LMFDB - Embedded newform 2.72.a.b.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2,72,Mod(1,2)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

N = Newforms(chi, 72, names="a")

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

chi := DirichletCharacter("2.1");

S:= CuspForms(chi, 72);

N := Newforms(S);

Level:	$ N $	$=$	$ 2 $
Weight:	$ k $	$=$	$ 72 $
Character orbit:	$[\chi]$	$=$	2.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$63.8492321122$
Analytic rank:	$0$
Dimension:	$3$
Coefficient field:	$\mathbb{Q}[x]/(x^{3} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - 71437129084791448795855051x - 180952663419752575975880178936282470070 $ x^3 - 71437129084791448795855051*x - 180952663419752575975880178936282470070
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{22}\cdot 3^{6}\cdot 5^{3}\cdot 7 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$9.51117e12$ of defining polynomial
Character	$\chi$	$=$	2.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-3.43597e10 q^{2} +4.72491e16 q^{3} +1.18059e21 q^{4} -7.30618e24 q^{5} -1.62347e27 q^{6} -2.33219e28 q^{7} -4.05648e31 q^{8} -5.27699e33 q^{9} +O(q^{10})$	\(q-3.43597e10 q^{2} +4.72491e16 q^{3} +1.18059e21 q^{4} -7.30618e24 q^{5} -1.62347e27 q^{6} -2.33219e28 q^{7} -4.05648e31 q^{8} -5.27699e33 q^{9} +2.51038e35 q^{10} -1.13918e37 q^{11} +5.57819e37 q^{12} -4.82382e39 q^{13} +8.01335e38 q^{14} -3.45211e41 q^{15} +1.39380e42 q^{16} +5.37011e43 q^{17} +1.81316e44 q^{18} +3.28254e44 q^{19} -8.62561e45 q^{20} -1.10194e45 q^{21} +3.91420e47 q^{22} +1.06232e48 q^{23} -1.91665e48 q^{24} +1.10286e49 q^{25} +1.65745e50 q^{26} -6.04149e50 q^{27} -2.75337e49 q^{28} -1.14189e52 q^{29} +1.18613e52 q^{30} +1.80143e52 q^{31} -4.78905e52 q^{32} -5.38254e53 q^{33} -1.84515e54 q^{34} +1.70394e53 q^{35} -6.22996e54 q^{36} -4.58287e55 q^{37} -1.12787e55 q^{38} -2.27921e56 q^{39} +2.96374e56 q^{40} +2.53761e57 q^{41} +3.78624e55 q^{42} +2.43971e57 q^{43} -1.34491e58 q^{44} +3.85546e58 q^{45} -3.65011e58 q^{46} +5.94323e58 q^{47} +6.58557e58 q^{48} -1.00398e60 q^{49} -3.78939e59 q^{50} +2.53733e60 q^{51} -5.69496e60 q^{52} -6.61258e60 q^{53} +2.07584e61 q^{54} +8.32306e61 q^{55} +9.46049e59 q^{56} +1.55097e61 q^{57} +3.92350e62 q^{58} -1.13910e63 q^{59} -4.07553e62 q^{60} +3.97263e63 q^{61} -6.18965e62 q^{62} +1.23069e62 q^{63} +1.64550e63 q^{64} +3.52437e64 q^{65} +1.84943e64 q^{66} +1.05200e65 q^{67} +6.33990e64 q^{68} +5.01938e64 q^{69} -5.85470e63 q^{70} +6.61153e65 q^{71} +2.14060e65 q^{72} +1.33268e66 q^{73} +1.57466e66 q^{74} +5.21091e65 q^{75} +3.87534e65 q^{76} +2.65679e65 q^{77} +7.83131e66 q^{78} +2.53823e67 q^{79} -1.01833e67 q^{80} +1.10818e67 q^{81} -8.71917e67 q^{82} -2.11949e68 q^{83} -1.30094e66 q^{84} -3.92350e68 q^{85} -8.38278e67 q^{86} -5.39532e68 q^{87} +4.62107e68 q^{88} -4.02156e66 q^{89} -1.32473e69 q^{90} +1.12501e68 q^{91} +1.25417e69 q^{92} +8.51158e68 q^{93} -2.04208e69 q^{94} -2.39828e69 q^{95} -2.26278e69 q^{96} +3.31804e70 q^{97} +3.44965e70 q^{98} +6.01144e70 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q - 103079215104 q^{2} + 23\!\cdots\!36 q^{3}+ \cdots - 45\!\cdots\!09 q^{9}+O(q^{10}) $ 3 * q - 103079215104 * q^2 + 2362570292707236 * q^3 + 3541774862152233910272 * q^4 + 4753308915533391960256650 * q^5 - 81177297133429807380430848 * q^6 - 685790799447997047084795426072 * q^7 - 121694457621910022543683507716096 * q^8 - 4505398350426548777838087948321009 * q^9	$ 3 q - 103079215104 q^{2} + 23\!\cdots\!36 q^{3}+ \cdots + 12\!\cdots\!32 q^{99}+O(q^{100}) $ 3 * q - 103079215104 * q^2 + 2362570292707236 * q^3 + 3541774862152233910272 * q^4 + 4753308915533391960256650 * q^5 - 81177297133429807380430848 * q^6 - 685790799447997047084795426072 * q^7 - 121694457621910022543683507716096 * q^8 - 4505398350426548777838087948321009 * q^9 - 163322450720009158922013148132147200 * q^10 + 3969518227834483364274834229858599756 * q^11 + 2789230690926044568084239380396376064 * q^12 + 2529641076874049546506304992034610800946 * q^13 + 23563592444214737359470147950637005930496 * q^14 + 407345545990301587458425269101161600167800 * q^15 + 4181389724724491839037947176121567782371328 * q^16 + 35492344011589917581644253423281452467295318 * q^17 + 154804308564274997207706858569683774117773312 * q^18 + 2841186907242840665111664111817927348680296820 * q^19 + 5611716676360087923124104685676605682063769600 * q^20 - 147880796471173011613366779703968478971439282464 * q^21 - 136391607755399863604931742184512261250988638208 * q^22 + 372858837194588698341491556777522114253679157816 * q^23 - 95837236788214762996482028094701909694377623552 * q^24 + 69862220765255200329820968690236540988174429613125 * q^25 - 86917805566338117706625687988721551121211486896128 * q^26 - 947955055507342807334349523771491542851454430730200 * q^27 - 809638871393400010881229450690138902710706952470528 * q^28 + 2838293454662119862597708158946776463408079116647170 * q^29 - 13996286385596874010486562323595907106653832898150400 * q^30 - 60985780592296898612188383347434281055674826984896864 * q^31 - 143671456956177080471095033795341485964256792704712704 * q^32 - 2226251555109516044503731418659397026281060527969942128 * q^33 - 1219507654305281127811979826874639066803295203071361024 * q^34 - 15012477392108224914953334499824623410367257977654315600 * q^35 - 5319035540507630615660738213693513175181501019052834816 * q^36 - 68176149937496232624484049167780541975937489767987119062 * q^37 - 97622438787451089494347884387159080552686908811782389760 * q^38 - 181103730680294442815742293797937418749802413053959521448 * q^39 - 192817116795075151596020734194091048294013313747832012800 * q^40 + 2552747372756675092691146114350576632165539159012967279886 * q^41 + 5081145476400962333097908122251049428777563489860690378752 * q^42 + 18909111020150337719256805153495922766806377418623683904236 * q^43 + 4686379958066419052688339975958270078272033990167488364544 * q^44 - 2721353093966297027357236277004028373408155461709353007950 * q^45 - 12811332094202774780383325409756677029090619443972342284288 * q^46 - 43968712731246921396266407709188709699073053268890920706832 * q^47 + 3292942381955123882354250189747983144048777985840314843136 * q^48 - 1026062827616062451582801453511096725123047657850544364580901 * q^49 - 2400447627301625428084075792476847184386981583454606458880000 * q^50 - 6642917231549727841284660449151726108810042035755118549288184 * q^51 + 2986473058780071792225246819400472631327963744947218472239104 * q^52 + 30871443618914543069766688718872801487605153889290407489338106 * q^53 + 32571487691855216362894881136253846029500634928164051196313600 * q^54 + 82883499258166400764153074170750404891861017028181553423013800 * q^55 + 27818979793640023975847397047889529734718496879205953310818304 * q^56 + 212035618958631297738882658287269296529392551878549426422723440 * q^57 - 97523020513797308319113361177830197719681924065441314567618560 * q^58 + 460247047764608873010378962302858647900183942836691252581585340 * q^59 + 480908738332708954518977169818481521140257570324838935114547200 * q^60 + 16775049429831179566881200695612811340299429511572993213743266 * q^61 + 2095455465319573512492615147746729941147165896884722534503677952 * q^62 + 7123265108840012936647472594777745274062746713593724228790075016 * q^63 + 4936513671963618126464907547672051514948207596900739590045827072 * q^64 + 94246518292142244320312430108492294401480277247156255007099586300 * q^65 + 76493420974916104876246455944878355127654459774619157686181167104 * q^66 + 294767885753586694210169114445805135103533346814314947921669563108 * q^67 + 41901963939702848352307595147506533469792897297801394818312568832 * q^68 + 528466810873440345877804349403437515478040457656947404876631762592 * q^69 + 515824795448353556018695624343162202264346882905763074362100940800 * q^70 + 919902509099705545860692207075672006856952727183920111456887673896 * q^71 + 182760669541935653861689728472248787637997325928180787446481420288 * q^72 + 2801172592879364865003588703151843916561463459054226277253242976686 * q^73 + 2342514674789910105962937920394187557534453899950714432964385570816 * q^74 + 11540065797237808994474506232223048759594775508100266283876440557500 * q^75 + 3354281455582914596622346722317098026585759026191516667903402311680 * q^76 + 9865200407486310864984017360081516522994693272661494127815675761056 * q^77 + 6222676803643651708353242446609318766280468564229117023415764516864 * q^78 + 35861415701696815437845171625266918505761182712600613769101529649040 * q^79 + 6625145685950880879737210056812239750953150201084205487022827110400 * q^80 - 77413789943620858546024097436886978978462391694997730724429179486277 * q^81 - 87711731847518727110449929519145623311142498769344304856227588866048 * q^82 - 491461197261236055126649090145388665192472846714449095644779700562764 * q^83 - 174586829178883784028666990008648217586232931580122342181773546356736 * q^84 - 1165838157532517419220567093290863687374587795758826921777398482729100 * q^85 - 649712107423831180060505660477673986822201803017772989597881726926848 * q^86 - 533065155655732635133140699091829032733726763688543635407301551318760 * q^87 - 161022789252200969817021768618161569975309969433357984705416047624192 * q^88 - 177072112231663993716456138855227097994172685795374860821951903002370 * q^89 + 93504980315629285269770776949416789792352830141803611411715824025600 * q^90 - 4639739553715545710656746238349490629903267972921545465730866402748304 * q^91 + 440194018902368870993599719829045817260629209057943315516279157161984 * q^92 + 890401138912307375413854706914858877690325831251184410358068258856832 * q^93 + 1510753465823394917581175020914942294799654122438019189017381150130176 * q^94 + 30260171170818092294903292510986000303485315694075825006268582939063000 * q^95 - 113144638704876780914720448412555056685190067823591226636899920642048 * q^96 + 41131919037209954991700932094148075864450433573097333943337676290089958 * q^97 + 35255250306018190990733725431131398459969530130539885613376564329709568 * q^98 + 126334151665356806749302419314959438273928289729980682281425205273054332 * 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 $

$2$	−3.43597e10	−0.707107
$2$	−3.43597e10	−0.707107
$3$	4.72491e16	0.545242	0.272621	−	0.962121i	$-0.412109\pi$
$3$	4.72491e16	0.545242	0.272621	+	0.962121i	$0.412109\pi$
$4$	1.18059e21	0.500000
$5$	−7.30618e24	−1.12268	−0.561339	−	0.827586i	$-0.689714\pi$
$5$	−7.30618e24	−1.12268	−0.561339	+	0.827586i	$0.689714\pi$
$6$	−1.62347e27	−0.385544
$7$	−2.33219e28	−0.0232693	−0.0116347	−	0.999932i	$-0.503704\pi$
$7$	−2.33219e28	−0.0232693	−0.0116347	+	0.999932i	$0.503704\pi$
$8$	−4.05648e31	−0.353553
$9$	−5.27699e33	−0.702711
$10$	2.51038e35	0.793853
$11$	−1.13918e37	−1.22223	−0.611115	−	0.791542i	$-0.709279\pi$
$11$	−1.13918e37	−1.22223	−0.611115	+	0.791542i	$0.709279\pi$
$12$	5.57819e37	0.272621
$13$	−4.82382e39	−1.37531	−0.687657	−	0.726036i	$-0.741361\pi$
$13$	−4.82382e39	−1.37531	−0.687657	+	0.726036i	$0.741361\pi$
$14$	8.01335e38	0.0164539
$15$	−3.45211e41	−0.612131
$16$	1.39380e42	0.250000
$17$	5.37011e43	1.11956	0.559779	−	0.828642i	$-0.310886\pi$
$17$	5.37011e43	1.11956	0.559779	+	0.828642i	$0.310886\pi$
$18$	1.81316e44	0.496892
$19$	3.28254e44	0.131964	0.0659822	−	0.997821i	$-0.478982\pi$
$19$	3.28254e44	0.131964	0.0659822	+	0.997821i	$0.478982\pi$
$20$	−8.62561e45	−0.561339
$21$	−1.10194e45	−0.0126874
$22$	3.91420e47	0.864247
$23$	1.06232e48	0.484081	0.242040	−	0.970266i	$-0.422183\pi$
$23$	1.06232e48	0.484081	0.242040	+	0.970266i	$0.422183\pi$
$24$	−1.91665e48	−0.192772
$25$	1.10286e49	0.260405
$26$	1.65745e50	0.972494
$27$	−6.04149e50	−0.928390
$28$	−2.75337e49	−0.0116347
$29$	−1.14189e52	−1.38834	−0.694168	−	0.719813i	$-0.744227\pi$
$29$	−1.14189e52	−1.38834	−0.694168	+	0.719813i	$0.744227\pi$
$30$	1.18613e52	0.432842
$31$	1.80143e52	0.205247	0.102623	−	0.994720i	$-0.467276\pi$
$31$	1.80143e52	0.205247	0.102623	+	0.994720i	$0.467276\pi$
$32$	−4.78905e52	−0.176777
$33$	−5.38254e53	−0.666411
$34$	−1.84515e54	−0.791646
$35$	1.70394e53	0.0261240
$36$	−6.22996e54	−0.351356
$37$	−4.58287e55	−0.977185	−0.488592	−	0.872512i	$-0.662489\pi$
$37$	−4.58287e55	−0.977185	−0.488592	+	0.872512i	$0.662489\pi$
$38$	−1.12787e55	−0.0933130
$39$	−2.27921e56	−0.749879
$40$	2.96374e56	0.396926
$41$	2.53761e57	1.41449	0.707243	−	0.706971i	$-0.249939\pi$
$41$	2.53761e57	1.41449	0.707243	+	0.706971i	$0.249939\pi$
$42$	3.78624e55	0.00897136
$43$	2.43971e57	0.250731	0.125365	−	0.992111i	$-0.459990\pi$
$43$	2.43971e57	0.250731	0.125365	+	0.992111i	$0.459990\pi$
$44$	−1.34491e58	−0.611115
$45$	3.85546e58	0.788918
$46$	−3.65011e58	−0.342297
$47$	5.94323e58	0.259746	0.129873	−	0.991531i	$-0.458543\pi$
$47$	5.94323e58	0.259746	0.129873	+	0.991531i	$0.458543\pi$
$48$	6.58557e58	0.136311
$49$	−1.00398e60	−0.999459
$50$	−3.78939e59	−0.184134
$51$	2.53733e60	0.610430
$52$	−5.69496e60	−0.687657
$53$	−6.61258e60	−0.406048	−0.203024	−	0.979174i	$-0.565077\pi$
$53$	−6.61258e60	−0.406048	−0.203024	+	0.979174i	$0.565077\pi$
$54$	2.07584e61	0.656471
$55$	8.32306e61	1.37217
$56$	9.46049e59	0.00822695
$57$	1.55097e61	0.0719526
$58$	3.92350e62	0.981701
$59$	−1.13910e63	−1.55352	−0.776759	−	0.629798i	$-0.783138\pi$
$59$	−1.13910e63	−1.55352	−0.776759	+	0.629798i	$0.783138\pi$
$60$	−4.07553e62	−0.306066
$61$	3.97263e63	1.65909	0.829543	−	0.558443i	$-0.188601\pi$
$61$	3.97263e63	1.65909	0.829543	+	0.558443i	$0.188601\pi$
$62$	−6.18965e62	−0.145131
$63$	1.23069e62	0.0163516
$64$	1.64550e63	0.125000
$65$	3.52437e64	1.54403
$66$	1.84943e64	0.471224
$67$	1.05200e65	1.57166	0.785830	−	0.618442i	$-0.212236\pi$
$67$	1.05200e65	1.57166	0.785830	+	0.618442i	$0.212236\pi$
$68$	6.33990e64	0.559779
$69$	5.01938e64	0.263941
$70$	−5.85470e63	−0.0184724
$71$	6.61153e65	1.26075	0.630377	−	0.776289i	$-0.282900\pi$
$71$	6.61153e65	1.26075	0.630377	+	0.776289i	$0.282900\pi$
$72$	2.14060e65	0.248446
$73$	1.33268e66	0.947904	0.473952	−	0.880551i	$-0.342827\pi$
$73$	1.33268e66	0.947904	0.473952	+	0.880551i	$0.342827\pi$
$74$	1.57466e66	0.690974
$75$	5.21091e65	0.141984
$76$	3.87534e65	0.0659822
$77$	2.65679e65	0.0284405
$78$	7.83131e66	0.530245
$79$	2.53823e67	1.09338	0.546688	−	0.837336i	$-0.315888\pi$
$79$	2.53823e67	1.09338	0.546688	+	0.837336i	$0.315888\pi$
$80$	−1.01833e67	−0.280669
$81$	1.10818e67	0.196514
$82$	−8.71917e67	−1.00019
$83$	−2.11949e68	−1.58110	−0.790549	−	0.612398i	$-0.790205\pi$
$83$	−2.11949e68	−1.58110	−0.790549	+	0.612398i	$0.790205\pi$
$84$	−1.30094e66	−0.00634371
$85$	−3.92350e68	−1.25690
$86$	−8.38278e67	−0.177294
$87$	−5.39532e68	−0.756979
$88$	4.62107e68	0.432123
$89$	−4.02156e66	−0.00251796	−0.00125898	−	0.999999i	$-0.500401\pi$
$89$	−4.02156e66	−0.00251796	−0.00125898	+	0.999999i	$0.500401\pi$
$90$	−1.32473e69	−0.557849
$91$	1.12501e68	0.0320026
$92$	1.25417e69	0.242040
$93$	8.51158e68	0.111909
$94$	−2.04208e69	−0.183668
$95$	−2.39828e69	−0.148154
$96$	−2.26278e69	−0.0963861
$97$	3.31804e70	0.978329	0.489165	−	0.872192i	$-0.337302\pi$
$97$	3.31804e70	0.978329	0.489165	+	0.872192i	$0.337302\pi$
$98$	3.44965e70	0.706724
$99$	6.01144e70	0.858874
$100$	1.30203e70	0.130203
$101$	1.36670e71	0.959986	0.479993	−	0.877272i	$-0.340639\pi$
$101$	1.36670e71	0.959986	0.479993	+	0.877272i	$0.340639\pi$
$102$	−8.71820e70	−0.431639
$103$	4.44634e69	0.0155697	0.00778486	−	0.999970i	$-0.497522\pi$
$103$	4.44634e69	0.0155697	0.00778486	+	0.999970i	$0.497522\pi$
$104$	1.95677e71	0.486247
$105$	8.05097e69	0.0142439
$106$	2.27206e71	0.287119
$107$	−2.00338e72	−1.81401	−0.907003	−	0.421124i	$-0.861636\pi$
$107$	−2.00338e72	−1.81401	−0.907003	+	0.421124i	$0.861636\pi$
$108$	−7.13253e71	−0.464195
$109$	−2.50828e70	−0.0117689	−0.00588444	−	0.999983i	$-0.501873\pi$
$109$	−2.50828e70	−0.0117689	−0.00588444	+	0.999983i	$0.501873\pi$
$110$	−2.85978e72	−0.970270
$111$	−2.16537e72	−0.532802
$112$	−3.25060e70	−0.00581733
$113$	4.70386e72	0.614002	0.307001	−	0.951709i	$-0.400674\pi$
$113$	4.70386e72	0.614002	0.307001	+	0.951709i	$0.400674\pi$
$114$	−5.32910e71	−0.0508782
$115$	−7.76151e72	−0.543467
$116$	−1.34810e73	−0.694168
$117$	2.54552e73	0.966448
$118$	3.91393e73	1.09850
$119$	−1.25241e72	−0.0260513
$120$	1.40034e73	0.216421
$121$	4.29013e73	0.493844
$122$	−1.36498e74	−1.17315
$123$	1.19900e74	0.771237
$124$	2.12675e73	0.102623
$125$	2.28852e74	0.830327
$126$	−4.22863e72	−0.0115623
$127$	6.39197e74	1.32009	0.660044	−	0.751227i	$-0.270538\pi$
$127$	6.39197e74	1.32009	0.660044	+	0.751227i	$0.270538\pi$
$128$	−5.65391e73	−0.0883883
$129$	1.15274e74	0.136709
$130$	−1.21096e75	−1.09180
$131$	−2.60096e75	−1.78650	−0.893251	−	0.449559i	$-0.851581\pi$
$131$	−2.60096e75	−1.78650	−0.893251	+	0.449559i	$0.851581\pi$
$132$	−6.35458e74	−0.333205
$133$	−7.65551e72	−0.00307073
$134$	−3.61463e75	−1.11133
$135$	4.41402e75	1.04228
$136$	−2.17837e75	−0.395823
$137$	−6.19752e75	−0.868236	−0.434118	−	0.900856i	$-0.642940\pi$
$137$	−6.19752e75	−0.868236	−0.434118	+	0.900856i	$0.642940\pi$
$138$	−1.72465e75	−0.186635
$139$	2.13310e76	1.78643	0.893214	−	0.449632i	$-0.148445\pi$
$139$	2.13310e76	1.78643	0.893214	+	0.449632i	$0.148445\pi$
$140$	2.01166e74	0.0130620
$141$	2.80813e75	0.141624
$142$	−2.27170e76	−0.891488
$143$	5.49520e76	1.68095
$144$	−7.35504e75	−0.175678
$145$	8.34283e76	1.55865
$146$	−4.57905e76	−0.670269
$147$	−4.74373e76	−0.544947
$148$	−5.41050e76	−0.488592
$149$	1.80883e77	1.28613	0.643067	−	0.765810i	$-0.277662\pi$
$149$	1.80883e77	1.28613	0.643067	+	0.765810i	$0.277662\pi$
$150$	−1.79046e76	−0.100398
$151$	−5.67496e76	−0.251352	−0.125676	−	0.992071i	$-0.540110\pi$
$151$	−5.67496e76	−0.251352	−0.125676	+	0.992071i	$0.540110\pi$
$152$	−1.33156e76	−0.0466565
$153$	−2.83380e77	−0.786725
$154$	−9.12866e75	−0.0201104
$155$	−1.31615e77	−0.230426
$156$	−2.69082e77	−0.374940
$157$	1.31081e77	0.145580	0.0727899	−	0.997347i	$-0.476810\pi$
$157$	1.31081e77	0.145580	0.0727899	+	0.997347i	$0.476810\pi$
$158$	−8.72130e77	−0.773133
$159$	−3.12439e77	−0.221394
$160$	3.49896e77	0.198463
$161$	−2.47754e76	−0.0112642
$162$	−3.80769e77	−0.138956
$163$	−3.97385e78	−1.16560	−0.582802	−	0.812614i	$-0.698044\pi$
$163$	−3.97385e78	−1.16560	−0.582802	+	0.812614i	$0.698044\pi$
$164$	2.99589e78	0.707243
$165$	3.93258e78	0.748164
$166$	7.28251e78	1.11801
$167$	1.55721e78	0.193158	0.0965788	−	0.995325i	$-0.469210\pi$
$167$	1.55721e78	0.193158	0.0965788	+	0.995325i	$0.469210\pi$
$168$	4.47000e76	0.00448568
$169$	1.09672e79	0.891489
$170$	1.34810e79	0.888764
$171$	−1.73219e78	−0.0927329
$172$	2.88030e78	0.125365
$173$	−5.01978e79	−1.77848	−0.889238	−	0.457444i	$-0.848765\pi$
$173$	−5.01978e79	−1.77848	−0.889238	+	0.457444i	$0.848765\pi$
$174$	1.85382e79	0.535265
$175$	−2.57208e77	−0.00605945
$176$	−1.58779e79	−0.305557
$177$	−5.38216e79	−0.847043
$178$	1.38180e77	0.00178047
$179$	−1.48614e80	−1.56956	−0.784781	−	0.619773i	$-0.787225\pi$
$179$	−1.48614e80	−1.56956	−0.784781	+	0.619773i	$0.787225\pi$
$180$	4.55172e79	0.394459
$181$	−1.54409e79	−0.109922	−0.0549610	−	0.998489i	$-0.517503\pi$
$181$	−1.54409e79	−0.109922	−0.0549610	+	0.998489i	$0.517503\pi$
$182$	−3.86549e78	−0.0226293
$183$	1.87703e80	0.904603
$184$	−4.30929e79	−0.171148
$185$	3.34833e80	1.09706
$186$	−2.92456e79	−0.0791317
$187$	−6.11753e80	−1.36836
$188$	7.01653e79	0.129873
$189$	1.40899e79	0.0216030
$190$	8.24043e79	0.104760
$191$	5.78406e80	0.610307	0.305154	−	0.952303i	$-0.401292\pi$
$191$	5.78406e80	0.610307	0.305154	+	0.952303i	$0.401292\pi$
$192$	7.77487e79	0.0681553
$193$	2.61375e81	1.90537	0.952686	−	0.303957i	$-0.0983078\pi$
$193$	2.61375e81	1.90537	0.952686	+	0.303957i	$0.0983078\pi$
$194$	−1.14007e81	−0.691783
$195$	1.66523e81	0.841872
$196$	−1.18529e81	−0.499729
$197$	1.78054e81	0.626615	0.313307	−	0.949652i	$-0.398563\pi$
$197$	1.78054e81	0.626615	0.313307	+	0.949652i	$0.398563\pi$
$198$	−2.06552e81	−0.607316
$199$	−6.02034e81	−1.48026	−0.740129	−	0.672465i	$-0.765235\pi$
$199$	−6.02034e81	−1.48026	−0.740129	+	0.672465i	$0.765235\pi$
$200$	−4.47372e80	−0.0920671
$201$	4.97059e81	0.856936
$202$	−4.69595e81	−0.678813
$203$	2.66310e80	0.0323056
$204$	2.99555e81	0.305215
$205$	−1.85403e82	−1.58801
$206$	−1.52775e80	−0.0110095
$207$	−5.60586e81	−0.340169
$208$	−6.72342e81	−0.343829
$209$	−3.73941e81	−0.161291
$210$	−2.76629e80	−0.0100719
$211$	4.38889e82	1.34998	0.674990	−	0.737826i	$-0.264148\pi$
$211$	4.38889e82	1.34998	0.674990	+	0.737826i	$0.264148\pi$
$212$	−7.80675e81	−0.203024
$213$	3.12389e82	0.687416
$214$	6.88355e82	1.28270
$215$	−1.78250e82	−0.281490
$216$	2.45072e82	0.328235
$217$	−4.20127e80	−0.00477595
$218$	8.61837e80	0.00832185
$219$	6.29680e82	0.516837
$220$	9.82614e82	0.686085
$221$	−2.59044e83	−1.53974
$222$	7.44015e82	0.376748
$223$	−1.83691e83	−0.792987	−0.396493	−	0.918038i	$-0.629773\pi$
$223$	−1.83691e83	−0.792987	−0.396493	+	0.918038i	$0.629773\pi$
$224$	1.11690e81	0.00411348
$225$	−5.81977e82	−0.182990
$226$	−1.61623e83	−0.434165
$227$	−2.03324e83	−0.466951	−0.233476	−	0.972363i	$-0.575010\pi$
$227$	−2.03324e83	−0.466951	−0.233476	+	0.972363i	$0.575010\pi$
$228$	1.83106e82	0.0359763
$229$	−3.01022e83	−0.506335	−0.253168	−	0.967422i	$-0.581472\pi$
$229$	−3.01022e83	−0.506335	−0.253168	+	0.967422i	$0.581472\pi$
$230$	2.66683e83	0.384289
$231$	1.25531e82	0.0155069
$232$	4.63205e83	0.490851
$233$	5.06680e83	0.460892	0.230446	−	0.973085i	$-0.425982\pi$
$233$	5.06680e83	0.460892	0.230446	+	0.973085i	$0.425982\pi$
$234$	−8.74635e83	−0.683382
$235$	−4.34223e83	−0.291611
$236$	−1.34481e84	−0.776759
$237$	1.19929e84	0.596155
$238$	4.30326e82	0.0184211
$239$	3.13482e84	1.15635	0.578173	−	0.815914i	$-0.303766\pi$
$239$	3.13482e84	1.15635	0.578173	+	0.815914i	$0.303766\pi$
$240$	−4.81153e83	−0.153033
$241$	−5.12529e83	−0.140641	−0.0703207	−	0.997524i	$-0.522402\pi$
$241$	−5.12529e83	−0.140641	−0.0703207	+	0.997524i	$0.522402\pi$
$242$	−1.47408e84	−0.349201
$243$	5.06044e84	1.03554
$244$	4.69005e84	0.829543
$245$	7.33527e84	1.12207
$246$	−4.11973e84	−0.545347
$247$	−1.58344e84	−0.181493
$248$	−7.30745e83	−0.0725657
$249$	−1.00144e85	−0.862081
$250$	−7.86329e84	−0.587130
$251$	5.87220e84	0.380525	0.190263	−	0.981733i	$-0.439066\pi$
$251$	5.87220e84	0.380525	0.190263	+	0.981733i	$0.439066\pi$
$252$	1.45295e83	0.00817581
$253$	−1.21018e85	−0.591658
$254$	−2.19627e85	−0.933443
$255$	−1.85382e85	−0.685316
$256$	1.94267e84	0.0625000
$257$	−2.03692e85	−0.570622	−0.285311	−	0.958435i	$-0.592097\pi$
$257$	−2.03692e85	−0.570622	−0.285311	+	0.958435i	$0.592097\pi$
$258$	−3.96079e84	−0.0966679
$259$	1.06881e84	0.0227384
$260$	4.16084e85	0.772017
$261$	6.02572e85	0.975599
$262$	8.93685e85	1.26325
$263$	−1.07762e86	−1.33056	−0.665281	−	0.746593i	$-0.731688\pi$
$263$	−1.07762e86	−1.33056	−0.665281	+	0.746593i	$0.731688\pi$
$264$	2.18342e85	0.235612
$265$	4.83127e85	0.455861
$266$	2.63041e83	0.00217133
$267$	−1.90015e83	−0.00137290
$268$	1.24198e86	0.785830
$269$	1.26089e86	0.698992	0.349496	−	0.936938i	$-0.386353\pi$
$269$	1.26089e86	0.698992	0.349496	+	0.936938i	$0.386353\pi$
$270$	−1.51665e86	−0.737005
$271$	−4.02205e85	−0.171411	−0.0857053	−	0.996321i	$-0.527314\pi$
$271$	−4.02205e85	−0.171411	−0.0857053	+	0.996321i	$0.527314\pi$
$272$	7.48484e85	0.279889
$273$	5.31556e84	0.0174492
$274$	2.12945e86	0.613936
$275$	−1.25636e86	−0.318275
$276$	5.92584e85	0.131971
$277$	−7.61221e86	−1.49100	−0.745502	−	0.666503i	$-0.767790\pi$
$277$	−7.61221e86	−1.49100	−0.745502	+	0.666503i	$0.767790\pi$
$278$	−7.32927e86	−1.26319
$279$	−9.50609e85	−0.144229
$280$	−6.91201e84	−0.00923621
$281$	2.98819e86	0.351830	0.175915	−	0.984405i	$-0.443712\pi$
$281$	2.98819e86	0.351830	0.175915	+	0.984405i	$0.443712\pi$
$282$	−9.64865e85	−0.100144
$283$	9.54597e86	0.873779	0.436889	−	0.899515i	$-0.356080\pi$
$283$	9.54597e86	0.873779	0.436889	+	0.899515i	$0.356080\pi$
$284$	7.80551e86	0.630377
$285$	−1.13317e86	−0.0807796
$286$	−1.88814e87	−1.18861
$287$	−5.91820e85	−0.0329141
$288$	2.52717e86	0.124223
$289$	5.83034e86	0.253408
$290$	−2.86658e87	−1.10213
$291$	1.56775e87	0.533426
$292$	1.57335e87	0.473952
$293$	−1.38390e87	−0.369237	−0.184618	−	0.982810i	$-0.559105\pi$
$293$	−1.38390e87	−0.369237	−0.184618	+	0.982810i	$0.559105\pi$
$294$	1.62993e87	0.385336
$295$	8.32248e87	1.74410
$296$	1.85903e87	0.345487
$297$	6.88235e87	1.13471
$298$	−6.21511e87	−0.909434
$299$	−5.12445e87	−0.665763
$300$	6.15196e86	0.0709919
$301$	−5.68987e85	−0.00583434
$302$	1.94990e87	0.177732
$303$	6.45755e87	0.523425
$304$	4.57519e86	0.0329911
$305$	−2.90247e88	−1.86262
$306$	9.73686e87	0.556299
$307$	−3.01627e88	−1.53482	−0.767411	−	0.641155i	$-0.778455\pi$
$307$	−3.01627e88	−1.53482	−0.767411	+	0.641155i	$0.778455\pi$
$308$	3.13658e86	0.0142202
$309$	2.10086e86	0.00848927
$310$	4.52227e87	0.162936
$311$	−5.53131e88	−1.77760	−0.888800	−	0.458295i	$-0.848460\pi$
$311$	−5.53131e88	−1.77760	−0.888800	+	0.458295i	$0.848460\pi$
$312$	9.24558e87	0.265122
$313$	2.88699e88	0.738962	0.369481	−	0.929238i	$-0.379536\pi$
$313$	2.88699e88	0.738962	0.369481	+	0.929238i	$0.379536\pi$
$314$	−4.50390e87	−0.102940
$315$	−8.99167e86	−0.0183576
$316$	2.99661e88	0.546688
$317$	6.28908e88	1.02561	0.512806	−	0.858505i	$-0.328606\pi$
$317$	6.28908e88	1.02561	0.512806	+	0.858505i	$0.328606\pi$
$318$	1.07353e88	0.156550
$319$	1.30082e89	1.69686
$320$	−1.20223e88	−0.140335
$321$	−9.46579e88	−0.989073
$322$	8.51276e86	0.00796502
$323$	1.76276e88	0.147742
$324$	1.30831e88	0.0982570
$325$	−5.31999e88	−0.358139
$326$	1.36540e89	0.824207
$327$	−1.18514e87	−0.00641688
$328$	−1.02938e89	−0.500096
$329$	−1.38608e87	−0.00604411
$330$	−1.35122e89	−0.529032
$331$	2.02940e89	0.713632	0.356816	−	0.934175i	$-0.383862\pi$
$331$	2.02940e89	0.713632	0.356816	+	0.934175i	$0.383862\pi$
$332$	−2.50225e89	−0.790549
$333$	2.41838e89	0.686678
$334$	−5.35052e88	−0.136583
$335$	−7.68607e89	−1.76447
$336$	−1.53588e87	−0.00317185
$337$	5.20726e89	0.967715	0.483857	−	0.875147i	$-0.339235\pi$
$337$	5.20726e89	0.967715	0.483857	+	0.875147i	$0.339235\pi$
$338$	−3.76828e89	−0.630378
$339$	2.22253e89	0.334780
$340$	−4.63205e89	−0.628451
$341$	−2.05215e89	−0.250858
$342$	5.95176e88	0.0655721
$343$	4.68422e88	0.0465261
$344$	−9.89664e88	−0.0886468
$345$	−3.66725e89	−0.296321
$346$	1.72478e90	1.25757
$347$	6.31179e89	0.415390	0.207695	−	0.978194i	$-0.433404\pi$
$347$	6.31179e89	0.415390	0.207695	+	0.978194i	$0.433404\pi$
$348$	−6.36967e89	−0.378489
$349$	−9.56833e89	−0.513492	−0.256746	−	0.966479i	$-0.582650\pi$
$349$	−9.56833e89	−0.513492	−0.256746	+	0.966479i	$0.582650\pi$
$350$	8.83759e87	0.00428468
$351$	2.91430e90	1.27683
$352$	5.45560e89	0.216062
$353$	2.29734e90	0.822665	0.411333	−	0.911485i	$-0.365063\pi$
$353$	2.29734e90	0.822665	0.411333	+	0.911485i	$0.365063\pi$
$354$	1.84930e90	0.598950
$355$	−4.83050e90	−1.41542
$356$	−4.74782e87	−0.00125898
$357$	−5.91754e88	−0.0142043
$358$	5.10635e90	1.10985
$359$	−7.60169e89	−0.149643	−0.0748216	−	0.997197i	$-0.523839\pi$
$359$	−7.60169e89	−0.149643	−0.0748216	+	0.997197i	$0.523839\pi$
$360$	−1.56396e90	−0.278925
$361$	−6.07961e90	−0.982585
$362$	5.30547e89	0.0777265
$363$	2.02705e90	0.269265
$364$	1.32817e89	0.0160013
$365$	−9.73679e90	−1.06419
$366$	−6.44944e90	−0.639651
$367$	−5.42266e89	−0.0488166	−0.0244083	−	0.999702i	$-0.507770\pi$
$367$	−5.42266e89	−0.0488166	−0.0244083	+	0.999702i	$0.507770\pi$
$368$	1.48066e90	0.121020
$369$	−1.33910e91	−0.993975
$370$	−1.15048e91	−0.775741
$371$	1.54218e89	0.00944846
$372$	1.00487e90	0.0559546
$373$	7.69351e90	0.389458	0.194729	−	0.980857i	$-0.437617\pi$
$373$	7.69351e90	0.389458	0.194729	+	0.980857i	$0.437617\pi$
$374$	2.10197e91	0.967573
$375$	1.08131e91	0.452729
$376$	−2.41086e90	−0.0918341
$377$	5.50826e91	1.90940
$378$	−4.84126e89	−0.0152756
$379$	1.38688e91	0.398425	0.199212	−	0.979956i	$-0.436162\pi$
$379$	1.38688e91	0.398425	0.199212	+	0.979956i	$0.436162\pi$
$380$	−2.83139e90	−0.0740768
$381$	3.02015e91	0.719767
$382$	−1.98739e91	−0.431552
$383$	−2.95611e91	−0.585011	−0.292506	−	0.956264i	$-0.594489\pi$
$383$	−2.95611e91	−0.585011	−0.292506	+	0.956264i	$0.594489\pi$
$384$	−2.67142e90	−0.0481930
$385$	−1.94110e90	−0.0319295
$386$	−8.98078e91	−1.34730
$387$	−1.28743e91	−0.176191
$388$	3.91725e91	0.489165
$389$	1.01670e92	1.15873	0.579365	−	0.815068i	$-0.303301\pi$
$389$	1.01670e92	1.15873	0.579365	+	0.815068i	$0.303301\pi$
$390$	−5.72170e91	−0.595294
$391$	5.70478e91	0.541956
$392$	4.07263e91	0.353362
$393$	−1.22893e92	−0.974076
$394$	−6.11789e91	−0.443084
$395$	−1.85448e92	−1.22751
$396$	7.09706e91	0.429437
$397$	−1.53409e92	−0.848767	−0.424384	−	0.905483i	$-0.639509\pi$
$397$	−1.53409e92	−0.848767	−0.424384	+	0.905483i	$0.639509\pi$
$398$	2.06857e92	1.04670
$399$	−3.61716e89	−0.00167429
$400$	1.53716e91	0.0651013
$401$	1.04002e91	0.0403104	0.0201552	−	0.999797i	$-0.493584\pi$
$401$	1.04002e91	0.0403104	0.0201552	+	0.999797i	$0.493584\pi$
$402$	−1.70788e92	−0.605945
$403$	−8.68975e91	−0.282279
$404$	1.61352e92	0.479993
$405$	−8.09658e91	−0.220622
$406$	−9.15034e90	−0.0228435
$407$	5.22072e92	1.19434
$408$	−1.02926e92	−0.215819
$409$	−4.25564e92	−0.818065	−0.409032	−	0.912520i	$-0.634134\pi$
$409$	−4.25564e92	−0.818065	−0.409032	+	0.912520i	$0.634134\pi$
$410$	6.37038e92	1.12289
$411$	−2.92828e92	−0.473399
$412$	5.24931e90	0.00778486
$413$	2.65661e91	0.0361493
$414$	1.92616e92	0.240536
$415$	1.54854e93	1.77506
$416$	2.31015e92	0.243123
$417$	1.00787e93	0.974035
$418$	1.28485e92	0.114050
$419$	−1.19211e93	−0.972117	−0.486058	−	0.873926i	$-0.661566\pi$
$419$	−1.19211e93	−0.972117	−0.486058	+	0.873926i	$0.661566\pi$
$420$	9.50491e90	0.00712194
$421$	−2.01512e93	−1.38767	−0.693835	−	0.720134i	$-0.744080\pi$
$421$	−2.01512e93	−1.38767	−0.693835	+	0.720134i	$0.744080\pi$
$422$	−1.50801e93	−0.954581
$423$	−3.13624e92	−0.182526
$424$	2.68238e92	0.143560
$425$	5.92247e92	0.291538
$426$	−1.07336e93	−0.486077
$427$	−9.26493e91	−0.0386058
$428$	−2.36517e93	−0.907003
$429$	2.59644e93	0.916524
$430$	6.12461e92	0.199044
$431$	−4.35439e93	−1.30312	−0.651559	−	0.758598i	$-0.725885\pi$
$431$	−4.35439e93	−1.30312	−0.651559	+	0.758598i	$0.725885\pi$
$432$	−8.42061e92	−0.232097
$433$	−6.20426e92	−0.157532	−0.0787662	−	0.996893i	$-0.525098\pi$
$433$	−6.20426e92	−0.157532	−0.0787662	+	0.996893i	$0.525098\pi$
$434$	1.44355e91	0.00337711
$435$	3.94192e93	0.849843
$436$	−2.96125e91	−0.00588444
$437$	3.48711e92	0.0638815
$438$	−2.16356e93	−0.365459
$439$	9.04825e93	1.40953	0.704764	−	0.709441i	$-0.251053\pi$
$439$	9.04825e93	1.40953	0.704764	+	0.709441i	$0.251053\pi$
$440$	−3.37624e93	−0.485135
$441$	5.29799e93	0.702331
$442$	8.90069e93	1.08876
$443$	1.09859e93	0.124024	0.0620118	−	0.998075i	$-0.480248\pi$
$443$	1.09859e93	0.124024	0.0620118	+	0.998075i	$0.480248\pi$
$444$	−2.55642e93	−0.266401
$445$	2.93822e91	0.00282686
$446$	6.31158e93	0.560726
$447$	8.54658e93	0.701254
$448$	−3.83763e91	−0.00290867
$449$	−1.39288e94	−0.975369	−0.487684	−	0.873020i	$-0.662158\pi$
$449$	−1.39288e94	−0.975369	−0.487684	+	0.873020i	$0.662158\pi$
$450$	1.99966e93	0.129393
$451$	−2.89080e94	−1.72883
$452$	5.55334e93	0.307001
$453$	−2.68137e93	−0.137047
$454$	6.98617e93	0.330184
$455$	−8.21950e92	−0.0359286
$456$	−6.29149e92	−0.0254391
$457$	−2.39151e94	−0.894636	−0.447318	−	0.894375i	$-0.647621\pi$
$457$	−2.39151e94	−0.894636	−0.447318	+	0.894375i	$0.647621\pi$
$458$	1.03430e94	0.358033
$459$	−3.24434e94	−1.03939
$460$	−9.16317e93	−0.271733
$461$	7.63538e93	0.209627	0.104814	−	0.994492i	$-0.466575\pi$
$461$	7.63538e93	0.209627	0.104814	+	0.994492i	$0.466575\pi$
$462$	−4.31321e92	−0.0109651
$463$	6.69305e94	1.57579	0.787896	−	0.615808i	$-0.211170\pi$
$463$	6.69305e94	1.57579	0.787896	+	0.615808i	$0.211170\pi$
$464$	−1.59156e94	−0.347084
$465$	−6.21871e93	−0.125638
$466$	−1.74094e94	−0.325900
$467$	−3.07783e94	−0.533944	−0.266972	−	0.963704i	$-0.586023\pi$
$467$	−3.07783e94	−0.533944	−0.266972	+	0.963704i	$0.586023\pi$
$468$	3.00522e94	0.483224
$469$	−2.45346e93	−0.0365715
$470$	1.49198e94	0.206200
$471$	6.19345e93	0.0793763
$472$	4.62075e94	0.549252
$473$	−2.77927e94	−0.306451
$474$	−4.12074e94	−0.421545
$475$	3.62018e93	0.0343642
$476$	−1.47859e93	−0.0130257
$477$	3.48945e94	0.285334
$478$	−1.07712e95	−0.817660
$479$	2.80878e95	1.97973	0.989867	−	0.141997i	$-0.0453522\pi$
$479$	2.80878e95	1.97973	0.989867	+	0.141997i	$0.0453522\pi$
$480$	1.65323e94	0.108211
$481$	2.21069e95	1.34394
$482$	1.76104e94	0.0994486
$483$	−1.17062e93	−0.00614173
$484$	5.06489e94	0.246922
$485$	−2.42422e95	−1.09835
$486$	−1.73875e95	−0.732236
$487$	2.23280e95	0.874123	0.437062	−	0.899432i	$-0.356019\pi$
$487$	2.23280e95	0.874123	0.437062	+	0.899432i	$0.356019\pi$
$488$	−1.61149e95	−0.586575
$489$	−1.87761e95	−0.635536
$490$	−2.52038e95	−0.793423
$491$	−2.11361e94	−0.0618916	−0.0309458	−	0.999521i	$-0.509852\pi$
$491$	−2.11361e94	−0.0618916	−0.0309458	+	0.999521i	$0.509852\pi$
$492$	1.41553e95	0.385619
$493$	−6.13206e95	−1.55432
$494$	5.44065e94	0.128335
$495$	−4.39207e95	−0.964239
$496$	2.51082e94	0.0513117
$497$	−1.54193e94	−0.0293369
$498$	3.44092e95	0.609584
$499$	3.69647e95	0.609843	0.304922	−	0.952377i	$-0.401370\pi$
$499$	3.69647e95	0.609843	0.304922	+	0.952377i	$0.401370\pi$
$500$	2.70181e95	0.415163
$501$	7.35767e94	0.105318
$502$	−2.01767e95	−0.269072
$503$	4.58753e95	0.570054	0.285027	−	0.958520i	$-0.407997\pi$
$503$	4.58753e95	0.570054	0.285027	+	0.958520i	$0.407997\pi$
$504$	−4.99229e93	−0.00578117
$505$	−9.98536e95	−1.07775
$506$	4.15814e95	0.418365
$507$	5.18188e95	0.486077
$508$	7.54631e95	0.660044
$509$	1.23564e96	1.00789	0.503944	−	0.863736i	$-0.331882\pi$
$509$	1.23564e96	1.00789	0.503944	+	0.863736i	$0.331882\pi$
$510$	6.36967e95	0.484591
$511$	−3.10806e94	−0.0220571
$512$	−6.67496e94	−0.0441942
$513$	−1.98314e95	−0.122514
$514$	6.99881e95	0.403490
$515$	−3.24857e94	−0.0174798
$516$	1.36092e95	0.0683545
$517$	−6.77042e95	−0.317469
$518$	−3.67242e94	−0.0160785
$519$	−2.37180e96	−0.969700
$520$	−1.42965e96	−0.545899
$521$	−8.62017e95	−0.307452	−0.153726	−	0.988114i	$-0.549127\pi$
$521$	−8.62017e95	−0.307452	−0.153726	+	0.988114i	$0.549127\pi$
$522$	−2.07042e96	−0.689852
$523$	2.04389e96	0.636279	0.318140	−	0.948044i	$-0.396942\pi$
$523$	2.04389e96	0.636279	0.318140	+	0.948044i	$0.396942\pi$
$524$	−3.07068e96	−0.893251
$525$	−1.21528e94	−0.00330387
$526$	3.70266e96	0.940850
$527$	9.67385e95	0.229785
$528$	−7.50216e95	−0.166603
$529$	−3.68736e96	−0.765666
$530$	−1.66001e96	−0.322342
$531$	6.01103e96	1.09167
$532$	−9.03803e93	−0.00153536
$533$	−1.22410e97	−1.94536
$534$	6.52888e93	0.000970787 0
$535$	1.46370e97	2.03654
$536$	−4.26741e96	−0.555666
$537$	−7.02191e96	−0.855791
$538$	−4.33239e96	−0.494262
$539$	1.14372e97	1.22157
$540$	5.21115e96	0.521141
$541$	1.14549e97	1.07273	0.536363	−	0.843987i	$-0.319798\pi$
$541$	1.14549e97	1.07273	0.536363	+	0.843987i	$0.319798\pi$
$542$	1.38197e96	0.121206
$543$	−7.29571e95	−0.0599341
$544$	−2.57177e96	−0.197912
$545$	1.83259e95	0.0132126
$546$	−1.82641e95	−0.0123384
$547$	1.56422e97	0.990256	0.495128	−	0.868820i	$-0.335121\pi$
$547$	1.56422e97	0.990256	0.495128	+	0.868820i	$0.335121\pi$
$548$	−7.31674e96	−0.434118
$549$	−2.09635e97	−1.16586
$550$	4.31681e96	0.225054
$551$	−3.74829e96	−0.183211
$552$	−2.03610e96	−0.0933173
$553$	−5.91964e95	−0.0254421
$554$	2.61553e97	1.05430
$555$	1.58206e97	0.598165
$556$	2.51832e97	0.893214
$557$	−4.30979e97	−1.43416	−0.717079	−	0.696992i	$-0.754521\pi$
$557$	−4.30979e97	−1.43416	−0.717079	+	0.696992i	$0.754521\pi$
$558$	3.26627e96	0.101985
$559$	−1.17687e97	−0.344834
$560$	2.37495e95	0.00653099
$561$	−2.89048e97	−0.746085
$562$	−1.02673e97	−0.248782
$563$	−2.27037e97	−0.516474	−0.258237	−	0.966082i	$-0.583142\pi$
$563$	−2.27037e97	−0.516474	−0.258237	+	0.966082i	$0.583142\pi$
$564$	3.31525e96	0.0708122
$565$	−3.43673e97	−0.689327
$566$	−3.27997e97	−0.617855
$567$	−2.58450e95	−0.00457275
$568$	−2.68195e97	−0.445744
$569$	−7.47572e97	−1.16726	−0.583630	−	0.812020i	$-0.698368\pi$
$569$	−7.47572e97	−1.16726	−0.583630	+	0.812020i	$0.698368\pi$
$570$	3.89353e96	0.0571198
$571$	1.15862e98	1.59720	0.798601	−	0.601861i	$-0.205574\pi$
$571$	1.15862e98	1.59720	0.798601	+	0.601861i	$0.205574\pi$
$572$	6.48759e97	0.840474
$573$	2.73292e97	0.332765
$574$	2.03348e96	0.0232738
$575$	1.17159e97	0.126057
$576$	−8.68330e96	−0.0878389
$577$	1.00727e98	0.958088	0.479044	−	0.877791i	$-0.340984\pi$
$577$	1.00727e98	0.958088	0.479044	+	0.877791i	$0.340984\pi$
$578$	−2.00329e97	−0.179187
$579$	1.23497e98	1.03889
$580$	9.84948e97	0.779327
$581$	4.94306e96	0.0367911
$582$	−5.38673e97	−0.377189
$583$	7.53293e97	0.496284
$584$	−5.40599e97	−0.335135
$585$	−1.85980e98	−1.08501
$586$	4.75505e97	0.261090
$587$	2.29774e98	1.18754	0.593771	−	0.804634i	$-0.297638\pi$
$587$	2.29774e98	1.18754	0.593771	+	0.804634i	$0.297638\pi$
$588$	−5.60040e97	−0.272473
$589$	5.91325e96	0.0270853
$590$	−2.85958e98	−1.23327
$591$	8.41290e97	0.341657
$592$	−6.38759e97	−0.244296
$593$	−4.87226e98	−1.75505	−0.877524	−	0.479533i	$-0.840806\pi$
$593$	−4.87226e98	−1.75505	−0.877524	+	0.479533i	$0.840806\pi$
$594$	−2.36476e98	−0.802358
$595$	9.15035e96	0.0292473
$596$	2.13549e98	0.643067
$597$	−2.84456e98	−0.807098
$598$	1.76075e98	0.470766
$599$	5.52581e98	1.39234	0.696168	−	0.717879i	$-0.254887\pi$
$599$	5.52581e98	1.39234	0.696168	+	0.717879i	$0.254887\pi$
$600$	−2.11380e97	−0.0501989
$601$	1.24790e98	0.279341	0.139671	−	0.990198i	$-0.455396\pi$
$601$	1.24790e98	0.279341	0.139671	+	0.990198i	$0.455396\pi$
$602$	1.95502e96	0.00412550
$603$	−5.55137e98	−1.10442
$604$	−6.69982e97	−0.125676
$605$	−3.13445e98	−0.554428
$606$	−2.21880e98	−0.370117
$607$	5.21368e98	0.820250	0.410125	−	0.912029i	$-0.365485\pi$
$607$	5.21368e98	0.820250	0.410125	+	0.912029i	$0.365485\pi$
$608$	−1.57202e97	−0.0233282
$609$	1.25829e97	0.0176144
$610$	9.97282e98	1.31707
$611$	−2.86691e98	−0.357232
$612$	−3.34556e98	−0.393363
$613$	2.99839e98	0.332691	0.166346	−	0.986068i	$-0.446803\pi$
$613$	2.99839e98	0.332691	0.166346	+	0.986068i	$0.446803\pi$
$614$	1.03638e99	1.08528
$615$	−8.76011e98	−0.865851
$616$	−1.07772e97	−0.0100552
$617$	1.62625e98	0.143240	0.0716198	−	0.997432i	$-0.477183\pi$
$617$	1.62625e98	0.143240	0.0716198	+	0.997432i	$0.477183\pi$
$618$	−7.21849e96	−0.00600282
$619$	1.78340e99	1.40033	0.700166	−	0.713980i	$-0.253109\pi$
$619$	1.78340e99	1.40033	0.700166	+	0.713980i	$0.253109\pi$
$620$	−1.55384e98	−0.115213
$621$	−6.41800e98	−0.449416
$622$	1.90054e99	1.25695
$623$	9.37905e94	5.85913e−5 0
$624$	−3.17676e98	−0.187470
$625$	−2.13911e99	−1.19259
$626$	−9.91963e98	−0.522525
$627$	−1.76684e98	−0.0879426
$628$	1.54753e98	0.0727899
$629$	−2.46105e99	−1.09401
$630$	3.08951e97	0.0129808
$631$	4.98801e99	1.98100	0.990501	−	0.137508i	$-0.0439094\pi$
$631$	4.98801e99	1.98100	0.990501	+	0.137508i	$0.0439094\pi$
$632$	−1.02963e99	−0.386567
$633$	2.07371e99	0.736066
$634$	−2.16091e99	−0.725217
$635$	−4.67009e99	−1.48203
$636$	−3.68862e98	−0.110697
$637$	4.84302e99	1.37457
$638$	−4.46957e99	−1.19986
$639$	−3.48889e99	−0.885946
$640$	4.13085e98	0.0992316
$641$	−3.01818e99	−0.685939	−0.342970	−	0.939346i	$-0.611433\pi$
$641$	−3.01818e99	−0.685939	−0.342970	+	0.939346i	$0.611433\pi$
$642$	3.25242e99	0.699380
$643$	−1.72844e99	−0.351694	−0.175847	−	0.984418i	$-0.556266\pi$
$643$	−1.72844e99	−0.351694	−0.175847	+	0.984418i	$0.556266\pi$
$644$	−2.92496e97	−0.00563212
$645$	−8.42214e98	−0.153480
$646$	−6.05679e98	−0.104469
$647$	−2.55126e96	−0.000416536 0	−0.000208268	−	1.00000i	$-0.500066\pi$
$647$	−2.55126e96	−0.000416536 0	−0.000208268		1.00000i	$0.500066\pi$
$648$	−4.49532e98	−0.0694782
$649$	1.29764e100	1.89876
$650$	1.82793e99	0.253242
$651$	−1.98506e97	−0.00260405
$652$	−4.69149e99	−0.582802
$653$	6.69505e99	0.787655	0.393827	−	0.919184i	$-0.371151\pi$
$653$	6.69505e99	0.787655	0.393827	+	0.919184i	$0.371151\pi$
$654$	4.07211e97	0.00453742
$655$	1.90031e100	2.00567
$656$	3.53692e99	0.353621
$657$	−7.03253e99	−0.666102
$658$	4.76252e97	0.00427383
$659$	−1.69393e100	−1.44033	−0.720167	−	0.693801i	$-0.755935\pi$
$659$	−1.69393e100	−1.44033	−0.720167	+	0.693801i	$0.755935\pi$
$660$	4.64277e99	0.374082
$661$	1.91790e100	1.46445	0.732226	−	0.681062i	$-0.238481\pi$
$661$	1.91790e100	1.46445	0.732226	+	0.681062i	$0.238481\pi$
$662$	−6.97297e99	−0.504614
$663$	−1.22396e100	−0.839532
$664$	8.59767e99	0.559003
$665$	5.59325e97	0.00344743
$666$	−8.30947e99	−0.485555
$667$	−1.21305e100	−0.672066
$668$	1.83843e99	0.0965788
$669$	−8.67925e99	−0.432370
$670$	2.64091e100	1.24767
$671$	−4.52555e100	−2.02778
$672$	5.27725e97	0.00224284
$673$	−2.15237e100	−0.867725	−0.433862	−	0.900979i	$-0.642850\pi$
$673$	−2.15237e100	−0.867725	−0.433862	+	0.900979i	$0.642850\pi$
$674$	−1.78920e100	−0.684278
$675$	−6.66291e99	−0.241757
$676$	1.29477e100	0.445744
$677$	1.59032e99	0.0519503	0.0259751	−	0.999663i	$-0.491731\pi$
$677$	1.59032e99	0.0519503	0.0259751	+	0.999663i	$0.491731\pi$
$678$	−7.63657e99	−0.236725
$679$	−7.73831e98	−0.0227651
$680$	1.59156e100	0.444382
$681$	−9.60690e99	−0.254602
$682$	7.05114e99	0.177384
$683$	7.65806e100	1.82887	0.914437	−	0.404728i	$-0.132634\pi$
$683$	7.65806e100	1.82887	0.914437	+	0.404728i	$0.132634\pi$
$684$	−2.04501e99	−0.0463665
$685$	4.52802e100	0.974750
$686$	−1.60949e99	−0.0328989
$687$	−1.42230e100	−0.276075
$688$	3.40046e99	0.0626827
$689$	3.18979e100	0.558443
$690$	1.26006e100	0.209531
$691$	2.01843e99	0.0318818	0.0159409	−	0.999873i	$-0.494926\pi$
$691$	2.01843e99	0.0318818	0.0159409	+	0.999873i	$0.494926\pi$
$692$	−5.92631e100	−0.889238
$693$	−1.40198e99	−0.0199854
$694$	−2.16871e100	−0.293725
$695$	−1.55848e101	−2.00558
$696$	2.18860e100	0.267632
$697$	1.36273e101	1.58360
$698$	3.28765e100	0.363094
$699$	2.39402e100	0.251298
$700$	−3.03657e98	−0.00302973
$701$	2.02517e101	1.92076	0.960379	−	0.278699i	$-0.0899031\pi$
$701$	2.02517e101	1.92076	0.960379	+	0.278699i	$0.0899031\pi$
$702$	−1.00135e101	−0.902853
$703$	−1.50435e100	−0.128954
$704$	−1.87453e100	−0.152779
$705$	−2.05167e100	−0.158999
$706$	−7.89360e100	−0.581712
$707$	−3.18741e99	−0.0223382
$708$	−6.35413e100	−0.423522
$709$	−7.94579e100	−0.503728	−0.251864	−	0.967763i	$-0.581043\pi$
$709$	−7.94579e100	−0.503728	−0.251864	+	0.967763i	$0.581043\pi$
$710$	1.65975e101	1.00085
$711$	−1.33942e101	−0.768327
$712$	1.63134e98	0.000890234 0
$713$	1.91369e100	0.0993560
$714$	2.03325e99	0.0100439
$715$	−4.01489e101	−1.88716
$716$	−1.75453e101	−0.784781
$717$	1.48118e101	0.630488
$718$	2.61192e100	0.105814
$719$	8.50599e100	0.327981	0.163991	−	0.986462i	$-0.447563\pi$
$719$	8.50599e100	0.327981	0.163991	+	0.986462i	$0.447563\pi$
$720$	5.37373e100	0.197230
$721$	−1.03697e98	−0.000362297 0
$722$	2.08894e101	0.694793
$723$	−2.42166e100	−0.0766837
$724$	−1.82294e100	−0.0549610
$725$	−1.25934e101	−0.361530
$726$	−6.96489e100	−0.190399
$727$	−5.06459e100	−0.131848	−0.0659239	−	0.997825i	$-0.520999\pi$
$727$	−5.06459e100	−0.131848	−0.0659239	+	0.997825i	$0.520999\pi$
$728$	−4.56357e99	−0.0113146
$729$	1.55883e101	0.368105
$730$	3.34554e101	0.752496
$731$	1.31015e101	0.280708
$732$	2.21601e101	0.452302
$733$	7.90471e101	1.53707	0.768537	−	0.639806i	$-0.220985\pi$
$733$	7.90471e101	1.53707	0.768537	+	0.639806i	$0.220985\pi$
$734$	1.86321e100	0.0345185
$735$	3.46585e101	0.611800
$736$	−5.08751e100	−0.0855742
$737$	−1.19842e102	−1.92093
$738$	4.60110e101	0.702846
$739$	−3.78561e100	−0.0551136	−0.0275568	−	0.999620i	$-0.508773\pi$
$739$	−3.78561e100	−0.0551136	−0.0275568	+	0.999620i	$0.508773\pi$
$740$	3.95301e101	0.548532
$741$	−7.48160e100	−0.0989574
$742$	−5.29889e99	−0.00668107
$743$	−1.68381e99	−0.00202391	−0.00101195	−	0.999999i	$-0.500322\pi$
$743$	−1.68381e99	−0.00202391	−0.00101195	+	0.999999i	$0.500322\pi$
$744$	−3.45271e100	−0.0395658
$745$	−1.32157e102	−1.44391
$746$	−2.64347e101	−0.275389
$747$	1.11845e102	1.11106
$748$	−7.22230e101	−0.684178
$749$	4.67226e100	0.0422107
$750$	−3.71534e101	−0.320128
$751$	−9.77486e101	−0.803328	−0.401664	−	0.915787i	$-0.631568\pi$
$751$	−9.77486e101	−0.803328	−0.401664	+	0.915787i	$0.631568\pi$
$752$	8.28366e100	0.0649365
$753$	2.77456e101	0.207478
$754$	−1.89262e102	−1.35015
$755$	4.14623e101	0.282187
$756$	1.66344e100	0.0108015
$757$	−2.24282e101	−0.138960	−0.0694800	−	0.997583i	$-0.522134\pi$
$757$	−2.24282e101	−0.138960	−0.0694800	+	0.997583i	$0.522134\pi$
$758$	−4.76527e101	−0.281729
$759$	−5.71798e101	−0.322597
$760$	9.72858e100	0.0523802
$761$	8.57100e101	0.440429	0.220215	−	0.975451i	$-0.429324\pi$
$761$	8.57100e101	0.440429	0.220215	+	0.975451i	$0.429324\pi$
$762$	−1.03772e102	−0.508952
$763$	5.84978e98	0.000273854 0
$764$	6.82862e101	0.305154
$765$	2.07042e102	0.883239
$766$	1.01571e102	0.413665
$767$	5.49482e102	2.13658
$768$	9.17894e100	0.0340776
$769$	−1.46162e102	−0.518142	−0.259071	−	0.965858i	$-0.583416\pi$
$769$	−1.46162e102	−0.518142	−0.259071	+	0.965858i	$0.583416\pi$
$770$	6.66956e100	0.0225775
$771$	−9.62427e101	−0.311127
$772$	3.08577e102	0.952686
$773$	−7.34446e100	−0.0216565	−0.0108282	−	0.999941i	$-0.503447\pi$
$773$	−7.34446e100	−0.0216565	−0.0108282	+	0.999941i	$0.503447\pi$
$774$	4.42358e101	0.124586
$775$	1.98672e101	0.0534473
$776$	−1.34596e102	−0.345892
$777$	5.05005e100	0.0123979
$778$	−3.49335e102	−0.819345
$779$	8.32982e101	0.186662
$780$	1.96596e102	0.420936
$781$	−7.53173e102	−1.54093
$782$	−1.96015e102	−0.383221
$783$	6.89870e102	1.28892
$784$	−1.39935e102	−0.249865
$785$	−9.57699e101	−0.163439
$786$	4.22258e102	0.688776
$787$	−3.09091e102	−0.481929	−0.240965	−	0.970534i	$-0.577464\pi$
$787$	−3.09091e102	−0.481929	−0.240965	+	0.970534i	$0.577464\pi$
$788$	2.10209e102	0.313307
$789$	−5.09165e102	−0.725479
$790$	6.37193e102	0.867980
$791$	−1.09703e101	−0.0142874
$792$	−2.43853e102	−0.303658
$793$	−1.91632e103	−2.28176
$794$	5.27110e102	0.600169
$795$	2.28273e102	0.248555
$796$	−7.10757e102	−0.740129
$797$	8.71056e102	0.867513	0.433756	−	0.901030i	$-0.357188\pi$
$797$	8.71056e102	0.867513	0.433756	+	0.901030i	$0.357188\pi$
$798$	1.24285e100	0.00118390
$799$	3.19158e102	0.290800
$800$	−5.28164e101	−0.0460335
$801$	2.12217e100	0.00176940
$802$	−3.57349e101	−0.0285038
$803$	−1.51816e103	−1.15856
$804$	5.86824e102	0.428468
$805$	1.81013e101	0.0126461
$806$	2.98577e102	0.199601
$807$	5.95761e102	0.381120
$808$	−5.54400e102	−0.339406
$809$	−7.08325e102	−0.415011	−0.207506	−	0.978234i	$-0.566535\pi$
$809$	−7.08325e102	−0.415011	−0.207506	+	0.978234i	$0.566535\pi$
$810$	2.78196e102	0.156003
$811$	2.41112e103	1.29413	0.647065	−	0.762435i	$-0.275996\pi$
$811$	2.41112e103	1.29413	0.647065	+	0.762435i	$0.275996\pi$
$812$	3.14403e101	0.0161528
$813$	−1.90038e102	−0.0934603
$814$	−1.79383e103	−0.844528
$815$	2.90336e103	1.30860
$816$	3.53652e102	0.152607
$817$	8.00844e101	0.0330876
$818$	1.46223e103	0.578459
$819$	−5.93664e101	−0.0224886
$820$	−2.18885e103	−0.794006
$821$	5.18111e103	1.79987	0.899934	−	0.436026i	$-0.143614\pi$
$821$	5.18111e103	1.79987	0.899934	+	0.436026i	$0.143614\pi$
$822$	1.00615e103	0.334744
$823$	−1.02240e103	−0.325782	−0.162891	−	0.986644i	$-0.552082\pi$
$823$	−1.02240e103	−0.325782	−0.162891	+	0.986644i	$0.552082\pi$
$824$	−1.80365e101	−0.00550473
$825$	−5.93617e102	−0.173537
$826$	−9.12803e101	−0.0255614
$827$	5.50266e103	1.47614	0.738069	−	0.674725i	$-0.235738\pi$
$827$	5.50266e103	1.47614	0.738069	+	0.674725i	$0.235738\pi$
$828$	−6.61823e102	−0.170084
$829$	−4.82843e103	−1.18883	−0.594415	−	0.804158i	$-0.702616\pi$
$829$	−4.82843e103	−1.18883	−0.594415	+	0.804158i	$0.702616\pi$
$830$	−5.32073e103	−1.25516
$831$	−3.59670e103	−0.812958
$832$	−7.93761e102	−0.171914
$833$	−5.39149e103	−1.11895
$834$	−3.46302e103	−0.688747
$835$	−1.13772e103	−0.216854
$836$	−4.41471e102	−0.0806454
$837$	−1.08833e103	−0.190549
$838$	4.09606e103	0.687390
$839$	−6.22383e103	−1.00117	−0.500585	−	0.865687i	$-0.666882\pi$
$839$	−6.22383e103	−1.00117	−0.500585	+	0.865687i	$0.666882\pi$
$840$	−3.26586e101	−0.00503597
$841$	6.27423e103	0.927475
$842$	6.92390e103	0.981231
$843$	1.41189e103	0.191833
$844$	5.18149e103	0.674990
$845$	−8.01280e103	−1.00085
$846$	1.07760e103	0.129066
$847$	−1.00054e102	−0.0114914
$848$	−9.21659e102	−0.101512
$849$	4.51039e103	0.476421
$850$	−2.03494e103	−0.206149
$851$	−4.86848e103	−0.473036
$852$	3.68804e103	0.343708
$853$	1.63607e104	1.46255	0.731276	−	0.682081i	$-0.238925\pi$
$853$	1.63607e104	1.46255	0.731276	+	0.682081i	$0.238925\pi$
$854$	3.18341e102	0.0272984
$855$	1.26557e103	0.104109
$856$	8.12667e103	0.641348
$857$	−1.31809e102	−0.00997990	−0.00498995	−	0.999988i	$-0.501588\pi$
$857$	−1.31809e102	−0.00997990	−0.00498995	+	0.999988i	$0.501588\pi$
$858$	−8.92129e103	−0.648080
$859$	2.76578e102	0.0192780	0.00963898	−	0.999954i	$-0.496932\pi$
$859$	2.76578e102	0.0192780	0.00963898	+	0.999954i	$0.496932\pi$
$860$	−2.10440e103	−0.140745
$861$	−2.79630e102	−0.0179462
$862$	1.49616e104	0.921444
$863$	−1.34409e104	−0.794412	−0.397206	−	0.917730i	$-0.630020\pi$
$863$	−1.34409e104	−0.794412	−0.397206	+	0.917730i	$0.630020\pi$
$864$	2.89330e103	0.164118
$865$	3.66754e104	1.99666
$866$	2.13177e103	0.111392
$867$	2.75479e103	0.138169
$868$	−4.95998e101	−0.00238798
$869$	−2.89151e104	−1.33636
$870$	−1.35443e104	−0.600930
$871$	−5.07464e104	−2.16153
$872$	1.01748e102	0.00416092
$873$	−1.75092e104	−0.687483
$874$	−1.19816e103	−0.0451710
$875$	−5.33727e102	−0.0193211
$876$	7.43395e103	0.258419
$877$	4.92071e104	1.64264	0.821319	−	0.570469i	$-0.193239\pi$
$877$	4.92071e104	1.64264	0.821319	+	0.570469i	$0.193239\pi$
$878$	−3.10895e104	−0.996687
$879$	−6.53882e103	−0.201323
$880$	1.16007e104	0.343042
$881$	2.93838e104	0.834570	0.417285	−	0.908776i	$-0.362982\pi$
$881$	2.93838e104	0.834570	0.417285	+	0.908776i	$0.362982\pi$
$882$	−1.82038e104	−0.496623
$883$	−3.26352e104	−0.855227	−0.427614	−	0.903962i	$-0.640646\pi$
$883$	−3.26352e104	−0.855227	−0.427614	+	0.903962i	$0.640646\pi$
$884$	−3.05825e104	−0.769871
$885$	3.93230e104	0.950957
$886$	−3.77474e103	−0.0876979
$887$	2.01172e104	0.449033	0.224516	−	0.974470i	$-0.427920\pi$
$887$	2.01172e104	0.449033	0.224516	+	0.974470i	$0.427920\pi$
$888$	8.78378e103	0.188374
$889$	−1.49073e103	−0.0307176
$890$	−1.00957e102	−0.00199889
$891$	−1.26242e104	−0.240185
$892$	−2.16864e104	−0.396493
$893$	1.95089e103	0.0342772
$894$	−2.93658e104	−0.495862
$895$	1.08580e105	1.76211
$896$	1.31860e102	0.00205674
$897$	−2.42126e104	−0.363002
$898$	4.78590e104	0.689690
$899$	−2.05702e104	−0.284951
$900$	−6.87077e103	−0.0914948
$901$	−3.55102e104	−0.454594
$902$	9.93272e104	1.22246
$903$	−2.68842e102	−0.00318113
$904$	−1.90811e104	−0.217083
$905$	1.12814e104	0.123407
$906$	9.21312e103	0.0969072
$907$	7.71153e104	0.779977	0.389989	−	0.920820i	$-0.372479\pi$
$907$	7.71153e104	0.779977	0.389989	+	0.920820i	$0.372479\pi$
$908$	−2.40043e104	−0.233476
$909$	−7.21206e104	−0.674593
$910$	2.82420e103	0.0254054
$911$	−8.50577e104	−0.735887	−0.367944	−	0.929848i	$-0.619938\pi$
$911$	−8.50577e104	−0.735887	−0.367944	+	0.929848i	$0.619938\pi$
$912$	2.16174e103	0.0179881
$913$	2.41448e105	1.93246
$914$	8.21715e104	0.632603
$915$	−1.37139e105	−1.01558
$916$	−3.55384e104	−0.253168
$917$	6.06595e103	0.0415707
$918$	1.11475e105	0.734956
$919$	−1.47365e105	−0.934744	−0.467372	−	0.884061i	$-0.654799\pi$
$919$	−1.47365e105	−0.934744	−0.467372	+	0.884061i	$0.654799\pi$
$920$	3.14844e104	0.192144
$921$	−1.42516e105	−0.836850
$922$	−2.62350e104	−0.148229
$923$	−3.18928e105	−1.73393
$924$	1.48201e103	0.00775347
$925$	−5.05426e104	−0.254464
$926$	−2.29971e105	−1.11425
$927$	−2.34633e103	−0.0109410
$928$	5.46855e104	0.245425
$929$	3.93948e104	0.170169	0.0850847	−	0.996374i	$-0.472884\pi$
$929$	3.93948e104	0.170169	0.0850847	+	0.996374i	$0.472884\pi$
$930$	2.13673e104	0.0888394
$931$	−3.29561e104	−0.131893
$932$	5.98183e104	0.230446
$933$	−2.61350e105	−0.969223
$934$	1.05754e105	0.377556
$935$	4.46957e105	1.53622
$936$	−1.03259e105	−0.341691
$937$	3.14941e105	1.00340	0.501699	−	0.865042i	$-0.332708\pi$
$937$	3.14941e105	1.00340	0.501699	+	0.865042i	$0.332708\pi$
$938$	8.43002e103	0.0258600
$939$	1.36408e105	0.402913
$940$	−5.12640e104	−0.145805
$941$	3.78812e105	1.03751	0.518755	−	0.854923i	$-0.326396\pi$
$941$	3.78812e105	1.03751	0.518755	+	0.854923i	$0.326396\pi$
$942$	−2.12805e104	−0.0561275
$943$	2.69576e105	0.684725
$944$	−1.58768e105	−0.388380
$945$	−1.02943e104	−0.0242532
$946$	9.54951e104	0.216693
$947$	4.12841e105	0.902316	0.451158	−	0.892444i	$-0.351011\pi$
$947$	4.12841e105	0.902316	0.451158	+	0.892444i	$0.351011\pi$
$948$	1.41587e105	0.298077
$949$	−6.42860e105	−1.30367
$950$	−1.24388e104	−0.0242992
$951$	2.97153e105	0.559207
$952$	5.08039e103	0.00921054
$953$	1.46735e104	0.0256292	0.0128146	−	0.999918i	$-0.495921\pi$
$953$	1.46735e104	0.0256292	0.0128146	+	0.999918i	$0.495921\pi$
$954$	−1.19896e105	−0.201762
$955$	−4.22594e105	−0.685178
$956$	3.70095e105	0.578173
$957$	6.14625e105	0.925202
$958$	−9.65089e105	−1.39988
$959$	1.44538e104	0.0202033
$960$	−5.68046e104	−0.0765164
$961$	−7.37885e105	−0.957874
$962$	−7.59589e105	−0.950306
$963$	1.05718e106	1.27472
$964$	−6.05088e104	−0.0703207
$965$	−1.90965e106	−2.13912
$966$	4.02220e103	0.00434286
$967$	−3.05195e105	−0.317642	−0.158821	−	0.987307i	$-0.550769\pi$
$967$	−3.05195e105	−0.317642	−0.158821	+	0.987307i	$0.550769\pi$
$968$	−1.74028e105	−0.174600
$969$	8.32888e104	0.0805550
$970$	8.32955e105	0.776649
$971$	1.28635e106	1.15631	0.578156	−	0.815926i	$-0.303772\pi$
$971$	1.28635e106	1.15631	0.578156	+	0.815926i	$0.303772\pi$
$972$	5.97432e105	0.517769
$973$	−4.97479e104	−0.0415690
$974$	−7.67186e105	−0.618098
$975$	−2.51365e105	−0.195272
$976$	5.53704e105	0.414771
$977$	−1.50192e106	−1.08490	−0.542450	−	0.840088i	$-0.682503\pi$
$977$	−1.50192e106	−1.08490	−0.542450	+	0.840088i	$0.682503\pi$
$978$	6.45141e105	0.449392
$979$	4.58129e103	0.00307753
$980$	8.65995e105	0.561035
$981$	1.32361e104	0.00827012
$982$	7.26231e104	0.0437640
$983$	1.54951e105	0.0900628	0.0450314	−	0.998986i	$-0.485661\pi$
$983$	1.54951e105	0.0900628	0.0450314	+	0.998986i	$0.485661\pi$
$984$	−4.86372e105	−0.272674
$985$	−1.30089e106	−0.703487
$986$	2.10696e106	1.09907
$987$	−6.54909e103	−0.00329551
$988$	−1.86939e105	−0.0907463
$989$	2.59176e105	0.121374
$990$	1.50910e106	0.681820
$991$	−1.80949e106	−0.788753	−0.394376	−	0.918949i	$-0.629039\pi$
$991$	−1.80949e106	−0.788753	−0.394376	+	0.918949i	$0.629039\pi$
$992$	−8.62711e104	−0.0362828
$993$	9.58875e105	0.389102
$994$	5.29805e104	0.0207443
$995$	4.39857e106	1.66185
$996$	−1.18229e106	−0.431041
$997$	2.71026e106	0.953528	0.476764	−	0.879031i	$-0.341810\pi$
$997$	2.71026e106	0.953528	0.476764	+	0.879031i	$0.341810\pi$
$998$	−1.27010e106	−0.431224
$999$	2.76874e106	0.907208

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2.72.a.b.1.2	✓	3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2.72.a.b.1.2	✓	3	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 2 \)
Weight:	\( k \)	\(=\)	\( 72 \)
Character orbit:	\([\chi]\)	\(=\)	2.a (trivial)

\(f(q)\)	\(=\)	\(q-3.43597e10 q^{2} +4.72491e16 q^{3} +1.18059e21 q^{4} -7.30618e24 q^{5} -1.62347e27 q^{6} -2.33219e28 q^{7} -4.05648e31 q^{8} -5.27699e33 q^{9} +O(q^{10})\)	\(q-3.43597e10 q^{2} +4.72491e16 q^{3} +1.18059e21 q^{4} -7.30618e24 q^{5} -1.62347e27 q^{6} -2.33219e28 q^{7} -4.05648e31 q^{8} -5.27699e33 q^{9} +2.51038e35 q^{10} -1.13918e37 q^{11} +5.57819e37 q^{12} -4.82382e39 q^{13} +8.01335e38 q^{14} -3.45211e41 q^{15} +1.39380e42 q^{16} +5.37011e43 q^{17} +1.81316e44 q^{18} +3.28254e44 q^{19} -8.62561e45 q^{20} -1.10194e45 q^{21} +3.91420e47 q^{22} +1.06232e48 q^{23} -1.91665e48 q^{24} +1.10286e49 q^{25} +1.65745e50 q^{26} -6.04149e50 q^{27} -2.75337e49 q^{28} -1.14189e52 q^{29} +1.18613e52 q^{30} +1.80143e52 q^{31} -4.78905e52 q^{32} -5.38254e53 q^{33} -1.84515e54 q^{34} +1.70394e53 q^{35} -6.22996e54 q^{36} -4.58287e55 q^{37} -1.12787e55 q^{38} -2.27921e56 q^{39} +2.96374e56 q^{40} +2.53761e57 q^{41} +3.78624e55 q^{42} +2.43971e57 q^{43} -1.34491e58 q^{44} +3.85546e58 q^{45} -3.65011e58 q^{46} +5.94323e58 q^{47} +6.58557e58 q^{48} -1.00398e60 q^{49} -3.78939e59 q^{50} +2.53733e60 q^{51} -5.69496e60 q^{52} -6.61258e60 q^{53} +2.07584e61 q^{54} +8.32306e61 q^{55} +9.46049e59 q^{56} +1.55097e61 q^{57} +3.92350e62 q^{58} -1.13910e63 q^{59} -4.07553e62 q^{60} +3.97263e63 q^{61} -6.18965e62 q^{62} +1.23069e62 q^{63} +1.64550e63 q^{64} +3.52437e64 q^{65} +1.84943e64 q^{66} +1.05200e65 q^{67} +6.33990e64 q^{68} +5.01938e64 q^{69} -5.85470e63 q^{70} +6.61153e65 q^{71} +2.14060e65 q^{72} +1.33268e66 q^{73} +1.57466e66 q^{74} +5.21091e65 q^{75} +3.87534e65 q^{76} +2.65679e65 q^{77} +7.83131e66 q^{78} +2.53823e67 q^{79} -1.01833e67 q^{80} +1.10818e67 q^{81} -8.71917e67 q^{82} -2.11949e68 q^{83} -1.30094e66 q^{84} -3.92350e68 q^{85} -8.38278e67 q^{86} -5.39532e68 q^{87} +4.62107e68 q^{88} -4.02156e66 q^{89} -1.32473e69 q^{90} +1.12501e68 q^{91} +1.25417e69 q^{92} +8.51158e68 q^{93} -2.04208e69 q^{94} -2.39828e69 q^{95} -2.26278e69 q^{96} +3.31804e70 q^{97} +3.44965e70 q^{98} +6.01144e70 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q - 103079215104 q^{2} + 23\!\cdots\!36 q^{3}+ \cdots - 45\!\cdots\!09 q^{9}+O(q^{10}) \) 3 * q - 103079215104 * q^2 + 2362570292707236 * q^3 + 3541774862152233910272 * q^4 + 4753308915533391960256650 * q^5 - 81177297133429807380430848 * q^6 - 685790799447997047084795426072 * q^7 - 121694457621910022543683507716096 * q^8 - 4505398350426548777838087948321009 * q^9	\( 3 q - 103079215104 q^{2} + 23\!\cdots\!36 q^{3}+ \cdots + 12\!\cdots\!32 q^{99}+O(q^{100}) \) 3 * q - 103079215104 * q^2 + 2362570292707236 * q^3 + 3541774862152233910272 * q^4 + 4753308915533391960256650 * q^5 - 81177297133429807380430848 * q^6 - 685790799447997047084795426072 * q^7 - 121694457621910022543683507716096 * q^8 - 4505398350426548777838087948321009 * q^9 - 163322450720009158922013148132147200 * q^10 + 3969518227834483364274834229858599756 * q^11 + 2789230690926044568084239380396376064 * q^12 + 2529641076874049546506304992034610800946 * q^13 + 23563592444214737359470147950637005930496 * q^14 + 407345545990301587458425269101161600167800 * q^15 + 4181389724724491839037947176121567782371328 * q^16 + 35492344011589917581644253423281452467295318 * q^17 + 154804308564274997207706858569683774117773312 * q^18 + 2841186907242840665111664111817927348680296820 * q^19 + 5611716676360087923124104685676605682063769600 * q^20 - 147880796471173011613366779703968478971439282464 * q^21 - 136391607755399863604931742184512261250988638208 * q^22 + 372858837194588698341491556777522114253679157816 * q^23 - 95837236788214762996482028094701909694377623552 * q^24 + 69862220765255200329820968690236540988174429613125 * q^25 - 86917805566338117706625687988721551121211486896128 * q^26 - 947955055507342807334349523771491542851454430730200 * q^27 - 809638871393400010881229450690138902710706952470528 * q^28 + 2838293454662119862597708158946776463408079116647170 * q^29 - 13996286385596874010486562323595907106653832898150400 * q^30 - 60985780592296898612188383347434281055674826984896864 * q^31 - 143671456956177080471095033795341485964256792704712704 * q^32 - 2226251555109516044503731418659397026281060527969942128 * q^33 - 1219507654305281127811979826874639066803295203071361024 * q^34 - 15012477392108224914953334499824623410367257977654315600 * q^35 - 5319035540507630615660738213693513175181501019052834816 * q^36 - 68176149937496232624484049167780541975937489767987119062 * q^37 - 97622438787451089494347884387159080552686908811782389760 * q^38 - 181103730680294442815742293797937418749802413053959521448 * q^39 - 192817116795075151596020734194091048294013313747832012800 * q^40 + 2552747372756675092691146114350576632165539159012967279886 * q^41 + 5081145476400962333097908122251049428777563489860690378752 * q^42 + 18909111020150337719256805153495922766806377418623683904236 * q^43 + 4686379958066419052688339975958270078272033990167488364544 * q^44 - 2721353093966297027357236277004028373408155461709353007950 * q^45 - 12811332094202774780383325409756677029090619443972342284288 * q^46 - 43968712731246921396266407709188709699073053268890920706832 * q^47 + 3292942381955123882354250189747983144048777985840314843136 * q^48 - 1026062827616062451582801453511096725123047657850544364580901 * q^49 - 2400447627301625428084075792476847184386981583454606458880000 * q^50 - 6642917231549727841284660449151726108810042035755118549288184 * q^51 + 2986473058780071792225246819400472631327963744947218472239104 * q^52 + 30871443618914543069766688718872801487605153889290407489338106 * q^53 + 32571487691855216362894881136253846029500634928164051196313600 * q^54 + 82883499258166400764153074170750404891861017028181553423013800 * q^55 + 27818979793640023975847397047889529734718496879205953310818304 * q^56 + 212035618958631297738882658287269296529392551878549426422723440 * q^57 - 97523020513797308319113361177830197719681924065441314567618560 * q^58 + 460247047764608873010378962302858647900183942836691252581585340 * q^59 + 480908738332708954518977169818481521140257570324838935114547200 * q^60 + 16775049429831179566881200695612811340299429511572993213743266 * q^61 + 2095455465319573512492615147746729941147165896884722534503677952 * q^62 + 7123265108840012936647472594777745274062746713593724228790075016 * q^63 + 4936513671963618126464907547672051514948207596900739590045827072 * q^64 + 94246518292142244320312430108492294401480277247156255007099586300 * q^65 + 76493420974916104876246455944878355127654459774619157686181167104 * q^66 + 294767885753586694210169114445805135103533346814314947921669563108 * q^67 + 41901963939702848352307595147506533469792897297801394818312568832 * q^68 + 528466810873440345877804349403437515478040457656947404876631762592 * q^69 + 515824795448353556018695624343162202264346882905763074362100940800 * q^70 + 919902509099705545860692207075672006856952727183920111456887673896 * q^71 + 182760669541935653861689728472248787637997325928180787446481420288 * q^72 + 2801172592879364865003588703151843916561463459054226277253242976686 * q^73 + 2342514674789910105962937920394187557534453899950714432964385570816 * q^74 + 11540065797237808994474506232223048759594775508100266283876440557500 * q^75 + 3354281455582914596622346722317098026585759026191516667903402311680 * q^76 + 9865200407486310864984017360081516522994693272661494127815675761056 * q^77 + 6222676803643651708353242446609318766280468564229117023415764516864 * q^78 + 35861415701696815437845171625266918505761182712600613769101529649040 * q^79 + 6625145685950880879737210056812239750953150201084205487022827110400 * q^80 - 77413789943620858546024097436886978978462391694997730724429179486277 * q^81 - 87711731847518727110449929519145623311142498769344304856227588866048 * q^82 - 491461197261236055126649090145388665192472846714449095644779700562764 * q^83 - 174586829178883784028666990008648217586232931580122342181773546356736 * q^84 - 1165838157532517419220567093290863687374587795758826921777398482729100 * q^85 - 649712107423831180060505660477673986822201803017772989597881726926848 * q^86 - 533065155655732635133140699091829032733726763688543635407301551318760 * q^87 - 161022789252200969817021768618161569975309969433357984705416047624192 * q^88 - 177072112231663993716456138855227097994172685795374860821951903002370 * q^89 + 93504980315629285269770776949416789792352830141803611411715824025600 * q^90 - 4639739553715545710656746238349490629903267972921545465730866402748304 * q^91 + 440194018902368870993599719829045817260629209057943315516279157161984 * q^92 + 890401138912307375413854706914858877690325831251184410358068258856832 * q^93 + 1510753465823394917581175020914942294799654122438019189017381150130176 * q^94 + 30260171170818092294903292510986000303485315694075825006268582939063000 * q^95 - 113144638704876780914720448412555056685190067823591226636899920642048 * q^96 + 41131919037209954991700932094148075864450433573097333943337676290089958 * q^97 + 35255250306018190990733725431131398459969530130539885613376564329709568 * q^98 + 126334151665356806749302419314959438273928289729980682281425205273054332 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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