LMFDB - Embedded newform 3.66.a.b.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3,66,Mod(1,3)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(3, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0]))

N = Newforms(chi, 66, names="a")

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

chi := DirichletCharacter("3.1");

S:= CuspForms(chi, 66);

N := Newforms(S);

Level:	$ N $	$=$	$ 3 $
Weight:	$ k $	$=$	$ 66 $
Character orbit:	$[\chi]$	$=$	3.a (trivial)

Newform invariants

comment: select newform

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

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

Self dual:	yes
Analytic conductor:	$80.2717069417$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	$\mathbb{Q}[x]/(x^{6} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 3 x^{5} + \cdots - 27\!\cdots\!48 $ x^6 - 3x^5 - 4253784014616993888x^4 - 329017052684987797861154944x^3 + 3760278921468113125234877358788007936x^2 + 22551593102849743113985540842573617614848*x - 272928737776547549611547193931962354302098378900635648
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	multiple of $ 2^{43}\cdot 3^{29}\cdot 5^{6}\cdot 7^{2}\cdot 11\cdot 13 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$-2.78112e8$ of defining polynomial
Character	$\chi$	$=$	3.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-6.33506e8 q^{2} +1.85302e15 q^{3} -3.64922e19 q^{4} -5.06462e22 q^{5} -1.17390e24 q^{6} -3.41514e27 q^{7} +4.64902e28 q^{8} +3.43368e30 q^{9} +O(q^{10})$	\(q-6.33506e8 q^{2} +1.85302e15 q^{3} -3.64922e19 q^{4} -5.06462e22 q^{5} -1.17390e24 q^{6} -3.41514e27 q^{7} +4.64902e28 q^{8} +3.43368e30 q^{9} +3.20846e31 q^{10} -1.72248e33 q^{11} -6.76207e34 q^{12} -1.67942e36 q^{13} +2.16351e36 q^{14} -9.38484e37 q^{15} +1.31687e39 q^{16} -1.71430e40 q^{17} -2.17526e39 q^{18} -6.76864e41 q^{19} +1.84819e42 q^{20} -6.32831e42 q^{21} +1.09120e42 q^{22} -1.74786e44 q^{23} +8.61473e43 q^{24} -1.45470e44 q^{25} +1.06392e45 q^{26} +6.36269e45 q^{27} +1.24626e47 q^{28} +4.57138e47 q^{29} +5.94535e46 q^{30} -2.29379e48 q^{31} -2.54943e48 q^{32} -3.19179e48 q^{33} +1.08602e49 q^{34} +1.72964e50 q^{35} -1.25303e50 q^{36} -9.53469e50 q^{37} +4.28798e50 q^{38} -3.11200e51 q^{39} -2.35455e51 q^{40} +1.14761e52 q^{41} +4.00902e51 q^{42} +7.37475e52 q^{43} +6.28570e52 q^{44} -1.73903e53 q^{45} +1.10728e53 q^{46} -3.76424e54 q^{47} +2.44019e54 q^{48} +3.12483e54 q^{49} +9.21558e52 q^{50} -3.17664e55 q^{51} +6.12856e55 q^{52} +6.87510e55 q^{53} -4.03080e54 q^{54} +8.72370e55 q^{55} -1.58770e56 q^{56} -1.25424e57 q^{57} -2.89600e56 q^{58} +1.49620e57 q^{59} +3.42473e57 q^{60} +3.03654e57 q^{61} +1.45313e57 q^{62} -1.17265e58 q^{63} -4.69689e58 q^{64} +8.50561e58 q^{65} +2.02202e57 q^{66} -2.20791e59 q^{67} +6.25586e59 q^{68} -3.23881e59 q^{69} -1.09573e59 q^{70} +2.29212e59 q^{71} +1.59633e59 q^{72} -4.99420e58 q^{73} +6.04028e59 q^{74} -2.69558e59 q^{75} +2.47002e61 q^{76} +5.88250e60 q^{77} +1.97147e60 q^{78} +1.27990e61 q^{79} -6.66945e61 q^{80} +1.17902e61 q^{81} -7.27019e60 q^{82} +4.41159e62 q^{83} +2.30934e62 q^{84} +8.68229e62 q^{85} -4.67194e61 q^{86} +8.47086e62 q^{87} -8.00785e61 q^{88} +1.08249e63 q^{89} +1.10169e62 q^{90} +5.73544e63 q^{91} +6.37830e63 q^{92} -4.25044e63 q^{93} +2.38467e63 q^{94} +3.42806e64 q^{95} -4.72415e63 q^{96} +2.77342e64 q^{97} -1.97960e63 q^{98} -5.91445e63 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 6210982962 q^{2} + 11\!\cdots\!46 q^{3}+ \cdots + 20\!\cdots\!86 q^{9}+O(q^{10}) $ 6 * q + 6210982962 * q^2 + 11118121133111046 * q^3 + 91340905060284656388 * q^4 + 35156143485265939841700 * q^5 + 11509076821200806793333042 * q^6 + 1317821413686135751883120304 * q^7 + 712695351135793704541979166216 * q^8 + 20602102921755074907947094535686 * q^9	$ 6 q + 6210982962 q^{2} + 11\!\cdots\!46 q^{3}+ \cdots - 79\!\cdots\!56 q^{99}+O(q^{100}) $ 6 * q + 6210982962 * q^2 + 11118121133111046 * q^3 + 91340905060284656388 * q^4 + 35156143485265939841700 * q^5 + 11509076821200806793333042 * q^6 + 1317821413686135751883120304 * q^7 + 712695351135793704541979166216 * q^8 + 20602102921755074907947094535686 * q^9 + 1279335362952214656095633710080300 * q^10 - 2320891225483098403783749293998776 * q^11 + 169256541144706753221065102926210308 * q^12 + 961121104514647333696741144147524948 * q^13 - 23129299274714313374806876102877367408 * q^14 + 65145043640369911498096047700293569700 * q^15 + 3823746510407049616170834753394080518160 * q^16 - 13299388459605389867520707035083919491732 * q^17 + 21326551704731864898382187093091507830322 * q^18 + 560292177581177184743091103452788118819192 * q^19 + 2639207549045807126411266673763877251826200 * q^20 + 2441949684861683354803792504764566234879664 * q^21 + 109087634208372169902244649477327815818480216 * q^22 + 47867967315720390505184778564365196445371792 * q^23 + 1320638874155477584526460333544399643536603656 * q^24 + 5903161610990991425391100671552625540789976250 * q^25 - 12767069733763684064339316615714552428734293828 * q^26 + 38176112646815654150848972575231205385341297926 * q^27 + 188981295845031762805361197391664671598468484128 * q^28 + 184598319743070439951214664118917344915749962804 * q^29 + 2370634255862551351967264008295295716324912832300 * q^30 + 2623293635847269610518889821610813093244853580096 * q^31 + 54517802865386487937006688151855327070440233101344 * q^32 - 4300658296949271697408611055488031957639099346616 * q^33 - 197051985794439999405618245255004158938931162716284 * q^34 - 336946198056174264271289046874497082169398437573600 * q^35 + 313635787836373904323815807955150893399463818977028 * q^36 - 1968820149934868134141337613116275247510383189922076 * q^37 - 4694460210295937878277310645733397353377543187928088 * q^38 + 1780976810597221813831295709299147451849422023229268 * q^39 + 49157095865813933882755882516506487928569967968330800 * q^40 + 44721887514455538638767198455359242350295739355243516 * q^41 - 42859058510041866039547467439355390841668392234198128 * q^42 + 153471498107711152104975153786874048016259113736389640 * q^43 + 587913931391616274066657207301553410768002198418789424 * q^44 + 120715081069239676913401645732104593549750878306817700 * q^45 - 849756306074338863410215581822356060828605711616030544 * q^46 - 2381436220471011081110439407418227465375144570579750880 * q^47 + 7085479480836039087453859606939812767013947556749932560 * q^48 - 13393548707851784006635575377379702474705118021474562730 * q^49 + 8605967224979103186898364333260236908007021440152308750 * q^50 - 24644035315031974302945230554182833693819016149372478612 * q^51 + 28103125715176726198206798610702185135717107604823332408 * q^52 + 96360078764216635005363901635422818697091613178374171332 * q^53 + 39518530867460791914301257749994379976512907662225322802 * q^54 + 618818415407556251266374500995172486288026360694877294000 * q^55 - 1594813238548124991376317569708337784666756662353002031040 * q^56 + 1038232716713682180976880962449952357714831981771155332472 * q^57 - 6219453968745032502669888624143069517040566250894307781156 * q^58 - 7164713795718274697330180132380143319550103232198323750552 * q^59 + 4890504870952065939781074525505374307433603429398482034200 * q^60 + 4054291215081390738422899746523994767920509085300201674100 * q^61 + 34958707902560547237040840127848348482406693907763612852288 * q^62 + 4524982066209090105617255500931244831346320008742959861424 * q^63 + 253886263593501163190345542000578846999323347305576212553792 * q^64 - 97713589375076675190034327138723287340652596444477353717000 * q^65 + 202141588542198348857919279578170075461005987681230613677656 * q^66 + 144969667137236336673901245696979200934490405700749088000408 * q^67 - 2043740729154231542349040029441864841610331954777068147532216 * q^68 + 88700309835329950515541486518405473374907183046958848669072 * q^69 - 376744368214432254685629568745965379661331246625643952048800 * q^70 + 4588679866778477404065022934148807666177872634340922809064112 * q^71 + 2447170495992665754108483599319590630800125228272471322930696 * q^72 + 5295912209896035983548777676613107350643482423356854790725052 * q^73 + 9350247807486544549899934039998290071104428513885721798684012 * q^74 + 10938677643221464887252782466723953018644303552582609158776250 * q^75 + 49431355703188799046581662321370260954206584827526057026382928 * q^76 - 1828833584476997625702724578991793773647028588398159948752832 * q^77 - 23657637969143405241553634968093771501075977806653249252737348 * q^78 + 54854215934838989987009222002160957436114851061876043050015840 * q^79 + 467229112107152547456622091810828686257369551958519790980194400 * q^80 + 70741107466431499029125237168475111994069269553655046654581766 * q^81 + 508922387706347567665108833107375226127873394210791088866943028 * q^82 + 1256260453192702935091990356349904699687077869271636880116177656 * q^83 + 350186156516226392013489515258489267145665356490052568052079648 * q^84 + 1852861842448226107460158067921550442047822098825611523802078600 * q^85 + 3831728770512664300176489776078486686399726517973532920621402264 * q^86 + 342064413312036915623899374372475723529966510246438451216922164 * q^87 + 9887117998185871649768434211230976034878006221151840213514086496 * q^88 + 6405745009095237591902398822994073231956083842634829017742480412 * q^89 + 4392833136497068463530245328708128567870257643882088544379264300 * q^90 + 15865450468547895312707699659652371514673487967941777300259476896 * q^91 + 29446826967437370900765953556333974961331800074484795273728913504 * q^92 + 4861016068511540147024173987086576965408216747184752296570556736 * q^93 + 56000185796626083903421554209308857253984887888617668932197528928 * q^94 + 72344957899327813087872537810796747182935722022569380946809723600 * q^95 + 101022589361405908280345556707156044958833243651227160537953974304 * q^96 + 129176222791613802297195096968916495723771832056570573627879422028 * q^97 - 31866926727825199330491058509226158803414878017058965243757311198 * q^98 - 7969206649600176331526748122851560060012392538244305510328720056 * 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 $

$2$	−6.33506e8	−0.104298	−0.0521490	−	0.998639i	$-0.516607\pi$
$2$	−6.33506e8	−0.104298	−0.0521490	+	0.998639i	$0.516607\pi$
$3$	1.85302e15	0.577350
$3$	1.85302e15	0.577350
$4$	−3.64922e19	−0.989122
$5$	−5.06462e22	−0.972796	−0.486398	−	0.873737i	$-0.661689\pi$
$5$	−5.06462e22	−0.972796	−0.486398	+	0.873737i	$0.661689\pi$
$6$	−1.17390e24	−0.0602164
$7$	−3.41514e27	−1.16875	−0.584375	−	0.811484i	$-0.698660\pi$
$7$	−3.41514e27	−1.16875	−0.584375	+	0.811484i	$0.698660\pi$
$8$	4.64902e28	0.207461
$9$	3.43368e30	0.333333
$10$	3.20846e31	0.101461
$11$	−1.72248e33	−0.245975	−0.122988	−	0.992408i	$-0.539248\pi$
$11$	−1.72248e33	−0.245975	−0.122988	+	0.992408i	$0.539248\pi$
$12$	−6.76207e34	−0.571070
$13$	−1.67942e36	−1.05196	−0.525981	−	0.850496i	$-0.676302\pi$
$13$	−1.67942e36	−1.05196	−0.525981	+	0.850496i	$0.676302\pi$
$14$	2.16351e36	0.121898
$15$	−9.38484e37	−0.561644
$16$	1.31687e39	0.967484
$17$	−1.71430e40	−1.75589	−0.877946	−	0.478760i	$-0.841087\pi$
$17$	−1.71430e40	−1.75589	−0.877946	+	0.478760i	$0.841087\pi$
$18$	−2.17526e39	−0.0347660
$19$	−6.76864e41	−1.86642	−0.933211	−	0.359330i	$-0.883005\pi$
$19$	−6.76864e41	−1.86642	−0.933211	+	0.359330i	$0.883005\pi$
$20$	1.84819e42	0.962213
$21$	−6.32831e42	−0.674778
$22$	1.09120e42	0.0256547
$23$	−1.74786e44	−0.969060	−0.484530	−	0.874775i	$-0.661009\pi$
$23$	−1.74786e44	−0.969060	−0.484530	+	0.874775i	$0.661009\pi$
$24$	8.61473e43	0.119778
$25$	−1.45470e44	−0.0536688
$26$	1.06392e45	0.109717
$27$	6.36269e45	0.192450
$28$	1.24626e47	1.15604
$29$	4.57138e47	1.35554	0.677770	−	0.735274i	$-0.262946\pi$
$29$	4.57138e47	1.35554	0.677770	+	0.735274i	$0.262946\pi$
$30$	5.94535e46	0.0585783
$31$	−2.29379e48	−0.778572	−0.389286	−	0.921117i	$-0.627278\pi$
$31$	−2.29379e48	−0.778572	−0.389286	+	0.921117i	$0.627278\pi$
$32$	−2.54943e48	−0.308368
$33$	−3.19179e48	−0.142014
$34$	1.08602e49	0.183136
$35$	1.72964e50	1.13695
$36$	−1.25303e50	−0.329707
$37$	−9.53469e50	−1.02979	−0.514897	−	0.857252i	$-0.672170\pi$
$37$	−9.53469e50	−1.02979	−0.514897	+	0.857252i	$0.672170\pi$
$38$	4.28798e50	0.194664
$39$	−3.11200e51	−0.607350
$40$	−2.35455e51	−0.201817
$41$	1.14761e52	0.440880	0.220440	−	0.975401i	$-0.429251\pi$
$41$	1.14761e52	0.440880	0.220440	+	0.975401i	$0.429251\pi$
$42$	4.00902e51	0.0703780
$43$	7.37475e52	0.602590	0.301295	−	0.953531i	$-0.402581\pi$
$43$	7.37475e52	0.602590	0.301295	+	0.953531i	$0.402581\pi$
$44$	6.28570e52	0.243300
$45$	−1.73903e53	−0.324265
$46$	1.10728e53	0.101071
$47$	−3.76424e54	−1.70804	−0.854018	−	0.520243i	$-0.825841\pi$
$47$	−3.76424e54	−1.70804	−0.854018	+	0.520243i	$0.825841\pi$
$48$	2.44019e54	0.558577
$49$	3.12483e54	0.365977
$50$	9.21558e52	0.00559754
$51$	−3.17664e55	−1.01376
$52$	6.12856e55	1.04052
$53$	6.87510e55	0.628511	0.314256	−	0.949338i	$-0.398245\pi$
$53$	6.87510e55	0.628511	0.314256	+	0.949338i	$0.398245\pi$
$54$	−4.03080e54	−0.0200721
$55$	8.72370e55	0.239284
$56$	−1.58770e56	−0.242470
$57$	−1.25424e57	−1.07758
$58$	−2.89600e56	−0.141380
$59$	1.49620e57	0.419083	0.209542	−	0.977800i	$-0.432803\pi$
$59$	1.49620e57	0.419083	0.209542	+	0.977800i	$0.432803\pi$
$60$	3.42473e57	0.555534
$61$	3.03654e57	0.287845	0.143923	−	0.989589i	$-0.454028\pi$
$61$	3.03654e57	0.287845	0.143923	+	0.989589i	$0.454028\pi$
$62$	1.45313e57	0.0812035
$63$	−1.17265e58	−0.389583
$64$	−4.69689e58	−0.935322
$65$	8.50561e58	1.02334
$66$	2.02202e57	0.0148118
$67$	−2.20791e59	−0.992088	−0.496044	−	0.868297i	$-0.665215\pi$
$67$	−2.20791e59	−0.992088	−0.496044	+	0.868297i	$0.665215\pi$
$68$	6.25586e59	1.73679
$69$	−3.23881e59	−0.559487
$70$	−1.09573e59	−0.118582
$71$	2.29212e59	0.156438	0.0782188	−	0.996936i	$-0.475077\pi$
$71$	2.29212e59	0.156438	0.0782188	+	0.996936i	$0.475077\pi$
$72$	1.59633e59	0.0691538
$73$	−4.99420e58	−0.0138189	−0.00690944	−	0.999976i	$-0.502199\pi$
$73$	−4.99420e58	−0.0138189	−0.00690944	+	0.999976i	$0.502199\pi$
$74$	6.04028e59	0.107405
$75$	−2.69558e59	−0.0309857
$76$	2.47002e61	1.84612
$77$	5.88250e60	0.287484
$78$	1.97147e60	0.0633454
$79$	1.27990e61	0.271829	0.135915	−	0.990721i	$-0.456603\pi$
$79$	1.27990e61	0.271829	0.135915	+	0.990721i	$0.456603\pi$
$80$	−6.66945e61	−0.941164
$81$	1.17902e61	0.111111
$82$	−7.27019e60	−0.0459828
$83$	4.41159e62	1.88173	0.940864	−	0.338784i	$-0.110015\pi$
$83$	4.41159e62	1.88173	0.940864	+	0.338784i	$0.110015\pi$
$84$	2.30934e62	0.667438
$85$	8.68229e62	1.70812
$86$	−4.67194e61	−0.0628489
$87$	8.47086e62	0.782622
$88$	−8.00785e61	−0.0510304
$89$	1.08249e63	0.477802	0.238901	−	0.971044i	$-0.423213\pi$
$89$	1.08249e63	0.477802	0.238901	+	0.971044i	$0.423213\pi$
$90$	1.10169e62	0.0338202
$91$	5.73544e63	1.22948
$92$	6.37830e63	0.958519
$93$	−4.25044e63	−0.449509
$94$	2.38467e63	0.178145
$95$	3.42806e64	1.81565
$96$	−4.72415e63	−0.178036
$97$	2.77342e64	0.746335	0.373167	−	0.927764i	$-0.378272\pi$
$97$	2.77342e64	0.746335	0.373167	+	0.927764i	$0.378272\pi$
$98$	−1.97960e63	−0.0381706
$99$	−5.91445e63	−0.0819918
$100$	5.30850e63	0.0530850
$101$	−5.39622e64	−0.390522	−0.195261	−	0.980751i	$-0.562555\pi$
$101$	−5.39622e64	−0.390522	−0.195261	+	0.980751i	$0.562555\pi$
$102$	2.01242e64	0.105734
$103$	−2.18065e65	−0.834404	−0.417202	−	0.908814i	$-0.636989\pi$
$103$	−2.18065e65	−0.834404	−0.417202	+	0.908814i	$0.636989\pi$
$104$	−7.80765e64	−0.218241
$105$	3.20505e65	0.656421
$106$	−4.35541e64	−0.0655524
$107$	−1.14479e66	−1.26985	−0.634927	−	0.772572i	$-0.718970\pi$
$107$	−1.14479e66	−1.26985	−0.634927	+	0.772572i	$0.718970\pi$
$108$	−2.32188e65	−0.190357
$109$	−7.38757e65	−0.448890	−0.224445	−	0.974487i	$-0.572057\pi$
$109$	−7.38757e65	−0.448890	−0.224445	+	0.974487i	$0.572057\pi$
$110$	−5.52652e64	−0.0249568
$111$	−1.76680e66	−0.594552
$112$	−4.49729e66	−1.13075
$113$	−4.52673e66	−0.852580	−0.426290	−	0.904587i	$-0.640180\pi$
$113$	−4.52673e66	−0.852580	−0.426290	+	0.904587i	$0.640180\pi$
$114$	7.94570e65	0.112389
$115$	8.85222e66	0.942698
$116$	−1.66820e67	−1.34079
$117$	−5.76659e66	−0.350654
$118$	−9.47854e65	−0.0437095
$119$	5.85458e67	2.05220
$120$	−4.36303e66	−0.116519
$121$	−4.60701e67	−0.939496
$122$	−1.92366e66	−0.0300216
$123$	2.12655e67	0.254542
$124$	8.37054e67	0.770103
$125$	1.44644e68	1.02500
$126$	7.42880e66	0.0406327
$127$	1.85460e68	0.784568	0.392284	−	0.919844i	$-0.371685\pi$
$127$	1.85460e68	0.784568	0.392284	+	0.919844i	$0.371685\pi$
$128$	1.23813e68	0.405920
$129$	1.36656e68	0.347906
$130$	−5.38835e67	−0.106733
$131$	−1.00556e69	−1.55271	−0.776354	−	0.630297i	$-0.782933\pi$
$131$	−1.00556e69	−1.55271	−0.776354	+	0.630297i	$0.782933\pi$
$132$	1.16475e68	0.140469
$133$	2.31158e69	2.18138
$134$	1.39872e68	0.103473
$135$	−3.22246e68	−0.187215
$136$	−7.96984e68	−0.364280
$137$	2.66582e69	0.960311	0.480156	−	0.877183i	$-0.340580\pi$
$137$	2.66582e69	0.960311	0.480156	+	0.877183i	$0.340580\pi$
$138$	2.05181e68	0.0583534
$139$	−7.82958e69	−1.76099	−0.880496	−	0.474053i	$-0.842791\pi$
$139$	−7.82958e69	−1.76099	−0.880496	+	0.474053i	$0.842791\pi$
$140$	−6.31181e69	−1.12459
$141$	−6.97522e69	−0.986135
$142$	−1.45207e68	−0.0163161
$143$	2.89276e69	0.258757
$144$	4.52172e69	0.322495
$145$	−2.31523e70	−1.31866
$146$	3.16385e67	0.00144128
$147$	5.79037e69	0.211297
$148$	3.47942e70	1.01859
$149$	−3.09690e70	−0.728406	−0.364203	−	0.931319i	$-0.618659\pi$
$149$	−3.09690e70	−0.728406	−0.364203	+	0.931319i	$0.618659\pi$
$150$	1.70767e68	0.00323174
$151$	−3.71839e69	−0.0567028	−0.0283514	−	0.999598i	$-0.509026\pi$
$151$	−3.71839e69	−0.0567028	−0.0283514	+	0.999598i	$0.509026\pi$
$152$	−3.14676e70	−0.387210
$153$	−5.88638e70	−0.585297
$154$	−3.72660e69	−0.0299840
$155$	1.16172e71	0.757392
$156$	1.13563e71	0.600744
$157$	3.68140e71	1.58225	0.791123	−	0.611658i	$-0.209497\pi$
$157$	3.68140e71	1.58225	0.791123	+	0.611658i	$0.209497\pi$
$158$	−8.10826e69	−0.0283512
$159$	1.27397e71	0.362871
$160$	1.29119e71	0.299979
$161$	5.96916e71	1.13259
$162$	−7.46915e69	−0.0115887
$163$	−8.60396e71	−1.09295	−0.546476	−	0.837475i	$-0.684031\pi$
$163$	−8.60396e71	−1.09295	−0.546476	+	0.837475i	$0.684031\pi$
$164$	−4.18789e71	−0.436084
$165$	1.61652e71	0.138151
$166$	−2.79477e71	−0.196260
$167$	1.26005e72	0.727950	0.363975	−	0.931409i	$-0.381419\pi$
$167$	1.26005e72	0.727950	0.363975	+	0.931409i	$0.381419\pi$
$168$	−2.94205e71	−0.139990
$169$	2.71751e71	0.106623
$170$	−5.50028e71	−0.178154
$171$	−2.32414e72	−0.622140
$172$	−2.69120e72	−0.596035
$173$	−3.48350e72	−0.639024	−0.319512	−	0.947582i	$-0.603519\pi$
$173$	−3.48350e72	−0.639024	−0.319512	+	0.947582i	$0.603519\pi$
$174$	−5.36634e71	−0.0816258
$175$	4.96798e71	0.0627254
$176$	−2.26828e72	−0.237977
$177$	2.77250e72	0.241958
$178$	−6.85763e71	−0.0498338
$179$	−2.60827e73	−1.57990	−0.789950	−	0.613172i	$-0.789893\pi$
$179$	−2.60827e73	−1.57990	−0.789950	+	0.613172i	$0.789893\pi$
$180$	6.34610e72	0.320738
$181$	−1.37130e71	−0.00578866	−0.00289433	−	0.999996i	$-0.500921\pi$
$181$	−1.37130e71	−0.00578866	−0.00289433	+	0.999996i	$0.500921\pi$
$182$	−3.63343e72	−0.128232
$183$	5.62676e72	0.166187
$184$	−8.12582e72	−0.201043
$185$	4.82896e73	1.00178
$186$	2.69268e72	0.0468828
$187$	2.95285e73	0.431906
$188$	1.37365e74	1.68946
$189$	−2.17294e73	−0.224926
$190$	−2.17170e73	−0.189368
$191$	−3.24991e73	−0.238939	−0.119469	−	0.992838i	$-0.538119\pi$
$191$	−3.24991e73	−0.238939	−0.119469	+	0.992838i	$0.538119\pi$
$192$	−8.70343e73	−0.540008
$193$	3.26291e74	1.70999	0.854994	−	0.518639i	$-0.173561\pi$
$193$	3.26291e74	1.70999	0.854994	+	0.518639i	$0.173561\pi$
$194$	−1.75698e73	−0.0778412
$195$	1.57611e74	0.590828
$196$	−1.14032e74	−0.361995
$197$	−9.18908e73	−0.247241	−0.123620	−	0.992330i	$-0.539450\pi$
$197$	−9.18908e73	−0.247241	−0.123620	+	0.992330i	$0.539450\pi$
$198$	3.74684e72	0.00855158
$199$	−1.66802e74	−0.323204	−0.161602	−	0.986856i	$-0.551666\pi$
$199$	−1.66802e74	−0.323204	−0.161602	+	0.986856i	$0.551666\pi$
$200$	−6.76291e72	−0.0111342
$201$	−4.09130e74	−0.572782
$202$	3.41854e73	0.0407306
$203$	−1.56119e75	−1.58429
$204$	1.15922e75	1.00274
$205$	−5.81222e74	−0.428886
$206$	1.38146e74	0.0870266
$207$	−6.00158e74	−0.323020
$208$	−2.21158e75	−1.01776
$209$	1.16589e75	0.459094
$210$	−2.03042e74	−0.0684634
$211$	9.04013e74	0.261213	0.130607	−	0.991434i	$-0.458308\pi$
$211$	9.04013e74	0.261213	0.130607	+	0.991434i	$0.458308\pi$
$212$	−2.50887e75	−0.621674
$213$	4.24734e74	0.0903193
$214$	7.25232e74	0.132443
$215$	−3.73503e75	−0.586197
$216$	2.95803e74	0.0399259
$217$	7.83361e75	0.909956
$218$	4.68007e74	0.0468183
$219$	−9.25435e73	−0.00797834
$220$	−3.18347e75	−0.236681
$221$	2.87903e76	1.84713
$222$	1.11928e75	0.0620106
$223$	2.46556e76	1.18034	0.590171	−	0.807278i	$-0.299060\pi$
$223$	2.46556e76	1.18034	0.590171	+	0.807278i	$0.299060\pi$
$224$	8.70666e75	0.360405
$225$	−4.99497e74	−0.0178896
$226$	2.86771e75	0.0889223
$227$	−7.08377e76	−1.90294	−0.951468	−	0.307749i	$-0.900424\pi$
$227$	−7.08377e76	−1.90294	−0.951468	+	0.307749i	$0.900424\pi$
$228$	4.57701e76	1.06586
$229$	−5.24688e76	−1.05986	−0.529930	−	0.848042i	$-0.677782\pi$
$229$	−5.24688e76	−1.05986	−0.529930	+	0.848042i	$0.677782\pi$
$230$	−5.60793e75	−0.0983214
$231$	1.09004e76	0.165979
$232$	2.12525e76	0.281222
$233$	−7.56731e76	−0.870711	−0.435355	−	0.900259i	$-0.643377\pi$
$233$	−7.56731e76	−0.870711	−0.435355	+	0.900259i	$0.643377\pi$
$234$	3.65317e75	0.0365725
$235$	1.90644e77	1.66157
$236$	−5.45997e76	−0.414525
$237$	2.37168e76	0.156941
$238$	−3.70891e76	−0.214040
$239$	−2.98369e77	−1.50252	−0.751262	−	0.660004i	$-0.770555\pi$
$239$	−2.98369e77	−1.50252	−0.751262	+	0.660004i	$0.770555\pi$
$240$	−1.23586e77	−0.543381
$241$	−3.79288e77	−1.45685	−0.728426	−	0.685124i	$-0.759748\pi$
$241$	−3.79288e77	−1.45685	−0.728426	+	0.685124i	$0.759748\pi$
$242$	2.91857e76	0.0979875
$243$	2.18475e76	0.0641500
$244$	−1.10810e77	−0.284714
$245$	−1.58261e77	−0.356020
$246$	−1.34718e76	−0.0265482
$247$	1.13674e78	1.96340
$248$	−1.06639e77	−0.161524
$249$	8.17476e77	1.08642
$250$	−9.16330e76	−0.106906
$251$	−3.66831e77	−0.375899	−0.187949	−	0.982179i	$-0.560184\pi$
$251$	−3.66831e77	−0.375899	−0.187949	+	0.982179i	$0.560184\pi$
$252$	4.27925e77	0.385345
$253$	3.01065e77	0.238365
$254$	−1.17490e77	−0.0818288
$255$	1.60885e78	0.986186
$256$	1.65441e78	0.892985
$257$	−3.04946e78	−1.45010	−0.725048	−	0.688699i	$-0.758182\pi$
$257$	−3.04946e78	−1.45010	−0.725048	+	0.688699i	$0.758182\pi$
$258$	−8.65721e76	−0.0362858
$259$	3.25623e78	1.20357
$260$	−3.10388e78	−1.01221
$261$	1.56967e78	0.451847
$262$	6.37026e77	0.161944
$263$	7.04372e77	0.158212	0.0791061	−	0.996866i	$-0.474793\pi$
$263$	7.04372e77	0.158212	0.0791061	+	0.996866i	$0.474793\pi$
$264$	−1.48387e77	−0.0294624
$265$	−3.48197e78	−0.611413
$266$	−1.46440e78	−0.227513
$267$	2.00587e78	0.275859
$268$	8.05714e78	0.981296
$269$	−1.47891e79	−1.59586	−0.797929	−	0.602752i	$-0.794071\pi$
$269$	−1.47891e79	−1.59586	−0.797929	+	0.602752i	$0.794071\pi$
$270$	2.04145e77	0.0195261
$271$	−6.57944e78	−0.558068	−0.279034	−	0.960281i	$-0.590014\pi$
$271$	−6.57944e78	−0.558068	−0.279034	+	0.960281i	$0.590014\pi$
$272$	−2.25752e79	−1.69880
$273$	1.06279e79	0.709841
$274$	−1.68881e78	−0.100158
$275$	2.50568e77	0.0132012
$276$	1.18191e79	0.553401
$277$	−7.13841e78	−0.297173	−0.148586	−	0.988899i	$-0.547472\pi$
$277$	−7.13841e78	−0.297173	−0.148586	+	0.988899i	$0.547472\pi$
$278$	4.96009e78	0.183668
$279$	−7.87616e78	−0.259524
$280$	8.04112e78	0.235874
$281$	−6.10493e79	−1.59487	−0.797435	−	0.603405i	$-0.793810\pi$
$281$	−6.10493e79	−1.59487	−0.797435	+	0.603405i	$0.793810\pi$
$282$	4.41884e78	0.102852
$283$	7.10142e79	1.47328	0.736642	−	0.676283i	$-0.236411\pi$
$283$	7.10142e79	1.47328	0.736642	+	0.676283i	$0.236411\pi$
$284$	−8.36444e78	−0.154736
$285$	6.35226e79	1.04826
$286$	−1.83258e78	−0.0269878
$287$	−3.91925e79	−0.515278
$288$	−8.75394e78	−0.102789
$289$	1.98565e80	2.08316
$290$	1.46671e79	0.137534
$291$	5.13920e79	0.430897
$292$	1.82249e78	0.0136686
$293$	−8.09868e79	−0.543521	−0.271761	−	0.962365i	$-0.587606\pi$
$293$	−8.09868e79	−0.543521	−0.271761	+	0.962365i	$0.587606\pi$
$294$	−3.66823e78	−0.0220378
$295$	−7.57770e79	−0.407682
$296$	−4.43270e79	−0.213643
$297$	−1.09596e79	−0.0473380
$298$	1.96191e79	0.0759713
$299$	2.93538e80	1.01941
$300$	9.83676e78	0.0306486
$301$	−2.51858e80	−0.704278
$302$	2.35562e78	0.00591398
$303$	−9.99931e79	−0.225468
$304$	−8.91343e80	−1.80573
$305$	−1.53789e80	−0.280014
$306$	3.72905e79	0.0610453
$307$	4.65784e80	0.685784	0.342892	−	0.939375i	$-0.388593\pi$
$307$	4.65784e80	0.685784	0.342892	+	0.939375i	$0.388593\pi$
$308$	−2.14665e80	−0.284357
$309$	−4.04079e80	−0.481743
$310$	−7.35955e79	−0.0789944
$311$	−2.78996e80	−0.269703	−0.134851	−	0.990866i	$-0.543056\pi$
$311$	−2.78996e80	−0.269703	−0.134851	+	0.990866i	$0.543056\pi$
$312$	−1.44677e80	−0.126002
$313$	8.76271e80	0.687777	0.343889	−	0.939010i	$-0.388256\pi$
$313$	8.76271e80	0.687777	0.343889	+	0.939010i	$0.388256\pi$
$314$	−2.33218e80	−0.165025
$315$	5.93902e80	0.378985
$316$	−4.67064e80	−0.268872
$317$	−8.80133e80	−0.457217	−0.228608	−	0.973518i	$-0.573418\pi$
$317$	−8.80133e80	−0.457217	−0.228608	+	0.973518i	$0.573418\pi$
$318$	−8.07067e79	−0.0378467
$319$	−7.87411e80	−0.333430
$320$	2.37880e81	0.909877
$321$	−2.12132e81	−0.733150
$322$	−3.78150e80	−0.118127
$323$	1.16035e82	3.27723
$324$	−4.30249e80	−0.109902
$325$	2.44304e80	0.0564575
$326$	5.45066e80	0.113993
$327$	−1.36893e81	−0.259167
$328$	5.33528e80	0.0914655
$329$	1.28554e82	1.99627
$330$	−1.02407e80	−0.0144088
$331$	−1.05526e82	−1.34571	−0.672855	−	0.739774i	$-0.734932\pi$
$331$	−1.05526e82	−1.34571	−0.672855	+	0.739774i	$0.734932\pi$
$332$	−1.60988e82	−1.86126
$333$	−3.27391e81	−0.343265
$334$	−7.98247e80	−0.0759237
$335$	1.11822e82	0.965099
$336$	−8.33358e81	−0.652837
$337$	1.37663e82	0.979142	0.489571	−	0.871963i	$-0.337153\pi$
$337$	1.37663e82	0.979142	0.489571	+	0.871963i	$0.337153\pi$
$338$	−1.72156e80	−0.0111206
$339$	−8.38812e81	−0.492237
$340$	−3.16836e82	−1.68954
$341$	3.95101e81	0.191510
$342$	1.47236e81	0.0648880
$343$	1.84878e82	0.741015
$344$	3.42854e81	0.125014
$345$	1.64033e82	0.544267
$346$	2.20681e81	0.0666489
$347$	−2.05270e82	−0.564440	−0.282220	−	0.959350i	$-0.591071\pi$
$347$	−2.05270e82	−0.564440	−0.282220	+	0.959350i	$0.591071\pi$
$348$	−3.09120e82	−0.774108
$349$	−7.04780e82	−1.60778	−0.803891	−	0.594777i	$-0.797240\pi$
$349$	−7.04780e82	−1.60778	−0.803891	+	0.594777i	$0.797240\pi$
$350$	−3.14725e80	−0.00654213
$351$	−1.06856e82	−0.202450
$352$	4.39134e81	0.0758509
$353$	6.31956e82	0.995426	0.497713	−	0.867342i	$-0.334173\pi$
$353$	6.31956e82	0.995426	0.497713	+	0.867342i	$0.334173\pi$
$354$	−1.75639e81	−0.0252357
$355$	−1.16087e82	−0.152182
$356$	−3.95024e82	−0.472605
$357$	1.08487e83	1.18484
$358$	1.65236e82	0.164780
$359$	1.44070e83	1.31222	0.656108	−	0.754667i	$-0.272202\pi$
$359$	1.44070e83	1.31222	0.656108	+	0.754667i	$0.272202\pi$
$360$	−8.08479e81	−0.0672725
$361$	3.26628e83	2.48353
$362$	8.68725e79	0.000603745 0
$363$	−8.53689e82	−0.542418
$364$	−2.09299e83	−1.21611
$365$	2.52937e81	0.0134429
$366$	−3.56459e81	−0.0173330
$367$	9.98083e82	0.444140	0.222070	−	0.975031i	$-0.428719\pi$
$367$	9.98083e82	0.444140	0.222070	+	0.975031i	$0.428719\pi$
$368$	−2.30170e83	−0.937550
$369$	3.94054e82	0.146960
$370$	−3.05917e82	−0.104484
$371$	−2.34794e83	−0.734573
$372$	1.55108e83	0.444619
$373$	3.39344e83	0.891462	0.445731	−	0.895167i	$-0.352944\pi$
$373$	3.39344e83	0.891462	0.445731	+	0.895167i	$0.352944\pi$
$374$	−1.87065e82	−0.0450469
$375$	2.68029e83	0.591787
$376$	−1.75000e83	−0.354351
$377$	−7.67726e83	−1.42598
$378$	1.37657e82	0.0234593
$379$	1.60152e82	0.0250471	0.0125235	−	0.999922i	$-0.496014\pi$
$379$	1.60152e82	0.0250471	0.0125235	+	0.999922i	$0.496014\pi$
$380$	−1.25097e84	−1.79590
$381$	3.43662e83	0.452970
$382$	2.05884e82	0.0249208
$383$	−3.38980e83	−0.376889	−0.188445	−	0.982084i	$-0.560345\pi$
$383$	−3.38980e83	−0.376889	−0.188445	+	0.982084i	$0.560345\pi$
$384$	2.29427e83	0.234358
$385$	−2.97926e83	−0.279663
$386$	−2.06707e83	−0.178348
$387$	2.53225e83	0.200863
$388$	−1.01208e84	−0.738216
$389$	1.23910e84	0.831277	0.415638	−	0.909530i	$-0.363558\pi$
$389$	1.23910e84	0.831277	0.415638	+	0.909530i	$0.363558\pi$
$390$	−9.98473e82	−0.0616221
$391$	2.99635e84	1.70157
$392$	1.45274e83	0.0759260
$393$	−1.86332e84	−0.896456
$394$	5.82134e82	0.0257867
$395$	−6.48222e83	−0.264434
$396$	2.15831e83	0.0810999
$397$	1.88177e84	0.651441	0.325720	−	0.945466i	$-0.394393\pi$
$397$	1.88177e84	0.651441	0.325720	+	0.945466i	$0.394393\pi$
$398$	1.05670e83	0.0337095
$399$	4.28341e84	1.25942
$400$	−1.91565e83	−0.0519237
$401$	−1.86689e84	−0.466580	−0.233290	−	0.972407i	$-0.574949\pi$
$401$	−1.86689e84	−0.466580	−0.233290	+	0.972407i	$0.574949\pi$
$402$	2.59186e83	0.0597400
$403$	3.85224e84	0.819028
$404$	1.96920e84	0.386273
$405$	−5.97128e83	−0.108088
$406$	9.89022e83	0.165238
$407$	1.64233e84	0.253304
$408$	−1.47683e84	−0.210317
$409$	−1.20190e85	−1.58074	−0.790372	−	0.612627i	$-0.790113\pi$
$409$	−1.20190e85	−1.58074	−0.790372	+	0.612627i	$0.790113\pi$
$410$	3.68208e83	0.0447319
$411$	4.93981e84	0.554436
$412$	7.95767e84	0.825327
$413$	−5.10974e84	−0.489804
$414$	3.80204e83	0.0336903
$415$	−2.23430e85	−1.83054
$416$	4.28156e84	0.324391
$417$	−1.45084e85	−1.01671
$418$	−7.38595e83	−0.0478825
$419$	1.41332e85	0.847782	0.423891	−	0.905713i	$-0.360664\pi$
$419$	1.41332e85	0.847782	0.423891	+	0.905713i	$0.360664\pi$
$420$	−1.16959e85	−0.649281
$421$	−1.95139e84	−0.100271	−0.0501355	−	0.998742i	$-0.515965\pi$
$421$	−1.95139e84	−0.100271	−0.0501355	+	0.998742i	$0.515965\pi$
$422$	−5.72698e83	−0.0272440
$423$	−1.29252e85	−0.569345
$424$	3.19625e84	0.130392
$425$	2.49379e84	0.0942366
$426$	−2.69072e83	−0.00942011
$427$	−1.03702e85	−0.336419
$428$	4.17759e85	1.25604
$429$	5.36035e84	0.149393
$430$	2.36616e84	0.0611392
$431$	−3.61529e84	−0.0866227	−0.0433113	−	0.999062i	$-0.513791\pi$
$431$	−3.61529e84	−0.0866227	−0.0433113	+	0.999062i	$0.513791\pi$
$432$	8.37884e84	0.186192
$433$	−3.37434e85	−0.695556	−0.347778	−	0.937577i	$-0.613064\pi$
$433$	−3.37434e85	−0.695556	−0.347778	+	0.937577i	$0.613064\pi$
$434$	−4.96264e84	−0.0949066
$435$	−4.29017e85	−0.761331
$436$	2.69588e85	0.444007
$437$	1.18306e86	1.80867
$438$	5.86269e82	0.000832124 0
$439$	2.67258e85	0.352235	0.176118	−	0.984369i	$-0.443646\pi$
$439$	2.67258e85	0.352235	0.176118	+	0.984369i	$0.443646\pi$
$440$	4.05567e84	0.0496421
$441$	1.07297e85	0.121992
$442$	−1.82388e85	−0.192652
$443$	9.24002e85	0.906885	0.453442	−	0.891286i	$-0.350196\pi$
$443$	9.24002e85	0.906885	0.453442	+	0.891286i	$0.350196\pi$
$444$	6.44743e85	0.588085
$445$	−5.48239e85	−0.464804
$446$	−1.56195e85	−0.123107
$447$	−5.73862e85	−0.420546
$448$	1.60405e86	1.09316
$449$	−2.11660e86	−1.34163	−0.670814	−	0.741626i	$-0.734055\pi$
$449$	−2.11660e86	−1.34163	−0.670814	+	0.741626i	$0.734055\pi$
$450$	3.16434e83	0.00186585
$451$	−1.97674e85	−0.108446
$452$	1.65190e86	0.843305
$453$	−6.89025e84	−0.0327374
$454$	4.48761e85	0.198472
$455$	−2.90478e86	−1.19603
$456$	−5.83101e85	−0.223556
$457$	−3.17556e86	−1.13382	−0.566909	−	0.823781i	$-0.691861\pi$
$457$	−3.17556e86	−1.13382	−0.566909	+	0.823781i	$0.691861\pi$
$458$	3.32393e85	0.110541
$459$	−1.09076e86	−0.337922
$460$	−3.23037e86	−0.932443
$461$	−5.11325e86	−1.37536	−0.687680	−	0.726013i	$-0.741371\pi$
$461$	−5.11325e86	−1.37536	−0.687680	+	0.726013i	$0.741371\pi$
$462$	−6.90546e84	−0.0173113
$463$	9.44616e85	0.220736	0.110368	−	0.993891i	$-0.464797\pi$
$463$	9.44616e85	0.220736	0.110368	+	0.993891i	$0.464797\pi$
$464$	6.01992e86	1.31146
$465$	2.15269e86	0.437280
$466$	4.79393e85	0.0908133
$467$	−3.16859e86	−0.559844	−0.279922	−	0.960023i	$-0.590309\pi$
$467$	−3.16859e86	−0.559844	−0.279922	+	0.960023i	$0.590309\pi$
$468$	2.10435e86	0.346839
$469$	7.54031e86	1.15950
$470$	−1.20774e86	−0.173298
$471$	6.82170e86	0.913510
$472$	6.95589e85	0.0869436
$473$	−1.27028e86	−0.148222
$474$	−1.50248e85	−0.0163686
$475$	9.84632e85	0.100169
$476$	−2.13646e87	−2.02987
$477$	2.36069e86	0.209504
$478$	1.89018e86	0.156710
$479$	2.11230e86	0.163626	0.0818130	−	0.996648i	$-0.473929\pi$
$479$	2.11230e86	0.163626	0.0818130	+	0.996648i	$0.473929\pi$
$480$	2.39260e86	0.173193
$481$	1.60127e87	1.08330
$482$	2.40281e86	0.151947
$483$	1.10610e87	0.653901
$484$	1.68120e87	0.929276
$485$	−1.40463e87	−0.726031
$486$	−1.38405e85	−0.00669072
$487$	2.39813e87	1.08438	0.542189	−	0.840256i	$-0.317596\pi$
$487$	2.39813e87	1.08438	0.542189	+	0.840256i	$0.317596\pi$
$488$	1.41169e86	0.0597167
$489$	−1.59433e87	−0.631016
$490$	1.00259e86	0.0371322
$491$	3.70537e87	1.28435	0.642174	−	0.766559i	$-0.278033\pi$
$491$	3.70537e87	1.28435	0.642174	+	0.766559i	$0.278033\pi$
$492$	−7.76024e86	−0.251773
$493$	−7.83674e87	−2.38018
$494$	−7.20130e86	−0.204779
$495$	2.99544e86	0.0797613
$496$	−3.02063e87	−0.753256
$497$	−7.82790e86	−0.182836
$498$	−5.17876e86	−0.113311
$499$	1.08158e87	0.221713	0.110856	−	0.993836i	$-0.464641\pi$
$499$	1.08158e87	0.221713	0.110856	+	0.993836i	$0.464641\pi$
$500$	−5.27838e87	−1.01385
$501$	2.33489e87	0.420282
$502$	2.32390e86	0.0392054
$503$	−4.05092e87	−0.640611	−0.320305	−	0.947314i	$-0.603786\pi$
$503$	−4.05092e87	−0.640611	−0.320305	+	0.947314i	$0.603786\pi$
$504$	−5.45167e86	−0.0808235
$505$	2.73298e87	0.379898
$506$	−1.90726e86	−0.0248610
$507$	5.03559e86	0.0615591
$508$	−6.76785e87	−0.776033
$509$	1.50416e88	1.61796	0.808978	−	0.587839i	$-0.200021\pi$
$509$	1.50416e88	1.61796	0.808978	+	0.587839i	$0.200021\pi$
$510$	−1.01921e87	−0.102857
$511$	1.70559e86	0.0161508
$512$	−5.61595e87	−0.499057
$513$	−4.30668e87	−0.359193
$514$	1.93185e87	0.151242
$515$	1.10442e88	0.811705
$516$	−4.98685e87	−0.344121
$517$	6.48383e87	0.420135
$518$	−2.06284e87	−0.125530
$519$	−6.45499e87	−0.368941
$520$	3.95428e87	0.212304
$521$	1.38304e88	0.697606	0.348803	−	0.937196i	$-0.386588\pi$
$521$	1.38304e88	0.697606	0.348803	+	0.937196i	$0.386588\pi$
$522$	−9.94394e86	−0.0471267
$523$	−4.67207e87	−0.208068	−0.104034	−	0.994574i	$-0.533175\pi$
$523$	−4.67207e87	−0.208068	−0.104034	+	0.994574i	$0.533175\pi$
$524$	3.66950e88	1.53582
$525$	9.20577e86	0.0362145
$526$	−4.46224e86	−0.0165012
$527$	3.93226e88	1.36709
$528$	−4.20318e87	−0.137396
$529$	−1.98191e87	−0.0609222
$530$	2.20585e87	0.0637691
$531$	5.13749e87	0.139694
$532$	−8.43547e88	−2.15765
$533$	−1.92732e88	−0.463789
$534$	−1.27073e87	−0.0287716
$535$	5.79793e88	1.23531
$536$	−1.02646e88	−0.205820
$537$	−4.83318e88	−0.912155
$538$	9.36901e87	0.166445
$539$	−5.38245e87	−0.0900213
$540$	1.17594e88	0.185178
$541$	−9.13037e88	−1.35387	−0.676935	−	0.736043i	$-0.736692\pi$
$541$	−9.13037e88	−1.35387	−0.676935	+	0.736043i	$0.736692\pi$
$542$	4.16811e87	0.0582053
$543$	−2.54104e86	−0.00334209
$544$	4.37050e88	0.541461
$545$	3.74152e88	0.436679
$546$	−6.73283e87	−0.0740349
$547$	1.10854e88	0.114859	0.0574293	−	0.998350i	$-0.481710\pi$
$547$	1.10854e88	0.114859	0.0574293	+	0.998350i	$0.481710\pi$
$548$	−9.72814e88	−0.949865
$549$	1.04265e88	0.0959483
$550$	−1.58737e86	−0.00137686
$551$	−3.09421e89	−2.53001
$552$	−1.50573e88	−0.116072
$553$	−4.37104e88	−0.317701
$554$	4.52222e87	0.0309945
$555$	8.94816e88	0.578378
$556$	2.85718e89	1.74184
$557$	1.93356e89	1.11189	0.555947	−	0.831217i	$-0.312356\pi$
$557$	1.93356e89	1.11189	0.555947	+	0.831217i	$0.312356\pi$
$558$	4.98959e87	0.0270678
$559$	−1.23853e89	−0.633902
$560$	2.27771e89	1.09999
$561$	5.47170e88	0.249361
$562$	3.86751e88	0.166342
$563$	−2.78081e89	−1.12888	−0.564441	−	0.825474i	$-0.690908\pi$
$563$	−2.78081e89	−1.12888	−0.564441	+	0.825474i	$0.690908\pi$
$564$	2.54541e89	0.975408
$565$	2.29261e89	0.829386
$566$	−4.49879e88	−0.153660
$567$	−4.02651e88	−0.129861
$568$	1.06561e88	0.0324547
$569$	2.58196e89	0.742678	0.371339	−	0.928497i	$-0.378899\pi$
$569$	2.58196e89	0.742678	0.371339	+	0.928497i	$0.378899\pi$
$570$	−4.02420e88	−0.109332
$571$	−1.12405e89	−0.288478	−0.144239	−	0.989543i	$-0.546073\pi$
$571$	−1.12405e89	−0.288478	−0.144239	+	0.989543i	$0.546073\pi$
$572$	−1.05563e89	−0.255942
$573$	−6.02215e88	−0.137951
$574$	2.48287e88	0.0537424
$575$	2.54260e88	0.0520083
$576$	−1.61276e89	−0.311774
$577$	−2.83679e89	−0.518339	−0.259170	−	0.965832i	$-0.583449\pi$
$577$	−2.83679e89	−0.518339	−0.259170	+	0.965832i	$0.583449\pi$
$578$	−1.25792e89	−0.217269
$579$	6.04624e89	0.987261
$580$	8.44877e89	1.30432
$581$	−1.50662e90	−2.19927
$582$	−3.25571e88	−0.0449416
$583$	−1.18422e89	−0.154598
$584$	−2.32181e87	−0.00286688
$585$	2.92056e89	0.341115
$586$	5.13056e88	0.0566881
$587$	−1.64147e90	−1.71591	−0.857954	−	0.513726i	$-0.828265\pi$
$587$	−1.64147e90	−1.71591	−0.857954	+	0.513726i	$0.828265\pi$
$588$	−2.11303e89	−0.208998
$589$	1.55259e90	1.45314
$590$	4.80052e88	0.0425204
$591$	−1.70276e89	−0.142744
$592$	−1.25560e90	−0.996310
$593$	1.03473e90	0.777233	0.388616	−	0.921400i	$-0.372953\pi$
$593$	1.03473e90	0.777233	0.388616	+	0.921400i	$0.372953\pi$
$594$	6.94297e87	0.00493726
$595$	−2.96512e90	−1.99637
$596$	1.13013e90	0.720483
$597$	−3.09088e89	−0.186602
$598$	−1.85958e89	−0.106323
$599$	5.14760e89	0.278762	0.139381	−	0.990239i	$-0.455489\pi$
$599$	5.14760e89	0.278762	0.139381	+	0.990239i	$0.455489\pi$
$600$	−1.25318e88	−0.00642833
$601$	−7.27152e89	−0.353350	−0.176675	−	0.984269i	$-0.556534\pi$
$601$	−7.27152e89	−0.353350	−0.176675	+	0.984269i	$0.556534\pi$
$602$	1.59553e89	0.0734547
$603$	−7.58126e89	−0.330696
$604$	1.35692e89	0.0560860
$605$	2.33328e90	0.913938
$606$	6.33462e88	0.0235158
$607$	4.94266e90	1.73911	0.869557	−	0.493832i	$-0.164404\pi$
$607$	4.94266e90	1.73911	0.869557	+	0.493832i	$0.164404\pi$
$608$	1.72562e90	0.575544
$609$	−2.89291e90	−0.914689
$610$	9.74262e88	0.0292049
$611$	6.32174e90	1.79679
$612$	2.14807e90	0.578930
$613$	−3.76570e90	−0.962454	−0.481227	−	0.876596i	$-0.659809\pi$
$613$	−3.76570e90	−0.962454	−0.481227	+	0.876596i	$0.659809\pi$
$614$	−2.95077e89	−0.0715259
$615$	−1.07702e90	−0.247617
$616$	2.73479e89	0.0596418
$617$	1.01694e90	0.210390	0.105195	−	0.994452i	$-0.466453\pi$
$617$	1.01694e90	0.210390	0.105195	+	0.994452i	$0.466453\pi$
$618$	2.55986e89	0.0502448
$619$	6.42970e90	1.19741	0.598707	−	0.800968i	$-0.295681\pi$
$619$	6.42970e90	1.19741	0.598707	+	0.800968i	$0.295681\pi$
$620$	−4.23936e90	−0.749153
$621$	−1.11211e90	−0.186496
$622$	1.76746e89	0.0281294
$623$	−3.69685e90	−0.558431
$624$	−4.09810e90	−0.587602
$625$	−6.93138e90	−0.943451
$626$	−5.55123e89	−0.0717337
$627$	2.16041e90	0.265058
$628$	−1.34342e91	−1.56503
$629$	1.63454e91	1.80821
$630$	−3.76240e89	−0.0395273
$631$	−1.49436e90	−0.149108	−0.0745540	−	0.997217i	$-0.523753\pi$
$631$	−1.49436e90	−0.149108	−0.0745540	+	0.997217i	$0.523753\pi$
$632$	5.95030e89	0.0563941
$633$	1.67516e90	0.150812
$634$	5.57569e89	0.0476868
$635$	−9.39286e90	−0.763224
$636$	−4.64899e90	−0.358924
$637$	−5.24789e90	−0.384993
$638$	4.98829e89	0.0347760
$639$	7.87042e89	0.0521459
$640$	−6.27063e90	−0.394877
$641$	1.33247e91	0.797577	0.398789	−	0.917043i	$-0.369431\pi$
$641$	1.33247e91	0.797577	0.398789	+	0.917043i	$0.369431\pi$
$642$	1.34387e90	0.0764660
$643$	1.45707e91	0.788179	0.394090	−	0.919072i	$-0.371060\pi$
$643$	1.45707e91	0.788179	0.394090	+	0.919072i	$0.371060\pi$
$644$	−2.17828e91	−1.12027
$645$	−6.92108e90	−0.338441
$646$	−7.35089e90	−0.341809
$647$	−3.37127e91	−1.49075	−0.745374	−	0.666646i	$-0.767729\pi$
$647$	−3.37127e91	−1.49075	−0.745374	+	0.666646i	$0.767729\pi$
$648$	5.48128e89	0.0230513
$649$	−2.57718e90	−0.103084
$650$	−1.54768e89	−0.00588840
$651$	1.45158e91	0.525364
$652$	3.13977e91	1.08106
$653$	5.59108e91	1.83154	0.915772	−	0.401699i	$-0.131580\pi$
$653$	5.59108e91	1.83154	0.915772	+	0.401699i	$0.131580\pi$
$654$	8.67226e89	0.0270306
$655$	5.09276e91	1.51047
$656$	1.51126e91	0.426544
$657$	−1.71485e89	−0.00460629
$658$	−8.14397e90	−0.208207
$659$	−2.31789e91	−0.564050	−0.282025	−	0.959407i	$-0.591006\pi$
$659$	−2.31789e91	−0.564050	−0.282025	+	0.959407i	$0.591006\pi$
$660$	−5.89903e90	−0.136648
$661$	2.90003e91	0.639521	0.319761	−	0.947498i	$-0.396397\pi$
$661$	2.90003e91	0.639521	0.319761	+	0.947498i	$0.396397\pi$
$662$	6.68516e90	0.140355
$663$	5.33491e91	1.06644
$664$	2.05096e91	0.390386
$665$	−1.17073e92	−2.12204
$666$	2.07404e90	0.0358018
$667$	−7.99011e91	−1.31360
$668$	−4.59818e91	−0.720031
$669$	4.56873e91	0.681470
$670$	−7.08400e90	−0.100658
$671$	−5.23037e90	−0.0708028
$672$	1.61336e91	0.208080
$673$	1.14120e92	1.40241	0.701203	−	0.712961i	$-0.252647\pi$
$673$	1.14120e92	1.40241	0.701203	+	0.712961i	$0.252647\pi$
$674$	−8.72104e90	−0.102123
$675$	−9.25577e89	−0.0103286
$676$	−9.91677e90	−0.105464
$677$	−5.06570e91	−0.513461	−0.256731	−	0.966483i	$-0.582645\pi$
$677$	−5.06570e91	−0.513461	−0.256731	+	0.966483i	$0.582645\pi$
$678$	5.31392e90	0.0513393
$679$	−9.47159e91	−0.872279
$680$	4.03642e91	0.354370
$681$	−1.31264e92	−1.09866
$682$	−2.50299e90	−0.0199741
$683$	−5.08890e91	−0.387214	−0.193607	−	0.981079i	$-0.562019\pi$
$683$	−5.08890e91	−0.387214	−0.193607	+	0.981079i	$0.562019\pi$
$684$	8.48128e91	0.615373
$685$	−1.35013e92	−0.934186
$686$	−1.17121e91	−0.0772863
$687$	−9.72258e91	−0.611910
$688$	9.71159e91	0.582997
$689$	−1.15462e92	−0.661170
$690$	−1.03916e91	−0.0567659
$691$	1.01478e91	0.0528852	0.0264426	−	0.999650i	$-0.491582\pi$
$691$	1.01478e91	0.0528852	0.0264426	+	0.999650i	$0.491582\pi$
$692$	1.27120e92	0.632072
$693$	2.01986e91	0.0958279
$694$	1.30040e91	0.0588699
$695$	3.96538e92	1.71309
$696$	3.93812e91	0.162364
$697$	−1.96736e92	−0.774137
$698$	4.46482e91	0.167688
$699$	−1.40224e92	−0.502705
$700$	−1.81292e91	−0.0620431
$701$	−2.45372e92	−0.801658	−0.400829	−	0.916153i	$-0.631278\pi$
$701$	−2.45372e92	−0.801658	−0.400829	+	0.916153i	$0.631278\pi$
$702$	6.76940e90	0.0211151
$703$	6.45370e92	1.92203
$704$	8.09030e91	0.230066
$705$	3.53268e92	0.959308
$706$	−4.00348e91	−0.103821
$707$	1.84288e92	0.456422
$708$	−1.01174e92	−0.239326
$709$	−6.06643e92	−1.37066	−0.685332	−	0.728231i	$-0.740343\pi$
$709$	−6.06643e92	−1.37066	−0.685332	+	0.728231i	$0.740343\pi$
$710$	7.35419e90	0.0158722
$711$	4.39478e91	0.0906098
$712$	5.03252e91	0.0991255
$713$	4.00922e92	0.754483
$714$	−6.87268e91	−0.123576
$715$	−1.46507e92	−0.251717
$716$	9.51815e92	1.56271
$717$	−5.52883e92	−0.867483
$718$	−9.12694e91	−0.136861
$719$	2.18530e92	0.313201	0.156600	−	0.987662i	$-0.449947\pi$
$719$	2.18530e92	0.313201	0.156600	+	0.987662i	$0.449947\pi$
$720$	−2.29008e92	−0.313721
$721$	7.44722e92	0.975210
$722$	−2.06921e92	−0.259027
$723$	−7.02829e92	−0.841114
$724$	5.00416e90	0.00572569
$725$	−6.64997e91	−0.0727502
$726$	5.40817e91	0.0565731
$727$	−1.54467e93	−1.54514	−0.772569	−	0.634931i	$-0.781028\pi$
$727$	−1.54467e93	−1.54514	−0.772569	+	0.634931i	$0.781028\pi$
$728$	2.66642e92	0.255070
$729$	4.04838e91	0.0370370
$730$	−1.60237e90	−0.00140207
$731$	−1.26426e93	−1.05808
$732$	−2.05333e92	−0.164380
$733$	−2.18739e93	−1.67512	−0.837561	−	0.546344i	$-0.816019\pi$
$733$	−2.18739e93	−1.67512	−0.837561	+	0.546344i	$0.816019\pi$
$734$	−6.32291e91	−0.0463229
$735$	−2.93260e92	−0.205548
$736$	4.45604e92	0.298827
$737$	3.80308e92	0.244029
$738$	−2.49635e91	−0.0153276
$739$	1.74755e93	1.02680	0.513400	−	0.858149i	$-0.328386\pi$
$739$	1.74755e93	1.02680	0.513400	+	0.858149i	$0.328386\pi$
$740$	−1.76219e93	−0.990882
$741$	2.10640e93	1.13357
$742$	1.48743e92	0.0766144
$743$	1.09932e93	0.541986	0.270993	−	0.962581i	$-0.412648\pi$
$743$	1.09932e93	0.541986	0.270993	+	0.962581i	$0.412648\pi$
$744$	−1.97604e92	−0.0932557
$745$	1.56846e93	0.708591
$746$	−2.14976e92	−0.0929776
$747$	1.51480e93	0.627243
$748$	−1.07756e93	−0.427208
$749$	3.90962e93	1.48414
$750$	−1.69798e92	−0.0617221
$751$	−1.12155e93	−0.390411	−0.195205	−	0.980762i	$-0.562537\pi$
$751$	−1.12155e93	−0.390411	−0.195205	+	0.980762i	$0.562537\pi$
$752$	−4.95702e93	−1.65250
$753$	−6.79746e92	−0.217025
$754$	4.86359e92	0.148726
$755$	1.88322e92	0.0551602
$756$	7.92954e92	0.222479
$757$	6.56685e93	1.76499	0.882493	−	0.470326i	$-0.155864\pi$
$757$	6.56685e93	1.76499	0.882493	+	0.470326i	$0.155864\pi$
$758$	−1.01457e91	−0.00261236
$759$	5.57879e92	0.137620
$760$	1.59371e93	0.376676
$761$	−5.03680e93	−1.14065	−0.570327	−	0.821418i	$-0.693183\pi$
$761$	−5.03680e93	−1.14065	−0.570327	+	0.821418i	$0.693183\pi$
$762$	−2.17712e92	−0.0472439
$763$	2.52295e93	0.524641
$764$	1.18596e93	0.236340
$765$	2.98123e93	0.569375
$766$	2.14746e92	0.0393088
$767$	−2.51275e93	−0.440860
$768$	3.06566e93	0.515565
$769$	3.18546e93	0.513530	0.256765	−	0.966474i	$-0.417343\pi$
$769$	3.18546e93	0.513530	0.256765	+	0.966474i	$0.417343\pi$
$770$	1.88738e92	0.0291683
$771$	−5.65071e93	−0.837213
$772$	−1.19071e94	−1.69139
$773$	−2.17972e92	−0.0296871	−0.0148435	−	0.999890i	$-0.504725\pi$
$773$	−2.17972e92	−0.0296871	−0.0148435	+	0.999890i	$0.504725\pi$
$774$	−1.60420e92	−0.0209496
$775$	3.33677e92	0.0417850
$776$	1.28937e93	0.154836
$777$	6.03385e93	0.694883
$778$	−7.84979e92	−0.0867004
$779$	−7.76778e93	−0.822867
$780$	−5.75156e93	−0.584401
$781$	−3.94813e92	−0.0384798
$782$	−1.89821e93	−0.177470
$783$	2.90863e93	0.260874
$784$	4.11499e93	0.354077
$785$	−1.86449e94	−1.53920
$786$	1.18042e93	0.0934985
$787$	−1.72602e94	−1.31180	−0.655899	−	0.754849i	$-0.727710\pi$
$787$	−1.72602e94	−1.31180	−0.655899	+	0.754849i	$0.727710\pi$
$788$	3.35329e93	0.244551
$789$	1.30522e93	0.0913439
$790$	4.10652e92	0.0275800
$791$	1.54594e94	0.996452
$792$	−2.74964e92	−0.0170101
$793$	−5.09961e93	−0.302802
$794$	−1.19211e93	−0.0679439
$795$	−6.45217e93	−0.352999
$796$	6.08698e93	0.319688
$797$	7.26703e93	0.366405	0.183203	−	0.983075i	$-0.441354\pi$
$797$	7.26703e93	0.366405	0.183203	+	0.983075i	$0.441354\pi$
$798$	−2.71357e93	−0.131355
$799$	6.45305e94	2.99913
$800$	3.70865e92	0.0165497
$801$	3.71692e93	0.159267
$802$	1.18269e93	0.0486634
$803$	8.60241e91	0.00339911
$804$	1.49300e94	0.566552
$805$	−3.02315e94	−1.10178
$806$	−2.44041e93	−0.0854229
$807$	−2.74046e94	−0.921368
$808$	−2.50872e93	−0.0810181
$809$	4.27655e94	1.32668	0.663341	−	0.748317i	$-0.269138\pi$
$809$	4.27655e94	1.32668	0.663341	+	0.748317i	$0.269138\pi$
$810$	3.78284e92	0.0112734
$811$	−4.93001e94	−1.41147	−0.705733	−	0.708478i	$-0.749382\pi$
$811$	−4.93001e94	−1.41147	−0.705733	+	0.708478i	$0.749382\pi$
$812$	5.69711e94	1.56705
$813$	−1.21918e94	−0.322201
$814$	−1.04043e93	−0.0264191
$815$	4.35758e94	1.06322
$816$	−4.18322e94	−0.980801
$817$	−4.99170e94	−1.12469
$818$	7.61412e93	0.164868
$819$	1.96937e94	0.409827
$820$	2.12101e94	0.424220
$821$	3.77685e94	0.726068	0.363034	−	0.931776i	$-0.381741\pi$
$821$	3.77685e94	0.726068	0.363034	+	0.931776i	$0.381741\pi$
$822$	−3.12940e93	−0.0578265
$823$	4.11741e94	0.731358	0.365679	−	0.930741i	$-0.380837\pi$
$823$	4.11741e94	0.731358	0.365679	+	0.930741i	$0.380837\pi$
$824$	−1.01379e94	−0.173107
$825$	4.64308e92	0.00762172
$826$	3.23705e93	0.0510855
$827$	−8.61522e94	−1.30719	−0.653593	−	0.756846i	$-0.726739\pi$
$827$	−8.61522e94	−1.30719	−0.653593	+	0.756846i	$0.726739\pi$
$828$	2.19011e94	0.319506
$829$	−1.36639e95	−1.91669	−0.958344	−	0.285616i	$-0.907802\pi$
$829$	−1.36639e95	−1.91669	−0.958344	+	0.285616i	$0.907802\pi$
$830$	1.41544e94	0.190921
$831$	−1.32276e94	−0.171573
$832$	7.88804e94	0.983923
$833$	−5.35690e94	−0.642615
$834$	9.19114e93	0.106041
$835$	−6.38166e94	−0.708146
$836$	−4.25457e94	−0.454100
$837$	−1.45947e94	−0.149836
$838$	−8.95345e93	−0.0884219
$839$	−1.17169e95	−1.11314	−0.556570	−	0.830801i	$-0.687883\pi$
$839$	−1.17169e95	−1.11314	−0.556570	+	0.830801i	$0.687883\pi$
$840$	1.49004e94	0.136182
$841$	9.52466e94	0.837490
$842$	1.23622e93	0.0104581
$843$	−1.13126e95	−0.920798
$844$	−3.29894e94	−0.258372
$845$	−1.37631e94	−0.103723
$846$	8.18820e93	0.0593816
$847$	1.57336e95	1.09804
$848$	9.05362e94	0.608075
$849$	1.31591e95	0.850600
$850$	−1.57983e93	−0.00982868
$851$	1.66653e95	0.997933
$852$	−1.54995e94	−0.0893368
$853$	−5.14803e94	−0.285626	−0.142813	−	0.989750i	$-0.545615\pi$
$853$	−5.14803e94	−0.285626	−0.142813	+	0.989750i	$0.545615\pi$
$854$	6.56957e93	0.0350878
$855$	1.17709e95	0.605215
$856$	−5.32216e94	−0.263445
$857$	−8.42573e94	−0.401542	−0.200771	−	0.979638i	$-0.564345\pi$
$857$	−8.42573e94	−0.401542	−0.200771	+	0.979638i	$0.564345\pi$
$858$	−3.39581e93	−0.0155814
$859$	2.23307e95	0.986561	0.493280	−	0.869870i	$-0.335798\pi$
$859$	2.23307e95	0.986561	0.493280	+	0.869870i	$0.335798\pi$
$860$	1.36299e95	0.579821
$861$	−7.26246e94	−0.297496
$862$	2.29031e93	0.00903457
$863$	−3.02098e95	−1.14762	−0.573808	−	0.818990i	$-0.694534\pi$
$863$	−3.02098e95	−1.14762	−0.573808	+	0.818990i	$0.694534\pi$
$864$	−1.62212e94	−0.0593454
$865$	1.76426e95	0.621639
$866$	2.13766e94	0.0725451
$867$	3.67944e95	1.20271
$868$	−2.85865e95	−0.900058
$869$	−2.20461e94	−0.0668634
$870$	2.71785e94	0.0794052
$871$	3.70800e95	1.04364
$872$	−3.43450e94	−0.0931274
$873$	9.52303e94	0.248778
$874$	−7.49476e94	−0.188641
$875$	−4.93980e95	−1.19797
$876$	3.37711e93	0.00789155
$877$	1.44119e95	0.324515	0.162257	−	0.986748i	$-0.448123\pi$
$877$	1.44119e95	0.324515	0.162257	+	0.986748i	$0.448123\pi$
$878$	−1.69309e94	−0.0367374
$879$	−1.50070e95	−0.313802
$880$	1.14880e95	0.231503
$881$	−4.03725e95	−0.784095	−0.392048	−	0.919945i	$-0.628233\pi$
$881$	−4.03725e95	−0.784095	−0.392048	+	0.919945i	$0.628233\pi$
$882$	−6.79730e93	−0.0127235
$883$	−5.36513e94	−0.0967961	−0.0483980	−	0.998828i	$-0.515412\pi$
$883$	−5.36513e94	−0.0967961	−0.0483980	+	0.998828i	$0.515412\pi$
$884$	−1.05062e96	−1.82704
$885$	−1.40416e95	−0.235376
$886$	−5.85361e94	−0.0945862
$887$	−7.01397e94	−0.109256	−0.0546281	−	0.998507i	$-0.517397\pi$
$887$	−7.01397e94	−0.109256	−0.0546281	+	0.998507i	$0.517397\pi$
$888$	−8.21388e94	−0.123347
$889$	−6.33373e95	−0.916963
$890$	3.47313e94	0.0484781
$891$	−2.03084e94	−0.0273306
$892$	−8.99736e95	−1.16750
$893$	2.54788e96	3.18792
$894$	3.63545e94	0.0438620
$895$	1.32099e96	1.53692
$896$	−4.22836e95	−0.474419
$897$	5.43932e95	0.588559
$898$	1.34088e95	0.139929
$899$	−1.04858e96	−1.05539
$900$	1.82277e94	0.0176950
$901$	−1.17860e96	−1.10360
$902$	1.25228e94	0.0113107
$903$	−4.66697e95	−0.406615
$904$	−2.10449e95	−0.176877
$905$	6.94510e93	0.00563118
$906$	4.36502e93	0.00341444
$907$	−1.00871e95	−0.0761254	−0.0380627	−	0.999275i	$-0.512119\pi$
$907$	−1.00871e95	−0.0761254	−0.0380627	+	0.999275i	$0.512119\pi$
$908$	2.58502e96	1.88223
$909$	−1.85289e95	−0.130174
$910$	1.84020e95	0.124744
$911$	8.20590e95	0.536758	0.268379	−	0.963313i	$-0.413512\pi$
$911$	8.20590e95	0.536758	0.268379	+	0.963313i	$0.413512\pi$
$912$	−1.65168e96	−1.04254
$913$	−7.59887e95	−0.462859
$914$	2.01173e95	0.118255
$915$	−2.84974e95	−0.161666
$916$	1.91470e96	1.04833
$917$	3.43411e96	1.81473
$918$	6.91001e94	0.0352445
$919$	9.80468e95	0.482702	0.241351	−	0.970438i	$-0.422409\pi$
$919$	9.80468e95	0.482702	0.241351	+	0.970438i	$0.422409\pi$
$920$	4.11542e95	0.195573
$921$	8.63108e95	0.395938
$922$	3.23927e95	0.143447
$923$	−3.84943e95	−0.164566
$924$	−3.97779e95	−0.164173
$925$	1.38701e95	0.0552679
$926$	−5.98419e94	−0.0230223
$927$	−7.48767e95	−0.278135
$928$	−1.16544e96	−0.418005
$929$	−5.33507e96	−1.84769	−0.923846	−	0.382765i	$-0.874972\pi$
$929$	−5.33507e96	−1.84769	−0.923846	+	0.382765i	$0.874972\pi$
$930$	−1.36374e95	−0.0456074
$931$	−2.11508e96	−0.683066
$932$	2.76147e96	0.861239
$933$	−5.16985e95	−0.155713
$934$	2.00732e95	0.0583905
$935$	−1.49551e96	−0.420157
$936$	−2.68090e95	−0.0727471
$937$	1.17141e96	0.307025	0.153513	−	0.988147i	$-0.450941\pi$
$937$	1.17141e96	0.307025	0.153513	+	0.988147i	$0.450941\pi$
$938$	−4.77683e95	−0.120934
$939$	1.62375e96	0.397088
$940$	−6.95703e96	−1.64350
$941$	−2.86067e96	−0.652838	−0.326419	−	0.945225i	$-0.605842\pi$
$941$	−2.86067e96	−0.652838	−0.326419	+	0.945225i	$0.605842\pi$
$942$	−4.32159e95	−0.0952772
$943$	−2.00586e96	−0.427239
$944$	1.97031e96	0.405457
$945$	1.10051e96	0.218807
$946$	8.04733e94	0.0154593
$947$	4.16025e96	0.772227	0.386113	−	0.922451i	$-0.373817\pi$
$947$	4.16025e96	0.772227	0.386113	+	0.922451i	$0.373817\pi$
$948$	−8.65479e95	−0.155234
$949$	8.38735e94	0.0145369
$950$	−6.23770e94	−0.0104474
$951$	−1.63090e96	−0.263974
$952$	2.72181e96	0.425752
$953$	−2.42066e96	−0.365944	−0.182972	−	0.983118i	$-0.558572\pi$
$953$	−2.42066e96	−0.365944	−0.182972	+	0.983118i	$0.558572\pi$
$954$	−1.49551e95	−0.0218508
$955$	1.64596e96	0.232439
$956$	1.08881e97	1.48618
$957$	−1.45909e96	−0.192506
$958$	−1.33816e95	−0.0170659
$959$	−9.10413e96	−1.12236
$960$	4.40796e96	0.525318
$961$	−3.41833e96	−0.393825
$962$	−1.01442e96	−0.112986
$963$	−3.93085e96	−0.423284
$964$	1.38411e97	1.44100
$965$	−1.65254e97	−1.66347
$966$	−7.00719e95	−0.0682005
$967$	1.52970e96	0.143961	0.0719805	−	0.997406i	$-0.477068\pi$
$967$	1.52970e96	0.143961	0.0719805	+	0.997406i	$0.477068\pi$
$968$	−2.14181e96	−0.194909
$969$	2.15015e97	1.89211
$970$	8.89841e95	0.0757235
$971$	6.45963e96	0.531597	0.265799	−	0.964029i	$-0.414364\pi$
$971$	6.45963e96	0.531597	0.265799	+	0.964029i	$0.414364\pi$
$972$	−7.97261e95	−0.0634522
$973$	2.67391e97	2.05816
$974$	−1.51923e96	−0.113098
$975$	4.52701e95	0.0325958
$976$	3.99873e96	0.278486
$977$	−1.18043e97	−0.795185	−0.397593	−	0.917562i	$-0.630154\pi$
$977$	−1.18043e97	−0.795185	−0.397593	+	0.917562i	$0.630154\pi$
$978$	1.01002e96	0.0658137
$979$	−1.86457e96	−0.117528
$980$	5.77527e96	0.352148
$981$	−2.53666e96	−0.149630
$982$	−2.34737e96	−0.133955
$983$	−1.77412e97	−0.979475	−0.489737	−	0.871870i	$-0.662907\pi$
$983$	−1.77412e97	−0.979475	−0.489737	+	0.871870i	$0.662907\pi$
$984$	9.88638e95	0.0528076
$985$	4.65392e96	0.240515
$986$	4.96462e96	0.248248
$987$	2.38213e97	1.15255
$988$	−4.14820e97	−1.94205
$989$	−1.28900e97	−0.583946
$990$	−1.89763e95	−0.00831894
$991$	−1.09335e97	−0.463836	−0.231918	−	0.972735i	$-0.574500\pi$
$991$	−1.09335e97	−0.463836	−0.231918	+	0.972735i	$0.574500\pi$
$992$	5.84787e96	0.240087
$993$	−1.95543e97	−0.776946
$994$	4.95902e95	0.0190695
$995$	8.44790e96	0.314412
$996$	−2.98315e97	−1.07460
$997$	3.84523e96	0.134070	0.0670348	−	0.997751i	$-0.478646\pi$
$997$	3.84523e96	0.134070	0.0670348	+	0.997751i	$0.478646\pi$
$998$	−6.85186e95	−0.0231242
$999$	−6.06663e96	−0.198184

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3.66.a.b.1.3	✓	6
3.2	odd	2		9.66.a.c.1.4		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
3.66.a.b.1.3	✓	6	1.1	even	1	trivial
9.66.a.c.1.4		6	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 3 \)
Weight:	\( k \)	\(=\)	\( 66 \)
Character orbit:	\([\chi]\)	\(=\)	3.a (trivial)

\(f(q)\)	\(=\)	\(q-6.33506e8 q^{2} +1.85302e15 q^{3} -3.64922e19 q^{4} -5.06462e22 q^{5} -1.17390e24 q^{6} -3.41514e27 q^{7} +4.64902e28 q^{8} +3.43368e30 q^{9} +O(q^{10})\)	\(q-6.33506e8 q^{2} +1.85302e15 q^{3} -3.64922e19 q^{4} -5.06462e22 q^{5} -1.17390e24 q^{6} -3.41514e27 q^{7} +4.64902e28 q^{8} +3.43368e30 q^{9} +3.20846e31 q^{10} -1.72248e33 q^{11} -6.76207e34 q^{12} -1.67942e36 q^{13} +2.16351e36 q^{14} -9.38484e37 q^{15} +1.31687e39 q^{16} -1.71430e40 q^{17} -2.17526e39 q^{18} -6.76864e41 q^{19} +1.84819e42 q^{20} -6.32831e42 q^{21} +1.09120e42 q^{22} -1.74786e44 q^{23} +8.61473e43 q^{24} -1.45470e44 q^{25} +1.06392e45 q^{26} +6.36269e45 q^{27} +1.24626e47 q^{28} +4.57138e47 q^{29} +5.94535e46 q^{30} -2.29379e48 q^{31} -2.54943e48 q^{32} -3.19179e48 q^{33} +1.08602e49 q^{34} +1.72964e50 q^{35} -1.25303e50 q^{36} -9.53469e50 q^{37} +4.28798e50 q^{38} -3.11200e51 q^{39} -2.35455e51 q^{40} +1.14761e52 q^{41} +4.00902e51 q^{42} +7.37475e52 q^{43} +6.28570e52 q^{44} -1.73903e53 q^{45} +1.10728e53 q^{46} -3.76424e54 q^{47} +2.44019e54 q^{48} +3.12483e54 q^{49} +9.21558e52 q^{50} -3.17664e55 q^{51} +6.12856e55 q^{52} +6.87510e55 q^{53} -4.03080e54 q^{54} +8.72370e55 q^{55} -1.58770e56 q^{56} -1.25424e57 q^{57} -2.89600e56 q^{58} +1.49620e57 q^{59} +3.42473e57 q^{60} +3.03654e57 q^{61} +1.45313e57 q^{62} -1.17265e58 q^{63} -4.69689e58 q^{64} +8.50561e58 q^{65} +2.02202e57 q^{66} -2.20791e59 q^{67} +6.25586e59 q^{68} -3.23881e59 q^{69} -1.09573e59 q^{70} +2.29212e59 q^{71} +1.59633e59 q^{72} -4.99420e58 q^{73} +6.04028e59 q^{74} -2.69558e59 q^{75} +2.47002e61 q^{76} +5.88250e60 q^{77} +1.97147e60 q^{78} +1.27990e61 q^{79} -6.66945e61 q^{80} +1.17902e61 q^{81} -7.27019e60 q^{82} +4.41159e62 q^{83} +2.30934e62 q^{84} +8.68229e62 q^{85} -4.67194e61 q^{86} +8.47086e62 q^{87} -8.00785e61 q^{88} +1.08249e63 q^{89} +1.10169e62 q^{90} +5.73544e63 q^{91} +6.37830e63 q^{92} -4.25044e63 q^{93} +2.38467e63 q^{94} +3.42806e64 q^{95} -4.72415e63 q^{96} +2.77342e64 q^{97} -1.97960e63 q^{98} -5.91445e63 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 6210982962 q^{2} + 11\!\cdots\!46 q^{3}+ \cdots + 20\!\cdots\!86 q^{9}+O(q^{10}) \) 6 * q + 6210982962 * q^2 + 11118121133111046 * q^3 + 91340905060284656388 * q^4 + 35156143485265939841700 * q^5 + 11509076821200806793333042 * q^6 + 1317821413686135751883120304 * q^7 + 712695351135793704541979166216 * q^8 + 20602102921755074907947094535686 * q^9	\( 6 q + 6210982962 q^{2} + 11\!\cdots\!46 q^{3}+ \cdots - 79\!\cdots\!56 q^{99}+O(q^{100}) \) 6 * q + 6210982962 * q^2 + 11118121133111046 * q^3 + 91340905060284656388 * q^4 + 35156143485265939841700 * q^5 + 11509076821200806793333042 * q^6 + 1317821413686135751883120304 * q^7 + 712695351135793704541979166216 * q^8 + 20602102921755074907947094535686 * q^9 + 1279335362952214656095633710080300 * q^10 - 2320891225483098403783749293998776 * q^11 + 169256541144706753221065102926210308 * q^12 + 961121104514647333696741144147524948 * q^13 - 23129299274714313374806876102877367408 * q^14 + 65145043640369911498096047700293569700 * q^15 + 3823746510407049616170834753394080518160 * q^16 - 13299388459605389867520707035083919491732 * q^17 + 21326551704731864898382187093091507830322 * q^18 + 560292177581177184743091103452788118819192 * q^19 + 2639207549045807126411266673763877251826200 * q^20 + 2441949684861683354803792504764566234879664 * q^21 + 109087634208372169902244649477327815818480216 * q^22 + 47867967315720390505184778564365196445371792 * q^23 + 1320638874155477584526460333544399643536603656 * q^24 + 5903161610990991425391100671552625540789976250 * q^25 - 12767069733763684064339316615714552428734293828 * q^26 + 38176112646815654150848972575231205385341297926 * q^27 + 188981295845031762805361197391664671598468484128 * q^28 + 184598319743070439951214664118917344915749962804 * q^29 + 2370634255862551351967264008295295716324912832300 * q^30 + 2623293635847269610518889821610813093244853580096 * q^31 + 54517802865386487937006688151855327070440233101344 * q^32 - 4300658296949271697408611055488031957639099346616 * q^33 - 197051985794439999405618245255004158938931162716284 * q^34 - 336946198056174264271289046874497082169398437573600 * q^35 + 313635787836373904323815807955150893399463818977028 * q^36 - 1968820149934868134141337613116275247510383189922076 * q^37 - 4694460210295937878277310645733397353377543187928088 * q^38 + 1780976810597221813831295709299147451849422023229268 * q^39 + 49157095865813933882755882516506487928569967968330800 * q^40 + 44721887514455538638767198455359242350295739355243516 * q^41 - 42859058510041866039547467439355390841668392234198128 * q^42 + 153471498107711152104975153786874048016259113736389640 * q^43 + 587913931391616274066657207301553410768002198418789424 * q^44 + 120715081069239676913401645732104593549750878306817700 * q^45 - 849756306074338863410215581822356060828605711616030544 * q^46 - 2381436220471011081110439407418227465375144570579750880 * q^47 + 7085479480836039087453859606939812767013947556749932560 * q^48 - 13393548707851784006635575377379702474705118021474562730 * q^49 + 8605967224979103186898364333260236908007021440152308750 * q^50 - 24644035315031974302945230554182833693819016149372478612 * q^51 + 28103125715176726198206798610702185135717107604823332408 * q^52 + 96360078764216635005363901635422818697091613178374171332 * q^53 + 39518530867460791914301257749994379976512907662225322802 * q^54 + 618818415407556251266374500995172486288026360694877294000 * q^55 - 1594813238548124991376317569708337784666756662353002031040 * q^56 + 1038232716713682180976880962449952357714831981771155332472 * q^57 - 6219453968745032502669888624143069517040566250894307781156 * q^58 - 7164713795718274697330180132380143319550103232198323750552 * q^59 + 4890504870952065939781074525505374307433603429398482034200 * q^60 + 4054291215081390738422899746523994767920509085300201674100 * q^61 + 34958707902560547237040840127848348482406693907763612852288 * q^62 + 4524982066209090105617255500931244831346320008742959861424 * q^63 + 253886263593501163190345542000578846999323347305576212553792 * q^64 - 97713589375076675190034327138723287340652596444477353717000 * q^65 + 202141588542198348857919279578170075461005987681230613677656 * q^66 + 144969667137236336673901245696979200934490405700749088000408 * q^67 - 2043740729154231542349040029441864841610331954777068147532216 * q^68 + 88700309835329950515541486518405473374907183046958848669072 * q^69 - 376744368214432254685629568745965379661331246625643952048800 * q^70 + 4588679866778477404065022934148807666177872634340922809064112 * q^71 + 2447170495992665754108483599319590630800125228272471322930696 * q^72 + 5295912209896035983548777676613107350643482423356854790725052 * q^73 + 9350247807486544549899934039998290071104428513885721798684012 * q^74 + 10938677643221464887252782466723953018644303552582609158776250 * q^75 + 49431355703188799046581662321370260954206584827526057026382928 * q^76 - 1828833584476997625702724578991793773647028588398159948752832 * q^77 - 23657637969143405241553634968093771501075977806653249252737348 * q^78 + 54854215934838989987009222002160957436114851061876043050015840 * q^79 + 467229112107152547456622091810828686257369551958519790980194400 * q^80 + 70741107466431499029125237168475111994069269553655046654581766 * q^81 + 508922387706347567665108833107375226127873394210791088866943028 * q^82 + 1256260453192702935091990356349904699687077869271636880116177656 * q^83 + 350186156516226392013489515258489267145665356490052568052079648 * q^84 + 1852861842448226107460158067921550442047822098825611523802078600 * q^85 + 3831728770512664300176489776078486686399726517973532920621402264 * q^86 + 342064413312036915623899374372475723529966510246438451216922164 * q^87 + 9887117998185871649768434211230976034878006221151840213514086496 * q^88 + 6405745009095237591902398822994073231956083842634829017742480412 * q^89 + 4392833136497068463530245328708128567870257643882088544379264300 * q^90 + 15865450468547895312707699659652371514673487967941777300259476896 * q^91 + 29446826967437370900765953556333974961331800074484795273728913504 * q^92 + 4861016068511540147024173987086576965408216747184752296570556736 * q^93 + 56000185796626083903421554209308857253984887888617668932197528928 * q^94 + 72344957899327813087872537810796747182935722022569380946809723600 * q^95 + 101022589361405908280345556707156044958833243651227160537953974304 * q^96 + 129176222791613802297195096968916495723771832056570573627879422028 * q^97 - 31866926727825199330491058509226158803414878017058965243757311198 * q^98 - 7969206649600176331526748122851560060012392538244305510328720056 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more