LMFDB - Embedded newform 1.94.a.a.1.1

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			1.1
Root			$-3.01170e11$ 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)

$f(q)$	$=$	$q-1.67226e14 q^{2} +1.22637e22 q^{3} +1.80609e28 q^{4} -5.69707e32 q^{5} -2.05080e36 q^{6} +3.48367e39 q^{7} -1.36413e42 q^{8} -8.52575e43 q^{9} +O(q^{10})$	\(q-1.67226e14 q^{2} +1.22637e22 q^{3} +1.80609e28 q^{4} -5.69707e32 q^{5} -2.05080e36 q^{6} +3.48367e39 q^{7} -1.36413e42 q^{8} -8.52575e43 q^{9} +9.52696e46 q^{10} -4.56983e47 q^{11} +2.21493e50 q^{12} -4.65568e49 q^{13} -5.82559e53 q^{14} -6.98669e54 q^{15} +4.92506e55 q^{16} -7.16300e56 q^{17} +1.42572e58 q^{18} -4.92840e58 q^{19} -1.02894e61 q^{20} +4.27226e61 q^{21} +7.64193e61 q^{22} +1.15698e63 q^{23} -1.67292e64 q^{24} +2.23592e65 q^{25} +7.78549e63 q^{26} -3.93556e66 q^{27} +6.29183e67 q^{28} +1.03850e68 q^{29} +1.16835e69 q^{30} -8.93363e67 q^{31} +5.27370e69 q^{32} -5.60428e69 q^{33} +1.19784e71 q^{34} -1.98467e72 q^{35} -1.53983e72 q^{36} +5.91204e72 q^{37} +8.24156e72 q^{38} -5.70957e71 q^{39} +7.77153e74 q^{40} +2.38541e74 q^{41} -7.14432e75 q^{42} -1.84207e75 q^{43} -8.25353e75 q^{44} +4.85718e76 q^{45} -1.93477e77 q^{46} +5.58584e77 q^{47} +6.03993e77 q^{48} +8.20845e78 q^{49} -3.73903e79 q^{50} -8.78446e78 q^{51} -8.40858e77 q^{52} -2.41979e80 q^{53} +6.58128e80 q^{54} +2.60346e80 q^{55} -4.75217e81 q^{56} -6.04403e80 q^{57} -1.73664e82 q^{58} -2.30840e82 q^{59} -1.26186e83 q^{60} +1.46410e83 q^{61} +1.49393e82 q^{62} -2.97009e83 q^{63} -1.36965e84 q^{64} +2.65237e82 q^{65} +9.37180e83 q^{66} +1.40138e84 q^{67} -1.29370e85 q^{68} +1.41889e85 q^{69} +3.31888e86 q^{70} -1.74082e86 q^{71} +1.16302e86 q^{72} -4.65018e86 q^{73} -9.88645e86 q^{74} +2.74205e87 q^{75} -8.90115e86 q^{76} -1.59198e87 q^{77} +9.54786e85 q^{78} -1.89450e88 q^{79} -2.80584e88 q^{80} -2.81731e88 q^{81} -3.98902e88 q^{82} -2.23742e89 q^{83} +7.71609e89 q^{84} +4.08081e89 q^{85} +3.08041e89 q^{86} +1.27358e90 q^{87} +6.23383e89 q^{88} -1.44081e90 q^{89} -8.12245e90 q^{90} -1.62188e89 q^{91} +2.08962e91 q^{92} -1.09559e90 q^{93} -9.34096e91 q^{94} +2.80774e91 q^{95} +6.46750e91 q^{96} -8.44825e91 q^{97} -1.37266e93 q^{98} +3.89612e91 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−1.67226e14	−1.68038	−0.840192	−	0.542290i	$-0.817558\pi$
$2$	−1.67226e14	−1.68038	−0.840192	+	0.542290i	$0.817558\pi$
$3$	1.22637e22	0.798881	0.399440	−	0.916759i	$-0.369204\pi$
$3$	1.22637e22	0.798881	0.399440	+	0.916759i	$0.369204\pi$
$4$	1.80609e28	1.82369
$5$	−5.69707e32	−1.79286	−0.896429	−	0.443186i	$-0.853848\pi$
$5$	−5.69707e32	−1.79286	−0.896429	+	0.443186i	$0.853848\pi$
$6$	−2.05080e36	−1.34243
$7$	3.48367e39	1.75784	0.878918	−	0.476973i	$-0.158266\pi$
$7$	3.48367e39	1.75784	0.878918	+	0.476973i	$0.158266\pi$
$8$	−1.36413e42	−1.38411
$9$	−8.52575e43	−0.361789
$10$	9.52696e46	3.01269
$11$	−4.56983e47	−0.171846	−0.0859231	−	0.996302i	$-0.527384\pi$
$11$	−4.56983e47	−0.171846	−0.0859231	+	0.996302i	$0.527384\pi$
$12$	2.21493e50	1.45691
$13$	−4.65568e49	−0.00740657	−0.00370328	−	0.999993i	$-0.501179\pi$
$13$	−4.65568e49	−0.00740657	−0.00370328	+	0.999993i	$0.501179\pi$
$14$	−5.82559e53	−2.95384
$15$	−6.98669e54	−1.43228
$16$	4.92506e55	0.502149
$17$	−7.16300e56	−0.435733	−0.217866	−	0.975979i	$-0.569910\pi$
$17$	−7.16300e56	−0.435733	−0.217866	+	0.975979i	$0.569910\pi$
$18$	1.42572e58	0.607945
$19$	−4.92840e58	−0.170084	−0.0850421	−	0.996377i	$-0.527102\pi$
$19$	−4.92840e58	−0.170084	−0.0850421	+	0.996377i	$0.527102\pi$
$20$	−1.02894e61	−3.26961
$21$	4.27226e61	1.40430
$22$	7.64193e61	0.288767
$23$	1.15698e63	0.553328	0.276664	−	0.960967i	$-0.410771\pi$
$23$	1.15698e63	0.553328	0.276664	+	0.960967i	$0.410771\pi$
$24$	−1.67292e64	−1.10574
$25$	2.23592e65	2.21434
$26$	7.78549e63	0.0124459
$27$	−3.93556e66	−1.08791
$28$	6.29183e67	3.20574
$29$	1.03850e68	1.03490	0.517452	−	0.855712i	$-0.326880\pi$
$29$	1.03850e68	1.03490	0.517452	+	0.855712i	$0.326880\pi$
$30$	1.16835e69	2.40678
$31$	−8.93363e67	−0.0400598	−0.0200299	−	0.999799i	$-0.506376\pi$
$31$	−8.93363e67	−0.0400598	−0.0200299	+	0.999799i	$0.506376\pi$
$32$	5.27370e69	0.540309
$33$	−5.60428e69	−0.137285
$34$	1.19784e71	0.732198
$35$	−1.98467e72	−3.15155
$36$	−1.53983e72	−0.659791
$37$	5.91204e72	0.708528	0.354264	−	0.935145i	$-0.384731\pi$
$37$	5.91204e72	0.708528	0.354264	+	0.935145i	$0.384731\pi$
$38$	8.24156e72	0.285807
$39$	−5.70957e71	−0.00591696
$40$	7.77153e74	2.48152
$41$	2.38541e74	0.241609	0.120805	−	0.992676i	$-0.461453\pi$
$41$	2.38541e74	0.241609	0.120805	+	0.992676i	$0.461453\pi$
$42$	−7.14432e75	−2.35976
$43$	−1.84207e75	−0.203715	−0.101857	−	0.994799i	$-0.532479\pi$
$43$	−1.84207e75	−0.203715	−0.101857	+	0.994799i	$0.532479\pi$
$44$	−8.25353e75	−0.313394
$45$	4.85718e76	0.648637
$46$	−1.93477e77	−0.929803
$47$	5.58584e77	0.987502	0.493751	−	0.869603i	$-0.335625\pi$
$47$	5.58584e77	0.987502	0.493751	+	0.869603i	$0.335625\pi$
$48$	6.03993e77	0.401157
$49$	8.20845e78	2.08999
$50$	−3.73903e79	−3.72095
$51$	−8.78446e78	−0.348098
$52$	−8.40858e77	−0.0135073
$53$	−2.41979e80	−1.60306	−0.801531	−	0.597953i	$-0.795981\pi$
$53$	−2.41979e80	−1.60306	−0.801531	+	0.597953i	$0.795981\pi$
$54$	6.58128e80	1.82810
$55$	2.60346e80	0.308096
$56$	−4.75217e81	−2.43304
$57$	−6.04403e80	−0.135877
$58$	−1.73664e82	−1.73904
$59$	−2.30840e82	−1.04398	−0.521990	−	0.852951i	$-0.674810\pi$
$59$	−2.30840e82	−1.04398	−0.521990	+	0.852951i	$0.674810\pi$
$60$	−1.26186e83	−2.61203
$61$	1.46410e83	1.40518	0.702591	−	0.711594i	$-0.252027\pi$
$61$	1.46410e83	1.40518	0.702591	+	0.711594i	$0.252027\pi$
$62$	1.49393e82	0.0673159
$63$	−2.97009e83	−0.635966
$64$	−1.36965e84	−1.41007
$65$	2.65237e82	0.0132789
$66$	9.37180e83	0.230691
$67$	1.40138e84	0.171426	0.0857131	−	0.996320i	$-0.472683\pi$
$67$	1.40138e84	0.171426	0.0857131	+	0.996320i	$0.472683\pi$
$68$	−1.29370e85	−0.794640
$69$	1.41889e85	0.442043
$70$	3.31888e86	5.29581
$71$	−1.74082e86	−1.43628	−0.718142	−	0.695897i	$-0.755007\pi$
$71$	−1.74082e86	−1.43628	−0.718142	+	0.695897i	$0.755007\pi$
$72$	1.16302e86	0.500757
$73$	−4.65018e86	−1.05428	−0.527141	−	0.849778i	$-0.676736\pi$
$73$	−4.65018e86	−1.05428	−0.527141	+	0.849778i	$0.676736\pi$
$74$	−9.88645e86	−1.19060
$75$	2.74205e87	1.76900
$76$	−8.90115e86	−0.310180
$77$	−1.59198e87	−0.302077
$78$	9.54786e85	0.00994277
$79$	−1.89450e88	−1.09103	−0.545513	−	0.838102i	$-0.683665\pi$
$79$	−1.89450e88	−1.09103	−0.545513	+	0.838102i	$0.683665\pi$
$80$	−2.80584e88	−0.900282
$81$	−2.81731e88	−0.507319
$82$	−3.98902e88	−0.405996
$83$	−2.23742e89	−1.29603	−0.648016	−	0.761627i	$-0.724401\pi$
$83$	−2.23742e89	−1.29603	−0.648016	+	0.761627i	$0.724401\pi$
$84$	7.71609e89	2.56101
$85$	4.08081e89	0.781207
$86$	3.08041e89	0.342319
$87$	1.27358e90	0.826766
$88$	6.23383e89	0.237854
$89$	−1.44081e90	−0.325066	−0.162533	−	0.986703i	$-0.551966\pi$
$89$	−1.44081e90	−0.325066	−0.162533	+	0.986703i	$0.551966\pi$
$90$	−8.12245e90	−1.08996
$91$	−1.62188e89	−0.0130195
$92$	2.08962e91	1.00910
$93$	−1.09559e90	−0.0320030
$94$	−9.34096e91	−1.65938
$95$	2.80774e91	0.304937
$96$	6.46750e91	0.431642
$97$	−8.44825e91	−0.348242	−0.174121	−	0.984724i	$-0.555708\pi$
$97$	−8.44825e91	−0.348242	−0.174121	+	0.984724i	$0.555708\pi$
$98$	−1.37266e93	−3.51198
$99$	3.89612e91	0.0621721
$100$	4.03827e93	4.03827
$101$	1.31306e93	0.826683	0.413342	−	0.910576i	$-0.364361\pi$
$101$	1.31306e93	0.826683	0.413342	+	0.910576i	$0.364361\pi$
$102$	1.46899e93	0.584939
$103$	−1.21301e93	−0.306854	−0.153427	−	0.988160i	$-0.549031\pi$
$103$	−1.21301e93	−0.306854	−0.153427	+	0.988160i	$0.549031\pi$
$104$	6.35094e91	0.0102515
$105$	−2.43393e94	−2.51771
$106$	4.04652e94	2.69376
$107$	−1.56019e94	−0.671168	−0.335584	−	0.942010i	$-0.608934\pi$
$107$	−1.56019e94	−0.671168	−0.335584	+	0.942010i	$0.608934\pi$
$108$	−7.10799e94	−1.98400
$109$	2.90925e94	0.528992	0.264496	−	0.964387i	$-0.414794\pi$
$109$	2.90925e94	0.528992	0.264496	+	0.964387i	$0.414794\pi$
$110$	−4.35366e94	−0.517719
$111$	7.25033e94	0.566030
$112$	1.71573e95	0.882695
$113$	−5.02384e95	−1.70957	−0.854787	−	0.518979i	$-0.826312\pi$
$113$	−5.02384e95	−1.70957	−0.854787	+	0.518979i	$0.826312\pi$
$114$	1.01072e95	0.228325
$115$	−6.59141e95	−0.992040
$116$	1.87563e96	1.88734
$117$	3.96931e93	0.00267962
$118$	3.86024e96	1.75429
$119$	−2.49535e96	−0.765946
$120$	9.53075e96	1.98243
$121$	−6.86280e96	−0.970469
$122$	−2.44835e97	−2.36124
$123$	2.92539e96	0.193017
$124$	−1.61350e96	−0.0730566
$125$	−6.98559e97	−2.17715
$126$	4.96676e97	1.06867
$127$	5.70958e96	0.0850611	0.0425306	−	0.999095i	$-0.486458\pi$
$127$	5.70958e96	0.0850611	0.0425306	+	0.999095i	$0.486458\pi$
$128$	1.76813e98	1.82916
$129$	−2.25905e97	−0.162744
$130$	−4.43545e96	−0.0223137
$131$	−6.34511e96	−0.0223524	−0.0111762	−	0.999938i	$-0.503558\pi$
$131$	−6.34511e96	−0.0223524	−0.0111762	+	0.999938i	$0.503558\pi$
$132$	−1.01219e98	−0.250364
$133$	−1.71689e98	−0.298980
$134$	−2.34346e98	−0.288062
$135$	2.24212e99	1.95046
$136$	9.77125e98	0.603102
$137$	−1.94391e99	−0.853436	−0.426718	−	0.904385i	$-0.640330\pi$
$137$	−1.94391e99	−0.853436	−0.426718	+	0.904385i	$0.640330\pi$
$138$	−2.37274e99	−0.742802
$139$	8.49504e99	1.90098	0.950489	−	0.310758i	$-0.100583\pi$
$139$	8.49504e99	1.90098	0.950489	+	0.310758i	$0.100583\pi$
$140$	−3.58450e100	−5.74745
$141$	6.85028e99	0.788896
$142$	2.91110e100	2.41351
$143$	2.12756e97	0.00127279
$144$	−4.19898e99	−0.181672
$145$	−5.91642e100	−1.85544
$146$	7.77630e100	1.77160
$147$	1.00666e101	1.66965
$148$	1.06777e101	1.29213
$149$	1.32597e101	1.17320	0.586599	−	0.809878i	$-0.300466\pi$
$149$	1.32597e101	1.17320	0.586599	+	0.809878i	$0.300466\pi$
$150$	−4.58542e101	−2.97259
$151$	−3.45701e101	−1.64541	−0.822703	−	0.568472i	$-0.807535\pi$
$151$	−3.45701e101	−1.64541	−0.822703	+	0.568472i	$0.807535\pi$
$152$	6.72298e100	0.235415
$153$	6.10699e100	0.157643
$154$	2.66220e101	0.507606
$155$	5.08955e100	0.0718216
$156$	−1.03120e100	−0.0107907
$157$	−1.50836e102	−1.17266	−0.586331	−	0.810072i	$-0.699428\pi$
$157$	−1.50836e102	−1.17266	−0.586331	+	0.810072i	$0.699428\pi$
$158$	3.16809e102	1.83334
$159$	−2.96755e102	−1.28066
$160$	−3.00447e102	−0.968697
$161$	4.03055e102	0.972660
$162$	4.71127e102	0.852490
$163$	−2.68240e102	−0.364586	−0.182293	−	0.983244i	$-0.558352\pi$
$163$	−2.68240e102	−0.364586	−0.182293	+	0.983244i	$0.558352\pi$
$164$	4.30827e102	0.440620
$165$	3.19280e102	0.246132
$166$	3.74153e103	2.17783
$167$	2.49429e102	0.109807	0.0549036	−	0.998492i	$-0.482515\pi$
$167$	2.49429e102	0.109807	0.0549036	+	0.998492i	$0.482515\pi$
$168$	−5.82791e103	−1.94371
$169$	−3.95101e103	−0.999945
$170$	−6.82416e103	−1.31273
$171$	4.20183e102	0.0615346
$172$	−3.32695e103	−0.371512
$173$	4.59720e103	0.392057	0.196029	−	0.980598i	$-0.437195\pi$
$173$	4.59720e103	0.392057	0.196029	+	0.980598i	$0.437195\pi$
$174$	−2.12976e104	−1.38928
$175$	7.78919e104	3.89245
$176$	−2.25067e103	−0.0862923
$177$	−2.83094e104	−0.834016
$178$	2.40941e104	0.546236
$179$	−3.50256e104	−0.611954	−0.305977	−	0.952039i	$-0.598983\pi$
$179$	−3.50256e104	−0.611954	−0.305977	+	0.952039i	$0.598983\pi$
$180$	8.77251e104	1.18291
$181$	−1.14588e105	−1.19422	−0.597111	−	0.802158i	$-0.703685\pi$
$181$	−1.14588e105	−1.19422	−0.597111	+	0.802158i	$0.703685\pi$
$182$	2.71221e103	0.0218778
$183$	1.79552e105	1.12257
$184$	−1.57827e105	−0.765867
$185$	−3.36813e105	−1.27029
$186$	1.83211e104	0.0537773
$187$	3.27337e104	0.0748790
$188$	1.00885e106	1.80089
$189$	−1.37102e106	−1.91236
$190$	−4.69527e105	−0.512411
$191$	1.60846e106	1.37518	0.687589	−	0.726100i	$-0.258669\pi$
$191$	1.60846e106	1.37518	0.687589	+	0.726100i	$0.258669\pi$
$192$	−1.67970e106	−1.12648
$193$	−1.70685e106	−0.899043	−0.449521	−	0.893270i	$-0.648405\pi$
$193$	−1.70685e106	−0.899043	−0.449521	+	0.893270i	$0.648405\pi$
$194$	1.41276e106	0.585180
$195$	3.25278e104	0.0106083
$196$	1.48252e107	3.81148
$197$	3.10588e106	0.630239	0.315119	−	0.949052i	$-0.397955\pi$
$197$	3.10588e106	0.630239	0.315119	+	0.949052i	$0.397955\pi$
$198$	−6.51531e105	−0.104473
$199$	−6.17602e106	−0.783504	−0.391752	−	0.920071i	$-0.628131\pi$
$199$	−6.17602e106	−0.783504	−0.391752	+	0.920071i	$0.628131\pi$
$200$	−3.05008e107	−3.06490
$201$	1.71860e106	0.136949
$202$	−2.19577e107	−1.38915
$203$	3.61780e107	1.81919
$204$	−1.58656e107	−0.634823
$205$	−1.35898e107	−0.433172
$206$	2.02846e107	0.515633
$207$	−9.86415e106	−0.200188
$208$	−2.29295e105	−0.00371920
$209$	2.25220e106	0.0292283
$210$	4.07016e108	4.23072
$211$	−8.25722e107	−0.688176	−0.344088	−	0.938937i	$-0.611812\pi$
$211$	−8.25722e107	−0.688176	−0.344088	+	0.938937i	$0.611812\pi$
$212$	−4.37037e108	−2.92349
$213$	−2.13488e108	−1.14742
$214$	2.60904e108	1.12782
$215$	1.04944e108	0.365232
$216$	5.36861e108	1.50578
$217$	−3.11218e107	−0.0704186
$218$	−4.86502e108	−0.888909
$219$	−5.70283e108	−0.842246
$220$	4.70209e108	0.561871
$221$	3.33486e106	0.00322728
$222$	−1.21244e109	−0.951147
$223$	−2.48798e109	−1.58369	−0.791846	−	0.610721i	$-0.790880\pi$
$223$	−2.48798e109	−1.58369	−0.791846	+	0.610721i	$0.790880\pi$
$224$	1.83719e109	0.949774
$225$	−1.90629e109	−0.801126
$226$	8.40115e109	2.87274
$227$	−4.23182e109	−1.17849	−0.589244	−	0.807955i	$-0.700574\pi$
$227$	−4.23182e109	−1.17849	−0.589244	+	0.807955i	$0.700574\pi$
$228$	−1.09161e109	−0.247797
$229$	5.89882e109	1.09248	0.546242	−	0.837627i	$-0.316058\pi$
$229$	5.89882e109	1.09248	0.546242	+	0.837627i	$0.316058\pi$
$230$	1.10225e110	1.66701
$231$	−1.95235e109	−0.241324
$232$	−1.41665e110	−1.43242
$233$	2.13090e110	1.76406	0.882031	−	0.471192i	$-0.156176\pi$
$233$	2.13090e110	1.76406	0.882031	+	0.471192i	$0.156176\pi$
$234$	−6.63771e107	−0.00450278
$235$	−3.18229e110	−1.77045
$236$	−4.16918e110	−1.90389
$237$	−2.32335e110	−0.871600
$238$	4.17287e110	1.28708
$239$	−8.20500e109	−0.208246	−0.104123	−	0.994564i	$-0.533204\pi$
$239$	−8.20500e109	−0.208246	−0.104123	+	0.994564i	$0.533204\pi$
$240$	−3.44099e110	−0.719218
$241$	3.90307e110	0.672378	0.336189	−	0.941795i	$-0.390862\pi$
$241$	3.90307e110	0.672378	0.336189	+	0.941795i	$0.390862\pi$
$242$	1.14764e111	1.63076
$243$	5.81930e110	0.682620
$244$	2.64429e111	2.56261
$245$	−4.67641e111	−3.74705
$246$	−4.89200e110	−0.324343
$247$	2.29451e108	0.00125974
$248$	1.21866e110	0.0554472
$249$	−2.74389e111	−1.03537
$250$	1.16817e112	3.65844
$251$	−1.23935e111	−0.322379	−0.161190	−	0.986923i	$-0.551533\pi$
$251$	−1.23935e111	−0.322379	−0.161190	+	0.986923i	$0.551533\pi$
$252$	−5.36426e111	−1.15980
$253$	−5.28721e110	−0.0950873
$254$	−9.54789e110	−0.142935
$255$	5.00457e111	0.624091
$256$	−1.60033e112	−1.66361
$257$	−1.72101e112	−1.49243	−0.746213	−	0.665707i	$-0.768130\pi$
$257$	−1.72101e112	−1.49243	−0.746213	+	0.665707i	$0.768130\pi$
$258$	3.77771e111	0.273472
$259$	2.05956e112	1.24548
$260$	4.79043e110	0.0242166
$261$	−8.85401e111	−0.374418
$262$	1.06107e111	0.0375606
$263$	−6.46068e111	−0.191574	−0.0957869	−	0.995402i	$-0.530537\pi$
$263$	−6.46068e111	−0.191574	−0.0957869	+	0.995402i	$0.530537\pi$
$264$	7.64496e111	0.190017
$265$	1.37857e113	2.87407
$266$	2.87109e112	0.502401
$267$	−1.76696e112	−0.259689
$268$	2.53102e112	0.312628
$269$	−7.61241e111	−0.0790753	−0.0395377	−	0.999218i	$-0.512589\pi$
$269$	−7.61241e111	−0.0790753	−0.0395377	+	0.999218i	$0.512589\pi$
$270$	−3.74940e113	−3.27753
$271$	−8.48308e112	−0.624427	−0.312213	−	0.950012i	$-0.601070\pi$
$271$	−8.48308e112	−0.624427	−0.312213	+	0.950012i	$0.601070\pi$
$272$	−3.52782e112	−0.218802
$273$	−1.98903e111	−0.0104011
$274$	3.25073e113	1.43410
$275$	−1.02177e113	−0.380526
$276$	2.56264e113	0.806149
$277$	1.01098e113	0.268802	0.134401	−	0.990927i	$-0.457089\pi$
$277$	1.01098e113	0.268802	0.134401	+	0.990927i	$0.457089\pi$
$278$	−1.42059e114	−3.19437
$279$	7.61659e111	0.0144932
$280$	2.70735e114	4.36210
$281$	2.93864e113	0.401146	0.200573	−	0.979679i	$-0.435720\pi$
$281$	2.93864e113	0.401146	0.200573	+	0.979679i	$0.435720\pi$
$282$	−1.14554e114	−1.32565
$283$	1.44060e114	1.41408	0.707042	−	0.707172i	$-0.250029\pi$
$283$	1.44060e114	1.41408	0.707042	+	0.707172i	$0.250029\pi$
$284$	−3.14408e114	−2.61933
$285$	3.44332e113	0.243608
$286$	−3.55783e111	−0.00213877
$287$	8.30999e113	0.424710
$288$	−4.49623e113	−0.195478
$289$	−2.18931e114	−0.810137
$290$	9.89377e114	3.11785
$291$	−1.03607e114	−0.278204
$292$	−8.39866e114	−1.92268
$293$	2.96400e114	0.578807	0.289403	−	0.957207i	$-0.406543\pi$
$293$	2.96400e114	0.578807	0.289403	+	0.957207i	$0.406543\pi$
$294$	−1.68339e115	−2.80565
$295$	1.31511e115	1.87171
$296$	−8.06478e114	−0.980682
$297$	1.79848e114	0.186953
$298$	−2.21736e115	−1.97142
$299$	−5.38654e112	−0.00409826
$300$	4.95240e115	3.22610
$301$	−6.41716e114	−0.358097
$302$	5.78102e115	2.76491
$303$	1.61029e115	0.660422
$304$	−2.42727e114	−0.0854075
$305$	−8.34105e115	−2.51929
$306$	−1.02125e115	−0.264901
$307$	1.05946e115	0.236129	0.118065	−	0.993006i	$-0.462331\pi$
$307$	1.05946e115	0.236129	0.118065	+	0.993006i	$0.462331\pi$
$308$	−2.87526e115	−0.550895
$309$	−1.48759e115	−0.245140
$310$	−8.51103e114	−0.120688
$311$	−9.04218e115	−1.10386	−0.551931	−	0.833890i	$-0.686109\pi$
$311$	−9.04218e115	−1.10386	−0.551931	+	0.833890i	$0.686109\pi$
$312$	7.78858e113	0.00818973
$313$	−8.51474e115	−0.771542	−0.385771	−	0.922595i	$-0.626064\pi$
$313$	−8.51474e115	−0.771542	−0.385771	+	0.922595i	$0.626064\pi$
$314$	2.52237e116	1.97052
$315$	1.69208e116	1.14020
$316$	−3.42164e116	−1.98969
$317$	−2.02778e116	−1.01804	−0.509021	−	0.860754i	$-0.669992\pi$
$317$	−2.02778e116	−1.01804	−0.509021	+	0.860754i	$0.669992\pi$
$318$	4.96252e116	2.15199
$319$	−4.74577e115	−0.177844
$320$	7.80301e116	2.52806
$321$	−1.91336e116	−0.536184
$322$	−6.74012e116	−1.63444
$323$	3.53021e115	0.0741112
$324$	−5.08832e116	−0.925191
$325$	−1.04097e115	−0.0164007
$326$	4.48566e116	0.612643
$327$	3.56781e116	0.422601
$328$	−3.25401e116	−0.334414
$329$	1.94592e117	1.73587
$330$	−5.33918e116	−0.413596
$331$	−1.27033e116	−0.0854901	−0.0427450	−	0.999086i	$-0.513610\pi$
$331$	−1.27033e116	−0.0854901	−0.0427450	+	0.999086i	$0.513610\pi$
$332$	−4.04098e117	−2.36356
$333$	−5.04046e116	−0.256338
$334$	−4.17109e116	−0.184518
$335$	−7.98374e116	−0.307343
$336$	2.10411e117	0.705168
$337$	−1.73776e117	−0.507225	−0.253612	−	0.967306i	$-0.581619\pi$
$337$	−1.73776e117	−0.507225	−0.253612	+	0.967306i	$0.581619\pi$
$338$	6.60710e117	1.68029
$339$	−6.16107e117	−1.36575
$340$	7.37032e117	1.42468
$341$	4.08251e115	0.00688413
$342$	−7.02655e116	−0.103402
$343$	1.49134e118	1.91602
$344$	2.51282e117	0.281964
$345$	−8.08349e117	−0.792521
$346$	−7.68770e117	−0.658806
$347$	1.27568e118	0.955921	0.477960	−	0.878381i	$-0.341376\pi$
$347$	1.27568e118	0.955921	0.477960	+	0.878381i	$0.341376\pi$
$348$	2.30021e118	1.50776
$349$	−9.04561e117	−0.518866	−0.259433	−	0.965761i	$-0.583536\pi$
$349$	−9.04561e117	−0.518866	−0.259433	+	0.965761i	$0.583536\pi$
$350$	−1.30255e119	−6.54081
$351$	1.83227e116	0.00805766
$352$	−2.40999e117	−0.0928500
$353$	4.00670e118	1.35289	0.676447	−	0.736492i	$-0.263519\pi$
$353$	4.00670e118	1.35289	0.676447	+	0.736492i	$0.263519\pi$
$354$	4.73407e118	1.40147
$355$	9.91756e118	2.57505
$356$	−2.60224e118	−0.592819
$357$	−3.06022e118	−0.611900
$358$	5.85717e118	1.02832
$359$	−3.72279e118	−0.574085	−0.287043	−	0.957918i	$-0.592672\pi$
$359$	−3.72279e118	−0.574085	−0.287043	+	0.957918i	$0.592672\pi$
$360$	−6.62581e118	−0.897786
$361$	−8.15335e118	−0.971071
$362$	1.91621e119	2.00675
$363$	−8.41631e118	−0.775289
$364$	−2.92927e117	−0.0237435
$365$	2.64924e119	1.89018
$366$	−3.00257e119	−1.88635
$367$	−1.79087e118	−0.0991043	−0.0495522	−	0.998772i	$-0.515779\pi$
$367$	−1.79087e118	−0.0991043	−0.0495522	+	0.998772i	$0.515779\pi$
$368$	5.69821e118	0.277853
$369$	−2.03374e118	−0.0874117
$370$	5.63238e119	2.13458
$371$	−8.42977e119	−2.81792
$372$	−1.97874e118	−0.0583635
$373$	4.39147e119	1.14327	0.571635	−	0.820508i	$-0.306309\pi$
$373$	4.39147e119	1.14327	0.571635	+	0.820508i	$0.306309\pi$
$374$	−5.47391e118	−0.125825
$375$	−8.56690e119	−1.73928
$376$	−7.61980e119	−1.36681
$377$	−4.83493e117	−0.00766509
$378$	2.29270e120	3.21350
$379$	−6.66278e119	−0.825909	−0.412954	−	0.910752i	$-0.635503\pi$
$379$	−6.66278e119	−0.825909	−0.412954	+	0.910752i	$0.635503\pi$
$380$	5.07105e119	0.556110
$381$	7.00204e118	0.0679537
$382$	−2.68976e120	−2.31083
$383$	1.79657e120	1.36679	0.683395	−	0.730049i	$-0.260503\pi$
$383$	1.79657e120	1.36679	0.683395	+	0.730049i	$0.260503\pi$
$384$	2.16838e120	1.46128
$385$	9.06960e119	0.541582
$386$	2.85429e120	1.51074
$387$	1.57050e119	0.0737018
$388$	−1.52583e120	−0.635085
$389$	−3.75042e120	−1.38492	−0.692459	−	0.721458i	$-0.743472\pi$
$389$	−3.75042e120	−1.38492	−0.692459	+	0.721458i	$0.743472\pi$
$390$	−5.43948e118	−0.0178260
$391$	−8.28747e119	−0.241103
$392$	−1.11974e121	−2.89277
$393$	−7.78144e118	−0.0178569
$394$	−5.19383e120	−1.05904
$395$	1.07931e121	1.95606
$396$	7.03675e119	0.113383
$397$	−6.93819e119	−0.0994232	−0.0497116	−	0.998764i	$-0.515830\pi$
$397$	−6.93819e119	−0.0994232	−0.0497116	+	0.998764i	$0.515830\pi$
$398$	1.03279e121	1.31659
$399$	−2.10554e120	−0.238849
$400$	1.10120e121	1.11193
$401$	−4.38284e120	−0.394042	−0.197021	−	0.980399i	$-0.563127\pi$
$401$	−4.38284e120	−0.394042	−0.197021	+	0.980399i	$0.563127\pi$
$402$	−2.87395e120	−0.230127
$403$	4.15921e117	0.000296706 0
$404$	2.37150e121	1.50761
$405$	1.60504e121	0.909551
$406$	−6.04989e121	−3.05694
$407$	−2.70170e120	−0.121758
$408$	1.19831e121	0.481807
$409$	1.19957e121	0.430421	0.215210	−	0.976568i	$-0.430956\pi$
$409$	1.19957e121	0.430421	0.215210	+	0.976568i	$0.430956\pi$
$410$	2.27257e121	0.727894
$411$	−2.38395e121	−0.681794
$412$	−2.19080e121	−0.559606
$413$	−8.04171e121	−1.83515
$414$	1.64954e121	0.336393
$415$	1.27467e122	2.32360
$416$	−2.45527e119	−0.00400183
$417$	1.04180e122	1.51866
$418$	−3.76625e120	−0.0491148
$419$	−1.55294e122	−1.81219	−0.906095	−	0.423074i	$-0.860951\pi$
$419$	−1.55294e122	−1.81219	−0.906095	+	0.423074i	$0.860951\pi$
$420$	−4.39591e122	−4.59152
$421$	1.20749e122	1.12919	0.564595	−	0.825368i	$-0.309032\pi$
$421$	1.20749e122	1.12919	0.564595	+	0.825368i	$0.309032\pi$
$422$	1.38082e122	1.15640
$423$	−4.76234e121	−0.357268
$424$	3.30091e122	2.21882
$425$	−1.60159e122	−0.964861
$426$	3.57007e122	1.92810
$427$	5.10043e122	2.47008
$428$	−2.81785e122	−1.22400
$429$	2.60917e119	0.00101681
$430$	−1.75493e122	−0.613729
$431$	1.44577e122	0.453842	0.226921	−	0.973913i	$-0.427134\pi$
$431$	1.44577e122	0.453842	0.226921	+	0.973913i	$0.427134\pi$
$432$	−1.93829e122	−0.546291
$433$	−6.73888e122	−1.70569	−0.852846	−	0.522163i	$-0.825125\pi$
$433$	−6.73888e122	−1.70569	−0.852846	+	0.522163i	$0.825125\pi$
$434$	5.20437e121	0.118330
$435$	−7.25569e122	−1.48227
$436$	5.25438e122	0.964716
$437$	−5.70208e121	−0.0941124
$438$	9.53659e122	1.41530
$439$	−1.23553e123	−1.64912	−0.824560	−	0.565775i	$-0.808577\pi$
$439$	−1.23553e123	−1.64912	−0.824560	+	0.565775i	$0.808577\pi$
$440$	−3.55145e122	−0.426439
$441$	−6.99832e122	−0.756135
$442$	−5.57674e120	−0.00542307
$443$	2.19056e122	0.191771	0.0958854	−	0.995392i	$-0.469432\pi$
$443$	2.19056e122	0.191771	0.0958854	+	0.995392i	$0.469432\pi$
$444$	1.30948e123	1.03226
$445$	8.20840e122	0.582798
$446$	4.16054e123	2.66121
$447$	1.62612e123	0.937245
$448$	−4.77142e123	−2.47868
$449$	7.18526e122	0.336502	0.168251	−	0.985744i	$-0.446188\pi$
$449$	7.18526e122	0.336502	0.168251	+	0.985744i	$0.446188\pi$
$450$	3.18780e123	1.34620
$451$	−1.09009e122	−0.0415197
$452$	−9.07351e123	−3.11773
$453$	−4.23957e123	−1.31448
$454$	7.07670e123	1.98031
$455$	9.23999e121	0.0233422
$456$	8.24483e122	0.188069
$457$	4.72549e123	0.973518	0.486759	−	0.873536i	$-0.338179\pi$
$457$	4.72549e123	0.973518	0.486759	+	0.873536i	$0.338179\pi$
$458$	−9.86434e123	−1.83579
$459$	2.81904e123	0.474037
$460$	−1.19047e124	−1.80917
$461$	1.23678e124	1.69902	0.849510	−	0.527573i	$-0.176898\pi$
$461$	1.23678e124	1.69902	0.849510	+	0.527573i	$0.176898\pi$
$462$	3.26483e123	0.405516
$463$	7.69925e123	0.864833	0.432417	−	0.901674i	$-0.357661\pi$
$463$	7.69925e123	0.864833	0.432417	+	0.901674i	$0.357661\pi$
$464$	5.11468e123	0.519676
$465$	6.24165e122	0.0573769
$466$	−3.56342e124	−2.96430
$467$	−1.64477e124	−1.23843	−0.619215	−	0.785222i	$-0.712549\pi$
$467$	−1.64477e124	−1.23843	−0.619215	+	0.785222i	$0.712549\pi$
$468$	7.16895e121	0.00488678
$469$	4.88194e123	0.301339
$470$	5.32161e124	2.97504
$471$	−1.84981e124	−0.936817
$472$	3.14895e124	1.44498
$473$	8.41793e122	0.0350076
$474$	3.88524e124	1.46462
$475$	−1.10195e124	−0.376625
$476$	−4.50684e124	−1.39685
$477$	2.06306e124	0.579971
$478$	1.37209e124	0.349933
$479$	−2.79704e124	−0.647287	−0.323643	−	0.946179i	$-0.604908\pi$
$479$	−2.79704e124	−0.647287	−0.323643	+	0.946179i	$0.604908\pi$
$480$	−3.68458e124	−0.773873
$481$	−2.75245e122	−0.00524776
$482$	−6.52693e124	−1.12985
$483$	4.94293e124	0.777040
$484$	−1.23949e125	−1.76983
$485$	4.81302e124	0.624349
$486$	−9.73137e124	−1.14706
$487$	2.15017e124	0.230343	0.115172	−	0.993346i	$-0.463258\pi$
$487$	2.15017e124	0.230343	0.115172	+	0.993346i	$0.463258\pi$
$488$	−1.99721e125	−1.94493
$489$	−3.28960e124	−0.291260
$490$	7.82016e125	6.29648
$491$	−2.58184e123	−0.0189077	−0.00945387	−	0.999955i	$-0.503009\pi$
$491$	−2.58184e123	−0.0189077	−0.00945387	+	0.999955i	$0.503009\pi$
$492$	5.28352e124	0.352003
$493$	−7.43879e124	−0.450942
$494$	−3.83700e122	−0.00211685
$495$	−2.21965e124	−0.111466
$496$	−4.39986e123	−0.0201160
$497$	−6.06444e125	−2.52475
$498$	4.58849e125	1.73983
$499$	4.24177e125	1.46511	0.732557	−	0.680706i	$-0.238327\pi$
$499$	4.24177e125	1.46511	0.732557	+	0.680706i	$0.238327\pi$
$500$	−1.26166e126	−3.97043
$501$	3.05891e124	0.0877228
$502$	2.07252e125	0.541721
$503$	6.20313e125	1.47809	0.739043	−	0.673658i	$-0.235278\pi$
$503$	6.20313e125	1.47809	0.739043	+	0.673658i	$0.235278\pi$
$504$	4.05158e125	0.880248
$505$	−7.48057e125	−1.48213
$506$	8.84158e124	0.159783
$507$	−4.84538e125	−0.798837
$508$	1.03120e125	0.155125
$509$	6.21343e125	0.853011	0.426505	−	0.904485i	$-0.359745\pi$
$509$	6.21343e125	0.853011	0.426505	+	0.904485i	$0.359745\pi$
$510$	−8.36892e125	−1.04871
$511$	−1.61997e126	−1.85325
$512$	9.25092e125	0.966344
$513$	1.93961e125	0.185036
$514$	2.87797e126	2.50785
$515$	6.91058e125	0.550146
$516$	−4.08006e125	−0.296794
$517$	−2.55263e125	−0.169698
$518$	−3.44412e126	−2.09288
$519$	5.63785e125	0.313207
$520$	−3.61817e124	−0.0183795
$521$	1.08310e126	0.503170	0.251585	−	0.967835i	$-0.419048\pi$
$521$	1.08310e126	0.503170	0.251585	+	0.967835i	$0.419048\pi$
$522$	1.48062e126	0.629165
$523$	−2.12144e126	−0.824711	−0.412356	−	0.911023i	$-0.635294\pi$
$523$	−2.12144e126	−0.824711	−0.412356	+	0.911023i	$0.635294\pi$
$524$	−1.14599e125	−0.0407638
$525$	9.55241e126	3.10961
$526$	1.08039e126	0.321917
$527$	6.39916e124	0.0174554
$528$	−2.76014e125	−0.0689373
$529$	−3.03348e126	−0.693828
$530$	−2.30533e127	−4.82953
$531$	1.96808e126	0.377701
$532$	−3.10087e126	−0.545246
$533$	−1.11057e124	−0.00178950
$534$	2.95482e126	0.436377
$535$	8.88850e126	1.20331
$536$	−1.91166e126	−0.237273
$537$	−4.29542e126	−0.488879
$538$	1.27299e126	0.132877
$539$	−3.75112e126	−0.359156
$540$	4.04947e127	3.55704
$541$	5.54574e126	0.446978	0.223489	−	0.974706i	$-0.428255\pi$
$541$	5.54574e126	0.446978	0.223489	+	0.974706i	$0.428255\pi$
$542$	1.41859e127	1.04928
$543$	−1.40527e127	−0.954042
$544$	−3.77755e126	−0.235430
$545$	−1.65742e127	−0.948408
$546$	3.32616e125	0.0174777
$547$	2.32636e127	1.12271	0.561354	−	0.827576i	$-0.310281\pi$
$547$	2.32636e127	1.12271	0.561354	+	0.827576i	$0.310281\pi$
$548$	−3.51089e127	−1.55640
$549$	−1.24825e127	−0.508380
$550$	1.70867e127	0.639430
$551$	−5.11816e126	−0.176021
$552$	−1.93554e127	−0.611837
$553$	−6.59982e127	−1.91784
$554$	−1.69061e127	−0.451690
$555$	−4.13056e127	−1.01481
$556$	1.53428e128	3.46679
$557$	5.86328e127	1.21864	0.609318	−	0.792926i	$-0.291443\pi$
$557$	5.86328e127	1.21864	0.609318	+	0.792926i	$0.291443\pi$
$558$	−1.27369e126	−0.0243542
$559$	8.57607e124	0.00150883
$560$	−9.77462e127	−1.58255
$561$	4.01435e126	0.0598194
$562$	−4.91416e127	−0.674079
$563$	−6.83447e127	−0.863107	−0.431554	−	0.902087i	$-0.642034\pi$
$563$	−6.83447e127	−0.863107	−0.431554	+	0.902087i	$0.642034\pi$
$564$	1.23722e128	1.43870
$565$	2.86211e128	3.06502
$566$	−2.40906e128	−2.37620
$567$	−9.81458e127	−0.891784
$568$	2.37470e128	1.98797
$569$	−1.82425e128	−1.40722	−0.703611	−	0.710585i	$-0.748430\pi$
$569$	−1.82425e128	−1.40722	−0.703611	+	0.710585i	$0.748430\pi$
$570$	−5.75813e127	−0.409355
$571$	8.22711e127	0.539099	0.269549	−	0.962987i	$-0.413125\pi$
$571$	8.22711e127	0.539099	0.269549	+	0.962987i	$0.413125\pi$
$572$	3.84258e125	0.00232117
$573$	1.97256e128	1.09860
$574$	−1.38964e128	−0.713675
$575$	2.58692e128	1.22526
$576$	1.16773e128	0.510150
$577$	−1.15417e128	−0.465150	−0.232575	−	0.972578i	$-0.574715\pi$
$577$	−1.15417e128	−0.465150	−0.232575	+	0.972578i	$0.574715\pi$
$578$	3.66110e128	1.36134
$579$	−2.09322e128	−0.718228
$580$	−1.06856e129	−3.38374
$581$	−7.79442e128	−2.27821
$582$	1.73257e128	0.467489
$583$	1.10580e128	0.275480
$584$	6.34344e128	1.45924
$585$	−2.26134e126	−0.00480418
$586$	−4.95657e128	−0.972617
$587$	4.28859e128	0.777397	0.388699	−	0.921365i	$-0.372925\pi$
$587$	4.28859e128	0.777397	0.388699	+	0.921365i	$0.372925\pi$
$588$	1.81812e129	3.04492
$589$	4.40285e126	0.00681354
$590$	−2.19920e129	−3.14519
$591$	3.80895e128	0.503486
$592$	2.91172e128	0.355787
$593$	8.20747e128	0.927184	0.463592	−	0.886049i	$-0.346560\pi$
$593$	8.20747e128	0.927184	0.463592	+	0.886049i	$0.346560\pi$
$594$	−3.00753e128	−0.314152
$595$	1.42162e129	1.37323
$596$	2.39482e129	2.13955
$597$	−7.57407e128	−0.625926
$598$	9.00768e126	0.00688665
$599$	4.54499e128	0.321504	0.160752	−	0.986995i	$-0.448608\pi$
$599$	4.54499e128	0.321504	0.160752	+	0.986995i	$0.448608\pi$
$600$	−3.74051e129	−2.44849
$601$	−2.06533e129	−1.25120	−0.625599	−	0.780145i	$-0.715145\pi$
$601$	−2.06533e129	−1.25120	−0.625599	+	0.780145i	$0.715145\pi$
$602$	1.07311e129	0.601740
$603$	−1.19478e128	−0.0620201
$604$	−6.24369e129	−3.00071
$605$	3.90978e129	1.73991
$606$	−2.69282e129	−1.10976
$607$	−3.80973e129	−1.45419	−0.727094	−	0.686538i	$-0.759130\pi$
$607$	−3.80973e129	−1.45419	−0.727094	+	0.686538i	$0.759130\pi$
$608$	−2.59909e128	−0.0918979
$609$	4.43675e129	1.45332
$610$	1.39484e130	4.23338
$611$	−2.60058e127	−0.00731400
$612$	1.10298e129	0.287492
$613$	−4.21082e129	−1.01731	−0.508656	−	0.860970i	$-0.669857\pi$
$613$	−4.21082e129	−1.01731	−0.508656	+	0.860970i	$0.669857\pi$
$614$	−1.77169e129	−0.396787
$615$	−1.66661e129	−0.346053
$616$	2.17166e129	0.418108
$617$	−4.88112e129	−0.871484	−0.435742	−	0.900072i	$-0.643514\pi$
$617$	−4.88112e129	−0.871484	−0.435742	+	0.900072i	$0.643514\pi$
$618$	2.48763e129	0.411929
$619$	−7.62026e129	−1.17045	−0.585227	−	0.810869i	$-0.698995\pi$
$619$	−7.62026e129	−1.17045	−0.585227	+	0.810869i	$0.698995\pi$
$620$	9.19219e128	0.130980
$621$	−4.55338e129	−0.601970
$622$	1.51208e130	1.85491
$623$	−5.01931e129	−0.571413
$624$	−2.81200e127	−0.00297120
$625$	1.72204e130	1.68897
$626$	1.42388e130	1.29649
$627$	2.76202e128	0.0233499
$628$	−2.72425e130	−2.13857
$629$	−4.23479e129	−0.308729
$630$	−2.82959e130	−1.91597
$631$	−4.44127e129	−0.279346	−0.139673	−	0.990198i	$-0.544605\pi$
$631$	−4.44127e129	−0.279346	−0.139673	+	0.990198i	$0.544605\pi$
$632$	2.58434e130	1.51010
$633$	−1.01264e130	−0.549771
$634$	3.39097e130	1.71070
$635$	−3.25279e129	−0.152503
$636$	−5.35968e130	−2.33552
$637$	−3.82159e128	−0.0154796
$638$	7.93615e129	0.298847
$639$	1.48418e130	0.519632
$640$	−1.00732e131	−3.27942
$641$	5.07224e130	1.53568	0.767841	−	0.640640i	$-0.221331\pi$
$641$	5.07224e130	1.53568	0.767841	+	0.640640i	$0.221331\pi$
$642$	3.19964e130	0.900994
$643$	5.10656e130	1.33757	0.668787	−	0.743454i	$-0.266814\pi$
$643$	5.10656e130	1.33757	0.668787	+	0.743454i	$0.266814\pi$
$644$	7.27955e130	1.77383
$645$	1.28700e130	0.291777
$646$	−5.90343e129	−0.124535
$647$	−1.41954e130	−0.278675	−0.139337	−	0.990245i	$-0.544497\pi$
$647$	−1.41954e130	−0.278675	−0.139337	+	0.990245i	$0.544497\pi$
$648$	3.84317e130	0.702186
$649$	1.05490e130	0.179404
$650$	1.74077e129	0.0275594
$651$	−3.81668e129	−0.0562561
$652$	−4.84466e130	−0.664890
$653$	−1.15140e131	−1.47150	−0.735752	−	0.677251i	$-0.763171\pi$
$653$	−1.15140e131	−1.47150	−0.735752	+	0.677251i	$0.763171\pi$
$654$	−5.96629e130	−0.710132
$655$	3.61485e129	0.0400747
$656$	1.17483e130	0.121324
$657$	3.96463e130	0.381428
$658$	−3.25408e131	−2.91692
$659$	1.96031e131	1.63740	0.818698	−	0.574224i	$-0.194696\pi$
$659$	1.96031e131	1.63740	0.818698	+	0.574224i	$0.194696\pi$
$660$	5.76649e130	0.448868
$661$	−2.17070e131	−1.57482	−0.787410	−	0.616429i	$-0.788579\pi$
$661$	−2.17070e131	−1.57482	−0.787410	+	0.616429i	$0.788579\pi$
$662$	2.12432e130	0.143656
$663$	4.08976e128	0.00257821
$664$	3.05212e131	1.79385
$665$	9.78126e130	0.536029
$666$	8.42894e130	0.430746
$667$	1.20153e131	0.572642
$668$	4.50492e130	0.200254
$669$	−3.05118e131	−1.26518
$670$	1.33509e131	0.516454
$671$	−6.69067e130	−0.241475
$672$	2.25306e131	0.758756
$673$	2.57783e131	0.810127	0.405063	−	0.914289i	$-0.367249\pi$
$673$	2.57783e131	0.810127	0.405063	+	0.914289i	$0.367249\pi$
$674$	2.90599e131	0.852332
$675$	−8.79959e131	−2.40900
$676$	−7.13589e131	−1.82359
$677$	3.80729e131	0.908328	0.454164	−	0.890918i	$-0.349938\pi$
$677$	3.80729e131	0.908328	0.454164	+	0.890918i	$0.349938\pi$
$678$	1.03029e132	2.29498
$679$	−2.94309e131	−0.612152
$680$	−5.56675e131	−1.08128
$681$	−5.18977e131	−0.941471
$682$	−6.82701e129	−0.0115680
$683$	6.39876e131	1.01282	0.506411	−	0.862292i	$-0.330972\pi$
$683$	6.39876e131	1.01282	0.506411	+	0.862292i	$0.330972\pi$
$684$	7.58890e130	0.112220
$685$	1.10746e132	1.53009
$686$	−2.49390e132	−3.21964
$687$	7.23412e131	0.872765
$688$	−9.07229e130	−0.102295
$689$	1.12658e130	0.0118732
$690$	1.35177e132	1.33174
$691$	1.56983e131	0.144585	0.0722925	−	0.997383i	$-0.476968\pi$
$691$	1.56983e131	0.144585	0.0722925	+	0.997383i	$0.476968\pi$
$692$	8.30297e131	0.714990
$693$	1.35728e131	0.109288
$694$	−2.13327e132	−1.60631
$695$	−4.83968e132	−3.40819
$696$	−1.73733e132	−1.14434
$697$	−1.70867e131	−0.105277
$698$	1.51266e132	0.871894
$699$	2.61327e132	1.40927
$700$	1.40680e133	7.09862
$701$	−1.73944e132	−0.821335	−0.410668	−	0.911785i	$-0.634704\pi$
$701$	−1.73944e132	−0.821335	−0.410668	+	0.911785i	$0.634704\pi$
$702$	−3.06403e130	−0.0135400
$703$	−2.91369e131	−0.120509
$704$	6.25908e131	0.242316
$705$	−3.90265e132	−1.41438
$706$	−6.70024e132	−2.27338
$707$	4.57425e132	1.45317
$708$	−5.11295e132	−1.52098
$709$	5.69886e132	1.58759	0.793794	−	0.608186i	$-0.208103\pi$
$709$	5.69886e132	1.58759	0.793794	+	0.608186i	$0.208103\pi$
$710$	−1.65847e133	−4.32708
$711$	1.61520e132	0.394722
$712$	1.96545e132	0.449928
$713$	−1.03361e131	−0.0221662
$714$	5.11747e132	1.02823
$715$	−1.21209e130	−0.00228193
$716$	−6.32594e132	−1.11601
$717$	−1.00623e132	−0.166363
$718$	6.22546e132	0.964683
$719$	−5.60725e131	−0.0814435	−0.0407218	−	0.999171i	$-0.512966\pi$
$719$	−5.60725e131	−0.0814435	−0.0407218	+	0.999171i	$0.512966\pi$
$720$	2.39219e132	0.325712
$721$	−4.22572e132	−0.539399
$722$	1.36345e133	1.63177
$723$	4.78659e132	0.537150
$724$	−2.06956e133	−2.17789
$725$	2.32200e133	2.29163
$726$	1.40742e133	1.30278
$727$	−3.95282e132	−0.343207	−0.171604	−	0.985166i	$-0.554895\pi$
$727$	−3.95282e132	−0.343207	−0.171604	+	0.985166i	$0.554895\pi$
$728$	2.21246e131	0.0180205
$729$	1.37757e133	1.05265
$730$	−4.43021e133	−3.17623
$731$	1.31947e132	0.0887652
$732$	3.24287e133	2.04722
$733$	−1.21179e133	−0.717950	−0.358975	−	0.933347i	$-0.616874\pi$
$733$	−1.21179e133	−0.717950	−0.358975	+	0.933347i	$0.616874\pi$
$734$	2.99480e132	0.166533
$735$	−5.73499e133	−2.99345
$736$	6.10159e132	0.298968
$737$	−6.40405e131	−0.0294589
$738$	3.40094e132	0.146885
$739$	2.87595e133	1.16631	0.583157	−	0.812360i	$-0.301817\pi$
$739$	2.87595e133	1.16631	0.583157	+	0.812360i	$0.301817\pi$
$740$	−6.08315e133	−2.31661
$741$	2.81390e130	0.00100638
$742$	1.40967e134	4.73519
$743$	−9.00234e132	−0.284037	−0.142019	−	0.989864i	$-0.545359\pi$
$743$	−9.00234e132	−0.284037	−0.142019	+	0.989864i	$0.545359\pi$
$744$	1.49453e132	0.0442957
$745$	−7.55412e133	−2.10338
$746$	−7.34366e133	−1.92113
$747$	1.90756e133	0.468890
$748$	5.91200e132	0.136556
$749$	−5.43518e133	−1.17980
$750$	1.43261e134	2.92266
$751$	−7.48940e133	−1.43612	−0.718059	−	0.695982i	$-0.754969\pi$
$751$	−7.48940e133	−1.43612	−0.718059	+	0.695982i	$0.754969\pi$
$752$	2.75106e133	0.495873
$753$	−1.51990e133	−0.257543
$754$	8.08525e131	0.0128803
$755$	1.96948e134	2.94998
$756$	−2.47619e134	−3.48755
$757$	1.10318e134	1.46113	0.730565	−	0.682843i	$-0.239257\pi$
$757$	1.10318e134	1.46113	0.730565	+	0.682843i	$0.239257\pi$
$758$	1.11419e134	1.38784
$759$	−6.48406e132	−0.0759635
$760$	−3.83012e133	−0.422066
$761$	−1.06465e134	−1.10362	−0.551811	−	0.833969i	$-0.686063\pi$
$761$	−1.06465e134	−1.10362	−0.551811	+	0.833969i	$0.686063\pi$
$762$	−1.17092e133	−0.114188
$763$	1.01349e134	0.929881
$764$	2.90503e134	2.50790
$765$	−3.47919e133	−0.282632
$766$	−3.00433e134	−2.29673
$767$	1.07472e132	0.00773231
$768$	−1.96259e134	−1.32903
$769$	2.64666e134	1.68703	0.843515	−	0.537105i	$-0.180482\pi$
$769$	2.64666e134	1.68703	0.843515	+	0.537105i	$0.180482\pi$
$770$	−1.51667e134	−0.910065
$771$	−2.11059e134	−1.19227
$772$	−3.08273e134	−1.63957
$773$	−1.28102e134	−0.641518	−0.320759	−	0.947161i	$-0.603938\pi$
$773$	−1.28102e134	−0.641518	−0.320759	+	0.947161i	$0.603938\pi$
$774$	−2.62628e133	−0.123847
$775$	−1.99748e133	−0.0887062
$776$	1.15245e134	0.482005
$777$	2.52578e134	0.994987
$778$	6.27167e134	2.32719
$779$	−1.17563e133	−0.0410939
$780$	5.87482e132	0.0193462
$781$	7.95523e133	0.246820
$782$	1.38588e134	0.405146
$783$	−4.08709e134	−1.12588
$784$	4.04271e134	1.04948
$785$	8.59326e134	2.10242
$786$	1.30126e133	0.0300064
$787$	2.01831e133	0.0438696	0.0219348	−	0.999759i	$-0.493017\pi$
$787$	2.01831e133	0.0438696	0.0219348	+	0.999759i	$0.493017\pi$
$788$	5.60951e134	1.14936
$789$	−7.92317e133	−0.153045
$790$	−1.80488e135	−3.28692
$791$	−1.75014e135	−3.00515
$792$	−5.31481e133	−0.0860531
$793$	−6.81636e132	−0.0104076
$794$	1.16024e134	0.167069
$795$	1.69064e135	2.29604
$796$	−1.11545e135	−1.42887
$797$	1.38083e134	0.166850	0.0834252	−	0.996514i	$-0.473414\pi$
$797$	1.38083e134	0.166850	0.0834252	+	0.996514i	$0.473414\pi$
$798$	3.52101e134	0.401359
$799$	−4.00113e134	−0.430287
$800$	1.17916e135	1.19643
$801$	1.22840e134	0.117606
$802$	7.32924e134	0.662141
$803$	2.12505e134	0.181174
$804$	3.10396e134	0.249752
$805$	−2.29623e135	−1.74384
$806$	−6.95527e131	−0.000498579 0
$807$	−9.33560e133	−0.0631717
$808$	−1.79118e135	−1.14422
$809$	6.20202e134	0.374047	0.187024	−	0.982355i	$-0.440116\pi$
$809$	6.20202e134	0.374047	0.187024	+	0.982355i	$0.440116\pi$
$810$	−2.68404e135	−1.52839
$811$	1.84479e135	0.991922	0.495961	−	0.868345i	$-0.334816\pi$
$811$	1.84479e135	0.991922	0.495961	+	0.868345i	$0.334816\pi$
$812$	6.53408e135	3.31764
$813$	−1.04034e135	−0.498843
$814$	4.51794e134	0.204600
$815$	1.52818e135	0.653650
$816$	−4.32640e134	−0.174797
$817$	9.07846e133	0.0346487
$818$	−2.00600e135	−0.723272
$819$	1.38278e133	0.00471033
$820$	−2.45445e135	−0.789970
$821$	−2.15187e135	−0.654425	−0.327213	−	0.944951i	$-0.606109\pi$
$821$	−2.15187e135	−0.654425	−0.327213	+	0.944951i	$0.606109\pi$
$822$	3.98658e135	1.14567
$823$	−5.23448e135	−1.42161	−0.710806	−	0.703388i	$-0.751670\pi$
$823$	−5.23448e135	−1.42161	−0.710806	+	0.703388i	$0.751670\pi$
$824$	1.65470e135	0.424720
$825$	−1.25307e135	−0.303995
$826$	1.34478e136	3.08375
$827$	−4.54736e135	−0.985719	−0.492860	−	0.870109i	$-0.664048\pi$
$827$	−4.54736e135	−0.985719	−0.492860	+	0.870109i	$0.664048\pi$
$828$	−1.78156e135	−0.365081
$829$	9.79485e135	1.89763	0.948816	−	0.315828i	$-0.102282\pi$
$829$	9.79485e135	1.89763	0.948816	+	0.315828i	$0.102282\pi$
$830$	−2.13158e136	−3.90454
$831$	1.23983e135	0.214740
$832$	6.37666e133	0.0104438
$833$	−5.87971e135	−0.910675
$834$	−1.74216e136	−2.55192
$835$	−1.42101e135	−0.196869
$836$	4.06767e134	0.0533033
$837$	3.51589e134	0.0435814
$838$	2.59692e136	3.04517
$839$	7.42245e135	0.823409	0.411705	−	0.911317i	$-0.364934\pi$
$839$	7.42245e135	0.823409	0.411705	+	0.911317i	$0.364934\pi$
$840$	3.32020e136	3.48479
$841$	7.15226e134	0.0710280
$842$	−2.01924e136	−1.89747
$843$	3.60385e135	0.320468
$844$	−1.49133e136	−1.25502
$845$	2.25092e136	1.79276
$846$	7.96386e135	0.600346
$847$	−2.39077e136	−1.70592
$848$	−1.19176e136	−0.804976
$849$	1.76671e136	1.12968
$850$	2.67826e136	1.62134
$851$	6.84013e135	0.392049
$852$	−3.85579e136	−2.09253
$853$	2.84936e135	0.146426	0.0732128	−	0.997316i	$-0.476675\pi$
$853$	2.84936e135	0.146426	0.0732128	+	0.997316i	$0.476675\pi$
$854$	−8.52923e136	−4.15068
$855$	−2.39381e135	−0.110323
$856$	2.12830e136	0.928971
$857$	1.21549e136	0.502507	0.251254	−	0.967921i	$-0.419157\pi$
$857$	1.21549e136	0.502507	0.251254	+	0.967921i	$0.419157\pi$
$858$	−4.36321e133	−0.00170863
$859$	−7.04217e135	−0.261231	−0.130615	−	0.991433i	$-0.541695\pi$
$859$	−7.04217e135	−0.261231	−0.130615	+	0.991433i	$0.541695\pi$
$860$	1.89538e136	0.666069
$861$	1.01911e136	0.339292
$862$	−2.41769e136	−0.762629
$863$	2.08063e136	0.621859	0.310930	−	0.950433i	$-0.399360\pi$
$863$	2.08063e136	0.621859	0.310930	+	0.950433i	$0.399360\pi$
$864$	−2.07550e136	−0.587806
$865$	−2.61906e136	−0.702903
$866$	1.12691e137	2.86621
$867$	−2.68490e136	−0.647203
$868$	−5.62089e135	−0.128422
$869$	8.65754e135	0.187489
$870$	1.21334e137	2.49079
$871$	−6.52436e133	−0.00126968
$872$	−3.96859e136	−0.732183
$873$	7.20277e135	0.125990
$874$	9.53535e135	0.158145
$875$	−2.43355e137	−3.82707
$876$	−1.02998e137	−1.53599
$877$	3.05763e136	0.432418	0.216209	−	0.976347i	$-0.430631\pi$
$877$	3.05763e136	0.432418	0.216209	+	0.976347i	$0.430631\pi$
$878$	2.06612e137	2.77115
$879$	3.63495e136	0.462397
$880$	1.28222e136	0.154710
$881$	−7.50481e136	−0.858935	−0.429467	−	0.903082i	$-0.641299\pi$
$881$	−7.50481e136	−0.858935	−0.429467	+	0.903082i	$0.641299\pi$
$882$	1.17030e137	1.27060
$883$	−5.64375e136	−0.581293	−0.290647	−	0.956830i	$-0.593870\pi$
$883$	−5.64375e136	−0.581293	−0.290647	+	0.956830i	$0.593870\pi$
$884$	6.02307e134	0.00588555
$885$	1.61281e137	1.49527
$886$	−3.66318e136	−0.322248
$887$	1.61696e136	0.134974	0.0674872	−	0.997720i	$-0.478502\pi$
$887$	1.61696e136	0.134974	0.0674872	+	0.997720i	$0.478502\pi$
$888$	−9.89038e136	−0.783448
$889$	1.98903e136	0.149523
$890$	−1.37266e137	−0.979324
$891$	1.28746e136	0.0871808
$892$	−4.49352e137	−2.88816
$893$	−2.75293e136	−0.167958
$894$	−2.71929e137	−1.57493
$895$	1.99543e137	1.09715
$896$	6.15959e137	3.21536
$897$	−6.60587e134	−0.00327402
$898$	−1.20156e137	−0.565452
$899$	−9.27759e135	−0.0414581
$900$	−3.44293e137	−1.46100
$901$	1.73330e137	0.698507
$902$	1.82291e136	0.0697689
$903$	−7.86979e136	−0.286077
$904$	6.85316e137	2.36624
$905$	6.52815e137	2.14107
$906$	7.08964e137	2.20884
$907$	−5.22741e137	−1.54721	−0.773603	−	0.633671i	$-0.781547\pi$
$907$	−5.22741e137	−1.54721	−0.773603	+	0.633671i	$0.781547\pi$
$908$	−7.64306e137	−2.14919
$909$	−1.11948e137	−0.299085
$910$	−1.54516e136	−0.0392238
$911$	2.17562e137	0.524781	0.262391	−	0.964962i	$-0.415489\pi$
$911$	2.17562e137	0.524781	0.262391	+	0.964962i	$0.415489\pi$
$912$	−2.97672e136	−0.0682304
$913$	1.02246e137	0.222718
$914$	−7.90224e137	−1.63588
$915$	−1.02292e138	−2.01261
$916$	1.06538e138	1.99235
$917$	−2.21043e136	−0.0392918
$918$	−4.71417e137	−0.796563
$919$	−2.13720e137	−0.343301	−0.171650	−	0.985158i	$-0.554910\pi$
$919$	−2.13720e137	−0.343301	−0.171650	+	0.985158i	$0.554910\pi$
$920$	8.99153e137	1.37309
$921$	1.29928e137	0.188639
$922$	−2.06821e138	−2.85500
$923$	8.10468e135	0.0106379
$924$	−3.52612e137	−0.440099
$925$	1.32188e138	1.56893
$926$	−1.28751e138	−1.45325
$927$	1.03418e137	0.111017
$928$	5.47675e137	0.559168
$929$	1.80381e138	1.75171	0.875853	−	0.482578i	$-0.160300\pi$
$929$	1.80381e138	1.75171	0.875853	+	0.482578i	$0.160300\pi$
$930$	−1.04376e137	−0.0964152
$931$	−4.04546e137	−0.355474
$932$	3.84861e138	3.21710
$933$	−1.10890e138	−0.881855
$934$	2.75048e138	2.08104
$935$	−1.86486e137	−0.134247
$936$	−5.41465e135	−0.00370889
$937$	−1.75823e138	−1.14600	−0.573001	−	0.819555i	$-0.694221\pi$
$937$	−1.75823e138	−1.14600	−0.573001	+	0.819555i	$0.694221\pi$
$938$	−8.16386e137	−0.506365
$939$	−1.04422e138	−0.616370
$940$	−5.74751e138	−3.22875
$941$	−2.47445e138	−1.32301	−0.661503	−	0.749943i	$-0.730081\pi$
$941$	−2.47445e138	−1.32301	−0.661503	+	0.749943i	$0.730081\pi$
$942$	3.09336e138	1.57421
$943$	2.75988e137	0.133689
$944$	−1.13690e138	−0.524233
$945$	7.81080e138	3.42860
$946$	−1.40769e137	−0.0588262
$947$	5.09791e137	0.202823	0.101412	−	0.994845i	$-0.467664\pi$
$947$	5.09791e137	0.202823	0.101412	+	0.994845i	$0.467664\pi$
$948$	−4.19619e138	−1.58953
$949$	2.16497e136	0.00780861
$950$	1.84274e138	0.632874
$951$	−2.48680e138	−0.813294
$952$	3.40398e138	1.06015
$953$	4.08950e138	1.21297	0.606485	−	0.795095i	$-0.292579\pi$
$953$	4.08950e138	1.21297	0.606485	+	0.795095i	$0.292579\pi$
$954$	−3.44996e138	−0.974574
$955$	−9.16351e138	−2.46550
$956$	−1.48190e138	−0.379775
$957$	−5.82006e137	−0.142077
$958$	4.67736e138	1.08769
$959$	−6.77196e138	−1.50020
$960$	9.56935e138	2.01962
$961$	−4.96524e138	−0.998395
$962$	4.60281e136	0.00881825
$963$	1.33018e138	0.242822
$964$	7.04930e138	1.22621
$965$	9.72403e138	1.61186
$966$	−8.26586e138	−1.30572
$967$	−8.90772e138	−1.34102	−0.670511	−	0.741900i	$-0.733925\pi$
$967$	−8.90772e138	−1.34102	−0.670511	+	0.741900i	$0.733925\pi$
$968$	9.36174e138	1.34324
$969$	4.32934e137	0.0592060
$970$	−8.04862e138	−1.04915
$971$	−9.30395e138	−1.15604	−0.578021	−	0.816022i	$-0.696175\pi$
$971$	−9.30395e138	−1.15604	−0.578021	+	0.816022i	$0.696175\pi$
$972$	1.05102e139	1.24489
$973$	2.95939e139	3.34161
$974$	−3.59563e138	−0.387065
$975$	−1.27661e137	−0.0131022
$976$	7.21076e138	0.705610
$977$	1.24550e139	1.16210	0.581052	−	0.813867i	$-0.302641\pi$
$977$	1.24550e139	1.16210	0.581052	+	0.813867i	$0.302641\pi$
$978$	5.50106e138	0.489429
$979$	6.58426e137	0.0558614
$980$	−8.44603e139	−6.83345
$981$	−2.48035e138	−0.191384
$982$	4.31750e137	0.0317723
$983$	−4.90628e138	−0.344361	−0.172181	−	0.985065i	$-0.555081\pi$
$983$	−4.90628e138	−0.344361	−0.172181	+	0.985065i	$0.555081\pi$
$984$	−3.99060e138	−0.267157
$985$	−1.76944e139	−1.12993
$986$	1.24396e139	0.757755
$987$	2.38641e139	1.38675
$988$	4.14409e136	0.00229737
$989$	−2.13124e138	−0.112721
$990$	3.71182e138	0.187305
$991$	−4.86403e138	−0.234192	−0.117096	−	0.993121i	$-0.537358\pi$
$991$	−4.86403e138	−0.234192	−0.117096	+	0.993121i	$0.537358\pi$
$992$	−4.71133e137	−0.0216447
$993$	−1.55789e138	−0.0682964
$994$	1.01413e140	4.24255
$995$	3.51852e139	1.40471
$996$	−4.95572e139	−1.88820
$997$	1.15939e139	0.421602	0.210801	−	0.977529i	$-0.432393\pi$
$997$	1.15939e139	0.421602	0.210801	+	0.977529i	$0.432393\pi$
$998$	−7.09332e139	−2.46195
$999$	−2.32672e139	−0.770813

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1.94.a.a.1.1	✓	7
3.2	odd	2		9.94.a.b.1.7		7

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1.94.a.a.1.1	✓	7	1.1	even	1	trivial
9.94.a.b.1.7		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)

\(f(q)\)	\(=\)	\(q-1.67226e14 q^{2} +1.22637e22 q^{3} +1.80609e28 q^{4} -5.69707e32 q^{5} -2.05080e36 q^{6} +3.48367e39 q^{7} -1.36413e42 q^{8} -8.52575e43 q^{9} +O(q^{10})\)	\(q-1.67226e14 q^{2} +1.22637e22 q^{3} +1.80609e28 q^{4} -5.69707e32 q^{5} -2.05080e36 q^{6} +3.48367e39 q^{7} -1.36413e42 q^{8} -8.52575e43 q^{9} +9.52696e46 q^{10} -4.56983e47 q^{11} +2.21493e50 q^{12} -4.65568e49 q^{13} -5.82559e53 q^{14} -6.98669e54 q^{15} +4.92506e55 q^{16} -7.16300e56 q^{17} +1.42572e58 q^{18} -4.92840e58 q^{19} -1.02894e61 q^{20} +4.27226e61 q^{21} +7.64193e61 q^{22} +1.15698e63 q^{23} -1.67292e64 q^{24} +2.23592e65 q^{25} +7.78549e63 q^{26} -3.93556e66 q^{27} +6.29183e67 q^{28} +1.03850e68 q^{29} +1.16835e69 q^{30} -8.93363e67 q^{31} +5.27370e69 q^{32} -5.60428e69 q^{33} +1.19784e71 q^{34} -1.98467e72 q^{35} -1.53983e72 q^{36} +5.91204e72 q^{37} +8.24156e72 q^{38} -5.70957e71 q^{39} +7.77153e74 q^{40} +2.38541e74 q^{41} -7.14432e75 q^{42} -1.84207e75 q^{43} -8.25353e75 q^{44} +4.85718e76 q^{45} -1.93477e77 q^{46} +5.58584e77 q^{47} +6.03993e77 q^{48} +8.20845e78 q^{49} -3.73903e79 q^{50} -8.78446e78 q^{51} -8.40858e77 q^{52} -2.41979e80 q^{53} +6.58128e80 q^{54} +2.60346e80 q^{55} -4.75217e81 q^{56} -6.04403e80 q^{57} -1.73664e82 q^{58} -2.30840e82 q^{59} -1.26186e83 q^{60} +1.46410e83 q^{61} +1.49393e82 q^{62} -2.97009e83 q^{63} -1.36965e84 q^{64} +2.65237e82 q^{65} +9.37180e83 q^{66} +1.40138e84 q^{67} -1.29370e85 q^{68} +1.41889e85 q^{69} +3.31888e86 q^{70} -1.74082e86 q^{71} +1.16302e86 q^{72} -4.65018e86 q^{73} -9.88645e86 q^{74} +2.74205e87 q^{75} -8.90115e86 q^{76} -1.59198e87 q^{77} +9.54786e85 q^{78} -1.89450e88 q^{79} -2.80584e88 q^{80} -2.81731e88 q^{81} -3.98902e88 q^{82} -2.23742e89 q^{83} +7.71609e89 q^{84} +4.08081e89 q^{85} +3.08041e89 q^{86} +1.27358e90 q^{87} +6.23383e89 q^{88} -1.44081e90 q^{89} -8.12245e90 q^{90} -1.62188e89 q^{91} +2.08962e91 q^{92} -1.09559e90 q^{93} -9.34096e91 q^{94} +2.80774e91 q^{95} +6.46750e91 q^{96} -8.44825e91 q^{97} -1.37266e93 q^{98} +3.89612e91 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 7 q + 43735426713792 q^{2} - 36\!\cdots\!84 q^{3}+ \cdots + 36\!\cdots\!11 q^{9}+O(q^{10}) \) 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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