LMFDB - Embedded newform 1.96.a.a.1.2

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			1.2
Root			$-1.46162e13$ 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)

$f(q)$	$=$	$q-3.51519e14 q^{2} +6.56090e22 q^{3} +8.39514e28 q^{4} +2.79946e33 q^{5} -2.30628e37 q^{6} +5.53054e39 q^{7} -1.55854e43 q^{8} +2.18364e45 q^{9} +O(q^{10})$	\(q-3.51519e14 q^{2} +6.56090e22 q^{3} +8.39514e28 q^{4} +2.79946e33 q^{5} -2.30628e37 q^{6} +5.53054e39 q^{7} -1.55854e43 q^{8} +2.18364e45 q^{9} -9.84062e47 q^{10} +3.60788e48 q^{11} +5.50796e51 q^{12} +1.06916e53 q^{13} -1.94409e54 q^{14} +1.83670e56 q^{15} +2.15290e57 q^{16} +3.05031e58 q^{17} -7.67592e59 q^{18} -5.36133e58 q^{19} +2.35018e62 q^{20} +3.62853e62 q^{21} -1.26824e63 q^{22} +3.27765e64 q^{23} -1.02254e66 q^{24} +5.31261e66 q^{25} -3.75830e67 q^{26} +4.11692e66 q^{27} +4.64296e68 q^{28} -3.24861e69 q^{29} -6.45633e70 q^{30} -4.63359e70 q^{31} -1.39384e71 q^{32} +2.36709e71 q^{33} -1.07224e73 q^{34} +1.54825e73 q^{35} +1.83320e74 q^{36} +2.22715e74 q^{37} +1.88461e73 q^{38} +7.01465e75 q^{39} -4.36306e76 q^{40} -8.69382e75 q^{41} -1.27550e77 q^{42} +4.86197e77 q^{43} +3.02887e77 q^{44} +6.11302e78 q^{45} -1.15216e79 q^{46} -1.28855e79 q^{47} +1.41250e80 q^{48} -1.61861e80 q^{49} -1.86748e81 q^{50} +2.00128e81 q^{51} +8.97574e81 q^{52} +4.42467e81 q^{53} -1.44717e81 q^{54} +1.01001e82 q^{55} -8.61956e82 q^{56} -3.51751e81 q^{57} +1.14195e84 q^{58} -1.94954e84 q^{59} +1.54193e85 q^{60} -5.98141e84 q^{61} +1.62879e85 q^{62} +1.20767e85 q^{63} -3.62891e85 q^{64} +2.99307e86 q^{65} -8.32078e85 q^{66} -6.60161e86 q^{67} +2.56078e87 q^{68} +2.15044e87 q^{69} -5.44240e87 q^{70} -7.94968e87 q^{71} -3.40329e88 q^{72} -4.40521e88 q^{73} -7.82883e88 q^{74} +3.48555e89 q^{75} -4.50091e87 q^{76} +1.99535e88 q^{77} -2.46578e90 q^{78} +1.51977e90 q^{79} +6.02695e90 q^{80} -4.36117e90 q^{81} +3.05604e90 q^{82} +1.48872e91 q^{83} +3.04620e91 q^{84} +8.53923e91 q^{85} -1.70907e92 q^{86} -2.13138e92 q^{87} -5.62302e91 q^{88} +5.31083e92 q^{89} -2.14884e93 q^{90} +5.91303e92 q^{91} +2.75163e93 q^{92} -3.04005e93 q^{93} +4.52949e93 q^{94} -1.50088e92 q^{95} -9.14485e93 q^{96} -2.46425e94 q^{97} +5.68973e94 q^{98} +7.87833e93 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−3.51519e14	−1.76613	−0.883067	−	0.469247i	$-0.844526\pi$
$2$	−3.51519e14	−1.76613	−0.883067	+	0.469247i	$0.844526\pi$
$3$	6.56090e22	1.42464	0.712318	−	0.701857i	$-0.247646\pi$
$3$	6.56090e22	1.42464	0.712318	+	0.701857i	$0.247646\pi$
$4$	8.39514e28	2.11923
$5$	2.79946e33	1.76197	0.880986	−	0.473143i	$-0.156881\pi$
$5$	2.79946e33	1.76197	0.880986	+	0.473143i	$0.156881\pi$
$6$	−2.30628e37	−2.51610
$7$	5.53054e39	0.398667	0.199334	−	0.979932i	$-0.436122\pi$
$7$	5.53054e39	0.398667	0.199334	+	0.979932i	$0.436122\pi$
$8$	−1.55854e43	−1.97671
$9$	2.18364e45	1.02959
$10$	−9.84062e47	−3.11188
$11$	3.60788e48	0.123339	0.0616694	−	0.998097i	$-0.480358\pi$
$11$	3.60788e48	0.123339	0.0616694	+	0.998097i	$0.480358\pi$
$12$	5.50796e51	3.01913
$13$	1.06916e53	1.30838	0.654189	−	0.756331i	$-0.273010\pi$
$13$	1.06916e53	1.30838	0.654189	+	0.756331i	$0.273010\pi$
$14$	−1.94409e54	−0.704100
$15$	1.83670e56	2.51017
$16$	2.15290e57	1.37191
$17$	3.05031e58	1.09149	0.545746	−	0.837950i	$-0.316246\pi$
$17$	3.05031e58	1.09149	0.545746	+	0.837950i	$0.316246\pi$
$18$	−7.67592e59	−1.81839
$19$	−5.36133e58	−0.00973815	−0.00486907	−	0.999988i	$-0.501550\pi$
$19$	−5.36133e58	−0.00973815	−0.00486907	+	0.999988i	$0.501550\pi$
$20$	2.35018e62	3.73402
$21$	3.62853e62	0.567956
$22$	−1.26824e63	−0.217833
$23$	3.27765e64	0.681539	0.340770	−	0.940147i	$-0.389312\pi$
$23$	3.27765e64	0.681539	0.340770	+	0.940147i	$0.389312\pi$
$24$	−1.02254e66	−2.81609
$25$	5.31261e66	2.10454
$26$	−3.75830e67	−2.31077
$27$	4.11692e66	0.0421496
$28$	4.64296e68	0.844868
$29$	−3.24861e69	−1.11633	−0.558165	−	0.829730i	$-0.688495\pi$
$29$	−3.24861e69	−1.11633	−0.558165	+	0.829730i	$0.688495\pi$
$30$	−6.45633e70	−4.43329
$31$	−4.63359e70	−0.670251	−0.335125	−	0.942174i	$-0.608779\pi$
$31$	−4.63359e70	−0.670251	−0.335125	+	0.942174i	$0.608779\pi$
$32$	−1.39384e71	−0.446261
$33$	2.36709e71	0.175713
$34$	−1.07224e73	−1.92772
$35$	1.54825e73	0.702440
$36$	1.83320e74	2.18193
$37$	2.22715e74	0.721384	0.360692	−	0.932685i	$-0.382541\pi$
$37$	2.22715e74	0.721384	0.360692	+	0.932685i	$0.382541\pi$
$38$	1.88461e73	0.0171989
$39$	7.01465e75	1.86396
$40$	−4.36306e76	−3.48291
$41$	−8.69382e75	−0.214772	−0.107386	−	0.994217i	$-0.534248\pi$
$41$	−8.69382e75	−0.214772	−0.107386	+	0.994217i	$0.534248\pi$
$42$	−1.27550e77	−1.00309
$43$	4.86197e77	1.25043	0.625217	−	0.780451i	$-0.285010\pi$
$43$	4.86197e77	1.25043	0.625217	+	0.780451i	$0.285010\pi$
$44$	3.02887e77	0.261383
$45$	6.11302e78	1.81410
$46$	−1.15216e79	−1.20369
$47$	−1.28855e79	−0.484677	−0.242339	−	0.970192i	$-0.577915\pi$
$47$	−1.28855e79	−0.484677	−0.242339	+	0.970192i	$0.577915\pi$
$48$	1.41250e80	1.95447
$49$	−1.61861e80	−0.841064
$50$	−1.86748e81	−3.71690
$51$	2.00128e81	1.55498
$52$	8.97574e81	2.77275
$53$	4.42467e81	0.553066	0.276533	−	0.961004i	$-0.410815\pi$
$53$	4.42467e81	0.553066	0.276533	+	0.961004i	$0.410815\pi$
$54$	−1.44717e81	−0.0744418
$55$	1.01001e82	0.217319
$56$	−8.61956e82	−0.788050
$57$	−3.51751e81	−0.0138733
$58$	1.14195e84	1.97159
$59$	−1.94954e84	−1.49438	−0.747190	−	0.664610i	$-0.768598\pi$
$59$	−1.94954e84	−1.49438	−0.747190	+	0.664610i	$0.768598\pi$
$60$	1.54193e85	5.31962
$61$	−5.98141e84	−0.941102	−0.470551	−	0.882373i	$-0.655945\pi$
$61$	−5.98141e84	−0.941102	−0.470551	+	0.882373i	$0.655945\pi$
$62$	1.62879e85	1.18375
$63$	1.20767e85	0.410462
$64$	−3.62891e85	−0.583750
$65$	2.99307e86	2.30532
$66$	−8.32078e85	−0.310332
$67$	−6.60161e86	−1.20530	−0.602652	−	0.798004i	$-0.705889\pi$
$67$	−6.60161e86	−1.20530	−0.602652	+	0.798004i	$0.705889\pi$
$68$	2.56078e87	2.31312
$69$	2.15044e87	0.970945
$70$	−5.44240e87	−1.24060
$71$	−7.94968e87	−0.923801	−0.461900	−	0.886932i	$-0.652832\pi$
$71$	−7.94968e87	−0.923801	−0.461900	+	0.886932i	$0.652832\pi$
$72$	−3.40329e88	−2.03519
$73$	−4.40521e88	−1.36814	−0.684070	−	0.729417i	$-0.739792\pi$
$73$	−4.40521e88	−1.36814	−0.684070	+	0.729417i	$0.739792\pi$
$74$	−7.82883e88	−1.27406
$75$	3.48555e89	2.99821
$76$	−4.50091e87	−0.0206374
$77$	1.99535e88	0.0491712
$78$	−2.46578e90	−3.29201
$79$	1.51977e90	1.10787	0.553937	−	0.832558i	$-0.313125\pi$
$79$	1.51977e90	1.10787	0.553937	+	0.832558i	$0.313125\pi$
$80$	6.02695e90	2.41726
$81$	−4.36117e90	−0.969538
$82$	3.05604e90	0.379316
$83$	1.48872e91	1.03897	0.519485	−	0.854479i	$-0.326124\pi$
$83$	1.48872e91	1.03897	0.519485	+	0.854479i	$0.326124\pi$
$84$	3.04620e91	1.20363
$85$	8.53923e91	1.92318
$86$	−1.70907e92	−2.20843
$87$	−2.13138e92	−1.59036
$88$	−5.62302e91	−0.243805
$89$	5.31083e92	1.34629	0.673143	−	0.739512i	$-0.264944\pi$
$89$	5.31083e92	1.34629	0.673143	+	0.739512i	$0.264944\pi$
$90$	−2.14884e93	−3.20395
$91$	5.91303e92	0.521608
$92$	2.75163e93	1.44434
$93$	−3.04005e93	−0.954863
$94$	4.52949e93	0.856005
$95$	−1.50088e92	−0.0171583
$96$	−9.14485e93	−0.635759
$97$	−2.46425e94	−1.04719	−0.523597	−	0.851966i	$-0.675410\pi$
$97$	−2.46425e94	−1.04719	−0.523597	+	0.851966i	$0.675410\pi$
$98$	5.68973e94	1.48543
$99$	7.87833e93	0.126988
$100$	4.46001e95	4.46001
$101$	−1.34497e95	−0.838394	−0.419197	−	0.907895i	$-0.637688\pi$
$101$	−1.34497e95	−0.838394	−0.419197	+	0.907895i	$0.637688\pi$
$102$	−7.03488e95	−2.74630
$103$	1.85813e95	0.456361	0.228180	−	0.973619i	$-0.426722\pi$
$103$	1.85813e95	0.456361	0.228180	+	0.973619i	$0.426722\pi$
$104$	−1.66633e96	−2.58629
$105$	1.01579e96	1.00072
$106$	−1.55535e96	−0.976788
$107$	2.19705e96	0.883303	0.441652	−	0.897187i	$-0.354393\pi$
$107$	2.19705e96	0.883303	0.441652	+	0.897187i	$0.354393\pi$
$108$	3.45621e95	0.0893247
$109$	−1.22056e96	−0.203610	−0.101805	−	0.994804i	$-0.532462\pi$
$109$	−1.22056e96	−0.203610	−0.101805	+	0.994804i	$0.532462\pi$
$110$	−3.55038e96	−0.383815
$111$	1.46121e97	1.02771
$112$	1.19067e97	0.546935
$113$	−7.13251e96	−0.214791	−0.107395	−	0.994216i	$-0.534251\pi$
$113$	−7.13251e96	−0.214791	−0.107395	+	0.994216i	$0.534251\pi$
$114$	1.23647e96	0.0245021
$115$	9.17565e97	1.20085
$116$	−2.72725e98	−2.36576
$117$	2.33466e98	1.34709
$118$	6.85299e98	2.63928
$119$	1.68699e98	0.435143
$120$	−2.86256e99	−4.96187
$121$	−8.42651e98	−0.984788
$122$	2.10258e99	1.66211
$123$	−5.70393e98	−0.305972
$124$	−3.88996e99	−1.42042
$125$	7.80561e99	1.94617
$126$	−4.24520e99	−0.724932
$127$	1.52656e100	1.79075	0.895377	−	0.445309i	$-0.146906\pi$
$127$	1.52656e100	1.79075	0.895377	+	0.445309i	$0.146906\pi$
$128$	1.82779e100	1.47724
$129$	3.18989e100	1.78141
$130$	−1.05212e101	−4.07151
$131$	−1.97188e100	−0.530266	−0.265133	−	0.964212i	$-0.585416\pi$
$131$	−1.97188e100	−0.530266	−0.265133	+	0.964212i	$0.585416\pi$
$132$	1.98721e100	0.372376
$133$	−2.96510e98	−0.00388228
$134$	2.32059e101	2.12873
$135$	1.15251e100	0.0742663
$136$	−4.75403e101	−2.15757
$137$	2.26969e101	0.727345	0.363672	−	0.931527i	$-0.381523\pi$
$137$	2.26969e101	0.727345	0.363672	+	0.931527i	$0.381523\pi$
$138$	−7.55918e101	−1.71482
$139$	−6.09466e101	−0.981175	−0.490587	−	0.871392i	$-0.663218\pi$
$139$	−6.09466e101	−0.981175	−0.490587	+	0.871392i	$0.663218\pi$
$140$	1.29978e102	1.48863
$141$	−8.45404e101	−0.690488
$142$	2.79446e102	1.63156
$143$	3.85740e101	0.161374
$144$	4.70117e102	1.41250
$145$	−9.09435e102	−1.96694
$146$	1.54851e103	2.41632
$147$	−1.06196e103	−1.19821
$148$	1.86972e103	1.52878
$149$	5.92217e102	0.351668	0.175834	−	0.984420i	$-0.443738\pi$
$149$	5.92217e102	0.351668	0.175834	+	0.984420i	$0.443738\pi$
$150$	−1.22524e104	−5.29523
$151$	2.56833e103	0.809555	0.404778	−	0.914415i	$-0.367349\pi$
$151$	2.56833e103	0.809555	0.404778	+	0.914415i	$0.367349\pi$
$152$	8.35584e101	0.0192495
$153$	6.66080e103	1.12379
$154$	−7.01404e102	−0.0868429
$155$	−1.29715e104	−1.18096
$156$	5.88889e104	3.95016
$157$	−1.93151e104	−0.956452	−0.478226	−	0.878237i	$-0.658720\pi$
$157$	−1.93151e104	−0.956452	−0.478226	+	0.878237i	$0.658720\pi$
$158$	−5.34227e104	−1.95666
$159$	2.90298e104	0.787917
$160$	−3.90200e104	−0.786299
$161$	1.81272e104	0.271707
$162$	1.53303e105	1.71234
$163$	7.24673e104	0.604270	0.302135	−	0.953265i	$-0.402301\pi$
$163$	7.24673e104	0.604270	0.302135	+	0.953265i	$0.402301\pi$
$164$	−7.29858e104	−0.455151
$165$	6.62658e104	0.309601
$166$	−5.23313e105	−1.83496
$167$	2.66985e105	0.703808	0.351904	−	0.936036i	$-0.385534\pi$
$167$	2.66985e105	0.703808	0.351904	+	0.936036i	$0.385534\pi$
$168$	−5.65521e105	−1.12268
$169$	4.75344e105	0.711852
$170$	−3.00170e106	−3.39659
$171$	−1.17072e104	−0.0100263
$172$	4.08169e106	2.64996
$173$	−8.11433e105	−0.400002	−0.200001	−	0.979796i	$-0.564095\pi$
$173$	−8.11433e105	−0.400002	−0.200001	+	0.979796i	$0.564095\pi$
$174$	7.49221e106	2.80880
$175$	2.93816e106	0.839012
$176$	7.76741e105	0.169209
$177$	−1.27907e107	−2.12895
$178$	−1.86686e107	−2.37772
$179$	8.86576e106	0.865360	0.432680	−	0.901548i	$-0.357568\pi$
$179$	8.86576e106	0.865360	0.432680	+	0.901548i	$0.357568\pi$
$180$	5.13196e107	3.84450
$181$	−3.14813e107	−1.81268	−0.906339	−	0.422550i	$-0.861135\pi$
$181$	−3.14813e107	−1.81268	−0.906339	+	0.422550i	$0.861135\pi$
$182$	−2.07854e107	−0.921229
$183$	−3.92435e107	−1.34073
$184$	−5.10835e107	−1.34721
$185$	6.23480e107	1.27106
$186$	1.06864e108	1.68642
$187$	1.10052e107	0.134623
$188$	−1.08175e108	−1.02714
$189$	2.27688e106	0.0168037
$190$	5.27588e106	0.0303039
$191$	1.19303e108	0.534031	0.267015	−	0.963692i	$-0.413963\pi$
$191$	1.19303e108	0.534031	0.267015	+	0.963692i	$0.413963\pi$
$192$	−2.38089e108	−0.831631
$193$	−3.23100e108	−0.881789	−0.440895	−	0.897559i	$-0.645339\pi$
$193$	−3.23100e108	−0.881789	−0.440895	+	0.897559i	$0.645339\pi$
$194$	8.66230e108	1.84949
$195$	1.96372e109	3.28425
$196$	−1.35885e109	−1.78241
$197$	−4.47509e108	−0.460952	−0.230476	−	0.973078i	$-0.574028\pi$
$197$	−4.47509e108	−0.460952	−0.230476	+	0.973078i	$0.574028\pi$
$198$	−2.76938e108	−0.224278
$199$	1.72995e109	1.10284	0.551421	−	0.834227i	$-0.314086\pi$
$199$	1.72995e109	1.10284	0.551421	+	0.834227i	$0.314086\pi$
$200$	−8.27991e109	−4.16007
$201$	−4.33125e109	−1.71712
$202$	4.72783e109	1.48072
$203$	−1.79666e109	−0.445045
$204$	1.68010e110	3.29536
$205$	−2.43380e109	−0.378422
$206$	−6.53168e109	−0.805995
$207$	7.15723e109	0.701703
$208$	2.30179e110	1.79497
$209$	−1.93430e107	−0.00120109
$210$	−3.57070e110	−1.76741
$211$	−3.21956e109	−0.127169	−0.0635844	−	0.997976i	$-0.520253\pi$
$211$	−3.21956e109	−0.127169	−0.0635844	+	0.997976i	$0.520253\pi$
$212$	3.71457e110	1.17207
$213$	−5.21571e110	−1.31608
$214$	−7.72303e110	−1.56003
$215$	1.36109e111	2.20323
$216$	−6.41637e109	−0.0833175
$217$	−2.56263e110	−0.267207
$218$	4.29049e110	0.359603
$219$	−2.89021e111	−1.94910
$220$	8.47918e110	0.460550
$221$	3.26127e111	1.42808
$222$	−5.13642e111	−1.81507
$223$	−1.68343e111	−0.480522	−0.240261	−	0.970708i	$-0.577233\pi$
$223$	−1.68343e111	−0.480522	−0.240261	+	0.970708i	$0.577233\pi$
$224$	−7.70869e110	−0.177910
$225$	1.16009e112	2.16681
$226$	2.50721e111	0.379350
$227$	1.33543e112	1.63830	0.819150	−	0.573579i	$-0.194446\pi$
$227$	1.33543e112	1.63830	0.819150	+	0.573579i	$0.194446\pi$
$228$	−2.95300e110	−0.0294007
$229$	−9.22326e111	−0.745932	−0.372966	−	0.927845i	$-0.621659\pi$
$229$	−9.22326e111	−0.745932	−0.372966	+	0.927845i	$0.621659\pi$
$230$	−3.22541e112	−2.12087
$231$	1.30913e111	0.0700510
$232$	5.06309e112	2.20666
$233$	2.87634e112	1.02196	0.510979	−	0.859593i	$-0.329283\pi$
$233$	2.87634e112	1.02196	0.510979	+	0.859593i	$0.329283\pi$
$234$	−8.20678e112	−2.37914
$235$	−3.60724e112	−0.853987
$236$	−1.63666e113	−3.16694
$237$	9.97105e112	1.57832
$238$	−5.93008e112	−0.768520
$239$	3.00850e112	0.319485	0.159742	−	0.987159i	$-0.448934\pi$
$239$	3.00850e112	0.319485	0.159742	+	0.987159i	$0.448934\pi$
$240$	3.95422e113	3.44372
$241$	1.57464e113	1.12557	0.562784	−	0.826604i	$-0.309730\pi$
$241$	1.57464e113	1.12557	0.562784	+	0.826604i	$0.309730\pi$
$242$	2.96208e113	1.73927
$243$	−2.94864e113	−1.42339
$244$	−5.02148e113	−1.99441
$245$	−4.53124e113	−1.48193
$246$	2.00504e113	0.540387
$247$	−5.73211e111	−0.0127412
$248$	7.22163e113	1.32489
$249$	9.76733e113	1.48015
$250$	−2.74382e114	−3.43720
$251$	1.45878e114	1.51178	0.755889	−	0.654700i	$-0.227205\pi$
$251$	1.45878e114	1.51178	0.755889	+	0.654700i	$0.227205\pi$
$252$	1.01386e114	0.869865
$253$	1.18254e113	0.0840602
$254$	−5.36613e114	−3.16271
$255$	5.60250e114	2.73983
$256$	−4.98745e114	−2.02526
$257$	3.19917e114	1.07948	0.539739	−	0.841832i	$-0.318523\pi$
$257$	3.19917e114	1.07948	0.539739	+	0.841832i	$0.318523\pi$
$258$	−1.12131e115	−3.14621
$259$	1.23173e114	0.287592
$260$	2.51272e115	4.88551
$261$	−7.09381e114	−1.14936
$262$	6.93152e114	0.936521
$263$	−7.13243e114	−0.804155	−0.402077	−	0.915606i	$-0.631712\pi$
$263$	−7.13243e114	−0.804155	−0.402077	+	0.915606i	$0.631712\pi$
$264$	−3.68921e114	−0.347334
$265$	1.23867e115	0.974485
$266$	1.04229e113	0.00685663
$267$	3.48438e115	1.91797
$268$	−5.54214e115	−2.55432
$269$	−4.72689e115	−1.82534	−0.912668	−	0.408703i	$-0.865981\pi$
$269$	−4.72689e115	−1.82534	−0.912668	+	0.408703i	$0.865981\pi$
$270$	−4.05130e114	−0.131164
$271$	−5.67261e115	−1.54078	−0.770392	−	0.637571i	$-0.779939\pi$
$271$	−5.67261e115	−1.54078	−0.770392	+	0.637571i	$0.779939\pi$
$272$	6.56702e115	1.49743
$273$	3.87948e115	0.743101
$274$	−7.97840e115	−1.28459
$275$	1.91673e115	0.259572
$276$	1.80532e116	2.05766
$277$	−8.10881e115	−0.778338	−0.389169	−	0.921166i	$-0.627238\pi$
$277$	−8.10881e115	−0.778338	−0.389169	+	0.921166i	$0.627238\pi$
$278$	2.14239e116	1.73289
$279$	−1.01181e116	−0.690081
$280$	−2.41301e116	−1.38852
$281$	2.94221e116	1.42930	0.714651	−	0.699481i	$-0.246585\pi$
$281$	2.94221e116	1.42930	0.714651	+	0.699481i	$0.246585\pi$
$282$	2.97175e116	1.21950
$283$	−9.29359e115	−0.322350	−0.161175	−	0.986926i	$-0.551528\pi$
$283$	−9.29359e115	−0.322350	−0.161175	+	0.986926i	$0.551528\pi$
$284$	−6.67387e116	−1.95775
$285$	−9.84713e114	−0.0244444
$286$	−1.35595e116	−0.285008
$287$	−4.80815e115	−0.0856226
$288$	−3.04365e116	−0.459464
$289$	1.49448e116	0.191356
$290$	3.19684e117	3.47389
$291$	−1.61677e117	−1.49187
$292$	−3.69823e117	−2.89940
$293$	1.78906e117	1.19238	0.596188	−	0.802845i	$-0.296681\pi$
$293$	1.78906e117	1.19238	0.596188	+	0.802845i	$0.296681\pi$
$294$	3.73297e117	2.11620
$295$	−5.45765e117	−2.63305
$296$	−3.47109e117	−1.42597
$297$	1.48533e115	0.00519868
$298$	−2.08176e117	−0.621094
$299$	3.50433e117	0.891711
$300$	2.92617e118	6.35389
$301$	2.68893e117	0.498507
$302$	−9.02818e117	−1.42978
$303$	−8.82423e117	−1.19441
$304$	−1.15424e116	−0.0133598
$305$	−1.67447e118	−1.65819
$306$	−2.34140e118	−1.98476
$307$	−2.98339e117	−0.216590	−0.108295	−	0.994119i	$-0.534539\pi$
$307$	−2.98339e117	−0.216590	−0.108295	+	0.994119i	$0.534539\pi$
$308$	1.67513e117	0.104205
$309$	1.21910e118	0.650148
$310$	4.55974e118	2.08574
$311$	2.89743e117	0.113735	0.0568675	−	0.998382i	$-0.481889\pi$
$311$	2.89743e117	0.113735	0.0568675	+	0.998382i	$0.481889\pi$
$312$	−1.09326e119	−3.68451
$313$	−1.13198e118	−0.327704	−0.163852	−	0.986485i	$-0.552392\pi$
$313$	−1.13198e118	−0.327704	−0.163852	+	0.986485i	$0.552392\pi$
$314$	6.78962e118	1.68922
$315$	3.38083e118	0.723223
$316$	1.27587e119	2.34784
$317$	3.28781e118	0.520705	0.260352	−	0.965514i	$-0.416161\pi$
$317$	3.28781e118	0.520705	0.260352	+	0.965514i	$0.416161\pi$
$318$	−1.02045e119	−1.39157
$319$	−1.17206e118	−0.137687
$320$	−1.01590e119	−1.02855
$321$	1.44146e119	1.25839
$322$	−6.37205e118	−0.479872
$323$	−1.63537e117	−0.0106291
$324$	−3.66127e119	−2.05468
$325$	5.68003e119	2.75354
$326$	−2.54736e119	−1.06722
$327$	−8.00795e118	−0.290070
$328$	1.35497e119	0.424542
$329$	−7.12637e118	−0.193225
$330$	−2.32937e119	−0.546797
$331$	−7.78507e119	−1.58282	−0.791412	−	0.611283i	$-0.790654\pi$
$331$	−7.78507e119	−1.58282	−0.791412	+	0.611283i	$0.790654\pi$
$332$	1.24980e120	2.20182
$333$	4.86329e119	0.742727
$334$	−9.38501e119	−1.24302
$335$	−1.84809e120	−2.12371
$336$	7.81187e119	0.779183
$337$	2.02317e120	1.75231	0.876156	−	0.482027i	$-0.160099\pi$
$337$	2.02317e120	1.75231	0.876156	+	0.482027i	$0.160099\pi$
$338$	−1.67093e120	−1.25723
$339$	−4.67956e119	−0.305999
$340$	7.16880e120	4.07566
$341$	−1.67175e119	−0.0826679
$342$	4.11531e118	0.0177077
$343$	−1.95952e120	−0.733972
$344$	−7.57757e120	−2.47175
$345$	6.02005e120	1.71078
$346$	2.85234e120	0.706458
$347$	3.11363e120	0.672384	0.336192	−	0.941794i	$-0.390861\pi$
$347$	3.11363e120	0.672384	0.336192	+	0.941794i	$0.390861\pi$
$348$	−1.78932e121	−3.37035
$349$	−4.69781e120	−0.772124	−0.386062	−	0.922473i	$-0.626165\pi$
$349$	−4.69781e120	−0.772124	−0.386062	+	0.922473i	$0.626165\pi$
$350$	−1.03282e121	−1.48181
$351$	4.40164e119	0.0551476
$352$	−5.02881e119	−0.0550413
$353$	6.93665e120	0.663516	0.331758	−	0.943364i	$-0.392358\pi$
$353$	6.93665e120	0.663516	0.331758	+	0.943364i	$0.392358\pi$
$354$	4.49618e121	3.76001
$355$	−2.22548e121	−1.62771
$356$	4.45852e121	2.85309
$357$	1.10682e121	0.619919
$358$	−3.11648e121	−1.52834
$359$	2.15720e121	0.926623	0.463312	−	0.886195i	$-0.346661\pi$
$359$	2.15720e121	0.926623	0.463312	+	0.886195i	$0.346661\pi$
$360$	−9.52738e121	−3.58595
$361$	−3.03076e121	−0.999905
$362$	1.10663e122	3.20143
$363$	−5.52855e121	−1.40296
$364$	4.96407e121	1.10541
$365$	−1.23322e122	−2.41062
$366$	1.37948e122	2.36790
$367$	1.01946e121	0.153720	0.0768600	−	0.997042i	$-0.475511\pi$
$367$	1.01946e121	0.153720	0.0768600	+	0.997042i	$0.475511\pi$
$368$	7.05646e121	0.935009
$369$	−1.89842e121	−0.221126
$370$	−2.19165e122	−2.24486
$371$	2.44708e121	0.220489
$372$	−2.55217e122	−2.02357
$373$	3.85444e121	0.269025	0.134512	−	0.990912i	$-0.457053\pi$
$373$	3.85444e121	0.269025	0.134512	+	0.990912i	$0.457053\pi$
$374$	−3.86852e121	−0.237763
$375$	5.12118e122	2.77258
$376$	2.00825e122	0.958067
$377$	−3.47328e122	−1.46058
$378$	−8.00365e120	−0.0296775
$379$	−2.09934e122	−0.686626	−0.343313	−	0.939221i	$-0.611549\pi$
$379$	−2.09934e122	−0.686626	−0.343313	+	0.939221i	$0.611549\pi$
$380$	−1.26001e121	−0.0363625
$381$	1.00156e123	2.55117
$382$	−4.19372e122	−0.943170
$383$	−8.32879e122	−1.65440	−0.827199	−	0.561908i	$-0.810067\pi$
$383$	−8.32879e122	−1.65440	−0.827199	+	0.561908i	$0.810067\pi$
$384$	1.19919e123	2.10453
$385$	5.58591e121	0.0866382
$386$	1.13576e123	1.55736
$387$	1.06168e123	1.28743
$388$	−2.06877e123	−2.21925
$389$	−3.62540e122	−0.344152	−0.172076	−	0.985084i	$-0.555047\pi$
$389$	−3.62540e122	−0.344152	−0.172076	+	0.985084i	$0.555047\pi$
$390$	−6.90285e123	−5.80042
$391$	9.99787e122	0.743895
$392$	2.52267e123	1.66254
$393$	−1.29373e123	−0.755436
$394$	1.57308e123	0.814103
$395$	4.25453e123	1.95204
$396$	6.61397e122	0.269117
$397$	9.72736e121	0.0351112	0.0175556	−	0.999846i	$-0.494412\pi$
$397$	9.72736e121	0.0351112	0.0175556	+	0.999846i	$0.494412\pi$
$398$	−6.08111e123	−1.94777
$399$	−1.94538e121	−0.00553084
$400$	1.14375e124	2.88724
$401$	−2.30711e123	−0.517262	−0.258631	−	0.965976i	$-0.583271\pi$
$401$	−2.30711e123	−0.517262	−0.258631	+	0.965976i	$0.583271\pi$
$402$	1.52252e124	3.03266
$403$	−4.95405e123	−0.876941
$404$	−1.12912e124	−1.77675
$405$	−1.22089e124	−1.70830
$406$	6.31559e123	0.786009
$407$	8.03528e122	0.0889747
$408$	−3.11907e124	−3.07374
$409$	1.29091e124	1.13250	0.566251	−	0.824233i	$-0.308393\pi$
$409$	1.29091e124	1.13250	0.566251	+	0.824233i	$0.308393\pi$
$410$	8.55526e123	0.668344
$411$	1.48912e124	1.03620
$412$	1.55993e124	0.967134
$413$	−1.07820e124	−0.595761
$414$	−2.51590e124	−1.23930
$415$	4.16761e124	1.83064
$416$	−1.49024e124	−0.583878
$417$	−3.99864e124	−1.39782
$418$	6.79944e121	0.00212129
$419$	−5.99514e124	−1.66968	−0.834840	−	0.550493i	$-0.814440\pi$
$419$	−5.99514e124	−1.66968	−0.834840	+	0.550493i	$0.814440\pi$
$420$	8.52772e124	2.12076
$421$	−1.20855e124	−0.268450	−0.134225	−	0.990951i	$-0.542854\pi$
$421$	−1.20855e124	−0.268450	−0.134225	+	0.990951i	$0.542854\pi$
$422$	1.13174e124	0.224597
$423$	−2.81373e124	−0.499017
$424$	−6.89601e124	−1.09325
$425$	1.62051e125	2.29709
$426$	1.83342e125	2.32437
$427$	−3.30805e124	−0.375187
$428$	1.84445e125	1.87192
$429$	2.53080e124	0.229899
$430$	−4.78448e125	−3.89120
$431$	−1.75841e125	−1.28071	−0.640355	−	0.768079i	$-0.721213\pi$
$431$	−1.75841e125	−1.28071	−0.640355	+	0.768079i	$0.721213\pi$
$432$	8.86331e123	0.0578253
$433$	6.77506e124	0.396039	0.198019	−	0.980198i	$-0.436549\pi$
$433$	6.77506e124	0.396039	0.198019	+	0.980198i	$0.436549\pi$
$434$	9.00812e124	0.471924
$435$	−5.96671e125	−2.80218
$436$	−1.02467e125	−0.431497
$437$	−1.75726e123	−0.00663693
$438$	1.01596e126	3.44237
$439$	3.61345e125	1.09864	0.549322	−	0.835611i	$-0.314886\pi$
$439$	3.61345e125	1.09864	0.549322	+	0.835611i	$0.314886\pi$
$440$	−1.57414e125	−0.429578
$441$	−3.53448e125	−0.865948
$442$	−1.14640e126	−2.52219
$443$	−3.21123e125	−0.634593	−0.317296	−	0.948326i	$-0.602775\pi$
$443$	−3.21123e125	−0.634593	−0.317296	+	0.948326i	$0.602775\pi$
$444$	1.22670e126	2.17795
$445$	1.48675e126	2.37212
$446$	5.91756e125	0.848667
$447$	3.88548e125	0.500999
$448$	−2.00698e125	−0.232722
$449$	1.14232e126	1.19148	0.595741	−	0.803177i	$-0.296858\pi$
$449$	1.14232e126	1.19148	0.595741	+	0.803177i	$0.296858\pi$
$450$	−4.07792e126	−3.82687
$451$	−3.13663e124	−0.0264897
$452$	−5.98784e125	−0.455192
$453$	1.68506e126	1.15332
$454$	−4.69429e126	−2.89346
$455$	1.65533e126	0.919057
$456$	5.48218e124	0.0274235
$457$	−1.24639e126	−0.561868	−0.280934	−	0.959727i	$-0.590644\pi$
$457$	−1.24639e126	−0.561868	−0.280934	+	0.959727i	$0.590644\pi$
$458$	3.24215e126	1.31742
$459$	1.25579e125	0.0460059
$460$	7.70309e126	2.54488
$461$	−6.08897e126	−1.81447	−0.907234	−	0.420625i	$-0.861811\pi$
$461$	−6.08897e126	−1.81447	−0.907234	+	0.420625i	$0.861811\pi$
$462$	−4.60184e125	−0.123719
$463$	7.59270e126	1.84204	0.921020	−	0.389516i	$-0.127358\pi$
$463$	7.59270e126	1.84204	0.921020	+	0.389516i	$0.127358\pi$
$464$	−6.99394e126	−1.53150
$465$	−8.51050e126	−1.68244
$466$	−1.01109e127	−1.80492
$467$	2.65217e126	0.427611	0.213806	−	0.976876i	$-0.431414\pi$
$467$	2.65217e126	0.427611	0.213806	+	0.976876i	$0.431414\pi$
$468$	1.95998e127	2.85479
$469$	−3.65105e126	−0.480515
$470$	1.26801e127	1.50826
$471$	−1.26724e127	−1.36260
$472$	3.03843e127	2.95396
$473$	1.75414e126	0.154227
$474$	−3.50501e127	−2.78752
$475$	−2.84827e125	−0.0204943
$476$	1.41625e127	0.922167
$477$	9.66190e126	0.569429
$478$	−1.05755e127	−0.564253
$479$	−1.00203e127	−0.484111	−0.242055	−	0.970262i	$-0.577822\pi$
$479$	−1.00203e127	−0.484111	−0.242055	+	0.970262i	$0.577822\pi$
$480$	−2.56006e127	−1.12019
$481$	2.38117e127	0.943843
$482$	−5.53516e127	−1.98791
$483$	1.18931e127	0.387084
$484$	−7.07417e127	−2.08699
$485$	−6.89856e127	−1.84513
$486$	1.03650e128	2.51390
$487$	2.76472e127	0.608171	0.304085	−	0.952645i	$-0.401649\pi$
$487$	2.76472e127	0.608171	0.304085	+	0.952645i	$0.401649\pi$
$488$	9.32227e127	1.86029
$489$	4.75451e127	0.860864
$490$	1.59282e128	2.61729
$491$	−1.49674e127	−0.223242	−0.111621	−	0.993751i	$-0.535604\pi$
$491$	−1.49674e127	−0.223242	−0.111621	+	0.993751i	$0.535604\pi$
$492$	−4.78853e127	−0.648425
$493$	−9.90929e127	−1.21847
$494$	2.01495e126	0.0225026
$495$	2.20551e127	0.223749
$496$	−9.97566e127	−0.919522
$497$	−4.39660e127	−0.368289
$498$	−3.43340e128	−2.61415
$499$	−1.45830e127	−0.100942	−0.0504708	−	0.998726i	$-0.516072\pi$
$499$	−1.45830e127	−0.100942	−0.0504708	+	0.998726i	$0.516072\pi$
$500$	6.55291e128	4.12439
$501$	1.75166e128	1.00267
$502$	−5.12788e128	−2.67000
$503$	−5.12730e127	−0.242890	−0.121445	−	0.992598i	$-0.538753\pi$
$503$	−5.12730e127	−0.242890	−0.121445	+	0.992598i	$0.538753\pi$
$504$	−1.88221e128	−0.811366
$505$	−3.76520e128	−1.47723
$506$	−4.15685e127	−0.148462
$507$	3.11869e128	1.01413
$508$	1.28156e129	3.79502
$509$	4.39810e128	1.18623	0.593117	−	0.805117i	$-0.297897\pi$
$509$	4.39810e128	1.18623	0.593117	+	0.805117i	$0.297897\pi$
$510$	−1.96938e129	−4.83890
$511$	−2.43632e128	−0.545433
$512$	1.02912e129	2.09964
$513$	−2.20721e125	−0.000410459 0
$514$	−1.12457e129	−1.90650
$515$	5.20176e128	0.804095
$516$	2.67796e129	3.77522
$517$	−4.64893e127	−0.0597795
$518$	−4.32977e128	−0.507927
$519$	−5.32373e128	−0.569858
$520$	−4.66481e129	−4.55696
$521$	2.15301e129	1.91979	0.959896	−	0.280358i	$-0.0904531\pi$
$521$	2.15301e129	1.91979	0.959896	+	0.280358i	$0.0904531\pi$
$522$	2.49361e129	2.02992
$523$	−2.63877e128	−0.196142	−0.0980712	−	0.995179i	$-0.531267\pi$
$523$	−2.63877e128	−0.196142	−0.0980712	+	0.995179i	$0.531267\pi$
$524$	−1.65542e129	−1.12376
$525$	1.92770e129	1.19529
$526$	2.50718e129	1.42025
$527$	−1.41339e129	−0.731574
$528$	5.09612e128	0.241062
$529$	−1.23853e129	−0.535504
$530$	−4.35415e129	−1.72107
$531$	−4.25710e129	−1.53859
$532$	−2.48925e127	−0.00822745
$533$	−9.29508e128	−0.281003
$534$	−1.22483e130	−3.38739
$535$	6.15054e129	1.55635
$536$	1.02889e130	2.38254
$537$	5.81673e129	1.23282
$538$	1.66159e130	3.22379
$539$	−5.83976e128	−0.103736
$540$	9.67551e128	0.157387
$541$	−7.31142e129	−1.08926	−0.544630	−	0.838676i	$-0.683330\pi$
$541$	−7.31142e129	−1.08926	−0.544630	+	0.838676i	$0.683330\pi$
$542$	1.99403e130	2.72123
$543$	−2.06546e130	−2.58241
$544$	−4.25165e129	−0.487091
$545$	−3.41690e129	−0.358755
$546$	−1.36371e130	−1.31242
$547$	−4.64925e129	−0.410190	−0.205095	−	0.978742i	$-0.565750\pi$
$547$	−4.64925e129	−0.410190	−0.205095	+	0.978742i	$0.565750\pi$
$548$	1.90544e130	1.54141
$549$	−1.30613e130	−0.968946
$550$	−6.73766e129	−0.458439
$551$	1.74169e128	0.0108710
$552$	−3.35154e130	−1.91928
$553$	8.40514e129	0.441674
$554$	2.85040e130	1.37465
$555$	4.09059e130	1.81079
$556$	−5.11655e130	−2.07933
$557$	−2.83174e130	−1.05665	−0.528325	−	0.849042i	$-0.677180\pi$
$557$	−2.83174e130	−1.05665	−0.528325	+	0.849042i	$0.677180\pi$
$558$	3.55671e130	1.21878
$559$	5.19822e130	1.63604
$560$	3.33323e130	0.963683
$561$	7.22038e129	0.191789
$562$	−1.03424e131	−2.52434
$563$	7.52281e130	1.68745	0.843725	−	0.536775i	$-0.180358\pi$
$563$	7.52281e130	1.68745	0.843725	+	0.536775i	$0.180358\pi$
$564$	−7.09728e130	−1.46330
$565$	−1.99672e130	−0.378456
$566$	3.26687e130	0.569314
$567$	−2.41197e130	−0.386523
$568$	1.23899e131	1.82609
$569$	−7.50173e130	−1.01702	−0.508509	−	0.861057i	$-0.669803\pi$
$569$	−7.50173e130	−1.01702	−0.508509	+	0.861057i	$0.669803\pi$
$570$	3.46145e129	0.0431720
$571$	−1.81042e130	−0.207761	−0.103881	−	0.994590i	$-0.533126\pi$
$571$	−1.81042e130	−0.207761	−0.103881	+	0.994590i	$0.533126\pi$
$572$	3.23834e130	0.341988
$573$	7.82735e130	0.760799
$574$	1.69016e130	0.151221
$575$	1.74129e131	1.43433
$576$	−7.92424e130	−0.601021
$577$	−1.96588e131	−1.37311	−0.686557	−	0.727076i	$-0.740879\pi$
$577$	−1.96588e131	−1.37311	−0.686557	+	0.727076i	$0.740879\pi$
$578$	−5.25338e130	−0.337961
$579$	−2.11983e131	−1.25623
$580$	−7.63483e131	−4.16841
$581$	8.23342e130	0.414204
$582$	5.68325e131	2.63484
$583$	1.59637e130	0.0682144
$584$	6.86568e131	2.70442
$585$	6.53579e131	2.37353
$586$	−6.28888e131	−2.10589
$587$	−5.49307e131	−1.69631	−0.848155	−	0.529748i	$-0.822287\pi$
$587$	−5.49307e131	−1.69631	−0.848155	+	0.529748i	$0.822287\pi$
$588$	−8.91526e131	−2.53928
$589$	2.48422e129	0.00652700
$590$	1.91847e132	4.65033
$591$	−2.93606e131	−0.656689
$592$	4.79482e131	0.989672
$593$	−4.19155e131	−0.798504	−0.399252	−	0.916841i	$-0.630730\pi$
$593$	−4.19155e131	−0.798504	−0.399252	+	0.916841i	$0.630730\pi$
$594$	−5.22123e129	−0.00918156
$595$	4.72265e131	0.766709
$596$	4.97175e131	0.745266
$597$	1.13501e132	1.57115
$598$	−1.23184e132	−1.57488
$599$	4.66145e131	0.550487	0.275244	−	0.961374i	$-0.411241\pi$
$599$	4.66145e131	0.550487	0.275244	+	0.961374i	$0.411241\pi$
$600$	−5.43237e132	−5.92659
$601$	1.62414e132	1.63714	0.818571	−	0.574405i	$-0.194767\pi$
$601$	1.62414e132	1.63714	0.818571	+	0.574405i	$0.194767\pi$
$602$	−9.45210e131	−0.880431
$603$	−1.44156e132	−1.24096
$604$	2.15615e132	1.71563
$605$	−2.35897e132	−1.73517
$606$	3.10188e132	2.10948
$607$	−1.40346e131	−0.0882547	−0.0441274	−	0.999026i	$-0.514051\pi$
$607$	−1.40346e131	−0.0882547	−0.0441274	+	0.999026i	$0.514051\pi$
$608$	7.47284e129	0.00434576
$609$	−1.17877e132	−0.634027
$610$	5.88608e132	2.92859
$611$	−1.37766e132	−0.634141
$612$	5.59183e132	2.38156
$613$	−3.11624e132	−1.22817	−0.614084	−	0.789240i	$-0.710475\pi$
$613$	−3.11624e132	−1.22817	−0.614084	+	0.789240i	$0.710475\pi$
$614$	1.04872e132	0.382526
$615$	−1.59679e132	−0.539113
$616$	−3.10984e131	−0.0971972
$617$	−4.99281e131	−0.144477	−0.0722386	−	0.997387i	$-0.523014\pi$
$617$	−4.99281e131	−0.144477	−0.0722386	+	0.997387i	$0.523014\pi$
$618$	−4.28537e132	−1.14825
$619$	2.50887e132	0.622547	0.311274	−	0.950320i	$-0.399244\pi$
$619$	2.50887e132	0.622547	0.311274	+	0.950320i	$0.399244\pi$
$620$	−1.08898e133	−2.50273
$621$	1.34938e131	0.0287266
$622$	−1.01850e132	−0.200871
$623$	2.93718e132	0.536720
$624$	1.51018e133	2.55718
$625$	8.44055e132	1.32456
$626$	3.97912e132	0.578770
$627$	−1.26908e130	−0.00171112
$628$	−1.62153e133	−2.02694
$629$	6.79349e132	0.787386
$630$	−1.18843e133	−1.27731
$631$	−1.20203e133	−1.19818	−0.599090	−	0.800682i	$-0.704471\pi$
$631$	−1.20203e133	−1.19818	−0.599090	+	0.800682i	$0.704471\pi$
$632$	−2.36862e133	−2.18995
$633$	−2.11232e132	−0.181169
$634$	−1.15573e133	−0.919635
$635$	4.27353e133	3.15526
$636$	2.43709e133	1.66978
$637$	−1.73055e133	−1.10043
$638$	4.12001e132	0.243174
$639$	−1.73593e133	−0.951132
$640$	5.11681e133	2.60286
$641$	−2.58997e133	−1.22331	−0.611657	−	0.791123i	$-0.709497\pi$
$641$	−2.58997e133	−1.22331	−0.611657	+	0.791123i	$0.709497\pi$
$642$	−5.06700e133	−2.22248
$643$	1.20445e133	0.490646	0.245323	−	0.969441i	$-0.421106\pi$
$643$	1.20445e133	0.490646	0.245323	+	0.969441i	$0.421106\pi$
$644$	1.52180e133	0.575811
$645$	8.92996e133	3.13880
$646$	5.74865e131	0.0187724
$647$	1.65024e133	0.500718	0.250359	−	0.968153i	$-0.419451\pi$
$647$	1.65024e133	0.500718	0.250359	+	0.968153i	$0.419451\pi$
$648$	6.79706e133	1.91650
$649$	−7.03370e132	−0.184315
$650$	−1.99664e134	−4.86311
$651$	−1.68131e133	−0.380673
$652$	6.08373e133	1.28059
$653$	−6.40154e133	−1.25288	−0.626438	−	0.779471i	$-0.715488\pi$
$653$	−6.40154e133	−1.25288	−0.626438	+	0.779471i	$0.715488\pi$
$654$	2.81494e133	0.512303
$655$	−5.52019e133	−0.934313
$656$	−1.87169e133	−0.294647
$657$	−9.61940e133	−1.40862
$658$	2.50505e133	0.341261
$659$	−1.90383e133	−0.241308	−0.120654	−	0.992695i	$-0.538499\pi$
$659$	−1.90383e133	−0.241308	−0.120654	+	0.992695i	$0.538499\pi$
$660$	5.56311e133	0.656116
$661$	−8.24900e132	−0.0905382	−0.0452691	−	0.998975i	$-0.514415\pi$
$661$	−8.24900e132	−0.0905382	−0.0452691	+	0.998975i	$0.514415\pi$
$662$	2.73660e134	2.79548
$663$	2.13969e134	2.03450
$664$	−2.32023e134	−2.05375
$665$	−8.30069e131	−0.00684047
$666$	−1.70954e134	−1.31176
$667$	−1.06478e134	−0.760823
$668$	2.24137e134	1.49153
$669$	−1.10448e134	−0.684569
$670$	6.49639e134	3.75076
$671$	−2.15802e133	−0.116074
$672$	−5.05759e133	−0.253457
$673$	−1.00679e134	−0.470137	−0.235069	−	0.971979i	$-0.575532\pi$
$673$	−1.00679e134	−0.470137	−0.235069	+	0.971979i	$0.575532\pi$
$674$	−7.11181e134	−3.09482
$675$	2.18716e133	0.0887056
$676$	3.99058e134	1.50858
$677$	−1.52482e134	−0.537349	−0.268674	−	0.963231i	$-0.586586\pi$
$677$	−1.52482e134	−0.537349	−0.268674	+	0.963231i	$0.586586\pi$
$678$	1.64495e134	0.540435
$679$	−1.36286e134	−0.417482
$680$	−1.33087e135	−3.80157
$681$	8.76163e134	2.33398
$682$	5.87650e133	0.146003
$683$	−1.11109e134	−0.257492	−0.128746	−	0.991678i	$-0.541095\pi$
$683$	−1.11109e134	−0.257492	−0.128746	+	0.991678i	$0.541095\pi$
$684$	−9.82838e132	−0.0212480
$685$	6.35391e134	1.28156
$686$	6.88809e134	1.29629
$687$	−6.05129e134	−1.06268
$688$	1.04673e135	1.71548
$689$	4.73067e134	0.723619
$690$	−2.11616e135	−3.02146
$691$	−2.78189e134	−0.370793	−0.185397	−	0.982664i	$-0.559357\pi$
$691$	−2.78189e134	−0.370793	−0.185397	+	0.982664i	$0.559357\pi$
$692$	−6.81209e134	−0.847697
$693$	4.35714e133	0.0506260
$694$	−1.09450e135	−1.18752
$695$	−1.70617e135	−1.72880
$696$	3.32184e135	3.14369
$697$	−2.65189e134	−0.234422
$698$	1.65137e135	1.36368
$699$	1.88713e135	1.45592
$700$	2.46663e135	1.77806
$701$	7.23519e134	0.487353	0.243677	−	0.969857i	$-0.421646\pi$
$701$	7.23519e134	0.487353	0.243677	+	0.969857i	$0.421646\pi$
$702$	−1.54726e134	−0.0973980
$703$	−1.19405e133	−0.00702495
$704$	−1.30927e134	−0.0719990
$705$	−2.36667e135	−1.21662
$706$	−2.43836e135	−1.17186
$707$	−7.43843e134	−0.334241
$708$	−1.07380e136	−4.51173
$709$	1.84460e135	0.724781	0.362391	−	0.932026i	$-0.381961\pi$
$709$	1.84460e135	0.724781	0.362391	+	0.932026i	$0.381961\pi$
$710$	7.82298e135	2.87475
$711$	3.31863e135	1.14065
$712$	−8.27714e135	−2.66122
$713$	−1.51873e135	−0.456802
$714$	−3.89067e135	−1.09486
$715$	1.07986e135	0.284336
$716$	7.44292e135	1.83390
$717$	1.97385e135	0.455149
$718$	−7.58295e135	−1.63654
$719$	5.21780e135	1.05406	0.527029	−	0.849847i	$-0.323306\pi$
$719$	5.21780e135	1.05406	0.527029	+	0.849847i	$0.323306\pi$
$720$	1.31607e136	2.48878
$721$	1.02765e135	0.181936
$722$	1.06537e136	1.76597
$723$	1.03311e136	1.60352
$724$	−2.64290e136	−3.84148
$725$	−1.72586e136	−2.34937
$726$	1.94339e136	2.47782
$727$	−4.76746e135	−0.569381	−0.284690	−	0.958619i	$-0.591891\pi$
$727$	−4.76746e135	−0.569381	−0.284690	+	0.958619i	$0.591891\pi$
$728$	−9.21569e135	−1.03107
$729$	−1.00961e136	−1.05827
$730$	4.33500e136	4.25748
$731$	1.48305e136	1.36484
$732$	−3.29454e136	−2.84131
$733$	−3.61594e135	−0.292268	−0.146134	−	0.989265i	$-0.546683\pi$
$733$	−3.61594e135	−0.292268	−0.146134	+	0.989265i	$0.546683\pi$
$734$	−3.58358e135	−0.271490
$735$	−2.97290e136	−2.11121
$736$	−4.56853e135	−0.304144
$737$	−2.38178e135	−0.148661
$738$	6.67331e135	0.390539
$739$	−1.82464e136	−1.00130	−0.500652	−	0.865648i	$-0.666907\pi$
$739$	−1.82464e136	−1.00130	−0.500652	+	0.865648i	$0.666907\pi$
$740$	5.23420e136	2.69367
$741$	−3.76078e134	−0.0181515
$742$	−8.60194e135	−0.389414
$743$	−3.17392e136	−1.34780	−0.673902	−	0.738820i	$-0.735383\pi$
$743$	−3.17392e136	−1.34780	−0.673902	+	0.738820i	$0.735383\pi$
$744$	4.73804e136	1.88749
$745$	1.65789e136	0.619630
$746$	−1.35491e136	−0.475134
$747$	3.25083e136	1.06971
$748$	9.23899e135	0.285298
$749$	1.21509e136	0.352144
$750$	−1.80019e137	−4.89676
$751$	−1.44685e136	−0.369426	−0.184713	−	0.982793i	$-0.559136\pi$
$751$	−1.44685e136	−0.369426	−0.184713	+	0.982793i	$0.559136\pi$
$752$	−2.77412e136	−0.664932
$753$	9.57091e136	2.15373
$754$	1.22092e137	2.57959
$755$	7.18994e136	1.42641
$756$	1.91147e135	0.0356108
$757$	−7.89873e136	−1.38198	−0.690992	−	0.722863i	$-0.742826\pi$
$757$	−7.89873e136	−1.38198	−0.690992	+	0.722863i	$0.742826\pi$
$758$	7.37957e136	1.21267
$759$	7.75852e135	0.119755
$760$	2.33918e135	0.0339171
$761$	2.24276e135	0.0305500	0.0152750	−	0.999883i	$-0.495138\pi$
$761$	2.24276e135	0.0305500	0.0152750	+	0.999883i	$0.495138\pi$
$762$	−3.52066e137	−4.50571
$763$	−6.75034e135	−0.0811727
$764$	1.00156e137	1.13173
$765$	1.86466e137	1.98008
$766$	2.92773e137	2.92189
$767$	−2.08437e137	−1.95521
$768$	−3.27222e137	−2.88525
$769$	−2.36115e136	−0.195714	−0.0978572	−	0.995200i	$-0.531199\pi$
$769$	−2.36115e136	−0.195714	−0.0978572	+	0.995200i	$0.531199\pi$
$770$	−1.96355e136	−0.153015
$771$	2.09894e137	1.53786
$772$	−2.71247e137	−1.86871
$773$	5.09447e136	0.330045	0.165023	−	0.986290i	$-0.447230\pi$
$773$	5.09447e136	0.330045	0.165023	+	0.986290i	$0.447230\pi$
$774$	−3.73201e137	−2.27377
$775$	−2.46165e137	−1.41057
$776$	3.84063e137	2.07000
$777$	8.08127e136	0.409714
$778$	1.27440e137	0.607818
$779$	4.66104e134	0.00209148
$780$	1.64857e138	6.96007
$781$	−2.86815e136	−0.113940
$782$	−3.51444e137	−1.31382
$783$	−1.33743e136	−0.0470529
$784$	−3.48471e137	−1.15386
$785$	−5.40718e137	−1.68524
$786$	4.54770e137	1.33420
$787$	5.48397e137	1.51459	0.757295	−	0.653073i	$-0.226521\pi$
$787$	5.48397e137	1.51459	0.757295	+	0.653073i	$0.226521\pi$
$788$	−3.75690e137	−0.976864
$789$	−4.67952e137	−1.14563
$790$	−1.49555e138	−3.44757
$791$	−3.94466e136	−0.0856302
$792$	−1.22787e137	−0.251018
$793$	−6.39508e137	−1.23132
$794$	−3.41935e136	−0.0620111
$795$	8.12677e137	1.38829
$796$	1.45232e138	2.33718
$797$	5.46947e137	0.829229	0.414615	−	0.909997i	$-0.363916\pi$
$797$	5.46947e137	0.829229	0.414615	+	0.909997i	$0.363916\pi$
$798$	6.83836e135	0.00976820
$799$	−3.93048e137	−0.529022
$800$	−7.40493e137	−0.939175
$801$	1.15970e138	1.38612
$802$	8.10992e137	0.913554
$803$	−1.58935e137	−0.168745
$804$	−3.63614e138	−3.63897
$805$	5.07463e137	0.478741
$806$	1.74144e138	1.54880
$807$	−3.10127e138	−2.60044
$808$	2.09619e138	1.65726
$809$	−3.84583e137	−0.286705	−0.143352	−	0.989672i	$-0.545788\pi$
$809$	−3.84583e137	−0.286705	−0.143352	+	0.989672i	$0.545788\pi$
$810$	4.29167e138	3.01708
$811$	1.19495e138	0.792241	0.396121	−	0.918198i	$-0.370356\pi$
$811$	1.19495e138	0.792241	0.396121	+	0.918198i	$0.370356\pi$
$812$	−1.50832e138	−0.943152
$813$	−3.72174e138	−2.19505
$814$	−2.82455e137	−0.157141
$815$	2.02869e138	1.06471
$816$	4.30856e138	2.13329
$817$	−2.60666e136	−0.0121769
$818$	−4.53779e138	−2.00015
$819$	1.29120e138	0.537040
$820$	−2.04321e138	−0.801963
$821$	1.65886e138	0.614483	0.307242	−	0.951632i	$-0.400594\pi$
$821$	1.65886e138	0.614483	0.307242	+	0.951632i	$0.400594\pi$
$822$	−5.23455e138	−1.83007
$823$	3.69056e138	1.21787	0.608933	−	0.793221i	$-0.291598\pi$
$823$	3.69056e138	1.21787	0.608933	+	0.793221i	$0.291598\pi$
$824$	−2.89597e138	−0.902094
$825$	1.25755e138	0.369795
$826$	3.79007e138	1.05219
$827$	−4.55962e137	−0.119513	−0.0597567	−	0.998213i	$-0.519032\pi$
$827$	−4.55962e137	−0.119513	−0.0597567	+	0.998213i	$0.519032\pi$
$828$	6.00859e138	1.48707
$829$	−1.93756e138	−0.452808	−0.226404	−	0.974034i	$-0.572697\pi$
$829$	−1.93756e138	−0.452808	−0.226404	+	0.974034i	$0.572697\pi$
$830$	−1.46499e139	−3.23315
$831$	−5.32011e138	−1.10885
$832$	−3.87988e138	−0.763766
$833$	−4.93728e138	−0.918015
$834$	1.40560e139	2.46873
$835$	7.47413e138	1.24009
$836$	−1.62387e136	−0.00254539
$837$	−1.90761e137	−0.0282508
$838$	2.10740e139	2.94888
$839$	−8.39985e138	−1.11065	−0.555326	−	0.831633i	$-0.687407\pi$
$839$	−8.39985e138	−1.11065	−0.555326	+	0.831633i	$0.687407\pi$
$840$	−1.58315e139	−1.97814
$841$	2.08492e138	0.246195
$842$	4.24826e138	0.474119
$843$	1.93036e139	2.03623
$844$	−2.70287e138	−0.269500
$845$	1.33071e139	1.25426
$846$	9.89080e138	0.881331
$847$	−4.66031e138	−0.392603
$848$	9.52586e138	0.758755
$849$	−6.09743e138	−0.459232
$850$	−5.69641e139	−4.05697
$851$	7.29981e138	0.491652
$852$	−4.37866e139	−2.78907
$853$	1.24777e139	0.751720	0.375860	−	0.926676i	$-0.377347\pi$
$853$	1.24777e139	0.751720	0.375860	+	0.926676i	$0.377347\pi$
$854$	1.16284e139	0.662630
$855$	−3.27739e137	−0.0176660
$856$	−3.42418e139	−1.74604
$857$	1.05197e139	0.507474	0.253737	−	0.967273i	$-0.418340\pi$
$857$	1.05197e139	0.507474	0.253737	+	0.967273i	$0.418340\pi$
$858$	−8.89624e138	−0.406032
$859$	−3.29167e139	−1.42148	−0.710740	−	0.703454i	$-0.751640\pi$
$859$	−3.29167e139	−1.42148	−0.710740	+	0.703454i	$0.751640\pi$
$860$	1.14265e140	4.66915
$861$	−3.15458e138	−0.121981
$862$	6.18116e139	2.26191
$863$	−5.15864e139	−1.78658	−0.893290	−	0.449481i	$-0.851609\pi$
$863$	−5.15864e139	−1.78658	−0.893290	+	0.449481i	$0.851609\pi$
$864$	−5.73832e137	−0.0188097
$865$	−2.27157e139	−0.704793
$866$	−2.38156e139	−0.699458
$867$	9.80513e138	0.272613
$868$	−2.15136e139	−0.566274
$869$	5.48315e138	0.136644
$870$	2.09741e140	4.94902
$871$	−7.05817e139	−1.57699
$872$	1.90228e139	0.402478
$873$	−5.38104e139	−1.07818
$874$	6.17709e137	0.0117217
$875$	4.31692e139	0.775875
$876$	−2.42637e140	−4.13059
$877$	−1.15355e139	−0.186018	−0.0930091	−	0.995665i	$-0.529649\pi$
$877$	−1.15355e139	−0.186018	−0.0930091	+	0.995665i	$0.529649\pi$
$878$	−1.27020e140	−1.94035
$879$	1.17378e140	1.69870
$880$	2.17445e139	0.298142
$881$	4.74588e139	0.616540	0.308270	−	0.951299i	$-0.400250\pi$
$881$	4.74588e139	0.616540	0.308270	+	0.951299i	$0.400250\pi$
$882$	1.24243e140	1.52938
$883$	8.57526e139	1.00026	0.500131	−	0.865950i	$-0.333285\pi$
$883$	8.57526e139	1.00026	0.500131	+	0.865950i	$0.333285\pi$
$884$	2.73788e140	3.02644
$885$	−3.58071e140	−3.75114
$886$	1.12881e140	1.12078
$887$	1.64928e140	1.55211	0.776053	−	0.630668i	$-0.217219\pi$
$887$	1.64928e140	1.55211	0.776053	+	0.630668i	$0.217219\pi$
$888$	−2.27735e140	−2.03149
$889$	8.44268e139	0.713915
$890$	−5.22619e140	−4.18948
$891$	−1.57346e139	−0.119582
$892$	−1.41326e140	−1.01834
$893$	6.90833e137	0.00471986
$894$	−1.36582e140	−0.884832
$895$	2.48193e140	1.52474
$896$	1.01086e140	0.588928
$897$	2.29916e140	1.27036
$898$	−4.01548e140	−2.10432
$899$	1.50527e140	0.748222
$900$	9.73908e140	4.59196
$901$	1.34966e140	0.603667
$902$	1.10258e139	0.0467844
$903$	1.76418e140	0.710191
$904$	1.11163e140	0.424580
$905$	−8.81307e140	−3.19389
$906$	−5.92329e140	−2.03692
$907$	−1.22023e140	−0.398195	−0.199098	−	0.979980i	$-0.563801\pi$
$907$	−1.22023e140	−0.398195	−0.199098	+	0.979980i	$0.563801\pi$
$908$	1.12111e141	3.47194
$909$	−2.93694e140	−0.863199
$910$	−5.81879e140	−1.62318
$911$	6.59191e140	1.74537	0.872687	−	0.488280i	$-0.162375\pi$
$911$	6.59191e140	1.74537	0.872687	+	0.488280i	$0.162375\pi$
$912$	−7.57286e138	−0.0190329
$913$	5.37112e139	0.128145
$914$	4.38129e140	0.992334
$915$	−1.09860e141	−2.36232
$916$	−7.74305e140	−1.58080
$917$	−1.09056e140	−0.211400
$918$	−4.41433e139	−0.0812527
$919$	6.22282e140	1.08768	0.543839	−	0.839190i	$-0.316970\pi$
$919$	6.22282e140	1.08768	0.543839	+	0.839190i	$0.316970\pi$
$920$	−1.43006e141	−2.37374
$921$	−1.95737e140	−0.308561
$922$	2.14039e141	3.20460
$923$	−8.49948e140	−1.20868
$924$	1.09903e140	0.148454
$925$	1.18320e141	1.51818
$926$	−2.66898e141	−3.25329
$927$	4.05750e140	0.469863
$928$	4.52805e140	0.498175
$929$	8.80044e140	0.919936	0.459968	−	0.887935i	$-0.347861\pi$
$929$	8.80044e140	0.919936	0.459968	+	0.887935i	$0.347861\pi$
$930$	2.99160e141	2.97142
$931$	8.67792e138	0.00819041
$932$	2.41472e141	2.16577
$933$	1.90097e140	0.162031
$934$	−9.32287e140	−0.755219
$935$	3.08085e140	0.237203
$936$	−3.63866e141	−2.66280
$937$	−1.86263e141	−1.29567	−0.647836	−	0.761780i	$-0.724326\pi$
$937$	−1.86263e141	−1.29567	−0.647836	+	0.761780i	$0.724326\pi$
$938$	1.28341e141	0.848655
$939$	−7.42680e140	−0.466859
$940$	−3.02833e141	−1.80980
$941$	−4.03868e140	−0.229473	−0.114737	−	0.993396i	$-0.536602\pi$
$941$	−4.03868e140	−0.229473	−0.114737	+	0.993396i	$0.536602\pi$
$942$	4.45460e141	2.40653
$943$	−2.84953e140	−0.146375
$944$	−4.19716e141	−2.05015
$945$	6.37402e139	0.0296076
$946$	−6.16614e140	−0.272386
$947$	1.98978e141	0.835950	0.417975	−	0.908459i	$-0.362740\pi$
$947$	1.98978e141	0.835950	0.417975	+	0.908459i	$0.362740\pi$
$948$	8.37083e141	3.34482
$949$	−4.70987e141	−1.79004
$950$	1.00122e140	0.0361958
$951$	2.15710e141	0.741815
$952$	−2.62924e141	−0.860151
$953$	−3.52250e141	−1.09632	−0.548161	−	0.836373i	$-0.684672\pi$
$953$	−3.52250e141	−1.09632	−0.548161	+	0.836373i	$0.684672\pi$
$954$	−3.39634e141	−1.00569
$955$	3.33984e141	0.940947
$956$	2.52568e141	0.677062
$957$	−7.68977e140	−0.196154
$958$	3.52233e141	0.855005
$959$	1.25526e141	0.289969
$960$	−6.66520e141	−1.46531
$961$	−2.63225e141	−0.550764
$962$	−8.37027e141	−1.66695
$963$	4.79757e141	0.909437
$964$	1.32193e142	2.38534
$965$	−9.04505e141	−1.55369
$966$	−4.18064e141	−0.683642
$967$	7.89135e141	1.22855	0.614276	−	0.789091i	$-0.289448\pi$
$967$	7.89135e141	1.22855	0.614276	+	0.789091i	$0.289448\pi$
$968$	1.31330e142	1.94664
$969$	−1.07295e140	−0.0151426
$970$	2.42497e142	3.25874
$971$	−4.10444e141	−0.525220	−0.262610	−	0.964902i	$-0.584583\pi$
$971$	−4.10444e141	−0.525220	−0.262610	+	0.964902i	$0.584583\pi$
$972$	−2.47542e142	−3.01649
$973$	−3.37068e141	−0.391162
$974$	−9.71851e141	−1.07411
$975$	3.72661e142	3.92279
$976$	−1.28774e142	−1.29110
$977$	3.95481e141	0.377688	0.188844	−	0.982007i	$-0.439526\pi$
$977$	3.95481e141	0.377688	0.188844	+	0.982007i	$0.439526\pi$
$978$	−1.67130e142	−1.52040
$979$	1.91609e141	0.166049
$980$	−3.80404e142	−3.14055
$981$	−2.66526e141	−0.209634
$982$	5.26133e141	0.394276
$983$	−2.68438e142	−1.91669	−0.958346	−	0.285608i	$-0.907804\pi$
$983$	−2.68438e142	−1.91669	−0.958346	+	0.285608i	$0.907804\pi$
$984$	8.88979e141	0.604818
$985$	−1.25278e142	−0.812184
$986$	3.48330e142	2.15198
$987$	−4.67554e141	−0.275275
$988$	−4.81219e140	−0.0270015
$989$	1.59359e142	0.852220
$990$	−7.75277e141	−0.395171
$991$	3.43061e142	1.66676	0.833378	−	0.552703i	$-0.186404\pi$
$991$	3.43061e142	1.66676	0.833378	+	0.552703i	$0.186404\pi$
$992$	6.45849e141	0.299107
$993$	−5.10770e142	−2.25495
$994$	1.54549e142	0.650448
$995$	4.84293e142	1.94318
$996$	8.19981e142	3.13679
$997$	2.28019e142	0.831669	0.415834	−	0.909440i	$-0.363490\pi$
$997$	2.28019e142	0.831669	0.415834	+	0.909440i	$0.363490\pi$
$998$	5.12619e141	0.178276
$999$	9.16897e140	0.0304060

Twists

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

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

\(f(q)\)	\(=\)	\(q-3.51519e14 q^{2} +6.56090e22 q^{3} +8.39514e28 q^{4} +2.79946e33 q^{5} -2.30628e37 q^{6} +5.53054e39 q^{7} -1.55854e43 q^{8} +2.18364e45 q^{9} +O(q^{10})\)	\(q-3.51519e14 q^{2} +6.56090e22 q^{3} +8.39514e28 q^{4} +2.79946e33 q^{5} -2.30628e37 q^{6} +5.53054e39 q^{7} -1.55854e43 q^{8} +2.18364e45 q^{9} -9.84062e47 q^{10} +3.60788e48 q^{11} +5.50796e51 q^{12} +1.06916e53 q^{13} -1.94409e54 q^{14} +1.83670e56 q^{15} +2.15290e57 q^{16} +3.05031e58 q^{17} -7.67592e59 q^{18} -5.36133e58 q^{19} +2.35018e62 q^{20} +3.62853e62 q^{21} -1.26824e63 q^{22} +3.27765e64 q^{23} -1.02254e66 q^{24} +5.31261e66 q^{25} -3.75830e67 q^{26} +4.11692e66 q^{27} +4.64296e68 q^{28} -3.24861e69 q^{29} -6.45633e70 q^{30} -4.63359e70 q^{31} -1.39384e71 q^{32} +2.36709e71 q^{33} -1.07224e73 q^{34} +1.54825e73 q^{35} +1.83320e74 q^{36} +2.22715e74 q^{37} +1.88461e73 q^{38} +7.01465e75 q^{39} -4.36306e76 q^{40} -8.69382e75 q^{41} -1.27550e77 q^{42} +4.86197e77 q^{43} +3.02887e77 q^{44} +6.11302e78 q^{45} -1.15216e79 q^{46} -1.28855e79 q^{47} +1.41250e80 q^{48} -1.61861e80 q^{49} -1.86748e81 q^{50} +2.00128e81 q^{51} +8.97574e81 q^{52} +4.42467e81 q^{53} -1.44717e81 q^{54} +1.01001e82 q^{55} -8.61956e82 q^{56} -3.51751e81 q^{57} +1.14195e84 q^{58} -1.94954e84 q^{59} +1.54193e85 q^{60} -5.98141e84 q^{61} +1.62879e85 q^{62} +1.20767e85 q^{63} -3.62891e85 q^{64} +2.99307e86 q^{65} -8.32078e85 q^{66} -6.60161e86 q^{67} +2.56078e87 q^{68} +2.15044e87 q^{69} -5.44240e87 q^{70} -7.94968e87 q^{71} -3.40329e88 q^{72} -4.40521e88 q^{73} -7.82883e88 q^{74} +3.48555e89 q^{75} -4.50091e87 q^{76} +1.99535e88 q^{77} -2.46578e90 q^{78} +1.51977e90 q^{79} +6.02695e90 q^{80} -4.36117e90 q^{81} +3.05604e90 q^{82} +1.48872e91 q^{83} +3.04620e91 q^{84} +8.53923e91 q^{85} -1.70907e92 q^{86} -2.13138e92 q^{87} -5.62302e91 q^{88} +5.31083e92 q^{89} -2.14884e93 q^{90} +5.91303e92 q^{91} +2.75163e93 q^{92} -3.04005e93 q^{93} +4.52949e93 q^{94} -1.50088e92 q^{95} -9.14485e93 q^{96} -2.46425e94 q^{97} +5.68973e94 q^{98} +7.87833e93 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 5835659138280 q^{2} - 95\!\cdots\!80 q^{3}+ \cdots + 92\!\cdots\!36 q^{9}+O(q^{10}) \) 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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