LMFDB - Embedded newform 338.10.a.o.1.12

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 = [12,-192,-399,3072,562] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)

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

Self dual:	yes
Analytic conductor:	$174.082112623$
Analytic rank:	$1$
Dimension:	$12$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - x^{11} - 136646 x^{10} - 2261265 x^{9} + 6422687308 x^{8} + 214352365700 x^{7} + \cdots - 14\!\cdots\!24 $ x^12 - x^11 - 136646x^10 - 2261265x^9 + 6422687308x^8 + 214352365700x^7 - 113292049988480x^6 - 5422180918282688x^5 + 449225802381939008x^4 + 23649776612717976832x^3 - 253873801835065913984x^2 - 19616063257504031524864x - 140050093578719428109824
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{9}\cdot 3^{3}\cdot 7\cdot 13^{8} $
Twist minimal:	yes
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.12
Root			$225.484$ 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)

$f(q)$	$=$	\(q-16.0000 q^{2} +214.068 q^{3} +256.000 q^{4} -543.184 q^{5} -3425.09 q^{6} +7002.26 q^{7} -4096.00 q^{8} +26142.1 q^{9} +8690.94 q^{10} +22073.5 q^{11} +54801.4 q^{12} -112036. q^{14} -116278. q^{15} +65536.0 q^{16} -160293. q^{17} -418273. q^{18} +319608. q^{19} -139055. q^{20} +1.49896e6 q^{21} -353176. q^{22} -1.94692e6 q^{23} -876822. q^{24} -1.65808e6 q^{25} +1.38268e6 q^{27} +1.79258e6 q^{28} -6.36416e6 q^{29} +1.86045e6 q^{30} -7.65952e6 q^{31} -1.04858e6 q^{32} +4.72523e6 q^{33} +2.56468e6 q^{34} -3.80352e6 q^{35} +6.69237e6 q^{36} +1.86035e6 q^{37} -5.11373e6 q^{38} +2.22488e6 q^{40} -1.49835e7 q^{41} -2.39834e7 q^{42} -1.31570e7 q^{43} +5.65082e6 q^{44} -1.42000e7 q^{45} +3.11507e7 q^{46} +5.07440e7 q^{47} +1.40292e7 q^{48} +8.67806e6 q^{49} +2.65292e7 q^{50} -3.43136e7 q^{51} +6.39570e7 q^{53} -2.21229e7 q^{54} -1.19900e7 q^{55} -2.86813e7 q^{56} +6.84179e7 q^{57} +1.01827e8 q^{58} -4.95386e7 q^{59} -2.97672e7 q^{60} -9.47554e7 q^{61} +1.22552e8 q^{62} +1.83054e8 q^{63} +1.67772e7 q^{64} -7.56037e7 q^{66} -3.03905e8 q^{67} -4.10350e7 q^{68} -4.16773e8 q^{69} +6.08563e7 q^{70} -3.10294e7 q^{71} -1.07078e8 q^{72} -9.77274e7 q^{73} -2.97656e7 q^{74} -3.54941e8 q^{75} +8.18197e7 q^{76} +1.54565e8 q^{77} -6.40154e8 q^{79} -3.55981e7 q^{80} -2.18566e8 q^{81} +2.39736e8 q^{82} +6.01226e8 q^{83} +3.83734e8 q^{84} +8.70685e7 q^{85} +2.10512e8 q^{86} -1.36236e9 q^{87} -9.04131e7 q^{88} -3.98742e8 q^{89} +2.27199e8 q^{90} -4.98411e8 q^{92} -1.63966e9 q^{93} -8.11903e8 q^{94} -1.73606e8 q^{95} -2.24467e8 q^{96} +1.54108e9 q^{97} -1.38849e8 q^{98} +5.77048e8 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 192 q^{2} - 399 q^{3} + 3072 q^{4} + 562 q^{5} + 6384 q^{6} - 3161 q^{7} - 49152 q^{8} + 54783 q^{9} - 8992 q^{10} + 164271 q^{11} - 102144 q^{12} + 50576 q^{14} - 434244 q^{15} + 786432 q^{16} - 649529 q^{17}+ \cdots + 4431369848 q^{99}+O(q^{100}) $ 12 * q - 192 * q^2 - 399 * q^3 + 3072 * q^4 + 562 * q^5 + 6384 * q^6 - 3161 * q^7 - 49152 * q^8 + 54783 * q^9 - 8992 * q^10 + 164271 * q^11 - 102144 * q^12 + 50576 * q^14 - 434244 * q^15 + 786432 * q^16 - 649529 * q^17 - 876528 * q^18 + 228567 * q^19 + 143872 * q^20 + 3321918 * q^21 - 2628336 * q^22 - 3365321 * q^23 + 1634304 * q^24 + 1357734 * q^25 - 7310211 * q^27 - 809216 * q^28 + 1210855 * q^29 + 6947904 * q^30 - 2031015 * q^31 - 12582912 * q^32 + 3709742 * q^33 + 10392464 * q^34 - 16818664 * q^35 + 14024448 * q^36 - 21152418 * q^37 - 3657072 * q^38 - 2301952 * q^40 + 20819170 * q^41 - 53150688 * q^42 - 37183522 * q^43 + 42053376 * q^44 + 51849705 * q^45 + 53845136 * q^46 - 20020222 * q^47 - 26148864 * q^48 - 79988801 * q^49 - 21723744 * q^50 - 72774687 * q^51 - 74983469 * q^53 + 116963376 * q^54 - 19133432 * q^55 + 12947456 * q^56 + 13760507 * q^57 - 19373680 * q^58 + 136123112 * q^59 - 111166464 * q^60 - 112790708 * q^61 + 32496240 * q^62 - 659441340 * q^63 + 201326592 * q^64 - 59355872 * q^66 + 61165134 * q^67 - 166279424 * q^68 - 69902864 * q^69 + 269098624 * q^70 - 212025009 * q^71 - 224391168 * q^72 - 71937292 * q^73 + 338438688 * q^74 - 628692958 * q^75 + 58513152 * q^76 - 527155758 * q^77 - 1146472537 * q^79 + 36831232 * q^80 + 1297690908 * q^81 - 333106720 * q^82 + 1318830968 * q^83 + 850411008 * q^84 + 1737694467 * q^85 + 594936352 * q^86 - 1405133144 * q^87 - 672854016 * q^88 + 3175197052 * q^89 - 829595280 * q^90 - 861522176 * q^92 + 2432770524 * q^93 + 320323552 * q^94 + 1551319209 * q^95 + 418381824 * q^96 + 5161204312 * q^97 + 1279820816 * q^98 + 4431369848 * 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
$3$	214.068	1.52583	0.762915	−	0.646499i	$-0.223768\pi$
$3$	214.068	1.52583	0.762915	+	0.646499i	$0.223768\pi$
$4$	256.000	0.500000
$5$	−543.184	−0.388671	−0.194335	−	0.980935i	$-0.562255\pi$
$5$	−543.184	−0.388671	−0.194335	+	0.980935i	$0.562255\pi$
$6$	−3425.09	−1.07892
$7$	7002.26	1.10229	0.551147	−	0.834408i	$-0.314190\pi$
$7$	7002.26	1.10229	0.551147	+	0.834408i	$0.314190\pi$
$8$	−4096.00	−0.353553
$9$	26142.1	1.32816
$10$	8690.94	0.274832
$11$	22073.5	0.454574	0.227287	−	0.973828i	$-0.427014\pi$
$11$	22073.5	0.454574	0.227287	+	0.973828i	$0.427014\pi$
$12$	54801.4	0.762915
$13$	0	0
$13$	0	0
$14$	−112036.	−0.779439
$15$	−116278.	−0.593045
$16$	65536.0	0.250000
$17$	−160293.	−0.465472	−0.232736	−	0.972540i	$-0.574768\pi$
$17$	−160293.	−0.465472	−0.232736	+	0.972540i	$0.574768\pi$
$18$	−418273.	−0.939148
$19$	319608.	0.562635	0.281318	−	0.959615i	$-0.409229\pi$
$19$	319608.	0.562635	0.281318	+	0.959615i	$0.409229\pi$
$20$	−139055.	−0.194335
$21$	1.49896e6	1.68191
$22$	−353176.	−0.321432
$23$	−1.94692e6	−1.45068	−0.725342	−	0.688389i	$-0.758318\pi$
$23$	−1.94692e6	−1.45068	−0.725342	+	0.688389i	$0.758318\pi$
$24$	−876822.	−0.539462
$25$	−1.65808e6	−0.848935
$26$	0	0
$27$	1.38268e6	0.500709
$28$	1.79258e6	0.551147
$29$	−6.36416e6	−1.67090	−0.835449	−	0.549568i	$-0.814792\pi$
$29$	−6.36416e6	−1.67090	−0.835449	+	0.549568i	$0.814792\pi$
$30$	1.86045e6	0.419346
$31$	−7.65952e6	−1.48961	−0.744807	−	0.667280i	$-0.767459\pi$
$31$	−7.65952e6	−1.48961	−0.744807	+	0.667280i	$0.767459\pi$
$32$	−1.04858e6	−0.176777
$33$	4.72523e6	0.693602
$34$	2.56468e6	0.329139
$35$	−3.80352e6	−0.428429
$36$	6.69237e6	0.664078
$37$	1.86035e6	0.163187	0.0815937	−	0.996666i	$-0.473999\pi$
$37$	1.86035e6	0.163187	0.0815937	+	0.996666i	$0.473999\pi$
$38$	−5.11373e6	−0.397843
$39$	0	0
$40$	2.22488e6	0.137416
$41$	−1.49835e7	−0.828104	−0.414052	−	0.910253i	$-0.635887\pi$
$41$	−1.49835e7	−0.828104	−0.414052	+	0.910253i	$0.635887\pi$
$42$	−2.39834e7	−1.18929
$43$	−1.31570e7	−0.586880	−0.293440	−	0.955977i	$-0.594800\pi$
$43$	−1.31570e7	−0.586880	−0.293440	+	0.955977i	$0.594800\pi$
$44$	5.65082e6	0.227287
$45$	−1.42000e7	−0.516215
$46$	3.11507e7	1.02579
$47$	5.07440e7	1.51685	0.758427	−	0.651758i	$-0.225968\pi$
$47$	5.07440e7	1.51685	0.758427	+	0.651758i	$0.225968\pi$
$48$	1.40292e7	0.381457
$49$	8.67806e6	0.215050
$50$	2.65292e7	0.600288
$51$	−3.43136e7	−0.710231
$52$	0	0
$53$	6.39570e7	1.11339	0.556694	−	0.830717i	$-0.312069\pi$
$53$	6.39570e7	1.11339	0.556694	+	0.830717i	$0.312069\pi$
$54$	−2.21229e7	−0.354055
$55$	−1.19900e7	−0.176680
$56$	−2.86813e7	−0.389720
$57$	6.84179e7	0.858485
$58$	1.01827e8	1.18150
$59$	−4.95386e7	−0.532242	−0.266121	−	0.963940i	$-0.585742\pi$
$59$	−4.95386e7	−0.532242	−0.266121	+	0.963940i	$0.585742\pi$
$60$	−2.97672e7	−0.296523
$61$	−9.47554e7	−0.876233	−0.438117	−	0.898918i	$-0.644354\pi$
$61$	−9.47554e7	−0.876233	−0.438117	+	0.898918i	$0.644354\pi$
$62$	1.22552e8	1.05332
$63$	1.83054e8	1.46402
$64$	1.67772e7	0.125000
$65$	0	0
$66$	−7.56037e7	−0.490451
$67$	−3.03905e8	−1.84248	−0.921238	−	0.388999i	$-0.872821\pi$
$67$	−3.03905e8	−1.84248	−0.921238	+	0.388999i	$0.872821\pi$
$68$	−4.10350e7	−0.232736
$69$	−4.16773e8	−2.21350
$70$	6.08563e7	0.302945
$71$	−3.10294e7	−0.144914	−0.0724571	−	0.997372i	$-0.523084\pi$
$71$	−3.10294e7	−0.144914	−0.0724571	+	0.997372i	$0.523084\pi$
$72$	−1.07078e8	−0.469574
$73$	−9.77274e7	−0.402776	−0.201388	−	0.979512i	$-0.564545\pi$
$73$	−9.77274e7	−0.402776	−0.201388	+	0.979512i	$0.564545\pi$
$74$	−2.97656e7	−0.115391
$75$	−3.54941e8	−1.29533
$76$	8.18197e7	0.281318
$77$	1.54565e8	0.501074
$78$	0	0
$79$	−6.40154e8	−1.84911	−0.924555	−	0.381050i	$-0.875563\pi$
$79$	−6.40154e8	−1.84911	−0.924555	+	0.381050i	$0.875563\pi$
$80$	−3.55981e7	−0.0971677
$81$	−2.18566e8	−0.564158
$82$	2.39736e8	0.585558
$83$	6.01226e8	1.39055	0.695274	−	0.718744i	$-0.255283\pi$
$83$	6.01226e8	1.39055	0.695274	+	0.718744i	$0.255283\pi$
$84$	3.83734e8	0.840956
$85$	8.70685e7	0.180916
$86$	2.10512e8	0.414987
$87$	−1.36236e9	−2.54951
$88$	−9.04131e7	−0.160716
$89$	−3.98742e8	−0.673655	−0.336827	−	0.941566i	$-0.609354\pi$
$89$	−3.98742e8	−0.673655	−0.336827	+	0.941566i	$0.609354\pi$
$90$	2.27199e8	0.365019
$91$	0	0
$92$	−4.98411e8	−0.725342
$93$	−1.63966e9	−2.27290
$94$	−8.11903e8	−1.07258
$95$	−1.73606e8	−0.218680
$96$	−2.24467e8	−0.269731
$97$	1.54108e9	1.76747	0.883733	−	0.467991i	$-0.155022\pi$
$97$	1.54108e9	1.76747	0.883733	+	0.467991i	$0.155022\pi$
$98$	−1.38849e8	−0.152064
$99$	5.77048e8	0.603745
$100$	−4.24467e8	−0.424467
$101$	1.97167e9	1.88533	0.942667	−	0.333735i	$-0.108309\pi$
$101$	1.97167e9	1.88533	0.942667	+	0.333735i	$0.108309\pi$
$102$	5.49017e8	0.502209
$103$	−7.94164e8	−0.695252	−0.347626	−	0.937633i	$-0.613012\pi$
$103$	−7.94164e8	−0.695252	−0.347626	+	0.937633i	$0.613012\pi$
$104$	0	0
$105$	−8.14211e8	−0.653710
$106$	−1.02331e9	−0.787285
$107$	1.04673e9	0.771981	0.385991	−	0.922503i	$-0.373860\pi$
$107$	1.04673e9	0.771981	0.385991	+	0.922503i	$0.373860\pi$
$108$	3.53967e8	0.250355
$109$	−9.16572e8	−0.621938	−0.310969	−	0.950420i	$-0.600654\pi$
$109$	−9.16572e8	−0.621938	−0.310969	+	0.950420i	$0.600654\pi$
$110$	1.91840e8	0.124931
$111$	3.98241e8	0.248996
$112$	4.58900e8	0.275573
$113$	6.62151e7	0.0382036	0.0191018	−	0.999818i	$-0.493919\pi$
$113$	6.62151e7	0.0382036	0.0191018	+	0.999818i	$0.493919\pi$
$114$	−1.09469e9	−0.607041
$115$	1.05754e9	0.563838
$116$	−1.62922e9	−0.835449
$117$	0	0
$118$	7.92617e8	0.376352
$119$	−1.12241e9	−0.513087
$120$	4.76276e8	0.209673
$121$	−1.87071e9	−0.793363
$122$	1.51609e9	0.619590
$123$	−3.20748e9	−1.26355
$124$	−1.96084e9	−0.744807
$125$	1.96155e9	0.718627
$126$	−2.92886e9	−1.03522
$127$	4.16674e9	1.42128	0.710639	−	0.703556i	$-0.248406\pi$
$127$	4.16674e9	1.42128	0.710639	+	0.703556i	$0.248406\pi$
$128$	−2.68435e8	−0.0883883
$129$	−2.81650e9	−0.895480
$130$	0	0
$131$	−1.62751e9	−0.482840	−0.241420	−	0.970421i	$-0.577613\pi$
$131$	−1.62751e9	−0.482840	−0.241420	+	0.970421i	$0.577613\pi$
$132$	1.20966e9	0.346801
$133$	2.23798e9	0.620189
$134$	4.86249e9	1.30283
$135$	−7.51052e8	−0.194611
$136$	6.56559e8	0.164569
$137$	5.28874e9	1.28265	0.641327	−	0.767267i	$-0.278384\pi$
$137$	5.28874e9	1.28265	0.641327	+	0.767267i	$0.278384\pi$
$138$	6.66837e9	1.56518
$139$	2.41456e8	0.0548619	0.0274310	−	0.999624i	$-0.491267\pi$
$139$	2.41456e8	0.0548619	0.0274310	+	0.999624i	$0.491267\pi$
$140$	−9.73700e8	−0.214215
$141$	1.08627e10	2.31446
$142$	4.96471e8	0.102470
$143$	0	0
$144$	1.71325e9	0.332039
$145$	3.45691e9	0.649429
$146$	1.56364e9	0.284806
$147$	1.85770e9	0.328130
$148$	4.76249e8	0.0815937
$149$	−3.77246e9	−0.627027	−0.313513	−	0.949584i	$-0.601506\pi$
$149$	−3.77246e9	−0.627027	−0.313513	+	0.949584i	$0.601506\pi$
$150$	5.67906e9	0.915937
$151$	−9.98101e9	−1.56235	−0.781175	−	0.624312i	$-0.785379\pi$
$151$	−9.98101e9	−1.56235	−0.781175	+	0.624312i	$0.785379\pi$
$152$	−1.30912e9	−0.198922
$153$	−4.19039e9	−0.618220
$154$	−2.47303e9	−0.354313
$155$	4.16053e9	0.578970
$156$	0	0
$157$	−6.60326e9	−0.867381	−0.433691	−	0.901062i	$-0.642789\pi$
$157$	−6.60326e9	−0.867381	−0.433691	+	0.901062i	$0.642789\pi$
$158$	1.02425e10	1.30752
$159$	1.36912e10	1.69884
$160$	5.69570e8	0.0687079
$161$	−1.36328e10	−1.59908
$162$	3.49706e9	0.398920
$163$	1.05234e10	1.16764	0.583821	−	0.811882i	$-0.301557\pi$
$163$	1.05234e10	1.16764	0.583821	+	0.811882i	$0.301557\pi$
$164$	−3.83577e9	−0.414052
$165$	−2.56667e9	−0.269583
$166$	−9.61961e9	−0.983267
$167$	−7.50019e8	−0.0746188	−0.0373094	−	0.999304i	$-0.511879\pi$
$167$	−7.50019e8	−0.0746188	−0.0373094	+	0.999304i	$0.511879\pi$
$168$	−6.13974e9	−0.594646
$169$	0	0
$170$	−1.39310e9	−0.127927
$171$	8.35523e9	0.747267
$172$	−3.36820e9	−0.293440
$173$	1.52159e10	1.29149	0.645745	−	0.763553i	$-0.276547\pi$
$173$	1.52159e10	1.29149	0.645745	+	0.763553i	$0.276547\pi$
$174$	2.17978e10	1.80277
$175$	−1.16103e10	−0.935775
$176$	1.44661e9	0.113643
$177$	−1.06046e10	−0.812111
$178$	6.37988e9	0.476346
$179$	−1.42967e10	−1.04087	−0.520434	−	0.853902i	$-0.674230\pi$
$179$	−1.42967e10	−1.04087	−0.520434	+	0.853902i	$0.674230\pi$
$180$	−3.63519e9	−0.258108
$181$	−1.61446e9	−0.111808	−0.0559041	−	0.998436i	$-0.517804\pi$
$181$	−1.61446e9	−0.111808	−0.0559041	+	0.998436i	$0.517804\pi$
$182$	0	0
$183$	−2.02841e10	−1.33698
$184$	7.97458e9	0.512894
$185$	−1.01051e9	−0.0634262
$186$	2.62345e10	1.60718
$187$	−3.53823e9	−0.211592
$188$	1.29905e10	0.758427
$189$	9.68191e9	0.551929
$190$	2.77770e9	0.154630
$191$	2.71988e10	1.47877	0.739385	−	0.673283i	$-0.235117\pi$
$191$	2.71988e10	1.47877	0.739385	+	0.673283i	$0.235117\pi$
$192$	3.59146e9	0.190729
$193$	1.15062e10	0.596931	0.298466	−	0.954420i	$-0.403525\pi$
$193$	1.15062e10	0.596931	0.298466	+	0.954420i	$0.403525\pi$
$194$	−2.46572e10	−1.24979
$195$	0	0
$196$	2.22158e9	0.107525
$197$	3.10270e9	0.146771	0.0733857	−	0.997304i	$-0.476620\pi$
$197$	3.10270e9	0.146771	0.0733857	+	0.997304i	$0.476620\pi$
$198$	−9.23276e9	−0.426912
$199$	3.08347e9	0.139380	0.0696900	−	0.997569i	$-0.477799\pi$
$199$	3.08347e9	0.139380	0.0696900	+	0.997569i	$0.477799\pi$
$200$	6.79148e9	0.300144
$201$	−6.50564e10	−2.81130
$202$	−3.15467e10	−1.33313
$203$	−4.45635e10	−1.84182
$204$	−8.78427e9	−0.355116
$205$	8.13878e9	0.321860
$206$	1.27066e10	0.491618
$207$	−5.08965e10	−1.92673
$208$	0	0
$209$	7.05488e9	0.255759
$210$	1.30274e10	0.462243
$211$	1.81636e10	0.630856	0.315428	−	0.948950i	$-0.397852\pi$
$211$	1.81636e10	0.630856	0.315428	+	0.948950i	$0.397852\pi$
$212$	1.63730e10	0.556694
$213$	−6.64240e9	−0.221114
$214$	−1.67476e10	−0.545873
$215$	7.14669e9	0.228103
$216$	−5.66347e9	−0.177028
$217$	−5.36339e10	−1.64199
$218$	1.46651e10	0.439777
$219$	−2.09203e10	−0.614567
$220$	−3.06944e9	−0.0883398
$221$	0	0
$222$	−6.37186e9	−0.176067
$223$	−4.07436e10	−1.10328	−0.551642	−	0.834081i	$-0.685998\pi$
$223$	−4.07436e10	−1.10328	−0.551642	+	0.834081i	$0.685998\pi$
$224$	−7.34240e9	−0.194860
$225$	−4.33456e10	−1.12752
$226$	−1.05944e9	−0.0270140
$227$	−2.94809e10	−0.736926	−0.368463	−	0.929642i	$-0.620116\pi$
$227$	−2.94809e10	−0.736926	−0.368463	+	0.929642i	$0.620116\pi$
$228$	1.75150e10	0.429243
$229$	−1.20107e10	−0.288607	−0.144304	−	0.989533i	$-0.546094\pi$
$229$	−1.20107e10	−0.288607	−0.144304	+	0.989533i	$0.546094\pi$
$230$	−1.69206e10	−0.398694
$231$	3.30873e10	0.764553
$232$	2.60676e10	0.590752
$233$	−2.13260e10	−0.474032	−0.237016	−	0.971506i	$-0.576169\pi$
$233$	−2.13260e10	−0.474032	−0.237016	+	0.971506i	$0.576169\pi$
$234$	0	0
$235$	−2.75633e10	−0.589557
$236$	−1.26819e10	−0.266121
$237$	−1.37036e11	−2.82143
$238$	1.79586e10	0.362807
$239$	3.87588e10	0.768386	0.384193	−	0.923253i	$-0.374480\pi$
$239$	3.87588e10	0.768386	0.384193	+	0.923253i	$0.374480\pi$
$240$	−7.62041e9	−0.148261
$241$	2.95025e10	0.563355	0.281677	−	0.959509i	$-0.409109\pi$
$241$	2.95025e10	0.563355	0.281677	+	0.959509i	$0.409109\pi$
$242$	2.99313e10	0.560992
$243$	−7.40034e10	−1.36152
$244$	−2.42574e10	−0.438117
$245$	−4.71379e9	−0.0835839
$246$	5.13197e10	0.893462
$247$	0	0
$248$	3.13734e10	0.526658
$249$	1.28703e11	2.12174
$250$	−3.13847e10	−0.508146
$251$	−7.72417e9	−0.122834	−0.0614172	−	0.998112i	$-0.519562\pi$
$251$	−7.72417e9	−0.122834	−0.0614172	+	0.998112i	$0.519562\pi$
$252$	4.68618e10	0.732008
$253$	−4.29754e10	−0.659443
$254$	−6.66678e10	−1.00500
$255$	1.86386e10	0.276046
$256$	4.29497e9	0.0625000
$257$	9.31679e10	1.33219	0.666097	−	0.745865i	$-0.267964\pi$
$257$	9.31679e10	1.33219	0.666097	+	0.745865i	$0.267964\pi$
$258$	4.50640e10	0.633200
$259$	1.30266e10	0.179880
$260$	0	0
$261$	−1.66372e11	−2.21921
$262$	2.60402e10	0.341419
$263$	−9.43492e10	−1.21601	−0.608006	−	0.793933i	$-0.708030\pi$
$263$	−9.43492e10	−1.21601	−0.608006	+	0.793933i	$0.708030\pi$
$264$	−1.93546e10	−0.245225
$265$	−3.47404e10	−0.432742
$266$	−3.58077e10	−0.438540
$267$	−8.53580e10	−1.02788
$268$	−7.77998e10	−0.921238
$269$	−1.55133e11	−1.80642	−0.903212	−	0.429194i	$-0.858798\pi$
$269$	−1.55133e11	−1.80642	−0.903212	+	0.429194i	$0.858798\pi$
$270$	1.20168e10	0.137611
$271$	8.46688e10	0.953590	0.476795	−	0.879014i	$-0.341798\pi$
$271$	8.46688e10	0.953590	0.476795	+	0.879014i	$0.341798\pi$
$272$	−1.05049e10	−0.116368
$273$	0	0
$274$	−8.46199e10	−0.906974
$275$	−3.65996e10	−0.385904
$276$	−1.06694e11	−1.10675
$277$	−1.08946e11	−1.11187	−0.555935	−	0.831226i	$-0.687640\pi$
$277$	−1.08946e11	−1.11187	−0.555935	+	0.831226i	$0.687640\pi$
$278$	−3.86329e9	−0.0387932
$279$	−2.00236e11	−1.97844
$280$	1.55792e10	0.151473
$281$	1.03370e11	0.989044	0.494522	−	0.869165i	$-0.335343\pi$
$281$	1.03370e11	0.989044	0.494522	+	0.869165i	$0.335343\pi$
$282$	−1.73802e11	−1.63657
$283$	9.16958e10	0.849788	0.424894	−	0.905243i	$-0.360311\pi$
$283$	9.16958e10	0.849788	0.424894	+	0.905243i	$0.360311\pi$
$284$	−7.94353e9	−0.0724571
$285$	−3.71635e10	−0.333668
$286$	0	0
$287$	−1.04918e11	−0.912814
$288$	−2.74120e10	−0.234787
$289$	−9.28941e10	−0.783336
$290$	−5.53105e10	−0.459216
$291$	3.29895e11	2.69685
$292$	−2.50182e10	−0.201388
$293$	−1.03773e11	−0.822583	−0.411292	−	0.911504i	$-0.634922\pi$
$293$	−1.03773e11	−0.822583	−0.411292	+	0.911504i	$0.634922\pi$
$294$	−2.97231e10	−0.232023
$295$	2.69086e10	0.206867
$296$	−7.61999e9	−0.0576954
$297$	3.05207e10	0.227609
$298$	6.03593e10	0.443375
$299$	0	0
$300$	−9.08649e10	−0.647665
$301$	−9.21289e10	−0.646914
$302$	1.59696e11	1.10475
$303$	4.22072e11	2.87670
$304$	2.09458e10	0.140659
$305$	5.14696e10	0.340566
$306$	6.70462e10	0.437147
$307$	−1.60123e11	−1.02880	−0.514401	−	0.857550i	$-0.671986\pi$
$307$	−1.60123e11	−1.02880	−0.514401	+	0.857550i	$0.671986\pi$
$308$	3.95685e10	0.250537
$309$	−1.70005e11	−1.06084
$310$	−6.65684e10	−0.409393
$311$	−2.22651e11	−1.34959	−0.674796	−	0.738004i	$-0.735768\pi$
$311$	−2.22651e11	−1.34959	−0.674796	+	0.738004i	$0.735768\pi$
$312$	0	0
$313$	1.04187e11	0.613573	0.306786	−	0.951778i	$-0.400746\pi$
$313$	1.04187e11	0.613573	0.306786	+	0.951778i	$0.400746\pi$
$314$	1.05652e11	0.613331
$315$	−9.94319e10	−0.569021
$316$	−1.63879e11	−0.924555
$317$	3.23443e10	0.179900	0.0899500	−	0.995946i	$-0.471329\pi$
$317$	3.23443e10	0.179900	0.0899500	+	0.995946i	$0.471329\pi$
$318$	−2.19058e11	−1.20126
$319$	−1.40479e11	−0.759547
$320$	−9.11312e9	−0.0485839
$321$	2.24071e11	1.17791
$322$	2.18125e11	1.13072
$323$	−5.12309e10	−0.261891
$324$	−5.59530e10	−0.282079
$325$	0	0
$326$	−1.68374e11	−0.825648
$327$	−1.96209e11	−0.948972
$328$	6.13723e10	0.292779
$329$	3.55322e11	1.67202
$330$	4.10667e10	0.190624
$331$	−2.85306e11	−1.30642	−0.653212	−	0.757175i	$-0.726579\pi$
$331$	−2.85306e11	−1.30642	−0.653212	+	0.757175i	$0.726579\pi$
$332$	1.53914e11	0.695274
$333$	4.86334e10	0.216738
$334$	1.20003e10	0.0527635
$335$	1.65077e11	0.716117
$336$	9.82358e10	0.420478
$337$	−2.47522e11	−1.04539	−0.522697	−	0.852519i	$-0.675074\pi$
$337$	−2.47522e11	−1.04539	−0.522697	+	0.852519i	$0.675074\pi$
$338$	0	0
$339$	1.41745e10	0.0582922
$340$	2.22895e10	0.0904578
$341$	−1.69072e11	−0.677140
$342$	−1.33684e11	−0.528397
$343$	−2.21800e11	−0.865245
$344$	5.38912e10	0.207494
$345$	2.26384e11	0.860321
$346$	−2.43455e11	−0.913221
$347$	−2.59297e11	−0.960098	−0.480049	−	0.877242i	$-0.659381\pi$
$347$	−2.59297e11	−0.960098	−0.480049	+	0.877242i	$0.659381\pi$
$348$	−3.48765e11	−1.27475
$349$	−1.65421e11	−0.596867	−0.298433	−	0.954430i	$-0.596464\pi$
$349$	−1.65421e11	−0.596867	−0.298433	+	0.954430i	$0.596464\pi$
$350$	1.85765e11	0.661693
$351$	0	0
$352$	−2.31458e10	−0.0803581
$353$	3.91322e11	1.34137	0.670684	−	0.741743i	$-0.266001\pi$
$353$	3.91322e11	1.34137	0.670684	+	0.741743i	$0.266001\pi$
$354$	1.69674e11	0.574249
$355$	1.68547e10	0.0563239
$356$	−1.02078e11	−0.336827
$357$	−2.40272e11	−0.782883
$358$	2.28746e11	0.736005
$359$	6.93669e9	0.0220408	0.0110204	−	0.999939i	$-0.496492\pi$
$359$	6.93669e9	0.0220408	0.0110204	+	0.999939i	$0.496492\pi$
$360$	5.81631e10	0.182510
$361$	−2.20538e11	−0.683442
$362$	2.58314e10	0.0790603
$363$	−4.00459e11	−1.21054
$364$	0	0
$365$	5.30840e10	0.156547
$366$	3.24546e11	0.945389
$367$	4.70305e11	1.35326	0.676631	−	0.736322i	$-0.263439\pi$
$367$	4.70305e11	1.35326	0.676631	+	0.736322i	$0.263439\pi$
$368$	−1.27593e11	−0.362671
$369$	−3.91699e11	−1.09985
$370$	1.61682e10	0.0448491
$371$	4.47844e11	1.22728
$372$	−4.19752e11	−1.13645
$373$	−2.97318e10	−0.0795300	−0.0397650	−	0.999209i	$-0.512661\pi$
$373$	−2.97318e10	−0.0795300	−0.0397650	+	0.999209i	$0.512661\pi$
$374$	5.66116e10	0.149618
$375$	4.19904e11	1.09650
$376$	−2.07847e11	−0.536289
$377$	0	0
$378$	−1.54911e11	−0.390273
$379$	6.21819e11	1.54806	0.774030	−	0.633149i	$-0.218238\pi$
$379$	6.21819e11	1.54806	0.774030	+	0.633149i	$0.218238\pi$
$380$	−4.44432e10	−0.109340
$381$	8.91965e11	2.16863
$382$	−4.35182e11	−1.04565
$383$	7.75402e11	1.84133	0.920667	−	0.390349i	$-0.127646\pi$
$383$	7.75402e11	1.84133	0.920667	+	0.390349i	$0.127646\pi$
$384$	−5.74634e10	−0.134866
$385$	−8.39570e10	−0.194753
$386$	−1.84099e11	−0.422094
$387$	−3.43952e11	−0.779469
$388$	3.94515e11	0.883733
$389$	−4.18910e11	−0.927573	−0.463786	−	0.885947i	$-0.653509\pi$
$389$	−4.18910e11	−0.927573	−0.463786	+	0.885947i	$0.653509\pi$
$390$	0	0
$391$	3.12077e11	0.675253
$392$	−3.55453e10	−0.0760318
$393$	−3.48398e11	−0.736731
$394$	−4.96431e10	−0.103783
$395$	3.47721e11	0.718695
$396$	1.47724e11	0.301872
$397$	−2.34885e11	−0.474567	−0.237283	−	0.971440i	$-0.576257\pi$
$397$	−2.34885e11	−0.474567	−0.237283	+	0.971440i	$0.576257\pi$
$398$	−4.93355e10	−0.0985566
$399$	4.79080e11	0.946302
$400$	−1.08664e11	−0.212234
$401$	4.85397e10	0.0937449	0.0468724	−	0.998901i	$-0.485075\pi$
$401$	4.85397e10	0.0937449	0.0468724	+	0.998901i	$0.485075\pi$
$402$	1.04090e12	1.98789
$403$	0	0
$404$	5.04748e11	0.942667
$405$	1.18722e11	0.219272
$406$	7.13016e11	1.30236
$407$	4.10644e10	0.0741807
$408$	1.40548e11	0.251105
$409$	−1.39589e11	−0.246659	−0.123329	−	0.992366i	$-0.539357\pi$
$409$	−1.39589e11	−0.246659	−0.123329	+	0.992366i	$0.539357\pi$
$410$	−1.30221e11	−0.227589
$411$	1.13215e12	1.95711
$412$	−2.03306e11	−0.347626
$413$	−3.46882e11	−0.586687
$414$	8.14345e11	1.36241
$415$	−3.26576e11	−0.540466
$416$	0	0
$417$	5.16879e10	0.0837099
$418$	−1.12878e11	−0.180849
$419$	1.05583e12	1.67352	0.836761	−	0.547568i	$-0.184446\pi$
$419$	1.05583e12	1.67352	0.836761	+	0.547568i	$0.184446\pi$
$420$	−2.08438e11	−0.326855
$421$	3.55252e10	0.0551147	0.0275574	−	0.999620i	$-0.491227\pi$
$421$	3.55252e10	0.0551147	0.0275574	+	0.999620i	$0.491227\pi$
$422$	−2.90617e11	−0.446082
$423$	1.32655e12	2.01462
$424$	−2.61968e11	−0.393642
$425$	2.65778e11	0.395156
$426$	1.06278e11	0.156351
$427$	−6.63502e11	−0.965866
$428$	2.67962e11	0.385991
$429$	0	0
$430$	−1.14347e11	−0.161293
$431$	−1.07951e12	−1.50688	−0.753442	−	0.657515i	$-0.771608\pi$
$431$	−1.07951e12	−1.50688	−0.753442	+	0.657515i	$0.771608\pi$
$432$	9.06155e10	0.125177
$433$	−9.37095e11	−1.28112	−0.640558	−	0.767910i	$-0.721297\pi$
$433$	−9.37095e11	−1.28112	−0.640558	+	0.767910i	$0.721297\pi$
$434$	8.58143e11	1.16106
$435$	7.40013e11	0.990918
$436$	−2.34642e11	−0.310969
$437$	−6.22252e11	−0.816205
$438$	3.34725e11	0.434565
$439$	8.32479e11	1.06975	0.534876	−	0.844931i	$-0.320358\pi$
$439$	8.32479e11	1.06975	0.534876	+	0.844931i	$0.320358\pi$
$440$	4.91110e10	0.0624657
$441$	2.26863e11	0.285621
$442$	0	0
$443$	1.05746e12	1.30451	0.652255	−	0.758000i	$-0.273823\pi$
$443$	1.05746e12	1.30451	0.652255	+	0.758000i	$0.273823\pi$
$444$	1.01950e11	0.124498
$445$	2.16591e11	0.261830
$446$	6.51897e11	0.780139
$447$	−8.07562e11	−0.956736
$448$	1.17478e11	0.137787
$449$	−1.09666e12	−1.27339	−0.636697	−	0.771114i	$-0.719700\pi$
$449$	−1.09666e12	−1.27339	−0.636697	+	0.771114i	$0.719700\pi$
$450$	6.93529e11	0.797275
$451$	−3.30738e11	−0.376435
$452$	1.69511e10	0.0191018
$453$	−2.13661e12	−2.38388
$454$	4.71694e11	0.521085
$455$	0	0
$456$	−2.80240e11	−0.303520
$457$	−1.38035e12	−1.48035	−0.740176	−	0.672413i	$-0.765258\pi$
$457$	−1.38035e12	−1.48035	−0.740176	+	0.672413i	$0.765258\pi$
$458$	1.92170e11	0.204076
$459$	−2.21634e11	−0.233066
$460$	2.70729e11	0.281919
$461$	9.70837e9	0.0100113	0.00500567	−	0.999987i	$-0.498407\pi$
$461$	9.70837e9	0.0100113	0.00500567	+	0.999987i	$0.498407\pi$
$462$	−5.29397e11	−0.540621
$463$	1.18016e12	1.19352	0.596758	−	0.802422i	$-0.296455\pi$
$463$	1.18016e12	1.19352	0.596758	+	0.802422i	$0.296455\pi$
$464$	−4.17081e11	−0.417725
$465$	8.90636e11	0.883409
$466$	3.41216e11	0.335192
$467$	−5.38177e11	−0.523600	−0.261800	−	0.965122i	$-0.584316\pi$
$467$	−5.38177e11	−0.523600	−0.261800	+	0.965122i	$0.584316\pi$
$468$	0	0
$469$	−2.12803e12	−2.03095
$470$	4.41013e11	0.416880
$471$	−1.41355e12	−1.32348
$472$	2.02910e11	0.188176
$473$	−2.90422e11	−0.266781
$474$	2.19258e12	1.99505
$475$	−5.29935e11	−0.477641
$476$	−2.87338e11	−0.256544
$477$	1.67197e12	1.47875
$478$	−6.20140e11	−0.543331
$479$	6.14553e11	0.533396	0.266698	−	0.963780i	$-0.414067\pi$
$479$	6.14553e11	0.533396	0.266698	+	0.963780i	$0.414067\pi$
$480$	1.21927e11	0.104837
$481$	0	0
$482$	−4.72040e11	−0.398352
$483$	−2.91835e12	−2.43992
$484$	−4.78901e11	−0.396681
$485$	−8.37088e11	−0.686963
$486$	1.18406e12	0.962739
$487$	−2.18229e10	−0.0175806	−0.00879028	−	0.999961i	$-0.502798\pi$
$487$	−2.18229e10	−0.0175806	−0.00879028	+	0.999961i	$0.502798\pi$
$488$	3.88118e11	0.309795
$489$	2.25271e12	1.78162
$490$	7.54206e10	0.0591027
$491$	−1.31071e11	−0.101775	−0.0508875	−	0.998704i	$-0.516205\pi$
$491$	−1.31071e11	−0.101775	−0.0508875	+	0.998704i	$0.516205\pi$
$492$	−8.21115e11	−0.631773
$493$	1.02013e12	0.777757
$494$	0	0
$495$	−3.13443e11	−0.234658
$496$	−5.01974e11	−0.372404
$497$	−2.17276e11	−0.159738
$498$	−2.05925e12	−1.50030
$499$	−2.11689e12	−1.52843	−0.764216	−	0.644961i	$-0.776874\pi$
$499$	−2.11689e12	−1.52843	−0.764216	+	0.644961i	$0.776874\pi$
$500$	5.02156e11	0.359314
$501$	−1.60555e11	−0.113856
$502$	1.23587e11	0.0868570
$503$	−4.25100e11	−0.296098	−0.148049	−	0.988980i	$-0.547299\pi$
$503$	−4.25100e11	−0.296098	−0.148049	+	0.988980i	$0.547299\pi$
$504$	−7.49788e11	−0.517608
$505$	−1.07098e12	−0.732774
$506$	6.87606e11	0.466297
$507$	0	0
$508$	1.06668e12	0.710639
$509$	−1.93072e12	−1.27494	−0.637469	−	0.770476i	$-0.720018\pi$
$509$	−1.93072e12	−1.27494	−0.637469	+	0.770476i	$0.720018\pi$
$510$	−2.98217e11	−0.195194
$511$	−6.84313e11	−0.443977
$512$	−6.87195e10	−0.0441942
$513$	4.41917e11	0.281717
$514$	−1.49069e12	−0.942003
$515$	4.31377e11	0.270224
$516$	−7.21023e11	−0.447740
$517$	1.12010e12	0.689522
$518$	−2.08426e11	−0.127195
$519$	3.25724e12	1.97059
$520$	0	0
$521$	2.60841e12	1.55098	0.775490	−	0.631360i	$-0.217503\pi$
$521$	2.60841e12	1.55098	0.775490	+	0.631360i	$0.217503\pi$
$522$	2.66196e12	1.56922
$523$	−2.23302e11	−0.130507	−0.0652537	−	0.997869i	$-0.520786\pi$
$523$	−2.23302e11	−0.130507	−0.0652537	+	0.997869i	$0.520786\pi$
$524$	−4.16643e11	−0.241420
$525$	−2.48539e12	−1.42783
$526$	1.50959e12	0.859850
$527$	1.22777e12	0.693374
$528$	3.09673e11	0.173401
$529$	1.98934e12	1.10448
$530$	5.55847e11	0.305995
$531$	−1.29504e12	−0.706901
$532$	5.72923e11	0.310094
$533$	0	0
$534$	1.36573e12	0.726823
$535$	−5.68566e11	−0.300047
$536$	1.24480e12	0.651414
$537$	−3.06045e12	−1.58819
$538$	2.48213e12	1.27733
$539$	1.91555e11	0.0977563
$540$	−1.92269e11	−0.0973056
$541$	−2.08096e12	−1.04442	−0.522212	−	0.852816i	$-0.674893\pi$
$541$	−2.08096e12	−1.04442	−0.522212	+	0.852816i	$0.674893\pi$
$542$	−1.35470e12	−0.674290
$543$	−3.45604e11	−0.170600
$544$	1.68079e11	0.0822847
$545$	4.97867e11	0.241729
$546$	0	0
$547$	2.54059e12	1.21337	0.606684	−	0.794943i	$-0.292499\pi$
$547$	2.54059e12	1.21337	0.606684	+	0.794943i	$0.292499\pi$
$548$	1.35392e12	0.641327
$549$	−2.47710e12	−1.16377
$550$	5.85593e11	0.272875
$551$	−2.03404e12	−0.940106
$552$	1.70710e12	0.782589
$553$	−4.48253e12	−2.03826
$554$	1.74314e12	0.786210
$555$	−2.16318e11	−0.0967775
$556$	6.18127e10	0.0274310
$557$	9.00442e11	0.396376	0.198188	−	0.980164i	$-0.436494\pi$
$557$	9.00442e11	0.396376	0.198188	+	0.980164i	$0.436494\pi$
$558$	3.20377e12	1.39897
$559$	0	0
$560$	−2.49267e11	−0.107107
$561$	−7.57421e11	−0.322853
$562$	−1.65392e12	−0.699360
$563$	2.04664e11	0.0858526	0.0429263	−	0.999078i	$-0.486332\pi$
$563$	2.04664e11	0.0858526	0.0429263	+	0.999078i	$0.486332\pi$
$564$	2.78084e12	1.15723
$565$	−3.59670e10	−0.0148486
$566$	−1.46713e12	−0.600891
$567$	−1.53046e12	−0.621868
$568$	1.27096e11	0.0512349
$569$	2.58109e12	1.03228	0.516141	−	0.856504i	$-0.327368\pi$
$569$	2.58109e12	1.03228	0.516141	+	0.856504i	$0.327368\pi$
$570$	5.94616e11	0.235939
$571$	−4.20505e12	−1.65542	−0.827710	−	0.561156i	$-0.810357\pi$
$571$	−4.20505e12	−1.65542	−0.827710	+	0.561156i	$0.810357\pi$
$572$	0	0
$573$	5.82240e12	2.25635
$574$	1.67869e12	0.645457
$575$	3.22814e12	1.23154
$576$	4.38591e11	0.166019
$577$	4.16728e12	1.56517	0.782585	−	0.622543i	$-0.213901\pi$
$577$	4.16728e12	1.56517	0.782585	+	0.622543i	$0.213901\pi$
$578$	1.48631e12	0.553902
$579$	2.46311e12	0.910815
$580$	8.84969e11	0.324715
$581$	4.20994e12	1.53279
$582$	−5.27832e12	−1.90696
$583$	1.41176e12	0.506117
$584$	4.00291e11	0.142403
$585$	0	0
$586$	1.66037e12	0.581654
$587$	1.03026e12	0.358160	0.179080	−	0.983835i	$-0.442688\pi$
$587$	1.03026e12	0.358160	0.179080	+	0.983835i	$0.442688\pi$
$588$	4.75570e11	0.164065
$589$	−2.44805e12	−0.838109
$590$	−4.30537e11	−0.146277
$591$	6.64188e11	0.223948
$592$	1.21920e11	0.0407968
$593$	−2.35250e12	−0.781238	−0.390619	−	0.920552i	$-0.627739\pi$
$593$	−2.35250e12	−0.781238	−0.390619	+	0.920552i	$0.627739\pi$
$594$	−4.88331e11	−0.160944
$595$	6.09676e11	0.199422
$596$	−9.65749e11	−0.313513
$597$	6.60072e11	0.212670
$598$	0	0
$599$	−1.55241e12	−0.492702	−0.246351	−	0.969181i	$-0.579232\pi$
$599$	−1.55241e12	−0.492702	−0.246351	+	0.969181i	$0.579232\pi$
$600$	1.45384e12	0.457968
$601$	1.61275e12	0.504235	0.252117	−	0.967697i	$-0.418873\pi$
$601$	1.61275e12	0.504235	0.252117	+	0.967697i	$0.418873\pi$
$602$	1.47406e12	0.457438
$603$	−7.94472e12	−2.44709
$604$	−2.55514e12	−0.781175
$605$	1.01614e12	0.308357
$606$	−6.75314e12	−2.03413
$607$	5.98358e12	1.78901	0.894504	−	0.447060i	$-0.147529\pi$
$607$	5.98358e12	1.78901	0.894504	+	0.447060i	$0.147529\pi$
$608$	−3.35134e11	−0.0994608
$609$	−9.53962e12	−2.81030
$610$	−8.23514e11	−0.240817
$611$	0	0
$612$	−1.07274e12	−0.309110
$613$	3.16702e12	0.905898	0.452949	−	0.891537i	$-0.350372\pi$
$613$	3.16702e12	0.905898	0.452949	+	0.891537i	$0.350372\pi$
$614$	2.56197e12	0.727472
$615$	1.74225e12	0.491104
$616$	−6.33096e11	−0.177156
$617$	−5.19353e12	−1.44271	−0.721356	−	0.692565i	$-0.756481\pi$
$617$	−5.19353e12	−1.44271	−0.721356	+	0.692565i	$0.756481\pi$
$618$	2.72008e12	0.750125
$619$	4.48823e12	1.22876	0.614380	−	0.789010i	$-0.289406\pi$
$619$	4.48823e12	1.22876	0.614380	+	0.789010i	$0.289406\pi$
$620$	1.06510e12	0.289485
$621$	−2.69197e12	−0.726371
$622$	3.56241e12	0.954306
$623$	−2.79210e12	−0.742565
$624$	0	0
$625$	2.17295e12	0.569626
$626$	−1.66700e12	−0.433861
$627$	1.51022e12	0.390245
$628$	−1.69044e12	−0.433691
$629$	−2.98200e11	−0.0759592
$630$	1.59091e12	0.402358
$631$	3.25343e12	0.816975	0.408487	−	0.912764i	$-0.366056\pi$
$631$	3.25343e12	0.816975	0.408487	+	0.912764i	$0.366056\pi$
$632$	2.62207e12	0.653759
$633$	3.88824e12	0.962578
$634$	−5.17509e11	−0.127208
$635$	−2.26330e12	−0.552410
$636$	3.50493e12	0.849421
$637$	0	0
$638$	2.24767e12	0.537081
$639$	−8.11174e11	−0.192469
$640$	1.45810e11	0.0343540
$641$	9.44836e11	0.221052	0.110526	−	0.993873i	$-0.464746\pi$
$641$	9.44836e11	0.221052	0.110526	+	0.993873i	$0.464746\pi$
$642$	−3.58514e12	−0.832910
$643$	6.61958e12	1.52715	0.763574	−	0.645720i	$-0.223443\pi$
$643$	6.61958e12	1.52715	0.763574	+	0.645720i	$0.223443\pi$
$644$	−3.49001e12	−0.799539
$645$	1.52988e12	0.348047
$646$	8.19694e11	0.185185
$647$	−1.72331e12	−0.386629	−0.193315	−	0.981137i	$-0.561924\pi$
$647$	−1.72331e12	−0.386629	−0.193315	+	0.981137i	$0.561924\pi$
$648$	8.95248e11	0.199460
$649$	−1.09349e12	−0.241943
$650$	0	0
$651$	−1.14813e13	−2.50540
$652$	2.69398e12	0.583821
$653$	−7.01466e12	−1.50972	−0.754861	−	0.655884i	$-0.772296\pi$
$653$	−7.01466e12	−1.50972	−0.754861	+	0.655884i	$0.772296\pi$
$654$	3.13934e12	0.671024
$655$	8.84038e11	0.187666
$656$	−9.81957e11	−0.207026
$657$	−2.55480e12	−0.534949
$658$	−5.68516e12	−1.18230
$659$	1.88109e12	0.388531	0.194265	−	0.980949i	$-0.437768\pi$
$659$	1.88109e12	0.388531	0.194265	+	0.980949i	$0.437768\pi$
$660$	−6.57068e11	−0.134791
$661$	−4.65444e12	−0.948332	−0.474166	−	0.880435i	$-0.657250\pi$
$661$	−4.65444e12	−0.948332	−0.474166	+	0.880435i	$0.657250\pi$
$662$	4.56489e12	0.923781
$663$	0	0
$664$	−2.46262e12	−0.491633
$665$	−1.21564e12	−0.241049
$666$	−7.78134e11	−0.153257
$667$	1.23905e13	2.42394
$668$	−1.92005e11	−0.0373094
$669$	−8.72189e12	−1.68342
$670$	−2.64123e12	−0.506371
$671$	−2.09158e12	−0.398313
$672$	−1.57177e12	−0.297323
$673$	−1.05746e12	−0.198699	−0.0993495	−	0.995053i	$-0.531676\pi$
$673$	−1.05746e12	−0.198699	−0.0993495	+	0.995053i	$0.531676\pi$
$674$	3.96036e12	0.739205
$675$	−2.29259e12	−0.425070
$676$	0	0
$677$	8.40145e12	1.53711	0.768555	−	0.639784i	$-0.220976\pi$
$677$	8.40145e12	1.53711	0.768555	+	0.639784i	$0.220976\pi$
$678$	−2.26793e11	−0.0412188
$679$	1.07910e13	1.94827
$680$	−3.56633e11	−0.0639633
$681$	−6.31091e12	−1.12442
$682$	2.70516e12	0.478810
$683$	8.60487e12	1.51304	0.756521	−	0.653969i	$-0.226897\pi$
$683$	8.60487e12	1.51304	0.756521	+	0.653969i	$0.226897\pi$
$684$	2.13894e12	0.373633
$685$	−2.87276e12	−0.498530
$686$	3.54881e12	0.611820
$687$	−2.57110e12	−0.440365
$688$	−8.62259e11	−0.146720
$689$	0	0
$690$	−3.62215e12	−0.608339
$691$	−5.12497e12	−0.855146	−0.427573	−	0.903981i	$-0.640631\pi$
$691$	−5.12497e12	−0.855146	−0.427573	+	0.903981i	$0.640631\pi$
$692$	3.89528e12	0.645745
$693$	4.04064e12	0.665504
$694$	4.14876e12	0.678892
$695$	−1.31155e11	−0.0213232
$696$	5.58024e12	0.901386
$697$	2.40174e12	0.385460
$698$	2.64674e12	0.422049
$699$	−4.56522e12	−0.723293
$700$	−2.97223e12	−0.467888
$701$	−7.08567e12	−1.10828	−0.554140	−	0.832423i	$-0.686953\pi$
$701$	−7.08567e12	−1.10828	−0.554140	+	0.832423i	$0.686953\pi$
$702$	0	0
$703$	5.94583e11	0.0918149
$704$	3.70332e11	0.0568217
$705$	−5.90042e12	−0.899564
$706$	−6.26115e12	−0.948490
$707$	1.38062e13	2.07819
$708$	−2.71478e12	−0.406056
$709$	−3.49375e12	−0.519259	−0.259630	−	0.965708i	$-0.583600\pi$
$709$	−3.49375e12	−0.519259	−0.259630	+	0.965708i	$0.583600\pi$
$710$	−2.69675e11	−0.0398270
$711$	−1.67350e13	−2.45590
$712$	1.63325e12	0.238173
$713$	1.49125e13	2.16096
$714$	3.84436e12	0.553582
$715$	0	0
$716$	−3.65994e12	−0.520434
$717$	8.29701e12	1.17243
$718$	−1.10987e11	−0.0155852
$719$	−5.96519e12	−0.832423	−0.416211	−	0.909268i	$-0.636642\pi$
$719$	−5.96519e12	−0.832423	−0.416211	+	0.909268i	$0.636642\pi$
$720$	−9.30609e11	−0.129054
$721$	−5.56094e12	−0.766372
$722$	3.52861e12	0.483266
$723$	6.31554e12	0.859583
$724$	−4.13302e11	−0.0559041
$725$	1.05523e13	1.41848
$726$	6.40734e12	0.855978
$727$	−4.12061e12	−0.547087	−0.273544	−	0.961860i	$-0.588196\pi$
$727$	−4.12061e12	−0.547087	−0.273544	+	0.961860i	$0.588196\pi$
$728$	0	0
$729$	−1.15397e13	−1.51329
$730$	−8.49343e11	−0.110696
$731$	2.10898e12	0.273177
$732$	−5.19273e12	−0.668491
$733$	1.19055e13	1.52328	0.761641	−	0.647999i	$-0.224394\pi$
$733$	1.19055e13	1.52328	0.761641	+	0.647999i	$0.224394\pi$
$734$	−7.52487e12	−0.956901
$735$	−1.00907e12	−0.127535
$736$	2.04149e12	0.256447
$737$	−6.70826e12	−0.837541
$738$	6.26719e12	0.777712
$739$	1.33277e13	1.64383	0.821914	−	0.569611i	$-0.192906\pi$
$739$	1.33277e13	1.64383	0.821914	+	0.569611i	$0.192906\pi$
$740$	−2.58691e11	−0.0317131
$741$	0	0
$742$	−7.16550e12	−0.867819
$743$	−7.00674e12	−0.843463	−0.421732	−	0.906721i	$-0.638578\pi$
$743$	−7.00674e12	−0.843463	−0.421732	+	0.906721i	$0.638578\pi$
$744$	6.71604e12	0.803591
$745$	2.04914e12	0.243707
$746$	4.75709e11	0.0562362
$747$	1.57173e13	1.84687
$748$	−9.05786e11	−0.105796
$749$	7.32946e12	0.850950
$750$	−6.71847e12	−0.775344
$751$	−1.50087e12	−0.172172	−0.0860861	−	0.996288i	$-0.527436\pi$
$751$	−1.50087e12	−0.172172	−0.0860861	+	0.996288i	$0.527436\pi$
$752$	3.32556e12	0.379214
$753$	−1.65350e12	−0.187424
$754$	0	0
$755$	5.42153e12	0.607240
$756$	2.47857e12	0.275964
$757$	−1.19276e13	−1.32015	−0.660075	−	0.751200i	$-0.729476\pi$
$757$	−1.19276e13	−1.32015	−0.660075	+	0.751200i	$0.729476\pi$
$758$	−9.94911e12	−1.09464
$759$	−9.19965e12	−1.00620
$760$	7.11091e11	0.0773150
$761$	−7.03886e12	−0.760802	−0.380401	−	0.924822i	$-0.624214\pi$
$761$	−7.03886e12	−0.760802	−0.380401	+	0.924822i	$0.624214\pi$
$762$	−1.42714e13	−1.53345
$763$	−6.41807e12	−0.685558
$764$	6.96291e12	0.739385
$765$	2.27615e12	0.240284
$766$	−1.24064e13	−1.30202
$767$	0	0
$768$	9.19415e11	0.0953643
$769$	5.61868e12	0.579383	0.289692	−	0.957120i	$-0.406447\pi$
$769$	5.61868e12	0.579383	0.289692	+	0.957120i	$0.406447\pi$
$770$	1.34331e12	0.137711
$771$	1.99443e13	2.03270
$772$	2.94559e12	0.298466
$773$	−4.24702e10	−0.00427836	−0.00213918	−	0.999998i	$-0.500681\pi$
$773$	−4.24702e10	−0.00427836	−0.00213918	+	0.999998i	$0.500681\pi$
$774$	5.50323e12	0.551168
$775$	1.27001e13	1.26459
$776$	−6.31225e12	−0.624894
$777$	2.78859e12	0.274467
$778$	6.70257e12	0.655893
$779$	−4.78884e12	−0.465921
$780$	0	0
$781$	−6.84928e11	−0.0658742
$782$	−4.99323e12	−0.477476
$783$	−8.79962e12	−0.836634
$784$	5.68726e11	0.0537626
$785$	3.58679e12	0.337126
$786$	5.57437e12	0.520948
$787$	−1.53467e13	−1.42603	−0.713013	−	0.701151i	$-0.752670\pi$
$787$	−1.53467e13	−1.42603	−0.713013	+	0.701151i	$0.752670\pi$
$788$	7.94290e11	0.0733857
$789$	−2.01971e13	−1.85543
$790$	−5.56354e12	−0.508194
$791$	4.63656e11	0.0421116
$792$	−2.36359e12	−0.213456
$793$	0	0
$794$	3.75815e12	0.335569
$795$	−7.43681e12	−0.660290
$796$	7.89368e11	0.0696900
$797$	−4.72604e12	−0.414892	−0.207446	−	0.978247i	$-0.566515\pi$
$797$	−4.72604e12	−0.414892	−0.207446	+	0.978247i	$0.566515\pi$
$798$	−7.66528e12	−0.669137
$799$	−8.13389e12	−0.706054
$800$	1.73862e12	0.150072
$801$	−1.04240e13	−0.894718
$802$	−7.76636e11	−0.0662877
$803$	−2.15719e12	−0.183091
$804$	−1.66544e13	−1.40565
$805$	7.40514e12	0.621515
$806$	0	0
$807$	−3.32091e13	−2.75630
$808$	−8.07596e12	−0.666566
$809$	−1.47237e13	−1.20850	−0.604251	−	0.796794i	$-0.706528\pi$
$809$	−1.47237e13	−1.20850	−0.604251	+	0.796794i	$0.706528\pi$
$810$	−1.89955e12	−0.155049
$811$	9.13263e12	0.741314	0.370657	−	0.928770i	$-0.379133\pi$
$811$	9.13263e12	0.741314	0.370657	+	0.928770i	$0.379133\pi$
$812$	−1.14083e13	−0.920910
$813$	1.81249e13	1.45502
$814$	−6.57031e11	−0.0524537
$815$	−5.71612e12	−0.453829
$816$	−2.24877e12	−0.177558
$817$	−4.20509e12	−0.330200
$818$	2.23343e12	0.174414
$819$	0	0
$820$	2.08353e12	0.160930
$821$	−9.37570e12	−0.720211	−0.360105	−	0.932912i	$-0.617259\pi$
$821$	−9.37570e12	−0.720211	−0.360105	+	0.932912i	$0.617259\pi$
$822$	−1.81144e13	−1.38389
$823$	−1.09602e13	−0.832762	−0.416381	−	0.909190i	$-0.636702\pi$
$823$	−1.09602e13	−0.832762	−0.416381	+	0.909190i	$0.636702\pi$
$824$	3.25289e12	0.245809
$825$	−7.83480e12	−0.588823
$826$	5.55011e12	0.414850
$827$	−1.24213e13	−0.923408	−0.461704	−	0.887034i	$-0.652762\pi$
$827$	−1.24213e13	−0.923408	−0.461704	+	0.887034i	$0.652762\pi$
$828$	−1.30295e13	−0.963367
$829$	8.95630e12	0.658618	0.329309	−	0.944222i	$-0.393184\pi$
$829$	8.95630e12	0.658618	0.329309	+	0.944222i	$0.393184\pi$
$830$	5.22522e12	0.382167
$831$	−2.33219e13	−1.69652
$832$	0	0
$833$	−1.39103e12	−0.100100
$834$	−8.27007e11	−0.0591918
$835$	4.07398e11	0.0290022
$836$	1.80605e12	0.127880
$837$	−1.05907e13	−0.745864
$838$	−1.68933e13	−1.18336
$839$	1.45875e13	1.01637	0.508185	−	0.861248i	$-0.330317\pi$
$839$	1.45875e13	1.01637	0.508185	+	0.861248i	$0.330317\pi$
$840$	3.33501e12	0.231121
$841$	2.59954e13	1.79190
$842$	−5.68404e11	−0.0389720
$843$	2.21282e13	1.50911
$844$	4.64987e12	0.315428
$845$	0	0
$846$	−2.12248e13	−1.42455
$847$	−1.30992e13	−0.874518
$848$	4.19149e12	0.278347
$849$	1.96291e13	1.29663
$850$	−4.25244e12	−0.279417
$851$	−3.62195e12	−0.236733
$852$	−1.70045e12	−0.110557
$853$	−1.83110e13	−1.18424	−0.592121	−	0.805849i	$-0.701709\pi$
$853$	−1.83110e13	−1.18424	−0.592121	+	0.805849i	$0.701709\pi$
$854$	1.06160e13	0.682970
$855$	−4.53843e12	−0.290441
$856$	−4.28740e12	−0.272937
$857$	−1.39674e12	−0.0884506	−0.0442253	−	0.999022i	$-0.514082\pi$
$857$	−1.39674e12	−0.0884506	−0.0442253	+	0.999022i	$0.514082\pi$
$858$	0	0
$859$	−8.17566e12	−0.512334	−0.256167	−	0.966633i	$-0.582460\pi$
$859$	−8.17566e12	−0.512334	−0.256167	+	0.966633i	$0.582460\pi$
$860$	1.82955e12	0.114052
$861$	−2.24596e13	−1.39280
$862$	1.72722e13	1.06553
$863$	5.86145e12	0.359713	0.179857	−	0.983693i	$-0.442437\pi$
$863$	5.86145e12	0.359713	0.179857	+	0.983693i	$0.442437\pi$
$864$	−1.44985e12	−0.0885138
$865$	−8.26505e12	−0.501965
$866$	1.49935e13	0.905885
$867$	−1.98856e13	−1.19524
$868$	−1.37303e13	−0.820996
$869$	−1.41304e13	−0.840557
$870$	−1.18402e13	−0.700685
$871$	0	0
$872$	3.75428e12	0.219888
$873$	4.02869e13	2.34747
$874$	9.95602e12	0.577144
$875$	1.37353e13	0.792138
$876$	−5.35560e12	−0.307284
$877$	1.21872e12	0.0695672	0.0347836	−	0.999395i	$-0.488926\pi$
$877$	1.21872e12	0.0695672	0.0347836	+	0.999395i	$0.488926\pi$
$878$	−1.33197e13	−0.756428
$879$	−2.22145e13	−1.25512
$880$	−7.85775e11	−0.0441699
$881$	−1.08861e13	−0.608806	−0.304403	−	0.952543i	$-0.598457\pi$
$881$	−1.08861e13	−0.608806	−0.304403	+	0.952543i	$0.598457\pi$
$882$	−3.62980e12	−0.201964
$883$	−2.77016e13	−1.53349	−0.766746	−	0.641950i	$-0.778126\pi$
$883$	−2.77016e13	−1.53349	−0.766746	+	0.641950i	$0.778126\pi$
$884$	0	0
$885$	5.76026e12	0.315644
$886$	−1.69194e13	−0.922428
$887$	3.64336e13	1.97627	0.988133	−	0.153600i	$-0.0490866\pi$
$887$	3.64336e13	1.97627	0.988133	+	0.153600i	$0.0490866\pi$
$888$	−1.63120e12	−0.0880334
$889$	2.91766e13	1.56667
$890$	−3.46545e12	−0.185142
$891$	−4.82453e12	−0.256452
$892$	−1.04304e13	−0.551642
$893$	1.62182e13	0.853435
$894$	1.29210e13	0.676514
$895$	7.76571e12	0.404555
$896$	−1.87966e12	−0.0974299
$897$	0	0
$898$	1.75465e13	0.900426
$899$	4.87464e13	2.48899
$900$	−1.10965e13	−0.563759
$901$	−1.02519e13	−0.518252
$902$	5.29181e12	0.266179
$903$	−1.97219e13	−0.987081
$904$	−2.71217e11	−0.0135070
$905$	8.76949e11	0.0434566
$906$	3.41858e13	1.68566
$907$	2.16470e13	1.06210	0.531049	−	0.847341i	$-0.321798\pi$
$907$	2.16470e13	1.06210	0.531049	+	0.847341i	$0.321798\pi$
$908$	−7.54710e12	−0.368463
$909$	5.15436e13	2.50402
$910$	0	0
$911$	1.54878e13	0.745002	0.372501	−	0.928032i	$-0.378500\pi$
$911$	1.54878e13	0.745002	0.372501	+	0.928032i	$0.378500\pi$
$912$	4.48383e12	0.214621
$913$	1.32712e13	0.632107
$914$	2.20855e13	1.04677
$915$	1.10180e13	0.519646
$916$	−3.07473e12	−0.144304
$917$	−1.13963e13	−0.532231
$918$	3.54615e12	0.164803
$919$	1.42584e13	0.659404	0.329702	−	0.944085i	$-0.393052\pi$
$919$	1.42584e13	0.659404	0.329702	+	0.944085i	$0.393052\pi$
$920$	−4.33167e12	−0.199347
$921$	−3.42772e13	−1.56978
$922$	−1.55334e11	−0.00707908
$923$	0	0
$924$	8.47035e12	0.382277
$925$	−3.08460e12	−0.138535
$926$	−1.88826e13	−0.843943
$927$	−2.07611e13	−0.923403
$928$	6.67330e12	0.295376
$929$	−2.94641e13	−1.29785	−0.648923	−	0.760854i	$-0.724780\pi$
$929$	−2.94641e13	−1.29785	−0.648923	+	0.760854i	$0.724780\pi$
$930$	−1.42502e13	−0.624664
$931$	2.77358e12	0.120995
$932$	−5.45946e12	−0.237016
$933$	−4.76624e13	−2.05925
$934$	8.61084e12	0.370241
$935$	1.92191e12	0.0822395
$936$	0	0
$937$	−1.48665e13	−0.630058	−0.315029	−	0.949082i	$-0.602014\pi$
$937$	−1.48665e13	−0.630058	−0.315029	+	0.949082i	$0.602014\pi$
$938$	3.40484e13	1.43610
$939$	2.23032e13	0.936207
$940$	−7.05621e12	−0.294779
$941$	1.07989e13	0.448979	0.224489	−	0.974477i	$-0.427929\pi$
$941$	1.07989e13	0.448979	0.224489	+	0.974477i	$0.427929\pi$
$942$	2.26167e13	0.935839
$943$	2.91716e13	1.20132
$944$	−3.24656e12	−0.133061
$945$	−5.25906e12	−0.214519
$946$	4.64675e12	0.188642
$947$	3.34338e13	1.35086	0.675431	−	0.737423i	$-0.263958\pi$
$947$	3.34338e13	1.35086	0.675431	+	0.737423i	$0.263958\pi$
$948$	−3.50813e13	−1.41071
$949$	0	0
$950$	8.47896e12	0.337743
$951$	6.92388e12	0.274497
$952$	4.59740e12	0.181404
$953$	−4.30973e13	−1.69251	−0.846257	−	0.532775i	$-0.821149\pi$
$953$	−4.30973e13	−1.69251	−0.846257	+	0.532775i	$0.821149\pi$
$954$	−2.67515e13	−1.04564
$955$	−1.47740e13	−0.574754
$956$	9.92224e12	0.384193
$957$	−3.00721e13	−1.15894
$958$	−9.83285e12	−0.377168
$959$	3.70331e13	1.41386
$960$	−1.95083e12	−0.0741307
$961$	3.22286e13	1.21895
$962$	0	0
$963$	2.73637e13	1.02531
$964$	7.55264e12	0.281677
$965$	−6.24999e12	−0.232010
$966$	4.66937e13	1.72529
$967$	−2.87351e13	−1.05680	−0.528401	−	0.848995i	$-0.677208\pi$
$967$	−2.87351e13	−1.05680	−0.528401	+	0.848995i	$0.677208\pi$
$968$	7.66242e12	0.280496
$969$	−1.09669e13	−0.399601
$970$	1.33934e13	0.485756
$971$	2.53809e13	0.916263	0.458132	−	0.888884i	$-0.348519\pi$
$971$	2.53809e13	0.916263	0.458132	+	0.888884i	$0.348519\pi$
$972$	−1.89449e13	−0.680759
$973$	1.69074e12	0.0604739
$974$	3.49167e11	0.0124313
$975$	0	0
$976$	−6.20989e12	−0.219058
$977$	4.19116e13	1.47166	0.735832	−	0.677165i	$-0.236792\pi$
$977$	4.19116e13	1.47166	0.735832	+	0.677165i	$0.236792\pi$
$978$	−3.60434e13	−1.25980
$979$	−8.80165e12	−0.306226
$980$	−1.20673e12	−0.0417919
$981$	−2.39611e13	−0.826031
$982$	2.09714e12	0.0719658
$983$	4.57288e12	0.156206	0.0781032	−	0.996945i	$-0.475114\pi$
$983$	4.57288e12	0.156206	0.0781032	+	0.996945i	$0.475114\pi$
$984$	1.31378e13	0.446731
$985$	−1.68534e12	−0.0570457
$986$	−1.63221e13	−0.549957
$987$	7.60631e13	2.55122
$988$	0	0
$989$	2.56157e13	0.851378
$990$	5.01509e12	0.165928
$991$	2.78674e13	0.917834	0.458917	−	0.888479i	$-0.348237\pi$
$991$	2.78674e13	0.917834	0.458917	+	0.888479i	$0.348237\pi$
$992$	8.03159e12	0.263329
$993$	−6.10748e13	−1.99338
$994$	3.47642e12	0.112952
$995$	−1.67489e12	−0.0541730
$996$	3.29480e13	1.06087
$997$	−1.72557e13	−0.553100	−0.276550	−	0.961000i	$-0.589191\pi$
$997$	−1.72557e13	−0.553100	−0.276550	+	0.961000i	$0.589191\pi$
$998$	3.38702e13	1.08076
$999$	2.57227e12	0.0817095

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	338.10.a.o.1.12	✓	12
13.12	even	2		338.10.a.p.1.12	yes	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
338.10.a.o.1.12	✓	12	1.1	even	1	trivial
338.10.a.p.1.12	yes	12	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)

\(f(q)\)	\(=\)	\(q-16.0000 q^{2} +214.068 q^{3} +256.000 q^{4} -543.184 q^{5} -3425.09 q^{6} +7002.26 q^{7} -4096.00 q^{8} +26142.1 q^{9} +8690.94 q^{10} +22073.5 q^{11} +54801.4 q^{12} -112036. q^{14} -116278. q^{15} +65536.0 q^{16} -160293. q^{17} -418273. q^{18} +319608. q^{19} -139055. q^{20} +1.49896e6 q^{21} -353176. q^{22} -1.94692e6 q^{23} -876822. q^{24} -1.65808e6 q^{25} +1.38268e6 q^{27} +1.79258e6 q^{28} -6.36416e6 q^{29} +1.86045e6 q^{30} -7.65952e6 q^{31} -1.04858e6 q^{32} +4.72523e6 q^{33} +2.56468e6 q^{34} -3.80352e6 q^{35} +6.69237e6 q^{36} +1.86035e6 q^{37} -5.11373e6 q^{38} +2.22488e6 q^{40} -1.49835e7 q^{41} -2.39834e7 q^{42} -1.31570e7 q^{43} +5.65082e6 q^{44} -1.42000e7 q^{45} +3.11507e7 q^{46} +5.07440e7 q^{47} +1.40292e7 q^{48} +8.67806e6 q^{49} +2.65292e7 q^{50} -3.43136e7 q^{51} +6.39570e7 q^{53} -2.21229e7 q^{54} -1.19900e7 q^{55} -2.86813e7 q^{56} +6.84179e7 q^{57} +1.01827e8 q^{58} -4.95386e7 q^{59} -2.97672e7 q^{60} -9.47554e7 q^{61} +1.22552e8 q^{62} +1.83054e8 q^{63} +1.67772e7 q^{64} -7.56037e7 q^{66} -3.03905e8 q^{67} -4.10350e7 q^{68} -4.16773e8 q^{69} +6.08563e7 q^{70} -3.10294e7 q^{71} -1.07078e8 q^{72} -9.77274e7 q^{73} -2.97656e7 q^{74} -3.54941e8 q^{75} +8.18197e7 q^{76} +1.54565e8 q^{77} -6.40154e8 q^{79} -3.55981e7 q^{80} -2.18566e8 q^{81} +2.39736e8 q^{82} +6.01226e8 q^{83} +3.83734e8 q^{84} +8.70685e7 q^{85} +2.10512e8 q^{86} -1.36236e9 q^{87} -9.04131e7 q^{88} -3.98742e8 q^{89} +2.27199e8 q^{90} -4.98411e8 q^{92} -1.63966e9 q^{93} -8.11903e8 q^{94} -1.73606e8 q^{95} -2.24467e8 q^{96} +1.54108e9 q^{97} -1.38849e8 q^{98} +5.77048e8 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 192 q^{2} - 399 q^{3} + 3072 q^{4} + 562 q^{5} + 6384 q^{6} - 3161 q^{7} - 49152 q^{8} + 54783 q^{9} - 8992 q^{10} + 164271 q^{11} - 102144 q^{12} + 50576 q^{14} - 434244 q^{15} + 786432 q^{16} - 649529 q^{17}+ \cdots + 4431369848 q^{99}+O(q^{100}) \) 12 * q - 192 * q^2 - 399 * q^3 + 3072 * q^4 + 562 * q^5 + 6384 * q^6 - 3161 * q^7 - 49152 * q^8 + 54783 * q^9 - 8992 * q^10 + 164271 * q^11 - 102144 * q^12 + 50576 * q^14 - 434244 * q^15 + 786432 * q^16 - 649529 * q^17 - 876528 * q^18 + 228567 * q^19 + 143872 * q^20 + 3321918 * q^21 - 2628336 * q^22 - 3365321 * q^23 + 1634304 * q^24 + 1357734 * q^25 - 7310211 * q^27 - 809216 * q^28 + 1210855 * q^29 + 6947904 * q^30 - 2031015 * q^31 - 12582912 * q^32 + 3709742 * q^33 + 10392464 * q^34 - 16818664 * q^35 + 14024448 * q^36 - 21152418 * q^37 - 3657072 * q^38 - 2301952 * q^40 + 20819170 * q^41 - 53150688 * q^42 - 37183522 * q^43 + 42053376 * q^44 + 51849705 * q^45 + 53845136 * q^46 - 20020222 * q^47 - 26148864 * q^48 - 79988801 * q^49 - 21723744 * q^50 - 72774687 * q^51 - 74983469 * q^53 + 116963376 * q^54 - 19133432 * q^55 + 12947456 * q^56 + 13760507 * q^57 - 19373680 * q^58 + 136123112 * q^59 - 111166464 * q^60 - 112790708 * q^61 + 32496240 * q^62 - 659441340 * q^63 + 201326592 * q^64 - 59355872 * q^66 + 61165134 * q^67 - 166279424 * q^68 - 69902864 * q^69 + 269098624 * q^70 - 212025009 * q^71 - 224391168 * q^72 - 71937292 * q^73 + 338438688 * q^74 - 628692958 * q^75 + 58513152 * q^76 - 527155758 * q^77 - 1146472537 * q^79 + 36831232 * q^80 + 1297690908 * q^81 - 333106720 * q^82 + 1318830968 * q^83 + 850411008 * q^84 + 1737694467 * q^85 + 594936352 * q^86 - 1405133144 * q^87 - 672854016 * q^88 + 3175197052 * q^89 - 829595280 * q^90 - 861522176 * q^92 + 2432770524 * q^93 + 320323552 * q^94 + 1551319209 * q^95 + 418381824 * q^96 + 5161204312 * q^97 + 1279820816 * q^98 + 4431369848 * q^99

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