LMFDB - Embedded newform 338.10.a.m.1.2

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 = [10,-160,-162,2560,3088] 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:	$10$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - 2 x^{9} - 124193 x^{8} - 182380 x^{7} + 5434866119 x^{6} + 59076086702 x^{5} + \cdots + 20\!\cdots\!04 $ x^10 - 2x^9 - 124193x^8 - 182380x^7 + 5434866119x^6 + 59076086702x^5 - 99239916178943x^4 - 2585100275453696x^3 + 637502596296640360x^2 + 28730203732505382432*x + 204373529570400572304
Coefficient ring:	$\Z[a_1, \ldots, a_{19}]$
Coefficient ring index:	$ 2^{10}\cdot 3\cdot 13^{6} $
Twist minimal:	no (minimal twist has level 26)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$192.242$ 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)

$f(q)$	$=$	\(q-16.0000 q^{2} -208.242 q^{3} +256.000 q^{4} +1666.10 q^{5} +3331.87 q^{6} +11980.1 q^{7} -4096.00 q^{8} +23681.6 q^{9} -26657.6 q^{10} -53713.7 q^{11} -53309.9 q^{12} -191681. q^{14} -346951. q^{15} +65536.0 q^{16} -430839. q^{17} -378905. q^{18} +709630. q^{19} +426521. q^{20} -2.49475e6 q^{21} +859419. q^{22} -776469. q^{23} +852958. q^{24} +822757. q^{25} -832673. q^{27} +3.06690e6 q^{28} +5.13509e6 q^{29} +5.55122e6 q^{30} -3.90910e6 q^{31} -1.04858e6 q^{32} +1.11854e7 q^{33} +6.89343e6 q^{34} +1.99600e7 q^{35} +6.06249e6 q^{36} -6.98795e6 q^{37} -1.13541e7 q^{38} -6.82434e6 q^{40} -6.93003e6 q^{41} +3.99160e7 q^{42} +3.35693e7 q^{43} -1.37507e7 q^{44} +3.94558e7 q^{45} +1.24235e7 q^{46} +5.50056e6 q^{47} -1.36473e7 q^{48} +1.03168e8 q^{49} -1.31641e7 q^{50} +8.97187e7 q^{51} +2.81373e7 q^{53} +1.33228e7 q^{54} -8.94923e7 q^{55} -4.90704e7 q^{56} -1.47775e8 q^{57} -8.21614e7 q^{58} -1.01485e8 q^{59} -8.88194e7 q^{60} +1.42297e6 q^{61} +6.25456e7 q^{62} +2.83707e8 q^{63} +1.67772e7 q^{64} -1.78967e8 q^{66} -5.61602e7 q^{67} -1.10295e8 q^{68} +1.61693e8 q^{69} -3.19359e8 q^{70} -9.50326e7 q^{71} -9.69998e7 q^{72} +2.74408e8 q^{73} +1.11807e8 q^{74} -1.71332e8 q^{75} +1.81665e8 q^{76} -6.43494e8 q^{77} -5.91897e7 q^{79} +1.09189e8 q^{80} -2.92728e8 q^{81} +1.10880e8 q^{82} +1.51961e8 q^{83} -6.38656e8 q^{84} -7.17821e8 q^{85} -5.37108e8 q^{86} -1.06934e9 q^{87} +2.20011e8 q^{88} +6.04142e8 q^{89} -6.31293e8 q^{90} -1.98776e8 q^{92} +8.14038e8 q^{93} -8.80090e7 q^{94} +1.18231e9 q^{95} +2.18357e8 q^{96} +1.45492e9 q^{97} -1.65069e9 q^{98} -1.27203e9 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q - 160 q^{2} - 162 q^{3} + 2560 q^{4} + 3088 q^{5} + 2592 q^{6} + 11376 q^{7} - 40960 q^{8} + 54184 q^{9} - 49408 q^{10} - 8784 q^{11} - 41472 q^{12} - 182016 q^{14} + 357296 q^{15} + 655360 q^{16}+ \cdots + 199174752 q^{99}+O(q^{100}) $ 10 * q - 160 * q^2 - 162 * q^3 + 2560 * q^4 + 3088 * q^5 + 2592 * q^6 + 11376 * q^7 - 40960 * q^8 + 54184 * q^9 - 49408 * q^10 - 8784 * q^11 - 41472 * q^12 - 182016 * q^14 + 357296 * q^15 + 655360 * q^16 - 7446 * q^17 - 866944 * q^18 + 1520064 * q^19 + 790528 * q^20 - 1711648 * q^21 + 140544 * q^22 - 1308510 * q^23 + 663552 * q^24 + 4279466 * q^25 - 6880230 * q^27 + 2912256 * q^28 - 2343210 * q^29 - 5716736 * q^30 + 2693808 * q^31 - 10485760 * q^32 + 4567872 * q^33 + 119136 * q^34 + 23179536 * q^35 + 13871104 * q^36 + 32978928 * q^37 - 24321024 * q^38 - 12648448 * q^40 + 32690912 * q^41 + 27386368 * q^42 - 8233882 * q^43 - 2248704 * q^44 + 83696528 * q^45 + 20936160 * q^46 + 67552944 * q^47 - 10616832 * q^48 + 69922092 * q^49 - 68471456 * q^50 + 107347798 * q^51 + 87904728 * q^53 + 110083680 * q^54 + 69423408 * q^55 - 46596096 * q^56 - 197088768 * q^57 + 37491360 * q^58 + 157323568 * q^59 + 91467776 * q^60 + 68245766 * q^61 - 43100928 * q^62 + 262927520 * q^63 + 167772160 * q^64 - 73085952 * q^66 + 461709408 * q^67 - 1906176 * q^68 - 552088886 * q^69 - 370872576 * q^70 + 124194624 * q^71 - 221937664 * q^72 + 382312704 * q^73 - 527662848 * q^74 + 844565210 * q^75 + 389136384 * q^76 - 647268798 * q^77 - 389187960 * q^79 + 202375168 * q^80 - 1371213878 * q^81 - 523054592 * q^82 - 174671840 * q^83 - 438181888 * q^84 + 1034710608 * q^85 + 131742112 * q^86 - 1806098150 * q^87 + 35979264 * q^88 + 1731111552 * q^89 - 1339144448 * q^90 - 334978560 * q^92 + 2368608064 * q^93 - 1080847104 * q^94 - 4221476160 * q^95 + 169869312 * q^96 + 2693726784 * q^97 - 1118753472 * q^98 + 199174752 * 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
$3$	−208.242	−1.48430	−0.742150	−	0.670233i	$-0.766194\pi$
$3$	−208.242	−1.48430	−0.742150	+	0.670233i	$0.766194\pi$
$4$	256.000	0.500000
$5$	1666.10	1.19216	0.596081	−	0.802924i	$-0.296724\pi$
$5$	1666.10	1.19216	0.596081	+	0.802924i	$0.296724\pi$
$6$	3331.87	1.04956
$7$	11980.1	1.88590	0.942949	−	0.332938i	$-0.108040\pi$
$7$	11980.1	1.88590	0.942949	+	0.332938i	$0.108040\pi$
$8$	−4096.00	−0.353553
$9$	23681.6	1.20315
$10$	−26657.6	−0.842986
$11$	−53713.7	−1.10616	−0.553080	−	0.833128i	$-0.686548\pi$
$11$	−53713.7	−1.10616	−0.553080	+	0.833128i	$0.686548\pi$
$12$	−53309.9	−0.742150
$13$	0	0
$13$	0	0
$14$	−191681.	−1.33353
$15$	−346951.	−1.76953
$16$	65536.0	0.250000
$17$	−430839.	−1.25111	−0.625555	−	0.780180i	$-0.715127\pi$
$17$	−430839.	−1.25111	−0.625555	+	0.780180i	$0.715127\pi$
$18$	−378905.	−0.850755
$19$	709630.	1.24923	0.624613	−	0.780935i	$-0.285257\pi$
$19$	709630.	1.24923	0.624613	+	0.780935i	$0.285257\pi$
$20$	426521.	0.596081
$21$	−2.49475e6	−2.79924
$22$	859419.	0.782174
$23$	−776469.	−0.578561	−0.289280	−	0.957244i	$-0.593416\pi$
$23$	−776469.	−0.578561	−0.289280	+	0.957244i	$0.593416\pi$
$24$	852958.	0.524780
$25$	822757.	0.421251
$26$	0	0
$27$	−832673.	−0.301535
$28$	3.06690e6	0.942949
$29$	5.13509e6	1.34821	0.674104	−	0.738636i	$-0.264530\pi$
$29$	5.13509e6	1.34821	0.674104	+	0.738636i	$0.264530\pi$
$30$	5.55122e6	1.25125
$31$	−3.90910e6	−0.760237	−0.380119	−	0.924938i	$-0.624117\pi$
$31$	−3.90910e6	−0.760237	−0.380119	+	0.924938i	$0.624117\pi$
$32$	−1.04858e6	−0.176777
$33$	1.11854e7	1.64188
$34$	6.89343e6	0.884668
$35$	1.99600e7	2.24830
$36$	6.06249e6	0.601575
$37$	−6.98795e6	−0.612974	−0.306487	−	0.951875i	$-0.599154\pi$
$37$	−6.98795e6	−0.612974	−0.306487	+	0.951875i	$0.599154\pi$
$38$	−1.13541e7	−0.883336
$39$	0	0
$40$	−6.82434e6	−0.421493
$41$	−6.93003e6	−0.383008	−0.191504	−	0.981492i	$-0.561336\pi$
$41$	−6.93003e6	−0.383008	−0.191504	+	0.981492i	$0.561336\pi$
$42$	3.99160e7	1.97936
$43$	3.35693e7	1.49739	0.748693	−	0.662917i	$-0.230682\pi$
$43$	3.35693e7	1.49739	0.748693	+	0.662917i	$0.230682\pi$
$44$	−1.37507e7	−0.553080
$45$	3.94558e7	1.43435
$46$	1.24235e7	0.409104
$47$	5.50056e6	0.164425	0.0822123	−	0.996615i	$-0.473801\pi$
$47$	5.50056e6	0.164425	0.0822123	+	0.996615i	$0.473801\pi$
$48$	−1.36473e7	−0.371075
$49$	1.03168e8	2.55661
$50$	−1.31641e7	−0.297870
$51$	8.97187e7	1.85702
$52$	0	0
$53$	2.81373e7	0.489826	0.244913	−	0.969545i	$-0.421241\pi$
$53$	2.81373e7	0.489826	0.244913	+	0.969545i	$0.421241\pi$
$54$	1.33228e7	0.213217
$55$	−8.94923e7	−1.31872
$56$	−4.90704e7	−0.666765
$57$	−1.47775e8	−1.85423
$58$	−8.21614e7	−0.953327
$59$	−1.01485e8	−1.09035	−0.545175	−	0.838322i	$-0.683537\pi$
$59$	−1.01485e8	−1.09035	−0.545175	+	0.838322i	$0.683537\pi$
$60$	−8.88194e7	−0.884764
$61$	1.42297e6	0.0131586	0.00657932	−	0.999978i	$-0.497906\pi$
$61$	1.42297e6	0.0131586	0.00657932	+	0.999978i	$0.497906\pi$
$62$	6.25456e7	0.537569
$63$	2.83707e8	2.26902
$64$	1.67772e7	0.125000
$65$	0	0
$66$	−1.78967e8	−1.16098
$67$	−5.61602e7	−0.340480	−0.170240	−	0.985403i	$-0.554454\pi$
$67$	−5.61602e7	−0.340480	−0.170240	+	0.985403i	$0.554454\pi$
$68$	−1.10295e8	−0.625555
$69$	1.61693e8	0.858758
$70$	−3.19359e8	−1.58979
$71$	−9.50326e7	−0.443823	−0.221912	−	0.975067i	$-0.571230\pi$
$71$	−9.50326e7	−0.443823	−0.221912	+	0.975067i	$0.571230\pi$
$72$	−9.69998e7	−0.425378
$73$	2.74408e8	1.13095	0.565476	−	0.824765i	$-0.308693\pi$
$73$	2.74408e8	1.13095	0.565476	+	0.824765i	$0.308693\pi$
$74$	1.11807e8	0.433438
$75$	−1.71332e8	−0.625264
$76$	1.81665e8	0.624613
$77$	−6.43494e8	−2.08611
$78$	0	0
$79$	−5.91897e7	−0.170972	−0.0854859	−	0.996339i	$-0.527244\pi$
$79$	−5.91897e7	−0.170972	−0.0854859	+	0.996339i	$0.527244\pi$
$80$	1.09189e8	0.298041
$81$	−2.92728e8	−0.755581
$82$	1.10880e8	0.270827
$83$	1.51961e8	0.351465	0.175732	−	0.984438i	$-0.443771\pi$
$83$	1.51961e8	0.351465	0.175732	+	0.984438i	$0.443771\pi$
$84$	−6.38656e8	−1.39962
$85$	−7.17821e8	−1.49153
$86$	−5.37108e8	−1.05881
$87$	−1.06934e9	−2.00115
$88$	2.20011e8	0.391087
$89$	6.04142e8	1.02067	0.510333	−	0.859977i	$-0.329522\pi$
$89$	6.04142e8	1.02067	0.510333	+	0.859977i	$0.329522\pi$
$90$	−6.31293e8	−1.01424
$91$	0	0
$92$	−1.98776e8	−0.289280
$93$	8.14038e8	1.12842
$94$	−8.80090e7	−0.116266
$95$	1.18231e9	1.48928
$96$	2.18357e8	0.262390
$97$	1.45492e9	1.66866	0.834328	−	0.551269i	$-0.185856\pi$
$97$	1.45492e9	1.66866	0.834328	+	0.551269i	$0.185856\pi$
$98$	−1.65069e9	−1.80780
$99$	−1.27203e9	−1.33088
$100$	2.10626e8	0.210626
$101$	−1.58851e8	−0.151895	−0.0759473	−	0.997112i	$-0.524198\pi$
$101$	−1.58851e8	−0.151895	−0.0759473	+	0.997112i	$0.524198\pi$
$102$	−1.43550e9	−1.31311
$103$	−3.74556e8	−0.327906	−0.163953	−	0.986468i	$-0.552425\pi$
$103$	−3.74556e8	−0.327906	−0.163953	+	0.986468i	$0.552425\pi$
$104$	0	0
$105$	−4.15650e9	−3.33715
$106$	−4.50197e8	−0.346359
$107$	−1.75577e9	−1.29491	−0.647456	−	0.762103i	$-0.724167\pi$
$107$	−1.75577e9	−1.29491	−0.647456	+	0.762103i	$0.724167\pi$
$108$	−2.13164e8	−0.150767
$109$	−1.96931e8	−0.133627	−0.0668135	−	0.997765i	$-0.521283\pi$
$109$	−1.96931e8	−0.133627	−0.0668135	+	0.997765i	$0.521283\pi$
$110$	1.43188e9	0.932478
$111$	1.45518e9	0.909838
$112$	7.85126e8	0.471474
$113$	1.35120e9	0.779588	0.389794	−	0.920902i	$-0.372546\pi$
$113$	1.35120e9	0.779588	0.389794	+	0.920902i	$0.372546\pi$
$114$	2.36439e9	1.31114
$115$	−1.29367e9	−0.689738
$116$	1.31458e9	0.674104
$117$	0	0
$118$	1.62375e9	0.770994
$119$	−5.16148e9	−2.35946
$120$	1.42111e9	0.625623
$121$	5.27216e8	0.223591
$122$	−2.27675e7	−0.00930456
$123$	1.44312e9	0.568499
$124$	−1.00073e9	−0.380119
$125$	−1.88330e9	−0.689962
$126$	−4.53931e9	−1.60444
$127$	2.72382e9	0.929100	0.464550	−	0.885547i	$-0.346216\pi$
$127$	2.72382e9	0.929100	0.464550	+	0.885547i	$0.346216\pi$
$128$	−2.68435e8	−0.0883883
$129$	−6.99052e9	−2.22257
$130$	0	0
$131$	2.76631e9	0.820690	0.410345	−	0.911930i	$-0.365408\pi$
$131$	2.76631e9	0.820690	0.410345	+	0.911930i	$0.365408\pi$
$132$	2.86347e9	0.820938
$133$	8.50142e9	2.35591
$134$	8.98564e8	0.240756
$135$	−1.38731e9	−0.359479
$136$	1.76472e9	0.442334
$137$	−2.58017e9	−0.625758	−0.312879	−	0.949793i	$-0.601293\pi$
$137$	−2.58017e9	−0.625758	−0.312879	+	0.949793i	$0.601293\pi$
$138$	−2.58709e9	−0.607234
$139$	1.47443e9	0.335010	0.167505	−	0.985871i	$-0.446429\pi$
$139$	1.47443e9	0.335010	0.167505	+	0.985871i	$0.446429\pi$
$140$	5.10975e9	1.12415
$141$	−1.14545e9	−0.244056
$142$	1.52052e9	0.313831
$143$	0	0
$144$	1.55200e9	0.300787
$145$	8.55556e9	1.60728
$146$	−4.39053e9	−0.799704
$147$	−2.14840e10	−3.79478
$148$	−1.78892e9	−0.306487
$149$	−6.78910e8	−0.112843	−0.0564214	−	0.998407i	$-0.517969\pi$
$149$	−6.78910e8	−0.112843	−0.0564214	+	0.998407i	$0.517969\pi$
$150$	2.74132e9	0.442128
$151$	1.04399e10	1.63418	0.817089	−	0.576512i	$-0.195587\pi$
$151$	1.04399e10	1.63418	0.817089	+	0.576512i	$0.195587\pi$
$152$	−2.90665e9	−0.441668
$153$	−1.02030e10	−1.50527
$154$	1.02959e10	1.47510
$155$	−6.51294e9	−0.906326
$156$	0	0
$157$	−1.24661e9	−0.163750	−0.0818749	−	0.996643i	$-0.526091\pi$
$157$	−1.24661e9	−0.163750	−0.0818749	+	0.996643i	$0.526091\pi$
$158$	9.47036e8	0.120895
$159$	−5.85937e9	−0.727049
$160$	−1.74703e9	−0.210747
$161$	−9.30215e9	−1.09111
$162$	4.68364e9	0.534276
$163$	7.33517e9	0.813891	0.406945	−	0.913453i	$-0.366594\pi$
$163$	7.33517e9	0.813891	0.406945	+	0.913453i	$0.366594\pi$
$164$	−1.77409e9	−0.191504
$165$	1.86360e10	1.95738
$166$	−2.43138e9	−0.248523
$167$	2.57636e9	0.256320	0.128160	−	0.991753i	$-0.459093\pi$
$167$	2.57636e9	0.256320	0.128160	+	0.991753i	$0.459093\pi$
$168$	1.02185e10	0.989681
$169$	0	0
$170$	1.14851e10	1.05467
$171$	1.68052e10	1.50301
$172$	8.59373e9	0.748693
$173$	−1.18751e10	−1.00793	−0.503964	−	0.863725i	$-0.668126\pi$
$173$	−1.18751e10	−1.00793	−0.503964	+	0.863725i	$0.668126\pi$
$174$	1.71094e10	1.41502
$175$	9.85668e9	0.794437
$176$	−3.52018e9	−0.276540
$177$	2.11333e10	1.61841
$178$	−9.66627e9	−0.721720
$179$	8.54356e9	0.622014	0.311007	−	0.950408i	$-0.399334\pi$
$179$	8.54356e9	0.622014	0.311007	+	0.950408i	$0.399334\pi$
$180$	1.01007e10	0.717175
$181$	1.31871e10	0.913265	0.456632	−	0.889655i	$-0.349055\pi$
$181$	1.31871e10	0.913265	0.456632	+	0.889655i	$0.349055\pi$
$182$	0	0
$183$	−2.96321e8	−0.0195314
$184$	3.18042e9	0.204552
$185$	−1.16426e10	−0.730765
$186$	−1.30246e10	−0.797914
$187$	2.31420e10	1.38393
$188$	1.40814e9	0.0822123
$189$	−9.97548e9	−0.568664
$190$	−1.89170e10	−1.05308
$191$	−2.68121e9	−0.145774	−0.0728872	−	0.997340i	$-0.523221\pi$
$191$	−2.68121e9	−0.145774	−0.0728872	+	0.997340i	$0.523221\pi$
$192$	−3.49372e9	−0.185538
$193$	−2.94629e10	−1.52851	−0.764253	−	0.644916i	$-0.776892\pi$
$193$	−2.94629e10	−1.52851	−0.764253	+	0.644916i	$0.776892\pi$
$194$	−2.32787e10	−1.17992
$195$	0	0
$196$	2.64111e10	1.27830
$197$	−1.50666e9	−0.0712718	−0.0356359	−	0.999365i	$-0.511346\pi$
$197$	−1.50666e9	−0.0712718	−0.0356359	+	0.999365i	$0.511346\pi$
$198$	2.03524e10	0.941072
$199$	−1.94000e10	−0.876928	−0.438464	−	0.898749i	$-0.644477\pi$
$199$	−1.94000e10	−0.876928	−0.438464	+	0.898749i	$0.644477\pi$
$200$	−3.37001e9	−0.148935
$201$	1.16949e10	0.505376
$202$	2.54161e9	0.107406
$203$	6.15187e10	2.54258
$204$	2.29680e10	0.928511
$205$	−1.15461e10	−0.456608
$206$	5.99290e9	0.231864
$207$	−1.83880e10	−0.696095
$208$	0	0
$209$	−3.81169e10	−1.38184
$210$	6.65039e10	2.35972
$211$	3.99058e10	1.38600	0.693002	−	0.720936i	$-0.256288\pi$
$211$	3.99058e10	1.38600	0.693002	+	0.720936i	$0.256288\pi$
$212$	7.20316e9	0.244913
$213$	1.97898e10	0.658768
$214$	2.80923e10	0.915641
$215$	5.59297e10	1.78513
$216$	3.41063e9	0.106609
$217$	−4.68313e10	−1.43373
$218$	3.15089e9	0.0944886
$219$	−5.71432e10	−1.67867
$220$	−2.29100e10	−0.659361
$221$	0	0
$222$	−2.32829e10	−0.643353
$223$	−3.03167e10	−0.820936	−0.410468	−	0.911875i	$-0.634635\pi$
$223$	−3.03167e10	−0.820936	−0.410468	+	0.911875i	$0.634635\pi$
$224$	−1.25620e10	−0.333383
$225$	1.94842e10	0.506828
$226$	−2.16191e10	−0.551252
$227$	−1.19536e9	−0.0298802	−0.0149401	−	0.999888i	$-0.504756\pi$
$227$	−1.19536e9	−0.0298802	−0.0149401	+	0.999888i	$0.504756\pi$
$228$	−3.78303e10	−0.927113
$229$	−2.38819e10	−0.573865	−0.286932	−	0.957951i	$-0.592636\pi$
$229$	−2.38819e10	−0.573865	−0.286932	+	0.957951i	$0.592636\pi$
$230$	2.06988e10	0.487719
$231$	1.34002e11	3.09641
$232$	−2.10333e10	−0.476663
$233$	−7.69294e10	−1.70998	−0.854989	−	0.518646i	$-0.826436\pi$
$233$	−7.69294e10	−1.70998	−0.854989	+	0.518646i	$0.826436\pi$
$234$	0	0
$235$	9.16448e9	0.196021
$236$	−2.59801e10	−0.545175
$237$	1.23258e10	0.253774
$238$	8.25838e10	1.66839
$239$	3.25919e10	0.646129	0.323064	−	0.946377i	$-0.395287\pi$
$239$	3.25919e10	0.646129	0.323064	+	0.946377i	$0.395287\pi$
$240$	−2.27378e10	−0.442382
$241$	−7.51023e10	−1.43409	−0.717045	−	0.697027i	$-0.754506\pi$
$241$	−7.51023e10	−1.43409	−0.717045	+	0.697027i	$0.754506\pi$
$242$	−8.43545e9	−0.158103
$243$	7.73476e10	1.42304
$244$	3.64280e8	0.00657932
$245$	1.71889e11	3.04789
$246$	−2.30899e10	−0.401989
$247$	0	0
$248$	1.60117e10	0.268784
$249$	−3.16447e10	−0.521679
$250$	3.01329e10	0.487877
$251$	4.28794e10	0.681895	0.340947	−	0.940082i	$-0.389252\pi$
$251$	4.28794e10	0.681895	0.340947	+	0.940082i	$0.389252\pi$
$252$	7.26290e10	1.13451
$253$	4.17070e10	0.639981
$254$	−4.35812e10	−0.656973
$255$	1.49480e11	2.21387
$256$	4.29497e9	0.0625000
$257$	−1.24210e11	−1.77605	−0.888027	−	0.459791i	$-0.847924\pi$
$257$	−1.24210e11	−1.77605	−0.888027	+	0.459791i	$0.847924\pi$
$258$	1.11848e11	1.57159
$259$	−8.37162e10	−1.15601
$260$	0	0
$261$	1.21607e11	1.62210
$262$	−4.42609e10	−0.580316
$263$	4.93843e10	0.636485	0.318243	−	0.948009i	$-0.396907\pi$
$263$	4.93843e10	0.636485	0.318243	+	0.948009i	$0.396907\pi$
$264$	−4.58155e10	−0.580490
$265$	4.68796e10	0.583952
$266$	−1.36023e11	−1.66588
$267$	−1.25808e11	−1.51498
$268$	−1.43770e10	−0.170240
$269$	1.66947e10	0.194399	0.0971996	−	0.995265i	$-0.469011\pi$
$269$	1.66947e10	0.194399	0.0971996	+	0.995265i	$0.469011\pi$
$270$	2.21970e10	0.254190
$271$	7.23487e10	0.814834	0.407417	−	0.913242i	$-0.366430\pi$
$271$	7.23487e10	0.814834	0.407417	+	0.913242i	$0.366430\pi$
$272$	−2.82355e10	−0.312777
$273$	0	0
$274$	4.12828e10	0.442478
$275$	−4.41933e10	−0.465972
$276$	4.13935e10	0.429379
$277$	2.14905e10	0.219325	0.109663	−	0.993969i	$-0.465023\pi$
$277$	2.14905e10	0.219325	0.109663	+	0.993969i	$0.465023\pi$
$278$	−2.35909e10	−0.236888
$279$	−9.25737e10	−0.914679
$280$	−8.17560e10	−0.794893
$281$	1.18358e11	1.13245	0.566224	−	0.824251i	$-0.308404\pi$
$281$	1.18358e11	1.13245	0.566224	+	0.824251i	$0.308404\pi$
$282$	1.83271e10	0.172573
$283$	1.57858e11	1.46294	0.731471	−	0.681873i	$-0.238834\pi$
$283$	1.57858e11	1.46294	0.731471	+	0.681873i	$0.238834\pi$
$284$	−2.43284e10	−0.221912
$285$	−2.46207e11	−2.21054
$286$	0	0
$287$	−8.30222e10	−0.722313
$288$	−2.48319e10	−0.212689
$289$	6.70347e10	0.565275
$290$	−1.36889e11	−1.13652
$291$	−3.02975e11	−2.47679
$292$	7.02485e10	0.565476
$293$	−4.39162e9	−0.0348113	−0.0174057	−	0.999849i	$-0.505541\pi$
$293$	−4.39162e9	−0.0348113	−0.0174057	+	0.999849i	$0.505541\pi$
$294$	3.43743e11	2.68331
$295$	−1.69083e11	−1.29988
$296$	2.86227e10	0.216719
$297$	4.47260e10	0.333546
$298$	1.08626e10	0.0797919
$299$	0	0
$300$	−4.38610e10	−0.312632
$301$	4.02162e11	2.82392
$302$	−1.67038e11	−1.15554
$303$	3.30793e10	0.225457
$304$	4.65063e10	0.312306
$305$	2.37080e9	0.0156872
$306$	1.63247e11	1.06439
$307$	−3.04196e11	−1.95448	−0.977239	−	0.212140i	$-0.931957\pi$
$307$	−3.04196e11	−1.95448	−0.977239	+	0.212140i	$0.931957\pi$
$308$	−1.64734e11	−1.04305
$309$	7.79982e10	0.486711
$310$	1.04207e11	0.640870
$311$	2.34858e11	1.42359	0.711794	−	0.702389i	$-0.247883\pi$
$311$	2.34858e11	1.42359	0.711794	+	0.702389i	$0.247883\pi$
$312$	0	0
$313$	1.72269e11	1.01452	0.507258	−	0.861794i	$-0.330659\pi$
$313$	1.72269e11	1.01452	0.507258	+	0.861794i	$0.330659\pi$
$314$	1.99457e10	0.115789
$315$	4.72684e11	2.70504
$316$	−1.51526e10	−0.0854859
$317$	2.91539e11	1.62155	0.810775	−	0.585358i	$-0.199046\pi$
$317$	2.91539e11	1.62155	0.810775	+	0.585358i	$0.199046\pi$
$318$	9.37499e10	0.514101
$319$	−2.75825e11	−1.49133
$320$	2.79525e10	0.149020
$321$	3.65624e11	1.92204
$322$	1.48834e11	0.771528
$323$	−3.05737e11	−1.56292
$324$	−7.49382e10	−0.377790
$325$	0	0
$326$	−1.17363e11	−0.575508
$327$	4.10092e10	0.198343
$328$	2.83854e10	0.135414
$329$	6.58971e10	0.310088
$330$	−2.98176e11	−1.38408
$331$	−2.19848e11	−1.00669	−0.503346	−	0.864085i	$-0.667898\pi$
$331$	−2.19848e11	−1.00669	−0.503346	+	0.864085i	$0.667898\pi$
$332$	3.89021e10	0.175732
$333$	−1.65486e11	−0.737500
$334$	−4.12218e10	−0.181246
$335$	−9.35684e10	−0.405908
$336$	−1.63496e11	−0.699810
$337$	3.17624e10	0.134146	0.0670732	−	0.997748i	$-0.478634\pi$
$337$	3.17624e10	0.134146	0.0670732	+	0.997748i	$0.478634\pi$
$338$	0	0
$339$	−2.81375e11	−1.15714
$340$	−1.83762e11	−0.745763
$341$	2.09972e11	0.840944
$342$	−2.68883e11	−1.06279
$343$	7.52525e11	2.93560
$344$	−1.37500e11	−0.529406
$345$	2.69397e11	1.02378
$346$	1.90001e11	0.712713
$347$	2.95477e11	1.09406	0.547030	−	0.837113i	$-0.315758\pi$
$347$	2.95477e11	1.09406	0.547030	+	0.837113i	$0.315758\pi$
$348$	−2.73751e11	−1.00057
$349$	5.13586e10	0.185310	0.0926550	−	0.995698i	$-0.470465\pi$
$349$	5.13586e10	0.185310	0.0926550	+	0.995698i	$0.470465\pi$
$350$	−1.57707e11	−0.561752
$351$	0	0
$352$	5.63229e10	0.195543
$353$	3.81104e11	1.30634	0.653172	−	0.757209i	$-0.273438\pi$
$353$	3.81104e11	1.30634	0.653172	+	0.757209i	$0.273438\pi$
$354$	−3.38133e11	−1.14439
$355$	−1.58334e11	−0.529110
$356$	1.54660e11	0.510333
$357$	1.07484e12	3.50215
$358$	−1.36697e11	−0.439831
$359$	5.69015e11	1.80800	0.904001	−	0.427530i	$-0.140616\pi$
$359$	5.69015e11	1.80800	0.904001	+	0.427530i	$0.140616\pi$
$360$	−1.61611e11	−0.507119
$361$	1.80887e11	0.560565
$362$	−2.10994e11	−0.645776
$363$	−1.09788e11	−0.331876
$364$	0	0
$365$	4.57191e11	1.34828
$366$	4.74114e9	0.0138108
$367$	−1.39298e11	−0.400817	−0.200409	−	0.979712i	$-0.564227\pi$
$367$	−1.39298e11	−0.400817	−0.200409	+	0.979712i	$0.564227\pi$
$368$	−5.08867e10	−0.144640
$369$	−1.64114e11	−0.460816
$370$	1.86282e11	0.516729
$371$	3.37087e11	0.923761
$372$	2.08394e11	0.564211
$373$	3.73405e11	0.998827	0.499414	−	0.866364i	$-0.333549\pi$
$373$	3.73405e11	0.998827	0.499414	+	0.866364i	$0.333549\pi$
$374$	−3.70272e11	−0.978585
$375$	3.92182e11	1.02411
$376$	−2.25303e10	−0.0581329
$377$	0	0
$378$	1.59608e11	0.402106
$379$	5.33114e11	1.32722	0.663611	−	0.748078i	$-0.269023\pi$
$379$	5.33114e11	1.32722	0.663611	+	0.748078i	$0.269023\pi$
$380$	3.02672e11	0.744640
$381$	−5.67214e11	−1.37906
$382$	4.28994e10	0.103078
$383$	7.34355e11	1.74386	0.871929	−	0.489632i	$-0.162869\pi$
$383$	7.34355e11	1.74386	0.871929	+	0.489632i	$0.162869\pi$
$384$	5.58994e10	0.131195
$385$	−1.07212e12	−2.48698
$386$	4.71406e11	1.08082
$387$	7.94973e11	1.80158
$388$	3.72460e11	0.834328
$389$	−5.51944e11	−1.22214	−0.611072	−	0.791575i	$-0.709261\pi$
$389$	−5.51944e11	−1.22214	−0.611072	+	0.791575i	$0.709261\pi$
$390$	0	0
$391$	3.34533e11	0.723842
$392$	−4.22578e11	−0.903898
$393$	−5.76060e11	−1.21815
$394$	2.41066e10	0.0503968
$395$	−9.86159e10	−0.203826
$396$	−3.25639e11	−0.665438
$397$	2.52178e11	0.509506	0.254753	−	0.967006i	$-0.418006\pi$
$397$	2.52178e11	0.509506	0.254753	+	0.967006i	$0.418006\pi$
$398$	3.10401e11	0.620082
$399$	−1.77035e12	−3.49688
$400$	5.39202e10	0.105313
$401$	−7.26470e11	−1.40303	−0.701517	−	0.712653i	$-0.747494\pi$
$401$	−7.26470e11	−1.40303	−0.701517	+	0.712653i	$0.747494\pi$
$402$	−1.87118e11	−0.357354
$403$	0	0
$404$	−4.06657e10	−0.0759473
$405$	−4.87713e11	−0.900775
$406$	−9.84299e11	−1.79788
$407$	3.75349e11	0.678048
$408$	−3.67488e11	−0.656557
$409$	4.76686e11	0.842320	0.421160	−	0.906986i	$-0.361623\pi$
$409$	4.76686e11	0.842320	0.421160	+	0.906986i	$0.361623\pi$
$410$	1.84738e11	0.322870
$411$	5.37300e11	0.928813
$412$	−9.58863e10	−0.163953
$413$	−1.21579e12	−2.05629
$414$	2.94208e11	0.492213
$415$	2.53182e11	0.419003
$416$	0	0
$417$	−3.07038e11	−0.497256
$418$	6.09870e11	0.977111
$419$	7.22556e10	0.114527	0.0572636	−	0.998359i	$-0.481762\pi$
$419$	7.22556e10	0.114527	0.0572636	+	0.998359i	$0.481762\pi$
$420$	−1.06406e12	−1.66857
$421$	−8.42735e11	−1.30744	−0.653719	−	0.756737i	$-0.726792\pi$
$421$	−8.42735e11	−1.30744	−0.653719	+	0.756737i	$0.726792\pi$
$422$	−6.38492e11	−0.980053
$423$	1.30262e11	0.197827
$424$	−1.15251e11	−0.173180
$425$	−3.54476e11	−0.527032
$426$	−3.16636e11	−0.465819
$427$	1.70473e10	0.0248158
$428$	−4.49477e11	−0.647456
$429$	0	0
$430$	−8.94875e11	−1.26228
$431$	−1.08748e12	−1.51801	−0.759004	−	0.651086i	$-0.774314\pi$
$431$	−1.08748e12	−1.51801	−0.759004	+	0.651086i	$0.774314\pi$
$432$	−5.45701e10	−0.0753837
$433$	−3.73018e11	−0.509958	−0.254979	−	0.966947i	$-0.582069\pi$
$433$	−3.73018e11	−0.509958	−0.254979	+	0.966947i	$0.582069\pi$
$434$	7.49301e11	1.01380
$435$	−1.78162e12	−2.38569
$436$	−5.04143e10	−0.0668135
$437$	−5.51006e11	−0.722753
$438$	9.14291e11	1.18700
$439$	7.46105e11	0.958759	0.479379	−	0.877608i	$-0.340862\pi$
$439$	7.46105e11	0.958759	0.479379	+	0.877608i	$0.340862\pi$
$440$	3.66560e11	0.466239
$441$	2.44319e12	3.07598
$442$	0	0
$443$	−6.23115e11	−0.768691	−0.384345	−	0.923189i	$-0.625573\pi$
$443$	−6.23115e11	−0.768691	−0.384345	+	0.923189i	$0.625573\pi$
$444$	3.72527e11	0.454919
$445$	1.00656e12	1.21680
$446$	4.85067e11	0.580490
$447$	1.41377e11	0.167493
$448$	2.00992e11	0.235737
$449$	−1.88104e11	−0.218419	−0.109209	−	0.994019i	$-0.534832\pi$
$449$	−1.88104e11	−0.218419	−0.109209	+	0.994019i	$0.534832\pi$
$450$	−3.11747e11	−0.358382
$451$	3.72238e11	0.423668
$452$	3.45906e11	0.389794
$453$	−2.17402e12	−2.42561
$454$	1.91258e10	0.0211285
$455$	0	0
$456$	6.05285e11	0.655568
$457$	−1.38987e11	−0.149057	−0.0745286	−	0.997219i	$-0.523745\pi$
$457$	−1.38987e11	−0.149057	−0.0745286	+	0.997219i	$0.523745\pi$
$458$	3.82111e11	0.405784
$459$	3.58748e11	0.377253
$460$	−3.31180e11	−0.344869
$461$	2.01094e11	0.207369	0.103685	−	0.994610i	$-0.466937\pi$
$461$	2.01094e11	0.207369	0.103685	+	0.994610i	$0.466937\pi$
$462$	−2.14404e12	−2.18949
$463$	−9.58309e11	−0.969151	−0.484575	−	0.874750i	$-0.661026\pi$
$463$	−9.58309e11	−0.969151	−0.484575	+	0.874750i	$0.661026\pi$
$464$	3.36533e11	0.337052
$465$	1.35627e12	1.34526
$466$	1.23087e12	1.20914
$467$	1.72451e12	1.67780	0.838902	−	0.544283i	$-0.183198\pi$
$467$	1.72451e12	1.67780	0.838902	+	0.544283i	$0.183198\pi$
$468$	0	0
$469$	−6.72803e11	−0.642111
$470$	−1.46632e11	−0.138608
$471$	2.59595e11	0.243054
$472$	4.15681e11	0.385497
$473$	−1.80313e12	−1.65635
$474$	−1.97212e11	−0.179445
$475$	5.83853e11	0.526238
$476$	−1.32134e12	−1.17973
$477$	6.66337e11	0.589334
$478$	−5.21470e11	−0.456882
$479$	−3.72242e11	−0.323084	−0.161542	−	0.986866i	$-0.551647\pi$
$479$	−3.72242e11	−0.323084	−0.161542	+	0.986866i	$0.551647\pi$
$480$	3.63804e11	0.312811
$481$	0	0
$482$	1.20164e12	1.01406
$483$	1.93710e12	1.61953
$484$	1.34967e11	0.111795
$485$	2.42404e12	1.98931
$486$	−1.23756e12	−1.00624
$487$	8.51374e11	0.685867	0.342934	−	0.939360i	$-0.388579\pi$
$487$	8.51374e11	0.685867	0.342934	+	0.939360i	$0.388579\pi$
$488$	−5.82848e9	−0.00465228
$489$	−1.52749e12	−1.20806
$490$	−2.75022e12	−2.15519
$491$	−9.31183e11	−0.723050	−0.361525	−	0.932362i	$-0.617744\pi$
$491$	−9.31183e11	−0.723050	−0.361525	+	0.932362i	$0.617744\pi$
$492$	3.69439e11	0.284249
$493$	−2.21240e12	−1.68676
$494$	0	0
$495$	−2.11932e12	−1.58662
$496$	−2.56187e11	−0.190059
$497$	−1.13850e12	−0.837006
$498$	5.06315e11	0.368883
$499$	1.50725e12	1.08826	0.544129	−	0.839002i	$-0.316860\pi$
$499$	1.50725e12	1.08826	0.544129	+	0.839002i	$0.316860\pi$
$500$	−4.82126e11	−0.344981
$501$	−5.36506e11	−0.380456
$502$	−6.86071e11	−0.482172
$503$	1.81828e12	1.26650	0.633250	−	0.773947i	$-0.281720\pi$
$503$	1.81828e12	1.26650	0.633250	+	0.773947i	$0.281720\pi$
$504$	−1.16206e12	−0.802218
$505$	−2.64660e11	−0.181083
$506$	−6.67312e11	−0.452535
$507$	0	0
$508$	6.97299e11	0.464550
$509$	−2.23212e12	−1.47397	−0.736984	−	0.675910i	$-0.763751\pi$
$509$	−2.23212e12	−1.47397	−0.736984	+	0.675910i	$0.763751\pi$
$510$	−2.39168e12	−1.56544
$511$	3.28743e12	2.13286
$512$	−6.87195e10	−0.0441942
$513$	−5.90890e11	−0.376685
$514$	1.98735e12	1.25586
$515$	−6.24047e11	−0.390917
$516$	−1.78957e12	−1.11129
$517$	−2.95456e11	−0.181880
$518$	1.33946e12	0.817420
$519$	2.47289e12	1.49607
$520$	0	0
$521$	−1.52179e12	−0.904865	−0.452433	−	0.891799i	$-0.649444\pi$
$521$	−1.52179e12	−0.904865	−0.452433	+	0.891799i	$0.649444\pi$
$522$	−1.94571e12	−1.14699
$523$	3.35095e11	0.195844	0.0979221	−	0.995194i	$-0.468780\pi$
$523$	3.35095e11	0.195844	0.0979221	+	0.995194i	$0.468780\pi$
$524$	7.08174e11	0.410345
$525$	−2.05257e12	−1.17918
$526$	−7.90149e11	−0.450063
$527$	1.68419e12	0.951140
$528$	7.33049e11	0.410469
$529$	−1.19825e12	−0.665268
$530$	−7.50073e11	−0.412916
$531$	−2.40332e12	−1.31185
$532$	2.17636e12	1.17796
$533$	0	0
$534$	2.01292e12	1.07125
$535$	−2.92528e12	−1.54375
$536$	2.30032e11	0.120378
$537$	−1.77913e12	−0.923257
$538$	−2.67116e11	−0.137461
$539$	−5.54156e12	−2.82802
$540$	−3.55153e11	−0.179739
$541$	1.84448e12	0.925734	0.462867	−	0.886428i	$-0.346821\pi$
$541$	1.84448e12	0.925734	0.462867	+	0.886428i	$0.346821\pi$
$542$	−1.15758e12	−0.576174
$543$	−2.74611e12	−1.35556
$544$	4.51768e11	0.221167
$545$	−3.28106e11	−0.159305
$546$	0	0
$547$	−1.90323e12	−0.908966	−0.454483	−	0.890755i	$-0.650176\pi$
$547$	−1.90323e12	−0.908966	−0.454483	+	0.890755i	$0.650176\pi$
$548$	−6.60524e11	−0.312879
$549$	3.36982e10	0.0158318
$550$	7.07093e11	0.329492
$551$	3.64401e12	1.68422
$552$	−6.62295e11	−0.303617
$553$	−7.09097e11	−0.322435
$554$	−3.43849e11	−0.155086
$555$	2.42448e12	1.08468
$556$	3.77454e11	0.167505
$557$	1.73780e12	0.764982	0.382491	−	0.923959i	$-0.375066\pi$
$557$	1.73780e12	0.764982	0.382491	+	0.923959i	$0.375066\pi$
$558$	1.48118e12	0.646776
$559$	0	0
$560$	1.30810e12	0.562074
$561$	−4.81913e12	−2.05417
$562$	−1.89372e12	−0.800762
$563$	4.07227e12	1.70824	0.854121	−	0.520075i	$-0.174096\pi$
$563$	4.07227e12	1.70824	0.854121	+	0.520075i	$0.174096\pi$
$564$	−2.93234e11	−0.122028
$565$	2.25122e12	0.929396
$566$	−2.52573e12	−1.03446
$567$	−3.50690e12	−1.42495
$568$	3.89254e11	0.156915
$569$	2.37343e12	0.949231	0.474615	−	0.880193i	$-0.342587\pi$
$569$	2.37343e12	0.949231	0.474615	+	0.880193i	$0.342587\pi$
$570$	3.93931e12	1.56309
$571$	−2.38248e12	−0.937924	−0.468962	−	0.883218i	$-0.655372\pi$
$571$	−2.38248e12	−0.937924	−0.468962	+	0.883218i	$0.655372\pi$
$572$	0	0
$573$	5.58340e11	0.216373
$574$	1.32836e12	0.510753
$575$	−6.38845e11	−0.243719
$576$	3.97311e11	0.150394
$577$	−2.45216e12	−0.920998	−0.460499	−	0.887660i	$-0.652329\pi$
$577$	−2.45216e12	−0.920998	−0.460499	+	0.887660i	$0.652329\pi$
$578$	−1.07256e12	−0.399709
$579$	6.13540e12	2.26876
$580$	2.19022e12	0.803641
$581$	1.82051e12	0.662826
$582$	4.84760e12	1.75135
$583$	−1.51136e12	−0.541826
$584$	−1.12398e12	−0.399852
$585$	0	0
$586$	7.02660e10	0.0246153
$587$	2.54616e12	0.885146	0.442573	−	0.896732i	$-0.354066\pi$
$587$	2.54616e12	0.885146	0.442573	+	0.896732i	$0.354066\pi$
$588$	−5.49989e12	−1.89739
$589$	−2.77402e12	−0.949708
$590$	2.70533e12	0.919151
$591$	3.13750e11	0.105789
$592$	−4.57963e11	−0.153244
$593$	2.24693e12	0.746180	0.373090	−	0.927795i	$-0.378298\pi$
$593$	2.24693e12	0.746180	0.373090	+	0.927795i	$0.378298\pi$
$594$	−7.15615e11	−0.235853
$595$	−8.59954e12	−2.81286
$596$	−1.73801e11	−0.0564214
$597$	4.03990e12	1.30163
$598$	0	0
$599$	3.22395e12	1.02322	0.511608	−	0.859219i	$-0.329050\pi$
$599$	3.22395e12	1.02322	0.511608	+	0.859219i	$0.329050\pi$
$600$	7.01777e11	0.221064
$601$	−2.70440e12	−0.845542	−0.422771	−	0.906237i	$-0.638943\pi$
$601$	−2.70440e12	−0.845542	−0.422771	+	0.906237i	$0.638943\pi$
$602$	−6.43459e12	−1.99681
$603$	−1.32996e12	−0.409649
$604$	2.67261e12	0.817089
$605$	8.78393e11	0.266557
$606$	−5.29269e11	−0.159422
$607$	5.66961e12	1.69513	0.847566	−	0.530689i	$-0.178067\pi$
$607$	5.66961e12	1.69513	0.847566	+	0.530689i	$0.178067\pi$
$608$	−7.44101e11	−0.220834
$609$	−1.28108e13	−3.77396
$610$	−3.79329e10	−0.0110926
$611$	0	0
$612$	−2.61196e12	−0.752636
$613$	6.10591e12	1.74654	0.873269	−	0.487238i	$-0.161996\pi$
$613$	6.10591e12	1.74654	0.873269	+	0.487238i	$0.161996\pi$
$614$	4.86714e12	1.38203
$615$	2.40438e12	0.677743
$616$	2.63575e12	0.737550
$617$	4.76455e12	1.32355	0.661773	−	0.749705i	$-0.269804\pi$
$617$	4.76455e12	1.32355	0.661773	+	0.749705i	$0.269804\pi$
$618$	−1.24797e12	−0.344157
$619$	3.87180e12	1.06000	0.530000	−	0.847998i	$-0.322192\pi$
$619$	3.87180e12	1.06000	0.530000	+	0.847998i	$0.322192\pi$
$620$	−1.66731e12	−0.453163
$621$	6.46545e11	0.174456
$622$	−3.75773e12	−1.00663
$623$	7.23766e12	1.92487
$624$	0	0
$625$	−4.74472e12	−1.24380
$626$	−2.75631e12	−0.717371
$627$	7.93752e12	2.05107
$628$	−3.19131e11	−0.0818749
$629$	3.01069e12	0.766898
$630$	−7.56294e12	−1.91275
$631$	6.74330e12	1.69333	0.846663	−	0.532130i	$-0.178608\pi$
$631$	6.74330e12	1.69333	0.846663	+	0.532130i	$0.178608\pi$
$632$	2.42441e11	0.0604477
$633$	−8.31004e12	−2.05725
$634$	−4.66463e12	−1.14661
$635$	4.53816e12	1.10764
$636$	−1.50000e12	−0.363524
$637$	0	0
$638$	4.41319e12	1.05453
$639$	−2.25052e12	−0.533986
$640$	−4.47240e11	−0.105373
$641$	3.63572e12	0.850609	0.425304	−	0.905050i	$-0.360167\pi$
$641$	3.63572e12	0.850609	0.425304	+	0.905050i	$0.360167\pi$
$642$	−5.84999e12	−1.35909
$643$	1.03213e12	0.238113	0.119057	−	0.992887i	$-0.462013\pi$
$643$	1.03213e12	0.238113	0.119057	+	0.992887i	$0.462013\pi$
$644$	−2.38135e12	−0.545553
$645$	−1.16469e13	−2.64967
$646$	4.89179e12	1.10515
$647$	−6.69734e12	−1.50256	−0.751282	−	0.659982i	$-0.770564\pi$
$647$	−6.69734e12	−1.50256	−0.751282	+	0.659982i	$0.770564\pi$
$648$	1.19901e12	0.267138
$649$	5.45112e12	1.20610
$650$	0	0
$651$	9.75222e12	2.12809
$652$	1.87780e12	0.406945
$653$	−4.30745e12	−0.927066	−0.463533	−	0.886080i	$-0.653418\pi$
$653$	−4.30745e12	−0.927066	−0.463533	+	0.886080i	$0.653418\pi$
$654$	−6.56147e11	−0.140249
$655$	4.60894e12	0.978396
$656$	−4.54166e11	−0.0957519
$657$	6.49842e12	1.36070
$658$	−1.05435e12	−0.219265
$659$	9.31298e11	0.192355	0.0961776	−	0.995364i	$-0.469338\pi$
$659$	9.31298e11	0.192355	0.0961776	+	0.995364i	$0.469338\pi$
$660$	4.77082e12	0.978691
$661$	2.47375e12	0.504022	0.252011	−	0.967724i	$-0.418908\pi$
$661$	2.47375e12	0.504022	0.252011	+	0.967724i	$0.418908\pi$
$662$	3.51757e12	0.711839
$663$	0	0
$664$	−6.22434e11	−0.124262
$665$	1.41642e13	2.80863
$666$	2.64777e12	0.521491
$667$	−3.98724e12	−0.780020
$668$	6.59549e11	0.128160
$669$	6.31319e12	1.21852
$670$	1.49709e12	0.287020
$671$	−7.64329e10	−0.0145556
$672$	2.61593e12	0.494840
$673$	9.41332e12	1.76878	0.884392	−	0.466744i	$-0.154573\pi$
$673$	9.41332e12	1.76878	0.884392	+	0.466744i	$0.154573\pi$
$674$	−5.08199e11	−0.0948559
$675$	−6.85087e11	−0.127022
$676$	0	0
$677$	−3.30199e10	−0.00604124	−0.00302062	−	0.999995i	$-0.500961\pi$
$677$	−3.30199e10	−0.00604124	−0.00302062	+	0.999995i	$0.500961\pi$
$678$	4.50200e12	0.818224
$679$	1.74301e13	3.14691
$680$	2.94019e12	0.527334
$681$	2.48925e11	0.0443512
$682$	−3.35956e12	−0.594638
$683$	−1.13606e12	−0.199760	−0.0998799	−	0.995000i	$-0.531846\pi$
$683$	−1.13606e12	−0.199760	−0.0998799	+	0.995000i	$0.531846\pi$
$684$	4.30212e12	0.751503
$685$	−4.29882e12	−0.746005
$686$	−1.20404e13	−2.07579
$687$	4.97321e12	0.851788
$688$	2.19999e12	0.374346
$689$	0	0
$690$	−4.31035e12	−0.723921
$691$	−1.06529e13	−1.77752	−0.888761	−	0.458371i	$-0.848433\pi$
$691$	−1.06529e13	−1.77752	−0.888761	+	0.458371i	$0.848433\pi$
$692$	−3.04002e12	−0.503964
$693$	−1.52390e13	−2.50990
$694$	−4.72764e12	−0.773618
$695$	2.45655e12	0.399386
$696$	4.38001e12	0.707512
$697$	2.98573e12	0.479185
$698$	−8.21738e11	−0.131034
$699$	1.60199e13	2.53812
$700$	2.52331e12	0.397218
$701$	−3.77795e12	−0.590915	−0.295458	−	0.955356i	$-0.595472\pi$
$701$	−3.77795e12	−0.590915	−0.295458	+	0.955356i	$0.595472\pi$
$702$	0	0
$703$	−4.95886e12	−0.765743
$704$	−9.01167e11	−0.138270
$705$	−1.90843e12	−0.290954
$706$	−6.09767e12	−0.923725
$707$	−1.90304e12	−0.286458
$708$	5.41013e12	0.809204
$709$	−1.07641e13	−1.59981	−0.799906	−	0.600125i	$-0.795117\pi$
$709$	−1.07641e13	−1.59981	−0.799906	+	0.600125i	$0.795117\pi$
$710$	2.53334e12	0.374137
$711$	−1.40171e12	−0.205705
$712$	−2.47457e12	−0.360860
$713$	3.03529e12	0.439843
$714$	−1.71974e13	−2.47640
$715$	0	0
$716$	2.18715e12	0.311007
$717$	−6.78699e12	−0.959049
$718$	−9.10425e12	−1.27845
$719$	5.68657e11	0.0793543	0.0396771	−	0.999213i	$-0.487367\pi$
$719$	5.68657e11	0.0793543	0.0396771	+	0.999213i	$0.487367\pi$
$720$	2.58578e12	0.358587
$721$	−4.48721e12	−0.618397
$722$	−2.89420e12	−0.396379
$723$	1.56394e13	2.12862
$724$	3.37591e12	0.456632
$725$	4.22493e12	0.567934
$726$	1.75661e12	0.234672
$727$	−1.19679e13	−1.58897	−0.794483	−	0.607286i	$-0.792258\pi$
$727$	−1.19679e13	−1.58897	−0.794483	+	0.607286i	$0.792258\pi$
$728$	0	0
$729$	−1.03452e13	−1.35665
$730$	−7.31505e12	−0.953377
$731$	−1.44630e13	−1.87339
$732$	−7.58583e10	−0.00976569
$733$	2.48128e12	0.317474	0.158737	−	0.987321i	$-0.449258\pi$
$733$	2.48128e12	0.317474	0.158737	+	0.987321i	$0.449258\pi$
$734$	2.22876e12	0.283421
$735$	−3.57944e13	−4.52399
$736$	8.14187e11	0.102276
$737$	3.01657e12	0.376626
$738$	2.62583e12	0.325846
$739$	−2.00191e12	−0.246914	−0.123457	−	0.992350i	$-0.539398\pi$
$739$	−2.00191e12	−0.246914	−0.123457	+	0.992350i	$0.539398\pi$
$740$	−2.98051e12	−0.365383
$741$	0	0
$742$	−5.39340e12	−0.653198
$743$	1.38092e13	1.66234	0.831169	−	0.556020i	$-0.187672\pi$
$743$	1.38092e13	1.66234	0.831169	+	0.556020i	$0.187672\pi$
$744$	−3.33430e12	−0.398957
$745$	−1.13113e12	−0.134527
$746$	−5.97448e12	−0.706278
$747$	3.59869e12	0.422864
$748$	5.92435e12	0.691964
$749$	−2.10342e13	−2.44207
$750$	−6.27492e12	−0.724156
$751$	9.14851e12	1.04947	0.524736	−	0.851265i	$-0.324164\pi$
$751$	9.14851e12	1.04947	0.524736	+	0.851265i	$0.324164\pi$
$752$	3.60485e11	0.0411062
$753$	−8.92928e12	−1.01214
$754$	0	0
$755$	1.73939e13	1.94821
$756$	−2.55372e12	−0.284332
$757$	8.63064e12	0.955237	0.477619	−	0.878567i	$-0.341500\pi$
$757$	8.63064e12	0.955237	0.477619	+	0.878567i	$0.341500\pi$
$758$	−8.52982e12	−0.938487
$759$	−8.68514e12	−0.949924
$760$	−4.84275e12	−0.526540
$761$	1.59040e12	0.171900	0.0859498	−	0.996299i	$-0.472608\pi$
$761$	1.59040e12	0.171900	0.0859498	+	0.996299i	$0.472608\pi$
$762$	9.07542e12	0.975145
$763$	−2.35924e12	−0.252007
$764$	−6.86390e11	−0.0728872
$765$	−1.69991e13	−1.79453
$766$	−1.17497e13	−1.23309
$767$	0	0
$768$	−8.94391e11	−0.0927688
$769$	3.83292e12	0.395241	0.197620	−	0.980279i	$-0.436679\pi$
$769$	3.83292e12	0.395241	0.197620	+	0.980279i	$0.436679\pi$
$770$	1.71540e13	1.75856
$771$	2.58656e13	2.63620
$772$	−7.54250e12	−0.764253
$773$	1.60472e12	0.161656	0.0808281	−	0.996728i	$-0.474244\pi$
$773$	1.60472e12	0.161656	0.0808281	+	0.996728i	$0.474244\pi$
$774$	−1.27196e13	−1.27391
$775$	−3.21624e12	−0.320251
$776$	−5.95936e12	−0.589959
$777$	1.74332e13	1.71586
$778$	8.83111e12	0.864186
$779$	−4.91776e12	−0.478463
$780$	0	0
$781$	5.10456e12	0.490940
$782$	−5.35253e12	−0.511834
$783$	−4.27585e12	−0.406532
$784$	6.76124e12	0.639152
$785$	−2.07697e12	−0.195216
$786$	9.21696e12	0.861363
$787$	1.77959e13	1.65361	0.826806	−	0.562487i	$-0.190155\pi$
$787$	1.77959e13	1.65361	0.826806	+	0.562487i	$0.190155\pi$
$788$	−3.85705e11	−0.0356359
$789$	−1.02839e13	−0.944735
$790$	1.57785e12	0.144127
$791$	1.61874e13	1.47022
$792$	5.21022e12	0.470536
$793$	0	0
$794$	−4.03484e12	−0.360275
$795$	−9.76228e12	−0.866760
$796$	−4.96641e12	−0.438464
$797$	4.01400e12	0.352383	0.176191	−	0.984356i	$-0.443622\pi$
$797$	4.01400e12	0.352383	0.176191	+	0.984356i	$0.443622\pi$
$798$	2.83256e13	2.47267
$799$	−2.36986e12	−0.205713
$800$	−8.62723e11	−0.0744674
$801$	1.43070e13	1.22801
$802$	1.16235e13	0.992095
$803$	−1.47395e13	−1.25101
$804$	2.99389e12	0.252688
$805$	−1.54983e13	−1.30078
$806$	0	0
$807$	−3.47654e12	−0.288547
$808$	6.50652e11	0.0537029
$809$	9.72226e12	0.797993	0.398996	−	0.916953i	$-0.369359\pi$
$809$	9.72226e12	0.797993	0.398996	+	0.916953i	$0.369359\pi$
$810$	7.80340e12	0.636944
$811$	6.66026e12	0.540626	0.270313	−	0.962772i	$-0.412873\pi$
$811$	6.66026e12	0.540626	0.270313	+	0.962772i	$0.412873\pi$
$812$	1.57488e13	1.27129
$813$	−1.50660e13	−1.20946
$814$	−6.00558e12	−0.479452
$815$	1.22211e13	0.970290
$816$	5.87981e12	0.464256
$817$	2.38218e13	1.87057
$818$	−7.62697e12	−0.595611
$819$	0	0
$820$	−2.95580e12	−0.228304
$821$	1.89842e13	1.45830	0.729151	−	0.684353i	$-0.239915\pi$
$821$	1.89842e13	1.45830	0.729151	+	0.684353i	$0.239915\pi$
$822$	−8.59679e12	−0.656770
$823$	6.62799e12	0.503596	0.251798	−	0.967780i	$-0.418978\pi$
$823$	6.62799e12	0.503596	0.251798	+	0.967780i	$0.418978\pi$
$824$	1.53418e12	0.115932
$825$	9.20289e12	0.691642
$826$	1.94527e13	1.45402
$827$	−4.06874e12	−0.302472	−0.151236	−	0.988498i	$-0.548325\pi$
$827$	−4.06874e12	−0.302472	−0.151236	+	0.988498i	$0.548325\pi$
$828$	−4.70733e12	−0.348047
$829$	−1.67223e13	−1.22970	−0.614850	−	0.788644i	$-0.710784\pi$
$829$	−1.67223e13	−1.22970	−0.614850	+	0.788644i	$0.710784\pi$
$830$	−4.05092e12	−0.296280
$831$	−4.47523e12	−0.325545
$832$	0	0
$833$	−4.44490e13	−3.19860
$834$	4.91261e12	0.351613
$835$	4.29247e12	0.305575
$836$	−9.75792e12	−0.690922
$837$	3.25500e12	0.229238
$838$	−1.15609e12	−0.0809829
$839$	−3.95231e12	−0.275373	−0.137687	−	0.990476i	$-0.543967\pi$
$839$	−3.95231e12	−0.275373	−0.137687	+	0.990476i	$0.543967\pi$
$840$	1.70250e13	1.17986
$841$	1.18620e13	0.817665
$842$	1.34838e13	0.924499
$843$	−2.46470e13	−1.68089
$844$	1.02159e13	0.693002
$845$	0	0
$846$	−2.08419e12	−0.139885
$847$	6.31608e12	0.421669
$848$	1.84401e12	0.122456
$849$	−3.28726e13	−2.17145
$850$	5.67162e12	0.372668
$851$	5.42593e12	0.354643
$852$	5.06618e12	0.329384
$853$	−1.80193e12	−0.116538	−0.0582691	−	0.998301i	$-0.518558\pi$
$853$	−1.80193e12	−0.116538	−0.0582691	+	0.998301i	$0.518558\pi$
$854$	−2.72756e11	−0.0175475
$855$	2.79991e13	1.79183
$856$	7.19163e12	0.457821
$857$	−2.14106e13	−1.35586	−0.677929	−	0.735127i	$-0.737122\pi$
$857$	−2.14106e13	−1.35586	−0.677929	+	0.735127i	$0.737122\pi$
$858$	0	0
$859$	1.84429e13	1.15574	0.577869	−	0.816129i	$-0.303884\pi$
$859$	1.84429e13	1.15574	0.577869	+	0.816129i	$0.303884\pi$
$860$	1.43180e13	0.892563
$861$	1.72887e13	1.07213
$862$	1.73997e13	1.07339
$863$	−1.24982e13	−0.767005	−0.383503	−	0.923540i	$-0.625282\pi$
$863$	−1.24982e13	−0.767005	−0.383503	+	0.923540i	$0.625282\pi$
$864$	8.73121e11	0.0533043
$865$	−1.97851e13	−1.20161
$866$	5.96830e12	0.360595
$867$	−1.39594e13	−0.839038
$868$	−1.19888e13	−0.716865
$869$	3.17930e12	0.189122
$870$	2.85060e13	1.68694
$871$	0	0
$872$	8.06628e11	0.0472443
$873$	3.44548e13	2.00764
$874$	8.81609e12	0.511063
$875$	−2.25621e13	−1.30120
$876$	−1.46287e13	−0.839336
$877$	2.72954e13	1.55809	0.779043	−	0.626971i	$-0.215705\pi$
$877$	2.72954e13	1.55809	0.779043	+	0.626971i	$0.215705\pi$
$878$	−1.19377e13	−0.677945
$879$	9.14519e11	0.0516705
$880$	−5.86497e12	−0.329681
$881$	3.94286e12	0.220505	0.110253	−	0.993904i	$-0.464834\pi$
$881$	3.94286e12	0.220505	0.110253	+	0.993904i	$0.464834\pi$
$882$	−3.90911e13	−2.17505
$883$	1.87096e13	1.03572	0.517859	−	0.855466i	$-0.326729\pi$
$883$	1.87096e13	1.03572	0.517859	+	0.855466i	$0.326729\pi$
$884$	0	0
$885$	3.52102e13	1.92941
$886$	9.96985e12	0.543546
$887$	1.16619e13	0.632576	0.316288	−	0.948663i	$-0.397563\pi$
$887$	1.16619e13	0.632576	0.316288	+	0.948663i	$0.397563\pi$
$888$	−5.96043e12	−0.321676
$889$	3.26316e13	1.75219
$890$	−1.61050e13	−0.860408
$891$	1.57235e13	0.835794
$892$	−7.76106e12	−0.410468
$893$	3.90337e12	0.205403
$894$	−2.26204e12	−0.118435
$895$	1.42344e13	0.741542
$896$	−3.21587e12	−0.166691
$897$	0	0
$898$	3.00966e12	0.154445
$899$	−2.00736e13	−1.02496
$900$	4.98795e12	0.253414
$901$	−1.21227e13	−0.612826
$902$	−5.95580e12	−0.299579
$903$	−8.37469e13	−4.19154
$904$	−5.53450e12	−0.275626
$905$	2.19711e13	1.08876
$906$	3.47843e13	1.71517
$907$	−1.60523e13	−0.787599	−0.393799	−	0.919196i	$-0.628840\pi$
$907$	−1.60523e13	−0.787599	−0.393799	+	0.919196i	$0.628840\pi$
$908$	−3.06013e11	−0.0149401
$909$	−3.76183e12	−0.182752
$910$	0	0
$911$	2.26003e13	1.08713	0.543564	−	0.839368i	$-0.317075\pi$
$911$	2.26003e13	1.08713	0.543564	+	0.839368i	$0.317075\pi$
$912$	−9.68455e12	−0.463557
$913$	−8.16241e12	−0.388776
$914$	2.22380e12	0.105399
$915$	−4.93700e11	−0.0232846
$916$	−6.11377e12	−0.286932
$917$	3.31405e13	1.54774
$918$	−5.73997e12	−0.266758
$919$	2.90227e13	1.34220	0.671102	−	0.741365i	$-0.265821\pi$
$919$	2.90227e13	1.34220	0.671102	+	0.741365i	$0.265821\pi$
$920$	5.29888e12	0.243859
$921$	6.33463e13	2.90103
$922$	−3.21750e12	−0.146632
$923$	0	0
$924$	3.43046e13	1.54820
$925$	−5.74939e12	−0.258216
$926$	1.53329e13	0.685293
$927$	−8.87008e12	−0.394520
$928$	−5.38453e12	−0.238332
$929$	1.99051e13	0.876784	0.438392	−	0.898784i	$-0.355548\pi$
$929$	1.99051e13	0.876784	0.438392	+	0.898784i	$0.355548\pi$
$930$	−2.17003e13	−0.951243
$931$	7.32114e13	3.19378
$932$	−1.96939e13	−0.854989
$933$	−4.89073e13	−2.11303
$934$	−2.75922e13	−1.18639
$935$	3.85568e13	1.64987
$936$	0	0
$937$	3.43703e13	1.45665	0.728326	−	0.685231i	$-0.240299\pi$
$937$	3.43703e13	1.45665	0.728326	+	0.685231i	$0.240299\pi$
$938$	1.07649e13	0.454041
$939$	−3.58737e13	−1.50585
$940$	2.34611e12	0.0980105
$941$	−2.03841e13	−0.847499	−0.423750	−	0.905779i	$-0.639286\pi$
$941$	−2.03841e13	−0.847499	−0.423750	+	0.905779i	$0.639286\pi$
$942$	−4.15352e12	−0.171865
$943$	5.38095e12	0.221593
$944$	−6.65090e12	−0.272588
$945$	−1.66201e13	−0.677940
$946$	2.88501e13	1.17122
$947$	−3.69932e13	−1.49467	−0.747337	−	0.664445i	$-0.768668\pi$
$947$	−3.69932e13	−1.49467	−0.747337	+	0.664445i	$0.768668\pi$
$948$	3.15540e12	0.126887
$949$	0	0
$950$	−9.34165e12	−0.372106
$951$	−6.07106e13	−2.40687
$952$	2.11414e13	0.834196
$953$	1.84856e13	0.725965	0.362982	−	0.931796i	$-0.381759\pi$
$953$	1.84856e13	0.725965	0.362982	+	0.931796i	$0.381759\pi$
$954$	−1.06614e13	−0.416722
$955$	−4.46716e12	−0.173787
$956$	8.34352e12	0.323064
$957$	5.74382e13	2.21359
$958$	5.95587e12	0.228455
$959$	−3.09107e13	−1.18012
$960$	−5.82087e12	−0.221191
$961$	−1.11586e13	−0.422039
$962$	0	0
$963$	−4.15794e13	−1.55797
$964$	−1.92262e13	−0.717045
$965$	−4.90880e13	−1.82223
$966$	−3.09935e13	−1.14518
$967$	1.82143e13	0.669873	0.334937	−	0.942241i	$-0.391285\pi$
$967$	1.82143e13	0.669873	0.334937	+	0.942241i	$0.391285\pi$
$968$	−2.15948e12	−0.0790513
$969$	6.36671e13	2.31984
$970$	−3.87847e13	−1.40665
$971$	4.63902e12	0.167471	0.0837355	−	0.996488i	$-0.473315\pi$
$971$	4.63902e12	0.167471	0.0837355	+	0.996488i	$0.473315\pi$
$972$	1.98010e13	0.711522
$973$	1.76638e13	0.631794
$974$	−1.36220e13	−0.484981
$975$	0	0
$976$	9.32557e10	0.00328966
$977$	−7.68621e10	−0.00269890	−0.00134945	−	0.999999i	$-0.500430\pi$
$977$	−7.68621e10	−0.00269890	−0.00134945	+	0.999999i	$0.500430\pi$
$978$	2.44398e13	0.854226
$979$	−3.24507e13	−1.12902
$980$	4.40035e13	1.52395
$981$	−4.66363e12	−0.160773
$982$	1.48989e13	0.511273
$983$	−3.19134e13	−1.09014	−0.545069	−	0.838391i	$-0.683497\pi$
$983$	−3.19134e13	−1.09014	−0.545069	+	0.838391i	$0.683497\pi$
$984$	−5.91102e12	−0.200995
$985$	−2.51025e12	−0.0849676
$986$	3.53984e13	1.19272
$987$	−1.37225e13	−0.460264
$988$	0	0
$989$	−2.60655e13	−0.866328
$990$	3.39091e13	1.12191
$991$	1.95782e13	0.644824	0.322412	−	0.946600i	$-0.395506\pi$
$991$	1.95782e13	0.644824	0.322412	+	0.946600i	$0.395506\pi$
$992$	4.09899e12	0.134392
$993$	4.57815e13	1.49423
$994$	1.82160e13	0.591852
$995$	−3.23224e13	−1.04544
$996$	−8.10104e12	−0.260840
$997$	2.52846e12	0.0810452	0.0405226	−	0.999179i	$-0.487098\pi$
$997$	2.52846e12	0.0810452	0.0405226	+	0.999179i	$0.487098\pi$
$998$	−2.41159e13	−0.769514
$999$	5.81868e12	0.184833

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	338.10.a.m.1.2		10
13.2	odd	12		26.10.e.a.17.5	✓	20
13.7	odd	12		26.10.e.a.23.5	yes	20
13.12	even	2		338.10.a.n.1.2		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
26.10.e.a.17.5	✓	20	13.2	odd	12
26.10.e.a.23.5	yes	20	13.7	odd	12
338.10.a.m.1.2		10	1.1	even	1	trivial
338.10.a.n.1.2		10	13.12	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

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

\(f(q)\)	\(=\)	\(q-16.0000 q^{2} -208.242 q^{3} +256.000 q^{4} +1666.10 q^{5} +3331.87 q^{6} +11980.1 q^{7} -4096.00 q^{8} +23681.6 q^{9} -26657.6 q^{10} -53713.7 q^{11} -53309.9 q^{12} -191681. q^{14} -346951. q^{15} +65536.0 q^{16} -430839. q^{17} -378905. q^{18} +709630. q^{19} +426521. q^{20} -2.49475e6 q^{21} +859419. q^{22} -776469. q^{23} +852958. q^{24} +822757. q^{25} -832673. q^{27} +3.06690e6 q^{28} +5.13509e6 q^{29} +5.55122e6 q^{30} -3.90910e6 q^{31} -1.04858e6 q^{32} +1.11854e7 q^{33} +6.89343e6 q^{34} +1.99600e7 q^{35} +6.06249e6 q^{36} -6.98795e6 q^{37} -1.13541e7 q^{38} -6.82434e6 q^{40} -6.93003e6 q^{41} +3.99160e7 q^{42} +3.35693e7 q^{43} -1.37507e7 q^{44} +3.94558e7 q^{45} +1.24235e7 q^{46} +5.50056e6 q^{47} -1.36473e7 q^{48} +1.03168e8 q^{49} -1.31641e7 q^{50} +8.97187e7 q^{51} +2.81373e7 q^{53} +1.33228e7 q^{54} -8.94923e7 q^{55} -4.90704e7 q^{56} -1.47775e8 q^{57} -8.21614e7 q^{58} -1.01485e8 q^{59} -8.88194e7 q^{60} +1.42297e6 q^{61} +6.25456e7 q^{62} +2.83707e8 q^{63} +1.67772e7 q^{64} -1.78967e8 q^{66} -5.61602e7 q^{67} -1.10295e8 q^{68} +1.61693e8 q^{69} -3.19359e8 q^{70} -9.50326e7 q^{71} -9.69998e7 q^{72} +2.74408e8 q^{73} +1.11807e8 q^{74} -1.71332e8 q^{75} +1.81665e8 q^{76} -6.43494e8 q^{77} -5.91897e7 q^{79} +1.09189e8 q^{80} -2.92728e8 q^{81} +1.10880e8 q^{82} +1.51961e8 q^{83} -6.38656e8 q^{84} -7.17821e8 q^{85} -5.37108e8 q^{86} -1.06934e9 q^{87} +2.20011e8 q^{88} +6.04142e8 q^{89} -6.31293e8 q^{90} -1.98776e8 q^{92} +8.14038e8 q^{93} -8.80090e7 q^{94} +1.18231e9 q^{95} +2.18357e8 q^{96} +1.45492e9 q^{97} -1.65069e9 q^{98} -1.27203e9 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - 160 q^{2} - 162 q^{3} + 2560 q^{4} + 3088 q^{5} + 2592 q^{6} + 11376 q^{7} - 40960 q^{8} + 54184 q^{9} - 49408 q^{10} - 8784 q^{11} - 41472 q^{12} - 182016 q^{14} + 357296 q^{15} + 655360 q^{16}+ \cdots + 199174752 q^{99}+O(q^{100}) \) 10 * q - 160 * q^2 - 162 * q^3 + 2560 * q^4 + 3088 * q^5 + 2592 * q^6 + 11376 * q^7 - 40960 * q^8 + 54184 * q^9 - 49408 * q^10 - 8784 * q^11 - 41472 * q^12 - 182016 * q^14 + 357296 * q^15 + 655360 * q^16 - 7446 * q^17 - 866944 * q^18 + 1520064 * q^19 + 790528 * q^20 - 1711648 * q^21 + 140544 * q^22 - 1308510 * q^23 + 663552 * q^24 + 4279466 * q^25 - 6880230 * q^27 + 2912256 * q^28 - 2343210 * q^29 - 5716736 * q^30 + 2693808 * q^31 - 10485760 * q^32 + 4567872 * q^33 + 119136 * q^34 + 23179536 * q^35 + 13871104 * q^36 + 32978928 * q^37 - 24321024 * q^38 - 12648448 * q^40 + 32690912 * q^41 + 27386368 * q^42 - 8233882 * q^43 - 2248704 * q^44 + 83696528 * q^45 + 20936160 * q^46 + 67552944 * q^47 - 10616832 * q^48 + 69922092 * q^49 - 68471456 * q^50 + 107347798 * q^51 + 87904728 * q^53 + 110083680 * q^54 + 69423408 * q^55 - 46596096 * q^56 - 197088768 * q^57 + 37491360 * q^58 + 157323568 * q^59 + 91467776 * q^60 + 68245766 * q^61 - 43100928 * q^62 + 262927520 * q^63 + 167772160 * q^64 - 73085952 * q^66 + 461709408 * q^67 - 1906176 * q^68 - 552088886 * q^69 - 370872576 * q^70 + 124194624 * q^71 - 221937664 * q^72 + 382312704 * q^73 - 527662848 * q^74 + 844565210 * q^75 + 389136384 * q^76 - 647268798 * q^77 - 389187960 * q^79 + 202375168 * q^80 - 1371213878 * q^81 - 523054592 * q^82 - 174671840 * q^83 - 438181888 * q^84 + 1034710608 * q^85 + 131742112 * q^86 - 1806098150 * q^87 + 35979264 * q^88 + 1731111552 * q^89 - 1339144448 * q^90 - 334978560 * q^92 + 2368608064 * q^93 - 1080847104 * q^94 - 4221476160 * q^95 + 169869312 * q^96 + 2693726784 * q^97 - 1118753472 * q^98 + 199174752 * q^99

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