LMFDB - Embedded newform 10.24.a.b.1.2

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			1.2
Root			$-170.781$ 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)

$f(q)$	$=$	\(q-2048.00 q^{2} +589887. q^{3} +4.19430e6 q^{4} -4.88281e7 q^{5} -1.20809e9 q^{6} -8.65943e9 q^{7} -8.58993e9 q^{8} +2.53823e11 q^{9} +1.00000e11 q^{10} -3.41600e11 q^{11} +2.47417e12 q^{12} +9.37599e12 q^{13} +1.77345e13 q^{14} -2.88031e13 q^{15} +1.75922e13 q^{16} +1.26651e14 q^{17} -5.19830e14 q^{18} +2.68434e14 q^{19} -2.04800e14 q^{20} -5.10808e15 q^{21} +6.99597e14 q^{22} +4.00352e15 q^{23} -5.06709e15 q^{24} +2.38419e15 q^{25} -1.92020e16 q^{26} +9.41933e16 q^{27} -3.63203e16 q^{28} +7.20419e16 q^{29} +5.89887e16 q^{30} +8.44456e16 q^{31} -3.60288e16 q^{32} -2.01505e17 q^{33} -2.59382e17 q^{34} +4.22824e17 q^{35} +1.06461e18 q^{36} -8.22837e17 q^{37} -5.49753e17 q^{38} +5.53078e18 q^{39} +4.19430e17 q^{40} -1.49837e18 q^{41} +1.04614e19 q^{42} +4.28965e18 q^{43} -1.43277e18 q^{44} -1.23937e19 q^{45} -8.19921e18 q^{46} -8.20255e18 q^{47} +1.03774e19 q^{48} +4.76169e19 q^{49} -4.88281e18 q^{50} +7.47099e19 q^{51} +3.93258e19 q^{52} -1.87100e19 q^{53} -1.92908e20 q^{54} +1.66797e19 q^{55} +7.43839e19 q^{56} +1.58346e20 q^{57} -1.47542e20 q^{58} -1.04739e20 q^{59} -1.20809e20 q^{60} -1.53791e20 q^{61} -1.72945e20 q^{62} -2.19797e21 q^{63} +7.37870e19 q^{64} -4.57812e20 q^{65} +4.12683e20 q^{66} +1.63830e21 q^{67} +5.31214e20 q^{68} +2.36163e21 q^{69} -8.65943e20 q^{70} +2.80919e21 q^{71} -2.18033e21 q^{72} -1.84822e21 q^{73} +1.68517e21 q^{74} +1.40640e21 q^{75} +1.12589e21 q^{76} +2.95806e21 q^{77} -1.13270e22 q^{78} -8.75087e21 q^{79} -8.58993e20 q^{80} +3.16676e22 q^{81} +3.06866e21 q^{82} +6.73667e21 q^{83} -2.14249e22 q^{84} -6.18414e21 q^{85} -8.78520e21 q^{86} +4.24965e22 q^{87} +2.93432e21 q^{88} +1.65512e22 q^{89} +2.53823e22 q^{90} -8.11907e22 q^{91} +1.67920e22 q^{92} +4.98134e22 q^{93} +1.67988e22 q^{94} -1.31071e22 q^{95} -2.12529e22 q^{96} -4.48228e22 q^{97} -9.75195e22 q^{98} -8.67060e22 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	589887.	1.92254	0.961268	−	0.275616i	$-0.0888820\pi$
$3$	589887.	1.92254	0.961268	+	0.275616i	$0.0888820\pi$
$4$	4.19430e6	0.500000
$5$	−4.88281e7	−0.447214
$5$	−4.88281e7	−0.447214
$6$	−1.20809e9	−1.35944
$7$	−8.65943e9	−1.65524	−0.827621	−	0.561287i	$-0.810307\pi$
$7$	−8.65943e9	−1.65524	−0.827621	+	0.561287i	$0.810307\pi$
$8$	−8.58993e9	−0.353553
$9$	2.53823e11	2.69614
$10$	1.00000e11	0.316228
$11$	−3.41600e11	−0.360996	−0.180498	−	0.983575i	$-0.557771\pi$
$11$	−3.41600e11	−0.360996	−0.180498	+	0.983575i	$0.557771\pi$
$12$	2.47417e12	0.961268
$13$	9.37599e12	1.45100	0.725502	−	0.688220i	$-0.241608\pi$
$13$	9.37599e12	1.45100	0.725502	+	0.688220i	$0.241608\pi$
$14$	1.77345e13	1.17043
$15$	−2.88031e13	−0.859784
$16$	1.75922e13	0.250000
$17$	1.26651e14	0.896286	0.448143	−	0.893962i	$-0.352085\pi$
$17$	1.26651e14	0.896286	0.448143	+	0.893962i	$0.352085\pi$
$18$	−5.19830e14	−1.90646
$19$	2.68434e14	0.528654	0.264327	−	0.964433i	$-0.414850\pi$
$19$	2.68434e14	0.528654	0.264327	+	0.964433i	$0.414850\pi$
$20$	−2.04800e14	−0.223607
$21$	−5.10808e15	−3.18226
$22$	6.99597e14	0.255262
$23$	4.00352e15	0.876137	0.438069	−	0.898942i	$-0.355663\pi$
$23$	4.00352e15	0.876137	0.438069	+	0.898942i	$0.355663\pi$
$24$	−5.06709e15	−0.679719
$25$	2.38419e15	0.200000
$26$	−1.92020e16	−1.02602
$27$	9.41933e16	3.26089
$28$	−3.63203e16	−0.827621
$29$	7.20419e16	1.09650	0.548249	−	0.836315i	$-0.315295\pi$
$29$	7.20419e16	1.09650	0.548249	+	0.836315i	$0.315295\pi$
$30$	5.89887e16	0.607959
$31$	8.44456e16	0.596922	0.298461	−	0.954422i	$-0.403527\pi$
$31$	8.44456e16	0.596922	0.298461	+	0.954422i	$0.403527\pi$
$32$	−3.60288e16	−0.176777
$33$	−2.01505e17	−0.694027
$34$	−2.59382e17	−0.633770
$35$	4.22824e17	0.740247
$36$	1.06461e18	1.34807
$37$	−8.22837e17	−0.760316	−0.380158	−	0.924922i	$-0.624130\pi$
$37$	−8.22837e17	−0.760316	−0.380158	+	0.924922i	$0.624130\pi$
$38$	−5.49753e17	−0.373815
$39$	5.53078e18	2.78961
$40$	4.19430e17	0.158114
$41$	−1.49837e18	−0.425211	−0.212605	−	0.977138i	$-0.568195\pi$
$41$	−1.49837e18	−0.425211	−0.212605	+	0.977138i	$0.568195\pi$
$42$	1.04614e19	2.25020
$43$	4.28965e18	0.703938	0.351969	−	0.936012i	$-0.385512\pi$
$43$	4.28965e18	0.703938	0.351969	+	0.936012i	$0.385512\pi$
$44$	−1.43277e18	−0.180498
$45$	−1.23937e19	−1.20575
$46$	−8.19921e18	−0.619523
$47$	−8.20255e18	−0.483976	−0.241988	−	0.970279i	$-0.577799\pi$
$47$	−8.20255e18	−0.483976	−0.241988	+	0.970279i	$0.577799\pi$
$48$	1.03774e19	0.480634
$49$	4.76169e19	1.73983
$50$	−4.88281e18	−0.141421
$51$	7.47099e19	1.72314
$52$	3.93258e19	0.725502
$53$	−1.87100e19	−0.277269	−0.138635	−	0.990344i	$-0.544271\pi$
$53$	−1.87100e19	−0.277269	−0.138635	+	0.990344i	$0.544271\pi$
$54$	−1.92908e20	−2.30580
$55$	1.66797e19	0.161442
$56$	7.43839e19	0.585217
$57$	1.58346e20	1.01636
$58$	−1.47542e20	−0.775341
$59$	−1.04739e20	−0.452178	−0.226089	−	0.974107i	$-0.572594\pi$
$59$	−1.04739e20	−0.452178	−0.226089	+	0.974107i	$0.572594\pi$
$60$	−1.20809e20	−0.429892
$61$	−1.53791e20	−0.452519	−0.226259	−	0.974067i	$-0.572650\pi$
$61$	−1.53791e20	−0.452519	−0.226259	+	0.974067i	$0.572650\pi$
$62$	−1.72945e20	−0.422088
$63$	−2.19797e21	−4.46277
$64$	7.37870e19	0.125000
$65$	−4.57812e20	−0.648909
$66$	4.12683e20	0.490751
$67$	1.63830e21	1.63883	0.819415	−	0.573200i	$-0.194298\pi$
$67$	1.63830e21	1.63883	0.819415	+	0.573200i	$0.194298\pi$
$68$	5.31214e20	0.448143
$69$	2.36163e21	1.68440
$70$	−8.65943e20	−0.523434
$71$	2.80919e21	1.44248	0.721241	−	0.692684i	$-0.243572\pi$
$71$	2.80919e21	1.44248	0.721241	+	0.692684i	$0.243572\pi$
$72$	−2.18033e21	−0.953230
$73$	−1.84822e21	−0.689510	−0.344755	−	0.938693i	$-0.612038\pi$
$73$	−1.84822e21	−0.689510	−0.344755	+	0.938693i	$0.612038\pi$
$74$	1.68517e21	0.537625
$75$	1.40640e21	0.384507
$76$	1.12589e21	0.264327
$77$	2.95806e21	0.597535
$78$	−1.13270e22	−1.97255
$79$	−8.75087e21	−1.31625	−0.658127	−	0.752907i	$-0.728651\pi$
$79$	−8.75087e21	−1.31625	−0.658127	+	0.752907i	$0.728651\pi$
$80$	−8.58993e20	−0.111803
$81$	3.16676e22	3.57304
$82$	3.06866e21	0.300669
$83$	6.73667e21	0.574179	0.287090	−	0.957904i	$-0.407312\pi$
$83$	6.73667e21	0.574179	0.287090	+	0.957904i	$0.407312\pi$
$84$	−2.14249e22	−1.59113
$85$	−6.18414e21	−0.400831
$86$	−8.78520e21	−0.497759
$87$	4.24965e22	2.10806
$88$	2.93432e21	0.127631
$89$	1.65512e22	0.632185	0.316092	−	0.948728i	$-0.397629\pi$
$89$	1.65512e22	0.632185	0.316092	+	0.948728i	$0.397629\pi$
$90$	2.53823e22	0.852595
$91$	−8.11907e22	−2.40176
$92$	1.67920e22	0.438069
$93$	4.98134e22	1.14760
$94$	1.67988e22	0.342223
$95$	−1.31071e22	−0.236421
$96$	−2.12529e22	−0.339859
$97$	−4.48228e22	−0.636244	−0.318122	−	0.948050i	$-0.603052\pi$
$97$	−4.48228e22	−0.636244	−0.318122	+	0.948050i	$0.603052\pi$
$98$	−9.75195e22	−1.23024
$99$	−8.67060e22	−0.973295
$100$	1.00000e22	0.100000
$101$	−1.48622e23	−1.32552	−0.662760	−	0.748832i	$-0.730615\pi$
$101$	−1.48622e23	−1.32552	−0.662760	+	0.748832i	$0.730615\pi$
$102$	−1.53006e23	−1.21845
$103$	6.64435e22	0.472960	0.236480	−	0.971636i	$-0.424006\pi$
$103$	6.64435e22	0.472960	0.236480	+	0.971636i	$0.424006\pi$
$104$	−8.05392e22	−0.513008
$105$	2.49418e23	1.42315
$106$	3.83181e22	0.196059
$107$	3.18955e22	0.146493	0.0732463	−	0.997314i	$-0.476664\pi$
$107$	3.18955e22	0.146493	0.0732463	+	0.997314i	$0.476664\pi$
$108$	3.95075e23	1.63045
$109$	1.27271e22	0.0472418	0.0236209	−	0.999721i	$-0.492481\pi$
$109$	1.27271e22	0.0472418	0.0236209	+	0.999721i	$0.492481\pi$
$110$	−3.41600e22	−0.114157
$111$	−4.85381e23	−1.46173
$112$	−1.52338e23	−0.413811
$113$	1.29270e23	0.317027	0.158513	−	0.987357i	$-0.449330\pi$
$113$	1.29270e23	0.317027	0.158513	+	0.987357i	$0.449330\pi$
$114$	−3.24292e23	−0.718672
$115$	−1.95484e23	−0.391820
$116$	3.02165e23	0.548249
$117$	2.37985e24	3.91211
$118$	2.14505e23	0.319738
$119$	−1.09673e24	−1.48357
$120$	2.47417e23	0.303980
$121$	−7.78740e23	−0.869682
$122$	3.14963e23	0.319979
$123$	−8.83868e23	−0.817482
$124$	3.54191e23	0.298461
$125$	−1.16415e23	−0.0894427
$126$	4.50143e24	3.15566
$127$	−2.37120e24	−1.51784	−0.758918	−	0.651187i	$-0.774271\pi$
$127$	−2.37120e24	−1.51784	−0.758918	+	0.651187i	$0.774271\pi$
$128$	−1.51116e23	−0.0883883
$129$	2.53041e24	1.35335
$130$	9.37599e23	0.458848
$131$	2.08233e24	0.933103	0.466551	−	0.884494i	$-0.345496\pi$
$131$	2.08233e24	0.933103	0.466551	+	0.884494i	$0.345496\pi$
$132$	−8.45175e23	−0.347013
$133$	−2.32449e24	−0.875051
$134$	−3.35525e24	−1.15883
$135$	−4.59928e24	−1.45832
$136$	−1.08793e24	−0.316885
$137$	−2.45853e24	−0.658248	−0.329124	−	0.944287i	$-0.606753\pi$
$137$	−2.45853e24	−0.658248	−0.329124	+	0.944287i	$0.606753\pi$
$138$	−4.83661e24	−1.19105
$139$	2.83898e24	0.643417	0.321708	−	0.946839i	$-0.395743\pi$
$139$	2.83898e24	0.643417	0.321708	+	0.946839i	$0.395743\pi$
$140$	1.77345e24	0.370124
$141$	−4.83858e24	−0.930461
$142$	−5.75323e24	−1.01999
$143$	−3.20284e24	−0.523806
$144$	4.46531e24	0.674036
$145$	−3.51767e24	−0.490369
$146$	3.78515e24	0.487557
$147$	2.80886e25	3.34488
$148$	−3.45123e24	−0.380158
$149$	−1.04342e25	−1.06370	−0.531849	−	0.846839i	$-0.678503\pi$
$149$	−1.04342e25	−1.06370	−0.531849	+	0.846839i	$0.678503\pi$
$150$	−2.88031e24	−0.271888
$151$	−3.94859e24	−0.345308	−0.172654	−	0.984982i	$-0.555234\pi$
$151$	−3.94859e24	−0.345308	−0.172654	+	0.984982i	$0.555234\pi$
$152$	−2.30583e24	−0.186907
$153$	3.21470e25	2.41652
$154$	−6.05811e24	−0.422521
$155$	−4.12332e24	−0.266952
$156$	2.31978e25	1.39480
$157$	−1.85824e25	−1.03814	−0.519070	−	0.854732i	$-0.673722\pi$
$157$	−1.85824e25	−1.03814	−0.519070	+	0.854732i	$0.673722\pi$
$158$	1.79218e25	0.930732
$159$	−1.10368e25	−0.533060
$160$	1.75922e24	0.0790569
$161$	−3.46682e25	−1.45022
$162$	−6.48553e25	−2.52652
$163$	4.00527e25	1.45370	0.726849	−	0.686798i	$-0.240984\pi$
$163$	4.00527e25	1.45370	0.726849	+	0.686798i	$0.240984\pi$
$164$	−6.28461e24	−0.212605
$165$	9.83913e24	0.310378
$166$	−1.37967e25	−0.406006
$167$	7.99548e24	0.219586	0.109793	−	0.993954i	$-0.464981\pi$
$167$	7.99548e24	0.219586	0.109793	+	0.993954i	$0.464981\pi$
$168$	4.38781e25	1.12510
$169$	4.61554e25	1.10541
$170$	1.26651e25	0.283431
$171$	6.81349e25	1.42533
$172$	1.79921e25	0.351969
$173$	8.98445e25	1.64423	0.822113	−	0.569325i	$-0.192795\pi$
$173$	8.98445e25	1.64423	0.822113	+	0.569325i	$0.192795\pi$
$174$	−8.70329e25	−1.49062
$175$	−2.06457e25	−0.331049
$176$	−6.00949e24	−0.0902489
$177$	−6.17841e25	−0.869329
$178$	−3.38968e25	−0.447022
$179$	1.18230e26	1.46190	0.730949	−	0.682433i	$-0.239078\pi$
$179$	1.18230e26	1.46190	0.730949	+	0.682433i	$0.239078\pi$
$180$	−5.19830e25	−0.602876
$181$	−1.17668e26	−1.28043	−0.640213	−	0.768198i	$-0.721154\pi$
$181$	−1.17668e26	−1.28043	−0.640213	+	0.768198i	$0.721154\pi$
$182$	1.66279e26	1.69830
$183$	−9.07191e25	−0.869983
$184$	−3.43900e25	−0.309761
$185$	4.01776e25	0.340024
$186$	−1.02018e26	−0.811478
$187$	−4.32640e25	−0.323555
$188$	−3.44040e25	−0.241988
$189$	−8.15660e26	−5.39757
$190$	2.68434e25	0.167175
$191$	2.94896e26	1.72896	0.864480	−	0.502668i	$-0.167648\pi$
$191$	2.94896e26	1.72896	0.864480	+	0.502668i	$0.167648\pi$
$192$	4.35260e25	0.240317
$193$	1.41854e26	0.737789	0.368894	−	0.929471i	$-0.379736\pi$
$193$	1.41854e26	0.737789	0.368894	+	0.929471i	$0.379736\pi$
$194$	9.17970e25	0.449892
$195$	−2.70057e26	−1.24755
$196$	1.99720e26	0.869915
$197$	−1.89037e25	−0.0776580	−0.0388290	−	0.999246i	$-0.512363\pi$
$197$	−1.89037e25	−0.0776580	−0.0388290	+	0.999246i	$0.512363\pi$
$198$	1.77574e26	0.688224
$199$	−4.29000e26	−1.56909	−0.784543	−	0.620074i	$-0.787102\pi$
$199$	−4.29000e26	−1.56909	−0.784543	+	0.620074i	$0.787102\pi$
$200$	−2.04800e25	−0.0707107
$201$	9.66414e26	3.15071
$202$	3.04377e26	0.937284
$203$	−6.23841e26	−1.81497
$204$	3.13356e26	0.861571
$205$	7.31625e25	0.190160
$206$	−1.36076e26	−0.334433
$207$	1.01619e27	2.36219
$208$	1.64944e26	0.362751
$209$	−9.16971e25	−0.190842
$210$	−5.10808e26	−1.00632
$211$	−5.54819e26	−1.03491	−0.517456	−	0.855710i	$-0.673121\pi$
$211$	−5.54819e26	−1.03491	−0.517456	+	0.855710i	$0.673121\pi$
$212$	−7.84756e25	−0.138635
$213$	1.65711e27	2.77322
$214$	−6.53220e25	−0.103586
$215$	−2.09456e26	−0.314811
$216$	−8.09114e26	−1.15290
$217$	−7.31251e26	−0.988051
$218$	−2.60652e25	−0.0334050
$219$	−1.09024e27	−1.32561
$220$	6.99597e25	0.0807211
$221$	1.18748e27	1.30052
$222$	9.94060e26	1.03360
$223$	−1.18597e26	−0.117103	−0.0585517	−	0.998284i	$-0.518648\pi$
$223$	−1.18597e26	−0.117103	−0.0585517	+	0.998284i	$0.518648\pi$
$224$	3.11989e26	0.292608
$225$	6.05162e26	0.539228
$226$	−2.64745e26	−0.224172
$227$	−4.65610e26	−0.374736	−0.187368	−	0.982290i	$-0.559996\pi$
$227$	−4.65610e26	−0.374736	−0.187368	+	0.982290i	$0.559996\pi$
$228$	6.64151e26	0.508178
$229$	−9.14229e26	−0.665192	−0.332596	−	0.943069i	$-0.607925\pi$
$229$	−9.14229e26	−0.665192	−0.332596	+	0.943069i	$0.607925\pi$
$230$	4.00352e26	0.277059
$231$	1.74492e27	1.14878
$232$	−6.18835e26	−0.387671
$233$	1.71939e25	0.0102514	0.00512569	−	0.999987i	$-0.498368\pi$
$233$	1.71939e25	0.0102514	0.00512569	+	0.999987i	$0.498368\pi$
$234$	−4.87393e27	−2.76628
$235$	4.00515e26	0.216441
$236$	−4.39307e26	−0.226089
$237$	−5.16203e27	−2.53055
$238$	2.24610e27	1.04904
$239$	−1.37899e27	−0.613741	−0.306870	−	0.951751i	$-0.599282\pi$
$239$	−1.37899e27	−0.613741	−0.306870	+	0.951751i	$0.599282\pi$
$240$	−5.06709e26	−0.214946
$241$	−4.72718e27	−1.91164	−0.955821	−	0.293950i	$-0.905030\pi$
$241$	−4.72718e27	−1.91164	−0.955821	+	0.293950i	$0.905030\pi$
$242$	1.59486e27	0.614958
$243$	9.81267e27	3.60840
$244$	−6.45044e26	−0.226259
$245$	−2.32505e27	−0.778075
$246$	1.81016e27	0.578047
$247$	2.51684e27	0.767079
$248$	−7.25382e26	−0.211044
$249$	3.97388e27	1.10388
$250$	2.38419e26	0.0632456
$251$	−4.79993e27	−1.21615	−0.608075	−	0.793879i	$-0.708058\pi$
$251$	−4.79993e27	−1.21615	−0.608075	+	0.793879i	$0.708058\pi$
$252$	−9.21894e27	−2.23139
$253$	−1.36760e27	−0.316282
$254$	4.85621e27	1.07327
$255$	−3.64794e27	−0.770613
$256$	3.09485e26	0.0625000
$257$	9.07525e27	1.75238	0.876189	−	0.481968i	$-0.160078\pi$
$257$	9.07525e27	1.75238	0.876189	+	0.481968i	$0.160078\pi$
$258$	−5.18228e27	−0.956960
$259$	7.12530e27	1.25851
$260$	−1.92020e27	−0.324454
$261$	1.82859e28	2.95632
$262$	−4.26461e27	−0.659803
$263$	−8.09758e25	−0.0119912	−0.00599562	−	0.999982i	$-0.501908\pi$
$263$	−8.09758e25	−0.0119912	−0.00599562	+	0.999982i	$0.501908\pi$
$264$	1.73092e27	0.245375
$265$	9.13576e26	0.123999
$266$	4.76055e27	0.618754
$267$	9.76333e27	1.21540
$268$	6.87154e27	0.819415
$269$	−1.72812e28	−1.97435	−0.987173	−	0.159656i	$-0.948962\pi$
$269$	−1.72812e28	−1.97435	−0.987173	+	0.159656i	$0.948962\pi$
$270$	9.41933e27	1.03119
$271$	−1.25531e28	−1.31706	−0.658528	−	0.752557i	$-0.728820\pi$
$271$	−1.25531e28	−1.31706	−0.658528	+	0.752557i	$0.728820\pi$
$272$	2.22807e27	0.224072
$273$	−4.78934e28	−4.61748
$274$	5.03507e27	0.465451
$275$	−8.14438e26	−0.0721991
$276$	9.90538e27	0.842202
$277$	−5.00554e27	−0.408257	−0.204129	−	0.978944i	$-0.565436\pi$
$277$	−5.00554e27	−0.408257	−0.204129	+	0.978944i	$0.565436\pi$
$278$	−5.81423e27	−0.454964
$279$	2.14343e28	1.60939
$280$	−3.63203e27	−0.261717
$281$	−2.40666e27	−0.166453	−0.0832265	−	0.996531i	$-0.526522\pi$
$281$	−2.40666e27	−0.166453	−0.0832265	+	0.996531i	$0.526522\pi$
$282$	9.90941e27	0.657935
$283$	2.62143e28	1.67107	0.835535	−	0.549438i	$-0.185158\pi$
$283$	2.62143e28	1.67107	0.835535	+	0.549438i	$0.185158\pi$
$284$	1.17826e28	0.721241
$285$	−7.73173e27	−0.454528
$286$	6.55941e27	0.370387
$287$	1.29750e28	0.703827
$288$	−9.14495e27	−0.476615
$289$	−3.92704e27	−0.196671
$290$	7.20419e27	0.346743
$291$	−2.64404e28	−1.22320
$292$	−7.75199e27	−0.344755
$293$	−3.01791e27	−0.129041	−0.0645206	−	0.997916i	$-0.520552\pi$
$293$	−3.01791e27	−0.129041	−0.0645206	+	0.997916i	$0.520552\pi$
$294$	−5.75255e28	−2.36519
$295$	5.11420e27	0.202220
$296$	7.06812e27	0.268812
$297$	−3.21764e28	−1.17717
$298$	2.13693e28	0.752149
$299$	3.75370e28	1.27128
$300$	5.89887e27	0.192254
$301$	−3.71459e28	−1.16519
$302$	8.08671e27	0.244170
$303$	−8.76699e28	−2.54836
$304$	4.72235e27	0.132164
$305$	7.50931e27	0.202373
$306$	−6.58371e28	−1.70873
$307$	−2.03128e28	−0.507784	−0.253892	−	0.967233i	$-0.581711\pi$
$307$	−2.03128e28	−0.507784	−0.253892	+	0.967233i	$0.581711\pi$
$308$	1.24070e28	0.298768
$309$	3.91941e28	0.909282
$310$	8.44456e27	0.188763
$311$	6.48885e28	1.39773	0.698865	−	0.715254i	$-0.253689\pi$
$311$	6.48885e28	1.39773	0.698865	+	0.715254i	$0.253689\pi$
$312$	−4.75090e28	−0.986275
$313$	4.80190e28	0.960845	0.480423	−	0.877037i	$-0.340483\pi$
$313$	4.80190e28	0.960845	0.480423	+	0.877037i	$0.340483\pi$
$314$	3.80568e28	0.734076
$315$	1.07323e29	1.99581
$316$	−3.67038e28	−0.658127
$317$	5.25019e28	0.907807	0.453903	−	0.891051i	$-0.350031\pi$
$317$	5.25019e28	0.907807	0.453903	+	0.891051i	$0.350031\pi$
$318$	2.26034e28	0.376931
$319$	−2.46095e28	−0.395831
$320$	−3.60288e27	−0.0559017
$321$	1.88147e28	0.281637
$322$	7.10005e28	1.02546
$323$	3.39975e28	0.473825
$324$	1.32824e29	1.78652
$325$	2.23541e28	0.290201
$326$	−8.20279e28	−1.02792
$327$	7.50758e27	0.0908240
$328$	1.28709e28	0.150335
$329$	7.10294e28	0.801097
$330$	−2.01505e28	−0.219471
$331$	−1.29656e28	−0.136386	−0.0681930	−	0.997672i	$-0.521723\pi$
$331$	−1.29656e28	−0.136386	−0.0681930	+	0.997672i	$0.521723\pi$
$332$	2.82557e28	0.287090
$333$	−2.08855e29	−2.04992
$334$	−1.63747e28	−0.155271
$335$	−7.99953e28	−0.732907
$336$	−8.98624e28	−0.795566
$337$	9.04429e28	0.773803	0.386902	−	0.922121i	$-0.373545\pi$
$337$	9.04429e28	0.773803	0.386902	+	0.922121i	$0.373545\pi$
$338$	−9.45262e28	−0.781646
$339$	7.62548e28	0.609495
$340$	−2.59382e28	−0.200416
$341$	−2.88466e28	−0.215486
$342$	−1.39540e29	−1.00786
$343$	−1.75338e29	−1.22460
$344$	−3.68478e28	−0.248880
$345$	−1.15314e29	−0.753289
$346$	−1.84002e29	−1.16264
$347$	−1.49288e29	−0.912504	−0.456252	−	0.889851i	$-0.650808\pi$
$347$	−1.49288e29	−0.912504	−0.456252	+	0.889851i	$0.650808\pi$
$348$	1.78243e29	1.05403
$349$	−1.52139e29	−0.870459	−0.435230	−	0.900319i	$-0.643333\pi$
$349$	−1.52139e29	−0.870459	−0.435230	+	0.900319i	$0.643333\pi$
$350$	4.22824e28	0.234087
$351$	8.83156e29	4.73157
$352$	1.23074e28	0.0638156
$353$	2.49410e29	1.25171	0.625857	−	0.779938i	$-0.284750\pi$
$353$	2.49410e29	1.25171	0.625857	+	0.779938i	$0.284750\pi$
$354$	1.26534e29	0.614708
$355$	−1.37168e29	−0.645098
$356$	6.94207e28	0.316092
$357$	−6.46945e29	−2.85222
$358$	−2.42134e29	−1.03372
$359$	3.91702e29	1.61946	0.809728	−	0.586805i	$-0.199614\pi$
$359$	3.91702e29	1.61946	0.809728	+	0.586805i	$0.199614\pi$
$360$	1.06461e29	0.426298
$361$	−1.85773e29	−0.720525
$362$	2.40984e29	0.905398
$363$	−4.59368e29	−1.67199
$364$	−3.40539e29	−1.20088
$365$	9.02451e28	0.308358
$366$	1.85793e29	0.615171
$367$	1.79517e29	0.576032	0.288016	−	0.957626i	$-0.407004\pi$
$367$	1.79517e29	0.576032	0.288016	+	0.957626i	$0.407004\pi$
$368$	7.04307e28	0.219034
$369$	−3.80321e29	−1.14643
$370$	−8.22837e28	−0.240433
$371$	1.62018e29	0.458948
$372$	2.08932e29	0.573802
$373$	−7.00737e29	−1.86597	−0.932983	−	0.359920i	$-0.882804\pi$
$373$	−7.00737e29	−1.86597	−0.932983	+	0.359920i	$0.882804\pi$
$374$	8.86048e28	0.228788
$375$	−6.86719e28	−0.171957
$376$	7.04594e28	0.171111
$377$	6.75464e29	1.59102
$378$	1.67047e30	3.81666
$379$	7.85722e28	0.174148	0.0870739	−	0.996202i	$-0.472248\pi$
$379$	7.85722e28	0.174148	0.0870739	+	0.996202i	$0.472248\pi$
$380$	−5.49753e28	−0.118211
$381$	−1.39874e30	−2.91809
$382$	−6.03947e29	−1.22256
$383$	4.36132e29	0.856707	0.428353	−	0.903611i	$-0.359094\pi$
$383$	4.36132e29	0.856707	0.428353	+	0.903611i	$0.359094\pi$
$384$	−8.91412e28	−0.169930
$385$	−1.44437e29	−0.267226
$386$	−2.90517e29	−0.521696
$387$	1.08881e30	1.89792
$388$	−1.88000e29	−0.318122
$389$	−8.02563e28	−0.131844	−0.0659218	−	0.997825i	$-0.520999\pi$
$389$	−8.02563e28	−0.131844	−0.0659218	+	0.997825i	$0.520999\pi$
$390$	5.53078e29	0.882151
$391$	5.07051e29	0.785270
$392$	−4.09026e29	−0.615122
$393$	1.22834e30	1.79392
$394$	3.87148e28	0.0549125
$395$	4.27289e29	0.588647
$396$	−3.63672e29	−0.486648
$397$	−1.82014e29	−0.236600	−0.118300	−	0.992978i	$-0.537744\pi$
$397$	−1.82014e29	−0.236600	−0.118300	+	0.992978i	$0.537744\pi$
$398$	8.78592e29	1.10951
$399$	−1.37118e30	−1.68232
$400$	4.19430e28	0.0500000
$401$	1.22321e30	1.41691	0.708454	−	0.705757i	$-0.249393\pi$
$401$	1.22321e30	1.41691	0.708454	+	0.705757i	$0.249393\pi$
$402$	−1.97922e30	−2.22789
$403$	7.91762e29	0.866137
$404$	−6.23364e29	−0.662760
$405$	−1.54627e30	−1.59791
$406$	1.27763e30	1.28338
$407$	2.81081e29	0.274471
$408$	−6.41753e29	−0.609223
$409$	−1.28273e30	−1.18391	−0.591954	−	0.805972i	$-0.701643\pi$
$409$	−1.28273e30	−1.18391	−0.591954	+	0.805972i	$0.701643\pi$
$410$	−1.49837e29	−0.134463
$411$	−1.45026e30	−1.26550
$412$	2.78684e29	0.236480
$413$	9.06979e29	0.748465
$414$	−2.08115e30	−1.67032
$415$	−3.28939e29	−0.256781
$416$	−3.37806e29	−0.256504
$417$	1.67468e30	1.23699
$418$	1.87796e29	0.134946
$419$	3.03804e29	0.212389	0.106194	−	0.994345i	$-0.466133\pi$
$419$	3.03804e29	0.212389	0.106194	+	0.994345i	$0.466133\pi$
$420$	1.04614e30	0.711576
$421$	1.27738e30	0.845427	0.422714	−	0.906263i	$-0.361078\pi$
$421$	1.27738e30	0.845427	0.422714	+	0.906263i	$0.361078\pi$
$422$	1.13627e30	0.731793
$423$	−2.08200e30	−1.30487
$424$	1.60718e29	0.0980296
$425$	3.01960e29	0.179257
$426$	−3.39375e30	−1.96097
$427$	1.33174e30	0.749029
$428$	1.33779e29	0.0732463
$429$	−1.88931e30	−1.00704
$430$	4.28965e29	0.222605
$431$	−1.22639e30	−0.619642	−0.309821	−	0.950795i	$-0.600269\pi$
$431$	−1.22639e30	−0.619642	−0.309821	+	0.950795i	$0.600269\pi$
$432$	1.65707e30	0.815223
$433$	−2.34066e30	−1.12132	−0.560658	−	0.828047i	$-0.689452\pi$
$433$	−2.34066e30	−1.12132	−0.560658	+	0.828047i	$0.689452\pi$
$434$	1.49760e30	0.698658
$435$	−2.07503e30	−0.942752
$436$	5.33815e28	0.0236209
$437$	1.07468e30	0.463174
$438$	2.23281e30	0.937346
$439$	2.33966e30	0.956779	0.478389	−	0.878148i	$-0.341221\pi$
$439$	2.33966e30	0.956779	0.478389	+	0.878148i	$0.341221\pi$
$440$	−1.43277e29	−0.0570784
$441$	1.20863e31	4.69083
$442$	−2.43196e30	−0.919603
$443$	−5.19485e30	−1.91395	−0.956974	−	0.290175i	$-0.906286\pi$
$443$	−5.19485e30	−1.91395	−0.956974	+	0.290175i	$0.906286\pi$
$444$	−2.03584e30	−0.730867
$445$	−8.08163e29	−0.282722
$446$	2.42888e29	0.0828046
$447$	−6.15502e30	−2.04500
$448$	−6.38953e29	−0.206905
$449$	8.46675e29	0.267229	0.133615	−	0.991033i	$-0.457342\pi$
$449$	8.46675e29	0.267229	0.133615	+	0.991033i	$0.457342\pi$
$450$	−1.23937e30	−0.381292
$451$	5.11842e29	0.153499
$452$	5.42198e29	0.158513
$453$	−2.32922e30	−0.663868
$454$	9.53569e29	0.264978
$455$	3.96439e30	1.07410
$456$	−1.36018e30	−0.359336
$457$	4.30243e30	1.10835	0.554176	−	0.832399i	$-0.313033\pi$
$457$	4.30243e30	1.10835	0.554176	+	0.832399i	$0.313033\pi$
$458$	1.87234e30	0.470362
$459$	1.19297e31	2.92269
$460$	−8.19921e29	−0.195910
$461$	5.59904e30	1.30483	0.652413	−	0.757863i	$-0.273757\pi$
$461$	5.59904e30	1.30483	0.652413	+	0.757863i	$0.273757\pi$
$462$	−3.57360e30	−0.812312
$463$	6.54677e30	1.45160	0.725798	−	0.687908i	$-0.241471\pi$
$463$	6.54677e30	1.45160	0.725798	+	0.687908i	$0.241471\pi$
$464$	1.26737e30	0.274125
$465$	−2.43229e30	−0.513224
$466$	−3.52132e28	−0.00724882
$467$	−2.46045e30	−0.494163	−0.247082	−	0.968995i	$-0.579472\pi$
$467$	−2.46045e30	−0.494163	−0.247082	+	0.968995i	$0.579472\pi$
$468$	9.98180e30	1.95606
$469$	−1.41868e31	−2.71266
$470$	−8.20255e29	−0.153047
$471$	−1.09615e31	−1.99586
$472$	8.99700e29	0.159869
$473$	−1.46534e30	−0.254119
$474$	1.05718e31	1.78937
$475$	6.39997e29	0.105731
$476$	−4.60001e30	−0.741786
$477$	−4.74904e30	−0.747558
$478$	2.82417e30	0.433980
$479$	−6.11043e30	−0.916671	−0.458336	−	0.888779i	$-0.651554\pi$
$479$	−6.11043e30	−0.916671	−0.458336	+	0.888779i	$0.651554\pi$
$480$	1.03774e30	0.151990
$481$	−7.71492e30	−1.10322
$482$	9.68127e30	1.35173
$483$	−2.04503e31	−2.78810
$484$	−3.26627e30	−0.434841
$485$	2.18861e30	0.284537
$486$	−2.00964e31	−2.55153
$487$	−5.95367e30	−0.738247	−0.369124	−	0.929380i	$-0.620342\pi$
$487$	−5.95367e30	−0.738247	−0.369124	+	0.929380i	$0.620342\pi$
$488$	1.32105e30	0.159990
$489$	2.36265e31	2.79478
$490$	4.76169e30	0.550182
$491$	−4.90871e30	−0.554026	−0.277013	−	0.960866i	$-0.589345\pi$
$491$	−4.90871e30	−0.554026	−0.277013	+	0.960866i	$0.589345\pi$
$492$	−3.70721e30	−0.408741
$493$	9.12419e30	0.982776
$494$	−5.15448e30	−0.542407
$495$	4.23369e30	0.435271
$496$	1.48558e30	0.149231
$497$	−2.43260e31	−2.38766
$498$	−8.13850e30	−0.780561
$499$	1.58005e29	0.0148087	0.00740433	−	0.999973i	$-0.497643\pi$
$499$	1.58005e29	0.0148087	0.00740433	+	0.999973i	$0.497643\pi$
$500$	−4.88281e29	−0.0447214
$501$	4.71643e30	0.422162
$502$	9.83026e30	0.859948
$503$	−7.88073e30	−0.673805	−0.336903	−	0.941539i	$-0.609379\pi$
$503$	−7.88073e30	−0.673805	−0.336903	+	0.941539i	$0.609379\pi$
$504$	1.88804e31	1.57783
$505$	7.25691e30	0.592790
$506$	2.80085e30	0.223645
$507$	2.72264e31	2.12520
$508$	−9.94552e30	−0.758918
$509$	−1.29230e31	−0.964070	−0.482035	−	0.876152i	$-0.660102\pi$
$509$	−1.29230e31	−0.964070	−0.482035	+	0.876152i	$0.660102\pi$
$510$	7.47099e30	0.544905
$511$	1.60045e31	1.14131
$512$	−6.33825e29	−0.0441942
$513$	2.52847e31	1.72388
$514$	−1.85861e31	−1.23912
$515$	−3.24431e30	−0.211514
$516$	1.06133e31	0.676673
$517$	2.80199e30	0.174713
$518$	−1.45926e31	−0.889899
$519$	5.29981e31	3.16108
$520$	3.93258e30	0.229424
$521$	2.00059e31	1.14163	0.570814	−	0.821079i	$-0.306628\pi$
$521$	2.00059e31	1.14163	0.570814	+	0.821079i	$0.306628\pi$
$522$	−3.74495e31	−2.09043
$523$	−3.24415e31	−1.77146	−0.885731	−	0.464199i	$-0.846342\pi$
$523$	−3.24415e31	−1.77146	−0.885731	+	0.464199i	$0.846342\pi$
$524$	8.73392e30	0.466551
$525$	−1.21786e31	−0.636453
$526$	1.65838e29	0.00847908
$527$	1.06951e31	0.535013
$528$	−3.54492e30	−0.173507
$529$	−4.85228e30	−0.232383
$530$	−1.87100e30	−0.0876803
$531$	−2.65852e31	−1.21914
$532$	−9.74961e30	−0.437525
$533$	−1.40487e31	−0.616982
$534$	−1.99953e31	−0.859416
$535$	−1.55740e30	−0.0655135
$536$	−1.40729e31	−0.579414
$537$	6.97422e31	2.81055
$538$	3.53919e31	1.39607
$539$	−1.62659e31	−0.628071
$540$	−1.92908e31	−0.729158
$541$	−3.62031e31	−1.33961	−0.669804	−	0.742538i	$-0.733622\pi$
$541$	−3.62031e31	−1.33961	−0.669804	+	0.742538i	$0.733622\pi$
$542$	2.57087e31	0.931299
$543$	−6.94108e31	−2.46166
$544$	−4.56309e30	−0.158443
$545$	−6.21443e29	−0.0211272
$546$	9.80856e31	3.26505
$547$	3.22624e31	1.05158	0.525791	−	0.850614i	$-0.323769\pi$
$547$	3.22624e31	1.05158	0.525791	+	0.850614i	$0.323769\pi$
$548$	−1.03118e31	−0.329124
$549$	−3.90357e31	−1.22006
$550$	1.66797e30	0.0510525
$551$	1.93385e31	0.579668
$552$	−2.02862e31	−0.595527
$553$	7.57776e31	2.17872
$554$	1.02514e31	0.288681
$555$	2.37002e31	0.653707
$556$	1.19076e31	0.321708
$557$	4.85642e31	1.28523	0.642616	−	0.766189i	$-0.277849\pi$
$557$	4.85642e31	1.28523	0.642616	+	0.766189i	$0.277849\pi$
$558$	−4.38974e31	−1.13801
$559$	4.02197e31	1.02142
$560$	7.43839e30	0.185062
$561$	−2.55209e31	−0.622047
$562$	4.92884e30	0.117700
$563$	−5.02515e31	−1.17572	−0.587858	−	0.808964i	$-0.700028\pi$
$563$	−5.02515e31	−1.17572	−0.587858	+	0.808964i	$0.700028\pi$
$564$	−2.02945e31	−0.465230
$565$	−6.31202e30	−0.141779
$566$	−5.36869e31	−1.18162
$567$	−2.74224e32	−5.91425
$568$	−2.41308e31	−0.509995
$569$	−7.80283e31	−1.61607	−0.808037	−	0.589132i	$-0.799470\pi$
$569$	−7.80283e31	−1.61607	−0.808037	+	0.589132i	$0.799470\pi$
$570$	1.58346e31	0.321400
$571$	−4.11699e31	−0.818963	−0.409481	−	0.912319i	$-0.634290\pi$
$571$	−4.11699e31	−0.818963	−0.409481	+	0.912319i	$0.634290\pi$
$572$	−1.34337e31	−0.261903
$573$	1.73955e32	3.32399
$574$	−2.65728e31	−0.497681
$575$	9.54514e30	0.175227
$576$	1.87289e31	0.337018
$577$	7.34525e31	1.29564	0.647820	−	0.761793i	$-0.275681\pi$
$577$	7.34525e31	1.29564	0.647820	+	0.761793i	$0.275681\pi$
$578$	8.04257e30	0.139067
$579$	8.36777e31	1.41843
$580$	−1.47542e31	−0.245184
$581$	−5.83357e31	−0.950406
$582$	5.41499e31	0.864934
$583$	6.39134e30	0.100093
$584$	1.58761e31	0.243779
$585$	−1.16203e32	−1.74955
$586$	6.18068e30	0.0912460
$587$	5.81709e31	0.842107	0.421054	−	0.907036i	$-0.361660\pi$
$587$	5.81709e31	0.842107	0.421054	+	0.907036i	$0.361660\pi$
$588$	1.17812e32	1.67244
$589$	2.26681e31	0.315565
$590$	−1.04739e31	−0.142991
$591$	−1.11511e31	−0.149300
$592$	−1.44755e31	−0.190079
$593$	7.52337e31	0.968909	0.484455	−	0.874816i	$-0.339018\pi$
$593$	7.52337e31	0.968909	0.484455	+	0.874816i	$0.339018\pi$
$594$	6.58973e31	0.832384
$595$	5.35511e31	0.663473
$596$	−4.37644e31	−0.531849
$597$	−2.53061e32	−3.01662
$598$	−7.68758e31	−0.898930
$599$	−5.59333e31	−0.641597	−0.320798	−	0.947147i	$-0.603951\pi$
$599$	−5.59333e31	−0.641597	−0.320798	+	0.947147i	$0.603951\pi$
$600$	−1.20809e31	−0.135944
$601$	5.72895e31	0.632439	0.316220	−	0.948686i	$-0.397586\pi$
$601$	5.72895e31	0.632439	0.316220	+	0.948686i	$0.397586\pi$
$602$	7.60748e31	0.823913
$603$	4.15840e32	4.41852
$604$	−1.65616e31	−0.172654
$605$	3.80244e31	0.388934
$606$	1.79548e32	1.80196
$607$	1.73060e32	1.70423	0.852114	−	0.523356i	$-0.175320\pi$
$607$	1.73060e32	1.70423	0.852114	+	0.523356i	$0.175320\pi$
$608$	−9.67136e30	−0.0934537
$609$	−3.67996e32	−3.48935
$610$	−1.53791e31	−0.143099
$611$	−7.69071e31	−0.702251
$612$	1.34834e32	1.20826
$613$	−4.07291e29	−0.00358186	−0.00179093	−	0.999998i	$-0.500570\pi$
$613$	−4.07291e29	−0.00358186	−0.00179093	+	0.999998i	$0.500570\pi$
$614$	4.16006e31	0.359057
$615$	4.31576e31	0.365589
$616$	−2.54095e31	−0.211261
$617$	−1.95659e32	−1.59669	−0.798346	−	0.602199i	$-0.794292\pi$
$617$	−1.95659e32	−1.59669	−0.798346	+	0.602199i	$0.794292\pi$
$618$	−8.02696e31	−0.642959
$619$	−2.00768e32	−1.57853	−0.789264	−	0.614054i	$-0.789538\pi$
$619$	−2.00768e32	−1.57853	−0.789264	+	0.614054i	$0.789538\pi$
$620$	−1.72945e31	−0.133476
$621$	3.77105e32	2.85699
$622$	−1.32892e32	−0.988344
$623$	−1.43324e32	−1.04642
$624$	9.72984e31	0.697402
$625$	5.68434e30	0.0400000
$626$	−9.83430e31	−0.679420
$627$	−5.40909e31	−0.366900
$628$	−7.79402e31	−0.519070
$629$	−1.04213e32	−0.681461
$630$	−2.19797e32	−1.41125
$631$	2.41339e32	1.52156	0.760782	−	0.649007i	$-0.224816\pi$
$631$	2.41339e32	1.52156	0.760782	+	0.649007i	$0.224816\pi$
$632$	7.51694e31	0.465366
$633$	−3.27281e32	−1.98965
$634$	−1.07524e32	−0.641916
$635$	1.15781e32	0.678797
$636$	−4.62917e31	−0.266530
$637$	4.46456e32	2.52450
$638$	5.04002e31	0.279895
$639$	7.13039e32	3.88914
$640$	7.37870e30	0.0395285
$641$	−1.22253e32	−0.643268	−0.321634	−	0.946864i	$-0.604232\pi$
$641$	−1.22253e32	−0.643268	−0.321634	+	0.946864i	$0.604232\pi$
$642$	−3.85326e31	−0.199148
$643$	−2.71424e32	−1.37792	−0.688958	−	0.724801i	$-0.741932\pi$
$643$	−2.71424e32	−1.37792	−0.688958	+	0.724801i	$0.741932\pi$
$644$	−1.45409e32	−0.725110
$645$	−1.23555e32	−0.605235
$646$	−6.96269e31	−0.335045
$647$	−2.71917e31	−0.128540	−0.0642699	−	0.997933i	$-0.520472\pi$
$647$	−2.71917e31	−0.128540	−0.0642699	+	0.997933i	$0.520472\pi$
$648$	−2.72023e32	−1.26326
$649$	3.57788e31	0.163234
$650$	−4.57812e31	−0.205203
$651$	−4.31355e32	−1.89956
$652$	1.67993e32	0.726849
$653$	1.78163e32	0.757384	0.378692	−	0.925523i	$-0.376374\pi$
$653$	1.78163e32	0.757384	0.378692	+	0.925523i	$0.376374\pi$
$654$	−1.53755e31	−0.0642223
$655$	−1.01676e32	−0.417296
$656$	−2.63596e31	−0.106303
$657$	−4.69121e32	−1.85902
$658$	−1.45468e32	−0.566461
$659$	−2.28601e32	−0.874774	−0.437387	−	0.899273i	$-0.644096\pi$
$659$	−2.28601e32	−0.874774	−0.437387	+	0.899273i	$0.644096\pi$
$660$	4.12683e31	0.155189
$661$	−1.82780e32	−0.675478	−0.337739	−	0.941240i	$-0.609662\pi$
$661$	−1.82780e32	−0.675478	−0.337739	+	0.941240i	$0.609662\pi$
$662$	2.65535e31	0.0964394
$663$	7.00480e32	2.50029
$664$	−5.78676e31	−0.203003
$665$	1.13500e32	0.391335
$666$	4.27736e32	1.44951
$667$	2.88421e32	0.960683
$668$	3.35355e31	0.109793
$669$	−6.99591e31	−0.225135
$670$	1.63830e32	0.518244
$671$	5.25348e31	0.163357
$672$	1.84038e32	0.562550
$673$	−4.40091e32	−1.32242	−0.661210	−	0.750201i	$-0.729957\pi$
$673$	−4.40091e32	−1.32242	−0.661210	+	0.750201i	$0.729957\pi$
$674$	−1.85227e32	−0.547162
$675$	2.24574e32	0.652179
$676$	1.93590e32	0.552707
$677$	3.63271e32	1.01967	0.509837	−	0.860271i	$-0.329706\pi$
$677$	3.63271e32	1.01967	0.509837	+	0.860271i	$0.329706\pi$
$678$	−1.56170e32	−0.430978
$679$	3.88139e32	1.05314
$680$	5.31214e31	0.141715
$681$	−2.74657e32	−0.720443
$682$	5.90779e31	0.152372
$683$	4.83335e31	0.122577	0.0612887	−	0.998120i	$-0.480479\pi$
$683$	4.83335e31	0.122577	0.0612887	+	0.998120i	$0.480479\pi$
$684$	2.85779e32	0.712663
$685$	1.20046e32	0.294377
$686$	3.59092e32	0.865921
$687$	−5.39292e32	−1.27885
$688$	7.54643e31	0.175985
$689$	−1.75425e32	−0.402319
$690$	2.36163e32	0.532656
$691$	1.13967e32	0.252802	0.126401	−	0.991979i	$-0.459657\pi$
$691$	1.13967e32	0.252802	0.126401	+	0.991979i	$0.459657\pi$
$692$	3.76835e32	0.822113
$693$	7.50825e32	1.61104
$694$	3.05741e32	0.645238
$695$	−1.38622e32	−0.287745
$696$	−3.65043e32	−0.745311
$697$	−1.89770e32	−0.381110
$698$	3.11581e32	0.615508
$699$	1.01425e31	0.0197086
$700$	−8.65943e31	−0.165524
$701$	−2.14787e32	−0.403879	−0.201939	−	0.979398i	$-0.564724\pi$
$701$	−2.14787e32	−0.403879	−0.201939	+	0.979398i	$0.564724\pi$
$702$	−1.80870e33	−3.34573
$703$	−2.20878e32	−0.401944
$704$	−2.52056e31	−0.0451244
$705$	2.36259e32	0.416115
$706$	−5.10792e32	−0.885095
$707$	1.28698e33	2.19406
$708$	−2.59141e32	−0.434664
$709$	−2.27478e32	−0.375412	−0.187706	−	0.982225i	$-0.560105\pi$
$709$	−2.27478e32	−0.375412	−0.187706	+	0.982225i	$0.560105\pi$
$710$	2.80919e32	0.456153
$711$	−2.22118e33	−3.54881
$712$	−1.42174e32	−0.223511
$713$	3.38080e32	0.522986
$714$	1.32494e33	2.01682
$715$	1.56389e32	0.234253
$716$	4.95891e32	0.730949
$717$	−8.13448e32	−1.17994
$718$	−8.02205e32	−1.14513
$719$	8.12373e32	1.14123	0.570615	−	0.821217i	$-0.306705\pi$
$719$	8.12373e32	1.14123	0.570615	+	0.821217i	$0.306705\pi$
$720$	−2.18033e32	−0.301438
$721$	−5.75362e32	−0.782863
$722$	3.80462e32	0.509488
$723$	−2.78850e33	−3.67520
$724$	−4.93535e32	−0.640213
$725$	1.71761e32	0.219300
$726$	9.40786e32	1.18228
$727$	−8.49369e32	−1.05063	−0.525316	−	0.850907i	$-0.676053\pi$
$727$	−8.49369e32	−1.05063	−0.525316	+	0.850907i	$0.676053\pi$
$728$	6.97423e32	0.849152
$729$	2.80708e33	3.36424
$730$	−1.84822e32	−0.218042
$731$	5.43289e32	0.630930
$732$	−3.80503e32	−0.434992
$733$	1.06482e33	1.19834	0.599171	−	0.800621i	$-0.295497\pi$
$733$	1.06482e33	1.19834	0.599171	+	0.800621i	$0.295497\pi$
$734$	−3.67651e32	−0.407316
$735$	−1.37151e33	−1.49588
$736$	−1.44242e32	−0.154881
$737$	−5.59644e32	−0.591611
$738$	7.78897e32	0.810647
$739$	−4.97066e32	−0.509334	−0.254667	−	0.967029i	$-0.581966\pi$
$739$	−4.97066e32	−0.509334	−0.254667	+	0.967029i	$0.581966\pi$
$740$	1.68517e32	0.170012
$741$	1.48465e33	1.47474
$742$	−3.31813e32	−0.324525
$743$	−6.27596e32	−0.604379	−0.302189	−	0.953248i	$-0.597717\pi$
$743$	−6.27596e32	−0.604379	−0.302189	+	0.953248i	$0.597717\pi$
$744$	−4.27894e32	−0.405739
$745$	5.09484e32	0.475701
$746$	1.43511e33	1.31944
$747$	1.70993e33	1.54807
$748$	−1.81463e32	−0.161778
$749$	−2.76197e32	−0.242481
$750$	1.40640e32	0.121592
$751$	2.25567e33	1.92051	0.960254	−	0.279128i	$-0.0900455\pi$
$751$	2.25567e33	1.92051	0.960254	+	0.279128i	$0.0900455\pi$
$752$	−1.44301e32	−0.120994
$753$	−2.83142e33	−2.33809
$754$	−1.38335e33	−1.12502
$755$	1.92802e32	0.154427
$756$	−3.42113e33	−2.69879
$757$	−5.24347e32	−0.407396	−0.203698	−	0.979034i	$-0.565296\pi$
$757$	−5.24347e32	−0.407396	−0.203698	+	0.979034i	$0.565296\pi$
$758$	−1.60916e32	−0.123141
$759$	−8.06731e32	−0.608063
$760$	1.12589e32	0.0835875
$761$	−1.07047e33	−0.782799	−0.391400	−	0.920221i	$-0.628009\pi$
$761$	−1.07047e33	−0.782799	−0.391400	+	0.920221i	$0.628009\pi$
$762$	2.86461e33	2.06340
$763$	−1.10210e32	−0.0781966
$764$	1.23688e33	0.864480
$765$	−1.56968e33	−1.08070
$766$	−8.93199e32	−0.605783
$767$	−9.82031e32	−0.656113
$768$	1.82561e32	0.120158
$769$	1.76963e32	0.114744	0.0573719	−	0.998353i	$-0.481728\pi$
$769$	1.76963e32	0.114744	0.0573719	+	0.998353i	$0.481728\pi$
$770$	2.95806e32	0.188957
$771$	5.35337e33	3.36901
$772$	5.94978e32	0.368894
$773$	−1.34952e32	−0.0824354	−0.0412177	−	0.999150i	$-0.513124\pi$
$773$	−1.34952e32	−0.0824354	−0.0412177	+	0.999150i	$0.513124\pi$
$774$	−2.22989e33	−1.34203
$775$	2.01334e32	0.119384
$776$	3.85025e32	0.224946
$777$	4.20312e33	2.41953
$778$	1.64365e32	0.0932275
$779$	−4.02213e32	−0.224789
$780$	−1.13270e33	−0.623775
$781$	−9.59620e32	−0.520730
$782$	−1.03844e33	−0.555270
$783$	6.78586e33	3.57556
$784$	8.37686e32	0.434957
$785$	9.07344e32	0.464270
$786$	−2.51564e33	−1.26849
$787$	2.58175e32	0.128293	0.0641467	−	0.997940i	$-0.479567\pi$
$787$	2.58175e32	0.128293	0.0641467	+	0.997940i	$0.479567\pi$
$788$	−7.92880e31	−0.0388290
$789$	−4.77665e31	−0.0230536
$790$	−8.75087e32	−0.416236
$791$	−1.11941e33	−0.524756
$792$	7.44799e32	0.344112
$793$	−1.44194e33	−0.656607
$794$	3.72765e32	0.167301
$795$	5.38906e32	0.238392
$796$	−1.79936e33	−0.784543
$797$	4.68701e32	0.201430	0.100715	−	0.994915i	$-0.467887\pi$
$797$	4.68701e32	0.201430	0.100715	+	0.994915i	$0.467887\pi$
$798$	2.80819e33	1.18958
$799$	−1.03886e33	−0.433781
$800$	−8.58993e31	−0.0353553
$801$	4.20108e33	1.70446
$802$	−2.50514e33	−1.00190
$803$	6.31352e32	0.248910
$804$	4.05343e33	1.57536
$805$	1.69278e33	0.648558
$806$	−1.62153e33	−0.612451
$807$	−1.01940e34	−3.79575
$808$	1.27665e33	0.468642
$809$	−1.32810e33	−0.480643	−0.240321	−	0.970693i	$-0.577253\pi$
$809$	−1.32810e33	−0.480643	−0.240321	+	0.970693i	$0.577253\pi$
$810$	3.16676e33	1.12989
$811$	5.54203e32	0.194952	0.0974762	−	0.995238i	$-0.468923\pi$
$811$	5.54203e32	0.194952	0.0974762	+	0.995238i	$0.468923\pi$
$812$	−2.61658e33	−0.907485
$813$	−7.40491e33	−2.53209
$814$	−5.75654e32	−0.194080
$815$	−1.95570e33	−0.650113
$816$	1.31431e33	0.430786
$817$	1.15149e33	0.372140
$818$	2.62704e33	0.837150
$819$	−2.06081e34	−6.47550
$820$	3.06866e32	0.0950800
$821$	−2.33985e33	−0.714895	−0.357448	−	0.933933i	$-0.616353\pi$
$821$	−2.33985e33	−0.714895	−0.357448	+	0.933933i	$0.616353\pi$
$822$	2.97012e33	0.894847
$823$	3.81112e33	1.13228	0.566141	−	0.824308i	$-0.308436\pi$
$823$	3.81112e33	1.13228	0.566141	+	0.824308i	$0.308436\pi$
$824$	−5.70745e32	−0.167217
$825$	−4.80426e32	−0.138805
$826$	−1.85749e33	−0.529245
$827$	3.90417e33	1.09702	0.548511	−	0.836143i	$-0.315195\pi$
$827$	3.90417e33	1.09702	0.548511	+	0.836143i	$0.315195\pi$
$828$	4.26220e33	1.18110
$829$	2.55686e33	0.698763	0.349382	−	0.936981i	$-0.386392\pi$
$829$	2.55686e33	0.698763	0.349382	+	0.936981i	$0.386392\pi$
$830$	6.73667e32	0.181571
$831$	−2.95270e33	−0.784889
$832$	6.91826e32	0.181376
$833$	6.03074e33	1.55939
$834$	−3.42974e33	−0.874685
$835$	−3.90404e32	−0.0982019
$836$	−3.84606e32	−0.0954209
$837$	7.95421e33	1.94650
$838$	−6.22190e32	−0.150182
$839$	5.90891e32	0.140684	0.0703420	−	0.997523i	$-0.477591\pi$
$839$	5.90891e32	0.140684	0.0703420	+	0.997523i	$0.477591\pi$
$840$	−2.14249e33	−0.503160
$841$	8.73308e32	0.202308
$842$	−2.61608e33	−0.597808
$843$	−1.41966e33	−0.320012
$844$	−2.32708e33	−0.517456
$845$	−2.25368e33	−0.494356
$846$	4.26394e33	0.922681
$847$	6.74344e33	1.43954
$848$	−3.29150e32	−0.0693174
$849$	1.54635e34	3.21269
$850$	−6.18414e32	−0.126754
$851$	−3.29425e33	−0.666141
$852$	6.95041e33	1.38661
$853$	−3.51995e33	−0.692823	−0.346412	−	0.938083i	$-0.612600\pi$
$853$	−3.51995e33	−0.692823	−0.346412	+	0.938083i	$0.612600\pi$
$854$	−2.72740e33	−0.529643
$855$	−3.32690e33	−0.637425
$856$	−2.73980e32	−0.0517930
$857$	−8.93522e33	−1.66658	−0.833289	−	0.552837i	$-0.813545\pi$
$857$	−8.93522e33	−1.66658	−0.833289	+	0.552837i	$0.813545\pi$
$858$	3.86931e33	0.712082
$859$	4.26448e33	0.774363	0.387181	−	0.922004i	$-0.373449\pi$
$859$	4.26448e33	0.774363	0.387181	+	0.922004i	$0.373449\pi$
$860$	−8.78520e32	−0.157405
$861$	7.65379e33	1.35313
$862$	2.51165e33	0.438153
$863$	−7.90521e31	−0.0136078	−0.00680392	−	0.999977i	$-0.502166\pi$
$863$	−7.90521e31	−0.0136078	−0.00680392	+	0.999977i	$0.502166\pi$
$864$	−3.39367e33	−0.576450
$865$	−4.38694e33	−0.735320
$866$	4.79368e33	0.792891
$867$	−2.31651e33	−0.378107
$868$	−3.06709e33	−0.494025
$869$	2.98930e33	0.475162
$870$	4.24965e33	0.666626
$871$	1.53607e34	2.37795
$872$	−1.09325e32	−0.0167025
$873$	−1.13771e34	−1.71540
$874$	−2.20095e33	−0.327513
$875$	1.00809e33	0.148049
$876$	−4.57280e33	−0.662804
$877$	−5.32153e33	−0.761275	−0.380638	−	0.924724i	$-0.624295\pi$
$877$	−5.32153e33	−0.761275	−0.380638	+	0.924724i	$0.624295\pi$
$878$	−4.79163e33	−0.676545
$879$	−1.78023e33	−0.248086
$880$	2.93432e32	0.0403605
$881$	−6.10795e33	−0.829225	−0.414613	−	0.909998i	$-0.636083\pi$
$881$	−6.10795e33	−0.829225	−0.414613	+	0.909998i	$0.636083\pi$
$882$	−2.47527e34	−3.31692
$883$	5.57230e33	0.737032	0.368516	−	0.929621i	$-0.379866\pi$
$883$	5.57230e33	0.737032	0.368516	+	0.929621i	$0.379866\pi$
$884$	4.98066e33	0.650258
$885$	3.01680e33	0.388776
$886$	1.06390e34	1.35336
$887$	−3.09075e33	−0.388099	−0.194050	−	0.980992i	$-0.562162\pi$
$887$	−3.09075e33	−0.388099	−0.194050	+	0.980992i	$0.562162\pi$
$888$	4.16939e33	0.516801
$889$	2.05332e34	2.51239
$890$	1.65512e33	0.199914
$891$	−1.08177e34	−1.28985
$892$	−4.97434e32	−0.0585517
$893$	−2.20185e33	−0.255856
$894$	1.26055e34	1.44603
$895$	−5.77294e33	−0.653780
$896$	1.30858e33	0.146304
$897$	2.21426e34	2.44408
$898$	−1.73399e33	−0.188960
$899$	6.08362e33	0.654524
$900$	2.53823e33	0.269614
$901$	−2.36965e33	−0.248513
$902$	−1.04825e33	−0.108540
$903$	−2.19119e34	−2.24012
$904$	−1.11042e33	−0.112086
$905$	5.74550e33	0.572624
$906$	4.77025e33	0.469425
$907$	1.19132e34	1.15756	0.578781	−	0.815483i	$-0.303529\pi$
$907$	1.19132e34	1.15756	0.578781	+	0.815483i	$0.303529\pi$
$908$	−1.95291e33	−0.187368
$909$	−3.77236e34	−3.57379
$910$	−8.11907e33	−0.759505
$911$	−1.48259e34	−1.36949	−0.684747	−	0.728781i	$-0.740087\pi$
$911$	−1.48259e34	−1.36949	−0.684747	+	0.728781i	$0.740087\pi$
$912$	2.78565e33	0.254089
$913$	−2.30125e33	−0.207276
$914$	−8.81138e33	−0.783723
$915$	4.42964e33	0.389068
$916$	−3.83455e33	−0.332596
$917$	−1.80318e34	−1.54451
$918$	−2.44320e34	−2.06666
$919$	1.05759e34	0.883461	0.441731	−	0.897148i	$-0.354365\pi$
$919$	1.05759e34	0.883461	0.441731	+	0.897148i	$0.354365\pi$
$920$	1.67920e33	0.138529
$921$	−1.19823e34	−0.976232
$922$	−1.14668e34	−0.922652
$923$	2.63390e34	2.09305
$924$	7.31873e33	0.574391
$925$	−1.96180e33	−0.152063
$926$	−1.34078e34	−1.02643
$927$	1.68649e34	1.27517
$928$	−2.59558e33	−0.193835
$929$	−4.72412e33	−0.348450	−0.174225	−	0.984706i	$-0.555742\pi$
$929$	−4.72412e33	−0.348450	−0.174225	+	0.984706i	$0.555742\pi$
$930$	4.98134e33	0.362904
$931$	1.27820e34	0.919768
$932$	7.21166e31	0.00512569
$933$	3.82769e34	2.68718
$934$	5.03900e33	0.349426
$935$	2.11250e33	0.144698
$936$	−2.04427e34	−1.38314
$937$	−2.82822e34	−1.89020	−0.945101	−	0.326779i	$-0.894037\pi$
$937$	−2.82822e34	−1.89020	−0.945101	+	0.326779i	$0.894037\pi$
$938$	2.90545e34	1.91814
$939$	2.83258e34	1.84726
$940$	1.67988e33	0.108220
$941$	−1.69342e34	−1.07767	−0.538833	−	0.842412i	$-0.681135\pi$
$941$	−1.69342e34	−1.07767	−0.538833	+	0.842412i	$0.681135\pi$
$942$	2.24492e34	1.41129
$943$	−5.99875e33	−0.372543
$944$	−1.84259e33	−0.113045
$945$	3.98271e34	2.41387
$946$	3.00102e33	0.179689
$947$	−8.74272e33	−0.517156	−0.258578	−	0.965990i	$-0.583254\pi$
$947$	−8.74272e33	−0.517156	−0.258578	+	0.965990i	$0.583254\pi$
$948$	−2.16511e34	−1.26527
$949$	−1.73289e34	−1.00048
$950$	−1.31071e33	−0.0747630
$951$	3.09702e34	1.74529
$952$	9.42081e33	0.524522
$953$	−2.80700e34	−1.54410	−0.772048	−	0.635564i	$-0.780768\pi$
$953$	−2.80700e34	−1.54410	−0.772048	+	0.635564i	$0.780768\pi$
$954$	9.72604e33	0.528603
$955$	−1.43992e34	−0.773214
$956$	−5.78390e33	−0.306870
$957$	−1.45168e34	−0.760999
$958$	1.25142e34	0.648185
$959$	2.12895e34	1.08956
$960$	−2.12529e33	−0.107473
$961$	−1.28823e34	−0.643684
$962$	1.58002e34	0.780096
$963$	8.09582e33	0.394965
$964$	−1.98272e34	−0.955821
$965$	−6.92646e33	−0.329949
$966$	4.18823e34	1.97148
$967$	−1.63293e34	−0.759562	−0.379781	−	0.925076i	$-0.624001\pi$
$967$	−1.63293e34	−0.759562	−0.379781	+	0.925076i	$0.624001\pi$
$968$	6.68932e33	0.307479
$969$	2.00547e34	0.910946
$970$	−4.48228e33	−0.201198
$971$	−2.94646e34	−1.30701	−0.653505	−	0.756922i	$-0.726702\pi$
$971$	−2.94646e34	−1.30701	−0.653505	+	0.756922i	$0.726702\pi$
$972$	4.11573e34	1.80420
$973$	−2.45840e34	−1.06501
$974$	1.21931e34	0.522020
$975$	1.31864e34	0.557922
$976$	−2.70551e33	−0.113130
$977$	−3.20852e34	−1.32592	−0.662960	−	0.748655i	$-0.730700\pi$
$977$	−3.20852e34	−1.32592	−0.662960	+	0.748655i	$0.730700\pi$
$978$	−4.83872e34	−1.97621
$979$	−5.65388e33	−0.228216
$980$	−9.75195e33	−0.389038
$981$	3.23045e33	0.127371
$982$	1.00530e34	0.391756
$983$	−1.27173e34	−0.489813	−0.244906	−	0.969547i	$-0.578757\pi$
$983$	−1.27173e34	−0.489813	−0.244906	+	0.969547i	$0.578757\pi$
$984$	7.59236e33	0.289024
$985$	9.23034e32	0.0347297
$986$	−1.86863e34	−0.694928
$987$	4.18993e34	1.54014
$988$	1.05564e34	0.383540
$989$	1.71737e34	0.616746
$990$	−8.67060e33	−0.307783
$991$	−3.20701e34	−1.12526	−0.562631	−	0.826708i	$-0.690211\pi$
$991$	−3.20701e34	−1.12526	−0.562631	+	0.826708i	$0.690211\pi$
$992$	−3.04247e33	−0.105522
$993$	−7.64822e33	−0.262207
$994$	4.98197e34	1.68833
$995$	2.09473e34	0.701717
$996$	1.66676e34	0.551940
$997$	4.63954e34	1.51873	0.759365	−	0.650665i	$-0.225510\pi$
$997$	4.63954e34	1.51873	0.759365	+	0.650665i	$0.225510\pi$
$998$	−3.23595e32	−0.0104713
$999$	−7.75057e34	−2.47931

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	10.24.a.b.1.2	✓	2
5.2	odd	4		50.24.b.b.49.1		4
5.3	odd	4		50.24.b.b.49.4		4
5.4	even	2		50.24.a.c.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
10.24.a.b.1.2	✓	2	1.1	even	1	trivial
50.24.a.c.1.1		2	5.4	even	2
50.24.b.b.49.1		4	5.2	odd	4
50.24.b.b.49.4		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)

\(f(q)\)	\(=\)	\(q-2048.00 q^{2} +589887. q^{3} +4.19430e6 q^{4} -4.88281e7 q^{5} -1.20809e9 q^{6} -8.65943e9 q^{7} -8.58993e9 q^{8} +2.53823e11 q^{9} +1.00000e11 q^{10} -3.41600e11 q^{11} +2.47417e12 q^{12} +9.37599e12 q^{13} +1.77345e13 q^{14} -2.88031e13 q^{15} +1.75922e13 q^{16} +1.26651e14 q^{17} -5.19830e14 q^{18} +2.68434e14 q^{19} -2.04800e14 q^{20} -5.10808e15 q^{21} +6.99597e14 q^{22} +4.00352e15 q^{23} -5.06709e15 q^{24} +2.38419e15 q^{25} -1.92020e16 q^{26} +9.41933e16 q^{27} -3.63203e16 q^{28} +7.20419e16 q^{29} +5.89887e16 q^{30} +8.44456e16 q^{31} -3.60288e16 q^{32} -2.01505e17 q^{33} -2.59382e17 q^{34} +4.22824e17 q^{35} +1.06461e18 q^{36} -8.22837e17 q^{37} -5.49753e17 q^{38} +5.53078e18 q^{39} +4.19430e17 q^{40} -1.49837e18 q^{41} +1.04614e19 q^{42} +4.28965e18 q^{43} -1.43277e18 q^{44} -1.23937e19 q^{45} -8.19921e18 q^{46} -8.20255e18 q^{47} +1.03774e19 q^{48} +4.76169e19 q^{49} -4.88281e18 q^{50} +7.47099e19 q^{51} +3.93258e19 q^{52} -1.87100e19 q^{53} -1.92908e20 q^{54} +1.66797e19 q^{55} +7.43839e19 q^{56} +1.58346e20 q^{57} -1.47542e20 q^{58} -1.04739e20 q^{59} -1.20809e20 q^{60} -1.53791e20 q^{61} -1.72945e20 q^{62} -2.19797e21 q^{63} +7.37870e19 q^{64} -4.57812e20 q^{65} +4.12683e20 q^{66} +1.63830e21 q^{67} +5.31214e20 q^{68} +2.36163e21 q^{69} -8.65943e20 q^{70} +2.80919e21 q^{71} -2.18033e21 q^{72} -1.84822e21 q^{73} +1.68517e21 q^{74} +1.40640e21 q^{75} +1.12589e21 q^{76} +2.95806e21 q^{77} -1.13270e22 q^{78} -8.75087e21 q^{79} -8.58993e20 q^{80} +3.16676e22 q^{81} +3.06866e21 q^{82} +6.73667e21 q^{83} -2.14249e22 q^{84} -6.18414e21 q^{85} -8.78520e21 q^{86} +4.24965e22 q^{87} +2.93432e21 q^{88} +1.65512e22 q^{89} +2.53823e22 q^{90} -8.11907e22 q^{91} +1.67920e22 q^{92} +4.98134e22 q^{93} +1.67988e22 q^{94} -1.31071e22 q^{95} -2.12529e22 q^{96} -4.48228e22 q^{97} -9.75195e22 q^{98} -8.67060e22 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 4096 q^{2} + 686484 q^{3} + 8388608 q^{4} - 97656250 q^{5} - 1405919232 q^{6} - 3529595108 q^{7} - 17179869184 q^{8} + 169011226674 q^{9} + 200000000000 q^{10} + 936557269824 q^{11} + 2879322587136 q^{12}+ \cdots - 19\!\cdots\!12 q^{99}+O(q^{100}) \) 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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