LMFDB - Embedded newform 3.66.a.b.1.4

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			1.4
Root			$2.86568e8$ 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)

$f(q)$	$=$	$q+2.75457e9 q^{2} +1.85302e15 q^{3} -2.93058e19 q^{4} +9.23075e22 q^{5} +5.10428e24 q^{6} -1.32074e27 q^{7} -1.82351e29 q^{8} +3.43368e30 q^{9} +O(q^{10})$	\(q+2.75457e9 q^{2} +1.85302e15 q^{3} -2.93058e19 q^{4} +9.23075e22 q^{5} +5.10428e24 q^{6} -1.32074e27 q^{7} -1.82351e29 q^{8} +3.43368e30 q^{9} +2.54268e32 q^{10} -1.13880e34 q^{11} -5.43043e34 q^{12} +1.26314e36 q^{13} -3.63806e36 q^{14} +1.71048e38 q^{15} +5.78896e38 q^{16} +1.26682e40 q^{17} +9.45833e39 q^{18} +5.39047e41 q^{19} -2.70515e42 q^{20} -2.44735e42 q^{21} -3.13692e43 q^{22} -2.86568e44 q^{23} -3.37900e44 q^{24} +5.81017e45 q^{25} +3.47942e45 q^{26} +6.36269e45 q^{27} +3.87053e46 q^{28} -8.89970e46 q^{29} +4.71163e47 q^{30} +7.20648e47 q^{31} +8.32216e48 q^{32} -2.11023e49 q^{33} +3.48956e49 q^{34} -1.21914e50 q^{35} -1.00627e50 q^{36} +3.10500e50 q^{37} +1.48484e51 q^{38} +2.34063e51 q^{39} -1.68323e52 q^{40} +1.45482e52 q^{41} -6.74141e51 q^{42} +1.60447e53 q^{43} +3.33736e53 q^{44} +3.16955e53 q^{45} -7.89372e53 q^{46} -1.74566e54 q^{47} +1.07271e54 q^{48} -6.79398e54 q^{49} +1.60045e55 q^{50} +2.34745e55 q^{51} -3.70175e55 q^{52} +1.10250e56 q^{53} +1.75265e55 q^{54} -1.05120e57 q^{55} +2.40837e56 q^{56} +9.98865e56 q^{57} -2.45149e56 q^{58} +8.05146e56 q^{59} -5.01269e57 q^{60} +7.28180e57 q^{61} +1.98507e57 q^{62} -4.53499e57 q^{63} +1.56649e57 q^{64} +1.16598e59 q^{65} -5.81277e58 q^{66} +2.30605e59 q^{67} -3.71253e59 q^{68} -5.31017e59 q^{69} -3.35821e59 q^{70} +1.89858e60 q^{71} -6.26135e59 q^{72} +1.33542e59 q^{73} +8.55294e59 q^{74} +1.07664e61 q^{75} -1.57972e61 q^{76} +1.50406e61 q^{77} +6.44743e60 q^{78} +6.07331e61 q^{79} +5.34365e61 q^{80} +1.17902e61 q^{81} +4.00741e61 q^{82} -1.13480e62 q^{83} +7.17217e61 q^{84} +1.16937e63 q^{85} +4.41963e62 q^{86} -1.64913e62 q^{87} +2.07662e63 q^{88} -1.42307e62 q^{89} +8.73074e62 q^{90} -1.66828e63 q^{91} +8.39812e63 q^{92} +1.33537e63 q^{93} -4.80856e63 q^{94} +4.97581e64 q^{95} +1.54211e64 q^{96} +5.82740e64 q^{97} -1.87145e64 q^{98} -3.91029e64 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	2.75457e9	0.453502	0.226751	−	0.973953i	$-0.427190\pi$
$2$	2.75457e9	0.453502	0.226751	+	0.973953i	$0.427190\pi$
$3$	1.85302e15	0.577350
$3$	1.85302e15	0.577350
$4$	−2.93058e19	−0.794336
$5$	9.23075e22	1.77301	0.886506	−	0.462717i	$-0.153125\pi$
$5$	9.23075e22	1.77301	0.886506	+	0.462717i	$0.153125\pi$
$6$	5.10428e24	0.261829
$7$	−1.32074e27	−0.451991	−0.225996	−	0.974128i	$-0.572564\pi$
$7$	−1.32074e27	−0.451991	−0.225996	+	0.974128i	$0.572564\pi$
$8$	−1.82351e29	−0.813735
$9$	3.43368e30	0.333333
$10$	2.54268e32	0.804064
$11$	−1.13880e34	−1.62625	−0.813124	−	0.582091i	$-0.802235\pi$
$11$	−1.13880e34	−1.62625	−0.813124	+	0.582091i	$0.802235\pi$
$12$	−5.43043e34	−0.458610
$13$	1.26314e36	0.791213	0.395607	−	0.918420i	$-0.370534\pi$
$13$	1.26314e36	0.791213	0.395607	+	0.918420i	$0.370534\pi$
$14$	−3.63806e36	−0.204979
$15$	1.71048e38	1.02365
$16$	5.78896e38	0.425306
$17$	1.26682e40	1.29756	0.648778	−	0.760977i	$-0.275280\pi$
$17$	1.26682e40	1.29756	0.648778	+	0.760977i	$0.275280\pi$
$18$	9.45833e39	0.151167
$19$	5.39047e41	1.48640	0.743198	−	0.669071i	$-0.233308\pi$
$19$	5.39047e41	1.48640	0.743198	+	0.669071i	$0.233308\pi$
$20$	−2.70515e42	−1.40837
$21$	−2.44735e42	−0.260957
$22$	−3.13692e43	−0.737506
$23$	−2.86568e44	−1.58882	−0.794408	−	0.607385i	$-0.792218\pi$
$23$	−2.86568e44	−1.58882	−0.794408	+	0.607385i	$0.792218\pi$
$24$	−3.37900e44	−0.469810
$25$	5.81017e45	2.14357
$26$	3.47942e45	0.358817
$27$	6.36269e45	0.192450
$28$	3.87053e46	0.359033
$29$	−8.89970e46	−0.263901	−0.131950	−	0.991256i	$-0.542124\pi$
$29$	−8.89970e46	−0.263901	−0.131950	+	0.991256i	$0.542124\pi$
$30$	4.71163e47	0.464227
$31$	7.20648e47	0.244606	0.122303	−	0.992493i	$-0.460972\pi$
$31$	7.20648e47	0.244606	0.122303	+	0.992493i	$0.460972\pi$
$32$	8.32216e48	1.00661
$33$	−2.11023e49	−0.938914
$34$	3.48956e49	0.588444
$35$	−1.21914e50	−0.801386
$36$	−1.00627e50	−0.264779
$37$	3.10500e50	0.335356	0.167678	−	0.985842i	$-0.446373\pi$
$37$	3.10500e50	0.335356	0.167678	+	0.985842i	$0.446373\pi$
$38$	1.48484e51	0.674084
$39$	2.34063e51	0.456807
$40$	−1.68323e52	−1.44276
$41$	1.45482e52	0.558901	0.279451	−	0.960160i	$-0.409848\pi$
$41$	1.45482e52	0.558901	0.279451	+	0.960160i	$0.409848\pi$
$42$	−6.74141e51	−0.118345
$43$	1.60447e53	1.31101	0.655507	−	0.755189i	$-0.272455\pi$
$43$	1.60447e53	1.31101	0.655507	+	0.755189i	$0.272455\pi$
$44$	3.33736e53	1.29179
$45$	3.16955e53	0.591004
$46$	−7.89372e53	−0.720531
$47$	−1.74566e54	−0.792101	−0.396050	−	0.918229i	$-0.629619\pi$
$47$	−1.74566e54	−0.792101	−0.396050	+	0.918229i	$0.629619\pi$
$48$	1.07271e54	0.245550
$49$	−6.79398e54	−0.795704
$50$	1.60045e55	0.972115
$51$	2.34745e55	0.749145
$52$	−3.70175e55	−0.628489
$53$	1.10250e56	1.00789	0.503946	−	0.863735i	$-0.331881\pi$
$53$	1.10250e56	1.00789	0.503946	+	0.863735i	$0.331881\pi$
$54$	1.75265e55	0.0872765
$55$	−1.05120e57	−2.88336
$56$	2.40837e56	0.367801
$57$	9.98865e56	0.858171
$58$	−2.45149e56	−0.119679
$59$	8.05146e56	0.225520	0.112760	−	0.993622i	$-0.464031\pi$
$59$	8.05146e56	0.225520	0.112760	+	0.993622i	$0.464031\pi$
$60$	−5.01269e57	−0.813122
$61$	7.28180e57	0.690270	0.345135	−	0.938553i	$-0.387833\pi$
$61$	7.28180e57	0.690270	0.345135	+	0.938553i	$0.387833\pi$
$62$	1.98507e57	0.110929
$63$	−4.53499e57	−0.150664
$64$	1.56649e57	0.0311945
$65$	1.16598e59	1.40283
$66$	−5.81277e58	−0.425799
$67$	2.30605e59	1.03619	0.518093	−	0.855324i	$-0.326642\pi$
$67$	2.30605e59	1.03619	0.518093	+	0.855324i	$0.326642\pi$
$68$	−3.71253e59	−1.03070
$69$	−5.31017e59	−0.917303
$70$	−3.35821e59	−0.363430
$71$	1.89858e60	1.29579	0.647894	−	0.761731i	$-0.275650\pi$
$71$	1.89858e60	1.29579	0.647894	+	0.761731i	$0.275650\pi$
$72$	−6.26135e59	−0.271245
$73$	1.33542e59	0.0369509	0.0184755	−	0.999829i	$-0.494119\pi$
$73$	1.33542e59	0.0369509	0.0184755	+	0.999829i	$0.494119\pi$
$74$	8.55294e59	0.152084
$75$	1.07664e61	1.23759
$76$	−1.57972e61	−1.18070
$77$	1.50406e61	0.735050
$78$	6.44743e60	0.207163
$79$	6.07331e61	1.28987	0.644933	−	0.764239i	$-0.276885\pi$
$79$	6.07331e61	1.28987	0.644933	+	0.764239i	$0.276885\pi$
$80$	5.34365e61	0.754073
$81$	1.17902e61	0.111111
$82$	4.00741e61	0.253463
$83$	−1.13480e62	−0.484040	−0.242020	−	0.970271i	$-0.577810\pi$
$83$	−1.13480e62	−0.484040	−0.242020	+	0.970271i	$0.577810\pi$
$84$	7.17217e61	0.207288
$85$	1.16937e63	2.30058
$86$	4.41963e62	0.594547
$87$	−1.64913e62	−0.152363
$88$	2.07662e63	1.32333
$89$	−1.42307e62	−0.0628131	−0.0314066	−	0.999507i	$-0.509999\pi$
$89$	−1.42307e62	−0.0628131	−0.0314066	+	0.999507i	$0.509999\pi$
$90$	8.73074e62	0.268021
$91$	−1.66828e63	−0.357622
$92$	8.39812e63	1.26205
$93$	1.33537e63	0.141224
$94$	−4.80856e63	−0.359219
$95$	4.97581e64	2.63540
$96$	1.54211e64	0.581168
$97$	5.82740e64	1.56817	0.784085	−	0.620653i	$-0.213132\pi$
$97$	5.82740e64	1.56817	0.784085	+	0.620653i	$0.213132\pi$
$98$	−1.87145e64	−0.360853
$99$	−3.91029e64	−0.542082
$100$	−1.70272e65	−1.70272
$101$	−5.65978e64	−0.409595	−0.204798	−	0.978804i	$-0.565654\pi$
$101$	−5.65978e64	−0.409595	−0.204798	+	0.978804i	$0.565654\pi$
$102$	6.46622e64	0.339739
$103$	1.89775e65	0.726155	0.363077	−	0.931759i	$-0.381726\pi$
$103$	1.89775e65	0.726155	0.363077	+	0.931759i	$0.381726\pi$
$104$	−2.30335e65	−0.643838
$105$	−2.25909e65	−0.462681
$106$	3.03692e65	0.457081
$107$	−8.68980e65	−0.963911	−0.481956	−	0.876196i	$-0.660073\pi$
$107$	−8.68980e65	−0.963911	−0.481956	+	0.876196i	$0.660073\pi$
$108$	−1.86464e65	−0.152870
$109$	−1.38051e66	−0.838836	−0.419418	−	0.907793i	$-0.637766\pi$
$109$	−1.38051e66	−0.838836	−0.419418	+	0.907793i	$0.637766\pi$
$110$	−2.89561e66	−1.30761
$111$	5.75363e65	0.193618
$112$	−7.64570e65	−0.192235
$113$	5.66434e66	1.06684	0.533421	−	0.845850i	$-0.320906\pi$
$113$	5.66434e66	1.06684	0.533421	+	0.845850i	$0.320906\pi$
$114$	2.75144e66	0.389182
$115$	−2.64524e67	−2.81699
$116$	2.60813e66	0.209626
$117$	4.33723e66	0.263738
$118$	2.21783e66	0.102274
$119$	−1.67314e67	−0.586484
$120$	−3.11907e67	−0.832979
$121$	8.06503e67	1.64468
$122$	2.00582e67	0.313039
$123$	2.69582e67	0.322682
$124$	−2.11192e67	−0.194300
$125$	2.86122e68	2.02757
$126$	−1.24920e67	−0.0683263
$127$	3.83188e67	0.162103	0.0810514	−	0.996710i	$-0.474172\pi$
$127$	3.83188e67	0.162103	0.0810514	+	0.996710i	$0.474172\pi$
$128$	−3.02719e68	−0.992465
$129$	2.97312e68	0.756914
$130$	3.21176e68	0.636187
$131$	5.34531e68	0.825384	0.412692	−	0.910871i	$-0.364589\pi$
$131$	5.34531e68	0.825384	0.412692	+	0.910871i	$0.364589\pi$
$132$	6.18419e68	0.745813
$133$	−7.11939e68	−0.671838
$134$	6.35218e68	0.469912
$135$	5.87324e68	0.341216
$136$	−2.31006e69	−1.05587
$137$	−1.69801e69	−0.611676	−0.305838	−	0.952084i	$-0.598937\pi$
$137$	−1.69801e69	−0.611676	−0.305838	+	0.952084i	$0.598937\pi$
$138$	−1.46272e69	−0.415999
$139$	−5.08502e69	−1.14370	−0.571850	−	0.820358i	$-0.693774\pi$
$139$	−5.08502e69	−1.14370	−0.571850	+	0.820358i	$0.693774\pi$
$140$	3.57279e69	0.636570
$141$	−3.23475e69	−0.457320
$142$	5.22979e69	0.587642
$143$	−1.43847e70	−1.28671
$144$	1.98775e69	0.141769
$145$	−8.21509e69	−0.467899
$146$	3.67851e68	0.0167573
$147$	−1.25894e70	−0.459400
$148$	−9.09946e69	−0.266385
$149$	4.13195e70	0.971855	0.485927	−	0.873999i	$-0.338482\pi$
$149$	4.13195e70	0.971855	0.485927	+	0.873999i	$0.338482\pi$
$150$	2.96567e70	0.561251
$151$	−3.71183e70	−0.566027	−0.283014	−	0.959116i	$-0.591334\pi$
$151$	−3.71183e70	−0.566027	−0.283014	+	0.959116i	$0.591334\pi$
$152$	−9.82956e70	−1.20953
$153$	4.34987e70	0.432519
$154$	4.14304e70	0.333346
$155$	6.65212e70	0.433690
$156$	−6.85941e70	−0.362859
$157$	−2.80660e70	−0.120626	−0.0603130	−	0.998180i	$-0.519210\pi$
$157$	−2.80660e70	−0.120626	−0.0603130	+	0.998180i	$0.519210\pi$
$158$	1.67294e71	0.584957
$159$	2.04296e71	0.581907
$160$	7.68198e71	1.78474
$161$	3.78481e71	0.718131
$162$	3.24769e70	0.0503891
$163$	1.03692e72	1.31719	0.658594	−	0.752498i	$-0.271151\pi$
$163$	1.03692e72	1.31719	0.658594	+	0.752498i	$0.271151\pi$
$164$	−4.26348e71	−0.443955
$165$	−1.94790e72	−1.66471
$166$	−3.12588e71	−0.219513
$167$	−1.81046e72	−1.04593	−0.522965	−	0.852354i	$-0.675174\pi$
$167$	−1.81046e72	−1.04593	−0.522965	+	0.852354i	$0.675174\pi$
$168$	4.46276e71	0.212350
$169$	−9.53164e71	−0.373981
$170$	3.22112e72	1.04332
$171$	1.85092e72	0.495466
$172$	−4.70204e72	−1.04139
$173$	−2.52067e72	−0.462400	−0.231200	−	0.972906i	$-0.574265\pi$
$173$	−2.52067e72	−0.462400	−0.231200	+	0.972906i	$0.574265\pi$
$174$	−4.54265e71	−0.0690970
$175$	−7.67370e72	−0.968876
$176$	−6.59249e72	−0.691652
$177$	1.49195e72	0.130204
$178$	−3.91994e71	−0.0284859
$179$	−1.31892e73	−0.798904	−0.399452	−	0.916754i	$-0.630800\pi$
$179$	−1.31892e73	−0.798904	−0.399452	+	0.916754i	$0.630800\pi$
$180$	−9.28862e72	−0.469456
$181$	3.05983e73	1.29164	0.645822	−	0.763488i	$-0.276515\pi$
$181$	3.05983e73	1.29164	0.645822	+	0.763488i	$0.276515\pi$
$182$	−4.59540e72	−0.162182
$183$	1.34933e73	0.398528
$184$	5.22559e73	1.29287
$185$	2.86615e73	0.594590
$186$	3.67838e72	0.0640452
$187$	−1.44266e74	−2.11015
$188$	5.11582e73	0.629194
$189$	−8.40343e72	−0.0869858
$190$	1.37062e74	1.19516
$191$	1.16760e74	0.858440	0.429220	−	0.903200i	$-0.358788\pi$
$191$	1.16760e74	0.858440	0.429220	+	0.903200i	$0.358788\pi$
$192$	2.90273e72	0.0180101
$193$	−1.93063e74	−1.01178	−0.505890	−	0.862598i	$-0.668836\pi$
$193$	−1.93063e74	−1.01178	−0.505890	+	0.862598i	$0.668836\pi$
$194$	1.60520e74	0.711168
$195$	2.16058e74	0.809925
$196$	1.99103e74	0.632056
$197$	8.69090e73	0.233837	0.116918	−	0.993142i	$-0.462698\pi$
$197$	8.69090e73	0.233837	0.116918	+	0.993142i	$0.462698\pi$
$198$	−1.07712e74	−0.245835
$199$	−4.70450e74	−0.911566	−0.455783	−	0.890091i	$-0.650641\pi$
$199$	−4.70450e74	−0.911566	−0.455783	+	0.890091i	$0.650641\pi$
$200$	−1.05949e75	−1.74430
$201$	4.27316e74	0.598242
$202$	−1.55903e74	−0.185752
$203$	1.17542e74	0.119281
$204$	−6.87940e74	−0.595073
$205$	1.34291e75	0.990939
$206$	5.22749e74	0.329312
$207$	−9.83985e74	−0.529605
$208$	7.31229e74	0.336508
$209$	−6.13869e75	−2.41725
$210$	−6.22282e74	−0.209826
$211$	−2.12606e75	−0.614320	−0.307160	−	0.951658i	$-0.599379\pi$
$211$	−2.12606e75	−0.614320	−0.307160	+	0.951658i	$0.599379\pi$
$212$	−3.23098e75	−0.800606
$213$	3.51812e75	0.748123
$214$	−2.39367e75	−0.437135
$215$	1.48105e76	2.32444
$216$	−1.16024e75	−0.156603
$217$	−9.51786e74	−0.110560
$218$	−3.80270e75	−0.380414
$219$	2.47456e74	0.0213336
$220$	3.08063e76	2.29035
$221$	1.60018e76	1.02664
$222$	1.58488e75	0.0878059
$223$	−1.68148e76	−0.804977	−0.402488	−	0.915425i	$-0.631855\pi$
$223$	−1.68148e76	−0.804977	−0.402488	+	0.915425i	$0.631855\pi$
$224$	−1.09914e76	−0.454980
$225$	1.99503e76	0.714524
$226$	1.56028e76	0.483815
$227$	−3.37633e76	−0.906995	−0.453498	−	0.891257i	$-0.649824\pi$
$227$	−3.37633e76	−0.906995	−0.453498	+	0.891257i	$0.649824\pi$
$228$	−2.92726e76	−0.681677
$229$	6.43837e76	1.30054	0.650268	−	0.759705i	$-0.274656\pi$
$229$	6.43837e76	1.30054	0.650268	+	0.759705i	$0.274656\pi$
$230$	−7.28650e76	−1.27751
$231$	2.78705e76	0.424381
$232$	1.62287e76	0.214745
$233$	−2.23067e76	−0.256665	−0.128333	−	0.991731i	$-0.540963\pi$
$233$	−2.23067e76	−0.256665	−0.128333	+	0.991731i	$0.540963\pi$
$234$	1.19472e76	0.119606
$235$	−1.61138e77	−1.40440
$236$	−2.35955e76	−0.179138
$237$	1.12540e77	0.744705
$238$	−4.60879e76	−0.265972
$239$	−1.26689e77	−0.637982	−0.318991	−	0.947758i	$-0.603344\pi$
$239$	−1.26689e77	−0.637982	−0.318991	+	0.947758i	$0.603344\pi$
$240$	9.90188e76	0.435364
$241$	−2.42925e77	−0.933079	−0.466539	−	0.884500i	$-0.654499\pi$
$241$	−2.42925e77	−0.933079	−0.466539	+	0.884500i	$0.654499\pi$
$242$	2.22157e77	0.745865
$243$	2.18475e76	0.0641500
$244$	−2.13399e77	−0.548306
$245$	−6.27135e77	−1.41079
$246$	7.42582e76	0.146337
$247$	6.80894e77	1.17606
$248$	−1.31411e77	−0.199045
$249$	−2.10281e77	−0.279460
$250$	7.88143e77	0.919507
$251$	−1.23366e78	−1.26415	−0.632077	−	0.774905i	$-0.717797\pi$
$251$	−1.23366e78	−1.26415	−0.632077	+	0.774905i	$0.717797\pi$
$252$	1.32902e77	0.119678
$253$	3.26345e78	2.58381
$254$	1.05552e77	0.0735139
$255$	2.16687e78	1.32824
$256$	−8.91653e77	−0.481279
$257$	−1.06737e78	−0.507560	−0.253780	−	0.967262i	$-0.581674\pi$
$257$	−1.06737e78	−0.507560	−0.253780	+	0.967262i	$0.581674\pi$
$258$	8.18966e77	0.343262
$259$	−4.10089e77	−0.151578
$260$	−3.41699e78	−1.11432
$261$	−3.05588e77	−0.0879669
$262$	1.47240e78	0.374313
$263$	−1.58670e78	−0.356395	−0.178198	−	0.983995i	$-0.557027\pi$
$263$	−1.58670e78	−0.356395	−0.178198	+	0.983995i	$0.557027\pi$
$264$	3.84801e78	0.764027
$265$	1.01769e79	1.78701
$266$	−1.96109e78	−0.304680
$267$	−2.63697e77	−0.0362652
$268$	−6.75807e78	−0.823080
$269$	−1.55488e79	−1.67783	−0.838913	−	0.544265i	$-0.816809\pi$
$269$	−1.55488e79	−1.67783	−0.838913	+	0.544265i	$0.816809\pi$
$270$	1.61782e78	0.154742
$271$	−1.02845e79	−0.872332	−0.436166	−	0.899866i	$-0.643664\pi$
$271$	−1.02845e79	−0.872332	−0.436166	+	0.899866i	$0.643664\pi$
$272$	7.33360e78	0.551858
$273$	−3.09136e78	−0.206473
$274$	−4.67729e78	−0.277396
$275$	−6.61664e79	−3.48598
$276$	1.55619e79	0.728647
$277$	4.40171e79	1.83244	0.916218	−	0.400681i	$-0.131226\pi$
$277$	4.40171e79	1.83244	0.916218	+	0.400681i	$0.131226\pi$
$278$	−1.40071e79	−0.518670
$279$	2.47448e78	0.0815355
$280$	2.22311e79	0.652116
$281$	6.49123e79	1.69579	0.847894	−	0.530166i	$-0.177870\pi$
$281$	6.49123e79	1.69579	0.847894	+	0.530166i	$0.177870\pi$
$282$	−8.91035e78	−0.207395
$283$	−7.99232e78	−0.165811	−0.0829056	−	0.996557i	$-0.526420\pi$
$283$	−7.99232e78	−0.165811	−0.0829056	+	0.996557i	$0.526420\pi$
$284$	−5.56396e79	−1.02929
$285$	9.22027e79	1.52155
$286$	−3.96237e79	−0.583525
$287$	−1.92144e79	−0.252618
$288$	2.85757e79	0.335537
$289$	6.51652e79	0.683654
$290$	−2.26291e79	−0.212193
$291$	1.07983e80	0.905384
$292$	−3.91356e78	−0.0293515
$293$	1.16933e80	0.784766	0.392383	−	0.919802i	$-0.371651\pi$
$293$	1.16933e80	0.784766	0.392383	+	0.919802i	$0.371651\pi$
$294$	−3.46783e79	−0.208339
$295$	7.43210e79	0.399849
$296$	−5.66199e79	−0.272890
$297$	−7.24585e79	−0.312971
$298$	1.13817e80	0.440738
$299$	−3.61977e80	−1.25709
$300$	−3.15517e80	−0.983064
$301$	−2.11908e80	−0.592567
$302$	−1.02245e80	−0.256694
$303$	−1.04877e80	−0.236480
$304$	3.12052e80	0.632173
$305$	6.72164e80	1.22386
$306$	1.19820e80	0.196148
$307$	−3.26296e80	−0.480412	−0.240206	−	0.970722i	$-0.577215\pi$
$307$	−3.26296e80	−0.480412	−0.240206	+	0.970722i	$0.577215\pi$
$308$	−4.40777e80	−0.583876
$309$	3.51657e80	0.419246
$310$	1.83237e80	0.196679
$311$	−7.45384e80	−0.720555	−0.360278	−	0.932845i	$-0.617318\pi$
$311$	−7.45384e80	−0.720555	−0.360278	+	0.932845i	$0.617318\pi$
$312$	−4.26816e80	−0.371720
$313$	−1.27784e81	−1.00297	−0.501483	−	0.865167i	$-0.667212\pi$
$313$	−1.27784e81	−1.00297	−0.501483	+	0.865167i	$0.667212\pi$
$314$	−7.73097e79	−0.0547041
$315$	−4.18614e80	−0.267129
$316$	−1.77983e81	−1.02459
$317$	2.45420e81	1.27493	0.637463	−	0.770481i	$-0.279984\pi$
$317$	2.45420e81	1.27493	0.637463	+	0.770481i	$0.279984\pi$
$318$	5.62748e80	0.263896
$319$	1.01350e81	0.429168
$320$	1.44598e80	0.0553082
$321$	−1.61024e81	−0.556514
$322$	1.04255e81	0.325674
$323$	6.82878e81	1.92868
$324$	−3.45521e80	−0.0882596
$325$	7.33907e81	1.69602
$326$	2.85627e81	0.597347
$327$	−2.55811e81	−0.484302
$328$	−2.65288e81	−0.454797
$329$	2.30556e81	0.358023
$330$	−5.36562e81	−0.754948
$331$	−9.84153e81	−1.25503	−0.627513	−	0.778606i	$-0.715927\pi$
$331$	−9.84153e81	−1.25503	−0.627513	+	0.778606i	$0.715927\pi$
$332$	3.32562e81	0.384490
$333$	1.06616e81	0.111785
$334$	−4.98703e81	−0.474331
$335$	2.12866e82	1.83717
$336$	−1.41676e81	−0.110987
$337$	−1.46609e82	−1.04277	−0.521387	−	0.853321i	$-0.674585\pi$
$337$	−1.46609e82	−1.04277	−0.521387	+	0.853321i	$0.674585\pi$
$338$	−2.62556e81	−0.169601
$339$	1.04961e82	0.615942
$340$	−3.42695e82	−1.82744
$341$	−8.20676e81	−0.397791
$342$	5.09848e81	0.224695
$343$	2.02499e82	0.811642
$344$	−2.92577e82	−1.06682
$345$	−4.90168e82	−1.62639
$346$	−6.94337e81	−0.209699
$347$	3.83459e82	1.05441	0.527207	−	0.849737i	$-0.323239\pi$
$347$	3.83459e82	1.05441	0.527207	+	0.849737i	$0.323239\pi$
$348$	4.83292e81	0.121028
$349$	4.47894e82	1.02176	0.510879	−	0.859652i	$-0.329320\pi$
$349$	4.47894e82	1.02176	0.510879	+	0.859652i	$0.329320\pi$
$350$	−2.11378e82	−0.439387
$351$	8.03698e81	0.152269
$352$	−9.47731e82	−1.63700
$353$	2.46644e82	0.388502	0.194251	−	0.980952i	$-0.437772\pi$
$353$	2.46644e82	0.388502	0.194251	+	0.980952i	$0.437772\pi$
$354$	4.10969e81	0.0590477
$355$	1.75254e83	2.29745
$356$	4.17042e81	0.0498947
$357$	−3.10036e82	−0.338607
$358$	−3.63306e82	−0.362304
$359$	9.56775e81	0.0871445	0.0435723	−	0.999050i	$-0.486126\pi$
$359$	9.56775e81	0.0871445	0.0435723	+	0.999050i	$0.486126\pi$
$360$	−5.77969e82	−0.480921
$361$	1.59054e83	1.20937
$362$	8.42851e82	0.585763
$363$	1.49447e83	0.949556
$364$	4.88903e82	0.284072
$365$	1.23269e82	0.0655145
$366$	3.71683e82	0.180733
$367$	−2.53741e83	−1.12913	−0.564565	−	0.825389i	$-0.690956\pi$
$367$	−2.53741e83	−1.12913	−0.564565	+	0.825389i	$0.690956\pi$
$368$	−1.65893e83	−0.675732
$369$	4.99540e82	0.186300
$370$	7.89500e82	0.269647
$371$	−1.45612e83	−0.455559
$372$	−3.91343e82	−0.112179
$373$	−3.01274e83	−0.791453	−0.395726	−	0.918368i	$-0.629507\pi$
$373$	−3.01274e83	−0.791453	−0.395726	+	0.918368i	$0.629507\pi$
$374$	−3.97392e83	−0.956956
$375$	5.30190e83	1.17062
$376$	3.18323e83	0.644560
$377$	−1.12416e83	−0.208802
$378$	−2.31479e82	−0.0394482
$379$	4.04643e83	0.632846	0.316423	−	0.948618i	$-0.397518\pi$
$379$	4.04643e83	0.632846	0.316423	+	0.948618i	$0.397518\pi$
$380$	−1.45820e84	−2.09339
$381$	7.10054e82	0.0935901
$382$	3.21624e83	0.389304
$383$	−7.19927e82	−0.0800439	−0.0400220	−	0.999199i	$-0.512743\pi$
$383$	−7.19927e82	−0.0800439	−0.0400220	+	0.999199i	$0.512743\pi$
$384$	−5.60944e83	−0.573000
$385$	1.38836e84	1.30325
$386$	−5.31806e83	−0.458844
$387$	5.50925e83	0.437005
$388$	−1.70777e84	−1.24565
$389$	−1.35411e84	−0.908434	−0.454217	−	0.890891i	$-0.650081\pi$
$389$	−1.35411e84	−0.908434	−0.454217	+	0.890891i	$0.650081\pi$
$390$	5.95146e83	0.367303
$391$	−3.63032e84	−2.06158
$392$	1.23889e84	0.647492
$393$	9.90497e83	0.476535
$394$	2.39397e83	0.106045
$395$	5.60612e84	2.28695
$396$	1.14594e84	0.430596
$397$	5.09033e84	1.76220	0.881099	−	0.472933i	$-0.156805\pi$
$397$	5.09033e84	1.76220	0.881099	+	0.472933i	$0.156805\pi$
$398$	−1.29589e84	−0.413397
$399$	−1.31924e84	−0.387886
$400$	3.36348e84	0.911674
$401$	−6.09581e84	−1.52349	−0.761744	−	0.647878i	$-0.775657\pi$
$401$	−6.09581e84	−1.52349	−0.761744	+	0.647878i	$0.775657\pi$
$402$	1.17707e84	0.271304
$403$	9.10281e83	0.193536
$404$	1.65865e84	0.325356
$405$	1.08832e84	0.197001
$406$	3.23777e83	0.0540941
$407$	−3.53598e84	−0.545371
$408$	−4.28059e84	−0.609605
$409$	1.13215e85	1.48901	0.744505	−	0.667617i	$-0.232686\pi$
$409$	1.13215e85	1.48901	0.744505	+	0.667617i	$0.232686\pi$
$410$	3.69914e84	0.449393
$411$	−3.14645e84	−0.353151
$412$	−5.56151e84	−0.576811
$413$	−1.06339e84	−0.101933
$414$	−2.71046e84	−0.240177
$415$	−1.04750e85	−0.858208
$416$	1.05121e85	0.796445
$417$	−9.42265e84	−0.660315
$418$	−1.69095e85	−1.09623
$419$	−2.14262e85	−1.28526	−0.642628	−	0.766178i	$-0.722156\pi$
$419$	−2.14262e85	−1.28526	−0.642628	+	0.766178i	$0.722156\pi$
$420$	6.62045e84	0.367524
$421$	−1.84657e85	−0.948852	−0.474426	−	0.880295i	$-0.657344\pi$
$421$	−1.84657e85	−0.948852	−0.474426	+	0.880295i	$0.657344\pi$
$422$	−5.85637e84	−0.278595
$423$	−5.99406e84	−0.264034
$424$	−2.01042e85	−0.820157
$425$	7.36046e85	2.78141
$426$	9.69090e84	0.339275
$427$	−9.61734e84	−0.311996
$428$	2.54662e85	0.765669
$429$	−2.66552e85	−0.742882
$430$	4.07965e85	1.05414
$431$	5.50227e85	1.31835	0.659175	−	0.751989i	$-0.270906\pi$
$431$	5.50227e85	1.31835	0.659175	+	0.751989i	$0.270906\pi$
$432$	3.68334e84	0.0818501
$433$	−5.50983e85	−1.13575	−0.567873	−	0.823116i	$-0.692234\pi$
$433$	−5.50983e85	−1.13575	−0.567873	+	0.823116i	$0.692234\pi$
$434$	−2.62176e84	−0.0501392
$435$	−1.52227e85	−0.270142
$436$	4.04569e85	0.666318
$437$	−1.54474e86	−2.36161
$438$	6.81636e83	0.00967484
$439$	3.79738e85	0.500481	0.250240	−	0.968184i	$-0.419490\pi$
$439$	3.79738e85	0.500481	0.250240	+	0.968184i	$0.419490\pi$
$440$	1.91687e86	2.34629
$441$	−2.33284e85	−0.265235
$442$	4.40781e85	0.465585
$443$	5.59527e85	0.549162	0.274581	−	0.961564i	$-0.411461\pi$
$443$	5.59527e85	0.549162	0.274581	+	0.961564i	$0.411461\pi$
$444$	−1.68615e85	−0.153797
$445$	−1.31360e85	−0.111368
$446$	−4.63175e85	−0.365059
$447$	7.65659e85	0.561101
$448$	−2.06892e84	−0.0140996
$449$	1.28151e86	0.812296	0.406148	−	0.913807i	$-0.366872\pi$
$449$	1.28151e86	0.812296	0.406148	+	0.913807i	$0.366872\pi$
$450$	5.49545e85	0.324038
$451$	−1.65676e86	−0.908911
$452$	−1.65998e86	−0.847431
$453$	−6.87810e85	−0.326796
$454$	−9.30035e85	−0.411324
$455$	−1.53995e86	−0.634068
$456$	−1.82144e86	−0.698324
$457$	−4.31091e86	−1.53919	−0.769595	−	0.638532i	$-0.779542\pi$
$457$	−4.31091e86	−1.53919	−0.769595	+	0.638532i	$0.779542\pi$
$458$	1.77349e86	0.589796
$459$	8.06040e85	0.249715
$460$	7.75209e86	2.23764
$461$	−6.81501e86	−1.83310	−0.916551	−	0.399918i	$-0.869039\pi$
$461$	−6.81501e86	−1.83310	−0.916551	+	0.399918i	$0.869039\pi$
$462$	7.67714e85	0.192458
$463$	1.64154e86	0.383591	0.191796	−	0.981435i	$-0.438569\pi$
$463$	1.64154e86	0.383591	0.191796	+	0.981435i	$0.438569\pi$
$464$	−5.15200e85	−0.112239
$465$	1.23265e86	0.250391
$466$	−6.14453e85	−0.116398
$467$	4.11907e86	0.727781	0.363891	−	0.931442i	$-0.381448\pi$
$467$	4.11907e86	0.727781	0.363891	+	0.931442i	$0.381448\pi$
$468$	−1.27106e86	−0.209496
$469$	−3.04569e86	−0.468347
$470$	−4.43866e86	−0.636900
$471$	−5.20068e85	−0.0696435
$472$	−1.46819e86	−0.183513
$473$	−1.82718e87	−2.13203
$474$	3.09998e86	0.337725
$475$	3.13195e87	3.18620
$476$	4.90328e86	0.465866
$477$	3.78565e86	0.335964
$478$	−3.48975e86	−0.289326
$479$	−9.16847e86	−0.710219	−0.355110	−	0.934825i	$-0.615557\pi$
$479$	−9.16847e86	−0.710219	−0.355110	+	0.934825i	$0.615557\pi$
$480$	1.42349e87	1.03042
$481$	3.92206e86	0.265338
$482$	−6.69154e86	−0.423153
$483$	7.01333e86	0.414613
$484$	−2.36352e87	−1.30643
$485$	5.37913e87	2.78039
$486$	6.01803e85	0.0290922
$487$	4.08178e86	0.184569	0.0922844	−	0.995733i	$-0.470583\pi$
$487$	4.08178e86	0.184569	0.0922844	+	0.995733i	$0.470583\pi$
$488$	−1.32784e87	−0.561697
$489$	1.92143e87	0.760479
$490$	−1.72749e87	−0.639797
$491$	−2.25556e87	−0.781817	−0.390908	−	0.920430i	$-0.627839\pi$
$491$	−2.25556e87	−0.781817	−0.390908	+	0.920430i	$0.627839\pi$
$492$	−7.90032e86	−0.256318
$493$	−1.12744e87	−0.342426
$494$	1.87557e87	0.533344
$495$	−3.60949e87	−0.961119
$496$	4.17180e86	0.104033
$497$	−2.50753e87	−0.585684
$498$	−5.79233e86	−0.126736
$499$	6.71691e87	1.37690	0.688449	−	0.725284i	$-0.258292\pi$
$499$	6.71691e87	1.37690	0.688449	+	0.725284i	$0.258292\pi$
$500$	−8.38504e87	−1.61057
$501$	−3.35481e87	−0.603868
$502$	−3.39821e87	−0.573296
$503$	−5.18036e87	−0.819220	−0.409610	−	0.912261i	$-0.634335\pi$
$503$	−5.18036e87	−0.819220	−0.409610	+	0.912261i	$0.634335\pi$
$504$	8.26959e86	0.122600
$505$	−5.22440e87	−0.726218
$506$	8.98940e87	1.17176
$507$	−1.76623e87	−0.215918
$508$	−1.12296e87	−0.128764
$509$	5.16474e86	0.0555546	0.0277773	−	0.999614i	$-0.491157\pi$
$509$	5.16474e86	0.0555546	0.0277773	+	0.999614i	$0.491157\pi$
$510$	5.96880e87	0.602361
$511$	−1.76374e86	−0.0167015
$512$	8.71223e87	0.774204
$513$	3.42979e87	0.286057
$514$	−2.94014e87	−0.230180
$515$	1.75176e88	1.28748
$516$	−8.71297e87	−0.601244
$517$	1.98797e88	1.28815
$518$	−1.12962e87	−0.0687408
$519$	−4.67086e87	−0.266967
$520$	−2.12617e88	−1.14153
$521$	3.28303e88	1.65595	0.827977	−	0.560762i	$-0.189492\pi$
$521$	3.28303e88	1.65595	0.827977	+	0.560762i	$0.189492\pi$
$522$	−8.41763e86	−0.0398932
$523$	−7.37591e87	−0.328481	−0.164241	−	0.986420i	$-0.552517\pi$
$523$	−7.37591e87	−0.328481	−0.164241	+	0.986420i	$0.552517\pi$
$524$	−1.56649e88	−0.655632
$525$	−1.42195e88	−0.559381
$526$	−4.37066e87	−0.161626
$527$	9.12934e87	0.317391
$528$	−1.22160e88	−0.399326
$529$	4.95894e88	1.52433
$530$	2.80331e88	0.810411
$531$	2.76462e87	0.0751732
$532$	2.08640e88	0.533665
$533$	1.83765e88	0.442210
$534$	−7.26373e86	−0.0164463
$535$	−8.02134e88	−1.70903
$536$	−4.20510e88	−0.843181
$537$	−2.44398e88	−0.461247
$538$	−4.28302e88	−0.760897
$539$	7.73701e88	1.29401
$540$	−1.72120e88	−0.271041
$541$	−7.86627e88	−1.16643	−0.583214	−	0.812319i	$-0.698205\pi$
$541$	−7.86627e88	−1.16643	−0.583214	+	0.812319i	$0.698205\pi$
$542$	−2.83294e88	−0.395604
$543$	5.66992e88	0.745731
$544$	1.05427e89	1.30614
$545$	−1.27431e89	−1.48727
$546$	−8.51536e87	−0.0936359
$547$	2.99732e87	0.0310560	0.0155280	−	0.999879i	$-0.495057\pi$
$547$	2.99732e87	0.0310560	0.0155280	+	0.999879i	$0.495057\pi$
$548$	4.97616e88	0.485876
$549$	2.50034e88	0.230090
$550$	−1.82260e89	−1.58090
$551$	−4.79736e88	−0.392261
$552$	9.68313e88	0.746441
$553$	−8.02124e88	−0.583008
$554$	1.21248e89	0.831013
$555$	5.31103e88	0.343286
$556$	1.49021e89	0.908482
$557$	−3.36120e89	−1.93286	−0.966429	−	0.256933i	$-0.917288\pi$
$557$	−3.36120e89	−1.93286	−0.966429	+	0.256933i	$0.917288\pi$
$558$	6.81612e87	0.0369765
$559$	2.02668e89	1.03729
$560$	−7.05755e88	−0.340834
$561$	−2.67329e89	−1.21829
$562$	1.78805e89	0.769043
$563$	1.56822e89	0.636624	0.318312	−	0.947986i	$-0.396884\pi$
$563$	1.56822e89	0.636624	0.318312	+	0.947986i	$0.396884\pi$
$564$	9.47971e88	0.363266
$565$	5.22861e89	1.89152
$566$	−2.20154e88	−0.0751957
$567$	−1.55717e88	−0.0502213
$568$	−3.46208e89	−1.05443
$569$	1.43335e89	0.412292	0.206146	−	0.978521i	$-0.433908\pi$
$569$	1.43335e89	0.412292	0.206146	+	0.978521i	$0.433908\pi$
$570$	2.53979e89	0.690025
$571$	6.02932e89	1.54737	0.773687	−	0.633569i	$-0.218411\pi$
$571$	6.02932e89	1.54737	0.773687	+	0.633569i	$0.218411\pi$
$572$	4.21556e89	1.02208
$573$	2.16359e89	0.495621
$574$	−5.29274e88	−0.114563
$575$	−1.66501e90	−3.40574
$576$	5.37882e87	0.0103982
$577$	−3.38961e89	−0.619350	−0.309675	−	0.950842i	$-0.600220\pi$
$577$	−3.38961e89	−0.619350	−0.309675	+	0.950842i	$0.600220\pi$
$578$	1.79502e89	0.310038
$579$	−3.57750e89	−0.584152
$580$	2.40750e89	0.371669
$581$	1.49877e89	0.218782
$582$	2.97446e89	0.410593
$583$	−1.25554e90	−1.63908
$584$	−2.43515e88	−0.0300683
$585$	4.00359e89	0.467610
$586$	3.22101e89	0.355893
$587$	−8.28087e89	−0.865641	−0.432820	−	0.901480i	$-0.642482\pi$
$587$	−8.28087e89	−0.865641	−0.432820	+	0.901480i	$0.642482\pi$
$588$	3.68942e89	0.364918
$589$	3.88463e89	0.363582
$590$	2.04723e89	0.181332
$591$	1.61044e89	0.135006
$592$	1.79747e89	0.142629
$593$	−1.06459e90	−0.799659	−0.399830	−	0.916589i	$-0.630931\pi$
$593$	−1.06459e90	−0.799659	−0.399830	+	0.916589i	$0.630931\pi$
$594$	−1.99592e89	−0.141933
$595$	−1.54443e90	−1.03984
$596$	−1.21090e90	−0.771979
$597$	−8.71753e89	−0.526293
$598$	−9.97090e89	−0.570093
$599$	1.87437e90	1.01504	0.507520	−	0.861640i	$-0.330563\pi$
$599$	1.87437e90	1.01504	0.507520	+	0.861640i	$0.330563\pi$
$600$	−1.96325e90	−1.00707
$601$	5.59029e89	0.271652	0.135826	−	0.990733i	$-0.456631\pi$
$601$	5.59029e89	0.271652	0.135826	+	0.990733i	$0.456631\pi$
$602$	−5.83717e89	−0.268730
$603$	7.91825e89	0.345395
$604$	1.08778e90	0.449616
$605$	7.44463e90	2.91604
$606$	−2.88891e89	−0.107244
$607$	3.60962e90	1.27008	0.635038	−	0.772481i	$-0.280985\pi$
$607$	3.60962e90	1.27008	0.635038	+	0.772481i	$0.280985\pi$
$608$	4.48604e90	1.49622
$609$	2.17807e89	0.0688668
$610$	1.85152e90	0.555021
$611$	−2.20502e90	−0.626721
$612$	−1.27477e90	−0.343565
$613$	−7.12106e90	−1.82003	−0.910016	−	0.414572i	$-0.863931\pi$
$613$	−7.12106e90	−1.82003	−0.910016	+	0.414572i	$0.863931\pi$
$614$	−8.98804e89	−0.217868
$615$	2.48844e90	0.572119
$616$	−2.74266e90	−0.598135
$617$	6.39023e90	1.32205	0.661026	−	0.750363i	$-0.270121\pi$
$617$	6.39023e90	1.32205	0.661026	+	0.750363i	$0.270121\pi$
$618$	9.68664e89	0.190129
$619$	−6.56756e90	−1.22309	−0.611545	−	0.791210i	$-0.709452\pi$
$619$	−6.56756e90	−1.22309	−0.611545	+	0.791210i	$0.709452\pi$
$620$	−1.94946e90	−0.344496
$621$	−1.82334e90	−0.305768
$622$	−2.05321e90	−0.326773
$623$	1.87950e89	0.0283910
$624$	1.35498e90	0.194283
$625$	1.06627e91	1.45133
$626$	−3.51991e90	−0.454847
$627$	−1.13751e91	−1.39560
$628$	8.22496e89	0.0958176
$629$	3.93349e90	0.435143
$630$	−1.15310e90	−0.121143
$631$	9.14236e90	0.912229	0.456115	−	0.889921i	$-0.349241\pi$
$631$	9.14236e90	0.912229	0.456115	+	0.889921i	$0.349241\pi$
$632$	−1.10747e91	−1.04961
$633$	−3.93962e90	−0.354678
$634$	6.76028e90	0.578181
$635$	3.53711e90	0.287410
$636$	−5.98707e90	−0.462230
$637$	−8.58177e90	−0.629572
$638$	2.79176e90	0.194628
$639$	6.51914e90	0.431929
$640$	−2.79432e91	−1.75965
$641$	−6.54798e90	−0.391941	−0.195971	−	0.980610i	$-0.562786\pi$
$641$	−6.54798e90	−0.391941	−0.195971	+	0.980610i	$0.562786\pi$
$642$	−4.43551e90	−0.252380
$643$	−4.01708e90	−0.217297	−0.108649	−	0.994080i	$-0.534652\pi$
$643$	−4.01708e90	−0.217297	−0.108649	+	0.994080i	$0.534652\pi$
$644$	−1.10917e91	−0.570437
$645$	2.74441e91	1.34202
$646$	1.88104e91	0.874662
$647$	2.04496e91	0.904264	0.452132	−	0.891951i	$-0.350664\pi$
$647$	2.04496e91	0.904264	0.452132	+	0.891951i	$0.350664\pi$
$648$	−2.14995e90	−0.0904150
$649$	−9.16904e90	−0.366751
$650$	2.02160e91	0.769150
$651$	−1.76368e90	−0.0638318
$652$	−3.03878e91	−1.04629
$653$	−2.91233e91	−0.954031	−0.477016	−	0.878895i	$-0.658281\pi$
$653$	−2.91233e91	−0.954031	−0.477016	+	0.878895i	$0.658281\pi$
$654$	−7.04648e90	−0.219632
$655$	4.93412e91	1.46342
$656$	8.42192e90	0.237704
$657$	4.58542e89	0.0123170
$658$	6.35084e90	0.162364
$659$	8.34563e90	0.203087	0.101544	−	0.994831i	$-0.467622\pi$
$659$	8.34563e90	0.203087	0.101544	+	0.994831i	$0.467622\pi$
$660$	5.70847e91	1.32234
$661$	3.17883e91	0.701002	0.350501	−	0.936562i	$-0.386011\pi$
$661$	3.17883e91	0.701002	0.350501	+	0.936562i	$0.386011\pi$
$662$	−2.71092e91	−0.569157
$663$	2.96517e91	0.592733
$664$	2.06931e91	0.393880
$665$	−6.57173e91	−1.19118
$666$	2.93681e90	0.0506948
$667$	2.55037e91	0.419289
$668$	5.30569e91	0.830820
$669$	−3.11581e91	−0.464754
$670$	5.86354e91	0.833161
$671$	−8.29254e91	−1.12255
$672$	−2.03673e91	−0.262683
$673$	−4.04085e91	−0.496573	−0.248287	−	0.968687i	$-0.579868\pi$
$673$	−4.04085e91	−0.496573	−0.248287	+	0.968687i	$0.579868\pi$
$674$	−4.03846e91	−0.472900
$675$	3.69683e91	0.412531
$676$	2.79333e91	0.297067
$677$	−1.02034e92	−1.03422	−0.517108	−	0.855920i	$-0.672992\pi$
$677$	−1.02034e92	−1.03422	−0.517108	+	0.855920i	$0.672992\pi$
$678$	2.89124e91	0.279331
$679$	−7.69646e91	−0.708799
$680$	−2.13236e92	−1.87207
$681$	−6.25642e91	−0.523654
$682$	−2.26061e91	−0.180399
$683$	2.53255e92	1.92702	0.963509	−	0.267675i	$-0.0862554\pi$
$683$	2.53255e92	1.92702	0.963509	+	0.267675i	$0.0862554\pi$
$684$	−5.42427e91	−0.393566
$685$	−1.56739e92	−1.08451
$686$	5.57799e91	0.368081
$687$	1.19304e92	0.750865
$688$	9.28823e91	0.557582
$689$	1.39262e92	0.797458
$690$	−1.35020e92	−0.737571
$691$	−2.59318e92	−1.35144	−0.675720	−	0.737159i	$-0.736167\pi$
$691$	−2.59318e92	−1.35144	−0.675720	+	0.737159i	$0.736167\pi$
$692$	7.38704e91	0.367301
$693$	5.16447e91	0.245017
$694$	1.05627e92	0.478179
$695$	−4.69386e92	−2.02779
$696$	3.00721e91	0.123983
$697$	1.84301e92	0.725206
$698$	1.23375e92	0.463370
$699$	−4.13347e91	−0.148186
$700$	2.24884e92	0.769614
$701$	5.03596e92	1.64531	0.822653	−	0.568544i	$-0.192493\pi$
$701$	5.03596e92	1.64531	0.822653	+	0.568544i	$0.192493\pi$
$702$	2.21384e91	0.0690543
$703$	1.67374e92	0.498471
$704$	−1.78392e91	−0.0507299
$705$	−2.98592e92	−0.810833
$706$	6.79399e91	0.176186
$707$	7.47508e91	0.185134
$708$	−4.37229e91	−0.103426
$709$	3.16103e92	0.714209	0.357105	−	0.934064i	$-0.383764\pi$
$709$	3.16103e92	0.714209	0.357105	+	0.934064i	$0.383764\pi$
$710$	4.82748e92	1.04190
$711$	2.08538e92	0.429955
$712$	2.59497e91	0.0511132
$713$	−2.06515e92	−0.388634
$714$	−8.54017e91	−0.153559
$715$	−1.32782e93	−2.28135
$716$	3.86520e92	0.634598
$717$	−2.34758e92	−0.368339
$718$	2.63550e91	0.0395202
$719$	4.32948e92	0.620508	0.310254	−	0.950654i	$-0.399586\pi$
$719$	4.32948e92	0.620508	0.310254	+	0.950654i	$0.399586\pi$
$720$	1.83484e92	0.251358
$721$	−2.50643e92	−0.328216
$722$	4.38126e92	0.548454
$723$	−4.50145e92	−0.538713
$724$	−8.96707e92	−1.02600
$725$	−5.17088e92	−0.565691
$726$	4.11661e92	0.430626
$727$	−1.18976e93	−1.19012	−0.595058	−	0.803683i	$-0.702871\pi$
$727$	−1.18976e93	−1.19012	−0.595058	+	0.803683i	$0.702871\pi$
$728$	3.04212e92	0.291009
$729$	4.04838e91	0.0370370
$730$	3.39554e91	0.0297109
$731$	2.03258e93	1.70111
$732$	−3.95433e92	−0.316565
$733$	9.37422e92	0.717887	0.358943	−	0.933359i	$-0.383137\pi$
$733$	9.37422e92	0.717887	0.358943	+	0.933359i	$0.383137\pi$
$734$	−6.98948e92	−0.512063
$735$	−1.16209e93	−0.814522
$736$	−2.38487e93	−1.59932
$737$	−2.62614e93	−1.68509
$738$	1.37602e92	0.0844876
$739$	2.47858e93	1.45633	0.728164	−	0.685403i	$-0.240374\pi$
$739$	2.47858e93	1.45633	0.728164	+	0.685403i	$0.240374\pi$
$740$	−8.39948e92	−0.472304
$741$	1.26171e93	0.678997
$742$	−4.01098e92	−0.206597
$743$	−4.12270e92	−0.203257	−0.101628	−	0.994822i	$-0.532405\pi$
$743$	−4.12270e92	−0.203257	−0.101628	+	0.994822i	$0.532405\pi$
$744$	−2.43506e92	−0.114919
$745$	3.81410e93	1.72311
$746$	−8.29881e92	−0.358925
$747$	−3.89654e92	−0.161347
$748$	4.22785e93	1.67617
$749$	1.14769e93	0.435679
$750$	1.46045e93	0.530877
$751$	1.17897e93	0.410396	0.205198	−	0.978720i	$-0.434216\pi$
$751$	1.17897e93	0.410396	0.205198	+	0.978720i	$0.434216\pi$
$752$	−1.01056e93	−0.336885
$753$	−2.28600e93	−0.729860
$754$	−3.09658e92	−0.0946920
$755$	−3.42630e93	−1.00357
$756$	2.46270e92	0.0690959
$757$	−1.29931e93	−0.349218	−0.174609	−	0.984638i	$-0.555866\pi$
$757$	−1.29931e93	−0.349218	−0.174609	+	0.984638i	$0.555866\pi$
$758$	1.11462e93	0.286997
$759$	6.04724e93	1.49176
$760$	−9.07342e93	−2.14452
$761$	4.93251e93	1.11703	0.558517	−	0.829493i	$-0.311371\pi$
$761$	4.93251e93	1.11703	0.558517	+	0.829493i	$0.311371\pi$
$762$	1.95589e92	0.0424433
$763$	1.82329e93	0.379147
$764$	−3.42175e93	−0.681890
$765$	4.01526e93	0.766861
$766$	−1.98309e92	−0.0363001
$767$	1.01702e93	0.178434
$768$	−1.65225e93	−0.277867
$769$	1.09108e94	1.75894	0.879471	−	0.475952i	$-0.157896\pi$
$769$	1.09108e94	1.75894	0.879471	+	0.475952i	$0.157896\pi$
$770$	3.82434e93	0.591027
$771$	−1.97785e93	−0.293040
$772$	5.65787e93	0.803694
$773$	−1.24086e94	−1.69001	−0.845006	−	0.534757i	$-0.820403\pi$
$773$	−1.24086e94	−1.69001	−0.845006	+	0.534757i	$0.820403\pi$
$774$	1.51756e93	0.198182
$775$	4.18708e93	0.524332
$776$	−1.06263e94	−1.27608
$777$	−7.59903e92	−0.0875135
$778$	−3.73001e93	−0.411977
$779$	7.84219e93	0.830749
$780$	−6.33175e93	−0.643353
$781$	−2.16212e94	−2.10727
$782$	−9.99996e93	−0.934929
$783$	−5.66260e92	−0.0507877
$784$	−3.93301e93	−0.338418
$785$	−2.59070e93	−0.213872
$786$	2.72839e93	0.216110
$787$	−1.31183e94	−0.997006	−0.498503	−	0.866888i	$-0.666117\pi$
$787$	−1.31183e94	−0.997006	−0.498503	+	0.866888i	$0.666117\pi$
$788$	−2.54694e93	−0.185745
$789$	−2.94018e93	−0.205765
$790$	1.54424e94	1.03714
$791$	−7.48111e93	−0.482203
$792$	7.13044e93	0.441111
$793$	9.19795e93	0.546151
$794$	1.40217e94	0.799160
$795$	1.88581e94	1.03173
$796$	1.37869e94	0.724090
$797$	4.58398e93	0.231125	0.115563	−	0.993300i	$-0.463133\pi$
$797$	4.58398e93	0.231125	0.115563	+	0.993300i	$0.463133\pi$
$798$	−3.63394e93	−0.175907
$799$	−2.21145e94	−1.02780
$800$	4.83532e94	2.15775
$801$	−4.88636e92	−0.0209377
$802$	−1.67913e94	−0.690905
$803$	−1.52078e93	−0.0600914
$804$	−1.25228e94	−0.475205
$805$	3.49367e94	1.27325
$806$	2.50743e93	0.0877689
$807$	−2.88122e94	−0.968694
$808$	1.03207e94	0.333302
$809$	7.83941e92	0.0243196	0.0121598	−	0.999926i	$-0.496129\pi$
$809$	7.83941e92	0.0243196	0.0121598	+	0.999926i	$0.496129\pi$
$810$	2.99786e93	0.0893405
$811$	−4.13662e94	−1.18432	−0.592158	−	0.805822i	$-0.701724\pi$
$811$	−4.13662e94	−1.18432	−0.592158	+	0.805822i	$0.701724\pi$
$812$	−3.44466e93	−0.0947491
$813$	−1.90574e94	−0.503641
$814$	−9.74012e93	−0.247327
$815$	9.57154e94	2.33539
$816$	1.35893e94	0.318616
$817$	8.64886e94	1.94869
$818$	3.11859e94	0.675269
$819$	−5.72835e93	−0.119207
$820$	−3.93551e94	−0.787138
$821$	−1.66834e94	−0.320724	−0.160362	−	0.987058i	$-0.551266\pi$
$821$	−1.66834e94	−0.320724	−0.160362	+	0.987058i	$0.551266\pi$
$822$	−8.66711e93	−0.160155
$823$	−8.28208e94	−1.47111	−0.735555	−	0.677465i	$-0.763078\pi$
$823$	−8.28208e94	−1.47111	−0.735555	+	0.677465i	$0.763078\pi$
$824$	−3.46056e94	−0.590897
$825$	−1.22608e95	−2.01263
$826$	−2.92917e93	−0.0462268
$827$	−1.00195e95	−1.52026	−0.760131	−	0.649770i	$-0.774865\pi$
$827$	−1.00195e95	−1.52026	−0.760131	+	0.649770i	$0.774865\pi$
$828$	2.88365e94	0.420684
$829$	1.37558e95	1.92958	0.964790	−	0.263021i	$-0.0847187\pi$
$829$	1.37558e95	1.92958	0.964790	+	0.263021i	$0.0847187\pi$
$830$	−2.88543e94	−0.389199
$831$	8.15645e94	1.05796
$832$	1.97870e93	0.0246815
$833$	−8.60677e94	−1.03247
$834$	−2.59554e94	−0.299454
$835$	−1.67119e95	−1.85445
$836$	1.79899e95	1.92011
$837$	4.58525e93	0.0470745
$838$	−5.90200e94	−0.582866
$839$	8.24660e94	0.783450	0.391725	−	0.920082i	$-0.371878\pi$
$839$	8.24660e94	0.783450	0.391725	+	0.920082i	$0.371878\pi$
$840$	4.11947e94	0.376499
$841$	−1.05808e95	−0.930356
$842$	−5.08652e94	−0.430306
$843$	1.20284e95	0.979063
$844$	6.23058e94	0.487977
$845$	−8.79842e94	−0.663073
$846$	−1.65111e94	−0.119740
$847$	−1.06518e95	−0.743381
$848$	6.38235e94	0.428663
$849$	−1.48099e94	−0.0957311
$850$	2.02749e95	1.26137
$851$	−8.89794e94	−0.532818
$852$	−1.03101e95	−0.594261
$853$	−5.24846e94	−0.291198	−0.145599	−	0.989344i	$-0.546511\pi$
$853$	−5.24846e94	−0.291198	−0.145599	+	0.989344i	$0.546511\pi$
$854$	−2.64916e94	−0.141491
$855$	1.70854e95	0.878467
$856$	1.58459e95	0.784368
$857$	2.09368e95	0.997775	0.498888	−	0.866667i	$-0.333742\pi$
$857$	2.09368e95	0.997775	0.498888	+	0.866667i	$0.333742\pi$
$858$	−7.34236e94	−0.336898
$859$	3.91536e95	1.72979	0.864896	−	0.501952i	$-0.167385\pi$
$859$	3.91536e95	1.72979	0.864896	+	0.501952i	$0.167385\pi$
$860$	−4.34033e95	−1.84639
$861$	−3.56047e94	−0.145849
$862$	1.51564e95	0.597874
$863$	4.83787e95	1.83782	0.918911	−	0.394464i	$-0.129070\pi$
$863$	4.83787e95	1.83782	0.918911	+	0.394464i	$0.129070\pi$
$864$	5.29513e94	0.193723
$865$	−2.32677e95	−0.819842
$866$	−1.51772e95	−0.515063
$867$	1.20752e95	0.394708
$868$	2.78929e94	0.0878218
$869$	−6.91630e95	−2.09764
$870$	−4.19321e94	−0.122510
$871$	2.91287e95	0.819844
$872$	2.51736e95	0.682590
$873$	2.00094e95	0.522724
$874$	−4.25509e95	−1.07099
$875$	−3.77892e95	−0.916444
$876$	−7.25191e93	−0.0169461
$877$	7.17585e95	1.61580	0.807898	−	0.589322i	$-0.200605\pi$
$877$	7.17585e95	1.61580	0.807898	+	0.589322i	$0.200605\pi$
$878$	1.04602e95	0.226969
$879$	2.16680e95	0.453085
$880$	−6.08536e95	−1.22631
$881$	−1.45924e95	−0.283407	−0.141704	−	0.989909i	$-0.545258\pi$
$881$	−1.45924e95	−0.283407	−0.141704	+	0.989909i	$0.545258\pi$
$882$	−6.42596e94	−0.120284
$883$	−4.28770e95	−0.773574	−0.386787	−	0.922169i	$-0.626415\pi$
$883$	−4.28770e95	−0.773574	−0.386787	+	0.922169i	$0.626415\pi$
$884$	−4.68946e95	−0.815501
$885$	1.37718e95	0.230853
$886$	1.54126e95	0.249046
$887$	1.97647e95	0.307874	0.153937	−	0.988081i	$-0.450805\pi$
$887$	1.97647e95	0.307874	0.153937	+	0.988081i	$0.450805\pi$
$888$	−1.04918e95	−0.157553
$889$	−5.06090e94	−0.0732690
$890$	−3.61840e94	−0.0505058
$891$	−1.34267e95	−0.180694
$892$	4.92771e95	0.639422
$893$	−9.40996e95	−1.17738
$894$	2.10906e95	0.254460
$895$	−1.21746e96	−1.41647
$896$	3.99812e95	0.448586
$897$	−6.70750e95	−0.725782
$898$	3.53000e95	0.368378
$899$	−6.41355e94	−0.0645518
$900$	−5.84659e95	−0.567573
$901$	1.39668e96	1.30780
$902$	−4.56366e95	−0.412193
$903$	−3.92671e95	−0.342119
$904$	−1.03290e96	−0.868127
$905$	2.82445e96	2.29010
$906$	−1.89462e95	−0.148203
$907$	1.06259e96	0.801914	0.400957	−	0.916097i	$-0.368678\pi$
$907$	1.06259e96	0.801914	0.400957	+	0.916097i	$0.368678\pi$
$908$	9.89463e95	0.720459
$909$	−1.94339e95	−0.136532
$910$	−4.24189e95	−0.287551
$911$	1.69934e96	1.11156	0.555779	−	0.831330i	$-0.312420\pi$
$911$	1.69934e96	1.11156	0.555779	+	0.831330i	$0.312420\pi$
$912$	5.78239e95	0.364985
$913$	1.29231e96	0.787168
$914$	−1.18747e96	−0.698025
$915$	1.24553e96	0.706594
$916$	−1.88682e96	−1.03306
$917$	−7.05975e95	−0.373066
$918$	2.22030e95	0.113246
$919$	−2.33574e96	−1.14993	−0.574964	−	0.818178i	$-0.694984\pi$
$919$	−2.33574e96	−1.14993	−0.574964	+	0.818178i	$0.694984\pi$
$920$	4.82361e96	2.29228
$921$	−6.04632e95	−0.277366
$922$	−1.87724e96	−0.831315
$923$	2.39818e96	1.02524
$924$	−8.16769e95	−0.337101
$925$	1.80406e96	0.718859
$926$	4.52173e95	0.173959
$927$	6.51627e95	0.242052
$928$	−7.40648e95	−0.265646
$929$	3.73179e95	0.129243	0.0646215	−	0.997910i	$-0.479416\pi$
$929$	3.73179e95	0.129243	0.0646215	+	0.997910i	$0.479416\pi$
$930$	3.39542e95	0.113553
$931$	−3.66227e96	−1.18273
$932$	6.53715e95	0.203878
$933$	−1.38121e96	−0.416013
$934$	1.13463e96	0.330050
$935$	−1.33169e97	−3.74132
$936$	−7.90898e95	−0.214613
$937$	3.51666e96	0.921709	0.460854	−	0.887476i	$-0.347543\pi$
$937$	3.51666e96	0.921709	0.460854	+	0.887476i	$0.347543\pi$
$938$	−8.38956e95	−0.212396
$939$	−2.36787e96	−0.579063
$940$	4.72228e96	1.11557
$941$	8.17139e94	0.0186480	0.00932402	−	0.999957i	$-0.497032\pi$
$941$	8.17139e94	0.0186480	0.00932402	+	0.999957i	$0.497032\pi$
$942$	−1.43256e95	−0.0315835
$943$	−4.16906e96	−0.887991
$944$	4.66096e95	0.0959148
$945$	−7.75700e95	−0.154227
$946$	−5.03309e96	−0.966881
$947$	1.41165e96	0.262032	0.131016	−	0.991380i	$-0.458176\pi$
$947$	1.41165e96	0.262032	0.131016	+	0.991380i	$0.458176\pi$
$948$	−3.29807e96	−0.591546
$949$	1.68683e95	0.0292361
$950$	8.62719e96	1.44495
$951$	4.54769e96	0.736078
$952$	3.05099e96	0.477243
$953$	−4.34504e96	−0.656862	−0.328431	−	0.944528i	$-0.606520\pi$
$953$	−4.34504e96	−0.656862	−0.328431	+	0.944528i	$0.606520\pi$
$954$	1.04278e96	0.152360
$955$	1.07778e97	1.52203
$956$	3.71274e96	0.506772
$957$	1.87804e96	0.247780
$958$	−2.52552e96	−0.322086
$959$	2.24262e96	0.276472
$960$	2.67944e95	0.0319322
$961$	−8.16047e96	−0.940168
$962$	1.08036e96	0.120331
$963$	−2.98380e96	−0.321304
$964$	7.11912e96	0.741178
$965$	−1.78212e97	−1.79390
$966$	1.93187e96	0.188028
$967$	−6.65522e96	−0.626328	−0.313164	−	0.949699i	$-0.601389\pi$
$967$	−6.65522e96	−0.626328	−0.313164	+	0.949699i	$0.601389\pi$
$968$	−1.47066e97	−1.33833
$969$	1.26539e97	1.11353
$970$	1.48172e97	1.26091
$971$	2.77316e96	0.228218	0.114109	−	0.993468i	$-0.463599\pi$
$971$	2.77316e96	0.228218	0.114109	+	0.993468i	$0.463599\pi$
$972$	−6.40258e95	−0.0509567
$973$	6.71598e96	0.516942
$974$	1.12436e96	0.0837023
$975$	1.35995e97	0.979200
$976$	4.21541e96	0.293576
$977$	−6.99746e95	−0.0471376	−0.0235688	−	0.999722i	$-0.507503\pi$
$977$	−6.99746e95	−0.0471376	−0.0235688	+	0.999722i	$0.507503\pi$
$978$	5.29272e96	0.344879
$979$	1.62059e96	0.102150
$980$	1.83787e97	1.12064
$981$	−4.74022e96	−0.279612
$982$	−6.21309e96	−0.354555
$983$	−1.03568e96	−0.0571788	−0.0285894	−	0.999591i	$-0.509102\pi$
$983$	−1.03568e96	−0.0571788	−0.0285894	+	0.999591i	$0.509102\pi$
$984$	−4.91584e96	−0.262577
$985$	8.02235e96	0.414595
$986$	−3.10560e96	−0.155291
$987$	4.27226e96	0.206704
$988$	−1.99542e97	−0.934185
$989$	−4.59791e97	−2.08296
$990$	−9.94260e96	−0.435869
$991$	3.59011e97	1.52305	0.761524	−	0.648137i	$-0.224452\pi$
$991$	3.59011e97	1.52305	0.761524	+	0.648137i	$0.224452\pi$
$992$	5.99735e96	0.246224
$993$	−1.82366e97	−0.724590
$994$	−6.90717e96	−0.265609
$995$	−4.34260e97	−1.61622
$996$	6.16245e96	0.221986
$997$	−2.39613e97	−0.835445	−0.417723	−	0.908575i	$-0.637172\pi$
$997$	−2.39613e97	−0.835445	−0.417723	+	0.908575i	$0.637172\pi$
$998$	1.85022e97	0.624426
$999$	1.97561e96	0.0645392

Twists

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

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

\(f(q)\)	\(=\)	\(q+2.75457e9 q^{2} +1.85302e15 q^{3} -2.93058e19 q^{4} +9.23075e22 q^{5} +5.10428e24 q^{6} -1.32074e27 q^{7} -1.82351e29 q^{8} +3.43368e30 q^{9} +O(q^{10})\)	\(q+2.75457e9 q^{2} +1.85302e15 q^{3} -2.93058e19 q^{4} +9.23075e22 q^{5} +5.10428e24 q^{6} -1.32074e27 q^{7} -1.82351e29 q^{8} +3.43368e30 q^{9} +2.54268e32 q^{10} -1.13880e34 q^{11} -5.43043e34 q^{12} +1.26314e36 q^{13} -3.63806e36 q^{14} +1.71048e38 q^{15} +5.78896e38 q^{16} +1.26682e40 q^{17} +9.45833e39 q^{18} +5.39047e41 q^{19} -2.70515e42 q^{20} -2.44735e42 q^{21} -3.13692e43 q^{22} -2.86568e44 q^{23} -3.37900e44 q^{24} +5.81017e45 q^{25} +3.47942e45 q^{26} +6.36269e45 q^{27} +3.87053e46 q^{28} -8.89970e46 q^{29} +4.71163e47 q^{30} +7.20648e47 q^{31} +8.32216e48 q^{32} -2.11023e49 q^{33} +3.48956e49 q^{34} -1.21914e50 q^{35} -1.00627e50 q^{36} +3.10500e50 q^{37} +1.48484e51 q^{38} +2.34063e51 q^{39} -1.68323e52 q^{40} +1.45482e52 q^{41} -6.74141e51 q^{42} +1.60447e53 q^{43} +3.33736e53 q^{44} +3.16955e53 q^{45} -7.89372e53 q^{46} -1.74566e54 q^{47} +1.07271e54 q^{48} -6.79398e54 q^{49} +1.60045e55 q^{50} +2.34745e55 q^{51} -3.70175e55 q^{52} +1.10250e56 q^{53} +1.75265e55 q^{54} -1.05120e57 q^{55} +2.40837e56 q^{56} +9.98865e56 q^{57} -2.45149e56 q^{58} +8.05146e56 q^{59} -5.01269e57 q^{60} +7.28180e57 q^{61} +1.98507e57 q^{62} -4.53499e57 q^{63} +1.56649e57 q^{64} +1.16598e59 q^{65} -5.81277e58 q^{66} +2.30605e59 q^{67} -3.71253e59 q^{68} -5.31017e59 q^{69} -3.35821e59 q^{70} +1.89858e60 q^{71} -6.26135e59 q^{72} +1.33542e59 q^{73} +8.55294e59 q^{74} +1.07664e61 q^{75} -1.57972e61 q^{76} +1.50406e61 q^{77} +6.44743e60 q^{78} +6.07331e61 q^{79} +5.34365e61 q^{80} +1.17902e61 q^{81} +4.00741e61 q^{82} -1.13480e62 q^{83} +7.17217e61 q^{84} +1.16937e63 q^{85} +4.41963e62 q^{86} -1.64913e62 q^{87} +2.07662e63 q^{88} -1.42307e62 q^{89} +8.73074e62 q^{90} -1.66828e63 q^{91} +8.39812e63 q^{92} +1.33537e63 q^{93} -4.80856e63 q^{94} +4.97581e64 q^{95} +1.54211e64 q^{96} +5.82740e64 q^{97} -1.87145e64 q^{98} -3.91029e64 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 6210982962 q^{2} + 11\!\cdots\!46 q^{3}+ \cdots + 20\!\cdots\!86 q^{9}+O(q^{10}) \) 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

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