LMFDB - Embedded newform 10.24.a.b.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [10,24,Mod(1,10)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(10, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0]))

N = Newforms(chi, 24, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("10.1");

S:= CuspForms(chi, 24);

N := Newforms(S);

Level:	$ N $	$=$	$ 10 = 2 \cdot 5 $
Weight:	$ k $	$=$	$ 24 $
Character orbit:	$[\chi]$	$=$	10.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	yes
Analytic conductor:	$33.5204037345$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\sqrt{117349}) $
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x - 29337 $ x^2 - x - 29337
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{5}\cdot 3\cdot 5 $
Twist minimal:	yes
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$171.781$ of defining polynomial
Character	$\chi$	$=$	10.1

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q-2048.00 q^{2} +96597.1 q^{3} +4.19430e6 q^{4} -4.88281e7 q^{5} -1.97831e8 q^{6} +5.12983e9 q^{7} -8.58993e9 q^{8} -8.48122e10 q^{9} +1.00000e11 q^{10} +1.27816e12 q^{11} +4.05157e11 q^{12} +5.85852e11 q^{13} -1.05059e13 q^{14} -4.71665e12 q^{15} +1.75922e13 q^{16} -1.28261e14 q^{17} +1.73695e14 q^{18} -5.25349e14 q^{19} -2.04800e14 q^{20} +4.95527e14 q^{21} -2.61767e15 q^{22} -4.09420e14 q^{23} -8.29763e14 q^{24} +2.38419e15 q^{25} -1.19983e15 q^{26} -1.72866e16 q^{27} +2.15161e16 q^{28} +1.23428e17 q^{29} +9.65971e15 q^{30} +8.43658e16 q^{31} -3.60288e16 q^{32} +1.23466e17 q^{33} +2.62678e17 q^{34} -2.50480e17 q^{35} -3.55728e17 q^{36} +1.73772e18 q^{37} +1.07591e18 q^{38} +5.65916e16 q^{39} +4.19430e17 q^{40} +3.44259e18 q^{41} -1.01484e18 q^{42} -2.12762e18 q^{43} +5.36098e18 q^{44} +4.14122e18 q^{45} +8.38492e17 q^{46} +2.91020e19 q^{47} +1.69935e18 q^{48} -1.05356e18 q^{49} -4.88281e18 q^{50} -1.23896e19 q^{51} +2.45724e18 q^{52} +9.13857e19 q^{53} +3.54029e19 q^{54} -6.24100e19 q^{55} -4.40649e19 q^{56} -5.07471e19 q^{57} -2.52781e20 q^{58} -1.56524e20 q^{59} -1.97831e19 q^{60} -1.87132e20 q^{61} -1.72781e20 q^{62} -4.35072e20 q^{63} +7.37870e19 q^{64} -2.86061e19 q^{65} -2.52859e20 q^{66} +8.07966e19 q^{67} -5.37965e20 q^{68} -3.95488e19 q^{69} +5.12983e20 q^{70} +2.90638e21 q^{71} +7.28531e20 q^{72} +7.57899e20 q^{73} -3.55884e21 q^{74} +2.30305e20 q^{75} -2.20347e21 q^{76} +6.55673e21 q^{77} -1.15900e20 q^{78} +3.63951e21 q^{79} -8.58993e20 q^{80} +6.31466e21 q^{81} -7.05043e21 q^{82} +2.01482e21 q^{83} +2.07839e21 q^{84} +6.26274e21 q^{85} +4.35736e21 q^{86} +1.19228e22 q^{87} -1.09793e22 q^{88} +7.78361e21 q^{89} -8.48122e21 q^{90} +3.00532e21 q^{91} -1.71723e21 q^{92} +8.14949e21 q^{93} -5.96009e22 q^{94} +2.56518e22 q^{95} -3.48028e21 q^{96} +7.35687e22 q^{97} +2.15770e21 q^{98} -1.08403e23 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 4096 q^{2} + 686484 q^{3} + 8388608 q^{4} - 97656250 q^{5} - 1405919232 q^{6} - 3529595108 q^{7} - 17179869184 q^{8} + 169011226674 q^{9} + 200000000000 q^{10} + 936557269824 q^{11} + 2879322587136 q^{12}+ \cdots - 19\!\cdots\!12 q^{99}+O(q^{100}) $ 2 * q - 4096 * q^2 + 686484 * q^3 + 8388608 * q^4 - 97656250 * q^5 - 1405919232 * q^6 - 3529595108 * q^7 - 17179869184 * q^8 + 169011226674 * q^9 + 200000000000 * q^10 + 936557269824 * q^11 + 2879322587136 * q^12 + 9961846393684 * q^13 + 7228610781184 * q^14 - 33519726562500 * q^15 + 35184372088832 * q^16 - 1609709739468 * q^17 - 346134992228352 * q^18 - 256914240498200 * q^19 - 409600000000000 * q^20 - 4612556435458536 * q^21 - 1918069288599552 * q^22 + 3594102326172564 * q^23 - 5896852658454528 * q^24 + 4768371582031250 * q^25 - 20401861414264832 * q^26 + 76906718569871640 * q^27 - 14804194879864832 * q^28 + 195470005256002620 * q^29 + 68648400000000000 * q^30 + 168811393572212104 * q^31 - 72057594037927936 * q^32 - 78039073845355392 * q^33 + 3296685546430464 * q^34 + 172343511132812500 * q^35 + 708884464083664896 * q^36 + 914879862377868532 * q^37 + 526160364540313600 * q^38 + 5587367999460857928 * q^39 + 838860800000000000 * q^40 + 1944225537689591724 * q^41 + 9446515579819081728 * q^42 + 2162030450882223364 * q^43 + 3928205903051882496 * q^44 - 8252501302441406250 * q^45 - 7360721564001411072 * q^46 + 20899427956391479692 * q^47 + 12076754244514873344 * q^48 + 46563376335520673946 * q^49 - 9765625000000000000 * q^50 + 62320269928250619144 * q^51 + 41783012176414375936 * q^52 + 72675644730523142244 * q^53 - 157504959631097118720 * q^54 - 45730335440625000000 * q^55 + 30318991113963175936 * q^56 + 107598748127858096400 * q^57 - 400322570764293365760 * q^58 - 261263082885806125560 * q^59 - 140591923200000000000 * q^60 - 340922118994570959596 * q^61 - 345725734035890388992 * q^62 - 2633037798049393980996 * q^63 + 147573952589676412928 * q^64 - 486418280941601562500 * q^65 + 159824023235287842816 * q^66 + 1719100191085929833452 * q^67 - 6751611999089590272 * q^68 + 2322076789711913279688 * q^69 - 352959510800000000000 * q^70 + 5715571620816449768664 * q^71 - 1451795382443345707008 * q^72 - 1090320686515726670876 * q^73 - 1873673958149874753536 * q^74 + 1636705398559570312500 * q^75 - 1077576426578562252800 * q^76 + 9514791828109879327104 * q^77 - 11442929662895837036544 * q^78 - 5111367769184022959120 * q^79 - 1717986918400000000000 * q^80 + 37982300618876935787082 * q^81 - 3981773901188283850752 * q^82 + 8751494681922030765444 * q^83 - 19346463907469479378944 * q^84 + 78599108372460937500 * q^85 - 4427838363406793449472 * q^86 + 54419346040895445239640 * q^87 - 8044965689450255351808 * q^88 + 24334798769961205033620 * q^89 + 16901122667400000000000 * q^90 - 78185419196088395301736 * q^91 + 15074757763074889875456 * q^92 + 57962850856840838879568 * q^93 - 42802028454689750409216 * q^94 + 12544640649326171875000 * q^95 - 24733192692766460608512 * q^96 + 28745948397303569150212 * q^97 - 95361794735146340241408 * q^98 - 195109350721035124600512 * 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 $

$2$	−2048.00	−0.707107
$2$	−2048.00	−0.707107
$3$	96597.1	0.314825	0.157413	−	0.987533i	$-0.449685\pi$
$3$	96597.1	0.314825	0.157413	+	0.987533i	$0.449685\pi$
$4$	4.19430e6	0.500000
$5$	−4.88281e7	−0.447214
$5$	−4.88281e7	−0.447214
$6$	−1.97831e8	−0.222615
$7$	5.12983e9	0.980564	0.490282	−	0.871564i	$-0.336894\pi$
$7$	5.12983e9	0.980564	0.490282	+	0.871564i	$0.336894\pi$
$8$	−8.58993e9	−0.353553
$9$	−8.48122e10	−0.900885
$10$	1.00000e11	0.316228
$11$	1.27816e12	1.35073	0.675365	−	0.737484i	$-0.263986\pi$
$11$	1.27816e12	1.35073	0.675365	+	0.737484i	$0.263986\pi$
$12$	4.05157e11	0.157413
$13$	5.85852e11	0.0906650	0.0453325	−	0.998972i	$-0.485565\pi$
$13$	5.85852e11	0.0906650	0.0453325	+	0.998972i	$0.485565\pi$
$14$	−1.05059e13	−0.693363
$15$	−4.71665e12	−0.140794
$16$	1.75922e13	0.250000
$17$	−1.28261e14	−0.907678	−0.453839	−	0.891084i	$-0.649946\pi$
$17$	−1.28261e14	−0.907678	−0.453839	+	0.891084i	$0.649946\pi$
$18$	1.73695e14	0.637022
$19$	−5.25349e14	−1.03462	−0.517310	−	0.855798i	$-0.673067\pi$
$19$	−5.25349e14	−1.03462	−0.517310	+	0.855798i	$0.673067\pi$
$20$	−2.04800e14	−0.223607
$21$	4.95527e14	0.308706
$22$	−2.61767e15	−0.955110
$23$	−4.09420e14	−0.0895982	−0.0447991	−	0.998996i	$-0.514265\pi$
$23$	−4.09420e14	−0.0895982	−0.0447991	+	0.998996i	$0.514265\pi$
$24$	−8.29763e14	−0.111308
$25$	2.38419e15	0.200000
$26$	−1.19983e15	−0.0641098
$27$	−1.72866e16	−0.598447
$28$	2.15161e16	0.490282
$29$	1.23428e17	1.87861	0.939306	−	0.343080i	$-0.111470\pi$
$29$	1.23428e17	1.87861	0.939306	+	0.343080i	$0.111470\pi$
$30$	9.65971e15	0.0995565
$31$	8.43658e16	0.596358	0.298179	−	0.954510i	$-0.403621\pi$
$31$	8.43658e16	0.596358	0.298179	+	0.954510i	$0.403621\pi$
$32$	−3.60288e16	−0.176777
$33$	1.23466e17	0.425244
$34$	2.62678e17	0.641825
$35$	−2.50480e17	−0.438521
$36$	−3.55728e17	−0.450443
$37$	1.73772e18	1.60568	0.802840	−	0.596194i	$-0.203321\pi$
$37$	1.73772e18	1.60568	0.802840	+	0.596194i	$0.203321\pi$
$38$	1.07591e18	0.731587
$39$	5.65916e16	0.0285436
$40$	4.19430e17	0.158114
$41$	3.44259e18	0.976948	0.488474	−	0.872579i	$-0.337554\pi$
$41$	3.44259e18	0.976948	0.488474	+	0.872579i	$0.337554\pi$
$42$	−1.01484e18	−0.218288
$43$	−2.12762e18	−0.349146	−0.174573	−	0.984644i	$-0.555854\pi$
$43$	−2.12762e18	−0.349146	−0.174573	+	0.984644i	$0.555854\pi$
$44$	5.36098e18	0.675365
$45$	4.14122e18	0.402888
$46$	8.38492e17	0.0633555
$47$	2.91020e19	1.71711	0.858553	−	0.512725i	$-0.171364\pi$
$47$	2.91020e19	1.71711	0.858553	+	0.512725i	$0.171364\pi$
$48$	1.69935e18	0.0787063
$49$	−1.05356e18	−0.0384952
$50$	−4.88281e18	−0.141421
$51$	−1.23896e19	−0.285760
$52$	2.45724e18	0.0453325
$53$	9.13857e19	1.35427	0.677136	−	0.735858i	$-0.263221\pi$
$53$	9.13857e19	1.35427	0.677136	+	0.735858i	$0.263221\pi$
$54$	3.54029e19	0.423166
$55$	−6.24100e19	−0.604065
$56$	−4.40649e19	−0.346682
$57$	−5.07471e19	−0.325725
$58$	−2.52781e20	−1.32838
$59$	−1.56524e20	−0.675746	−0.337873	−	0.941192i	$-0.609707\pi$
$59$	−1.56524e20	−0.675746	−0.337873	+	0.941192i	$0.609707\pi$
$60$	−1.97831e19	−0.0703971
$61$	−1.87132e20	−0.550622	−0.275311	−	0.961355i	$-0.588781\pi$
$61$	−1.87132e20	−0.550622	−0.275311	+	0.961355i	$0.588781\pi$
$62$	−1.72781e20	−0.421689
$63$	−4.35072e20	−0.883375
$64$	7.37870e19	0.125000
$65$	−2.86061e19	−0.0405466
$66$	−2.52859e20	−0.300693
$67$	8.07966e19	0.0808226	0.0404113	−	0.999183i	$-0.487133\pi$
$67$	8.07966e19	0.0808226	0.0404113	+	0.999183i	$0.487133\pi$
$68$	−5.37965e20	−0.453839
$69$	−3.95488e19	−0.0282078
$70$	5.12983e20	0.310081
$71$	2.90638e21	1.49239	0.746193	−	0.665730i	$-0.231880\pi$
$71$	2.90638e21	1.49239	0.746193	+	0.665730i	$0.231880\pi$
$72$	7.28531e20	0.318511
$73$	7.57899e20	0.282747	0.141374	−	0.989956i	$-0.454848\pi$
$73$	7.57899e20	0.282747	0.141374	+	0.989956i	$0.454848\pi$
$74$	−3.55884e21	−1.13539
$75$	2.30305e20	0.0629650
$76$	−2.20347e21	−0.517310
$77$	6.55673e21	1.32448
$78$	−1.15900e20	−0.0201834
$79$	3.63951e21	0.547433	0.273716	−	0.961810i	$-0.411747\pi$
$79$	3.63951e21	0.547433	0.273716	+	0.961810i	$0.411747\pi$
$80$	−8.58993e20	−0.111803
$81$	6.31466e21	0.712479
$82$	−7.05043e21	−0.690806
$83$	2.01482e21	0.171727	0.0858635	−	0.996307i	$-0.472635\pi$
$83$	2.01482e21	0.171727	0.0858635	+	0.996307i	$0.472635\pi$
$84$	2.07839e21	0.154353
$85$	6.26274e21	0.405926
$86$	4.35736e21	0.246883
$87$	1.19228e22	0.591435
$88$	−1.09793e22	−0.477555
$89$	7.78361e21	0.297301	0.148650	−	0.988890i	$-0.452507\pi$
$89$	7.78361e21	0.297301	0.148650	+	0.988890i	$0.452507\pi$
$90$	−8.48122e21	−0.284885
$91$	3.00532e21	0.0889028
$92$	−1.71723e21	−0.0447991
$93$	8.14949e21	0.187748
$94$	−5.96009e22	−1.21418
$95$	2.56518e22	0.462696
$96$	−3.48028e21	−0.0556538
$97$	7.35687e22	1.04428	0.522141	−	0.852859i	$-0.325133\pi$
$97$	7.35687e22	1.04428	0.522141	+	0.852859i	$0.325133\pi$
$98$	2.15770e21	0.0272202
$99$	−1.08403e23	−1.21685
$100$	1.00000e22	0.100000
$101$	−1.90412e23	−1.69823	−0.849117	−	0.528205i	$-0.822865\pi$
$101$	−1.90412e23	−1.69823	−0.849117	+	0.528205i	$0.822865\pi$
$102$	2.53740e22	0.202063
$103$	−1.26775e23	−0.902417	−0.451208	−	0.892419i	$-0.649007\pi$
$103$	−1.26775e23	−0.902417	−0.451208	+	0.892419i	$0.649007\pi$
$104$	−5.03243e21	−0.0320549
$105$	−2.41956e22	−0.138058
$106$	−1.87158e23	−0.957614
$107$	1.51150e23	0.694218	0.347109	−	0.937825i	$-0.387163\pi$
$107$	1.51150e23	0.694218	0.347109	+	0.937825i	$0.387163\pi$
$108$	−7.25051e22	−0.299223
$109$	−6.22872e22	−0.231203	−0.115602	−	0.993296i	$-0.536880\pi$
$109$	−6.22872e22	−0.231203	−0.115602	+	0.993296i	$0.536880\pi$
$110$	1.27816e23	0.427138
$111$	1.67858e23	0.505509
$112$	9.02450e22	0.245141
$113$	2.44237e23	0.598976	0.299488	−	0.954100i	$-0.403184\pi$
$113$	2.44237e23	0.598976	0.299488	+	0.954100i	$0.403184\pi$
$114$	1.03930e23	0.230322
$115$	1.99912e22	0.0400695
$116$	5.17695e23	0.939306
$117$	−4.96874e22	−0.0816787
$118$	3.20562e23	0.477825
$119$	−6.57957e23	−0.890036
$120$	4.05157e22	0.0497782
$121$	7.38255e23	0.824470
$122$	3.83245e23	0.389349
$123$	3.32544e23	0.307568
$124$	3.53856e23	0.298179
$125$	−1.16415e23	−0.0894427
$126$	8.91028e23	0.624640
$127$	7.30411e23	0.467546	0.233773	−	0.972291i	$-0.424893\pi$
$127$	7.30411e23	0.467546	0.233773	+	0.972291i	$0.424893\pi$
$128$	−1.51116e23	−0.0883883
$129$	−2.05522e23	−0.109920
$130$	5.85852e22	0.0286708
$131$	−3.63647e24	−1.62952	−0.814760	−	0.579798i	$-0.803131\pi$
$131$	−3.63647e24	−1.62952	−0.814760	+	0.579798i	$0.803131\pi$
$132$	5.17855e23	0.212622
$133$	−2.69495e24	−1.01451
$134$	−1.65471e23	−0.0571502
$135$	8.44070e23	0.267633
$136$	1.10175e24	0.320913
$137$	−1.38361e24	−0.370448	−0.185224	−	0.982696i	$-0.559301\pi$
$137$	−1.38361e24	−0.370448	−0.185224	+	0.982696i	$0.559301\pi$
$138$	8.09959e22	0.0199459
$139$	−4.41623e24	−1.00088	−0.500439	−	0.865772i	$-0.666828\pi$
$139$	−4.41623e24	−1.00088	−0.500439	+	0.865772i	$0.666828\pi$
$140$	−1.05059e24	−0.219261
$141$	2.81117e24	0.540588
$142$	−5.95226e24	−1.05528
$143$	7.48811e23	0.122464
$144$	−1.49203e24	−0.225221
$145$	−6.02677e24	−0.840141
$146$	−1.55218e24	−0.199932
$147$	−1.01771e23	−0.0121193
$148$	7.28851e24	0.802840
$149$	1.34290e25	1.36899	0.684497	−	0.729016i	$-0.260022\pi$
$149$	1.34290e25	1.36899	0.684497	+	0.729016i	$0.260022\pi$
$150$	−4.71665e23	−0.0445230
$151$	3.64303e24	0.318587	0.159294	−	0.987231i	$-0.449078\pi$
$151$	3.64303e24	0.318587	0.159294	+	0.987231i	$0.449078\pi$
$152$	4.51271e24	0.365794
$153$	1.08781e25	0.817714
$154$	−1.34282e25	−0.936546
$155$	−4.11942e24	−0.266699
$156$	2.37362e23	0.0142718
$157$	−1.59126e25	−0.888984	−0.444492	−	0.895783i	$-0.646616\pi$
$157$	−1.59126e25	−0.888984	−0.444492	+	0.895783i	$0.646616\pi$
$158$	−7.45371e24	−0.387093
$159$	8.82759e24	0.426359
$160$	1.75922e24	0.0790569
$161$	−2.10026e24	−0.0878567
$162$	−1.29324e25	−0.503799
$163$	4.75035e25	1.72412	0.862062	−	0.506803i	$-0.169173\pi$
$163$	4.75035e25	1.72412	0.862062	+	0.506803i	$0.169173\pi$
$164$	1.44393e25	0.488474
$165$	−6.02862e24	−0.190175
$166$	−4.12635e24	−0.121429
$167$	4.51339e25	1.23955	0.619774	−	0.784780i	$-0.287224\pi$
$167$	4.51339e25	1.23955	0.619774	+	0.784780i	$0.287224\pi$
$168$	−4.25654e24	−0.109144
$169$	−4.14107e25	−0.991780
$170$	−1.28261e25	−0.287033
$171$	4.45560e25	0.932074
$172$	−8.92388e24	−0.174573
$173$	7.96874e25	1.45834	0.729171	−	0.684332i	$-0.239906\pi$
$173$	7.96874e25	1.45834	0.729171	+	0.684332i	$0.239906\pi$
$174$	−2.44179e25	−0.418207
$175$	1.22305e25	0.196113
$176$	2.24856e25	0.337682
$177$	−1.51198e25	−0.212742
$178$	−1.59408e25	−0.210223
$179$	−1.43711e26	−1.77697	−0.888485	−	0.458905i	$-0.848242\pi$
$179$	−1.43711e26	−1.77697	−0.888485	+	0.458905i	$0.848242\pi$
$180$	1.73695e25	0.201444
$181$	5.76556e25	0.627390	0.313695	−	0.949524i	$-0.398433\pi$
$181$	5.76556e25	0.627390	0.313695	+	0.949524i	$0.398433\pi$
$182$	−6.15490e24	−0.0628638
$183$	−1.80764e25	−0.173350
$184$	3.51689e24	0.0316777
$185$	−8.48495e25	−0.718082
$186$	−1.66901e25	−0.132758
$187$	−1.63938e26	−1.22603
$188$	1.22063e26	0.858553
$189$	−8.86772e25	−0.586815
$190$	−5.25349e25	−0.327176
$191$	−7.50288e25	−0.439890	−0.219945	−	0.975512i	$-0.570588\pi$
$191$	−7.50288e25	−0.439890	−0.219945	+	0.975512i	$0.570588\pi$
$192$	7.12761e24	0.0393532
$193$	−2.16639e26	−1.12675	−0.563376	−	0.826201i	$-0.690498\pi$
$193$	−2.16639e26	−1.12675	−0.563376	+	0.826201i	$0.690498\pi$
$194$	−1.50669e26	−0.738419
$195$	−2.76326e24	−0.0127651
$196$	−4.41897e24	−0.0192476
$197$	4.39361e26	1.80493	0.902464	−	0.430766i	$-0.141757\pi$
$197$	4.39361e26	1.80493	0.902464	+	0.430766i	$0.141757\pi$
$198$	2.22010e26	0.860444
$199$	−4.86048e26	−1.77774	−0.888870	−	0.458159i	$-0.848509\pi$
$199$	−4.86048e26	−1.77774	−0.888870	+	0.458159i	$0.848509\pi$
$200$	−2.04800e25	−0.0707107
$201$	7.80472e24	0.0254450
$202$	3.89963e26	1.20083
$203$	6.33166e26	1.84210
$204$	−5.19659e25	−0.142880
$205$	−1.68095e26	−0.436904
$206$	2.59636e26	0.638105
$207$	3.47238e25	0.0807176
$208$	1.03064e25	0.0226662
$209$	−6.71478e26	−1.39749
$210$	4.95527e25	0.0976215
$211$	7.27703e26	1.35739	0.678697	−	0.734419i	$-0.262545\pi$
$211$	7.27703e26	1.35739	0.678697	+	0.734419i	$0.262545\pi$
$212$	3.83299e26	0.677136
$213$	2.80748e26	0.469841
$214$	−3.09556e26	−0.490886
$215$	1.03888e26	0.156143
$216$	1.48490e26	0.211583
$217$	4.32782e26	0.584767
$218$	1.27564e26	0.163485
$219$	7.32108e25	0.0890160
$220$	−2.61767e26	−0.302032
$221$	−7.51420e25	−0.0822946
$222$	−3.43774e26	−0.357449
$223$	5.98167e26	0.590631	0.295315	−	0.955400i	$-0.404575\pi$
$223$	5.98167e26	0.590631	0.295315	+	0.955400i	$0.404575\pi$
$224$	−1.84822e26	−0.173341
$225$	−2.02208e26	−0.180177
$226$	−5.00197e26	−0.423540
$227$	−1.11932e27	−0.900856	−0.450428	−	0.892813i	$-0.648729\pi$
$227$	−1.11932e27	−0.900856	−0.450428	+	0.892813i	$0.648729\pi$
$228$	−2.12849e26	−0.162862
$229$	−1.94352e27	−1.41410	−0.707050	−	0.707164i	$-0.749974\pi$
$229$	−1.94352e27	−1.41410	−0.707050	+	0.707164i	$0.749974\pi$
$230$	−4.09420e25	−0.0283334
$231$	6.33361e26	0.416978
$232$	−1.06024e27	−0.664190
$233$	1.63857e27	0.976950	0.488475	−	0.872578i	$-0.337553\pi$
$233$	1.63857e27	0.976950	0.488475	+	0.872578i	$0.337553\pi$
$234$	1.01760e26	0.0577556
$235$	−1.42100e27	−0.767913
$236$	−6.56510e26	−0.337873
$237$	3.51566e26	0.172346
$238$	1.34750e27	0.629350
$239$	−2.04624e27	−0.910712	−0.455356	−	0.890309i	$-0.650488\pi$
$239$	−2.04624e27	−0.910712	−0.455356	+	0.890309i	$0.650488\pi$
$240$	−8.29763e25	−0.0351985
$241$	8.86273e26	0.358403	0.179202	−	0.983812i	$-0.442649\pi$
$241$	8.86273e26	0.358403	0.179202	+	0.983812i	$0.442649\pi$
$242$	−1.51195e27	−0.582988
$243$	2.23739e27	0.822753
$244$	−7.84887e26	−0.275311
$245$	5.14436e25	0.0172156
$246$	−6.81051e26	−0.217483
$247$	−3.07777e26	−0.0938039
$248$	−7.24697e26	−0.210844
$249$	1.94626e26	0.0540640
$250$	2.38419e26	0.0632456
$251$	5.18484e27	1.31367	0.656837	−	0.754033i	$-0.271894\pi$
$251$	5.18484e27	1.31367	0.656837	+	0.754033i	$0.271894\pi$
$252$	−1.82483e27	−0.441688
$253$	−5.23303e26	−0.121023
$254$	−1.49588e27	−0.330605
$255$	6.04962e26	0.127796
$256$	3.09485e26	0.0625000
$257$	3.40999e26	0.0658448	0.0329224	−	0.999458i	$-0.489519\pi$
$257$	3.40999e26	0.0658448	0.0329224	+	0.999458i	$0.489519\pi$
$258$	4.20908e26	0.0777251
$259$	8.91420e27	1.57447
$260$	−1.19983e26	−0.0202733
$261$	−1.04682e28	−1.69241
$262$	7.44749e27	1.15224
$263$	−1.92562e26	−0.0285154	−0.0142577	−	0.999898i	$-0.504539\pi$
$263$	−1.92562e26	−0.0285154	−0.0142577	+	0.999898i	$0.504539\pi$
$264$	−1.06057e27	−0.150346
$265$	−4.46219e27	−0.605648
$266$	5.51926e27	0.717368
$267$	7.51874e26	0.0935978
$268$	3.38886e26	0.0404113
$269$	7.57249e27	0.865142	0.432571	−	0.901600i	$-0.357606\pi$
$269$	7.57249e27	0.865142	0.432571	+	0.901600i	$0.357606\pi$
$270$	−1.72866e27	−0.189245
$271$	7.36490e27	0.772716	0.386358	−	0.922349i	$-0.373733\pi$
$271$	7.36490e27	0.772716	0.386358	+	0.922349i	$0.373733\pi$
$272$	−2.25639e27	−0.226919
$273$	2.90306e26	0.0279888
$274$	2.83363e27	0.261946
$275$	3.04736e27	0.270146
$276$	−1.65880e26	−0.0141039
$277$	−7.09557e27	−0.578722	−0.289361	−	0.957220i	$-0.593443\pi$
$277$	−7.09557e27	−0.578722	−0.289361	+	0.957220i	$0.593443\pi$
$278$	9.04443e27	0.707728
$279$	−7.15525e27	−0.537250
$280$	2.15161e27	0.155041
$281$	−1.37982e28	−0.954335	−0.477167	−	0.878812i	$-0.658336\pi$
$281$	−1.37982e28	−0.954335	−0.477167	+	0.878812i	$0.658336\pi$
$282$	−5.75727e27	−0.382254
$283$	−2.58038e28	−1.64490	−0.822451	−	0.568836i	$-0.807394\pi$
$283$	−2.58038e28	−1.64490	−0.822451	+	0.568836i	$0.807394\pi$
$284$	1.21902e28	0.746193
$285$	2.47789e27	0.145668
$286$	−1.53357e27	−0.0865950
$287$	1.76599e28	0.957959
$288$	3.05568e27	0.159255
$289$	−3.51670e27	−0.176121
$290$	1.23428e28	0.594069
$291$	7.10652e27	0.328767
$292$	3.17886e27	0.141374
$293$	−3.76122e28	−1.60824	−0.804121	−	0.594465i	$-0.797364\pi$
$293$	−3.76122e28	−1.60824	−0.804121	+	0.594465i	$0.797364\pi$
$294$	2.08428e26	0.00856961
$295$	7.64278e27	0.302203
$296$	−1.49269e28	−0.567694
$297$	−2.20949e28	−0.808339
$298$	−2.75026e28	−0.968025
$299$	−2.39860e26	−0.00812342
$300$	9.65971e26	0.0314825
$301$	−1.09143e28	−0.342359
$302$	−7.46093e27	−0.225275
$303$	−1.83932e28	−0.534647
$304$	−9.24203e27	−0.258655
$305$	9.13728e27	0.246246
$306$	−2.22783e28	−0.578211
$307$	4.21582e28	1.05388	0.526940	−	0.849903i	$-0.323339\pi$
$307$	4.21582e28	1.05388	0.526940	+	0.849903i	$0.323339\pi$
$308$	2.75009e28	0.662238
$309$	−1.22461e28	−0.284104
$310$	8.43658e27	0.188585
$311$	5.94875e26	0.0128139	0.00640695	−	0.999979i	$-0.497961\pi$
$311$	5.94875e26	0.0128139	0.00640695	+	0.999979i	$0.497961\pi$
$312$	−4.86118e26	−0.0100917
$313$	−1.94352e28	−0.388892	−0.194446	−	0.980913i	$-0.562291\pi$
$313$	−1.94352e28	−0.388892	−0.194446	+	0.980913i	$0.562291\pi$
$314$	3.25889e28	0.628607
$315$	2.12438e28	0.395057
$316$	1.52652e28	0.273716
$317$	2.90468e28	0.502247	0.251123	−	0.967955i	$-0.419200\pi$
$317$	2.90468e28	0.502247	0.251123	+	0.967955i	$0.419200\pi$
$318$	−1.80789e28	−0.301481
$319$	1.57761e29	2.53750
$320$	−3.60288e27	−0.0559017
$321$	1.46007e28	0.218557
$322$	4.30133e27	0.0621241
$323$	6.73817e28	0.939102
$324$	2.64856e28	0.356239
$325$	1.39678e27	0.0181330
$326$	−9.72872e28	−1.21914
$327$	−6.01676e27	−0.0727887
$328$	−2.95717e28	−0.345403
$329$	1.49288e29	1.68373
$330$	1.23466e28	0.134474
$331$	1.15568e27	0.0121567	0.00607836	−	0.999982i	$-0.498065\pi$
$331$	1.15568e27	0.0121567	0.00607836	+	0.999982i	$0.498065\pi$
$332$	8.45077e27	0.0858635
$333$	−1.47380e29	−1.44653
$334$	−9.24342e28	−0.876493
$335$	−3.94515e27	−0.0361450
$336$	8.71740e27	0.0771765
$337$	−1.71663e29	−1.46870	−0.734350	−	0.678770i	$-0.762513\pi$
$337$	−1.71663e29	−1.46870	−0.734350	+	0.678770i	$0.762513\pi$
$338$	8.48091e28	0.701294
$339$	2.35926e28	0.188573
$340$	2.62678e28	0.202963
$341$	1.07833e29	0.805518
$342$	−9.12506e28	−0.659076
$343$	−1.45802e29	−1.01831
$344$	1.82761e28	0.123442
$345$	1.93109e27	0.0126149
$346$	−1.63200e29	−1.03120
$347$	2.28248e29	1.39514	0.697571	−	0.716515i	$-0.254264\pi$
$347$	2.28248e29	1.39514	0.697571	+	0.716515i	$0.254264\pi$
$348$	5.00078e28	0.295717
$349$	−2.74075e29	−1.56811	−0.784055	−	0.620691i	$-0.786852\pi$
$349$	−2.74075e29	−1.56811	−0.784055	+	0.620691i	$0.786852\pi$
$350$	−2.50480e28	−0.138673
$351$	−1.01274e28	−0.0542581
$352$	−4.60505e28	−0.238777
$353$	−2.35796e29	−1.18339	−0.591695	−	0.806162i	$-0.701541\pi$
$353$	−2.35796e29	−1.18339	−0.591695	+	0.806162i	$0.701541\pi$
$354$	3.09653e28	0.150431
$355$	−1.41913e29	−0.667415
$356$	3.26468e28	0.148650
$357$	−6.35567e28	−0.280206
$358$	2.94320e29	1.25651
$359$	3.64190e29	1.50571	0.752855	−	0.658186i	$-0.228676\pi$
$359$	3.64190e29	1.50571	0.752855	+	0.658186i	$0.228676\pi$
$360$	−3.55728e28	−0.142442
$361$	1.81614e28	0.0704397
$362$	−1.18079e29	−0.443632
$363$	7.13133e28	0.259564
$364$	1.26052e28	0.0444514
$365$	−3.70068e28	−0.126448
$366$	3.70204e28	0.122577
$367$	−3.48766e29	−1.11911	−0.559557	−	0.828792i	$-0.689029\pi$
$367$	−3.48766e29	−1.11911	−0.559557	+	0.828792i	$0.689029\pi$
$368$	−7.20260e27	−0.0223995
$369$	−2.91974e29	−0.880118
$370$	1.73772e29	0.507761
$371$	4.68793e29	1.32795
$372$	3.41814e28	0.0938742
$373$	−1.01384e29	−0.269973	−0.134986	−	0.990847i	$-0.543099\pi$
$373$	−1.01384e29	−0.269973	−0.134986	+	0.990847i	$0.543099\pi$
$374$	3.35744e29	0.866932
$375$	−1.12454e28	−0.0281588
$376$	−2.49984e29	−0.607089
$377$	7.23107e28	0.170324
$378$	1.81611e29	0.414941
$379$	−3.31120e29	−0.733896	−0.366948	−	0.930241i	$-0.619597\pi$
$379$	−3.31120e29	−0.733896	−0.366948	+	0.930241i	$0.619597\pi$
$380$	1.07591e29	0.231348
$381$	7.05556e28	0.147195
$382$	1.53659e29	0.311049
$383$	7.73906e29	1.52021	0.760103	−	0.649803i	$-0.225149\pi$
$383$	7.73906e29	1.52021	0.760103	+	0.649803i	$0.225149\pi$
$384$	−1.45973e28	−0.0278269
$385$	−3.20153e29	−0.592324
$386$	4.43677e29	0.796734
$387$	1.80448e29	0.314540
$388$	3.08570e29	0.522141
$389$	−4.63657e29	−0.761687	−0.380844	−	0.924639i	$-0.624366\pi$
$389$	−4.63657e29	−0.761687	−0.380844	+	0.924639i	$0.624366\pi$
$390$	5.65916e27	0.00902629
$391$	5.25126e28	0.0813263
$392$	9.05005e27	0.0136101
$393$	−3.51272e29	−0.513014
$394$	−8.99811e29	−1.27628
$395$	−1.77710e29	−0.244819
$396$	−4.54676e29	−0.608426
$397$	8.34883e29	1.08526	0.542631	−	0.839971i	$-0.317428\pi$
$397$	8.34883e29	1.08526	0.542631	+	0.839971i	$0.317428\pi$
$398$	9.95425e29	1.25705
$399$	−2.60324e29	−0.319394
$400$	4.19430e28	0.0500000
$401$	7.15041e29	0.828267	0.414134	−	0.910216i	$-0.364085\pi$
$401$	7.15041e29	0.828267	0.414134	+	0.910216i	$0.364085\pi$
$402$	−1.59841e28	−0.0179923
$403$	4.94259e28	0.0540688
$404$	−7.98644e29	−0.849117
$405$	−3.08333e29	−0.318630
$406$	−1.29672e30	−1.30256
$407$	2.22108e30	2.16884
$408$	1.06426e29	0.101031
$409$	−9.14108e29	−0.843683	−0.421842	−	0.906670i	$-0.638616\pi$
$409$	−9.14108e29	−0.843683	−0.421842	+	0.906670i	$0.638616\pi$
$410$	3.44259e29	0.308938
$411$	−1.33653e29	−0.116626
$412$	−5.31735e29	−0.451208
$413$	−8.02943e29	−0.662612
$414$	−7.11144e28	−0.0570760
$415$	−9.83800e28	−0.0767986
$416$	−2.11076e28	−0.0160275
$417$	−4.26595e29	−0.315102
$418$	1.37519e30	0.988176
$419$	−8.72251e29	−0.609790	−0.304895	−	0.952386i	$-0.598621\pi$
$419$	−8.72251e29	−0.609790	−0.304895	+	0.952386i	$0.598621\pi$
$420$	−1.01484e29	−0.0690288
$421$	1.00203e30	0.663188	0.331594	−	0.943422i	$-0.392414\pi$
$421$	1.00203e30	0.663188	0.331594	+	0.943422i	$0.392414\pi$
$422$	−1.49034e30	−0.959822
$423$	−2.46820e30	−1.54692
$424$	−7.84997e29	−0.478807
$425$	−3.05798e29	−0.181536
$426$	−5.74971e29	−0.332228
$427$	−9.59953e29	−0.539920
$428$	6.33971e29	0.347109
$429$	7.23330e28	0.0385547
$430$	−2.12762e29	−0.110410
$431$	2.54277e30	1.28475	0.642376	−	0.766390i	$-0.277949\pi$
$431$	2.54277e30	1.28475	0.642376	+	0.766390i	$0.277949\pi$
$432$	−3.04108e29	−0.149612
$433$	3.98569e30	1.90938	0.954690	−	0.297602i	$-0.0961869\pi$
$433$	3.98569e30	1.90938	0.954690	+	0.297602i	$0.0961869\pi$
$434$	−8.86338e29	−0.413492
$435$	−5.82168e29	−0.264498
$436$	−2.61252e29	−0.115602
$437$	2.15088e29	0.0927001
$438$	−1.49936e29	−0.0629438
$439$	−1.67709e30	−0.685828	−0.342914	−	0.939367i	$-0.611414\pi$
$439$	−1.67709e30	−0.685828	−0.342914	+	0.939367i	$0.611414\pi$
$440$	5.36098e29	0.213569
$441$	8.93551e28	0.0346797
$442$	1.53891e29	0.0581911
$443$	−2.50087e30	−0.921402	−0.460701	−	0.887555i	$-0.652402\pi$
$443$	−2.50087e30	−0.921402	−0.460701	+	0.887555i	$0.652402\pi$
$444$	7.04049e29	0.252754
$445$	−3.80059e29	−0.132957
$446$	−1.22505e30	−0.417639
$447$	1.29720e30	0.430994
$448$	3.78515e29	0.122570
$449$	4.01190e30	1.26624	0.633121	−	0.774053i	$-0.281774\pi$
$449$	4.01190e30	1.26624	0.633121	+	0.774053i	$0.281774\pi$
$450$	4.14122e29	0.127404
$451$	4.40018e30	1.31959
$452$	1.02440e30	0.299488
$453$	3.51906e29	0.100299
$454$	2.29236e30	0.637002
$455$	−1.46744e29	−0.0397585
$456$	4.35915e29	0.115161
$457$	2.65155e30	0.683067	0.341534	−	0.939870i	$-0.389054\pi$
$457$	2.65155e30	0.683067	0.341534	+	0.939870i	$0.389054\pi$
$458$	3.98032e30	0.999919
$459$	2.21719e30	0.543197
$460$	8.38492e28	0.0200348
$461$	−4.46767e29	−0.104117	−0.0520583	−	0.998644i	$-0.516578\pi$
$461$	−4.46767e29	−0.104117	−0.0520583	+	0.998644i	$0.516578\pi$
$462$	−1.29712e30	−0.294848
$463$	−6.05418e30	−1.34238	−0.671188	−	0.741287i	$-0.734216\pi$
$463$	−6.05418e30	−1.34238	−0.671188	+	0.741287i	$0.734216\pi$
$464$	2.17137e30	0.469653
$465$	−3.97924e29	−0.0839637
$466$	−3.35580e30	−0.690808
$467$	−3.71792e30	−0.746716	−0.373358	−	0.927687i	$-0.621794\pi$
$467$	−3.71792e30	−0.746716	−0.373358	+	0.927687i	$0.621794\pi$
$468$	−2.08404e29	−0.0408394
$469$	4.14473e29	0.0792517
$470$	2.91020e30	0.542997
$471$	−1.53711e30	−0.279875
$472$	1.34453e30	0.238912
$473$	−2.71943e30	−0.471601
$474$	−7.20006e29	−0.121867
$475$	−1.25253e30	−0.206924
$476$	−2.75967e30	−0.445018
$477$	−7.75062e30	−1.22004
$478$	4.19070e30	0.643971
$479$	1.06439e30	0.159677	0.0798387	−	0.996808i	$-0.474559\pi$
$479$	1.06439e30	0.159677	0.0798387	+	0.996808i	$0.474559\pi$
$480$	1.69935e29	0.0248891
$481$	1.01805e30	0.145579
$482$	−1.81509e30	−0.253429
$483$	−2.02879e29	−0.0276595
$484$	3.09647e30	0.412235
$485$	−3.59222e30	−0.467017
$486$	−4.58217e30	−0.581774
$487$	−1.04192e31	−1.29197	−0.645985	−	0.763350i	$-0.723553\pi$
$487$	−1.04192e31	−1.29197	−0.645985	+	0.763350i	$0.723553\pi$
$488$	1.60745e30	0.194674
$489$	4.58870e30	0.542798
$490$	−1.05356e29	−0.0121732
$491$	−1.39431e31	−1.57370	−0.786850	−	0.617145i	$-0.788289\pi$
$491$	−1.39431e31	−1.57370	−0.786850	+	0.617145i	$0.788289\pi$
$492$	1.39479e30	0.153784
$493$	−1.58310e31	−1.70518
$494$	6.30327e29	0.0663293
$495$	5.29313e30	0.544193
$496$	1.48418e30	0.149089
$497$	1.49092e31	1.46338
$498$	−3.98594e29	−0.0382290
$499$	7.97788e30	0.747707	0.373853	−	0.927488i	$-0.378036\pi$
$499$	7.97788e30	0.747707	0.373853	+	0.927488i	$0.378036\pi$
$500$	−4.88281e29	−0.0447214
$501$	4.35980e30	0.390241
$502$	−1.06186e31	−0.928908
$503$	−1.42305e31	−1.21671	−0.608356	−	0.793664i	$-0.708171\pi$
$503$	−1.42305e31	−1.21671	−0.608356	+	0.793664i	$0.708171\pi$
$504$	3.73724e30	0.312320
$505$	9.29744e30	0.759473
$506$	1.07173e30	0.0855761
$507$	−4.00015e30	−0.312237
$508$	3.06357e30	0.233773
$509$	1.65075e31	1.23148	0.615738	−	0.787951i	$-0.288858\pi$
$509$	1.65075e31	1.23148	0.615738	+	0.787951i	$0.288858\pi$
$510$	−1.23896e30	−0.0903652
$511$	3.88789e30	0.277252
$512$	−6.33825e29	−0.0441942
$513$	9.08147e30	0.619165
$514$	−6.98365e29	−0.0465593
$515$	6.19021e30	0.403573
$516$	−8.62021e29	−0.0549599
$517$	3.71969e31	2.31935
$518$	−1.82563e31	−1.11332
$519$	7.69756e30	0.459123
$520$	2.45724e29	0.0143354
$521$	−7.10111e30	−0.405221	−0.202611	−	0.979259i	$-0.564943\pi$
$521$	−7.10111e30	−0.405221	−0.202611	+	0.979259i	$0.564943\pi$
$522$	2.14389e31	1.19672
$523$	−4.37438e30	−0.238862	−0.119431	−	0.992843i	$-0.538107\pi$
$523$	−4.37438e30	−0.238862	−0.119431	+	0.992843i	$0.538107\pi$
$524$	−1.52525e31	−0.814760
$525$	1.18143e30	0.0617412
$526$	3.94366e29	0.0201634
$527$	−1.08208e31	−0.541301
$528$	2.17204e30	0.106311
$529$	−2.07128e31	−0.991972
$530$	9.13857e30	0.428258
$531$	1.32752e31	0.608769
$532$	−1.13034e31	−0.507256
$533$	2.01685e30	0.0885750
$534$	−1.53984e30	−0.0661836
$535$	−7.38039e30	−0.310464
$536$	−6.94038e29	−0.0285751
$537$	−1.38821e31	−0.559435
$538$	−1.55085e31	−0.611748
$539$	−1.34662e30	−0.0519966
$540$	3.54029e30	0.133817
$541$	4.49548e31	1.66344	0.831720	−	0.555196i	$-0.187357\pi$
$541$	4.49548e31	1.66344	0.831720	+	0.555196i	$0.187357\pi$
$542$	−1.50833e31	−0.546393
$543$	5.56936e30	0.197518
$544$	4.62109e30	0.160456
$545$	3.04137e30	0.103397
$546$	−5.94546e29	−0.0197911
$547$	2.88414e31	0.940073	0.470037	−	0.882647i	$-0.344241\pi$
$547$	2.88414e31	0.940073	0.470037	+	0.882647i	$0.344241\pi$
$548$	−5.80328e30	−0.185224
$549$	1.58710e31	0.496047
$550$	−6.24100e30	−0.191022
$551$	−6.48428e31	−1.94365
$552$	3.39721e29	0.00997295
$553$	1.86701e31	0.536793
$554$	1.45317e31	0.409218
$555$	−8.19621e30	−0.226070
$556$	−1.85230e31	−0.500439
$557$	−3.57987e31	−0.947399	−0.473699	−	0.880687i	$-0.657082\pi$
$557$	−3.57987e31	−0.947399	−0.473699	+	0.880687i	$0.657082\pi$
$558$	1.46539e31	0.379893
$559$	−1.24647e30	−0.0316553
$560$	−4.40649e30	−0.109630
$561$	−1.58359e31	−0.385984
$562$	2.82588e31	0.674816
$563$	−1.08547e31	−0.253963	−0.126981	−	0.991905i	$-0.540529\pi$
$563$	−1.08547e31	−0.253963	−0.126981	+	0.991905i	$0.540529\pi$
$564$	1.17909e31	0.270294
$565$	−1.19256e31	−0.267870
$566$	5.28462e31	1.16312
$567$	3.23931e31	0.698631
$568$	−2.49656e31	−0.527638
$569$	−6.35163e31	−1.31551	−0.657755	−	0.753232i	$-0.728494\pi$
$569$	−6.35163e31	−1.31551	−0.657755	+	0.753232i	$0.728494\pi$
$570$	−5.07471e30	−0.103003
$571$	−5.61161e31	−1.11628	−0.558139	−	0.829748i	$-0.688484\pi$
$571$	−5.61161e31	−1.11628	−0.558139	+	0.829748i	$0.688484\pi$
$572$	3.14074e30	0.0612319
$573$	−7.24756e30	−0.138488
$574$	−3.61675e31	−0.677380
$575$	−9.76134e29	−0.0179196
$576$	−6.25803e30	−0.112611
$577$	−4.70124e31	−0.829260	−0.414630	−	0.909990i	$-0.636089\pi$
$577$	−4.70124e31	−0.829260	−0.414630	+	0.909990i	$0.636089\pi$
$578$	7.20221e30	0.124536
$579$	−2.09267e31	−0.354730
$580$	−2.52781e31	−0.420071
$581$	1.03357e31	0.168389
$582$	−1.45542e31	−0.232473
$583$	1.16805e32	1.82925
$584$	−6.51030e30	−0.0999662
$585$	2.42614e30	0.0365278
$586$	7.70299e31	1.13720
$587$	−4.84136e31	−0.700856	−0.350428	−	0.936590i	$-0.613964\pi$
$587$	−4.84136e31	−0.700856	−0.350428	+	0.936590i	$0.613964\pi$
$588$	−4.26860e29	−0.00605963
$589$	−4.43214e31	−0.617004
$590$	−1.56524e31	−0.213690
$591$	4.24410e31	0.568237
$592$	3.05702e31	0.401420
$593$	1.51819e32	1.95522	0.977611	−	0.210421i	$-0.0674836\pi$
$593$	1.51819e32	1.95522	0.977611	+	0.210421i	$0.0674836\pi$
$594$	4.52504e31	0.571582
$595$	3.21268e31	0.398036
$596$	5.63253e31	0.684497
$597$	−4.69508e31	−0.559678
$598$	4.91233e29	0.00574412
$599$	−8.36725e31	−0.959785	−0.479893	−	0.877327i	$-0.659324\pi$
$599$	−8.36725e31	−0.959785	−0.479893	+	0.877327i	$0.659324\pi$
$600$	−1.97831e30	−0.0222615
$601$	−1.63771e31	−0.180792	−0.0903962	−	0.995906i	$-0.528813\pi$
$601$	−1.63771e31	−0.180792	−0.0903962	+	0.995906i	$0.528813\pi$
$602$	2.23525e31	0.242085
$603$	−6.85254e30	−0.0728119
$604$	1.52800e31	0.159294
$605$	−3.60476e31	−0.368714
$606$	3.76693e31	0.378052
$607$	3.14222e31	0.309433	0.154717	−	0.987959i	$-0.450554\pi$
$607$	3.14222e31	0.309433	0.154717	+	0.987959i	$0.450554\pi$
$608$	1.89277e31	0.182897
$609$	6.11620e31	0.579939
$610$	−1.87132e31	−0.174122
$611$	1.70495e31	0.155681
$612$	4.56260e31	0.408857
$613$	8.36754e31	0.735872	0.367936	−	0.929851i	$-0.380064\pi$
$613$	8.36754e31	0.735872	0.367936	+	0.929851i	$0.380064\pi$
$614$	−8.63401e31	−0.745206
$615$	−1.62375e31	−0.137549
$616$	−5.63219e31	−0.468273
$617$	−5.63274e31	−0.459664	−0.229832	−	0.973230i	$-0.573818\pi$
$617$	−5.63274e31	−0.459664	−0.229832	+	0.973230i	$0.573818\pi$
$618$	2.50801e31	0.200892
$619$	1.71215e32	1.34617	0.673085	−	0.739565i	$-0.264969\pi$
$619$	1.71215e32	1.34617	0.673085	+	0.739565i	$0.264969\pi$
$620$	−1.72781e31	−0.133350
$621$	7.07747e30	0.0536197
$622$	−1.21830e30	−0.00906079
$623$	3.99286e31	0.291522
$624$	9.95570e29	0.00713591
$625$	5.68434e30	0.0400000
$626$	3.98033e31	0.274988
$627$	−6.48628e31	−0.439966
$628$	−6.67421e31	−0.444492
$629$	−2.22881e32	−1.45744
$630$	−4.35072e31	−0.279348
$631$	1.89962e32	1.19765	0.598823	−	0.800882i	$-0.295635\pi$
$631$	1.89962e32	1.19765	0.598823	+	0.800882i	$0.295635\pi$
$632$	−3.12631e31	−0.193547
$633$	7.02939e31	0.427342
$634$	−5.94879e31	−0.355142
$635$	−3.56646e31	−0.209093
$636$	3.70256e31	0.213179
$637$	−6.17233e29	−0.00349016
$638$	−3.23094e32	−1.79428
$639$	−2.46496e32	−1.34447
$640$	7.37870e30	0.0395285
$641$	−3.21032e32	−1.68920	−0.844600	−	0.535398i	$-0.820162\pi$
$641$	−3.21032e32	−1.68920	−0.844600	+	0.535398i	$0.820162\pi$
$642$	−2.99022e31	−0.154543
$643$	1.99375e32	1.01215	0.506074	−	0.862490i	$-0.331096\pi$
$643$	1.99375e32	1.01215	0.506074	+	0.862490i	$0.331096\pi$
$644$	−8.80912e30	−0.0439283
$645$	1.00352e31	0.0491576
$646$	−1.37998e32	−0.664046
$647$	2.96466e32	1.40144	0.700721	−	0.713435i	$-0.252862\pi$
$647$	2.96466e32	1.40144	0.700721	+	0.713435i	$0.252862\pi$
$648$	−5.42425e31	−0.251899
$649$	−2.00063e32	−0.912750
$650$	−2.86061e30	−0.0128220
$651$	4.18055e31	0.184099
$652$	1.99244e32	0.862062
$653$	−2.49597e32	−1.06106	−0.530528	−	0.847668i	$-0.678006\pi$
$653$	−2.49597e32	−1.06106	−0.530528	+	0.847668i	$0.678006\pi$
$654$	1.23223e31	0.0514694
$655$	1.77562e32	0.728744
$656$	6.05627e31	0.244237
$657$	−6.42791e31	−0.254723
$658$	−3.05742e32	−1.19058
$659$	2.96418e32	1.13428	0.567142	−	0.823620i	$-0.308049\pi$
$659$	2.96418e32	1.13428	0.567142	+	0.823620i	$0.308049\pi$
$660$	−2.52859e31	−0.0950874
$661$	−1.53911e32	−0.568793	−0.284396	−	0.958707i	$-0.591793\pi$
$661$	−1.53911e32	−0.568793	−0.284396	+	0.958707i	$0.591793\pi$
$662$	−2.36684e30	−0.00859610
$663$	−7.25849e30	−0.0259084
$664$	−1.73072e31	−0.0607147
$665$	1.31589e32	0.453703
$666$	3.01833e32	1.02285
$667$	−5.05340e31	−0.168320
$668$	1.89305e32	0.619774
$669$	5.77811e31	0.185946
$670$	8.07966e30	0.0255584
$671$	−2.39184e32	−0.743742
$672$	−1.78532e31	−0.0545720
$673$	2.36902e32	0.711863	0.355931	−	0.934512i	$-0.384164\pi$
$673$	2.36902e32	0.711863	0.355931	+	0.934512i	$0.384164\pi$
$674$	3.51566e32	1.03853
$675$	−4.12144e31	−0.119689
$676$	−1.73689e32	−0.495890
$677$	5.52473e32	1.55075	0.775375	−	0.631501i	$-0.217561\pi$
$677$	5.52473e32	1.55075	0.775375	+	0.631501i	$0.217561\pi$
$678$	−4.83176e31	−0.133341
$679$	3.77395e32	1.02399
$680$	−5.37965e31	−0.143516
$681$	−1.08123e32	−0.283612
$682$	−2.20841e32	−0.569587
$683$	2.02178e32	0.512737	0.256369	−	0.966579i	$-0.417474\pi$
$683$	2.02178e32	0.512737	0.256369	+	0.966579i	$0.417474\pi$
$684$	1.86881e32	0.466037
$685$	6.75591e31	0.165669
$686$	2.98602e32	0.720054
$687$	−1.87738e32	−0.445194
$688$	−3.74295e31	−0.0872864
$689$	5.35385e31	0.122785
$690$	−3.95488e30	−0.00892008
$691$	7.61688e31	0.168958	0.0844791	−	0.996425i	$-0.473077\pi$
$691$	7.61688e31	0.168958	0.0844791	+	0.996425i	$0.473077\pi$
$692$	3.34233e32	0.729171
$693$	−5.56091e32	−1.19320
$694$	−4.67453e32	−0.986515
$695$	2.15636e32	0.447606
$696$	−1.02416e32	−0.209104
$697$	−4.41550e32	−0.886754
$698$	5.61305e32	1.10882
$699$	1.58281e32	0.307569
$700$	5.12983e31	0.0980564
$701$	1.14010e31	0.0214382	0.0107191	−	0.999943i	$-0.496588\pi$
$701$	1.14010e31	0.0214382	0.0107191	+	0.999943i	$0.496588\pi$
$702$	2.07409e31	0.0383663
$703$	−9.12907e32	−1.66127
$704$	9.43114e31	0.168841
$705$	−1.37264e32	−0.241758
$706$	4.82911e32	0.836783
$707$	−9.76779e32	−1.66523
$708$	−6.34170e31	−0.106371
$709$	1.01717e33	1.67865	0.839327	−	0.543627i	$-0.182949\pi$
$709$	1.01717e33	1.67865	0.839327	+	0.543627i	$0.182949\pi$
$710$	2.90638e32	0.471934
$711$	−3.08674e32	−0.493174
$712$	−6.68607e31	−0.105112
$713$	−3.45410e31	−0.0534326
$714$	1.30164e32	0.198135
$715$	−3.65631e31	−0.0547675
$716$	−6.02768e32	−0.888485
$717$	−1.97661e32	−0.286715
$718$	−7.45860e32	−1.06470
$719$	1.86740e32	0.262335	0.131167	−	0.991360i	$-0.458127\pi$
$719$	1.86740e32	0.262335	0.131167	+	0.991360i	$0.458127\pi$
$720$	7.28531e31	0.100722
$721$	−6.50337e32	−0.884877
$722$	−3.71946e31	−0.0498084
$723$	8.56114e31	0.112834
$724$	2.41825e32	0.313695
$725$	2.94276e32	0.375723
$726$	−1.46050e32	−0.183539
$727$	4.12802e32	0.510618	0.255309	−	0.966860i	$-0.417823\pi$
$727$	4.12802e32	0.510618	0.255309	+	0.966860i	$0.417823\pi$
$728$	−2.58155e31	−0.0314319
$729$	−3.78357e32	−0.453456
$730$	7.57899e31	0.0894125
$731$	2.72890e32	0.316912
$732$	−7.58177e31	−0.0866749
$733$	−1.10621e33	−1.24492	−0.622462	−	0.782650i	$-0.713868\pi$
$733$	−1.10621e33	−1.24492	−0.622462	+	0.782650i	$0.713868\pi$
$734$	7.14273e32	0.791334
$735$	4.96930e30	0.00541989
$736$	1.47509e31	0.0158389
$737$	1.03271e32	0.109170
$738$	5.97962e32	0.622337
$739$	−3.81239e31	−0.0390649	−0.0195324	−	0.999809i	$-0.506218\pi$
$739$	−3.81239e31	−0.0390649	−0.0195324	+	0.999809i	$0.506218\pi$
$740$	−3.55884e32	−0.359041
$741$	−2.97303e31	−0.0295318
$742$	−9.60089e32	−0.939002
$743$	8.34595e32	0.803720	0.401860	−	0.915701i	$-0.368364\pi$
$743$	8.34595e32	0.803720	0.401860	+	0.915701i	$0.368364\pi$
$744$	−7.00036e31	−0.0663791
$745$	−6.55713e32	−0.612233
$746$	2.07635e32	0.190899
$747$	−1.70881e32	−0.154706
$748$	−6.87604e32	−0.613014
$749$	7.75376e32	0.680725
$750$	2.30305e31	0.0199113
$751$	−4.78669e32	−0.407545	−0.203773	−	0.979018i	$-0.565320\pi$
$751$	−4.78669e32	−0.407545	−0.203773	+	0.979018i	$0.565320\pi$
$752$	5.11967e32	0.429277
$753$	5.00840e32	0.413578
$754$	−1.48092e32	−0.120438
$755$	−1.77882e32	−0.142476
$756$	−3.71939e32	−0.293407
$757$	8.03371e32	0.624185	0.312093	−	0.950052i	$-0.398970\pi$
$757$	8.03371e32	0.624185	0.312093	+	0.950052i	$0.398970\pi$
$758$	6.78134e32	0.518943
$759$	−5.05496e31	−0.0381011
$760$	−2.20347e32	−0.163588
$761$	2.20093e33	1.60947	0.804733	−	0.593636i	$-0.202308\pi$
$761$	2.20093e33	1.60947	0.804733	+	0.593636i	$0.202308\pi$
$762$	−1.44498e32	−0.104083
$763$	−3.19523e32	−0.226710
$764$	−3.14693e32	−0.219945
$765$	−5.31157e32	−0.365693
$766$	−1.58496e33	−1.07495
$767$	−9.17001e31	−0.0612665
$768$	2.98953e31	0.0196766
$769$	1.27642e33	0.827640	0.413820	−	0.910359i	$-0.364194\pi$
$769$	1.27642e33	0.827640	0.413820	+	0.910359i	$0.364194\pi$
$770$	6.55673e32	0.418836
$771$	3.29395e31	0.0207296
$772$	−9.08651e32	−0.563376
$773$	7.13411e32	0.435789	0.217894	−	0.975972i	$-0.430081\pi$
$773$	7.13411e32	0.435789	0.217894	+	0.975972i	$0.430081\pi$
$774$	−3.69557e32	−0.222413
$775$	2.01144e32	0.119272
$776$	−6.31950e32	−0.369210
$777$	8.61085e32	0.495684
$778$	9.49570e32	0.538594
$779$	−1.80856e33	−1.01077
$780$	−1.15900e31	−0.00638255
$781$	3.71481e33	2.01581
$782$	−1.07546e32	−0.0575064
$783$	−2.13365e33	−1.12425
$784$	−1.85345e31	−0.00962379
$785$	7.76980e32	0.397566
$786$	7.19405e32	0.362756
$787$	3.74186e33	1.85942	0.929711	−	0.368290i	$-0.120057\pi$
$787$	3.74186e33	1.85942	0.929711	+	0.368290i	$0.120057\pi$
$788$	1.84281e33	0.902464
$789$	−1.86009e31	−0.00897736
$790$	3.63951e32	0.173113
$791$	1.25289e33	0.587334
$792$	9.31177e32	0.430222
$793$	−1.09631e32	−0.0499222
$794$	−1.70984e33	−0.767396
$795$	−4.31035e32	−0.190673
$796$	−2.03863e33	−0.888870
$797$	−2.09675e33	−0.901106	−0.450553	−	0.892750i	$-0.648773\pi$
$797$	−2.09675e33	−0.901106	−0.450553	+	0.892750i	$0.648773\pi$
$798$	5.33144e32	0.225845
$799$	−3.73265e33	−1.55858
$800$	−8.58993e31	−0.0353553
$801$	−6.60145e32	−0.267834
$802$	−1.46440e33	−0.585673
$803$	9.68714e32	0.381915
$804$	3.27354e31	0.0127225
$805$	1.02552e32	0.0392907
$806$	−1.01224e32	−0.0382324
$807$	7.31480e32	0.272369
$808$	1.63562e33	0.600416
$809$	−3.43370e33	−1.24267	−0.621334	−	0.783546i	$-0.713409\pi$
$809$	−3.43370e33	−1.24267	−0.621334	+	0.783546i	$0.713409\pi$
$810$	6.31466e32	0.225306
$811$	7.84005e32	0.275790	0.137895	−	0.990447i	$-0.455966\pi$
$811$	7.84005e32	0.275790	0.137895	+	0.990447i	$0.455966\pi$
$812$	2.65569e33	0.921050
$813$	7.11428e32	0.243270
$814$	−4.54876e33	−1.53360
$815$	−2.31951e33	−0.771052
$816$	−2.17961e32	−0.0714400
$817$	1.11774e33	0.361233
$818$	1.87209e33	0.596574
$819$	−2.54888e32	−0.0800912
$820$	−7.05043e32	−0.218452
$821$	−5.68448e33	−1.73678	−0.868389	−	0.495884i	$-0.834844\pi$
$821$	−5.68448e33	−1.73678	−0.868389	+	0.495884i	$0.834844\pi$
$822$	2.73721e32	0.0824673
$823$	−2.94087e33	−0.873730	−0.436865	−	0.899527i	$-0.643911\pi$
$823$	−2.94087e33	−0.873730	−0.436865	+	0.899527i	$0.643911\pi$
$824$	1.08899e33	0.319053
$825$	2.94366e32	0.0850487
$826$	1.64443e33	0.468537
$827$	−5.39861e33	−1.51694	−0.758471	−	0.651707i	$-0.774053\pi$
$827$	−5.39861e33	−1.51694	−0.758471	+	0.651707i	$0.774053\pi$
$828$	1.45642e32	0.0403588
$829$	−1.55567e33	−0.425148	−0.212574	−	0.977145i	$-0.568185\pi$
$829$	−1.55567e33	−0.425148	−0.212574	+	0.977145i	$0.568185\pi$
$830$	2.01482e32	0.0543048
$831$	−6.85411e32	−0.182196
$832$	4.32283e31	0.0113331
$833$	1.35131e32	0.0349412
$834$	8.73666e32	0.222811
$835$	−2.20380e33	−0.554343
$836$	−2.81638e33	−0.698746
$837$	−1.45839e33	−0.356888
$838$	1.78637e33	0.431187
$839$	−1.92891e33	−0.459249	−0.229625	−	0.973279i	$-0.573750\pi$
$839$	−1.92891e33	−0.459249	−0.229625	+	0.973279i	$0.573750\pi$
$840$	2.07839e32	0.0488107
$841$	1.09178e34	2.52919
$842$	−2.05216e33	−0.468945
$843$	−1.33287e33	−0.300449
$844$	3.05221e33	0.678697
$845$	2.02201e33	0.443537
$846$	5.05488e33	1.09383
$847$	3.78713e33	0.808445
$848$	1.60767e33	0.338568
$849$	−2.49257e33	−0.517857
$850$	6.26274e32	0.128365
$851$	−7.11456e32	−0.143866
$852$	1.17754e33	0.234920
$853$	5.61734e33	1.10565	0.552824	−	0.833298i	$-0.313550\pi$
$853$	5.61734e33	1.10565	0.552824	+	0.833298i	$0.313550\pi$
$854$	1.96598e33	0.381781
$855$	−2.17558e33	−0.416836
$856$	−1.29837e33	−0.245443
$857$	7.42776e33	1.38541	0.692705	−	0.721221i	$-0.256419\pi$
$857$	7.42776e33	1.38541	0.692705	+	0.721221i	$0.256419\pi$
$858$	−1.48138e32	−0.0272623
$859$	4.35697e33	0.791158	0.395579	−	0.918432i	$-0.370544\pi$
$859$	4.35697e33	0.791158	0.395579	+	0.918432i	$0.370544\pi$
$860$	4.35736e32	0.0780713
$861$	1.70590e33	0.301590
$862$	−5.20760e33	−0.908457
$863$	3.05708e33	0.526239	0.263119	−	0.964763i	$-0.415249\pi$
$863$	3.05708e33	0.526239	0.263119	+	0.964763i	$0.415249\pi$
$864$	6.22814e32	0.105791
$865$	−3.89098e33	−0.652190
$866$	−8.16269e33	−1.35014
$867$	−3.39703e32	−0.0554472
$868$	1.81522e33	0.292383
$869$	4.65186e33	0.739434
$870$	1.19228e33	0.187028
$871$	4.73349e31	0.00732778
$872$	5.35043e32	0.0817427
$873$	−6.23952e33	−0.940779
$874$	−4.40501e32	−0.0655489
$875$	−5.97191e32	−0.0877043
$876$	3.07068e32	0.0445080
$877$	3.83111e33	0.548061	0.274031	−	0.961721i	$-0.411643\pi$
$877$	3.83111e33	0.548061	0.274031	+	0.961721i	$0.411643\pi$
$878$	3.43469e33	0.484953
$879$	−3.63323e33	−0.506315
$880$	−1.09793e33	−0.151016
$881$	−3.46831e33	−0.470864	−0.235432	−	0.971891i	$-0.575650\pi$
$881$	−3.46831e33	−0.470864	−0.235432	+	0.971891i	$0.575650\pi$
$882$	−1.82999e32	−0.0245223
$883$	4.45714e33	0.589533	0.294767	−	0.955569i	$-0.404758\pi$
$883$	4.45714e33	0.589533	0.294767	+	0.955569i	$0.404758\pi$
$884$	−3.15168e32	−0.0411473
$885$	7.38271e32	0.0951410
$886$	5.12179e33	0.651529
$887$	−6.02507e33	−0.756555	−0.378278	−	0.925692i	$-0.623484\pi$
$887$	−6.02507e33	−0.756555	−0.378278	+	0.925692i	$0.623484\pi$
$888$	−1.44189e33	−0.178724
$889$	3.74689e33	0.458459
$890$	7.78361e32	0.0940148
$891$	8.07112e33	0.962366
$892$	2.50889e33	0.295315
$893$	−1.52887e34	−1.77655
$894$	−2.65667e33	−0.304759
$895$	7.01714e33	0.794685
$896$	−7.75198e32	−0.0866704
$897$	−2.31697e31	−0.00255746
$898$	−8.21636e33	−0.895368
$899$	1.04131e34	1.12033
$900$	−8.48122e32	−0.0900885
$901$	−1.17212e34	−1.22924
$902$	−9.01156e33	−0.933093
$903$	−1.05429e33	−0.107783
$904$	−2.09798e33	−0.211770
$905$	−2.81521e33	−0.280577
$906$	−7.20704e32	−0.0709223
$907$	−1.36671e34	−1.32798	−0.663992	−	0.747740i	$-0.731139\pi$
$907$	−1.36671e34	−1.32798	−0.663992	+	0.747740i	$0.731139\pi$
$908$	−4.69475e33	−0.450428
$909$	1.61492e34	1.52991
$910$	3.00532e32	0.0281135
$911$	−3.04666e33	−0.281425	−0.140713	−	0.990050i	$-0.544939\pi$
$911$	−3.04666e33	−0.281425	−0.140713	+	0.990050i	$0.544939\pi$
$912$	−8.92753e32	−0.0814312
$913$	2.57526e33	0.231957
$914$	−5.43037e33	−0.483001
$915$	8.82635e32	0.0775244
$916$	−8.15169e33	−0.707050
$917$	−1.86545e34	−1.59785
$918$	−4.54081e33	−0.384098
$919$	1.15749e34	0.966914	0.483457	−	0.875368i	$-0.339381\pi$
$919$	1.15749e34	0.966914	0.483457	+	0.875368i	$0.339381\pi$
$920$	−1.71723e32	−0.0141667
$921$	4.07236e33	0.331788
$922$	9.14978e32	0.0736216
$923$	1.70271e33	0.135307
$924$	2.65651e33	0.208489
$925$	4.14304e33	0.321136
$926$	1.23990e34	0.949203
$927$	1.07521e34	0.812974
$928$	−4.44697e33	−0.332095
$929$	−1.30644e34	−0.963625	−0.481813	−	0.876274i	$-0.660021\pi$
$929$	−1.30644e34	−0.963625	−0.481813	+	0.876274i	$0.660021\pi$
$930$	8.14949e32	0.0593713
$931$	5.53489e32	0.0398279
$932$	6.87267e33	0.488475
$933$	5.74632e31	0.00403414
$934$	7.61429e33	0.528008
$935$	8.00477e33	0.548296
$936$	4.26812e32	0.0288778
$937$	5.31518e33	0.355233	0.177616	−	0.984100i	$-0.443161\pi$
$937$	5.31518e33	0.355233	0.177616	+	0.984100i	$0.443161\pi$
$938$	−8.48841e32	−0.0560394
$939$	−1.87738e33	−0.122433
$940$	−5.96009e33	−0.383957
$941$	−2.68773e34	−1.71043	−0.855215	−	0.518273i	$-0.826575\pi$
$941$	−2.68773e34	−1.71043	−0.855215	+	0.518273i	$0.826575\pi$
$942$	3.14799e33	0.197901
$943$	−1.40947e33	−0.0875327
$944$	−2.75360e33	−0.168936
$945$	4.32994e33	0.262432
$946$	5.56939e33	0.333472
$947$	2.30574e34	1.36391	0.681954	−	0.731395i	$-0.261130\pi$
$947$	2.30574e34	1.36391	0.681954	+	0.731395i	$0.261130\pi$
$948$	1.47457e33	0.0861728
$949$	4.44017e32	0.0256353
$950$	2.56518e33	0.146317
$951$	2.80584e33	0.158120
$952$	5.65181e33	0.314675
$953$	2.81392e33	0.154790	0.0773951	−	0.997000i	$-0.475340\pi$
$953$	2.81392e33	0.154790	0.0773951	+	0.997000i	$0.475340\pi$
$954$	1.58733e34	0.862700
$955$	3.66351e33	0.196725
$956$	−8.58256e33	−0.455356
$957$	1.52392e34	0.798868
$958$	−2.17987e33	−0.112909
$959$	−7.09769e33	−0.363248
$960$	−3.48028e32	−0.0175993
$961$	−1.28957e34	−0.644357
$962$	−2.08496e33	−0.102940
$963$	−1.28194e34	−0.625411
$964$	3.71730e33	0.179202
$965$	1.05781e34	0.503899
$966$	4.15495e32	0.0195582
$967$	−6.80922e33	−0.316733	−0.158366	−	0.987380i	$-0.550623\pi$
$967$	−6.80922e33	−0.316733	−0.158366	+	0.987380i	$0.550623\pi$
$968$	−6.34157e33	−0.291494
$969$	6.50887e33	0.295653
$970$	7.35687e33	0.330231
$971$	−1.01372e34	−0.449672	−0.224836	−	0.974397i	$-0.572185\pi$
$971$	−1.01372e34	−0.449672	−0.224836	+	0.974397i	$0.572185\pi$
$972$	9.38429e33	0.411376
$973$	−2.26545e34	−0.981425
$974$	2.13386e34	0.913561
$975$	1.34925e32	0.00570872
$976$	−3.29205e33	−0.137656
$977$	−2.44303e34	−1.00958	−0.504791	−	0.863241i	$-0.668431\pi$
$977$	−2.44303e34	−1.00958	−0.504791	+	0.863241i	$0.668431\pi$
$978$	−9.39766e33	−0.383816
$979$	9.94868e33	0.401573
$980$	2.15770e32	0.00860778
$981$	5.28271e33	0.208288
$982$	2.85554e34	1.11277
$983$	2.69854e34	1.03935	0.519677	−	0.854363i	$-0.326052\pi$
$983$	2.69854e34	1.03935	0.519677	+	0.854363i	$0.326052\pi$
$984$	−2.85653e33	−0.108742
$985$	−2.14532e34	−0.807188
$986$	3.24219e34	1.20574
$987$	1.44208e34	0.530081
$988$	−1.29091e33	−0.0469019
$989$	8.71090e32	0.0312828
$990$	−1.08403e34	−0.384802
$991$	7.07919e33	0.248391	0.124196	−	0.992258i	$-0.460365\pi$
$991$	7.07919e33	0.248391	0.124196	+	0.992258i	$0.460365\pi$
$992$	−3.03960e33	−0.105422
$993$	1.11636e32	0.00382724
$994$	−3.05341e34	−1.03477
$995$	2.37328e34	0.795030
$996$	8.16320e32	0.0270320
$997$	−1.40997e34	−0.461545	−0.230773	−	0.973008i	$-0.574125\pi$
$997$	−1.40997e34	−0.461545	−0.230773	+	0.973008i	$0.574125\pi$
$998$	−1.63387e34	−0.528708
$999$	−3.00392e34	−0.960914

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	10.24.a.b.1.1	✓	2
5.2	odd	4		50.24.b.b.49.2		4
5.3	odd	4		50.24.b.b.49.3		4
5.4	even	2		50.24.a.c.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
10.24.a.b.1.1	✓	2	1.1	even	1	trivial
50.24.a.c.1.2		2	5.4	even	2
50.24.b.b.49.2		4	5.2	odd	4
50.24.b.b.49.3		4	5.3	odd	4

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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 10 = 2 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 24 \)
Character orbit:	\([\chi]\)	\(=\)	10.a (trivial)

\(f(q)\)	\(=\)	\(q-2048.00 q^{2} +96597.1 q^{3} +4.19430e6 q^{4} -4.88281e7 q^{5} -1.97831e8 q^{6} +5.12983e9 q^{7} -8.58993e9 q^{8} -8.48122e10 q^{9} +1.00000e11 q^{10} +1.27816e12 q^{11} +4.05157e11 q^{12} +5.85852e11 q^{13} -1.05059e13 q^{14} -4.71665e12 q^{15} +1.75922e13 q^{16} -1.28261e14 q^{17} +1.73695e14 q^{18} -5.25349e14 q^{19} -2.04800e14 q^{20} +4.95527e14 q^{21} -2.61767e15 q^{22} -4.09420e14 q^{23} -8.29763e14 q^{24} +2.38419e15 q^{25} -1.19983e15 q^{26} -1.72866e16 q^{27} +2.15161e16 q^{28} +1.23428e17 q^{29} +9.65971e15 q^{30} +8.43658e16 q^{31} -3.60288e16 q^{32} +1.23466e17 q^{33} +2.62678e17 q^{34} -2.50480e17 q^{35} -3.55728e17 q^{36} +1.73772e18 q^{37} +1.07591e18 q^{38} +5.65916e16 q^{39} +4.19430e17 q^{40} +3.44259e18 q^{41} -1.01484e18 q^{42} -2.12762e18 q^{43} +5.36098e18 q^{44} +4.14122e18 q^{45} +8.38492e17 q^{46} +2.91020e19 q^{47} +1.69935e18 q^{48} -1.05356e18 q^{49} -4.88281e18 q^{50} -1.23896e19 q^{51} +2.45724e18 q^{52} +9.13857e19 q^{53} +3.54029e19 q^{54} -6.24100e19 q^{55} -4.40649e19 q^{56} -5.07471e19 q^{57} -2.52781e20 q^{58} -1.56524e20 q^{59} -1.97831e19 q^{60} -1.87132e20 q^{61} -1.72781e20 q^{62} -4.35072e20 q^{63} +7.37870e19 q^{64} -2.86061e19 q^{65} -2.52859e20 q^{66} +8.07966e19 q^{67} -5.37965e20 q^{68} -3.95488e19 q^{69} +5.12983e20 q^{70} +2.90638e21 q^{71} +7.28531e20 q^{72} +7.57899e20 q^{73} -3.55884e21 q^{74} +2.30305e20 q^{75} -2.20347e21 q^{76} +6.55673e21 q^{77} -1.15900e20 q^{78} +3.63951e21 q^{79} -8.58993e20 q^{80} +6.31466e21 q^{81} -7.05043e21 q^{82} +2.01482e21 q^{83} +2.07839e21 q^{84} +6.26274e21 q^{85} +4.35736e21 q^{86} +1.19228e22 q^{87} -1.09793e22 q^{88} +7.78361e21 q^{89} -8.48122e21 q^{90} +3.00532e21 q^{91} -1.71723e21 q^{92} +8.14949e21 q^{93} -5.96009e22 q^{94} +2.56518e22 q^{95} -3.48028e21 q^{96} +7.35687e22 q^{97} +2.15770e21 q^{98} -1.08403e23 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 4096 q^{2} + 686484 q^{3} + 8388608 q^{4} - 97656250 q^{5} - 1405919232 q^{6} - 3529595108 q^{7} - 17179869184 q^{8} + 169011226674 q^{9} + 200000000000 q^{10} + 936557269824 q^{11} + 2879322587136 q^{12}+ \cdots - 19\!\cdots\!12 q^{99}+O(q^{100}) \) 2 * q - 4096 * q^2 + 686484 * q^3 + 8388608 * q^4 - 97656250 * q^5 - 1405919232 * q^6 - 3529595108 * q^7 - 17179869184 * q^8 + 169011226674 * q^9 + 200000000000 * q^10 + 936557269824 * q^11 + 2879322587136 * q^12 + 9961846393684 * q^13 + 7228610781184 * q^14 - 33519726562500 * q^15 + 35184372088832 * q^16 - 1609709739468 * q^17 - 346134992228352 * q^18 - 256914240498200 * q^19 - 409600000000000 * q^20 - 4612556435458536 * q^21 - 1918069288599552 * q^22 + 3594102326172564 * q^23 - 5896852658454528 * q^24 + 4768371582031250 * q^25 - 20401861414264832 * q^26 + 76906718569871640 * q^27 - 14804194879864832 * q^28 + 195470005256002620 * q^29 + 68648400000000000 * q^30 + 168811393572212104 * q^31 - 72057594037927936 * q^32 - 78039073845355392 * q^33 + 3296685546430464 * q^34 + 172343511132812500 * q^35 + 708884464083664896 * q^36 + 914879862377868532 * q^37 + 526160364540313600 * q^38 + 5587367999460857928 * q^39 + 838860800000000000 * q^40 + 1944225537689591724 * q^41 + 9446515579819081728 * q^42 + 2162030450882223364 * q^43 + 3928205903051882496 * q^44 - 8252501302441406250 * q^45 - 7360721564001411072 * q^46 + 20899427956391479692 * q^47 + 12076754244514873344 * q^48 + 46563376335520673946 * q^49 - 9765625000000000000 * q^50 + 62320269928250619144 * q^51 + 41783012176414375936 * q^52 + 72675644730523142244 * q^53 - 157504959631097118720 * q^54 - 45730335440625000000 * q^55 + 30318991113963175936 * q^56 + 107598748127858096400 * q^57 - 400322570764293365760 * q^58 - 261263082885806125560 * q^59 - 140591923200000000000 * q^60 - 340922118994570959596 * q^61 - 345725734035890388992 * q^62 - 2633037798049393980996 * q^63 + 147573952589676412928 * q^64 - 486418280941601562500 * q^65 + 159824023235287842816 * q^66 + 1719100191085929833452 * q^67 - 6751611999089590272 * q^68 + 2322076789711913279688 * q^69 - 352959510800000000000 * q^70 + 5715571620816449768664 * q^71 - 1451795382443345707008 * q^72 - 1090320686515726670876 * q^73 - 1873673958149874753536 * q^74 + 1636705398559570312500 * q^75 - 1077576426578562252800 * q^76 + 9514791828109879327104 * q^77 - 11442929662895837036544 * q^78 - 5111367769184022959120 * q^79 - 1717986918400000000000 * q^80 + 37982300618876935787082 * q^81 - 3981773901188283850752 * q^82 + 8751494681922030765444 * q^83 - 19346463907469479378944 * q^84 + 78599108372460937500 * q^85 - 4427838363406793449472 * q^86 + 54419346040895445239640 * q^87 - 8044965689450255351808 * q^88 + 24334798769961205033620 * q^89 + 16901122667400000000000 * q^90 - 78185419196088395301736 * q^91 + 15074757763074889875456 * q^92 + 57962850856840838879568 * q^93 - 42802028454689750409216 * q^94 + 12544640649326171875000 * q^95 - 24733192692766460608512 * q^96 + 28745948397303569150212 * q^97 - 95361794735146340241408 * q^98 - 195109350721035124600512 * q^99

Introduction

L-functions

Modular forms

Varieties

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Database

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