LMFDB - Embedded newform 338.10.a.r.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 = [15,240,324,3840,2164] 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:	$15$
Coefficient field:	$\mathbb{Q}[x]/(x^{15} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{15} - 4 x^{14} - 189447 x^{13} - 2075910 x^{12} + 13427724566 x^{11} + 240902663602 x^{10} + \cdots - 13\!\cdots\!64 $ x^15 - 4x^14 - 189447x^13 - 2075910x^12 + 13427724566x^11 + 240902663602x^10 - 443655654567001x^9 - 6615893817054688x^8 + 7115286003316448188x^7 + 24277759902481977312x^6 - 51707718239515932824096x^5 + 542415804353313005652352x^4 + 123474200669609970033074304x^3 - 1840146860618814818678953344x^2 - 54256006845924411243904364032x - 138658441142855576538884248064
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{12}\cdot 3^{3}\cdot 13^{13} $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.12
Root			$96.2913$ 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)

$f(q)$	$=$	\(q+16.0000 q^{2} +163.789 q^{3} +256.000 q^{4} -328.410 q^{5} +2620.62 q^{6} +11627.7 q^{7} +4096.00 q^{8} +7143.79 q^{9} -5254.55 q^{10} +65659.4 q^{11} +41929.9 q^{12} +186043. q^{14} -53789.8 q^{15} +65536.0 q^{16} +150400. q^{17} +114301. q^{18} -180202. q^{19} -84072.8 q^{20} +1.90449e6 q^{21} +1.05055e6 q^{22} +1.01492e6 q^{23} +670879. q^{24} -1.84527e6 q^{25} -2.05378e6 q^{27} +2.97669e6 q^{28} +4.65597e6 q^{29} -860637. q^{30} +449634. q^{31} +1.04858e6 q^{32} +1.07543e7 q^{33} +2.40640e6 q^{34} -3.81865e6 q^{35} +1.82881e6 q^{36} +1.77914e7 q^{37} -2.88323e6 q^{38} -1.34517e6 q^{40} +1.14044e7 q^{41} +3.04718e7 q^{42} -4.03420e7 q^{43} +1.68088e7 q^{44} -2.34609e6 q^{45} +1.62387e7 q^{46} -1.06710e7 q^{47} +1.07341e7 q^{48} +9.48499e7 q^{49} -2.95244e7 q^{50} +2.46339e7 q^{51} -7.92920e7 q^{53} -3.28605e7 q^{54} -2.15632e7 q^{55} +4.76271e7 q^{56} -2.95151e7 q^{57} +7.44956e7 q^{58} -7.70667e7 q^{59} -1.37702e7 q^{60} +1.05698e8 q^{61} +7.19415e6 q^{62} +8.30658e7 q^{63} +1.67772e7 q^{64} +1.72068e8 q^{66} -1.04892e8 q^{67} +3.85025e7 q^{68} +1.66232e8 q^{69} -6.10984e7 q^{70} +1.44246e8 q^{71} +2.92610e7 q^{72} +1.96637e7 q^{73} +2.84662e8 q^{74} -3.02235e8 q^{75} -4.61317e7 q^{76} +7.63468e8 q^{77} -5.52966e8 q^{79} -2.15226e7 q^{80} -4.76998e8 q^{81} +1.82470e8 q^{82} -7.29864e8 q^{83} +4.87549e8 q^{84} -4.93929e7 q^{85} -6.45472e8 q^{86} +7.62596e8 q^{87} +2.68941e8 q^{88} -2.46836e8 q^{89} -3.75374e7 q^{90} +2.59819e8 q^{92} +7.36451e7 q^{93} -1.70735e8 q^{94} +5.91801e7 q^{95} +1.71745e8 q^{96} -7.21914e8 q^{97} +1.51760e9 q^{98} +4.69057e8 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 15 q + 240 q^{2} + 324 q^{3} + 3840 q^{4} + 2164 q^{5} + 5184 q^{6} + 4227 q^{7} + 61440 q^{8} + 112199 q^{9} + 34624 q^{10} - 58782 q^{11} + 82944 q^{12} + 67632 q^{14} + 488672 q^{15} + 983040 q^{16}+ \cdots + 3437295177 q^{99}+O(q^{100}) $ 15 * q + 240 * q^2 + 324 * q^3 + 3840 * q^4 + 2164 * q^5 + 5184 * q^6 + 4227 * q^7 + 61440 * q^8 + 112199 * q^9 + 34624 * q^10 - 58782 * q^11 + 82944 * q^12 + 67632 * q^14 + 488672 * q^15 + 983040 * q^16 + 47308 * q^17 + 1795184 * q^18 + 1027864 * q^19 + 553984 * q^20 - 1332838 * q^21 - 940512 * q^22 - 697897 * q^23 + 1327104 * q^24 + 12121163 * q^25 + 11934723 * q^27 + 1082112 * q^28 + 4970557 * q^29 + 7818752 * q^30 + 8962601 * q^31 + 15728640 * q^32 + 3541482 * q^33 + 756928 * q^34 - 5785412 * q^35 + 28722944 * q^36 + 25045552 * q^37 + 16445824 * q^38 + 8863744 * q^40 + 26390985 * q^41 - 21325408 * q^42 + 11355145 * q^43 - 15048192 * q^44 + 221235525 * q^45 - 11166352 * q^46 + 79882208 * q^47 + 21233664 * q^48 + 150275074 * q^49 + 193938608 * q^50 + 118779121 * q^51 - 21678349 * q^53 + 190955568 * q^54 + 290281352 * q^55 + 17313792 * q^56 - 617732541 * q^57 + 79528912 * q^58 - 264523979 * q^59 + 125100032 * q^60 + 379367976 * q^61 + 143401616 * q^62 + 270769230 * q^63 + 251658240 * q^64 + 56663712 * q^66 - 250185789 * q^67 + 12110848 * q^68 + 281627650 * q^69 - 92566592 * q^70 + 173178579 * q^71 + 459567104 * q^72 + 153358293 * q^73 + 400728832 * q^74 + 20980603 * q^75 + 263133184 * q^76 + 1172911296 * q^77 + 217644101 * q^79 + 141819904 * q^80 + 2373566723 * q^81 + 422255760 * q^82 - 76435497 * q^83 - 341206528 * q^84 + 2676674151 * q^85 + 181682320 * q^86 + 4874616750 * q^87 - 240771072 * q^88 + 2250224949 * q^89 + 3539768400 * q^90 - 178661632 * q^92 + 2915972474 * q^93 + 1278115328 * q^94 + 3329480199 * q^95 + 339738624 * q^96 + 2720440815 * q^97 + 2404401184 * q^98 + 3437295177 * 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
$3$	163.789	1.16745	0.583726	−	0.811951i	$-0.301594\pi$
$3$	163.789	1.16745	0.583726	+	0.811951i	$0.301594\pi$
$4$	256.000	0.500000
$5$	−328.410	−0.234991	−0.117495	−	0.993073i	$-0.537487\pi$
$5$	−328.410	−0.234991	−0.117495	+	0.993073i	$0.537487\pi$
$6$	2620.62	0.825513
$7$	11627.7	1.83043	0.915214	−	0.402968i	$-0.132021\pi$
$7$	11627.7	1.83043	0.915214	+	0.402968i	$0.132021\pi$
$8$	4096.00	0.353553
$9$	7143.79	0.362942
$10$	−5254.55	−0.166164
$11$	65659.4	1.35216	0.676082	−	0.736826i	$-0.263676\pi$
$11$	65659.4	1.35216	0.676082	+	0.736826i	$0.263676\pi$
$12$	41929.9	0.583726
$13$	0	0
$13$	0	0
$14$	186043.	1.29431
$15$	−53789.8	−0.274340
$16$	65536.0	0.250000
$17$	150400.	0.436746	0.218373	−	0.975865i	$-0.429925\pi$
$17$	150400.	0.436746	0.218373	+	0.975865i	$0.429925\pi$
$18$	114301.	0.256639
$19$	−180202.	−0.317226	−0.158613	−	0.987341i	$-0.550702\pi$
$19$	−180202.	−0.317226	−0.158613	+	0.987341i	$0.550702\pi$
$20$	−84072.8	−0.117495
$21$	1.90449e6	2.13694
$22$	1.05055e6	0.956125
$23$	1.01492e6	0.756232	0.378116	−	0.925758i	$-0.376572\pi$
$23$	1.01492e6	0.756232	0.378116	+	0.925758i	$0.376572\pi$
$24$	670879.	0.412756
$25$	−1.84527e6	−0.944779
$26$	0	0
$27$	−2.05378e6	−0.743734
$28$	2.97669e6	0.915214
$29$	4.65597e6	1.22242	0.611209	−	0.791470i	$-0.290684\pi$
$29$	4.65597e6	1.22242	0.611209	+	0.791470i	$0.290684\pi$
$30$	−860637.	−0.193988
$31$	449634.	0.0874443	0.0437222	−	0.999044i	$-0.486078\pi$
$31$	449634.	0.0874443	0.0437222	+	0.999044i	$0.486078\pi$
$32$	1.04858e6	0.176777
$33$	1.07543e7	1.57859
$34$	2.40640e6	0.308826
$35$	−3.81865e6	−0.430134
$36$	1.82881e6	0.181471
$37$	1.77914e7	1.56063	0.780317	−	0.625384i	$-0.215058\pi$
$37$	1.77914e7	1.56063	0.780317	+	0.625384i	$0.215058\pi$
$38$	−2.88323e6	−0.224313
$39$	0	0
$40$	−1.34517e6	−0.0830818
$41$	1.14044e7	0.630295	0.315148	−	0.949043i	$-0.397946\pi$
$41$	1.14044e7	0.630295	0.315148	+	0.949043i	$0.397946\pi$
$42$	3.04718e7	1.51104
$43$	−4.03420e7	−1.79949	−0.899744	−	0.436418i	$-0.856247\pi$
$43$	−4.03420e7	−1.79949	−0.899744	+	0.436418i	$0.856247\pi$
$44$	1.68088e7	0.676082
$45$	−2.34609e6	−0.0852880
$46$	1.62387e7	0.534737
$47$	−1.06710e7	−0.318980	−0.159490	−	0.987200i	$-0.550985\pi$
$47$	−1.06710e7	−0.318980	−0.159490	+	0.987200i	$0.550985\pi$
$48$	1.07341e7	0.291863
$49$	9.48499e7	2.35047
$50$	−2.95244e7	−0.668060
$51$	2.46339e7	0.509879
$52$	0	0
$53$	−7.92920e7	−1.38035	−0.690173	−	0.723645i	$-0.742465\pi$
$53$	−7.92920e7	−1.38035	−0.690173	+	0.723645i	$0.742465\pi$
$54$	−3.28605e7	−0.525899
$55$	−2.15632e7	−0.317746
$56$	4.76271e7	0.647154
$57$	−2.95151e7	−0.370346
$58$	7.44956e7	0.864379
$59$	−7.70667e7	−0.828004	−0.414002	−	0.910276i	$-0.635869\pi$
$59$	−7.70667e7	−0.828004	−0.414002	+	0.910276i	$0.635869\pi$
$60$	−1.37702e7	−0.137170
$61$	1.05698e8	0.977423	0.488712	−	0.872445i	$-0.337467\pi$
$61$	1.05698e8	0.977423	0.488712	+	0.872445i	$0.337467\pi$
$62$	7.19415e6	0.0618325
$63$	8.30658e7	0.664339
$64$	1.67772e7	0.125000
$65$	0	0
$66$	1.72068e8	1.11623
$67$	−1.04892e8	−0.635925	−0.317963	−	0.948103i	$-0.602999\pi$
$67$	−1.04892e8	−0.635925	−0.317963	+	0.948103i	$0.602999\pi$
$68$	3.85025e7	0.218373
$69$	1.66232e8	0.882864
$70$	−6.10984e7	−0.304150
$71$	1.44246e8	0.673660	0.336830	−	0.941565i	$-0.390645\pi$
$71$	1.44246e8	0.673660	0.336830	+	0.941565i	$0.390645\pi$
$72$	2.92610e7	0.128319
$73$	1.96637e7	0.0810423	0.0405211	−	0.999179i	$-0.487098\pi$
$73$	1.96637e7	0.0810423	0.0405211	+	0.999179i	$0.487098\pi$
$74$	2.84662e8	1.10354
$75$	−3.02235e8	−1.10298
$76$	−4.61317e7	−0.158613
$77$	7.63468e8	2.47504
$78$	0	0
$79$	−5.52966e8	−1.59726	−0.798632	−	0.601820i	$-0.794443\pi$
$79$	−5.52966e8	−1.59726	−0.798632	+	0.601820i	$0.794443\pi$
$80$	−2.15226e7	−0.0587477
$81$	−4.76998e8	−1.23122
$82$	1.82470e8	0.445686
$83$	−7.29864e8	−1.68807	−0.844035	−	0.536288i	$-0.819826\pi$
$83$	−7.29864e8	−1.68807	−0.844035	+	0.536288i	$0.819826\pi$
$84$	4.87549e8	1.06847
$85$	−4.93929e7	−0.102631
$86$	−6.45472e8	−1.27243
$87$	7.62596e8	1.42711
$88$	2.68941e8	0.478063
$89$	−2.46836e8	−0.417017	−0.208508	−	0.978021i	$-0.566861\pi$
$89$	−2.46836e8	−0.417017	−0.208508	+	0.978021i	$0.566861\pi$
$90$	−3.75374e7	−0.0603077
$91$	0	0
$92$	2.59819e8	0.378116
$93$	7.36451e7	0.102087
$94$	−1.70735e8	−0.225553
$95$	5.91801e7	0.0745451
$96$	1.71745e8	0.206378
$97$	−7.21914e8	−0.827966	−0.413983	−	0.910284i	$-0.635863\pi$
$97$	−7.21914e8	−0.827966	−0.413983	+	0.910284i	$0.635863\pi$
$98$	1.51760e9	1.66203
$99$	4.69057e8	0.490757
$100$	−4.72390e8	−0.472390
$101$	1.89413e9	1.81119	0.905593	−	0.424147i	$-0.139426\pi$
$101$	1.89413e9	1.81119	0.905593	+	0.424147i	$0.139426\pi$
$102$	3.94142e8	0.360539
$103$	1.69630e9	1.48503	0.742516	−	0.669828i	$-0.233632\pi$
$103$	1.69630e9	1.48503	0.742516	+	0.669828i	$0.233632\pi$
$104$	0	0
$105$	−6.25452e8	−0.502160
$106$	−1.26867e9	−0.976052
$107$	8.82869e8	0.651132	0.325566	−	0.945519i	$-0.394445\pi$
$107$	8.82869e8	0.651132	0.325566	+	0.945519i	$0.394445\pi$
$108$	−5.25769e8	−0.371867
$109$	2.06960e9	1.40432	0.702161	−	0.712018i	$-0.252219\pi$
$109$	2.06960e9	1.40432	0.702161	+	0.712018i	$0.252219\pi$
$110$	−3.45011e8	−0.224681
$111$	2.91403e9	1.82196
$112$	7.62033e8	0.457607
$113$	1.50809e9	0.870110	0.435055	−	0.900404i	$-0.356729\pi$
$113$	1.50809e9	0.870110	0.435055	+	0.900404i	$0.356729\pi$
$114$	−4.72241e8	−0.261874
$115$	−3.33308e8	−0.177707
$116$	1.19193e9	0.611209
$117$	0	0
$118$	−1.23307e9	−0.585487
$119$	1.74881e9	0.799432
$120$	−2.20323e8	−0.0969939
$121$	1.95321e9	0.828350
$122$	1.69117e9	0.691143
$123$	1.86791e9	0.735839
$124$	1.15106e8	0.0437222
$125$	1.24743e9	0.457005
$126$	1.32905e9	0.469759
$127$	1.34579e9	0.459052	0.229526	−	0.973303i	$-0.426282\pi$
$127$	1.34579e9	0.459052	0.229526	+	0.973303i	$0.426282\pi$
$128$	2.68435e8	0.0883883
$129$	−6.60757e9	−2.10081
$130$	0	0
$131$	−4.65874e9	−1.38213	−0.691064	−	0.722794i	$-0.742858\pi$
$131$	−4.65874e9	−1.38213	−0.691064	+	0.722794i	$0.742858\pi$
$132$	2.75309e9	0.789293
$133$	−2.09534e9	−0.580659
$134$	−1.67827e9	−0.449667
$135$	6.74482e8	0.174771
$136$	6.16040e8	0.154413
$137$	2.76109e8	0.0669634	0.0334817	−	0.999439i	$-0.489340\pi$
$137$	2.76109e8	0.0669634	0.0334817	+	0.999439i	$0.489340\pi$
$138$	2.65971e9	0.624279
$139$	−1.76402e9	−0.400809	−0.200405	−	0.979713i	$-0.564226\pi$
$139$	−1.76402e9	−0.400809	−0.200405	+	0.979713i	$0.564226\pi$
$140$	−9.77574e8	−0.215067
$141$	−1.74778e9	−0.372393
$142$	2.30793e9	0.476350
$143$	0	0
$144$	4.68175e8	0.0907355
$145$	−1.52907e9	−0.287257
$146$	3.14619e8	0.0573055
$147$	1.55353e10	2.74406
$148$	4.55459e9	0.780317
$149$	4.88939e8	0.0812675	0.0406337	−	0.999174i	$-0.487062\pi$
$149$	4.88939e8	0.0812675	0.0406337	+	0.999174i	$0.487062\pi$
$150$	−4.83576e9	−0.779927
$151$	−9.14820e9	−1.43199	−0.715994	−	0.698107i	$-0.754026\pi$
$151$	−9.14820e9	−1.43199	−0.715994	+	0.698107i	$0.754026\pi$
$152$	−7.38108e8	−0.112156
$153$	1.07443e9	0.158513
$154$	1.22155e10	1.75012
$155$	−1.47664e8	−0.0205486
$156$	0	0
$157$	7.52516e9	0.988478	0.494239	−	0.869326i	$-0.335447\pi$
$157$	7.52516e9	0.988478	0.494239	+	0.869326i	$0.335447\pi$
$158$	−8.84746e9	−1.12944
$159$	−1.29871e10	−1.61149
$160$	−3.44362e8	−0.0415409
$161$	1.18011e10	1.38423
$162$	−7.63197e9	−0.870601
$163$	−9.93974e9	−1.10289	−0.551443	−	0.834212i	$-0.685923\pi$
$163$	−9.93974e9	−1.10289	−0.551443	+	0.834212i	$0.685923\pi$
$164$	2.91952e9	0.315148
$165$	−3.53181e9	−0.370953
$166$	−1.16778e10	−1.19365
$167$	−6.44084e9	−0.640793	−0.320397	−	0.947283i	$-0.603816\pi$
$167$	−6.44084e9	−0.640793	−0.320397	+	0.947283i	$0.603816\pi$
$168$	7.80078e9	0.755521
$169$	0	0
$170$	−7.90286e8	−0.0725712
$171$	−1.28732e9	−0.115135
$172$	−1.03275e10	−0.899744
$173$	2.30296e9	0.195469	0.0977346	−	0.995213i	$-0.468840\pi$
$173$	2.30296e9	0.195469	0.0977346	+	0.995213i	$0.468840\pi$
$174$	1.22015e10	1.00912
$175$	−2.14563e10	−1.72935
$176$	4.30305e9	0.338041
$177$	−1.26227e10	−0.966654
$178$	−3.94938e9	−0.294875
$179$	1.97601e10	1.43864	0.719318	−	0.694681i	$-0.244454\pi$
$179$	1.97601e10	1.43864	0.719318	+	0.694681i	$0.244454\pi$
$180$	−6.00598e8	−0.0426440
$181$	−1.91454e10	−1.32590	−0.662950	−	0.748664i	$-0.730696\pi$
$181$	−1.91454e10	−1.32590	−0.662950	+	0.748664i	$0.730696\pi$
$182$	0	0
$183$	1.73122e10	1.14109
$184$	4.15710e9	0.267368
$185$	−5.84285e9	−0.366735
$186$	1.17832e9	0.0721864
$187$	9.87519e9	0.590552
$188$	−2.73177e9	−0.159490
$189$	−2.38808e10	−1.36135
$190$	9.46881e8	0.0527114
$191$	2.75444e10	1.49756	0.748778	−	0.662821i	$-0.230641\pi$
$191$	2.75444e10	1.49756	0.748778	+	0.662821i	$0.230641\pi$
$192$	2.74792e9	0.145931
$193$	−3.71081e9	−0.192513	−0.0962567	−	0.995357i	$-0.530687\pi$
$193$	−3.71081e9	−0.192513	−0.0962567	+	0.995357i	$0.530687\pi$
$194$	−1.15506e10	−0.585461
$195$	0	0
$196$	2.42816e10	1.17523
$197$	1.79150e10	0.847460	0.423730	−	0.905789i	$-0.360721\pi$
$197$	1.79150e10	0.847460	0.423730	+	0.905789i	$0.360721\pi$
$198$	7.50491e9	0.347018
$199$	3.66919e9	0.165856	0.0829281	−	0.996556i	$-0.473573\pi$
$199$	3.66919e9	0.165856	0.0829281	+	0.996556i	$0.473573\pi$
$200$	−7.55823e9	−0.334030
$201$	−1.71802e10	−0.742412
$202$	3.03061e10	1.28070
$203$	5.41383e10	2.23755
$204$	6.30628e9	0.254940
$205$	−3.74530e9	−0.148114
$206$	2.71408e10	1.05008
$207$	7.25035e9	0.274468
$208$	0	0
$209$	−1.18320e10	−0.428942
$210$	−1.00072e10	−0.355081
$211$	5.95397e9	0.206793	0.103396	−	0.994640i	$-0.467029\pi$
$211$	5.95397e9	0.206793	0.103396	+	0.994640i	$0.467029\pi$
$212$	−2.02987e10	−0.690173
$213$	2.36259e10	0.786465
$214$	1.41259e10	0.460420
$215$	1.32487e10	0.422863
$216$	−8.41230e9	−0.262950
$217$	5.22821e9	0.160061
$218$	3.31136e10	0.993006
$219$	3.22069e9	0.0946129
$220$	−5.52017e9	−0.158873
$221$	0	0
$222$	4.66244e10	1.28832
$223$	−3.50622e10	−0.949438	−0.474719	−	0.880137i	$-0.657450\pi$
$223$	−3.50622e10	−0.949438	−0.474719	+	0.880137i	$0.657450\pi$
$224$	1.21925e10	0.323577
$225$	−1.31822e10	−0.342900
$226$	2.41294e10	0.615261
$227$	−4.96849e10	−1.24196	−0.620980	−	0.783826i	$-0.713265\pi$
$227$	−4.96849e10	−1.24196	−0.620980	+	0.783826i	$0.713265\pi$
$228$	−7.55586e9	−0.185173
$229$	7.62879e10	1.83314	0.916571	−	0.399872i	$-0.130945\pi$
$229$	7.62879e10	1.83314	0.916571	+	0.399872i	$0.130945\pi$
$230$	−5.33293e9	−0.125658
$231$	1.25047e11	2.88949
$232$	1.90709e10	0.432190
$233$	−3.39395e10	−0.754404	−0.377202	−	0.926131i	$-0.623114\pi$
$233$	−3.39395e10	−0.754404	−0.377202	+	0.926131i	$0.623114\pi$
$234$	0	0
$235$	3.50444e9	0.0749573
$236$	−1.97291e10	−0.414002
$237$	−9.05697e10	−1.86473
$238$	2.79810e10	0.565283
$239$	−6.71629e10	−1.33149	−0.665747	−	0.746178i	$-0.731887\pi$
$239$	−6.71629e10	−1.33149	−0.665747	+	0.746178i	$0.731887\pi$
$240$	−3.52517e9	−0.0685850
$241$	−7.95207e10	−1.51846	−0.759230	−	0.650822i	$-0.774424\pi$
$241$	−7.95207e10	−1.51846	−0.759230	+	0.650822i	$0.774424\pi$
$242$	3.12513e10	0.585732
$243$	−3.77023e10	−0.693649
$244$	2.70587e10	0.488712
$245$	−3.11496e10	−0.552338
$246$	2.98865e10	0.520317
$247$	0	0
$248$	1.84170e9	0.0309162
$249$	−1.19544e11	−1.97074
$250$	1.99589e10	0.323151
$251$	1.11412e11	1.77174	0.885868	−	0.463938i	$-0.153564\pi$
$251$	1.11412e11	1.77174	0.885868	+	0.463938i	$0.153564\pi$
$252$	2.12649e10	0.332170
$253$	6.66388e10	1.02255
$254$	2.15327e10	0.324599
$255$	−8.09000e9	−0.119817
$256$	4.29497e9	0.0625000
$257$	1.14075e11	1.63114	0.815571	−	0.578657i	$-0.196423\pi$
$257$	1.14075e11	1.63114	0.815571	+	0.578657i	$0.196423\pi$
$258$	−1.05721e11	−1.48550
$259$	2.06873e11	2.85663
$260$	0	0
$261$	3.32613e10	0.443666
$262$	−7.45399e10	−0.977312
$263$	3.77214e10	0.486168	0.243084	−	0.970005i	$-0.421841\pi$
$263$	3.77214e10	0.486168	0.243084	+	0.970005i	$0.421841\pi$
$264$	4.40495e10	0.558115
$265$	2.60402e10	0.324368
$266$	−3.35254e10	−0.410588
$267$	−4.04290e10	−0.486847
$268$	−2.68524e10	−0.317963
$269$	−2.91455e8	−0.00339379	−0.00169690	−	0.999999i	$-0.500540\pi$
$269$	−2.91455e8	−0.00339379	−0.00169690	+	0.999999i	$0.500540\pi$
$270$	1.07917e10	0.123581
$271$	1.41433e11	1.59290	0.796450	−	0.604705i	$-0.206709\pi$
$271$	1.41433e11	1.59290	0.796450	+	0.604705i	$0.206709\pi$
$272$	9.85663e9	0.109186
$273$	0	0
$274$	4.41774e9	0.0473503
$275$	−1.21159e11	−1.27750
$276$	4.25554e10	0.441432
$277$	−5.00160e10	−0.510446	−0.255223	−	0.966882i	$-0.582149\pi$
$277$	−5.00160e10	−0.510446	−0.255223	+	0.966882i	$0.582149\pi$
$278$	−2.82244e10	−0.283415
$279$	3.21209e9	0.0317372
$280$	−1.56412e10	−0.152075
$281$	6.67975e10	0.639119	0.319560	−	0.947566i	$-0.396465\pi$
$281$	6.67975e10	0.639119	0.319560	+	0.947566i	$0.396465\pi$
$282$	−2.79645e10	−0.263322
$283$	−1.19718e11	−1.10948	−0.554742	−	0.832022i	$-0.687183\pi$
$283$	−1.19718e11	−1.10948	−0.554742	+	0.832022i	$0.687183\pi$
$284$	3.69269e10	0.336830
$285$	9.69304e9	0.0870278
$286$	0	0
$287$	1.32607e11	1.15371
$288$	7.49080e9	0.0641597
$289$	−9.59676e10	−0.809253
$290$	−2.44651e10	−0.203121
$291$	−1.18241e11	−0.966610
$292$	5.03390e9	0.0405211
$293$	1.43370e10	0.113646	0.0568230	−	0.998384i	$-0.481903\pi$
$293$	1.43370e10	0.113646	0.0568230	+	0.998384i	$0.481903\pi$
$294$	2.48566e11	1.94034
$295$	2.53094e10	0.194573
$296$	7.28734e10	0.551768
$297$	−1.34850e11	−1.00565
$298$	7.82303e9	0.0574648
$299$	0	0
$300$	−7.73722e10	−0.551492
$301$	−4.69084e11	−3.29383
$302$	−1.46371e11	−1.01257
$303$	3.10237e11	2.11447
$304$	−1.18097e10	−0.0793064
$305$	−3.47122e10	−0.229685
$306$	1.71908e10	0.112086
$307$	9.85124e10	0.632948	0.316474	−	0.948601i	$-0.397501\pi$
$307$	9.85124e10	0.632948	0.316474	+	0.948601i	$0.397501\pi$
$308$	1.95448e11	1.23752
$309$	2.77835e11	1.73370
$310$	−2.36263e9	−0.0145301
$311$	−1.88850e11	−1.14471	−0.572355	−	0.820006i	$-0.693970\pi$
$311$	−1.88850e11	−1.14471	−0.572355	+	0.820006i	$0.693970\pi$
$312$	0	0
$313$	2.57591e11	1.51698	0.758492	−	0.651683i	$-0.225937\pi$
$313$	2.57591e11	1.51698	0.758492	+	0.651683i	$0.225937\pi$
$314$	1.20402e11	0.698960
$315$	−2.72796e10	−0.156114
$316$	−1.41559e11	−0.798632
$317$	1.91020e11	1.06246	0.531231	−	0.847227i	$-0.321730\pi$
$317$	1.91020e11	1.06246	0.531231	+	0.847227i	$0.321730\pi$
$318$	−2.07794e11	−1.13949
$319$	3.05708e11	1.65291
$320$	−5.50980e9	−0.0293738
$321$	1.44604e11	0.760165
$322$	1.88818e11	0.978797
$323$	−2.71024e10	−0.138547
$324$	−1.22111e11	−0.615608
$325$	0	0
$326$	−1.59036e11	−0.779859
$327$	3.38977e11	1.63948
$328$	4.67123e10	0.222843
$329$	−1.24079e11	−0.583870
$330$	−5.65089e10	−0.262304
$331$	−3.87909e11	−1.77625	−0.888126	−	0.459601i	$-0.847992\pi$
$331$	−3.87909e11	−1.77625	−0.888126	+	0.459601i	$0.847992\pi$
$332$	−1.86845e11	−0.844035
$333$	1.27098e11	0.566420
$334$	−1.03053e11	−0.453109
$335$	3.44476e10	0.149437
$336$	1.24813e11	0.534234
$337$	1.65154e11	0.697515	0.348757	−	0.937213i	$-0.386604\pi$
$337$	1.65154e11	0.697515	0.348757	+	0.937213i	$0.386604\pi$
$338$	0	0
$339$	2.47008e11	1.01581
$340$	−1.26446e10	−0.0513156
$341$	2.95227e10	0.118239
$342$	−2.05972e10	−0.0814124
$343$	6.33666e11	2.47193
$344$	−1.65241e11	−0.636215
$345$	−5.45922e10	−0.207465
$346$	3.68473e10	0.138218
$347$	−2.12668e11	−0.787445	−0.393723	−	0.919229i	$-0.628813\pi$
$347$	−2.12668e11	−0.787445	−0.393723	+	0.919229i	$0.628813\pi$
$348$	1.95225e11	0.713556
$349$	3.44314e11	1.24234	0.621169	−	0.783676i	$-0.286658\pi$
$349$	3.44314e11	1.24234	0.621169	+	0.783676i	$0.286658\pi$
$350$	−3.43300e11	−1.22284
$351$	0	0
$352$	6.88488e10	0.239031
$353$	−9.65241e10	−0.330864	−0.165432	−	0.986221i	$-0.552902\pi$
$353$	−9.65241e10	−0.330864	−0.165432	+	0.986221i	$0.552902\pi$
$354$	−2.01963e11	−0.683528
$355$	−4.73717e10	−0.158304
$356$	−6.31900e10	−0.208508
$357$	2.86436e11	0.933297
$358$	3.16162e11	1.01727
$359$	−4.68238e11	−1.48779	−0.743894	−	0.668297i	$-0.767024\pi$
$359$	−4.68238e11	−1.48779	−0.743894	+	0.668297i	$0.767024\pi$
$360$	−9.60958e9	−0.0301539
$361$	−2.90215e11	−0.899368
$362$	−3.06326e11	−0.937553
$363$	3.19913e11	0.967058
$364$	0	0
$365$	−6.45773e9	−0.0190442
$366$	2.76995e11	0.806875
$367$	7.99775e10	0.230129	0.115064	−	0.993358i	$-0.463293\pi$
$367$	7.99775e10	0.230129	0.115064	+	0.993358i	$0.463293\pi$
$368$	6.65136e10	0.189058
$369$	8.14704e10	0.228761
$370$	−9.34856e10	−0.259321
$371$	−9.21983e11	−2.52662
$372$	1.88531e10	0.0510435
$373$	1.93642e11	0.517977	0.258988	−	0.965880i	$-0.416611\pi$
$373$	1.93642e11	0.517977	0.258988	+	0.965880i	$0.416611\pi$
$374$	1.58003e11	0.417583
$375$	2.04315e11	0.533531
$376$	−4.37082e10	−0.112776
$377$	0	0
$378$	−3.82092e11	−0.962621
$379$	1.39160e11	0.346448	0.173224	−	0.984882i	$-0.444582\pi$
$379$	1.39160e11	0.346448	0.173224	+	0.984882i	$0.444582\pi$
$380$	1.51501e10	0.0372726
$381$	2.20426e11	0.535921
$382$	4.40710e11	1.05893
$383$	1.09951e11	0.261099	0.130550	−	0.991442i	$-0.458326\pi$
$383$	1.09951e11	0.261099	0.130550	+	0.991442i	$0.458326\pi$
$384$	4.39667e10	0.103189
$385$	−2.50730e11	−0.581612
$386$	−5.93730e10	−0.136128
$387$	−2.88194e11	−0.653110
$388$	−1.84810e11	−0.413983
$389$	−3.65716e11	−0.809787	−0.404893	−	0.914364i	$-0.632691\pi$
$389$	−3.65716e11	−0.809787	−0.404893	+	0.914364i	$0.632691\pi$
$390$	0	0
$391$	1.52644e11	0.330281
$392$	3.88505e11	0.831016
$393$	−7.63050e11	−1.61357
$394$	2.86640e11	0.599245
$395$	1.81599e11	0.375342
$396$	1.20078e11	0.245379
$397$	−3.46976e11	−0.701039	−0.350519	−	0.936555i	$-0.613995\pi$
$397$	−3.46976e11	−0.701039	−0.350519	+	0.936555i	$0.613995\pi$
$398$	5.87071e10	0.117278
$399$	−3.43193e11	−0.677891
$400$	−1.20932e11	−0.236195
$401$	1.36930e11	0.264453	0.132226	−	0.991220i	$-0.457787\pi$
$401$	1.36930e11	0.264453	0.132226	+	0.991220i	$0.457787\pi$
$402$	−2.74883e11	−0.524964
$403$	0	0
$404$	4.84897e11	0.905593
$405$	1.56651e11	0.289324
$406$	8.66212e11	1.58218
$407$	1.16817e12	2.11024
$408$	1.00900e11	0.180269
$409$	5.61335e11	0.991899	0.495949	−	0.868351i	$-0.334820\pi$
$409$	5.61335e11	0.991899	0.495949	+	0.868351i	$0.334820\pi$
$410$	−5.99249e10	−0.104732
$411$	4.52235e10	0.0781765
$412$	4.34253e11	0.742516
$413$	−8.96108e11	−1.51560
$414$	1.16006e11	0.194078
$415$	2.39694e11	0.396681
$416$	0	0
$417$	−2.88927e11	−0.467925
$418$	−1.89311e11	−0.303308
$419$	−1.23264e12	−1.95376	−0.976882	−	0.213778i	$-0.931423\pi$
$419$	−1.23264e12	−1.95376	−0.976882	+	0.213778i	$0.931423\pi$
$420$	−1.60116e11	−0.251080
$421$	−1.31000e11	−0.203236	−0.101618	−	0.994823i	$-0.532402\pi$
$421$	−1.31000e11	−0.203236	−0.101618	+	0.994823i	$0.532402\pi$
$422$	9.52636e10	0.146225
$423$	−7.62311e10	−0.115771
$424$	−3.24780e11	−0.488026
$425$	−2.77529e11	−0.412628
$426$	3.78014e11	0.556115
$427$	1.22903e12	1.78910
$428$	2.26014e11	0.325566
$429$	0	0
$430$	2.11979e11	0.299009
$431$	−8.26151e11	−1.15322	−0.576609	−	0.817020i	$-0.695625\pi$
$431$	−8.26151e11	−1.15322	−0.576609	+	0.817020i	$0.695625\pi$
$432$	−1.34597e11	−0.185934
$433$	−1.10299e12	−1.50792	−0.753959	−	0.656922i	$-0.771858\pi$
$433$	−1.10299e12	−1.50792	−0.753959	+	0.656922i	$0.771858\pi$
$434$	8.36514e10	0.113180
$435$	−2.50444e11	−0.335358
$436$	5.29817e11	0.702161
$437$	−1.82890e11	−0.239896
$438$	5.15310e10	0.0669014
$439$	−7.44262e11	−0.956391	−0.478196	−	0.878253i	$-0.658709\pi$
$439$	−7.44262e11	−0.956391	−0.478196	+	0.878253i	$0.658709\pi$
$440$	−8.83227e10	−0.112340
$441$	6.77587e11	0.853083
$442$	0	0
$443$	−1.48555e12	−1.83262	−0.916309	−	0.400473i	$-0.868846\pi$
$443$	−1.48555e12	−1.83262	−0.916309	+	0.400473i	$0.868846\pi$
$444$	7.45991e11	0.910982
$445$	8.10633e10	0.0979951
$446$	−5.60995e11	−0.671354
$447$	8.00828e10	0.0948758
$448$	1.95080e11	0.228804
$449$	7.99853e11	0.928756	0.464378	−	0.885637i	$-0.346278\pi$
$449$	7.99853e11	0.928756	0.464378	+	0.885637i	$0.346278\pi$
$450$	−2.10916e11	−0.242467
$451$	7.48804e11	0.852263
$452$	3.86071e11	0.435055
$453$	−1.49837e12	−1.67178
$454$	−7.94958e11	−0.878199
$455$	0	0
$456$	−1.20894e11	−0.130937
$457$	3.25370e11	0.348943	0.174472	−	0.984662i	$-0.444178\pi$
$457$	3.25370e11	0.348943	0.174472	+	0.984662i	$0.444178\pi$
$458$	1.22061e12	1.29623
$459$	−3.08890e11	−0.324823
$460$	−8.53269e10	−0.0888537
$461$	3.59994e11	0.371229	0.185614	−	0.982623i	$-0.440573\pi$
$461$	3.59994e11	0.371229	0.185614	+	0.982623i	$0.440573\pi$
$462$	2.00076e12	2.04318
$463$	−5.79365e11	−0.585919	−0.292960	−	0.956125i	$-0.594640\pi$
$463$	−5.79365e11	−0.585919	−0.292960	+	0.956125i	$0.594640\pi$
$464$	3.05134e11	0.305604
$465$	−2.41857e10	−0.0239895
$466$	−5.43032e11	−0.533444
$467$	2.20112e11	0.214150	0.107075	−	0.994251i	$-0.465852\pi$
$467$	2.20112e11	0.214150	0.107075	+	0.994251i	$0.465852\pi$
$468$	0	0
$469$	−1.21965e12	−1.16402
$470$	5.60711e10	0.0530028
$471$	1.23254e12	1.15400
$472$	−3.15665e11	−0.292744
$473$	−2.64883e12	−2.43321
$474$	−1.44912e12	−1.31856
$475$	3.32522e11	0.299708
$476$	4.47695e11	0.399716
$477$	−5.66445e11	−0.500985
$478$	−1.07461e12	−0.941508
$479$	−2.07550e12	−1.80141	−0.900706	−	0.434428i	$-0.856950\pi$
$479$	−2.07550e12	−1.80141	−0.900706	+	0.434428i	$0.856950\pi$
$480$	−5.64027e10	−0.0484970
$481$	0	0
$482$	−1.27233e12	−1.07371
$483$	1.93290e12	1.61602
$484$	5.00021e11	0.414175
$485$	2.37084e11	0.194564
$486$	−6.03237e11	−0.490484
$487$	1.00844e12	0.812400	0.406200	−	0.913784i	$-0.366854\pi$
$487$	1.00844e12	0.812400	0.406200	+	0.913784i	$0.366854\pi$
$488$	4.32939e11	0.345571
$489$	−1.62802e12	−1.28757
$490$	−4.98394e11	−0.390562
$491$	−2.60858e11	−0.202553	−0.101276	−	0.994858i	$-0.532293\pi$
$491$	−2.60858e11	−0.202553	−0.101276	+	0.994858i	$0.532293\pi$
$492$	4.78185e11	0.367919
$493$	7.00260e11	0.533885
$494$	0	0
$495$	−1.54043e11	−0.115323
$496$	2.94672e10	0.0218611
$497$	1.67725e12	1.23309
$498$	−1.91270e12	−1.39352
$499$	−3.53821e11	−0.255465	−0.127732	−	0.991809i	$-0.540770\pi$
$499$	−3.53821e11	−0.255465	−0.127732	+	0.991809i	$0.540770\pi$
$500$	3.19342e11	0.228503
$501$	−1.05494e12	−0.748095
$502$	1.78259e12	1.25281
$503$	1.10638e12	0.770634	0.385317	−	0.922784i	$-0.374092\pi$
$503$	1.10638e12	0.770634	0.385317	+	0.922784i	$0.374092\pi$
$504$	3.40238e11	0.234879
$505$	−6.22050e11	−0.425612
$506$	1.06622e12	0.723052
$507$	0	0
$508$	3.44523e11	0.229526
$509$	−1.92581e12	−1.27170	−0.635848	−	0.771814i	$-0.719349\pi$
$509$	−1.92581e12	−1.27170	−0.635848	+	0.771814i	$0.719349\pi$
$510$	−1.29440e11	−0.0847233
$511$	2.28643e11	0.148342
$512$	6.87195e10	0.0441942
$513$	3.70096e11	0.235932
$514$	1.82520e12	1.15339
$515$	−5.57082e11	−0.348969
$516$	−1.69154e12	−1.05041
$517$	−7.00649e11	−0.431313
$518$	3.30996e12	2.01994
$519$	3.77199e11	0.228201
$520$	0	0
$521$	1.72837e12	1.02770	0.513851	−	0.857879i	$-0.328218\pi$
$521$	1.72837e12	1.02770	0.513851	+	0.857879i	$0.328218\pi$
$522$	5.32180e11	0.313720
$523$	−1.62219e11	−0.0948080	−0.0474040	−	0.998876i	$-0.515095\pi$
$523$	−1.62219e11	−0.0948080	−0.0474040	+	0.998876i	$0.515095\pi$
$524$	−1.19264e12	−0.691064
$525$	−3.51430e12	−2.01893
$526$	6.03542e11	0.343773
$527$	6.76251e10	0.0381909
$528$	7.04792e11	0.394647
$529$	−7.71097e11	−0.428113
$530$	4.16644e11	0.229363
$531$	−5.50548e11	−0.300517
$532$	−5.36406e11	−0.290330
$533$	0	0
$534$	−6.46864e11	−0.344253
$535$	−2.89943e11	−0.153010
$536$	−4.29638e11	−0.224834
$537$	3.23649e12	1.67954
$538$	−4.66327e9	−0.00239978
$539$	6.22778e12	3.17822
$540$	1.72667e11	0.0873853
$541$	3.99004e11	0.200258	0.100129	−	0.994974i	$-0.468074\pi$
$541$	3.99004e11	0.200258	0.100129	+	0.994974i	$0.468074\pi$
$542$	2.26293e12	1.12635
$543$	−3.13580e12	−1.54792
$544$	1.57706e11	0.0772064
$545$	−6.79676e11	−0.330003
$546$	0	0
$547$	−2.72848e12	−1.30310	−0.651551	−	0.758605i	$-0.725881\pi$
$547$	−2.72848e12	−1.30310	−0.651551	+	0.758605i	$0.725881\pi$
$548$	7.06839e10	0.0334817
$549$	7.55084e11	0.354748
$550$	−1.93855e12	−0.903327
$551$	−8.39016e11	−0.387782
$552$	6.80886e11	0.312139
$553$	−6.42973e12	−2.92368
$554$	−8.00256e11	−0.360940
$555$	−9.56994e11	−0.428145
$556$	−4.51590e11	−0.200405
$557$	−6.68129e11	−0.294111	−0.147056	−	0.989128i	$-0.546980\pi$
$557$	−6.68129e11	−0.294111	−0.147056	+	0.989128i	$0.546980\pi$
$558$	5.13934e10	0.0224416
$559$	0	0
$560$	−2.50259e11	−0.107533
$561$	1.61745e12	0.689441
$562$	1.06876e12	0.451926
$563$	−2.16253e12	−0.907139	−0.453570	−	0.891221i	$-0.649850\pi$
$563$	−2.16253e12	−0.907139	−0.453570	+	0.891221i	$0.649850\pi$
$564$	−4.47433e11	−0.186197
$565$	−4.95271e11	−0.204468
$566$	−1.91549e12	−0.784524
$567$	−5.54639e12	−2.25365
$568$	5.90831e11	0.238175
$569$	−1.17553e12	−0.470140	−0.235070	−	0.971978i	$-0.575532\pi$
$569$	−1.17553e12	−0.470140	−0.235070	+	0.971978i	$0.575532\pi$
$570$	1.55089e11	0.0615379
$571$	−1.68861e11	−0.0664761	−0.0332381	−	0.999447i	$-0.510582\pi$
$571$	−1.68861e11	−0.0664761	−0.0332381	+	0.999447i	$0.510582\pi$
$572$	0	0
$573$	4.51146e12	1.74832
$574$	2.12171e12	0.815796
$575$	−1.87280e12	−0.714472
$576$	1.19853e11	0.0453677
$577$	−2.62228e12	−0.984890	−0.492445	−	0.870344i	$-0.663897\pi$
$577$	−2.62228e12	−0.984890	−0.492445	+	0.870344i	$0.663897\pi$
$578$	−1.53548e12	−0.572228
$579$	−6.07789e11	−0.224750
$580$	−3.91441e11	−0.143628
$581$	−8.48664e12	−3.08989
$582$	−1.89186e12	−0.683497
$583$	−5.20626e12	−1.86645
$584$	8.05424e10	0.0286528
$585$	0	0
$586$	2.29392e11	0.0803598
$587$	−7.63488e11	−0.265418	−0.132709	−	0.991155i	$-0.542368\pi$
$587$	−7.63488e11	−0.265418	−0.132709	+	0.991155i	$0.542368\pi$
$588$	3.97705e12	1.37203
$589$	−8.10250e10	−0.0277396
$590$	4.04951e11	0.137584
$591$	2.93428e12	0.989368
$592$	1.16597e12	0.390159
$593$	−1.98675e12	−0.659776	−0.329888	−	0.944020i	$-0.607011\pi$
$593$	−1.98675e12	−0.659776	−0.329888	+	0.944020i	$0.607011\pi$
$594$	−2.15760e12	−0.711103
$595$	−5.74326e11	−0.187859
$596$	1.25168e11	0.0406337
$597$	6.00973e11	0.193629
$598$	0	0
$599$	−3.57967e12	−1.13611	−0.568057	−	0.822989i	$-0.692305\pi$
$599$	−3.57967e12	−1.13611	−0.568057	+	0.822989i	$0.692305\pi$
$600$	−1.23795e12	−0.389964
$601$	4.51274e11	0.141093	0.0705465	−	0.997508i	$-0.477526\pi$
$601$	4.51274e11	0.141093	0.0705465	+	0.997508i	$0.477526\pi$
$602$	−7.50535e12	−2.32909
$603$	−7.49327e11	−0.230804
$604$	−2.34194e12	−0.715994
$605$	−6.41452e11	−0.194655
$606$	4.96379e12	1.49516
$607$	5.29060e12	1.58181	0.790907	−	0.611936i	$-0.209609\pi$
$607$	5.29060e12	1.58181	0.790907	+	0.611936i	$0.209609\pi$
$608$	−1.88956e11	−0.0560781
$609$	8.86724e12	2.61223
$610$	−5.55396e11	−0.162412
$611$	0	0
$612$	2.75053e11	0.0792567
$613$	3.73141e12	1.06734	0.533668	−	0.845694i	$-0.320813\pi$
$613$	3.73141e12	1.06734	0.533668	+	0.845694i	$0.320813\pi$
$614$	1.57620e12	0.447562
$615$	−6.13439e11	−0.172915
$616$	3.12716e12	0.875059
$617$	−5.22525e12	−1.45152	−0.725761	−	0.687947i	$-0.758512\pi$
$617$	−5.22525e12	−1.45152	−0.725761	+	0.687947i	$0.758512\pi$
$618$	4.44537e12	1.22591
$619$	−3.68332e11	−0.100840	−0.0504198	−	0.998728i	$-0.516056\pi$
$619$	−3.68332e11	−0.100840	−0.0504198	+	0.998728i	$0.516056\pi$
$620$	−3.78020e10	−0.0102743
$621$	−2.08442e12	−0.562435
$622$	−3.02160e12	−0.809432
$623$	−2.87014e12	−0.763319
$624$	0	0
$625$	3.19438e12	0.837387
$626$	4.12145e12	1.07267
$627$	−1.93794e12	−0.500768
$628$	1.92644e12	0.494239
$629$	2.67582e12	0.681600
$630$	−4.36474e11	−0.110389
$631$	−5.66616e12	−1.42284	−0.711421	−	0.702766i	$-0.751948\pi$
$631$	−5.66616e12	−1.42284	−0.711421	+	0.702766i	$0.751948\pi$
$632$	−2.26495e12	−0.564718
$633$	9.75194e11	0.241421
$634$	3.05633e12	0.751274
$635$	−4.41971e11	−0.107873
$636$	−3.32471e12	−0.805743
$637$	0	0
$638$	4.89133e12	1.16878
$639$	1.03046e12	0.244499
$640$	−8.81568e10	−0.0207704
$641$	−4.18212e12	−0.978443	−0.489221	−	0.872160i	$-0.662719\pi$
$641$	−4.18212e12	−0.978443	−0.489221	+	0.872160i	$0.662719\pi$
$642$	2.31366e12	0.537518
$643$	−4.59095e12	−1.05914	−0.529569	−	0.848267i	$-0.677646\pi$
$643$	−4.59095e12	−1.05914	−0.529569	+	0.848267i	$0.677646\pi$
$644$	3.02109e12	0.692114
$645$	2.16999e12	0.493672
$646$	−4.33639e11	−0.0979675
$647$	−1.21485e12	−0.272555	−0.136277	−	0.990671i	$-0.543514\pi$
$647$	−1.21485e12	−0.272555	−0.136277	+	0.990671i	$0.543514\pi$
$648$	−1.95378e12	−0.435300
$649$	−5.06015e12	−1.11960
$650$	0	0
$651$	8.56323e11	0.186863
$652$	−2.54457e12	−0.551443
$653$	9.26075e11	0.199314	0.0996568	−	0.995022i	$-0.468226\pi$
$653$	9.26075e11	0.199314	0.0996568	+	0.995022i	$0.468226\pi$
$654$	5.42363e12	1.15929
$655$	1.52998e12	0.324787
$656$	7.47397e11	0.157574
$657$	1.40473e11	0.0294136
$658$	−1.98526e12	−0.412858
$659$	2.76107e11	0.0570286	0.0285143	−	0.999593i	$-0.490922\pi$
$659$	2.76107e11	0.0570286	0.0285143	+	0.999593i	$0.490922\pi$
$660$	−9.04142e11	−0.185477
$661$	−6.62032e12	−1.34888	−0.674438	−	0.738331i	$-0.735614\pi$
$661$	−6.62032e12	−1.34888	−0.674438	+	0.738331i	$0.735614\pi$
$662$	−6.20655e12	−1.25600
$663$	0	0
$664$	−2.98952e12	−0.596823
$665$	6.88128e11	0.136450
$666$	2.03356e12	0.400519
$667$	4.72542e12	0.924431
$668$	−1.64885e12	−0.320397
$669$	−5.74279e12	−1.10842
$670$	5.51161e11	0.105668
$671$	6.94007e12	1.32164
$672$	1.99700e12	0.377760
$673$	−9.49262e11	−0.178369	−0.0891843	−	0.996015i	$-0.528426\pi$
$673$	−9.49262e11	−0.178369	−0.0891843	+	0.996015i	$0.528426\pi$
$674$	2.64246e12	0.493217
$675$	3.78979e12	0.702665
$676$	0	0
$677$	−4.09158e12	−0.748586	−0.374293	−	0.927311i	$-0.622115\pi$
$677$	−4.09158e12	−0.748586	−0.374293	+	0.927311i	$0.622115\pi$
$678$	3.95213e12	0.718287
$679$	−8.39420e12	−1.51553
$680$	−2.02313e11	−0.0362856
$681$	−8.13783e12	−1.44993
$682$	4.72363e11	0.0836077
$683$	9.22255e12	1.62165	0.810826	−	0.585287i	$-0.199018\pi$
$683$	9.22255e12	1.62165	0.810826	+	0.585287i	$0.199018\pi$
$684$	−3.29555e11	−0.0575673
$685$	−9.06768e10	−0.0157358
$686$	1.01387e13	1.74792
$687$	1.24951e13	2.14010
$688$	−2.64385e12	−0.449872
$689$	0	0
$690$	−8.73475e11	−0.146700
$691$	−5.56624e12	−0.928775	−0.464388	−	0.885632i	$-0.653726\pi$
$691$	−5.56624e12	−0.928775	−0.464388	+	0.885632i	$0.653726\pi$
$692$	5.89557e11	0.0977346
$693$	5.45405e12	0.898296
$694$	−3.40270e12	−0.556808
$695$	5.79322e11	0.0941865
$696$	3.12359e12	0.504560
$697$	1.71522e12	0.275279
$698$	5.50902e12	0.878466
$699$	−5.55891e12	−0.880730
$700$	−5.49281e12	−0.864675
$701$	6.38372e12	0.998487	0.499244	−	0.866462i	$-0.333611\pi$
$701$	6.38372e12	0.998487	0.499244	+	0.866462i	$0.333611\pi$
$702$	0	0
$703$	−3.20604e12	−0.495074
$704$	1.10158e12	0.169021
$705$	5.73989e11	0.0875090
$706$	−1.54439e12	−0.233956
$707$	2.20244e13	3.31525
$708$	−3.23140e12	−0.483327
$709$	−4.57498e12	−0.679957	−0.339979	−	0.940433i	$-0.610420\pi$
$709$	−4.57498e12	−0.679957	−0.339979	+	0.940433i	$0.610420\pi$
$710$	−7.57947e11	−0.111938
$711$	−3.95027e12	−0.579714
$712$	−1.01104e12	−0.147438
$713$	4.56341e11	0.0661282
$714$	4.58297e12	0.659941
$715$	0	0
$716$	5.05859e12	0.719318
$717$	−1.10005e13	−1.55445
$718$	−7.49180e12	−1.05203
$719$	2.81561e12	0.392910	0.196455	−	0.980513i	$-0.437057\pi$
$719$	2.81561e12	0.392910	0.196455	+	0.980513i	$0.437057\pi$
$720$	−1.53753e11	−0.0213220
$721$	1.97241e13	2.71824
$722$	−4.64344e12	−0.635949
$723$	−1.30246e13	−1.77273
$724$	−4.90122e12	−0.662950
$725$	−8.59154e12	−1.15491
$726$	5.11861e12	0.683813
$727$	8.80768e12	1.16938	0.584692	−	0.811256i	$-0.301216\pi$
$727$	8.80768e12	1.16938	0.584692	+	0.811256i	$0.301216\pi$
$728$	0	0
$729$	3.21353e12	0.421413
$730$	−1.03324e11	−0.0134663
$731$	−6.06744e12	−0.785919
$732$	4.43191e12	0.570547
$733$	9.56473e11	0.122378	0.0611892	−	0.998126i	$-0.480511\pi$
$733$	9.56473e11	0.122378	0.0611892	+	0.998126i	$0.480511\pi$
$734$	1.27964e12	0.162726
$735$	−5.10196e12	−0.644828
$736$	1.06422e12	0.133684
$737$	−6.88715e12	−0.859876
$738$	1.30353e12	0.161758
$739$	−8.07521e12	−0.995988	−0.497994	−	0.867181i	$-0.665930\pi$
$739$	−8.07521e12	−0.995988	−0.497994	+	0.867181i	$0.665930\pi$
$740$	−1.49577e12	−0.183367
$741$	0	0
$742$	−1.47517e13	−1.78659
$743$	−8.34279e12	−1.00430	−0.502148	−	0.864782i	$-0.667457\pi$
$743$	−8.34279e12	−1.00430	−0.502148	+	0.864782i	$0.667457\pi$
$744$	3.01650e11	0.0360932
$745$	−1.60572e11	−0.0190971
$746$	3.09827e12	0.366265
$747$	−5.21399e12	−0.612671
$748$	2.52805e12	0.295276
$749$	1.02657e13	1.19185
$750$	3.26904e12	0.377263
$751$	1.37838e13	1.58121	0.790605	−	0.612327i	$-0.209766\pi$
$751$	1.37838e13	1.58121	0.790605	+	0.612327i	$0.209766\pi$
$752$	−6.99332e11	−0.0797449
$753$	1.82480e13	2.06841
$754$	0	0
$755$	3.00436e12	0.336504
$756$	−6.11348e12	−0.680676
$757$	5.99121e12	0.663107	0.331553	−	0.943437i	$-0.392427\pi$
$757$	5.99121e12	0.663107	0.331553	+	0.943437i	$0.392427\pi$
$758$	2.22656e12	0.244976
$759$	1.09147e13	1.19378
$760$	2.42402e11	0.0263557
$761$	−5.19855e12	−0.561890	−0.280945	−	0.959724i	$-0.590648\pi$
$761$	−5.19855e12	−0.561890	−0.280945	+	0.959724i	$0.590648\pi$
$762$	3.52682e12	0.378953
$763$	2.40647e13	2.57051
$764$	7.05136e12	0.748778
$765$	−3.52852e11	−0.0372492
$766$	1.75922e12	0.184625
$767$	0	0
$768$	7.03468e11	0.0729657
$769$	−6.67066e12	−0.687860	−0.343930	−	0.938995i	$-0.611758\pi$
$769$	−6.67066e12	−0.687860	−0.343930	+	0.938995i	$0.611758\pi$
$770$	−4.01168e12	−0.411262
$771$	1.86842e13	1.90428
$772$	−9.49968e11	−0.0962567
$773$	5.10637e12	0.514404	0.257202	−	0.966358i	$-0.417199\pi$
$773$	5.10637e12	0.514404	0.257202	+	0.966358i	$0.417199\pi$
$774$	−4.61111e12	−0.461818
$775$	−8.29697e11	−0.0826156
$776$	−2.95696e12	−0.292730
$777$	3.38834e13	3.33498
$778$	−5.85146e12	−0.572606
$779$	−2.05509e12	−0.199946
$780$	0	0
$781$	9.47109e12	0.910899
$782$	2.44230e12	0.233544
$783$	−9.56236e12	−0.909153
$784$	6.21608e12	0.587617
$785$	−2.47133e12	−0.232283
$786$	−1.22088e13	−1.14096
$787$	1.64204e13	1.52580	0.762899	−	0.646518i	$-0.223775\pi$
$787$	1.64204e13	1.52580	0.762899	+	0.646518i	$0.223775\pi$
$788$	4.58624e12	0.423730
$789$	6.17834e12	0.567578
$790$	2.90559e12	0.265407
$791$	1.75356e13	1.59267
$792$	1.92126e12	0.173509
$793$	0	0
$794$	−5.55162e12	−0.495709
$795$	4.26510e12	0.378684
$796$	9.39314e11	0.0829281
$797$	1.12683e12	0.0989230	0.0494615	−	0.998776i	$-0.484249\pi$
$797$	1.12683e12	0.0989230	0.0494615	+	0.998776i	$0.484249\pi$
$798$	−5.49108e12	−0.479341
$799$	−1.60492e12	−0.139313
$800$	−1.93491e12	−0.167015
$801$	−1.76334e12	−0.151353
$802$	2.19088e12	0.186997
$803$	1.29110e12	0.109583
$804$	−4.39812e12	−0.371206
$805$	−3.87561e12	−0.325281
$806$	0	0
$807$	−4.77370e10	−0.00396209
$808$	7.75835e12	0.640351
$809$	−7.36603e12	−0.604596	−0.302298	−	0.953214i	$-0.597754\pi$
$809$	−7.36603e12	−0.604596	−0.302298	+	0.953214i	$0.597754\pi$
$810$	2.50641e12	0.204583
$811$	3.01694e12	0.244891	0.122446	−	0.992475i	$-0.460926\pi$
$811$	3.01694e12	0.244891	0.122446	+	0.992475i	$0.460926\pi$
$812$	1.38594e13	1.11877
$813$	2.31651e13	1.85963
$814$	1.86907e13	1.49216
$815$	3.26431e12	0.259168
$816$	1.61441e12	0.127470
$817$	7.26971e12	0.570844
$818$	8.98136e12	0.701378
$819$	0	0
$820$	−9.58798e11	−0.0740568
$821$	−1.95823e13	−1.50425	−0.752125	−	0.659021i	$-0.770971\pi$
$821$	−1.95823e13	−1.50425	−0.752125	+	0.659021i	$0.770971\pi$
$822$	7.23577e11	0.0552792
$823$	−3.88389e12	−0.295099	−0.147549	−	0.989055i	$-0.547139\pi$
$823$	−3.88389e12	−0.295099	−0.147549	+	0.989055i	$0.547139\pi$
$824$	6.94805e12	0.525038
$825$	−1.98446e13	−1.49142
$826$	−1.43377e13	−1.07169
$827$	8.71895e12	0.648171	0.324085	−	0.946028i	$-0.394943\pi$
$827$	8.71895e12	0.648171	0.324085	+	0.946028i	$0.394943\pi$
$828$	1.85609e12	0.137234
$829$	4.28594e12	0.315174	0.157587	−	0.987505i	$-0.449628\pi$
$829$	4.28594e12	0.315174	0.157587	+	0.987505i	$0.449628\pi$
$830$	3.83511e12	0.280496
$831$	−8.19206e12	−0.595921
$832$	0	0
$833$	1.42654e13	1.02656
$834$	−4.62284e12	−0.330873
$835$	2.11523e12	0.150581
$836$	−3.02898e12	−0.214471
$837$	−9.23451e11	−0.0650353
$838$	−1.97222e13	−1.38152
$839$	1.39822e13	0.974198	0.487099	−	0.873347i	$-0.338055\pi$
$839$	1.39822e13	0.974198	0.487099	+	0.873347i	$0.338055\pi$
$840$	−2.56185e12	−0.177540
$841$	7.17094e12	0.494304
$842$	−2.09599e12	−0.143710
$843$	1.09407e13	0.746141
$844$	1.52422e12	0.103396
$845$	0	0
$846$	−1.21970e12	−0.0818625
$847$	2.27113e13	1.51624
$848$	−5.19648e12	−0.345086
$849$	−1.96085e13	−1.29527
$850$	−4.44047e12	−0.291772
$851$	1.80567e13	1.18020
$852$	6.04822e12	0.393233
$853$	1.97610e13	1.27802	0.639012	−	0.769197i	$-0.279343\pi$
$853$	1.97610e13	1.27802	0.639012	+	0.769197i	$0.279343\pi$
$854$	1.96644e13	1.26509
$855$	4.22770e11	0.0270556
$856$	3.61623e12	0.230210
$857$	−2.36152e13	−1.49547	−0.747736	−	0.663996i	$-0.768859\pi$
$857$	−2.36152e13	−1.49547	−0.747736	+	0.663996i	$0.768859\pi$
$858$	0	0
$859$	1.78743e13	1.12011	0.560054	−	0.828456i	$-0.310781\pi$
$859$	1.78743e13	1.12011	0.560054	+	0.828456i	$0.310781\pi$
$860$	3.39166e12	0.211432
$861$	2.17195e13	1.34690
$862$	−1.32184e13	−0.815449
$863$	−8.93009e12	−0.548033	−0.274017	−	0.961725i	$-0.588352\pi$
$863$	−8.93009e12	−0.548033	−0.274017	+	0.961725i	$0.588352\pi$
$864$	−2.15355e12	−0.131475
$865$	−7.56313e11	−0.0459334
$866$	−1.76479e13	−1.06626
$867$	−1.57184e13	−0.944764
$868$	1.33842e12	0.0800303
$869$	−3.63074e13	−2.15976
$870$	−4.00710e12	−0.237134
$871$	0	0
$872$	8.47708e12	0.496503
$873$	−5.15720e12	−0.300504
$874$	−2.92624e12	−0.169632
$875$	1.45047e13	0.836515
$876$	8.24496e11	0.0473064
$877$	−1.36331e13	−0.778209	−0.389104	−	0.921194i	$-0.627215\pi$
$877$	−1.36331e13	−0.778209	−0.389104	+	0.921194i	$0.627215\pi$
$878$	−1.19082e13	−0.676271
$879$	2.34824e12	0.132676
$880$	−1.41316e12	−0.0794366
$881$	2.21086e13	1.23643	0.618214	−	0.786010i	$-0.287857\pi$
$881$	2.21086e13	1.23643	0.618214	+	0.786010i	$0.287857\pi$
$882$	1.08414e13	0.603221
$883$	−2.18016e12	−0.120688	−0.0603442	−	0.998178i	$-0.519220\pi$
$883$	−2.18016e12	−0.120688	−0.0603442	+	0.998178i	$0.519220\pi$
$884$	0	0
$885$	4.14540e12	0.227155
$886$	−2.37689e13	−1.29586
$887$	8.98386e11	0.0487312	0.0243656	−	0.999703i	$-0.492243\pi$
$887$	8.98386e11	0.0487312	0.0243656	+	0.999703i	$0.492243\pi$
$888$	1.19358e13	0.644162
$889$	1.56485e13	0.840262
$890$	1.29701e12	0.0692930
$891$	−3.13194e13	−1.66481
$892$	−8.97591e12	−0.474719
$893$	1.92293e12	0.101189
$894$	1.28133e12	0.0670873
$895$	−6.48941e12	−0.338066
$896$	3.12129e12	0.161789
$897$	0	0
$898$	1.27976e13	0.656730
$899$	2.09348e12	0.106893
$900$	−3.37465e12	−0.171450
$901$	−1.19255e13	−0.602860
$902$	1.19809e13	0.602641
$903$	−7.68308e13	−3.84539
$904$	6.17713e12	0.307630
$905$	6.28753e12	0.311574
$906$	−2.39740e13	−1.18212
$907$	4.12871e12	0.202573	0.101286	−	0.994857i	$-0.467704\pi$
$907$	4.12871e12	0.202573	0.101286	+	0.994857i	$0.467704\pi$
$908$	−1.27193e13	−0.620980
$909$	1.35312e13	0.657356
$910$	0	0
$911$	−3.43032e13	−1.65007	−0.825034	−	0.565084i	$-0.808844\pi$
$911$	−3.43032e13	−1.65007	−0.825034	+	0.565084i	$0.808844\pi$
$912$	−1.93430e12	−0.0925864
$913$	−4.79224e13	−2.28255
$914$	5.20592e12	0.246740
$915$	−5.68548e12	−0.268146
$916$	1.95297e13	0.916571
$917$	−5.41705e13	−2.52989
$918$	−4.94223e12	−0.229684
$919$	−1.46188e13	−0.676071	−0.338035	−	0.941133i	$-0.609762\pi$
$919$	−1.46188e13	−0.676071	−0.338035	+	0.941133i	$0.609762\pi$
$920$	−1.36523e12	−0.0628291
$921$	1.61352e13	0.738936
$922$	5.75991e12	0.262498
$923$	0	0
$924$	3.20122e13	1.44474
$925$	−3.28299e13	−1.47446
$926$	−9.26984e12	−0.414307
$927$	1.21180e13	0.538980
$928$	4.88214e12	0.216095
$929$	2.82624e13	1.24491	0.622455	−	0.782656i	$-0.286136\pi$
$929$	2.82624e13	1.24491	0.622455	+	0.782656i	$0.286136\pi$
$930$	−3.86972e11	−0.0169631
$931$	−1.70921e13	−0.745629
$932$	−8.68851e12	−0.377202
$933$	−3.09315e13	−1.33639
$934$	3.52179e12	0.151427
$935$	−3.24311e12	−0.138774
$936$	0	0
$937$	2.56705e13	1.08794	0.543972	−	0.839103i	$-0.316920\pi$
$937$	2.56705e13	1.08794	0.543972	+	0.839103i	$0.316920\pi$
$938$	−1.95145e13	−0.823084
$939$	4.21905e13	1.77100
$940$	8.97138e11	0.0374786
$941$	2.19542e13	0.912774	0.456387	−	0.889781i	$-0.349143\pi$
$941$	2.19542e13	0.912774	0.456387	+	0.889781i	$0.349143\pi$
$942$	1.97206e13	0.816001
$943$	1.15745e13	0.476649
$944$	−5.05064e12	−0.207001
$945$	7.84268e12	0.319905
$946$	−4.23813e13	−1.72054
$947$	2.54204e13	1.02709	0.513544	−	0.858064i	$-0.328332\pi$
$947$	2.54204e13	1.02709	0.513544	+	0.858064i	$0.328332\pi$
$948$	−2.31858e13	−0.932364
$949$	0	0
$950$	5.32035e12	0.211926
$951$	3.12870e13	1.24037
$952$	7.16313e12	0.282642
$953$	−2.37513e13	−0.932760	−0.466380	−	0.884585i	$-0.654442\pi$
$953$	−2.37513e13	−0.932760	−0.466380	+	0.884585i	$0.654442\pi$
$954$	−9.06312e12	−0.354250
$955$	−9.04584e12	−0.351912
$956$	−1.71937e13	−0.665747
$957$	5.00716e13	1.92969
$958$	−3.32080e13	−1.27379
$959$	3.21051e12	0.122572
$960$	−9.02443e11	−0.0342925
$961$	−2.62375e13	−0.992353
$962$	0	0
$963$	6.30703e12	0.236323
$964$	−2.03573e13	−0.759230
$965$	1.21867e12	0.0452389
$966$	3.09263e13	1.14270
$967$	1.52013e12	0.0559064	0.0279532	−	0.999609i	$-0.491101\pi$
$967$	1.52013e12	0.0559064	0.0279532	+	0.999609i	$0.491101\pi$
$968$	8.00033e12	0.292866
$969$	−4.43908e12	−0.161747
$970$	3.79334e12	0.137578
$971$	−3.22330e13	−1.16363	−0.581814	−	0.813322i	$-0.697657\pi$
$971$	−3.22330e13	−1.16363	−0.581814	+	0.813322i	$0.697657\pi$
$972$	−9.65180e12	−0.346825
$973$	−2.05115e13	−0.733653
$974$	1.61350e13	0.574453
$975$	0	0
$976$	6.92703e12	0.244356
$977$	3.09104e13	1.08537	0.542687	−	0.839935i	$-0.317407\pi$
$977$	3.09104e13	1.08537	0.542687	+	0.839935i	$0.317407\pi$
$978$	−2.60483e13	−0.910447
$979$	−1.62071e13	−0.563875
$980$	−7.97430e12	−0.276169
$981$	1.47848e13	0.509688
$982$	−4.17374e12	−0.143226
$983$	4.06941e12	0.139008	0.0695042	−	0.997582i	$-0.477858\pi$
$983$	4.06941e12	0.139008	0.0695042	+	0.997582i	$0.477858\pi$
$984$	7.65096e12	0.260158
$985$	−5.88346e12	−0.199145
$986$	1.12042e13	0.377514
$987$	−2.03227e13	−0.681639
$988$	0	0
$989$	−4.09437e13	−1.36083
$990$	−2.46468e12	−0.0815460
$991$	2.35584e13	0.775914	0.387957	−	0.921677i	$-0.373181\pi$
$991$	2.35584e13	0.775914	0.387957	+	0.921677i	$0.373181\pi$
$992$	4.71476e11	0.0154581
$993$	−6.35352e13	−2.07369
$994$	2.68360e13	0.871924
$995$	−1.20500e12	−0.0389747
$996$	−3.06032e13	−0.985370
$997$	−2.00207e13	−0.641727	−0.320863	−	0.947125i	$-0.603973\pi$
$997$	−2.00207e13	−0.641727	−0.320863	+	0.947125i	$0.603973\pi$
$998$	−5.66114e12	−0.180641
$999$	−3.65396e13	−1.16070

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	338.10.a.r.1.12	yes	15
13.12	even	2		338.10.a.q.1.12	✓	15

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
338.10.a.q.1.12	✓	15	13.12	even	2
338.10.a.r.1.12	yes	15	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+16.0000 q^{2} +163.789 q^{3} +256.000 q^{4} -328.410 q^{5} +2620.62 q^{6} +11627.7 q^{7} +4096.00 q^{8} +7143.79 q^{9} -5254.55 q^{10} +65659.4 q^{11} +41929.9 q^{12} +186043. q^{14} -53789.8 q^{15} +65536.0 q^{16} +150400. q^{17} +114301. q^{18} -180202. q^{19} -84072.8 q^{20} +1.90449e6 q^{21} +1.05055e6 q^{22} +1.01492e6 q^{23} +670879. q^{24} -1.84527e6 q^{25} -2.05378e6 q^{27} +2.97669e6 q^{28} +4.65597e6 q^{29} -860637. q^{30} +449634. q^{31} +1.04858e6 q^{32} +1.07543e7 q^{33} +2.40640e6 q^{34} -3.81865e6 q^{35} +1.82881e6 q^{36} +1.77914e7 q^{37} -2.88323e6 q^{38} -1.34517e6 q^{40} +1.14044e7 q^{41} +3.04718e7 q^{42} -4.03420e7 q^{43} +1.68088e7 q^{44} -2.34609e6 q^{45} +1.62387e7 q^{46} -1.06710e7 q^{47} +1.07341e7 q^{48} +9.48499e7 q^{49} -2.95244e7 q^{50} +2.46339e7 q^{51} -7.92920e7 q^{53} -3.28605e7 q^{54} -2.15632e7 q^{55} +4.76271e7 q^{56} -2.95151e7 q^{57} +7.44956e7 q^{58} -7.70667e7 q^{59} -1.37702e7 q^{60} +1.05698e8 q^{61} +7.19415e6 q^{62} +8.30658e7 q^{63} +1.67772e7 q^{64} +1.72068e8 q^{66} -1.04892e8 q^{67} +3.85025e7 q^{68} +1.66232e8 q^{69} -6.10984e7 q^{70} +1.44246e8 q^{71} +2.92610e7 q^{72} +1.96637e7 q^{73} +2.84662e8 q^{74} -3.02235e8 q^{75} -4.61317e7 q^{76} +7.63468e8 q^{77} -5.52966e8 q^{79} -2.15226e7 q^{80} -4.76998e8 q^{81} +1.82470e8 q^{82} -7.29864e8 q^{83} +4.87549e8 q^{84} -4.93929e7 q^{85} -6.45472e8 q^{86} +7.62596e8 q^{87} +2.68941e8 q^{88} -2.46836e8 q^{89} -3.75374e7 q^{90} +2.59819e8 q^{92} +7.36451e7 q^{93} -1.70735e8 q^{94} +5.91801e7 q^{95} +1.71745e8 q^{96} -7.21914e8 q^{97} +1.51760e9 q^{98} +4.69057e8 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 15 q + 240 q^{2} + 324 q^{3} + 3840 q^{4} + 2164 q^{5} + 5184 q^{6} + 4227 q^{7} + 61440 q^{8} + 112199 q^{9} + 34624 q^{10} - 58782 q^{11} + 82944 q^{12} + 67632 q^{14} + 488672 q^{15} + 983040 q^{16}+ \cdots + 3437295177 q^{99}+O(q^{100}) \) 15 * q + 240 * q^2 + 324 * q^3 + 3840 * q^4 + 2164 * q^5 + 5184 * q^6 + 4227 * q^7 + 61440 * q^8 + 112199 * q^9 + 34624 * q^10 - 58782 * q^11 + 82944 * q^12 + 67632 * q^14 + 488672 * q^15 + 983040 * q^16 + 47308 * q^17 + 1795184 * q^18 + 1027864 * q^19 + 553984 * q^20 - 1332838 * q^21 - 940512 * q^22 - 697897 * q^23 + 1327104 * q^24 + 12121163 * q^25 + 11934723 * q^27 + 1082112 * q^28 + 4970557 * q^29 + 7818752 * q^30 + 8962601 * q^31 + 15728640 * q^32 + 3541482 * q^33 + 756928 * q^34 - 5785412 * q^35 + 28722944 * q^36 + 25045552 * q^37 + 16445824 * q^38 + 8863744 * q^40 + 26390985 * q^41 - 21325408 * q^42 + 11355145 * q^43 - 15048192 * q^44 + 221235525 * q^45 - 11166352 * q^46 + 79882208 * q^47 + 21233664 * q^48 + 150275074 * q^49 + 193938608 * q^50 + 118779121 * q^51 - 21678349 * q^53 + 190955568 * q^54 + 290281352 * q^55 + 17313792 * q^56 - 617732541 * q^57 + 79528912 * q^58 - 264523979 * q^59 + 125100032 * q^60 + 379367976 * q^61 + 143401616 * q^62 + 270769230 * q^63 + 251658240 * q^64 + 56663712 * q^66 - 250185789 * q^67 + 12110848 * q^68 + 281627650 * q^69 - 92566592 * q^70 + 173178579 * q^71 + 459567104 * q^72 + 153358293 * q^73 + 400728832 * q^74 + 20980603 * q^75 + 263133184 * q^76 + 1172911296 * q^77 + 217644101 * q^79 + 141819904 * q^80 + 2373566723 * q^81 + 422255760 * q^82 - 76435497 * q^83 - 341206528 * q^84 + 2676674151 * q^85 + 181682320 * q^86 + 4874616750 * q^87 - 240771072 * q^88 + 2250224949 * q^89 + 3539768400 * q^90 - 178661632 * q^92 + 2915972474 * q^93 + 1278115328 * q^94 + 3329480199 * q^95 + 339738624 * q^96 + 2720440815 * q^97 + 2404401184 * q^98 + 3437295177 * q^99

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