LMFDB - Embedded newform 2.72.a.b.1.3

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			1.3
Root			$-2.86077e12$ 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)

$f(q)$	$=$	$q-3.43597e10 q^{2} +6.35309e16 q^{3} +1.18059e21 q^{4} +1.19804e25 q^{5} -2.18290e27 q^{6} -1.27132e30 q^{7} -4.05648e31 q^{8} -3.47329e33 q^{9} +O(q^{10})$	\(q-3.43597e10 q^{2} +6.35309e16 q^{3} +1.18059e21 q^{4} +1.19804e25 q^{5} -2.18290e27 q^{6} -1.27132e30 q^{7} -4.05648e31 q^{8} -3.47329e33 q^{9} -4.11644e35 q^{10} -1.31209e35 q^{11} +7.50040e37 q^{12} +4.90880e39 q^{13} +4.36824e40 q^{14} +7.61127e41 q^{15} +1.39380e42 q^{16} -6.48706e43 q^{17} +1.19341e44 q^{18} +2.72740e45 q^{19} +1.41440e46 q^{20} -8.07683e46 q^{21} +4.50829e45 q^{22} +2.34677e48 q^{23} -2.57712e48 q^{24} +1.01179e50 q^{25} -1.68665e50 q^{26} -6.97744e50 q^{27} -1.50091e51 q^{28} +9.02709e51 q^{29} -2.61521e52 q^{30} -4.95831e52 q^{31} -4.78905e52 q^{32} -8.33579e51 q^{33} +2.22894e54 q^{34} -1.52310e55 q^{35} -4.10054e54 q^{36} -1.80430e55 q^{37} -9.37127e55 q^{38} +3.11861e56 q^{39} -4.85984e56 q^{40} +6.04763e56 q^{41} +2.77518e57 q^{42} +1.03698e58 q^{43} -1.54904e56 q^{44} -4.16115e58 q^{45} -8.06344e58 q^{46} +2.53196e59 q^{47} +8.85491e58 q^{48} +6.11739e59 q^{49} -3.47649e60 q^{50} -4.12129e60 q^{51} +5.79529e60 q^{52} +6.53033e60 q^{53} +2.39743e61 q^{54} -1.57193e60 q^{55} +5.15710e61 q^{56} +1.73274e62 q^{57} -3.10168e62 q^{58} +2.34221e62 q^{59} +8.98581e62 q^{60} -2.75624e63 q^{61} +1.70366e63 q^{62} +4.41568e63 q^{63} +1.64550e63 q^{64} +5.88096e64 q^{65} +2.86416e62 q^{66} +6.97669e64 q^{67} -7.65857e64 q^{68} +1.49092e65 q^{69} +5.23333e65 q^{70} +5.81114e65 q^{71} +1.40893e65 q^{72} -8.45661e65 q^{73} +6.19952e65 q^{74} +6.42799e66 q^{75} +3.21994e66 q^{76} +1.66809e65 q^{77} -1.07155e67 q^{78} +1.96236e67 q^{79} +1.66983e67 q^{80} -1.82458e67 q^{81} -2.07795e67 q^{82} -1.11774e68 q^{83} -9.53544e67 q^{84} -7.77178e68 q^{85} -3.56304e68 q^{86} +5.73499e68 q^{87} +5.32245e66 q^{88} +5.42522e68 q^{89} +1.42976e69 q^{90} -6.24068e69 q^{91} +2.77058e69 q^{92} -3.15006e69 q^{93} -8.69974e69 q^{94} +3.26754e70 q^{95} -3.04253e69 q^{96} +2.87774e70 q^{97} -2.10192e70 q^{98} +4.55726e68 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	6.35309e16	0.733129	0.366565	−	0.930393i	$-0.380534\pi$
$3$	6.35309e16	0.733129	0.366565	+	0.930393i	$0.380534\pi$
$4$	1.18059e21	0.500000
$5$	1.19804e25	1.84093	0.920465	−	0.390825i	$-0.127810\pi$
$5$	1.19804e25	1.84093	0.920465	+	0.390825i	$0.127810\pi$
$6$	−2.18290e27	−0.518400
$7$	−1.27132e30	−1.26846	−0.634229	−	0.773146i	$-0.718682\pi$
$7$	−1.27132e30	−1.26846	−0.634229	+	0.773146i	$0.718682\pi$
$8$	−4.05648e31	−0.353553
$9$	−3.47329e33	−0.462522
$10$	−4.11644e35	−1.30173
$11$	−1.31209e35	−0.0140774	−0.00703869	−	0.999975i	$-0.502241\pi$
$11$	−1.31209e35	−0.0140774	−0.00703869	+	0.999975i	$0.502241\pi$
$12$	7.50040e37	0.366565
$13$	4.90880e39	1.39954	0.699772	−	0.714366i	$-0.253285\pi$
$13$	4.90880e39	1.39954	0.699772	+	0.714366i	$0.253285\pi$
$14$	4.36824e40	0.896935
$15$	7.61127e41	1.34964
$16$	1.39380e42	0.250000
$17$	−6.48706e43	−1.35242	−0.676209	−	0.736710i	$-0.736379\pi$
$17$	−6.48706e43	−1.35242	−0.676209	+	0.736710i	$0.736379\pi$
$18$	1.19341e44	0.327052
$19$	2.72740e45	1.09647	0.548234	−	0.836325i	$-0.315300\pi$
$19$	2.72740e45	1.09647	0.548234	+	0.836325i	$0.315300\pi$
$20$	1.41440e46	0.920465
$21$	−8.07683e46	−0.929943
$22$	4.50829e45	0.00995421
$23$	2.34677e48	1.06938	0.534690	−	0.845048i	$-0.320428\pi$
$23$	2.34677e48	1.06938	0.534690	+	0.845048i	$0.320428\pi$
$24$	−2.57712e48	−0.259200
$25$	1.01179e50	2.38902
$26$	−1.68665e50	−0.989627
$27$	−6.97744e50	−1.07222
$28$	−1.50091e51	−0.634229
$29$	9.02709e51	1.09754	0.548768	−	0.835975i	$-0.315097\pi$
$29$	9.02709e51	1.09754	0.548768	+	0.835975i	$0.315097\pi$
$30$	−2.61521e52	−0.954339
$31$	−4.95831e52	−0.564929	−0.282465	−	0.959278i	$-0.591152\pi$
$31$	−4.95831e52	−0.564929	−0.282465	+	0.959278i	$0.591152\pi$
$32$	−4.78905e52	−0.176777
$33$	−8.33579e51	−0.0103205
$34$	2.22894e54	0.956304
$35$	−1.52310e55	−2.33514
$36$	−4.10054e54	−0.231261
$37$	−1.80430e55	−0.384722	−0.192361	−	0.981324i	$-0.561614\pi$
$37$	−1.80430e55	−0.384722	−0.192361	+	0.981324i	$0.561614\pi$
$38$	−9.37127e55	−0.775320
$39$	3.11861e56	1.02605
$40$	−4.85984e56	−0.650867
$41$	6.04763e56	0.337099	0.168550	−	0.985693i	$-0.446092\pi$
$41$	6.04763e56	0.337099	0.168550	+	0.985693i	$0.446092\pi$
$42$	2.77518e57	0.657569
$43$	1.03698e58	1.06571	0.532857	−	0.846206i	$-0.321119\pi$
$43$	1.03698e58	1.06571	0.532857	+	0.846206i	$0.321119\pi$
$44$	−1.54904e56	−0.00703869
$45$	−4.16115e58	−0.851470
$46$	−8.06344e58	−0.756166
$47$	2.53196e59	1.10658	0.553289	−	0.832989i	$-0.313372\pi$
$47$	2.53196e59	1.10658	0.553289	+	0.832989i	$0.313372\pi$
$48$	8.85491e58	0.183282
$49$	6.11739e59	0.608983
$50$	−3.47649e60	−1.68929
$51$	−4.12129e60	−0.991497
$52$	5.79529e60	0.699772
$53$	6.53033e60	0.400997	0.200499	−	0.979694i	$-0.435744\pi$
$53$	6.53033e60	0.400997	0.200499	+	0.979694i	$0.435744\pi$
$54$	2.39743e61	0.758172
$55$	−1.57193e60	−0.0259155
$56$	5.15710e61	0.448467
$57$	1.73274e62	0.803852
$58$	−3.10168e62	−0.776075
$59$	2.34221e62	0.319433	0.159716	−	0.987163i	$-0.448942\pi$
$59$	2.34221e62	0.319433	0.159716	+	0.987163i	$0.448942\pi$
$60$	8.98581e62	0.674820
$61$	−2.75624e63	−1.15109	−0.575543	−	0.817771i	$-0.695209\pi$
$61$	−2.75624e63	−1.15109	−0.575543	+	0.817771i	$0.695209\pi$
$62$	1.70366e63	0.399465
$63$	4.41568e63	0.586689
$64$	1.64550e63	0.125000
$65$	5.88096e64	2.57646
$66$	2.86416e62	0.00729772
$67$	6.97669e64	1.04230	0.521151	−	0.853464i	$-0.325503\pi$
$67$	6.97669e64	1.04230	0.521151	+	0.853464i	$0.325503\pi$
$68$	−7.65857e64	−0.676209
$69$	1.49092e65	0.783994
$70$	5.23333e65	1.65119
$71$	5.81114e65	1.10813	0.554064	−	0.832474i	$-0.313076\pi$
$71$	5.81114e65	1.10813	0.554064	+	0.832474i	$0.313076\pi$
$72$	1.40893e65	0.163526
$73$	−8.45661e65	−0.601499	−0.300749	−	0.953703i	$-0.597237\pi$
$73$	−8.45661e65	−0.601499	−0.300749	+	0.953703i	$0.597237\pi$
$74$	6.19952e65	0.272040
$75$	6.42799e66	1.75146
$76$	3.21994e66	0.548234
$77$	1.66809e65	0.0178565
$78$	−1.07155e67	−0.725525
$79$	1.96236e67	0.845312	0.422656	−	0.906290i	$-0.361098\pi$
$79$	1.96236e67	0.845312	0.422656	+	0.906290i	$0.361098\pi$
$80$	1.66983e67	0.460232
$81$	−1.82458e67	−0.323552
$82$	−2.07795e67	−0.238365
$83$	−1.11774e68	−0.833816	−0.416908	−	0.908949i	$-0.636886\pi$
$83$	−1.11774e68	−0.833816	−0.416908	+	0.908949i	$0.636886\pi$
$84$	−9.53544e67	−0.464971
$85$	−7.77178e68	−2.48971
$86$	−3.56304e68	−0.753573
$87$	5.73499e68	0.804635
$88$	5.32245e66	0.00497710
$89$	5.42522e68	0.339682	0.169841	−	0.985472i	$-0.445675\pi$
$89$	5.42522e68	0.339682	0.169841	+	0.985472i	$0.445675\pi$
$90$	1.42976e69	0.602080
$91$	−6.24068e69	−1.77526
$92$	2.77058e69	0.534690
$93$	−3.15006e69	−0.414166
$94$	−8.69974e69	−0.782469
$95$	3.26754e70	2.01852
$96$	−3.04253e69	−0.129600
$97$	2.87774e70	0.848505	0.424252	−	0.905544i	$-0.360537\pi$
$97$	2.87774e70	0.848505	0.424252	+	0.905544i	$0.360537\pi$
$98$	−2.10192e70	−0.430616
$99$	4.55726e68	0.00651109
$100$	1.19451e71	1.19451
$101$	1.12568e71	0.790689	0.395344	−	0.918533i	$-0.370625\pi$
$101$	1.12568e71	0.790689	0.395344	+	0.918533i	$0.370625\pi$
$102$	1.41606e71	0.701094
$103$	1.67384e71	0.586129	0.293064	−	0.956093i	$-0.405325\pi$
$103$	1.67384e71	0.586129	0.293064	+	0.956093i	$0.405325\pi$
$104$	−1.99125e71	−0.494814
$105$	−9.67639e71	−1.71196
$106$	−2.24380e71	−0.283548
$107$	1.28125e72	1.16013	0.580067	−	0.814569i	$-0.303026\pi$
$107$	1.28125e72	1.16013	0.580067	+	0.814569i	$0.303026\pi$
$108$	−8.23751e71	−0.536109
$109$	−3.28017e72	−1.53906	−0.769530	−	0.638611i	$-0.779509\pi$
$109$	−3.28017e72	−1.53906	−0.769530	+	0.638611i	$0.779509\pi$
$110$	5.40113e70	0.0183250
$111$	−1.14629e72	−0.282051
$112$	−1.77197e72	−0.317114
$113$	−8.49850e72	−1.10932	−0.554661	−	0.832077i	$-0.687152\pi$
$113$	−8.49850e72	−1.10932	−0.554661	+	0.832077i	$0.687152\pi$
$114$	−5.95365e72	−0.568409
$115$	2.81153e73	1.96865
$116$	1.06573e73	0.548768
$117$	−1.70497e73	−0.647320
$118$	−8.04778e72	−0.225873
$119$	8.24715e73	1.71549
$120$	−3.08750e73	−0.477169
$121$	−8.68549e73	−0.999802
$122$	9.47037e73	0.813941
$123$	3.84211e73	0.247137
$124$	−5.85374e73	−0.282465
$125$	7.04777e74	2.55709
$126$	−1.51722e74	−0.414852
$127$	−2.49935e74	−0.516174	−0.258087	−	0.966122i	$-0.583092\pi$
$127$	−2.49935e74	−0.516174	−0.258087	+	0.966122i	$0.583092\pi$
$128$	−5.65391e73	−0.0883883
$129$	6.58803e74	0.781305
$130$	−2.02068e75	−1.82183
$131$	6.52258e74	0.448011	0.224005	−	0.974588i	$-0.428087\pi$
$131$	6.52258e74	0.448011	0.224005	+	0.974588i	$0.428087\pi$
$132$	−9.84117e72	−0.00516027
$133$	−3.46741e75	−1.39082
$134$	−2.39717e75	−0.737019
$135$	−8.35928e75	−1.97388
$136$	2.63146e75	0.478152
$137$	1.38004e76	1.93336	0.966679	−	0.255992i	$-0.0824020\pi$
$137$	1.38004e76	1.93336	0.966679	+	0.255992i	$0.0824020\pi$
$138$	−5.12278e75	−0.554367
$139$	2.20913e76	1.85010	0.925052	−	0.379840i	$-0.124021\pi$
$139$	2.20913e76	1.85010	0.925052	+	0.379840i	$0.124021\pi$
$140$	−1.79816e76	−1.16757
$141$	1.60857e76	0.811265
$142$	−1.99669e76	−0.783565
$143$	−6.44077e74	−0.0197019
$144$	−4.84106e75	−0.115630
$145$	1.08148e77	2.02049
$146$	2.90567e76	0.425324
$147$	3.88643e76	0.446463
$148$	−2.13014e76	−0.192361
$149$	−1.01281e77	−0.720139	−0.360069	−	0.932926i	$-0.617247\pi$
$149$	−1.01281e77	−0.720139	−0.360069	+	0.932926i	$0.617247\pi$
$150$	−2.20864e77	−1.23847
$151$	1.65388e77	0.732526	0.366263	−	0.930511i	$-0.380637\pi$
$151$	1.65388e77	0.732526	0.366263	+	0.930511i	$0.380637\pi$
$152$	−1.10636e77	−0.387660
$153$	2.25315e77	0.625523
$154$	−5.73150e75	−0.0126265
$155$	−5.94027e77	−1.03999
$156$	3.68180e77	0.513023
$157$	−7.47828e77	−0.830547	−0.415274	−	0.909697i	$-0.636314\pi$
$157$	−7.47828e77	−0.830547	−0.415274	+	0.909697i	$0.636314\pi$
$158$	−6.74262e77	−0.597726
$159$	4.14878e77	0.293983
$160$	−5.73749e77	−0.325433
$161$	−2.98350e78	−1.35646
$162$	6.26919e77	0.228786
$163$	5.69846e78	1.67147	0.835734	−	0.549135i	$-0.185043\pi$
$163$	5.69846e78	1.67147	0.835734	+	0.549135i	$0.185043\pi$
$164$	7.13978e77	0.168550
$165$	−9.98664e76	−0.0189994
$166$	3.84054e78	0.589597
$167$	−6.16609e78	−0.764849	−0.382424	−	0.923987i	$-0.624911\pi$
$167$	−6.16609e78	−0.764849	−0.382424	+	0.923987i	$0.624911\pi$
$168$	3.27635e78	0.328784
$169$	1.17943e79	0.958725
$170$	2.67036e79	1.76049
$171$	−9.47305e78	−0.507140
$172$	1.22425e79	0.532857
$173$	1.10789e79	0.392520	0.196260	−	0.980552i	$-0.437120\pi$
$173$	1.10789e79	0.392520	0.196260	+	0.980552i	$0.437120\pi$
$174$	−1.97053e79	−0.568963
$175$	−1.28631e80	−3.03037
$176$	−1.82878e77	−0.00351934
$177$	1.48803e79	0.234186
$178$	−1.86409e79	−0.240191
$179$	−3.78746e79	−0.400005	−0.200003	−	0.979795i	$-0.564095\pi$
$179$	−3.78746e79	−0.400005	−0.200003	+	0.979795i	$0.564095\pi$
$180$	−4.91262e79	−0.425735
$181$	1.13894e80	0.810794	0.405397	−	0.914141i	$-0.367133\pi$
$181$	1.13894e80	0.810794	0.405397	+	0.914141i	$0.367133\pi$
$182$	2.14428e80	1.25530
$183$	−1.75106e80	−0.843895
$184$	−9.51963e79	−0.378083
$185$	−2.16163e80	−0.708247
$186$	1.08235e80	0.292860
$187$	8.51157e78	0.0190385
$188$	2.98921e80	0.553289
$189$	8.87059e80	1.36006
$190$	−1.12272e81	−1.42731
$191$	6.70060e80	0.707016	0.353508	−	0.935432i	$-0.384989\pi$
$191$	6.70060e80	0.707016	0.353508	+	0.935432i	$0.384989\pi$
$192$	1.04540e80	0.0916411
$193$	7.59342e80	0.553545	0.276772	−	0.960936i	$-0.410735\pi$
$193$	7.59342e80	0.553545	0.276772	+	0.960936i	$0.410735\pi$
$194$	−9.88783e80	−0.599984
$195$	3.73623e81	1.88888
$196$	7.22214e80	0.304492
$197$	−3.09240e81	−1.08829	−0.544145	−	0.838991i	$-0.683146\pi$
$197$	−3.09240e81	−1.08829	−0.544145	+	0.838991i	$0.683146\pi$
$198$	−1.56586e79	−0.00460404
$199$	−3.56339e80	−0.0876151	−0.0438076	−	0.999040i	$-0.513949\pi$
$199$	−3.56339e80	−0.0876151	−0.0438076	+	0.999040i	$0.513949\pi$
$200$	−4.10431e81	−0.844647
$201$	4.43235e81	0.764142
$202$	−3.86780e81	−0.559101
$203$	−1.14764e82	−1.39218
$204$	−4.86556e81	−0.495749
$205$	7.24532e81	0.620576
$206$	−5.75128e81	−0.414456
$207$	−8.15102e81	−0.494612
$208$	6.84187e81	0.349886
$209$	−3.57858e80	−0.0154354
$210$	3.32478e82	1.21054
$211$	−4.41478e82	−1.35794	−0.678972	−	0.734164i	$-0.737574\pi$
$211$	−4.41478e82	−1.35794	−0.678972	+	0.734164i	$0.737574\pi$
$212$	7.70965e81	0.200499
$213$	3.69187e82	0.812401
$214$	−4.40233e82	−0.820339
$215$	1.24235e83	1.96190
$216$	2.83039e82	0.379086
$217$	6.30362e82	0.716588
$218$	1.12706e83	1.08828
$219$	−5.37256e82	−0.440976
$220$	−1.85581e81	−0.0129577
$221$	−3.18437e83	−1.89277
$222$	3.93861e82	0.199440
$223$	−2.48721e83	−1.07372	−0.536858	−	0.843672i	$-0.680389\pi$
$223$	−2.48721e83	−1.07372	−0.536858	+	0.843672i	$0.680389\pi$
$224$	6.08843e82	0.224234
$225$	−3.51424e83	−1.10498
$226$	2.92006e83	0.784409
$227$	3.74337e83	0.859695	0.429847	−	0.902902i	$-0.358567\pi$
$227$	3.74337e83	0.859695	0.429847	+	0.902902i	$0.358567\pi$
$228$	2.04566e83	0.401926
$229$	−2.18566e83	−0.367641	−0.183820	−	0.982960i	$-0.558846\pi$
$229$	−2.18566e83	−0.367641	−0.183820	+	0.982960i	$0.558846\pi$
$230$	−9.66035e83	−1.39205
$231$	1.05975e82	0.0130912
$232$	−3.66182e83	−0.388038
$233$	−1.07513e84	−0.977969	−0.488984	−	0.872293i	$-0.662632\pi$
$233$	−1.07513e84	−0.977969	−0.488984	+	0.872293i	$0.662632\pi$
$234$	5.85824e83	0.457724
$235$	3.03339e84	2.03713
$236$	2.76520e83	0.159716
$237$	1.24670e84	0.619723
$238$	−2.83370e84	−1.21303
$239$	−3.17105e84	−1.16971	−0.584854	−	0.811139i	$-0.698848\pi$
$239$	−3.17105e84	−1.16971	−0.584854	+	0.811139i	$0.698848\pi$
$240$	1.06086e84	0.337410
$241$	2.09314e84	0.574371	0.287186	−	0.957875i	$-0.407280\pi$
$241$	2.09314e84	0.574371	0.287186	+	0.957875i	$0.407280\pi$
$242$	2.98431e84	0.706967
$243$	4.08052e84	0.835012
$244$	−3.25399e84	−0.575543
$245$	7.32890e84	1.12110
$246$	−1.32014e84	−0.174753
$247$	1.33883e85	1.53456
$248$	2.01133e84	0.199733
$249$	−7.10113e84	−0.611295
$250$	−2.42160e85	−1.80814
$251$	−2.60584e85	−1.68862	−0.844308	−	0.535857i	$-0.819988\pi$
$251$	−2.60584e85	−1.68862	−0.844308	+	0.535857i	$0.819988\pi$
$252$	5.21311e84	0.293345
$253$	−3.07916e83	−0.0150541
$254$	8.58772e84	0.364990
$255$	−4.93748e85	−1.82528
$256$	1.94267e84	0.0625000
$257$	3.62235e85	1.01476	0.507381	−	0.861722i	$-0.330614\pi$
$257$	3.62235e85	1.01476	0.507381	+	0.861722i	$0.330614\pi$
$258$	−2.26363e85	−0.552466
$259$	2.29385e85	0.488004
$260$	6.94301e85	1.28823
$261$	−3.13537e85	−0.507634
$262$	−2.24114e85	−0.316791
$263$	−3.33182e85	−0.411389	−0.205695	−	0.978616i	$-0.565945\pi$
$263$	−3.33182e85	−0.411389	−0.205695	+	0.978616i	$0.565945\pi$
$264$	3.38140e83	0.00364886
$265$	7.82361e85	0.738208
$266$	1.19139e86	0.983460
$267$	3.44669e85	0.249030
$268$	8.23662e85	0.521151
$269$	−1.47569e86	−0.818066	−0.409033	−	0.912519i	$-0.634134\pi$
$269$	−1.47569e86	−0.818066	−0.409033	+	0.912519i	$0.634134\pi$
$270$	2.87223e86	1.39574
$271$	1.38297e86	0.589392	0.294696	−	0.955591i	$-0.404782\pi$
$271$	1.38297e86	0.589392	0.294696	+	0.955591i	$0.404782\pi$
$272$	−9.04164e85	−0.338105
$273$	−3.96476e86	−1.30150
$274$	−4.74179e86	−1.36709
$275$	−1.32756e85	−0.0336312
$276$	1.76017e86	0.391997
$277$	5.77313e86	1.13078	0.565391	−	0.824823i	$-0.308725\pi$
$277$	5.77313e86	1.13078	0.565391	+	0.824823i	$0.308725\pi$
$278$	−7.59052e86	−1.30822
$279$	1.72217e86	0.261292
$280$	6.17843e86	0.825597
$281$	−1.22238e87	−1.43924	−0.719618	−	0.694370i	$-0.755683\pi$
$281$	−1.22238e87	−1.43924	−0.719618	+	0.694370i	$0.755683\pi$
$282$	−5.52702e86	−0.573651
$283$	−1.17533e87	−1.07582	−0.537911	−	0.843002i	$-0.680786\pi$
$283$	−1.17533e87	−1.07582	−0.537911	+	0.843002i	$0.680786\pi$
$284$	6.86058e86	0.554064
$285$	2.07590e87	1.47984
$286$	2.21303e85	0.0139314
$287$	−7.68849e86	−0.427596
$288$	1.66338e86	0.0817631
$289$	1.90742e87	0.829036
$290$	−3.71595e87	−1.42870
$291$	1.82825e87	0.622064
$292$	−9.98380e86	−0.300749
$293$	2.82961e87	0.754965	0.377482	−	0.926017i	$-0.376790\pi$
$293$	2.82961e87	0.754965	0.377482	+	0.926017i	$0.376790\pi$
$294$	−1.33537e87	−0.315697
$295$	2.80607e87	0.588054
$296$	7.31911e86	0.136020
$297$	9.15500e85	0.0150940
$298$	3.47999e87	0.509215
$299$	1.15198e88	1.49665
$300$	7.58884e87	0.875731
$301$	−1.31834e88	−1.35181
$302$	−5.68270e87	−0.517974
$303$	7.15154e87	0.579677
$304$	3.80144e87	0.274117
$305$	−3.30209e88	−2.11907
$306$	−7.74175e87	−0.442312
$307$	−3.07076e88	−1.56255	−0.781274	−	0.624189i	$-0.785430\pi$
$307$	−3.07076e88	−1.56255	−0.781274	+	0.624189i	$0.785430\pi$
$308$	1.96933e86	0.00892827
$309$	1.06341e88	0.429708
$310$	2.04106e88	0.735387
$311$	−2.22902e88	−0.716342	−0.358171	−	0.933656i	$-0.616600\pi$
$311$	−2.22902e88	−0.716342	−0.358171	+	0.933656i	$0.616600\pi$
$312$	−1.26506e88	−0.362762
$313$	−1.43486e88	−0.367270	−0.183635	−	0.982994i	$-0.558786\pi$
$313$	−1.43486e88	−0.367270	−0.183635	+	0.982994i	$0.558786\pi$
$314$	2.56952e88	0.587286
$315$	5.29017e88	1.08005
$316$	2.31675e88	0.422656
$317$	1.21756e87	0.0198558	0.00992789	−	0.999951i	$-0.496840\pi$
$317$	1.21756e87	0.0198558	0.00992789	+	0.999951i	$0.496840\pi$
$318$	−1.42551e88	−0.207877
$319$	−1.18443e87	−0.0154504
$320$	1.97139e88	0.230116
$321$	8.13987e88	0.850528
$322$	1.02512e89	0.959165
$323$	−1.76928e89	−1.48288
$324$	−2.15408e88	−0.161776
$325$	4.96668e89	3.34354
$326$	−1.95798e89	−1.18191
$327$	−2.08392e89	−1.12833
$328$	−2.45321e88	−0.119183
$329$	−3.21894e89	−1.40365
$330$	3.43138e87	0.0134346
$331$	5.13420e88	0.180542	0.0902711	−	0.995917i	$-0.471227\pi$
$331$	5.13420e88	0.180542	0.0902711	+	0.995917i	$0.471227\pi$
$332$	−1.31960e89	−0.416908
$333$	6.26686e88	0.177942
$334$	2.11865e89	0.540830
$335$	8.35837e89	1.91881
$336$	−1.12575e89	−0.232486
$337$	−7.69122e89	−1.42933	−0.714667	−	0.699465i	$-0.753422\pi$
$337$	−7.69122e89	−1.42933	−0.714667	+	0.699465i	$0.753422\pi$
$338$	−4.05249e89	−0.677921
$339$	−5.39917e89	−0.813276
$340$	−9.17529e89	−1.24485
$341$	6.50573e87	0.00795272
$342$	3.25492e89	0.358602
$343$	4.99358e89	0.495988
$344$	−4.20649e89	−0.376786
$345$	1.78619e90	1.44328
$346$	−3.80670e89	−0.277553
$347$	1.93762e90	1.27518	0.637590	−	0.770376i	$-0.279932\pi$
$347$	1.93762e90	1.27518	0.637590	+	0.770376i	$0.279932\pi$
$348$	6.77068e89	0.402318
$349$	−1.86154e90	−0.999012	−0.499506	−	0.866311i	$-0.666485\pi$
$349$	−1.86154e90	−0.999012	−0.499506	+	0.866311i	$0.666485\pi$
$350$	4.41974e90	2.14280
$351$	−3.42509e90	−1.50062
$352$	6.28364e87	0.00248855
$353$	−4.65298e90	−1.66621	−0.833103	−	0.553118i	$-0.813438\pi$
$353$	−4.65298e90	−1.66621	−0.833103	+	0.553118i	$0.813438\pi$
$354$	−5.11282e89	−0.165594
$355$	6.96199e90	2.03999
$356$	6.40497e89	0.169841
$357$	5.23949e90	1.25767
$358$	1.30136e90	0.282847
$359$	−5.17585e90	−1.01889	−0.509446	−	0.860502i	$-0.670150\pi$
$359$	−5.17585e90	−1.01889	−0.509446	+	0.860502i	$0.670150\pi$
$360$	1.68796e90	0.301040
$361$	1.25134e90	0.202241
$362$	−3.91336e90	−0.573318
$363$	−5.51797e90	−0.732984
$364$	−7.36769e90	−0.887631
$365$	−1.01314e91	−1.10732
$366$	6.01661e90	0.596724
$367$	−1.43156e91	−1.28873	−0.644367	−	0.764716i	$-0.722879\pi$
$367$	−1.43156e91	−1.28873	−0.644367	+	0.764716i	$0.722879\pi$
$368$	3.27092e90	0.267345
$369$	−2.10052e90	−0.155916
$370$	7.42729e90	0.500806
$371$	−8.30216e90	−0.508648
$372$	−3.71894e90	−0.207083
$373$	5.23714e90	0.265113	0.132556	−	0.991175i	$-0.457681\pi$
$373$	5.23714e90	0.265113	0.132556	+	0.991175i	$0.457681\pi$
$374$	−2.92455e89	−0.0134623
$375$	4.47751e91	1.87468
$376$	−1.02708e91	−0.391235
$377$	4.43122e91	1.53605
$378$	−3.04791e91	−0.961709
$379$	1.52174e91	0.437167	0.218584	−	0.975818i	$-0.429856\pi$
$379$	1.52174e91	0.437167	0.218584	+	0.975818i	$0.429856\pi$
$380$	3.85763e91	1.00926
$381$	−1.58786e91	−0.378422
$382$	−2.30231e91	−0.499936
$383$	3.81971e91	0.755917	0.377958	−	0.925823i	$-0.376626\pi$
$383$	3.81971e91	0.755917	0.377958	+	0.925823i	$0.376626\pi$
$384$	−3.59198e90	−0.0648001
$385$	1.99844e90	0.0328727
$386$	−2.60908e91	−0.391415
$387$	−3.60174e91	−0.492916
$388$	3.39743e91	0.424252
$389$	4.20949e91	0.479754	0.239877	−	0.970803i	$-0.422893\pi$
$389$	4.20949e91	0.479754	0.239877	+	0.970803i	$0.422893\pi$
$390$	−1.28376e92	−1.33564
$391$	−1.52236e92	−1.44625
$392$	−2.48151e91	−0.215308
$393$	4.14385e91	0.328450
$394$	1.06254e92	0.769537
$395$	2.35099e92	1.55616
$396$	5.38026e89	0.00325555
$397$	−2.08665e92	−1.15448	−0.577240	−	0.816574i	$-0.695870\pi$
$397$	−2.08665e92	−1.15448	−0.577240	+	0.816574i	$0.695870\pi$
$398$	1.22437e91	0.0619532
$399$	−2.20287e92	−1.01965
$400$	1.41023e92	0.597256
$401$	−7.91681e91	−0.306849	−0.153425	−	0.988160i	$-0.549030\pi$
$401$	−7.91681e91	−0.306849	−0.153425	+	0.988160i	$0.549030\pi$
$402$	−1.52294e92	−0.540330
$403$	−2.43394e92	−0.790643
$404$	1.32897e92	0.395344
$405$	−2.18592e92	−0.595636
$406$	3.94324e92	0.984418
$407$	2.36739e90	0.00541588
$408$	1.67179e92	0.350547
$409$	6.32880e92	1.21659	0.608294	−	0.793712i	$-0.291854\pi$
$409$	6.32880e92	1.21659	0.608294	+	0.793712i	$0.291854\pi$
$410$	−2.48947e92	−0.438814
$411$	8.76753e92	1.41740
$412$	1.97612e92	0.293064
$413$	−2.97771e92	−0.405187
$414$	2.80067e92	0.349743
$415$	−1.33911e93	−1.53500
$416$	−2.35085e92	−0.247407
$417$	1.40348e93	1.35637
$418$	1.22959e91	0.0109145
$419$	1.41223e93	1.15162	0.575810	−	0.817584i	$-0.304687\pi$
$419$	1.41223e93	1.15162	0.575810	+	0.817584i	$0.304687\pi$
$420$	−1.14239e93	−0.855980
$421$	−3.41326e92	−0.235047	−0.117523	−	0.993070i	$-0.537496\pi$
$421$	−3.41326e92	−0.235047	−0.117523	+	0.993070i	$0.537496\pi$
$422$	1.51691e93	0.960211
$423$	−8.79422e92	−0.511817
$424$	−2.64902e92	−0.141774
$425$	−6.56354e93	−3.23096
$426$	−1.26852e93	−0.574454
$427$	3.50407e93	1.46010
$428$	1.51263e93	0.580067
$429$	−4.09188e91	−0.0144440
$430$	−4.26867e93	−1.38727
$431$	−1.79555e93	−0.537346	−0.268673	−	0.963231i	$-0.586585\pi$
$431$	−1.79555e93	−0.537346	−0.268673	+	0.963231i	$0.586585\pi$
$432$	−9.72514e92	−0.268054
$433$	3.29618e93	0.836933	0.418467	−	0.908232i	$-0.362568\pi$
$433$	3.29618e93	0.836933	0.418467	+	0.908232i	$0.362568\pi$
$434$	−2.16591e93	−0.506704
$435$	6.87076e93	1.48128
$436$	−3.87254e93	−0.769530
$437$	6.40058e93	1.17254
$438$	1.84600e93	0.311817
$439$	−1.11024e93	−0.172952	−0.0864762	−	0.996254i	$-0.527561\pi$
$439$	−1.11024e93	−0.172952	−0.0864762	+	0.996254i	$0.527561\pi$
$440$	6.37652e91	0.00916250
$441$	−2.12475e93	−0.281668
$442$	1.09414e94	1.33839
$443$	−3.60978e93	−0.407519	−0.203760	−	0.979021i	$-0.565316\pi$
$443$	−3.60978e93	−0.407519	−0.203760	+	0.979021i	$0.565316\pi$
$444$	−1.35330e93	−0.141025
$445$	6.49965e93	0.625330
$446$	8.54599e93	0.759232
$447$	−6.43448e93	−0.527954
$448$	−2.09197e93	−0.158557
$449$	4.55344e93	0.318856	0.159428	−	0.987210i	$-0.449035\pi$
$449$	4.55344e93	0.318856	0.159428	+	0.987210i	$0.449035\pi$
$450$	1.20748e94	0.781335
$451$	−7.93500e91	−0.00474548
$452$	−1.00333e94	−0.554661
$453$	1.05073e94	0.537036
$454$	−1.28621e94	−0.607896
$455$	−7.47660e94	−3.26813
$456$	−7.02883e93	−0.284205
$457$	−2.49400e94	−0.932979	−0.466490	−	0.884527i	$-0.654482\pi$
$457$	−2.49400e94	−0.932979	−0.466490	+	0.884527i	$0.654482\pi$
$458$	7.50988e93	0.259961
$459$	4.52631e94	1.45009
$460$	3.31927e94	0.984327
$461$	−9.77697e93	−0.268424	−0.134212	−	0.990953i	$-0.542850\pi$
$461$	−9.77697e93	−0.268424	−0.134212	+	0.990953i	$0.542850\pi$
$462$	−3.64127e92	−0.00925684
$463$	2.81645e93	0.0663097	0.0331548	−	0.999450i	$-0.489445\pi$
$463$	2.81645e93	0.0663097	0.0331548	+	0.999450i	$0.489445\pi$
$464$	1.25819e94	0.274384
$465$	−3.77391e94	−0.762450
$466$	3.69411e94	0.691528
$467$	1.02417e95	1.77674	0.888368	−	0.459131i	$-0.151839\pi$
$467$	1.02417e95	1.77674	0.888368	+	0.459131i	$0.151839\pi$
$468$	−2.01287e94	−0.323660
$469$	−8.86963e94	−1.32212
$470$	−1.04227e95	−1.44047
$471$	−4.75102e94	−0.608898
$472$	−9.50114e93	−0.112937
$473$	−1.36061e93	−0.0150024
$474$	−4.28365e94	−0.438210
$475$	2.75956e95	2.61949
$476$	9.73652e94	0.857743
$477$	−2.26817e94	−0.185470
$478$	1.08956e95	0.827108
$479$	1.99811e95	1.40834	0.704170	−	0.710031i	$-0.251319\pi$
$479$	1.99811e95	1.40834	0.704170	+	0.710031i	$0.251319\pi$
$480$	−3.64508e94	−0.238585
$481$	−8.85695e94	−0.538436
$482$	−7.19197e94	−0.406142
$483$	−1.89545e95	−0.994463
$484$	−1.02540e95	−0.499901
$485$	3.44765e95	1.56204
$486$	−1.40206e95	−0.590443
$487$	−2.84568e95	−1.11406	−0.557029	−	0.830493i	$-0.688059\pi$
$487$	−2.84568e95	−1.11406	−0.557029	+	0.830493i	$0.688059\pi$
$488$	1.11806e95	0.406971
$489$	3.62028e95	1.22540
$490$	−2.51819e95	−0.792734
$491$	−7.10643e94	−0.208094	−0.104047	−	0.994572i	$-0.533179\pi$
$491$	−7.10643e94	−0.208094	−0.104047	+	0.994572i	$0.533179\pi$
$492$	4.53596e94	0.123569
$493$	−5.85593e95	−1.48433
$494$	−4.60017e95	−1.08509
$495$	5.45979e93	0.0119865
$496$	−6.91088e94	−0.141232
$497$	−7.38784e95	−1.40561
$498$	2.43993e95	0.432251
$499$	3.63312e95	0.599391	0.299695	−	0.954035i	$-0.403115\pi$
$499$	3.63312e95	0.599391	0.299695	+	0.954035i	$0.403115\pi$
$500$	8.32054e95	1.27855
$501$	−3.91738e95	−0.560733
$502$	8.95361e95	1.19403
$503$	−3.07878e95	−0.382574	−0.191287	−	0.981534i	$-0.561266\pi$
$503$	−3.07878e95	−0.382574	−0.191287	+	0.981534i	$0.561266\pi$
$504$	−1.79121e95	−0.207426
$505$	1.34861e96	1.45560
$506$	1.05799e94	0.0106448
$507$	7.49302e95	0.702869
$508$	−2.95072e95	−0.258087
$509$	−1.29339e96	−1.05499	−0.527496	−	0.849557i	$-0.676869\pi$
$509$	−1.29339e96	−1.05499	−0.527496	+	0.849557i	$0.676869\pi$
$510$	1.69650e96	1.29067
$511$	1.07511e96	0.762975
$512$	−6.67496e94	−0.0441942
$513$	−1.90303e96	−1.17565
$514$	−1.24463e96	−0.717545
$515$	2.00534e96	1.07902
$516$	7.77777e95	0.390653
$517$	−3.32214e94	−0.0155777
$518$	−7.88160e95	−0.345071
$519$	7.03855e95	0.287768
$520$	−2.38560e96	−0.910917
$521$	1.18658e96	0.423210	0.211605	−	0.977355i	$-0.432131\pi$
$521$	1.18658e96	0.423210	0.211605	+	0.977355i	$0.432131\pi$
$522$	1.07731e96	0.358952
$523$	−3.82430e96	−1.19054	−0.595268	−	0.803527i	$-0.702954\pi$
$523$	−3.82430e96	−1.19054	−0.595268	+	0.803527i	$0.702954\pi$
$524$	7.70050e95	0.224005
$525$	−8.17206e96	−2.22165
$526$	1.14481e96	0.290896
$527$	3.21649e96	0.764021
$528$	−1.16184e94	−0.00258013
$529$	6.91442e95	0.143575
$530$	−2.68817e96	−0.521992
$531$	−8.13518e95	−0.147745
$532$	−4.09359e96	−0.695411
$533$	2.96866e96	0.471786
$534$	−1.18427e96	−0.176091
$535$	1.53499e97	2.13573
$536$	−2.83008e96	−0.368510
$537$	−2.40621e96	−0.293256
$538$	5.07042e96	0.578460
$539$	−8.02654e94	−0.00857289
$540$	−9.86889e96	−0.986938
$541$	1.33177e97	1.24717	0.623586	−	0.781754i	$-0.285675\pi$
$541$	1.33177e97	1.24717	0.623586	+	0.781754i	$0.285675\pi$
$542$	−4.75186e96	−0.416763
$543$	7.23577e96	0.594416
$544$	3.10668e96	0.239076
$545$	−3.92978e97	−2.83330
$546$	1.36228e97	0.920297
$547$	1.67497e97	1.06037	0.530183	−	0.847883i	$-0.322123\pi$
$547$	1.67497e97	1.06037	0.530183	+	0.847883i	$0.322123\pi$
$548$	1.62927e97	0.966679
$549$	9.57323e96	0.532403
$550$	4.56144e95	0.0237808
$551$	2.46205e97	1.20341
$552$	−6.04791e96	−0.277184
$553$	−2.49480e97	−1.07224
$554$	−1.98363e97	−0.799584
$555$	−1.37330e97	−0.519236
$556$	2.60808e97	0.925052
$557$	−4.68525e97	−1.55910	−0.779549	−	0.626342i	$-0.784552\pi$
$557$	−4.68525e97	−1.55910	−0.779549	+	0.626342i	$0.784552\pi$
$558$	−5.91732e96	−0.184761
$559$	5.09033e97	1.49151
$560$	−2.12289e97	−0.583785
$561$	5.40748e95	0.0139577
$562$	4.20007e97	1.01769
$563$	−6.32562e97	−1.43898	−0.719491	−	0.694502i	$-0.755625\pi$
$563$	−6.32562e97	−1.43898	−0.719491	+	0.694502i	$0.755625\pi$
$564$	1.89907e97	0.405632
$565$	−1.01816e98	−2.04218
$566$	4.03839e97	0.760721
$567$	2.31963e97	0.410411
$568$	−2.35728e97	−0.391782
$569$	−6.22645e97	−0.972198	−0.486099	−	0.873904i	$-0.661581\pi$
$569$	−6.22645e97	−0.972198	−0.486099	+	0.873904i	$0.661581\pi$
$570$	−7.13273e97	−1.04640
$571$	−1.75074e97	−0.241346	−0.120673	−	0.992692i	$-0.538505\pi$
$571$	−1.75074e97	−0.241346	−0.120673	+	0.992692i	$0.538505\pi$
$572$	−7.60392e95	−0.00985096
$573$	4.25695e97	0.518334
$574$	2.64175e97	0.302356
$575$	2.37444e98	2.55477
$576$	−5.71532e96	−0.0578152
$577$	1.26858e98	1.20664	0.603318	−	0.797500i	$-0.293845\pi$
$577$	1.26858e98	1.20664	0.603318	+	0.797500i	$0.293845\pi$
$578$	−6.55385e97	−0.586217
$579$	4.82416e97	0.405820
$580$	1.27679e98	1.01024
$581$	1.42102e98	1.05766
$582$	−6.28182e97	−0.439865
$583$	−8.56835e95	−0.00564499
$584$	3.43041e97	0.212662
$585$	−2.04263e98	−1.19167
$586$	−9.72248e97	−0.533841
$587$	−3.42133e97	−0.176824	−0.0884122	−	0.996084i	$-0.528179\pi$
$587$	−3.42133e97	−0.176824	−0.0884122	+	0.996084i	$0.528179\pi$
$588$	4.58829e97	0.223232
$589$	−1.35233e98	−0.619426
$590$	−9.64158e97	−0.415817
$591$	−1.96463e98	−0.797857
$592$	−2.51483e97	−0.0961805
$593$	−3.13381e98	−1.12884	−0.564418	−	0.825489i	$-0.690899\pi$
$593$	−3.13381e98	−1.12884	−0.564418	+	0.825489i	$0.690899\pi$
$594$	−3.14563e96	−0.0106731
$595$	9.88044e98	3.15809
$596$	−1.19572e98	−0.360069
$597$	−2.26385e97	−0.0642332
$598$	−3.95819e98	−1.05829
$599$	−3.97239e98	−1.00092	−0.500460	−	0.865760i	$-0.666836\pi$
$599$	−3.97239e98	−1.00092	−0.500460	+	0.865760i	$0.666836\pi$
$600$	−2.60750e98	−0.619235
$601$	3.97435e98	0.889657	0.444829	−	0.895616i	$-0.353265\pi$
$601$	3.97435e98	0.889657	0.444829	+	0.895616i	$0.353265\pi$
$602$	4.52977e98	0.955875
$603$	−2.42321e98	−0.482088
$604$	1.95256e98	0.366263
$605$	−1.04056e99	−1.84056
$606$	−2.45725e98	−0.409893
$607$	5.63124e98	0.885942	0.442971	−	0.896536i	$-0.353924\pi$
$607$	5.63124e98	0.885942	0.442971	+	0.896536i	$0.353924\pi$
$608$	−1.30616e98	−0.193830
$609$	−7.29103e98	−1.02065
$610$	1.13459e99	1.49841
$611$	1.24289e99	1.54871
$612$	2.66004e98	0.312762
$613$	−4.47432e98	−0.496455	−0.248228	−	0.968702i	$-0.579848\pi$
$613$	−4.47432e98	−0.496455	−0.248228	+	0.968702i	$0.579848\pi$
$614$	1.05510e99	1.10489
$615$	4.60301e98	0.454963
$616$	−6.76656e96	−0.00631324
$617$	−9.61698e98	−0.847063	−0.423531	−	0.905881i	$-0.639210\pi$
$617$	−9.61698e98	−0.847063	−0.423531	+	0.905881i	$0.639210\pi$
$618$	−3.65384e98	−0.303850
$619$	5.21001e98	0.409092	0.204546	−	0.978857i	$-0.434428\pi$
$619$	5.21001e98	0.409092	0.204546	+	0.978857i	$0.434428\pi$
$620$	−7.01304e98	−0.519997
$621$	−1.63745e99	−1.14661
$622$	7.65886e98	0.506530
$623$	−6.89721e98	−0.430872
$624$	4.34670e98	0.256512
$625$	4.15844e99	2.31841
$626$	4.93014e98	0.259699
$627$	−2.27350e97	−0.0113161
$628$	−8.82880e98	−0.415274
$629$	1.17046e99	0.520305
$630$	−1.81769e99	−0.763713
$631$	−2.51153e99	−0.997460	−0.498730	−	0.866757i	$-0.666200\pi$
$631$	−2.51153e99	−0.997460	−0.498730	+	0.866757i	$0.666200\pi$
$632$	−7.96028e98	−0.298863
$633$	−2.80475e99	−0.995548
$634$	−4.18351e97	−0.0140402
$635$	−2.99433e99	−0.950239
$636$	4.89801e98	0.146991
$637$	3.00291e99	0.852299
$638$	4.06967e97	0.0109251
$639$	−2.01838e99	−0.512533
$640$	−6.77363e98	−0.162717
$641$	−9.49005e98	−0.215679	−0.107840	−	0.994168i	$-0.534393\pi$
$641$	−9.49005e98	−0.215679	−0.107840	+	0.994168i	$0.534393\pi$
$642$	−2.79684e99	−0.601414
$643$	5.64108e99	1.14782	0.573909	−	0.818919i	$-0.305426\pi$
$643$	5.64108e99	1.14782	0.573909	+	0.818919i	$0.305426\pi$
$644$	−3.52230e99	−0.678232
$645$	7.89274e99	1.43833
$646$	6.07920e99	1.04856
$647$	−8.13337e99	−1.32791	−0.663955	−	0.747773i	$-0.731123\pi$
$647$	−8.13337e99	−1.32791	−0.663955	+	0.747773i	$0.731123\pi$
$648$	7.40136e98	0.114393
$649$	−3.07318e97	−0.00449678
$650$	−1.70654e100	−2.36424
$651$	4.00475e99	0.525352
$652$	6.72756e99	0.835734
$653$	8.00212e99	0.941427	0.470714	−	0.882286i	$-0.343996\pi$
$653$	8.00212e99	0.941427	0.470714	+	0.882286i	$0.343996\pi$
$654$	7.16029e99	0.797849
$655$	7.81433e99	0.824756
$656$	8.42916e98	0.0842749
$657$	2.93723e99	0.278206
$658$	1.10602e100	0.992529
$659$	4.60333e99	0.391417	0.195709	−	0.980662i	$-0.437299\pi$
$659$	4.60333e99	0.391417	0.195709	+	0.980662i	$0.437299\pi$
$660$	−1.17901e98	−0.00949969
$661$	8.71421e99	0.665390	0.332695	−	0.943034i	$-0.392042\pi$
$661$	8.71421e99	0.665390	0.332695	+	0.943034i	$0.392042\pi$
$662$	−1.76410e99	−0.127663
$663$	−2.02306e100	−1.38764
$664$	4.53411e99	0.294798
$665$	−4.15410e100	−2.56041
$666$	−2.15328e99	−0.125824
$667$	2.11845e100	1.17368
$668$	−7.27964e99	−0.382424
$669$	−1.58015e100	−0.787173
$670$	−2.87191e100	−1.35680
$671$	3.61642e98	0.0162043
$672$	3.86804e99	0.164392
$673$	2.40707e100	0.970406	0.485203	−	0.874402i	$-0.338746\pi$
$673$	2.40707e100	0.970406	0.485203	+	0.874402i	$0.338746\pi$
$674$	2.64268e100	1.01069
$675$	−7.05971e100	−2.56155
$676$	1.39242e100	0.479362
$677$	−8.57367e99	−0.280072	−0.140036	−	0.990146i	$-0.544722\pi$
$677$	−8.57367e99	−0.280072	−0.140036	+	0.990146i	$0.544722\pi$
$678$	1.85514e100	0.575073
$679$	−3.65853e100	−1.07629
$680$	3.15261e100	0.880245
$681$	2.37819e100	0.630267
$682$	−2.23535e98	−0.00562342
$683$	−4.03210e100	−0.962934	−0.481467	−	0.876464i	$-0.659896\pi$
$683$	−4.03210e100	−0.962934	−0.481467	+	0.876464i	$0.659896\pi$
$684$	−1.11838e100	−0.253570
$685$	1.65335e101	3.55918
$686$	−1.71578e100	−0.350716
$687$	−1.38857e100	−0.269528
$688$	1.44534e100	0.266428
$689$	3.20561e100	0.561214
$690$	−6.13730e100	−1.02055
$691$	−6.86618e100	−1.08454	−0.542269	−	0.840205i	$-0.682434\pi$
$691$	−6.86618e100	−1.08454	−0.542269	+	0.840205i	$0.682434\pi$
$692$	1.30797e100	0.196260
$693$	−5.79375e98	−0.00825904
$694$	−6.65760e100	−0.901688
$695$	2.64664e101	3.40591
$696$	−2.32639e100	−0.284482
$697$	−3.92313e100	−0.455900
$698$	6.39622e100	0.706408
$699$	−6.83038e100	−0.716977
$700$	−1.51861e101	−1.51519
$701$	−1.20468e101	−1.14257	−0.571285	−	0.820752i	$-0.693555\pi$
$701$	−1.20468e101	−1.14257	−0.571285	+	0.820752i	$0.693555\pi$
$702$	1.17685e101	1.06110
$703$	−4.92104e100	−0.421835
$704$	−2.15904e98	−0.00175967
$705$	1.92714e101	1.49348
$706$	1.59875e101	1.17819
$707$	−1.43110e101	−1.00295
$708$	1.75675e100	0.117093
$709$	1.96324e101	1.24461	0.622303	−	0.782776i	$-0.286197\pi$
$709$	1.96324e101	1.24461	0.622303	+	0.782776i	$0.286197\pi$
$710$	−2.39212e101	−1.44249
$711$	−6.81585e100	−0.390975
$712$	−2.20073e100	−0.120096
$713$	−1.16360e101	−0.604124
$714$	−1.80028e101	−0.889308
$715$	−7.71632e99	−0.0362698
$716$	−4.47145e100	−0.200003
$717$	−2.01459e101	−0.857546
$718$	1.77841e101	0.720466
$719$	−2.14600e101	−0.827474	−0.413737	−	0.910396i	$-0.635777\pi$
$719$	−2.14600e101	−0.827474	−0.413737	+	0.910396i	$0.635777\pi$
$720$	−5.79980e100	−0.212868
$721$	−2.12800e101	−0.743479
$722$	−4.29957e100	−0.143006
$723$	1.32979e101	0.421088
$724$	1.34462e101	0.405397
$725$	9.13352e101	2.62204
$726$	1.89596e101	0.518298
$727$	−2.73223e101	−0.711289	−0.355644	−	0.934621i	$-0.615739\pi$
$727$	−2.73223e101	−0.711289	−0.355644	+	0.934621i	$0.615739\pi$
$728$	2.53152e101	0.627650
$729$	3.96255e101	0.935723
$730$	3.48112e101	0.782991
$731$	−6.72695e101	−1.44129
$732$	−2.06729e101	−0.421947
$733$	−4.99877e101	−0.972013	−0.486007	−	0.873955i	$-0.661547\pi$
$733$	−4.99877e101	−0.972013	−0.486007	+	0.873955i	$0.661547\pi$
$734$	4.91879e101	0.911273
$735$	4.65611e101	0.821908
$736$	−1.12388e101	−0.189042
$737$	−9.15401e99	−0.0146729
$738$	7.21732e100	0.110249
$739$	−6.56244e101	−0.955406	−0.477703	−	0.878521i	$-0.658530\pi$
$739$	−6.56244e101	−0.955406	−0.477703	+	0.878521i	$0.658530\pi$
$740$	−2.55200e101	−0.354123
$741$	8.50569e101	1.12503
$742$	2.85260e101	0.359668
$743$	1.43734e102	1.72766	0.863830	−	0.503784i	$-0.168059\pi$
$743$	1.43734e102	1.72766	0.863830	+	0.503784i	$0.168059\pi$
$744$	1.27782e101	0.146430
$745$	−1.21339e102	−1.32572
$746$	−1.79947e101	−0.187463
$747$	3.88225e101	0.385658
$748$	1.00487e100	0.00951925
$749$	−1.62888e102	−1.47158
$750$	−1.53846e102	−1.32560
$751$	−1.15761e102	−0.951360	−0.475680	−	0.879618i	$-0.657798\pi$
$751$	−1.15761e102	−0.951360	−0.475680	+	0.879618i	$0.657798\pi$
$752$	3.52903e101	0.276645
$753$	−1.65552e102	−1.23797
$754$	−1.52256e102	−1.08615
$755$	1.98142e102	1.34853
$756$	1.04725e102	0.680031
$757$	1.51102e102	0.936196	0.468098	−	0.883677i	$-0.344939\pi$
$757$	1.51102e102	0.936196	0.468098	+	0.883677i	$0.344939\pi$
$758$	−5.22865e101	−0.309124
$759$	−1.95622e100	−0.0110366
$760$	−1.32547e102	−0.713655
$761$	−2.62214e102	−1.34741	−0.673705	−	0.739000i	$-0.735298\pi$
$761$	−2.62214e102	−1.34741	−0.673705	+	0.739000i	$0.735298\pi$
$762$	5.45585e101	0.267585
$763$	4.17016e102	1.95223
$764$	7.91067e101	0.353508
$765$	2.69936e102	1.15154
$766$	−1.31244e102	−0.534514
$767$	1.14975e102	0.447061
$768$	1.23419e101	0.0458206
$769$	−6.78375e101	−0.240483	−0.120242	−	0.992745i	$-0.538367\pi$
$769$	−6.78375e101	−0.240483	−0.120242	+	0.992745i	$0.538367\pi$
$770$	−6.86658e100	−0.0232445
$771$	2.30131e102	0.743951
$772$	8.96472e101	0.276772
$773$	1.18478e102	0.349353	0.174677	−	0.984626i	$-0.444112\pi$
$773$	1.18478e102	0.349353	0.174677	+	0.984626i	$0.444112\pi$
$774$	1.23755e102	0.348544
$775$	−5.01677e102	−1.34963
$776$	−1.16735e102	−0.299992
$777$	1.45730e102	0.357770
$778$	−1.44637e102	−0.339237
$779$	1.64943e102	0.369619
$780$	4.41096e102	0.944440
$781$	−7.62471e100	−0.0155995
$782$	5.23080e102	1.02265
$783$	−6.29860e102	−1.17680
$784$	8.52640e101	0.152246
$785$	−8.95931e102	−1.52898
$786$	−1.42382e102	−0.232249
$787$	1.29941e102	0.202601	0.101301	−	0.994856i	$-0.467700\pi$
$787$	1.29941e102	0.202601	0.101301	+	0.994856i	$0.467700\pi$
$788$	−3.65086e102	−0.544145
$789$	−2.11674e102	−0.301601
$790$	−8.07795e102	−1.10037
$791$	1.08043e103	1.40713
$792$	−1.84864e100	−0.00230202
$793$	−1.35298e103	−1.61100
$794$	7.16968e102	0.816341
$795$	4.97041e102	0.541202
$796$	−4.20691e101	−0.0438076
$797$	1.65316e103	1.64643	0.823217	−	0.567727i	$-0.192177\pi$
$797$	1.65316e103	1.64643	0.823217	+	0.567727i	$0.192177\pi$
$798$	7.56902e102	0.721003
$799$	−1.64250e103	−1.49656
$800$	−4.84551e102	−0.422323
$801$	−1.88434e102	−0.157110
$802$	2.72019e102	0.216975
$803$	1.10958e101	0.00846753
$804$	5.23280e102	0.382071
$805$	−3.57437e103	−2.49715
$806$	8.36295e102	0.559069
$807$	−9.37518e102	−0.599748
$808$	−4.56629e102	−0.279551
$809$	2.52855e102	0.148149	0.0740745	−	0.997253i	$-0.476400\pi$
$809$	2.52855e102	0.148149	0.0740745	+	0.997253i	$0.476400\pi$
$810$	7.51076e102	0.421178
$811$	2.54635e103	1.36671	0.683357	−	0.730084i	$-0.260519\pi$
$811$	2.54635e103	1.36671	0.683357	+	0.730084i	$0.260519\pi$
$812$	−1.35489e103	−0.696089
$813$	8.78616e102	0.432100
$814$	−8.13430e100	−0.00382960
$815$	6.82700e103	3.07705
$816$	−5.74424e102	−0.247874
$817$	2.82826e103	1.16852
$818$	−2.17456e103	−0.860258
$819$	2.16757e103	0.821098
$820$	8.55376e102	0.310288
$821$	−3.39236e103	−1.17847	−0.589237	−	0.807960i	$-0.700572\pi$
$821$	−3.39236e103	−1.17847	−0.589237	+	0.807960i	$0.700572\pi$
$822$	−3.01250e103	−1.00225
$823$	1.57208e103	0.500935	0.250467	−	0.968125i	$-0.419416\pi$
$823$	1.57208e103	0.500935	0.250467	+	0.968125i	$0.419416\pi$
$824$	−6.78991e102	−0.207228
$825$	−8.43408e101	−0.0246560
$826$	1.02313e103	0.286510
$827$	−4.52040e103	−1.21264	−0.606319	−	0.795222i	$-0.707354\pi$
$827$	−4.52040e103	−1.21264	−0.606319	+	0.795222i	$0.707354\pi$
$828$	−9.62302e102	−0.247306
$829$	−2.39429e103	−0.589511	−0.294755	−	0.955573i	$-0.595238\pi$
$829$	−2.39429e103	−0.589511	−0.294755	+	0.955573i	$0.595238\pi$
$830$	4.60113e103	1.08541
$831$	3.66772e103	0.829010
$832$	8.07746e102	0.174943
$833$	−3.96839e103	−0.823601
$834$	−4.82232e103	−0.959095
$835$	−7.38725e103	−1.40803
$836$	−4.22484e101	−0.00771769
$837$	3.45964e103	0.605727
$838$	−4.85240e103	−0.814318
$839$	−7.31868e103	−1.17729	−0.588644	−	0.808392i	$-0.700338\pi$
$839$	−7.31868e103	−1.17729	−0.588644	+	0.808392i	$0.700338\pi$
$840$	3.92521e103	0.605269
$841$	1.38399e103	0.204585
$842$	1.17279e103	0.166203
$843$	−7.76589e103	−1.05515
$844$	−5.21205e103	−0.678972
$845$	1.41301e104	1.76495
$846$	3.02167e103	0.361909
$847$	1.10421e104	1.26821
$848$	9.10195e102	0.100249
$849$	−7.46696e103	−0.788716
$850$	2.25522e104	2.28463
$851$	−4.23427e103	−0.411414
$852$	4.35859e103	0.406200
$853$	3.32008e103	0.296796	0.148398	−	0.988928i	$-0.452588\pi$
$853$	3.32008e103	0.296796	0.148398	+	0.988928i	$0.452588\pi$
$854$	−1.20399e104	−1.03245
$855$	−1.13491e104	−0.933610
$856$	−5.19735e103	−0.410169
$857$	1.77473e104	1.34374	0.671868	−	0.740671i	$-0.265492\pi$
$857$	1.77473e104	1.34374	0.671868	+	0.740671i	$0.265492\pi$
$858$	1.40596e102	0.0102135
$859$	4.47292e103	0.311770	0.155885	−	0.987775i	$-0.450177\pi$
$859$	4.47292e103	0.311770	0.155885	+	0.987775i	$0.450177\pi$
$860$	1.46670e104	0.980952
$861$	−4.88457e103	−0.313483
$862$	6.16946e103	0.379961
$863$	−2.77727e104	−1.64147	−0.820737	−	0.571306i	$-0.806437\pi$
$863$	−2.77727e104	−1.64147	−0.820737	+	0.571306i	$0.806437\pi$
$864$	3.34153e103	0.189543
$865$	1.32730e104	0.722602
$866$	−1.13256e104	−0.591801
$867$	1.21180e104	0.607790
$868$	7.44201e103	0.358294
$869$	−2.57478e102	−0.0118998
$870$	−2.36078e104	−1.04742
$871$	3.42472e104	1.45875
$872$	1.33059e104	0.544140
$873$	−9.99522e103	−0.392452
$874$	−2.19922e104	−0.829112
$875$	−8.96000e104	−3.24356
$876$	−6.34280e103	−0.220488
$877$	−3.68205e103	−0.122915	−0.0614574	−	0.998110i	$-0.519575\pi$
$877$	−3.68205e103	−0.122915	−0.0614574	+	0.998110i	$0.519575\pi$
$878$	3.81476e103	0.122296
$879$	1.79768e104	0.553487
$880$	−2.19096e102	−0.00647887
$881$	−1.37268e104	−0.389873	−0.194937	−	0.980816i	$-0.562450\pi$
$881$	−1.37268e104	−0.389873	−0.194937	+	0.980816i	$0.562450\pi$
$882$	7.30058e103	0.199169
$883$	4.13122e104	1.08261	0.541307	−	0.840825i	$-0.317930\pi$
$883$	4.13122e104	1.08261	0.541307	+	0.840825i	$0.317930\pi$
$884$	−3.75944e104	−0.946385
$885$	1.78272e104	0.431119
$886$	1.24031e104	0.288160
$887$	9.46061e103	0.211169	0.105585	−	0.994410i	$-0.466329\pi$
$887$	9.46061e103	0.211169	0.105585	+	0.994410i	$0.466329\pi$
$888$	4.64989e103	0.0997201
$889$	3.17749e104	0.654744
$890$	−2.23326e104	−0.442175
$891$	2.39400e102	0.00455476
$892$	−2.93638e104	−0.536858
$893$	6.90565e104	1.21333
$894$	2.21087e104	0.373320
$895$	−4.53754e104	−0.736382
$896$	7.18795e103	0.112117
$897$	7.31865e104	1.09723
$898$	−1.56455e104	−0.225465
$899$	−4.47591e104	−0.620030
$900$	−4.14889e104	−0.552488
$901$	−4.23626e104	−0.542316
$902$	2.72645e102	0.00335556
$903$	−8.37552e104	−0.991052
$904$	3.44740e104	0.392204
$905$	1.36450e105	1.49261
$906$	−3.61027e104	−0.379742
$907$	1.47913e105	1.49606	0.748030	−	0.663665i	$-0.231000\pi$
$907$	1.47913e105	1.49606	0.748030	+	0.663665i	$0.231000\pi$
$908$	4.41939e104	0.429847
$909$	−3.90981e104	−0.365711
$910$	2.56894e105	2.31092
$911$	−1.08909e105	−0.942239	−0.471120	−	0.882069i	$-0.656150\pi$
$911$	−1.08909e105	−0.942239	−0.471120	+	0.882069i	$0.656150\pi$
$912$	2.41509e104	0.200963
$913$	1.46658e103	0.0117379
$914$	8.56933e104	0.659716
$915$	−2.09785e105	−1.55355
$916$	−2.58037e104	−0.183820
$917$	−8.29231e104	−0.568282
$918$	−1.55523e105	−1.02537
$919$	−8.20150e104	−0.520227	−0.260113	−	0.965578i	$-0.583760\pi$
$919$	−8.20150e104	−0.520227	−0.260113	+	0.965578i	$0.583760\pi$
$920$	−1.14049e105	−0.696025
$921$	−1.95088e105	−1.14555
$922$	3.35934e104	0.189804
$923$	2.85257e105	1.55087
$924$	1.25113e103	0.00654558
$925$	−1.82557e105	−0.919110
$926$	−9.67725e103	−0.0468880
$927$	−5.81374e104	−0.271097
$928$	−4.32312e104	−0.194019
$929$	3.60099e104	0.155548	0.0777740	−	0.996971i	$-0.475219\pi$
$929$	3.60099e104	0.155548	0.0777740	+	0.996971i	$0.475219\pi$
$930$	1.29671e105	0.539134
$931$	1.66846e105	0.667731
$932$	−1.26929e105	−0.488984
$933$	−1.41612e105	−0.525171
$934$	−3.51902e105	−1.25634
$935$	1.01972e104	0.0350486
$936$	6.91619e104	0.228862
$937$	1.78381e105	0.568321	0.284160	−	0.958777i	$-0.408285\pi$
$937$	1.78381e105	0.568321	0.284160	+	0.958777i	$0.408285\pi$
$938$	3.04758e105	0.934877
$939$	−9.11580e104	−0.269256
$940$	3.58120e105	1.01857
$941$	−1.48657e105	−0.407149	−0.203575	−	0.979059i	$-0.565256\pi$
$941$	−1.48657e105	−0.407149	−0.203575	+	0.979059i	$0.565256\pi$
$942$	1.63244e105	0.430556
$943$	1.41924e105	0.360488
$944$	3.26457e104	0.0798582
$945$	1.06274e106	2.50378
$946$	4.67501e103	0.0106083
$947$	5.26769e105	1.15132	0.575660	−	0.817689i	$-0.304745\pi$
$947$	5.26769e105	1.15132	0.575660	+	0.817689i	$0.304745\pi$
$948$	1.47185e105	0.309861
$949$	−4.15118e105	−0.841824
$950$	−9.48176e105	−1.85226
$951$	7.73527e103	0.0145568
$952$	−3.34544e105	−0.606516
$953$	1.45719e105	0.254517	0.127259	−	0.991870i	$-0.459382\pi$
$953$	1.45719e105	0.254517	0.127259	+	0.991870i	$0.459382\pi$
$954$	7.79338e104	0.131147
$955$	8.02761e105	1.30157
$956$	−3.74371e105	−0.584854
$957$	−7.52479e103	−0.0113272
$958$	−6.86544e105	−0.995847
$959$	−1.75448e106	−2.45238
$960$	1.25244e105	0.168705
$961$	−5.24487e105	−0.680855
$962$	3.04322e105	0.380732
$963$	−4.45014e105	−0.536587
$964$	2.47114e105	0.287186
$965$	9.09724e105	1.01904
$966$	6.51271e105	0.703191
$967$	1.17983e106	1.22795	0.613975	−	0.789326i	$-0.289570\pi$
$967$	1.17983e106	1.22795	0.613975	+	0.789326i	$0.289570\pi$
$968$	3.52326e105	0.353483
$969$	−1.12404e106	−1.08714
$970$	−1.18460e106	−1.10453
$971$	−1.43187e105	−0.128712	−0.0643562	−	0.997927i	$-0.520499\pi$
$971$	−1.43187e105	−0.128712	−0.0643562	+	0.997927i	$0.520499\pi$
$972$	4.81743e105	0.417506
$973$	−2.80852e106	−2.34678
$974$	9.77768e105	0.787758
$975$	3.15538e106	2.45125
$976$	−3.84164e105	−0.287772
$977$	−2.06913e106	−1.49462	−0.747308	−	0.664477i	$-0.768654\pi$
$977$	−2.06913e106	−1.49462	−0.747308	+	0.664477i	$0.768654\pi$
$978$	−1.24392e106	−0.866489
$979$	−7.11835e103	−0.00478183
$980$	8.65244e105	0.560548
$981$	1.13930e106	0.711849
$982$	2.44175e105	0.147144
$983$	2.23867e106	1.30119	0.650594	−	0.759426i	$-0.274520\pi$
$983$	2.23867e106	1.30119	0.650594	+	0.759426i	$0.274520\pi$
$984$	−1.55855e105	−0.0873763
$985$	−3.70483e106	−2.00347
$986$	2.01208e106	1.04958
$987$	−2.04502e106	−1.02905
$988$	1.58061e106	0.767278
$989$	2.43355e106	1.13965
$990$	−1.87597e104	−0.00847571
$991$	2.93416e106	1.27900	0.639499	−	0.768792i	$-0.279142\pi$
$991$	2.93416e106	1.27900	0.639499	+	0.768792i	$0.279142\pi$
$992$	2.37456e105	0.0998663
$993$	3.26180e105	0.132361
$994$	2.53844e106	0.993918
$995$	−4.26909e105	−0.161293
$996$	−8.38353e105	−0.305647
$997$	−4.13322e106	−1.45415	−0.727076	−	0.686557i	$-0.759121\pi$
$997$	−4.13322e106	−1.45415	−0.727076	+	0.686557i	$0.759121\pi$
$998$	−1.24833e106	−0.423833
$999$	1.25894e106	0.412506

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2.72.a.b.1.3	✓	3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2.72.a.b.1.3	✓	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)

\(f(q)\)	\(=\)	\(q-3.43597e10 q^{2} +6.35309e16 q^{3} +1.18059e21 q^{4} +1.19804e25 q^{5} -2.18290e27 q^{6} -1.27132e30 q^{7} -4.05648e31 q^{8} -3.47329e33 q^{9} +O(q^{10})\)	\(q-3.43597e10 q^{2} +6.35309e16 q^{3} +1.18059e21 q^{4} +1.19804e25 q^{5} -2.18290e27 q^{6} -1.27132e30 q^{7} -4.05648e31 q^{8} -3.47329e33 q^{9} -4.11644e35 q^{10} -1.31209e35 q^{11} +7.50040e37 q^{12} +4.90880e39 q^{13} +4.36824e40 q^{14} +7.61127e41 q^{15} +1.39380e42 q^{16} -6.48706e43 q^{17} +1.19341e44 q^{18} +2.72740e45 q^{19} +1.41440e46 q^{20} -8.07683e46 q^{21} +4.50829e45 q^{22} +2.34677e48 q^{23} -2.57712e48 q^{24} +1.01179e50 q^{25} -1.68665e50 q^{26} -6.97744e50 q^{27} -1.50091e51 q^{28} +9.02709e51 q^{29} -2.61521e52 q^{30} -4.95831e52 q^{31} -4.78905e52 q^{32} -8.33579e51 q^{33} +2.22894e54 q^{34} -1.52310e55 q^{35} -4.10054e54 q^{36} -1.80430e55 q^{37} -9.37127e55 q^{38} +3.11861e56 q^{39} -4.85984e56 q^{40} +6.04763e56 q^{41} +2.77518e57 q^{42} +1.03698e58 q^{43} -1.54904e56 q^{44} -4.16115e58 q^{45} -8.06344e58 q^{46} +2.53196e59 q^{47} +8.85491e58 q^{48} +6.11739e59 q^{49} -3.47649e60 q^{50} -4.12129e60 q^{51} +5.79529e60 q^{52} +6.53033e60 q^{53} +2.39743e61 q^{54} -1.57193e60 q^{55} +5.15710e61 q^{56} +1.73274e62 q^{57} -3.10168e62 q^{58} +2.34221e62 q^{59} +8.98581e62 q^{60} -2.75624e63 q^{61} +1.70366e63 q^{62} +4.41568e63 q^{63} +1.64550e63 q^{64} +5.88096e64 q^{65} +2.86416e62 q^{66} +6.97669e64 q^{67} -7.65857e64 q^{68} +1.49092e65 q^{69} +5.23333e65 q^{70} +5.81114e65 q^{71} +1.40893e65 q^{72} -8.45661e65 q^{73} +6.19952e65 q^{74} +6.42799e66 q^{75} +3.21994e66 q^{76} +1.66809e65 q^{77} -1.07155e67 q^{78} +1.96236e67 q^{79} +1.66983e67 q^{80} -1.82458e67 q^{81} -2.07795e67 q^{82} -1.11774e68 q^{83} -9.53544e67 q^{84} -7.77178e68 q^{85} -3.56304e68 q^{86} +5.73499e68 q^{87} +5.32245e66 q^{88} +5.42522e68 q^{89} +1.42976e69 q^{90} -6.24068e69 q^{91} +2.77058e69 q^{92} -3.15006e69 q^{93} -8.69974e69 q^{94} +3.26754e70 q^{95} -3.04253e69 q^{96} +2.87774e70 q^{97} -2.10192e70 q^{98} +4.55726e68 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q - 103079215104 q^{2} + 23\!\cdots\!36 q^{3}+ \cdots - 45\!\cdots\!09 q^{9}+O(q^{10}) \) 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

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Groups

Database

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