LMFDB - Embedded newform 2.50.a.a.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2,50,Mod(1,2)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2, base_ring=CyclotomicField(1))

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

N = Newforms(chi, 50, names="a")

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

chi := DirichletCharacter("2.1");

S:= CuspForms(chi, 50);

N := Newforms(S);

Level:	$ N $	$=$	$ 2 $
Weight:	$ k $	$=$	$ 50 $
Character orbit:	$[\chi]$	$=$	2.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:	$30.4132410198$
Analytic rank:	$1$
Dimension:	$2$
Coefficient field:	$\mathbb{Q}[x]/(x^{2} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x - 22129540960032 $ x^2 - x - 22129540960032
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{7}\cdot 3^{3}\cdot 5^{2} $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$-4.70420e6$ of defining polynomial
Character	$\chi$	$=$	2.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.67772e7 q^{2} +5.46969e11 q^{3} +2.81475e14 q^{4} +1.83444e17 q^{5} -9.17661e18 q^{6} -6.94316e20 q^{7} -4.72237e21 q^{8} +5.98756e22 q^{9} +O(q^{10})$	\(q-1.67772e7 q^{2} +5.46969e11 q^{3} +2.81475e14 q^{4} +1.83444e17 q^{5} -9.17661e18 q^{6} -6.94316e20 q^{7} -4.72237e21 q^{8} +5.98756e22 q^{9} -3.07768e24 q^{10} -3.82951e25 q^{11} +1.53958e26 q^{12} -2.81665e27 q^{13} +1.16487e28 q^{14} +1.00338e29 q^{15} +7.92282e28 q^{16} -8.61007e28 q^{17} -1.00455e30 q^{18} +2.22241e31 q^{19} +5.16349e31 q^{20} -3.79769e32 q^{21} +6.42485e32 q^{22} -3.43692e33 q^{23} -2.58299e33 q^{24} +1.58882e34 q^{25} +4.72555e34 q^{26} -9.81392e34 q^{27} -1.95433e35 q^{28} -8.08917e34 q^{29} -1.68340e36 q^{30} -2.10125e36 q^{31} -1.32923e36 q^{32} -2.09462e37 q^{33} +1.44453e36 q^{34} -1.27368e38 q^{35} +1.68535e37 q^{36} +1.93999e37 q^{37} -3.72858e38 q^{38} -1.54062e39 q^{39} -8.66290e38 q^{40} +5.03702e39 q^{41} +6.37147e39 q^{42} +1.24860e40 q^{43} -1.07791e40 q^{44} +1.09838e40 q^{45} +5.76620e40 q^{46} -8.45536e40 q^{47} +4.33353e40 q^{48} +2.25151e41 q^{49} -2.66559e41 q^{50} -4.70944e40 q^{51} -7.92816e41 q^{52} -2.42683e42 q^{53} +1.64650e42 q^{54} -7.02501e42 q^{55} +3.27881e42 q^{56} +1.21559e43 q^{57} +1.35714e42 q^{58} -1.80798e43 q^{59} +2.82427e43 q^{60} +9.36304e43 q^{61} +3.52532e43 q^{62} -4.15725e43 q^{63} +2.23007e43 q^{64} -5.16698e44 q^{65} +3.51419e44 q^{66} -2.03720e44 q^{67} -2.42352e43 q^{68} -1.87989e45 q^{69} +2.13688e45 q^{70} +4.45012e44 q^{71} -2.82754e44 q^{72} -7.35314e45 q^{73} -3.25477e44 q^{74} +8.69033e45 q^{75} +6.25552e45 q^{76} +2.65889e46 q^{77} +2.58473e46 q^{78} -3.49765e46 q^{79} +1.45339e46 q^{80} -6.80073e46 q^{81} -8.45072e46 q^{82} +1.11659e47 q^{83} -1.06895e47 q^{84} -1.57947e46 q^{85} -2.09480e47 q^{86} -4.42452e46 q^{87} +1.80843e47 q^{88} +1.64975e47 q^{89} -1.84278e47 q^{90} +1.95564e48 q^{91} -9.67407e47 q^{92} -1.14932e48 q^{93} +1.41857e48 q^{94} +4.07687e48 q^{95} -7.27046e47 q^{96} -3.51280e48 q^{97} -3.77740e48 q^{98} -2.29294e48 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 33554432 q^{2} + 281051075592 q^{3} + 562949953421312 q^{4} + 83\!\cdots\!00 q^{5}+ \cdots - 10\!\cdots\!34 q^{9}+O(q^{10}) $ 2 * q - 33554432 * q^2 + 281051075592 * q^3 + 562949953421312 * q^4 + 83174531182543500 * q^5 - 4715254602239311872 * q^6 - 432389265285998218736 * q^7 - 9444732965739290427392 * q^8 - 108711528745520320184934 * q^9	$ 2 q - 33554432 q^{2} + 281051075592 q^{3} + 562949953421312 q^{4} + 83\!\cdots\!00 q^{5}+ \cdots - 83\!\cdots\!88 q^{99}+O(q^{100}) $ 2 * q - 33554432 * q^2 + 281051075592 * q^3 + 562949953421312 * q^4 + 83174531182543500 * q^5 - 4715254602239311872 * q^6 - 432389265285998218736 * q^7 - 9444732965739290427392 * q^8 - 108711528745520320184934 * q^9 - 1395437075348267728896000 * q^10 - 2505571492867298738664936 * q^11 + 79108844956763018967908352 * q^12 - 1673639931069227126134717028 * q^13 + 7254288099784493891349118976 * q^14 + 127001657954212134060542526000 * q^15 + 158456325028528675187087900672 * q^16 + 1242185964859741101801103139364 * q^17 + 1823876799453803444131797663744 * q^18 + 31751134463818510134391653857320 * q^19 + 23411549227526162913517633536000 * q^20 - 449419956159673170901966356305856 * q^21 + 42036514139277130275109182898176 * q^22 - 2878171210013224318486705571467728 * q^23 - 1327226179350123830036695489708032 * q^24 + 8178586568827926193122430485218750 * q^25 + 28079018629773534448221392677634048 * q^26 + 10325024674570189620203761899320400 * q^27 - 121706758376314007465844700470050816 * q^28 - 1184833247028586089467361473487066180 * q^29 - 2130734247855935082954679035887616000 * q^30 - 7105311682527075962924679523835996096 * q^31 - 2658455991569831745807614120560689152 * q^32 - 30463287003660767303795140420914481056 * q^33 - 20840422244620286168995096407387930624 * q^34 - 153631379897937223253539499790216708000 * q^35 - 30599575021825142403743101872928456704 * q^36 - 450602837422002559898874775434541099316 * q^37 - 532695641144527329322877805361490821120 * q^38 - 1844565860254881158789650811268042150288 * q^39 - 392780618284839580851274657642315776000 * q^40 + 6980390908841383456250364112135442830164 * q^41 + 7540015679201367277627204384476308176896 * q^42 + 23005349788522089920652198271012421804632 * q^43 - 705255677601706498485646185066204758016 * q^44 + 27887971423437826407657644077983762985500 * q^45 + 48287700075373227247704252500917509685248 * q^46 - 11845558119045913680201694380285648264096 * q^47 + 22267160291811767123272928157057429798912 * q^48 + 36832674584096520693651334136269148555634 * q^49 - 137213913439924984574072730695499776000000 * q^50 - 400309416097057296812546757700179931238256 * q^51 - 471087760619734618521251120773484792250368 * q^52 - 3995941967102752634563056816023520583445268 * q^53 - 173225169170593778419116477397468604006400 * q^54 - 10613607478462837375186572114612688143558000 * q^55 + 2041900573939229387080089162241344071008256 * q^56 + 9622454719526896343609264017960761786306720 * q^57 + 19878203309379946997589248390770782508154880 * q^58 + 21714921312003050521860441061723392092382840 * q^59 + 35747788714876559768708568395758285357056000 * q^60 + 57835793538935399324202832959454753282039804 * q^61 + 119207348845080179278395340102173655077748736 * q^62 - 85729962342781357158809844980279689420458288 * q^63 + 44601490397061246283071436545296723011960832 * q^64 - 631306767245427642112526729506636646807559000 * q^65 + 511089146130409483781508690592013166204420096 * q^66 - 1132689219365496932068743832028246172304100216 * q^67 + 349644265529199379039043235367571307871862784 * q^68 - 2028469745805465818965418074868217428589127488 * q^69 + 2577506844925750748964854952512420396924928000 * q^70 - 2581062199613136895595155085939596851144015216 * q^71 + 513375679649365128338357228632125270669656064 * q^72 - 9741247004630734466730318432740133532244065388 * q^73 + 7559861133641820099976360264416789884101984256 * q^74 + 10740447594643201176358815057388298782852875000 * q^75 + 8937149833740222221953054682155689587947601920 * q^76 + 35963105293022811785641876043939586820028000448 * q^77 + 30946679863721956255344270225219177052486238208 * q^78 - 16980842222977013563575057931860781555913425760 * q^79 + 6589765273578303173291298806591182514159616000 * q^80 - 56507054670978661477896482621261594252148312078 * q^81 - 117111526042068199984338908787944545617312743424 * q^82 - 24532280715782170299281847013445659051689117528 * q^83 - 126500471693348046312083575434506069166350401536 * q^84 - 148981404862178656936917823933576821852486633000 * q^85 - 385965722557589423370204791267601939299420864512 * q^86 + 249312411293548103558555079681567027901136340720 * q^87 + 11832226838350191893697358946431691525462163456 * q^88 + 1016887356645909629915356530428621471206692153780 * q^89 - 467882520372843876211776348747454436100538368000 * q^90 + 2255028438334749866892926186990858608923879598304 * q^91 - 810133174307752914151819748326433258171497709568 * q^92 + 181349176304449265724939153173691107739800035584 * q^93 + 198735487203787007730098750184038462626763636736 * q^94 + 3121598780165095291602283998223694567559507510000 * q^95 - 373580957922349048368848542643434424141183188992 * q^96 + 862374182033100841941070901898381458438293782724 * q^97 - 617949737355097492525858261492360939453959634944 * q^98 - 8326590145602153633338172323505805232970312882888 * q^99

Display 100 coefficients 10 coefficients

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 $

$2$	−1.67772e7	−0.707107
$2$	−1.67772e7	−0.707107
$3$	5.46969e11	1.11813	0.559064	−	0.829124i	$-0.311160\pi$
$3$	5.46969e11	1.11813	0.559064	+	0.829124i	$0.311160\pi$
$4$	2.81475e14	0.500000
$5$	1.83444e17	1.37638	0.688190	−	0.725530i	$-0.258405\pi$
$5$	1.83444e17	1.37638	0.688190	+	0.725530i	$0.258405\pi$
$6$	−9.17661e18	−0.790636
$7$	−6.94316e20	−1.36979	−0.684897	−	0.728640i	$-0.740153\pi$
$7$	−6.94316e20	−1.36979	−0.684897	+	0.728640i	$0.740153\pi$
$8$	−4.72237e21	−0.353553
$9$	5.98756e22	0.250212
$10$	−3.07768e24	−0.973248
$11$	−3.82951e25	−1.17226	−0.586128	−	0.810219i	$-0.699348\pi$
$11$	−3.82951e25	−1.17226	−0.586128	+	0.810219i	$0.699348\pi$
$12$	1.53958e26	0.559064
$13$	−2.81665e27	−1.43920	−0.719599	−	0.694390i	$-0.755674\pi$
$13$	−2.81665e27	−1.43920	−0.719599	+	0.694390i	$0.755674\pi$
$14$	1.16487e28	0.968590
$15$	1.00338e29	1.53897
$16$	7.92282e28	0.250000
$17$	−8.61007e28	−0.0615189	−0.0307594	−	0.999527i	$-0.509793\pi$
$17$	−8.61007e28	−0.0615189	−0.0307594	+	0.999527i	$0.509793\pi$
$18$	−1.00455e30	−0.176927
$19$	2.22241e31	1.04078	0.520392	−	0.853928i	$-0.325786\pi$
$19$	2.22241e31	1.04078	0.520392	+	0.853928i	$0.325786\pi$
$20$	5.16349e31	0.688190
$21$	−3.79769e32	−1.53161
$22$	6.42485e32	0.828910
$23$	−3.43692e33	−1.49224	−0.746118	−	0.665814i	$-0.768085\pi$
$23$	−3.43692e33	−1.49224	−0.746118	+	0.665814i	$0.768085\pi$
$24$	−2.58299e33	−0.395318
$25$	1.58882e34	0.894424
$26$	4.72555e34	1.01767
$27$	−9.81392e34	−0.838360
$28$	−1.95433e35	−0.684897
$29$	−8.08917e34	−0.119992	−0.0599961	−	0.998199i	$-0.519109\pi$
$29$	−8.08917e34	−0.119992	−0.0599961	+	0.998199i	$0.519109\pi$
$30$	−1.68340e36	−1.08822
$31$	−2.10125e36	−0.608298	−0.304149	−	0.952624i	$-0.598372\pi$
$31$	−2.10125e36	−0.608298	−0.304149	+	0.952624i	$0.598372\pi$
$32$	−1.32923e36	−0.176777
$33$	−2.09462e37	−1.31073
$34$	1.44453e36	0.0435004
$35$	−1.27368e38	−1.88536
$36$	1.68535e37	0.125106
$37$	1.93999e37	0.0735966	0.0367983	−	0.999323i	$-0.488284\pi$
$37$	1.93999e37	0.0735966	0.0367983	+	0.999323i	$0.488284\pi$
$38$	−3.72858e38	−0.735945
$39$	−1.54062e39	−1.60921
$40$	−8.66290e38	−0.486624
$41$	5.03702e39	1.54515	0.772573	−	0.634926i	$-0.218969\pi$
$41$	5.03702e39	1.54515	0.772573	+	0.634926i	$0.218969\pi$
$42$	6.37147e39	1.08301
$43$	1.24860e40	1.19247	0.596234	−	0.802811i	$-0.296663\pi$
$43$	1.24860e40	1.19247	0.596234	+	0.802811i	$0.296663\pi$
$44$	−1.07791e40	−0.586128
$45$	1.09838e40	0.344387
$46$	5.76620e40	1.05517
$47$	−8.45536e40	−0.913554	−0.456777	−	0.889581i	$-0.650996\pi$
$47$	−8.45536e40	−0.913554	−0.456777	+	0.889581i	$0.650996\pi$
$48$	4.33353e40	0.279532
$49$	2.25151e41	0.876334
$50$	−2.66559e41	−0.632454
$51$	−4.70944e40	−0.0687860
$52$	−7.92816e41	−0.719599
$53$	−2.42683e42	−1.38128	−0.690638	−	0.723201i	$-0.742670\pi$
$53$	−2.42683e42	−1.38128	−0.690638	+	0.723201i	$0.742670\pi$
$54$	1.64650e42	0.592810
$55$	−7.02501e42	−1.61347
$56$	3.27881e42	0.484295
$57$	1.21559e43	1.16373
$58$	1.35714e42	0.0848473
$59$	−1.80798e43	−0.743566	−0.371783	−	0.928320i	$-0.621254\pi$
$59$	−1.80798e43	−0.743566	−0.371783	+	0.928320i	$0.621254\pi$
$60$	2.82427e43	0.769486
$61$	9.36304e43	1.70152	0.850758	−	0.525558i	$-0.176144\pi$
$61$	9.36304e43	1.70152	0.850758	+	0.525558i	$0.176144\pi$
$62$	3.52532e43	0.430132
$63$	−4.15725e43	−0.342739
$64$	2.23007e43	0.125000
$65$	−5.16698e44	−1.98089
$66$	3.51419e44	0.926828
$67$	−2.03720e44	−0.371707	−0.185854	−	0.982577i	$-0.559505\pi$
$67$	−2.03720e44	−0.371707	−0.185854	+	0.982577i	$0.559505\pi$
$68$	−2.42352e43	−0.0307594
$69$	−1.87989e45	−1.66851
$70$	2.13688e45	1.33315
$71$	4.45012e44	0.196129	0.0980646	−	0.995180i	$-0.468735\pi$
$71$	4.45012e44	0.196129	0.0980646	+	0.995180i	$0.468735\pi$
$72$	−2.82754e44	−0.0884633
$73$	−7.35314e45	−1.64083	−0.820414	−	0.571771i	$-0.806257\pi$
$73$	−7.35314e45	−1.64083	−0.820414	+	0.571771i	$0.806257\pi$
$74$	−3.25477e44	−0.0520407
$75$	8.69033e45	1.00008
$76$	6.25552e45	0.520392
$77$	2.65889e46	1.60575
$78$	2.58473e46	1.13788
$79$	−3.49765e46	−1.12697	−0.563485	−	0.826126i	$-0.690540\pi$
$79$	−3.49765e46	−1.12697	−0.563485	+	0.826126i	$0.690540\pi$
$80$	1.45339e46	0.344095
$81$	−6.80073e46	−1.18761
$82$	−8.45072e46	−1.09258
$83$	1.11659e47	1.07270	0.536352	−	0.843994i	$-0.319802\pi$
$83$	1.11659e47	1.07270	0.536352	+	0.843994i	$0.319802\pi$
$84$	−1.06895e47	−0.765803
$85$	−1.57947e46	−0.0846734
$86$	−2.09480e47	−0.843202
$87$	−4.42452e46	−0.134167
$88$	1.80843e47	0.414455
$89$	1.64975e47	0.286658	0.143329	−	0.989675i	$-0.454219\pi$
$89$	1.64975e47	0.286658	0.143329	+	0.989675i	$0.454219\pi$
$90$	−1.84278e47	−0.243518
$91$	1.95564e48	1.97140
$92$	−9.67407e47	−0.746118
$93$	−1.14932e48	−0.680156
$94$	1.41857e48	0.645980
$95$	4.07687e48	1.43251
$96$	−7.27046e47	−0.197659
$97$	−3.51280e48	−0.740876	−0.370438	−	0.928857i	$-0.620792\pi$
$97$	−3.51280e48	−0.740876	−0.370438	+	0.928857i	$0.620792\pi$
$98$	−3.77740e48	−0.619661
$99$	−2.29294e48	−0.293312
$100$	4.47212e48	0.447212
$101$	−5.36346e48	−0.420312	−0.210156	−	0.977668i	$-0.567397\pi$
$101$	−5.36346e48	−0.420312	−0.210156	+	0.977668i	$0.567397\pi$
$102$	7.90113e47	0.0486391
$103$	−1.19106e49	−0.577328	−0.288664	−	0.957430i	$-0.593211\pi$
$103$	−1.19106e49	−0.577328	−0.288664	+	0.957430i	$0.593211\pi$
$104$	1.33013e49	0.508833
$105$	−6.96664e49	−2.10807
$106$	4.07154e49	0.976709
$107$	9.39849e48	0.179125	0.0895624	−	0.995981i	$-0.471453\pi$
$107$	9.39849e48	0.179125	0.0895624	+	0.995981i	$0.471453\pi$
$108$	−2.76237e49	−0.419180
$109$	1.53768e50	1.86173	0.930863	−	0.365368i	$-0.119057\pi$
$109$	1.53768e50	1.86173	0.930863	+	0.365368i	$0.119057\pi$
$110$	1.17860e50	1.14090
$111$	1.06112e49	0.0822905
$112$	−5.50094e49	−0.342448
$113$	2.40031e50	1.20184	0.600918	−	0.799311i	$-0.294802\pi$
$113$	2.40031e50	1.20184	0.600918	+	0.799311i	$0.294802\pi$
$114$	−2.03942e50	−0.822881
$115$	−6.30483e50	−2.05389
$116$	−2.27690e49	−0.0599961
$117$	−1.68648e50	−0.360105
$118$	3.03329e50	0.525781
$119$	5.97811e49	0.0842681
$120$	−4.73834e50	−0.544108
$121$	3.99324e50	0.374183
$122$	−1.57086e51	−1.20315
$123$	2.75509e51	1.72767
$124$	−5.91450e50	−0.304149
$125$	−3.44031e50	−0.145312
$126$	6.97472e50	0.242353
$127$	−2.26514e51	−0.648490	−0.324245	−	0.945973i	$-0.605110\pi$
$127$	−2.26514e51	−0.648490	−0.324245	+	0.945973i	$0.605110\pi$
$128$	−3.74144e50	−0.0883883
$129$	6.82946e51	1.33333
$130$	8.66875e51	1.40070
$131$	3.05993e51	0.409794	0.204897	−	0.978784i	$-0.434314\pi$
$131$	3.05993e51	0.409794	0.204897	+	0.978784i	$0.434314\pi$
$132$	−5.89584e51	−0.655366
$133$	−1.54305e52	−1.42566
$134$	3.41786e51	0.262837
$135$	−1.80031e52	−1.15390
$136$	4.06599e50	0.0217502
$137$	5.61652e51	0.251081	0.125540	−	0.992089i	$-0.459934\pi$
$137$	5.61652e51	0.251081	0.125540	+	0.992089i	$0.459934\pi$
$138$	3.15393e52	1.17982
$139$	−2.82771e52	−0.886282	−0.443141	−	0.896452i	$-0.646136\pi$
$139$	−2.82771e52	−0.886282	−0.443141	+	0.896452i	$0.646136\pi$
$140$	−3.58509e52	−0.942679
$141$	−4.62482e52	−1.02147
$142$	−7.46606e51	−0.138684
$143$	1.07864e53	1.68711
$144$	4.74383e51	0.0625530
$145$	−1.48391e52	−0.165155
$146$	1.23365e53	1.16024
$147$	1.23150e53	0.979854
$148$	5.46059e51	0.0367983
$149$	−3.54063e52	−0.202310	−0.101155	−	0.994871i	$-0.532254\pi$
$149$	−3.54063e52	−0.202310	−0.101155	+	0.994871i	$0.532254\pi$
$150$	−1.45800e53	−0.707165
$151$	1.90012e53	0.783152	0.391576	−	0.920146i	$-0.371930\pi$
$151$	1.90012e53	0.783152	0.391576	+	0.920146i	$0.371930\pi$
$152$	−1.04950e53	−0.367972
$153$	−5.15533e51	−0.0153928
$154$	−4.46087e53	−1.13544
$155$	−3.85462e53	−0.837250
$156$	−4.33646e53	−0.804605
$157$	5.21006e53	0.826612	0.413306	−	0.910592i	$-0.364374\pi$
$157$	5.21006e53	0.826612	0.413306	+	0.910592i	$0.364374\pi$
$158$	5.86808e53	0.796888
$159$	−1.32740e54	−1.54444
$160$	−2.43839e53	−0.243312
$161$	2.38631e54	2.04405
$162$	1.14097e54	0.839764
$163$	−1.13103e54	−0.715943	−0.357971	−	0.933733i	$-0.616531\pi$
$163$	−1.13103e54	−0.715943	−0.357971	+	0.933733i	$0.616531\pi$
$164$	1.41780e54	0.772573
$165$	−3.84246e54	−1.80407
$166$	−1.87332e54	−0.758516
$167$	3.02957e54	1.05883	0.529417	−	0.848362i	$-0.322411\pi$
$167$	3.02957e54	1.05883	0.529417	+	0.848362i	$0.322411\pi$
$168$	1.79341e54	0.541504
$169$	4.10329e54	1.07129
$170$	2.64991e53	0.0598731
$171$	1.33068e54	0.260416
$172$	3.51450e54	0.596234
$173$	−7.05590e54	−1.03854	−0.519270	−	0.854611i	$-0.673796\pi$
$173$	−7.05590e54	−1.03854	−0.519270	+	0.854611i	$0.673796\pi$
$174$	7.42312e53	0.0948702
$175$	−1.10314e55	−1.22518
$176$	−3.03405e54	−0.293064
$177$	−9.88910e54	−0.831403
$178$	−2.76783e54	−0.202698
$179$	2.68322e54	0.171300	0.0856499	−	0.996325i	$-0.472703\pi$
$179$	2.68322e54	0.171300	0.0856499	+	0.996325i	$0.472703\pi$
$180$	3.09167e54	0.172193
$181$	3.29637e54	0.160292	0.0801459	−	0.996783i	$-0.474461\pi$
$181$	3.29637e54	0.160292	0.0801459	+	0.996783i	$0.474461\pi$
$182$	−3.28103e55	−1.39399
$183$	5.12129e55	1.90251
$184$	1.62304e55	0.527585
$185$	3.55880e54	0.101297
$186$	1.92824e55	0.480943
$187$	3.29724e54	0.0721158
$188$	−2.37997e55	−0.456777
$189$	6.81396e55	1.14838
$190$	−6.83986e55	−1.01294
$191$	5.42627e55	0.706616	0.353308	−	0.935507i	$-0.385057\pi$
$191$	5.42627e55	0.706616	0.353308	+	0.935507i	$0.385057\pi$
$192$	1.21978e55	0.139766
$193$	−1.54330e55	−0.155703	−0.0778516	−	0.996965i	$-0.524806\pi$
$193$	−1.54330e55	−0.155703	−0.0778516	+	0.996965i	$0.524806\pi$
$194$	5.89350e55	0.523879
$195$	−2.82618e56	−2.21488
$196$	6.33743e55	0.438167
$197$	−1.24089e56	−0.757372	−0.378686	−	0.925525i	$-0.623624\pi$
$197$	−1.24089e56	−0.757372	−0.378686	+	0.925525i	$0.623624\pi$
$198$	3.84691e55	0.207403
$199$	−4.92211e55	−0.234558	−0.117279	−	0.993099i	$-0.537417\pi$
$199$	−4.92211e55	−0.234558	−0.117279	+	0.993099i	$0.537417\pi$
$200$	−7.50298e55	−0.316227
$201$	−1.11429e56	−0.415617
$202$	8.99839e55	0.297205
$203$	5.61644e55	0.164364
$204$	−1.32559e55	−0.0343930
$205$	9.24012e56	2.12671
$206$	1.99827e56	0.408233
$207$	−2.05788e56	−0.373375
$208$	−2.23158e56	−0.359800
$209$	−8.51073e56	−1.22006
$210$	1.16881e57	1.49063
$211$	−4.03237e56	−0.457763	−0.228881	−	0.973454i	$-0.573507\pi$
$211$	−4.03237e56	−0.457763	−0.228881	+	0.973454i	$0.573507\pi$
$212$	−6.83092e56	−0.690638
$213$	2.43408e56	0.219298
$214$	−1.57681e56	−0.126660
$215$	2.29048e57	1.64129
$216$	4.63449e56	0.296405
$217$	1.45893e57	0.833243
$218$	−2.57979e57	−1.31644
$219$	−4.02194e57	−1.83466
$220$	−1.97736e57	−0.806735
$221$	2.42516e56	0.0885378
$222$	−1.78026e56	−0.0581882
$223$	1.25272e57	0.366764	0.183382	−	0.983042i	$-0.441296\pi$
$223$	1.25272e57	0.366764	0.183382	+	0.983042i	$0.441296\pi$
$224$	9.22904e56	0.242148
$225$	9.51313e56	0.223796
$226$	−4.02705e57	−0.849827
$227$	−2.03385e57	−0.385200	−0.192600	−	0.981277i	$-0.561692\pi$
$227$	−2.03385e57	−0.385200	−0.192600	+	0.981277i	$0.561692\pi$
$228$	3.42157e57	0.581865
$229$	−4.08825e57	−0.624551	−0.312275	−	0.949992i	$-0.601091\pi$
$229$	−4.08825e57	−0.624551	−0.312275	+	0.949992i	$0.601091\pi$
$230$	1.05777e58	1.45232
$231$	1.45433e58	1.79543
$232$	3.82000e56	0.0424236
$233$	1.21098e58	1.21036	0.605182	−	0.796087i	$-0.293100\pi$
$233$	1.21098e58	1.21036	0.605182	+	0.796087i	$0.293100\pi$
$234$	2.82945e57	0.254632
$235$	−1.55109e58	−1.25740
$236$	−5.08902e57	−0.371783
$237$	−1.91311e58	−1.26010
$238$	−1.00296e57	−0.0595866
$239$	−1.30989e58	−0.702243	−0.351121	−	0.936330i	$-0.614200\pi$
$239$	−1.30989e58	−0.702243	−0.351121	+	0.936330i	$0.614200\pi$
$240$	7.94961e57	0.384743
$241$	−2.38239e57	−0.104134	−0.0520672	−	0.998644i	$-0.516581\pi$
$241$	−2.38239e57	−0.104134	−0.0520672	+	0.998644i	$0.516581\pi$
$242$	−6.69955e57	−0.264587
$243$	−1.37132e58	−0.489537
$244$	2.63546e58	0.850758
$245$	4.13026e58	1.20617
$246$	−4.62228e58	−1.22165
$247$	−6.25974e58	−1.49789
$248$	9.92288e57	0.215066
$249$	6.10739e58	1.19942
$250$	5.77188e57	0.102751
$251$	−5.82711e58	−0.940692	−0.470346	−	0.882482i	$-0.655871\pi$
$251$	−5.82711e58	−0.940692	−0.470346	+	0.882482i	$0.655871\pi$
$252$	−1.17016e58	−0.171369
$253$	1.31617e59	1.74928
$254$	3.80027e58	0.458552
$255$	−8.63919e57	−0.0946758
$256$	6.27710e57	0.0625000
$257$	1.67432e59	1.51523	0.757613	−	0.652704i	$-0.226365\pi$
$257$	1.67432e59	1.51523	0.757613	+	0.652704i	$0.226365\pi$
$258$	−1.14579e59	−0.942808
$259$	−1.34697e58	−0.100812
$260$	−1.45437e59	−0.990443
$261$	−4.84343e57	−0.0300235
$262$	−5.13371e58	−0.289768
$263$	1.10522e59	0.568240	0.284120	−	0.958789i	$-0.408299\pi$
$263$	1.10522e59	0.568240	0.284120	+	0.958789i	$0.408299\pi$
$264$	9.89157e58	0.463414
$265$	−4.45187e59	−1.90116
$266$	2.58881e59	1.00809
$267$	9.02364e58	0.320520
$268$	−5.73421e58	−0.185854
$269$	−3.67439e59	−1.08706	−0.543532	−	0.839389i	$-0.682913\pi$
$269$	−3.67439e59	−1.08706	−0.543532	+	0.839389i	$0.682913\pi$
$270$	3.02041e59	0.815932
$271$	−8.00463e59	−1.97512	−0.987561	−	0.157237i	$-0.949741\pi$
$271$	−8.00463e59	−1.97512	−0.987561	+	0.157237i	$0.949741\pi$
$272$	−6.82160e57	−0.0153797
$273$	1.06968e60	2.20428
$274$	−9.42296e58	−0.177541
$275$	−6.08439e59	−1.04849
$276$	−5.29142e59	−0.834256
$277$	7.47402e59	1.07845	0.539225	−	0.842162i	$-0.318717\pi$
$277$	7.47402e59	1.07845	0.539225	+	0.842162i	$0.318717\pi$
$278$	4.74410e59	0.626696
$279$	−1.25814e59	−0.152204
$280$	6.01479e59	0.666574
$281$	4.12737e59	0.419149	0.209574	−	0.977793i	$-0.432792\pi$
$281$	4.12737e59	0.419149	0.209574	+	0.977793i	$0.432792\pi$
$282$	7.75915e59	0.722289
$283$	6.41861e59	0.547865	0.273932	−	0.961749i	$-0.411676\pi$
$283$	6.41861e59	0.547865	0.273932	+	0.961749i	$0.411676\pi$
$284$	1.25260e59	0.0980646
$285$	2.22992e60	1.60174
$286$	−1.80965e60	−1.19297
$287$	−3.49728e60	−2.11653
$288$	−7.95883e58	−0.0442316
$289$	−1.95142e60	−0.996215
$290$	2.48959e59	0.116782
$291$	−1.92139e60	−0.828395
$292$	−2.06973e60	−0.820414
$293$	5.06226e60	1.84539	0.922694	−	0.385534i	$-0.125983\pi$
$293$	5.06226e60	1.84539	0.922694	+	0.385534i	$0.125983\pi$
$294$	−2.06612e60	−0.692861
$295$	−3.31664e60	−1.02343
$296$	−9.16135e58	−0.0260203
$297$	3.75825e60	0.982772
$298$	5.94018e59	0.143054
$299$	9.68060e60	2.14762
$300$	2.44611e60	0.500041
$301$	−8.66923e60	−1.63343
$302$	−3.18788e60	−0.553772
$303$	−2.93364e60	−0.469962
$304$	1.76077e60	0.260196
$305$	1.71759e61	2.34193
$306$	8.64921e58	0.0108843
$307$	−1.48574e61	−1.72605	−0.863025	−	0.505160i	$-0.831433\pi$
$307$	−1.48574e61	−1.72605	−0.863025	+	0.505160i	$0.831433\pi$
$308$	7.48411e60	0.802874
$309$	−6.51475e60	−0.645528
$310$	6.46698e60	0.592025
$311$	2.81771e60	0.238378	0.119189	−	0.992872i	$-0.461970\pi$
$311$	2.81771e60	0.238378	0.119189	+	0.992872i	$0.461970\pi$
$312$	7.27537e60	0.568941
$313$	−1.67694e60	−0.121250	−0.0606249	−	0.998161i	$-0.519309\pi$
$313$	−1.67694e60	−0.121250	−0.0606249	+	0.998161i	$0.519309\pi$
$314$	−8.74104e60	−0.584503
$315$	−7.62624e60	−0.471739
$316$	−9.84501e60	−0.563485
$317$	−1.83062e61	−0.969718	−0.484859	−	0.874592i	$-0.661129\pi$
$317$	−1.83062e61	−0.969718	−0.484859	+	0.874592i	$0.661129\pi$
$318$	2.22701e61	1.09209
$319$	3.09775e60	0.140662
$320$	4.09094e60	0.172048
$321$	5.14068e60	0.200285
$322$	−4.00356e61	−1.44537
$323$	−1.91351e60	−0.0640278
$324$	−1.91423e61	−0.593803
$325$	−4.47514e61	−1.28725
$326$	1.89756e61	0.506248
$327$	8.41061e61	2.08165
$328$	−2.37867e61	−0.546292
$329$	5.87069e61	1.25138
$330$	6.44658e61	1.27567
$331$	−2.17720e61	−0.400049	−0.200024	−	0.979791i	$-0.564102\pi$
$331$	−2.17720e61	−0.400049	−0.200024	+	0.979791i	$0.564102\pi$
$332$	3.14292e61	0.536352
$333$	1.16158e60	0.0184147
$334$	−5.08278e61	−0.748708
$335$	−3.73712e61	−0.511611
$336$	−3.00884e61	−0.382901
$337$	3.29883e61	0.390326	0.195163	−	0.980771i	$-0.437476\pi$
$337$	3.29883e61	0.390326	0.195163	+	0.980771i	$0.437476\pi$
$338$	−6.88418e61	−0.757518
$339$	1.31289e62	1.34381
$340$	−4.44580e60	−0.0423367
$341$	8.04676e61	0.713081
$342$	−2.23251e61	−0.184142
$343$	2.20604e61	0.169397
$344$	−5.89635e61	−0.421601
$345$	−3.44854e62	−2.29651
$346$	1.18378e62	0.734358
$347$	−2.91357e62	−1.68404	−0.842020	−	0.539446i	$-0.818634\pi$
$347$	−2.91357e62	−1.68404	−0.842020	+	0.539446i	$0.818634\pi$
$348$	−1.24539e61	−0.0670834
$349$	−3.41535e62	−1.71479	−0.857397	−	0.514656i	$-0.827920\pi$
$349$	−3.41535e62	−1.71479	−0.857397	+	0.514656i	$0.827920\pi$
$350$	1.85076e62	0.866331
$351$	2.76424e62	1.20657
$352$	5.09029e61	0.207227
$353$	2.89274e62	1.09858	0.549288	−	0.835633i	$-0.314899\pi$
$353$	2.89274e62	1.09858	0.549288	+	0.835633i	$0.314899\pi$
$354$	1.65912e62	0.587891
$355$	8.16348e61	0.269948
$356$	4.64364e61	0.143329
$357$	3.26984e61	0.0942226
$358$	−4.50169e61	−0.121127
$359$	2.98428e62	0.749939	0.374970	−	0.927037i	$-0.377653\pi$
$359$	2.98428e62	0.749939	0.374970	+	0.927037i	$0.377653\pi$
$360$	−5.18696e61	−0.121759
$361$	3.79494e61	0.0832298
$362$	−5.53039e61	−0.113343
$363$	2.18418e62	0.418385
$364$	5.50465e62	0.985702
$365$	−1.34889e63	−2.25840
$366$	−8.59210e62	−1.34528
$367$	3.88819e62	0.569414	0.284707	−	0.958615i	$-0.408104\pi$
$367$	3.88819e62	0.569414	0.284707	+	0.958615i	$0.408104\pi$
$368$	−2.72301e62	−0.373059
$369$	3.01595e62	0.386614
$370$	−5.97068e61	−0.0716278
$371$	1.68499e63	1.89206
$372$	−3.23505e62	−0.340078
$373$	−1.60662e63	−1.58142	−0.790711	−	0.612190i	$-0.790289\pi$
$373$	−1.60662e63	−1.58142	−0.790711	+	0.612190i	$0.790289\pi$
$374$	−5.53184e61	−0.0509936
$375$	−1.88174e62	−0.162478
$376$	3.99293e62	0.322990
$377$	2.27844e62	0.172693
$378$	−1.14319e63	−0.812027
$379$	8.33077e62	0.554657	0.277328	−	0.960775i	$-0.410551\pi$
$379$	8.33077e62	0.554657	0.277328	+	0.960775i	$0.410551\pi$
$380$	1.14754e63	0.716257
$381$	−1.23896e63	−0.725096
$382$	−9.10377e62	−0.499653
$383$	−2.73152e63	−1.40616	−0.703078	−	0.711112i	$-0.748192\pi$
$383$	−2.73152e63	−1.40616	−0.703078	+	0.711112i	$0.748192\pi$
$384$	−2.04645e62	−0.0988296
$385$	4.87757e63	2.21012
$386$	2.58923e62	0.110099
$387$	7.47607e62	0.298370
$388$	−9.88765e62	−0.370438
$389$	1.94880e63	0.685490	0.342745	−	0.939428i	$-0.388643\pi$
$389$	1.94880e63	0.685490	0.342745	+	0.939428i	$0.388643\pi$
$390$	4.74154e63	1.56616
$391$	2.95921e62	0.0918007
$392$	−1.06324e63	−0.309831
$393$	1.67369e63	0.458202
$394$	2.08186e63	0.535543
$395$	−6.41623e63	−1.55114
$396$	−6.45405e62	−0.146656
$397$	−2.53642e63	−0.541819	−0.270910	−	0.962605i	$-0.587324\pi$
$397$	−2.53642e63	−0.541819	−0.270910	+	0.962605i	$0.587324\pi$
$398$	8.25793e62	0.165858
$399$	−8.44001e63	−1.59407
$400$	1.25879e63	0.223606
$401$	−1.66146e63	−0.277621	−0.138810	−	0.990319i	$-0.544328\pi$
$401$	−1.66146e63	−0.277621	−0.138810	+	0.990319i	$0.544328\pi$
$402$	1.86946e63	0.293885
$403$	5.91849e63	0.875462
$404$	−1.50968e63	−0.210156
$405$	−1.24755e64	−1.63460
$406$	−9.42282e62	−0.116223
$407$	−7.42922e62	−0.0862740
$408$	2.22397e62	0.0243195
$409$	1.75781e64	1.81030	0.905150	−	0.425093i	$-0.139759\pi$
$409$	1.75781e64	1.81030	0.905150	+	0.425093i	$0.139759\pi$
$410$	−1.55024e64	−1.50381
$411$	3.07206e63	0.280741
$412$	−3.35255e63	−0.288664
$413$	1.25531e64	1.01853
$414$	3.45254e63	0.264016
$415$	2.04832e64	1.47645
$416$	3.74397e63	0.254417
$417$	−1.54667e64	−0.990977
$418$	1.42786e64	0.862715
$419$	−3.77116e63	−0.214898	−0.107449	−	0.994211i	$-0.534268\pi$
$419$	−3.77116e63	−0.214898	−0.107449	+	0.994211i	$0.534268\pi$
$420$	−1.96093e64	−1.05404
$421$	2.15371e64	1.09213	0.546066	−	0.837742i	$-0.316125\pi$
$421$	2.15371e64	1.09213	0.546066	+	0.837742i	$0.316125\pi$
$422$	6.76520e63	0.323687
$423$	−5.06269e63	−0.228582
$424$	1.14604e64	0.488355
$425$	−1.36798e63	−0.0550240
$426$	−4.08370e63	−0.155067
$427$	−6.50090e64	−2.33072
$428$	2.64544e63	0.0895624
$429$	5.89982e64	1.88640
$430$	−3.84280e64	−1.16057
$431$	−4.00866e64	−1.14369	−0.571843	−	0.820363i	$-0.693771\pi$
$431$	−4.00866e64	−1.14369	−0.571843	+	0.820363i	$0.693771\pi$
$432$	−7.77539e63	−0.209590
$433$	1.96173e64	0.499672	0.249836	−	0.968288i	$-0.419623\pi$
$433$	1.96173e64	0.499672	0.249836	+	0.968288i	$0.419623\pi$
$434$	−2.44768e64	−0.589192
$435$	−8.11653e63	−0.184665
$436$	4.32817e64	0.930863
$437$	−7.63824e64	−1.55309
$438$	6.74769e64	1.29730
$439$	−6.61036e63	−0.120183	−0.0600917	−	0.998193i	$-0.519139\pi$
$439$	−6.61036e63	−0.120183	−0.0600917	+	0.998193i	$0.519139\pi$
$440$	3.31747e64	0.570448
$441$	1.34810e64	0.219269
$442$	−4.06874e63	−0.0626057
$443$	6.49071e64	0.944933	0.472467	−	0.881349i	$-0.343364\pi$
$443$	6.49071e64	0.944933	0.472467	+	0.881349i	$0.343364\pi$
$444$	2.98677e63	0.0411452
$445$	3.02637e64	0.394550
$446$	−2.10172e64	−0.259341
$447$	−1.93661e64	−0.226208
$448$	−1.54838e64	−0.171224
$449$	−2.97057e64	−0.311032	−0.155516	−	0.987833i	$-0.549704\pi$
$449$	−2.97057e64	−0.311032	−0.155516	+	0.987833i	$0.549704\pi$
$450$	−1.59604e64	−0.158247
$451$	−1.92893e65	−1.81131
$452$	6.75627e64	0.600918
$453$	1.03931e65	0.875665
$454$	3.41224e64	0.272378
$455$	3.58751e65	2.71340
$456$	−5.74045e64	−0.411441
$457$	−9.53881e60	−6.47959e−5 0	−3.23979e−5	−	1.00000i	$-0.500010\pi$
$457$	−9.53881e60	−6.47959e−5 0	−3.23979e−5		1.00000i	$0.500010\pi$
$458$	6.85894e64	0.441624
$459$	8.44986e63	0.0515749
$460$	−1.77465e65	−1.02694
$461$	−2.70016e63	−0.0148155	−0.00740776	−	0.999973i	$-0.502358\pi$
$461$	−2.70016e63	−0.0148155	−0.00740776	+	0.999973i	$0.502358\pi$
$462$	−2.43996e65	−1.26956
$463$	−3.03424e65	−1.49732	−0.748661	−	0.662953i	$-0.769303\pi$
$463$	−3.03424e65	−1.49732	−0.748661	+	0.662953i	$0.769303\pi$
$464$	−6.40890e63	−0.0299980
$465$	−2.10836e65	−0.936153
$466$	−2.03168e65	−0.855857
$467$	9.36667e64	0.374388	0.187194	−	0.982323i	$-0.440061\pi$
$467$	9.36667e64	0.374388	0.187194	+	0.982323i	$0.440061\pi$
$468$	−4.74703e64	−0.180052
$469$	1.41446e65	0.509162
$470$	2.60229e65	0.889115
$471$	2.84974e65	0.924258
$472$	8.53795e64	0.262890
$473$	−4.78153e65	−1.39788
$474$	3.20966e65	0.891024
$475$	3.53100e65	0.930902
$476$	1.68269e64	0.0421341
$477$	−1.45308e65	−0.345612
$478$	2.19764e65	0.496561
$479$	2.77494e65	0.595708	0.297854	−	0.954611i	$-0.403729\pi$
$479$	2.77494e65	0.595708	0.297854	+	0.954611i	$0.403729\pi$
$480$	−1.33372e65	−0.272054
$481$	−5.46428e64	−0.105920
$482$	3.99698e64	0.0736342
$483$	1.30524e66	2.28552
$484$	1.12400e65	0.187092
$485$	−6.44402e65	−1.01973
$486$	2.30069e65	0.346155
$487$	−1.35054e66	−1.93218	−0.966092	−	0.258197i	$-0.916872\pi$
$487$	−1.35054e66	−1.93218	−0.966092	+	0.258197i	$0.916872\pi$
$488$	−4.42157e65	−0.601576
$489$	−6.18639e65	−0.800516
$490$	−6.92942e65	−0.852890
$491$	3.82866e65	0.448280	0.224140	−	0.974557i	$-0.428043\pi$
$491$	3.82866e65	0.448280	0.224140	+	0.974557i	$0.428043\pi$
$492$	7.75490e65	0.863836
$493$	6.96483e63	0.00738178
$494$	1.05021e66	1.05917
$495$	−4.20626e65	−0.403710
$496$	−1.66478e65	−0.152075
$497$	−3.08979e65	−0.268656
$498$	−1.02465e66	−0.848119
$499$	−1.64091e66	−1.29307	−0.646533	−	0.762886i	$-0.723782\pi$
$499$	−1.64091e66	−1.29307	−0.646533	+	0.762886i	$0.723782\pi$
$500$	−9.68361e64	−0.0726561
$501$	1.65708e66	1.18391
$502$	9.77628e65	0.665170
$503$	6.21357e64	0.0402648	0.0201324	−	0.999797i	$-0.493591\pi$
$503$	6.21357e64	0.0402648	0.0201324	+	0.999797i	$0.493591\pi$
$504$	1.96321e65	0.121176
$505$	−9.83895e65	−0.578509
$506$	−2.20817e66	−1.23693
$507$	2.24437e66	1.19784
$508$	−6.37580e65	−0.324245
$509$	2.93731e66	1.42352	0.711760	−	0.702422i	$-0.247898\pi$
$509$	2.93731e66	1.42352	0.711760	+	0.702422i	$0.247898\pi$
$510$	1.44942e65	0.0669459
$511$	5.10540e66	2.24759
$512$	−1.05312e65	−0.0441942
$513$	−2.18105e66	−0.872551
$514$	−2.80905e66	−1.07143
$515$	−2.18494e66	−0.794624
$516$	1.92232e66	0.666666
$517$	3.23799e66	1.07092
$518$	2.25984e65	0.0712849
$519$	−3.85936e66	−1.16122
$520$	2.44004e66	0.700349
$521$	−1.44593e66	−0.395934	−0.197967	−	0.980209i	$-0.563434\pi$
$521$	−1.44593e66	−0.395934	−0.197967	+	0.980209i	$0.563434\pi$
$522$	8.12594e64	0.0212298
$523$	−2.05511e65	−0.0512323	−0.0256161	−	0.999672i	$-0.508155\pi$
$523$	−2.05511e65	−0.0512323	−0.0256161	+	0.999672i	$0.508155\pi$
$524$	8.61294e65	0.204897
$525$	−6.03383e66	−1.36991
$526$	−1.85425e66	−0.401807
$527$	1.80919e65	0.0374218
$528$	−1.65953e66	−0.327683
$529$	6.50768e66	1.22677
$530$	7.46900e66	1.34432
$531$	−1.08254e66	−0.186049
$532$	−4.34330e66	−0.712829
$533$	−1.41875e67	−2.22377
$534$	−1.51391e66	−0.226642
$535$	1.72410e66	0.246544
$536$	9.62041e65	0.131418
$537$	1.46764e66	0.191535
$538$	6.16461e66	0.768670
$539$	−8.62217e66	−1.02729
$540$	−5.06741e66	−0.576951
$541$	5.94963e66	0.647377	0.323688	−	0.946164i	$-0.395077\pi$
$541$	5.94963e66	0.647377	0.323688	+	0.946164i	$0.395077\pi$
$542$	1.34295e67	1.39662
$543$	1.80301e66	0.179227
$544$	1.14448e65	0.0108751
$545$	2.82078e67	2.56244
$546$	−1.79462e67	−1.55866
$547$	−9.51607e66	−0.790257	−0.395128	−	0.918626i	$-0.629300\pi$
$547$	−9.51607e66	−0.790257	−0.395128	+	0.918626i	$0.629300\pi$
$548$	1.58091e66	0.125540
$549$	5.60617e66	0.425739
$550$	1.02079e67	0.741397
$551$	−1.79774e66	−0.124886
$552$	8.87752e66	0.589908
$553$	2.42847e67	1.54372
$554$	−1.25393e67	−0.762579
$555$	1.94655e66	0.113263
$556$	−7.95929e66	−0.443141
$557$	−3.18474e67	−1.69677	−0.848383	−	0.529383i	$-0.822423\pi$
$557$	−3.18474e67	−1.69677	−0.848383	+	0.529383i	$0.822423\pi$
$558$	2.11080e66	0.107624
$559$	−3.51687e67	−1.71620
$560$	−1.00911e67	−0.471339
$561$	1.80348e66	0.0806348
$562$	−6.92457e66	−0.296383
$563$	−3.73857e67	−1.53197	−0.765984	−	0.642860i	$-0.777748\pi$
$563$	−3.73857e67	−1.53197	−0.765984	+	0.642860i	$0.777748\pi$
$564$	−1.30177e67	−0.510736
$565$	4.40323e67	1.65418
$566$	−1.07686e67	−0.387399
$567$	4.72185e67	1.62677
$568$	−2.10151e66	−0.0693421
$569$	5.52070e66	0.174479	0.0872395	−	0.996187i	$-0.472195\pi$
$569$	5.52070e66	0.174479	0.0872395	+	0.996187i	$0.472195\pi$
$570$	−3.74119e67	−1.13260
$571$	3.62901e67	1.05245	0.526227	−	0.850344i	$-0.323606\pi$
$571$	3.62901e67	1.05245	0.526227	+	0.850344i	$0.323606\pi$
$572$	3.03610e67	0.843554
$573$	2.96800e67	0.790088
$574$	5.86747e67	1.49661
$575$	−5.46064e67	−1.33469
$576$	1.33527e66	0.0312765
$577$	−6.45533e67	−1.44914	−0.724571	−	0.689200i	$-0.757962\pi$
$577$	−6.45533e67	−1.44914	−0.724571	+	0.689200i	$0.757962\pi$
$578$	3.27394e67	0.704431
$579$	−8.44139e66	−0.174096
$580$	−4.17684e66	−0.0825775
$581$	−7.75265e67	−1.46938
$582$	3.22356e67	0.585764
$583$	9.29356e67	1.61921
$584$	3.47242e67	0.580120
$585$	−3.09376e67	−0.495641
$586$	−8.49306e67	−1.30489
$587$	1.15266e68	1.69851	0.849255	−	0.527983i	$-0.177052\pi$
$587$	1.15266e68	1.69851	0.849255	+	0.527983i	$0.177052\pi$
$588$	3.46638e67	0.489927
$589$	−4.66984e67	−0.633107
$590$	5.56439e67	0.723675
$591$	−6.78726e67	−0.846840
$592$	1.53702e66	0.0183991
$593$	−1.18137e66	−0.0135690	−0.00678448	−	0.999977i	$-0.502160\pi$
$593$	−1.18137e66	−0.0135690	−0.00678448	+	0.999977i	$0.502160\pi$
$594$	−6.30530e67	−0.694925
$595$	1.09665e67	0.115985
$596$	−9.96598e66	−0.101155
$597$	−2.69224e67	−0.262267
$598$	−1.62414e68	−1.51860
$599$	−1.41814e68	−1.27281	−0.636404	−	0.771356i	$-0.719579\pi$
$599$	−1.41814e68	−1.27281	−0.636404	+	0.771356i	$0.719579\pi$
$600$	−4.10389e67	−0.353582
$601$	1.12391e68	0.929621	0.464811	−	0.885410i	$-0.346122\pi$
$601$	1.12391e68	0.929621	0.464811	+	0.885410i	$0.346122\pi$
$602$	1.45446e68	1.15501
$603$	−1.21979e67	−0.0930056
$604$	5.34837e67	0.391576
$605$	7.32537e67	0.515018
$606$	4.92184e67	0.332314
$607$	−6.75870e67	−0.438268	−0.219134	−	0.975695i	$-0.570323\pi$
$607$	−6.75870e67	−0.438268	−0.219134	+	0.975695i	$0.570323\pi$
$608$	−2.95409e67	−0.183986
$609$	3.07202e67	0.183781
$610$	−2.88164e68	−1.65600
$611$	2.38158e68	1.31479
$612$	−1.45110e66	−0.00769638
$613$	−2.95475e68	−1.50570	−0.752850	−	0.658192i	$-0.771322\pi$
$613$	−2.95475e68	−1.50570	−0.752850	+	0.658192i	$0.771322\pi$
$614$	2.49266e68	1.22050
$615$	5.05406e68	2.37793
$616$	−1.25562e68	−0.567718
$617$	−1.12660e68	−0.489536	−0.244768	−	0.969582i	$-0.578712\pi$
$617$	−1.12660e68	−0.489536	−0.244768	+	0.969582i	$0.578712\pi$
$618$	1.09299e68	0.456457
$619$	2.31878e68	0.930761	0.465381	−	0.885111i	$-0.345917\pi$
$619$	2.31878e68	0.930761	0.465381	+	0.885111i	$0.345917\pi$
$620$	−1.08498e68	−0.418625
$621$	3.37297e68	1.25103
$622$	−4.72733e67	−0.168559
$623$	−1.14545e68	−0.392662
$624$	−1.22060e68	−0.402302
$625$	−3.45341e68	−1.09443
$626$	2.81344e67	0.0857365
$627$	−4.65510e68	−1.36419
$628$	1.46650e68	0.413306
$629$	−1.67035e66	−0.00452758
$630$	1.27947e68	0.333570
$631$	1.18119e68	0.296211	0.148105	−	0.988972i	$-0.452683\pi$
$631$	1.18119e68	0.296211	0.148105	+	0.988972i	$0.452683\pi$
$632$	1.65172e68	0.398444
$633$	−2.20558e68	−0.511838
$634$	3.07126e68	0.685694
$635$	−4.15526e68	−0.892570
$636$	−3.73630e68	−0.772222
$637$	−6.34171e68	−1.26122
$638$	−5.19717e67	−0.0994627
$639$	2.66453e67	0.0490739
$640$	−6.86346e67	−0.121656
$641$	−3.04622e68	−0.519685	−0.259842	−	0.965651i	$-0.583671\pi$
$641$	−3.04622e68	−0.519685	−0.259842	+	0.965651i	$0.583671\pi$
$642$	−8.62463e67	−0.141623
$643$	−4.07673e68	−0.644382	−0.322191	−	0.946675i	$-0.604419\pi$
$643$	−4.07673e68	−0.644382	−0.322191	+	0.946675i	$0.604419\pi$
$644$	6.71686e68	1.02203
$645$	1.25282e69	1.83517
$646$	3.21033e67	0.0452745
$647$	3.17405e68	0.430982	0.215491	−	0.976506i	$-0.430865\pi$
$647$	3.17405e68	0.430982	0.215491	+	0.976506i	$0.430865\pi$
$648$	3.21155e68	0.419882
$649$	6.92368e68	0.871650
$650$	7.50804e68	0.910226
$651$	7.97990e68	0.931673
$652$	−3.18357e68	−0.357971
$653$	−2.07482e68	−0.224702	−0.112351	−	0.993669i	$-0.535838\pi$
$653$	−2.07482e68	−0.224702	−0.112351	+	0.993669i	$0.535838\pi$
$654$	−1.41107e69	−1.47195
$655$	5.61327e68	0.564032
$656$	3.99074e68	0.386286
$657$	−4.40273e68	−0.410555
$658$	−9.84938e68	−0.884860
$659$	−4.41699e68	−0.382326	−0.191163	−	0.981558i	$-0.561226\pi$
$659$	−4.41699e68	−0.382326	−0.191163	+	0.981558i	$0.561226\pi$
$660$	−1.08156e69	−0.902034
$661$	1.79546e69	1.44291	0.721455	−	0.692462i	$-0.243474\pi$
$661$	1.79546e69	1.44291	0.721455	+	0.692462i	$0.243474\pi$
$662$	3.65274e68	0.282877
$663$	1.32648e68	0.0989967
$664$	−5.27294e68	−0.379258
$665$	−2.83064e69	−1.96225
$666$	−1.94881e67	−0.0130212
$667$	2.78018e68	0.179057
$668$	8.52749e68	0.529417
$669$	6.85201e68	0.410089
$670$	6.26985e68	0.361764
$671$	−3.58558e69	−1.99461
$672$	5.04800e68	0.270752
$673$	2.68307e69	1.38760	0.693798	−	0.720169i	$-0.255936\pi$
$673$	2.68307e69	1.38760	0.693798	+	0.720169i	$0.255936\pi$
$674$	−5.53451e68	−0.276002
$675$	−1.55925e69	−0.749849
$676$	1.15497e69	0.535646
$677$	1.82448e69	0.816051	0.408026	−	0.912970i	$-0.366217\pi$
$677$	1.82448e69	0.816051	0.408026	+	0.912970i	$0.366217\pi$
$678$	−2.20267e69	−0.950216
$679$	2.43899e69	1.01485
$680$	7.45882e67	0.0299366
$681$	−1.11245e69	−0.430703
$682$	−1.35002e69	−0.504224
$683$	−3.01839e69	−1.08760	−0.543798	−	0.839216i	$-0.683014\pi$
$683$	−3.01839e69	−1.08760	−0.543798	+	0.839216i	$0.683014\pi$
$684$	3.74553e68	0.130208
$685$	1.03032e69	0.345583
$686$	−3.70111e68	−0.119782
$687$	−2.23614e69	−0.698328
$688$	9.89244e68	0.298117
$689$	6.83553e69	1.98793
$690$	5.78570e69	1.62388
$691$	−2.98347e69	−0.808182	−0.404091	−	0.914719i	$-0.632412\pi$
$691$	−2.98347e69	−0.808182	−0.404091	+	0.914719i	$0.632412\pi$
$692$	−1.98606e69	−0.519270
$693$	1.59202e69	0.401777
$694$	4.88815e69	1.19080
$695$	−5.18726e69	−1.21986
$696$	2.08942e68	0.0474351
$697$	−4.33691e68	−0.0950556
$698$	5.73000e69	1.21254
$699$	6.62367e69	1.35334
$700$	−3.10506e69	−0.612588
$701$	−4.23251e69	−0.806318	−0.403159	−	0.915130i	$-0.632088\pi$
$701$	−4.23251e69	−0.806318	−0.403159	+	0.915130i	$0.632088\pi$
$702$	−4.63762e69	−0.853171
$703$	4.31145e68	0.0765981
$704$	−8.54009e68	−0.146532
$705$	−8.48395e69	−1.40593
$706$	−4.85322e69	−0.776810
$707$	3.72393e69	0.575740
$708$	−2.78353e69	−0.415702
$709$	−9.81430e69	−1.41588	−0.707940	−	0.706272i	$-0.750376\pi$
$709$	−9.81430e69	−1.41588	−0.707940	+	0.706272i	$0.750376\pi$
$710$	−1.36961e69	−0.190882
$711$	−2.09424e69	−0.281981
$712$	−7.79074e68	−0.101349
$713$	7.22184e69	0.907725
$714$	−5.48588e68	−0.0666255
$715$	1.97870e70	2.32210
$716$	7.55259e68	0.0856499
$717$	−7.16471e69	−0.785198
$718$	−5.00680e69	−0.530287
$719$	6.17065e68	0.0631645	0.0315823	−	0.999501i	$-0.489945\pi$
$719$	6.17065e68	0.0631645	0.0315823	+	0.999501i	$0.489945\pi$
$720$	8.70228e68	0.0860967
$721$	8.26974e69	0.790821
$722$	−6.36686e68	−0.0588524
$723$	−1.30309e69	−0.116436
$724$	9.27846e68	0.0801459
$725$	−1.28522e69	−0.107324
$726$	−3.66444e69	−0.295843
$727$	3.56583e69	0.278335	0.139167	−	0.990269i	$-0.455557\pi$
$727$	3.56583e69	0.278335	0.139167	+	0.990269i	$0.455557\pi$
$728$	−9.23527e69	−0.696997
$729$	8.77340e69	0.640241
$730$	2.26306e70	1.59693
$731$	−1.07505e69	−0.0733592
$732$	1.44151e70	0.951257
$733$	−5.19344e69	−0.331442	−0.165721	−	0.986173i	$-0.552995\pi$
$733$	−5.19344e69	−0.331442	−0.165721	+	0.986173i	$0.552995\pi$
$734$	−6.52329e69	−0.402637
$735$	2.25912e70	1.34865
$736$	4.56845e69	0.263793
$737$	7.80148e69	0.435736
$738$	−5.05992e69	−0.273377
$739$	−3.59123e70	−1.87696	−0.938478	−	0.345340i	$-0.887764\pi$
$739$	−3.59123e70	−1.87696	−0.938478	+	0.345340i	$0.887764\pi$
$740$	1.00171e69	0.0506485
$741$	−3.42388e70	−1.67484
$742$	−2.82694e70	−1.33789
$743$	−4.82971e69	−0.221154	−0.110577	−	0.993868i	$-0.535270\pi$
$743$	−4.82971e69	−0.221154	−0.110577	+	0.993868i	$0.535270\pi$
$744$	5.42751e69	0.240471
$745$	−6.49507e69	−0.278455
$746$	2.69547e70	1.11823
$747$	6.68564e69	0.268403
$748$	9.28089e68	0.0360579
$749$	−6.52552e69	−0.245364
$750$	3.15704e69	0.114889
$751$	−2.71224e70	−0.955322	−0.477661	−	0.878544i	$-0.658515\pi$
$751$	−2.71224e70	−0.955322	−0.477661	+	0.878544i	$0.658515\pi$
$752$	−6.69902e69	−0.228389
$753$	−3.18725e70	−1.05181
$754$	−3.82258e69	−0.122112
$755$	3.48566e70	1.07792
$756$	1.91796e70	0.574190
$757$	5.68718e70	1.64834	0.824172	−	0.566339i	$-0.191641\pi$
$757$	5.68718e70	1.64834	0.824172	+	0.566339i	$0.191641\pi$
$758$	−1.39767e70	−0.392202
$759$	7.19905e70	1.95592
$760$	−1.92525e70	−0.506470
$761$	−3.27369e70	−0.833899	−0.416950	−	0.908930i	$-0.636901\pi$
$761$	−3.27369e70	−0.833899	−0.416950	+	0.908930i	$0.636901\pi$
$762$	2.07863e70	0.512720
$763$	−1.06763e71	−2.55018
$764$	1.52736e70	0.353308
$765$	−9.45715e68	−0.0211863
$766$	4.58272e70	0.994303
$767$	5.09245e70	1.07014
$768$	3.43338e69	0.0698830
$769$	3.16849e70	0.624679	0.312339	−	0.949971i	$-0.398887\pi$
$769$	3.16849e70	0.624679	0.312339	+	0.949971i	$0.398887\pi$
$770$	−8.18321e70	−1.56279
$771$	9.15802e70	1.69422
$772$	−4.34401e69	−0.0778516
$773$	−4.24812e70	−0.737564	−0.368782	−	0.929516i	$-0.620225\pi$
$773$	−4.24812e70	−0.737564	−0.368782	+	0.929516i	$0.620225\pi$
$774$	−1.25428e70	−0.210979
$775$	−3.33850e70	−0.544077
$776$	1.65887e70	0.261939
$777$	−7.36749e69	−0.112721
$778$	−3.26954e70	−0.484715
$779$	1.11943e71	1.60816
$780$	−7.95498e70	−1.10744
$781$	−1.70418e70	−0.229914
$782$	−4.96474e69	−0.0649129
$783$	7.93865e69	0.100597
$784$	1.78383e70	0.219083
$785$	9.55755e70	1.13773
$786$	−2.80798e70	−0.323998
$787$	−7.11099e70	−0.795333	−0.397667	−	0.917530i	$-0.630180\pi$
$787$	−7.11099e70	−0.795333	−0.397667	+	0.917530i	$0.630180\pi$
$788$	−3.49278e70	−0.378686
$789$	6.04520e70	0.635366
$790$	1.07646e71	1.09682
$791$	−1.66657e71	−1.64627
$792$	1.08281e70	0.103702
$793$	−2.63724e71	−2.44882
$794$	4.25541e70	0.383124
$795$	−2.43504e71	−2.12574
$796$	−1.38545e70	−0.117279
$797$	8.80755e70	0.722980	0.361490	−	0.932376i	$-0.382268\pi$
$797$	8.80755e70	0.722980	0.361490	+	0.932376i	$0.382268\pi$
$798$	1.41600e71	1.12718
$799$	7.28012e69	0.0562008
$800$	−2.11190e70	−0.158113
$801$	9.87799e69	0.0717252
$802$	2.78746e70	0.196307
$803$	2.81589e71	1.92347
$804$	−3.13643e70	−0.207808
$805$	4.37754e71	2.81340
$806$	−9.92958e70	−0.619045
$807$	−2.00978e71	−1.21548
$808$	2.53282e70	0.148603
$809$	3.34391e71	1.90334	0.951668	−	0.307128i	$-0.0993679\pi$
$809$	3.34391e71	1.90334	0.951668	+	0.307128i	$0.0993679\pi$
$810$	2.09305e71	1.15584
$811$	−1.23812e71	−0.663365	−0.331683	−	0.943391i	$-0.607616\pi$
$811$	−1.23812e71	−0.663365	−0.331683	+	0.943391i	$0.607616\pi$
$812$	1.58089e70	0.0821822
$813$	−4.37829e71	−2.20844
$814$	1.24642e70	0.0610049
$815$	−2.07481e71	−0.985410
$816$	−3.73120e69	−0.0171965
$817$	2.77490e71	1.24110
$818$	−2.94911e71	−1.28008
$819$	1.17095e71	0.493269
$820$	2.60086e71	1.06335
$821$	−4.94321e70	−0.196156	−0.0980779	−	0.995179i	$-0.531269\pi$
$821$	−4.94321e70	−0.196156	−0.0980779	+	0.995179i	$0.531269\pi$
$822$	−5.15406e70	−0.198514
$823$	−5.94924e70	−0.222416	−0.111208	−	0.993797i	$-0.535472\pi$
$823$	−5.94924e70	−0.222416	−0.111208	+	0.993797i	$0.535472\pi$
$824$	5.62464e70	0.204116
$825$	−3.32797e71	−1.17235
$826$	−2.10606e71	−0.720211
$827$	−4.16062e71	−1.38125	−0.690626	−	0.723212i	$-0.742665\pi$
$827$	−4.16062e71	−1.38125	−0.690626	+	0.723212i	$0.742665\pi$
$828$	−5.79240e70	−0.186688
$829$	1.09472e71	0.342545	0.171273	−	0.985224i	$-0.445212\pi$
$829$	1.09472e71	0.342545	0.171273	+	0.985224i	$0.445212\pi$
$830$	−3.43650e71	−1.04401
$831$	4.08805e71	1.20585
$832$	−6.28134e70	−0.179900
$833$	−1.93856e70	−0.0539110
$834$	2.59488e71	0.700727
$835$	5.55757e71	1.45736
$836$	−2.39556e71	−0.610032
$837$	2.06215e71	0.509973
$838$	6.32696e70	0.151956
$839$	−2.86343e71	−0.667911	−0.333955	−	0.942589i	$-0.608383\pi$
$839$	−2.86343e71	−0.667911	−0.333955	+	0.942589i	$0.608383\pi$
$840$	3.28990e71	0.745316
$841$	−4.47923e71	−0.985602
$842$	−3.61332e71	−0.772254
$843$	2.25754e71	0.468662
$844$	−1.13501e71	−0.228881
$845$	7.52724e71	1.47451
$846$	8.49379e70	0.161632
$847$	−2.77257e71	−0.512553
$848$	−1.92273e71	−0.345319
$849$	3.51078e71	0.612583
$850$	2.29509e70	0.0389078
$851$	−6.66760e70	−0.109823
$852$	6.85132e70	0.109649
$853$	7.72297e71	1.20097	0.600486	−	0.799635i	$-0.294974\pi$
$853$	7.72297e71	1.20097	0.600486	+	0.799635i	$0.294974\pi$
$854$	1.09067e72	1.64807
$855$	2.44105e71	0.358432
$856$	−4.43831e70	−0.0633302
$857$	−1.38988e72	−1.92730	−0.963649	−	0.267173i	$-0.913911\pi$
$857$	−1.38988e72	−1.92730	−0.963649	+	0.267173i	$0.913911\pi$
$858$	−9.89825e71	−1.33389
$859$	1.33369e72	1.74672	0.873360	−	0.487074i	$-0.161936\pi$
$859$	1.33369e72	1.74672	0.873360	+	0.487074i	$0.161936\pi$
$860$	6.44714e71	0.820645
$861$	−1.91291e72	−2.36655
$862$	6.72542e71	0.808707
$863$	−6.63753e71	−0.775786	−0.387893	−	0.921704i	$-0.626797\pi$
$863$	−6.63753e71	−0.775786	−0.387893	+	0.921704i	$0.626797\pi$
$864$	1.30449e71	0.148202
$865$	−1.29436e72	−1.42943
$866$	−3.29123e71	−0.353322
$867$	−1.06737e72	−1.11390
$868$	4.10653e71	0.416621
$869$	1.33943e72	1.32110
$870$	1.36173e71	0.130578
$871$	5.73808e71	0.534961
$872$	−7.26147e71	−0.658220
$873$	−2.10331e71	−0.185376
$874$	1.28148e72	1.09820
$875$	2.38866e71	0.199048
$876$	−1.13208e72	−0.917328
$877$	−2.34548e72	−1.84817	−0.924086	−	0.382185i	$-0.875172\pi$
$877$	−2.34548e72	−1.84817	−0.924086	+	0.382185i	$0.875172\pi$
$878$	1.10904e71	0.0849825
$879$	2.76890e72	2.06338
$880$	−5.56578e71	−0.403368
$881$	2.76948e72	1.95204	0.976018	−	0.217690i	$-0.0698521\pi$
$881$	2.76948e72	1.95204	0.976018	+	0.217690i	$0.0698521\pi$
$882$	−2.26174e71	−0.155047
$883$	−2.54226e72	−1.69505	−0.847525	−	0.530755i	$-0.821908\pi$
$883$	−2.54226e72	−1.69505	−0.847525	+	0.530755i	$0.821908\pi$
$884$	6.82621e70	0.0442689
$885$	−1.81410e72	−1.14433
$886$	−1.08896e72	−0.668169
$887$	9.13774e71	0.545394	0.272697	−	0.962100i	$-0.412084\pi$
$887$	9.13774e71	0.545394	0.272697	+	0.962100i	$0.412084\pi$
$888$	−5.01098e70	−0.0290941
$889$	1.57272e72	0.888298
$890$	−5.07741e71	−0.278989
$891$	2.60434e72	1.39218
$892$	3.52610e71	0.183382
$893$	−1.87912e72	−0.950812
$894$	3.24910e71	0.159953
$895$	4.92221e71	0.235774
$896$	2.59774e71	0.121074
$897$	5.29499e72	2.40132
$898$	4.98379e71	0.219933
$899$	1.69974e71	0.0729910
$900$	2.67771e71	0.111898
$901$	2.08952e71	0.0849745
$902$	3.23621e72	1.28079
$903$	−4.74180e72	−1.82639
$904$	−1.13351e72	−0.424913
$905$	6.04700e71	0.220622
$906$	−1.74367e72	−0.619189
$907$	−1.21182e72	−0.418849	−0.209425	−	0.977825i	$-0.567159\pi$
$907$	−1.21182e72	−0.418849	−0.209425	+	0.977825i	$0.567159\pi$
$908$	−5.72479e71	−0.192600
$909$	−3.21140e71	−0.105167
$910$	−6.01885e72	−1.91867
$911$	−3.15652e72	−0.979508	−0.489754	−	0.871861i	$-0.662913\pi$
$911$	−3.15652e72	−0.979508	−0.489754	+	0.871861i	$0.662913\pi$
$912$	9.63087e71	0.290932
$913$	−4.27599e72	−1.25748
$914$	1.60035e68	4.58176e−5 0
$915$	9.39470e72	2.61858
$916$	−1.15074e72	−0.312275
$917$	−2.12456e72	−0.561332
$918$	−1.41765e71	−0.0364690
$919$	−5.08605e70	−0.0127395	−0.00636973	−	0.999980i	$-0.502028\pi$
$919$	−5.08605e70	−0.0127395	−0.00636973	+	0.999980i	$0.502028\pi$
$920$	2.97737e72	0.726158
$921$	−8.12655e72	−1.92995
$922$	4.53012e70	0.0104762
$923$	−1.25344e72	−0.282269
$924$	4.09357e72	0.897716
$925$	3.08229e71	0.0658266
$926$	5.09060e72	1.05877
$927$	−7.13156e71	−0.144454
$928$	1.07524e71	0.0212118
$929$	1.96142e72	0.376866	0.188433	−	0.982086i	$-0.439659\pi$
$929$	1.96142e72	0.376866	0.188433	+	0.982086i	$0.439659\pi$
$930$	3.53724e72	0.661960
$931$	5.00377e72	0.912073
$932$	3.40860e72	0.605182
$933$	1.54120e72	0.266538
$934$	−1.57147e72	−0.264732
$935$	6.04858e71	0.0992588
$936$	7.96420e71	0.127316
$937$	6.81725e72	1.06167	0.530835	−	0.847475i	$-0.321878\pi$
$937$	6.81725e72	1.06167	0.530835	+	0.847475i	$0.321878\pi$
$938$	−2.37307e72	−0.360032
$939$	−9.17233e71	−0.135573
$940$	−4.36592e72	−0.628699
$941$	−1.76332e72	−0.247391	−0.123696	−	0.992320i	$-0.539475\pi$
$941$	−1.76332e72	−0.247391	−0.123696	+	0.992320i	$0.539475\pi$
$942$	−4.78107e72	−0.653549
$943$	−1.73119e73	−2.30572
$944$	−1.43243e72	−0.185892
$945$	1.24998e73	1.58061
$946$	8.02207e72	0.988448
$947$	−9.56788e72	−1.14879	−0.574396	−	0.818578i	$-0.694763\pi$
$947$	−9.56788e72	−1.14879	−0.574396	+	0.818578i	$0.694763\pi$
$948$	−5.38491e72	−0.630049
$949$	2.07112e73	2.36148
$950$	−5.92403e72	−0.658247
$951$	−1.00129e73	−1.08427
$952$	−2.82308e71	−0.0297933
$953$	−2.85071e72	−0.293209	−0.146604	−	0.989195i	$-0.546834\pi$
$953$	−2.85071e72	−0.293209	−0.146604	+	0.989195i	$0.546834\pi$
$954$	2.43786e72	0.244384
$955$	9.95417e72	0.972573
$956$	−3.68702e72	−0.351121
$957$	1.69438e72	0.157278
$958$	−4.65557e72	−0.421229
$959$	−3.89964e72	−0.343929
$960$	2.23762e72	0.192371
$961$	−7.51701e72	−0.629973
$962$	9.16754e71	0.0748968
$963$	5.62740e71	0.0448192
$964$	−6.70582e71	−0.0520672
$965$	−2.83110e72	−0.214307
$966$	−2.18982e73	−1.61610
$967$	−2.08488e71	−0.0150014	−0.00750071	−	0.999972i	$-0.502388\pi$
$967$	−2.08488e71	−0.0150014	−0.00750071	+	0.999972i	$0.502388\pi$
$968$	−1.88576e72	−0.132294
$969$	−1.04663e72	−0.0715913
$970$	1.08113e73	0.721056
$971$	9.81497e72	0.638290	0.319145	−	0.947706i	$-0.396604\pi$
$971$	9.81497e72	0.638290	0.319145	+	0.947706i	$0.396604\pi$
$972$	−3.85992e72	−0.244768
$973$	1.96332e73	1.21402
$974$	2.26583e73	1.36626
$975$	−2.44776e73	−1.43932
$976$	7.41816e72	0.425379
$977$	3.84869e72	0.215226	0.107613	−	0.994193i	$-0.465679\pi$
$977$	3.84869e72	0.215226	0.107613	+	0.994193i	$0.465679\pi$
$978$	1.03790e73	0.566050
$979$	−6.31774e72	−0.336036
$980$	1.16256e73	0.603084
$981$	9.20692e72	0.465826
$982$	−6.42342e72	−0.316982
$983$	2.90652e73	1.39898	0.699492	−	0.714640i	$-0.253410\pi$
$983$	2.90652e73	1.39898	0.699492	+	0.714640i	$0.253410\pi$
$984$	−1.30106e73	−0.610824
$985$	−2.27633e73	−1.04243
$986$	−1.16851e71	−0.00521971
$987$	3.21108e73	1.39920
$988$	−1.76196e73	−0.748947
$989$	−4.29134e73	−1.77944
$990$	7.05694e72	0.285466
$991$	7.20046e72	0.284155	0.142078	−	0.989856i	$-0.454622\pi$
$991$	7.20046e72	0.284155	0.142078	+	0.989856i	$0.454622\pi$
$992$	2.79304e72	0.107533
$993$	−1.19086e73	−0.447306
$994$	5.18381e72	0.189969
$995$	−9.02932e72	−0.322842
$996$	1.71908e73	0.599711
$997$	2.83383e73	0.964590	0.482295	−	0.876009i	$-0.339803\pi$
$997$	2.83383e73	0.964590	0.482295	+	0.876009i	$0.339803\pi$
$998$	2.75299e73	0.914336
$999$	−1.90389e72	−0.0617004

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2.50.a.a.1.2	✓	2
4.3	odd	2		16.50.a.a.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2.50.a.a.1.2	✓	2	1.1	even	1	trivial
16.50.a.a.1.1		2	4.3	odd	2

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:	\( N \)	\(=\)	\( 2 \)
Weight:	\( k \)	\(=\)	\( 50 \)
Character orbit:	\([\chi]\)	\(=\)	2.a (trivial)

\(f(q)\)	\(=\)	\(q-1.67772e7 q^{2} +5.46969e11 q^{3} +2.81475e14 q^{4} +1.83444e17 q^{5} -9.17661e18 q^{6} -6.94316e20 q^{7} -4.72237e21 q^{8} +5.98756e22 q^{9} +O(q^{10})\)	\(q-1.67772e7 q^{2} +5.46969e11 q^{3} +2.81475e14 q^{4} +1.83444e17 q^{5} -9.17661e18 q^{6} -6.94316e20 q^{7} -4.72237e21 q^{8} +5.98756e22 q^{9} -3.07768e24 q^{10} -3.82951e25 q^{11} +1.53958e26 q^{12} -2.81665e27 q^{13} +1.16487e28 q^{14} +1.00338e29 q^{15} +7.92282e28 q^{16} -8.61007e28 q^{17} -1.00455e30 q^{18} +2.22241e31 q^{19} +5.16349e31 q^{20} -3.79769e32 q^{21} +6.42485e32 q^{22} -3.43692e33 q^{23} -2.58299e33 q^{24} +1.58882e34 q^{25} +4.72555e34 q^{26} -9.81392e34 q^{27} -1.95433e35 q^{28} -8.08917e34 q^{29} -1.68340e36 q^{30} -2.10125e36 q^{31} -1.32923e36 q^{32} -2.09462e37 q^{33} +1.44453e36 q^{34} -1.27368e38 q^{35} +1.68535e37 q^{36} +1.93999e37 q^{37} -3.72858e38 q^{38} -1.54062e39 q^{39} -8.66290e38 q^{40} +5.03702e39 q^{41} +6.37147e39 q^{42} +1.24860e40 q^{43} -1.07791e40 q^{44} +1.09838e40 q^{45} +5.76620e40 q^{46} -8.45536e40 q^{47} +4.33353e40 q^{48} +2.25151e41 q^{49} -2.66559e41 q^{50} -4.70944e40 q^{51} -7.92816e41 q^{52} -2.42683e42 q^{53} +1.64650e42 q^{54} -7.02501e42 q^{55} +3.27881e42 q^{56} +1.21559e43 q^{57} +1.35714e42 q^{58} -1.80798e43 q^{59} +2.82427e43 q^{60} +9.36304e43 q^{61} +3.52532e43 q^{62} -4.15725e43 q^{63} +2.23007e43 q^{64} -5.16698e44 q^{65} +3.51419e44 q^{66} -2.03720e44 q^{67} -2.42352e43 q^{68} -1.87989e45 q^{69} +2.13688e45 q^{70} +4.45012e44 q^{71} -2.82754e44 q^{72} -7.35314e45 q^{73} -3.25477e44 q^{74} +8.69033e45 q^{75} +6.25552e45 q^{76} +2.65889e46 q^{77} +2.58473e46 q^{78} -3.49765e46 q^{79} +1.45339e46 q^{80} -6.80073e46 q^{81} -8.45072e46 q^{82} +1.11659e47 q^{83} -1.06895e47 q^{84} -1.57947e46 q^{85} -2.09480e47 q^{86} -4.42452e46 q^{87} +1.80843e47 q^{88} +1.64975e47 q^{89} -1.84278e47 q^{90} +1.95564e48 q^{91} -9.67407e47 q^{92} -1.14932e48 q^{93} +1.41857e48 q^{94} +4.07687e48 q^{95} -7.27046e47 q^{96} -3.51280e48 q^{97} -3.77740e48 q^{98} -2.29294e48 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 33554432 q^{2} + 281051075592 q^{3} + 562949953421312 q^{4} + 83\!\cdots\!00 q^{5}+ \cdots - 10\!\cdots\!34 q^{9}+O(q^{10}) \) 2 * q - 33554432 * q^2 + 281051075592 * q^3 + 562949953421312 * q^4 + 83174531182543500 * q^5 - 4715254602239311872 * q^6 - 432389265285998218736 * q^7 - 9444732965739290427392 * q^8 - 108711528745520320184934 * q^9	\( 2 q - 33554432 q^{2} + 281051075592 q^{3} + 562949953421312 q^{4} + 83\!\cdots\!00 q^{5}+ \cdots - 83\!\cdots\!88 q^{99}+O(q^{100}) \) 2 * q - 33554432 * q^2 + 281051075592 * q^3 + 562949953421312 * q^4 + 83174531182543500 * q^5 - 4715254602239311872 * q^6 - 432389265285998218736 * q^7 - 9444732965739290427392 * q^8 - 108711528745520320184934 * q^9 - 1395437075348267728896000 * q^10 - 2505571492867298738664936 * q^11 + 79108844956763018967908352 * q^12 - 1673639931069227126134717028 * q^13 + 7254288099784493891349118976 * q^14 + 127001657954212134060542526000 * q^15 + 158456325028528675187087900672 * q^16 + 1242185964859741101801103139364 * q^17 + 1823876799453803444131797663744 * q^18 + 31751134463818510134391653857320 * q^19 + 23411549227526162913517633536000 * q^20 - 449419956159673170901966356305856 * q^21 + 42036514139277130275109182898176 * q^22 - 2878171210013224318486705571467728 * q^23 - 1327226179350123830036695489708032 * q^24 + 8178586568827926193122430485218750 * q^25 + 28079018629773534448221392677634048 * q^26 + 10325024674570189620203761899320400 * q^27 - 121706758376314007465844700470050816 * q^28 - 1184833247028586089467361473487066180 * q^29 - 2130734247855935082954679035887616000 * q^30 - 7105311682527075962924679523835996096 * q^31 - 2658455991569831745807614120560689152 * q^32 - 30463287003660767303795140420914481056 * q^33 - 20840422244620286168995096407387930624 * q^34 - 153631379897937223253539499790216708000 * q^35 - 30599575021825142403743101872928456704 * q^36 - 450602837422002559898874775434541099316 * q^37 - 532695641144527329322877805361490821120 * q^38 - 1844565860254881158789650811268042150288 * q^39 - 392780618284839580851274657642315776000 * q^40 + 6980390908841383456250364112135442830164 * q^41 + 7540015679201367277627204384476308176896 * q^42 + 23005349788522089920652198271012421804632 * q^43 - 705255677601706498485646185066204758016 * q^44 + 27887971423437826407657644077983762985500 * q^45 + 48287700075373227247704252500917509685248 * q^46 - 11845558119045913680201694380285648264096 * q^47 + 22267160291811767123272928157057429798912 * q^48 + 36832674584096520693651334136269148555634 * q^49 - 137213913439924984574072730695499776000000 * q^50 - 400309416097057296812546757700179931238256 * q^51 - 471087760619734618521251120773484792250368 * q^52 - 3995941967102752634563056816023520583445268 * q^53 - 173225169170593778419116477397468604006400 * q^54 - 10613607478462837375186572114612688143558000 * q^55 + 2041900573939229387080089162241344071008256 * q^56 + 9622454719526896343609264017960761786306720 * q^57 + 19878203309379946997589248390770782508154880 * q^58 + 21714921312003050521860441061723392092382840 * q^59 + 35747788714876559768708568395758285357056000 * q^60 + 57835793538935399324202832959454753282039804 * q^61 + 119207348845080179278395340102173655077748736 * q^62 - 85729962342781357158809844980279689420458288 * q^63 + 44601490397061246283071436545296723011960832 * q^64 - 631306767245427642112526729506636646807559000 * q^65 + 511089146130409483781508690592013166204420096 * q^66 - 1132689219365496932068743832028246172304100216 * q^67 + 349644265529199379039043235367571307871862784 * q^68 - 2028469745805465818965418074868217428589127488 * q^69 + 2577506844925750748964854952512420396924928000 * q^70 - 2581062199613136895595155085939596851144015216 * q^71 + 513375679649365128338357228632125270669656064 * q^72 - 9741247004630734466730318432740133532244065388 * q^73 + 7559861133641820099976360264416789884101984256 * q^74 + 10740447594643201176358815057388298782852875000 * q^75 + 8937149833740222221953054682155689587947601920 * q^76 + 35963105293022811785641876043939586820028000448 * q^77 + 30946679863721956255344270225219177052486238208 * q^78 - 16980842222977013563575057931860781555913425760 * q^79 + 6589765273578303173291298806591182514159616000 * q^80 - 56507054670978661477896482621261594252148312078 * q^81 - 117111526042068199984338908787944545617312743424 * q^82 - 24532280715782170299281847013445659051689117528 * q^83 - 126500471693348046312083575434506069166350401536 * q^84 - 148981404862178656936917823933576821852486633000 * q^85 - 385965722557589423370204791267601939299420864512 * q^86 + 249312411293548103558555079681567027901136340720 * q^87 + 11832226838350191893697358946431691525462163456 * q^88 + 1016887356645909629915356530428621471206692153780 * q^89 - 467882520372843876211776348747454436100538368000 * q^90 + 2255028438334749866892926186990858608923879598304 * q^91 - 810133174307752914151819748326433258171497709568 * q^92 + 181349176304449265724939153173691107739800035584 * q^93 + 198735487203787007730098750184038462626763636736 * q^94 + 3121598780165095291602283998223694567559507510000 * q^95 - 373580957922349048368848542643434424141183188992 * q^96 + 862374182033100841941070901898381458438293782724 * q^97 - 617949737355097492525858261492360939453959634944 * q^98 - 8326590145602153633338172323505805232970312882888 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

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Groups

Database

Properties

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