LMFDB - Embedded newform 3.70.a.a.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3,70,Mod(1,3)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(3, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 70, names="a")

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

chi := DirichletCharacter("3.1");

S:= CuspForms(chi, 70);

N := Newforms(S);

Level:	$ N $	$=$	$ 3 $
Weight:	$ k $	$=$	$ 70 $
Character orbit:	$[\chi]$	$=$	3.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:	$90.4544859877$
Analytic rank:	$1$
Dimension:	$6$
Coefficient field:	$\mathbb{Q}[x]/(x^{6} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 3 x^{5} + \cdots - 14\!\cdots\!28 $ x^6 - 3x^5 - 1895395655112138158x^4 - 215343254036998938223429254x^3 + 753811615313247966666178630793780821x^2 + 48156657138617542519489631631312055499331993*x - 14832095927450491582029231424734280560496715550059928
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{51}\cdot 3^{33}\cdot 5^{6}\cdot 7^{3}\cdot 11\cdot 17\cdot 23^{2} $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$-8.84844e8$ of defining polynomial
Character	$\chi$	$=$	3.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-3.19993e10 q^{2} -1.66772e16 q^{3} +4.33658e20 q^{4} -1.19891e23 q^{5} +5.33658e26 q^{6} +2.02540e29 q^{7} +5.01228e30 q^{8} +2.78128e32 q^{9} +O(q^{10})$	\(q-3.19993e10 q^{2} -1.66772e16 q^{3} +4.33658e20 q^{4} -1.19891e23 q^{5} +5.33658e26 q^{6} +2.02540e29 q^{7} +5.01228e30 q^{8} +2.78128e32 q^{9} +3.83642e33 q^{10} -9.10928e35 q^{11} -7.23220e36 q^{12} -3.11194e37 q^{13} -6.48112e39 q^{14} +1.99944e39 q^{15} -4.16376e41 q^{16} +2.29590e42 q^{17} -8.89991e42 q^{18} +4.71273e43 q^{19} -5.19916e43 q^{20} -3.37779e45 q^{21} +2.91490e46 q^{22} -1.39652e47 q^{23} -8.35908e46 q^{24} -1.67969e48 q^{25} +9.95797e47 q^{26} -4.63840e48 q^{27} +8.78330e49 q^{28} -1.66042e50 q^{29} -6.39806e49 q^{30} +2.79238e51 q^{31} +1.03650e52 q^{32} +1.51917e52 q^{33} -7.34673e52 q^{34} -2.42826e52 q^{35} +1.20613e53 q^{36} +1.41933e54 q^{37} -1.50804e54 q^{38} +5.18983e53 q^{39} -6.00926e53 q^{40} -2.72825e55 q^{41} +1.08087e56 q^{42} +1.02563e56 q^{43} -3.95032e56 q^{44} -3.33450e55 q^{45} +4.46877e57 q^{46} +5.64329e57 q^{47} +6.94398e57 q^{48} +2.05218e58 q^{49} +5.37489e58 q^{50} -3.82892e58 q^{51} -1.34952e58 q^{52} +3.40856e59 q^{53} +1.48425e59 q^{54} +1.09212e59 q^{55} +1.01519e60 q^{56} -7.85951e59 q^{57} +5.31324e60 q^{58} -2.01257e61 q^{59} +8.67074e59 q^{60} -4.23832e61 q^{61} -8.93541e61 q^{62} +5.63320e61 q^{63} -8.58879e61 q^{64} +3.73092e60 q^{65} -4.86124e62 q^{66} +7.65850e62 q^{67} +9.95638e62 q^{68} +2.32901e63 q^{69} +7.77026e62 q^{70} +4.39641e63 q^{71} +1.39406e63 q^{72} +2.02475e64 q^{73} -4.54176e64 q^{74} +2.80125e64 q^{75} +2.04372e64 q^{76} -1.84499e65 q^{77} -1.66071e64 q^{78} -5.59183e65 q^{79} +4.99196e64 q^{80} +7.73554e64 q^{81} +8.73019e65 q^{82} +1.81704e63 q^{83} -1.46481e66 q^{84} -2.75257e65 q^{85} -3.28195e66 q^{86} +2.76912e66 q^{87} -4.56583e66 q^{88} +1.30321e67 q^{89} +1.06702e66 q^{90} -6.30290e66 q^{91} -6.05614e67 q^{92} -4.65690e67 q^{93} -1.80581e68 q^{94} -5.65013e66 q^{95} -1.72859e68 q^{96} -5.99916e68 q^{97} -6.56683e68 q^{98} -2.53355e68 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 869363388 q^{2} - 10\!\cdots\!14 q^{3}+ \cdots + 16\!\cdots\!66 q^{9}+O(q^{10}) $ 6 * q - 869363388 * q^2 - 100063090197999414 * q^3 + 1371216641348494011408 * q^4 + 536749102286059793452020 * q^5 + 14498531184713726896175772 * q^6 - 165486212832272947603119602016 * q^7 + 29031977276772288550932250437696 * q^8 + 1668770336662161067543714657390566 * q^9	$ 6 q - 869363388 q^{2} - 10\!\cdots\!14 q^{3}+ \cdots - 53\!\cdots\!36 q^{99}+O(q^{100}) $ 6 * q - 869363388 * q^2 - 100063090197999414 * q^3 + 1371216641348494011408 * q^4 + 536749102286059793452020 * q^5 + 14498531184713726896175772 * q^6 - 165486212832272947603119602016 * q^7 + 29031977276772288550932250437696 * q^8 + 1668770336662161067543714657390566 * q^9 - 30539001465788028222087378612341640 * q^10 - 1920537066516616187668579962543158376 * q^11 - 22868029077375361513671619126882219152 * q^12 - 47217968885374199615397355356796191852 * q^13 + 7064585334174201405371837809050003141312 * q^14 - 8951462305957535762539464569043499519380 * q^15 + 377157429568235813937466329721859576398080 * q^16 - 5058270084832851177273994934925110056607412 * q^17 - 241794638945752826180250102109053616166268 * q^18 - 65818466266910893781669604806057906253992088 * q^19 - 74276832342140585406878490976963545328073760 * q^20 + 2759843640193509337740927488460262535180203104 * q^21 - 57200945629382567456443201741175335542976506864 * q^22 - 51318359662817614748704757772348805853962165488 * q^23 - 484171560145322484473355383995534830167508585024 * q^24 + 1351900008806516831015099778033783730620565906650 * q^25 - 16207493799167654397027294571148058082290306700488 * q^26 - 27830386119528611875968901007343548725913806188054 * q^27 + 121390433570468044194114098496551362783272349932288 * q^28 + 785579239339018365983000259217156564097330312249124 * q^29 + 509304476371330630546739998356596576017896314633160 * q^30 + 6912833464261058549529914367563374193660948950153296 * q^31 + 36737392694691819442392877818076822209799633285776384 * q^32 + 32029145619242227636284505564240924042938191359531944 * q^33 + 253117449563254571066779054180560057695840514055176 * q^34 + 276611165060305397158461820821003699537527995207930560 * q^35 + 381374276036647353263390282147345081660028453185929488 * q^36 - 759040697498936685975105001963916849352981208607118396 * q^37 + 2103369059703889244990286400717050872850491394651970032 * q^38 + 787462646590588064894632608232796865789891597354595788 * q^39 - 32664751344775020838298315886208043642737757270980944000 * q^40 - 25768671104884673827847532722814331858226170126017093924 * q^41 - 117817373250822824537222457055662269520721648792989198528 * q^42 - 677055351038557514071054609066516734267888940905925188840 * q^43 + 238305524760672609941760876572355183014168119775154744384 * q^44 + 149285163354170121367980976931811340477842188257753607220 * q^45 + 8376385103625214805959746309869879529208374887220505747296 * q^46 + 7598599404092453023795535768684988784173129214818972342720 * q^47 - 6289922982288665238584151982726579281690322330718011787520 * q^48 + 39520658833284024797097689208298803008912245306300761939990 * q^49 - 28568855233568347359168873341651630916131610440562956535300 * q^50 + 84357689290745289159801421813736090901392081119475734009428 * q^51 - 841291935994679864415054059209490217537323675729185299370272 * q^52 - 449047684897777378052965016724937358227157858973850840458828 * q^53 + 4032453127703594497238226593730133400050584990603665094492 * q^54 + 2254548165992828810812926827082553754343205233701600459282640 * q^55 + 1641356236071085469964848605225791359818442190977904466652160 * q^56 + 1097666521126647756280461762493305085319303708198214764106072 * q^57 + 10854840022358605054892033620996887145323506082370467922396824 * q^58 + 9739940026219086244132886290748367338175220661414782584592728 * q^59 + 1238728229045548911290208746311830657587532274639907038129440 * q^60 - 59315134126314210963145084137204520506665661947323124957508780 * q^61 - 58284415626578488701665533854996023611020152283699473273044512 * q^62 - 46026413850176360961358753239584156335498095610944326498830176 * q^63 - 196087603577998032685001038699358078224720081884631691829178368 * q^64 - 368792752455446531625971790511790913672736652263934282973351720 * q^65 + 953950563653961367781459452317768129208925530496794989139829616 * q^66 + 1284404845637086838528947432298267008623636941858083561714308648 * q^67 - 1893312213205272549692225847826950804709005883992500832775643616 * q^68 + 855845608625648963144016144920672894915758664084152710799170672 * q^69 + 5651141511141393939253777145916410305809660448417857533217598080 * q^70 - 8028908380018744267365790936955359727729274918181835022662164368 * q^71 + 8074617082354583671186761526246370992341166934797564305786862656 * q^72 + 23917666927401813793494400679686156753046201104575562189407759612 * q^73 - 66571567863995212404482808802342117220480190894464062470316692648 * q^74 - 22545882086647115963110648728416884279973448838942742394179783850 * q^75 - 117137080475037691773181405327212499216032011801755896581802226752 * q^76 - 370001686623730076506835954110410638316696132431439489747825466752 * q^77 + 270295318984938200277077861249204534384356528838329715416149585672 * q^78 + 151166116158225305435965330589298930972238439200795534257670973040 * q^79 - 103132668838130690471303376617648857617362361028013189202842042880 * q^80 + 464132406087257065130090681062365209793088477541530761100710966726 * q^81 + 37460932835681010277915179679262266245084578260611880863596729448 * q^82 - 2199869100513279294476979658003407541858593100082068956813742116504 * q^83 - 2024450317255999993413036160714996242543447082962560389819327279872 * q^84 - 6491952514505341124698414891022457176579387500885906219615755954840 * q^85 - 23144659602467499127119271177953663689526653967585956674347553430256 * q^86 - 13101247713942660717783546201323542017367838371972839670487262335556 * q^87 - 65249604729672858795836798510445455460410612360663171240882606141184 * q^88 - 6686194196194507079670325678793857718304620226396138544648538601828 * q^89 - 8493763292898219695542584151776832427456280937959354979087550828040 * q^90 - 82097466714973722451927498084842810568687277892210020260162088564544 * q^91 + 4359811041243409323098555915712612735158801326895369127311689835904 * q^92 - 115286579743017176690026802480066668815283610415364196376484636361424 * q^93 - 560087180092970937289054350368454974923005535872515030885741348295552 * q^94 - 914644999797608066644469983517358223242420981276970458662113135611600 * q^95 - 612676173141378712760794918109470208907664831994025080010863094506496 * q^96 - 1193245591335854049619056301286742793562875638671855181199561300009332 * q^97 - 3639892838212491311414089259694594431294943863329296694030071739108188 * q^98 - 534155881177182136550108656986512933865188403627723332959024704380136 * 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 $

$2$	−3.19993e10	−1.31706	−0.658530	−	0.752555i	$-0.728821\pi$
$2$	−3.19993e10	−1.31706	−0.658530	+	0.752555i	$0.728821\pi$
$3$	−1.66772e16	−0.577350
$3$	−1.66772e16	−0.577350
$4$	4.33658e20	0.734646
$5$	−1.19891e23	−0.0921129	−0.0460564	−	0.998939i	$-0.514665\pi$
$5$	−1.19891e23	−0.0921129	−0.0460564	+	0.998939i	$0.514665\pi$
$6$	5.33658e26	0.760405
$7$	2.02540e29	1.41458	0.707290	−	0.706923i	$-0.249917\pi$
$7$	2.02540e29	1.41458	0.707290	+	0.706923i	$0.249917\pi$
$8$	5.01228e30	0.349487
$9$	2.78128e32	0.333333
$10$	3.83642e33	0.121318
$11$	−9.10928e35	−1.07507	−0.537535	−	0.843242i	$-0.680644\pi$
$11$	−9.10928e35	−1.07507	−0.537535	+	0.843242i	$0.680644\pi$
$12$	−7.23220e36	−0.424148
$13$	−3.11194e37	−0.115341	−0.0576707	−	0.998336i	$-0.518367\pi$
$13$	−3.11194e37	−0.115341	−0.0576707	+	0.998336i	$0.518367\pi$
$14$	−6.48112e39	−1.86309
$15$	1.99944e39	0.0531814
$16$	−4.16376e41	−1.19494
$17$	2.29590e42	0.813703	0.406851	−	0.913494i	$-0.366627\pi$
$17$	2.29590e42	0.813703	0.406851	+	0.913494i	$0.366627\pi$
$18$	−8.89991e42	−0.439020
$19$	4.71273e43	0.359976	0.179988	−	0.983669i	$-0.442394\pi$
$19$	4.71273e43	0.359976	0.179988	+	0.983669i	$0.442394\pi$
$20$	−5.19916e43	−0.0676703
$21$	−3.37779e45	−0.816708
$22$	2.91490e46	1.41593
$23$	−1.39652e47	−1.46365	−0.731825	−	0.681492i	$-0.761331\pi$
$23$	−1.39652e47	−1.46365	−0.731825	+	0.681492i	$0.761331\pi$
$24$	−8.35908e46	−0.201776
$25$	−1.67969e48	−0.991515
$26$	9.95797e47	0.151911
$27$	−4.63840e48	−0.192450
$28$	8.78330e49	1.03922
$29$	−1.66042e50	−0.585448	−0.292724	−	0.956197i	$-0.594562\pi$
$29$	−1.66042e50	−0.585448	−0.292724	+	0.956197i	$0.594562\pi$
$30$	−6.39806e49	−0.0700431
$31$	2.79238e51	0.986270	0.493135	−	0.869953i	$-0.335851\pi$
$31$	2.79238e51	0.986270	0.493135	+	0.869953i	$0.335851\pi$
$32$	1.03650e52	1.22432
$33$	1.51917e52	0.620691
$34$	−7.34673e52	−1.07169
$35$	−2.42826e52	−0.130301
$36$	1.20613e53	0.244882
$37$	1.41933e54	1.11976	0.559879	−	0.828575i	$-0.310848\pi$
$37$	1.41933e54	1.11976	0.559879	+	0.828575i	$0.310848\pi$
$38$	−1.50804e54	−0.474110
$39$	5.18983e53	0.0665923
$40$	−6.00926e53	−0.0321922
$41$	−2.72825e55	−0.623506	−0.311753	−	0.950163i	$-0.600916\pi$
$41$	−2.72825e55	−0.623506	−0.311753	+	0.950163i	$0.600916\pi$
$42$	1.08087e56	1.07565
$43$	1.02563e56	0.453241	0.226621	−	0.973983i	$-0.427232\pi$
$43$	1.02563e56	0.453241	0.226621	+	0.973983i	$0.427232\pi$
$44$	−3.95032e56	−0.789795
$45$	−3.33450e55	−0.0307043
$46$	4.46877e57	1.92772
$47$	5.64329e57	1.15919	0.579597	−	0.814903i	$-0.303210\pi$
$47$	5.64329e57	1.15919	0.579597	+	0.814903i	$0.303210\pi$
$48$	6.94398e57	0.689900
$49$	2.05218e58	1.00104
$50$	5.37489e58	1.30588
$51$	−3.82892e58	−0.469791
$52$	−1.34952e58	−0.0847350
$53$	3.40856e59	1.10931	0.554656	−	0.832080i	$-0.312850\pi$
$53$	3.40856e59	1.10931	0.554656	+	0.832080i	$0.312850\pi$
$54$	1.48425e59	0.253468
$55$	1.09212e59	0.0990277
$56$	1.01519e60	0.494378
$57$	−7.85951e59	−0.207832
$58$	5.31324e60	0.771069
$59$	−2.01257e61	−1.61941	−0.809705	−	0.586837i	$-0.800373\pi$
$59$	−2.01257e61	−1.61941	−0.809705	+	0.586837i	$0.800373\pi$
$60$	8.67074e59	0.0390695
$61$	−4.23832e61	−1.07973	−0.539864	−	0.841752i	$-0.681524\pi$
$61$	−4.23832e61	−1.07973	−0.539864	+	0.841752i	$0.681524\pi$
$62$	−8.93541e61	−1.29898
$63$	5.63320e61	0.471527
$64$	−8.58879e61	−0.417564
$65$	3.73092e60	0.0106244
$66$	−4.86124e62	−0.817488
$67$	7.65850e62	0.766590	0.383295	−	0.923626i	$-0.374789\pi$
$67$	7.65850e62	0.766590	0.383295	+	0.923626i	$0.374789\pi$
$68$	9.95638e62	0.597783
$69$	2.32901e63	0.845039
$70$	7.77026e62	0.171614
$71$	4.39641e63	0.595230	0.297615	−	0.954686i	$-0.403809\pi$
$71$	4.39641e63	0.595230	0.297615	+	0.954686i	$0.403809\pi$
$72$	1.39406e63	0.116496
$73$	2.02475e64	1.05131	0.525657	−	0.850696i	$-0.323819\pi$
$73$	2.02475e64	1.05131	0.525657	+	0.850696i	$0.323819\pi$
$74$	−4.54176e64	−1.47479
$75$	2.80125e64	0.572452
$76$	2.04372e64	0.264455
$77$	−1.84499e65	−1.52077
$78$	−1.66071e64	−0.0877061
$79$	−5.59183e65	−1.90291	−0.951457	−	0.307782i	$-0.900413\pi$
$79$	−5.59183e65	−1.90291	−0.951457	+	0.307782i	$0.900413\pi$
$80$	4.99196e64	0.110069
$81$	7.73554e64	0.111111
$82$	8.73019e65	0.821194
$83$	1.81704e63	0.00112504	0.000562522	−	1.00000i	$-0.499821\pi$
$83$	1.81704e63	0.00112504	0.000562522		1.00000i	$0.499821\pi$
$84$	−1.46481e66	−0.599992
$85$	−2.75257e65	−0.0749525
$86$	−3.28195e66	−0.596946
$87$	2.76912e66	0.338008
$88$	−4.56583e66	−0.375723
$89$	1.30321e67	0.726206	0.363103	−	0.931749i	$-0.381717\pi$
$89$	1.30321e67	0.726206	0.363103	+	0.931749i	$0.381717\pi$
$90$	1.06702e66	0.0404394
$91$	−6.30290e66	−0.163160
$92$	−6.05614e67	−1.07527
$93$	−4.65690e67	−0.569423
$94$	−1.80581e68	−1.52673
$95$	−5.65013e66	−0.0331584
$96$	−1.72859e68	−0.706863
$97$	−5.99916e68	−1.71580	−0.857898	−	0.513820i	$-0.828230\pi$
$97$	−5.99916e68	−1.71580	−0.857898	+	0.513820i	$0.828230\pi$
$98$	−6.56683e68	−1.31843
$99$	−2.53355e68	−0.358356
$100$	−7.28413e68	−0.728413
$101$	−1.26497e69	−0.897412	−0.448706	−	0.893679i	$-0.648115\pi$
$101$	−1.26497e69	−0.897412	−0.448706	+	0.893679i	$0.648115\pi$
$102$	1.22523e69	0.618743
$103$	3.79094e69	1.36730	0.683648	−	0.729812i	$-0.260392\pi$
$103$	3.79094e69	1.36730	0.683648	+	0.729812i	$0.260392\pi$
$104$	−1.55979e68	−0.0403103
$105$	4.04966e68	0.0752294
$106$	−1.09072e70	−1.46103
$107$	−1.74513e70	−1.69078	−0.845390	−	0.534150i	$-0.820632\pi$
$107$	−1.74513e70	−1.69078	−0.845390	+	0.534150i	$0.820632\pi$
$108$	−2.01148e69	−0.141383
$109$	1.32131e70	0.675759	0.337879	−	0.941189i	$-0.390290\pi$
$109$	1.32131e70	0.675759	0.337879	+	0.941189i	$0.390290\pi$
$110$	−3.49470e69	−0.130425
$111$	−2.36704e70	−0.646492
$112$	−8.43327e70	−1.69034
$113$	3.60557e70	0.531824	0.265912	−	0.963997i	$-0.414327\pi$
$113$	3.60557e70	0.531824	0.265912	+	0.963997i	$0.414327\pi$
$114$	2.51499e70	0.273727
$115$	1.67430e70	0.134821
$116$	−7.20057e70	−0.430097
$117$	−8.65518e69	−0.0384471
$118$	6.44009e71	2.13286
$119$	4.65011e71	1.15105
$120$	1.00218e70	0.0185862
$121$	1.11838e71	0.155774
$122$	1.35623e72	1.42207
$123$	4.54995e71	0.359981
$124$	1.21094e72	0.724559
$125$	4.04482e71	0.183444
$126$	−1.80258e72	−0.621029
$127$	3.59785e72	0.943659	0.471829	−	0.881690i	$-0.343594\pi$
$127$	3.59785e72	0.943659	0.471829	+	0.881690i	$0.343594\pi$
$128$	−3.37007e72	−0.674366
$129$	−1.71046e72	−0.261679
$130$	−1.19387e71	−0.0139930
$131$	−5.63360e72	−0.506904	−0.253452	−	0.967348i	$-0.581566\pi$
$131$	−5.63360e72	−0.506904	−0.253452	+	0.967348i	$0.581566\pi$
$132$	6.58801e72	0.455989
$133$	9.54515e72	0.509215
$134$	−2.45066e73	−1.00964
$135$	5.56101e71	0.0177271
$136$	1.15077e73	0.284379
$137$	−2.95903e73	−0.567923	−0.283961	−	0.958836i	$-0.591649\pi$
$137$	−2.95903e73	−0.567923	−0.283961	+	0.958836i	$0.591649\pi$
$138$	−7.45265e73	−1.11297
$139$	1.20118e74	1.39830	0.699148	−	0.714977i	$-0.253563\pi$
$139$	1.20118e74	1.39830	0.699148	+	0.714977i	$0.253563\pi$
$140$	−1.05304e73	−0.0957252
$141$	−9.41141e73	−0.669261
$142$	−1.40682e74	−0.783954
$143$	2.83475e73	0.124000
$144$	−1.15806e74	−0.398314
$145$	1.99069e73	0.0539273
$146$	−6.47905e74	−1.38464
$147$	−3.42246e74	−0.577950
$148$	6.15505e74	0.822625
$149$	−1.45780e75	−1.54444	−0.772222	−	0.635353i	$-0.780855\pi$
$149$	−1.45780e75	−1.54444	−0.772222	+	0.635353i	$0.780855\pi$
$150$	−8.96381e74	−0.753953
$151$	1.75138e75	1.17132	0.585661	−	0.810556i	$-0.300835\pi$
$151$	1.75138e75	1.17132	0.585661	+	0.810556i	$0.300835\pi$
$152$	2.36215e74	0.125807
$153$	6.38556e74	0.271234
$154$	5.90384e75	2.00295
$155$	−3.34780e74	−0.0908482
$156$	2.25061e74	0.0489218
$157$	1.09843e76	1.91530	0.957649	−	0.287939i	$-0.0929699\pi$
$157$	1.09843e76	1.91530	0.957649	+	0.287939i	$0.0929699\pi$
$158$	1.78934e76	2.50625
$159$	−5.68452e75	−0.640462
$160$	−1.24267e75	−0.112776
$161$	−2.82851e76	−2.07045
$162$	−2.47532e75	−0.146340
$163$	1.63225e76	0.780394	0.390197	−	0.920731i	$-0.372407\pi$
$163$	1.63225e76	0.780394	0.390197	+	0.920731i	$0.372407\pi$
$164$	−1.18313e76	−0.458056
$165$	−1.82134e75	−0.0571737
$166$	−5.81439e73	−0.00148175
$167$	3.81312e75	0.0789882	0.0394941	−	0.999220i	$-0.487425\pi$
$167$	3.81312e75	0.0789882	0.0394941	+	0.999220i	$0.487425\pi$
$168$	−1.69304e76	−0.285429
$169$	−7.18249e76	−0.986696
$170$	8.80804e75	0.0987169
$171$	1.31074e76	0.119992
$172$	4.44774e76	0.332972
$173$	−3.52320e75	−0.0215947	−0.0107973	−	0.999942i	$-0.503437\pi$
$173$	−3.52320e75	−0.0215947	−0.0107973	+	0.999942i	$0.503437\pi$
$174$	−8.86098e76	−0.445177
$175$	−3.40204e77	−1.40258
$176$	3.79289e77	1.28464
$177$	3.35640e77	0.934967
$178$	−4.17019e77	−0.956457
$179$	−9.12286e77	−1.72465	−0.862326	−	0.506353i	$-0.830993\pi$
$179$	−9.12286e77	−1.72465	−0.862326	+	0.506353i	$0.830993\pi$
$180$	−1.44603e76	−0.0225568
$181$	−1.56522e77	−0.201681	−0.100841	−	0.994903i	$-0.532153\pi$
$181$	−1.56522e77	−0.201681	−0.100841	+	0.994903i	$0.532153\pi$
$182$	2.01688e77	0.214891
$183$	7.06832e77	0.623381
$184$	−6.99976e77	−0.511527
$185$	−1.70164e77	−0.103144
$186$	1.49018e78	0.749965
$187$	−2.09140e78	−0.874787
$188$	2.44726e78	0.851597
$189$	−9.39459e77	−0.272236
$190$	1.80800e77	0.0436716
$191$	6.79427e78	1.36928	0.684639	−	0.728883i	$-0.259960\pi$
$191$	6.79427e78	1.36928	0.684639	+	0.728883i	$0.259960\pi$
$192$	1.43237e78	0.241080
$193$	3.55804e78	0.500592	0.250296	−	0.968169i	$-0.419472\pi$
$193$	3.55804e78	0.500592	0.250296	+	0.968169i	$0.419472\pi$
$194$	1.91969e79	2.25981
$195$	−6.22212e76	−0.00613401
$196$	8.89945e78	0.735409
$197$	−1.90619e79	−1.32154	−0.660771	−	0.750587i	$-0.729771\pi$
$197$	−1.90619e79	−1.32154	−0.660771	+	0.750587i	$0.729771\pi$
$198$	8.10718e78	0.471977
$199$	−3.10140e79	−1.51749	−0.758747	−	0.651385i	$-0.774188\pi$
$199$	−3.10140e79	−1.51749	−0.758747	+	0.651385i	$0.774188\pi$
$200$	−8.41909e78	−0.346522
$201$	−1.27722e79	−0.442591
$202$	4.04780e79	1.18195
$203$	−3.36302e79	−0.828163
$204$	−1.66044e79	−0.345130
$205$	3.27091e78	0.0574329
$206$	−1.21307e80	−1.80081
$207$	−3.88412e79	−0.487884
$208$	1.29574e79	0.137826
$209$	−4.29296e79	−0.386999
$210$	−1.29586e79	−0.0990815
$211$	−1.61706e80	−1.04950	−0.524749	−	0.851257i	$-0.675841\pi$
$211$	−1.61706e80	−1.04950	−0.524749	+	0.851257i	$0.675841\pi$
$212$	1.47815e80	0.814952
$213$	−7.33197e79	−0.343656
$214$	5.58428e80	2.22686
$215$	−1.22964e79	−0.0417494
$216$	−2.32490e79	−0.0672588
$217$	5.65567e80	1.39516
$218$	−4.22811e80	−0.890014
$219$	−3.37671e80	−0.606977
$220$	4.73606e79	0.0727503
$221$	−7.14470e79	−0.0938535
$222$	7.57437e80	0.851469
$223$	−1.27381e81	−1.22627	−0.613137	−	0.789977i	$-0.710093\pi$
$223$	−1.27381e81	−1.22627	−0.613137	+	0.789977i	$0.710093\pi$
$224$	2.09933e81	1.73190
$225$	−4.67170e80	−0.330505
$226$	−1.15376e81	−0.700444
$227$	−1.02819e81	−0.536020	−0.268010	−	0.963416i	$-0.586366\pi$
$227$	−1.02819e81	−0.536020	−0.268010	+	0.963416i	$0.586366\pi$
$228$	−3.40834e80	−0.152683
$229$	3.80930e81	1.46731	0.733653	−	0.679524i	$-0.237814\pi$
$229$	3.80930e81	1.46731	0.733653	+	0.679524i	$0.237814\pi$
$230$	−5.35764e80	−0.177567
$231$	3.07692e81	0.878018
$232$	−8.32251e80	−0.204606
$233$	9.24550e81	1.95953	0.979763	−	0.200159i	$-0.0641458\pi$
$233$	9.24550e81	1.95953	0.979763	+	0.200159i	$0.0641458\pi$
$234$	2.76959e80	0.0506371
$235$	−6.76578e80	−0.106777
$236$	−8.72769e81	−1.18969
$237$	9.32559e81	1.09865
$238$	−1.48800e82	−1.51600
$239$	−1.34595e82	−1.18659	−0.593297	−	0.804984i	$-0.702174\pi$
$239$	−1.34595e82	−1.18659	−0.593297	+	0.804984i	$0.702174\pi$
$240$	−8.32519e80	−0.0635486
$241$	−1.54576e82	−1.02224	−0.511122	−	0.859508i	$-0.670770\pi$
$241$	−1.54576e82	−1.02224	−0.511122	+	0.859508i	$0.670770\pi$
$242$	−3.57874e81	−0.205163
$243$	−1.29007e81	−0.0641500
$244$	−1.83798e82	−0.793218
$245$	−2.46037e81	−0.0922085
$246$	−1.45595e82	−0.474117
$247$	−1.46657e81	−0.0415201
$248$	1.39962e82	0.344689
$249$	−3.03031e79	−0.000649545 0
$250$	−1.29431e82	−0.241607
$251$	5.78024e82	0.940162	0.470081	−	0.882623i	$-0.344225\pi$
$251$	5.78024e82	0.940162	0.470081	+	0.882623i	$0.344225\pi$
$252$	2.44289e82	0.346405
$253$	1.27213e83	1.57353
$254$	−1.15129e83	−1.24285
$255$	4.59052e81	0.0432738
$256$	1.58539e83	1.30574
$257$	−6.62209e82	−0.476763	−0.238381	−	0.971172i	$-0.576617\pi$
$257$	−6.62209e82	−0.476763	−0.238381	+	0.971172i	$0.576617\pi$
$258$	5.47336e82	0.344647
$259$	2.87471e83	1.58399
$260$	1.61795e81	0.00780519
$261$	−4.61811e82	−0.195149
$262$	1.80271e83	0.667623
$263$	−1.73718e83	−0.564120	−0.282060	−	0.959397i	$-0.591018\pi$
$263$	−1.73718e83	−0.564120	−0.282060	+	0.959397i	$0.591018\pi$
$264$	7.61452e82	0.216924
$265$	−4.08655e82	−0.102182
$266$	−3.05438e83	−0.670667
$267$	−2.17339e83	−0.419275
$268$	3.32117e83	0.563172
$269$	−7.83021e83	−1.16767	−0.583835	−	0.811872i	$-0.698448\pi$
$269$	−7.83021e83	−1.16767	−0.583835	+	0.811872i	$0.698448\pi$
$270$	−1.77948e82	−0.0233477
$271$	−8.45999e83	−0.977079	−0.488539	−	0.872542i	$-0.662470\pi$
$271$	−8.45999e83	−0.977079	−0.488539	+	0.872542i	$0.662470\pi$
$272$	−9.55959e83	−0.972327
$273$	1.05115e83	0.0942002
$274$	9.46867e83	0.747988
$275$	1.53008e84	1.06595
$276$	1.00999e84	0.620805
$277$	−9.34489e82	−0.0507017	−0.0253508	−	0.999679i	$-0.508070\pi$
$277$	−9.34489e82	−0.0507017	−0.0253508	+	0.999679i	$0.508070\pi$
$278$	−3.84371e84	−1.84164
$279$	7.76640e83	0.328757
$280$	−1.21711e83	−0.0455385
$281$	−1.14166e84	−0.377718	−0.188859	−	0.982004i	$-0.560479\pi$
$281$	−1.14166e84	−0.377718	−0.188859	+	0.982004i	$0.560479\pi$
$282$	3.01158e84	0.881456
$283$	−2.91028e84	−0.753881	−0.376941	−	0.926237i	$-0.623024\pi$
$283$	−2.91028e84	−0.753881	−0.376941	+	0.926237i	$0.623024\pi$
$284$	1.90654e84	0.437284
$285$	9.42282e82	0.0191440
$286$	−9.07099e83	−0.163315
$287$	−5.52578e84	−0.881999
$288$	2.88280e84	0.408107
$289$	−2.68998e84	−0.337888
$290$	−6.37008e83	−0.0710254
$291$	1.00049e85	0.990616
$292$	8.78050e84	0.772344
$293$	−1.96830e85	−1.53872	−0.769358	−	0.638818i	$-0.779424\pi$
$293$	−1.96830e85	−1.53872	−0.769358	+	0.638818i	$0.779424\pi$
$294$	1.09516e85	0.761194
$295$	2.41289e84	0.149169
$296$	7.11409e84	0.391341
$297$	4.22525e84	0.206897
$298$	4.66486e85	2.03413
$299$	4.34589e84	0.168819
$300$	1.21479e85	0.420549
$301$	2.07731e85	0.641146
$302$	−5.60430e85	−1.54270
$303$	2.10961e85	0.518121
$304$	−1.96227e85	−0.430150
$305$	5.08135e84	0.0994568
$306$	−2.04333e85	−0.357232
$307$	2.68183e85	0.418945	0.209473	−	0.977814i	$-0.432825\pi$
$307$	2.68183e85	0.418945	0.209473	+	0.977814i	$0.432825\pi$
$308$	−8.00096e85	−1.11723
$309$	−6.32222e85	−0.789409
$310$	1.07127e85	0.119652
$311$	−1.65967e86	−1.65878	−0.829390	−	0.558671i	$-0.811312\pi$
$311$	−1.65967e86	−1.65878	−0.829390	+	0.558671i	$0.811312\pi$
$312$	2.60129e84	0.0232732
$313$	1.72230e86	1.37984	0.689920	−	0.723885i	$-0.257646\pi$
$313$	1.72230e86	1.37984	0.689920	+	0.723885i	$0.257646\pi$
$314$	−3.51491e86	−2.52256
$315$	−6.75369e84	−0.0434337
$316$	−2.42494e86	−1.39797
$317$	−5.90355e85	−0.305189	−0.152594	−	0.988289i	$-0.548763\pi$
$317$	−5.90355e85	−0.305189	−0.152594	+	0.988289i	$0.548763\pi$
$318$	1.81901e86	0.843526
$319$	1.51253e86	0.629397
$320$	1.02972e85	0.0384630
$321$	2.91038e86	0.976172
$322$	9.05103e86	2.72691
$323$	1.08200e86	0.292913
$324$	3.35458e85	0.0816273
$325$	5.22709e85	0.114363
$326$	−5.22308e86	−1.02783
$327$	−2.20358e86	−0.390149
$328$	−1.36747e86	−0.217907
$329$	1.14299e87	1.63977
$330$	5.82817e85	0.0753011
$331$	−1.09019e87	−1.26893	−0.634464	−	0.772952i	$-0.718779\pi$
$331$	−1.09019e87	−1.26893	−0.634464	+	0.772952i	$0.718779\pi$
$332$	7.87974e83	0.000826509 0
$333$	3.94756e86	0.373253
$334$	−1.22017e86	−0.104032
$335$	−9.18182e85	−0.0706128
$336$	1.40643e87	0.975919
$337$	−1.66011e87	−1.03969	−0.519846	−	0.854260i	$-0.674011\pi$
$337$	−1.66011e87	−1.03969	−0.519846	+	0.854260i	$0.674011\pi$
$338$	2.29834e87	1.29954
$339$	−6.01308e86	−0.307049
$340$	−1.19368e86	−0.0550635
$341$	−2.54366e87	−1.06031
$342$	−4.19429e86	−0.158037
$343$	4.31030e84	0.00146845
$344$	5.14075e86	0.158402
$345$	−2.79226e86	−0.0778390
$346$	1.12740e86	0.0284415
$347$	−2.98086e87	−0.680730	−0.340365	−	0.940293i	$-0.610551\pi$
$347$	−2.98086e87	−0.680730	−0.340365	+	0.940293i	$0.610551\pi$
$348$	1.20085e87	0.248316
$349$	−2.36481e87	−0.442913	−0.221456	−	0.975170i	$-0.571081\pi$
$349$	−2.36481e87	−0.442913	−0.221456	+	0.975170i	$0.571081\pi$
$350$	1.08863e88	1.84728
$351$	1.44344e86	0.0221974
$352$	−9.44178e87	−1.31623
$353$	−7.93872e87	−1.00351	−0.501757	−	0.865009i	$-0.667313\pi$
$353$	−7.93872e87	−1.00351	−0.501757	+	0.865009i	$0.667313\pi$
$354$	−1.07402e88	−1.23141
$355$	−5.27089e86	−0.0548284
$356$	5.65149e87	0.533505
$357$	−7.75508e87	−0.664558
$358$	2.91925e88	2.27147
$359$	−1.89368e87	−0.133828	−0.0669142	−	0.997759i	$-0.521315\pi$
$359$	−1.89368e87	−0.133828	−0.0669142	+	0.997759i	$0.521315\pi$
$360$	−1.67135e86	−0.0107307
$361$	−1.49185e88	−0.870417
$362$	5.00861e87	0.265626
$363$	−1.86514e87	−0.0899360
$364$	−2.73331e87	−0.119865
$365$	−2.42749e87	−0.0968396
$366$	−2.26181e88	−0.821030
$367$	1.51614e88	0.500911	0.250456	−	0.968128i	$-0.419420\pi$
$367$	1.51614e88	0.500911	0.250456	+	0.968128i	$0.419420\pi$
$368$	5.81479e88	1.74898
$369$	−7.58803e87	−0.207835
$370$	5.44514e87	0.135847
$371$	6.90369e88	1.56921
$372$	−2.01950e88	−0.418325
$373$	3.65155e88	0.689481	0.344741	−	0.938698i	$-0.387967\pi$
$373$	3.65155e88	0.689481	0.344741	+	0.938698i	$0.387967\pi$
$374$	6.69234e88	1.15215
$375$	−6.74562e87	−0.105912
$376$	2.82858e88	0.405123
$377$	5.16713e87	0.0675263
$378$	3.00620e88	0.358551
$379$	−1.59882e89	−1.74079	−0.870397	−	0.492351i	$-0.836138\pi$
$379$	−1.59882e89	−1.74079	−0.870397	+	0.492351i	$0.836138\pi$
$380$	−2.45023e87	−0.0243597
$381$	−6.00020e88	−0.544822
$382$	−2.17412e89	−1.80342
$383$	−6.88490e88	−0.521843	−0.260922	−	0.965360i	$-0.584026\pi$
$383$	−6.88490e88	−0.521843	−0.260922	+	0.965360i	$0.584026\pi$
$384$	5.62033e88	0.389345
$385$	2.21197e88	0.140083
$386$	−1.13855e89	−0.659309
$387$	2.85257e88	0.151080
$388$	−2.60159e89	−1.26050
$389$	−3.97050e88	−0.176029	−0.0880144	−	0.996119i	$-0.528052\pi$
$389$	−3.97050e88	−0.176029	−0.0880144	+	0.996119i	$0.528052\pi$
$390$	1.99104e87	0.00807886
$391$	−3.20628e89	−1.19098
$392$	1.02861e89	0.349850
$393$	9.39525e88	0.292661
$394$	6.09967e89	1.74055
$395$	6.70408e88	0.175283
$396$	−1.09870e89	−0.263265
$397$	−6.14480e89	−1.34969	−0.674847	−	0.737958i	$-0.735790\pi$
$397$	−6.14480e89	−1.34969	−0.674847	+	0.737958i	$0.735790\pi$
$398$	9.92427e89	1.99863
$399$	−1.59186e89	−0.293995
$400$	6.99384e89	1.18480
$401$	2.40258e89	0.373419	0.186709	−	0.982415i	$-0.440218\pi$
$401$	2.40258e89	0.373419	0.186709	+	0.982415i	$0.440218\pi$
$402$	4.08702e89	0.582918
$403$	−8.68970e88	−0.113758
$404$	−5.48564e89	−0.659280
$405$	−9.27419e87	−0.0102348
$406$	1.07614e90	1.09074
$407$	−1.29291e90	−1.20382
$408$	−1.91916e89	−0.164186
$409$	9.18114e89	0.721843	0.360921	−	0.932596i	$-0.382462\pi$
$409$	9.18114e89	0.721843	0.360921	+	0.932596i	$0.382462\pi$
$410$	−1.04667e89	−0.0756426
$411$	4.93482e89	0.327890
$412$	1.64397e90	1.00448
$413$	−4.07626e90	−2.29079
$414$	1.24289e90	0.642572
$415$	−2.17846e86	−0.000103631 0
$416$	−3.22553e89	−0.141215
$417$	−2.00324e90	−0.807307
$418$	1.37372e90	0.509701
$419$	−4.32312e90	−1.47711	−0.738556	−	0.674192i	$-0.764492\pi$
$419$	−4.32312e90	−1.47711	−0.738556	+	0.674192i	$0.764492\pi$
$420$	1.75617e89	0.0552669
$421$	4.46617e90	1.29480	0.647400	−	0.762150i	$-0.275856\pi$
$421$	4.46617e90	1.29480	0.647400	+	0.762150i	$0.275856\pi$
$422$	5.17448e90	1.38225
$423$	1.56956e90	0.386398
$424$	1.70847e90	0.387690
$425$	−3.85641e90	−0.806799
$426$	2.34618e90	0.452616
$427$	−8.58427e90	−1.52736
$428$	−7.56789e90	−1.24212
$429$	−4.72756e89	−0.0715914
$430$	3.93475e89	0.0549864
$431$	9.02177e90	1.16366	0.581830	−	0.813311i	$-0.302337\pi$
$431$	9.02177e90	1.16366	0.581830	+	0.813311i	$0.302337\pi$
$432$	1.93132e90	0.229967
$433$	−1.12774e91	−1.23987	−0.619935	−	0.784653i	$-0.712841\pi$
$433$	−1.12774e91	−1.23987	−0.619935	+	0.784653i	$0.712841\pi$
$434$	−1.80978e91	−1.83751
$435$	−3.31992e89	−0.0311349
$436$	5.72999e90	0.496443
$437$	−6.58143e90	−0.526879
$438$	1.08052e91	0.799425
$439$	−3.30958e90	−0.226332	−0.113166	−	0.993576i	$-0.536099\pi$
$439$	−3.30958e90	−0.226332	−0.113166	+	0.993576i	$0.536099\pi$
$440$	5.47400e89	0.0346089
$441$	5.70769e90	0.333679
$442$	2.28625e90	0.123611
$443$	1.86206e91	0.931245	0.465623	−	0.884983i	$-0.345830\pi$
$443$	1.86206e91	0.931245	0.465623	+	0.884983i	$0.345830\pi$
$444$	−1.02649e91	−0.474943
$445$	−1.56243e90	−0.0668929
$446$	4.07611e91	1.61508
$447$	2.43120e91	0.891685
$448$	−1.73957e91	−0.590677
$449$	1.24411e91	0.391164	0.195582	−	0.980687i	$-0.437340\pi$
$449$	1.24411e91	0.391164	0.195582	+	0.980687i	$0.437340\pi$
$450$	1.49491e91	0.435295
$451$	2.48524e91	0.670312
$452$	1.56359e91	0.390703
$453$	−2.92081e91	−0.676263
$454$	3.29013e91	0.705971
$455$	7.55659e89	0.0150291
$456$	−3.93941e90	−0.0726347
$457$	1.06704e91	0.182420	0.0912101	−	0.995832i	$-0.470927\pi$
$457$	1.06704e91	0.182420	0.0912101	+	0.995832i	$0.470927\pi$
$458$	−1.21895e92	−1.93253
$459$	−1.06493e91	−0.156597
$460$	7.26074e90	0.0990458
$461$	6.17862e91	0.782004	0.391002	−	0.920390i	$-0.372128\pi$
$461$	6.17862e91	0.782004	0.391002	+	0.920390i	$0.372128\pi$
$462$	−9.84594e91	−1.15640
$463$	7.32959e90	0.0798979	0.0399490	−	0.999202i	$-0.487280\pi$
$463$	7.32959e90	0.0798979	0.0399490	+	0.999202i	$0.487280\pi$
$464$	6.91361e91	0.699575
$465$	5.58319e90	0.0524512
$466$	−2.95849e92	−2.58081
$467$	−1.95599e91	−0.158466	−0.0792328	−	0.996856i	$-0.525247\pi$
$467$	−1.95599e91	−0.158466	−0.0792328	+	0.996856i	$0.525247\pi$
$468$	−3.75339e90	−0.0282450
$469$	1.55115e92	1.08440
$470$	2.16500e91	0.140631
$471$	−1.83188e92	−1.10580
$472$	−1.00876e92	−0.565963
$473$	−9.34276e91	−0.487266
$474$	−2.98412e92	−1.44698
$475$	−7.91594e91	−0.356922
$476$	2.01656e92	0.845613
$477$	9.48018e91	0.369771
$478$	4.30695e92	1.56281
$479$	2.36057e92	0.796970	0.398485	−	0.917175i	$-0.369536\pi$
$479$	2.36057e92	0.796970	0.398485	+	0.917175i	$0.369536\pi$
$480$	2.07242e91	0.0651111
$481$	−4.41686e91	−0.129154
$482$	4.94633e92	1.34636
$483$	4.71716e92	1.19538
$484$	4.84995e91	0.114439
$485$	7.19244e91	0.158047
$486$	4.12813e91	0.0844894
$487$	−3.42444e92	−0.652891	−0.326445	−	0.945216i	$-0.605851\pi$
$487$	−3.42444e92	−0.652891	−0.326445	+	0.945216i	$0.605851\pi$
$488$	−2.12436e92	−0.377351
$489$	−2.72213e92	−0.450561
$490$	7.87301e91	0.121444
$491$	5.45077e91	0.0783694	0.0391847	−	0.999232i	$-0.487524\pi$
$491$	5.45077e91	0.0783694	0.0391847	+	0.999232i	$0.487524\pi$
$492$	1.97312e92	0.264459
$493$	−3.81217e92	−0.476380
$494$	4.69293e91	0.0546845
$495$	3.03749e91	0.0330092
$496$	−1.16268e93	−1.17853
$497$	8.90447e92	0.842001
$498$	9.69676e89	0.000855489 0
$499$	2.88108e91	0.0237184	0.0118592	−	0.999930i	$-0.496225\pi$
$499$	2.88108e91	0.0237184	0.0118592	+	0.999930i	$0.496225\pi$
$500$	1.75407e92	0.134767
$501$	−6.35921e91	−0.0456039
$502$	−1.84964e93	−1.23825
$503$	2.73923e93	1.71212	0.856058	−	0.516879i	$-0.172906\pi$
$503$	2.73923e93	1.71212	0.856058	+	0.516879i	$0.172906\pi$
$504$	2.82352e92	0.164793
$505$	1.51658e92	0.0826632
$506$	−4.07073e93	−2.07243
$507$	1.19784e93	0.569669
$508$	1.56024e93	0.693255
$509$	−7.20201e92	−0.299013	−0.149507	−	0.988761i	$-0.547769\pi$
$509$	−7.20201e92	−0.299013	−0.149507	+	0.988761i	$0.547769\pi$
$510$	−1.46893e92	−0.0569942
$511$	4.10092e93	1.48717
$512$	−3.08380e93	−1.04538
$513$	−2.18595e92	−0.0692774
$514$	2.11902e93	0.627925
$515$	−4.54498e92	−0.125946
$516$	−7.41757e92	−0.192241
$517$	−5.14063e93	−1.24621
$518$	−9.19886e93	−2.08621
$519$	5.87571e91	0.0124677
$520$	1.87004e91	0.00371310
$521$	−5.88826e93	−1.09417	−0.547085	−	0.837077i	$-0.684263\pi$
$521$	−5.88826e93	−1.09417	−0.547085	+	0.837077i	$0.684263\pi$
$522$	1.47776e93	0.257023
$523$	6.86490e93	1.11770	0.558851	−	0.829268i	$-0.311242\pi$
$523$	6.86490e93	1.11770	0.558851	+	0.829268i	$0.311242\pi$
$524$	−2.44306e93	−0.372395
$525$	5.67365e93	0.809779
$526$	5.55885e93	0.742980
$527$	6.41103e93	0.802531
$528$	−6.32547e93	−0.741690
$529$	1.03990e94	1.14227
$530$	1.30767e93	0.134580
$531$	−5.59753e93	−0.539804
$532$	4.13934e93	0.374093
$533$	8.49013e92	0.0719160
$534$	6.95470e93	0.552211
$535$	2.09225e93	0.155743
$536$	3.83866e93	0.267913
$537$	1.52144e94	0.995729
$538$	2.50561e94	1.53789
$539$	−1.86939e94	−1.07619
$540$	2.41158e92	0.0130232
$541$	−3.09356e94	−1.56730	−0.783650	−	0.621202i	$-0.786645\pi$
$541$	−3.09356e94	−1.56730	−0.783650	+	0.621202i	$0.786645\pi$
$542$	2.70714e94	1.28687
$543$	2.61035e93	0.116441
$544$	2.37971e94	0.996234
$545$	−1.58413e93	−0.0622461
$546$	−3.36359e93	−0.124067
$547$	−4.60546e94	−1.59482	−0.797408	−	0.603441i	$-0.793796\pi$
$547$	−4.60546e94	−1.59482	−0.797408	+	0.603441i	$0.793796\pi$
$548$	−1.28321e94	−0.417222
$549$	−1.17880e94	−0.359909
$550$	−4.89614e94	−1.40392
$551$	−7.82513e93	−0.210747
$552$	1.16736e94	0.295330
$553$	−1.13257e95	−2.69182
$554$	2.99030e93	0.0667771
$555$	2.83786e93	0.0595503
$556$	5.20904e94	1.02725
$557$	5.58090e93	0.103443	0.0517214	−	0.998662i	$-0.483529\pi$
$557$	5.58090e93	0.103443	0.0517214	+	0.998662i	$0.483529\pi$
$558$	−2.48519e94	−0.432992
$559$	−3.19170e93	−0.0522775
$560$	1.01107e94	0.155702
$561$	3.48787e94	0.505058
$562$	3.65323e94	0.497478
$563$	2.17333e94	0.278346	0.139173	−	0.990268i	$-0.455556\pi$
$563$	2.17333e94	0.278346	0.139173	+	0.990268i	$0.455556\pi$
$564$	−4.08134e94	−0.491670
$565$	−4.32275e93	−0.0489878
$566$	9.31270e94	0.992907
$567$	1.56675e94	0.157176
$568$	2.20360e94	0.208025
$569$	2.71323e94	0.241053	0.120527	−	0.992710i	$-0.461542\pi$
$569$	2.71323e94	0.241053	0.120527	+	0.992710i	$0.461542\pi$
$570$	−3.01523e93	−0.0252138
$571$	−2.83777e94	−0.223373	−0.111687	−	0.993743i	$-0.535625\pi$
$571$	−2.83777e94	−0.223373	−0.111687	+	0.993743i	$0.535625\pi$
$572$	1.22931e94	0.0910960
$573$	−1.13309e95	−0.790553
$574$	1.76821e95	1.16165
$575$	2.34573e95	1.45123
$576$	−2.38879e94	−0.139188
$577$	−1.86384e94	−0.102292	−0.0511462	−	0.998691i	$-0.516287\pi$
$577$	−1.86384e94	−0.102292	−0.0511462	+	0.998691i	$0.516287\pi$
$578$	8.60773e94	0.445019
$579$	−5.93381e94	−0.289017
$580$	8.63281e93	0.0396174
$581$	3.68022e92	0.00159147
$582$	−3.20150e95	−1.30470
$583$	−3.10496e95	−1.19259
$584$	1.01486e95	0.367421
$585$	1.03767e93	0.00354147
$586$	6.29842e95	2.02658
$587$	9.74295e93	0.0295581	0.0147790	−	0.999891i	$-0.495296\pi$
$587$	9.74295e93	0.0295581	0.0147790	+	0.999891i	$0.495296\pi$
$588$	−1.48418e95	−0.424588
$589$	1.31597e95	0.355034
$590$	−7.72106e94	−0.196464
$591$	3.17899e95	0.762993
$592$	−5.90975e95	−1.33804
$593$	−5.27276e95	−1.12629	−0.563146	−	0.826358i	$-0.690409\pi$
$593$	−5.27276e95	−1.12629	−0.563146	+	0.826358i	$0.690409\pi$
$594$	−1.35205e95	−0.272496
$595$	−5.57505e94	−0.106026
$596$	−6.32188e95	−1.13462
$597$	5.17227e95	0.876126
$598$	−1.39065e95	−0.222345
$599$	9.97640e95	1.50573	0.752867	−	0.658173i	$-0.228670\pi$
$599$	9.97640e95	1.50573	0.752867	+	0.658173i	$0.228670\pi$
$600$	1.40407e95	0.200064
$601$	−3.17569e95	−0.427236	−0.213618	−	0.976917i	$-0.568525\pi$
$601$	−3.17569e95	−0.427236	−0.213618	+	0.976917i	$0.568525\pi$
$602$	−6.64724e95	−0.844428
$603$	2.13005e95	0.255530
$604$	7.59501e95	0.860507
$605$	−1.34083e94	−0.0143488
$606$	−6.75060e95	−0.682396
$607$	−9.83214e95	−0.938941	−0.469470	−	0.882948i	$-0.655555\pi$
$607$	−9.83214e95	−0.938941	−0.469470	+	0.882948i	$0.655555\pi$
$608$	4.88475e95	0.440726
$609$	5.60856e95	0.478140
$610$	−1.62600e95	−0.130991
$611$	−1.75615e95	−0.133703
$612$	2.76915e95	0.199261
$613$	−1.11551e96	−0.758729	−0.379365	−	0.925247i	$-0.623857\pi$
$613$	−1.11551e96	−0.758729	−0.379365	+	0.925247i	$0.623857\pi$
$614$	−8.58167e95	−0.551776
$615$	−5.45496e94	−0.0331589
$616$	−9.24761e95	−0.531490
$617$	−4.73971e95	−0.257581	−0.128791	−	0.991672i	$-0.541109\pi$
$617$	−4.73971e95	−0.257581	−0.128791	+	0.991672i	$0.541109\pi$
$618$	2.02306e96	1.03970
$619$	−2.20537e96	−1.07190	−0.535950	−	0.844249i	$-0.680047\pi$
$619$	−2.20537e96	−1.07190	−0.535950	+	0.844249i	$0.680047\pi$
$620$	−1.45180e95	−0.0667412
$621$	6.47762e95	0.281680
$622$	5.31083e96	2.18471
$623$	2.63952e96	1.02728
$624$	−2.16092e95	−0.0795739
$625$	2.79702e96	0.974618
$626$	−5.51123e96	−1.81733
$627$	7.15945e95	0.223434
$628$	4.76346e96	1.40707
$629$	3.25864e96	0.911150
$630$	2.16113e95	0.0572048
$631$	2.83406e96	0.710225	0.355112	−	0.934824i	$-0.384443\pi$
$631$	2.83406e96	0.710225	0.355112	+	0.934824i	$0.384443\pi$
$632$	−2.80278e96	−0.665044
$633$	2.69680e96	0.605928
$634$	1.88909e96	0.401952
$635$	−4.31349e95	−0.0869231
$636$	−2.46514e96	−0.470513
$637$	−6.38625e95	−0.115461
$638$	−4.83998e96	−0.828953
$639$	1.22277e96	0.198410
$640$	4.04040e95	0.0621178
$641$	−1.41801e96	−0.206575	−0.103288	−	0.994652i	$-0.532936\pi$
$641$	−1.41801e96	−0.206575	−0.103288	+	0.994652i	$0.532936\pi$
$642$	−9.31301e96	−1.28568
$643$	−1.51469e97	−1.98173	−0.990866	−	0.134847i	$-0.956946\pi$
$643$	−1.51469e97	−1.98173	−0.990866	+	0.134847i	$0.956946\pi$
$644$	−1.22661e97	−1.52105
$645$	2.05069e95	0.0241040
$646$	−3.46232e96	−0.385784
$647$	−5.83859e96	−0.616752	−0.308376	−	0.951265i	$-0.599785\pi$
$647$	−5.83859e96	−0.616752	−0.308376	+	0.951265i	$0.599785\pi$
$648$	3.87727e95	0.0388319
$649$	1.83331e97	1.74098
$650$	−1.67263e96	−0.150622
$651$	−9.43207e96	−0.805495
$652$	7.07838e96	0.573313
$653$	3.87149e95	0.0297422	0.0148711	−	0.999889i	$-0.495266\pi$
$653$	3.87149e95	0.0297422	0.0148711	+	0.999889i	$0.495266\pi$
$654$	7.05129e96	0.513850
$655$	6.75416e95	0.0466924
$656$	1.13598e97	0.745053
$657$	5.63140e96	0.350438
$658$	−3.65748e97	−2.15968
$659$	3.21866e97	1.80355	0.901775	−	0.432206i	$-0.142265\pi$
$659$	3.21866e97	1.80355	0.901775	+	0.432206i	$0.142265\pi$
$660$	−7.89842e95	−0.0420024
$661$	−8.70284e96	−0.439249	−0.219624	−	0.975584i	$-0.570483\pi$
$661$	−8.70284e96	−0.439249	−0.219624	+	0.975584i	$0.570483\pi$
$662$	3.48854e97	1.67125
$663$	1.19153e96	0.0541864
$664$	9.10750e93	0.000393188 0
$665$	−1.14437e96	−0.0469053
$666$	−1.26319e97	−0.491596
$667$	2.31882e97	0.856891
$668$	1.65359e96	0.0580284
$669$	2.12436e97	0.707990
$670$	2.93812e96	0.0930012
$671$	3.86080e97	1.16078
$672$	−3.50108e97	−0.999914
$673$	−1.68681e97	−0.457663	−0.228832	−	0.973466i	$-0.573491\pi$
$673$	−1.68681e97	−0.457663	−0.228832	+	0.973466i	$0.573491\pi$
$674$	5.31222e97	1.36934
$675$	7.79108e96	0.190817
$676$	−3.11475e97	−0.724873
$677$	−4.58295e97	−1.01353	−0.506765	−	0.862084i	$-0.669159\pi$
$677$	−4.58295e97	−1.01353	−0.506765	+	0.862084i	$0.669159\pi$
$678$	1.92414e97	0.404402
$679$	−1.21507e98	−2.42713
$680$	−1.37967e96	−0.0261949
$681$	1.71473e97	0.309471
$682$	8.13952e97	1.39649
$683$	−1.04750e96	−0.0170860	−0.00854301	−	0.999964i	$-0.502719\pi$
$683$	−1.04750e96	−0.0170860	−0.00854301	+	0.999964i	$0.502719\pi$
$684$	5.68416e96	0.0881516
$685$	3.54760e96	0.0523130
$686$	−1.37926e95	−0.00193404
$687$	−6.35284e97	−0.847150
$688$	−4.27048e97	−0.541597
$689$	−1.06072e97	−0.127950
$690$	8.93503e96	0.102519
$691$	7.96363e97	0.869197	0.434599	−	0.900624i	$-0.356890\pi$
$691$	7.96363e97	0.869197	0.434599	+	0.900624i	$0.356890\pi$
$692$	−1.52787e96	−0.0158645
$693$	−5.13144e97	−0.506924
$694$	9.53854e97	0.896561
$695$	−1.44011e97	−0.128801
$696$	1.38796e97	0.118130
$697$	−6.26379e97	−0.507348
$698$	7.56721e97	0.583343
$699$	−1.54189e98	−1.13133
$700$	−1.47532e98	−1.03040
$701$	−1.01079e98	−0.672028	−0.336014	−	0.941857i	$-0.609079\pi$
$701$	−1.01079e98	−0.672028	−0.336014	+	0.941857i	$0.609079\pi$
$702$	−4.61890e96	−0.0292354
$703$	6.68892e97	0.403086
$704$	7.82376e97	0.448910
$705$	1.12834e97	0.0616475
$706$	2.54033e98	1.32169
$707$	−2.56206e98	−1.26946
$708$	1.45553e98	0.686870
$709$	3.80931e97	0.171219	0.0856093	−	0.996329i	$-0.472716\pi$
$709$	3.80931e97	0.171219	0.0856093	+	0.996329i	$0.472716\pi$
$710$	1.68665e97	0.0722122
$711$	−1.55525e98	−0.634305
$712$	6.53207e97	0.253800
$713$	−3.89962e98	−1.44356
$714$	2.48157e98	0.875262
$715$	−3.39860e96	−0.0114220
$716$	−3.95621e98	−1.26701
$717$	2.24467e98	0.685080
$718$	6.05965e97	0.176260
$719$	4.50548e97	0.124909	0.0624545	−	0.998048i	$-0.480107\pi$
$719$	4.50548e97	0.124909	0.0624545	+	0.998048i	$0.480107\pi$
$720$	1.38841e97	0.0366898
$721$	7.67816e98	1.93415
$722$	4.77382e98	1.14639
$723$	2.57790e98	0.590193
$724$	−6.78773e97	−0.148164
$725$	2.78900e98	0.580480
$726$	5.96832e97	0.118451
$727$	−4.41597e98	−0.835775	−0.417888	−	0.908499i	$-0.637229\pi$
$727$	−4.41597e98	−0.835775	−0.417888	+	0.908499i	$0.637229\pi$
$728$	−3.15919e97	−0.0570222
$729$	2.15147e97	0.0370370
$730$	7.76778e97	0.127544
$731$	2.35475e98	0.368804
$732$	3.06524e98	0.457964
$733$	2.77026e97	0.0394851	0.0197425	−	0.999805i	$-0.493715\pi$
$733$	2.77026e97	0.0394851	0.0197425	+	0.999805i	$0.493715\pi$
$734$	−4.85155e98	−0.659730
$735$	4.10321e97	0.0532366
$736$	−1.44750e99	−1.79198
$737$	−6.97634e98	−0.824137
$738$	2.42811e98	0.273731
$739$	8.56008e98	0.920969	0.460484	−	0.887668i	$-0.347676\pi$
$739$	8.56008e98	0.920969	0.460484	+	0.887668i	$0.347676\pi$
$740$	−7.37933e97	−0.0757744
$741$	2.44583e97	0.0239716
$742$	−2.20913e99	−2.06675
$743$	2.20951e99	1.97325	0.986626	−	0.162999i	$-0.0521167\pi$
$743$	2.20951e99	1.97325	0.986626	+	0.162999i	$0.0521167\pi$
$744$	−2.33417e98	−0.199006
$745$	1.74777e98	0.142263
$746$	−1.16847e99	−0.908088
$747$	5.05370e95	0.000375015 0
$748$	−9.06954e98	−0.642659
$749$	−3.53458e99	−2.39174
$750$	2.15855e98	0.139492
$751$	2.08554e99	1.28718	0.643592	−	0.765368i	$-0.277443\pi$
$751$	2.08554e99	1.28718	0.643592	+	0.765368i	$0.277443\pi$
$752$	−2.34973e99	−1.38517
$753$	−9.63981e98	−0.542803
$754$	−1.65345e98	−0.0889362
$755$	−2.09974e98	−0.107894
$756$	−4.07405e98	−0.199997
$757$	5.69283e98	0.267005	0.133503	−	0.991048i	$-0.457378\pi$
$757$	5.69283e98	0.267005	0.133503	+	0.991048i	$0.457378\pi$
$758$	5.11611e99	2.29273
$759$	−2.12156e99	−0.908476
$760$	−2.83200e97	−0.0115884
$761$	3.38178e99	1.32244	0.661219	−	0.750193i	$-0.270039\pi$
$761$	3.38178e99	1.32244	0.661219	+	0.750193i	$0.270039\pi$
$762$	1.92002e99	0.717563
$763$	2.67618e99	0.955915
$764$	2.94639e99	1.00593
$765$	−7.65569e97	−0.0249842
$766$	2.20312e99	0.687299
$767$	6.26299e98	0.186785
$768$	−2.64399e99	−0.753871
$769$	3.46377e99	0.944256	0.472128	−	0.881530i	$-0.343486\pi$
$769$	3.46377e99	0.944256	0.472128	+	0.881530i	$0.343486\pi$
$770$	−7.07815e98	−0.184497
$771$	1.10438e99	0.275259
$772$	1.54297e99	0.367758
$773$	1.34124e99	0.305713	0.152856	−	0.988248i	$-0.451153\pi$
$773$	1.34124e99	0.305713	0.152856	+	0.988248i	$0.451153\pi$
$774$	−9.12803e98	−0.198982
$775$	−4.69034e99	−0.977902
$776$	−3.00695e99	−0.599649
$777$	−4.79420e99	−0.914515
$778$	1.27053e99	0.231840
$779$	−1.28575e99	−0.224447
$780$	−2.69828e97	−0.00450633
$781$	−4.00481e99	−0.639914
$782$	1.02599e100	1.56859
$783$	7.70171e98	0.112669
$784$	−8.54479e99	−1.19618
$785$	−1.31692e99	−0.176424
$786$	−3.00641e99	−0.385452
$787$	−8.29989e99	−1.01846	−0.509230	−	0.860630i	$-0.670070\pi$
$787$	−8.29989e99	−1.01846	−0.509230	+	0.860630i	$0.670070\pi$
$788$	−8.26635e99	−0.970866
$789$	2.89713e99	0.325695
$790$	−2.14526e99	−0.230858
$791$	7.30272e99	0.752308
$792$	−1.26989e99	−0.125241
$793$	1.31894e99	0.124537
$794$	1.96629e100	1.77763
$795$	6.81521e98	0.0589948
$796$	−1.34495e100	−1.11482
$797$	1.12639e100	0.894083	0.447041	−	0.894513i	$-0.352478\pi$
$797$	1.12639e100	0.894083	0.447041	+	0.894513i	$0.352478\pi$
$798$	5.09385e99	0.387210
$799$	1.29564e100	0.943239
$800$	−1.74100e100	−1.21393
$801$	3.62460e99	0.242069
$802$	−7.68807e99	−0.491815
$803$	−1.84440e100	−1.13024
$804$	−5.53878e99	−0.325147
$805$	3.39112e99	0.190715
$806$	2.78064e99	0.149826
$807$	1.30586e100	0.674154
$808$	−6.34037e99	−0.313634
$809$	−1.21398e100	−0.575423	−0.287711	−	0.957717i	$-0.592894\pi$
$809$	−1.21398e100	−0.575423	−0.287711	+	0.957717i	$0.592894\pi$
$810$	2.96768e98	0.0134798
$811$	−3.05647e100	−1.33046	−0.665228	−	0.746640i	$-0.731666\pi$
$811$	−3.05647e100	−1.33046	−0.665228	+	0.746640i	$0.731666\pi$
$812$	−1.45840e100	−0.608406
$813$	1.41089e100	0.564117
$814$	4.13721e100	1.58550
$815$	−1.95691e99	−0.0718843
$816$	1.59427e100	0.561373
$817$	4.83353e99	0.163156
$818$	−2.93790e100	−0.950710
$819$	−1.75302e99	−0.0543865
$820$	1.41846e99	0.0421929
$821$	2.82208e100	0.804879	0.402439	−	0.915447i	$-0.368162\pi$
$821$	2.82208e100	0.804879	0.402439	+	0.915447i	$0.368162\pi$
$822$	−1.57911e100	−0.431851
$823$	5.34589e100	1.40193	0.700964	−	0.713197i	$-0.252753\pi$
$823$	5.34589e100	1.40193	0.700964	+	0.713197i	$0.252753\pi$
$824$	1.90013e100	0.477852
$825$	−2.55174e100	−0.615425
$826$	1.30437e101	3.01710
$827$	−4.20961e100	−0.933903	−0.466951	−	0.884283i	$-0.654648\pi$
$827$	−4.20961e100	−0.933903	−0.466951	+	0.884283i	$0.654648\pi$
$828$	−1.68438e100	−0.358422
$829$	−8.93027e100	−1.82278	−0.911388	−	0.411548i	$-0.864988\pi$
$829$	−8.93027e100	−1.82278	−0.911388	+	0.411548i	$0.864988\pi$
$830$	6.97091e96	0.000136488 0
$831$	1.55846e99	0.0292726
$832$	2.67277e99	0.0481623
$833$	4.71161e100	0.814547
$834$	6.41022e100	1.06327
$835$	−4.57158e98	−0.00727583
$836$	−1.86168e100	−0.284307
$837$	−1.29522e100	−0.189808
$838$	1.38337e101	1.94544
$839$	−5.41900e100	−0.731360	−0.365680	−	0.930741i	$-0.619164\pi$
$839$	−5.41900e100	−0.731360	−0.365680	+	0.930741i	$0.619164\pi$
$840$	2.02980e99	0.0262917
$841$	−5.28680e100	−0.657251
$842$	−1.42914e101	−1.70533
$843$	1.90396e100	0.218076
$844$	−7.01253e100	−0.771010
$845$	8.61113e99	0.0908874
$846$	−5.02247e100	−0.508909
$847$	2.26516e100	0.220354
$848$	−1.41924e101	−1.32556
$849$	4.85353e100	0.435254
$850$	1.23402e101	1.06260
$851$	−1.98213e101	−1.63893
$852$	−3.17957e100	−0.252466
$853$	−2.17106e101	−1.65551	−0.827754	−	0.561092i	$-0.810381\pi$
$853$	−2.17106e101	−1.65551	−0.827754	+	0.561092i	$0.810381\pi$
$854$	2.74691e101	2.01163
$855$	−1.57146e99	−0.0110528
$856$	−8.74707e100	−0.590905
$857$	−1.13232e100	−0.0734733	−0.0367367	−	0.999325i	$-0.511696\pi$
$857$	−1.13232e100	−0.0734733	−0.0367367	+	0.999325i	$0.511696\pi$
$858$	1.51279e100	0.0942901
$859$	−1.61410e101	−0.966422	−0.483211	−	0.875504i	$-0.660530\pi$
$859$	−1.61410e101	−0.966422	−0.483211	+	0.875504i	$0.660530\pi$
$860$	−5.33242e99	−0.0306710
$861$	9.21545e100	0.509223
$862$	−2.88690e101	−1.53261
$863$	1.65983e101	0.846624	0.423312	−	0.905984i	$-0.360867\pi$
$863$	1.65983e101	0.846624	0.423312	+	0.905984i	$0.360867\pi$
$864$	−4.80771e100	−0.235621
$865$	4.22399e98	0.00198915
$866$	3.60868e101	1.63298
$867$	4.48612e100	0.195080
$868$	2.45263e101	1.02495
$869$	5.09375e101	2.04576
$870$	1.06235e100	0.0410065
$871$	−2.38327e100	−0.0884194
$872$	6.62280e100	0.236169
$873$	−1.66854e101	−0.571932
$874$	2.10601e101	0.693931
$875$	8.19237e100	0.259497
$876$	−1.46434e101	−0.445913
$877$	1.62781e101	0.476560	0.238280	−	0.971197i	$-0.423416\pi$
$877$	1.62781e101	0.476560	0.238280	+	0.971197i	$0.423416\pi$
$878$	1.05904e101	0.298093
$879$	3.28257e101	0.888378
$880$	−4.54732e100	−0.118332
$881$	−2.09915e101	−0.525259	−0.262630	−	0.964897i	$-0.584590\pi$
$881$	−2.09915e101	−0.525259	−0.262630	+	0.964897i	$0.584590\pi$
$882$	−1.82642e101	−0.439476
$883$	−2.59271e101	−0.599943	−0.299971	−	0.953948i	$-0.596977\pi$
$883$	−2.59271e101	−0.599943	−0.299971	+	0.953948i	$0.596977\pi$
$884$	−3.09836e100	−0.0689491
$885$	−4.02401e100	−0.0861225
$886$	−5.95845e101	−1.22651
$887$	2.67781e101	0.530169	0.265085	−	0.964225i	$-0.414600\pi$
$887$	2.67781e101	0.530169	0.265085	+	0.964225i	$0.414600\pi$
$888$	−1.18643e101	−0.225941
$889$	7.28708e101	1.33488
$890$	4.99967e100	0.0881020
$891$	−7.04652e100	−0.119452
$892$	−5.52399e101	−0.900877
$893$	2.65953e101	0.417282
$894$	−7.77968e101	−1.17440
$895$	1.09375e101	0.158863
$896$	−6.82574e101	−0.953945
$897$	−7.24771e100	−0.0974679
$898$	−3.98105e101	−0.515187
$899$	−4.63653e101	−0.577410
$900$	−2.02592e101	−0.242804
$901$	7.82573e101	0.902650
$902$	−7.95258e101	−0.882841
$903$	−3.46437e101	−0.370166
$904$	1.80722e101	0.185866
$905$	1.87656e100	0.0185774
$906$	9.34638e101	0.890678
$907$	4.36327e101	0.400277	0.200138	−	0.979768i	$-0.435861\pi$
$907$	4.36327e101	0.400277	0.200138	+	0.979768i	$0.435861\pi$
$908$	−4.45883e101	−0.393785
$909$	−3.51823e101	−0.299137
$910$	−2.41806e100	−0.0197942
$911$	1.57554e102	1.24178	0.620891	−	0.783897i	$-0.286771\pi$
$911$	1.57554e102	1.24178	0.620891	+	0.783897i	$0.286771\pi$
$912$	3.27251e101	0.248347
$913$	−1.65519e99	−0.00120950
$914$	−3.41446e101	−0.240258
$915$	−8.47426e100	−0.0574214
$916$	1.65193e102	1.07795
$917$	−1.14103e102	−0.717057
$918$	3.40770e101	0.206248
$919$	1.26377e102	0.736685	0.368343	−	0.929690i	$-0.379925\pi$
$919$	1.26377e102	0.736685	0.368343	+	0.929690i	$0.379925\pi$
$920$	8.39206e100	0.0471182
$921$	−4.47254e101	−0.241878
$922$	−1.97711e102	−1.02995
$923$	−1.36813e101	−0.0686547
$924$	1.33433e102	0.645032
$925$	−2.38404e102	−1.11026
$926$	−2.34542e101	−0.105230
$927$	1.05437e102	0.455765
$928$	−1.72103e102	−0.716776
$929$	−1.99813e101	−0.0801831	−0.0400915	−	0.999196i	$-0.512765\pi$
$929$	−1.99813e101	−0.0801831	−0.0400915	+	0.999196i	$0.512765\pi$
$930$	−1.78658e101	−0.0690814
$931$	9.67137e101	0.360350
$932$	4.00939e102	1.43956
$933$	2.76786e102	0.957697
$934$	6.25904e101	0.208709
$935$	2.50740e101	0.0805791
$936$	−4.33822e100	−0.0134368
$937$	3.37707e101	0.100815	0.0504073	−	0.998729i	$-0.483948\pi$
$937$	3.37707e101	0.100815	0.0504073	+	0.998729i	$0.483948\pi$
$938$	−4.96357e102	−1.42822
$939$	−2.87231e102	−0.796651
$940$	−2.93404e101	−0.0784431
$941$	−6.86980e102	−1.77053	−0.885263	−	0.465092i	$-0.846021\pi$
$941$	−6.86980e102	−1.77053	−0.885263	+	0.465092i	$0.846021\pi$
$942$	5.86188e102	1.45640
$943$	3.81006e102	0.912595
$944$	8.37987e102	1.93510
$945$	1.12632e101	0.0250765
$946$	2.98962e102	0.641758
$947$	−2.76001e102	−0.571264	−0.285632	−	0.958339i	$-0.592203\pi$
$947$	−2.76001e102	−0.571264	−0.285632	+	0.958339i	$0.592203\pi$
$948$	4.04412e102	0.807117
$949$	−6.30089e101	−0.121260
$950$	2.53304e102	0.470087
$951$	9.84546e101	0.176201
$952$	2.33077e102	0.402276
$953$	−7.19441e102	−1.19754	−0.598770	−	0.800921i	$-0.704344\pi$
$953$	−7.19441e102	−1.19754	−0.598770	+	0.800921i	$0.704344\pi$
$954$	−3.03359e102	−0.487010
$955$	−8.14569e101	−0.126128
$956$	−5.83684e102	−0.871726
$957$	−2.52247e102	−0.363382
$958$	−7.55366e102	−1.04966
$959$	−5.99320e102	−0.803373
$960$	−1.71727e101	−0.0222066
$961$	−2.18605e101	−0.0272711
$962$	1.41337e102	0.170104
$963$	−4.85370e102	−0.563593
$964$	−6.70333e102	−0.750988
$965$	−4.26576e101	−0.0461110
$966$	−1.50946e103	−1.57438
$967$	−4.44192e102	−0.447051	−0.223526	−	0.974698i	$-0.571757\pi$
$967$	−4.44192e102	−0.447051	−0.223526	+	0.974698i	$0.571757\pi$
$968$	5.60564e101	0.0544409
$969$	−1.80447e102	−0.169114
$970$	−2.30153e102	−0.208157
$971$	2.98116e102	0.260209	0.130105	−	0.991500i	$-0.458469\pi$
$971$	2.98116e102	0.260209	0.130105	+	0.991500i	$0.458469\pi$
$972$	−5.59450e101	−0.0471276
$973$	2.43288e103	1.97800
$974$	1.09580e103	0.859896
$975$	−8.71732e101	−0.0660273
$976$	1.76473e103	1.29021
$977$	1.18061e103	0.833189	0.416594	−	0.909093i	$-0.363224\pi$
$977$	1.18061e103	0.833189	0.416594	+	0.909093i	$0.363224\pi$
$978$	8.71062e102	0.593415
$979$	−1.18713e103	−0.780722
$980$	−1.06696e102	−0.0677406
$981$	3.67495e102	0.225253
$982$	−1.74421e102	−0.103217
$983$	1.48589e103	0.848969	0.424484	−	0.905435i	$-0.360455\pi$
$983$	1.48589e103	0.848969	0.424484	+	0.905435i	$0.360455\pi$
$984$	2.28056e102	0.125809
$985$	2.28534e102	0.121731
$986$	1.21987e103	0.627421
$987$	−1.90618e103	−0.946723
$988$	−6.35991e101	−0.0305026
$989$	−1.43232e103	−0.663387
$990$	−9.71975e101	−0.0434751
$991$	2.83885e103	1.22631	0.613157	−	0.789961i	$-0.289899\pi$
$991$	2.83885e103	1.22631	0.613157	+	0.789961i	$0.289899\pi$
$992$	2.89430e103	1.20751
$993$	1.81813e103	0.732616
$994$	−2.84937e103	−1.10897
$995$	3.71829e102	0.139781
$996$	−1.31412e100	−0.000477185 0
$997$	−2.06981e102	−0.0726018	−0.0363009	−	0.999341i	$-0.511557\pi$
$997$	−2.06981e102	−0.0726018	−0.0363009	+	0.999341i	$0.511557\pi$
$998$	−9.21923e101	−0.0312386
$999$	−6.58342e102	−0.215497

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3.70.a.a.1.2	✓	6
3.2	odd	2		9.70.a.d.1.5		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
3.70.a.a.1.2	✓	6	1.1	even	1	trivial
9.70.a.d.1.5		6	3.2	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:	\( N \)	\(=\)	\( 3 \)
Weight:	\( k \)	\(=\)	\( 70 \)
Character orbit:	\([\chi]\)	\(=\)	3.a (trivial)

\(f(q)\)	\(=\)	\(q-3.19993e10 q^{2} -1.66772e16 q^{3} +4.33658e20 q^{4} -1.19891e23 q^{5} +5.33658e26 q^{6} +2.02540e29 q^{7} +5.01228e30 q^{8} +2.78128e32 q^{9} +O(q^{10})\)	\(q-3.19993e10 q^{2} -1.66772e16 q^{3} +4.33658e20 q^{4} -1.19891e23 q^{5} +5.33658e26 q^{6} +2.02540e29 q^{7} +5.01228e30 q^{8} +2.78128e32 q^{9} +3.83642e33 q^{10} -9.10928e35 q^{11} -7.23220e36 q^{12} -3.11194e37 q^{13} -6.48112e39 q^{14} +1.99944e39 q^{15} -4.16376e41 q^{16} +2.29590e42 q^{17} -8.89991e42 q^{18} +4.71273e43 q^{19} -5.19916e43 q^{20} -3.37779e45 q^{21} +2.91490e46 q^{22} -1.39652e47 q^{23} -8.35908e46 q^{24} -1.67969e48 q^{25} +9.95797e47 q^{26} -4.63840e48 q^{27} +8.78330e49 q^{28} -1.66042e50 q^{29} -6.39806e49 q^{30} +2.79238e51 q^{31} +1.03650e52 q^{32} +1.51917e52 q^{33} -7.34673e52 q^{34} -2.42826e52 q^{35} +1.20613e53 q^{36} +1.41933e54 q^{37} -1.50804e54 q^{38} +5.18983e53 q^{39} -6.00926e53 q^{40} -2.72825e55 q^{41} +1.08087e56 q^{42} +1.02563e56 q^{43} -3.95032e56 q^{44} -3.33450e55 q^{45} +4.46877e57 q^{46} +5.64329e57 q^{47} +6.94398e57 q^{48} +2.05218e58 q^{49} +5.37489e58 q^{50} -3.82892e58 q^{51} -1.34952e58 q^{52} +3.40856e59 q^{53} +1.48425e59 q^{54} +1.09212e59 q^{55} +1.01519e60 q^{56} -7.85951e59 q^{57} +5.31324e60 q^{58} -2.01257e61 q^{59} +8.67074e59 q^{60} -4.23832e61 q^{61} -8.93541e61 q^{62} +5.63320e61 q^{63} -8.58879e61 q^{64} +3.73092e60 q^{65} -4.86124e62 q^{66} +7.65850e62 q^{67} +9.95638e62 q^{68} +2.32901e63 q^{69} +7.77026e62 q^{70} +4.39641e63 q^{71} +1.39406e63 q^{72} +2.02475e64 q^{73} -4.54176e64 q^{74} +2.80125e64 q^{75} +2.04372e64 q^{76} -1.84499e65 q^{77} -1.66071e64 q^{78} -5.59183e65 q^{79} +4.99196e64 q^{80} +7.73554e64 q^{81} +8.73019e65 q^{82} +1.81704e63 q^{83} -1.46481e66 q^{84} -2.75257e65 q^{85} -3.28195e66 q^{86} +2.76912e66 q^{87} -4.56583e66 q^{88} +1.30321e67 q^{89} +1.06702e66 q^{90} -6.30290e66 q^{91} -6.05614e67 q^{92} -4.65690e67 q^{93} -1.80581e68 q^{94} -5.65013e66 q^{95} -1.72859e68 q^{96} -5.99916e68 q^{97} -6.56683e68 q^{98} -2.53355e68 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 869363388 q^{2} - 10\!\cdots\!14 q^{3}+ \cdots + 16\!\cdots\!66 q^{9}+O(q^{10}) \) 6 * q - 869363388 * q^2 - 100063090197999414 * q^3 + 1371216641348494011408 * q^4 + 536749102286059793452020 * q^5 + 14498531184713726896175772 * q^6 - 165486212832272947603119602016 * q^7 + 29031977276772288550932250437696 * q^8 + 1668770336662161067543714657390566 * q^9	\( 6 q - 869363388 q^{2} - 10\!\cdots\!14 q^{3}+ \cdots - 53\!\cdots\!36 q^{99}+O(q^{100}) \) 6 * q - 869363388 * q^2 - 100063090197999414 * q^3 + 1371216641348494011408 * q^4 + 536749102286059793452020 * q^5 + 14498531184713726896175772 * q^6 - 165486212832272947603119602016 * q^7 + 29031977276772288550932250437696 * q^8 + 1668770336662161067543714657390566 * q^9 - 30539001465788028222087378612341640 * q^10 - 1920537066516616187668579962543158376 * q^11 - 22868029077375361513671619126882219152 * q^12 - 47217968885374199615397355356796191852 * q^13 + 7064585334174201405371837809050003141312 * q^14 - 8951462305957535762539464569043499519380 * q^15 + 377157429568235813937466329721859576398080 * q^16 - 5058270084832851177273994934925110056607412 * q^17 - 241794638945752826180250102109053616166268 * q^18 - 65818466266910893781669604806057906253992088 * q^19 - 74276832342140585406878490976963545328073760 * q^20 + 2759843640193509337740927488460262535180203104 * q^21 - 57200945629382567456443201741175335542976506864 * q^22 - 51318359662817614748704757772348805853962165488 * q^23 - 484171560145322484473355383995534830167508585024 * q^24 + 1351900008806516831015099778033783730620565906650 * q^25 - 16207493799167654397027294571148058082290306700488 * q^26 - 27830386119528611875968901007343548725913806188054 * q^27 + 121390433570468044194114098496551362783272349932288 * q^28 + 785579239339018365983000259217156564097330312249124 * q^29 + 509304476371330630546739998356596576017896314633160 * q^30 + 6912833464261058549529914367563374193660948950153296 * q^31 + 36737392694691819442392877818076822209799633285776384 * q^32 + 32029145619242227636284505564240924042938191359531944 * q^33 + 253117449563254571066779054180560057695840514055176 * q^34 + 276611165060305397158461820821003699537527995207930560 * q^35 + 381374276036647353263390282147345081660028453185929488 * q^36 - 759040697498936685975105001963916849352981208607118396 * q^37 + 2103369059703889244990286400717050872850491394651970032 * q^38 + 787462646590588064894632608232796865789891597354595788 * q^39 - 32664751344775020838298315886208043642737757270980944000 * q^40 - 25768671104884673827847532722814331858226170126017093924 * q^41 - 117817373250822824537222457055662269520721648792989198528 * q^42 - 677055351038557514071054609066516734267888940905925188840 * q^43 + 238305524760672609941760876572355183014168119775154744384 * q^44 + 149285163354170121367980976931811340477842188257753607220 * q^45 + 8376385103625214805959746309869879529208374887220505747296 * q^46 + 7598599404092453023795535768684988784173129214818972342720 * q^47 - 6289922982288665238584151982726579281690322330718011787520 * q^48 + 39520658833284024797097689208298803008912245306300761939990 * q^49 - 28568855233568347359168873341651630916131610440562956535300 * q^50 + 84357689290745289159801421813736090901392081119475734009428 * q^51 - 841291935994679864415054059209490217537323675729185299370272 * q^52 - 449047684897777378052965016724937358227157858973850840458828 * q^53 + 4032453127703594497238226593730133400050584990603665094492 * q^54 + 2254548165992828810812926827082553754343205233701600459282640 * q^55 + 1641356236071085469964848605225791359818442190977904466652160 * q^56 + 1097666521126647756280461762493305085319303708198214764106072 * q^57 + 10854840022358605054892033620996887145323506082370467922396824 * q^58 + 9739940026219086244132886290748367338175220661414782584592728 * q^59 + 1238728229045548911290208746311830657587532274639907038129440 * q^60 - 59315134126314210963145084137204520506665661947323124957508780 * q^61 - 58284415626578488701665533854996023611020152283699473273044512 * q^62 - 46026413850176360961358753239584156335498095610944326498830176 * q^63 - 196087603577998032685001038699358078224720081884631691829178368 * q^64 - 368792752455446531625971790511790913672736652263934282973351720 * q^65 + 953950563653961367781459452317768129208925530496794989139829616 * q^66 + 1284404845637086838528947432298267008623636941858083561714308648 * q^67 - 1893312213205272549692225847826950804709005883992500832775643616 * q^68 + 855845608625648963144016144920672894915758664084152710799170672 * q^69 + 5651141511141393939253777145916410305809660448417857533217598080 * q^70 - 8028908380018744267365790936955359727729274918181835022662164368 * q^71 + 8074617082354583671186761526246370992341166934797564305786862656 * q^72 + 23917666927401813793494400679686156753046201104575562189407759612 * q^73 - 66571567863995212404482808802342117220480190894464062470316692648 * q^74 - 22545882086647115963110648728416884279973448838942742394179783850 * q^75 - 117137080475037691773181405327212499216032011801755896581802226752 * q^76 - 370001686623730076506835954110410638316696132431439489747825466752 * q^77 + 270295318984938200277077861249204534384356528838329715416149585672 * q^78 + 151166116158225305435965330589298930972238439200795534257670973040 * q^79 - 103132668838130690471303376617648857617362361028013189202842042880 * q^80 + 464132406087257065130090681062365209793088477541530761100710966726 * q^81 + 37460932835681010277915179679262266245084578260611880863596729448 * q^82 - 2199869100513279294476979658003407541858593100082068956813742116504 * q^83 - 2024450317255999993413036160714996242543447082962560389819327279872 * q^84 - 6491952514505341124698414891022457176579387500885906219615755954840 * q^85 - 23144659602467499127119271177953663689526653967585956674347553430256 * q^86 - 13101247713942660717783546201323542017367838371972839670487262335556 * q^87 - 65249604729672858795836798510445455460410612360663171240882606141184 * q^88 - 6686194196194507079670325678793857718304620226396138544648538601828 * q^89 - 8493763292898219695542584151776832427456280937959354979087550828040 * q^90 - 82097466714973722451927498084842810568687277892210020260162088564544 * q^91 + 4359811041243409323098555915712612735158801326895369127311689835904 * q^92 - 115286579743017176690026802480066668815283610415364196376484636361424 * q^93 - 560087180092970937289054350368454974923005535872515030885741348295552 * q^94 - 914644999797608066644469983517358223242420981276970458662113135611600 * q^95 - 612676173141378712760794918109470208907664831994025080010863094506496 * q^96 - 1193245591335854049619056301286742793562875638671855181199561300009332 * q^97 - 3639892838212491311414089259694594431294943863329296694030071739108188 * q^98 - 534155881177182136550108656986512933865188403627723332959024704380136 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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