.949973i	$0.398889\pi$
$360$	1.91738e10	0.0601655
$361$	6.75147e11	2.09226
$362$	2.70461e11	0.827783
$363$	3.61763e11	1.09357
$364$	0	0
$365$	1.09236e10	0.0322144
$366$	−1.22261e11	−0.356141
$367$	6.62820e10	0.190721	0.0953605	−	0.995443i	$-0.469600\pi$
$367$	6.62820e10	0.190721	0.0953605	+	0.995443i	$0.469600\pi$
$368$	7.74217e9	0.0220063
$369$	−2.82607e11	−0.793530
$370$	1.95814e10	0.0543169
$371$	−2.22869e11	−0.610755
$372$	−4.38341e10	−0.118678
$373$	3.50337e11	0.937122	0.468561	−	0.883431i	$-0.344773\pi$
$373$	3.50337e11	0.937122	0.468561	+	0.883431i	$0.344773\pi$
$374$	−8.24466e10	−0.217897
$375$	1.84133e11	0.480830
$376$	2.65011e11	0.683784
$377$	0	0
$378$	2.21824e11	0.558850
$379$	6.46678e11	1.60995	0.804974	−	0.593311i	$-0.202179\pi$
$379$	6.46678e11	1.60995	0.804974	+	0.593311i	$0.202179\pi$
$380$	−1.27033e11	−0.312528
$381$	3.66228e11	0.890407
$382$	1.05598e11	0.253729
$383$	3.89455e11	0.924832	0.462416	−	0.886663i	$-0.346983\pi$
$383$	3.89455e11	0.924832	0.462416	+	0.886663i	$0.346983\pi$
$384$	2.71899e10	0.0638141
$385$	−1.79883e11	−0.417269
$386$	5.65989e11	1.29767
$387$	−8.96336e10	−0.203129
$388$	−3.13977e11	−0.703324
$389$	−1.09573e11	−0.242622	−0.121311	−	0.992615i	$-0.538710\pi$
$389$	−1.09573e11	−0.242622	−0.121311	+	0.992615i	$0.538710\pi$
$390$	0	0
$391$	7.90544e9	0.0171053
$392$	−7.47091e10	−0.159803
$393$	−3.50336e11	−0.740830
$394$	3.69674e11	0.772833
$395$	1.18715e10	0.0245369
$396$	1.85760e11	0.379598
$397$	−6.77015e11	−1.36786	−0.683929	−	0.729548i	$-0.739730\pi$
$397$	−6.77015e11	−1.36786	−0.683929	+	0.729548i	$0.739730\pi$
$398$	−4.80826e11	−0.960538
$399$	−4.75807e11	−0.939838
$400$	−1.11828e11	−0.218414
$401$	7.84448e10	0.151501	0.0757504	−	0.997127i	$-0.475865\pi$
$401$	7.84448e10	0.151501	0.0757504	+	0.997127i	$0.475865\pi$
$402$	−8.66518e10	−0.165486
$403$	0	0
$404$	2.15265e11	0.402029
$405$	5.62046e10	0.103806
$406$	−6.97041e10	−0.127318
$407$	1.89708e11	0.342698
$408$	2.77633e10	0.0496021
$409$	6.73620e11	1.19031	0.595155	−	0.803611i	$-0.297091\pi$
$409$	6.73620e11	1.19031	0.595155	+	0.803611i	$0.297091\pi$
$410$	−2.38366e11	−0.416598
$411$	−2.93932e11	−0.508111
$412$	3.63752e11	0.621967
$413$	−3.09308e11	−0.523138
$414$	−1.78117e10	−0.0297992
$415$	−1.79606e11	−0.297238
$416$	0	0
$417$	−5.85844e10	−0.0948789
$418$	−1.23072e12	−1.97181
$419$	4.42161e11	0.700837	0.350419	−	0.936593i	$-0.386039\pi$
$419$	4.42161e11	0.700837	0.350419	+	0.936593i	$0.386039\pi$
$420$	6.05741e10	0.0949872
$421$	6.78641e11	1.05286	0.526430	−	0.850218i	$-0.323530\pi$
$421$	6.78641e11	1.05286	0.526430	+	0.850218i	$0.323530\pi$
$422$	−6.85695e11	−1.05251
$423$	−6.09688e11	−0.925926
$424$	1.94122e11	0.291695
$425$	−1.14186e11	−0.169771
$426$	4.30404e11	0.633189
$427$	3.54760e11	0.516427
$428$	1.03594e11	0.149223
$429$	0	0
$430$	−7.56020e10	−0.106641
$431$	−9.44035e11	−1.31777	−0.658886	−	0.752243i	$-0.728972\pi$
$431$	−9.44035e11	−1.31777	−0.658886	+	0.752243i	$0.728972\pi$
$432$	−1.93212e11	−0.266905
$433$	−5.80138e11	−0.793114	−0.396557	−	0.918010i	$-0.629795\pi$
$433$	−5.80138e11	−0.793114	−0.396557	+	0.918010i	$0.629795\pi$
$434$	1.27192e11	0.172090
$435$	−4.66140e10	−0.0624188
$436$	2.35459e11	0.312052
$437$	1.18008e11	0.154791
$438$	−3.56376e10	−0.0462674
$439$	4.59761e11	0.590801	0.295401	−	0.955373i	$-0.404547\pi$
$439$	4.59761e11	0.590801	0.295401	+	0.955373i	$0.404547\pi$
$440$	1.56680e11	0.199286
$441$	1.71877e11	0.216393
$442$	0	0
$443$	8.88513e11	1.09609	0.548046	−	0.836448i	$-0.315372\pi$
$443$	8.88513e11	1.09609	0.548046	+	0.836448i	$0.315372\pi$
$444$	−6.38829e10	−0.0780120
$445$	−3.33092e11	−0.402665
$446$	5.08371e11	0.608379
$447$	−1.49772e11	−0.177439
$448$	−7.88959e10	−0.0925344
$449$	2.23151e11	0.259114	0.129557	−	0.991572i	$-0.458645\pi$
$449$	2.23151e11	0.259114	0.129557	+	0.991572i	$0.458645\pi$
$450$	2.57272e11	0.295758
$451$	−2.30934e12	−2.62841
$452$	−6.48688e11	−0.730992
$453$	−1.11020e12	−1.23868
$454$	−1.13803e11	−0.125720
$455$	0	0
$456$	4.14435e11	0.448864
$457$	1.56152e12	1.67466	0.837328	−	0.546701i	$-0.184117\pi$
$457$	1.56152e12	1.67466	0.837328	+	0.546701i	$0.184117\pi$
$458$	5.43368e11	0.577031
$459$	−1.97287e11	−0.207463
$460$	−1.50234e10	−0.0156444
$461$	−4.99833e11	−0.515432	−0.257716	−	0.966221i	$-0.582970\pi$
$461$	−4.99833e11	−0.515432	−0.257716	+	0.966221i	$0.582970\pi$
$462$	5.86855e11	0.599297
$463$	9.34281e11	0.944850	0.472425	−	0.881371i	$-0.343379\pi$
$463$	9.34281e11	0.944850	0.472425	+	0.881371i	$0.343379\pi$
$464$	6.07133e10	0.0608069
$465$	8.50585e10	0.0843684
$466$	3.31339e11	0.325489
$467$	−5.01006e11	−0.487435	−0.243717	−	0.969846i	$-0.578367\pi$
$467$	−5.01006e11	−0.487435	−0.243717	+	0.969846i	$0.578367\pi$
$468$	0	0
$469$	2.51435e11	0.239965
$470$	−5.14245e11	−0.486104
$471$	4.80861e11	0.450221
$472$	2.69412e11	0.249849
$473$	−7.32448e11	−0.672824
$474$	−3.87301e10	−0.0352408
$475$	−1.70451e12	−1.53631
$476$	−8.05597e10	−0.0719261
$477$	−4.46600e11	−0.394990
$478$	−9.22546e11	−0.808281
$479$	−1.95563e12	−1.69737	−0.848686	−	0.528897i	$-0.822606\pi$
$479$	−1.95563e12	−1.69737	−0.848686	+	0.528897i	$0.822606\pi$
$480$	−5.27609e10	−0.0453656
$481$	0	0
$482$	1.58937e12	1.34127
$483$	−5.62709e10	−0.0470459
$484$	9.14318e11	0.757344
$485$	6.09262e11	0.499996
$486$	7.45101e11	0.605832
$487$	−1.11907e12	−0.901523	−0.450762	−	0.892644i	$-0.648848\pi$
$487$	−1.11907e12	−0.901523	−0.450762	+	0.892644i	$0.648848\pi$
$488$	−3.09001e11	−0.246644
$489$	7.32073e11	0.578982
$490$	1.44970e11	0.113605
$491$	−5.24548e11	−0.407304	−0.203652	−	0.979043i	$-0.565281\pi$
$491$	−5.24548e11	−0.407304	−0.203652	+	0.979043i	$0.565281\pi$
$492$	7.77653e11	0.598333
$493$	6.19937e10	0.0472646
$494$	0	0
$495$	−3.60461e11	−0.269858
$496$	−1.10786e11	−0.0821898
$497$	−1.24889e12	−0.918164
$498$	5.85952e11	0.426904
$499$	4.23413e11	0.305712	0.152856	−	0.988248i	$-0.451153\pi$
$499$	4.23413e11	0.305712	0.152856	+	0.988248i	$0.451153\pi$
$500$	4.65377e11	0.332997
$501$	−1.62586e12	−1.15296
$502$	−1.13517e12	−0.797798
$503$	−1.16252e12	−0.809736	−0.404868	−	0.914375i	$-0.632683\pi$
$503$	−1.16252e12	−0.809736	−0.404868	+	0.914375i	$0.632683\pi$
$504$	1.81509e11	0.125303
$505$	−4.17714e11	−0.285804
$506$	−1.45550e11	−0.0987039
$507$	0	0
$508$	9.25601e11	0.616648
$509$	5.37636e11	0.355025	0.177512	−	0.984119i	$-0.443195\pi$
$509$	5.37636e11	0.355025	0.177512	+	0.984119i	$0.443195\pi$
$510$	−5.38736e10	−0.0352623
$511$	1.03408e11	0.0670907
$512$	6.87195e10	0.0441942
$513$	−2.94499e12	−1.87739
$514$	5.83236e11	0.368561
$515$	−7.05847e11	−0.442158
$516$	2.46646e11	0.153162
$517$	−4.98211e12	−3.06695
$518$	1.85367e11	0.113122
$519$	−1.34562e12	−0.814085
$520$	0	0
$521$	−1.67587e12	−0.996486	−0.498243	−	0.867037i	$-0.666021\pi$
$521$	−1.67587e12	−0.996486	−0.498243	+	0.867037i	$0.666021\pi$
$522$	−1.39678e11	−0.0823399
$523$	−1.18623e12	−0.693285	−0.346643	−	0.937997i	$-0.612678\pi$
$523$	−1.18623e12	−0.693285	−0.346643	+	0.937997i	$0.612678\pi$
$524$	−8.85438e11	−0.513059
$525$	8.12776e11	0.466933
$526$	1.55622e12	0.886408
$527$	−1.13122e11	−0.0638853
$528$	−5.11159e11	−0.286222
$529$	−1.78720e12	−0.992252
$530$	−3.76687e11	−0.207367
$531$	−6.19813e11	−0.338326
$532$	−1.20255e12	−0.650881
$533$	0	0
$534$	1.08669e12	0.578323
$535$	−2.01020e11	−0.106083
$536$	−2.19003e11	−0.114606
$537$	2.18495e12	1.13385
$538$	−1.16635e12	−0.600218
$539$	1.40450e12	0.716759
$540$	3.74921e11	0.189744
$541$	3.39486e11	0.170386	0.0851932	−	0.996364i	$-0.472849\pi$
$541$	3.39486e11	0.170386	0.0851932	+	0.996364i	$0.472849\pi$
$542$	2.35608e12	1.17272
$543$	1.71219e12	0.845187
$544$	7.01687e10	0.0343517
$545$	−4.56900e11	−0.221839
$546$	0	0
$547$	2.09386e12	1.00001	0.500006	−	0.866022i	$-0.333331\pi$
$547$	2.09386e12	1.00001	0.500006	+	0.866022i	$0.333331\pi$
$548$	−7.42882e11	−0.351890
$549$	7.10892e11	0.333986
$550$	2.10232e12	0.979640
$551$	9.25408e11	0.427712
$552$	4.90128e10	0.0224690
$553$	1.12382e11	0.0511013
$554$	−1.18668e12	−0.535227
$555$	1.23962e11	0.0554590
$556$	−1.48066e11	−0.0657080
$557$	−4.22682e12	−1.86065	−0.930327	−	0.366732i	$-0.880477\pi$
$557$	−4.22682e12	−1.86065	−0.930327	+	0.366732i	$0.880477\pi$
$558$	2.54876e11	0.111295
$559$	0	0
$560$	1.53095e11	0.0657830
$561$	−5.21939e11	−0.222478
$562$	1.88317e12	0.796299
$563$	1.42927e12	0.599552	0.299776	−	0.954010i	$-0.403088\pi$
$563$	1.42927e12	0.599552	0.299776	+	0.954010i	$0.403088\pi$
$564$	1.67769e12	0.698161
$565$	1.25875e12	0.519665
$566$	−3.84677e11	−0.157551
$567$	5.32060e11	0.216191
$568$	1.08780e12	0.438513
$569$	−1.13224e12	−0.452826	−0.226413	−	0.974031i	$-0.572700\pi$
$569$	−1.13224e12	−0.452826	−0.226413	+	0.974031i	$0.572700\pi$
$570$	−8.04196e11	−0.319099
$571$	−2.72935e11	−0.107448	−0.0537238	−	0.998556i	$-0.517109\pi$
$571$	−2.72935e11	−0.107448	−0.0537238	+	0.998556i	$0.517109\pi$
$572$	0	0
$573$	6.68502e11	0.259064
$574$	−2.25649e12	−0.867620
$575$	−2.01582e11	−0.0769036
$576$	−1.58097e11	−0.0598442
$577$	−3.68253e12	−1.38311	−0.691553	−	0.722326i	$-0.743073\pi$
$577$	−3.68253e12	−1.38311	−0.691553	+	0.722326i	$0.743073\pi$
$578$	−1.82576e12	−0.680406
$579$	3.58307e12	1.32496
$580$	−1.17812e11	−0.0432279
$581$	−1.70024e12	−0.619038
$582$	−1.98768e12	−0.718112
$583$	−3.64943e12	−1.30833
$584$	−9.00703e10	−0.0320423
$585$	0	0
$586$	2.47976e12	0.868700
$587$	3.73912e12	1.29986	0.649932	−	0.759992i	$-0.274797\pi$
$587$	3.73912e12	1.29986	0.649932	+	0.759992i	$0.274797\pi$
$588$	−4.72956e11	−0.163163
$589$	−1.68863e12	−0.578117
$590$	−5.22785e11	−0.177619
$591$	2.34027e12	0.789082
$592$	−1.61457e11	−0.0540269
$593$	3.36951e11	0.111898	0.0559488	−	0.998434i	$-0.482182\pi$
$593$	3.36951e11	0.111898	0.0559488	+	0.998434i	$0.482182\pi$
$594$	3.63231e12	1.19714
$595$	1.56323e11	0.0511325
$596$	−3.78534e11	−0.122884
$597$	−3.04393e12	−0.980733
$598$	0	0
$599$	−2.35939e12	−0.748823	−0.374412	−	0.927263i	$-0.622155\pi$
$599$	−2.35939e12	−0.748823	−0.374412	+	0.927263i	$0.622155\pi$
$600$	−7.07940e11	−0.223006
$601$	2.73229e12	0.854264	0.427132	−	0.904189i	$-0.359524\pi$
$601$	2.73229e12	0.854264	0.427132	+	0.904189i	$0.359524\pi$
$602$	−7.15685e11	−0.222094
$603$	5.03842e11	0.155191
$604$	−2.80590e12	−0.857840
$605$	−1.77420e12	−0.538399
$606$	1.36276e12	0.410482
$607$	1.41433e12	0.422866	0.211433	−	0.977392i	$-0.432187\pi$
$607$	1.41433e12	0.422866	0.211433	+	0.977392i	$0.432187\pi$
$608$	1.04744e12	0.310859
$609$	−4.41271e11	−0.129995
$610$	5.99606e11	0.175340
$611$	0	0
$612$	−1.61431e11	−0.0465163
$613$	4.58402e12	1.31122	0.655608	−	0.755101i	$-0.272412\pi$
$613$	4.58402e12	1.31122	0.655608	+	0.755101i	$0.272412\pi$
$614$	1.46723e12	0.416621
$615$	−1.50901e12	−0.425357
$616$	1.48321e12	0.415040
$617$	−3.76391e12	−1.04558	−0.522788	−	0.852463i	$-0.675108\pi$
$617$	−3.76391e12	−1.04558	−0.522788	+	0.852463i	$0.675108\pi$
$618$	2.30278e12	0.635044
$619$	−4.45737e12	−1.22031	−0.610156	−	0.792281i	$-0.708893\pi$
$619$	−4.45737e12	−1.22031	−0.610156	+	0.792281i	$0.708893\pi$
$620$	2.14976e11	0.0584290
$621$	−3.48287e11	−0.0939777
$622$	1.85088e12	0.495817
$623$	−3.15321e12	−0.838604
$624$	0	0
$625$	2.42968e12	0.636926
$626$	−2.87865e12	−0.749211
$627$	−7.79122e12	−2.01327
$628$	1.21532e12	0.311798
$629$	−1.64862e11	−0.0419945
$630$	−3.52212e11	−0.0890781
$631$	−7.09673e12	−1.78208	−0.891038	−	0.453928i	$-0.850022\pi$
$631$	−7.09673e12	−1.78208	−0.891038	+	0.453928i	$0.850022\pi$
$632$	−9.78861e10	−0.0244059
$633$	−4.34088e12	−1.07464
$634$	−4.56717e12	−1.12265
$635$	−1.79610e12	−0.438377
$636$	1.22892e12	0.297828
$637$	0	0
$638$	−1.14139e12	−0.272735
$639$	−2.50261e12	−0.593799
$640$	−1.33348e11	−0.0314178
$641$	−3.91333e12	−0.915556	−0.457778	−	0.889066i	$-0.651355\pi$
$641$	−3.91333e12	−0.915556	−0.457778	+	0.889066i	$0.651355\pi$
$642$	6.55813e11	0.152360
$643$	1.96199e12	0.452634	0.226317	−	0.974054i	$-0.427332\pi$
$643$	1.96199e12	0.452634	0.226317	+	0.974054i	$0.427332\pi$
$644$	−1.42219e11	−0.0325815
$645$	−4.78608e11	−0.108883
$646$	1.06953e12	0.241628
$647$	−2.05456e12	−0.460946	−0.230473	−	0.973079i	$-0.574027\pi$
$647$	−2.05456e12	−0.460946	−0.230473	+	0.973079i	$0.574027\pi$
$648$	−4.63432e11	−0.103252
$649$	−5.06485e12	−1.12064
$650$	0	0
$651$	8.05206e11	0.175708
$652$	1.85024e12	0.400971
$653$	−1.86912e12	−0.402280	−0.201140	−	0.979563i	$-0.564465\pi$
$653$	−1.86912e12	−0.402280	−0.201140	+	0.979563i	$0.564465\pi$
$654$	1.49061e12	0.318613
$655$	1.71816e12	0.364735
$656$	1.96543e12	0.414373
$657$	2.07217e11	0.0433891
$658$	−4.86809e12	−1.01238
$659$	−6.92414e10	−0.0143015	−0.00715074	−	0.999974i	$-0.502276\pi$
$659$	−6.92414e10	−0.0143015	−0.00715074	+	0.999974i	$0.502276\pi$
$660$	9.91886e11	0.203476
$661$	3.41365e12	0.695525	0.347762	−	0.937583i	$-0.386942\pi$
$661$	3.41365e12	0.695525	0.347762	+	0.937583i	$0.386942\pi$
$662$	−8.59308e11	−0.173895
$663$	0	0
$664$	1.48093e12	0.295651
$665$	2.33351e12	0.462713
$666$	3.71451e11	0.0731589
$667$	1.09443e11	0.0214102
$668$	−4.10918e12	−0.798475
$669$	3.21831e12	0.621170
$670$	4.24968e11	0.0814741
$671$	5.80911e12	1.10626
$672$	−4.99461e11	−0.0944800
$673$	1.00166e13	1.88214	0.941072	−	0.338208i	$-0.109821\pi$
$673$	1.00166e13	1.88214	0.941072	+	0.338208i	$0.109821\pi$
$674$	−2.09981e12	−0.391932
$675$	5.03065e12	0.932732
$676$	0	0
$677$	−1.04118e13	−1.90492	−0.952458	−	0.304669i	$-0.901454\pi$
$677$	−1.04118e13	−1.90492	−0.952458	+	0.304669i	$0.901454\pi$
$678$	−4.10660e12	−0.746361
$679$	5.76757e12	1.04131
$680$	−1.36160e11	−0.0244207
$681$	−7.20446e11	−0.128363
$682$	2.08274e12	0.368642
$683$	−9.64615e12	−1.69614	−0.848069	−	0.529886i	$-0.822235\pi$
$683$	−9.64615e12	−1.69614	−0.848069	+	0.529886i	$0.822235\pi$
$684$	−2.40975e12	−0.420940
$685$	1.44154e12	0.250160
$686$	4.40860e12	0.760051
$687$	3.43986e12	0.589164
$688$	6.23372e11	0.106072
$689$	0	0
$690$	−9.51076e10	−0.0159733
$691$	−3.06746e12	−0.511832	−0.255916	−	0.966699i	$-0.582377\pi$
$691$	−3.06746e12	−0.511832	−0.255916	+	0.966699i	$0.582377\pi$
$692$	−3.40091e12	−0.563791
$693$	−3.41230e12	−0.562015
$694$	2.98743e12	0.488856
$695$	2.87316e11	0.0467120
$696$	3.84354e11	0.0620854
$697$	2.00688e12	0.322088
$698$	−6.78149e12	−1.08137
$699$	2.09759e12	0.332332
$700$	2.05421e12	0.323372
$701$	1.05088e13	1.64370	0.821849	−	0.569705i	$-0.192943\pi$
$701$	1.05088e13	1.64370	0.821849	+	0.569705i	$0.192943\pi$
$702$	0	0
$703$	−2.46097e12	−0.380021
$704$	−1.29190e12	−0.198222
$705$	−3.25549e12	−0.496325
$706$	−2.88172e12	−0.436546
$707$	−3.95429e12	−0.595224
$708$	1.70555e12	0.255102
$709$	9.77052e12	1.45214	0.726072	−	0.687619i	$-0.241344\pi$
$709$	9.77052e12	1.45214	0.726072	+	0.687619i	$0.241344\pi$
$710$	−2.11084e12	−0.311740
$711$	2.25198e11	0.0330485
$712$	2.74649e12	0.400515
$713$	−1.99704e11	−0.0289391
$714$	−5.09994e11	−0.0734384
$715$	0	0
$716$	5.52222e12	0.785245
$717$	−5.84030e12	−0.825275
$718$	3.14552e12	0.441706
$719$	3.18190e12	0.444025	0.222012	−	0.975044i	$-0.428737\pi$
$719$	3.18190e12	0.444025	0.222012	+	0.975044i	$0.428737\pi$
$720$	3.06781e11	0.0425435
$721$	−6.68189e12	−0.920854
$722$	1.08024e13	1.47945
$723$	1.00617e13	1.36947
$724$	4.32738e12	0.585331
$725$	−1.58079e12	−0.212497
$726$	5.78821e12	0.773268
$727$	3.49152e12	0.463565	0.231782	−	0.972768i	$-0.425544\pi$
$727$	3.49152e12	0.463565	0.231782	+	0.972768i	$0.425544\pi$
$728$	0	0
$729$	6.94395e12	0.910611
$730$	1.74778e11	0.0227790
$731$	6.36518e11	0.0824485
$732$	−1.95617e12	−0.251830
$733$	−1.89661e12	−0.242667	−0.121333	−	0.992612i	$-0.538717\pi$
$733$	−1.89661e12	−0.242667	−0.121333	+	0.992612i	$0.538717\pi$
$734$	1.06051e12	0.134860
$735$	9.17754e11	0.115993
$736$	1.23875e11	0.0155608
$737$	4.11718e12	0.514039
$738$	−4.52170e12	−0.561111
$739$	1.42558e13	1.75829	0.879145	−	0.476554i	$-0.158114\pi$
$739$	1.42558e13	1.75829	0.879145	+	0.476554i	$0.158114\pi$
$740$	3.13302e11	0.0384079
$741$	0	0
$742$	−3.56591e12	−0.431869
$743$	8.28027e12	0.996770	0.498385	−	0.866956i	$-0.333927\pi$
$743$	8.28027e12	0.996770	0.498385	+	0.866956i	$0.333927\pi$
$744$	−7.01346e11	−0.0839178
$745$	7.34532e11	0.0873589
$746$	5.60539e12	0.662645
$747$	−3.40705e12	−0.400346
$748$	−1.31914e12	−0.154076
$749$	−1.90295e12	−0.220932
$750$	2.94613e12	0.339998
$751$	1.62220e13	1.86091	0.930456	−	0.366405i	$-0.119411\pi$
$751$	1.62220e13	1.86091	0.930456	+	0.366405i	$0.119411\pi$
$752$	4.24018e12	0.483508
$753$	−7.18633e12	−0.814572
$754$	0	0
$755$	5.44475e12	0.609841
$756$	3.54919e12	0.395167
$757$	1.48658e13	1.64535	0.822674	−	0.568514i	$-0.192481\pi$
$757$	1.48658e13	1.64535	0.822674	+	0.568514i	$0.192481\pi$
$758$	1.03468e13	1.13840
$759$	−9.21423e11	−0.100779
$760$	−2.03252e12	−0.220991
$761$	−3.76818e12	−0.407287	−0.203644	−	0.979045i	$-0.565278\pi$
$761$	−3.76818e12	−0.407287	−0.203644	+	0.979045i	$0.565278\pi$
$762$	5.85964e12	0.629613
$763$	−4.32524e12	−0.462008
$764$	1.68957e12	0.179414
$765$	3.13251e11	0.0330686
$766$	6.23128e12	0.653955
$767$	0	0
$768$	4.35038e11	0.0451234
$769$	5.13616e12	0.529627	0.264814	−	0.964300i	$-0.414690\pi$
$769$	5.13616e12	0.529627	0.264814	+	0.964300i	$0.414690\pi$
$770$	−2.87812e12	−0.295054
$771$	3.69225e12	0.376311
$772$	9.05582e12	0.917593
$773$	1.14329e13	1.15172	0.575861	−	0.817548i	$-0.304667\pi$
$773$	1.14329e13	1.15172	0.575861	+	0.817548i	$0.304667\pi$
$774$	−1.43414e12	−0.143634
$775$	2.88453e12	0.287222
$776$	−5.02364e12	−0.497325
$777$	1.17349e12	0.115501
$778$	−1.75317e12	−0.171560
$779$	2.99577e13	2.91467
$780$	0	0
$781$	−2.04503e13	−1.96684
$782$	1.26487e11	0.0120953
$783$	−2.73123e12	−0.259675
$784$	−1.19535e12	−0.112998
$785$	−2.35829e12	−0.221659
$786$	−5.60538e12	−0.523846
$787$	2.50726e12	0.232977	0.116488	−	0.993192i	$-0.462836\pi$
$787$	2.50726e12	0.232977	0.116488	+	0.993192i	$0.462836\pi$
$788$	5.91478e12	0.546476
$789$	9.85183e12	0.905045
$790$	1.89944e11	0.0173502
$791$	1.19160e13	1.08227
$792$	2.97216e12	0.268417
$793$	0	0
$794$	−1.08322e13	−0.967222
$795$	−2.38467e12	−0.211727
$796$	−7.69322e12	−0.679203
$797$	−8.66588e12	−0.760764	−0.380382	−	0.924829i	$-0.624208\pi$
$797$	−8.66588e12	−0.760764	−0.380382	+	0.924829i	$0.624208\pi$
$798$	−7.61291e12	−0.664566
$799$	4.32960e12	0.375826
$800$	−1.78924e12	−0.154442
$801$	−6.31862e12	−0.542345
$802$	1.25512e12	0.107127
$803$	1.69329e12	0.143718
$804$	−1.38643e12	−0.117016
$805$	2.75970e11	0.0231623
$806$	0	0
$807$	−7.38374e12	−0.612838
$808$	3.44424e12	0.284277
$809$	2.35307e12	0.193137	0.0965686	−	0.995326i	$-0.469213\pi$
$809$	2.35307e12	0.193137	0.0965686	+	0.995326i	$0.469213\pi$
$810$	8.99274e11	0.0734022
$811$	−3.27323e12	−0.265695	−0.132847	−	0.991137i	$-0.542412\pi$
$811$	−3.27323e12	−0.265695	−0.132847	+	0.991137i	$0.542412\pi$
$812$	−1.11527e12	−0.0900278
$813$	1.49155e13	1.19737
$814$	3.03533e12	0.242324
$815$	−3.59032e12	−0.285052
$816$	4.44212e11	0.0350740
$817$	9.50160e12	0.746101
$818$	1.07779e13	0.841676
$819$	0	0
$820$	−3.81385e12	−0.294579
$821$	1.17584e13	0.903244	0.451622	−	0.892209i	$-0.350846\pi$
$821$	1.17584e13	0.903244	0.451622	+	0.892209i	$0.350846\pi$
$822$	−4.70291e12	−0.359289
$823$	−4.19155e12	−0.318475	−0.159238	−	0.987240i	$-0.550904\pi$
$823$	−4.19155e12	−0.318475	−0.159238	+	0.987240i	$0.550904\pi$
$824$	5.82002e12	0.439797
$825$	1.33090e13	1.00024
$826$	−4.94893e12	−0.369915
$827$	−7.54455e12	−0.560866	−0.280433	−	0.959874i	$-0.590478\pi$
$827$	−7.54455e12	−0.560866	−0.280433	+	0.959874i	$0.590478\pi$
$828$	−2.84988e11	−0.0210712
$829$	−6.79874e12	−0.499958	−0.249979	−	0.968251i	$-0.580424\pi$
$829$	−6.79874e12	−0.499958	−0.249979	+	0.968251i	$0.580424\pi$
$830$	−2.87370e12	−0.210179
$831$	−7.51241e12	−0.546480
$832$	0	0
$833$	−1.22055e12	−0.0878323
$834$	−9.37350e11	−0.0670895
$835$	7.97372e12	0.567638
$836$	−1.96915e13	−1.39428
$837$	4.98379e12	0.350990
$838$	7.07457e12	0.495567
$839$	7.28219e12	0.507380	0.253690	−	0.967286i	$-0.418356\pi$
$839$	7.28219e12	0.507380	0.253690	+	0.967286i	$0.418356\pi$
$840$	9.69186e11	0.0671661
$841$	−1.36489e13	−0.940840
$842$	1.08583e13	0.744485
$843$	1.19217e13	0.813041
$844$	−1.09711e13	−0.744234
$845$	0	0
$846$	−9.75501e12	−0.654728
$847$	−1.67955e13	−1.12129
$848$	3.10596e12	0.206259
$849$	−2.43525e12	−0.160864
$850$	−1.82698e12	−0.120046
$851$	−2.91045e11	−0.0190229
$852$	6.88647e12	0.447732
$853$	1.07546e13	0.695544	0.347772	−	0.937579i	$-0.386938\pi$
$853$	1.07546e13	0.695544	0.347772	+	0.937579i	$0.386938\pi$
$854$	5.67616e12	0.365169
$855$	4.67604e12	0.299248
$856$	1.65750e12	0.105517
$857$	−1.46070e13	−0.925010	−0.462505	−	0.886617i	$-0.653049\pi$
$857$	−1.46070e13	−0.925010	−0.462505	+	0.886617i	$0.653049\pi$
$858$	0	0
$859$	−2.51984e13	−1.57908	−0.789541	−	0.613698i	$-0.789681\pi$
$859$	−2.51984e13	−1.57908	−0.789541	+	0.613698i	$0.789681\pi$
$860$	−1.20963e12	−0.0754067
$861$	−1.42850e13	−0.885862
$862$	−1.51046e13	−0.931806
$863$	7.53859e12	0.462639	0.231319	−	0.972878i	$-0.425696\pi$
$863$	7.53859e12	0.462639	0.231319	+	0.972878i	$0.425696\pi$
$864$	−3.09139e12	−0.188731
$865$	6.59935e12	0.400801
$866$	−9.28220e12	−0.560816
$867$	−1.15582e13	−0.694711
$868$	2.03507e12	0.121686
$869$	1.84022e12	0.109466
$870$	−7.45825e11	−0.0441367
$871$	0	0
$872$	3.76735e12	0.220654
$873$	1.15575e13	0.673439
$874$	1.88813e12	0.109454
$875$	−8.54869e12	−0.493019
$876$	−5.70202e11	−0.0327160
$877$	−1.14927e13	−0.656031	−0.328016	−	0.944672i	$-0.606380\pi$
$877$	−1.14927e13	−0.656031	−0.328016	+	0.944672i	$0.606380\pi$
$878$	7.35617e12	0.417760
$879$	1.56984e13	0.886965
$880$	2.50689e12	0.140917
$881$	5.66962e12	0.317075	0.158538	−	0.987353i	$-0.449322\pi$
$881$	5.66962e12	0.317075	0.158538	+	0.987353i	$0.449322\pi$
$882$	2.75003e12	0.153013
$883$	7.46294e12	0.413130	0.206565	−	0.978433i	$-0.433771\pi$
$883$	7.46294e12	0.413130	0.206565	+	0.978433i	$0.433771\pi$
$884$	0	0
$885$	−3.30956e12	−0.181353
$886$	1.42162e13	0.775054
$887$	1.84813e13	1.00248	0.501241	−	0.865308i	$-0.332877\pi$
$887$	1.84813e13	1.00248	0.501241	+	0.865308i	$0.332877\pi$
$888$	−1.02213e12	−0.0551628
$889$	−1.70027e13	−0.912979
$890$	−5.32947e12	−0.284727
$891$	8.71235e12	0.463112
$892$	8.13394e12	0.430189
$893$	6.46299e13	3.40096
$894$	−2.39636e12	−0.125468
$895$	−1.07157e13	−0.558233
$896$	−1.26233e12	−0.0654317
$897$	0	0
$898$	3.57041e12	0.183221
$899$	−1.56606e12	−0.0799633
$900$	4.11636e12	0.209133
$901$	3.17146e12	0.160323
$902$	−3.69494e13	−1.85857
$903$	−4.53074e12	−0.226764
$904$	−1.03790e13	−0.516889
$905$	−8.39712e12	−0.416113
$906$	−1.77631e13	−0.875876
$907$	−2.57747e13	−1.26462	−0.632311	−	0.774715i	$-0.717893\pi$
$907$	−2.57747e13	−1.26462	−0.632311	+	0.774715i	$0.717893\pi$
$908$	−1.82085e12	−0.0888972
$909$	−7.92387e12	−0.384946
$910$	0	0
$911$	2.01177e13	0.967711	0.483855	−	0.875148i	$-0.339236\pi$
$911$	2.01177e13	0.967711	0.483855	+	0.875148i	$0.339236\pi$
$912$	6.63096e12	0.317395
$913$	−2.78410e13	−1.32607
$914$	2.49844e13	1.18416
$915$	3.79588e12	0.179027
$916$	8.69389e12	0.408023
$917$	1.62649e13	0.759610
$918$	−3.15659e12	−0.146698
$919$	2.82215e13	1.30515	0.652575	−	0.757724i	$-0.273689\pi$
$919$	2.82215e13	1.30515	0.652575	+	0.757724i	$0.273689\pi$
$920$	−2.40374e11	−0.0110622
$921$	9.28850e12	0.425380
$922$	−7.99733e12	−0.364465
$923$	0	0
$924$	9.38968e12	0.423767
$925$	4.20385e12	0.188803
$926$	1.49485e13	0.668110
$927$	−1.33896e13	−0.595538
$928$	9.71413e11	0.0429970
$929$	−1.80531e13	−0.795207	−0.397603	−	0.917557i	$-0.630158\pi$
$929$	−1.80531e13	−0.795207	−0.397603	+	0.917557i	$0.630158\pi$
$930$	1.36094e12	0.0596574
$931$	−1.82198e13	−0.794821
$932$	5.30142e12	0.230155
$933$	1.17172e13	0.506241
$934$	−8.01609e12	−0.344669
$935$	2.55975e12	0.109533
$936$	0	0
$937$	3.60858e13	1.52936	0.764678	−	0.644412i	$-0.222898\pi$
$937$	3.60858e13	1.52936	0.764678	+	0.644412i	$0.222898\pi$
$938$	4.02296e12	0.169681
$939$	−1.82237e13	−0.764964
$940$	−8.22792e12	−0.343728
$941$	−3.72613e12	−0.154919	−0.0774594	−	0.996996i	$-0.524681\pi$
$941$	−3.72613e12	−0.154919	−0.0774594	+	0.996996i	$0.524681\pi$
$942$	7.69377e12	0.318354
$943$	3.54292e12	0.145901
$944$	4.31059e12	0.176670
$945$	−6.88707e12	−0.280925
$946$	−1.17192e13	−0.475758
$947$	−2.97301e13	−1.20122	−0.600609	−	0.799543i	$-0.705075\pi$
$947$	−2.97301e13	−1.20122	−0.600609	+	0.799543i	$0.705075\pi$
$948$	−6.19681e11	−0.0249190
$949$	0	0
$950$	−2.72721e13	−1.08633
$951$	−2.89131e13	−1.14626
$952$	−1.28896e12	−0.0508594
$953$	4.04208e13	1.58740	0.793702	−	0.608307i	$-0.208151\pi$
$953$	4.04208e13	1.58740	0.793702	+	0.608307i	$0.208151\pi$
$954$	−7.14560e12	−0.279300
$955$	−3.27855e12	−0.127546
$956$	−1.47607e13	−0.571541
$957$	−7.22571e12	−0.278469
$958$	−3.12901e13	−1.20022
$959$	1.36463e13	0.520991
$960$	−8.44175e11	−0.0320783
$961$	−2.35820e13	−0.891918
$962$	0	0
$963$	−3.81326e12	−0.142882
$964$	2.54300e13	0.948418
$965$	−1.75725e13	−0.652320
$966$	−9.00335e11	−0.0332665
$967$	6.05671e12	0.222750	0.111375	−	0.993778i	$-0.464475\pi$
$967$	6.05671e12	0.222750	0.111375	+	0.993778i	$0.464475\pi$
$968$	1.46291e13	0.535523
$969$	6.77080e12	0.246708
$970$	9.74819e12	0.353550
$971$	1.65027e13	0.595755	0.297878	−	0.954604i	$-0.403721\pi$
$971$	1.65027e13	0.595755	0.297878	+	0.954604i	$0.403721\pi$
$972$	1.19216e13	0.428388
$973$	2.71988e12	0.0972840
$974$	−1.79051e13	−0.637473
$975$	0	0
$976$	−4.94402e12	−0.174404
$977$	−4.17148e13	−1.46475	−0.732377	−	0.680899i	$-0.761589\pi$
$977$	−4.17148e13	−1.46475	−0.732377	+	0.680899i	$0.761589\pi$
$978$	1.17132e13	0.409402
$979$	−5.16331e13	−1.79641
$980$	2.31952e12	0.0803307
$981$	−8.66721e12	−0.298792
$982$	−8.39277e12	−0.288007
$983$	−2.06209e13	−0.704397	−0.352198	−	0.935925i	$-0.614566\pi$
$983$	−2.06209e13	−0.704397	−0.352198	+	0.935925i	$0.614566\pi$
$984$	1.24424e13	0.423085
$985$	−1.14774e13	−0.388491
$986$	9.91899e11	0.0334211
$987$	−3.08181e13	−1.03366
$988$	0	0
$989$	1.12370e12	0.0373479
$990$	−5.76738e12	−0.190818
$991$	−8.03119e11	−0.0264514	−0.0132257	−	0.999913i	$-0.504210\pi$
$991$	−8.03119e11	−0.0264514	−0.0132257	+	0.999913i	$0.504210\pi$
$992$	−1.77258e12	−0.0581169
$993$	−5.43997e12	−0.177552
$994$	−1.99822e13	−0.649240
$995$	1.49284e13	0.482847
$996$	9.37524e12	0.301867
$997$	−2.93266e13	−0.940011	−0.470005	−	0.882664i	$-0.655748\pi$
$997$	−2.93266e13	−0.940011	−0.470005	+	0.882664i	$0.655748\pi$
$998$	6.77461e12	0.216171
$999$	7.26326e12	0.230721

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	338.10.a.i.1.4		5
13.4	even	6		26.10.c.a.3.2	✓	10
13.10	even	6		26.10.c.a.9.2	yes	10
13.12	even	2		338.10.a.h.1.4		5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
26.10.c.a.3.2	✓	10	13.4	even	6
26.10.c.a.9.2	yes	10	13.10	even	6
338.10.a.h.1.4		5	13.12	even	2
338.10.a.i.1.4		5	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)

\(f(q)\)	\(=\)	\(q+16.0000 q^{2} +101.290 q^{3} +256.000 q^{4} -496.759 q^{5} +1620.64 q^{6} -4702.56 q^{7} +4096.00 q^{8} -9423.31 q^{9} -7948.14 q^{10} -77003.3 q^{11} +25930.3 q^{12} -75241.0 q^{14} -50316.8 q^{15} +65536.0 q^{16} +66918.1 q^{17} -150773. q^{18} +998917. q^{19} -127170. q^{20} -476323. q^{21} -1.23205e6 q^{22} +118136. q^{23} +414884. q^{24} -1.70636e6 q^{25} -2.94818e6 q^{27} -1.20386e6 q^{28} +926412. q^{29} -805068. q^{30} -1.69046e6 q^{31} +1.04858e6 q^{32} -7.79967e6 q^{33} +1.07069e6 q^{34} +2.33604e6 q^{35} -2.41237e6 q^{36} -2.46364e6 q^{37} +1.59827e7 q^{38} -2.03472e6 q^{40} +2.99902e7 q^{41} -7.62117e6 q^{42} +9.51190e6 q^{43} -1.97128e7 q^{44} +4.68111e6 q^{45} +1.89018e6 q^{46} +6.47000e7 q^{47} +6.63815e6 q^{48} -1.82395e7 q^{49} -2.73017e7 q^{50} +6.77814e6 q^{51} +4.73931e7 q^{53} -4.71709e7 q^{54} +3.82521e7 q^{55} -1.92617e7 q^{56} +1.01180e8 q^{57} +1.48226e7 q^{58} +6.57744e7 q^{59} -1.28811e7 q^{60} -7.54398e7 q^{61} -2.70474e7 q^{62} +4.43137e7 q^{63} +1.67772e7 q^{64} -1.24795e8 q^{66} -5.34676e7 q^{67} +1.71310e7 q^{68} +1.19660e7 q^{69} +3.73766e7 q^{70} +2.65576e8 q^{71} -3.85979e7 q^{72} -2.19898e7 q^{73} -3.94183e7 q^{74} -1.72837e8 q^{75} +2.55723e8 q^{76} +3.62113e8 q^{77} -2.38980e7 q^{79} -3.25556e7 q^{80} -1.13143e8 q^{81} +4.79842e8 q^{82} +3.61556e8 q^{83} -1.21939e8 q^{84} -3.32421e7 q^{85} +1.52190e8 q^{86} +9.38364e7 q^{87} -3.15405e8 q^{88} +6.70531e8 q^{89} +7.48978e7 q^{90} +3.02428e7 q^{92} -1.71227e8 q^{93} +1.03520e9 q^{94} -4.96221e8 q^{95} +1.06210e8 q^{96} -1.22647e9 q^{97} -2.91832e8 q^{98} +7.25626e8 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 5 q + 80 q^{2} + 81 q^{3} + 1280 q^{4} + 914 q^{5} + 1296 q^{6} + 3323 q^{7} + 20480 q^{8} + 13784 q^{9} + 14624 q^{10} + 53337 q^{11} + 20736 q^{12} + 53168 q^{14} + 65996 q^{15} + 327680 q^{16} + 173255 q^{17}+ \cdots + 970554586 q^{99}+O(q^{100}) \) 5 * q + 80 * q^2 + 81 * q^3 + 1280 * q^4 + 914 * q^5 + 1296 * q^6 + 3323 * q^7 + 20480 * q^8 + 13784 * q^9 + 14624 * q^10 + 53337 * q^11 + 20736 * q^12 + 53168 * q^14 + 65996 * q^15 + 327680 * q^16 + 173255 * q^17 + 220544 * q^18 - 32351 * q^19 + 233984 * q^20 + 1198763 * q^21 + 853392 * q^22 + 695969 * q^23 + 331776 * q^24 - 245227 * q^25 + 2545821 * q^27 + 850688 * q^28 + 3162725 * q^29 + 1055936 * q^30 - 2956286 * q^31 + 5242880 * q^32 + 329501 * q^33 + 2772080 * q^34 + 19935514 * q^35 + 3528704 * q^36 + 5891731 * q^37 - 517616 * q^38 + 3743744 * q^40 - 1800323 * q^41 + 19180208 * q^42 + 29311717 * q^43 + 13654272 * q^44 + 50968384 * q^45 + 11135504 * q^46 - 19266174 * q^47 + 5308416 * q^48 - 64680864 * q^49 - 3923632 * q^50 + 133318747 * q^51 - 145385254 * q^53 + 40733136 * q^54 + 61117082 * q^55 + 13611008 * q^56 + 235331279 * q^57 + 50603600 * q^58 + 12606999 * q^59 + 16894976 * q^60 + 33553237 * q^61 - 47300576 * q^62 - 107603502 * q^63 + 83886080 * q^64 + 5272016 * q^66 + 50917531 * q^67 + 44353280 * q^68 + 1842303 * q^69 + 318968224 * q^70 + 395345149 * q^71 + 56459264 * q^72 + 75481772 * q^73 + 94267696 * q^74 - 150047035 * q^75 - 8281856 * q^76 + 850958589 * q^77 - 244279556 * q^79 + 59899904 * q^80 + 561233537 * q^81 - 28805168 * q^82 + 1085718192 * q^83 + 306883328 * q^84 - 605879602 * q^85 + 468987472 * q^86 - 493630617 * q^87 + 218468352 * q^88 + 1420841923 * q^89 + 815494144 * q^90 + 178168064 * q^92 - 1050116916 * q^93 - 308258784 * q^94 + 432108524 * q^95 + 84934656 * q^96 + 1806622227 * q^97 - 1034893824 * q^98 + 970554586 * q^99

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