LMFDB - Embedded newform 1.90.a.a.1.5

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			1.5
Root			$-4.68207e11$ 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)

$f(q)$	$=$	$q+1.79872e13 q^{2} -3.11193e21 q^{3} -2.95431e26 q^{4} -4.75717e30 q^{5} -5.59749e34 q^{6} +3.90338e37 q^{7} -1.64475e40 q^{8} +6.77478e42 q^{9} +O(q^{10})$	\(q+1.79872e13 q^{2} -3.11193e21 q^{3} -2.95431e26 q^{4} -4.75717e30 q^{5} -5.59749e34 q^{6} +3.90338e37 q^{7} -1.64475e40 q^{8} +6.77478e42 q^{9} -8.55680e43 q^{10} -2.01197e45 q^{11} +9.19360e47 q^{12} -1.05046e49 q^{13} +7.02109e50 q^{14} +1.48040e52 q^{15} -1.12982e53 q^{16} +1.05148e55 q^{17} +1.21859e56 q^{18} +1.08050e57 q^{19} +1.40541e57 q^{20} -1.21471e59 q^{21} -3.61897e58 q^{22} -5.03802e60 q^{23} +5.11835e61 q^{24} -1.38928e62 q^{25} -1.88949e62 q^{26} -1.20290e64 q^{27} -1.15318e64 q^{28} +1.12164e65 q^{29} +2.66282e65 q^{30} -3.18722e66 q^{31} +8.14829e66 q^{32} +6.26111e66 q^{33} +1.89132e68 q^{34} -1.85690e68 q^{35} -2.00148e69 q^{36} -6.99627e69 q^{37} +1.94351e70 q^{38} +3.26897e70 q^{39} +7.82435e70 q^{40} -7.38883e70 q^{41} -2.18491e72 q^{42} +4.97212e72 q^{43} +5.94398e71 q^{44} -3.22288e73 q^{45} -9.06197e73 q^{46} +5.91267e73 q^{47} +3.51590e74 q^{48} -1.12142e74 q^{49} -2.49893e75 q^{50} -3.27213e76 q^{51} +3.10339e75 q^{52} +2.39386e76 q^{53} -2.16369e77 q^{54} +9.57127e75 q^{55} -6.42009e77 q^{56} -3.36243e78 q^{57} +2.01752e78 q^{58} -1.72292e78 q^{59} -4.37355e78 q^{60} +1.90453e79 q^{61} -5.73291e79 q^{62} +2.64446e80 q^{63} +2.16497e80 q^{64} +4.99723e79 q^{65} +1.12620e80 q^{66} +7.04228e80 q^{67} -3.10640e81 q^{68} +1.56779e82 q^{69} -3.34005e81 q^{70} -1.27373e82 q^{71} -1.11428e83 q^{72} -3.75786e82 q^{73} -1.25843e83 q^{74} +4.32334e83 q^{75} -3.19212e83 q^{76} -7.85349e82 q^{77} +5.87995e83 q^{78} +3.21546e83 q^{79} +5.37472e83 q^{80} +1.77235e85 q^{81} -1.32904e84 q^{82} -2.22227e85 q^{83} +3.58862e85 q^{84} -5.00207e85 q^{85} +8.94344e85 q^{86} -3.49047e86 q^{87} +3.30919e85 q^{88} -5.54352e86 q^{89} -5.79705e86 q^{90} -4.10036e86 q^{91} +1.48839e87 q^{92} +9.91840e87 q^{93} +1.06352e87 q^{94} -5.14011e87 q^{95} -2.53569e88 q^{96} +4.88818e88 q^{97} -2.01713e87 q^{98} -1.36307e88 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	1.79872e13	0.722984	0.361492	−	0.932375i	$-0.382268\pi$
$2$	1.79872e13	0.722984	0.361492	+	0.932375i	$0.382268\pi$
$3$	−3.11193e21	−1.82446	−0.912229	−	0.409680i	$-0.865640\pi$
$3$	−3.11193e21	−1.82446	−0.912229	+	0.409680i	$0.865640\pi$
$4$	−2.95431e26	−0.477294
$5$	−4.75717e30	−0.374268	−0.187134	−	0.982334i	$-0.559920\pi$
$5$	−4.75717e30	−0.374268	−0.187134	+	0.982334i	$0.559920\pi$
$6$	−5.59749e34	−1.31905
$7$	3.90338e37	0.965114	0.482557	−	0.875865i	$-0.339708\pi$
$7$	3.90338e37	0.965114	0.482557	+	0.875865i	$0.339708\pi$
$8$	−1.64475e40	−1.06806
$9$	6.77478e42	2.32865
$10$	−8.55680e43	−0.270590
$11$	−2.01197e45	−0.0915476	−0.0457738	−	0.998952i	$-0.514575\pi$
$11$	−2.01197e45	−0.0915476	−0.0457738	+	0.998952i	$0.514575\pi$
$12$	9.19360e47	0.870804
$13$	−1.05046e49	−0.282424	−0.141212	−	0.989979i	$-0.545100\pi$
$13$	−1.05046e49	−0.282424	−0.141212	+	0.989979i	$0.545100\pi$
$14$	7.02109e50	0.697761
$15$	1.48040e52	0.682837
$16$	−1.12982e53	−0.294895
$17$	1.05148e55	1.84852	0.924260	−	0.381763i	$-0.124683\pi$
$17$	1.05148e55	1.84852	0.924260	+	0.381763i	$0.124683\pi$
$18$	1.21859e56	1.68357
$19$	1.08050e57	1.34613	0.673067	−	0.739581i	$-0.264976\pi$
$19$	1.08050e57	1.34613	0.673067	+	0.739581i	$0.264976\pi$
$20$	1.40541e57	0.178636
$21$	−1.21471e59	−1.76081
$22$	−3.61897e58	−0.0661874
$23$	−5.03802e60	−1.27459	−0.637295	−	0.770620i	$-0.719947\pi$
$23$	−5.03802e60	−1.27459	−0.637295	+	0.770620i	$0.719947\pi$
$24$	5.11835e61	1.94863
$25$	−1.38928e62	−0.859923
$26$	−1.88949e62	−0.204188
$27$	−1.20290e64	−2.42406
$28$	−1.15318e64	−0.460643
$29$	1.12164e65	0.940032	0.470016	−	0.882658i	$-0.344248\pi$
$29$	1.12164e65	0.940032	0.470016	+	0.882658i	$0.344248\pi$
$30$	2.66282e65	0.493680
$31$	−3.18722e66	−1.37346	−0.686731	−	0.726912i	$-0.740955\pi$
$31$	−3.18722e66	−1.37346	−0.686731	+	0.726912i	$0.740955\pi$
$32$	8.14829e66	0.854855
$33$	6.26111e66	0.167025
$34$	1.89132e68	1.33645
$35$	−1.85690e68	−0.361211
$36$	−2.00148e69	−1.11145
$37$	−6.99627e69	−1.14786	−0.573931	−	0.818904i	$-0.694582\pi$
$37$	−6.99627e69	−1.14786	−0.573931	+	0.818904i	$0.694582\pi$
$38$	1.94351e70	0.973233
$39$	3.26897e70	0.515271
$40$	7.82435e70	0.399741
$41$	−7.38883e70	−0.125804	−0.0629020	−	0.998020i	$-0.520036\pi$
$41$	−7.38883e70	−0.125804	−0.0629020	+	0.998020i	$0.520036\pi$
$42$	−2.18491e72	−1.27304
$43$	4.97212e72	1.01671	0.508353	−	0.861149i	$-0.330255\pi$
$43$	4.97212e72	1.01671	0.508353	+	0.861149i	$0.330255\pi$
$44$	5.94398e71	0.0436952
$45$	−3.22288e73	−0.871539
$46$	−9.06197e73	−0.921508
$47$	5.91267e73	0.230903	0.115451	−	0.993313i	$-0.463169\pi$
$47$	5.91267e73	0.230903	0.115451	+	0.993313i	$0.463169\pi$
$48$	3.51590e74	0.538025
$49$	−1.12142e74	−0.0685558
$50$	−2.49893e75	−0.621711
$51$	−3.27213e76	−3.37255
$52$	3.10339e75	0.134799
$53$	2.39386e76	0.445475	0.222738	−	0.974878i	$-0.428501\pi$
$53$	2.39386e76	0.445475	0.222738	+	0.974878i	$0.428501\pi$
$54$	−2.16369e77	−1.75256
$55$	9.57127e75	0.0342634
$56$	−6.42009e77	−1.03080
$57$	−3.36243e78	−2.45597
$58$	2.01752e78	0.679628
$59$	−1.72292e78	−0.271239	−0.135619	−	0.990761i	$-0.543302\pi$
$59$	−1.72292e78	−0.271239	−0.135619	+	0.990761i	$0.543302\pi$
$60$	−4.37355e78	−0.325914
$61$	1.90453e79	0.680158	0.340079	−	0.940397i	$-0.389546\pi$
$61$	1.90453e79	0.680158	0.340079	+	0.940397i	$0.389546\pi$
$62$	−5.73291e79	−0.992990
$63$	2.64446e80	2.24741
$64$	2.16497e80	0.912942
$65$	4.99723e79	0.105702
$66$	1.12620e80	0.120756
$67$	7.04228e80	0.386709	0.193355	−	0.981129i	$-0.438063\pi$
$67$	7.04228e80	0.386709	0.193355	+	0.981129i	$0.438063\pi$
$68$	−3.10640e81	−0.882289
$69$	1.56779e82	2.32544
$70$	−3.34005e81	−0.261150
$71$	−1.27373e82	−0.529762	−0.264881	−	0.964281i	$-0.585333\pi$
$71$	−1.27373e82	−0.529762	−0.264881	+	0.964281i	$0.585333\pi$
$72$	−1.11428e83	−2.48714
$73$	−3.75786e82	−0.454018	−0.227009	−	0.973893i	$-0.572895\pi$
$73$	−3.75786e82	−0.454018	−0.227009	+	0.973893i	$0.572895\pi$
$74$	−1.25843e83	−0.829886
$75$	4.32334e83	1.56889
$76$	−3.19212e83	−0.642503
$77$	−7.85349e82	−0.0883538
$78$	5.87995e83	0.372532
$79$	3.21546e83	0.115568	0.0577840	−	0.998329i	$-0.481597\pi$
$79$	3.21546e83	0.115568	0.0577840	+	0.998329i	$0.481597\pi$
$80$	5.37472e83	0.110370
$81$	1.77235e85	2.09395
$82$	−1.32904e84	−0.0909542
$83$	−2.22227e85	−0.886793	−0.443396	−	0.896326i	$-0.646227\pi$
$83$	−2.22227e85	−0.886793	−0.443396	+	0.896326i	$0.646227\pi$
$84$	3.58862e85	0.840425
$85$	−5.00207e85	−0.691843
$86$	8.94344e85	0.735062
$87$	−3.49047e86	−1.71505
$88$	3.30919e85	0.0977783
$89$	−5.54352e86	−0.990672	−0.495336	−	0.868701i	$-0.664955\pi$
$89$	−5.54352e86	−0.990672	−0.495336	+	0.868701i	$0.664955\pi$
$90$	−5.79705e86	−0.630109
$91$	−4.10036e86	−0.272571
$92$	1.48839e87	0.608355
$93$	9.91840e87	2.50582
$94$	1.06352e87	0.166939
$95$	−5.14011e87	−0.503816
$96$	−2.53569e88	−1.55965
$97$	4.88818e88	1.89585	0.947927	−	0.318488i	$-0.103175\pi$
$97$	4.88818e88	1.89585	0.947927	+	0.318488i	$0.103175\pi$
$98$	−2.01713e87	−0.0495647
$99$	−1.36307e88	−0.213182
$100$	4.10437e88	0.410437
$101$	6.30836e88	0.405150	0.202575	−	0.979267i	$-0.435069\pi$
$101$	6.30836e88	0.405150	0.202575	+	0.979267i	$0.435069\pi$
$102$	−5.88565e89	−2.43830
$103$	−3.95925e89	−1.06257	−0.531284	−	0.847194i	$-0.678290\pi$
$103$	−3.95925e89	−1.06257	−0.531284	+	0.847194i	$0.678290\pi$
$104$	1.72775e89	0.301646
$105$	5.77855e89	0.659015
$106$	4.30589e89	0.322071
$107$	5.08196e88	0.0250296	0.0125148	−	0.999922i	$-0.496016\pi$
$107$	5.08196e88	0.0250296	0.0125148	+	0.999922i	$0.496016\pi$
$108$	3.55375e90	1.15699
$109$	−3.00179e90	−0.648487	−0.324244	−	0.945974i	$-0.605110\pi$
$109$	−3.00179e90	−0.648487	−0.324244	+	0.945974i	$0.605110\pi$
$110$	1.72160e89	0.0247719
$111$	2.17719e91	2.09423
$112$	−4.41010e90	−0.284608
$113$	−1.01787e91	−0.442284	−0.221142	−	0.975242i	$-0.570978\pi$
$113$	−1.01787e91	−0.442284	−0.221142	+	0.975242i	$0.570978\pi$
$114$	−6.04807e91	−1.77562
$115$	2.39667e91	0.477039
$116$	−3.31367e91	−0.448672
$117$	−7.11666e91	−0.657666
$118$	−3.09906e91	−0.196101
$119$	4.10433e92	1.78403
$120$	−2.43488e92	−0.729311
$121$	−4.78954e92	−0.991619
$122$	3.42571e92	0.491743
$123$	2.29935e92	0.229524
$124$	9.41603e92	0.655546
$125$	1.42947e93	0.696110
$126$	4.75664e93	1.62484
$127$	−3.42465e93	−0.822908	−0.411454	−	0.911431i	$-0.634979\pi$
$127$	−3.42465e93	−0.822908	−0.411454	+	0.911431i	$0.634979\pi$
$128$	−1.14937e93	−0.194813
$129$	−1.54729e94	−1.85494
$130$	8.98861e92	0.0764211
$131$	−2.21360e94	−1.33821	−0.669107	−	0.743166i	$-0.733323\pi$
$131$	−2.21360e94	−1.33821	−0.669107	+	0.743166i	$0.733323\pi$
$132$	−1.84973e93	−0.0797200
$133$	4.21760e94	1.29917
$134$	1.26671e94	0.279585
$135$	5.72242e94	0.907250
$136$	−1.72942e95	−1.97433
$137$	1.50357e93	0.0123896	0.00619482	−	0.999981i	$-0.498028\pi$
$137$	1.50357e93	0.0123896	0.00619482	+	0.999981i	$0.498028\pi$
$138$	2.82002e95	1.68125
$139$	1.85854e95	0.803550	0.401775	−	0.915738i	$-0.368393\pi$
$139$	1.85854e95	0.803550	0.401775	+	0.915738i	$0.368393\pi$
$140$	5.48587e94	0.172404
$141$	−1.83998e95	−0.421272
$142$	−2.29108e95	−0.383009
$143$	2.11350e94	0.0258552
$144$	−7.65425e95	−0.686708
$145$	−5.33583e95	−0.351824
$146$	−6.75933e95	−0.328248
$147$	3.48979e95	0.125077
$148$	2.06691e96	0.547868
$149$	−6.69346e96	−1.31481	−0.657403	−	0.753539i	$-0.728345\pi$
$149$	−6.69346e96	−1.31481	−0.657403	+	0.753539i	$0.728345\pi$
$150$	7.77648e96	1.13428
$151$	−8.94714e96	−0.970980	−0.485490	−	0.874242i	$-0.661359\pi$
$151$	−8.94714e96	−0.970980	−0.485490	+	0.874242i	$0.661359\pi$
$152$	−1.77715e97	−1.43775
$153$	7.12356e97	4.30455
$154$	−1.41262e96	−0.0638784
$155$	1.51621e97	0.514043
$156$	−9.65754e96	−0.245936
$157$	−7.99466e97	−1.53202	−0.766012	−	0.642826i	$-0.777762\pi$
$157$	−7.99466e97	−1.53202	−0.766012	+	0.642826i	$0.777762\pi$
$158$	5.78371e96	0.0835538
$159$	−7.44954e97	−0.812751
$160$	−3.87628e97	−0.319945
$161$	−1.96653e98	−1.23012
$162$	3.18797e98	1.51389
$163$	8.25331e97	0.298044	0.149022	−	0.988834i	$-0.452388\pi$
$163$	8.25331e97	0.298044	0.149022	+	0.988834i	$0.452388\pi$
$164$	2.18289e97	0.0600455
$165$	−2.97851e97	−0.0625121
$166$	−3.99724e98	−0.641137
$167$	−2.58266e98	−0.317091	−0.158546	−	0.987352i	$-0.550680\pi$
$167$	−2.58266e98	−0.317091	−0.158546	+	0.987352i	$0.550680\pi$
$168$	1.99789e99	1.88065
$169$	−1.27309e99	−0.920237
$170$	−8.99732e98	−0.500191
$171$	7.32014e99	3.13467
$172$	−1.46892e99	−0.485268
$173$	−2.87467e99	−0.733730	−0.366865	−	0.930274i	$-0.619569\pi$
$173$	−2.87467e99	−0.733730	−0.366865	+	0.930274i	$0.619569\pi$
$174$	−6.27837e99	−1.23995
$175$	−5.42290e99	−0.829924
$176$	2.27315e98	0.0269970
$177$	5.36162e99	0.494864
$178$	−9.97123e99	−0.716240
$179$	−7.10087e99	−0.397513	−0.198757	−	0.980049i	$-0.563690\pi$
$179$	−7.10087e99	−0.397513	−0.198757	+	0.980049i	$0.563690\pi$
$180$	9.52138e99	0.415981
$181$	3.14165e100	1.07266	0.536329	−	0.844009i	$-0.319811\pi$
$181$	3.14165e100	1.07266	0.536329	+	0.844009i	$0.319811\pi$
$182$	−7.37540e99	−0.197065
$183$	−5.92676e100	−1.24092
$184$	8.28628e100	1.36134
$185$	3.32824e100	0.429608
$186$	1.78404e101	1.81167
$187$	−2.11555e100	−0.169228
$188$	−1.74679e100	−0.110209
$189$	−4.69540e101	−2.33950
$190$	−9.24561e100	−0.364250
$191$	1.75148e101	0.546285	0.273142	−	0.961974i	$-0.411937\pi$
$191$	1.75148e101	0.546285	0.273142	+	0.961974i	$0.411937\pi$
$192$	−6.73724e101	−1.66562
$193$	3.08614e101	0.605502	0.302751	−	0.953070i	$-0.402095\pi$
$193$	3.08614e101	0.605502	0.302751	+	0.953070i	$0.402095\pi$
$194$	8.79246e101	1.37067
$195$	−1.55510e101	−0.192850
$196$	3.31303e100	0.0327213
$197$	−6.10297e101	−0.480612	−0.240306	−	0.970697i	$-0.577248\pi$
$197$	−6.10297e101	−0.480612	−0.240306	+	0.970697i	$0.577248\pi$
$198$	−2.45177e101	−0.154127
$199$	9.92591e100	0.0498665	0.0249332	−	0.999689i	$-0.492063\pi$
$199$	9.92591e100	0.0498665	0.0249332	+	0.999689i	$0.492063\pi$
$200$	2.28502e102	0.918450
$201$	−2.19151e102	−0.705535
$202$	1.13470e102	0.292917
$203$	4.37819e102	0.907238
$204$	9.66690e102	1.60970
$205$	3.51499e101	0.0470844
$206$	−7.12158e102	−0.768219
$207$	−3.41315e103	−2.96807
$208$	1.18683e102	0.0832856
$209$	−2.17393e102	−0.123235
$210$	1.03940e103	0.476457
$211$	−8.33167e102	−0.309145	−0.154573	−	0.987981i	$-0.549400\pi$
$211$	−8.33167e102	−0.309145	−0.154573	+	0.987981i	$0.549400\pi$
$212$	−7.07222e102	−0.212623
$213$	3.96376e103	0.966529
$214$	9.14103e101	0.0180960
$215$	−2.36532e103	−0.380521
$216$	1.97848e104	2.58904
$217$	−1.24409e104	−1.32555
$218$	−5.39938e103	−0.468846
$219$	1.16942e104	0.828337
$220$	−2.82765e102	−0.0163537
$221$	−1.10454e104	−0.522067
$222$	3.91615e104	1.51409
$223$	−5.60785e104	−1.77513	−0.887564	−	0.460684i	$-0.847604\pi$
$223$	−5.60785e104	−1.77513	−0.887564	+	0.460684i	$0.847604\pi$
$224$	3.18059e104	0.825032
$225$	−9.41208e104	−2.00246
$226$	−1.83086e104	−0.319764
$227$	−4.37425e104	−0.627701	−0.313851	−	0.949472i	$-0.601619\pi$
$227$	−4.37425e104	−0.627701	−0.313851	+	0.949472i	$0.601619\pi$
$228$	9.93367e104	1.17222
$229$	6.98125e104	0.678038	0.339019	−	0.940779i	$-0.389905\pi$
$229$	6.98125e104	0.678038	0.339019	+	0.940779i	$0.389905\pi$
$230$	4.31093e104	0.344891
$231$	2.44395e104	0.161198
$232$	−1.84482e105	−1.00401
$233$	2.70074e105	1.21379	0.606897	−	0.794781i	$-0.292414\pi$
$233$	2.70074e105	1.21379	0.606897	+	0.794781i	$0.292414\pi$
$234$	−1.28009e105	−0.475482
$235$	−2.81276e104	−0.0864196
$236$	5.09005e104	0.129461
$237$	−1.00063e105	−0.210849
$238$	7.38254e105	1.28983
$239$	8.33363e105	1.20817	0.604084	−	0.796920i	$-0.293539\pi$
$239$	8.33363e105	1.20817	0.604084	+	0.796920i	$0.293539\pi$
$240$	−1.67257e105	−0.201366
$241$	−1.56610e106	−1.56697	−0.783487	−	0.621408i	$-0.786561\pi$
$241$	−1.56610e106	−1.56697	−0.783487	+	0.621408i	$0.786561\pi$
$242$	−8.61504e105	−0.716924
$243$	−2.01580e106	−1.39627
$244$	−5.62657e105	−0.324636
$245$	5.33480e104	0.0256583
$246$	4.13589e105	0.165942
$247$	−1.13502e106	−0.380181
$248$	5.24218e106	1.46694
$249$	6.91555e106	1.61792
$250$	2.57121e106	0.503276
$251$	−1.03640e106	−0.169843	−0.0849217	−	0.996388i	$-0.527064\pi$
$251$	−1.03640e106	−0.169843	−0.0849217	+	0.996388i	$0.527064\pi$
$252$	−7.81255e106	−1.07268
$253$	1.01363e106	0.116686
$254$	−6.15999e106	−0.594949
$255$	1.55661e107	1.26224
$256$	−1.54679e107	−1.05379
$257$	2.59608e107	1.48694	0.743471	−	0.668768i	$-0.233178\pi$
$257$	2.59608e107	1.48694	0.743471	+	0.668768i	$0.233178\pi$
$258$	−2.78314e107	−1.34109
$259$	−2.73091e107	−1.10782
$260$	−1.47634e106	−0.0504512
$261$	7.59887e107	2.18900
$262$	−3.98164e107	−0.967508
$263$	−9.18230e107	−1.88331	−0.941653	−	0.336586i	$-0.890728\pi$
$263$	−9.18230e107	−1.88331	−0.941653	+	0.336586i	$0.890728\pi$
$264$	−1.02980e107	−0.178392
$265$	−1.13880e107	−0.166727
$266$	7.58627e107	0.939281
$267$	1.72510e108	1.80744
$268$	−2.08051e107	−0.184574
$269$	−4.34307e107	−0.326453	−0.163227	−	0.986589i	$-0.552190\pi$
$269$	−4.34307e107	−0.326453	−0.163227	+	0.986589i	$0.552190\pi$
$270$	1.02930e108	0.655927
$271$	−2.01852e107	−0.109119	−0.0545595	−	0.998511i	$-0.517375\pi$
$271$	−2.01852e107	−0.109119	−0.0545595	+	0.998511i	$0.517375\pi$
$272$	−1.18798e108	−0.545120
$273$	1.27600e108	0.497295
$274$	2.70450e106	0.00895751
$275$	2.79519e107	0.0787239
$276$	−4.63175e108	−1.10992
$277$	6.30470e108	1.28622	0.643109	−	0.765774i	$-0.277644\pi$
$277$	6.30470e108	1.28622	0.643109	+	0.765774i	$0.277644\pi$
$278$	3.34299e108	0.580954
$279$	−2.15927e109	−3.19831
$280$	3.05414e108	0.385795
$281$	2.21025e108	0.238238	0.119119	−	0.992880i	$-0.461993\pi$
$281$	2.21025e108	0.238238	0.119119	+	0.992880i	$0.461993\pi$
$282$	−3.30961e108	−0.304573
$283$	−5.73795e108	−0.451087	−0.225544	−	0.974233i	$-0.572416\pi$
$283$	−5.73795e108	−0.451087	−0.225544	+	0.974233i	$0.572416\pi$
$284$	3.76299e108	0.252853
$285$	1.59956e109	0.919190
$286$	3.80159e107	0.0186929
$287$	−2.88414e108	−0.121415
$288$	5.52029e109	1.99066
$289$	7.82052e109	2.41703
$290$	−9.59766e108	−0.254363
$291$	−1.52117e110	−3.45891
$292$	1.11019e109	0.216700
$293$	−8.06470e109	−1.35201	−0.676004	−	0.736898i	$-0.736290\pi$
$293$	−8.06470e109	−1.35201	−0.676004	+	0.736898i	$0.736290\pi$
$294$	6.27715e108	0.0904288
$295$	8.19624e108	0.101516
$296$	1.15071e110	1.22599
$297$	2.42021e109	0.221917
$298$	−1.20397e110	−0.950584
$299$	5.29225e109	0.359975
$300$	−1.27725e110	−0.748824
$301$	1.94081e110	0.981236
$302$	−1.60934e110	−0.702002
$303$	−1.96312e110	−0.739178
$304$	−1.22076e110	−0.396969
$305$	−9.06015e109	−0.254562
$306$	1.28133e111	3.11212
$307$	−5.28891e110	−1.11099	−0.555493	−	0.831521i	$-0.687471\pi$
$307$	−5.28891e110	−1.11099	−0.555493	+	0.831521i	$0.687471\pi$
$308$	2.32016e109	0.0421708
$309$	1.23209e111	1.93861
$310$	2.72724e110	0.371645
$311$	−1.09333e111	−1.29097	−0.645484	−	0.763773i	$-0.723344\pi$
$311$	−1.09333e111	−1.29097	−0.645484	+	0.763773i	$0.723344\pi$
$312$	−5.37664e110	−0.550340
$313$	4.11236e110	0.365063	0.182531	−	0.983200i	$-0.441571\pi$
$313$	4.11236e110	0.365063	0.182531	+	0.983200i	$0.441571\pi$
$314$	−1.43802e111	−1.10763
$315$	−1.25801e111	−0.841134
$316$	−9.49947e109	−0.0551600
$317$	1.98612e111	1.00200	0.501000	−	0.865447i	$-0.332966\pi$
$317$	1.98612e111	1.00200	0.501000	+	0.865447i	$0.332966\pi$
$318$	−1.33996e111	−0.587605
$319$	−2.25671e110	−0.0860577
$320$	−1.02991e111	−0.341685
$321$	−1.58147e110	−0.0456654
$322$	−3.53724e111	−0.889360
$323$	1.13612e112	2.48836
$324$	−5.23608e111	−0.999432
$325$	1.45939e111	0.242863
$326$	1.48454e111	0.215481
$327$	9.34137e111	1.18314
$328$	1.21528e111	0.134366
$329$	2.30794e111	0.222847
$330$	−5.35751e110	−0.0451952
$331$	6.49334e110	0.0478765	0.0239383	−	0.999713i	$-0.492379\pi$
$331$	6.49334e110	0.0478765	0.0239383	+	0.999713i	$0.492379\pi$
$332$	6.56528e111	0.423261
$333$	−4.73982e112	−2.67297
$334$	−4.64548e111	−0.229252
$335$	−3.35013e111	−0.144733
$336$	1.37239e112	0.519255
$337$	−1.31744e112	−0.436718	−0.218359	−	0.975869i	$-0.570070\pi$
$337$	−1.31744e112	−0.436718	−0.218359	+	0.975869i	$0.570070\pi$
$338$	−2.28992e112	−0.665316
$339$	3.16754e112	0.806929
$340$	1.47777e112	0.330213
$341$	6.41259e111	0.125737
$342$	1.31669e113	2.26632
$343$	−6.82282e112	−1.03128
$344$	−8.17789e112	−1.08590
$345$	−7.45826e112	−0.870338
$346$	−5.17072e112	−0.530475
$347$	1.51622e113	1.36805	0.684023	−	0.729461i	$-0.260229\pi$
$347$	1.51622e113	1.36805	0.684023	+	0.729461i	$0.260229\pi$
$348$	1.03119e113	0.818584
$349$	1.52478e113	1.06531	0.532653	−	0.846334i	$-0.321195\pi$
$349$	1.52478e113	1.06531	0.532653	+	0.846334i	$0.321195\pi$
$350$	−9.75427e112	−0.600021
$351$	1.26361e113	0.684614
$352$	−1.63941e112	−0.0782600
$353$	−2.78663e113	−1.17248	−0.586239	−	0.810138i	$-0.699392\pi$
$353$	−2.78663e113	−1.17248	−0.586239	+	0.810138i	$0.699392\pi$
$354$	9.64405e112	0.357778
$355$	6.05934e112	0.198273
$356$	1.63773e113	0.472842
$357$	−1.27724e114	−3.25489
$358$	−1.27725e113	−0.287396
$359$	−5.91157e113	−1.17490	−0.587448	−	0.809262i	$-0.699867\pi$
$359$	−5.91157e113	−1.17490	−0.587448	+	0.809262i	$0.699867\pi$
$360$	5.30083e113	0.930856
$361$	5.23201e113	0.812078
$362$	5.65094e113	0.775514
$363$	1.49047e114	1.80917
$364$	1.21137e113	0.130097
$365$	1.78768e113	0.169925
$366$	−1.06606e114	−0.897165
$367$	−2.85230e113	−0.212596	−0.106298	−	0.994334i	$-0.533900\pi$
$367$	−2.85230e113	−0.212596	−0.106298	+	0.994334i	$0.533900\pi$
$368$	5.69203e113	0.375871
$369$	−5.00577e113	−0.292953
$370$	5.98657e113	0.310600
$371$	9.34417e113	0.429934
$372$	−2.93020e114	−1.19602
$373$	4.52146e114	1.63770	0.818852	−	0.574005i	$-0.194611\pi$
$373$	4.52146e114	1.63770	0.818852	+	0.574005i	$0.194611\pi$
$374$	−3.80528e113	−0.122349
$375$	−4.44840e114	−1.27002
$376$	−9.72487e113	−0.246618
$377$	−1.17824e114	−0.265488
$378$	−8.44570e114	−1.69142
$379$	9.92623e113	0.176742	0.0883709	−	0.996088i	$-0.471834\pi$
$379$	9.92623e113	0.176742	0.0883709	+	0.996088i	$0.471834\pi$
$380$	1.51855e114	0.240468
$381$	1.06573e115	1.50136
$382$	3.15041e114	0.394955
$383$	−1.05705e115	−1.17964	−0.589821	−	0.807534i	$-0.700802\pi$
$383$	−1.05705e115	−1.17964	−0.589821	+	0.807534i	$0.700802\pi$
$384$	3.57677e114	0.355428
$385$	3.73604e113	0.0330680
$386$	5.55110e114	0.437768
$387$	3.36850e115	2.36755
$388$	−1.44412e115	−0.904881
$389$	−2.17710e114	−0.121653	−0.0608263	−	0.998148i	$-0.519374\pi$
$389$	−2.17710e114	−0.121653	−0.0608263	+	0.998148i	$0.519374\pi$
$390$	−2.79719e114	−0.139427
$391$	−5.29738e115	−2.35611
$392$	1.84446e114	0.0732217
$393$	6.88856e115	2.44152
$394$	−1.09775e115	−0.347475
$395$	−1.52965e114	−0.0432535
$396$	4.02692e114	0.101751
$397$	4.00607e113	0.00904776	0.00452388	−	0.999990i	$-0.498560\pi$
$397$	4.00607e113	0.00904776	0.00452388	+	0.999990i	$0.498560\pi$
$398$	1.78539e114	0.0360526
$399$	−1.31249e116	−2.37029
$400$	1.56963e115	0.253587
$401$	6.23287e114	0.0901080	0.0450540	−	0.998985i	$-0.485654\pi$
$401$	6.23287e114	0.0901080	0.0450540	+	0.998985i	$0.485654\pi$
$402$	−3.94191e115	−0.510091
$403$	3.34806e115	0.387899
$404$	−1.86368e115	−0.193376
$405$	−8.43138e115	−0.783700
$406$	7.87514e115	0.655918
$407$	1.40763e115	0.105084
$408$	5.38184e116	3.60208
$409$	−6.55225e115	−0.393281	−0.196641	−	0.980476i	$-0.563003\pi$
$409$	−6.55225e115	−0.393281	−0.196641	+	0.980476i	$0.563003\pi$
$410$	6.32248e114	0.0340413
$411$	−4.67901e114	−0.0226044
$412$	1.16969e116	0.507158
$413$	−6.72523e115	−0.261776
$414$	−6.13929e116	−2.14587
$415$	1.05717e116	0.331898
$416$	−8.55948e115	−0.241432
$417$	−5.78364e116	−1.46604
$418$	−3.91029e115	−0.0890972
$419$	3.38221e116	0.692909	0.346454	−	0.938067i	$-0.387386\pi$
$419$	3.38221e116	0.692909	0.346454	+	0.938067i	$0.387386\pi$
$420$	−1.70716e116	−0.314544
$421$	7.60301e116	1.26018	0.630090	−	0.776522i	$-0.283018\pi$
$421$	7.60301e116	1.26018	0.630090	+	0.776522i	$0.283018\pi$
$422$	−1.49863e116	−0.223507
$423$	4.00571e116	0.537691
$424$	−3.93731e116	−0.475794
$425$	−1.46080e117	−1.58959
$426$	7.12969e116	0.698785
$427$	7.43410e116	0.656430
$428$	−1.50137e115	−0.0119465
$429$	−6.57706e115	−0.0471718
$430$	−4.25454e116	−0.275110
$431$	1.02975e117	0.600470	0.300235	−	0.953865i	$-0.402935\pi$
$431$	1.02975e117	0.600470	0.300235	+	0.953865i	$0.402935\pi$
$432$	1.35906e117	0.714845
$433$	2.72587e117	1.29358	0.646791	−	0.762668i	$-0.276111\pi$
$433$	2.72587e117	1.29358	0.646791	+	0.762668i	$0.276111\pi$
$434$	−2.23777e117	−0.958348
$435$	1.66047e117	0.641889
$436$	8.86823e116	0.309519
$437$	−5.44356e117	−1.71577
$438$	2.10346e117	0.598874
$439$	−5.39464e117	−1.38769	−0.693843	−	0.720126i	$-0.744084\pi$
$439$	−5.39464e117	−1.38769	−0.693843	+	0.720126i	$0.744084\pi$
$440$	−1.57424e116	−0.0365953
$441$	−7.59740e116	−0.159642
$442$	−1.98676e117	−0.377446
$443$	5.69469e117	0.978372	0.489186	−	0.872179i	$-0.337294\pi$
$443$	5.69469e117	0.978372	0.489186	+	0.872179i	$0.337294\pi$
$444$	−6.43209e117	−0.999563
$445$	2.63714e117	0.370777
$446$	−1.00869e118	−1.28339
$447$	2.08296e118	2.39881
$448$	8.45071e117	0.881093
$449$	−1.50535e118	−1.42126	−0.710631	−	0.703565i	$-0.751590\pi$
$449$	−1.50535e118	−1.42126	−0.710631	+	0.703565i	$0.751590\pi$
$450$	−1.69297e118	−1.44774
$451$	1.48661e116	0.0115170
$452$	3.00710e117	0.211100
$453$	2.78429e118	1.77151
$454$	−7.86805e117	−0.453818
$455$	1.95061e117	0.102015
$456$	5.53036e118	2.62312
$457$	2.94233e118	1.26596	0.632980	−	0.774168i	$-0.281831\pi$
$457$	2.94233e118	1.26596	0.632980	+	0.774168i	$0.281831\pi$
$458$	1.25573e118	0.490211
$459$	−1.26483e119	−4.48093
$460$	−7.08050e117	−0.227688
$461$	1.09403e117	0.0319402	0.0159701	−	0.999872i	$-0.494916\pi$
$461$	1.09403e117	0.0319402	0.0159701	+	0.999872i	$0.494916\pi$
$462$	4.39598e117	0.116543
$463$	−1.51518e118	−0.364847	−0.182423	−	0.983220i	$-0.558394\pi$
$463$	−1.51518e118	−0.364847	−0.182423	+	0.983220i	$0.558394\pi$
$464$	−1.26725e118	−0.277211
$465$	−4.71835e118	−0.937850
$466$	4.85788e118	0.877553
$467$	−8.24498e118	−1.35391	−0.676953	−	0.736026i	$-0.736700\pi$
$467$	−8.24498e118	−1.35391	−0.676953	+	0.736026i	$0.736700\pi$
$468$	2.10248e118	0.313900
$469$	2.74887e118	0.373219
$470$	−5.05936e117	−0.0624799
$471$	2.48788e119	2.79511
$472$	2.83378e118	0.289699
$473$	−1.00038e118	−0.0930770
$474$	−1.79985e118	−0.152440
$475$	−1.50111e119	−1.15757
$476$	−1.21255e119	−0.851509
$477$	1.62179e119	1.03735
$478$	1.49899e119	0.873487
$479$	−3.05065e119	−1.61980	−0.809900	−	0.586567i	$-0.800479\pi$
$479$	−3.05065e119	−1.61980	−0.809900	+	0.586567i	$0.800479\pi$
$480$	1.20627e119	0.583727
$481$	7.34932e118	0.324184
$482$	−2.81698e119	−1.13290
$483$	6.11970e119	2.24431
$484$	1.41498e119	0.473294
$485$	−2.32539e119	−0.709558
$486$	−3.62586e119	−1.00948
$487$	−1.88865e118	−0.0479857	−0.0239929	−	0.999712i	$-0.507638\pi$
$487$	−1.88865e118	−0.0479857	−0.0239929	+	0.999712i	$0.507638\pi$
$488$	−3.13247e119	−0.726449
$489$	−2.56837e119	−0.543768
$490$	9.59580e117	0.0185505
$491$	−7.35262e119	−1.29812	−0.649061	−	0.760736i	$-0.724838\pi$
$491$	−7.35262e119	−1.29812	−0.649061	+	0.760736i	$0.724838\pi$
$492$	−6.79300e118	−0.109551
$493$	1.17938e120	1.73767
$494$	−2.04159e119	−0.274865
$495$	6.48433e118	0.0797873
$496$	3.60097e119	0.405028
$497$	−4.97186e119	−0.511281
$498$	1.24391e120	1.16973
$499$	1.88248e120	1.61903	0.809515	−	0.587099i	$-0.199730\pi$
$499$	1.88248e120	1.61903	0.809515	+	0.587099i	$0.199730\pi$
$500$	−4.22308e119	−0.332250
$501$	8.03706e119	0.578520
$502$	−1.86420e119	−0.122794
$503$	−2.65462e119	−0.160039	−0.0800197	−	0.996793i	$-0.525498\pi$
$503$	−2.65462e119	−0.160039	−0.0800197	+	0.996793i	$0.525498\pi$
$504$	−4.34947e120	−2.40037
$505$	−3.00099e119	−0.151635
$506$	1.82324e119	0.0843619
$507$	3.96176e120	1.67893
$508$	1.01175e120	0.392769
$509$	−3.57212e120	−1.27053	−0.635265	−	0.772294i	$-0.719109\pi$
$509$	−3.57212e120	−1.27053	−0.635265	+	0.772294i	$0.719109\pi$
$510$	2.79990e120	0.912578
$511$	−1.46684e120	−0.438179
$512$	−2.07082e120	−0.567059
$513$	−1.29974e121	−3.26311
$514$	4.66962e120	1.07503
$515$	1.88348e120	0.397685
$516$	4.57117e120	0.885351
$517$	−1.18961e119	−0.0211386
$518$	−4.91214e120	−0.800934
$519$	8.94577e120	1.33866
$520$	−8.21919e119	−0.112896
$521$	9.79424e119	0.123507	0.0617535	−	0.998091i	$-0.480331\pi$
$521$	9.79424e119	0.123507	0.0617535	+	0.998091i	$0.480331\pi$
$522$	1.36682e121	1.58261
$523$	1.44190e120	0.153324	0.0766618	−	0.997057i	$-0.475574\pi$
$523$	1.44190e120	0.153324	0.0766618	+	0.997057i	$0.475574\pi$
$524$	6.53965e120	0.638722
$525$	1.68757e121	1.51416
$526$	−1.65164e121	−1.36160
$527$	−3.35130e121	−2.53887
$528$	−7.07390e119	−0.0492549
$529$	9.75813e120	0.624582
$530$	−2.04838e120	−0.120541
$531$	−1.16724e121	−0.631620
$532$	−1.24601e121	−0.620088
$533$	7.76170e119	0.0355301
$534$	3.10298e121	1.30675
$535$	−2.41757e119	−0.00936778
$536$	−1.15828e121	−0.413029
$537$	2.20974e121	0.725247
$538$	−7.81197e120	−0.236020
$539$	2.25627e119	0.00627612
$540$	−1.69058e121	−0.433025
$541$	−3.32756e121	−0.784960	−0.392480	−	0.919761i	$-0.628383\pi$
$541$	−3.32756e121	−0.784960	−0.392480	+	0.919761i	$0.628383\pi$
$542$	−3.63076e120	−0.0788913
$543$	−9.77659e121	−1.95702
$544$	8.56777e121	1.58022
$545$	1.42800e121	0.242708
$546$	2.29517e121	0.359536
$547$	8.03429e121	1.16014	0.580072	−	0.814565i	$-0.303025\pi$
$547$	8.03429e121	1.16014	0.580072	+	0.814565i	$0.303025\pi$
$548$	−4.44201e119	−0.00591351
$549$	1.29028e122	1.58385
$550$	5.02776e120	0.0569161
$551$	1.21193e122	1.26541
$552$	−2.57863e122	−2.48371
$553$	1.25512e121	0.111536
$554$	1.13404e122	0.929915
$555$	−1.03573e122	−0.783803
$556$	−5.49070e121	−0.383530
$557$	4.95449e121	0.319479	0.159740	−	0.987159i	$-0.448935\pi$
$557$	4.95449e121	0.319479	0.159740	+	0.987159i	$0.448935\pi$
$558$	−3.88392e122	−2.31232
$559$	−5.22303e121	−0.287142
$560$	2.09796e121	0.106520
$561$	6.58344e121	0.308749
$562$	3.97562e121	0.172242
$563$	−1.54057e122	−0.616679	−0.308340	−	0.951276i	$-0.599773\pi$
$563$	−1.54057e122	−0.616679	−0.308340	+	0.951276i	$0.599773\pi$
$564$	5.43588e121	0.201071
$565$	4.84217e121	0.165533
$566$	−1.03210e122	−0.326129
$567$	6.91817e122	2.02090
$568$	2.09497e122	0.565818
$569$	−5.08576e121	−0.127017	−0.0635083	−	0.997981i	$-0.520229\pi$
$569$	−5.08576e121	−0.127017	−0.0635083	+	0.997981i	$0.520229\pi$
$570$	2.87717e122	0.664560
$571$	−6.07440e122	−1.29777	−0.648883	−	0.760888i	$-0.724764\pi$
$571$	−6.07440e122	−1.29777	−0.648883	+	0.760888i	$0.724764\pi$
$572$	−6.24394e120	−0.0123406
$573$	−5.45047e122	−0.996674
$574$	−5.18777e121	−0.0877811
$575$	6.99922e122	1.09605
$576$	1.46672e123	2.12592
$577$	−9.97444e122	−1.33834	−0.669168	−	0.743111i	$-0.733349\pi$
$577$	−9.97444e122	−1.33834	−0.669168	+	0.743111i	$0.733349\pi$
$578$	1.40669e123	1.74747
$579$	−9.60385e122	−1.10471
$580$	1.57637e122	0.167924
$581$	−8.67438e122	−0.855856
$582$	−2.73615e123	−2.50073
$583$	−4.81638e121	−0.0407822
$584$	6.18074e122	0.484919
$585$	3.38551e122	0.246144
$586$	−1.45061e123	−0.977479
$587$	3.03625e123	1.89645	0.948226	−	0.317595i	$-0.102875\pi$
$587$	3.03625e123	1.89645	0.948226	+	0.317595i	$0.102875\pi$
$588$	−1.03099e122	−0.0596986
$589$	−3.44378e123	−1.84886
$590$	1.47427e122	0.0733945
$591$	1.89920e123	0.876856
$592$	7.90449e122	0.338499
$593$	3.31837e123	1.31823	0.659114	−	0.752043i	$-0.270931\pi$
$593$	3.31837e123	1.31823	0.659114	+	0.752043i	$0.270931\pi$
$594$	4.35328e122	0.160442
$595$	−1.95250e123	−0.667707
$596$	1.97746e123	0.627550
$597$	−3.08887e122	−0.0909793
$598$	9.51927e122	0.260256
$599$	−4.88132e123	−1.23892	−0.619460	−	0.785028i	$-0.712648\pi$
$599$	−4.88132e123	−1.23892	−0.619460	+	0.785028i	$0.712648\pi$
$600$	−7.11082e123	−1.67567
$601$	6.45254e123	1.41194	0.705970	−	0.708241i	$-0.250511\pi$
$601$	6.45254e123	1.41194	0.705970	+	0.708241i	$0.250511\pi$
$602$	3.49097e123	0.709418
$603$	4.77100e123	0.900510
$604$	2.64326e123	0.463443
$605$	2.27846e123	0.371132
$606$	−3.53110e123	−0.534414
$607$	−3.71680e123	−0.522724	−0.261362	−	0.965241i	$-0.584172\pi$
$607$	−3.71680e123	−0.522724	−0.261362	+	0.965241i	$0.584172\pi$
$608$	8.80421e123	1.15075
$609$	−1.36246e124	−1.65522
$610$	−1.62967e123	−0.184044
$611$	−6.21104e122	−0.0652125
$612$	−2.10452e124	−2.05454
$613$	−2.51871e123	−0.228658	−0.114329	−	0.993443i	$-0.536472\pi$
$613$	−2.51871e123	−0.228658	−0.114329	+	0.993443i	$0.536472\pi$
$614$	−9.51327e123	−0.803225
$615$	−1.09384e123	−0.0859036
$616$	1.29170e123	0.0943672
$617$	1.46315e124	0.994484	0.497242	−	0.867612i	$-0.334346\pi$
$617$	1.46315e124	0.994484	0.497242	+	0.867612i	$0.334346\pi$
$618$	2.21619e124	1.40158
$619$	7.24631e123	0.426465	0.213232	−	0.977002i	$-0.431601\pi$
$619$	7.24631e123	0.426465	0.213232	+	0.977002i	$0.431601\pi$
$620$	−4.47936e123	−0.245350
$621$	6.06025e124	3.08969
$622$	−1.96660e124	−0.933350
$623$	−2.16385e124	−0.956111
$624$	−3.69333e123	−0.151951
$625$	1.56448e124	0.599391
$626$	7.39697e123	0.263935
$627$	6.76511e123	0.224838
$628$	2.36187e124	0.731227
$629$	−7.35644e124	−2.12185
$630$	−2.26281e124	−0.608126
$631$	−4.53146e124	−1.13483	−0.567416	−	0.823431i	$-0.692057\pi$
$631$	−4.53146e124	−1.13483	−0.567416	+	0.823431i	$0.692057\pi$
$632$	−5.28863e123	−0.123434
$633$	2.59276e124	0.564023
$634$	3.57247e124	0.724430
$635$	1.62916e124	0.307988
$636$	2.20082e124	0.387921
$637$	1.17801e123	0.0193618
$638$	−4.05918e123	−0.0622183
$639$	−8.62925e124	−1.23363
$640$	5.46777e123	0.0729124
$641$	−7.56055e124	−0.940526	−0.470263	−	0.882526i	$-0.655841\pi$
$641$	−7.56055e124	−0.940526	−0.470263	+	0.882526i	$0.655841\pi$
$642$	−2.84462e123	−0.0330154
$643$	−4.06237e124	−0.439937	−0.219969	−	0.975507i	$-0.570596\pi$
$643$	−4.06237e124	−0.439937	−0.219969	+	0.975507i	$0.570596\pi$
$644$	5.80974e124	0.587132
$645$	7.36071e124	0.694244
$646$	2.04356e125	1.79904
$647$	7.70585e124	0.633257	0.316629	−	0.948550i	$-0.397449\pi$
$647$	7.70585e124	0.633257	0.316629	+	0.948550i	$0.397449\pi$
$648$	−2.91508e125	−2.23647
$649$	3.46647e123	0.0248313
$650$	2.62503e124	0.175586
$651$	3.87153e125	2.41840
$652$	−2.43828e124	−0.142255
$653$	−2.83307e125	−1.54391	−0.771954	−	0.635678i	$-0.780721\pi$
$653$	−2.83307e125	−1.54391	−0.771954	+	0.635678i	$0.780721\pi$
$654$	1.68025e125	0.855390
$655$	1.05304e125	0.500851
$656$	8.34801e123	0.0370990
$657$	−2.54587e125	−1.05725
$658$	4.15134e124	0.161115
$659$	−3.52918e125	−1.28018	−0.640092	−	0.768298i	$-0.721104\pi$
$659$	−3.52918e125	−1.28018	−0.640092	+	0.768298i	$0.721104\pi$
$660$	8.79945e123	0.0298367
$661$	−1.91190e125	−0.606037	−0.303019	−	0.952985i	$-0.597994\pi$
$661$	−1.91190e125	−0.606037	−0.303019	+	0.952985i	$0.597994\pi$
$662$	1.16797e124	0.0346139
$663$	3.43726e125	0.952489
$664$	3.65508e125	0.947148
$665$	−2.00638e125	−0.486239
$666$	−8.52561e125	−1.93251
$667$	−5.65084e125	−1.19816
$668$	7.62998e124	0.151346
$669$	1.74512e126	3.23865
$670$	−6.02594e124	−0.104640
$671$	−3.83185e124	−0.0622668
$672$	−9.89778e125	−1.50524
$673$	−6.51200e125	−0.926924	−0.463462	−	0.886117i	$-0.653393\pi$
$673$	−6.51200e125	−0.926924	−0.463462	+	0.886117i	$0.653393\pi$
$674$	−2.36971e125	−0.315740
$675$	1.67117e126	2.08451
$676$	3.76109e125	0.439224
$677$	−7.27595e125	−0.795599	−0.397799	−	0.917472i	$-0.630226\pi$
$677$	−7.27595e125	−0.795599	−0.397799	+	0.917472i	$0.630226\pi$
$678$	5.69751e125	0.583396
$679$	1.90804e126	1.82971
$680$	8.22715e125	0.738930
$681$	1.36124e126	1.14521
$682$	1.15344e125	0.0909059
$683$	−2.25576e126	−1.66560	−0.832802	−	0.553571i	$-0.813265\pi$
$683$	−2.25576e126	−1.66560	−0.832802	+	0.553571i	$0.813265\pi$
$684$	−2.16260e126	−1.49616
$685$	−7.15274e123	−0.00463705
$686$	−1.22723e126	−0.745597
$687$	−2.17252e126	−1.23705
$688$	−5.61757e125	−0.299822
$689$	−2.51467e125	−0.125813
$690$	−1.34153e126	−0.629240
$691$	9.57630e125	0.421138	0.210569	−	0.977579i	$-0.432468\pi$
$691$	9.57630e125	0.421138	0.210569	+	0.977579i	$0.432468\pi$
$692$	8.49267e125	0.350205
$693$	−5.32057e125	−0.205745
$694$	2.72725e126	0.989075
$695$	−8.84137e125	−0.300743
$696$	5.74095e126	1.83178
$697$	−7.76921e125	−0.232551
$698$	2.74264e126	0.770199
$699$	−8.40452e126	−2.21452
$700$	1.60209e126	0.396118
$701$	7.40940e126	1.71922	0.859610	−	0.510951i	$-0.170707\pi$
$701$	7.40940e126	1.71922	0.859610	+	0.510951i	$0.170707\pi$
$702$	2.27287e126	0.494964
$703$	−7.55945e126	−1.54518
$704$	−4.35586e125	−0.0835777
$705$	8.75310e125	0.157669
$706$	−5.01237e126	−0.847683
$707$	2.46239e126	0.391015
$708$	−1.58399e126	−0.236196
$709$	5.85411e126	0.819792	0.409896	−	0.912132i	$-0.365565\pi$
$709$	5.85411e126	0.819792	0.409896	+	0.912132i	$0.365565\pi$
$710$	1.08991e126	0.143348
$711$	2.17841e126	0.269117
$712$	9.11770e126	1.05810
$713$	1.60573e127	1.75060
$714$	−2.29739e127	−2.35323
$715$	−1.00543e125	−0.00967680
$716$	2.09782e126	0.189731
$717$	−2.59337e127	−2.20425
$718$	−1.06332e127	−0.849431
$719$	−8.16889e126	−0.613377	−0.306689	−	0.951810i	$-0.599221\pi$
$719$	−8.16889e126	−0.613377	−0.306689	+	0.951810i	$0.599221\pi$
$720$	3.64126e126	0.257013
$721$	−1.54545e127	−1.02550
$722$	9.41091e126	0.587119
$723$	4.87360e127	2.85888
$724$	−9.28141e126	−0.511974
$725$	−1.55827e127	−0.808356
$726$	2.68094e127	1.30800
$727$	−3.60710e127	−1.65530	−0.827651	−	0.561243i	$-0.810323\pi$
$727$	−3.60710e127	−1.65530	−0.827651	+	0.561243i	$0.810323\pi$
$728$	6.74407e126	0.291122
$729$	1.11669e127	0.453478
$730$	3.21553e126	0.122853
$731$	5.22809e127	1.87940
$732$	1.75095e127	0.592284
$733$	−1.35200e127	−0.430377	−0.215188	−	0.976573i	$-0.569037\pi$
$733$	−1.35200e127	−0.430377	−0.215188	+	0.976573i	$0.569037\pi$
$734$	−5.13048e126	−0.153703
$735$	−1.66015e126	−0.0468124
$736$	−4.10512e127	−1.08959
$737$	−1.41689e126	−0.0354023
$738$	−9.00398e126	−0.211800
$739$	2.74269e127	0.607434	0.303717	−	0.952762i	$-0.401772\pi$
$739$	2.74269e127	0.607434	0.303717	+	0.952762i	$0.401772\pi$
$740$	−9.83265e126	−0.205050
$741$	3.53211e127	0.693624
$742$	1.68075e127	0.310835
$743$	−3.00345e126	−0.0523139	−0.0261570	−	0.999658i	$-0.508327\pi$
$743$	−3.00345e126	−0.0523139	−0.0261570	+	0.999658i	$0.508327\pi$
$744$	−1.63133e128	−2.67637
$745$	3.18419e127	0.492091
$746$	8.13283e127	1.18403
$747$	−1.50554e128	−2.06503
$748$	6.24998e126	0.0807714
$749$	1.98369e126	0.0241564
$750$	−8.00141e127	−0.918207
$751$	7.58766e127	0.820599	0.410299	−	0.911951i	$-0.365424\pi$
$751$	7.58766e127	0.820599	0.410299	+	0.911951i	$0.365424\pi$
$752$	−6.68022e126	−0.0680922
$753$	3.22522e127	0.309872
$754$	−2.11933e127	−0.191943
$755$	4.25630e127	0.363407
$756$	1.38717e128	1.11663
$757$	1.94772e128	1.47829	0.739145	−	0.673546i	$-0.235230\pi$
$757$	1.94772e128	1.47829	0.739145	+	0.673546i	$0.235230\pi$
$758$	1.78545e127	0.127782
$759$	−3.15436e127	−0.212888
$760$	8.45419e127	0.538105
$761$	−9.33020e127	−0.560111	−0.280055	−	0.959984i	$-0.590353\pi$
$761$	−9.33020e127	−0.560111	−0.280055	+	0.959984i	$0.590353\pi$
$762$	1.91695e128	1.08546
$763$	−1.17171e128	−0.625864
$764$	−5.17440e127	−0.260739
$765$	−3.38879e128	−1.61106
$766$	−1.90134e128	−0.852861
$767$	1.80987e127	0.0766043
$768$	4.81351e128	1.92259
$769$	1.54824e127	0.0583602	0.0291801	−	0.999574i	$-0.490710\pi$
$769$	1.54824e127	0.0583602	0.0291801	+	0.999574i	$0.490710\pi$
$770$	6.72008e126	0.0239077
$771$	−8.07882e128	−2.71286
$772$	−9.11742e127	−0.289003
$773$	−5.49356e127	−0.164387	−0.0821933	−	0.996616i	$-0.526192\pi$
$773$	−5.49356e127	−0.164387	−0.0821933	+	0.996616i	$0.526192\pi$
$774$	6.05899e128	1.71170
$775$	4.42794e128	1.18107
$776$	−8.03983e128	−2.02489
$777$	8.49840e128	2.02117
$778$	−3.91599e127	−0.0879528
$779$	−7.98361e127	−0.169349
$780$	4.59425e127	0.0920460
$781$	2.56271e127	0.0484985
$782$	−9.52849e128	−1.70343
$783$	−1.34923e129	−2.27870
$784$	1.26700e127	0.0202168
$785$	3.80319e128	0.573388
$786$	1.23906e129	1.76518
$787$	−3.53123e128	−0.475391	−0.237695	−	0.971340i	$-0.576392\pi$
$787$	−3.53123e128	−0.475391	−0.237695	+	0.971340i	$0.576392\pi$
$788$	1.80301e128	0.229393
$789$	2.85747e129	3.43601
$790$	−2.75141e127	−0.0312716
$791$	−3.97313e128	−0.426854
$792$	2.24190e128	0.227691
$793$	−2.00064e128	−0.192093
$794$	7.20579e126	0.00654138
$795$	3.54387e128	0.304187
$796$	−2.93242e127	−0.0238010
$797$	−7.97738e127	−0.0612301	−0.0306151	−	0.999531i	$-0.509747\pi$
$797$	−7.97738e127	−0.0612301	−0.0306151	+	0.999531i	$0.509747\pi$
$798$	−2.36079e129	−1.71368
$799$	6.21706e128	0.426828
$800$	−1.13203e129	−0.735110
$801$	−3.75561e129	−2.30693
$802$	1.12112e128	0.0651466
$803$	7.56070e127	0.0415643
$804$	6.47440e128	0.336748
$805$	9.35511e128	0.460397
$806$	6.02221e128	0.280444
$807$	1.35153e129	0.595600
$808$	−1.03757e129	−0.432724
$809$	1.78703e129	0.705379	0.352690	−	0.935740i	$-0.385267\pi$
$809$	1.78703e129	0.705379	0.352690	+	0.935740i	$0.385267\pi$
$810$	−1.51657e129	−0.566603
$811$	1.09543e129	0.387396	0.193698	−	0.981061i	$-0.437952\pi$
$811$	1.09543e129	0.387396	0.193698	+	0.981061i	$0.437952\pi$
$812$	−1.29345e129	−0.433020
$813$	6.28151e128	0.199083
$814$	2.53193e128	0.0759740
$815$	−3.92624e128	−0.111548
$816$	3.69691e129	0.994549
$817$	5.37236e129	1.36862
$818$	−1.17857e129	−0.284336
$819$	−2.77791e129	−0.634723
$820$	−1.03844e128	−0.0224731
$821$	−3.64821e129	−0.747840	−0.373920	−	0.927461i	$-0.621987\pi$
$821$	−3.64821e129	−0.747840	−0.373920	+	0.927461i	$0.621987\pi$
$822$	−8.41622e127	−0.0163426
$823$	3.97364e129	0.730964	0.365482	−	0.930818i	$-0.380904\pi$
$823$	3.97364e129	0.730964	0.365482	+	0.930818i	$0.380904\pi$
$824$	6.51198e129	1.13489
$825$	−8.69844e128	−0.143628
$826$	−1.20968e129	−0.189260
$827$	−5.47831e129	−0.812178	−0.406089	−	0.913834i	$-0.633108\pi$
$827$	−5.47831e129	−0.812178	−0.406089	+	0.913834i	$0.633108\pi$
$828$	1.00835e130	1.41664
$829$	−1.19299e130	−1.58840	−0.794199	−	0.607658i	$-0.792109\pi$
$829$	−1.19299e130	−1.58840	−0.794199	+	0.607658i	$0.792109\pi$
$830$	1.90155e129	0.239957
$831$	−1.96198e130	−2.34665
$832$	−2.27422e129	−0.257837
$833$	−1.17916e129	−0.126727
$834$	−1.04031e130	−1.05993
$835$	1.22861e129	0.118677
$836$	6.42246e128	0.0588196
$837$	3.83392e130	3.32936
$838$	6.08364e129	0.500962
$839$	−9.99439e129	−0.780457	−0.390228	−	0.920718i	$-0.627604\pi$
$839$	−9.99439e129	−0.780457	−0.390228	+	0.920718i	$0.627604\pi$
$840$	−9.50428e129	−0.703868
$841$	−1.65633e129	−0.116339
$842$	1.36757e130	0.911089
$843$	−6.87814e129	−0.434655
$844$	2.46143e129	0.147553
$845$	6.05628e129	0.344415
$846$	7.20514e129	0.388742
$847$	−1.86954e130	−0.957025
$848$	−2.70462e129	−0.131369
$849$	1.78561e130	0.822990
$850$	−2.62757e130	−1.14924
$851$	3.52473e130	1.46305
$852$	−1.17102e130	−0.461319
$853$	1.76906e130	0.661470	0.330735	−	0.943724i	$-0.392703\pi$
$853$	1.76906e130	0.661470	0.330735	+	0.943724i	$0.392703\pi$
$854$	1.33719e130	0.474588
$855$	−3.48231e130	−1.17321
$856$	−8.35856e128	−0.0267331
$857$	4.47933e130	1.36009	0.680044	−	0.733171i	$-0.261961\pi$
$857$	4.47933e130	1.36009	0.680044	+	0.733171i	$0.261961\pi$
$858$	−1.18303e129	−0.0341045
$859$	−4.95328e130	−1.35580	−0.677902	−	0.735152i	$-0.737111\pi$
$859$	−4.95328e130	−1.35580	−0.677902	+	0.735152i	$0.737111\pi$
$860$	6.98789e129	0.181620
$861$	8.97525e129	0.221517
$862$	1.85222e130	0.434130
$863$	2.69455e129	0.0599798	0.0299899	−	0.999550i	$-0.490452\pi$
$863$	2.69455e129	0.0599798	0.0299899	+	0.999550i	$0.490452\pi$
$864$	−9.80162e130	−2.07222
$865$	1.36753e130	0.274612
$866$	4.90307e130	0.935238
$867$	−2.43369e131	−4.40977
$868$	3.67544e130	0.632676
$869$	−6.46941e128	−0.0105800
$870$	2.98672e130	0.464075
$871$	−7.39766e129	−0.109216
$872$	4.93720e130	0.692623
$873$	3.31164e131	4.41478
$874$	−9.79144e130	−1.24047
$875$	5.57975e130	0.671826
$876$	−3.45483e130	−0.395361
$877$	2.89651e130	0.315060	0.157530	−	0.987514i	$-0.449647\pi$
$877$	2.89651e130	0.315060	0.157530	+	0.987514i	$0.449647\pi$
$878$	−9.70344e130	−1.00327
$879$	2.50968e131	2.46668
$880$	−1.08138e129	−0.0101041
$881$	−1.34623e131	−1.19589	−0.597944	−	0.801538i	$-0.704015\pi$
$881$	−1.34623e131	−1.19589	−0.597944	+	0.801538i	$0.704015\pi$
$882$	−1.36656e130	−0.115419
$883$	−8.82317e130	−0.708554	−0.354277	−	0.935140i	$-0.615273\pi$
$883$	−8.82317e130	−0.708554	−0.354277	+	0.935140i	$0.615273\pi$
$884$	3.26316e130	0.249180
$885$	−2.55061e130	−0.185212
$886$	1.02431e131	0.707347
$887$	−8.56098e130	−0.562241	−0.281120	−	0.959673i	$-0.590706\pi$
$887$	−8.56098e130	−0.562241	−0.281120	+	0.959673i	$0.590706\pi$
$888$	−3.58093e131	−2.23676
$889$	−1.33677e131	−0.794199
$890$	4.74348e130	0.268066
$891$	−3.56592e130	−0.191696
$892$	1.65673e131	0.847259
$893$	6.38863e130	0.310826
$894$	3.74666e131	1.73430
$895$	3.37800e130	0.148777
$896$	−4.48645e130	−0.188017
$897$	−1.64691e131	−0.656759
$898$	−2.70769e131	−1.02755
$899$	−3.57491e131	−1.29110
$900$	2.78062e131	0.955762
$901$	2.51710e131	0.823470
$902$	2.67400e129	0.00832664
$903$	−6.03966e131	−1.79022
$904$	1.67414e131	0.472386
$905$	−1.49453e131	−0.401462
$906$	5.00815e131	1.28077
$907$	5.43134e131	1.32246	0.661230	−	0.750184i	$-0.270035\pi$
$907$	5.43134e131	1.32246	0.661230	+	0.750184i	$0.270035\pi$
$908$	1.29229e131	0.299598
$909$	4.27378e131	0.943451
$910$	3.50860e130	0.0737550
$911$	−6.55369e131	−1.31195	−0.655976	−	0.754782i	$-0.727743\pi$
$911$	−6.55369e131	−1.31195	−0.655976	+	0.754782i	$0.727743\pi$
$912$	3.79893e131	0.724253
$913$	4.47114e130	0.0811837
$914$	5.29242e131	0.915269
$915$	2.81946e131	0.464437
$916$	−2.06248e131	−0.323624
$917$	−8.64052e131	−1.29153
$918$	−2.27508e132	−3.23964
$919$	3.69672e131	0.501506	0.250753	−	0.968051i	$-0.419322\pi$
$919$	3.69672e131	0.501506	0.250753	+	0.968051i	$0.419322\pi$
$920$	−3.94192e131	−0.509506
$921$	1.64587e132	2.02695
$922$	1.96785e130	0.0230922
$923$	1.33801e131	0.149618
$924$	−7.22019e130	−0.0769389
$925$	9.71978e131	0.987073
$926$	−2.72539e131	−0.263778
$927$	−2.68231e132	−2.47435
$928$	9.13946e131	0.803592
$929$	2.08057e131	0.174375	0.0871873	−	0.996192i	$-0.472212\pi$
$929$	2.08057e131	0.174375	0.0871873	+	0.996192i	$0.472212\pi$
$930$	−8.48698e131	−0.678050
$931$	−1.21170e131	−0.0922853
$932$	−7.97883e131	−0.579337
$933$	3.40238e132	2.35532
$934$	−1.48304e132	−0.978852
$935$	1.00640e131	0.0633366
$936$	1.17051e132	0.702427
$937$	−1.38597e132	−0.793124	−0.396562	−	0.918008i	$-0.629797\pi$
$937$	−1.38597e132	−0.793124	−0.396562	+	0.918008i	$0.629797\pi$
$938$	4.94445e131	0.269831
$939$	−1.27974e132	−0.666042
$940$	8.30975e130	0.0412476
$941$	1.36215e132	0.644890	0.322445	−	0.946588i	$-0.395495\pi$
$941$	1.36215e132	0.644890	0.322445	+	0.946588i	$0.395495\pi$
$942$	4.47500e132	2.02082
$943$	3.72250e131	0.160349
$944$	1.94659e131	0.0799871
$945$	2.23368e132	0.875599
$946$	−1.79939e131	−0.0672931
$947$	1.23478e130	0.00440572	0.00220286	−	0.999998i	$-0.499299\pi$
$947$	1.23478e130	0.00440572	0.00220286	+	0.999998i	$0.499299\pi$
$948$	2.95617e131	0.100637
$949$	3.94749e131	0.128226
$950$	−2.70008e132	−0.836906
$951$	−6.18066e132	−1.82811
$952$	−6.75060e132	−1.90545
$953$	−2.21160e130	−0.00595762	−0.00297881	−	0.999996i	$-0.500948\pi$
$953$	−2.21160e130	−0.00595762	−0.00297881	+	0.999996i	$0.500948\pi$
$954$	2.91715e132	0.749990
$955$	−8.33206e131	−0.204457
$956$	−2.46201e132	−0.576652
$957$	7.02271e131	0.157009
$958$	−5.48726e132	−1.17109
$959$	5.86901e130	0.0119574
$960$	3.20501e132	0.623390
$961$	4.77330e132	0.886396
$962$	1.32194e132	0.234380
$963$	3.44292e131	0.0582851
$964$	4.62675e132	0.747908
$965$	−1.46813e132	−0.226620
$966$	1.10076e133	1.62260
$967$	1.28780e133	1.81288	0.906440	−	0.422334i	$-0.138789\pi$
$967$	1.28780e133	1.81288	0.906440	+	0.422334i	$0.138789\pi$
$968$	7.87760e132	1.05911
$969$	−3.53553e133	−4.53990
$970$	−4.18272e132	−0.512999
$971$	1.86631e132	0.218639	0.109320	−	0.994007i	$-0.465133\pi$
$971$	1.86631e132	0.218639	0.109320	+	0.994007i	$0.465133\pi$
$972$	5.95530e132	0.666431
$973$	7.25459e132	0.775517
$974$	−3.39715e131	−0.0346929
$975$	−4.54151e132	−0.443093
$976$	−2.15176e132	−0.200575
$977$	1.65586e133	1.47474	0.737370	−	0.675489i	$-0.236067\pi$
$977$	1.65586e133	1.47474	0.737370	+	0.675489i	$0.236067\pi$
$978$	−4.61978e132	−0.393136
$979$	1.11534e132	0.0906937
$980$	−1.57606e131	−0.0122465
$981$	−2.03365e133	−1.51010
$982$	−1.32253e133	−0.938522
$983$	2.57060e133	1.74342	0.871711	−	0.490021i	$-0.163011\pi$
$983$	2.57060e133	1.74342	0.871711	+	0.490021i	$0.163011\pi$
$984$	−3.78186e132	−0.245145
$985$	2.90329e132	0.179878
$986$	2.12138e133	1.25631
$987$	−7.18215e132	−0.406576
$988$	3.35321e132	0.181458
$989$	−2.50496e133	−1.29588
$990$	1.16635e132	0.0576849
$991$	−2.75768e133	−1.30397	−0.651984	−	0.758233i	$-0.726063\pi$
$991$	−2.75768e133	−1.30397	−0.651984	+	0.758233i	$0.726063\pi$
$992$	−2.59704e133	−1.17411
$993$	−2.02068e132	−0.0873487
$994$	−8.94297e132	−0.369648
$995$	−4.72192e131	−0.0186634
$996$	−2.04307e133	−0.772222
$997$	3.36932e133	1.21789	0.608945	−	0.793213i	$-0.291593\pi$
$997$	3.36932e133	1.21789	0.608945	+	0.793213i	$0.291593\pi$
$998$	3.38604e133	1.17053
$999$	8.41585e133	2.78249

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1.90.a.a.1.5	✓	7
3.2	odd	2		9.90.a.b.1.3		7

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1.90.a.a.1.5	✓	7	1.1	even	1	trivial
9.90.a.b.1.3		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)

\(f(q)\)	\(=\)	\(q+1.79872e13 q^{2} -3.11193e21 q^{3} -2.95431e26 q^{4} -4.75717e30 q^{5} -5.59749e34 q^{6} +3.90338e37 q^{7} -1.64475e40 q^{8} +6.77478e42 q^{9} +O(q^{10})\)	\(q+1.79872e13 q^{2} -3.11193e21 q^{3} -2.95431e26 q^{4} -4.75717e30 q^{5} -5.59749e34 q^{6} +3.90338e37 q^{7} -1.64475e40 q^{8} +6.77478e42 q^{9} -8.55680e43 q^{10} -2.01197e45 q^{11} +9.19360e47 q^{12} -1.05046e49 q^{13} +7.02109e50 q^{14} +1.48040e52 q^{15} -1.12982e53 q^{16} +1.05148e55 q^{17} +1.21859e56 q^{18} +1.08050e57 q^{19} +1.40541e57 q^{20} -1.21471e59 q^{21} -3.61897e58 q^{22} -5.03802e60 q^{23} +5.11835e61 q^{24} -1.38928e62 q^{25} -1.88949e62 q^{26} -1.20290e64 q^{27} -1.15318e64 q^{28} +1.12164e65 q^{29} +2.66282e65 q^{30} -3.18722e66 q^{31} +8.14829e66 q^{32} +6.26111e66 q^{33} +1.89132e68 q^{34} -1.85690e68 q^{35} -2.00148e69 q^{36} -6.99627e69 q^{37} +1.94351e70 q^{38} +3.26897e70 q^{39} +7.82435e70 q^{40} -7.38883e70 q^{41} -2.18491e72 q^{42} +4.97212e72 q^{43} +5.94398e71 q^{44} -3.22288e73 q^{45} -9.06197e73 q^{46} +5.91267e73 q^{47} +3.51590e74 q^{48} -1.12142e74 q^{49} -2.49893e75 q^{50} -3.27213e76 q^{51} +3.10339e75 q^{52} +2.39386e76 q^{53} -2.16369e77 q^{54} +9.57127e75 q^{55} -6.42009e77 q^{56} -3.36243e78 q^{57} +2.01752e78 q^{58} -1.72292e78 q^{59} -4.37355e78 q^{60} +1.90453e79 q^{61} -5.73291e79 q^{62} +2.64446e80 q^{63} +2.16497e80 q^{64} +4.99723e79 q^{65} +1.12620e80 q^{66} +7.04228e80 q^{67} -3.10640e81 q^{68} +1.56779e82 q^{69} -3.34005e81 q^{70} -1.27373e82 q^{71} -1.11428e83 q^{72} -3.75786e82 q^{73} -1.25843e83 q^{74} +4.32334e83 q^{75} -3.19212e83 q^{76} -7.85349e82 q^{77} +5.87995e83 q^{78} +3.21546e83 q^{79} +5.37472e83 q^{80} +1.77235e85 q^{81} -1.32904e84 q^{82} -2.22227e85 q^{83} +3.58862e85 q^{84} -5.00207e85 q^{85} +8.94344e85 q^{86} -3.49047e86 q^{87} +3.30919e85 q^{88} -5.54352e86 q^{89} -5.79705e86 q^{90} -4.10036e86 q^{91} +1.48839e87 q^{92} +9.91840e87 q^{93} +1.06352e87 q^{94} -5.14011e87 q^{95} -2.53569e88 q^{96} +4.88818e88 q^{97} -2.01713e87 q^{98} -1.36307e88 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 7 q - 31407330351408 q^{2} - 13\!\cdots\!64 q^{3}+ \cdots + 56\!\cdots\!71 q^{9}+O(q^{10}) \) 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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