LMFDB - Embedded newform 1.94.a.a.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1,94,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, 94, names="a")

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

chi := DirichletCharacter("1.1");

S:= CuspForms(chi, 94);

N := Newforms(S);

Level:	$ N $	$=$	$ 1 $
Weight:	$ k $	$=$	$ 94 $
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:	$54.7725430605$
Analytic rank:	$1$
Dimension:	$7$
Coefficient field:	$\mathbb{Q}[x]/(x^{7} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{7} - x^{6} + \cdots - 13\!\cdots\!00 $ x^7 - x^6 - 160477500301516091326739x^5 + 877016488484326647371325741724874x^4 + 7260529465737129707868752892581169765229378456x^3 - 20781038399188480098606854392326662967337072615105929280x^2 - 71309214652872234197294752847774640455181142633761719353245451878000*x - 1353216958878139720025204995487184336935523797943751976847532373756765247900000
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	multiple of $ 2^{88}\cdot 3^{34}\cdot 5^{10}\cdot 7^{6}\cdot 13^{2}\cdot 19\cdot 23\cdot 31^{2} $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$-9.86534e10$ 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)

$f(q)$	$=$	$q-5.05764e13 q^{2} +2.16277e22 q^{3} -7.34554e27 q^{4} +1.20105e32 q^{5} -1.09385e36 q^{6} -1.85159e39 q^{7} +8.72396e41 q^{8} +2.32102e44 q^{9} +O(q^{10})$	\(q-5.05764e13 q^{2} +2.16277e22 q^{3} -7.34554e27 q^{4} +1.20105e32 q^{5} -1.09385e36 q^{6} -1.85159e39 q^{7} +8.72396e41 q^{8} +2.32102e44 q^{9} -6.07451e45 q^{10} +6.89038e47 q^{11} -1.58867e50 q^{12} +5.57716e51 q^{13} +9.36469e52 q^{14} +2.59760e54 q^{15} +2.86240e55 q^{16} -1.91697e57 q^{17} -1.17389e58 q^{18} -4.84589e59 q^{19} -8.82240e59 q^{20} -4.00457e61 q^{21} -3.48491e61 q^{22} +2.71891e63 q^{23} +1.88679e64 q^{24} -8.65489e64 q^{25} -2.82073e65 q^{26} -7.68416e64 q^{27} +1.36009e67 q^{28} +1.52941e68 q^{29} -1.31378e68 q^{30} +1.67865e69 q^{31} -1.00875e70 q^{32} +1.49023e70 q^{33} +9.69535e70 q^{34} -2.22386e71 q^{35} -1.70492e72 q^{36} -8.48939e72 q^{37} +2.45088e73 q^{38} +1.20621e74 q^{39} +1.04780e74 q^{40} -1.65968e75 q^{41} +2.02537e75 q^{42} -1.12790e75 q^{43} -5.06136e75 q^{44} +2.78767e76 q^{45} -1.37513e77 q^{46} +5.85334e76 q^{47} +6.19072e77 q^{48} -4.99122e77 q^{49} +4.37733e78 q^{50} -4.14596e79 q^{51} -4.09673e79 q^{52} -1.38747e79 q^{53} +3.88637e78 q^{54} +8.27573e79 q^{55} -1.61532e81 q^{56} -1.04806e82 q^{57} -7.73524e81 q^{58} -4.69043e81 q^{59} -1.90808e82 q^{60} -1.85512e83 q^{61} -8.49001e82 q^{62} -4.29758e83 q^{63} +2.26711e83 q^{64} +6.69848e83 q^{65} -7.53706e83 q^{66} -7.55695e84 q^{67} +1.40812e85 q^{68} +5.88037e85 q^{69} +1.12475e85 q^{70} +1.37506e86 q^{71} +2.02485e86 q^{72} -4.41142e86 q^{73} +4.29363e86 q^{74} -1.87185e87 q^{75} +3.55957e87 q^{76} -1.27582e87 q^{77} -6.10059e87 q^{78} -3.34870e88 q^{79} +3.43790e87 q^{80} -5.63579e88 q^{81} +8.39409e88 q^{82} -4.06731e88 q^{83} +2.94157e89 q^{84} -2.30239e89 q^{85} +5.70450e88 q^{86} +3.30777e90 q^{87} +6.01114e89 q^{88} +2.67415e89 q^{89} -1.40991e90 q^{90} -1.03266e91 q^{91} -1.99718e91 q^{92} +3.63053e91 q^{93} -2.96041e90 q^{94} -5.82018e91 q^{95} -2.18169e92 q^{96} -5.40723e91 q^{97} +2.52438e91 q^{98} +1.59927e92 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 7 q + 43735426713792 q^{2} - 36\!\cdots\!84 q^{3}+ \cdots + 36\!\cdots\!11 q^{9}+O(q^{10}) $ 7 * q + 43735426713792 * q^2 - 3678766354327579216884 * q^3 + 37433779444352805880587218944 * q^4 - 242501922056818695041616562179750 * q^5 - 3422349689703076907975614807426150656 * q^6 - 921137753903839555947108372394316103208 * q^7 + 628568314501252186502498490389635108700160 * q^8 + 362824653360866901561998689210341299050559211 * q^9	$ 7 q + 43735426713792 q^{2} - 36\!\cdots\!84 q^{3}+ \cdots + 30\!\cdots\!52 q^{99}+O(q^{100}) $ 7 * q + 43735426713792 * q^2 - 3678766354327579216884 * q^3 + 37433779444352805880587218944 * q^4 - 242501922056818695041616562179750 * q^5 - 3422349689703076907975614807426150656 * q^6 - 921137753903839555947108372394316103208 * q^7 + 628568314501252186502498490389635108700160 * q^8 + 362824653360866901561998689210341299050559211 * q^9 + 56663128890275718532856219951648854919834448000 * q^10 + 1081566396126190174166498109003279139923369012324 * q^11 - 163904625261310040243241458042755377696324875010048 * q^12 + 1923851638471797431690458036346871401286646408469426 * q^13 - 827492161115181455891429526236298470299001717526508032 * q^14 - 16711611501720521025854082681912174509227777477242411000 * q^15 - 183863117199568288307852091185855957272115704336744448 * q^16 + 809325537307953309871783611300921224816172571619454935742 * q^17 + 79483944128603792717921302063558947044650774054000109708736 * q^18 - 491316328040151561437984621759105514680907320256463264658500 * q^19 - 5819101371751539891329503686613738398860076574931824253952000 * q^20 + 54451750333719895476183963426175615210898459319681281516277984 * q^21 + 341061341496448817039487179432626029859991533289656810924326144 * q^22 - 2595697104202345855126053487687658963668179272707633091075699064 * q^23 - 29432689846399066174371175818785662556182882963620634526849433600 * q^24 + 184388886386678531186865888507627315189418933935123407708899515625 * q^25 + 793059166145746283698718389909557916534745558035448772312212840064 * q^26 - 10506923232698637098067136941837198924358450251426727402321208664840 * q^27 + 1916814131388145595393790805747801246689773266225672358812878209024 * q^28 + 115585291038420509795092429775705167101645550654624527668945364036450 * q^29 - 646359246874848354315998274237243944693324584248820365706098812352000 * q^30 - 1163635467946810748613893942791764663199899897323284701513531956983456 * q^31 - 7066990866795922437106429389517828098400874624281122281464920526553088 * q^32 + 66569296470254314915045188377632673804554883301553196046747543676316112 * q^33 + 80911624156374405155780927188384543491071504244617539921495324380294528 * q^34 - 1672188852118103650980495790489284130570309869892526153633308501275462000 * q^35 + 5276416924359744904633666070671763693285317535397001093231145577416896512 * q^36 + 11072759435314078994932599484815080247923078570346623467670584315337670842 * q^37 - 42692186143014046654789275667852179938472092905944200699148410427788924160 * q^38 - 205635087839752927920079557406846610376307390801963146422737416149757222168 * q^39 + 760187696799287916151508882607919116749295190931669242261910585944965120000 * q^40 - 509603803596826806676973650829096820638503322986104149790656476262528674746 * q^41 - 542653738615875619591084295077236547022836265832353730045755853854336280576 * q^42 - 7275658116979055674748970912580687053338617746072325435955591393683798211644 * q^43 + 9423347779397833928027118997217234224491886242773059800183027480258516369408 * q^44 + 164505351109492760826482356226220602919737242087979463171032783958351054923250 * q^45 - 639778771092842366359510076082228574613573083413403803040568658686807125218816 * q^46 - 371149830895115606730684780470708713676568637183334957675426341554516993409008 * q^47 - 416843258596979693775599022471376378646238618283847940753742770006189894795264 * q^48 + 2561975156227711495237514871966779964501558283497058708235084248829398599957999 * q^49 - 31492320141514234591073138519794385457712593727985587891779934655429621403000000 * q^50 - 55702073279983479511744597938778959921377812834972727705529236388320801422608936 * q^51 - 55278983045853834535146427408736596689073596604984335518990233309047240924848128 * q^52 - 363766241548602923075270727552075967170433033161760056492510229436384310833635734 * q^53 - 1988318954489765046302005332528558912554496159988340641069330680002958019070937600 * q^54 - 3520855393890604949232827617669938515471701214675853816941159595183623184386577000 * q^55 - 12936956692485908268365121199611114191360014164491088694387999166431300696512921600 * q^56 - 13862265625178226892264597068584427924864963571452022505627535112981742091059296080 * q^57 - 73663001170657752665346575473371223431752845037418753763472734766611572171441325440 * q^58 - 119839908140624573484226478891501296275544385047787439213910489726968365086286210700 * q^59 - 468107546718994029022024884762568911834725078620349067042941227204209206458724352000 * q^60 - 328281166748320542242523532793984772143143166398612931227281116669834617338050603326 * q^61 - 999402477792071119370831029463209574610493980381087626216590758004912070795081435136 * q^62 - 2240117215552784969170617635914585450026055291898885166701984645532069514866650525064 * q^63 - 4748321960274080197621802735261780227229800262185345649692550833454877416714840047616 * q^64 + 2401958293154067008332922023669433962969772004736123854920087208208149417890196631500 * q^65 + 12481418287827593167181900965724458478832175604254852160085986797561206241884769502208 * q^66 + 9715050085721519766982024893817705652242604355912950898916137527198529527932523084492 * q^67 + 51110178162381015351883898716980001063480395685110983605059672645927223406195391258624 * q^68 + 125665844363573358610510037253282595268580727449546920119880250916295279742987985413792 * q^69 + 437770522317274261347763126091338009235407849188339858200284725822565513739255154816000 * q^70 + 420099768445021912291978352393445519280746916987347799091649913407485898651223357176984 * q^71 + 1153857576733974210773243583317262094473717150308417455216249971043377175999426453831680 * q^72 + 249990884773795871360906735022065792056914028590737521750721031757996649920054698123686 * q^73 + 988848152146322932205109547460090361956964236264222955609677033303897103570301064734848 * q^74 + 944080624555199942138536838755965622984512203073943882229003778583589699488457416312500 * q^75 - 9872924363930092749183448370538218854882826462181838927155554514487863834399954370969600 * q^76 - 16552736755381232703525388842736711985373990693881749218915711388952768140257306836693856 * q^77 - 73115054525877473148472082243219461137606249175371809547554984327725748004401082971708928 * q^78 - 43369884997252312790262999909905208728154246791055779943371432494520439561399960810221200 * q^79 - 88894687813962777903012798348655018553862729556819104796394604135123942915181092274176000 * q^80 - 70612572309757383558801217018071484518377724651384007545224773102476238636837549694743953 * q^81 - 236357995159599133663604843384379044643064499685381579522884048932961281765779447211829376 * q^82 - 206459225650342475045148123542600401116221913586781003327705338223920418727874732010864004 * q^83 + 1649840105905513745515070352659141454913812021851911846045941535531840033929951137654243328 * q^84 + 1637661121678145282281696006564110640734919603287375198985971859556394144920752854974380500 * q^85 + 3239900597437756786176903087412721547247433713557247371056571790561416975430434191434708224 * q^86 + 6559051070263618632233284423714108103382010904819072234989172243851503736785525745425626280 * q^87 + 6336674026069399594730100443279513731166873520796702455565229756349453295686310223539077120 * q^88 + 5580799156439265704685765323272125687903700231557911629488221982292995723510480958101067350 * q^89 + 19840068851074490675120863444780810644229753682905466429373855007108663777299926218608144000 * q^90 - 18025272478314007503227783954648499409552734863956310123113904904033321293148703549329112496 * q^91 - 81750027044574246291550532241925751638073881610946649428268147310600744342795416362583031808 * q^92 - 125975338781791055721238628453160089358246167768072651306884109747935024714536192316708787328 * q^93 - 306478475429892162274969547511367839192733042761577860914963828391848832364650578690812603392 * q^94 - 216711696129933523762297615654778954621414663971673687874218846402427636558070586043601335000 * q^95 - 229425406959806321843310706398725653116223652026933598684053060220054993118393316925679599616 * q^96 + 43971291171253027759915173352741872464098193495293359649108047104658615767375645954946743342 * q^97 - 690328280759812206538864038068682435013428219472201721649324072601042235191425205897720616256 * q^98 + 306809773352993420176583539450272713060724644284625495060244639714128125893072287559839588052 * 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 $

$2$	−5.05764e13	−0.508222	−0.254111	−	0.967175i	$-0.581783\pi$
$2$	−5.05764e13	−0.508222	−0.254111	+	0.967175i	$0.581783\pi$
$3$	2.16277e22	1.40887	0.704437	−	0.709767i	$-0.251200\pi$
$3$	2.16277e22	1.40887	0.704437	+	0.709767i	$0.251200\pi$
$4$	−7.34554e27	−0.741710
$5$	1.20105e32	0.377970	0.188985	−	0.981980i	$-0.439480\pi$
$5$	1.20105e32	0.377970	0.188985	+	0.981980i	$0.439480\pi$
$6$	−1.09385e36	−0.716020
$7$	−1.85159e39	−0.934300	−0.467150	−	0.884178i	$-0.654719\pi$
$7$	−1.85159e39	−0.934300	−0.467150	+	0.884178i	$0.654719\pi$
$8$	8.72396e41	0.885176
$9$	2.32102e44	0.984923
$10$	−6.07451e45	−0.192093
$11$	6.89038e47	0.259110	0.129555	−	0.991572i	$-0.458645\pi$
$11$	6.89038e47	0.259110	0.129555	+	0.991572i	$0.458645\pi$
$12$	−1.58867e50	−1.04498
$13$	5.57716e51	0.887253	0.443626	−	0.896212i	$-0.353692\pi$
$13$	5.57716e51	0.887253	0.443626	+	0.896212i	$0.353692\pi$
$14$	9.36469e52	0.474832
$15$	2.59760e54	0.532512
$16$	2.86240e55	0.291845
$17$	−1.91697e57	−1.16611	−0.583056	−	0.812432i	$-0.698143\pi$
$17$	−1.91697e57	−1.16611	−0.583056	+	0.812432i	$0.698143\pi$
$18$	−1.17389e58	−0.500560
$19$	−4.84589e59	−1.67237	−0.836183	−	0.548450i	$-0.815218\pi$
$19$	−4.84589e59	−1.67237	−0.836183	+	0.548450i	$0.815218\pi$
$20$	−8.82240e59	−0.280344
$21$	−4.00457e61	−1.31631
$22$	−3.48491e61	−0.131685
$23$	2.71891e63	1.30032	0.650159	−	0.759798i	$-0.274702\pi$
$23$	2.71891e63	1.30032	0.650159	+	0.759798i	$0.274702\pi$
$24$	1.88679e64	1.24710
$25$	−8.65489e64	−0.857139
$26$	−2.82073e65	−0.450921
$27$	−7.68416e64	−0.0212413
$28$	1.36009e67	0.692980
$29$	1.52941e68	1.52412	0.762059	−	0.647508i	$-0.224189\pi$
$29$	1.52941e68	1.52412	0.762059	+	0.647508i	$0.224189\pi$
$30$	−1.31378e68	−0.270634
$31$	1.67865e69	0.752733	0.376367	−	0.926471i	$-0.377173\pi$
$31$	1.67865e69	0.752733	0.376367	+	0.926471i	$0.377173\pi$
$32$	−1.00875e70	−1.03350
$33$	1.49023e70	0.365052
$34$	9.69535e70	0.592644
$35$	−2.22386e71	−0.353138
$36$	−1.70492e72	−0.730528
$37$	−8.48939e72	−1.01741	−0.508705	−	0.860941i	$-0.669876\pi$
$37$	−8.48939e72	−1.01741	−0.508705	+	0.860941i	$0.669876\pi$
$38$	2.45088e73	0.849934
$39$	1.20621e74	1.25003
$40$	1.04780e74	0.334570
$41$	−1.65968e75	−1.68103	−0.840516	−	0.541787i	$-0.817748\pi$
$41$	−1.65968e75	−1.68103	−0.840516	+	0.541787i	$0.817748\pi$
$42$	2.02537e75	0.668978
$43$	−1.12790e75	−0.124734	−0.0623672	−	0.998053i	$-0.519865\pi$
$43$	−1.12790e75	−0.124734	−0.0623672	+	0.998053i	$0.519865\pi$
$44$	−5.06136e75	−0.192184
$45$	2.78767e76	0.372272
$46$	−1.37513e77	−0.660851
$47$	5.85334e76	0.103479	0.0517396	−	0.998661i	$-0.483523\pi$
$47$	5.85334e76	0.103479	0.0517396	+	0.998661i	$0.483523\pi$
$48$	6.19072e77	0.411172
$49$	−4.99122e77	−0.127083
$50$	4.37733e78	0.435617
$51$	−4.14596e79	−1.64290
$52$	−4.09673e79	−0.658085
$53$	−1.38747e79	−0.0919173	−0.0459586	−	0.998943i	$-0.514634\pi$
$53$	−1.38747e79	−0.0919173	−0.0459586	+	0.998943i	$0.514634\pi$
$54$	3.88637e78	0.0107953
$55$	8.27573e79	0.0979357
$56$	−1.61532e81	−0.827020
$57$	−1.04806e82	−2.35615
$58$	−7.73524e81	−0.774590
$59$	−4.69043e81	−0.212126	−0.106063	−	0.994359i	$-0.533825\pi$
$59$	−4.69043e81	−0.212126	−0.106063	+	0.994359i	$0.533825\pi$
$60$	−1.90808e82	−0.394970
$61$	−1.85512e83	−1.78047	−0.890234	−	0.455504i	$-0.849459\pi$
$61$	−1.85512e83	−1.78047	−0.890234	+	0.455504i	$0.849459\pi$
$62$	−8.49001e82	−0.382556
$63$	−4.29758e83	−0.920214
$64$	2.26711e83	0.233402
$65$	6.69848e83	0.335355
$66$	−7.53706e83	−0.185528
$67$	−7.55695e84	−0.924417	−0.462209	−	0.886771i	$-0.652943\pi$
$67$	−7.55695e84	−0.924417	−0.462209	+	0.886771i	$0.652943\pi$
$68$	1.40812e85	0.864918
$69$	5.88037e85	1.83198
$70$	1.12475e85	0.179472
$71$	1.37506e86	1.13451	0.567257	−	0.823541i	$-0.308005\pi$
$71$	1.37506e86	1.13451	0.567257	+	0.823541i	$0.308005\pi$
$72$	2.02485e86	0.871830
$73$	−4.41142e86	−1.00015	−0.500076	−	0.865982i	$-0.666694\pi$
$73$	−4.41142e86	−1.00015	−0.500076	+	0.865982i	$0.666694\pi$
$74$	4.29363e86	0.517071
$75$	−1.87185e87	−1.20760
$76$	3.55957e87	1.24041
$77$	−1.27582e87	−0.242086
$78$	−6.10059e87	−0.635291
$79$	−3.34870e88	−1.92849	−0.964244	−	0.265015i	$-0.914623\pi$
$79$	−3.34870e88	−1.92849	−0.964244	+	0.265015i	$0.914623\pi$
$80$	3.43790e87	0.110309
$81$	−5.63579e88	−1.01485
$82$	8.39409e88	0.854337
$83$	−4.06731e88	−0.235600	−0.117800	−	0.993037i	$-0.537584\pi$
$83$	−4.06731e88	−0.235600	−0.117800	+	0.993037i	$0.537584\pi$
$84$	2.94157e89	0.976321
$85$	−2.30239e89	−0.440756
$86$	5.70450e88	0.0633927
$87$	3.30777e90	2.14729
$88$	6.01114e89	0.229357
$89$	2.67415e89	0.0603324	0.0301662	−	0.999545i	$-0.490396\pi$
$89$	2.67415e89	0.0603324	0.0301662	+	0.999545i	$0.490396\pi$
$90$	−1.40991e90	−0.189197
$91$	−1.03266e91	−0.828960
$92$	−1.99718e91	−0.964460
$93$	3.63053e91	1.06051
$94$	−2.96041e90	−0.0525904
$95$	−5.82018e91	−0.632105
$96$	−2.18169e92	−1.45607
$97$	−5.40723e91	−0.222889	−0.111445	−	0.993771i	$-0.535548\pi$
$97$	−5.40723e91	−0.222889	−0.111445	+	0.993771i	$0.535548\pi$
$98$	2.52438e91	0.0645866
$99$	1.59927e92	0.255203
$100$	6.35749e92	0.635749
$101$	2.20531e93	1.38844	0.694218	−	0.719764i	$-0.255750\pi$
$101$	2.20531e93	1.38844	0.694218	+	0.719764i	$0.255750\pi$
$102$	2.09688e93	0.834960
$103$	−3.68693e93	−0.932684	−0.466342	−	0.884605i	$-0.654428\pi$
$103$	−3.68693e93	−0.932684	−0.466342	+	0.884605i	$0.654428\pi$
$104$	4.86549e93	0.785374
$105$	−4.80970e93	−0.497526
$106$	7.01735e92	0.0467144
$107$	−1.33971e94	−0.576321	−0.288161	−	0.957582i	$-0.593044\pi$
$107$	−1.33971e94	−0.576321	−0.288161	+	0.957582i	$0.593044\pi$
$108$	5.64443e92	0.0157549
$109$	−2.23851e94	−0.407031	−0.203515	−	0.979072i	$-0.565237\pi$
$109$	−2.23851e94	−0.407031	−0.203515	+	0.979072i	$0.565237\pi$
$110$	−4.18557e93	−0.0497731
$111$	−1.83606e95	−1.43340
$112$	−5.30000e94	−0.272670
$113$	1.75390e95	0.596840	0.298420	−	0.954435i	$-0.403540\pi$
$113$	1.75390e95	0.596840	0.298420	+	0.954435i	$0.403540\pi$
$114$	5.30069e95	1.19745
$115$	3.26556e95	0.491482
$116$	−1.12344e96	−1.13045
$117$	1.29447e96	0.873876
$118$	2.37225e95	0.107807
$119$	3.54945e96	1.08950
$120$	2.26614e96	0.471367
$121$	−6.59686e96	−0.932862
$122$	9.38252e96	0.904873
$123$	−3.58951e97	−2.36836
$124$	−1.23306e97	−0.558310
$125$	−2.25225e97	−0.701943
$126$	2.17356e97	0.467673
$127$	3.30674e97	0.492637	0.246319	−	0.969189i	$-0.420779\pi$
$127$	3.30674e97	0.492637	0.246319	+	0.969189i	$0.420779\pi$
$128$	8.84355e97	0.914878
$129$	−2.43938e97	−0.175735
$130$	−3.38785e97	−0.170435
$131$	−7.10571e96	−0.0250318	−0.0125159	−	0.999922i	$-0.503984\pi$
$131$	−7.10571e96	−0.0250318	−0.0125159	+	0.999922i	$0.503984\pi$
$132$	−1.09466e98	−0.270763
$133$	8.97262e98	1.56249
$134$	3.82204e98	0.469809
$135$	−9.22909e96	−0.00802858
$136$	−1.67236e99	−1.03221
$137$	1.91186e99	0.839362	0.419681	−	0.907672i	$-0.362142\pi$
$137$	1.91186e99	0.839362	0.419681	+	0.907672i	$0.362142\pi$
$138$	−2.97408e99	−0.931055
$139$	−6.59713e99	−1.47627	−0.738136	−	0.674652i	$-0.764294\pi$
$139$	−6.59713e99	−1.47627	−0.738136	+	0.674652i	$0.764294\pi$
$140$	1.63355e99	0.261926
$141$	1.26594e99	0.145789
$142$	−6.95459e99	−0.576585
$143$	3.84288e99	0.229896
$144$	6.64370e99	0.287445
$145$	1.83691e100	0.576071
$146$	2.23114e100	0.508299
$147$	−1.07949e100	−0.179044
$148$	6.23592e100	0.754624
$149$	1.72761e100	0.152857	0.0764284	−	0.997075i	$-0.475648\pi$
$149$	1.72761e100	0.152857	0.0764284	+	0.997075i	$0.475648\pi$
$150$	9.46716e100	0.613729
$151$	2.99143e100	0.142381	0.0711904	−	0.997463i	$-0.477320\pi$
$151$	2.99143e100	0.142381	0.0711904	+	0.997463i	$0.477320\pi$
$152$	−4.22754e101	−1.48034
$153$	−4.44933e101	−1.14853
$154$	6.45263e100	0.123033
$155$	2.01615e101	0.284511
$156$	−8.86028e101	−0.927158
$157$	7.17255e101	0.557622	0.278811	−	0.960346i	$-0.410060\pi$
$157$	7.17255e101	0.557622	0.278811	+	0.960346i	$0.410060\pi$
$158$	1.69366e102	0.980100
$159$	−3.00079e101	−0.129500
$160$	−1.21156e102	−0.390631
$161$	−5.03430e102	−1.21489
$162$	2.85038e102	0.515769
$163$	1.07628e103	1.46285	0.731426	−	0.681921i	$-0.238855\pi$
$163$	1.07628e103	1.46285	0.731426	+	0.681921i	$0.238855\pi$
$164$	1.21913e103	1.24684
$165$	1.78985e102	0.137979
$166$	2.05710e102	0.119737
$167$	−1.94781e103	−0.857492	−0.428746	−	0.903425i	$-0.641044\pi$
$167$	−1.94781e103	−0.857492	−0.428746	+	0.903425i	$0.641044\pi$
$168$	−3.49357e103	−1.16517
$169$	−8.40752e102	−0.212783
$170$	1.16446e103	0.224002
$171$	−1.12474e104	−1.64715
$172$	8.28501e102	0.0925168
$173$	1.97197e104	1.68173	0.840864	−	0.541247i	$-0.182047\pi$
$173$	1.97197e104	1.68173	0.840864	+	0.541247i	$0.182047\pi$
$174$	−1.67295e104	−1.09130
$175$	1.60253e104	0.800825
$176$	1.97231e103	0.0756197
$177$	−1.01443e104	−0.298859
$178$	−1.35249e103	−0.0306623
$179$	1.05683e105	1.84645	0.923224	−	0.384262i	$-0.125544\pi$
$179$	1.05683e105	1.84645	0.923224	+	0.384262i	$0.125544\pi$
$180$	−2.04770e104	−0.276118
$181$	3.41629e104	0.356042	0.178021	−	0.984027i	$-0.443031\pi$
$181$	3.41629e104	0.356042	0.178021	+	0.984027i	$0.443031\pi$
$182$	5.22284e104	0.421296
$183$	−4.01219e105	−2.50845
$184$	2.37196e105	1.15101
$185$	−1.01962e105	−0.384551
$186$	−1.83619e105	−0.538972
$187$	−1.32087e105	−0.302151
$188$	−4.29959e104	−0.0767516
$189$	1.42279e104	0.0198458
$190$	2.94364e105	0.321250
$191$	−4.66141e105	−0.398534	−0.199267	−	0.979945i	$-0.563856\pi$
$191$	−4.66141e105	−0.398534	−0.199267	+	0.979945i	$0.563856\pi$
$192$	4.90323e105	0.328833
$193$	3.64694e105	0.192094	0.0960471	−	0.995377i	$-0.469380\pi$
$193$	3.64694e105	0.192094	0.0960471	+	0.995377i	$0.469380\pi$
$194$	2.73478e105	0.113277
$195$	1.44873e106	0.472473
$196$	3.66632e105	0.0942591
$197$	6.37141e106	1.29287	0.646437	−	0.762967i	$-0.276258\pi$
$197$	6.37141e106	1.29287	0.646437	+	0.762967i	$0.276258\pi$
$198$	−8.08855e105	−0.129700
$199$	4.40148e106	0.558381	0.279190	−	0.960236i	$-0.409934\pi$
$199$	4.40148e106	0.558381	0.279190	+	0.960236i	$0.409934\pi$
$200$	−7.55049e106	−0.758718
$201$	−1.63439e107	−1.30239
$202$	−1.11537e107	−0.705634
$203$	−2.83185e107	−1.42398
$204$	3.04544e107	1.21856
$205$	−1.99337e107	−0.635380
$206$	1.86472e107	0.474011
$207$	6.31064e107	1.28071
$208$	1.59641e107	0.258940
$209$	−3.33901e107	−0.433326
$210$	2.43258e107	0.252854
$211$	−1.08995e108	−0.908392	−0.454196	−	0.890902i	$-0.650073\pi$
$211$	−1.08995e108	−0.908392	−0.454196	+	0.890902i	$0.650073\pi$
$212$	1.01918e107	0.0681760
$213$	2.97395e108	1.59839
$214$	6.77577e107	0.292899
$215$	−1.35467e107	−0.0471459
$216$	−6.70363e106	−0.0188023
$217$	−3.10817e108	−0.703279
$218$	1.13216e108	0.206862
$219$	−9.54089e108	−1.40909
$220$	−6.07897e107	−0.0726399
$221$	−1.06912e109	−1.03464
$222$	9.28613e108	0.728487
$223$	4.86481e108	0.309663	0.154832	−	0.987941i	$-0.450517\pi$
$223$	4.86481e108	0.309663	0.154832	+	0.987941i	$0.450517\pi$
$224$	1.86779e109	0.965597
$225$	−2.00882e109	−0.844216
$226$	−8.87062e108	−0.303327
$227$	−9.58249e108	−0.266855	−0.133428	−	0.991059i	$-0.542598\pi$
$227$	−9.58249e108	−0.266855	−0.133428	+	0.991059i	$0.542598\pi$
$228$	7.69854e109	1.74758
$229$	2.66341e109	0.493274	0.246637	−	0.969108i	$-0.420674\pi$
$229$	2.66341e109	0.493274	0.246637	+	0.969108i	$0.420674\pi$
$230$	−1.65160e109	−0.249782
$231$	−2.75930e109	−0.341069
$232$	1.33426e110	1.34911
$233$	−7.83842e109	−0.648900	−0.324450	−	0.945903i	$-0.605179\pi$
$233$	−7.83842e109	−0.648900	−0.324450	+	0.945903i	$0.605179\pi$
$234$	−6.54697e109	−0.444123
$235$	7.03018e108	0.0391121
$236$	3.44538e109	0.157336
$237$	−7.24247e110	−2.71700
$238$	−1.79518e110	−0.553707
$239$	3.53328e110	0.896760	0.448380	−	0.893843i	$-0.352001\pi$
$239$	3.53328e110	0.896760	0.448380	+	0.893843i	$0.352001\pi$
$240$	7.43539e109	0.155411
$241$	6.85756e110	1.18135	0.590673	−	0.806911i	$-0.298862\pi$
$241$	6.85756e110	1.18135	0.590673	+	0.806911i	$0.298862\pi$
$242$	3.33646e110	0.474101
$243$	−1.20078e111	−1.40855
$244$	1.36268e111	1.32059
$245$	−5.99473e109	−0.0480338
$246$	1.81545e111	1.20365
$247$	−2.70263e111	−1.48381
$248$	1.46445e111	0.666301
$249$	−8.79664e110	−0.331931
$250$	1.13911e111	0.356743
$251$	−2.00152e111	−0.520633	−0.260317	−	0.965523i	$-0.583827\pi$
$251$	−2.00152e111	−0.520633	−0.260317	+	0.965523i	$0.583827\pi$
$252$	3.15681e111	0.682532
$253$	1.87343e111	0.336925
$254$	−1.67243e111	−0.250369
$255$	−4.97953e111	−0.620969
$256$	−6.71799e111	−0.698362
$257$	−2.15173e112	−1.86594	−0.932972	−	0.359949i	$-0.882794\pi$
$257$	−2.15173e112	−1.86594	−0.932972	+	0.359949i	$0.882794\pi$
$258$	1.23375e111	0.0893123
$259$	1.57189e112	0.950567
$260$	−4.92039e111	−0.248736
$261$	3.54980e112	1.50114
$262$	3.59381e110	0.0127217
$263$	2.80215e112	0.830899	0.415450	−	0.909616i	$-0.363624\pi$
$263$	2.80215e112	0.830899	0.415450	+	0.909616i	$0.363624\pi$
$264$	1.30007e112	0.323136
$265$	−1.66643e111	−0.0347420
$266$	−4.53803e112	−0.794093
$267$	5.78358e111	0.0850008
$268$	5.55099e112	0.685650
$269$	−6.54356e112	−0.679725	−0.339862	−	0.940475i	$-0.610380\pi$
$269$	−6.54356e112	−0.679725	−0.339862	+	0.940475i	$0.610380\pi$
$270$	4.66775e110	0.00408030
$271$	8.26366e112	0.608276	0.304138	−	0.952628i	$-0.401632\pi$
$271$	8.26366e112	0.608276	0.304138	+	0.952628i	$0.401632\pi$
$272$	−5.48714e112	−0.340324
$273$	−2.23341e113	−1.16790
$274$	−9.66950e112	−0.426582
$275$	−5.96355e112	−0.222093
$276$	−4.31945e113	−1.35880
$277$	3.61986e113	0.962460	0.481230	−	0.876595i	$-0.340190\pi$
$277$	3.61986e113	0.962460	0.481230	+	0.876595i	$0.340190\pi$
$278$	3.33659e113	0.750274
$279$	3.89618e113	0.741385
$280$	−1.94009e113	−0.312589
$281$	8.73104e113	1.19185	0.595926	−	0.803040i	$-0.296785\pi$
$281$	8.73104e113	1.19185	0.595926	+	0.803040i	$0.296785\pi$
$282$	−6.40268e112	−0.0740932
$283$	8.05802e113	0.790968	0.395484	−	0.918473i	$-0.370577\pi$
$283$	8.05802e113	0.790968	0.395484	+	0.918473i	$0.370577\pi$
$284$	−1.01006e114	−0.841481
$285$	−1.25877e114	−0.890555
$286$	−1.94359e113	−0.116838
$287$	3.07306e114	1.57059
$288$	−2.34133e114	−1.01792
$289$	9.72373e113	0.359818
$290$	−9.29044e113	−0.292772
$291$	−1.16946e114	−0.314023
$292$	3.24043e114	0.741822
$293$	−7.90158e114	−1.54301	−0.771507	−	0.636221i	$-0.780497\pi$
$293$	−7.90158e114	−1.54301	−0.771507	+	0.636221i	$0.780497\pi$
$294$	5.45965e113	0.0909943
$295$	−5.63346e113	−0.0801773
$296$	−7.40611e114	−0.900587
$297$	−5.29468e112	−0.00550383
$298$	−8.73764e113	−0.0776852
$299$	1.51638e115	1.15371
$300$	1.37498e115	0.895689
$301$	2.08840e114	0.116539
$302$	−1.51296e114	−0.0723610
$303$	4.76958e115	1.95613
$304$	−1.38709e115	−0.488071
$305$	−2.22810e115	−0.672964
$306$	2.25031e115	0.583709
$307$	−7.39463e115	−1.64809	−0.824047	−	0.566521i	$-0.808289\pi$
$307$	−7.39463e115	−1.64809	−0.824047	+	0.566521i	$0.808289\pi$
$308$	9.37157e114	0.179558
$309$	−7.97399e115	−1.31403
$310$	−1.01970e115	−0.144595
$311$	6.85748e115	0.837156	0.418578	−	0.908181i	$-0.362529\pi$
$311$	6.85748e115	0.837156	0.418578	+	0.908181i	$0.362529\pi$
$312$	1.05229e116	1.10649
$313$	−1.86223e116	−1.68741	−0.843706	−	0.536805i	$-0.819631\pi$
$313$	−1.86223e116	−1.68741	−0.843706	+	0.536805i	$0.819631\pi$
$314$	−3.62762e115	−0.283396
$315$	−5.16163e115	−0.347813
$316$	2.45981e116	1.43038
$317$	−6.89517e115	−0.346170	−0.173085	−	0.984907i	$-0.555374\pi$
$317$	−6.89517e115	−0.346170	−0.173085	+	0.984907i	$0.555374\pi$
$318$	1.51769e115	0.0658146
$319$	1.05383e116	0.394913
$320$	2.72292e115	0.0882188
$321$	−2.89748e116	−0.811964
$322$	2.54617e116	0.617433
$323$	9.28943e116	1.95017
$324$	4.13980e116	0.752724
$325$	−4.82697e116	−0.760498
$326$	−5.44342e116	−0.743453
$327$	−4.84139e116	−0.573455
$328$	−1.44790e117	−1.48801
$329$	−1.08380e116	−0.0966806
$330$	−9.05242e115	−0.0701240
$331$	2.05417e117	1.38240	0.691201	−	0.722663i	$-0.257082\pi$
$331$	2.05417e117	1.38240	0.691201	+	0.722663i	$0.257082\pi$
$332$	2.98766e116	0.174747
$333$	−1.97041e117	−1.00207
$334$	9.85131e116	0.435796
$335$	−9.07631e116	−0.349402
$336$	−1.14627e117	−0.384158
$337$	−2.14639e117	−0.626496	−0.313248	−	0.949671i	$-0.601417\pi$
$337$	−2.14639e117	−0.626496	−0.313248	+	0.949671i	$0.601417\pi$
$338$	4.25223e116	0.108141
$339$	3.79329e117	0.840872
$340$	1.69123e117	0.326913
$341$	1.15665e117	0.195040
$342$	5.68855e117	0.837119
$343$	8.19632e117	1.05303
$344$	−9.83973e116	−0.110412
$345$	7.06264e117	0.692435
$346$	−9.97350e117	−0.854691
$347$	−2.55511e117	−0.191465	−0.0957323	−	0.995407i	$-0.530519\pi$
$347$	−2.55511e117	−0.191465	−0.0957323	+	0.995407i	$0.530519\pi$
$348$	−2.42974e118	−1.59267
$349$	−7.79802e117	−0.447303	−0.223652	−	0.974669i	$-0.571798\pi$
$349$	−7.79802e117	−0.447303	−0.223652	+	0.974669i	$0.571798\pi$
$350$	−8.10504e117	−0.406997
$351$	−4.28558e116	−0.0188464
$352$	−6.95067e117	−0.267789
$353$	4.16579e117	0.140661	0.0703305	−	0.997524i	$-0.477595\pi$
$353$	4.16579e117	0.140661	0.0703305	+	0.997524i	$0.477595\pi$
$354$	5.13063e117	0.151887
$355$	1.65153e118	0.428812
$356$	−1.96431e117	−0.0447492
$357$	7.67663e118	1.53497
$358$	−5.34505e118	−0.938406
$359$	−4.71590e118	−0.727232	−0.363616	−	0.931549i	$-0.618458\pi$
$359$	−4.71590e118	−0.727232	−0.363616	+	0.931549i	$0.618458\pi$
$360$	2.43196e118	0.329526
$361$	1.50865e119	1.79681
$362$	−1.72784e118	−0.180948
$363$	−1.42675e119	−1.31428
$364$	7.58547e118	0.614848
$365$	−5.29836e118	−0.378027
$366$	2.02922e119	1.27485
$367$	−1.13188e118	−0.0626368	−0.0313184	−	0.999509i	$-0.509971\pi$
$367$	−1.13188e118	−0.0626368	−0.0313184	+	0.999509i	$0.509971\pi$
$368$	7.78261e118	0.379491
$369$	−3.85216e119	−1.65569
$370$	5.15689e118	0.195437
$371$	2.56904e118	0.0858783
$372$	−2.66682e119	−0.786588
$373$	−2.27689e119	−0.592765	−0.296382	−	0.955069i	$-0.595780\pi$
$373$	−2.27689e119	−0.592765	−0.296382	+	0.955069i	$0.595780\pi$
$374$	6.68047e118	0.153560
$375$	−4.87111e119	−0.988949
$376$	5.10643e118	0.0915973
$377$	8.52979e119	1.35228
$378$	−7.19598e117	−0.0100860
$379$	9.67039e118	0.119873	0.0599364	−	0.998202i	$-0.480910\pi$
$379$	9.67039e118	0.119873	0.0599364	+	0.998202i	$0.480910\pi$
$380$	4.27524e119	0.468839
$381$	7.15172e119	0.694063
$382$	2.35757e119	0.202544
$383$	−1.71702e120	−1.30627	−0.653135	−	0.757241i	$-0.726547\pi$
$383$	−1.71702e120	−1.30627	−0.653135	+	0.757241i	$0.726547\pi$
$384$	1.91266e120	1.28895
$385$	−1.53233e119	−0.0915013
$386$	−1.84449e119	−0.0976265
$387$	−2.61787e119	−0.122854
$388$	3.97190e119	0.165319
$389$	2.27940e120	0.841715	0.420857	−	0.907127i	$-0.361729\pi$
$389$	2.27940e120	0.841715	0.420857	+	0.907127i	$0.361729\pi$
$390$	−7.32714e119	−0.240121
$391$	−5.21206e120	−1.51632
$392$	−4.35432e119	−0.112491
$393$	−1.53680e119	−0.0352666
$394$	−3.22243e120	−0.657067
$395$	−4.02198e120	−0.728911
$396$	−1.17475e120	−0.189287
$397$	−2.02832e120	−0.290655	−0.145327	−	0.989384i	$-0.546424\pi$
$397$	−2.02832e120	−0.290655	−0.145327	+	0.989384i	$0.546424\pi$
$398$	−2.22611e120	−0.283781
$399$	1.94057e121	2.20135
$400$	−2.47738e120	−0.250151
$401$	1.22235e121	1.09896	0.549480	−	0.835507i	$-0.314826\pi$
$401$	1.22235e121	1.09896	0.549480	+	0.835507i	$0.314826\pi$
$402$	8.26618e120	0.661902
$403$	9.36210e120	0.667865
$404$	−1.61992e121	−1.02982
$405$	−6.76890e120	−0.383583
$406$	1.43225e121	0.723699
$407$	−5.84951e120	−0.263621
$408$	−3.61692e121	−1.45426
$409$	−1.63408e121	−0.586326	−0.293163	−	0.956063i	$-0.594708\pi$
$409$	−1.63408e121	−0.586326	−0.293163	+	0.956063i	$0.594708\pi$
$410$	1.00818e121	0.322914
$411$	4.13491e121	1.18255
$412$	2.70825e121	0.691781
$413$	8.68476e120	0.198189
$414$	−3.19170e121	−0.650887
$415$	−4.88506e120	−0.0890498
$416$	−5.62596e121	−0.916973
$417$	−1.42681e122	−2.07988
$418$	1.68875e121	0.220226
$419$	6.80062e121	0.793590	0.396795	−	0.917907i	$-0.370122\pi$
$419$	6.80062e121	0.793590	0.396795	+	0.917907i	$0.370122\pi$
$420$	3.53299e121	0.369020
$421$	9.07457e120	0.0848611	0.0424306	−	0.999099i	$-0.486490\pi$
$421$	9.07457e120	0.0848611	0.0424306	+	0.999099i	$0.486490\pi$
$422$	5.51259e121	0.461665
$423$	1.35857e121	0.101919
$424$	−1.21043e121	−0.0813629
$425$	1.65912e122	0.999520
$426$	−1.50412e122	−0.812335
$427$	3.43492e122	1.66349
$428$	9.84089e121	0.427464
$429$	8.31126e121	0.323894
$430$	6.85142e120	0.0239606
$431$	−6.00864e122	−1.88618	−0.943090	−	0.332537i	$-0.892096\pi$
$431$	−6.00864e122	−1.88618	−0.943090	+	0.332537i	$0.892096\pi$
$432$	−2.19952e120	−0.00619916
$433$	−4.16397e122	−1.05395	−0.526976	−	0.849880i	$-0.676674\pi$
$433$	−4.16397e122	−1.05395	−0.526976	+	0.849880i	$0.676674\pi$
$434$	1.57200e122	0.357422
$435$	3.97281e122	0.811611
$436$	1.64431e122	0.301899
$437$	−1.31755e123	−2.17461
$438$	4.82544e122	0.716128
$439$	−3.92818e122	−0.524314	−0.262157	−	0.965025i	$-0.584434\pi$
$439$	−3.92818e122	−0.524314	−0.262157	+	0.965025i	$0.584434\pi$
$440$	7.21971e121	0.0866903
$441$	−1.15847e122	−0.125167
$442$	5.40725e122	0.525825
$443$	−4.72253e122	−0.413429	−0.206715	−	0.978401i	$-0.566277\pi$
$443$	−4.72253e122	−0.413429	−0.206715	+	0.978401i	$0.566277\pi$
$444$	1.34869e123	1.06317
$445$	3.21180e121	0.0228039
$446$	−2.46045e122	−0.157378
$447$	3.73643e122	0.215356
$448$	−4.19776e122	−0.218067
$449$	3.72064e123	1.74246	0.871230	−	0.490875i	$-0.163323\pi$
$449$	3.72064e123	1.74246	0.871230	+	0.490875i	$0.163323\pi$
$450$	1.01599e123	0.429049
$451$	−1.14359e123	−0.435571
$452$	−1.28834e123	−0.442682
$453$	6.46978e122	0.200596
$454$	4.84648e122	0.135622
$455$	−1.24028e123	−0.313322
$456$	−9.14319e123	−2.08561
$457$	1.39159e123	0.286687	0.143344	−	0.989673i	$-0.454215\pi$
$457$	1.39159e123	0.286687	0.143344	+	0.989673i	$0.454215\pi$
$458$	−1.34706e123	−0.250693
$459$	1.47303e122	0.0247698
$460$	−2.39873e123	−0.364537
$461$	6.88216e123	0.945435	0.472718	−	0.881214i	$-0.343273\pi$
$461$	6.88216e123	0.945435	0.472718	+	0.881214i	$0.343273\pi$
$462$	1.39556e123	0.173339
$463$	−4.77146e123	−0.535964	−0.267982	−	0.963424i	$-0.586357\pi$
$463$	−4.77146e123	−0.535964	−0.267982	+	0.963424i	$0.586357\pi$
$464$	4.37780e123	0.444805
$465$	4.36047e123	0.400840
$466$	3.96439e123	0.329785
$467$	−1.67559e124	−1.26163	−0.630815	−	0.775934i	$-0.717279\pi$
$467$	−1.67559e124	−1.26163	−0.630815	+	0.775934i	$0.717279\pi$
$468$	−9.50859e123	−0.648163
$469$	1.39924e124	0.863683
$470$	−3.55561e122	−0.0198776
$471$	1.55126e124	0.785618
$472$	−4.09191e123	−0.187769
$473$	−7.77164e122	−0.0323199
$474$	3.66299e124	1.38084
$475$	4.19407e124	1.43345
$476$	−2.60726e124	−0.808093
$477$	−3.22036e123	−0.0905315
$478$	−1.78701e124	−0.455753
$479$	−1.44179e124	−0.333656	−0.166828	−	0.985986i	$-0.553352\pi$
$479$	−1.44179e124	−0.333656	−0.166828	+	0.985986i	$0.553352\pi$
$480$	−2.62033e124	−0.550350
$481$	−4.73467e124	−0.902700
$482$	−3.46831e124	−0.600386
$483$	−1.08880e125	−1.71162
$484$	4.84575e124	0.691914
$485$	−6.49438e123	−0.0842455
$486$	6.07314e124	0.715858
$487$	1.20536e125	1.29128	0.645641	−	0.763641i	$-0.276590\pi$
$487$	1.20536e125	1.29128	0.645641	+	0.763641i	$0.276590\pi$
$488$	−1.61840e125	−1.57603
$489$	2.32774e125	2.06097
$490$	3.03192e123	0.0244118
$491$	−9.38769e124	−0.687495	−0.343747	−	0.939062i	$-0.611696\pi$
$491$	−9.38769e124	−0.687495	−0.343747	+	0.939062i	$0.611696\pi$
$492$	2.63669e125	1.75664
$493$	−2.93184e125	−1.77729
$494$	1.36690e125	0.754106
$495$	1.92081e124	0.0964591
$496$	4.80497e124	0.219681
$497$	−2.54606e125	−1.05998
$498$	4.44903e124	0.168694
$499$	5.48346e125	1.89400	0.946999	−	0.321237i	$-0.104099\pi$
$499$	5.48346e125	1.89400	0.946999	+	0.321237i	$0.104099\pi$
$500$	1.65440e125	0.520638
$501$	−4.21266e125	−1.20810
$502$	1.01230e125	0.264597
$503$	−6.31756e125	−1.50535	−0.752676	−	0.658391i	$-0.771237\pi$
$503$	−6.31756e125	−1.50535	−0.752676	+	0.658391i	$0.771237\pi$
$504$	−3.74920e125	−0.814551
$505$	2.64870e125	0.524788
$506$	−9.47514e124	−0.171233
$507$	−1.81835e125	−0.299784
$508$	−2.42898e125	−0.365394
$509$	−1.89152e125	−0.259677	−0.129838	−	0.991535i	$-0.541446\pi$
$509$	−1.89152e125	−0.259677	−0.129838	+	0.991535i	$0.541446\pi$
$510$	2.51847e125	0.315590
$511$	8.16815e125	0.934441
$512$	−5.36051e125	−0.559954
$513$	3.72366e124	0.0355233
$514$	1.08827e126	0.948314
$515$	−4.42821e125	−0.352527
$516$	1.79186e125	0.130344
$517$	4.03317e124	0.0268125
$518$	−7.95005e125	−0.483099
$519$	4.26491e126	2.36934
$520$	5.84373e125	0.296848
$521$	−2.43131e126	−1.12950	−0.564750	−	0.825262i	$-0.691027\pi$
$521$	−2.43131e126	−1.12950	−0.564750	+	0.825262i	$0.691027\pi$
$522$	−1.79536e126	−0.762912
$523$	−3.48691e125	−0.135554	−0.0677770	−	0.997700i	$-0.521591\pi$
$523$	−3.48691e125	−0.135554	−0.0677770	+	0.997700i	$0.521591\pi$
$524$	5.21953e124	0.0185663
$525$	3.46591e126	1.12826
$526$	−1.41723e126	−0.422281
$527$	−3.21792e126	−0.877772
$528$	4.26564e125	0.106539
$529$	3.02036e126	0.690829
$530$	8.42822e124	0.0176566
$531$	−1.08866e126	−0.208928
$532$	−6.59088e126	−1.15892
$533$	−9.25632e126	−1.49150
$534$	−2.92513e125	−0.0431993
$535$	−1.60906e126	−0.217832
$536$	−6.59265e126	−0.818272
$537$	2.28567e127	2.60141
$538$	3.30950e126	0.345451
$539$	−3.43914e125	−0.0329285
$540$	6.77927e124	0.00595488
$541$	1.30995e127	1.05580	0.527902	−	0.849305i	$-0.322979\pi$
$541$	1.30995e127	1.05580	0.527902	+	0.849305i	$0.322979\pi$
$542$	−4.17947e126	−0.309139
$543$	7.38865e126	0.501618
$544$	1.93374e127	1.20517
$545$	−2.68858e126	−0.153846
$546$	1.12958e127	0.593552
$547$	−1.55998e127	−0.752848	−0.376424	−	0.926447i	$-0.622846\pi$
$547$	−1.55998e127	−0.752848	−0.376424	+	0.926447i	$0.622846\pi$
$548$	−1.40436e127	−0.622563
$549$	−4.30577e127	−1.75362
$550$	3.01615e126	0.112872
$551$	−7.41138e127	−2.54888
$552$	5.13001e127	1.62163
$553$	6.20043e127	1.80179
$554$	−1.83080e127	−0.489143
$555$	−2.20521e127	−0.541783
$556$	4.84595e127	1.09497
$557$	−3.34419e127	−0.695063	−0.347531	−	0.937668i	$-0.612980\pi$
$557$	−3.34419e127	−0.695063	−0.347531	+	0.937668i	$0.612980\pi$
$558$	−1.97055e127	−0.376788
$559$	−6.29046e126	−0.110671
$560$	−6.36559e126	−0.103061
$561$	−2.85673e127	−0.425692
$562$	−4.41585e127	−0.605725
$563$	1.02212e128	1.29080	0.645402	−	0.763843i	$-0.276690\pi$
$563$	1.02212e128	1.29080	0.645402	+	0.763843i	$0.276690\pi$
$564$	−9.29903e126	−0.108133
$565$	2.10653e127	0.225588
$566$	−4.07546e127	−0.401987
$567$	1.04352e128	0.948174
$568$	1.19960e128	1.00424
$569$	−7.09301e127	−0.547155	−0.273577	−	0.961850i	$-0.588207\pi$
$569$	−7.09301e127	−0.547155	−0.273577	+	0.961850i	$0.588207\pi$
$570$	6.36642e127	0.452600
$571$	1.97537e128	1.29440	0.647201	−	0.762319i	$-0.275939\pi$
$571$	1.97537e128	1.29440	0.647201	+	0.762319i	$0.275939\pi$
$572$	−2.82280e127	−0.170516
$573$	−1.00815e128	−0.561484
$574$	−1.55424e128	−0.798208
$575$	−2.35318e128	−1.11455
$576$	5.26201e127	0.229883
$577$	−1.23481e128	−0.497652	−0.248826	−	0.968548i	$-0.580045\pi$
$577$	−1.23481e128	−0.497652	−0.248826	+	0.968548i	$0.580045\pi$
$578$	−4.91792e127	−0.182868
$579$	7.88750e127	0.270636
$580$	−1.34931e128	−0.427278
$581$	7.53099e127	0.220121
$582$	5.91470e127	0.159593
$583$	−9.56023e126	−0.0238166
$584$	−3.84851e128	−0.885309
$585$	1.55473e128	0.330299
$586$	3.99634e128	0.784194
$587$	−1.66918e128	−0.302574	−0.151287	−	0.988490i	$-0.548342\pi$
$587$	−1.66918e128	−0.302574	−0.151287	+	0.988490i	$0.548342\pi$
$588$	7.92941e127	0.132799
$589$	−8.13456e128	−1.25885
$590$	2.84920e127	0.0407479
$591$	1.37799e129	1.82150
$592$	−2.43001e128	−0.296926
$593$	1.16393e129	1.31487	0.657434	−	0.753512i	$-0.271642\pi$
$593$	1.16393e129	1.31487	0.657434	+	0.753512i	$0.271642\pi$
$594$	2.67786e126	0.00279717
$595$	4.26308e128	0.411798
$596$	−1.26902e128	−0.113375
$597$	9.51938e128	0.786687
$598$	−7.66930e128	−0.586342
$599$	1.69191e127	0.0119682	0.00598412	−	0.999982i	$-0.498095\pi$
$599$	1.69191e127	0.0119682	0.00598412	+	0.999982i	$0.498095\pi$
$600$	−1.63300e129	−1.06894
$601$	−5.01379e128	−0.303741	−0.151870	−	0.988400i	$-0.548530\pi$
$601$	−5.01379e128	−0.303741	−0.151870	+	0.988400i	$0.548530\pi$
$602$	−1.05624e128	−0.0592278
$603$	−1.75398e129	−0.910480
$604$	−2.19737e128	−0.105605
$605$	−7.92319e128	−0.352594
$606$	−2.41228e129	−0.994149
$607$	1.33417e129	0.509258	0.254629	−	0.967039i	$-0.418047\pi$
$607$	1.33417e129	0.509258	0.254629	+	0.967039i	$0.418047\pi$
$608$	4.88829e129	1.72839
$609$	−6.12464e129	−2.00621
$610$	1.12689e129	0.342015
$611$	3.26450e128	0.0918122
$612$	3.26827e129	0.851878
$613$	2.92658e129	0.707046	0.353523	−	0.935426i	$-0.384984\pi$
$613$	2.92658e129	0.707046	0.353523	+	0.935426i	$0.384984\pi$
$614$	3.73994e129	0.837598
$615$	−4.31120e129	−0.895170
$616$	−1.11302e129	−0.214289
$617$	6.96398e129	1.24336	0.621681	−	0.783270i	$-0.286450\pi$
$617$	6.96398e129	1.24336	0.621681	+	0.783270i	$0.286450\pi$
$618$	4.03296e129	0.667821
$619$	−8.69061e129	−1.33486	−0.667429	−	0.744673i	$-0.732605\pi$
$619$	−8.69061e129	−1.33486	−0.667429	+	0.744673i	$0.732605\pi$
$620$	−1.48097e129	−0.211025
$621$	−2.08925e128	−0.0276205
$622$	−3.46827e129	−0.425461
$623$	−4.95144e128	−0.0563686
$624$	3.45266e129	0.364814
$625$	6.03412e129	0.591825
$626$	9.41849e129	0.857580
$627$	−7.22150e129	−0.610502
$628$	−5.26863e129	−0.413594
$629$	1.62739e130	1.18642
$630$	2.61057e129	0.176766
$631$	−1.68043e130	−1.05695	−0.528475	−	0.848949i	$-0.677236\pi$
$631$	−1.68043e130	−1.05695	−0.528475	+	0.848949i	$0.677236\pi$
$632$	−2.92140e130	−1.70705
$633$	−2.35732e130	−1.27981
$634$	3.48733e129	0.175931
$635$	3.97158e129	0.186202
$636$	2.20424e129	0.0960513
$637$	−2.78368e129	−0.112755
$638$	−5.32987e129	−0.200704
$639$	3.19155e130	1.11741
$640$	1.06216e130	0.345797
$641$	1.12855e130	0.341683	0.170841	−	0.985299i	$-0.445351\pi$
$641$	1.12855e130	0.341683	0.170841	+	0.985299i	$0.445351\pi$
$642$	1.46544e130	0.412658
$643$	1.78740e130	0.468178	0.234089	−	0.972215i	$-0.424789\pi$
$643$	1.78740e130	0.468178	0.234089	+	0.972215i	$0.424789\pi$
$644$	3.69797e130	0.901095
$645$	−2.92983e129	−0.0664225
$646$	−4.69827e130	−0.991118
$647$	7.40078e130	1.45288	0.726438	−	0.687232i	$-0.241175\pi$
$647$	7.40078e130	1.45288	0.726438	+	0.687232i	$0.241175\pi$
$648$	−4.91664e130	−0.898320
$649$	−3.23189e129	−0.0549639
$650$	2.44131e130	0.386502
$651$	−6.72226e130	−0.990830
$652$	−7.90584e130	−1.08501
$653$	8.19216e130	1.04697	0.523487	−	0.852034i	$-0.324631\pi$
$653$	8.19216e130	1.04697	0.523487	+	0.852034i	$0.324631\pi$
$654$	2.44860e130	0.291442
$655$	−8.53434e128	−0.00946127
$656$	−4.75069e130	−0.490600
$657$	−1.02390e131	−0.985072
$658$	5.48147e129	0.0491352
$659$	1.38301e131	1.15519	0.577597	−	0.816322i	$-0.303991\pi$
$659$	1.38301e131	1.15519	0.577597	+	0.816322i	$0.303991\pi$
$660$	−1.31474e130	−0.102340
$661$	−1.17338e131	−0.851279	−0.425640	−	0.904893i	$-0.639951\pi$
$661$	−1.17338e131	−0.851279	−0.425640	+	0.904893i	$0.639951\pi$
$662$	−1.03892e131	−0.702567
$663$	−2.31227e131	−1.45767
$664$	−3.54830e130	−0.208547
$665$	1.07766e131	0.590576
$666$	9.96561e130	0.509275
$667$	4.15834e131	1.98184
$668$	1.43077e131	0.636010
$669$	1.05215e131	0.436276
$670$	4.59047e130	0.177574
$671$	−1.27825e131	−0.461336
$672$	4.03960e131	1.36040
$673$	−5.22348e131	−1.64157	−0.820786	−	0.571236i	$-0.806464\pi$
$673$	−5.22348e131	−1.64157	−0.820786	+	0.571236i	$0.806464\pi$
$674$	1.08557e131	0.318399
$675$	6.65055e129	0.0182067
$676$	6.17578e130	0.157823
$677$	−1.57989e131	−0.376925	−0.188462	−	0.982080i	$-0.560350\pi$
$677$	−1.57989e131	−0.376925	−0.188462	+	0.982080i	$0.560350\pi$
$678$	−1.91851e131	−0.427350
$679$	1.00120e131	0.208245
$680$	−2.00859e131	−0.390146
$681$	−2.07247e131	−0.375965
$682$	−5.84994e130	−0.0991238
$683$	−7.37705e131	−1.16767	−0.583834	−	0.811873i	$-0.698448\pi$
$683$	−7.37705e131	−1.16767	−0.583834	+	0.811873i	$0.698448\pi$
$684$	8.26184e131	1.22171
$685$	2.29625e131	0.317254
$686$	−4.14541e131	−0.535175
$687$	5.76034e131	0.694961
$688$	−3.22850e130	−0.0364031
$689$	−7.73817e130	−0.0815538
$690$	−3.57203e131	−0.351911
$691$	−3.20174e131	−0.294888	−0.147444	−	0.989070i	$-0.547105\pi$
$691$	−3.20174e131	−0.294888	−0.147444	+	0.989070i	$0.547105\pi$
$692$	−1.44852e132	−1.24735
$693$	−2.96120e131	−0.238436
$694$	1.29228e131	0.0973065
$695$	−7.92351e131	−0.557987
$696$	2.88569e132	1.90073
$697$	3.18156e132	1.96027
$698$	3.94396e131	0.227329
$699$	−1.69527e132	−0.914218
$700$	−1.17715e132	−0.593980
$701$	7.57694e131	0.357772	0.178886	−	0.983870i	$-0.442751\pi$
$701$	7.57694e131	0.357772	0.178886	+	0.983870i	$0.442751\pi$
$702$	2.16749e130	0.00957816
$703$	4.11387e132	1.70148
$704$	1.56212e131	0.0604766
$705$	1.52047e131	0.0551039
$706$	−2.10691e131	−0.0714870
$707$	−4.08334e132	−1.29722
$708$	7.45155e131	0.221667
$709$	−2.69771e132	−0.751529	−0.375764	−	0.926715i	$-0.622620\pi$
$709$	−2.69771e132	−0.751529	−0.375764	+	0.926715i	$0.622620\pi$
$710$	−8.35284e131	−0.217932
$711$	−7.77241e132	−1.89941
$712$	2.33292e131	0.0534048
$713$	4.56409e132	0.978793
$714$	−3.88257e132	−0.780103
$715$	4.61551e131	0.0868937
$716$	−7.76296e132	−1.36953
$717$	7.64168e132	1.26342
$718$	2.38514e132	0.369595
$719$	4.75148e132	0.690137	0.345069	−	0.938577i	$-0.387856\pi$
$719$	4.75148e132	0.690137	0.345069	+	0.938577i	$0.387856\pi$
$720$	7.97945e131	0.108645
$721$	6.82670e132	0.871407
$722$	−7.63019e132	−0.913179
$723$	1.48313e133	1.66437
$724$	−2.50945e132	−0.264080
$725$	−1.32369e133	−1.30638
$726$	7.21599e132	0.667948
$727$	1.00321e133	0.871051	0.435526	−	0.900176i	$-0.356563\pi$
$727$	1.00321e133	0.871051	0.435526	+	0.900176i	$0.356563\pi$
$728$	−9.00891e132	−0.733775
$729$	−1.26892e133	−0.969623
$730$	2.67972e132	0.192122
$731$	2.16214e132	0.145454
$732$	2.94717e133	1.86055
$733$	2.91877e132	0.172928	0.0864640	−	0.996255i	$-0.472443\pi$
$733$	2.91877e132	0.172928	0.0864640	+	0.996255i	$0.472443\pi$
$734$	5.72467e131	0.0318334
$735$	−1.29652e132	−0.0676735
$736$	−2.74270e133	−1.34388
$737$	−5.20703e132	−0.239525
$738$	1.94829e133	0.841457
$739$	−3.91770e133	−1.58878	−0.794391	−	0.607406i	$-0.792210\pi$
$739$	−3.91770e133	−1.58878	−0.794391	+	0.607406i	$0.792210\pi$
$740$	7.48968e132	0.285225
$741$	−5.84517e133	−2.09050
$742$	−1.29933e132	−0.0436452
$743$	6.95679e132	0.219497	0.109749	−	0.993959i	$-0.464995\pi$
$743$	6.95679e132	0.219497	0.109749	+	0.993959i	$0.464995\pi$
$744$	3.16726e133	0.938734
$745$	2.07496e132	0.0577753
$746$	1.15157e133	0.301256
$747$	−9.44030e132	−0.232048
$748$	9.70248e132	0.224108
$749$	2.48059e133	0.538457
$750$	2.46363e133	0.502605
$751$	4.33173e133	0.830624	0.415312	−	0.909679i	$-0.363672\pi$
$751$	4.33173e133	0.830624	0.415312	+	0.909679i	$0.363672\pi$
$752$	1.67546e132	0.0301999
$753$	−4.32883e133	−0.733506
$754$	−4.31407e133	−0.687257
$755$	3.59287e132	0.0538157
$756$	−1.04512e132	−0.0147198
$757$	7.50220e133	0.993643	0.496821	−	0.867853i	$-0.334500\pi$
$757$	7.50220e133	0.993643	0.496821	+	0.867853i	$0.334500\pi$
$758$	−4.89094e132	−0.0609220
$759$	4.05180e133	0.474685
$760$	−5.07751e133	−0.559524
$761$	3.42648e133	0.355191	0.177595	−	0.984104i	$-0.443168\pi$
$761$	3.42648e133	0.355191	0.177595	+	0.984104i	$0.443168\pi$
$762$	−3.61708e133	−0.352738
$763$	4.14481e133	0.380289
$764$	3.42406e133	0.295597
$765$	−5.34389e133	−0.434111
$766$	8.68409e133	0.663875
$767$	−2.61593e133	−0.188209
$768$	−1.45295e134	−0.983904
$769$	4.49538e132	0.0286544	0.0143272	−	0.999897i	$-0.495439\pi$
$769$	4.49538e132	0.0286544	0.0143272	+	0.999897i	$0.495439\pi$
$770$	7.74996e132	0.0465030
$771$	−4.65371e134	−2.62888
$772$	−2.67888e133	−0.142478
$773$	6.94124e133	0.347609	0.173804	−	0.984780i	$-0.444394\pi$
$773$	6.94124e133	0.347609	0.173804	+	0.984780i	$0.444394\pi$
$774$	1.32403e133	0.0624370
$775$	−1.45285e134	−0.645197
$776$	−4.71724e133	−0.197296
$777$	3.39963e134	1.33923
$778$	−1.15284e134	−0.427778
$779$	8.04265e134	2.81130
$780$	−1.06417e134	−0.350438
$781$	9.47472e133	0.293963
$782$	2.63608e134	0.770626
$783$	−1.17523e133	−0.0323742
$784$	−1.42869e133	−0.0370886
$785$	8.61462e133	0.210764
$786$	7.77259e132	0.0179233
$787$	−4.53355e134	−0.985401	−0.492700	−	0.870199i	$-0.663990\pi$
$787$	−4.53355e134	−0.985401	−0.492700	+	0.870199i	$0.663990\pi$
$788$	−4.68015e134	−0.958938
$789$	6.06040e134	1.17063
$790$	2.03417e134	0.370449
$791$	−3.24751e134	−0.557628
$792$	1.39520e134	0.225899
$793$	−1.03463e135	−1.57972
$794$	1.02585e134	0.147717
$795$	−3.60411e133	−0.0489471
$796$	−3.23312e134	−0.414157
$797$	8.18029e134	0.988455	0.494228	−	0.869333i	$-0.335451\pi$
$797$	8.18029e134	0.988455	0.494228	+	0.869333i	$0.335451\pi$
$798$	−9.81471e134	−1.11878
$799$	−1.12207e134	−0.120668
$800$	8.73061e134	0.885850
$801$	6.20676e133	0.0594228
$802$	−6.18220e134	−0.558516
$803$	−3.03964e134	−0.259149
$804$	1.20055e135	0.965994
$805$	−6.04647e134	−0.459191
$806$	−4.73502e134	−0.339424
$807$	−1.41522e135	−0.957646
$808$	1.92391e135	1.22901
$809$	−7.01065e134	−0.422816	−0.211408	−	0.977398i	$-0.567805\pi$
$809$	−7.01065e134	−0.422816	−0.211408	+	0.977398i	$0.567805\pi$
$810$	3.42347e134	0.194945
$811$	−2.27619e134	−0.122388	−0.0611940	−	0.998126i	$-0.519491\pi$
$811$	−2.27619e134	−0.122388	−0.0611940	+	0.998126i	$0.519491\pi$
$812$	2.08015e135	1.05618
$813$	1.78724e135	0.856983
$814$	2.95848e134	0.133978
$815$	1.29267e135	0.552914
$816$	−1.18674e135	−0.479473
$817$	5.46567e134	0.208602
$818$	8.26458e134	0.297984
$819$	−2.39683e135	−0.816462
$820$	1.46424e135	0.471268
$821$	−2.38392e135	−0.724996	−0.362498	−	0.931985i	$-0.618076\pi$
$821$	−2.38392e135	−0.724996	−0.362498	+	0.931985i	$0.618076\pi$
$822$	−2.09129e135	−0.601000
$823$	4.89963e135	1.33067	0.665335	−	0.746545i	$-0.268289\pi$
$823$	4.89963e135	1.33067	0.665335	+	0.746545i	$0.268289\pi$
$824$	−3.21647e135	−0.825589
$825$	−1.28978e135	−0.312901
$826$	−4.39244e134	−0.100724
$827$	−2.84246e135	−0.616152	−0.308076	−	0.951362i	$-0.599685\pi$
$827$	−2.84246e135	−0.616152	−0.308076	+	0.951362i	$0.599685\pi$
$828$	−4.63551e135	−0.949919
$829$	−5.72864e135	−1.10985	−0.554927	−	0.831899i	$-0.687254\pi$
$829$	−5.72864e135	−1.10985	−0.554927	+	0.831899i	$0.687254\pi$
$830$	2.47069e134	0.0452571
$831$	7.82892e135	1.35598
$832$	1.26440e135	0.207086
$833$	9.56802e134	0.148194
$834$	7.21628e135	1.05704
$835$	−2.33942e135	−0.324106
$836$	2.45268e135	0.321403
$837$	−1.28990e134	−0.0159890
$838$	−3.43951e135	−0.403320
$839$	−1.53346e136	−1.70114	−0.850571	−	0.525860i	$-0.823743\pi$
$839$	−1.53346e136	−1.70114	−0.850571	+	0.525860i	$0.823743\pi$
$840$	−4.19597e135	−0.440398
$841$	1.33215e136	1.32293
$842$	−4.58960e134	−0.0431283
$843$	1.88832e136	1.67917
$844$	8.00629e135	0.673764
$845$	−1.00979e135	−0.0804255
$846$	−6.87117e134	−0.0517975
$847$	1.22147e136	0.871573
$848$	−3.97151e134	−0.0268256
$849$	1.74276e136	1.11437
$850$	−8.39122e135	−0.507978
$851$	−2.30819e136	−1.32296
$852$	−2.18453e136	−1.18554
$853$	1.78771e136	0.918684	0.459342	−	0.888260i	$-0.348085\pi$
$853$	1.78771e136	0.918684	0.459342	+	0.888260i	$0.348085\pi$
$854$	−1.73726e136	−0.845423
$855$	−1.35088e136	−0.622575
$856$	−1.16876e136	−0.510146
$857$	−1.68084e136	−0.694894	−0.347447	−	0.937700i	$-0.612951\pi$
$857$	−1.68084e136	−0.694894	−0.347447	+	0.937700i	$0.612951\pi$
$858$	−4.20354e135	−0.164610
$859$	−4.56777e136	−1.69442	−0.847212	−	0.531255i	$-0.821721\pi$
$859$	−4.56777e136	−1.69442	−0.847212	+	0.531255i	$0.821721\pi$
$860$	9.95075e134	0.0349686
$861$	6.64631e136	2.21276
$862$	3.03896e136	0.958599
$863$	−2.14397e136	−0.640791	−0.320395	−	0.947284i	$-0.603816\pi$
$863$	−2.14397e136	−0.640791	−0.320395	+	0.947284i	$0.603816\pi$
$864$	7.75139e134	0.0219528
$865$	2.36844e136	0.635643
$866$	2.10599e136	0.535641
$867$	2.10302e136	0.506938
$868$	2.28312e136	0.521629
$869$	−2.30739e136	−0.499690
$870$	−2.00931e136	−0.412478
$871$	−4.21463e136	−0.820192
$872$	−1.95287e136	−0.360294
$873$	−1.25503e136	−0.219529
$874$	6.66372e136	1.10518
$875$	4.17026e136	0.655825
$876$	7.00830e136	1.04513
$877$	−4.90563e136	−0.693767	−0.346883	−	0.937908i	$-0.612760\pi$
$877$	−4.90563e136	−0.693767	−0.346883	+	0.937908i	$0.612760\pi$
$878$	1.98673e136	0.266468
$879$	−1.70893e137	−2.17391
$880$	2.36885e135	0.0285820
$881$	1.65361e137	1.89257	0.946287	−	0.323328i	$-0.104802\pi$
$881$	1.65361e137	1.89257	0.946287	+	0.323328i	$0.104802\pi$
$882$	5.85914e135	0.0636128
$883$	−3.55857e136	−0.366524	−0.183262	−	0.983064i	$-0.558666\pi$
$883$	−3.55857e136	−0.366524	−0.183262	+	0.983064i	$0.558666\pi$
$884$	7.85330e136	0.767401
$885$	−1.21839e136	−0.112960
$886$	2.38849e136	0.210114
$887$	−1.45980e137	−1.21856	−0.609278	−	0.792956i	$-0.708541\pi$
$887$	−1.45980e137	−1.21856	−0.609278	+	0.792956i	$0.708541\pi$
$888$	−1.60177e137	−1.26881
$889$	−6.12273e136	−0.460271
$890$	−1.62442e135	−0.0115894
$891$	−3.88328e136	−0.262957
$892$	−3.57346e136	−0.229680
$893$	−2.83646e136	−0.173055
$894$	−1.88975e136	−0.109449
$895$	1.26930e137	0.697903
$896$	−1.63746e137	−0.854770
$897$	3.27958e137	1.62543
$898$	−1.88177e137	−0.885556
$899$	2.56735e137	1.14725
$900$	1.47559e137	0.626163
$901$	2.65975e136	0.107186
$902$	5.78385e136	0.221367
$903$	4.51674e136	0.164189
$904$	1.53010e137	0.528308
$905$	4.10315e136	0.134573
$906$	−3.27218e136	−0.101947
$907$	−4.43491e137	−1.31264	−0.656321	−	0.754482i	$-0.727888\pi$
$907$	−4.43491e137	−1.31264	−0.656321	+	0.754482i	$0.727888\pi$
$908$	7.03886e136	0.197929
$909$	5.11857e137	1.36750
$910$	6.27292e136	0.159237
$911$	−5.56999e136	−0.134354	−0.0671769	−	0.997741i	$-0.521399\pi$
$911$	−5.56999e136	−0.134354	−0.0671769	+	0.997741i	$0.521399\pi$
$912$	−2.99996e137	−0.687630
$913$	−2.80253e136	−0.0610463
$914$	−7.03818e136	−0.145701
$915$	−4.81886e137	−0.948120
$916$	−1.95642e137	−0.365867
$917$	1.31569e136	0.0233872
$918$	−7.45006e135	−0.0125885
$919$	3.23898e137	0.520280	0.260140	−	0.965571i	$-0.416231\pi$
$919$	3.23898e137	0.520280	0.260140	+	0.965571i	$0.416231\pi$
$920$	2.84886e137	0.435048
$921$	−1.59929e138	−2.32196
$922$	−3.48075e137	−0.480491
$923$	7.66896e137	1.00660
$924$	2.02686e137	0.252974
$925$	7.34747e137	0.872062
$926$	2.41324e137	0.272389
$927$	−8.55745e137	−0.918622
$928$	−1.54280e138	−1.57517
$929$	1.34434e138	1.30551	0.652753	−	0.757571i	$-0.273614\pi$
$929$	1.34434e138	1.30551	0.652753	+	0.757571i	$0.273614\pi$
$930$	−2.20537e137	−0.203715
$931$	2.41869e137	0.212530
$932$	5.75774e137	0.481296
$933$	1.48311e138	1.17945
$934$	8.47452e137	0.641188
$935$	−1.58643e137	−0.114204
$936$	1.12929e138	0.773533
$937$	2.26993e138	1.47952	0.739761	−	0.672870i	$-0.234938\pi$
$937$	2.26993e138	1.47952	0.739761	+	0.672870i	$0.234938\pi$
$938$	−7.07685e137	−0.438943
$939$	−4.02757e138	−2.37735
$940$	−5.16405e136	−0.0290098
$941$	3.49457e138	1.86843	0.934213	−	0.356716i	$-0.116104\pi$
$941$	3.49457e138	1.86843	0.934213	+	0.356716i	$0.116104\pi$
$942$	−7.84571e137	−0.399269
$943$	−4.51252e138	−2.18588
$944$	−1.34259e137	−0.0619079
$945$	1.70885e136	0.00750110
$946$	3.93062e136	0.0164257
$947$	−3.15534e138	−1.25537	−0.627685	−	0.778467i	$-0.715997\pi$
$947$	−3.15534e138	−1.25537	−0.627685	+	0.778467i	$0.715997\pi$
$948$	5.31999e138	2.01522
$949$	−2.46032e138	−0.887387
$950$	−2.12121e138	−0.728511
$951$	−1.49127e138	−0.487710
$952$	3.09652e138	0.964398
$953$	2.76357e138	0.819692	0.409846	−	0.912155i	$-0.365582\pi$
$953$	2.76357e138	0.819692	0.409846	+	0.912155i	$0.365582\pi$
$954$	1.62874e137	0.0460101
$955$	−5.59860e137	−0.150634
$956$	−2.59539e138	−0.665136
$957$	2.27918e138	0.556383
$958$	7.29204e137	0.169571
$959$	−3.53998e138	−0.784216
$960$	5.88905e137	0.124289
$961$	−2.15536e138	−0.433393
$962$	2.39463e138	0.458772
$963$	−3.10949e138	−0.567632
$964$	−5.03725e138	−0.876217
$965$	4.38018e137	0.0726059
$966$	5.50678e138	0.869884
$967$	6.63903e138	0.999479	0.499740	−	0.866176i	$-0.333429\pi$
$967$	6.63903e138	0.999479	0.499740	+	0.866176i	$0.333429\pi$
$968$	−5.75508e138	−0.825747
$969$	2.00909e139	2.74754
$970$	3.28462e137	0.0428154
$971$	−1.84814e138	−0.229636	−0.114818	−	0.993387i	$-0.536628\pi$
$971$	−1.84814e138	−0.229636	−0.114818	+	0.993387i	$0.536628\pi$
$972$	8.82041e138	1.04474
$973$	1.22152e139	1.37928
$974$	−6.09629e138	−0.656258
$975$	−1.04396e139	−1.07145
$976$	−5.31009e138	−0.519620
$977$	−1.80423e139	−1.68342	−0.841712	−	0.539926i	$-0.818452\pi$
$977$	−1.80423e139	−1.68342	−0.841712	+	0.539926i	$0.818452\pi$
$978$	−1.17729e139	−1.04743
$979$	1.84259e137	0.0156327
$980$	4.40345e137	0.0356271
$981$	−5.19563e138	−0.400894
$982$	4.74796e138	0.349400
$983$	5.12719e138	0.359866	0.179933	−	0.983679i	$-0.442412\pi$
$983$	5.12719e138	0.359866	0.179933	+	0.983679i	$0.442412\pi$
$984$	−3.13148e139	−2.09641
$985$	7.65242e138	0.488668
$986$	1.48282e139	0.903259
$987$	−2.34401e138	−0.136211
$988$	1.98523e139	1.10056
$989$	−3.06664e138	−0.162194
$990$	−9.71479e137	−0.0490227
$991$	−2.29485e139	−1.10491	−0.552457	−	0.833541i	$-0.686310\pi$
$991$	−2.29485e139	−1.10491	−0.552457	+	0.833541i	$0.686310\pi$
$992$	−1.69334e139	−0.777948
$993$	4.44269e139	1.94763
$994$	1.28771e139	0.538703
$995$	5.28641e138	0.211051
$996$	6.46161e138	0.246196
$997$	3.11371e139	1.13228	0.566139	−	0.824310i	$-0.308436\pi$
$997$	3.11371e139	1.13228	0.566139	+	0.824310i	$0.308436\pi$
$998$	−2.77334e139	−0.962571
$999$	6.52338e137	0.0216111

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1.94.a.a.1.3	✓	7
3.2	odd	2		9.94.a.b.1.5		7

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1.94.a.a.1.3	✓	7	1.1	even	1	trivial
9.94.a.b.1.5		7	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:	\( k \)	\(=\)	\( 94 \)
Character orbit:	\([\chi]\)	\(=\)	1.a (trivial)

\(f(q)\)	\(=\)	\(q-5.05764e13 q^{2} +2.16277e22 q^{3} -7.34554e27 q^{4} +1.20105e32 q^{5} -1.09385e36 q^{6} -1.85159e39 q^{7} +8.72396e41 q^{8} +2.32102e44 q^{9} +O(q^{10})\)	\(q-5.05764e13 q^{2} +2.16277e22 q^{3} -7.34554e27 q^{4} +1.20105e32 q^{5} -1.09385e36 q^{6} -1.85159e39 q^{7} +8.72396e41 q^{8} +2.32102e44 q^{9} -6.07451e45 q^{10} +6.89038e47 q^{11} -1.58867e50 q^{12} +5.57716e51 q^{13} +9.36469e52 q^{14} +2.59760e54 q^{15} +2.86240e55 q^{16} -1.91697e57 q^{17} -1.17389e58 q^{18} -4.84589e59 q^{19} -8.82240e59 q^{20} -4.00457e61 q^{21} -3.48491e61 q^{22} +2.71891e63 q^{23} +1.88679e64 q^{24} -8.65489e64 q^{25} -2.82073e65 q^{26} -7.68416e64 q^{27} +1.36009e67 q^{28} +1.52941e68 q^{29} -1.31378e68 q^{30} +1.67865e69 q^{31} -1.00875e70 q^{32} +1.49023e70 q^{33} +9.69535e70 q^{34} -2.22386e71 q^{35} -1.70492e72 q^{36} -8.48939e72 q^{37} +2.45088e73 q^{38} +1.20621e74 q^{39} +1.04780e74 q^{40} -1.65968e75 q^{41} +2.02537e75 q^{42} -1.12790e75 q^{43} -5.06136e75 q^{44} +2.78767e76 q^{45} -1.37513e77 q^{46} +5.85334e76 q^{47} +6.19072e77 q^{48} -4.99122e77 q^{49} +4.37733e78 q^{50} -4.14596e79 q^{51} -4.09673e79 q^{52} -1.38747e79 q^{53} +3.88637e78 q^{54} +8.27573e79 q^{55} -1.61532e81 q^{56} -1.04806e82 q^{57} -7.73524e81 q^{58} -4.69043e81 q^{59} -1.90808e82 q^{60} -1.85512e83 q^{61} -8.49001e82 q^{62} -4.29758e83 q^{63} +2.26711e83 q^{64} +6.69848e83 q^{65} -7.53706e83 q^{66} -7.55695e84 q^{67} +1.40812e85 q^{68} +5.88037e85 q^{69} +1.12475e85 q^{70} +1.37506e86 q^{71} +2.02485e86 q^{72} -4.41142e86 q^{73} +4.29363e86 q^{74} -1.87185e87 q^{75} +3.55957e87 q^{76} -1.27582e87 q^{77} -6.10059e87 q^{78} -3.34870e88 q^{79} +3.43790e87 q^{80} -5.63579e88 q^{81} +8.39409e88 q^{82} -4.06731e88 q^{83} +2.94157e89 q^{84} -2.30239e89 q^{85} +5.70450e88 q^{86} +3.30777e90 q^{87} +6.01114e89 q^{88} +2.67415e89 q^{89} -1.40991e90 q^{90} -1.03266e91 q^{91} -1.99718e91 q^{92} +3.63053e91 q^{93} -2.96041e90 q^{94} -5.82018e91 q^{95} -2.18169e92 q^{96} -5.40723e91 q^{97} +2.52438e91 q^{98} +1.59927e92 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 7 q + 43735426713792 q^{2} - 36\!\cdots\!84 q^{3}+ \cdots + 36\!\cdots\!11 q^{9}+O(q^{10}) \) 7 * q + 43735426713792 * q^2 - 3678766354327579216884 * q^3 + 37433779444352805880587218944 * q^4 - 242501922056818695041616562179750 * q^5 - 3422349689703076907975614807426150656 * q^6 - 921137753903839555947108372394316103208 * q^7 + 628568314501252186502498490389635108700160 * q^8 + 362824653360866901561998689210341299050559211 * q^9	\( 7 q + 43735426713792 q^{2} - 36\!\cdots\!84 q^{3}+ \cdots + 30\!\cdots\!52 q^{99}+O(q^{100}) \) 7 * q + 43735426713792 * q^2 - 3678766354327579216884 * q^3 + 37433779444352805880587218944 * q^4 - 242501922056818695041616562179750 * q^5 - 3422349689703076907975614807426150656 * q^6 - 921137753903839555947108372394316103208 * q^7 + 628568314501252186502498490389635108700160 * q^8 + 362824653360866901561998689210341299050559211 * q^9 + 56663128890275718532856219951648854919834448000 * q^10 + 1081566396126190174166498109003279139923369012324 * q^11 - 163904625261310040243241458042755377696324875010048 * q^12 + 1923851638471797431690458036346871401286646408469426 * q^13 - 827492161115181455891429526236298470299001717526508032 * q^14 - 16711611501720521025854082681912174509227777477242411000 * q^15 - 183863117199568288307852091185855957272115704336744448 * q^16 + 809325537307953309871783611300921224816172571619454935742 * q^17 + 79483944128603792717921302063558947044650774054000109708736 * q^18 - 491316328040151561437984621759105514680907320256463264658500 * q^19 - 5819101371751539891329503686613738398860076574931824253952000 * q^20 + 54451750333719895476183963426175615210898459319681281516277984 * q^21 + 341061341496448817039487179432626029859991533289656810924326144 * q^22 - 2595697104202345855126053487687658963668179272707633091075699064 * q^23 - 29432689846399066174371175818785662556182882963620634526849433600 * q^24 + 184388886386678531186865888507627315189418933935123407708899515625 * q^25 + 793059166145746283698718389909557916534745558035448772312212840064 * q^26 - 10506923232698637098067136941837198924358450251426727402321208664840 * q^27 + 1916814131388145595393790805747801246689773266225672358812878209024 * q^28 + 115585291038420509795092429775705167101645550654624527668945364036450 * q^29 - 646359246874848354315998274237243944693324584248820365706098812352000 * q^30 - 1163635467946810748613893942791764663199899897323284701513531956983456 * q^31 - 7066990866795922437106429389517828098400874624281122281464920526553088 * q^32 + 66569296470254314915045188377632673804554883301553196046747543676316112 * q^33 + 80911624156374405155780927188384543491071504244617539921495324380294528 * q^34 - 1672188852118103650980495790489284130570309869892526153633308501275462000 * q^35 + 5276416924359744904633666070671763693285317535397001093231145577416896512 * q^36 + 11072759435314078994932599484815080247923078570346623467670584315337670842 * q^37 - 42692186143014046654789275667852179938472092905944200699148410427788924160 * q^38 - 205635087839752927920079557406846610376307390801963146422737416149757222168 * q^39 + 760187696799287916151508882607919116749295190931669242261910585944965120000 * q^40 - 509603803596826806676973650829096820638503322986104149790656476262528674746 * q^41 - 542653738615875619591084295077236547022836265832353730045755853854336280576 * q^42 - 7275658116979055674748970912580687053338617746072325435955591393683798211644 * q^43 + 9423347779397833928027118997217234224491886242773059800183027480258516369408 * q^44 + 164505351109492760826482356226220602919737242087979463171032783958351054923250 * q^45 - 639778771092842366359510076082228574613573083413403803040568658686807125218816 * q^46 - 371149830895115606730684780470708713676568637183334957675426341554516993409008 * q^47 - 416843258596979693775599022471376378646238618283847940753742770006189894795264 * q^48 + 2561975156227711495237514871966779964501558283497058708235084248829398599957999 * q^49 - 31492320141514234591073138519794385457712593727985587891779934655429621403000000 * q^50 - 55702073279983479511744597938778959921377812834972727705529236388320801422608936 * q^51 - 55278983045853834535146427408736596689073596604984335518990233309047240924848128 * q^52 - 363766241548602923075270727552075967170433033161760056492510229436384310833635734 * q^53 - 1988318954489765046302005332528558912554496159988340641069330680002958019070937600 * q^54 - 3520855393890604949232827617669938515471701214675853816941159595183623184386577000 * q^55 - 12936956692485908268365121199611114191360014164491088694387999166431300696512921600 * q^56 - 13862265625178226892264597068584427924864963571452022505627535112981742091059296080 * q^57 - 73663001170657752665346575473371223431752845037418753763472734766611572171441325440 * q^58 - 119839908140624573484226478891501296275544385047787439213910489726968365086286210700 * q^59 - 468107546718994029022024884762568911834725078620349067042941227204209206458724352000 * q^60 - 328281166748320542242523532793984772143143166398612931227281116669834617338050603326 * q^61 - 999402477792071119370831029463209574610493980381087626216590758004912070795081435136 * q^62 - 2240117215552784969170617635914585450026055291898885166701984645532069514866650525064 * q^63 - 4748321960274080197621802735261780227229800262185345649692550833454877416714840047616 * q^64 + 2401958293154067008332922023669433962969772004736123854920087208208149417890196631500 * q^65 + 12481418287827593167181900965724458478832175604254852160085986797561206241884769502208 * q^66 + 9715050085721519766982024893817705652242604355912950898916137527198529527932523084492 * q^67 + 51110178162381015351883898716980001063480395685110983605059672645927223406195391258624 * q^68 + 125665844363573358610510037253282595268580727449546920119880250916295279742987985413792 * q^69 + 437770522317274261347763126091338009235407849188339858200284725822565513739255154816000 * q^70 + 420099768445021912291978352393445519280746916987347799091649913407485898651223357176984 * q^71 + 1153857576733974210773243583317262094473717150308417455216249971043377175999426453831680 * q^72 + 249990884773795871360906735022065792056914028590737521750721031757996649920054698123686 * q^73 + 988848152146322932205109547460090361956964236264222955609677033303897103570301064734848 * q^74 + 944080624555199942138536838755965622984512203073943882229003778583589699488457416312500 * q^75 - 9872924363930092749183448370538218854882826462181838927155554514487863834399954370969600 * q^76 - 16552736755381232703525388842736711985373990693881749218915711388952768140257306836693856 * q^77 - 73115054525877473148472082243219461137606249175371809547554984327725748004401082971708928 * q^78 - 43369884997252312790262999909905208728154246791055779943371432494520439561399960810221200 * q^79 - 88894687813962777903012798348655018553862729556819104796394604135123942915181092274176000 * q^80 - 70612572309757383558801217018071484518377724651384007545224773102476238636837549694743953 * q^81 - 236357995159599133663604843384379044643064499685381579522884048932961281765779447211829376 * q^82 - 206459225650342475045148123542600401116221913586781003327705338223920418727874732010864004 * q^83 + 1649840105905513745515070352659141454913812021851911846045941535531840033929951137654243328 * q^84 + 1637661121678145282281696006564110640734919603287375198985971859556394144920752854974380500 * q^85 + 3239900597437756786176903087412721547247433713557247371056571790561416975430434191434708224 * q^86 + 6559051070263618632233284423714108103382010904819072234989172243851503736785525745425626280 * q^87 + 6336674026069399594730100443279513731166873520796702455565229756349453295686310223539077120 * q^88 + 5580799156439265704685765323272125687903700231557911629488221982292995723510480958101067350 * q^89 + 19840068851074490675120863444780810644229753682905466429373855007108663777299926218608144000 * q^90 - 18025272478314007503227783954648499409552734863956310123113904904033321293148703549329112496 * q^91 - 81750027044574246291550532241925751638073881610946649428268147310600744342795416362583031808 * q^92 - 125975338781791055721238628453160089358246167768072651306884109747935024714536192316708787328 * q^93 - 306478475429892162274969547511367839192733042761577860914963828391848832364650578690812603392 * q^94 - 216711696129933523762297615654778954621414663971673687874218846402427636558070586043601335000 * q^95 - 229425406959806321843310706398725653116223652026933598684053060220054993118393316925679599616 * q^96 + 43971291171253027759915173352741872464098193495293359649108047104658615767375645954946743342 * q^97 - 690328280759812206538864038068682435013428219472201721649324072601042235191425205897720616256 * q^98 + 306809773352993420176583539450272713060724644284625495060244639714128125893072287559839588052 * q^99

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