LMFDB - Embedded newform 1.120.a.a.1.10

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			1.10
Root			$-5.98866e16$ 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)

$f(q)$	$=$	$q+1.52927e18 q^{2} +3.29001e28 q^{3} +1.67406e36 q^{4} +6.57038e41 q^{5} +5.03133e46 q^{6} -6.63364e49 q^{7} +1.54372e54 q^{8} +4.83416e56 q^{9} +O(q^{10})$	\(q+1.52927e18 q^{2} +3.29001e28 q^{3} +1.67406e36 q^{4} +6.57038e41 q^{5} +5.03133e46 q^{6} -6.63364e49 q^{7} +1.54372e54 q^{8} +4.83416e56 q^{9} +1.00479e60 q^{10} -2.55605e61 q^{11} +5.50768e64 q^{12} -1.55726e66 q^{13} -1.01446e68 q^{14} +2.16166e70 q^{15} +1.24816e72 q^{16} -5.44174e71 q^{17} +7.39274e74 q^{18} -1.66513e76 q^{19} +1.09992e78 q^{20} -2.18248e78 q^{21} -3.90890e79 q^{22} +1.53937e81 q^{23} +5.07885e82 q^{24} +2.81235e83 q^{25} -2.38148e84 q^{26} -3.80285e84 q^{27} -1.11051e86 q^{28} -8.98160e86 q^{29} +3.30577e88 q^{30} -2.64247e88 q^{31} +8.82801e89 q^{32} -8.40945e89 q^{33} -8.32191e89 q^{34} -4.35855e91 q^{35} +8.09267e92 q^{36} -2.34243e93 q^{37} -2.54644e94 q^{38} -5.12342e94 q^{39} +1.01428e96 q^{40} -2.60933e94 q^{41} -3.33760e96 q^{42} +1.81186e97 q^{43} -4.27899e97 q^{44} +3.17622e98 q^{45} +2.35412e99 q^{46} -9.77887e97 q^{47} +4.10647e100 q^{48} -3.24689e100 q^{49} +4.30085e101 q^{50} -1.79034e100 q^{51} -2.60695e102 q^{52} +2.98856e102 q^{53} -5.81559e102 q^{54} -1.67942e103 q^{55} -1.02405e104 q^{56} -5.47830e104 q^{57} -1.37353e105 q^{58} +2.79833e102 q^{59} +3.61875e106 q^{60} -9.69327e105 q^{61} -4.04105e106 q^{62} -3.20681e106 q^{63} +5.20498e107 q^{64} -1.02318e108 q^{65} -1.28603e108 q^{66} -8.21656e108 q^{67} -9.10980e107 q^{68} +5.06456e109 q^{69} -6.66541e109 q^{70} +9.76729e108 q^{71} +7.46257e110 q^{72} +6.12342e110 q^{73} -3.58221e111 q^{74} +9.25268e111 q^{75} -2.78753e112 q^{76} +1.69559e111 q^{77} -7.83510e112 q^{78} +6.14218e112 q^{79} +8.20088e113 q^{80} -4.14682e113 q^{81} -3.99038e112 q^{82} +3.99829e113 q^{83} -3.65360e114 q^{84} -3.57543e113 q^{85} +2.77082e115 q^{86} -2.95496e115 q^{87} -3.94582e115 q^{88} +5.13160e115 q^{89} +4.85731e116 q^{90} +1.03303e116 q^{91} +2.57700e117 q^{92} -8.69375e116 q^{93} -1.49545e116 q^{94} -1.09405e118 q^{95} +2.90443e118 q^{96} +2.85807e118 q^{97} -4.96539e118 q^{98} -1.23564e118 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	1.52927e18	1.87586	0.937929	−	0.346827i	$-0.112741\pi$
$2$	1.52927e18	1.87586	0.937929	+	0.346827i	$0.112741\pi$
$3$	3.29001e28	1.34426	0.672130	−	0.740433i	$-0.265380\pi$
$3$	3.29001e28	1.34426	0.672130	+	0.740433i	$0.265380\pi$
$4$	1.67406e36	2.51885
$5$	6.57038e41	1.69385	0.846925	−	0.531712i	$-0.178451\pi$
$5$	6.57038e41	1.69385	0.846925	+	0.531712i	$0.178451\pi$
$6$	5.03133e46	2.52164
$7$	−6.63364e49	−0.345476	−0.172738	−	0.984968i	$-0.555261\pi$
$7$	−6.63364e49	−0.345476	−0.172738	+	0.984968i	$0.555261\pi$
$8$	1.54372e54	2.84914
$9$	4.83416e56	0.807033
$10$	1.00479e60	3.17742
$11$	−2.55605e61	−0.278423	−0.139212	−	0.990263i	$-0.544457\pi$
$11$	−2.55605e61	−0.278423	−0.139212	+	0.990263i	$0.544457\pi$
$12$	5.50768e64	3.38598
$13$	−1.55726e66	−0.817961	−0.408981	−	0.912543i	$-0.634116\pi$
$13$	−1.55726e66	−0.817961	−0.408981	+	0.912543i	$0.634116\pi$
$14$	−1.01446e68	−0.648065
$15$	2.16166e70	2.27697
$16$	1.24816e72	2.82574
$17$	−5.44174e71	−0.0334216	−0.0167108	−	0.999860i	$-0.505319\pi$
$17$	−5.44174e71	−0.0334216	−0.0167108	+	0.999860i	$0.505319\pi$
$18$	7.39274e74	1.51388
$19$	−1.66513e76	−1.36650	−0.683248	−	0.730186i	$-0.739433\pi$
$19$	−1.66513e76	−1.36650	−0.683248	+	0.730186i	$0.739433\pi$
$20$	1.09992e78	4.26655
$21$	−2.18248e78	−0.464410
$22$	−3.90890e79	−0.522282
$23$	1.53937e81	1.46062	0.730311	−	0.683115i	$-0.239375\pi$
$23$	1.53937e81	1.46062	0.730311	+	0.683115i	$0.239375\pi$
$24$	5.07885e82	3.82998
$25$	2.81235e83	1.86913
$26$	−2.38148e84	−1.53438
$27$	−3.80285e84	−0.259397
$28$	−1.11051e86	−0.870202
$29$	−8.98160e86	−0.872314	−0.436157	−	0.899871i	$-0.643661\pi$
$29$	−8.98160e86	−0.872314	−0.436157	+	0.899871i	$0.643661\pi$
$30$	3.30577e88	4.27128
$31$	−2.64247e88	−0.485276	−0.242638	−	0.970117i	$-0.578013\pi$
$31$	−2.64247e88	−0.485276	−0.242638	+	0.970117i	$0.578013\pi$
$32$	8.82801e89	2.45154
$33$	−8.40945e89	−0.374273
$34$	−8.32191e89	−0.0626942
$35$	−4.35855e91	−0.585185
$36$	8.09267e92	2.03279
$37$	−2.34243e93	−1.15256	−0.576281	−	0.817252i	$-0.695497\pi$
$37$	−2.34243e93	−1.15256	−0.576281	+	0.817252i	$0.695497\pi$
$38$	−2.54644e94	−2.56335
$39$	−5.12342e94	−1.09955
$40$	1.01428e96	4.82601
$41$	−2.60933e94	−0.0285687	−0.0142843	−	0.999898i	$-0.504547\pi$
$41$	−2.60933e94	−0.0285687	−0.0142843	+	0.999898i	$0.504547\pi$
$42$	−3.33760e96	−0.871167
$43$	1.81186e97	1.16614	0.583070	−	0.812422i	$-0.301851\pi$
$43$	1.81186e97	1.16614	0.583070	+	0.812422i	$0.301851\pi$
$44$	−4.27899e97	−0.701305
$45$	3.17622e98	1.36699
$46$	2.35412e99	2.73992
$47$	−9.77887e97	−0.0316567	−0.0158284	−	0.999875i	$-0.505039\pi$
$47$	−9.77887e97	−0.0316567	−0.0158284	+	0.999875i	$0.505039\pi$
$48$	4.10647e100	3.79852
$49$	−3.24689e100	−0.880646
$50$	4.30085e101	3.50622
$51$	−1.79034e100	−0.0449273
$52$	−2.60695e102	−2.06032
$53$	2.98856e102	0.760410	0.380205	−	0.924902i	$-0.375853\pi$
$53$	2.98856e102	0.760410	0.380205	+	0.924902i	$0.375853\pi$
$54$	−5.81559e102	−0.486592
$55$	−1.67942e103	−0.471607
$56$	−1.02405e104	−0.984310
$57$	−5.47830e104	−1.83693
$58$	−1.37353e105	−1.63634
$59$	2.79833e102	0.00120560	0.000602801	−	1.00000i	$-0.499808\pi$
$59$	2.79833e102	0.00120560	0.000602801		1.00000i	$0.499808\pi$
$60$	3.61875e106	5.73534
$61$	−9.69327e105	−0.574573	−0.287286	−	0.957845i	$-0.592753\pi$
$61$	−9.69327e105	−0.574573	−0.287286	+	0.957845i	$0.592753\pi$
$62$	−4.04105e106	−0.910308
$63$	−3.20681e106	−0.278811
$64$	5.20498e107	1.77301
$65$	−1.02318e108	−1.38550
$66$	−1.28603e108	−0.702083
$67$	−8.21656e108	−1.83332	−0.916662	−	0.399663i	$-0.869127\pi$
$67$	−8.21656e108	−1.83332	−0.916662	+	0.399663i	$0.869127\pi$
$68$	−9.10980e107	−0.0841838
$69$	5.06456e109	1.96345
$70$	−6.66541e109	−1.09772
$71$	9.76729e108	0.0691675	0.0345838	−	0.999402i	$-0.488989\pi$
$71$	9.76729e108	0.0691675	0.0345838	+	0.999402i	$0.488989\pi$
$72$	7.46257e110	2.29935
$73$	6.12342e110	0.830394	0.415197	−	0.909732i	$-0.363713\pi$
$73$	6.12342e110	0.830394	0.415197	+	0.909732i	$0.363713\pi$
$74$	−3.58221e111	−2.16204
$75$	9.25268e111	2.51259
$76$	−2.78753e112	−3.44199
$77$	1.69559e111	0.0961886
$78$	−7.83510e112	−2.06260
$79$	6.14218e112	0.757723	0.378861	−	0.925453i	$-0.376316\pi$
$79$	6.14218e112	0.757723	0.378861	+	0.925453i	$0.376316\pi$
$80$	8.20088e113	4.78637
$81$	−4.14682e113	−1.15573
$82$	−3.99038e112	−0.0535908
$83$	3.99829e113	0.261052	0.130526	−	0.991445i	$-0.458333\pi$
$83$	3.99829e113	0.261052	0.130526	+	0.991445i	$0.458333\pi$
$84$	−3.65360e114	−1.16978
$85$	−3.57543e113	−0.0566112
$86$	2.77082e115	2.18752
$87$	−2.95496e115	−1.17262
$88$	−3.94582e115	−0.793266
$89$	5.13160e115	0.526680	0.263340	−	0.964703i	$-0.415176\pi$
$89$	5.13160e115	0.526680	0.263340	+	0.964703i	$0.415176\pi$
$90$	4.85731e116	2.56429
$91$	1.03303e116	0.282586
$92$	2.57700e117	3.67908
$93$	−8.69375e116	−0.652336
$94$	−1.49545e116	−0.0593835
$95$	−1.09405e118	−2.31464
$96$	2.90443e118	3.29551
$97$	2.85807e118	1.75047	0.875235	−	0.483699i	$-0.160707\pi$
$97$	2.85807e118	1.75047	0.875235	+	0.483699i	$0.160707\pi$
$98$	−4.96539e118	−1.65197
$99$	−1.23564e118	−0.224697
$100$	4.70804e119	4.70804
$101$	2.51086e119	1.38900	0.694498	−	0.719495i	$-0.255627\pi$
$101$	2.51086e119	1.38900	0.694498	+	0.719495i	$0.255627\pi$
$102$	−2.73792e118	−0.0842773
$103$	−3.16930e119	−0.545945	−0.272973	−	0.962022i	$-0.588007\pi$
$103$	−3.16930e119	−0.545945	−0.272973	+	0.962022i	$0.588007\pi$
$104$	−2.40397e120	−2.33048
$105$	−1.43397e120	−0.786641
$106$	4.57033e120	1.42642
$107$	−4.42333e120	−0.789613	−0.394807	−	0.918764i	$-0.629188\pi$
$107$	−4.42333e120	−0.789613	−0.394807	+	0.918764i	$0.629188\pi$
$108$	−6.36620e120	−0.653381
$109$	2.29288e121	1.35989	0.679947	−	0.733261i	$-0.262003\pi$
$109$	2.29288e121	1.35989	0.679947	+	0.733261i	$0.262003\pi$
$110$	−2.56830e121	−0.884668
$111$	−7.70663e121	−1.54934
$112$	−8.27985e121	−0.976225
$113$	2.13020e122	1.47997	0.739987	−	0.672622i	$-0.234832\pi$
$113$	2.13020e122	1.47997	0.739987	+	0.672622i	$0.234832\pi$
$114$	−8.37781e122	−3.44581
$115$	1.01143e123	2.47407
$116$	−1.50357e123	−2.19722
$117$	−7.52806e122	−0.660122
$118$	4.27940e120	0.00226154
$119$	3.60986e121	0.0115464
$120$	3.33700e124	6.48741
$121$	−7.77476e123	−0.922481
$122$	−1.48236e124	−1.07782
$123$	−8.58474e122	−0.0384037
$124$	−4.42364e124	−1.22233
$125$	8.59220e124	1.47217
$126$	−4.90408e124	−0.523010
$127$	2.99546e124	0.199591	0.0997957	−	0.995008i	$-0.468181\pi$
$127$	2.99546e124	0.199591	0.0997957	+	0.995008i	$0.468181\pi$
$128$	2.09262e125	0.874373
$129$	5.96104e125	1.56760
$130$	−1.56472e126	−2.59901
$131$	9.16983e125	0.965427	0.482713	−	0.875778i	$-0.339651\pi$
$131$	9.16983e125	0.965427	0.482713	+	0.875778i	$0.339651\pi$
$132$	−1.40779e126	−0.942735
$133$	1.10459e126	0.472092
$134$	−1.25654e127	−3.43906
$135$	−2.49862e126	−0.439380
$136$	−8.40051e125	−0.0952228
$137$	−1.75367e127	−1.28551	−0.642753	−	0.766073i	$-0.722208\pi$
$137$	−1.75367e127	−1.28551	−0.642753	+	0.766073i	$0.722208\pi$
$138$	7.74509e127	3.68316
$139$	5.09339e127	1.57625	0.788127	−	0.615512i	$-0.211051\pi$
$139$	5.09339e127	1.57625	0.788127	+	0.615512i	$0.211051\pi$
$140$	−7.29647e127	−1.47399
$141$	−3.21726e126	−0.0425549
$142$	1.49368e127	0.129749
$143$	3.98045e127	0.227739
$144$	6.03380e128	2.28046
$145$	−5.90125e128	−1.47757
$146$	9.36438e128	1.55770
$147$	−1.06823e129	−1.18382
$148$	−3.92137e129	−2.90312
$149$	1.32579e129	0.657496	0.328748	−	0.944418i	$-0.393373\pi$
$149$	1.32579e129	0.657496	0.328748	+	0.944418i	$0.393373\pi$
$150$	1.41499e130	4.71327
$151$	−8.05308e128	−0.180648	−0.0903241	−	0.995912i	$-0.528790\pi$
$151$	−8.05308e128	−0.180648	−0.0903241	+	0.995912i	$0.528790\pi$
$152$	−2.57049e130	−3.89334
$153$	−2.63062e128	−0.0269723
$154$	2.59302e129	0.180436
$155$	−1.73620e130	−0.821984
$156$	−8.57691e130	−2.76960
$157$	3.65978e129	0.0808026	0.0404013	−	0.999184i	$-0.487136\pi$
$157$	3.65978e129	0.0808026	0.0404013	+	0.999184i	$0.487136\pi$
$158$	9.39306e130	1.42138
$159$	9.83241e130	1.02219
$160$	5.80034e131	4.15254
$161$	−1.02116e131	−0.504610
$162$	−6.34162e131	−2.16799
$163$	3.68879e131	0.874424	0.437212	−	0.899359i	$-0.355966\pi$
$163$	3.68879e131	0.874424	0.437212	+	0.899359i	$0.355966\pi$
$164$	−4.36818e130	−0.0719601
$165$	−5.52533e131	−0.633962
$166$	6.11447e131	0.489697
$167$	1.72144e132	0.964413	0.482206	−	0.876058i	$-0.339835\pi$
$167$	1.72144e132	0.964413	0.482206	+	0.876058i	$0.339835\pi$
$168$	−3.36913e132	−1.32317
$169$	−1.19952e132	−0.330940
$170$	−5.46781e131	−0.106195
$171$	−8.04950e132	−1.10281
$172$	3.03316e133	2.93733
$173$	−9.82466e132	−0.673867	−0.336934	−	0.941528i	$-0.609390\pi$
$173$	−9.82466e132	−0.673867	−0.336934	+	0.941528i	$0.609390\pi$
$174$	−4.51894e133	−2.19966
$175$	−1.86561e133	−0.645740
$176$	−3.19037e133	−0.786750
$177$	9.20654e130	0.00162064
$178$	7.84761e133	0.987978
$179$	−3.76791e132	−0.0339896	−0.0169948	−	0.999856i	$-0.505410\pi$
$179$	−3.76791e132	−0.0339896	−0.0169948	+	0.999856i	$0.505410\pi$
$180$	5.31719e134	3.44324
$181$	−3.70115e134	−1.72370	−0.861849	−	0.507164i	$-0.830694\pi$
$181$	−3.70115e134	−1.72370	−0.861849	+	0.507164i	$0.830694\pi$
$182$	1.57979e134	0.530092
$183$	−3.18910e134	−0.772375
$184$	2.37636e135	4.16151
$185$	−1.53906e135	−1.95227
$186$	−1.32951e135	−1.22369
$187$	1.39094e133	0.00930534
$188$	−1.63704e134	−0.0797384
$189$	2.52267e134	0.0896156
$190$	−1.67310e136	−4.34194
$191$	−1.47224e135	−0.279572	−0.139786	−	0.990182i	$-0.544641\pi$
$191$	−1.47224e135	−0.279572	−0.139786	+	0.990182i	$0.544641\pi$
$192$	1.71245e136	2.38338
$193$	1.03264e136	1.05509	0.527543	−	0.849528i	$-0.323113\pi$
$193$	1.03264e136	1.05509	0.527543	+	0.849528i	$0.323113\pi$
$194$	4.37077e136	3.28363
$195$	−3.36628e136	−1.86248
$196$	−5.43549e136	−2.21821
$197$	−1.25508e136	−0.378381	−0.189191	−	0.981940i	$-0.560586\pi$
$197$	−1.25508e136	−0.378381	−0.189191	+	0.981940i	$0.560586\pi$
$198$	−1.88962e136	−0.421499
$199$	−1.10902e137	−1.83308	−0.916542	−	0.399939i	$-0.869031\pi$
$199$	−1.10902e137	−1.83308	−0.916542	+	0.399939i	$0.869031\pi$
$200$	4.34148e137	5.32540
$201$	−2.70326e137	−2.46446
$202$	3.83979e137	2.60556
$203$	5.95807e136	0.301364
$204$	−2.99714e136	−0.113165
$205$	−1.71443e136	−0.0483911
$206$	−4.84673e137	−1.02412
$207$	7.44157e137	1.17877
$208$	−1.94371e138	−2.31134
$209$	4.25616e137	0.380464
$210$	−2.19293e138	−1.47563
$211$	−3.14703e138	−1.59623	−0.798114	−	0.602507i	$-0.794169\pi$
$211$	−3.14703e138	−1.59623	−0.798114	+	0.602507i	$0.794169\pi$
$212$	5.00303e138	1.91536
$213$	3.21345e137	0.0929791
$214$	−6.76447e138	−1.48120
$215$	1.19046e139	1.97527
$216$	−5.87053e138	−0.739059
$217$	1.75292e138	0.167651
$218$	3.50644e139	2.55097
$219$	2.01461e139	1.11626
$220$	−2.81145e139	−1.18790
$221$	8.47423e137	0.0273376
$222$	−1.17855e140	−2.90635
$223$	6.35579e139	1.19958	0.599792	−	0.800156i	$-0.295250\pi$
$223$	6.35579e139	1.19958	0.599792	+	0.800156i	$0.295250\pi$
$224$	−5.85618e139	−0.846950
$225$	1.35953e140	1.50845
$226$	3.25766e140	2.77622
$227$	−8.45733e139	−0.554236	−0.277118	−	0.960836i	$-0.589379\pi$
$227$	−8.45733e139	−0.554236	−0.277118	+	0.960836i	$0.589379\pi$
$228$	−9.17100e140	−4.62693
$229$	−2.99469e140	−1.16450	−0.582252	−	0.813009i	$-0.697828\pi$
$229$	−2.99469e140	−1.16450	−0.582252	+	0.813009i	$0.697828\pi$
$230$	1.54675e141	4.64101
$231$	5.57853e139	0.129302
$232$	−1.38651e141	−2.48534
$233$	−1.23731e140	−0.171712	−0.0858562	−	0.996308i	$-0.527363\pi$
$233$	−1.23731e140	−0.171712	−0.0858562	+	0.996308i	$0.527363\pi$
$234$	−1.15124e141	−1.23830
$235$	−6.42508e139	−0.0536217
$236$	4.68457e138	0.00303672
$237$	2.02078e141	1.01858
$238$	5.52045e139	0.0216594
$239$	−6.74103e140	−0.206087	−0.103044	−	0.994677i	$-0.532858\pi$
$239$	−6.74103e140	−0.206087	−0.103044	+	0.994677i	$0.532858\pi$
$240$	2.69810e142	6.43413
$241$	−1.84128e141	−0.342852	−0.171426	−	0.985197i	$-0.554837\pi$
$241$	−1.84128e141	−0.342852	−0.171426	+	0.985197i	$0.554837\pi$
$242$	−1.18897e142	−1.73044
$243$	−1.13652e142	−1.29420
$244$	−1.62271e142	−1.44726
$245$	−2.13333e142	−1.49168
$246$	−1.31284e141	−0.0720399
$247$	2.59304e142	1.11774
$248$	−4.07922e142	−1.38262
$249$	1.31544e142	0.350922
$250$	1.31398e143	2.76159
$251$	−9.42928e142	−1.56276	−0.781380	−	0.624056i	$-0.785484\pi$
$251$	−9.42928e142	−1.56276	−0.781380	+	0.624056i	$0.785484\pi$
$252$	−5.36838e142	−0.702282
$253$	−3.93472e142	−0.406671
$254$	4.58087e142	0.374405
$255$	−1.17632e142	−0.0761001
$256$	−2.59123e142	−0.132809
$257$	5.92947e142	0.240988	0.120494	−	0.992714i	$-0.461552\pi$
$257$	5.92947e142	0.240988	0.120494	+	0.992714i	$0.461552\pi$
$258$	9.11605e143	2.94059
$259$	1.55388e143	0.398183
$260$	−1.71287e144	−3.48987
$261$	−4.34185e143	−0.703986
$262$	1.40232e144	1.81100
$263$	1.28649e144	1.32447	0.662233	−	0.749298i	$-0.269609\pi$
$263$	1.28649e144	1.32447	0.662233	+	0.749298i	$0.269609\pi$
$264$	−1.29818e144	−1.06636
$265$	1.96360e144	1.28802
$266$	1.68921e144	0.885579
$267$	1.68830e144	0.707995
$268$	−1.37550e145	−4.61786
$269$	1.13365e144	0.304942	0.152471	−	0.988308i	$-0.451277\pi$
$269$	1.13365e144	0.304942	0.152471	+	0.988308i	$0.451277\pi$
$270$	−3.82106e144	−0.824215
$271$	3.16302e144	0.547557	0.273778	−	0.961793i	$-0.411727\pi$
$271$	3.16302e144	0.547557	0.273778	+	0.961793i	$0.411727\pi$
$272$	−6.79217e143	−0.0944406
$273$	3.39869e144	0.379869
$274$	−2.68184e145	−2.41143
$275$	−7.18852e144	−0.520408
$276$	8.47837e145	4.94564
$277$	−1.88733e145	−0.887771	−0.443885	−	0.896084i	$-0.646400\pi$
$277$	−1.88733e145	−0.887771	−0.443885	+	0.896084i	$0.646400\pi$
$278$	7.78918e145	2.95683
$279$	−1.27741e145	−0.391634
$280$	−6.72837e145	−1.66727
$281$	−2.60884e144	−0.0522904	−0.0261452	−	0.999658i	$-0.508323\pi$
$281$	−2.60884e144	−0.0522904	−0.0261452	+	0.999658i	$0.508323\pi$
$282$	−4.92007e144	−0.0798269
$283$	4.01135e145	0.527227	0.263614	−	0.964628i	$-0.415086\pi$
$283$	4.01135e145	0.527227	0.263614	+	0.964628i	$0.415086\pi$
$284$	1.63510e145	0.174222
$285$	−3.59945e146	−3.11148
$286$	6.08719e145	0.427207
$287$	1.73094e144	0.00986981
$288$	4.26760e146	1.97848
$289$	−2.64811e146	−0.998883
$290$	−9.02462e146	−2.77171
$291$	9.40309e146	2.35308
$292$	1.02510e147	2.09163
$293$	3.97821e146	0.662314	0.331157	−	0.943576i	$-0.392561\pi$
$293$	3.97821e146	0.662314	0.331157	+	0.943576i	$0.392561\pi$
$294$	−1.63362e147	−2.22067
$295$	1.83861e144	0.00204211
$296$	−3.61605e147	−3.28381
$297$	9.72029e145	0.0722222
$298$	2.02750e147	1.23337
$299$	−2.39721e147	−1.19473
$300$	1.54895e148	6.32883
$301$	−1.20192e147	−0.402874
$302$	−1.23154e147	−0.338871
$303$	8.26077e147	1.86717
$304$	−2.07835e148	−3.86136
$305$	−6.36884e147	−0.973240
$306$	−4.02294e146	−0.0505963
$307$	1.46028e148	1.51252	0.756262	−	0.654269i	$-0.227023\pi$
$307$	1.46028e148	1.51252	0.756262	+	0.654269i	$0.227023\pi$
$308$	2.83853e147	0.242284
$309$	−1.04271e148	−0.733892
$310$	−2.65512e148	−1.54193
$311$	3.12215e148	1.49696	0.748481	−	0.663157i	$-0.230784\pi$
$311$	3.12215e148	1.49696	0.748481	+	0.663157i	$0.230784\pi$
$312$	−7.90911e148	−3.13278
$313$	1.87671e148	0.614480	0.307240	−	0.951632i	$-0.400595\pi$
$313$	1.87671e148	0.614480	0.307240	+	0.951632i	$0.400595\pi$
$314$	5.59680e147	0.151574
$315$	−2.10699e148	−0.472264
$316$	1.02824e149	1.90859
$317$	−5.50842e148	−0.847230	−0.423615	−	0.905842i	$-0.639239\pi$
$317$	−5.50842e148	−0.847230	−0.423615	+	0.905842i	$0.639239\pi$
$318$	1.50364e149	1.91748
$319$	2.29575e148	0.242872
$320$	3.41987e149	3.00321
$321$	−1.45528e149	−1.06144
$322$	−1.56164e149	−0.946577
$323$	9.06120e147	0.0456705
$324$	−6.94202e149	−2.91111
$325$	−4.37957e149	−1.52887
$326$	5.64117e149	1.64030
$327$	7.54361e149	1.82805
$328$	−4.02807e148	−0.0813961
$329$	6.48695e147	0.0109367
$330$	−8.44973e149	−1.18922
$331$	4.05433e149	0.476599	0.238299	−	0.971192i	$-0.423410\pi$
$331$	4.05433e149	0.476599	0.238299	+	0.971192i	$0.423410\pi$
$332$	6.69337e149	0.657550
$333$	−1.13237e150	−0.930156
$334$	2.63256e150	1.80910
$335$	−5.39859e150	−3.10538
$336$	−2.72408e150	−1.31230
$337$	3.62203e150	1.46209	0.731044	−	0.682331i	$-0.239034\pi$
$337$	3.62203e150	1.46209	0.731044	+	0.682331i	$0.239034\pi$
$338$	−1.83439e150	−0.620796
$339$	7.00840e150	1.98947
$340$	−5.98548e149	−0.142595
$341$	6.75428e149	0.135112
$342$	−1.23099e151	−2.06871
$343$	4.59966e150	0.649719
$344$	2.79700e151	3.32250
$345$	3.32761e151	3.32580
$346$	−1.50246e151	−1.26408
$347$	−1.60519e151	−1.13742	−0.568711	−	0.822537i	$-0.692558\pi$
$347$	−1.60519e151	−1.13742	−0.568711	+	0.822537i	$0.692558\pi$
$348$	−4.94678e151	−2.95364
$349$	1.35608e151	0.682610	0.341305	−	0.939953i	$-0.389131\pi$
$349$	1.35608e151	0.682610	0.341305	+	0.939953i	$0.389131\pi$
$350$	−2.85303e151	−1.21132
$351$	5.92204e150	0.212177
$352$	−2.25649e151	−0.682566
$353$	−4.33392e151	−1.10735	−0.553676	−	0.832732i	$-0.686775\pi$
$353$	−4.33392e151	−1.10735	−0.553676	+	0.832732i	$0.686775\pi$
$354$	1.40793e149	0.00304009
$355$	6.41748e150	0.117159
$356$	8.59060e151	1.32663
$357$	1.18765e150	0.0155213
$358$	−5.76216e150	−0.0637596
$359$	−7.21561e151	−0.676322	−0.338161	−	0.941088i	$-0.609805\pi$
$359$	−7.21561e151	−0.676322	−0.338161	+	0.941088i	$0.609805\pi$
$360$	4.90319e152	3.89475
$361$	1.28782e152	0.867313
$362$	−5.66006e152	−3.23342
$363$	−2.55791e152	−1.24005
$364$	1.72936e152	0.711791
$365$	4.02332e152	1.40656
$366$	−4.87700e152	−1.44887
$367$	2.43650e151	0.0615369	0.0307685	−	0.999527i	$-0.490205\pi$
$367$	2.43650e151	0.0615369	0.0307685	+	0.999527i	$0.490205\pi$
$368$	1.92138e153	4.12733
$369$	−1.26139e151	−0.0230559
$370$	−2.35365e153	−3.66218
$371$	−1.98250e152	−0.262704
$372$	−1.45539e153	−1.64313
$373$	4.50739e152	0.433760	0.216880	−	0.976198i	$-0.430412\pi$
$373$	4.50739e152	0.433760	0.216880	+	0.976198i	$0.430412\pi$
$374$	2.12712e151	0.0174555
$375$	2.82685e153	1.97898
$376$	−1.50958e152	−0.0901944
$377$	1.39867e153	0.713519
$378$	3.85786e152	0.168106
$379$	4.29848e153	1.60060	0.800298	−	0.599602i	$-0.204675\pi$
$379$	4.29848e153	1.60060	0.800298	+	0.599602i	$0.204675\pi$
$380$	−1.83151e154	−5.83022
$381$	9.85510e152	0.268303
$382$	−2.25146e153	−0.524437
$383$	1.68037e153	0.335025	0.167512	−	0.985870i	$-0.446427\pi$
$383$	1.68037e153	0.335025	0.167512	+	0.985870i	$0.446427\pi$
$384$	6.88474e153	1.17538
$385$	1.11407e153	0.162929
$386$	1.57918e154	1.97919
$387$	8.75881e153	0.941115
$388$	4.78458e154	4.40916
$389$	−8.95683e153	−0.708195	−0.354098	−	0.935208i	$-0.615212\pi$
$389$	−8.95683e153	−0.708195	−0.354098	+	0.935208i	$0.615212\pi$
$390$	−5.14796e154	−3.49374
$391$	−8.37687e152	−0.0488163
$392$	−5.01229e154	−2.50908
$393$	3.01689e154	1.29778
$394$	−1.91935e154	−0.709790
$395$	4.03564e154	1.28347
$396$	−2.06853e154	−0.565976
$397$	−8.23979e154	−1.94036	−0.970178	−	0.242395i	$-0.922067\pi$
$397$	−8.23979e154	−1.94036	−0.970178	+	0.242395i	$0.922067\pi$
$398$	−1.69600e155	−3.43861
$399$	3.63410e154	0.634615
$400$	3.51027e155	5.28166
$401$	1.27487e155	1.65339	0.826694	−	0.562651i	$-0.190219\pi$
$401$	1.27487e155	1.65339	0.826694	+	0.562651i	$0.190219\pi$
$402$	−4.13402e155	−4.62299
$403$	4.11501e154	0.396937
$404$	4.20333e155	3.49866
$405$	−2.72462e155	−1.95763
$406$	9.11151e154	0.565316
$407$	5.98738e154	0.320900
$408$	−2.76378e154	−0.128004
$409$	2.93941e155	1.17686	0.588428	−	0.808549i	$-0.299747\pi$
$409$	2.93941e155	1.17686	0.588428	+	0.808549i	$0.299747\pi$
$410$	−2.62183e154	−0.0907748
$411$	−5.76960e155	−1.72805
$412$	−5.30561e155	−1.37515
$413$	−1.85631e152	−0.000416507 0
$414$	1.13802e156	2.21121
$415$	2.62703e155	0.442184
$416$	−1.37475e156	−2.00527
$417$	1.67573e156	2.11890
$418$	6.50883e155	0.713697
$419$	2.85231e155	0.271308	0.135654	−	0.990756i	$-0.456687\pi$
$419$	2.85231e155	0.271308	0.135654	+	0.990756i	$0.456687\pi$
$420$	−2.40055e156	−1.98143
$421$	−3.60503e155	−0.258300	−0.129150	−	0.991625i	$-0.541225\pi$
$421$	−3.60503e155	−0.258300	−0.129150	+	0.991625i	$0.541225\pi$
$422$	−4.81266e156	−2.99430
$423$	−4.72726e154	−0.0255480
$424$	4.61349e156	2.16651
$425$	−1.53041e155	−0.0624692
$426$	4.91424e155	0.174416
$427$	6.43016e155	0.198501
$428$	−7.40492e156	−1.98891
$429$	1.30957e156	0.306141
$430$	1.82054e157	3.70532
$431$	−5.21505e156	−0.924402	−0.462201	−	0.886775i	$-0.652940\pi$
$431$	−5.21505e156	−0.924402	−0.462201	+	0.886775i	$0.652940\pi$
$432$	−4.74657e156	−0.732988
$433$	1.09819e157	1.47791	0.738957	−	0.673752i	$-0.235318\pi$
$433$	1.09819e157	1.47791	0.738957	+	0.673752i	$0.235318\pi$
$434$	2.68069e156	0.314490
$435$	−1.94152e157	−1.98624
$436$	3.83842e157	3.42536
$437$	−2.56325e157	−1.99593
$438$	3.08089e157	2.09395
$439$	−2.19184e157	−1.30068	−0.650338	−	0.759645i	$-0.725373\pi$
$439$	−2.19184e157	−1.30068	−0.650338	+	0.759645i	$0.725373\pi$
$440$	−2.59255e157	−1.34367
$441$	−1.56960e157	−0.710711
$442$	1.29594e156	0.0512814
$443$	−2.02293e157	−0.699775	−0.349887	−	0.936792i	$-0.613780\pi$
$443$	−2.02293e157	−0.699775	−0.349887	+	0.936792i	$0.613780\pi$
$444$	−1.29014e158	−3.90255
$445$	3.37165e157	0.892118
$446$	9.71974e157	2.25025
$447$	4.36188e157	0.883845
$448$	−3.45280e157	−0.612533
$449$	−9.24929e157	−1.43698	−0.718490	−	0.695537i	$-0.755167\pi$
$449$	−9.24929e157	−1.43698	−0.718490	+	0.695537i	$0.755167\pi$
$450$	2.07910e158	2.82964
$451$	6.66960e155	0.00795418
$452$	3.56609e158	3.72782
$453$	−2.64948e157	−0.242838
$454$	−1.29336e158	−1.03967
$455$	6.78741e157	0.478659
$456$	−8.45694e158	−5.23366
$457$	2.58797e157	0.140587	0.0702934	−	0.997526i	$-0.477606\pi$
$457$	2.58797e157	0.140587	0.0702934	+	0.997526i	$0.477606\pi$
$458$	−4.57970e158	−2.18444
$459$	2.06941e156	0.00866947
$460$	1.69319e159	6.23181
$461$	2.14308e158	0.693158	0.346579	−	0.938021i	$-0.387343\pi$
$461$	2.14308e158	0.693158	0.346579	+	0.938021i	$0.387343\pi$
$462$	8.53109e157	0.242553
$463$	2.30375e158	0.575927	0.287963	−	0.957641i	$-0.407022\pi$
$463$	2.30375e158	0.575927	0.287963	+	0.957641i	$0.407022\pi$
$464$	−1.12105e159	−2.46493
$465$	−5.71212e158	−1.10496
$466$	−1.89219e158	−0.322108
$467$	2.80066e158	0.419668	0.209834	−	0.977737i	$-0.432708\pi$
$467$	2.80066e158	0.419668	0.209834	+	0.977737i	$0.432708\pi$
$468$	−1.26024e159	−1.66274
$469$	5.45057e158	0.633370
$470$	−9.82570e157	−0.100587
$471$	1.20407e158	0.108620
$472$	4.31983e156	0.00343493
$473$	−4.63121e158	−0.324681
$474$	3.09033e159	1.91070
$475$	−4.68293e159	−2.55416
$476$	6.04311e157	0.0290835
$477$	1.44472e159	0.613677
$478$	−1.03089e159	−0.386591
$479$	−2.91926e159	−0.966741	−0.483371	−	0.875416i	$-0.660588\pi$
$479$	−2.91926e159	−0.966741	−0.483371	+	0.875416i	$0.660588\pi$
$480$	1.90832e160	5.58210
$481$	3.64778e159	0.942750
$482$	−2.81582e159	−0.643142
$483$	−3.35965e159	−0.678327
$484$	−1.30154e160	−2.32359
$485$	1.87786e160	2.96503
$486$	−1.73804e160	−2.42774
$487$	1.47518e159	0.182336	0.0911679	−	0.995836i	$-0.470940\pi$
$487$	1.47518e159	0.182336	0.0911679	+	0.995836i	$0.470940\pi$
$488$	−1.49637e160	−1.63704
$489$	1.21362e160	1.17545
$490$	−3.26244e160	−2.79818
$491$	4.78836e159	0.363779	0.181890	−	0.983319i	$-0.441779\pi$
$491$	4.78836e159	0.363779	0.181890	+	0.983319i	$0.441779\pi$
$492$	−1.43714e159	−0.0967330
$493$	4.88756e158	0.0291541
$494$	3.96547e160	2.09672
$495$	−8.11860e159	−0.380603
$496$	−3.29822e160	−1.37126
$497$	−6.47927e158	−0.0238958
$498$	2.01167e160	0.658280
$499$	−3.00379e160	−0.872343	−0.436172	−	0.899863i	$-0.643666\pi$
$499$	−3.00379e160	−0.872343	−0.436172	+	0.899863i	$0.643666\pi$
$500$	1.43839e161	3.70817
$501$	5.66358e160	1.29642
$502$	−1.44199e161	−2.93152
$503$	8.49663e159	0.153445	0.0767223	−	0.997053i	$-0.475555\pi$
$503$	8.49663e159	0.153445	0.0767223	+	0.997053i	$0.475555\pi$
$504$	−4.95040e160	−0.794371
$505$	1.64973e161	2.35275
$506$	−6.01726e160	−0.762857
$507$	−3.94644e160	−0.444869
$508$	5.01458e160	0.502740
$509$	−1.16262e161	−1.03688	−0.518441	−	0.855113i	$-0.673487\pi$
$509$	−1.16262e161	−1.03688	−0.518441	+	0.855113i	$0.673487\pi$
$510$	−1.79892e160	−0.142753
$511$	−4.06206e160	−0.286882
$512$	−1.78705e161	−1.12350
$513$	6.33224e160	0.354465
$514$	9.06777e160	0.452059
$515$	−2.08235e161	−0.924750
$516$	9.97913e161	3.94853
$517$	2.49953e159	0.00881396
$518$	2.37631e161	0.746935
$519$	−3.23233e161	−0.905853
$520$	−1.57950e162	−3.94749
$521$	−2.18291e161	−0.486621	−0.243310	−	0.969949i	$-0.578233\pi$
$521$	−2.18291e161	−0.486621	−0.243310	+	0.969949i	$0.578233\pi$
$522$	−6.63987e161	−1.32058
$523$	−4.31381e161	−0.765615	−0.382807	−	0.923828i	$-0.625043\pi$
$523$	−4.31381e161	−0.765615	−0.382807	+	0.923828i	$0.625043\pi$
$524$	1.53508e162	2.43176
$525$	−6.13789e161	−0.868042
$526$	1.96740e162	2.48451
$527$	1.43796e160	0.0162187
$528$	−1.04963e162	−1.05760
$529$	1.25893e162	1.13341
$530$	3.00288e162	2.41615
$531$	1.35276e159	0.000972961 0
$532$	1.84914e162	1.18913
$533$	4.06342e160	0.0233681
$534$	2.58187e162	1.32810
$535$	−2.90629e162	−1.33749
$536$	−1.26840e163	−5.22340
$537$	−1.23965e161	−0.0456908
$538$	1.73365e162	0.572027
$539$	8.29924e161	0.245192
$540$	−4.18283e162	−1.10673
$541$	4.37516e162	1.03695	0.518473	−	0.855094i	$-0.326501\pi$
$541$	4.37516e162	1.03695	0.518473	+	0.855094i	$0.326501\pi$
$542$	4.83712e162	1.02714
$543$	−1.21768e163	−2.31710
$544$	−4.80398e161	−0.0819344
$545$	1.50651e163	2.30346
$546$	5.19752e162	0.712581
$547$	6.83403e162	0.840294	0.420147	−	0.907456i	$-0.361979\pi$
$547$	6.83403e162	0.840294	0.420147	+	0.907456i	$0.361979\pi$
$548$	−2.93575e163	−3.23799
$549$	−4.68588e162	−0.463699
$550$	−1.09932e163	−0.976212
$551$	1.49555e163	1.19201
$552$	7.81825e163	5.59415
$553$	−4.07450e162	−0.261775
$554$	−2.88624e163	−1.66533
$555$	−5.06354e163	−2.62435
$556$	8.52664e163	3.97034
$557$	−2.64394e163	−1.10629	−0.553143	−	0.833086i	$-0.686572\pi$
$557$	−2.64394e163	−1.10629	−0.553143	+	0.833086i	$0.686572\pi$
$558$	−1.95351e163	−0.734649
$559$	−2.82154e163	−0.953858
$560$	−5.44017e163	−1.65358
$561$	4.57621e161	0.0125088
$562$	−3.98963e162	−0.0980893
$563$	2.31842e163	0.512794	0.256397	−	0.966572i	$-0.417465\pi$
$563$	2.31842e163	0.512794	0.256397	+	0.966572i	$0.417465\pi$
$564$	−5.38589e162	−0.107189
$565$	1.39962e164	2.50685
$566$	6.13445e163	0.989004
$567$	2.75085e163	0.399278
$568$	1.50779e163	0.197068
$569$	−1.20199e164	−1.41488	−0.707440	−	0.706773i	$-0.750150\pi$
$569$	−1.20199e164	−1.41488	−0.707440	+	0.706773i	$0.750150\pi$
$570$	−5.50453e164	−5.83669
$571$	1.57964e164	1.50907	0.754533	−	0.656262i	$-0.227863\pi$
$571$	1.57964e164	1.50907	0.754533	+	0.656262i	$0.227863\pi$
$572$	6.66351e163	0.573640
$573$	−4.84369e163	−0.375817
$574$	2.64708e162	0.0185144
$575$	4.32926e164	2.73009
$576$	2.51617e164	1.43088
$577$	−1.07794e164	−0.552881	−0.276441	−	0.961031i	$-0.589155\pi$
$577$	−1.07794e164	−0.552881	−0.276441	+	0.961031i	$0.589155\pi$
$578$	−4.04968e164	−1.87376
$579$	3.39739e164	1.41831
$580$	−9.87904e164	−3.72177
$581$	−2.65232e163	−0.0901875
$582$	1.43799e165	4.41405
$583$	−7.63893e163	−0.211716
$584$	9.45283e164	2.36591
$585$	−4.94622e164	−1.11815
$586$	6.08376e164	1.24241
$587$	2.47585e164	0.456832	0.228416	−	0.973564i	$-0.426645\pi$
$587$	2.47585e164	0.456832	0.228416	+	0.973564i	$0.426645\pi$
$588$	−1.78829e165	−2.98185
$589$	4.40005e164	0.663128
$590$	2.81173e162	0.00383071
$591$	−4.12922e164	−0.508643
$592$	−2.92373e165	−3.25683
$593$	−5.92571e164	−0.597016	−0.298508	−	0.954407i	$-0.596489\pi$
$593$	−5.92571e164	−0.597016	−0.298508	+	0.954407i	$0.596489\pi$
$594$	1.48650e164	0.135479
$595$	2.37181e163	0.0195578
$596$	2.21946e165	1.65613
$597$	−3.64870e165	−2.46414
$598$	−3.66599e165	−2.24115
$599$	2.11330e165	1.16967	0.584837	−	0.811151i	$-0.301158\pi$
$599$	2.11330e165	1.16967	0.584837	+	0.811151i	$0.301158\pi$
$600$	1.42835e166	7.15873
$601$	1.52061e165	0.690220	0.345110	−	0.938562i	$-0.387842\pi$
$601$	1.52061e165	0.690220	0.345110	+	0.938562i	$0.387842\pi$
$602$	−1.83806e165	−0.755735
$603$	−3.97202e165	−1.47955
$604$	−1.34813e165	−0.455025
$605$	−5.10831e165	−1.56254
$606$	1.26330e166	3.50255
$607$	2.83185e165	0.711775	0.355888	−	0.934529i	$-0.384179\pi$
$607$	2.83185e165	0.711775	0.355888	+	0.934529i	$0.384179\pi$
$608$	−1.46998e166	−3.35002
$609$	1.96021e165	0.405111
$610$	−9.73969e165	−1.82566
$611$	1.52283e164	0.0258940
$612$	−4.40382e164	−0.0679392
$613$	−6.63063e164	−0.0928232	−0.0464116	−	0.998922i	$-0.514779\pi$
$613$	−6.63063e164	−0.0928232	−0.0464116	+	0.998922i	$0.514779\pi$
$614$	2.23316e166	2.83728
$615$	−5.64050e164	−0.0650501
$616$	2.61752e165	0.274055
$617$	1.78705e166	1.69891	0.849454	−	0.527662i	$-0.176931\pi$
$617$	1.78705e166	1.69891	0.849454	+	0.527662i	$0.176931\pi$
$618$	−1.59458e166	−1.37668
$619$	−2.04222e166	−1.60143	−0.800716	−	0.599044i	$-0.795547\pi$
$619$	−2.04222e166	−1.60143	−0.800716	+	0.599044i	$0.795547\pi$
$620$	−2.90650e166	−2.07045
$621$	−5.85401e165	−0.378881
$622$	4.77462e166	2.80809
$623$	−3.40412e165	−0.181956
$624$	−6.39485e166	−3.10704
$625$	1.41384e166	0.624512
$626$	2.86999e166	1.15268
$627$	1.40028e166	0.511443
$628$	6.12669e165	0.203529
$629$	1.27469e165	0.0385204
$630$	−3.22216e166	−0.885901
$631$	2.34944e166	0.587783	0.293892	−	0.955839i	$-0.405050\pi$
$631$	2.34944e166	0.587783	0.293892	+	0.955839i	$0.405050\pi$
$632$	9.48179e166	2.15886
$633$	−1.03538e167	−2.14574
$634$	−8.42388e166	−1.58928
$635$	1.96813e166	0.338078
$636$	1.64600e167	2.57474
$637$	5.05627e166	0.720334
$638$	3.51082e166	0.455594
$639$	4.72166e165	0.0558205
$640$	1.37493e167	1.48106
$641$	−1.05062e167	−1.03132	−0.515660	−	0.856793i	$-0.672453\pi$
$641$	−1.05062e167	−1.03132	−0.515660	+	0.856793i	$0.672453\pi$
$642$	−2.22552e167	−1.99112
$643$	4.42397e166	0.360794	0.180397	−	0.983594i	$-0.442262\pi$
$643$	4.42397e166	0.360794	0.180397	+	0.983594i	$0.442262\pi$
$644$	−1.70949e167	−1.27104
$645$	3.91663e167	2.65527
$646$	1.38570e166	0.0856714
$647$	−3.11975e167	−1.75920	−0.879600	−	0.475713i	$-0.842190\pi$
$647$	−3.11975e167	−1.75920	−0.879600	+	0.475713i	$0.842190\pi$
$648$	−6.40152e167	−3.29284
$649$	−7.15267e163	−0.000335667 0
$650$	−6.69756e167	−2.86795
$651$	5.76712e166	0.225367
$652$	6.17526e167	2.20254
$653$	−6.08544e166	−0.198133	−0.0990666	−	0.995081i	$-0.531586\pi$
$653$	−6.08544e166	−0.198133	−0.0990666	+	0.995081i	$0.531586\pi$
$654$	1.15362e168	3.42916
$655$	6.02493e167	1.63529
$656$	−3.25687e166	−0.0807275
$657$	2.96016e167	0.670156
$658$	9.92031e165	0.0205156
$659$	−7.56449e167	−1.42921	−0.714607	−	0.699526i	$-0.753395\pi$
$659$	−7.56449e167	−1.42921	−0.714607	+	0.699526i	$0.753395\pi$
$660$	−9.24973e167	−1.59685
$661$	3.78775e167	0.597578	0.298789	−	0.954319i	$-0.403417\pi$
$661$	3.78775e167	0.597578	0.298789	+	0.954319i	$0.403417\pi$
$662$	6.20017e167	0.894032
$663$	2.78803e166	0.0367488
$664$	6.17223e167	0.743774
$665$	7.25755e167	0.799654
$666$	−1.73170e168	−1.74484
$667$	−1.38260e168	−1.27412
$668$	2.88180e168	2.42921
$669$	2.09107e168	1.61255
$670$	−8.25591e168	−5.82525
$671$	2.47765e167	0.159974
$672$	−1.92669e168	−1.13852
$673$	2.74172e168	1.48295	0.741476	−	0.670979i	$-0.234126\pi$
$673$	2.74172e168	1.48295	0.741476	+	0.670979i	$0.234126\pi$
$674$	5.53908e168	2.74267
$675$	−1.06950e168	−0.484847
$676$	−2.00807e168	−0.833586
$677$	−2.71359e168	−1.03162	−0.515808	−	0.856704i	$-0.672508\pi$
$677$	−2.71359e168	−1.03162	−0.515808	+	0.856704i	$0.672508\pi$
$678$	1.07178e169	3.73196
$679$	−1.89594e168	−0.604746
$680$	−5.51945e167	−0.161293
$681$	−2.78247e168	−0.745037
$682$	1.03291e168	0.253451
$683$	−3.00229e168	−0.675181	−0.337591	−	0.941293i	$-0.609612\pi$
$683$	−3.00229e168	−0.675181	−0.337591	+	0.941293i	$0.609612\pi$
$684$	−1.34753e169	−2.77780
$685$	−1.15223e169	−2.17746
$686$	7.03413e168	1.21878
$687$	−9.85258e168	−1.56539
$688$	2.26149e169	3.29521
$689$	−4.65398e168	−0.621986
$690$	5.08881e169	6.23872
$691$	7.75476e168	0.872217	0.436108	−	0.899894i	$-0.356356\pi$
$691$	7.75476e168	0.872217	0.436108	+	0.899894i	$0.356356\pi$
$692$	−1.64471e169	−1.69737
$693$	8.19677e167	0.0776274
$694$	−2.45477e169	−2.13364
$695$	3.34655e169	2.66994
$696$	−4.56162e169	−3.34095
$697$	1.41993e166	0.000954811 0
$698$	2.07382e169	1.28048
$699$	−4.07077e168	−0.230826
$700$	−3.12315e169	−1.62652
$701$	−3.31834e169	−1.58745	−0.793724	−	0.608279i	$-0.791860\pi$
$701$	−3.31834e169	−1.58745	−0.793724	+	0.608279i	$0.791860\pi$
$702$	9.05641e168	0.398014
$703$	3.90045e169	1.57497
$704$	−1.33042e169	−0.493647
$705$	−2.11386e168	−0.0720815
$706$	−6.62774e169	−2.07723
$707$	−1.66561e169	−0.479865
$708$	1.54123e167	0.00408214
$709$	5.73838e169	1.39746	0.698728	−	0.715387i	$-0.253750\pi$
$709$	5.73838e169	1.39746	0.698728	+	0.715387i	$0.253750\pi$
$710$	9.81407e168	0.219775
$711$	2.96923e169	0.611508
$712$	7.92174e169	1.50059
$713$	−4.06774e169	−0.708804
$714$	1.81624e168	0.0291158
$715$	2.61530e169	0.385756
$716$	−6.30771e168	−0.0856144
$717$	−2.21781e169	−0.277035
$718$	−1.10346e170	−1.26868
$719$	8.47957e169	0.897439	0.448720	−	0.893673i	$-0.351880\pi$
$719$	8.47957e169	0.897439	0.448720	+	0.893673i	$0.351880\pi$
$720$	3.96444e170	3.86276
$721$	2.10240e169	0.188611
$722$	1.96942e170	1.62696
$723$	−6.05785e169	−0.460882
$724$	−6.19594e170	−4.34173
$725$	−2.52594e170	−1.63047
$726$	−3.91173e170	−2.32616
$727$	1.09664e170	0.600850	0.300425	−	0.953805i	$-0.402872\pi$
$727$	1.09664e170	0.600850	0.300425	+	0.953805i	$0.402872\pi$
$728$	1.59471e170	0.805128
$729$	−1.25520e170	−0.584016
$730$	6.15275e170	2.63851
$731$	−9.85967e168	−0.0389743
$732$	−5.33874e170	−1.94549
$733$	5.06453e170	1.70158	0.850790	−	0.525506i	$-0.176124\pi$
$733$	5.06453e170	1.70158	0.850790	+	0.525506i	$0.176124\pi$
$734$	3.72607e169	0.115435
$735$	−7.01869e170	−2.00521
$736$	1.35896e171	3.58077
$737$	2.10020e170	0.510440
$738$	−1.92901e169	−0.0432496
$739$	1.82351e170	0.377192	0.188596	−	0.982055i	$-0.439606\pi$
$739$	1.82351e170	0.377192	0.188596	+	0.982055i	$0.439606\pi$
$740$	−2.57649e171	−4.91746
$741$	8.53115e170	1.50253
$742$	−3.03179e170	−0.492795
$743$	4.88003e170	0.732130	0.366065	−	0.930589i	$-0.380705\pi$
$743$	4.88003e170	0.732130	0.366065	+	0.930589i	$0.380705\pi$
$744$	−1.34207e171	−1.85860
$745$	8.71097e170	1.11370
$746$	6.89303e170	0.813673
$747$	1.93284e170	0.210678
$748$	2.32851e169	0.0234387
$749$	2.93428e170	0.272793
$750$	4.32302e171	3.71229
$751$	−1.36236e171	−1.08073	−0.540363	−	0.841432i	$-0.681713\pi$
$751$	−1.36236e171	−1.08073	−0.540363	+	0.841432i	$0.681713\pi$
$752$	−1.22056e170	−0.0894535
$753$	−3.10225e171	−2.10075
$754$	2.13895e171	1.33846
$755$	−5.29118e170	−0.305991
$756$	4.22311e170	0.225728
$757$	−1.09259e171	−0.539822	−0.269911	−	0.962885i	$-0.586994\pi$
$757$	−1.09259e171	−0.539822	−0.269911	+	0.962885i	$0.586994\pi$
$758$	6.57354e171	3.00249
$759$	−1.29453e171	−0.546671
$760$	−1.68891e172	−6.59473
$761$	4.05740e171	1.46508	0.732539	−	0.680725i	$-0.238335\pi$
$761$	4.05740e171	1.46508	0.732539	+	0.680725i	$0.238335\pi$
$762$	1.50711e171	0.503298
$763$	−1.52102e171	−0.469811
$764$	−2.46462e171	−0.704198
$765$	−1.72842e170	−0.0456871
$766$	2.56974e171	0.628459
$767$	−4.35773e168	−0.000986135 0
$768$	−8.52520e170	−0.178530
$769$	−2.38685e171	−0.462602	−0.231301	−	0.972882i	$-0.574298\pi$
$769$	−2.38685e171	−0.462602	−0.231301	+	0.972882i	$0.574298\pi$
$770$	1.70371e171	0.305632
$771$	1.95080e171	0.323950
$772$	1.72870e172	2.65760
$773$	−1.11294e172	−1.58413	−0.792067	−	0.610435i	$-0.790995\pi$
$773$	−1.11294e172	−1.58413	−0.792067	+	0.610435i	$0.790995\pi$
$774$	1.33946e172	1.76540
$775$	−7.43154e171	−0.907042
$776$	4.41205e172	4.98733
$777$	5.11230e171	0.535261
$778$	−1.36974e172	−1.32847
$779$	4.34488e170	0.0390390
$780$	−5.63535e172	−4.69129
$781$	−2.49657e170	−0.0192578
$782$	−1.28105e171	−0.0915725
$783$	3.41557e171	0.226276
$784$	−4.05265e172	−2.48847
$785$	2.40461e171	0.136867
$786$	4.61364e172	2.43446
$787$	−1.43449e172	−0.701782	−0.350891	−	0.936416i	$-0.614121\pi$
$787$	−1.43449e172	−0.701782	−0.350891	+	0.936416i	$0.614121\pi$
$788$	−2.10107e172	−0.953084
$789$	4.23259e172	1.78043
$790$	6.17159e172	2.40761
$791$	−1.41310e172	−0.511296
$792$	−1.90747e172	−0.640192
$793$	1.50950e172	0.469978
$794$	−1.26009e173	−3.63983
$795$	6.46026e172	1.73143
$796$	−1.85657e173	−4.61725
$797$	2.77388e172	0.640203	0.320101	−	0.947383i	$-0.396283\pi$
$797$	2.77388e172	0.640203	0.320101	+	0.947383i	$0.396283\pi$
$798$	5.55754e172	1.19045
$799$	5.32141e169	0.00105802
$800$	2.48275e173	4.58224
$801$	2.48070e172	0.425049
$802$	1.94962e173	3.10152
$803$	−1.56518e172	−0.231201
$804$	−4.52542e173	−6.20760
$805$	−6.70943e172	−0.854734
$806$	6.29298e172	0.744597
$807$	3.72971e172	0.409920
$808$	3.87606e173	3.95744
$809$	−1.16441e173	−1.10451	−0.552255	−	0.833675i	$-0.686232\pi$
$809$	−1.16441e173	−1.10451	−0.552255	+	0.833675i	$0.686232\pi$
$810$	−4.16668e173	−3.67224
$811$	4.62866e172	0.379066	0.189533	−	0.981874i	$-0.439303\pi$
$811$	4.62866e172	0.379066	0.189533	+	0.981874i	$0.439303\pi$
$812$	9.97416e172	0.759089
$813$	1.04064e173	0.736058
$814$	9.15633e172	0.601962
$815$	2.42368e173	1.48114
$816$	−2.23463e172	−0.126953
$817$	−3.01698e173	−1.59353
$818$	4.49516e173	2.20762
$819$	4.99384e172	0.228057
$820$	−2.87006e172	−0.121890
$821$	−1.37938e173	−0.544837	−0.272419	−	0.962179i	$-0.587824\pi$
$821$	−1.37938e173	−0.544837	−0.272419	+	0.962179i	$0.587824\pi$
$822$	−8.82329e173	−3.24158
$823$	−8.26855e172	−0.282578	−0.141289	−	0.989968i	$-0.545125\pi$
$823$	−8.26855e172	−0.282578	−0.141289	+	0.989968i	$0.545125\pi$
$824$	−4.89251e173	−1.55547
$825$	−2.36503e173	−0.699564
$826$	−2.83880e170	−0.000781308 0
$827$	−1.00252e173	−0.256754	−0.128377	−	0.991725i	$-0.540977\pi$
$827$	−1.00252e173	−0.256754	−0.128377	+	0.991725i	$0.540977\pi$
$828$	1.24576e174	2.96914
$829$	−2.58199e173	−0.572743	−0.286372	−	0.958119i	$-0.592449\pi$
$829$	−2.58199e173	−0.572743	−0.286372	+	0.958119i	$0.592449\pi$
$830$	4.01744e173	0.829474
$831$	−6.20933e173	−1.19339
$832$	−8.10553e173	−1.45025
$833$	1.76688e172	0.0294326
$834$	2.56265e174	3.97475
$835$	1.13105e174	1.63357
$836$	7.12506e173	0.958330
$837$	1.00489e173	0.125879
$838$	4.36196e173	0.508935
$839$	9.93578e173	1.07985	0.539927	−	0.841712i	$-0.318452\pi$
$839$	9.93578e173	1.07985	0.539927	+	0.841712i	$0.318452\pi$
$840$	−2.21364e174	−2.24125
$841$	−2.53445e173	−0.239068
$842$	−5.51308e173	−0.484534
$843$	−8.58312e172	−0.0702918
$844$	−5.26832e174	−4.02065
$845$	−7.88130e173	−0.560562
$846$	−7.22926e172	−0.0479245
$847$	5.15749e173	0.318695
$848$	3.73021e174	2.14872
$849$	1.31974e174	0.708730
$850$	−2.34041e173	−0.117183
$851$	−3.60587e174	−1.68346
$852$	5.37951e173	0.234200
$853$	2.54974e174	1.03521	0.517605	−	0.855620i	$-0.326824\pi$
$853$	2.54974e174	1.03521	0.517605	+	0.855620i	$0.326824\pi$
$854$	9.83347e173	0.372360
$855$	−5.28882e174	−1.86799
$856$	−6.82837e174	−2.24972
$857$	5.21083e174	1.60158	0.800788	−	0.598947i	$-0.204414\pi$
$857$	5.21083e174	1.60158	0.800788	+	0.598947i	$0.204414\pi$
$858$	2.00269e174	0.574276
$859$	−3.35819e173	−0.0898486	−0.0449243	−	0.998990i	$-0.514305\pi$
$859$	−3.35819e173	−0.0898486	−0.0449243	+	0.998990i	$0.514305\pi$
$860$	1.99290e175	4.97539
$861$	5.69481e172	0.0132676
$862$	−7.97523e174	−1.73405
$863$	−5.93257e174	−1.20393	−0.601964	−	0.798523i	$-0.705615\pi$
$863$	−5.93257e174	−1.20393	−0.601964	+	0.798523i	$0.705615\pi$
$864$	−3.35716e174	−0.635923
$865$	−6.45517e174	−1.14143
$866$	1.67944e175	2.77236
$867$	−8.71232e174	−1.34276
$868$	2.93449e174	0.422288
$869$	−1.56997e174	−0.210968
$870$	−2.96911e175	−3.72590
$871$	1.27954e175	1.49959
$872$	3.53956e175	3.87453
$873$	1.38164e175	1.41269
$874$	−3.91991e175	−3.74409
$875$	−5.69976e174	−0.508601
$876$	3.37259e175	2.81170
$877$	2.13182e175	1.66063	0.830317	−	0.557291i	$-0.188159\pi$
$877$	2.13182e175	1.66063	0.830317	+	0.557291i	$0.188159\pi$
$878$	−3.35191e175	−2.43988
$879$	1.30884e175	0.890322
$880$	−2.09619e175	−1.33264
$881$	3.61115e172	0.00214575	0.00107287	−	0.999999i	$-0.499658\pi$
$881$	3.61115e172	0.00214575	0.00107287	+	0.999999i	$0.499658\pi$
$882$	−2.40035e175	−1.33319
$883$	1.24529e175	0.646559	0.323280	−	0.946304i	$-0.395215\pi$
$883$	1.24529e175	0.646559	0.323280	+	0.946304i	$0.395215\pi$
$884$	1.41864e174	0.0688591
$885$	6.04904e172	0.00274512
$886$	−3.09360e175	−1.31268
$887$	2.48341e175	0.985357	0.492678	−	0.870212i	$-0.336018\pi$
$887$	2.48341e175	0.985357	0.492678	+	0.870212i	$0.336018\pi$
$888$	−1.18969e176	−4.41429
$889$	−1.98708e174	−0.0689541
$890$	5.15618e175	1.67349
$891$	1.05995e175	0.321782
$892$	1.06400e176	3.02156
$893$	1.62831e174	0.0432588
$894$	6.67051e175	1.65797
$895$	−2.47566e174	−0.0575732
$896$	−1.38817e175	−0.302075
$897$	−7.88685e175	−1.60603
$898$	−1.41447e176	−2.69557
$899$	2.37336e175	0.423313
$900$	2.27594e176	3.79955
$901$	−1.62630e174	−0.0254141
$902$	1.01996e174	0.0149209
$903$	−3.95434e175	−0.541567
$904$	3.28843e176	4.21665
$905$	−2.43179e176	−2.91969
$906$	−4.05177e175	−0.455530
$907$	1.40848e175	0.148292	0.0741459	−	0.997247i	$-0.476377\pi$
$907$	1.40848e175	0.148292	0.0741459	+	0.997247i	$0.476377\pi$
$908$	−1.41581e176	−1.39603
$909$	1.21379e176	1.12097
$910$	1.03798e176	0.897896
$911$	1.07372e176	0.870058	0.435029	−	0.900416i	$-0.356738\pi$
$911$	1.07372e176	0.870058	0.435029	+	0.900416i	$0.356738\pi$
$912$	−6.83779e176	−5.19067
$913$	−1.02198e175	−0.0726830
$914$	3.95770e175	0.263721
$915$	−2.09536e176	−1.30829
$916$	−5.01329e176	−2.93320
$917$	−6.08294e175	−0.333532
$918$	3.16470e174	0.0162627
$919$	−1.26462e176	−0.609096	−0.304548	−	0.952497i	$-0.598505\pi$
$919$	−1.26462e176	−0.609096	−0.304548	+	0.952497i	$0.598505\pi$
$920$	1.56136e177	7.04898
$921$	4.80434e176	2.03323
$922$	3.27735e176	1.30027
$923$	−1.52102e175	−0.0565764
$924$	9.33879e175	0.325693
$925$	−6.58774e176	−2.15429
$926$	3.52307e176	1.08036
$927$	−1.53209e176	−0.440596
$928$	−7.92897e176	−2.13851
$929$	−3.36258e176	−0.850625	−0.425313	−	0.905047i	$-0.639836\pi$
$929$	−3.36258e176	−0.850625	−0.425313	+	0.905047i	$0.639836\pi$
$930$	−8.73539e176	−2.07275
$931$	5.40650e176	1.20340
$932$	−2.07133e176	−0.432517
$933$	1.02719e177	2.01230
$934$	4.28297e176	0.787237
$935$	9.13899e174	0.0157619
$936$	−1.16212e177	−1.88078
$937$	5.93824e176	0.901887	0.450943	−	0.892552i	$-0.351088\pi$
$937$	5.93824e176	0.901887	0.450943	+	0.892552i	$0.351088\pi$
$938$	8.33541e176	1.18811
$939$	6.17439e176	0.826021
$940$	−1.07560e176	−0.135065
$941$	−1.53498e177	−1.80934	−0.904671	−	0.426110i	$-0.859884\pi$
$941$	−1.53498e177	−1.80934	−0.904671	+	0.426110i	$0.859884\pi$
$942$	1.84135e176	0.203755
$943$	−4.01674e175	−0.0417280
$944$	3.49276e174	0.00340671
$945$	1.65749e176	0.151795
$946$	−7.08237e176	−0.609055
$947$	1.10187e177	0.889829	0.444915	−	0.895573i	$-0.353234\pi$
$947$	1.10187e177	0.889829	0.444915	+	0.895573i	$0.353234\pi$
$948$	3.38291e177	2.56564
$949$	−9.53578e176	−0.679230
$950$	−7.16147e177	−4.79124
$951$	−1.81228e177	−1.13890
$952$	5.57260e175	0.0328972
$953$	2.67184e177	1.48178	0.740889	−	0.671627i	$-0.234404\pi$
$953$	2.67184e177	1.48178	0.740889	+	0.671627i	$0.234404\pi$
$954$	2.20937e177	1.15117
$955$	−9.67318e176	−0.473553
$956$	−1.12849e177	−0.519102
$957$	7.55303e176	0.326483
$958$	−4.46435e177	−1.81347
$959$	1.16332e177	0.444112
$960$	1.12514e178	4.03710
$961$	−2.26685e177	−0.764508
$962$	5.57845e177	1.76847
$963$	−2.13831e177	−0.637244
$964$	−3.08242e177	−0.863591
$965$	6.78482e177	1.78716
$966$	−5.13781e177	−1.27245
$967$	1.79999e177	0.419175	0.209587	−	0.977790i	$-0.432788\pi$
$967$	1.79999e177	0.419175	0.209587	+	0.977790i	$0.432788\pi$
$968$	−1.20020e178	−2.62827
$969$	2.98115e176	0.0613930
$970$	2.87176e178	5.56198
$971$	4.17824e177	0.761113	0.380557	−	0.924758i	$-0.375732\pi$
$971$	4.17824e177	0.761113	0.380557	+	0.924758i	$0.375732\pi$
$972$	−1.90260e178	−3.25990
$973$	−3.37877e177	−0.544559
$974$	2.25595e177	0.342036
$975$	−1.44089e178	−2.05520
$976$	−1.20988e178	−1.62359
$977$	−6.68152e177	−0.843624	−0.421812	−	0.906683i	$-0.638606\pi$
$977$	−6.68152e177	−0.843624	−0.421812	+	0.906683i	$0.638606\pi$
$978$	1.85595e178	2.20498
$979$	−1.31166e177	−0.146640
$980$	−3.57132e178	−3.75732
$981$	1.10842e178	1.09748
$982$	7.32271e177	0.682399
$983$	1.01983e178	0.894525	0.447262	−	0.894403i	$-0.352399\pi$
$983$	1.01983e178	0.894525	0.447262	+	0.894403i	$0.352399\pi$
$984$	−1.32524e177	−0.109418
$985$	−8.24633e177	−0.640921
$986$	7.47440e176	0.0546890
$987$	2.13421e176	0.0147017
$988$	4.34091e178	2.81542
$989$	2.78912e178	1.70329
$990$	−1.24155e178	−0.713956
$991$	1.57482e178	0.852804	0.426402	−	0.904534i	$-0.359781\pi$
$991$	1.57482e178	0.852804	0.426402	+	0.904534i	$0.359781\pi$
$992$	−2.33277e178	−1.18967
$993$	1.33388e178	0.640673
$994$	−9.90856e176	−0.0448251
$995$	−7.28669e178	−3.10497
$996$	2.20213e178	0.883918
$997$	1.49345e178	0.564715	0.282358	−	0.959309i	$-0.408883\pi$
$997$	1.49345e178	0.564715	0.282358	+	0.959309i	$0.408883\pi$
$998$	−4.59362e178	−1.63639
$999$	8.90791e177	0.298971

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1.120.a.a.1.10	✓	10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1.120.a.a.1.10	✓	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)

\(f(q)\)	\(=\)	\(q+1.52927e18 q^{2} +3.29001e28 q^{3} +1.67406e36 q^{4} +6.57038e41 q^{5} +5.03133e46 q^{6} -6.63364e49 q^{7} +1.54372e54 q^{8} +4.83416e56 q^{9} +O(q^{10})\)	\(q+1.52927e18 q^{2} +3.29001e28 q^{3} +1.67406e36 q^{4} +6.57038e41 q^{5} +5.03133e46 q^{6} -6.63364e49 q^{7} +1.54372e54 q^{8} +4.83416e56 q^{9} +1.00479e60 q^{10} -2.55605e61 q^{11} +5.50768e64 q^{12} -1.55726e66 q^{13} -1.01446e68 q^{14} +2.16166e70 q^{15} +1.24816e72 q^{16} -5.44174e71 q^{17} +7.39274e74 q^{18} -1.66513e76 q^{19} +1.09992e78 q^{20} -2.18248e78 q^{21} -3.90890e79 q^{22} +1.53937e81 q^{23} +5.07885e82 q^{24} +2.81235e83 q^{25} -2.38148e84 q^{26} -3.80285e84 q^{27} -1.11051e86 q^{28} -8.98160e86 q^{29} +3.30577e88 q^{30} -2.64247e88 q^{31} +8.82801e89 q^{32} -8.40945e89 q^{33} -8.32191e89 q^{34} -4.35855e91 q^{35} +8.09267e92 q^{36} -2.34243e93 q^{37} -2.54644e94 q^{38} -5.12342e94 q^{39} +1.01428e96 q^{40} -2.60933e94 q^{41} -3.33760e96 q^{42} +1.81186e97 q^{43} -4.27899e97 q^{44} +3.17622e98 q^{45} +2.35412e99 q^{46} -9.77887e97 q^{47} +4.10647e100 q^{48} -3.24689e100 q^{49} +4.30085e101 q^{50} -1.79034e100 q^{51} -2.60695e102 q^{52} +2.98856e102 q^{53} -5.81559e102 q^{54} -1.67942e103 q^{55} -1.02405e104 q^{56} -5.47830e104 q^{57} -1.37353e105 q^{58} +2.79833e102 q^{59} +3.61875e106 q^{60} -9.69327e105 q^{61} -4.04105e106 q^{62} -3.20681e106 q^{63} +5.20498e107 q^{64} -1.02318e108 q^{65} -1.28603e108 q^{66} -8.21656e108 q^{67} -9.10980e107 q^{68} +5.06456e109 q^{69} -6.66541e109 q^{70} +9.76729e108 q^{71} +7.46257e110 q^{72} +6.12342e110 q^{73} -3.58221e111 q^{74} +9.25268e111 q^{75} -2.78753e112 q^{76} +1.69559e111 q^{77} -7.83510e112 q^{78} +6.14218e112 q^{79} +8.20088e113 q^{80} -4.14682e113 q^{81} -3.99038e112 q^{82} +3.99829e113 q^{83} -3.65360e114 q^{84} -3.57543e113 q^{85} +2.77082e115 q^{86} -2.95496e115 q^{87} -3.94582e115 q^{88} +5.13160e115 q^{89} +4.85731e116 q^{90} +1.03303e116 q^{91} +2.57700e117 q^{92} -8.69375e116 q^{93} -1.49545e116 q^{94} -1.09405e118 q^{95} +2.90443e118 q^{96} +2.85807e118 q^{97} -4.96539e118 q^{98} -1.23564e118 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + 91\!\cdots\!00 q^{2}+ \cdots + 18\!\cdots\!70 q^{9}+O(q^{10}) \) 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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