LMFDB - Embedded newform 10.24.a.c.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:	$1$
Dimension:	$2$
Coefficient field:	$\Q(\sqrt{1492261}) $
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x - 373065 $ x^2 - x - 373065
Coefficient ring:	$\Z[a_1, a_2, a_3]$
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			$-610.291$ 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)

$f(q)$	$=$	\(q+2048.00 q^{2} +247238. q^{3} +4.19430e6 q^{4} -4.88281e7 q^{5} +5.06342e8 q^{6} -3.52608e9 q^{7} +8.58993e9 q^{8} -3.30168e10 q^{9} -1.00000e11 q^{10} -6.19384e11 q^{11} +1.03699e12 q^{12} -9.21814e12 q^{13} -7.22141e12 q^{14} -1.20721e13 q^{15} +1.75922e13 q^{16} +2.96454e13 q^{17} -6.76184e13 q^{18} -3.56432e14 q^{19} -2.04800e14 q^{20} -8.71779e14 q^{21} -1.26850e15 q^{22} +2.73214e15 q^{23} +2.12375e15 q^{24} +2.38419e15 q^{25} -1.88788e16 q^{26} -3.14387e16 q^{27} -1.47894e16 q^{28} +5.96584e16 q^{29} -2.47238e16 q^{30} +5.61319e16 q^{31} +3.60288e16 q^{32} -1.53135e17 q^{33} +6.07138e16 q^{34} +1.72172e17 q^{35} -1.38482e17 q^{36} -1.59225e18 q^{37} -7.29973e17 q^{38} -2.27907e18 q^{39} -4.19430e17 q^{40} -4.81098e18 q^{41} -1.78540e18 q^{42} -7.53412e18 q^{43} -2.59788e18 q^{44} +1.61215e18 q^{45} +5.59542e18 q^{46} +1.70653e18 q^{47} +4.34945e18 q^{48} -1.49355e19 q^{49} +4.88281e18 q^{50} +7.32946e18 q^{51} -3.86637e19 q^{52} +7.71411e19 q^{53} -6.43865e19 q^{54} +3.02434e19 q^{55} -3.02888e19 q^{56} -8.81234e19 q^{57} +1.22180e20 q^{58} +2.22753e20 q^{59} -5.06342e19 q^{60} +2.72118e20 q^{61} +1.14958e20 q^{62} +1.16420e20 q^{63} +7.37870e19 q^{64} +4.50105e20 q^{65} -3.13620e20 q^{66} +6.39125e20 q^{67} +1.24342e20 q^{68} +6.75487e20 q^{69} +3.52608e20 q^{70} -2.68803e21 q^{71} -2.83612e20 q^{72} +4.36224e21 q^{73} -3.26093e21 q^{74} +5.89460e20 q^{75} -1.49498e21 q^{76} +2.18400e21 q^{77} -4.66754e21 q^{78} -3.18360e21 q^{79} -8.58993e20 q^{80} -4.66452e21 q^{81} -9.85289e21 q^{82} -2.75933e21 q^{83} -3.65651e21 q^{84} -1.44753e21 q^{85} -1.54299e22 q^{86} +1.47498e22 q^{87} -5.32047e21 q^{88} -1.40148e22 q^{89} +3.30168e21 q^{90} +3.25039e22 q^{91} +1.14594e22 q^{92} +1.38779e22 q^{93} +3.49498e21 q^{94} +1.74039e22 q^{95} +8.90767e21 q^{96} +1.12387e23 q^{97} -3.05880e22 q^{98} +2.04501e22 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 4096 q^{2} - 91884 q^{3} + 8388608 q^{4} - 97656250 q^{5} - 188178432 q^{6} + 2146058908 q^{7} + 17179869184 q^{8} - 12156555726 q^{9} - 200000000000 q^{10} - 692289571776 q^{11} - 385389428736 q^{12}+ \cdots + 18\!\cdots\!88 q^{99}+O(q^{100}) $ 2 * q + 4096 * q^2 - 91884 * q^3 + 8388608 * q^4 - 97656250 * q^5 - 188178432 * q^6 + 2146058908 * q^7 + 17179869184 * q^8 - 12156555726 * q^9 - 200000000000 * q^10 - 692289571776 * q^11 - 385389428736 * q^12 - 1708452301484 * q^13 + 4395128643584 * q^14 + 4486523437500 * q^15 + 35184372088832 * q^16 - 93149332240332 * q^17 - 24896626126848 * q^18 - 970438534616600 * q^19 - 409600000000000 * q^20 - 2795322363317736 * q^21 - 1417809042997248 * q^22 - 962002498409964 * q^23 - 789277550051328 * q^24 + 4768371582031250 * q^25 - 3498910313439232 * q^26 - 6586889273700840 * q^27 + 9001223462060032 * q^28 - 40394756391690180 * q^29 + 9188400000000000 * q^30 - 54819002015519096 * q^31 + 72057594037927936 * q^32 - 128411117205326208 * q^33 - 190769832428199936 * q^34 - 104788032617187500 * q^35 - 50988290307784704 * q^36 - 2098544042837784332 * q^37 - 1987458118894796800 * q^38 - 4825767984454719672 * q^39 - 838860800000000000 * q^40 - 4273739814696341076 * q^41 - 5724820200074723328 * q^42 - 10838321168303261564 * q^43 - 2903672920058363904 * q^44 + 593581822558593750 * q^45 - 1970181116743606272 * q^46 - 26680537462560731892 * q^47 - 1616440422505119744 * q^48 - 10131136165510839654 * q^49 + 9765625000000000000 * q^50 + 48971798778005595144 * q^51 - 7165768321923547136 * q^52 + 33753250226251705956 * q^53 - 13489949232539320320 * q^54 + 33803201746875000000 * q^55 + 18434505650298945536 * q^56 + 120099366912137840400 * q^57 - 82728461090181488640 * q^58 + 40199521927491576840 * q^59 + 18817843200000000000 * q^60 + 803606238589543626004 * q^61 - 112269316127783108608 * q^62 + 234741824681222343996 * q^63 + 147573952589676412928 * q^64 + 83420522533398437500 * q^65 - 262985968036508073984 * q^66 + 2102618843174916067948 * q^67 - 390696616812953468928 * q^68 + 1928248820541872217288 * q^69 - 214605890800000000000 * q^70 + 718243220673362466264 * q^71 - 104424018550343073792 * q^72 + 3142915833207124335076 * q^73 - 4297818199731782311936 * q^74 - 219068527221679687500 * q^75 - 4070314227496543846400 * q^76 + 1770465757062240180096 * q^77 - 9883172832163265888256 * q^78 - 7052319452018896981520 * q^79 - 1717986918400000000000 * q^80 - 15056162150854903841718 * q^81 - 8752619140498106523648 * q^82 - 21904593841262540808444 * q^83 - 11724431769753033375744 * q^84 + 4548307238297460937500 * q^85 - 22196881752685079683072 * q^86 + 48679951535733201231960 * q^87 - 5946722140279529275392 * q^88 - 198123608118313558380 * q^89 + 1215655572600000000000 * q^90 + 75099870901057528941464 * q^91 - 4034930927090905645056 * q^92 + 51503746828643496862032 * q^93 - 54641740723324378914816 * q^94 + 47384694073076171875000 * q^95 - 3310469985290485235712 * q^96 + 115777326079591770710788 * q^97 - 20748566866966199611392 * q^98 + 18929241483376281127488 * 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
$3$	247238.	0.805786	0.402893	−	0.915247i	$-0.368005\pi$
$3$	247238.	0.805786	0.402893	+	0.915247i	$0.368005\pi$
$4$	4.19430e6	0.500000
$5$	−4.88281e7	−0.447214
$5$	−4.88281e7	−0.447214
$6$	5.06342e8	0.569777
$7$	−3.52608e9	−0.674007	−0.337004	−	0.941503i	$-0.609413\pi$
$7$	−3.52608e9	−0.674007	−0.337004	+	0.941503i	$0.609413\pi$
$8$	8.58993e9	0.353553
$9$	−3.30168e10	−0.350708
$10$	−1.00000e11	−0.316228
$11$	−6.19384e11	−0.654552	−0.327276	−	0.944929i	$-0.606131\pi$
$11$	−6.19384e11	−0.654552	−0.327276	+	0.944929i	$0.606131\pi$
$12$	1.03699e12	0.402893
$13$	−9.21814e12	−1.42658	−0.713288	−	0.700871i	$-0.752795\pi$
$13$	−9.21814e12	−1.42658	−0.713288	+	0.700871i	$0.752795\pi$
$14$	−7.22141e12	−0.476595
$15$	−1.20721e13	−0.360359
$16$	1.75922e13	0.250000
$17$	2.96454e13	0.209795	0.104897	−	0.994483i	$-0.466549\pi$
$17$	2.96454e13	0.209795	0.104897	+	0.994483i	$0.466549\pi$
$18$	−6.76184e13	−0.247988
$19$	−3.56432e14	−0.701957	−0.350978	−	0.936384i	$-0.614151\pi$
$19$	−3.56432e14	−0.701957	−0.350978	+	0.936384i	$0.614151\pi$
$20$	−2.04800e14	−0.223607
$21$	−8.71779e14	−0.543106
$22$	−1.26850e15	−0.462838
$23$	2.73214e15	0.597905	0.298953	−	0.954268i	$-0.403363\pi$
$23$	2.73214e15	0.597905	0.298953	+	0.954268i	$0.403363\pi$
$24$	2.12375e15	0.284889
$25$	2.38419e15	0.200000
$26$	−1.88788e16	−1.00874
$27$	−3.14387e16	−1.08838
$28$	−1.47894e16	−0.337004
$29$	5.96584e16	0.908018	0.454009	−	0.890997i	$-0.349993\pi$
$29$	5.96584e16	0.908018	0.454009	+	0.890997i	$0.349993\pi$
$30$	−2.47238e16	−0.254812
$31$	5.61319e16	0.396780	0.198390	−	0.980123i	$-0.436429\pi$
$31$	5.61319e16	0.396780	0.198390	+	0.980123i	$0.436429\pi$
$32$	3.60288e16	0.176777
$33$	−1.53135e17	−0.527429
$34$	6.07138e16	0.148347
$35$	1.72172e17	0.301425
$36$	−1.38482e17	−0.175354
$37$	−1.59225e18	−1.47127	−0.735634	−	0.677380i	$-0.763115\pi$
$37$	−1.59225e18	−1.47127	−0.735634	+	0.677380i	$0.763115\pi$
$38$	−7.29973e17	−0.496359
$39$	−2.27907e18	−1.14952
$40$	−4.19430e17	−0.158114
$41$	−4.81098e18	−1.36527	−0.682636	−	0.730759i	$-0.739167\pi$
$41$	−4.81098e18	−1.36527	−0.682636	+	0.730759i	$0.739167\pi$
$42$	−1.78540e18	−0.384034
$43$	−7.53412e18	−1.23636	−0.618180	−	0.786036i	$-0.712130\pi$
$43$	−7.53412e18	−1.23636	−0.618180	+	0.786036i	$0.712130\pi$
$44$	−2.59788e18	−0.327276
$45$	1.61215e18	0.156841
$46$	5.59542e18	0.422783
$47$	1.70653e18	0.100691	0.0503454	−	0.998732i	$-0.483968\pi$
$47$	1.70653e18	0.100691	0.0503454	+	0.998732i	$0.483968\pi$
$48$	4.34945e18	0.201447
$49$	−1.49355e19	−0.545715
$50$	4.88281e18	0.141421
$51$	7.32946e18	0.169050
$52$	−3.86637e19	−0.713288
$53$	7.71411e19	1.14318	0.571589	−	0.820540i	$-0.306327\pi$
$53$	7.71411e19	1.14318	0.571589	+	0.820540i	$0.306327\pi$
$54$	−6.43865e19	−0.769603
$55$	3.02434e19	0.292725
$56$	−3.02888e19	−0.238297
$57$	−8.81234e19	−0.565627
$58$	1.22180e20	0.642066
$59$	2.22753e20	0.961668	0.480834	−	0.876812i	$-0.340334\pi$
$59$	2.22753e20	0.961668	0.480834	+	0.876812i	$0.340334\pi$
$60$	−5.06342e19	−0.180179
$61$	2.72118e20	0.800690	0.400345	−	0.916364i	$-0.368890\pi$
$61$	2.72118e20	0.800690	0.400345	+	0.916364i	$0.368890\pi$
$62$	1.14958e20	0.280566
$63$	1.16420e20	0.236380
$64$	7.37870e19	0.125000
$65$	4.50105e20	0.637984
$66$	−3.13620e20	−0.372949
$67$	6.39125e20	0.639331	0.319665	−	0.947531i	$-0.396430\pi$
$67$	6.39125e20	0.639331	0.319665	+	0.947531i	$0.396430\pi$
$68$	1.24342e20	0.104897
$69$	6.75487e20	0.481784
$70$	3.52608e20	0.213140
$71$	−2.68803e21	−1.38027	−0.690134	−	0.723681i	$-0.742448\pi$
$71$	−2.68803e21	−1.38027	−0.690134	+	0.723681i	$0.742448\pi$
$72$	−2.83612e20	−0.123994
$73$	4.36224e21	1.62741	0.813704	−	0.581280i	$-0.197448\pi$
$73$	4.36224e21	1.62741	0.813704	+	0.581280i	$0.197448\pi$
$74$	−3.26093e21	−1.04034
$75$	5.89460e20	0.161157
$76$	−1.49498e21	−0.350978
$77$	2.18400e21	0.441173
$78$	−4.66754e21	−0.812830
$79$	−3.18360e21	−0.478859	−0.239429	−	0.970914i	$-0.576960\pi$
$79$	−3.18360e21	−0.478859	−0.239429	+	0.970914i	$0.576960\pi$
$80$	−8.58993e20	−0.111803
$81$	−4.66452e21	−0.526296
$82$	−9.85289e21	−0.965393
$83$	−2.75933e21	−0.235183	−0.117592	−	0.993062i	$-0.537517\pi$
$83$	−2.75933e21	−0.235183	−0.117592	+	0.993062i	$0.537517\pi$
$84$	−3.65651e21	−0.271553
$85$	−1.44753e21	−0.0938231
$86$	−1.54299e22	−0.874239
$87$	1.47498e22	0.731668
$88$	−5.32047e21	−0.231419
$89$	−1.40148e22	−0.535304	−0.267652	−	0.963516i	$-0.586248\pi$
$89$	−1.40148e22	−0.535304	−0.267652	+	0.963516i	$0.586248\pi$
$90$	3.30168e21	0.110904
$91$	3.25039e22	0.961522
$92$	1.14594e22	0.298953
$93$	1.38779e22	0.319720
$94$	3.49498e21	0.0711991
$95$	1.74039e22	0.313925
$96$	8.90767e21	0.142444
$97$	1.12387e23	1.59529	0.797644	−	0.603128i	$-0.206079\pi$
$97$	1.12387e23	1.59529	0.797644	+	0.603128i	$0.206079\pi$
$98$	−3.05880e22	−0.385878
$99$	2.04501e22	0.229557
$100$	1.00000e22	0.100000
$101$	1.15829e23	1.03305	0.516525	−	0.856272i	$-0.327225\pi$
$101$	1.15829e23	1.03305	0.516525	+	0.856272i	$0.327225\pi$
$102$	1.50107e22	0.119536
$103$	−1.69254e23	−1.20479	−0.602394	−	0.798199i	$-0.705786\pi$
$103$	−1.69254e23	−1.20479	−0.602394	+	0.798199i	$0.705786\pi$
$104$	−7.91832e22	−0.504371
$105$	4.25673e22	0.242884
$106$	1.57985e23	0.808348
$107$	1.60256e23	0.736041	0.368020	−	0.929818i	$-0.380036\pi$
$107$	1.60256e23	0.736041	0.368020	+	0.929818i	$0.380036\pi$
$108$	−1.31864e23	−0.544191
$109$	−1.24517e23	−0.462193	−0.231096	−	0.972931i	$-0.574231\pi$
$109$	−1.24517e23	−0.462193	−0.231096	+	0.972931i	$0.574231\pi$
$110$	6.19384e22	0.206987
$111$	−3.93664e23	−1.18553
$112$	−6.20314e22	−0.168502
$113$	−8.30660e22	−0.203714	−0.101857	−	0.994799i	$-0.532478\pi$
$113$	−8.30660e22	−0.203714	−0.101857	+	0.994799i	$0.532478\pi$
$114$	−1.80477e23	−0.399959
$115$	−1.33405e23	−0.267391
$116$	2.50225e23	0.454009
$117$	3.04353e23	0.500312
$118$	4.56198e23	0.680002
$119$	−1.04532e23	−0.141403
$120$	−1.03699e23	−0.127406
$121$	−5.11794e23	−0.571562
$122$	5.57298e23	0.566174
$123$	−1.18945e24	−1.10012
$124$	2.35434e23	0.198390
$125$	−1.16415e23	−0.0894427
$126$	2.38428e23	0.167146
$127$	−1.35449e24	−0.867031	−0.433515	−	0.901146i	$-0.642727\pi$
$127$	−1.35449e24	−0.867031	−0.433515	+	0.901146i	$0.642727\pi$
$128$	1.51116e23	0.0883883
$129$	−1.86272e24	−0.996243
$130$	9.21814e23	0.451123
$131$	−3.88681e24	−1.74170	−0.870850	−	0.491548i	$-0.836431\pi$
$131$	−3.88681e24	−1.74170	−0.870850	+	0.491548i	$0.836431\pi$
$132$	−6.42295e23	−0.263715
$133$	1.25681e24	0.473124
$134$	1.30893e24	0.452075
$135$	1.53509e24	0.486739
$136$	2.54652e23	0.0741737
$137$	4.74583e24	1.27065	0.635324	−	0.772246i	$-0.280867\pi$
$137$	4.74583e24	1.27065	0.635324	+	0.772246i	$0.280867\pi$
$138$	1.38340e24	0.340673
$139$	8.52208e24	1.93141	0.965707	−	0.259633i	$-0.0836015\pi$
$139$	8.52208e24	1.93141	0.965707	+	0.259633i	$0.0836015\pi$
$140$	7.22141e23	0.150713
$141$	4.21919e23	0.0811352
$142$	−5.50509e24	−0.975997
$143$	5.70957e24	0.933768
$144$	−5.80837e23	−0.0876771
$145$	−2.91301e24	−0.406078
$146$	8.93386e24	1.15075
$147$	−3.69262e24	−0.439729
$148$	−6.67838e24	−0.735634
$149$	4.97391e24	0.507056	0.253528	−	0.967328i	$-0.418409\pi$
$149$	4.97391e24	0.507056	0.253528	+	0.967328i	$0.418409\pi$
$150$	1.20721e24	0.113955
$151$	2.56571e24	0.224374	0.112187	−	0.993687i	$-0.464214\pi$
$151$	2.56571e24	0.224374	0.112187	+	0.993687i	$0.464214\pi$
$152$	−3.06173e24	−0.248179
$153$	−9.78796e23	−0.0735768
$154$	4.47282e24	0.311956
$155$	−2.74082e24	−0.177446
$156$	−9.55911e24	−0.574758
$157$	−2.22180e25	−1.24125	−0.620623	−	0.784109i	$-0.713120\pi$
$157$	−2.22180e25	−1.24125	−0.620623	+	0.784109i	$0.713120\pi$
$158$	−6.52002e24	−0.338604
$159$	1.90722e25	0.921157
$160$	−1.75922e24	−0.0790569
$161$	−9.63373e24	−0.402992
$162$	−9.55295e24	−0.372147
$163$	−2.96191e25	−1.07501	−0.537507	−	0.843259i	$-0.680634\pi$
$163$	−2.96191e25	−1.07501	−0.537507	+	0.843259i	$0.680634\pi$
$164$	−2.01787e25	−0.682636
$165$	7.47729e24	0.235873
$166$	−5.65112e24	−0.166300
$167$	1.84259e25	0.506044	0.253022	−	0.967460i	$-0.418575\pi$
$167$	1.84259e25	0.506044	0.253022	+	0.967460i	$0.418575\pi$
$168$	−7.48852e24	−0.192017
$169$	4.32202e25	1.03512
$170$	−2.96454e24	−0.0663430
$171$	1.17682e25	0.246182
$172$	−3.16004e25	−0.618180
$173$	−9.26470e25	−1.69551	−0.847757	−	0.530385i	$-0.822047\pi$
$173$	−9.26470e25	−1.69551	−0.847757	+	0.530385i	$0.822047\pi$
$174$	3.02076e25	0.517368
$175$	−8.40682e24	−0.134801
$176$	−1.08963e25	−0.163638
$177$	5.50728e25	0.774899
$178$	−2.87022e25	−0.378517
$179$	1.33235e26	1.64744	0.823719	−	0.566998i	$-0.191895\pi$
$179$	1.33235e26	1.64744	0.823719	+	0.566998i	$0.191895\pi$
$180$	6.76184e24	0.0784207
$181$	−3.72764e25	−0.405630	−0.202815	−	0.979217i	$-0.565009\pi$
$181$	−3.72764e25	−0.405630	−0.202815	+	0.979217i	$0.565009\pi$
$182$	6.65680e25	0.679899
$183$	6.72779e25	0.645185
$184$	2.34689e25	0.211391
$185$	7.77466e25	0.657971
$186$	2.84220e25	0.226076
$187$	−1.83619e25	−0.137322
$188$	7.15772e24	0.0503454
$189$	1.10855e26	0.733577
$190$	3.56432e25	0.221978
$191$	−1.74153e26	−1.02105	−0.510525	−	0.859863i	$-0.670549\pi$
$191$	−1.74153e26	−1.02105	−0.510525	+	0.859863i	$0.670549\pi$
$192$	1.82429e25	0.100723
$193$	−2.40877e26	−1.25281	−0.626407	−	0.779496i	$-0.715475\pi$
$193$	−2.40877e26	−1.25281	−0.626407	+	0.779496i	$0.715475\pi$
$194$	2.30168e26	1.12804
$195$	1.11283e26	0.514079
$196$	−6.26441e25	−0.272857
$197$	−2.32299e26	−0.954303	−0.477152	−	0.878821i	$-0.658331\pi$
$197$	−2.32299e26	−0.954303	−0.477152	+	0.878821i	$0.658331\pi$
$198$	4.18817e25	0.162321
$199$	−3.32534e26	−1.21626	−0.608129	−	0.793838i	$-0.708080\pi$
$199$	−3.32534e26	−1.21626	−0.608129	+	0.793838i	$0.708080\pi$
$200$	2.04800e25	0.0707107
$201$	1.58016e26	0.515164
$202$	2.37218e26	0.730476
$203$	−2.10360e26	−0.612010
$204$	3.07420e25	0.0845249
$205$	2.34911e26	0.610568
$206$	−3.46632e26	−0.851913
$207$	−9.02064e25	−0.209690
$208$	−1.62167e26	−0.356644
$209$	2.20768e26	0.459467
$210$	8.71779e25	0.171745
$211$	−4.88737e26	−0.911647	−0.455823	−	0.890070i	$-0.650655\pi$
$211$	−4.88737e26	−0.911647	−0.455823	+	0.890070i	$0.650655\pi$
$212$	3.23553e26	0.571589
$213$	−6.64583e26	−1.11220
$214$	3.28205e26	0.520459
$215$	3.67877e26	0.552917
$216$	−2.70057e26	−0.384801
$217$	−1.97925e26	−0.267433
$218$	−2.55010e26	−0.326820
$219$	1.07851e27	1.31134
$220$	1.26850e26	0.146362
$221$	−2.73276e26	−0.299288
$222$	−8.06224e26	−0.838294
$223$	−1.80253e27	−1.77982	−0.889909	−	0.456138i	$-0.849232\pi$
$223$	−1.80253e27	−1.77982	−0.889909	+	0.456138i	$0.849232\pi$
$224$	−1.27040e26	−0.119149
$225$	−7.87182e25	−0.0701416
$226$	−1.70119e26	−0.144048
$227$	7.37727e26	0.593743	0.296871	−	0.954917i	$-0.404057\pi$
$227$	7.37727e26	0.593743	0.296871	+	0.954917i	$0.404057\pi$
$228$	−3.69616e26	−0.282814
$229$	1.94352e27	1.41410	0.707052	−	0.707162i	$-0.250025\pi$
$229$	1.94352e27	1.41410	0.707052	+	0.707162i	$0.250025\pi$
$230$	−2.73214e26	−0.189074
$231$	5.39966e26	0.355491
$232$	5.12461e26	0.321033
$233$	−2.43138e26	−0.144964	−0.0724820	−	0.997370i	$-0.523092\pi$
$233$	−2.43138e26	−0.144964	−0.0724820	+	0.997370i	$0.523092\pi$
$234$	6.23316e26	0.353774
$235$	−8.33269e25	−0.0450303
$236$	9.34293e26	0.480834
$237$	−7.87106e26	−0.385858
$238$	−2.14082e26	−0.0999872
$239$	3.60889e27	1.60619	0.803097	−	0.595848i	$-0.203184\pi$
$239$	3.60889e27	1.60619	0.803097	+	0.595848i	$0.203184\pi$
$240$	−2.12375e26	−0.0900897
$241$	2.00066e27	0.809056	0.404528	−	0.914526i	$-0.367436\pi$
$241$	2.00066e27	0.809056	0.404528	+	0.914526i	$0.367436\pi$
$242$	−1.04815e27	−0.404155
$243$	1.80649e27	0.664301
$244$	1.14135e27	0.400345
$245$	7.29274e26	0.244051
$246$	−2.43600e27	−0.777901
$247$	3.28564e27	1.00139
$248$	4.82169e26	0.140283
$249$	−6.82211e26	−0.189507
$250$	−2.38419e26	−0.0632456
$251$	−1.85132e27	−0.469065	−0.234533	−	0.972108i	$-0.575356\pi$
$251$	−1.85132e27	−0.469065	−0.234533	+	0.972108i	$0.575356\pi$
$252$	4.88300e26	0.118190
$253$	−1.69224e27	−0.391360
$254$	−2.77400e27	−0.613083
$255$	−3.57884e26	−0.0756014
$256$	3.09485e26	0.0625000
$257$	−7.13742e27	−1.37819	−0.689097	−	0.724669i	$-0.741992\pi$
$257$	−7.13742e27	−1.37819	−0.689097	+	0.724669i	$0.741992\pi$
$258$	−3.81484e27	−0.704450
$259$	5.61440e27	0.991644
$260$	1.88788e27	0.318992
$261$	−1.96973e27	−0.318449
$262$	−7.96019e27	−1.23157
$263$	−5.02930e27	−0.744761	−0.372380	−	0.928080i	$-0.621458\pi$
$263$	−5.02930e27	−0.744761	−0.372380	+	0.928080i	$0.621458\pi$
$264$	−1.31542e27	−0.186474
$265$	−3.76666e27	−0.511244
$266$	2.57394e27	0.334549
$267$	−3.46497e27	−0.431341
$268$	2.68068e27	0.319665
$269$	−1.17031e28	−1.33705	−0.668527	−	0.743688i	$-0.733075\pi$
$269$	−1.17031e28	−1.33705	−0.668527	+	0.743688i	$0.733075\pi$
$270$	3.14387e27	0.344177
$271$	−1.49314e27	−0.156659	−0.0783294	−	0.996928i	$-0.524959\pi$
$271$	−1.49314e27	−0.156659	−0.0783294	+	0.996928i	$0.524959\pi$
$272$	5.21528e26	0.0524487
$273$	8.03618e27	0.774781
$274$	9.71945e27	0.898484
$275$	−1.47673e27	−0.130910
$276$	2.83320e27	0.240892
$277$	3.00946e27	0.245454	0.122727	−	0.992440i	$-0.460836\pi$
$277$	3.00946e27	0.245454	0.122727	+	0.992440i	$0.460836\pi$
$278$	1.74532e28	1.36572
$279$	−1.85329e27	−0.139154
$280$	1.47894e27	0.106570
$281$	−1.97459e28	−1.36569	−0.682847	−	0.730562i	$-0.739258\pi$
$281$	−1.97459e28	−1.36569	−0.682847	+	0.730562i	$0.739258\pi$
$282$	8.64091e26	0.0573713
$283$	2.06841e28	1.31854	0.659270	−	0.751906i	$-0.270866\pi$
$283$	2.06841e28	1.31854	0.659270	+	0.751906i	$0.270866\pi$
$284$	−1.12744e28	−0.690134
$285$	4.30290e27	0.252956
$286$	1.16932e28	0.660274
$287$	1.69639e28	0.920203
$288$	−1.18956e27	−0.0619970
$289$	−1.90887e28	−0.955986
$290$	−5.96584e27	−0.287140
$291$	2.77862e28	1.28546
$292$	1.82965e28	0.813704
$293$	−2.59950e28	−1.11151	−0.555754	−	0.831347i	$-0.687570\pi$
$293$	−2.59950e28	−1.11151	−0.555754	+	0.831347i	$0.687570\pi$
$294$	−7.56249e27	−0.310936
$295$	−1.08766e28	−0.430071
$296$	−1.36773e28	−0.520171
$297$	1.94726e28	0.712403
$298$	1.01866e28	0.358543
$299$	−2.51852e28	−0.852957
$300$	2.47238e27	0.0805786
$301$	2.65659e28	0.833316
$302$	5.25458e27	0.158657
$303$	2.86372e28	0.832417
$304$	−6.27042e27	−0.175489
$305$	−1.32870e28	−0.358080
$306$	−2.00457e27	−0.0520266
$307$	5.17015e28	1.29245	0.646223	−	0.763149i	$-0.276348\pi$
$307$	5.17015e28	1.29245	0.646223	+	0.763149i	$0.276348\pi$
$308$	9.16034e27	0.220586
$309$	−4.18459e28	−0.970801
$310$	−5.61319e27	−0.125473
$311$	2.19009e28	0.471756	0.235878	−	0.971783i	$-0.424203\pi$
$311$	2.19009e28	0.471756	0.235878	+	0.971783i	$0.424203\pi$
$312$	−1.95771e28	−0.406415
$313$	−3.44520e28	−0.689373	−0.344686	−	0.938718i	$-0.612015\pi$
$313$	−3.44520e28	−0.689373	−0.344686	+	0.938718i	$0.612015\pi$
$314$	−4.55024e28	−0.877694
$315$	−5.68456e27	−0.105712
$316$	−1.33530e28	−0.239429
$317$	−4.25122e28	−0.735075	−0.367538	−	0.930009i	$-0.619799\pi$
$317$	−4.25122e28	−0.735075	−0.367538	+	0.930009i	$0.619799\pi$
$318$	3.90598e28	0.651356
$319$	−3.69514e28	−0.594345
$320$	−3.60288e27	−0.0559017
$321$	3.96214e28	0.593092
$322$	−1.97299e28	−0.284959
$323$	−1.05666e28	−0.147267
$324$	−1.95644e28	−0.263148
$325$	−2.19778e28	−0.285315
$326$	−6.06599e28	−0.760150
$327$	−3.07852e28	−0.372429
$328$	−4.13260e28	−0.482697
$329$	−6.01737e27	−0.0678663
$330$	1.53135e28	0.166788
$331$	1.43295e29	1.50733	0.753667	−	0.657256i	$-0.228283\pi$
$331$	1.43295e29	1.50733	0.753667	+	0.657256i	$0.228283\pi$
$332$	−1.15735e28	−0.117592
$333$	5.25710e28	0.515985
$334$	3.77362e28	0.357827
$335$	−3.12073e28	−0.285917
$336$	−1.53365e28	−0.135776
$337$	1.66695e28	0.142619	0.0713095	−	0.997454i	$-0.477282\pi$
$337$	1.66695e28	0.142619	0.0713095	+	0.997454i	$0.477282\pi$
$338$	8.85150e28	0.731939
$339$	−2.05370e28	−0.164150
$340$	−6.07138e27	−0.0469116
$341$	−3.47672e28	−0.259713
$342$	2.41014e28	0.174077
$343$	1.49168e29	1.04182
$344$	−6.47176e28	−0.437120
$345$	−3.29827e28	−0.215460
$346$	−1.89741e29	−1.19891
$347$	−7.87942e28	−0.481621	−0.240811	−	0.970572i	$-0.577413\pi$
$347$	−7.87942e28	−0.481621	−0.240811	+	0.970572i	$0.577413\pi$
$348$	6.18651e28	0.365834
$349$	−1.45984e29	−0.835244	−0.417622	−	0.908621i	$-0.637136\pi$
$349$	−1.45984e29	−0.835244	−0.417622	+	0.908621i	$0.637136\pi$
$350$	−1.72172e28	−0.0953190
$351$	2.89807e29	1.55266
$352$	−2.23157e28	−0.115710
$353$	5.29769e28	0.265875	0.132937	−	0.991124i	$-0.457559\pi$
$353$	5.29769e28	0.265875	0.132937	+	0.991124i	$0.457559\pi$
$354$	1.12789e29	0.547936
$355$	1.31252e29	0.617275
$356$	−5.87822e28	−0.267652
$357$	−2.58442e28	−0.113941
$358$	2.72866e29	1.16492
$359$	2.82466e29	1.16783	0.583915	−	0.811815i	$-0.301520\pi$
$359$	2.82466e29	1.16783	0.583915	+	0.811815i	$0.301520\pi$
$360$	1.38482e28	0.0554518
$361$	−1.30786e29	−0.507256
$362$	−7.63420e28	−0.286824
$363$	−1.26535e29	−0.460557
$364$	1.36331e29	0.480761
$365$	−2.13000e29	−0.727799
$366$	1.37785e29	0.456215
$367$	2.59135e29	0.831509	0.415755	−	0.909477i	$-0.363517\pi$
$367$	2.59135e29	0.831509	0.415755	+	0.909477i	$0.363517\pi$
$368$	4.80643e28	0.149476
$369$	1.58843e29	0.478812
$370$	1.59225e29	0.465255
$371$	−2.72006e29	−0.770509
$372$	5.82082e28	0.159860
$373$	−6.81722e29	−1.81533	−0.907665	−	0.419695i	$-0.862137\pi$
$373$	−6.81722e29	−1.81533	−0.907665	+	0.419695i	$0.862137\pi$
$374$	−3.76052e28	−0.0971011
$375$	−2.87822e28	−0.0720717
$376$	1.46590e28	0.0355996
$377$	−5.49939e29	−1.29536
$378$	2.27032e29	0.518718
$379$	8.03139e29	1.78008	0.890041	−	0.455881i	$-0.150676\pi$
$379$	8.03139e29	1.78008	0.890041	+	0.455881i	$0.150676\pi$
$380$	7.29973e28	0.156962
$381$	−3.34882e29	−0.698642
$382$	−3.56665e29	−0.721992
$383$	−9.93629e29	−1.95181	−0.975907	−	0.218189i	$-0.929985\pi$
$383$	−9.93629e29	−1.95181	−0.975907	+	0.218189i	$0.929985\pi$
$384$	3.73615e28	0.0712221
$385$	−1.06640e29	−0.197298
$386$	−4.93317e29	−0.885874
$387$	2.48752e29	0.433602
$388$	4.71383e29	0.797644
$389$	−8.33130e29	−1.36865	−0.684325	−	0.729177i	$-0.739903\pi$
$389$	−8.33130e29	−1.36865	−0.684325	+	0.729177i	$0.739903\pi$
$390$	2.27907e29	0.363509
$391$	8.09953e28	0.125437
$392$	−1.28295e29	−0.192939
$393$	−9.60966e29	−1.40344
$394$	−4.75749e29	−0.674794
$395$	1.55449e29	0.214152
$396$	8.57738e28	0.114778
$397$	6.39815e29	0.831694	0.415847	−	0.909435i	$-0.363485\pi$
$397$	6.39815e29	0.831694	0.415847	+	0.909435i	$0.363485\pi$
$398$	−6.81030e29	−0.860025
$399$	3.10730e29	0.381237
$400$	4.19430e28	0.0500000
$401$	1.37492e30	1.59264	0.796318	−	0.604879i	$-0.206778\pi$
$401$	1.37492e30	1.59264	0.796318	+	0.604879i	$0.206778\pi$
$402$	3.23616e29	0.364276
$403$	−5.17432e29	−0.566037
$404$	4.85821e29	0.516525
$405$	2.27760e29	0.235367
$406$	−4.30817e29	−0.432757
$407$	9.86214e29	0.963021
$408$	6.29596e28	0.0597682
$409$	2.04005e30	1.88288	0.941440	−	0.337181i	$-0.109473\pi$
$409$	2.04005e30	1.88288	0.941440	+	0.337181i	$0.109473\pi$
$410$	4.81098e29	0.431737
$411$	1.17335e30	1.02387
$412$	−7.09902e29	−0.602394
$413$	−7.85444e29	−0.648171
$414$	−1.84743e29	−0.148273
$415$	1.34733e29	0.105177
$416$	−3.32119e29	−0.252185
$417$	2.10698e30	1.55631
$418$	4.52134e29	0.324892
$419$	−5.19038e29	−0.362859	−0.181430	−	0.983404i	$-0.558072\pi$
$419$	−5.19038e29	−0.362859	−0.181430	+	0.983404i	$0.558072\pi$
$420$	1.78540e29	0.121442
$421$	−1.09510e30	−0.724787	−0.362394	−	0.932025i	$-0.618040\pi$
$421$	−1.09510e30	−0.724787	−0.362394	+	0.932025i	$0.618040\pi$
$422$	−1.00093e30	−0.644632
$423$	−5.63443e28	−0.0353131
$424$	6.62637e29	0.404174
$425$	7.06802e28	0.0419590
$426$	−1.36106e30	−0.786445
$427$	−9.59510e29	−0.539671
$428$	6.72164e29	0.368020
$429$	1.41162e30	0.752418
$430$	7.53412e29	0.390972
$431$	−1.78506e30	−0.901911	−0.450956	−	0.892546i	$-0.648917\pi$
$431$	−1.78506e30	−0.901911	−0.450956	+	0.892546i	$0.648917\pi$
$432$	−5.53076e29	−0.272096
$433$	1.83380e27	0.000878501 0	0.000439250	−	1.00000i	$-0.499860\pi$
$433$	1.83380e27	0.000878501 0	0.000439250		1.00000i	$0.499860\pi$
$434$	−4.05351e29	−0.189104
$435$	−7.20204e29	−0.327212
$436$	−5.22261e29	−0.231096
$437$	−9.73821e29	−0.419704
$438$	2.20879e30	0.927260
$439$	2.76531e30	1.13084	0.565420	−	0.824803i	$-0.308714\pi$
$439$	2.76531e30	1.13084	0.565420	+	0.824803i	$0.308714\pi$
$440$	2.59788e29	0.103494
$441$	4.93123e29	0.191387
$442$	−5.59668e29	−0.211629
$443$	−4.05895e30	−1.49545	−0.747724	−	0.664010i	$-0.768853\pi$
$443$	−4.05895e30	−1.49545	−0.747724	+	0.664010i	$0.768853\pi$
$444$	−1.65115e30	−0.592764
$445$	6.84314e29	0.239395
$446$	−3.69157e30	−1.25852
$447$	1.22974e30	0.408579
$448$	−2.60179e29	−0.0842509
$449$	−2.95251e30	−0.931876	−0.465938	−	0.884817i	$-0.654283\pi$
$449$	−2.95251e30	−0.931876	−0.465938	+	0.884817i	$0.654283\pi$
$450$	−1.61215e29	−0.0495976
$451$	2.97984e30	0.893641
$452$	−3.48404e29	−0.101857
$453$	6.34340e29	0.180798
$454$	1.51086e30	0.419840
$455$	−1.58710e30	−0.430006
$456$	−7.56974e29	−0.199979
$457$	−7.87636e29	−0.202903	−0.101452	−	0.994840i	$-0.532349\pi$
$457$	−7.87636e29	−0.202903	−0.101452	+	0.994840i	$0.532349\pi$
$458$	3.98033e30	0.999923
$459$	−9.32014e29	−0.228337
$460$	−5.59542e29	−0.133696
$461$	5.04802e30	1.17641	0.588207	−	0.808710i	$-0.299834\pi$
$461$	5.04802e30	1.17641	0.588207	+	0.808710i	$0.299834\pi$
$462$	1.10585e30	0.251370
$463$	−3.07277e30	−0.681316	−0.340658	−	0.940187i	$-0.610650\pi$
$463$	−3.07277e30	−0.681316	−0.340658	+	0.940187i	$0.610650\pi$
$464$	1.04952e30	0.227004
$465$	−6.77632e29	−0.142983
$466$	−4.97947e29	−0.102505
$467$	−7.91191e30	−1.58905	−0.794524	−	0.607233i	$-0.792279\pi$
$467$	−7.91191e30	−1.58905	−0.794524	+	0.607233i	$0.792279\pi$
$468$	1.27655e30	0.250156
$469$	−2.25360e30	−0.430913
$470$	−1.70653e29	−0.0318412
$471$	−5.49311e30	−1.00018
$472$	1.91343e30	0.340001
$473$	4.66651e30	0.809262
$474$	−1.61199e30	−0.272843
$475$	−8.49801e29	−0.140391
$476$	−4.38439e29	−0.0707016
$477$	−2.54695e30	−0.400922
$478$	7.39101e30	1.13575
$479$	−1.14342e30	−0.171533	−0.0857664	−	0.996315i	$-0.527334\pi$
$479$	−1.14342e30	−0.171533	−0.0857664	+	0.996315i	$0.527334\pi$
$480$	−4.34945e29	−0.0637030
$481$	1.46776e31	2.09887
$482$	4.09736e30	0.572089
$483$	−2.38182e30	−0.324726
$484$	−2.14662e30	−0.285781
$485$	−5.48762e30	−0.713435
$486$	3.69970e30	0.469731
$487$	3.69536e30	0.458220	0.229110	−	0.973401i	$-0.426419\pi$
$487$	3.69536e30	0.458220	0.229110	+	0.973401i	$0.426419\pi$
$488$	2.33748e30	0.283087
$489$	−7.32295e30	−0.866232
$490$	1.49355e30	0.172570
$491$	9.29094e30	1.04863	0.524315	−	0.851524i	$-0.324321\pi$
$491$	9.29094e30	1.04863	0.524315	+	0.851524i	$0.324321\pi$
$492$	−4.98894e30	−0.550059
$493$	1.76860e30	0.190497
$494$	6.72900e30	0.708093
$495$	−9.98539e29	−0.102661
$496$	9.87483e29	0.0991951
$497$	9.47821e30	0.930311
$498$	−1.39717e30	−0.134002
$499$	3.27584e29	0.0307019	0.0153510	−	0.999882i	$-0.495113\pi$
$499$	3.27584e29	0.0307019	0.0153510	+	0.999882i	$0.495113\pi$
$500$	−4.88281e29	−0.0447214
$501$	4.55557e30	0.407764
$502$	−3.79150e30	−0.331679
$503$	1.69287e30	0.144741	0.0723705	−	0.997378i	$-0.476944\pi$
$503$	1.69287e30	0.144741	0.0723705	+	0.997378i	$0.476944\pi$
$504$	1.00004e30	0.0835729
$505$	−5.65571e30	−0.461994
$506$	−3.46571e30	−0.276733
$507$	1.06857e31	0.834084
$508$	−5.68116e30	−0.433515
$509$	−7.45718e30	−0.556315	−0.278157	−	0.960536i	$-0.589724\pi$
$509$	−7.45718e30	−0.556315	−0.278157	+	0.960536i	$0.589724\pi$
$510$	−7.32946e29	−0.0534583
$511$	−1.53816e31	−1.09688
$512$	6.33825e29	0.0441942
$513$	1.12058e31	0.763998
$514$	−1.46174e31	−0.974530
$515$	8.26435e30	0.538797
$516$	−7.81280e30	−0.498121
$517$	−1.05700e30	−0.0659073
$518$	1.14983e31	0.701198
$519$	−2.29058e31	−1.36622
$520$	3.86637e30	0.225561
$521$	9.54796e30	0.544850	0.272425	−	0.962177i	$-0.412174\pi$
$521$	9.54796e30	0.544850	0.272425	+	0.962177i	$0.412174\pi$
$522$	−4.03400e30	−0.225178
$523$	−1.33111e31	−0.726851	−0.363425	−	0.931623i	$-0.618393\pi$
$523$	−1.33111e31	−0.726851	−0.363425	+	0.931623i	$0.618393\pi$
$524$	−1.63025e31	−0.870850
$525$	−2.07848e30	−0.108621
$526$	−1.03000e31	−0.526625
$527$	1.66405e30	0.0832425
$528$	−2.69398e30	−0.131857
$529$	−1.34159e31	−0.642509
$530$	−7.71411e30	−0.361504
$531$	−7.35458e30	−0.337265
$532$	5.27143e30	0.236562
$533$	4.43483e31	1.94766
$534$	−7.09627e30	−0.305004
$535$	−7.82502e30	−0.329167
$536$	5.49004e30	0.226038
$537$	3.29408e31	1.32748
$538$	−2.39679e31	−0.945440
$539$	9.25082e30	0.357198
$540$	6.43865e30	0.243370
$541$	−2.43916e31	−0.902551	−0.451275	−	0.892385i	$-0.649031\pi$
$541$	−2.43916e31	−0.902551	−0.451275	+	0.892385i	$0.649031\pi$
$542$	−3.05796e30	−0.110775
$543$	−9.21611e30	−0.326851
$544$	1.06809e30	0.0370868
$545$	6.07992e30	0.206699
$546$	1.64581e31	0.547853
$547$	−3.76722e31	−1.22791	−0.613955	−	0.789341i	$-0.710422\pi$
$547$	−3.76722e31	−1.22791	−0.613955	+	0.789341i	$0.710422\pi$
$548$	1.99054e31	0.635324
$549$	−8.98447e30	−0.280809
$550$	−3.02434e30	−0.0925676
$551$	−2.12642e31	−0.637389
$552$	5.80239e30	0.170336
$553$	1.12256e31	0.322754
$554$	6.16337e30	0.173563
$555$	1.92219e31	0.530184
$556$	3.57442e31	0.965707
$557$	6.10400e30	0.161540	0.0807700	−	0.996733i	$-0.474262\pi$
$557$	6.10400e30	0.161540	0.0807700	+	0.996733i	$0.474262\pi$
$558$	−3.79555e30	−0.0983968
$559$	6.94506e31	1.76376
$560$	3.02888e30	0.0753563
$561$	−4.53975e30	−0.110652
$562$	−4.04395e31	−0.965691
$563$	1.68208e31	0.393549	0.196775	−	0.980449i	$-0.436953\pi$
$563$	1.68208e31	0.393549	0.196775	+	0.980449i	$0.436953\pi$
$564$	1.76966e30	0.0405676
$565$	4.05596e30	0.0911038
$566$	4.23611e31	0.932348
$567$	1.64475e31	0.354727
$568$	−2.30900e31	−0.487999
$569$	6.94377e31	1.43815	0.719076	−	0.694932i	$-0.244566\pi$
$569$	6.94377e31	1.43815	0.719076	+	0.694932i	$0.244566\pi$
$570$	8.81234e30	0.178867
$571$	2.16544e31	0.430756	0.215378	−	0.976531i	$-0.430902\pi$
$571$	2.16544e31	0.430756	0.215378	+	0.976531i	$0.430902\pi$
$572$	2.39477e31	0.466884
$573$	−4.30572e31	−0.822749
$574$	3.47420e31	0.650682
$575$	6.51392e30	0.119581
$576$	−2.43621e30	−0.0438385
$577$	−2.82605e30	−0.0498492	−0.0249246	−	0.999689i	$-0.507935\pi$
$577$	−2.82605e30	−0.0498492	−0.0249246	+	0.999689i	$0.507935\pi$
$578$	−3.90937e31	−0.675984
$579$	−5.95539e31	−1.00950
$580$	−1.22180e31	−0.203039
$581$	9.72963e30	0.158515
$582$	5.69061e31	0.908959
$583$	−4.77800e31	−0.748269
$584$	3.74713e31	0.575376
$585$	−1.48610e31	−0.223746
$586$	−5.32378e31	−0.785955
$587$	−8.73921e31	−1.26513	−0.632563	−	0.774509i	$-0.717997\pi$
$587$	−8.73921e31	−1.26513	−0.632563	+	0.774509i	$0.717997\pi$
$588$	−1.54880e31	−0.219865
$589$	−2.00072e31	−0.278523
$590$	−2.22753e31	−0.304106
$591$	−5.74331e31	−0.768965
$592$	−2.80112e31	−0.367817
$593$	−7.84285e31	−1.01005	−0.505027	−	0.863103i	$-0.668518\pi$
$593$	−7.84285e31	−1.01005	−0.505027	+	0.863103i	$0.668518\pi$
$594$	3.98800e31	0.503745
$595$	5.10410e30	0.0632374
$596$	2.08621e31	0.253528
$597$	−8.22149e31	−0.980045
$598$	−5.15793e31	−0.603132
$599$	1.13954e32	1.30714	0.653570	−	0.756866i	$-0.273271\pi$
$599$	1.13954e32	1.30714	0.653570	+	0.756866i	$0.273271\pi$
$600$	5.06342e30	0.0569777
$601$	−1.12055e32	−1.23701	−0.618506	−	0.785780i	$-0.712262\pi$
$601$	−1.12055e32	−1.23701	−0.618506	+	0.785780i	$0.712262\pi$
$602$	5.44069e31	0.589243
$603$	−2.11019e31	−0.224219
$604$	1.07614e31	0.112187
$605$	2.49899e31	0.255610
$606$	5.86491e31	0.588608
$607$	−2.47121e31	−0.243355	−0.121677	−	0.992570i	$-0.538827\pi$
$607$	−2.47121e31	−0.243355	−0.121677	+	0.992570i	$0.538827\pi$
$608$	−1.28418e31	−0.124090
$609$	−5.20089e31	−0.493150
$610$	−2.72118e31	−0.253201
$611$	−1.57311e31	−0.143643
$612$	−4.10537e30	−0.0367884
$613$	2.06753e32	1.81826	0.909131	−	0.416511i	$-0.136747\pi$
$613$	2.06753e32	1.81826	0.909131	+	0.416511i	$0.136747\pi$
$614$	1.05885e32	0.913897
$615$	5.80788e31	0.491988
$616$	1.87604e31	0.155978
$617$	−1.21753e32	−0.993572	−0.496786	−	0.867873i	$-0.665487\pi$
$617$	−1.21753e32	−0.993572	−0.496786	+	0.867873i	$0.665487\pi$
$618$	−8.57004e31	−0.686460
$619$	2.23981e32	1.76104	0.880518	−	0.474012i	$-0.157195\pi$
$619$	2.23981e32	1.76104	0.880518	+	0.474012i	$0.157195\pi$
$620$	−1.14958e31	−0.0887228
$621$	−8.58949e31	−0.650749
$622$	4.48530e31	0.333582
$623$	4.94171e31	0.360799
$624$	−4.00938e31	−0.287379
$625$	5.68434e30	0.0400000
$626$	−7.05576e31	−0.487460
$627$	5.45822e31	0.370233
$628$	−9.31889e31	−0.620623
$629$	−4.72029e31	−0.308664
$630$	−1.16420e31	−0.0747499
$631$	7.64725e31	0.482134	0.241067	−	0.970508i	$-0.422503\pi$
$631$	7.64725e31	0.482134	0.241067	+	0.970508i	$0.422503\pi$
$632$	−2.73469e31	−0.169302
$633$	−1.20834e32	−0.734593
$634$	−8.70649e31	−0.519777
$635$	6.61374e31	0.387748
$636$	7.99945e31	0.460578
$637$	1.37678e32	0.778503
$638$	−7.56765e31	−0.420265
$639$	8.87502e31	0.484071
$640$	−7.37870e30	−0.0395285
$641$	−5.00356e31	−0.263276	−0.131638	−	0.991298i	$-0.542024\pi$
$641$	−5.00356e31	−0.263276	−0.131638	+	0.991298i	$0.542024\pi$
$642$	8.11446e31	0.419379
$643$	1.82713e32	0.927565	0.463783	−	0.885949i	$-0.346492\pi$
$643$	1.82713e32	0.927565	0.463783	+	0.885949i	$0.346492\pi$
$644$	−4.04068e31	−0.201496
$645$	9.09530e31	0.445533
$646$	−2.16404e31	−0.104133
$647$	1.03583e32	0.489653	0.244826	−	0.969567i	$-0.421269\pi$
$647$	1.03583e32	0.489653	0.244826	+	0.969567i	$0.421269\pi$
$648$	−4.00680e31	−0.186074
$649$	−1.37970e32	−0.629461
$650$	−4.50105e31	−0.201748
$651$	−4.89346e31	−0.215494
$652$	−1.24231e32	−0.537507
$653$	2.79465e32	1.18802	0.594012	−	0.804456i	$-0.297543\pi$
$653$	2.79465e32	1.18802	0.594012	+	0.804456i	$0.297543\pi$
$654$	−6.30481e31	−0.263347
$655$	1.89786e32	0.778912
$656$	−8.46357e31	−0.341318
$657$	−1.44027e32	−0.570745
$658$	−1.23236e31	−0.0479887
$659$	1.29327e32	0.494886	0.247443	−	0.968902i	$-0.420410\pi$
$659$	1.29327e32	0.494886	0.247443	+	0.968902i	$0.420410\pi$
$660$	3.13620e31	0.117937
$661$	1.04268e32	0.385330	0.192665	−	0.981265i	$-0.438287\pi$
$661$	1.04268e32	0.385330	0.192665	+	0.981265i	$0.438287\pi$
$662$	2.93468e32	1.06585
$663$	−6.75640e31	−0.241162
$664$	−2.37025e31	−0.0831498
$665$	−6.13676e31	−0.211587
$666$	1.07665e32	0.364857
$667$	1.62995e32	0.542909
$668$	7.72837e31	0.253022
$669$	−4.45652e32	−1.43415
$670$	−6.39125e31	−0.202174
$671$	−1.68546e32	−0.524093
$672$	−3.14091e31	−0.0960084
$673$	9.42317e31	0.283155	0.141577	−	0.989927i	$-0.454783\pi$
$673$	9.42317e31	0.283155	0.141577	+	0.989927i	$0.454783\pi$
$674$	3.41390e31	0.100847
$675$	−7.49557e31	−0.217676
$676$	1.81279e32	0.517559
$677$	−2.82722e32	−0.793577	−0.396789	−	0.917910i	$-0.629875\pi$
$677$	−2.82722e32	−0.793577	−0.396789	+	0.917910i	$0.629875\pi$
$678$	−4.20599e31	−0.116072
$679$	−3.96284e32	−1.07524
$680$	−1.24342e31	−0.0331715
$681$	1.82394e32	0.478430
$682$	−7.12032e31	−0.183645
$683$	−6.52604e31	−0.165505	−0.0827525	−	0.996570i	$-0.526371\pi$
$683$	−6.52604e31	−0.165505	−0.0827525	+	0.996570i	$0.526371\pi$
$684$	4.93596e31	0.123091
$685$	−2.31730e32	−0.568251
$686$	3.05496e32	0.736680
$687$	4.80512e32	1.13947
$688$	−1.32542e32	−0.309090
$689$	−7.11098e32	−1.63083
$690$	−6.75487e31	−0.152353
$691$	−5.18137e31	−0.114934	−0.0574668	−	0.998347i	$-0.518302\pi$
$691$	−5.18137e31	−0.114934	−0.0574668	+	0.998347i	$0.518302\pi$
$692$	−3.88590e32	−0.847757
$693$	−7.21085e31	−0.154723
$694$	−1.61371e32	−0.340558
$695$	−4.16117e32	−0.863755
$696$	1.26700e32	0.258684
$697$	−1.42623e32	−0.286427
$698$	−2.98976e32	−0.590607
$699$	−6.01129e31	−0.116810
$700$	−3.52608e31	−0.0674007
$701$	−6.09165e32	−1.14545	−0.572727	−	0.819746i	$-0.694114\pi$
$701$	−6.09165e32	−1.14545	−0.572727	+	0.819746i	$0.694114\pi$
$702$	5.93524e32	1.09790
$703$	5.67529e32	1.03277
$704$	−4.57025e31	−0.0818190
$705$	−2.06015e31	−0.0362848
$706$	1.08497e32	0.188002
$707$	−4.08422e32	−0.696282
$708$	2.30992e32	0.387449
$709$	8.97201e32	1.48067	0.740334	−	0.672239i	$-0.234667\pi$
$709$	8.97201e32	1.48067	0.740334	+	0.672239i	$0.234667\pi$
$710$	2.68803e32	0.436479
$711$	1.05112e32	0.167940
$712$	−1.20386e32	−0.189259
$713$	1.53360e32	0.237237
$714$	−5.29290e31	−0.0805683
$715$	−2.78788e32	−0.417594
$716$	5.58829e32	0.823719
$717$	8.92254e32	1.29425
$718$	5.78490e32	0.825780
$719$	−7.87343e32	−1.10607	−0.553034	−	0.833159i	$-0.686530\pi$
$719$	−7.87343e32	−1.10607	−0.553034	+	0.833159i	$0.686530\pi$
$720$	2.83612e31	0.0392104
$721$	5.96802e32	0.812035
$722$	−2.67849e32	−0.358684
$723$	4.94639e32	0.651926
$724$	−1.56348e32	−0.202815
$725$	1.42237e32	0.181604
$726$	−2.59143e32	−0.325663
$727$	−3.15970e32	−0.390841	−0.195421	−	0.980720i	$-0.562607\pi$
$727$	−3.15970e32	−0.390841	−0.195421	+	0.980720i	$0.562607\pi$
$728$	2.79206e32	0.339949
$729$	8.85767e32	1.06158
$730$	−4.36224e32	−0.514631
$731$	−2.23352e32	−0.259382
$732$	2.82184e32	0.322593
$733$	9.47917e31	0.106678	0.0533389	−	0.998576i	$-0.483014\pi$
$733$	9.47917e31	0.106678	0.0533389	+	0.998576i	$0.483014\pi$
$734$	5.30709e32	0.587966
$735$	1.80304e32	0.196653
$736$	9.84356e31	0.105696
$737$	−3.95864e32	−0.418475
$738$	3.25311e32	0.338571
$739$	−4.13181e32	−0.423379	−0.211689	−	0.977337i	$-0.567897\pi$
$739$	−4.13181e32	−0.423379	−0.211689	+	0.977337i	$0.567897\pi$
$740$	3.26093e32	0.328985
$741$	8.12334e32	0.806910
$742$	−5.57068e32	−0.544832
$743$	2.23848e32	0.215566	0.107783	−	0.994174i	$-0.465625\pi$
$743$	2.23848e32	0.215566	0.107783	+	0.994174i	$0.465625\pi$
$744$	1.19210e32	0.113038
$745$	−2.42867e32	−0.226763
$746$	−1.39617e33	−1.28363
$747$	9.11043e31	0.0824807
$748$	−7.70154e31	−0.0686608
$749$	−5.65076e32	−0.496097
$750$	−5.89460e31	−0.0509624
$751$	1.65408e33	1.40831	0.704154	−	0.710047i	$-0.251326\pi$
$751$	1.65408e33	1.40831	0.704154	+	0.710047i	$0.251326\pi$
$752$	3.00217e31	0.0251727
$753$	−4.57715e32	−0.377967
$754$	−1.12628e33	−0.915955
$755$	−1.25279e32	−0.100343
$756$	4.64961e32	0.366789
$757$	−6.98662e32	−0.542831	−0.271415	−	0.962462i	$-0.587492\pi$
$757$	−6.98662e32	−0.542831	−0.271415	+	0.962462i	$0.587492\pi$
$758$	1.64483e33	1.25871
$759$	−4.18386e32	−0.315353
$760$	1.49498e32	0.110989
$761$	−9.28523e32	−0.678999	−0.339499	−	0.940606i	$-0.610258\pi$
$761$	−9.28523e32	−0.678999	−0.339499	+	0.940606i	$0.610258\pi$
$762$	−6.85838e32	−0.494014
$763$	4.39056e32	0.311521
$764$	−7.30451e32	−0.510525
$765$	4.77928e31	0.0329045
$766$	−2.03495e33	−1.38014
$767$	−2.05337e33	−1.37189
$768$	7.65163e31	0.0503617
$769$	1.31566e33	0.853081	0.426540	−	0.904469i	$-0.359732\pi$
$769$	1.31566e33	0.853081	0.426540	+	0.904469i	$0.359732\pi$
$770$	−2.18400e32	−0.139511
$771$	−1.76464e33	−1.11053
$772$	−1.01031e33	−0.626407
$773$	−1.01794e33	−0.621813	−0.310906	−	0.950441i	$-0.600633\pi$
$773$	−1.01794e33	−0.621813	−0.310906	+	0.950441i	$0.600633\pi$
$774$	5.09445e32	0.306603
$775$	1.33829e32	0.0793561
$776$	9.65393e32	0.564020
$777$	1.38809e33	0.799054
$778$	−1.70625e33	−0.967781
$779$	1.71479e33	0.958362
$780$	4.66754e32	0.257039
$781$	1.66492e33	0.903457
$782$	1.65878e32	0.0886977
$783$	−1.87558e33	−0.988271
$784$	−2.62749e32	−0.136429
$785$	1.08486e33	0.555102
$786$	−1.96806e33	−0.992381
$787$	3.95568e33	1.96567	0.982837	−	0.184475i	$-0.0590583\pi$
$787$	3.95568e33	1.96567	0.982837	+	0.184475i	$0.0590583\pi$
$788$	−9.74334e32	−0.477152
$789$	−1.24343e33	−0.600118
$790$	3.18360e32	0.151428
$791$	2.92897e32	0.137305
$792$	1.75665e32	0.0811606
$793$	−2.50842e33	−1.14225
$794$	1.31034e33	0.588097
$795$	−9.31259e32	−0.411954
$796$	−1.39475e33	−0.608129
$797$	2.05790e33	0.884408	0.442204	−	0.896914i	$-0.354197\pi$
$797$	2.05790e33	0.884408	0.442204	+	0.896914i	$0.354197\pi$
$798$	6.36375e32	0.269575
$799$	5.05909e31	0.0211244
$800$	8.58993e31	0.0353553
$801$	4.62722e32	0.187736
$802$	2.81583e33	1.12616
$803$	−2.70190e33	−1.06522
$804$	6.62766e32	0.257582
$805$	4.70397e32	0.180224
$806$	−1.05970e33	−0.400249
$807$	−2.89344e33	−1.07738
$808$	9.94962e32	0.365238
$809$	3.34033e33	1.20887	0.604437	−	0.796653i	$-0.293398\pi$
$809$	3.34033e33	1.20887	0.604437	+	0.796653i	$0.293398\pi$
$810$	4.66452e32	0.166429
$811$	4.70664e33	1.65566	0.827830	−	0.560980i	$-0.189575\pi$
$811$	4.70664e33	1.65566	0.827830	+	0.560980i	$0.189575\pi$
$812$	−8.82314e32	−0.306005
$813$	−3.69161e32	−0.126234
$814$	2.01977e33	0.680958
$815$	1.44624e33	0.480761
$816$	1.28941e32	0.0422625
$817$	2.68540e33	0.867872
$818$	4.17802e33	1.33140
$819$	−1.07317e33	−0.337214
$820$	9.85289e32	0.305284
$821$	−1.93945e33	−0.592561	−0.296281	−	0.955101i	$-0.595746\pi$
$821$	−1.93945e33	−0.592561	−0.296281	+	0.955101i	$0.595746\pi$
$822$	2.40301e33	0.723986
$823$	−6.10374e33	−1.81342	−0.906709	−	0.421756i	$-0.861414\pi$
$823$	−6.10374e33	−1.81342	−0.906709	+	0.421756i	$0.861414\pi$
$824$	−1.45388e33	−0.425957
$825$	−3.65102e32	−0.105486
$826$	−1.60859e33	−0.458326
$827$	−2.51659e33	−0.707129	−0.353564	−	0.935410i	$-0.615030\pi$
$827$	−2.51659e33	−0.707129	−0.353564	+	0.935410i	$0.615030\pi$
$828$	−3.78353e32	−0.104845
$829$	3.51989e33	0.961948	0.480974	−	0.876735i	$-0.340283\pi$
$829$	3.51989e33	0.961948	0.480974	+	0.876735i	$0.340283\pi$
$830$	2.75933e32	0.0743714
$831$	7.44051e32	0.197784
$832$	−6.80179e32	−0.178322
$833$	−4.42770e32	−0.114488
$834$	4.31509e33	1.10048
$835$	−8.99701e32	−0.226310
$836$	9.25970e32	0.229734
$837$	−1.76471e33	−0.431849
$838$	−1.06299e33	−0.256580
$839$	−2.21395e33	−0.527116	−0.263558	−	0.964644i	$-0.584896\pi$
$839$	−2.21395e33	−0.527116	−0.263558	+	0.964644i	$0.584896\pi$
$840$	3.65651e32	0.0858726
$841$	−7.57601e32	−0.175504
$842$	−2.24277e33	−0.512502
$843$	−4.88192e33	−1.10046
$844$	−2.04991e33	−0.455823
$845$	−2.11036e33	−0.462919
$846$	−1.15393e32	−0.0249701
$847$	1.80462e33	0.385237
$848$	1.35708e33	0.285794
$849$	5.11389e33	1.06246
$850$	1.44753e32	0.0296695
$851$	−4.35025e33	−0.879678
$852$	−2.78746e33	−0.556101
$853$	−1.33116e33	−0.262008	−0.131004	−	0.991382i	$-0.541820\pi$
$853$	−1.33116e33	−0.262008	−0.131004	+	0.991382i	$0.541820\pi$
$854$	−1.96508e33	−0.381605
$855$	−5.74621e32	−0.110096
$856$	1.37659e33	0.260230
$857$	2.64308e33	0.492982	0.246491	−	0.969145i	$-0.420722\pi$
$857$	2.64308e33	0.492982	0.246491	+	0.969145i	$0.420722\pi$
$858$	2.89100e33	0.532040
$859$	−8.59233e32	−0.156023	−0.0780117	−	0.996952i	$-0.524857\pi$
$859$	−8.59233e32	−0.156023	−0.0780117	+	0.996952i	$0.524857\pi$
$860$	1.54299e33	0.276459
$861$	4.19411e33	0.741487
$862$	−3.65580e33	−0.637748
$863$	6.91408e33	1.19017	0.595087	−	0.803661i	$-0.297118\pi$
$863$	6.91408e33	1.19017	0.595087	+	0.803661i	$0.297118\pi$
$864$	−1.13270e33	−0.192401
$865$	4.52378e33	0.758257
$866$	3.75563e30	0.000621194 0
$867$	−4.71945e33	−0.770321
$868$	−8.30159e32	−0.133716
$869$	1.97187e33	0.313438
$870$	−1.47498e33	−0.231374
$871$	−5.89154e33	−0.912054
$872$	−1.06959e33	−0.163410
$873$	−3.71064e33	−0.559481
$874$	−1.99439e33	−0.296775
$875$	4.10489e32	0.0602850
$876$	4.52359e33	0.655672
$877$	−8.45783e33	−1.20994	−0.604969	−	0.796249i	$-0.706815\pi$
$877$	−8.45783e33	−1.20994	−0.604969	+	0.796249i	$0.706815\pi$
$878$	5.66335e33	0.799625
$879$	−6.42694e33	−0.895638
$880$	5.32047e32	0.0731811
$881$	−6.75908e33	−0.917623	−0.458812	−	0.888534i	$-0.651725\pi$
$881$	−6.75908e33	−0.917623	−0.458812	+	0.888534i	$0.651725\pi$
$882$	1.00992e33	0.135331
$883$	1.02125e34	1.35077	0.675386	−	0.737464i	$-0.263977\pi$
$883$	1.02125e34	1.35077	0.675386	+	0.737464i	$0.263977\pi$
$884$	−1.14620e33	−0.149644
$885$	−2.68910e33	−0.346545
$886$	−8.31273e33	−1.05744
$887$	9.62143e33	1.20814	0.604071	−	0.796931i	$-0.293544\pi$
$887$	9.62143e33	1.20814	0.604071	+	0.796931i	$0.293544\pi$
$888$	−3.38155e33	−0.419147
$889$	4.77605e33	0.584385
$890$	1.40148e33	0.169278
$891$	2.88913e33	0.344488
$892$	−7.56034e33	−0.889909
$893$	−6.08264e32	−0.0706806
$894$	2.51850e33	0.288909
$895$	−6.50563e33	−0.736757
$896$	−5.32846e32	−0.0595744
$897$	−6.22673e33	−0.687301
$898$	−6.04673e33	−0.658936
$899$	3.34874e33	0.360284
$900$	−3.30168e32	−0.0350708
$901$	2.28688e33	0.239833
$902$	6.10272e33	0.631900
$903$	6.56808e33	0.671475
$904$	−7.13532e32	−0.0720239
$905$	1.82013e33	0.181403
$906$	1.29913e33	0.127843
$907$	4.24872e33	0.412833	0.206416	−	0.978464i	$-0.433820\pi$
$907$	4.24872e33	0.412833	0.206416	+	0.978464i	$0.433820\pi$
$908$	3.09425e33	0.296871
$909$	−3.82430e33	−0.362299
$910$	−3.25039e33	−0.304060
$911$	1.36929e34	1.26483	0.632417	−	0.774628i	$-0.282063\pi$
$911$	1.36929e34	1.26483	0.632417	+	0.774628i	$0.282063\pi$
$912$	−1.55028e33	−0.141407
$913$	1.70909e33	0.153940
$914$	−1.61308e33	−0.143474
$915$	−3.28505e33	−0.288536
$916$	8.15172e33	0.707052
$917$	1.37052e34	1.17392
$918$	−1.90876e33	−0.161459
$919$	5.57801e33	0.465963	0.232981	−	0.972481i	$-0.425152\pi$
$919$	5.57801e33	0.465963	0.232981	+	0.972481i	$0.425152\pi$
$920$	−1.14594e33	−0.0945371
$921$	1.27826e34	1.04143
$922$	1.03383e34	0.831851
$923$	2.47787e34	1.96906
$924$	2.26478e33	0.177745
$925$	−3.79622e33	−0.294253
$926$	−6.29304e33	−0.481763
$927$	5.58822e33	0.422529
$928$	2.14942e33	0.160516
$929$	−1.60947e34	−1.18714	−0.593571	−	0.804782i	$-0.702282\pi$
$929$	−1.60947e34	−1.18714	−0.593571	+	0.804782i	$0.702282\pi$
$930$	−1.38779e33	−0.101104
$931$	5.32350e33	0.383068
$932$	−1.01980e33	−0.0724820
$933$	5.41473e33	0.380135
$934$	−1.62036e34	−1.12363
$935$	8.96577e32	0.0614121
$936$	2.61438e33	0.176887
$937$	2.39248e33	0.159898	0.0799489	−	0.996799i	$-0.474524\pi$
$937$	2.39248e33	0.159898	0.0799489	+	0.996799i	$0.474524\pi$
$938$	−4.61538e33	−0.304702
$939$	−8.51782e33	−0.555487
$940$	−3.49498e32	−0.0225151
$941$	−1.12281e34	−0.714537	−0.357268	−	0.934002i	$-0.616292\pi$
$941$	−1.12281e34	−0.714537	−0.357268	+	0.934002i	$0.616292\pi$
$942$	−1.12499e34	−0.707234
$943$	−1.31443e34	−0.816303
$944$	3.91871e33	0.240417
$945$	−5.41286e33	−0.328066
$946$	9.55702e33	0.572235
$947$	−4.28978e33	−0.253752	−0.126876	−	0.991919i	$-0.540495\pi$
$947$	−4.28978e33	−0.253752	−0.126876	+	0.991919i	$0.540495\pi$
$948$	−3.30136e33	−0.192929
$949$	−4.02117e34	−2.32162
$950$	−1.74039e33	−0.0992717
$951$	−1.05106e34	−0.592314
$952$	−8.97923e32	−0.0499936
$953$	3.92575e33	0.215951	0.107975	−	0.994154i	$-0.465563\pi$
$953$	3.92575e33	0.215951	0.107975	+	0.994154i	$0.465563\pi$
$954$	−5.21616e33	−0.283494
$955$	8.50357e33	0.456628
$956$	1.51368e34	0.803097
$957$	−9.13578e33	−0.478915
$958$	−2.34172e33	−0.121292
$959$	−1.67341e34	−0.856426
$960$	−8.90767e32	−0.0450448
$961$	−1.68625e34	−0.842565
$962$	3.00597e34	1.48413
$963$	−5.29115e33	−0.258136
$964$	8.39140e33	0.404528
$965$	1.17616e34	0.560276
$966$	−4.87796e33	−0.229616
$967$	−2.44005e33	−0.113500	−0.0567498	−	0.998388i	$-0.518074\pi$
$967$	−2.44005e33	−0.113500	−0.0567498	+	0.998388i	$0.518074\pi$
$968$	−4.39627e33	−0.202078
$969$	−2.61245e33	−0.118666
$970$	−1.12387e34	−0.504475
$971$	1.61207e34	0.715094	0.357547	−	0.933895i	$-0.383613\pi$
$971$	1.61207e34	0.715094	0.357547	+	0.933895i	$0.383613\pi$
$972$	7.57699e33	0.332150
$973$	−3.00495e34	−1.30179
$974$	7.56810e33	0.324010
$975$	−5.43373e33	−0.229903
$976$	4.78716e33	0.200173
$977$	−3.11737e34	−1.28825	−0.644126	−	0.764920i	$-0.722779\pi$
$977$	−3.11737e34	−1.28825	−0.644126	+	0.764920i	$0.722779\pi$
$978$	−1.49974e34	−0.612519
$979$	8.68052e33	0.350384
$980$	3.05880e33	0.122025
$981$	4.11114e33	0.162095
$982$	1.90278e34	0.741494
$983$	3.16423e34	1.21872	0.609358	−	0.792895i	$-0.291427\pi$
$983$	3.16423e34	1.21872	0.609358	+	0.792895i	$0.291427\pi$
$984$	−1.02173e34	−0.388950
$985$	1.13427e34	0.426777
$986$	3.62209e33	0.134702
$987$	−1.48772e33	−0.0546857
$988$	1.37810e34	0.500697
$989$	−2.05842e34	−0.739227
$990$	−2.04501e33	−0.0725922
$991$	−2.83514e34	−0.994779	−0.497390	−	0.867527i	$-0.665708\pi$
$991$	−2.83514e34	−0.994779	−0.497390	+	0.867527i	$0.665708\pi$
$992$	2.02236e33	0.0701415
$993$	3.54279e34	1.21459
$994$	1.94114e34	0.657829
$995$	1.62370e34	0.543927
$996$	−2.86140e33	−0.0947537
$997$	1.22327e34	0.400430	0.200215	−	0.979752i	$-0.435836\pi$
$997$	1.22327e34	0.400430	0.200215	+	0.979752i	$0.435836\pi$
$998$	6.70891e32	0.0217096
$999$	5.00583e34	1.60130

Twists

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

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

\(f(q)\)	\(=\)	\(q+2048.00 q^{2} +247238. q^{3} +4.19430e6 q^{4} -4.88281e7 q^{5} +5.06342e8 q^{6} -3.52608e9 q^{7} +8.58993e9 q^{8} -3.30168e10 q^{9} -1.00000e11 q^{10} -6.19384e11 q^{11} +1.03699e12 q^{12} -9.21814e12 q^{13} -7.22141e12 q^{14} -1.20721e13 q^{15} +1.75922e13 q^{16} +2.96454e13 q^{17} -6.76184e13 q^{18} -3.56432e14 q^{19} -2.04800e14 q^{20} -8.71779e14 q^{21} -1.26850e15 q^{22} +2.73214e15 q^{23} +2.12375e15 q^{24} +2.38419e15 q^{25} -1.88788e16 q^{26} -3.14387e16 q^{27} -1.47894e16 q^{28} +5.96584e16 q^{29} -2.47238e16 q^{30} +5.61319e16 q^{31} +3.60288e16 q^{32} -1.53135e17 q^{33} +6.07138e16 q^{34} +1.72172e17 q^{35} -1.38482e17 q^{36} -1.59225e18 q^{37} -7.29973e17 q^{38} -2.27907e18 q^{39} -4.19430e17 q^{40} -4.81098e18 q^{41} -1.78540e18 q^{42} -7.53412e18 q^{43} -2.59788e18 q^{44} +1.61215e18 q^{45} +5.59542e18 q^{46} +1.70653e18 q^{47} +4.34945e18 q^{48} -1.49355e19 q^{49} +4.88281e18 q^{50} +7.32946e18 q^{51} -3.86637e19 q^{52} +7.71411e19 q^{53} -6.43865e19 q^{54} +3.02434e19 q^{55} -3.02888e19 q^{56} -8.81234e19 q^{57} +1.22180e20 q^{58} +2.22753e20 q^{59} -5.06342e19 q^{60} +2.72118e20 q^{61} +1.14958e20 q^{62} +1.16420e20 q^{63} +7.37870e19 q^{64} +4.50105e20 q^{65} -3.13620e20 q^{66} +6.39125e20 q^{67} +1.24342e20 q^{68} +6.75487e20 q^{69} +3.52608e20 q^{70} -2.68803e21 q^{71} -2.83612e20 q^{72} +4.36224e21 q^{73} -3.26093e21 q^{74} +5.89460e20 q^{75} -1.49498e21 q^{76} +2.18400e21 q^{77} -4.66754e21 q^{78} -3.18360e21 q^{79} -8.58993e20 q^{80} -4.66452e21 q^{81} -9.85289e21 q^{82} -2.75933e21 q^{83} -3.65651e21 q^{84} -1.44753e21 q^{85} -1.54299e22 q^{86} +1.47498e22 q^{87} -5.32047e21 q^{88} -1.40148e22 q^{89} +3.30168e21 q^{90} +3.25039e22 q^{91} +1.14594e22 q^{92} +1.38779e22 q^{93} +3.49498e21 q^{94} +1.74039e22 q^{95} +8.90767e21 q^{96} +1.12387e23 q^{97} -3.05880e22 q^{98} +2.04501e22 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 4096 q^{2} - 91884 q^{3} + 8388608 q^{4} - 97656250 q^{5} - 188178432 q^{6} + 2146058908 q^{7} + 17179869184 q^{8} - 12156555726 q^{9} - 200000000000 q^{10} - 692289571776 q^{11} - 385389428736 q^{12}+ \cdots + 18\!\cdots\!88 q^{99}+O(q^{100}) \) 2 * q + 4096 * q^2 - 91884 * q^3 + 8388608 * q^4 - 97656250 * q^5 - 188178432 * q^6 + 2146058908 * q^7 + 17179869184 * q^8 - 12156555726 * q^9 - 200000000000 * q^10 - 692289571776 * q^11 - 385389428736 * q^12 - 1708452301484 * q^13 + 4395128643584 * q^14 + 4486523437500 * q^15 + 35184372088832 * q^16 - 93149332240332 * q^17 - 24896626126848 * q^18 - 970438534616600 * q^19 - 409600000000000 * q^20 - 2795322363317736 * q^21 - 1417809042997248 * q^22 - 962002498409964 * q^23 - 789277550051328 * q^24 + 4768371582031250 * q^25 - 3498910313439232 * q^26 - 6586889273700840 * q^27 + 9001223462060032 * q^28 - 40394756391690180 * q^29 + 9188400000000000 * q^30 - 54819002015519096 * q^31 + 72057594037927936 * q^32 - 128411117205326208 * q^33 - 190769832428199936 * q^34 - 104788032617187500 * q^35 - 50988290307784704 * q^36 - 2098544042837784332 * q^37 - 1987458118894796800 * q^38 - 4825767984454719672 * q^39 - 838860800000000000 * q^40 - 4273739814696341076 * q^41 - 5724820200074723328 * q^42 - 10838321168303261564 * q^43 - 2903672920058363904 * q^44 + 593581822558593750 * q^45 - 1970181116743606272 * q^46 - 26680537462560731892 * q^47 - 1616440422505119744 * q^48 - 10131136165510839654 * q^49 + 9765625000000000000 * q^50 + 48971798778005595144 * q^51 - 7165768321923547136 * q^52 + 33753250226251705956 * q^53 - 13489949232539320320 * q^54 + 33803201746875000000 * q^55 + 18434505650298945536 * q^56 + 120099366912137840400 * q^57 - 82728461090181488640 * q^58 + 40199521927491576840 * q^59 + 18817843200000000000 * q^60 + 803606238589543626004 * q^61 - 112269316127783108608 * q^62 + 234741824681222343996 * q^63 + 147573952589676412928 * q^64 + 83420522533398437500 * q^65 - 262985968036508073984 * q^66 + 2102618843174916067948 * q^67 - 390696616812953468928 * q^68 + 1928248820541872217288 * q^69 - 214605890800000000000 * q^70 + 718243220673362466264 * q^71 - 104424018550343073792 * q^72 + 3142915833207124335076 * q^73 - 4297818199731782311936 * q^74 - 219068527221679687500 * q^75 - 4070314227496543846400 * q^76 + 1770465757062240180096 * q^77 - 9883172832163265888256 * q^78 - 7052319452018896981520 * q^79 - 1717986918400000000000 * q^80 - 15056162150854903841718 * q^81 - 8752619140498106523648 * q^82 - 21904593841262540808444 * q^83 - 11724431769753033375744 * q^84 + 4548307238297460937500 * q^85 - 22196881752685079683072 * q^86 + 48679951535733201231960 * q^87 - 5946722140279529275392 * q^88 - 198123608118313558380 * q^89 + 1215655572600000000000 * q^90 + 75099870901057528941464 * q^91 - 4034930927090905645056 * q^92 + 51503746828643496862032 * q^93 - 54641740723324378914816 * q^94 + 47384694073076171875000 * q^95 - 3310469985290485235712 * q^96 + 115777326079591770710788 * q^97 - 20748566866966199611392 * q^98 + 18929241483376281127488 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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