LMFDB - Embedded newform 1.98.a.a.1.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1,98,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, 98, names="a")

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

chi := DirichletCharacter("1.1");

S:= CuspForms(chi, 98);

N := Newforms(S);

Level:	$ N $	$=$	$ 1 $
Weight:	$ k $	$=$	$ 98 $
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:	$59.5852992940$
Analytic rank:	$1$
Dimension:	$7$
Coefficient field:	$\mathbb{Q}[x]/(x^{7} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{7} - x^{6} + \cdots - 60\!\cdots\!00 $ x^7 - x^6 - 276087571804405990752665088x^5 - 120083887007184048105302098667336699968x^4 + 19373155893793813105741918625198082602849023860244480x^3 + 17598423525325549028964286424215233146805218189713573416303513600x^2 - 58411389055962077878580852277509525104521481793026738328029906710656876544000*x - 6001611580367435872109665775701806052295874267155389813520177925124906158334928977920000
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	multiple of $ 2^{83}\cdot 3^{30}\cdot 5^{10}\cdot 7^{8}\cdot 11^{2}\cdot 19 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Root			$-1.00063e11$ 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)

$f(q)$	$=$	$q-7.18835e12 q^{2} +1.45423e23 q^{3} -1.58405e29 q^{4} +1.38920e34 q^{5} -1.04535e36 q^{6} -1.18505e40 q^{7} +2.27771e42 q^{8} +2.05969e45 q^{9} +O(q^{10})$	\(q-7.18835e12 q^{2} +1.45423e23 q^{3} -1.58405e29 q^{4} +1.38920e34 q^{5} -1.04535e36 q^{6} -1.18505e40 q^{7} +2.27771e42 q^{8} +2.05969e45 q^{9} -9.98605e46 q^{10} -1.43215e50 q^{11} -2.30356e52 q^{12} -1.66109e54 q^{13} +8.51852e52 q^{14} +2.02021e57 q^{15} +2.50838e58 q^{16} -2.44836e59 q^{17} -1.48058e58 q^{18} -3.82319e61 q^{19} -2.20056e63 q^{20} -1.72333e63 q^{21} +1.02948e63 q^{22} -1.93525e66 q^{23} +3.31230e65 q^{24} +1.29878e68 q^{25} +1.19405e67 q^{26} -2.47631e69 q^{27} +1.87717e69 q^{28} -3.44723e70 q^{29} -1.45220e70 q^{30} +1.99479e72 q^{31} -5.41229e71 q^{32} -2.08267e73 q^{33} +1.75996e72 q^{34} -1.64626e74 q^{35} -3.26265e74 q^{36} +1.29033e76 q^{37} +2.74824e74 q^{38} -2.41561e77 q^{39} +3.16419e76 q^{40} +2.61787e78 q^{41} +1.23879e76 q^{42} -2.22828e79 q^{43} +2.26859e79 q^{44} +2.86133e79 q^{45} +1.39112e79 q^{46} -5.24832e80 q^{47} +3.64776e81 q^{48} -9.28953e81 q^{49} -9.33612e80 q^{50} -3.56047e82 q^{51} +2.63125e83 q^{52} -4.67367e83 q^{53} +1.78006e82 q^{54} -1.98954e84 q^{55} -2.69919e82 q^{56} -5.55979e84 q^{57} +2.47799e83 q^{58} -8.05790e84 q^{59} -3.20011e86 q^{60} -4.59498e86 q^{61} -1.43393e85 q^{62} -2.44083e85 q^{63} -3.97080e87 q^{64} -2.30759e88 q^{65} +1.49710e86 q^{66} -2.23736e88 q^{67} +3.87831e88 q^{68} -2.81429e89 q^{69} +1.18339e87 q^{70} +3.17929e89 q^{71} +4.69138e87 q^{72} +9.38407e89 q^{73} -9.27532e88 q^{74} +1.88873e91 q^{75} +6.05612e90 q^{76} +1.69716e90 q^{77} +1.73642e90 q^{78} +2.26645e91 q^{79} +3.48465e92 q^{80} -3.99427e92 q^{81} -1.88182e91 q^{82} -2.02604e93 q^{83} +2.72983e92 q^{84} -3.40125e93 q^{85} +1.60176e92 q^{86} -5.01305e93 q^{87} -3.26202e92 q^{88} -1.75683e94 q^{89} -2.05682e92 q^{90} +1.96847e94 q^{91} +3.06553e95 q^{92} +2.90088e95 q^{93} +3.77267e93 q^{94} -5.31118e95 q^{95} -7.87069e94 q^{96} +2.38093e96 q^{97} +6.67764e94 q^{98} -2.94979e95 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 7 q - 16697241085008 q^{2} + 10\!\cdots\!96 q^{3}+ \cdots + 34\!\cdots\!51 q^{9}+O(q^{10}) $ 7 * q - 16697241085008 * q^2 + 100515854497394358147996 * q^3 + 163057083940695061811962902784 * q^4 - 3658387999529088680958306590731350 * q^5 - 30592714388364079315260992082788233536 * q^6 - 184642311743115370607493500489904481438408 * q^7 + 36028528195426625427479134330455698506199040 * q^8 + 34775775472129528349857305774273773877811641051 * q^9	$ 7 q - 16697241085008 q^{2} + 10\!\cdots\!96 q^{3}+ \cdots - 13\!\cdots\!28 q^{99}+O(q^{100}) $ 7 * q - 16697241085008 * q^2 + 100515854497394358147996 * q^3 + 163057083940695061811962902784 * q^4 - 3658387999529088680958306590731350 * q^5 - 30592714388364079315260992082788233536 * q^6 - 184642311743115370607493500489904481438408 * q^7 + 36028528195426625427479134330455698506199040 * q^8 + 34775775472129528349857305774273773877811641051 * q^9 + 2369114123959441270700616822719459966510786272800 * q^10 - 211379321299339211995860033669883746379479318698796 * q^11 + 29500590587146562092031430274877546417191966208812032 * q^12 - 883667637845783834437332163606692334928033653755299614 * q^13 + 24884922778173528138085777326574033504771595080747613568 * q^14 - 1421739776861319561135033238174867421082029896683725376600 * q^15 - 31468671341370205538262999960370611414173356196203424841728 * q^16 + 163250436637003263661570089512096377905088225334685131721342 * q^17 - 7054606772048003028382413409749231596837718873737440667537424 * q^18 + 133084372359310898958448501523235681541051727436663191570359820 * q^19 - 1318696260534044061297364386263469065025874939722479973417331200 * q^20 - 8226961344750528298533572507576209983448935264598913374247505696 * q^21 - 193421584410477868290586506488587370358898549812529751083484246976 * q^22 + 925260914184001305416523826357059292226482310773339215111132964776 * q^23 + 1719359518493251306391725804700467921422689016189510541760687554560 * q^24 - 15111829774373494694703308579556617230149980669179989285410298974375 * q^25 + 252570839996871764139482603418038366978372757286009959646749464447904 * q^26 - 16291464003153760806194022590188439733978909915063668620863256233960 * q^27 + 2270023864280230580582797832096861251181573169347509612847861972977664 * q^28 - 119228645746988213289933973286594685848645193803889692652451844737975470 * q^29 + 350448354156350400480979435069989695492221249186335731168327070817564800 * q^30 + 1783283666881858864849681148885200501497581294973934227348751364131906784 * q^31 - 5665372498136527985720301619489703024215195383428523596691479514791804928 * q^32 + 31524650657546522511070078635079454480923539002999356172307109465073458512 * q^33 - 360491523041063125717708388027762293189396999595568175085448186659598970272 * q^34 + 1278268341035082746531666145800358760269267683649420892787253371588938750800 * q^35 - 216561481226385812264597126278375191173372906326221899147967914271513631488 * q^36 - 4532061622841943284542390241171859851726205146853788500539269747469617514358 * q^37 - 2979582210919721773595405461863152858097797783237497905501709239616681227840 * q^38 + 43268347489134056222423767530379619668087154910038087692852374564634305176712 * q^39 - 252514831298472678734291758335102132215188475493571956673272319739362987008000 * q^40 + 123663386655433999860484853403953500874113711440208020678841289201379470695974 * q^41 + 3296122851141924824443574220618174749418258893075867148421980920155200276985344 * q^42 - 6595249409358954185694714287710218939626711013706300289026511229489118746183244 * q^43 + 31427981619155317050453798326367420934595218826815326227502736274099059309390848 * q^44 - 252057107931731391251960224707597558538839631727412739243273361199825466582835550 * q^45 + 333743461536679365083903174537100831945624746347277312419032904840551699600111744 * q^46 + 1582413179705462665936960636748613012540566075462612818643843634715630112826042192 * q^47 - 5861556434117332280930374286873664455351210291383528056190272983552191849213722624 * q^48 + 4345635008055985505106601346877321132027699788278385269907095782368403364891488399 * q^49 - 26742593205970009143775889336520990050133941492259748319418427757724876722706030000 * q^50 + 7043565089506559965061572069632281800522096763383079376468682406398600422146676984 * q^51 + 45800222007571685487736059984048709986270205428489770979037497696929384027946163712 * q^52 - 653999931744204429821742741003701830521617657540517458768483866216741544701292475654 * q^53 - 1692275654206728716605786947196644220317392594111136065941704729626944069981837438080 * q^54 - 2797264930804680667438884831689324464716285797264284803651188210713133784740241832200 * q^55 - 13571511538900847480549793700693331801076437559096966169392506220987757777557857402880 * q^56 - 32156245276763940566100505959698139630384956043693169857398532690693294678041975751120 * q^57 - 110275012470967940484400158535846043036245771061355495516009955997986614502808104491360 * q^58 - 289716843512018767811919727809674339112407721830489506743846640027004030301179845118940 * q^59 - 910863091257112962110410128770927709732237428874631129572443550789630933691032398899200 * q^60 - 1779644273771380099149369471014727845406783738447834645166296866716596067825339549188046 * q^61 - 4893410323209515393605311670149478112622973098189152140516775294151722525768562137565696 * q^62 - 12773855755538157144284595252262546905649007916763284311597736303148976241726684562602024 * q^63 - 24329532034212074257236420324752039539459926287390018025638252399891746834835822530789376 * q^64 - 40979880706222898178317998710539228015340375450212825952623031288613904725454054500850100 * q^65 - 142841613731497146561089386918878946227924637814625892149907766833242924230825872606056192 * q^66 - 183094181851902905703789039636502649221241410347877100016575616698548103898875205122783908 * q^67 - 250132580738896836682574414547500843555901286243235420681429272583107380144497499057716736 * q^68 - 372244836961332226973480986215431578494847115740354696097669790201492502675456308855459168 * q^69 - 587389541033882485666068522391834191601610745639266949076956170254929472707526921059782400 * q^70 - 36618527208607574135274147674246343687098099724640001025727994874106062220116534447931656 * q^71 + 2495502705800463241319297965149724088435827677064467496346161624547668625438549984339128320 * q^72 + 5937141741627411574629383951784847225959103237898806939243808260531064318159784943464907526 * q^73 + 25603418812897773069861990064614106209712057876935905208225093500026599325689360114519970848 * q^74 + 43416229043729585532262686371625117245611844558141193068941674421259839404159894884059222500 * q^75 + 64491781461168277038374423376126180174707623388661413952117963143585395013082375272839869440 * q^76 + 122801524700573133455664123216977109508839271312008866744292206338517188364407357732160152224 * q^77 + 256518622739178273010532892375526005382856863147760611859324715551823107217212845963281985152 * q^78 + 155279975164311735091235448536513906273532801204307686975280157544842456609207922540776901680 * q^79 + 343037548751841740038666995050634479050946344382038763901789904170114217394648666813900390400 * q^80 - 799336653019442009471583631583081099983526554777301855450568718504605547656753900698628831153 * q^81 - 2054599455199243418451530458808296516745297582440826399667363552358055209069956455679452833056 * q^82 - 2745080838526935126539434486643898932954125805020264508203796620734019354440308801326974021684 * q^83 - 12055830667015300843296227009204563031159870111997209215974794552386444770918151507927520305152 * q^84 - 16156906986132970771716277890961343081101351325821342812927748903601690598916612215092853170700 * q^85 - 16073101085057033129856695763368798351047883803740227513388827997968391823543719379002604387776 * q^86 - 44931373084677669249994770736329381356923858000626008622029156778901658182110994195783000791480 * q^87 - 20900444501134905678673788524771632932447417317035512416151379720801969394444956958395302789120 * q^88 + 8652425236627243255051028260917634407304730072980172181544783646255542601500269383337979350390 * q^89 + 169914380219009102880054256907856294069041898142575788262717672760376053145875718225670932330400 * q^90 + 235279610532724372901602846332263408075886672274330172793822218199845308058643167074949650230544 * q^91 + 622950794384614085632156625042963081233986358617743991991586248417198315809579918444522808891392 * q^92 + 1619655729334717431421579797164299646702152339363664709672746834797775058100318492643375449441152 * q^93 + 1784387548746436753701888750274366538460858609156963702431495773056050960861585984793528939671808 * q^94 + 1109691419127482658877926123378178695834970817464791602098716148821958373905367930889408748989000 * q^95 + 2773817117979873680694700349927475687549477810523157816910439588411515192104026991177258420404224 * q^96 - 462826972284038426621245345324758076530452205891330025493894671876723283114629445572915788984658 * q^97 - 10100804559243313775965110405631054964918520327952856127425837778067309219959758215138751854831056 * q^98 - 13792894935722775136702660269810636953813664741795563019740674282913700184659028566406972539495228 * 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 $

$2$	−7.18835e12	−0.0180582	−0.00902910	−	0.999959i	$-0.502874\pi$
$2$	−7.18835e12	−0.0180582	−0.00902910	+	0.999959i	$0.502874\pi$
$3$	1.45423e23	1.05257	0.526285	−	0.850308i	$-0.323584\pi$
$3$	1.45423e23	1.05257	0.526285	+	0.850308i	$0.323584\pi$
$4$	−1.58405e29	−0.999674
$5$	1.38920e34	1.74872	0.874358	−	0.485282i	$-0.161283\pi$
$5$	1.38920e34	1.74872	0.874358	+	0.485282i	$0.161283\pi$
$6$	−1.04535e36	−0.0190075
$7$	−1.18505e40	−0.122034	−0.0610169	−	0.998137i	$-0.519434\pi$
$7$	−1.18505e40	−0.122034	−0.0610169	+	0.998137i	$0.519434\pi$
$8$	2.27771e42	0.0361105
$9$	2.05969e45	0.107905
$10$	−9.98605e46	−0.0315787
$11$	−1.43215e50	−0.445086	−0.222543	−	0.974923i	$-0.571436\pi$
$11$	−1.43215e50	−0.445086	−0.222543	+	0.974923i	$0.571436\pi$
$12$	−2.30356e52	−1.05223
$13$	−1.66109e54	−1.56366	−0.781829	−	0.623493i	$-0.785713\pi$
$13$	−1.66109e54	−1.56366	−0.781829	+	0.623493i	$0.785713\pi$
$14$	8.51852e52	0.00220371
$15$	2.02021e57	1.84065
$16$	2.50838e58	0.999022
$17$	−2.44836e59	−0.515350	−0.257675	−	0.966232i	$-0.582956\pi$
$17$	−2.44836e59	−0.515350	−0.257675	+	0.966232i	$0.582956\pi$
$18$	−1.48058e58	−0.00194857
$19$	−3.82319e61	−0.365491	−0.182745	−	0.983160i	$-0.558498\pi$
$19$	−3.82319e61	−0.365491	−0.182745	+	0.983160i	$0.558498\pi$
$20$	−2.20056e63	−1.74815
$21$	−1.72333e63	−0.128449
$22$	1.02948e63	0.00803744
$23$	−1.93525e66	−1.74959	−0.874796	−	0.484491i	$-0.839005\pi$
$23$	−1.93525e66	−1.74959	−0.874796	+	0.484491i	$0.839005\pi$
$24$	3.31230e65	0.0380089
$25$	1.29878e68	2.05801
$26$	1.19405e67	0.0282368
$27$	−2.47631e69	−0.938993
$28$	1.87717e69	0.121994
$29$	−3.44723e70	−0.408476	−0.204238	−	0.978921i	$-0.565472\pi$
$29$	−3.44723e70	−0.408476	−0.204238	+	0.978921i	$0.565472\pi$
$30$	−1.45220e70	−0.0332388
$31$	1.99479e72	0.930797	0.465399	−	0.885101i	$-0.345911\pi$
$31$	1.99479e72	0.930797	0.465399	+	0.885101i	$0.345911\pi$
$32$	−5.41229e71	−0.0541510
$33$	−2.08267e73	−0.468484
$34$	1.75996e72	0.00930628
$35$	−1.64626e74	−0.213402
$36$	−3.26265e74	−0.107870
$37$	1.29033e76	1.12958	0.564789	−	0.825236i	$-0.308958\pi$
$37$	1.29033e76	1.12958	0.564789	+	0.825236i	$0.308958\pi$
$38$	2.74824e74	0.00660011
$39$	−2.41561e77	−1.64586
$40$	3.16419e76	0.0631470
$41$	2.61787e78	1.57736	0.788682	−	0.614802i	$-0.210764\pi$
$41$	2.61787e78	1.57736	0.788682	+	0.614802i	$0.210764\pi$
$42$	1.23879e76	0.00231956
$43$	−2.22828e79	−1.33275	−0.666376	−	0.745616i	$-0.732155\pi$
$43$	−2.22828e79	−1.33275	−0.666376	+	0.745616i	$0.732155\pi$
$44$	2.26859e79	0.444940
$45$	2.86133e79	0.188695
$46$	1.39112e79	0.0315945
$47$	−5.24832e80	−0.420024	−0.210012	−	0.977699i	$-0.567350\pi$
$47$	−5.24832e80	−0.420024	−0.210012	+	0.977699i	$0.567350\pi$
$48$	3.64776e81	1.05154
$49$	−9.28953e81	−0.985108
$50$	−9.33612e80	−0.0371639
$51$	−3.56047e82	−0.542442
$52$	2.63125e83	1.56315
$53$	−4.67367e83	−1.10225	−0.551123	−	0.834424i	$-0.685801\pi$
$53$	−4.67367e83	−1.10225	−0.551123	+	0.834424i	$0.685801\pi$
$54$	1.78006e82	0.0169565
$55$	−1.98954e84	−0.778328
$56$	−2.69919e82	−0.00440670
$57$	−5.55979e84	−0.384705
$58$	2.47799e83	0.00737635
$59$	−8.05790e84	−0.104689	−0.0523443	−	0.998629i	$-0.516669\pi$
$59$	−8.05790e84	−0.104689	−0.0523443	+	0.998629i	$0.516669\pi$
$60$	−3.20011e86	−1.84005
$61$	−4.59498e86	−1.18519	−0.592594	−	0.805501i	$-0.701896\pi$
$61$	−4.59498e86	−1.18519	−0.592594	+	0.805501i	$0.701896\pi$
$62$	−1.43393e85	−0.0168085
$63$	−2.44083e85	−0.0131680
$64$	−3.97080e87	−0.998044
$65$	−2.30759e88	−2.73439
$66$	1.49710e86	0.00845998
$67$	−2.23736e88	−0.609688	−0.304844	−	0.952402i	$-0.598604\pi$
$67$	−2.23736e88	−0.609688	−0.304844	+	0.952402i	$0.598604\pi$
$68$	3.87831e88	0.515182
$69$	−2.81429e89	−1.84157
$70$	1.18339e87	0.00385366
$71$	3.17929e89	0.520355	0.260177	−	0.965561i	$-0.416219\pi$
$71$	3.17929e89	0.520355	0.260177	+	0.965561i	$0.416219\pi$
$72$	4.69138e87	0.00389650
$73$	9.38407e89	0.399239	0.199619	−	0.979874i	$-0.436029\pi$
$73$	9.38407e89	0.399239	0.199619	+	0.979874i	$0.436029\pi$
$74$	−9.27532e88	−0.0203981
$75$	1.88873e91	2.16620
$76$	6.05612e90	0.365372
$77$	1.69716e90	0.0543155
$78$	1.73642e90	0.0297213
$79$	2.26645e91	0.209138	0.104569	−	0.994518i	$-0.466654\pi$
$79$	2.26645e91	0.209138	0.104569	+	0.994518i	$0.466654\pi$
$80$	3.48465e92	1.74701
$81$	−3.99427e92	−1.09626
$82$	−1.88182e91	−0.0284843
$83$	−2.02604e93	−1.70357	−0.851786	−	0.523890i	$-0.824480\pi$
$83$	−2.02604e93	−1.70357	−0.851786	+	0.523890i	$0.824480\pi$
$84$	2.72983e92	0.128407
$85$	−3.40125e93	−0.901200
$86$	1.60176e92	0.0240671
$87$	−5.01305e93	−0.429950
$88$	−3.26202e92	−0.0160723
$89$	−1.75683e94	−0.500398	−0.250199	−	0.968194i	$-0.580496\pi$
$89$	−1.75683e94	−0.500398	−0.250199	+	0.968194i	$0.580496\pi$
$90$	−2.05682e92	−0.00340749
$91$	1.96847e94	0.190819
$92$	3.06553e95	1.74902
$93$	2.90088e95	0.979730
$94$	3.77267e93	0.00758487
$95$	−5.31118e95	−0.639140
$96$	−7.87069e94	−0.0569978
$97$	2.38093e96	1.04308	0.521540	−	0.853227i	$-0.325358\pi$
$97$	2.38093e96	1.04308	0.521540	+	0.853227i	$0.325358\pi$
$98$	6.67764e94	0.0177893
$99$	−2.94979e95	−0.0480269
$100$	−2.05734e97	−2.05734
$101$	−3.34717e96	−0.206581	−0.103291	−	0.994651i	$-0.532937\pi$
$101$	−3.34717e96	−0.206581	−0.103291	+	0.994651i	$0.532937\pi$
$102$	2.55939e95	0.00979552
$103$	−1.96504e97	−0.468560	−0.234280	−	0.972169i	$-0.575273\pi$
$103$	−1.96504e97	−0.468560	−0.234280	+	0.972169i	$0.575273\pi$
$104$	−3.78349e96	−0.0564645
$105$	−2.39404e97	−0.224621
$106$	3.35960e96	0.0199046
$107$	3.54177e98	1.33078	0.665391	−	0.746495i	$-0.268265\pi$
$107$	3.54177e98	1.33078	0.665391	+	0.746495i	$0.268265\pi$
$108$	3.92259e98	0.938687
$109$	−5.26606e98	−0.805936	−0.402968	−	0.915214i	$-0.632021\pi$
$109$	−5.26606e98	−0.805936	−0.402968	+	0.915214i	$0.632021\pi$
$110$	1.43015e97	0.0140552
$111$	1.87643e99	1.18896
$112$	−2.97255e98	−0.121914
$113$	3.55528e99	0.947478	0.473739	−	0.880665i	$-0.342904\pi$
$113$	3.55528e99	0.947478	0.473739	+	0.880665i	$0.342904\pi$
$114$	3.99657e97	0.00694708
$115$	−2.68845e100	−3.05954
$116$	5.46057e99	0.408343
$117$	−3.42135e99	−0.168726
$118$	5.79230e97	0.00189049
$119$	2.90141e99	0.0628901
$120$	4.60145e99	0.0664667
$121$	−8.30252e100	−0.801899
$122$	3.30304e99	0.0214023
$123$	3.80698e101	1.66029
$124$	−3.15984e101	−0.930494
$125$	9.27563e101	1.85015
$126$	1.75456e98	0.000237791 0
$127$	4.77872e101	0.441399	0.220699	−	0.975342i	$-0.429166\pi$
$127$	4.77872e101	0.441399	0.220699	+	0.975342i	$0.429166\pi$
$128$	1.14305e101	0.0721739
$129$	−3.24042e102	−1.40282
$130$	1.65878e101	0.0493782
$131$	−4.64169e102	−0.952837	−0.476419	−	0.879219i	$-0.658065\pi$
$131$	−4.64169e102	−0.952837	−0.476419	+	0.879219i	$0.658065\pi$
$132$	3.29905e102	0.468331
$133$	4.53066e101	0.0446023
$134$	1.60829e101	0.0110099
$135$	−3.44009e103	−1.64203
$136$	−5.57664e101	−0.0186095
$137$	3.15159e103	0.737194	0.368597	−	0.929589i	$-0.379838\pi$
$137$	3.15159e103	0.737194	0.368597	+	0.929589i	$0.379838\pi$
$138$	2.02301e102	0.0332554
$139$	1.54281e104	1.78687	0.893437	−	0.449189i	$-0.148287\pi$
$139$	1.54281e104	1.78687	0.893437	+	0.449189i	$0.148287\pi$
$140$	2.60776e103	0.213333
$141$	−7.63224e103	−0.442105
$142$	−2.28538e102	−0.00939667
$143$	2.37894e104	0.695962
$144$	5.16651e103	0.107799
$145$	−4.78888e104	−0.714309
$146$	−6.74560e102	−0.00720953
$147$	−1.35091e105	−1.03690
$148$	−2.04394e105	−1.12921
$149$	3.68892e105	1.47016	0.735080	−	0.677980i	$-0.237144\pi$
$149$	3.68892e105	1.47016	0.735080	+	0.677980i	$0.237144\pi$
$150$	−1.35768e104	−0.0391176
$151$	−5.66627e105	−1.18281	−0.591406	−	0.806374i	$-0.701427\pi$
$151$	−5.66627e105	−1.18281	−0.591406	+	0.806374i	$0.701427\pi$
$152$	−8.70811e103	−0.0131981
$153$	−5.04287e104	−0.0556088
$154$	−1.21998e103	−0.000980840 0
$155$	2.77116e106	1.62770
$156$	3.82644e106	1.64532
$157$	−1.71640e106	−0.541358	−0.270679	−	0.962670i	$-0.587248\pi$
$157$	−1.71640e106	−0.541358	−0.270679	+	0.962670i	$0.587248\pi$
$158$	−1.62921e104	−0.00377665
$159$	−6.79658e106	−1.16019
$160$	−7.51874e105	−0.0946948
$161$	2.29336e106	0.213509
$162$	2.87122e105	0.0197965
$163$	1.76624e107	0.903549	0.451775	−	0.892132i	$-0.350791\pi$
$163$	1.76624e107	0.903549	0.451775	+	0.892132i	$0.350791\pi$
$164$	−4.14684e107	−1.57685
$165$	−2.89325e107	−0.819245
$166$	1.45639e106	0.0307634
$167$	−3.48515e107	−0.550139	−0.275069	−	0.961424i	$-0.588701\pi$
$167$	−3.48515e107	−0.550139	−0.275069	+	0.961424i	$0.588701\pi$
$168$	−3.92523e105	−0.00463837
$169$	1.63073e108	1.44503
$170$	2.44494e106	0.0162740
$171$	−7.87461e106	−0.0394383
$172$	3.52970e108	1.33232
$173$	1.08369e107	0.0308794	0.0154397	−	0.999881i	$-0.495085\pi$
$173$	1.08369e107	0.0308794	0.0154397	+	0.999881i	$0.495085\pi$
$174$	3.60355e106	0.00776413
$175$	−1.53912e108	−0.251146
$176$	−3.59239e108	−0.444650
$177$	−1.17180e108	−0.110192
$178$	1.26287e107	0.00903629
$179$	2.62307e108	0.143034	0.0715169	−	0.997439i	$-0.477216\pi$
$179$	2.62307e108	0.143034	0.0715169	+	0.997439i	$0.477216\pi$
$180$	−4.53247e108	−0.188633
$181$	−3.35426e109	−1.06705	−0.533527	−	0.845783i	$-0.679134\pi$
$181$	−3.35426e109	−1.06705	−0.533527	+	0.845783i	$0.679134\pi$
$182$	−1.41501e107	−0.00344585
$183$	−6.68215e109	−1.24749
$184$	−4.40793e108	−0.0631787
$185$	1.79252e110	1.97531
$186$	−2.08525e108	−0.0176922
$187$	3.50642e109	0.229375
$188$	8.31358e109	0.419887
$189$	2.93454e109	0.114589
$190$	3.81786e108	0.0115417
$191$	3.13801e110	0.735422	0.367711	−	0.929940i	$-0.380142\pi$
$191$	3.13801e110	0.735422	0.367711	+	0.929940i	$0.380142\pi$
$192$	−5.77445e110	−1.05051
$193$	8.26938e110	1.16935	0.584673	−	0.811269i	$-0.301223\pi$
$193$	8.26938e110	1.16935	0.584673	+	0.811269i	$0.301223\pi$
$194$	−1.71150e109	−0.0188361
$195$	−3.35576e111	−2.87814
$196$	1.47150e111	0.984787
$197$	4.65675e110	0.243485	0.121742	−	0.992562i	$-0.461152\pi$
$197$	4.65675e110	0.243485	0.121742	+	0.992562i	$0.461152\pi$
$198$	2.12041e108	0.000867279 0
$199$	−2.03902e111	−0.653200	−0.326600	−	0.945163i	$-0.605903\pi$
$199$	−2.03902e111	−0.653200	−0.326600	+	0.945163i	$0.605903\pi$
$200$	2.95825e110	0.0743157
$201$	−3.25363e111	−0.641740
$202$	2.40606e109	0.00373049
$203$	4.08512e110	0.0498479
$204$	5.63994e111	0.542265
$205$	3.63675e112	2.75836
$206$	1.41254e110	0.00846135
$207$	−3.98602e111	−0.188790
$208$	−4.16666e112	−1.56213
$209$	5.47539e111	0.162675
$210$	1.72092e110	0.00405625
$211$	−5.69625e112	−1.06633	−0.533163	−	0.846012i	$-0.678997\pi$
$211$	−5.69625e112	−1.06633	−0.533163	+	0.846012i	$0.678997\pi$
$212$	7.40332e112	1.10189
$213$	4.62340e112	0.547710
$214$	−2.54595e111	−0.0240315
$215$	−3.09552e113	−2.33060
$216$	−5.64031e111	−0.0339075
$217$	−2.36392e112	−0.113589
$218$	3.78543e111	0.0145538
$219$	1.36466e113	0.420227
$220$	3.15153e113	0.778074
$221$	4.06695e113	0.805831
$222$	−1.34884e112	−0.0214705
$223$	3.24676e113	0.415589	0.207794	−	0.978173i	$-0.433371\pi$
$223$	3.24676e113	0.415589	0.207794	+	0.978173i	$0.433371\pi$
$224$	6.41381e111	0.00660826
$225$	2.67510e113	0.222069
$226$	−2.55566e112	−0.0171097
$227$	−1.02156e114	−0.552091	−0.276046	−	0.961144i	$-0.589024\pi$
$227$	−1.02156e114	−0.552091	−0.276046	+	0.961144i	$0.589024\pi$
$228$	8.80697e113	0.384580
$229$	−3.45852e114	−1.22143	−0.610716	−	0.791850i	$-0.709118\pi$
$229$	−3.45852e114	−1.22143	−0.610716	+	0.791850i	$0.709118\pi$
$230$	1.93255e113	0.0552498
$231$	2.46806e113	0.0571709
$232$	−7.85177e112	−0.0147503
$233$	−3.15797e114	−0.481554	−0.240777	−	0.970580i	$-0.577402\pi$
$233$	−3.15797e114	−0.481554	−0.240777	+	0.970580i	$0.577402\pi$
$234$	2.45938e112	0.00304689
$235$	−7.29095e114	−0.734502
$236$	1.27641e114	0.104654
$237$	3.29594e114	0.220132
$238$	−2.08564e112	−0.00113568
$239$	2.70118e115	1.20020	0.600102	−	0.799923i	$-0.295127\pi$
$239$	2.70118e115	1.20020	0.600102	+	0.799923i	$0.295127\pi$
$240$	5.06746e115	1.83885
$241$	−3.73170e115	−1.10683	−0.553415	−	0.832906i	$-0.686675\pi$
$241$	−3.73170e115	−1.10683	−0.553415	+	0.832906i	$0.686675\pi$
$242$	5.96814e113	0.0144808
$243$	−1.08178e115	−0.214899
$244$	7.27867e115	1.18480
$245$	−1.29050e116	−1.72267
$246$	−2.73659e114	−0.0299818
$247$	6.35069e115	0.571503
$248$	4.54355e114	0.0336116
$249$	−2.94632e116	−1.79313
$250$	−6.66764e114	−0.0334104
$251$	2.38502e115	0.0984729	0.0492365	−	0.998787i	$-0.484321\pi$
$251$	2.38502e115	0.0984729	0.0492365	+	0.998787i	$0.484321\pi$
$252$	3.86639e114	0.0131638
$253$	2.77157e116	0.778718
$254$	−3.43511e114	−0.00797087
$255$	−4.94619e116	−0.948577
$256$	6.28377e116	0.996741
$257$	−1.88499e116	−0.247488	−0.123744	−	0.992314i	$-0.539490\pi$
$257$	−1.88499e116	−0.247488	−0.123744	+	0.992314i	$0.539490\pi$
$258$	2.32933e115	0.0253323
$259$	−1.52910e116	−0.137847
$260$	3.65533e117	2.73350
$261$	−7.10024e115	−0.0440766
$262$	3.33661e115	0.0172065
$263$	−2.60440e117	−1.11649	−0.558244	−	0.829677i	$-0.688525\pi$
$263$	−2.60440e117	−1.11649	−0.558244	+	0.829677i	$0.688525\pi$
$264$	−4.74372e115	−0.0169172
$265$	−6.49266e117	−1.92752
$266$	−3.25680e114	−0.000805436 0
$267$	−2.55484e117	−0.526704
$268$	3.54408e117	0.609489
$269$	8.64887e117	1.24158	0.620789	−	0.783978i	$-0.286812\pi$
$269$	8.64887e117	1.24158	0.620789	+	0.783978i	$0.286812\pi$
$270$	2.47285e116	0.0296521
$271$	−1.10413e118	−1.10665	−0.553325	−	0.832965i	$-0.686641\pi$
$271$	−1.10413e118	−1.10665	−0.553325	+	0.832965i	$0.686641\pi$
$272$	−6.14142e117	−0.514846
$273$	2.86261e117	0.200851
$274$	−2.26547e116	−0.0133124
$275$	−1.86006e118	−0.915989
$276$	4.45797e118	1.84097
$277$	4.61233e118	1.59828	0.799138	−	0.601147i	$-0.205289\pi$
$277$	4.61233e118	1.59828	0.799138	+	0.601147i	$0.205289\pi$
$278$	−1.10902e117	−0.0322677
$279$	4.10866e117	0.100438
$280$	−3.74971e116	−0.00770607
$281$	−6.27898e118	−1.08551	−0.542753	−	0.839892i	$-0.682618\pi$
$281$	−6.27898e118	−1.08551	−0.542753	+	0.839892i	$0.682618\pi$
$282$	5.48632e116	0.00798361
$283$	1.94757e118	0.238699	0.119350	−	0.992852i	$-0.461919\pi$
$283$	1.94757e118	0.238699	0.119350	+	0.992852i	$0.461919\pi$
$284$	−5.03614e118	−0.520185
$285$	−7.72365e118	−0.672740
$286$	−1.71006e117	−0.0125678
$287$	−3.10230e118	−0.192492
$288$	−1.11477e117	−0.00584316
$289$	−1.65763e119	−0.734415
$290$	3.44242e117	0.0128991
$291$	3.46241e119	1.09791
$292$	−1.48648e119	−0.399108
$293$	2.92842e119	0.666121	0.333061	−	0.942905i	$-0.391919\pi$
$293$	2.92842e119	0.666121	0.333061	+	0.942905i	$0.391919\pi$
$294$	9.71080e117	0.0187245
$295$	−1.11940e119	−0.183071
$296$	2.93899e118	0.0407896
$297$	3.54645e119	0.417932
$298$	−2.65172e118	−0.0265485
$299$	3.21463e120	2.73576
$300$	−2.99183e120	−2.16549
$301$	2.64061e119	0.162641
$302$	4.07312e118	0.0213594
$303$	−4.86754e119	−0.217441
$304$	−9.59004e119	−0.365133
$305$	−6.38335e120	−2.07256
$306$	3.62499e117	0.00100419
$307$	4.92322e120	1.16423	0.582114	−	0.813107i	$-0.302226\pi$
$307$	4.92322e120	1.16423	0.582114	+	0.813107i	$0.302226\pi$
$308$	−2.68839e119	−0.0542978
$309$	−2.85761e120	−0.493193
$310$	−1.99201e119	−0.0293933
$311$	1.40438e120	0.177258	0.0886288	−	0.996065i	$-0.471751\pi$
$311$	1.40438e120	0.177258	0.0886288	+	0.996065i	$0.471751\pi$
$312$	−5.50205e119	−0.0594328
$313$	1.44599e121	1.33741	0.668705	−	0.743528i	$-0.266849\pi$
$313$	1.44599e121	1.33741	0.668705	+	0.743528i	$0.266849\pi$
$314$	1.23381e119	0.00977595
$315$	−3.39080e119	−0.0230272
$316$	−3.59017e120	−0.209070
$317$	1.72065e121	0.859642	0.429821	−	0.902914i	$-0.358577\pi$
$317$	1.72065e121	0.859642	0.429821	+	0.902914i	$0.358577\pi$
$318$	4.88562e119	0.0209510
$319$	4.93695e120	0.181807
$320$	−5.51624e121	−1.74530
$321$	5.15054e121	1.40074
$322$	−1.64855e119	−0.00385560
$323$	9.36054e120	0.188356
$324$	6.32711e121	1.09590
$325$	−2.15740e122	−3.21802
$326$	−1.26964e120	−0.0163165
$327$	−7.65805e121	−0.848305
$328$	5.96275e120	0.0569594
$329$	6.21949e120	0.0512571
$330$	2.07977e120	0.0147941
$331$	1.78842e122	1.09853	0.549266	−	0.835647i	$-0.314907\pi$
$331$	1.78842e122	1.09853	0.549266	+	0.835647i	$0.314907\pi$
$332$	3.20934e122	1.70302
$333$	2.65768e121	0.121887
$334$	2.50525e120	0.00993451
$335$	−3.10814e122	−1.06617
$336$	−4.32276e121	−0.128324
$337$	−6.75660e121	−0.173651	−0.0868256	−	0.996224i	$-0.527672\pi$
$337$	−6.75660e121	−0.173651	−0.0868256	+	0.996224i	$0.527672\pi$
$338$	−1.17222e121	−0.0260946
$339$	5.17018e122	0.997287
$340$	5.38775e122	0.900906
$341$	−2.85684e122	−0.414285
$342$	5.66055e119	0.000712184 0
$343$	2.21834e122	0.242250
$344$	−5.07536e121	−0.0481263
$345$	−3.90961e123	−3.22038
$346$	−7.78995e119	−0.000557627 0
$347$	8.12614e122	0.505714	0.252857	−	0.967504i	$-0.418630\pi$
$347$	8.12614e122	0.505714	0.252857	+	0.967504i	$0.418630\pi$
$348$	7.94090e122	0.429810
$349$	−1.34495e123	−0.633395	−0.316697	−	0.948527i	$-0.602574\pi$
$349$	−1.34495e123	−0.633395	−0.316697	+	0.948527i	$0.602574\pi$
$350$	1.10637e121	0.00453525
$351$	4.11338e123	1.46826
$352$	7.75121e121	0.0241018
$353$	−2.13408e123	−0.578278	−0.289139	−	0.957287i	$-0.593369\pi$
$353$	−2.13408e123	−0.578278	−0.289139	+	0.957287i	$0.593369\pi$
$354$	8.42332e120	0.00198987
$355$	4.41666e123	0.909953
$356$	2.78291e123	0.500235
$357$	4.21931e122	0.0661963
$358$	−1.88556e121	−0.00258293
$359$	4.33416e123	0.518590	0.259295	−	0.965798i	$-0.416510\pi$
$359$	4.33416e123	0.518590	0.259295	+	0.965798i	$0.416510\pi$
$360$	6.51726e121	0.00681387
$361$	−9.48038e123	−0.866416
$362$	2.41116e122	0.0192691
$363$	−1.20737e124	−0.844055
$364$	−3.11815e123	−0.190757
$365$	1.30363e124	0.698155
$366$	4.80336e122	0.0225275
$367$	5.13534e123	0.210992	0.105496	−	0.994420i	$-0.466357\pi$
$367$	5.13534e123	0.210992	0.105496	+	0.994420i	$0.466357\pi$
$368$	−4.85435e124	−1.74788
$369$	5.39202e123	0.170205
$370$	−1.28853e123	−0.0356705
$371$	5.53852e123	0.134511
$372$	−4.59513e124	−0.979411
$373$	4.47602e124	0.837555	0.418777	−	0.908089i	$-0.362459\pi$
$373$	4.47602e124	0.837555	0.418777	+	0.908089i	$0.362459\pi$
$374$	−2.52053e122	−0.00414209
$375$	1.34889e125	1.94742
$376$	−1.19541e123	−0.0151673
$377$	5.72617e124	0.638717
$378$	−2.10945e122	−0.00206927
$379$	−1.28648e125	−1.11020	−0.555099	−	0.831784i	$-0.687320\pi$
$379$	−1.28648e125	−1.11020	−0.555099	+	0.831784i	$0.687320\pi$
$380$	8.41315e124	0.638931
$381$	6.94934e124	0.464603
$382$	−2.25571e123	−0.0132804
$383$	−2.80920e125	−1.45694	−0.728471	−	0.685077i	$-0.759769\pi$
$383$	−2.80920e125	−1.45694	−0.728471	+	0.685077i	$0.759769\pi$
$384$	1.66225e124	0.0759681
$385$	2.35770e124	0.0949824
$386$	−5.94432e123	−0.0211163
$387$	−4.58957e124	−0.143810
$388$	−3.77150e125	−1.04274
$389$	3.13265e122	0.000764462 0	0.000382231	−	1.00000i	$-0.499878\pi$
$389$	3.13265e122	0.000764462 0	0.000382231		1.00000i	$0.499878\pi$
$390$	2.41224e124	0.0519740
$391$	4.73818e125	0.901652
$392$	−2.11588e124	−0.0355727
$393$	−6.75007e125	−1.00293
$394$	−3.34744e123	−0.00439689
$395$	3.14855e125	0.365723
$396$	4.67261e124	0.0480113
$397$	6.11706e125	0.556164	0.278082	−	0.960557i	$-0.410301\pi$
$397$	6.11706e125	0.556164	0.278082	+	0.960557i	$0.410301\pi$
$398$	1.46572e124	0.0117956
$399$	6.58860e124	0.0469470
$400$	3.25785e126	2.05599
$401$	1.33814e126	0.748171	0.374085	−	0.927394i	$-0.377957\pi$
$401$	1.33814e126	0.748171	0.374085	+	0.927394i	$0.377957\pi$
$402$	2.33882e124	0.0115887
$403$	−3.31354e126	−1.45545
$404$	5.30207e125	0.206514
$405$	−5.54884e126	−1.91705
$406$	−2.93653e123	−0.000900164 0
$407$	−1.84794e126	−0.502759
$408$	−8.10970e124	−0.0195878
$409$	9.06205e125	0.194377	0.0971887	−	0.995266i	$-0.469015\pi$
$409$	9.06205e125	0.194377	0.0971887	+	0.995266i	$0.469015\pi$
$410$	−2.61422e125	−0.0498110
$411$	4.58312e126	0.775949
$412$	3.11271e126	0.468408
$413$	9.54898e124	0.0127755
$414$	2.86529e124	0.00340920
$415$	−2.81457e127	−2.97906
$416$	8.99032e125	0.0846737
$417$	2.24359e127	1.88081
$418$	−3.93590e124	−0.00293761
$419$	9.14158e126	0.607633	0.303816	−	0.952731i	$-0.401739\pi$
$419$	9.14158e126	0.607633	0.303816	+	0.952731i	$0.401739\pi$
$420$	3.79227e126	0.224548
$421$	2.89338e127	1.52660	0.763298	−	0.646046i	$-0.223579\pi$
$421$	2.89338e127	1.52660	0.763298	+	0.646046i	$0.223579\pi$
$422$	4.09467e125	0.0192559
$423$	−1.08099e126	−0.0453226
$424$	−1.06453e126	−0.0398027
$425$	−3.17989e127	−1.06059
$426$	−3.32346e125	−0.00989066
$427$	5.44527e126	0.144633
$428$	−5.61033e127	−1.33035
$429$	3.45951e127	0.732549
$430$	2.22517e126	0.0420865
$431$	5.14096e126	0.0868753	0.0434376	−	0.999056i	$-0.486169\pi$
$431$	5.14096e126	0.0868753	0.0434376	+	0.999056i	$0.486169\pi$
$432$	−6.21154e127	−0.938075
$433$	−4.49608e127	−0.606975	−0.303487	−	0.952835i	$-0.598151\pi$
$433$	−4.49608e127	−0.606975	−0.303487	+	0.952835i	$0.598151\pi$
$434$	1.69927e125	0.00205121
$435$	−6.96412e127	−0.751861
$436$	8.34169e127	0.805673
$437$	7.39883e127	0.639460
$438$	−9.80962e125	−0.00758854
$439$	1.16439e128	0.806438	0.403219	−	0.915104i	$-0.367891\pi$
$439$	1.16439e128	0.806438	0.403219	+	0.915104i	$0.367891\pi$
$440$	−4.53160e126	−0.0281058
$441$	−1.91336e127	−0.106298
$442$	−2.92347e126	−0.0145518
$443$	3.81052e128	1.69982	0.849910	−	0.526927i	$-0.176656\pi$
$443$	3.81052e128	1.69982	0.849910	+	0.526927i	$0.176656\pi$
$444$	−2.97235e128	−1.18857
$445$	−2.44059e128	−0.875054
$446$	−2.33388e126	−0.00750479
$447$	5.36452e128	1.54745
$448$	4.70558e127	0.121795
$449$	1.73919e128	0.404017	0.202008	−	0.979384i	$-0.435253\pi$
$449$	1.73919e128	0.404017	0.202008	+	0.979384i	$0.435253\pi$
$450$	−1.92296e126	−0.00401017
$451$	−3.74919e128	−0.702062
$452$	−5.63172e128	−0.947169
$453$	−8.24005e128	−1.24499
$454$	7.34335e126	0.00996978
$455$	2.73460e128	0.333688
$456$	−1.26636e127	−0.0138919
$457$	−1.51297e129	−1.49243	−0.746214	−	0.665706i	$-0.768130\pi$
$457$	−1.51297e129	−1.49243	−0.746214	+	0.665706i	$0.768130\pi$
$458$	2.48610e127	0.0220569
$459$	6.06289e128	0.483910
$460$	4.25862e129	3.05854
$461$	−2.07943e129	−1.34415	−0.672076	−	0.740482i	$-0.734597\pi$
$461$	−2.07943e129	−1.34415	−0.672076	+	0.740482i	$0.734597\pi$
$462$	−1.77413e126	−0.00103240
$463$	−2.26390e128	−0.118626	−0.0593129	−	0.998239i	$-0.518891\pi$
$463$	−2.26390e128	−0.118626	−0.0593129	+	0.998239i	$0.518891\pi$
$464$	−8.64697e128	−0.408077
$465$	4.02990e129	1.71327
$466$	2.27006e127	0.00869600
$467$	−1.37574e129	−0.474972	−0.237486	−	0.971391i	$-0.576323\pi$
$467$	−1.37574e129	−0.474972	−0.237486	+	0.971391i	$0.576323\pi$
$468$	5.41957e128	0.168671
$469$	2.65137e128	0.0744026
$470$	5.24099e127	0.0132638
$471$	−2.49603e129	−0.569818
$472$	−1.83535e127	−0.00378036
$473$	3.19123e129	0.593188
$474$	−2.36923e127	−0.00397519
$475$	−4.96551e129	−0.752183
$476$	−4.59598e128	−0.0628696
$477$	−9.62634e128	−0.118938
$478$	−1.94170e128	−0.0216735
$479$	−6.15945e129	−0.621255	−0.310627	−	0.950532i	$-0.600539\pi$
$479$	−6.15945e129	−0.621255	−0.310627	+	0.950532i	$0.600539\pi$
$480$	−1.09340e129	−0.0996729
$481$	−2.14335e130	−1.76627
$482$	2.68248e128	0.0199873
$483$	3.33506e129	0.224734
$484$	1.31516e130	0.801637
$485$	3.30758e130	1.82405
$486$	7.77622e127	0.00388070
$487$	1.31061e130	0.591998	0.295999	−	0.955188i	$-0.404347\pi$
$487$	1.31061e130	0.591998	0.295999	+	0.955188i	$0.404347\pi$
$488$	−1.04660e129	−0.0427977
$489$	2.56852e130	0.951050
$490$	9.27656e128	0.0311084
$491$	−1.55726e130	−0.473053	−0.236526	−	0.971625i	$-0.576009\pi$
$491$	−1.55726e130	−0.473053	−0.236526	+	0.971625i	$0.576009\pi$
$492$	−6.03044e130	−1.65975
$493$	8.44004e129	0.210508
$494$	−4.56509e128	−0.0103203
$495$	−4.09785e129	−0.0839854
$496$	5.00370e130	0.929887
$497$	−3.76760e129	−0.0635009
$498$	2.11792e129	0.0323807
$499$	8.04555e130	1.11604	0.558019	−	0.829828i	$-0.311561\pi$
$499$	8.04555e130	1.11604	0.558019	+	0.829828i	$0.311561\pi$
$500$	−1.46930e131	−1.84955
$501$	−5.06819e130	−0.579060
$502$	−1.71444e128	−0.00177824
$503$	−1.22923e131	−1.15767	−0.578837	−	0.815443i	$-0.696493\pi$
$503$	−1.22923e131	−1.15767	−0.578837	+	0.815443i	$0.696493\pi$
$504$	−5.55950e127	−0.000475505 0
$505$	−4.64988e130	−0.361252
$506$	−1.99230e129	−0.0140622
$507$	2.37144e131	1.52099
$508$	−7.56971e130	−0.441255
$509$	2.80317e131	1.48538	0.742688	−	0.669637i	$-0.233550\pi$
$509$	2.80317e131	1.48538	0.742688	+	0.669637i	$0.233550\pi$
$510$	3.55550e129	0.0171296
$511$	−1.11205e130	−0.0487206
$512$	−2.26293e130	−0.0901732
$513$	9.46741e130	0.343193
$514$	1.35500e129	0.00446918
$515$	−2.72983e131	−0.819379
$516$	5.13298e131	1.40236
$517$	7.51638e130	0.186946
$518$	1.09917e129	0.00248926
$519$	1.57593e130	0.0325028
$520$	−5.25602e130	−0.0987403
$521$	−6.66469e131	−1.14064	−0.570322	−	0.821421i	$-0.693182\pi$
$521$	−6.66469e131	−1.14064	−0.570322	+	0.821421i	$0.693182\pi$
$522$	5.10390e128	0.000795944 0
$523$	−1.30728e132	−1.85797	−0.928983	−	0.370122i	$-0.879316\pi$
$523$	−1.30728e132	−1.85797	−0.928983	+	0.370122i	$0.879316\pi$
$524$	7.35266e131	0.952526
$525$	−2.23823e131	−0.264349
$526$	1.87213e130	0.0201618
$527$	−4.88396e131	−0.479686
$528$	−5.22414e131	−0.468026
$529$	2.52170e132	2.06107
$530$	4.66715e130	0.0348075
$531$	−1.65968e130	−0.0112964
$532$	−7.17677e130	−0.0445877
$533$	−4.34854e132	−2.46646
$534$	1.83651e130	0.00951133
$535$	4.92022e132	2.32716
$536$	−5.09605e130	−0.0220161
$537$	3.81454e131	0.150553
$538$	−6.21711e130	−0.0224206
$539$	1.33040e132	0.438457
$540$	5.44926e132	1.64150
$541$	3.54370e131	0.0975865	0.0487933	−	0.998809i	$-0.484462\pi$
$541$	3.54370e131	0.0975865	0.0487933	+	0.998809i	$0.484462\pi$
$542$	7.93689e130	0.0199841
$543$	−4.87786e132	−1.12315
$544$	1.32512e131	0.0279067
$545$	−7.31561e132	−1.40935
$546$	−2.05774e130	−0.00362700
$547$	−8.36515e131	−0.134924	−0.0674619	−	0.997722i	$-0.521490\pi$
$547$	−8.36515e131	−0.134924	−0.0674619	+	0.997722i	$0.521490\pi$
$548$	−4.99226e132	−0.736954
$549$	−9.46427e131	−0.127888
$550$	1.33707e131	0.0165411
$551$	1.31794e132	0.149294
$552$	−6.41013e131	−0.0665000
$553$	−2.68585e131	−0.0255219
$554$	−3.31551e131	−0.0288620
$555$	2.60673e133	2.07915
$556$	−2.44388e133	−1.78629
$557$	−9.51333e132	−0.637317	−0.318659	−	0.947870i	$-0.603232\pi$
$557$	−9.51333e132	−0.637317	−0.318659	+	0.947870i	$0.603232\pi$
$558$	−2.95345e130	−0.00181372
$559$	3.70138e133	2.08397
$560$	−4.12946e132	−0.213194
$561$	5.09912e132	0.241433
$562$	4.51355e131	0.0196023
$563$	−3.67256e133	−1.46323	−0.731615	−	0.681719i	$-0.761233\pi$
$563$	−3.67256e133	−1.46323	−0.731615	+	0.681719i	$0.761233\pi$
$564$	1.20898e133	0.441960
$565$	4.93899e133	1.65687
$566$	−1.39998e131	−0.00431048
$567$	4.73339e132	0.133781
$568$	7.24148e131	0.0187903
$569$	−4.93003e132	−0.117464	−0.0587319	−	0.998274i	$-0.518706\pi$
$569$	−4.93003e132	−0.117464	−0.0587319	+	0.998274i	$0.518706\pi$
$570$	5.55203e131	0.0121485
$571$	−3.38143e133	−0.679593	−0.339796	−	0.940499i	$-0.610358\pi$
$571$	−3.38143e133	−0.679593	−0.339796	+	0.940499i	$0.610358\pi$
$572$	−3.76835e133	−0.695735
$573$	4.56338e133	0.774084
$574$	2.23004e131	0.00347605
$575$	−2.51347e134	−3.60067
$576$	−8.17864e132	−0.107694
$577$	6.21645e133	0.752516	0.376258	−	0.926515i	$-0.377211\pi$
$577$	6.21645e133	0.752516	0.376258	+	0.926515i	$0.377211\pi$
$578$	1.19156e132	0.0132622
$579$	1.20256e134	1.23082
$580$	7.58582e133	0.714076
$581$	2.40095e133	0.207893
$582$	−2.48890e132	−0.0198264
$583$	6.69341e133	0.490594
$584$	2.13742e132	0.0144167
$585$	−4.75293e133	−0.295054
$586$	−2.10505e132	−0.0120289
$587$	−1.46383e134	−0.770094	−0.385047	−	0.922897i	$-0.625815\pi$
$587$	−1.46383e134	−0.770094	−0.385047	+	0.922897i	$0.625815\pi$
$588$	2.13990e134	1.03656
$589$	−7.62647e133	−0.340198
$590$	8.04666e131	0.00330592
$591$	6.77198e133	0.256285
$592$	3.23663e134	1.12847
$593$	1.66086e134	0.533557	0.266778	−	0.963758i	$-0.414041\pi$
$593$	1.66086e134	0.533557	0.266778	+	0.963758i	$0.414041\pi$
$594$	−2.54931e132	−0.00754710
$595$	4.03064e133	0.109977
$596$	−5.84342e134	−1.46968
$597$	−2.96519e134	−0.687539
$598$	−2.31079e133	−0.0494030
$599$	−6.32210e134	−1.24641	−0.623204	−	0.782059i	$-0.714169\pi$
$599$	−6.32210e134	−1.24641	−0.623204	+	0.782059i	$0.714169\pi$
$600$	4.30197e133	0.0782225
$601$	8.50967e133	0.142725	0.0713626	−	0.997450i	$-0.477265\pi$
$601$	8.50967e133	0.142725	0.0713626	+	0.997450i	$0.477265\pi$
$602$	−1.89816e132	−0.00293700
$603$	−4.60828e133	−0.0657883
$604$	8.97564e134	1.18243
$605$	−1.15339e135	−1.40229
$606$	3.49896e132	0.00392660
$607$	6.42879e134	0.666005	0.333003	−	0.942926i	$-0.391938\pi$
$607$	6.42879e134	0.666005	0.333003	+	0.942926i	$0.391938\pi$
$608$	2.06922e133	0.0197917
$609$	5.94069e133	0.0524685
$610$	4.58857e133	0.0374266
$611$	8.71795e134	0.656773
$612$	7.98814e133	0.0555906
$613$	−3.71508e133	−0.0238856	−0.0119428	−	0.999929i	$-0.503802\pi$
$613$	−3.71508e133	−0.0238856	−0.0119428	+	0.999929i	$0.503802\pi$
$614$	−3.53898e133	−0.0210239
$615$	5.28866e135	2.90337
$616$	3.86564e132	0.00196136
$617$	−2.63533e135	−1.23596	−0.617981	−	0.786193i	$-0.712049\pi$
$617$	−2.63533e135	−1.23596	−0.617981	+	0.786193i	$0.712049\pi$
$618$	2.05415e133	0.00890617
$619$	−3.69925e135	−1.48292	−0.741458	−	0.670999i	$-0.765866\pi$
$619$	−3.69925e135	−1.48292	−0.741458	+	0.670999i	$0.765866\pi$
$620$	−4.38965e135	−1.62717
$621$	4.79228e135	1.64286
$622$	−1.00952e133	−0.00320095
$623$	2.08193e134	0.0610655
$624$	−6.05927e135	−1.64425
$625$	4.68921e135	1.17739
$626$	−1.03943e134	−0.0241512
$627$	7.96246e134	0.171227
$628$	2.71885e135	0.541182
$629$	−3.15918e135	−0.582127
$630$	2.43743e132	0.000415829 0
$631$	−9.12463e135	−1.44142	−0.720712	−	0.693235i	$-0.756185\pi$
$631$	−9.12463e135	−1.44142	−0.720712	+	0.693235i	$0.756185\pi$
$632$	5.16232e133	0.00755208
$633$	−8.28365e135	−1.12238
$634$	−1.23686e134	−0.0155236
$635$	6.63859e135	0.771881
$636$	1.07661e136	1.15981
$637$	1.54308e136	1.54037
$638$	−3.54885e133	−0.00328311
$639$	6.54836e134	0.0561488
$640$	1.58792e135	0.126212
$641$	9.21096e135	0.678720	0.339360	−	0.940657i	$-0.389790\pi$
$641$	9.21096e135	0.678720	0.339360	+	0.940657i	$0.389790\pi$
$642$	−3.70239e134	−0.0252949
$643$	1.31045e136	0.830214	0.415107	−	0.909773i	$-0.363744\pi$
$643$	1.31045e136	0.830214	0.415107	+	0.909773i	$0.363744\pi$
$644$	−3.63279e135	−0.213440
$645$	−4.50159e136	−2.45312
$646$	−6.72868e133	−0.00340136
$647$	5.11313e135	0.239789	0.119894	−	0.992787i	$-0.461744\pi$
$647$	5.11313e135	0.239789	0.119894	+	0.992787i	$0.461744\pi$
$648$	−9.09778e134	−0.0395866
$649$	1.15401e135	0.0465954
$650$	1.55082e135	0.0581116
$651$	−3.43767e135	−0.119560
$652$	−2.79781e136	−0.903255
$653$	1.66354e136	0.498592	0.249296	−	0.968427i	$-0.419801\pi$
$653$	1.66354e136	0.498592	0.249296	+	0.968427i	$0.419801\pi$
$654$	5.50487e134	0.0153189
$655$	−6.44824e136	−1.66624
$656$	6.56664e136	1.57582
$657$	1.93283e135	0.0430798
$658$	−4.47079e133	−0.000925611 0
$659$	−5.16159e136	−0.992752	−0.496376	−	0.868108i	$-0.665336\pi$
$659$	−5.16159e136	−0.992752	−0.496376	+	0.868108i	$0.665336\pi$
$660$	4.58304e136	0.818978
$661$	−2.97480e136	−0.493954	−0.246977	−	0.969021i	$-0.579437\pi$
$661$	−2.97480e136	−0.493954	−0.246977	+	0.969021i	$0.579437\pi$
$662$	−1.28558e135	−0.0198375
$663$	5.91427e136	0.848194
$664$	−4.61472e135	−0.0615168
$665$	6.29399e135	0.0779967
$666$	−1.91043e134	−0.00220106
$667$	6.67124e136	0.714667
$668$	5.52064e136	0.549959
$669$	4.72152e136	0.437437
$670$	2.23424e135	0.0192531
$671$	6.58071e136	0.527510
$672$	9.32713e134	0.00695566
$673$	1.94949e136	0.135266	0.0676332	−	0.997710i	$-0.478455\pi$
$673$	1.94949e136	0.135266	0.0676332	+	0.997710i	$0.478455\pi$
$674$	4.85688e134	0.00313583
$675$	−3.21619e137	−1.93245
$676$	−2.58315e137	−1.44455
$677$	7.26258e136	0.378043	0.189021	−	0.981973i	$-0.439468\pi$
$677$	7.26258e136	0.378043	0.189021	+	0.981973i	$0.439468\pi$
$678$	−3.71650e135	−0.0180092
$679$	−2.82151e136	−0.127291
$680$	−7.74706e135	−0.0325428
$681$	−1.48558e137	−0.581115
$682$	2.05360e135	0.00748123
$683$	2.47480e137	0.839723	0.419862	−	0.907588i	$-0.362079\pi$
$683$	2.47480e137	0.839723	0.419862	+	0.907588i	$0.362079\pi$
$684$	1.24738e136	0.0394254
$685$	4.37818e137	1.28914
$686$	−1.59462e135	−0.00437460
$687$	−5.02947e137	−1.28564
$688$	−5.58938e137	−1.33145
$689$	7.76342e137	1.72354
$690$	2.81036e136	0.0581543
$691$	−2.10969e137	−0.406943	−0.203472	−	0.979081i	$-0.565222\pi$
$691$	−2.10969e137	−0.406943	−0.203472	+	0.979081i	$0.565222\pi$
$692$	−1.71662e136	−0.0308694
$693$	3.49564e135	0.00586091
$694$	−5.84135e135	−0.00913228
$695$	2.14327e138	3.12473
$696$	−1.14183e136	−0.0155257
$697$	−6.40949e137	−0.812894
$698$	9.66800e135	0.0114380
$699$	−4.59240e137	−0.506870
$700$	2.43804e137	0.251065
$701$	−9.31470e137	−0.895045	−0.447523	−	0.894273i	$-0.647694\pi$
$701$	−9.31470e137	−0.895045	−0.447523	+	0.894273i	$0.647694\pi$
$702$	−2.95684e136	−0.0265142
$703$	−4.93317e137	−0.412850
$704$	5.68679e137	0.444215
$705$	−1.06027e138	−0.773115
$706$	1.53405e136	0.0104427
$707$	3.96655e136	0.0252099
$708$	1.85619e137	0.110156
$709$	−1.32575e138	−0.734716	−0.367358	−	0.930080i	$-0.619738\pi$
$709$	−1.32575e138	−0.734716	−0.367358	+	0.930080i	$0.619738\pi$
$710$	−3.17485e136	−0.0164321
$711$	4.66820e136	0.0225670
$712$	−4.00156e136	−0.0180696
$713$	−3.86042e138	−1.62852
$714$	−3.03299e135	−0.00119538
$715$	3.30482e138	1.21704
$716$	−4.15507e137	−0.142987
$717$	3.92813e138	1.26330
$718$	−3.11555e136	−0.00936481
$719$	5.78595e138	1.62564	0.812818	−	0.582518i	$-0.197932\pi$
$719$	5.78595e138	1.62564	0.812818	+	0.582518i	$0.197932\pi$
$720$	7.17731e137	0.188510
$721$	2.32866e137	0.0571802
$722$	6.81483e136	0.0156459
$723$	−5.42674e138	−1.16502
$724$	5.31331e138	1.06671
$725$	−4.47721e138	−0.840647
$726$	8.67903e136	0.0152421
$727$	−8.90090e138	−1.46223	−0.731114	−	0.682256i	$-0.760999\pi$
$727$	−8.90090e138	−1.46223	−0.731114	+	0.682256i	$0.760999\pi$
$728$	4.48360e136	0.00689057
$729$	6.05113e138	0.870065
$730$	−9.37097e136	−0.0126074
$731$	5.45562e138	0.686833
$732$	1.05848e139	1.24709
$733$	−8.14739e138	−0.898413	−0.449206	−	0.893428i	$-0.648293\pi$
$733$	−8.14739e138	−0.898413	−0.449206	+	0.893428i	$0.648293\pi$
$734$	−3.69146e136	−0.00381013
$735$	−1.87668e139	−1.81324
$736$	1.04741e138	0.0947422
$737$	3.20424e138	0.271363
$738$	−3.87597e136	−0.00307360
$739$	−1.64505e139	−1.22158	−0.610792	−	0.791791i	$-0.709149\pi$
$739$	−1.64505e139	−1.22158	−0.610792	+	0.791791i	$0.709149\pi$
$740$	−2.83944e139	−1.97467
$741$	9.23534e138	0.601547
$742$	−3.98128e136	−0.00242903
$743$	2.40615e139	1.37520	0.687600	−	0.726090i	$-0.258664\pi$
$743$	2.40615e139	1.37520	0.687600	+	0.726090i	$0.258664\pi$
$744$	6.60735e137	0.0353785
$745$	5.12464e139	2.57089
$746$	−3.21752e137	−0.0151247
$747$	−4.17302e138	−0.183824
$748$	−5.55433e138	−0.229300
$749$	−4.19716e138	−0.162401
$750$	−9.69627e137	−0.0351668
$751$	4.03164e139	1.37071	0.685353	−	0.728211i	$-0.259648\pi$
$751$	4.03164e139	1.37071	0.685353	+	0.728211i	$0.259648\pi$
$752$	−1.31648e139	−0.419613
$753$	3.46836e138	0.103650
$754$	−4.11617e137	−0.0115341
$755$	−7.87158e139	−2.06840
$756$	−4.64845e138	−0.114552
$757$	5.23770e139	1.21057	0.605286	−	0.796008i	$-0.293059\pi$
$757$	5.23770e139	1.21057	0.605286	+	0.796008i	$0.293059\pi$
$758$	9.24765e137	0.0200482
$759$	4.03049e139	0.819656
$760$	−1.20973e138	−0.0230797
$761$	−9.19907e139	−1.64660	−0.823300	−	0.567606i	$-0.807870\pi$
$761$	−9.19907e139	−1.64660	−0.823300	+	0.567606i	$0.807870\pi$
$762$	−4.99543e137	−0.00838990
$763$	6.24052e138	0.0983515
$764$	−4.97076e139	−0.735182
$765$	−7.00555e138	−0.0972439
$766$	2.01935e138	0.0263097
$767$	1.33849e139	0.163697
$768$	9.13803e139	1.04914
$769$	−1.05878e140	−1.14124	−0.570621	−	0.821213i	$-0.693298\pi$
$769$	−1.05878e140	−1.14124	−0.570621	+	0.821213i	$0.693298\pi$
$770$	−1.69480e137	−0.00171521
$771$	−2.74121e139	−0.260498
$772$	−1.30991e140	−1.16897
$773$	8.05261e139	0.674887	0.337443	−	0.941346i	$-0.390438\pi$
$773$	8.05261e139	0.674887	0.337443	+	0.941346i	$0.390438\pi$
$774$	3.29914e137	0.00259696
$775$	2.59080e140	1.91559
$776$	5.42306e138	0.0376661
$777$	−2.22365e139	−0.145093
$778$	−2.25186e135	−1.38048e−5 0
$779$	−1.00086e140	−0.576512
$780$	5.31568e140	2.87720
$781$	−4.55322e139	−0.231602
$782$	−3.40597e138	−0.0162822
$783$	8.53640e139	0.383557
$784$	−2.33017e140	−0.984144
$785$	−2.38442e140	−0.946681
$786$	4.85219e138	0.0181111
$787$	−6.27406e139	−0.220178	−0.110089	−	0.993922i	$-0.535114\pi$
$787$	−6.27406e139	−0.220178	−0.110089	+	0.993922i	$0.535114\pi$
$788$	−7.37652e139	−0.243405
$789$	−3.78739e140	−1.17518
$790$	−2.26329e138	−0.00660429
$791$	−4.21317e139	−0.115624
$792$	−6.71877e137	−0.00173428
$793$	7.63270e140	1.85323
$794$	−4.39715e138	−0.0100433
$795$	−9.44181e140	−2.02885
$796$	3.22989e140	0.652987
$797$	−2.67141e140	−0.508173	−0.254086	−	0.967182i	$-0.581775\pi$
$797$	−2.67141e140	−0.508173	−0.254086	+	0.967182i	$0.581775\pi$
$798$	−4.73612e137	−0.000847778 0
$799$	1.28497e140	0.216459
$800$	−7.02939e139	−0.111443
$801$	−3.61854e139	−0.0539954
$802$	−9.61904e138	−0.0135106
$803$	−1.34394e140	−0.177695
$804$	5.15390e140	0.641531
$805$	3.18593e140	0.373367
$806$	2.38188e139	0.0262828
$807$	1.25774e141	1.30685
$808$	−7.62387e138	−0.00745976
$809$	6.98654e140	0.643812	0.321906	−	0.946772i	$-0.395677\pi$
$809$	6.98654e140	0.643812	0.321906	+	0.946772i	$0.395677\pi$
$810$	3.98870e139	0.0346185
$811$	−7.60502e140	−0.621712	−0.310856	−	0.950457i	$-0.600616\pi$
$811$	−7.60502e140	−0.621712	−0.310856	+	0.950457i	$0.600616\pi$
$812$	−6.47102e139	−0.0498317
$813$	−1.60566e141	−1.16483
$814$	1.32837e139	0.00907891
$815$	2.45366e141	1.58005
$816$	−8.93102e140	−0.541911
$817$	8.51914e140	0.487109
$818$	−6.51412e138	−0.00351011
$819$	4.05445e139	0.0205903
$820$	−5.76078e141	−2.75746
$821$	3.34728e141	1.51025	0.755125	−	0.655581i	$-0.227576\pi$
$821$	3.34728e141	1.51025	0.755125	+	0.655581i	$0.227576\pi$
$822$	−3.29451e139	−0.0140122
$823$	−2.61110e141	−1.04696	−0.523482	−	0.852037i	$-0.675367\pi$
$823$	−2.61110e141	−1.04696	−0.523482	+	0.852037i	$0.675367\pi$
$824$	−4.47578e139	−0.0169200
$825$	−2.70494e141	−0.964143
$826$	−6.86414e137	−0.000230703 0
$827$	−2.73135e141	−0.865685	−0.432843	−	0.901470i	$-0.642489\pi$
$827$	−2.73135e141	−0.865685	−0.432843	+	0.901470i	$0.642489\pi$
$828$	6.31405e140	0.188728
$829$	1.58755e141	0.447541	0.223770	−	0.974642i	$-0.428163\pi$
$829$	1.58755e141	0.447541	0.223770	+	0.974642i	$0.428163\pi$
$830$	2.02321e140	0.0537965
$831$	6.70738e141	1.68230
$832$	6.59588e141	1.56060
$833$	2.27441e141	0.507675
$834$	−1.61277e140	−0.0339641
$835$	−4.84156e141	−0.962036
$836$	−8.67327e140	−0.162622
$837$	−4.93972e141	−0.874012
$838$	−6.57129e139	−0.0109727
$839$	7.14953e141	1.12674	0.563369	−	0.826206i	$-0.309505\pi$
$839$	7.14953e141	1.12674	0.563369	+	0.826206i	$0.309505\pi$
$840$	−5.45293e139	−0.00811118
$841$	−5.93373e141	−0.833147
$842$	−2.07986e140	−0.0275676
$843$	−9.13106e141	−1.14257
$844$	9.02313e141	1.06598
$845$	2.26540e142	2.52694
$846$	7.77055e138	0.000818445 0
$847$	9.83887e140	0.0978588
$848$	−1.17234e142	−1.10117
$849$	2.83221e141	0.251248
$850$	2.28581e140	0.0191524
$851$	−2.49710e142	−1.97630
$852$	−7.32368e141	−0.547532
$853$	−1.74551e142	−1.23281	−0.616403	−	0.787431i	$-0.711411\pi$
$853$	−1.74551e142	−1.23281	−0.616403	+	0.787431i	$0.711411\pi$
$854$	−3.91425e139	−0.00261181
$855$	−1.09394e141	−0.0689663
$856$	8.06712e140	0.0480552
$857$	7.44033e141	0.418815	0.209408	−	0.977828i	$-0.432846\pi$
$857$	7.44033e141	0.418815	0.209408	+	0.977828i	$0.432846\pi$
$858$	−2.48682e140	−0.0132285
$859$	−1.94019e142	−0.975382	−0.487691	−	0.873016i	$-0.662161\pi$
$859$	−1.94019e142	−0.975382	−0.487691	+	0.873016i	$0.662161\pi$
$860$	4.90345e142	2.32984
$861$	−4.51145e141	−0.202611
$862$	−3.69550e139	−0.00156881
$863$	3.46439e142	1.39028	0.695142	−	0.718872i	$-0.255341\pi$
$863$	3.46439e142	1.39028	0.695142	+	0.718872i	$0.255341\pi$
$864$	1.34025e141	0.0508474
$865$	1.50546e141	0.0539994
$866$	3.23194e140	0.0109609
$867$	−2.41057e142	−0.773023
$868$	3.74456e141	0.113552
$869$	−3.24590e141	−0.0930843
$870$	5.00605e140	0.0135772
$871$	3.71646e142	0.953344
$872$	−1.19945e141	−0.0291028
$873$	4.90399e141	0.112553
$874$	−5.31854e140	−0.0115475
$875$	−1.09920e142	−0.225781
$876$	−2.16168e142	−0.420090
$877$	−9.62603e141	−0.176997	−0.0884987	−	0.996076i	$-0.528207\pi$
$877$	−9.62603e141	−0.176997	−0.0884987	+	0.996076i	$0.528207\pi$
$878$	−8.37007e140	−0.0145628
$879$	4.25858e142	0.701139
$880$	−4.99054e142	−0.777567
$881$	−7.83287e142	−1.15502	−0.577510	−	0.816384i	$-0.695975\pi$
$881$	−7.83287e142	−1.15502	−0.577510	+	0.816384i	$0.695975\pi$
$882$	1.37539e140	0.00191955
$883$	9.62429e142	1.27138	0.635689	−	0.771945i	$-0.280716\pi$
$883$	9.62429e142	1.27138	0.635689	+	0.771945i	$0.280716\pi$
$884$	−6.44224e142	−0.805568
$885$	−1.62787e142	−0.192695
$886$	−2.73913e141	−0.0306957
$887$	−8.78608e142	−0.932180	−0.466090	−	0.884737i	$-0.654338\pi$
$887$	−8.78608e142	−0.932180	−0.466090	+	0.884737i	$0.654338\pi$
$888$	4.27395e141	0.0429339
$889$	−5.66300e141	−0.0538656
$890$	1.75438e141	0.0158019
$891$	5.72040e142	0.487930
$892$	−5.14302e142	−0.415453
$893$	2.00653e142	0.153515
$894$	−3.85620e141	−0.0279441
$895$	3.64397e142	0.250125
$896$	−1.35456e141	−0.00880766
$897$	4.67480e143	2.87959
$898$	−1.25019e141	−0.00729582
$899$	−6.87650e142	−0.380209
$900$	−4.23748e142	−0.221997
$901$	1.14428e143	0.568042
$902$	2.69505e141	0.0126780
$903$	3.84005e142	0.171191
$904$	8.09788e141	0.0342139
$905$	−4.65974e143	−1.86597
$906$	5.92323e141	0.0224823
$907$	−1.02294e143	−0.368041	−0.184020	−	0.982922i	$-0.558911\pi$
$907$	−1.02294e143	−0.368041	−0.184020	+	0.982922i	$0.558911\pi$
$908$	1.61820e143	0.551911
$909$	−6.89415e141	−0.0222911
$910$	−1.96573e141	−0.00602581
$911$	−1.10351e143	−0.320727	−0.160364	−	0.987058i	$-0.551267\pi$
$911$	−1.10351e143	−0.320727	−0.160364	+	0.987058i	$0.551267\pi$
$912$	−1.39461e143	−0.384329
$913$	2.90159e143	0.758235
$914$	1.08757e142	0.0269506
$915$	−9.28283e143	−2.18151
$916$	5.47846e143	1.22103
$917$	5.50062e142	0.116278
$918$	−4.35822e141	−0.00873854
$919$	−8.13461e143	−1.54716	−0.773579	−	0.633700i	$-0.781535\pi$
$919$	−8.13461e143	−1.54716	−0.773579	+	0.633700i	$0.781535\pi$
$920$	−6.12349e142	−0.110482
$921$	7.15948e143	1.22543
$922$	1.49476e142	0.0242730
$923$	−5.28109e143	−0.813657
$924$	−3.90952e142	−0.0571522
$925$	1.67586e144	2.32468
$926$	1.62737e141	0.00214217
$927$	−4.04738e142	−0.0505600
$928$	1.86574e142	0.0221194
$929$	−5.02152e143	−0.565032	−0.282516	−	0.959263i	$-0.591169\pi$
$929$	−5.02152e143	−0.565032	−0.282516	+	0.959263i	$0.591169\pi$
$930$	−2.89683e142	−0.0309386
$931$	3.55157e143	0.360048
$932$	5.00237e143	0.481397
$933$	2.04228e143	0.186576
$934$	9.88930e141	0.00857713
$935$	4.87111e143	0.401111
$936$	−7.79283e141	−0.00609279
$937$	−6.53245e143	−0.484960	−0.242480	−	0.970156i	$-0.577961\pi$
$937$	−6.53245e143	−0.484960	−0.242480	+	0.970156i	$0.577961\pi$
$938$	−1.90590e141	−0.00134358
$939$	2.10280e144	1.40772
$940$	1.15492e144	0.734263
$941$	−2.91023e144	−1.75724	−0.878620	−	0.477522i	$-0.841535\pi$
$941$	−2.91023e144	−1.75724	−0.878620	+	0.477522i	$0.841535\pi$
$942$	1.79423e142	0.0102899
$943$	−5.06624e144	−2.75974
$944$	−2.02123e143	−0.104586
$945$	4.07666e143	0.200383
$946$	−2.29397e142	−0.0107119
$947$	−4.80326e143	−0.213089	−0.106545	−	0.994308i	$-0.533979\pi$
$947$	−4.80326e143	−0.213089	−0.106545	+	0.994308i	$0.533979\pi$
$948$	−5.22092e143	−0.220061
$949$	−1.55878e144	−0.624272
$950$	3.56938e142	0.0135831
$951$	2.50221e144	0.904834
$952$	6.60857e141	0.00227099
$953$	5.83705e144	1.90628	0.953142	−	0.302524i	$-0.0978293\pi$
$953$	5.83705e144	1.90628	0.953142	+	0.302524i	$0.0978293\pi$
$954$	6.91975e141	0.00214780
$955$	4.35933e144	1.28604
$956$	−4.27879e144	−1.19981
$957$	7.17944e143	0.191365
$958$	4.42763e142	0.0112187
$959$	−3.73478e143	−0.0899626
$960$	−8.02186e144	−1.83705
$961$	−6.13682e143	−0.133616
$962$	1.54072e143	0.0318957
$963$	7.29497e143	0.143598
$964$	5.91119e144	1.10647
$965$	1.14878e145	2.04486
$966$	−2.39736e142	−0.00405829
$967$	−3.81465e144	−0.614145	−0.307072	−	0.951686i	$-0.599349\pi$
$967$	−3.81465e144	−0.614145	−0.307072	+	0.951686i	$0.599349\pi$
$968$	−1.89107e143	−0.0289570
$969$	1.36123e144	0.198258
$970$	−2.37761e143	−0.0329390
$971$	7.10022e144	0.935705	0.467853	−	0.883806i	$-0.345028\pi$
$971$	7.10022e144	0.935705	0.467853	+	0.883806i	$0.345028\pi$
$972$	1.71359e144	0.214829
$973$	−1.82830e144	−0.218059
$974$	−9.42115e142	−0.0106904
$975$	−3.13735e145	−3.38719
$976$	−1.15260e145	−1.18403
$977$	−5.80564e144	−0.567497	−0.283749	−	0.958899i	$-0.591578\pi$
$977$	−5.80564e144	−0.567497	−0.283749	+	0.958899i	$0.591578\pi$
$978$	−1.84634e143	−0.0171742
$979$	2.51605e144	0.222720
$980$	2.04421e145	1.72211
$981$	−1.08465e144	−0.0869645
$982$	1.11941e143	0.00854247
$983$	−3.78271e144	−0.274762	−0.137381	−	0.990518i	$-0.543869\pi$
$983$	−3.78271e144	−0.274762	−0.137381	+	0.990518i	$0.543869\pi$
$984$	8.67119e143	0.0599538
$985$	6.46916e144	0.425785
$986$	−6.06700e142	−0.00380140
$987$	9.04455e143	0.0539517
$988$	−1.00598e145	−0.571316
$989$	4.31227e145	2.33177
$990$	2.94568e142	0.00151663
$991$	−3.44249e145	−1.68772	−0.843860	−	0.536564i	$-0.819722\pi$
$991$	−3.44249e145	−1.68772	−0.843860	+	0.536564i	$0.819722\pi$
$992$	−1.07964e144	−0.0504036
$993$	2.60077e145	1.15628
$994$	2.70828e142	0.00114671
$995$	−2.83260e145	−1.14226
$996$	4.66711e145	1.79254
$997$	2.27867e145	0.833617	0.416808	−	0.908994i	$-0.363149\pi$
$997$	2.27867e145	0.833617	0.416808	+	0.908994i	$0.363149\pi$
$998$	−5.78342e143	−0.0201536
$999$	−3.19525e145	−1.06067

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1.98.a.a.1.4	✓	7
3.2	odd	2		9.98.a.a.1.4		7

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1.98.a.a.1.4	✓	7	1.1	even	1	trivial
9.98.a.a.1.4		7	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 1 \)
Weight:	\( k \)	\(=\)	\( 98 \)
Character orbit:	\([\chi]\)	\(=\)	1.a (trivial)

\(f(q)\)	\(=\)	\(q-7.18835e12 q^{2} +1.45423e23 q^{3} -1.58405e29 q^{4} +1.38920e34 q^{5} -1.04535e36 q^{6} -1.18505e40 q^{7} +2.27771e42 q^{8} +2.05969e45 q^{9} +O(q^{10})\)	\(q-7.18835e12 q^{2} +1.45423e23 q^{3} -1.58405e29 q^{4} +1.38920e34 q^{5} -1.04535e36 q^{6} -1.18505e40 q^{7} +2.27771e42 q^{8} +2.05969e45 q^{9} -9.98605e46 q^{10} -1.43215e50 q^{11} -2.30356e52 q^{12} -1.66109e54 q^{13} +8.51852e52 q^{14} +2.02021e57 q^{15} +2.50838e58 q^{16} -2.44836e59 q^{17} -1.48058e58 q^{18} -3.82319e61 q^{19} -2.20056e63 q^{20} -1.72333e63 q^{21} +1.02948e63 q^{22} -1.93525e66 q^{23} +3.31230e65 q^{24} +1.29878e68 q^{25} +1.19405e67 q^{26} -2.47631e69 q^{27} +1.87717e69 q^{28} -3.44723e70 q^{29} -1.45220e70 q^{30} +1.99479e72 q^{31} -5.41229e71 q^{32} -2.08267e73 q^{33} +1.75996e72 q^{34} -1.64626e74 q^{35} -3.26265e74 q^{36} +1.29033e76 q^{37} +2.74824e74 q^{38} -2.41561e77 q^{39} +3.16419e76 q^{40} +2.61787e78 q^{41} +1.23879e76 q^{42} -2.22828e79 q^{43} +2.26859e79 q^{44} +2.86133e79 q^{45} +1.39112e79 q^{46} -5.24832e80 q^{47} +3.64776e81 q^{48} -9.28953e81 q^{49} -9.33612e80 q^{50} -3.56047e82 q^{51} +2.63125e83 q^{52} -4.67367e83 q^{53} +1.78006e82 q^{54} -1.98954e84 q^{55} -2.69919e82 q^{56} -5.55979e84 q^{57} +2.47799e83 q^{58} -8.05790e84 q^{59} -3.20011e86 q^{60} -4.59498e86 q^{61} -1.43393e85 q^{62} -2.44083e85 q^{63} -3.97080e87 q^{64} -2.30759e88 q^{65} +1.49710e86 q^{66} -2.23736e88 q^{67} +3.87831e88 q^{68} -2.81429e89 q^{69} +1.18339e87 q^{70} +3.17929e89 q^{71} +4.69138e87 q^{72} +9.38407e89 q^{73} -9.27532e88 q^{74} +1.88873e91 q^{75} +6.05612e90 q^{76} +1.69716e90 q^{77} +1.73642e90 q^{78} +2.26645e91 q^{79} +3.48465e92 q^{80} -3.99427e92 q^{81} -1.88182e91 q^{82} -2.02604e93 q^{83} +2.72983e92 q^{84} -3.40125e93 q^{85} +1.60176e92 q^{86} -5.01305e93 q^{87} -3.26202e92 q^{88} -1.75683e94 q^{89} -2.05682e92 q^{90} +1.96847e94 q^{91} +3.06553e95 q^{92} +2.90088e95 q^{93} +3.77267e93 q^{94} -5.31118e95 q^{95} -7.87069e94 q^{96} +2.38093e96 q^{97} +6.67764e94 q^{98} -2.94979e95 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 7 q - 16697241085008 q^{2} + 10\!\cdots\!96 q^{3}+ \cdots + 34\!\cdots\!51 q^{9}+O(q^{10}) \) 7 * q - 16697241085008 * q^2 + 100515854497394358147996 * q^3 + 163057083940695061811962902784 * q^4 - 3658387999529088680958306590731350 * q^5 - 30592714388364079315260992082788233536 * q^6 - 184642311743115370607493500489904481438408 * q^7 + 36028528195426625427479134330455698506199040 * q^8 + 34775775472129528349857305774273773877811641051 * q^9	\( 7 q - 16697241085008 q^{2} + 10\!\cdots\!96 q^{3}+ \cdots - 13\!\cdots\!28 q^{99}+O(q^{100}) \) 7 * q - 16697241085008 * q^2 + 100515854497394358147996 * q^3 + 163057083940695061811962902784 * q^4 - 3658387999529088680958306590731350 * q^5 - 30592714388364079315260992082788233536 * q^6 - 184642311743115370607493500489904481438408 * q^7 + 36028528195426625427479134330455698506199040 * q^8 + 34775775472129528349857305774273773877811641051 * q^9 + 2369114123959441270700616822719459966510786272800 * q^10 - 211379321299339211995860033669883746379479318698796 * q^11 + 29500590587146562092031430274877546417191966208812032 * q^12 - 883667637845783834437332163606692334928033653755299614 * q^13 + 24884922778173528138085777326574033504771595080747613568 * q^14 - 1421739776861319561135033238174867421082029896683725376600 * q^15 - 31468671341370205538262999960370611414173356196203424841728 * q^16 + 163250436637003263661570089512096377905088225334685131721342 * q^17 - 7054606772048003028382413409749231596837718873737440667537424 * q^18 + 133084372359310898958448501523235681541051727436663191570359820 * q^19 - 1318696260534044061297364386263469065025874939722479973417331200 * q^20 - 8226961344750528298533572507576209983448935264598913374247505696 * q^21 - 193421584410477868290586506488587370358898549812529751083484246976 * q^22 + 925260914184001305416523826357059292226482310773339215111132964776 * q^23 + 1719359518493251306391725804700467921422689016189510541760687554560 * q^24 - 15111829774373494694703308579556617230149980669179989285410298974375 * q^25 + 252570839996871764139482603418038366978372757286009959646749464447904 * q^26 - 16291464003153760806194022590188439733978909915063668620863256233960 * q^27 + 2270023864280230580582797832096861251181573169347509612847861972977664 * q^28 - 119228645746988213289933973286594685848645193803889692652451844737975470 * q^29 + 350448354156350400480979435069989695492221249186335731168327070817564800 * q^30 + 1783283666881858864849681148885200501497581294973934227348751364131906784 * q^31 - 5665372498136527985720301619489703024215195383428523596691479514791804928 * q^32 + 31524650657546522511070078635079454480923539002999356172307109465073458512 * q^33 - 360491523041063125717708388027762293189396999595568175085448186659598970272 * q^34 + 1278268341035082746531666145800358760269267683649420892787253371588938750800 * q^35 - 216561481226385812264597126278375191173372906326221899147967914271513631488 * q^36 - 4532061622841943284542390241171859851726205146853788500539269747469617514358 * q^37 - 2979582210919721773595405461863152858097797783237497905501709239616681227840 * q^38 + 43268347489134056222423767530379619668087154910038087692852374564634305176712 * q^39 - 252514831298472678734291758335102132215188475493571956673272319739362987008000 * q^40 + 123663386655433999860484853403953500874113711440208020678841289201379470695974 * q^41 + 3296122851141924824443574220618174749418258893075867148421980920155200276985344 * q^42 - 6595249409358954185694714287710218939626711013706300289026511229489118746183244 * q^43 + 31427981619155317050453798326367420934595218826815326227502736274099059309390848 * q^44 - 252057107931731391251960224707597558538839631727412739243273361199825466582835550 * q^45 + 333743461536679365083903174537100831945624746347277312419032904840551699600111744 * q^46 + 1582413179705462665936960636748613012540566075462612818643843634715630112826042192 * q^47 - 5861556434117332280930374286873664455351210291383528056190272983552191849213722624 * q^48 + 4345635008055985505106601346877321132027699788278385269907095782368403364891488399 * q^49 - 26742593205970009143775889336520990050133941492259748319418427757724876722706030000 * q^50 + 7043565089506559965061572069632281800522096763383079376468682406398600422146676984 * q^51 + 45800222007571685487736059984048709986270205428489770979037497696929384027946163712 * q^52 - 653999931744204429821742741003701830521617657540517458768483866216741544701292475654 * q^53 - 1692275654206728716605786947196644220317392594111136065941704729626944069981837438080 * q^54 - 2797264930804680667438884831689324464716285797264284803651188210713133784740241832200 * q^55 - 13571511538900847480549793700693331801076437559096966169392506220987757777557857402880 * q^56 - 32156245276763940566100505959698139630384956043693169857398532690693294678041975751120 * q^57 - 110275012470967940484400158535846043036245771061355495516009955997986614502808104491360 * q^58 - 289716843512018767811919727809674339112407721830489506743846640027004030301179845118940 * q^59 - 910863091257112962110410128770927709732237428874631129572443550789630933691032398899200 * q^60 - 1779644273771380099149369471014727845406783738447834645166296866716596067825339549188046 * q^61 - 4893410323209515393605311670149478112622973098189152140516775294151722525768562137565696 * q^62 - 12773855755538157144284595252262546905649007916763284311597736303148976241726684562602024 * q^63 - 24329532034212074257236420324752039539459926287390018025638252399891746834835822530789376 * q^64 - 40979880706222898178317998710539228015340375450212825952623031288613904725454054500850100 * q^65 - 142841613731497146561089386918878946227924637814625892149907766833242924230825872606056192 * q^66 - 183094181851902905703789039636502649221241410347877100016575616698548103898875205122783908 * q^67 - 250132580738896836682574414547500843555901286243235420681429272583107380144497499057716736 * q^68 - 372244836961332226973480986215431578494847115740354696097669790201492502675456308855459168 * q^69 - 587389541033882485666068522391834191601610745639266949076956170254929472707526921059782400 * q^70 - 36618527208607574135274147674246343687098099724640001025727994874106062220116534447931656 * q^71 + 2495502705800463241319297965149724088435827677064467496346161624547668625438549984339128320 * q^72 + 5937141741627411574629383951784847225959103237898806939243808260531064318159784943464907526 * q^73 + 25603418812897773069861990064614106209712057876935905208225093500026599325689360114519970848 * q^74 + 43416229043729585532262686371625117245611844558141193068941674421259839404159894884059222500 * q^75 + 64491781461168277038374423376126180174707623388661413952117963143585395013082375272839869440 * q^76 + 122801524700573133455664123216977109508839271312008866744292206338517188364407357732160152224 * q^77 + 256518622739178273010532892375526005382856863147760611859324715551823107217212845963281985152 * q^78 + 155279975164311735091235448536513906273532801204307686975280157544842456609207922540776901680 * q^79 + 343037548751841740038666995050634479050946344382038763901789904170114217394648666813900390400 * q^80 - 799336653019442009471583631583081099983526554777301855450568718504605547656753900698628831153 * q^81 - 2054599455199243418451530458808296516745297582440826399667363552358055209069956455679452833056 * q^82 - 2745080838526935126539434486643898932954125805020264508203796620734019354440308801326974021684 * q^83 - 12055830667015300843296227009204563031159870111997209215974794552386444770918151507927520305152 * q^84 - 16156906986132970771716277890961343081101351325821342812927748903601690598916612215092853170700 * q^85 - 16073101085057033129856695763368798351047883803740227513388827997968391823543719379002604387776 * q^86 - 44931373084677669249994770736329381356923858000626008622029156778901658182110994195783000791480 * q^87 - 20900444501134905678673788524771632932447417317035512416151379720801969394444956958395302789120 * q^88 + 8652425236627243255051028260917634407304730072980172181544783646255542601500269383337979350390 * q^89 + 169914380219009102880054256907856294069041898142575788262717672760376053145875718225670932330400 * q^90 + 235279610532724372901602846332263408075886672274330172793822218199845308058643167074949650230544 * q^91 + 622950794384614085632156625042963081233986358617743991991586248417198315809579918444522808891392 * q^92 + 1619655729334717431421579797164299646702152339363664709672746834797775058100318492643375449441152 * q^93 + 1784387548746436753701888750274366538460858609156963702431495773056050960861585984793528939671808 * q^94 + 1109691419127482658877926123378178695834970817464791602098716148821958373905367930889408748989000 * q^95 + 2773817117979873680694700349927475687549477810523157816910439588411515192104026991177258420404224 * q^96 - 462826972284038426621245345324758076530452205891330025493894671876723283114629445572915788984658 * q^97 - 10100804559243313775965110405631054964918520327952856127425837778067309219959758215138751854831056 * q^98 - 13792894935722775136702660269810636953813664741795563019740674282913700184659028566406972539495228 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more