LMFDB - Embedded newform 3.70.a.a.1.6

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			1.6
Root			$1.25227e9$ 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)

$f(q)$	$=$	$q+4.49367e10 q^{2} -1.66772e16 q^{3} +1.42901e21 q^{4} -2.66474e23 q^{5} -7.49418e26 q^{6} +6.09654e28 q^{7} +3.76892e31 q^{8} +2.78128e32 q^{9} +O(q^{10})$	\(q+4.49367e10 q^{2} -1.66772e16 q^{3} +1.42901e21 q^{4} -2.66474e23 q^{5} -7.49418e26 q^{6} +6.09654e28 q^{7} +3.76892e31 q^{8} +2.78128e32 q^{9} -1.19745e34 q^{10} -1.12126e36 q^{11} -2.38319e37 q^{12} -4.59233e38 q^{13} +2.73959e39 q^{14} +4.44404e39 q^{15} +8.50089e41 q^{16} -3.29400e42 q^{17} +1.24982e43 q^{18} +1.91422e43 q^{19} -3.80795e44 q^{20} -1.01673e45 q^{21} -5.03857e46 q^{22} +8.47703e46 q^{23} -6.28550e47 q^{24} -1.62306e48 q^{25} -2.06364e49 q^{26} -4.63840e48 q^{27} +8.71204e49 q^{28} +3.99793e50 q^{29} +1.99701e50 q^{30} +1.61187e51 q^{31} +1.59524e52 q^{32} +1.86994e52 q^{33} -1.48021e53 q^{34} -1.62457e52 q^{35} +3.97449e53 q^{36} -1.70002e54 q^{37} +8.60188e53 q^{38} +7.65871e54 q^{39} -1.00432e55 q^{40} +2.99251e55 q^{41} -4.56886e55 q^{42} -4.05226e56 q^{43} -1.60229e57 q^{44} -7.41140e55 q^{45} +3.80930e57 q^{46} -1.26384e57 q^{47} -1.41771e58 q^{48} -1.67837e58 q^{49} -7.29349e58 q^{50} +5.49346e58 q^{51} -6.56250e59 q^{52} -3.07119e59 q^{53} -2.08434e59 q^{54} +2.98787e59 q^{55} +2.29774e60 q^{56} -3.19238e59 q^{57} +1.79654e61 q^{58} -1.80886e61 q^{59} +6.35059e60 q^{60} +2.21022e61 q^{61} +7.24322e61 q^{62} +1.69562e61 q^{63} +2.15046e62 q^{64} +1.22374e62 q^{65} +8.40292e62 q^{66} -7.33428e62 q^{67} -4.70717e63 q^{68} -1.41373e63 q^{69} -7.30029e62 q^{70} -1.20368e64 q^{71} +1.04824e64 q^{72} +3.04271e64 q^{73} -7.63935e64 q^{74} +2.70680e64 q^{75} +2.73545e64 q^{76} -6.83580e64 q^{77} +3.44157e65 q^{78} +1.07189e65 q^{79} -2.26527e65 q^{80} +7.73554e64 q^{81} +1.34474e66 q^{82} +1.00375e66 q^{83} -1.45292e66 q^{84} +8.77765e65 q^{85} -1.82095e67 q^{86} -6.66742e66 q^{87} -4.22594e67 q^{88} +2.42069e67 q^{89} -3.33044e66 q^{90} -2.79973e67 q^{91} +1.21138e68 q^{92} -2.68815e67 q^{93} -5.67930e67 q^{94} -5.10090e66 q^{95} -2.66042e68 q^{96} +1.94649e68 q^{97} -7.54206e68 q^{98} -3.11854e68 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	4.49367e10	1.84955	0.924776	−	0.380512i	$-0.124252\pi$
$2$	4.49367e10	1.84955	0.924776	+	0.380512i	$0.124252\pi$
$3$	−1.66772e16	−0.577350
$3$	−1.66772e16	−0.577350
$4$	1.42901e21	2.42084
$5$	−2.66474e23	−0.204734	−0.102367	−	0.994747i	$-0.532642\pi$
$5$	−2.66474e23	−0.204734	−0.102367	+	0.994747i	$0.532642\pi$
$6$	−7.49418e26	−1.06784
$7$	6.09654e28	0.425796	0.212898	−	0.977074i	$-0.431710\pi$
$7$	6.09654e28	0.425796	0.212898	+	0.977074i	$0.431710\pi$
$8$	3.76892e31	2.62792
$9$	2.78128e32	0.333333
$10$	−1.19745e34	−0.378666
$11$	−1.12126e36	−1.32330	−0.661650	−	0.749813i	$-0.730144\pi$
$11$	−1.12126e36	−1.32330	−0.661650	+	0.749813i	$0.730144\pi$
$12$	−2.38319e37	−1.39767
$13$	−4.59233e38	−1.70211	−0.851054	−	0.525078i	$-0.824036\pi$
$13$	−4.59233e38	−1.70211	−0.851054	+	0.525078i	$0.824036\pi$
$14$	2.73959e39	0.787531
$15$	4.44404e39	0.118203
$16$	8.50089e41	2.43964
$17$	−3.29400e42	−1.16744	−0.583721	−	0.811954i	$-0.698404\pi$
$17$	−3.29400e42	−1.16744	−0.583721	+	0.811954i	$0.698404\pi$
$18$	1.24982e43	0.616517
$19$	1.91422e43	0.146215	0.0731076	−	0.997324i	$-0.476708\pi$
$19$	1.91422e43	0.146215	0.0731076	+	0.997324i	$0.476708\pi$
$20$	−3.80795e44	−0.495629
$21$	−1.01673e45	−0.245833
$22$	−5.03857e46	−2.44751
$23$	8.47703e46	0.888451	0.444225	−	0.895915i	$-0.353479\pi$
$23$	8.47703e46	0.888451	0.444225	+	0.895915i	$0.353479\pi$
$24$	−6.28550e47	−1.51723
$25$	−1.62306e48	−0.958084
$26$	−2.06364e49	−3.14814
$27$	−4.63840e48	−0.192450
$28$	8.71204e49	1.03078
$29$	3.99793e50	1.40963	0.704814	−	0.709393i	$-0.251031\pi$
$29$	3.99793e50	1.40963	0.704814	+	0.709393i	$0.251031\pi$
$30$	1.99701e50	0.218623
$31$	1.61187e51	0.569314	0.284657	−	0.958629i	$-0.408120\pi$
$31$	1.61187e51	0.569314	0.284657	+	0.958629i	$0.408120\pi$
$32$	1.59524e52	1.88431
$33$	1.86994e52	0.764008
$34$	−1.48021e53	−2.15925
$35$	−1.62457e52	−0.0871748
$36$	3.97449e53	0.806948
$37$	−1.70002e54	−1.34121	−0.670603	−	0.741817i	$-0.733964\pi$
$37$	−1.70002e54	−1.34121	−0.670603	+	0.741817i	$0.733964\pi$
$38$	8.60188e53	0.270433
$39$	7.65871e54	0.982713
$40$	−1.00432e55	−0.538025
$41$	2.99251e55	0.683901	0.341950	−	0.939718i	$-0.388913\pi$
$41$	2.99251e55	0.683901	0.341950	+	0.939718i	$0.388913\pi$
$42$	−4.56886e55	−0.454681
$43$	−4.05226e56	−1.79075	−0.895376	−	0.445311i	$-0.853093\pi$
$43$	−4.05226e56	−1.79075	−0.895376	+	0.445311i	$0.853093\pi$
$44$	−1.60229e57	−3.20350
$45$	−7.41140e55	−0.0682447
$46$	3.80930e57	1.64324
$47$	−1.26384e57	−0.259607	−0.129804	−	0.991540i	$-0.541435\pi$
$47$	−1.26384e57	−0.259607	−0.129804	+	0.991540i	$0.541435\pi$
$48$	−1.41771e58	−1.40852
$49$	−1.67837e58	−0.818698
$50$	−7.29349e58	−1.77203
$51$	5.49346e58	0.674023
$52$	−6.56250e59	−4.12054
$53$	−3.07119e59	−0.999514	−0.499757	−	0.866166i	$-0.666577\pi$
$53$	−3.07119e59	−0.999514	−0.499757	+	0.866166i	$0.666577\pi$
$54$	−2.08434e59	−0.355946
$55$	2.98787e59	0.270925
$56$	2.29774e60	1.11896
$57$	−3.19238e59	−0.0844174
$58$	1.79654e61	2.60718
$59$	−1.80886e61	−1.45550	−0.727749	−	0.685844i	$-0.759433\pi$
$59$	−1.80886e61	−1.45550	−0.727749	+	0.685844i	$0.759433\pi$
$60$	6.35059e60	0.286151
$61$	2.21022e61	0.563061	0.281531	−	0.959552i	$-0.409158\pi$
$61$	2.21022e61	0.563061	0.281531	+	0.959552i	$0.409158\pi$
$62$	7.24322e61	1.05298
$63$	1.69562e61	0.141932
$64$	2.15046e62	1.04550
$65$	1.22374e62	0.348480
$66$	8.40292e62	1.41307
$67$	−7.33428e62	−0.734136	−0.367068	−	0.930194i	$-0.619638\pi$
$67$	−7.33428e62	−0.734136	−0.367068	+	0.930194i	$0.619638\pi$
$68$	−4.70717e63	−2.82620
$69$	−1.41373e63	−0.512947
$70$	−7.30029e62	−0.161234
$71$	−1.20368e64	−1.62966	−0.814830	−	0.579700i	$-0.803170\pi$
$71$	−1.20368e64	−1.62966	−0.814830	+	0.579700i	$0.803170\pi$
$72$	1.04824e64	0.875974
$73$	3.04271e64	1.57987	0.789936	−	0.613189i	$-0.210114\pi$
$73$	3.04271e64	1.57987	0.789936	+	0.613189i	$0.210114\pi$
$74$	−7.63935e64	−2.48063
$75$	2.70680e64	0.553150
$76$	2.73545e64	0.353964
$77$	−6.83580e64	−0.563455
$78$	3.44157e65	1.81758
$79$	1.07189e65	0.364767	0.182384	−	0.983227i	$-0.441619\pi$
$79$	1.07189e65	0.364767	0.182384	+	0.983227i	$0.441619\pi$
$80$	−2.26527e65	−0.499477
$81$	7.73554e64	0.111111
$82$	1.34474e66	1.26491
$83$	1.00375e66	0.621489	0.310745	−	0.950493i	$-0.399422\pi$
$83$	1.00375e66	0.621489	0.310745	+	0.950493i	$0.399422\pi$
$84$	−1.45292e66	−0.595123
$85$	8.77765e65	0.239015
$86$	−1.82095e67	−3.31209
$87$	−6.66742e66	−0.813849
$88$	−4.22594e67	−3.47753
$89$	2.42069e67	1.34891	0.674456	−	0.738315i	$-0.264378\pi$
$89$	2.42069e67	1.34891	0.674456	+	0.738315i	$0.264378\pi$
$90$	−3.33044e66	−0.126222
$91$	−2.79973e67	−0.724750
$92$	1.21138e68	2.15080
$93$	−2.68815e67	−0.328694
$94$	−5.67930e67	−0.480157
$95$	−5.10090e66	−0.0299352
$96$	−2.66042e68	−1.08791
$97$	1.94649e68	0.556707	0.278354	−	0.960479i	$-0.410211\pi$
$97$	1.94649e68	0.556707	0.278354	+	0.960479i	$0.410211\pi$
$98$	−7.54206e68	−1.51422
$99$	−3.11854e68	−0.441100
$100$	−2.31937e69	−2.31937
$101$	7.14587e68	0.506953	0.253477	−	0.967342i	$-0.418426\pi$
$101$	7.14587e68	0.506953	0.253477	+	0.967342i	$0.418426\pi$
$102$	2.46858e69	1.24664
$103$	1.13614e69	0.409776	0.204888	−	0.978785i	$-0.434317\pi$
$103$	1.13614e69	0.409776	0.204888	+	0.978785i	$0.434317\pi$
$104$	−1.73081e70	−4.47301
$105$	2.70933e68	0.0503304
$106$	−1.38009e70	−1.84865
$107$	−9.62315e69	−0.932346	−0.466173	−	0.884694i	$-0.654368\pi$
$107$	−9.62315e69	−0.932346	−0.466173	+	0.884694i	$0.654368\pi$
$108$	−6.62833e69	−0.465891
$109$	2.31086e70	1.18184	0.590922	−	0.806729i	$-0.298764\pi$
$109$	2.31086e70	1.18184	0.590922	+	0.806729i	$0.298764\pi$
$110$	1.34265e70	0.501089
$111$	2.83516e70	0.774345
$112$	5.18260e70	1.03879
$113$	−1.04026e70	−0.153439	−0.0767193	−	0.997053i	$-0.524445\pi$
$113$	−1.04026e70	−0.153439	−0.0767193	+	0.997053i	$0.524445\pi$
$114$	−1.43455e70	−0.156134
$115$	−2.25891e70	−0.181896
$116$	5.71309e71	3.41249
$117$	−1.27726e71	−0.567370
$118$	−8.12844e71	−2.69202
$119$	−2.00820e71	−0.497092
$120$	1.67492e71	0.310629
$121$	5.39271e71	0.751124
$122$	9.93199e71	1.04141
$123$	−4.99067e71	−0.394850
$124$	2.30339e72	1.37822
$125$	8.83928e71	0.400886
$126$	7.61957e71	0.262510
$127$	−2.24522e72	−0.588885	−0.294442	−	0.955669i	$-0.595134\pi$
$127$	−2.24522e72	−0.588885	−0.294442	+	0.955669i	$0.595134\pi$
$128$	2.46818e71	0.0493893
$129$	6.75803e72	1.03389
$130$	5.49907e72	0.644531
$131$	1.13537e73	1.02159	0.510796	−	0.859702i	$-0.329351\pi$
$131$	1.13537e73	1.02159	0.510796	+	0.859702i	$0.329351\pi$
$132$	2.67218e73	1.84954
$133$	1.16701e72	0.0622578
$134$	−3.29578e73	−1.35782
$135$	1.23601e72	0.0394011
$136$	−1.24148e74	−3.06795
$137$	−3.65292e73	−0.701101	−0.350551	−	0.936544i	$-0.614006\pi$
$137$	−3.65292e73	−0.701101	−0.350551	+	0.936544i	$0.614006\pi$
$138$	−6.35284e73	−0.948722
$139$	−6.67171e73	−0.776652	−0.388326	−	0.921522i	$-0.626947\pi$
$139$	−6.67171e73	−0.776652	−0.388326	+	0.921522i	$0.626947\pi$
$140$	−2.32153e73	−0.211037
$141$	2.10773e73	0.149884
$142$	−5.40893e74	−3.01414
$143$	5.14919e74	2.25240
$144$	2.36434e74	0.813212
$145$	−1.06534e74	−0.288599
$146$	1.36729e75	2.92206
$147$	2.79905e74	0.472676
$148$	−2.42936e75	−3.24685
$149$	−1.33839e75	−1.41793	−0.708966	−	0.705243i	$-0.750838\pi$
$149$	−1.33839e75	−1.41793	−0.708966	+	0.705243i	$0.750838\pi$
$150$	1.21635e75	1.02308
$151$	2.34250e75	1.56666	0.783329	−	0.621607i	$-0.213520\pi$
$151$	2.34250e75	1.56666	0.783329	+	0.621607i	$0.213520\pi$
$152$	7.21455e74	0.384242
$153$	−9.16154e74	−0.389148
$154$	−3.07179e75	−1.04214
$155$	−4.29522e74	−0.116558
$156$	1.09444e76	2.37899
$157$	−6.91134e75	−1.20510	−0.602552	−	0.798080i	$-0.705849\pi$
$157$	−6.91134e75	−1.20510	−0.602552	+	0.798080i	$0.705849\pi$
$158$	4.81672e75	0.674656
$159$	5.12188e75	0.577070
$160$	−4.25091e75	−0.385783
$161$	5.16805e75	0.378298
$162$	3.47610e75	0.205506
$163$	−2.72297e76	−1.30188	−0.650939	−	0.759130i	$-0.725625\pi$
$163$	−2.72297e76	−1.30188	−0.650939	+	0.759130i	$0.725625\pi$
$164$	4.27634e76	1.65562
$165$	−4.98292e75	−0.156418
$166$	4.51055e76	1.14948
$167$	2.77926e76	0.575720	0.287860	−	0.957672i	$-0.407056\pi$
$167$	2.77926e76	0.575720	0.287860	+	0.957672i	$0.407056\pi$
$168$	−3.83198e76	−0.646031
$169$	1.38102e77	1.89717
$170$	3.94439e76	0.442071
$171$	5.32399e75	0.0487384
$172$	−5.79073e77	−4.33513
$173$	−8.52367e76	−0.522440	−0.261220	−	0.965279i	$-0.584125\pi$
$173$	−8.52367e76	−0.522440	−0.261220	+	0.965279i	$0.584125\pi$
$174$	−2.99612e77	−1.50526
$175$	−9.89504e76	−0.407948
$176$	−9.53171e77	−3.22837
$177$	3.01668e77	0.840332
$178$	1.08778e78	2.49488
$179$	1.25511e77	0.237275	0.118637	−	0.992938i	$-0.462147\pi$
$179$	1.25511e77	0.237275	0.118637	+	0.992938i	$0.462147\pi$
$180$	−1.05910e77	−0.165210
$181$	9.52402e77	1.22718	0.613592	−	0.789623i	$-0.289724\pi$
$181$	9.52402e77	1.22718	0.613592	+	0.789623i	$0.289724\pi$
$182$	−1.25811e78	−1.34046
$183$	−3.68602e77	−0.325083
$184$	3.19493e78	2.33478
$185$	4.53012e77	0.274590
$186$	−1.20797e78	−0.607936
$187$	3.69343e78	1.54488
$188$	−1.80605e78	−0.628469
$189$	−2.82782e77	−0.0819444
$190$	−2.29218e77	−0.0553668
$191$	4.94319e78	0.996222	0.498111	−	0.867113i	$-0.334027\pi$
$191$	4.94319e78	0.996222	0.498111	+	0.867113i	$0.334027\pi$
$192$	−3.58637e78	−0.603618
$193$	−1.87009e77	−0.0263108	−0.0131554	−	0.999913i	$-0.504188\pi$
$193$	−1.87009e77	−0.0263108	−0.0131554	+	0.999913i	$0.504188\pi$
$194$	8.74688e78	1.02966
$195$	−2.04085e78	−0.201195
$196$	−2.39842e79	−1.98194
$197$	1.86757e79	1.29477	0.647385	−	0.762163i	$-0.275863\pi$
$197$	1.86757e79	1.29477	0.647385	+	0.762163i	$0.275863\pi$
$198$	−1.40137e79	−0.815838
$199$	2.98103e79	1.45859	0.729297	−	0.684197i	$-0.239847\pi$
$199$	2.98103e79	1.45859	0.729297	+	0.684197i	$0.239847\pi$
$200$	−6.11718e79	−2.51777
$201$	1.22315e79	0.423854
$202$	3.21112e79	0.937636
$203$	2.43735e79	0.600213
$204$	7.85023e79	1.63170
$205$	−7.97427e78	−0.140018
$206$	5.10543e79	0.757902
$207$	2.35770e79	0.296150
$208$	−3.90389e80	−4.15253
$209$	−2.14634e79	−0.193487
$210$	1.21748e79	0.0930887
$211$	4.92852e79	0.319868	0.159934	−	0.987128i	$-0.448872\pi$
$211$	4.92852e79	0.319868	0.159934	+	0.987128i	$0.448872\pi$
$212$	−4.38877e80	−2.41967
$213$	2.00739e80	0.940885
$214$	−4.32433e80	−1.72442
$215$	1.07982e80	0.366628
$216$	−1.74818e80	−0.505744
$217$	9.82684e79	0.242411
$218$	1.03843e81	2.18588
$219$	−5.07439e80	−0.912140
$220$	4.26970e80	0.655866
$221$	1.51271e81	1.98711
$222$	1.27403e81	1.43219
$223$	−4.31375e80	−0.415276	−0.207638	−	0.978206i	$-0.566578\pi$
$223$	−4.31375e80	−0.415276	−0.207638	+	0.978206i	$0.566578\pi$
$224$	9.72547e80	0.802332
$225$	−4.51418e80	−0.319361
$226$	−4.67458e80	−0.283793
$227$	−1.71059e81	−0.891772	−0.445886	−	0.895090i	$-0.647111\pi$
$227$	−1.71059e81	−0.891772	−0.445886	+	0.895090i	$0.647111\pi$
$228$	−4.56195e80	−0.204361
$229$	1.94874e81	0.750637	0.375319	−	0.926896i	$-0.377533\pi$
$229$	1.94874e81	0.750637	0.375319	+	0.926896i	$0.377533\pi$
$230$	−1.01508e81	−0.336426
$231$	1.14002e81	0.325311
$232$	1.50679e82	3.70439
$233$	−5.84862e81	−1.23958	−0.619789	−	0.784768i	$-0.712782\pi$
$233$	−5.84862e81	−1.23958	−0.619789	+	0.784768i	$0.712782\pi$
$234$	−5.73957e81	−1.04938
$235$	3.36782e80	0.0531505
$236$	−2.58489e82	−3.52353
$237$	−1.78761e81	−0.210598
$238$	−9.02419e81	−0.919397
$239$	−7.49139e81	−0.660443	−0.330221	−	0.943904i	$-0.607123\pi$
$239$	−7.49139e81	−0.660443	−0.330221	+	0.943904i	$0.607123\pi$
$240$	3.77783e81	0.288373
$241$	−6.62865e81	−0.438366	−0.219183	−	0.975684i	$-0.570339\pi$
$241$	−6.62865e81	−0.438366	−0.219183	+	0.975684i	$0.570339\pi$
$242$	2.42331e82	1.38924
$243$	−1.29007e81	−0.0641500
$244$	3.15843e82	1.36308
$245$	4.47243e81	0.167615
$246$	−2.24264e82	−0.730296
$247$	−8.79073e81	−0.248874
$248$	6.07502e82	1.49611
$249$	−1.67398e82	−0.358817
$250$	3.97208e82	0.741460
$251$	−3.15302e82	−0.512842	−0.256421	−	0.966565i	$-0.582543\pi$
$251$	−3.15302e82	−0.512842	−0.256421	+	0.966565i	$0.582543\pi$
$252$	2.42307e82	0.343595
$253$	−9.50495e82	−1.17569
$254$	−1.00893e83	−1.08917
$255$	−1.46387e82	−0.137995
$256$	−1.15850e83	−0.954149
$257$	−8.31953e82	−0.598971	−0.299486	−	0.954101i	$-0.596815\pi$
$257$	−8.31953e82	−0.598971	−0.299486	+	0.954101i	$0.596815\pi$
$258$	3.03684e83	1.91224
$259$	−1.03643e83	−0.571079
$260$	1.74874e83	0.843614
$261$	1.11194e83	0.469876
$262$	5.10198e83	1.88949
$263$	5.24503e81	0.0170324	0.00851618	−	0.999964i	$-0.497289\pi$
$263$	5.24503e81	0.0170324	0.00851618	+	0.999964i	$0.497289\pi$
$264$	7.04767e83	2.00775
$265$	8.18392e82	0.204635
$266$	5.24417e82	0.115149
$267$	−4.03702e83	−0.778794
$268$	−1.04808e84	−1.77723
$269$	3.29711e83	0.491676	0.245838	−	0.969311i	$-0.420937\pi$
$269$	3.29711e83	0.491676	0.245838	+	0.969311i	$0.420937\pi$
$270$	5.55424e82	0.0728743
$271$	1.08002e84	1.24736	0.623679	−	0.781681i	$-0.285637\pi$
$271$	1.08002e84	1.24736	0.623679	+	0.781681i	$0.285637\pi$
$272$	−2.80019e84	−2.84814
$273$	4.66916e83	0.418435
$274$	−1.64150e84	−1.29672
$275$	1.81987e84	1.26783
$276$	−2.02024e84	−1.24176
$277$	−2.99359e83	−0.162420	−0.0812101	−	0.996697i	$-0.525878\pi$
$277$	−2.99359e83	−0.162420	−0.0812101	+	0.996697i	$0.525878\pi$
$278$	−2.99805e84	−1.43646
$279$	4.48307e83	0.189771
$280$	−6.12288e83	−0.229089
$281$	1.57096e84	0.519752	0.259876	−	0.965642i	$-0.416318\pi$
$281$	1.57096e84	0.519752	0.259876	+	0.965642i	$0.416318\pi$
$282$	9.47147e83	0.277219
$283$	6.31338e83	0.163542	0.0817711	−	0.996651i	$-0.473942\pi$
$283$	6.31338e83	0.163542	0.0817711	+	0.996651i	$0.473942\pi$
$284$	−1.72007e85	−3.94515
$285$	8.50687e82	0.0172831
$286$	2.31388e85	4.16593
$287$	1.82440e84	0.291202
$288$	4.43683e84	0.628104
$289$	2.88928e84	0.362922
$290$	−4.78731e84	−0.533778
$291$	−3.24619e84	−0.321415
$292$	4.34808e85	3.82462
$293$	9.95254e84	0.778039	0.389019	−	0.921230i	$-0.372814\pi$
$293$	9.95254e84	0.778039	0.389019	+	0.921230i	$0.372814\pi$
$294$	1.25780e85	0.874238
$295$	4.82016e84	0.297990
$296$	−6.40725e85	−3.52458
$297$	5.20085e84	0.254669
$298$	−6.01427e85	−2.62254
$299$	−3.89293e85	−1.51224
$300$	3.86806e85	1.33909
$301$	−2.47048e85	−0.762494
$302$	1.05264e86	2.89762
$303$	−1.19173e85	−0.292690
$304$	1.62726e85	0.356712
$305$	−5.88966e84	−0.115278
$306$	−4.11690e85	−0.719749
$307$	4.27104e85	0.667205	0.333603	−	0.942714i	$-0.391736\pi$
$307$	4.27104e85	0.667205	0.333603	+	0.942714i	$0.391736\pi$
$308$	−9.76845e85	−1.36404
$309$	−1.89476e85	−0.236584
$310$	−1.93013e85	−0.215580
$311$	8.77908e85	0.877436	0.438718	−	0.898625i	$-0.355433\pi$
$311$	8.77908e85	0.877436	0.438718	+	0.898625i	$0.355433\pi$
$312$	2.88651e86	2.58249
$313$	−2.19232e86	−1.75640	−0.878202	−	0.478289i	$-0.841257\pi$
$313$	−2.19232e86	−1.75640	−0.878202	+	0.478289i	$0.841257\pi$
$314$	−3.10573e86	−2.22890
$315$	−4.51839e84	−0.0290583
$316$	1.53175e86	0.883044
$317$	−1.25374e86	−0.648131	−0.324066	−	0.946035i	$-0.605050\pi$
$317$	−1.25374e86	−0.648131	−0.324066	+	0.946035i	$0.605050\pi$
$318$	2.30160e86	1.06732
$319$	−4.48272e86	−1.86536
$320$	−5.73043e85	−0.214049
$321$	1.60487e86	0.538290
$322$	2.32235e86	0.699682
$323$	−6.30544e85	−0.170698
$324$	1.10542e86	0.268983
$325$	7.45361e86	1.63076
$326$	−1.22361e87	−2.40789
$327$	−3.85387e86	−0.682337
$328$	1.12785e87	1.79724
$329$	−7.70507e85	−0.110540
$330$	−2.23916e86	−0.289304
$331$	−5.22460e86	−0.608117	−0.304058	−	0.952653i	$-0.598342\pi$
$331$	−5.22460e86	−0.608117	−0.304058	+	0.952653i	$0.598342\pi$
$332$	1.43438e87	1.50453
$333$	−4.72825e86	−0.447068
$334$	1.24891e87	1.06482
$335$	1.95440e86	0.150303
$336$	−8.64312e86	−0.599744
$337$	1.57192e87	0.984465	0.492232	−	0.870464i	$-0.336181\pi$
$337$	1.57192e87	0.984465	0.492232	+	0.870464i	$0.336181\pi$
$338$	6.20583e87	3.50892
$339$	1.73486e86	0.0885878
$340$	1.25434e87	0.578618
$341$	−1.80733e87	−0.753374
$342$	2.39243e86	0.0901443
$343$	−2.27305e87	−0.774394
$344$	−1.52726e88	−4.70596
$345$	3.76722e86	0.105018
$346$	−3.83026e87	−0.966279
$347$	3.98273e87	0.909523	0.454762	−	0.890613i	$-0.349724\pi$
$347$	3.98273e87	0.909523	0.454762	+	0.890613i	$0.349724\pi$
$348$	−9.52783e87	−1.97020
$349$	5.60810e87	1.05036	0.525181	−	0.850991i	$-0.323998\pi$
$349$	5.60810e87	1.05036	0.525181	+	0.850991i	$0.323998\pi$
$350$	−4.44651e87	−0.754521
$351$	2.13010e87	0.327571
$352$	−1.78868e88	−2.49351
$353$	−9.25329e87	−1.16969	−0.584843	−	0.811147i	$-0.698844\pi$
$353$	−9.25329e87	−1.16969	−0.584843	+	0.811147i	$0.698844\pi$
$354$	1.35560e88	1.55424
$355$	3.20749e87	0.333647
$356$	3.45919e88	3.26550
$357$	3.34911e87	0.286996
$358$	5.64005e87	0.438852
$359$	1.77421e88	1.25385	0.626927	−	0.779078i	$-0.284312\pi$
$359$	1.77421e88	1.25385	0.626927	+	0.779078i	$0.284312\pi$
$360$	−2.79330e87	−0.179342
$361$	−1.67731e88	−0.978621
$362$	4.27978e88	2.26974
$363$	−8.99351e87	−0.433661
$364$	−4.00085e88	−1.75451
$365$	−8.10804e87	−0.323454
$366$	−1.65638e88	−0.601259
$367$	−3.13901e88	−1.03708	−0.518541	−	0.855053i	$-0.673525\pi$
$367$	−3.13901e88	−1.03708	−0.518541	+	0.855053i	$0.673525\pi$
$368$	7.20623e88	2.16750
$369$	8.32303e87	0.227967
$370$	2.03569e88	0.507869
$371$	−1.87236e88	−0.425589
$372$	−3.84140e88	−0.795716
$373$	9.24279e87	0.174521	0.0872606	−	0.996186i	$-0.472189\pi$
$373$	9.24279e87	0.174521	0.0872606	+	0.996186i	$0.472189\pi$
$374$	1.65970e89	2.85733
$375$	−1.47414e88	−0.231452
$376$	−4.76333e88	−0.682228
$377$	−1.83598e89	−2.39934
$378$	−1.27073e88	−0.151560
$379$	−6.43865e88	−0.701038	−0.350519	−	0.936556i	$-0.613995\pi$
$379$	−6.43865e88	−0.701038	−0.350519	+	0.936556i	$0.613995\pi$
$380$	−7.28926e87	−0.0724685
$381$	3.74439e88	0.339993
$382$	2.22131e89	1.84256
$383$	−9.00739e88	−0.682718	−0.341359	−	0.939933i	$-0.610887\pi$
$383$	−9.00739e88	−0.682718	−0.341359	+	0.939933i	$0.610887\pi$
$384$	−4.11623e87	−0.0285149
$385$	1.82156e88	0.115358
$386$	−8.40355e87	−0.0486632
$387$	−1.12705e89	−0.596917
$388$	2.78156e89	1.34770
$389$	9.34313e88	0.414220	0.207110	−	0.978318i	$-0.433594\pi$
$389$	9.34313e88	0.414220	0.207110	+	0.978318i	$0.433594\pi$
$390$	−9.17090e88	−0.372120
$391$	−2.79233e89	−1.03722
$392$	−6.32566e89	−2.15148
$393$	−1.89348e89	−0.589816
$394$	8.39225e89	2.39474
$395$	−2.85631e88	−0.0746802
$396$	−4.45644e89	−1.06783
$397$	−4.45619e89	−0.978794	−0.489397	−	0.872061i	$-0.662783\pi$
$397$	−4.45619e89	−0.978794	−0.489397	+	0.872061i	$0.662783\pi$
$398$	1.33958e90	2.69775
$399$	−1.94625e88	−0.0359446
$400$	−1.37974e90	−2.33738
$401$	−1.21587e90	−1.88975	−0.944876	−	0.327428i	$-0.893818\pi$
$401$	−1.21587e90	−1.88975	−0.944876	+	0.327428i	$0.893818\pi$
$402$	5.49644e89	0.783939
$403$	−7.40224e89	−0.969035
$404$	1.02115e90	1.22725
$405$	−2.06132e88	−0.0227482
$406$	1.09527e90	1.11013
$407$	1.90617e90	1.77482
$408$	2.07044e90	1.77128
$409$	1.84343e90	1.44935	0.724673	−	0.689093i	$-0.241991\pi$
$409$	1.84343e90	1.44935	0.724673	+	0.689093i	$0.241991\pi$
$410$	−3.58338e89	−0.258970
$411$	6.09204e89	0.404781
$412$	1.62356e90	0.992003
$413$	−1.10278e90	−0.619745
$414$	1.05947e90	0.547745
$415$	−2.67475e89	−0.127240
$416$	−7.32589e90	−3.20731
$417$	1.11265e90	0.448400
$418$	−9.64494e89	−0.357864
$419$	−2.06168e90	−0.704431	−0.352216	−	0.935919i	$-0.614572\pi$
$419$	−2.06168e90	−0.704431	−0.352216	+	0.935919i	$0.614572\pi$
$420$	3.87166e89	0.121842
$421$	−1.67203e90	−0.484744	−0.242372	−	0.970183i	$-0.577925\pi$
$421$	−1.67203e90	−0.484744	−0.242372	+	0.970183i	$0.577925\pi$
$422$	2.21471e90	0.591613
$423$	−3.51511e89	−0.0865358
$424$	−1.15751e91	−2.62665
$425$	5.34635e90	1.11851
$426$	9.02057e90	1.74022
$427$	1.34747e90	0.239749
$428$	−1.37516e91	−2.25706
$429$	−8.58740e90	−1.30042
$430$	4.85237e90	0.678097
$431$	−7.81140e90	−1.00754	−0.503771	−	0.863837i	$-0.668054\pi$
$431$	−7.81140e90	−1.00754	−0.503771	+	0.863837i	$0.668054\pi$
$432$	−3.94305e90	−0.469508
$433$	−2.60876e89	−0.0286815	−0.0143408	−	0.999897i	$-0.504565\pi$
$433$	−2.60876e89	−0.0286815	−0.0143408	+	0.999897i	$0.504565\pi$
$434$	4.41586e90	0.448353
$435$	1.77670e90	0.166622
$436$	3.30225e91	2.86106
$437$	1.62269e90	0.129905
$438$	−2.28026e91	−1.68705
$439$	−1.62970e91	−1.11451	−0.557254	−	0.830342i	$-0.688145\pi$
$439$	−1.62970e91	−1.11451	−0.557254	+	0.830342i	$0.688145\pi$
$440$	1.12610e91	0.711969
$441$	−4.66803e90	−0.272899
$442$	6.79763e91	3.67527
$443$	3.01228e90	0.150649	0.0753245	−	0.997159i	$-0.476001\pi$
$443$	3.01228e90	0.150649	0.0753245	+	0.997159i	$0.476001\pi$
$444$	4.05148e91	1.87457
$445$	−6.45050e90	−0.276168
$446$	−1.93846e91	−0.768075
$447$	2.23205e91	0.818643
$448$	1.31104e91	0.445168
$449$	−5.15334e91	−1.62028	−0.810140	−	0.586236i	$-0.800609\pi$
$449$	−5.15334e91	−1.62028	−0.810140	+	0.586236i	$0.800609\pi$
$450$	−2.02853e91	−0.590675
$451$	−3.35538e91	−0.905006
$452$	−1.48654e91	−0.371451
$453$	−3.90663e91	−0.904511
$454$	−7.68683e91	−1.64938
$455$	7.46056e90	0.148381
$456$	−1.20318e91	−0.221842
$457$	6.35622e91	1.08665	0.543326	−	0.839522i	$-0.317165\pi$
$457$	6.35622e91	1.08665	0.543326	+	0.839522i	$0.317165\pi$
$458$	8.75701e91	1.38834
$459$	1.52789e91	0.224674
$460$	−3.22801e91	−0.440342
$461$	−4.71832e91	−0.597180	−0.298590	−	0.954382i	$-0.596516\pi$
$461$	−4.71832e91	−0.597180	−0.298590	+	0.954382i	$0.596516\pi$
$462$	5.12287e91	0.601680
$463$	4.60871e91	0.502383	0.251192	−	0.967937i	$-0.419178\pi$
$463$	4.60871e91	0.502383	0.251192	+	0.967937i	$0.419178\pi$
$464$	3.39860e92	3.43898
$465$	7.16322e90	0.0672948
$466$	−2.62818e92	−2.29267
$467$	7.18603e91	0.582179	0.291089	−	0.956696i	$-0.405982\pi$
$467$	7.18603e91	0.582179	0.291089	+	0.956696i	$0.405982\pi$
$468$	−1.82522e92	−1.37351
$469$	−4.47137e91	−0.312592
$470$	1.51339e91	0.0983046
$471$	1.15262e92	0.695767
$472$	−6.81747e92	−3.82494
$473$	4.54363e92	2.36970
$474$	−8.03294e91	−0.389513
$475$	−3.10689e91	−0.140087
$476$	−2.86974e92	−1.20338
$477$	−8.54185e91	−0.333171
$478$	−3.36639e92	−1.22152
$479$	−2.86248e92	−0.966424	−0.483212	−	0.875503i	$-0.660530\pi$
$479$	−2.86248e92	−0.966424	−0.483212	+	0.875503i	$0.660530\pi$
$480$	7.08933e91	0.222732
$481$	7.80706e92	2.28288
$482$	−2.97870e92	−0.810782
$483$	−8.61886e91	−0.218411
$484$	7.70625e92	1.81835
$485$	−5.18689e91	−0.113977
$486$	−5.79715e91	−0.118649
$487$	8.18663e92	1.56083	0.780416	−	0.625261i	$-0.215007\pi$
$487$	8.18663e92	1.56083	0.780416	+	0.625261i	$0.215007\pi$
$488$	8.33013e92	1.47968
$489$	4.54114e92	0.751639
$490$	2.00976e92	0.310013
$491$	4.60884e92	0.662643	0.331322	−	0.943518i	$-0.392505\pi$
$491$	4.60884e92	0.662643	0.331322	+	0.943518i	$0.392505\pi$
$492$	−7.13173e92	−0.955870
$493$	−1.31692e93	−1.64566
$494$	−3.95027e92	−0.460306
$495$	8.31010e91	0.0903082
$496$	1.37023e93	1.38892
$497$	−7.33827e92	−0.693902
$498$	−7.52232e92	−0.663650
$499$	1.76577e93	1.45367	0.726833	−	0.686814i	$-0.240991\pi$
$499$	1.76577e93	1.45367	0.726833	+	0.686814i	$0.240991\pi$
$500$	1.26314e93	0.970483
$501$	−4.63503e92	−0.332392
$502$	−1.41687e93	−0.948529
$503$	2.62126e93	1.63838	0.819189	−	0.573523i	$-0.194424\pi$
$503$	2.62126e93	1.63838	0.819189	+	0.573523i	$0.194424\pi$
$504$	6.39066e92	0.372986
$505$	−1.90419e92	−0.103791
$506$	−4.27121e93	−2.17449
$507$	−2.30314e93	−1.09533
$508$	−3.20845e93	−1.42560
$509$	−1.99347e93	−0.827649	−0.413824	−	0.910357i	$-0.635807\pi$
$509$	−1.99347e93	−0.827649	−0.413824	+	0.910357i	$0.635807\pi$
$510$	−6.57813e92	−0.255230
$511$	1.85500e93	0.672703
$512$	−5.35160e93	−1.81414
$513$	−8.87892e91	−0.0281391
$514$	−3.73852e93	−1.10783
$515$	−3.02751e92	−0.0838951
$516$	9.65731e93	2.50289
$517$	1.41710e93	0.343539
$518$	−4.65736e93	−1.05624
$519$	1.42151e93	0.301631
$520$	4.61217e93	0.915777
$521$	−2.85225e90	−0.000530013 0	−0.000265007	−	1.00000i	$-0.500084\pi$
$521$	−2.85225e90	−0.000530013 0	−0.000265007		1.00000i	$0.500084\pi$
$522$	4.99668e93	0.869060
$523$	−3.15760e93	−0.514101	−0.257051	−	0.966398i	$-0.582751\pi$
$523$	−3.15760e93	−0.514101	−0.257051	+	0.966398i	$0.582751\pi$
$524$	1.62246e94	2.47311
$525$	1.65021e93	0.235529
$526$	2.35695e92	0.0315022
$527$	−5.30950e93	−0.664642
$528$	1.58962e94	1.86390
$529$	−1.91776e93	−0.210656
$530$	3.67759e93	0.378482
$531$	−5.03097e93	−0.485166
$532$	1.66768e93	0.150716
$533$	−1.37426e94	−1.16407
$534$	−1.81411e94	−1.44042
$535$	2.56432e93	0.190883
$536$	−2.76423e94	−1.92925
$537$	−2.09317e93	−0.136991
$538$	1.48161e94	0.909381
$539$	1.88189e94	1.08338
$540$	1.76628e93	0.0953838
$541$	7.86442e93	0.398438	0.199219	−	0.979955i	$-0.436159\pi$
$541$	7.86442e93	0.398438	0.199219	+	0.979955i	$0.436159\pi$
$542$	4.85325e94	2.30705
$543$	−1.58834e94	−0.708515
$544$	−5.25473e94	−2.19983
$545$	−6.15785e93	−0.241963
$546$	2.09817e94	0.773917
$547$	1.26682e94	0.438686	0.219343	−	0.975648i	$-0.429609\pi$
$547$	1.26682e94	0.438686	0.219343	+	0.975648i	$0.429609\pi$
$548$	−5.22007e94	−1.69726
$549$	6.14724e93	0.187687
$550$	8.17789e94	2.34492
$551$	7.65292e93	0.206109
$552$	−5.32824e94	−1.34799
$553$	6.53482e93	0.155316
$554$	−1.34522e94	−0.300405
$555$	−7.55497e93	−0.158535
$556$	−9.53396e94	−1.88015
$557$	−4.71380e94	−0.873710	−0.436855	−	0.899532i	$-0.643908\pi$
$557$	−4.71380e94	−0.873710	−0.436855	+	0.899532i	$0.643908\pi$
$558$	2.01455e94	0.350992
$559$	1.86093e95	3.04805
$560$	−1.38103e94	−0.212675
$561$	−6.15959e94	−0.891935
$562$	7.05936e94	0.961308
$563$	−1.22186e95	−1.56488	−0.782442	−	0.622724i	$-0.786026\pi$
$563$	−1.22186e95	−1.56488	−0.782442	+	0.622724i	$0.786026\pi$
$564$	3.01198e94	0.362847
$565$	2.77202e93	0.0314141
$566$	2.83703e94	0.302480
$567$	4.71600e93	0.0473106
$568$	−4.53657e95	−4.28262
$569$	4.75462e94	0.422418	0.211209	−	0.977441i	$-0.432260\pi$
$569$	4.75462e94	0.422418	0.211209	+	0.977441i	$0.432260\pi$
$570$	3.82271e93	0.0319660
$571$	−1.61556e95	−1.27168	−0.635839	−	0.771822i	$-0.719346\pi$
$571$	−1.61556e95	−1.27168	−0.635839	+	0.771822i	$0.719346\pi$
$572$	7.35826e95	5.45271
$573$	−8.24385e94	−0.575169
$574$	8.19825e94	0.538593
$575$	−1.37587e95	−0.851210
$576$	5.98105e94	0.348499
$577$	−1.16048e95	−0.636901	−0.318450	−	0.947940i	$-0.603162\pi$
$577$	−1.16048e95	−0.636901	−0.318450	+	0.947940i	$0.603162\pi$
$578$	1.29835e95	0.671244
$579$	3.11878e93	0.0151906
$580$	−1.52239e95	−0.698652
$581$	6.11943e94	0.264627
$582$	−1.45873e95	−0.594474
$583$	3.44360e95	1.32266
$584$	1.14677e96	4.15178
$585$	3.40356e94	0.116160
$586$	4.47235e95	1.43902
$587$	−4.47411e95	−1.35735	−0.678675	−	0.734438i	$-0.737446\pi$
$587$	−4.47411e95	−1.35735	−0.678675	+	0.734438i	$0.737446\pi$
$588$	3.99988e95	1.14427
$589$	3.08548e94	0.0832424
$590$	2.16602e95	0.551148
$591$	−3.11458e95	−0.747535
$592$	−1.44517e96	−3.27205
$593$	−8.73204e95	−1.86521	−0.932607	−	0.360894i	$-0.882472\pi$
$593$	−8.73204e95	−1.86521	−0.932607	+	0.360894i	$0.882472\pi$
$594$	2.33709e95	0.471024
$595$	5.35133e94	0.101772
$596$	−1.91257e96	−3.43259
$597$	−4.97151e95	−0.842120
$598$	−1.74936e96	−2.79697
$599$	3.48465e95	0.525937	0.262968	−	0.964804i	$-0.415299\pi$
$599$	3.48465e95	0.525937	0.262968	+	0.964804i	$0.415299\pi$
$600$	1.02017e96	1.45364
$601$	9.66420e95	1.30016	0.650080	−	0.759866i	$-0.274736\pi$
$601$	9.66420e95	1.30016	0.650080	+	0.759866i	$0.274736\pi$
$602$	−1.11015e96	−1.41027
$603$	−2.03987e95	−0.244712
$604$	3.34746e96	3.79263
$605$	−1.43702e95	−0.153781
$606$	−5.35524e95	−0.541344
$607$	7.70118e95	0.735440	0.367720	−	0.929936i	$-0.380138\pi$
$607$	7.70118e95	0.735440	0.367720	+	0.929936i	$0.380138\pi$
$608$	3.05365e95	0.275515
$609$	−4.06482e95	−0.346533
$610$	−2.64662e95	−0.213212
$611$	5.80398e95	0.441880
$612$	−1.30920e96	−0.942065
$613$	2.65795e96	1.80784	0.903920	−	0.427702i	$-0.140677\pi$
$613$	2.65795e96	1.80784	0.903920	+	0.427702i	$0.140677\pi$
$614$	1.91926e96	1.23403
$615$	1.32988e95	0.0808393
$616$	−2.57636e96	−1.48072
$617$	−1.10138e96	−0.598549	−0.299274	−	0.954167i	$-0.596745\pi$
$617$	−1.10138e96	−0.598549	−0.299274	+	0.954167i	$0.596745\pi$
$618$	−8.51441e95	−0.437575
$619$	9.13514e95	0.444005	0.222003	−	0.975046i	$-0.428741\pi$
$619$	9.13514e95	0.444005	0.222003	+	0.975046i	$0.428741\pi$
$620$	−6.13793e95	−0.282169
$621$	−3.93198e95	−0.170982
$622$	3.94503e96	1.62286
$623$	1.47578e96	0.574360
$624$	6.51059e96	2.39746
$625$	2.51402e96	0.876009
$626$	−9.85158e96	−3.24856
$627$	3.57949e95	0.111710
$628$	−9.87640e96	−2.91736
$629$	5.59987e96	1.56578
$630$	−2.03042e95	−0.0537448
$631$	3.26321e96	0.817772	0.408886	−	0.912586i	$-0.365917\pi$
$631$	3.26321e96	0.817772	0.408886	+	0.912586i	$0.365917\pi$
$632$	4.03987e96	0.958580
$633$	−8.21938e95	−0.184676
$634$	−5.63390e96	−1.19875
$635$	5.98293e95	0.120565
$636$	7.31923e96	1.39700
$637$	7.70764e96	1.39351
$638$	−2.01439e97	−3.45008
$639$	−3.34777e96	−0.543220
$640$	−6.57706e94	−0.0101117
$641$	−8.27835e96	−1.20599	−0.602993	−	0.797747i	$-0.706025\pi$
$641$	−8.27835e96	−1.20599	−0.602993	+	0.797747i	$0.706025\pi$
$642$	7.21176e96	0.995596
$643$	−1.21933e97	−1.59530	−0.797649	−	0.603122i	$-0.793923\pi$
$643$	−1.21933e97	−1.59530	−0.797649	+	0.603122i	$0.793923\pi$
$644$	7.38522e96	0.915801
$645$	−1.80084e96	−0.211673
$646$	−2.83346e96	−0.315715
$647$	7.71717e96	0.815193	0.407597	−	0.913162i	$-0.366367\pi$
$647$	7.71717e96	0.815193	0.407597	+	0.913162i	$0.366367\pi$
$648$	2.91546e96	0.291991
$649$	2.02821e97	1.92606
$650$	3.34941e97	3.01618
$651$	−1.63884e96	−0.139956
$652$	−3.89116e97	−3.15164
$653$	−9.62755e96	−0.739624	−0.369812	−	0.929107i	$-0.620578\pi$
$653$	−9.62755e96	−0.739624	−0.369812	+	0.929107i	$0.620578\pi$
$654$	−1.73180e97	−1.26202
$655$	−3.02547e96	−0.209155
$656$	2.54390e97	1.66847
$657$	8.46264e96	0.526624
$658$	−3.46241e96	−0.204449
$659$	−1.81593e97	−1.01754	−0.508771	−	0.860902i	$-0.669900\pi$
$659$	−1.81593e97	−1.01754	−0.508771	+	0.860902i	$0.669900\pi$
$660$	−7.12066e96	−0.378664
$661$	−1.90506e97	−0.961519	−0.480760	−	0.876852i	$-0.659639\pi$
$661$	−1.90506e97	−0.961519	−0.480760	+	0.876852i	$0.659639\pi$
$662$	−2.34776e97	−1.12474
$663$	−2.52278e97	−1.14726
$664$	3.78307e97	1.63323
$665$	−3.10979e95	−0.0127463
$666$	−2.12472e97	−0.826876
$667$	3.38906e97	1.25238
$668$	3.97161e97	1.39373
$669$	7.19411e96	0.239760
$670$	8.78241e96	0.277992
$671$	−2.47823e97	−0.745099
$672$	−1.62193e97	−0.463227
$673$	−2.87518e97	−0.780092	−0.390046	−	0.920795i	$-0.627541\pi$
$673$	−2.87518e97	−0.780092	−0.390046	+	0.920795i	$0.627541\pi$
$674$	7.06371e97	1.82082
$675$	7.52839e96	0.184383
$676$	1.97349e98	4.59276
$677$	−4.19371e97	−0.927448	−0.463724	−	0.885980i	$-0.653487\pi$
$677$	−4.19371e97	−0.927448	−0.463724	+	0.885980i	$0.653487\pi$
$678$	7.79588e96	0.163848
$679$	1.18668e97	0.237043
$680$	3.30823e97	0.628113
$681$	2.85278e97	0.514865
$682$	−8.12153e97	−1.39340
$683$	6.43512e96	0.104965	0.0524823	−	0.998622i	$-0.483287\pi$
$683$	6.43512e96	0.104965	0.0524823	+	0.998622i	$0.483287\pi$
$684$	7.60805e96	0.117988
$685$	9.73409e96	0.143539
$686$	−1.02143e98	−1.43228
$687$	−3.24995e97	−0.433381
$688$	−3.44478e98	−4.36878
$689$	1.41039e98	1.70128
$690$	1.69287e97	0.194236
$691$	−5.03705e97	−0.549774	−0.274887	−	0.961477i	$-0.588640\pi$
$691$	−5.03705e97	−0.549774	−0.274887	+	0.961477i	$0.588640\pi$
$692$	−1.21804e98	−1.26474
$693$	−1.90123e97	−0.187818
$694$	1.78971e98	1.68221
$695$	1.77784e97	0.159007
$696$	−2.51290e98	−2.13873
$697$	−9.85733e97	−0.798415
$698$	2.52010e98	1.94270
$699$	9.75385e97	0.715671
$700$	−1.41401e98	−0.987578
$701$	2.97803e97	0.197996	0.0989982	−	0.995088i	$-0.468436\pi$
$701$	2.97803e97	0.197996	0.0989982	+	0.995088i	$0.468436\pi$
$702$	9.57199e97	0.605860
$703$	−3.25422e97	−0.196105
$704$	−2.41123e98	−1.38351
$705$	−5.61657e96	−0.0306864
$706$	−4.15813e98	−2.16339
$707$	4.35651e97	0.215858
$708$	4.31087e98	2.03431
$709$	−2.19534e98	−0.986748	−0.493374	−	0.869817i	$-0.664237\pi$
$709$	−2.19534e98	−0.986748	−0.493374	+	0.869817i	$0.664237\pi$
$710$	1.44134e98	0.617097
$711$	2.98123e97	0.121589
$712$	9.12338e98	3.54483
$713$	1.36639e98	0.505808
$714$	1.50498e98	0.530814
$715$	−1.37213e98	−0.461143
$716$	1.79357e98	0.574405
$717$	1.24935e98	0.381307
$718$	7.97272e98	2.31907
$719$	−6.00122e98	−1.66377	−0.831884	−	0.554950i	$-0.812737\pi$
$719$	−6.00122e98	−1.66377	−0.831884	+	0.554950i	$0.812737\pi$
$720$	−6.30035e97	−0.166492
$721$	6.92651e97	0.174481
$722$	−7.53728e98	−1.81001
$723$	1.10547e98	0.253091
$724$	1.36100e99	2.97082
$725$	−6.48887e98	−1.35054
$726$	−4.04139e98	−0.802079
$727$	−3.54961e98	−0.671805	−0.335902	−	0.941897i	$-0.609041\pi$
$727$	−3.54961e98	−0.671805	−0.335902	+	0.941897i	$0.609041\pi$
$728$	−1.05520e99	−1.90459
$729$	2.15147e97	0.0370370
$730$	−3.64349e98	−0.598244
$731$	1.33481e99	2.09060
$732$	−5.26737e98	−0.786976
$733$	−1.20212e99	−1.71340	−0.856701	−	0.515814i	$-0.827490\pi$
$733$	−1.20212e99	−1.71340	−0.856701	+	0.515814i	$0.827490\pi$
$734$	−1.41057e99	−1.91814
$735$	−7.45875e97	−0.0967728
$736$	1.35229e99	1.67412
$737$	8.22363e98	0.971482
$738$	3.74010e98	0.421637
$739$	−6.67029e98	−0.717649	−0.358824	−	0.933405i	$-0.616822\pi$
$739$	−6.67029e98	−0.717649	−0.358824	+	0.933405i	$0.616822\pi$
$740$	6.47360e98	0.664740
$741$	1.46605e98	0.143688
$742$	−8.41379e98	−0.787149
$743$	1.00423e99	0.896845	0.448422	−	0.893822i	$-0.351986\pi$
$743$	1.00423e99	0.896845	0.448422	+	0.893822i	$0.351986\pi$
$744$	−1.01314e99	−0.863782
$745$	3.56645e98	0.290299
$746$	4.15341e98	0.322786
$747$	2.79173e98	0.207163
$748$	5.27795e99	3.73990
$749$	−5.86679e98	−0.396989
$750$	−6.62431e98	−0.428082
$751$	−8.00866e98	−0.494291	−0.247145	−	0.968978i	$-0.579492\pi$
$751$	−8.00866e98	−0.494291	−0.247145	+	0.968978i	$0.579492\pi$
$752$	−1.07438e99	−0.633348
$753$	5.25836e98	0.296090
$754$	−8.25030e99	−4.43770
$755$	−6.24215e98	−0.320748
$756$	−4.04099e98	−0.198374
$757$	2.10190e99	0.985833	0.492916	−	0.870077i	$-0.335931\pi$
$757$	2.10190e99	0.985833	0.492916	+	0.870077i	$0.335931\pi$
$758$	−2.89332e99	−1.29661
$759$	1.58516e99	0.678783
$760$	−1.92249e98	−0.0786675
$761$	−3.87689e99	−1.51605	−0.758024	−	0.652227i	$-0.773835\pi$
$761$	−3.87689e99	−1.51605	−0.758024	+	0.652227i	$0.773835\pi$
$762$	1.68261e99	0.628834
$763$	1.40883e99	0.503224
$764$	7.06388e99	2.41170
$765$	2.44131e98	0.0796717
$766$	−4.04763e99	−1.26272
$767$	8.30690e99	2.47742
$768$	1.93205e99	0.550878
$769$	−4.80235e99	−1.30917	−0.654584	−	0.755989i	$-0.727156\pi$
$769$	−4.80235e99	−1.30917	−0.654584	+	0.755989i	$0.727156\pi$
$770$	8.18552e98	0.213361
$771$	1.38746e99	0.345816
$772$	−2.67238e98	−0.0636944
$773$	5.82222e99	1.32708	0.663539	−	0.748142i	$-0.269054\pi$
$773$	5.82222e99	1.32708	0.663539	+	0.748142i	$0.269054\pi$
$774$	−5.06459e99	−1.10403
$775$	−2.61616e99	−0.545451
$776$	7.33616e99	1.46298
$777$	1.72847e99	0.329713
$778$	4.19850e99	0.766122
$779$	5.72833e98	0.0999967
$780$	−2.91640e99	−0.487061
$781$	1.34963e100	2.15653
$782$	−1.25478e100	−1.91838
$783$	−1.85440e99	−0.271283
$784$	−1.42677e100	−1.99733
$785$	1.84169e99	0.246726
$786$	−8.50866e99	−1.09090
$787$	−1.62907e99	−0.199899	−0.0999496	−	0.994993i	$-0.531868\pi$
$787$	−1.62907e99	−0.199899	−0.0999496	+	0.994993i	$0.531868\pi$
$788$	2.66878e100	3.13443
$789$	−8.74724e97	−0.00983364
$790$	−1.28353e99	−0.138125
$791$	−6.34197e98	−0.0653335
$792$	−1.17535e100	−1.15918
$793$	−1.01500e100	−0.958391
$794$	−2.00247e100	−1.81033
$795$	−1.36485e99	−0.118146
$796$	4.25993e100	3.53103
$797$	1.34921e98	0.0107095	0.00535474	−	0.999986i	$-0.498296\pi$
$797$	1.34921e98	0.0107095	0.00535474	+	0.999986i	$0.498296\pi$
$798$	−8.74580e98	−0.0664814
$799$	4.16310e99	0.303077
$800$	−2.58917e100	−1.80533
$801$	6.73262e99	0.449637
$802$	−5.46370e100	−3.49520
$803$	−3.41167e100	−2.09065
$804$	1.74790e100	1.02608
$805$	−1.37715e99	−0.0774505
$806$	−3.32633e100	−1.79228
$807$	−5.49864e99	−0.283869
$808$	2.69322e100	1.33223
$809$	−6.00206e99	−0.284496	−0.142248	−	0.989831i	$-0.545433\pi$
$809$	−6.00206e99	−0.284496	−0.142248	+	0.989831i	$0.545433\pi$
$810$	−9.26290e98	−0.0420740
$811$	2.72763e100	1.18732	0.593658	−	0.804718i	$-0.297683\pi$
$811$	2.72763e100	1.18732	0.593658	+	0.804718i	$0.297683\pi$
$812$	3.48301e100	1.45302
$813$	−1.80117e100	−0.720162
$814$	8.56569e100	3.28262
$815$	7.25601e99	0.266539
$816$	4.66993e100	1.64437
$817$	−7.75692e99	−0.261835
$818$	8.28376e100	2.68064
$819$	−7.78685e99	−0.241583
$820$	−1.13953e100	−0.338961
$821$	−1.70717e100	−0.486898	−0.243449	−	0.969914i	$-0.578279\pi$
$821$	−1.70717e100	−0.486898	−0.243449	+	0.969914i	$0.578279\pi$
$822$	2.73756e100	0.748663
$823$	−3.42370e99	−0.0897846	−0.0448923	−	0.998992i	$-0.514294\pi$
$823$	−3.42370e99	−0.0897846	−0.0448923	+	0.998992i	$0.514294\pi$
$824$	4.28201e100	1.07686
$825$	−3.03503e100	−0.731984
$826$	−4.95554e100	−1.14625
$827$	−7.13292e100	−1.58244	−0.791220	−	0.611531i	$-0.790554\pi$
$827$	−7.13292e100	−1.58244	−0.791220	+	0.611531i	$0.790554\pi$
$828$	3.36919e100	0.716933
$829$	−7.03577e100	−1.43609	−0.718043	−	0.695999i	$-0.754962\pi$
$829$	−7.03577e100	−1.43609	−0.718043	+	0.695999i	$0.754962\pi$
$830$	−1.20194e100	−0.235337
$831$	4.99246e99	0.0937734
$832$	−9.87564e100	−1.77955
$833$	5.52856e100	0.955783
$834$	4.99990e100	0.829339
$835$	−7.40602e99	−0.117870
$836$	−3.06715e100	−0.468401
$837$	−7.47650e99	−0.109565
$838$	−9.26454e100	−1.30288
$839$	2.07269e100	0.279735	0.139867	−	0.990170i	$-0.455332\pi$
$839$	2.07269e100	0.279735	0.139867	+	0.990170i	$0.455332\pi$
$840$	1.02112e100	0.132264
$841$	7.93963e100	0.987048
$842$	−7.51357e100	−0.896559
$843$	−2.61991e100	−0.300079
$844$	7.04291e100	0.774351
$845$	−3.68005e100	−0.388416
$846$	−1.57957e100	−0.160052
$847$	3.28769e100	0.319825
$848$	−2.61079e101	−2.43845
$849$	−1.05289e100	−0.0944211
$850$	2.40247e101	2.06874
$851$	−1.44111e101	−1.19159
$852$	2.86859e101	2.27773
$853$	2.42689e101	1.85058	0.925292	−	0.379256i	$-0.123820\pi$
$853$	2.42689e101	1.85058	0.925292	+	0.379256i	$0.123820\pi$
$854$	6.05508e100	0.443428
$855$	−1.41871e99	−0.00997841
$856$	−3.62689e101	−2.45013
$857$	1.90075e101	1.23335	0.616675	−	0.787218i	$-0.288479\pi$
$857$	1.90075e101	1.23335	0.616675	+	0.787218i	$0.288479\pi$
$858$	−3.85890e101	−2.40520
$859$	1.64755e101	0.986447	0.493224	−	0.869903i	$-0.335818\pi$
$859$	1.64755e101	0.986447	0.493224	+	0.869903i	$0.335818\pi$
$860$	1.54308e101	0.887548
$861$	−3.04258e100	−0.168125
$862$	−3.51019e101	−1.86350
$863$	−4.98333e100	−0.254183	−0.127092	−	0.991891i	$-0.540564\pi$
$863$	−4.98333e100	−0.254183	−0.127092	+	0.991891i	$0.540564\pi$
$864$	−7.39938e100	−0.362636
$865$	2.27134e100	0.106961
$866$	−1.17229e100	−0.0530479
$867$	−4.81850e100	−0.209533
$868$	1.40427e101	0.586840
$869$	−1.20187e101	−0.482696
$870$	7.98389e100	0.308177
$871$	3.36814e101	1.24958
$872$	8.70946e101	3.10579
$873$	5.41374e100	0.185569
$874$	7.29184e100	0.240266
$875$	5.38890e100	0.170696
$876$	−7.25136e101	−2.20815
$877$	−2.43771e101	−0.713669	−0.356834	−	0.934168i	$-0.616144\pi$
$877$	−2.43771e101	−0.713669	−0.356834	+	0.934168i	$0.616144\pi$
$878$	−7.32336e101	−2.06134
$879$	−1.65980e101	−0.449201
$880$	2.53995e101	0.660957
$881$	−2.81770e101	−0.705061	−0.352530	−	0.935800i	$-0.614679\pi$
$881$	−2.81770e101	−0.705061	−0.352530	+	0.935800i	$0.614679\pi$
$882$	−2.09766e101	−0.504742
$883$	−1.96203e101	−0.454006	−0.227003	−	0.973894i	$-0.572893\pi$
$883$	−1.96203e101	−0.454006	−0.227003	+	0.973894i	$0.572893\pi$
$884$	2.16169e102	4.81049
$885$	−8.03866e100	−0.172045
$886$	1.35362e101	0.278633
$887$	−8.62132e99	−0.0170690	−0.00853451	−	0.999964i	$-0.502717\pi$
$887$	−8.62132e99	−0.0170690	−0.00853451	+	0.999964i	$0.502717\pi$
$888$	1.06855e102	2.03492
$889$	−1.36881e101	−0.250745
$890$	−2.89865e101	−0.510787
$891$	−8.67355e100	−0.147033
$892$	−6.16440e101	−1.00532
$893$	−2.41928e100	−0.0379586
$894$	1.00301e102	1.51412
$895$	−3.34454e100	−0.0485783
$896$	1.50474e100	0.0210298
$897$	6.49231e101	0.873092
$898$	−2.31574e102	−2.99679
$899$	6.44415e101	0.802521
$900$	−6.45083e101	−0.773124
$901$	1.01165e102	1.16688
$902$	−1.50780e102	−1.67386
$903$	4.12006e101	0.440226
$904$	−3.92065e101	−0.403225
$905$	−2.53791e101	−0.251246
$906$	−1.75551e102	−1.67294
$907$	−1.55180e102	−1.42359	−0.711796	−	0.702386i	$-0.752118\pi$
$907$	−1.55180e102	−1.42359	−0.711796	+	0.702386i	$0.752118\pi$
$908$	−2.44445e102	−2.15884
$909$	1.98747e101	0.168984
$910$	3.35253e101	0.274438
$911$	−1.00365e102	−0.791038	−0.395519	−	0.918458i	$-0.629435\pi$
$911$	−1.00365e102	−0.791038	−0.395519	+	0.918458i	$0.629435\pi$
$912$	−2.71381e101	−0.205948
$913$	−1.12547e102	−0.822417
$914$	2.85628e102	2.00982
$915$	9.82229e100	0.0665556
$916$	2.78478e102	1.81718
$917$	6.92183e101	0.434989
$918$	6.86583e101	0.415547
$919$	4.05829e101	0.236569	0.118285	−	0.992980i	$-0.462260\pi$
$919$	4.05829e101	0.236569	0.118285	+	0.992980i	$0.462260\pi$
$920$	−8.51365e101	−0.478009
$921$	−7.12289e101	−0.385211
$922$	−2.12026e102	−1.10452
$923$	5.52768e102	2.77386
$924$	1.62910e102	0.787527
$925$	2.75923e102	1.28499
$926$	2.07100e102	0.929184
$927$	3.15992e101	0.136592
$928$	6.37767e102	2.65618
$929$	−2.11166e102	−0.847385	−0.423693	−	0.905806i	$-0.639266\pi$
$929$	−2.11166e102	−0.847385	−0.423693	+	0.905806i	$0.639266\pi$
$930$	3.21892e101	0.124465
$931$	−3.21278e101	−0.119706
$932$	−8.35776e102	−3.00083
$933$	−1.46410e102	−0.506588
$934$	3.22916e102	1.07677
$935$	−9.84203e101	−0.316289
$936$	−4.81388e102	−1.49100
$937$	−1.08050e102	−0.322559	−0.161279	−	0.986909i	$-0.551562\pi$
$937$	−1.08050e102	−0.322559	−0.161279	+	0.986909i	$0.551562\pi$
$938$	−2.00929e102	−0.578155
$939$	3.65617e102	1.01406
$940$	4.81265e101	0.128669
$941$	3.40516e102	0.877599	0.438799	−	0.898585i	$-0.355404\pi$
$941$	3.40516e102	0.877599	0.438799	+	0.898585i	$0.355404\pi$
$942$	5.17948e102	1.28686
$943$	2.53676e102	0.607612
$944$	−1.53770e103	−3.55089
$945$	7.53540e100	0.0167768
$946$	2.04176e103	4.38289
$947$	−1.43689e102	−0.297405	−0.148703	−	0.988882i	$-0.547510\pi$
$947$	−1.43689e102	−0.297405	−0.148703	+	0.988882i	$0.547510\pi$
$948$	−2.55452e102	−0.509826
$949$	−1.39731e103	−2.68912
$950$	−1.39613e102	−0.259097
$951$	2.09088e102	0.374199
$952$	−7.56875e102	−1.30632
$953$	9.66998e101	0.160961	0.0804805	−	0.996756i	$-0.474355\pi$
$953$	9.66998e101	0.160961	0.0804805	+	0.996756i	$0.474355\pi$
$954$	−3.83843e102	−0.616218
$955$	−1.31723e102	−0.203960
$956$	−1.07053e103	−1.59883
$957$	7.47591e102	1.07697
$958$	−1.28631e103	−1.78745
$959$	−2.22702e102	−0.298526
$960$	9.55674e101	0.123581
$961$	−5.41785e102	−0.675881
$962$	3.50824e103	4.22230
$963$	−2.67647e102	−0.310782
$964$	−9.47243e102	−1.06122
$965$	4.98330e100	0.00538672
$966$	−3.87303e102	−0.403962
$967$	−1.19480e101	−0.0120250	−0.00601248	−	0.999982i	$-0.501914\pi$
$967$	−1.19480e101	−0.0120250	−0.00601248	+	0.999982i	$0.501914\pi$
$968$	2.03247e103	1.97389
$969$	1.05157e102	0.0985525
$970$	−2.33082e102	−0.210806
$971$	−1.95902e103	−1.70992	−0.854961	−	0.518692i	$-0.826419\pi$
$971$	−1.95902e103	−1.70992	−0.854961	+	0.518692i	$0.826419\pi$
$972$	−1.84353e102	−0.155297
$973$	−4.06743e102	−0.330695
$974$	3.67880e103	2.88684
$975$	−1.24305e103	−0.941522
$976$	1.87888e103	1.37366
$977$	6.73512e102	0.475317	0.237658	−	0.971349i	$-0.423620\pi$
$977$	6.73512e102	0.475317	0.237658	+	0.971349i	$0.423620\pi$
$978$	2.04064e103	1.39020
$979$	−2.71422e103	−1.78501
$980$	6.39116e102	0.405770
$981$	6.42716e102	0.393948
$982$	2.07106e103	1.22559
$983$	1.04218e103	0.595453	0.297727	−	0.954651i	$-0.403772\pi$
$983$	1.04218e103	0.595453	0.297727	+	0.954651i	$0.403772\pi$
$984$	−1.88094e103	−1.03764
$985$	−4.97659e102	−0.265083
$986$	−5.91780e103	−3.04373
$987$	1.28499e102	0.0638201
$988$	−1.25621e103	−0.602486
$989$	−3.43511e103	−1.59099
$990$	3.73429e102	0.167030
$991$	1.51442e103	0.654190	0.327095	−	0.944991i	$-0.393930\pi$
$991$	1.51442e103	0.654190	0.327095	+	0.944991i	$0.393930\pi$
$992$	2.57133e103	1.07277
$993$	8.71315e102	0.351096
$994$	−3.29758e103	−1.28341
$995$	−7.94366e102	−0.298624
$996$	−2.39214e103	−0.868639
$997$	−1.77984e102	−0.0624306	−0.0312153	−	0.999513i	$-0.509938\pi$
$997$	−1.77984e102	−0.0624306	−0.0312153	+	0.999513i	$0.509938\pi$
$998$	7.93478e103	2.68863
$999$	7.88538e102	0.258115

Twists

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

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

\(f(q)\)	\(=\)	\(q+4.49367e10 q^{2} -1.66772e16 q^{3} +1.42901e21 q^{4} -2.66474e23 q^{5} -7.49418e26 q^{6} +6.09654e28 q^{7} +3.76892e31 q^{8} +2.78128e32 q^{9} +O(q^{10})\)	\(q+4.49367e10 q^{2} -1.66772e16 q^{3} +1.42901e21 q^{4} -2.66474e23 q^{5} -7.49418e26 q^{6} +6.09654e28 q^{7} +3.76892e31 q^{8} +2.78128e32 q^{9} -1.19745e34 q^{10} -1.12126e36 q^{11} -2.38319e37 q^{12} -4.59233e38 q^{13} +2.73959e39 q^{14} +4.44404e39 q^{15} +8.50089e41 q^{16} -3.29400e42 q^{17} +1.24982e43 q^{18} +1.91422e43 q^{19} -3.80795e44 q^{20} -1.01673e45 q^{21} -5.03857e46 q^{22} +8.47703e46 q^{23} -6.28550e47 q^{24} -1.62306e48 q^{25} -2.06364e49 q^{26} -4.63840e48 q^{27} +8.71204e49 q^{28} +3.99793e50 q^{29} +1.99701e50 q^{30} +1.61187e51 q^{31} +1.59524e52 q^{32} +1.86994e52 q^{33} -1.48021e53 q^{34} -1.62457e52 q^{35} +3.97449e53 q^{36} -1.70002e54 q^{37} +8.60188e53 q^{38} +7.65871e54 q^{39} -1.00432e55 q^{40} +2.99251e55 q^{41} -4.56886e55 q^{42} -4.05226e56 q^{43} -1.60229e57 q^{44} -7.41140e55 q^{45} +3.80930e57 q^{46} -1.26384e57 q^{47} -1.41771e58 q^{48} -1.67837e58 q^{49} -7.29349e58 q^{50} +5.49346e58 q^{51} -6.56250e59 q^{52} -3.07119e59 q^{53} -2.08434e59 q^{54} +2.98787e59 q^{55} +2.29774e60 q^{56} -3.19238e59 q^{57} +1.79654e61 q^{58} -1.80886e61 q^{59} +6.35059e60 q^{60} +2.21022e61 q^{61} +7.24322e61 q^{62} +1.69562e61 q^{63} +2.15046e62 q^{64} +1.22374e62 q^{65} +8.40292e62 q^{66} -7.33428e62 q^{67} -4.70717e63 q^{68} -1.41373e63 q^{69} -7.30029e62 q^{70} -1.20368e64 q^{71} +1.04824e64 q^{72} +3.04271e64 q^{73} -7.63935e64 q^{74} +2.70680e64 q^{75} +2.73545e64 q^{76} -6.83580e64 q^{77} +3.44157e65 q^{78} +1.07189e65 q^{79} -2.26527e65 q^{80} +7.73554e64 q^{81} +1.34474e66 q^{82} +1.00375e66 q^{83} -1.45292e66 q^{84} +8.77765e65 q^{85} -1.82095e67 q^{86} -6.66742e66 q^{87} -4.22594e67 q^{88} +2.42069e67 q^{89} -3.33044e66 q^{90} -2.79973e67 q^{91} +1.21138e68 q^{92} -2.68815e67 q^{93} -5.67930e67 q^{94} -5.10090e66 q^{95} -2.66042e68 q^{96} +1.94649e68 q^{97} -7.54206e68 q^{98} -3.11854e68 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 869363388 q^{2} - 10\!\cdots\!14 q^{3}+ \cdots + 16\!\cdots\!66 q^{9}+O(q^{10}) \) 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