LMFDB - Embedded newform 1.94.a.a.1.7

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			1.7
Root			$2.74671e11$ 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)

$f(q)$	$=$	$q+1.64459e14 q^{2} -2.77426e22 q^{3} +1.71431e28 q^{4} +3.18897e32 q^{5} -4.56250e36 q^{6} -2.05341e39 q^{7} +1.19061e42 q^{8} +5.33996e44 q^{9} +O(q^{10})$	\(q+1.64459e14 q^{2} -2.77426e22 q^{3} +1.71431e28 q^{4} +3.18897e32 q^{5} -4.56250e36 q^{6} -2.05341e39 q^{7} +1.19061e42 q^{8} +5.33996e44 q^{9} +5.24454e46 q^{10} -1.16805e48 q^{11} -4.75594e50 q^{12} +9.03622e51 q^{13} -3.37700e53 q^{14} -8.84704e54 q^{15} +2.60289e55 q^{16} +2.65663e56 q^{17} +8.78202e58 q^{18} -2.80384e59 q^{19} +5.46689e60 q^{20} +5.69668e61 q^{21} -1.92096e62 q^{22} -1.45691e63 q^{23} -3.30306e64 q^{24} +7.21293e62 q^{25} +1.48608e66 q^{26} -8.27675e66 q^{27} -3.52017e67 q^{28} -8.91760e67 q^{29} -1.45497e69 q^{30} +8.50292e68 q^{31} -7.51055e69 q^{32} +3.24048e70 q^{33} +4.36905e70 q^{34} -6.54826e71 q^{35} +9.15434e72 q^{36} +2.81703e72 q^{37} -4.61116e73 q^{38} -2.50688e74 q^{39} +3.79682e74 q^{40} -1.66230e75 q^{41} +9.36868e75 q^{42} -6.95533e75 q^{43} -2.00240e76 q^{44} +1.70290e77 q^{45} -2.39601e77 q^{46} -7.32306e77 q^{47} -7.22109e77 q^{48} +2.88966e77 q^{49} +1.18623e77 q^{50} -7.37017e78 q^{51} +1.54909e80 q^{52} -1.26790e80 q^{53} -1.36118e81 q^{54} -3.72488e80 q^{55} -2.44481e81 q^{56} +7.77858e81 q^{57} -1.46658e82 q^{58} +2.67897e81 q^{59} -1.51666e83 q^{60} -1.91064e82 q^{61} +1.39838e83 q^{62} -1.09651e84 q^{63} -1.49295e84 q^{64} +2.88163e84 q^{65} +5.32924e84 q^{66} +1.94035e84 q^{67} +4.55428e84 q^{68} +4.04184e85 q^{69} -1.07692e86 q^{70} -1.09152e85 q^{71} +6.35781e86 q^{72} +3.20901e86 q^{73} +4.63285e86 q^{74} -2.00105e85 q^{75} -4.80665e87 q^{76} +2.39848e87 q^{77} -4.12278e88 q^{78} +3.00437e88 q^{79} +8.30055e87 q^{80} +1.03780e89 q^{81} -2.73380e89 q^{82} -2.46149e89 q^{83} +9.76587e89 q^{84} +8.47191e88 q^{85} -1.14386e90 q^{86} +2.47397e90 q^{87} -1.39069e90 q^{88} -2.79307e89 q^{89} +2.80056e91 q^{90} -1.85550e91 q^{91} -2.49759e91 q^{92} -2.35893e91 q^{93} -1.20434e92 q^{94} -8.94137e91 q^{95} +2.08362e92 q^{96} +3.53812e92 q^{97} +4.75229e91 q^{98} -6.23735e92 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	1.64459e14	1.65258	0.826288	−	0.563247i	$-0.190448\pi$
$2$	1.64459e14	1.65258	0.826288	+	0.563247i	$0.190448\pi$
$3$	−2.77426e22	−1.80721	−0.903605	−	0.428367i	$-0.859089\pi$
$3$	−2.77426e22	−1.80721	−0.903605	+	0.428367i	$0.859089\pi$
$4$	1.71431e28	1.73101
$5$	3.18897e32	1.00357	0.501783	−	0.864994i	$-0.332678\pi$
$5$	3.18897e32	1.00357	0.501783	+	0.864994i	$0.332678\pi$
$6$	−4.56250e36	−2.98655
$7$	−2.05341e39	−1.03613	−0.518067	−	0.855340i	$-0.673348\pi$
$7$	−2.05341e39	−1.03613	−0.518067	+	0.855340i	$0.673348\pi$
$8$	1.19061e42	1.20805
$9$	5.33996e44	2.26601
$10$	5.24454e46	1.65847
$11$	−1.16805e48	−0.439240	−0.219620	−	0.975585i	$-0.570482\pi$
$11$	−1.16805e48	−0.439240	−0.219620	+	0.975585i	$0.570482\pi$
$12$	−4.75594e50	−3.12830
$13$	9.03622e51	1.43754	0.718772	−	0.695246i	$-0.244705\pi$
$13$	9.03622e51	1.43754	0.718772	+	0.695246i	$0.244705\pi$
$14$	−3.37700e53	−1.71229
$15$	−8.84704e54	−1.81365
$16$	2.60289e55	0.265385
$17$	2.65663e56	0.161605	0.0808027	−	0.996730i	$-0.474252\pi$
$17$	2.65663e56	0.161605	0.0808027	+	0.996730i	$0.474252\pi$
$18$	8.78202e58	3.74475
$19$	−2.80384e59	−0.967634	−0.483817	−	0.875169i	$-0.660750\pi$
$19$	−2.80384e59	−0.967634	−0.483817	+	0.875169i	$0.660750\pi$
$20$	5.46689e60	1.73718
$21$	5.69668e61	1.87251
$22$	−1.92096e62	−0.725878
$23$	−1.45691e63	−0.696767	−0.348384	−	0.937352i	$-0.613269\pi$
$23$	−1.45691e63	−0.696767	−0.348384	+	0.937352i	$0.613269\pi$
$24$	−3.30306e64	−2.18320
$25$	7.21293e62	0.00714334
$26$	1.48608e66	2.37565
$27$	−8.27675e66	−2.28794
$28$	−3.52017e67	−1.79356
$29$	−8.91760e67	−0.888671	−0.444336	−	0.895860i	$-0.646560\pi$
$29$	−8.91760e67	−0.888671	−0.444336	+	0.895860i	$0.646560\pi$
$30$	−1.45497e69	−2.99720
$31$	8.50292e68	0.381285	0.190642	−	0.981660i	$-0.438943\pi$
$31$	8.50292e68	0.381285	0.190642	+	0.981660i	$0.438943\pi$
$32$	−7.51055e69	−0.769480
$33$	3.24048e70	0.793799
$34$	4.36905e70	0.267065
$35$	−6.54826e71	−1.03983
$36$	9.15434e72	3.92248
$37$	2.81703e72	0.337607	0.168804	−	0.985650i	$-0.446010\pi$
$37$	2.81703e72	0.337607	0.168804	+	0.985650i	$0.446010\pi$
$38$	−4.61116e73	−1.59909
$39$	−2.50688e74	−2.59794
$40$	3.79682e74	1.21236
$41$	−1.66230e75	−1.68369	−0.841843	−	0.539722i	$-0.818529\pi$
$41$	−1.66230e75	−1.68369	−0.841843	+	0.539722i	$0.818529\pi$
$42$	9.36868e75	3.09447
$43$	−6.95533e75	−0.769192	−0.384596	−	0.923085i	$-0.625659\pi$
$43$	−6.95533e75	−0.769192	−0.384596	+	0.923085i	$0.625659\pi$
$44$	−2.00240e76	−0.760329
$45$	1.70290e77	2.27409
$46$	−2.39601e77	−1.15146
$47$	−7.32306e77	−1.29462	−0.647310	−	0.762227i	$-0.724106\pi$
$47$	−7.32306e77	−1.29462	−0.647310	+	0.762227i	$0.724106\pi$
$48$	−7.22109e77	−0.479607
$49$	2.88966e77	0.0735748
$50$	1.18623e77	0.0118049
$51$	−7.37017e78	−0.292055
$52$	1.54909e80	2.48840
$53$	−1.26790e80	−0.839956	−0.419978	−	0.907534i	$-0.637962\pi$
$53$	−1.26790e80	−0.839956	−0.419978	+	0.907534i	$0.637962\pi$
$54$	−1.36118e81	−3.78100
$55$	−3.72488e80	−0.440806
$56$	−2.44481e81	−1.25170
$57$	7.77858e81	1.74872
$58$	−1.46658e82	−1.46860
$59$	2.67897e81	0.121157	0.0605787	−	0.998163i	$-0.480705\pi$
$59$	2.67897e81	0.121157	0.0605787	+	0.998163i	$0.480705\pi$
$60$	−1.51666e83	−3.13945
$61$	−1.91064e82	−0.183376	−0.0916878	−	0.995788i	$-0.529226\pi$
$61$	−1.91064e82	−0.183376	−0.0916878	+	0.995788i	$0.529226\pi$
$62$	1.39838e83	0.630102
$63$	−1.09651e84	−2.34789
$64$	−1.49295e84	−1.53701
$65$	2.88163e84	1.44267
$66$	5.32924e84	1.31181
$67$	1.94035e84	0.237356	0.118678	−	0.992933i	$-0.462134\pi$
$67$	1.94035e84	0.237356	0.118678	+	0.992933i	$0.462134\pi$
$68$	4.55428e84	0.279741
$69$	4.04184e85	1.25920
$70$	−1.07692e86	−1.71840
$71$	−1.09152e85	−0.0900573	−0.0450286	−	0.998986i	$-0.514338\pi$
$71$	−1.09152e85	−0.0900573	−0.0450286	+	0.998986i	$0.514338\pi$
$72$	6.35781e86	2.73745
$73$	3.20901e86	0.727543	0.363771	−	0.931488i	$-0.381489\pi$
$73$	3.20901e86	0.727543	0.363771	+	0.931488i	$0.381489\pi$
$74$	4.63285e86	0.557922
$75$	−2.00105e85	−0.0129095
$76$	−4.80665e87	−1.67498
$77$	2.39848e87	0.455112
$78$	−4.12278e88	−4.29330
$79$	3.00437e88	1.73019	0.865095	−	0.501607i	$-0.167258\pi$
$79$	3.00437e88	1.73019	0.865095	+	0.501607i	$0.167258\pi$
$80$	8.30055e87	0.266331
$81$	1.03780e89	1.86878
$82$	−2.73380e89	−2.78242
$83$	−2.46149e89	−1.42583	−0.712914	−	0.701251i	$-0.752625\pi$
$83$	−2.46149e89	−1.42583	−0.712914	+	0.701251i	$0.752625\pi$
$84$	9.76587e89	3.24134
$85$	8.47191e88	0.162182
$86$	−1.14386e90	−1.27115
$87$	2.47397e90	1.60601
$88$	−1.39069e90	−0.530624
$89$	−2.79307e89	−0.0630155	−0.0315077	−	0.999504i	$-0.510031\pi$
$89$	−2.79307e89	−0.0630155	−0.0315077	+	0.999504i	$0.510031\pi$
$90$	2.80056e91	3.75810
$91$	−1.85550e91	−1.48949
$92$	−2.49759e91	−1.20611
$93$	−2.35893e91	−0.689062
$94$	−1.20434e92	−2.13946
$95$	−8.94137e91	−0.971084
$96$	2.08362e92	1.39061
$97$	3.53812e92	1.45843	0.729217	−	0.684282i	$-0.239884\pi$
$97$	3.53812e92	1.45843	0.729217	+	0.684282i	$0.239884\pi$
$98$	4.75229e91	0.121588
$99$	−6.23735e92	−0.995321
$100$	1.23652e91	0.0123652
$101$	1.67913e93	1.05716	0.528579	−	0.848884i	$-0.322725\pi$
$101$	1.67913e93	1.05716	0.528579	+	0.848884i	$0.322725\pi$
$102$	−1.21209e93	−0.482643
$103$	−2.72877e93	−0.690298	−0.345149	−	0.938548i	$-0.612172\pi$
$103$	−2.72877e93	−0.690298	−0.345149	+	0.938548i	$0.612172\pi$
$104$	1.07586e94	1.73662
$105$	1.81666e94	1.87919
$106$	−2.08517e94	−1.38809
$107$	2.57521e94	1.10782	0.553908	−	0.832578i	$-0.313136\pi$
$107$	2.57521e94	1.10782	0.553908	+	0.832578i	$0.313136\pi$
$108$	−1.41889e95	−3.96045
$109$	7.43481e94	1.35188	0.675939	−	0.736958i	$-0.263738\pi$
$109$	7.43481e94	1.35188	0.675939	+	0.736958i	$0.263738\pi$
$110$	−6.12589e94	−0.728466
$111$	−7.81518e94	−0.610127
$112$	−5.34479e94	−0.274975
$113$	−9.21006e94	−0.313412	−0.156706	−	0.987645i	$-0.550087\pi$
$113$	−9.21006e94	−0.313412	−0.156706	+	0.987645i	$0.550087\pi$
$114$	1.27925e96	2.88989
$115$	−4.64604e95	−0.699251
$116$	−1.52875e96	−1.53830
$117$	4.82530e96	3.25748
$118$	4.40580e95	0.200222
$119$	−5.45514e95	−0.167445
$120$	−1.05334e97	−2.19098
$121$	−5.70729e96	−0.807068
$122$	−3.14221e96	−0.303042
$123$	4.61166e97	3.04278
$124$	1.45766e97	0.660008
$125$	−3.19704e97	−0.996397
$126$	−1.80331e98	−3.88007
$127$	8.56364e97	1.27581	0.637904	−	0.770116i	$-0.279802\pi$
$127$	8.56364e97	1.27581	0.637904	+	0.770116i	$0.279802\pi$
$128$	−1.71148e98	−1.77055
$129$	1.92959e98	1.39009
$130$	4.73908e98	2.38412
$131$	−2.59789e98	−0.915177	−0.457588	−	0.889164i	$-0.651287\pi$
$131$	−2.59789e98	−0.915177	−0.457588	+	0.889164i	$0.651287\pi$
$132$	5.55518e98	1.37407
$133$	5.75743e98	1.00260
$134$	3.19106e98	0.392249
$135$	−2.63943e99	−2.29610
$136$	3.16301e98	0.195227
$137$	−3.51555e99	−1.54343	−0.771714	−	0.635969i	$-0.780601\pi$
$137$	−3.51555e99	−1.54343	−0.771714	+	0.635969i	$0.780601\pi$
$138$	6.64715e99	2.08093
$139$	−6.67319e99	−1.49329	−0.746647	−	0.665221i	$-0.768337\pi$
$139$	−6.67319e99	−1.49329	−0.746647	+	0.665221i	$0.768337\pi$
$140$	−1.12257e100	−1.79995
$141$	2.03161e100	2.33965
$142$	−1.79510e99	−0.148827
$143$	−1.05548e100	−0.631427
$144$	1.38993e100	0.601365
$145$	−2.84380e100	−0.891839
$146$	5.27750e100	1.20232
$147$	−8.01666e99	−0.132965
$148$	4.82926e100	0.584401
$149$	1.48590e100	0.131470	0.0657351	−	0.997837i	$-0.479061\pi$
$149$	1.48590e100	0.131470	0.0657351	+	0.997837i	$0.479061\pi$
$150$	−3.29091e99	−0.0213340
$151$	1.51425e101	0.720723	0.360362	−	0.932813i	$-0.382653\pi$
$151$	1.51425e101	0.720723	0.360362	+	0.932813i	$0.382653\pi$
$152$	−3.33828e101	−1.16895
$153$	1.41863e101	0.366199
$154$	3.94451e101	0.752107
$155$	2.71156e101	0.382644
$156$	−4.29757e102	−4.49706
$157$	−2.25114e102	−1.75012	−0.875060	−	0.484014i	$-0.839179\pi$
$157$	−2.25114e102	−1.75012	−0.875060	+	0.484014i	$0.839179\pi$
$158$	4.94095e102	2.85927
$159$	3.51748e102	1.51798
$160$	−2.39509e102	−0.772224
$161$	2.99162e102	0.721945
$162$	1.70674e103	3.08830
$163$	5.71396e101	0.0776629	0.0388315	−	0.999246i	$-0.487636\pi$
$163$	5.71396e101	0.0776629	0.0388315	+	0.999246i	$0.487636\pi$
$164$	−2.84970e103	−2.91448
$165$	1.03338e103	0.796629
$166$	−4.04814e103	−2.35629
$167$	−5.24708e102	−0.230995	−0.115497	−	0.993308i	$-0.536846\pi$
$167$	−5.24708e102	−0.230995	−0.115497	+	0.993308i	$0.536846\pi$
$168$	6.78252e103	2.26209
$169$	4.21410e103	1.06653
$170$	1.39328e103	0.268017
$171$	−1.49724e104	−2.19266
$172$	−1.19236e104	−1.33148
$173$	−1.36592e104	−1.16488	−0.582441	−	0.812873i	$-0.697902\pi$
$173$	−1.36592e104	−1.16488	−0.582441	+	0.812873i	$0.697902\pi$
$174$	4.06866e104	2.65406
$175$	−1.48111e102	−0.00740147
$176$	−3.04031e103	−0.116568
$177$	−7.43217e103	−0.218957
$178$	−4.59345e103	−0.104138
$179$	−5.69683e104	−0.995331	−0.497665	−	0.867369i	$-0.665809\pi$
$179$	−5.69683e104	−0.995331	−0.497665	+	0.867369i	$0.665809\pi$
$180$	2.91929e105	3.93647
$181$	8.04012e104	0.837932	0.418966	−	0.908002i	$-0.362393\pi$
$181$	8.04012e104	0.837932	0.418966	+	0.908002i	$0.362393\pi$
$182$	−3.05153e105	−2.46149
$183$	5.30061e104	0.331398
$184$	−1.73461e105	−0.841729
$185$	8.98344e104	0.338811
$186$	−3.87946e105	−1.13873
$187$	−3.10308e104	−0.0709836
$188$	−1.25540e106	−2.24100
$189$	1.69955e106	2.37061
$190$	−1.47049e106	−1.60479
$191$	6.07307e105	0.519226	0.259613	−	0.965713i	$-0.416405\pi$
$191$	6.07307e105	0.519226	0.259613	+	0.965713i	$0.416405\pi$
$192$	4.14183e106	2.77770
$193$	−1.56914e106	−0.826509	−0.413255	−	0.910616i	$-0.635608\pi$
$193$	−1.56914e106	−0.826509	−0.413255	+	0.910616i	$0.635608\pi$
$194$	5.81874e106	2.41017
$195$	−7.99437e106	−2.60720
$196$	4.95377e105	0.127359
$197$	5.15564e106	1.04617	0.523086	−	0.852280i	$-0.324781\pi$
$197$	5.15564e106	1.04617	0.523086	+	0.852280i	$0.324781\pi$
$198$	−1.02578e107	−1.64484
$199$	−6.16450e105	−0.0782042	−0.0391021	−	0.999235i	$-0.512450\pi$
$199$	−6.16450e105	−0.0782042	−0.0391021	+	0.999235i	$0.512450\pi$
$200$	8.58779e104	0.00862952
$201$	−5.38302e106	−0.428953
$202$	2.76147e107	1.74704
$203$	1.83115e107	0.920783
$204$	−1.26348e107	−0.505550
$205$	−5.30105e107	−1.68969
$206$	−4.48770e107	−1.14077
$207$	−7.77983e107	−1.57888
$208$	2.35203e107	0.381503
$209$	3.27503e107	0.425024
$210$	2.98765e108	3.10550
$211$	1.70503e108	1.42101	0.710505	−	0.703692i	$-0.248467\pi$
$211$	1.70503e108	1.42101	0.710505	+	0.703692i	$0.248467\pi$
$212$	−2.17357e108	−1.45397
$213$	3.02816e107	0.162752
$214$	4.23516e108	1.83075
$215$	−2.21804e108	−0.771934
$216$	−9.85437e108	−2.76395
$217$	−1.74600e108	−0.395062
$218$	1.22272e109	2.23408
$219$	−8.90263e108	−1.31482
$220$	−6.38560e108	−0.763040
$221$	2.40059e108	0.232315
$222$	−1.28527e109	−1.00828
$223$	6.25747e108	0.398311	0.199156	−	0.979968i	$-0.436180\pi$
$223$	6.25747e108	0.398311	0.199156	+	0.979968i	$0.436180\pi$
$224$	1.54222e109	0.797285
$225$	3.85168e107	0.0161869
$226$	−1.51467e109	−0.517937
$227$	4.56314e109	1.27075	0.635377	−	0.772202i	$-0.280845\pi$
$227$	4.56314e109	1.27075	0.635377	+	0.772202i	$0.280845\pi$
$228$	1.33349e110	3.02705
$229$	−8.76282e109	−1.62291	−0.811454	−	0.584416i	$-0.801324\pi$
$229$	−8.76282e109	−1.62291	−0.811454	+	0.584416i	$0.801324\pi$
$230$	−7.64081e109	−1.15557
$231$	−6.65402e109	−0.822483
$232$	−1.06174e110	−1.07356
$233$	−1.12526e110	−0.931541	−0.465770	−	0.884906i	$-0.654223\pi$
$233$	−1.12526e110	−0.931541	−0.465770	+	0.884906i	$0.654223\pi$
$234$	7.93563e110	5.38324
$235$	−2.33530e110	−1.29924
$236$	4.59259e109	0.209725
$237$	−8.33491e110	−3.12682
$238$	−8.97144e109	−0.276716
$239$	4.94210e110	1.25432	0.627161	−	0.778889i	$-0.284217\pi$
$239$	4.94210e110	1.25432	0.627161	+	0.778889i	$0.284217\pi$
$240$	−2.30279e110	−0.481317
$241$	5.44752e110	0.938440	0.469220	−	0.883081i	$-0.344535\pi$
$241$	5.44752e110	0.938440	0.469220	+	0.883081i	$0.344535\pi$
$242$	−9.38612e110	−1.33374
$243$	−9.28656e110	−1.08934
$244$	−3.27543e110	−0.317425
$245$	9.21505e109	0.0738371
$246$	7.58427e111	5.02842
$247$	−2.53361e111	−1.39101
$248$	1.01237e111	0.460611
$249$	6.82882e111	2.57677
$250$	−5.25780e111	−1.64662
$251$	−4.01618e111	−1.04468	−0.522342	−	0.852736i	$-0.674942\pi$
$251$	−4.01618e111	−1.04468	−0.522342	+	0.852736i	$0.674942\pi$
$252$	−1.87976e112	−4.06422
$253$	1.70174e111	0.306048
$254$	1.40836e112	2.10837
$255$	−2.35033e111	−0.293096
$256$	−1.33612e112	−1.38896
$257$	−5.20895e111	−0.451710	−0.225855	−	0.974161i	$-0.572518\pi$
$257$	−5.20895e111	−0.451710	−0.225855	+	0.974161i	$0.572518\pi$
$258$	3.17337e112	2.29723
$259$	−5.78451e111	−0.349806
$260$	4.94000e112	2.49727
$261$	−4.76196e112	−2.01373
$262$	−4.27245e112	−1.51240
$263$	1.79958e112	0.533616	0.266808	−	0.963750i	$-0.414031\pi$
$263$	1.79958e112	0.533616	0.266808	+	0.963750i	$0.414031\pi$
$264$	3.85814e112	0.958949
$265$	−4.04329e112	−0.842951
$266$	9.46858e112	1.65687
$267$	7.74871e111	0.113882
$268$	3.32635e112	0.410866
$269$	1.32093e113	1.37214	0.686072	−	0.727534i	$-0.259334\pi$
$269$	1.32093e113	1.37214	0.686072	+	0.727534i	$0.259334\pi$
$270$	−4.34077e113	−3.79448
$271$	−2.97524e112	−0.219003	−0.109501	−	0.993987i	$-0.534925\pi$
$271$	−2.97524e112	−0.219003	−0.109501	+	0.993987i	$0.534925\pi$
$272$	6.91491e111	0.0428877
$273$	5.14765e113	2.69182
$274$	−5.78162e113	−2.55063
$275$	−8.42508e110	−0.00313764
$276$	6.92896e113	2.17970
$277$	−4.03987e113	−1.07413	−0.537066	−	0.843540i	$-0.680467\pi$
$277$	−4.03987e113	−1.07413	−0.537066	+	0.843540i	$0.680467\pi$
$278$	−1.09746e114	−2.46778
$279$	4.54053e113	0.863994
$280$	−7.79642e113	−1.25616
$281$	2.87863e113	0.392954	0.196477	−	0.980508i	$-0.437050\pi$
$281$	2.87863e113	0.392954	0.196477	+	0.980508i	$0.437050\pi$
$282$	3.34115e114	3.86645
$283$	−5.62457e113	−0.552103	−0.276051	−	0.961143i	$-0.589026\pi$
$283$	−5.62457e113	−0.552103	−0.276051	+	0.961143i	$0.589026\pi$
$284$	−1.87120e113	−0.155890
$285$	2.48057e114	1.75495
$286$	−1.73582e114	−1.04348
$287$	3.41339e114	1.74453
$288$	−4.01060e114	−1.74365
$289$	−2.63182e114	−0.973884
$290$	−4.67687e114	−1.47383
$291$	−9.81566e114	−2.63570
$292$	5.50124e114	1.25938
$293$	7.76401e114	1.51615	0.758074	−	0.652169i	$-0.226141\pi$
$293$	7.76401e114	1.51615	0.758074	+	0.652169i	$0.226141\pi$
$294$	−1.31841e114	−0.219735
$295$	8.54318e113	0.121589
$296$	3.35398e114	0.407846
$297$	9.66767e114	1.00496
$298$	2.44368e114	0.217265
$299$	−1.31649e115	−1.00163
$300$	−3.43043e113	−0.0223465
$301$	1.42821e115	0.796986
$302$	2.49031e115	1.19105
$303$	−4.65834e115	−1.91051
$304$	−7.29809e114	−0.256796
$305$	−6.09298e114	−0.184029
$306$	2.33306e115	0.605172
$307$	−6.39360e114	−0.142499	−0.0712494	−	0.997459i	$-0.522699\pi$
$307$	−6.39360e114	−0.142499	−0.0712494	+	0.997459i	$0.522699\pi$
$308$	4.11174e115	0.787803
$309$	7.57032e115	1.24751
$310$	4.45939e115	0.632349
$311$	−7.51185e115	−0.917041	−0.458521	−	0.888684i	$-0.651621\pi$
$311$	−7.51185e115	−0.917041	−0.458521	+	0.888684i	$0.651621\pi$
$312$	−2.98472e116	−3.13844
$313$	1.96544e116	1.78094	0.890469	−	0.455044i	$-0.150377\pi$
$313$	1.96544e116	1.78094	0.890469	+	0.455044i	$0.150377\pi$
$314$	−3.70219e116	−2.89221
$315$	−3.49674e116	−2.35626
$316$	5.15042e116	2.99498
$317$	2.24637e116	1.12778	0.563892	−	0.825849i	$-0.309304\pi$
$317$	2.24637e116	1.12778	0.563892	+	0.825849i	$0.309304\pi$
$318$	5.78479e116	2.50857
$319$	1.04162e116	0.390340
$320$	−4.76098e116	−1.54249
$321$	−7.14431e116	−2.00205
$322$	4.91998e116	1.19307
$323$	−7.44876e115	−0.156375
$324$	1.77910e117	3.23488
$325$	6.51777e114	0.0102689
$326$	9.39710e115	0.128344
$327$	−2.06261e117	−2.44313
$328$	−1.97916e117	−2.03398
$329$	1.50372e117	1.34140
$330$	1.69948e117	1.31649
$331$	−1.83238e117	−1.23315	−0.616573	−	0.787298i	$-0.711479\pi$
$331$	−1.83238e117	−1.23315	−0.616573	+	0.787298i	$0.711479\pi$
$332$	−4.21976e117	−2.46812
$333$	1.50428e117	0.765020
$334$	−8.62927e116	−0.381736
$335$	6.18771e116	0.238202
$336$	1.48278e117	0.496937
$337$	4.69113e117	1.36926	0.684632	−	0.728889i	$-0.259963\pi$
$337$	4.69113e117	1.36926	0.684632	+	0.728889i	$0.259963\pi$
$338$	6.93045e117	1.76252
$339$	2.55511e117	0.566400
$340$	1.45235e117	0.280738
$341$	−9.93185e116	−0.167476
$342$	−2.46234e118	−3.62355
$343$	7.47142e117	0.959901
$344$	−8.28108e117	−0.929222
$345$	1.28893e118	1.26369
$346$	−2.24637e118	−1.92506
$347$	2.19991e118	1.64848	0.824242	−	0.566238i	$-0.191602\pi$
$347$	2.19991e118	1.64848	0.824242	+	0.566238i	$0.191602\pi$
$348$	4.24115e118	2.78003
$349$	−5.28040e116	−0.0302890	−0.0151445	−	0.999885i	$-0.504821\pi$
$349$	−5.28040e116	−0.0302890	−0.0151445	+	0.999885i	$0.504821\pi$
$350$	−2.43581e116	−0.0122315
$351$	−7.47905e118	−3.28901
$352$	8.77270e117	0.337987
$353$	−8.12471e117	−0.274337	−0.137168	−	0.990548i	$-0.543800\pi$
$353$	−8.12471e117	−0.274337	−0.137168	+	0.990548i	$0.543800\pi$
$354$	−1.22228e118	−0.361843
$355$	−3.48083e117	−0.0903784
$356$	−4.78819e117	−0.109080
$357$	1.51340e118	0.302608
$358$	−9.36892e118	−1.64486
$359$	2.33635e118	0.360284	0.180142	−	0.983641i	$-0.442344\pi$
$359$	2.33635e118	0.360284	0.180142	+	0.983641i	$0.442344\pi$
$360$	2.02749e119	2.74721
$361$	−5.34716e117	−0.0636852
$362$	1.32227e119	1.38475
$363$	1.58335e119	1.45854
$364$	−3.18091e119	−2.57832
$365$	1.02335e119	0.730137
$366$	8.71731e118	0.547661
$367$	3.31122e118	0.183238	0.0916190	−	0.995794i	$-0.470796\pi$
$367$	3.31122e118	0.183238	0.0916190	+	0.995794i	$0.470796\pi$
$368$	−3.79217e118	−0.184912
$369$	−8.87664e119	−3.81525
$370$	1.47740e119	0.559911
$371$	2.60351e119	0.870307
$372$	−4.04394e119	−1.19277
$373$	7.34542e118	0.191230	0.0956149	−	0.995418i	$-0.469518\pi$
$373$	7.34542e118	0.191230	0.0956149	+	0.995418i	$0.469518\pi$
$374$	−5.10328e118	−0.117306
$375$	8.86941e119	1.80070
$376$	−8.71890e119	−1.56397
$377$	−8.05814e119	−1.27750
$378$	2.79506e120	3.91762
$379$	9.84272e119	1.22009	0.610045	−	0.792367i	$-0.291151\pi$
$379$	9.84272e119	1.22009	0.610045	+	0.792367i	$0.291151\pi$
$380$	−1.53283e120	−1.68096
$381$	−2.37578e120	−2.30565
$382$	9.98768e119	0.858061
$383$	−5.93733e119	−0.451698	−0.225849	−	0.974162i	$-0.572516\pi$
$383$	−5.93733e119	−0.451698	−0.225849	+	0.974162i	$0.572516\pi$
$384$	4.74808e120	3.19975
$385$	7.64870e119	0.456735
$386$	−2.58059e120	−1.36587
$387$	−3.71412e120	−1.74299
$388$	6.06543e120	2.52456
$389$	1.81278e119	0.0669404	0.0334702	−	0.999440i	$-0.489344\pi$
$389$	1.81278e119	0.0669404	0.0334702	+	0.999440i	$0.489344\pi$
$390$	−1.31474e121	−4.30861
$391$	−3.87046e119	−0.112601
$392$	3.44046e119	0.0888820
$393$	7.20721e120	1.65392
$394$	8.47889e120	1.72888
$395$	9.58086e120	1.73636
$396$	−1.06927e121	−1.72291
$397$	−9.51402e120	−1.36334	−0.681672	−	0.731658i	$-0.738747\pi$
$397$	−9.51402e120	−1.36334	−0.681672	+	0.731658i	$0.738747\pi$
$398$	−1.01380e120	−0.129238
$399$	−1.59726e121	−1.81191
$400$	1.87745e118	0.00189574
$401$	4.50368e120	0.404906	0.202453	−	0.979292i	$-0.435109\pi$
$401$	4.50368e120	0.404906	0.202453	+	0.979292i	$0.435109\pi$
$402$	−8.85283e120	−0.708877
$403$	7.68343e120	0.548113
$404$	2.87855e121	1.82995
$405$	3.30950e121	1.87544
$406$	3.01148e121	1.52166
$407$	−3.29044e120	−0.148291
$408$	−8.77499e120	−0.352817
$409$	−2.08198e121	−0.747040	−0.373520	−	0.927622i	$-0.621849\pi$
$409$	−2.08198e121	−0.747040	−0.373520	+	0.927622i	$0.621849\pi$
$410$	−8.71802e121	−2.79234
$411$	9.75304e121	2.78930
$412$	−4.67796e121	−1.19491
$413$	−5.50102e120	−0.125535
$414$	−1.27946e122	−2.60922
$415$	−7.84964e121	−1.43091
$416$	−6.78670e121	−1.10616
$417$	1.85132e122	2.69870
$418$	5.38607e121	0.702384
$419$	−6.99167e121	−0.815885	−0.407943	−	0.913008i	$-0.633754\pi$
$419$	−6.99167e121	−0.815885	−0.407943	+	0.913008i	$0.633754\pi$
$420$	3.11431e122	3.25289
$421$	−5.99741e121	−0.560849	−0.280425	−	0.959876i	$-0.590475\pi$
$421$	−5.99741e121	−0.560849	−0.280425	+	0.959876i	$0.590475\pi$
$422$	2.80406e122	2.34833
$423$	−3.91048e122	−2.93362
$424$	−1.50957e122	−1.01471
$425$	1.91621e119	0.00115440
$426$	4.98007e121	0.268961
$427$	3.92332e121	0.190002
$428$	4.41471e122	1.91764
$429$	2.92817e122	1.14112
$430$	−3.64775e122	−1.27568
$431$	−2.88391e122	−0.905293	−0.452646	−	0.891690i	$-0.649520\pi$
$431$	−2.88391e122	−0.905293	−0.452646	+	0.891690i	$0.649520\pi$
$432$	−2.15435e122	−0.607185
$433$	−6.05429e122	−1.53241	−0.766207	−	0.642594i	$-0.777858\pi$
$433$	−6.05429e122	−1.53241	−0.766207	+	0.642594i	$0.777858\pi$
$434$	−2.87144e122	−0.652871
$435$	7.88943e122	1.61174
$436$	1.27456e123	2.34011
$437$	4.08494e122	0.674215
$438$	−1.46411e123	−2.17284
$439$	−1.03981e123	−1.38788	−0.693940	−	0.720033i	$-0.744127\pi$
$439$	−1.03981e123	−1.38788	−0.693940	+	0.720033i	$0.744127\pi$
$440$	−4.43488e122	−0.532516
$441$	1.54307e122	0.166721
$442$	3.94797e122	0.383918
$443$	1.27414e123	1.11544	0.557719	−	0.830030i	$-0.311677\pi$
$443$	1.27414e123	1.11544	0.557719	+	0.830030i	$0.311677\pi$
$444$	−1.33976e123	−1.05614
$445$	−8.90704e121	−0.0632402
$446$	1.02909e123	0.658240
$447$	−4.12226e122	−0.237594
$448$	3.06564e123	1.59255
$449$	−1.96102e122	−0.0918389	−0.0459195	−	0.998945i	$-0.514622\pi$
$449$	−1.96102e122	−0.0918389	−0.0459195	+	0.998945i	$0.514622\pi$
$450$	6.33441e121	0.0267500
$451$	1.94166e123	0.739543
$452$	−1.57889e123	−0.542518
$453$	−4.20091e123	−1.30250
$454$	7.50448e123	2.10002
$455$	−5.91715e123	−1.49480
$456$	9.26125e123	2.11254
$457$	1.00769e123	0.207598	0.103799	−	0.994598i	$-0.466900\pi$
$457$	1.00769e123	0.207598	0.103799	+	0.994598i	$0.466900\pi$
$458$	−1.44112e124	−2.68198
$459$	−2.19882e123	−0.369744
$460$	−7.96475e123	−1.21041
$461$	−1.03588e123	−0.142304	−0.0711522	−	0.997465i	$-0.522668\pi$
$461$	−1.03588e123	−0.142304	−0.0711522	+	0.997465i	$0.522668\pi$
$462$	−1.09431e124	−1.35922
$463$	1.69373e124	1.90252	0.951260	−	0.308391i	$-0.0997906\pi$
$463$	1.69373e124	1.90252	0.951260	+	0.308391i	$0.0997906\pi$
$464$	−2.32115e123	−0.235840
$465$	−7.52257e123	−0.691518
$466$	−1.85058e124	−1.53944
$467$	1.30804e124	0.984886	0.492443	−	0.870345i	$-0.336104\pi$
$467$	1.30804e124	0.984886	0.492443	+	0.870345i	$0.336104\pi$
$468$	8.27206e124	5.63873
$469$	−3.98432e123	−0.245933
$470$	−3.84061e124	−2.14709
$471$	6.24524e124	3.16284
$472$	3.18961e123	0.146364
$473$	8.12419e123	0.337860
$474$	−1.37075e125	−5.16731
$475$	−2.02239e122	−0.00691214
$476$	−9.35179e123	−0.289849
$477$	−6.77053e124	−1.90335
$478$	8.12771e124	2.07286
$479$	3.97794e122	0.00920571	0.00460285	−	0.999989i	$-0.498535\pi$
$479$	3.97794e122	0.00920571	0.00460285	+	0.999989i	$0.498535\pi$
$480$	6.64461e124	1.39557
$481$	2.54553e124	0.485325
$482$	8.95891e124	1.55084
$483$	−8.29954e124	−1.30471
$484$	−9.78406e124	−1.39704
$485$	1.12830e125	1.46363
$486$	−1.52725e125	−1.80022
$487$	−7.90319e124	−0.846653	−0.423327	−	0.905977i	$-0.639138\pi$
$487$	−7.90319e124	−0.846653	−0.423327	+	0.905977i	$0.639138\pi$
$488$	−2.27483e124	−0.221527
$489$	−1.58520e124	−0.140353
$490$	1.51549e124	0.122021
$491$	−1.51789e125	−1.11160	−0.555802	−	0.831315i	$-0.687589\pi$
$491$	−1.51789e125	−1.11160	−0.555802	+	0.831315i	$0.687589\pi$
$492$	7.90582e125	5.26707
$493$	−2.36907e124	−0.143614
$494$	−4.16674e125	−2.29876
$495$	−1.98907e125	−0.998870
$496$	2.21322e124	0.101187
$497$	2.24134e124	0.0933115
$498$	1.12306e126	4.25831
$499$	−2.29978e124	−0.0794348	−0.0397174	−	0.999211i	$-0.512646\pi$
$499$	−2.29978e124	−0.0794348	−0.0397174	+	0.999211i	$0.512646\pi$
$500$	−5.48071e125	−1.72477
$501$	1.45568e125	0.417456
$502$	−6.60495e125	−1.72642
$503$	4.01248e125	0.956097	0.478048	−	0.878334i	$-0.341344\pi$
$503$	4.01248e125	0.956097	0.478048	+	0.878334i	$0.341344\pi$
$504$	−1.30552e126	−2.83637
$505$	5.35470e125	1.06093
$506$	2.79866e125	0.505768
$507$	−1.16910e126	−1.92744
$508$	1.46807e126	2.20844
$509$	−8.19933e125	−1.12565	−0.562823	−	0.826578i	$-0.690285\pi$
$509$	−8.19933e125	−1.12565	−0.562823	+	0.826578i	$0.690285\pi$
$510$	−3.86531e125	−0.484364
$511$	−6.58941e125	−0.753832
$512$	−5.02404e125	−0.524807
$513$	2.32067e126	2.21389
$514$	−8.56656e125	−0.746486
$515$	−8.70198e125	−0.692759
$516$	3.30791e126	2.40626
$517$	8.55371e125	0.568649
$518$	−9.51313e125	−0.578082
$519$	3.78942e126	2.10518
$520$	3.43089e126	1.74282
$521$	−1.97404e126	−0.917069	−0.458534	−	0.888677i	$-0.651625\pi$
$521$	−1.97404e126	−0.917069	−0.458534	+	0.888677i	$0.651625\pi$
$522$	−7.83145e126	−3.32785
$523$	1.23071e126	0.478441	0.239220	−	0.970965i	$-0.423108\pi$
$523$	1.23071e126	0.478441	0.239220	+	0.970965i	$0.423108\pi$
$524$	−4.45358e126	−1.58418
$525$	4.10898e124	0.0133760
$526$	2.95956e126	0.881841
$527$	2.25891e125	0.0616177
$528$	8.43460e125	0.210662
$529$	−2.24951e126	−0.514515
$530$	−6.64954e126	−1.39304
$531$	1.43056e126	0.274544
$532$	9.87001e126	1.73551
$533$	−1.50210e127	−2.42037
$534$	1.27434e126	0.188199
$535$	8.21228e126	1.11177
$536$	2.31019e126	0.286738
$537$	1.58045e127	1.79877
$538$	2.17239e127	2.26757
$539$	−3.37527e125	−0.0323170
$540$	−4.52480e127	−3.97457
$541$	−9.82340e126	−0.791752	−0.395876	−	0.918304i	$-0.629559\pi$
$541$	−9.82340e126	−0.791752	−0.395876	+	0.918304i	$0.629559\pi$
$542$	−4.89303e126	−0.361919
$543$	−2.23054e127	−1.51432
$544$	−1.99527e126	−0.124352
$545$	2.37094e127	1.35670
$546$	8.46574e127	4.44843
$547$	3.53717e127	1.70704	0.853522	−	0.521056i	$-0.174462\pi$
$547$	3.53717e127	1.70704	0.853522	+	0.521056i	$0.174462\pi$
$548$	−6.02674e127	−2.67169
$549$	−1.02027e127	−0.415530
$550$	−1.38558e125	−0.00518520
$551$	2.50035e127	0.859908
$552$	4.81225e127	1.52118
$553$	−6.16920e127	−1.79271
$554$	−6.64391e127	−1.77509
$555$	−2.49224e127	−0.612302
$556$	−1.14399e128	−2.58491
$557$	1.20728e127	0.250924	0.125462	−	0.992098i	$-0.459959\pi$
$557$	1.20728e127	0.250924	0.125462	+	0.992098i	$0.459959\pi$
$558$	7.46729e127	1.42782
$559$	−6.28499e127	−1.10575
$560$	−1.70444e127	−0.275955
$561$	8.60874e126	0.128282
$562$	4.73415e127	0.649386
$563$	1.26048e128	1.59182	0.795911	−	0.605414i	$-0.206992\pi$
$563$	1.26048e128	1.59182	0.795911	+	0.605414i	$0.206992\pi$
$564$	3.48280e128	4.04996
$565$	−2.93706e127	−0.314529
$566$	−9.25008e127	−0.912392
$567$	−2.13102e128	−1.93631
$568$	−1.29957e127	−0.108794
$569$	−1.77963e128	−1.37280	−0.686402	−	0.727222i	$-0.740811\pi$
$569$	−1.77963e128	−1.37280	−0.686402	+	0.727222i	$0.740811\pi$
$570$	4.07951e128	2.90019
$571$	−1.45624e127	−0.0954230	−0.0477115	−	0.998861i	$-0.515193\pi$
$571$	−1.45624e127	−0.0954230	−0.0477115	+	0.998861i	$0.515193\pi$
$572$	−1.80941e128	−1.09301
$573$	−1.68483e128	−0.938351
$574$	5.61361e128	2.88296
$575$	−1.05086e126	−0.00497725
$576$	−7.97230e128	−3.48288
$577$	3.39638e128	1.36880	0.684401	−	0.729106i	$-0.260064\pi$
$577$	3.39638e128	1.36880	0.684401	+	0.729106i	$0.260064\pi$
$578$	−4.32826e128	−1.60942
$579$	4.35321e128	1.49368
$580$	−4.87515e128	−1.54378
$581$	5.05445e128	1.47735
$582$	−1.61427e129	−4.35569
$583$	1.48097e128	0.368942
$584$	3.82068e128	0.878908
$585$	1.53878e129	3.26910
$586$	1.27686e129	2.50555
$587$	−9.03917e128	−1.63854	−0.819270	−	0.573408i	$-0.805621\pi$
$587$	−9.03917e128	−1.63854	−0.819270	+	0.573408i	$0.805621\pi$
$588$	−1.37430e128	−0.230164
$589$	−2.38408e128	−0.368944
$590$	1.40500e128	0.200936
$591$	−1.43031e129	−1.89065
$592$	7.33243e127	0.0895959
$593$	3.48429e128	0.393615	0.196807	−	0.980442i	$-0.436943\pi$
$593$	3.48429e128	0.393615	0.196807	+	0.980442i	$0.436943\pi$
$594$	1.58993e129	1.66077
$595$	−1.73963e128	−0.168042
$596$	2.54729e128	0.227576
$597$	1.71019e128	0.141331
$598$	−2.16509e129	−1.65528
$599$	2.02715e128	0.143397	0.0716984	−	0.997426i	$-0.477158\pi$
$599$	2.02715e128	0.143397	0.0716984	+	0.997426i	$0.477158\pi$
$600$	−2.38247e127	−0.0155953
$601$	−5.80105e128	−0.351434	−0.175717	−	0.984441i	$-0.556224\pi$
$601$	−5.80105e128	−0.351434	−0.175717	+	0.984441i	$0.556224\pi$
$602$	2.34882e129	1.31708
$603$	1.03614e129	0.537851
$604$	2.59589e129	1.24758
$605$	−1.82004e129	−0.809946
$606$	−7.66104e129	−3.15726
$607$	4.21620e129	1.60934	0.804668	−	0.593725i	$-0.202343\pi$
$607$	4.21620e129	1.60934	0.804668	+	0.593725i	$0.202343\pi$
$608$	2.10584e129	0.744575
$609$	−5.08007e129	−1.66405
$610$	−1.00204e129	−0.304123
$611$	−6.61728e129	−1.86107
$612$	2.43197e129	0.633894
$613$	−5.05723e129	−1.22180	−0.610901	−	0.791707i	$-0.709193\pi$
$613$	−5.05723e129	−1.22180	−0.610901	+	0.791707i	$0.709193\pi$
$614$	−1.05148e129	−0.235490
$615$	1.47065e130	3.05362
$616$	2.85566e129	0.549798
$617$	2.60006e129	0.464220	0.232110	−	0.972690i	$-0.425437\pi$
$617$	2.60006e129	0.464220	0.232110	+	0.972690i	$0.425437\pi$
$618$	1.24500e130	2.06161
$619$	−7.58633e129	−1.16524	−0.582622	−	0.812744i	$-0.697973\pi$
$619$	−7.58633e129	−1.16524	−0.582622	+	0.812744i	$0.697973\pi$
$620$	4.64845e129	0.662361
$621$	1.20585e130	1.59416
$622$	−1.23539e130	−1.51548
$623$	5.73532e128	0.0652925
$624$	−6.52513e129	−0.689455
$625$	−1.02681e130	−1.00709
$626$	3.23234e130	2.94314
$627$	−9.08578e129	−0.768107
$628$	−3.85914e130	−3.02948
$629$	7.48381e128	0.0545591
$630$	−5.75069e130	−3.89390
$631$	1.12795e130	0.709456	0.354728	−	0.934970i	$-0.384574\pi$
$631$	1.12795e130	0.709456	0.354728	+	0.934970i	$0.384574\pi$
$632$	3.57703e130	2.09016
$633$	−4.73018e130	−2.56806
$634$	3.69435e130	1.86375
$635$	2.73092e130	1.28036
$636$	6.03004e130	2.62763
$637$	2.61116e129	0.105767
$638$	1.71304e130	0.645067
$639$	−5.82868e129	−0.204070
$640$	−5.45786e130	−1.77686
$641$	6.71910e129	0.203429	0.101715	−	0.994814i	$-0.467567\pi$
$641$	6.71910e129	0.203429	0.101715	+	0.994814i	$0.467567\pi$
$642$	−1.17494e131	−3.30855
$643$	2.52742e130	0.662015	0.331007	−	0.943628i	$-0.392612\pi$
$643$	2.52742e130	0.662015	0.331007	+	0.943628i	$0.392612\pi$
$644$	5.12857e130	1.24969
$645$	6.15341e130	1.39505
$646$	−1.22501e130	−0.258421
$647$	−5.15142e130	−1.01130	−0.505648	−	0.862740i	$-0.668746\pi$
$647$	−5.15142e130	−1.01130	−0.505648	+	0.862740i	$0.668746\pi$
$648$	1.23561e131	2.25758
$649$	−3.12918e129	−0.0532172
$650$	1.07190e129	0.0169701
$651$	4.84385e130	0.713961
$652$	9.79550e129	0.134435
$653$	1.88412e130	0.240794	0.120397	−	0.992726i	$-0.461583\pi$
$653$	1.88412e130	0.240794	0.120397	+	0.992726i	$0.461583\pi$
$654$	−3.39213e131	−4.03745
$655$	−8.28459e130	−0.918439
$656$	−4.32680e130	−0.446826
$657$	1.71360e131	1.64862
$658$	2.47300e131	2.21677
$659$	−1.86982e131	−1.56181	−0.780903	−	0.624653i	$-0.785241\pi$
$659$	−1.86982e131	−1.56181	−0.780903	+	0.624653i	$0.785241\pi$
$660$	1.77153e131	1.37897
$661$	8.10316e130	0.587877	0.293938	−	0.955824i	$-0.405034\pi$
$661$	8.10316e130	0.587877	0.293938	+	0.955824i	$0.405034\pi$
$662$	−3.01351e131	−2.03787
$663$	−6.65985e130	−0.419841
$664$	−2.93068e131	−1.72247
$665$	1.83603e131	1.00617
$666$	2.47392e131	1.26425
$667$	1.29921e131	0.619197
$668$	−8.99512e130	−0.399854
$669$	−1.73598e131	−0.719832
$670$	1.01762e131	0.393648
$671$	2.23173e130	0.0805459
$672$	−4.27852e131	−1.44086
$673$	1.80585e131	0.567519	0.283760	−	0.958895i	$-0.408418\pi$
$673$	1.80585e131	0.567519	0.283760	+	0.958895i	$0.408418\pi$
$674$	7.71497e131	2.26281
$675$	−5.96997e129	−0.0163435
$676$	7.22427e131	1.84617
$677$	3.06664e131	0.731627	0.365813	−	0.930688i	$-0.380791\pi$
$677$	3.06664e131	0.731627	0.365813	+	0.930688i	$0.380791\pi$
$678$	4.20210e131	0.936020
$679$	−7.26520e131	−1.51113
$680$	1.00867e131	0.195923
$681$	−1.26593e132	−2.29652
$682$	−1.63338e131	−0.276766
$683$	−2.46209e131	−0.389710	−0.194855	−	0.980832i	$-0.562424\pi$
$683$	−2.46209e131	−0.389710	−0.194855	+	0.980832i	$0.562424\pi$
$684$	−2.56673e132	−3.79552
$685$	−1.12110e132	−1.54893
$686$	1.22874e132	1.58631
$687$	2.43103e132	2.93294
$688$	−1.81040e131	−0.204132
$689$	−1.14570e132	−1.20747
$690$	2.11976e132	2.08835
$691$	−5.87683e131	−0.541270	−0.270635	−	0.962682i	$-0.587234\pi$
$691$	−5.87683e131	−0.541270	−0.270635	+	0.962682i	$0.587234\pi$
$692$	−2.34161e132	−2.01642
$693$	1.28078e132	1.03129
$694$	3.61794e132	2.72425
$695$	−2.12806e132	−1.49862
$696$	2.94553e132	1.94015
$697$	−4.41612e131	−0.272093
$698$	−8.68407e130	−0.0500549
$699$	3.12176e132	1.68349
$700$	−2.53908e130	−0.0128120
$701$	1.49796e132	0.707313	0.353657	−	0.935375i	$-0.384938\pi$
$701$	1.49796e132	0.707313	0.353657	+	0.935375i	$0.384938\pi$
$702$	−1.22999e133	−5.43535
$703$	−7.89851e131	−0.326680
$704$	1.74384e132	0.675117
$705$	6.47874e132	2.34799
$706$	−1.33618e132	−0.453362
$707$	−3.44794e132	−1.09536
$708$	−1.27410e132	−0.379016
$709$	−3.30985e132	−0.922059	−0.461029	−	0.887385i	$-0.652520\pi$
$709$	−3.30985e132	−0.922059	−0.461029	+	0.887385i	$0.652520\pi$
$710$	−5.72452e131	−0.149357
$711$	1.60432e133	3.92062
$712$	−3.32546e131	−0.0761258
$713$	−1.23880e132	−0.265667
$714$	2.48891e132	0.500083
$715$	−3.36589e132	−0.633678
$716$	−9.76613e132	−1.72293
$717$	−1.37107e133	−2.26682
$718$	3.84232e132	0.595397
$719$	−5.03271e131	−0.0730985	−0.0365492	−	0.999332i	$-0.511637\pi$
$719$	−5.03271e131	−0.0730985	−0.0365492	+	0.999332i	$0.511637\pi$
$720$	4.43246e132	0.603509
$721$	5.60328e132	0.715241
$722$	−8.79387e131	−0.105245
$723$	−1.51128e133	−1.69596
$724$	1.37833e133	1.45047
$725$	−6.43221e130	−0.00634808
$726$	2.60395e133	2.41035
$727$	8.36481e132	0.726283	0.363141	−	0.931734i	$-0.381704\pi$
$727$	8.36481e132	0.726283	0.363141	+	0.931734i	$0.381704\pi$
$728$	−2.20918e133	−1.79938
$729$	1.30715e132	0.0998836
$730$	1.68298e133	1.20661
$731$	−1.84777e132	−0.124306
$732$	9.08688e132	0.573654
$733$	−8.18691e131	−0.0485049	−0.0242524	−	0.999706i	$-0.507721\pi$
$733$	−8.18691e131	−0.0485049	−0.0242524	+	0.999706i	$0.507721\pi$
$734$	5.44558e132	0.302815
$735$	−2.55649e132	−0.133439
$736$	1.09422e133	0.536149
$737$	−2.26642e132	−0.104256
$738$	−1.45984e134	−6.30499
$739$	−2.27978e132	−0.0924543	−0.0462271	−	0.998931i	$-0.514720\pi$
$739$	−2.27978e132	−0.0924543	−0.0462271	+	0.998931i	$0.514720\pi$
$740$	1.54004e133	0.586485
$741$	7.02889e133	2.51386
$742$	4.28170e133	1.43825
$743$	2.14775e132	0.0677648	0.0338824	−	0.999426i	$-0.489213\pi$
$743$	2.14775e132	0.0677648	0.0338824	+	0.999426i	$0.489213\pi$
$744$	−2.80856e133	−0.832421
$745$	4.73849e132	0.131939
$746$	1.20802e133	0.316022
$747$	−1.31443e134	−3.23094
$748$	−5.31963e132	−0.122873
$749$	−5.28796e133	−1.14785
$750$	1.45865e134	2.97579
$751$	3.97986e133	0.763151	0.381575	−	0.924338i	$-0.375382\pi$
$751$	3.97986e133	0.763151	0.381575	+	0.924338i	$0.375382\pi$
$752$	−1.90611e133	−0.343573
$753$	1.11419e134	1.88796
$754$	−1.32523e134	−2.11117
$755$	4.82889e133	0.723293
$756$	2.91356e134	4.10356
$757$	−4.10840e133	−0.544145	−0.272072	−	0.962277i	$-0.587709\pi$
$757$	−4.10840e133	−0.544145	−0.272072	+	0.962277i	$0.587709\pi$
$758$	1.61872e134	2.01629
$759$	−4.72107e133	−0.553093
$760$	−1.06457e134	−1.17312
$761$	−1.71355e134	−1.77627	−0.888136	−	0.459580i	$-0.848000\pi$
$761$	−1.71355e134	−1.77627	−0.888136	+	0.459580i	$0.848000\pi$
$762$	−3.90717e134	−3.81027
$763$	−1.52667e134	−1.40073
$764$	1.04111e134	0.898786
$765$	4.52397e133	0.367505
$766$	−9.76445e133	−0.746466
$767$	2.42078e133	0.174169
$768$	3.70675e134	2.51013
$769$	3.69304e133	0.235401	0.117701	−	0.993049i	$-0.462448\pi$
$769$	3.69304e133	0.235401	0.117701	+	0.993049i	$0.462448\pi$
$770$	1.25789e134	0.754789
$771$	1.44510e134	0.816335
$772$	−2.69000e134	−1.43070
$773$	1.91572e134	0.959369	0.479684	−	0.877441i	$-0.340751\pi$
$773$	1.91572e134	0.959369	0.479684	+	0.877441i	$0.340751\pi$
$774$	−6.10819e134	−2.88043
$775$	6.13310e131	0.00272365
$776$	4.21252e134	1.76186
$777$	1.60477e134	0.632174
$778$	2.98127e133	0.110624
$779$	4.66084e134	1.62919
$780$	−1.37048e135	−4.51310
$781$	1.27495e133	0.0395568
$782$	−6.36530e133	−0.186082
$783$	7.38087e134	2.03323
$784$	7.52147e132	0.0195257
$785$	−7.17881e134	−1.75636
$786$	1.18529e135	2.73322
$787$	−5.96118e134	−1.29571	−0.647854	−	0.761765i	$-0.724333\pi$
$787$	−5.96118e134	−1.29571	−0.647854	+	0.761765i	$0.724333\pi$
$788$	8.83836e134	1.81093
$789$	−4.99250e134	−0.964355
$790$	1.57565e135	2.86947
$791$	1.89120e134	0.324737
$792$	−7.42624e134	−1.20240
$793$	−1.72650e134	−0.263610
$794$	−1.56466e135	−2.25303
$795$	1.12171e135	1.52339
$796$	−1.05679e134	−0.135372
$797$	7.29944e133	0.0882018	0.0441009	−	0.999027i	$-0.485958\pi$
$797$	7.29944e133	0.0882018	0.0441009	+	0.999027i	$0.485958\pi$
$798$	−2.62683e135	−2.99431
$799$	−1.94546e134	−0.209218
$800$	−5.41731e132	−0.00549666
$801$	−1.49149e134	−0.142794
$802$	7.40668e134	0.669138
$803$	−3.74829e134	−0.319566
$804$	−9.22816e134	−0.742521
$805$	9.54021e134	0.724519
$806$	1.26361e135	0.905799
$807$	−3.66461e135	−2.47975
$808$	1.99919e135	1.27710
$809$	5.84885e134	0.352748	0.176374	−	0.984323i	$-0.443563\pi$
$809$	5.84885e134	0.352748	0.176374	+	0.984323i	$0.443563\pi$
$810$	5.44276e135	3.09932
$811$	−1.10103e135	−0.592010	−0.296005	−	0.955186i	$-0.595655\pi$
$811$	−1.10103e135	−0.592010	−0.296005	+	0.955186i	$0.595655\pi$
$812$	3.13915e135	1.59388
$813$	8.25408e134	0.395784
$814$	−5.41141e134	−0.245062
$815$	1.82217e134	0.0779398
$816$	−1.91837e134	−0.0775070
$817$	1.95016e135	0.744296
$818$	−3.42400e135	−1.23454
$819$	−9.90831e135	−3.37519
$820$	−9.08763e135	−2.92487
$821$	2.55189e135	0.776079	0.388039	−	0.921643i	$-0.373152\pi$
$821$	2.55189e135	0.776079	0.388039	+	0.921643i	$0.373152\pi$
$822$	1.60397e136	4.60953
$823$	3.68807e135	1.00163	0.500815	−	0.865554i	$-0.333034\pi$
$823$	3.68807e135	1.00163	0.500815	+	0.865554i	$0.333034\pi$
$824$	−3.24890e135	−0.833914
$825$	2.33733e133	0.00567038
$826$	−9.04690e134	−0.207457
$827$	−3.38429e135	−0.733604	−0.366802	−	0.930299i	$-0.619547\pi$
$827$	−3.38429e135	−0.733604	−0.366802	+	0.930299i	$0.619547\pi$
$828$	−1.33370e136	−2.73306
$829$	7.09533e135	1.37463	0.687317	−	0.726357i	$-0.258788\pi$
$829$	7.09533e135	1.37463	0.687317	+	0.726357i	$0.258788\pi$
$830$	−1.29094e136	−2.36469
$831$	1.12076e136	1.94118
$832$	−1.34906e136	−2.20952
$833$	7.67675e133	0.0118901
$834$	3.04465e136	4.45980
$835$	−1.67328e135	−0.231818
$836$	5.61441e135	0.735720
$837$	−7.03766e135	−0.872357
$838$	−1.14984e136	−1.34831
$839$	1.42976e135	0.158611	0.0793053	−	0.996850i	$-0.474730\pi$
$839$	1.42976e135	0.158611	0.0793053	+	0.996850i	$0.474730\pi$
$840$	2.16293e136	2.27015
$841$	−2.11728e135	−0.210264
$842$	−9.86325e135	−0.926847
$843$	−7.98606e135	−0.710150
$844$	2.92294e136	2.45978
$845$	1.34387e136	1.07033
$846$	−6.43113e136	−4.84803
$847$	1.17194e136	0.836231
$848$	−3.30020e135	−0.222912
$849$	1.56040e136	0.997766
$850$	3.15137e133	0.00190774
$851$	−4.10416e135	−0.235234
$852$	5.19120e135	0.281726
$853$	8.68850e135	0.446493	0.223247	−	0.974762i	$-0.428334\pi$
$853$	8.68850e135	0.446493	0.223247	+	0.974762i	$0.428334\pi$
$854$	6.45224e135	0.313993
$855$	−4.77466e136	−2.20048
$856$	3.06607e136	1.33830
$857$	3.33416e136	1.37841	0.689205	−	0.724567i	$-0.257960\pi$
$857$	3.33416e136	1.37841	0.689205	+	0.724567i	$0.257960\pi$
$858$	4.81562e136	1.88579
$859$	8.15089e135	0.302359	0.151179	−	0.988506i	$-0.451693\pi$
$859$	8.15089e135	0.302359	0.151179	+	0.988506i	$0.451693\pi$
$860$	−3.80240e136	−1.33623
$861$	−9.46962e136	−3.15272
$862$	−4.74284e136	−1.49607
$863$	−9.31789e135	−0.278494	−0.139247	−	0.990258i	$-0.544468\pi$
$863$	−9.31789e135	−0.278494	−0.139247	+	0.990258i	$0.544468\pi$
$864$	6.21629e136	1.76053
$865$	−4.35588e136	−1.16903
$866$	−9.95680e136	−2.53243
$867$	7.30136e136	1.76001
$868$	−2.99318e136	−0.683857
$869$	−3.50926e136	−0.759969
$870$	1.29748e137	2.66353
$871$	1.75334e136	0.341210
$872$	8.85195e136	1.63314
$873$	1.88934e137	3.30482
$874$	6.71803e136	1.11419
$875$	6.56482e136	1.03240
$876$	−1.52619e137	−2.27597
$877$	1.16539e137	1.64812	0.824061	−	0.566501i	$-0.191703\pi$
$877$	1.16539e137	1.64812	0.824061	+	0.566501i	$0.191703\pi$
$878$	−1.71005e137	−2.29358
$879$	−2.15394e137	−2.74000
$880$	−9.69546e135	−0.116983
$881$	−1.45824e137	−1.66897	−0.834487	−	0.551028i	$-0.814236\pi$
$881$	−1.45824e137	−1.66897	−0.834487	+	0.551028i	$0.814236\pi$
$882$	2.53770e136	0.275519
$883$	6.58283e136	0.678016	0.339008	−	0.940784i	$-0.389909\pi$
$883$	6.58283e136	0.678016	0.339008	+	0.940784i	$0.389909\pi$
$884$	4.11535e136	0.402139
$885$	−2.37010e136	−0.219737
$886$	2.09544e137	1.84335
$887$	−1.39279e137	−1.16262	−0.581310	−	0.813682i	$-0.697460\pi$
$887$	−1.39279e137	−1.16262	−0.581310	+	0.813682i	$0.697460\pi$
$888$	−9.30482e136	−0.737064
$889$	−1.75846e137	−1.32191
$890$	−1.46484e136	−0.104509
$891$	−1.21220e137	−0.820844
$892$	1.07272e137	0.689480
$893$	2.05327e137	1.25272
$894$	−6.77941e136	−0.392643
$895$	−1.81670e137	−0.998879
$896$	3.51436e137	1.83453
$897$	3.65229e137	1.81016
$898$	−3.22506e136	−0.151771
$899$	−7.58257e136	−0.338837
$900$	6.60297e135	0.0280196
$901$	−3.36833e136	−0.135741
$902$	3.19322e137	1.22215
$903$	−3.96223e137	−1.44032
$904$	−1.09656e137	−0.378617
$905$	2.56397e137	0.840920
$906$	−6.90876e137	−2.15248
$907$	−2.41067e137	−0.713508	−0.356754	−	0.934198i	$-0.616117\pi$
$907$	−2.41067e137	−0.713508	−0.356754	+	0.934198i	$0.616117\pi$
$908$	7.82264e137	2.19969
$909$	8.96648e137	2.39553
$910$	−9.73126e137	−2.47027
$911$	−9.93661e136	−0.239681	−0.119841	−	0.992793i	$-0.538238\pi$
$911$	−9.93661e136	−0.239681	−0.119841	+	0.992793i	$0.538238\pi$
$912$	2.02468e137	0.464084
$913$	2.87515e137	0.626281
$914$	1.65723e137	0.343072
$915$	1.69035e137	0.332580
$916$	−1.50222e138	−2.80927
$917$	5.33452e137	0.948246
$918$	−3.61615e137	−0.611030
$919$	6.14650e137	0.987317	0.493658	−	0.869656i	$-0.335659\pi$
$919$	6.14650e137	0.987317	0.493658	+	0.869656i	$0.335659\pi$
$920$	−5.53162e137	−0.844730
$921$	1.77375e137	0.257525
$922$	−1.70360e137	−0.235169
$923$	−9.86322e136	−0.129461
$924$	−1.14070e138	−1.42373
$925$	2.03191e135	0.00241164
$926$	2.78549e138	3.14406
$927$	−1.45715e138	−1.56422
$928$	6.69760e137	0.683815
$929$	−6.24054e137	−0.606026	−0.303013	−	0.952986i	$-0.597993\pi$
$929$	−6.24054e137	−0.606026	−0.303013	+	0.952986i	$0.597993\pi$
$930$	−1.23715e138	−1.14279
$931$	−8.10215e136	−0.0711934
$932$	−1.92904e138	−1.61251
$933$	2.08398e138	1.65729
$934$	2.15118e138	1.62760
$935$	−9.89563e136	−0.0712367
$936$	5.74505e138	3.93520
$937$	−8.37503e137	−0.545877	−0.272939	−	0.962031i	$-0.587996\pi$
$937$	−8.37503e137	−0.545877	−0.272939	+	0.962031i	$0.587996\pi$
$938$	−6.55255e137	−0.406423
$939$	−5.45265e138	−3.21853
$940$	−4.00343e138	−2.24899
$941$	−2.62324e138	−1.40256	−0.701278	−	0.712887i	$-0.747387\pi$
$941$	−2.62324e138	−1.40256	−0.701278	+	0.712887i	$0.747387\pi$
$942$	1.02708e139	5.22683
$943$	2.42182e138	1.17314
$944$	6.97307e136	0.0321534
$945$	5.41983e138	2.37907
$946$	1.33609e138	0.558340
$947$	−2.87773e138	−1.14492	−0.572461	−	0.819932i	$-0.694011\pi$
$947$	−2.87773e138	−1.14492	−0.572461	+	0.819932i	$0.694011\pi$
$948$	−1.42886e139	−5.41255
$949$	2.89973e138	1.04587
$950$	−3.32600e136	−0.0114228
$951$	−6.23201e138	−2.03814
$952$	−6.49494e137	−0.202282
$953$	4.21352e136	0.0124976	0.00624878	−	0.999980i	$-0.498011\pi$
$953$	4.21352e136	0.0124976	0.00624878	+	0.999980i	$0.498011\pi$
$954$	−1.11347e139	−3.14543
$955$	1.93668e138	0.521077
$956$	8.47229e138	2.17124
$957$	−2.88973e138	−0.705426
$958$	6.54207e136	0.0152131
$959$	7.21885e138	1.59920
$960$	1.32082e139	2.78760
$961$	−4.25022e138	−0.854622
$962$	4.18634e138	0.802037
$963$	1.37515e139	2.51032
$964$	9.33874e138	1.62445
$965$	−5.00396e138	−0.829456
$966$	−1.36493e139	−2.15613
$967$	−1.04448e139	−1.57242	−0.786211	−	0.617958i	$-0.787960\pi$
$967$	−1.04448e139	−1.57242	−0.786211	+	0.617958i	$0.787960\pi$
$968$	−6.79515e138	−0.974978
$969$	2.06648e138	0.282602
$970$	1.85558e139	2.41877
$971$	−8.38938e138	−1.04240	−0.521201	−	0.853434i	$-0.674516\pi$
$971$	−8.38938e138	−1.04240	−0.521201	+	0.853434i	$0.674516\pi$
$972$	−1.59200e139	−1.88566
$973$	1.37028e139	1.54725
$974$	−1.29975e139	−1.39916
$975$	−1.80820e137	−0.0185580
$976$	−4.97319e137	−0.0486652
$977$	−4.89824e138	−0.457028	−0.228514	−	0.973541i	$-0.573387\pi$
$977$	−4.89824e138	−0.457028	−0.228514	+	0.973541i	$0.573387\pi$
$978$	−2.60700e138	−0.231944
$979$	3.26245e137	0.0276789
$980$	1.57974e138	0.127813
$981$	3.97016e139	3.06336
$982$	−2.49629e139	−1.83701
$983$	−2.09544e139	−1.47074	−0.735371	−	0.677664i	$-0.762992\pi$
$983$	−2.09544e139	−1.47074	−0.735371	+	0.677664i	$0.762992\pi$
$984$	5.49069e139	3.67582
$985$	1.64412e139	1.04990
$986$	−3.89614e138	−0.237333
$987$	−4.17171e139	−2.42419
$988$	−4.34339e139	−2.40786
$989$	1.01333e139	0.535948
$990$	−3.27120e139	−1.65071
$991$	−2.03468e139	−0.979648	−0.489824	−	0.871821i	$-0.662939\pi$
$991$	−2.03468e139	−0.979648	−0.489824	+	0.871821i	$0.662939\pi$
$992$	−6.38616e138	−0.293391
$993$	5.08350e139	2.22855
$994$	3.68607e138	0.154204
$995$	−1.96584e138	−0.0784830
$996$	1.17067e140	4.46042
$997$	−1.57813e139	−0.573875	−0.286938	−	0.957949i	$-0.592637\pi$
$997$	−1.57813e139	−0.573875	−0.286938	+	0.957949i	$0.592637\pi$
$998$	−3.78218e138	−0.131272
$999$	−2.33159e139	−0.772425

Twists

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

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

\(f(q)\)	\(=\)	\(q+1.64459e14 q^{2} -2.77426e22 q^{3} +1.71431e28 q^{4} +3.18897e32 q^{5} -4.56250e36 q^{6} -2.05341e39 q^{7} +1.19061e42 q^{8} +5.33996e44 q^{9} +O(q^{10})\)	\(q+1.64459e14 q^{2} -2.77426e22 q^{3} +1.71431e28 q^{4} +3.18897e32 q^{5} -4.56250e36 q^{6} -2.05341e39 q^{7} +1.19061e42 q^{8} +5.33996e44 q^{9} +5.24454e46 q^{10} -1.16805e48 q^{11} -4.75594e50 q^{12} +9.03622e51 q^{13} -3.37700e53 q^{14} -8.84704e54 q^{15} +2.60289e55 q^{16} +2.65663e56 q^{17} +8.78202e58 q^{18} -2.80384e59 q^{19} +5.46689e60 q^{20} +5.69668e61 q^{21} -1.92096e62 q^{22} -1.45691e63 q^{23} -3.30306e64 q^{24} +7.21293e62 q^{25} +1.48608e66 q^{26} -8.27675e66 q^{27} -3.52017e67 q^{28} -8.91760e67 q^{29} -1.45497e69 q^{30} +8.50292e68 q^{31} -7.51055e69 q^{32} +3.24048e70 q^{33} +4.36905e70 q^{34} -6.54826e71 q^{35} +9.15434e72 q^{36} +2.81703e72 q^{37} -4.61116e73 q^{38} -2.50688e74 q^{39} +3.79682e74 q^{40} -1.66230e75 q^{41} +9.36868e75 q^{42} -6.95533e75 q^{43} -2.00240e76 q^{44} +1.70290e77 q^{45} -2.39601e77 q^{46} -7.32306e77 q^{47} -7.22109e77 q^{48} +2.88966e77 q^{49} +1.18623e77 q^{50} -7.37017e78 q^{51} +1.54909e80 q^{52} -1.26790e80 q^{53} -1.36118e81 q^{54} -3.72488e80 q^{55} -2.44481e81 q^{56} +7.77858e81 q^{57} -1.46658e82 q^{58} +2.67897e81 q^{59} -1.51666e83 q^{60} -1.91064e82 q^{61} +1.39838e83 q^{62} -1.09651e84 q^{63} -1.49295e84 q^{64} +2.88163e84 q^{65} +5.32924e84 q^{66} +1.94035e84 q^{67} +4.55428e84 q^{68} +4.04184e85 q^{69} -1.07692e86 q^{70} -1.09152e85 q^{71} +6.35781e86 q^{72} +3.20901e86 q^{73} +4.63285e86 q^{74} -2.00105e85 q^{75} -4.80665e87 q^{76} +2.39848e87 q^{77} -4.12278e88 q^{78} +3.00437e88 q^{79} +8.30055e87 q^{80} +1.03780e89 q^{81} -2.73380e89 q^{82} -2.46149e89 q^{83} +9.76587e89 q^{84} +8.47191e88 q^{85} -1.14386e90 q^{86} +2.47397e90 q^{87} -1.39069e90 q^{88} -2.79307e89 q^{89} +2.80056e91 q^{90} -1.85550e91 q^{91} -2.49759e91 q^{92} -2.35893e91 q^{93} -1.20434e92 q^{94} -8.94137e91 q^{95} +2.08362e92 q^{96} +3.53812e92 q^{97} +4.75229e91 q^{98} -6.23735e92 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 7 q + 43735426713792 q^{2} - 36\!\cdots\!84 q^{3}+ \cdots + 36\!\cdots\!11 q^{9}+O(q^{10}) \) 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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