LMFDB - Embedded newform 1.74.a.a.1.4

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			1.4
Root			$-6.50494e8$ 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)

$f(q)$	$=$	$q+1.28059e10 q^{2} -4.48831e17 q^{3} -9.28074e21 q^{4} +4.05981e25 q^{5} -5.74767e27 q^{6} -7.12492e30 q^{7} -2.39796e32 q^{8} +1.33864e35 q^{9} +O(q^{10})$	\(q+1.28059e10 q^{2} -4.48831e17 q^{3} -9.28074e21 q^{4} +4.05981e25 q^{5} -5.74767e27 q^{6} -7.12492e30 q^{7} -2.39796e32 q^{8} +1.33864e35 q^{9} +5.19894e35 q^{10} +5.42440e37 q^{11} +4.16549e39 q^{12} +7.16246e40 q^{13} -9.12407e40 q^{14} -1.82217e43 q^{15} +8.45834e43 q^{16} +1.30590e44 q^{17} +1.71425e45 q^{18} -2.65578e46 q^{19} -3.76781e47 q^{20} +3.19789e48 q^{21} +6.94640e47 q^{22} -6.34296e49 q^{23} +1.07628e50 q^{24} +5.89418e50 q^{25} +9.17214e50 q^{26} -2.97482e52 q^{27} +6.61246e52 q^{28} +8.00076e52 q^{29} -2.33345e53 q^{30} -3.53071e54 q^{31} +3.34797e54 q^{32} -2.43464e55 q^{33} +1.67231e54 q^{34} -2.89259e56 q^{35} -1.24236e57 q^{36} +1.61097e56 q^{37} -3.40096e56 q^{38} -3.21474e58 q^{39} -9.73526e57 q^{40} +6.62324e58 q^{41} +4.09517e58 q^{42} +5.13946e57 q^{43} -5.03424e59 q^{44} +5.43465e60 q^{45} -8.12270e59 q^{46} +1.87105e61 q^{47} -3.79637e61 q^{48} +1.54278e60 q^{49} +7.54801e60 q^{50} -5.86128e61 q^{51} -6.64729e62 q^{52} -2.36299e62 q^{53} -3.80951e62 q^{54} +2.20220e63 q^{55} +1.70853e63 q^{56} +1.19200e64 q^{57} +1.02457e63 q^{58} -2.19113e64 q^{59} +1.69111e65 q^{60} -1.30217e65 q^{61} -4.52138e64 q^{62} -9.53773e65 q^{63} -7.55994e65 q^{64} +2.90783e66 q^{65} -3.11776e65 q^{66} -5.38484e66 q^{67} -1.21197e66 q^{68} +2.84692e67 q^{69} -3.70420e66 q^{70} +3.88431e67 q^{71} -3.21001e67 q^{72} -9.28505e67 q^{73} +2.06298e66 q^{74} -2.64549e68 q^{75} +2.46476e68 q^{76} -3.86484e68 q^{77} -4.11674e68 q^{78} -4.44441e68 q^{79} +3.43393e69 q^{80} +4.30467e69 q^{81} +8.48163e68 q^{82} +9.20761e69 q^{83} -2.96788e70 q^{84} +5.30170e69 q^{85} +6.58152e67 q^{86} -3.59099e70 q^{87} -1.30075e70 q^{88} -3.27546e70 q^{89} +6.95953e70 q^{90} -5.10320e71 q^{91} +5.88674e71 q^{92} +1.58469e72 q^{93} +2.39603e71 q^{94} -1.07820e72 q^{95} -1.50267e72 q^{96} -2.09156e72 q^{97} +1.97567e70 q^{98} +7.26133e72 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	1.28059e10	0.131769	0.0658846	−	0.997827i	$-0.479013\pi$
$2$	1.28059e10	0.131769	0.0658846	+	0.997827i	$0.479013\pi$
$3$	−4.48831e17	−1.72646	−0.863232	−	0.504808i	$-0.831563\pi$
$3$	−4.48831e17	−1.72646	−0.863232	+	0.504808i	$0.831563\pi$
$4$	−9.28074e21	−0.982637
$5$	4.05981e25	1.24767	0.623837	−	0.781555i	$-0.285573\pi$
$5$	4.05981e25	1.24767	0.623837	+	0.781555i	$0.285573\pi$
$6$	−5.74767e27	−0.227495
$7$	−7.12492e30	−1.01555	−0.507775	−	0.861489i	$-0.669532\pi$
$7$	−7.12492e30	−1.01555	−0.507775	+	0.861489i	$0.669532\pi$
$8$	−2.39796e32	−0.261250
$9$	1.33864e35	1.98068
$10$	5.19894e35	0.164405
$11$	5.42440e37	0.529076	0.264538	−	0.964375i	$-0.414780\pi$
$11$	5.42440e37	0.529076	0.264538	+	0.964375i	$0.414780\pi$
$12$	4.16549e39	1.69649
$13$	7.16246e40	1.57083	0.785416	−	0.618968i	$-0.212449\pi$
$13$	7.16246e40	1.57083	0.785416	+	0.618968i	$0.212449\pi$
$14$	−9.12407e40	−0.133818
$15$	−1.82217e43	−2.15406
$16$	8.45834e43	0.948212
$17$	1.30590e44	0.160149	0.0800744	−	0.996789i	$-0.474484\pi$
$17$	1.30590e44	0.160149	0.0800744	+	0.996789i	$0.474484\pi$
$18$	1.71425e45	0.260992
$19$	−2.65578e46	−0.561935	−0.280968	−	0.959717i	$-0.590655\pi$
$19$	−2.65578e46	−0.561935	−0.280968	+	0.959717i	$0.590655\pi$
$20$	−3.76781e47	−1.22601
$21$	3.19789e48	1.75331
$22$	6.94640e47	0.0697159
$23$	−6.34296e49	−1.25668	−0.628342	−	0.777937i	$-0.716266\pi$
$23$	−6.34296e49	−1.25668	−0.628342	+	0.777937i	$0.716266\pi$
$24$	1.07628e50	0.451039
$25$	5.89418e50	0.556690
$26$	9.17214e50	0.206987
$27$	−2.97482e52	−1.69310
$28$	6.61246e52	0.997918
$29$	8.00076e52	0.335432	0.167716	−	0.985835i	$-0.446361\pi$
$29$	8.00076e52	0.335432	0.167716	+	0.985835i	$0.446361\pi$
$30$	−2.33345e53	−0.283839
$31$	−3.53071e54	−1.29766	−0.648829	−	0.760934i	$-0.724741\pi$
$31$	−3.53071e54	−1.29766	−0.648829	+	0.760934i	$0.724741\pi$
$32$	3.34797e54	0.386195
$33$	−2.43464e55	−0.913431
$34$	1.67231e54	0.0211027
$35$	−2.89259e56	−1.26708
$36$	−1.24236e57	−1.94629
$37$	1.61097e56	0.0928376	0.0464188	−	0.998922i	$-0.485219\pi$
$37$	1.61097e56	0.0928376	0.0464188	+	0.998922i	$0.485219\pi$
$38$	−3.40096e56	−0.0740457
$39$	−3.21474e58	−2.71198
$40$	−9.73526e57	−0.325955
$41$	6.62324e58	0.900450	0.450225	−	0.892915i	$-0.351344\pi$
$41$	6.62324e58	0.900450	0.450225	+	0.892915i	$0.351344\pi$
$42$	4.09517e58	0.231032
$43$	5.13946e57	0.0122834	0.00614171	−	0.999981i	$-0.498045\pi$
$43$	5.13946e57	0.0122834	0.00614171	+	0.999981i	$0.498045\pi$
$44$	−5.03424e59	−0.519890
$45$	5.43465e60	2.47124
$46$	−8.12270e59	−0.165592
$47$	1.87105e61	1.73985	0.869927	−	0.493181i	$-0.164166\pi$
$47$	1.87105e61	1.73985	0.869927	+	0.493181i	$0.164166\pi$
$48$	−3.79637e61	−1.63705
$49$	1.54278e60	0.0313436
$50$	7.54801e60	0.0733545
$51$	−5.86128e61	−0.276491
$52$	−6.64729e62	−1.54356
$53$	−2.36299e62	−0.273774	−0.136887	−	0.990587i	$-0.543710\pi$
$53$	−2.36299e62	−0.273774	−0.136887	+	0.990587i	$0.543710\pi$
$54$	−3.80951e62	−0.223099
$55$	2.20220e63	0.660115
$56$	1.70853e63	0.265313
$57$	1.19200e64	0.970160
$58$	1.02457e63	0.0441996
$59$	−2.19113e64	−0.506489	−0.253244	−	0.967402i	$-0.581498\pi$
$59$	−2.19113e64	−0.506489	−0.253244	+	0.967402i	$0.581498\pi$
$60$	1.69111e65	2.11666
$61$	−1.30217e65	−0.891513	−0.445756	−	0.895154i	$-0.647065\pi$
$61$	−1.30217e65	−0.891513	−0.445756	+	0.895154i	$0.647065\pi$
$62$	−4.52138e64	−0.170991
$63$	−9.53773e65	−2.01148
$64$	−7.55994e65	−0.897324
$65$	2.90783e66	1.95989
$66$	−3.11776e65	−0.120362
$67$	−5.38484e66	−1.20072	−0.600361	−	0.799729i	$-0.704977\pi$
$67$	−5.38484e66	−1.20072	−0.600361	+	0.799729i	$0.704977\pi$
$68$	−1.21197e66	−0.157368
$69$	2.84692e67	2.16962
$70$	−3.70420e66	−0.166962
$71$	3.88431e67	1.04324	0.521620	−	0.853178i	$-0.325328\pi$
$71$	3.88431e67	1.04324	0.521620	+	0.853178i	$0.325328\pi$
$72$	−3.21001e67	−0.517452
$73$	−9.28505e67	−0.904690	−0.452345	−	0.891843i	$-0.649412\pi$
$73$	−9.28505e67	−0.904690	−0.452345	+	0.891843i	$0.649412\pi$
$74$	2.06298e66	0.0122331
$75$	−2.64549e68	−0.961105
$76$	2.46476e68	0.552178
$77$	−3.86484e68	−0.537304
$78$	−4.11674e68	−0.357356
$79$	−4.44441e68	−0.242340	−0.121170	−	0.992632i	$-0.538665\pi$
$79$	−4.44441e68	−0.242340	−0.121170	+	0.992632i	$0.538665\pi$
$80$	3.43393e69	1.18306
$81$	4.30467e69	0.942402
$82$	8.48163e68	0.118652
$83$	9.20761e69	0.827555	0.413777	−	0.910378i	$-0.364209\pi$
$83$	9.20761e69	0.827555	0.413777	+	0.910378i	$0.364209\pi$
$84$	−2.96788e70	−1.72287
$85$	5.30170e69	0.199813
$86$	6.58152e67	0.00161858
$87$	−3.59099e70	−0.579111
$88$	−1.30075e70	−0.138221
$89$	−3.27546e70	−0.230429	−0.115214	−	0.993341i	$-0.536755\pi$
$89$	−3.27546e70	−0.230429	−0.115214	+	0.993341i	$0.536755\pi$
$90$	6.95953e70	0.325633
$91$	−5.10320e71	−1.59526
$92$	5.88674e71	1.23486
$93$	1.58469e72	2.24036
$94$	2.39603e71	0.229259
$95$	−1.07820e72	−0.701112
$96$	−1.50267e72	−0.666752
$97$	−2.09156e72	−0.635773	−0.317886	−	0.948129i	$-0.602973\pi$
$97$	−2.09156e72	−0.635773	−0.317886	+	0.948129i	$0.602973\pi$
$98$	1.97567e70	0.00413011
$99$	7.26133e72	1.04793
$100$	−5.47024e72	−0.547024
$101$	−2.75339e73	−1.91486	−0.957430	−	0.288664i	$-0.906789\pi$
$101$	−2.75339e73	−1.91486	−0.957430	+	0.288664i	$0.906789\pi$
$102$	−7.50587e71	−0.0364330
$103$	4.01406e73	1.36466	0.682332	−	0.731043i	$-0.260966\pi$
$103$	4.01406e73	1.36466	0.682332	+	0.731043i	$0.260966\pi$
$104$	−1.71753e73	−0.410380
$105$	1.29828e74	2.18756
$106$	−3.02601e72	−0.0360750
$107$	−1.95235e74	−1.65215	−0.826077	−	0.563557i	$-0.809432\pi$
$107$	−1.95235e74	−1.65215	−0.826077	+	0.563557i	$0.809432\pi$
$108$	2.76085e74	1.66370
$109$	−2.72452e74	−1.17280	−0.586398	−	0.810023i	$-0.699454\pi$
$109$	−2.72452e74	−1.17280	−0.586398	+	0.810023i	$0.699454\pi$
$110$	2.82011e73	0.0869827
$111$	−7.23053e73	−0.160281
$112$	−6.02650e74	−0.962958
$113$	4.60081e74	0.531461	0.265730	−	0.964047i	$-0.414387\pi$
$113$	4.60081e74	0.531461	0.265730	+	0.964047i	$0.414387\pi$
$114$	1.52646e74	0.127837
$115$	−2.57512e75	−1.56793
$116$	−7.42530e74	−0.329608
$117$	9.58798e75	3.11131
$118$	−2.80593e74	−0.0667396
$119$	−9.30442e74	−0.162639
$120$	4.36949e75	0.562750
$121$	−7.56913e75	−0.720078
$122$	−1.66754e75	−0.117474
$123$	−2.97272e76	−1.55459
$124$	3.27676e76	1.27513
$125$	−1.90557e76	−0.553106
$126$	−1.22139e76	−0.265051
$127$	5.34262e75	0.0868798	0.0434399	−	0.999056i	$-0.486168\pi$
$127$	5.34262e75	0.0868798	0.0434399	+	0.999056i	$0.486168\pi$
$128$	−4.13018e76	−0.504435
$129$	−2.30675e75	−0.0212069
$130$	3.72372e76	0.258252
$131$	2.08365e77	1.09250	0.546252	−	0.837621i	$-0.316054\pi$
$131$	2.08365e77	1.09250	0.546252	+	0.837621i	$0.316054\pi$
$132$	2.25953e77	0.897571
$133$	1.89222e77	0.570674
$134$	−6.89575e76	−0.158218
$135$	−1.20772e78	−2.11244
$136$	−3.13149e76	−0.0418389
$137$	1.66251e76	0.0170006	0.00850030	−	0.999964i	$-0.497294\pi$
$137$	1.66251e76	0.0170006	0.00850030	+	0.999964i	$0.497294\pi$
$138$	3.64572e77	0.285889
$139$	−9.14130e76	−0.0550767	−0.0275383	−	0.999621i	$-0.508767\pi$
$139$	−9.14130e76	−0.0550767	−0.0275383	+	0.999621i	$0.508767\pi$
$140$	2.68454e78	1.24508
$141$	−8.39784e78	−3.00379
$142$	4.97419e77	0.137467
$143$	3.88520e78	0.831090
$144$	1.13227e79	1.87810
$145$	3.24816e78	0.418510
$146$	−1.18903e78	−0.119210
$147$	−6.92450e77	−0.0541135
$148$	−1.49510e78	−0.0912257
$149$	−1.98294e79	−0.946260	−0.473130	−	0.880993i	$-0.656876\pi$
$149$	−1.98294e79	−0.946260	−0.473130	+	0.880993i	$0.656876\pi$
$150$	−3.38778e78	−0.126644
$151$	−2.17790e79	−0.638821	−0.319410	−	0.947617i	$-0.603485\pi$
$151$	−2.17790e79	−0.638821	−0.319410	+	0.947617i	$0.603485\pi$
$152$	6.36845e78	0.146806
$153$	1.74813e79	0.317203
$154$	−4.94926e78	−0.0708001
$155$	−1.43340e80	−1.61905
$156$	2.98351e80	2.66490
$157$	−1.69128e80	−1.19641	−0.598204	−	0.801344i	$-0.704119\pi$
$157$	−1.69128e80	−1.19641	−0.598204	+	0.801344i	$0.704119\pi$
$158$	−5.69145e78	−0.0319330
$159$	1.06058e80	0.472661
$160$	1.35921e80	0.481846
$161$	4.51931e80	1.27623
$162$	5.51249e79	0.124180
$163$	−4.96403e80	−0.893279	−0.446640	−	0.894714i	$-0.647379\pi$
$163$	−4.96403e80	−0.893279	−0.446640	+	0.894714i	$0.647379\pi$
$164$	−6.14686e80	−0.884816
$165$	−9.88418e80	−1.13966
$166$	1.17911e80	0.109046
$167$	1.76051e80	0.130764	0.0653818	−	0.997860i	$-0.479173\pi$
$167$	1.76051e80	0.130764	0.0653818	+	0.997860i	$0.479173\pi$
$168$	−7.66840e80	−0.458053
$169$	3.05103e81	1.46751
$170$	6.78928e79	0.0263292
$171$	−3.55515e81	−1.11301
$172$	−4.76981e79	−0.0120701
$173$	8.57658e81	1.75643	0.878216	−	0.478265i	$-0.158734\pi$
$173$	8.57658e81	1.75643	0.878216	+	0.478265i	$0.158734\pi$
$174$	−4.59857e80	−0.0763090
$175$	−4.19956e81	−0.565347
$176$	4.58814e81	0.501677
$177$	9.83449e81	0.874435
$178$	−4.19450e80	−0.0303634
$179$	−1.04344e82	−0.615646	−0.307823	−	0.951444i	$-0.599600\pi$
$179$	−1.04344e82	−0.615646	−0.307823	+	0.951444i	$0.599600\pi$
$180$	−5.04376e82	−2.42833
$181$	−5.37748e81	−0.211500	−0.105750	−	0.994393i	$-0.533724\pi$
$181$	−5.37748e81	−0.211500	−0.105750	+	0.994393i	$0.533724\pi$
$182$	−6.53508e81	−0.210206
$183$	5.84453e82	1.53916
$184$	1.52101e82	0.328309
$185$	6.54023e81	0.115831
$186$	2.02934e82	0.295210
$187$	7.08371e81	0.0847309
$188$	−1.73647e83	−1.70964
$189$	2.11954e83	1.71943
$190$	−1.38073e82	−0.0923849
$191$	2.08649e82	0.115265	0.0576325	−	0.998338i	$-0.481645\pi$
$191$	2.08649e82	0.115265	0.0576325	+	0.998338i	$0.481645\pi$
$192$	3.39314e83	1.54920
$193$	−1.09262e83	−0.412693	−0.206347	−	0.978479i	$-0.566157\pi$
$193$	−1.09262e83	−0.412693	−0.206347	+	0.978479i	$0.566157\pi$
$194$	−2.67842e82	−0.0837752
$195$	−1.30512e84	−3.38367
$196$	−1.43182e82	−0.0307993
$197$	7.56333e83	1.35113	0.675563	−	0.737302i	$-0.263901\pi$
$197$	7.56333e83	1.35113	0.675563	+	0.737302i	$0.263901\pi$
$198$	9.29876e82	0.138085
$199$	−7.27551e83	−0.898930	−0.449465	−	0.893298i	$-0.648385\pi$
$199$	−7.27551e83	−0.898930	−0.449465	+	0.893298i	$0.648385\pi$
$200$	−1.41340e83	−0.145435
$201$	2.41689e84	2.07300
$202$	−3.52595e83	−0.252320
$203$	−5.70048e83	−0.340648
$204$	5.43970e83	0.271690
$205$	2.68891e84	1.12347
$206$	5.14035e83	0.179820
$207$	−8.49097e84	−2.48908
$208$	6.05825e84	1.48948
$209$	−1.44060e84	−0.297307
$210$	1.66256e84	0.288253
$211$	−3.42639e84	−0.499491	−0.249745	−	0.968312i	$-0.580347\pi$
$211$	−3.42639e84	−0.499491	−0.249745	+	0.968312i	$0.580347\pi$
$212$	2.19303e84	0.269021
$213$	−1.74340e85	−1.80112
$214$	−2.50015e84	−0.217703
$215$	2.08653e83	0.0153257
$216$	7.13349e84	0.442323
$217$	2.51560e85	1.31784
$218$	−3.48898e84	−0.154538
$219$	4.16742e85	1.56191
$220$	−2.04381e85	−0.648653
$221$	9.35344e84	0.251567
$222$	−9.25931e83	−0.0211201
$223$	−7.17475e85	−1.38893	−0.694463	−	0.719528i	$-0.744358\pi$
$223$	−7.17475e85	−1.38893	−0.694463	+	0.719528i	$0.744358\pi$
$224$	−2.38540e85	−0.392201
$225$	7.89021e85	1.10262
$226$	5.89173e84	0.0700301
$227$	5.26645e85	0.532813	0.266406	−	0.963861i	$-0.414164\pi$
$227$	5.26645e85	0.532813	0.266406	+	0.963861i	$0.414164\pi$
$228$	−1.10626e86	−0.953315
$229$	−1.96927e86	−1.44648	−0.723238	−	0.690599i	$-0.757347\pi$
$229$	−1.96927e86	−1.44648	−0.723238	+	0.690599i	$0.757347\pi$
$230$	−3.29767e85	−0.206605
$231$	1.73466e86	0.927636
$232$	−1.91855e85	−0.0876317
$233$	−2.47311e86	−0.965499	−0.482750	−	0.875758i	$-0.660362\pi$
$233$	−2.47311e86	−0.965499	−0.482750	+	0.875758i	$0.660362\pi$
$234$	1.22782e86	0.409975
$235$	7.59610e86	2.17077
$236$	2.03353e86	0.497695
$237$	1.99479e86	0.418392
$238$	−1.19151e85	−0.0214308
$239$	−9.15532e85	−0.141303	−0.0706513	−	0.997501i	$-0.522508\pi$
$239$	−9.15532e85	−0.141303	−0.0706513	+	0.997501i	$0.522508\pi$
$240$	−1.54125e87	−2.04251
$241$	−1.90452e86	−0.216852	−0.108426	−	0.994104i	$-0.534581\pi$
$241$	−1.90452e86	−0.216852	−0.108426	+	0.994104i	$0.534581\pi$
$242$	−9.69291e85	−0.0948841
$243$	7.84674e85	0.0660786
$244$	1.20851e87	0.876033
$245$	6.26342e85	0.0391065
$246$	−3.80682e86	−0.204848
$247$	−1.90219e87	−0.882706
$248$	8.46649e86	0.339014
$249$	−4.13267e87	−1.42874
$250$	−2.44024e86	−0.0728823
$251$	6.30464e87	1.62768	0.813841	−	0.581087i	$-0.197373\pi$
$251$	6.30464e87	1.62768	0.813841	+	0.581087i	$0.197373\pi$
$252$	8.85173e87	1.97655
$253$	−3.44067e87	−0.664882
$254$	6.84168e85	0.0114481
$255$	−2.37957e87	−0.344971
$256$	6.61125e87	0.830855
$257$	−6.84443e87	−0.746068	−0.373034	−	0.927818i	$-0.621683\pi$
$257$	−6.84443e87	−0.746068	−0.373034	+	0.927818i	$0.621683\pi$
$258$	−2.95399e85	−0.00279441
$259$	−1.14780e87	−0.0942814
$260$	−2.69868e88	−1.92586
$261$	1.07102e88	0.664382
$262$	2.66829e87	0.143958
$263$	−7.68237e87	−0.360670	−0.180335	−	0.983605i	$-0.557718\pi$
$263$	−7.68237e87	−0.360670	−0.180335	+	0.983605i	$0.557718\pi$
$264$	5.83816e87	0.238634
$265$	−9.59330e87	−0.341581
$266$	2.42316e87	0.0751972
$267$	1.47013e88	0.397827
$268$	4.99753e88	1.17987
$269$	−6.48183e87	−0.133579	−0.0667897	−	0.997767i	$-0.521276\pi$
$269$	−6.48183e87	−0.133579	−0.0667897	+	0.997767i	$0.521276\pi$
$270$	−1.54659e88	−0.278354
$271$	−7.02783e88	−1.10520	−0.552602	−	0.833445i	$-0.686365\pi$
$271$	−7.02783e88	−1.10520	−0.552602	+	0.833445i	$0.686365\pi$
$272$	1.10457e88	0.151855
$273$	2.29047e89	2.75416
$274$	2.12899e86	0.00224016
$275$	3.19724e88	0.294531
$276$	−2.64215e89	−2.13195
$277$	−2.35295e88	−0.166380	−0.0831901	−	0.996534i	$-0.526511\pi$
$277$	−2.35295e88	−0.166380	−0.0831901	+	0.996534i	$0.526511\pi$
$278$	−1.17062e87	−0.00725740
$279$	−4.72637e89	−2.57024
$280$	6.93630e88	0.331024
$281$	3.29283e89	1.37971	0.689856	−	0.723947i	$-0.257674\pi$
$281$	3.29283e89	1.37971	0.689856	+	0.723947i	$0.257674\pi$
$282$	−1.07542e89	−0.395807
$283$	5.00752e89	1.61964	0.809819	−	0.586680i	$-0.199565\pi$
$283$	5.00752e89	1.61964	0.809819	+	0.586680i	$0.199565\pi$
$284$	−3.60493e89	−1.02513
$285$	4.83929e89	1.21044
$286$	4.97533e88	0.109512
$287$	−4.71901e89	−0.914453
$288$	4.48174e89	0.764928
$289$	−6.47869e89	−0.974352
$290$	4.15955e88	0.0551467
$291$	9.38757e89	1.09764
$292$	8.61722e89	0.888982
$293$	−6.16045e89	−0.560976	−0.280488	−	0.959858i	$-0.590496\pi$
$293$	−6.16045e89	−0.560976	−0.280488	+	0.959858i	$0.590496\pi$
$294$	−8.86741e87	−0.00713049
$295$	−8.89559e89	−0.631933
$296$	−3.86303e88	−0.0242539
$297$	−1.61366e90	−0.895780
$298$	−2.53932e89	−0.124688
$299$	−4.54312e90	−1.97404
$300$	2.45522e90	0.944417
$301$	−3.66183e88	−0.0124744
$302$	−2.78898e89	−0.0841768
$303$	1.23581e91	3.30594
$304$	−2.24635e90	−0.532834
$305$	−5.28656e90	−1.11232
$306$	2.23863e89	0.0417975
$307$	9.29015e90	1.53983	0.769914	−	0.638148i	$-0.220299\pi$
$307$	9.29015e90	1.53983	0.769914	+	0.638148i	$0.220299\pi$
$308$	3.58686e90	0.527975
$309$	−1.80164e91	−2.35604
$310$	−1.83560e90	−0.213341
$311$	2.50281e90	0.258627	0.129314	−	0.991604i	$-0.458723\pi$
$311$	2.50281e90	0.258627	0.129314	+	0.991604i	$0.458723\pi$
$312$	7.70880e90	0.708507
$313$	1.82125e91	1.48937	0.744684	−	0.667417i	$-0.232600\pi$
$313$	1.82125e91	1.48937	0.744684	+	0.667417i	$0.232600\pi$
$314$	−2.16583e90	−0.157650
$315$	−3.87214e91	−2.50967
$316$	4.12475e90	0.238133
$317$	−2.15612e91	−1.10920	−0.554601	−	0.832117i	$-0.687129\pi$
$317$	−2.15612e91	−1.10920	−0.554601	+	0.832117i	$0.687129\pi$
$318$	1.35817e90	0.0622821
$319$	4.33993e90	0.177469
$320$	−3.06919e91	−1.11957
$321$	8.76277e91	2.85238
$322$	5.78736e90	0.168167
$323$	−3.46818e90	−0.0899932
$324$	−3.99505e91	−0.926039
$325$	4.22168e91	0.874466
$326$	−6.35687e90	−0.117707
$327$	1.22285e92	2.02479
$328$	−1.58822e91	−0.235243
$329$	−1.33311e92	−1.76691
$330$	−1.26575e91	−0.150173
$331$	2.31408e91	0.245842	0.122921	−	0.992416i	$-0.460774\pi$
$331$	2.31408e91	0.245842	0.122921	+	0.992416i	$0.460774\pi$
$332$	−8.54535e91	−0.813186
$333$	2.15651e91	0.183881
$334$	2.25448e90	0.0172306
$335$	−2.18615e92	−1.49811
$336$	2.70488e92	1.66251
$337$	2.57115e91	0.141787	0.0708935	−	0.997484i	$-0.477415\pi$
$337$	2.57115e91	0.141787	0.0708935	+	0.997484i	$0.477415\pi$
$338$	3.90710e91	0.193373
$339$	−2.06499e92	−0.917548
$340$	−4.92037e91	−0.196344
$341$	−1.91520e92	−0.686560
$342$	−4.55267e91	−0.146661
$343$	3.39709e92	0.983720
$344$	−1.23242e90	−0.00320905
$345$	1.15580e93	2.70698
$346$	1.09830e92	0.231443
$347$	−5.43093e92	−1.03003	−0.515013	−	0.857182i	$-0.672213\pi$
$347$	−5.43093e92	−1.03003	−0.515013	+	0.857182i	$0.672213\pi$
$348$	3.33271e92	0.569056
$349$	−1.29977e90	−0.00199866	−0.000999328	−	1.00000i	$-0.500318\pi$
$349$	−1.29977e90	−0.00199866	−0.000999328		1.00000i	$0.500318\pi$
$350$	−5.37790e91	−0.0744953
$351$	−2.13070e93	−2.65958
$352$	1.81607e92	0.204327
$353$	−1.12268e93	−1.13888	−0.569442	−	0.822032i	$-0.692841\pi$
$353$	−1.12268e93	−1.13888	−0.569442	+	0.822032i	$0.692841\pi$
$354$	1.25939e92	0.115224
$355$	1.57696e93	1.30162
$356$	3.03987e92	0.226428
$357$	4.17612e92	0.280791
$358$	−1.33621e92	−0.0811231
$359$	8.79228e91	0.0482119	0.0241059	−	0.999709i	$-0.492326\pi$
$359$	8.79228e91	0.0482119	0.0241059	+	0.999709i	$0.492326\pi$
$360$	−1.30320e93	−0.645612
$361$	−1.52832e93	−0.684229
$362$	−6.88633e91	−0.0278692
$363$	3.39726e93	1.24319
$364$	4.73614e93	1.56756
$365$	−3.76956e93	−1.12876
$366$	7.48442e92	0.202814
$367$	3.02870e93	0.742925	0.371462	−	0.928448i	$-0.378856\pi$
$367$	3.02870e93	0.742925	0.371462	+	0.928448i	$0.378856\pi$
$368$	−5.36509e93	−1.19160
$369$	8.86616e93	1.78350
$370$	8.37533e91	0.0152630
$371$	1.68361e93	0.278032
$372$	−1.47071e94	−2.20146
$373$	−1.41066e94	−1.91448	−0.957239	−	0.289297i	$-0.906579\pi$
$373$	−1.41066e94	−1.91448	−0.957239	+	0.289297i	$0.906579\pi$
$374$	9.07129e91	0.0111649
$375$	8.55278e93	0.954918
$376$	−4.48669e93	−0.454537
$377$	5.73051e93	0.526907
$378$	2.71425e93	0.226568
$379$	3.09449e93	0.234562	0.117281	−	0.993099i	$-0.462582\pi$
$379$	3.09449e93	0.234562	0.117281	+	0.993099i	$0.462582\pi$
$380$	1.00065e94	0.688938
$381$	−2.39794e93	−0.149995
$382$	2.67192e92	0.0151884
$383$	−5.62498e93	−0.290647	−0.145323	−	0.989384i	$-0.546422\pi$
$383$	−5.62498e93	−0.290647	−0.145323	+	0.989384i	$0.546422\pi$
$384$	1.85375e94	0.870889
$385$	−1.56905e94	−0.670380
$386$	−1.39919e93	−0.0543802
$387$	6.87991e92	0.0243295
$388$	1.94112e94	0.624734
$389$	4.55175e94	1.33358	0.666789	−	0.745247i	$-0.267668\pi$
$389$	4.55175e94	1.33358	0.666789	+	0.745247i	$0.267668\pi$
$390$	−1.67132e94	−0.445863
$391$	−8.28326e93	−0.201256
$392$	−3.69953e92	−0.00818852
$393$	−9.35208e94	−1.88617
$394$	9.68549e93	0.178037
$395$	−1.80435e94	−0.302362
$396$	−6.73906e94	−1.02973
$397$	6.04038e94	0.841804	0.420902	−	0.907106i	$-0.361714\pi$
$397$	6.04038e94	0.841804	0.420902	+	0.907106i	$0.361714\pi$
$398$	−9.31691e93	−0.118451
$399$	−8.49290e94	−0.985247
$400$	4.98550e94	0.527860
$401$	1.81150e95	1.75093	0.875465	−	0.483281i	$-0.160555\pi$
$401$	1.81150e95	1.75093	0.875465	+	0.483281i	$0.160555\pi$
$402$	3.09503e94	0.273158
$403$	−2.52886e95	−2.03840
$404$	2.55535e95	1.88161
$405$	1.74762e95	1.17581
$406$	−7.29995e93	−0.0448869
$407$	8.73853e93	0.0491182
$408$	1.40551e94	0.0722334
$409$	−2.92901e95	−1.37664	−0.688318	−	0.725409i	$-0.741651\pi$
$409$	−2.92901e95	−1.37664	−0.688318	+	0.725409i	$0.741651\pi$
$410$	3.44338e94	0.148038
$411$	−7.46188e93	−0.0293509
$412$	−3.72535e95	−1.34097
$413$	1.56116e95	0.514365
$414$	−1.08734e95	−0.327984
$415$	3.73812e95	1.03252
$416$	2.39797e95	0.606648
$417$	4.10290e94	0.0950878
$418$	−1.84481e94	−0.0391758
$419$	−8.12273e95	−1.58085	−0.790424	−	0.612560i	$-0.790140\pi$
$419$	−8.12273e95	−1.58085	−0.790424	+	0.612560i	$0.790140\pi$
$420$	−1.20490e96	−2.14958
$421$	−1.37700e95	−0.225236	−0.112618	−	0.993638i	$-0.535924\pi$
$421$	−1.37700e95	−0.225236	−0.112618	+	0.993638i	$0.535924\pi$
$422$	−4.38779e94	−0.0658175
$423$	2.50467e96	3.44609
$424$	5.66635e94	0.0715236
$425$	7.69720e94	0.0891532
$426$	−2.23257e95	−0.237331
$427$	9.27784e95	0.905377
$428$	1.81193e96	1.62347
$429$	−1.74380e96	−1.43485
$430$	2.67198e93	0.00201945
$431$	2.16300e95	0.150189	0.0750943	−	0.997176i	$-0.476074\pi$
$431$	2.16300e95	0.150189	0.0750943	+	0.997176i	$0.476074\pi$
$432$	−2.51620e96	−1.60542
$433$	−1.06805e96	−0.626299	−0.313149	−	0.949704i	$-0.601384\pi$
$433$	−1.06805e96	−0.626299	−0.313149	+	0.949704i	$0.601384\pi$
$434$	3.22145e95	0.173650
$435$	−1.45788e96	−0.722542
$436$	2.52855e96	1.15243
$437$	1.68455e96	0.706175
$438$	5.33674e95	0.205812
$439$	−4.18327e96	−1.48443	−0.742217	−	0.670160i	$-0.766225\pi$
$439$	−4.18327e96	−1.48443	−0.742217	+	0.670160i	$0.766225\pi$
$440$	−5.28079e95	−0.172455
$441$	2.06524e95	0.0620814
$442$	1.19779e95	0.0331487
$443$	−1.44956e96	−0.369403	−0.184701	−	0.982795i	$-0.559132\pi$
$443$	−1.44956e96	−0.369403	−0.184701	+	0.982795i	$0.559132\pi$
$444$	6.71047e95	0.157498
$445$	−1.32977e96	−0.287500
$446$	−9.18788e95	−0.183018
$447$	8.90005e96	1.63368
$448$	5.38640e96	0.911278
$449$	−8.52316e95	−0.132926	−0.0664629	−	0.997789i	$-0.521171\pi$
$449$	−8.52316e95	−0.132926	−0.0664629	+	0.997789i	$0.521171\pi$
$450$	1.01041e96	0.145292
$451$	3.59271e96	0.476407
$452$	−4.26990e96	−0.522233
$453$	9.77509e96	1.10290
$454$	6.74414e95	0.0702083
$455$	−2.07180e97	−1.99036
$456$	−2.85836e96	−0.253455
$457$	−1.28421e97	−1.05122	−0.525610	−	0.850726i	$-0.676163\pi$
$457$	−1.28421e97	−1.05122	−0.525610	+	0.850726i	$0.676163\pi$
$458$	−2.52182e96	−0.190601
$459$	−3.88481e96	−0.271148
$460$	2.38991e97	1.54071
$461$	−2.16592e97	−1.28991	−0.644954	−	0.764221i	$-0.723124\pi$
$461$	−2.16592e97	−1.28991	−0.644954	+	0.764221i	$0.723124\pi$
$462$	2.22138e96	0.122234
$463$	−7.61030e96	−0.386986	−0.193493	−	0.981102i	$-0.561982\pi$
$463$	−7.61030e96	−0.386986	−0.193493	+	0.981102i	$0.561982\pi$
$464$	6.76731e96	0.318061
$465$	6.43356e97	2.79524
$466$	−3.16703e96	−0.127223
$467$	−2.32926e97	−0.865270	−0.432635	−	0.901569i	$-0.642416\pi$
$467$	−2.32926e97	−0.865270	−0.432635	+	0.901569i	$0.642416\pi$
$468$	−8.89836e97	−3.05729
$469$	3.83666e97	1.21939
$470$	9.72746e96	0.286040
$471$	7.59101e97	2.06555
$472$	5.25424e96	0.132320
$473$	2.78785e95	0.00649887
$474$	2.55450e96	0.0551311
$475$	−1.56537e97	−0.312824
$476$	8.63519e96	0.159815
$477$	−3.16320e97	−0.542258
$478$	−1.17242e96	−0.0186193
$479$	2.29746e97	0.338066	0.169033	−	0.985610i	$-0.445936\pi$
$479$	2.29746e97	0.338066	0.169033	+	0.985610i	$0.445936\pi$
$480$	−6.10057e97	−0.831889
$481$	1.15385e97	0.145832
$482$	−2.43890e96	−0.0285745
$483$	−2.02841e98	−2.20336
$484$	7.02471e97	0.707575
$485$	−8.49134e97	−0.793237
$486$	1.00484e96	0.00870711
$487$	9.83578e97	0.790682	0.395341	−	0.918534i	$-0.370626\pi$
$487$	9.83578e97	0.790682	0.395341	+	0.918534i	$0.370626\pi$
$488$	3.12254e97	0.232908
$489$	2.22801e98	1.54221
$490$	8.02084e95	0.00515303
$491$	−1.73954e98	−1.03743	−0.518716	−	0.854947i	$-0.673590\pi$
$491$	−1.73954e98	−1.03743	−0.518716	+	0.854947i	$0.673590\pi$
$492$	2.75890e98	1.52760
$493$	1.04482e97	0.0537190
$494$	−2.43592e97	−0.116313
$495$	2.94797e98	1.30747
$496$	−2.98639e98	−1.23046
$497$	−2.76754e98	−1.05946
$498$	−5.29223e97	−0.188264
$499$	−4.48498e97	−0.148283	−0.0741413	−	0.997248i	$-0.523622\pi$
$499$	−4.48498e97	−0.148283	−0.0741413	+	0.997248i	$0.523622\pi$
$500$	1.76851e98	0.543503
$501$	−7.90172e97	−0.225759
$502$	8.07363e97	0.214478
$503$	7.59682e98	1.87672	0.938362	−	0.345655i	$-0.112343\pi$
$503$	7.59682e98	1.87672	0.938362	+	0.345655i	$0.112343\pi$
$504$	2.28711e98	0.525499
$505$	−1.11782e99	−2.38912
$506$	−4.40608e97	−0.0876109
$507$	−1.36940e99	−2.53361
$508$	−4.95835e97	−0.0853713
$509$	1.10612e98	0.177257	0.0886284	−	0.996065i	$-0.471752\pi$
$509$	1.10612e98	0.177257	0.0886284	+	0.996065i	$0.471752\pi$
$510$	−3.04724e97	−0.0454565
$511$	6.61553e98	0.918759
$512$	4.74747e98	0.613916
$513$	7.90047e98	0.951413
$514$	−8.76488e97	−0.0983087
$515$	1.62964e99	1.70265
$516$	2.14084e97	0.0208387
$517$	1.01493e99	0.920516
$518$	−1.46986e97	−0.0124234
$519$	−3.84944e99	−3.03242
$520$	−6.97284e98	−0.512021
$521$	1.94380e99	1.33068	0.665341	−	0.746540i	$-0.268286\pi$
$521$	1.94380e99	1.33068	0.665341	+	0.746540i	$0.268286\pi$
$522$	1.37153e98	0.0875451
$523$	3.22586e98	0.192014	0.0960072	−	0.995381i	$-0.469393\pi$
$523$	3.22586e98	0.192014	0.0960072	+	0.995381i	$0.469393\pi$
$524$	−1.93378e99	−1.07353
$525$	1.88489e99	0.976051
$526$	−9.83793e97	−0.0475252
$527$	−4.61075e98	−0.207818
$528$	−2.05930e99	−0.866126
$529$	1.47571e99	0.579255
$530$	−1.22850e98	−0.0450098
$531$	−2.93315e99	−1.00319
$532$	−1.75613e99	−0.560765
$533$	4.74387e99	1.41446
$534$	1.88262e98	0.0524213
$535$	−7.92619e99	−2.06135
$536$	1.29126e99	0.313689
$537$	4.68327e99	1.06289
$538$	−8.30054e97	−0.0176016
$539$	8.36867e97	0.0165831
$540$	1.12086e100	2.07576
$541$	2.75772e99	0.477364	0.238682	−	0.971098i	$-0.423285\pi$
$541$	2.75772e99	0.477364	0.238682	+	0.971098i	$0.423285\pi$
$542$	−8.99974e98	−0.145632
$543$	2.41358e99	0.365148
$544$	4.37210e98	0.0618487
$545$	−1.10610e100	−1.46327
$546$	2.93315e99	0.362913
$547$	2.20581e99	0.255288	0.127644	−	0.991820i	$-0.459258\pi$
$547$	2.20581e99	0.255288	0.127644	+	0.991820i	$0.459258\pi$
$548$	−1.54294e98	−0.0167054
$549$	−1.74314e100	−1.76580
$550$	4.09434e98	0.0388102
$551$	−2.12483e99	−0.188491
$552$	−6.82679e99	−0.566814
$553$	3.16661e99	0.246109
$554$	−3.01316e98	−0.0219238
$555$	−2.93546e99	−0.199978
$556$	8.48380e98	0.0541204
$557$	3.12775e100	1.86860	0.934302	−	0.356482i	$-0.116024\pi$
$557$	3.12775e100	1.86860	0.934302	+	0.356482i	$0.116024\pi$
$558$	−6.05251e99	−0.338678
$559$	3.68112e98	0.0192952
$560$	−2.44665e100	−1.20146
$561$	−3.17939e99	−0.146285
$562$	4.21674e99	0.181803
$563$	−3.06947e100	−1.24024	−0.620122	−	0.784505i	$-0.712917\pi$
$563$	−3.06947e100	−1.24024	−0.620122	+	0.784505i	$0.712917\pi$
$564$	7.79382e100	2.95164
$565$	1.86784e100	0.663090
$566$	6.41256e99	0.213418
$567$	−3.06704e100	−0.957058
$568$	−9.31441e99	−0.272547
$569$	5.43050e99	0.149019	0.0745095	−	0.997220i	$-0.476261\pi$
$569$	5.43050e99	0.149019	0.0745095	+	0.997220i	$0.476261\pi$
$570$	6.19713e99	0.159499
$571$	5.10752e100	1.23308	0.616541	−	0.787323i	$-0.288534\pi$
$571$	5.10752e100	1.23308	0.616541	+	0.787323i	$0.288534\pi$
$572$	−3.60575e100	−0.816660
$573$	−9.36481e99	−0.199001
$574$	−6.04309e99	−0.120497
$575$	−3.73866e100	−0.699583
$576$	−1.01201e101	−1.77731
$577$	1.75584e100	0.289447	0.144723	−	0.989472i	$-0.453771\pi$
$577$	1.75584e100	0.289447	0.144723	+	0.989472i	$0.453771\pi$
$578$	−8.29652e99	−0.128390
$579$	4.90402e100	0.712500
$580$	−3.01454e100	−0.411243
$581$	−6.56035e100	−0.840424
$582$	1.20216e100	0.144635
$583$	−1.28178e100	−0.144847
$584$	2.22652e100	0.236351
$585$	3.89254e101	3.88190
$586$	−7.88898e99	−0.0739193
$587$	−1.85514e101	−1.63337	−0.816687	−	0.577081i	$-0.804192\pi$
$587$	−1.85514e101	−1.63337	−0.816687	+	0.577081i	$0.804192\pi$
$588$	6.42645e99	0.0531739
$589$	9.37680e100	0.729200
$590$	−1.13916e100	−0.0832693
$591$	−3.39466e101	−2.33267
$592$	1.36261e100	0.0880298
$593$	2.31200e101	1.40440	0.702202	−	0.711978i	$-0.252200\pi$
$593$	2.31200e101	1.40440	0.702202	+	0.711978i	$0.252200\pi$
$594$	−2.06643e100	−0.118036
$595$	−3.77742e100	−0.202921
$596$	1.84031e101	0.929830
$597$	3.26548e101	1.55197
$598$	−5.81785e100	−0.260117
$599$	−2.30638e101	−0.970178	−0.485089	−	0.874465i	$-0.661213\pi$
$599$	−2.30638e101	−0.970178	−0.485089	+	0.874465i	$0.661213\pi$
$600$	6.34378e100	0.251089
$601$	−3.98037e101	−1.48254	−0.741269	−	0.671209i	$-0.765775\pi$
$601$	−3.98037e101	−1.48254	−0.741269	+	0.671209i	$0.765775\pi$
$602$	−4.68928e98	−0.00164375
$603$	−7.20839e101	−2.37824
$604$	2.02125e101	0.627729
$605$	−3.07292e101	−0.898423
$606$	1.58256e101	0.435620
$607$	2.03446e101	0.527306	0.263653	−	0.964618i	$-0.415073\pi$
$607$	2.03446e101	0.527306	0.263653	+	0.964618i	$0.415073\pi$
$608$	−8.89148e100	−0.217017
$609$	2.55856e101	0.588117
$610$	−6.76989e100	−0.146569
$611$	1.34013e102	2.73302
$612$	−1.62240e101	−0.311695
$613$	8.11549e101	1.46895	0.734476	−	0.678635i	$-0.237428\pi$
$613$	8.11549e101	1.46895	0.734476	+	0.678635i	$0.237428\pi$
$614$	1.18968e101	0.202902
$615$	−1.20687e102	−1.93963
$616$	9.26772e100	0.140371
$617$	−4.85215e101	−0.692669	−0.346335	−	0.938111i	$-0.612574\pi$
$617$	−4.85215e101	−0.692669	−0.346335	+	0.938111i	$0.612574\pi$
$618$	−2.30715e101	−0.310453
$619$	−1.16809e102	−1.48173	−0.740864	−	0.671655i	$-0.765584\pi$
$619$	−1.16809e102	−1.48173	−0.740864	+	0.671655i	$0.765584\pi$
$620$	1.33030e102	1.59094
$621$	1.88692e102	2.12769
$622$	3.20507e100	0.0340791
$623$	2.33374e101	0.234012
$624$	−2.71913e102	−2.57154
$625$	−1.39770e102	−1.24679
$626$	2.33227e101	0.196253
$627$	6.46587e101	0.513289
$628$	1.56964e102	1.17563
$629$	2.10376e100	0.0148678
$630$	−4.95861e101	−0.330697
$631$	−2.95061e102	−1.85712	−0.928559	−	0.371185i	$-0.878952\pi$
$631$	−2.95061e102	−1.85712	−0.928559	+	0.371185i	$0.878952\pi$
$632$	1.06575e101	0.0633115
$633$	1.53787e102	0.862353
$634$	−2.76110e101	−0.146159
$635$	2.16901e101	0.108398
$636$	−9.84300e101	−0.464454
$637$	1.10501e101	0.0492355
$638$	5.55765e100	0.0233850
$639$	5.19971e102	2.06632
$640$	−1.67678e102	−0.629370
$641$	4.29395e102	1.52244	0.761218	−	0.648496i	$-0.224602\pi$
$641$	4.29395e102	1.52244	0.761218	+	0.648496i	$0.224602\pi$
$642$	1.12215e102	0.375856
$643$	1.03978e102	0.329034	0.164517	−	0.986374i	$-0.447393\pi$
$643$	1.03978e102	0.329034	0.164517	+	0.986374i	$0.447393\pi$
$644$	−4.19426e102	−1.25407
$645$	−9.36499e100	−0.0264593
$646$	−4.44130e100	−0.0118583
$647$	−9.92922e101	−0.250558	−0.125279	−	0.992122i	$-0.539983\pi$
$647$	−9.92922e101	−0.250558	−0.125279	+	0.992122i	$0.539983\pi$
$648$	−1.03224e102	−0.246203
$649$	−1.18856e102	−0.267971
$650$	5.40623e101	0.115228
$651$	−1.12908e103	−2.27520
$652$	4.60699e102	0.877769
$653$	−2.55572e102	−0.460450	−0.230225	−	0.973137i	$-0.573946\pi$
$653$	−2.55572e102	−0.460450	−0.230225	+	0.973137i	$0.573946\pi$
$654$	1.56596e102	0.266805
$655$	8.45924e102	1.36309
$656$	5.60216e102	0.853818
$657$	−1.24294e103	−1.79190
$658$	−1.70716e102	−0.232824
$659$	−9.61531e102	−1.24064	−0.620320	−	0.784349i	$-0.712997\pi$
$659$	−9.61531e102	−1.24064	−0.620320	+	0.784349i	$0.712997\pi$
$660$	9.17326e102	1.11988
$661$	8.19473e102	0.946633	0.473316	−	0.880893i	$-0.343057\pi$
$661$	8.19473e102	0.946633	0.473316	+	0.880893i	$0.343057\pi$
$662$	2.96337e101	0.0323944
$663$	−4.19812e102	−0.434321
$664$	−2.20795e102	−0.216199
$665$	7.68208e102	0.712015
$666$	2.76160e101	0.0242299
$667$	−5.07485e102	−0.421532
$668$	−1.63388e102	−0.128493
$669$	3.22025e103	2.39793
$670$	−2.79955e102	−0.197405
$671$	−7.06347e102	−0.471678
$672$	1.07064e103	0.677121
$673$	9.08707e102	0.544344	0.272172	−	0.962249i	$-0.412258\pi$
$673$	9.08707e102	0.544344	0.272172	+	0.962249i	$0.412258\pi$
$674$	3.29258e101	0.0186831
$675$	−1.75341e103	−0.942533
$676$	−2.83158e103	−1.44203
$677$	−2.19434e103	−1.05881	−0.529405	−	0.848369i	$-0.677585\pi$
$677$	−2.19434e103	−1.05881	−0.529405	+	0.848369i	$0.677585\pi$
$678$	−2.64439e102	−0.120904
$679$	1.49022e103	0.645659
$680$	−1.27133e102	−0.0522013
$681$	−2.36375e103	−0.919882
$682$	−2.45257e102	−0.0904675
$683$	−3.52716e103	−1.23330	−0.616651	−	0.787236i	$-0.711511\pi$
$683$	−3.52716e103	−1.23330	−0.616651	+	0.787236i	$0.711511\pi$
$684$	3.29944e103	1.09369
$685$	6.74950e101	0.0212112
$686$	4.35026e102	0.129624
$687$	8.83872e103	2.49729
$688$	4.34713e101	0.0116473
$689$	−1.69248e103	−0.430053
$690$	1.48010e103	0.356696
$691$	5.99882e103	1.37125	0.685626	−	0.727954i	$-0.259528\pi$
$691$	5.99882e103	1.37125	0.685626	+	0.727954i	$0.259528\pi$
$692$	−7.95970e103	−1.72593
$693$	−5.17364e103	−1.06423
$694$	−6.95477e102	−0.135726
$695$	−3.71120e102	−0.0687177
$696$	8.61105e102	0.151293
$697$	8.64928e102	0.144206
$698$	−1.66446e100	−0.000263361 0
$699$	1.11001e104	1.66690
$700$	3.89750e103	0.555531
$701$	8.24063e103	1.11494	0.557472	−	0.830196i	$-0.311771\pi$
$701$	8.24063e103	1.11494	0.557472	+	0.830196i	$0.311771\pi$
$702$	−2.72854e103	−0.350450
$703$	−4.27838e102	−0.0521687
$704$	−4.10081e103	−0.474753
$705$	−3.40937e104	−3.74776
$706$	−1.43769e103	−0.150070
$707$	1.96177e104	1.94464
$708$	−9.12713e103	−0.859252
$709$	−1.70430e104	−1.52391	−0.761953	−	0.647632i	$-0.775760\pi$
$709$	−1.70430e104	−1.52391	−0.761953	+	0.647632i	$0.775760\pi$
$710$	2.01943e103	0.171514
$711$	−5.94949e103	−0.479998
$712$	7.85440e102	0.0601996
$713$	2.23952e104	1.63075
$714$	5.34787e102	0.0369995
$715$	1.57732e104	1.03693
$716$	9.68387e103	0.604956
$717$	4.10919e103	0.243954
$718$	1.12593e102	0.00635284
$719$	−3.17489e104	−1.70265	−0.851323	−	0.524642i	$-0.824199\pi$
$719$	−3.17489e104	−1.70265	−0.851323	+	0.524642i	$0.824199\pi$
$720$	4.59681e104	2.34326
$721$	−2.85999e104	−1.38588
$722$	−1.95714e103	−0.0901602
$723$	8.54810e103	0.374388
$724$	4.99070e103	0.207828
$725$	4.71580e103	0.186732
$726$	4.35048e103	0.163814
$727$	−2.53957e102	−0.00909398	−0.00454699	−	0.999990i	$-0.501447\pi$
$727$	−2.53957e102	−0.00909398	−0.00454699	+	0.999990i	$0.501447\pi$
$728$	1.22372e104	0.416762
$729$	−3.26150e104	−1.05648
$730$	−4.82724e103	−0.148736
$731$	6.71162e101	0.00196717
$732$	−5.42416e104	−1.51244
$733$	5.13601e104	1.36248	0.681242	−	0.732059i	$-0.261440\pi$
$733$	5.13601e104	1.36248	0.681242	+	0.732059i	$0.261440\pi$
$734$	3.87851e103	0.0978946
$735$	−2.81122e103	−0.0675160
$736$	−2.12360e104	−0.485326
$737$	−2.92095e104	−0.635274
$738$	1.13539e104	0.235010
$739$	−8.61961e104	−1.69811	−0.849054	−	0.528306i	$-0.822828\pi$
$739$	−8.61961e104	−1.69811	−0.849054	+	0.528306i	$0.822828\pi$
$740$	−6.06982e103	−0.113820
$741$	8.53764e104	1.52396
$742$	2.15601e103	0.0366360
$743$	8.31834e104	1.34569	0.672845	−	0.739784i	$-0.265072\pi$
$743$	8.31834e104	1.34569	0.672845	+	0.739784i	$0.265072\pi$
$744$	−3.80003e104	−0.585295
$745$	−8.05036e104	−1.18062
$746$	−1.80647e104	−0.252269
$747$	1.23257e105	1.63912
$748$	−6.57421e103	−0.0832597
$749$	1.39104e105	1.67785
$750$	1.09526e104	0.125829
$751$	8.23505e104	0.901174	0.450587	−	0.892733i	$-0.351215\pi$
$751$	8.23505e104	0.901174	0.450587	+	0.892733i	$0.351215\pi$
$752$	1.58259e105	1.64975
$753$	−2.82972e105	−2.81013
$754$	7.33841e103	0.0694301
$755$	−8.84186e104	−0.797040
$756$	−1.96709e105	−1.68958
$757$	−2.18065e104	−0.178479	−0.0892394	−	0.996010i	$-0.528444\pi$
$757$	−2.18065e104	−0.178479	−0.0892394	+	0.996010i	$0.528444\pi$
$758$	3.96275e103	0.0309080
$759$	1.54428e105	1.14789
$760$	2.58547e104	0.183166
$761$	−2.07078e105	−1.39828	−0.699140	−	0.714985i	$-0.746433\pi$
$761$	−2.07078e105	−1.39828	−0.699140	+	0.714985i	$0.746433\pi$
$762$	−3.07076e103	−0.0197647
$763$	1.94120e105	1.19103
$764$	−1.93641e104	−0.113264
$765$	7.09709e104	0.395766
$766$	−7.20327e103	−0.0382983
$767$	−1.56939e105	−0.795609
$768$	−2.96734e105	−1.43444
$769$	1.22335e105	0.563947	0.281973	−	0.959422i	$-0.409011\pi$
$769$	1.22335e105	0.563947	0.281973	+	0.959422i	$0.409011\pi$
$770$	−2.00931e104	−0.0883354
$771$	3.07200e105	1.28806
$772$	1.01403e105	0.405528
$773$	−8.34378e104	−0.318281	−0.159141	−	0.987256i	$-0.550872\pi$
$773$	−8.34378e104	−0.318281	−0.159141	+	0.987256i	$0.550872\pi$
$774$	8.81032e102	0.00320587
$775$	−2.08107e105	−0.722393
$776$	5.01547e104	0.166096
$777$	5.15170e104	0.162773
$778$	5.82891e104	0.175724
$779$	−1.75899e105	−0.505995
$780$	1.21125e106	3.32492
$781$	2.10700e105	0.551953
$782$	−1.06074e104	−0.0265194
$783$	−2.38008e105	−0.567921
$784$	1.30494e104	0.0297203
$785$	−6.86630e105	−1.49273
$786$	−1.19761e105	−0.248539
$787$	−2.99942e105	−0.594236	−0.297118	−	0.954841i	$-0.596026\pi$
$787$	−2.99942e105	−0.594236	−0.297118	+	0.954841i	$0.596026\pi$
$788$	−7.01933e105	−1.32767
$789$	3.44809e105	0.622684
$790$	−2.31062e104	−0.0398419
$791$	−3.27804e105	−0.539726
$792$	−1.74124e105	−0.273772
$793$	−9.32671e105	−1.40042
$794$	7.73522e104	0.110924
$795$	4.30577e105	0.589727
$796$	6.75221e105	0.883322
$797$	1.44943e106	1.81121	0.905604	−	0.424124i	$-0.139418\pi$
$797$	1.44943e106	1.81121	0.905604	+	0.424124i	$0.139418\pi$
$798$	−1.08759e105	−0.129825
$799$	2.44340e105	0.278635
$800$	1.97335e105	0.214991
$801$	−4.38467e105	−0.456405
$802$	2.31978e105	0.230719
$803$	−5.03658e105	−0.478650
$804$	−2.24305e106	−2.03701
$805$	1.83476e106	1.59231
$806$	−3.23842e105	−0.268599
$807$	2.90925e105	0.230620
$808$	6.60250e105	0.500258
$809$	1.25435e106	0.908442	0.454221	−	0.890889i	$-0.349918\pi$
$809$	1.25435e106	0.908442	0.454221	+	0.890889i	$0.349918\pi$
$810$	2.23797e105	0.154936
$811$	−1.31775e106	−0.872112	−0.436056	−	0.899920i	$-0.643625\pi$
$811$	−1.31775e106	−0.872112	−0.436056	+	0.899920i	$0.643625\pi$
$812$	5.29047e105	0.334734
$813$	3.15431e106	1.90809
$814$	1.11904e104	0.00647226
$815$	−2.01531e106	−1.11452
$816$	−4.95767e105	−0.262172
$817$	−1.36493e104	−0.00690248
$818$	−3.75084e105	−0.181398
$819$	−6.83136e106	−3.15969
$820$	−2.49551e106	−1.10396
$821$	2.12804e106	0.900439	0.450219	−	0.892918i	$-0.351346\pi$
$821$	2.12804e106	0.900439	0.450219	+	0.892918i	$0.351346\pi$
$822$	−9.55558e103	−0.00386755
$823$	2.97912e106	1.15344	0.576720	−	0.816942i	$-0.304333\pi$
$823$	2.97912e106	1.15344	0.576720	+	0.816942i	$0.304333\pi$
$824$	−9.62555e105	−0.356519
$825$	−1.43502e106	−0.508498
$826$	1.99920e105	0.0677775
$827$	3.05296e106	0.990306	0.495153	−	0.868806i	$-0.335112\pi$
$827$	3.05296e106	0.990306	0.495153	+	0.868806i	$0.335112\pi$
$828$	7.88025e106	2.44587
$829$	−3.55563e106	−1.05603	−0.528015	−	0.849235i	$-0.677064\pi$
$829$	−3.55563e106	−1.05603	−0.528015	+	0.849235i	$0.677064\pi$
$830$	4.78698e105	0.136054
$831$	1.05608e106	0.287249
$832$	−5.41477e106	−1.40954
$833$	2.01472e104	0.00501963
$834$	5.25411e104	0.0125296
$835$	7.14734e105	0.163150
$836$	1.33699e106	0.292144
$837$	1.05032e107	2.19707
$838$	−1.04019e106	−0.208307
$839$	1.13258e106	0.217148	0.108574	−	0.994088i	$-0.465372\pi$
$839$	1.13258e106	0.217148	0.108574	+	0.994088i	$0.465372\pi$
$840$	−3.11323e106	−0.571501
$841$	−5.04911e106	−0.887485
$842$	−1.76337e105	−0.0296792
$843$	−1.47792e107	−2.38202
$844$	3.17995e106	0.490818
$845$	1.23866e107	1.83098
$846$	3.20744e106	0.454088
$847$	5.39294e106	0.731276
$848$	−1.99870e106	−0.259596
$849$	−2.24753e107	−2.79625
$850$	9.85692e104	0.0117476
$851$	−1.02183e106	−0.116668
$852$	1.61800e107	1.76984
$853$	−9.81188e106	−1.02828	−0.514141	−	0.857706i	$-0.671889\pi$
$853$	−9.81188e106	−1.02828	−0.514141	+	0.857706i	$0.671889\pi$
$854$	1.18811e106	0.119301
$855$	−1.44332e107	−1.38868
$856$	4.68166e106	0.431626
$857$	−7.41614e106	−0.655206	−0.327603	−	0.944815i	$-0.606241\pi$
$857$	−7.41614e106	−0.655206	−0.327603	+	0.944815i	$0.606241\pi$
$858$	−2.23308e106	−0.189068
$859$	8.57042e106	0.695427	0.347714	−	0.937601i	$-0.386958\pi$
$859$	8.57042e106	0.695427	0.347714	+	0.937601i	$0.386958\pi$
$860$	−1.93645e105	−0.0150596
$861$	2.11804e107	1.57877
$862$	2.76991e105	0.0197902
$863$	7.22821e106	0.495036	0.247518	−	0.968883i	$-0.420385\pi$
$863$	7.22821e106	0.495036	0.247518	+	0.968883i	$0.420385\pi$
$864$	−9.95960e106	−0.653868
$865$	3.48193e107	2.19145
$866$	−1.36772e106	−0.0825269
$867$	2.90784e107	1.68218
$868$	−2.33467e107	−1.29496
$869$	−2.41083e106	−0.128217
$870$	−1.86694e106	−0.0952087
$871$	−3.85687e107	−1.88613
$872$	6.53327e106	0.306393
$873$	−2.79985e107	−1.25926
$874$	2.15721e106	0.0930520
$875$	1.35770e107	0.561708
$876$	−3.86768e107	−1.53480
$877$	1.98341e107	0.754967	0.377483	−	0.926016i	$-0.376790\pi$
$877$	1.98341e107	0.754967	0.377483	+	0.926016i	$0.376790\pi$
$878$	−5.35703e106	−0.195602
$879$	2.76500e107	0.968504
$880$	1.86270e107	0.625929
$881$	−3.33655e107	−1.07567	−0.537833	−	0.843052i	$-0.680757\pi$
$881$	−3.33655e107	−1.07567	−0.537833	+	0.843052i	$0.680757\pi$
$882$	2.64471e105	0.00818042
$883$	−4.17223e106	−0.123823	−0.0619116	−	0.998082i	$-0.519720\pi$
$883$	−4.17223e106	−0.123823	−0.0619116	+	0.998082i	$0.519720\pi$
$884$	−8.68068e106	−0.247199
$885$	3.99262e107	1.09101
$886$	−1.85628e106	−0.0486759
$887$	−5.76985e107	−1.45195	−0.725976	−	0.687720i	$-0.758612\pi$
$887$	−5.76985e107	−1.45195	−0.725976	+	0.687720i	$0.758612\pi$
$888$	1.73385e106	0.0418734
$889$	−3.80658e106	−0.0882308
$890$	−1.70289e106	−0.0378836
$891$	2.33502e107	0.498603
$892$	6.65870e107	1.36481
$893$	−4.96909e107	−0.977685
$894$	1.13973e107	0.215269
$895$	−4.23616e107	−0.768125
$896$	2.94272e107	0.512279
$897$	2.03909e108	3.40811
$898$	−1.09146e106	−0.0175155
$899$	−2.82484e107	−0.435276
$900$	−7.32270e107	−1.08348
$901$	−3.08582e106	−0.0438446
$902$	4.60077e106	0.0627757
$903$	1.64354e106	0.0215367
$904$	−1.10325e107	−0.138844
$905$	−2.18316e107	−0.263883
$906$	1.25178e107	0.145328
$907$	−1.62085e107	−0.180749	−0.0903746	−	0.995908i	$-0.528806\pi$
$907$	−1.62085e107	−0.180749	−0.0903746	+	0.995908i	$0.528806\pi$
$908$	−4.88766e107	−0.523561
$909$	−3.68581e108	−3.79272
$910$	−2.65312e107	−0.262268
$911$	7.78998e107	0.739802	0.369901	−	0.929071i	$-0.379392\pi$
$911$	7.78998e107	0.739802	0.369901	+	0.929071i	$0.379392\pi$
$912$	1.00823e108	0.919918
$913$	4.99457e107	0.437840
$914$	−1.64454e107	−0.138518
$915$	2.37277e108	1.92038
$916$	1.82763e108	1.42136
$917$	−1.48459e108	−1.10949
$918$	−4.97483e106	−0.0357290
$919$	1.01773e107	0.0702448	0.0351224	−	0.999383i	$-0.488818\pi$
$919$	1.01773e107	0.0702448	0.0351224	+	0.999383i	$0.488818\pi$
$920$	6.17504e107	0.409623
$921$	−4.16971e108	−2.65846
$922$	−2.77365e107	−0.169970
$923$	2.78212e108	1.63875
$924$	−1.60989e108	−0.911529
$925$	9.49534e106	0.0516818
$926$	−9.74564e106	−0.0509929
$927$	5.37340e108	2.70296
$928$	2.67863e107	0.129542
$929$	−1.93150e108	−0.898092	−0.449046	−	0.893509i	$-0.648236\pi$
$929$	−1.93150e108	−0.898092	−0.449046	+	0.893509i	$0.648236\pi$
$930$	8.23873e107	0.368326
$931$	−4.09730e106	−0.0176130
$932$	2.29523e108	0.948735
$933$	−1.12334e108	−0.446511
$934$	−2.98281e107	−0.114016
$935$	2.87585e107	0.105717
$936$	−2.29916e108	−0.812831
$937$	3.17605e108	1.07992	0.539960	−	0.841691i	$-0.318439\pi$
$937$	3.17605e108	1.07992	0.539960	+	0.841691i	$0.318439\pi$
$938$	4.91317e107	0.160679
$939$	−8.17436e108	−2.57134
$940$	−7.04975e108	−2.13308
$941$	2.32516e108	0.676756	0.338378	−	0.941010i	$-0.390122\pi$
$941$	2.32516e108	0.676756	0.338378	+	0.941010i	$0.390122\pi$
$942$	9.72094e107	0.272176
$943$	−4.20110e108	−1.13158
$944$	−1.85333e108	−0.480259
$945$	8.60492e108	2.14529
$946$	3.57008e105	0.000856350 0
$947$	6.27531e108	1.44831	0.724154	−	0.689638i	$-0.242230\pi$
$947$	6.27531e108	1.44831	0.724154	+	0.689638i	$0.242230\pi$
$948$	−1.85132e108	−0.411127
$949$	−6.65038e108	−1.42112
$950$	−2.00459e107	−0.0412205
$951$	9.67736e108	1.91500
$952$	2.23116e107	0.0424895
$953$	−1.78151e107	−0.0326511	−0.0163255	−	0.999867i	$-0.505197\pi$
$953$	−1.78151e107	−0.0326511	−0.0163255	+	0.999867i	$0.505197\pi$
$954$	−4.05075e107	−0.0714529
$955$	8.47075e107	0.143813
$956$	8.49682e107	0.138849
$957$	−1.94790e108	−0.306394
$958$	2.94209e107	0.0445467
$959$	−1.18453e107	−0.0172650
$960$	1.37755e109	1.93289
$961$	5.06299e108	0.683917
$962$	1.47760e107	0.0192162
$963$	−2.61351e109	−3.27238
$964$	1.76754e108	0.213087
$965$	−4.43584e108	−0.514907
$966$	−2.59755e108	−0.290335
$967$	9.41056e108	1.01286	0.506430	−	0.862281i	$-0.330965\pi$
$967$	9.41056e108	1.01286	0.506430	+	0.862281i	$0.330965\pi$
$968$	1.81504e108	0.188121
$969$	1.55663e108	0.155370
$970$	−1.08739e108	−0.104524
$971$	5.54960e107	0.0513759	0.0256879	−	0.999670i	$-0.491822\pi$
$971$	5.54960e107	0.0513759	0.0256879	+	0.999670i	$0.491822\pi$
$972$	−7.28236e107	−0.0649312
$973$	6.51310e107	0.0559331
$974$	1.25956e108	0.104187
$975$	−1.89482e109	−1.50973
$976$	−1.10142e109	−0.845343
$977$	1.67241e109	1.23649	0.618245	−	0.785985i	$-0.287844\pi$
$977$	1.67241e109	1.23649	0.618245	+	0.785985i	$0.287844\pi$
$978$	2.85316e108	0.203216
$979$	−1.77674e108	−0.121914
$980$	−5.81292e107	−0.0384275
$981$	−3.64716e109	−2.32293
$982$	−2.22763e108	−0.136701
$983$	2.14789e108	0.127002	0.0635008	−	0.997982i	$-0.479773\pi$
$983$	2.14789e108	0.127002	0.0635008	+	0.997982i	$0.479773\pi$
$984$	7.12845e108	0.406138
$985$	3.07057e109	1.68576
$986$	1.33798e107	0.00707851
$987$	5.98340e109	3.05051
$988$	1.76538e109	0.867379
$989$	−3.25994e107	−0.0154364
$990$	3.77512e108	0.172285
$991$	−2.88916e109	−1.27082	−0.635410	−	0.772175i	$-0.719169\pi$
$991$	−2.88916e109	−1.27082	−0.635410	+	0.772175i	$0.719169\pi$
$992$	−1.18207e109	−0.501150
$993$	−1.03863e109	−0.424437
$994$	−3.54407e108	−0.139605
$995$	−2.95372e109	−1.12157
$996$	3.83542e109	1.40394
$997$	−2.76095e109	−0.974284	−0.487142	−	0.873323i	$-0.661961\pi$
$997$	−2.76095e109	−0.974284	−0.487142	+	0.873323i	$0.661961\pi$
$998$	−5.74340e107	−0.0195391
$999$	−4.79234e108	−0.157184

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1.74.a.a.1.4	✓	5
3.2	odd	2		9.74.a.a.1.2		5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1.74.a.a.1.4	✓	5	1.1	even	1	trivial
9.74.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:	\( N \)	\(=\)	\( 1 \)
Weight:	\( k \)	\(=\)	\( 74 \)
Character orbit:	\([\chi]\)	\(=\)	1.a (trivial)

\(f(q)\)	\(=\)	\(q+1.28059e10 q^{2} -4.48831e17 q^{3} -9.28074e21 q^{4} +4.05981e25 q^{5} -5.74767e27 q^{6} -7.12492e30 q^{7} -2.39796e32 q^{8} +1.33864e35 q^{9} +O(q^{10})\)	\(q+1.28059e10 q^{2} -4.48831e17 q^{3} -9.28074e21 q^{4} +4.05981e25 q^{5} -5.74767e27 q^{6} -7.12492e30 q^{7} -2.39796e32 q^{8} +1.33864e35 q^{9} +5.19894e35 q^{10} +5.42440e37 q^{11} +4.16549e39 q^{12} +7.16246e40 q^{13} -9.12407e40 q^{14} -1.82217e43 q^{15} +8.45834e43 q^{16} +1.30590e44 q^{17} +1.71425e45 q^{18} -2.65578e46 q^{19} -3.76781e47 q^{20} +3.19789e48 q^{21} +6.94640e47 q^{22} -6.34296e49 q^{23} +1.07628e50 q^{24} +5.89418e50 q^{25} +9.17214e50 q^{26} -2.97482e52 q^{27} +6.61246e52 q^{28} +8.00076e52 q^{29} -2.33345e53 q^{30} -3.53071e54 q^{31} +3.34797e54 q^{32} -2.43464e55 q^{33} +1.67231e54 q^{34} -2.89259e56 q^{35} -1.24236e57 q^{36} +1.61097e56 q^{37} -3.40096e56 q^{38} -3.21474e58 q^{39} -9.73526e57 q^{40} +6.62324e58 q^{41} +4.09517e58 q^{42} +5.13946e57 q^{43} -5.03424e59 q^{44} +5.43465e60 q^{45} -8.12270e59 q^{46} +1.87105e61 q^{47} -3.79637e61 q^{48} +1.54278e60 q^{49} +7.54801e60 q^{50} -5.86128e61 q^{51} -6.64729e62 q^{52} -2.36299e62 q^{53} -3.80951e62 q^{54} +2.20220e63 q^{55} +1.70853e63 q^{56} +1.19200e64 q^{57} +1.02457e63 q^{58} -2.19113e64 q^{59} +1.69111e65 q^{60} -1.30217e65 q^{61} -4.52138e64 q^{62} -9.53773e65 q^{63} -7.55994e65 q^{64} +2.90783e66 q^{65} -3.11776e65 q^{66} -5.38484e66 q^{67} -1.21197e66 q^{68} +2.84692e67 q^{69} -3.70420e66 q^{70} +3.88431e67 q^{71} -3.21001e67 q^{72} -9.28505e67 q^{73} +2.06298e66 q^{74} -2.64549e68 q^{75} +2.46476e68 q^{76} -3.86484e68 q^{77} -4.11674e68 q^{78} -4.44441e68 q^{79} +3.43393e69 q^{80} +4.30467e69 q^{81} +8.48163e68 q^{82} +9.20761e69 q^{83} -2.96788e70 q^{84} +5.30170e69 q^{85} +6.58152e67 q^{86} -3.59099e70 q^{87} -1.30075e70 q^{88} -3.27546e70 q^{89} +6.95953e70 q^{90} -5.10320e71 q^{91} +5.88674e71 q^{92} +1.58469e72 q^{93} +2.39603e71 q^{94} -1.07820e72 q^{95} -1.50267e72 q^{96} -2.09156e72 q^{97} +1.97567e70 q^{98} +7.26133e72 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 5 q - 92089333488 q^{2} - 12\!\cdots\!04 q^{3}+ \cdots + 32\!\cdots\!65 q^{9}+O(q^{10}) \) 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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