LMFDB - Embedded newform 1.90.a.a.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1,90,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, 90, names="a")

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

chi := DirichletCharacter("1.1");

S:= CuspForms(chi, 90);

N := Newforms(S);

Level:	$ N $	$=$	$ 1 $
Weight:	$ k $	$=$	$ 90 $
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:	$50.1624291928$
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} - 3 x^{6} + \cdots + 56\!\cdots\!00 $ x^7 - 3x^6 - 1400531600527934473811256x^5 + 92429106535860966322690362643440028x^4 + 486502004825754823566786579226467181483733375376x^3 - 41390338158988484679355574715314473323669246141474080139600x^2 - 47785461930919140795588898989186212855196409324706742802409577734342400x + 5612439960923763868733925256800794059272997589318959539312206365735127554315560000
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	multiple of $ 2^{83}\cdot 3^{29}\cdot 5^{9}\cdot 7^{5}\cdot 11^{2}\cdot 13^{2} $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$9.08809e11$ 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)

$f(q)$	$=$	$q-4.81096e13 q^{2} -1.58991e21 q^{3} +1.69556e27 q^{4} +1.07790e31 q^{5} +7.64900e34 q^{6} +5.70296e37 q^{7} -5.17945e40 q^{8} -3.81503e41 q^{9} +O(q^{10})$	\(q-4.81096e13 q^{2} -1.58991e21 q^{3} +1.69556e27 q^{4} +1.07790e31 q^{5} +7.64900e34 q^{6} +5.70296e37 q^{7} -5.17945e40 q^{8} -3.81503e41 q^{9} -5.18572e44 q^{10} +1.25806e46 q^{11} -2.69579e48 q^{12} -3.04674e49 q^{13} -2.74367e51 q^{14} -1.71376e52 q^{15} +1.44231e54 q^{16} -1.44307e54 q^{17} +1.83540e55 q^{18} -2.63820e56 q^{19} +1.82764e58 q^{20} -9.06721e58 q^{21} -6.05246e59 q^{22} +1.82853e60 q^{23} +8.23486e61 q^{24} -4.53723e61 q^{25} +1.46577e63 q^{26} +5.23212e63 q^{27} +9.66973e64 q^{28} -1.87067e65 q^{29} +8.24484e65 q^{30} +9.55617e65 q^{31} -3.73296e67 q^{32} -2.00020e67 q^{33} +6.94257e67 q^{34} +6.14721e68 q^{35} -6.46863e68 q^{36} +6.40520e69 q^{37} +1.26923e70 q^{38} +4.84404e70 q^{39} -5.58291e71 q^{40} -1.04557e72 q^{41} +4.36220e72 q^{42} -3.49195e72 q^{43} +2.13312e73 q^{44} -4.11221e72 q^{45} -8.79700e73 q^{46} +6.29528e72 q^{47} -2.29314e75 q^{48} +1.61660e75 q^{49} +2.18284e75 q^{50} +2.29436e75 q^{51} -5.16593e76 q^{52} +6.67038e75 q^{53} -2.51715e77 q^{54} +1.35606e77 q^{55} -2.95382e78 q^{56} +4.19451e77 q^{57} +8.99970e78 q^{58} -1.69313e78 q^{59} -2.90579e79 q^{60} +1.46459e79 q^{61} -4.59743e79 q^{62} -2.17570e79 q^{63} +9.03167e80 q^{64} -3.28407e80 q^{65} +9.62288e80 q^{66} +2.58895e81 q^{67} -2.44682e81 q^{68} -2.90720e81 q^{69} -2.95740e82 q^{70} +2.08753e82 q^{71} +1.97597e82 q^{72} +2.80058e82 q^{73} -3.08152e83 q^{74} +7.21380e82 q^{75} -4.47324e83 q^{76} +7.17466e83 q^{77} -2.33045e84 q^{78} +1.45733e84 q^{79} +1.55466e85 q^{80} -7.20869e84 q^{81} +5.03020e85 q^{82} -3.27919e85 q^{83} -1.53740e86 q^{84} -1.55549e85 q^{85} +1.67996e86 q^{86} +2.97419e86 q^{87} -6.51604e86 q^{88} -3.07472e86 q^{89} +1.97837e86 q^{90} -1.73754e87 q^{91} +3.10039e87 q^{92} -1.51935e87 q^{93} -3.02863e86 q^{94} -2.84371e87 q^{95} +5.93508e88 q^{96} +1.70392e88 q^{97} -7.77738e88 q^{98} -4.79953e87 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 7 q - 31407330351408 q^{2} - 13\!\cdots\!64 q^{3}+ \cdots + 56\!\cdots\!71 q^{9}+O(q^{10}) $ 7 * q - 31407330351408 * q^2 - 1359636564127989407364 * q^3 + 2261776677705673116713576704 * q^4 + 10232470009089362495458987082250 * q^5 - 47224471979937892179333042051869376 * q^6 + 38501341543555466088619988316514959992 * q^7 - 17954070319777658933153680910224754257920 * q^8 + 5642786905031106277764534052585801627237371 * q^9	$ 7 q - 31407330351408 q^{2} - 13\!\cdots\!64 q^{3}+ \cdots - 19\!\cdots\!68 q^{99}+O(q^{100}) $ 7 * q - 31407330351408 * q^2 - 1359636564127989407364 * q^3 + 2261776677705673116713576704 * q^4 + 10232470009089362495458987082250 * q^5 - 47224471979937892179333042051869376 * q^6 + 38501341543555466088619988316514959992 * q^7 - 17954070319777658933153680910224754257920 * q^8 + 5642786905031106277764534052585801627237371 * q^9 - 339886969508111355644737639996417314840948000 * q^10 - 33185398429231418991729589216300973489966079756 * q^11 - 1004632700194650448641313614558096018594697264128 * q^12 - 103208963062610039235367083636366996420076737975934 * q^13 - 3327254465892753266340667920543396227686510656335232 * q^14 - 3928505137426182309397624104867069340549391446959000 * q^15 + 1162914962909596823700454711087105707311468348200517632 * q^16 + 8319478335928844788789086096491382896131016464480742142 * q^17 - 147732328649241019658282821579260643023785726547655592304 * q^18 + 566291740319213482378495952187194771397009633898137615980 * q^19 + 17240116916193408372006373658712519601040539123805641152000 * q^20 - 90598178803547150933473132922481297065025295806785914127136 * q^21 - 572030171884928043470630402880877439080047260844354367465536 * q^22 - 1162243907076079309616831317442805749267469267057101679089304 * q^23 + 102292564315938855068370806246211339063831852161969337222512640 * q^24 - 212322678457531006783078558385295515929862869778299899884234375 * q^25 + 256954281475267715641749604093742676189922873609159508555728224 * q^26 + 11230609565348224313895297191070036430584541766541637832713861080 * q^27 + 42271634017038816624971599134243423766860094950653754695170525184 * q^28 - 141971615822865442921693407341400369750322173654805889340125766030 * q^29 + 685316390944098153207628047778140189726339714889914380742075312000 * q^30 + 683664012826903943332640912357777981916064560235376021892996967904 * q^31 - 18295616415211966307849618677858007212056173228946481610958698446848 * q^32 - 86562711553720527899763440849945042911790491733183542919656093165488 * q^33 + 310076023324380793221121009797602653729382139402481891183326564397728 * q^34 + 330170304491374501797216156307803170564453659546779205972398673602000 * q^35 - 1640012020416196297725034563971477848297008731151338285245876678380288 * q^36 - 54562371243327727239087361205689070078467002527262667251534613287958 * q^37 + 45443543517981085735407850236293406047335765118416513555057178362067520 * q^38 - 52864527349249866236351055677173599634948671842685563480478962199294648 * q^39 - 361606215568925170012071637858292899677067482636237269829164280222720000 * q^40 - 657970372131031022656393678727303783670430723595160145307484502660397466 * q^41 + 1194858754087456269163194270977035799298048792026970828715903204437563904 * q^42 + 3219260988489925248073148176207907480629490254450229462745931521229023956 * q^43 - 15518629834856028222698238418543583045824703222318379119582671434892588032 * q^44 - 47660318642997018016862592256216157339280861352258819392244471941754530750 * q^45 - 56495859283654895727924020960810320205382055229302825603343235358563739776 * q^46 - 589986405817377998239864975519322982713028461832176517663311475432884156208 * q^47 - 3832565523894613734560398647870601248628652435813709455578147238513735368704 * q^48 - 3087918931516952942471049623523578487683423584779916315782412290559435137201 * q^49 - 11186377093883721132072449077187321801629226446489467367094029042775729250000 * q^50 - 44749224651513683358510561546459122133403179429459901007904418343196358896456 * q^51 - 195074413541392068451275175025603658303895820240091441880921515457689944416768 * q^52 - 181430063765559371241038742666701312033549399057740391278794421145415983301414 * q^53 - 1069768557347791789565342861771646012899754433224109219876568781015744643201920 * q^54 - 1251959124114414009910203618775792485005181014548185493458611647835407269933000 * q^55 - 5833843183212315752254903583581814862872931164492369538677714690034795155128320 * q^56 - 6636053151264088660994009243658731470064177381062469866816802824914691937541840 * q^57 - 3085757480392710136283141086455357758895171179069060863542747741259905831138720 * q^58 - 9086646688135460130541149101651496775878005651006843822379595086967226946739260 * q^59 - 28597614595134268752948807453761124021285695193298938696320462632027102503168000 * q^60 + 8774545844023482806788207542368099480171833682235332719617911769894989384384594 * q^61 + 169526530141162019514362685680407627845528510541984421132250792903222430290676224 * q^62 + 600060998677337137803649489067962875140223680130818894152235224596331850847343896 * q^63 + 1452176441912468141297252840801366807510309025606268702123180748140039039923257344 * q^64 + 1324597647382660271811574639166235036730362819738030027679321346411726630592583500 * q^65 + 5794073040567151132693317781366382943170107912751606019648469980133340516392228608 * q^66 + 5843793535214317245370457729815716742376089805910350107798697912590172409883288892 * q^67 + 3383522446313435458738303622044969561038087184549368481666865721250715220292329984 * q^68 - 5947153100304692873901208875288315645744737627052374011935588797613066907438186848 * q^69 - 48530199945646178573467957795368744286471165824229177345686884714666072932491936000 * q^70 - 54831722251632385251791847370899308335600102141533329655944703784411212003030405576 * q^71 - 193536676908511823968799310909661267914860871284938663775925036280217916976534056960 * q^72 - 199687593578972105167207004100293505918603845674208378633352670689487827039532442554 * q^73 - 965066694195901068911432718812601386557508653596585879236882657245078468484355531552 * q^74 - 449845818551229824067343835155681595861236685828593692926866173145835890979882437500 * q^75 - 624789819902471734428103435859366276136204176410553236414159885942801809403293936640 * q^76 + 1343091849772730830408738350805190184311976794055420918621708129900429278982204783264 * q^77 + 5115170224904826933556340523459220074577237696572659886093176102046008883684662673792 * q^78 + 2673613187258858564803647217355170619960582874636639491339476674654505245882753222320 * q^79 + 27680777280715589878137850302356927719666260300976702690203906698201250115244507136000 * q^80 + 48638608516196512054280935503541026926798324553759401775728207287806340272179807855247 * q^81 + 63127032979305734173962933747182283580799525530431609292523424735220314498528511785504 * q^82 - 35017619719051015255233069909205249521130641969249674783596011796500257235899597331924 * q^83 - 91271218351884570971920288208768314031909543306789609723100776475256076481746994388992 * q^84 - 141384913067859944856588220403027346022605850144801355881993121940858052671602572135500 * q^85 - 246618390628075722158819620850499384970086160242141588082920865473574265424952752922176 * q^86 - 414485418912512080488627714148474005618211107267303271323056368803909094640534785472760 * q^87 - 1874747156501905660418588549009712256169985369393565612731235328175018372894817920368640 * q^88 - 1625431592570174192786638376427668495469444301472287736732287307560402850485922205836490 * q^89 - 1500534342888898564405033173718589632643579855463696593286927469992128698108056410724000 * q^90 - 304928345599594097428899578613442396706625647498145800328408392926012721126646204980336 * q^91 + 7281329003117440073848907204538369781556431009214831685528490675028895216006021740500992 * q^92 + 8725785078968826322471270683478576510125821912788765392594960100289595008684983594910592 * q^93 + 22964567086699943860517240071514688733928422760236698641236969735081204002206026310078208 * q^94 + 22546113414761055806340378014072491896390775587517280959221325649524340597082183574485000 * q^95 + 84826971262863357834463681679311846519023363534588497414160609596759417378202987836473344 * q^96 + 71386807957160533061753038101994485650273149078658846323482657056181047793902162983463342 * q^97 - 17615586549862077419320336328445909012296979015379167958274818444332513071671081562433456 * q^98 - 197573613824864988900062481565182229817848341132748736551935840297576094108952766009175068 * 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 $

$2$	−4.81096e13	−1.93373	−0.966867	−	0.255279i	$-0.917833\pi$
$2$	−4.81096e13	−1.93373	−0.966867	+	0.255279i	$0.917833\pi$
$3$	−1.58991e21	−0.932131	−0.466066	−	0.884750i	$-0.654329\pi$
$3$	−1.58991e21	−0.932131	−0.466066	+	0.884750i	$0.654329\pi$
$4$	1.69556e27	2.73933
$5$	1.07790e31	0.848032	0.424016	−	0.905655i	$-0.360620\pi$
$5$	1.07790e31	0.848032	0.424016	+	0.905655i	$0.360620\pi$
$6$	7.64900e34	1.80249
$7$	5.70296e37	1.41006	0.705030	−	0.709177i	$-0.250933\pi$
$7$	5.70296e37	1.41006	0.705030	+	0.709177i	$0.250933\pi$
$8$	−5.17945e40	−3.36340
$9$	−3.81503e41	−0.131131
$10$	−5.18572e44	−1.63987
$11$	1.25806e46	0.572435	0.286217	−	0.958165i	$-0.407602\pi$
$11$	1.25806e46	0.572435	0.286217	+	0.958165i	$0.407602\pi$
$12$	−2.69579e48	−2.55341
$13$	−3.04674e49	−0.819136	−0.409568	−	0.912280i	$-0.634320\pi$
$13$	−3.04674e49	−0.819136	−0.409568	+	0.912280i	$0.634320\pi$
$14$	−2.74367e51	−2.72668
$15$	−1.71376e52	−0.790477
$16$	1.44231e54	3.76460
$17$	−1.44307e54	−0.253695	−0.126847	−	0.991922i	$-0.540486\pi$
$17$	−1.44307e54	−0.253695	−0.126847	+	0.991922i	$0.540486\pi$
$18$	1.83540e55	0.253573
$19$	−2.63820e56	−0.328680	−0.164340	−	0.986404i	$-0.552549\pi$
$19$	−2.63820e56	−0.328680	−0.164340	+	0.986404i	$0.552549\pi$
$20$	1.82764e58	2.32304
$21$	−9.06721e58	−1.31436
$22$	−6.05246e59	−1.10694
$23$	1.82853e60	0.462609	0.231304	−	0.972881i	$-0.425701\pi$
$23$	1.82853e60	0.462609	0.231304	+	0.972881i	$0.425701\pi$
$24$	8.23486e61	3.13513
$25$	−4.53723e61	−0.280841
$26$	1.46577e63	1.58399
$27$	5.23212e63	1.05436
$28$	9.66973e64	3.86262
$29$	−1.87067e65	−1.56778	−0.783890	−	0.620899i	$-0.786768\pi$
$29$	−1.87067e65	−1.56778	−0.783890	+	0.620899i	$0.786768\pi$
$30$	8.24484e65	1.52857
$31$	9.55617e65	0.411802	0.205901	−	0.978573i	$-0.433988\pi$
$31$	9.55617e65	0.411802	0.205901	+	0.978573i	$0.433988\pi$
$32$	−3.73296e67	−3.91633
$33$	−2.00020e67	−0.533584
$34$	6.94257e67	0.490579
$35$	6.14721e68	1.19578
$36$	−6.46863e68	−0.359212
$37$	6.40520e69	1.05089	0.525443	−	0.850829i	$-0.323899\pi$
$37$	6.40520e69	1.05089	0.525443	+	0.850829i	$0.323899\pi$
$38$	1.26923e70	0.635580
$39$	4.84404e70	0.763542
$40$	−5.58291e71	−2.85227
$41$	−1.04557e72	−1.78021	−0.890106	−	0.455754i	$-0.849370\pi$
$41$	−1.04557e72	−1.78021	−0.890106	+	0.455754i	$0.849370\pi$
$42$	4.36220e72	2.54163
$43$	−3.49195e72	−0.714039	−0.357019	−	0.934097i	$-0.616207\pi$
$43$	−3.49195e72	−0.714039	−0.357019	+	0.934097i	$0.616207\pi$
$44$	2.13312e73	1.56809
$45$	−4.11221e72	−0.111204
$46$	−8.79700e73	−0.894563
$47$	6.29528e72	0.0245845	0.0122922	−	0.999924i	$-0.496087\pi$
$47$	6.29528e72	0.0245845	0.0122922	+	0.999924i	$0.496087\pi$
$48$	−2.29314e75	−3.50910
$49$	1.61660e75	0.988271
$50$	2.18284e75	0.543072
$51$	2.29436e75	0.236477
$52$	−5.16593e76	−2.24388
$53$	6.67038e75	0.124129	0.0620647	−	0.998072i	$-0.480231\pi$
$53$	6.67038e75	0.124129	0.0620647	+	0.998072i	$0.480231\pi$
$54$	−2.51715e77	−2.03886
$55$	1.35606e77	0.485443
$56$	−2.95382e78	−4.74260
$57$	4.19451e77	0.306373
$58$	8.99970e78	3.03167
$59$	−1.69313e78	−0.266549	−0.133274	−	0.991079i	$-0.542549\pi$
$59$	−1.69313e78	−0.266549	−0.133274	+	0.991079i	$0.542549\pi$
$60$	−2.90579e79	−2.16538
$61$	1.46459e79	0.523044	0.261522	−	0.965197i	$-0.415776\pi$
$61$	1.46459e79	0.523044	0.261522	+	0.965197i	$0.415776\pi$
$62$	−4.59743e79	−0.796316
$63$	−2.17570e79	−0.184903
$64$	9.03167e80	3.80855
$65$	−3.28407e80	−0.694653
$66$	9.62288e80	1.03181
$67$	2.58895e81	1.42166	0.710828	−	0.703366i	$-0.248321\pi$
$67$	2.58895e81	1.42166	0.710828	+	0.703366i	$0.248321\pi$
$68$	−2.44682e81	−0.694954
$69$	−2.90720e81	−0.431212
$70$	−2.95740e82	−2.31232
$71$	2.08753e82	0.868234	0.434117	−	0.900856i	$-0.357060\pi$
$71$	2.08753e82	0.868234	0.434117	+	0.900856i	$0.357060\pi$
$72$	1.97597e82	0.441047
$73$	2.80058e82	0.338361	0.169181	−	0.985585i	$-0.445888\pi$
$73$	2.80058e82	0.338361	0.169181	+	0.985585i	$0.445888\pi$
$74$	−3.08152e83	−2.03214
$75$	7.21380e82	0.261781
$76$	−4.47324e83	−0.900362
$77$	7.17466e83	0.807168
$78$	−2.33045e84	−1.47649
$79$	1.45733e84	0.523783	0.261892	−	0.965097i	$-0.415654\pi$
$79$	1.45733e84	0.523783	0.261892	+	0.965097i	$0.415654\pi$
$80$	1.55466e85	3.19250
$81$	−7.20869e84	−0.851673
$82$	5.03020e85	3.44246
$83$	−3.27919e85	−1.30855	−0.654276	−	0.756256i	$-0.727027\pi$
$83$	−3.27919e85	−1.30855	−0.654276	+	0.756256i	$0.727027\pi$
$84$	−1.53740e86	−3.60047
$85$	−1.55549e85	−0.215141
$86$	1.67996e86	1.38076
$87$	2.97419e86	1.46138
$88$	−6.51604e86	−1.92533
$89$	−3.07472e86	−0.549478	−0.274739	−	0.961519i	$-0.588591\pi$
$89$	−3.07472e86	−0.549478	−0.274739	+	0.961519i	$0.588591\pi$
$90$	1.97837e86	0.215038
$91$	−1.73754e87	−1.15503
$92$	3.10039e87	1.26724
$93$	−1.51935e87	−0.383854
$94$	−3.02863e86	−0.0475398
$95$	−2.84371e87	−0.278731
$96$	5.93508e88	3.65053
$97$	1.70392e88	0.660856	0.330428	−	0.943831i	$-0.392807\pi$
$97$	1.70392e88	0.660856	0.330428	+	0.943831i	$0.392807\pi$
$98$	−7.77738e88	−1.91105
$99$	−4.79953e87	−0.0750641
$100$	−7.69317e88	−0.769317
$101$	−1.94636e89	−1.25003	−0.625016	−	0.780612i	$-0.714908\pi$
$101$	−1.94636e89	−1.25003	−0.625016	+	0.780612i	$0.714908\pi$
$102$	−1.10381e89	−0.457284
$103$	−2.49750e89	−0.670270	−0.335135	−	0.942170i	$-0.608782\pi$
$103$	−2.49750e89	−0.670270	−0.335135	+	0.942170i	$0.608782\pi$
$104$	1.57804e90	2.75508
$105$	−9.77352e89	−1.11462
$106$	−3.20909e89	−0.240033
$107$	−1.15673e90	−0.569708	−0.284854	−	0.958571i	$-0.591945\pi$
$107$	−1.15673e90	−0.569708	−0.284854	+	0.958571i	$0.591945\pi$
$108$	8.87139e90	2.88825
$109$	−7.89198e90	−1.70493	−0.852466	−	0.522783i	$-0.824894\pi$
$109$	−7.89198e90	−1.70493	−0.852466	+	0.522783i	$0.824894\pi$
$110$	−6.52394e90	−0.938718
$111$	−1.01837e91	−0.979564
$112$	8.22543e91	5.30831
$113$	−2.57271e91	−1.11789	−0.558946	−	0.829204i	$-0.688794\pi$
$113$	−2.57271e91	−1.11789	−0.558946	+	0.829204i	$0.688794\pi$
$114$	−2.01796e91	−0.592444
$115$	1.97097e91	0.392307
$116$	−3.17183e92	−4.29467
$117$	1.16234e91	0.107414
$118$	8.14559e91	0.515434
$119$	−8.22980e91	−0.357725
$120$	8.87634e92	2.65869
$121$	−3.24731e92	−0.672318
$122$	−7.04609e92	−1.01143
$123$	1.66236e93	1.65939
$124$	1.62031e93	1.12806
$125$	−2.23051e93	−1.08619
$126$	1.04672e93	0.357554
$127$	2.77892e93	0.667744	0.333872	−	0.942618i	$-0.391645\pi$
$127$	2.77892e93	0.667744	0.333872	+	0.942618i	$0.391645\pi$
$128$	−2.03451e94	−3.44839
$129$	5.55189e93	0.665578
$130$	1.57995e94	1.34328
$131$	2.61791e94	1.58264	0.791318	−	0.611404i	$-0.209395\pi$
$131$	2.61791e94	1.58264	0.791318	+	0.611404i	$0.209395\pi$
$132$	−3.39147e94	−1.46166
$133$	−1.50456e94	−0.463458
$134$	−1.24553e95	−2.74910
$135$	5.63969e94	0.894134
$136$	7.47433e94	0.853278
$137$	1.28376e95	1.05784	0.528920	−	0.848672i	$-0.322597\pi$
$137$	1.28376e95	1.05784	0.528920	+	0.848672i	$0.322597\pi$
$138$	1.39864e95	0.833850
$139$	−3.19520e95	−1.38146	−0.690732	−	0.723111i	$-0.742712\pi$
$139$	−3.19520e95	−1.38146	−0.690732	+	0.723111i	$0.742712\pi$
$140$	1.04230e96	3.27563
$141$	−1.00089e94	−0.0229159
$142$	−1.00430e96	−1.67893
$143$	−3.83297e95	−0.468902
$144$	−5.50245e95	−0.493657
$145$	−2.01639e96	−1.32953
$146$	−1.34735e96	−0.654301
$147$	−2.57024e96	−0.921198
$148$	1.08604e97	2.87873
$149$	5.65429e96	1.11068	0.555340	−	0.831624i	$-0.312588\pi$
$149$	5.65429e96	1.11068	0.555340	+	0.831624i	$0.312588\pi$
$150$	−3.47053e96	−0.506215
$151$	−1.22003e97	−1.32402	−0.662011	−	0.749495i	$-0.730297\pi$
$151$	−1.22003e97	−1.32402	−0.662011	+	0.749495i	$0.730297\pi$
$152$	1.36644e97	1.10548
$153$	5.50538e95	0.0332674
$154$	−3.45170e97	−1.56085
$155$	1.03006e97	0.349221
$156$	8.21338e97	2.09159
$157$	5.80043e97	1.11154	0.555771	−	0.831335i	$-0.312423\pi$
$157$	5.80043e97	1.11154	0.555771	+	0.831335i	$0.312423\pi$
$158$	−7.01114e97	−1.01286
$159$	−1.06053e97	−0.115705
$160$	−4.02375e98	−3.32118
$161$	1.04281e98	0.652307
$162$	3.46807e98	1.64691
$163$	4.97994e98	1.79835	0.899177	−	0.437584i	$-0.144166\pi$
$163$	4.97994e98	1.79835	0.899177	+	0.437584i	$0.144166\pi$
$164$	−1.77283e99	−4.87659
$165$	−2.15601e98	−0.452497
$166$	1.57760e99	2.53039
$167$	−1.16618e99	−1.43180	−0.715900	−	0.698202i	$-0.753984\pi$
$167$	−1.16618e99	−1.43180	−0.715900	+	0.698202i	$0.753984\pi$
$168$	4.69631e99	4.42073
$169$	−4.55173e98	−0.329017
$170$	7.48338e98	0.416027
$171$	1.00648e98	0.0431002
$172$	−5.92082e99	−1.95599
$173$	1.56484e99	0.399410	0.199705	−	0.979856i	$-0.436002\pi$
$173$	1.56484e99	0.399410	0.199705	+	0.979856i	$0.436002\pi$
$174$	−1.43087e100	−2.82592
$175$	−2.58757e99	−0.396003
$176$	1.81451e100	2.15499
$177$	2.69193e99	0.248458
$178$	1.47924e100	1.06254
$179$	−3.09061e100	−1.73015	−0.865077	−	0.501639i	$-0.832730\pi$
$179$	−3.09061e100	−1.73015	−0.865077	+	0.501639i	$0.832730\pi$
$180$	−6.97252e99	−0.304623
$181$	−9.98755e99	−0.341006	−0.170503	−	0.985357i	$-0.554539\pi$
$181$	−9.98755e99	−0.341006	−0.170503	+	0.985357i	$0.554539\pi$
$182$	8.35925e100	2.23352
$183$	−2.32857e100	−0.487546
$184$	−9.47078e100	−1.55594
$185$	6.90415e100	0.891186
$186$	7.30951e100	0.742271
$187$	−1.81547e100	−0.145224
$188$	1.06740e100	0.0673449
$189$	2.98386e101	1.48672
$190$	1.36810e101	0.538992
$191$	−8.28952e100	−0.258550	−0.129275	−	0.991609i	$-0.541265\pi$
$191$	−8.28952e100	−0.258550	−0.129275	+	0.991609i	$0.541265\pi$
$192$	−1.43596e102	−3.55007
$193$	−2.59064e101	−0.508284	−0.254142	−	0.967167i	$-0.581793\pi$
$193$	−2.59064e101	−0.508284	−0.254142	+	0.967167i	$0.581793\pi$
$194$	−8.19749e101	−1.27792
$195$	5.22138e101	0.647508
$196$	2.74104e102	2.70720
$197$	−1.12650e102	−0.887121	−0.443560	−	0.896244i	$-0.646285\pi$
$197$	−1.12650e102	−0.887121	−0.443560	+	0.896244i	$0.646285\pi$
$198$	2.30903e101	0.145154
$199$	2.12882e102	1.06949	0.534745	−	0.845013i	$-0.320408\pi$
$199$	2.12882e102	1.06949	0.534745	+	0.845013i	$0.320408\pi$
$200$	2.35004e102	0.944582
$201$	−4.11620e102	−1.32517
$202$	9.36385e102	2.41723
$203$	−1.06683e103	−2.21067
$204$	3.89023e102	0.647788
$205$	−1.12702e103	−1.50968
$206$	1.20154e103	1.29612
$207$	−6.97591e101	−0.0606625
$208$	−4.39433e103	−3.08372
$209$	−3.31901e102	−0.188148
$210$	4.70200e103	2.15538
$211$	2.09663e103	0.777950	0.388975	−	0.921248i	$-0.372829\pi$
$211$	2.09663e103	0.777950	0.388975	+	0.921248i	$0.372829\pi$
$212$	1.13101e103	0.340031
$213$	−3.31899e103	−0.809308
$214$	5.56496e103	1.10166
$215$	−3.76396e103	−0.605528
$216$	−2.70995e104	−3.54625
$217$	5.44985e103	0.580666
$218$	3.79680e104	3.29688
$219$	−4.45267e103	−0.315397
$220$	2.29928e104	1.32979
$221$	4.39667e103	0.207811
$222$	4.89934e104	1.89422
$223$	−3.38231e104	−1.07065	−0.535325	−	0.844646i	$-0.679811\pi$
$223$	−3.38231e104	−1.07065	−0.535325	+	0.844646i	$0.679811\pi$
$224$	−2.12889e105	−5.52226
$225$	1.73097e103	0.0368271
$226$	1.23772e105	2.16171
$227$	−3.05939e104	−0.439020	−0.219510	−	0.975610i	$-0.570446\pi$
$227$	−3.05939e104	−0.439020	−0.219510	+	0.975610i	$0.570446\pi$
$228$	7.11205e104	0.839256
$229$	−1.51461e105	−1.47103	−0.735514	−	0.677509i	$-0.763059\pi$
$229$	−1.51461e105	−1.47103	−0.735514	+	0.677509i	$0.763059\pi$
$230$	−9.48226e104	−0.758618
$231$	−1.14071e105	−0.752386
$232$	9.68901e105	5.27308
$233$	−8.75172e104	−0.393328	−0.196664	−	0.980471i	$-0.563011\pi$
$233$	−8.75172e104	−0.393328	−0.196664	+	0.980471i	$0.563011\pi$
$234$	−5.59197e104	−0.207711
$235$	6.78567e103	0.0208484
$236$	−2.87081e105	−0.730165
$237$	−2.31702e105	−0.488235
$238$	3.95932e105	0.691746
$239$	−2.25016e105	−0.326217	−0.163109	−	0.986608i	$-0.552152\pi$
$239$	−2.25016e105	−0.326217	−0.163109	+	0.986608i	$0.552152\pi$
$240$	−2.47177e106	−2.97583
$241$	7.69108e105	0.769536	0.384768	−	0.923013i	$-0.374281\pi$
$241$	7.69108e105	0.769536	0.384768	+	0.923013i	$0.374281\pi$
$242$	1.56227e106	1.30009
$243$	−3.76074e105	−0.260492
$244$	2.48331e106	1.43279
$245$	1.74253e106	0.838086
$246$	−7.99757e106	−3.20882
$247$	8.03791e105	0.269233
$248$	−4.94957e106	−1.38506
$249$	5.21362e106	1.21974
$250$	1.07309e107	2.10041
$251$	2.20478e105	0.0361314	0.0180657	−	0.999837i	$-0.494249\pi$
$251$	2.20478e105	0.0361314	0.0180657	+	0.999837i	$0.494249\pi$
$252$	−3.68903e106	−0.506511
$253$	2.30040e106	0.264813
$254$	−1.33693e107	−1.29124
$255$	2.47309e106	0.200540
$256$	4.19761e107	2.85972
$257$	−9.37238e106	−0.536816	−0.268408	−	0.963305i	$-0.586498\pi$
$257$	−9.37238e106	−0.536816	−0.268408	+	0.963305i	$0.586498\pi$
$258$	−2.67099e107	−1.28705
$259$	3.65286e107	1.48181
$260$	−5.56835e107	−1.90288
$261$	7.13665e106	0.205585
$262$	−1.25946e108	−3.06040
$263$	−6.07350e107	−1.24569	−0.622843	−	0.782347i	$-0.714022\pi$
$263$	−6.07350e107	−1.24569	−0.622843	+	0.782347i	$0.714022\pi$
$264$	1.03599e108	1.79466
$265$	7.18999e106	0.105266
$266$	7.23837e107	0.896206
$267$	4.88853e107	0.512186
$268$	4.38972e108	3.89438
$269$	−3.10570e107	−0.233444	−0.116722	−	0.993165i	$-0.537239\pi$
$269$	−3.10570e107	−0.233444	−0.116722	+	0.993165i	$0.537239\pi$
$270$	−2.71323e108	−1.72902
$271$	−3.28545e107	−0.177607	−0.0888037	−	0.996049i	$-0.528304\pi$
$271$	−3.28545e107	−0.177607	−0.0888037	+	0.996049i	$0.528304\pi$
$272$	−2.08136e108	−0.955059
$273$	2.76254e108	1.07664
$274$	−6.17614e108	−2.04558
$275$	−5.70810e107	−0.160763
$276$	−4.92935e108	−1.18123
$277$	8.23734e108	1.68050	0.840248	−	0.542203i	$-0.182410\pi$
$277$	8.23734e108	1.68050	0.840248	+	0.542203i	$0.182410\pi$
$278$	1.53720e109	2.67139
$279$	−3.64571e107	−0.0540001
$280$	−3.18391e109	−4.02188
$281$	7.73806e108	0.834067	0.417034	−	0.908891i	$-0.363070\pi$
$281$	7.73806e108	0.834067	0.417034	+	0.908891i	$0.363070\pi$
$282$	4.81526e107	0.0443133
$283$	−1.50030e109	−1.17946	−0.589728	−	0.807602i	$-0.700765\pi$
$283$	−1.50030e109	−1.17946	−0.589728	+	0.807602i	$0.700765\pi$
$284$	3.53954e109	2.37838
$285$	4.52125e108	0.259814
$286$	1.84403e109	0.906732
$287$	−5.96285e109	−2.51021
$288$	1.42414e109	0.513554
$289$	−3.02735e109	−0.935639
$290$	9.70076e109	2.57096
$291$	−2.70908e109	−0.616005
$292$	4.74856e109	0.926883
$293$	−2.42775e108	−0.0407001	−0.0203500	−	0.999793i	$-0.506478\pi$
$293$	−2.42775e108	−0.0407001	−0.0203500	+	0.999793i	$0.506478\pi$
$294$	1.23653e110	1.78135
$295$	−1.82502e109	−0.226042
$296$	−3.31754e110	−3.53456
$297$	6.58231e109	0.603554
$298$	−2.72025e110	−2.14776
$299$	−5.57106e109	−0.378939
$300$	1.22315e110	0.717104
$301$	−1.99145e110	−1.00684
$302$	5.86949e110	2.56031
$303$	3.09454e110	1.16519
$304$	−3.80510e110	−1.23735
$305$	1.57868e110	0.443559
$306$	−2.64861e109	−0.0643302
$307$	−2.66215e107	−0.000559209 0	−0.000279604	−	1.00000i	$-0.500089\pi$
$307$	−2.66215e107	−0.000559209 0	−0.000279604		1.00000i	$0.500089\pi$
$308$	1.21651e111	2.21110
$309$	3.97081e110	0.624780
$310$	−4.95556e110	−0.675302
$311$	−5.79663e110	−0.684444	−0.342222	−	0.939619i	$-0.611179\pi$
$311$	−5.79663e110	−0.684444	−0.342222	+	0.939619i	$0.611179\pi$
$312$	−2.50894e111	−2.56810
$313$	1.83417e111	1.62823	0.814117	−	0.580701i	$-0.197221\pi$
$313$	1.83417e111	1.62823	0.814117	+	0.580701i	$0.197221\pi$
$314$	−2.79057e111	−2.14943
$315$	−2.34518e110	−0.156804
$316$	2.47099e111	1.43481
$317$	−1.33808e111	−0.675062	−0.337531	−	0.941314i	$-0.609592\pi$
$317$	−1.33808e111	−0.675062	−0.337531	+	0.941314i	$0.609592\pi$
$318$	5.10217e110	0.223742
$319$	−2.35341e111	−0.897452
$320$	9.73522e111	3.22977
$321$	1.83909e111	0.531043
$322$	−5.01689e111	−1.26139
$323$	3.80712e110	0.0833844
$324$	−1.22228e112	−2.33301
$325$	1.38238e111	0.230047
$326$	−2.39583e112	−3.47754
$327$	1.25475e112	1.58922
$328$	5.41548e112	5.98757
$329$	3.59018e110	0.0346656
$330$	1.03725e112	0.875009
$331$	−1.40461e112	−1.03564	−0.517821	−	0.855489i	$-0.673257\pi$
$331$	−1.40461e112	−1.03564	−0.517821	+	0.855489i	$0.673257\pi$
$332$	−5.56007e112	−3.58456
$333$	−2.44360e111	−0.137804
$334$	5.61044e112	2.76872
$335$	2.79062e112	1.20561
$336$	−1.30777e113	−4.94804
$337$	−1.78572e112	−0.591949	−0.295974	−	0.955196i	$-0.595644\pi$
$337$	−1.78572e112	−0.591949	−0.295974	+	0.955196i	$0.595644\pi$
$338$	2.18982e112	0.636232
$339$	4.09038e112	1.04202
$340$	−2.63743e112	−0.589344
$341$	1.20222e112	0.235730
$342$	−4.84215e111	−0.0833444
$343$	−1.09418e111	−0.0165386
$344$	1.80864e113	2.40160
$345$	−3.13367e112	−0.365682
$346$	−7.52838e112	−0.772352
$347$	−1.99873e112	−0.180340	−0.0901700	−	0.995926i	$-0.528741\pi$
$347$	−1.99873e112	−0.180340	−0.0901700	+	0.995926i	$0.528741\pi$
$348$	5.04293e113	4.00320
$349$	−2.76100e113	−1.92901	−0.964504	−	0.264067i	$-0.914936\pi$
$349$	−2.76100e113	−1.92901	−0.964504	+	0.264067i	$0.914936\pi$
$350$	1.24487e113	0.765765
$351$	−1.59409e113	−0.863666
$352$	−4.69628e113	−2.24184
$353$	−1.57593e113	−0.663075	−0.331537	−	0.943442i	$-0.607567\pi$
$353$	−1.57593e113	−0.663075	−0.331537	+	0.943442i	$0.607567\pi$
$354$	−1.29508e113	−0.480453
$355$	2.25015e113	0.736291
$356$	−5.21338e113	−1.50520
$357$	1.30847e113	0.333447
$358$	1.48688e114	3.34566
$359$	−4.80149e113	−0.954274	−0.477137	−	0.878829i	$-0.658325\pi$
$359$	−4.80149e113	−0.954274	−0.477137	+	0.878829i	$0.658325\pi$
$360$	2.12990e113	0.374022
$361$	−5.74673e113	−0.891970
$362$	4.80497e113	0.659416
$363$	5.16294e113	0.626689
$364$	−2.94611e114	−3.16401
$365$	3.01874e113	0.286941
$366$	1.12027e114	0.942785
$367$	1.15953e114	0.864255	0.432128	−	0.901812i	$-0.357763\pi$
$367$	1.15953e114	0.864255	0.432128	+	0.901812i	$0.357763\pi$
$368$	2.63731e114	1.74154
$369$	3.98888e113	0.233442
$370$	−3.32156e114	−1.72332
$371$	3.80409e113	0.175030
$372$	−2.57615e114	−1.05150
$373$	2.55903e114	0.926900	0.463450	−	0.886123i	$-0.346611\pi$
$373$	2.55903e114	0.926900	0.463450	+	0.886123i	$0.346611\pi$
$374$	8.73416e113	0.280824
$375$	3.54631e114	1.01248
$376$	−3.26061e113	−0.0826874
$377$	5.69943e114	1.28423
$378$	−1.43552e115	−2.87491
$379$	−9.87836e114	−1.75890	−0.879448	−	0.475995i	$-0.842088\pi$
$379$	−9.87836e114	−1.75890	−0.879448	+	0.475995i	$0.842088\pi$
$380$	−4.82170e114	−0.763536
$381$	−4.41823e114	−0.622425
$382$	3.98805e114	0.499967
$383$	−9.67896e114	−1.08015	−0.540074	−	0.841617i	$-0.681604\pi$
$383$	−9.67896e114	−1.08015	−0.540074	+	0.841617i	$0.681604\pi$
$384$	3.23469e115	3.21435
$385$	7.73355e114	0.684504
$386$	1.24635e115	0.982887
$387$	1.33219e114	0.0936328
$388$	2.88910e115	1.81030
$389$	1.42694e115	0.797352	0.398676	−	0.917092i	$-0.369470\pi$
$389$	1.42694e115	0.797352	0.398676	+	0.917092i	$0.369470\pi$
$390$	−2.51199e115	−1.25211
$391$	−2.63871e114	−0.117362
$392$	−8.37307e115	−3.32395
$393$	−4.16224e115	−1.47523
$394$	5.41953e115	1.71546
$395$	1.57085e115	0.444185
$396$	−8.13791e114	−0.205625
$397$	5.95174e115	1.34421	0.672104	−	0.740456i	$-0.265391\pi$
$397$	5.95174e115	1.34421	0.672104	+	0.740456i	$0.265391\pi$
$398$	−1.02417e116	−2.06811
$399$	2.39211e115	0.432004
$400$	−6.54409e115	−1.05725
$401$	4.18136e115	0.604495	0.302248	−	0.953229i	$-0.402263\pi$
$401$	4.18136e115	0.604495	0.302248	+	0.953229i	$0.402263\pi$
$402$	1.98028e116	2.56253
$403$	−2.91151e115	−0.337322
$404$	−3.30017e116	−3.42425
$405$	−7.77023e115	−0.722246
$406$	5.13249e116	4.27484
$407$	8.05811e115	0.601564
$408$	−1.18835e116	−0.795367
$409$	−2.79410e116	−1.67709	−0.838543	−	0.544836i	$-0.816592\pi$
$409$	−2.79410e116	−1.67709	−0.838543	+	0.544836i	$0.816592\pi$
$410$	5.42204e116	2.91932
$411$	−2.04107e116	−0.986045
$412$	−4.23468e116	−1.83609
$413$	−9.65587e115	−0.375850
$414$	3.35608e115	0.117305
$415$	−3.53463e116	−1.10969
$416$	1.13733e117	3.20801
$417$	5.08009e116	1.28771
$418$	1.59676e116	0.363828
$419$	−7.53082e115	−0.154283	−0.0771415	−	0.997020i	$-0.524579\pi$
$419$	−7.53082e115	−0.154283	−0.0771415	+	0.997020i	$0.524579\pi$
$420$	−1.65716e117	−3.05331
$421$	−1.74478e116	−0.289193	−0.144596	−	0.989491i	$-0.546188\pi$
$421$	−1.74478e116	−0.289193	−0.144596	+	0.989491i	$0.546188\pi$
$422$	−1.00868e117	−1.50435
$423$	−2.40167e114	−0.00322379
$424$	−3.45489e116	−0.417497
$425$	6.54757e115	0.0712480
$426$	1.59675e117	1.56499
$427$	8.35251e116	0.737524
$428$	−1.96130e117	−1.56062
$429$	6.09408e116	0.437078
$430$	1.81083e117	1.17093
$431$	6.52772e116	0.380648	0.190324	−	0.981721i	$-0.439046\pi$
$431$	6.52772e116	0.380648	0.190324	+	0.981721i	$0.439046\pi$
$432$	7.54632e117	3.96925
$433$	−1.58060e117	−0.750083	−0.375042	−	0.927008i	$-0.622372\pi$
$433$	−1.58060e117	−0.750083	−0.375042	+	0.927008i	$0.622372\pi$
$434$	−2.62190e117	−1.12285
$435$	3.20588e117	1.23930
$436$	−1.33813e118	−4.67037
$437$	−4.82404e116	−0.152050
$438$	2.14216e117	0.609894
$439$	6.33463e117	1.62948	0.814742	−	0.579823i	$-0.196878\pi$
$439$	6.33463e117	1.62948	0.814742	+	0.579823i	$0.196878\pi$
$440$	−7.02363e117	−1.63274
$441$	−6.16737e116	−0.129593
$442$	−2.11522e117	−0.401850
$443$	4.84950e117	0.833165	0.416583	−	0.909098i	$-0.363228\pi$
$443$	4.84950e117	0.833165	0.416583	+	0.909098i	$0.363228\pi$
$444$	−1.72671e118	−2.68335
$445$	−3.31424e117	−0.465975
$446$	1.62722e118	2.07035
$447$	−8.98981e117	−1.03530
$448$	5.15073e118	5.37028
$449$	−2.82363e117	−0.266591	−0.133296	−	0.991076i	$-0.542556\pi$
$449$	−2.82363e117	−0.266591	−0.133296	+	0.991076i	$0.542556\pi$
$450$	−8.32762e116	−0.0712138
$451$	−1.31539e118	−1.01906
$452$	−4.36219e118	−3.06228
$453$	1.93973e118	1.23416
$454$	1.47186e118	0.848948
$455$	−1.87289e118	−0.979503
$456$	−2.17252e118	−1.03045
$457$	−1.85598e118	−0.798552	−0.399276	−	0.916831i	$-0.630738\pi$
$457$	−1.85598e118	−0.798552	−0.399276	+	0.916831i	$0.630738\pi$
$458$	7.28671e118	2.84458
$459$	−7.55034e117	−0.267487
$460$	3.34191e118	1.07466
$461$	1.46775e118	0.428510	0.214255	−	0.976778i	$-0.431268\pi$
$461$	1.46775e118	0.428510	0.214255	+	0.976778i	$0.431268\pi$
$462$	5.48789e118	1.45492
$463$	2.77498e118	0.668198	0.334099	−	0.942538i	$-0.391568\pi$
$463$	2.77498e118	0.668198	0.334099	+	0.942538i	$0.391568\pi$
$464$	−2.69808e119	−5.90206
$465$	−1.63770e118	−0.325520
$466$	4.21042e118	0.760592
$467$	−6.20631e118	−1.01914	−0.509568	−	0.860430i	$-0.670195\pi$
$467$	−6.20631e118	−1.01914	−0.509568	+	0.860430i	$0.670195\pi$
$468$	1.97082e118	0.294243
$469$	1.47647e119	2.00462
$470$	−3.26456e117	−0.0403153
$471$	−9.22218e118	−1.03610
$472$	8.76949e118	0.896510
$473$	−4.39307e118	−0.408741
$474$	1.11471e119	0.944116
$475$	1.19701e118	0.0923068
$476$	−1.39541e119	−0.979927
$477$	−2.54477e117	−0.0162772
$478$	1.08254e119	0.630817
$479$	2.47010e119	1.31155	0.655774	−	0.754958i	$-0.272343\pi$
$479$	2.47010e119	1.31155	0.655774	+	0.754958i	$0.272343\pi$
$480$	6.39741e119	3.09577
$481$	−1.95150e119	−0.860819
$482$	−3.70015e119	−1.48808
$483$	−1.65797e119	−0.608035
$484$	−5.50602e119	−1.84170
$485$	1.83665e119	0.560427
$486$	1.80928e119	0.503722
$487$	−3.27475e119	−0.832031	−0.416015	−	0.909358i	$-0.636574\pi$
$487$	−3.27475e119	−0.832031	−0.416015	+	0.909358i	$0.636574\pi$
$488$	−7.58577e119	−1.75921
$489$	−7.91766e119	−1.67630
$490$	−8.38322e119	−1.62064
$491$	7.69474e119	1.35852	0.679262	−	0.733896i	$-0.262300\pi$
$491$	7.69474e119	1.35852	0.679262	+	0.733896i	$0.262300\pi$
$492$	2.81864e120	4.54562
$493$	2.69951e119	0.397738
$494$	−3.86701e119	−0.520626
$495$	−5.17340e118	−0.0636568
$496$	1.37829e120	1.55027
$497$	1.19051e120	1.22426
$498$	−2.50825e120	−2.35866
$499$	6.79740e119	0.584613	0.292306	−	0.956325i	$-0.405577\pi$
$499$	6.79740e119	0.584613	0.292306	+	0.956325i	$0.405577\pi$
$500$	−3.78196e120	−2.97545
$501$	1.85412e120	1.33463
$502$	−1.06071e119	−0.0698686
$503$	9.48767e119	0.571985	0.285992	−	0.958232i	$-0.407677\pi$
$503$	9.48767e119	0.571985	0.285992	+	0.958232i	$0.407677\pi$
$504$	1.12689e120	0.621904
$505$	−2.09797e120	−1.06007
$506$	−1.10671e120	−0.512079
$507$	7.23685e119	0.306687
$508$	4.71183e120	1.82917
$509$	−1.57324e120	−0.559569	−0.279784	−	0.960063i	$-0.590263\pi$
$509$	−1.57324e120	−0.559569	−0.279784	+	0.960063i	$0.590263\pi$
$510$	−1.18979e120	−0.387791
$511$	1.59716e120	0.477110
$512$	−7.60153e120	−2.08155
$513$	−1.38034e120	−0.346548
$514$	4.50901e120	1.03806
$515$	−2.69206e120	−0.568411
$516$	9.41358e120	1.82324
$517$	7.91983e118	0.0140730
$518$	−1.75738e121	−2.86544
$519$	−2.48796e120	−0.372302
$520$	1.70097e121	2.33640
$521$	−1.40305e121	−1.76927	−0.884637	−	0.466280i	$-0.845594\pi$
$521$	−1.40305e121	−1.76927	−0.884637	+	0.466280i	$0.845594\pi$
$522$	−3.43341e120	−0.397547
$523$	−7.70708e120	−0.819530	−0.409765	−	0.912191i	$-0.634389\pi$
$523$	−7.70708e120	−0.819530	−0.409765	+	0.912191i	$0.634389\pi$
$524$	4.43882e121	4.33536
$525$	4.11400e120	0.369127
$526$	2.92194e121	2.40882
$527$	−1.37903e120	−0.104472
$528$	−2.88490e121	−2.00873
$529$	−1.22799e121	−0.785993
$530$	−3.45908e120	−0.203556
$531$	6.45936e119	0.0349529
$532$	−2.55107e121	−1.26957
$533$	3.18558e121	1.45823
$534$	−2.35185e121	−0.990431
$535$	−1.24683e121	−0.483131
$536$	−1.34093e122	−4.78160
$537$	4.91380e121	1.61273
$538$	1.49414e121	0.451419
$539$	2.03377e121	0.565721
$540$	9.56245e121	2.44933
$541$	1.41172e121	0.333019	0.166510	−	0.986040i	$-0.446750\pi$
$541$	1.41172e121	0.333019	0.166510	+	0.986040i	$0.446750\pi$
$542$	1.58061e121	0.343445
$543$	1.58793e121	0.317863
$544$	5.38694e121	0.993553
$545$	−8.50675e121	−1.44584
$546$	−1.32905e122	−2.08194
$547$	−2.47148e121	−0.356879	−0.178440	−	0.983951i	$-0.557105\pi$
$547$	−2.47148e121	−0.356879	−0.178440	+	0.983951i	$0.557105\pi$
$548$	2.17670e122	2.89777
$549$	−5.58746e120	−0.0685875
$550$	2.74614e121	0.310874
$551$	4.93520e121	0.515298
$552$	1.50577e122	1.45034
$553$	8.31108e121	0.738566
$554$	−3.96295e122	−3.24963
$555$	−1.09770e122	−0.830702
$556$	−5.41767e122	−3.78429
$557$	9.31061e121	0.600374	0.300187	−	0.953880i	$-0.402951\pi$
$557$	9.31061e121	0.600374	0.300187	+	0.953880i	$0.402951\pi$
$558$	1.75394e121	0.104422
$559$	1.06391e122	0.584894
$560$	8.86617e122	4.50162
$561$	2.88644e121	0.135368
$562$	−3.72275e122	−1.61286
$563$	3.11201e121	0.124571	0.0622855	−	0.998058i	$-0.480161\pi$
$563$	3.11201e121	0.124571	0.0622855	+	0.998058i	$0.480161\pi$
$564$	−1.69708e121	−0.0627743
$565$	−2.77312e122	−0.948009
$566$	7.21788e122	2.28075
$567$	−4.11109e122	−1.20091
$568$	−1.08123e123	−2.92022
$569$	2.71930e122	0.679142	0.339571	−	0.940580i	$-0.389718\pi$
$569$	2.71930e122	0.679142	0.339571	+	0.940580i	$0.389718\pi$
$570$	−2.17516e122	−0.502411
$571$	2.89172e122	0.617801	0.308901	−	0.951094i	$-0.400039\pi$
$571$	2.89172e122	0.617801	0.308901	+	0.951094i	$0.400039\pi$
$572$	−6.49904e122	−1.28448
$573$	1.31796e122	0.241003
$574$	2.86870e123	4.85407
$575$	−8.29648e121	−0.129920
$576$	−3.44561e122	−0.499420
$577$	3.49596e122	0.469075	0.234538	−	0.972107i	$-0.424642\pi$
$577$	3.49596e122	0.469075	0.234538	+	0.972107i	$0.424642\pi$
$578$	1.45644e123	1.80928
$579$	4.11889e122	0.473788
$580$	−3.41891e123	−3.64202
$581$	−1.87011e123	−1.84514
$582$	1.30333e123	1.19119
$583$	8.39173e121	0.0710560
$584$	−1.45054e123	−1.13804
$585$	1.25288e122	0.0910908
$586$	1.16798e122	0.0787031
$587$	−5.88136e121	−0.0367352	−0.0183676	−	0.999831i	$-0.505847\pi$
$587$	−5.88136e121	−0.0367352	−0.0183676	+	0.999831i	$0.505847\pi$
$588$	−4.35801e123	−2.52347
$589$	−2.52111e122	−0.135351
$590$	8.78012e122	0.437105
$591$	1.79103e123	0.826913
$592$	9.23827e123	3.95617
$593$	−3.21670e123	−1.27784	−0.638920	−	0.769273i	$-0.720618\pi$
$593$	−3.21670e123	−1.27784	−0.638920	+	0.769273i	$0.720618\pi$
$594$	−3.16672e123	−1.16711
$595$	−8.87088e122	−0.303363
$596$	9.58720e123	3.04252
$597$	−3.38463e123	−0.996905
$598$	2.68021e123	0.732768
$599$	−3.33166e122	−0.0845603	−0.0422802	−	0.999106i	$-0.513462\pi$
$599$	−3.33166e122	−0.0845603	−0.0422802	+	0.999106i	$0.513462\pi$
$600$	−3.73635e123	−0.880474
$601$	3.45390e123	0.755781	0.377890	−	0.925850i	$-0.376650\pi$
$601$	3.45390e123	0.755781	0.377890	+	0.925850i	$0.376650\pi$
$602$	9.58077e123	1.94696
$603$	−9.87691e122	−0.186424
$604$	−2.06863e124	−3.62693
$605$	−3.50027e123	−0.570148
$606$	−1.48877e124	−2.25318
$607$	8.57587e122	0.120609	0.0603047	−	0.998180i	$-0.480793\pi$
$607$	8.57587e122	0.120609	0.0603047	+	0.998180i	$0.480793\pi$
$608$	9.84831e123	1.28722
$609$	1.69617e124	2.06063
$610$	−7.59496e123	−0.857725
$611$	−1.91801e122	−0.0201380
$612$	9.33471e122	0.0911303
$613$	7.99900e123	0.726180	0.363090	−	0.931754i	$-0.381722\pi$
$613$	7.99900e123	0.726180	0.363090	+	0.931754i	$0.381722\pi$
$614$	1.28075e121	0.00108136
$615$	1.79186e124	1.40722
$616$	−3.71607e124	−2.71483
$617$	2.42228e124	1.64640	0.823199	−	0.567752i	$-0.192187\pi$
$617$	2.42228e124	1.64640	0.823199	+	0.567752i	$0.192187\pi$
$618$	−1.91034e124	−1.20816
$619$	−3.19334e124	−1.87936	−0.939682	−	0.342050i	$-0.888879\pi$
$619$	−3.19334e124	−1.87936	−0.939682	+	0.342050i	$0.888879\pi$
$620$	1.74653e124	0.956633
$621$	9.56710e123	0.487758
$622$	2.78873e124	1.32353
$623$	−1.75350e124	−0.774798
$624$	6.98660e124	2.87443
$625$	−1.67123e124	−0.640287
$626$	−8.82412e124	−3.14857
$627$	5.27693e123	0.175378
$628$	9.83500e124	3.04488
$629$	−9.24318e123	−0.266605
$630$	1.12826e124	0.303217
$631$	−1.27838e124	−0.320151	−0.160076	−	0.987105i	$-0.551174\pi$
$631$	−1.27838e124	−0.320151	−0.160076	+	0.987105i	$0.551174\pi$
$632$	−7.54815e124	−1.76169
$633$	−3.33345e124	−0.725151
$634$	6.43743e124	1.30539
$635$	2.99539e124	0.566269
$636$	−1.79820e124	−0.316954
$637$	−4.92534e124	−0.809528
$638$	1.13221e125	1.73543
$639$	−7.96400e123	−0.113853
$640$	−2.19299e125	−2.92435
$641$	−1.15177e125	−1.43279	−0.716393	−	0.697697i	$-0.754208\pi$
$641$	−1.15177e125	−1.43279	−0.716393	+	0.697697i	$0.754208\pi$
$642$	−8.84780e124	−1.02690
$643$	1.29646e123	0.0140401	0.00702004	−	0.999975i	$-0.497765\pi$
$643$	1.29646e123	0.0140401	0.00702004	+	0.999975i	$0.497765\pi$
$644$	1.76814e125	1.78688
$645$	5.98437e124	0.564431
$646$	−1.83159e124	−0.161243
$647$	4.09400e124	0.336440	0.168220	−	0.985750i	$-0.446198\pi$
$647$	4.09400e124	0.336440	0.168220	+	0.985750i	$0.446198\pi$
$648$	3.73370e125	2.86452
$649$	−2.13006e124	−0.152582
$650$	−6.65055e124	−0.444850
$651$	−8.66478e124	−0.541257
$652$	8.44380e125	4.92629
$653$	2.61194e125	1.42340	0.711698	−	0.702485i	$-0.247926\pi$
$653$	2.61194e125	1.42340	0.711698	+	0.702485i	$0.247926\pi$
$654$	−6.03657e125	−3.07313
$655$	2.82183e125	1.34213
$656$	−1.50803e126	−6.70178
$657$	−1.06843e124	−0.0443698
$658$	−1.72722e124	−0.0670340
$659$	−4.17300e124	−0.151373	−0.0756864	−	0.997132i	$-0.524115\pi$
$659$	−4.17300e124	−0.151373	−0.0756864	+	0.997132i	$0.524115\pi$
$660$	−3.65565e125	−1.23954
$661$	−1.80404e125	−0.571850	−0.285925	−	0.958252i	$-0.592301\pi$
$661$	−1.80404e125	−0.571850	−0.285925	+	0.958252i	$0.592301\pi$
$662$	6.75752e125	2.00266
$663$	−6.99031e124	−0.193707
$664$	1.69844e126	4.40119
$665$	−1.62176e125	−0.393028
$666$	1.17561e125	0.266477
$667$	−3.42057e125	−0.725269
$668$	−1.97733e126	−3.92217
$669$	5.37758e125	0.997986
$670$	−1.34256e126	−2.33133
$671$	1.84254e125	0.299409
$672$	3.38475e126	5.14748
$673$	−4.58978e125	−0.653313	−0.326656	−	0.945143i	$-0.605922\pi$
$673$	−4.58978e125	−0.653313	−0.326656	+	0.945143i	$0.605922\pi$
$674$	8.59105e125	1.14467
$675$	−2.37393e125	−0.296109
$676$	−7.71775e125	−0.901286
$677$	−4.89209e125	−0.534932	−0.267466	−	0.963567i	$-0.586186\pi$
$677$	−4.89209e125	−0.534932	−0.267466	+	0.963567i	$0.586186\pi$
$678$	−1.96786e126	−2.01499
$679$	9.71739e125	0.931847
$680$	8.05656e125	0.723607
$681$	4.86416e125	0.409224
$682$	−5.78384e125	−0.455839
$683$	2.01226e124	0.0148581	0.00742905	−	0.999972i	$-0.497635\pi$
$683$	2.01226e124	0.0148581	0.00742905	+	0.999972i	$0.497635\pi$
$684$	1.70656e125	0.118066
$685$	1.38377e126	0.897082
$686$	5.26404e124	0.0319813
$687$	2.40809e126	1.37119
$688$	−5.03646e126	−2.68807
$689$	−2.03229e125	−0.101679
$690$	1.50760e126	0.707132
$691$	−2.29357e126	−1.00865	−0.504324	−	0.863515i	$-0.668258\pi$
$691$	−2.29357e126	−1.00865	−0.504324	+	0.863515i	$0.668258\pi$
$692$	2.65329e126	1.09411
$693$	−2.73715e125	−0.105845
$694$	9.61580e125	0.348730
$695$	−3.44410e126	−1.17153
$696$	−1.54047e127	−4.91520
$697$	1.50884e126	0.451631
$698$	1.32830e127	3.73019
$699$	1.39145e126	0.366634
$700$	−4.38738e126	−1.08478
$701$	2.57316e126	0.597057	0.298528	−	0.954401i	$-0.403504\pi$
$701$	2.57316e126	0.597057	0.298528	+	0.954401i	$0.403504\pi$
$702$	7.66910e126	1.67010
$703$	−1.68982e126	−0.345405
$704$	1.13624e127	2.18015
$705$	−1.07886e125	−0.0194335
$706$	7.58173e126	1.28221
$707$	−1.11000e127	−1.76262
$708$	4.56434e126	0.680609
$709$	−6.78467e126	−0.950104	−0.475052	−	0.879958i	$-0.657571\pi$
$709$	−6.78467e126	−0.950104	−0.475052	+	0.879958i	$0.657571\pi$
$710$	−1.08254e127	−1.42379
$711$	−5.55975e125	−0.0686844
$712$	1.59253e127	1.84812
$713$	1.74738e126	0.190503
$714$	−6.29497e126	−0.644798
$715$	−4.13155e126	−0.397644
$716$	−5.24033e127	−4.73946
$717$	3.57755e126	0.304077
$718$	2.30998e127	1.84531
$719$	1.13360e127	0.851182	0.425591	−	0.904916i	$-0.360066\pi$
$719$	1.13360e127	0.851182	0.425591	+	0.904916i	$0.360066\pi$
$720$	−5.93108e126	−0.418637
$721$	−1.42432e127	−0.945121
$722$	2.76473e127	1.72483
$723$	−1.22281e127	−0.717309
$724$	−1.69345e127	−0.934129
$725$	8.48765e126	0.440297
$726$	−2.48387e127	−1.21185
$727$	3.79015e127	1.73930	0.869651	−	0.493666i	$-0.164344\pi$
$727$	3.79015e127	1.73930	0.869651	+	0.493666i	$0.164344\pi$
$728$	8.99951e127	3.88483
$729$	2.69516e127	1.09449
$730$	−1.45230e127	−0.554868
$731$	5.03914e126	0.181148
$732$	−3.94824e127	−1.33555
$733$	−1.80508e127	−0.574606	−0.287303	−	0.957840i	$-0.592759\pi$
$733$	−1.80508e127	−0.574606	−0.287303	+	0.957840i	$0.592759\pi$
$734$	−5.57845e127	−1.67124
$735$	−2.77046e127	−0.781206
$736$	−6.82584e127	−1.81173
$737$	3.25704e127	0.813805
$738$	−1.91904e127	−0.451414
$739$	4.14460e127	0.917921	0.458960	−	0.888457i	$-0.348222\pi$
$739$	4.14460e127	0.917921	0.458960	+	0.888457i	$0.348222\pi$
$740$	1.17064e128	2.44125
$741$	−1.27796e127	−0.250961
$742$	−1.83013e127	−0.338461
$743$	−3.30910e126	−0.0576379	−0.0288189	−	0.999585i	$-0.509175\pi$
$743$	−3.30910e126	−0.0576379	−0.0288189	+	0.999585i	$0.509175\pi$
$744$	7.86937e127	1.29105
$745$	6.09474e127	0.941892
$746$	−1.23114e128	−1.79238
$747$	1.25102e127	0.171592
$748$	−3.07825e127	−0.397816
$749$	−6.59677e127	−0.803323
$750$	−1.70611e128	−1.95786
$751$	6.11801e127	0.661657	0.330829	−	0.943691i	$-0.392672\pi$
$751$	6.11801e127	0.661657	0.330829	+	0.943691i	$0.392672\pi$
$752$	9.07973e126	0.0925506
$753$	−3.50541e126	−0.0336793
$754$	−2.74197e128	−2.48335
$755$	−1.31506e128	−1.12281
$756$	5.05932e128	4.07260
$757$	−1.17540e128	−0.892110	−0.446055	−	0.895005i	$-0.647171\pi$
$757$	−1.17540e128	−0.892110	−0.446055	+	0.895005i	$0.647171\pi$
$758$	4.75244e128	3.40124
$759$	−3.65743e127	−0.246841
$760$	1.47289e128	0.937485
$761$	−3.45209e127	−0.207236	−0.103618	−	0.994617i	$-0.533042\pi$
$761$	−3.45209e127	−0.207236	−0.103618	+	0.994617i	$0.533042\pi$
$762$	2.12559e128	1.20361
$763$	−4.50077e128	−2.40406
$764$	−1.40554e128	−0.708254
$765$	5.93423e126	0.0282118
$766$	4.65651e128	2.08872
$767$	5.15853e127	0.218339
$768$	−6.67383e128	−2.66564
$769$	4.31920e128	1.62810	0.814050	−	0.580794i	$-0.197258\pi$
$769$	4.31920e128	1.62810	0.814050	+	0.580794i	$0.197258\pi$
$770$	−3.72058e128	−1.32365
$771$	1.49013e128	0.500383
$772$	−4.39259e128	−1.39236
$773$	5.58575e128	1.67145	0.835727	−	0.549145i	$-0.185047\pi$
$773$	5.58575e128	1.67145	0.835727	+	0.549145i	$0.185047\pi$
$774$	−6.40911e127	−0.181061
$775$	−4.33586e127	−0.115651
$776$	−8.82536e128	−2.22272
$777$	−5.80773e128	−1.38125
$778$	−6.86497e128	−1.54187
$779$	2.75843e128	0.585120
$780$	8.85318e128	1.77374
$781$	2.62624e128	0.497007
$782$	1.26947e128	0.226946
$783$	−9.78755e128	−1.65301
$784$	2.33163e129	3.72044
$785$	6.25228e128	0.942624
$786$	2.00244e129	2.85269
$787$	−2.16044e128	−0.290849	−0.145424	−	0.989369i	$-0.546455\pi$
$787$	−2.16044e128	−0.290849	−0.145424	+	0.989369i	$0.546455\pi$
$788$	−1.91005e129	−2.43012
$789$	9.65633e128	1.16114
$790$	−7.55729e128	−0.858936
$791$	−1.46721e129	−1.57630
$792$	2.48589e128	0.252471
$793$	−4.46222e128	−0.428444
$794$	−2.86336e129	−2.59934
$795$	−1.14314e128	−0.0981215
$796$	3.60955e129	2.92969
$797$	5.79107e128	0.444492	0.222246	−	0.974991i	$-0.428661\pi$
$797$	5.79107e128	0.444492	0.222246	+	0.974991i	$0.428661\pi$
$798$	−1.15084e129	−0.835381
$799$	−9.08456e126	−0.00623695
$800$	1.69373e129	1.09987
$801$	1.17302e128	0.0720538
$802$	−2.01164e129	−1.16893
$803$	3.52329e128	0.193690
$804$	−6.97927e129	−3.63008
$805$	1.12404e129	0.553177
$806$	1.40072e129	0.652291
$807$	4.93779e128	0.217601
$808$	1.00810e130	4.20436
$809$	−1.68676e129	−0.665799	−0.332899	−	0.942962i	$-0.608027\pi$
$809$	−1.68676e129	−0.665799	−0.332899	+	0.942962i	$0.608027\pi$
$810$	3.73823e129	1.39663
$811$	1.55157e129	0.548712	0.274356	−	0.961628i	$-0.411535\pi$
$811$	1.55157e129	0.548712	0.274356	+	0.961628i	$0.411535\pi$
$812$	−1.80888e130	−6.05574
$813$	5.22357e128	0.165553
$814$	−3.87672e129	−1.16327
$815$	5.36786e129	1.52506
$816$	3.30917e129	0.890241
$817$	9.21247e128	0.234690
$818$	1.34423e130	3.24304
$819$	6.62878e128	0.151461
$820$	−1.91093e130	−4.13550
$821$	3.14500e129	0.644689	0.322345	−	0.946622i	$-0.395529\pi$
$821$	3.14500e129	0.644689	0.322345	+	0.946622i	$0.395529\pi$
$822$	9.81951e129	1.90675
$823$	−9.23589e129	−1.69897	−0.849486	−	0.527612i	$-0.823088\pi$
$823$	−9.23589e129	−1.69897	−0.849486	+	0.527612i	$0.823088\pi$
$824$	1.29357e130	2.25439
$825$	9.07538e128	0.149852
$826$	4.64540e129	0.726794
$827$	−3.35499e129	−0.497389	−0.248694	−	0.968582i	$-0.580001\pi$
$827$	−3.35499e129	−0.497389	−0.248694	+	0.968582i	$0.580001\pi$
$828$	−1.18281e129	−0.166175
$829$	4.80463e129	0.639711	0.319855	−	0.947466i	$-0.396366\pi$
$829$	4.80463e129	0.639711	0.319855	+	0.947466i	$0.396366\pi$
$830$	1.70050e130	2.14586
$831$	−1.30966e130	−1.56644
$832$	−2.75171e130	−3.11972
$833$	−2.33287e129	−0.250719
$834$	−2.44401e130	−2.49008
$835$	−1.25702e130	−1.21421
$836$	−5.62759e129	−0.515399
$837$	4.99990e129	0.434189
$838$	3.62305e129	0.298342
$839$	−1.24765e130	−0.974282	−0.487141	−	0.873323i	$-0.661960\pi$
$839$	−1.24765e130	−0.974282	−0.487141	+	0.873323i	$0.661960\pi$
$840$	5.06214e130	3.74892
$841$	2.07568e130	1.45794
$842$	8.39407e129	0.559222
$843$	−1.23028e130	−0.777460
$844$	3.55496e130	2.13106
$845$	−4.90630e129	−0.279017
$846$	1.15543e128	0.00623396
$847$	−1.85193e130	−0.948010
$848$	9.62074e129	0.467297
$849$	2.38534e130	1.09941
$850$	−3.15001e129	−0.137775
$851$	1.17121e130	0.486150
$852$	−5.62756e130	−2.21696
$853$	−3.16115e130	−1.18199	−0.590993	−	0.806676i	$-0.701264\pi$
$853$	−3.16115e130	−1.18199	−0.590993	+	0.806676i	$0.701264\pi$
$854$	−4.01836e130	−1.42618
$855$	1.08489e129	0.0365504
$856$	5.99120e130	1.91616
$857$	4.85246e130	1.47338	0.736692	−	0.676229i	$-0.236387\pi$
$857$	4.85246e130	1.47338	0.736692	+	0.676229i	$0.236387\pi$
$858$	−2.93184e130	−0.845193
$859$	1.53494e129	0.0420141	0.0210070	−	0.999779i	$-0.493313\pi$
$859$	1.53494e129	0.0420141	0.0210070	+	0.999779i	$0.493313\pi$
$860$	−6.38204e130	−1.65874
$861$	9.48040e130	2.33984
$862$	−3.14046e130	−0.736072
$863$	−2.23394e130	−0.497269	−0.248634	−	0.968597i	$-0.579982\pi$
$863$	−2.23394e130	−0.497269	−0.248634	+	0.968597i	$0.579982\pi$
$864$	−1.95313e131	−4.12923
$865$	1.68674e130	0.338712
$866$	7.60418e130	1.45046
$867$	4.81321e130	0.872138
$868$	9.24056e130	1.59064
$869$	1.83340e130	0.299832
$870$	−1.54233e131	−2.39647
$871$	−7.88784e130	−1.16453
$872$	4.08761e131	5.73437
$873$	−6.50051e129	−0.0866589
$874$	2.32083e130	0.294025
$875$	−1.27205e131	−1.53160
$876$	−7.54979e130	−0.863977
$877$	−9.11800e129	−0.0991785	−0.0495892	−	0.998770i	$-0.515791\pi$
$877$	−9.11800e129	−0.0991785	−0.0495892	+	0.998770i	$0.515791\pi$
$878$	−3.04757e131	−3.15099
$879$	3.85991e129	0.0379378
$880$	1.95585e131	1.82750
$881$	1.41911e131	1.26063	0.630314	−	0.776340i	$-0.282926\pi$
$881$	1.41911e131	1.26063	0.630314	+	0.776340i	$0.282926\pi$
$882$	2.96709e130	0.250599
$883$	−6.40533e130	−0.514388	−0.257194	−	0.966360i	$-0.582798\pi$
$883$	−6.40533e130	−0.514388	−0.257194	+	0.966360i	$0.582798\pi$
$884$	7.45483e130	0.569262
$885$	2.90163e130	0.210701
$886$	−2.33307e131	−1.61112
$887$	−1.13778e131	−0.747235	−0.373617	−	0.927583i	$-0.621883\pi$
$887$	−1.13778e131	−0.747235	−0.373617	+	0.927583i	$0.621883\pi$
$888$	5.27459e131	3.29467
$889$	1.58481e131	0.941560
$890$	1.59447e131	0.901072
$891$	−9.06895e130	−0.487527
$892$	−5.73492e131	−2.93286
$893$	−1.66082e129	−0.00808041
$894$	4.32496e131	2.00199
$895$	−3.33136e131	−1.46723
$896$	−1.16027e132	−4.86244
$897$	8.85749e130	0.353221
$898$	1.35844e131	0.515517
$899$	−1.78764e131	−0.645615
$900$	2.93497e130	0.100882
$901$	−9.62586e129	−0.0314910
$902$	6.32828e131	1.97058
$903$	3.16622e131	0.938505
$904$	1.33252e132	3.75992
$905$	−1.07656e131	−0.289184
$906$	−9.33198e131	−2.38654
$907$	−2.07157e131	−0.504401	−0.252201	−	0.967675i	$-0.581154\pi$
$907$	−2.07157e131	−0.504401	−0.252201	+	0.967675i	$0.581154\pi$
$908$	−5.18739e131	−1.20262
$909$	7.42541e130	0.163918
$910$	9.01042e131	1.89410
$911$	7.32060e131	1.46548	0.732738	−	0.680511i	$-0.238242\pi$
$911$	7.32060e131	1.46548	0.732738	+	0.680511i	$0.238242\pi$
$912$	6.04977e131	1.15337
$913$	−4.12541e131	−0.749061
$914$	8.92906e131	1.54419
$915$	−2.50996e131	−0.413455
$916$	−2.56811e132	−4.02963
$917$	1.49298e132	2.23161
$918$	3.63244e131	0.517248
$919$	−9.54003e131	−1.29422	−0.647112	−	0.762395i	$-0.724023\pi$
$919$	−9.54003e131	−1.29422	−0.647112	+	0.762395i	$0.724023\pi$
$920$	−1.02085e132	−1.31949
$921$	4.23258e128	0.000521256 0
$922$	−7.06128e131	−0.828624
$923$	−6.36016e131	−0.711201
$924$	−1.93414e132	−2.06103
$925$	−2.90619e131	−0.295132
$926$	−1.33503e132	−1.29212
$927$	9.52806e130	0.0878934
$928$	6.98312e132	6.13995
$929$	−6.90699e130	−0.0578882	−0.0289441	−	0.999581i	$-0.509214\pi$
$929$	−6.90699e130	−0.0578882	−0.0289441	+	0.999581i	$0.509214\pi$
$930$	7.87891e131	0.629470
$931$	−4.26491e131	−0.324825
$932$	−1.48391e132	−1.07746
$933$	9.21612e131	0.637992
$934$	2.98583e132	1.97074
$935$	−1.95689e131	−0.123154
$936$	−6.02027e131	−0.361278
$937$	9.96476e131	0.570237	0.285118	−	0.958492i	$-0.407967\pi$
$937$	9.96476e131	0.570237	0.285118	+	0.958492i	$0.407967\pi$
$938$	−7.10322e132	−3.87640
$939$	−2.91617e132	−1.51773
$940$	1.15055e131	0.0571107
$941$	3.96538e132	1.87736	0.938678	−	0.344795i	$-0.112052\pi$
$941$	3.96538e132	1.87736	0.938678	+	0.344795i	$0.112052\pi$
$942$	4.43675e132	2.00355
$943$	−1.91186e132	−0.823542
$944$	−2.44202e132	−1.00345
$945$	3.21629e132	1.26078
$946$	2.11349e132	0.790396
$947$	7.97066e131	0.284394	0.142197	−	0.989838i	$-0.454583\pi$
$947$	7.97066e131	0.284394	0.142197	+	0.989838i	$0.454583\pi$
$948$	−3.92865e132	−1.33744
$949$	−8.53263e131	−0.277164
$950$	−5.75879e131	−0.178497
$951$	2.12742e132	0.629246
$952$	4.26258e132	1.20317
$953$	−1.94714e132	−0.524521	−0.262260	−	0.964997i	$-0.584468\pi$
$953$	−1.94714e132	−0.524521	−0.262260	+	0.964997i	$0.584468\pi$
$954$	1.22428e131	0.0314759
$955$	−8.93526e131	−0.219259
$956$	−3.81529e132	−0.893616
$957$	3.74171e132	0.836543
$958$	−1.18835e133	−2.53618
$959$	7.32126e132	1.49162
$960$	−1.54781e133	−3.01057
$961$	−4.47186e132	−0.830419
$962$	9.38857e132	1.66459
$963$	4.41295e131	0.0747066
$964$	1.30407e133	2.10801
$965$	−2.79244e132	−0.431041
$966$	7.97642e132	1.17578
$967$	−1.33124e133	−1.87403	−0.937017	−	0.349283i	$-0.886425\pi$
$967$	−1.33124e133	−1.87403	−0.937017	+	0.349283i	$0.886425\pi$
$968$	1.68193e133	2.26128
$969$	−6.05299e131	−0.0777252
$970$	−8.83605e132	−1.08372
$971$	2.41972e132	0.283471	0.141735	−	0.989905i	$-0.454732\pi$
$971$	2.41972e132	0.283471	0.141735	+	0.989905i	$0.454732\pi$
$972$	−6.37657e132	−0.713572
$973$	−1.82221e133	−1.94795
$974$	1.57547e133	1.60893
$975$	−2.19785e132	−0.214434
$976$	2.11239e133	1.96905
$977$	−3.12470e132	−0.278292	−0.139146	−	0.990272i	$-0.544436\pi$
$977$	−3.12470e132	−0.278292	−0.139146	+	0.990272i	$0.544436\pi$
$978$	3.80915e133	3.24152
$979$	−3.86818e132	−0.314540
$980$	2.95456e133	2.29579
$981$	3.01082e132	0.223570
$982$	−3.70191e133	−2.62703
$983$	6.48939e132	0.440121	0.220061	−	0.975486i	$-0.429374\pi$
$983$	6.48939e132	0.440121	0.220061	+	0.975486i	$0.429374\pi$
$984$	−8.61013e133	−5.58120
$985$	−1.21425e133	−0.752307
$986$	−1.29872e133	−0.769120
$987$	−5.70806e131	−0.0323129
$988$	1.36288e133	0.737519
$989$	−6.38514e132	−0.330321
$990$	2.48890e132	0.123095
$991$	3.49977e133	1.65486	0.827432	−	0.561566i	$-0.189801\pi$
$991$	3.49977e133	1.65486	0.827432	+	0.561566i	$0.189801\pi$
$992$	−3.56728e133	−1.61275
$993$	2.23320e133	0.965355
$994$	−5.72751e133	−2.36740
$995$	2.29465e133	0.906962
$996$	8.84002e133	3.34128
$997$	2.65956e133	0.961336	0.480668	−	0.876903i	$-0.340394\pi$
$997$	2.65956e133	0.961336	0.480668	+	0.876903i	$0.340394\pi$
$998$	−3.27020e133	−1.13049
$999$	3.35128e133	1.10802

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1.90.a.a.1.1	✓	7
3.2	odd	2		9.90.a.b.1.7		7

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1.90.a.a.1.1	✓	7	1.1	even	1	trivial
9.90.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:	\( k \)	\(=\)	\( 90 \)
Character orbit:	\([\chi]\)	\(=\)	1.a (trivial)

\(f(q)\)	\(=\)	\(q-4.81096e13 q^{2} -1.58991e21 q^{3} +1.69556e27 q^{4} +1.07790e31 q^{5} +7.64900e34 q^{6} +5.70296e37 q^{7} -5.17945e40 q^{8} -3.81503e41 q^{9} +O(q^{10})\)	\(q-4.81096e13 q^{2} -1.58991e21 q^{3} +1.69556e27 q^{4} +1.07790e31 q^{5} +7.64900e34 q^{6} +5.70296e37 q^{7} -5.17945e40 q^{8} -3.81503e41 q^{9} -5.18572e44 q^{10} +1.25806e46 q^{11} -2.69579e48 q^{12} -3.04674e49 q^{13} -2.74367e51 q^{14} -1.71376e52 q^{15} +1.44231e54 q^{16} -1.44307e54 q^{17} +1.83540e55 q^{18} -2.63820e56 q^{19} +1.82764e58 q^{20} -9.06721e58 q^{21} -6.05246e59 q^{22} +1.82853e60 q^{23} +8.23486e61 q^{24} -4.53723e61 q^{25} +1.46577e63 q^{26} +5.23212e63 q^{27} +9.66973e64 q^{28} -1.87067e65 q^{29} +8.24484e65 q^{30} +9.55617e65 q^{31} -3.73296e67 q^{32} -2.00020e67 q^{33} +6.94257e67 q^{34} +6.14721e68 q^{35} -6.46863e68 q^{36} +6.40520e69 q^{37} +1.26923e70 q^{38} +4.84404e70 q^{39} -5.58291e71 q^{40} -1.04557e72 q^{41} +4.36220e72 q^{42} -3.49195e72 q^{43} +2.13312e73 q^{44} -4.11221e72 q^{45} -8.79700e73 q^{46} +6.29528e72 q^{47} -2.29314e75 q^{48} +1.61660e75 q^{49} +2.18284e75 q^{50} +2.29436e75 q^{51} -5.16593e76 q^{52} +6.67038e75 q^{53} -2.51715e77 q^{54} +1.35606e77 q^{55} -2.95382e78 q^{56} +4.19451e77 q^{57} +8.99970e78 q^{58} -1.69313e78 q^{59} -2.90579e79 q^{60} +1.46459e79 q^{61} -4.59743e79 q^{62} -2.17570e79 q^{63} +9.03167e80 q^{64} -3.28407e80 q^{65} +9.62288e80 q^{66} +2.58895e81 q^{67} -2.44682e81 q^{68} -2.90720e81 q^{69} -2.95740e82 q^{70} +2.08753e82 q^{71} +1.97597e82 q^{72} +2.80058e82 q^{73} -3.08152e83 q^{74} +7.21380e82 q^{75} -4.47324e83 q^{76} +7.17466e83 q^{77} -2.33045e84 q^{78} +1.45733e84 q^{79} +1.55466e85 q^{80} -7.20869e84 q^{81} +5.03020e85 q^{82} -3.27919e85 q^{83} -1.53740e86 q^{84} -1.55549e85 q^{85} +1.67996e86 q^{86} +2.97419e86 q^{87} -6.51604e86 q^{88} -3.07472e86 q^{89} +1.97837e86 q^{90} -1.73754e87 q^{91} +3.10039e87 q^{92} -1.51935e87 q^{93} -3.02863e86 q^{94} -2.84371e87 q^{95} +5.93508e88 q^{96} +1.70392e88 q^{97} -7.77738e88 q^{98} -4.79953e87 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 7 q - 31407330351408 q^{2} - 13\!\cdots\!64 q^{3}+ \cdots + 56\!\cdots\!71 q^{9}+O(q^{10}) \) 7 * q - 31407330351408 * q^2 - 1359636564127989407364 * q^3 + 2261776677705673116713576704 * q^4 + 10232470009089362495458987082250 * q^5 - 47224471979937892179333042051869376 * q^6 + 38501341543555466088619988316514959992 * q^7 - 17954070319777658933153680910224754257920 * q^8 + 5642786905031106277764534052585801627237371 * q^9	\( 7 q - 31407330351408 q^{2} - 13\!\cdots\!64 q^{3}+ \cdots - 19\!\cdots\!68 q^{99}+O(q^{100}) \) 7 * q - 31407330351408 * q^2 - 1359636564127989407364 * q^3 + 2261776677705673116713576704 * q^4 + 10232470009089362495458987082250 * q^5 - 47224471979937892179333042051869376 * q^6 + 38501341543555466088619988316514959992 * q^7 - 17954070319777658933153680910224754257920 * q^8 + 5642786905031106277764534052585801627237371 * q^9 - 339886969508111355644737639996417314840948000 * q^10 - 33185398429231418991729589216300973489966079756 * q^11 - 1004632700194650448641313614558096018594697264128 * q^12 - 103208963062610039235367083636366996420076737975934 * q^13 - 3327254465892753266340667920543396227686510656335232 * q^14 - 3928505137426182309397624104867069340549391446959000 * q^15 + 1162914962909596823700454711087105707311468348200517632 * q^16 + 8319478335928844788789086096491382896131016464480742142 * q^17 - 147732328649241019658282821579260643023785726547655592304 * q^18 + 566291740319213482378495952187194771397009633898137615980 * q^19 + 17240116916193408372006373658712519601040539123805641152000 * q^20 - 90598178803547150933473132922481297065025295806785914127136 * q^21 - 572030171884928043470630402880877439080047260844354367465536 * q^22 - 1162243907076079309616831317442805749267469267057101679089304 * q^23 + 102292564315938855068370806246211339063831852161969337222512640 * q^24 - 212322678457531006783078558385295515929862869778299899884234375 * q^25 + 256954281475267715641749604093742676189922873609159508555728224 * q^26 + 11230609565348224313895297191070036430584541766541637832713861080 * q^27 + 42271634017038816624971599134243423766860094950653754695170525184 * q^28 - 141971615822865442921693407341400369750322173654805889340125766030 * q^29 + 685316390944098153207628047778140189726339714889914380742075312000 * q^30 + 683664012826903943332640912357777981916064560235376021892996967904 * q^31 - 18295616415211966307849618677858007212056173228946481610958698446848 * q^32 - 86562711553720527899763440849945042911790491733183542919656093165488 * q^33 + 310076023324380793221121009797602653729382139402481891183326564397728 * q^34 + 330170304491374501797216156307803170564453659546779205972398673602000 * q^35 - 1640012020416196297725034563971477848297008731151338285245876678380288 * q^36 - 54562371243327727239087361205689070078467002527262667251534613287958 * q^37 + 45443543517981085735407850236293406047335765118416513555057178362067520 * q^38 - 52864527349249866236351055677173599634948671842685563480478962199294648 * q^39 - 361606215568925170012071637858292899677067482636237269829164280222720000 * q^40 - 657970372131031022656393678727303783670430723595160145307484502660397466 * q^41 + 1194858754087456269163194270977035799298048792026970828715903204437563904 * q^42 + 3219260988489925248073148176207907480629490254450229462745931521229023956 * q^43 - 15518629834856028222698238418543583045824703222318379119582671434892588032 * q^44 - 47660318642997018016862592256216157339280861352258819392244471941754530750 * q^45 - 56495859283654895727924020960810320205382055229302825603343235358563739776 * q^46 - 589986405817377998239864975519322982713028461832176517663311475432884156208 * q^47 - 3832565523894613734560398647870601248628652435813709455578147238513735368704 * q^48 - 3087918931516952942471049623523578487683423584779916315782412290559435137201 * q^49 - 11186377093883721132072449077187321801629226446489467367094029042775729250000 * q^50 - 44749224651513683358510561546459122133403179429459901007904418343196358896456 * q^51 - 195074413541392068451275175025603658303895820240091441880921515457689944416768 * q^52 - 181430063765559371241038742666701312033549399057740391278794421145415983301414 * q^53 - 1069768557347791789565342861771646012899754433224109219876568781015744643201920 * q^54 - 1251959124114414009910203618775792485005181014548185493458611647835407269933000 * q^55 - 5833843183212315752254903583581814862872931164492369538677714690034795155128320 * q^56 - 6636053151264088660994009243658731470064177381062469866816802824914691937541840 * q^57 - 3085757480392710136283141086455357758895171179069060863542747741259905831138720 * q^58 - 9086646688135460130541149101651496775878005651006843822379595086967226946739260 * q^59 - 28597614595134268752948807453761124021285695193298938696320462632027102503168000 * q^60 + 8774545844023482806788207542368099480171833682235332719617911769894989384384594 * q^61 + 169526530141162019514362685680407627845528510541984421132250792903222430290676224 * q^62 + 600060998677337137803649489067962875140223680130818894152235224596331850847343896 * q^63 + 1452176441912468141297252840801366807510309025606268702123180748140039039923257344 * q^64 + 1324597647382660271811574639166235036730362819738030027679321346411726630592583500 * q^65 + 5794073040567151132693317781366382943170107912751606019648469980133340516392228608 * q^66 + 5843793535214317245370457729815716742376089805910350107798697912590172409883288892 * q^67 + 3383522446313435458738303622044969561038087184549368481666865721250715220292329984 * q^68 - 5947153100304692873901208875288315645744737627052374011935588797613066907438186848 * q^69 - 48530199945646178573467957795368744286471165824229177345686884714666072932491936000 * q^70 - 54831722251632385251791847370899308335600102141533329655944703784411212003030405576 * q^71 - 193536676908511823968799310909661267914860871284938663775925036280217916976534056960 * q^72 - 199687593578972105167207004100293505918603845674208378633352670689487827039532442554 * q^73 - 965066694195901068911432718812601386557508653596585879236882657245078468484355531552 * q^74 - 449845818551229824067343835155681595861236685828593692926866173145835890979882437500 * q^75 - 624789819902471734428103435859366276136204176410553236414159885942801809403293936640 * q^76 + 1343091849772730830408738350805190184311976794055420918621708129900429278982204783264 * q^77 + 5115170224904826933556340523459220074577237696572659886093176102046008883684662673792 * q^78 + 2673613187258858564803647217355170619960582874636639491339476674654505245882753222320 * q^79 + 27680777280715589878137850302356927719666260300976702690203906698201250115244507136000 * q^80 + 48638608516196512054280935503541026926798324553759401775728207287806340272179807855247 * q^81 + 63127032979305734173962933747182283580799525530431609292523424735220314498528511785504 * q^82 - 35017619719051015255233069909205249521130641969249674783596011796500257235899597331924 * q^83 - 91271218351884570971920288208768314031909543306789609723100776475256076481746994388992 * q^84 - 141384913067859944856588220403027346022605850144801355881993121940858052671602572135500 * q^85 - 246618390628075722158819620850499384970086160242141588082920865473574265424952752922176 * q^86 - 414485418912512080488627714148474005618211107267303271323056368803909094640534785472760 * q^87 - 1874747156501905660418588549009712256169985369393565612731235328175018372894817920368640 * q^88 - 1625431592570174192786638376427668495469444301472287736732287307560402850485922205836490 * q^89 - 1500534342888898564405033173718589632643579855463696593286927469992128698108056410724000 * q^90 - 304928345599594097428899578613442396706625647498145800328408392926012721126646204980336 * q^91 + 7281329003117440073848907204538369781556431009214831685528490675028895216006021740500992 * q^92 + 8725785078968826322471270683478576510125821912788765392594960100289595008684983594910592 * q^93 + 22964567086699943860517240071514688733928422760236698641236969735081204002206026310078208 * q^94 + 22546113414761055806340378014072491896390775587517280959221325649524340597082183574485000 * q^95 + 84826971262863357834463681679311846519023363534588497414160609596759417378202987836473344 * q^96 + 71386807957160533061753038101994485650273149078658846323482657056181047793902162983463342 * q^97 - 17615586549862077419320336328445909012296979015379167958274818444332513071671081562433456 * q^98 - 197573613824864988900062481565182229817848341132748736551935840297576094108952766009175068 * q^99

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