LMFDB - Embedded newform 1.74.a.a.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1,74,Mod(1,1)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1, base_ring=CyclotomicField(1))

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

N = Newforms(chi, 74, names="a")

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

chi := DirichletCharacter("1.1");

S:= CuspForms(chi, 74);

N := Newforms(S);

Level:	$ N $	$=$	$ 1 $
Weight:	$ k $	$=$	$ 74 $
Character orbit:	$[\chi]$	$=$	1.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:	$33.7483973737$
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} - x^{4} + \cdots + 17\!\cdots\!00 $ x^5 - x^4 - 10073499617947743056x^3 + 1429272143092482488433869600x^2 + 7661214288514935343595600445215756800*x + 1722510836040319301450745177697157900206688000
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{39}\cdot 3^{15}\cdot 5^{6}\cdot 7^{2} $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$-2.60629e8$ of defining polynomial
Character	$\chi$	$=$	1.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-5.90767e9 q^{2} +3.95253e17 q^{3} -9.40983e21 q^{4} +1.69056e25 q^{5} -2.33502e27 q^{6} -2.69951e30 q^{7} +1.11387e32 q^{8} +8.86395e34 q^{9} +O(q^{10})$	\(q-5.90767e9 q^{2} +3.95253e17 q^{3} -9.40983e21 q^{4} +1.69056e25 q^{5} -2.33502e27 q^{6} -2.69951e30 q^{7} +1.11387e32 q^{8} +8.86395e34 q^{9} -9.98727e34 q^{10} -1.46803e38 q^{11} -3.71926e39 q^{12} -3.34896e40 q^{13} +1.59478e40 q^{14} +6.68198e42 q^{15} +8.82153e43 q^{16} -1.35791e45 q^{17} -5.23653e44 q^{18} +7.35113e46 q^{19} -1.59079e47 q^{20} -1.06699e48 q^{21} +8.67264e47 q^{22} +2.07741e49 q^{23} +4.40258e49 q^{24} -7.72992e50 q^{25} +1.97845e50 q^{26} +8.32175e51 q^{27} +2.54020e52 q^{28} -3.30017e53 q^{29} -3.94750e52 q^{30} +1.78429e54 q^{31} -1.57316e54 q^{32} -5.80243e55 q^{33} +8.02211e54 q^{34} -4.56369e55 q^{35} -8.34082e56 q^{36} -3.22112e57 q^{37} -4.34280e56 q^{38} -1.32368e58 q^{39} +1.88306e57 q^{40} -6.12341e58 q^{41} +6.30343e57 q^{42} +2.07892e59 q^{43} +1.38139e60 q^{44} +1.49850e60 q^{45} -1.22727e59 q^{46} +5.09761e58 q^{47} +3.48673e61 q^{48} -4.19344e61 q^{49} +4.56658e60 q^{50} -5.36719e62 q^{51} +3.15131e62 q^{52} -1.65493e62 q^{53} -4.91622e61 q^{54} -2.48179e63 q^{55} -3.00690e62 q^{56} +2.90555e64 q^{57} +1.94963e63 q^{58} +1.57646e64 q^{59} -6.28764e64 q^{60} +3.70457e64 q^{61} -1.05410e64 q^{62} -2.39283e65 q^{63} -8.23876e65 q^{64} -5.66162e65 q^{65} +3.42788e65 q^{66} -2.21412e66 q^{67} +1.27777e67 q^{68} +8.21103e66 q^{69} +2.69608e65 q^{70} -1.08186e67 q^{71} +9.87324e66 q^{72} +2.15731e67 q^{73} +1.90293e67 q^{74} -3.05527e68 q^{75} -6.91729e68 q^{76} +3.96297e68 q^{77} +7.81989e67 q^{78} +1.93510e69 q^{79} +1.49133e69 q^{80} -2.70152e69 q^{81} +3.61751e68 q^{82} +1.17002e70 q^{83} +1.00402e70 q^{84} -2.29564e70 q^{85} -1.22816e69 q^{86} -1.30440e71 q^{87} -1.63519e70 q^{88} +1.65587e71 q^{89} -8.85267e69 q^{90} +9.04056e70 q^{91} -1.95481e71 q^{92} +7.05247e71 q^{93} -3.01150e68 q^{94} +1.24275e72 q^{95} -6.21797e71 q^{96} -9.74539e71 q^{97} +2.47734e71 q^{98} -1.30125e73 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 5 q - 92089333488 q^{2} - 12\!\cdots\!04 q^{3}+ \cdots + 32\!\cdots\!65 q^{9}+O(q^{10}) $ 5 * q - 92089333488 * q^2 - 129195798226305804 * q^3 + 891110479259563516160 * q^4 + 23099529720469471562826750 * q^5 - 3335695451789843173883221440 * q^6 - 4356178487147579439806268090008 * q^7 - 382321348565178801062509850849280 * q^8 + 32335028924861937033188022998788065 * q^9	$ 5 q - 92089333488 q^{2} - 12\!\cdots\!04 q^{3}+ \cdots - 15\!\cdots\!20 q^{99}+O(q^{100}) $ 5 * q - 92089333488 * q^2 - 129195798226305804 * q^3 + 891110479259563516160 * q^4 + 23099529720469471562826750 * q^5 - 3335695451789843173883221440 * q^6 - 4356178487147579439806268090008 * q^7 - 382321348565178801062509850849280 * q^8 + 32335028924861937033188022998788065 * q^9 - 1082726120403847340426026649690244000 * q^10 + 50083756421782317855880849016778496860 * q^11 + 1389386159501111619787899997887234696192 * q^12 + 4753748397471720291047553799357192278886 * q^13 + 263363595637460329420141722180437171694720 * q^14 - 5053973124818591694478703469878924549517000 * q^15 + 57509595349357883169785087518099233197588480 * q^16 + 663279725175909884624200257401822351394256602 * q^17 + 6936746909593304334038759770389897835631806416 * q^18 + 31387402430958534058855312636541530201995765700 * q^19 + 68535205735011202400715856751699460073169856000 * q^20 + 873650260100519441483759434874628458149545804960 * q^21 - 9492394168845783423791120540922405517833204177216 * q^22 - 41173446223173693726617088414497261153026772718024 * q^23 + 16216566841440134675070566439222517257116824780800 * q^24 + 321010940201155914585034686800814006311220324546875 * q^25 + 4496438035379975943261998606627087983483848085006560 * q^26 - 12482045195529499122248281309176768796522105943881080 * q^27 - 37814301174111882879202704910382387341459683517577216 * q^28 - 217397685843681573854388291537651452827057882148450250 * q^29 - 809277931163833776121134244746469476931174350662544000 * q^30 - 3959918978904396097569386510196715694840286709585401440 * q^31 - 9479144378484593489541015426974249650207814007382867968 * q^32 - 73769578315518021607552488579011739564089308117835328528 * q^33 - 324638192385754362369074018224584035205208569018875155680 * q^34 - 1051811671165262926972759981500117019527196204743409914000 * q^35 - 3440544904928519792841567448764696150680442862608580965120 * q^36 - 6710426612911460903226679780416929578822322356442579950178 * q^37 - 20075776649866586500887218371135359952534984707306414947520 * q^38 - 53266590853912928667191550341591883996636524676049287303720 * q^39 - 87443314425210154156114784714128373503740284779633935360000 * q^40 - 89999556000464227434562342749528590851939245788450434103790 * q^41 + 151860645080061390785566939100205618848419219581171296592384 * q^42 + 1171421579861687300375905115748875459141635816468653452284156 * q^43 + 3620387401482413711753562750789250834104238410455247119723520 * q^44 + 8637496301209289669216900677161766462676265859857821184867750 * q^45 + 13122337792181100518478081314861771936057558300377044573644160 * q^46 + 26407117391117866585989236437476333636637017745173062895096432 * q^47 - 305063509192507618357183882504465545852009436962512246145024 * q^48 - 47859785088079990485612756297590896342589260563105328803969315 * q^49 - 198341627273982740927873511630518057650356858808871192258250000 * q^50 - 666572032421535161197734372534298884381369595464382997470670040 * q^51 - 1819820853930882517149424007699825989256997486995920851867734528 * q^52 - 2253672757277210109476755074185818948452790752453662372858468754 * q^53 - 981929879310881011928466994898412465282666955980051795540412800 * q^54 + 5272301841223840031246441919708126997046467528986443289345081000 * q^55 + 17369101267271748189623122493455314696373137673860233497989120000 * q^56 + 39672259194438733138452388186436605652387179030172301666478212240 * q^57 + 63080485469034924979732075223792805715626817023343777138220605920 * q^58 + 49827032054541030737892137385762950528020446432538215007741437900 * q^59 + 91369267546356596727702377377074204109693912478731602288473856000 * q^60 - 200207946356755779993110124671040230418699916707275462827300034090 * q^61 - 456512716932753516995161459627410738703514050956609499700325060096 * q^62 - 1444699606935245693297879065147738830138012519879166909023399465144 * q^63 - 2671988611100492125931167910213768824231319631401339943695669002240 * q^64 - 2221078323698894670419341126197735507928898751783246157619800369500 * q^65 - 797490624045567852983392967901985951789407586519264116965780839680 * q^66 + 1726934463658866670044856129309631728944059099751189118466533017652 * q^67 + 25844159932565717701710366021885253281928511625890180327915132834304 * q^68 + 43307862567803975621848996603714756131647359083362619530437754803680 * q^69 + 60019715162941233136874683443010604187189046779871920798680662752000 * q^70 + 29528228383509762365399718501357560736875772117852859701209862331560 * q^71 + 5937319857025079492793067138582418624443592391466592842045028290560 * q^72 - 237248424072934328617284197336037660641948064767277176027665176375374 * q^73 - 385668396032745357868624366253781435784895053179379214963132226802080 * q^74 - 785444151134296088966742788487546108897483082972592363003091781312500 * q^75 - 402469771116557587325960702574461860644965601604695023105081798528000 * q^76 - 1160921420345569675442649510235573702285949327395662717704239852301856 * q^77 + 339124438335685564147183055565832879915531514801135920231578753382272 * q^78 + 1210019475236668608258558597507004925943189831192425236151129201347600 * q^79 + 7695510793835037324754830224890315360926193938062866122926593916928000 * q^80 + 12895807280425851869767179003361520763349212513521199742652083367867805 * q^81 + 19869905655996015892436375229312420723635630923691072274009372051144864 * q^82 + 10633758535693793129462935403233565634399957806616398467042339222483716 * q^83 - 17104473919241589848125111473450344991721950406193981672669373028884480 * q^84 - 28641392301460491393930553180957463692521548910270676165772874742366500 * q^85 - 130748824105220136322401247193488038601024385677355691179590030869522240 * q^86 - 158256246334086183408933559981662943488738078279070353132629771124728040 * q^87 - 221808067516055560593893382793377773024661552295403957235825845052456960 * q^88 - 44230399340933247556508628049428956972940692248797881370004235332026750 * q^89 + 205005728265438963974181523583877066710560749255482389735945594174668000 * q^90 + 503963419362898329804217905595235878617892804641236823955454638331741360 * q^91 + 1056276182251025158869277711594662138415929570173882076378175681365399552 * q^92 + 2087551224100544830404247844376209582022159740935531745376318713047458432 * q^93 + 1211599009021421323842808603980852406277919665987296133682388929757489920 * q^94 + 1134809355692277446299742482002998127744674957590385906379174039024255000 * q^95 - 1239624362529508037215561089866383709629049658259836228855181445997527040 * q^96 - 4705643796144250410051227741367571092615369303801441364082016351450032918 * q^97 - 7645702282951838206479981702299956043322685777549671658293752892775157616 * q^98 - 15823110517274977002648456256699492623727665140588002701017544901953092820 * 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 $

$2$	−5.90767e9	−0.0607885	−0.0303943	−	0.999538i	$-0.509676\pi$
$2$	−5.90767e9	−0.0607885	−0.0303943	+	0.999538i	$0.509676\pi$
$3$	3.95253e17	1.52037	0.760184	−	0.649707i	$-0.225109\pi$
$3$	3.95253e17	1.52037	0.760184	+	0.649707i	$0.225109\pi$
$4$	−9.40983e21	−0.996305
$5$	1.69056e25	0.519548	0.259774	−	0.965669i	$-0.416352\pi$
$5$	1.69056e25	0.519548	0.259774	+	0.965669i	$0.416352\pi$
$6$	−2.33502e27	−0.0924209
$7$	−2.69951e30	−0.384775	−0.192388	−	0.981319i	$-0.561623\pi$
$7$	−2.69951e30	−0.384775	−0.192388	+	0.981319i	$0.561623\pi$
$8$	1.11387e32	0.121352
$9$	8.86395e34	1.31152
$10$	−9.98727e34	−0.0315825
$11$	−1.46803e38	−1.43187	−0.715933	−	0.698169i	$-0.753998\pi$
$11$	−1.46803e38	−1.43187	−0.715933	+	0.698169i	$0.753998\pi$
$12$	−3.71926e39	−1.51475
$13$	−3.34896e40	−0.734476	−0.367238	−	0.930127i	$-0.619696\pi$
$13$	−3.34896e40	−0.734476	−0.367238	+	0.930127i	$0.619696\pi$
$14$	1.59478e40	0.0233899
$15$	6.68198e42	0.789904
$16$	8.82153e43	0.988928
$17$	−1.35791e45	−1.66528	−0.832639	−	0.553817i	$-0.813171\pi$
$17$	−1.35791e45	−1.66528	−0.832639	+	0.553817i	$0.813171\pi$
$18$	−5.23653e44	−0.0797254
$19$	7.35113e46	1.55542	0.777710	−	0.628624i	$-0.216381\pi$
$19$	7.35113e46	1.55542	0.777710	+	0.628624i	$0.216381\pi$
$20$	−1.59079e47	−0.517628
$21$	−1.06699e48	−0.585000
$22$	8.67264e47	0.0870409
$23$	2.07741e49	0.411583	0.205791	−	0.978596i	$-0.434023\pi$
$23$	2.07741e49	0.411583	0.205791	+	0.978596i	$0.434023\pi$
$24$	4.40258e49	0.184500
$25$	−7.72992e50	−0.730070
$26$	1.97845e50	0.0446477
$27$	8.32175e51	0.473628
$28$	2.54020e52	0.383353
$29$	−3.30017e53	−1.38360	−0.691799	−	0.722091i	$-0.743181\pi$
$29$	−3.30017e53	−1.38360	−0.691799	+	0.722091i	$0.743181\pi$
$30$	−3.94750e52	−0.0480171
$31$	1.78429e54	0.655790	0.327895	−	0.944714i	$-0.393661\pi$
$31$	1.78429e54	0.655790	0.327895	+	0.944714i	$0.393661\pi$
$32$	−1.57316e54	−0.181468
$33$	−5.80243e55	−2.17696
$34$	8.02211e54	0.101230
$35$	−4.56369e55	−0.199909
$36$	−8.34082e56	−1.30668
$37$	−3.22112e57	−1.85628	−0.928140	−	0.372230i	$-0.878593\pi$
$37$	−3.22112e57	−1.85628	−0.928140	+	0.372230i	$0.878593\pi$
$38$	−4.34280e56	−0.0945516
$39$	−1.32368e58	−1.11667
$40$	1.88306e57	0.0630484
$41$	−6.12341e58	−0.832497	−0.416249	−	0.909251i	$-0.636655\pi$
$41$	−6.12341e58	−0.832497	−0.416249	+	0.909251i	$0.636655\pi$
$42$	6.30343e57	0.0355613
$43$	2.07892e59	0.496867	0.248434	−	0.968649i	$-0.420084\pi$
$43$	2.07892e59	0.496867	0.248434	+	0.968649i	$0.420084\pi$
$44$	1.38139e60	1.42657
$45$	1.49850e60	0.681398
$46$	−1.22727e59	−0.0250195
$47$	5.09761e58	0.00474018	0.00237009	−	0.999997i	$-0.499246\pi$
$47$	5.09761e58	0.00474018	0.00237009	+	0.999997i	$0.499246\pi$
$48$	3.48673e61	1.50354
$49$	−4.19344e61	−0.851948
$50$	4.56658e60	0.0443799
$51$	−5.36719e62	−2.53184
$52$	3.15131e62	0.731762
$53$	−1.65493e62	−0.191739	−0.0958697	−	0.995394i	$-0.530563\pi$
$53$	−1.65493e62	−0.191739	−0.0958697	+	0.995394i	$0.530563\pi$
$54$	−4.91622e61	−0.0287911
$55$	−2.48179e63	−0.743923
$56$	−3.00690e62	−0.0466934
$57$	2.90555e64	2.36481
$58$	1.94963e63	0.0841068
$59$	1.57646e64	0.364404	0.182202	−	0.983261i	$-0.441677\pi$
$59$	1.57646e64	0.364404	0.182202	+	0.983261i	$0.441677\pi$
$60$	−6.28764e64	−0.786985
$61$	3.70457e64	0.253629	0.126814	−	0.991926i	$-0.459525\pi$
$61$	3.70457e64	0.253629	0.126814	+	0.991926i	$0.459525\pi$
$62$	−1.05410e64	−0.0398645
$63$	−2.39283e65	−0.504641
$64$	−8.23876e65	−0.977897
$65$	−5.66162e65	−0.381595
$66$	3.42788e65	0.132334
$67$	−2.21412e66	−0.493709	−0.246855	−	0.969053i	$-0.579397\pi$
$67$	−2.21412e66	−0.493709	−0.246855	+	0.969053i	$0.579397\pi$
$68$	1.27777e67	1.65912
$69$	8.21103e66	0.625757
$70$	2.69608e65	0.0121522
$71$	−1.08186e67	−0.290564	−0.145282	−	0.989390i	$-0.546409\pi$
$71$	−1.08186e67	−0.290564	−0.145282	+	0.989390i	$0.546409\pi$
$72$	9.87324e66	0.159156
$73$	2.15731e67	0.210197	0.105099	−	0.994462i	$-0.466484\pi$
$73$	2.15731e67	0.210197	0.105099	+	0.994462i	$0.466484\pi$
$74$	1.90293e67	0.112841
$75$	−3.05527e68	−1.10998
$76$	−6.91729e68	−1.54967
$77$	3.96297e68	0.550946
$78$	7.81989e67	0.0678809
$79$	1.93510e69	1.05515	0.527575	−	0.849508i	$-0.323101\pi$
$79$	1.93510e69	1.05515	0.527575	+	0.849508i	$0.323101\pi$
$80$	1.49133e69	0.513795
$81$	−2.70152e69	−0.591433
$82$	3.61751e68	0.0506063
$83$	1.17002e70	1.05158	0.525791	−	0.850614i	$-0.323769\pi$
$83$	1.17002e70	1.05158	0.525791	+	0.850614i	$0.323769\pi$
$84$	1.00402e70	0.582839
$85$	−2.29564e70	−0.865191
$86$	−1.22816e69	−0.0302038
$87$	−1.30440e71	−2.10358
$88$	−1.63519e70	−0.173760
$89$	1.65587e71	1.16490	0.582452	−	0.812865i	$-0.302093\pi$
$89$	1.65587e71	1.16490	0.582452	+	0.812865i	$0.302093\pi$
$90$	−8.85267e69	−0.0414212
$91$	9.04056e70	0.282608
$92$	−1.95481e71	−0.410062
$93$	7.05247e71	0.997043
$94$	−3.01150e68	−0.000288149 0
$95$	1.24275e72	0.808115
$96$	−6.21797e71	−0.275898
$97$	−9.74539e71	−0.296231	−0.148116	−	0.988970i	$-0.547321\pi$
$97$	−9.74539e71	−0.296231	−0.148116	+	0.988970i	$0.547321\pi$
$98$	2.47734e71	0.0517886
$99$	−1.30125e73	−1.87792
$100$	7.27372e72	0.727372
$101$	−1.40279e73	−0.975582	−0.487791	−	0.872961i	$-0.662197\pi$
$101$	−1.40279e73	−0.975582	−0.487791	+	0.872961i	$0.662197\pi$
$102$	3.17076e72	0.153907
$103$	4.70385e73	1.59917	0.799586	−	0.600552i	$-0.205052\pi$
$103$	4.70385e73	1.59917	0.799586	+	0.600552i	$0.205052\pi$
$104$	−3.73029e72	−0.0891304
$105$	−1.80381e73	−0.303936
$106$	9.77680e71	0.0116555
$107$	1.24306e74	1.05192	0.525962	−	0.850508i	$-0.323705\pi$
$107$	1.24306e74	1.05192	0.525962	+	0.850508i	$0.323705\pi$
$108$	−7.83063e73	−0.471878
$109$	2.39112e74	1.02928	0.514641	−	0.857406i	$-0.327925\pi$
$109$	2.39112e74	1.02928	0.514641	+	0.857406i	$0.327925\pi$
$110$	1.46616e73	0.0452219
$111$	−1.27316e75	−2.82223
$112$	−2.38139e74	−0.380515
$113$	7.57224e74	0.874704	0.437352	−	0.899290i	$-0.355916\pi$
$113$	7.57224e74	0.874704	0.437352	+	0.899290i	$0.355916\pi$
$114$	−1.71650e74	−0.143753
$115$	3.51199e74	0.213837
$116$	3.10541e75	1.37848
$117$	−2.96850e75	−0.963281
$118$	−9.31319e73	−0.0221516
$119$	3.66571e75	0.640758
$120$	7.44283e74	0.0958568
$121$	1.10396e76	1.05024
$122$	−2.18854e74	−0.0154177
$123$	−2.42030e76	−1.26570
$124$	−1.67899e76	−0.653367
$125$	−3.09674e76	−0.898854
$126$	1.41361e75	0.0306764
$127$	3.10832e76	0.505463	0.252732	−	0.967536i	$-0.418671\pi$
$127$	3.10832e76	0.505463	0.252732	+	0.967536i	$0.418671\pi$
$128$	1.97253e76	0.240913
$129$	8.21701e76	0.755421
$130$	3.34470e75	0.0231966
$131$	−2.13454e77	−1.11919	−0.559593	−	0.828768i	$-0.689042\pi$
$131$	−2.13454e77	−1.11919	−0.559593	+	0.828768i	$0.689042\pi$
$132$	5.45999e77	2.16892
$133$	−1.98445e77	−0.598487
$134$	1.30803e76	0.0300118
$135$	1.40684e77	0.246072
$136$	−1.51253e77	−0.202085
$137$	−1.04031e78	−1.06381	−0.531905	−	0.846804i	$-0.678524\pi$
$137$	−1.04031e78	−1.06381	−0.531905	+	0.846804i	$0.678524\pi$
$138$	−4.85081e76	−0.0380388
$139$	−1.48817e78	−0.896626	−0.448313	−	0.893877i	$-0.647975\pi$
$139$	−1.48817e78	−0.896626	−0.448313	+	0.893877i	$0.647975\pi$
$140$	4.29436e77	0.199170
$141$	2.01484e76	0.00720682
$142$	6.39128e76	0.0176630
$143$	4.91637e78	1.05167
$144$	7.81936e78	1.29700
$145$	−5.57914e78	−0.718845
$146$	−1.27447e77	−0.0127776
$147$	−1.65747e79	−1.29528
$148$	3.03102e79	1.84942
$149$	−8.64312e78	−0.412450	−0.206225	−	0.978505i	$-0.566118\pi$
$149$	−8.64312e78	−0.412450	−0.206225	+	0.978505i	$0.566118\pi$
$150$	1.80495e78	0.0674738
$151$	−2.28898e79	−0.671403	−0.335701	−	0.941968i	$-0.608973\pi$
$151$	−2.28898e79	−0.671403	−0.335701	+	0.941968i	$0.608973\pi$
$152$	8.18817e78	0.188754
$153$	−1.20365e80	−2.18405
$154$	−2.34119e78	−0.0334912
$155$	3.01646e79	0.340714
$156$	1.24557e80	1.11255
$157$	1.93279e80	1.36725	0.683623	−	0.729835i	$-0.260403\pi$
$157$	1.93279e80	1.36725	0.683623	+	0.729835i	$0.260403\pi$
$158$	−1.14319e79	−0.0641410
$159$	−6.54117e79	−0.291515
$160$	−2.65953e79	−0.0942812
$161$	−5.60801e79	−0.158367
$162$	1.59597e79	0.0359523
$163$	−9.29339e78	−0.0167235	−0.00836174	−	0.999965i	$-0.502662\pi$
$163$	−9.29339e78	−0.0167235	−0.00836174	+	0.999965i	$0.502662\pi$
$164$	5.76203e80	0.829421
$165$	−9.80936e80	−1.13104
$166$	−6.91210e79	−0.0639241
$167$	−1.36355e81	−1.01279	−0.506397	−	0.862300i	$-0.669023\pi$
$167$	−1.36355e81	−1.01279	−0.506397	+	0.862300i	$0.669023\pi$
$168$	−1.18848e80	−0.0709912
$169$	−9.57497e80	−0.460546
$170$	1.35619e80	0.0525937
$171$	6.51600e81	2.03997
$172$	−1.95623e81	−0.495031
$173$	4.09283e81	0.838188	0.419094	−	0.907943i	$-0.362348\pi$
$173$	4.09283e81	0.838188	0.419094	+	0.907943i	$0.362348\pi$
$174$	7.70597e80	0.127873
$175$	2.08670e81	0.280913
$176$	−1.29503e82	−1.41601
$177$	6.23099e81	0.554029
$178$	−9.78231e80	−0.0708127
$179$	6.62628e81	0.390962	0.195481	−	0.980708i	$-0.437373\pi$
$179$	6.62628e81	0.390962	0.195481	+	0.980708i	$0.437373\pi$
$180$	−1.41007e82	−0.678880
$181$	−2.47756e82	−0.974442	−0.487221	−	0.873279i	$-0.661989\pi$
$181$	−2.47756e82	−0.974442	−0.487221	+	0.873279i	$0.661989\pi$
$182$	−5.34087e80	−0.0171793
$183$	1.46424e82	0.385609
$184$	2.31396e81	0.0499465
$185$	−5.44549e82	−0.964427
$186$	−4.16637e81	−0.0606087
$187$	1.99346e83	2.38445
$188$	−4.79677e80	−0.00472267
$189$	−2.24647e82	−0.182240
$190$	−7.34177e81	−0.0491241
$191$	3.23309e83	1.78608	0.893038	−	0.449981i	$-0.148569\pi$
$191$	3.23309e83	1.78608	0.893038	+	0.449981i	$0.148569\pi$
$192$	−3.25639e83	−1.48676
$193$	−3.80588e83	−1.43752	−0.718759	−	0.695259i	$-0.755290\pi$
$193$	−3.80588e83	−1.43752	−0.718759	+	0.695259i	$0.755290\pi$
$194$	5.75725e81	0.0180075
$195$	−2.23777e83	−0.580166
$196$	3.94595e83	0.848800
$197$	−5.12328e80	−0.000915232 0	−0.000457616	−	1.00000i	$-0.500146\pi$
$197$	−5.12328e80	−0.000915232 0	−0.000457616		1.00000i	$0.500146\pi$
$198$	7.68738e82	0.114156
$199$	−2.77399e83	−0.342742	−0.171371	−	0.985207i	$-0.554820\pi$
$199$	−2.77399e83	−0.342742	−0.171371	+	0.985207i	$0.554820\pi$
$200$	−8.61009e82	−0.0885957
$201$	−8.75138e83	−0.750620
$202$	8.28724e82	0.0593042
$203$	8.90886e83	0.532374
$204$	5.05044e84	2.52248
$205$	−1.03520e84	−0.432522
$206$	−2.77888e83	−0.0972113
$207$	1.84141e84	0.539799
$208$	−2.95429e84	−0.726343
$209$	−1.07917e85	−2.22715
$210$	1.06563e83	0.0184758
$211$	4.96555e84	0.723865	0.361932	−	0.932204i	$-0.382117\pi$
$211$	4.96555e84	0.723865	0.361932	+	0.932204i	$0.382117\pi$
$212$	1.55726e84	0.191031
$213$	−4.27609e84	−0.441765
$214$	−7.34359e83	−0.0639449
$215$	3.51455e84	0.258146
$216$	9.26931e83	0.0574759
$217$	−4.81673e84	−0.252332
$218$	−1.41259e84	−0.0625685
$219$	8.52681e84	0.319578
$220$	2.33533e85	0.741174
$221$	4.54760e85	1.22311
$222$	7.52138e84	0.171559
$223$	−4.40493e85	−0.852730	−0.426365	−	0.904551i	$-0.640206\pi$
$223$	−4.40493e85	−0.852730	−0.426365	+	0.904551i	$0.640206\pi$
$224$	4.24678e84	0.0698243
$225$	−6.85176e85	−0.957503
$226$	−4.47343e84	−0.0531720
$227$	2.14705e85	0.217220	0.108610	−	0.994084i	$-0.465360\pi$
$227$	2.14705e85	0.217220	0.108610	+	0.994084i	$0.465360\pi$
$228$	−2.73408e86	−2.35607
$229$	1.57271e86	1.15519	0.577595	−	0.816323i	$-0.303991\pi$
$229$	1.57271e86	1.15519	0.577595	+	0.816323i	$0.303991\pi$
$230$	−2.07477e84	−0.0129988
$231$	1.56637e86	0.837642
$232$	−3.67595e85	−0.167903
$233$	7.07062e85	0.276036	0.138018	−	0.990430i	$-0.455927\pi$
$233$	7.07062e85	0.276036	0.138018	+	0.990430i	$0.455927\pi$
$234$	1.75369e85	0.0585564
$235$	8.61782e83	0.00246275
$236$	−1.48342e86	−0.363058
$237$	7.64853e86	1.60422
$238$	−2.16558e85	−0.0389507
$239$	−7.62711e86	−1.17716	−0.588582	−	0.808438i	$-0.700313\pi$
$239$	−7.62711e86	−1.17716	−0.588582	+	0.808438i	$0.700313\pi$
$240$	5.89453e86	0.781159
$241$	3.73671e86	0.425468	0.212734	−	0.977110i	$-0.431763\pi$
$241$	3.73671e86	0.425468	0.212734	+	0.977110i	$0.431763\pi$
$242$	−6.52184e85	−0.0638424
$243$	−1.63021e87	−1.37282
$244$	−3.48594e86	−0.252692
$245$	−7.08926e86	−0.442628
$246$	1.42983e86	0.0769402
$247$	−2.46186e87	−1.14242
$248$	1.98746e86	0.0795817
$249$	4.62454e87	1.59879
$250$	1.82945e86	0.0546400
$251$	4.47993e87	1.15659	0.578296	−	0.815827i	$-0.303718\pi$
$251$	4.47993e87	1.15659	0.578296	+	0.815827i	$0.303718\pi$
$252$	2.25162e87	0.502776
$253$	−3.04971e87	−0.589331
$254$	−1.83629e86	−0.0307264
$255$	−9.07356e87	−1.31541
$256$	7.66476e87	0.963252
$257$	−6.05754e86	−0.0660294	−0.0330147	−	0.999455i	$-0.510511\pi$
$257$	−6.05754e86	−0.0660294	−0.0330147	+	0.999455i	$0.510511\pi$
$258$	−4.85434e86	−0.0459209
$259$	8.69545e87	0.714251
$260$	5.32749e87	0.380185
$261$	−2.92525e88	−1.81462
$262$	1.26102e87	0.0680336
$263$	−2.40877e88	−1.13086	−0.565432	−	0.824795i	$-0.691290\pi$
$263$	−2.40877e88	−1.13086	−0.565432	+	0.824795i	$0.691290\pi$
$264$	−6.46313e87	−0.264180
$265$	−2.79776e87	−0.0996178
$266$	1.17235e87	0.0363811
$267$	6.54485e88	1.77108
$268$	2.08345e88	0.491885
$269$	4.13585e88	0.852328	0.426164	−	0.904646i	$-0.359865\pi$
$269$	4.13585e88	0.852328	0.426164	+	0.904646i	$0.359865\pi$
$270$	−8.31116e86	−0.0149584
$271$	3.37612e87	0.0530932	0.0265466	−	0.999648i	$-0.491549\pi$
$271$	3.37612e87	0.0530932	0.0265466	+	0.999648i	$0.491549\pi$
$272$	−1.19789e89	−1.64684
$273$	3.57331e88	0.429669
$274$	6.14583e87	0.0646674
$275$	1.13478e89	1.04536
$276$	−7.72644e88	−0.623445
$277$	−1.55810e89	−1.10175	−0.550875	−	0.834588i	$-0.685706\pi$
$277$	−1.55810e89	−1.10175	−0.550875	+	0.834588i	$0.685706\pi$
$278$	8.79160e87	0.0545046
$279$	1.58159e89	0.860083
$280$	−5.08334e87	−0.0242595
$281$	−4.48983e89	−1.88126	−0.940630	−	0.339432i	$-0.889765\pi$
$281$	−4.48983e89	−1.88126	−0.940630	+	0.339432i	$0.889765\pi$
$282$	−1.19030e86	−0.000438092 0
$283$	−3.25365e88	−0.105236	−0.0526182	−	0.998615i	$-0.516757\pi$
$283$	−3.25365e88	−0.105236	−0.0526182	+	0.998615i	$0.516757\pi$
$284$	1.01801e89	0.289490
$285$	4.91201e89	1.22863
$286$	−2.90443e88	−0.0639295
$287$	1.65302e89	0.320324
$288$	−1.39444e89	−0.237999
$289$	1.17901e90	1.77315
$290$	3.29597e88	0.0436975
$291$	−3.85189e89	−0.450381
$292$	−2.02999e89	−0.209421
$293$	−1.51494e90	−1.37952	−0.689760	−	0.724038i	$-0.742284\pi$
$293$	−1.51494e90	−1.37952	−0.689760	+	0.724038i	$0.742284\pi$
$294$	9.79177e88	0.0787378
$295$	2.66509e89	0.189325
$296$	−3.58789e89	−0.225264
$297$	−1.22166e90	−0.678171
$298$	5.10607e88	0.0250722
$299$	−6.95717e89	−0.302297
$300$	2.87496e90	1.10587
$301$	−5.61209e89	−0.191182
$302$	1.35225e89	0.0408136
$303$	−5.54458e90	−1.48324
$304$	6.48482e90	1.53820
$305$	6.26280e89	0.131772
$306$	7.11075e89	0.132765
$307$	1.83701e90	0.304482	0.152241	−	0.988343i	$-0.451351\pi$
$307$	1.83701e90	0.304482	0.152241	+	0.988343i	$0.451351\pi$
$308$	−3.72909e90	−0.548910
$309$	1.85921e91	2.43133
$310$	−1.78202e89	−0.0207115
$311$	−1.36709e91	−1.41268	−0.706339	−	0.707874i	$-0.749655\pi$
$311$	−1.36709e91	−1.41268	−0.706339	+	0.707874i	$0.749655\pi$
$312$	−1.47441e90	−0.135511
$313$	−1.01164e91	−0.827292	−0.413646	−	0.910438i	$-0.635745\pi$
$313$	−1.01164e91	−0.827292	−0.413646	+	0.910438i	$0.635745\pi$
$314$	−1.14183e90	−0.0831128
$315$	−4.04523e90	−0.262185
$316$	−1.82090e91	−1.05125
$317$	−8.49508e90	−0.437023	−0.218512	−	0.975834i	$-0.570120\pi$
$317$	−8.49508e90	−0.437023	−0.218512	+	0.975834i	$0.570120\pi$
$318$	3.86431e89	0.0177207
$319$	4.84475e91	1.98112
$320$	−1.39281e91	−0.508064
$321$	4.91323e91	1.59931
$322$	3.31303e89	0.00962688
$323$	−9.98220e91	−2.59020
$324$	2.54209e91	0.589247
$325$	2.58872e91	0.536219
$326$	5.49023e88	0.00101659
$327$	9.45096e91	1.56489
$328$	−6.82066e90	−0.101026
$329$	−1.37611e89	−0.00182390
$330$	5.79505e90	0.0687540
$331$	1.05949e92	1.12558	0.562790	−	0.826600i	$-0.309728\pi$
$331$	1.05949e92	1.12558	0.562790	+	0.826600i	$0.309728\pi$
$332$	−1.10097e92	−1.04770
$333$	−2.85518e92	−2.43455
$334$	8.05543e90	0.0615662
$335$	−3.74311e91	−0.256506
$336$	−9.41249e91	−0.578523
$337$	7.23797e91	0.399140	0.199570	−	0.979884i	$-0.436045\pi$
$337$	7.23797e91	0.399140	0.199570	+	0.979884i	$0.436045\pi$
$338$	5.65658e90	0.0279959
$339$	2.99295e92	1.32987
$340$	2.16015e92	0.861994
$341$	−2.61940e92	−0.939003
$342$	−3.84944e91	−0.124006
$343$	2.46077e92	0.712584
$344$	2.31564e91	0.0602960
$345$	1.38812e92	0.325111
$346$	−2.41791e91	−0.0509522
$347$	−6.97644e92	−1.32315	−0.661574	−	0.749880i	$-0.730111\pi$
$347$	−6.97644e92	−1.32315	−0.661574	+	0.749880i	$0.730111\pi$
$348$	1.22742e93	2.09580
$349$	−3.78993e92	−0.582778	−0.291389	−	0.956605i	$-0.594117\pi$
$349$	−3.78993e92	−0.582778	−0.291389	+	0.956605i	$0.594117\pi$
$350$	−1.23275e91	−0.0170763
$351$	−2.78692e92	−0.347868
$352$	2.30945e92	0.259837
$353$	−1.10203e93	−1.11794	−0.558970	−	0.829188i	$-0.688803\pi$
$353$	−1.10203e93	−1.11794	−0.558970	+	0.829188i	$0.688803\pi$
$354$	−3.68106e91	−0.0336786
$355$	−1.82895e92	−0.150962
$356$	−1.55814e93	−1.16060
$357$	1.44888e93	0.974188
$358$	−3.91459e91	−0.0237660
$359$	−1.96885e93	−1.07961	−0.539804	−	0.841791i	$-0.681502\pi$
$359$	−1.96885e93	−1.07961	−0.539804	+	0.841791i	$0.681502\pi$
$360$	1.66913e92	0.0826893
$361$	3.17027e93	1.41933
$362$	1.46366e92	0.0592349
$363$	4.36344e93	1.59675
$364$	−8.50702e92	−0.281564
$365$	3.64706e92	0.109208
$366$	−8.65025e91	−0.0234406
$367$	−1.57037e93	−0.385205	−0.192603	−	0.981277i	$-0.561693\pi$
$367$	−1.57037e93	−0.385205	−0.192603	+	0.981277i	$0.561693\pi$
$368$	1.83260e93	0.407025
$369$	−5.42776e93	−1.09184
$370$	3.21702e92	0.0586261
$371$	4.46752e92	0.0737766
$372$	−6.63626e93	−0.993358
$373$	9.09346e93	1.23412	0.617059	−	0.786917i	$-0.288324\pi$
$373$	9.09346e93	1.23412	0.617059	+	0.786917i	$0.288324\pi$
$374$	−1.17767e93	−0.144947
$375$	−1.22399e94	−1.36659
$376$	5.67805e90	0.000575232 0
$377$	1.10521e94	1.01622
$378$	1.32714e92	0.0110781
$379$	−1.61012e94	−1.22047	−0.610235	−	0.792220i	$-0.708925\pi$
$379$	−1.61012e94	−1.22047	−0.610235	+	0.792220i	$0.708925\pi$
$380$	−1.16941e94	−0.805129
$381$	1.22857e94	0.768491
$382$	−1.91000e93	−0.108573
$383$	3.65366e94	1.88787	0.943937	−	0.330125i	$-0.107091\pi$
$383$	3.65366e94	1.88787	0.943937	+	0.330125i	$0.107091\pi$
$384$	7.79648e93	0.366276
$385$	6.69964e93	0.286243
$386$	2.24839e93	0.0873846
$387$	1.84275e94	0.651652
$388$	9.17025e93	0.295137
$389$	−5.06109e94	−1.48280	−0.741402	−	0.671061i	$-0.765839\pi$
$389$	−5.06109e94	−1.48280	−0.741402	+	0.671061i	$0.765839\pi$
$390$	1.32200e93	0.0352674
$391$	−2.82095e94	−0.685399
$392$	−4.67092e93	−0.103386
$393$	−8.43683e94	−1.70157
$394$	3.02667e90	5.56356e−5 0
$395$	3.27140e94	0.548201
$396$	1.22446e95	1.87098
$397$	−2.77522e94	−0.386762	−0.193381	−	0.981124i	$-0.561945\pi$
$397$	−2.77522e94	−0.386762	−0.193381	+	0.981124i	$0.561945\pi$
$398$	1.63878e93	0.0208348
$399$	−7.84358e94	−0.909921
$400$	−6.81897e94	−0.721987
$401$	6.35711e94	0.614455	0.307228	−	0.951636i	$-0.400599\pi$
$401$	6.35711e94	0.614455	0.307228	+	0.951636i	$0.400599\pi$
$402$	5.17002e93	0.0456291
$403$	−5.97553e94	−0.481662
$404$	1.32001e95	0.971977
$405$	−4.56709e94	−0.307278
$406$	−5.26306e93	−0.0323622
$407$	4.72870e95	2.65794
$408$	−5.97833e94	−0.307244
$409$	1.42308e95	0.668851	0.334426	−	0.942422i	$-0.391458\pi$
$409$	1.42308e95	0.668851	0.334426	+	0.942422i	$0.391458\pi$
$410$	6.11562e93	0.0262924
$411$	−4.11187e95	−1.61738
$412$	−4.42625e95	−1.59326
$413$	−4.25567e94	−0.140214
$414$	−1.08784e94	−0.0328136
$415$	1.97799e95	0.546347
$416$	5.26846e94	0.133284
$417$	−5.88202e95	−1.36320
$418$	6.37537e94	0.135385
$419$	3.45923e95	0.673237	0.336618	−	0.941641i	$-0.390717\pi$
$419$	3.45923e95	0.673237	0.336618	+	0.941641i	$0.390717\pi$
$420$	1.69736e95	0.302813
$421$	−3.52446e94	−0.0576495	−0.0288248	−	0.999584i	$-0.509176\pi$
$421$	−3.52446e94	−0.0576495	−0.0288248	+	0.999584i	$0.509176\pi$
$422$	−2.93348e94	−0.0440026
$423$	4.51850e93	0.00621685
$424$	−1.84337e94	−0.0232680
$425$	1.04966e96	1.21577
$426$	2.52617e94	0.0268542
$427$	−1.00005e95	−0.0975901
$428$	−1.16970e96	−1.04804
$429$	1.94321e96	1.59893
$430$	−2.07628e94	−0.0156923
$431$	−7.25552e95	−0.503788	−0.251894	−	0.967755i	$-0.581053\pi$
$431$	−7.25552e95	−0.503788	−0.251894	+	0.967755i	$0.581053\pi$
$432$	7.34106e95	0.468384
$433$	1.48595e95	0.0871354	0.0435677	−	0.999050i	$-0.486128\pi$
$433$	1.48595e95	0.0871354	0.0435677	+	0.999050i	$0.486128\pi$
$434$	2.84556e94	0.0153389
$435$	−2.20517e96	−1.09291
$436$	−2.25000e96	−1.02548
$437$	1.52713e96	0.640183
$438$	−5.03736e94	−0.0194266
$439$	−1.75652e96	−0.623302	−0.311651	−	0.950197i	$-0.600882\pi$
$439$	−1.75652e96	−0.623302	−0.311651	+	0.950197i	$0.600882\pi$
$440$	−2.76439e95	−0.0902768
$441$	−3.71704e96	−1.11735
$442$	−2.68657e95	−0.0743508
$443$	−7.67761e95	−0.195654	−0.0978272	−	0.995203i	$-0.531189\pi$
$443$	−7.67761e95	−0.195654	−0.0978272	+	0.995203i	$0.531189\pi$
$444$	1.19802e97	2.81180
$445$	2.79934e96	0.605223
$446$	2.60229e95	0.0518362
$447$	−3.41621e96	−0.627077
$448$	2.22407e96	0.376270
$449$	−2.38413e96	−0.371826	−0.185913	−	0.982566i	$-0.559524\pi$
$449$	−2.38413e96	−0.371826	−0.185913	+	0.982566i	$0.559524\pi$
$450$	4.04779e95	0.0582052
$451$	8.98936e96	1.19202
$452$	−7.12535e96	−0.871472
$453$	−9.04725e96	−1.02078
$454$	−1.26841e95	−0.0132045
$455$	1.52836e96	0.146828
$456$	3.23640e96	0.286975
$457$	1.08572e97	0.888744	0.444372	−	0.895842i	$-0.353427\pi$
$457$	1.08572e97	0.888744	0.444372	+	0.895842i	$0.353427\pi$
$458$	−9.29105e95	−0.0702223
$459$	−1.13002e97	−0.788722
$460$	−3.30473e96	−0.213047
$461$	−2.25885e97	−1.34525	−0.672625	−	0.739984i	$-0.734833\pi$
$461$	−2.25885e97	−1.34525	−0.672625	+	0.739984i	$0.734833\pi$
$462$	−9.25362e95	−0.0509190
$463$	1.05828e97	0.538137	0.269068	−	0.963121i	$-0.413284\pi$
$463$	1.05828e97	0.538137	0.269068	+	0.963121i	$0.413284\pi$
$464$	−2.91126e97	−1.36828
$465$	1.19226e97	0.518011
$466$	−4.17709e95	−0.0167798
$467$	2.18220e97	0.810642	0.405321	−	0.914174i	$-0.367160\pi$
$467$	2.18220e97	0.810642	0.405321	+	0.914174i	$0.367160\pi$
$468$	2.79331e97	0.959721
$469$	5.97705e96	0.189967
$470$	−5.09112e93	−0.000149707 0
$471$	7.63939e97	2.07872
$472$	1.75596e96	0.0442213
$473$	−3.05193e97	−0.711447
$474$	−4.51850e96	−0.0975180
$475$	−5.68236e97	−1.13557
$476$	−3.44937e97	−0.638390
$477$	−1.46692e97	−0.251470
$478$	4.50585e96	0.0715580
$479$	−1.96022e97	−0.288442	−0.144221	−	0.989546i	$-0.546068\pi$
$479$	−1.96022e97	−0.288442	−0.144221	+	0.989546i	$0.546068\pi$
$480$	−1.05119e97	−0.143342
$481$	1.07874e98	1.36339
$482$	−2.20753e96	−0.0258636
$483$	−2.21658e97	−0.240776
$484$	−1.03881e98	−1.04636
$485$	−1.64752e97	−0.153906
$486$	9.63075e96	0.0834519
$487$	−4.70183e97	−0.377972	−0.188986	−	0.981980i	$-0.560520\pi$
$487$	−4.70183e97	−0.377972	−0.188986	+	0.981980i	$0.560520\pi$
$488$	4.12639e96	0.0307785
$489$	−3.67324e96	−0.0254258
$490$	4.18810e96	0.0269067
$491$	−8.71377e97	−0.519675	−0.259838	−	0.965652i	$-0.583669\pi$
$491$	−8.71377e97	−0.519675	−0.259838	+	0.965652i	$0.583669\pi$
$492$	2.27746e98	1.26103
$493$	4.48135e98	2.30407
$494$	1.45439e97	0.0694459
$495$	−2.19985e98	−0.975670
$496$	1.57402e98	0.648529
$497$	2.92050e97	0.111802
$498$	−2.73203e97	−0.0971882
$499$	−4.82312e98	−1.59462	−0.797312	−	0.603567i	$-0.793745\pi$
$499$	−4.82312e98	−1.59462	−0.797312	+	0.603567i	$0.793745\pi$
$500$	2.91398e98	0.895533
$501$	−5.38948e98	−1.53982
$502$	−2.64659e97	−0.0703075
$503$	2.59870e98	0.641985	0.320992	−	0.947082i	$-0.395984\pi$
$503$	2.59870e98	0.641985	0.320992	+	0.947082i	$0.395984\pi$
$504$	−2.66530e97	−0.0612394
$505$	−2.37151e98	−0.506861
$506$	1.80167e97	0.0358245
$507$	−3.78453e98	−0.700199
$508$	−2.92488e98	−0.503596
$509$	7.47042e98	1.19714	0.598572	−	0.801069i	$-0.295735\pi$
$509$	7.47042e98	1.19714	0.598572	+	0.801069i	$0.295735\pi$
$510$	5.36036e97	0.0799618
$511$	−5.82368e97	−0.0808788
$512$	−2.31581e98	−0.299467
$513$	6.11742e98	0.736690
$514$	3.57859e96	0.00401383
$515$	7.95215e98	0.830846
$516$	−7.73206e98	−0.752630
$517$	−7.48345e96	−0.00678730
$518$	−5.13699e97	−0.0434182
$519$	1.61770e99	1.27435
$520$	−6.30628e97	−0.0463075
$521$	2.02966e98	0.138946	0.0694729	−	0.997584i	$-0.477868\pi$
$521$	2.02966e98	0.138946	0.0694729	+	0.997584i	$0.477868\pi$
$522$	1.72814e98	0.110308
$523$	−2.22396e99	−1.32378	−0.661890	−	0.749601i	$-0.730245\pi$
$523$	−2.22396e99	−1.32378	−0.661890	+	0.749601i	$0.730245\pi$
$524$	2.00857e99	1.11505
$525$	8.24775e98	0.427091
$526$	1.42302e98	0.0687435
$527$	−2.42292e99	−1.09207
$528$	−5.11863e99	−2.15286
$529$	−2.11604e99	−0.830600
$530$	1.65283e97	0.00605561
$531$	1.39736e99	0.477924
$532$	1.86733e99	0.596275
$533$	2.05071e99	0.611449
$534$	−3.86648e98	−0.107661
$535$	2.10147e99	0.546525
$536$	−2.46623e98	−0.0599128
$537$	2.61906e99	0.594406
$538$	−2.44333e98	−0.0518117
$539$	6.15609e99	1.21987
$540$	−1.32381e99	−0.245163
$541$	−1.61237e99	−0.279102	−0.139551	−	0.990215i	$-0.544566\pi$
$541$	−1.61237e99	−0.279102	−0.139551	+	0.990215i	$0.544566\pi$
$542$	−1.99450e97	−0.00322746
$543$	−9.79262e99	−1.48151
$544$	2.13622e99	0.302194
$545$	4.04233e99	0.534761
$546$	−2.11099e98	−0.0261189
$547$	1.79750e99	0.208033	0.104016	−	0.994576i	$-0.466831\pi$
$547$	1.79750e99	0.208033	0.104016	+	0.994576i	$0.466831\pi$
$548$	9.78918e99	1.05988
$549$	3.28371e99	0.332640
$550$	−6.70388e98	−0.0635460
$551$	−2.42600e100	−2.15207
$552$	9.14599e98	0.0759371
$553$	−5.22383e99	−0.405996
$554$	9.20473e98	0.0669738
$555$	−2.15235e100	−1.46628
$556$	1.40034e100	0.893313
$557$	−8.70004e99	−0.519764	−0.259882	−	0.965640i	$-0.583684\pi$
$557$	−8.70004e99	−0.519764	−0.259882	+	0.965640i	$0.583684\pi$
$558$	−9.34351e98	−0.0522831
$559$	−6.96223e99	−0.364937
$560$	−4.02588e99	−0.197696
$561$	7.87920e100	3.62525
$562$	2.65244e99	0.114359
$563$	−1.34453e100	−0.543267	−0.271634	−	0.962401i	$-0.587564\pi$
$563$	−1.34453e100	−0.543267	−0.271634	+	0.962401i	$0.587564\pi$
$564$	−1.89593e98	−0.00718019
$565$	1.28013e100	0.454451
$566$	1.92215e98	0.00639717
$567$	7.29280e99	0.227569
$568$	−1.20505e99	−0.0352606
$569$	−4.71804e100	−1.29468	−0.647342	−	0.762200i	$-0.724119\pi$
$569$	−4.71804e100	−1.29468	−0.647342	+	0.762200i	$0.724119\pi$
$570$	−2.90185e99	−0.0746867
$571$	−2.57174e100	−0.620882	−0.310441	−	0.950593i	$-0.600477\pi$
$571$	−2.57174e100	−0.620882	−0.310441	+	0.950593i	$0.600477\pi$
$572$	−4.62623e100	−1.04778
$573$	1.27789e101	2.71549
$574$	−9.76552e98	−0.0194720
$575$	−1.60582e100	−0.300484
$576$	−7.30280e100	−1.28253
$577$	5.80535e100	0.956998	0.478499	−	0.878088i	$-0.341181\pi$
$577$	5.80535e100	0.956998	0.478499	+	0.878088i	$0.341181\pi$
$578$	−6.96519e99	−0.107787
$579$	−1.50428e101	−2.18556
$580$	5.24988e100	0.716189
$581$	−3.15849e100	−0.404623
$582$	2.27557e99	0.0273780
$583$	2.42949e100	0.274545
$584$	2.40295e99	0.0255080
$585$	−5.01843e100	−0.500470
$586$	8.94978e99	0.0838589
$587$	1.38113e101	1.21603	0.608013	−	0.793927i	$-0.291967\pi$
$587$	1.38113e101	1.21603	0.608013	+	0.793927i	$0.291967\pi$
$588$	1.55965e101	1.29049
$589$	1.31166e101	1.02003
$590$	−1.57445e99	−0.0115088
$591$	−2.02499e98	−0.00139149
$592$	−2.84152e101	−1.83573
$593$	9.03719e100	0.548956	0.274478	−	0.961593i	$-0.411495\pi$
$593$	9.03719e100	0.548956	0.274478	+	0.961593i	$0.411495\pi$
$594$	7.21716e99	0.0412250
$595$	6.19710e100	0.332904
$596$	8.13303e100	0.410926
$597$	−1.09643e101	−0.521095
$598$	4.11007e99	0.0183762
$599$	−4.41983e101	−1.85920	−0.929601	−	0.368568i	$-0.879848\pi$
$599$	−4.41983e101	−1.85920	−0.929601	+	0.368568i	$0.879848\pi$
$600$	−3.40316e100	−0.134698
$601$	5.61076e100	0.208980	0.104490	−	0.994526i	$-0.466679\pi$
$601$	5.61076e100	0.208980	0.104490	+	0.994526i	$0.466679\pi$
$602$	3.31544e99	0.0116217
$603$	−1.96259e101	−0.647510
$604$	2.15389e101	0.668922
$605$	1.86631e101	0.545649
$606$	3.27555e100	0.0901642
$607$	−3.42040e101	−0.886524	−0.443262	−	0.896392i	$-0.646179\pi$
$607$	−3.42040e101	−0.886524	−0.443262	+	0.896392i	$0.646179\pi$
$608$	−1.15645e101	−0.282259
$609$	3.52125e101	0.809405
$610$	−3.69985e99	−0.00801024
$611$	−1.70717e99	−0.00348155
$612$	1.13261e102	2.17598
$613$	−1.01689e102	−1.84062	−0.920312	−	0.391185i	$-0.872065\pi$
$613$	−1.01689e102	−1.84062	−0.920312	+	0.391185i	$0.872065\pi$
$614$	−1.08525e100	−0.0185090
$615$	−4.09165e101	−0.657593
$616$	4.41422e100	0.0668586
$617$	1.26801e102	1.81015	0.905077	−	0.425247i	$-0.139813\pi$
$617$	1.26801e102	1.81015	0.905077	+	0.425247i	$0.139813\pi$
$618$	−1.09836e101	−0.147797
$619$	8.97168e101	1.13806	0.569030	−	0.822317i	$-0.307319\pi$
$619$	8.97168e101	1.13806	0.569030	+	0.822317i	$0.307319\pi$
$620$	−2.83844e101	−0.339455
$621$	1.72877e101	0.194937
$622$	8.07632e100	0.0858746
$623$	−4.47003e101	−0.448226
$624$	−1.16769e102	−1.10431
$625$	2.94914e101	0.263072
$626$	5.97645e100	0.0502898
$627$	−4.26544e102	−3.38609
$628$	−1.81872e102	−1.36219
$629$	4.37400e102	3.09122
$630$	2.38979e100	0.0159378
$631$	−1.05597e102	−0.664629	−0.332314	−	0.943169i	$-0.607829\pi$
$631$	−1.05597e102	−0.664629	−0.332314	+	0.943169i	$0.607829\pi$
$632$	2.15544e101	0.128045
$633$	1.96265e102	1.10054
$634$	5.01862e100	0.0265660
$635$	5.25480e101	0.262612
$636$	6.15513e101	0.290437
$637$	1.40436e102	0.625735
$638$	−2.86212e101	−0.120430
$639$	−9.58956e101	−0.381081
$640$	3.33468e101	0.125166
$641$	−1.64809e102	−0.584336	−0.292168	−	0.956367i	$-0.594377\pi$
$641$	−1.64809e102	−0.584336	−0.292168	+	0.956367i	$0.594377\pi$
$642$	−2.90258e101	−0.0972198
$643$	1.19000e102	0.376570	0.188285	−	0.982114i	$-0.439707\pi$
$643$	1.19000e102	0.376570	0.188285	+	0.982114i	$0.439707\pi$
$644$	5.27704e101	0.157782
$645$	1.38913e102	0.392477
$646$	5.89715e101	0.157455
$647$	3.27438e102	0.826273	0.413136	−	0.910669i	$-0.364433\pi$
$647$	3.27438e102	0.826273	0.413136	+	0.910669i	$0.364433\pi$
$648$	−3.00913e101	−0.0717717
$649$	−2.31429e102	−0.521778
$650$	−1.52933e101	−0.0325959
$651$	−1.90382e102	−0.383637
$652$	8.74492e100	0.0166617
$653$	−7.85065e102	−1.41441	−0.707204	−	0.707010i	$-0.750044\pi$
$653$	−7.85065e102	−1.41441	−0.707204	+	0.707010i	$0.750044\pi$
$654$	−5.58332e101	−0.0951272
$655$	−3.60857e102	−0.581470
$656$	−5.40179e102	−0.823280
$657$	1.91222e102	0.275679
$658$	8.12959e98	0.000110872 0
$659$	−2.63756e102	−0.340318	−0.170159	−	0.985417i	$-0.554428\pi$
$659$	−2.63756e102	−0.340318	−0.170159	+	0.985417i	$0.554428\pi$
$660$	9.23044e102	1.12686
$661$	4.82101e102	0.556910	0.278455	−	0.960449i	$-0.410178\pi$
$661$	4.82101e102	0.556910	0.278455	+	0.960449i	$0.410178\pi$
$662$	−6.25914e101	−0.0684224
$663$	1.79745e103	1.85957
$664$	1.30325e102	0.127612
$665$	−3.35483e102	−0.310943
$666$	1.68675e102	0.147993
$667$	−6.85582e102	−0.569464
$668$	1.28308e103	1.00905
$669$	−1.74106e103	−1.29646
$670$	2.21130e101	0.0155926
$671$	−5.43842e102	−0.363162
$672$	1.67855e102	0.106159
$673$	1.51214e103	0.905822	0.452911	−	0.891556i	$-0.350386\pi$
$673$	1.51214e103	0.905822	0.452911	+	0.891556i	$0.350386\pi$
$674$	−4.27595e101	−0.0242631
$675$	−6.43264e102	−0.345782
$676$	9.00988e102	0.458844
$677$	−2.33256e103	−1.12550	−0.562751	−	0.826626i	$-0.690257\pi$
$677$	−2.33256e103	−1.12550	−0.562751	+	0.826626i	$0.690257\pi$
$678$	−1.76814e102	−0.0808410
$679$	2.63078e102	0.113982
$680$	−2.55703e102	−0.104993
$681$	8.48628e102	0.330254
$682$	1.54745e102	0.0570806
$683$	−1.30508e103	−0.456334	−0.228167	−	0.973622i	$-0.573273\pi$
$683$	−1.30508e103	−0.456334	−0.228167	+	0.973622i	$0.573273\pi$
$684$	−6.13145e103	−2.03243
$685$	−1.75871e103	−0.552700
$686$	−1.45374e102	−0.0433169
$687$	6.21618e103	1.75632
$688$	1.83393e103	0.491366
$689$	5.54230e102	0.140828
$690$	−8.20058e101	−0.0197630
$691$	6.78656e103	1.55132	0.775660	−	0.631151i	$-0.217417\pi$
$691$	6.78656e103	1.55132	0.775660	+	0.631151i	$0.217417\pi$
$692$	−3.85129e103	−0.835090
$693$	3.51275e103	0.722578
$694$	4.12145e102	0.0804321
$695$	−2.51584e103	−0.465840
$696$	−1.45293e103	−0.255274
$697$	8.31507e103	1.38634
$698$	2.23897e102	0.0354262
$699$	2.79468e103	0.419677
$700$	−1.96355e103	−0.279875
$701$	−7.61065e103	−1.02971	−0.514854	−	0.857278i	$-0.672154\pi$
$701$	−7.61065e103	−1.02971	−0.514854	+	0.857278i	$0.672154\pi$
$702$	1.64642e102	0.0211464
$703$	−2.36788e104	−2.88730
$704$	1.20948e104	1.40022
$705$	3.40622e101	0.00374429
$706$	6.51045e102	0.0679579
$707$	3.78686e103	0.375380
$708$	−5.86325e103	−0.551982
$709$	−1.25155e104	−1.11908	−0.559538	−	0.828805i	$-0.689021\pi$
$709$	−1.25155e104	−1.11908	−0.559538	+	0.828805i	$0.689021\pi$
$710$	1.08048e102	0.00917675
$711$	1.71526e104	1.38385
$712$	1.84441e103	0.141364
$713$	3.70672e103	0.269912
$714$	−8.55951e102	−0.0592194
$715$	8.31143e103	0.546393
$716$	−6.23522e103	−0.389517
$717$	−3.01464e104	−1.78972
$718$	1.16313e103	0.0656277
$719$	2.65219e104	1.42233	0.711164	−	0.703026i	$-0.248168\pi$
$719$	2.65219e104	1.42233	0.711164	+	0.703026i	$0.248168\pi$
$720$	1.32191e104	0.673854
$721$	−1.26981e104	−0.615322
$722$	−1.87289e103	−0.0862789
$723$	1.47694e104	0.646869
$724$	2.33134e104	0.970842
$725$	2.55101e104	1.01012
$726$	−2.57777e103	−0.0970640
$727$	2.80516e103	0.100451	0.0502253	−	0.998738i	$-0.484006\pi$
$727$	2.80516e103	0.100451	0.0502253	+	0.998738i	$0.484006\pi$
$728$	1.00700e103	0.0342952
$729$	−4.61762e104	−1.49577
$730$	−2.15456e102	−0.00663857
$731$	−2.82300e104	−0.827421
$732$	−1.37783e104	−0.384184
$733$	−4.71011e104	−1.24950	−0.624750	−	0.780825i	$-0.714799\pi$
$733$	−4.71011e104	−1.24950	−0.624750	+	0.780825i	$0.714799\pi$
$734$	9.27726e102	0.0234160
$735$	−2.80205e104	−0.672957
$736$	−3.26811e103	−0.0746890
$737$	3.25040e104	0.706925
$738$	3.20654e103	0.0663712
$739$	7.23905e104	1.42613	0.713065	−	0.701098i	$-0.247306\pi$
$739$	7.23905e104	1.42613	0.713065	+	0.701098i	$0.247306\pi$
$740$	5.12412e104	0.960863
$741$	−9.73057e104	−1.73690
$742$	−2.63926e102	−0.00448477
$743$	7.11987e104	1.15181	0.575905	−	0.817517i	$-0.304650\pi$
$743$	7.11987e104	1.15181	0.575905	+	0.817517i	$0.304650\pi$
$744$	7.85551e103	0.120993
$745$	−1.46117e104	−0.214288
$746$	−5.37212e103	−0.0750202
$747$	1.03710e105	1.37917
$748$	−1.87581e105	−2.37564
$749$	−3.35566e104	−0.404754
$750$	7.23096e103	0.0830730
$751$	1.54302e105	1.68855	0.844277	−	0.535907i	$-0.180030\pi$
$751$	1.54302e105	1.68855	0.844277	+	0.535907i	$0.180030\pi$
$752$	4.49687e102	0.00468770
$753$	1.77070e105	1.75845
$754$	−6.52924e103	−0.0617744
$755$	−3.86966e104	−0.348826
$756$	2.11389e104	0.181567
$757$	−1.58740e105	−1.29923	−0.649617	−	0.760262i	$-0.725071\pi$
$757$	−1.58740e105	−1.29923	−0.649617	+	0.760262i	$0.725071\pi$
$758$	9.51207e103	0.0741906
$759$	−1.20540e105	−0.896000
$760$	1.38426e104	0.0980666
$761$	7.55382e104	0.510066	0.255033	−	0.966932i	$-0.417914\pi$
$761$	7.55382e104	0.510066	0.255033	+	0.966932i	$0.417914\pi$
$762$	−7.25799e103	−0.0467154
$763$	−6.45486e104	−0.396042
$764$	−3.04228e105	−1.77948
$765$	−2.03484e105	−1.13472
$766$	−2.15846e104	−0.114761
$767$	−5.27949e104	−0.267646
$768$	3.02952e105	1.46450
$769$	3.16605e105	1.45951	0.729754	−	0.683710i	$-0.239635\pi$
$769$	3.16605e105	1.45951	0.729754	+	0.683710i	$0.239635\pi$
$770$	−3.95793e103	−0.0174003
$771$	−2.39426e104	−0.100389
$772$	3.58127e105	1.43221
$773$	−6.80947e104	−0.259754	−0.129877	−	0.991530i	$-0.541458\pi$
$773$	−6.80947e104	−0.259754	−0.129877	+	0.991530i	$0.541458\pi$
$774$	−1.08863e104	−0.0396129
$775$	−1.37925e105	−0.478773
$776$	−1.08551e104	−0.0359484
$777$	3.43690e105	1.08593
$778$	2.98993e104	0.0901374
$779$	−4.50140e105	−1.29488
$780$	2.10570e105	0.578022
$781$	1.58821e105	0.416049
$782$	1.66652e104	0.0416644
$783$	−2.74632e105	−0.655310
$784$	−3.69925e105	−0.842515
$785$	3.26749e105	0.710350
$786$	4.98420e104	0.103436
$787$	5.43922e105	1.07760	0.538801	−	0.842433i	$-0.318877\pi$
$787$	5.43922e105	1.07760	0.538801	+	0.842433i	$0.318877\pi$
$788$	4.82092e102	0.000911850 0
$789$	−9.52072e105	−1.71933
$790$	−1.93264e104	−0.0333243
$791$	−2.04414e105	−0.336565
$792$	−1.44942e105	−0.227890
$793$	−1.24064e105	−0.186284
$794$	1.63951e104	0.0235107
$795$	−1.10582e105	−0.151456
$796$	2.61028e105	0.341476
$797$	−7.11246e105	−0.888773	−0.444387	−	0.895835i	$-0.646578\pi$
$797$	−7.11246e105	−0.888773	−0.444387	+	0.895835i	$0.646578\pi$
$798$	4.63373e104	0.0553127
$799$	−6.92212e103	−0.00789372
$800$	1.21604e105	0.132484
$801$	1.46775e106	1.52780
$802$	−3.75557e104	−0.0373518
$803$	−3.16699e105	−0.300974
$804$	8.23490e105	0.747846
$805$	−9.48068e104	−0.0822791
$806$	3.53015e104	0.0292795
$807$	1.63471e106	1.29585
$808$	−1.56252e105	−0.118389
$809$	7.46404e105	0.540571	0.270286	−	0.962780i	$-0.412882\pi$
$809$	7.46404e105	0.540571	0.270286	+	0.962780i	$0.412882\pi$
$810$	2.69808e104	0.0186789
$811$	−1.03340e106	−0.683920	−0.341960	−	0.939715i	$-0.611091\pi$
$811$	−1.03340e106	−0.683920	−0.341960	+	0.939715i	$0.611091\pi$
$812$	−8.38309e105	−0.530407
$813$	1.33442e105	0.0807213
$814$	−2.79356e105	−0.161572
$815$	−1.57110e104	−0.00868864
$816$	−4.73468e106	−2.50380
$817$	1.52824e106	0.772837
$818$	−8.40711e104	−0.0406585
$819$	8.01350e105	0.370647
$820$	9.74106e105	0.430924
$821$	−1.85960e106	−0.786855	−0.393428	−	0.919356i	$-0.628711\pi$
$821$	−1.85960e106	−0.786855	−0.393428	+	0.919356i	$0.628711\pi$
$822$	2.42916e105	0.0983183
$823$	−1.97114e106	−0.763172	−0.381586	−	0.924333i	$-0.624622\pi$
$823$	−1.97114e106	−0.763172	−0.381586	+	0.924333i	$0.624622\pi$
$824$	5.23946e105	0.194063
$825$	4.48523e106	1.58934
$826$	2.51411e104	0.00852339
$827$	1.57846e106	0.512014	0.256007	−	0.966675i	$-0.417593\pi$
$827$	1.57846e106	0.512014	0.256007	+	0.966675i	$0.417593\pi$
$828$	−1.73273e106	−0.537805
$829$	−3.37721e106	−1.00304	−0.501519	−	0.865146i	$-0.667225\pi$
$829$	−3.37721e106	−1.00304	−0.501519	+	0.865146i	$0.667225\pi$
$830$	−1.16853e105	−0.0332116
$831$	−6.15843e106	−1.67507
$832$	2.75913e106	0.718241
$833$	5.69432e106	1.41873
$834$	3.47490e105	0.0828670
$835$	−2.30517e106	−0.526195
$836$	1.01548e107	2.21892
$837$	1.48485e106	0.310600
$838$	−2.04360e105	−0.0409251
$839$	4.15571e106	0.796771	0.398385	−	0.917218i	$-0.369571\pi$
$839$	4.15571e106	0.796771	0.398385	+	0.917218i	$0.369571\pi$
$840$	−2.00920e105	−0.0368833
$841$	5.20190e106	0.914341
$842$	2.08213e104	0.00350443
$843$	−1.77462e107	−2.86021
$844$	−4.67250e106	−0.721190
$845$	−1.61871e106	−0.239275
$846$	−2.66938e103	−0.000377913 0
$847$	−2.98016e106	−0.404106
$848$	−1.45990e106	−0.189616
$849$	−1.28601e106	−0.159998
$850$	−6.20102e105	−0.0739048
$851$	−6.69159e106	−0.764013
$852$	4.02373e106	0.440132
$853$	3.24533e106	0.340110	0.170055	−	0.985435i	$-0.445605\pi$
$853$	3.24533e106	0.340110	0.170055	+	0.985435i	$0.445605\pi$
$854$	5.90799e104	0.00593236
$855$	1.10157e107	1.05986
$856$	1.38460e106	0.127654
$857$	1.48340e107	1.31056	0.655282	−	0.755385i	$-0.272550\pi$
$857$	1.48340e107	1.31056	0.655282	+	0.755385i	$0.272550\pi$
$858$	−1.14798e106	−0.0971964
$859$	−1.87004e107	−1.51740	−0.758699	−	0.651441i	$-0.774165\pi$
$859$	−1.87004e107	−1.51740	−0.758699	+	0.651441i	$0.774165\pi$
$860$	−3.30713e106	−0.257192
$861$	6.53362e106	0.487011
$862$	4.28632e105	0.0306245
$863$	−1.06435e107	−0.728939	−0.364469	−	0.931215i	$-0.618750\pi$
$863$	−1.06435e107	−0.728939	−0.364469	+	0.931215i	$0.618750\pi$
$864$	−1.30915e106	−0.0859482
$865$	6.91918e106	0.435479
$866$	−8.77848e104	−0.00529683
$867$	4.66006e107	2.69584
$868$	4.53246e106	0.251399
$869$	−2.84078e107	−1.51083
$870$	1.30274e106	0.0664363
$871$	7.41500e106	0.362617
$872$	2.66339e106	0.124906
$873$	−8.63826e106	−0.388514
$874$	−9.02180e105	−0.0389158
$875$	8.35969e106	0.345857
$876$	−8.02359e106	−0.318397
$877$	−7.50757e106	−0.285768	−0.142884	−	0.989739i	$-0.545638\pi$
$877$	−7.50757e106	−0.285768	−0.142884	+	0.989739i	$0.545638\pi$
$878$	1.03769e106	0.0378896
$879$	−5.98785e107	−2.09738
$880$	−2.18932e107	−0.735686
$881$	−1.46469e107	−0.472199	−0.236099	−	0.971729i	$-0.575869\pi$
$881$	−1.46469e107	−0.472199	−0.236099	+	0.971729i	$0.575869\pi$
$882$	2.19590e106	0.0679219
$883$	6.01925e107	1.78639	0.893196	−	0.449667i	$-0.148457\pi$
$883$	6.01925e107	1.78639	0.893196	+	0.449667i	$0.148457\pi$
$884$	−4.27921e107	−1.21859
$885$	1.05339e107	0.287845
$886$	4.53568e105	0.0118935
$887$	5.72253e107	1.44004	0.720022	−	0.693951i	$-0.244132\pi$
$887$	5.72253e107	1.44004	0.720022	+	0.693951i	$0.244132\pi$
$888$	−1.41812e107	−0.342485
$889$	−8.39095e106	−0.194490
$890$	−1.65376e106	−0.0367906
$891$	3.96592e107	0.846852
$892$	4.14497e107	0.849579
$893$	3.74732e105	0.00737297
$894$	2.01819e106	0.0381190
$895$	1.12021e107	0.203123
$896$	−5.32487e106	−0.0926972
$897$	−2.74984e107	−0.459603
$898$	1.40847e106	0.0226027
$899$	−5.88848e107	−0.907349
$900$	6.44739e107	0.953964
$901$	2.24726e107	0.319299
$902$	−5.31062e106	−0.0724613
$903$	−2.21819e107	−0.290667
$904$	8.43446e106	0.106147
$905$	−4.18846e107	−0.506269
$906$	5.34482e106	0.0620517
$907$	4.68331e107	0.522261	0.261130	−	0.965304i	$-0.415905\pi$
$907$	4.68331e107	0.522261	0.261130	+	0.965304i	$0.415905\pi$
$908$	−2.02034e107	−0.216417
$909$	−1.24343e108	−1.27950
$910$	−9.02906e105	−0.00892548
$911$	−1.35405e108	−1.28592	−0.642959	−	0.765901i	$-0.722293\pi$
$911$	−1.35405e108	−1.28592	−0.642959	+	0.765901i	$0.722293\pi$
$912$	2.56314e108	2.33863
$913$	−1.71763e108	−1.50572
$914$	−6.41408e106	−0.0540254
$915$	2.47539e107	0.200343
$916$	−1.47989e108	−1.15092
$917$	5.76222e107	0.430635
$918$	6.67580e106	0.0479452
$919$	1.02309e108	0.706148	0.353074	−	0.935595i	$-0.385136\pi$
$919$	1.02309e108	0.706148	0.353074	+	0.935595i	$0.385136\pi$
$920$	3.91189e106	0.0259496
$921$	7.26084e107	0.462925
$922$	1.33445e107	0.0817757
$923$	3.62311e107	0.213412
$924$	−1.47393e108	−0.834546
$925$	2.48990e108	1.35522
$926$	−6.25194e106	−0.0327125
$927$	4.16947e108	2.09735
$928$	5.19171e107	0.251078
$929$	4.67277e107	0.217271	0.108635	−	0.994082i	$-0.465352\pi$
$929$	4.67277e107	0.217271	0.108635	+	0.994082i	$0.465352\pi$
$930$	−7.04350e106	−0.0314891
$931$	−3.08265e108	−1.32514
$932$	−6.65333e107	−0.275016
$933$	−5.40346e108	−2.14779
$934$	−1.28917e107	−0.0492777
$935$	3.37006e108	1.23884
$936$	−3.30651e107	−0.116896
$937$	−1.30332e108	−0.443156	−0.221578	−	0.975143i	$-0.571121\pi$
$937$	−1.30332e108	−0.443156	−0.221578	+	0.975143i	$0.571121\pi$
$938$	−3.53105e106	−0.0115478
$939$	−3.99854e108	−1.25779
$940$	−8.10923e105	−0.00245365
$941$	3.96389e108	1.15372	0.576860	−	0.816843i	$-0.304278\pi$
$941$	3.96389e108	1.15372	0.576860	+	0.816843i	$0.304278\pi$
$942$	−4.51310e107	−0.126362
$943$	−1.27209e108	−0.342641
$944$	1.39068e108	0.360370
$945$	−3.79779e107	−0.0946825
$946$	1.80298e107	0.0432478
$947$	7.26911e108	1.67767	0.838835	−	0.544385i	$-0.183237\pi$
$947$	7.26911e108	1.67767	0.838835	+	0.544385i	$0.183237\pi$
$948$	−7.19714e108	−1.59829
$949$	−7.22473e107	−0.154385
$950$	3.35695e107	0.0690293
$951$	−3.35770e108	−0.664437
$952$	4.08311e107	0.0777575
$953$	−9.62132e108	−1.76337	−0.881685	−	0.471838i	$-0.843591\pi$
$953$	−9.62132e108	−1.76337	−0.881685	+	0.471838i	$0.843591\pi$
$954$	8.66610e106	0.0152865
$955$	5.46573e108	0.927952
$956$	7.17698e108	1.17281
$957$	1.91490e109	3.01204
$958$	1.15803e107	0.0175340
$959$	2.80834e108	0.409328
$960$	−5.50513e108	−0.772445
$961$	−4.21922e108	−0.569940
$962$	−6.37283e107	−0.0828786
$963$	1.10184e109	1.37962
$964$	−3.51618e108	−0.423896
$965$	−6.43407e108	−0.746859
$966$	1.30948e107	0.0146364
$967$	−1.54885e108	−0.166703	−0.0833513	−	0.996520i	$-0.526562\pi$
$967$	−1.54885e108	−0.166703	−0.0833513	+	0.996520i	$0.526562\pi$
$968$	1.22966e108	0.127449
$969$	−3.94549e109	−3.93807
$970$	9.73299e106	0.00935573
$971$	−5.52113e108	−0.511124	−0.255562	−	0.966793i	$-0.582260\pi$
$971$	−5.52113e108	−0.511124	−0.255562	+	0.966793i	$0.582260\pi$
$972$	1.53400e109	1.36775
$973$	4.01733e108	0.345000
$974$	2.77769e107	0.0229764
$975$	1.02320e109	0.815250
$976$	3.26800e108	0.250821
$977$	2.30000e108	0.170050	0.0850250	−	0.996379i	$-0.472903\pi$
$977$	2.30000e108	0.170050	0.0850250	+	0.996379i	$0.472903\pi$
$978$	2.17003e106	0.00154560
$979$	−2.43086e109	−1.66799
$980$	6.67087e108	0.440992
$981$	2.11948e109	1.34992
$982$	5.14781e107	0.0315903
$983$	−8.64281e108	−0.511036	−0.255518	−	0.966804i	$-0.582246\pi$
$983$	−8.64281e108	−0.511036	−0.255518	+	0.966804i	$0.582246\pi$
$984$	−2.69588e108	−0.153596
$985$	−8.66122e105	−0.000475507 0
$986$	−2.64743e108	−0.140061
$987$	−5.43910e106	−0.00277301
$988$	2.31657e109	1.13820
$989$	4.31879e108	0.204502
$990$	1.29960e108	0.0593095
$991$	−1.02125e109	−0.449202	−0.224601	−	0.974451i	$-0.572108\pi$
$991$	−1.02125e109	−0.449202	−0.224601	+	0.974451i	$0.572108\pi$
$992$	−2.80699e108	−0.119005
$993$	4.18768e109	1.71130
$994$	−1.72534e107	−0.00679627
$995$	−4.68960e108	−0.178071
$996$	−4.35161e109	−1.59289
$997$	4.58848e109	1.61918	0.809592	−	0.586994i	$-0.199689\pi$
$997$	4.58848e109	1.61918	0.809592	+	0.586994i	$0.199689\pi$
$998$	2.84934e108	0.0969348
$999$	−2.68053e109	−0.879186

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1.74.a.a.1.3	✓	5
3.2	odd	2		9.74.a.a.1.3		5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1.74.a.a.1.3	✓	5	1.1	even	1	trivial
9.74.a.a.1.3		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:	\( N \)	\(=\)	\( 1 \)
Weight:	\( k \)	\(=\)	\( 74 \)
Character orbit:	\([\chi]\)	\(=\)	1.a (trivial)

\(f(q)\)	\(=\)	\(q-5.90767e9 q^{2} +3.95253e17 q^{3} -9.40983e21 q^{4} +1.69056e25 q^{5} -2.33502e27 q^{6} -2.69951e30 q^{7} +1.11387e32 q^{8} +8.86395e34 q^{9} +O(q^{10})\)	\(q-5.90767e9 q^{2} +3.95253e17 q^{3} -9.40983e21 q^{4} +1.69056e25 q^{5} -2.33502e27 q^{6} -2.69951e30 q^{7} +1.11387e32 q^{8} +8.86395e34 q^{9} -9.98727e34 q^{10} -1.46803e38 q^{11} -3.71926e39 q^{12} -3.34896e40 q^{13} +1.59478e40 q^{14} +6.68198e42 q^{15} +8.82153e43 q^{16} -1.35791e45 q^{17} -5.23653e44 q^{18} +7.35113e46 q^{19} -1.59079e47 q^{20} -1.06699e48 q^{21} +8.67264e47 q^{22} +2.07741e49 q^{23} +4.40258e49 q^{24} -7.72992e50 q^{25} +1.97845e50 q^{26} +8.32175e51 q^{27} +2.54020e52 q^{28} -3.30017e53 q^{29} -3.94750e52 q^{30} +1.78429e54 q^{31} -1.57316e54 q^{32} -5.80243e55 q^{33} +8.02211e54 q^{34} -4.56369e55 q^{35} -8.34082e56 q^{36} -3.22112e57 q^{37} -4.34280e56 q^{38} -1.32368e58 q^{39} +1.88306e57 q^{40} -6.12341e58 q^{41} +6.30343e57 q^{42} +2.07892e59 q^{43} +1.38139e60 q^{44} +1.49850e60 q^{45} -1.22727e59 q^{46} +5.09761e58 q^{47} +3.48673e61 q^{48} -4.19344e61 q^{49} +4.56658e60 q^{50} -5.36719e62 q^{51} +3.15131e62 q^{52} -1.65493e62 q^{53} -4.91622e61 q^{54} -2.48179e63 q^{55} -3.00690e62 q^{56} +2.90555e64 q^{57} +1.94963e63 q^{58} +1.57646e64 q^{59} -6.28764e64 q^{60} +3.70457e64 q^{61} -1.05410e64 q^{62} -2.39283e65 q^{63} -8.23876e65 q^{64} -5.66162e65 q^{65} +3.42788e65 q^{66} -2.21412e66 q^{67} +1.27777e67 q^{68} +8.21103e66 q^{69} +2.69608e65 q^{70} -1.08186e67 q^{71} +9.87324e66 q^{72} +2.15731e67 q^{73} +1.90293e67 q^{74} -3.05527e68 q^{75} -6.91729e68 q^{76} +3.96297e68 q^{77} +7.81989e67 q^{78} +1.93510e69 q^{79} +1.49133e69 q^{80} -2.70152e69 q^{81} +3.61751e68 q^{82} +1.17002e70 q^{83} +1.00402e70 q^{84} -2.29564e70 q^{85} -1.22816e69 q^{86} -1.30440e71 q^{87} -1.63519e70 q^{88} +1.65587e71 q^{89} -8.85267e69 q^{90} +9.04056e70 q^{91} -1.95481e71 q^{92} +7.05247e71 q^{93} -3.01150e68 q^{94} +1.24275e72 q^{95} -6.21797e71 q^{96} -9.74539e71 q^{97} +2.47734e71 q^{98} -1.30125e73 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 5 q - 92089333488 q^{2} - 12\!\cdots\!04 q^{3}+ \cdots + 32\!\cdots\!65 q^{9}+O(q^{10}) \) 5 * q - 92089333488 * q^2 - 129195798226305804 * q^3 + 891110479259563516160 * q^4 + 23099529720469471562826750 * q^5 - 3335695451789843173883221440 * q^6 - 4356178487147579439806268090008 * q^7 - 382321348565178801062509850849280 * q^8 + 32335028924861937033188022998788065 * q^9	\( 5 q - 92089333488 q^{2} - 12\!\cdots\!04 q^{3}+ \cdots - 15\!\cdots\!20 q^{99}+O(q^{100}) \) 5 * q - 92089333488 * q^2 - 129195798226305804 * q^3 + 891110479259563516160 * q^4 + 23099529720469471562826750 * q^5 - 3335695451789843173883221440 * q^6 - 4356178487147579439806268090008 * q^7 - 382321348565178801062509850849280 * q^8 + 32335028924861937033188022998788065 * q^9 - 1082726120403847340426026649690244000 * q^10 + 50083756421782317855880849016778496860 * q^11 + 1389386159501111619787899997887234696192 * q^12 + 4753748397471720291047553799357192278886 * q^13 + 263363595637460329420141722180437171694720 * q^14 - 5053973124818591694478703469878924549517000 * q^15 + 57509595349357883169785087518099233197588480 * q^16 + 663279725175909884624200257401822351394256602 * q^17 + 6936746909593304334038759770389897835631806416 * q^18 + 31387402430958534058855312636541530201995765700 * q^19 + 68535205735011202400715856751699460073169856000 * q^20 + 873650260100519441483759434874628458149545804960 * q^21 - 9492394168845783423791120540922405517833204177216 * q^22 - 41173446223173693726617088414497261153026772718024 * q^23 + 16216566841440134675070566439222517257116824780800 * q^24 + 321010940201155914585034686800814006311220324546875 * q^25 + 4496438035379975943261998606627087983483848085006560 * q^26 - 12482045195529499122248281309176768796522105943881080 * q^27 - 37814301174111882879202704910382387341459683517577216 * q^28 - 217397685843681573854388291537651452827057882148450250 * q^29 - 809277931163833776121134244746469476931174350662544000 * q^30 - 3959918978904396097569386510196715694840286709585401440 * q^31 - 9479144378484593489541015426974249650207814007382867968 * q^32 - 73769578315518021607552488579011739564089308117835328528 * q^33 - 324638192385754362369074018224584035205208569018875155680 * q^34 - 1051811671165262926972759981500117019527196204743409914000 * q^35 - 3440544904928519792841567448764696150680442862608580965120 * q^36 - 6710426612911460903226679780416929578822322356442579950178 * q^37 - 20075776649866586500887218371135359952534984707306414947520 * q^38 - 53266590853912928667191550341591883996636524676049287303720 * q^39 - 87443314425210154156114784714128373503740284779633935360000 * q^40 - 89999556000464227434562342749528590851939245788450434103790 * q^41 + 151860645080061390785566939100205618848419219581171296592384 * q^42 + 1171421579861687300375905115748875459141635816468653452284156 * q^43 + 3620387401482413711753562750789250834104238410455247119723520 * q^44 + 8637496301209289669216900677161766462676265859857821184867750 * q^45 + 13122337792181100518478081314861771936057558300377044573644160 * q^46 + 26407117391117866585989236437476333636637017745173062895096432 * q^47 - 305063509192507618357183882504465545852009436962512246145024 * q^48 - 47859785088079990485612756297590896342589260563105328803969315 * q^49 - 198341627273982740927873511630518057650356858808871192258250000 * q^50 - 666572032421535161197734372534298884381369595464382997470670040 * q^51 - 1819820853930882517149424007699825989256997486995920851867734528 * q^52 - 2253672757277210109476755074185818948452790752453662372858468754 * q^53 - 981929879310881011928466994898412465282666955980051795540412800 * q^54 + 5272301841223840031246441919708126997046467528986443289345081000 * q^55 + 17369101267271748189623122493455314696373137673860233497989120000 * q^56 + 39672259194438733138452388186436605652387179030172301666478212240 * q^57 + 63080485469034924979732075223792805715626817023343777138220605920 * q^58 + 49827032054541030737892137385762950528020446432538215007741437900 * q^59 + 91369267546356596727702377377074204109693912478731602288473856000 * q^60 - 200207946356755779993110124671040230418699916707275462827300034090 * q^61 - 456512716932753516995161459627410738703514050956609499700325060096 * q^62 - 1444699606935245693297879065147738830138012519879166909023399465144 * q^63 - 2671988611100492125931167910213768824231319631401339943695669002240 * q^64 - 2221078323698894670419341126197735507928898751783246157619800369500 * q^65 - 797490624045567852983392967901985951789407586519264116965780839680 * q^66 + 1726934463658866670044856129309631728944059099751189118466533017652 * q^67 + 25844159932565717701710366021885253281928511625890180327915132834304 * q^68 + 43307862567803975621848996603714756131647359083362619530437754803680 * q^69 + 60019715162941233136874683443010604187189046779871920798680662752000 * q^70 + 29528228383509762365399718501357560736875772117852859701209862331560 * q^71 + 5937319857025079492793067138582418624443592391466592842045028290560 * q^72 - 237248424072934328617284197336037660641948064767277176027665176375374 * q^73 - 385668396032745357868624366253781435784895053179379214963132226802080 * q^74 - 785444151134296088966742788487546108897483082972592363003091781312500 * q^75 - 402469771116557587325960702574461860644965601604695023105081798528000 * q^76 - 1160921420345569675442649510235573702285949327395662717704239852301856 * q^77 + 339124438335685564147183055565832879915531514801135920231578753382272 * q^78 + 1210019475236668608258558597507004925943189831192425236151129201347600 * q^79 + 7695510793835037324754830224890315360926193938062866122926593916928000 * q^80 + 12895807280425851869767179003361520763349212513521199742652083367867805 * q^81 + 19869905655996015892436375229312420723635630923691072274009372051144864 * q^82 + 10633758535693793129462935403233565634399957806616398467042339222483716 * q^83 - 17104473919241589848125111473450344991721950406193981672669373028884480 * q^84 - 28641392301460491393930553180957463692521548910270676165772874742366500 * q^85 - 130748824105220136322401247193488038601024385677355691179590030869522240 * q^86 - 158256246334086183408933559981662943488738078279070353132629771124728040 * q^87 - 221808067516055560593893382793377773024661552295403957235825845052456960 * q^88 - 44230399340933247556508628049428956972940692248797881370004235332026750 * q^89 + 205005728265438963974181523583877066710560749255482389735945594174668000 * q^90 + 503963419362898329804217905595235878617892804641236823955454638331741360 * q^91 + 1056276182251025158869277711594662138415929570173882076378175681365399552 * q^92 + 2087551224100544830404247844376209582022159740935531745376318713047458432 * q^93 + 1211599009021421323842808603980852406277919665987296133682388929757489920 * q^94 + 1134809355692277446299742482002998127744674957590385906379174039024255000 * q^95 - 1239624362529508037215561089866383709629049658259836228855181445997527040 * q^96 - 4705643796144250410051227741367571092615369303801441364082016351450032918 * q^97 - 7645702282951838206479981702299956043322685777549671658293752892775157616 * q^98 - 15823110517274977002648456256699492623727665140588002701017544901953092820 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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