LMFDB - Embedded newform 338.10.a.l.1.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

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

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

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

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

Newform invariants

comment:select newform

sage:traces = [6,96,81,1536,1693] 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:	$6$
Coefficient field:	$\mathbb{Q}[x]/(x^{6} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 3x^{5} - 10375x^{4} - 44865x^{3} + 25702990x^{2} + 68900300x - 16723086000 $ x^6 - 3x^5 - 10375x^4 - 44865x^3 + 25702990x^2 + 68900300*x - 16723086000
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{6}\cdot 3^{4}\cdot 13 $
Twist minimal:	no (minimal twist has level 26)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$31.0068$ 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)

$f(q)$	$=$	\(q+16.0000 q^{2} -78.0204 q^{3} +256.000 q^{4} -1338.85 q^{5} -1248.33 q^{6} -132.180 q^{7} +4096.00 q^{8} -13595.8 q^{9} -21421.6 q^{10} -24257.6 q^{11} -19973.2 q^{12} -2114.88 q^{14} +104457. q^{15} +65536.0 q^{16} -427172. q^{17} -217533. q^{18} -949104. q^{19} -342745. q^{20} +10312.8 q^{21} -388121. q^{22} +972785. q^{23} -319572. q^{24} -160614. q^{25} +2.59643e6 q^{27} -33838.1 q^{28} -3.04579e6 q^{29} +1.67132e6 q^{30} +2.57547e6 q^{31} +1.04858e6 q^{32} +1.89258e6 q^{33} -6.83475e6 q^{34} +176969. q^{35} -3.48053e6 q^{36} -1.08742e7 q^{37} -1.51857e7 q^{38} -5.48392e6 q^{40} +1.20652e7 q^{41} +165004. q^{42} -2.13875e7 q^{43} -6.20994e6 q^{44} +1.82027e7 q^{45} +1.55646e7 q^{46} -2.69913e7 q^{47} -5.11314e6 q^{48} -4.03361e7 q^{49} -2.56982e6 q^{50} +3.33281e7 q^{51} +3.73277e7 q^{53} +4.15428e7 q^{54} +3.24772e7 q^{55} -541410. q^{56} +7.40495e7 q^{57} -4.87326e7 q^{58} +3.49075e7 q^{59} +2.67411e7 q^{60} -1.58329e8 q^{61} +4.12075e7 q^{62} +1.79710e6 q^{63} +1.67772e7 q^{64} +3.02814e7 q^{66} +6.76408e7 q^{67} -1.09356e8 q^{68} -7.58970e7 q^{69} +2.83150e6 q^{70} +1.14781e8 q^{71} -5.56885e7 q^{72} -1.49856e8 q^{73} -1.73988e8 q^{74} +1.25311e7 q^{75} -2.42971e8 q^{76} +3.20637e6 q^{77} +6.16681e7 q^{79} -8.77427e7 q^{80} +6.50322e7 q^{81} +1.93043e8 q^{82} -4.82674e8 q^{83} +2.64006e6 q^{84} +5.71918e8 q^{85} -3.42200e8 q^{86} +2.37633e8 q^{87} -9.93590e7 q^{88} -1.91320e8 q^{89} +2.91244e8 q^{90} +2.49033e8 q^{92} -2.00939e8 q^{93} -4.31861e8 q^{94} +1.27070e9 q^{95} -8.18103e7 q^{96} -1.07090e8 q^{97} -6.45378e8 q^{98} +3.29801e8 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 96 q^{2} + 81 q^{3} + 1536 q^{4} + 1693 q^{5} + 1296 q^{6} + 473 q^{7} + 24576 q^{8} + 69813 q^{9} + 27088 q^{10} + 14011 q^{11} + 20736 q^{12} + 7568 q^{14} - 294780 q^{15} + 393216 q^{16} - 173558 q^{17}+ \cdots - 881769510 q^{99}+O(q^{100}) $ 6 * q + 96 * q^2 + 81 * q^3 + 1536 * q^4 + 1693 * q^5 + 1296 * q^6 + 473 * q^7 + 24576 * q^8 + 69813 * q^9 + 27088 * q^10 + 14011 * q^11 + 20736 * q^12 + 7568 * q^14 - 294780 * q^15 + 393216 * q^16 - 173558 * q^17 + 1117008 * q^18 + 322367 * q^19 + 433408 * q^20 + 2256885 * q^21 + 224176 * q^22 - 1644771 * q^23 + 331776 * q^24 + 2687569 * q^25 - 922995 * q^27 + 121088 * q^28 + 10801236 * q^29 - 4716480 * q^30 + 10435122 * q^31 + 6291456 * q^32 + 26201763 * q^33 - 2776928 * q^34 + 2168950 * q^35 + 17872128 * q^36 - 15710464 * q^37 + 5157872 * q^38 + 6934528 * q^40 - 1525478 * q^41 + 36110160 * q^42 + 50959661 * q^43 + 3586816 * q^44 + 18619731 * q^45 - 26316336 * q^46 + 68156998 * q^47 + 5308416 * q^48 + 162536361 * q^49 + 43001104 * q^50 - 84678981 * q^51 + 72278209 * q^53 - 14767920 * q^54 - 353372330 * q^55 + 1937408 * q^56 + 17951025 * q^57 + 172819776 * q^58 - 5665291 * q^59 - 75463680 * q^60 - 353387956 * q^61 + 166961952 * q^62 - 224088894 * q^63 + 100663296 * q^64 + 419228208 * q^66 + 371115369 * q^67 - 44430848 * q^68 + 280317279 * q^69 + 34703200 * q^70 + 156688763 * q^71 + 285954048 * q^72 + 466401663 * q^73 - 251367424 * q^74 + 1149481845 * q^75 + 82525952 * q^76 + 312460333 * q^77 + 162543480 * q^79 + 110952448 * q^80 + 295496586 * q^81 - 24407648 * q^82 - 435114576 * q^83 + 577762560 * q^84 + 2307296767 * q^85 + 815354576 * q^86 - 617376057 * q^87 + 57389056 * q^88 + 163315063 * q^89 + 297915696 * q^90 - 421061376 * q^92 + 2056270836 * q^93 + 1090511968 * q^94 - 537110948 * q^95 + 84934656 * q^96 - 1500514705 * q^97 + 2600581776 * q^98 - 881769510 * 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
$3$	−78.0204	−0.556112	−0.278056	−	0.960565i	$-0.589690\pi$
$3$	−78.0204	−0.556112	−0.278056	+	0.960565i	$0.589690\pi$
$4$	256.000	0.500000
$5$	−1338.85	−0.958001	−0.479000	−	0.877815i	$-0.659001\pi$
$5$	−1338.85	−0.958001	−0.479000	+	0.877815i	$0.659001\pi$
$6$	−1248.33	−0.393231
$7$	−132.180	−0.0208078	−0.0104039	−	0.999946i	$-0.503312\pi$
$7$	−132.180	−0.0208078	−0.0104039	+	0.999946i	$0.503312\pi$
$8$	4096.00	0.353553
$9$	−13595.8	−0.690739
$10$	−21421.6	−0.677409
$11$	−24257.6	−0.499551	−0.249776	−	0.968304i	$-0.580357\pi$
$11$	−24257.6	−0.499551	−0.249776	+	0.968304i	$0.580357\pi$
$12$	−19973.2	−0.278056
$13$	0	0
$13$	0	0
$14$	−2114.88	−0.0147133
$15$	104457.	0.532756
$16$	65536.0	0.250000
$17$	−427172.	−1.24046	−0.620230	−	0.784420i	$-0.712961\pi$
$17$	−427172.	−1.24046	−0.620230	+	0.784420i	$0.712961\pi$
$18$	−217533.	−0.488426
$19$	−949104.	−1.67079	−0.835396	−	0.549648i	$-0.814762\pi$
$19$	−949104.	−1.67079	−0.835396	+	0.549648i	$0.814762\pi$
$20$	−342745.	−0.479000
$21$	10312.8	0.0115714
$22$	−388121.	−0.353236
$23$	972785.	0.724839	0.362419	−	0.932015i	$-0.381951\pi$
$23$	972785.	0.724839	0.362419	+	0.932015i	$0.381951\pi$
$24$	−319572.	−0.196615
$25$	−160614.	−0.0822342
$26$	0	0
$27$	2.59643e6	0.940241
$28$	−33838.1	−0.0104039
$29$	−3.04579e6	−0.799666	−0.399833	−	0.916588i	$-0.630932\pi$
$29$	−3.04579e6	−0.799666	−0.399833	+	0.916588i	$0.630932\pi$
$30$	1.67132e6	0.376715
$31$	2.57547e6	0.500874	0.250437	−	0.968133i	$-0.419426\pi$
$31$	2.57547e6	0.500874	0.250437	+	0.968133i	$0.419426\pi$
$32$	1.04858e6	0.176777
$33$	1.89258e6	0.277807
$34$	−6.83475e6	−0.877138
$35$	176969.	0.0199338
$36$	−3.48053e6	−0.345370
$37$	−1.08742e7	−0.953874	−0.476937	−	0.878937i	$-0.658253\pi$
$37$	−1.08742e7	−0.953874	−0.476937	+	0.878937i	$0.658253\pi$
$38$	−1.51857e7	−1.18143
$39$	0	0
$40$	−5.48392e6	−0.338704
$41$	1.20652e7	0.666817	0.333408	−	0.942782i	$-0.391801\pi$
$41$	1.20652e7	0.666817	0.333408	+	0.942782i	$0.391801\pi$
$42$	165004.	0.00818225
$43$	−2.13875e7	−0.954008	−0.477004	−	0.878901i	$-0.658277\pi$
$43$	−2.13875e7	−0.954008	−0.477004	+	0.878901i	$0.658277\pi$
$44$	−6.20994e6	−0.249776
$45$	1.82027e7	0.661729
$46$	1.55646e7	0.512538
$47$	−2.69913e7	−0.806833	−0.403417	−	0.915016i	$-0.632177\pi$
$47$	−2.69913e7	−0.806833	−0.403417	+	0.915016i	$0.632177\pi$
$48$	−5.11314e6	−0.139028
$49$	−4.03361e7	−0.999567
$50$	−2.56982e6	−0.0581484
$51$	3.33281e7	0.689835
$52$	0	0
$53$	3.73277e7	0.649815	0.324908	−	0.945746i	$-0.394667\pi$
$53$	3.73277e7	0.649815	0.324908	+	0.945746i	$0.394667\pi$
$54$	4.15428e7	0.664851
$55$	3.24772e7	0.478571
$56$	−541410.	−0.00735665
$57$	7.40495e7	0.929148
$58$	−4.87326e7	−0.565449
$59$	3.49075e7	0.375046	0.187523	−	0.982260i	$-0.439954\pi$
$59$	3.49075e7	0.375046	0.187523	+	0.982260i	$0.439954\pi$
$60$	2.67411e7	0.266378
$61$	−1.58329e8	−1.46412	−0.732058	−	0.681242i	$-0.761440\pi$
$61$	−1.58329e8	−1.46412	−0.732058	+	0.681242i	$0.761440\pi$
$62$	4.12075e7	0.354171
$63$	1.79710e6	0.0143727
$64$	1.67772e7	0.125000
$65$	0	0
$66$	3.02814e7	0.196439
$67$	6.76408e7	0.410083	0.205042	−	0.978753i	$-0.434267\pi$
$67$	6.76408e7	0.410083	0.205042	+	0.978753i	$0.434267\pi$
$68$	−1.09356e8	−0.620230
$69$	−7.58970e7	−0.403092
$70$	2.83150e6	0.0140954
$71$	1.14781e8	0.536053	0.268026	−	0.963412i	$-0.413629\pi$
$71$	1.14781e8	0.536053	0.268026	+	0.963412i	$0.413629\pi$
$72$	−5.56885e7	−0.244213
$73$	−1.49856e8	−0.617620	−0.308810	−	0.951124i	$-0.599931\pi$
$73$	−1.49856e8	−0.617620	−0.308810	+	0.951124i	$0.599931\pi$
$74$	−1.73988e8	−0.674491
$75$	1.25311e7	0.0457315
$76$	−2.42971e8	−0.835396
$77$	3.20637e6	0.0103945
$78$	0	0
$79$	6.16681e7	0.178131	0.0890654	−	0.996026i	$-0.471612\pi$
$79$	6.16681e7	0.178131	0.0890654	+	0.996026i	$0.471612\pi$
$80$	−8.77427e7	−0.239500
$81$	6.50322e7	0.167860
$82$	1.93043e8	0.471511
$83$	−4.82674e8	−1.11636	−0.558178	−	0.829721i	$-0.688499\pi$
$83$	−4.82674e8	−1.11636	−0.558178	+	0.829721i	$0.688499\pi$
$84$	2.64006e6	0.00578572
$85$	5.71918e8	1.18836
$86$	−3.42200e8	−0.674585
$87$	2.37633e8	0.444704
$88$	−9.93590e7	−0.176618
$89$	−1.91320e8	−0.323225	−0.161612	−	0.986854i	$-0.551669\pi$
$89$	−1.91320e8	−0.323225	−0.161612	+	0.986854i	$0.551669\pi$
$90$	2.91244e8	0.467913
$91$	0	0
$92$	2.49033e8	0.362419
$93$	−2.00939e8	−0.278542
$94$	−4.31861e8	−0.570517
$95$	1.27070e9	1.60062
$96$	−8.18103e7	−0.0983077
$97$	−1.07090e8	−0.122822	−0.0614110	−	0.998113i	$-0.519560\pi$
$97$	−1.07090e8	−0.122822	−0.0614110	+	0.998113i	$0.519560\pi$
$98$	−6.45378e8	−0.706801
$99$	3.29801e8	0.345060
$100$	−4.11171e7	−0.0411171
$101$	1.37121e9	1.31117	0.655583	−	0.755123i	$-0.272423\pi$
$101$	1.37121e9	1.31117	0.655583	+	0.755123i	$0.272423\pi$
$102$	5.33250e8	0.487787
$103$	1.97511e9	1.72911	0.864555	−	0.502537i	$-0.167600\pi$
$103$	1.97511e9	1.72911	0.864555	+	0.502537i	$0.167600\pi$
$104$	0	0
$105$	−1.38072e7	−0.0110855
$106$	5.97243e8	0.459489
$107$	2.25459e9	1.66280	0.831400	−	0.555674i	$-0.187540\pi$
$107$	2.25459e9	1.66280	0.831400	+	0.555674i	$0.187540\pi$
$108$	6.64685e8	0.470120
$109$	6.84819e7	0.0464683	0.0232341	−	0.999730i	$-0.492604\pi$
$109$	6.84819e7	0.0464683	0.0232341	+	0.999730i	$0.492604\pi$
$110$	5.19635e8	0.338401
$111$	8.48412e8	0.530461
$112$	−8.66256e6	−0.00520194
$113$	−2.69288e9	−1.55369	−0.776844	−	0.629693i	$-0.783181\pi$
$113$	−2.69288e9	−1.55369	−0.776844	+	0.629693i	$0.783181\pi$
$114$	1.18479e9	0.657007
$115$	−1.30241e9	−0.694396
$116$	−7.79721e8	−0.399833
$117$	0	0
$118$	5.58520e8	0.265197
$119$	5.64637e7	0.0258112
$120$	4.27857e8	0.188358
$121$	−1.76952e9	−0.750448
$122$	−2.53326e9	−1.03529
$123$	−9.41330e8	−0.370825
$124$	6.59320e8	0.250437
$125$	2.82997e9	1.03678
$126$	2.87536e7	0.0101631
$127$	−4.79639e9	−1.63605	−0.818027	−	0.575180i	$-0.804932\pi$
$127$	−4.79639e9	−1.63605	−0.818027	+	0.575180i	$0.804932\pi$
$128$	2.68435e8	0.0883883
$129$	1.66866e9	0.530536
$130$	0	0
$131$	−2.25488e8	−0.0668965	−0.0334483	−	0.999440i	$-0.510649\pi$
$131$	−2.25488e8	−0.0668965	−0.0334483	+	0.999440i	$0.510649\pi$
$132$	4.84502e8	0.138903
$133$	1.25453e8	0.0347654
$134$	1.08225e9	0.289973
$135$	−3.47622e9	−0.900752
$136$	−1.74970e9	−0.438569
$137$	5.88169e9	1.42646	0.713230	−	0.700930i	$-0.247231\pi$
$137$	5.88169e9	1.42646	0.713230	+	0.700930i	$0.247231\pi$
$138$	−1.21435e9	−0.285029
$139$	4.98569e9	1.13281	0.566407	−	0.824126i	$-0.308333\pi$
$139$	4.98569e9	1.13281	0.566407	+	0.824126i	$0.308333\pi$
$140$	4.53041e7	0.00996692
$141$	2.10587e9	0.448690
$142$	1.83650e9	0.379046
$143$	0	0
$144$	−8.91015e8	−0.172685
$145$	4.07784e9	0.766080
$146$	−2.39770e9	−0.436723
$147$	3.14704e9	0.555872
$148$	−2.78381e9	−0.476937
$149$	−4.11445e9	−0.683871	−0.341935	−	0.939723i	$-0.611082\pi$
$149$	−4.11445e9	−0.683871	−0.341935	+	0.939723i	$0.611082\pi$
$150$	2.00498e8	0.0323370
$151$	−4.09807e9	−0.641480	−0.320740	−	0.947167i	$-0.603932\pi$
$151$	−4.09807e9	−0.641480	−0.320740	+	0.947167i	$0.603932\pi$
$152$	−3.88753e9	−0.590714
$153$	5.80775e9	0.856834
$154$	5.13019e7	0.00735005
$155$	−3.44816e9	−0.479838
$156$	0	0
$157$	1.11279e10	1.46173	0.730863	−	0.682524i	$-0.239118\pi$
$157$	1.11279e10	1.46173	0.730863	+	0.682524i	$0.239118\pi$
$158$	9.86690e8	0.125957
$159$	−2.91232e9	−0.361370
$160$	−1.40388e9	−0.169352
$161$	−1.28583e8	−0.0150823
$162$	1.04052e9	0.118695
$163$	1.35306e10	1.50132	0.750661	−	0.660688i	$-0.229735\pi$
$163$	1.35306e10	1.50132	0.750661	+	0.660688i	$0.229735\pi$
$164$	3.08869e9	0.333408
$165$	−2.53388e9	−0.266139
$166$	−7.72279e9	−0.789383
$167$	7.60541e9	0.756656	0.378328	−	0.925672i	$-0.376499\pi$
$167$	7.60541e9	0.756656	0.378328	+	0.925672i	$0.376499\pi$
$168$	4.22410e7	0.00409112
$169$	0	0
$170$	9.15069e9	0.840299
$171$	1.29038e10	1.15408
$172$	−5.47520e9	−0.477004
$173$	−4.57829e9	−0.388594	−0.194297	−	0.980943i	$-0.562243\pi$
$173$	−4.57829e9	−0.388594	−0.194297	+	0.980943i	$0.562243\pi$
$174$	3.80214e9	0.314453
$175$	2.12300e7	0.00171111
$176$	−1.58974e9	−0.124888
$177$	−2.72350e9	−0.208568
$178$	−3.06111e9	−0.228554
$179$	2.99951e9	0.218379	0.109190	−	0.994021i	$-0.465174\pi$
$179$	2.99951e9	0.218379	0.109190	+	0.994021i	$0.465174\pi$
$180$	4.65990e9	0.330864
$181$	−9.34858e9	−0.647429	−0.323714	−	0.946155i	$-0.604932\pi$
$181$	−9.34858e9	−0.647429	−0.323714	+	0.946155i	$0.604932\pi$
$182$	0	0
$183$	1.23529e10	0.814213
$184$	3.98453e9	0.256269
$185$	1.45589e10	0.913812
$186$	−3.21502e9	−0.196959
$187$	1.03622e10	0.619673
$188$	−6.90978e9	−0.403417
$189$	−3.43196e8	−0.0195643
$190$	2.03313e10	1.13181
$191$	−5.09241e9	−0.276868	−0.138434	−	0.990372i	$-0.544207\pi$
$191$	−5.09241e9	−0.276868	−0.138434	+	0.990372i	$0.544207\pi$
$192$	−1.30897e9	−0.0695140
$193$	1.36610e10	0.708722	0.354361	−	0.935109i	$-0.384698\pi$
$193$	1.36610e10	0.708722	0.354361	+	0.935109i	$0.384698\pi$
$194$	−1.71344e9	−0.0868483
$195$	0	0
$196$	−1.03261e10	−0.499784
$197$	−2.47334e9	−0.117000	−0.0585001	−	0.998287i	$-0.518632\pi$
$197$	−2.47334e9	−0.117000	−0.0585001	+	0.998287i	$0.518632\pi$
$198$	5.27682e9	0.243994
$199$	4.35407e10	1.96814	0.984071	−	0.177777i	$-0.0568905\pi$
$199$	4.35407e10	1.96814	0.984071	+	0.177777i	$0.0568905\pi$
$200$	−6.57874e8	−0.0290742
$201$	−5.27736e9	−0.228052
$202$	2.19394e10	0.927134
$203$	4.02593e8	0.0166392
$204$	8.53200e9	0.344918
$205$	−1.61534e10	−0.638811
$206$	3.16017e10	1.22267
$207$	−1.32258e10	−0.500674
$208$	0	0
$209$	2.30230e10	0.834647
$210$	−2.20915e8	−0.00783860
$211$	−2.27973e10	−0.791795	−0.395898	−	0.918295i	$-0.629566\pi$
$211$	−2.27973e10	−0.791795	−0.395898	+	0.918295i	$0.629566\pi$
$212$	9.55589e9	0.324908
$213$	−8.95526e9	−0.298105
$214$	3.60734e10	1.17578
$215$	2.86346e10	0.913940
$216$	1.06350e10	0.332425
$217$	−3.40426e8	−0.0104221
$218$	1.09571e9	0.0328580
$219$	1.16918e10	0.343466
$220$	8.31416e9	0.239285
$221$	0	0
$222$	1.35746e10	0.375093
$223$	−3.15215e10	−0.853561	−0.426780	−	0.904355i	$-0.640352\pi$
$223$	−3.15215e10	−0.853561	−0.426780	+	0.904355i	$0.640352\pi$
$224$	−1.38601e8	−0.00367833
$225$	2.18367e9	0.0568024
$226$	−4.30861e10	−1.09862
$227$	5.59976e10	1.39976	0.699880	−	0.714261i	$-0.253237\pi$
$227$	5.59976e10	1.39976	0.699880	+	0.714261i	$0.253237\pi$
$228$	1.89567e10	0.464574
$229$	5.70932e10	1.37191	0.685953	−	0.727646i	$-0.259385\pi$
$229$	5.70932e10	1.37191	0.685953	+	0.727646i	$0.259385\pi$
$230$	−2.08386e10	−0.491012
$231$	−2.50162e8	−0.00578053
$232$	−1.24755e10	−0.282724
$233$	−6.90380e10	−1.53457	−0.767285	−	0.641306i	$-0.778393\pi$
$233$	−6.90380e10	−1.53457	−0.767285	+	0.641306i	$0.778393\pi$
$234$	0	0
$235$	3.61372e10	0.772947
$236$	8.93631e9	0.187523
$237$	−4.81137e9	−0.0990607
$238$	9.03419e8	0.0182513
$239$	1.10735e10	0.219530	0.109765	−	0.993958i	$-0.464990\pi$
$239$	1.10735e10	0.219530	0.109765	+	0.993958i	$0.464990\pi$
$240$	6.84572e9	0.133189
$241$	−2.50128e10	−0.477624	−0.238812	−	0.971066i	$-0.576758\pi$
$241$	−2.50128e10	−0.477624	−0.238812	+	0.971066i	$0.576758\pi$
$242$	−2.83123e10	−0.530647
$243$	−5.61793e10	−1.03359
$244$	−4.05322e10	−0.732058
$245$	5.40039e10	0.957586
$246$	−1.50613e10	−0.262213
$247$	0	0
$248$	1.05491e10	0.177086
$249$	3.76585e10	0.620820
$250$	4.52796e10	0.733115
$251$	1.07464e10	0.170896	0.0854478	−	0.996343i	$-0.472768\pi$
$251$	1.07464e10	0.170896	0.0854478	+	0.996343i	$0.472768\pi$
$252$	4.60057e8	0.00718636
$253$	−2.35974e10	−0.362094
$254$	−7.67422e10	−1.15686
$255$	−4.46213e10	−0.660863
$256$	4.29497e9	0.0625000
$257$	−1.31427e11	−1.87925	−0.939626	−	0.342202i	$-0.888827\pi$
$257$	−1.31427e11	−1.87925	−0.939626	+	0.342202i	$0.888827\pi$
$258$	2.66986e10	0.375145
$259$	1.43736e9	0.0198480
$260$	0	0
$261$	4.14100e10	0.552360
$262$	−3.60782e9	−0.0473030
$263$	1.15856e9	0.0149320	0.00746600	−	0.999972i	$-0.497623\pi$
$263$	1.15856e9	0.0149320	0.00746600	+	0.999972i	$0.497623\pi$
$264$	7.75203e9	0.0982195
$265$	−4.99761e10	−0.622523
$266$	2.00724e9	0.0245829
$267$	1.49268e10	0.179749
$268$	1.73160e10	0.205042
$269$	−3.20648e10	−0.373373	−0.186687	−	0.982420i	$-0.559775\pi$
$269$	−3.20648e10	−0.373373	−0.186687	+	0.982420i	$0.559775\pi$
$270$	−5.56195e10	−0.636928
$271$	1.63517e11	1.84162	0.920812	−	0.390007i	$-0.127527\pi$
$271$	1.63517e11	1.84162	0.920812	+	0.390007i	$0.127527\pi$
$272$	−2.79952e10	−0.310115
$273$	0	0
$274$	9.41071e10	1.00866
$275$	3.89610e9	0.0410802
$276$	−1.94296e10	−0.201546
$277$	1.28133e11	1.30768	0.653839	−	0.756634i	$-0.273157\pi$
$277$	1.28133e11	1.30768	0.653839	+	0.756634i	$0.273157\pi$
$278$	7.97710e10	0.801021
$279$	−3.50156e10	−0.345973
$280$	7.24865e8	0.00704768
$281$	−6.67853e10	−0.639003	−0.319501	−	0.947586i	$-0.603515\pi$
$281$	−6.67853e10	−0.639003	−0.319501	+	0.947586i	$0.603515\pi$
$282$	3.36940e10	0.317272
$283$	−1.58033e11	−1.46457	−0.732285	−	0.680998i	$-0.761546\pi$
$283$	−1.58033e11	−1.46457	−0.732285	+	0.680998i	$0.761546\pi$
$284$	2.93839e10	0.268026
$285$	−9.91409e10	−0.890125
$286$	0	0
$287$	−1.59478e9	−0.0138750
$288$	−1.42562e10	−0.122107
$289$	6.38881e10	0.538741
$290$	6.52455e10	0.541701
$291$	8.35521e9	0.0683028
$292$	−3.83631e10	−0.308810
$293$	2.34407e11	1.85809	0.929043	−	0.369971i	$-0.120632\pi$
$293$	2.34407e11	1.85809	0.929043	+	0.369971i	$0.120632\pi$
$294$	5.03527e10	0.393061
$295$	−4.67358e10	−0.359294
$296$	−4.45409e10	−0.337245
$297$	−6.29830e10	−0.469699
$298$	−6.58313e10	−0.483570
$299$	0	0
$300$	3.20797e9	0.0228657
$301$	2.82700e9	0.0198508
$302$	−6.55692e10	−0.453595
$303$	−1.06982e11	−0.729155
$304$	−6.22005e10	−0.417698
$305$	2.11978e11	1.40263
$306$	9.29241e10	0.605873
$307$	−5.83393e10	−0.374833	−0.187417	−	0.982281i	$-0.560011\pi$
$307$	−5.83393e10	−0.374833	−0.187417	+	0.982281i	$0.560011\pi$
$308$	8.20831e8	0.00519727
$309$	−1.54099e11	−0.961580
$310$	−5.51705e10	−0.339297
$311$	−6.30562e9	−0.0382213	−0.0191107	−	0.999817i	$-0.506083\pi$
$311$	−6.30562e9	−0.0382213	−0.0191107	+	0.999817i	$0.506083\pi$
$312$	0	0
$313$	2.01041e10	0.118396	0.0591978	−	0.998246i	$-0.481146\pi$
$313$	2.01041e10	0.118396	0.0591978	+	0.998246i	$0.481146\pi$
$314$	1.78047e11	1.03360
$315$	−2.40604e9	−0.0137691
$316$	1.57870e10	0.0890654
$317$	−3.31339e9	−0.0184292	−0.00921458	−	0.999958i	$-0.502933\pi$
$317$	−3.31339e9	−0.0184292	−0.00921458	+	0.999958i	$0.502933\pi$
$318$	−4.65971e10	−0.255527
$319$	7.38834e10	0.399474
$320$	−2.24621e10	−0.119750
$321$	−1.75904e11	−0.924704
$322$	−2.05733e9	−0.0106648
$323$	4.05431e11	2.07255
$324$	1.66483e10	0.0839298
$325$	0	0
$326$	2.16490e11	1.06159
$327$	−5.34299e9	−0.0258416
$328$	4.94190e10	0.235755
$329$	3.56772e9	0.0167884
$330$	−4.05421e10	−0.188189
$331$	−1.44793e11	−0.663011	−0.331506	−	0.943453i	$-0.607557\pi$
$331$	−1.44793e11	−0.663011	−0.331506	+	0.943453i	$0.607557\pi$
$332$	−1.23565e11	−0.558178
$333$	1.47844e11	0.658878
$334$	1.21686e11	0.535036
$335$	−9.05607e10	−0.392860
$336$	6.75856e8	0.00289286
$337$	−2.45134e10	−0.103531	−0.0517654	−	0.998659i	$-0.516485\pi$
$337$	−2.45134e10	−0.103531	−0.0517654	+	0.998659i	$0.516485\pi$
$338$	0	0
$339$	2.10100e11	0.864026
$340$	1.46411e11	0.594181
$341$	−6.24746e10	−0.250212
$342$	2.06462e11	0.816059
$343$	1.06656e10	0.0416065
$344$	−8.76032e10	−0.337293
$345$	1.01615e11	0.386162
$346$	−7.32527e10	−0.274777
$347$	7.87399e10	0.291549	0.145775	−	0.989318i	$-0.453433\pi$
$347$	7.87399e10	0.291549	0.145775	+	0.989318i	$0.453433\pi$
$348$	6.08342e10	0.222352
$349$	3.63227e11	1.31058	0.655290	−	0.755377i	$-0.272546\pi$
$349$	3.63227e11	1.31058	0.655290	+	0.755377i	$0.272546\pi$
$350$	3.39679e8	0.00120994
$351$	0	0
$352$	−2.54359e10	−0.0883090
$353$	−5.70238e11	−1.95465	−0.977327	−	0.211737i	$-0.932088\pi$
$353$	−5.70238e11	−1.95465	−0.977327	+	0.211737i	$0.932088\pi$
$354$	−4.35759e10	−0.147480
$355$	−1.53674e11	−0.513539
$356$	−4.89778e10	−0.161612
$357$	−4.40532e9	−0.0143539
$358$	4.79921e10	0.154417
$359$	4.97640e11	1.58121	0.790607	−	0.612324i	$-0.209765\pi$
$359$	4.97640e11	1.58121	0.790607	+	0.612324i	$0.209765\pi$
$360$	7.45583e10	0.233956
$361$	5.78111e11	1.79155
$362$	−1.49577e11	−0.457801
$363$	1.38059e11	0.417334
$364$	0	0
$365$	2.00634e11	0.591681
$366$	1.97646e11	0.575736
$367$	−1.98143e11	−0.570141	−0.285070	−	0.958507i	$-0.592017\pi$
$367$	−1.98143e11	−0.570141	−0.285070	+	0.958507i	$0.592017\pi$
$368$	6.37524e10	0.181210
$369$	−1.64036e11	−0.460597
$370$	2.32943e11	0.646163
$371$	−4.93398e9	−0.0135212
$372$	−5.14404e10	−0.139271
$373$	−6.15553e11	−1.64655	−0.823276	−	0.567642i	$-0.807856\pi$
$373$	−6.15553e11	−1.64655	−0.823276	+	0.567642i	$0.807856\pi$
$374$	1.65794e11	0.438175
$375$	−2.20796e11	−0.576567
$376$	−1.10556e11	−0.285259
$377$	0	0
$378$	−5.49114e9	−0.0138340
$379$	7.33929e11	1.82716	0.913582	−	0.406654i	$-0.133305\pi$
$379$	7.33929e11	1.82716	0.913582	+	0.406654i	$0.133305\pi$
$380$	3.25300e11	0.800310
$381$	3.74216e11	0.909830
$382$	−8.14785e10	−0.195775
$383$	4.59205e11	1.09047	0.545233	−	0.838284i	$-0.316441\pi$
$383$	4.59205e11	1.09047	0.545233	+	0.838284i	$0.316441\pi$
$384$	−2.09434e10	−0.0491538
$385$	−4.29284e9	−0.00995798
$386$	2.18577e11	0.501142
$387$	2.90781e11	0.658970
$388$	−2.74151e10	−0.0614110
$389$	−3.60025e11	−0.797185	−0.398593	−	0.917128i	$-0.630501\pi$
$389$	−3.60025e11	−0.797185	−0.398593	+	0.917128i	$0.630501\pi$
$390$	0	0
$391$	−4.15546e11	−0.899134
$392$	−1.65217e11	−0.353400
$393$	1.75927e10	0.0372020
$394$	−3.95735e10	−0.0827316
$395$	−8.25642e10	−0.170649
$396$	8.44292e10	0.172530
$397$	8.51526e11	1.72044	0.860222	−	0.509919i	$-0.170325\pi$
$397$	8.51526e11	1.72044	0.860222	+	0.509919i	$0.170325\pi$
$398$	6.96651e11	1.39169
$399$	−9.78787e9	−0.0193335
$400$	−1.05260e10	−0.0205586
$401$	−4.18560e11	−0.808365	−0.404183	−	0.914678i	$-0.632444\pi$
$401$	−4.18560e11	−0.808365	−0.404183	+	0.914678i	$0.632444\pi$
$402$	−8.44378e10	−0.161257
$403$	0	0
$404$	3.51030e11	0.655583
$405$	−8.70682e10	−0.160810
$406$	6.44148e9	0.0117657
$407$	2.63783e11	0.476509
$408$	1.36512e11	0.243894
$409$	−4.98140e11	−0.880231	−0.440116	−	0.897941i	$-0.645063\pi$
$409$	−4.98140e11	−0.880231	−0.440116	+	0.897941i	$0.645063\pi$
$410$	−2.58455e11	−0.451708
$411$	−4.58892e11	−0.793273
$412$	5.05627e11	0.864555
$413$	−4.61408e9	−0.00780386
$414$	−2.11613e11	−0.354030
$415$	6.46227e11	1.06947
$416$	0	0
$417$	−3.88986e11	−0.629972
$418$	3.68367e11	0.590184
$419$	−3.28439e11	−0.520584	−0.260292	−	0.965530i	$-0.583819\pi$
$419$	−3.28439e11	−0.520584	−0.260292	+	0.965530i	$0.583819\pi$
$420$	−3.53464e9	−0.00554273
$421$	−1.25167e11	−0.194187	−0.0970937	−	0.995275i	$-0.530955\pi$
$421$	−1.25167e11	−0.194187	−0.0970937	+	0.995275i	$0.530955\pi$
$422$	−3.64757e11	−0.559884
$423$	3.66969e11	0.557311
$424$	1.52894e11	0.229744
$425$	6.86097e10	0.102008
$426$	−1.43284e11	−0.210792
$427$	2.09279e10	0.0304650
$428$	5.77174e11	0.831400
$429$	0	0
$430$	4.58153e11	0.646253
$431$	−6.77654e11	−0.945933	−0.472966	−	0.881080i	$-0.656817\pi$
$431$	−6.77654e11	−0.945933	−0.472966	+	0.881080i	$0.656817\pi$
$432$	1.70159e11	0.235060
$433$	−7.49888e11	−1.02518	−0.512591	−	0.858633i	$-0.671314\pi$
$433$	−7.49888e11	−1.02518	−0.512591	+	0.858633i	$0.671314\pi$
$434$	−5.44681e9	−0.00736951
$435$	−3.18155e11	−0.426027
$436$	1.75314e10	0.0232341
$437$	−9.23274e11	−1.21106
$438$	1.87069e11	0.242867
$439$	7.09009e11	0.911091	0.455545	−	0.890213i	$-0.349444\pi$
$439$	7.09009e11	0.911091	0.455545	+	0.890213i	$0.349444\pi$
$440$	1.33026e11	0.169200
$441$	5.48403e11	0.690440
$442$	0	0
$443$	−1.27698e12	−1.57532	−0.787659	−	0.616112i	$-0.788707\pi$
$443$	−1.27698e12	−1.57532	−0.787659	+	0.616112i	$0.788707\pi$
$444$	2.17194e11	0.265231
$445$	2.56148e11	0.309649
$446$	−5.04343e11	−0.603559
$447$	3.21011e11	0.380309
$448$	−2.21762e9	−0.00260097
$449$	−1.35014e12	−1.56773	−0.783865	−	0.620931i	$-0.786755\pi$
$449$	−1.35014e12	−1.56773	−0.783865	+	0.620931i	$0.786755\pi$
$450$	3.49388e10	0.0401654
$451$	−2.92672e11	−0.333109
$452$	−6.89377e11	−0.776844
$453$	3.19733e11	0.356735
$454$	8.95962e11	0.989779
$455$	0	0
$456$	3.03307e11	0.328504
$457$	−5.05907e11	−0.542560	−0.271280	−	0.962500i	$-0.587447\pi$
$457$	−5.05907e11	−0.542560	−0.271280	+	0.962500i	$0.587447\pi$
$458$	9.13491e11	0.970085
$459$	−1.10912e12	−1.16633
$460$	−3.33417e11	−0.347198
$461$	−1.58511e12	−1.63458	−0.817289	−	0.576228i	$-0.804524\pi$
$461$	−1.58511e12	−1.63458	−0.817289	+	0.576228i	$0.804524\pi$
$462$	−4.00260e9	−0.00408745
$463$	−6.78962e11	−0.686643	−0.343321	−	0.939218i	$-0.611552\pi$
$463$	−6.78962e11	−0.686643	−0.343321	+	0.939218i	$0.611552\pi$
$464$	−1.99609e11	−0.199916
$465$	2.69027e11	0.266844
$466$	−1.10461e12	−1.08510
$467$	−1.16699e12	−1.13538	−0.567689	−	0.823243i	$-0.692162\pi$
$467$	−1.16699e12	−1.13538	−0.567689	+	0.823243i	$0.692162\pi$
$468$	0	0
$469$	−8.94077e9	−0.00853291
$470$	5.78196e11	0.546556
$471$	−8.68205e11	−0.812884
$472$	1.42981e11	0.132599
$473$	5.18809e11	0.476576
$474$	−7.69819e10	−0.0700465
$475$	1.52439e11	0.137396
$476$	1.44547e10	0.0129056
$477$	−5.07501e11	−0.448853
$478$	1.77176e11	0.155231
$479$	−9.58400e11	−0.831835	−0.415917	−	0.909402i	$-0.636539\pi$
$479$	−9.58400e11	−0.831835	−0.415917	+	0.909402i	$0.636539\pi$
$480$	1.09531e11	0.0941789
$481$	0	0
$482$	−4.00205e11	−0.337731
$483$	1.00321e10	0.00838743
$484$	−4.52997e11	−0.375224
$485$	1.43377e11	0.117664
$486$	−8.98869e11	−0.730858
$487$	2.16464e12	1.74384	0.871919	−	0.489650i	$-0.162875\pi$
$487$	2.16464e12	1.74384	0.871919	+	0.489650i	$0.162875\pi$
$488$	−6.48515e11	−0.517643
$489$	−1.05567e12	−0.834904
$490$	8.64063e11	0.677116
$491$	−3.11272e11	−0.241698	−0.120849	−	0.992671i	$-0.538562\pi$
$491$	−3.11272e11	−0.241698	−0.120849	+	0.992671i	$0.538562\pi$
$492$	−2.40981e11	−0.185413
$493$	1.30107e12	0.991953
$494$	0	0
$495$	−4.41554e11	−0.330567
$496$	1.68786e11	0.125219
$497$	−1.51718e10	−0.0111540
$498$	6.02535e11	0.438986
$499$	1.41915e12	1.02465	0.512325	−	0.858792i	$-0.328784\pi$
$499$	1.41915e12	1.02465	0.512325	+	0.858792i	$0.328784\pi$
$500$	7.24473e11	0.518391
$501$	−5.93377e11	−0.420785
$502$	1.71942e11	0.120841
$503$	5.24058e11	0.365026	0.182513	−	0.983203i	$-0.441577\pi$
$503$	5.24058e11	0.365026	0.182513	+	0.983203i	$0.441577\pi$
$504$	7.36091e9	0.00508153
$505$	−1.83584e12	−1.25610
$506$	−3.77558e11	−0.256039
$507$	0	0
$508$	−1.22788e12	−0.818027
$509$	−2.02882e12	−1.33972	−0.669859	−	0.742488i	$-0.733646\pi$
$509$	−2.02882e12	−1.33972	−0.669859	+	0.742488i	$0.733646\pi$
$510$	−7.13940e11	−0.467300
$511$	1.98080e10	0.0128513
$512$	6.87195e10	0.0441942
$513$	−2.46428e12	−1.57095
$514$	−2.10283e12	−1.32883
$515$	−2.64436e12	−1.65649
$516$	4.27177e11	0.265268
$517$	6.54744e11	0.403055
$518$	2.29977e10	0.0140346
$519$	3.57200e11	0.216102
$520$	0	0
$521$	−2.41913e12	−1.43843	−0.719216	−	0.694787i	$-0.755499\pi$
$521$	−2.41913e12	−1.43843	−0.719216	+	0.694787i	$0.755499\pi$
$522$	6.62559e11	0.390578
$523$	1.87796e11	0.109756	0.0548782	−	0.998493i	$-0.482523\pi$
$523$	1.87796e11	0.109756	0.0548782	+	0.998493i	$0.482523\pi$
$524$	−5.77251e10	−0.0334483
$525$	−1.65637e9	−0.000951569 0
$526$	1.85370e10	0.0105585
$527$	−1.10017e12	−0.621314
$528$	1.24032e11	0.0694517
$529$	−8.54843e11	−0.474609
$530$	−7.99617e11	−0.440191
$531$	−4.74596e11	−0.259059
$532$	3.21159e10	0.0173827
$533$	0	0
$534$	2.38829e11	0.127102
$535$	−3.01855e12	−1.59296
$536$	2.77057e11	0.144986
$537$	−2.34023e11	−0.121443
$538$	−5.13037e11	−0.264015
$539$	9.78456e11	0.499335
$540$	−8.89912e11	−0.450376
$541$	2.23118e12	1.11982	0.559908	−	0.828554i	$-0.310836\pi$
$541$	2.23118e12	1.11982	0.559908	+	0.828554i	$0.310836\pi$
$542$	2.61627e12	1.30222
$543$	7.29380e11	0.360043
$544$	−4.47922e11	−0.219284
$545$	−9.16868e10	−0.0445167
$546$	0	0
$547$	−3.74325e12	−1.78775	−0.893874	−	0.448318i	$-0.852023\pi$
$547$	−3.74325e12	−1.78775	−0.893874	+	0.448318i	$0.852023\pi$
$548$	1.50571e12	0.713230
$549$	2.15261e12	1.01132
$550$	6.23376e10	0.0290481
$551$	2.89077e12	1.33608
$552$	−3.10874e11	−0.142514
$553$	−8.15130e9	−0.00370650
$554$	2.05012e12	0.924668
$555$	−1.13589e12	−0.508182
$556$	1.27634e12	0.566407
$557$	6.79800e10	0.0299249	0.0149625	−	0.999888i	$-0.495237\pi$
$557$	6.79800e10	0.0299249	0.0149625	+	0.999888i	$0.495237\pi$
$558$	−5.60250e11	−0.244640
$559$	0	0
$560$	1.15978e10	0.00498346
$561$	−8.08460e11	−0.344608
$562$	−1.06857e12	−0.451843
$563$	−4.39345e12	−1.84297	−0.921485	−	0.388415i	$-0.873023\pi$
$563$	−4.39345e12	−1.84297	−0.921485	+	0.388415i	$0.873023\pi$
$564$	5.39104e11	0.224345
$565$	3.60535e12	1.48844
$566$	−2.52854e12	−1.03561
$567$	−8.59597e9	−0.00349278
$568$	4.70143e11	0.189523
$569$	4.19303e12	1.67696	0.838480	−	0.544932i	$-0.183444\pi$
$569$	4.19303e12	1.67696	0.838480	+	0.544932i	$0.183444\pi$
$570$	−1.58625e12	−0.629413
$571$	9.45651e10	0.0372279	0.0186139	−	0.999827i	$-0.494075\pi$
$571$	9.45651e10	0.0372279	0.0186139	+	0.999827i	$0.494075\pi$
$572$	0	0
$573$	3.97312e11	0.153970
$574$	−2.55165e10	−0.00981108
$575$	−1.56243e11	−0.0596066
$576$	−2.28100e11	−0.0863424
$577$	1.78911e12	0.671963	0.335981	−	0.941869i	$-0.390932\pi$
$577$	1.78911e12	0.671963	0.335981	+	0.941869i	$0.390932\pi$
$578$	1.02221e12	0.380947
$579$	−1.06584e12	−0.394129
$580$	1.04393e12	0.383040
$581$	6.38000e10	0.0232289
$582$	1.33683e11	0.0482974
$583$	−9.05479e11	−0.324616
$584$	−6.13810e11	−0.218362
$585$	0	0
$586$	3.75051e12	1.31387
$587$	−2.73299e12	−0.950096	−0.475048	−	0.879960i	$-0.657569\pi$
$587$	−2.73299e12	−0.950096	−0.475048	+	0.879960i	$0.657569\pi$
$588$	8.05643e11	0.277936
$589$	−2.44439e12	−0.836857
$590$	−7.47772e11	−0.254059
$591$	1.92971e11	0.0650652
$592$	−7.12654e11	−0.238469
$593$	5.86251e11	0.194687	0.0973436	−	0.995251i	$-0.468965\pi$
$593$	5.86251e11	0.194687	0.0973436	+	0.995251i	$0.468965\pi$
$594$	−1.00773e12	−0.332127
$595$	−7.55962e10	−0.0247271
$596$	−1.05330e12	−0.341935
$597$	−3.39706e12	−1.09451
$598$	0	0
$599$	−3.70853e12	−1.17701	−0.588506	−	0.808493i	$-0.700284\pi$
$599$	−3.70853e12	−1.17701	−0.588506	+	0.808493i	$0.700284\pi$
$600$	5.13276e10	0.0161685
$601$	−1.30269e12	−0.407293	−0.203646	−	0.979044i	$-0.565279\pi$
$601$	−1.30269e12	−0.407293	−0.203646	+	0.979044i	$0.565279\pi$
$602$	4.52321e10	0.0140366
$603$	−9.19632e11	−0.283261
$604$	−1.04911e12	−0.320740
$605$	2.36911e12	0.718930
$606$	−1.71172e12	−0.515591
$607$	4.23450e12	1.26606	0.633029	−	0.774128i	$-0.281812\pi$
$607$	4.23450e12	1.26606	0.633029	+	0.774128i	$0.281812\pi$
$608$	−9.95208e11	−0.295357
$609$	−3.14104e10	−0.00925329
$610$	3.39165e12	0.991806
$611$	0	0
$612$	1.48679e12	0.428417
$613$	−5.74314e8	−0.000164277 0	−8.21386e−5	−	1.00000i	$-0.500026\pi$
$613$	−5.74314e8	−0.000164277 0	−8.21386e−5		1.00000i	$0.500026\pi$
$614$	−9.33428e11	−0.265047
$615$	1.26030e12	0.355251
$616$	1.31333e10	0.00367503
$617$	−6.51466e11	−0.180971	−0.0904854	−	0.995898i	$-0.528842\pi$
$617$	−6.51466e11	−0.180971	−0.0904854	+	0.995898i	$0.528842\pi$
$618$	−2.46558e12	−0.679940
$619$	−2.12694e12	−0.582301	−0.291150	−	0.956677i	$-0.594038\pi$
$619$	−2.12694e12	−0.582301	−0.291150	+	0.956677i	$0.594038\pi$
$620$	−8.82728e11	−0.239919
$621$	2.52576e12	0.681523
$622$	−1.00890e11	−0.0270266
$623$	2.52887e10	0.00672558
$624$	0	0
$625$	−3.47520e12	−0.911003
$626$	3.21666e11	0.0837183
$627$	−1.79626e12	−0.464157
$628$	2.84875e12	0.730863
$629$	4.64517e12	1.18324
$630$	−3.84966e10	−0.00973621
$631$	2.12362e12	0.533268	0.266634	−	0.963798i	$-0.414089\pi$
$631$	2.12362e12	0.533268	0.266634	+	0.963798i	$0.414089\pi$
$632$	2.52593e11	0.0629787
$633$	1.77866e12	0.440327
$634$	−5.30142e10	−0.0130314
$635$	6.42163e12	1.56734
$636$	−7.45554e11	−0.180685
$637$	0	0
$638$	1.18213e12	0.282471
$639$	−1.56054e12	−0.370272
$640$	−3.59394e11	−0.0846761
$641$	8.88570e11	0.207888	0.103944	−	0.994583i	$-0.466854\pi$
$641$	8.88570e11	0.207888	0.103944	+	0.994583i	$0.466854\pi$
$642$	−2.81446e12	−0.653864
$643$	−5.75199e12	−1.32699	−0.663497	−	0.748179i	$-0.730928\pi$
$643$	−5.75199e12	−1.32699	−0.663497	+	0.748179i	$0.730928\pi$
$644$	−3.29172e10	−0.00754113
$645$	−2.23408e12	−0.508254
$646$	6.48689e12	1.46552
$647$	−4.48594e12	−1.00643	−0.503216	−	0.864161i	$-0.667850\pi$
$647$	−4.48594e12	−1.00643	−0.503216	+	0.864161i	$0.667850\pi$
$648$	2.66372e11	0.0593473
$649$	−8.46770e11	−0.187355
$650$	0	0
$651$	2.65602e10	0.00579584
$652$	3.46384e12	0.750661
$653$	−2.76591e12	−0.595291	−0.297645	−	0.954676i	$-0.596201\pi$
$653$	−2.76591e12	−0.595291	−0.297645	+	0.954676i	$0.596201\pi$
$654$	−8.54878e10	−0.0182728
$655$	3.01895e11	0.0640869
$656$	7.90704e11	0.166704
$657$	2.03742e12	0.426614
$658$	5.70835e10	0.0118712
$659$	−7.37449e12	−1.52317	−0.761584	−	0.648066i	$-0.775578\pi$
$659$	−7.37449e12	−1.52317	−0.761584	+	0.648066i	$0.775578\pi$
$660$	−6.48674e11	−0.133070
$661$	7.09718e11	0.144604	0.0723019	−	0.997383i	$-0.476966\pi$
$661$	7.09718e11	0.144604	0.0723019	+	0.997383i	$0.476966\pi$
$662$	−2.31669e12	−0.468820
$663$	0	0
$664$	−1.97703e12	−0.394692
$665$	−1.67962e11	−0.0333053
$666$	2.36551e12	0.465897
$667$	−2.96289e12	−0.579629
$668$	1.94698e12	0.378328
$669$	2.45932e12	0.474676
$670$	−1.44897e12	−0.277794
$671$	3.84067e12	0.731401
$672$	1.08137e10	0.00204556
$673$	−5.09781e12	−0.957891	−0.478945	−	0.877845i	$-0.658981\pi$
$673$	−5.09781e12	−0.957891	−0.478945	+	0.877845i	$0.658981\pi$
$674$	−3.92215e11	−0.0732073
$675$	−4.17022e11	−0.0773200
$676$	0	0
$677$	9.32854e11	0.170673	0.0853365	−	0.996352i	$-0.472803\pi$
$677$	9.32854e11	0.170673	0.0853365	+	0.996352i	$0.472803\pi$
$678$	3.36159e12	0.610958
$679$	1.41552e10	0.00255565
$680$	2.34258e12	0.420149
$681$	−4.36896e12	−0.778423
$682$	−9.99593e11	−0.176927
$683$	−2.85151e12	−0.501396	−0.250698	−	0.968065i	$-0.580660\pi$
$683$	−2.85151e12	−0.501396	−0.250698	+	0.968065i	$0.580660\pi$
$684$	3.30338e12	0.577041
$685$	−7.87469e12	−1.36655
$686$	1.70649e11	0.0294202
$687$	−4.45443e12	−0.762934
$688$	−1.40165e12	−0.238502
$689$	0	0
$690$	1.62583e12	0.273058
$691$	7.72439e12	1.28888	0.644441	−	0.764654i	$-0.277090\pi$
$691$	7.72439e12	1.28888	0.644441	+	0.764654i	$0.277090\pi$
$692$	−1.17204e12	−0.194297
$693$	−4.35932e10	−0.00717992
$694$	1.25984e12	0.206157
$695$	−6.67508e12	−1.08524
$696$	9.73347e11	0.157227
$697$	−5.15391e12	−0.827160
$698$	5.81163e12	0.926720
$699$	5.38637e12	0.853393
$700$	5.43487e9	0.000855555 0
$701$	9.46243e12	1.48003	0.740017	−	0.672588i	$-0.234817\pi$
$701$	9.46243e12	1.48003	0.740017	+	0.672588i	$0.234817\pi$
$702$	0	0
$703$	1.03208e13	1.59373
$704$	−4.06974e11	−0.0624439
$705$	−2.81944e12	−0.429845
$706$	−9.12380e12	−1.38215
$707$	−1.81247e11	−0.0272824
$708$	−6.97215e11	−0.104284
$709$	1.14047e13	1.69503	0.847515	−	0.530771i	$-0.178098\pi$
$709$	1.14047e13	1.69503	0.847515	+	0.530771i	$0.178098\pi$
$710$	−2.45879e12	−0.363127
$711$	−8.38429e11	−0.123042
$712$	−7.83645e11	−0.114277
$713$	2.50538e12	0.363053
$714$	−7.04851e10	−0.0101498
$715$	0	0
$716$	7.67874e11	0.109190
$717$	−8.63959e11	−0.122083
$718$	7.96225e12	1.11809
$719$	4.49589e12	0.627387	0.313694	−	0.949524i	$-0.398434\pi$
$719$	4.49589e12	0.627387	0.313694	+	0.949524i	$0.398434\pi$
$720$	1.19293e12	0.165432
$721$	−2.61070e11	−0.0359789
$722$	9.24977e12	1.26682
$723$	1.95151e12	0.265612
$724$	−2.39324e12	−0.323714
$725$	4.89195e11	0.0657599
$726$	2.20894e12	0.295099
$727$	−4.49807e11	−0.0597203	−0.0298601	−	0.999554i	$-0.509506\pi$
$727$	−4.49807e11	−0.0597203	−0.0298601	+	0.999554i	$0.509506\pi$
$728$	0	0
$729$	3.10310e12	0.406932
$730$	3.21015e12	0.418381
$731$	9.13614e12	1.18341
$732$	3.16234e12	0.407107
$733$	−1.37779e13	−1.76285	−0.881424	−	0.472326i	$-0.843415\pi$
$733$	−1.37779e13	−1.76285	−0.881424	+	0.472326i	$0.843415\pi$
$734$	−3.17029e12	−0.403150
$735$	−4.21341e12	−0.532525
$736$	1.02004e12	0.128135
$737$	−1.64080e12	−0.204858
$738$	−2.62458e12	−0.325691
$739$	1.38664e13	1.71027	0.855135	−	0.518406i	$-0.173474\pi$
$739$	1.38664e13	1.71027	0.855135	+	0.518406i	$0.173474\pi$
$740$	3.72709e12	0.456906
$741$	0	0
$742$	−7.89437e10	−0.00956093
$743$	−1.05429e13	−1.26914	−0.634571	−	0.772865i	$-0.718823\pi$
$743$	−1.05429e13	−1.26914	−0.634571	+	0.772865i	$0.718823\pi$
$744$	−8.23046e11	−0.0984796
$745$	5.50863e12	0.655149
$746$	−9.84884e12	−1.16429
$747$	6.56235e12	0.771111
$748$	2.65271e12	0.309837
$749$	−2.98012e11	−0.0345991
$750$	−3.53273e12	−0.407694
$751$	−7.51483e12	−0.862063	−0.431032	−	0.902337i	$-0.641850\pi$
$751$	−7.51483e12	−0.862063	−0.431032	+	0.902337i	$0.641850\pi$
$752$	−1.76890e12	−0.201708
$753$	−8.38438e11	−0.0950372
$754$	0	0
$755$	5.48669e12	0.614539
$756$	−8.78582e10	−0.00978215
$757$	1.20035e12	0.132855	0.0664274	−	0.997791i	$-0.478840\pi$
$757$	1.20035e12	0.132855	0.0664274	+	0.997791i	$0.478840\pi$
$758$	1.17429e13	1.29200
$759$	1.84108e12	0.201365
$760$	5.20481e12	0.565905
$761$	1.10016e13	1.18912	0.594561	−	0.804050i	$-0.297326\pi$
$761$	1.10016e13	1.18912	0.594561	+	0.804050i	$0.297326\pi$
$762$	5.98746e12	0.643347
$763$	−9.05195e9	−0.000966900 0
$764$	−1.30366e12	−0.138434
$765$	−7.77569e12	−0.820848
$766$	7.34728e12	0.771076
$767$	0	0
$768$	−3.35095e11	−0.0347570
$769$	6.04153e12	0.622986	0.311493	−	0.950248i	$-0.399171\pi$
$769$	6.04153e12	0.622986	0.311493	+	0.950248i	$0.399171\pi$
$770$	−6.86854e10	−0.00704135
$771$	1.02540e13	1.04508
$772$	3.49723e12	0.354361
$773$	4.13748e12	0.416801	0.208400	−	0.978044i	$-0.433174\pi$
$773$	4.13748e12	0.416801	0.208400	+	0.978044i	$0.433174\pi$
$774$	4.65249e12	0.465963
$775$	−4.13656e11	−0.0411890
$776$	−4.38641e11	−0.0434241
$777$	−1.12143e11	−0.0110377
$778$	−5.76040e12	−0.563695
$779$	−1.14511e13	−1.11411
$780$	0	0
$781$	−2.78431e12	−0.267786
$782$	−6.64874e12	−0.635783
$783$	−7.90816e12	−0.751878
$784$	−2.64347e12	−0.249892
$785$	−1.48986e13	−1.40033
$786$	2.81483e11	0.0263058
$787$	4.97253e11	0.0462052	0.0231026	−	0.999733i	$-0.492646\pi$
$787$	4.97253e11	0.0462052	0.0231026	+	0.999733i	$0.492646\pi$
$788$	−6.33176e11	−0.0585001
$789$	−9.03914e10	−0.00830387
$790$	−1.32103e12	−0.120667
$791$	3.55945e11	0.0323288
$792$	1.35087e12	0.121997
$793$	0	0
$794$	1.36244e13	1.21654
$795$	3.89915e12	0.346193
$796$	1.11464e13	0.984071
$797$	2.56117e12	0.224841	0.112421	−	0.993661i	$-0.464140\pi$
$797$	2.56117e12	0.224841	0.112421	+	0.993661i	$0.464140\pi$
$798$	−1.56606e11	−0.0136708
$799$	1.15299e13	1.00084
$800$	−1.68416e11	−0.0145371
$801$	2.60115e12	0.223264
$802$	−6.69695e12	−0.571601
$803$	3.63514e12	0.308533
$804$	−1.35100e12	−0.114026
$805$	1.72153e11	0.0144488
$806$	0	0
$807$	2.50171e12	0.207637
$808$	5.61647e12	0.463567
$809$	−5.40754e11	−0.0443845	−0.0221923	−	0.999754i	$-0.507065\pi$
$809$	−5.40754e11	−0.0443845	−0.0221923	+	0.999754i	$0.507065\pi$
$810$	−1.39309e12	−0.113710
$811$	−1.95940e12	−0.159048	−0.0795242	−	0.996833i	$-0.525340\pi$
$811$	−1.95940e12	−0.159048	−0.0795242	+	0.996833i	$0.525340\pi$
$812$	1.03064e11	0.00831962
$813$	−1.27577e13	−1.02415
$814$	4.22052e12	0.336943
$815$	−1.81154e13	−1.43827
$816$	2.18419e12	0.172459
$817$	2.02990e13	1.59395
$818$	−7.97025e12	−0.622418
$819$	0	0
$820$	−4.13528e12	−0.319406
$821$	2.09751e13	1.61124	0.805620	−	0.592432i	$-0.201832\pi$
$821$	2.09751e13	1.61124	0.805620	+	0.592432i	$0.201832\pi$
$822$	−7.34227e12	−0.560928
$823$	7.56818e12	0.575032	0.287516	−	0.957776i	$-0.407171\pi$
$823$	7.56818e12	0.575032	0.287516	+	0.957776i	$0.407171\pi$
$824$	8.09003e12	0.611333
$825$	−3.03975e11	−0.0228452
$826$	−7.38252e10	−0.00551816
$827$	3.34596e12	0.248740	0.124370	−	0.992236i	$-0.460309\pi$
$827$	3.34596e12	0.248740	0.124370	+	0.992236i	$0.460309\pi$
$828$	−3.38581e12	−0.250337
$829$	5.10496e12	0.375403	0.187701	−	0.982226i	$-0.439896\pi$
$829$	5.10496e12	0.375403	0.187701	+	0.982226i	$0.439896\pi$
$830$	1.03396e13	0.756230
$831$	−9.99696e12	−0.727216
$832$	0	0
$833$	1.72305e13	1.23992
$834$	−6.22377e12	−0.445457
$835$	−1.01825e13	−0.724877
$836$	5.89388e12	0.417323
$837$	6.68701e12	0.470942
$838$	−5.25502e12	−0.368109
$839$	1.96315e13	1.36781	0.683903	−	0.729573i	$-0.260281\pi$
$839$	1.96315e13	1.36781	0.683903	+	0.729573i	$0.260281\pi$
$840$	−5.65543e10	−0.00391930
$841$	−5.23033e12	−0.360535
$842$	−2.00268e12	−0.137311
$843$	5.21062e12	0.355357
$844$	−5.83611e12	−0.395898
$845$	0	0
$846$	5.87150e12	0.394078
$847$	2.33895e11	0.0156151
$848$	2.44631e12	0.162454
$849$	1.23298e13	0.814465
$850$	1.09776e12	0.0721307
$851$	−1.05783e13	−0.691405
$852$	−2.29255e12	−0.149053
$853$	1.41852e13	0.917411	0.458706	−	0.888588i	$-0.348313\pi$
$853$	1.41852e13	0.917411	0.458706	+	0.888588i	$0.348313\pi$
$854$	3.34847e11	0.0215420
$855$	−1.72763e13	−1.10561
$856$	9.23479e12	0.587889
$857$	3.06579e13	1.94146	0.970732	−	0.240167i	$-0.0772021\pi$
$857$	3.06579e13	1.94146	0.970732	+	0.240167i	$0.0772021\pi$
$858$	0	0
$859$	1.13754e13	0.712848	0.356424	−	0.934324i	$-0.383996\pi$
$859$	1.13754e13	0.712848	0.356424	+	0.934324i	$0.383996\pi$
$860$	7.33045e12	0.456970
$861$	1.24425e11	0.00771604
$862$	−1.08425e13	−0.668875
$863$	1.07114e13	0.657349	0.328675	−	0.944443i	$-0.393398\pi$
$863$	1.07114e13	0.657349	0.328675	+	0.944443i	$0.393398\pi$
$864$	2.72255e12	0.166213
$865$	6.12963e12	0.372273
$866$	−1.19982e13	−0.724913
$867$	−4.98458e12	−0.299600
$868$	−8.71490e10	−0.00521103
$869$	−1.49592e12	−0.0889854
$870$	−5.09048e12	−0.301246
$871$	0	0
$872$	2.80502e11	0.0164290
$873$	1.45598e12	0.0848380
$874$	−1.47724e13	−0.856345
$875$	−3.74066e11	−0.0215731
$876$	2.99311e12	0.171733
$877$	−3.70350e12	−0.211405	−0.105702	−	0.994398i	$-0.533709\pi$
$877$	−3.70350e12	−0.211405	−0.105702	+	0.994398i	$0.533709\pi$
$878$	1.13441e13	0.644238
$879$	−1.82885e13	−1.03330
$880$	2.12842e12	0.119643
$881$	−1.78613e13	−0.998897	−0.499449	−	0.866344i	$-0.666464\pi$
$881$	−1.78613e13	−0.998897	−0.499449	+	0.866344i	$0.666464\pi$
$882$	8.77444e12	0.488215
$883$	−1.97547e13	−1.09357	−0.546785	−	0.837273i	$-0.684149\pi$
$883$	−1.97547e13	−1.09357	−0.546785	+	0.837273i	$0.684149\pi$
$884$	0	0
$885$	3.64634e12	0.199808
$886$	−2.04317e13	−1.11392
$887$	1.68967e13	0.916527	0.458263	−	0.888816i	$-0.348472\pi$
$887$	1.68967e13	0.916527	0.458263	+	0.888816i	$0.348472\pi$
$888$	3.47510e12	0.187546
$889$	6.33988e11	0.0340426
$890$	4.09836e12	0.218955
$891$	−1.57752e12	−0.0838545
$892$	−8.06950e12	−0.426780
$893$	2.56176e13	1.34805
$894$	5.13618e12	0.268919
$895$	−4.01588e12	−0.209207
$896$	−3.54818e10	−0.00183916
$897$	0	0
$898$	−2.16023e13	−1.10855
$899$	−7.84433e12	−0.400532
$900$	5.59021e11	0.0284012
$901$	−1.59454e13	−0.806070
$902$	−4.68275e12	−0.235544
$903$	−2.20564e11	−0.0110393
$904$	−1.10300e13	−0.549312
$905$	1.25163e13	0.620237
$906$	5.11573e12	0.252250
$907$	−2.64871e13	−1.29958	−0.649788	−	0.760115i	$-0.725142\pi$
$907$	−2.64871e13	−1.29958	−0.649788	+	0.760115i	$0.725142\pi$
$908$	1.43354e13	0.699880
$909$	−1.86427e13	−0.905673
$910$	0	0
$911$	8.31999e12	0.400212	0.200106	−	0.979774i	$-0.435871\pi$
$911$	8.31999e12	0.400212	0.200106	+	0.979774i	$0.435871\pi$
$912$	4.85291e12	0.232287
$913$	1.17085e13	0.557677
$914$	−8.09452e12	−0.383648
$915$	−1.65386e13	−0.780017
$916$	1.46159e13	0.685953
$917$	2.98051e10	0.00139197
$918$	−1.77459e13	−0.824721
$919$	3.21794e13	1.48819	0.744095	−	0.668074i	$-0.232881\pi$
$919$	3.21794e13	1.48819	0.744095	+	0.668074i	$0.232881\pi$
$920$	−5.33467e12	−0.245506
$921$	4.55165e12	0.208449
$922$	−2.53618e13	−1.15582
$923$	0	0
$924$	−6.40415e10	−0.00289027
$925$	1.74655e12	0.0784411
$926$	−1.08634e13	−0.485530
$927$	−2.68532e13	−1.19436
$928$	−3.19374e12	−0.141362
$929$	7.79638e12	0.343417	0.171709	−	0.985148i	$-0.445071\pi$
$929$	7.79638e12	0.343417	0.171709	+	0.985148i	$0.445071\pi$
$930$	4.30443e12	0.188687
$931$	3.82832e13	1.67007
$932$	−1.76737e13	−0.767285
$933$	4.91967e11	0.0212553
$934$	−1.86718e13	−0.802833
$935$	−1.38733e13	−0.593648
$936$	0	0
$937$	1.98759e13	0.842361	0.421181	−	0.906977i	$-0.361616\pi$
$937$	1.98759e13	0.842361	0.421181	+	0.906977i	$0.361616\pi$
$938$	−1.43052e11	−0.00603368
$939$	−1.56853e12	−0.0658412
$940$	9.25113e12	0.386473
$941$	3.05247e13	1.26910	0.634552	−	0.772880i	$-0.281184\pi$
$941$	3.05247e13	1.26910	0.634552	+	0.772880i	$0.281184\pi$
$942$	−1.38913e13	−0.574796
$943$	1.17368e13	0.483335
$944$	2.28770e12	0.0937615
$945$	4.59487e11	0.0187426
$946$	8.30094e12	0.336990
$947$	1.20948e13	0.488677	0.244339	−	0.969690i	$-0.421429\pi$
$947$	1.20948e13	0.488677	0.244339	+	0.969690i	$0.421429\pi$
$948$	−1.23171e12	−0.0495303
$949$	0	0
$950$	2.43903e12	0.0971539
$951$	2.58512e11	0.0102487
$952$	2.31275e11	0.00912563
$953$	−2.96674e12	−0.116510	−0.0582548	−	0.998302i	$-0.518554\pi$
$953$	−2.96674e12	−0.116510	−0.0582548	+	0.998302i	$0.518554\pi$
$954$	−8.12001e12	−0.317387
$955$	6.81796e12	0.265240
$956$	2.83481e12	0.109765
$957$	−5.76441e12	−0.222152
$958$	−1.53344e13	−0.588196
$959$	−7.77443e11	−0.0296814
$960$	1.75250e12	0.0665945
$961$	−1.98066e13	−0.749125
$962$	0	0
$963$	−3.06530e13	−1.14856
$964$	−6.40328e12	−0.238812
$965$	−1.82901e13	−0.678957
$966$	1.60513e11	0.00593081
$967$	2.38826e13	0.878341	0.439170	−	0.898404i	$-0.355272\pi$
$967$	2.38826e13	0.878341	0.439170	+	0.898404i	$0.355272\pi$
$968$	−7.24795e12	−0.265324
$969$	−3.16319e13	−1.15257
$970$	2.29403e12	0.0832007
$971$	3.98840e13	1.43983	0.719916	−	0.694061i	$-0.244180\pi$
$971$	3.98840e13	1.43983	0.719916	+	0.694061i	$0.244180\pi$
$972$	−1.43819e13	−0.516795
$973$	−6.59009e11	−0.0235713
$974$	3.46343e13	1.23308
$975$	0	0
$976$	−1.03762e13	−0.366029
$977$	2.32835e13	0.817567	0.408783	−	0.912631i	$-0.365953\pi$
$977$	2.32835e13	0.817567	0.408783	+	0.912631i	$0.365953\pi$
$978$	−1.68906e13	−0.590366
$979$	4.64095e12	0.161467
$980$	1.38250e13	0.478793
$981$	−9.31067e11	−0.0320975
$982$	−4.98034e12	−0.170906
$983$	−1.80946e13	−0.618099	−0.309050	−	0.951046i	$-0.600011\pi$
$983$	−1.80946e13	−0.618099	−0.309050	+	0.951046i	$0.600011\pi$
$984$	−3.85569e12	−0.131106
$985$	3.31143e12	0.112086
$986$	2.08172e13	0.701417
$987$	−2.78355e11	−0.00933623
$988$	0	0
$989$	−2.08054e13	−0.691502
$990$	−7.06486e12	−0.233746
$991$	2.89588e13	0.953780	0.476890	−	0.878963i	$-0.341764\pi$
$991$	2.89588e13	0.953780	0.476890	+	0.878963i	$0.341764\pi$
$992$	2.70057e12	0.0885429
$993$	1.12968e13	0.368709
$994$	−2.42748e11	−0.00788710
$995$	−5.82943e13	−1.88548
$996$	9.64056e12	0.310410
$997$	−3.17778e12	−0.101858	−0.0509291	−	0.998702i	$-0.516218\pi$
$997$	−3.17778e12	−0.101858	−0.0509291	+	0.998702i	$0.516218\pi$
$998$	2.27064e13	0.724537
$999$	−2.82342e13	−0.896872

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	338.10.a.l.1.3		6
13.3	even	3		26.10.c.b.9.4	yes	12
13.9	even	3		26.10.c.b.3.4	✓	12
13.12	even	2		338.10.a.k.1.3		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
26.10.c.b.3.4	✓	12	13.9	even	3
26.10.c.b.9.4	yes	12	13.3	even	3
338.10.a.k.1.3		6	13.12	even	2
338.10.a.l.1.3		6	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)

\(f(q)\)	\(=\)	\(q+16.0000 q^{2} -78.0204 q^{3} +256.000 q^{4} -1338.85 q^{5} -1248.33 q^{6} -132.180 q^{7} +4096.00 q^{8} -13595.8 q^{9} -21421.6 q^{10} -24257.6 q^{11} -19973.2 q^{12} -2114.88 q^{14} +104457. q^{15} +65536.0 q^{16} -427172. q^{17} -217533. q^{18} -949104. q^{19} -342745. q^{20} +10312.8 q^{21} -388121. q^{22} +972785. q^{23} -319572. q^{24} -160614. q^{25} +2.59643e6 q^{27} -33838.1 q^{28} -3.04579e6 q^{29} +1.67132e6 q^{30} +2.57547e6 q^{31} +1.04858e6 q^{32} +1.89258e6 q^{33} -6.83475e6 q^{34} +176969. q^{35} -3.48053e6 q^{36} -1.08742e7 q^{37} -1.51857e7 q^{38} -5.48392e6 q^{40} +1.20652e7 q^{41} +165004. q^{42} -2.13875e7 q^{43} -6.20994e6 q^{44} +1.82027e7 q^{45} +1.55646e7 q^{46} -2.69913e7 q^{47} -5.11314e6 q^{48} -4.03361e7 q^{49} -2.56982e6 q^{50} +3.33281e7 q^{51} +3.73277e7 q^{53} +4.15428e7 q^{54} +3.24772e7 q^{55} -541410. q^{56} +7.40495e7 q^{57} -4.87326e7 q^{58} +3.49075e7 q^{59} +2.67411e7 q^{60} -1.58329e8 q^{61} +4.12075e7 q^{62} +1.79710e6 q^{63} +1.67772e7 q^{64} +3.02814e7 q^{66} +6.76408e7 q^{67} -1.09356e8 q^{68} -7.58970e7 q^{69} +2.83150e6 q^{70} +1.14781e8 q^{71} -5.56885e7 q^{72} -1.49856e8 q^{73} -1.73988e8 q^{74} +1.25311e7 q^{75} -2.42971e8 q^{76} +3.20637e6 q^{77} +6.16681e7 q^{79} -8.77427e7 q^{80} +6.50322e7 q^{81} +1.93043e8 q^{82} -4.82674e8 q^{83} +2.64006e6 q^{84} +5.71918e8 q^{85} -3.42200e8 q^{86} +2.37633e8 q^{87} -9.93590e7 q^{88} -1.91320e8 q^{89} +2.91244e8 q^{90} +2.49033e8 q^{92} -2.00939e8 q^{93} -4.31861e8 q^{94} +1.27070e9 q^{95} -8.18103e7 q^{96} -1.07090e8 q^{97} -6.45378e8 q^{98} +3.29801e8 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 96 q^{2} + 81 q^{3} + 1536 q^{4} + 1693 q^{5} + 1296 q^{6} + 473 q^{7} + 24576 q^{8} + 69813 q^{9} + 27088 q^{10} + 14011 q^{11} + 20736 q^{12} + 7568 q^{14} - 294780 q^{15} + 393216 q^{16} - 173558 q^{17}+ \cdots - 881769510 q^{99}+O(q^{100}) \) 6 * q + 96 * q^2 + 81 * q^3 + 1536 * q^4 + 1693 * q^5 + 1296 * q^6 + 473 * q^7 + 24576 * q^8 + 69813 * q^9 + 27088 * q^10 + 14011 * q^11 + 20736 * q^12 + 7568 * q^14 - 294780 * q^15 + 393216 * q^16 - 173558 * q^17 + 1117008 * q^18 + 322367 * q^19 + 433408 * q^20 + 2256885 * q^21 + 224176 * q^22 - 1644771 * q^23 + 331776 * q^24 + 2687569 * q^25 - 922995 * q^27 + 121088 * q^28 + 10801236 * q^29 - 4716480 * q^30 + 10435122 * q^31 + 6291456 * q^32 + 26201763 * q^33 - 2776928 * q^34 + 2168950 * q^35 + 17872128 * q^36 - 15710464 * q^37 + 5157872 * q^38 + 6934528 * q^40 - 1525478 * q^41 + 36110160 * q^42 + 50959661 * q^43 + 3586816 * q^44 + 18619731 * q^45 - 26316336 * q^46 + 68156998 * q^47 + 5308416 * q^48 + 162536361 * q^49 + 43001104 * q^50 - 84678981 * q^51 + 72278209 * q^53 - 14767920 * q^54 - 353372330 * q^55 + 1937408 * q^56 + 17951025 * q^57 + 172819776 * q^58 - 5665291 * q^59 - 75463680 * q^60 - 353387956 * q^61 + 166961952 * q^62 - 224088894 * q^63 + 100663296 * q^64 + 419228208 * q^66 + 371115369 * q^67 - 44430848 * q^68 + 280317279 * q^69 + 34703200 * q^70 + 156688763 * q^71 + 285954048 * q^72 + 466401663 * q^73 - 251367424 * q^74 + 1149481845 * q^75 + 82525952 * q^76 + 312460333 * q^77 + 162543480 * q^79 + 110952448 * q^80 + 295496586 * q^81 - 24407648 * q^82 - 435114576 * q^83 + 577762560 * q^84 + 2307296767 * q^85 + 815354576 * q^86 - 617376057 * q^87 + 57389056 * q^88 + 163315063 * q^89 + 297915696 * q^90 - 421061376 * q^92 + 2056270836 * q^93 + 1090511968 * q^94 - 537110948 * q^95 + 84934656 * q^96 - 1500514705 * q^97 + 2600581776 * q^98 - 881769510 * q^99

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