LMFDB - Embedded newform 2.50.a.a.1.1

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			1.1
Root			$4.70421e6$ 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)

$f(q)$	$=$	$q-1.67772e7 q^{2} -2.65918e11 q^{3} +2.81475e14 q^{4} -1.00270e17 q^{5} +4.46136e18 q^{6} +2.61926e20 q^{7} -4.72237e21 q^{8} -1.68587e23 q^{9} +O(q^{10})$	\(q-1.67772e7 q^{2} -2.65918e11 q^{3} +2.81475e14 q^{4} -1.00270e17 q^{5} +4.46136e18 q^{6} +2.61926e20 q^{7} -4.72237e21 q^{8} -1.68587e23 q^{9} +1.68224e24 q^{10} +3.57895e25 q^{11} -7.48492e25 q^{12} +1.14301e27 q^{13} -4.39440e27 q^{14} +2.66635e28 q^{15} +7.92282e28 q^{16} +1.32829e30 q^{17} +2.82842e30 q^{18} +9.52707e30 q^{19} -2.82234e31 q^{20} -6.96509e31 q^{21} -6.00448e32 q^{22} +5.58749e32 q^{23} +1.25576e33 q^{24} -7.70958e33 q^{25} -1.91765e34 q^{26} +1.08464e35 q^{27} +7.37257e34 q^{28} -1.10394e36 q^{29} -4.47339e35 q^{30} -5.00406e36 q^{31} -1.32923e36 q^{32} -9.51707e36 q^{33} -2.22850e37 q^{34} -2.62633e37 q^{35} -4.74530e37 q^{36} -4.70003e38 q^{37} -1.59838e38 q^{38} -3.03946e38 q^{39} +4.73510e38 q^{40} +1.94337e39 q^{41} +1.16855e39 q^{42} +1.05193e40 q^{43} +1.00739e40 q^{44} +1.69042e40 q^{45} -9.37426e39 q^{46} +7.27080e40 q^{47} -2.10682e40 q^{48} -1.88318e41 q^{49} +1.29345e41 q^{50} -3.53215e41 q^{51} +3.21729e41 q^{52} -1.56911e42 q^{53} -1.81973e42 q^{54} -3.58860e42 q^{55} -1.23691e42 q^{56} -2.53342e42 q^{57} +1.85211e43 q^{58} +3.97947e43 q^{59} +7.50510e42 q^{60} -3.57946e43 q^{61} +8.39542e43 q^{62} -4.41574e43 q^{63} +2.23007e43 q^{64} -1.14609e44 q^{65} +1.59670e44 q^{66} -9.28969e44 q^{67} +3.73879e44 q^{68} -1.48581e44 q^{69} +4.40624e44 q^{70} -3.02607e45 q^{71} +7.96130e44 q^{72} -2.38811e45 q^{73} +7.88534e45 q^{74} +2.05011e45 q^{75} +2.68163e45 q^{76} +9.37422e45 q^{77} +5.09938e45 q^{78} +1.79957e46 q^{79} -7.94417e45 q^{80} +1.15002e46 q^{81} -3.26043e46 q^{82} -1.36191e47 q^{83} -1.96050e46 q^{84} -1.33187e47 q^{85} -1.76485e47 q^{86} +2.93558e47 q^{87} -1.69011e47 q^{88} +8.51912e47 q^{89} -2.83605e47 q^{90} +2.99384e47 q^{91} +1.57274e47 q^{92} +1.33067e48 q^{93} -1.21984e48 q^{94} -9.55275e47 q^{95} +3.53465e47 q^{96} +4.37517e48 q^{97} +3.15945e48 q^{98} -6.03365e48 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	−2.65918e11	−0.543596	−0.271798	−	0.962354i	$-0.587618\pi$
$3$	−2.65918e11	−0.543596	−0.271798	+	0.962354i	$0.587618\pi$
$4$	2.81475e14	0.500000
$5$	−1.00270e17	−0.752322	−0.376161	−	0.926554i	$-0.622756\pi$
$5$	−1.00270e17	−0.752322	−0.376161	+	0.926554i	$0.622756\pi$
$6$	4.46136e18	0.384381
$7$	2.61926e20	0.516746	0.258373	−	0.966045i	$-0.416814\pi$
$7$	2.61926e20	0.516746	0.258373	+	0.966045i	$0.416814\pi$
$8$	−4.72237e21	−0.353553
$9$	−1.68587e23	−0.704503
$10$	1.68224e24	0.531972
$11$	3.57895e25	1.09556	0.547779	−	0.836623i	$-0.315474\pi$
$11$	3.57895e25	1.09556	0.547779	+	0.836623i	$0.315474\pi$
$12$	−7.48492e25	−0.271798
$13$	1.14301e27	0.584033	0.292017	−	0.956413i	$-0.405674\pi$
$13$	1.14301e27	0.584033	0.292017	+	0.956413i	$0.405674\pi$
$14$	−4.39440e27	−0.365395
$15$	2.66635e28	0.408960
$16$	7.92282e28	0.250000
$17$	1.32829e30	0.949059	0.474530	−	0.880240i	$-0.342618\pi$
$17$	1.32829e30	0.949059	0.474530	+	0.880240i	$0.342618\pi$
$18$	2.82842e30	0.498159
$19$	9.52707e30	0.446166	0.223083	−	0.974800i	$-0.428388\pi$
$19$	9.52707e30	0.446166	0.223083	+	0.974800i	$0.428388\pi$
$20$	−2.82234e31	−0.376161
$21$	−6.96509e31	−0.280901
$22$	−6.00448e32	−0.774676
$23$	5.58749e32	0.242597	0.121298	−	0.992616i	$-0.461294\pi$
$23$	5.58749e32	0.242597	0.121298	+	0.992616i	$0.461294\pi$
$24$	1.25576e33	0.192190
$25$	−7.70958e33	−0.434011
$26$	−1.91765e34	−0.412974
$27$	1.08464e35	0.926562
$28$	7.37257e34	0.258373
$29$	−1.10394e36	−1.63755	−0.818776	−	0.574113i	$-0.805347\pi$
$29$	−1.10394e36	−1.63755	−0.818776	+	0.574113i	$0.805347\pi$
$30$	−4.47339e35	−0.289178
$31$	−5.00406e36	−1.44864	−0.724321	−	0.689463i	$-0.757847\pi$
$31$	−5.00406e36	−1.44864	−0.724321	+	0.689463i	$0.757847\pi$
$32$	−1.32923e36	−0.176777
$33$	−9.51707e36	−0.595541
$34$	−2.22850e37	−0.671086
$35$	−2.62633e37	−0.388760
$36$	−4.74530e37	−0.352251
$37$	−4.70003e38	−1.78303	−0.891514	−	0.452993i	$-0.850356\pi$
$37$	−4.70003e38	−1.78303	−0.891514	+	0.452993i	$0.850356\pi$
$38$	−1.59838e38	−0.315487
$39$	−3.03946e38	−0.317478
$40$	4.73510e38	0.265986
$41$	1.94337e39	0.596143	0.298071	−	0.954544i	$-0.403657\pi$
$41$	1.94337e39	0.596143	0.298071	+	0.954544i	$0.403657\pi$
$42$	1.16855e39	0.198627
$43$	1.05193e40	1.00464	0.502321	−	0.864681i	$-0.332480\pi$
$43$	1.05193e40	1.00464	0.502321	+	0.864681i	$0.332480\pi$
$44$	1.00739e40	0.547779
$45$	1.69042e40	0.530013
$46$	−9.37426e39	−0.171542
$47$	7.27080e40	0.785570	0.392785	−	0.919630i	$-0.371512\pi$
$47$	7.27080e40	0.785570	0.392785	+	0.919630i	$0.371512\pi$
$48$	−2.10682e40	−0.135899
$49$	−1.88318e41	−0.732973
$50$	1.29345e41	0.306892
$51$	−3.53215e41	−0.515905
$52$	3.21729e41	0.292017
$53$	−1.56911e42	−0.893091	−0.446545	−	0.894761i	$-0.647346\pi$
$53$	−1.56911e42	−0.893091	−0.446545	+	0.894761i	$0.647346\pi$
$54$	−1.81973e42	−0.655178
$55$	−3.58860e42	−0.824212
$56$	−1.23691e42	−0.182697
$57$	−2.53342e42	−0.242534
$58$	1.85211e43	1.15792
$59$	3.97947e43	1.63663	0.818317	−	0.574768i	$-0.194908\pi$
$59$	3.97947e43	1.63663	0.818317	+	0.574768i	$0.194908\pi$
$60$	7.50510e42	0.204480
$61$	−3.57946e43	−0.650484	−0.325242	−	0.945631i	$-0.605446\pi$
$61$	−3.57946e43	−0.650484	−0.325242	+	0.945631i	$0.605446\pi$
$62$	8.39542e43	1.02434
$63$	−4.41574e43	−0.364049
$64$	2.23007e43	0.125000
$65$	−1.14609e44	−0.439381
$66$	1.59670e44	0.421111
$67$	−9.28969e44	−1.69500	−0.847498	−	0.530799i	$-0.821892\pi$
$67$	−9.28969e44	−1.69500	−0.847498	+	0.530799i	$0.821892\pi$
$68$	3.73879e44	0.474530
$69$	−1.48581e44	−0.131875
$70$	4.40624e44	0.274895
$71$	−3.02607e45	−1.33368	−0.666838	−	0.745203i	$-0.732353\pi$
$71$	−3.02607e45	−1.33368	−0.666838	+	0.745203i	$0.732353\pi$
$72$	7.96130e44	0.249079
$73$	−2.38811e45	−0.532897	−0.266449	−	0.963849i	$-0.585850\pi$
$73$	−2.38811e45	−0.532897	−0.266449	+	0.963849i	$0.585850\pi$
$74$	7.88534e45	1.26079
$75$	2.05011e45	0.235927
$76$	2.68163e45	0.223083
$77$	9.37422e45	0.566125
$78$	5.09938e45	0.224491
$79$	1.79957e46	0.579834	0.289917	−	0.957052i	$-0.406372\pi$
$79$	1.79957e46	0.579834	0.289917	+	0.957052i	$0.406372\pi$
$80$	−7.94417e45	−0.188081
$81$	1.15002e46	0.200827
$82$	−3.26043e46	−0.421537
$83$	−1.36191e47	−1.30839	−0.654193	−	0.756328i	$-0.726991\pi$
$83$	−1.36191e47	−1.30839	−0.654193	+	0.756328i	$0.726991\pi$
$84$	−1.96050e46	−0.140451
$85$	−1.33187e47	−0.713998
$86$	−1.76485e47	−0.710389
$87$	2.93558e47	0.890167
$88$	−1.69011e47	−0.387338
$89$	8.51912e47	1.48027	0.740133	−	0.672461i	$-0.234763\pi$
$89$	8.51912e47	1.48027	0.740133	+	0.672461i	$0.234763\pi$
$90$	−2.83605e47	−0.374776
$91$	2.99384e47	0.301797
$92$	1.57274e47	0.121298
$93$	1.33067e48	0.787476
$94$	−1.21984e48	−0.555482
$95$	−9.55275e47	−0.335660
$96$	3.53465e47	0.0960952
$97$	4.37517e48	0.922758	0.461379	−	0.887203i	$-0.347355\pi$
$97$	4.37517e48	0.922758	0.461379	+	0.887203i	$0.347355\pi$
$98$	3.15945e48	0.518290
$99$	−6.03365e48	−0.771823
$100$	−2.17005e48	−0.217005
$101$	−1.85228e49	−1.45156	−0.725778	−	0.687929i	$-0.758520\pi$
$101$	−1.85228e49	−1.45156	−0.725778	+	0.687929i	$0.758520\pi$
$102$	5.92596e48	0.364800
$103$	−1.81937e49	−0.881879	−0.440939	−	0.897537i	$-0.645355\pi$
$103$	−1.81937e49	−0.881879	−0.440939	+	0.897537i	$0.645355\pi$
$104$	−5.39771e48	−0.206487
$105$	6.98387e48	0.211328
$106$	2.63254e49	0.631510
$107$	4.67775e48	0.0891527	0.0445763	−	0.999006i	$-0.485806\pi$
$107$	4.67775e48	0.0891527	0.0445763	+	0.999006i	$0.485806\pi$
$108$	3.05300e49	0.463281
$109$	−6.50009e47	−0.00786992	−0.00393496	−	0.999992i	$-0.501253\pi$
$109$	−6.50009e47	−0.00786992	−0.00393496	+	0.999992i	$0.501253\pi$
$110$	6.02067e49	0.582806
$111$	1.24982e50	0.969248
$112$	2.07520e49	0.129187
$113$	−8.67960e49	−0.434588	−0.217294	−	0.976106i	$-0.569723\pi$
$113$	−8.67960e49	−0.434588	−0.217294	+	0.976106i	$0.569723\pi$
$114$	4.25037e49	0.171497
$115$	−5.60256e49	−0.182511
$116$	−3.10732e50	−0.818776
$117$	−1.92697e50	−0.411453
$118$	−6.67645e50	−1.15727
$119$	3.47913e50	0.490423
$120$	−1.25915e50	−0.144589
$121$	2.13700e50	0.200246
$122$	6.00534e50	0.459961
$123$	−5.16776e50	−0.324061
$124$	−1.40852e51	−0.724321
$125$	2.55418e51	1.07884
$126$	7.40839e50	0.257422
$127$	3.05394e51	0.874318	0.437159	−	0.899384i	$-0.355985\pi$
$127$	3.05394e51	0.874318	0.437159	+	0.899384i	$0.355985\pi$
$128$	−3.74144e50	−0.0883883
$129$	−2.79728e51	−0.546120
$130$	1.92282e51	0.310690
$131$	3.26289e50	0.0436974	0.0218487	−	0.999761i	$-0.493045\pi$
$131$	3.26289e50	0.0436974	0.0218487	+	0.999761i	$0.493045\pi$
$132$	−2.67882e51	−0.297770
$133$	2.49539e51	0.230554
$134$	1.55855e52	1.19854
$135$	−1.08757e52	−0.697073
$136$	−6.27266e51	−0.335543
$137$	−2.61433e52	−1.16871	−0.584354	−	0.811499i	$-0.698652\pi$
$137$	−2.61433e52	−1.16871	−0.584354	+	0.811499i	$0.698652\pi$
$138$	2.49278e51	0.0932495
$139$	−3.57225e52	−1.11964	−0.559821	−	0.828614i	$-0.689130\pi$
$139$	−3.57225e52	−1.11964	−0.559821	+	0.828614i	$0.689130\pi$
$140$	−7.39245e51	−0.194380
$141$	−1.93343e52	−0.427033
$142$	5.07691e52	0.943051
$143$	4.09078e52	0.639842
$144$	−1.33568e52	−0.176126
$145$	1.10692e53	1.23197
$146$	4.00658e52	0.376815
$147$	5.00771e52	0.398442
$148$	−1.32294e53	−0.891514
$149$	2.70432e53	1.54524	0.772618	−	0.634872i	$-0.218947\pi$
$149$	2.70432e53	1.54524	0.772618	+	0.634872i	$0.218947\pi$
$150$	−3.43952e52	−0.166825
$151$	−2.85333e53	−1.17602	−0.588012	−	0.808852i	$-0.700089\pi$
$151$	−2.85333e53	−1.17602	−0.588012	+	0.808852i	$0.700089\pi$
$152$	−4.49903e52	−0.157743
$153$	−2.23932e53	−0.668615
$154$	−1.57273e53	−0.400311
$155$	5.01755e53	1.08985
$156$	−8.55533e52	−0.158739
$157$	−8.08434e53	−1.28264	−0.641318	−	0.767275i	$-0.721612\pi$
$157$	−8.08434e53	−1.28264	−0.641318	+	0.767275i	$0.721612\pi$
$158$	−3.01917e53	−0.410005
$159$	4.17255e53	0.485481
$160$	1.33281e53	0.132993
$161$	1.46351e53	0.125361
$162$	−1.92942e53	−0.142006
$163$	3.32354e53	0.210380	0.105190	−	0.994452i	$-0.466455\pi$
$163$	3.32354e53	0.210380	0.105190	+	0.994452i	$0.466455\pi$
$164$	5.47009e53	0.298071
$165$	9.54272e53	0.448039
$166$	2.28491e54	0.925168
$167$	−1.06154e54	−0.371006	−0.185503	−	0.982644i	$-0.559391\pi$
$167$	−1.06154e54	−0.371006	−0.185503	+	0.982644i	$0.559391\pi$
$168$	3.28917e53	0.0993137
$169$	−2.52375e54	−0.658905
$170$	2.23450e54	0.504873
$171$	−1.60614e54	−0.314325
$172$	2.96093e54	0.502321
$173$	3.01118e54	0.443207	0.221604	−	0.975137i	$-0.428871\pi$
$173$	3.01118e54	0.443207	0.221604	+	0.975137i	$0.428871\pi$
$174$	−4.92508e54	−0.629443
$175$	−2.01934e54	−0.224274
$176$	2.83554e54	0.273889
$177$	−1.05821e55	−0.889668
$178$	−1.42927e55	−1.04671
$179$	−1.05012e55	−0.670411	−0.335206	−	0.942145i	$-0.608806\pi$
$179$	−1.05012e55	−0.670411	−0.335206	+	0.942145i	$0.608806\pi$
$180$	4.75810e54	0.265007
$181$	1.17965e55	0.573625	0.286813	−	0.957987i	$-0.407404\pi$
$181$	1.17965e55	0.573625	0.286813	+	0.957987i	$0.407404\pi$
$182$	−5.02284e54	−0.213403
$183$	9.51842e54	0.353601
$184$	−2.63862e54	−0.0857709
$185$	4.71270e55	1.34141
$186$	−2.23249e55	−0.556830
$187$	4.75387e55	1.03975
$188$	2.04655e55	0.392785
$189$	2.84097e55	0.478797
$190$	1.60269e55	0.237348
$191$	−4.67371e55	−0.608618	−0.304309	−	0.952573i	$-0.598426\pi$
$191$	−4.67371e55	−0.608618	−0.304309	+	0.952573i	$0.598426\pi$
$192$	−5.93016e54	−0.0679495
$193$	−5.93332e55	−0.598609	−0.299305	−	0.954158i	$-0.596755\pi$
$193$	−5.93332e55	−0.598609	−0.299305	+	0.954158i	$0.596755\pi$
$194$	−7.34032e55	−0.652488
$195$	3.04766e55	0.238846
$196$	−5.30068e55	−0.366487
$197$	−2.52231e56	−1.53949	−0.769743	−	0.638354i	$-0.779615\pi$
$197$	−2.52231e56	−1.53949	−0.769743	+	0.638354i	$0.779615\pi$
$198$	1.01228e56	0.545761
$199$	−6.43702e55	−0.306750	−0.153375	−	0.988168i	$-0.549014\pi$
$199$	−6.43702e55	−0.306750	−0.153375	+	0.988168i	$0.549014\pi$
$200$	3.64075e55	0.153446
$201$	2.47029e56	0.921394
$202$	3.10761e56	1.02640
$203$	−2.89152e56	−0.846199
$204$	−9.94212e55	−0.257953
$205$	−1.94861e56	−0.448492
$206$	3.05240e56	0.623582
$207$	−9.41979e55	−0.170910
$208$	9.05585e55	0.146008
$209$	3.40969e56	0.488800
$210$	−1.17170e56	−0.149432
$211$	1.17514e57	1.33404	0.667018	−	0.745041i	$-0.267570\pi$
$211$	1.17514e57	1.33404	0.667018	+	0.745041i	$0.267570\pi$
$212$	−4.41666e56	−0.446545
$213$	8.04687e56	0.724981
$214$	−7.84796e55	−0.0630405
$215$	−1.05477e57	−0.755815
$216$	−5.12208e56	−0.327589
$217$	−1.31070e57	−0.748580
$218$	1.09053e55	0.00556487
$219$	6.35040e56	0.289681
$220$	−1.01010e57	−0.412106
$221$	1.51824e57	0.554282
$222$	−2.09685e57	−0.685362
$223$	−4.26530e57	−1.24876	−0.624382	−	0.781119i	$-0.714649\pi$
$223$	−4.26530e57	−1.24876	−0.624382	+	0.781119i	$0.714649\pi$
$224$	−3.48160e56	−0.0913487
$225$	1.29974e57	0.305762
$226$	1.45619e57	0.307300
$227$	3.30988e57	0.626872	0.313436	−	0.949609i	$-0.398520\pi$
$227$	3.30988e57	0.626872	0.313436	+	0.949609i	$0.398520\pi$
$228$	−7.13093e56	−0.121267
$229$	4.89193e57	0.747328	0.373664	−	0.927564i	$-0.378101\pi$
$229$	4.89193e57	0.747328	0.373664	+	0.927564i	$0.378101\pi$
$230$	9.39953e56	0.129055
$231$	−2.49277e57	−0.307744
$232$	5.21322e57	0.578962
$233$	9.91157e57	0.990655	0.495327	−	0.868706i	$-0.335048\pi$
$233$	9.91157e57	0.990655	0.495327	+	0.868706i	$0.335048\pi$
$234$	3.23291e57	0.290941
$235$	−7.29040e57	−0.591002
$236$	1.12012e58	0.818317
$237$	−4.78536e57	−0.315196
$238$	−5.83702e57	−0.346781
$239$	−1.97517e58	−1.05890	−0.529450	−	0.848341i	$-0.677602\pi$
$239$	−1.97517e58	−1.05890	−0.529450	+	0.848341i	$0.677602\pi$
$240$	2.11250e57	0.102240
$241$	−1.88136e58	−0.822347	−0.411173	−	0.911557i	$-0.634881\pi$
$241$	−1.88136e58	−0.822347	−0.411173	+	0.911557i	$0.634881\pi$
$242$	−3.58529e57	−0.141595
$243$	−2.90135e58	−1.03573
$244$	−1.00753e58	−0.325242
$245$	1.88826e58	0.551432
$246$	8.67006e57	0.229146
$247$	1.08895e58	0.260576
$248$	2.36310e58	0.512172
$249$	3.62156e58	0.711233
$250$	−4.28521e58	−0.762854
$251$	4.64323e58	0.749573	0.374787	−	0.927111i	$-0.377716\pi$
$251$	4.64323e58	0.749573	0.374787	+	0.927111i	$0.377716\pi$
$252$	−1.24292e58	−0.182025
$253$	1.99974e58	0.265779
$254$	−5.12366e58	−0.618236
$255$	3.54167e58	0.388127
$256$	6.27710e57	0.0625000
$257$	8.40120e58	0.760291	0.380146	−	0.924927i	$-0.375874\pi$
$257$	8.40120e58	0.760291	0.380146	+	0.924927i	$0.375874\pi$
$258$	4.69306e58	0.386165
$259$	−1.23106e59	−0.921373
$260$	−3.22596e58	−0.219691
$261$	1.86110e59	1.15366
$262$	−5.47422e57	−0.0308987
$263$	−2.69735e59	−1.38682	−0.693411	−	0.720542i	$-0.743893\pi$
$263$	−2.69735e59	−1.38682	−0.693411	+	0.720542i	$0.743893\pi$
$264$	4.49431e58	0.210556
$265$	1.57334e59	0.671892
$266$	−4.18657e58	−0.163027
$267$	−2.26539e59	−0.804667
$268$	−2.61482e59	−0.847498
$269$	1.62188e59	0.479832	0.239916	−	0.970794i	$-0.422880\pi$
$269$	1.62188e59	0.479832	0.239916	+	0.970794i	$0.422880\pi$
$270$	1.82463e59	0.492905
$271$	−7.10925e59	−1.75419	−0.877094	−	0.480320i	$-0.840521\pi$
$271$	−7.10925e59	−1.75419	−0.877094	+	0.480320i	$0.840521\pi$
$272$	1.05238e59	0.237265
$273$	−7.96116e58	−0.164056
$274$	4.38611e59	0.826401
$275$	−2.75922e59	−0.475484
$276$	−4.18219e58	−0.0659374
$277$	3.82735e59	0.552260	0.276130	−	0.961120i	$-0.410948\pi$
$277$	3.82735e59	0.552260	0.276130	+	0.961120i	$0.410948\pi$
$278$	5.99324e59	0.791707
$279$	8.43620e59	1.02057
$280$	1.24025e59	0.137447
$281$	1.30910e60	1.32944	0.664720	−	0.747092i	$-0.268551\pi$
$281$	1.30910e60	1.32944	0.664720	+	0.747092i	$0.268551\pi$
$282$	3.24376e59	0.301958
$283$	−1.65200e60	−1.41008	−0.705038	−	0.709169i	$-0.749070\pi$
$283$	−1.65200e60	−1.41008	−0.705038	+	0.709169i	$0.749070\pi$
$284$	−8.51764e59	−0.666838
$285$	2.54025e59	0.182464
$286$	−6.86318e59	−0.452437
$287$	5.09019e59	0.308055
$288$	2.24091e59	0.124540
$289$	−1.94486e59	−0.0992869
$290$	−1.85710e60	−0.871132
$291$	−1.16344e60	−0.501608
$292$	−6.72192e59	−0.266449
$293$	1.19892e60	0.437054	0.218527	−	0.975831i	$-0.429875\pi$
$293$	1.19892e60	0.437054	0.218527	+	0.975831i	$0.429875\pi$
$294$	−8.40155e59	−0.281741
$295$	−3.99020e60	−1.23128
$296$	2.21953e60	0.630396
$297$	3.88188e60	1.01510
$298$	−4.53710e60	−1.09265
$299$	6.38656e59	0.141685
$300$	5.77056e59	0.117963
$301$	2.75529e60	0.519145
$302$	4.78709e60	0.831574
$303$	4.92555e60	0.789060
$304$	7.54812e59	0.111541
$305$	3.58911e60	0.489374
$306$	3.75696e60	0.472782
$307$	−1.42835e61	−1.65937	−0.829687	−	0.558230i	$-0.811481\pi$
$307$	−1.42835e61	−1.65937	−0.829687	+	0.558230i	$0.811481\pi$
$308$	2.63861e60	0.283063
$309$	4.83803e60	0.479386
$310$	−8.41805e60	−0.770637
$311$	3.46632e60	0.293250	0.146625	−	0.989192i	$-0.453159\pi$
$311$	3.46632e60	0.293250	0.146625	+	0.989192i	$0.453159\pi$
$312$	1.43535e60	0.112246
$313$	−2.40220e61	−1.73689	−0.868447	−	0.495781i	$-0.834882\pi$
$313$	−2.40220e61	−1.73689	−0.868447	+	0.495781i	$0.834882\pi$
$314$	1.35633e61	0.906960
$315$	4.42765e60	0.273882
$316$	5.06533e60	0.289917
$317$	1.40824e61	0.745974	0.372987	−	0.927837i	$-0.378334\pi$
$317$	1.40824e61	0.745974	0.372987	+	0.927837i	$0.378334\pi$
$318$	−7.00038e60	−0.343287
$319$	−3.95095e61	−1.79403
$320$	−2.23609e60	−0.0940403
$321$	−1.24390e60	−0.0484631
$322$	−2.45537e60	−0.0886436
$323$	1.26547e61	0.423437
$324$	3.23702e60	0.100414
$325$	−8.81213e60	−0.253477
$326$	−5.57598e60	−0.148761
$327$	1.72849e59	0.00427806
$328$	−9.17729e60	−0.210768
$329$	1.90441e61	0.405940
$330$	−1.60100e61	−0.316811
$331$	8.55134e61	1.57126	0.785630	−	0.618696i	$-0.212339\pi$
$331$	8.55134e61	1.57126	0.785630	+	0.618696i	$0.212339\pi$
$332$	−3.83344e61	−0.654193
$333$	7.92364e61	1.25615
$334$	1.78096e61	0.262341
$335$	9.31473e61	1.27518
$336$	−5.51831e60	−0.0702254
$337$	−1.11012e62	−1.31352	−0.656759	−	0.754101i	$-0.728073\pi$
$337$	−1.11012e62	−1.31352	−0.656759	+	0.754101i	$0.728073\pi$
$338$	4.23416e61	0.465916
$339$	2.30806e61	0.236240
$340$	−3.74887e61	−0.356999
$341$	−1.79093e62	−1.58707
$342$	2.69466e61	0.222261
$343$	−1.16621e62	−0.895508
$344$	−4.96762e61	−0.355195
$345$	1.48982e61	0.0992123
$346$	−5.05192e61	−0.313395
$347$	3.07741e60	0.0177874	0.00889370	−	0.999960i	$-0.497169\pi$
$347$	3.07741e60	0.0177874	0.00889370	+	0.999960i	$0.497169\pi$
$348$	8.26291e61	0.445084
$349$	−1.29508e62	−0.650242	−0.325121	−	0.945673i	$-0.605405\pi$
$349$	−1.29508e62	−0.650242	−0.325121	+	0.945673i	$0.605405\pi$
$350$	3.38790e61	0.158585
$351$	1.23976e62	0.541143
$352$	−4.75724e61	−0.193669
$353$	−1.97962e62	−0.751798	−0.375899	−	0.926661i	$-0.622666\pi$
$353$	−1.97962e62	−0.751798	−0.375899	+	0.926661i	$0.622666\pi$
$354$	1.77539e62	0.629090
$355$	3.03423e62	1.00335
$356$	2.39792e62	0.740133
$357$	−9.25164e61	−0.266592
$358$	1.76182e62	0.474052
$359$	4.09885e62	1.03003	0.515013	−	0.857182i	$-0.327787\pi$
$359$	4.09885e62	1.03003	0.515013	+	0.857182i	$0.327787\pi$
$360$	−7.98276e61	−0.187388
$361$	−3.65195e62	−0.800936
$362$	−1.97913e62	−0.405614
$363$	−5.68266e61	−0.108853
$364$	8.42692e61	0.150899
$365$	2.39454e62	0.400911
$366$	−1.59693e62	−0.250033
$367$	1.36973e62	0.200594	0.100297	−	0.994958i	$-0.468021\pi$
$367$	1.36973e62	0.200594	0.100297	+	0.994958i	$0.468021\pi$
$368$	4.42687e61	0.0606492
$369$	−3.27627e62	−0.419984
$370$	−7.90659e62	−0.948522
$371$	−4.10992e62	−0.461501
$372$	3.74550e62	0.393738
$373$	1.37831e63	1.35669	0.678347	−	0.734742i	$-0.262697\pi$
$373$	1.37831e63	1.35669	0.678347	+	0.734742i	$0.262697\pi$
$374$	−7.97568e62	−0.735213
$375$	−6.79202e62	−0.586453
$376$	−3.43354e62	−0.277741
$377$	−1.26182e63	−0.956385
$378$	−4.76635e62	−0.338561
$379$	1.79111e63	1.19251	0.596255	−	0.802795i	$-0.296655\pi$
$379$	1.79111e63	1.19251	0.596255	+	0.802795i	$0.296655\pi$
$380$	−2.68886e62	−0.167830
$381$	−8.12097e62	−0.475276
$382$	7.84119e62	0.430358
$383$	2.85224e63	1.46831	0.734153	−	0.678984i	$-0.237580\pi$
$383$	2.85224e63	1.46831	0.734153	+	0.678984i	$0.237580\pi$
$384$	9.94916e61	0.0480476
$385$	−9.39949e62	−0.425909
$386$	9.95445e62	0.423281
$387$	−1.77342e63	−0.707773
$388$	1.23150e63	0.461379
$389$	6.76212e62	0.237858	0.118929	−	0.992903i	$-0.462054\pi$
$389$	6.76212e62	0.237858	0.118929	+	0.992903i	$0.462054\pi$
$390$	−5.11312e62	−0.168890
$391$	7.42179e62	0.230239
$392$	8.89307e62	0.259145
$393$	−8.67660e61	−0.0237538
$394$	4.23173e63	1.08858
$395$	−1.80442e63	−0.436222
$396$	−1.69832e63	−0.385912
$397$	1.10514e63	0.236076	0.118038	−	0.993009i	$-0.462340\pi$
$397$	1.10514e63	0.236076	0.118038	+	0.993009i	$0.462340\pi$
$398$	1.07995e63	0.216905
$399$	−6.63569e62	−0.125329
$400$	−6.10816e62	−0.108503
$401$	−5.10307e63	−0.852696	−0.426348	−	0.904559i	$-0.640200\pi$
$401$	−5.10307e63	−0.852696	−0.426348	+	0.904559i	$0.640200\pi$
$402$	−4.14447e63	−0.651524
$403$	−5.71969e63	−0.846055
$404$	−5.21371e63	−0.725778
$405$	−1.15312e63	−0.151087
$406$	4.85116e63	0.598353
$407$	−1.68212e64	−1.95341
$408$	1.66801e63	0.182400
$409$	1.82914e64	1.88376	0.941878	−	0.335954i	$-0.109059\pi$
$409$	1.82914e64	1.88376	0.941878	+	0.335954i	$0.109059\pi$
$410$	3.26922e63	0.317132
$411$	6.95195e63	0.635305
$412$	−5.12107e63	−0.440939
$413$	1.04233e64	0.845724
$414$	1.58038e63	0.120852
$415$	1.36558e64	0.984328
$416$	−1.51932e63	−0.103243
$417$	9.49925e63	0.608633
$418$	−5.72051e63	−0.345634
$419$	−1.12533e64	−0.641263	−0.320631	−	0.947204i	$-0.603895\pi$
$419$	−1.12533e64	−0.641263	−0.320631	+	0.947204i	$0.603895\pi$
$420$	1.96578e63	0.105664
$421$	2.85472e64	1.44761	0.723807	−	0.690003i	$-0.242391\pi$
$421$	2.85472e64	1.44761	0.723807	+	0.690003i	$0.242391\pi$
$422$	−1.97155e64	−0.943306
$423$	−1.22576e64	−0.553436
$424$	7.40993e63	0.315755
$425$	−1.02405e64	−0.411902
$426$	−1.35004e64	−0.512639
$427$	−9.37555e63	−0.336135
$428$	1.31667e63	0.0445763
$429$	−1.08781e64	−0.347816
$430$	1.76961e64	0.534442
$431$	−2.02886e64	−0.578842	−0.289421	−	0.957202i	$-0.593463\pi$
$431$	−2.02886e64	−0.578842	−0.289421	+	0.957202i	$0.593463\pi$
$432$	8.59342e63	0.231640
$433$	−1.93258e64	−0.492248	−0.246124	−	0.969238i	$-0.579157\pi$
$433$	−1.93258e64	−0.492248	−0.246124	+	0.969238i	$0.579157\pi$
$434$	2.19898e64	0.529326
$435$	−2.94349e64	−0.669693
$436$	−1.82961e62	−0.00393496
$437$	5.32324e63	0.108238
$438$	−1.06542e64	−0.204835
$439$	1.64251e62	0.00298625	0.00149313	−	0.999999i	$-0.499525\pi$
$439$	1.64251e62	0.00298625	0.00149313	+	0.999999i	$0.499525\pi$
$440$	1.69467e64	0.291403
$441$	3.17480e64	0.516382
$442$	−2.54719e64	−0.391937
$443$	2.50698e64	0.364973	0.182486	−	0.983208i	$-0.441585\pi$
$443$	2.50698e64	0.364973	0.182486	+	0.983208i	$0.441585\pi$
$444$	3.51793e64	0.484624
$445$	−8.54209e64	−1.11364
$446$	7.15599e64	0.883010
$447$	−7.19127e64	−0.839984
$448$	5.84116e63	0.0645933
$449$	1.82403e65	1.90983	0.954917	−	0.296874i	$-0.0959442\pi$
$449$	1.82403e65	1.90983	0.954917	+	0.296874i	$0.0959442\pi$
$450$	−2.18060e64	−0.216206
$451$	6.95522e64	0.653109
$452$	−2.44309e64	−0.217294
$453$	7.58750e64	0.639282
$454$	−5.55306e64	−0.443265
$455$	−3.00191e64	−0.227049
$456$	1.19637e64	0.0857487
$457$	−1.71770e65	−1.16681	−0.583406	−	0.812181i	$-0.698280\pi$
$457$	−1.71770e65	−1.16681	−0.583406	+	0.812181i	$0.698280\pi$
$458$	−8.20730e64	−0.528441
$459$	1.44072e65	0.879362
$460$	−1.57698e64	−0.0912555
$461$	−7.91793e64	−0.434449	−0.217225	−	0.976122i	$-0.569700\pi$
$461$	−7.91793e64	−0.434449	−0.217225	+	0.976122i	$0.569700\pi$
$462$	4.18218e64	0.217608
$463$	3.31899e64	0.163784	0.0818920	−	0.996641i	$-0.473904\pi$
$463$	3.31899e64	0.163784	0.0818920	+	0.996641i	$0.473904\pi$
$464$	−8.74633e64	−0.409388
$465$	−1.33426e65	−0.592436
$466$	−1.66289e65	−0.700499
$467$	−2.75842e64	−0.110254	−0.0551272	−	0.998479i	$-0.517556\pi$
$467$	−2.75842e64	−0.110254	−0.0551272	+	0.998479i	$0.517556\pi$
$468$	−5.42393e64	−0.205727
$469$	−2.43322e65	−0.875883
$470$	1.22313e65	0.417901
$471$	2.14977e65	0.697236
$472$	−1.87925e65	−0.578637
$473$	3.76482e65	1.10064
$474$	8.02851e64	0.222877
$475$	−7.34497e64	−0.193641
$476$	9.79289e64	0.245211
$477$	2.64532e65	0.629185
$478$	3.31378e65	0.748756
$479$	4.69833e65	1.00861	0.504305	−	0.863526i	$-0.331749\pi$
$479$	4.69833e65	1.00861	0.504305	+	0.863526i	$0.331749\pi$
$480$	−3.54418e64	−0.0722946
$481$	−5.37218e65	−1.04135
$482$	3.15640e65	0.581487
$483$	−3.89174e64	−0.0681458
$484$	6.01512e64	0.100123
$485$	−4.38697e65	−0.694211
$486$	4.86766e65	0.732372
$487$	1.94534e65	0.278315	0.139157	−	0.990270i	$-0.455561\pi$
$487$	1.94534e65	0.278315	0.139157	+	0.990270i	$0.455561\pi$
$488$	1.69035e65	0.229981
$489$	−8.83789e64	−0.114362
$490$	−3.16797e65	−0.389921
$491$	−9.63449e65	−1.12806	−0.564030	−	0.825754i	$-0.690750\pi$
$491$	−9.63449e65	−1.12806	−0.564030	+	0.825754i	$0.690750\pi$
$492$	−1.45459e65	−0.162031
$493$	−1.46635e66	−1.55413
$494$	−1.82696e65	−0.184255
$495$	6.04992e65	0.580660
$496$	−3.96462e65	−0.362160
$497$	−7.92609e65	−0.689172
$498$	−6.07598e65	−0.502918
$499$	1.48675e66	1.17159	0.585794	−	0.810460i	$-0.300783\pi$
$499$	1.48675e66	1.17159	0.585794	+	0.810460i	$0.300783\pi$
$500$	7.18938e65	0.539419
$501$	2.82281e65	0.201678
$502$	−7.79005e65	−0.530028
$503$	1.04127e66	0.674759	0.337379	−	0.941369i	$-0.390459\pi$
$503$	1.04127e66	0.674759	0.337379	+	0.941369i	$0.390459\pi$
$504$	2.08528e65	0.128711
$505$	1.85728e66	1.09204
$506$	−3.35500e65	−0.187934
$507$	6.71111e65	0.358178
$508$	8.59608e65	0.437159
$509$	−2.02314e66	−0.980483	−0.490242	−	0.871587i	$-0.663092\pi$
$509$	−2.02314e66	−0.980483	−0.490242	+	0.871587i	$0.663092\pi$
$510$	−5.94194e65	−0.274447
$511$	−6.25508e65	−0.275373
$512$	−1.05312e65	−0.0441942
$513$	1.03335e66	0.413400
$514$	−1.40949e66	−0.537607
$515$	1.82427e66	0.663457
$516$	−7.87364e65	−0.273060
$517$	2.60218e66	0.860636
$518$	2.06538e66	0.651509
$519$	−8.00725e65	−0.240926
$520$	5.41226e65	0.155345
$521$	1.06580e66	0.291844	0.145922	−	0.989296i	$-0.453385\pi$
$521$	1.06580e66	0.291844	0.145922	+	0.989296i	$0.453385\pi$
$522$	−3.12241e66	−0.815761
$523$	−9.70027e65	−0.241820	−0.120910	−	0.992663i	$-0.538581\pi$
$523$	−9.70027e65	−0.241820	−0.120910	+	0.992663i	$0.538581\pi$
$524$	9.18422e64	0.0218487
$525$	5.36979e65	0.121914
$526$	4.52540e66	0.980632
$527$	−6.64683e66	−1.37485
$528$	−7.54020e65	−0.148885
$529$	−4.99254e66	−0.941147
$530$	−2.63963e66	−0.475099
$531$	−6.70888e66	−1.15301
$532$	7.02390e65	0.115277
$533$	2.22129e66	0.348167
$534$	3.80069e66	0.568985
$535$	−4.69036e65	−0.0670716
$536$	4.38693e66	0.599272
$537$	2.79247e66	0.364433
$538$	−2.72107e66	−0.339292
$539$	−6.73981e66	−0.803014
$540$	−3.06123e66	−0.348537
$541$	1.05015e67	1.14266	0.571331	−	0.820719i	$-0.306427\pi$
$541$	1.05015e67	1.14266	0.571331	+	0.820719i	$0.306427\pi$
$542$	1.19273e67	1.24040
$543$	−3.13690e66	−0.311821
$544$	−1.76560e66	−0.167772
$545$	6.51762e64	0.00592072
$546$	1.33566e66	0.116005
$547$	2.34084e67	1.94394	0.971970	−	0.235105i	$-0.0755433\pi$
$547$	2.34084e67	1.94394	0.971970	+	0.235105i	$0.0755433\pi$
$548$	−7.35867e66	−0.584354
$549$	6.03451e66	0.458268
$550$	4.62921e66	0.336218
$551$	−1.05173e67	−0.730619
$552$	7.01656e65	0.0466248
$553$	4.71354e66	0.299627
$554$	−6.42122e66	−0.390507
$555$	−1.25319e67	−0.729187
$556$	−1.00550e67	−0.559821
$557$	8.47917e66	0.451753	0.225877	−	0.974156i	$-0.427475\pi$
$557$	8.47917e66	0.451753	0.225877	+	0.974156i	$0.427475\pi$
$558$	−1.41536e67	−0.721654
$559$	1.20237e67	0.586745
$560$	−2.08079e66	−0.0971900
$561$	−1.26414e67	−0.565204
$562$	−2.19631e67	−0.940056
$563$	−2.78437e67	−1.14096	−0.570481	−	0.821311i	$-0.693243\pi$
$563$	−2.78437e67	−1.14096	−0.570481	+	0.821311i	$0.693243\pi$
$564$	−5.44213e66	−0.213516
$565$	8.70300e66	0.326950
$566$	2.77160e67	0.997075
$567$	3.01221e66	0.103777
$568$	1.42902e67	0.471525
$569$	−2.68979e67	−0.850097	−0.425048	−	0.905171i	$-0.639743\pi$
$569$	−2.68979e67	−0.850097	−0.425048	+	0.905171i	$0.639743\pi$
$570$	−4.26183e66	−0.129021
$571$	1.42375e67	0.412904	0.206452	−	0.978457i	$-0.433808\pi$
$571$	1.42375e67	0.412904	0.206452	+	0.978457i	$0.433808\pi$
$572$	1.15145e67	0.319921
$573$	1.24282e67	0.330842
$574$	−8.53993e66	−0.217828
$575$	−4.30772e66	−0.105290
$576$	−3.75962e66	−0.0880629
$577$	8.28960e67	1.86091	0.930456	−	0.366403i	$-0.119411\pi$
$577$	8.28960e67	1.86091	0.930456	+	0.366403i	$0.119411\pi$
$578$	3.26294e66	0.0702064
$579$	1.57777e67	0.325402
$580$	3.11570e67	0.615984
$581$	−3.56721e67	−0.676103
$582$	1.95192e67	0.354690
$583$	−5.61578e67	−0.978432
$584$	1.12775e67	0.188408
$585$	1.93216e67	0.309546
$586$	−2.01146e67	−0.309044
$587$	−4.82922e67	−0.711612	−0.355806	−	0.934560i	$-0.615794\pi$
$587$	−4.82922e67	−0.711612	−0.355806	+	0.934560i	$0.615794\pi$
$588$	1.40955e67	0.199221
$589$	−4.76740e67	−0.646334
$590$	6.69445e67	0.870644
$591$	6.70726e67	0.836859
$592$	−3.72375e67	−0.445757
$593$	−9.74161e67	−1.11890	−0.559450	−	0.828864i	$-0.688987\pi$
$593$	−9.74161e67	−1.11890	−0.559450	+	0.828864i	$0.688987\pi$
$594$	−6.51272e67	−0.717785
$595$	−3.48851e67	−0.368956
$596$	7.61199e67	0.772618
$597$	1.71172e67	0.166748
$598$	−1.07149e67	−0.100186
$599$	1.14351e68	1.02632	0.513159	−	0.858293i	$-0.328475\pi$
$599$	1.14351e68	1.02632	0.513159	+	0.858293i	$0.328475\pi$
$600$	−9.68139e66	−0.0834127
$601$	−2.02507e68	−1.67500	−0.837500	−	0.546437i	$-0.815984\pi$
$601$	−2.02507e68	−1.67500	−0.837500	+	0.546437i	$0.815984\pi$
$602$	−4.62262e67	−0.367091
$603$	1.56612e68	1.19413
$604$	−8.03140e67	−0.588012
$605$	−2.14276e67	−0.150649
$606$	−8.26370e67	−0.557950
$607$	5.17102e67	0.335315	0.167658	−	0.985845i	$-0.446380\pi$
$607$	5.17102e67	0.335315	0.167658	+	0.985845i	$0.446380\pi$
$608$	−1.26636e67	−0.0788717
$609$	7.68905e67	0.459991
$610$	−6.02152e67	−0.346039
$611$	8.31059e67	0.458799
$612$	−6.30312e67	−0.334307
$613$	4.95964e67	0.252737	0.126368	−	0.991983i	$-0.459668\pi$
$613$	4.95964e67	0.252737	0.126368	+	0.991983i	$0.459668\pi$
$614$	2.39637e68	1.17335
$615$	5.18169e67	0.243798
$616$	−4.42685e67	−0.200155
$617$	1.02789e68	0.446645	0.223322	−	0.974745i	$-0.428310\pi$
$617$	1.02789e68	0.446645	0.223322	+	0.974745i	$0.428310\pi$
$618$	−8.11686e67	−0.338977
$619$	8.14987e67	0.327137	0.163568	−	0.986532i	$-0.447700\pi$
$619$	8.14987e67	0.327137	0.163568	+	0.986532i	$0.447700\pi$
$620$	1.41231e68	0.544923
$621$	6.06043e67	0.224781
$622$	−5.81551e67	−0.207359
$623$	2.23138e68	0.764922
$624$	−2.40811e67	−0.0793696
$625$	−1.19157e68	−0.377624
$626$	4.03023e68	1.22817
$627$	−9.06698e67	−0.265710
$628$	−2.27554e68	−0.641318
$629$	−6.24298e68	−1.69220
$630$	−7.42836e67	−0.193664
$631$	−3.83950e68	−0.962843	−0.481422	−	0.876489i	$-0.659879\pi$
$631$	−3.83950e68	−0.962843	−0.481422	+	0.876489i	$0.659879\pi$
$632$	−8.49821e67	−0.205002
$633$	−3.12489e68	−0.725178
$634$	−2.36263e68	−0.527483
$635$	−3.06217e68	−0.657769
$636$	1.17447e68	0.242740
$637$	−2.15249e68	−0.428081
$638$	6.62860e68	1.26857
$639$	5.10157e68	0.939578
$640$	3.75153e67	0.0664965
$641$	6.86038e67	0.117038	0.0585189	−	0.998286i	$-0.481362\pi$
$641$	6.86038e67	0.117038	0.0585189	+	0.998286i	$0.481362\pi$
$642$	2.08691e67	0.0342686
$643$	4.67689e68	0.739245	0.369623	−	0.929182i	$-0.379487\pi$
$643$	4.67689e68	0.739245	0.369623	+	0.929182i	$0.379487\pi$
$644$	4.11942e67	0.0626805
$645$	2.80482e68	0.410858
$646$	−2.12310e68	−0.299416
$647$	−1.18951e69	−1.61515	−0.807574	−	0.589766i	$-0.799220\pi$
$647$	−1.18951e69	−1.61515	−0.807574	+	0.589766i	$0.799220\pi$
$648$	−5.43082e67	−0.0710032
$649$	1.42423e69	1.79303
$650$	1.47843e68	0.179235
$651$	3.48537e68	0.406926
$652$	9.35494e67	0.105190
$653$	1.01234e68	0.109636	0.0548179	−	0.998496i	$-0.482542\pi$
$653$	1.01234e68	0.109636	0.0548179	+	0.998496i	$0.482542\pi$
$654$	−2.89993e66	−0.00302505
$655$	−3.27169e67	−0.0328745
$656$	1.53969e68	0.149036
$657$	4.02604e68	0.375428
$658$	−3.19508e68	−0.287043
$659$	1.56033e68	0.135059	0.0675296	−	0.997717i	$-0.478488\pi$
$659$	1.56033e68	0.135059	0.0675296	+	0.997717i	$0.478488\pi$
$660$	2.68604e68	0.224019
$661$	−1.05434e67	−0.00847318	−0.00423659	−	0.999991i	$-0.501349\pi$
$661$	−1.05434e67	−0.00847318	−0.00423659	+	0.999991i	$0.501349\pi$
$662$	−1.43468e69	−1.11105
$663$	−4.03728e68	−0.301306
$664$	6.43144e68	0.462584
$665$	−2.50212e68	−0.173451
$666$	−1.32937e69	−0.888231
$667$	−6.16827e68	−0.397265
$668$	−2.98796e68	−0.185503
$669$	1.13422e69	0.678824
$670$	−1.56275e69	−0.901691
$671$	−1.28107e69	−0.712642
$672$	9.25819e67	0.0496568
$673$	1.77205e69	0.916446	0.458223	−	0.888837i	$-0.348486\pi$
$673$	1.77205e69	0.916446	0.458223	+	0.888837i	$0.348486\pi$
$674$	1.86247e69	0.928798
$675$	−8.36214e68	−0.402138
$676$	−7.10374e68	−0.329452
$677$	−8.15931e68	−0.364948	−0.182474	−	0.983211i	$-0.558411\pi$
$677$	−8.15931e68	−0.364948	−0.182474	+	0.983211i	$0.558411\pi$
$678$	−3.87228e68	−0.167047
$679$	1.14597e69	0.476832
$680$	6.28957e68	0.252437
$681$	−8.80156e68	−0.340765
$682$	3.00468e69	1.12223
$683$	−3.52443e69	−1.26993	−0.634967	−	0.772539i	$-0.718986\pi$
$683$	−3.52443e69	−1.26993	−0.634967	+	0.772539i	$0.718986\pi$
$684$	−4.52088e68	−0.157162
$685$	2.62137e69	0.879245
$686$	1.95657e69	0.633219
$687$	−1.30085e69	−0.406245
$688$	8.33428e68	0.251161
$689$	−1.79351e69	−0.521595
$690$	−2.49950e68	−0.0701537
$691$	4.21607e69	1.14208	0.571038	−	0.820923i	$-0.306541\pi$
$691$	4.21607e69	1.14208	0.571038	+	0.820923i	$0.306541\pi$
$692$	8.47571e68	0.221604
$693$	−1.58037e69	−0.398837
$694$	−5.16303e67	−0.0125776
$695$	3.58188e69	0.842332
$696$	−1.38629e69	−0.314722
$697$	2.58135e69	0.565775
$698$	2.17279e69	0.459790
$699$	−2.63566e69	−0.538516
$700$	−5.68395e68	−0.112137
$701$	−1.52450e69	−0.290427	−0.145213	−	0.989400i	$-0.546387\pi$
$701$	−1.52450e69	−0.290427	−0.145213	+	0.989400i	$0.546387\pi$
$702$	−2.07997e69	−0.382646
$703$	−4.47775e69	−0.795526
$704$	7.98133e68	0.136945
$705$	1.93865e69	0.321266
$706$	3.32125e69	0.531601
$707$	−4.85162e69	−0.750086
$708$	−2.97860e69	−0.444834
$709$	1.93716e69	0.279469	0.139734	−	0.990189i	$-0.455375\pi$
$709$	1.93716e69	0.279469	0.139734	+	0.990189i	$0.455375\pi$
$710$	−5.09060e69	−0.709478
$711$	−3.03383e69	−0.408495
$712$	−4.02304e69	−0.523353
$713$	−2.79602e69	−0.351436
$714$	1.55217e69	0.188509
$715$	−4.10180e69	−0.481368
$716$	−2.95584e69	−0.335206
$717$	5.25232e69	0.575615
$718$	−6.87673e69	−0.728339
$719$	1.35437e70	1.38638	0.693188	−	0.720757i	$-0.256206\pi$
$719$	1.35437e70	1.38638	0.693188	+	0.720757i	$0.256206\pi$
$720$	1.33929e69	0.132503
$721$	−4.76541e69	−0.455708
$722$	6.12695e69	0.566347
$723$	5.00288e69	0.447025
$724$	3.32042e69	0.286813
$725$	8.51093e69	0.710715
$726$	9.53392e68	0.0769705
$727$	1.71359e70	1.33756	0.668781	−	0.743459i	$-0.266816\pi$
$727$	1.71359e70	1.33756	0.668781	+	0.743459i	$0.266816\pi$
$728$	−1.41380e69	−0.106701
$729$	4.96322e69	0.362192
$730$	−4.01738e69	−0.283487
$731$	1.39727e70	0.953465
$732$	2.67920e69	0.176800
$733$	−1.42680e70	−0.910575	−0.455287	−	0.890344i	$-0.650464\pi$
$733$	−1.42680e70	−0.910575	−0.455287	+	0.890344i	$0.650464\pi$
$734$	−2.29803e69	−0.141841
$735$	−5.02121e69	−0.299757
$736$	−7.42705e68	−0.0428855
$737$	−3.32474e70	−1.85696
$738$	5.49666e69	0.296974
$739$	3.54443e69	0.185250	0.0926248	−	0.995701i	$-0.470474\pi$
$739$	3.54443e69	0.185250	0.0926248	+	0.995701i	$0.470474\pi$
$740$	1.32651e70	0.670706
$741$	−2.89572e69	−0.141648
$742$	6.89531e69	0.326331
$743$	−2.47010e70	−1.13107	−0.565534	−	0.824725i	$-0.691330\pi$
$743$	−2.47010e70	−1.13107	−0.565534	+	0.824725i	$0.691330\pi$
$744$	−6.28390e69	−0.278415
$745$	−2.71161e70	−1.16252
$746$	−2.31243e70	−0.959327
$747$	2.29601e70	0.921761
$748$	1.33810e70	0.519874
$749$	1.22523e69	0.0460693
$750$	1.13951e70	0.414685
$751$	−1.25896e70	−0.443440	−0.221720	−	0.975110i	$-0.571167\pi$
$751$	−1.25896e70	−0.443440	−0.221720	+	0.975110i	$0.571167\pi$
$752$	5.76052e69	0.196392
$753$	−1.23472e70	−0.407465
$754$	2.11698e70	0.676266
$755$	2.86102e70	0.884749
$756$	7.99661e69	0.239399
$757$	−3.64959e70	−1.05778	−0.528890	−	0.848690i	$-0.677392\pi$
$757$	−3.64959e70	−1.05778	−0.528890	+	0.848690i	$0.677392\pi$
$758$	−3.00499e70	−0.843232
$759$	−5.31766e69	−0.144476
$760$	4.51116e69	0.118674
$761$	5.40000e70	1.37553	0.687764	−	0.725934i	$-0.258592\pi$
$761$	5.40000e70	1.37553	0.687764	+	0.725934i	$0.258592\pi$
$762$	1.36247e70	0.336071
$763$	−1.70255e68	−0.00406675
$764$	−1.31553e70	−0.304309
$765$	2.24536e70	0.503014
$766$	−4.78527e70	−1.03825
$767$	4.54858e70	0.955849
$768$	−1.66919e69	−0.0339748
$769$	4.36340e69	0.0860260	0.0430130	−	0.999075i	$-0.486304\pi$
$769$	4.36340e69	0.0860260	0.0430130	+	0.999075i	$0.486304\pi$
$770$	1.57697e70	0.301163
$771$	−2.23403e70	−0.413291
$772$	−1.67008e70	−0.299305
$773$	3.88162e70	0.673931	0.336965	−	0.941517i	$-0.390599\pi$
$773$	3.88162e70	0.673931	0.336965	+	0.941517i	$0.390599\pi$
$774$	2.97531e70	0.500471
$775$	3.85792e70	0.628726
$776$	−2.06612e70	−0.326244
$777$	3.27361e70	0.500855
$778$	−1.13450e70	−0.168191
$779$	1.85146e70	0.265978
$780$	8.57840e69	0.119423
$781$	−1.08302e71	−1.46112
$782$	−1.24517e70	−0.162803
$783$	−1.19738e71	−1.51729
$784$	−1.49201e70	−0.183243
$785$	8.10614e70	0.964956
$786$	1.45569e69	0.0167964
$787$	−7.58128e70	−0.847933	−0.423966	−	0.905678i	$-0.639363\pi$
$787$	−7.58128e70	−0.847933	−0.423966	+	0.905678i	$0.639363\pi$
$788$	−7.09967e70	−0.769743
$789$	7.17272e70	0.753872
$790$	3.02731e70	0.308456
$791$	−2.27342e70	−0.224572
$792$	2.84931e70	0.272881
$793$	−4.09136e70	−0.379904
$794$	−1.85412e70	−0.166931
$795$	−4.18380e70	−0.365238
$796$	−1.81186e70	−0.153375
$797$	5.68943e70	0.467025	0.233512	−	0.972354i	$-0.424978\pi$
$797$	5.68943e70	0.467025	0.233512	+	0.972354i	$0.424978\pi$
$798$	1.11328e70	0.0886207
$799$	9.65771e70	0.745552
$800$	1.02478e70	0.0767230
$801$	−1.43621e71	−1.04285
$802$	8.56153e70	0.602947
$803$	−8.54692e70	−0.583819
$804$	6.95326e70	0.460697
$805$	−1.46746e70	−0.0943119
$806$	9.59604e70	0.598251
$807$	−4.31288e70	−0.260835
$808$	8.74716e70	0.513202
$809$	1.76866e71	1.00671	0.503356	−	0.864079i	$-0.332099\pi$
$809$	1.76866e71	1.00671	0.503356	+	0.864079i	$0.332099\pi$
$810$	1.93462e70	0.106835
$811$	8.62595e70	0.462164	0.231082	−	0.972934i	$-0.425773\pi$
$811$	8.62595e70	0.462164	0.231082	+	0.972934i	$0.425773\pi$
$812$	−8.13889e70	−0.423100
$813$	1.89047e71	0.953570
$814$	2.82212e71	1.38127
$815$	−3.33250e70	−0.158274
$816$	−2.79846e70	−0.128976
$817$	1.00218e71	0.448237
$818$	−3.06878e71	−1.33202
$819$	−5.04723e70	−0.212617
$820$	−5.48484e70	−0.224246
$821$	−2.91911e71	−1.15836	−0.579179	−	0.815201i	$-0.696627\pi$
$821$	−2.91911e71	−1.15836	−0.579179	+	0.815201i	$0.696627\pi$
$822$	−1.16634e71	−0.449228
$823$	−5.03932e71	−1.88398	−0.941989	−	0.335644i	$-0.891046\pi$
$823$	−5.03932e71	−1.88398	−0.941989	+	0.335644i	$0.891046\pi$
$824$	8.59173e70	0.311791
$825$	7.33726e70	0.258471
$826$	−1.74874e71	−0.598017
$827$	6.61084e70	0.219468	0.109734	−	0.993961i	$-0.465000\pi$
$827$	6.61084e70	0.219468	0.109734	+	0.993961i	$0.465000\pi$
$828$	−2.65144e70	−0.0854551
$829$	5.11811e71	1.60149	0.800745	−	0.599006i	$-0.204437\pi$
$829$	5.11811e71	1.60149	0.800745	+	0.599006i	$0.204437\pi$
$830$	−2.29107e71	−0.696025
$831$	−1.01776e71	−0.300206
$832$	2.54900e70	0.0730042
$833$	−2.50140e71	−0.695635
$834$	−1.59371e71	−0.430369
$835$	1.06440e71	0.279116
$836$	9.59743e70	0.244400
$837$	−5.42762e71	−1.34226
$838$	1.88799e71	0.453441
$839$	8.21238e71	1.91558	0.957792	−	0.287463i	$-0.0928118\pi$
$839$	8.21238e71	1.91558	0.957792	+	0.287463i	$0.0928118\pi$
$840$	−3.29804e70	−0.0747159
$841$	7.64220e71	1.68158
$842$	−4.78943e71	−1.02362
$843$	−3.48114e71	−0.722679
$844$	3.30771e71	0.667018
$845$	2.53056e71	0.495709
$846$	2.05649e71	0.391338
$847$	5.59737e70	0.103476
$848$	−1.24318e71	−0.223273
$849$	4.39297e71	0.766513
$850$	1.71808e71	0.291259
$851$	−2.62614e71	−0.432557
$852$	2.26499e71	0.362490
$853$	−9.19425e71	−1.42977	−0.714883	−	0.699244i	$-0.753520\pi$
$853$	−9.19425e71	−1.42977	−0.714883	+	0.699244i	$0.753520\pi$
$854$	1.57296e71	0.237683
$855$	1.61047e71	0.236474
$856$	−2.20901e70	−0.0315202
$857$	−9.35670e71	−1.29746	−0.648728	−	0.761020i	$-0.724699\pi$
$857$	−9.35670e71	−1.29746	−0.648728	+	0.761020i	$0.724699\pi$
$858$	1.82504e71	0.245943
$859$	1.22416e72	1.60327	0.801635	−	0.597814i	$-0.203964\pi$
$859$	1.22416e72	1.60327	0.801635	+	0.597814i	$0.203964\pi$
$860$	−2.96891e71	−0.377907
$861$	−1.35357e71	−0.167457
$862$	3.40387e71	0.409303
$863$	−8.53536e71	−0.997602	−0.498801	−	0.866717i	$-0.666226\pi$
$863$	−8.53536e71	−0.997602	−0.498801	+	0.866717i	$0.666226\pi$
$864$	−1.44174e71	−0.163795
$865$	−3.01929e71	−0.333435
$866$	3.24233e71	0.348072
$867$	5.17173e70	0.0539720
$868$	−3.68928e71	−0.374290
$869$	6.44056e71	0.635241
$870$	4.93836e71	0.473544
$871$	−1.06182e72	−0.989934
$872$	3.06958e69	0.00278244
$873$	−7.37597e71	−0.650085
$874$	−8.93092e70	−0.0765361
$875$	6.69008e71	0.557486
$876$	1.78748e71	0.144841
$877$	−1.02731e72	−0.809491	−0.404746	−	0.914429i	$-0.632640\pi$
$877$	−1.02731e72	−0.809491	−0.404746	+	0.914429i	$0.632640\pi$
$878$	−2.75567e69	−0.00211160
$879$	−3.18815e71	−0.237581
$880$	−2.84318e71	−0.206053
$881$	−1.59062e72	−1.12113	−0.560566	−	0.828110i	$-0.689416\pi$
$881$	−1.59062e72	−1.12113	−0.560566	+	0.828110i	$0.689416\pi$
$882$	−5.32643e71	−0.365137
$883$	1.16807e72	0.778811	0.389405	−	0.921066i	$-0.372681\pi$
$883$	1.16807e72	0.778811	0.389405	+	0.921066i	$0.372681\pi$
$884$	4.27348e71	0.277141
$885$	1.06107e72	0.669317
$886$	−4.20602e71	−0.258075
$887$	2.23169e72	1.33200	0.666000	−	0.745952i	$-0.268005\pi$
$887$	2.23169e72	1.33200	0.666000	+	0.745952i	$0.268005\pi$
$888$	−5.90211e71	−0.342681
$889$	7.99908e71	0.451801
$890$	1.43312e72	0.787460
$891$	4.11587e71	0.220018
$892$	−1.20058e72	−0.624382
$893$	6.92694e71	0.350494
$894$	1.20649e72	0.593959
$895$	1.05296e72	0.504366
$896$	−9.79983e70	−0.0456744
$897$	−1.69830e71	−0.0770193
$898$	−3.06021e72	−1.35046
$899$	5.52419e72	2.37223
$900$	3.65843e71	0.152881
$901$	−2.08423e72	−0.847596
$902$	−1.16689e72	−0.461818
$903$	−7.32682e71	−0.282205
$904$	4.09882e71	0.153650
$905$	−1.18283e72	−0.431551
$906$	−1.27297e72	−0.452041
$907$	−2.74919e72	−0.950224	−0.475112	−	0.879925i	$-0.657592\pi$
$907$	−2.74919e72	−0.950224	−0.475112	+	0.879925i	$0.657592\pi$
$908$	9.31648e71	0.313436
$909$	3.12271e72	1.02262
$910$	5.03638e71	0.160548
$911$	−5.18996e72	−1.61051	−0.805256	−	0.592927i	$-0.797972\pi$
$911$	−5.18996e72	−1.61051	−0.805256	+	0.592927i	$0.797972\pi$
$912$	−2.00718e71	−0.0606335
$913$	−4.87422e72	−1.43341
$914$	2.88182e72	0.825060
$915$	−9.54407e71	−0.266022
$916$	1.37696e72	0.373664
$917$	8.54637e70	0.0225805
$918$	−2.41712e72	−0.621803
$919$	−2.91412e72	−0.729923	−0.364961	−	0.931023i	$-0.618918\pi$
$919$	−2.91412e72	−0.729923	−0.364961	+	0.931023i	$0.618918\pi$
$920$	2.64573e71	0.0645274
$921$	3.79823e72	0.902029
$922$	1.32841e72	0.307202
$923$	−3.45883e72	−0.778911
$924$	−7.01653e71	−0.153872
$925$	3.62352e72	0.773854
$926$	−5.56834e71	−0.115813
$927$	3.06722e72	0.621286
$928$	1.46739e72	0.289481
$929$	2.86503e72	0.550483	0.275241	−	0.961375i	$-0.411242\pi$
$929$	2.86503e72	0.550483	0.275241	+	0.961375i	$0.411242\pi$
$930$	2.23851e72	0.418916
$931$	−1.79412e72	−0.327027
$932$	2.78986e72	0.495327
$933$	−9.21755e71	−0.159410
$934$	4.62786e71	0.0779617
$935$	−4.76669e72	−0.782226
$936$	9.09984e71	0.145471
$937$	9.31686e72	1.45094	0.725470	−	0.688253i	$-0.241622\pi$
$937$	9.31686e72	1.45094	0.725470	+	0.688253i	$0.241622\pi$
$938$	4.08226e72	0.619343
$939$	6.38788e72	0.944170
$940$	−2.05206e72	−0.295501
$941$	−3.56143e72	−0.499664	−0.249832	−	0.968289i	$-0.580375\pi$
$941$	−3.56143e72	−0.499664	−0.249832	+	0.968289i	$0.580375\pi$
$942$	−3.60672e72	−0.493020
$943$	1.08586e72	0.144622
$944$	3.15286e72	0.409158
$945$	−2.84862e72	−0.360210
$946$	−6.31632e72	−0.778272
$947$	−5.10172e72	−0.612551	−0.306275	−	0.951943i	$-0.599083\pi$
$947$	−5.10172e72	−0.612551	−0.306275	+	0.951943i	$0.599083\pi$
$948$	−1.34696e72	−0.157598
$949$	−2.72963e72	−0.311230
$950$	1.23228e72	0.136925
$951$	−3.74475e72	−0.405509
$952$	−1.64297e72	−0.173391
$953$	−5.72894e72	−0.589248	−0.294624	−	0.955613i	$-0.595194\pi$
$953$	−5.72894e72	−0.589248	−0.294624	+	0.955613i	$0.595194\pi$
$954$	−4.43811e72	−0.444901
$955$	4.68631e72	0.457877
$956$	−5.55960e72	−0.529450
$957$	1.05063e73	0.975229
$958$	−7.88248e72	−0.713195
$959$	−6.84761e72	−0.603925
$960$	5.94615e71	0.0511200
$961$	1.31083e73	1.09856
$962$	9.01302e72	0.736344
$963$	−7.88608e71	−0.0628083
$964$	−5.29557e72	−0.411173
$965$	5.94931e72	0.450347
$966$	6.52926e71	0.0481864
$967$	−3.98636e72	−0.286832	−0.143416	−	0.989662i	$-0.545809\pi$
$967$	−3.98636e72	−0.286832	−0.143416	+	0.989662i	$0.545809\pi$
$968$	−1.00917e72	−0.0707975
$969$	−3.36510e72	−0.230179
$970$	7.36011e72	0.490881
$971$	1.25926e72	0.0818925	0.0409463	−	0.999161i	$-0.486963\pi$
$971$	1.25926e72	0.0818925	0.0409463	+	0.999161i	$0.486963\pi$
$972$	−8.16658e72	−0.517865
$973$	−9.35667e72	−0.578571
$974$	−3.26374e72	−0.196798
$975$	2.34330e72	0.137789
$976$	−2.83594e72	−0.162621
$977$	−2.61383e72	−0.146170	−0.0730852	−	0.997326i	$-0.523285\pi$
$977$	−2.61383e72	−0.146170	−0.0730852	+	0.997326i	$0.523285\pi$
$978$	1.48275e72	0.0808661
$979$	3.04895e73	1.62172
$980$	5.31497e72	0.275716
$981$	1.09583e71	0.00554438
$982$	1.61640e73	0.797659
$983$	−2.91819e73	−1.40460	−0.702299	−	0.711882i	$-0.747843\pi$
$983$	−2.91819e73	−1.40460	−0.702299	+	0.711882i	$0.747843\pi$
$984$	2.44040e72	0.114573
$985$	2.52911e73	1.15819
$986$	2.46013e73	1.09894
$987$	−5.06418e72	−0.220668
$988$	3.06513e72	0.130288
$989$	5.87767e72	0.243723
$990$	−1.01501e73	−0.410589
$991$	−1.29576e73	−0.511354	−0.255677	−	0.966762i	$-0.582298\pi$
$991$	−1.29576e73	−0.511354	−0.255677	+	0.966762i	$0.582298\pi$
$992$	6.65154e72	0.256086
$993$	−2.27395e73	−0.854132
$994$	1.32978e73	0.487318
$995$	6.45438e72	0.230775
$996$	1.01938e73	0.355617
$997$	−2.43676e73	−0.829433	−0.414716	−	0.909951i	$-0.636119\pi$
$997$	−2.43676e73	−0.829433	−0.414716	+	0.909951i	$0.636119\pi$
$998$	−2.49436e73	−0.828438
$999$	−5.09785e73	−1.65209

Twists

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

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

\(f(q)\)	\(=\)	\(q-1.67772e7 q^{2} -2.65918e11 q^{3} +2.81475e14 q^{4} -1.00270e17 q^{5} +4.46136e18 q^{6} +2.61926e20 q^{7} -4.72237e21 q^{8} -1.68587e23 q^{9} +O(q^{10})\)	\(q-1.67772e7 q^{2} -2.65918e11 q^{3} +2.81475e14 q^{4} -1.00270e17 q^{5} +4.46136e18 q^{6} +2.61926e20 q^{7} -4.72237e21 q^{8} -1.68587e23 q^{9} +1.68224e24 q^{10} +3.57895e25 q^{11} -7.48492e25 q^{12} +1.14301e27 q^{13} -4.39440e27 q^{14} +2.66635e28 q^{15} +7.92282e28 q^{16} +1.32829e30 q^{17} +2.82842e30 q^{18} +9.52707e30 q^{19} -2.82234e31 q^{20} -6.96509e31 q^{21} -6.00448e32 q^{22} +5.58749e32 q^{23} +1.25576e33 q^{24} -7.70958e33 q^{25} -1.91765e34 q^{26} +1.08464e35 q^{27} +7.37257e34 q^{28} -1.10394e36 q^{29} -4.47339e35 q^{30} -5.00406e36 q^{31} -1.32923e36 q^{32} -9.51707e36 q^{33} -2.22850e37 q^{34} -2.62633e37 q^{35} -4.74530e37 q^{36} -4.70003e38 q^{37} -1.59838e38 q^{38} -3.03946e38 q^{39} +4.73510e38 q^{40} +1.94337e39 q^{41} +1.16855e39 q^{42} +1.05193e40 q^{43} +1.00739e40 q^{44} +1.69042e40 q^{45} -9.37426e39 q^{46} +7.27080e40 q^{47} -2.10682e40 q^{48} -1.88318e41 q^{49} +1.29345e41 q^{50} -3.53215e41 q^{51} +3.21729e41 q^{52} -1.56911e42 q^{53} -1.81973e42 q^{54} -3.58860e42 q^{55} -1.23691e42 q^{56} -2.53342e42 q^{57} +1.85211e43 q^{58} +3.97947e43 q^{59} +7.50510e42 q^{60} -3.57946e43 q^{61} +8.39542e43 q^{62} -4.41574e43 q^{63} +2.23007e43 q^{64} -1.14609e44 q^{65} +1.59670e44 q^{66} -9.28969e44 q^{67} +3.73879e44 q^{68} -1.48581e44 q^{69} +4.40624e44 q^{70} -3.02607e45 q^{71} +7.96130e44 q^{72} -2.38811e45 q^{73} +7.88534e45 q^{74} +2.05011e45 q^{75} +2.68163e45 q^{76} +9.37422e45 q^{77} +5.09938e45 q^{78} +1.79957e46 q^{79} -7.94417e45 q^{80} +1.15002e46 q^{81} -3.26043e46 q^{82} -1.36191e47 q^{83} -1.96050e46 q^{84} -1.33187e47 q^{85} -1.76485e47 q^{86} +2.93558e47 q^{87} -1.69011e47 q^{88} +8.51912e47 q^{89} -2.83605e47 q^{90} +2.99384e47 q^{91} +1.57274e47 q^{92} +1.33067e48 q^{93} -1.21984e48 q^{94} -9.55275e47 q^{95} +3.53465e47 q^{96} +4.37517e48 q^{97} +3.15945e48 q^{98} -6.03365e48 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 33554432 q^{2} + 281051075592 q^{3} + 562949953421312 q^{4} + 83\!\cdots\!00 q^{5}+ \cdots - 10\!\cdots\!34 q^{9}+O(q^{10}) \) 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

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