LMFDB - Embedded newform 2.72.a.b.1.1

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			1.1
Root			$-6.65040e12$ 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)

$f(q)$	$=$	$q-3.43597e10 q^{2} -1.08417e17 q^{3} +1.18059e21 q^{4} +7.90573e22 q^{5} +3.72520e27 q^{6} +6.08855e29 q^{7} -4.05648e31 q^{8} +4.24488e33 q^{9} +O(q^{10})$	\(q-3.43597e10 q^{2} -1.08417e17 q^{3} +1.18059e21 q^{4} +7.90573e22 q^{5} +3.72520e27 q^{6} +6.08855e29 q^{7} -4.05648e31 q^{8} +4.24488e33 q^{9} -2.71639e33 q^{10} +1.54925e37 q^{11} -1.27997e38 q^{12} +2.44465e39 q^{13} -2.09201e40 q^{14} -8.57119e39 q^{15} +1.39380e42 q^{16} +4.66619e43 q^{17} -1.45853e44 q^{18} -2.14466e44 q^{19} +9.33344e43 q^{20} -6.60105e46 q^{21} -5.32320e47 q^{22} -3.03623e48 q^{23} +4.39793e48 q^{24} -4.23454e49 q^{25} -8.39977e49 q^{26} +3.53938e50 q^{27} +7.18809e50 q^{28} +5.23008e51 q^{29} +2.94504e50 q^{30} -2.94169e52 q^{31} -4.78905e52 q^{32} -1.67966e54 q^{33} -1.60329e54 q^{34} +4.81344e52 q^{35} +5.01147e54 q^{36} -4.30443e54 q^{37} +7.36899e54 q^{38} -2.65043e56 q^{39} -3.20694e54 q^{40} -5.89629e56 q^{41} +2.26810e57 q^{42} +6.09960e57 q^{43} +1.82904e58 q^{44} +3.35589e56 q^{45} +1.04324e59 q^{46} -3.56597e59 q^{47} -1.51112e59 q^{48} -6.33821e59 q^{49} +1.45498e60 q^{50} -5.05896e60 q^{51} +2.88614e60 q^{52} +3.09537e61 q^{53} -1.21612e61 q^{54} +1.22480e60 q^{55} -2.46981e61 q^{56} +2.32518e61 q^{57} -1.79704e62 q^{58} +1.36513e63 q^{59} -1.01191e61 q^{60} -1.19961e63 q^{61} +1.01076e63 q^{62} +2.58452e63 q^{63} +1.64550e63 q^{64} +1.93268e62 q^{65} +5.77128e64 q^{66} +1.19801e65 q^{67} +5.50886e64 q^{68} +3.29181e65 q^{69} -1.65389e63 q^{70} -3.22364e65 q^{71} -1.72193e65 q^{72} +2.31415e66 q^{73} +1.47899e65 q^{74} +4.59098e66 q^{75} -2.53196e65 q^{76} +9.43271e66 q^{77} +9.10682e66 q^{78} -9.14450e66 q^{79} +1.10190e65 q^{80} -7.02499e67 q^{81} +2.02595e67 q^{82} -1.67738e68 q^{83} -7.79315e67 q^{84} +3.68896e66 q^{85} -2.09581e68 q^{86} -5.67032e68 q^{87} -6.28452e68 q^{88} -7.15572e68 q^{89} -1.15307e67 q^{90} +1.48844e69 q^{91} -3.58455e69 q^{92} +3.18930e69 q^{93} +1.22526e70 q^{94} -1.69551e67 q^{95} +5.19216e69 q^{96} -2.08258e70 q^{97} +2.17779e70 q^{98} +6.57640e70 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	−1.08417e17	−1.25111	−0.625554	−	0.780181i	$-0.715127\pi$
$3$	−1.08417e17	−1.25111	−0.625554	+	0.780181i	$0.715127\pi$
$4$	1.18059e21	0.500000
$5$	7.90573e22	0.0121481	0.00607403	−	0.999982i	$-0.498067\pi$
$5$	7.90573e22	0.0121481	0.00607403	+	0.999982i	$0.498067\pi$
$6$	3.72520e27	0.884667
$7$	6.08855e29	0.607482	0.303741	−	0.952755i	$-0.401764\pi$
$7$	6.08855e29	0.607482	0.303741	+	0.952755i	$0.401764\pi$
$8$	−4.05648e31	−0.353553
$9$	4.24488e33	0.565270
$10$	−2.71639e33	−0.00858997
$11$	1.54925e37	1.66220	0.831098	−	0.556126i	$-0.187713\pi$
$11$	1.54925e37	1.66220	0.831098	+	0.556126i	$0.187713\pi$
$12$	−1.27997e38	−0.625554
$13$	2.44465e39	0.696993	0.348497	−	0.937310i	$-0.386692\pi$
$13$	2.44465e39	0.696993	0.348497	+	0.937310i	$0.386692\pi$
$14$	−2.09201e40	−0.429555
$15$	−8.57119e39	−0.0151985
$16$	1.39380e42	0.250000
$17$	4.66619e43	0.972804	0.486402	−	0.873735i	$-0.338309\pi$
$17$	4.66619e43	0.972804	0.486402	+	0.873735i	$0.338309\pi$
$18$	−1.45853e44	−0.399707
$19$	−2.14466e44	−0.0862194	−0.0431097	−	0.999070i	$-0.513727\pi$
$19$	−2.14466e44	−0.0862194	−0.0431097	+	0.999070i	$0.513727\pi$
$20$	9.33344e43	0.00607403
$21$	−6.60105e46	−0.760025
$22$	−5.32320e47	−1.17535
$23$	−3.03623e48	−1.38356	−0.691778	−	0.722110i	$-0.743172\pi$
$23$	−3.03623e48	−1.38356	−0.691778	+	0.722110i	$0.743172\pi$
$24$	4.39793e48	0.442333
$25$	−4.23454e49	−0.999852
$26$	−8.39977e49	−0.492849
$27$	3.53938e50	0.543894
$28$	7.18809e50	0.303741
$29$	5.23008e51	0.635886	0.317943	−	0.948110i	$-0.397008\pi$
$29$	5.23008e51	0.635886	0.317943	+	0.948110i	$0.397008\pi$
$30$	2.94504e50	0.0107470
$31$	−2.94169e52	−0.335163	−0.167582	−	0.985858i	$-0.553596\pi$
$31$	−2.94169e52	−0.335163	−0.167582	+	0.985858i	$0.553596\pi$
$32$	−4.78905e52	−0.176777
$33$	−1.67966e54	−2.07959
$34$	−1.60329e54	−0.687876
$35$	4.81344e52	0.00737973
$36$	5.01147e54	0.282635
$37$	−4.30443e54	−0.0917814	−0.0458907	−	0.998946i	$-0.514613\pi$
$37$	−4.30443e54	−0.0917814	−0.0458907	+	0.998946i	$0.514613\pi$
$38$	7.36899e54	0.0609663
$39$	−2.65043e56	−0.872013
$40$	−3.20694e54	−0.00429499
$41$	−5.89629e56	−0.328664	−0.164332	−	0.986405i	$-0.552547\pi$
$41$	−5.89629e56	−0.328664	−0.164332	+	0.986405i	$0.552547\pi$
$42$	2.26810e57	0.537419
$43$	6.09960e57	0.626861	0.313430	−	0.949611i	$-0.398522\pi$
$43$	6.09960e57	0.626861	0.313430	+	0.949611i	$0.398522\pi$
$44$	1.82904e58	0.831098
$45$	3.35589e56	0.00686694
$46$	1.04324e59	0.978322
$47$	−3.56597e59	−1.55849	−0.779244	−	0.626721i	$-0.784397\pi$
$47$	−3.56597e59	−1.55849	−0.779244	+	0.626721i	$0.784397\pi$
$48$	−1.51112e59	−0.312777
$49$	−6.33821e59	−0.630966
$50$	1.45498e60	0.707002
$51$	−5.05896e60	−1.21708
$52$	2.88614e60	0.348497
$53$	3.09537e61	1.90072	0.950362	−	0.311146i	$-0.100713\pi$
$53$	3.09537e61	1.90072	0.950362	+	0.311146i	$0.100713\pi$
$54$	−1.21612e61	−0.384591
$55$	1.22480e60	0.0201925
$56$	−2.46981e61	−0.214777
$57$	2.32518e61	0.107870
$58$	−1.79704e62	−0.449640
$59$	1.36513e63	1.86177	0.930887	−	0.365307i	$-0.119036\pi$
$59$	1.36513e63	1.86177	0.930887	+	0.365307i	$0.119036\pi$
$60$	−1.01191e61	−0.00759926
$61$	−1.19961e63	−0.500994	−0.250497	−	0.968117i	$-0.580594\pi$
$61$	−1.19961e63	−0.500994	−0.250497	+	0.968117i	$0.580594\pi$
$62$	1.01076e63	0.236996
$63$	2.58452e63	0.343392
$64$	1.64550e63	0.125000
$65$	1.93268e62	0.00846711
$66$	5.77128e64	1.47049
$67$	1.19801e65	1.78981	0.894904	−	0.446260i	$-0.147244\pi$
$67$	1.19801e65	1.78981	0.894904	+	0.446260i	$0.147244\pi$
$68$	5.50886e64	0.486402
$69$	3.29181e65	1.73098
$70$	−1.65389e63	−0.00521825
$71$	−3.22364e65	−0.614717	−0.307358	−	0.951594i	$-0.599445\pi$
$71$	−3.22364e65	−0.614717	−0.307358	+	0.951594i	$0.599445\pi$
$72$	−1.72193e65	−0.199853
$73$	2.31415e66	1.64600	0.823002	−	0.568039i	$-0.192298\pi$
$73$	2.31415e66	1.64600	0.823002	+	0.568039i	$0.192298\pi$
$74$	1.47899e65	0.0648993
$75$	4.59098e66	1.25092
$76$	−2.53196e65	−0.0431097
$77$	9.43271e66	1.00975
$78$	9.10682e66	0.616607
$79$	−9.14450e66	−0.393911	−0.196956	−	0.980412i	$-0.563105\pi$
$79$	−9.14450e66	−0.393911	−0.196956	+	0.980412i	$0.563105\pi$
$80$	1.10190e65	0.00303701
$81$	−7.02499e67	−1.24574
$82$	2.02595e67	0.232400
$83$	−1.67738e68	−1.25129	−0.625646	−	0.780107i	$-0.715165\pi$
$83$	−1.67738e68	−1.25129	−0.625646	+	0.780107i	$0.715165\pi$
$84$	−7.79315e67	−0.380013
$85$	3.68896e66	0.0118177
$86$	−2.09581e68	−0.443257
$87$	−5.67032e68	−0.795562
$88$	−6.28452e68	−0.587675
$89$	−7.15572e68	−0.448031	−0.224016	−	0.974586i	$-0.571917\pi$
$89$	−7.15572e68	−0.448031	−0.224016	+	0.974586i	$0.571917\pi$
$90$	−1.15307e67	−0.00485566
$91$	1.48844e69	0.423411
$92$	−3.58455e69	−0.691778
$93$	3.18930e69	0.419326
$94$	1.22526e70	1.10202
$95$	−1.69551e67	−0.00104740
$96$	5.19216e69	0.221167
$97$	−2.08258e70	−0.614053	−0.307027	−	0.951701i	$-0.599334\pi$
$97$	−2.08258e70	−0.614053	−0.307027	+	0.951701i	$0.599334\pi$
$98$	2.17779e70	0.446160
$99$	6.57640e70	0.939591
$100$	−4.99926e70	−0.499926
$101$	1.72267e71	1.21002	0.605012	−	0.796216i	$-0.293168\pi$
$101$	1.72267e71	1.21002	0.605012	+	0.796216i	$0.293168\pi$
$102$	1.73825e71	0.860607
$103$	3.46755e71	1.21423	0.607115	−	0.794614i	$-0.292327\pi$
$103$	3.46755e71	1.21423	0.607115	+	0.794614i	$0.292327\pi$
$104$	−9.91670e70	−0.246424
$105$	−5.21861e69	−0.00923283
$106$	−1.06356e72	−1.34401
$107$	−2.12004e72	−1.91964	−0.959820	−	0.280615i	$-0.909462\pi$
$107$	−2.12004e72	−1.91964	−0.959820	+	0.280615i	$0.909462\pi$
$108$	4.17857e71	0.271947
$109$	−1.81480e72	−0.851507	−0.425754	−	0.904839i	$-0.639991\pi$
$109$	−1.81480e72	−0.851507	−0.425754	+	0.904839i	$0.639991\pi$
$110$	−4.20838e70	−0.0142782
$111$	4.66676e71	0.114828
$112$	8.48620e71	0.151871
$113$	−2.85789e72	−0.373045	−0.186522	−	0.982451i	$-0.559722\pi$
$113$	−2.85789e72	−0.373045	−0.186522	+	0.982451i	$0.559722\pi$
$114$	−7.98927e71	−0.0762755
$115$	−2.40036e71	−0.0168075
$116$	6.17459e72	0.317943
$117$	1.03773e73	0.393990
$118$	−4.69055e73	−1.31647
$119$	2.84103e73	0.590961
$120$	3.47689e71	0.00537349
$121$	1.53147e74	1.76290
$122$	4.12184e73	0.354256
$123$	6.39261e73	0.411194
$124$	−3.47293e73	−0.167582
$125$	−6.69592e72	−0.0242943
$126$	−8.88033e73	−0.242815
$127$	4.30888e74	0.889882	0.444941	−	0.895560i	$-0.353225\pi$
$127$	4.30888e74	0.889882	0.444941	+	0.895560i	$0.353225\pi$
$128$	−5.65391e73	−0.0883883
$129$	−6.61303e74	−0.784270
$130$	−6.64063e72	−0.00598715
$131$	1.32037e74	0.0906914	0.0453457	−	0.998971i	$-0.485561\pi$
$131$	1.32037e74	0.0906914	0.0453457	+	0.998971i	$0.485561\pi$
$132$	−1.98300e75	−1.03979
$133$	−1.30579e74	−0.0523768
$134$	−4.11634e75	−1.26558
$135$	2.79814e73	0.00660725
$136$	−1.89283e75	−0.343938
$137$	5.58406e75	0.782293	0.391147	−	0.920328i	$-0.372078\pi$
$137$	5.58406e75	0.782293	0.391147	+	0.920328i	$0.372078\pi$
$138$	−1.13106e76	−1.22399
$139$	−7.17584e74	−0.0600962	−0.0300481	−	0.999548i	$-0.509566\pi$
$139$	−7.17584e74	−0.0600962	−0.0300481	+	0.999548i	$0.509566\pi$
$140$	5.68271e73	0.00368986
$141$	3.86613e76	1.94984
$142$	1.10763e76	0.434670
$143$	3.78739e76	1.15854
$144$	5.91650e75	0.141318
$145$	4.13476e74	0.00772478
$146$	−7.95137e76	−1.16390
$147$	6.87172e76	0.789406
$148$	−5.08178e75	−0.0458907
$149$	−9.08606e76	−0.646045	−0.323023	−	0.946391i	$-0.604699\pi$
$149$	−9.08606e76	−0.646045	−0.323023	+	0.946391i	$0.604699\pi$
$150$	−1.57745e77	−0.884536
$151$	2.84202e77	1.25877	0.629383	−	0.777095i	$-0.283308\pi$
$151$	2.84202e77	1.25877	0.629383	+	0.777095i	$0.283308\pi$
$152$	8.69976e75	0.0304832
$153$	1.98074e77	0.549897
$154$	−3.24106e77	−0.714004
$155$	−2.32562e75	−0.00407158
$156$	−3.12908e77	−0.436007
$157$	−3.41124e77	−0.378856	−0.189428	−	0.981895i	$-0.560663\pi$
$157$	−3.41124e77	−0.378856	−0.189428	+	0.981895i	$0.560663\pi$
$158$	3.14203e77	0.278537
$159$	−3.35592e78	−2.37801
$160$	−3.78609e75	−0.00214749
$161$	−1.84863e78	−0.840486
$162$	2.41377e78	0.880871
$163$	6.27266e78	1.83989	0.919944	−	0.392049i	$-0.128234\pi$
$163$	6.27266e78	1.83989	0.919944	+	0.392049i	$0.128234\pi$
$164$	−6.96111e77	−0.164332
$165$	−1.32790e77	−0.0252629
$166$	5.76343e78	0.884797
$167$	6.74880e78	0.837128	0.418564	−	0.908187i	$-0.362534\pi$
$167$	6.74880e78	0.837128	0.418564	+	0.908187i	$0.362534\pi$
$168$	2.67770e78	0.268710
$169$	−6.32573e78	−0.514201
$170$	−1.26752e77	−0.00835636
$171$	−9.10381e77	−0.0487373
$172$	7.20113e78	0.313430
$173$	9.26145e75	0.000328127 0	0.000164064	−	1.00000i	$-0.499948\pi$
$173$	9.26145e75	0.000328127 0	0.000164064		1.00000i	$0.499948\pi$
$174$	1.94831e79	0.562547
$175$	−2.57822e79	−0.607392
$176$	2.15935e79	0.415549
$177$	−1.48004e80	−2.32928
$178$	2.45869e79	0.316806
$179$	1.97933e78	0.0209043	0.0104522	−	0.999945i	$-0.496673\pi$
$179$	1.97933e78	0.0209043	0.0104522	+	0.999945i	$0.496673\pi$
$180$	3.96193e77	0.00343347
$181$	−1.77140e80	−1.26103	−0.630517	−	0.776175i	$-0.717157\pi$
$181$	−1.77140e80	−1.26103	−0.630517	+	0.776175i	$0.717157\pi$
$182$	−5.11424e79	−0.299397
$183$	1.30059e80	0.626797
$184$	1.23164e80	0.489161
$185$	−3.40297e77	−0.00111497
$186$	−1.09584e80	−0.296508
$187$	7.22911e80	1.61699
$188$	−4.20995e80	−0.779244
$189$	2.15497e80	0.330406
$190$	5.82572e77	0.000740622 0
$191$	9.43324e80	0.995351	0.497676	−	0.867363i	$-0.334187\pi$
$191$	9.43324e80	0.995351	0.497676	+	0.867363i	$0.334187\pi$
$192$	−1.78401e80	−0.156388
$193$	−1.13467e81	−0.827155	−0.413577	−	0.910469i	$-0.635721\pi$
$193$	−1.13467e81	−0.827155	−0.413577	+	0.910469i	$0.635721\pi$
$194$	7.15570e80	0.434201
$195$	−2.09536e79	−0.0105933
$196$	−7.48283e80	−0.315483
$197$	4.09862e81	1.44240	0.721202	−	0.692725i	$-0.243590\pi$
$197$	4.09862e81	1.44240	0.721202	+	0.692725i	$0.243590\pi$
$198$	−2.25963e81	−0.664391
$199$	5.84283e81	1.43661	0.718305	−	0.695728i	$-0.244918\pi$
$199$	5.84283e81	1.43661	0.718305	+	0.695728i	$0.244918\pi$
$200$	1.71773e81	0.353501
$201$	−1.29886e82	−2.23924
$202$	−5.91906e81	−0.855616
$203$	3.18436e81	0.386290
$204$	−5.97257e81	−0.608541
$205$	−4.66145e79	−0.00399263
$206$	−1.19144e82	−0.858590
$207$	−1.28884e82	−0.782084
$208$	3.40735e81	0.174248
$209$	−3.32262e81	−0.143314
$210$	1.79310e80	0.00652860
$211$	2.85737e82	0.878900	0.439450	−	0.898267i	$-0.355173\pi$
$211$	2.85737e82	0.878900	0.439450	+	0.898267i	$0.355173\pi$
$212$	3.65437e82	0.950362
$213$	3.49499e82	0.769077
$214$	7.28440e82	1.35739
$215$	4.82218e80	0.00761514
$216$	−1.43574e82	−0.192295
$217$	−1.79106e82	−0.203606
$218$	6.23561e82	0.602106
$219$	−2.50895e83	−2.05933
$220$	1.44599e81	0.0100962
$221$	1.14072e83	0.678038
$222$	−1.60349e82	−0.0811960
$223$	1.60386e83	0.692379	0.346189	−	0.938165i	$-0.387475\pi$
$223$	1.60386e83	0.692379	0.346189	+	0.938165i	$0.387475\pi$
$224$	−2.91584e82	−0.107389
$225$	−1.79751e83	−0.565187
$226$	9.81964e82	0.263783
$227$	−5.39066e83	−1.23801	−0.619005	−	0.785387i	$-0.712464\pi$
$227$	−5.39066e83	−1.23801	−0.619005	+	0.785387i	$0.712464\pi$
$228$	2.74509e82	0.0539349
$229$	7.71941e82	0.129845	0.0649224	−	0.997890i	$-0.479320\pi$
$229$	7.71941e82	0.129845	0.0649224	+	0.997890i	$0.479320\pi$
$230$	8.24759e81	0.0118847
$231$	−1.02267e84	−1.26331
$232$	−2.12157e83	−0.224820
$233$	6.55236e83	0.596023	0.298011	−	0.954562i	$-0.403677\pi$
$233$	6.55236e83	0.596023	0.298011	+	0.954562i	$0.403677\pi$
$234$	−3.56560e83	−0.278593
$235$	−2.81916e82	−0.0189326
$236$	1.61166e84	0.930887
$237$	9.91423e83	0.492825
$238$	−9.76171e83	−0.417873
$239$	1.90214e84	0.701645	0.350822	−	0.936442i	$-0.385902\pi$
$239$	1.90214e84	0.701645	0.350822	+	0.936442i	$0.385902\pi$
$240$	−1.19465e82	−0.00379963
$241$	3.92217e84	1.07627	0.538136	−	0.842858i	$-0.319129\pi$
$241$	3.92217e84	1.07627	0.538136	+	0.842858i	$0.319129\pi$
$242$	−5.26208e84	−1.24656
$243$	4.95842e84	1.01466
$244$	−1.41625e84	−0.250497
$245$	−5.01082e82	−0.00766500
$246$	−2.19648e84	−0.290758
$247$	−5.24295e83	−0.0600943
$248$	1.19329e84	0.118498
$249$	1.81857e85	1.56550
$250$	2.30070e83	0.0171787
$251$	−1.05793e85	−0.685549	−0.342775	−	0.939418i	$-0.611367\pi$
$251$	−1.05793e85	−0.685549	−0.342775	+	0.939418i	$0.611367\pi$
$252$	3.05126e84	0.171696
$253$	−4.70390e85	−2.29974
$254$	−1.48052e85	−0.629242
$255$	−3.99948e83	−0.0147852
$256$	1.94267e84	0.0625000
$257$	−4.16992e85	−1.16816	−0.584079	−	0.811697i	$-0.698544\pi$
$257$	−4.16992e85	−1.16816	−0.584079	+	0.811697i	$0.698544\pi$
$258$	2.27222e85	0.554563
$259$	−2.62078e84	−0.0557556
$260$	2.28170e83	0.00423356
$261$	2.22011e85	0.359448
$262$	−4.53677e84	−0.0641285
$263$	1.30793e86	1.61493	0.807466	−	0.589914i	$-0.200838\pi$
$263$	1.30793e86	1.61493	0.807466	+	0.589914i	$0.200838\pi$
$264$	6.81352e85	0.735245
$265$	2.44712e84	0.0230901
$266$	4.48664e84	0.0370360
$267$	7.75806e85	0.560535
$268$	1.41436e86	0.894904
$269$	−2.23293e86	−1.23785	−0.618927	−	0.785449i	$-0.712432\pi$
$269$	−2.23293e86	−1.23785	−0.618927	+	0.785449i	$0.712432\pi$
$270$	−9.61434e83	−0.00467203
$271$	3.14182e85	0.133897	0.0669486	−	0.997756i	$-0.478674\pi$
$271$	3.14182e85	0.133897	0.0669486	+	0.997756i	$0.478674\pi$
$272$	6.50371e85	0.243201
$273$	−1.61373e86	−0.529732
$274$	−1.91867e86	−0.553165
$275$	−6.56038e86	−1.66195
$276$	3.88628e86	0.865489
$277$	4.63652e86	0.908156	0.454078	−	0.890962i	$-0.349969\pi$
$277$	4.63652e86	0.908156	0.454078	+	0.890962i	$0.349969\pi$
$278$	2.46560e85	0.0424944
$279$	−1.24871e86	−0.189458
$280$	−1.95256e84	−0.00260913
$281$	1.44083e86	0.169644	0.0848219	−	0.996396i	$-0.472968\pi$
$281$	1.44083e86	0.169644	0.0848219	+	0.996396i	$0.472968\pi$
$282$	−1.32839e87	−1.37874
$283$	7.45940e86	0.682788	0.341394	−	0.939920i	$-0.389101\pi$
$283$	7.45940e86	0.682788	0.341394	+	0.939920i	$0.389101\pi$
$284$	−3.80580e86	−0.307358
$285$	1.83823e84	0.00131041
$286$	−1.30134e87	−0.819211
$287$	−3.58999e86	−0.199657
$288$	−2.03289e86	−0.0999266
$289$	−1.23442e86	−0.0536524
$290$	−1.42069e85	−0.00546225
$291$	2.25788e87	0.768246
$292$	2.73207e87	0.823002
$293$	5.25334e87	1.40163	0.700817	−	0.713341i	$-0.252819\pi$
$293$	5.25334e87	1.40163	0.700817	+	0.713341i	$0.252819\pi$
$294$	−2.36111e87	−0.558194
$295$	1.07923e86	0.0226169
$296$	1.74609e86	0.0324496
$297$	5.48340e87	0.904058
$298$	3.12195e87	0.456823
$299$	−7.42254e87	−0.964329
$300$	5.42007e87	0.625462
$301$	3.71377e87	0.380807
$302$	−9.76509e87	−0.890082
$303$	−1.86768e88	−1.51387
$304$	−2.98922e86	−0.0215549
$305$	−9.48382e85	−0.00608610
$306$	−6.80577e87	−0.388836
$307$	1.66055e88	0.844967	0.422484	−	0.906371i	$-0.361158\pi$
$307$	1.66055e88	0.844967	0.422484	+	0.906371i	$0.361158\pi$
$308$	1.11362e88	0.504877
$309$	−3.75943e88	−1.51913
$310$	7.99077e85	0.00287904
$311$	−1.71648e88	−0.551627	−0.275814	−	0.961211i	$-0.588947\pi$
$311$	−1.71648e88	−0.551627	−0.275814	+	0.961211i	$0.588947\pi$
$312$	1.07514e88	0.308303
$313$	−2.06197e88	−0.527787	−0.263893	−	0.964552i	$-0.585007\pi$
$313$	−2.06197e88	−0.527787	−0.263893	+	0.964552i	$0.585007\pi$
$314$	1.17209e88	0.267892
$315$	2.04325e86	0.00417154
$316$	−1.07959e88	−0.196956
$317$	−8.92142e88	−1.45489	−0.727445	−	0.686166i	$-0.759293\pi$
$317$	−8.92142e88	−1.45489	−0.727445	+	0.686166i	$0.759293\pi$
$318$	1.15309e89	1.68151
$319$	8.10273e88	1.05697
$320$	1.30089e86	0.00151851
$321$	2.29849e89	2.40168
$322$	6.35183e88	0.594313
$323$	−1.00074e88	−0.0838746
$324$	−8.29364e88	−0.622870
$325$	−1.03520e89	−0.696890
$326$	−2.15527e89	−1.30100
$327$	1.96756e89	1.06533
$328$	2.39182e88	0.116200
$329$	−2.17116e89	−0.946753
$330$	4.56261e87	0.0178636
$331$	4.48290e88	0.157639	0.0788197	−	0.996889i	$-0.474885\pi$
$331$	4.48290e88	0.157639	0.0788197	+	0.996889i	$0.474885\pi$
$332$	−1.98030e89	−0.625646
$333$	−1.82718e88	−0.0518813
$334$	−2.31887e89	−0.591939
$335$	9.47117e87	0.0217427
$336$	−9.20052e88	−0.190006
$337$	2.65936e89	0.494215	0.247108	−	0.968988i	$-0.420520\pi$
$337$	2.65936e89	0.494215	0.247108	+	0.968988i	$0.420520\pi$
$338$	2.17350e89	0.363595
$339$	3.09845e89	0.466719
$340$	4.35516e87	0.00590884
$341$	−4.55742e89	−0.557108
$342$	3.12805e88	0.0344625
$343$	−9.97515e89	−0.990782
$344$	−2.47429e89	−0.221629
$345$	2.60241e88	0.0210280
$346$	−3.18221e86	−0.000232021 0
$347$	−6.17481e89	−0.406375	−0.203188	−	0.979140i	$-0.565130\pi$
$347$	−6.17481e89	−0.406375	−0.203188	+	0.979140i	$0.565130\pi$
$348$	−6.69433e89	−0.397781
$349$	3.59395e90	1.92872	0.964360	−	0.264595i	$-0.0852384\pi$
$349$	3.59395e90	1.92872	0.964360	+	0.264595i	$0.0852384\pi$
$350$	8.85870e89	0.429491
$351$	8.65257e89	0.379090
$352$	−7.41945e89	−0.293838
$353$	1.40761e90	0.504057	0.252028	−	0.967720i	$-0.418902\pi$
$353$	1.40761e90	0.504057	0.252028	+	0.967720i	$0.418902\pi$
$354$	5.08537e90	1.64705
$355$	−2.54852e88	−0.00746761
$356$	−8.44799e89	−0.224016
$357$	−3.08017e90	−0.739356
$358$	−6.80093e88	−0.0147816
$359$	4.19832e89	0.0826462	0.0413231	−	0.999146i	$-0.486843\pi$
$359$	4.19832e89	0.0826462	0.0413231	+	0.999146i	$0.486843\pi$
$360$	−1.36131e88	−0.00242783
$361$	−6.14137e90	−0.992566
$362$	6.08648e90	0.891686
$363$	−1.66038e91	−2.20557
$364$	1.75724e90	0.211705
$365$	1.82951e89	0.0199957
$366$	−4.46879e90	−0.443212
$367$	−8.13209e90	−0.732077	−0.366038	−	0.930600i	$-0.619286\pi$
$367$	−8.13209e90	−0.732077	−0.366038	+	0.930600i	$0.619286\pi$
$368$	−4.23189e90	−0.345889
$369$	−2.50290e90	−0.185784
$370$	1.16925e88	0.000788400 0
$371$	1.88463e91	1.15466
$372$	3.76527e90	0.209663
$373$	2.39425e91	1.21201	0.606006	−	0.795460i	$-0.292771\pi$
$373$	2.39425e91	1.21201	0.606006	+	0.795460i	$0.292771\pi$
$374$	−2.48390e91	−1.14339
$375$	7.25955e89	0.0303948
$376$	1.44653e91	0.551009
$377$	1.27857e91	0.443208
$378$	−7.40442e90	−0.233632
$379$	3.67253e91	1.05505	0.527526	−	0.849539i	$-0.323120\pi$
$379$	3.67253e91	1.05505	0.527526	+	0.849539i	$0.323120\pi$
$380$	−2.00170e88	−0.000523699 0
$381$	−4.67158e91	−1.11334
$382$	−3.24124e91	−0.703820
$383$	9.66684e91	1.91306	0.956529	−	0.291639i	$-0.0942005\pi$
$383$	9.66684e91	1.91306	0.956529	+	0.291639i	$0.0942005\pi$
$384$	6.12983e90	0.110583
$385$	7.45725e89	0.0122666
$386$	3.89871e91	0.584887
$387$	2.58921e91	0.354346
$388$	−2.45868e91	−0.307027
$389$	−6.23321e91	−0.710397	−0.355199	−	0.934791i	$-0.615587\pi$
$389$	−6.23321e91	−0.710397	−0.355199	+	0.934791i	$0.615587\pi$
$390$	7.19960e89	0.00749057
$391$	−1.41676e92	−1.34593
$392$	2.57108e91	0.223080
$393$	−1.43152e91	−0.113465
$394$	−1.40828e92	−1.01993
$395$	−7.22939e89	−0.00478525
$396$	7.76404e91	0.469795
$397$	4.26060e91	0.235726	0.117863	−	0.993030i	$-0.462396\pi$
$397$	4.26060e91	0.235726	0.117863	+	0.993030i	$0.462396\pi$
$398$	−2.00758e92	−1.01584
$399$	1.41570e91	0.0655290
$400$	−5.90209e91	−0.249963
$401$	−5.66288e91	−0.219489	−0.109744	−	0.993960i	$-0.535003\pi$
$401$	−5.66288e91	−0.219489	−0.109744	+	0.993960i	$0.535003\pi$
$402$	4.46283e92	1.58338
$403$	−7.19141e91	−0.233607
$404$	2.03377e92	0.605012
$405$	−5.55376e90	−0.0151333
$406$	−1.09414e92	−0.273148
$407$	−6.66866e91	−0.152559
$408$	2.05216e92	0.430304
$409$	−2.72890e92	−0.524577	−0.262289	−	0.964989i	$-0.584477\pi$
$409$	−2.72890e92	−0.524577	−0.262289	+	0.964989i	$0.584477\pi$
$410$	1.60166e90	0.00282321
$411$	−6.05409e92	−0.978733
$412$	4.09376e92	0.607115
$413$	8.31165e92	1.13099
$414$	4.42843e92	0.553017
$415$	−1.32609e91	−0.0152008
$416$	−1.17076e92	−0.123212
$417$	7.77986e91	0.0751868
$418$	1.14164e92	0.101338
$419$	1.10409e93	0.900342	0.450171	−	0.892942i	$-0.351363\pi$
$419$	1.10409e93	0.900342	0.450171	+	0.892942i	$0.351363\pi$
$420$	−6.16105e90	−0.00461642
$421$	2.05977e93	1.41842	0.709210	−	0.704997i	$-0.249052\pi$
$421$	2.05977e93	1.41842	0.709210	+	0.704997i	$0.249052\pi$
$422$	−9.81785e92	−0.621476
$423$	−1.51371e93	−0.880967
$424$	−1.25563e93	−0.672007
$425$	−1.97591e93	−0.972660
$426$	−1.20087e93	−0.543819
$427$	−7.30391e92	−0.304345
$428$	−2.50290e93	−0.959820
$429$	−4.10619e93	−1.44946
$430$	−1.65689e91	−0.00538472
$431$	1.23738e93	0.370306	0.185153	−	0.982710i	$-0.440722\pi$
$431$	1.23738e93	0.370306	0.185153	+	0.982710i	$0.440722\pi$
$432$	4.93318e92	0.135973
$433$	5.91980e93	1.50310	0.751549	−	0.659678i	$-0.229307\pi$
$433$	5.91980e93	1.50310	0.751549	+	0.659678i	$0.229307\pi$
$434$	6.15404e92	0.143971
$435$	−4.48280e91	−0.00966453
$436$	−2.14254e93	−0.425754
$437$	6.51168e92	0.119289
$438$	8.62068e93	1.45616
$439$	7.71156e93	1.20130	0.600651	−	0.799512i	$-0.294908\pi$
$439$	7.71156e93	1.20130	0.600651	+	0.799512i	$0.294908\pi$
$440$	−4.96837e91	−0.00713911
$441$	−2.69049e93	−0.356666
$442$	−3.91949e93	−0.479445
$443$	3.75945e93	0.424416	0.212208	−	0.977225i	$-0.431935\pi$
$443$	3.75945e93	0.424416	0.212208	+	0.977225i	$0.431935\pi$
$444$	5.50954e92	0.0574142
$445$	−5.65712e91	−0.00544271
$446$	−5.51082e93	−0.489586
$447$	9.85087e93	0.808272
$448$	1.00187e93	0.0759353
$449$	−5.19594e93	−0.363848	−0.181924	−	0.983313i	$-0.558232\pi$
$449$	−5.19594e93	−0.363848	−0.181924	+	0.983313i	$0.558232\pi$
$450$	6.17620e93	0.399648
$451$	−9.13485e93	−0.546304
$452$	−3.37400e93	−0.186522
$453$	−3.08124e94	−1.57485
$454$	1.85222e94	0.875405
$455$	1.17672e92	0.00514362
$456$	−9.43206e92	−0.0381377
$457$	7.28756e93	0.272619	0.136310	−	0.990666i	$-0.456476\pi$
$457$	7.28756e93	0.272619	0.136310	+	0.990666i	$0.456476\pi$
$458$	−2.65237e93	−0.0918141
$459$	1.65154e94	0.529102
$460$	−2.83385e92	−0.00840376
$461$	−6.60287e94	−1.81280	−0.906400	−	0.422420i	$-0.861181\pi$
$461$	−6.60287e94	−1.81280	−0.906400	+	0.422420i	$0.861181\pi$
$462$	3.51387e94	0.893296
$463$	−6.02451e94	−1.41839	−0.709196	−	0.705011i	$-0.750942\pi$
$463$	−6.02451e94	−1.41839	−0.709196	+	0.705011i	$0.750942\pi$
$464$	7.28967e93	0.158972
$465$	2.52138e92	0.00509399
$466$	−2.25137e94	−0.421452
$467$	1.01422e94	0.175947	0.0879735	−	0.996123i	$-0.471961\pi$
$467$	1.01422e94	0.175947	0.0879735	+	0.996123i	$0.471961\pi$
$468$	1.22513e94	0.196995
$469$	7.29417e94	1.08728
$470$	9.68655e92	0.0133874
$471$	3.69837e94	0.473989
$472$	−5.53762e94	−0.658237
$473$	9.44983e94	1.04197
$474$	−3.40650e94	−0.348480
$475$	9.08164e93	0.0862067
$476$	3.35410e94	0.295480
$477$	1.31395e95	1.07442
$478$	−6.53571e94	−0.496138
$479$	−1.17917e94	−0.0831125	−0.0415562	−	0.999136i	$-0.513232\pi$
$479$	−1.17917e94	−0.0831125	−0.0415562	+	0.999136i	$0.513232\pi$
$480$	4.10479e92	0.00268675
$481$	−1.05229e94	−0.0639710
$482$	−1.34765e95	−0.761039
$483$	2.00423e95	1.05154
$484$	1.80804e95	0.881449
$485$	−1.64643e93	−0.00745955
$486$	−1.70370e95	−0.717474
$487$	−3.03660e94	−0.118880	−0.0594401	−	0.998232i	$-0.518932\pi$
$487$	−3.03660e94	−0.118880	−0.0594401	+	0.998232i	$0.518932\pi$
$488$	4.86621e94	0.177128
$489$	−6.80066e95	−2.30190
$490$	1.72170e93	0.00541998
$491$	5.42401e94	0.158828	0.0794141	−	0.996842i	$-0.474695\pi$
$491$	5.42401e94	0.158828	0.0794141	+	0.996842i	$0.474695\pi$
$492$	7.54706e94	0.205597
$493$	2.44045e95	0.618593
$494$	1.80146e94	0.0424931
$495$	5.19912e93	0.0114142
$496$	−4.10012e94	−0.0837909
$497$	−1.96273e95	−0.373429
$498$	−6.24856e95	−1.10698
$499$	−6.08843e95	−1.00447	−0.502234	−	0.864732i	$-0.667488\pi$
$499$	−6.08843e95	−1.00447	−0.502234	+	0.864732i	$0.667488\pi$
$500$	−7.90515e93	−0.0121472
$501$	−7.31688e95	−1.04734
$502$	3.63501e95	0.484757
$503$	1.31961e96	1.63976	0.819881	−	0.572534i	$-0.194040\pi$
$503$	1.31961e96	1.63976	0.819881	+	0.572534i	$0.194040\pi$
$504$	−1.04840e95	−0.121407
$505$	1.36190e94	0.0146994
$506$	1.61625e96	1.62616
$507$	6.85820e95	0.643320
$508$	5.08703e95	0.444941
$509$	1.05049e95	0.0856864	0.0428432	−	0.999082i	$-0.486358\pi$
$509$	1.05049e95	0.0856864	0.0428432	+	0.999082i	$0.486358\pi$
$510$	1.37421e94	0.0104547
$511$	1.40898e96	0.999918
$512$	−6.67496e94	−0.0441942
$513$	−7.59076e94	−0.0468942
$514$	1.43277e96	0.826012
$515$	2.74135e94	0.0147505
$516$	−7.80729e95	−0.392135
$517$	−5.52459e96	−2.59051
$518$	9.00492e94	0.0394251
$519$	−1.00410e93	−0.000410522 0
$520$	−7.83987e93	−0.00299358
$521$	−4.81101e96	−1.71592	−0.857960	−	0.513716i	$-0.828268\pi$
$521$	−4.81101e96	−1.71592	−0.857960	+	0.513716i	$0.828268\pi$
$522$	−7.62823e95	−0.254168
$523$	4.50131e96	1.40129	0.700647	−	0.713508i	$-0.252895\pi$
$523$	4.50131e96	1.40129	0.700647	+	0.713508i	$0.252895\pi$
$524$	1.55882e95	0.0453457
$525$	2.79524e96	0.759913
$526$	−4.49400e96	−1.14193
$527$	−1.37265e96	−0.326048
$528$	−2.34111e96	−0.519897
$529$	4.40282e96	0.914228
$530$	−8.40822e94	−0.0163272
$531$	5.79480e96	1.05241
$532$	−1.54160e95	−0.0261884
$533$	−1.44144e96	−0.229076
$534$	−2.66565e96	−0.396358
$535$	−1.67605e95	−0.0233199
$536$	−4.85972e96	−0.632792
$537$	−2.14594e95	−0.0261535
$538$	7.67229e96	0.875295
$539$	−9.81950e96	−1.04879
$540$	3.30346e94	0.00330362
$541$	−2.42313e96	−0.226920	−0.113460	−	0.993543i	$-0.536193\pi$
$541$	−2.42313e96	−0.226920	−0.113460	+	0.993543i	$0.536193\pi$
$542$	−1.07952e96	−0.0946796
$543$	1.92051e97	1.57769
$544$	−2.23466e96	−0.171969
$545$	−1.43473e95	−0.0103442
$546$	5.54473e96	0.374577
$547$	1.73234e97	1.09669	0.548343	−	0.836254i	$-0.315259\pi$
$547$	1.73234e97	1.09669	0.548343	+	0.836254i	$0.315259\pi$
$548$	6.59249e96	0.391147
$549$	−5.09221e96	−0.283197
$550$	2.25413e97	1.17518
$551$	−1.12167e96	−0.0548257
$552$	−1.33532e97	−0.611993
$553$	−5.56767e96	−0.239294
$554$	−1.59310e97	−0.642163
$555$	3.68941e94	0.00139494
$556$	−8.47173e95	−0.0300481
$557$	−3.67457e97	−1.22278	−0.611388	−	0.791331i	$-0.709389\pi$
$557$	−3.67457e97	−1.22278	−0.611388	+	0.791331i	$0.709389\pi$
$558$	4.29054e96	0.133967
$559$	1.49114e97	0.436918
$560$	6.70896e94	0.00184493
$561$	−7.83762e97	−2.02303
$562$	−4.95065e96	−0.119956
$563$	1.74764e97	0.397561	0.198781	−	0.980044i	$-0.436302\pi$
$563$	1.74764e97	0.397561	0.198781	+	0.980044i	$0.436302\pi$
$564$	4.56432e97	0.974918
$565$	−2.25937e95	−0.00453177
$566$	−2.56303e97	−0.482804
$567$	−4.27720e97	−0.756765
$568$	1.30766e97	0.217335
$569$	−4.83411e97	−0.754799	−0.377400	−	0.926050i	$-0.623182\pi$
$569$	−4.83411e97	−0.754799	−0.377400	+	0.926050i	$0.623182\pi$
$570$	−6.31610e94	−0.000926598 0
$571$	8.57504e97	1.18210	0.591050	−	0.806635i	$-0.298713\pi$
$571$	8.57504e97	1.18210	0.591050	+	0.806635i	$0.298713\pi$
$572$	4.47136e97	0.579270
$573$	−1.02273e98	−1.24529
$574$	1.23351e97	0.141179
$575$	1.28570e98	1.38335
$576$	6.98497e96	0.0706588
$577$	−3.71702e96	−0.0353552	−0.0176776	−	0.999844i	$-0.505627\pi$
$577$	−3.71702e96	−0.0353552	−0.0176776	+	0.999844i	$0.505627\pi$
$578$	4.24143e96	0.0379380
$579$	1.23019e98	1.03486
$580$	4.88146e95	0.00386239
$581$	−1.02128e98	−0.760138
$582$	−7.75803e97	−0.543232
$583$	4.79551e98	3.15938
$584$	−9.38732e97	−0.581950
$585$	8.20398e95	0.00478621
$586$	−1.80503e98	−0.991106
$587$	1.38877e97	0.0717755	0.0358878	−	0.999356i	$-0.488574\pi$
$587$	1.38877e97	0.0717755	0.0358878	+	0.999356i	$0.488574\pi$
$588$	8.11270e97	0.394703
$589$	6.30892e96	0.0288976
$590$	−3.70822e96	−0.0159926
$591$	−4.44362e98	−1.80460
$592$	−5.99951e96	−0.0229454
$593$	3.18365e98	1.14679	0.573395	−	0.819279i	$-0.305626\pi$
$593$	3.18365e98	1.14679	0.573395	+	0.819279i	$0.305626\pi$
$594$	−1.88408e98	−0.639266
$595$	2.24604e96	0.00717903
$596$	−1.07269e98	−0.323023
$597$	−6.33465e98	−1.79735
$598$	2.55037e98	0.681884
$599$	−2.02276e98	−0.509675	−0.254837	−	0.966984i	$-0.582022\pi$
$599$	−2.02276e98	−0.509675	−0.254837	+	0.966984i	$0.582022\pi$
$600$	−1.86232e98	−0.442268
$601$	−4.68245e98	−1.04816	−0.524082	−	0.851668i	$-0.675592\pi$
$601$	−4.68245e98	−1.04816	−0.524082	+	0.851668i	$0.675592\pi$
$602$	−1.27604e98	−0.269271
$603$	5.08542e98	1.01173
$604$	3.35526e98	0.629383
$605$	1.21074e97	0.0214158
$606$	6.41729e98	1.07047
$607$	8.96839e98	1.41096	0.705482	−	0.708728i	$-0.250731\pi$
$607$	8.96839e98	1.41096	0.705482	+	0.708728i	$0.250731\pi$
$608$	1.02709e97	0.0152416
$609$	−3.45240e98	−0.483290
$610$	3.25862e96	0.00430352
$611$	−8.71756e98	−1.08625
$612$	2.33844e98	0.274949
$613$	1.48120e99	1.64349	0.821743	−	0.569858i	$-0.193002\pi$
$613$	1.48120e99	1.64349	0.821743	+	0.569858i	$0.193002\pi$
$614$	−5.70561e98	−0.597482
$615$	5.05382e96	0.00499521
$616$	−3.82636e98	−0.357002
$617$	−6.76299e98	−0.595683	−0.297842	−	0.954615i	$-0.596267\pi$
$617$	−6.76299e98	−0.595683	−0.297842	+	0.954615i	$0.596267\pi$
$618$	1.29173e99	1.07419
$619$	−1.66102e98	−0.130424	−0.0652120	−	0.997871i	$-0.520772\pi$
$619$	−1.66102e98	−0.130424	−0.0652120	+	0.997871i	$0.520772\pi$
$620$	−2.74561e96	−0.00203579
$621$	−1.07464e99	−0.752507
$622$	5.89779e98	0.390060
$623$	−4.35680e98	−0.272171
$624$	−3.69416e98	−0.218003
$625$	1.79287e99	0.999557
$626$	7.08487e98	0.373201
$627$	3.60230e98	0.179301
$628$	−4.02728e98	−0.189428
$629$	−2.00853e98	−0.0892853
$630$	−7.02055e96	−0.00294973
$631$	4.09616e98	0.162680	0.0813401	−	0.996686i	$-0.474080\pi$
$631$	4.09616e98	0.162680	0.0813401	+	0.996686i	$0.474080\pi$
$632$	3.70945e98	0.139269
$633$	−3.09789e99	−1.09960
$634$	3.06538e99	1.02876
$635$	3.40649e97	0.0108103
$636$	−3.96197e99	−1.18901
$637$	−1.54947e99	−0.439779
$638$	−2.78408e99	−0.747389
$639$	−1.36840e99	−0.347481
$640$	−4.46983e96	−0.00107375
$641$	−4.83494e99	−1.09883	−0.549416	−	0.835549i	$-0.685150\pi$
$641$	−4.83494e99	−1.09883	−0.549416	+	0.835549i	$0.685150\pi$
$642$	−7.89756e99	−1.69824
$643$	8.28095e99	1.68496	0.842482	−	0.538725i	$-0.181094\pi$
$643$	8.28095e99	1.68496	0.842482	+	0.538725i	$0.181094\pi$
$644$	−2.18247e99	−0.420243
$645$	−5.22808e97	−0.00952736
$646$	3.43851e98	0.0593083
$647$	2.80499e99	0.457961	0.228981	−	0.973431i	$-0.426461\pi$
$647$	2.80499e99	0.457961	0.228981	+	0.973431i	$0.426461\pi$
$648$	2.84967e99	0.440436
$649$	2.11493e100	3.09464
$650$	3.55692e99	0.492776
$651$	1.94182e99	0.254733
$652$	7.40545e99	0.919944
$653$	−1.01434e100	−1.19335	−0.596674	−	0.802484i	$-0.703512\pi$
$653$	−1.01434e100	−1.19335	−0.596674	+	0.802484i	$0.703512\pi$
$654$	−6.76049e99	−0.753300
$655$	1.04385e97	0.00110172
$656$	−8.21823e98	−0.0821660
$657$	9.82330e99	0.930437
$658$	7.46004e99	0.669456
$659$	−1.62029e100	−1.37772	−0.688858	−	0.724896i	$-0.741888\pi$
$659$	−1.62029e100	−1.37772	−0.688858	+	0.724896i	$0.741888\pi$
$660$	−1.56770e98	−0.0126315
$661$	7.85423e99	0.599725	0.299862	−	0.953983i	$-0.403059\pi$
$661$	7.85423e99	0.599725	0.299862	+	0.953983i	$0.403059\pi$
$662$	−1.54031e99	−0.111468
$663$	−1.23674e100	−0.848298
$664$	6.80425e99	0.442399
$665$	−1.03232e97	−0.000636276 0
$666$	6.27814e98	0.0366856
$667$	−1.58797e100	−0.879785
$668$	7.96758e99	0.418564
$669$	−1.73886e100	−0.866240
$670$	−3.25427e98	−0.0153744
$671$	−1.85851e100	−0.832750
$672$	3.16128e99	0.134355
$673$	2.42910e100	0.979288	0.489644	−	0.871923i	$-0.337127\pi$
$673$	2.42910e100	0.979288	0.489644	+	0.871923i	$0.337127\pi$
$674$	−9.13750e99	−0.349463
$675$	−1.49877e100	−0.543813
$676$	−7.46810e99	−0.257100
$677$	−5.37614e99	−0.175619	−0.0878097	−	0.996137i	$-0.527987\pi$
$677$	−5.37614e99	−0.175619	−0.0878097	+	0.996137i	$0.527987\pi$
$678$	−1.06462e100	−0.330020
$679$	−1.26799e100	−0.373026
$680$	−1.49642e98	−0.00417818
$681$	5.84442e100	1.54888
$682$	1.56592e100	0.393935
$683$	−6.44927e100	−1.54019	−0.770097	−	0.637927i	$-0.779792\pi$
$683$	−6.44927e100	−1.54019	−0.770097	+	0.637927i	$0.779792\pi$
$684$	−1.07479e99	−0.0243686
$685$	4.41460e98	0.00950334
$686$	3.42744e100	0.700589
$687$	−8.36919e99	−0.162450
$688$	8.50160e99	0.156715
$689$	7.56711e100	1.32479
$690$	−8.94182e98	−0.0148691
$691$	5.51090e100	0.870467	0.435233	−	0.900318i	$-0.356666\pi$
$691$	5.51090e100	0.870467	0.435233	+	0.900318i	$0.356666\pi$
$692$	1.09340e97	0.000164064 0
$693$	4.00407e100	0.570784
$694$	2.12165e100	0.287351
$695$	−5.67302e97	−0.000730052 0
$696$	2.30016e100	0.281274
$697$	−2.75132e100	−0.319725
$698$	−1.23487e101	−1.36381
$699$	−7.10390e100	−0.745688
$700$	−3.04383e100	−0.303696
$701$	1.10097e101	1.04420	0.522102	−	0.852883i	$-0.325148\pi$
$701$	1.10097e101	1.04420	0.522102	+	0.852883i	$0.325148\pi$
$702$	−2.97300e100	−0.268057
$703$	9.23154e98	0.00791334
$704$	2.54931e100	0.207775
$705$	3.05646e99	0.0236867
$706$	−4.83650e100	−0.356422
$707$	1.04886e101	0.735068
$708$	−1.74732e101	−1.16464
$709$	−6.79427e100	−0.430726	−0.215363	−	0.976534i	$-0.569093\pi$
$709$	−6.79427e100	−0.430726	−0.215363	+	0.976534i	$0.569093\pi$
$710$	8.75665e98	0.00528040
$711$	−3.88173e100	−0.222666
$712$	2.90271e100	0.158403
$713$	8.93165e100	0.463718
$714$	1.05834e101	0.522804
$715$	2.99421e99	0.0140740
$716$	2.33678e99	0.0104522
$717$	−2.06225e101	−0.877833
$718$	−1.44253e100	−0.0584397
$719$	−3.31606e101	−1.27864	−0.639318	−	0.768942i	$-0.720783\pi$
$719$	−3.31606e101	−1.27864	−0.639318	+	0.768942i	$0.720783\pi$
$720$	4.67742e98	0.00171673
$721$	2.11123e101	0.737623
$722$	2.11016e101	0.701850
$723$	−4.25232e101	−1.34653
$724$	−2.09130e101	−0.630517
$725$	−2.21470e101	−0.635792
$726$	5.70502e101	1.55958
$727$	4.93711e101	1.28529	0.642646	−	0.766163i	$-0.277837\pi$
$727$	4.93711e101	1.28529	0.642646	+	0.766163i	$0.277837\pi$
$728$	−6.03783e100	−0.149698
$729$	−1.00408e100	−0.0237105
$730$	−6.28614e99	−0.0141391
$731$	2.84619e101	0.609813
$732$	1.53547e101	0.313398
$733$	−7.45694e101	−1.45001	−0.725003	−	0.688746i	$-0.758162\pi$
$733$	−7.45694e101	−1.45001	−0.725003	+	0.688746i	$0.758162\pi$
$734$	2.79416e101	0.517656
$735$	5.43260e99	0.00958975
$736$	1.45407e101	0.244581
$737$	1.85603e102	2.97501
$738$	8.59991e100	0.131369
$739$	4.87994e101	0.710455	0.355228	−	0.934780i	$-0.384403\pi$
$739$	4.87994e101	0.710455	0.355228	+	0.934780i	$0.384403\pi$
$740$	−4.01752e98	−0.000557483 0
$741$	5.68427e100	0.0751845
$742$	−6.47554e101	−0.816465
$743$	−1.17408e102	−1.41122	−0.705612	−	0.708598i	$-0.749328\pi$
$743$	−1.17408e102	−1.41122	−0.705612	+	0.708598i	$0.749328\pi$
$744$	−1.29374e101	−0.148254
$745$	−7.18319e99	−0.00784819
$746$	−8.22659e101	−0.857021
$747$	−7.12027e101	−0.707318
$748$	8.53463e101	0.808496
$749$	−1.29080e102	−1.16615
$750$	−2.49436e100	−0.0214924
$751$	−2.18587e102	−1.79641	−0.898205	−	0.439576i	$-0.855129\pi$
$751$	−2.18587e102	−1.79641	−0.898205	+	0.439576i	$0.855129\pi$
$752$	−4.97023e101	−0.389622
$753$	1.14698e102	0.857696
$754$	−4.39315e101	−0.313396
$755$	2.24682e100	0.0152916
$756$	2.54414e101	0.165203
$757$	−1.75623e102	−1.08812	−0.544062	−	0.839045i	$-0.683114\pi$
$757$	−1.75623e102	−1.08812	−0.544062	+	0.839045i	$0.683114\pi$
$758$	−1.26187e102	−0.746034
$759$	5.09985e102	2.87723
$760$	6.87780e98	0.000370311 0
$761$	1.37687e102	0.707517	0.353758	−	0.935337i	$-0.384904\pi$
$761$	1.37687e102	0.707517	0.353758	+	0.935337i	$0.384904\pi$
$762$	1.60514e102	0.787249
$763$	−1.10495e102	−0.517275
$764$	1.11368e102	0.497676
$765$	1.56592e100	0.00668018
$766$	−3.32150e102	−1.35274
$767$	3.33727e102	1.29764
$768$	−2.10619e101	−0.0781942
$769$	−1.23531e102	−0.437916	−0.218958	−	0.975734i	$-0.570266\pi$
$769$	−1.23531e102	−0.437916	−0.218958	+	0.975734i	$0.570266\pi$
$770$	−2.56229e100	−0.00867377
$771$	4.52092e102	1.46149
$772$	−1.33959e102	−0.413577
$773$	−2.73478e102	−0.806399	−0.403199	−	0.915112i	$-0.632102\pi$
$773$	−2.73478e102	−0.806399	−0.403199	+	0.915112i	$0.632102\pi$
$774$	−8.89644e101	−0.250560
$775$	1.24567e102	0.335114
$776$	8.44796e101	0.217101
$777$	2.84138e101	0.0697562
$778$	2.14172e102	0.502327
$779$	1.26455e101	0.0283372
$780$	−2.47376e100	−0.00529663
$781$	−4.99424e102	−1.02178
$782$	4.86796e102	0.951716
$783$	1.85113e102	0.345854
$784$	−8.83417e101	−0.157741
$785$	−2.69683e100	−0.00460236
$786$	4.91865e101	0.0802317
$787$	6.29219e101	0.0981068	0.0490534	−	0.998796i	$-0.484380\pi$
$787$	6.29219e101	0.0981068	0.0490534	+	0.998796i	$0.484380\pi$
$788$	4.83880e102	0.721202
$789$	−1.41802e103	−2.02045
$790$	2.48400e100	0.00338369
$791$	−1.74004e102	−0.226618
$792$	−2.66770e102	−0.332195
$793$	−2.93264e102	−0.349189
$794$	−1.46393e102	−0.166683
$795$	−2.65310e101	−0.0288882
$796$	6.89800e102	0.718305
$797$	−8.84208e102	−0.880611	−0.440305	−	0.897848i	$-0.645130\pi$
$797$	−8.84208e102	−0.880611	−0.440305	+	0.897848i	$0.645130\pi$
$798$	−4.86431e101	−0.0463360
$799$	−1.66395e103	−1.51610
$800$	2.02794e102	0.176751
$801$	−3.03752e102	−0.253259
$802$	1.94575e102	0.155202
$803$	3.58521e103	2.73598
$804$	−1.53342e103	−1.11962
$805$	−1.46147e101	−0.0102103
$806$	2.47095e102	0.165185
$807$	2.42089e103	1.54869
$808$	−6.98799e102	−0.427808
$809$	1.65699e103	0.970841	0.485421	−	0.874281i	$-0.338667\pi$
$809$	1.65699e103	0.970841	0.485421	+	0.874281i	$0.338667\pi$
$810$	1.90826e101	0.0107009
$811$	−2.39680e103	−1.28645	−0.643224	−	0.765678i	$-0.722404\pi$
$811$	−2.39680e103	−1.28645	−0.643224	+	0.765678i	$0.722404\pi$
$812$	3.75943e102	0.193145
$813$	−3.40628e102	−0.167520
$814$	2.29134e102	0.107875
$815$	4.95899e101	0.0223511
$816$	−7.05116e102	−0.304271
$817$	−1.30815e102	−0.0540476
$818$	9.37641e102	0.370932
$819$	6.31825e102	0.239342
$820$	−5.50327e100	−0.00199631
$821$	4.26124e102	0.148031	0.0740157	−	0.997257i	$-0.476419\pi$
$821$	4.26124e102	0.148031	0.0740157	+	0.997257i	$0.476419\pi$
$822$	2.08017e103	0.692069
$823$	2.60841e103	0.831154	0.415577	−	0.909558i	$-0.363580\pi$
$823$	2.60841e103	0.831154	0.415577	+	0.909558i	$0.363580\pi$
$824$	−1.40660e103	−0.429295
$825$	7.11260e103	2.07928
$826$	−2.85586e103	−0.799734
$827$	−2.77148e103	−0.743474	−0.371737	−	0.928338i	$-0.621238\pi$
$827$	−2.77148e103	−0.743474	−0.371737	+	0.928338i	$0.621238\pi$
$828$	−1.52160e103	−0.391042
$829$	−1.86490e103	−0.459165	−0.229582	−	0.973289i	$-0.573736\pi$
$829$	−1.86490e103	−0.459165	−0.229582	+	0.973289i	$0.573736\pi$
$830$	4.55641e101	0.0107486
$831$	−5.02680e103	−1.13620
$832$	4.02269e102	0.0871241
$833$	−2.95753e103	−0.613806
$834$	−2.67314e102	−0.0531651
$835$	5.33542e101	0.0101695
$836$	−3.92266e102	−0.0716568
$837$	−1.04118e103	−0.182293
$838$	−3.79363e103	−0.636638
$839$	−1.13404e103	−0.182423	−0.0912114	−	0.995832i	$-0.529074\pi$
$839$	−1.13404e103	−0.182423	−0.0912114	+	0.995832i	$0.529074\pi$
$840$	2.11692e101	0.00326430
$841$	−4.02947e103	−0.595649
$842$	−7.07733e103	−1.00297
$843$	−1.56211e103	−0.212243
$844$	3.37339e103	0.439450
$845$	−5.00095e101	−0.00624654
$846$	5.20107e103	0.622938
$847$	9.32442e103	1.07093
$848$	4.31432e103	0.475181
$849$	−8.08730e103	−0.854241
$850$	6.78919e103	0.687775
$851$	1.30693e103	0.126985
$852$	4.12615e103	0.384538
$853$	1.52267e104	1.36118	0.680590	−	0.732664i	$-0.261723\pi$
$853$	1.52267e104	1.36118	0.680590	+	0.732664i	$0.261723\pi$
$854$	2.50960e103	0.215204
$855$	−7.19723e100	−0.000592063 0
$856$	8.59990e103	0.678695
$857$	6.39056e102	0.0483860	0.0241930	−	0.999707i	$-0.492298\pi$
$857$	6.39056e102	0.0483860	0.0241930	+	0.999707i	$0.492298\pi$
$858$	1.41088e104	1.02492
$859$	−4.19896e103	−0.292674	−0.146337	−	0.989235i	$-0.546748\pi$
$859$	−4.19896e103	−0.292674	−0.146337	+	0.989235i	$0.546748\pi$
$860$	5.69302e101	0.00380757
$861$	3.89217e103	0.249793
$862$	−4.25161e103	−0.261846
$863$	−2.96988e104	−1.75532	−0.877658	−	0.479287i	$-0.840895\pi$
$863$	−2.96988e104	−1.75532	−0.877658	+	0.479287i	$0.840895\pi$
$864$	−1.69503e103	−0.0961477
$865$	7.32185e98	3.98611e−6 0
$866$	−2.03403e104	−1.06285
$867$	1.33833e103	0.0671250
$868$	−2.11451e103	−0.101803
$869$	−1.41672e104	−0.654758
$870$	1.54028e102	0.00683386
$871$	2.92873e104	1.24748
$872$	7.36171e103	0.301053
$873$	−8.84032e103	−0.347106
$874$	−2.23740e103	−0.0843504
$875$	−4.07684e102	−0.0147584
$876$	−2.96204e104	−1.02966
$877$	4.89308e104	1.63342	0.816708	−	0.577052i	$-0.195797\pi$
$877$	4.89308e104	1.63342	0.816708	+	0.577052i	$0.195797\pi$
$878$	−2.64967e104	−0.849448
$879$	−5.69554e104	−1.75360
$880$	1.70712e102	0.00504811
$881$	3.03671e104	0.862500	0.431250	−	0.902233i	$-0.358073\pi$
$881$	3.03671e104	0.862500	0.431250	+	0.902233i	$0.358073\pi$
$882$	9.24446e103	0.252201
$883$	2.91425e103	0.0763699	0.0381849	−	0.999271i	$-0.487842\pi$
$883$	2.91425e103	0.0763699	0.0381849	+	0.999271i	$0.487842\pi$
$884$	1.34673e104	0.339019
$885$	−1.17008e103	−0.0282962
$886$	−1.29174e104	−0.300107
$887$	1.86513e104	0.416313	0.208157	−	0.978096i	$-0.433254\pi$
$887$	1.86513e104	0.416313	0.208157	+	0.978096i	$0.433254\pi$
$888$	−1.89306e103	−0.0405980
$889$	2.62348e104	0.540588
$890$	1.94377e102	0.00384858
$891$	−1.08835e105	−2.07066
$892$	1.89350e104	0.346189
$893$	7.64778e103	0.134372
$894$	−3.38473e104	−0.571535
$895$	1.56481e101	0.000253947 0
$896$	−3.44241e103	−0.0536943
$897$	8.04733e104	1.20648
$898$	1.78531e104	0.257279
$899$	−1.53853e104	−0.213126
$900$	−2.12213e104	−0.282594
$901$	1.44436e105	1.84903
$902$	3.13871e104	0.386295
$903$	−4.02638e104	−0.476430
$904$	1.15930e104	0.131891
$905$	−1.40042e103	−0.0153191
$906$	1.05871e105	1.11359
$907$	7.56043e104	0.764695	0.382347	−	0.924019i	$-0.375116\pi$
$907$	7.56043e104	0.764695	0.382347	+	0.924019i	$0.375116\pi$
$908$	−6.36417e104	−0.619005
$909$	7.31254e104	0.683991
$910$	−4.04318e102	−0.00363709
$911$	−1.06937e104	−0.0925180	−0.0462590	−	0.998929i	$-0.514730\pi$
$911$	−1.06937e104	−0.0925180	−0.0462590	+	0.998929i	$0.514730\pi$
$912$	3.24083e103	0.0269674
$913$	−2.59869e105	−2.07989
$914$	−2.50399e104	−0.192771
$915$	1.02821e103	0.00761436
$916$	9.11347e103	0.0649224
$917$	8.03917e103	0.0550934
$918$	−5.67465e104	−0.374131
$919$	−2.01508e105	−1.27818	−0.639089	−	0.769133i	$-0.720689\pi$
$919$	−2.01508e105	−1.27818	−0.639089	+	0.769133i	$0.720689\pi$
$920$	9.73703e102	0.00594236
$921$	−1.80033e105	−1.05715
$922$	2.26873e105	1.28184
$923$	−7.88068e104	−0.428453
$924$	−1.20736e105	−0.631656
$925$	1.82273e104	0.0917679
$926$	2.07000e105	1.00295
$927$	1.47193e105	0.686368
$928$	−2.50471e104	−0.112410
$929$	−3.83029e105	−1.65453	−0.827264	−	0.561813i	$-0.810104\pi$
$929$	−3.83029e105	−1.65453	−0.827264	+	0.561813i	$0.810104\pi$
$930$	−8.66339e102	−0.00360200
$931$	1.35933e104	0.0544015
$932$	7.73566e104	0.298011
$933$	1.86097e105	0.690145
$934$	−3.48482e104	−0.124413
$935$	5.71514e103	0.0196433
$936$	−4.20952e104	−0.139296
$937$	4.66279e104	0.148556	0.0742780	−	0.997238i	$-0.476335\pi$
$937$	4.66279e104	0.148556	0.0742780	+	0.997238i	$0.476335\pi$
$938$	−2.50626e105	−0.768820
$939$	2.23554e105	0.660318
$940$	−3.32827e103	−0.00946630
$941$	2.77125e105	0.759004	0.379502	−	0.925191i	$-0.376095\pi$
$941$	2.77125e105	0.759004	0.379502	+	0.925191i	$0.376095\pi$
$942$	−1.27075e105	−0.335161
$943$	1.79025e105	0.454725
$944$	1.90271e105	0.465444
$945$	1.70366e103	0.00401379
$946$	−3.24694e105	−0.736781
$947$	5.79302e105	1.26614	0.633069	−	0.774096i	$-0.281795\pi$
$947$	5.79302e105	1.26614	0.633069	+	0.774096i	$0.281795\pi$
$948$	1.17047e105	0.246413
$949$	5.65731e105	1.14725
$950$	−3.12043e104	−0.0609573
$951$	9.67238e105	1.82023
$952$	−1.15246e105	−0.208936
$953$	−7.88146e105	−1.37660	−0.688302	−	0.725425i	$-0.741643\pi$
$953$	−7.88146e105	−1.37660	−0.688302	+	0.725425i	$0.741643\pi$
$954$	−4.51469e105	−0.759732
$955$	7.45766e103	0.0120916
$956$	2.24565e105	0.350822
$957$	−8.78477e105	−1.32238
$958$	4.05160e104	0.0587694
$959$	3.39988e105	0.475229
$960$	−1.41039e103	−0.00189982
$961$	−6.83801e105	−0.887665
$962$	3.61562e104	0.0452343
$963$	−8.99931e105	−1.08512
$964$	4.63048e105	0.538136
$965$	−8.97043e103	−0.0100483
$966$	−6.88649e105	−0.743550
$967$	−1.50824e106	−1.56975	−0.784876	−	0.619652i	$-0.787274\pi$
$967$	−1.50824e106	−1.56975	−0.784876	+	0.619652i	$0.787274\pi$
$968$	−6.21237e105	−0.623278
$969$	1.08497e105	0.104936
$970$	5.65711e103	0.00527470
$971$	3.90862e105	0.351351	0.175675	−	0.984448i	$-0.443789\pi$
$971$	3.90862e105	0.351351	0.175675	+	0.984448i	$0.443789\pi$
$972$	5.85387e105	0.507331
$973$	−4.36904e104	−0.0365074
$974$	1.04337e105	0.0840611
$975$	1.12234e106	0.871885
$976$	−1.67202e105	−0.125248
$977$	1.80640e106	1.30484	0.652418	−	0.757859i	$-0.273755\pi$
$977$	1.80640e106	1.30484	0.652418	+	0.757859i	$0.273755\pi$
$978$	2.33669e106	1.62769
$979$	−1.10860e106	−0.744716
$980$	−5.91573e103	−0.00383250
$981$	−7.70361e105	−0.481332
$982$	−1.86368e105	−0.112309
$983$	−4.00954e105	−0.233047	−0.116524	−	0.993188i	$-0.537175\pi$
$983$	−4.00954e105	−0.233047	−0.116524	+	0.993188i	$0.537175\pi$
$984$	−2.59315e105	−0.145379
$985$	3.24026e104	0.0175224
$986$	−8.38533e105	−0.437411
$987$	2.35391e106	1.18449
$988$	−6.18978e104	−0.0300472
$989$	−1.85198e106	−0.867297
$990$	−1.78640e104	−0.00807106
$991$	7.98725e105	0.348163	0.174081	−	0.984731i	$-0.444304\pi$
$991$	7.98725e105	0.348163	0.174081	+	0.984731i	$0.444304\pi$
$992$	1.40879e105	0.0592491
$993$	−4.86024e105	−0.197224
$994$	6.74388e105	0.264054
$995$	4.61918e104	0.0174520
$996$	2.14699e106	0.782751
$997$	−4.68674e106	−1.64889	−0.824446	−	0.565940i	$-0.808513\pi$
$997$	−4.68674e106	−1.64889	−0.824446	+	0.565940i	$0.808513\pi$
$998$	2.09197e106	0.710266
$999$	−1.52350e105	−0.0499193

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2.72.a.b.1.1	✓	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)

\(f(q)\)	\(=\)	\(q-3.43597e10 q^{2} -1.08417e17 q^{3} +1.18059e21 q^{4} +7.90573e22 q^{5} +3.72520e27 q^{6} +6.08855e29 q^{7} -4.05648e31 q^{8} +4.24488e33 q^{9} +O(q^{10})\)	\(q-3.43597e10 q^{2} -1.08417e17 q^{3} +1.18059e21 q^{4} +7.90573e22 q^{5} +3.72520e27 q^{6} +6.08855e29 q^{7} -4.05648e31 q^{8} +4.24488e33 q^{9} -2.71639e33 q^{10} +1.54925e37 q^{11} -1.27997e38 q^{12} +2.44465e39 q^{13} -2.09201e40 q^{14} -8.57119e39 q^{15} +1.39380e42 q^{16} +4.66619e43 q^{17} -1.45853e44 q^{18} -2.14466e44 q^{19} +9.33344e43 q^{20} -6.60105e46 q^{21} -5.32320e47 q^{22} -3.03623e48 q^{23} +4.39793e48 q^{24} -4.23454e49 q^{25} -8.39977e49 q^{26} +3.53938e50 q^{27} +7.18809e50 q^{28} +5.23008e51 q^{29} +2.94504e50 q^{30} -2.94169e52 q^{31} -4.78905e52 q^{32} -1.67966e54 q^{33} -1.60329e54 q^{34} +4.81344e52 q^{35} +5.01147e54 q^{36} -4.30443e54 q^{37} +7.36899e54 q^{38} -2.65043e56 q^{39} -3.20694e54 q^{40} -5.89629e56 q^{41} +2.26810e57 q^{42} +6.09960e57 q^{43} +1.82904e58 q^{44} +3.35589e56 q^{45} +1.04324e59 q^{46} -3.56597e59 q^{47} -1.51112e59 q^{48} -6.33821e59 q^{49} +1.45498e60 q^{50} -5.05896e60 q^{51} +2.88614e60 q^{52} +3.09537e61 q^{53} -1.21612e61 q^{54} +1.22480e60 q^{55} -2.46981e61 q^{56} +2.32518e61 q^{57} -1.79704e62 q^{58} +1.36513e63 q^{59} -1.01191e61 q^{60} -1.19961e63 q^{61} +1.01076e63 q^{62} +2.58452e63 q^{63} +1.64550e63 q^{64} +1.93268e62 q^{65} +5.77128e64 q^{66} +1.19801e65 q^{67} +5.50886e64 q^{68} +3.29181e65 q^{69} -1.65389e63 q^{70} -3.22364e65 q^{71} -1.72193e65 q^{72} +2.31415e66 q^{73} +1.47899e65 q^{74} +4.59098e66 q^{75} -2.53196e65 q^{76} +9.43271e66 q^{77} +9.10682e66 q^{78} -9.14450e66 q^{79} +1.10190e65 q^{80} -7.02499e67 q^{81} +2.02595e67 q^{82} -1.67738e68 q^{83} -7.79315e67 q^{84} +3.68896e66 q^{85} -2.09581e68 q^{86} -5.67032e68 q^{87} -6.28452e68 q^{88} -7.15572e68 q^{89} -1.15307e67 q^{90} +1.48844e69 q^{91} -3.58455e69 q^{92} +3.18930e69 q^{93} +1.22526e70 q^{94} -1.69551e67 q^{95} +5.19216e69 q^{96} -2.08258e70 q^{97} +2.17779e70 q^{98} +6.57640e70 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q - 103079215104 q^{2} + 23\!\cdots\!36 q^{3}+ \cdots - 45\!\cdots\!09 q^{9}+O(q^{10}) \) 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

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