LMFDB - Embedded newform 1.96.a.a.1.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1,96,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, 96, names="a")

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

chi := DirichletCharacter("1.1");

S:= CuspForms(chi, 96);

N := Newforms(S);

Level:	$ N $	$=$	$ 1 $
Weight:	$ k $	$=$	$ 96 $
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:	$57.1535908815$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{7} + \cdots + 12\!\cdots\!76 $ x^8 - x^7 - 456480027345544641394773612x^6 + 339329782338279955661332506368261395760x^5 + 59416097258977044989967193525017781867755241062538816x^4 - 123333481272707766511586825940129187946017943991568425334323966720x^3 - 2095214953359612636412863727366527579550578420280500659704186845017628059993088x^2 + 4629118030090922642937991592467690897026031030167011441378882798867864401974811543004909568x + 12580947281346973442685392853423155834893282648684156383693372843595042753411312943646281706520481611776
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	multiple of $ 2^{104}\cdot 3^{38}\cdot 5^{12}\cdot 7^{7}\cdot 11\cdot 13\cdot 19^{3} $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.5
Root			$4.79736e12$ 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)

$f(q)$	$=$	$q+1.14407e14 q^{2} +8.75958e22 q^{3} -2.65251e28 q^{4} -1.07741e33 q^{5} +1.00216e37 q^{6} +1.86215e40 q^{7} -7.56680e42 q^{8} +5.55214e45 q^{9} +O(q^{10})$	\(q+1.14407e14 q^{2} +8.75958e22 q^{3} -2.65251e28 q^{4} -1.07741e33 q^{5} +1.00216e37 q^{6} +1.86215e40 q^{7} -7.56680e42 q^{8} +5.55214e45 q^{9} -1.23264e47 q^{10} +1.86898e49 q^{11} -2.32348e51 q^{12} -5.82728e52 q^{13} +2.13044e54 q^{14} -9.43769e55 q^{15} +1.85069e56 q^{16} -1.12709e58 q^{17} +6.35205e59 q^{18} +8.30862e60 q^{19} +2.85785e61 q^{20} +1.63117e63 q^{21} +2.13824e63 q^{22} +1.09549e64 q^{23} -6.62820e65 q^{24} -1.36353e66 q^{25} -6.66683e66 q^{26} +3.00562e68 q^{27} -4.93937e68 q^{28} +2.28760e69 q^{29} -1.07974e70 q^{30} +3.05026e70 q^{31} +3.20925e71 q^{32} +1.63715e72 q^{33} -1.28947e72 q^{34} -2.00631e73 q^{35} -1.47271e74 q^{36} +3.99750e74 q^{37} +9.50566e74 q^{38} -5.10446e75 q^{39} +8.15257e75 q^{40} -3.81589e76 q^{41} +1.86617e77 q^{42} +2.50487e77 q^{43} -4.95747e77 q^{44} -5.98195e78 q^{45} +1.25332e78 q^{46} +2.28370e79 q^{47} +1.62113e79 q^{48} +1.54313e80 q^{49} -1.55998e80 q^{50} -9.87281e80 q^{51} +1.54569e81 q^{52} -5.87919e80 q^{53} +3.43865e82 q^{54} -2.01366e82 q^{55} -1.40905e83 q^{56} +7.27800e83 q^{57} +2.61719e83 q^{58} +1.48881e84 q^{59} +2.50335e84 q^{60} -5.46013e84 q^{61} +3.48972e84 q^{62} +1.03389e86 q^{63} +2.93848e85 q^{64} +6.27839e85 q^{65} +1.87301e86 q^{66} -6.62877e86 q^{67} +2.98960e86 q^{68} +9.59605e86 q^{69} -2.29536e87 q^{70} +5.25075e87 q^{71} -4.20119e88 q^{72} -2.09882e88 q^{73} +4.57343e88 q^{74} -1.19440e89 q^{75} -2.20387e89 q^{76} +3.48032e89 q^{77} -5.83987e89 q^{78} +6.42811e89 q^{79} -1.99396e89 q^{80} +1.45525e91 q^{81} -4.36566e90 q^{82} +1.28783e91 q^{83} -4.32668e91 q^{84} +1.21434e91 q^{85} +2.86575e91 q^{86} +2.00385e92 q^{87} -1.41422e92 q^{88} -5.79584e92 q^{89} -6.84378e92 q^{90} -1.08513e93 q^{91} -2.90580e92 q^{92} +2.67190e93 q^{93} +2.61272e93 q^{94} -8.95182e93 q^{95} +2.81117e94 q^{96} -1.99071e94 q^{97} +1.76545e94 q^{98} +1.03768e95 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 5835659138280 q^{2} - 95\!\cdots\!80 q^{3}+ \cdots + 92\!\cdots\!36 q^{9}+O(q^{10}) $ 8 * q - 5835659138280 * q^2 - 9565982513916703570080 * q^3 + 208956598309707350371623569984 * q^4 + 1941568507475850402526904141070960 * q^5 + 10651800775920653731297343298528492576 * q^6 + 31232311735415758067806325356531573912000 * q^7 - 14761127603920085098561309094124598702287360 * q^8 + 9274438133561954597944854467482391143953072936 * q^9	$ 8 q - 5835659138280 q^{2} - 95\!\cdots\!80 q^{3}+ \cdots + 30\!\cdots\!72 q^{99}+O(q^{100}) $ 8 * q - 5835659138280 * q^2 - 9565982513916703570080 * q^3 + 208956598309707350371623569984 * q^4 + 1941568507475850402526904141070960 * q^5 + 10651800775920653731297343298528492576 * q^6 + 31232311735415758067806325356531573912000 * q^7 - 14761127603920085098561309094124598702287360 * q^8 + 9274438133561954597944854467482391143953072936 * q^9 - 355384205613899841010372205704985147108657534640 * q^10 + 53080108095821756826858489331993621982645992125216 * q^11 + 1065031032961827853079380844579017283696993846403840 * q^12 + 117293508281179239843264964380833942161194396039342640 * q^13 + 8850886815767090581799564344683737269936151852930265408 * q^14 + 187812376414067333691564154745798290909917959215041625920 * q^15 + 9517116971431211282501221161054789131283343644054948220928 * q^16 - 13655041265063090981829171372625119189425374473948274915440 * q^17 - 1790266901749030205580776247252673430153004351197542602854280 * q^18 - 5232175975370167369536369873888207394303637759872553281713440 * q^19 + 136065209104116992530471413843386338746929879497239386344644480 * q^20 + 1346571177849118208545064341536207444072396945735327627682503936 * q^21 - 20365500099170357171519767897869972385636855003458825137197491360 * q^22 - 7129054072165937484825035531327773489156117409617881426435061440 * q^23 + 288860682603965362857322541557744811472884721216169744526242990080 * q^24 + 8177806376085721196783759852983887433280593317172609841487587996600 * q^25 - 69072273179717436642550386629266724895941590936463282023015399323504 * q^26 + 64049503386294800673569522679695786753122795388715525750679249767360 * q^27 + 303354815522537415860404332264897505740906926923909508834765584637440 * q^28 + 7715272198415359380593902919630157934289467091855373333108685675435440 * q^29 - 62913685170287068298704199843316213881225133796680396150164526710345280 * q^30 + 48520677903801540370519073843711920597057994260920479636592334181199616 * q^31 + 911347110324473008775326747695560179887781374647708612161794209209221120 * q^32 - 1535322742350198888271103254480947687741587903792512354063710702943493760 * q^33 - 16409772766982648656985219134942803587399227958333745923026675404562961232 * q^34 + 58800416933815614414155173269063056087887600285328689246425433374756677760 * q^35 + 51665208441213434468989869710710146210173003797753332160946711226240568128 * q^36 - 181116344963557296256979160619337453378797091102974834966000994855965247120 * q^37 - 1676466315180766681626408275142200947978975839695306622930354052184199692640 * q^38 + 465478714369259758144024065308323445042256641733578800363164365799686202432 * q^39 + 39028182173606372825635252450401491624189758401191157685601991729209269171200 * q^40 - 87541390126560450267544465567119030351560808726320656469732601708266148308784 * q^41 - 157435820560022140348706044721413472652300880194209574021901207450891596867840 * q^42 + 360093033489081253538156425248276463103949347025569853491672117723107522861600 * q^43 + 1942224484251042670482996667732829207493398934442399145050649033803969221005568 * q^44 - 1611554371538604569657837598986488298494511731253236200388961579880024486332880 * q^45 - 19332434944442851407749457669991401004991143268030327859543986888040547882373184 * q^46 + 38672453335683563852366980570346257355794761888911368752480783496161211070336640 * q^47 + 93863838769591236482712272126012963144755254935077324856132076191099747033333760 * q^48 + 265668043093542548841947390620517395072194945166225827717144824590425137465244744 * q^49 - 1423963459280866882678609595824694565889878038511273700600414891648711070234429400 * q^50 + 2434476695354895883532253554814552047229450451049452072207263289482820720406821056 * q^51 + 15678746704556392183126484026214298441253990030076674973212546269606119207477104000 * q^52 - 2922690482809426126710991861168746969788895886261814706776237561500358605037675280 * q^53 + 44393564079821957628952458152403809172972567715888333832276777433089826621820157760 * q^54 + 77963865832782922646862204005771036172886494149999882551809226033579503680996905920 * q^55 + 723822110434297992891221750986765045769194525611914833690699475848521019635777392640 * q^56 + 1459603943948321457517074656112276013643674313689343212415092604638087582879924782720 * q^57 + 2398120500739528001867383787619453843290390222445601081527493426426916763954522209040 * q^58 + 2444569112045817337560949868287606200158569651761097862873350630901953709318185022880 * q^59 + 41015921945833187827435663222575462810347191746192004435818365735996703011205515880960 * q^60 + 26252719580888049069066995575288184611473664654647035829209505915961690057602967485616 * q^61 + 109318411457586083204284032417457169492313955459811319765445849679642744506848521207040 * q^62 + 170984018880767416687602973051010439420211230624233991381305273834268390445660056281280 * q^63 + 407545659960425058121678577897271227683793728749313452587765989597513138495845491277824 * q^64 + 711217468942010938456527729098183388378886665557115838437689631605619958224435834575520 * q^65 + 1747938075646007071584137716302374690644541046339320226994976444199784352790302021223552 * q^66 - 646475642994207391400653355260241732956721934256209274545597969100350739031184431188640 * q^67 + 91675839067201266020688320385568861573762045194469769590554263557238860857176520405120 * q^68 - 1671348258106164448387617904756675195481964064504427142194954632911883632406377850960128 * q^69 - 15589682350948763132524633727148211085350313303119537319661619119948806738470696493235840 * q^70 - 14595295080721751466823982356267079020901744922845645857244436108167397828048945561374784 * q^71 - 168731956650076191328348463912100975176233311308158667034794509156143705616303905637470720 * q^72 - 167722859263497180232486905674536831998056258335586734743256934373976249561602911979579440 * q^73 - 209312489678791718598684146630297797595302804804578868479635191055424978871400486510408112 * q^74 - 319918492419260578418623942107150301135641877679303067145274604119881385565549842206216800 * q^75 - 959273209575432254809587692424149415253949631691365417587931662952012091653615772375589120 * q^76 - 358973379150050060834656745211596557040941835816686113329022190288009228708654757892460800 * q^77 + 590425535394410417923583601115147442109710886806797004396557673983317347484688655751672000 * q^78 + 4672642903096907209502768293890247708239627672362847349478671278970829923925879535283527040 * q^79 + 18415268594255335517079731605762998550074832241200743044677945286622776635630921688252866560 * q^80 + 12509737552066767544095911653095580991572013599361129872125476231341584536182121238921405768 * q^81 + 32657845092209493410036294321958173121440540177602229019397776717126981442788576405027965040 * q^82 + 34387792212015780744754986808561666458900302762495709021597904850967930099747337487085254880 * q^83 + 173836457542583880184373241725060178629119564679421678850358203433258194499103546320231344128 * q^84 + 58585978711733607272815047107060888289878133655773893600270763487144112403111490135244590560 * q^85 - 153511472921832187435283964804212642635464712353485304877046031498544471884447149897205104544 * q^86 - 544464219458114578116693663783217812912359092004929393234553696235186032730900539616052969920 * q^87 - 1202425497404423912185881933157195269872332267934742515736241252480851349730675866727622174720 * q^88 - 342673661311688548077760584785109887358595471462214186557789870415877447806348084055852796080 * q^89 - 3514062299884453064121468346218192535289244482618329972865712072788945397515179474700715316080 * q^90 - 3490211360016960529246147249335483533013067701963330513611222538458526220206688421639066690944 * q^91 - 12008074146638359830472895966704879561255070000267734630900014099911412498586265442549753546240 * q^92 + 197667690727810326296814984504358164807428856713575716952413727748092885643497784281407575040 * q^93 + 15433462798640093333378242254437202047220637579307237556798289796157532672617883642933732299648 * q^94 + 15321400721190643816477985005690604983976540891819618748501840926190750159388834713154020724800 * q^95 + 97555071644510782149318139986276901553221426854121546320985366392022081200430710682001871077376 * q^96 + 10072532354157458294768094296505188523874048354320514397914144859011793551098974691865811668240 * q^97 + 146363464831387371243245039459581022362075942196915081212239417921551560440470151788055390975960 * q^98 + 307096415144337525387251975813943414746365371627429389615225939474864146107991251707726185786272 * 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 $

$2$	1.14407e14	0.574816	0.287408	−	0.957808i	$-0.407206\pi$
$2$	1.14407e14	0.574816	0.287408	+	0.957808i	$0.407206\pi$
$3$	8.75958e22	1.90206	0.951029	−	0.309101i	$-0.100028\pi$
$3$	8.75958e22	1.90206	0.951029	+	0.309101i	$0.100028\pi$
$4$	−2.65251e28	−0.669587
$5$	−1.07741e33	−0.678121	−0.339061	−	0.940765i	$-0.610109\pi$
$5$	−1.07741e33	−0.678121	−0.339061	+	0.940765i	$0.610109\pi$
$6$	1.00216e37	1.09333
$7$	1.86215e40	1.34233	0.671163	−	0.741309i	$-0.265795\pi$
$7$	1.86215e40	1.34233	0.671163	+	0.741309i	$0.265795\pi$
$8$	−7.56680e42	−0.959705
$9$	5.55214e45	2.61783
$10$	−1.23264e47	−0.389795
$11$	1.86898e49	0.638927	0.319464	−	0.947599i	$-0.396497\pi$
$11$	1.86898e49	0.638927	0.319464	+	0.947599i	$0.396497\pi$
$12$	−2.32348e51	−1.27359
$13$	−5.82728e52	−0.713110	−0.356555	−	0.934274i	$-0.616049\pi$
$13$	−5.82728e52	−0.713110	−0.356555	+	0.934274i	$0.616049\pi$
$14$	2.13044e54	0.771591
$15$	−9.43769e55	−1.28983
$16$	1.85069e56	0.117933
$17$	−1.12709e58	−0.403305	−0.201652	−	0.979457i	$-0.564631\pi$
$17$	−1.12709e58	−0.403305	−0.201652	+	0.979457i	$0.564631\pi$
$18$	6.35205e59	1.50477
$19$	8.30862e60	1.50915	0.754576	−	0.656213i	$-0.227843\pi$
$19$	8.30862e60	1.50915	0.754576	+	0.656213i	$0.227843\pi$
$20$	2.85785e61	0.454061
$21$	1.63117e63	2.55318
$22$	2.13824e63	0.367265
$23$	1.09549e64	0.227791	0.113896	−	0.993493i	$-0.463667\pi$
$23$	1.09549e64	0.227791	0.113896	+	0.993493i	$0.463667\pi$
$24$	−6.62820e65	−1.82542
$25$	−1.36353e66	−0.540152
$26$	−6.66683e66	−0.409907
$27$	3.00562e68	3.07720
$28$	−4.93937e68	−0.898804
$29$	2.28760e69	0.786097	0.393048	−	0.919518i	$-0.371421\pi$
$29$	2.28760e69	0.786097	0.393048	+	0.919518i	$0.371421\pi$
$30$	−1.07974e70	−0.741413
$31$	3.05026e70	0.441221	0.220610	−	0.975362i	$-0.429195\pi$
$31$	3.05026e70	0.441221	0.220610	+	0.975362i	$0.429195\pi$
$32$	3.20925e71	1.02749
$33$	1.63715e72	1.21528
$34$	−1.28947e72	−0.231826
$35$	−2.00631e73	−0.910260
$36$	−1.47271e74	−1.75286
$37$	3.99750e74	1.29481	0.647406	−	0.762145i	$-0.275854\pi$
$37$	3.99750e74	1.29481	0.647406	+	0.762145i	$0.275854\pi$
$38$	9.50566e74	0.867484
$39$	−5.10446e75	−1.35638
$40$	8.15257e75	0.650796
$41$	−3.81589e76	−0.942677	−0.471338	−	0.881952i	$-0.656229\pi$
$41$	−3.81589e76	−0.942677	−0.471338	+	0.881952i	$0.656229\pi$
$42$	1.86617e77	1.46761
$43$	2.50487e77	0.644219	0.322110	−	0.946702i	$-0.395608\pi$
$43$	2.50487e77	0.644219	0.322110	+	0.946702i	$0.395608\pi$
$44$	−4.95747e77	−0.427817
$45$	−5.98195e78	−1.77520
$46$	1.25332e78	0.130938
$47$	2.28370e79	0.858994	0.429497	−	0.903068i	$-0.358691\pi$
$47$	2.28370e79	0.858994	0.429497	+	0.903068i	$0.358691\pi$
$48$	1.62113e79	0.224315
$49$	1.54313e80	0.801841
$50$	−1.55998e80	−0.310488
$51$	−9.87281e80	−0.767109
$52$	1.54569e81	0.477489
$53$	−5.87919e80	−0.0734875	−0.0367438	−	0.999325i	$-0.511699\pi$
$53$	−5.87919e80	−0.0734875	−0.0367438	+	0.999325i	$0.511699\pi$
$54$	3.43865e82	1.76882
$55$	−2.01366e82	−0.433270
$56$	−1.40905e83	−1.28824
$57$	7.27800e83	2.87049
$58$	2.61719e83	0.451861
$59$	1.48881e84	1.14122	0.570610	−	0.821221i	$-0.306707\pi$
$59$	1.48881e84	1.14122	0.570610	+	0.821221i	$0.306707\pi$
$60$	2.50335e84	0.863650
$61$	−5.46013e84	−0.859084	−0.429542	−	0.903047i	$-0.641325\pi$
$61$	−5.46013e84	−0.859084	−0.429542	+	0.903047i	$0.641325\pi$
$62$	3.48972e84	0.253621
$63$	1.03389e86	3.51398
$64$	2.93848e85	0.472688
$65$	6.27839e85	0.483575
$66$	1.87301e86	0.698560
$67$	−6.62877e86	−1.21026	−0.605132	−	0.796125i	$-0.706880\pi$
$67$	−6.62877e86	−1.21026	−0.605132	+	0.796125i	$0.706880\pi$
$68$	2.98960e86	0.270047
$69$	9.59605e86	0.433272
$70$	−2.29536e87	−0.523232
$71$	5.25075e87	0.610168	0.305084	−	0.952325i	$-0.401315\pi$
$71$	5.25075e87	0.610168	0.305084	+	0.952325i	$0.401315\pi$
$72$	−4.20119e88	−2.51234
$73$	−2.09882e88	−0.651838	−0.325919	−	0.945398i	$-0.605674\pi$
$73$	−2.09882e88	−0.651838	−0.325919	+	0.945398i	$0.605674\pi$
$74$	4.57343e88	0.744279
$75$	−1.19440e89	−1.02740
$76$	−2.20387e89	−1.01051
$77$	3.48032e89	0.857649
$78$	−5.83987e89	−0.779668
$79$	6.42811e89	0.468594	0.234297	−	0.972165i	$-0.424721\pi$
$79$	6.42811e89	0.468594	0.234297	+	0.972165i	$0.424721\pi$
$80$	−1.99396e89	−0.0799727
$81$	1.45525e91	3.23519
$82$	−4.36566e90	−0.541866
$83$	1.28783e91	0.898770	0.449385	−	0.893338i	$-0.351643\pi$
$83$	1.28783e91	0.898770	0.449385	+	0.893338i	$0.351643\pi$
$84$	−4.32668e91	−1.70958
$85$	1.21434e91	0.273489
$86$	2.86575e91	0.370307
$87$	2.00385e92	1.49520
$88$	−1.41422e92	−0.613182
$89$	−5.79584e92	−1.46923	−0.734617	−	0.678482i	$-0.762638\pi$
$89$	−5.79584e92	−1.46923	−0.734617	+	0.678482i	$0.762638\pi$
$90$	−6.84378e92	−1.02042
$91$	−1.08513e93	−0.957227
$92$	−2.90580e92	−0.152526
$93$	2.67190e93	0.839228
$94$	2.61272e93	0.493764
$95$	−8.95182e93	−1.02339
$96$	2.81117e94	1.95436
$97$	−1.99071e94	−0.845960	−0.422980	−	0.906139i	$-0.639016\pi$
$97$	−1.99071e94	−0.845960	−0.422980	+	0.906139i	$0.639016\pi$
$98$	1.76545e94	0.460911
$99$	1.03768e95	1.67260
$100$	3.61678e94	0.361678
$101$	−1.49360e95	−0.931044	−0.465522	−	0.885036i	$-0.654133\pi$
$101$	−1.49360e95	−0.931044	−0.465522	+	0.885036i	$0.654133\pi$
$102$	−1.12952e95	−0.440947
$103$	−1.96607e95	−0.482871	−0.241436	−	0.970417i	$-0.577618\pi$
$103$	−1.96607e95	−0.482871	−0.241436	+	0.970417i	$0.577618\pi$
$104$	4.40939e95	0.684376
$105$	−1.75744e96	−1.73137
$106$	−6.72622e94	−0.0422418
$107$	4.75478e96	1.91162	0.955810	−	0.293987i	$-0.0949821\pi$
$107$	4.75478e96	1.91162	0.955810	+	0.293987i	$0.0949821\pi$
$108$	−7.97243e96	−2.06045
$109$	−7.14568e96	−1.19202	−0.596012	−	0.802975i	$-0.703249\pi$
$109$	−7.14568e96	−1.19202	−0.596012	+	0.802975i	$0.703249\pi$
$110$	−2.30377e96	−0.249050
$111$	3.50164e97	2.46281
$112$	3.44627e96	0.158304
$113$	1.00967e97	0.304056	0.152028	−	0.988376i	$-0.451420\pi$
$113$	1.00967e97	0.304056	0.152028	+	0.988376i	$0.451420\pi$
$114$	8.32657e97	1.65001
$115$	−1.18030e97	−0.154470
$116$	−6.06788e97	−0.526360
$117$	−3.23539e98	−1.86680
$118$	1.70331e98	0.655991
$119$	−2.09881e98	−0.541367
$120$	7.14131e98	1.23785
$121$	−5.06360e98	−0.591772
$122$	−6.24678e98	−0.493815
$123$	−3.34256e99	−1.79303
$124$	−8.09082e98	−0.295436
$125$	4.18887e99	1.04441
$126$	1.18285e100	2.01989
$127$	−3.20381e99	−0.375828	−0.187914	−	0.982185i	$-0.560173\pi$
$127$	−3.20381e99	−0.375828	−0.187914	+	0.982185i	$0.560173\pi$
$128$	−9.35131e99	−0.755786
$129$	2.19416e100	1.22534
$130$	7.18294e99	0.277967
$131$	−8.76864e99	−0.235801	−0.117901	−	0.993025i	$-0.537616\pi$
$131$	−8.76864e99	−0.235801	−0.117901	+	0.993025i	$0.537616\pi$
$132$	−4.34254e100	−0.813733
$133$	1.54719e101	2.02577
$134$	−7.58380e100	−0.695679
$135$	−3.23830e101	−2.08671
$136$	8.52843e100	0.387054
$137$	−4.51916e101	−1.44821	−0.724104	−	0.689690i	$-0.757747\pi$
$137$	−4.51916e101	−1.44821	−0.724104	+	0.689690i	$0.757747\pi$
$138$	1.09786e101	0.249052
$139$	−1.59027e101	−0.256016	−0.128008	−	0.991773i	$-0.540858\pi$
$139$	−1.59027e101	−0.256016	−0.128008	+	0.991773i	$0.540858\pi$
$140$	5.32174e101	0.609498
$141$	2.00042e102	1.63386
$142$	6.00724e101	0.350734
$143$	−1.08911e102	−0.455626
$144$	1.02753e102	0.308728
$145$	−2.46470e102	−0.533069
$146$	−2.40120e102	−0.374687
$147$	1.35172e103	1.52515
$148$	−1.06034e103	−0.866989
$149$	1.71379e103	1.01767	0.508837	−	0.860863i	$-0.330076\pi$
$149$	1.71379e103	1.01767	0.508837	+	0.860863i	$0.330076\pi$
$150$	−1.36648e103	−0.590566
$151$	−1.14182e103	−0.359910	−0.179955	−	0.983675i	$-0.557595\pi$
$151$	−1.14182e103	−0.359910	−0.179955	+	0.983675i	$0.557595\pi$
$152$	−6.28696e103	−1.44834
$153$	−6.25774e103	−1.05578
$154$	3.98174e103	0.492990
$155$	−3.28639e103	−0.299201
$156$	1.35396e104	0.908212
$157$	2.80778e104	1.39037	0.695183	−	0.718833i	$-0.255323\pi$
$157$	2.80778e104	1.39037	0.695183	+	0.718833i	$0.255323\pi$
$158$	7.35423e103	0.269355
$159$	−5.14992e103	−0.139778
$160$	−3.45769e104	−0.696766
$161$	2.03997e104	0.305770
$162$	1.66491e105	1.85964
$163$	−1.96014e105	−1.63447	−0.817233	−	0.576307i	$-0.804493\pi$
$163$	−1.96014e105	−1.63447	−0.817233	+	0.576307i	$0.804493\pi$
$164$	1.01217e105	0.631204
$165$	−1.76388e105	−0.824105
$166$	1.47337e105	0.516628
$167$	−1.64238e105	−0.432953	−0.216476	−	0.976288i	$-0.569456\pi$
$167$	−1.64238e105	−0.432953	−0.216476	+	0.976288i	$0.569456\pi$
$168$	−1.23427e106	−2.45030
$169$	−3.28185e105	−0.491474
$170$	1.38929e105	0.157206
$171$	4.61306e106	3.95070
$172$	−6.64418e105	−0.431360
$173$	−3.79233e106	−1.86946	−0.934729	−	0.355361i	$-0.884358\pi$
$173$	−3.79233e106	−1.86946	−0.934729	+	0.355361i	$0.884358\pi$
$174$	2.29255e106	0.859466
$175$	−2.53911e106	−0.725060
$176$	3.45890e105	0.0753505
$177$	1.30414e107	2.17067
$178$	−6.63086e106	−0.844539
$179$	−1.93342e106	−0.188715	−0.0943575	−	0.995538i	$-0.530080\pi$
$179$	−1.93342e106	−0.188715	−0.0943575	+	0.995538i	$0.530080\pi$
$180$	1.58671e107	1.18865
$181$	−6.25383e106	−0.360092	−0.180046	−	0.983658i	$-0.557625\pi$
$181$	−6.25383e106	−0.360092	−0.180046	+	0.983658i	$0.557625\pi$
$182$	−1.24147e107	−0.550229
$183$	−4.78285e107	−1.63403
$184$	−8.28936e106	−0.218612
$185$	−4.30696e107	−0.878039
$186$	3.05685e107	0.482401
$187$	−2.10650e107	−0.257682
$188$	−6.05752e107	−0.575171
$189$	5.59693e108	4.13061
$190$	−1.02415e108	−0.588259
$191$	−3.51064e108	−1.57145	−0.785727	−	0.618574i	$-0.787711\pi$
$191$	−3.51064e108	−1.57145	−0.785727	+	0.618574i	$0.787711\pi$
$192$	2.57399e108	0.899079
$193$	2.92480e107	0.0798222	0.0399111	−	0.999203i	$-0.487293\pi$
$193$	2.92480e107	0.0798222	0.0399111	+	0.999203i	$0.487293\pi$
$194$	−2.27751e108	−0.486271
$195$	5.49961e108	0.919788
$196$	−4.09316e108	−0.536902
$197$	−4.45025e108	−0.458394	−0.229197	−	0.973380i	$-0.573610\pi$
$197$	−4.45025e108	−0.458394	−0.229197	+	0.973380i	$0.573610\pi$
$198$	1.18718e109	0.961437
$199$	−1.61011e109	−1.02644	−0.513221	−	0.858257i	$-0.671548\pi$
$199$	−1.61011e109	−1.02644	−0.513221	+	0.858257i	$0.671548\pi$
$200$	1.03176e109	0.518386
$201$	−5.80653e109	−2.30199
$202$	−1.70879e109	−0.535179
$203$	4.25987e109	1.05520
$204$	2.61877e109	0.513646
$205$	4.11129e109	0.639249
$206$	−2.24933e109	−0.277562
$207$	6.08232e109	0.596317
$208$	−1.07845e109	−0.0840991
$209$	1.55286e110	0.964238
$210$	−2.01064e110	−0.995218
$211$	−3.31253e109	−0.130841	−0.0654204	−	0.997858i	$-0.520839\pi$
$211$	−3.31253e109	−0.130841	−0.0654204	+	0.997858i	$0.520839\pi$
$212$	1.55946e109	0.0492063
$213$	4.59944e110	1.16058
$214$	5.43982e110	1.09883
$215$	−2.69878e110	−0.436859
$216$	−2.27429e111	−2.95320
$217$	5.68004e110	0.592262
$218$	−8.17518e110	−0.685195
$219$	−1.83848e111	−1.23983
$220$	5.34125e110	0.290112
$221$	6.56785e110	0.287601
$222$	4.00614e111	1.41566
$223$	3.24943e111	0.927525	0.463762	−	0.885960i	$-0.346499\pi$
$223$	3.24943e111	0.927525	0.463762	+	0.885960i	$0.346499\pi$
$224$	5.97611e111	1.37923
$225$	−7.57053e111	−1.41402
$226$	1.15514e111	0.174777
$227$	4.89470e111	0.600479	0.300239	−	0.953864i	$-0.402933\pi$
$227$	4.89470e111	0.600479	0.300239	+	0.953864i	$0.402933\pi$
$228$	−1.93049e112	−1.92204
$229$	8.09008e111	0.654285	0.327143	−	0.944975i	$-0.393914\pi$
$229$	8.09008e111	0.654285	0.327143	+	0.944975i	$0.393914\pi$
$230$	−1.35035e111	−0.0887918
$231$	3.04861e112	1.63130
$232$	−1.73098e112	−0.754421
$233$	1.29046e111	0.0458499	0.0229249	−	0.999737i	$-0.492702\pi$
$233$	1.29046e111	0.0458499	0.0229249	+	0.999737i	$0.492702\pi$
$234$	−3.70152e112	−1.07307
$235$	−2.46049e112	−0.582502
$236$	−3.94908e112	−0.764145
$237$	5.63076e112	0.891293
$238$	−2.40119e112	−0.311186
$239$	1.08843e112	0.115585	0.0577925	−	0.998329i	$-0.481594\pi$
$239$	1.08843e112	0.115585	0.0577925	+	0.998329i	$0.481594\pi$
$240$	−1.74663e112	−0.152113
$241$	4.88485e111	0.0349174	0.0174587	−	0.999848i	$-0.494442\pi$
$241$	4.88485e111	0.0349174	0.0174587	+	0.999848i	$0.494442\pi$
$242$	−5.79313e112	−0.340160
$243$	6.37278e113	3.07632
$244$	1.44830e113	0.575231
$245$	−1.66259e113	−0.543745
$246$	−3.82413e113	−1.03066
$247$	−4.84167e113	−1.07619
$248$	−2.30807e113	−0.423442
$249$	1.12808e114	1.70951
$250$	4.79237e113	0.600343
$251$	−3.41272e113	−0.353671	−0.176835	−	0.984240i	$-0.556586\pi$
$251$	−3.41272e113	−0.353671	−0.176835	+	0.984240i	$0.556586\pi$
$252$	−2.74240e114	−2.35291
$253$	2.04745e113	0.145542
$254$	−3.66539e113	−0.216032
$255$	1.06371e114	0.520193
$256$	−2.23391e114	−0.907126
$257$	−1.29687e114	−0.437596	−0.218798	−	0.975770i	$-0.570214\pi$
$257$	−1.29687e114	−0.437596	−0.218798	+	0.975770i	$0.570214\pi$
$258$	2.51028e114	0.704346
$259$	7.44396e114	1.73806
$260$	−1.66535e114	−0.323795
$261$	1.27011e115	2.05786
$262$	−1.00320e114	−0.135542
$263$	−6.44551e114	−0.726707	−0.363353	−	0.931651i	$-0.618368\pi$
$263$	−6.44551e114	−0.726707	−0.363353	+	0.931651i	$0.618368\pi$
$264$	−1.23880e115	−1.16631
$265$	6.33432e113	0.0498334
$266$	1.77010e115	1.16445
$267$	−5.07691e115	−2.79457
$268$	1.75829e115	0.810376
$269$	3.56451e115	1.37647	0.688235	−	0.725488i	$-0.258386\pi$
$269$	3.56451e115	1.37647	0.688235	+	0.725488i	$0.258386\pi$
$270$	−3.70485e115	−1.19948
$271$	5.89389e115	1.60089	0.800444	−	0.599407i	$-0.204597\pi$
$271$	5.89389e115	1.60089	0.800444	+	0.599407i	$0.204597\pi$
$272$	−2.08589e114	−0.0475629
$273$	−9.50527e115	−1.82070
$274$	−5.17025e115	−0.832454
$275$	−2.54841e115	−0.345118
$276$	−2.54536e115	−0.290113
$277$	1.57132e116	1.50825	0.754127	−	0.656729i	$-0.228060\pi$
$277$	1.57132e116	1.50825	0.754127	+	0.656729i	$0.228060\pi$
$278$	−1.81938e115	−0.147162
$279$	1.69354e116	1.15504
$280$	1.51813e116	0.873581
$281$	−7.65627e114	−0.0371935	−0.0185968	−	0.999827i	$-0.505920\pi$
$281$	−7.65627e114	−0.0371935	−0.0185968	+	0.999827i	$0.505920\pi$
$282$	2.28863e116	0.939167
$283$	2.92782e115	0.101552	0.0507760	−	0.998710i	$-0.483831\pi$
$283$	2.92782e115	0.101552	0.0507760	+	0.998710i	$0.483831\pi$
$284$	−1.39276e116	−0.408560
$285$	−7.84142e116	−1.94654
$286$	−1.24602e116	−0.261901
$287$	−7.10577e116	−1.26538
$288$	1.78182e117	2.68980
$289$	−6.53961e116	−0.837345
$290$	−2.81979e116	−0.306416
$291$	−1.74378e117	−1.60906
$292$	5.56713e116	0.436462
$293$	7.90530e116	0.526874	0.263437	−	0.964677i	$-0.415144\pi$
$293$	7.90530e116	0.526874	0.263437	+	0.964677i	$0.415144\pi$
$294$	1.54646e117	0.876680
$295$	−1.60407e117	−0.773885
$296$	−3.02483e117	−1.24264
$297$	5.61744e117	1.96611
$298$	1.96070e117	0.584976
$299$	−6.38374e116	−0.162440
$300$	3.16815e117	0.687933
$301$	4.66445e117	0.864753
$302$	−1.30633e117	−0.206882
$303$	−1.30833e118	−1.77090
$304$	1.53767e117	0.177978
$305$	5.88282e117	0.582563
$306$	−7.15930e117	−0.606880
$307$	−2.08767e117	−0.151561	−0.0757807	−	0.997125i	$-0.524145\pi$
$307$	−2.08767e117	−0.151561	−0.0757807	+	0.997125i	$0.524145\pi$
$308$	−9.23156e117	−0.574270
$309$	−1.72220e118	−0.918450
$310$	−3.75987e117	−0.171986
$311$	2.44843e118	0.961100	0.480550	−	0.876967i	$-0.340437\pi$
$311$	2.44843e118	0.961100	0.480550	+	0.876967i	$0.340437\pi$
$312$	3.86244e118	1.30172
$313$	−1.91407e118	−0.554117	−0.277058	−	0.960853i	$-0.589360\pi$
$313$	−1.91407e118	−0.554117	−0.277058	+	0.960853i	$0.589360\pi$
$314$	3.21230e118	0.799204
$315$	−1.11393e119	−2.38290
$316$	−1.70506e118	−0.313764
$317$	7.65791e118	1.21282	0.606409	−	0.795153i	$-0.292610\pi$
$317$	7.65791e118	1.21282	0.606409	+	0.795153i	$0.292610\pi$
$318$	−5.89189e117	−0.0803464
$319$	4.27548e118	0.502258
$320$	−3.16596e118	−0.320539
$321$	4.16499e119	3.63601
$322$	2.33388e118	0.175761
$323$	−9.36453e118	−0.608648
$324$	−3.86006e119	−2.16624
$325$	7.94570e118	0.385188
$326$	−2.24254e119	−0.939517
$327$	−6.25932e119	−2.26730
$328$	2.88741e119	0.904692
$329$	4.25259e119	1.15305
$330$	−2.01801e119	−0.473709
$331$	−7.45763e119	−1.51625	−0.758126	−	0.652108i	$-0.773885\pi$
$331$	−7.45763e119	−1.51625	−0.758126	+	0.652108i	$0.773885\pi$
$332$	−3.41597e119	−0.601805
$333$	2.21947e120	3.38959
$334$	−1.87900e119	−0.248868
$335$	7.14193e119	0.820705
$336$	3.01879e119	0.301104
$337$	−2.14150e120	−1.85480	−0.927401	−	0.374068i	$-0.877963\pi$
$337$	−2.14150e120	−1.85480	−0.927401	+	0.374068i	$0.877963\pi$
$338$	−3.75467e119	−0.282507
$339$	8.84431e119	0.578333
$340$	−3.22104e119	−0.183125
$341$	5.70086e119	0.281908
$342$	5.27767e120	2.27092
$343$	−7.10138e119	−0.265994
$344$	−1.89538e120	−0.618260
$345$	−1.03389e120	−0.293811
$346$	−4.33870e120	−1.07459
$347$	−1.97192e120	−0.425834	−0.212917	−	0.977070i	$-0.568296\pi$
$347$	−1.97192e120	−0.425834	−0.212917	+	0.977070i	$0.568296\pi$
$348$	−5.31521e120	−1.00117
$349$	9.46806e120	1.55616	0.778078	−	0.628167i	$-0.216195\pi$
$349$	9.46806e120	1.55616	0.778078	+	0.628167i	$0.216195\pi$
$350$	−2.90493e120	−0.416776
$351$	−1.75146e121	−2.19438
$352$	5.99801e120	0.656494
$353$	9.73961e120	0.931629	0.465814	−	0.884882i	$-0.345761\pi$
$353$	9.73961e120	0.931629	0.465814	+	0.884882i	$0.345761\pi$
$354$	1.49203e121	1.24773
$355$	−5.65723e120	−0.413768
$356$	1.53735e121	0.983780
$357$	−1.83847e121	−1.02971
$358$	−2.21197e120	−0.108476
$359$	−2.47022e121	−1.06108	−0.530541	−	0.847660i	$-0.678011\pi$
$359$	−2.47022e121	−1.06108	−0.530541	+	0.847660i	$0.678011\pi$
$360$	4.52642e121	1.70367
$361$	3.87227e121	1.27754
$362$	−7.15484e120	−0.206987
$363$	−4.43551e121	−1.12559
$364$	2.87831e121	0.640946
$365$	2.26130e121	0.442025
$366$	−5.47192e121	−0.939266
$367$	5.30267e121	0.799569	0.399785	−	0.916609i	$-0.369085\pi$
$367$	5.30267e121	0.799569	0.399785	+	0.916609i	$0.369085\pi$
$368$	2.02742e120	0.0268640
$369$	−2.11863e122	−2.46776
$370$	−4.92748e121	−0.504711
$371$	−1.09479e121	−0.0986442
$372$	−7.08722e121	−0.561936
$373$	9.90937e121	0.691634	0.345817	−	0.938302i	$-0.387602\pi$
$373$	9.90937e121	0.691634	0.345817	+	0.938302i	$0.387602\pi$
$374$	−2.40999e121	−0.148120
$375$	3.66927e122	1.98653
$376$	−1.72803e122	−0.824381
$377$	−1.33305e122	−0.560574
$378$	6.40329e122	2.37434
$379$	1.31454e122	0.429945	0.214972	−	0.976620i	$-0.431034\pi$
$379$	1.31454e122	0.429945	0.214972	+	0.976620i	$0.431034\pi$
$380$	2.37448e122	0.685246
$381$	−2.80640e122	−0.714848
$382$	−4.01643e122	−0.903297
$383$	1.20580e122	0.239516	0.119758	−	0.992803i	$-0.461788\pi$
$383$	1.20580e122	0.239516	0.119758	+	0.992803i	$0.461788\pi$
$384$	−8.19136e122	−1.43755
$385$	−3.74974e122	−0.581590
$386$	3.34618e121	0.0458831
$387$	1.39074e123	1.68645
$388$	5.28036e122	0.566443
$389$	−1.21812e123	−1.15633	−0.578167	−	0.815918i	$-0.696232\pi$
$389$	−1.21812e123	−1.15633	−0.578167	+	0.815918i	$0.696232\pi$
$390$	6.29195e122	0.528709
$391$	−1.23471e122	−0.0918692
$392$	−1.16765e123	−0.769531
$393$	−7.68096e122	−0.448507
$394$	−5.09141e122	−0.263492
$395$	−6.92574e122	−0.317763
$396$	−2.75245e123	−1.11995
$397$	7.23754e122	0.261241	0.130621	−	0.991432i	$-0.458303\pi$
$397$	7.23754e122	0.261241	0.130621	+	0.991432i	$0.458303\pi$
$398$	−1.84208e123	−0.590015
$399$	1.35527e124	3.85314
$400$	−2.52348e122	−0.0637016
$401$	7.18701e123	1.61135	0.805676	−	0.592356i	$-0.201802\pi$
$401$	7.18701e123	1.61135	0.805676	+	0.592356i	$0.201802\pi$
$402$	−6.64309e123	−1.32322
$403$	−1.77747e123	−0.314639
$404$	3.96179e123	0.623414
$405$	−1.56791e124	−2.19385
$406$	4.87360e123	0.606545
$407$	7.47124e123	0.827291
$408$	7.47055e123	0.736199
$409$	−1.32614e124	−1.16341	−0.581704	−	0.813400i	$-0.697614\pi$
$409$	−1.32614e124	−1.16341	−0.581704	+	0.813400i	$0.697614\pi$
$410$	4.70362e123	0.367451
$411$	−3.95860e124	−2.75458
$412$	5.21502e123	0.323324
$413$	2.77239e124	1.53189
$414$	6.95861e123	0.342773
$415$	−1.38752e124	−0.609475
$416$	−1.87012e124	−0.732717
$417$	−1.39301e124	−0.486957
$418$	1.77659e124	0.554259
$419$	−4.30372e124	−1.19861	−0.599305	−	0.800521i	$-0.704556\pi$
$419$	−4.30372e124	−1.19861	−0.599305	+	0.800521i	$0.704556\pi$
$420$	4.66163e124	1.15930
$421$	3.32481e124	0.738530	0.369265	−	0.929324i	$-0.379610\pi$
$421$	3.32481e124	0.738530	0.369265	+	0.929324i	$0.379610\pi$
$422$	−3.78977e123	−0.0752094
$423$	1.26794e125	2.24870
$424$	4.44866e123	0.0705263
$425$	1.53682e124	0.217846
$426$	5.26209e124	0.667117
$427$	−1.01676e125	−1.15317
$428$	−1.26121e125	−1.27999
$429$	−9.54011e124	−0.866626
$430$	−3.08760e124	−0.251113
$431$	−2.01518e124	−0.146772	−0.0733861	−	0.997304i	$-0.523381\pi$
$431$	−2.01518e124	−0.146772	−0.0733861	+	0.997304i	$0.523381\pi$
$432$	5.56248e124	0.362903
$433$	2.41699e124	0.141286	0.0706430	−	0.997502i	$-0.477495\pi$
$433$	2.41699e124	0.141286	0.0706430	+	0.997502i	$0.477495\pi$
$434$	6.49838e124	0.340442
$435$	−2.15897e125	−1.01393
$436$	1.89540e125	0.798163
$437$	9.10202e124	0.343771
$438$	−2.10335e125	−0.712676
$439$	−2.94011e125	−0.893921	−0.446961	−	0.894554i	$-0.647494\pi$
$439$	−2.94011e125	−0.893921	−0.446961	+	0.894554i	$0.647494\pi$
$440$	1.52370e125	0.415811
$441$	8.56766e125	2.09908
$442$	7.51410e124	0.165318
$443$	−9.53250e125	−1.88378	−0.941889	−	0.335924i	$-0.890951\pi$
$443$	−9.53250e125	−1.88378	−0.941889	+	0.335924i	$0.890951\pi$
$444$	−9.28813e125	−1.64906
$445$	6.24452e125	0.996319
$446$	3.71758e125	0.533156
$447$	1.50121e126	1.93568
$448$	5.47190e125	0.634501
$449$	9.58358e125	0.999600	0.499800	−	0.866141i	$-0.333407\pi$
$449$	9.58358e125	0.999600	0.499800	+	0.866141i	$0.333407\pi$
$450$	−8.66124e125	−0.812803
$451$	−7.13181e125	−0.602302
$452$	−2.67816e125	−0.203592
$453$	−1.00019e126	−0.684569
$454$	5.59989e125	0.345165
$455$	1.16913e126	0.649116
$456$	−5.50712e126	−2.75483
$457$	−8.93478e125	−0.402777	−0.201388	−	0.979511i	$-0.564545\pi$
$457$	−8.93478e125	−0.402777	−0.201388	+	0.979511i	$0.564545\pi$
$458$	9.25564e125	0.376094
$459$	−3.38760e126	−1.24105
$460$	3.13074e125	0.103431
$461$	2.72707e126	0.812648	0.406324	−	0.913729i	$-0.366810\pi$
$461$	2.72707e126	0.812648	0.406324	+	0.913729i	$0.366810\pi$
$462$	3.48784e126	0.937696
$463$	6.50980e126	1.57932	0.789660	−	0.613544i	$-0.210257\pi$
$463$	6.50980e126	1.57932	0.789660	+	0.613544i	$0.210257\pi$
$464$	4.23365e125	0.0927066
$465$	−2.87874e126	−0.569098
$466$	1.47638e125	0.0263552
$467$	−3.39970e126	−0.548137	−0.274069	−	0.961710i	$-0.588370\pi$
$467$	−3.39970e126	−0.548137	−0.274069	+	0.961710i	$0.588370\pi$
$468$	8.58188e126	1.24998
$469$	−1.23438e127	−1.62457
$470$	−2.81498e126	−0.334832
$471$	2.45949e127	2.64456
$472$	−1.12655e127	−1.09523
$473$	4.68154e126	0.411609
$474$	6.44200e126	0.512329
$475$	−1.13291e127	−0.815171
$476$	5.56709e126	0.362492
$477$	−3.26420e126	−0.192378
$478$	1.24525e126	0.0664401
$479$	−2.63247e127	−1.27182	−0.635911	−	0.771763i	$-0.719375\pi$
$479$	−2.63247e127	−1.27182	−0.635911	+	0.771763i	$0.719375\pi$
$480$	−3.02879e127	−1.32529
$481$	−2.32946e127	−0.923344
$482$	5.58862e125	0.0200711
$483$	1.78693e127	0.581592
$484$	1.34312e127	0.396243
$485$	2.14481e127	0.573663
$486$	7.29093e127	1.76832
$487$	1.28035e127	0.281645	0.140823	−	0.990035i	$-0.455025\pi$
$487$	1.28035e127	0.281645	0.140823	+	0.990035i	$0.455025\pi$
$488$	4.13157e127	0.824467
$489$	−1.71700e128	−3.10885
$490$	−1.90212e127	−0.312553
$491$	1.17215e128	1.74829	0.874145	−	0.485664i	$-0.161422\pi$
$491$	1.17215e128	1.74829	0.874145	+	0.485664i	$0.161422\pi$
$492$	8.86617e127	1.20059
$493$	−2.57833e127	−0.317037
$494$	−5.53922e127	−0.618612
$495$	−1.11801e128	−1.13423
$496$	5.64508e126	0.0520344
$497$	9.77769e127	0.819045
$498$	1.29061e128	0.982656
$499$	1.23344e128	0.853769	0.426885	−	0.904306i	$-0.359611\pi$
$499$	1.23344e128	0.853769	0.426885	+	0.904306i	$0.359611\pi$
$500$	−1.11110e128	−0.699323
$501$	−1.43865e128	−0.823502
$502$	−3.90440e127	−0.203296
$503$	2.66821e128	1.26398	0.631991	−	0.774976i	$-0.282238\pi$
$503$	2.66821e128	1.26398	0.631991	+	0.774976i	$0.282238\pi$
$504$	−7.82325e128	−3.37238
$505$	1.60923e128	0.631360
$506$	2.34243e127	0.0836598
$507$	−2.87476e128	−0.934812
$508$	8.49812e127	0.251650
$509$	−1.41380e128	−0.381324	−0.190662	−	0.981656i	$-0.561063\pi$
$509$	−1.41380e128	−0.381324	−0.190662	+	0.981656i	$0.561063\pi$
$510$	1.21696e128	0.299015
$511$	−3.90832e128	−0.874979
$512$	1.14868e128	0.234356
$513$	2.49726e129	4.64396
$514$	−1.48372e128	−0.251537
$515$	2.11827e128	0.327445
$516$	−5.82003e128	−0.820473
$517$	4.26818e128	0.548835
$518$	8.51643e128	0.999065
$519$	−3.32192e129	−3.55582
$520$	−4.75073e128	−0.464090
$521$	7.36119e128	0.656381	0.328190	−	0.944612i	$-0.393561\pi$
$521$	7.36119e128	0.656381	0.328190	+	0.944612i	$0.393561\pi$
$522$	1.45310e129	1.18289
$523$	9.21109e127	0.0684669	0.0342335	−	0.999414i	$-0.489101\pi$
$523$	9.21109e127	0.0684669	0.0342335	+	0.999414i	$0.489101\pi$
$524$	2.32589e128	0.157889
$525$	−2.22415e129	−1.37911
$526$	−7.37413e128	−0.417723
$527$	−3.43790e128	−0.177946
$528$	3.02985e128	0.143321
$529$	−2.19282e129	−0.948111
$530$	7.24692e127	0.0286451
$531$	8.26608e129	2.98751
$532$	−4.10393e129	−1.35643
$533$	2.22363e129	0.672233
$534$	−5.80836e129	−1.60636
$535$	−5.12287e129	−1.29631
$536$	5.01586e129	1.16150
$537$	−1.69359e129	−0.358947
$538$	4.07806e129	0.791217
$539$	2.88407e129	0.512318
$540$	8.58961e129	1.39724
$541$	8.43709e128	0.125696	0.0628481	−	0.998023i	$-0.479982\pi$
$541$	8.43709e128	0.125696	0.0628481	+	0.998023i	$0.479982\pi$
$542$	6.74304e129	0.920216
$543$	−5.47810e129	−0.684917
$544$	−3.61710e129	−0.414394
$545$	7.69886e129	0.808337
$546$	−1.08747e130	−1.04657
$547$	−1.12457e130	−0.992172	−0.496086	−	0.868273i	$-0.665230\pi$
$547$	−1.12457e130	−0.992172	−0.496086	+	0.868273i	$0.665230\pi$
$548$	1.19871e130	0.969701
$549$	−3.03154e130	−2.24893
$550$	−2.91557e129	−0.198379
$551$	1.90068e130	1.18634
$552$	−7.26113e129	−0.415813
$553$	1.19701e130	0.629006
$554$	1.79770e130	0.866968
$555$	−3.77272e130	−1.67008
$556$	4.21819e129	0.171425
$557$	−5.73188e129	−0.213883	−0.106941	−	0.994265i	$-0.534106\pi$
$557$	−5.73188e129	−0.213883	−0.106941	+	0.994265i	$0.534106\pi$
$558$	1.93754e130	0.663935
$559$	−1.45966e130	−0.459399
$560$	−3.71305e129	−0.107350
$561$	−1.84520e130	−0.490127
$562$	−8.75933e128	−0.0213794
$563$	7.23872e130	1.62373	0.811864	−	0.583847i	$-0.198453\pi$
$563$	7.23872e130	1.62373	0.811864	+	0.583847i	$0.198453\pi$
$564$	−5.30614e130	−1.09401
$565$	−1.08783e130	−0.206187
$566$	3.34964e129	0.0583737
$567$	2.70990e131	4.34268
$568$	−3.97313e130	−0.585581
$569$	9.75582e130	1.32261	0.661304	−	0.750118i	$-0.270003\pi$
$569$	9.75582e130	1.32261	0.661304	+	0.750118i	$0.270003\pi$
$570$	−8.97116e130	−1.11890
$571$	−1.13086e131	−1.29775	−0.648876	−	0.760894i	$-0.724761\pi$
$571$	−1.13086e131	−1.29775	−0.648876	+	0.760894i	$0.724761\pi$
$572$	2.88886e130	0.305081
$573$	−3.07518e131	−2.98900
$574$	−8.12952e130	−0.727361
$575$	−1.49374e130	−0.123042
$576$	1.63148e131	1.23741
$577$	−8.80595e130	−0.615071	−0.307536	−	0.951537i	$-0.599504\pi$
$577$	−8.80595e130	−0.615071	−0.307536	+	0.951537i	$0.599504\pi$
$578$	−7.48179e130	−0.481319
$579$	2.56200e130	0.151827
$580$	6.53762e130	0.356936
$581$	2.39813e131	1.20644
$582$	−1.99501e131	−0.924916
$583$	−1.09881e130	−0.0469532
$584$	1.58813e131	0.625572
$585$	3.48585e131	1.26592
$586$	9.04424e130	0.302856
$587$	−1.79188e131	−0.553348	−0.276674	−	0.960964i	$-0.589232\pi$
$587$	−1.79188e131	−0.553348	−0.276674	+	0.960964i	$0.589232\pi$
$588$	−3.58544e131	−1.02122
$589$	2.53434e131	0.665869
$590$	−1.83517e131	−0.444842
$591$	−3.89823e131	−0.871891
$592$	7.39814e130	0.152701
$593$	8.32855e131	1.58662	0.793308	−	0.608821i	$-0.208357\pi$
$593$	8.32855e131	1.58662	0.793308	+	0.608821i	$0.208357\pi$
$594$	6.42676e131	1.13015
$595$	2.26128e131	0.367112
$596$	−4.54583e131	−0.681421
$597$	−1.41039e132	−1.95235
$598$	−7.30346e130	−0.0933732
$599$	1.35667e132	1.60214	0.801069	−	0.598572i	$-0.204265\pi$
$599$	1.35667e132	1.60214	0.801069	+	0.598572i	$0.204265\pi$
$600$	9.03778e131	0.986001
$601$	−1.04918e132	−1.05758	−0.528792	−	0.848752i	$-0.677355\pi$
$601$	−1.04918e132	−1.05758	−0.528792	+	0.848752i	$0.677355\pi$
$602$	5.33647e131	0.497074
$603$	−3.68038e132	−3.16826
$604$	3.02869e131	0.240991
$605$	5.45559e131	0.401293
$606$	−1.49683e132	−1.01794
$607$	−2.82460e132	−1.77621	−0.888104	−	0.459643i	$-0.847977\pi$
$607$	−2.82460e132	−1.77621	−0.888104	+	0.459643i	$0.847977\pi$
$608$	2.66644e132	1.55064
$609$	3.73147e132	2.00705
$610$	6.73037e131	0.334867
$611$	−1.33077e132	−0.612558
$612$	1.65987e132	0.706937
$613$	3.79050e131	0.149391	0.0746954	−	0.997206i	$-0.476202\pi$
$613$	3.79050e131	0.149391	0.0746954	+	0.997206i	$0.476202\pi$
$614$	−2.38844e131	−0.0871199
$615$	3.60132e132	1.21589
$616$	−2.63349e132	−0.823090
$617$	−7.28475e131	−0.210799	−0.105400	−	0.994430i	$-0.533612\pi$
$617$	−7.28475e131	−0.210799	−0.105400	+	0.994430i	$0.533612\pi$
$618$	−1.97032e132	−0.527940
$619$	3.61647e132	0.897385	0.448692	−	0.893686i	$-0.351890\pi$
$619$	3.61647e132	0.897385	0.448692	+	0.893686i	$0.351890\pi$
$620$	8.71716e131	0.200341
$621$	3.29263e132	0.700959
$622$	2.80118e132	0.552455
$623$	−1.07927e133	−1.97219
$624$	−9.44677e131	−0.159961
$625$	−1.07109e132	−0.168084
$626$	−2.18983e132	−0.318515
$627$	1.36024e133	1.83404
$628$	−7.44764e132	−0.930970
$629$	−4.50553e132	−0.522204
$630$	−1.27442e133	−1.36973
$631$	−5.79307e131	−0.0577450	−0.0288725	−	0.999583i	$-0.509192\pi$
$631$	−5.79307e131	−0.0577450	−0.0288725	+	0.999583i	$0.509192\pi$
$632$	−4.86402e132	−0.449712
$633$	−2.90164e132	−0.248867
$634$	8.76121e132	0.697147
$635$	3.45183e132	0.254857
$636$	1.36602e132	0.0935932
$637$	−8.99224e132	−0.571801
$638$	4.89146e132	0.288706
$639$	2.91529e133	1.59731
$640$	1.00752e133	0.512515
$641$	−2.37379e133	−1.12121	−0.560604	−	0.828084i	$-0.689431\pi$
$641$	−2.37379e133	−1.12121	−0.560604	+	0.828084i	$0.689431\pi$
$642$	4.76505e133	2.09004
$643$	4.51189e133	1.83797	0.918983	−	0.394296i	$-0.129012\pi$
$643$	4.51189e133	1.83797	0.918983	+	0.394296i	$0.129012\pi$
$644$	−5.41104e132	−0.204740
$645$	−2.36402e133	−0.830931
$646$	−1.07137e133	−0.349861
$647$	−6.09518e133	−1.84941	−0.924705	−	0.380684i	$-0.875688\pi$
$647$	−6.09518e133	−1.84941	−0.924705	+	0.380684i	$0.875688\pi$
$648$	−1.10116e134	−3.10483
$649$	2.78255e133	0.729156
$650$	9.09046e132	0.221412
$651$	4.97548e133	1.12652
$652$	5.19928e133	1.09442
$653$	8.32773e133	1.62986	0.814931	−	0.579558i	$-0.196775\pi$
$653$	8.32773e133	1.62986	0.814931	+	0.579558i	$0.196775\pi$
$654$	−7.16112e133	−1.30328
$655$	9.44745e132	0.159902
$656$	−7.06204e132	−0.111173
$657$	−1.16529e134	−1.70640
$658$	4.86527e133	0.662792
$659$	−7.29231e133	−0.924289	−0.462145	−	0.886805i	$-0.652920\pi$
$659$	−7.29231e133	−0.924289	−0.462145	+	0.886805i	$0.652920\pi$
$660$	4.67871e133	0.551809
$661$	1.56158e133	0.171393	0.0856967	−	0.996321i	$-0.472688\pi$
$661$	1.56158e133	0.171393	0.0856967	+	0.996321i	$0.472688\pi$
$662$	−8.53208e133	−0.871566
$663$	5.75316e133	0.547034
$664$	−9.74474e133	−0.862554
$665$	−1.66696e134	−1.37372
$666$	2.53923e134	1.94839
$667$	2.50605e133	0.179066
$668$	4.35642e133	0.289899
$669$	2.84636e134	1.76421
$670$	8.17088e133	0.471754
$671$	−1.02049e134	−0.548892
$672$	5.23482e134	2.62338
$673$	−6.13539e133	−0.286501	−0.143251	−	0.989686i	$-0.545755\pi$
$673$	−6.13539e133	−0.286501	−0.143251	+	0.989686i	$0.545755\pi$
$674$	−2.45003e134	−1.06617
$675$	−4.09827e134	−1.66216
$676$	8.70512e133	0.329084
$677$	−3.48029e134	−1.22646	−0.613230	−	0.789905i	$-0.710130\pi$
$677$	−3.48029e134	−1.22646	−0.613230	+	0.789905i	$0.710130\pi$
$678$	1.01185e134	0.332435
$679$	−3.70700e134	−1.13555
$680$	−9.18865e133	−0.262469
$681$	4.28755e134	1.14215
$682$	6.52220e133	0.162045
$683$	6.68574e133	0.154941	0.0774705	−	0.996995i	$-0.475316\pi$
$683$	6.68574e133	0.154941	0.0774705	+	0.996995i	$0.475316\pi$
$684$	−1.22362e135	−2.64533
$685$	4.86901e134	0.982061
$686$	−8.12449e133	−0.152898
$687$	7.08657e134	1.24449
$688$	4.63574e133	0.0759746
$689$	3.42597e133	0.0524047
$690$	−1.18285e134	−0.168887
$691$	−1.47122e135	−1.96097	−0.980483	−	0.196603i	$-0.937009\pi$
$691$	−1.47122e135	−1.96097	−0.980483	+	0.196603i	$0.937009\pi$
$692$	1.00592e135	1.25176
$693$	1.93232e135	2.24518
$694$	−2.25602e134	−0.244776
$695$	1.71338e134	0.173610
$696$	−1.51627e135	−1.43495
$697$	4.30084e134	0.380186
$698$	1.08322e135	0.894504
$699$	1.13039e134	0.0872091
$700$	6.73500e134	0.485491
$701$	−2.06509e134	−0.139102	−0.0695511	−	0.997578i	$-0.522157\pi$
$701$	−2.06509e134	−0.139102	−0.0695511	+	0.997578i	$0.522157\pi$
$702$	−2.00380e135	−1.26137
$703$	3.32137e135	1.95407
$704$	5.49195e134	0.302013
$705$	−2.15528e135	−1.10795
$706$	1.11428e135	0.535515
$707$	−2.78132e135	−1.24976
$708$	−3.45923e135	−1.45345
$709$	−4.71684e135	−1.85334	−0.926670	−	0.375876i	$-0.877342\pi$
$709$	−4.71684e135	−1.85334	−0.926670	+	0.375876i	$0.877342\pi$
$710$	−6.47228e134	−0.237840
$711$	3.56898e135	1.22670
$712$	4.38559e135	1.41003
$713$	3.34153e134	0.100506
$714$	−2.10334e135	−0.591894
$715$	1.17342e135	0.308969
$716$	5.12840e134	0.126361
$717$	9.53422e134	0.219849
$718$	−2.82611e135	−0.609926
$719$	7.04696e135	1.42357	0.711786	−	0.702397i	$-0.247887\pi$
$719$	7.04696e135	1.42357	0.711786	+	0.702397i	$0.247887\pi$
$720$	−1.10707e135	−0.209355
$721$	−3.66113e135	−0.648171
$722$	4.43016e135	0.734349
$723$	4.27892e134	0.0664149
$724$	1.65883e135	0.241113
$725$	−3.11923e135	−0.424612
$726$	−5.07454e135	−0.647004
$727$	−1.26918e136	−1.51579	−0.757895	−	0.652377i	$-0.773772\pi$
$727$	−1.26918e136	−1.51579	−0.757895	+	0.652377i	$0.773772\pi$
$728$	8.21095e135	0.918656
$729$	2.49586e136	2.61615
$730$	2.58709e135	0.254083
$731$	−2.82320e135	−0.259817
$732$	1.26865e136	1.09412
$733$	−1.90987e136	−1.54371	−0.771854	−	0.635799i	$-0.780671\pi$
$733$	−1.90987e136	−1.54371	−0.771854	+	0.635799i	$0.780671\pi$
$734$	6.06663e135	0.459605
$735$	−1.45636e136	−1.03424
$736$	3.51571e135	0.234054
$737$	−1.23890e136	−0.773270
$738$	−2.42387e136	−1.41851
$739$	1.05861e136	0.580930	0.290465	−	0.956886i	$-0.406190\pi$
$739$	1.05861e136	0.580930	0.290465	+	0.956886i	$0.406190\pi$
$740$	1.14242e136	0.587923
$741$	−4.24110e136	−2.04698
$742$	−1.25252e135	−0.0567023
$743$	5.62340e135	0.238798	0.119399	−	0.992846i	$-0.461903\pi$
$743$	5.62340e135	0.238798	0.119399	+	0.992846i	$0.461903\pi$
$744$	−2.02177e136	−0.805411
$745$	−1.84646e136	−0.690106
$746$	1.13370e136	0.397562
$747$	7.15020e136	2.35282
$748$	5.58750e135	0.172541
$749$	8.85413e136	2.56602
$750$	4.19791e136	1.14189
$751$	−2.83733e136	−0.724457	−0.362228	−	0.932089i	$-0.617984\pi$
$751$	−2.83733e136	−0.724457	−0.362228	+	0.932089i	$0.617984\pi$
$752$	4.22642e135	0.101304
$753$	−2.98940e136	−0.672703
$754$	−1.52511e136	−0.322227
$755$	1.23021e136	0.244062
$756$	−1.48459e137	−2.76580
$757$	1.18088e136	0.206610	0.103305	−	0.994650i	$-0.467058\pi$
$757$	1.18088e136	0.206610	0.103305	+	0.994650i	$0.467058\pi$
$758$	1.50393e136	0.247139
$759$	1.79348e136	0.276829
$760$	6.77366e136	0.982150
$761$	3.27266e136	0.445789	0.222894	−	0.974843i	$-0.428449\pi$
$761$	3.27266e136	0.445789	0.222894	+	0.974843i	$0.428449\pi$
$762$	−3.21073e136	−0.410906
$763$	−1.33063e137	−1.60009
$764$	9.31200e136	1.05222
$765$	6.74217e136	0.715948
$766$	1.37953e136	0.137678
$767$	−8.67572e136	−0.813816
$768$	−1.95681e137	−1.72541
$769$	1.30590e137	1.08245	0.541226	−	0.840877i	$-0.317960\pi$
$769$	1.30590e137	1.08245	0.541226	+	0.840877i	$0.317960\pi$
$770$	−4.28998e136	−0.334307
$771$	−1.13601e137	−0.832334
$772$	−7.75804e135	−0.0534479
$773$	−1.61886e137	−1.04878	−0.524389	−	0.851479i	$-0.675706\pi$
$773$	−1.61886e137	−1.04878	−0.524389	+	0.851479i	$0.675706\pi$
$774$	1.59111e137	0.969401
$775$	−4.15913e136	−0.238326
$776$	1.50633e137	0.811872
$777$	6.52060e137	3.30589
$778$	−1.39362e137	−0.664680
$779$	−3.17048e137	−1.42264
$780$	−1.45877e137	−0.615878
$781$	9.81352e136	0.389853
$782$	−1.41260e136	−0.0528079
$783$	6.87568e137	2.41898
$784$	2.85585e136	0.0945634
$785$	−3.02514e137	−0.942836
$786$	−8.78758e136	−0.257809
$787$	4.12249e136	0.113857	0.0569286	−	0.998378i	$-0.481869\pi$
$787$	4.12249e136	0.113857	0.0569286	+	0.998378i	$0.481869\pi$
$788$	1.18043e137	0.306934
$789$	−5.64600e137	−1.38224
$790$	−7.92355e136	−0.182655
$791$	1.88016e137	0.408143
$792$	−7.85192e137	−1.60520
$793$	3.18177e137	0.612622
$794$	8.28027e136	0.150166
$795$	5.54860e136	0.0947861
$796$	4.27082e137	0.687291
$797$	−7.57575e137	−1.14856	−0.574282	−	0.818658i	$-0.694719\pi$
$797$	−7.57575e137	−1.14856	−0.574282	+	0.818658i	$0.694719\pi$
$798$	1.55053e138	2.21485
$799$	−2.57392e137	−0.346437
$800$	−4.37592e137	−0.555003
$801$	−3.21793e138	−3.84620
$802$	8.22246e137	0.926231
$803$	−3.92265e137	−0.416477
$804$	1.54018e138	1.54138
$805$	−2.19789e137	−0.207349
$806$	−2.03356e137	−0.180860
$807$	3.12236e138	2.61813
$808$	1.13018e138	0.893527
$809$	−1.43006e138	−1.06610	−0.533051	−	0.846083i	$-0.678955\pi$
$809$	−1.43006e138	−1.06610	−0.533051	+	0.846083i	$0.678955\pi$
$810$	−1.79380e138	−1.26106
$811$	−4.32850e137	−0.286977	−0.143488	−	0.989652i	$-0.545832\pi$
$811$	−4.32850e137	−0.286977	−0.143488	+	0.989652i	$0.545832\pi$
$812$	−1.12993e138	−0.706547
$813$	5.16281e138	3.04498
$814$	8.54764e137	0.475540
$815$	2.11188e138	1.10837
$816$	−1.82715e137	−0.0904673
$817$	2.08120e138	0.972224
$818$	−1.51720e138	−0.668746
$819$	−6.02478e138	−2.50585
$820$	−1.09052e138	−0.428033
$821$	−1.65106e138	−0.611595	−0.305797	−	0.952097i	$-0.598923\pi$
$821$	−1.65106e138	−0.611595	−0.305797	+	0.952097i	$0.598923\pi$
$822$	−4.52893e138	−1.58338
$823$	−2.10906e138	−0.695981	−0.347991	−	0.937498i	$-0.613136\pi$
$823$	−2.10906e138	−0.695981	−0.347991	+	0.937498i	$0.613136\pi$
$824$	1.48769e138	0.463414
$825$	−2.23231e138	−0.656434
$826$	3.17182e138	0.880555
$827$	4.77571e138	1.25177	0.625887	−	0.779914i	$-0.284737\pi$
$827$	4.77571e138	1.25177	0.625887	+	0.779914i	$0.284737\pi$
$828$	−1.61334e138	−0.399286
$829$	−2.47120e138	−0.577522	−0.288761	−	0.957401i	$-0.593243\pi$
$829$	−2.47120e138	−0.577522	−0.288761	+	0.957401i	$0.593243\pi$
$830$	−1.58743e138	−0.350336
$831$	1.37641e139	2.86879
$832$	−1.71234e138	−0.337078
$833$	−1.73924e138	−0.323386
$834$	−1.59370e138	−0.279911
$835$	1.76952e138	0.293594
$836$	−4.11897e138	−0.645641
$837$	9.16792e138	1.35772
$838$	−4.92377e138	−0.688981
$839$	−1.42759e139	−1.88760	−0.943802	−	0.330512i	$-0.892778\pi$
$839$	−1.42759e139	−1.88760	−0.943802	+	0.330512i	$0.892778\pi$
$840$	1.32982e139	1.66160
$841$	−3.23543e138	−0.382052
$842$	3.80383e138	0.424519
$843$	−6.70658e137	−0.0707442
$844$	8.78650e137	0.0876092
$845$	3.53591e138	0.333279
$846$	1.45062e139	1.29259
$847$	−9.42920e138	−0.794352
$848$	−1.08806e137	−0.00866659
$849$	2.56465e138	0.193158
$850$	1.75824e138	0.125221
$851$	4.37923e138	0.294947
$852$	−1.22000e139	−0.777106
$853$	2.20829e139	1.33039	0.665193	−	0.746671i	$-0.268349\pi$
$853$	2.20829e139	1.33039	0.665193	+	0.746671i	$0.268349\pi$
$854$	−1.16325e139	−0.662862
$855$	−4.97017e139	−2.67905
$856$	−3.59785e139	−1.83459
$857$	1.71311e139	0.826409	0.413205	−	0.910638i	$-0.364409\pi$
$857$	1.71311e139	0.826409	0.413205	+	0.910638i	$0.364409\pi$
$858$	−1.09146e139	−0.498151
$859$	3.82863e139	1.65336	0.826681	−	0.562671i	$-0.190226\pi$
$859$	3.82863e139	1.65336	0.826681	+	0.562671i	$0.190226\pi$
$860$	7.15853e138	0.292515
$861$	−6.22436e139	−2.40683
$862$	−2.30551e138	−0.0843670
$863$	2.07564e139	0.718850	0.359425	−	0.933174i	$-0.382973\pi$
$863$	2.07564e139	0.718850	0.359425	+	0.933174i	$0.382973\pi$
$864$	9.64580e139	3.16181
$865$	4.08590e139	1.26772
$866$	2.76521e138	0.0812134
$867$	−5.72843e139	−1.59268
$868$	−1.50663e139	−0.396571
$869$	1.20140e139	0.299397
$870$	−2.47002e139	−0.582822
$871$	3.86277e139	0.863051
$872$	5.40699e139	1.14399
$873$	−1.10527e140	−2.21458
$874$	1.04134e139	0.197605
$875$	7.80030e139	1.40194
$876$	4.87658e139	0.830176
$877$	−9.49190e139	−1.53064	−0.765319	−	0.643651i	$-0.777419\pi$
$877$	−9.49190e139	−1.53064	−0.765319	+	0.643651i	$0.777419\pi$
$878$	−3.36370e139	−0.513840
$879$	6.92472e139	1.00214
$880$	−3.72666e138	−0.0510967
$881$	3.40666e139	0.442561	0.221280	−	0.975210i	$-0.428976\pi$
$881$	3.40666e139	0.442561	0.221280	+	0.975210i	$0.428976\pi$
$882$	9.80202e139	1.20659
$883$	−7.69675e139	−0.897788	−0.448894	−	0.893585i	$-0.648182\pi$
$883$	−7.69675e139	−0.897788	−0.448894	+	0.893585i	$0.648182\pi$
$884$	−1.74213e139	−0.192574
$885$	−1.40510e140	−1.47197
$886$	−1.09059e140	−1.08283
$887$	1.45856e138	0.0137262	0.00686311	−	0.999976i	$-0.497815\pi$
$887$	1.45856e138	0.0137262	0.00686311	+	0.999976i	$0.497815\pi$
$888$	−2.64962e140	−2.36357
$889$	−5.96598e139	−0.504485
$890$	7.14418e139	0.572700
$891$	2.71983e140	2.06705
$892$	−8.61912e139	−0.621058
$893$	1.89744e140	1.29635
$894$	1.71749e140	1.11266
$895$	2.08309e139	0.127972
$896$	−1.74136e140	−1.01451
$897$	−5.59189e139	−0.308971
$898$	1.09643e140	0.574586
$899$	6.97778e139	0.346842
$900$	2.00809e140	0.946811
$901$	6.62635e138	0.0296379
$902$	−8.15931e139	−0.346213
$903$	4.08586e140	1.64481
$904$	−7.63998e139	−0.291805
$905$	6.73796e139	0.244186
$906$	−1.14429e140	−0.393501
$907$	−3.03400e140	−0.990077	−0.495039	−	0.868871i	$-0.664846\pi$
$907$	−3.03400e140	−0.990077	−0.495039	+	0.868871i	$0.664846\pi$
$908$	−1.29832e140	−0.402072
$909$	−8.29269e140	−2.43731
$910$	1.33757e140	0.373122
$911$	1.96916e140	0.521384	0.260692	−	0.965422i	$-0.416049\pi$
$911$	1.96916e140	0.521384	0.260692	+	0.965422i	$0.416049\pi$
$912$	1.34693e140	0.338525
$913$	2.40692e140	0.574249
$914$	−1.02220e140	−0.231522
$915$	5.15310e140	1.10807
$916$	−2.14590e140	−0.438101
$917$	−1.63285e140	−0.316522
$918$	−3.87566e140	−0.713375
$919$	2.76791e140	0.483799	0.241900	−	0.970301i	$-0.422230\pi$
$919$	2.76791e140	0.483799	0.241900	+	0.970301i	$0.422230\pi$
$920$	8.93107e139	0.148246
$921$	−1.82871e140	−0.288279
$922$	3.11997e140	0.467123
$923$	−3.05976e140	−0.435117
$924$	−8.08647e140	−1.09230
$925$	−5.45073e140	−0.699395
$926$	7.44768e140	0.907819
$927$	−1.09159e141	−1.26407
$928$	7.34149e140	0.807710
$929$	2.70807e140	0.283083	0.141541	−	0.989932i	$-0.454794\pi$
$929$	2.70807e140	0.283083	0.141541	+	0.989932i	$0.454794\pi$
$930$	−3.29349e140	−0.327127
$931$	1.28213e141	1.21010
$932$	−3.42295e139	−0.0307004
$933$	2.14472e141	1.82807
$934$	−3.88951e140	−0.315078
$935$	2.26957e140	0.174740
$936$	2.44815e141	1.79158
$937$	3.38747e140	0.235638	0.117819	−	0.993035i	$-0.462410\pi$
$937$	3.38747e140	0.235638	0.117819	+	0.993035i	$0.462410\pi$
$938$	−1.41222e141	−0.933828
$939$	−1.67664e141	−1.05396
$940$	6.52646e140	0.390036
$941$	−2.48262e141	−1.41060	−0.705298	−	0.708911i	$-0.749187\pi$
$941$	−2.48262e141	−1.41060	−0.705298	+	0.708911i	$0.749187\pi$
$942$	2.81384e141	1.52013
$943$	−4.18028e140	−0.214733
$944$	2.75533e140	0.134587
$945$	−6.03021e141	−2.80105
$946$	5.35603e140	0.236599
$947$	−3.57048e141	−1.50004	−0.750020	−	0.661415i	$-0.769956\pi$
$947$	−3.57048e141	−1.50004	−0.750020	+	0.661415i	$0.769956\pi$
$948$	−1.49356e141	−0.596798
$949$	1.22304e141	0.464832
$950$	−1.29613e141	−0.468573
$951$	6.70801e141	2.30685
$952$	1.58812e141	0.519552
$953$	−1.38191e141	−0.430098	−0.215049	−	0.976603i	$-0.568991\pi$
$953$	−1.38191e141	−0.430098	−0.215049	+	0.976603i	$0.568991\pi$
$954$	−3.73449e140	−0.110582
$955$	3.78241e141	1.06564
$956$	−2.88708e140	−0.0773942
$957$	3.74514e141	0.955325
$958$	−3.01173e141	−0.731063
$959$	−8.41537e141	−1.94397
$960$	−2.77325e141	−0.609685
$961$	−3.84886e141	−0.805324
$962$	−2.66507e141	−0.530753
$963$	2.63992e142	5.00429
$964$	−1.29571e140	−0.0233802
$965$	−3.15122e140	−0.0541291
$966$	2.04438e141	0.334309
$967$	−4.60228e141	−0.716499	−0.358250	−	0.933626i	$-0.616626\pi$
$967$	−4.60228e141	−0.716499	−0.358250	+	0.933626i	$0.616626\pi$
$968$	3.83153e141	0.567927
$969$	−8.20294e141	−1.15768
$970$	2.45382e141	0.329751
$971$	1.42645e142	1.82534	0.912670	−	0.408696i	$-0.134016\pi$
$971$	1.42645e142	1.82534	0.912670	+	0.408696i	$0.134016\pi$
$972$	−1.69038e142	−2.05986
$973$	−2.96132e141	−0.343657
$974$	1.46481e141	0.161894
$975$	6.96010e141	0.732650
$976$	−1.01050e141	−0.101314
$977$	6.70156e141	0.640006	0.320003	−	0.947417i	$-0.396316\pi$
$977$	6.70156e141	0.640006	0.320003	+	0.947417i	$0.396316\pi$
$978$	−1.96437e142	−1.78702
$979$	−1.08323e142	−0.938734
$980$	4.41002e141	0.364085
$981$	−3.96738e142	−3.12051
$982$	1.34103e142	1.00495
$983$	−1.38643e142	−0.989936	−0.494968	−	0.868911i	$-0.664820\pi$
$983$	−1.38643e142	−0.989936	−0.494968	+	0.868911i	$0.664820\pi$
$984$	2.52925e142	1.72078
$985$	4.79476e141	0.310846
$986$	−2.94979e141	−0.182238
$987$	3.72509e142	2.19317
$988$	1.28425e142	0.720603
$989$	2.74406e141	0.146747
$990$	−1.27909e142	−0.651971
$991$	1.77596e142	0.862850	0.431425	−	0.902149i	$-0.358011\pi$
$991$	1.77596e142	0.862850	0.431425	+	0.902149i	$0.358011\pi$
$992$	9.78904e141	0.453352
$993$	−6.53258e142	−2.88400
$994$	1.11864e142	0.470800
$995$	1.73475e142	0.696051
$996$	−2.99225e142	−1.14467
$997$	−3.21730e142	−1.17347	−0.586734	−	0.809779i	$-0.699587\pi$
$997$	−3.21730e142	−1.17347	−0.586734	+	0.809779i	$0.699587\pi$
$998$	1.41114e142	0.490760
$999$	1.20150e143	3.98440

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1.96.a.a.1.5	✓	8
3.2	odd	2		9.96.a.c.1.4		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1.96.a.a.1.5	✓	8	1.1	even	1	trivial
9.96.a.c.1.4		8	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:	\( k \)	\(=\)	\( 96 \)
Character orbit:	\([\chi]\)	\(=\)	1.a (trivial)

\(f(q)\)	\(=\)	\(q+1.14407e14 q^{2} +8.75958e22 q^{3} -2.65251e28 q^{4} -1.07741e33 q^{5} +1.00216e37 q^{6} +1.86215e40 q^{7} -7.56680e42 q^{8} +5.55214e45 q^{9} +O(q^{10})\)	\(q+1.14407e14 q^{2} +8.75958e22 q^{3} -2.65251e28 q^{4} -1.07741e33 q^{5} +1.00216e37 q^{6} +1.86215e40 q^{7} -7.56680e42 q^{8} +5.55214e45 q^{9} -1.23264e47 q^{10} +1.86898e49 q^{11} -2.32348e51 q^{12} -5.82728e52 q^{13} +2.13044e54 q^{14} -9.43769e55 q^{15} +1.85069e56 q^{16} -1.12709e58 q^{17} +6.35205e59 q^{18} +8.30862e60 q^{19} +2.85785e61 q^{20} +1.63117e63 q^{21} +2.13824e63 q^{22} +1.09549e64 q^{23} -6.62820e65 q^{24} -1.36353e66 q^{25} -6.66683e66 q^{26} +3.00562e68 q^{27} -4.93937e68 q^{28} +2.28760e69 q^{29} -1.07974e70 q^{30} +3.05026e70 q^{31} +3.20925e71 q^{32} +1.63715e72 q^{33} -1.28947e72 q^{34} -2.00631e73 q^{35} -1.47271e74 q^{36} +3.99750e74 q^{37} +9.50566e74 q^{38} -5.10446e75 q^{39} +8.15257e75 q^{40} -3.81589e76 q^{41} +1.86617e77 q^{42} +2.50487e77 q^{43} -4.95747e77 q^{44} -5.98195e78 q^{45} +1.25332e78 q^{46} +2.28370e79 q^{47} +1.62113e79 q^{48} +1.54313e80 q^{49} -1.55998e80 q^{50} -9.87281e80 q^{51} +1.54569e81 q^{52} -5.87919e80 q^{53} +3.43865e82 q^{54} -2.01366e82 q^{55} -1.40905e83 q^{56} +7.27800e83 q^{57} +2.61719e83 q^{58} +1.48881e84 q^{59} +2.50335e84 q^{60} -5.46013e84 q^{61} +3.48972e84 q^{62} +1.03389e86 q^{63} +2.93848e85 q^{64} +6.27839e85 q^{65} +1.87301e86 q^{66} -6.62877e86 q^{67} +2.98960e86 q^{68} +9.59605e86 q^{69} -2.29536e87 q^{70} +5.25075e87 q^{71} -4.20119e88 q^{72} -2.09882e88 q^{73} +4.57343e88 q^{74} -1.19440e89 q^{75} -2.20387e89 q^{76} +3.48032e89 q^{77} -5.83987e89 q^{78} +6.42811e89 q^{79} -1.99396e89 q^{80} +1.45525e91 q^{81} -4.36566e90 q^{82} +1.28783e91 q^{83} -4.32668e91 q^{84} +1.21434e91 q^{85} +2.86575e91 q^{86} +2.00385e92 q^{87} -1.41422e92 q^{88} -5.79584e92 q^{89} -6.84378e92 q^{90} -1.08513e93 q^{91} -2.90580e92 q^{92} +2.67190e93 q^{93} +2.61272e93 q^{94} -8.95182e93 q^{95} +2.81117e94 q^{96} -1.99071e94 q^{97} +1.76545e94 q^{98} +1.03768e95 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 5835659138280 q^{2} - 95\!\cdots\!80 q^{3}+ \cdots + 92\!\cdots\!36 q^{9}+O(q^{10}) \) 8 * q - 5835659138280 * q^2 - 9565982513916703570080 * q^3 + 208956598309707350371623569984 * q^4 + 1941568507475850402526904141070960 * q^5 + 10651800775920653731297343298528492576 * q^6 + 31232311735415758067806325356531573912000 * q^7 - 14761127603920085098561309094124598702287360 * q^8 + 9274438133561954597944854467482391143953072936 * q^9	\( 8 q - 5835659138280 q^{2} - 95\!\cdots\!80 q^{3}+ \cdots + 30\!\cdots\!72 q^{99}+O(q^{100}) \) 8 * q - 5835659138280 * q^2 - 9565982513916703570080 * q^3 + 208956598309707350371623569984 * q^4 + 1941568507475850402526904141070960 * q^5 + 10651800775920653731297343298528492576 * q^6 + 31232311735415758067806325356531573912000 * q^7 - 14761127603920085098561309094124598702287360 * q^8 + 9274438133561954597944854467482391143953072936 * q^9 - 355384205613899841010372205704985147108657534640 * q^10 + 53080108095821756826858489331993621982645992125216 * q^11 + 1065031032961827853079380844579017283696993846403840 * q^12 + 117293508281179239843264964380833942161194396039342640 * q^13 + 8850886815767090581799564344683737269936151852930265408 * q^14 + 187812376414067333691564154745798290909917959215041625920 * q^15 + 9517116971431211282501221161054789131283343644054948220928 * q^16 - 13655041265063090981829171372625119189425374473948274915440 * q^17 - 1790266901749030205580776247252673430153004351197542602854280 * q^18 - 5232175975370167369536369873888207394303637759872553281713440 * q^19 + 136065209104116992530471413843386338746929879497239386344644480 * q^20 + 1346571177849118208545064341536207444072396945735327627682503936 * q^21 - 20365500099170357171519767897869972385636855003458825137197491360 * q^22 - 7129054072165937484825035531327773489156117409617881426435061440 * q^23 + 288860682603965362857322541557744811472884721216169744526242990080 * q^24 + 8177806376085721196783759852983887433280593317172609841487587996600 * q^25 - 69072273179717436642550386629266724895941590936463282023015399323504 * q^26 + 64049503386294800673569522679695786753122795388715525750679249767360 * q^27 + 303354815522537415860404332264897505740906926923909508834765584637440 * q^28 + 7715272198415359380593902919630157934289467091855373333108685675435440 * q^29 - 62913685170287068298704199843316213881225133796680396150164526710345280 * q^30 + 48520677903801540370519073843711920597057994260920479636592334181199616 * q^31 + 911347110324473008775326747695560179887781374647708612161794209209221120 * q^32 - 1535322742350198888271103254480947687741587903792512354063710702943493760 * q^33 - 16409772766982648656985219134942803587399227958333745923026675404562961232 * q^34 + 58800416933815614414155173269063056087887600285328689246425433374756677760 * q^35 + 51665208441213434468989869710710146210173003797753332160946711226240568128 * q^36 - 181116344963557296256979160619337453378797091102974834966000994855965247120 * q^37 - 1676466315180766681626408275142200947978975839695306622930354052184199692640 * q^38 + 465478714369259758144024065308323445042256641733578800363164365799686202432 * q^39 + 39028182173606372825635252450401491624189758401191157685601991729209269171200 * q^40 - 87541390126560450267544465567119030351560808726320656469732601708266148308784 * q^41 - 157435820560022140348706044721413472652300880194209574021901207450891596867840 * q^42 + 360093033489081253538156425248276463103949347025569853491672117723107522861600 * q^43 + 1942224484251042670482996667732829207493398934442399145050649033803969221005568 * q^44 - 1611554371538604569657837598986488298494511731253236200388961579880024486332880 * q^45 - 19332434944442851407749457669991401004991143268030327859543986888040547882373184 * q^46 + 38672453335683563852366980570346257355794761888911368752480783496161211070336640 * q^47 + 93863838769591236482712272126012963144755254935077324856132076191099747033333760 * q^48 + 265668043093542548841947390620517395072194945166225827717144824590425137465244744 * q^49 - 1423963459280866882678609595824694565889878038511273700600414891648711070234429400 * q^50 + 2434476695354895883532253554814552047229450451049452072207263289482820720406821056 * q^51 + 15678746704556392183126484026214298441253990030076674973212546269606119207477104000 * q^52 - 2922690482809426126710991861168746969788895886261814706776237561500358605037675280 * q^53 + 44393564079821957628952458152403809172972567715888333832276777433089826621820157760 * q^54 + 77963865832782922646862204005771036172886494149999882551809226033579503680996905920 * q^55 + 723822110434297992891221750986765045769194525611914833690699475848521019635777392640 * q^56 + 1459603943948321457517074656112276013643674313689343212415092604638087582879924782720 * q^57 + 2398120500739528001867383787619453843290390222445601081527493426426916763954522209040 * q^58 + 2444569112045817337560949868287606200158569651761097862873350630901953709318185022880 * q^59 + 41015921945833187827435663222575462810347191746192004435818365735996703011205515880960 * q^60 + 26252719580888049069066995575288184611473664654647035829209505915961690057602967485616 * q^61 + 109318411457586083204284032417457169492313955459811319765445849679642744506848521207040 * q^62 + 170984018880767416687602973051010439420211230624233991381305273834268390445660056281280 * q^63 + 407545659960425058121678577897271227683793728749313452587765989597513138495845491277824 * q^64 + 711217468942010938456527729098183388378886665557115838437689631605619958224435834575520 * q^65 + 1747938075646007071584137716302374690644541046339320226994976444199784352790302021223552 * q^66 - 646475642994207391400653355260241732956721934256209274545597969100350739031184431188640 * q^67 + 91675839067201266020688320385568861573762045194469769590554263557238860857176520405120 * q^68 - 1671348258106164448387617904756675195481964064504427142194954632911883632406377850960128 * q^69 - 15589682350948763132524633727148211085350313303119537319661619119948806738470696493235840 * q^70 - 14595295080721751466823982356267079020901744922845645857244436108167397828048945561374784 * q^71 - 168731956650076191328348463912100975176233311308158667034794509156143705616303905637470720 * q^72 - 167722859263497180232486905674536831998056258335586734743256934373976249561602911979579440 * q^73 - 209312489678791718598684146630297797595302804804578868479635191055424978871400486510408112 * q^74 - 319918492419260578418623942107150301135641877679303067145274604119881385565549842206216800 * q^75 - 959273209575432254809587692424149415253949631691365417587931662952012091653615772375589120 * q^76 - 358973379150050060834656745211596557040941835816686113329022190288009228708654757892460800 * q^77 + 590425535394410417923583601115147442109710886806797004396557673983317347484688655751672000 * q^78 + 4672642903096907209502768293890247708239627672362847349478671278970829923925879535283527040 * q^79 + 18415268594255335517079731605762998550074832241200743044677945286622776635630921688252866560 * q^80 + 12509737552066767544095911653095580991572013599361129872125476231341584536182121238921405768 * q^81 + 32657845092209493410036294321958173121440540177602229019397776717126981442788576405027965040 * q^82 + 34387792212015780744754986808561666458900302762495709021597904850967930099747337487085254880 * q^83 + 173836457542583880184373241725060178629119564679421678850358203433258194499103546320231344128 * q^84 + 58585978711733607272815047107060888289878133655773893600270763487144112403111490135244590560 * q^85 - 153511472921832187435283964804212642635464712353485304877046031498544471884447149897205104544 * q^86 - 544464219458114578116693663783217812912359092004929393234553696235186032730900539616052969920 * q^87 - 1202425497404423912185881933157195269872332267934742515736241252480851349730675866727622174720 * q^88 - 342673661311688548077760584785109887358595471462214186557789870415877447806348084055852796080 * q^89 - 3514062299884453064121468346218192535289244482618329972865712072788945397515179474700715316080 * q^90 - 3490211360016960529246147249335483533013067701963330513611222538458526220206688421639066690944 * q^91 - 12008074146638359830472895966704879561255070000267734630900014099911412498586265442549753546240 * q^92 + 197667690727810326296814984504358164807428856713575716952413727748092885643497784281407575040 * q^93 + 15433462798640093333378242254437202047220637579307237556798289796157532672617883642933732299648 * q^94 + 15321400721190643816477985005690604983976540891819618748501840926190750159388834713154020724800 * q^95 + 97555071644510782149318139986276901553221426854121546320985366392022081200430710682001871077376 * q^96 + 10072532354157458294768094296505188523874048354320514397914144859011793551098974691865811668240 * q^97 + 146363464831387371243245039459581022362075942196915081212239417921551560440470151788055390975960 * q^98 + 307096415144337525387251975813943414746365371627429389615225939474864146107991251707726185786272 * q^99

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