LMFDB - Embedded newform 1.96.a.a.1.7

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			1.7
Root			$9.80521e12$ 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)

$f(q)$	$=$	$q+2.34596e14 q^{2} -5.48368e22 q^{3} +1.54210e28 q^{4} -2.52565e33 q^{5} -1.28645e37 q^{6} +4.80687e39 q^{7} -5.67559e42 q^{8} +8.86182e44 q^{9} +O(q^{10})$	\(q+2.34596e14 q^{2} -5.48368e22 q^{3} +1.54210e28 q^{4} -2.52565e33 q^{5} -1.28645e37 q^{6} +4.80687e39 q^{7} -5.67559e42 q^{8} +8.86182e44 q^{9} -5.92506e47 q^{10} -3.16113e49 q^{11} -8.45638e50 q^{12} -9.97774e52 q^{13} +1.12767e54 q^{14} +1.38499e56 q^{15} -1.94236e57 q^{16} -3.48353e57 q^{17} +2.07894e59 q^{18} -1.04863e61 q^{19} -3.89480e61 q^{20} -2.63593e62 q^{21} -7.41586e63 q^{22} +1.70644e64 q^{23} +3.11231e65 q^{24} +3.85455e66 q^{25} -2.34073e67 q^{26} +6.77078e67 q^{27} +7.41266e67 q^{28} +1.55539e69 q^{29} +3.24912e70 q^{30} +1.02679e71 q^{31} -2.30835e71 q^{32} +1.73346e72 q^{33} -8.17221e71 q^{34} -1.21405e73 q^{35} +1.36658e73 q^{36} -2.81257e74 q^{37} -2.46005e75 q^{38} +5.47148e75 q^{39} +1.43346e76 q^{40} +3.26782e76 q^{41} -6.18378e76 q^{42} +7.50961e75 q^{43} -4.87477e77 q^{44} -2.23818e78 q^{45} +4.00322e78 q^{46} -2.42784e79 q^{47} +1.06513e80 q^{48} -1.69342e80 q^{49} +9.04260e80 q^{50} +1.91026e80 q^{51} -1.53867e81 q^{52} -1.40525e82 q^{53} +1.58839e82 q^{54} +7.98389e82 q^{55} -2.72818e82 q^{56} +5.75037e83 q^{57} +3.64887e83 q^{58} -1.17208e84 q^{59} +2.13578e84 q^{60} +7.58248e84 q^{61} +2.40880e85 q^{62} +4.25976e84 q^{63} +2.27918e85 q^{64} +2.52003e86 q^{65} +4.06662e86 q^{66} -8.84858e86 q^{67} -5.37195e85 q^{68} -9.35755e86 q^{69} -2.84810e87 q^{70} +6.46617e86 q^{71} -5.02961e87 q^{72} +1.01177e88 q^{73} -6.59817e88 q^{74} -2.11371e89 q^{75} -1.61710e89 q^{76} -1.51951e89 q^{77} +1.28358e90 q^{78} +1.04527e89 q^{79} +4.90571e90 q^{80} -5.59238e90 q^{81} +7.66617e90 q^{82} +1.05596e91 q^{83} -4.06487e90 q^{84} +8.79818e90 q^{85} +1.76172e90 q^{86} -8.52926e91 q^{87} +1.79413e92 q^{88} -3.90606e92 q^{89} -5.25068e92 q^{90} -4.79617e92 q^{91} +2.63149e92 q^{92} -5.63058e93 q^{93} -5.69559e93 q^{94} +2.64848e94 q^{95} +1.26583e94 q^{96} +3.16941e94 q^{97} -3.97269e94 q^{98} -2.80133e94 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	2.34596e14	1.17868	0.589339	−	0.807886i	$-0.299388\pi$
$2$	2.34596e14	1.17868	0.589339	+	0.807886i	$0.299388\pi$
$3$	−5.48368e22	−1.19073	−0.595364	−	0.803456i	$-0.702992\pi$
$3$	−5.48368e22	−1.19073	−0.595364	+	0.803456i	$0.702992\pi$
$4$	1.54210e28	0.389280
$5$	−2.52565e33	−1.58964	−0.794818	−	0.606847i	$-0.792434\pi$
$5$	−2.52565e33	−1.58964	−0.794818	+	0.606847i	$0.792434\pi$
$6$	−1.28645e37	−1.40348
$7$	4.80687e39	0.346502	0.173251	−	0.984878i	$-0.444573\pi$
$7$	4.80687e39	0.346502	0.173251	+	0.984878i	$0.444573\pi$
$8$	−5.67559e42	−0.719841
$9$	8.86182e44	0.417834
$10$	−5.92506e47	−1.87367
$11$	−3.16113e49	−1.08066	−0.540330	−	0.841453i	$-0.681701\pi$
$11$	−3.16113e49	−1.08066	−0.540330	+	0.841453i	$0.681701\pi$
$12$	−8.45638e50	−0.463527
$13$	−9.97774e52	−1.22102	−0.610510	−	0.792008i	$-0.709036\pi$
$13$	−9.97774e52	−1.22102	−0.610510	+	0.792008i	$0.709036\pi$
$14$	1.12767e54	0.408414
$15$	1.38499e56	1.89283
$16$	−1.94236e57	−1.23774
$17$	−3.48353e57	−0.124651	−0.0623256	−	0.998056i	$-0.519852\pi$
$17$	−3.48353e57	−0.124651	−0.0623256	+	0.998056i	$0.519852\pi$
$18$	2.07894e59	0.492491
$19$	−1.04863e61	−1.90470	−0.952352	−	0.305002i	$-0.901343\pi$
$19$	−1.04863e61	−1.90470	−0.952352	+	0.305002i	$0.901343\pi$
$20$	−3.89480e61	−0.618814
$21$	−2.63593e62	−0.412589
$22$	−7.41586e63	−1.27375
$23$	1.70644e64	0.354828	0.177414	−	0.984136i	$-0.443227\pi$
$23$	1.70644e64	0.354828	0.177414	+	0.984136i	$0.443227\pi$
$24$	3.11231e65	0.857135
$25$	3.85455e66	1.52694
$26$	−2.34073e67	−1.43919
$27$	6.77078e67	0.693202
$28$	7.41266e67	0.134886
$29$	1.55539e69	0.534483	0.267242	−	0.963630i	$-0.413888\pi$
$29$	1.55539e69	0.534483	0.267242	+	0.963630i	$0.413888\pi$
$30$	3.24912e70	2.23103
$31$	1.02679e71	1.48525	0.742626	−	0.669706i	$-0.233580\pi$
$31$	1.02679e71	1.48525	0.742626	+	0.669706i	$0.233580\pi$
$32$	−2.30835e71	−0.739056
$33$	1.73346e72	1.28677
$34$	−8.17221e71	−0.146923
$35$	−1.21405e73	−0.550812
$36$	1.36658e73	0.162655
$37$	−2.81257e74	−0.911007	−0.455503	−	0.890234i	$-0.650541\pi$
$37$	−2.81257e74	−0.911007	−0.455503	+	0.890234i	$0.650541\pi$
$38$	−2.46005e75	−2.24503
$39$	5.47148e75	1.45390
$40$	1.43346e76	1.14429
$41$	3.26782e76	0.807282	0.403641	−	0.914917i	$-0.367744\pi$
$41$	3.26782e76	0.807282	0.403641	+	0.914917i	$0.367744\pi$
$42$	−6.18378e76	−0.486310
$43$	7.50961e75	0.0193137	0.00965686	−	0.999953i	$-0.496926\pi$
$43$	7.50961e75	0.0193137	0.00965686	+	0.999953i	$0.496926\pi$
$44$	−4.87477e77	−0.420680
$45$	−2.23818e78	−0.664204
$46$	4.00322e78	0.418227
$47$	−2.42784e79	−0.913211	−0.456605	−	0.889669i	$-0.650935\pi$
$47$	−2.42784e79	−0.913211	−0.456605	+	0.889669i	$0.650935\pi$
$48$	1.06513e80	1.47381
$49$	−1.69342e80	−0.879937
$50$	9.04260e80	1.79978
$51$	1.91026e80	0.148426
$52$	−1.53867e81	−0.475320
$53$	−1.40525e82	−1.75650	−0.878252	−	0.478197i	$-0.841290\pi$
$53$	−1.40525e82	−1.75650	−0.878252	+	0.478197i	$0.841290\pi$
$54$	1.58839e82	0.817061
$55$	7.98389e82	1.71786
$56$	−2.72818e82	−0.249426
$57$	5.75037e83	2.26798
$58$	3.64887e83	0.629983
$59$	−1.17208e84	−0.898437	−0.449218	−	0.893422i	$-0.648297\pi$
$59$	−1.17208e84	−0.898437	−0.449218	+	0.893422i	$0.648297\pi$
$60$	2.13578e84	0.736840
$61$	7.58248e84	1.19301	0.596505	−	0.802609i	$-0.296555\pi$
$61$	7.58248e84	1.19301	0.596505	+	0.802609i	$0.296555\pi$
$62$	2.40880e85	1.75063
$63$	4.25976e84	0.144780
$64$	2.27918e85	0.366632
$65$	2.52003e86	1.94098
$66$	4.06662e86	1.51669
$67$	−8.84858e86	−1.61555	−0.807775	−	0.589491i	$-0.799328\pi$
$67$	−8.84858e86	−1.61555	−0.807775	+	0.589491i	$0.799328\pi$
$68$	−5.37195e85	−0.0485242
$69$	−9.35755e86	−0.422503
$70$	−2.84810e87	−0.649229
$71$	6.46617e86	0.0751407	0.0375704	−	0.999294i	$-0.488038\pi$
$71$	6.46617e86	0.0751407	0.0375704	+	0.999294i	$0.488038\pi$
$72$	−5.02961e87	−0.300774
$73$	1.01177e88	0.314229	0.157115	−	0.987580i	$-0.449781\pi$
$73$	1.01177e88	0.314229	0.157115	+	0.987580i	$0.449781\pi$
$74$	−6.59817e88	−1.07378
$75$	−2.11371e89	−1.81818
$76$	−1.61710e89	−0.741464
$77$	−1.51951e89	−0.374450
$78$	1.28358e90	1.71368
$79$	1.04527e89	0.0761980	0.0380990	−	0.999274i	$-0.487870\pi$
$79$	1.04527e89	0.0761980	0.0380990	+	0.999274i	$0.487870\pi$
$80$	4.90571e90	1.96756
$81$	−5.59238e90	−1.24325
$82$	7.66617e90	0.951525
$83$	1.05596e91	0.736952	0.368476	−	0.929637i	$-0.379880\pi$
$83$	1.05596e91	0.736952	0.368476	+	0.929637i	$0.379880\pi$
$84$	−4.06487e90	−0.160613
$85$	8.79818e90	0.198150
$86$	1.76172e90	0.0227646
$87$	−8.52926e91	−0.636424
$88$	1.79413e92	0.777904
$89$	−3.90606e92	−0.990178	−0.495089	−	0.868842i	$-0.664865\pi$
$89$	−3.90606e92	−0.990178	−0.495089	+	0.868842i	$0.664865\pi$
$90$	−5.25068e92	−0.782882
$91$	−4.79617e92	−0.423086
$92$	2.63149e92	0.138128
$93$	−5.63058e93	−1.76853
$94$	−5.69559e93	−1.07638
$95$	2.64848e94	3.02779
$96$	1.26583e94	0.880015
$97$	3.16941e94	1.34685	0.673427	−	0.739253i	$-0.264821\pi$
$97$	3.16941e94	1.34685	0.673427	+	0.739253i	$0.264821\pi$
$98$	−3.97269e94	−1.03716
$99$	−2.80133e94	−0.451536
$100$	5.94410e94	0.594410
$101$	−3.19125e93	−0.0198928	−0.00994639	−	0.999951i	$-0.503166\pi$
$101$	−3.19125e93	−0.0198928	−0.00994639	+	0.999951i	$0.503166\pi$
$102$	4.48138e94	0.174946
$103$	−4.65433e95	−1.14311	−0.571557	−	0.820563i	$-0.693660\pi$
$103$	−4.65433e95	−1.14311	−0.571557	+	0.820563i	$0.693660\pi$
$104$	5.66296e95	0.878941
$105$	6.65744e95	0.655867
$106$	−3.29665e96	−2.07035
$107$	−2.14933e96	−0.864120	−0.432060	−	0.901845i	$-0.642213\pi$
$107$	−2.14933e96	−0.864120	−0.432060	+	0.901845i	$0.642213\pi$
$108$	1.04412e96	0.269850
$109$	−9.13418e96	−1.52374	−0.761870	−	0.647730i	$-0.775718\pi$
$109$	−9.13418e96	−1.52374	−0.761870	+	0.647730i	$0.775718\pi$
$110$	1.87299e97	2.02480
$111$	1.54232e97	1.08476
$112$	−9.33665e96	−0.428879
$113$	−1.86534e97	−0.561737	−0.280869	−	0.959746i	$-0.590622\pi$
$113$	−1.86534e97	−0.561737	−0.280869	+	0.959746i	$0.590622\pi$
$114$	1.34901e98	2.67322
$115$	−4.30986e97	−0.564047
$116$	2.39856e97	0.208064
$117$	−8.84209e97	−0.510184
$118$	−2.74965e98	−1.05897
$119$	−1.67449e97	−0.0431918
$120$	−7.86062e98	−1.36253
$121$	1.43604e98	0.167826
$122$	1.77882e99	1.40617
$123$	−1.79197e99	−0.961254
$124$	1.58341e99	0.578180
$125$	−3.35961e99	−0.837651
$126$	9.99320e98	0.170649
$127$	−4.70738e99	−0.552208	−0.276104	−	0.961128i	$-0.589043\pi$
$127$	−4.70738e99	−0.552208	−0.276104	+	0.961128i	$0.589043\pi$
$128$	1.44912e100	1.17120
$129$	−4.11803e98	−0.0229974
$130$	5.91187e100	2.28779
$131$	−1.31142e100	−0.352660	−0.176330	−	0.984331i	$-0.556423\pi$
$131$	−1.31142e100	−0.352660	−0.176330	+	0.984331i	$0.556423\pi$
$132$	2.67317e100	0.500915
$133$	−5.04064e100	−0.659983
$134$	−2.07584e101	−1.90421
$135$	−1.71006e101	−1.10194
$136$	1.97711e100	0.0897290
$137$	2.88473e101	0.924440	0.462220	−	0.886765i	$-0.347053\pi$
$137$	2.88473e101	0.924440	0.462220	+	0.886765i	$0.347053\pi$
$138$	−2.19524e101	−0.497995
$139$	−9.04382e100	−0.145596	−0.0727979	−	0.997347i	$-0.523193\pi$
$139$	−9.04382e100	−0.145596	−0.0727979	+	0.997347i	$0.523193\pi$
$140$	−1.87218e101	−0.214420
$141$	1.33135e102	1.08739
$142$	1.51693e101	0.0885667
$143$	3.15409e102	1.31951
$144$	−1.72128e102	−0.517170
$145$	−3.92837e102	−0.849634
$146$	2.37357e102	0.370375
$147$	9.28619e102	1.04777
$148$	−4.33726e102	−0.354637
$149$	1.04129e103	0.618335	0.309167	−	0.951008i	$-0.399950\pi$
$149$	1.04129e103	0.618335	0.309167	+	0.951008i	$0.399950\pi$
$150$	−4.95868e103	−2.14304
$151$	−1.59249e103	−0.501964	−0.250982	−	0.967992i	$-0.580753\pi$
$151$	−1.59249e103	−0.501964	−0.250982	+	0.967992i	$0.580753\pi$
$152$	5.95161e103	1.37108
$153$	−3.08704e102	−0.0520834
$154$	−3.56470e103	−0.441356
$155$	−2.59331e104	−2.36101
$156$	8.43756e103	0.565976
$157$	1.96027e104	0.970695	0.485348	−	0.874321i	$-0.338693\pi$
$157$	1.96027e104	0.970695	0.485348	+	0.874321i	$0.338693\pi$
$158$	2.45217e103	0.0898129
$159$	7.70594e104	2.09152
$160$	5.83008e104	1.17483
$161$	8.20261e103	0.122948
$162$	−1.31195e105	−1.46539
$163$	−5.17949e104	−0.431893	−0.215946	−	0.976405i	$-0.569284\pi$
$163$	−5.17949e104	−0.431893	−0.215946	+	0.976405i	$0.569284\pi$
$164$	5.03931e104	0.314259
$165$	−4.37811e105	−2.04550
$166$	2.47724e105	0.868629
$167$	−2.44321e105	−0.644064	−0.322032	−	0.946729i	$-0.604366\pi$
$167$	−2.44321e105	−0.644064	−0.322032	+	0.946729i	$0.604366\pi$
$168$	1.49605e105	0.296999
$169$	3.27797e105	0.490892
$170$	2.06401e105	0.233555
$171$	−9.29279e105	−0.795850
$172$	1.15806e104	0.00751845
$173$	8.48274e105	0.418164	0.209082	−	0.977898i	$-0.432953\pi$
$173$	8.48274e105	0.418164	0.209082	+	0.977898i	$0.432953\pi$
$174$	−2.00093e106	−0.750139
$175$	1.85283e106	0.529089
$176$	6.14003e106	1.33758
$177$	6.42733e106	1.06979
$178$	−9.16344e106	−1.16710
$179$	4.09354e106	0.399559	0.199779	−	0.979841i	$-0.435977\pi$
$179$	4.09354e106	0.399559	0.199779	+	0.979841i	$0.435977\pi$
$180$	−3.45150e106	−0.258562
$181$	3.39061e106	0.195229	0.0976147	−	0.995224i	$-0.468879\pi$
$181$	3.39061e106	0.195229	0.0976147	+	0.995224i	$0.468879\pi$
$182$	−1.12516e107	−0.498681
$183$	−4.15799e107	−1.42055
$184$	−9.68503e106	−0.255420
$185$	7.10357e107	1.44817
$186$	−1.32091e108	−2.08453
$187$	1.10119e107	0.134705
$188$	−3.74396e107	−0.355495
$189$	3.25462e107	0.240195
$190$	6.21321e108	3.56878
$191$	−1.24535e108	−0.557450	−0.278725	−	0.960371i	$-0.589912\pi$
$191$	−1.24535e108	−0.557450	−0.278725	+	0.960371i	$0.589912\pi$
$192$	−1.24983e108	−0.436559
$193$	1.34117e107	0.0366026	0.0183013	−	0.999833i	$-0.494174\pi$
$193$	1.34117e107	0.0366026	0.0183013	+	0.999833i	$0.494174\pi$
$194$	7.43529e108	1.58751
$195$	−1.38190e109	−2.31118
$196$	−2.61142e108	−0.342542
$197$	7.02757e108	0.723868	0.361934	−	0.932204i	$-0.382117\pi$
$197$	7.02757e108	0.723868	0.361934	+	0.932204i	$0.382117\pi$
$198$	−6.57180e108	−0.532216
$199$	−1.04024e109	−0.663149	−0.331575	−	0.943429i	$-0.607580\pi$
$199$	−1.04024e109	−0.663149	−0.331575	+	0.943429i	$0.607580\pi$
$200$	−2.18769e109	−1.09916
$201$	4.85228e109	1.92368
$202$	−7.48653e107	−0.0234472
$203$	7.47655e108	0.185199
$204$	2.94581e108	0.0577792
$205$	−8.25338e109	−1.28329
$206$	−1.09189e110	−1.34736
$207$	1.51221e109	0.148259
$208$	1.93803e110	1.51131
$209$	3.31486e110	2.05834
$210$	1.56181e110	0.773055
$211$	−6.82443e109	−0.269556	−0.134778	−	0.990876i	$-0.543032\pi$
$211$	−6.82443e109	−0.269556	−0.134778	+	0.990876i	$0.543032\pi$
$212$	−2.16703e110	−0.683773
$213$	−3.54584e109	−0.0894722
$214$	−5.04224e110	−1.01852
$215$	−1.89667e109	−0.0307018
$216$	−3.84282e110	−0.498995
$217$	4.93563e110	0.514642
$218$	−2.14284e111	−1.79600
$219$	−5.54823e110	−0.374162
$220$	1.23120e111	0.668728
$221$	3.47578e110	0.152202
$222$	3.61822e111	1.27858
$223$	5.51903e110	0.157537	0.0787683	−	0.996893i	$-0.474901\pi$
$223$	5.51903e110	0.157537	0.0787683	+	0.996893i	$0.474901\pi$
$224$	−1.10959e111	−0.256084
$225$	3.41583e111	0.638009
$226$	−4.37602e111	−0.662107
$227$	1.13992e112	1.39844	0.699222	−	0.714905i	$-0.253530\pi$
$227$	1.13992e112	1.39844	0.699222	+	0.714905i	$0.253530\pi$
$228$	8.86764e111	0.882882
$229$	−2.01230e112	−1.62745	−0.813724	−	0.581252i	$-0.802563\pi$
$229$	−2.01230e112	−1.62745	−0.813724	+	0.581252i	$0.802563\pi$
$230$	−1.01107e112	−0.664830
$231$	8.33251e111	0.445869
$232$	−8.82775e111	−0.384743
$233$	−1.66461e112	−0.591435	−0.295718	−	0.955275i	$-0.595559\pi$
$233$	−1.66461e112	−0.591435	−0.295718	+	0.955275i	$0.595559\pi$
$234$	−2.07432e112	−0.601342
$235$	6.13186e112	1.45167
$236$	−1.80747e112	−0.349744
$237$	−5.73195e111	−0.0907311
$238$	−3.92827e111	−0.0509092
$239$	1.78548e112	0.189608	0.0948038	−	0.995496i	$-0.469778\pi$
$239$	1.78548e112	0.189608	0.0948038	+	0.995496i	$0.469778\pi$
$240$	−2.69014e113	−2.34283
$241$	1.84544e113	1.31914	0.659571	−	0.751643i	$-0.270738\pi$
$241$	1.84544e113	1.31914	0.659571	+	0.751643i	$0.270738\pi$
$242$	3.36888e112	0.197813
$243$	1.63067e113	0.787170
$244$	1.16929e113	0.464416
$245$	4.27699e113	1.39878
$246$	−4.20388e113	−1.13301
$247$	1.04630e114	2.32568
$248$	−5.82763e113	−1.06915
$249$	−5.79056e113	−0.877510
$250$	−7.88149e113	−0.987320
$251$	−9.74969e113	−1.01039	−0.505195	−	0.863005i	$-0.668579\pi$
$251$	−9.74969e113	−1.01039	−0.505195	+	0.863005i	$0.668579\pi$
$252$	6.56897e112	0.0563600
$253$	−5.39426e113	−0.383448
$254$	−1.10433e114	−0.650875
$255$	−4.82464e113	−0.235943
$256$	2.49669e114	1.01383
$257$	4.79912e114	1.61934	0.809671	−	0.586884i	$-0.199646\pi$
$257$	4.79912e114	1.61934	0.809671	+	0.586884i	$0.199646\pi$
$258$	−9.66072e112	−0.0271065
$259$	−1.35197e114	−0.315665
$260$	3.88613e114	0.755585
$261$	1.37836e114	0.223325
$262$	−3.07654e114	−0.415673
$263$	−8.59726e114	−0.969309	−0.484654	−	0.874706i	$-0.661055\pi$
$263$	−8.59726e114	−0.969309	−0.484654	+	0.874706i	$0.661055\pi$
$264$	−9.83841e114	−0.926272
$265$	3.54917e115	2.79220
$266$	−1.18251e115	−0.777907
$267$	2.14196e115	1.17903
$268$	−1.36454e115	−0.628902
$269$	−4.76127e115	−1.83861	−0.919305	−	0.393546i	$-0.871248\pi$
$269$	−4.76127e115	−1.83861	−0.919305	+	0.393546i	$0.871248\pi$
$270$	−4.01173e115	−1.29883
$271$	3.00132e115	0.815212	0.407606	−	0.913158i	$-0.366364\pi$
$271$	3.00132e115	0.815212	0.407606	+	0.913158i	$0.366364\pi$
$272$	6.76626e114	0.154286
$273$	2.63007e115	0.503780
$274$	6.76745e115	1.08962
$275$	−1.21847e116	−1.65011
$276$	−1.44303e115	−0.164472
$277$	1.42446e115	0.136729	0.0683647	−	0.997660i	$-0.478222\pi$
$277$	1.42446e115	0.136729	0.0683647	+	0.997660i	$0.478222\pi$
$278$	−2.12164e115	−0.171610
$279$	9.09921e115	0.620589
$280$	6.89043e115	0.396497
$281$	5.39650e115	0.262158	0.131079	−	0.991372i	$-0.458156\pi$
$281$	5.39650e115	0.262158	0.131079	+	0.991372i	$0.458156\pi$
$282$	3.12328e116	1.28168
$283$	3.65205e116	1.26672	0.633361	−	0.773857i	$-0.281675\pi$
$283$	3.65205e116	1.26672	0.633361	+	0.773857i	$0.281675\pi$
$284$	9.97147e114	0.0292508
$285$	−1.45234e117	−3.60527
$286$	7.39935e116	1.55528
$287$	1.57080e116	0.279725
$288$	−2.04562e116	−0.308803
$289$	−7.68859e116	−0.984462
$290$	−9.21578e116	−1.00144
$291$	−1.73800e117	−1.60374
$292$	1.56025e116	0.122323
$293$	1.22883e117	0.818990	0.409495	−	0.912312i	$-0.365705\pi$
$293$	1.22883e117	0.818990	0.409495	+	0.912312i	$0.365705\pi$
$294$	2.17850e117	1.23498
$295$	2.96027e117	1.42819
$296$	1.59630e117	0.655780
$297$	−2.14033e117	−0.749115
$298$	2.44282e117	0.728817
$299$	−1.70264e117	−0.433252
$300$	−3.25955e117	−0.707780
$301$	3.60977e115	0.00669223
$302$	−3.73592e117	−0.591653
$303$	1.74998e116	0.0236869
$304$	2.03682e118	2.35753
$305$	−1.91507e118	−1.89645
$306$	−7.24207e116	−0.0613896
$307$	1.46735e117	0.106527	0.0532635	−	0.998580i	$-0.483038\pi$
$307$	1.46735e117	0.106527	0.0532635	+	0.998580i	$0.483038\pi$
$308$	−2.34324e117	−0.145766
$309$	2.55229e118	1.36114
$310$	−6.08378e118	−2.78287
$311$	3.27509e118	1.28560	0.642799	−	0.766035i	$-0.277773\pi$
$311$	3.27509e118	1.28560	0.642799	+	0.766035i	$0.277773\pi$
$312$	−3.10539e118	−1.04658
$313$	−2.81510e118	−0.814964	−0.407482	−	0.913213i	$-0.633593\pi$
$313$	−2.81510e118	−0.814964	−0.407482	+	0.913213i	$0.633593\pi$
$314$	4.59871e118	1.14414
$315$	−1.07587e118	−0.230148
$316$	1.61192e117	0.0296624
$317$	1.14868e118	0.181921	0.0909604	−	0.995855i	$-0.471006\pi$
$317$	1.14868e118	0.181921	0.0909604	+	0.995855i	$0.471006\pi$
$318$	1.80778e119	2.46523
$319$	−4.91678e118	−0.577595
$320$	−5.75642e118	−0.582812
$321$	1.17863e119	1.02893
$322$	1.92429e118	0.144916
$323$	3.65295e118	0.237423
$324$	−8.62400e118	−0.483972
$325$	−3.84597e119	−1.86443
$326$	−1.21509e119	−0.509062
$327$	5.00889e119	1.81436
$328$	−1.85468e119	−0.581115
$329$	−1.16703e119	−0.316429
$330$	−1.02709e120	−2.41099
$331$	4.87830e119	0.991834	0.495917	−	0.868370i	$-0.334832\pi$
$331$	4.87830e119	0.991834	0.495917	+	0.868370i	$0.334832\pi$
$332$	1.62840e119	0.286881
$333$	−2.49245e119	−0.380649
$334$	−5.73167e119	−0.759143
$335$	2.23484e120	2.56814
$336$	5.11992e119	0.510679
$337$	2.24839e119	0.194738	0.0973691	−	0.995248i	$-0.468957\pi$
$337$	2.24839e119	0.194738	0.0973691	+	0.995248i	$0.468957\pi$
$338$	7.68996e119	0.578603
$339$	1.02290e120	0.668876
$340$	1.35677e119	0.0771359
$341$	−3.24581e120	−1.60505
$342$	−2.18005e120	−0.938050
$343$	−1.73908e120	−0.651401
$344$	−4.26215e118	−0.0139028
$345$	2.36339e120	0.671627
$346$	1.99001e120	0.492880
$347$	5.72676e120	1.23668	0.618342	−	0.785909i	$-0.287805\pi$
$347$	5.72676e120	1.23668	0.618342	+	0.785909i	$0.287805\pi$
$348$	−1.31530e120	−0.247748
$349$	−1.19478e121	−1.96372	−0.981860	−	0.189608i	$-0.939278\pi$
$349$	−1.19478e121	−1.96372	−0.981860	+	0.189608i	$0.939278\pi$
$350$	4.34666e120	0.623625
$351$	−6.75571e120	−0.846414
$352$	7.29698e120	0.798669
$353$	−1.63379e121	−1.56278	−0.781391	−	0.624042i	$-0.785489\pi$
$353$	−1.63379e121	−1.56278	−0.781391	+	0.624042i	$0.785489\pi$
$354$	1.50782e121	1.26094
$355$	−1.63313e120	−0.119446
$356$	−6.02353e120	−0.385457
$357$	9.18236e119	0.0514297
$358$	9.60327e120	0.470951
$359$	−4.74165e120	−0.203677	−0.101839	−	0.994801i	$-0.532473\pi$
$359$	−4.74165e120	−0.203677	−0.101839	+	0.994801i	$0.532473\pi$
$360$	1.27030e121	0.478122
$361$	7.96526e121	2.62790
$362$	7.95421e120	0.230112
$363$	−7.87476e120	−0.199836
$364$	−7.39616e120	−0.164699
$365$	−2.55538e121	−0.499510
$366$	−9.75447e121	−1.67437
$367$	−1.06281e122	−1.60258	−0.801288	−	0.598278i	$-0.795852\pi$
$367$	−1.06281e122	−1.60258	−0.801288	+	0.598278i	$0.795852\pi$
$368$	−3.31451e121	−0.439185
$369$	2.89589e121	0.337310
$370$	1.66647e122	1.70692
$371$	−6.75484e121	−0.608632
$372$	−8.68291e121	−0.688455
$373$	−5.89096e121	−0.411165	−0.205583	−	0.978640i	$-0.565909\pi$
$373$	−5.89096e121	−0.411165	−0.205583	+	0.978640i	$0.565909\pi$
$374$	2.58334e121	0.158774
$375$	1.84230e122	0.997415
$376$	1.37794e122	0.657367
$377$	−1.55193e122	−0.652615
$378$	7.63520e121	0.283113
$379$	1.50810e122	0.493251	0.246625	−	0.969111i	$-0.420678\pi$
$379$	1.50810e122	0.493251	0.246625	+	0.969111i	$0.420678\pi$
$380$	4.08422e122	1.17866
$381$	2.58138e122	0.657530
$382$	−2.92153e122	−0.657054
$383$	−2.95525e122	−0.587019	−0.293510	−	0.955956i	$-0.594823\pi$
$383$	−2.95525e122	−0.587019	−0.293510	+	0.955956i	$0.594823\pi$
$384$	−7.94650e122	−1.39458
$385$	3.83775e122	0.595240
$386$	3.14633e121	0.0431426
$387$	6.65488e120	0.00806993
$388$	4.88754e122	0.524304
$389$	3.87600e122	0.367940	0.183970	−	0.982932i	$-0.441105\pi$
$389$	3.87600e122	0.367940	0.183970	+	0.982932i	$0.441105\pi$
$390$	−3.24188e123	−2.72413
$391$	−5.94442e121	−0.0442297
$392$	9.61117e122	0.633415
$393$	7.19143e122	0.419922
$394$	1.64864e123	0.853207
$395$	−2.64000e122	−0.121127
$396$	−4.31993e122	−0.175774
$397$	−1.52456e122	−0.0550294	−0.0275147	−	0.999621i	$-0.508759\pi$
$397$	−1.52456e122	−0.0550294	−0.0275147	+	0.999621i	$0.508759\pi$
$398$	−2.44035e123	−0.781639
$399$	2.76413e123	0.785860
$400$	−7.48691e123	−1.88996
$401$	5.92751e123	1.32897	0.664484	−	0.747303i	$-0.268651\pi$
$401$	5.92751e123	1.32897	0.664484	+	0.747303i	$0.268651\pi$
$402$	1.13832e124	2.26740
$403$	−1.02450e124	−1.81352
$404$	−4.92122e121	−0.00774387
$405$	1.41244e124	1.97631
$406$	1.75396e123	0.218290
$407$	8.89089e123	0.984489
$408$	−1.08418e123	−0.106843
$409$	−1.54933e124	−1.35921	−0.679606	−	0.733577i	$-0.737849\pi$
$409$	−1.54933e124	−1.35921	−0.679606	+	0.733577i	$0.737849\pi$
$410$	−1.93621e124	−1.51258
$411$	−1.58190e124	−1.10076
$412$	−7.17744e123	−0.444992
$413$	−5.63404e123	−0.311310
$414$	3.54758e123	0.174750
$415$	−2.66699e124	−1.17149
$416$	2.30321e124	0.902403
$417$	4.95934e123	0.173365
$418$	7.77651e124	2.42612
$419$	6.74054e123	0.187728	0.0938639	−	0.995585i	$-0.470078\pi$
$419$	6.74054e123	0.187728	0.0938639	+	0.995585i	$0.470078\pi$
$420$	1.02664e124	0.255316
$421$	−1.49665e124	−0.332446	−0.166223	−	0.986088i	$-0.553157\pi$
$421$	−1.49665e124	−0.332446	−0.166223	+	0.986088i	$0.553157\pi$
$422$	−1.60098e124	−0.317720
$423$	−2.15150e124	−0.381570
$424$	7.97562e124	1.26440
$425$	−1.34275e124	−0.190335
$426$	−8.31839e123	−0.105459
$427$	3.64480e124	0.413380
$428$	−3.31448e124	−0.336385
$429$	−1.72960e125	−1.57118
$430$	−4.44949e123	−0.0361875
$431$	1.57092e125	1.14415	0.572076	−	0.820201i	$-0.306138\pi$
$431$	1.57092e125	1.14415	0.572076	+	0.820201i	$0.306138\pi$
$432$	−1.31513e125	−0.858004
$433$	−1.36231e125	−0.796344	−0.398172	−	0.917311i	$-0.630355\pi$
$433$	−1.36231e125	−0.796344	−0.398172	+	0.917311i	$0.630355\pi$
$434$	1.15788e125	0.606597
$435$	2.15419e125	1.01168
$436$	−1.40858e125	−0.593162
$437$	−1.78942e125	−0.675842
$438$	−1.30159e125	−0.441016
$439$	4.13575e125	1.25745	0.628723	−	0.777629i	$-0.283578\pi$
$439$	4.13575e125	1.25745	0.628723	+	0.777629i	$0.283578\pi$
$440$	−4.53133e125	−1.23658
$441$	−1.50068e125	−0.367667
$442$	8.15402e124	0.179397
$443$	3.49485e125	0.690639	0.345319	−	0.938485i	$-0.387771\pi$
$443$	3.49485e125	0.690639	0.345319	+	0.938485i	$0.387771\pi$
$444$	2.37842e125	0.422276
$445$	9.86534e125	1.57402
$446$	1.29474e125	0.185685
$447$	−5.71010e125	−0.736269
$448$	1.09557e125	0.127039
$449$	−7.11658e125	−0.742284	−0.371142	−	0.928576i	$-0.621034\pi$
$449$	−7.11658e125	−0.742284	−0.371142	+	0.928576i	$0.621034\pi$
$450$	8.01339e125	0.752007
$451$	−1.03300e126	−0.872398
$452$	−2.87655e125	−0.218673
$453$	8.73272e125	0.597702
$454$	2.67419e126	1.64831
$455$	1.21134e126	0.672552
$456$	−3.26367e126	−1.63259
$457$	−3.50368e126	−1.57945	−0.789724	−	0.613462i	$-0.789776\pi$
$457$	−3.50368e126	−1.57945	−0.789724	+	0.613462i	$0.789776\pi$
$458$	−4.72076e126	−1.91824
$459$	−2.35862e125	−0.0864084
$460$	−6.64623e125	−0.219573
$461$	3.10796e126	0.926150	0.463075	−	0.886319i	$-0.346746\pi$
$461$	3.10796e126	0.926150	0.463075	+	0.886319i	$0.346746\pi$
$462$	1.95477e126	0.525535
$463$	−7.74133e125	−0.187810	−0.0939050	−	0.995581i	$-0.529935\pi$
$463$	−7.74133e125	−0.187810	−0.0939050	+	0.995581i	$0.529935\pi$
$464$	−3.02112e126	−0.661552
$465$	1.42209e127	2.81132
$466$	−3.90511e126	−0.697111
$467$	8.79545e126	1.41810	0.709049	−	0.705159i	$-0.249125\pi$
$467$	8.79545e126	1.41810	0.709049	+	0.705159i	$0.249125\pi$
$468$	−1.36354e126	−0.198605
$469$	−4.25339e126	−0.559790
$470$	1.43851e127	1.71105
$471$	−1.07495e127	−1.15583
$472$	6.65226e126	0.646732
$473$	−2.37388e125	−0.0208716
$474$	−1.34469e126	−0.106943
$475$	−4.04201e127	−2.90838
$476$	−2.58222e125	−0.0168137
$477$	−1.24531e127	−0.733927
$478$	4.18867e126	0.223486
$479$	2.97559e127	1.43760	0.718798	−	0.695219i	$-0.244693\pi$
$479$	2.97559e127	1.43760	0.718798	+	0.695219i	$0.244693\pi$
$480$	−3.19703e127	−1.39890
$481$	2.80631e127	1.11236
$482$	4.32933e127	1.55484
$483$	−4.49805e126	−0.146398
$484$	2.21451e126	0.0653315
$485$	−8.00481e127	−2.14101
$486$	3.82548e127	0.927819
$487$	−3.69546e127	−0.812911	−0.406455	−	0.913671i	$-0.633235\pi$
$487$	−3.69546e127	−0.812911	−0.406455	+	0.913671i	$0.633235\pi$
$488$	−4.30351e127	−0.858779
$489$	2.84027e127	0.514267
$490$	1.00336e128	1.64871
$491$	−2.26267e127	−0.337481	−0.168741	−	0.985660i	$-0.553970\pi$
$491$	−2.26267e127	−0.337481	−0.168741	+	0.985660i	$0.553970\pi$
$492$	−2.76340e127	−0.374197
$493$	−5.41825e126	−0.0666239
$494$	2.45457e128	2.74123
$495$	7.07518e127	0.717779
$496$	−1.99439e128	−1.83836
$497$	3.10820e126	0.0260364
$498$	−1.35844e128	−1.03430
$499$	1.13378e128	0.784786	0.392393	−	0.919798i	$-0.371647\pi$
$499$	1.13378e128	0.784786	0.392393	+	0.919798i	$0.371647\pi$
$500$	−5.18085e127	−0.326081
$501$	1.33978e128	0.766905
$502$	−2.28723e128	−1.19092
$503$	−1.72721e128	−0.818214	−0.409107	−	0.912486i	$-0.634160\pi$
$503$	−1.72721e128	−0.818214	−0.409107	+	0.912486i	$0.634160\pi$
$504$	−2.41766e127	−0.104219
$505$	8.05997e126	0.0316223
$506$	−1.26547e128	−0.451962
$507$	−1.79753e128	−0.584519
$508$	−7.25925e127	−0.214964
$509$	5.19969e128	1.40243	0.701217	−	0.712948i	$-0.252640\pi$
$509$	5.19969e128	1.40243	0.701217	+	0.712948i	$0.252640\pi$
$510$	−1.13184e128	−0.278100
$511$	4.86345e127	0.108881
$512$	1.16571e127	0.0237830
$513$	−7.10006e128	−1.32034
$514$	1.12585e129	1.90868
$515$	1.17552e129	1.81713
$516$	−6.35041e126	−0.00895244
$517$	7.67469e128	0.986871
$518$	−3.17165e128	−0.372067
$519$	−4.65166e128	−0.497919
$520$	−1.43027e129	−1.39720
$521$	−2.82044e128	−0.251492	−0.125746	−	0.992062i	$-0.540133\pi$
$521$	−2.82044e128	−0.251492	−0.125746	+	0.992062i	$0.540133\pi$
$522$	3.23357e128	0.263228
$523$	1.04986e129	0.780373	0.390186	−	0.920736i	$-0.372411\pi$
$523$	1.04986e129	0.780373	0.390186	+	0.920736i	$0.372411\pi$
$524$	−2.02234e128	−0.137284
$525$	−1.01603e129	−0.630001
$526$	−2.01688e129	−1.14250
$527$	−3.57685e128	−0.185138
$528$	−3.36700e129	−1.59269
$529$	−2.02164e129	−0.874097
$530$	8.32618e129	3.29111
$531$	−1.03868e129	−0.375397
$532$	−7.77316e128	−0.256918
$533$	−3.26055e129	−0.985708
$534$	5.02494e129	1.38970
$535$	5.42846e129	1.37364
$536$	5.02209e129	1.16294
$537$	−2.24477e129	−0.475766
$538$	−1.11697e130	−2.16713
$539$	5.35312e129	0.950913
$540$	−2.63708e129	−0.428963
$541$	−1.09474e130	−1.63095	−0.815475	−	0.578792i	$-0.803524\pi$
$541$	−1.09474e130	−1.63095	−0.815475	+	0.578792i	$0.803524\pi$
$542$	7.04096e129	0.960872
$543$	−1.85930e129	−0.232465
$544$	8.04121e128	0.0921242
$545$	2.30697e130	2.42219
$546$	6.17002e129	0.593794
$547$	−9.31044e129	−0.821433	−0.410717	−	0.911763i	$-0.634721\pi$
$547$	−9.31044e129	−0.821433	−0.410717	+	0.911763i	$0.634721\pi$
$548$	4.44854e129	0.359866
$549$	6.71946e129	0.498480
$550$	−2.85848e130	−1.94495
$551$	−1.63103e130	−1.01803
$552$	5.31096e129	0.304135
$553$	5.02450e128	0.0264027
$554$	3.34173e129	0.161160
$555$	−3.89537e130	−1.72438
$556$	−1.39465e129	−0.0566776
$557$	−9.20667e129	−0.343543	−0.171771	−	0.985137i	$-0.554949\pi$
$557$	−9.20667e129	−0.343543	−0.171771	+	0.985137i	$0.554949\pi$
$558$	2.13463e130	0.731474
$559$	−7.49290e128	−0.0235825
$560$	2.35811e130	0.681762
$561$	−6.03857e129	−0.160398
$562$	1.26600e130	0.308999
$563$	3.58585e130	0.804348	0.402174	−	0.915563i	$-0.368255\pi$
$563$	3.58585e130	0.804348	0.402174	+	0.915563i	$0.368255\pi$
$564$	2.05307e130	0.423298
$565$	4.71121e130	0.892958
$566$	8.56755e130	1.49306
$567$	−2.68818e130	−0.430788
$568$	−3.66993e129	−0.0540894
$569$	1.14908e131	1.55782	0.778911	−	0.627134i	$-0.215772\pi$
$569$	1.14908e131	1.55782	0.778911	+	0.627134i	$0.215772\pi$
$570$	−3.40713e131	−4.24945
$571$	−1.05014e131	−1.20513	−0.602564	−	0.798071i	$-0.705854\pi$
$571$	−1.05014e131	−1.20513	−0.602564	+	0.798071i	$0.705854\pi$
$572$	4.86392e130	0.513659
$573$	6.82910e130	0.663772
$574$	3.68502e130	0.329705
$575$	6.57754e130	0.541802
$576$	2.01977e130	0.153191
$577$	−8.12255e130	−0.567337	−0.283669	−	0.958922i	$-0.591552\pi$
$577$	−8.12255e130	−0.567337	−0.283669	+	0.958922i	$0.591552\pi$
$578$	−1.80371e131	−1.16036
$579$	−7.35455e129	−0.0435837
$580$	−6.05793e130	−0.330746
$581$	5.07587e130	0.255355
$582$	−4.07728e131	−1.89029
$583$	4.44217e131	1.89818
$584$	−5.74240e130	−0.226195
$585$	2.23320e131	0.811007
$586$	2.88277e131	0.965325
$587$	4.95615e131	1.53051	0.765253	−	0.643730i	$-0.222614\pi$
$587$	4.95615e131	1.53051	0.765253	+	0.643730i	$0.222614\pi$
$588$	1.43202e131	0.407875
$589$	−1.07672e132	−2.82897
$590$	6.94466e131	1.68337
$591$	−3.85370e131	−0.861930
$592$	5.46302e131	1.12759
$593$	−4.41739e131	−0.841527	−0.420763	−	0.907170i	$-0.638238\pi$
$593$	−4.41739e131	−0.841527	−0.420763	+	0.907170i	$0.638238\pi$
$594$	−5.02111e131	−0.882965
$595$	4.22917e130	0.0686593
$596$	1.60577e131	0.240706
$597$	5.70433e131	0.789631
$598$	−3.99431e131	−0.510665
$599$	−5.19239e131	−0.613187	−0.306594	−	0.951841i	$-0.599189\pi$
$599$	−5.19239e131	−0.613187	−0.306594	+	0.951841i	$0.599189\pi$
$600$	1.19966e132	1.30880
$601$	−4.50468e131	−0.454074	−0.227037	−	0.973886i	$-0.572904\pi$
$601$	−4.50468e131	−0.454074	−0.227037	+	0.973886i	$0.572904\pi$
$602$	8.46836e129	0.00788798
$603$	−7.84145e131	−0.675031
$604$	−2.45578e131	−0.195405
$605$	−3.62692e131	−0.266783
$606$	4.10537e130	0.0279192
$607$	−1.48875e132	−0.936178	−0.468089	−	0.883681i	$-0.655057\pi$
$607$	−1.48875e132	−0.936178	−0.468089	+	0.883681i	$0.655057\pi$
$608$	2.42061e132	1.40768
$609$	−4.09990e131	−0.220522
$610$	−4.49267e132	−2.23531
$611$	2.42243e132	1.11505
$612$	−4.76053e130	−0.0202751
$613$	−1.17585e131	−0.0463423	−0.0231712	−	0.999732i	$-0.507376\pi$
$613$	−1.17585e131	−0.0463423	−0.0231712	+	0.999732i	$0.507376\pi$
$614$	3.44233e131	0.125561
$615$	4.52589e132	1.52804
$616$	8.62412e131	0.269545
$617$	1.28747e132	0.372556	0.186278	−	0.982497i	$-0.440358\pi$
$617$	1.28747e132	0.372556	0.186278	+	0.982497i	$0.440358\pi$
$618$	5.98755e132	1.60434
$619$	−3.57292e131	−0.0886578	−0.0443289	−	0.999017i	$-0.514115\pi$
$619$	−3.57292e131	−0.0886578	−0.0443289	+	0.999017i	$0.514115\pi$
$620$	−3.99913e132	−0.919096
$621$	1.15539e132	0.245967
$622$	7.68323e132	1.51531
$623$	−1.87759e132	−0.343098
$624$	−1.06276e133	−1.79956
$625$	−1.24506e132	−0.195384
$626$	−6.60411e132	−0.960580
$627$	−1.81776e133	−2.45092
$628$	3.02293e132	0.377873
$629$	9.79768e131	0.113558
$630$	−2.52393e132	−0.271270
$631$	8.05657e132	0.803074	0.401537	−	0.915843i	$-0.368476\pi$
$631$	8.05657e132	0.803074	0.401537	+	0.915843i	$0.368476\pi$
$632$	−5.93255e131	−0.0548505
$633$	3.74230e132	0.320968
$634$	2.69474e132	0.214426
$635$	1.18892e133	0.877810
$636$	1.18833e133	0.814188
$637$	1.68965e133	1.07442
$638$	−1.15345e133	−0.680798
$639$	5.73020e131	0.0313963
$640$	−3.65996e133	−1.86178
$641$	−1.70084e133	−0.803354	−0.401677	−	0.915781i	$-0.631572\pi$
$641$	−1.70084e133	−0.803354	−0.401677	+	0.915781i	$0.631572\pi$
$642$	2.76500e133	1.21278
$643$	3.55754e133	1.44920	0.724600	−	0.689170i	$-0.242025\pi$
$643$	3.55754e133	1.44920	0.724600	+	0.689170i	$0.242025\pi$
$644$	1.26492e132	0.0478614
$645$	1.04007e132	0.0365575
$646$	8.56965e132	0.279846
$647$	−3.43446e133	−1.04209	−0.521044	−	0.853530i	$-0.674457\pi$
$647$	−3.43446e133	−1.04209	−0.521044	+	0.853530i	$0.674457\pi$
$648$	3.17400e133	0.894942
$649$	3.70510e133	0.970905
$650$	−9.02248e133	−2.19756
$651$	−2.70654e133	−0.612799
$652$	−7.98729e132	−0.168127
$653$	−4.55143e133	−0.890783	−0.445391	−	0.895336i	$-0.646935\pi$
$653$	−4.55143e133	−0.890783	−0.445391	+	0.895336i	$0.646935\pi$
$654$	1.17506e134	2.13855
$655$	3.31220e133	0.560602
$656$	−6.34728e133	−0.999206
$657$	8.96613e132	0.131296
$658$	−2.73780e133	−0.372968
$659$	−1.09030e134	−1.38194	−0.690969	−	0.722884i	$-0.742816\pi$
$659$	−1.09030e134	−1.38194	−0.690969	+	0.722884i	$0.742816\pi$
$660$	−6.75148e133	−0.796273
$661$	7.88900e133	0.865870	0.432935	−	0.901425i	$-0.357478\pi$
$661$	7.88900e133	0.865870	0.432935	+	0.901425i	$0.357478\pi$
$662$	1.14443e134	1.16905
$663$	−1.90601e133	−0.181231
$664$	−5.99321e133	−0.530489
$665$	1.27309e134	1.04913
$666$	−5.84717e133	−0.448663
$667$	2.65417e133	0.189650
$668$	−3.76767e133	−0.250721
$669$	−3.02646e133	−0.187583
$670$	5.24284e134	3.02700
$671$	−2.39692e134	−1.28924
$672$	6.08465e133	0.304927
$673$	−3.42957e134	−1.60149	−0.800745	−	0.599006i	$-0.795563\pi$
$673$	−3.42957e134	−1.60149	−0.800745	+	0.599006i	$0.795563\pi$
$674$	5.27462e133	0.229534
$675$	2.60983e134	1.05848
$676$	5.05495e133	0.191095
$677$	4.77519e133	0.168278	0.0841392	−	0.996454i	$-0.473186\pi$
$677$	4.77519e133	0.168278	0.0841392	+	0.996454i	$0.473186\pi$
$678$	2.39967e134	0.788389
$679$	1.52349e134	0.466687
$680$	−4.99349e133	−0.142637
$681$	−6.25094e134	−1.66517
$682$	−7.61451e134	−1.89184
$683$	−3.47812e134	−0.806048	−0.403024	−	0.915189i	$-0.632041\pi$
$683$	−3.47812e134	−0.806048	−0.403024	+	0.915189i	$0.632041\pi$
$684$	−1.43304e134	−0.309809
$685$	−7.28582e134	−1.46952
$686$	−4.07980e134	−0.767792
$687$	1.10348e135	1.93785
$688$	−1.45863e133	−0.0239054
$689$	1.40212e135	2.14473
$690$	5.54440e134	0.791632
$691$	−3.20714e134	−0.427475	−0.213738	−	0.976891i	$-0.568564\pi$
$691$	−3.20714e134	−0.427475	−0.213738	+	0.976891i	$0.568564\pi$
$692$	1.30812e134	0.162783
$693$	−1.34656e134	−0.156458
$694$	1.34347e135	1.45765
$695$	2.28415e134	0.231444
$696$	4.84086e134	0.458125
$697$	−1.13836e134	−0.100629
$698$	−2.80290e135	−2.31459
$699$	9.12821e134	0.704239
$700$	2.85725e134	0.205964
$701$	7.30037e134	0.491744	0.245872	−	0.969302i	$-0.420926\pi$
$701$	7.30037e134	0.491744	0.245872	+	0.969302i	$0.420926\pi$
$702$	−1.58486e135	−0.997649
$703$	2.94935e135	1.73520
$704$	−7.20479e134	−0.396205
$705$	−3.36252e135	−1.72855
$706$	−3.83280e135	−1.84202
$707$	−1.53399e133	−0.00689288
$708$	9.91157e134	0.416450
$709$	4.15680e135	1.63329	0.816644	−	0.577142i	$-0.195832\pi$
$709$	4.15680e135	1.63329	0.816644	+	0.577142i	$0.195832\pi$
$710$	−3.83124e134	−0.140789
$711$	9.26303e133	0.0318381
$712$	2.21692e135	0.712771
$713$	1.75215e135	0.527009
$714$	2.15414e134	0.0606190
$715$	−7.96612e135	−2.09754
$716$	6.31265e134	0.155540
$717$	−9.79103e134	−0.225771
$718$	−1.11237e135	−0.240070
$719$	−5.33664e135	−1.07807	−0.539033	−	0.842285i	$-0.681210\pi$
$719$	−5.33664e135	−1.07807	−0.539033	+	0.842285i	$0.681210\pi$
$720$	4.34735e135	0.822113
$721$	−2.23728e135	−0.396090
$722$	1.86862e136	3.09744
$723$	−1.01198e136	−1.57074
$724$	5.22865e134	0.0759990
$725$	5.99533e135	0.816127
$726$	−1.84738e135	−0.235542
$727$	1.15888e136	1.38406	0.692031	−	0.721868i	$-0.256716\pi$
$727$	1.15888e136	1.38406	0.692031	+	0.721868i	$0.256716\pi$
$728$	2.72211e135	0.304555
$729$	2.91876e135	0.305943
$730$	−5.99481e135	−0.588761
$731$	−2.61600e133	−0.00240748
$732$	−6.41204e135	−0.552993
$733$	1.10067e136	0.889645	0.444822	−	0.895619i	$-0.353267\pi$
$733$	1.10067e136	0.889645	0.444822	+	0.895619i	$0.353267\pi$
$734$	−2.49331e136	−1.88892
$735$	−2.34537e136	−1.66557
$736$	−3.93905e135	−0.262238
$737$	2.79715e136	1.74586
$738$	6.79362e135	0.397579
$739$	−7.30942e135	−0.401118	−0.200559	−	0.979682i	$-0.564276\pi$
$739$	−7.30942e135	−0.401118	−0.200559	+	0.979682i	$0.564276\pi$
$740$	1.09544e136	0.563744
$741$	−5.73757e136	−2.76926
$742$	−1.58466e136	−0.717380
$743$	3.66143e136	1.55483	0.777414	−	0.628989i	$-0.216531\pi$
$743$	3.66143e136	1.55483	0.777414	+	0.628989i	$0.216531\pi$
$744$	3.19569e136	1.27306
$745$	−2.62993e136	−0.982928
$746$	−1.38199e136	−0.484631
$747$	9.35775e135	0.307923
$748$	1.69814e135	0.0524382
$749$	−1.03316e136	−0.299419
$750$	4.32196e136	1.17563
$751$	2.09910e136	0.535964	0.267982	−	0.963424i	$-0.413643\pi$
$751$	2.09910e136	0.535964	0.267982	+	0.963424i	$0.413643\pi$
$752$	4.71572e136	1.13032
$753$	5.34642e136	1.20310
$754$	−3.64075e136	−0.769223
$755$	4.02208e136	0.797940
$756$	5.01895e135	0.0935034
$757$	−7.34784e136	−1.28560	−0.642799	−	0.766035i	$-0.722227\pi$
$757$	−7.34784e136	−1.28560	−0.642799	+	0.766035i	$0.722227\pi$
$758$	3.53793e136	0.581383
$759$	2.95804e136	0.456583
$760$	−1.50317e137	−2.17953
$761$	−9.58660e136	−1.30585	−0.652925	−	0.757422i	$-0.726459\pi$
$761$	−9.58660e136	−1.30585	−0.652925	+	0.757422i	$0.726459\pi$
$762$	6.05580e136	0.775015
$763$	−4.39068e136	−0.527978
$764$	−1.92045e136	−0.217005
$765$	7.79679e135	0.0827938
$766$	−6.93288e136	−0.691906
$767$	1.16947e137	1.09701
$768$	−1.36910e137	−1.20720
$769$	1.57789e137	1.30790	0.653950	−	0.756538i	$-0.273111\pi$
$769$	1.57789e137	1.30790	0.653950	+	0.756538i	$0.273111\pi$
$770$	9.00319e136	0.701596
$771$	−2.63169e137	−1.92820
$772$	2.06822e135	0.0142487
$773$	1.75047e137	1.13404	0.567021	−	0.823703i	$-0.308096\pi$
$773$	1.75047e137	1.13404	0.567021	+	0.823703i	$0.308096\pi$
$774$	1.56121e135	0.00951184
$775$	3.95781e137	2.26790
$776$	−1.79883e137	−0.969522
$777$	7.41375e136	0.375871
$778$	9.09291e136	0.433683
$779$	−3.42675e137	−1.53763
$780$	−2.13103e137	−0.899697
$781$	−2.04404e136	−0.0812016
$782$	−1.39454e136	−0.0521325
$783$	1.05312e137	0.370505
$784$	3.28923e137	1.08913
$785$	−4.95096e137	−1.54305
$786$	1.68708e137	0.494953
$787$	6.72817e137	1.85822	0.929110	−	0.369804i	$-0.120575\pi$
$787$	6.72817e137	1.85822	0.929110	+	0.369804i	$0.120575\pi$
$788$	1.08372e137	0.281788
$789$	4.71447e137	1.15418
$790$	−6.19332e136	−0.142770
$791$	−8.96646e136	−0.194643
$792$	1.58992e137	0.325035
$793$	−7.56561e137	−1.45669
$794$	−3.57655e136	−0.0648620
$795$	−1.94625e138	−3.32476
$796$	−1.60415e137	−0.258151
$797$	3.20907e137	0.486530	0.243265	−	0.969960i	$-0.421782\pi$
$797$	3.20907e137	0.486530	0.243265	+	0.969960i	$0.421782\pi$
$798$	6.48451e137	0.926275
$799$	8.45745e136	0.113833
$800$	−8.89765e137	−1.12850
$801$	−3.46148e137	−0.413730
$802$	1.39057e138	1.56642
$803$	−3.19834e137	−0.339575
$804$	7.48269e137	0.748851
$805$	−2.07169e137	−0.195443
$806$	−2.40344e138	−2.13756
$807$	2.61093e138	2.18928
$808$	1.81122e136	0.0143196
$809$	1.47751e138	1.10147	0.550737	−	0.834679i	$-0.314347\pi$
$809$	1.47751e138	1.10147	0.550737	+	0.834679i	$0.314347\pi$
$810$	3.31352e138	2.32944
$811$	−1.90707e138	−1.26438	−0.632189	−	0.774814i	$-0.717844\pi$
$811$	−1.90707e138	−1.26438	−0.632189	+	0.774814i	$0.717844\pi$
$812$	1.15296e137	0.0720945
$813$	−1.64583e138	−0.970696
$814$	2.08576e138	1.16039
$815$	1.30816e138	0.686553
$816$	−3.71040e137	−0.183712
$817$	−7.87483e136	−0.0367869
$818$	−3.63466e138	−1.60207
$819$	−4.25028e137	−0.176779
$820$	−1.27275e138	−0.499558
$821$	−2.39011e138	−0.885358	−0.442679	−	0.896680i	$-0.645972\pi$
$821$	−2.39011e138	−0.885358	−0.442679	+	0.896680i	$0.645972\pi$
$822$	−3.71106e138	−1.29744
$823$	−9.95240e136	−0.0328424	−0.0164212	−	0.999865i	$-0.505227\pi$
$823$	−9.95240e136	−0.0328424	−0.0164212	+	0.999865i	$0.505227\pi$
$824$	2.64161e138	0.822860
$825$	6.68171e138	1.96483
$826$	−1.32172e138	−0.366934
$827$	−2.03165e138	−0.532521	−0.266261	−	0.963901i	$-0.585788\pi$
$827$	−2.03165e138	−0.532521	−0.266261	+	0.963901i	$0.585788\pi$
$828$	2.33198e137	0.0577143
$829$	5.35269e137	0.125093	0.0625463	−	0.998042i	$-0.480078\pi$
$829$	5.35269e137	0.125093	0.0625463	+	0.998042i	$0.480078\pi$
$830$	−6.25664e138	−1.38080
$831$	−7.81130e137	−0.162808
$832$	−2.27411e138	−0.447666
$833$	5.89909e137	0.109685
$834$	1.16344e138	0.204341
$835$	6.17070e138	1.02383
$836$	5.11184e138	0.801270
$837$	6.95215e138	1.02958
$838$	1.58130e138	0.221271
$839$	9.72921e138	1.28642	0.643212	−	0.765688i	$-0.277601\pi$
$839$	9.72921e138	1.28642	0.643212	+	0.765688i	$0.277601\pi$
$840$	−3.77849e138	−0.472120
$841$	−6.04933e138	−0.714328
$842$	−3.51108e138	−0.391847
$843$	−2.95927e138	−0.312158
$844$	−1.05239e138	−0.104933
$845$	−8.27900e138	−0.780340
$846$	−5.04733e138	−0.449748
$847$	6.90283e137	0.0581521
$848$	2.72949e139	2.17410
$849$	−2.00267e139	−1.50832
$850$	−3.15002e138	−0.224344
$851$	−4.79947e138	−0.323250
$852$	−5.46804e137	−0.0348298
$853$	8.37087e138	0.504303	0.252152	−	0.967688i	$-0.418862\pi$
$853$	8.37087e138	0.504303	0.252152	+	0.967688i	$0.418862\pi$
$854$	8.55054e138	0.487242
$855$	2.34703e139	1.26511
$856$	1.21987e139	0.622029
$857$	−2.70903e139	−1.30685	−0.653424	−	0.756992i	$-0.726668\pi$
$857$	−2.70903e139	−1.30685	−0.653424	+	0.756992i	$0.726668\pi$
$858$	−4.05757e139	−1.85191
$859$	−2.18967e139	−0.945589	−0.472795	−	0.881173i	$-0.656755\pi$
$859$	−2.18967e139	−0.945589	−0.472795	+	0.881173i	$0.656755\pi$
$860$	−2.92484e137	−0.0119516
$861$	−8.61376e138	−0.333076
$862$	3.68531e139	1.34859
$863$	2.16635e138	0.0750267	0.0375133	−	0.999296i	$-0.488056\pi$
$863$	2.16635e138	0.0750267	0.0375133	+	0.999296i	$0.488056\pi$
$864$	−1.56293e139	−0.512315
$865$	−2.14244e139	−0.664728
$866$	−3.19592e139	−0.938633
$867$	4.21618e139	1.17223
$868$	7.61123e138	0.200340
$869$	−3.30424e138	−0.0823442
$870$	5.05364e139	1.19245
$871$	8.82888e139	1.97262
$872$	5.18419e139	1.09685
$873$	2.80867e139	0.562761
$874$	−4.19791e139	−0.796599
$875$	−1.61492e139	−0.290247
$876$	−8.55592e138	−0.145654
$877$	−5.83625e139	−0.941137	−0.470569	−	0.882363i	$-0.655951\pi$
$877$	−5.83625e139	−0.941137	−0.470569	+	0.882363i	$0.655951\pi$
$878$	9.70228e139	1.48212
$879$	−6.73849e139	−0.975194
$880$	−1.55076e140	−2.12626
$881$	9.21046e139	1.19654	0.598268	−	0.801296i	$-0.295856\pi$
$881$	9.21046e139	1.19654	0.598268	+	0.801296i	$0.295856\pi$
$882$	−3.52053e139	−0.433361
$883$	−4.51820e139	−0.527026	−0.263513	−	0.964656i	$-0.584881\pi$
$883$	−4.51820e139	−0.527026	−0.263513	+	0.964656i	$0.584881\pi$
$884$	5.36000e138	0.0592491
$885$	−1.62332e140	−1.70058
$886$	8.19875e139	0.814040
$887$	−1.77330e140	−1.66883	−0.834414	−	0.551139i	$-0.814193\pi$
$887$	−1.77330e140	−1.66883	−0.834414	+	0.551139i	$0.814193\pi$
$888$	−8.75360e139	−0.780856
$889$	−2.26278e139	−0.191341
$890$	2.31436e140	1.85527
$891$	1.76782e140	1.34353
$892$	8.51089e138	0.0613259
$893$	2.54591e140	1.73940
$894$	−1.33956e140	−0.867823
$895$	−1.03389e140	−0.635153
$896$	6.96572e139	0.405822
$897$	9.33672e139	0.515886
$898$	−1.66952e140	−0.874914
$899$	1.59705e140	0.793843
$900$	5.26755e139	0.248365
$901$	4.89523e139	0.218950
$902$	−2.42337e140	−1.02828
$903$	−1.97948e138	−0.00796863
$904$	1.05869e140	0.404362
$905$	−8.56348e139	−0.310344
$906$	2.04866e140	0.704498
$907$	−1.25161e140	−0.408435	−0.204217	−	0.978926i	$-0.565465\pi$
$907$	−1.25161e140	−0.408435	−0.204217	+	0.978926i	$0.565465\pi$
$908$	1.75786e140	0.544387
$909$	−2.82803e138	−0.00831187
$910$	2.84176e140	0.792722
$911$	4.72772e140	1.25178	0.625892	−	0.779910i	$-0.284735\pi$
$911$	4.72772e140	1.25178	0.625892	+	0.779910i	$0.284735\pi$
$912$	−1.11693e141	−2.80718
$913$	−3.33803e140	−0.796395
$914$	−8.21949e140	−1.86166
$915$	1.05016e141	2.25816
$916$	−3.10316e140	−0.633533
$917$	−6.30384e139	−0.122197
$918$	−5.53322e139	−0.101848
$919$	4.73889e139	0.0828305	0.0414152	−	0.999142i	$-0.486813\pi$
$919$	4.73889e139	0.0828305	0.0414152	+	0.999142i	$0.486813\pi$
$920$	2.44610e140	0.406025
$921$	−8.04646e139	−0.126845
$922$	7.29113e140	1.09163
$923$	−6.45178e139	−0.0917484
$924$	1.28496e140	0.173568
$925$	−1.08412e141	−1.39106
$926$	−1.81608e140	−0.221367
$927$	−4.12458e140	−0.477631
$928$	−3.59038e140	−0.395013
$929$	−1.52587e141	−1.59504	−0.797520	−	0.603293i	$-0.793855\pi$
$929$	−1.52587e141	−1.59504	−0.797520	+	0.603293i	$0.793855\pi$
$930$	3.33615e141	3.31364
$931$	1.77578e141	1.67602
$932$	−2.56700e140	−0.230234
$933$	−1.79596e141	−1.53080
$934$	2.06337e141	1.67148
$935$	−2.78122e140	−0.214133
$936$	5.01841e140	0.367251
$937$	−4.18019e140	−0.290780	−0.145390	−	0.989374i	$-0.546444\pi$
$937$	−4.18019e140	−0.290780	−0.145390	+	0.989374i	$0.546444\pi$
$938$	−9.97827e140	−0.659812
$939$	1.54371e141	0.970401
$940$	9.45594e140	0.565108
$941$	−1.40551e141	−0.798593	−0.399297	−	0.916822i	$-0.630746\pi$
$941$	−1.40551e141	−0.798593	−0.399297	+	0.916822i	$0.630746\pi$
$942$	−2.52179e141	−1.36236
$943$	5.57633e140	0.286446
$944$	2.27660e141	1.11203
$945$	−8.22003e140	−0.381823
$946$	−5.56902e139	−0.0246008
$947$	1.37847e141	0.579127	0.289564	−	0.957159i	$-0.406490\pi$
$947$	1.37847e141	0.579127	0.289564	+	0.957159i	$0.406490\pi$
$948$	−8.83924e139	−0.0353199
$949$	−1.00952e141	−0.383680
$950$	−9.48237e141	−3.42804
$951$	−6.29897e140	−0.216618
$952$	9.50371e139	0.0310912
$953$	−1.95030e141	−0.607000	−0.303500	−	0.952831i	$-0.598155\pi$
$953$	−1.95030e141	−0.607000	−0.303500	+	0.952831i	$0.598155\pi$
$954$	−2.92143e141	−0.865063
$955$	3.14532e141	0.886144
$956$	2.75339e140	0.0738105
$957$	2.69621e141	0.687758
$958$	6.98061e141	1.69446
$959$	1.38665e141	0.320320
$960$	3.15664e141	0.693971
$961$	5.76367e141	1.20598
$962$	6.58348e141	1.31111
$963$	−1.90470e141	−0.361059
$964$	2.84586e141	0.513516
$965$	−3.38733e140	−0.0581848
$966$	−1.05522e141	−0.172556
$967$	−1.09243e142	−1.70073	−0.850365	−	0.526193i	$-0.823619\pi$
$967$	−1.09243e142	−1.70073	−0.850365	+	0.526193i	$0.823619\pi$
$968$	−8.15035e140	−0.120808
$969$	−2.00316e141	−0.282707
$970$	−1.87789e142	−2.52356
$971$	1.31822e142	1.68685	0.843423	−	0.537251i	$-0.180537\pi$
$971$	1.31822e142	1.68685	0.843423	+	0.537251i	$0.180537\pi$
$972$	2.51466e141	0.306430
$973$	−4.34724e140	−0.0504492
$974$	−8.66938e141	−0.958160
$975$	2.10901e142	2.22003
$976$	−1.47279e142	−1.47664
$977$	−1.47379e142	−1.40748	−0.703742	−	0.710456i	$-0.748489\pi$
$977$	−1.47379e142	−1.40748	−0.703742	+	0.710456i	$0.748489\pi$
$978$	6.66314e141	0.606155
$979$	1.23475e142	1.07005
$980$	6.59554e141	0.544518
$981$	−8.09454e141	−0.636670
$982$	−5.30812e141	−0.397782
$983$	−7.00451e141	−0.500133	−0.250067	−	0.968229i	$-0.580453\pi$
$983$	−7.00451e141	−0.500133	−0.250067	+	0.968229i	$0.580453\pi$
$984$	1.01705e142	0.691950
$985$	−1.77492e142	−1.15069
$986$	−1.27110e141	−0.0785281
$987$	6.39961e141	0.376781
$988$	1.61350e142	0.905343
$989$	1.28147e140	0.00685304
$990$	1.65981e142	0.846030
$991$	−9.23865e141	−0.448859	−0.224430	−	0.974490i	$-0.572052\pi$
$991$	−9.23865e141	−0.448859	−0.224430	+	0.974490i	$0.572052\pi$
$992$	−2.37018e142	−1.09769
$993$	−2.67511e142	−1.18101
$994$	7.29170e140	0.0306885
$995$	2.62728e142	1.05417
$996$	−8.92962e141	−0.341597
$997$	4.50334e142	1.64254	0.821268	−	0.570543i	$-0.193267\pi$
$997$	4.50334e142	1.64254	0.821268	+	0.570543i	$0.193267\pi$
$998$	2.65979e142	0.925009
$999$	−1.90433e142	−0.631511

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1.96.a.a.1.7	✓	8
3.2	odd	2		9.96.a.c.1.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1.96.a.a.1.7	✓	8	1.1	even	1	trivial
9.96.a.c.1.2		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)

\(f(q)\)	\(=\)	\(q+2.34596e14 q^{2} -5.48368e22 q^{3} +1.54210e28 q^{4} -2.52565e33 q^{5} -1.28645e37 q^{6} +4.80687e39 q^{7} -5.67559e42 q^{8} +8.86182e44 q^{9} +O(q^{10})\)	\(q+2.34596e14 q^{2} -5.48368e22 q^{3} +1.54210e28 q^{4} -2.52565e33 q^{5} -1.28645e37 q^{6} +4.80687e39 q^{7} -5.67559e42 q^{8} +8.86182e44 q^{9} -5.92506e47 q^{10} -3.16113e49 q^{11} -8.45638e50 q^{12} -9.97774e52 q^{13} +1.12767e54 q^{14} +1.38499e56 q^{15} -1.94236e57 q^{16} -3.48353e57 q^{17} +2.07894e59 q^{18} -1.04863e61 q^{19} -3.89480e61 q^{20} -2.63593e62 q^{21} -7.41586e63 q^{22} +1.70644e64 q^{23} +3.11231e65 q^{24} +3.85455e66 q^{25} -2.34073e67 q^{26} +6.77078e67 q^{27} +7.41266e67 q^{28} +1.55539e69 q^{29} +3.24912e70 q^{30} +1.02679e71 q^{31} -2.30835e71 q^{32} +1.73346e72 q^{33} -8.17221e71 q^{34} -1.21405e73 q^{35} +1.36658e73 q^{36} -2.81257e74 q^{37} -2.46005e75 q^{38} +5.47148e75 q^{39} +1.43346e76 q^{40} +3.26782e76 q^{41} -6.18378e76 q^{42} +7.50961e75 q^{43} -4.87477e77 q^{44} -2.23818e78 q^{45} +4.00322e78 q^{46} -2.42784e79 q^{47} +1.06513e80 q^{48} -1.69342e80 q^{49} +9.04260e80 q^{50} +1.91026e80 q^{51} -1.53867e81 q^{52} -1.40525e82 q^{53} +1.58839e82 q^{54} +7.98389e82 q^{55} -2.72818e82 q^{56} +5.75037e83 q^{57} +3.64887e83 q^{58} -1.17208e84 q^{59} +2.13578e84 q^{60} +7.58248e84 q^{61} +2.40880e85 q^{62} +4.25976e84 q^{63} +2.27918e85 q^{64} +2.52003e86 q^{65} +4.06662e86 q^{66} -8.84858e86 q^{67} -5.37195e85 q^{68} -9.35755e86 q^{69} -2.84810e87 q^{70} +6.46617e86 q^{71} -5.02961e87 q^{72} +1.01177e88 q^{73} -6.59817e88 q^{74} -2.11371e89 q^{75} -1.61710e89 q^{76} -1.51951e89 q^{77} +1.28358e90 q^{78} +1.04527e89 q^{79} +4.90571e90 q^{80} -5.59238e90 q^{81} +7.66617e90 q^{82} +1.05596e91 q^{83} -4.06487e90 q^{84} +8.79818e90 q^{85} +1.76172e90 q^{86} -8.52926e91 q^{87} +1.79413e92 q^{88} -3.90606e92 q^{89} -5.25068e92 q^{90} -4.79617e92 q^{91} +2.63149e92 q^{92} -5.63058e93 q^{93} -5.69559e93 q^{94} +2.64848e94 q^{95} +1.26583e94 q^{96} +3.16941e94 q^{97} -3.97269e94 q^{98} -2.80133e94 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 5835659138280 q^{2} - 95\!\cdots\!80 q^{3}+ \cdots + 92\!\cdots\!36 q^{9}+O(q^{10}) \) 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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