LMFDB - Embedded newform 1.120.a.a.1.7

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			1.7
Root			$-3.19227e16$ 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)

$f(q)$	$=$	$q+8.58138e17 q^{2} +9.54518e27 q^{3} +7.17860e34 q^{4} -1.94208e41 q^{5} +8.19107e45 q^{6} +3.78566e50 q^{7} -5.08728e53 q^{8} -5.07893e56 q^{9} +O(q^{10})$	\(q+8.58138e17 q^{2} +9.54518e27 q^{3} +7.17860e34 q^{4} -1.94208e41 q^{5} +8.19107e45 q^{6} +3.78566e50 q^{7} -5.08728e53 q^{8} -5.07893e56 q^{9} -1.66657e59 q^{10} -8.28552e61 q^{11} +6.85210e62 q^{12} +2.29727e66 q^{13} +3.24861e68 q^{14} -1.85375e69 q^{15} -4.84269e71 q^{16} +2.23869e73 q^{17} -4.35842e74 q^{18} -9.99106e75 q^{19} -1.39414e76 q^{20} +3.61348e78 q^{21} -7.11012e79 q^{22} +1.34928e81 q^{23} -4.85590e81 q^{24} -1.12746e83 q^{25} +1.97138e84 q^{26} -1.05655e85 q^{27} +2.71757e85 q^{28} +2.05034e86 q^{29} -1.59077e87 q^{30} +6.89597e88 q^{31} -7.74612e88 q^{32} -7.90868e89 q^{33} +1.92110e91 q^{34} -7.35206e91 q^{35} -3.64596e91 q^{36} +6.69127e92 q^{37} -8.57370e93 q^{38} +2.19279e94 q^{39} +9.87991e94 q^{40} -1.85272e95 q^{41} +3.10086e96 q^{42} +3.94503e96 q^{43} -5.94784e96 q^{44} +9.86370e97 q^{45} +1.15787e99 q^{46} +3.59690e99 q^{47} -4.62243e99 q^{48} +1.06443e101 q^{49} -9.67520e100 q^{50} +2.13687e101 q^{51} +1.64912e101 q^{52} -1.01746e102 q^{53} -9.06667e102 q^{54} +1.60912e103 q^{55} -1.92587e104 q^{56} -9.53664e103 q^{57} +1.75947e104 q^{58} +7.81017e104 q^{59} -1.33073e104 q^{60} +2.02233e106 q^{61} +5.91769e106 q^{62} -1.92271e107 q^{63} +2.55379e107 q^{64} -4.46149e107 q^{65} -6.78673e107 q^{66} -3.75667e108 q^{67} +1.60707e108 q^{68} +1.28791e109 q^{69} -6.30908e109 q^{70} +2.20728e110 q^{71} +2.58379e110 q^{72} -4.83130e110 q^{73} +5.74203e110 q^{74} -1.07618e111 q^{75} -7.17218e110 q^{76} -3.13661e112 q^{77} +1.88171e112 q^{78} +6.29729e112 q^{79} +9.40489e112 q^{80} +2.03380e113 q^{81} -1.58989e113 q^{82} +1.13104e114 q^{83} +2.59397e113 q^{84} -4.34772e114 q^{85} +3.38538e114 q^{86} +1.95708e114 q^{87} +4.21508e115 q^{88} +3.58879e115 q^{89} +8.46441e115 q^{90} +8.69669e116 q^{91} +9.68593e115 q^{92} +6.58233e116 q^{93} +3.08664e117 q^{94} +1.94035e117 q^{95} -7.39381e116 q^{96} -6.16605e117 q^{97} +9.13424e118 q^{98} +4.20816e118 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	8.58138e17	1.05262	0.526311	−	0.850292i	$-0.323575\pi$
$2$	8.58138e17	1.05262	0.526311	+	0.850292i	$0.323575\pi$
$3$	9.54518e27	0.390004	0.195002	−	0.980803i	$-0.437529\pi$
$3$	9.54518e27	0.390004	0.195002	+	0.980803i	$0.437529\pi$
$4$	7.17860e34	0.108012
$5$	−1.94208e41	−0.500671	−0.250335	−	0.968159i	$-0.580541\pi$
$5$	−1.94208e41	−0.500671	−0.250335	+	0.968159i	$0.580541\pi$
$6$	8.19107e45	0.410527
$7$	3.78566e50	1.97155	0.985775	−	0.168068i	$-0.0537529\pi$
$7$	3.78566e50	1.97155	0.985775	+	0.168068i	$0.0537529\pi$
$8$	−5.08728e53	−0.938926
$9$	−5.07893e56	−0.847897
$10$	−1.66657e59	−0.527017
$11$	−8.28552e61	−0.902516	−0.451258	−	0.892393i	$-0.649025\pi$
$11$	−8.28552e61	−0.902516	−0.451258	+	0.892393i	$0.649025\pi$
$12$	6.85210e62	0.0421250
$13$	2.29727e66	1.20666	0.603328	−	0.797493i	$-0.293841\pi$
$13$	2.29727e66	1.20666	0.603328	+	0.797493i	$0.293841\pi$
$14$	3.24861e68	2.07530
$15$	−1.85375e69	−0.195264
$16$	−4.84269e71	−1.09635
$17$	2.23869e73	1.37494	0.687469	−	0.726213i	$-0.258722\pi$
$17$	2.23869e73	1.37494	0.687469	+	0.726213i	$0.258722\pi$
$18$	−4.35842e74	−0.892514
$19$	−9.99106e75	−0.819922	−0.409961	−	0.912103i	$-0.634458\pi$
$19$	−9.99106e75	−0.819922	−0.409961	+	0.912103i	$0.634458\pi$
$20$	−1.39414e76	−0.0540782
$21$	3.61348e78	0.768913
$22$	−7.11012e79	−0.950008
$23$	1.34928e81	1.28025	0.640126	−	0.768270i	$-0.278882\pi$
$23$	1.34928e81	1.28025	0.640126	+	0.768270i	$0.278882\pi$
$24$	−4.85590e81	−0.366185
$25$	−1.12746e83	−0.749329
$26$	1.97138e84	1.27015
$27$	−1.05655e85	−0.720688
$28$	2.71757e85	0.212950
$29$	2.05034e86	0.199134	0.0995668	−	0.995031i	$-0.468254\pi$
$29$	2.05034e86	0.199134	0.0995668	+	0.995031i	$0.468254\pi$
$30$	−1.59077e87	−0.205539
$31$	6.89597e88	1.26641	0.633206	−	0.773984i	$-0.281739\pi$
$31$	6.89597e88	1.26641	0.633206	+	0.773984i	$0.281739\pi$
$32$	−7.74612e88	−0.215110
$33$	−7.90868e89	−0.351985
$34$	1.92110e91	1.44729
$35$	−7.35206e91	−0.987098
$36$	−3.64596e91	−0.0915826
$37$	6.69127e92	0.329235	0.164618	−	0.986357i	$-0.447361\pi$
$37$	6.69127e92	0.329235	0.164618	+	0.986357i	$0.447361\pi$
$38$	−8.57370e93	−0.863067
$39$	2.19279e94	0.470601
$40$	9.87991e94	0.470093
$41$	−1.85272e95	−0.202848	−0.101424	−	0.994843i	$-0.532340\pi$
$41$	−1.85272e95	−0.202848	−0.101424	+	0.994843i	$0.532340\pi$
$42$	3.10086e96	0.809374
$43$	3.94503e96	0.253908	0.126954	−	0.991909i	$-0.459480\pi$
$43$	3.94503e96	0.253908	0.126954	+	0.991909i	$0.459480\pi$
$44$	−5.94784e96	−0.0974822
$45$	9.86370e97	0.424517
$46$	1.15787e99	1.34762
$47$	3.59690e99	1.16441	0.582205	−	0.813042i	$-0.302190\pi$
$47$	3.59690e99	1.16441	0.582205	+	0.813042i	$0.302190\pi$
$48$	−4.62243e99	−0.427579
$49$	1.06443e101	2.88701
$50$	−9.67520e100	−0.788759
$51$	2.13687e101	0.536232
$52$	1.64912e101	0.130333
$53$	−1.01746e102	−0.258884	−0.129442	−	0.991587i	$-0.541319\pi$
$53$	−1.01746e102	−0.258884	−0.129442	+	0.991587i	$0.541319\pi$
$54$	−9.06667e102	−0.758611
$55$	1.60912e103	0.451864
$56$	−1.92587e104	−1.85114
$57$	−9.53664e103	−0.319773
$58$	1.75947e104	0.209612
$59$	7.81017e104	0.336485	0.168243	−	0.985746i	$-0.446191\pi$
$59$	7.81017e104	0.336485	0.168243	+	0.985746i	$0.446191\pi$
$60$	−1.33073e104	−0.0210907
$61$	2.02233e106	1.19874	0.599372	−	0.800470i	$-0.295417\pi$
$61$	2.02233e106	1.19874	0.599372	+	0.800470i	$0.295417\pi$
$62$	5.91769e106	1.33305
$63$	−1.92271e107	−1.67167
$64$	2.55379e107	0.869916
$65$	−4.46149e107	−0.604137
$66$	−6.78673e107	−0.370507
$67$	−3.75667e108	−0.838208	−0.419104	−	0.907938i	$-0.637656\pi$
$67$	−3.75667e108	−0.838208	−0.419104	+	0.907938i	$0.637656\pi$
$68$	1.60707e108	0.148509
$69$	1.28791e109	0.499303
$70$	−6.30908e109	−1.03904
$71$	2.20728e110	1.56309	0.781547	−	0.623846i	$-0.214431\pi$
$71$	2.20728e110	1.56309	0.781547	+	0.623846i	$0.214431\pi$
$72$	2.58379e110	0.796112
$73$	−4.83130e110	−0.655169	−0.327585	−	0.944822i	$-0.606235\pi$
$73$	−4.83130e110	−0.655169	−0.327585	+	0.944822i	$0.606235\pi$
$74$	5.74203e110	0.346560
$75$	−1.07618e111	−0.292241
$76$	−7.17218e110	−0.0885610
$77$	−3.13661e112	−1.77936
$78$	1.88171e112	0.495364
$79$	6.29729e112	0.776858	0.388429	−	0.921479i	$-0.373018\pi$
$79$	6.29729e112	0.776858	0.388429	+	0.921479i	$0.373018\pi$
$80$	9.40489e112	0.548908
$81$	2.03380e113	0.566826
$82$	−1.58989e113	−0.213522
$83$	1.13104e114	0.738469	0.369234	−	0.929336i	$-0.379620\pi$
$83$	1.13104e114	0.738469	0.369234	+	0.929336i	$0.379620\pi$
$84$	2.59397e113	0.0830515
$85$	−4.34772e114	−0.688392
$86$	3.38538e114	0.267269
$87$	1.95708e114	0.0776629
$88$	4.21508e115	0.847396
$89$	3.58879e115	0.368335	0.184167	−	0.982895i	$-0.441041\pi$
$89$	3.58879e115	0.368335	0.184167	+	0.982895i	$0.441041\pi$
$90$	8.46441e115	0.446856
$91$	8.69669e116	2.37898
$92$	9.68593e115	0.138282
$93$	6.58233e116	0.493906
$94$	3.08664e117	1.22568
$95$	1.94035e117	0.410511
$96$	−7.39381e116	−0.0838938
$97$	−6.16605e117	−0.377649	−0.188825	−	0.982011i	$-0.560468\pi$
$97$	−6.16605e117	−0.377649	−0.188825	+	0.982011i	$0.560468\pi$
$98$	9.13424e118	3.03893
$99$	4.20816e118	0.765241
$100$	−8.09362e117	−0.0809362
$101$	2.96166e119	1.63838	0.819189	−	0.573524i	$-0.194424\pi$
$101$	2.96166e119	1.63838	0.819189	+	0.573524i	$0.194424\pi$
$102$	1.83373e119	0.564449
$103$	1.17319e118	0.0202093	0.0101047	−	0.999949i	$-0.496784\pi$
$103$	1.17319e118	0.0202093	0.0101047	+	0.999949i	$0.496784\pi$
$104$	−1.16869e120	−1.13296
$105$	−7.01767e119	−0.384972
$106$	−8.73124e119	−0.272507
$107$	−8.53651e118	−0.0152386	−0.00761931	−	0.999971i	$-0.502425\pi$
$107$	−8.53651e118	−0.0152386	−0.00761931	+	0.999971i	$0.502425\pi$
$108$	−7.58456e119	−0.0778426
$109$	−2.29938e121	−1.36375	−0.681875	−	0.731469i	$-0.738835\pi$
$109$	−2.29938e121	−1.36375	−0.681875	+	0.731469i	$0.738835\pi$
$110$	1.38084e121	0.475641
$111$	6.38694e120	0.128403
$112$	−1.83327e122	−2.16150
$113$	−2.37206e121	−0.164800	−0.0824001	−	0.996599i	$-0.526259\pi$
$113$	−2.37206e121	−0.164800	−0.0824001	+	0.996599i	$0.526259\pi$
$114$	−8.18375e121	−0.336600
$115$	−2.62041e122	−0.640985
$116$	1.47185e121	0.0215087
$117$	−1.16677e123	−1.02312
$118$	6.70220e122	0.354191
$119$	8.47492e123	2.71076
$120$	9.43055e122	0.183338
$121$	−1.56311e123	−0.185464
$122$	1.73544e124	1.26182
$123$	−1.76845e123	−0.0791115
$124$	4.95034e123	0.136787
$125$	5.11175e124	0.875838
$126$	−1.64995e125	−1.75964
$127$	1.15453e125	0.769277	0.384638	−	0.923067i	$-0.374326\pi$
$127$	1.15453e125	0.769277	0.384638	+	0.923067i	$0.374326\pi$
$128$	2.70632e125	1.13080
$129$	3.76560e124	0.0990253
$130$	−3.82858e125	−0.635928
$131$	−6.51746e125	−0.686177	−0.343089	−	0.939303i	$-0.611473\pi$
$131$	−6.51746e125	−0.686177	−0.343089	+	0.939303i	$0.611473\pi$
$132$	−5.67732e124	−0.0380185
$133$	−3.78227e126	−1.61652
$134$	−3.22374e126	−0.882315
$135$	2.05191e126	0.360827
$136$	−1.13888e127	−1.29097
$137$	6.41681e126	0.470376	0.235188	−	0.971950i	$-0.424429\pi$
$137$	6.41681e126	0.470376	0.235188	+	0.971950i	$0.424429\pi$
$138$	1.10520e127	0.525577
$139$	3.11228e127	0.963161	0.481580	−	0.876402i	$-0.340063\pi$
$139$	3.11228e127	0.963161	0.481580	+	0.876402i	$0.340063\pi$
$140$	−5.27775e126	−0.106618
$141$	3.43331e127	0.454125
$142$	1.89415e128	1.64535
$143$	−1.90341e128	−1.08903
$144$	2.45957e128	0.929587
$145$	−3.98192e127	−0.0997004
$146$	−4.14592e128	−0.689645
$147$	1.01601e129	1.12595
$148$	4.80340e127	0.0355612
$149$	−1.31759e129	−0.653426	−0.326713	−	0.945124i	$-0.605941\pi$
$149$	−1.31759e129	−0.653426	−0.326713	+	0.945124i	$0.605941\pi$
$150$	−9.23515e128	−0.307619
$151$	6.22066e127	0.0139543	0.00697715	−	0.999976i	$-0.497779\pi$
$151$	6.22066e127	0.0139543	0.00697715	+	0.999976i	$0.497779\pi$
$152$	5.08273e129	0.769846
$153$	−1.13702e130	−1.16581
$154$	−2.69165e130	−1.87299
$155$	−1.33925e130	−0.634055
$156$	1.57412e129	0.0508303
$157$	1.47261e130	0.325130	0.162565	−	0.986698i	$-0.448023\pi$
$157$	1.47261e130	0.325130	0.162565	+	0.986698i	$0.448023\pi$
$158$	5.40394e130	0.817737
$159$	−9.71188e129	−0.100966
$160$	1.50436e130	0.107699
$161$	5.10791e131	2.52408
$162$	1.74528e131	0.596653
$163$	−5.52329e131	−1.30929	−0.654644	−	0.755937i	$-0.727182\pi$
$163$	−5.52329e131	−1.30929	−0.654644	+	0.755937i	$0.727182\pi$
$164$	−1.32999e130	−0.0219099
$165$	1.53593e131	0.176229
$166$	9.70589e131	0.777328
$167$	−1.31181e132	−0.734920	−0.367460	−	0.930039i	$-0.619773\pi$
$167$	−1.31181e132	−0.734920	−0.367460	+	0.930039i	$0.619773\pi$
$168$	−1.83828e132	−0.721953
$169$	1.65288e132	0.456018
$170$	−3.73094e132	−0.724616
$171$	5.07439e132	0.695209
$172$	2.83198e131	0.0274250
$173$	−2.29883e133	−1.57675	−0.788377	−	0.615192i	$-0.789078\pi$
$173$	−2.29883e133	−1.57675	−0.788377	+	0.615192i	$0.789078\pi$
$174$	1.67945e132	0.0817497
$175$	−4.26819e133	−1.47734
$176$	4.01242e133	0.989469
$177$	7.45495e132	0.131231
$178$	3.07968e133	0.387717
$179$	−1.71028e133	−0.154281	−0.0771403	−	0.997020i	$-0.524579\pi$
$179$	−1.71028e133	−0.154281	−0.0771403	+	0.997020i	$0.524579\pi$
$180$	7.08075e132	0.0458527
$181$	1.20766e134	0.562431	0.281215	−	0.959645i	$-0.409262\pi$
$181$	1.20766e134	0.562431	0.281215	+	0.959645i	$0.409262\pi$
$182$	7.46296e134	2.50417
$183$	1.93035e134	0.467515
$184$	−6.86416e134	−1.20206
$185$	−1.29950e134	−0.164838
$186$	5.64854e134	0.519896
$187$	−1.85487e135	−1.24090
$188$	2.58207e134	0.125770
$189$	−3.99974e135	−1.42087
$190$	1.66508e135	0.432112
$191$	−6.63492e135	−1.25994	−0.629971	−	0.776619i	$-0.716933\pi$
$191$	−6.63492e135	−1.25994	−0.629971	+	0.776619i	$0.716933\pi$
$192$	2.43764e135	0.339271
$193$	1.15783e136	1.18300	0.591502	−	0.806304i	$-0.298535\pi$
$193$	1.15783e136	1.18300	0.591502	+	0.806304i	$0.298535\pi$
$194$	−5.29132e135	−0.397522
$195$	−4.25858e135	−0.235616
$196$	7.64108e135	0.311831
$197$	−2.62330e136	−0.790873	−0.395437	−	0.918493i	$-0.629407\pi$
$197$	−2.62330e136	−0.790873	−0.395437	+	0.918493i	$0.629407\pi$
$198$	3.61118e136	0.805508
$199$	−2.55089e136	−0.421632	−0.210816	−	0.977526i	$-0.567612\pi$
$199$	−2.55089e136	−0.421632	−0.210816	+	0.977526i	$0.567612\pi$
$200$	5.73573e136	0.703564
$201$	−3.58580e136	−0.326905
$202$	2.54151e137	1.72459
$203$	7.76188e136	0.392602
$204$	1.53397e136	0.0579192
$205$	3.59813e136	0.101560
$206$	1.00675e136	0.0212728
$207$	−6.85289e137	−1.08552
$208$	−1.11250e138	−1.32291
$209$	8.27811e137	0.739993
$210$	−6.02212e137	−0.405230
$211$	−3.37785e138	−1.71330	−0.856652	−	0.515895i	$-0.827459\pi$
$211$	−3.37785e138	−1.71330	−0.856652	+	0.515895i	$0.827459\pi$
$212$	−7.30397e136	−0.0279624
$213$	2.10689e138	0.609613
$214$	−7.32550e136	−0.0160405
$215$	−7.66157e137	−0.127124
$216$	5.37498e138	0.676672
$217$	2.61058e139	2.49679
$218$	−1.97319e139	−1.43551
$219$	−4.61156e138	−0.255519
$220$	1.15512e138	0.0488065
$221$	5.14289e139	1.65908
$222$	5.48087e138	0.135160
$223$	−7.64028e139	−1.44202	−0.721008	−	0.692927i	$-0.756321\pi$
$223$	−7.64028e139	−1.44202	−0.721008	+	0.692927i	$0.756321\pi$
$224$	−2.93242e139	−0.424100
$225$	5.72631e139	0.635353
$226$	−2.03555e139	−0.173472
$227$	3.27984e139	0.214939	0.107469	−	0.994208i	$-0.465725\pi$
$227$	3.27984e139	0.214939	0.107469	+	0.994208i	$0.465725\pi$
$228$	−6.84597e138	−0.0345392
$229$	−7.74198e139	−0.301052	−0.150526	−	0.988606i	$-0.548097\pi$
$229$	−7.74198e139	−0.301052	−0.150526	+	0.988606i	$0.548097\pi$
$230$	−2.24867e140	−0.674714
$231$	−2.99395e140	−0.693957
$232$	−1.04306e140	−0.186972
$233$	6.22388e140	0.863742	0.431871	−	0.901935i	$-0.357854\pi$
$233$	6.22388e140	0.863742	0.431871	+	0.901935i	$0.357854\pi$
$234$	−1.00125e141	−1.07696
$235$	−6.98548e140	−0.582986
$236$	5.60661e139	0.0363443
$237$	6.01087e140	0.302978
$238$	7.27265e141	2.85341
$239$	2.20608e141	0.674445	0.337223	−	0.941425i	$-0.390512\pi$
$239$	2.20608e141	0.674445	0.337223	+	0.941425i	$0.390512\pi$
$240$	8.97713e140	0.214076
$241$	−5.29228e141	−0.985437	−0.492718	−	0.870189i	$-0.663997\pi$
$241$	−5.29228e141	−0.985437	−0.492718	+	0.870189i	$0.663997\pi$
$242$	−1.34137e141	−0.195224
$243$	8.27008e141	0.941752
$244$	1.45175e141	0.129478
$245$	−2.06720e142	−1.44544
$246$	−1.51758e141	−0.0832744
$247$	−2.29522e142	−0.989363
$248$	−3.50817e142	−1.18907
$249$	1.07960e142	0.288006
$250$	4.38658e142	0.921926
$251$	3.20600e142	0.531346	0.265673	−	0.964063i	$-0.414406\pi$
$251$	3.20600e142	0.531346	0.265673	+	0.964063i	$0.414406\pi$
$252$	−1.38024e142	−0.180560
$253$	−1.11795e143	−1.15545
$254$	9.90743e142	0.809757
$255$	−4.14998e142	−0.268476
$256$	6.25111e142	0.320390
$257$	1.20927e143	0.491475	0.245738	−	0.969336i	$-0.420970\pi$
$257$	1.20927e143	0.491475	0.245738	+	0.969336i	$0.420970\pi$
$258$	3.23140e142	0.104236
$259$	2.53309e143	0.649104
$260$	−3.20273e142	−0.0652538
$261$	−1.04135e143	−0.168845
$262$	−5.59288e143	−0.722285
$263$	1.64158e144	1.69003	0.845015	−	0.534742i	$-0.179591\pi$
$263$	1.64158e144	1.69003	0.845015	+	0.534742i	$0.179591\pi$
$264$	4.02336e143	0.330488
$265$	1.97600e143	0.129616
$266$	−3.24571e144	−1.70158
$267$	3.42557e143	0.143652
$268$	−2.69676e143	−0.0905361
$269$	−3.10920e144	−0.836349	−0.418175	−	0.908367i	$-0.637330\pi$
$269$	−3.10920e144	−0.836349	−0.418175	+	0.908367i	$0.637330\pi$
$270$	1.76082e144	0.379814
$271$	−6.89894e144	−1.19429	−0.597145	−	0.802133i	$-0.703698\pi$
$271$	−6.89894e144	−1.19429	−0.597145	+	0.802133i	$0.703698\pi$
$272$	−1.08413e145	−1.50741
$273$	8.30115e144	0.927813
$274$	5.50650e144	0.495128
$275$	9.34163e144	0.676281
$276$	9.24539e143	0.0539305
$277$	2.57648e145	1.21194	0.605969	−	0.795488i	$-0.292785\pi$
$277$	2.57648e145	1.21194	0.605969	+	0.795488i	$0.292785\pi$
$278$	2.67077e145	1.01384
$279$	−3.50242e145	−1.07379
$280$	3.74020e145	0.926812
$281$	2.08011e145	0.416927	0.208463	−	0.978030i	$-0.433154\pi$
$281$	2.08011e145	0.416927	0.208463	+	0.978030i	$0.433154\pi$
$282$	2.94625e145	0.478021
$283$	−1.48107e146	−1.94662	−0.973311	−	0.229491i	$-0.926294\pi$
$283$	−1.48107e146	−1.94662	−0.973311	+	0.229491i	$0.926294\pi$
$284$	1.58452e145	0.168832
$285$	1.85209e145	0.160101
$286$	−1.63339e146	−1.14633
$287$	−7.01376e145	−0.399925
$288$	3.93420e145	0.182391
$289$	2.36067e146	0.890457
$290$	−3.41704e145	−0.104947
$291$	−5.88560e145	−0.147285
$292$	−3.46819e145	−0.0707659
$293$	−9.84017e146	−1.63825	−0.819123	−	0.573618i	$-0.805540\pi$
$293$	−9.84017e146	−1.63825	−0.819123	+	0.573618i	$0.805540\pi$
$294$	8.71879e146	1.18520
$295$	−1.51680e146	−0.168468
$296$	−3.40404e146	−0.309127
$297$	8.75408e146	0.650432
$298$	−1.13067e147	−0.687810
$299$	3.09966e147	1.54482
$300$	−7.72550e145	−0.0315654
$301$	1.49345e147	0.500593
$302$	5.33818e145	0.0146886
$303$	2.82696e147	0.638974
$304$	4.83836e147	0.898917
$305$	−3.92753e147	−0.600176
$306$	−9.75716e147	−1.22715
$307$	−3.51009e147	−0.363567	−0.181784	−	0.983339i	$-0.558187\pi$
$307$	−3.51009e147	−0.363567	−0.181784	+	0.983339i	$0.558187\pi$
$308$	−2.25165e147	−0.192191
$309$	1.11983e146	0.00788172
$310$	−1.14926e148	−0.667420
$311$	−1.40825e148	−0.675204	−0.337602	−	0.941289i	$-0.609616\pi$
$311$	−1.40825e148	−0.675204	−0.337602	+	0.941289i	$0.609616\pi$
$312$	−1.11553e148	−0.441859
$313$	−1.46450e148	−0.479513	−0.239756	−	0.970833i	$-0.577068\pi$
$313$	−1.46450e148	−0.479513	−0.239756	+	0.970833i	$0.577068\pi$
$314$	1.26370e148	0.342239
$315$	3.73406e148	0.836957
$316$	4.52057e147	0.0839096
$317$	1.10579e149	1.70078	0.850389	−	0.526155i	$-0.176367\pi$
$317$	1.10579e149	1.70078	0.850389	+	0.526155i	$0.176367\pi$
$318$	−8.33413e147	−0.106279
$319$	−1.69881e148	−0.179721
$320$	−4.95967e148	−0.435541
$321$	−8.14825e146	−0.00594312
$322$	4.38329e149	2.65690
$323$	−2.23669e149	−1.12734
$324$	1.45998e148	0.0612237
$325$	−2.59010e149	−0.904182
$326$	−4.73974e149	−1.37818
$327$	−2.19480e149	−0.531868
$328$	9.42530e148	0.190459
$329$	1.36166e150	2.29569
$330$	1.31804e149	0.185502
$331$	−1.50918e150	−1.77409	−0.887045	−	0.461682i	$-0.847246\pi$
$331$	−1.50918e150	−1.77409	−0.887045	+	0.461682i	$0.847246\pi$
$332$	8.11929e148	0.0797631
$333$	−3.39845e149	−0.279157
$334$	−1.12571e150	−0.773593
$335$	7.29575e149	0.419666
$336$	−1.74989e150	−0.842994
$337$	1.95168e150	0.787826	0.393913	−	0.919148i	$-0.371121\pi$
$337$	1.95168e150	0.787826	0.393913	+	0.919148i	$0.371121\pi$
$338$	1.41840e150	0.480014
$339$	−2.26417e149	−0.0642728
$340$	−3.12105e149	−0.0743542
$341$	−5.71367e150	−1.14296
$342$	4.35452e150	0.731792
$343$	2.63380e151	3.72034
$344$	−2.00695e150	−0.238401
$345$	−2.50123e150	−0.249987
$346$	−1.97271e151	−1.65973
$347$	1.42891e151	1.01252	0.506258	−	0.862382i	$-0.331028\pi$
$347$	1.42891e151	1.01252	0.506258	+	0.862382i	$0.331028\pi$
$348$	1.40491e149	0.00838849
$349$	−5.15235e150	−0.259354	−0.129677	−	0.991556i	$-0.541394\pi$
$349$	−5.15235e150	−0.259354	−0.129677	+	0.991556i	$0.541394\pi$
$350$	−3.66270e151	−1.55508
$351$	−2.42719e151	−0.869622
$352$	6.41807e150	0.194140
$353$	−1.52874e151	−0.390605	−0.195302	−	0.980743i	$-0.562569\pi$
$353$	−1.52874e151	−0.390605	−0.195302	+	0.980743i	$0.562569\pi$
$354$	6.39737e150	0.138136
$355$	−4.28671e151	−0.782596
$356$	2.57625e150	0.0397844
$357$	8.08946e151	1.05721
$358$	−1.46765e151	−0.162399
$359$	1.63166e152	1.52936	0.764679	−	0.644411i	$-0.222898\pi$
$359$	1.63166e152	1.52936	0.764679	+	0.644411i	$0.222898\pi$
$360$	−5.01794e151	−0.398590
$361$	−4.86623e151	−0.327728
$362$	1.03634e152	0.592027
$363$	−1.49202e151	−0.0723319
$364$	6.24301e151	0.256958
$365$	9.38278e151	0.328024
$366$	1.65650e152	0.492117
$367$	6.80797e151	0.171944	0.0859720	−	0.996298i	$-0.472600\pi$
$367$	6.80797e151	0.171944	0.0859720	+	0.996298i	$0.472600\pi$
$368$	−6.53413e152	−1.40360
$369$	9.40984e151	0.171994
$370$	−1.11515e152	−0.173512
$371$	−3.85177e152	−0.510403
$372$	4.72519e151	0.0533475
$373$	1.64864e153	1.58654	0.793268	−	0.608873i	$-0.208378\pi$
$373$	1.64864e153	1.58654	0.793268	+	0.608873i	$0.208378\pi$
$374$	−1.59174e153	−1.30620
$375$	4.87925e152	0.341580
$376$	−1.82984e153	−1.09329
$377$	4.71019e152	0.240286
$378$	−3.43233e153	−1.49564
$379$	3.13537e153	1.16750	0.583748	−	0.811935i	$-0.301586\pi$
$379$	3.13537e153	1.16750	0.583748	+	0.811935i	$0.301586\pi$
$380$	1.39290e152	0.0443399
$381$	1.10202e153	0.300021
$382$	−5.69368e153	−1.32624
$383$	2.35942e153	0.470412	0.235206	−	0.971945i	$-0.424423\pi$
$383$	2.35942e153	0.470412	0.235206	+	0.971945i	$0.424423\pi$
$384$	2.58323e153	0.441017
$385$	6.09156e153	0.890872
$386$	9.93580e153	1.24525
$387$	−2.00365e153	−0.215288
$388$	−4.42636e152	−0.0407905
$389$	1.31173e154	1.03715	0.518577	−	0.855031i	$-0.326462\pi$
$389$	1.31173e154	1.03715	0.518577	+	0.855031i	$0.326462\pi$
$390$	−3.65444e153	−0.248015
$391$	3.02062e154	1.76027
$392$	−5.41503e154	−2.71069
$393$	−6.22103e153	−0.267612
$394$	−2.25115e154	−0.832490
$395$	−1.22298e154	−0.388950
$396$	3.02087e153	0.0826548
$397$	−2.46416e154	−0.580275	−0.290137	−	0.956985i	$-0.593701\pi$
$397$	−2.46416e154	−0.580275	−0.290137	+	0.956985i	$0.593701\pi$
$398$	−2.18901e154	−0.443818
$399$	−3.61025e154	−0.630448
$400$	5.45996e154	0.821523
$401$	3.78280e154	0.490595	0.245298	−	0.969448i	$-0.421114\pi$
$401$	3.78280e154	0.490595	0.245298	+	0.969448i	$0.421114\pi$
$402$	−3.07711e154	−0.344107
$403$	1.58419e155	1.52812
$404$	2.12606e154	0.176964
$405$	−3.94980e154	−0.283793
$406$	6.66076e154	0.413261
$407$	−5.54407e154	−0.297140
$408$	−1.08709e155	−0.503482
$409$	2.05328e155	0.822077	0.411038	−	0.911618i	$-0.365166\pi$
$409$	2.05328e155	0.822077	0.411038	+	0.911618i	$0.365166\pi$
$410$	3.08769e154	0.106904
$411$	6.12496e154	0.183449
$412$	8.42182e152	0.00218284
$413$	2.95666e155	0.663398
$414$	−5.88072e155	−1.14264
$415$	−2.19658e155	−0.369730
$416$	−1.77950e155	−0.259564
$417$	2.97073e155	0.375637
$418$	7.10376e155	0.778932
$419$	−6.27418e155	−0.596792	−0.298396	−	0.954442i	$-0.596452\pi$
$419$	−6.27418e155	−0.596792	−0.298396	+	0.954442i	$0.596452\pi$
$420$	−5.03770e154	−0.0415815
$421$	8.68079e155	0.621977	0.310989	−	0.950414i	$-0.399340\pi$
$421$	8.68079e155	0.621977	0.310989	+	0.950414i	$0.399340\pi$
$422$	−2.89866e156	−1.80346
$423$	−1.82684e156	−0.987299
$424$	5.17613e155	0.243073
$425$	−2.52405e156	−1.03028
$426$	1.80800e156	0.641692
$427$	7.65585e156	2.36339
$428$	−6.12802e153	−0.00164595
$429$	−1.81684e156	−0.424725
$430$	−6.57468e155	−0.133814
$431$	−4.18443e156	−0.741719	−0.370859	−	0.928689i	$-0.620937\pi$
$431$	−4.18443e156	−0.741719	−0.370859	+	0.928689i	$0.620937\pi$
$432$	5.11655e156	0.790122
$433$	1.72502e156	0.232148	0.116074	−	0.993241i	$-0.462969\pi$
$433$	1.72502e156	0.232148	0.116074	+	0.993241i	$0.462969\pi$
$434$	2.24024e157	2.62818
$435$	−3.80082e155	−0.0388836
$436$	−1.65063e156	−0.147301
$437$	−1.34807e157	−1.04971
$438$	−3.95735e156	−0.268965
$439$	−3.46553e156	−0.205651	−0.102826	−	0.994699i	$-0.532788\pi$
$439$	−3.46553e156	−0.205651	−0.102826	+	0.994699i	$0.532788\pi$
$440$	−8.18602e156	−0.424266
$441$	−5.40614e157	−2.44789
$442$	4.41331e157	1.74638
$443$	−2.11379e157	−0.731206	−0.365603	−	0.930771i	$-0.619137\pi$
$443$	−2.11379e157	−0.731206	−0.365603	+	0.930771i	$0.619137\pi$
$444$	4.58493e155	0.0138690
$445$	−6.96973e156	−0.184415
$446$	−6.55641e157	−1.51790
$447$	−1.25766e157	−0.254839
$448$	9.66778e157	1.71508
$449$	5.87660e157	0.912997	0.456498	−	0.889724i	$-0.349103\pi$
$449$	5.87660e157	0.912997	0.456498	+	0.889724i	$0.349103\pi$
$450$	4.91397e157	0.668786
$451$	1.53507e157	0.183073
$452$	−1.70280e156	−0.0178003
$453$	5.93773e155	0.00544224
$454$	2.81456e157	0.226249
$455$	−1.68897e158	−1.19109
$456$	4.85156e157	0.300243
$457$	2.39604e158	1.30161	0.650804	−	0.759246i	$-0.274432\pi$
$457$	2.39604e158	1.30161	0.650804	+	0.759246i	$0.274432\pi$
$458$	−6.64368e157	−0.316893
$459$	−2.36529e158	−0.990901
$460$	−1.88109e157	−0.0692337
$461$	5.25820e158	1.70072	0.850358	−	0.526205i	$-0.176385\pi$
$461$	5.25820e158	1.70072	0.850358	+	0.526205i	$0.176385\pi$
$462$	−2.56922e158	−0.730473
$463$	−2.52727e158	−0.631804	−0.315902	−	0.948792i	$-0.602307\pi$
$463$	−2.52727e158	−0.631804	−0.315902	+	0.948792i	$0.602307\pi$
$464$	−9.92914e157	−0.218319
$465$	−1.27834e158	−0.247284
$466$	5.34094e158	0.909193
$467$	1.27263e158	0.190698	0.0953491	−	0.995444i	$-0.469603\pi$
$467$	1.27263e158	0.190698	0.0953491	+	0.995444i	$0.469603\pi$
$468$	−8.37577e157	−0.110509
$469$	−1.42214e159	−1.65257
$470$	−5.99450e158	−0.613663
$471$	1.40563e158	0.126802
$472$	−3.97325e158	−0.315935
$473$	−3.26866e158	−0.229156
$474$	5.15815e158	0.318921
$475$	1.12646e159	0.614391
$476$	6.08380e158	0.292794
$477$	5.16763e158	0.219507
$478$	1.89312e159	0.709935
$479$	2.79482e159	0.925531	0.462766	−	0.886481i	$-0.346857\pi$
$479$	2.79482e159	0.925531	0.462766	+	0.886481i	$0.346857\pi$
$480$	1.43594e158	0.0420032
$481$	1.53717e159	0.397274
$482$	−4.54150e159	−1.03729
$483$	4.87559e159	0.984402
$484$	−1.12210e158	−0.0200323
$485$	1.19750e159	0.189078
$486$	7.09687e159	0.991308
$487$	−1.37960e160	−1.70522	−0.852612	−	0.522544i	$-0.824983\pi$
$487$	−1.37960e160	−1.70522	−0.852612	+	0.522544i	$0.824983\pi$
$488$	−1.02882e160	−1.12553
$489$	−5.27208e159	−0.510628
$490$	−1.77394e160	−1.52150
$491$	1.88307e160	1.43060	0.715298	−	0.698819i	$-0.246291\pi$
$491$	1.88307e160	1.43060	0.715298	+	0.698819i	$0.246291\pi$
$492$	−1.26950e158	−0.00854496
$493$	4.59007e159	0.273796
$494$	−1.96962e160	−1.04142
$495$	−8.17259e159	−0.383134
$496$	−3.33950e160	−1.38842
$497$	8.35600e160	3.08172
$498$	9.26445e159	0.303161
$499$	4.58191e159	0.133065	0.0665326	−	0.997784i	$-0.478806\pi$
$499$	4.58191e159	0.133065	0.0665326	+	0.997784i	$0.478806\pi$
$500$	3.66952e159	0.0946006
$501$	−1.25214e160	−0.286622
$502$	2.75119e160	0.559307
$503$	−1.46036e160	−0.263733	−0.131866	−	0.991267i	$-0.542097\pi$
$503$	−1.46036e160	−0.263733	−0.131866	+	0.991267i	$0.542097\pi$
$504$	9.78136e160	1.56958
$505$	−5.75179e160	−0.820288
$506$	−9.59352e160	−1.21625
$507$	1.57770e160	0.177849
$508$	8.28788e159	0.0830908
$509$	1.72490e161	1.53835	0.769176	−	0.639037i	$-0.220667\pi$
$509$	1.72490e161	1.53835	0.769176	+	0.639037i	$0.220667\pi$
$510$	−3.56125e160	−0.282603
$511$	−1.82896e161	−1.29170
$512$	−1.26223e161	−0.793552
$513$	1.05561e161	0.590907
$514$	1.03772e161	0.517337
$515$	−2.27842e159	−0.0101182
$516$	2.70317e159	0.0106959
$517$	−2.98022e161	−1.05090
$518$	2.17374e161	0.683260
$519$	−2.19428e161	−0.614941
$520$	2.26969e161	0.567240
$521$	−4.31670e161	−0.962292	−0.481146	−	0.876640i	$-0.659779\pi$
$521$	−4.31670e161	−0.962292	−0.481146	+	0.876640i	$0.659779\pi$
$522$	−8.93623e160	−0.177730
$523$	−6.22261e161	−1.10439	−0.552194	−	0.833715i	$-0.686209\pi$
$523$	−6.22261e161	−1.10439	−0.552194	+	0.833715i	$0.686209\pi$
$524$	−4.67862e160	−0.0741151
$525$	−4.07407e161	−0.576169
$526$	1.40870e162	1.77896
$527$	1.54380e162	1.74124
$528$	3.82992e161	0.385897
$529$	7.09812e161	0.639044
$530$	1.69568e161	0.136436
$531$	−3.96673e161	−0.285305
$532$	−2.71514e161	−0.174603
$533$	−4.25621e161	−0.244767
$534$	2.93961e161	0.151211
$535$	1.65786e160	0.00762953
$536$	1.91112e162	0.787015
$537$	−1.63249e161	−0.0601701
$538$	−2.66812e162	−0.880359
$539$	−8.81932e162	−2.60558
$540$	1.47298e161	0.0389735
$541$	2.91872e162	0.691759	0.345880	−	0.938279i	$-0.387581\pi$
$541$	2.91872e162	0.691759	0.345880	+	0.938279i	$0.387581\pi$
$542$	−5.92024e162	−1.25713
$543$	1.15273e162	0.219350
$544$	−1.73412e162	−0.295763
$545$	4.46559e162	0.682789
$546$	7.12353e162	0.976636
$547$	4.01305e162	0.493433	0.246717	−	0.969088i	$-0.420648\pi$
$547$	4.01305e162	0.493433	0.246717	+	0.969088i	$0.420648\pi$
$548$	4.60637e161	0.0508060
$549$	−1.02713e163	−1.01641
$550$	8.01640e162	0.711868
$551$	−2.04850e162	−0.163274
$552$	−6.55196e162	−0.468809
$553$	2.38394e163	1.53161
$554$	2.21097e163	1.27571
$555$	−1.24040e162	−0.0642877
$556$	2.23418e162	0.104032
$557$	−3.53626e163	−1.47965	−0.739826	−	0.672798i	$-0.765092\pi$
$557$	−3.53626e163	−1.47965	−0.739826	+	0.672798i	$0.765092\pi$
$558$	−3.00556e163	−1.13029
$559$	9.06281e162	0.306380
$560$	3.56037e163	1.08220
$561$	−1.77051e163	−0.483958
$562$	1.78502e163	0.438866
$563$	4.45884e162	0.0986217	0.0493108	−	0.998783i	$-0.484298\pi$
$563$	4.45884e162	0.0986217	0.0493108	+	0.998783i	$0.484298\pi$
$564$	2.46463e162	0.0490507
$565$	4.60673e162	0.0825106
$566$	−1.27096e164	−2.04906
$567$	7.69927e163	1.11753
$568$	−1.12290e164	−1.46763
$569$	3.04526e163	0.358463	0.179232	−	0.983807i	$-0.442639\pi$
$569$	3.04526e163	0.358463	0.179232	+	0.983807i	$0.442639\pi$
$570$	1.58935e163	0.168526
$571$	1.17429e164	1.12183	0.560914	−	0.827874i	$-0.310450\pi$
$571$	1.17429e164	1.12183	0.560914	+	0.827874i	$0.310450\pi$
$572$	−1.36638e163	−0.117627
$573$	−6.33315e163	−0.491383
$574$	−6.01877e163	−0.420969
$575$	−1.52126e164	−0.959329
$576$	−1.29705e164	−0.737599
$577$	2.05337e164	1.05319	0.526594	−	0.850117i	$-0.323469\pi$
$577$	2.05337e164	1.05319	0.526594	+	0.850117i	$0.323469\pi$
$578$	2.02578e164	0.937314
$579$	1.10517e164	0.461376
$580$	−2.85846e162	−0.0107688
$581$	4.28174e164	1.45593
$582$	−5.05066e163	−0.155035
$583$	8.43022e163	0.233647
$584$	2.45782e164	0.615156
$585$	2.26596e164	0.512246
$586$	−8.44422e164	−1.72445
$587$	3.96650e164	0.731881	0.365940	−	0.930638i	$-0.380747\pi$
$587$	3.96650e164	0.731881	0.365940	+	0.930638i	$0.380747\pi$
$588$	7.29355e163	0.121615
$589$	−6.88981e164	−1.03836
$590$	−1.30162e164	−0.177333
$591$	−2.50398e164	−0.308444
$592$	−3.24037e164	−0.360955
$593$	−1.51686e165	−1.52824	−0.764121	−	0.645073i	$-0.776827\pi$
$593$	−1.51686e165	−1.52824	−0.764121	+	0.645073i	$0.776827\pi$
$594$	7.51221e164	0.684659
$595$	−1.64590e165	−1.35720
$596$	−9.45842e163	−0.0705775
$597$	−2.43487e164	−0.164438
$598$	2.65994e165	1.62611
$599$	−1.98142e164	−0.109668	−0.0548341	−	0.998495i	$-0.517463\pi$
$599$	−1.98142e164	−0.109668	−0.0548341	+	0.998495i	$0.517463\pi$
$600$	5.47485e164	0.274393
$601$	9.56489e164	0.434159	0.217080	−	0.976154i	$-0.430347\pi$
$601$	9.56489e164	0.434159	0.217080	+	0.976154i	$0.430347\pi$
$602$	1.28159e165	0.526935
$603$	1.90798e165	0.710714
$604$	4.46556e162	0.00150723
$605$	3.03569e164	0.0928566
$606$	2.42592e165	0.672598
$607$	−4.96406e165	−1.24770	−0.623849	−	0.781545i	$-0.714432\pi$
$607$	−4.96406e165	−1.24770	−0.623849	+	0.781545i	$0.714432\pi$
$608$	7.73920e164	0.176373
$609$	7.40885e164	0.153116
$610$	−3.37036e165	−0.631759
$611$	8.26307e165	1.40504
$612$	−8.16218e164	−0.125921
$613$	−1.07176e166	−1.50037	−0.750186	−	0.661226i	$-0.770036\pi$
$613$	−1.07176e166	−1.50037	−0.750186	+	0.661226i	$0.770036\pi$
$614$	−3.01214e165	−0.382698
$615$	3.43448e164	0.0396088
$616$	1.59568e166	1.67068
$617$	−6.52456e165	−0.620275	−0.310137	−	0.950692i	$-0.600375\pi$
$617$	−6.52456e165	−0.620275	−0.310137	+	0.950692i	$0.600375\pi$
$618$	9.60965e163	0.00829647
$619$	−3.07578e165	−0.241192	−0.120596	−	0.992702i	$-0.538480\pi$
$619$	−3.07578e165	−0.241192	−0.120596	+	0.992702i	$0.538480\pi$
$620$	−9.61397e164	−0.0684853
$621$	−1.42558e166	−0.922661
$622$	−1.20847e166	−0.710734
$623$	1.35859e166	0.726191
$624$	−1.06190e166	−0.515941
$625$	7.03677e165	0.310822
$626$	−1.25674e166	−0.504745
$627$	7.90161e165	0.288600
$628$	1.05713e165	0.0351178
$629$	1.49797e166	0.452678
$630$	3.20434e166	0.880999
$631$	−1.44937e166	−0.362604	−0.181302	−	0.983427i	$-0.558031\pi$
$631$	−1.44937e166	−0.362604	−0.181302	+	0.983427i	$0.558031\pi$
$632$	−3.20361e166	−0.729412
$633$	−3.22422e166	−0.668196
$634$	9.48922e166	1.79027
$635$	−2.24219e166	−0.385154
$636$	−6.97177e164	−0.0109055
$637$	2.44528e167	3.48363
$638$	−1.45781e166	−0.189178
$639$	−1.12106e167	−1.32534
$640$	−5.25590e166	−0.566159
$641$	−2.21600e166	−0.217529	−0.108765	−	0.994068i	$-0.534689\pi$
$641$	−2.21600e166	−0.217529	−0.108765	+	0.994068i	$0.534689\pi$
$642$	−6.99232e164	−0.00625586
$643$	−1.06101e167	−0.865301	−0.432651	−	0.901562i	$-0.642422\pi$
$643$	−1.06101e167	−0.865301	−0.432651	+	0.901562i	$0.642422\pi$
$644$	3.66676e166	0.272630
$645$	−7.31310e165	−0.0495791
$646$	−1.91939e167	−1.18666
$647$	1.68650e166	0.0951004	0.0475502	−	0.998869i	$-0.484859\pi$
$647$	1.68650e166	0.0951004	0.0475502	+	0.998869i	$0.484859\pi$
$648$	−1.03465e167	−0.532207
$649$	−6.47113e166	−0.303683
$650$	−2.22266e167	−0.951761
$651$	2.49184e167	0.973760
$652$	−3.96495e166	−0.141418
$653$	5.46379e166	0.177893	0.0889467	−	0.996036i	$-0.471650\pi$
$653$	5.46379e166	0.177893	0.0889467	+	0.996036i	$0.471650\pi$
$654$	−1.88344e167	−0.559856
$655$	1.26574e167	0.343549
$656$	8.97214e166	0.222391
$657$	2.45378e167	0.555516
$658$	1.16849e168	2.41650
$659$	5.30930e167	1.00313	0.501563	−	0.865121i	$-0.332759\pi$
$659$	5.30930e167	1.00313	0.501563	+	0.865121i	$0.332759\pi$
$660$	1.10258e166	0.0190347
$661$	−3.64877e167	−0.575652	−0.287826	−	0.957683i	$-0.592932\pi$
$661$	−3.64877e167	−0.575652	−0.287826	+	0.957683i	$0.592932\pi$
$662$	−1.29509e168	−1.86745
$663$	4.90898e167	0.647047
$664$	−5.75392e167	−0.693367
$665$	7.34548e167	0.809343
$666$	−2.91634e167	−0.293847
$667$	2.76648e167	0.254941
$668$	−9.41694e166	−0.0793799
$669$	−7.29278e167	−0.562392
$670$	6.26076e167	0.441750
$671$	−1.67561e168	−1.08189
$672$	−2.79904e167	−0.165401
$673$	−1.68177e168	−0.909640	−0.454820	−	0.890583i	$-0.650296\pi$
$673$	−1.68177e168	−0.909640	−0.454820	+	0.890583i	$0.650296\pi$
$674$	1.67481e168	0.829282
$675$	1.19123e168	0.540032
$676$	1.18654e167	0.0492552
$677$	7.31012e167	0.277906	0.138953	−	0.990299i	$-0.455626\pi$
$677$	7.31012e167	0.277906	0.138953	+	0.990299i	$0.455626\pi$
$678$	−1.94297e167	−0.0676549
$679$	−2.33426e168	−0.744555
$680$	2.21181e168	0.646349
$681$	3.13067e167	0.0838270
$682$	−4.90312e168	−1.20310
$683$	−7.00318e168	−1.57494	−0.787469	−	0.616355i	$-0.788609\pi$
$683$	−7.00318e168	−1.57494	−0.787469	+	0.616355i	$0.788609\pi$
$684$	3.64270e167	0.0750906
$685$	−1.24620e168	−0.235504
$686$	2.26016e169	3.91611
$687$	−7.38986e167	−0.117411
$688$	−1.91045e168	−0.278371
$689$	−2.33739e168	−0.312384
$690$	−2.14640e168	−0.263141
$691$	−1.00661e168	−0.113219	−0.0566093	−	0.998396i	$-0.518029\pi$
$691$	−1.00661e168	−0.113219	−0.0566093	+	0.998396i	$0.518029\pi$
$692$	−1.65024e168	−0.170308
$693$	1.59306e169	1.50871
$694$	1.22620e169	1.06580
$695$	−6.04431e168	−0.482226
$696$	−9.95623e167	−0.0729198
$697$	−4.14767e168	−0.278903
$698$	−4.42143e168	−0.273001
$699$	5.94080e168	0.336863
$700$	−3.06397e168	−0.159570
$701$	−3.90734e169	−1.86922	−0.934608	−	0.355680i	$-0.884249\pi$
$701$	−3.90734e169	−1.86922	−0.934608	+	0.355680i	$0.884249\pi$
$702$	−2.08286e169	−0.915382
$703$	−6.68529e168	−0.269947
$704$	−2.11595e169	−0.785113
$705$	−6.66776e168	−0.227367
$706$	−1.31187e169	−0.411159
$707$	1.12118e170	3.23014
$708$	5.35161e167	0.0141744
$709$	−3.54142e169	−0.862436	−0.431218	−	0.902248i	$-0.641916\pi$
$709$	−3.54142e169	−0.862436	−0.431218	+	0.902248i	$0.641916\pi$
$710$	−3.67859e169	−0.823777
$711$	−3.19835e169	−0.658695
$712$	−1.82572e169	−0.345839
$713$	9.30459e169	1.62132
$714$	6.94187e169	1.11284
$715$	3.69658e169	0.545244
$716$	−1.22774e168	−0.0166641
$717$	2.10574e169	0.263036
$718$	1.40019e170	1.60983
$719$	−8.43012e169	−0.892205	−0.446103	−	0.894982i	$-0.647188\pi$
$719$	−8.43012e169	−0.892205	−0.446103	+	0.894982i	$0.647188\pi$
$720$	−4.77668e169	−0.465417
$721$	4.44128e168	0.0398437
$722$	−4.17590e169	−0.344974
$723$	−5.05157e169	−0.384324
$724$	8.66930e168	0.0607490
$725$	−2.31168e169	−0.149217
$726$	−1.28036e169	−0.0761381
$727$	8.92436e169	0.488967	0.244484	−	0.969653i	$-0.421382\pi$
$727$	8.92436e169	0.488967	0.244484	+	0.969653i	$0.421382\pi$
$728$	−4.42425e170	−2.23369
$729$	−4.28859e169	−0.199538
$730$	8.05171e169	0.345285
$731$	8.83170e169	0.349108
$732$	1.38572e169	0.0504971
$733$	1.03403e170	0.347413	0.173707	−	0.984797i	$-0.444426\pi$
$733$	1.03403e170	0.347413	0.173707	+	0.984797i	$0.444426\pi$
$734$	5.84218e169	0.180992
$735$	−1.97318e170	−0.563729
$736$	−1.04517e170	−0.275395
$737$	3.11259e170	0.756496
$738$	8.07493e169	0.181045
$739$	−6.78305e169	−0.140308	−0.0701538	−	0.997536i	$-0.522349\pi$
$739$	−6.78305e169	−0.140308	−0.0701538	+	0.997536i	$0.522349\pi$
$740$	−9.32859e168	−0.0178045
$741$	−2.19083e170	−0.385856
$742$	−3.30535e170	−0.537261
$743$	3.89940e170	0.585010	0.292505	−	0.956264i	$-0.405511\pi$
$743$	3.89940e170	0.585010	0.292505	+	0.956264i	$0.405511\pi$
$744$	−3.34861e170	−0.463741
$745$	2.55886e170	0.327151
$746$	1.41476e171	1.67002
$747$	−5.74448e170	−0.626145
$748$	−1.33154e170	−0.134032
$749$	−3.23163e169	−0.0300437
$750$	4.18707e170	0.359555
$751$	2.24569e171	1.78145	0.890724	−	0.454545i	$-0.150198\pi$
$751$	2.24569e171	1.78145	0.890724	+	0.454545i	$0.150198\pi$
$752$	−1.74187e171	−1.27660
$753$	3.06019e170	0.207227
$754$	4.04199e170	0.252930
$755$	−1.20810e169	−0.00698651
$756$	−2.87126e170	−0.153471
$757$	−2.06634e171	−1.02093	−0.510466	−	0.859898i	$-0.670527\pi$
$757$	−2.06634e171	−1.02093	−0.510466	+	0.859898i	$0.670527\pi$
$758$	2.69057e171	1.22893
$759$	−1.06710e171	−0.450629
$760$	−9.87108e170	−0.385439
$761$	−3.97256e171	−1.43444	−0.717221	−	0.696846i	$-0.754586\pi$
$761$	−3.97256e171	−1.43444	−0.717221	+	0.696846i	$0.754586\pi$
$762$	9.45681e170	0.315809
$763$	−8.70467e171	−2.68870
$764$	−4.76294e170	−0.136088
$765$	2.20818e171	0.583685
$766$	2.02471e171	0.495166
$767$	1.79421e171	0.406022
$768$	5.96680e170	0.124954
$769$	2.12837e171	0.412506	0.206253	−	0.978499i	$-0.433873\pi$
$769$	2.12837e171	0.412506	0.206253	+	0.978499i	$0.433873\pi$
$770$	5.22740e171	0.937751
$771$	1.15427e171	0.191677
$772$	8.31162e170	0.127778
$773$	9.51680e171	1.35460	0.677300	−	0.735707i	$-0.263150\pi$
$773$	9.51680e171	1.35460	0.677300	+	0.735707i	$0.263150\pi$
$774$	−1.71941e171	−0.226617
$775$	−7.77497e171	−0.948958
$776$	3.13684e171	0.354585
$777$	2.41788e171	0.253153
$778$	1.12565e172	1.09173
$779$	1.85106e171	0.166319
$780$	−3.05706e170	−0.0254493
$781$	−1.82884e172	−1.41072
$782$	2.59211e172	1.85289
$783$	−2.16629e171	−0.143513
$784$	−5.15468e172	−3.16516
$785$	−2.85992e171	−0.162783
$786$	−5.33850e171	−0.281694
$787$	1.24887e172	0.610971	0.305485	−	0.952197i	$-0.401181\pi$
$787$	1.24887e172	0.610971	0.305485	+	0.952197i	$0.401181\pi$
$788$	−1.88316e171	−0.0854234
$789$	1.56692e172	0.659119
$790$	−1.04949e172	−0.409417
$791$	−8.97980e171	−0.324912
$792$	−2.14081e172	−0.718504
$793$	4.64585e172	1.44647
$794$	−2.11459e172	−0.610810
$795$	1.88613e171	0.0505506
$796$	−1.83118e171	−0.0455411
$797$	−2.11625e172	−0.488424	−0.244212	−	0.969722i	$-0.578529\pi$
$797$	−2.11625e172	−0.488424	−0.244212	+	0.969722i	$0.578529\pi$
$798$	−3.09809e172	−0.663623
$799$	8.05235e172	1.60099
$800$	8.73348e171	0.161188
$801$	−1.82272e172	−0.312310
$802$	3.24616e172	0.516411
$803$	4.00298e172	0.591301
$804$	−2.57410e171	−0.0353095
$805$	−9.91997e172	−1.26373
$806$	1.35946e173	1.60853
$807$	−2.96778e172	−0.326180
$808$	−1.50668e173	−1.53832
$809$	1.06567e173	1.01085	0.505423	−	0.862872i	$-0.331336\pi$
$809$	1.06567e173	1.01085	0.505423	+	0.862872i	$0.331336\pi$
$810$	−3.38948e172	−0.298727
$811$	2.10894e173	1.72713	0.863563	−	0.504242i	$-0.168228\pi$
$811$	2.10894e173	1.72713	0.863563	+	0.504242i	$0.168228\pi$
$812$	5.57194e171	0.0424055
$813$	−6.58516e172	−0.465778
$814$	−4.75757e172	−0.312776
$815$	1.07267e173	0.655523
$816$	−1.03482e173	−0.587895
$817$	−3.94150e172	−0.208185
$818$	1.76200e173	0.865335
$819$	−4.41699e173	−2.01713
$820$	2.58296e171	0.0109696
$821$	−1.11573e173	−0.440697	−0.220348	−	0.975421i	$-0.570719\pi$
$821$	−1.11573e173	−0.440697	−0.220348	+	0.975421i	$0.570719\pi$
$822$	5.25605e172	0.193102
$823$	−1.27860e173	−0.436961	−0.218481	−	0.975841i	$-0.570110\pi$
$823$	−1.27860e173	−0.436961	−0.218481	+	0.975841i	$0.570110\pi$
$824$	−5.96832e171	−0.0189751
$825$	8.91675e172	0.263753
$826$	2.53722e173	0.698306
$827$	−6.25712e173	−1.60250	−0.801248	−	0.598332i	$-0.795830\pi$
$827$	−6.25712e173	−1.60250	−0.801248	+	0.598332i	$0.795830\pi$
$828$	−4.91941e172	−0.117249
$829$	−6.21691e173	−1.37905	−0.689525	−	0.724262i	$-0.742181\pi$
$829$	−6.21691e173	−1.37905	−0.689525	+	0.724262i	$0.742181\pi$
$830$	−1.88496e173	−0.389185
$831$	2.45930e173	0.472661
$832$	5.86676e173	1.04969
$833$	2.38292e174	3.96947
$834$	2.54930e173	0.395403
$835$	2.54764e173	0.367953
$836$	5.94253e172	0.0799277
$837$	−7.28596e173	−0.912687
$838$	−5.38411e173	−0.628196
$839$	1.24063e173	0.134836	0.0674182	−	0.997725i	$-0.478524\pi$
$839$	1.24063e173	0.134836	0.0674182	+	0.997725i	$0.478524\pi$
$840$	3.57008e173	0.361461
$841$	−1.01810e174	−0.960346
$842$	7.44931e173	0.654706
$843$	1.98550e173	0.162603
$844$	−2.42482e173	−0.185057
$845$	−3.21003e173	−0.228315
$846$	−1.56768e174	−1.03925
$847$	−5.91741e173	−0.365653
$848$	4.92726e173	0.283826
$849$	−1.41370e174	−0.759191
$850$	−2.16598e174	−1.08450
$851$	9.02839e173	0.421504
$852$	1.51245e173	0.0658453
$853$	−4.64077e174	−1.88418	−0.942090	−	0.335360i	$-0.891142\pi$
$853$	−4.64077e174	−1.88418	−0.942090	+	0.335360i	$0.891142\pi$
$854$	6.56977e174	2.48775
$855$	−9.85488e173	−0.348071
$856$	4.34276e172	0.0143079
$857$	6.11301e174	1.87887	0.939434	−	0.342731i	$-0.111352\pi$
$857$	6.11301e174	1.87887	0.939434	+	0.342731i	$0.111352\pi$
$858$	−1.55910e174	−0.447074
$859$	−1.13419e174	−0.303453	−0.151727	−	0.988422i	$-0.548483\pi$
$859$	−1.13419e174	−0.303453	−0.151727	+	0.988422i	$0.548483\pi$
$860$	−5.49993e172	−0.0137309
$861$	−6.69476e173	−0.155972
$862$	−3.59082e174	−0.780749
$863$	1.52305e174	0.309081	0.154540	−	0.987986i	$-0.450610\pi$
$863$	1.52305e174	0.309081	0.154540	+	0.987986i	$0.450610\pi$
$864$	8.18419e173	0.155027
$865$	4.46452e174	0.789435
$866$	1.48030e174	0.244364
$867$	2.25330e174	0.347282
$868$	1.87403e174	0.269683
$869$	−5.21763e174	−0.701127
$870$	−3.26162e173	−0.0409297
$871$	−8.63009e174	−1.01143
$872$	1.16976e175	1.28046
$873$	3.13169e174	0.320208
$874$	−1.15683e175	−1.10494
$875$	1.93513e175	1.72676
$876$	−3.31045e173	−0.0275990
$877$	−4.41786e174	−0.344141	−0.172071	−	0.985085i	$-0.555046\pi$
$877$	−4.41786e174	−0.344141	−0.172071	+	0.985085i	$0.555046\pi$
$878$	−2.97390e174	−0.216473
$879$	−9.39262e174	−0.638923
$880$	−7.79244e174	−0.495398
$881$	2.84094e175	1.68809	0.844045	−	0.536272i	$-0.180168\pi$
$881$	2.84094e175	1.68809	0.844045	+	0.536272i	$0.180168\pi$
$882$	−4.63922e175	−2.57670
$883$	−2.96104e174	−0.153739	−0.0768693	−	0.997041i	$-0.524492\pi$
$883$	−2.96104e174	−0.153739	−0.0768693	+	0.997041i	$0.524492\pi$
$884$	3.69187e174	0.179200
$885$	−1.44781e174	−0.0657033
$886$	−1.81392e175	−0.769683
$887$	3.94751e174	0.156628	0.0783138	−	0.996929i	$-0.475046\pi$
$887$	3.94751e174	0.156628	0.0783138	+	0.996929i	$0.475046\pi$
$888$	−3.24921e174	−0.120561
$889$	4.37064e175	1.51667
$890$	−5.98099e174	−0.194119
$891$	−1.68511e175	−0.511569
$892$	−5.48465e174	−0.155754
$893$	−3.59369e175	−0.954725
$894$	−1.07924e175	−0.268249
$895$	3.32150e174	0.0772437
$896$	1.02452e176	2.22943
$897$	2.95868e175	0.602487
$898$	5.04293e175	0.961040
$899$	1.41391e175	0.252185
$900$	4.11069e174	0.0686255
$901$	−2.27779e175	−0.355949
$902$	1.31731e175	0.192707
$903$	1.42553e175	0.195233
$904$	1.20673e175	0.154735
$905$	−2.34537e175	−0.281593
$906$	5.09539e173	0.00572862
$907$	−2.01655e175	−0.212313	−0.106156	−	0.994349i	$-0.533854\pi$
$907$	−2.01655e175	−0.212313	−0.106156	+	0.994349i	$0.533854\pi$
$908$	2.35447e174	0.0232159
$909$	−1.50421e176	−1.38917
$910$	−1.44937e176	−1.25376
$911$	−4.34335e175	−0.351950	−0.175975	−	0.984395i	$-0.556308\pi$
$911$	−4.34335e175	−0.351950	−0.175975	+	0.984395i	$0.556308\pi$
$912$	4.61830e175	0.350581
$913$	−9.37127e175	−0.666480
$914$	2.05613e176	1.37010
$915$	−3.74890e175	−0.234071
$916$	−5.55766e174	−0.0325170
$917$	−2.46729e176	−1.35283
$918$	−2.02975e176	−1.04304
$919$	5.62270e175	0.270815	0.135407	−	0.990790i	$-0.456766\pi$
$919$	5.62270e175	0.270815	0.135407	+	0.990790i	$0.456766\pi$
$920$	1.33308e176	0.601837
$921$	−3.35044e175	−0.141793
$922$	4.51226e176	1.79021
$923$	5.07072e176	1.88612
$924$	−2.14924e175	−0.0749553
$925$	−7.54417e175	−0.246705
$926$	−2.16874e176	−0.665050
$927$	−5.95853e174	−0.0171354
$928$	−1.58822e175	−0.0428356
$929$	7.24307e176	1.83226	0.916132	−	0.400878i	$-0.131295\pi$
$929$	7.24307e176	1.83226	0.916132	+	0.400878i	$0.131295\pi$
$930$	−1.09699e176	−0.260297
$931$	−1.06347e177	−2.36712
$932$	4.46787e175	0.0932941
$933$	−1.34420e176	−0.263333
$934$	1.09209e176	0.200733
$935$	3.60231e176	0.621285
$936$	5.93568e176	0.960634
$937$	7.00607e176	1.06407	0.532033	−	0.846724i	$-0.321428\pi$
$937$	7.00607e176	1.06407	0.532033	+	0.846724i	$0.321428\pi$
$938$	−1.22040e177	−1.73953
$939$	−1.39789e176	−0.187012
$940$	−5.01459e175	−0.0629692
$941$	6.11118e175	0.0720348	0.0360174	−	0.999351i	$-0.488533\pi$
$941$	6.11118e175	0.0720348	0.0360174	+	0.999351i	$0.488533\pi$
$942$	1.20622e176	0.133475
$943$	−2.49983e176	−0.259696
$944$	−3.78222e176	−0.368904
$945$	7.76783e176	0.711389
$946$	−2.80496e176	−0.241215
$947$	−5.77344e176	−0.466241	−0.233121	−	0.972448i	$-0.574894\pi$
$947$	−5.77344e176	−0.466241	−0.233121	+	0.972448i	$0.574894\pi$
$948$	4.31496e175	0.0327251
$949$	−1.10988e177	−0.790564
$950$	9.66655e176	0.646721
$951$	1.05550e177	0.663310
$952$	−4.31143e177	−2.54520
$953$	−8.21073e176	−0.455359	−0.227680	−	0.973736i	$-0.573114\pi$
$953$	−8.21073e176	−0.455359	−0.227680	+	0.973736i	$0.573114\pi$
$954$	4.43454e176	0.231057
$955$	1.28856e177	0.630816
$956$	1.58366e176	0.0728479
$957$	−1.62155e176	−0.0700921
$958$	2.39834e177	0.974234
$959$	2.42918e177	0.927370
$960$	−4.73410e176	−0.169863
$961$	1.79033e177	0.603797
$962$	1.31910e177	0.418179
$963$	4.33563e175	0.0129208
$964$	−3.79911e176	−0.106439
$965$	−2.24861e177	−0.592295
$966$	4.18392e177	1.03620
$967$	2.51233e177	0.585062	0.292531	−	0.956256i	$-0.405502\pi$
$967$	2.51233e177	0.585062	0.292531	+	0.956256i	$0.405502\pi$
$968$	7.95199e176	0.174137
$969$	−2.13496e177	−0.439668
$970$	1.02762e177	0.199028
$971$	−4.81387e177	−0.876900	−0.438450	−	0.898756i	$-0.644472\pi$
$971$	−4.81387e177	−0.876900	−0.438450	+	0.898756i	$0.644472\pi$
$972$	5.93676e176	0.101720
$973$	1.17820e178	1.89892
$974$	−1.18389e178	−1.79496
$975$	−2.47229e177	−0.352635
$976$	−9.79350e177	−1.31424
$977$	−1.01560e178	−1.28231	−0.641157	−	0.767410i	$-0.721545\pi$
$977$	−1.01560e178	−1.28231	−0.641157	+	0.767410i	$0.721545\pi$
$978$	−4.52417e177	−0.537498
$979$	−2.97350e177	−0.332428
$980$	−1.48396e177	−0.156124
$981$	1.16784e178	1.15632
$982$	1.61593e178	1.50588
$983$	−1.99401e178	−1.74901	−0.874506	−	0.485015i	$-0.838814\pi$
$983$	−1.99401e178	−1.74901	−0.874506	+	0.485015i	$0.838814\pi$
$984$	8.99662e176	0.0742798
$985$	5.09466e177	0.395967
$986$	3.93891e177	0.288204
$987$	1.29973e178	0.895330
$988$	−1.64765e177	−0.106863
$989$	5.32294e177	0.325066
$990$	−7.01320e177	−0.403295
$991$	−1.47936e177	−0.0801107	−0.0400553	−	0.999197i	$-0.512753\pi$
$991$	−1.47936e177	−0.0801107	−0.0400553	+	0.999197i	$0.512753\pi$
$992$	−5.34171e177	−0.272418
$993$	−1.44054e178	−0.691903
$994$	7.17059e178	3.24388
$995$	4.95403e177	0.211099
$996$	7.75001e176	0.0311080
$997$	1.16178e178	0.439302	0.219651	−	0.975579i	$-0.429508\pi$
$997$	1.16178e178	0.439302	0.219651	+	0.975579i	$0.429508\pi$
$998$	3.93191e177	0.140067
$999$	−7.06968e177	−0.237276

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1.120.a.a.1.7	✓	10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1.120.a.a.1.7	✓	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)

\(f(q)\)	\(=\)	\(q+8.58138e17 q^{2} +9.54518e27 q^{3} +7.17860e34 q^{4} -1.94208e41 q^{5} +8.19107e45 q^{6} +3.78566e50 q^{7} -5.08728e53 q^{8} -5.07893e56 q^{9} +O(q^{10})\)	\(q+8.58138e17 q^{2} +9.54518e27 q^{3} +7.17860e34 q^{4} -1.94208e41 q^{5} +8.19107e45 q^{6} +3.78566e50 q^{7} -5.08728e53 q^{8} -5.07893e56 q^{9} -1.66657e59 q^{10} -8.28552e61 q^{11} +6.85210e62 q^{12} +2.29727e66 q^{13} +3.24861e68 q^{14} -1.85375e69 q^{15} -4.84269e71 q^{16} +2.23869e73 q^{17} -4.35842e74 q^{18} -9.99106e75 q^{19} -1.39414e76 q^{20} +3.61348e78 q^{21} -7.11012e79 q^{22} +1.34928e81 q^{23} -4.85590e81 q^{24} -1.12746e83 q^{25} +1.97138e84 q^{26} -1.05655e85 q^{27} +2.71757e85 q^{28} +2.05034e86 q^{29} -1.59077e87 q^{30} +6.89597e88 q^{31} -7.74612e88 q^{32} -7.90868e89 q^{33} +1.92110e91 q^{34} -7.35206e91 q^{35} -3.64596e91 q^{36} +6.69127e92 q^{37} -8.57370e93 q^{38} +2.19279e94 q^{39} +9.87991e94 q^{40} -1.85272e95 q^{41} +3.10086e96 q^{42} +3.94503e96 q^{43} -5.94784e96 q^{44} +9.86370e97 q^{45} +1.15787e99 q^{46} +3.59690e99 q^{47} -4.62243e99 q^{48} +1.06443e101 q^{49} -9.67520e100 q^{50} +2.13687e101 q^{51} +1.64912e101 q^{52} -1.01746e102 q^{53} -9.06667e102 q^{54} +1.60912e103 q^{55} -1.92587e104 q^{56} -9.53664e103 q^{57} +1.75947e104 q^{58} +7.81017e104 q^{59} -1.33073e104 q^{60} +2.02233e106 q^{61} +5.91769e106 q^{62} -1.92271e107 q^{63} +2.55379e107 q^{64} -4.46149e107 q^{65} -6.78673e107 q^{66} -3.75667e108 q^{67} +1.60707e108 q^{68} +1.28791e109 q^{69} -6.30908e109 q^{70} +2.20728e110 q^{71} +2.58379e110 q^{72} -4.83130e110 q^{73} +5.74203e110 q^{74} -1.07618e111 q^{75} -7.17218e110 q^{76} -3.13661e112 q^{77} +1.88171e112 q^{78} +6.29729e112 q^{79} +9.40489e112 q^{80} +2.03380e113 q^{81} -1.58989e113 q^{82} +1.13104e114 q^{83} +2.59397e113 q^{84} -4.34772e114 q^{85} +3.38538e114 q^{86} +1.95708e114 q^{87} +4.21508e115 q^{88} +3.58879e115 q^{89} +8.46441e115 q^{90} +8.69669e116 q^{91} +9.68593e115 q^{92} +6.58233e116 q^{93} +3.08664e117 q^{94} +1.94035e117 q^{95} -7.39381e116 q^{96} -6.16605e117 q^{97} +9.13424e118 q^{98} +4.20816e118 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + 91\!\cdots\!00 q^{2}+ \cdots + 18\!\cdots\!70 q^{9}+O(q^{10}) \) 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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