LMFDB - Embedded newform 1.120.a.a.1.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1,120,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, 120, names="a")

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

chi := DirichletCharacter("1.1");

S:= CuspForms(chi, 120);

N := Newforms(S);

Level:	$ N $	$=$	$ 1 $
Weight:	$ k $	$=$	$ 120 $
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:	$89.6776908760$
Analytic rank:	$0$
Dimension:	$10$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - 5 x^{9} + \cdots + 23\!\cdots\!68 $ x^10 - 5x^9 - 9404703345787384536294563884297100x^8 - 56437488986319546905620662547371236705587734966820x^7 + 29639140109584307591053258695711885914328690189713977843938211566110x^6 + 302320857760746893918849906190665722105536110585047402238063990554086373127779618394x^5 - 35710306278640081530319345579053585523958115296012847290249734470317750445455776758602646818902850220x^4 - 445100005786946110126339043566954480210221599946077713973116224858519979503918563142233399991602485684676838691646580x^3 + 12111564406778326992233841084911489562945191258853609898079398729364716543796816162023709225083671762179935562524829088932227191957225x^2 + 124309768227350287898431974323399479001175728476861830859454663442291359471846962662042666026947182289555101166686363185407032551518863101947349788995*x + 23558257629308685607471906626237287073167696282463668426160514244215304598190480627096203724741982428417614929950299439430849802178287249226345997305074584081617968
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	multiple of $ 2^{171}\cdot 3^{61}\cdot 5^{22}\cdot 7^{9}\cdot 11^{6}\cdot 13^{3}\cdot 17^{4} $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.6
Root			$-9.26226e15$ 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)

$f(q)$	$=$	$q+3.14287e17 q^{2} -2.85616e27 q^{3} -5.65837e35 q^{4} +3.01555e41 q^{5} -8.97656e44 q^{6} -2.21350e50 q^{7} -3.86715e53 q^{8} -5.90846e56 q^{9} +O(q^{10})$	\(q+3.14287e17 q^{2} -2.85616e27 q^{3} -5.65837e35 q^{4} +3.01555e41 q^{5} -8.97656e44 q^{6} -2.21350e50 q^{7} -3.86715e53 q^{8} -5.90846e56 q^{9} +9.47749e58 q^{10} -1.59915e62 q^{11} +1.61612e63 q^{12} -2.31155e66 q^{13} -6.95675e67 q^{14} -8.61290e68 q^{15} +2.54524e71 q^{16} +2.98092e72 q^{17} -1.85695e74 q^{18} +2.37014e76 q^{19} -1.70631e77 q^{20} +6.32212e77 q^{21} -5.02593e79 q^{22} -1.39203e81 q^{23} +1.10452e81 q^{24} -5.95279e82 q^{25} -7.26490e83 q^{26} +3.39840e84 q^{27} +1.25248e86 q^{28} -2.65083e86 q^{29} -2.70693e86 q^{30} -8.19375e88 q^{31} +3.37010e89 q^{32} +4.56744e89 q^{33} +9.36866e89 q^{34} -6.67492e91 q^{35} +3.34323e92 q^{36} -1.39280e93 q^{37} +7.44906e93 q^{38} +6.60216e93 q^{39} -1.16616e95 q^{40} +9.61174e94 q^{41} +1.98696e95 q^{42} -1.59918e96 q^{43} +9.04860e97 q^{44} -1.78172e98 q^{45} -4.37498e98 q^{46} +5.19724e99 q^{47} -7.26961e98 q^{48} +1.21264e100 q^{49} -1.87089e100 q^{50} -8.51400e99 q^{51} +1.30796e102 q^{52} -2.71633e102 q^{53} +1.06808e102 q^{54} -4.82232e103 q^{55} +8.55995e103 q^{56} -6.76951e103 q^{57} -8.33123e103 q^{58} -8.62119e103 q^{59} +4.87350e104 q^{60} +9.74865e105 q^{61} -2.57519e106 q^{62} +1.30784e107 q^{63} -6.32420e106 q^{64} -6.97058e107 q^{65} +1.43549e107 q^{66} +6.81129e107 q^{67} -1.68672e108 q^{68} +3.97587e108 q^{69} -2.09784e109 q^{70} +3.25932e109 q^{71} +2.28489e110 q^{72} +3.58903e109 q^{73} -4.37738e110 q^{74} +1.70021e110 q^{75} -1.34111e112 q^{76} +3.53972e112 q^{77} +2.07497e111 q^{78} -1.11583e113 q^{79} +7.67529e112 q^{80} +3.44212e113 q^{81} +3.02085e112 q^{82} +6.81972e113 q^{83} -3.57729e113 q^{84} +8.98911e113 q^{85} -5.02602e113 q^{86} +7.57121e113 q^{87} +6.18416e115 q^{88} +7.44440e115 q^{89} -5.59974e115 q^{90} +5.11661e116 q^{91} +7.87664e116 q^{92} +2.34027e116 q^{93} +1.63343e117 q^{94} +7.14728e117 q^{95} -9.62556e116 q^{96} +2.08213e118 q^{97} +3.81116e117 q^{98} +9.44852e118 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q + 91\!\cdots\!00 q^{2}+ \cdots + 18\!\cdots\!70 q^{9}+O(q^{10}) $ 10 * q + 919932722605769400 * q^2 - 9570159827289248935296702600 * q^3 + 4272705896834573968338259309906185280 * q^4 + 606257200226243383006472566047160160843340 * q^5 + 36401504491894467383240980519952999483223273120 * q^6 - 219254218938377593670425814743273520801802467026000 * q^7 - 565565131741559483416651174475719665908207742245491200 * q^8 + 1834851904582599922503319964983981808160026773815306152370 * q^9	$ 10 q + 91\!\cdots\!00 q^{2}+ \cdots + 32\!\cdots\!40 q^{99}+O(q^{100}) $ 10 * q + 919932722605769400 * q^2 - 9570159827289248935296702600 * q^3 + 4272705896834573968338259309906185280 * q^4 + 606257200226243383006472566047160160843340 * q^5 + 36401504491894467383240980519952999483223273120 * q^6 - 219254218938377593670425814743273520801802467026000 * q^7 - 565565131741559483416651174475719665908207742245491200 * q^8 + 1834851904582599922503319964983981808160026773815306152370 * q^9 + 634986125367587740207204302796387131018009187401381869153040 * q^10 + 101699246725606790738835774661895063480820812124313881877201320 * q^11 - 38454913569966405167762742595438498566456999771452096076177235200 * q^12 - 1185748520257577664060559883259066024596136377436810629686687725700 * q^13 + 128663533898726556350640086194927332426384167007882730622864072285760 * q^14 - 3710554087524006716347381761626904165187860707894445603427280739742320 * q^15 + 1692157270872518872969972729913243365739971167225638932987297451499458560 * q^16 - 7864283005617688192060113380368906686779951730371226323040594773109948300 * q^17 + 332729677344108131883156941184784577100879720076210912205274121852966805400 * q^18 + 6933132543714084280010692900040098202807958189097871055544810749569091843800 * q^19 + 739362437091413007058366615825358922208924736756157332674630660292607013864320 * q^20 + 2956525867496139343216584028476962325502089413634709218759412375063065769235520 * q^21 + 182048505569729359245793025478209587997846812992510021821256296609773333925464800 * q^22 + 2899273707160329485617593679008001931087825074180318868634550223688404754013405200 * q^23 + 114076958190963694629504891381029963295654961523414627262670720636843992879159552000 * q^24 + 438494787182106380867327117170026697103640781467523702437104047242833362602352949350 * q^25 - 318317418521249562365279268571874153839124425225189223040103737098442975265906223280 * q^26 - 45551493493769742679374192788006036083495765633221136999776547459453349750382686446800 * q^27 - 523381565894005037423609946706950604481078110602387257868273228698395911628601559155200 * q^28 - 239780648672002576188201702569667845017734503354477933365275721637750281457865124433700 * q^29 + 21029395143482710334699445468847496946126462842956505426185423480948664554653809442982080 * q^30 + 160165221449158413670086721746271710279050125440150480736499480204572300135092293246793920 * q^31 - 834373398020641818369077524061840548626893881879494325415144208186283168678479622990233600 * q^32 - 3570238663181267586336948085267071808900587562867500514533738739767476967040829429822599200 * q^33 - 41095955432266996557490146601397116658486035720992194797885692480580962506776105495084173840 * q^34 + 138699704976096510485603716990768616767579130103693747880984703716174722976398003170335643040 * q^35 + 1968770682959423831661461799770758836110419126467351452806841613209828415998369150047869168960 * q^36 - 2929977505416183984446606444699920153402867583929450347729318630774282158879219717208971398900 * q^37 - 34132539768785031258064307777998769213197932649565990492157910428905434754702082210597346456800 * q^38 - 37083836176586549326655714409651173972060300017562592944355756464743632231154290665689117350960 * q^39 + 671451534852984850954224825661781753416230993956537124458730875650510059526361261848342923494400 * q^40 + 2514540111291426044482406571860470483406800557710096621771586537326874081984886304684316806834820 * q^41 - 15273274580038512441282769157227926832173790524876405090470612324607958771986447522111977427436800 * q^42 + 3044753550753493053954517812078986490614702618943897995955026804229546439117864461911484146129000 * q^43 - 12194938044986814191839006674776852072893778556175391506781528253940392493592913843485049137975040 * q^44 + 986746799250062956400338006861900986362523619062838880021292887355485855896798596485569080571667580 * q^45 + 752141612087076748912715482380878319001154104492332189173260174861749530869824058097798503110563520 * q^46 - 1918977170076493454170487365406413018340521940535245265635752086808026838196958796824029488596607200 * q^47 - 9413963382571179425636093740415075791073794954566518162212892225259707570459169592567092964578508800 * q^48 + 4424167233212972548308367231382645770920683128881486958515725055988725408868499618515518765011399130 * q^49 + 680722065409115183760100309976569125874165206805654527502038796615083137012712040535401772639602878600 * q^50 - 32319807059595921198119329763639094466370593528876750378364913074838896902840034535481214151885659280 * q^51 - 3672350508615918706988315428535798947878272949374804570220967811956449680004938673562235859140924944000 * q^52 - 2009211479238083119390289905543378382308797873461290277025114374748986032309712284340399015223172958100 * q^53 - 1931801935997371383558162239941092584008314189522805286105797190362500280610458221586931216805738379200 * q^54 + 30511878931073238316415921138278986771644957150459948535911136025774807284294416560913953468660882079280 * q^55 + 126877575660686062164799530657771058499408094328546461202608068856064827832632677097022676050516125388800 * q^56 - 1412245636613402987583566403928499689907673096626013381053749242060772374057239140716128737047059987589600 * q^57 - 136877557224662485454400622855348052940229394353948623607073498889520831920878560332024651715699006897200 * q^58 + 3299933671312970318014224510035438974811878541147756441623760703525598387045261537239059812342521105337800 * q^59 + 21522094490079259713051153429507985158270932148578747769685503036840800025279058274203907556876957730736640 * q^60 + 4837190174129518173385919119672257037555828391936321041643076409836299786530753347575068109568740623595420 * q^61 - 160819201153827870914932578626796393716485319064275718134936059959659604110154771581583794810946018351763200 * q^62 - 29983538095598409492955452543692543839392503094995599971655215910869017565718274766970279553480154472448400 * q^63 + 1211010735266408368721880715435373923494644777241361683572485488080139913559735067537574947639643472539156480 * q^64 + 275596405736800076158618605370878142954922604093367429122958466182625164052330625944843847143685944773387080 * q^65 - 4571556792821411386452986160291211039829949386539474994568046789054354433826530257625242189399890177231308160 * q^66 - 14492255044540068397146202787177666038978329738091966816085948596075196182415583867767491778681013197600129800 * q^67 + 11412020923423724971791403006719373171687704529451822317715709895446884725238988347133907742324217053213750400 * q^68 + 26214069579412214259271827314973627996718651539417118198340276923109493510587408283690746644729049025547573440 * q^69 + 123614110386251874656201195782002919137175900573453806468611285513805590311860970064321111121804039130548666240 * q^70 + 167986438720991202535175844535056202103467058420138032407837057205213862880922938218281473241336848029824726320 * q^71 - 1214027676200915397665818515850699616086911975452482717359179924343053006357499126921626784766543068325763750400 * q^72 + 1233949202586186335303917316898506861995019601998317675708778649302958930766175545348120938476925924328720549700 * q^73 + 543442580799452155829153254268968536321414860958435747186750896729081968075855332008879736531095204288140166160 * q^74 + 5400719330138615967684042552542859592218848409512888981139070352575924621197393023272032307312948409698674976200 * q^75 - 1947681364249266128008278515237592495027779127950973160394084152671569960150463509448195360313803381416385798400 * q^76 - 16683659822909228960950374914003452078135467020374567292986163653878590289822431170045744715362904216698143432000 * q^77 - 89072355889618061913236422961170201709148241333748665798116496667029121445925030388457750939459839052612461352000 * q^78 + 157508184913938702697109095010204757626061191800741192129723961816007368467430024268154560701305365480554014277600 * q^79 + 717738694171956562725550070775822043413971269412641242062469275441459076310474017521997792969717993348643119882240 * q^80 + 685377716933108811002635995136680562114143448286890027079208804131082571599201228615213084084612556502713839645210 * q^81 - 81231248886594142360412634887129249452756426241963903730935732338634849662649563859028187215008243901359954917200 * q^82 - 1206868514083202720232704577481117752069506004611956039833793542006699255448280107179126221895523030200058209215400 * q^83 + 14126467866143646431573189552438805296686170961752631529359503040694891931287469221548265077514565520405417102632960 * q^84 + 14020561046474179165946028061965977084369651578728211422336420822319994099510809728088754276111040551899070188910040 * q^85 + 66344225309049944615999973318384392854563837752586977497952258411148013864305631982269419370065960537615017456509920 * q^86 + 42211584651436829046971577208962080119193312751750182233070614864898561469568330009329188990317590094811388534891600 * q^87 + 137328180658233895389586672135196831011178161508672801678233870639146210732539922411594570311726409571327613009049600 * q^88 + 419216508652667251481624162222063794117236701682826141556295380005381004122845062519830860537035472363408866073492900 * q^89 + 1960186172906516738137093246273215583954033628616907194913300477767254569348788187788783980642894284377261444786246480 * q^90 + 2117961972511642186570565583354551994813643511649789410299502995928572494930166279095010158484303424328709161629477920 * q^91 + 7643877538850487094208225981990239274508968935126003265201353928208290718282344963218624186914954600357688007403379200 * q^92 + 4145125513717754925972762047991995413704692770483070724240680311937909051760759841371162072158739134468687943292012800 * q^93 + 18905124986143721068825997229954909071618392026686975237140598903838373039063178431388647564880138863772474056628453760 * q^94 + 24103470106743892259389808018645838698305984759500570316746447180409251673952803385627315633849766600459698430524475600 * q^95 + 145148996310095551220695234868863345553364456500073995562810300405246452541716926663419327678590987234751701850742456320 * q^96 + 107546374851676082038883438148873453454117013661188535495956674032604491178648329876169635437402337745265739065665481300 * q^97 + 174218963757049243228974277723290518756443094205275131612770946890670481716398629353987179661401811795718431811507182200 * q^98 + 323496911757957747789115751830719500571150759171653307778212471313230140211264055128690873120449943627772784580871392840 * 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 $

$2$	3.14287e17	0.385516	0.192758	−	0.981246i	$-0.438257\pi$
$2$	3.14287e17	0.385516	0.192758	+	0.981246i	$0.438257\pi$
$3$	−2.85616e27	−0.116699	−0.0583497	−	0.998296i	$-0.518584\pi$
$3$	−2.85616e27	−0.116699	−0.0583497	+	0.998296i	$0.518584\pi$
$4$	−5.65837e35	−0.851378
$5$	3.01555e41	0.777412	0.388706	−	0.921362i	$-0.372922\pi$
$5$	3.01555e41	0.777412	0.388706	+	0.921362i	$0.372922\pi$
$6$	−8.97656e44	−0.0449894
$7$	−2.21350e50	−1.15278	−0.576390	−	0.817175i	$-0.695539\pi$
$7$	−2.21350e50	−1.15278	−0.576390	+	0.817175i	$0.695539\pi$
$8$	−3.86715e53	−0.713735
$9$	−5.90846e56	−0.986381
$10$	9.47749e58	0.299705
$11$	−1.59915e62	−1.74191	−0.870953	−	0.491366i	$-0.836498\pi$
$11$	−1.59915e62	−1.74191	−0.870953	+	0.491366i	$0.836498\pi$
$12$	1.61612e63	0.0993552
$13$	−2.31155e66	−1.21415	−0.607076	−	0.794644i	$-0.707658\pi$
$13$	−2.31155e66	−1.21415	−0.607076	+	0.794644i	$0.707658\pi$
$14$	−6.95675e67	−0.444415
$15$	−8.61290e68	−0.0907235
$16$	2.54524e71	0.576221
$17$	2.98092e72	0.183079	0.0915397	−	0.995801i	$-0.470821\pi$
$17$	2.98092e72	0.183079	0.0915397	+	0.995801i	$0.470821\pi$
$18$	−1.85695e74	−0.380266
$19$	2.37014e76	1.94507	0.972535	−	0.232758i	$-0.0747750\pi$
$19$	2.37014e76	1.94507	0.972535	+	0.232758i	$0.0747750\pi$
$20$	−1.70631e77	−0.661871
$21$	6.32212e77	0.134529
$22$	−5.02593e79	−0.671532
$23$	−1.39203e81	−1.32082	−0.660409	−	0.750906i	$-0.729617\pi$
$23$	−1.39203e81	−1.32082	−0.660409	+	0.750906i	$0.729617\pi$
$24$	1.10452e81	0.0832925
$25$	−5.95279e82	−0.395631
$26$	−7.26490e83	−0.468075
$27$	3.39840e84	0.231809
$28$	1.25248e86	0.981450
$29$	−2.65083e86	−0.257455	−0.128727	−	0.991680i	$-0.541089\pi$
$29$	−2.65083e86	−0.257455	−0.128727	+	0.991680i	$0.541089\pi$
$30$	−2.70693e86	−0.0349753
$31$	−8.19375e88	−1.50474	−0.752371	−	0.658739i	$-0.771090\pi$
$31$	−8.19375e88	−1.50474	−0.752371	+	0.658739i	$0.771090\pi$
$32$	3.37010e89	0.935878
$33$	4.56744e89	0.203279
$34$	9.36866e89	0.0705800
$35$	−6.67492e91	−0.896184
$36$	3.34323e92	0.839783
$37$	−1.39280e93	−0.685307	−0.342653	−	0.939462i	$-0.611326\pi$
$37$	−1.39280e93	−0.685307	−0.342653	+	0.939462i	$0.611326\pi$
$38$	7.44906e93	0.749855
$39$	6.60216e93	0.141691
$40$	−1.16616e95	−0.554866
$41$	9.61174e94	0.105236	0.0526178	−	0.998615i	$-0.483244\pi$
$41$	9.61174e94	0.105236	0.0526178	+	0.998615i	$0.483244\pi$
$42$	1.98696e95	0.0518629
$43$	−1.59918e96	−0.102926	−0.0514629	−	0.998675i	$-0.516388\pi$
$43$	−1.59918e96	−0.102926	−0.0514629	+	0.998675i	$0.516388\pi$
$44$	9.04860e97	1.48302
$45$	−1.78172e98	−0.766825
$46$	−4.37498e98	−0.509196
$47$	5.19724e99	1.68248	0.841240	−	0.540662i	$-0.181826\pi$
$47$	5.19724e99	1.68248	0.841240	+	0.540662i	$0.181826\pi$
$48$	−7.26961e98	−0.0672446
$49$	1.21264e100	0.328900
$50$	−1.87089e100	−0.152522
$51$	−8.51400e99	−0.0213652
$52$	1.30796e102	1.03370
$53$	−2.71633e102	−0.691144	−0.345572	−	0.938392i	$-0.612315\pi$
$53$	−2.71633e102	−0.691144	−0.345572	+	0.938392i	$0.612315\pi$
$54$	1.06808e102	0.0893662
$55$	−4.82232e103	−1.35418
$56$	8.55995e103	0.822779
$57$	−6.76951e103	−0.226988
$58$	−8.33123e103	−0.0992529
$59$	−8.62119e103	−0.0371426	−0.0185713	−	0.999828i	$-0.505912\pi$
$59$	−8.62119e103	−0.0371426	−0.0185713	+	0.999828i	$0.505912\pi$
$60$	4.87350e104	0.0772399
$61$	9.74865e105	0.577856	0.288928	−	0.957351i	$-0.406701\pi$
$61$	9.74865e105	0.577856	0.288928	+	0.957351i	$0.406701\pi$
$62$	−2.57519e106	−0.580102
$63$	1.30784e107	1.13708
$64$	−6.32420e106	−0.215426
$65$	−6.97058e107	−0.943897
$66$	1.43549e107	0.0783674
$67$	6.81129e107	0.151977	0.0759886	−	0.997109i	$-0.475789\pi$
$67$	6.81129e107	0.151977	0.0759886	+	0.997109i	$0.475789\pi$
$68$	−1.68672e108	−0.155870
$69$	3.97587e108	0.154139
$70$	−2.09784e109	−0.345493
$71$	3.25932e109	0.230810	0.115405	−	0.993318i	$-0.463183\pi$
$71$	3.25932e109	0.230810	0.115405	+	0.993318i	$0.463183\pi$
$72$	2.28489e110	0.704015
$73$	3.58903e109	0.0486706	0.0243353	−	0.999704i	$-0.492253\pi$
$73$	3.58903e109	0.0486706	0.0243353	+	0.999704i	$0.492253\pi$
$74$	−4.37738e110	−0.264197
$75$	1.70021e110	0.0461698
$76$	−1.34111e112	−1.65599
$77$	3.53972e112	2.00803
$78$	2.07497e111	0.0546241
$79$	−1.11583e113	−1.37653	−0.688266	−	0.725459i	$-0.741628\pi$
$79$	−1.11583e113	−1.37653	−0.688266	+	0.725459i	$0.741628\pi$
$80$	7.67529e112	0.447961
$81$	3.44212e113	0.959329
$82$	3.02085e112	0.0405700
$83$	6.81972e113	0.445266	0.222633	−	0.974902i	$-0.428535\pi$
$83$	6.81972e113	0.445266	0.222633	+	0.974902i	$0.428535\pi$
$84$	−3.57729e113	−0.114535
$85$	8.98911e113	0.142328
$86$	−5.02602e113	−0.0396795
$87$	7.57121e113	0.0300448
$88$	6.18416e115	1.24326
$89$	7.44440e115	0.764055	0.382027	−	0.924151i	$-0.375226\pi$
$89$	7.44440e115	0.764055	0.382027	+	0.924151i	$0.375226\pi$
$90$	−5.59974e115	−0.295623
$91$	5.11661e116	1.39965
$92$	7.87664e116	1.12451
$93$	2.34027e116	0.175602
$94$	1.63343e117	0.648623
$95$	7.14728e117	1.51212
$96$	−9.62556e116	−0.109216
$97$	2.08213e118	1.27524	0.637618	−	0.770353i	$-0.279920\pi$
$97$	2.08213e118	1.27524	0.637618	+	0.770353i	$0.279920\pi$
$98$	3.81116e117	0.126796
$99$	9.44852e118	1.71818
$100$	3.36831e118	0.336831
$101$	2.28320e119	1.26305	0.631527	−	0.775354i	$-0.282428\pi$
$101$	2.28320e119	1.26305	0.631527	+	0.775354i	$0.282428\pi$
$102$	−2.67584e117	−0.00823664
$103$	−5.09109e119	−0.876993	−0.438496	−	0.898733i	$-0.644489\pi$
$103$	−5.09109e119	−0.876993	−0.438496	+	0.898733i	$0.644489\pi$
$104$	8.93911e119	0.866584
$105$	1.90647e119	0.104584
$106$	−8.53709e119	−0.266447
$107$	−7.69979e120	−1.37450	−0.687249	−	0.726422i	$-0.741182\pi$
$107$	−7.69979e120	−1.37450	−0.687249	+	0.726422i	$0.741182\pi$
$108$	−1.92294e120	−0.197357
$109$	−7.16334e120	−0.424853	−0.212427	−	0.977177i	$-0.568137\pi$
$109$	−7.16334e120	−0.424853	−0.212427	+	0.977177i	$0.568137\pi$
$110$	−1.51559e121	−0.522057
$111$	3.97806e120	0.0799749
$112$	−5.63388e121	−0.664256
$113$	−2.14303e122	−1.48888	−0.744441	−	0.667689i	$-0.767284\pi$
$113$	−2.14303e122	−1.48888	−0.744441	+	0.667689i	$0.767284\pi$
$114$	−2.12757e121	−0.0875076
$115$	−4.19774e122	−1.02682
$116$	1.49994e122	0.219191
$117$	1.36577e123	1.19762
$118$	−2.70953e121	−0.0143191
$119$	−6.59827e122	−0.211050
$120$	3.33074e122	0.0647525
$121$	1.71447e124	2.03424
$122$	3.06388e123	0.222773
$123$	−2.74527e122	−0.0122809
$124$	4.63633e124	1.28110
$125$	−6.33239e124	−1.08498
$126$	4.11037e124	0.438362
$127$	1.77263e125	1.18113	0.590563	−	0.806991i	$-0.298906\pi$
$127$	1.77263e125	1.18113	0.590563	+	0.806991i	$0.298906\pi$
$128$	−2.43858e125	−1.01893
$129$	4.56752e123	0.0120114
$130$	−2.19077e125	−0.363887
$131$	−8.97739e124	−0.0945166	−0.0472583	−	0.998883i	$-0.515048\pi$
$131$	−8.97739e124	−0.0945166	−0.0472583	+	0.998883i	$0.515048\pi$
$132$	−2.58443e125	−0.173067
$133$	−5.24631e126	−2.24224
$134$	2.14070e125	0.0585896
$135$	1.02481e126	0.180211
$136$	−1.15277e126	−0.130670
$137$	−1.14502e127	−0.839343	−0.419671	−	0.907676i	$-0.637855\pi$
$137$	−1.14502e127	−0.839343	−0.419671	+	0.907676i	$0.637855\pi$
$138$	1.24957e126	0.0594229
$139$	3.41036e127	1.05541	0.527703	−	0.849429i	$-0.323053\pi$
$139$	3.41036e127	1.05541	0.527703	+	0.849429i	$0.323053\pi$
$140$	3.77692e127	0.762991
$141$	−1.48442e127	−0.196344
$142$	1.02436e127	0.0889811
$143$	3.69651e128	2.11494
$144$	−1.50384e128	−0.568374
$145$	−7.99371e127	−0.200148
$146$	1.12799e127	0.0187633
$147$	−3.46349e127	−0.0383824
$148$	7.88097e128	0.583455
$149$	2.63955e128	0.130902	0.0654511	−	0.997856i	$-0.479151\pi$
$149$	2.63955e128	0.130902	0.0654511	+	0.997856i	$0.479151\pi$
$150$	5.34356e127	0.0177992
$151$	−5.46569e129	−1.22607	−0.613037	−	0.790054i	$-0.710052\pi$
$151$	−5.46569e129	−1.22607	−0.613037	+	0.790054i	$0.710052\pi$
$152$	−9.16570e129	−1.38826
$153$	−1.76126e129	−0.180586
$154$	1.11249e130	0.774129
$155$	−2.47087e130	−1.16980
$156$	−3.73575e129	−0.120632
$157$	2.51292e130	0.554816	0.277408	−	0.960752i	$-0.410525\pi$
$157$	2.51292e130	0.554816	0.277408	+	0.960752i	$0.410525\pi$
$158$	−3.50691e130	−0.530675
$159$	7.75829e129	0.0806560
$160$	1.01627e131	0.727563
$161$	3.08126e131	1.52261
$162$	1.08182e131	0.369837
$163$	2.97472e130	0.0705154	0.0352577	−	0.999378i	$-0.488775\pi$
$163$	2.97472e130	0.0705154	0.0352577	+	0.999378i	$0.488775\pi$
$164$	−5.43868e130	−0.0895952
$165$	1.37733e131	0.158032
$166$	2.14335e131	0.171657
$167$	−1.15713e132	−0.648266	−0.324133	−	0.946012i	$-0.605072\pi$
$167$	−1.15713e132	−0.648266	−0.324133	+	0.946012i	$0.605072\pi$
$168$	−2.44486e131	−0.0960178
$169$	1.71866e132	0.474167
$170$	2.82516e131	0.0548697
$171$	−1.40039e133	−1.91858
$172$	9.04876e131	0.0876287
$173$	−5.95307e132	−0.408318	−0.204159	−	0.978938i	$-0.565446\pi$
$173$	−5.95307e132	−0.408318	−0.204159	+	0.978938i	$0.565446\pi$
$174$	2.37953e131	0.0115828
$175$	1.31765e133	0.456075
$176$	−4.07022e133	−1.00372
$177$	2.46235e131	0.00433452
$178$	2.33968e133	0.294555
$179$	7.79524e133	0.703192	0.351596	−	0.936152i	$-0.385639\pi$
$179$	7.79524e133	0.703192	0.351596	+	0.936152i	$0.385639\pi$
$180$	1.00817e134	0.652857
$181$	1.05055e134	0.489260	0.244630	−	0.969616i	$-0.421333\pi$
$181$	1.05055e134	0.489260	0.244630	+	0.969616i	$0.421333\pi$
$182$	1.60809e134	0.539587
$183$	−2.78437e133	−0.0674354
$184$	5.38320e134	0.942714
$185$	−4.20005e134	−0.532766
$186$	7.35517e133	0.0676975
$187$	−4.76694e134	−0.318907
$188$	−2.94079e135	−1.43243
$189$	−7.52237e134	−0.267225
$190$	2.24630e135	0.582946
$191$	−1.84549e135	−0.350451	−0.175225	−	0.984528i	$-0.556065\pi$
$191$	−1.84549e135	−0.350451	−0.175225	+	0.984528i	$0.556065\pi$
$192$	1.80630e134	0.0251400
$193$	−1.39846e136	−1.42886	−0.714431	−	0.699706i	$-0.753314\pi$
$193$	−1.39846e136	−1.42886	−0.714431	+	0.699706i	$0.753314\pi$
$194$	6.54388e135	0.491623
$195$	1.99091e135	0.110152
$196$	−6.86155e135	−0.280018
$197$	2.02847e136	0.611544	0.305772	−	0.952105i	$-0.401085\pi$
$197$	2.02847e136	0.611544	0.305772	+	0.952105i	$0.401085\pi$
$198$	2.96955e136	0.662387
$199$	1.32599e136	0.219171	0.109586	−	0.993977i	$-0.465048\pi$
$199$	1.32599e136	0.219171	0.109586	+	0.993977i	$0.465048\pi$
$200$	2.30204e136	0.282376
$201$	−1.94542e135	−0.0177356
$202$	7.17581e136	0.486927
$203$	5.86761e136	0.296789
$204$	4.81754e135	0.0181899
$205$	2.89847e136	0.0818114
$206$	−1.60007e137	−0.338095
$207$	8.22476e137	1.30283
$208$	−5.88344e137	−0.699621
$209$	−3.79022e138	−3.38813
$210$	5.99178e136	0.0403188
$211$	1.14045e138	0.578456	0.289228	−	0.957260i	$-0.406602\pi$
$211$	1.14045e138	0.578456	0.289228	+	0.957260i	$0.406602\pi$
$212$	1.53700e138	0.588424
$213$	−9.30915e136	−0.0269354
$214$	−2.41995e138	−0.529891
$215$	−4.82241e137	−0.0800158
$216$	−1.31422e138	−0.165451
$217$	1.81369e139	1.73464
$218$	−2.25135e138	−0.163788
$219$	−1.02509e137	−0.00567983
$220$	2.72865e139	1.15292
$221$	−6.89054e138	−0.222286
$222$	1.25025e138	0.0308316
$223$	2.25773e139	0.426120	0.213060	−	0.977039i	$-0.431657\pi$
$223$	2.25773e139	0.426120	0.213060	+	0.977039i	$0.431657\pi$
$224$	−7.45972e139	−1.07886
$225$	3.51718e139	0.390243
$226$	−6.73526e139	−0.573987
$227$	5.78570e139	0.379156	0.189578	−	0.981866i	$-0.439288\pi$
$227$	5.78570e139	0.379156	0.189578	+	0.981866i	$0.439288\pi$
$228$	3.83044e139	0.193253
$229$	−2.93548e140	−1.14148	−0.570740	−	0.821131i	$-0.693343\pi$
$229$	−2.93548e140	−1.14148	−0.570740	+	0.821131i	$0.693343\pi$
$230$	−1.31930e140	−0.395855
$231$	−1.01100e140	−0.234336
$232$	1.02512e140	0.183755
$233$	−1.03698e141	−1.43910	−0.719551	−	0.694439i	$-0.755652\pi$
$233$	−1.03698e141	−1.43910	−0.719551	+	0.694439i	$0.755652\pi$
$234$	4.29244e140	0.461701
$235$	1.56725e141	1.30798
$236$	4.87819e139	0.0316224
$237$	3.18699e140	0.160640
$238$	−2.07375e140	−0.0813632
$239$	4.69138e141	1.43425	0.717126	−	0.696944i	$-0.245457\pi$
$239$	4.69138e141	1.43425	0.717126	+	0.696944i	$0.245457\pi$
$240$	−2.19219e140	−0.0522768
$241$	−6.74900e140	−0.125668	−0.0628341	−	0.998024i	$-0.520014\pi$
$241$	−6.74900e140	−0.125668	−0.0628341	+	0.998024i	$0.520014\pi$
$242$	5.38838e141	0.784231
$243$	−3.01878e141	−0.343762
$244$	−5.51615e141	−0.491973
$245$	3.65677e141	0.255691
$246$	−8.62804e139	−0.00473449
$247$	−5.47869e142	−2.36161
$248$	3.16865e142	1.07399
$249$	−1.94782e141	−0.0519623
$250$	−1.99019e142	−0.418277
$251$	−6.41589e142	−1.06334	−0.531668	−	0.846953i	$-0.678435\pi$
$251$	−6.41589e142	−1.06334	−0.531668	+	0.846953i	$0.678435\pi$
$252$	−7.40023e142	−0.968084
$253$	2.22607e143	2.30074
$254$	5.57115e142	0.455343
$255$	−2.56744e141	−0.0166096
$256$	−3.46099e142	−0.177387
$257$	−1.32214e143	−0.537348	−0.268674	−	0.963231i	$-0.586585\pi$
$257$	−1.32214e143	−0.537348	−0.268674	+	0.963231i	$0.586585\pi$
$258$	1.43551e141	0.00463058
$259$	3.08296e143	0.790008
$260$	3.94422e143	0.803612
$261$	1.56623e143	0.253949
$262$	−2.82148e142	−0.0364377
$263$	4.77384e143	0.491474	0.245737	−	0.969336i	$-0.420970\pi$
$263$	4.77384e143	0.491474	0.245737	+	0.969336i	$0.420970\pi$
$264$	−1.76630e143	−0.145088
$265$	−8.19123e143	−0.537303
$266$	−1.64885e144	−0.864417
$267$	−2.12624e143	−0.0891647
$268$	−3.85408e143	−0.129390
$269$	−2.48659e144	−0.668871	−0.334436	−	0.942419i	$-0.608546\pi$
$269$	−2.48659e144	−0.668871	−0.334436	+	0.942419i	$0.608546\pi$
$270$	3.22083e143	0.0694743
$271$	−2.77622e144	−0.480598	−0.240299	−	0.970699i	$-0.577245\pi$
$271$	−2.77622e144	−0.480598	−0.240299	+	0.970699i	$0.577245\pi$
$272$	7.58715e143	0.105494
$273$	−1.46139e144	−0.163338
$274$	−3.59865e144	−0.323580
$275$	9.51941e144	0.689152
$276$	−2.24970e144	−0.131230
$277$	1.76922e145	0.832215	0.416107	−	0.909315i	$-0.363394\pi$
$277$	1.76922e145	0.832215	0.416107	+	0.909315i	$0.363394\pi$
$278$	1.07183e145	0.406876
$279$	4.84125e145	1.48425
$280$	2.58129e145	0.639638
$281$	−7.38218e145	−1.47965	−0.739825	−	0.672800i	$-0.765092\pi$
$281$	−7.38218e145	−1.47965	−0.739825	+	0.672800i	$0.765092\pi$
$282$	−4.66533e144	−0.0756939
$283$	−1.41495e145	−0.185972	−0.0929859	−	0.995667i	$-0.529641\pi$
$283$	−1.41495e145	−0.185972	−0.0929859	+	0.995667i	$0.529641\pi$
$284$	−1.84425e145	−0.196507
$285$	−2.04138e145	−0.176463
$286$	1.16177e146	0.815343
$287$	−2.12756e145	−0.121313
$288$	−1.99121e146	−0.923132
$289$	−2.56221e146	−0.966482
$290$	−2.51232e145	−0.0771604
$291$	−5.94691e145	−0.148819
$292$	−2.03081e145	−0.0414371
$293$	2.78485e146	0.463637	0.231818	−	0.972759i	$-0.425532\pi$
$293$	2.78485e146	0.463637	0.231818	+	0.972759i	$0.425532\pi$
$294$	−1.08853e145	−0.0147970
$295$	−2.59976e145	−0.0288751
$296$	5.38616e146	0.489128
$297$	−5.43456e146	−0.403790
$298$	8.29578e145	0.0504649
$299$	3.21775e147	1.60367
$300$	−9.62045e145	−0.0393080
$301$	3.53979e146	0.118651
$302$	−1.71780e147	−0.472671
$303$	−6.52119e146	−0.147398
$304$	6.03257e147	1.12079
$305$	2.93975e147	0.449232
$306$	−5.53543e146	−0.0696188
$307$	−9.78903e147	−1.01393	−0.506963	−	0.861968i	$-0.669232\pi$
$307$	−9.78903e147	−1.01393	−0.506963	+	0.861968i	$0.669232\pi$
$308$	−2.00291e148	−1.70959
$309$	1.45410e147	0.102344
$310$	−7.76562e147	−0.450978
$311$	1.37969e148	0.661515	0.330757	−	0.943716i	$-0.392696\pi$
$311$	1.37969e148	0.661515	0.330757	+	0.943716i	$0.392696\pi$
$312$	−2.55316e147	−0.101130
$313$	−4.84117e148	−1.58512	−0.792560	−	0.609794i	$-0.791252\pi$
$313$	−4.84117e148	−1.58512	−0.792560	+	0.609794i	$0.791252\pi$
$314$	7.89779e147	0.213890
$315$	3.94385e148	0.883979
$316$	6.31378e148	1.17195
$317$	−5.12943e147	−0.0788939	−0.0394469	−	0.999222i	$-0.512560\pi$
$317$	−5.12943e147	−0.0788939	−0.0394469	+	0.999222i	$0.512560\pi$
$318$	2.43833e147	0.0310942
$319$	4.23908e148	0.448462
$320$	−1.90709e148	−0.167474
$321$	2.19919e148	0.160403
$322$	9.68402e148	0.586991
$323$	7.06520e148	0.356102
$324$	−1.94768e149	−0.816751
$325$	1.37602e149	0.480356
$326$	9.34917e147	0.0271848
$327$	2.04597e148	0.0495801
$328$	−3.71701e148	−0.0751103
$329$	−1.15041e150	−1.93953
$330$	4.32879e148	0.0609237
$331$	1.08780e149	0.127874	0.0639372	−	0.997954i	$-0.479634\pi$
$331$	1.08780e149	0.127874	0.0639372	+	0.997954i	$0.479634\pi$
$332$	−3.85885e149	−0.379090
$333$	8.22928e149	0.675974
$334$	−3.63672e149	−0.249917
$335$	2.05398e149	0.118149
$336$	1.60913e149	0.0775182
$337$	−2.54018e150	−1.02538	−0.512691	−	0.858573i	$-0.671352\pi$
$337$	−2.54018e150	−1.02538	−0.512691	+	0.858573i	$0.671352\pi$
$338$	5.40153e149	0.182799
$339$	6.12083e149	0.173751
$340$	−5.08638e149	−0.121175
$341$	1.31031e151	2.62112
$342$	−4.40124e150	−0.739643
$343$	5.47688e150	0.773630
$344$	6.18428e149	0.0734618
$345$	1.19894e150	0.119829
$346$	−1.87098e150	−0.157413
$347$	−1.23537e151	−0.875372	−0.437686	−	0.899128i	$-0.644202\pi$
$347$	−1.23537e151	−0.875372	−0.437686	+	0.899128i	$0.644202\pi$
$348$	−4.28407e149	−0.0255795
$349$	−8.48898e149	−0.0427310	−0.0213655	−	0.999772i	$-0.506801\pi$
$349$	−8.48898e149	−0.0427310	−0.0213655	+	0.999772i	$0.506801\pi$
$350$	4.14121e150	0.175824
$351$	−7.85557e150	−0.281452
$352$	−5.38930e151	−1.63021
$353$	1.10405e151	0.282095	0.141047	−	0.990003i	$-0.454953\pi$
$353$	1.10405e151	0.282095	0.141047	+	0.990003i	$0.454953\pi$
$354$	7.73887e148	0.00167103
$355$	9.82864e150	0.179435
$356$	−4.21232e151	−0.650499
$357$	1.88457e150	0.0246294
$358$	2.44994e151	0.271092
$359$	−8.02561e151	−0.752244	−0.376122	−	0.926570i	$-0.622743\pi$
$359$	−8.02561e151	−0.752244	−0.376122	+	0.926570i	$0.622743\pi$
$360$	6.89020e151	0.547310
$361$	4.13274e152	2.78329
$362$	3.30173e151	0.188617
$363$	−4.89682e151	−0.237394
$364$	−2.89517e152	−1.19163
$365$	1.08229e151	0.0378371
$366$	−8.75094e150	−0.0259974
$367$	4.88480e152	1.23372	0.616859	−	0.787073i	$-0.288405\pi$
$367$	4.88480e152	1.23372	0.616859	+	0.787073i	$0.288405\pi$
$368$	−3.54305e152	−0.761083
$369$	−5.67905e151	−0.103802
$370$	−1.32002e152	−0.205390
$371$	6.01260e152	0.796736
$372$	−1.32421e152	−0.149504
$373$	−1.36860e153	−1.31704	−0.658521	−	0.752562i	$-0.728818\pi$
$373$	−1.36860e153	−1.31704	−0.658521	+	0.752562i	$0.728818\pi$
$374$	−1.49819e152	−0.122944
$375$	1.80863e152	0.126616
$376$	−2.00985e153	−1.20085
$377$	6.12752e152	0.312590
$378$	−2.36419e152	−0.103019
$379$	3.20043e153	1.19172	0.595861	−	0.803087i	$-0.296811\pi$
$379$	3.20043e153	1.19172	0.595861	+	0.803087i	$0.296811\pi$
$380$	−4.04420e153	−1.28739
$381$	−5.06292e152	−0.137837
$382$	−5.80015e152	−0.135104
$383$	7.29425e153	1.45430	0.727150	−	0.686479i	$-0.240845\pi$
$383$	7.29425e153	1.45430	0.727150	+	0.686479i	$0.240845\pi$
$384$	6.96498e152	0.118908
$385$	1.06742e154	1.56107
$386$	−4.39519e153	−0.550849
$387$	9.44869e152	0.101524
$388$	−1.17815e154	−1.08571
$389$	1.83617e154	1.45181	0.725907	−	0.687793i	$-0.241420\pi$
$389$	1.83617e154	1.45181	0.725907	+	0.687793i	$0.241420\pi$
$390$	6.25719e152	0.0424654
$391$	−4.14954e153	−0.241815
$392$	−4.68945e153	−0.234748
$393$	2.56409e152	0.0110300
$394$	6.37522e153	0.235760
$395$	−3.36484e154	−1.07013
$396$	−5.34632e154	−1.46282
$397$	4.80840e152	0.0113231	0.00566155	−	0.999984i	$-0.498198\pi$
$397$	4.80840e152	0.0113231	0.00566155	+	0.999984i	$0.498198\pi$
$398$	4.16743e153	0.0844939
$399$	1.49843e154	0.261667
$400$	−1.51513e154	−0.227971
$401$	−3.49075e154	−0.452719	−0.226360	−	0.974044i	$-0.572682\pi$
$401$	−3.49075e154	−0.452719	−0.226360	+	0.974044i	$0.572682\pi$
$402$	−6.11420e152	−0.00683737
$403$	1.89403e155	1.82699
$404$	−1.29192e155	−1.07534
$405$	1.03799e155	0.745794
$406$	1.84412e154	0.114417
$407$	2.22729e155	1.19374
$408$	3.29249e153	0.0152491
$409$	−2.69768e155	−1.08007	−0.540037	−	0.841641i	$-0.681590\pi$
$409$	−2.69768e155	−1.08007	−0.540037	+	0.841641i	$0.681590\pi$
$410$	9.10952e153	0.0315396
$411$	3.27036e154	0.0979507
$412$	2.88073e155	0.746652
$413$	1.90830e154	0.0428172
$414$	2.58494e155	0.502262
$415$	2.05652e155	0.346155
$416$	−7.79015e155	−1.13630
$417$	−9.74055e154	−0.123165
$418$	−1.19122e156	−1.30618
$419$	−7.75813e155	−0.737943	−0.368971	−	0.929441i	$-0.620290\pi$
$419$	−7.75813e155	−0.737943	−0.368971	+	0.929441i	$0.620290\pi$
$420$	−1.07875e155	−0.0890406
$421$	2.22649e156	1.59528	0.797639	−	0.603135i	$-0.206082\pi$
$421$	2.22649e156	1.59528	0.797639	+	0.603135i	$0.206082\pi$
$422$	3.58429e155	0.223004
$423$	−3.07077e156	−1.65957
$424$	1.05045e156	0.493294
$425$	−1.77448e155	−0.0724318
$426$	−2.92575e154	−0.0103840
$427$	−2.15786e156	−0.666140
$428$	4.35683e156	1.17022
$429$	−1.05578e156	−0.246812
$430$	−1.51562e155	−0.0308473
$431$	5.17246e156	0.916853	0.458426	−	0.888732i	$-0.348413\pi$
$431$	5.17246e156	0.916853	0.458426	+	0.888732i	$0.348413\pi$
$432$	8.64974e155	0.133573
$433$	9.47774e156	1.27548	0.637742	−	0.770250i	$-0.279869\pi$
$433$	9.47774e156	1.27548	0.637742	+	0.770250i	$0.279869\pi$
$434$	5.70019e156	0.668730
$435$	2.28313e155	0.0233572
$436$	4.05328e156	0.361710
$437$	−3.29931e157	−2.56908
$438$	−3.22172e154	−0.00218967
$439$	−6.50172e156	−0.385824	−0.192912	−	0.981216i	$-0.561793\pi$
$439$	−6.50172e156	−0.385824	−0.192912	+	0.981216i	$0.561793\pi$
$440$	1.86487e157	0.966525
$441$	−7.16481e156	−0.324421
$442$	−2.16561e156	−0.0856949
$443$	−5.05369e157	−1.74818	−0.874092	−	0.485761i	$-0.838543\pi$
$443$	−5.05369e157	−1.74818	−0.874092	+	0.485761i	$0.838543\pi$
$444$	−2.25093e156	−0.0680888
$445$	2.24490e157	0.593985
$446$	7.09576e156	0.164276
$447$	−7.53899e155	−0.0152762
$448$	1.39986e157	0.248338
$449$	−4.47728e157	−0.695596	−0.347798	−	0.937569i	$-0.613071\pi$
$449$	−4.47728e157	−0.695596	−0.347798	+	0.937569i	$0.613071\pi$
$450$	1.10541e157	0.150445
$451$	−1.53706e157	−0.183310
$452$	1.21260e158	1.26760
$453$	1.56109e157	0.143082
$454$	1.81837e157	0.146171
$455$	1.54294e158	1.08810
$456$	2.61787e157	0.162010
$457$	−7.52691e157	−0.408887	−0.204443	−	0.978878i	$-0.565538\pi$
$457$	−7.52691e157	−0.408887	−0.204443	+	0.978878i	$0.565538\pi$
$458$	−9.22585e157	−0.440058
$459$	1.01304e157	0.0424395
$460$	2.37524e158	0.874211
$461$	−4.74098e158	−1.53343	−0.766714	−	0.641989i	$-0.778110\pi$
$461$	−4.74098e158	−1.53343	−0.766714	+	0.641989i	$0.778110\pi$
$462$	−3.17745e157	−0.0903403
$463$	3.13898e158	0.784729	0.392365	−	0.919810i	$-0.371657\pi$
$463$	3.13898e158	0.784729	0.392365	+	0.919810i	$0.371657\pi$
$464$	−6.74699e157	−0.148351
$465$	7.05720e157	0.136515
$466$	−3.25909e158	−0.554797
$467$	−2.65343e158	−0.397606	−0.198803	−	0.980039i	$-0.563705\pi$
$467$	−2.65343e158	−0.397606	−0.198803	+	0.980039i	$0.563705\pi$
$468$	−7.72803e158	−1.01962
$469$	−1.50768e158	−0.175196
$470$	4.92568e158	0.504247
$471$	−7.17731e157	−0.0647467
$472$	3.33395e157	0.0265100
$473$	2.55733e158	0.179287
$474$	1.00163e158	0.0619294
$475$	−1.41090e159	−0.769529
$476$	3.73355e158	0.179683
$477$	1.60493e159	0.681731
$478$	1.47444e159	0.552927
$479$	3.91769e159	1.29738	0.648690	−	0.761053i	$-0.275317\pi$
$479$	3.91769e159	1.29738	0.648690	+	0.761053i	$0.275317\pi$
$480$	−2.90263e158	−0.0849061
$481$	3.21952e159	0.832067
$482$	−2.12112e158	−0.0484471
$483$	−8.80059e158	−0.177688
$484$	−9.70114e159	−1.73190
$485$	6.27877e159	0.991383
$486$	−9.48765e158	−0.132526
$487$	−1.76831e159	−0.218568	−0.109284	−	0.994011i	$-0.534856\pi$
$487$	−1.76831e159	−0.218568	−0.109284	+	0.994011i	$0.534856\pi$
$488$	−3.76995e159	−0.412436
$489$	−8.49629e157	−0.00822910
$490$	1.14928e159	0.0985729
$491$	−1.76772e160	−1.34296	−0.671481	−	0.741021i	$-0.734342\pi$
$491$	−1.76772e160	−1.34296	−0.671481	+	0.741021i	$0.734342\pi$
$492$	1.55338e158	0.0104557
$493$	−7.90191e158	−0.0471347
$494$	−1.72188e160	−0.910439
$495$	2.84925e160	1.33574
$496$	−2.08550e160	−0.867065
$497$	−7.21451e159	−0.266073
$498$	−6.12176e158	−0.0200323
$499$	5.62803e160	1.63446	0.817229	−	0.576313i	$-0.195509\pi$
$499$	5.62803e160	1.63446	0.817229	+	0.576313i	$0.195509\pi$
$500$	3.58310e160	0.923728
$501$	3.30496e159	0.0756522
$502$	−2.01643e160	−0.409933
$503$	5.97237e159	0.107858	0.0539289	−	0.998545i	$-0.482826\pi$
$503$	5.97237e159	0.107858	0.0539289	+	0.998545i	$0.482826\pi$
$504$	−5.05761e160	−0.811574
$505$	6.88510e160	0.981914
$506$	6.99626e160	0.886972
$507$	−4.90877e159	−0.0553349
$508$	−1.00302e161	−1.00558
$509$	−5.00382e160	−0.446265	−0.223133	−	0.974788i	$-0.571628\pi$
$509$	−5.00382e160	−0.446265	−0.223133	+	0.974788i	$0.571628\pi$
$510$	−8.06913e158	−0.00640326
$511$	−7.94432e159	−0.0561065
$512$	1.51194e161	0.950542
$513$	8.05470e160	0.450885
$514$	−4.15531e160	−0.207156
$515$	−1.53524e161	−0.681785
$516$	−2.58447e159	−0.0102262
$517$	−8.31117e161	−2.93072
$518$	9.68934e160	0.304560
$519$	1.70030e160	0.0476504
$520$	2.69563e161	0.673692
$521$	1.83893e161	0.409940	0.204970	−	0.978768i	$-0.434290\pi$
$521$	1.83893e161	0.409940	0.204970	+	0.978768i	$0.434290\pi$
$522$	4.92247e160	0.0979012
$523$	3.00597e161	0.533500	0.266750	−	0.963766i	$-0.414050\pi$
$523$	3.00597e161	0.533500	0.266750	+	0.963766i	$0.414050\pi$
$524$	5.07975e160	0.0804693
$525$	−3.76342e160	−0.0532236
$526$	1.50036e161	0.189471
$527$	−2.44249e161	−0.275487
$528$	1.16252e161	0.117134
$529$	8.27012e161	0.744559
$530$	−2.57440e161	−0.207139
$531$	5.09379e160	0.0366368
$532$	2.96856e162	1.90899
$533$	−2.22180e161	−0.127772
$534$	−6.68251e160	−0.0343744
$535$	−2.32191e162	−1.06855
$536$	−2.63403e161	−0.108472
$537$	−2.22645e161	−0.0820621
$538$	−7.81502e161	−0.257861
$539$	−1.93919e162	−0.572913
$540$	−5.79873e161	−0.153428
$541$	−4.57365e162	−1.08399	−0.541995	−	0.840382i	$-0.682331\pi$
$541$	−4.57365e162	−1.08399	−0.541995	+	0.840382i	$0.682331\pi$
$542$	−8.72532e161	−0.185278
$543$	−3.00053e161	−0.0570963
$544$	1.00460e162	0.171340
$545$	−2.16014e162	−0.330286
$546$	−4.59296e161	−0.0629695
$547$	9.70288e162	1.19304	0.596519	−	0.802599i	$-0.296550\pi$
$547$	9.70288e162	1.19304	0.596519	+	0.802599i	$0.296550\pi$
$548$	6.47895e162	0.714597
$549$	−5.75995e162	−0.569986
$550$	2.99183e162	0.265679
$551$	−6.28284e162	−0.500768
$552$	−1.53753e162	−0.110014
$553$	2.46989e163	1.58684
$554$	5.56043e162	0.320832
$555$	1.19960e162	0.0621734
$556$	−1.92971e163	−0.898549
$557$	7.19132e162	0.300902	0.150451	−	0.988617i	$-0.451927\pi$
$557$	7.19132e162	0.300902	0.150451	+	0.988617i	$0.451927\pi$
$558$	1.52154e163	0.572202
$559$	3.69658e162	0.124968
$560$	−1.69893e163	−0.516400
$561$	1.36152e162	0.0372163
$562$	−2.32013e163	−0.570428
$563$	2.30981e163	0.510889	0.255445	−	0.966824i	$-0.417778\pi$
$563$	2.30981e163	0.510889	0.255445	+	0.966824i	$0.417778\pi$
$564$	8.39938e162	0.167163
$565$	−6.46240e163	−1.15747
$566$	−4.44700e162	−0.0716951
$567$	−7.61914e163	−1.10589
$568$	−1.26043e163	−0.164738
$569$	1.18612e164	1.39621	0.698103	−	0.715997i	$-0.254028\pi$
$569$	1.18612e164	1.39621	0.698103	+	0.715997i	$0.254028\pi$
$570$	−6.41580e162	−0.0680294
$571$	2.91534e163	0.278510	0.139255	−	0.990257i	$-0.455529\pi$
$571$	2.91534e163	0.278510	0.139255	+	0.990257i	$0.455529\pi$
$572$	−2.09163e164	−1.80061
$573$	5.27103e162	0.0408973
$574$	−6.68665e162	−0.0467682
$575$	8.28647e163	0.522556
$576$	3.73663e163	0.212492
$577$	3.12659e164	1.60365	0.801825	−	0.597559i	$-0.203863\pi$
$577$	3.12659e164	1.60365	0.801825	+	0.597559i	$0.203863\pi$
$578$	−8.05272e163	−0.372594
$579$	3.99423e163	0.166747
$580$	4.52314e163	0.170402
$581$	−1.50954e164	−0.513294
$582$	−1.86904e163	−0.0573721
$583$	4.34382e164	1.20391
$584$	−1.38793e163	−0.0347380
$585$	4.11854e164	0.931042
$586$	8.75242e163	0.178739
$587$	4.47953e162	0.00826544	0.00413272	−	0.999991i	$-0.498685\pi$
$587$	4.47953e162	0.00826544	0.00413272	+	0.999991i	$0.498685\pi$
$588$	1.95977e163	0.0326779
$589$	−1.94204e165	−2.92683
$590$	−8.17073e162	−0.0111318
$591$	−5.79364e163	−0.0713668
$592$	−3.54500e164	−0.394888
$593$	2.88330e164	0.290493	0.145247	−	0.989395i	$-0.453602\pi$
$593$	2.88330e164	0.290493	0.145247	+	0.989395i	$0.453602\pi$
$594$	−1.70801e164	−0.155668
$595$	−1.98974e164	−0.164073
$596$	−1.49356e164	−0.111447
$597$	−3.78725e163	−0.0255771
$598$	1.01130e165	0.618242
$599$	4.83882e164	0.267820	0.133910	−	0.990993i	$-0.457247\pi$
$599$	4.83882e164	0.267820	0.133910	+	0.990993i	$0.457247\pi$
$600$	−6.57499e163	−0.0329531
$601$	−2.03139e165	−0.922065	−0.461032	−	0.887383i	$-0.652521\pi$
$601$	−2.03139e165	−0.922065	−0.461032	+	0.887383i	$0.652521\pi$
$602$	1.11251e164	0.0457417
$603$	−4.02442e164	−0.149908
$604$	3.09269e165	1.04385
$605$	5.17008e165	1.58144
$606$	−2.04953e164	−0.0568241
$607$	−4.24683e165	−1.06743	−0.533713	−	0.845666i	$-0.679204\pi$
$607$	−4.24683e165	−1.06743	−0.533713	+	0.845666i	$0.679204\pi$
$608$	7.98762e165	1.82035
$609$	−1.67589e164	−0.0346350
$610$	9.23928e164	0.173186
$611$	−1.20137e166	−2.04279
$612$	9.96589e164	0.153747
$613$	1.03660e166	1.45115	0.725577	−	0.688141i	$-0.241573\pi$
$613$	1.03660e166	1.45115	0.725577	+	0.688141i	$0.241573\pi$
$614$	−3.07657e165	−0.390884
$615$	−8.27850e163	−0.00954733
$616$	−1.36886e166	−1.43320
$617$	−1.11204e166	−1.05719	−0.528597	−	0.848873i	$-0.677282\pi$
$617$	−1.11204e166	−1.05719	−0.528597	+	0.848873i	$0.677282\pi$
$618$	4.57005e164	0.0394554
$619$	7.37915e165	0.578646	0.289323	−	0.957232i	$-0.406570\pi$
$619$	7.37915e165	0.578646	0.289323	+	0.957232i	$0.406570\pi$
$620$	1.39811e166	0.995945
$621$	−4.73069e165	−0.306178
$622$	4.33620e165	0.255024
$623$	−1.64782e166	−0.880786
$624$	1.68041e165	0.0816453
$625$	−1.01389e166	−0.447846
$626$	−1.52152e166	−0.611089
$627$	1.08255e166	0.395392
$628$	−1.42190e166	−0.472358
$629$	−4.15182e165	−0.125466
$630$	1.23950e166	0.340788
$631$	5.36523e166	1.34227	0.671137	−	0.741333i	$-0.265806\pi$
$631$	5.36523e166	1.34227	0.671137	+	0.741333i	$0.265806\pi$
$632$	4.31509e166	0.982479
$633$	−3.25731e165	−0.0675054
$634$	−1.61212e165	−0.0304148
$635$	5.34545e166	0.918222
$636$	−4.38993e165	−0.0686687
$637$	−2.80307e166	−0.399335
$638$	1.33229e166	0.172889
$639$	−1.92576e166	−0.227667
$640$	−7.35365e166	−0.792127
$641$	7.59401e165	0.0745450	0.0372725	−	0.999305i	$-0.488133\pi$
$641$	7.59401e165	0.0745450	0.0372725	+	0.999305i	$0.488133\pi$
$642$	6.91177e165	0.0618379
$643$	1.48555e167	1.21153	0.605764	−	0.795644i	$-0.292867\pi$
$643$	1.48555e167	1.21153	0.605764	+	0.795644i	$0.292867\pi$
$644$	−1.74349e167	−1.29632
$645$	1.37736e165	0.00933779
$646$	2.22050e166	0.137283
$647$	−2.96523e167	−1.67207	−0.836035	−	0.548677i	$-0.815132\pi$
$647$	−2.96523e167	−1.67207	−0.836035	+	0.548677i	$0.815132\pi$
$648$	−1.33112e167	−0.684707
$649$	1.37866e166	0.0646990
$650$	4.32464e166	0.185185
$651$	−5.18019e166	−0.202431
$652$	−1.68321e166	−0.0600352
$653$	3.77075e167	1.22770	0.613852	−	0.789421i	$-0.289619\pi$
$653$	3.77075e167	1.22770	0.613852	+	0.789421i	$0.289619\pi$
$654$	6.43022e165	0.0191139
$655$	−2.70718e166	−0.0734783
$656$	2.44642e166	0.0606390
$657$	−2.12056e166	−0.0480078
$658$	−3.61559e167	−0.747719
$659$	1.02347e168	1.93372	0.966862	−	0.255300i	$-0.0821743\pi$
$659$	1.02347e168	1.93372	0.966862	+	0.255300i	$0.0821743\pi$
$660$	−7.79347e166	−0.134545
$661$	8.93385e167	1.40946	0.704728	−	0.709477i	$-0.251069\pi$
$661$	8.93385e167	1.40946	0.704728	+	0.709477i	$0.251069\pi$
$662$	3.41882e166	0.0492976
$663$	1.96805e166	0.0259407
$664$	−2.63729e167	−0.317802
$665$	−1.58205e168	−1.74314
$666$	2.58636e167	0.260599
$667$	3.69004e167	0.340051
$668$	6.54749e167	0.551919
$669$	−6.44844e166	−0.0497280
$670$	6.45539e166	0.0455483
$671$	−1.55896e168	−1.00657
$672$	2.13062e167	0.125902
$673$	−6.50909e167	−0.352066	−0.176033	−	0.984384i	$-0.556326\pi$
$673$	−6.50909e167	−0.352066	−0.176033	+	0.984384i	$0.556326\pi$
$674$	−7.98348e167	−0.395301
$675$	−2.02300e167	−0.0917109
$676$	−9.72482e167	−0.403695
$677$	2.61302e168	0.993382	0.496691	−	0.867927i	$-0.334548\pi$
$677$	2.61302e168	0.993382	0.496691	+	0.867927i	$0.334548\pi$
$678$	1.92370e167	0.0669839
$679$	−4.60880e168	−1.47006
$680$	−3.47623e167	−0.101585
$681$	−1.65249e167	−0.0442472
$682$	4.11812e168	1.01048
$683$	−3.95391e168	−0.889190	−0.444595	−	0.895732i	$-0.646652\pi$
$683$	−3.95391e168	−0.889190	−0.444595	+	0.895732i	$0.646652\pi$
$684$	7.92392e168	1.63344
$685$	−3.45286e168	−0.652515
$686$	1.72132e168	0.298247
$687$	8.38422e167	0.133210
$688$	−4.07029e167	−0.0593080
$689$	6.27893e168	0.839154
$690$	3.76813e167	0.0461960
$691$	1.24460e169	1.39986	0.699932	−	0.714209i	$-0.253213\pi$
$691$	1.24460e169	1.39986	0.699932	+	0.714209i	$0.253213\pi$
$692$	3.36847e168	0.347633
$693$	−2.09143e169	−1.98069
$694$	−3.88261e168	−0.337470
$695$	1.02841e169	0.820485
$696$	−2.92790e167	−0.0214440
$697$	2.86518e167	0.0192665
$698$	−2.66798e167	−0.0164735
$699$	2.96177e168	0.167942
$700$	−7.45576e168	−0.388292
$701$	−8.71378e168	−0.416855	−0.208427	−	0.978038i	$-0.566834\pi$
$701$	−8.71378e168	−0.416855	−0.208427	+	0.978038i	$0.566834\pi$
$702$	−2.46891e168	−0.108504
$703$	−3.30113e169	−1.33297
$704$	1.01134e169	0.375251
$705$	−4.47633e168	−0.152640
$706$	3.46990e168	0.108752
$707$	−5.05386e169	−1.45602
$708$	−1.39329e167	−0.00369031
$709$	−1.73891e168	−0.0423473	−0.0211737	−	0.999776i	$-0.506740\pi$
$709$	−1.73891e168	−0.0423473	−0.0211737	+	0.999776i	$0.506740\pi$
$710$	3.08902e168	0.0691749
$711$	6.59283e169	1.35778
$712$	−2.87886e169	−0.545333
$713$	1.14060e170	1.98749
$714$	5.92298e167	0.00949503
$715$	1.11470e170	1.64418
$716$	−4.41084e169	−0.598682
$717$	−1.33993e169	−0.167376
$718$	−2.52235e169	−0.290002
$719$	−1.25283e170	−1.32594	−0.662970	−	0.748646i	$-0.730704\pi$
$719$	−1.25283e170	−1.32594	−0.662970	+	0.748646i	$0.730704\pi$
$720$	−4.53491e169	−0.441861
$721$	1.12691e170	1.01098
$722$	1.29887e170	1.07300
$723$	1.92762e168	0.0146654
$724$	−5.94438e169	−0.416545
$725$	1.57798e169	0.101857
$726$	−1.53901e169	−0.0915192
$727$	2.43071e169	0.133179	0.0665894	−	0.997780i	$-0.478788\pi$
$727$	2.43071e169	0.133179	0.0665894	+	0.997780i	$0.478788\pi$
$728$	−1.97867e170	−0.998980
$729$	−1.97562e170	−0.919212
$730$	3.40150e168	0.0145868
$731$	−4.76703e168	−0.0188436
$732$	1.57550e169	0.0574130
$733$	−7.66498e169	−0.257528	−0.128764	−	0.991675i	$-0.541101\pi$
$733$	−7.66498e169	−0.257528	−0.128764	+	0.991675i	$0.541101\pi$
$734$	1.53523e170	0.475618
$735$	−1.04443e169	−0.0298390
$736$	−4.69129e170	−1.23612
$737$	−1.08923e170	−0.264730
$738$	−1.78486e169	−0.0400175
$739$	6.17242e170	1.27677	0.638383	−	0.769719i	$-0.279604\pi$
$739$	6.17242e170	1.27677	0.638383	+	0.769719i	$0.279604\pi$
$740$	2.37654e170	0.453585
$741$	1.56480e170	0.275598
$742$	1.88968e170	0.307154
$743$	6.71239e169	0.100703	0.0503516	−	0.998732i	$-0.483966\pi$
$743$	6.71239e169	0.100703	0.0503516	+	0.998732i	$0.483966\pi$
$744$	−9.05019e169	−0.125334
$745$	7.95970e169	0.101765
$746$	−4.30133e170	−0.507741
$747$	−4.02940e170	−0.439202
$748$	2.69731e170	0.271510
$749$	1.70435e171	1.58449
$750$	5.68431e169	0.0488126
$751$	−6.94530e170	−0.550953	−0.275477	−	0.961308i	$-0.588836\pi$
$751$	−6.94530e170	−0.550953	−0.275477	+	0.961308i	$0.588836\pi$
$752$	1.32282e171	0.969481
$753$	1.83248e170	0.124091
$754$	1.92580e170	0.120508
$755$	−1.64821e171	−0.953164
$756$	4.25644e170	0.227509
$757$	−2.49006e171	−1.23029	−0.615143	−	0.788416i	$-0.710902\pi$
$757$	−2.49006e171	−1.23029	−0.615143	+	0.788416i	$0.710902\pi$
$758$	1.00585e171	0.459428
$759$	−6.35802e170	−0.268495
$760$	−2.76396e171	−1.07925
$761$	−2.59213e171	−0.935988	−0.467994	−	0.883732i	$-0.655023\pi$
$761$	−2.59213e171	−0.935988	−0.467994	+	0.883732i	$0.655023\pi$
$762$	−1.59121e170	−0.0531382
$763$	1.58560e171	0.489762
$764$	1.04425e171	0.298366
$765$	−5.31118e170	−0.140390
$766$	2.29249e171	0.560656
$767$	1.99283e170	0.0450968
$768$	9.88515e169	0.0207010
$769$	−9.02982e171	−1.75010	−0.875048	−	0.484036i	$-0.839170\pi$
$769$	−9.02982e171	−1.75010	−0.875048	+	0.484036i	$0.839170\pi$
$770$	3.35477e171	0.601817
$771$	3.77624e170	0.0627082
$772$	7.91301e171	1.21650
$773$	1.05349e172	1.49951	0.749755	−	0.661715i	$-0.230171\pi$
$773$	1.05349e172	1.49951	0.749755	+	0.661715i	$0.230171\pi$
$774$	2.96960e170	0.0391392
$775$	4.87757e171	0.595322
$776$	−8.05193e171	−0.910180
$777$	−8.80543e170	−0.0921934
$778$	5.77085e171	0.559698
$779$	2.27812e171	0.204690
$780$	−1.12653e171	−0.0937811
$781$	−5.21215e171	−0.402050
$782$	−1.30415e171	−0.0932233
$783$	−9.00859e170	−0.0596805
$784$	3.08645e171	0.189519
$785$	7.57783e171	0.431321
$786$	8.05861e169	0.00425225
$787$	−3.95045e172	−1.93264	−0.966318	−	0.257352i	$-0.917150\pi$
$787$	−3.95045e172	−1.93264	−0.966318	+	0.257352i	$0.917150\pi$
$788$	−1.14778e172	−0.520655
$789$	−1.36349e171	−0.0573547
$790$	−1.05753e172	−0.412553
$791$	4.74359e172	1.71635
$792$	−3.65389e172	−1.22633
$793$	−2.25345e172	−0.701605
$794$	1.51122e170	0.00436523
$795$	2.33955e171	0.0627030
$796$	−7.50296e171	−0.186597
$797$	8.39543e172	1.93764	0.968819	−	0.247769i	$-0.0796973\pi$
$797$	8.39543e172	1.93764	0.968819	+	0.247769i	$0.0796973\pi$
$798$	4.70938e171	0.100877
$799$	1.54925e172	0.308028
$800$	−2.00615e172	−0.370262
$801$	−4.39849e172	−0.753649
$802$	−1.09710e172	−0.174530
$803$	−5.73940e171	−0.0847797
$804$	1.10079e171	0.0150997
$805$	9.29170e172	1.18370
$806$	5.95268e172	0.704332
$807$	7.10209e171	0.0780569
$808$	−8.82948e172	−0.901487
$809$	1.01606e173	0.963792	0.481896	−	0.876228i	$-0.339948\pi$
$809$	1.01606e173	0.963792	0.481896	+	0.876228i	$0.339948\pi$
$810$	3.26227e172	0.287515
$811$	−4.64766e172	−0.380621	−0.190311	−	0.981724i	$-0.560950\pi$
$811$	−4.64766e172	−0.380621	−0.190311	+	0.981724i	$0.560950\pi$
$812$	−3.32012e172	−0.252679
$813$	7.92935e171	0.0560854
$814$	7.00010e172	0.460206
$815$	8.97042e171	0.0548195
$816$	−2.16701e171	−0.0123111
$817$	−3.79028e172	−0.200198
$818$	−8.47847e172	−0.416386
$819$	−3.02313e173	−1.38059
$820$	−1.64006e172	−0.0696524
$821$	−3.66204e173	−1.44646	−0.723228	−	0.690609i	$-0.757342\pi$
$821$	−3.66204e173	−1.44646	−0.723228	+	0.690609i	$0.757342\pi$
$822$	1.02783e172	0.0377616
$823$	4.04144e172	0.138116	0.0690582	−	0.997613i	$-0.478001\pi$
$823$	4.04144e172	0.138116	0.0690582	+	0.997613i	$0.478001\pi$
$824$	1.96880e173	0.625941
$825$	−2.71890e172	−0.0804235
$826$	5.99755e171	0.0165067
$827$	7.61381e173	1.94995	0.974977	−	0.222307i	$-0.0713588\pi$
$827$	7.61381e173	1.94995	0.974977	+	0.222307i	$0.0713588\pi$
$828$	−4.65388e173	−1.10920
$829$	−1.75082e173	−0.388371	−0.194186	−	0.980965i	$-0.562206\pi$
$829$	−1.75082e173	−0.388371	−0.194186	+	0.980965i	$0.562206\pi$
$830$	6.46338e172	0.133448
$831$	−5.05318e172	−0.0971189
$832$	1.46187e173	0.261559
$833$	3.61477e172	0.0602148
$834$	−3.06133e172	−0.0474821
$835$	−3.48939e173	−0.503969
$836$	2.14465e174	2.88458
$837$	−2.78457e173	−0.348813
$838$	−2.43828e173	−0.284489
$839$	9.01539e173	0.979823	0.489912	−	0.871772i	$-0.337029\pi$
$839$	9.01539e173	0.979823	0.489912	+	0.871772i	$0.337029\pi$
$840$	−7.37260e172	−0.0746454
$841$	−9.89867e173	−0.933717
$842$	6.99759e173	0.615005
$843$	2.10847e173	0.172674
$844$	−6.45309e173	−0.492484
$845$	5.18270e173	0.368623
$846$	−9.65103e173	−0.639789
$847$	−3.79499e174	−2.34503
$848$	−6.91371e173	−0.398252
$849$	4.04132e172	0.0217028
$850$	−5.57696e172	−0.0279236
$851$	1.93882e174	0.905166
$852$	5.26747e172	0.0229322
$853$	1.61870e174	0.657201	0.328601	−	0.944469i	$-0.393423\pi$
$853$	1.61870e174	0.657201	0.328601	+	0.944469i	$0.393423\pi$
$854$	−6.78190e173	−0.256808
$855$	−4.22294e174	−1.49153
$856$	2.97763e174	0.981028
$857$	8.97385e173	0.275816	0.137908	−	0.990445i	$-0.455962\pi$
$857$	8.97385e173	0.275816	0.137908	+	0.990445i	$0.455962\pi$
$858$	−3.31820e173	−0.0951500
$859$	−2.47533e174	−0.662279	−0.331139	−	0.943582i	$-0.607433\pi$
$859$	−2.47533e174	−0.662279	−0.331139	+	0.943582i	$0.607433\pi$
$860$	2.72870e173	0.0681236
$861$	6.07665e172	0.0141572
$862$	1.62564e174	0.353461
$863$	5.66242e174	1.14911	0.574553	−	0.818468i	$-0.305176\pi$
$863$	5.66242e174	1.14911	0.574553	+	0.818468i	$0.305176\pi$
$864$	1.14530e174	0.216945
$865$	−1.79518e174	−0.317431
$866$	2.97873e174	0.491719
$867$	7.31810e173	0.112788
$868$	−1.02625e175	−1.47683
$869$	1.78438e175	2.39779
$870$	7.17560e172	0.00900457
$871$	−1.57446e174	−0.184524
$872$	2.77017e174	0.303233
$873$	−1.23022e175	−1.25787
$874$	−1.03693e175	−0.990422
$875$	1.40167e175	1.25074
$876$	5.80032e172	0.00483568
$877$	2.29628e174	0.178874	0.0894372	−	0.995992i	$-0.471493\pi$
$877$	2.29628e174	0.178874	0.0894372	+	0.995992i	$0.471493\pi$
$878$	−2.04341e174	−0.148741
$879$	−7.95398e173	−0.0541061
$880$	−1.22739e175	−0.780306
$881$	−2.82242e175	−1.67708	−0.838542	−	0.544836i	$-0.816592\pi$
$881$	−2.82242e175	−1.67708	−0.838542	+	0.544836i	$0.816592\pi$
$882$	−2.25181e174	−0.125069
$883$	2.71910e175	1.41177	0.705883	−	0.708329i	$-0.250550\pi$
$883$	2.71910e175	1.41177	0.705883	+	0.708329i	$0.250550\pi$
$884$	3.89892e174	0.189250
$885$	7.42535e172	0.00336971
$886$	−1.58831e175	−0.673952
$887$	1.15838e175	0.459618	0.229809	−	0.973236i	$-0.426190\pi$
$887$	1.15838e175	0.459618	0.229809	+	0.973236i	$0.426190\pi$
$888$	−1.53838e174	−0.0570809
$889$	−3.92372e175	−1.36158
$890$	7.05542e174	0.228991
$891$	−5.50447e175	−1.67106
$892$	−1.27751e175	−0.362789
$893$	1.23182e176	3.27254
$894$	−2.36941e173	−0.00588922
$895$	2.35069e175	0.546670
$896$	5.39779e175	1.17460
$897$	−9.19041e174	−0.187148
$898$	−1.40715e175	−0.268163
$899$	2.17203e175	0.387403
$900$	−1.99015e175	−0.332244
$901$	−8.09717e174	−0.126534
$902$	−4.83079e174	−0.0706691
$903$	−1.01102e174	−0.0138465
$904$	8.28741e175	1.06267
$905$	3.16797e175	0.380357
$906$	4.90631e174	0.0551604
$907$	−9.99338e175	−1.05215	−0.526076	−	0.850437i	$-0.676337\pi$
$907$	−9.99338e175	−1.05215	−0.526076	+	0.850437i	$0.676337\pi$
$908$	−3.27377e175	−0.322805
$909$	−1.34902e176	−1.24585
$910$	4.84926e175	0.419482
$911$	−8.61932e175	−0.698440	−0.349220	−	0.937041i	$-0.613553\pi$
$911$	−8.61932e175	−0.698440	−0.349220	+	0.937041i	$0.613553\pi$
$912$	−1.72300e175	−0.130795
$913$	−1.09058e176	−0.775612
$914$	−2.36561e175	−0.157632
$915$	−8.39642e174	−0.0524251
$916$	1.66101e176	0.971830
$917$	1.98715e175	0.108957
$918$	3.18385e174	0.0163611
$919$	−1.35446e176	−0.652371	−0.326185	−	0.945306i	$-0.605763\pi$
$919$	−1.35446e176	−0.652371	−0.326185	+	0.945306i	$0.605763\pi$
$920$	1.62333e176	0.732877
$921$	2.79591e175	0.118324
$922$	−1.49003e176	−0.591161
$923$	−7.53408e175	−0.280239
$924$	5.72063e175	0.199509
$925$	8.29103e175	0.271129
$926$	9.86543e175	0.302526
$927$	3.00805e176	0.865049
$928$	−8.93357e175	−0.240946
$929$	6.69140e175	0.169271	0.0846354	−	0.996412i	$-0.473027\pi$
$929$	6.69140e175	0.169271	0.0846354	+	0.996412i	$0.473027\pi$
$930$	2.21799e175	0.0526289
$931$	2.87412e176	0.639733
$932$	5.86760e176	1.22522
$933$	−3.94063e175	−0.0771984
$934$	−8.33938e175	−0.153283
$935$	−1.43750e176	−0.247922
$936$	−5.28163e176	−0.854782
$937$	−3.51567e176	−0.533952	−0.266976	−	0.963703i	$-0.586024\pi$
$937$	−3.51567e176	−0.533952	−0.266976	+	0.963703i	$0.586024\pi$
$938$	−4.73845e175	−0.0675409
$939$	1.38272e176	0.184983
$940$	−8.86810e176	−1.11358
$941$	8.56490e176	1.00958	0.504789	−	0.863243i	$-0.331570\pi$
$941$	8.56490e176	1.00958	0.504789	+	0.863243i	$0.331570\pi$
$942$	−2.25574e175	−0.0249609
$943$	−1.33798e176	−0.138997
$944$	−2.19430e175	−0.0214024
$945$	−2.26841e176	−0.207744
$946$	8.03737e175	0.0691180
$947$	−8.57105e176	−0.692166	−0.346083	−	0.938204i	$-0.612488\pi$
$947$	−8.57105e176	−0.692166	−0.346083	+	0.938204i	$0.612488\pi$
$948$	−1.80332e176	−0.136766
$949$	−8.29621e175	−0.0590936
$950$	−4.43427e176	−0.296666
$951$	1.46505e175	0.00920686
$952$	2.55165e176	0.150634
$953$	3.37686e176	0.187277	0.0936387	−	0.995606i	$-0.470150\pi$
$953$	3.37686e176	0.187277	0.0936387	+	0.995606i	$0.470150\pi$
$954$	5.04410e176	0.262818
$955$	−5.56517e176	−0.272444
$956$	−2.65456e177	−1.22109
$957$	−1.21075e176	−0.0523352
$958$	1.23128e177	0.500161
$959$	2.53450e177	0.967577
$960$	5.44697e175	0.0195441
$961$	3.74865e177	1.26425
$962$	1.01185e177	0.320775
$963$	4.54939e177	1.35578
$964$	3.81884e176	0.106991
$965$	−4.21713e177	−1.11081
$966$	−2.76591e176	−0.0685014
$967$	4.88040e177	1.13653	0.568264	−	0.822846i	$-0.307615\pi$
$967$	4.88040e177	1.13653	0.568264	+	0.822846i	$0.307615\pi$
$968$	−6.63014e177	−1.45191
$969$	−2.01794e176	−0.0415569
$970$	1.97334e177	0.382194
$971$	−2.83596e177	−0.516602	−0.258301	−	0.966065i	$-0.583163\pi$
$971$	−2.83596e177	−0.516602	−0.258301	+	0.966065i	$0.583163\pi$
$972$	1.70814e177	0.292672
$973$	−7.54883e177	−1.21665
$974$	−5.55759e176	−0.0842614
$975$	−3.93013e176	−0.0560572
$976$	2.48126e177	0.332973
$977$	4.49416e177	0.567443	0.283721	−	0.958907i	$-0.408431\pi$
$977$	4.49416e177	0.567443	0.283721	+	0.958907i	$0.408431\pi$
$978$	−2.67028e175	−0.00317245
$979$	−1.19047e178	−1.33091
$980$	−2.06913e177	−0.217689
$981$	4.23243e177	0.419067
$982$	−5.55571e177	−0.517733
$983$	−1.99883e178	−1.75324	−0.876620	−	0.481184i	$-0.840207\pi$
$983$	−1.99883e178	−1.75324	−0.876620	+	0.481184i	$0.840207\pi$
$984$	1.06164e176	0.00876533
$985$	6.11694e177	0.475422
$986$	−2.48347e176	−0.0181712
$987$	3.28575e177	0.226342
$988$	3.10005e178	2.01062
$989$	2.22611e177	0.135946
$990$	8.95482e177	0.514948
$991$	2.43020e178	1.31601	0.658006	−	0.753013i	$-0.271400\pi$
$991$	2.43020e178	1.31601	0.658006	+	0.753013i	$0.271400\pi$
$992$	−2.76138e178	−1.40826
$993$	−3.10693e176	−0.0149229
$994$	−2.26743e177	−0.102576
$995$	3.99860e177	0.170386
$996$	1.10215e177	0.0442395
$997$	1.50168e178	0.567825	0.283912	−	0.958850i	$-0.408368\pi$
$997$	1.50168e178	0.567825	0.283912	+	0.958850i	$0.408368\pi$
$998$	1.76882e178	0.630109
$999$	−4.73329e177	−0.158861

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1.120.a.a.1.6	✓	10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1.120.a.a.1.6	✓	10	1.1	even	1	trivial

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:	\( k \)	\(=\)	\( 120 \)
Character orbit:	\([\chi]\)	\(=\)	1.a (trivial)

\(f(q)\)	\(=\)	\(q+3.14287e17 q^{2} -2.85616e27 q^{3} -5.65837e35 q^{4} +3.01555e41 q^{5} -8.97656e44 q^{6} -2.21350e50 q^{7} -3.86715e53 q^{8} -5.90846e56 q^{9} +O(q^{10})\)	\(q+3.14287e17 q^{2} -2.85616e27 q^{3} -5.65837e35 q^{4} +3.01555e41 q^{5} -8.97656e44 q^{6} -2.21350e50 q^{7} -3.86715e53 q^{8} -5.90846e56 q^{9} +9.47749e58 q^{10} -1.59915e62 q^{11} +1.61612e63 q^{12} -2.31155e66 q^{13} -6.95675e67 q^{14} -8.61290e68 q^{15} +2.54524e71 q^{16} +2.98092e72 q^{17} -1.85695e74 q^{18} +2.37014e76 q^{19} -1.70631e77 q^{20} +6.32212e77 q^{21} -5.02593e79 q^{22} -1.39203e81 q^{23} +1.10452e81 q^{24} -5.95279e82 q^{25} -7.26490e83 q^{26} +3.39840e84 q^{27} +1.25248e86 q^{28} -2.65083e86 q^{29} -2.70693e86 q^{30} -8.19375e88 q^{31} +3.37010e89 q^{32} +4.56744e89 q^{33} +9.36866e89 q^{34} -6.67492e91 q^{35} +3.34323e92 q^{36} -1.39280e93 q^{37} +7.44906e93 q^{38} +6.60216e93 q^{39} -1.16616e95 q^{40} +9.61174e94 q^{41} +1.98696e95 q^{42} -1.59918e96 q^{43} +9.04860e97 q^{44} -1.78172e98 q^{45} -4.37498e98 q^{46} +5.19724e99 q^{47} -7.26961e98 q^{48} +1.21264e100 q^{49} -1.87089e100 q^{50} -8.51400e99 q^{51} +1.30796e102 q^{52} -2.71633e102 q^{53} +1.06808e102 q^{54} -4.82232e103 q^{55} +8.55995e103 q^{56} -6.76951e103 q^{57} -8.33123e103 q^{58} -8.62119e103 q^{59} +4.87350e104 q^{60} +9.74865e105 q^{61} -2.57519e106 q^{62} +1.30784e107 q^{63} -6.32420e106 q^{64} -6.97058e107 q^{65} +1.43549e107 q^{66} +6.81129e107 q^{67} -1.68672e108 q^{68} +3.97587e108 q^{69} -2.09784e109 q^{70} +3.25932e109 q^{71} +2.28489e110 q^{72} +3.58903e109 q^{73} -4.37738e110 q^{74} +1.70021e110 q^{75} -1.34111e112 q^{76} +3.53972e112 q^{77} +2.07497e111 q^{78} -1.11583e113 q^{79} +7.67529e112 q^{80} +3.44212e113 q^{81} +3.02085e112 q^{82} +6.81972e113 q^{83} -3.57729e113 q^{84} +8.98911e113 q^{85} -5.02602e113 q^{86} +7.57121e113 q^{87} +6.18416e115 q^{88} +7.44440e115 q^{89} -5.59974e115 q^{90} +5.11661e116 q^{91} +7.87664e116 q^{92} +2.34027e116 q^{93} +1.63343e117 q^{94} +7.14728e117 q^{95} -9.62556e116 q^{96} +2.08213e118 q^{97} +3.81116e117 q^{98} +9.44852e118 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + 91\!\cdots\!00 q^{2}+ \cdots + 18\!\cdots\!70 q^{9}+O(q^{10}) \) 10 * q + 919932722605769400 * q^2 - 9570159827289248935296702600 * q^3 + 4272705896834573968338259309906185280 * q^4 + 606257200226243383006472566047160160843340 * q^5 + 36401504491894467383240980519952999483223273120 * q^6 - 219254218938377593670425814743273520801802467026000 * q^7 - 565565131741559483416651174475719665908207742245491200 * q^8 + 1834851904582599922503319964983981808160026773815306152370 * q^9	\( 10 q + 91\!\cdots\!00 q^{2}+ \cdots + 32\!\cdots\!40 q^{99}+O(q^{100}) \) 10 * q + 919932722605769400 * q^2 - 9570159827289248935296702600 * q^3 + 4272705896834573968338259309906185280 * q^4 + 606257200226243383006472566047160160843340 * q^5 + 36401504491894467383240980519952999483223273120 * q^6 - 219254218938377593670425814743273520801802467026000 * q^7 - 565565131741559483416651174475719665908207742245491200 * q^8 + 1834851904582599922503319964983981808160026773815306152370 * q^9 + 634986125367587740207204302796387131018009187401381869153040 * q^10 + 101699246725606790738835774661895063480820812124313881877201320 * q^11 - 38454913569966405167762742595438498566456999771452096076177235200 * q^12 - 1185748520257577664060559883259066024596136377436810629686687725700 * q^13 + 128663533898726556350640086194927332426384167007882730622864072285760 * q^14 - 3710554087524006716347381761626904165187860707894445603427280739742320 * q^15 + 1692157270872518872969972729913243365739971167225638932987297451499458560 * q^16 - 7864283005617688192060113380368906686779951730371226323040594773109948300 * q^17 + 332729677344108131883156941184784577100879720076210912205274121852966805400 * q^18 + 6933132543714084280010692900040098202807958189097871055544810749569091843800 * q^19 + 739362437091413007058366615825358922208924736756157332674630660292607013864320 * q^20 + 2956525867496139343216584028476962325502089413634709218759412375063065769235520 * q^21 + 182048505569729359245793025478209587997846812992510021821256296609773333925464800 * q^22 + 2899273707160329485617593679008001931087825074180318868634550223688404754013405200 * q^23 + 114076958190963694629504891381029963295654961523414627262670720636843992879159552000 * q^24 + 438494787182106380867327117170026697103640781467523702437104047242833362602352949350 * q^25 - 318317418521249562365279268571874153839124425225189223040103737098442975265906223280 * q^26 - 45551493493769742679374192788006036083495765633221136999776547459453349750382686446800 * q^27 - 523381565894005037423609946706950604481078110602387257868273228698395911628601559155200 * q^28 - 239780648672002576188201702569667845017734503354477933365275721637750281457865124433700 * q^29 + 21029395143482710334699445468847496946126462842956505426185423480948664554653809442982080 * q^30 + 160165221449158413670086721746271710279050125440150480736499480204572300135092293246793920 * q^31 - 834373398020641818369077524061840548626893881879494325415144208186283168678479622990233600 * q^32 - 3570238663181267586336948085267071808900587562867500514533738739767476967040829429822599200 * q^33 - 41095955432266996557490146601397116658486035720992194797885692480580962506776105495084173840 * q^34 + 138699704976096510485603716990768616767579130103693747880984703716174722976398003170335643040 * q^35 + 1968770682959423831661461799770758836110419126467351452806841613209828415998369150047869168960 * q^36 - 2929977505416183984446606444699920153402867583929450347729318630774282158879219717208971398900 * q^37 - 34132539768785031258064307777998769213197932649565990492157910428905434754702082210597346456800 * q^38 - 37083836176586549326655714409651173972060300017562592944355756464743632231154290665689117350960 * q^39 + 671451534852984850954224825661781753416230993956537124458730875650510059526361261848342923494400 * q^40 + 2514540111291426044482406571860470483406800557710096621771586537326874081984886304684316806834820 * q^41 - 15273274580038512441282769157227926832173790524876405090470612324607958771986447522111977427436800 * q^42 + 3044753550753493053954517812078986490614702618943897995955026804229546439117864461911484146129000 * q^43 - 12194938044986814191839006674776852072893778556175391506781528253940392493592913843485049137975040 * q^44 + 986746799250062956400338006861900986362523619062838880021292887355485855896798596485569080571667580 * q^45 + 752141612087076748912715482380878319001154104492332189173260174861749530869824058097798503110563520 * q^46 - 1918977170076493454170487365406413018340521940535245265635752086808026838196958796824029488596607200 * q^47 - 9413963382571179425636093740415075791073794954566518162212892225259707570459169592567092964578508800 * q^48 + 4424167233212972548308367231382645770920683128881486958515725055988725408868499618515518765011399130 * q^49 + 680722065409115183760100309976569125874165206805654527502038796615083137012712040535401772639602878600 * q^50 - 32319807059595921198119329763639094466370593528876750378364913074838896902840034535481214151885659280 * q^51 - 3672350508615918706988315428535798947878272949374804570220967811956449680004938673562235859140924944000 * q^52 - 2009211479238083119390289905543378382308797873461290277025114374748986032309712284340399015223172958100 * q^53 - 1931801935997371383558162239941092584008314189522805286105797190362500280610458221586931216805738379200 * q^54 + 30511878931073238316415921138278986771644957150459948535911136025774807284294416560913953468660882079280 * q^55 + 126877575660686062164799530657771058499408094328546461202608068856064827832632677097022676050516125388800 * q^56 - 1412245636613402987583566403928499689907673096626013381053749242060772374057239140716128737047059987589600 * q^57 - 136877557224662485454400622855348052940229394353948623607073498889520831920878560332024651715699006897200 * q^58 + 3299933671312970318014224510035438974811878541147756441623760703525598387045261537239059812342521105337800 * q^59 + 21522094490079259713051153429507985158270932148578747769685503036840800025279058274203907556876957730736640 * q^60 + 4837190174129518173385919119672257037555828391936321041643076409836299786530753347575068109568740623595420 * q^61 - 160819201153827870914932578626796393716485319064275718134936059959659604110154771581583794810946018351763200 * q^62 - 29983538095598409492955452543692543839392503094995599971655215910869017565718274766970279553480154472448400 * q^63 + 1211010735266408368721880715435373923494644777241361683572485488080139913559735067537574947639643472539156480 * q^64 + 275596405736800076158618605370878142954922604093367429122958466182625164052330625944843847143685944773387080 * q^65 - 4571556792821411386452986160291211039829949386539474994568046789054354433826530257625242189399890177231308160 * q^66 - 14492255044540068397146202787177666038978329738091966816085948596075196182415583867767491778681013197600129800 * q^67 + 11412020923423724971791403006719373171687704529451822317715709895446884725238988347133907742324217053213750400 * q^68 + 26214069579412214259271827314973627996718651539417118198340276923109493510587408283690746644729049025547573440 * q^69 + 123614110386251874656201195782002919137175900573453806468611285513805590311860970064321111121804039130548666240 * q^70 + 167986438720991202535175844535056202103467058420138032407837057205213862880922938218281473241336848029824726320 * q^71 - 1214027676200915397665818515850699616086911975452482717359179924343053006357499126921626784766543068325763750400 * q^72 + 1233949202586186335303917316898506861995019601998317675708778649302958930766175545348120938476925924328720549700 * q^73 + 543442580799452155829153254268968536321414860958435747186750896729081968075855332008879736531095204288140166160 * q^74 + 5400719330138615967684042552542859592218848409512888981139070352575924621197393023272032307312948409698674976200 * q^75 - 1947681364249266128008278515237592495027779127950973160394084152671569960150463509448195360313803381416385798400 * q^76 - 16683659822909228960950374914003452078135467020374567292986163653878590289822431170045744715362904216698143432000 * q^77 - 89072355889618061913236422961170201709148241333748665798116496667029121445925030388457750939459839052612461352000 * q^78 + 157508184913938702697109095010204757626061191800741192129723961816007368467430024268154560701305365480554014277600 * q^79 + 717738694171956562725550070775822043413971269412641242062469275441459076310474017521997792969717993348643119882240 * q^80 + 685377716933108811002635995136680562114143448286890027079208804131082571599201228615213084084612556502713839645210 * q^81 - 81231248886594142360412634887129249452756426241963903730935732338634849662649563859028187215008243901359954917200 * q^82 - 1206868514083202720232704577481117752069506004611956039833793542006699255448280107179126221895523030200058209215400 * q^83 + 14126467866143646431573189552438805296686170961752631529359503040694891931287469221548265077514565520405417102632960 * q^84 + 14020561046474179165946028061965977084369651578728211422336420822319994099510809728088754276111040551899070188910040 * q^85 + 66344225309049944615999973318384392854563837752586977497952258411148013864305631982269419370065960537615017456509920 * q^86 + 42211584651436829046971577208962080119193312751750182233070614864898561469568330009329188990317590094811388534891600 * q^87 + 137328180658233895389586672135196831011178161508672801678233870639146210732539922411594570311726409571327613009049600 * q^88 + 419216508652667251481624162222063794117236701682826141556295380005381004122845062519830860537035472363408866073492900 * q^89 + 1960186172906516738137093246273215583954033628616907194913300477767254569348788187788783980642894284377261444786246480 * q^90 + 2117961972511642186570565583354551994813643511649789410299502995928572494930166279095010158484303424328709161629477920 * q^91 + 7643877538850487094208225981990239274508968935126003265201353928208290718282344963218624186914954600357688007403379200 * q^92 + 4145125513717754925972762047991995413704692770483070724240680311937909051760759841371162072158739134468687943292012800 * q^93 + 18905124986143721068825997229954909071618392026686975237140598903838373039063178431388647564880138863772474056628453760 * q^94 + 24103470106743892259389808018645838698305984759500570316746447180409251673952803385627315633849766600459698430524475600 * q^95 + 145148996310095551220695234868863345553364456500073995562810300405246452541716926663419327678590987234751701850742456320 * q^96 + 107546374851676082038883438148873453454117013661188535495956674032604491178648329876169635437402337745265739065665481300 * q^97 + 174218963757049243228974277723290518756443094205275131612770946890670481716398629353987179661401811795718431811507182200 * q^98 + 323496911757957747789115751830719500571150759171653307778212471313230140211264055128690873120449943627772784580871392840 * q^99

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