LMFDB - Embedded newform 3.70.a.a.1.1

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			1.1
Root			$-9.72827e8$ 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)

$f(q)$	$=$	$q-3.51667e10 q^{2} -1.66772e16 q^{3} +6.46400e20 q^{4} +9.85410e23 q^{5} +5.86481e26 q^{6} -2.48063e29 q^{7} -1.97299e30 q^{8} +2.78128e32 q^{9} +O(q^{10})$	\(q-3.51667e10 q^{2} -1.66772e16 q^{3} +6.46400e20 q^{4} +9.85410e23 q^{5} +5.86481e26 q^{6} -2.48063e29 q^{7} -1.97299e30 q^{8} +2.78128e32 q^{9} -3.46536e34 q^{10} +1.61399e36 q^{11} -1.07801e37 q^{12} -1.81132e37 q^{13} +8.72356e39 q^{14} -1.64339e40 q^{15} -3.12184e41 q^{16} -2.66911e42 q^{17} -9.78085e42 q^{18} -1.74886e44 q^{19} +6.36969e44 q^{20} +4.13700e45 q^{21} -5.67588e46 q^{22} -1.67108e46 q^{23} +3.29039e46 q^{24} -7.23033e47 q^{25} +6.36982e47 q^{26} -4.63840e48 q^{27} -1.60348e50 q^{28} +4.55964e50 q^{29} +5.77924e50 q^{30} +2.05939e51 q^{31} +1.21431e52 q^{32} -2.69169e52 q^{33} +9.38637e52 q^{34} -2.44444e53 q^{35} +1.79782e53 q^{36} -1.25481e54 q^{37} +6.15017e54 q^{38} +3.02078e53 q^{39} -1.94420e54 q^{40} +2.09570e55 q^{41} -1.45484e56 q^{42} -5.15221e55 q^{43} +1.04329e57 q^{44} +2.74070e56 q^{45} +5.87663e56 q^{46} +7.23496e57 q^{47} +5.20634e57 q^{48} +4.10349e58 q^{49} +2.54267e58 q^{50} +4.45132e58 q^{51} -1.17084e58 q^{52} -6.23754e58 q^{53} +1.63117e59 q^{54} +1.59045e60 q^{55} +4.89426e59 q^{56} +2.91661e60 q^{57} -1.60348e61 q^{58} +7.35705e60 q^{59} -1.06228e61 q^{60} -2.83358e61 q^{61} -7.24220e61 q^{62} -6.89934e61 q^{63} -2.42752e62 q^{64} -1.78490e61 q^{65} +9.46577e62 q^{66} +9.29917e62 q^{67} -1.72531e63 q^{68} +2.78689e62 q^{69} +8.59629e63 q^{70} -4.20941e63 q^{71} -5.48744e62 q^{72} +1.66564e64 q^{73} +4.41274e64 q^{74} +1.20582e64 q^{75} -1.13046e65 q^{76} -4.00373e65 q^{77} -1.06231e64 q^{78} +3.60971e65 q^{79} -3.07629e65 q^{80} +7.73554e64 q^{81} -7.36988e65 q^{82} -3.04752e65 q^{83} +2.67415e66 q^{84} -2.63017e66 q^{85} +1.81186e66 q^{86} -7.60420e66 q^{87} -3.18439e66 q^{88} +1.81353e67 q^{89} -9.63815e66 q^{90} +4.49323e66 q^{91} -1.08019e67 q^{92} -3.43449e67 q^{93} -2.54430e68 q^{94} -1.72335e68 q^{95} -2.02513e68 q^{96} -1.57068e68 q^{97} -1.44306e69 q^{98} +4.48897e68 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−3.51667e10	−1.44743	−0.723713	−	0.690101i	$-0.757566\pi$
$2$	−3.51667e10	−1.44743	−0.723713	+	0.690101i	$0.757566\pi$
$3$	−1.66772e16	−0.577350
$3$	−1.66772e16	−0.577350
$4$	6.46400e20	1.09504
$5$	9.85410e23	0.757098	0.378549	−	0.925581i	$-0.376423\pi$
$5$	9.85410e23	0.757098	0.378549	+	0.925581i	$0.376423\pi$
$6$	5.86481e26	0.835672
$7$	−2.48063e29	−1.73253	−0.866264	−	0.499587i	$-0.833485\pi$
$7$	−2.48063e29	−1.73253	−0.866264	+	0.499587i	$0.833485\pi$
$8$	−1.97299e30	−0.137569
$9$	2.78128e32	0.333333
$10$	−3.46536e34	−1.09584
$11$	1.61399e36	1.90482	0.952411	−	0.304818i	$-0.0985956\pi$
$11$	1.61399e36	1.90482	0.952411	+	0.304818i	$0.0985956\pi$
$12$	−1.07801e37	−0.632224
$13$	−1.81132e37	−0.0671352	−0.0335676	−	0.999436i	$-0.510687\pi$
$13$	−1.81132e37	−0.0671352	−0.0335676	+	0.999436i	$0.510687\pi$
$14$	8.72356e39	2.50771
$15$	−1.64339e40	−0.437110
$16$	−3.12184e41	−0.895923
$17$	−2.66911e42	−0.945973	−0.472986	−	0.881070i	$-0.656824\pi$
$17$	−2.66911e42	−0.945973	−0.472986	+	0.881070i	$0.656824\pi$
$18$	−9.78085e42	−0.482476
$19$	−1.74886e44	−1.33585	−0.667923	−	0.744230i	$-0.732817\pi$
$19$	−1.74886e44	−1.33585	−0.667923	+	0.744230i	$0.732817\pi$
$20$	6.36969e44	0.829055
$21$	4.13700e45	1.00028
$22$	−5.67588e46	−2.75709
$23$	−1.67108e46	−0.175141	−0.0875703	−	0.996158i	$-0.527910\pi$
$23$	−1.67108e46	−0.175141	−0.0875703	+	0.996158i	$0.527910\pi$
$24$	3.29039e46	0.0794254
$25$	−7.23033e47	−0.426803
$26$	6.36982e47	0.0971732
$27$	−4.63840e48	−0.192450
$28$	−1.60348e50	−1.89719
$29$	4.55964e50	1.60768	0.803841	−	0.594844i	$-0.202786\pi$
$29$	4.55964e50	1.60768	0.803841	+	0.594844i	$0.202786\pi$
$30$	5.77924e50	0.632685
$31$	2.05939e51	0.727379	0.363690	−	0.931520i	$-0.381517\pi$
$31$	2.05939e51	0.727379	0.363690	+	0.931520i	$0.381517\pi$
$32$	1.21431e52	1.43435
$33$	−2.69169e52	−1.09975
$34$	9.38637e52	1.36923
$35$	−2.44444e53	−1.31169
$36$	1.79782e53	0.365015
$37$	−1.25481e54	−0.989960	−0.494980	−	0.868904i	$-0.664825\pi$
$37$	−1.25481e54	−0.989960	−0.494980	+	0.868904i	$0.664825\pi$
$38$	6.15017e54	1.93354
$39$	3.02078e53	0.0387605
$40$	−1.94420e54	−0.104153
$41$	2.09570e55	0.478945	0.239473	−	0.970903i	$-0.423025\pi$
$41$	2.09570e55	0.478945	0.239473	+	0.970903i	$0.423025\pi$
$42$	−1.45484e56	−1.44782
$43$	−5.15221e55	−0.227684	−0.113842	−	0.993499i	$-0.536316\pi$
$43$	−5.15221e55	−0.227684	−0.113842	+	0.993499i	$0.536316\pi$
$44$	1.04329e57	2.08586
$45$	2.74070e56	0.252366
$46$	5.87663e56	0.253503
$47$	7.23496e57	1.48614	0.743071	−	0.669213i	$-0.233368\pi$
$47$	7.23496e57	1.48614	0.743071	+	0.669213i	$0.233368\pi$
$48$	5.20634e57	0.517261
$49$	4.10349e58	2.00165
$50$	2.54267e58	0.617767
$51$	4.45132e58	0.546158
$52$	−1.17084e58	−0.0735160
$53$	−6.23754e58	−0.203000	−0.101500	−	0.994836i	$-0.532364\pi$
$53$	−6.23754e58	−0.203000	−0.101500	+	0.994836i	$0.532364\pi$
$54$	1.63117e59	0.278557
$55$	1.59045e60	1.44214
$56$	4.89426e59	0.238342
$57$	2.91661e60	0.771251
$58$	−1.60348e61	−2.32700
$59$	7.35705e60	0.591983	0.295992	−	0.955191i	$-0.404350\pi$
$59$	7.35705e60	0.591983	0.295992	+	0.955191i	$0.404350\pi$
$60$	−1.06228e61	−0.478655
$61$	−2.83358e61	−0.721866	−0.360933	−	0.932592i	$-0.617542\pi$
$61$	−2.83358e61	−0.721866	−0.360933	+	0.932592i	$0.617542\pi$
$62$	−7.24220e61	−1.05283
$63$	−6.89934e61	−0.577509
$64$	−2.42752e62	−1.18020
$65$	−1.78490e61	−0.0508279
$66$	9.46577e62	1.59181
$67$	9.29917e62	0.930815	0.465408	−	0.885097i	$-0.345908\pi$
$67$	9.29917e62	0.930815	0.465408	+	0.885097i	$0.345908\pi$
$68$	−1.72531e63	−1.03588
$69$	2.78689e62	0.101117
$70$	8.59629e63	1.89858
$71$	−4.20941e63	−0.569913	−0.284956	−	0.958540i	$-0.591979\pi$
$71$	−4.20941e63	−0.569913	−0.284956	+	0.958540i	$0.591979\pi$
$72$	−5.48744e62	−0.0458563
$73$	1.66564e64	0.864851	0.432426	−	0.901670i	$-0.357658\pi$
$73$	1.66564e64	0.864851	0.432426	+	0.901670i	$0.357658\pi$
$74$	4.41274e64	1.43289
$75$	1.20582e64	0.246415
$76$	−1.13046e65	−1.46281
$77$	−4.00373e65	−3.30016
$78$	−1.06231e64	−0.0561030
$79$	3.60971e65	1.22839	0.614196	−	0.789153i	$-0.289480\pi$
$79$	3.60971e65	1.22839	0.614196	+	0.789153i	$0.289480\pi$
$80$	−3.07629e65	−0.678301
$81$	7.73554e64	0.111111
$82$	−7.36988e65	−0.693238
$83$	−3.04752e65	−0.188692	−0.0943459	−	0.995539i	$-0.530076\pi$
$83$	−3.04752e65	−0.188692	−0.0943459	+	0.995539i	$0.530076\pi$
$84$	2.67415e66	1.09535
$85$	−2.63017e66	−0.716194
$86$	1.81186e66	0.329555
$87$	−7.60420e66	−0.928195
$88$	−3.18439e66	−0.262044
$89$	1.81353e67	1.01058	0.505289	−	0.862950i	$-0.331386\pi$
$89$	1.81353e67	1.01058	0.505289	+	0.862950i	$0.331386\pi$
$90$	−9.63815e66	−0.365281
$91$	4.49323e66	0.116314
$92$	−1.08019e67	−0.191787
$93$	−3.43449e67	−0.419953
$94$	−2.54430e68	−2.15108
$95$	−1.72335e68	−1.01137
$96$	−2.02513e68	−0.828123
$97$	−1.57068e68	−0.449223	−0.224612	−	0.974448i	$-0.572111\pi$
$97$	−1.57068e68	−0.449223	−0.224612	+	0.974448i	$0.572111\pi$
$98$	−1.44306e69	−2.89724
$99$	4.48897e68	0.634940
$100$	−4.67368e68	−0.467368
$101$	1.24634e69	0.884195	0.442098	−	0.896967i	$-0.354234\pi$
$101$	1.24634e69	0.884195	0.442098	+	0.896967i	$0.354234\pi$
$102$	−1.56538e69	−0.790523
$103$	−1.77478e69	−0.640117	−0.320059	−	0.947398i	$-0.603703\pi$
$103$	−1.77478e69	−0.640117	−0.320059	+	0.947398i	$0.603703\pi$
$104$	3.57372e67	0.00923571
$105$	4.07664e69	0.757306
$106$	2.19354e69	0.293827
$107$	−8.18632e69	−0.793137	−0.396569	−	0.918005i	$-0.629799\pi$
$107$	−8.18632e69	−0.793137	−0.396569	+	0.918005i	$0.629799\pi$
$108$	−2.99826e69	−0.210741
$109$	−3.44065e70	−1.75965	−0.879824	−	0.475300i	$-0.842340\pi$
$109$	−3.44065e70	−1.75965	−0.879824	+	0.475300i	$0.842340\pi$
$110$	−5.59307e70	−2.08739
$111$	2.09266e70	0.571553
$112$	7.74413e70	1.55221
$113$	−3.90110e70	−0.575415	−0.287707	−	0.957718i	$-0.592893\pi$
$113$	−3.90110e70	−0.575415	−0.287707	+	0.957718i	$0.592893\pi$
$114$	−1.02568e71	−1.11633
$115$	−1.64670e70	−0.132598
$116$	2.94735e71	1.76048
$117$	−5.03780e69	−0.0223784
$118$	−2.58723e71	−0.856852
$119$	6.62108e71	1.63892
$120$	3.24238e70	0.0601328
$121$	1.88702e72	2.62834
$122$	9.96476e71	1.04485
$123$	−3.49504e71	−0.276519
$124$	1.33119e72	0.796512
$125$	−2.38183e72	−1.08023
$126$	2.42627e72	0.835902
$127$	−1.98607e72	−0.520915	−0.260457	−	0.965485i	$-0.583873\pi$
$127$	−1.98607e72	−0.520915	−0.260457	+	0.965485i	$0.583873\pi$
$128$	1.36876e72	0.273895
$129$	8.59243e71	0.131453
$130$	6.27689e71	0.0735696
$131$	−1.09863e73	−0.988538	−0.494269	−	0.869309i	$-0.664564\pi$
$131$	−1.09863e73	−0.988538	−0.494269	+	0.869309i	$0.664564\pi$
$132$	−1.73991e73	−1.20427
$133$	4.33829e73	2.31439
$134$	−3.27021e73	−1.34729
$135$	−4.57072e72	−0.145703
$136$	5.26612e72	0.130136
$137$	4.56223e73	0.875624	0.437812	−	0.899067i	$-0.355754\pi$
$137$	4.56223e73	0.875624	0.437812	+	0.899067i	$0.355754\pi$
$138$	−9.80056e72	−0.146360
$139$	−4.56951e73	−0.531935	−0.265968	−	0.963982i	$-0.585691\pi$
$139$	−4.56951e73	−0.531935	−0.265968	+	0.963982i	$0.585691\pi$
$140$	−1.58009e74	−1.43636
$141$	−1.20659e74	−0.858024
$142$	1.48031e74	0.824907
$143$	−2.92346e73	−0.127881
$144$	−8.68271e73	−0.298641
$145$	4.49312e74	1.21717
$146$	−5.85749e74	−1.25181
$147$	−6.84346e74	−1.15565
$148$	−8.11107e74	−1.08405
$149$	−5.36784e74	−0.568687	−0.284344	−	0.958722i	$-0.591776\pi$
$149$	−5.36784e74	−0.568687	−0.284344	+	0.958722i	$0.591776\pi$
$150$	−4.24045e74	−0.356668
$151$	−9.42518e73	−0.0630355	−0.0315177	−	0.999503i	$-0.510034\pi$
$151$	−9.42518e73	−0.0630355	−0.0315177	+	0.999503i	$0.510034\pi$
$152$	3.45049e74	0.183771
$153$	−7.42355e74	−0.315324
$154$	1.40798e76	4.77673
$155$	2.02935e75	0.550697
$156$	1.95263e74	0.0424445
$157$	9.58865e75	1.67194	0.835968	−	0.548779i	$-0.184907\pi$
$157$	9.58865e75	1.67194	0.835968	+	0.548779i	$0.184907\pi$
$158$	−1.26941e76	−1.77801
$159$	1.04025e75	0.117202
$160$	1.19659e76	1.08594
$161$	4.14533e75	0.303436
$162$	−2.72033e75	−0.160825
$163$	−2.98521e76	−1.42726	−0.713630	−	0.700523i	$-0.752950\pi$
$163$	−2.98521e76	−1.42726	−0.713630	+	0.700523i	$0.752950\pi$
$164$	1.35466e76	0.524466
$165$	−2.65242e76	−0.832617
$166$	1.07171e76	0.273117
$167$	−7.51205e75	−0.155611	−0.0778055	−	0.996969i	$-0.524791\pi$
$167$	−7.51205e75	−0.155611	−0.0778055	+	0.996969i	$0.524791\pi$
$168$	−8.16225e75	−0.137607
$169$	−7.24652e76	−0.995493
$170$	9.24942e76	1.03664
$171$	−4.86408e76	−0.445282
$172$	−3.33039e76	−0.249323
$173$	−1.41214e77	−0.865539	−0.432770	−	0.901505i	$-0.642464\pi$
$173$	−1.41214e77	−0.865539	−0.432770	+	0.901505i	$0.642464\pi$
$174$	2.67415e77	1.34349
$175$	1.79358e77	0.739449
$176$	−5.03862e77	−1.70657
$177$	−1.22695e77	−0.341782
$178$	−6.37758e77	−1.46274
$179$	9.25676e77	1.74997	0.874983	−	0.484154i	$-0.160873\pi$
$179$	9.25676e77	1.74997	0.874983	+	0.484154i	$0.160873\pi$
$180$	1.77159e77	0.276352
$181$	−1.14474e78	−1.47502	−0.737509	−	0.675338i	$-0.763998\pi$
$181$	−1.14474e78	−1.47502	−0.737509	+	0.675338i	$0.763998\pi$
$182$	−1.58012e77	−0.168355
$183$	4.72561e77	0.416769
$184$	3.29702e76	0.0240939
$185$	−1.23650e78	−0.749496
$186$	1.20780e78	0.607851
$187$	−4.30793e78	−1.80191
$188$	4.67668e78	1.62739
$189$	1.15062e78	0.333425
$190$	6.06044e78	1.46388
$191$	5.34057e78	1.07631	0.538154	−	0.842847i	$-0.319122\pi$
$191$	5.34057e78	1.07631	0.538154	+	0.842847i	$0.319122\pi$
$192$	4.04842e78	0.681386
$193$	−1.01482e79	−1.42778	−0.713891	−	0.700257i	$-0.753069\pi$
$193$	−1.01482e79	−1.42778	−0.713891	+	0.700257i	$0.753069\pi$
$194$	5.52355e78	0.650218
$195$	2.97670e77	0.0293455
$196$	2.65249e79	2.19190
$197$	8.73930e78	0.605887	0.302944	−	0.953008i	$-0.402031\pi$
$197$	8.73930e78	0.605887	0.302944	+	0.953008i	$0.402031\pi$
$198$	−1.57862e79	−0.919030
$199$	−4.17904e78	−0.204477	−0.102239	−	0.994760i	$-0.532601\pi$
$199$	−4.17904e78	−0.204477	−0.102239	+	0.994760i	$0.532601\pi$
$200$	1.42654e78	0.0587149
$201$	−1.55084e79	−0.537406
$202$	−4.38295e79	−1.27981
$203$	−1.13108e80	−2.78535
$204$	2.87733e79	0.598066
$205$	2.06512e79	0.362608
$206$	6.24130e79	0.926523
$207$	−4.64775e78	−0.0583802
$208$	5.65465e78	0.0601479
$209$	−2.82265e80	−2.54455
$210$	−1.43362e80	−1.09614
$211$	2.57827e80	1.67334	0.836668	−	0.547710i	$-0.184500\pi$
$211$	2.57827e80	1.67334	0.836668	+	0.547710i	$0.184500\pi$
$212$	−4.03194e79	−0.222294
$213$	7.02011e79	0.329039
$214$	2.87886e80	1.14801
$215$	−5.07704e79	−0.172379
$216$	9.15151e78	0.0264751
$217$	−5.10860e80	−1.26020
$218$	1.20996e81	2.54696
$219$	−2.77781e80	−0.499322
$220$	1.02806e81	1.57920
$221$	4.83462e79	0.0635080
$222$	−7.35921e80	−0.827282
$223$	−5.16234e80	−0.496969	−0.248484	−	0.968636i	$-0.579932\pi$
$223$	−5.16234e80	−0.496969	−0.248484	+	0.968636i	$0.579932\pi$
$224$	−3.01226e81	−2.48505
$225$	−2.01096e80	−0.142268
$226$	1.37189e81	0.832870
$227$	3.43237e81	1.78938	0.894690	−	0.446688i	$-0.147397\pi$
$227$	3.43237e81	1.78938	0.894690	+	0.446688i	$0.147397\pi$
$228$	1.88530e81	0.844554
$229$	−3.06168e81	−1.17933	−0.589666	−	0.807647i	$-0.700741\pi$
$229$	−3.06168e81	−1.17933	−0.589666	+	0.807647i	$0.700741\pi$
$230$	5.79089e80	0.191927
$231$	6.67709e81	1.90535
$232$	−8.99613e80	−0.221167
$233$	−1.13997e81	−0.241609	−0.120804	−	0.992676i	$-0.538547\pi$
$233$	−1.13997e81	−0.241609	−0.120804	+	0.992676i	$0.538547\pi$
$234$	1.77163e80	0.0323911
$235$	7.12941e81	1.12515
$236$	4.75559e81	0.648247
$237$	−6.01997e81	−0.709213
$238$	−2.32841e82	−2.37222
$239$	1.24558e82	1.09811	0.549054	−	0.835787i	$-0.314988\pi$
$239$	1.24558e82	1.09811	0.549054	+	0.835787i	$0.314988\pi$
$240$	5.13038e81	0.391617
$241$	−1.59128e82	−1.05234	−0.526172	−	0.850378i	$-0.676373\pi$
$241$	−1.59128e82	−1.05234	−0.526172	+	0.850378i	$0.676373\pi$
$242$	−6.63604e82	−3.80433
$243$	−1.29007e81	−0.0641500
$244$	−1.83163e82	−0.790474
$245$	4.04362e82	1.51545
$246$	1.22909e82	0.400241
$247$	3.16776e81	0.0896823
$248$	−4.06316e81	−0.100065
$249$	5.08241e81	0.108941
$250$	8.37612e82	1.56355
$251$	−4.97759e82	−0.809609	−0.404805	−	0.914403i	$-0.632660\pi$
$251$	−4.97759e82	−0.809609	−0.404805	+	0.914403i	$0.632660\pi$
$252$	−4.45973e82	−0.632398
$253$	−2.69711e82	−0.333611
$254$	6.98436e82	0.753986
$255$	4.38638e82	0.413495
$256$	9.51607e82	0.783753
$257$	7.89050e82	0.568083	0.284042	−	0.958812i	$-0.408325\pi$
$257$	7.89050e82	0.568083	0.284042	+	0.958812i	$0.408325\pi$
$258$	−3.02167e82	−0.190269
$259$	3.11272e83	1.71513
$260$	−1.15376e82	−0.0556587
$261$	1.26817e83	0.535894
$262$	3.86353e83	1.43084
$263$	−3.66249e83	−1.18933	−0.594666	−	0.803973i	$-0.702716\pi$
$263$	−3.66249e83	−1.18933	−0.594666	+	0.803973i	$0.702716\pi$
$264$	5.31067e82	0.151291
$265$	−6.14653e82	−0.153691
$266$	−1.52563e84	−3.34991
$267$	−3.02446e83	−0.583457
$268$	6.01098e83	1.01928
$269$	−1.36900e83	−0.204151	−0.102075	−	0.994777i	$-0.532548\pi$
$269$	−1.36900e83	−0.204151	−0.102075	+	0.994777i	$0.532548\pi$
$270$	1.60737e83	0.210895
$271$	2.50816e83	0.289677	0.144839	−	0.989455i	$-0.453734\pi$
$271$	2.50816e83	0.289677	0.144839	+	0.989455i	$0.453734\pi$
$272$	8.33252e83	0.847519
$273$	−7.49344e82	−0.0671537
$274$	−1.60439e84	−1.26740
$275$	−1.16697e84	−0.812984
$276$	1.80144e83	0.110728
$277$	−3.58455e83	−0.194483	−0.0972416	−	0.995261i	$-0.531002\pi$
$277$	−3.58455e83	−0.194483	−0.0972416	+	0.995261i	$0.531002\pi$
$278$	1.60694e84	0.769937
$279$	5.72776e83	0.242460
$280$	4.82286e83	0.180448
$281$	−2.22558e84	−0.736336	−0.368168	−	0.929759i	$-0.620015\pi$
$281$	−2.22558e84	−0.736336	−0.368168	+	0.929759i	$0.620015\pi$
$282$	4.24317e84	1.24193
$283$	−3.91943e84	−1.01529	−0.507646	−	0.861566i	$-0.669484\pi$
$283$	−3.91943e84	−1.01529	−0.507646	+	0.861566i	$0.669484\pi$
$284$	−2.72096e84	−0.624079
$285$	2.87406e84	0.583912
$286$	1.02809e84	0.185098
$287$	−5.19866e84	−0.829786
$288$	3.37734e84	0.478117
$289$	−8.37001e83	−0.105136
$290$	−1.58008e85	−1.76177
$291$	2.61945e84	0.259359
$292$	1.07667e85	0.947050
$293$	3.62772e84	0.283597	0.141798	−	0.989896i	$-0.454712\pi$
$293$	3.62772e84	0.283597	0.141798	+	0.989896i	$0.454712\pi$
$294$	2.40662e85	1.67272
$295$	7.24971e84	0.448189
$296$	2.47572e84	0.136188
$297$	−7.48635e84	−0.366583
$298$	1.88769e85	0.823133
$299$	3.02686e83	0.0117581
$300$	7.79439e84	0.269835
$301$	1.27807e85	0.394468
$302$	3.31452e84	0.0912392
$303$	−2.07854e85	−0.510490
$304$	5.45966e85	1.19682
$305$	−2.79224e85	−0.546523
$306$	2.61062e85	0.456409
$307$	2.34344e85	0.366083	0.183041	−	0.983105i	$-0.441406\pi$
$307$	2.34344e85	0.366083	0.183041	+	0.983105i	$0.441406\pi$
$308$	−2.58801e86	−3.61381
$309$	2.95983e85	0.369572
$310$	−7.13654e85	−0.797093
$311$	4.27294e85	0.427064	0.213532	−	0.976936i	$-0.431503\pi$
$311$	4.27294e85	0.427064	0.213532	+	0.976936i	$0.431503\pi$
$312$	−5.95996e83	−0.00533224
$313$	−9.90788e85	−0.793782	−0.396891	−	0.917866i	$-0.629911\pi$
$313$	−9.90788e85	−0.793782	−0.396891	+	0.917866i	$0.629911\pi$
$314$	−3.37201e86	−2.42000
$315$	−6.79868e85	−0.437231
$316$	2.33331e86	1.34514
$317$	−1.84192e86	−0.952195	−0.476097	−	0.879393i	$-0.657949\pi$
$317$	−1.84192e86	−0.952195	−0.476097	+	0.879393i	$0.657949\pi$
$318$	−3.65820e85	−0.169641
$319$	7.35924e86	3.06235
$320$	−2.39210e86	−0.893523
$321$	1.36525e86	0.457918
$322$	−1.45778e86	−0.439201
$323$	4.66791e86	1.26367
$324$	5.00025e85	0.121672
$325$	1.30965e85	0.0286535
$326$	1.04980e87	2.06585
$327$	5.73803e86	1.01593
$328$	−4.13479e85	−0.0658880
$329$	−1.79473e87	−2.57478
$330$	9.32766e86	1.20515
$331$	−7.14079e86	−0.831152	−0.415576	−	0.909558i	$-0.636420\pi$
$331$	−7.14079e86	−0.831152	−0.415576	+	0.909558i	$0.636420\pi$
$332$	−1.96992e86	−0.206626
$333$	−3.48997e86	−0.329987
$334$	2.64174e86	0.225235
$335$	9.16349e86	0.704718
$336$	−1.29150e87	−0.896169
$337$	−1.37501e87	−0.861139	−0.430570	−	0.902557i	$-0.641687\pi$
$337$	−1.37501e87	−0.861139	−0.430570	+	0.902557i	$0.641687\pi$
$338$	2.54836e87	1.44090
$339$	6.50594e86	0.332216
$340$	−1.70014e87	−0.784263
$341$	3.32385e87	1.38553
$342$	1.71054e87	0.644513
$343$	−5.09382e87	−1.73539
$344$	1.01653e86	0.0313222
$345$	2.74623e86	0.0765558
$346$	4.96602e87	1.25280
$347$	−6.60515e87	−1.50840	−0.754199	−	0.656646i	$-0.771975\pi$
$347$	−6.60515e87	−1.50840	−0.754199	+	0.656646i	$0.771975\pi$
$348$	−4.91535e87	−1.01641
$349$	−5.58686e87	−1.04638	−0.523191	−	0.852215i	$-0.675259\pi$
$349$	−5.58686e87	−1.04638	−0.523191	+	0.852215i	$0.675259\pi$
$350$	−6.30742e87	−1.07030
$351$	8.40163e85	0.0129202
$352$	1.95989e88	2.73218
$353$	1.74105e86	0.0220081	0.0110041	−	0.999939i	$-0.496497\pi$
$353$	1.74105e86	0.0220081	0.0110041	+	0.999939i	$0.496497\pi$
$354$	4.31477e87	0.494704
$355$	−4.14800e87	−0.431479
$356$	1.17227e88	1.10663
$357$	−1.10421e88	−0.946233
$358$	−3.25530e88	−2.53295
$359$	−8.95828e87	−0.633091	−0.316545	−	0.948577i	$-0.602523\pi$
$359$	−8.95828e87	−0.633091	−0.316545	+	0.948577i	$0.602523\pi$
$360$	−5.40738e86	−0.0347177
$361$	1.34457e88	0.784486
$362$	4.02568e88	2.13498
$363$	−3.14702e88	−1.51748
$364$	2.90442e87	0.127368
$365$	1.64133e88	0.654777
$366$	−1.66184e88	−0.603243
$367$	2.15946e88	0.713455	0.356727	−	0.934209i	$-0.383893\pi$
$367$	2.15946e88	0.713455	0.356727	+	0.934209i	$0.383893\pi$
$368$	5.21683e87	0.156912
$369$	5.82874e87	0.159648
$370$	4.34836e88	1.08484
$371$	1.54730e88	0.351703
$372$	−2.22005e88	−0.459866
$373$	8.52861e87	0.161036	0.0805182	−	0.996753i	$-0.474343\pi$
$373$	8.52861e87	0.161036	0.0805182	+	0.996753i	$0.474343\pi$
$374$	1.51495e89	2.60813
$375$	3.97223e88	0.623671
$376$	−1.42745e88	−0.204447
$377$	−8.25899e87	−0.107932
$378$	−4.04634e88	−0.482608
$379$	−2.00718e88	−0.218541	−0.109271	−	0.994012i	$-0.534852\pi$
$379$	−2.00718e88	−0.218541	−0.109271	+	0.994012i	$0.534852\pi$
$380$	−1.11397e89	−1.10749
$381$	3.31221e88	0.300750
$382$	−1.87810e89	−1.55788
$383$	−1.82024e89	−1.37966	−0.689829	−	0.723973i	$-0.742314\pi$
$383$	−1.82024e89	−1.37966	−0.689829	+	0.723973i	$0.742314\pi$
$384$	−2.28271e88	−0.158133
$385$	−3.94531e89	−2.49854
$386$	3.56879e89	2.06661
$387$	−1.43298e88	−0.0758945
$388$	−1.01529e89	−0.491919
$389$	−5.65241e88	−0.250595	−0.125298	−	0.992119i	$-0.539989\pi$
$389$	−5.65241e88	−0.250595	−0.125298	+	0.992119i	$0.539989\pi$
$390$	−1.04681e88	−0.0424754
$391$	4.46029e88	0.165678
$392$	−8.09614e88	−0.275365
$393$	1.83221e89	0.570733
$394$	−3.07332e89	−0.876977
$395$	3.55704e89	0.930013
$396$	2.90167e89	0.695288
$397$	3.41051e89	0.749113	0.374556	−	0.927204i	$-0.377795\pi$
$397$	3.41051e89	0.749113	0.374556	+	0.927204i	$0.377795\pi$
$398$	1.46963e89	0.295966
$399$	−7.23504e89	−1.33621
$400$	2.25719e89	0.382383
$401$	−7.25201e88	−0.112714	−0.0563569	−	0.998411i	$-0.517948\pi$
$401$	−7.25201e88	−0.112714	−0.0563569	+	0.998411i	$0.517948\pi$
$402$	5.45379e89	0.777856
$403$	−3.73023e88	−0.0488327
$404$	8.05632e89	0.968233
$405$	7.62268e88	0.0841219
$406$	3.97763e90	4.03159
$407$	−2.02525e90	−1.88570
$408$	−8.78241e88	−0.0751343
$409$	−1.77734e90	−1.39738	−0.698692	−	0.715422i	$-0.746234\pi$
$409$	−1.77734e90	−1.39738	−0.698692	+	0.715422i	$0.746234\pi$
$410$	−7.26236e89	−0.524849
$411$	−7.60852e89	−0.505542
$412$	−1.14722e90	−0.700957
$413$	−1.82501e90	−1.02563
$414$	1.63446e89	0.0845010
$415$	−3.00306e89	−0.142858
$416$	−2.19951e89	−0.0962954
$417$	7.62065e89	0.307113
$418$	9.92634e90	3.68305
$419$	−4.67577e89	−0.159760	−0.0798802	−	0.996804i	$-0.525454\pi$
$419$	−4.67577e89	−0.159760	−0.0798802	+	0.996804i	$0.525454\pi$
$420$	2.63514e90	0.829283
$421$	−4.80425e90	−1.39281	−0.696407	−	0.717647i	$-0.745219\pi$
$421$	−4.80425e90	−1.39281	−0.696407	+	0.717647i	$0.745219\pi$
$422$	−9.06691e90	−2.42203
$423$	2.01225e90	0.495381
$424$	1.23066e89	0.0279265
$425$	1.92985e90	0.403744
$426$	−2.46874e90	−0.476260
$427$	7.02907e90	1.25065
$428$	−5.29163e90	−0.868520
$429$	4.87551e89	0.0738319
$430$	1.78543e90	0.249505
$431$	−9.17368e90	−1.18325	−0.591627	−	0.806212i	$-0.701514\pi$
$431$	−9.17368e90	−1.18325	−0.591627	+	0.806212i	$0.701514\pi$
$432$	1.44803e90	0.172420
$433$	−1.46631e91	−1.61211	−0.806053	−	0.591843i	$-0.798400\pi$
$433$	−1.46631e91	−1.61211	−0.806053	+	0.591843i	$0.798400\pi$
$434$	1.79652e91	1.82405
$435$	−7.49326e90	−0.702734
$436$	−2.22403e91	−1.92689
$437$	2.92249e90	0.233961
$438$	9.76864e90	0.722732
$439$	−4.90165e90	−0.335209	−0.167605	−	0.985854i	$-0.553603\pi$
$439$	−4.90165e90	−0.335209	−0.167605	+	0.985854i	$0.553603\pi$
$440$	−3.13793e90	−0.198393
$441$	1.14130e91	0.667217
$442$	−1.70017e90	−0.0919232
$443$	−1.18252e91	−0.591396	−0.295698	−	0.955281i	$-0.595552\pi$
$443$	−1.18252e91	−0.591396	−0.295698	+	0.955281i	$0.595552\pi$
$444$	1.35270e91	0.625876
$445$	1.78707e91	0.765105
$446$	1.81543e91	0.719326
$447$	8.95205e90	0.328332
$448$	6.02179e91	2.04472
$449$	2.24200e91	0.704916	0.352458	−	0.935828i	$-0.385346\pi$
$449$	2.24200e91	0.704916	0.352458	+	0.935828i	$0.385346\pi$
$450$	7.07188e90	0.205922
$451$	3.38245e91	0.912305
$452$	−2.52167e91	−0.630104
$453$	1.57185e90	0.0363935
$454$	−1.20705e92	−2.59000
$455$	4.42767e90	0.0880607
$456$	−5.75444e90	−0.106100
$457$	−9.55157e90	−0.163292	−0.0816462	−	0.996661i	$-0.526018\pi$
$457$	−9.55157e90	−0.163292	−0.0816462	+	0.996661i	$0.526018\pi$
$458$	1.07669e92	1.70700
$459$	1.23804e91	0.182053
$460$	−1.06443e91	−0.145201
$461$	1.72349e91	0.218136	0.109068	−	0.994034i	$-0.465213\pi$
$461$	1.72349e91	0.218136	0.109068	+	0.994034i	$0.465213\pi$
$462$	−2.34811e92	−2.75785
$463$	1.25648e92	1.36966	0.684829	−	0.728704i	$-0.259877\pi$
$463$	1.25648e92	1.36966	0.684829	+	0.728704i	$0.259877\pi$
$464$	−1.42345e92	−1.44036
$465$	−3.38438e91	−0.317945
$466$	4.00888e91	0.349711
$467$	1.32393e92	1.07259	0.536293	−	0.844032i	$-0.319824\pi$
$467$	1.32393e92	1.07259	0.536293	+	0.844032i	$0.319824\pi$
$468$	−3.25643e90	−0.0245053
$469$	−2.30678e92	−1.61266
$470$	−2.50718e92	−1.62858
$471$	−1.59912e92	−0.965292
$472$	−1.45154e91	−0.0814384
$473$	−8.31563e91	−0.433697
$474$	2.11702e92	1.02653
$475$	1.26449e92	0.570144
$476$	4.27986e92	1.79469
$477$	−1.73484e91	−0.0676666
$478$	−4.38030e92	−1.58943
$479$	2.95780e92	0.998604	0.499302	−	0.866428i	$-0.333590\pi$
$479$	2.95780e92	0.998604	0.499302	+	0.866428i	$0.333590\pi$
$480$	−1.99558e92	−0.626970
$481$	2.27286e91	0.0664611
$482$	5.59599e92	1.52319
$483$	−6.91325e91	−0.175189
$484$	1.21977e93	2.87815
$485$	−1.54776e92	−0.340106
$486$	4.53675e91	0.0928525
$487$	1.75651e92	0.334889	0.167444	−	0.985882i	$-0.446449\pi$
$487$	1.75651e92	0.334889	0.167444	+	0.985882i	$0.446449\pi$
$488$	5.59063e91	0.0993062
$489$	4.97849e92	0.824029
$490$	−1.42201e93	−2.19350
$491$	1.72108e92	0.247451	0.123726	−	0.992316i	$-0.460516\pi$
$491$	1.72108e92	0.247451	0.123726	+	0.992316i	$0.460516\pi$
$492$	−2.25919e92	−0.302801
$493$	−1.21702e93	−1.52082
$494$	−1.11399e92	−0.129809
$495$	4.42348e92	0.480712
$496$	−6.42909e92	−0.651676
$497$	1.04420e93	0.987389
$498$	−1.78732e92	−0.157684
$499$	−7.93614e91	−0.0653342	−0.0326671	−	0.999466i	$-0.510400\pi$
$499$	−7.93614e91	−0.0653342	−0.0326671	+	0.999466i	$0.510400\pi$
$500$	−1.53962e93	−1.18290
$501$	1.25280e92	0.0898420
$502$	1.75045e93	1.17185
$503$	3.05600e92	0.191011	0.0955055	−	0.995429i	$-0.469553\pi$
$503$	3.05600e92	0.191011	0.0955055	+	0.995429i	$0.469553\pi$
$504$	1.36123e92	0.0794473
$505$	1.22815e93	0.669422
$506$	9.48485e92	0.482878
$507$	1.20852e93	0.574748
$508$	−1.28380e93	−0.570425
$509$	2.08088e93	0.863940	0.431970	−	0.901888i	$-0.357819\pi$
$509$	2.08088e93	0.863940	0.431970	+	0.901888i	$0.357819\pi$
$510$	−1.54254e93	−0.598503
$511$	−4.13183e93	−1.49838
$512$	−4.15446e93	−1.40832
$513$	8.11192e92	0.257084
$514$	−2.77483e93	−0.822259
$515$	−1.74888e93	−0.484631
$516$	5.55415e92	0.143947
$517$	1.16772e94	2.83083
$518$	−1.09464e94	−2.48253
$519$	2.35505e93	0.499719
$520$	3.52158e91	0.00699233
$521$	−2.60350e93	−0.483788	−0.241894	−	0.970303i	$-0.577769\pi$
$521$	−2.60350e93	−0.483788	−0.241894	+	0.970303i	$0.577769\pi$
$522$	−4.45972e93	−0.775667
$523$	6.33071e93	1.03073	0.515364	−	0.856971i	$-0.327657\pi$
$523$	6.33071e93	1.03073	0.515364	+	0.856971i	$0.327657\pi$
$524$	−7.10157e93	−1.08249
$525$	−2.99119e93	−0.426921
$526$	1.28798e94	1.72147
$527$	−5.49675e93	−0.688081
$528$	8.40300e93	0.985290
$529$	−8.82451e93	−0.969326
$530$	2.16153e93	0.222456
$531$	2.04620e93	0.197328
$532$	2.80427e94	2.53436
$533$	−3.79599e92	−0.0321541
$534$	1.06360e94	0.844511
$535$	−8.06688e93	−0.600482
$536$	−1.83472e93	−0.128051
$537$	−1.54377e94	−1.01034
$538$	4.81433e93	0.295493
$539$	6.62301e94	3.81279
$540$	−2.95451e93	−0.159552
$541$	−1.31637e94	−0.666916	−0.333458	−	0.942765i	$-0.608216\pi$
$541$	−1.31637e94	−0.666916	−0.333458	+	0.942765i	$0.608216\pi$
$542$	−8.82035e93	−0.419286
$543$	1.90911e94	0.851602
$544$	−3.24113e94	−1.35686
$545$	−3.39045e94	−1.33223
$546$	2.63519e93	0.0972000
$547$	−3.81016e94	−1.31941	−0.659705	−	0.751524i	$-0.729319\pi$
$547$	−3.81016e94	−1.31941	−0.659705	+	0.751524i	$0.729319\pi$
$548$	2.94902e94	0.958847
$549$	−7.88099e93	−0.240622
$550$	4.10385e94	1.17673
$551$	−7.97419e94	−2.14762
$552$	−5.49850e92	−0.0139106
$553$	−8.95436e94	−2.12822
$554$	1.26057e94	0.281500
$555$	2.06213e94	0.432722
$556$	−2.95373e94	−0.582493
$557$	−9.59178e94	−1.77785	−0.888925	−	0.458053i	$-0.848547\pi$
$557$	−9.59178e94	−1.77785	−0.888925	+	0.458053i	$0.848547\pi$
$558$	−2.01426e94	−0.350943
$559$	9.33231e92	0.0152856
$560$	7.63114e94	1.17518
$561$	7.18441e94	1.04033
$562$	7.82664e94	1.06579
$563$	9.96146e94	1.27580	0.637901	−	0.770118i	$-0.279803\pi$
$563$	9.96146e94	1.27580	0.637901	+	0.770118i	$0.279803\pi$
$564$	−7.79938e94	−0.939574
$565$	−3.84418e94	−0.435645
$566$	1.37833e95	1.46956
$567$	−1.91890e94	−0.192503
$568$	8.30512e93	0.0784022
$569$	1.54943e95	1.37657	0.688285	−	0.725441i	$-0.258364\pi$
$569$	1.54943e95	1.37657	0.688285	+	0.725441i	$0.258364\pi$
$570$	−1.01071e95	−0.845170
$571$	−1.09698e95	−0.863485	−0.431743	−	0.901997i	$-0.642101\pi$
$571$	−1.09698e95	−0.863485	−0.431743	+	0.901997i	$0.642101\pi$
$572$	−1.88973e94	−0.140035
$573$	−8.90657e94	−0.621407
$574$	1.82820e95	1.20105
$575$	1.20825e94	0.0747506
$576$	−6.75163e94	−0.393399
$577$	1.16611e94	0.0639989	0.0319995	−	0.999488i	$-0.489813\pi$
$577$	1.16611e94	0.0639989	0.0319995	+	0.999488i	$0.489813\pi$
$578$	2.94346e94	0.152176
$579$	1.69243e95	0.824330
$580$	2.90435e95	1.33286
$581$	7.55979e94	0.326914
$582$	−9.21173e94	−0.375403
$583$	−1.00674e95	−0.386679
$584$	−3.28628e94	−0.118977
$585$	−4.96430e93	−0.0169426
$586$	−1.27575e95	−0.410485
$587$	−1.39736e94	−0.0423929	−0.0211964	−	0.999775i	$-0.506748\pi$
$587$	−1.39736e94	−0.0423929	−0.0211964	+	0.999775i	$0.506748\pi$
$588$	−4.42361e95	−1.26549
$589$	−3.60160e95	−0.971667
$590$	−2.54948e95	−0.648720
$591$	−1.45747e95	−0.349809
$592$	3.91730e95	0.886927
$593$	3.88262e95	0.829351	0.414676	−	0.909969i	$-0.363895\pi$
$593$	3.88262e95	0.829351	0.414676	+	0.909969i	$0.363895\pi$
$594$	2.63270e95	0.530602
$595$	6.52448e95	1.24082
$596$	−3.46977e95	−0.622737
$597$	6.96945e94	0.118055
$598$	−1.06445e94	−0.0170190
$599$	−4.04711e95	−0.610829	−0.305414	−	0.952220i	$-0.598795\pi$
$599$	−4.04711e95	−0.610829	−0.305414	+	0.952220i	$0.598795\pi$
$600$	−2.37906e94	−0.0338990
$601$	−1.11377e96	−1.49839	−0.749197	−	0.662347i	$-0.769560\pi$
$601$	−1.11377e96	−1.49839	−0.749197	+	0.662347i	$0.769560\pi$
$602$	−4.49456e95	−0.570964
$603$	2.58636e95	0.310272
$604$	−6.09243e94	−0.0690266
$605$	1.85949e96	1.98991
$606$	7.30953e95	0.738897
$607$	−2.04295e96	−1.95096	−0.975481	−	0.220086i	$-0.929366\pi$
$607$	−2.04295e96	−1.95096	−0.975481	+	0.220086i	$0.929366\pi$
$608$	−2.12366e96	−1.91607
$609$	1.88632e96	1.60812
$610$	9.81938e95	0.791051
$611$	−1.31049e95	−0.0997724
$612$	−4.79858e95	−0.345294
$613$	−1.47296e96	−1.00185	−0.500926	−	0.865490i	$-0.667007\pi$
$613$	−1.47296e96	−1.00185	−0.500926	+	0.865490i	$0.667007\pi$
$614$	−8.24108e95	−0.529878
$615$	−3.44404e95	−0.209352
$616$	7.89931e95	0.453999
$617$	1.46292e96	0.795029	0.397514	−	0.917596i	$-0.369873\pi$
$617$	1.46292e96	0.795029	0.397514	+	0.917596i	$0.369873\pi$
$618$	−1.04087e96	−0.534928
$619$	2.19380e96	1.06627	0.533137	−	0.846029i	$-0.321013\pi$
$619$	2.19380e96	1.06627	0.533137	+	0.846029i	$0.321013\pi$
$620$	1.31177e96	0.603037
$621$	7.75113e94	0.0337058
$622$	−1.50265e96	−0.618144
$623$	−4.49870e96	−1.75085
$624$	−9.43037e94	−0.0347264
$625$	−1.12222e96	−0.391036
$626$	3.48427e96	1.14894
$627$	4.70739e96	1.46910
$628$	6.19810e96	1.83084
$629$	3.34922e96	0.936475
$630$	2.39087e96	0.632859
$631$	6.86379e96	1.72009	0.860045	−	0.510219i	$-0.170436\pi$
$631$	6.86379e96	1.72009	0.860045	+	0.510219i	$0.170436\pi$
$632$	−7.12191e95	−0.168989
$633$	−4.29982e96	−0.966102
$634$	6.47741e96	1.37823
$635$	−1.95710e96	−0.394383
$636$	6.72415e95	0.128341
$637$	−7.43274e95	−0.134381
$638$	−2.58800e97	−4.43252
$639$	−1.17076e96	−0.189971
$640$	1.34879e96	0.207365
$641$	−5.79908e96	−0.844805	−0.422403	−	0.906408i	$-0.638813\pi$
$641$	−5.79908e96	−0.844805	−0.422403	+	0.906408i	$0.638813\pi$
$642$	−4.80112e96	−0.662803
$643$	−7.60412e96	−0.994879	−0.497439	−	0.867499i	$-0.665726\pi$
$643$	−7.60412e96	−0.994879	−0.497439	+	0.867499i	$0.665726\pi$
$644$	2.67954e96	0.332275
$645$	8.46707e95	0.0995229
$646$	−1.64155e97	−1.82908
$647$	7.35255e96	0.776677	0.388338	−	0.921517i	$-0.373049\pi$
$647$	7.35255e96	0.776677	0.388338	+	0.921517i	$0.373049\pi$
$648$	−1.52621e95	−0.0152854
$649$	1.18742e97	1.12762
$650$	−4.60559e95	−0.0414739
$651$	8.51970e96	0.727579
$652$	−1.92964e97	−1.56291
$653$	1.57527e97	1.21018	0.605092	−	0.796156i	$-0.293136\pi$
$653$	1.57527e97	1.21018	0.605092	+	0.796156i	$0.293136\pi$
$654$	−2.01787e97	−1.47049
$655$	−1.08260e97	−0.748420
$656$	−6.54243e96	−0.429098
$657$	4.63261e96	0.288284
$658$	6.31147e97	3.72681
$659$	2.03379e97	1.13962	0.569810	−	0.821777i	$-0.307017\pi$
$659$	2.03379e97	1.13962	0.569810	+	0.821777i	$0.307017\pi$
$660$	−1.71452e97	−0.911752
$661$	−3.86362e97	−1.95004	−0.975022	−	0.222107i	$-0.928707\pi$
$661$	−3.86362e97	−1.95004	−0.975022	+	0.222107i	$0.928707\pi$
$662$	2.51118e97	1.20303
$663$	−8.06278e95	−0.0366664
$664$	6.01273e95	0.0259581
$665$	4.27499e97	1.75222
$666$	1.22731e97	0.477631
$667$	−7.61953e96	−0.281570
$668$	−4.85579e96	−0.170401
$669$	8.60934e96	0.286925
$670$	−3.22250e97	−1.02003
$671$	−4.57338e97	−1.37502
$672$	5.02360e97	1.43475
$673$	8.24954e96	0.223826	0.111913	−	0.993718i	$-0.464302\pi$
$673$	8.24954e96	0.223826	0.111913	+	0.993718i	$0.464302\pi$
$674$	4.83544e97	1.24644
$675$	3.35371e96	0.0821383
$676$	−4.68415e97	−1.09011
$677$	4.95763e97	1.09639	0.548195	−	0.836350i	$-0.315315\pi$
$677$	4.95763e97	1.09639	0.548195	+	0.836350i	$0.315315\pi$
$678$	−2.28792e97	−0.480858
$679$	3.89627e97	0.778292
$680$	5.18929e96	0.0985259
$681$	−5.72423e97	−1.03310
$682$	−1.16889e98	−2.00545
$683$	−1.18469e98	−1.93238	−0.966189	−	0.257835i	$-0.916991\pi$
$683$	−1.18469e98	−1.93238	−0.966189	+	0.257835i	$0.916991\pi$
$684$	−3.14414e97	−0.487603
$685$	4.49567e97	0.662933
$686$	1.79133e98	2.51185
$687$	5.10603e97	0.680888
$688$	1.60843e97	0.203987
$689$	1.12982e96	0.0136284
$690$	−9.65757e96	−0.110809
$691$	−1.45401e98	−1.58699	−0.793496	−	0.608576i	$-0.791741\pi$
$691$	−1.45401e98	−1.58699	−0.793496	+	0.608576i	$0.791741\pi$
$692$	−9.12806e97	−0.947803
$693$	−1.11355e98	−1.10005
$694$	2.32281e98	2.18330
$695$	−4.50284e97	−0.402727
$696$	1.50030e97	0.127691
$697$	−5.59365e97	−0.453069
$698$	1.96471e98	1.51456
$699$	1.90114e97	0.139493
$700$	1.15937e98	0.809729
$701$	−1.31861e98	−0.876689	−0.438345	−	0.898807i	$-0.644435\pi$
$701$	−1.31861e98	−0.876689	−0.438345	+	0.898807i	$0.644435\pi$
$702$	−2.95458e96	−0.0187010
$703$	2.19449e98	1.32243
$704$	−3.91800e98	−2.24806
$705$	−1.18898e98	−0.649608
$706$	−6.12268e96	−0.0318551
$707$	−3.09171e98	−1.53189
$708$	−7.93099e97	−0.374266
$709$	−9.79468e97	−0.440246	−0.220123	−	0.975472i	$-0.570646\pi$
$709$	−9.79468e97	−0.440246	−0.220123	+	0.975472i	$0.570646\pi$
$710$	1.45871e98	0.624535
$711$	1.00396e98	0.409464
$712$	−3.57808e97	−0.139024
$713$	−3.44141e97	−0.127394
$714$	3.88314e98	1.36960
$715$	−2.88081e97	−0.0968180
$716$	5.98357e98	1.91629
$717$	−2.07728e98	−0.633993
$718$	3.15033e98	0.916353
$719$	−2.70824e97	−0.0750828	−0.0375414	−	0.999295i	$-0.511953\pi$
$719$	−2.70824e97	−0.0750828	−0.0375414	+	0.999295i	$0.511953\pi$
$720$	−8.55603e97	−0.226100
$721$	4.40257e98	1.10902
$722$	−4.72841e98	−1.13549
$723$	2.65380e98	0.607571
$724$	−7.39962e98	−1.61521
$725$	−3.29677e98	−0.686164
$726$	1.10670e99	2.19643
$727$	1.04255e99	1.97315	0.986575	−	0.163309i	$-0.0522166\pi$
$727$	1.04255e99	1.97315	0.986575	+	0.163309i	$0.0522166\pi$
$728$	−8.86509e96	−0.0160011
$729$	2.15147e97	0.0370370
$730$	−5.77203e98	−0.947741
$731$	1.37518e98	0.215382
$732$	3.05464e98	0.456381
$733$	−3.17514e97	−0.0452560	−0.0226280	−	0.999744i	$-0.507203\pi$
$733$	−3.17514e97	−0.0452560	−0.0226280	+	0.999744i	$0.507203\pi$
$734$	−7.59411e98	−1.03267
$735$	−6.74362e98	−0.874943
$736$	−2.02921e98	−0.251213
$737$	1.50088e99	1.77304
$738$	−2.04977e98	−0.231079
$739$	−3.87487e98	−0.416892	−0.208446	−	0.978034i	$-0.566841\pi$
$739$	−3.87487e98	−0.416892	−0.208446	+	0.978034i	$0.566841\pi$
$740$	−7.99273e98	−0.820731
$741$	−5.28292e97	−0.0517781
$742$	−5.44136e98	−0.509064
$743$	−6.91718e98	−0.617753	−0.308876	−	0.951102i	$-0.599953\pi$
$743$	−6.91718e98	−0.617753	−0.308876	+	0.951102i	$0.599953\pi$
$744$	6.77621e97	0.0577724
$745$	−5.28952e98	−0.430552
$746$	−2.99923e98	−0.233088
$747$	−8.47603e97	−0.0628973
$748$	−2.78464e99	−1.97317
$749$	2.03073e99	1.37413
$750$	−1.39690e99	−0.902718
$751$	−3.34660e98	−0.206550	−0.103275	−	0.994653i	$-0.532932\pi$
$751$	−3.34660e98	−0.206550	−0.103275	+	0.994653i	$0.532932\pi$
$752$	−2.25864e99	−1.33147
$753$	8.30121e98	0.467428
$754$	2.90441e98	0.156224
$755$	−9.28767e97	−0.0477240
$756$	7.43758e98	0.365115
$757$	2.08822e99	0.979419	0.489710	−	0.871886i	$-0.337103\pi$
$757$	2.08822e99	0.979419	0.489710	+	0.871886i	$0.337103\pi$
$758$	7.05858e98	0.316322
$759$	4.49802e98	0.192611
$760$	3.40015e98	0.139132
$761$	−3.79309e99	−1.48328	−0.741639	−	0.670799i	$-0.765951\pi$
$761$	−3.79309e99	−1.48328	−0.741639	+	0.670799i	$0.765951\pi$
$762$	−1.16479e99	−0.435314
$763$	8.53498e99	3.04864
$764$	3.45214e99	1.17860
$765$	−7.31524e98	−0.238731
$766$	6.40118e99	1.99695
$767$	−1.33260e98	−0.0397429
$768$	−1.58701e99	−0.452500
$769$	−2.03688e99	−0.555274	−0.277637	−	0.960686i	$-0.589551\pi$
$769$	−2.03688e99	−0.555274	−0.277637	+	0.960686i	$0.589551\pi$
$770$	1.38744e100	3.61645
$771$	−1.31591e99	−0.327983
$772$	−6.55979e99	−1.56348
$773$	−4.01567e99	−0.915305	−0.457652	−	0.889131i	$-0.651310\pi$
$773$	−4.01567e99	−0.915305	−0.457652	+	0.889131i	$0.651310\pi$
$774$	5.03930e98	0.109852
$775$	−1.48901e99	−0.310448
$776$	3.09893e98	0.0617991
$777$	−5.19113e99	−0.990232
$778$	1.98777e99	0.362718
$779$	−3.66509e99	−0.639798
$780$	1.92414e98	0.0321346
$781$	−6.79396e99	−1.08558
$782$	−1.56854e99	−0.239807
$783$	−2.11494e99	−0.309398
$784$	−1.28104e100	−1.79333
$785$	9.44875e99	1.26582
$786$	−6.44328e99	−0.826094
$787$	1.14924e100	1.41021	0.705104	−	0.709104i	$-0.250900\pi$
$787$	1.14924e100	1.41021	0.705104	+	0.709104i	$0.250900\pi$
$788$	5.64908e99	0.663473
$789$	6.10801e99	0.686662
$790$	−1.25089e100	−1.34613
$791$	9.67720e99	0.996922
$792$	−8.85670e98	−0.0873480
$793$	5.13253e98	0.0484626
$794$	−1.19936e100	−1.08429
$795$	1.02507e99	0.0887334
$796$	−2.70133e99	−0.223912
$797$	−5.15259e99	−0.408991	−0.204496	−	0.978868i	$-0.565555\pi$
$797$	−5.15259e99	−0.408991	−0.204496	+	0.978868i	$0.565555\pi$
$798$	2.54432e100	1.93407
$799$	−1.93109e100	−1.40585
$800$	−8.77987e99	−0.612186
$801$	5.04394e99	0.336859
$802$	2.55029e99	0.163145
$803$	2.68833e100	1.64739
$804$	−1.00246e100	−0.588483
$805$	4.08485e99	0.229731
$806$	1.31180e99	0.0706818
$807$	2.28311e99	0.117866
$808$	−2.45901e99	−0.121638
$809$	−3.63082e99	−0.172100	−0.0860500	−	0.996291i	$-0.527424\pi$
$809$	−3.63082e99	−0.172100	−0.0860500	+	0.996291i	$0.527424\pi$
$810$	−2.68064e99	−0.121760
$811$	−2.49265e100	−1.08503	−0.542514	−	0.840047i	$-0.682528\pi$
$811$	−2.49265e100	−1.08503	−0.542514	+	0.840047i	$0.682528\pi$
$812$	−7.31130e100	−3.05008
$813$	−4.18290e99	−0.167245
$814$	7.12213e100	2.72941
$815$	−2.94166e100	−1.08057
$816$	−1.38963e100	−0.489315
$817$	9.01051e99	0.304150
$818$	6.25031e100	2.02261
$819$	1.24969e99	0.0387712
$820$	1.33490e100	0.397072
$821$	−1.74128e99	−0.0496626	−0.0248313	−	0.999692i	$-0.507905\pi$
$821$	−1.74128e99	−0.0496626	−0.0248313	+	0.999692i	$0.507905\pi$
$822$	2.67566e100	0.731735
$823$	−5.12045e100	−1.34281	−0.671404	−	0.741092i	$-0.734308\pi$
$823$	−5.12045e100	−1.34281	−0.671404	+	0.741092i	$0.734308\pi$
$824$	3.50162e99	0.0880602
$825$	1.94618e100	0.469377
$826$	6.41797e100	1.48452
$827$	4.10981e100	0.911763	0.455881	−	0.890041i	$-0.349324\pi$
$827$	4.10981e100	0.911763	0.455881	+	0.890041i	$0.349324\pi$
$828$	−3.00430e99	−0.0639289
$829$	8.11010e100	1.65537	0.827684	−	0.561194i	$-0.189658\pi$
$829$	8.11010e100	1.65537	0.827684	+	0.561194i	$0.189658\pi$
$830$	1.05608e100	0.206777
$831$	5.97801e99	0.112285
$832$	4.39702e99	0.0792326
$833$	−1.09527e101	−1.89351
$834$	−2.67993e100	−0.444524
$835$	−7.40245e99	−0.117813
$836$	−1.82456e101	−2.78639
$837$	−9.55229e99	−0.139984
$838$	1.64431e100	0.231241
$839$	1.51125e100	0.203962	0.101981	−	0.994786i	$-0.467482\pi$
$839$	1.51125e100	0.203962	0.101981	+	0.994786i	$0.467482\pi$
$840$	−8.04316e99	−0.104182
$841$	1.27465e101	1.58464
$842$	1.68949e101	2.01600
$843$	3.71165e100	0.425124
$844$	1.66659e101	1.83238
$845$	−7.14079e100	−0.753685
$846$	−7.07641e100	−0.717027
$847$	−4.68101e101	−4.55368
$848$	1.94726e100	0.181872
$849$	6.53651e100	0.586179
$850$	−6.78666e100	−0.584390
$851$	2.09688e100	0.173382
$852$	4.53780e100	0.360312
$853$	−1.38983e101	−1.05979	−0.529897	−	0.848062i	$-0.677769\pi$
$853$	−1.38983e101	−1.05979	−0.529897	+	0.848062i	$0.677769\pi$
$854$	−2.47189e101	−1.81023
$855$	−4.79312e100	−0.337122
$856$	1.61515e100	0.109111
$857$	−1.73701e101	−1.12711	−0.563553	−	0.826080i	$-0.690566\pi$
$857$	−1.73701e101	−1.12711	−0.563553	+	0.826080i	$0.690566\pi$
$858$	−1.71456e100	−0.106866
$859$	1.07792e101	0.645388	0.322694	−	0.946503i	$-0.395412\pi$
$859$	1.07792e101	0.645388	0.322694	+	0.946503i	$0.395412\pi$
$860$	−3.28180e100	−0.188762
$861$	8.66990e100	0.479077
$862$	3.22608e101	1.71267
$863$	5.40835e100	0.275862	0.137931	−	0.990442i	$-0.455955\pi$
$863$	5.40835e100	0.275862	0.137931	+	0.990442i	$0.455955\pi$
$864$	−5.63246e100	−0.276041
$865$	−1.39154e101	−0.655298
$866$	5.15653e101	2.33340
$867$	1.39588e100	0.0607002
$868$	−3.30220e101	−1.37998
$869$	5.82604e101	2.33987
$870$	2.63513e101	1.01716
$871$	−1.68438e100	−0.0624904
$872$	6.78836e100	0.242073
$873$	−4.36850e100	−0.149741
$874$	−1.02774e101	−0.338641
$875$	5.90845e101	1.87153
$876$	−1.79558e101	−0.546780
$877$	−1.68712e101	−0.493923	−0.246961	−	0.969025i	$-0.579432\pi$
$877$	−1.68712e101	−0.493923	−0.246961	+	0.969025i	$0.579432\pi$
$878$	1.72375e101	0.485191
$879$	−6.05002e100	−0.163735
$880$	−4.96511e101	−1.29204
$881$	3.63411e101	0.909346	0.454673	−	0.890659i	$-0.349756\pi$
$881$	3.63411e101	0.909346	0.454673	+	0.890659i	$0.349756\pi$
$882$	−4.01356e101	−0.965748
$883$	2.09080e101	0.483803	0.241901	−	0.970301i	$-0.422229\pi$
$883$	2.09080e101	0.483803	0.241901	+	0.970301i	$0.422229\pi$
$884$	3.12510e100	0.0695441
$885$	−1.20905e101	−0.258762
$886$	4.15852e101	0.856003
$887$	−3.70484e101	−0.733507	−0.366753	−	0.930318i	$-0.619531\pi$
$887$	−3.70484e101	−0.733507	−0.366753	+	0.930318i	$0.619531\pi$
$888$	−4.12880e100	−0.0786280
$889$	4.92672e101	0.902499
$890$	−6.28453e101	−1.10743
$891$	1.24851e101	0.211647
$892$	−3.33694e101	−0.544203
$893$	−1.26530e102	−1.98526
$894$	−3.14814e101	−0.475236
$895$	9.12170e101	1.32489
$896$	−3.39540e101	−0.474531
$897$	−5.04796e99	−0.00678854
$898$	−7.88438e101	−1.02031
$899$	9.39010e101	1.16939
$900$	−1.29988e101	−0.155789
$901$	1.66487e101	0.192032
$902$	−1.18949e102	−1.32050
$903$	−2.13147e101	−0.227746
$904$	7.69683e100	0.0791591
$905$	−1.12804e102	−1.11673
$906$	−5.52769e100	−0.0526770
$907$	1.29476e102	1.18778	0.593891	−	0.804546i	$-0.297591\pi$
$907$	1.29476e102	1.18778	0.593891	+	0.804546i	$0.297591\pi$
$908$	2.21869e102	1.95945
$909$	3.46642e101	0.294732
$910$	−1.55706e101	−0.127461
$911$	−3.71508e101	−0.292809	−0.146405	−	0.989225i	$-0.546770\pi$
$911$	−3.71508e101	−0.292809	−0.146405	+	0.989225i	$0.546770\pi$
$912$	−9.10518e101	−0.690982
$913$	−4.91868e101	−0.359424
$914$	3.35897e101	0.236354
$915$	4.65667e101	0.315535
$916$	−1.97907e102	−1.29142
$917$	2.72531e102	1.71267
$918$	−4.35377e101	−0.263508
$919$	9.76035e101	0.568958	0.284479	−	0.958682i	$-0.408179\pi$
$919$	9.76035e101	0.568958	0.284479	+	0.958682i	$0.408179\pi$
$920$	3.24892e100	0.0182414
$921$	−3.90819e101	−0.211358
$922$	−6.06095e101	−0.315736
$923$	7.62460e100	0.0382612
$924$	4.31607e102	2.08644
$925$	9.07267e101	0.422518
$926$	−4.41863e102	−1.98248
$927$	−4.93616e101	−0.213372
$928$	5.53683e102	2.30598
$929$	−1.95930e102	−0.786246	−0.393123	−	0.919486i	$-0.628605\pi$
$929$	−1.95930e102	−0.786246	−0.393123	+	0.919486i	$0.628605\pi$
$930$	1.19017e102	0.460202
$931$	−7.17644e102	−2.67390
$932$	−7.36874e101	−0.264572
$933$	−7.12606e101	−0.246566
$934$	−4.65582e102	−1.55249
$935$	−4.24507e102	−1.36422
$936$	9.93953e99	0.00307857
$937$	4.70525e102	1.40465	0.702323	−	0.711858i	$-0.252146\pi$
$937$	4.70525e102	1.40465	0.702323	+	0.711858i	$0.252146\pi$
$938$	8.11219e102	2.33421
$939$	1.65236e102	0.458290
$940$	4.60845e102	1.23209
$941$	2.97279e102	0.766165	0.383083	−	0.923714i	$-0.374862\pi$
$941$	2.97279e102	0.766165	0.383083	+	0.923714i	$0.374862\pi$
$942$	5.62356e102	1.39719
$943$	−3.50208e101	−0.0838828
$944$	−2.29675e102	−0.530371
$945$	1.13383e102	0.252435
$946$	2.92433e102	0.627744
$947$	−2.92027e102	−0.604434	−0.302217	−	0.953239i	$-0.597727\pi$
$947$	−2.92027e102	−0.604434	−0.302217	+	0.953239i	$0.597727\pi$
$948$	−3.89131e102	−0.776619
$949$	−3.01700e101	−0.0580619
$950$	−4.44678e102	−0.825241
$951$	3.07180e102	0.549750
$952$	−1.30633e102	−0.225465
$953$	−3.44705e102	−0.573776	−0.286888	−	0.957964i	$-0.592621\pi$
$953$	−3.44705e102	−0.573776	−0.286888	+	0.957964i	$0.592621\pi$
$954$	6.10085e101	0.0979425
$955$	5.26265e102	0.814870
$956$	8.05145e102	1.20248
$957$	−1.22731e103	−1.76805
$958$	−1.04016e103	−1.44541
$959$	−1.13172e103	−1.51704
$960$	3.98936e102	0.515876
$961$	−3.77488e102	−0.470919
$962$	−7.99290e101	−0.0961976
$963$	−2.27685e102	−0.264379
$964$	−1.02860e103	−1.15236
$965$	−1.00001e103	−1.08097
$966$	2.43116e102	0.253573
$967$	1.16447e102	0.117197	0.0585984	−	0.998282i	$-0.481337\pi$
$967$	1.16447e102	0.117197	0.0585984	+	0.998282i	$0.481337\pi$
$968$	−3.72308e102	−0.361578
$969$	−7.78475e102	−0.729583
$970$	5.44296e102	0.492278
$971$	2.03673e103	1.77775	0.888874	−	0.458152i	$-0.151488\pi$
$971$	2.03673e103	1.77775	0.888874	+	0.458152i	$0.151488\pi$
$972$	−8.33901e101	−0.0702471
$973$	1.13353e103	0.921593
$974$	−6.17705e102	−0.484727
$975$	−2.18412e101	−0.0165431
$976$	8.84597e102	0.646736
$977$	2.81951e102	0.198981	0.0994903	−	0.995039i	$-0.468279\pi$
$977$	2.81951e102	0.198981	0.0994903	+	0.995039i	$0.468279\pi$
$978$	−1.75077e103	−1.19272
$979$	2.92703e103	1.92497
$980$	2.61379e103	1.65948
$981$	−9.56941e102	−0.586549
$982$	−6.05247e102	−0.358168
$983$	−1.42726e103	−0.815469	−0.407735	−	0.913101i	$-0.633681\pi$
$983$	−1.42726e103	−0.815469	−0.407735	+	0.913101i	$0.633681\pi$
$984$	6.89567e101	0.0380404
$985$	8.61179e102	0.458716
$986$	4.27985e103	2.20128
$987$	2.99310e103	1.48655
$988$	2.04764e102	0.0982060
$989$	8.60975e101	0.0398766
$990$	−1.55559e103	−0.695795
$991$	−3.14342e103	−1.35788	−0.678940	−	0.734193i	$-0.737561\pi$
$991$	−3.14342e103	−1.35788	−0.678940	+	0.734193i	$0.737561\pi$
$992$	2.50074e103	1.04332
$993$	1.19088e103	0.479866
$994$	−3.67211e103	−1.42917
$995$	−4.11806e102	−0.154809
$996$	3.28527e102	0.119295
$997$	−9.67674e102	−0.339427	−0.169713	−	0.985493i	$-0.554284\pi$
$997$	−9.67674e102	−0.339427	−0.169713	+	0.985493i	$0.554284\pi$
$998$	2.79088e102	0.0945665
$999$	5.82029e102	0.190518

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3.70.a.a.1.1	✓	6
3.2	odd	2		9.70.a.d.1.6		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
3.70.a.a.1.1	✓	6	1.1	even	1	trivial
9.70.a.d.1.6		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)

\(f(q)\)	\(=\)	\(q-3.51667e10 q^{2} -1.66772e16 q^{3} +6.46400e20 q^{4} +9.85410e23 q^{5} +5.86481e26 q^{6} -2.48063e29 q^{7} -1.97299e30 q^{8} +2.78128e32 q^{9} +O(q^{10})\)	\(q-3.51667e10 q^{2} -1.66772e16 q^{3} +6.46400e20 q^{4} +9.85410e23 q^{5} +5.86481e26 q^{6} -2.48063e29 q^{7} -1.97299e30 q^{8} +2.78128e32 q^{9} -3.46536e34 q^{10} +1.61399e36 q^{11} -1.07801e37 q^{12} -1.81132e37 q^{13} +8.72356e39 q^{14} -1.64339e40 q^{15} -3.12184e41 q^{16} -2.66911e42 q^{17} -9.78085e42 q^{18} -1.74886e44 q^{19} +6.36969e44 q^{20} +4.13700e45 q^{21} -5.67588e46 q^{22} -1.67108e46 q^{23} +3.29039e46 q^{24} -7.23033e47 q^{25} +6.36982e47 q^{26} -4.63840e48 q^{27} -1.60348e50 q^{28} +4.55964e50 q^{29} +5.77924e50 q^{30} +2.05939e51 q^{31} +1.21431e52 q^{32} -2.69169e52 q^{33} +9.38637e52 q^{34} -2.44444e53 q^{35} +1.79782e53 q^{36} -1.25481e54 q^{37} +6.15017e54 q^{38} +3.02078e53 q^{39} -1.94420e54 q^{40} +2.09570e55 q^{41} -1.45484e56 q^{42} -5.15221e55 q^{43} +1.04329e57 q^{44} +2.74070e56 q^{45} +5.87663e56 q^{46} +7.23496e57 q^{47} +5.20634e57 q^{48} +4.10349e58 q^{49} +2.54267e58 q^{50} +4.45132e58 q^{51} -1.17084e58 q^{52} -6.23754e58 q^{53} +1.63117e59 q^{54} +1.59045e60 q^{55} +4.89426e59 q^{56} +2.91661e60 q^{57} -1.60348e61 q^{58} +7.35705e60 q^{59} -1.06228e61 q^{60} -2.83358e61 q^{61} -7.24220e61 q^{62} -6.89934e61 q^{63} -2.42752e62 q^{64} -1.78490e61 q^{65} +9.46577e62 q^{66} +9.29917e62 q^{67} -1.72531e63 q^{68} +2.78689e62 q^{69} +8.59629e63 q^{70} -4.20941e63 q^{71} -5.48744e62 q^{72} +1.66564e64 q^{73} +4.41274e64 q^{74} +1.20582e64 q^{75} -1.13046e65 q^{76} -4.00373e65 q^{77} -1.06231e64 q^{78} +3.60971e65 q^{79} -3.07629e65 q^{80} +7.73554e64 q^{81} -7.36988e65 q^{82} -3.04752e65 q^{83} +2.67415e66 q^{84} -2.63017e66 q^{85} +1.81186e66 q^{86} -7.60420e66 q^{87} -3.18439e66 q^{88} +1.81353e67 q^{89} -9.63815e66 q^{90} +4.49323e66 q^{91} -1.08019e67 q^{92} -3.43449e67 q^{93} -2.54430e68 q^{94} -1.72335e68 q^{95} -2.02513e68 q^{96} -1.57068e68 q^{97} -1.44306e69 q^{98} +4.48897e68 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 869363388 q^{2} - 10\!\cdots\!14 q^{3}+ \cdots + 16\!\cdots\!66 q^{9}+O(q^{10}) \) 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

Related objects

Downloads

Learn more