LMFDB - Embedded newform 3.66.a.a.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:	$1$
Dimension:	$5$
Coefficient field:	$\mathbb{Q}[x]/(x^{5} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{5} - 2 x^{4} + \cdots + 11\!\cdots\!50 $ x^5 - 2x^4 - 951687707356162322x^3 + 12324255588111120031125216x^2 + 110893397087607196931833643857303785x + 11092688481415693693368751083964140538880250
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{37}\cdot 3^{20}\cdot 5^{2}\cdot 7^{2}\cdot 11^{2}\cdot 13^{2} $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Root			$-2.77962e8$ 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)

$f(q)$	$=$	$q+2.81824e9 q^{2} -1.85302e15 q^{3} -2.89510e19 q^{4} +1.31338e22 q^{5} -5.22225e24 q^{6} -3.12329e27 q^{7} -1.85565e29 q^{8} +3.43368e30 q^{9} +O(q^{10})$	\(q+2.81824e9 q^{2} -1.85302e15 q^{3} -2.89510e19 q^{4} +1.31338e22 q^{5} -5.22225e24 q^{6} -3.12329e27 q^{7} -1.85565e29 q^{8} +3.43368e30 q^{9} +3.70141e31 q^{10} +7.74457e33 q^{11} +5.36469e34 q^{12} +1.76637e36 q^{13} -8.80217e36 q^{14} -2.43371e37 q^{15} +5.45138e38 q^{16} -6.76655e39 q^{17} +9.67693e39 q^{18} +1.80453e41 q^{19} -3.80236e41 q^{20} +5.78752e42 q^{21} +2.18260e43 q^{22} +1.68093e44 q^{23} +3.43856e44 q^{24} -2.53801e45 q^{25} +4.97804e45 q^{26} -6.36269e45 q^{27} +9.04225e46 q^{28} -1.85611e47 q^{29} -6.85878e46 q^{30} +3.74610e48 q^{31} +8.38248e48 q^{32} -1.43508e49 q^{33} -1.90697e49 q^{34} -4.10206e49 q^{35} -9.94087e49 q^{36} -6.66522e50 q^{37} +5.08559e50 q^{38} -3.27311e51 q^{39} -2.43717e51 q^{40} +2.75020e52 q^{41} +1.63106e52 q^{42} -1.48339e53 q^{43} -2.24213e53 q^{44} +4.50972e52 q^{45} +4.73725e53 q^{46} -1.81185e54 q^{47} -1.01015e54 q^{48} +1.21661e54 q^{49} -7.15271e54 q^{50} +1.25386e55 q^{51} -5.11381e55 q^{52} +1.62834e56 q^{53} -1.79315e55 q^{54} +1.01715e56 q^{55} +5.79574e56 q^{56} -3.34383e56 q^{57} -5.23096e56 q^{58} -3.03042e57 q^{59} +7.04586e56 q^{60} -1.98960e57 q^{61} +1.05574e58 q^{62} -1.07244e58 q^{63} +3.51176e57 q^{64} +2.31991e58 q^{65} -4.04440e58 q^{66} -2.37742e59 q^{67} +1.95899e59 q^{68} -3.11479e59 q^{69} -1.15606e59 q^{70} +1.04373e60 q^{71} -6.37173e59 q^{72} +1.63023e60 q^{73} -1.87842e60 q^{74} +4.70298e60 q^{75} -5.22430e60 q^{76} -2.41885e61 q^{77} -9.22440e60 q^{78} -8.50011e61 q^{79} +7.15972e60 q^{80} +1.17902e61 q^{81} +7.75070e61 q^{82} -4.31694e62 q^{83} -1.67555e62 q^{84} -8.88703e61 q^{85} -4.18054e62 q^{86} +3.43941e62 q^{87} -1.43712e63 q^{88} -1.94171e63 q^{89} +1.27095e62 q^{90} -5.51687e63 q^{91} -4.86646e63 q^{92} -6.94161e63 q^{93} -5.10623e63 q^{94} +2.37003e63 q^{95} -1.55329e64 q^{96} -5.72475e64 q^{97} +3.42871e63 q^{98} +2.65924e64 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 5 q - 2586530964 q^{2} - 92\!\cdots\!05 q^{3}+ \cdots + 17\!\cdots\!05 q^{9}+O(q^{10}) $ 5 * q - 2586530964 * q^2 - 9265100944259205 * q^3 + 90956647467025386896 * q^4 - 86326129898993074537194 * q^5 + 4792894095382414354904724 * q^6 + 5727531915019826651630441824 * q^7 - 171310184604381688819720685376 * q^8 + 17168419101462562423289245446405 * q^9	$ 5 q - 2586530964 q^{2} - 92\!\cdots\!05 q^{3}+ \cdots + 83\!\cdots\!12 q^{99}+O(q^{100}) $ 5 * q - 2586530964 * q^2 - 9265100944259205 * q^3 + 90956647467025386896 * q^4 - 86326129898993074537194 * q^5 + 4792894095382414354904724 * q^6 + 5727531915019826651630441824 * q^7 - 171310184604381688819720685376 * q^8 + 17168419101462562423289245446405 * q^9 - 659896383621335348194397701499736 * q^10 + 2423670936929044310926676000247252 * q^11 - 168544504066677707761757029046875536 * q^12 + 1275682308849370318735355413877537206 * q^13 - 49982312455633392023473970602516559232 * q^14 + 159964061528280704808897398479309874154 * q^15 + 4993462918087349121596715635252022735104 * q^16 - 14309939744126060363431428635715654504630 * q^17 - 8881329521772395078924101615064506996884 * q^18 + 505698133245450788939168217707371295193772 * q^19 - 2392412709256462478682330993076561136959776 * q^20 - 10613232270824985719754055969983070105797984 * q^21 - 137756426131570501611689002373657418979559760 * q^22 - 230360184409184050962312611330412345814929768 * q^23 + 317441230627855101604057424708804059039377216 * q^24 + 130572856113249510620811280312450547680114811 * q^25 + 44579953518799489855288790990258594868841710120 * q^26 - 31813427205679711792374143812692671154451081605 * q^27 + 367972371100886988316449196636850968953833778688 * q^28 + 652807732796864695792958071571718718887562702974 * q^29 + 1222801321400653743042610213721072617113604613976 * q^30 + 3581649354549322445208888229299534409749377229064 * q^31 - 2294508588173344143229543858391788222944135238656 * q^32 - 4491111177262976106278253651057341558249995390932 * q^33 + 106009618192883428412510933273135649343581836564952 * q^34 - 440771650608122791407015684618838754335319696936640 * q^35 + 312316368755575009460762874432245635911640271461776 * q^36 - 1172919468819631279715021157080009190889506495424226 * q^37 - 1342153935543987221244867931117925994792583662033072 * q^38 - 2363865072859012745357164672952015693551969899096246 * q^39 + 6732673491145233171964344219335775749594077923182208 * q^40 - 31982157562646981598434088890071836535840877160069726 * q^41 + 92618234065789512770934641713649798453212083948746112 * q^42 + 334877331045247829802327806663521554334341796684864084 * q^43 + 765921589904004792600073853631095307075801590287172160 * q^44 - 296416635502642225078067725267957665933115223461217514 * q^45 - 1110786269552442011050694204097985240019345559259829856 * q^46 - 4739916099041293147061619254167248169010271632238793152 * q^47 - 9252987599498884715329226429707310439431406578245726464 * q^48 - 1034115523044747562960726145206837328993313613574344227 * q^49 + 17979150603446614626452006162693701157007696601013121684 * q^50 + 26516607247118937651921141601708197225189188319318523830 * q^51 + 196783095275672862675056518704849747440137799355569402080 * q^52 - 170349965491878622775963275845161284943336335955115530538 * q^53 + 16457282907690114243514332408903722031371469798924663444 * q^54 + 229872003287660350640021345393036601027517632014351462616 * q^55 - 1700645281408649030356235569424664257832623944355798292480 * q^56 - 937068850368508674586743856840468080145831759338293934252 * q^57 - 696261775514704784879329791831143710762267301706537573624 * q^58 - 474745263568883969772349493682768733261242489336725334252 * q^59 + 4433189050317954677128613223372191531876028787426840547616 * q^60 + 16730379071820983834994499297475454972698844660036791965558 * q^61 - 32044230246813109420262523738727183452436444722941621340192 * q^62 + 19666533666812568344327802767761565715789308623694052488544 * q^63 - 6799996890991484025916228043599795294772269798542795304960 * q^64 + 98327236007925367657039618198273012082179961727092352428628 * q^65 + 255265438765877455424089405839369888236077304073402045518160 * q^66 - 157867546999669568987249916138496240685031332689194550821140 * q^67 - 1841419506634516386840778640672442997018991116523035775279328 * q^68 + 426862072417851148888089847118038952307811954977491972502888 * q^69 + 23291625706079904056449388536721692805076454252911576349440 * q^70 - 2043321526264647509032986684728405185145183590127912842838040 * q^71 - 588225009127388873750372308302205823457682226651398735054656 * q^72 - 1660934711906093644806157827567781169064101732089773004438478 * q^73 - 9200664498225283568864642819789868487958640990578272114106232 * q^74 - 241954138493897869785850291733840314435547497927181148717051 * q^75 - 5070235637155727844283962057122934109243885036643776429316672 * q^76 + 4616082562248437504836495905290988893883262463306988896984448 * q^77 - 82607553888412124411359004512880746638409772740472893750330920 * q^78 - 163509551671043484183806641788315287501186266983650622023282120 * q^79 - 287668452024434390504869182936693895988801429402000504952930816 * q^80 + 58950922888692915857604364307062593328391057961379205545484805 * q^81 - 677341656519699641817805800073183557931663668916119169144445832 * q^82 - 589633406515402133745211638063307147435988708987095453910208852 * q^83 - 681860232589625326627851166858938950331146998149790873215364608 * q^84 - 1066061999513499352091796913743581330797689631268396473996237908 * q^85 + 137148023832501554228942959312729645276819917245413885813851312 * q^86 - 1209665908311188376322243994188912872601875035942569939576075134 * q^87 - 11964353423109418345237661686710948652415377217786770171449052416 * q^88 - 10941920179046539778574748322212359805621940112257230199924523678 * q^89 - 2265875535510120122678975555367302287591875858382145015461929816 * q^90 - 16180146413603976436779593298107073378132804995273218800058622656 * q^91 - 48721899282574156202978669144522080387547664616447238186528493696 * q^92 - 6636868563368059900522243146976794918401004717018411592215106824 * q^93 - 5234723903677352863882525356783160839602260999433933056496630016 * q^94 - 28228453100889608049374802221925083368230728387835292904406462936 * q^95 + 4251770737379141231134077935944194660412446665052721093159965696 * q^96 + 32463915428803989473801328163474800827209052066062755964127978890 * q^97 - 140921747559822123463058353811762401049788378559606700759676581876 * q^98 + 8322119681846453946246108390142135321418956300625182459022905812 * 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 $

$2$	2.81824e9	0.463983	0.231992	−	0.972718i	$-0.425476\pi$
$2$	2.81824e9	0.463983	0.231992	+	0.972718i	$0.425476\pi$
$3$	−1.85302e15	−0.577350
$3$	−1.85302e15	−0.577350
$4$	−2.89510e19	−0.784719
$5$	1.31338e22	0.252269	0.126135	−	0.992013i	$-0.459743\pi$
$5$	1.31338e22	0.252269	0.126135	+	0.992013i	$0.459743\pi$
$6$	−5.22225e24	−0.267881
$7$	−3.12329e27	−1.06887	−0.534436	−	0.845209i	$-0.679476\pi$
$7$	−3.12329e27	−1.06887	−0.534436	+	0.845209i	$0.679476\pi$
$8$	−1.85565e29	−0.828080
$9$	3.43368e30	0.333333
$10$	3.70141e31	0.117049
$11$	7.74457e33	1.10595	0.552974	−	0.833198i	$-0.313493\pi$
$11$	7.74457e33	1.10595	0.552974	+	0.833198i	$0.313493\pi$
$12$	5.36469e34	0.453058
$13$	1.76637e36	1.10642	0.553212	−	0.833040i	$-0.313402\pi$
$13$	1.76637e36	1.10642	0.553212	+	0.833040i	$0.313402\pi$
$14$	−8.80217e36	−0.495939
$15$	−2.43371e37	−0.145648
$16$	5.45138e38	0.400504
$17$	−6.76655e39	−0.693070	−0.346535	−	0.938037i	$-0.612642\pi$
$17$	−6.76655e39	−0.693070	−0.346535	+	0.938037i	$0.612642\pi$
$18$	9.67693e39	0.154661
$19$	1.80453e41	0.497590	0.248795	−	0.968556i	$-0.419965\pi$
$19$	1.80453e41	0.497590	0.248795	+	0.968556i	$0.419965\pi$
$20$	−3.80236e41	−0.197961
$21$	5.78752e42	0.617114
$22$	2.18260e43	0.513142
$23$	1.68093e44	0.931954	0.465977	−	0.884797i	$-0.345703\pi$
$23$	1.68093e44	0.931954	0.465977	+	0.884797i	$0.345703\pi$
$24$	3.43856e44	0.478092
$25$	−2.53801e45	−0.936360
$26$	4.97804e45	0.513363
$27$	−6.36269e45	−0.192450
$28$	9.04225e46	0.838765
$29$	−1.85611e47	−0.550389	−0.275194	−	0.961389i	$-0.588742\pi$
$29$	−1.85611e47	−0.550389	−0.275194	+	0.961389i	$0.588742\pi$
$30$	−6.85878e46	−0.0675781
$31$	3.74610e48	1.27152	0.635762	−	0.771885i	$-0.280686\pi$
$31$	3.74610e48	1.27152	0.635762	+	0.771885i	$0.280686\pi$
$32$	8.38248e48	1.01391
$33$	−1.43508e49	−0.638520
$34$	−1.90697e49	−0.321573
$35$	−4.10206e49	−0.269644
$36$	−9.94087e49	−0.261573
$37$	−6.66522e50	−0.719877	−0.359939	−	0.932976i	$-0.617202\pi$
$37$	−6.66522e50	−0.719877	−0.359939	+	0.932976i	$0.617202\pi$
$38$	5.08559e50	0.230874
$39$	−3.27311e51	−0.638795
$40$	−2.43717e51	−0.208899
$41$	2.75020e52	1.05655	0.528273	−	0.849075i	$-0.322840\pi$
$41$	2.75020e52	1.05655	0.528273	+	0.849075i	$0.322840\pi$
$42$	1.63106e52	0.286331
$43$	−1.48339e53	−1.21208	−0.606039	−	0.795435i	$-0.707242\pi$
$43$	−1.48339e53	−1.21208	−0.606039	+	0.795435i	$0.707242\pi$
$44$	−2.24213e53	−0.867859
$45$	4.50972e52	0.0840898
$46$	4.73725e53	0.432411
$47$	−1.81185e54	−0.822134	−0.411067	−	0.911605i	$-0.634844\pi$
$47$	−1.81185e54	−0.822134	−0.411067	+	0.911605i	$0.634844\pi$
$48$	−1.01015e54	−0.231231
$49$	1.21661e54	0.142489
$50$	−7.15271e54	−0.434456
$51$	1.25386e55	0.400144
$52$	−5.11381e55	−0.868233
$53$	1.62834e56	1.48861	0.744303	−	0.667842i	$-0.232782\pi$
$53$	1.62834e56	1.48861	0.744303	+	0.667842i	$0.232782\pi$
$54$	−1.79315e55	−0.0892936
$55$	1.01715e56	0.278997
$56$	5.79574e56	0.885112
$57$	−3.34383e56	−0.287284
$58$	−5.23096e56	−0.255371
$59$	−3.03042e57	−0.848815	−0.424407	−	0.905471i	$-0.639518\pi$
$59$	−3.03042e57	−0.848815	−0.424407	+	0.905471i	$0.639518\pi$
$60$	7.04586e56	0.114293
$61$	−1.98960e57	−0.188602	−0.0943010	−	0.995544i	$-0.530062\pi$
$61$	−1.98960e57	−0.188602	−0.0943010	+	0.995544i	$0.530062\pi$
$62$	1.05574e58	0.589966
$63$	−1.07244e58	−0.356291
$64$	3.51176e57	0.0699320
$65$	2.31991e58	0.279117
$66$	−4.04440e58	−0.296263
$67$	−2.37742e59	−1.06825	−0.534126	−	0.845405i	$-0.679359\pi$
$67$	−2.37742e59	−1.06825	−0.534126	+	0.845405i	$0.679359\pi$
$68$	1.95899e59	0.543866
$69$	−3.11479e59	−0.538064
$70$	−1.15606e59	−0.125110
$71$	1.04373e60	0.712348	0.356174	−	0.934420i	$-0.384081\pi$
$71$	1.04373e60	0.712348	0.356174	+	0.934420i	$0.384081\pi$
$72$	−6.37173e59	−0.276027
$73$	1.63023e60	0.451083	0.225541	−	0.974234i	$-0.427585\pi$
$73$	1.63023e60	0.451083	0.225541	+	0.974234i	$0.427585\pi$
$74$	−1.87842e60	−0.334011
$75$	4.70298e60	0.540608
$76$	−5.22430e60	−0.390469
$77$	−2.41885e61	−1.18212
$78$	−9.22440e60	−0.296390
$79$	−8.50011e61	−1.80528	−0.902639	−	0.430398i	$-0.858373\pi$
$79$	−8.50011e61	−1.80528	−0.902639	+	0.430398i	$0.858373\pi$
$80$	7.15972e60	0.101035
$81$	1.17902e61	0.111111
$82$	7.75070e61	0.490220
$83$	−4.31694e62	−1.84136	−0.920679	−	0.390321i	$-0.872364\pi$
$83$	−4.31694e62	−1.84136	−0.920679	+	0.390321i	$0.872364\pi$
$84$	−1.67555e62	−0.484261
$85$	−8.88703e61	−0.174840
$86$	−4.18054e62	−0.562384
$87$	3.43941e62	0.317767
$88$	−1.43712e63	−0.915814
$89$	−1.94171e63	−0.857054	−0.428527	−	0.903529i	$-0.640967\pi$
$89$	−1.94171e63	−0.857054	−0.428527	+	0.903529i	$0.640967\pi$
$90$	1.27095e62	0.0390162
$91$	−5.51687e63	−1.18263
$92$	−4.86646e63	−0.731322
$93$	−6.94161e63	−0.734115
$94$	−5.10623e63	−0.381456
$95$	2.37003e63	0.125527
$96$	−1.55329e64	−0.585380
$97$	−5.72475e64	−1.54055	−0.770274	−	0.637713i	$-0.779880\pi$
$97$	−5.72475e64	−1.54055	−0.770274	+	0.637713i	$0.779880\pi$
$98$	3.42871e63	0.0661124
$99$	2.65924e64	0.368650
$100$	7.34780e64	0.734780
$101$	2.32662e64	0.168376	0.0841880	−	0.996450i	$-0.473170\pi$
$101$	2.32662e64	0.168376	0.0841880	+	0.996450i	$0.473170\pi$
$102$	3.53366e64	0.185660
$103$	4.51792e64	0.172874	0.0864368	−	0.996257i	$-0.472452\pi$
$103$	4.51792e64	0.172874	0.0864368	+	0.996257i	$0.472452\pi$
$104$	−3.27776e65	−0.916208
$105$	7.60120e64	0.155679
$106$	4.58905e65	0.690688
$107$	1.34617e66	1.49323	0.746614	−	0.665257i	$-0.231678\pi$
$107$	1.34617e66	1.49323	0.746614	+	0.665257i	$0.231678\pi$
$108$	1.84206e65	0.151019
$109$	1.76313e66	1.07133	0.535666	−	0.844430i	$-0.320061\pi$
$109$	1.76313e66	1.07133	0.535666	+	0.844430i	$0.320061\pi$
$110$	2.86658e65	0.129450
$111$	1.23508e66	0.415621
$112$	−1.70262e66	−0.428088
$113$	1.59084e66	0.299624	0.149812	−	0.988714i	$-0.452133\pi$
$113$	1.59084e66	0.299624	0.149812	+	0.988714i	$0.452133\pi$
$114$	−9.42370e65	−0.133295
$115$	2.20769e66	0.235103
$116$	5.37364e66	0.431901
$117$	6.06514e66	0.368808
$118$	−8.54045e66	−0.393836
$119$	2.11339e67	0.740804
$120$	4.51613e66	0.120608
$121$	1.09413e67	0.223122
$122$	−5.60716e66	−0.0875082
$123$	−5.09617e67	−0.609997
$124$	−1.08454e68	−0.997790
$125$	−6.89328e67	−0.488484
$126$	−3.02239e67	−0.165313
$127$	−4.09722e68	−1.73328	−0.866639	−	0.498935i	$-0.833725\pi$
$127$	−4.09722e68	−1.73328	−0.866639	+	0.498935i	$0.833725\pi$
$128$	−2.99362e68	−0.981460
$129$	2.74875e68	0.699793
$130$	6.53804e67	0.129506
$131$	−1.53872e68	−0.237597	−0.118799	−	0.992918i	$-0.537904\pi$
$131$	−1.53872e68	−0.237597	−0.118799	+	0.992918i	$0.537904\pi$
$132$	4.15472e68	0.501059
$133$	−5.63607e68	−0.531861
$134$	−6.70012e68	−0.495651
$135$	−8.35661e67	−0.0485492
$136$	1.25564e69	0.573918
$137$	4.42875e69	1.59537	0.797687	−	0.603071i	$-0.206057\pi$
$137$	4.42875e69	1.59537	0.797687	+	0.603071i	$0.206057\pi$
$138$	−8.77822e68	−0.249653
$139$	−3.37741e69	−0.759630	−0.379815	−	0.925062i	$-0.624012\pi$
$139$	−3.37741e69	−0.759630	−0.379815	+	0.925062i	$0.624012\pi$
$140$	1.18759e69	0.211595
$141$	3.35740e69	0.474659
$142$	2.94148e69	0.330518
$143$	1.36797e70	1.22365
$144$	1.87183e69	0.133501
$145$	−2.43778e69	−0.138846
$146$	4.59438e69	0.209295
$147$	−2.25441e69	−0.0822659
$148$	1.92965e70	0.564902
$149$	−1.72056e70	−0.404684	−0.202342	−	0.979315i	$-0.564855\pi$
$149$	−1.72056e70	−0.404684	−0.202342	+	0.979315i	$0.564855\pi$
$150$	1.32541e70	0.250833
$151$	2.54097e70	0.387480	0.193740	−	0.981053i	$-0.437938\pi$
$151$	2.54097e70	0.387480	0.193740	+	0.981053i	$0.437938\pi$
$152$	−3.34858e70	−0.412045
$153$	−2.32342e70	−0.231023
$154$	−6.81690e70	−0.548483
$155$	4.92005e70	0.320767
$156$	9.47600e70	0.501274
$157$	−2.28779e71	−0.983280	−0.491640	−	0.870799i	$-0.663602\pi$
$157$	−2.28779e71	−0.983280	−0.491640	+	0.870799i	$0.663602\pi$
$158$	−2.39553e71	−0.837619
$159$	−3.01735e71	−0.859447
$160$	1.10094e71	0.255778
$161$	−5.25002e71	−0.996140
$162$	3.32275e70	0.0515537
$163$	7.85387e71	0.997669	0.498834	−	0.866697i	$-0.333762\pi$
$163$	7.85387e71	0.997669	0.498834	+	0.866697i	$0.333762\pi$
$164$	−7.96210e71	−0.829092
$165$	−1.88481e71	−0.161079
$166$	−1.21662e72	−0.854359
$167$	2.61195e72	1.50897	0.754483	−	0.656320i	$-0.227888\pi$
$167$	2.61195e72	1.50897	0.754483	+	0.656320i	$0.227888\pi$
$168$	−1.07396e72	−0.511020
$169$	5.71355e71	0.224175
$170$	−2.50457e71	−0.0811230
$171$	6.19618e71	0.165863
$172$	4.29457e72	0.951141
$173$	4.36593e72	0.800900	0.400450	−	0.916319i	$-0.368854\pi$
$173$	4.36593e72	0.800900	0.400450	+	0.916319i	$0.368854\pi$
$174$	9.69308e71	0.147439
$175$	7.92694e72	1.00085
$176$	4.22186e72	0.442937
$177$	5.61544e72	0.490063
$178$	−5.47218e72	−0.397659
$179$	−1.48864e73	−0.901706	−0.450853	−	0.892598i	$-0.648880\pi$
$179$	−1.48864e73	−0.901706	−0.450853	+	0.892598i	$0.648880\pi$
$180$	−1.30561e72	−0.0659869
$181$	1.31999e73	0.557206	0.278603	−	0.960406i	$-0.410129\pi$
$181$	1.31999e73	0.557206	0.278603	+	0.960406i	$0.410129\pi$
$182$	−1.55478e73	−0.548719
$183$	3.68677e72	0.108889
$184$	−3.11922e73	−0.771732
$185$	−8.75395e72	−0.181603
$186$	−1.95631e73	−0.340617
$187$	−5.24040e73	−0.766500
$188$	5.24550e73	0.645144
$189$	1.98725e73	0.205705
$190$	6.67930e72	0.0582423
$191$	1.08860e74	0.800359	0.400180	−	0.916437i	$-0.368948\pi$
$191$	1.08860e74	0.800359	0.400180	+	0.916437i	$0.368948\pi$
$192$	−6.50737e72	−0.0403753
$193$	−3.05336e74	−1.60017	−0.800083	−	0.599890i	$-0.795211\pi$
$193$	−3.05336e74	−1.60017	−0.800083	+	0.599890i	$0.795211\pi$
$194$	−1.61337e74	−0.714788
$195$	−4.29883e73	−0.161148
$196$	−3.52223e73	−0.111814
$197$	−5.29549e74	−1.42480	−0.712400	−	0.701773i	$-0.752392\pi$
$197$	−5.29549e74	−1.42480	−0.712400	+	0.701773i	$0.752392\pi$
$198$	7.49436e73	0.171047
$199$	5.72758e74	1.10980	0.554902	−	0.831916i	$-0.312756\pi$
$199$	5.72758e74	1.10980	0.554902	+	0.831916i	$0.312756\pi$
$200$	4.70967e74	0.775381
$201$	4.40540e74	0.616756
$202$	6.55695e73	0.0781236
$203$	5.79718e74	0.588295
$204$	−3.63004e74	−0.314001
$205$	3.61205e74	0.266534
$206$	1.27326e74	0.0802105
$207$	5.77177e74	0.310651
$208$	9.62913e74	0.443128
$209$	1.39753e75	0.550309
$210$	2.14220e74	0.0722324
$211$	3.68631e75	1.06515	0.532577	−	0.846382i	$-0.321224\pi$
$211$	3.68631e75	1.06515	0.532577	+	0.846382i	$0.321224\pi$
$212$	−4.71422e75	−1.16814
$213$	−1.93406e75	−0.411274
$214$	3.79382e75	0.692833
$215$	−1.94825e75	−0.305770
$216$	1.18069e75	0.159364
$217$	−1.17002e76	−1.35910
$218$	4.96892e75	0.497080
$219$	−3.02085e75	−0.260433
$220$	−2.94477e75	−0.218934
$221$	−1.19522e76	−0.766830
$222$	3.48074e75	0.192841
$223$	−8.93055e75	−0.427533	−0.213767	−	0.976885i	$-0.568573\pi$
$223$	−8.93055e75	−0.427533	−0.213767	+	0.976885i	$0.568573\pi$
$224$	−2.61809e76	−1.08374
$225$	−8.71472e75	−0.312120
$226$	4.48336e75	0.139021
$227$	−1.51209e76	−0.406198	−0.203099	−	0.979158i	$-0.565101\pi$
$227$	−1.51209e76	−0.406198	−0.203099	+	0.979158i	$0.565101\pi$
$228$	9.68073e75	0.225437
$229$	4.94598e76	0.999078	0.499539	−	0.866291i	$-0.333503\pi$
$229$	4.94598e76	0.999078	0.499539	+	0.866291i	$0.333503\pi$
$230$	6.22180e75	0.109084
$231$	4.48218e76	0.682496
$232$	3.44430e76	0.455766
$233$	−9.30495e76	−1.07065	−0.535324	−	0.844647i	$-0.679811\pi$
$233$	−9.30495e76	−1.07065	−0.535324	+	0.844647i	$0.679811\pi$
$234$	1.70930e76	0.171121
$235$	−2.37965e76	−0.207399
$236$	8.77339e76	0.666081
$237$	1.57509e77	1.04228
$238$	5.95603e76	0.343721
$239$	2.42614e76	0.122175	0.0610877	−	0.998132i	$-0.480543\pi$
$239$	2.42614e76	0.122175	0.0610877	+	0.998132i	$0.480543\pi$
$240$	−1.32671e76	−0.0583325
$241$	−3.48800e76	−0.133975	−0.0669873	−	0.997754i	$-0.521339\pi$
$241$	−3.48800e76	−0.133975	−0.0669873	+	0.997754i	$0.521339\pi$
$242$	3.08351e76	0.103525
$243$	−2.18475e76	−0.0641500
$244$	5.76010e76	0.148000
$245$	1.59787e76	0.0359455
$246$	−1.43622e77	−0.283028
$247$	3.18746e77	0.550546
$248$	−6.95147e77	−1.05292
$249$	7.99938e77	1.06311
$250$	−1.94269e77	−0.226649
$251$	−1.44256e78	−1.47822	−0.739110	−	0.673585i	$-0.764754\pi$
$251$	−1.44256e78	−1.47822	−0.739110	+	0.673585i	$0.764754\pi$
$252$	3.10482e77	0.279588
$253$	1.30181e78	1.03069
$254$	−1.15469e78	−0.804212
$255$	1.64679e77	0.100944
$256$	−9.73234e77	−0.525313
$257$	−3.54167e78	−1.68415	−0.842077	−	0.539357i	$-0.818667\pi$
$257$	−3.54167e78	−1.68415	−0.842077	+	0.539357i	$0.818667\pi$
$258$	7.74663e77	0.324692
$259$	2.08174e78	0.769457
$260$	−6.71637e77	−0.219028
$261$	−6.37330e77	−0.183463
$262$	−4.33647e77	−0.110241
$263$	−7.31339e78	−1.64269	−0.821347	−	0.570428i	$-0.806777\pi$
$263$	−7.31339e78	−1.64269	−0.821347	+	0.570428i	$0.806777\pi$
$264$	2.66302e78	0.528745
$265$	2.13863e78	0.375529
$266$	−1.58838e78	−0.246775
$267$	3.59802e78	0.494820
$268$	6.88286e78	0.838279
$269$	7.35142e78	0.793272	0.396636	−	0.917976i	$-0.370177\pi$
$269$	7.35142e78	0.793272	0.396636	+	0.917976i	$0.370177\pi$
$270$	−2.35509e77	−0.0225260
$271$	2.13141e79	1.80786	0.903930	−	0.427680i	$-0.140669\pi$
$271$	2.13141e79	1.80786	0.903930	+	0.427680i	$0.140669\pi$
$272$	−3.68870e78	−0.277578
$273$	1.02229e79	0.682790
$274$	1.24813e79	0.740227
$275$	−1.96558e79	−1.03557
$276$	9.01765e78	0.422229
$277$	−2.70707e79	−1.12696	−0.563478	−	0.826131i	$-0.690537\pi$
$277$	−2.70707e79	−1.12696	−0.563478	+	0.826131i	$0.690537\pi$
$278$	−9.51832e78	−0.352456
$279$	1.28629e79	0.423842
$280$	7.61200e78	0.223287
$281$	−3.09108e79	−0.807523	−0.403762	−	0.914864i	$-0.632298\pi$
$281$	−3.09108e79	−0.807523	−0.403762	+	0.914864i	$0.632298\pi$
$282$	9.46194e78	0.220234
$283$	−3.31971e78	−0.0688718	−0.0344359	−	0.999407i	$-0.510963\pi$
$283$	−3.31971e78	−0.0688718	−0.0344359	+	0.999407i	$0.510963\pi$
$284$	−3.02171e79	−0.558994
$285$	−4.39171e78	−0.0724729
$286$	3.85527e79	0.567753
$287$	−8.58966e79	−1.12931
$288$	2.87828e79	0.337969
$289$	−4.95329e79	−0.519653
$290$	−6.87023e78	−0.0644223
$291$	1.06081e80	0.889436
$292$	−4.71969e79	−0.353974
$293$	−2.58650e80	−1.73586	−0.867931	−	0.496684i	$-0.834551\pi$
$293$	−2.58650e80	−1.73586	−0.867931	+	0.496684i	$0.834551\pi$
$294$	−6.35346e78	−0.0381700
$295$	−3.98009e79	−0.214130
$296$	1.23683e80	0.596116
$297$	−4.92763e79	−0.212840
$298$	−4.84894e79	−0.187766
$299$	2.96913e80	1.03114
$300$	−1.36156e80	−0.424225
$301$	4.63306e80	1.29556
$302$	7.16106e79	0.179784
$303$	−4.31127e79	−0.0972119
$304$	9.83717e79	0.199287
$305$	−2.61310e79	−0.0475785
$306$	−6.54794e79	−0.107191
$307$	3.91916e80	0.577026	0.288513	−	0.957476i	$-0.406839\pi$
$307$	3.91916e80	0.577026	0.288513	+	0.957476i	$0.406839\pi$
$308$	7.00283e80	0.927631
$309$	−8.37180e79	−0.0998086
$310$	1.38659e80	0.148830
$311$	−6.63571e80	−0.641468	−0.320734	−	0.947169i	$-0.603929\pi$
$311$	−6.63571e80	−0.641468	−0.320734	+	0.947169i	$0.603929\pi$
$312$	6.07376e80	0.528973
$313$	−1.73522e81	−1.36196	−0.680980	−	0.732302i	$-0.738446\pi$
$313$	−1.73522e81	−1.36196	−0.680980	+	0.732302i	$0.738446\pi$
$314$	−6.44753e80	−0.456226
$315$	−1.40852e80	−0.0898812
$316$	2.46087e81	1.41664
$317$	3.13934e81	1.63085	0.815423	−	0.578866i	$-0.196505\pi$
$317$	3.13934e81	1.63085	0.815423	+	0.578866i	$0.196505\pi$
$318$	−8.50360e80	−0.398769
$319$	−1.43748e81	−0.608701
$320$	4.61227e79	0.0176417
$321$	−2.49447e81	−0.862116
$322$	−1.47958e81	−0.462192
$323$	−1.22104e81	−0.344865
$324$	−3.41338e80	−0.0871911
$325$	−4.48305e81	−1.03601
$326$	2.21340e81	0.462902
$327$	−3.26712e81	−0.618533
$328$	−5.10341e81	−0.874905
$329$	5.65894e81	0.878756
$330$	−5.31183e80	−0.0747379
$331$	−1.21733e82	−1.55238	−0.776190	−	0.630500i	$-0.782850\pi$
$331$	−1.21733e82	−1.55238	−0.776190	+	0.630500i	$0.782850\pi$
$332$	1.24980e82	1.44495
$333$	−2.28863e81	−0.239959
$334$	7.36108e81	0.700135
$335$	−3.12244e81	−0.269487
$336$	3.15500e81	0.247157
$337$	−9.87026e80	−0.0702032	−0.0351016	−	0.999384i	$-0.511175\pi$
$337$	−9.87026e80	−0.0702032	−0.0351016	+	0.999384i	$0.511175\pi$
$338$	1.61021e81	0.104014
$339$	−2.94786e81	−0.172988
$340$	2.57289e81	0.137201
$341$	2.90120e82	1.40624
$342$	1.74623e81	0.0769579
$343$	2.28678e82	0.916570
$344$	2.75266e82	1.00370
$345$	−4.09090e81	−0.135737
$346$	1.23042e82	0.371604
$347$	−1.70568e80	−0.00469019	−0.00234509	−	0.999997i	$-0.500746\pi$
$347$	−1.70568e80	−0.00469019	−0.00234509	+	0.999997i	$0.500746\pi$
$348$	−9.95746e81	−0.249358
$349$	−8.27261e82	−1.88719	−0.943596	−	0.331099i	$-0.892581\pi$
$349$	−8.27261e82	−1.88719	−0.943596	+	0.331099i	$0.892581\pi$
$350$	2.23400e82	0.464378
$351$	−1.12388e82	−0.212932
$352$	6.49187e82	1.12133
$353$	−1.01900e83	−1.60508	−0.802542	−	0.596596i	$-0.796519\pi$
$353$	−1.01900e83	−1.60508	−0.802542	+	0.596596i	$0.796519\pi$
$354$	1.58256e82	0.227381
$355$	1.37081e82	0.179704
$356$	5.62144e82	0.672547
$357$	−3.91615e82	−0.427703
$358$	−4.19532e82	−0.418376
$359$	−1.71822e83	−1.56498	−0.782492	−	0.622661i	$-0.786052\pi$
$359$	−1.71822e83	−1.56498	−0.782492	+	0.622661i	$0.786052\pi$
$360$	−8.36848e81	−0.0696331
$361$	−9.89544e82	−0.752404
$362$	3.72003e82	0.258534
$363$	−2.02744e82	−0.128820
$364$	1.59719e83	0.928030
$365$	2.14111e82	0.113794
$366$	1.03902e82	0.0505229
$367$	1.21072e81	0.00538762	0.00269381	−	0.999996i	$-0.499143\pi$
$367$	1.21072e81	0.00538762	0.00269381	+	0.999996i	$0.499143\pi$
$368$	9.16337e82	0.373251
$369$	9.44330e82	0.352182
$370$	−2.46707e82	−0.0842607
$371$	−5.08578e83	−1.59113
$372$	2.00967e83	0.576074
$373$	−2.73814e81	−0.00719315	−0.00359657	−	0.999994i	$-0.501145\pi$
$373$	−2.73814e81	−0.00719315	−0.00359657	+	0.999994i	$0.501145\pi$
$374$	−1.47687e83	−0.355643
$375$	1.27734e83	0.282026
$376$	3.36217e83	0.680793
$377$	−3.27857e83	−0.608963
$378$	5.60054e82	0.0954435
$379$	5.43728e83	0.850369	0.425184	−	0.905107i	$-0.360209\pi$
$379$	5.43728e83	0.850369	0.425184	+	0.905107i	$0.360209\pi$
$380$	−6.86148e82	−0.0985033
$381$	7.59223e83	1.00071
$382$	3.06794e83	0.371353
$383$	5.30222e83	0.589518	0.294759	−	0.955572i	$-0.404761\pi$
$383$	5.30222e83	0.589518	0.294759	+	0.955572i	$0.404761\pi$
$384$	5.54724e83	0.566646
$385$	−3.17687e83	−0.298212
$386$	−8.60507e83	−0.742450
$387$	−5.09349e83	−0.404026
$388$	1.65737e84	1.20890
$389$	−1.12058e83	−0.0751762	−0.0375881	−	0.999293i	$-0.511967\pi$
$389$	−1.12058e83	−0.0751762	−0.0375881	+	0.999293i	$0.511967\pi$
$390$	−1.21151e83	−0.0747701
$391$	−1.13741e84	−0.645910
$392$	−2.25762e83	−0.117992
$393$	2.85127e83	0.137177
$394$	−1.49240e84	−0.661084
$395$	−1.11639e84	−0.455416
$396$	−7.69878e83	−0.289286
$397$	−2.32414e84	−0.804584	−0.402292	−	0.915511i	$-0.631786\pi$
$397$	−2.32414e84	−0.804584	−0.402292	+	0.915511i	$0.631786\pi$
$398$	1.61417e84	0.514930
$399$	1.04437e84	0.307070
$400$	−1.38357e84	−0.375016
$401$	−7.26629e84	−1.81602	−0.908010	−	0.418949i	$-0.862398\pi$
$401$	−7.26629e84	−1.81602	−0.908010	+	0.418949i	$0.862398\pi$
$402$	1.24155e84	0.286164
$403$	6.61699e84	1.40685
$404$	−6.73579e83	−0.132128
$405$	1.54850e83	0.0280299
$406$	1.63378e84	0.272959
$407$	−5.16192e84	−0.796147
$408$	−2.32672e84	−0.331352
$409$	1.72349e84	0.226674	0.113337	−	0.993557i	$-0.463846\pi$
$409$	1.72349e84	0.226674	0.113337	+	0.993557i	$0.463846\pi$
$410$	1.01796e84	0.123667
$411$	−8.20656e84	−0.921090
$412$	−1.30798e84	−0.135657
$413$	9.46489e84	0.907275
$414$	1.62662e84	0.144137
$415$	−5.66977e84	−0.464518
$416$	1.48065e85	1.12181
$417$	6.25840e84	0.438573
$418$	3.93857e84	0.255334
$419$	2.85967e85	1.71538	0.857688	−	0.514170i	$-0.171900\pi$
$419$	2.85967e85	1.71538	0.857688	+	0.514170i	$0.171900\pi$
$420$	−2.20062e84	−0.122164
$421$	1.51027e85	0.776045	0.388023	−	0.921650i	$-0.373158\pi$
$421$	1.51027e85	0.776045	0.388023	+	0.921650i	$0.373158\pi$
$422$	1.03889e85	0.494213
$423$	−6.22133e84	−0.274045
$424$	−3.02164e85	−1.23268
$425$	1.71736e85	0.648964
$426$	−5.45062e84	−0.190825
$427$	6.21410e84	0.201592
$428$	−3.89729e85	−1.17177
$429$	−2.53488e85	−0.706474
$430$	−5.49063e84	−0.141872
$431$	6.28723e85	1.50643	0.753213	−	0.657776i	$-0.228503\pi$
$431$	6.28723e85	1.50643	0.753213	+	0.657776i	$0.228503\pi$
$432$	−3.46854e84	−0.0770770
$433$	−7.61048e85	−1.56876	−0.784378	−	0.620284i	$-0.787018\pi$
$433$	−7.61048e85	−1.56876	−0.784378	+	0.620284i	$0.787018\pi$
$434$	−3.29738e85	−0.630599
$435$	4.51725e84	0.0801628
$436$	−5.10445e85	−0.840694
$437$	3.03328e85	0.463731
$438$	−8.51347e84	−0.120837
$439$	3.18698e85	0.420032	0.210016	−	0.977698i	$-0.432648\pi$
$439$	3.18698e85	0.420032	0.210016	+	0.977698i	$0.432648\pi$
$440$	−1.88749e85	−0.231032
$441$	4.17747e84	0.0474962
$442$	−3.36841e85	−0.355796
$443$	6.99195e85	0.686242	0.343121	−	0.939291i	$-0.388516\pi$
$443$	6.99195e85	0.686242	0.343121	+	0.939291i	$0.388516\pi$
$444$	−3.57568e85	−0.326146
$445$	−2.55019e85	−0.216208
$446$	−2.51684e85	−0.198368
$447$	3.18823e85	0.233644
$448$	−1.09683e85	−0.0747484
$449$	−1.37951e85	−0.0874417	−0.0437209	−	0.999044i	$-0.513921\pi$
$449$	−1.37951e85	−0.0874417	−0.0437209	+	0.999044i	$0.513921\pi$
$450$	−2.45601e85	−0.144819
$451$	2.12991e86	1.16849
$452$	−4.60565e85	−0.235121
$453$	−4.70848e85	−0.223712
$454$	−4.26143e85	−0.188469
$455$	−7.24574e85	−0.298340
$456$	6.20499e85	0.237894
$457$	1.79309e86	0.640216	0.320108	−	0.947381i	$-0.396281\pi$
$457$	1.79309e86	0.640216	0.320108	+	0.947381i	$0.396281\pi$
$458$	1.39389e86	0.463556
$459$	4.30534e85	0.133381
$460$	−6.39150e85	−0.184490
$461$	2.70199e86	0.726782	0.363391	−	0.931637i	$-0.381619\pi$
$461$	2.70199e86	0.726782	0.363391	+	0.931637i	$0.381619\pi$
$462$	1.26318e86	0.316667
$463$	3.30461e86	0.772215	0.386108	−	0.922454i	$-0.373819\pi$
$463$	3.30461e86	0.772215	0.386108	+	0.922454i	$0.373819\pi$
$464$	−1.01184e86	−0.220433
$465$	−9.11695e85	−0.185195
$466$	−2.62236e86	−0.496763
$467$	−3.93282e86	−0.694873	−0.347437	−	0.937704i	$-0.612948\pi$
$467$	−3.93282e86	−0.694873	−0.347437	+	0.937704i	$0.612948\pi$
$468$	−1.75592e86	−0.289411
$469$	7.42536e86	1.14183
$470$	−6.70640e85	−0.0962297
$471$	4.23932e86	0.567697
$472$	5.62342e86	0.702887
$473$	−1.14882e87	−1.34050
$474$	4.43897e86	0.483600
$475$	−4.57991e86	−0.465924
$476$	−6.11848e86	−0.581323
$477$	5.59121e86	0.496202
$478$	6.83743e85	0.0566874
$479$	−2.52690e87	−1.95742	−0.978711	−	0.205244i	$-0.934201\pi$
$479$	−2.52690e87	−1.95742	−0.978711	+	0.205244i	$0.934201\pi$
$480$	−2.04006e86	−0.147673
$481$	−1.17732e87	−0.796490
$482$	−9.83000e85	−0.0621620
$483$	9.72840e86	0.575122
$484$	−3.16761e86	−0.175088
$485$	−7.51875e86	−0.388633
$486$	−6.15713e85	−0.0297645
$487$	−1.29045e87	−0.583514	−0.291757	−	0.956492i	$-0.594240\pi$
$487$	−1.29045e87	−0.583514	−0.291757	+	0.956492i	$0.594240\pi$
$488$	3.69201e86	0.156178
$489$	−1.45534e87	−0.576004
$490$	4.50319e85	0.0166781
$491$	4.78518e87	1.65863	0.829316	−	0.558780i	$-0.188730\pi$
$491$	4.78518e87	1.65863	0.829316	+	0.558780i	$0.188730\pi$
$492$	1.47539e87	0.478677
$493$	1.25595e87	0.381458
$494$	8.98301e86	0.255444
$495$	3.49258e86	0.0929989
$496$	2.04214e87	0.509251
$497$	−3.25988e87	−0.761410
$498$	2.25441e87	0.493265
$499$	4.88853e87	1.00210	0.501050	−	0.865418i	$-0.332947\pi$
$499$	4.88853e87	1.00210	0.501050	+	0.865418i	$0.332947\pi$
$500$	1.99568e87	0.383323
$501$	−4.83999e87	−0.871202
$502$	−4.06548e87	−0.685870
$503$	4.20214e87	0.664525	0.332262	−	0.943187i	$-0.392188\pi$
$503$	4.20214e87	0.664525	0.332262	+	0.943187i	$0.392188\pi$
$504$	1.99008e87	0.295037
$505$	3.05572e86	0.0424761
$506$	3.66880e87	0.478224
$507$	−1.05873e87	−0.129428
$508$	1.18619e88	1.36014
$509$	−1.21628e88	−1.30830	−0.654149	−	0.756366i	$-0.726973\pi$
$509$	−1.21628e88	−1.30830	−0.654149	+	0.756366i	$0.726973\pi$
$510$	4.64103e86	0.0468364
$511$	−5.09169e87	−0.482150
$512$	8.30171e87	0.737723
$513$	−1.14817e87	−0.0957613
$514$	−9.98127e87	−0.781420
$515$	5.93373e86	0.0436107
$516$	−7.95792e87	−0.549141
$517$	−1.40320e88	−0.909238
$518$	5.86684e87	0.357015
$519$	−8.09015e87	−0.462400
$520$	−4.30494e87	−0.231131
$521$	1.58598e88	0.799967	0.399984	−	0.916522i	$-0.369016\pi$
$521$	1.58598e88	0.799967	0.399984	+	0.916522i	$0.369016\pi$
$522$	−1.79615e87	−0.0851237
$523$	−2.22737e87	−0.0991946	−0.0495973	−	0.998769i	$-0.515794\pi$
$523$	−2.22737e87	−0.0991946	−0.0495973	+	0.998769i	$0.515794\pi$
$524$	4.45475e87	0.186447
$525$	−1.46888e88	−0.577841
$526$	−2.06109e88	−0.762183
$527$	−2.53482e88	−0.881256
$528$	−7.82319e87	−0.255730
$529$	−4.27671e87	−0.131462
$530$	6.02715e87	0.174239
$531$	−1.04055e88	−0.282938
$532$	1.63170e88	0.417361
$533$	4.85785e88	1.16899
$534$	1.01401e88	0.229588
$535$	1.76803e88	0.376696
$536$	4.41166e88	0.884599
$537$	2.75847e88	0.520600
$538$	2.07180e88	0.368065
$539$	9.42216e87	0.157585
$540$	2.41932e87	0.0380975
$541$	−1.03663e89	−1.53713	−0.768566	−	0.639771i	$-0.779029\pi$
$541$	−1.03663e89	−1.53713	−0.768566	+	0.639771i	$0.779029\pi$
$542$	6.00681e88	0.838817
$543$	−2.44596e88	−0.321703
$544$	−5.67205e88	−0.702709
$545$	2.31566e88	0.270264
$546$	2.88105e88	0.316803
$547$	1.38342e89	1.43340	0.716698	−	0.697383i	$-0.245652\pi$
$547$	1.38342e89	1.43340	0.716698	+	0.697383i	$0.245652\pi$
$548$	−1.28217e89	−1.25192
$549$	−6.83166e87	−0.0628673
$550$	−5.53946e88	−0.480486
$551$	−3.34941e88	−0.273868
$552$	5.77998e88	0.445560
$553$	2.65483e89	1.92961
$554$	−7.62916e88	−0.522889
$555$	1.62212e88	0.104848
$556$	9.77794e88	0.596097
$557$	1.90876e87	0.0109763	0.00548817	−	0.999985i	$-0.498253\pi$
$557$	1.90876e87	0.0109763	0.00548817	+	0.999985i	$0.498253\pi$
$558$	3.62508e88	0.196655
$559$	−2.62021e89	−1.34107
$560$	−2.23619e88	−0.107993
$561$	9.71057e88	0.442539
$562$	−8.71140e88	−0.374677
$563$	−2.06722e89	−0.839196	−0.419598	−	0.907710i	$-0.637829\pi$
$563$	−2.06722e89	−0.839196	−0.419598	+	0.907710i	$0.637829\pi$
$564$	−9.72002e88	−0.372474
$565$	2.08937e88	0.0755860
$566$	−9.35574e87	−0.0319554
$567$	−3.68242e88	−0.118764
$568$	−1.93680e89	−0.589881
$569$	−3.43335e89	−0.987573	−0.493787	−	0.869583i	$-0.664388\pi$
$569$	−3.43335e89	−0.987573	−0.493787	+	0.869583i	$0.664388\pi$
$570$	−1.23769e88	−0.0336262
$571$	5.43170e89	1.39400	0.696999	−	0.717072i	$-0.254518\pi$
$571$	5.43170e89	1.39400	0.696999	+	0.717072i	$0.254518\pi$
$572$	−3.96043e89	−0.960221
$573$	−2.01720e89	−0.462088
$574$	−2.42077e89	−0.523982
$575$	−4.26621e89	−0.872644
$576$	1.20583e88	0.0233107
$577$	2.65291e89	0.484740	0.242370	−	0.970184i	$-0.422075\pi$
$577$	2.65291e89	0.484740	0.242370	+	0.970184i	$0.422075\pi$
$578$	−1.39595e89	−0.241111
$579$	5.65793e89	0.923856
$580$	7.05761e88	0.108955
$581$	1.34831e90	1.96818
$582$	2.98961e89	0.412683
$583$	1.26108e90	1.64632
$584$	−3.02515e89	−0.373533
$585$	7.96582e88	0.0930390
$586$	−7.28937e89	−0.805411
$587$	−1.11013e90	−1.16048	−0.580238	−	0.814447i	$-0.697040\pi$
$587$	−1.11013e90	−1.16048	−0.580238	+	0.814447i	$0.697040\pi$
$588$	6.52676e88	0.0645557
$589$	6.75996e89	0.632698
$590$	−1.12168e89	−0.0993527
$591$	9.81266e89	0.822609
$592$	−3.63346e89	−0.288314
$593$	1.39555e90	1.04826	0.524129	−	0.851639i	$-0.324391\pi$
$593$	1.39555e90	1.04826	0.524129	+	0.851639i	$0.324391\pi$
$594$	−1.38872e89	−0.0987542
$595$	2.77568e89	0.186882
$596$	4.98120e89	0.317563
$597$	−1.06133e90	−0.640745
$598$	8.36772e89	0.478430
$599$	5.21589e89	0.282460	0.141230	−	0.989977i	$-0.454894\pi$
$599$	5.21589e89	0.282460	0.141230	+	0.989977i	$0.454894\pi$
$600$	−8.72711e89	−0.447667
$601$	−3.32843e90	−1.61740	−0.808702	−	0.588218i	$-0.799830\pi$
$601$	−3.32843e90	−1.61740	−0.808702	+	0.588218i	$0.799830\pi$
$602$	1.30570e90	0.601117
$603$	−8.16329e89	−0.356084
$604$	−7.35638e89	−0.304063
$605$	1.43700e89	0.0562869
$606$	−1.21502e89	−0.0451047
$607$	−3.51288e90	−1.23603	−0.618017	−	0.786165i	$-0.712064\pi$
$607$	−3.51288e90	−1.23603	−0.618017	+	0.786165i	$0.712064\pi$
$608$	1.51264e90	0.504511
$609$	−1.07423e90	−0.339652
$610$	−7.36432e88	−0.0220756
$611$	−3.20040e90	−0.909629
$612$	6.72654e89	0.181289
$613$	−1.81949e90	−0.465034	−0.232517	−	0.972592i	$-0.574696\pi$
$613$	−1.81949e90	−0.465034	−0.232517	+	0.972592i	$0.574696\pi$
$614$	1.10451e90	0.267731
$615$	−6.69319e89	−0.153884
$616$	4.48855e90	0.978889
$617$	3.54601e90	0.733621	0.366810	−	0.930296i	$-0.380450\pi$
$617$	3.54601e90	0.733621	0.366810	+	0.930296i	$0.380450\pi$
$618$	−2.35937e89	−0.0463095
$619$	−4.99203e90	−0.929675	−0.464838	−	0.885396i	$-0.653887\pi$
$619$	−4.99203e90	−0.929675	−0.464838	+	0.885396i	$0.653887\pi$
$620$	−1.42441e90	−0.251712
$621$	−1.06952e90	−0.179355
$622$	−1.87010e90	−0.297630
$623$	6.06451e90	0.916081
$624$	−1.78430e90	−0.255840
$625$	5.97394e90	0.813131
$626$	−4.89026e90	−0.631926
$627$	−2.58965e90	−0.317721
$628$	6.62339e90	0.771599
$629$	4.51005e90	0.498926
$630$	−3.96953e89	−0.0417034
$631$	−7.03349e90	−0.701805	−0.350902	−	0.936412i	$-0.614125\pi$
$631$	−7.03349e90	−0.701805	−0.350902	+	0.936412i	$0.614125\pi$
$632$	1.57733e91	1.49492
$633$	−6.83081e90	−0.614967
$634$	8.84741e90	0.756685
$635$	−5.38120e90	−0.437253
$636$	8.73554e90	0.674425
$637$	2.14899e90	0.157653
$638$	−4.05115e90	−0.282427
$639$	3.58384e90	0.237449
$640$	−3.93175e90	−0.247592
$641$	−9.51406e89	−0.0569482	−0.0284741	−	0.999595i	$-0.509065\pi$
$641$	−9.51406e89	−0.0569482	−0.0284741	+	0.999595i	$0.509065\pi$
$642$	−7.03002e90	−0.400007
$643$	1.61532e91	0.873779	0.436890	−	0.899515i	$-0.356080\pi$
$643$	1.61532e91	0.873779	0.436890	+	0.899515i	$0.356080\pi$
$644$	1.51994e91	0.781690
$645$	3.61015e90	0.176536
$646$	−3.44119e90	−0.160012
$647$	−3.07787e90	−0.136101	−0.0680504	−	0.997682i	$-0.521678\pi$
$647$	−3.07787e90	−0.136101	−0.0680504	+	0.997682i	$0.521678\pi$
$648$	−2.18785e90	−0.0920089
$649$	−2.34693e91	−0.938745
$650$	−1.26343e91	−0.480692
$651$	2.16807e91	0.784676
$652$	−2.27378e91	−0.782890
$653$	−3.97759e91	−1.30299	−0.651496	−	0.758652i	$-0.725858\pi$
$653$	−3.97759e91	−1.30299	−0.651496	+	0.758652i	$0.725858\pi$
$654$	−9.20751e90	−0.286989
$655$	−2.02092e90	−0.0599385
$656$	1.49924e91	0.423151
$657$	5.59770e90	0.150361
$658$	1.59482e91	0.407728
$659$	−3.25263e91	−0.791513	−0.395757	−	0.918355i	$-0.629518\pi$
$659$	−3.25263e91	−0.791513	−0.395757	+	0.918355i	$0.629518\pi$
$660$	5.45671e90	0.126402
$661$	−1.87984e91	−0.414546	−0.207273	−	0.978283i	$-0.566459\pi$
$661$	−1.87984e91	−0.414546	−0.207273	+	0.978283i	$0.566459\pi$
$662$	−3.43072e91	−0.720278
$663$	2.21477e91	0.442730
$664$	8.01075e91	1.52479
$665$	−7.40228e90	−0.134172
$666$	−6.44989e90	−0.111337
$667$	−3.11999e91	−0.512937
$668$	−7.56186e91	−1.18411
$669$	1.65485e91	0.246836
$670$	−8.79978e90	−0.125038
$671$	−1.54086e91	−0.208584
$672$	4.85138e91	0.625696
$673$	−1.13747e91	−0.139781	−0.0698907	−	0.997555i	$-0.522265\pi$
$673$	−1.13747e91	−0.139781	−0.0698907	+	0.997555i	$0.522265\pi$
$674$	−2.78167e90	−0.0325731
$675$	1.61486e91	0.180203
$676$	−1.65413e91	−0.175915
$677$	−1.50485e91	−0.152532	−0.0762661	−	0.997088i	$-0.524300\pi$
$677$	−1.50485e91	−0.152532	−0.0762661	+	0.997088i	$0.524300\pi$
$678$	−8.30776e90	−0.0802636
$679$	1.78800e92	1.64665
$680$	1.64913e91	0.144782
$681$	2.80194e91	0.234519
$682$	8.17625e91	0.652472
$683$	9.05945e91	0.689333	0.344667	−	0.938725i	$-0.387992\pi$
$683$	9.05945e91	0.689333	0.344667	+	0.938725i	$0.387992\pi$
$684$	−1.79386e91	−0.130156
$685$	5.81662e91	0.402464
$686$	6.44469e91	0.425273
$687$	−9.16501e91	−0.576818
$688$	−8.08652e91	−0.485442
$689$	2.87625e92	1.64703
$690$	−1.15291e91	−0.0629797
$691$	7.32561e91	0.381775	0.190887	−	0.981612i	$-0.438863\pi$
$691$	7.32561e91	0.381775	0.190887	+	0.981612i	$0.438863\pi$
$692$	−1.26398e92	−0.628482
$693$	−8.30558e91	−0.394039
$694$	−4.80702e89	−0.00217617
$695$	−4.43581e91	−0.191631
$696$	−6.38236e91	−0.263136
$697$	−1.86093e92	−0.732261
$698$	−2.33142e92	−0.875626
$699$	1.72423e92	0.618139
$700$	−2.29493e92	−0.785386
$701$	−1.84397e92	−0.602447	−0.301223	−	0.953554i	$-0.597395\pi$
$701$	−1.84397e92	−0.602447	−0.301223	+	0.953554i	$0.597395\pi$
$702$	−3.16737e91	−0.0987967
$703$	−1.20276e92	−0.358204
$704$	2.71971e91	0.0773412
$705$	4.40953e91	0.119742
$706$	−2.87179e92	−0.744732
$707$	−7.26670e91	−0.179972
$708$	−1.62573e92	−0.384562
$709$	−5.69174e91	−0.128600	−0.0643002	−	0.997931i	$-0.520482\pi$
$709$	−5.69174e91	−0.128600	−0.0643002	+	0.997931i	$0.520482\pi$
$710$	3.86327e91	0.0833795
$711$	−2.91867e92	−0.601760
$712$	3.60313e92	0.709709
$713$	6.29693e92	1.18500
$714$	−1.10366e92	−0.198447
$715$	1.79667e92	0.308689
$716$	4.30975e92	0.707586
$717$	−4.49569e91	−0.0705380
$718$	−4.84236e92	−0.726127
$719$	8.42701e92	1.20777	0.603885	−	0.797071i	$-0.293618\pi$
$719$	8.42701e92	1.20777	0.603885	+	0.797071i	$0.293618\pi$
$720$	2.45842e91	0.0336783
$721$	−1.41108e92	−0.184780
$722$	−2.78877e92	−0.349103
$723$	6.46333e91	0.0773503
$724$	−3.82150e92	−0.437251
$725$	4.71083e92	0.515362
$726$	−5.71380e91	−0.0597702
$727$	−1.30498e93	−1.30537	−0.652686	−	0.757629i	$-0.726358\pi$
$727$	−1.30498e93	−1.30537	−0.652686	+	0.757629i	$0.726358\pi$
$728$	1.02374e93	0.979310
$729$	4.04838e91	0.0370370
$730$	6.03415e91	0.0527987
$731$	1.00374e93	0.840055
$732$	−1.06736e92	−0.0854477
$733$	7.24055e92	0.554488	0.277244	−	0.960799i	$-0.410579\pi$
$733$	7.24055e92	0.554488	0.277244	+	0.960799i	$0.410579\pi$
$734$	3.41210e90	0.00249977
$735$	−2.96089e91	−0.0207532
$736$	1.40903e93	0.944915
$737$	−1.84121e93	−1.18143
$738$	2.66135e92	0.163407
$739$	2.94993e93	1.73327	0.866637	−	0.498939i	$-0.166277\pi$
$739$	2.94993e93	1.73327	0.866637	+	0.498939i	$0.166277\pi$
$740$	2.53436e92	0.142507
$741$	−5.90643e92	−0.317858
$742$	−1.43329e93	−0.738258
$743$	−1.14796e93	−0.565968	−0.282984	−	0.959125i	$-0.591324\pi$
$743$	−1.14796e93	−0.565968	−0.282984	+	0.959125i	$0.591324\pi$
$744$	1.28812e93	0.607906
$745$	−2.25974e92	−0.102089
$746$	−7.71673e90	−0.00333750
$747$	−1.48230e93	−0.613786
$748$	1.51715e93	0.601488
$749$	−4.20447e93	−1.59607
$750$	3.59984e92	0.130856
$751$	−3.79422e93	−1.32076	−0.660382	−	0.750930i	$-0.729605\pi$
$751$	−3.79422e93	−1.32076	−0.660382	+	0.750930i	$0.729605\pi$
$752$	−9.87709e92	−0.329268
$753$	2.67310e93	0.853451
$754$	−9.23979e92	−0.282549
$755$	3.33726e92	0.0977493
$756$	−5.75330e92	−0.161420
$757$	5.50567e93	1.47977	0.739885	−	0.672733i	$-0.234880\pi$
$757$	5.50567e93	1.47977	0.739885	+	0.672733i	$0.234880\pi$
$758$	1.53235e93	0.394557
$759$	−2.41227e93	−0.595071
$760$	−4.39795e92	−0.103946
$761$	−5.24357e93	−1.18748	−0.593739	−	0.804658i	$-0.702349\pi$
$761$	−5.24357e93	−1.18748	−0.593739	+	0.804658i	$0.702349\pi$
$762$	2.13967e93	0.464312
$763$	−5.50677e93	−1.14512
$764$	−3.15162e93	−0.628057
$765$	−3.05153e92	−0.0582801
$766$	1.49429e93	0.273527
$767$	−5.35284e93	−0.939150
$768$	1.80342e93	0.303290
$769$	4.38267e93	0.706533	0.353267	−	0.935523i	$-0.385071\pi$
$769$	4.38267e93	0.706533	0.353267	+	0.935523i	$0.385071\pi$
$770$	−8.95316e92	−0.138365
$771$	6.56279e93	0.972347
$772$	8.83978e93	1.25568
$773$	1.05829e93	0.144135	0.0720677	−	0.997400i	$-0.477040\pi$
$773$	1.05829e93	0.144135	0.0720677	+	0.997400i	$0.477040\pi$
$774$	−1.43547e93	−0.187461
$775$	−9.50765e93	−1.19061
$776$	1.06232e94	1.27570
$777$	−3.85751e93	−0.444246
$778$	−3.15806e92	−0.0348805
$779$	4.96281e93	0.525727
$780$	1.24456e93	0.126456
$781$	8.08325e93	0.787821
$782$	−3.20548e93	−0.299691
$783$	1.18099e93	0.105922
$784$	6.63223e92	0.0570673
$785$	−3.00473e93	−0.248051
$786$	8.03556e92	0.0636478
$787$	6.88024e93	0.522908	0.261454	−	0.965216i	$-0.415798\pi$
$787$	6.88024e93	0.522908	0.261454	+	0.965216i	$0.415798\pi$
$788$	1.53310e94	1.11807
$789$	1.35519e94	0.948410
$790$	−3.14624e93	−0.211306
$791$	−4.96865e93	−0.320260
$792$	−4.93463e93	−0.305271
$793$	−3.51436e93	−0.208674
$794$	−6.54998e93	−0.373313
$795$	−3.96292e93	−0.216812
$796$	−1.65819e94	−0.870884
$797$	−5.72955e93	−0.288885	−0.144442	−	0.989513i	$-0.546139\pi$
$797$	−5.72955e93	−0.288885	−0.144442	+	0.989513i	$0.546139\pi$
$798$	2.94329e93	0.142475
$799$	1.22600e94	0.569797
$800$	−2.12748e94	−0.949382
$801$	−6.66720e93	−0.285685
$802$	−2.04781e94	−0.842603
$803$	1.26254e94	0.498875
$804$	−1.27541e94	−0.483980
$805$	−6.89526e93	−0.251295
$806$	1.86482e94	0.652753
$807$	−1.36223e94	−0.457996
$808$	−4.31739e93	−0.139429
$809$	2.80994e94	0.871706	0.435853	−	0.900018i	$-0.356447\pi$
$809$	2.80994e94	0.871706	0.435853	+	0.900018i	$0.356447\pi$
$810$	4.36403e92	0.0130054
$811$	−1.06728e94	−0.305563	−0.152782	−	0.988260i	$-0.548823\pi$
$811$	−1.06728e94	−0.305563	−0.152782	+	0.988260i	$0.548823\pi$
$812$	−1.67834e94	−0.461647
$813$	−3.94954e94	−1.04377
$814$	−1.45475e94	−0.369399
$815$	1.03151e94	0.251681
$816$	6.83524e93	0.160259
$817$	−2.67682e94	−0.603118
$818$	4.85720e93	0.105173
$819$	−1.89432e94	−0.394209
$820$	−1.04572e94	−0.209154
$821$	6.43540e94	1.23715	0.618576	−	0.785725i	$-0.287710\pi$
$821$	6.43540e94	1.23715	0.618576	+	0.785725i	$0.287710\pi$
$822$	−2.31280e94	−0.427370
$823$	5.91463e94	1.05059	0.525294	−	0.850921i	$-0.323955\pi$
$823$	5.91463e94	1.05059	0.525294	+	0.850921i	$0.323955\pi$
$824$	−8.38369e93	−0.143153
$825$	3.64226e94	0.597884
$826$	2.66743e94	0.420960
$827$	1.03811e95	1.57513	0.787563	−	0.616234i	$-0.211343\pi$
$827$	1.03811e95	1.57513	0.787563	+	0.616234i	$0.211343\pi$
$828$	−1.67099e94	−0.243774
$829$	1.18911e94	0.166802	0.0834010	−	0.996516i	$-0.473422\pi$
$829$	1.18911e94	0.166802	0.0834010	+	0.996516i	$0.473422\pi$
$830$	−1.59788e94	−0.215529
$831$	5.01625e94	0.650648
$832$	6.20306e93	0.0773745
$833$	−8.23229e93	−0.0987547
$834$	1.76376e94	0.203490
$835$	3.43047e94	0.380666
$836$	−4.04600e94	−0.431838
$837$	−2.38353e94	−0.244705
$838$	8.05921e94	0.795906
$839$	−1.10886e95	−1.05345	−0.526723	−	0.850037i	$-0.676579\pi$
$839$	−1.10886e95	−1.05345	−0.526723	+	0.850037i	$0.676579\pi$
$840$	−1.41052e94	−0.128915
$841$	−7.92771e94	−0.697072
$842$	4.25630e94	0.360072
$843$	5.72784e94	0.466224
$844$	−1.06723e95	−0.835847
$845$	7.50404e93	0.0565526
$846$	−1.75332e94	−0.127152
$847$	−3.41727e94	−0.238489
$848$	8.87671e94	0.596193
$849$	6.15150e93	0.0397632
$850$	4.83992e94	0.301108
$851$	−1.12038e95	−0.670892
$852$	5.59929e94	0.322735
$853$	−9.42595e94	−0.522976	−0.261488	−	0.965207i	$-0.584213\pi$
$853$	−9.42595e94	−0.522976	−0.261488	+	0.965207i	$0.584213\pi$
$854$	1.75128e94	0.0935351
$855$	8.13793e93	0.0418423
$856$	−2.49802e95	−1.23651
$857$	−5.32023e94	−0.253544	−0.126772	−	0.991932i	$-0.540462\pi$
$857$	−5.32023e94	−0.253544	−0.126772	+	0.991932i	$0.540462\pi$
$858$	−7.14390e94	−0.327792
$859$	2.07133e95	0.915105	0.457553	−	0.889183i	$-0.348726\pi$
$859$	2.07133e95	0.915105	0.457553	+	0.889183i	$0.348726\pi$
$860$	5.64039e94	0.239944
$861$	1.59168e95	0.652009
$862$	1.77189e95	0.698957
$863$	−2.24621e95	−0.853296	−0.426648	−	0.904418i	$-0.640306\pi$
$863$	−2.24621e95	−0.853296	−0.426648	+	0.904418i	$0.640306\pi$
$864$	−5.33351e94	−0.195127
$865$	5.73411e94	0.202042
$866$	−2.14481e95	−0.727876
$867$	9.17854e94	0.300022
$868$	3.38732e95	1.06651
$869$	−6.58297e95	−1.99655
$870$	1.27307e94	0.0371942
$871$	−4.19939e95	−1.18194
$872$	−3.27176e95	−0.887148
$873$	−1.96570e95	−0.513516
$874$	8.54851e94	0.215164
$875$	2.15297e95	0.522127
$876$	8.74568e94	0.204367
$877$	2.94241e95	0.662546	0.331273	−	0.943535i	$-0.392522\pi$
$877$	2.94241e95	0.662546	0.331273	+	0.943535i	$0.392522\pi$
$878$	8.98166e94	0.194888
$879$	4.79284e95	1.00220
$880$	5.54489e94	0.111739
$881$	6.29216e95	1.22203	0.611016	−	0.791618i	$-0.290761\pi$
$881$	6.29216e95	1.22203	0.611016	+	0.791618i	$0.290761\pi$
$882$	1.17731e94	0.0220375
$883$	−1.88431e95	−0.339961	−0.169980	−	0.985447i	$-0.554370\pi$
$883$	−1.88431e95	−0.339961	−0.169980	+	0.985447i	$0.554370\pi$
$884$	3.46029e95	0.601747
$885$	7.37518e94	0.123628
$886$	1.97050e95	0.318405
$887$	−3.86988e95	−0.602809	−0.301405	−	0.953496i	$-0.597456\pi$
$887$	−3.86988e95	−0.602809	−0.301405	+	0.953496i	$0.597456\pi$
$888$	−2.29188e95	−0.344168
$889$	1.27968e96	1.85265
$890$	−7.18704e94	−0.100317
$891$	9.13099e94	0.122883
$892$	2.58549e95	0.335494
$893$	−3.26954e95	−0.409086
$894$	8.98518e94	0.108407
$895$	−1.95514e95	−0.227473
$896$	9.34994e95	1.04906
$897$	−5.50187e95	−0.595327
$898$	−3.88778e94	−0.0405715
$899$	−6.95319e95	−0.699833
$900$	2.52300e95	0.244927
$901$	−1.10183e96	−1.03171
$902$	6.00258e95	0.542158
$903$	−8.58515e95	−0.747990
$904$	−2.95205e95	−0.248113
$905$	1.73364e95	0.140566
$906$	−1.32696e95	−0.103799
$907$	−4.85828e95	−0.366645	−0.183322	−	0.983053i	$-0.558685\pi$
$907$	−4.85828e95	−0.366645	−0.183322	+	0.983053i	$0.558685\pi$
$908$	4.37766e95	0.318752
$909$	7.98886e94	0.0561253
$910$	−2.04202e95	−0.138425
$911$	4.63622e95	0.303261	0.151631	−	0.988437i	$-0.451548\pi$
$911$	4.63622e95	0.303261	0.151631	+	0.988437i	$0.451548\pi$
$912$	−1.82285e95	−0.115058
$913$	−3.34329e96	−2.03645
$914$	5.05336e95	0.297049
$915$	4.84212e94	0.0274695
$916$	−1.43191e96	−0.783996
$917$	4.80586e95	0.253961
$918$	1.21335e95	0.0618868
$919$	9.98324e94	0.0491493	0.0245746	−	0.999698i	$-0.492177\pi$
$919$	9.98324e94	0.0491493	0.0245746	+	0.999698i	$0.492177\pi$
$920$	−4.09671e95	−0.194684
$921$	−7.26228e95	−0.333146
$922$	7.61485e95	0.337215
$923$	1.84361e96	0.788160
$924$	−1.29764e96	−0.535568
$925$	1.69164e96	0.674064
$926$	9.31318e95	0.358295
$927$	1.55131e95	0.0576245
$928$	−1.55588e96	−0.558043
$929$	−2.75419e96	−0.953855	−0.476928	−	0.878943i	$-0.658250\pi$
$929$	−2.75419e96	−0.953855	−0.476928	+	0.878943i	$0.658250\pi$
$930$	−2.56937e95	−0.0859273
$931$	2.19542e95	0.0709010
$932$	2.69388e96	0.840158
$933$	1.22961e96	0.370351
$934$	−1.10836e96	−0.322410
$935$	−6.88262e95	−0.193364
$936$	−1.12548e96	−0.305403
$937$	5.38990e96	1.41268	0.706341	−	0.707872i	$-0.250345\pi$
$937$	5.38990e96	1.41268	0.706341	+	0.707872i	$0.250345\pi$
$938$	2.09264e96	0.529788
$939$	3.21540e96	0.786328
$940$	6.88932e95	0.162750
$941$	2.81350e96	0.642072	0.321036	−	0.947067i	$-0.395969\pi$
$941$	2.81350e96	0.642072	0.321036	+	0.947067i	$0.395969\pi$
$942$	1.19474e96	0.263402
$943$	4.62288e96	0.984652
$944$	−1.65200e96	−0.339954
$945$	2.61001e95	0.0518930
$946$	−3.23765e96	−0.621968
$947$	7.91810e95	0.146976	0.0734881	−	0.997296i	$-0.476587\pi$
$947$	7.91810e95	0.146976	0.0734881	+	0.997296i	$0.476587\pi$
$948$	−4.56004e96	−0.817896
$949$	2.87959e96	0.499089
$950$	−1.29073e96	−0.216181
$951$	−5.81727e96	−0.941569
$952$	−3.92172e96	−0.613445
$953$	5.89207e96	0.890735	0.445368	−	0.895348i	$-0.353073\pi$
$953$	5.89207e96	0.890735	0.445368	+	0.895348i	$0.353073\pi$
$954$	1.57573e96	0.230229
$955$	1.42975e96	0.201906
$956$	−7.02393e95	−0.0958735
$957$	2.66368e96	0.351434
$958$	−7.12141e96	−0.908211
$959$	−1.38323e97	−1.70525
$960$	−8.54663e94	−0.0101854
$961$	5.35349e96	0.616775
$962$	−3.31797e96	−0.369558
$963$	4.62231e96	0.497743
$964$	1.00981e96	0.105133
$965$	−4.01021e96	−0.403672
$966$	2.74169e96	0.266847
$967$	2.15117e96	0.202448	0.101224	−	0.994864i	$-0.467724\pi$
$967$	2.15117e96	0.202448	0.101224	+	0.994864i	$0.467724\pi$
$968$	−2.03032e96	−0.184763
$969$	2.26262e96	0.199108
$970$	−2.11896e96	−0.180319
$971$	−1.80469e97	−1.48518	−0.742589	−	0.669748i	$-0.766402\pi$
$971$	−1.80469e97	−1.48518	−0.742589	+	0.669748i	$0.766402\pi$
$972$	6.32506e95	0.0503398
$973$	1.05486e97	0.811948
$974$	−3.63681e96	−0.270741
$975$	8.30719e96	0.598142
$976$	−1.08461e96	−0.0755359
$977$	−2.13932e97	−1.44113	−0.720563	−	0.693389i	$-0.756117\pi$
$977$	−2.13932e97	−1.44113	−0.720563	+	0.693389i	$0.756117\pi$
$978$	−4.10148e96	−0.267256
$979$	−1.50377e97	−0.947858
$980$	−4.62601e95	−0.0282072
$981$	6.05404e96	0.357110
$982$	1.34858e97	0.769578
$983$	2.99452e97	1.65325	0.826624	−	0.562755i	$-0.190259\pi$
$983$	2.99452e97	1.65325	0.826624	+	0.562755i	$0.190259\pi$
$984$	9.45673e96	0.505126
$985$	−6.95498e96	−0.359433
$986$	3.53956e96	0.176990
$987$	−1.04861e97	−0.507350
$988$	−9.22803e96	−0.432024
$989$	−2.49347e97	−1.12960
$990$	9.84293e95	0.0431500
$991$	3.43296e97	1.45638	0.728191	−	0.685374i	$-0.240361\pi$
$991$	3.43296e97	1.45638	0.728191	+	0.685374i	$0.240361\pi$
$992$	3.14016e97	1.28921
$993$	2.25573e97	0.896267
$994$	−9.18710e96	−0.353281
$995$	7.52247e96	0.279969
$996$	−2.31590e97	−0.834242
$997$	−2.55537e97	−0.890968	−0.445484	−	0.895290i	$-0.646968\pi$
$997$	−2.55537e97	−0.890968	−0.445484	+	0.895290i	$0.646968\pi$
$998$	1.37770e97	0.464958
$999$	4.24087e96	0.138540

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3.66.a.a.1.4	✓	5
3.2	odd	2		9.66.a.a.1.2		5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
3.66.a.a.1.4	✓	5	1.1	even	1	trivial
9.66.a.a.1.2		5	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)

\(f(q)\)	\(=\)	\(q+2.81824e9 q^{2} -1.85302e15 q^{3} -2.89510e19 q^{4} +1.31338e22 q^{5} -5.22225e24 q^{6} -3.12329e27 q^{7} -1.85565e29 q^{8} +3.43368e30 q^{9} +O(q^{10})\)	\(q+2.81824e9 q^{2} -1.85302e15 q^{3} -2.89510e19 q^{4} +1.31338e22 q^{5} -5.22225e24 q^{6} -3.12329e27 q^{7} -1.85565e29 q^{8} +3.43368e30 q^{9} +3.70141e31 q^{10} +7.74457e33 q^{11} +5.36469e34 q^{12} +1.76637e36 q^{13} -8.80217e36 q^{14} -2.43371e37 q^{15} +5.45138e38 q^{16} -6.76655e39 q^{17} +9.67693e39 q^{18} +1.80453e41 q^{19} -3.80236e41 q^{20} +5.78752e42 q^{21} +2.18260e43 q^{22} +1.68093e44 q^{23} +3.43856e44 q^{24} -2.53801e45 q^{25} +4.97804e45 q^{26} -6.36269e45 q^{27} +9.04225e46 q^{28} -1.85611e47 q^{29} -6.85878e46 q^{30} +3.74610e48 q^{31} +8.38248e48 q^{32} -1.43508e49 q^{33} -1.90697e49 q^{34} -4.10206e49 q^{35} -9.94087e49 q^{36} -6.66522e50 q^{37} +5.08559e50 q^{38} -3.27311e51 q^{39} -2.43717e51 q^{40} +2.75020e52 q^{41} +1.63106e52 q^{42} -1.48339e53 q^{43} -2.24213e53 q^{44} +4.50972e52 q^{45} +4.73725e53 q^{46} -1.81185e54 q^{47} -1.01015e54 q^{48} +1.21661e54 q^{49} -7.15271e54 q^{50} +1.25386e55 q^{51} -5.11381e55 q^{52} +1.62834e56 q^{53} -1.79315e55 q^{54} +1.01715e56 q^{55} +5.79574e56 q^{56} -3.34383e56 q^{57} -5.23096e56 q^{58} -3.03042e57 q^{59} +7.04586e56 q^{60} -1.98960e57 q^{61} +1.05574e58 q^{62} -1.07244e58 q^{63} +3.51176e57 q^{64} +2.31991e58 q^{65} -4.04440e58 q^{66} -2.37742e59 q^{67} +1.95899e59 q^{68} -3.11479e59 q^{69} -1.15606e59 q^{70} +1.04373e60 q^{71} -6.37173e59 q^{72} +1.63023e60 q^{73} -1.87842e60 q^{74} +4.70298e60 q^{75} -5.22430e60 q^{76} -2.41885e61 q^{77} -9.22440e60 q^{78} -8.50011e61 q^{79} +7.15972e60 q^{80} +1.17902e61 q^{81} +7.75070e61 q^{82} -4.31694e62 q^{83} -1.67555e62 q^{84} -8.88703e61 q^{85} -4.18054e62 q^{86} +3.43941e62 q^{87} -1.43712e63 q^{88} -1.94171e63 q^{89} +1.27095e62 q^{90} -5.51687e63 q^{91} -4.86646e63 q^{92} -6.94161e63 q^{93} -5.10623e63 q^{94} +2.37003e63 q^{95} -1.55329e64 q^{96} -5.72475e64 q^{97} +3.42871e63 q^{98} +2.65924e64 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 5 q - 2586530964 q^{2} - 92\!\cdots\!05 q^{3}+ \cdots + 17\!\cdots\!05 q^{9}+O(q^{10}) \) 5 * q - 2586530964 * q^2 - 9265100944259205 * q^3 + 90956647467025386896 * q^4 - 86326129898993074537194 * q^5 + 4792894095382414354904724 * q^6 + 5727531915019826651630441824 * q^7 - 171310184604381688819720685376 * q^8 + 17168419101462562423289245446405 * q^9	\( 5 q - 2586530964 q^{2} - 92\!\cdots\!05 q^{3}+ \cdots + 83\!\cdots\!12 q^{99}+O(q^{100}) \) 5 * q - 2586530964 * q^2 - 9265100944259205 * q^3 + 90956647467025386896 * q^4 - 86326129898993074537194 * q^5 + 4792894095382414354904724 * q^6 + 5727531915019826651630441824 * q^7 - 171310184604381688819720685376 * q^8 + 17168419101462562423289245446405 * q^9 - 659896383621335348194397701499736 * q^10 + 2423670936929044310926676000247252 * q^11 - 168544504066677707761757029046875536 * q^12 + 1275682308849370318735355413877537206 * q^13 - 49982312455633392023473970602516559232 * q^14 + 159964061528280704808897398479309874154 * q^15 + 4993462918087349121596715635252022735104 * q^16 - 14309939744126060363431428635715654504630 * q^17 - 8881329521772395078924101615064506996884 * q^18 + 505698133245450788939168217707371295193772 * q^19 - 2392412709256462478682330993076561136959776 * q^20 - 10613232270824985719754055969983070105797984 * q^21 - 137756426131570501611689002373657418979559760 * q^22 - 230360184409184050962312611330412345814929768 * q^23 + 317441230627855101604057424708804059039377216 * q^24 + 130572856113249510620811280312450547680114811 * q^25 + 44579953518799489855288790990258594868841710120 * q^26 - 31813427205679711792374143812692671154451081605 * q^27 + 367972371100886988316449196636850968953833778688 * q^28 + 652807732796864695792958071571718718887562702974 * q^29 + 1222801321400653743042610213721072617113604613976 * q^30 + 3581649354549322445208888229299534409749377229064 * q^31 - 2294508588173344143229543858391788222944135238656 * q^32 - 4491111177262976106278253651057341558249995390932 * q^33 + 106009618192883428412510933273135649343581836564952 * q^34 - 440771650608122791407015684618838754335319696936640 * q^35 + 312316368755575009460762874432245635911640271461776 * q^36 - 1172919468819631279715021157080009190889506495424226 * q^37 - 1342153935543987221244867931117925994792583662033072 * q^38 - 2363865072859012745357164672952015693551969899096246 * q^39 + 6732673491145233171964344219335775749594077923182208 * q^40 - 31982157562646981598434088890071836535840877160069726 * q^41 + 92618234065789512770934641713649798453212083948746112 * q^42 + 334877331045247829802327806663521554334341796684864084 * q^43 + 765921589904004792600073853631095307075801590287172160 * q^44 - 296416635502642225078067725267957665933115223461217514 * q^45 - 1110786269552442011050694204097985240019345559259829856 * q^46 - 4739916099041293147061619254167248169010271632238793152 * q^47 - 9252987599498884715329226429707310439431406578245726464 * q^48 - 1034115523044747562960726145206837328993313613574344227 * q^49 + 17979150603446614626452006162693701157007696601013121684 * q^50 + 26516607247118937651921141601708197225189188319318523830 * q^51 + 196783095275672862675056518704849747440137799355569402080 * q^52 - 170349965491878622775963275845161284943336335955115530538 * q^53 + 16457282907690114243514332408903722031371469798924663444 * q^54 + 229872003287660350640021345393036601027517632014351462616 * q^55 - 1700645281408649030356235569424664257832623944355798292480 * q^56 - 937068850368508674586743856840468080145831759338293934252 * q^57 - 696261775514704784879329791831143710762267301706537573624 * q^58 - 474745263568883969772349493682768733261242489336725334252 * q^59 + 4433189050317954677128613223372191531876028787426840547616 * q^60 + 16730379071820983834994499297475454972698844660036791965558 * q^61 - 32044230246813109420262523738727183452436444722941621340192 * q^62 + 19666533666812568344327802767761565715789308623694052488544 * q^63 - 6799996890991484025916228043599795294772269798542795304960 * q^64 + 98327236007925367657039618198273012082179961727092352428628 * q^65 + 255265438765877455424089405839369888236077304073402045518160 * q^66 - 157867546999669568987249916138496240685031332689194550821140 * q^67 - 1841419506634516386840778640672442997018991116523035775279328 * q^68 + 426862072417851148888089847118038952307811954977491972502888 * q^69 + 23291625706079904056449388536721692805076454252911576349440 * q^70 - 2043321526264647509032986684728405185145183590127912842838040 * q^71 - 588225009127388873750372308302205823457682226651398735054656 * q^72 - 1660934711906093644806157827567781169064101732089773004438478 * q^73 - 9200664498225283568864642819789868487958640990578272114106232 * q^74 - 241954138493897869785850291733840314435547497927181148717051 * q^75 - 5070235637155727844283962057122934109243885036643776429316672 * q^76 + 4616082562248437504836495905290988893883262463306988896984448 * q^77 - 82607553888412124411359004512880746638409772740472893750330920 * q^78 - 163509551671043484183806641788315287501186266983650622023282120 * q^79 - 287668452024434390504869182936693895988801429402000504952930816 * q^80 + 58950922888692915857604364307062593328391057961379205545484805 * q^81 - 677341656519699641817805800073183557931663668916119169144445832 * q^82 - 589633406515402133745211638063307147435988708987095453910208852 * q^83 - 681860232589625326627851166858938950331146998149790873215364608 * q^84 - 1066061999513499352091796913743581330797689631268396473996237908 * q^85 + 137148023832501554228942959312729645276819917245413885813851312 * q^86 - 1209665908311188376322243994188912872601875035942569939576075134 * q^87 - 11964353423109418345237661686710948652415377217786770171449052416 * q^88 - 10941920179046539778574748322212359805621940112257230199924523678 * q^89 - 2265875535510120122678975555367302287591875858382145015461929816 * q^90 - 16180146413603976436779593298107073378132804995273218800058622656 * q^91 - 48721899282574156202978669144522080387547664616447238186528493696 * q^92 - 6636868563368059900522243146976794918401004717018411592215106824 * q^93 - 5234723903677352863882525356783160839602260999433933056496630016 * q^94 - 28228453100889608049374802221925083368230728387835292904406462936 * q^95 + 4251770737379141231134077935944194660412446665052721093159965696 * q^96 + 32463915428803989473801328163474800827209052066062755964127978890 * q^97 - 140921747559822123463058353811762401049788378559606700759676581876 * q^98 + 8322119681846453946246108390142135321418956300625182459022905812 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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