LMFDB - Embedded newform 10.24.a.c.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("10.1");

S:= CuspForms(chi, 24);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

Self dual:	yes
Analytic conductor:	$33.5204037345$
Analytic rank:	$1$
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			1.1
Root			$611.291$ 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)

$f(q)$	$=$	\(q+2048.00 q^{2} -339122. q^{3} +4.19430e6 q^{4} -4.88281e7 q^{5} -6.94521e8 q^{6} +5.67214e9 q^{7} +8.58993e9 q^{8} +2.08602e10 q^{9} -1.00000e11 q^{10} -7.29056e10 q^{11} -1.42238e12 q^{12} +7.50969e12 q^{13} +1.16165e13 q^{14} +1.65587e13 q^{15} +1.75922e13 q^{16} -1.22795e14 q^{17} +4.27218e13 q^{18} -6.14006e14 q^{19} -2.04800e14 q^{20} -1.92354e15 q^{21} -1.49311e14 q^{22} -3.69414e15 q^{23} -2.91303e15 q^{24} +2.38419e15 q^{25} +1.53798e16 q^{26} +2.48518e16 q^{27} +2.37907e16 q^{28} -1.00053e17 q^{29} +3.39122e16 q^{30} -1.10951e17 q^{31} +3.60288e16 q^{32} +2.47238e16 q^{33} -2.51484e17 q^{34} -2.76960e17 q^{35} +8.74941e16 q^{36} -5.06294e17 q^{37} -1.25749e18 q^{38} -2.54670e18 q^{39} -4.19430e17 q^{40} +5.37240e17 q^{41} -3.93942e18 q^{42} -3.30420e18 q^{43} -3.05788e17 q^{44} -1.01857e18 q^{45} -7.56560e18 q^{46} -2.83871e19 q^{47} -5.96589e18 q^{48} +4.80439e18 q^{49} +4.88281e18 q^{50} +4.16423e19 q^{51} +3.14979e19 q^{52} -4.33879e19 q^{53} +5.08965e19 q^{54} +3.55984e18 q^{55} +4.87233e19 q^{56} +2.08223e20 q^{57} -2.04909e20 q^{58} -1.82553e20 q^{59} +6.94521e19 q^{60} +5.31488e20 q^{61} -2.27227e20 q^{62} +1.18322e20 q^{63} +7.37870e19 q^{64} -3.66684e20 q^{65} +5.06344e19 q^{66} +1.46349e21 q^{67} -5.15038e20 q^{68} +1.25276e21 q^{69} -5.67214e20 q^{70} +3.40628e21 q^{71} +1.79188e20 q^{72} -1.21932e21 q^{73} -1.03689e21 q^{74} -8.08529e20 q^{75} -2.57533e21 q^{76} -4.13530e20 q^{77} -5.21564e21 q^{78} -3.86872e21 q^{79} -8.58993e20 q^{80} -1.03916e22 q^{81} +1.10027e21 q^{82} -1.91453e22 q^{83} -8.06793e21 q^{84} +5.99584e21 q^{85} -6.76701e21 q^{86} +3.39302e22 q^{87} -6.26254e20 q^{88} +1.38166e22 q^{89} -2.08602e21 q^{90} +4.25960e22 q^{91} -1.54943e22 q^{92} +3.76258e22 q^{93} -5.81367e22 q^{94} +2.99808e22 q^{95} -1.22181e22 q^{96} +3.39080e21 q^{97} +9.83938e21 q^{98} -1.52083e21 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	−339122.	−1.10525	−0.552626	−	0.833430i	$-0.686374\pi$
$3$	−339122.	−1.10525	−0.552626	+	0.833430i	$0.686374\pi$
$4$	4.19430e6	0.500000
$5$	−4.88281e7	−0.447214
$5$	−4.88281e7	−0.447214
$6$	−6.94521e8	−0.781530
$7$	5.67214e9	1.08422	0.542112	−	0.840306i	$-0.317625\pi$
$7$	5.67214e9	1.08422	0.542112	+	0.840306i	$0.317625\pi$
$8$	8.58993e9	0.353553
$9$	2.08602e10	0.221580
$10$	−1.00000e11	−0.316228
$11$	−7.29056e10	−0.0770451	−0.0385225	−	0.999258i	$-0.512265\pi$
$11$	−7.29056e10	−0.0770451	−0.0385225	+	0.999258i	$0.512265\pi$
$12$	−1.42238e12	−0.552626
$13$	7.50969e12	1.16218	0.581090	−	0.813839i	$-0.302626\pi$
$13$	7.50969e12	1.16218	0.581090	+	0.813839i	$0.302626\pi$
$14$	1.16165e13	0.766663
$15$	1.65587e13	0.494283
$16$	1.75922e13	0.250000
$17$	−1.22795e14	−0.868995	−0.434497	−	0.900673i	$-0.643074\pi$
$17$	−1.22795e14	−0.868995	−0.434497	+	0.900673i	$0.643074\pi$
$18$	4.27218e13	0.156681
$19$	−6.14006e14	−1.20922	−0.604612	−	0.796520i	$-0.706672\pi$
$19$	−6.14006e14	−1.20922	−0.604612	+	0.796520i	$0.706672\pi$
$20$	−2.04800e14	−0.223607
$21$	−1.92354e15	−1.19834
$22$	−1.49311e14	−0.0544791
$23$	−3.69414e15	−0.808431	−0.404216	−	0.914664i	$-0.632455\pi$
$23$	−3.69414e15	−0.808431	−0.404216	+	0.914664i	$0.632455\pi$
$24$	−2.91303e15	−0.390765
$25$	2.38419e15	0.200000
$26$	1.53798e16	0.821785
$27$	2.48518e16	0.860350
$28$	2.37907e16	0.542112
$29$	−1.00053e17	−1.52284	−0.761419	−	0.648260i	$-0.775497\pi$
$29$	−1.00053e17	−1.52284	−0.761419	+	0.648260i	$0.775497\pi$
$30$	3.39122e16	0.349511
$31$	−1.10951e17	−0.784280	−0.392140	−	0.919905i	$-0.628265\pi$
$31$	−1.10951e17	−0.784280	−0.392140	+	0.919905i	$0.628265\pi$
$32$	3.60288e16	0.176777
$33$	2.47238e16	0.0851541
$34$	−2.51484e17	−0.614472
$35$	−2.76960e17	−0.484880
$36$	8.74941e16	0.110790
$37$	−5.06294e17	−0.467824	−0.233912	−	0.972258i	$-0.575153\pi$
$37$	−5.06294e17	−0.467824	−0.233912	+	0.972258i	$0.575153\pi$
$38$	−1.25749e18	−0.855050
$39$	−2.54670e18	−1.28450
$40$	−4.19430e17	−0.158114
$41$	5.37240e17	0.152459	0.0762297	−	0.997090i	$-0.475712\pi$
$41$	5.37240e17	0.152459	0.0762297	+	0.997090i	$0.475712\pi$
$42$	−3.93942e18	−0.847355
$43$	−3.30420e18	−0.542225	−0.271112	−	0.962548i	$-0.587392\pi$
$43$	−3.30420e18	−0.542225	−0.271112	+	0.962548i	$0.587392\pi$
$44$	−3.05788e17	−0.0385225
$45$	−1.01857e18	−0.0990935
$46$	−7.56560e18	−0.571647
$47$	−2.83871e19	−1.67492	−0.837462	−	0.546495i	$-0.815962\pi$
$47$	−2.83871e19	−1.67492	−0.837462	+	0.546495i	$0.815962\pi$
$48$	−5.96589e18	−0.276313
$49$	4.80439e18	0.175543
$50$	4.88281e18	0.141421
$51$	4.16423e19	0.960457
$52$	3.14979e19	0.581090
$53$	−4.33879e19	−0.642978	−0.321489	−	0.946913i	$-0.604183\pi$
$53$	−4.33879e19	−0.642978	−0.321489	+	0.946913i	$0.604183\pi$
$54$	5.08965e19	0.608359
$55$	3.55984e18	0.0344556
$56$	4.87233e19	0.383331
$57$	2.08223e20	1.33650
$58$	−2.04909e20	−1.07681
$59$	−1.82553e20	−0.788118	−0.394059	−	0.919085i	$-0.628930\pi$
$59$	−1.82553e20	−0.788118	−0.394059	+	0.919085i	$0.628930\pi$
$60$	6.94521e19	0.247142
$61$	5.31488e20	1.56387	0.781934	−	0.623361i	$-0.214233\pi$
$61$	5.31488e20	1.56387	0.781934	+	0.623361i	$0.214233\pi$
$62$	−2.27227e20	−0.554570
$63$	1.18322e20	0.240242
$64$	7.37870e19	0.125000
$65$	−3.66684e20	−0.519743
$66$	5.06344e19	0.0602131
$67$	1.46349e21	1.46396	0.731982	−	0.681323i	$-0.238595\pi$
$67$	1.46349e21	1.46396	0.731982	+	0.681323i	$0.238595\pi$
$68$	−5.15038e20	−0.434497
$69$	1.25276e21	0.893520
$70$	−5.67214e20	−0.342862
$71$	3.40628e21	1.74908	0.874538	−	0.484957i	$-0.161165\pi$
$71$	3.40628e21	1.74908	0.874538	+	0.484957i	$0.161165\pi$
$72$	1.79188e20	0.0783403
$73$	−1.21932e21	−0.454889	−0.227444	−	0.973791i	$-0.573037\pi$
$73$	−1.21932e21	−0.454889	−0.227444	+	0.973791i	$0.573037\pi$
$74$	−1.03689e21	−0.330802
$75$	−8.08529e20	−0.221050
$76$	−2.57533e21	−0.604612
$77$	−4.13530e20	−0.0835342
$78$	−5.21564e21	−0.908279
$79$	−3.86872e21	−0.581909	−0.290955	−	0.956737i	$-0.593973\pi$
$79$	−3.86872e21	−0.581909	−0.290955	+	0.956737i	$0.593973\pi$
$80$	−8.58993e20	−0.111803
$81$	−1.03916e22	−1.17248
$82$	1.10027e21	0.107805
$83$	−1.91453e22	−1.63179	−0.815893	−	0.578203i	$-0.803754\pi$
$83$	−1.91453e22	−1.63179	−0.815893	+	0.578203i	$0.803754\pi$
$84$	−8.06793e21	−0.599170
$85$	5.99584e21	0.388626
$86$	−6.76701e21	−0.383411
$87$	3.39302e22	1.68312
$88$	−6.26254e20	−0.0272395
$89$	1.38166e22	0.527737	0.263868	−	0.964559i	$-0.415002\pi$
$89$	1.38166e22	0.527737	0.263868	+	0.964559i	$0.415002\pi$
$90$	−2.08602e21	−0.0700697
$91$	4.25960e22	1.26006
$92$	−1.54943e22	−0.404216
$93$	3.76258e22	0.866827
$94$	−5.81367e22	−1.18435
$95$	2.99808e22	0.540781
$96$	−1.22181e22	−0.195383
$97$	3.39080e21	0.0481312	0.0240656	−	0.999710i	$-0.492339\pi$
$97$	3.39080e21	0.0481312	0.0240656	+	0.999710i	$0.492339\pi$
$98$	9.83938e21	0.124128
$99$	−1.52083e21	−0.0170716
$100$	1.00000e22	0.100000
$101$	−6.91624e22	−0.616842	−0.308421	−	0.951250i	$-0.599801\pi$
$101$	−6.91624e22	−0.616842	−0.308421	+	0.951250i	$0.599801\pi$
$102$	8.52835e22	0.679146
$103$	2.42869e23	1.72880	0.864398	−	0.502809i	$-0.167700\pi$
$103$	2.42869e23	1.72880	0.864398	+	0.502809i	$0.167700\pi$
$104$	6.45077e22	0.410893
$105$	9.39230e22	0.535914
$106$	−8.88584e22	−0.454654
$107$	−3.44606e22	−0.158274	−0.0791371	−	0.996864i	$-0.525216\pi$
$107$	−3.44606e22	−0.158274	−0.0791371	+	0.996864i	$0.525216\pi$
$108$	1.04236e23	0.430175
$109$	−4.80102e23	−1.78209	−0.891043	−	0.453918i	$-0.850026\pi$
$109$	−4.80102e23	−1.78209	−0.891043	+	0.453918i	$0.850026\pi$
$110$	7.29056e21	0.0243638
$111$	1.71695e23	0.517063
$112$	9.97853e22	0.271056
$113$	−6.76991e23	−1.66028	−0.830139	−	0.557556i	$-0.811739\pi$
$113$	−6.76991e23	−1.66028	−0.830139	+	0.557556i	$0.811739\pi$
$114$	4.26440e23	0.945045
$115$	1.80378e23	0.361541
$116$	−4.19653e23	−0.761419
$117$	1.56654e23	0.257516
$118$	−3.73869e23	−0.557284
$119$	−6.96509e23	−0.942185
$120$	1.42238e23	0.174756
$121$	−8.90115e23	−0.994064
$122$	1.08849e24	1.10582
$123$	−1.82190e23	−0.168506
$124$	−4.65362e23	−0.392140
$125$	−1.16415e23	−0.0894427
$126$	2.42324e23	0.169877
$127$	−6.00234e23	−0.384218	−0.192109	−	0.981374i	$-0.561533\pi$
$127$	−6.00234e23	−0.384218	−0.192109	+	0.981374i	$0.561533\pi$
$128$	1.51116e23	0.0883883
$129$	1.12053e24	0.599294
$130$	−7.50969e23	−0.367514
$131$	1.78064e24	0.797914	0.398957	−	0.916970i	$-0.369372\pi$
$131$	1.78064e24	0.797914	0.398957	+	0.916970i	$0.369372\pi$
$132$	1.03699e23	0.0425771
$133$	−3.48273e24	−1.31107
$134$	2.99724e24	1.03518
$135$	−1.21347e24	−0.384760
$136$	−1.05480e24	−0.307236
$137$	−3.22877e24	−0.864471	−0.432236	−	0.901761i	$-0.642275\pi$
$137$	−3.22877e24	−0.864471	−0.432236	+	0.901761i	$0.642275\pi$
$138$	2.56566e24	0.631814
$139$	−3.01015e23	−0.0682210	−0.0341105	−	0.999418i	$-0.510860\pi$
$139$	−3.01015e23	−0.0682210	−0.0341105	+	0.999418i	$0.510860\pi$
$140$	−1.16165e24	−0.242440
$141$	9.62667e24	1.85121
$142$	6.97605e24	1.23678
$143$	−5.47498e23	−0.0895402
$144$	3.66977e23	0.0553950
$145$	4.88541e24	0.681034
$146$	−2.49717e24	−0.321655
$147$	−1.62927e24	−0.194019
$148$	−2.12355e24	−0.233912
$149$	1.49284e25	1.52185	0.760925	−	0.648840i	$-0.224746\pi$
$149$	1.49284e25	1.52185	0.760925	+	0.648840i	$0.224746\pi$
$150$	−1.65587e24	−0.156306
$151$	2.25537e24	0.197235	0.0986173	−	0.995125i	$-0.468558\pi$
$151$	2.25537e24	0.197235	0.0986173	+	0.995125i	$0.468558\pi$
$152$	−5.27427e24	−0.427525
$153$	−2.56153e24	−0.192552
$154$	−8.46910e23	−0.0590676
$155$	5.41752e24	0.350741
$156$	−1.06816e25	−0.642250
$157$	−2.00139e25	−1.11812	−0.559058	−	0.829129i	$-0.688837\pi$
$157$	−2.00139e25	−1.11812	−0.559058	+	0.829129i	$0.688837\pi$
$158$	−7.92313e24	−0.411472
$159$	1.47138e25	0.710652
$160$	−1.75922e24	−0.0790569
$161$	−2.09537e25	−0.876521
$162$	−2.12821e25	−0.829070
$163$	−5.04020e24	−0.182932	−0.0914661	−	0.995808i	$-0.529155\pi$
$163$	−5.04020e24	−0.182932	−0.0914661	+	0.995808i	$0.529155\pi$
$164$	2.25335e24	0.0762297
$165$	−1.20722e24	−0.0380821
$166$	−3.92095e25	−1.15385
$167$	−4.08368e25	−1.12153	−0.560767	−	0.827974i	$-0.689494\pi$
$167$	−4.08368e25	−1.12153	−0.560767	+	0.827974i	$0.689494\pi$
$168$	−1.65231e25	−0.423677
$169$	1.46415e25	0.350663
$170$	1.22795e25	0.274800
$171$	−1.28083e25	−0.267939
$172$	−1.38588e25	−0.271112
$173$	8.79177e25	1.60896	0.804482	−	0.593978i	$-0.202443\pi$
$173$	8.79177e25	1.60896	0.804482	+	0.593978i	$0.202443\pi$
$174$	6.94890e25	1.19014
$175$	1.35234e25	0.216845
$176$	−1.28257e24	−0.0192613
$177$	6.19077e25	0.871069
$178$	2.82965e25	0.373166
$179$	6.44672e25	0.797129	0.398565	−	0.917140i	$-0.369508\pi$
$179$	6.44672e25	0.797129	0.398565	+	0.917140i	$0.369508\pi$
$180$	−4.27218e24	−0.0495468
$181$	−4.53664e25	−0.493663	−0.246832	−	0.969058i	$-0.579389\pi$
$181$	−4.53664e25	−0.493663	−0.246832	+	0.969058i	$0.579389\pi$
$182$	8.72366e25	0.891000
$183$	−1.80239e26	−1.72847
$184$	−3.17324e25	−0.285824
$185$	2.47214e25	0.209217
$186$	7.70577e25	0.612939
$187$	8.95242e24	0.0669518
$188$	−1.19064e26	−0.837462
$189$	1.40963e26	0.932812
$190$	6.14006e25	0.382390
$191$	4.01824e25	0.235587	0.117794	−	0.993038i	$-0.462418\pi$
$191$	4.01824e25	0.235587	0.117794	+	0.993038i	$0.462418\pi$
$192$	−2.50228e25	−0.138156
$193$	−3.37563e26	−1.75568	−0.877841	−	0.478952i	$-0.841017\pi$
$193$	−3.37563e26	−1.75568	−0.877841	+	0.478952i	$0.841017\pi$
$194$	6.94435e24	0.0340339
$195$	1.24350e26	0.574446
$196$	2.01511e25	0.0877714
$197$	3.28937e26	1.35130	0.675649	−	0.737223i	$-0.263863\pi$
$197$	3.28937e26	1.35130	0.675649	+	0.737223i	$0.263863\pi$
$198$	−3.11465e24	−0.0120715
$199$	3.82254e26	1.39811	0.699055	−	0.715068i	$-0.253604\pi$
$199$	3.82254e26	1.39811	0.699055	+	0.715068i	$0.253604\pi$
$200$	2.04800e25	0.0707107
$201$	−4.96302e26	−1.61805
$202$	−1.41645e26	−0.436173
$203$	−5.67515e26	−1.65110
$204$	1.74661e26	0.480229
$205$	−2.62324e25	−0.0681819
$206$	4.97395e26	1.22244
$207$	−7.70606e25	−0.179132
$208$	1.32112e26	0.290545
$209$	4.47645e25	0.0931647
$210$	1.92354e26	0.378948
$211$	−1.52630e26	−0.284703	−0.142352	−	0.989816i	$-0.545466\pi$
$211$	−1.52630e26	−0.284703	−0.142352	+	0.989816i	$0.545466\pi$
$212$	−1.81982e26	−0.321489
$213$	−1.15514e27	−1.93317
$214$	−7.05754e25	−0.111917
$215$	1.61338e26	0.242490
$216$	2.13476e26	0.304180
$217$	−6.29329e26	−0.850336
$218$	−9.83249e26	−1.26013
$219$	4.13498e26	0.502766
$220$	1.49311e25	0.0172278
$221$	−9.22150e26	−1.00993
$222$	3.51632e26	0.365619
$223$	7.09326e26	0.700390	0.350195	−	0.936677i	$-0.386115\pi$
$223$	7.09326e26	0.700390	0.350195	+	0.936677i	$0.386115\pi$
$224$	2.04360e26	0.191666
$225$	4.97347e25	0.0443160
$226$	−1.38648e27	−1.17399
$227$	1.34868e27	1.08545	0.542727	−	0.839909i	$-0.317392\pi$
$227$	1.34868e27	1.08545	0.542727	+	0.839909i	$0.317392\pi$
$228$	8.73350e26	0.668248
$229$	1.71030e27	1.24441	0.622207	−	0.782853i	$-0.286236\pi$
$229$	1.71030e27	1.24441	0.622207	+	0.782853i	$0.286236\pi$
$230$	3.69414e26	0.255648
$231$	1.40237e26	0.0923262
$232$	−8.59450e26	−0.538404
$233$	7.74363e26	0.461691	0.230846	−	0.972990i	$-0.425851\pi$
$233$	7.74363e26	0.461691	0.230846	+	0.972990i	$0.425851\pi$
$234$	3.20827e26	0.182091
$235$	1.38609e27	0.749049
$236$	−7.65684e26	−0.394059
$237$	1.31196e27	0.643156
$238$	−1.42645e27	−0.666226
$239$	2.12271e27	0.944744	0.472372	−	0.881399i	$-0.343398\pi$
$239$	2.12271e27	0.944744	0.472372	+	0.881399i	$0.343398\pi$
$240$	2.91303e26	0.123571
$241$	−1.93749e27	−0.783508	−0.391754	−	0.920070i	$-0.628132\pi$
$241$	−1.93749e27	−0.783508	−0.391754	+	0.920070i	$0.628132\pi$
$242$	−1.82296e27	−0.702909
$243$	1.18440e27	0.435537
$244$	2.22922e27	0.781934
$245$	−2.34589e26	−0.0785051
$246$	−3.73125e26	−0.119152
$247$	−4.61100e27	−1.40534
$248$	−9.53061e26	−0.277285
$249$	6.49257e27	1.80353
$250$	−2.38419e26	−0.0632456
$251$	4.58522e27	1.16175	0.580875	−	0.813993i	$-0.302711\pi$
$251$	4.58522e27	1.16175	0.580875	+	0.813993i	$0.302711\pi$
$252$	4.96279e26	0.120121
$253$	2.69323e26	0.0622856
$254$	−1.22928e27	−0.271683
$255$	−2.03332e27	−0.429530
$256$	3.09485e26	0.0625000
$257$	−5.64317e27	−1.08966	−0.544832	−	0.838545i	$-0.683407\pi$
$257$	−5.64317e27	−1.08966	−0.544832	+	0.838545i	$0.683407\pi$
$258$	2.29484e27	0.423765
$259$	−2.87177e27	−0.507227
$260$	−1.53798e27	−0.259871
$261$	−2.08713e27	−0.337430
$262$	3.64675e27	0.564210
$263$	−1.17070e28	−1.73363	−0.866813	−	0.498633i	$-0.833836\pi$
$263$	−1.17070e28	−1.73363	−0.866813	+	0.498633i	$0.833836\pi$
$264$	2.12376e26	0.0301065
$265$	2.11855e27	0.287548
$266$	−7.13263e27	−0.927066
$267$	−4.68552e27	−0.583282
$268$	6.13834e27	0.731982
$269$	−1.41632e28	−1.61812	−0.809060	−	0.587726i	$-0.800023\pi$
$269$	−1.41632e28	−1.61812	−0.809060	+	0.587726i	$0.800023\pi$
$270$	−2.48518e27	−0.272066
$271$	1.48604e28	1.55913	0.779566	−	0.626320i	$-0.215439\pi$
$271$	1.48604e28	1.55913	0.779566	+	0.626320i	$0.215439\pi$
$272$	−2.16023e27	−0.217249
$273$	−1.44452e28	−1.39269
$274$	−6.61252e27	−0.611273
$275$	−1.73820e26	−0.0154090
$276$	5.25447e27	0.446760
$277$	1.32716e28	1.08245	0.541223	−	0.840879i	$-0.317962\pi$
$277$	1.32716e28	1.08245	0.541223	+	0.840879i	$0.317962\pi$
$278$	−6.16479e26	−0.0482395
$279$	−2.31446e27	−0.173781
$280$	−2.37907e27	−0.171431
$281$	1.06254e28	0.734892	0.367446	−	0.930045i	$-0.380232\pi$
$281$	1.06254e28	0.734892	0.367446	+	0.930045i	$0.380232\pi$
$282$	1.97154e28	1.30900
$283$	2.71424e28	1.73023	0.865117	−	0.501570i	$-0.167244\pi$
$283$	2.71424e28	1.73023	0.865117	+	0.501570i	$0.167244\pi$
$284$	1.42870e28	0.874538
$285$	−1.01671e28	−0.597699
$286$	−1.12128e27	−0.0633145
$287$	3.04730e27	0.165300
$288$	7.51569e26	0.0391702
$289$	−4.88902e27	−0.244848
$290$	1.00053e28	0.481564
$291$	−1.14989e27	−0.0531971
$292$	−5.11420e27	−0.227444
$293$	−1.41085e27	−0.0603257	−0.0301629	−	0.999545i	$-0.509603\pi$
$293$	−1.41085e27	−0.0603257	−0.0301629	+	0.999545i	$0.509603\pi$
$294$	−3.33675e27	−0.137192
$295$	8.91373e27	0.352457
$296$	−4.34903e27	−0.165401
$297$	−1.81184e27	−0.0662857
$298$	3.05734e28	1.07611
$299$	−2.77418e28	−0.939543
$300$	−3.39122e27	−0.110525
$301$	−1.87419e28	−0.587893
$302$	4.61900e27	0.139466
$303$	2.34544e28	0.681765
$304$	−1.08017e28	−0.302306
$305$	−2.59516e28	−0.699383
$306$	−5.24601e27	−0.136155
$307$	4.70277e28	1.17561	0.587804	−	0.809003i	$-0.299993\pi$
$307$	4.70277e28	1.17561	0.587804	+	0.809003i	$0.299993\pi$
$308$	−1.73447e27	−0.0417671
$309$	−8.23620e28	−1.91075
$310$	1.10951e28	0.248011
$311$	2.33572e28	0.503126	0.251563	−	0.967841i	$-0.419055\pi$
$311$	2.33572e28	0.503126	0.251563	+	0.967841i	$0.419055\pi$
$312$	−2.18760e28	−0.454140
$313$	3.37396e28	0.675119	0.337560	−	0.941304i	$-0.390399\pi$
$313$	3.37396e28	0.675119	0.337560	+	0.941304i	$0.390399\pi$
$314$	−4.09886e28	−0.790627
$315$	−5.77744e27	−0.107440
$316$	−1.62266e28	−0.290955
$317$	−2.97844e28	−0.515000	−0.257500	−	0.966278i	$-0.582899\pi$
$317$	−2.97844e28	−0.515000	−0.257500	+	0.966278i	$0.582899\pi$
$318$	3.01338e28	0.502507
$319$	7.29443e27	0.117327
$320$	−3.60288e27	−0.0559017
$321$	1.16863e28	0.174933
$322$	−4.29131e28	−0.619794
$323$	7.53968e28	1.05081
$324$	−4.35857e28	−0.586241
$325$	1.79045e28	0.232436
$326$	−1.03223e28	−0.129353
$327$	1.62813e29	1.96965
$328$	4.61486e27	0.0539025
$329$	−1.61015e29	−1.81599
$330$	−2.47238e27	−0.0269281
$331$	5.24477e28	0.551702	0.275851	−	0.961200i	$-0.411040\pi$
$331$	5.24477e28	0.551702	0.275851	+	0.961200i	$0.411040\pi$
$332$	−8.03010e28	−0.815893
$333$	−1.05614e28	−0.103660
$334$	−8.36338e28	−0.793044
$335$	−7.14597e28	−0.654705
$336$	−3.38393e28	−0.299585
$337$	−1.64340e29	−1.40605	−0.703024	−	0.711166i	$-0.748167\pi$
$337$	−1.64340e29	−1.40605	−0.703024	+	0.711166i	$0.748167\pi$
$338$	2.99859e28	0.247956
$339$	2.29582e29	1.83502
$340$	2.51484e28	0.194313
$341$	8.08894e27	0.0604249
$342$	−2.62314e28	−0.189462
$343$	−1.27988e29	−0.893897
$344$	−2.83829e28	−0.191705
$345$	−6.11700e28	−0.399594
$346$	1.80055e29	1.13771
$347$	2.04136e28	0.124776	0.0623881	−	0.998052i	$-0.480128\pi$
$347$	2.04136e28	0.124776	0.0623881	+	0.998052i	$0.480128\pi$
$348$	1.42313e29	0.841559
$349$	2.60772e29	1.49200	0.745999	−	0.665947i	$-0.231972\pi$
$349$	2.60772e29	1.49200	0.745999	+	0.665947i	$0.231972\pi$
$350$	2.76960e28	0.153333
$351$	1.86629e29	0.999881
$352$	−2.62670e27	−0.0136198
$353$	−3.17093e29	−1.59139	−0.795696	−	0.605696i	$-0.792895\pi$
$353$	−3.17093e29	−1.59139	−0.795696	+	0.605696i	$0.792895\pi$
$354$	1.26787e29	0.615939
$355$	−1.66322e29	−0.782211
$356$	5.79512e28	0.263868
$357$	2.36201e29	1.04135
$358$	1.32029e29	0.563656
$359$	3.06761e27	0.0126828	0.00634138	−	0.999980i	$-0.497981\pi$
$359$	3.06761e27	0.0126828	0.00634138	+	0.999980i	$0.497981\pi$
$360$	−8.74941e27	−0.0350348
$361$	1.19174e29	0.462221
$362$	−9.29104e28	−0.349073
$363$	3.01857e29	1.09869
$364$	1.78661e29	0.630032
$365$	5.95372e28	0.203432
$366$	−3.69129e29	−1.22221
$367$	1.46745e29	0.470874	0.235437	−	0.971890i	$-0.424348\pi$
$367$	1.46745e29	0.470874	0.235437	+	0.971890i	$0.424348\pi$
$368$	−6.49880e28	−0.202108
$369$	1.12070e28	0.0337819
$370$	5.06294e28	0.147939
$371$	−2.46102e29	−0.697132
$372$	1.57814e29	0.433413
$373$	−5.22732e29	−1.39196	−0.695981	−	0.718060i	$-0.745030\pi$
$373$	−5.22732e29	−1.39196	−0.695981	+	0.718060i	$0.745030\pi$
$374$	1.83346e28	0.0473420
$375$	3.94789e28	0.0988567
$376$	−2.43843e29	−0.592175
$377$	−7.51368e29	−1.76981
$378$	2.88692e29	0.659598
$379$	−5.96093e29	−1.32118	−0.660592	−	0.750745i	$-0.729694\pi$
$379$	−5.96093e29	−1.32118	−0.660592	+	0.750745i	$0.729694\pi$
$380$	1.25749e29	0.270391
$381$	2.03552e29	0.424657
$382$	8.22935e28	0.166585
$383$	−4.94929e29	−0.972203	−0.486101	−	0.873902i	$-0.661581\pi$
$383$	−4.94929e29	−0.972203	−0.486101	+	0.873902i	$0.661581\pi$
$384$	−5.12466e28	−0.0976913
$385$	2.01919e28	0.0373576
$386$	−6.91329e29	−1.24145
$387$	−6.89264e28	−0.120146
$388$	1.42220e28	0.0240656
$389$	5.66942e28	0.0931361	0.0465681	−	0.998915i	$-0.485172\pi$
$389$	5.66942e28	0.0931361	0.0465681	+	0.998915i	$0.485172\pi$
$390$	2.54670e29	0.406195
$391$	4.53621e29	0.702523
$392$	4.12694e28	0.0620638
$393$	−6.03853e29	−0.881895
$394$	6.73663e29	0.955512
$395$	1.88902e29	0.260238
$396$	−6.37881e27	−0.00853582
$397$	3.68342e29	0.478807	0.239403	−	0.970920i	$-0.423048\pi$
$397$	3.68342e29	0.478807	0.239403	+	0.970920i	$0.423048\pi$
$398$	7.82856e29	0.988613
$399$	1.18107e30	1.44906
$400$	4.19430e28	0.0500000
$401$	−1.21847e30	−1.41142	−0.705710	−	0.708501i	$-0.749372\pi$
$401$	−1.21847e30	−1.41142	−0.705710	+	0.708501i	$0.749372\pi$
$402$	−1.01643e30	−1.14413
$403$	−8.33207e29	−0.911475
$404$	−2.90088e29	−0.308421
$405$	5.07404e29	0.524350
$406$	−1.16227e30	−1.16750
$407$	3.69116e28	0.0360436
$408$	3.57705e29	0.339573
$409$	1.47992e30	1.36590	0.682952	−	0.730464i	$-0.260696\pi$
$409$	1.47992e30	1.36590	0.682952	+	0.730464i	$0.260696\pi$
$410$	−5.37240e28	−0.0482119
$411$	1.09495e30	0.955458
$412$	1.01867e30	0.864398
$413$	−1.03547e30	−0.854497
$414$	−1.57820e29	−0.126666
$415$	9.34827e29	0.729757
$416$	2.70565e29	0.205446
$417$	1.02081e29	0.0754014
$418$	9.16777e28	0.0658774
$419$	4.36760e29	0.305339	0.152669	−	0.988277i	$-0.451213\pi$
$419$	4.36760e29	0.305339	0.152669	+	0.988277i	$0.451213\pi$
$420$	3.93942e29	0.267957
$421$	2.90507e30	1.92271	0.961353	−	0.275319i	$-0.0887836\pi$
$421$	2.90507e30	1.92271	0.961353	+	0.275319i	$0.0887836\pi$
$422$	−3.12587e29	−0.201316
$423$	−5.92161e29	−0.371129
$424$	−3.72699e29	−0.227327
$425$	−2.92765e29	−0.173799
$426$	−2.36573e30	−1.36696
$427$	3.01467e30	1.69558
$428$	−1.44538e29	−0.0791371
$429$	1.85668e29	0.0989644
$430$	3.30420e29	0.171467
$431$	5.61010e29	0.283454	0.141727	−	0.989906i	$-0.454735\pi$
$431$	5.61010e29	0.283454	0.141727	+	0.989906i	$0.454735\pi$
$432$	4.37198e29	0.215087
$433$	−2.91680e30	−1.39732	−0.698659	−	0.715455i	$-0.746220\pi$
$433$	−2.91680e30	−1.39732	−0.698659	+	0.715455i	$0.746220\pi$
$434$	−1.28887e30	−0.601278
$435$	−1.65675e30	−0.752713
$436$	−2.01369e30	−0.891043
$437$	2.26822e30	0.977574
$438$	8.46844e29	0.355509
$439$	1.03028e30	0.421322	0.210661	−	0.977559i	$-0.432438\pi$
$439$	1.03028e30	0.421322	0.210661	+	0.977559i	$0.432438\pi$
$440$	3.05788e28	0.0121819
$441$	1.00221e29	0.0388967
$442$	−1.88856e30	−0.714127
$443$	−2.53393e30	−0.933582	−0.466791	−	0.884368i	$-0.654590\pi$
$443$	−2.53393e30	−0.933582	−0.466791	+	0.884368i	$0.654590\pi$
$444$	7.20142e29	0.258532
$445$	−6.74640e29	−0.236011
$446$	1.45270e30	0.495250
$447$	−5.06255e30	−1.68203
$448$	4.18530e29	0.135528
$449$	−4.77953e29	−0.150852	−0.0754262	−	0.997151i	$-0.524032\pi$
$449$	−4.77953e29	−0.150852	−0.0754262	+	0.997151i	$0.524032\pi$
$450$	1.01857e29	0.0313361
$451$	−3.91678e28	−0.0117462
$452$	−2.83951e30	−0.830139
$453$	−7.64845e29	−0.217994
$454$	2.76209e30	0.767531
$455$	−2.07988e30	−0.563518
$456$	1.78862e30	0.472522
$457$	5.53212e29	0.142513	0.0712566	−	0.997458i	$-0.477299\pi$
$457$	5.53212e29	0.142513	0.0712566	+	0.997458i	$0.477299\pi$
$458$	3.50270e30	0.879934
$459$	−3.05167e30	−0.747639
$460$	7.56560e29	0.180771
$461$	−3.77831e30	−0.880516	−0.440258	−	0.897871i	$-0.645113\pi$
$461$	−3.77831e30	−0.880516	−0.440258	+	0.897871i	$0.645113\pi$
$462$	2.87205e29	0.0652845
$463$	9.57536e29	0.212312	0.106156	−	0.994350i	$-0.466146\pi$
$463$	9.57536e29	0.212312	0.106156	+	0.994350i	$0.466146\pi$
$464$	−1.76015e30	−0.380709
$465$	−1.83720e30	−0.387657
$466$	1.58590e30	0.326465
$467$	1.81078e30	0.363681	0.181841	−	0.983328i	$-0.441795\pi$
$467$	1.81078e30	0.363681	0.181841	+	0.983328i	$0.441795\pi$
$468$	6.57054e29	0.128758
$469$	8.30114e30	1.58727
$470$	2.83871e30	0.529658
$471$	6.78716e30	1.23580
$472$	−1.56812e30	−0.278642
$473$	2.40895e29	0.0417757
$474$	2.68690e30	0.454780
$475$	−1.46391e30	−0.241845
$476$	−2.92137e30	−0.471093
$477$	−9.05081e29	−0.142471
$478$	4.34730e30	0.668035
$479$	−1.31018e31	−1.96550	−0.982751	−	0.184936i	$-0.940792\pi$
$479$	−1.31018e31	−1.96550	−0.982751	+	0.184936i	$0.940792\pi$
$480$	5.96589e29	0.0873778
$481$	−3.80211e30	−0.543696
$482$	−3.96798e30	−0.554024
$483$	7.10584e30	0.968776
$484$	−3.73341e30	−0.497032
$485$	−1.65566e29	−0.0215249
$486$	2.42565e30	0.307972
$487$	−7.78763e30	−0.965656	−0.482828	−	0.875715i	$-0.660390\pi$
$487$	−7.78763e30	−0.965656	−0.482828	+	0.875715i	$0.660390\pi$
$488$	4.56545e30	0.552911
$489$	1.70924e30	0.202186
$490$	−4.80439e29	−0.0555115
$491$	−2.96392e28	−0.00334526	−0.00167263	−	0.999999i	$-0.500532\pi$
$491$	−2.96392e28	−0.00334526	−0.00167263	+	0.999999i	$0.500532\pi$
$492$	−7.64159e29	−0.0842530
$493$	1.22860e31	1.32334
$494$	−9.44332e30	−0.993722
$495$	7.42591e28	0.00763467
$496$	−1.95187e30	−0.196070
$497$	1.93209e31	1.89639
$498$	1.32968e31	1.27529
$499$	−1.73299e31	−1.62420	−0.812101	−	0.583517i	$-0.801676\pi$
$499$	−1.73299e31	−1.62420	−0.812101	+	0.583517i	$0.801676\pi$
$500$	−4.88281e29	−0.0447214
$501$	1.38486e31	1.23958
$502$	9.39054e30	0.821481
$503$	6.74488e30	0.576690	0.288345	−	0.957527i	$-0.406895\pi$
$503$	6.74488e30	0.576690	0.288345	+	0.957527i	$0.406895\pi$
$504$	1.01638e30	0.0849385
$505$	3.37707e30	0.275860
$506$	5.51574e29	0.0440426
$507$	−4.96526e30	−0.387570
$508$	−2.51756e30	−0.192109
$509$	1.67540e31	1.24987	0.624935	−	0.780677i	$-0.285126\pi$
$509$	1.67540e31	1.24987	0.624935	+	0.780677i	$0.285126\pi$
$510$	−4.16423e30	−0.303723
$511$	−6.91616e30	−0.493202
$512$	6.33825e29	0.0441942
$513$	−1.52592e31	−1.04035
$514$	−1.15572e31	−0.770509
$515$	−1.18588e31	−0.773141
$516$	4.69983e30	0.299647
$517$	2.06958e30	0.129045
$518$	−5.88138e30	−0.358663
$519$	−2.98148e31	−1.77831
$520$	−3.14979e30	−0.183757
$521$	9.00283e30	0.513742	0.256871	−	0.966446i	$-0.417308\pi$
$521$	9.00283e30	0.513742	0.256871	+	0.966446i	$0.417308\pi$
$522$	−4.27444e30	−0.238599
$523$	−1.06079e31	−0.579239	−0.289620	−	0.957142i	$-0.593529\pi$
$523$	−1.06079e31	−0.579239	−0.289620	+	0.957142i	$0.593529\pi$
$524$	7.46854e30	0.398957
$525$	−4.58609e30	−0.239668
$526$	−2.39760e31	−1.22586
$527$	1.36242e31	0.681536
$528$	4.34947e29	0.0212885
$529$	−7.23380e30	−0.346439
$530$	4.33879e30	0.203327
$531$	−3.80810e30	−0.174631
$532$	−1.46076e31	−0.655535
$533$	4.03451e30	0.177185
$534$	−9.59594e30	−0.412442
$535$	1.68265e30	0.0707823
$536$	1.25713e31	0.517590
$537$	−2.18622e31	−0.881028
$538$	−2.90063e31	−1.14418
$539$	−3.50267e29	−0.0135247
$540$	−5.08965e30	−0.192380
$541$	1.12742e31	0.417175	0.208588	−	0.978004i	$-0.433113\pi$
$541$	1.12742e31	0.417175	0.208588	+	0.978004i	$0.433113\pi$
$542$	3.04341e31	1.10247
$543$	1.53847e31	0.545622
$544$	−4.42415e30	−0.153618
$545$	2.34425e31	0.796973
$546$	−2.95838e31	−0.984779
$547$	4.29561e31	1.40014	0.700069	−	0.714075i	$-0.253153\pi$
$547$	4.29561e31	1.40014	0.700069	+	0.714075i	$0.253153\pi$
$548$	−1.35424e31	−0.432236
$549$	1.10870e31	0.346522
$550$	−3.55984e29	−0.0108958
$551$	6.14333e31	1.84145
$552$	1.07611e31	0.315907
$553$	−2.19439e31	−0.630920
$554$	2.71803e31	0.765405
$555$	−8.38355e30	−0.231238
$556$	−1.26255e30	−0.0341105
$557$	1.28388e31	0.339772	0.169886	−	0.985464i	$-0.445660\pi$
$557$	1.28388e31	0.339772	0.169886	+	0.985464i	$0.445660\pi$
$558$	−4.74002e30	−0.122882
$559$	−2.48135e31	−0.630163
$560$	−4.87233e30	−0.121220
$561$	−3.03596e30	−0.0739985
$562$	2.17609e31	0.519647
$563$	4.67401e31	1.09356	0.546780	−	0.837276i	$-0.315853\pi$
$563$	4.67401e31	1.09356	0.546780	+	0.837276i	$0.315853\pi$
$564$	4.03772e31	0.925606
$565$	3.30562e31	0.742499
$566$	5.55877e31	1.22346
$567$	−5.89428e31	−1.27123
$568$	2.92597e31	0.618392
$569$	−1.56288e31	−0.323694	−0.161847	−	0.986816i	$-0.551745\pi$
$569$	−1.56288e31	−0.323694	−0.161847	+	0.986816i	$0.551745\pi$
$570$	−2.08223e31	−0.422637
$571$	−3.73702e31	−0.743378	−0.371689	−	0.928357i	$-0.621221\pi$
$571$	−3.73702e31	−0.743378	−0.371689	+	0.928357i	$0.621221\pi$
$572$	−2.29637e30	−0.0447701
$573$	−1.36267e31	−0.260383
$574$	6.24087e30	0.116885
$575$	−8.80751e30	−0.161686
$576$	1.53921e30	0.0276975
$577$	−9.29399e31	−1.63938	−0.819692	−	0.572805i	$-0.805855\pi$
$577$	−9.29399e31	−1.63938	−0.819692	+	0.572805i	$0.805855\pi$
$578$	−1.00127e31	−0.173134
$579$	1.14475e32	1.94047
$580$	2.04909e31	0.340517
$581$	−1.08595e32	−1.76922
$582$	−2.35498e30	−0.0376160
$583$	3.16322e30	0.0495383
$584$	−1.04739e31	−0.160827
$585$	−7.64911e30	−0.115165
$586$	−2.88942e30	−0.0426567
$587$	−4.03960e31	−0.584791	−0.292395	−	0.956298i	$-0.594452\pi$
$587$	−4.03960e31	−0.584791	−0.292395	+	0.956298i	$0.594452\pi$
$588$	−6.83366e30	−0.0970094
$589$	6.81246e31	0.948370
$590$	1.82553e31	0.249225
$591$	−1.11550e32	−1.49352
$592$	−8.90681e30	−0.116956
$593$	1.98679e31	0.255872	0.127936	−	0.991782i	$-0.459165\pi$
$593$	1.98679e31	0.255872	0.127936	+	0.991782i	$0.459165\pi$
$594$	−3.71064e30	−0.0468711
$595$	3.40092e31	0.421358
$596$	6.26143e31	0.760925
$597$	−1.29630e32	−1.54526
$598$	−5.68153e31	−0.664357
$599$	−4.06122e30	−0.0465852	−0.0232926	−	0.999729i	$-0.507415\pi$
$599$	−4.06122e30	−0.0465852	−0.0232926	+	0.999729i	$0.507415\pi$
$600$	−6.94521e30	−0.0781530
$601$	−2.13201e31	−0.235360	−0.117680	−	0.993052i	$-0.537546\pi$
$601$	−2.13201e31	−0.235360	−0.117680	+	0.993052i	$0.537546\pi$
$602$	−3.83834e31	−0.415703
$603$	3.05288e31	0.324385
$604$	9.45971e30	0.0986173
$605$	4.34626e31	0.444559
$606$	4.80347e31	0.482081
$607$	1.05290e32	1.03685	0.518425	−	0.855123i	$-0.326519\pi$
$607$	1.05290e32	1.03685	0.518425	+	0.855123i	$0.326519\pi$
$608$	−2.21219e31	−0.213762
$609$	1.92457e32	1.82488
$610$	−5.31488e31	−0.494539
$611$	−2.13178e32	−1.94656
$612$	−1.07438e31	−0.0962759
$613$	−1.91908e32	−1.68771	−0.843855	−	0.536572i	$-0.819719\pi$
$613$	−1.91908e32	−1.68771	−0.843855	+	0.536572i	$0.819719\pi$
$614$	9.63128e31	0.831281
$615$	8.89598e30	0.0753581
$616$	−3.55220e30	−0.0295338
$617$	1.64022e32	1.33851	0.669256	−	0.743032i	$-0.266613\pi$
$617$	1.64022e32	1.33851	0.669256	+	0.743032i	$0.266613\pi$
$618$	−1.68677e32	−1.35111
$619$	−9.18518e31	−0.722180	−0.361090	−	0.932531i	$-0.617595\pi$
$619$	−9.18518e31	−0.722180	−0.361090	+	0.932531i	$0.617595\pi$
$620$	2.27227e31	0.175370
$621$	−9.18061e31	−0.695534
$622$	4.78356e31	0.355764
$623$	7.83699e31	0.572185
$624$	−4.48020e31	−0.321125
$625$	5.68434e30	0.0400000
$626$	6.90987e31	0.477381
$627$	−1.51806e31	−0.102970
$628$	−8.39446e31	−0.559058
$629$	6.21702e31	0.406537
$630$	−1.18322e31	−0.0759713
$631$	2.95348e32	1.86207	0.931035	−	0.364930i	$-0.118907\pi$
$631$	2.95348e32	1.86207	0.931035	+	0.364930i	$0.118907\pi$
$632$	−3.32320e31	−0.205736
$633$	5.17602e31	0.314669
$634$	−6.09984e31	−0.364160
$635$	2.93083e31	0.171827
$636$	6.17140e31	0.355326
$637$	3.60795e31	0.204012
$638$	1.49390e31	0.0829628
$639$	7.10557e31	0.387560
$640$	−7.37870e30	−0.0395285
$641$	−2.62963e31	−0.138365	−0.0691826	−	0.997604i	$-0.522039\pi$
$641$	−2.62963e31	−0.138365	−0.0691826	+	0.997604i	$0.522039\pi$
$642$	2.39336e31	0.123696
$643$	2.59835e32	1.31908	0.659541	−	0.751668i	$-0.270751\pi$
$643$	2.59835e32	1.31908	0.659541	+	0.751668i	$0.270751\pi$
$644$	−8.78860e31	−0.438261
$645$	−5.47132e31	−0.268013
$646$	1.54413e32	0.743034
$647$	1.64878e31	0.0779403	0.0389702	−	0.999240i	$-0.487592\pi$
$647$	1.64878e31	0.0779403	0.0389702	+	0.999240i	$0.487592\pi$
$648$	−8.92635e31	−0.414535
$649$	1.33091e31	0.0607206
$650$	3.66684e31	0.164357
$651$	2.13419e32	0.939835
$652$	−2.11401e31	−0.0914661
$653$	−2.31883e32	−0.985751	−0.492876	−	0.870100i	$-0.664054\pi$
$653$	−2.31883e32	−0.985751	−0.492876	+	0.870100i	$0.664054\pi$
$654$	3.33441e32	1.39276
$655$	−8.69453e31	−0.356838
$656$	9.45123e30	0.0381149
$657$	−2.54353e31	−0.100794
$658$	−3.29759e32	−1.28410
$659$	−3.55456e32	−1.36020	−0.680102	−	0.733118i	$-0.738064\pi$
$659$	−3.55456e32	−1.36020	−0.680102	+	0.733118i	$0.738064\pi$
$660$	−5.06344e30	−0.0190410
$661$	−2.00631e32	−0.741447	−0.370724	−	0.928743i	$-0.620890\pi$
$661$	−2.00631e32	−0.741447	−0.370724	+	0.928743i	$0.620890\pi$
$662$	1.07413e32	0.390112
$663$	3.12721e32	1.11622
$664$	−1.64457e32	−0.576923
$665$	1.70055e32	0.586328
$666$	−2.16298e31	−0.0732990
$667$	3.69610e32	1.23111
$668$	−1.71282e32	−0.560767
$669$	−2.40548e32	−0.774106
$670$	−1.46349e32	−0.462946
$671$	−3.87484e31	−0.120488
$672$	−6.93030e31	−0.211839
$673$	3.34870e32	1.00624	0.503122	−	0.864215i	$-0.332185\pi$
$673$	3.34870e32	1.00624	0.503122	+	0.864215i	$0.332185\pi$
$674$	−3.36569e32	−0.994226
$675$	5.92514e31	0.172070
$676$	6.14110e31	0.175331
$677$	−9.65120e31	−0.270902	−0.135451	−	0.990784i	$-0.543248\pi$
$677$	−9.65120e31	−0.270902	−0.135451	+	0.990784i	$0.543248\pi$
$678$	4.70184e32	1.29756
$679$	1.92331e31	0.0521850
$680$	5.15038e31	0.137400
$681$	−4.57366e32	−1.19970
$682$	1.65661e31	0.0427269
$683$	−1.74605e32	−0.442811	−0.221406	−	0.975182i	$-0.571065\pi$
$683$	−1.74605e32	−0.442811	−0.221406	+	0.975182i	$0.571065\pi$
$684$	−5.37220e31	−0.133970
$685$	1.57655e32	0.386603
$686$	−2.62120e32	−0.632080
$687$	−5.80001e32	−1.37539
$688$	−5.81281e31	−0.135556
$689$	−3.25830e32	−0.747256
$690$	−1.25276e32	−0.282556
$691$	4.17873e32	0.926931	0.463465	−	0.886115i	$-0.346606\pi$
$691$	4.17873e32	0.926931	0.463465	+	0.886115i	$0.346606\pi$
$692$	3.68754e32	0.804482
$693$	−8.62634e30	−0.0185095
$694$	4.18071e31	0.0882300
$695$	1.46980e31	0.0305094
$696$	2.91458e32	0.595072
$697$	−6.59703e31	−0.132486
$698$	5.34061e32	1.05500
$699$	−2.62603e32	−0.510285
$700$	5.67214e31	0.108422
$701$	−5.54616e32	−1.04288	−0.521441	−	0.853288i	$-0.674605\pi$
$701$	−5.54616e32	−1.04288	−0.521441	+	0.853288i	$0.674605\pi$
$702$	3.82217e32	0.707023
$703$	3.10868e32	0.565704
$704$	−5.37948e30	−0.00963063
$705$	−4.70052e32	−0.827887
$706$	−6.49406e32	−1.12528
$707$	−3.92298e32	−0.668795
$708$	2.59660e32	0.435534
$709$	−9.37126e32	−1.54656	−0.773279	−	0.634066i	$-0.781385\pi$
$709$	−9.37126e32	−1.54656	−0.773279	+	0.634066i	$0.781385\pi$
$710$	−3.40628e32	−0.553107
$711$	−8.07023e31	−0.128939
$712$	1.18684e32	0.186583
$713$	4.09868e32	0.634037
$714$	4.83740e32	0.736347
$715$	2.67333e31	0.0400436
$716$	2.70395e32	0.398565
$717$	−7.19855e32	−1.04418
$718$	6.28246e30	0.00896806
$719$	−7.22362e31	−0.101478	−0.0507391	−	0.998712i	$-0.516158\pi$
$719$	−7.22362e31	−0.101478	−0.0507391	+	0.998712i	$0.516158\pi$
$720$	−1.79188e31	−0.0247734
$721$	1.37759e33	1.87440
$722$	2.44069e32	0.326839
$723$	6.57045e32	0.865973
$724$	−1.90281e32	−0.246832
$725$	−2.38545e32	−0.304568
$726$	6.18203e32	0.776891
$727$	9.11706e32	1.12774	0.563870	−	0.825863i	$-0.309312\pi$
$727$	9.11706e32	1.12774	0.563870	+	0.825863i	$0.309312\pi$
$728$	3.65897e32	0.445500
$729$	5.76647e32	0.691104
$730$	1.21932e32	0.143848
$731$	4.05739e32	0.471191
$732$	−7.55977e32	−0.864234
$733$	1.25151e33	1.40844	0.704221	−	0.709981i	$-0.251296\pi$
$733$	1.25151e33	1.40844	0.704221	+	0.709981i	$0.251296\pi$
$734$	3.00535e32	0.332958
$735$	7.95542e31	0.0867679
$736$	−1.33095e32	−0.142912
$737$	−1.06697e32	−0.112791
$738$	2.29518e31	0.0238874
$739$	7.62517e32	0.781337	0.390669	−	0.920531i	$-0.372244\pi$
$739$	7.62517e32	0.781337	0.390669	+	0.920531i	$0.372244\pi$
$740$	1.03689e32	0.104609
$741$	1.56369e33	1.55325
$742$	−5.04017e32	−0.492947
$743$	−6.76133e32	−0.651119	−0.325560	−	0.945521i	$-0.605553\pi$
$743$	−6.76133e32	−0.651119	−0.325560	+	0.945521i	$0.605553\pi$
$744$	3.23203e32	0.306470
$745$	−7.28927e32	−0.680592
$746$	−1.07055e33	−0.984265
$747$	−3.99375e32	−0.361571
$748$	3.75492e31	0.0334759
$749$	−1.95465e32	−0.171605
$750$	8.08529e31	0.0699022
$751$	−9.33180e32	−0.794522	−0.397261	−	0.917706i	$-0.630039\pi$
$751$	−9.33180e32	−0.794522	−0.397261	+	0.917706i	$0.630039\pi$
$752$	−4.99391e32	−0.418731
$753$	−1.55495e33	−1.28403
$754$	−1.53880e33	−1.25145
$755$	−1.10126e32	−0.0882060
$756$	5.91241e32	0.466406
$757$	2.41509e33	1.87642	0.938211	−	0.346065i	$-0.112482\pi$
$757$	2.41509e33	1.87642	0.938211	+	0.346065i	$0.112482\pi$
$758$	−1.22080e33	−0.934218
$759$	−9.13333e31	−0.0688413
$760$	2.57533e32	0.191195
$761$	−1.31749e32	−0.0963435	−0.0481718	−	0.998839i	$-0.515339\pi$
$761$	−1.31749e32	−0.0963435	−0.0481718	+	0.998839i	$0.515339\pi$
$762$	4.16875e32	0.300278
$763$	−2.72320e33	−1.93218
$764$	1.68537e32	0.117794
$765$	1.25075e32	0.0861117
$766$	−1.01361e33	−0.687451
$767$	−1.37092e33	−0.915935
$768$	−1.04953e32	−0.0690782
$769$	−7.19550e32	−0.466561	−0.233280	−	0.972410i	$-0.574946\pi$
$769$	−7.19550e32	−0.466561	−0.233280	+	0.972410i	$0.574946\pi$
$770$	4.13530e31	0.0264158
$771$	1.91372e33	1.20435
$772$	−1.41584e33	−0.877841
$773$	−3.05497e32	−0.186613	−0.0933066	−	0.995637i	$-0.529744\pi$
$773$	−3.05497e32	−0.186613	−0.0933066	+	0.995637i	$0.529744\pi$
$774$	−1.41161e32	−0.0849561
$775$	−2.64528e32	−0.156856
$776$	2.91267e31	0.0170170
$777$	9.73878e32	0.560613
$778$	1.16110e32	0.0658572
$779$	−3.29869e32	−0.184357
$780$	5.21564e32	0.287223
$781$	−2.48336e32	−0.134758
$782$	9.29016e32	0.496759
$783$	−2.48650e33	−1.31017
$784$	8.45197e31	0.0438857
$785$	9.77243e32	0.500036
$786$	−1.23669e33	−0.623594
$787$	−3.70046e32	−0.183885	−0.0919426	−	0.995764i	$-0.529308\pi$
$787$	−3.70046e32	−0.183885	−0.0919426	+	0.995764i	$0.529308\pi$
$788$	1.37966e33	0.675649
$789$	3.97011e33	1.91609
$790$	3.86872e32	0.184016
$791$	−3.83999e33	−1.80011
$792$	−1.30638e31	−0.00603573
$793$	3.99131e33	1.81750
$794$	7.54364e32	0.338567
$795$	−7.18446e32	−0.317813
$796$	1.60329e33	0.699055
$797$	1.56557e32	0.0672823	0.0336412	−	0.999434i	$-0.489290\pi$
$797$	1.56557e32	0.0672823	0.0336412	+	0.999434i	$0.489290\pi$
$798$	2.41883e33	1.02464
$799$	3.48578e33	1.45550
$800$	8.58993e31	0.0353553
$801$	2.88218e32	0.116936
$802$	−2.49544e33	−0.998024
$803$	8.88953e31	0.0350469
$804$	−2.08164e33	−0.809024
$805$	1.02313e33	0.391992
$806$	−1.70641e33	−0.644510
$807$	4.80305e33	1.78843
$808$	−5.94100e32	−0.218087
$809$	−3.53778e33	−1.28033	−0.640167	−	0.768236i	$-0.721135\pi$
$809$	−3.53778e33	−1.28033	−0.640167	+	0.768236i	$0.721135\pi$
$810$	1.03916e33	0.370771
$811$	−2.93265e33	−1.03162	−0.515811	−	0.856702i	$-0.672509\pi$
$811$	−2.93265e33	−1.03162	−0.515811	+	0.856702i	$0.672509\pi$
$812$	−2.38033e33	−0.825549
$813$	−5.03948e33	−1.72323
$814$	7.55950e31	0.0254866
$815$	2.46103e32	0.0818098
$816$	7.32580e32	0.240114
$817$	2.02880e33	0.655671
$818$	3.03087e33	0.965840
$819$	8.88562e32	0.279205
$820$	−1.10027e32	−0.0340910
$821$	2.49297e33	0.761677	0.380838	−	0.924642i	$-0.375635\pi$
$821$	2.49297e33	0.761677	0.380838	+	0.924642i	$0.375635\pi$
$822$	2.24245e33	0.675611
$823$	−3.98570e33	−1.18415	−0.592075	−	0.805883i	$-0.701691\pi$
$823$	−3.98570e33	−1.18415	−0.592075	+	0.805883i	$0.701691\pi$
$824$	2.08623e33	0.611222
$825$	5.89463e31	0.0170308
$826$	−2.12064e33	−0.604221
$827$	1.70726e32	0.0479718	0.0239859	−	0.999712i	$-0.492364\pi$
$827$	1.70726e32	0.0479718	0.0239859	+	0.999712i	$0.492364\pi$
$828$	−3.23216e32	−0.0895660
$829$	5.89567e33	1.61123	0.805613	−	0.592443i	$-0.201836\pi$
$829$	5.89567e33	1.61123	0.805613	+	0.592443i	$0.201836\pi$
$830$	1.91453e33	0.516016
$831$	−4.50069e33	−1.19637
$832$	5.54117e32	0.145273
$833$	−5.89953e32	−0.152546
$834$	2.09061e32	0.0533168
$835$	1.99399e33	0.501565
$836$	1.87756e32	0.0465823
$837$	−2.75733e33	−0.674755
$838$	8.94485e32	0.215907
$839$	2.81133e33	0.669345	0.334672	−	0.942335i	$-0.391374\pi$
$839$	2.81133e33	0.669345	0.334672	+	0.942335i	$0.391374\pi$
$840$	8.06793e32	0.189474
$841$	5.69391e33	1.31903
$842$	5.94959e33	1.35956
$843$	−3.60331e33	−0.812241
$844$	−6.40178e32	−0.142352
$845$	−7.14919e32	−0.156821
$846$	−1.21275e33	−0.262428
$847$	−5.04885e33	−1.07779
$848$	−7.63288e32	−0.160744
$849$	−9.20459e33	−1.91234
$850$	−5.99584e32	−0.122894
$851$	1.87032e33	0.378204
$852$	−4.84501e33	−0.966584
$853$	−3.10315e33	−0.610787	−0.305393	−	0.952226i	$-0.598788\pi$
$853$	−3.10315e33	−0.610787	−0.305393	+	0.952226i	$0.598788\pi$
$854$	6.17405e33	1.19896
$855$	6.25406e32	0.119826
$856$	−2.96015e32	−0.0559584
$857$	−5.09943e33	−0.951134	−0.475567	−	0.879679i	$-0.657757\pi$
$857$	−5.09943e33	−0.951134	−0.475567	+	0.879679i	$0.657757\pi$
$858$	3.80249e32	0.0699784
$859$	1.31743e33	0.239224	0.119612	−	0.992821i	$-0.461835\pi$
$859$	1.31743e33	0.239224	0.119612	+	0.992821i	$0.461835\pi$
$860$	6.76701e32	0.121245
$861$	−1.03341e33	−0.182698
$862$	1.14895e33	0.200432
$863$	−1.29184e33	−0.222375	−0.111188	−	0.993799i	$-0.535465\pi$
$863$	−1.29184e33	−0.222375	−0.111188	+	0.993799i	$0.535465\pi$
$864$	8.95381e32	0.152090
$865$	−4.29286e33	−0.719550
$866$	−5.97360e33	−0.988053
$867$	1.65797e33	0.270619
$868$	−2.63960e33	−0.425168
$869$	2.82051e32	0.0448332
$870$	−3.39302e33	−0.532249
$871$	1.09904e34	1.70139
$872$	−4.12405e33	−0.630063
$873$	7.07328e31	0.0106649
$874$	4.64532e33	0.691249
$875$	−6.60324e32	−0.0969760
$876$	1.73434e33	0.251383
$877$	−1.10353e33	−0.157866	−0.0789329	−	0.996880i	$-0.525151\pi$
$877$	−1.10353e33	−0.157866	−0.0789329	+	0.996880i	$0.525151\pi$
$878$	2.11002e33	0.297920
$879$	4.78449e32	0.0666750
$880$	6.26254e31	0.00861390
$881$	3.42468e33	0.464940	0.232470	−	0.972604i	$-0.425319\pi$
$881$	3.42468e33	0.464940	0.232470	+	0.972604i	$0.425319\pi$
$882$	2.05252e32	0.0275042
$883$	−7.33051e33	−0.969585	−0.484792	−	0.874629i	$-0.661105\pi$
$883$	−7.33051e33	−0.969585	−0.484792	+	0.874629i	$0.661105\pi$
$884$	−3.86778e33	−0.504964
$885$	−3.02284e33	−0.389554
$886$	−5.18950e33	−0.660142
$887$	−7.64645e33	−0.960148	−0.480074	−	0.877228i	$-0.659390\pi$
$887$	−7.64645e33	−0.960148	−0.480074	+	0.877228i	$0.659390\pi$
$888$	1.47485e33	0.182809
$889$	−3.40461e33	−0.416578
$890$	−1.38166e33	−0.166885
$891$	7.57608e32	0.0903340
$892$	2.97513e33	0.350195
$893$	1.74298e34	2.02536
$894$	−1.03681e34	−1.18937
$895$	−3.14781e33	−0.356487
$896$	8.57149e32	0.0958328
$897$	9.40785e33	1.03843
$898$	−9.78848e32	−0.106669
$899$	1.11010e34	1.19433
$900$	2.08602e32	0.0221580
$901$	5.32780e33	0.558744
$902$	−8.02157e31	−0.00830585
$903$	6.35578e33	0.649770
$904$	−5.81531e33	−0.586997
$905$	2.21516e33	0.220773
$906$	−1.56640e33	−0.154145
$907$	2.55586e33	0.248344	0.124172	−	0.992261i	$-0.460373\pi$
$907$	2.55586e33	0.248344	0.124172	+	0.992261i	$0.460373\pi$
$908$	5.65677e33	0.542727
$909$	−1.44274e33	−0.136680
$910$	−4.25960e33	−0.398467
$911$	6.46941e33	0.597590	0.298795	−	0.954317i	$-0.403415\pi$
$911$	6.46941e33	0.597590	0.298795	+	0.954317i	$0.403415\pi$
$912$	3.66309e33	0.334124
$913$	1.39580e33	0.125721
$914$	1.13298e33	0.100772
$915$	8.80073e33	0.772994
$916$	7.17353e33	0.622207
$917$	1.01000e34	0.865118
$918$	−6.24983e33	−0.528661
$919$	−5.58007e33	−0.466134	−0.233067	−	0.972461i	$-0.574876\pi$
$919$	−5.58007e33	−0.466134	−0.233067	+	0.972461i	$0.574876\pi$
$920$	1.54943e33	0.127824
$921$	−1.59481e34	−1.29934
$922$	−7.73798e33	−0.622619
$923$	2.55801e34	2.03274
$924$	5.88197e32	0.0461631
$925$	−1.20710e33	−0.0935649
$926$	1.96103e33	0.150127
$927$	5.06630e33	0.383066
$928$	−3.60479e33	−0.269202
$929$	−1.37312e34	−1.01281	−0.506406	−	0.862295i	$-0.669026\pi$
$929$	−1.37312e34	−1.01281	−0.506406	+	0.862295i	$0.669026\pi$
$930$	−3.76258e33	−0.274115
$931$	−2.94992e33	−0.212270
$932$	3.24791e33	0.230846
$933$	−7.92093e33	−0.556080
$934$	3.70847e33	0.257161
$935$	−4.37130e32	−0.0299417
$936$	1.34565e33	0.0910455
$937$	−6.15639e33	−0.411454	−0.205727	−	0.978609i	$-0.565956\pi$
$937$	−6.15639e33	−0.411454	−0.205727	+	0.978609i	$0.565956\pi$
$938$	1.70007e34	1.12237
$939$	−1.14418e34	−0.746176
$940$	5.81367e33	0.374524
$941$	−1.54804e34	−0.985147	−0.492574	−	0.870271i	$-0.663944\pi$
$941$	−1.54804e34	−0.985147	−0.492574	+	0.870271i	$0.663944\pi$
$942$	1.39001e34	0.873841
$943$	−1.98464e33	−0.123253
$944$	−3.21151e33	−0.197030
$945$	−6.88296e33	−0.417166
$946$	4.93352e32	0.0295399
$947$	−1.09161e34	−0.645720	−0.322860	−	0.946447i	$-0.604644\pi$
$947$	−1.09161e34	−0.645720	−0.322860	+	0.946447i	$0.604644\pi$
$948$	5.50278e33	0.321578
$949$	−9.15672e33	−0.528663
$950$	−2.99808e33	−0.171010
$951$	1.01005e34	0.569204
$952$	−5.98296e33	−0.333113
$953$	3.06171e34	1.68421	0.842103	−	0.539317i	$-0.181318\pi$
$953$	3.06171e34	1.68421	0.842103	+	0.539317i	$0.181318\pi$
$954$	−1.85361e33	−0.100742
$955$	−1.96203e33	−0.105358
$956$	8.90327e33	0.472372
$957$	−2.47370e33	−0.129676
$958$	−2.68325e34	−1.38982
$959$	−1.83140e34	−0.937281
$960$	1.22181e33	0.0617854
$961$	−7.70321e33	−0.384904
$962$	−7.78672e33	−0.384451
$963$	−7.18857e32	−0.0350704
$964$	−8.12642e33	−0.391754
$965$	1.64826e34	0.785165
$966$	1.45528e34	0.685028
$967$	−1.52535e34	−0.709519	−0.354759	−	0.934958i	$-0.615437\pi$
$967$	−1.52535e34	−0.709519	−0.354759	+	0.934958i	$0.615437\pi$
$968$	−7.64603e33	−0.351455
$969$	−2.55687e34	−1.16141
$970$	−3.39080e32	−0.0152204
$971$	−2.92889e34	−1.29922	−0.649610	−	0.760268i	$-0.725068\pi$
$971$	−2.92889e34	−1.29922	−0.649610	+	0.760268i	$0.725068\pi$
$972$	4.96773e33	0.217769
$973$	−1.70740e33	−0.0739669
$974$	−1.59491e34	−0.682822
$975$	−6.07180e33	−0.256900
$976$	9.35003e33	0.390967
$977$	−6.75647e33	−0.279211	−0.139605	−	0.990207i	$-0.544583\pi$
$977$	−6.75647e33	−0.279211	−0.139605	+	0.990207i	$0.544583\pi$
$978$	3.50052e33	0.142967
$979$	−1.00731e33	−0.0406595
$980$	−9.83938e32	−0.0392526
$981$	−1.00150e34	−0.394874
$982$	−6.07012e31	−0.00236546
$983$	2.01524e34	0.776178	0.388089	−	0.921622i	$-0.373135\pi$
$983$	2.01524e34	0.776178	0.388089	+	0.921622i	$0.373135\pi$
$984$	−1.56500e33	−0.0595758
$985$	−1.60614e34	−0.604319
$986$	2.51617e34	0.935741
$987$	5.46038e34	2.00713
$988$	−1.93399e34	−0.702668
$989$	1.22062e34	0.438352
$990$	1.52083e32	0.00539852
$991$	6.56935e33	0.230502	0.115251	−	0.993336i	$-0.463233\pi$
$991$	6.56935e33	0.230502	0.115251	+	0.993336i	$0.463233\pi$
$992$	−3.99743e33	−0.138642
$993$	−1.77861e34	−0.609769
$994$	3.95691e34	1.34095
$995$	−1.86647e34	−0.625254
$996$	2.72318e34	0.901767
$997$	8.17693e33	0.267668	0.133834	−	0.991004i	$-0.457271\pi$
$997$	8.17693e33	0.267668	0.133834	+	0.991004i	$0.457271\pi$
$998$	−3.54917e34	−1.14848
$999$	−1.25823e34	−0.402493

Twists

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

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

\(f(q)\)	\(=\)	\(q+2048.00 q^{2} -339122. q^{3} +4.19430e6 q^{4} -4.88281e7 q^{5} -6.94521e8 q^{6} +5.67214e9 q^{7} +8.58993e9 q^{8} +2.08602e10 q^{9} -1.00000e11 q^{10} -7.29056e10 q^{11} -1.42238e12 q^{12} +7.50969e12 q^{13} +1.16165e13 q^{14} +1.65587e13 q^{15} +1.75922e13 q^{16} -1.22795e14 q^{17} +4.27218e13 q^{18} -6.14006e14 q^{19} -2.04800e14 q^{20} -1.92354e15 q^{21} -1.49311e14 q^{22} -3.69414e15 q^{23} -2.91303e15 q^{24} +2.38419e15 q^{25} +1.53798e16 q^{26} +2.48518e16 q^{27} +2.37907e16 q^{28} -1.00053e17 q^{29} +3.39122e16 q^{30} -1.10951e17 q^{31} +3.60288e16 q^{32} +2.47238e16 q^{33} -2.51484e17 q^{34} -2.76960e17 q^{35} +8.74941e16 q^{36} -5.06294e17 q^{37} -1.25749e18 q^{38} -2.54670e18 q^{39} -4.19430e17 q^{40} +5.37240e17 q^{41} -3.93942e18 q^{42} -3.30420e18 q^{43} -3.05788e17 q^{44} -1.01857e18 q^{45} -7.56560e18 q^{46} -2.83871e19 q^{47} -5.96589e18 q^{48} +4.80439e18 q^{49} +4.88281e18 q^{50} +4.16423e19 q^{51} +3.14979e19 q^{52} -4.33879e19 q^{53} +5.08965e19 q^{54} +3.55984e18 q^{55} +4.87233e19 q^{56} +2.08223e20 q^{57} -2.04909e20 q^{58} -1.82553e20 q^{59} +6.94521e19 q^{60} +5.31488e20 q^{61} -2.27227e20 q^{62} +1.18322e20 q^{63} +7.37870e19 q^{64} -3.66684e20 q^{65} +5.06344e19 q^{66} +1.46349e21 q^{67} -5.15038e20 q^{68} +1.25276e21 q^{69} -5.67214e20 q^{70} +3.40628e21 q^{71} +1.79188e20 q^{72} -1.21932e21 q^{73} -1.03689e21 q^{74} -8.08529e20 q^{75} -2.57533e21 q^{76} -4.13530e20 q^{77} -5.21564e21 q^{78} -3.86872e21 q^{79} -8.58993e20 q^{80} -1.03916e22 q^{81} +1.10027e21 q^{82} -1.91453e22 q^{83} -8.06793e21 q^{84} +5.99584e21 q^{85} -6.76701e21 q^{86} +3.39302e22 q^{87} -6.26254e20 q^{88} +1.38166e22 q^{89} -2.08602e21 q^{90} +4.25960e22 q^{91} -1.54943e22 q^{92} +3.76258e22 q^{93} -5.81367e22 q^{94} +2.99808e22 q^{95} -1.22181e22 q^{96} +3.39080e21 q^{97} +9.83938e21 q^{98} -1.52083e21 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 4096 q^{2} - 91884 q^{3} + 8388608 q^{4} - 97656250 q^{5} - 188178432 q^{6} + 2146058908 q^{7} + 17179869184 q^{8} - 12156555726 q^{9} - 200000000000 q^{10} - 692289571776 q^{11} - 385389428736 q^{12}+ \cdots + 18\!\cdots\!88 q^{99}+O(q^{100}) \) 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

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Database

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