LMFDB - Embedded newform 1.120.a.a.1.9

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			1.9
Root			$-4.85771e16$ 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)

$f(q)$	$=$	$q+1.25784e18 q^{2} -1.09661e28 q^{3} +9.17555e35 q^{4} -6.18260e41 q^{5} -1.37937e46 q^{6} -3.09107e50 q^{7} +3.18161e53 q^{8} -4.78748e56 q^{9} +O(q^{10})$	\(q+1.25784e18 q^{2} -1.09661e28 q^{3} +9.17555e35 q^{4} -6.18260e41 q^{5} -1.37937e46 q^{6} -3.09107e50 q^{7} +3.18161e53 q^{8} -4.78748e56 q^{9} -7.77674e59 q^{10} +1.28542e62 q^{11} -1.00620e64 q^{12} -7.15965e65 q^{13} -3.88808e68 q^{14} +6.77992e69 q^{15} -2.09624e71 q^{16} -1.37834e73 q^{17} -6.02189e74 q^{18} +1.31086e75 q^{19} -5.67288e77 q^{20} +3.38970e78 q^{21} +1.61685e80 q^{22} +1.25014e81 q^{23} -3.48899e81 q^{24} +2.31782e83 q^{25} -9.00571e83 q^{26} +1.18188e85 q^{27} -2.83622e86 q^{28} -5.10549e86 q^{29} +8.52807e87 q^{30} +3.03978e88 q^{31} -4.75128e89 q^{32} -1.40961e90 q^{33} -1.73373e91 q^{34} +1.91108e92 q^{35} -4.39277e92 q^{36} +9.96990e92 q^{37} +1.64885e93 q^{38} +7.85136e93 q^{39} -1.96706e95 q^{40} +9.49364e95 q^{41} +4.26371e96 q^{42} -2.68491e97 q^{43} +1.17944e98 q^{44} +2.95991e98 q^{45} +1.57248e99 q^{46} +1.25610e99 q^{47} +2.29876e99 q^{48} +5.86774e100 q^{49} +2.91546e101 q^{50} +1.51150e101 q^{51} -6.56937e101 q^{52} -5.87315e102 q^{53} +1.48661e103 q^{54} -7.94723e103 q^{55} -9.83456e103 q^{56} -1.43750e103 q^{57} -6.42190e104 q^{58} +2.33809e105 q^{59} +6.22095e105 q^{60} -5.10278e104 q^{61} +3.82356e106 q^{62} +1.47984e107 q^{63} -4.58318e107 q^{64} +4.42652e107 q^{65} -1.77306e108 q^{66} -4.46187e108 q^{67} -1.26470e109 q^{68} -1.37092e109 q^{69} +2.40384e110 q^{70} -8.71194e109 q^{71} -1.52319e110 q^{72} +1.10832e110 q^{73} +1.25406e111 q^{74} -2.54175e111 q^{75} +1.20278e111 q^{76} -3.97331e112 q^{77} +9.87578e111 q^{78} +6.92138e112 q^{79} +1.29602e113 q^{80} +1.57166e113 q^{81} +1.19415e114 q^{82} -2.69937e114 q^{83} +3.11024e114 q^{84} +8.52172e114 q^{85} -3.37720e115 q^{86} +5.59874e114 q^{87} +4.08969e115 q^{88} +9.23733e115 q^{89} +3.72310e116 q^{90} +2.21309e116 q^{91} +1.14707e117 q^{92} -3.33346e116 q^{93} +1.57998e117 q^{94} -8.10451e116 q^{95} +5.21031e117 q^{96} +1.37232e118 q^{97} +7.38070e118 q^{98} -6.15391e118 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	1.25784e18	1.54291	0.771457	−	0.636281i	$-0.219528\pi$
$2$	1.25784e18	1.54291	0.771457	+	0.636281i	$0.219528\pi$
$3$	−1.09661e28	−0.448062	−0.224031	−	0.974582i	$-0.571922\pi$
$3$	−1.09661e28	−0.448062	−0.224031	+	0.974582i	$0.571922\pi$
$4$	9.17555e35	1.38058
$5$	−6.18260e41	−1.59388	−0.796941	−	0.604058i	$-0.793550\pi$
$5$	−6.18260e41	−1.59388	−0.796941	+	0.604058i	$0.793550\pi$
$6$	−1.37937e46	−0.691322
$7$	−3.09107e50	−1.60981	−0.804906	−	0.593403i	$-0.797784\pi$
$7$	−3.09107e50	−1.60981	−0.804906	+	0.593403i	$0.797784\pi$
$8$	3.18161e53	0.587208
$9$	−4.78748e56	−0.799240
$10$	−7.77674e59	−2.45922
$11$	1.28542e62	1.40017	0.700083	−	0.714061i	$-0.253146\pi$
$11$	1.28542e62	1.40017	0.700083	+	0.714061i	$0.253146\pi$
$12$	−1.00620e64	−0.618588
$13$	−7.15965e65	−0.376064	−0.188032	−	0.982163i	$-0.560211\pi$
$13$	−7.15965e65	−0.376064	−0.188032	+	0.982163i	$0.560211\pi$
$14$	−3.88808e68	−2.48380
$15$	6.77992e69	0.714158
$16$	−2.09624e71	−0.474572
$17$	−1.37834e73	−0.846536	−0.423268	−	0.906005i	$-0.639117\pi$
$17$	−1.37834e73	−0.846536	−0.423268	+	0.906005i	$0.639117\pi$
$18$	−6.02189e74	−1.23316
$19$	1.31086e75	0.107576	0.0537881	−	0.998552i	$-0.482870\pi$
$19$	1.31086e75	0.107576	0.0537881	+	0.998552i	$0.482870\pi$
$20$	−5.67288e77	−2.20049
$21$	3.38970e78	0.721296
$22$	1.61685e80	2.16034
$23$	1.25014e81	1.18618	0.593091	−	0.805135i	$-0.297907\pi$
$23$	1.25014e81	1.18618	0.593091	+	0.805135i	$0.297907\pi$
$24$	−3.48899e81	−0.263106
$25$	2.31782e83	1.54046
$26$	−9.00571e83	−0.580235
$27$	1.18188e85	0.806172
$28$	−2.83622e86	−2.22248
$29$	−5.10549e86	−0.495857	−0.247929	−	0.968778i	$-0.579750\pi$
$29$	−5.10549e86	−0.495857	−0.247929	+	0.968778i	$0.579750\pi$
$30$	8.52807e87	1.10189
$31$	3.03978e88	0.558240	0.279120	−	0.960256i	$-0.409957\pi$
$31$	3.03978e88	0.558240	0.279120	+	0.960256i	$0.409957\pi$
$32$	−4.75128e89	−1.31943
$33$	−1.40961e90	−0.627362
$34$	−1.73373e91	−1.30613
$35$	1.91108e92	2.56585
$36$	−4.39277e92	−1.10342
$37$	9.96990e92	0.490556	0.245278	−	0.969453i	$-0.421121\pi$
$37$	9.96990e92	0.490556	0.245278	+	0.969453i	$0.421121\pi$
$38$	1.64885e93	0.165981
$39$	7.85136e93	0.168500
$40$	−1.96706e95	−0.935941
$41$	9.49364e95	1.03943	0.519713	−	0.854341i	$-0.326039\pi$
$41$	9.49364e95	1.03943	0.519713	+	0.854341i	$0.326039\pi$
$42$	4.26371e96	1.11290
$43$	−2.68491e97	−1.72805	−0.864026	−	0.503446i	$-0.832065\pi$
$43$	−2.68491e97	−1.72805	−0.864026	+	0.503446i	$0.832065\pi$
$44$	1.17944e98	1.93305
$45$	2.95991e98	1.27389
$46$	1.57248e99	1.83018
$47$	1.25610e99	0.406632	0.203316	−	0.979113i	$-0.434828\pi$
$47$	1.25610e99	0.406632	0.203316	+	0.979113i	$0.434828\pi$
$48$	2.29876e99	0.212638
$49$	5.86774e100	1.59149
$50$	2.91546e101	2.37679
$51$	1.51150e101	0.379301
$52$	−6.56937e101	−0.519188
$53$	−5.87315e102	−1.49437	−0.747183	−	0.664618i	$-0.768594\pi$
$53$	−5.87315e102	−1.49437	−0.747183	+	0.664618i	$0.768594\pi$
$54$	1.48661e103	1.24385
$55$	−7.94723e103	−2.23170
$56$	−9.83456e103	−0.945295
$57$	−1.43750e103	−0.0482008
$58$	−6.42190e104	−0.765065
$59$	2.33809e105	1.00732	0.503659	−	0.863903i	$-0.331987\pi$
$59$	2.33809e105	1.00732	0.503659	+	0.863903i	$0.331987\pi$
$60$	6.22095e105	0.985956
$61$	−5.10278e104	−0.0302470	−0.0151235	−	0.999886i	$-0.504814\pi$
$61$	−5.10278e104	−0.0302470	−0.0151235	+	0.999886i	$0.504814\pi$
$62$	3.82356e106	0.861317
$63$	1.47984e107	1.28663
$64$	−4.58318e107	−1.56120
$65$	4.42652e107	0.599402
$66$	−1.77306e108	−0.967965
$67$	−4.46187e108	−0.995556	−0.497778	−	0.867304i	$-0.665851\pi$
$67$	−4.46187e108	−0.995556	−0.497778	+	0.867304i	$0.665851\pi$
$68$	−1.26470e109	−1.16871
$69$	−1.37092e109	−0.531484
$70$	2.40384e110	3.95888
$71$	−8.71194e109	−0.616940	−0.308470	−	0.951234i	$-0.599817\pi$
$71$	−8.71194e109	−0.616940	−0.308470	+	0.951234i	$0.599817\pi$
$72$	−1.52319e110	−0.469321
$73$	1.10832e110	0.150298	0.0751491	−	0.997172i	$-0.476057\pi$
$73$	1.10832e110	0.150298	0.0751491	+	0.997172i	$0.476057\pi$
$74$	1.25406e111	0.756885
$75$	−2.54175e111	−0.690221
$76$	1.20278e111	0.148518
$77$	−3.97331e112	−2.25400
$78$	9.87578e111	0.259981
$79$	6.92138e112	0.853848	0.426924	−	0.904288i	$-0.359597\pi$
$79$	6.92138e112	0.853848	0.426924	+	0.904288i	$0.359597\pi$
$80$	1.29602e113	0.756411
$81$	1.57166e113	0.438025
$82$	1.19415e114	1.60374
$83$	−2.69937e114	−1.76245	−0.881224	−	0.472698i	$-0.843280\pi$
$83$	−2.69937e114	−1.76245	−0.881224	+	0.472698i	$0.843280\pi$
$84$	3.11024e114	0.995809
$85$	8.52172e114	1.34928
$86$	−3.37720e115	−2.66624
$87$	5.59874e114	0.222175
$88$	4.08969e115	0.822189
$89$	9.23733e115	0.948071	0.474036	−	0.880506i	$-0.342797\pi$
$89$	9.23733e115	0.948071	0.474036	+	0.880506i	$0.342797\pi$
$90$	3.72310e116	1.96551
$91$	2.21309e116	0.605393
$92$	1.14707e117	1.63762
$93$	−3.33346e116	−0.250126
$94$	1.57998e117	0.627399
$95$	−8.10451e116	−0.171464
$96$	5.21031e117	0.591188
$97$	1.37232e118	0.840496	0.420248	−	0.907409i	$-0.361943\pi$
$97$	1.37232e118	0.840496	0.420248	+	0.907409i	$0.361943\pi$
$98$	7.38070e118	2.45553
$99$	−6.15391e118	−1.11907
$100$	2.12673e119	2.12673
$101$	1.38643e119	0.766964	0.383482	−	0.923548i	$-0.374725\pi$
$101$	1.38643e119	0.766964	0.383482	+	0.923548i	$0.374725\pi$
$102$	1.90123e119	0.585229
$103$	2.79208e119	0.480964	0.240482	−	0.970654i	$-0.422694\pi$
$103$	2.79208e119	0.480964	0.240482	+	0.970654i	$0.422694\pi$
$104$	−2.27792e119	−0.220828
$105$	−2.09572e120	−1.14966
$106$	−7.38750e120	−2.30568
$107$	6.52833e119	0.116538	0.0582690	−	0.998301i	$-0.481442\pi$
$107$	6.52833e119	0.116538	0.0582690	+	0.998301i	$0.481442\pi$
$108$	1.08444e121	1.11299
$109$	3.00924e121	1.78476	0.892380	−	0.451285i	$-0.149034\pi$
$109$	3.00924e121	1.78476	0.892380	+	0.451285i	$0.149034\pi$
$110$	−9.99636e121	−3.44332
$111$	−1.09331e121	−0.219800
$112$	6.47961e121	0.763971
$113$	−2.10859e122	−1.46495	−0.732477	−	0.680792i	$-0.761636\pi$
$113$	−2.10859e122	−1.46495	−0.732477	+	0.680792i	$0.761636\pi$
$114$	−1.80815e121	−0.0743697
$115$	−7.72910e122	−1.89063
$116$	−4.68457e122	−0.684572
$117$	3.42766e122	0.300566
$118$	2.94095e123	1.55420
$119$	4.26054e123	1.36276
$120$	2.15710e123	0.419360
$121$	8.09489e123	0.960465
$122$	−6.41850e122	−0.0466685
$123$	−1.04108e124	−0.465728
$124$	2.78917e124	0.770698
$125$	−5.02764e124	−0.861426
$126$	1.86141e125	1.98515
$127$	−9.16382e124	−0.610598	−0.305299	−	0.952257i	$-0.598756\pi$
$127$	−9.16382e124	−0.610598	−0.305299	+	0.952257i	$0.598756\pi$
$128$	−2.60715e125	−1.08936
$129$	2.94431e125	0.774276
$130$	5.56787e125	0.924826
$131$	−8.51129e125	−0.896093	−0.448047	−	0.894010i	$-0.647880\pi$
$131$	−8.51129e125	−0.896093	−0.448047	+	0.894010i	$0.647880\pi$
$132$	−1.29339e126	−0.866126
$133$	−4.05195e125	−0.173177
$134$	−5.61233e126	−1.53606
$135$	−7.30706e126	−1.28494
$136$	−4.38533e126	−0.497093
$137$	1.68731e127	1.23686	0.618430	−	0.785840i	$-0.287769\pi$
$137$	1.68731e127	1.23686	0.618430	+	0.785840i	$0.287769\pi$
$138$	−1.72440e127	−0.820033
$139$	1.94065e127	0.600573	0.300286	−	0.953849i	$-0.402918\pi$
$139$	1.94065e127	0.600573	0.300286	+	0.953849i	$0.402918\pi$
$140$	1.75352e128	3.54237
$141$	−1.37746e127	−0.182197
$142$	−1.09583e128	−0.951886
$143$	−9.20314e127	−0.526553
$144$	1.00357e128	0.379297
$145$	3.15652e128	0.790337
$146$	1.39409e128	0.231897
$147$	−6.43464e128	−0.713088
$148$	9.14794e128	0.677253
$149$	7.76513e128	0.385093	0.192546	−	0.981288i	$-0.438325\pi$
$149$	7.76513e128	0.385093	0.192546	+	0.981288i	$0.438325\pi$
$150$	−3.19713e129	−1.06495
$151$	9.79573e128	0.219740	0.109870	−	0.993946i	$-0.464957\pi$
$151$	9.79573e128	0.219740	0.109870	+	0.993946i	$0.464957\pi$
$152$	4.17063e128	0.0631696
$153$	6.59876e129	0.676585
$154$	−4.99780e130	−3.47773
$155$	−1.87937e130	−0.889769
$156$	7.20406e129	0.232629
$157$	3.81025e128	0.00841247	0.00420624	−	0.999991i	$-0.498661\pi$
$157$	3.81025e128	0.00841247	0.00420624	+	0.999991i	$0.498661\pi$
$158$	8.70601e130	1.31741
$159$	6.44057e130	0.669569
$160$	2.93753e131	2.10302
$161$	−3.86426e131	−1.90953
$162$	1.97690e131	0.675835
$163$	1.81684e131	0.430680	0.215340	−	0.976539i	$-0.430914\pi$
$163$	1.81684e131	0.430680	0.215340	+	0.976539i	$0.430914\pi$
$164$	8.71095e131	1.43501
$165$	8.71503e131	0.999940
$166$	−3.39539e132	−2.71931
$167$	−1.32054e132	−0.739811	−0.369906	−	0.929069i	$-0.620610\pi$
$167$	−1.32054e132	−0.739811	−0.369906	+	0.929069i	$0.620610\pi$
$168$	1.07847e132	0.423551
$169$	−3.11198e132	−0.858576
$170$	1.07190e133	2.08182
$171$	−6.27570e131	−0.0859792
$172$	−2.46356e133	−2.38572
$173$	2.24056e133	1.53679	0.768393	−	0.639978i	$-0.221057\pi$
$173$	2.24056e133	1.53679	0.768393	+	0.639978i	$0.221057\pi$
$174$	7.04234e132	0.342797
$175$	−7.16455e133	−2.47985
$176$	−2.69454e133	−0.664479
$177$	−2.56398e133	−0.451341
$178$	1.16191e134	1.46279
$179$	8.07135e132	0.0728099	0.0364050	−	0.999337i	$-0.488409\pi$
$179$	8.07135e132	0.0728099	0.0364050	+	0.999337i	$0.488409\pi$
$180$	2.71588e134	1.75872
$181$	6.90738e133	0.321691	0.160845	−	0.986980i	$-0.448578\pi$
$181$	6.90738e133	0.321691	0.160845	+	0.986980i	$0.448578\pi$
$182$	2.78373e134	0.934069
$183$	5.59578e132	0.0135525
$184$	3.97744e134	0.696536
$185$	−6.16399e134	−0.781888
$186$	−4.19297e134	−0.385924
$187$	−1.77174e135	−1.18529
$188$	1.15254e135	0.561390
$189$	−3.65325e135	−1.29778
$190$	−1.01942e135	−0.264554
$191$	5.06881e134	0.0962545	0.0481273	−	0.998841i	$-0.484675\pi$
$191$	5.06881e134	0.0962545	0.0481273	+	0.998841i	$0.484675\pi$
$192$	5.02597e135	0.699514
$193$	−1.66807e136	−1.70433	−0.852166	−	0.523272i	$-0.824711\pi$
$193$	−1.66807e136	−1.70433	−0.852166	+	0.523272i	$0.824711\pi$
$194$	1.72616e136	1.29681
$195$	−4.85418e135	−0.268569
$196$	5.38398e136	2.19719
$197$	−5.21647e136	−1.57267	−0.786333	−	0.617803i	$-0.788023\pi$
$197$	−5.21647e136	−1.57267	−0.786333	+	0.617803i	$0.788023\pi$
$198$	−7.74065e136	−1.72663
$199$	3.41482e136	0.564429	0.282215	−	0.959351i	$-0.408931\pi$
$199$	3.41482e136	0.564429	0.282215	+	0.959351i	$0.408931\pi$
$200$	7.37440e136	0.904570
$201$	4.89294e136	0.446071
$202$	1.74391e137	1.18336
$203$	1.57814e137	0.798236
$204$	1.38689e137	0.523657
$205$	−5.86954e137	−1.65672
$206$	3.51200e137	0.742087
$207$	−5.98500e137	−0.948044
$208$	1.50083e137	0.178470
$209$	1.68500e137	0.150624
$210$	−2.63608e138	−1.77383
$211$	−4.31619e137	−0.218925	−0.109462	−	0.993991i	$-0.534913\pi$
$211$	−4.31619e137	−0.218925	−0.109462	+	0.993991i	$0.534913\pi$
$212$	−5.38894e138	−2.06310
$213$	9.55362e137	0.276428
$214$	8.21162e137	0.179808
$215$	1.65997e139	2.75431
$216$	3.76026e138	0.473391
$217$	−9.39616e138	−0.898661
$218$	3.78515e139	2.75373
$219$	−1.21539e138	−0.0673430
$220$	−7.29202e139	−3.08105
$221$	9.86842e138	0.318352
$222$	−1.37522e139	−0.339132
$223$	6.58452e139	1.24275	0.621376	−	0.783512i	$-0.286574\pi$
$223$	6.58452e139	1.24275	0.621376	+	0.783512i	$0.286574\pi$
$224$	1.46865e140	2.12404
$225$	−1.10965e140	−1.23120
$226$	−2.65227e140	−2.26030
$227$	2.06478e140	1.35312	0.676560	−	0.736388i	$-0.263470\pi$
$227$	2.06478e140	1.35312	0.676560	+	0.736388i	$0.263470\pi$
$228$	−1.31899e139	−0.0665453
$229$	3.02251e140	1.17532	0.587660	−	0.809108i	$-0.300049\pi$
$229$	3.02251e140	1.17532	0.587660	+	0.809108i	$0.300049\pi$
$230$	−9.72199e140	−2.91709
$231$	4.35718e140	1.00993
$232$	−1.62437e140	−0.291171
$233$	−1.02108e141	−1.41704	−0.708519	−	0.705692i	$-0.750636\pi$
$233$	−1.02108e141	−1.41704	−0.708519	+	0.705692i	$0.750636\pi$
$234$	4.31146e140	0.463747
$235$	−7.76597e140	−0.648124
$236$	2.14533e141	1.39069
$237$	−7.59007e140	−0.382577
$238$	5.35909e141	2.10263
$239$	−8.14282e140	−0.248943	−0.124471	−	0.992223i	$-0.539724\pi$
$239$	−8.14282e140	−0.248943	−0.124471	+	0.992223i	$0.539724\pi$
$240$	−1.42123e141	−0.338919
$241$	7.78344e141	1.44930	0.724649	−	0.689118i	$-0.242002\pi$
$241$	7.78344e141	1.44930	0.724649	+	0.689118i	$0.242002\pi$
$242$	1.01821e142	1.48191
$243$	−8.80297e141	−1.00243
$244$	−4.68209e140	−0.0417585
$245$	−3.62779e142	−2.53665
$246$	−1.30952e142	−0.718578
$247$	−9.38527e140	−0.0404556
$248$	9.67138e141	0.327803
$249$	2.96017e142	0.789687
$250$	−6.32398e142	−1.32911
$251$	−6.81877e142	−1.13011	−0.565054	−	0.825054i	$-0.691145\pi$
$251$	−6.81877e142	−1.13011	−0.565054	+	0.825054i	$0.691145\pi$
$252$	1.35784e143	1.77629
$253$	1.60695e143	1.66085
$254$	−1.15267e143	−0.942100
$255$	−9.34503e142	−0.604560
$256$	−2.33342e142	−0.119595
$257$	9.16217e141	0.0372372	0.0186186	−	0.999827i	$-0.494073\pi$
$257$	9.16217e141	0.0372372	0.0186186	+	0.999827i	$0.494073\pi$
$258$	3.70348e143	1.19464
$259$	−3.08176e143	−0.789702
$260$	4.06158e143	0.827525
$261$	2.44424e143	0.396309
$262$	−1.07059e144	−1.38260
$263$	9.51999e143	0.980098	0.490049	−	0.871695i	$-0.336979\pi$
$263$	9.51999e143	0.980098	0.490049	+	0.871695i	$0.336979\pi$
$264$	−4.48481e143	−0.368392
$265$	3.63114e144	2.38184
$266$	−5.09671e143	−0.267198
$267$	−1.01298e144	−0.424795
$268$	−4.09401e144	−1.37445
$269$	−3.63997e144	−0.979123	−0.489561	−	0.871969i	$-0.662843\pi$
$269$	−3.63997e144	−0.979123	−0.489561	+	0.871969i	$0.662843\pi$
$270$	−9.19114e144	−1.98256
$271$	−3.04394e144	−0.526943	−0.263472	−	0.964667i	$-0.584868\pi$
$271$	−3.04394e144	−0.526943	−0.263472	+	0.964667i	$0.584868\pi$
$272$	2.88933e144	0.401742
$273$	−2.42691e144	−0.271254
$274$	2.12237e145	1.90837
$275$	2.97937e145	2.15690
$276$	−1.25789e145	−0.733758
$277$	−2.00507e145	−0.943157	−0.471578	−	0.881824i	$-0.656316\pi$
$277$	−2.00507e145	−0.943157	−0.471578	+	0.881824i	$0.656316\pi$
$278$	2.44103e145	0.926632
$279$	−1.45529e145	−0.446168
$280$	6.08032e145	1.50669
$281$	1.64677e145	0.330071	0.165035	−	0.986288i	$-0.447226\pi$
$281$	1.64677e145	0.330071	0.165035	+	0.986288i	$0.447226\pi$
$282$	−1.73262e145	−0.281114
$283$	−1.26710e145	−0.166540	−0.0832700	−	0.996527i	$-0.526536\pi$
$283$	−1.26710e145	−0.166540	−0.0832700	+	0.996527i	$0.526536\pi$
$284$	−7.99369e145	−0.851738
$285$	8.88750e144	0.0768264
$286$	−1.15761e146	−0.812425
$287$	−2.93455e146	−1.67328
$288$	2.27466e146	1.05454
$289$	−7.51254e145	−0.283377
$290$	3.97041e146	1.21942
$291$	−1.50490e146	−0.376595
$292$	1.01694e146	0.207499
$293$	4.41217e146	0.734563	0.367282	−	0.930110i	$-0.380288\pi$
$293$	4.41217e146	0.734563	0.367282	+	0.930110i	$0.380288\pi$
$294$	−8.09377e146	−1.10023
$295$	−1.44555e147	−1.60555
$296$	3.17203e146	0.288058
$297$	1.51920e147	1.12877
$298$	9.76731e146	0.594165
$299$	−8.95054e146	−0.446081
$300$	−2.33220e147	−0.952909
$301$	8.29924e147	2.78184
$302$	1.23215e147	0.339039
$303$	−1.52037e147	−0.343648
$304$	−2.74787e146	−0.0510526
$305$	3.15485e146	0.0482101
$306$	8.30021e147	1.04391
$307$	1.19276e147	0.123543	0.0617715	−	0.998090i	$-0.480325\pi$
$307$	1.19276e147	0.123543	0.0617715	+	0.998090i	$0.480325\pi$
$308$	−3.64573e148	−3.11184
$309$	−3.06183e147	−0.215502
$310$	−2.36396e148	−1.37284
$311$	−2.24273e147	−0.107531	−0.0537656	−	0.998554i	$-0.517122\pi$
$311$	−2.24273e147	−0.107531	−0.0537656	+	0.998554i	$0.517122\pi$
$312$	2.49799e147	0.0989448
$313$	4.66916e148	1.52880	0.764401	−	0.644741i	$-0.223035\pi$
$313$	4.66916e148	1.52880	0.764401	+	0.644741i	$0.223035\pi$
$314$	4.79269e146	0.0129797
$315$	−9.14926e148	−2.05073
$316$	6.35075e148	1.17881
$317$	9.76434e148	1.50182	0.750908	−	0.660407i	$-0.229616\pi$
$317$	9.76434e148	1.50182	0.750908	+	0.660407i	$0.229616\pi$
$318$	8.10123e148	1.03309
$319$	−6.56269e148	−0.694282
$320$	2.83360e149	2.48837
$321$	−7.15905e147	−0.0522163
$322$	−4.86063e149	−2.94624
$323$	−1.80681e148	−0.0910671
$324$	1.44208e149	0.604730
$325$	−1.65948e149	−0.579311
$326$	2.28530e149	0.664503
$327$	−3.29997e149	−0.799684
$328$	3.02050e149	0.610360
$329$	−3.88269e149	−0.654601
$330$	1.09621e150	1.54282
$331$	5.64852e149	0.664001	0.332001	−	0.943279i	$-0.392276\pi$
$331$	5.64852e149	0.664001	0.332001	+	0.943279i	$0.392276\pi$
$332$	−2.47683e150	−2.43321
$333$	−4.77307e149	−0.392072
$334$	−1.66103e150	−1.14147
$335$	2.75859e150	1.58680
$336$	−7.10563e149	−0.342307
$337$	2.40122e149	0.0969289	0.0484645	−	0.998825i	$-0.484567\pi$
$337$	2.40122e149	0.0969289	0.0484645	+	0.998825i	$0.484567\pi$
$338$	−3.91439e150	−1.32471
$339$	2.31230e150	0.656391
$340$	7.81915e150	1.86279
$341$	3.90739e150	0.781629
$342$	−7.89384e149	−0.132658
$343$	−6.74099e150	−0.952190
$344$	−8.54234e150	−1.01473
$345$	8.47583e150	0.847122
$346$	2.81827e151	2.37113
$347$	1.43760e151	1.01867	0.509335	−	0.860569i	$-0.329892\pi$
$347$	1.43760e151	1.01867	0.509335	+	0.860569i	$0.329892\pi$
$348$	5.13716e150	0.306731
$349$	−1.01999e151	−0.513432	−0.256716	−	0.966487i	$-0.582640\pi$
$349$	−1.01999e151	−0.513432	−0.256716	+	0.966487i	$0.582640\pi$
$350$	−9.01188e151	−3.82619
$351$	−8.46181e150	−0.303172
$352$	−6.10738e151	−1.84742
$353$	3.24616e151	0.829421	0.414710	−	0.909953i	$-0.363883\pi$
$353$	3.24616e151	0.829421	0.414710	+	0.909953i	$0.363883\pi$
$354$	−3.22508e151	−0.696381
$355$	5.38625e151	0.983330
$356$	8.47576e151	1.30889
$357$	−4.67216e151	−0.610603
$358$	1.01525e151	0.112339
$359$	1.39073e152	1.30354	0.651768	−	0.758419i	$-0.274028\pi$
$359$	1.39073e152	1.30354	0.651768	+	0.758419i	$0.274028\pi$
$360$	9.41726e151	0.748041
$361$	−1.46765e152	−0.988427
$362$	8.68841e151	0.496341
$363$	−8.87696e151	−0.430348
$364$	2.03064e152	0.835795
$365$	−6.85228e151	−0.239558
$366$	7.03861e150	0.0209104
$367$	1.18310e152	0.298808	0.149404	−	0.988776i	$-0.452264\pi$
$367$	1.18310e152	0.298808	0.149404	+	0.988776i	$0.452264\pi$
$368$	−2.62059e152	−0.562928
$369$	−4.54506e152	−0.830751
$370$	−7.75334e152	−1.20639
$371$	1.81543e153	2.40565
$372$	−3.05863e152	−0.345321
$373$	9.46273e152	0.910627	0.455314	−	0.890331i	$-0.349527\pi$
$373$	9.46273e152	0.910627	0.455314	+	0.890331i	$0.349527\pi$
$374$	−2.22857e153	−1.82880
$375$	5.51337e152	0.385973
$376$	3.99642e152	0.238778
$377$	3.65535e152	0.186474
$378$	−4.59522e153	−2.00237
$379$	−6.50992e151	−0.0242405	−0.0121203	−	0.999927i	$-0.503858\pi$
$379$	−6.50992e151	−0.0242405	−0.0121203	+	0.999927i	$0.503858\pi$
$380$	−7.43633e152	−0.236720
$381$	1.00492e153	0.273586
$382$	6.37577e152	0.148512
$383$	−2.20037e153	−0.438700	−0.219350	−	0.975646i	$-0.570394\pi$
$383$	−2.20037e153	−0.438700	−0.219350	+	0.975646i	$0.570394\pi$
$384$	2.85903e153	0.488103
$385$	2.45654e154	3.59261
$386$	−2.09817e154	−2.62964
$387$	1.28540e154	1.38113
$388$	1.25918e154	1.16038
$389$	2.94504e153	0.232857	0.116429	−	0.993199i	$-0.462855\pi$
$389$	2.94504e153	0.232857	0.116429	+	0.993199i	$0.462855\pi$
$390$	−6.10580e153	−0.414380
$391$	−1.72311e154	−1.00415
$392$	1.86689e154	0.934537
$393$	9.33359e153	0.401506
$394$	−6.56151e154	−2.42649
$395$	−4.27921e154	−1.36093
$396$	−5.64655e154	−1.54497
$397$	6.80064e154	1.60146	0.800728	−	0.599028i	$-0.204446\pi$
$397$	6.80064e154	1.60146	0.800728	+	0.599028i	$0.204446\pi$
$398$	4.29531e154	0.870866
$399$	4.44341e153	0.0775942
$400$	−4.85871e154	−0.731058
$401$	−3.33984e154	−0.433147	−0.216574	−	0.976266i	$-0.569488\pi$
$401$	−3.33984e154	−0.433147	−0.216574	+	0.976266i	$0.569488\pi$
$402$	6.15455e154	0.688250
$403$	−2.17637e154	−0.209934
$404$	1.27212e155	1.05886
$405$	−9.71692e154	−0.698160
$406$	1.98505e155	1.23161
$407$	1.28155e155	0.686859
$408$	4.80901e154	0.222729
$409$	4.56356e155	1.82712	0.913560	−	0.406705i	$-0.133322\pi$
$409$	4.56356e155	1.82712	0.913560	+	0.406705i	$0.133322\pi$
$410$	−7.38296e155	−2.55618
$411$	−1.85032e155	−0.554191
$412$	2.56189e155	0.664012
$413$	−7.22719e155	−1.62159
$414$	−7.52819e155	−1.46275
$415$	1.66892e156	2.80913
$416$	3.40175e155	0.496191
$417$	−2.12814e155	−0.269094
$418$	2.11946e155	0.232401
$419$	1.01337e156	0.963899	0.481950	−	0.876199i	$-0.339929\pi$
$419$	1.01337e156	0.963899	0.481950	+	0.876199i	$0.339929\pi$
$420$	−1.92294e156	−1.58720
$421$	−2.40325e155	−0.172192	−0.0860962	−	0.996287i	$-0.527439\pi$
$421$	−2.40325e155	−0.172192	−0.0860962	+	0.996287i	$0.527439\pi$
$422$	−5.42910e155	−0.337782
$423$	−6.01355e155	−0.324997
$424$	−1.86861e156	−0.877504
$425$	−3.19475e156	−1.30405
$426$	1.20170e156	0.426504
$427$	1.57730e155	0.0486919
$428$	5.99011e155	0.160890
$429$	1.00923e156	0.235928
$430$	2.08799e157	4.24967
$431$	−3.45797e156	−0.612948	−0.306474	−	0.951879i	$-0.599149\pi$
$431$	−3.45797e156	−0.612948	−0.306474	+	0.951879i	$0.599149\pi$
$432$	−2.47749e156	−0.382586
$433$	1.12623e156	0.151564	0.0757819	−	0.997124i	$-0.475855\pi$
$433$	1.12623e156	0.151564	0.0757819	+	0.997124i	$0.475855\pi$
$434$	−1.18189e157	−1.38656
$435$	−3.46148e156	−0.354120
$436$	2.76114e157	2.46401
$437$	1.63875e156	0.127605
$438$	−1.52878e156	−0.103904
$439$	−9.37275e156	−0.556197	−0.278098	−	0.960553i	$-0.589704\pi$
$439$	−9.37275e156	−0.556197	−0.278098	+	0.960553i	$0.589704\pi$
$440$	−2.52850e157	−1.31047
$441$	−2.80917e157	−1.27198
$442$	1.24129e157	0.491190
$443$	−4.57275e157	−1.58181	−0.790907	−	0.611936i	$-0.790391\pi$
$443$	−4.57275e157	−1.58181	−0.790907	+	0.611936i	$0.790391\pi$
$444$	−1.00317e157	−0.303452
$445$	−5.71107e157	−1.51111
$446$	8.28229e157	1.91746
$447$	−8.51533e156	−0.172546
$448$	1.41669e158	2.51323
$449$	7.66272e157	1.19049	0.595245	−	0.803544i	$-0.297055\pi$
$449$	7.66272e157	1.19049	0.595245	+	0.803544i	$0.297055\pi$
$450$	−1.39577e158	−1.89963
$451$	1.22033e158	1.45537
$452$	−1.93474e158	−2.02249
$453$	−1.07421e157	−0.0984571
$454$	2.59717e158	2.08775
$455$	−1.36827e158	−0.964924
$456$	−4.57357e156	−0.0283039
$457$	3.14166e157	0.170665	0.0853327	−	0.996353i	$-0.472805\pi$
$457$	3.14166e157	0.170665	0.0853327	+	0.996353i	$0.472805\pi$
$458$	3.80184e158	1.81342
$459$	−1.62902e158	−0.682453
$460$	−7.09188e158	−2.61018
$461$	−8.18582e157	−0.264763	−0.132381	−	0.991199i	$-0.542262\pi$
$461$	−8.18582e157	−0.264763	−0.132381	+	0.991199i	$0.542262\pi$
$462$	5.48065e158	1.55824
$463$	4.08271e158	1.02066	0.510329	−	0.859979i	$-0.329524\pi$
$463$	4.08271e158	1.02066	0.510329	+	0.859979i	$0.329524\pi$
$464$	1.07023e158	0.235320
$465$	2.06094e158	0.398672
$466$	−1.28436e159	−2.18637
$467$	−7.47562e158	−1.12019	−0.560096	−	0.828427i	$-0.689236\pi$
$467$	−7.47562e158	−1.12019	−0.560096	+	0.828427i	$0.689236\pi$
$468$	3.14507e158	0.414956
$469$	1.37919e159	1.60266
$470$	−9.76838e158	−1.00000
$471$	−4.17836e156	−0.00376931
$472$	7.43888e158	0.591506
$473$	−3.45123e159	−2.41956
$474$	−9.54711e158	−0.590284
$475$	3.03834e158	0.165717
$476$	3.90928e159	1.88141
$477$	2.81176e159	1.19436
$478$	−1.02424e159	−0.384098
$479$	2.29871e159	0.761238	0.380619	−	0.924732i	$-0.375711\pi$
$479$	2.29871e159	0.761238	0.380619	+	0.924732i	$0.375711\pi$
$480$	−3.22133e159	−0.942283
$481$	−7.13810e158	−0.184481
$482$	9.79035e159	2.23614
$483$	4.23759e159	0.855588
$484$	7.42751e159	1.32600
$485$	−8.48448e159	−1.33965
$486$	−1.10728e160	−1.54667
$487$	−3.51236e159	−0.434136	−0.217068	−	0.976156i	$-0.569649\pi$
$487$	−3.51236e159	−0.434136	−0.217068	+	0.976156i	$0.569649\pi$
$488$	−1.62351e158	−0.0177613
$489$	−1.99237e159	−0.192972
$490$	−4.56319e160	−3.91383
$491$	1.75799e160	1.33557	0.667787	−	0.744352i	$-0.267242\pi$
$491$	1.75799e160	1.33557	0.667787	+	0.744352i	$0.267242\pi$
$492$	−9.55253e159	−0.642976
$493$	7.03710e159	0.419761
$494$	−1.18052e159	−0.0624195
$495$	3.80472e160	1.78366
$496$	−6.37210e159	−0.264925
$497$	2.69292e160	0.993157
$498$	3.72343e160	1.21842
$499$	−6.38912e159	−0.185549	−0.0927744	−	0.995687i	$-0.529574\pi$
$499$	−6.38912e159	−0.185549	−0.0927744	+	0.995687i	$0.529574\pi$
$500$	−4.61313e160	−1.18927
$501$	1.44812e160	0.331482
$502$	−8.57695e160	−1.74366
$503$	6.54375e160	1.18177	0.590883	−	0.806757i	$-0.298779\pi$
$503$	6.54375e160	1.18177	0.590883	+	0.806757i	$0.298779\pi$
$504$	4.70827e160	0.755517
$505$	−8.57172e160	−1.22245
$506$	2.02129e161	2.56255
$507$	3.41264e160	0.384695
$508$	−8.40831e160	−0.842982
$509$	−1.10352e161	−0.984177	−0.492088	−	0.870545i	$-0.663766\pi$
$509$	−1.10352e161	−0.984177	−0.492088	+	0.870545i	$0.663766\pi$
$510$	−1.17546e161	−0.932785
$511$	−3.42588e160	−0.241952
$512$	1.43924e161	0.904838
$513$	1.54927e160	0.0867249
$514$	1.15246e160	0.0574538
$515$	−1.72623e161	−0.766600
$516$	2.70157e161	1.06895
$517$	1.61461e161	0.569353
$518$	−3.87637e161	−1.21844
$519$	−2.45703e161	−0.688576
$520$	1.40835e161	0.351974
$521$	−5.08279e161	−1.13307	−0.566536	−	0.824037i	$-0.691717\pi$
$521$	−5.08279e161	−1.13307	−0.566536	+	0.824037i	$0.691717\pi$
$522$	3.07447e161	0.611470
$523$	−5.29055e161	−0.938966	−0.469483	−	0.882941i	$-0.655560\pi$
$523$	−5.29055e161	−0.938966	−0.469483	+	0.882941i	$0.655560\pi$
$524$	−7.80958e161	−1.23713
$525$	7.85673e161	1.11113
$526$	1.19747e162	1.51221
$527$	−4.18985e161	−0.472570
$528$	2.95487e161	0.297728
$529$	4.52102e161	0.407028
$530$	4.56740e162	3.67498
$531$	−1.11935e162	−0.805089
$532$	−3.71788e161	−0.239086
$533$	−6.79711e161	−0.390891
$534$	−1.27417e162	−0.655422
$535$	−4.03621e161	−0.185748
$536$	−1.41959e162	−0.584599
$537$	−8.85114e160	−0.0326234
$538$	−4.57851e162	−1.51070
$539$	7.54250e162	2.22835
$540$	−6.70464e162	−1.77397
$541$	−7.01048e161	−0.166154	−0.0830769	−	0.996543i	$-0.526475\pi$
$541$	−7.01048e161	−0.166154	−0.0830769	+	0.996543i	$0.526475\pi$
$542$	−3.82881e162	−0.813028
$543$	−7.57472e161	−0.144137
$544$	6.54888e162	1.11695
$545$	−1.86049e163	−2.84470
$546$	−3.05267e162	−0.418521
$547$	1.10945e163	1.36415	0.682073	−	0.731284i	$-0.261079\pi$
$547$	1.10945e163	1.36415	0.682073	+	0.731284i	$0.261079\pi$
$548$	1.54820e163	1.70759
$549$	2.44295e161	0.0241746
$550$	3.74758e163	3.32791
$551$	−6.69257e161	−0.0533424
$552$	−4.36171e162	−0.312092
$553$	−2.13944e163	−1.37453
$554$	−2.52207e163	−1.45521
$555$	6.75951e162	0.350334
$556$	1.78065e163	0.829141
$557$	3.90736e162	0.163493	0.0817465	−	0.996653i	$-0.473950\pi$
$557$	3.90736e162	0.163493	0.0817465	+	0.996653i	$0.473950\pi$
$558$	−1.83052e163	−0.688399
$559$	1.92230e163	0.649859
$560$	−4.00609e163	−1.21768
$561$	1.94291e163	0.531084
$562$	2.07138e163	0.509270
$563$	−5.81203e163	−1.28552	−0.642759	−	0.766068i	$-0.722210\pi$
$563$	−5.81203e163	−1.28552	−0.642759	+	0.766068i	$0.722210\pi$
$564$	−1.26389e163	−0.251538
$565$	1.30365e164	2.33496
$566$	−1.59382e163	−0.256957
$567$	−4.85809e163	−0.705137
$568$	−2.77180e163	−0.362273
$569$	2.27394e163	0.267670	0.133835	−	0.991004i	$-0.457271\pi$
$569$	2.27394e163	0.267670	0.133835	+	0.991004i	$0.457271\pi$
$570$	1.11791e163	0.118537
$571$	−1.14185e164	−1.09084	−0.545419	−	0.838163i	$-0.683630\pi$
$571$	−1.14185e164	−1.09084	−0.545419	+	0.838163i	$0.683630\pi$
$572$	−8.44439e163	−0.726950
$573$	−5.55853e162	−0.0431280
$574$	−3.69120e164	−2.58173
$575$	2.89760e164	1.82726
$576$	2.19418e164	1.24777
$577$	5.16324e162	0.0264826	0.0132413	−	0.999912i	$-0.495785\pi$
$577$	5.16324e162	0.0264826	0.0132413	+	0.999912i	$0.495785\pi$
$578$	−9.44960e163	−0.437227
$579$	1.82923e164	0.763647
$580$	2.89628e164	1.09113
$581$	8.34394e164	2.83721
$582$	−1.89293e164	−0.581053
$583$	−7.54945e164	−2.09236
$584$	3.52623e163	0.0882564
$585$	−2.11919e164	−0.479066
$586$	5.54982e164	1.13337
$587$	6.53400e164	1.20563	0.602813	−	0.797883i	$-0.294047\pi$
$587$	6.53400e164	1.20563	0.602813	+	0.797883i	$0.294047\pi$
$588$	−5.90414e164	−0.984477
$589$	3.98471e163	0.0600533
$590$	−1.81827e165	−2.47722
$591$	5.72045e164	0.704653
$592$	−2.08993e164	−0.232804
$593$	−1.40505e165	−1.41559	−0.707795	−	0.706418i	$-0.750310\pi$
$593$	−1.40505e165	−1.41559	−0.707795	+	0.706418i	$0.750310\pi$
$594$	1.91092e165	1.74160
$595$	−2.63412e165	−2.17208
$596$	7.12493e164	0.531653
$597$	−3.74473e164	−0.252900
$598$	−1.12584e165	−0.688264
$599$	−6.15751e164	−0.340808	−0.170404	−	0.985374i	$-0.554507\pi$
$599$	−6.15751e164	−0.340808	−0.170404	+	0.985374i	$0.554507\pi$
$600$	−8.08686e164	−0.405304
$601$	2.43685e165	1.10611	0.553055	−	0.833145i	$-0.313462\pi$
$601$	2.43685e165	1.10611	0.553055	+	0.833145i	$0.313462\pi$
$602$	1.04391e166	4.29214
$603$	2.13611e165	0.795688
$604$	8.98813e164	0.303369
$605$	−5.00475e165	−1.53087
$606$	−1.91239e165	−0.530219
$607$	−2.96916e165	−0.746289	−0.373145	−	0.927773i	$-0.621720\pi$
$607$	−2.96916e165	−0.746289	−0.373145	+	0.927773i	$0.621720\pi$
$608$	−6.22825e164	−0.141939
$609$	−1.73061e165	−0.357660
$610$	3.96830e164	0.0743841
$611$	−8.99324e164	−0.152920
$612$	6.05473e165	0.934083
$613$	−4.69838e165	−0.657733	−0.328867	−	0.944376i	$-0.606667\pi$
$613$	−4.69838e165	−0.657733	−0.328867	+	0.944376i	$0.606667\pi$
$614$	1.50030e165	0.190616
$615$	6.43661e165	0.742315
$616$	−1.26415e166	−1.32357
$617$	6.79897e165	0.646362	0.323181	−	0.946337i	$-0.395248\pi$
$617$	6.79897e165	0.646362	0.323181	+	0.946337i	$0.395248\pi$
$618$	−3.85130e165	−0.332501
$619$	5.55641e165	0.435713	0.217857	−	0.975981i	$-0.430094\pi$
$619$	5.55641e165	0.435713	0.217857	+	0.975981i	$0.430094\pi$
$620$	−1.72443e166	−1.22840
$621$	1.47751e166	0.956267
$622$	−2.82101e165	−0.165912
$623$	−2.85532e166	−1.52622
$624$	−1.64583e165	−0.0799655
$625$	−3.79087e165	−0.167447
$626$	5.87308e166	2.35881
$627$	−1.84779e165	−0.0674892
$628$	3.49611e164	0.0116141
$629$	−1.37419e166	−0.415273
$630$	−1.15083e167	−3.16410
$631$	2.22035e166	0.555489	0.277744	−	0.960655i	$-0.410413\pi$
$631$	2.22035e166	0.555489	0.277744	+	0.960655i	$0.410413\pi$
$632$	2.20211e166	0.501387
$633$	4.73319e165	0.0980920
$634$	1.22820e167	2.31717
$635$	5.66563e166	0.973220
$636$	5.90958e166	0.924397
$637$	−4.20110e166	−0.598503
$638$	−8.25483e166	−1.07122
$639$	4.17082e166	0.493083
$640$	1.61190e167	1.73632
$641$	4.29015e166	0.421134	0.210567	−	0.977579i	$-0.432469\pi$
$641$	4.29015e166	0.421134	0.210567	+	0.977579i	$0.432469\pi$
$642$	−9.00496e165	−0.0805652
$643$	−7.90133e166	−0.644388	−0.322194	−	0.946674i	$-0.604420\pi$
$643$	−7.90133e166	−0.644388	−0.322194	+	0.946674i	$0.604420\pi$
$644$	−3.54567e167	−2.63626
$645$	−1.82035e167	−1.23410
$646$	−2.27268e166	−0.140509
$647$	−3.21852e167	−1.81489	−0.907447	−	0.420167i	$-0.861971\pi$
$647$	−3.21852e167	−1.81489	−0.907447	+	0.420167i	$0.861971\pi$
$648$	5.00039e166	0.257212
$649$	3.00542e167	1.41041
$650$	−2.08737e167	−0.893828
$651$	1.03039e167	0.402656
$652$	1.66705e167	0.594590
$653$	5.19173e167	1.69035	0.845177	−	0.534487i	$-0.179495\pi$
$653$	5.19173e167	1.69035	0.845177	+	0.534487i	$0.179495\pi$
$654$	−4.15084e167	−1.23384
$655$	5.26219e167	1.42827
$656$	−1.99010e167	−0.493282
$657$	−5.30604e166	−0.120124
$658$	−4.88382e167	−1.00999
$659$	7.86104e167	1.48524	0.742622	−	0.669711i	$-0.233582\pi$
$659$	7.86104e167	1.48524	0.742622	+	0.669711i	$0.233582\pi$
$660$	7.99652e167	1.38050
$661$	−3.24639e167	−0.512169	−0.256085	−	0.966654i	$-0.582433\pi$
$661$	−3.24639e167	−0.512169	−0.256085	+	0.966654i	$0.582433\pi$
$662$	7.10495e167	1.02450
$663$	−1.08218e167	−0.142641
$664$	−8.58835e167	−1.03492
$665$	2.50516e167	0.276024
$666$	−6.00377e167	−0.604933
$667$	−6.38256e167	−0.588177
$668$	−1.21167e168	−1.02137
$669$	−7.22066e167	−0.556831
$670$	3.46988e168	2.44829
$671$	−6.55921e166	−0.0423508
$672$	−1.61054e168	−0.951701
$673$	−1.27707e168	−0.690745	−0.345372	−	0.938466i	$-0.612247\pi$
$673$	−1.27707e168	−0.690745	−0.345372	+	0.938466i	$0.612247\pi$
$674$	3.02036e167	0.149553
$675$	2.73938e168	1.24187
$676$	−2.85542e168	−1.18534
$677$	−1.98510e168	−0.754668	−0.377334	−	0.926077i	$-0.623159\pi$
$677$	−1.98510e168	−0.754668	−0.377334	+	0.926077i	$0.623159\pi$
$678$	2.90851e168	1.01275
$679$	−4.24192e168	−1.35304
$680$	2.71128e168	0.792307
$681$	−2.26427e168	−0.606282
$682$	4.91488e168	1.20599
$683$	8.39342e168	1.88759	0.943794	−	0.330535i	$-0.107229\pi$
$683$	8.39342e168	1.88759	0.943794	+	0.330535i	$0.107229\pi$
$684$	−5.75830e167	−0.118701
$685$	−1.04320e169	−1.97141
$686$	−8.47911e168	−1.46915
$687$	−3.31452e168	−0.526617
$688$	5.62822e168	0.820085
$689$	4.20497e168	0.561978
$690$	1.06613e169	1.30704
$691$	−1.71347e169	−1.92723	−0.963615	−	0.267293i	$-0.913871\pi$
$691$	−1.71347e169	−1.92723	−0.963615	+	0.267293i	$0.913871\pi$
$692$	2.05584e169	2.12166
$693$	1.90221e169	1.80149
$694$	1.80827e169	1.57172
$695$	−1.19982e169	−0.957242
$696$	1.78130e168	0.130463
$697$	−1.30855e169	−0.879911
$698$	−1.28299e169	−0.792181
$699$	1.11973e169	0.634922
$700$	−6.57387e169	−3.42364
$701$	2.91654e169	1.39523	0.697614	−	0.716474i	$-0.254245\pi$
$701$	2.91654e169	1.39523	0.697614	+	0.716474i	$0.254245\pi$
$702$	−1.06436e169	−0.467769
$703$	1.30691e168	0.0527721
$704$	−5.89130e169	−2.18594
$705$	8.51626e168	0.290400
$706$	4.08316e169	1.27972
$707$	−4.28554e169	−1.23467
$708$	−2.35259e169	−0.623115
$709$	4.52414e169	1.10175	0.550877	−	0.834586i	$-0.314293\pi$
$709$	4.52414e169	1.10175	0.550877	+	0.834586i	$0.314293\pi$
$710$	6.77505e169	1.51719
$711$	−3.31359e169	−0.682429
$712$	2.93895e169	0.556715
$713$	3.80014e169	0.662175
$714$	−5.87684e169	−0.942107
$715$	5.68993e169	0.839262
$716$	7.40591e168	0.100520
$717$	8.92952e168	0.111542
$718$	1.74932e170	2.01124
$719$	1.37453e170	1.45473	0.727367	−	0.686248i	$-0.240744\pi$
$719$	1.37453e170	1.45473	0.727367	+	0.686248i	$0.240744\pi$
$720$	−6.20467e169	−0.604554
$721$	−8.63050e169	−0.774262
$722$	−1.84608e170	−1.52506
$723$	−8.53542e169	−0.649376
$724$	6.33791e169	0.444121
$725$	−1.18336e170	−0.763847
$726$	−1.11658e170	−0.663990
$727$	−1.98319e170	−1.08659	−0.543297	−	0.839541i	$-0.682824\pi$
$727$	−1.98319e170	−1.08659	−0.543297	+	0.839541i	$0.682824\pi$
$728$	7.04120e169	0.355492
$729$	2.39177e168	0.0111284
$730$	−8.61910e169	−0.369617
$731$	3.70072e170	1.46286
$732$	5.13444e168	0.0187104
$733$	3.20089e170	1.07543	0.537717	−	0.843125i	$-0.319287\pi$
$733$	3.20089e170	1.07543	0.537717	+	0.843125i	$0.319287\pi$
$734$	1.48816e170	0.461035
$735$	3.97828e170	1.13658
$736$	−5.93975e170	−1.56509
$737$	−5.73536e170	−1.39394
$738$	−5.71697e170	−1.28178
$739$	1.51579e170	0.313542	0.156771	−	0.987635i	$-0.449891\pi$
$739$	1.51579e170	0.313542	0.156771	+	0.987635i	$0.449891\pi$
$740$	−5.65581e170	−1.07946
$741$	1.02920e169	0.0181266
$742$	2.28353e171	3.71171
$743$	−8.69795e170	−1.30492	−0.652458	−	0.757825i	$-0.726262\pi$
$743$	−8.69795e170	−1.30492	−0.652458	+	0.757825i	$0.726262\pi$
$744$	−1.06058e170	−0.146876
$745$	−4.80087e170	−0.613792
$746$	1.19026e171	1.40502
$747$	1.29232e171	1.40862
$748$	−1.62567e171	−1.63639
$749$	−2.01795e170	−0.187604
$750$	6.93495e170	0.595523
$751$	1.12852e171	0.895224	0.447612	−	0.894228i	$-0.352275\pi$
$751$	1.12852e171	0.895224	0.447612	+	0.894228i	$0.352275\pi$
$752$	−2.63309e170	−0.192976
$753$	7.47755e170	0.506359
$754$	4.59786e170	0.287714
$755$	−6.05631e170	−0.350239
$756$	−3.35206e171	−1.79170
$757$	1.48750e171	0.734942	0.367471	−	0.930035i	$-0.380224\pi$
$757$	1.48750e171	0.734942	0.367471	+	0.930035i	$0.380224\pi$
$758$	−8.18845e169	−0.0374011
$759$	−1.76220e171	−0.744165
$760$	−2.57854e170	−0.100685
$761$	3.19347e171	1.15312	0.576561	−	0.817054i	$-0.304394\pi$
$761$	3.19347e171	1.15312	0.576561	+	0.817054i	$0.304394\pi$
$762$	1.26403e171	0.422120
$763$	−9.30175e171	−2.87313
$764$	4.65092e170	0.132887
$765$	−4.07975e171	−1.07840
$766$	−2.76771e171	−0.676877
$767$	−1.67399e171	−0.378816
$768$	2.55886e170	0.0535862
$769$	−2.71738e171	−0.526663	−0.263331	−	0.964705i	$-0.584821\pi$
$769$	−2.71738e171	−0.526663	−0.263331	+	0.964705i	$0.584821\pi$
$770$	3.08994e172	5.54309
$771$	−1.00473e170	−0.0166846
$772$	−1.53055e172	−2.35297
$773$	−3.75965e171	−0.535140	−0.267570	−	0.963538i	$-0.586221\pi$
$773$	−3.75965e171	−0.535140	−0.267570	+	0.963538i	$0.586221\pi$
$774$	1.61683e172	2.13096
$775$	7.04567e171	0.859946
$776$	4.36617e171	0.493546
$777$	3.37950e171	0.353836
$778$	3.70440e171	0.359279
$779$	1.24448e171	0.111817
$780$	−4.45398e171	−0.370783
$781$	−1.11985e172	−0.863819
$782$	−2.16741e172	−1.54931
$783$	−6.03405e171	−0.399746
$784$	−1.23002e172	−0.755277
$785$	−2.35572e170	−0.0134085
$786$	1.17402e172	0.619489
$787$	3.53728e172	1.73051	0.865253	−	0.501335i	$-0.167158\pi$
$787$	3.53728e172	1.73051	0.865253	+	0.501335i	$0.167158\pi$
$788$	−4.78640e172	−2.17120
$789$	−1.04397e172	−0.439145
$790$	−5.38258e172	−2.09980
$791$	6.51778e172	2.35830
$792$	−1.95793e172	−0.657127
$793$	3.65341e170	0.0113748
$794$	8.55414e172	2.47091
$795$	−3.98195e172	−1.06721
$796$	3.13329e172	0.779242
$797$	3.04135e172	0.701934	0.350967	−	0.936388i	$-0.385853\pi$
$797$	3.04135e172	0.701934	0.350967	+	0.936388i	$0.385853\pi$
$798$	5.58912e171	0.119721
$799$	−1.73133e172	−0.344229
$800$	−1.10126e173	−2.03253
$801$	−4.42235e172	−0.757736
$802$	−4.20100e172	−0.668309
$803$	1.42465e172	0.210442
$804$	4.48954e172	0.615839
$805$	2.38912e173	3.04356
$806$	−2.73754e172	−0.323911
$807$	3.99164e172	0.438708
$808$	4.41107e172	0.450368
$809$	−5.82176e172	−0.552226	−0.276113	−	0.961125i	$-0.589046\pi$
$809$	−5.82176e172	−0.552226	−0.276113	+	0.961125i	$0.589046\pi$
$810$	−1.22224e173	−1.07720
$811$	−1.62862e173	−1.33376	−0.666881	−	0.745164i	$-0.732371\pi$
$811$	−1.62862e173	−1.33376	−0.666881	+	0.745164i	$0.732371\pi$
$812$	1.44803e173	1.10203
$813$	3.33803e172	0.236104
$814$	1.61199e173	1.05977
$815$	−1.12328e173	−0.686453
$816$	−3.16847e172	−0.180005
$817$	−3.51954e172	−0.185897
$818$	5.74024e173	2.81909
$819$	−1.05951e173	−0.483854
$820$	−5.38563e173	−2.28724
$821$	−1.40317e173	−0.554232	−0.277116	−	0.960836i	$-0.589379\pi$
$821$	−1.40317e173	−0.554232	−0.277116	+	0.960836i	$0.589379\pi$
$822$	−2.32742e173	−0.855069
$823$	4.21904e172	0.144186	0.0720930	−	0.997398i	$-0.477032\pi$
$823$	4.21904e172	0.144186	0.0720930	+	0.997398i	$0.477032\pi$
$824$	8.88330e172	0.282426
$825$	−3.26722e173	−0.966424
$826$	−9.09067e173	−2.50198
$827$	−1.05591e173	−0.270427	−0.135213	−	0.990817i	$-0.543172\pi$
$827$	−1.05591e173	−0.270427	−0.135213	+	0.990817i	$0.543172\pi$
$828$	−5.49157e173	−1.30885
$829$	8.80480e173	1.95310	0.976551	−	0.215284i	$-0.0690678\pi$
$829$	8.80480e173	1.95310	0.976551	+	0.215284i	$0.0690678\pi$
$830$	2.09923e174	4.33425
$831$	2.19879e173	0.422593
$832$	3.28139e173	0.587111
$833$	−8.08774e173	−1.34725
$834$	−2.67686e173	−0.415189
$835$	8.16436e173	1.17917
$836$	1.54608e173	0.207950
$837$	3.59264e173	0.450038
$838$	1.27465e174	1.48721
$839$	−8.93031e173	−0.970577	−0.485288	−	0.874354i	$-0.661285\pi$
$839$	−8.93031e173	−0.970577	−0.485288	+	0.874354i	$0.661285\pi$
$840$	−6.66775e173	−0.675090
$841$	−7.99476e173	−0.754126
$842$	−3.02291e173	−0.265678
$843$	−1.80587e173	−0.147892
$844$	−3.96035e173	−0.302244
$845$	1.92402e174	1.36847
$846$	−7.56411e173	−0.501442
$847$	−2.50218e174	−1.54617
$848$	1.23115e174	0.709184
$849$	1.38952e173	0.0746203
$850$	−4.01849e174	−2.01204
$851$	1.24637e174	0.581888
$852$	8.76598e173	0.381632
$853$	−3.07037e174	−1.24659	−0.623295	−	0.781987i	$-0.714206\pi$
$853$	−3.07037e174	−1.24659	−0.623295	+	0.781987i	$0.714206\pi$
$854$	1.98400e173	0.0751275
$855$	3.88001e173	0.137041
$856$	2.07706e173	0.0684321
$857$	−1.19991e174	−0.368800	−0.184400	−	0.982851i	$-0.559034\pi$
$857$	−1.19991e174	−0.368800	−0.184400	+	0.982851i	$0.559034\pi$
$858$	1.26945e174	0.364017
$859$	−9.59016e173	−0.256586	−0.128293	−	0.991736i	$-0.540950\pi$
$859$	−9.59016e173	−0.256586	−0.128293	+	0.991736i	$0.540950\pi$
$860$	1.52312e175	3.80256
$861$	3.21806e174	0.749734
$862$	−4.34959e174	−0.945726
$863$	6.91293e174	1.40288	0.701438	−	0.712730i	$-0.252542\pi$
$863$	6.91293e174	1.40288	0.701438	+	0.712730i	$0.252542\pi$
$864$	−5.61542e174	−1.06369
$865$	−1.38525e175	−2.44945
$866$	1.41661e174	0.233850
$867$	8.23835e173	0.126971
$868$	−8.62149e174	−1.24068
$869$	8.89686e174	1.19553
$870$	−4.35400e174	−0.546377
$871$	3.19454e174	0.374393
$872$	9.57421e174	1.04803
$873$	−6.56993e174	−0.671758
$874$	2.06129e174	0.196883
$875$	1.55408e175	1.38673
$876$	−1.11519e174	−0.0929726
$877$	4.02303e174	0.313384	0.156692	−	0.987647i	$-0.449917\pi$
$877$	4.02303e174	0.313384	0.156692	+	0.987647i	$0.449917\pi$
$878$	−1.17895e175	−0.858163
$879$	−4.83845e174	−0.329130
$880$	1.66593e175	1.05910
$881$	2.82462e174	0.167839	0.0839196	−	0.996473i	$-0.473256\pi$
$881$	2.82462e174	0.167839	0.0839196	+	0.996473i	$0.473256\pi$
$882$	−3.53349e175	−1.96256
$883$	−1.18908e175	−0.617377	−0.308688	−	0.951163i	$-0.599890\pi$
$883$	−1.18908e175	−0.617377	−0.308688	+	0.951163i	$0.599890\pi$
$884$	9.05482e174	0.439511
$885$	1.58521e175	0.719384
$886$	−5.75180e175	−2.44060
$887$	1.69948e174	0.0674312	0.0337156	−	0.999431i	$-0.489266\pi$
$887$	1.69948e174	0.0674312	0.0337156	+	0.999431i	$0.489266\pi$
$888$	−3.47849e174	−0.129068
$889$	2.83260e175	0.982947
$890$	−7.18363e175	−2.33152
$891$	2.02023e175	0.613307
$892$	6.04166e175	1.71572
$893$	1.64657e174	0.0437440
$894$	−1.07110e175	−0.266223
$895$	−4.99019e174	−0.116050
$896$	8.05887e175	1.75367
$897$	9.81527e174	0.199872
$898$	9.63851e175	1.83682
$899$	−1.55196e175	−0.276807
$900$	−1.01817e176	−1.69977
$901$	8.09519e175	1.26503
$902$	1.53498e176	2.24551
$903$	−9.10105e175	−1.24644
$904$	−6.70869e175	−0.860233
$905$	−4.27056e175	−0.512737
$906$	−1.35119e175	−0.151911
$907$	−7.60382e175	−0.800568	−0.400284	−	0.916391i	$-0.631089\pi$
$907$	−7.60382e175	−0.800568	−0.400284	+	0.916391i	$0.631089\pi$
$908$	1.89455e176	1.86810
$909$	−6.63748e175	−0.612989
$910$	−1.72107e176	−1.48879
$911$	−1.12091e176	−0.908292	−0.454146	−	0.890927i	$-0.650056\pi$
$911$	−1.12091e176	−0.908292	−0.454146	+	0.890927i	$0.650056\pi$
$912$	3.01335e174	0.0228748
$913$	−3.46982e176	−2.46772
$914$	3.95172e175	0.263322
$915$	−3.45965e174	−0.0216011
$916$	2.77332e176	1.62263
$917$	2.63090e176	1.44254
$918$	−2.04906e176	−1.05297
$919$	1.76582e176	0.850499	0.425250	−	0.905076i	$-0.360186\pi$
$919$	1.76582e176	0.850499	0.425250	+	0.905076i	$0.360186\pi$
$920$	−2.45910e176	−1.11020
$921$	−1.30799e175	−0.0553549
$922$	−1.02965e176	−0.408506
$923$	6.23744e175	0.232009
$924$	3.99796e176	1.39430
$925$	2.31085e176	0.755681
$926$	5.13541e176	1.57479
$927$	−1.33670e176	−0.384406
$928$	2.42576e176	0.654250
$929$	−6.78656e176	−1.71678	−0.858390	−	0.512998i	$-0.828535\pi$
$929$	−6.78656e176	−1.71678	−0.858390	+	0.512998i	$0.828535\pi$
$930$	2.59235e176	0.615117
$931$	7.69177e175	0.171207
$932$	−9.36896e176	−1.95634
$933$	2.45941e175	0.0481807
$934$	−9.40316e176	−1.72836
$935$	1.09540e177	1.88921
$936$	1.09055e176	0.176495
$937$	−2.53202e176	−0.384557	−0.192279	−	0.981340i	$-0.561588\pi$
$937$	−2.53202e176	−0.384557	−0.192279	+	0.981340i	$0.561588\pi$
$938$	1.73481e177	2.47276
$939$	−5.12026e176	−0.684999
$940$	−7.12571e176	−0.894789
$941$	−2.31842e176	−0.273281	−0.136641	−	0.990621i	$-0.543631\pi$
$941$	−2.31842e176	−0.273281	−0.136641	+	0.990621i	$0.543631\pi$
$942$	−5.25572e174	−0.00581573
$943$	1.18684e177	1.23295
$944$	−4.90120e176	−0.478045
$945$	2.25866e177	2.06851
$946$	−4.34111e177	−3.73317
$947$	−5.03885e176	−0.406919	−0.203459	−	0.979083i	$-0.565218\pi$
$947$	−5.03885e176	−0.406919	−0.203459	+	0.979083i	$0.565218\pi$
$948$	−6.96431e176	−0.528180
$949$	−7.93516e175	−0.0565218
$950$	3.82175e176	0.255686
$951$	−1.07077e177	−0.672907
$952$	1.35554e177	0.800226
$953$	−5.01897e176	−0.278347	−0.139174	−	0.990268i	$-0.544445\pi$
$953$	−5.01897e176	−0.278347	−0.139174	+	0.990268i	$0.544445\pi$
$954$	3.53675e177	1.84279
$955$	−3.13385e176	−0.153418
$956$	−7.47149e176	−0.343687
$957$	7.19672e176	0.311082
$958$	2.89141e177	1.17453
$959$	−5.21558e177	−1.99111
$960$	−3.10736e177	−1.11494
$961$	−2.04109e177	−0.688368
$962$	−8.97861e176	−0.284638
$963$	−3.12542e176	−0.0931418
$964$	7.14174e177	2.00088
$965$	1.03130e178	2.71650
$966$	5.33022e177	1.32010
$967$	4.71522e177	1.09806	0.549031	−	0.835802i	$-0.314997\pi$
$967$	4.71522e177	1.09806	0.549031	+	0.835802i	$0.314997\pi$
$968$	2.57548e177	0.563993
$969$	1.98137e176	0.0408037
$970$	−1.06721e178	−2.06697
$971$	−1.94614e176	−0.0354512	−0.0177256	−	0.999843i	$-0.505643\pi$
$971$	−1.94614e176	−0.0354512	−0.0177256	+	0.999843i	$0.505643\pi$
$972$	−8.07721e177	−1.38394
$973$	−5.99866e177	−0.966809
$974$	−4.41800e177	−0.669835
$975$	1.81981e177	0.259568
$976$	1.06967e176	0.0143544
$977$	−1.03381e178	−1.30531	−0.652656	−	0.757654i	$-0.726345\pi$
$977$	−1.03381e178	−1.30531	−0.652656	+	0.757654i	$0.726345\pi$
$978$	−2.50609e177	−0.297739
$979$	1.18738e178	1.32746
$980$	−3.32870e178	−3.50206
$981$	−1.44067e178	−1.42645
$982$	2.21128e178	2.06068
$983$	1.02914e178	0.902697	0.451348	−	0.892348i	$-0.350943\pi$
$983$	1.02914e178	0.902697	0.451348	+	0.892348i	$0.350943\pi$
$984$	−3.31232e177	−0.273479
$985$	3.22514e178	2.50664
$986$	8.85156e177	0.647655
$987$	4.25781e177	0.293302
$988$	−8.61151e176	−0.0558523
$989$	−3.35651e178	−2.04979
$990$	4.78573e178	2.75204
$991$	−1.04866e178	−0.567873	−0.283937	−	0.958843i	$-0.591641\pi$
$991$	−1.04866e178	−0.567873	−0.283937	+	0.958843i	$0.591641\pi$
$992$	−1.44428e178	−0.736560
$993$	−6.19424e177	−0.297514
$994$	3.38727e178	1.53236
$995$	−2.11125e178	−0.899634
$996$	2.71612e178	1.09023
$997$	−2.17329e178	−0.821781	−0.410891	−	0.911685i	$-0.634782\pi$
$997$	−2.17329e178	−0.821781	−0.410891	+	0.911685i	$0.634782\pi$
$998$	−8.03651e177	−0.286286
$999$	1.17832e178	0.395472

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1.120.a.a.1.9	✓	10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1.120.a.a.1.9	✓	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)

\(f(q)\)	\(=\)	\(q+1.25784e18 q^{2} -1.09661e28 q^{3} +9.17555e35 q^{4} -6.18260e41 q^{5} -1.37937e46 q^{6} -3.09107e50 q^{7} +3.18161e53 q^{8} -4.78748e56 q^{9} +O(q^{10})\)	\(q+1.25784e18 q^{2} -1.09661e28 q^{3} +9.17555e35 q^{4} -6.18260e41 q^{5} -1.37937e46 q^{6} -3.09107e50 q^{7} +3.18161e53 q^{8} -4.78748e56 q^{9} -7.77674e59 q^{10} +1.28542e62 q^{11} -1.00620e64 q^{12} -7.15965e65 q^{13} -3.88808e68 q^{14} +6.77992e69 q^{15} -2.09624e71 q^{16} -1.37834e73 q^{17} -6.02189e74 q^{18} +1.31086e75 q^{19} -5.67288e77 q^{20} +3.38970e78 q^{21} +1.61685e80 q^{22} +1.25014e81 q^{23} -3.48899e81 q^{24} +2.31782e83 q^{25} -9.00571e83 q^{26} +1.18188e85 q^{27} -2.83622e86 q^{28} -5.10549e86 q^{29} +8.52807e87 q^{30} +3.03978e88 q^{31} -4.75128e89 q^{32} -1.40961e90 q^{33} -1.73373e91 q^{34} +1.91108e92 q^{35} -4.39277e92 q^{36} +9.96990e92 q^{37} +1.64885e93 q^{38} +7.85136e93 q^{39} -1.96706e95 q^{40} +9.49364e95 q^{41} +4.26371e96 q^{42} -2.68491e97 q^{43} +1.17944e98 q^{44} +2.95991e98 q^{45} +1.57248e99 q^{46} +1.25610e99 q^{47} +2.29876e99 q^{48} +5.86774e100 q^{49} +2.91546e101 q^{50} +1.51150e101 q^{51} -6.56937e101 q^{52} -5.87315e102 q^{53} +1.48661e103 q^{54} -7.94723e103 q^{55} -9.83456e103 q^{56} -1.43750e103 q^{57} -6.42190e104 q^{58} +2.33809e105 q^{59} +6.22095e105 q^{60} -5.10278e104 q^{61} +3.82356e106 q^{62} +1.47984e107 q^{63} -4.58318e107 q^{64} +4.42652e107 q^{65} -1.77306e108 q^{66} -4.46187e108 q^{67} -1.26470e109 q^{68} -1.37092e109 q^{69} +2.40384e110 q^{70} -8.71194e109 q^{71} -1.52319e110 q^{72} +1.10832e110 q^{73} +1.25406e111 q^{74} -2.54175e111 q^{75} +1.20278e111 q^{76} -3.97331e112 q^{77} +9.87578e111 q^{78} +6.92138e112 q^{79} +1.29602e113 q^{80} +1.57166e113 q^{81} +1.19415e114 q^{82} -2.69937e114 q^{83} +3.11024e114 q^{84} +8.52172e114 q^{85} -3.37720e115 q^{86} +5.59874e114 q^{87} +4.08969e115 q^{88} +9.23733e115 q^{89} +3.72310e116 q^{90} +2.21309e116 q^{91} +1.14707e117 q^{92} -3.33346e116 q^{93} +1.57998e117 q^{94} -8.10451e116 q^{95} +5.21031e117 q^{96} +1.37232e118 q^{97} +7.38070e118 q^{98} -6.15391e118 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + 91\!\cdots\!00 q^{2}+ \cdots + 18\!\cdots\!70 q^{9}+O(q^{10}) \) 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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