LMFDB - Embedded newform 1.96.a.a.1.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1,96,Mod(1,1)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://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);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1, base_ring=CyclotomicField(1)) chi = DirichletCharacter(H, H._module([])) N = Newforms(chi, 96, names="a")

Level:	$ N $	$=$	$ 1 $
Weight:	$ k $	$=$	$ 96 $
Character orbit:	$[\chi]$	$=$	1.a (trivial)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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			1.4
Root			$-1.67307e12$ 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)

$f(q)$	$=$	\(q-4.08831e13 q^{2} -7.46060e22 q^{3} -3.79427e28 q^{4} +2.52173e33 q^{5} +3.05013e36 q^{6} +2.11876e40 q^{7} +3.17076e42 q^{8} +3.44515e45 q^{9} -1.03096e47 q^{10} +2.27998e49 q^{11} +2.83075e51 q^{12} +2.29728e52 q^{13} -8.66214e53 q^{14} -1.88136e56 q^{15} +1.37343e57 q^{16} -1.90158e58 q^{17} -1.40849e59 q^{18} -1.95604e60 q^{19} -9.56809e61 q^{20} -1.58072e63 q^{21} -9.32129e62 q^{22} +6.96784e64 q^{23} -2.36558e65 q^{24} +3.83474e66 q^{25} -9.39201e65 q^{26} -9.87975e67 q^{27} -8.03912e68 q^{28} +3.29733e69 q^{29} +7.69158e69 q^{30} -1.05470e70 q^{31} -1.81757e71 q^{32} -1.70100e72 q^{33} +7.77425e71 q^{34} +5.34292e73 q^{35} -1.30718e74 q^{36} +6.15205e73 q^{37} +7.99690e73 q^{38} -1.71391e75 q^{39} +7.99579e75 q^{40} -5.28549e75 q^{41} +6.46247e76 q^{42} -5.20413e77 q^{43} -8.65086e77 q^{44} +8.68773e78 q^{45} -2.84867e78 q^{46} -1.26681e79 q^{47} -1.02466e80 q^{48} +2.56465e80 q^{49} -1.56776e80 q^{50} +1.41869e81 q^{51} -8.71650e80 q^{52} -3.16779e81 q^{53} +4.03915e81 q^{54} +5.74949e82 q^{55} +6.71807e82 q^{56} +1.45932e83 q^{57} -1.34805e83 q^{58} +4.60990e83 q^{59} +7.13837e84 q^{60} +4.35502e84 q^{61} +4.31195e83 q^{62} +7.29944e85 q^{63} -4.69765e85 q^{64} +5.79311e85 q^{65} +6.95424e85 q^{66} +1.06266e87 q^{67} +7.21510e86 q^{68} -5.19842e87 q^{69} -2.18435e87 q^{70} -2.68493e87 q^{71} +1.09238e88 q^{72} -4.60158e88 q^{73} -2.51515e87 q^{74} -2.86095e89 q^{75} +7.42173e88 q^{76} +4.83073e89 q^{77} +7.00700e88 q^{78} -9.17980e89 q^{79} +3.46342e90 q^{80} +6.40740e88 q^{81} +2.16088e89 q^{82} +9.48142e90 q^{83} +5.99766e91 q^{84} -4.79526e91 q^{85} +2.12761e91 q^{86} -2.46001e92 q^{87} +7.22929e91 q^{88} -2.01039e92 q^{89} -3.55182e92 q^{90} +4.86738e92 q^{91} -2.64378e93 q^{92} +7.86870e92 q^{93} +5.17914e92 q^{94} -4.93259e93 q^{95} +1.35602e94 q^{96} +4.06342e94 q^{97} -1.04851e94 q^{98} +7.85489e94 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 5835659138280 q^{2} - 95\!\cdots\!80 q^{3} + 20\!\cdots\!84 q^{4} + 19\!\cdots\!60 q^{5} + 10\!\cdots\!76 q^{6} + 31\!\cdots\!00 q^{7} - 14\!\cdots\!60 q^{8} + 92\!\cdots\!36 q^{9} - 35\!\cdots\!40 q^{10}+ \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

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 $

$2$	−4.08831e13	−0.205409	−0.102704	−	0.994712i	$-0.532750\pi$
$2$	−4.08831e13	−0.205409	−0.102704	+	0.994712i	$0.532750\pi$
$3$	−7.46060e22	−1.62000	−0.809998	−	0.586433i	$-0.800532\pi$
$3$	−7.46060e22	−1.62000	−0.809998	+	0.586433i	$0.800532\pi$
$4$	−3.79427e28	−0.957807
$5$	2.52173e33	1.58717	0.793583	−	0.608461i	$-0.208213\pi$
$5$	2.52173e33	1.58717	0.793583	+	0.608461i	$0.208213\pi$
$6$	3.05013e36	0.332762
$7$	2.11876e40	1.52730	0.763650	−	0.645631i	$-0.223406\pi$
$7$	2.11876e40	1.52730	0.763650	+	0.645631i	$0.223406\pi$
$8$	3.17076e42	0.402151
$9$	3.44515e45	1.62439
$10$	−1.03096e47	−0.326018
$11$	2.27998e49	0.779434	0.389717	−	0.920935i	$-0.372573\pi$
$11$	2.27998e49	0.779434	0.389717	+	0.920935i	$0.372573\pi$
$12$	2.83075e51	1.55164
$13$	2.29728e52	0.281129	0.140564	−	0.990072i	$-0.455108\pi$
$13$	2.29728e52	0.281129	0.140564	+	0.990072i	$0.455108\pi$
$14$	−8.66214e53	−0.313721
$15$	−1.88136e56	−2.57120
$16$	1.37343e57	0.875202
$17$	−1.90158e58	−0.680441	−0.340221	−	0.940346i	$-0.610502\pi$
$17$	−1.90158e58	−0.680441	−0.340221	+	0.940346i	$0.610502\pi$
$18$	−1.40849e59	−0.333664
$19$	−1.95604e60	−0.355289	−0.177644	−	0.984095i	$-0.556848\pi$
$19$	−1.95604e60	−0.355289	−0.177644	+	0.984095i	$0.556848\pi$
$20$	−9.56809e61	−1.52020
$21$	−1.58072e63	−2.47422
$22$	−9.32129e62	−0.160103
$23$	6.96784e64	1.44886	0.724429	−	0.689350i	$-0.242104\pi$
$23$	6.96784e64	1.44886	0.724429	+	0.689350i	$0.242104\pi$
$24$	−2.36558e65	−0.651483
$25$	3.83474e66	1.51910
$26$	−9.39201e65	−0.0577463
$27$	−9.87975e67	−1.01150
$28$	−8.03912e68	−1.46286
$29$	3.29733e69	1.13307	0.566536	−	0.824037i	$-0.308283\pi$
$29$	3.29733e69	1.13307	0.566536	+	0.824037i	$0.308283\pi$
$30$	7.69158e69	0.528148
$31$	−1.05470e70	−0.152563	−0.0762815	−	0.997086i	$-0.524305\pi$
$31$	−1.05470e70	−0.152563	−0.0762815	+	0.997086i	$0.524305\pi$
$32$	−1.81757e71	−0.581925
$33$	−1.70100e72	−1.26268
$34$	7.77425e71	0.139769
$35$	5.34292e73	2.42408
$36$	−1.30718e74	−1.55585
$37$	6.15205e73	0.199268	0.0996341	−	0.995024i	$-0.468233\pi$
$37$	6.15205e73	0.199268	0.0996341	+	0.995024i	$0.468233\pi$
$38$	7.99690e73	0.0729795
$39$	−1.71391e75	−0.455427
$40$	7.99579e75	0.638281
$41$	−5.28549e75	−0.130573	−0.0652864	−	0.997867i	$-0.520796\pi$
$41$	−5.28549e75	−0.130573	−0.0652864	+	0.997867i	$0.520796\pi$
$42$	6.46247e76	0.508227
$43$	−5.20413e77	−1.33843	−0.669217	−	0.743067i	$-0.733370\pi$
$43$	−5.20413e77	−1.33843	−0.669217	+	0.743067i	$0.733370\pi$
$44$	−8.65086e77	−0.746547
$45$	8.68773e78	2.57817
$46$	−2.84867e78	−0.297608
$47$	−1.26681e79	−0.476502	−0.238251	−	0.971204i	$-0.576574\pi$
$47$	−1.26681e79	−0.476502	−0.238251	+	0.971204i	$0.576574\pi$
$48$	−1.02466e80	−1.41782
$49$	2.56465e80	1.33264
$50$	−1.56776e80	−0.312037
$51$	1.41869e81	1.10231
$52$	−8.71650e80	−0.269267
$53$	−3.16779e81	−0.395961	−0.197981	−	0.980206i	$-0.563438\pi$
$53$	−3.16779e81	−0.395961	−0.197981	+	0.980206i	$0.563438\pi$
$54$	4.03915e81	0.207772
$55$	5.74949e82	1.23709
$56$	6.71807e82	0.614205
$57$	1.45932e83	0.575566
$58$	−1.34805e83	−0.232743
$59$	4.60990e83	0.353363	0.176682	−	0.984268i	$-0.443464\pi$
$59$	4.60990e83	0.353363	0.176682	+	0.984268i	$0.443464\pi$
$60$	7.13837e84	2.46272
$61$	4.35502e84	0.685209	0.342605	−	0.939480i	$-0.388691\pi$
$61$	4.35502e84	0.685209	0.342605	+	0.939480i	$0.388691\pi$
$62$	4.31195e83	0.0313378
$63$	7.29944e85	2.48092
$64$	−4.69765e85	−0.755669
$65$	5.79311e85	0.446198
$66$	6.95424e85	0.259366
$67$	1.06266e87	1.94017	0.970085	−	0.242764i	$-0.0780539\pi$
$67$	1.06266e87	1.94017	0.970085	+	0.242764i	$0.0780539\pi$
$68$	7.21510e86	0.651732
$69$	−5.19842e87	−2.34714
$70$	−2.18435e87	−0.497928
$71$	−2.68493e87	−0.312005	−0.156003	−	0.987757i	$-0.549861\pi$
$71$	−2.68493e87	−0.312005	−0.156003	+	0.987757i	$0.549861\pi$
$72$	1.09238e88	0.653249
$73$	−4.60158e88	−1.42913	−0.714564	−	0.699570i	$-0.753375\pi$
$73$	−4.60158e88	−1.42913	−0.714564	+	0.699570i	$0.753375\pi$
$74$	−2.51515e87	−0.0409315
$75$	−2.86095e89	−2.46093
$76$	7.42173e88	0.340298
$77$	4.83073e89	1.19043
$78$	7.00700e88	0.0935488
$79$	−9.17980e89	−0.669185	−0.334593	−	0.942363i	$-0.608599\pi$
$79$	−9.17980e89	−0.669185	−0.334593	+	0.942363i	$0.608599\pi$
$80$	3.46342e90	1.38909
$81$	6.40740e88	0.0142444
$82$	2.16088e89	0.0268208
$83$	9.48142e90	0.661704	0.330852	−	0.943683i	$-0.392664\pi$
$83$	9.48142e90	0.661704	0.330852	+	0.943683i	$0.392664\pi$
$84$	5.99766e91	2.36982
$85$	−4.79526e91	−1.07997
$86$	2.12761e91	0.274926
$87$	−2.46001e92	−1.83557
$88$	7.22929e91	0.313450
$89$	−2.01039e92	−0.509630	−0.254815	−	0.966990i	$-0.582015\pi$
$89$	−2.01039e92	−0.509630	−0.254815	+	0.966990i	$0.582015\pi$
$90$	−3.55182e92	−0.529580
$91$	4.86738e92	0.429367
$92$	−2.64378e93	−1.38773
$93$	7.86870e92	0.247151
$94$	5.17914e92	0.0978778
$95$	−4.93259e93	−0.563903
$96$	1.35602e94	0.942717
$97$	4.06342e94	1.72677	0.863384	−	0.504548i	$-0.168341\pi$
$97$	4.06342e94	1.72677	0.863384	+	0.504548i	$0.168341\pi$
$98$	−1.04851e94	−0.273737
$99$	7.85489e94	1.26610
$100$	−1.45500e95	−1.45500
$101$	1.86177e94	0.116054	0.0580271	−	0.998315i	$-0.481519\pi$
$101$	1.86177e94	0.116054	0.0580271	+	0.998315i	$0.481519\pi$
$102$	−5.80006e94	−0.226425
$103$	7.25788e95	1.78255	0.891275	−	0.453464i	$-0.149812\pi$
$103$	7.25788e95	1.78255	0.891275	+	0.453464i	$0.149812\pi$
$104$	7.28413e94	0.113056
$105$	−3.98614e96	−3.92700
$106$	1.29509e95	0.0813340
$107$	−7.14056e95	−0.287080	−0.143540	−	0.989645i	$-0.545849\pi$
$107$	−7.14056e95	−0.287080	−0.143540	+	0.989645i	$0.545849\pi$
$108$	3.74864e96	0.968825
$109$	3.83591e96	0.639896	0.319948	−	0.947435i	$-0.396334\pi$
$109$	3.83591e96	0.639896	0.319948	+	0.947435i	$0.396334\pi$
$110$	−2.35057e96	−0.254110
$111$	−4.58980e96	−0.322814
$112$	2.90997e97	1.33669
$113$	−1.95393e97	−0.588413	−0.294207	−	0.955742i	$-0.595055\pi$
$113$	−1.95393e97	−0.588413	−0.294207	+	0.955742i	$0.595055\pi$
$114$	−5.96616e96	−0.118226
$115$	1.75710e98	2.29958
$116$	−1.25110e98	−1.08527
$117$	7.91449e97	0.456661
$118$	−1.88467e97	−0.0725840
$119$	−4.02898e98	−1.03924
$120$	−5.96534e98	−1.03401
$121$	−3.35835e98	−0.392483
$122$	−1.78047e98	−0.140748
$123$	3.94329e98	0.211527
$124$	4.00182e98	0.146126
$125$	3.30444e99	0.823897
$126$	−2.98424e99	−0.509604
$127$	−4.48700e99	−0.526355	−0.263178	−	0.964747i	$-0.584771\pi$
$127$	−4.48700e99	−0.526355	−0.263178	+	0.964747i	$0.584771\pi$
$128$	9.12069e99	0.737147
$129$	3.88259e100	2.16826
$130$	−2.36841e99	−0.0916531
$131$	−5.20402e100	−1.39944	−0.699718	−	0.714420i	$-0.746691\pi$
$131$	−5.20402e100	−1.39944	−0.699718	+	0.714420i	$0.746691\pi$
$132$	6.45406e100	1.20940
$133$	−4.14437e100	−0.542632
$134$	−4.34448e100	−0.398529
$135$	−2.49140e101	−1.60542
$136$	−6.02946e100	−0.273640
$137$	1.76335e101	0.565081	0.282541	−	0.959255i	$-0.408823\pi$
$137$	1.76335e101	0.565081	0.282541	+	0.959255i	$0.408823\pi$
$138$	2.12528e101	0.482124
$139$	4.61090e101	0.742305	0.371152	−	0.928572i	$-0.378963\pi$
$139$	4.61090e101	0.742305	0.371152	+	0.928572i	$0.378963\pi$
$140$	−2.02725e102	−2.32180
$141$	9.45119e101	0.771932
$142$	1.09768e101	0.0640886
$143$	5.23776e101	0.219121
$144$	4.73168e102	1.42167
$145$	8.31497e102	1.79838
$146$	1.88127e102	0.293556
$147$	−1.91338e103	−2.15888
$148$	−2.33425e102	−0.190860
$149$	−2.12538e103	−1.26209	−0.631043	−	0.775748i	$-0.717373\pi$
$149$	−2.12538e103	−1.26209	−0.631043	+	0.775748i	$0.717373\pi$
$150$	1.16965e103	0.505498
$151$	2.15586e103	0.679542	0.339771	−	0.940508i	$-0.389650\pi$
$151$	2.15586e103	0.679542	0.339771	+	0.940508i	$0.389650\pi$
$152$	−6.20213e102	−0.142880
$153$	−6.55123e103	−1.10530
$154$	−1.97495e103	−0.244525
$155$	−2.65967e103	−0.242143
$156$	6.50302e103	0.436211
$157$	1.54158e104	0.763363	0.381682	−	0.924294i	$-0.375345\pi$
$157$	1.54158e104	0.763363	0.381682	+	0.924294i	$0.375345\pi$
$158$	3.75299e103	0.137457
$159$	2.36336e104	0.641455
$160$	−4.58341e104	−0.923613
$161$	1.47631e105	2.21284
$162$	−2.61954e102	−0.00292592
$163$	−1.03228e105	−0.860769	−0.430385	−	0.902646i	$-0.641622\pi$
$163$	−1.03228e105	−0.860769	−0.430385	+	0.902646i	$0.641622\pi$
$164$	2.00546e104	0.125063
$165$	−4.28946e105	−2.00408
$166$	−3.87630e104	−0.135920
$167$	7.02027e105	1.85064	0.925319	−	0.379189i	$-0.123797\pi$
$167$	7.02027e105	1.85064	0.925319	+	0.379189i	$0.123797\pi$
$168$	−5.01208e105	−0.995010
$169$	−6.14982e105	−0.920967
$170$	1.96045e105	0.221836
$171$	−6.73885e105	−0.577126
$172$	1.97459e106	1.28196
$173$	−2.77879e106	−1.36982	−0.684912	−	0.728625i	$-0.740160\pi$
$173$	−2.77879e106	−1.36982	−0.684912	+	0.728625i	$0.740160\pi$
$174$	1.00573e106	0.377043
$175$	8.12489e106	2.32012
$176$	3.13140e106	0.682162
$177$	−3.43926e106	−0.572447
$178$	8.21910e105	0.104683
$179$	3.49562e106	0.341197	0.170599	−	0.985341i	$-0.445430\pi$
$179$	3.49562e106	0.341197	0.170599	+	0.985341i	$0.445430\pi$
$180$	−3.29635e107	−2.46939
$181$	1.51871e107	0.874465	0.437232	−	0.899349i	$-0.355959\pi$
$181$	1.51871e107	0.874465	0.437232	+	0.899349i	$0.355959\pi$
$182$	−1.98994e106	−0.0881959
$183$	−3.24911e107	−1.11004
$184$	2.20934e107	0.582660
$185$	1.55138e107	0.316272
$186$	−3.21697e106	−0.0507671
$187$	−4.33557e107	−0.530359
$188$	4.80663e107	0.456397
$189$	−2.09328e108	−1.54487
$190$	2.01660e107	0.115831
$191$	3.78959e108	1.69632	0.848159	−	0.529741i	$-0.177711\pi$
$191$	3.78959e108	1.69632	0.848159	+	0.529741i	$0.177711\pi$
$192$	3.50472e108	1.22418
$193$	4.50954e108	1.23072	0.615361	−	0.788245i	$-0.289010\pi$
$193$	4.50954e108	1.23072	0.615361	+	0.788245i	$0.289010\pi$
$194$	−1.66125e108	−0.354694
$195$	−4.32201e108	−0.722839
$196$	−9.73095e108	−1.27642
$197$	−7.56582e108	−0.779310	−0.389655	−	0.920961i	$-0.627406\pi$
$197$	−7.56582e108	−0.779310	−0.389655	+	0.920961i	$0.627406\pi$
$198$	−3.21133e108	−0.260069
$199$	2.81191e109	1.79259	0.896294	−	0.443461i	$-0.146250\pi$
$199$	2.81191e109	1.79259	0.896294	+	0.443461i	$0.146250\pi$
$200$	1.21591e109	0.610907
$201$	−7.92805e109	−3.14307
$202$	−7.61151e107	−0.0238386
$203$	6.98624e109	1.73054
$204$	−5.38289e109	−1.05580
$205$	−1.33286e109	−0.207241
$206$	−2.96725e109	−0.366152
$207$	2.40053e110	2.35350
$208$	3.15516e109	0.246044
$209$	−4.45974e109	−0.276924
$210$	1.62966e110	0.806641
$211$	−2.48806e110	−0.982751	−0.491375	−	0.870948i	$-0.663506\pi$
$211$	−2.48806e110	−0.982751	−0.491375	+	0.870948i	$0.663506\pi$
$212$	1.20194e110	0.379254
$213$	2.00312e110	0.505447
$214$	2.91928e109	0.0589688
$215$	−1.31234e111	−2.12432
$216$	−3.13263e110	−0.406777
$217$	−2.23466e110	−0.233009
$218$	−1.56824e110	−0.131440
$219$	3.43305e111	2.31518
$220$	−2.18151e111	−1.18490
$221$	−4.36846e110	−0.191291
$222$	1.87645e110	0.0663088
$223$	−2.59063e111	−0.739477	−0.369738	−	0.929136i	$-0.620553\pi$
$223$	−2.59063e111	−0.739477	−0.369738	+	0.929136i	$0.620553\pi$
$224$	−3.85099e111	−0.888774
$225$	1.32113e112	2.46760
$226$	7.98827e110	0.120865
$227$	9.27134e111	1.13740	0.568701	−	0.822544i	$-0.307446\pi$
$227$	9.27134e111	1.13740	0.568701	+	0.822544i	$0.307446\pi$
$228$	−5.53705e111	−0.551281
$229$	1.36440e112	1.10346	0.551730	−	0.834023i	$-0.313968\pi$
$229$	1.36440e112	1.10346	0.551730	+	0.834023i	$0.313968\pi$
$230$	−7.18356e111	−0.472354
$231$	−3.60401e112	−1.92849
$232$	1.04551e112	0.455666
$233$	−2.20207e112	−0.782393	−0.391197	−	0.920307i	$-0.627939\pi$
$233$	−2.20207e112	−0.782393	−0.391197	+	0.920307i	$0.627939\pi$
$234$	−3.23569e111	−0.0938023
$235$	−3.19456e112	−0.756289
$236$	−1.74912e112	−0.338454
$237$	6.84868e112	1.08408
$238$	1.64717e112	0.213469
$239$	1.47369e113	1.56497	0.782486	−	0.622669i	$-0.213952\pi$
$239$	1.47369e113	1.56497	0.782486	+	0.622669i	$0.213952\pi$
$240$	−2.58392e113	−2.25032
$241$	4.05551e112	0.289892	0.144946	−	0.989440i	$-0.453699\pi$
$241$	4.05551e112	0.289892	0.144946	+	0.989440i	$0.453699\pi$
$242$	1.37300e112	0.0806195
$243$	2.04759e113	0.988427
$244$	−1.65241e113	−0.656298
$245$	6.46734e113	2.11513
$246$	−1.61214e112	−0.0434496
$247$	−4.49357e112	−0.0998818
$248$	−3.34421e112	−0.0613534
$249$	−7.07370e113	−1.07196
$250$	−1.35096e113	−0.169236
$251$	−3.94780e113	−0.409123	−0.204561	−	0.978854i	$-0.565577\pi$
$251$	−3.94780e113	−0.409123	−0.204561	+	0.978854i	$0.565577\pi$
$252$	−2.76960e114	−2.37625
$253$	1.58866e114	1.12929
$254$	1.83442e113	0.108118
$255$	3.57755e114	1.74955
$256$	1.48805e114	0.604252
$257$	−5.58088e114	−1.88313	−0.941563	−	0.336838i	$-0.890643\pi$
$257$	−5.58088e114	−1.88313	−0.941563	+	0.336838i	$0.890643\pi$
$258$	−1.58733e114	−0.445379
$259$	1.30347e114	0.304342
$260$	−2.19806e114	−0.427372
$261$	1.13598e115	1.84055
$262$	2.12757e114	0.287457
$263$	9.70917e114	1.09467	0.547336	−	0.836913i	$-0.315642\pi$
$263$	9.70917e114	1.09467	0.547336	+	0.836913i	$0.315642\pi$
$264$	−5.39348e114	−0.507788
$265$	−7.98830e114	−0.628456
$266$	1.69435e114	0.111462
$267$	1.49987e115	0.825598
$268$	−4.03200e115	−1.85831
$269$	5.38725e114	0.208034	0.104017	−	0.994576i	$-0.466830\pi$
$269$	5.38725e114	0.208034	0.104017	+	0.994576i	$0.466830\pi$
$270$	1.01856e115	0.329769
$271$	−4.37144e115	−1.18736	−0.593681	−	0.804701i	$-0.702326\pi$
$271$	−4.37144e115	−1.18736	−0.593681	+	0.804701i	$0.702326\pi$
$272$	−2.61169e115	−0.595523
$273$	−3.63136e115	−0.695573
$274$	−7.20911e114	−0.116073
$275$	8.74316e115	1.18404
$276$	1.97242e116	2.24811
$277$	−7.04017e115	−0.675762	−0.337881	−	0.941189i	$-0.609710\pi$
$277$	−7.04017e115	−0.675762	−0.337881	+	0.941189i	$0.609710\pi$
$278$	−1.88508e115	−0.152476
$279$	−3.63361e115	−0.247821
$280$	1.69411e116	0.974846
$281$	−2.18798e116	−1.06290	−0.531451	−	0.847089i	$-0.678353\pi$
$281$	−2.18798e116	−1.06290	−0.531451	+	0.847089i	$0.678353\pi$
$282$	−3.86394e115	−0.158562
$283$	1.26882e116	0.440092	0.220046	−	0.975489i	$-0.429379\pi$
$283$	1.26882e116	0.440092	0.220046	+	0.975489i	$0.429379\pi$
$284$	1.01873e116	0.298841
$285$	3.68001e116	0.913520
$286$	−2.14136e115	−0.0450094
$287$	−1.11987e116	−0.199424
$288$	−6.26181e116	−0.945272
$289$	−4.19393e116	−0.537000
$290$	−3.39942e116	−0.369402
$291$	−3.03155e117	−2.79736
$292$	1.74596e117	1.36883
$293$	1.87445e117	1.24928	0.624642	−	0.780911i	$-0.285245\pi$
$293$	1.87445e117	1.24928	0.624642	+	0.780911i	$0.285245\pi$
$294$	7.82250e116	0.443453
$295$	1.16249e117	0.560846
$296$	1.95067e116	0.0801359
$297$	−2.25257e117	−0.788400
$298$	8.68922e116	0.259244
$299$	1.60071e117	0.407315
$300$	1.08552e118	2.35710
$301$	−1.10263e118	−2.04419
$302$	−8.81385e116	−0.139584
$303$	−1.38899e117	−0.188007
$304$	−2.68649e117	−0.310949
$305$	1.09822e118	1.08754
$306$	2.67835e117	0.227038
$307$	1.09189e118	0.792692	0.396346	−	0.918101i	$-0.370278\pi$
$307$	1.09189e118	0.792692	0.396346	+	0.918101i	$0.370278\pi$
$308$	−1.83291e118	−1.14020
$309$	−5.41481e118	−2.88772
$310$	1.08736e117	0.0497383
$311$	2.39607e118	0.940549	0.470275	−	0.882520i	$-0.344155\pi$
$311$	2.39607e118	0.940549	0.470275	+	0.882520i	$0.344155\pi$
$312$	−5.43440e117	−0.183151
$313$	−4.34700e118	−1.25844	−0.629221	−	0.777226i	$-0.716626\pi$
$313$	−4.34700e118	−1.25844	−0.629221	+	0.777226i	$0.716626\pi$
$314$	−6.30244e117	−0.156802
$315$	1.84072e119	3.93764
$316$	3.48306e118	0.640950
$317$	−8.21619e118	−1.30123	−0.650617	−	0.759406i	$-0.725490\pi$
$317$	−8.21619e118	−1.30123	−0.650617	+	0.759406i	$0.725490\pi$
$318$	−9.66216e117	−0.131761
$319$	7.51786e118	0.883155
$320$	−1.18462e119	−1.19937
$321$	5.32728e118	0.465068
$322$	−6.03564e118	−0.454537
$323$	3.71956e118	0.241753
$324$	−2.43114e117	−0.0136434
$325$	8.80949e118	0.427062
$326$	4.22029e118	0.176810
$327$	−2.86182e119	−1.03663
$328$	−1.67590e118	−0.0525100
$329$	−2.68407e119	−0.727761
$330$	1.75367e119	0.411657
$331$	−3.32807e119	−0.676648	−0.338324	−	0.941030i	$-0.609860\pi$
$331$	−3.32807e119	−0.676648	−0.338324	+	0.941030i	$0.609860\pi$
$332$	−3.59750e119	−0.633785
$333$	2.11948e119	0.323688
$334$	−2.87011e119	−0.380138
$335$	2.67973e120	3.07938
$336$	−2.17101e120	−2.16544
$337$	5.06186e119	0.438419	0.219210	−	0.975678i	$-0.429652\pi$
$337$	5.06186e119	0.438419	0.219210	+	0.975678i	$0.429652\pi$
$338$	2.51424e119	0.189175
$339$	1.45775e120	0.953227
$340$	1.81945e120	1.03441
$341$	−2.40470e119	−0.118913
$342$	2.75505e119	0.118547
$343$	1.35635e120	0.508046
$344$	−1.65011e120	−0.538253
$345$	−1.31090e121	−3.72531
$346$	1.13605e120	0.281374
$347$	1.16918e120	0.252483	0.126242	−	0.992000i	$-0.459709\pi$
$347$	1.16918e120	0.252483	0.126242	+	0.992000i	$0.459709\pi$
$348$	9.33391e120	1.75812
$349$	2.15983e120	0.354986	0.177493	−	0.984122i	$-0.443201\pi$
$349$	2.15983e120	0.354986	0.177493	+	0.984122i	$0.443201\pi$
$350$	−3.32171e120	−0.476573
$351$	−2.26966e120	−0.284362
$352$	−4.14403e120	−0.453572
$353$	−1.04122e121	−0.995963	−0.497981	−	0.867188i	$-0.665925\pi$
$353$	−1.04122e121	−0.995963	−0.497981	+	0.867188i	$0.665925\pi$
$354$	1.40608e120	0.117586
$355$	−6.77066e120	−0.495204
$356$	7.62795e120	0.488127
$357$	3.00586e121	1.68356
$358$	−1.42912e120	−0.0700849
$359$	2.49154e121	1.07024	0.535121	−	0.844776i	$-0.320266\pi$
$359$	2.49154e121	1.07024	0.535121	+	0.844776i	$0.320266\pi$
$360$	2.75467e121	1.03681
$361$	−2.64843e121	−0.873770
$362$	−6.20896e120	−0.179623
$363$	2.50553e121	0.635821
$364$	−1.84681e121	−0.411251
$365$	−1.16039e122	−2.26826
$366$	1.32834e121	0.228011
$367$	−4.45359e121	−0.671540	−0.335770	−	0.941944i	$-0.608996\pi$
$367$	−4.45359e121	−0.671540	−0.335770	+	0.941944i	$0.608996\pi$
$368$	9.56985e121	1.26804
$369$	−1.82093e121	−0.212101
$370$	−6.34252e120	−0.0649651
$371$	−6.71177e121	−0.604751
$372$	−2.98560e121	−0.236723
$373$	1.81276e122	1.26524	0.632618	−	0.774464i	$-0.281980\pi$
$373$	1.81276e122	1.26524	0.632618	+	0.774464i	$0.281980\pi$
$374$	1.77252e121	0.108940
$375$	−2.46531e122	−1.33471
$376$	−4.01677e121	−0.191626
$377$	7.57490e121	0.318539
$378$	8.55798e121	0.317330
$379$	1.02935e122	0.336668	0.168334	−	0.985730i	$-0.446161\pi$
$379$	1.02935e122	0.336668	0.168334	+	0.985730i	$0.446161\pi$
$380$	1.87156e122	0.540110
$381$	3.34757e122	0.852693
$382$	−1.54930e122	−0.348439
$383$	6.67846e122	1.32658	0.663292	−	0.748361i	$-0.269159\pi$
$383$	6.67846e122	1.32658	0.663292	+	0.748361i	$0.269159\pi$
$384$	−6.80457e122	−1.19417
$385$	1.21818e123	1.88941
$386$	−1.84364e122	−0.252801
$387$	−1.79290e123	−2.17413
$388$	−1.54177e123	−1.65391
$389$	−9.31427e121	−0.0884184	−0.0442092	−	0.999022i	$-0.514077\pi$
$389$	−9.31427e121	−0.0884184	−0.0442092	+	0.999022i	$0.514077\pi$
$390$	1.76697e122	0.148478
$391$	−1.32499e123	−0.985863
$392$	8.13189e122	0.535924
$393$	3.88251e123	2.26708
$394$	3.09314e122	0.160077
$395$	−2.31489e123	−1.06211
$396$	−2.98035e123	−1.21268
$397$	2.09036e123	0.754524	0.377262	−	0.926107i	$-0.376866\pi$
$397$	2.09036e123	0.754524	0.377262	+	0.926107i	$0.376866\pi$
$398$	−1.14960e123	−0.368214
$399$	3.09195e123	0.879062
$400$	5.26676e123	1.32952
$401$	−3.05610e123	−0.685187	−0.342594	−	0.939484i	$-0.611305\pi$
$401$	−3.05610e123	−0.685187	−0.342594	+	0.939484i	$0.611305\pi$
$402$	3.24124e123	0.645615
$403$	−2.42295e122	−0.0428898
$404$	−7.06405e122	−0.111158
$405$	1.61577e122	0.0226082
$406$	−2.85620e123	−0.355469
$407$	1.40266e123	0.155316
$408$	4.49833e123	0.443296
$409$	−2.64150e123	−0.231736	−0.115868	−	0.993265i	$-0.536965\pi$
$409$	−2.64150e123	−0.231736	−0.115868	+	0.993265i	$0.536965\pi$
$410$	5.44914e122	0.0425691
$411$	−1.31556e124	−0.915429
$412$	−2.75383e124	−1.70734
$413$	9.76726e123	0.539691
$414$	−9.81410e123	−0.483431
$415$	2.39095e124	1.05024
$416$	−4.17547e123	−0.163596
$417$	−3.44000e124	−1.20253
$418$	1.82328e123	0.0568827
$419$	8.57191e123	0.238733	0.119366	−	0.992850i	$-0.461914\pi$
$419$	8.57191e123	0.238733	0.119366	+	0.992850i	$0.461914\pi$
$420$	1.51245e125	3.76131
$421$	−3.57310e124	−0.793681	−0.396841	−	0.917888i	$-0.629893\pi$
$421$	−3.57310e124	−0.793681	−0.396841	+	0.917888i	$0.629893\pi$
$422$	1.01720e124	0.201866
$423$	−4.36437e124	−0.774024
$424$	−1.00443e124	−0.159236
$425$	−7.29207e124	−1.03366
$426$	−8.18938e123	−0.103823
$427$	9.22723e124	1.04652
$428$	2.70932e124	0.274967
$429$	−3.90768e124	−0.354975
$430$	5.36526e124	0.436354
$431$	1.73372e125	1.26272	0.631362	−	0.775488i	$-0.282496\pi$
$431$	1.73372e125	1.26272	0.631362	+	0.775488i	$0.282496\pi$
$432$	−1.35692e125	−0.885269
$433$	−2.07959e124	−0.121564	−0.0607818	−	0.998151i	$-0.519359\pi$
$433$	−2.07959e124	−0.121564	−0.0607818	+	0.998151i	$0.519359\pi$
$434$	9.13598e123	0.0478622
$435$	−6.20346e125	−2.91336
$436$	−1.45545e125	−0.612897
$437$	−1.36294e125	−0.514763
$438$	−1.40354e125	−0.475559
$439$	5.77780e125	1.75670	0.878350	−	0.478018i	$-0.158645\pi$
$439$	5.77780e125	1.75670	0.878350	+	0.478018i	$0.158645\pi$
$440$	1.82303e125	0.497498
$441$	8.83560e125	2.16473
$442$	1.78596e124	0.0392930
$443$	−2.96767e125	−0.586460	−0.293230	−	0.956042i	$-0.594730\pi$
$443$	−2.96767e125	−0.586460	−0.293230	+	0.956042i	$0.594730\pi$
$444$	1.74149e125	0.309193
$445$	−5.06965e125	−0.808868
$446$	1.05913e125	0.151895
$447$	1.58566e126	2.04457
$448$	−9.95317e125	−1.15413
$449$	−1.90165e125	−0.198349	−0.0991746	−	0.995070i	$-0.531620\pi$
$449$	−1.90165e125	−0.198349	−0.0991746	+	0.995070i	$0.531620\pi$
$450$	−5.40119e125	−0.506868
$451$	−1.20508e125	−0.101773
$452$	7.41372e125	0.563586
$453$	−1.60840e126	−1.10086
$454$	−3.79041e125	−0.233633
$455$	1.22742e126	0.681478
$456$	4.62716e125	0.231465
$457$	−3.97496e125	−0.179190	−0.0895950	−	0.995978i	$-0.528557\pi$
$457$	−3.97496e125	−0.179190	−0.0895950	+	0.995978i	$0.528557\pi$
$458$	−5.57810e125	−0.226661
$459$	1.87871e126	0.688268
$460$	−6.66689e126	−2.20255
$461$	−3.63717e126	−1.08385	−0.541926	−	0.840426i	$-0.682305\pi$
$461$	−3.63717e126	−1.08385	−0.541926	+	0.840426i	$0.682305\pi$
$462$	1.47343e126	0.396129
$463$	3.21928e126	0.781020	0.390510	−	0.920599i	$-0.372299\pi$
$463$	3.21928e126	0.781020	0.390510	+	0.920599i	$0.372299\pi$
$464$	4.52866e126	0.991667
$465$	1.98427e126	0.392271
$466$	9.00276e125	0.160711
$467$	−1.36728e126	−0.220447	−0.110224	−	0.993907i	$-0.535157\pi$
$467$	−1.36728e126	−0.220447	−0.110224	+	0.993907i	$0.535157\pi$
$468$	−3.00297e126	−0.437394
$469$	2.25151e127	2.96322
$470$	1.30604e126	0.155348
$471$	−1.15011e127	−1.23665
$472$	1.46169e126	0.142105
$473$	−1.18653e127	−1.04322
$474$	−2.79995e126	−0.222679
$475$	−7.50091e126	−0.539719
$476$	1.52870e127	0.995389
$477$	−1.09135e127	−0.643194
$478$	−6.02491e126	−0.321459
$479$	−1.40633e127	−0.679440	−0.339720	−	0.940527i	$-0.610332\pi$
$479$	−1.40633e127	−0.679440	−0.339720	+	0.940527i	$0.610332\pi$
$480$	3.41950e127	1.49625
$481$	1.41330e126	0.0560200
$482$	−1.65802e126	−0.0595464
$483$	−1.10142e128	−3.58479
$484$	1.27425e127	0.375923
$485$	1.02468e128	2.74067
$486$	−8.37118e126	−0.203032
$487$	−5.77282e127	−1.26988	−0.634940	−	0.772562i	$-0.718975\pi$
$487$	−5.77282e127	−1.26988	−0.634940	+	0.772562i	$0.718975\pi$
$488$	1.38087e127	0.275558
$489$	7.70143e127	1.39444
$490$	−2.64405e127	−0.434466
$491$	8.21573e127	1.22539	0.612697	−	0.790318i	$-0.290085\pi$
$491$	8.21573e127	1.22539	0.612697	+	0.790318i	$0.290085\pi$
$492$	−1.49619e127	−0.202602
$493$	−6.27014e127	−0.770989
$494$	1.83711e126	0.0205166
$495$	1.98079e128	2.00951
$496$	−1.44856e127	−0.133523
$497$	−5.68872e127	−0.476525
$498$	2.89195e127	0.220190
$499$	6.32170e127	0.437580	0.218790	−	0.975772i	$-0.429789\pi$
$499$	6.32170e127	0.437580	0.218790	+	0.975772i	$0.429789\pi$
$500$	−1.25379e128	−0.789134
$501$	−5.23754e128	−2.99803
$502$	1.61398e127	0.0840375
$503$	−2.22222e128	−1.05271	−0.526354	−	0.850266i	$-0.676441\pi$
$503$	−2.22222e128	−1.05271	−0.526354	+	0.850266i	$0.676441\pi$
$504$	2.31448e128	0.997706
$505$	4.69488e127	0.184197
$506$	−6.49492e127	−0.231966
$507$	4.58813e128	1.49196
$508$	1.70249e128	0.504147
$509$	4.96882e128	1.34017	0.670083	−	0.742286i	$-0.266259\pi$
$509$	4.96882e128	1.34017	0.670083	+	0.742286i	$0.266259\pi$
$510$	−1.46261e128	−0.359374
$511$	−9.74963e128	−2.18271
$512$	−4.22144e128	−0.861266
$513$	1.93252e128	0.359376
$514$	2.28164e128	0.386811
$515$	1.83024e129	2.82920
$516$	−1.47316e129	−2.07677
$517$	−2.88832e128	−0.371402
$518$	−5.32899e127	−0.0625146
$519$	2.07314e129	2.21911
$520$	1.83686e128	0.179439
$521$	1.58063e129	1.40942	0.704709	−	0.709497i	$-0.251078\pi$
$521$	1.58063e129	1.40942	0.704709	+	0.709497i	$0.251078\pi$
$522$	−4.64425e128	−0.378065
$523$	−2.18953e129	−1.62750	−0.813749	−	0.581216i	$-0.802577\pi$
$523$	−2.18953e129	−1.62750	−0.813749	+	0.581216i	$0.802577\pi$
$524$	1.97454e129	1.34039
$525$	−6.06165e129	−3.75858
$526$	−3.96941e128	−0.224856
$527$	2.00560e128	0.103810
$528$	−2.33621e129	−1.10510
$529$	2.54224e129	1.09919
$530$	3.26587e128	0.129091
$531$	1.58818e129	0.573998
$532$	1.57248e129	0.519737
$533$	−1.21423e128	−0.0367077
$534$	−6.13194e128	−0.169585
$535$	−1.80065e129	−0.455644
$536$	3.36943e129	0.780242
$537$	−2.60794e129	−0.552738
$538$	−2.20248e128	−0.0427320
$539$	5.84735e129	1.03871
$540$	9.45304e129	1.53769
$541$	−5.80289e129	−0.864519	−0.432260	−	0.901749i	$-0.642284\pi$
$541$	−5.80289e129	−0.864519	−0.432260	+	0.901749i	$0.642284\pi$
$542$	1.78718e129	0.243895
$543$	−1.13305e130	−1.41663
$544$	3.45625e129	0.395966
$545$	9.67311e129	1.01562
$546$	1.48461e129	0.142877
$547$	−9.09608e129	−0.802521	−0.401260	−	0.915964i	$-0.631428\pi$
$547$	−9.09608e129	−0.802521	−0.401260	+	0.915964i	$0.631428\pi$
$548$	−6.69060e129	−0.541239
$549$	1.50037e130	1.11304
$550$	−3.57448e129	−0.243212
$551$	−6.44971e129	−0.402568
$552$	−1.64830e130	−0.943906
$553$	−1.94498e130	−1.02205
$554$	2.87824e129	0.138808
$555$	−1.15742e130	−0.512359
$556$	−1.74950e130	−0.710985
$557$	2.46146e130	0.918484	0.459242	−	0.888311i	$-0.348121\pi$
$557$	2.46146e130	0.918484	0.459242	+	0.888311i	$0.348121\pi$
$558$	1.48553e129	0.0509047
$559$	−1.19554e130	−0.376272
$560$	7.33814e130	2.12156
$561$	3.23459e130	0.859179
$562$	8.94515e129	0.218330
$563$	2.05139e130	0.460149	0.230075	−	0.973173i	$-0.426103\pi$
$563$	2.05139e130	0.460149	0.230075	+	0.973173i	$0.426103\pi$
$564$	−3.58603e130	−0.739362
$565$	−4.92727e130	−0.933910
$566$	−5.18733e129	−0.0903989
$567$	1.35757e129	0.0217554
$568$	−8.51328e129	−0.125473
$569$	1.35598e131	1.83832	0.919158	−	0.393890i	$-0.128871\pi$
$569$	1.35598e131	1.83832	0.919158	+	0.393890i	$0.128871\pi$
$570$	−1.50450e130	−0.187645
$571$	2.68308e129	0.0307906	0.0153953	−	0.999881i	$-0.495099\pi$
$571$	2.68308e129	0.0307906	0.0153953	+	0.999881i	$0.495099\pi$
$572$	−1.98735e130	−0.209876
$573$	−2.82726e131	−2.74803
$574$	4.57837e129	0.0409634
$575$	2.67199e131	2.20096
$576$	−1.61841e131	−1.22750
$577$	2.26523e131	1.58220	0.791101	−	0.611686i	$-0.209508\pi$
$577$	2.26523e131	1.58220	0.791101	+	0.611686i	$0.209508\pi$
$578$	1.71461e130	0.110305
$579$	−3.36438e131	−1.99376
$580$	−3.15492e131	−1.72250
$581$	2.00888e131	1.01062
$582$	1.23939e131	0.574602
$583$	−7.22251e130	−0.308625
$584$	−1.45905e131	−0.574726
$585$	1.99582e131	0.724798
$586$	−7.66333e130	−0.256614
$587$	−1.44403e131	−0.445930	−0.222965	−	0.974827i	$-0.571573\pi$
$587$	−1.44403e131	−0.445930	−0.222965	+	0.974827i	$0.571573\pi$
$588$	7.25987e131	2.06779
$589$	2.06304e130	0.0542039
$590$	−4.75263e130	−0.115203
$591$	5.64455e131	1.26248
$592$	8.44943e130	0.174400
$593$	5.41209e131	1.03102	0.515510	−	0.856883i	$-0.327602\pi$
$593$	5.41209e131	1.03102	0.515510	+	0.856883i	$0.327602\pi$
$594$	9.20920e130	0.161944
$595$	−1.01600e132	−1.64944
$596$	8.06425e131	1.20883
$597$	−2.09785e132	−2.90398
$598$	−6.54420e130	−0.0836662
$599$	−4.64792e131	−0.548889	−0.274444	−	0.961603i	$-0.588494\pi$
$599$	−4.64792e131	−0.548889	−0.274444	+	0.961603i	$0.588494\pi$
$600$	−9.07139e131	−0.989667
$601$	−1.60710e131	−0.161996	−0.0809982	−	0.996714i	$-0.525811\pi$
$601$	−1.60710e131	−0.161996	−0.0809982	+	0.996714i	$0.525811\pi$
$602$	4.50789e131	0.419895
$603$	3.66102e132	3.15159
$604$	−8.17992e131	−0.650870
$605$	−8.46884e131	−0.622936
$606$	5.67864e130	0.0386184
$607$	2.40574e131	0.151282	0.0756409	−	0.997135i	$-0.475900\pi$
$607$	2.40574e131	0.151282	0.0756409	+	0.997135i	$0.475900\pi$
$608$	3.55524e131	0.206752
$609$	−5.21215e132	−2.80347
$610$	−4.48986e131	−0.223391
$611$	−2.91023e131	−0.133958
$612$	2.48571e132	1.05866
$613$	4.35545e132	1.71657	0.858284	−	0.513176i	$-0.171531\pi$
$613$	4.35545e132	1.71657	0.858284	+	0.513176i	$0.171531\pi$
$614$	−4.46397e131	−0.162826
$615$	9.94390e131	0.335729
$616$	1.53171e132	0.478732
$617$	2.46864e132	0.714354	0.357177	−	0.934037i	$-0.383739\pi$
$617$	2.46864e132	0.714354	0.357177	+	0.934037i	$0.383739\pi$
$618$	2.21374e132	0.593164
$619$	8.93087e131	0.221609	0.110805	−	0.993842i	$-0.464657\pi$
$619$	8.93087e131	0.221609	0.110805	+	0.993842i	$0.464657\pi$
$620$	1.00915e132	0.231926
$621$	−6.88405e132	−1.46552
$622$	−9.79590e131	−0.193197
$623$	−4.25953e132	−0.778357
$624$	−2.35394e132	−0.398591
$625$	−1.34736e132	−0.211437
$626$	1.77719e132	0.258495
$627$	3.32723e132	0.448616
$628$	−5.84915e132	−0.731155
$629$	−1.16986e132	−0.135590
$630$	−7.52543e132	−0.808827
$631$	2.49650e132	0.248850	0.124425	−	0.992229i	$-0.460291\pi$
$631$	2.49650e132	0.248850	0.124425	+	0.992229i	$0.460291\pi$
$632$	−2.91070e132	−0.269114
$633$	1.85624e133	1.59205
$634$	3.35904e132	0.267285
$635$	−1.13150e133	−0.835414
$636$	−8.96721e132	−0.614390
$637$	5.89172e132	0.374644
$638$	−3.07354e132	−0.181408
$639$	−9.25000e132	−0.506817
$640$	2.29999e133	1.16997
$641$	2.40692e133	1.13685	0.568427	−	0.822733i	$-0.307552\pi$
$641$	2.40692e133	1.13685	0.568427	+	0.822733i	$0.307552\pi$
$642$	−2.17796e132	−0.0955292
$643$	−1.54332e132	−0.0628687	−0.0314343	−	0.999506i	$-0.510008\pi$
$643$	−1.54332e132	−0.0628687	−0.0314343	+	0.999506i	$0.510008\pi$
$644$	−5.60153e133	−2.11947
$645$	9.79083e133	3.44138
$646$	−1.52067e132	−0.0496583
$647$	−3.92082e133	−1.18966	−0.594831	−	0.803851i	$-0.702781\pi$
$647$	−3.92082e133	−1.18966	−0.594831	+	0.803851i	$0.702781\pi$
$648$	2.03163e131	0.00572839
$649$	1.05105e133	0.275423
$650$	−3.60160e132	−0.0877224
$651$	1.66719e133	0.377474
$652$	3.91675e133	0.824451
$653$	−8.16486e133	−1.59798	−0.798992	−	0.601341i	$-0.794633\pi$
$653$	−8.16486e133	−1.59798	−0.798992	+	0.601341i	$0.794633\pi$
$654$	1.17000e133	0.212933
$655$	−1.31231e134	−2.22114
$656$	−7.25927e132	−0.114277
$657$	−1.58531e134	−2.32146
$658$	1.09733e133	0.149489
$659$	9.80773e133	1.24312	0.621558	−	0.783368i	$-0.286500\pi$
$659$	9.80773e133	1.24312	0.621558	+	0.783368i	$0.286500\pi$
$660$	1.62754e134	1.91952
$661$	3.42559e133	0.375981	0.187990	−	0.982171i	$-0.439803\pi$
$661$	3.42559e133	0.375981	0.187990	+	0.982171i	$0.439803\pi$
$662$	1.36062e133	0.138990
$663$	3.25913e133	0.309891
$664$	3.00633e133	0.266105
$665$	−1.04510e134	−0.861248
$666$	−8.66508e132	−0.0664885
$667$	2.29753e134	1.64166
$668$	−2.66368e134	−1.77255
$669$	1.93276e134	1.19795
$670$	−1.09556e134	−0.632531
$671$	9.92938e133	0.534075
$672$	2.87307e134	1.43981
$673$	−1.74787e134	−0.816195	−0.408098	−	0.912938i	$-0.633808\pi$
$673$	−1.74787e134	−0.816195	−0.408098	+	0.912938i	$0.633808\pi$
$674$	−2.06945e133	−0.0900552
$675$	−3.78863e134	−1.53657
$676$	2.33340e134	0.882109
$677$	−2.40368e134	−0.847060	−0.423530	−	0.905882i	$-0.639209\pi$
$677$	−2.40368e134	−0.847060	−0.423530	+	0.905882i	$0.639209\pi$
$678$	−5.95972e133	−0.195801
$679$	8.60939e134	2.63729
$680$	−1.52046e134	−0.434313
$681$	−6.91697e134	−1.84259
$682$	9.83118e132	0.0244258
$683$	−4.71094e134	−1.09175	−0.545876	−	0.837866i	$-0.683803\pi$
$683$	−4.71094e134	−1.09175	−0.545876	+	0.837866i	$0.683803\pi$
$684$	2.55690e134	0.552776
$685$	4.44668e134	0.896878
$686$	−5.54520e133	−0.104357
$687$	−1.01792e135	−1.78760
$688$	−7.14752e134	−1.17140
$689$	−7.27730e133	−0.111316
$690$	5.35937e134	0.765212
$691$	4.33118e133	0.0577297	0.0288648	−	0.999583i	$-0.490811\pi$
$691$	4.33118e133	0.0577297	0.0288648	+	0.999583i	$0.490811\pi$
$692$	1.05434e135	1.31203
$693$	1.66426e135	1.93372
$694$	−4.77999e133	−0.0518623
$695$	1.16274e135	1.17816
$696$	−7.80009e134	−0.738178
$697$	1.00508e134	0.0888471
$698$	−8.83004e133	−0.0729173
$699$	1.64288e135	1.26747
$700$	−3.08280e135	−2.22223
$701$	−1.30322e135	−0.877832	−0.438916	−	0.898528i	$-0.644637\pi$
$701$	−1.30322e135	−0.877832	−0.438916	+	0.898528i	$0.644637\pi$
$702$	9.27907e133	0.0584106
$703$	−1.20336e134	−0.0707977
$704$	−1.07106e135	−0.588994
$705$	2.38333e135	1.22518
$706$	4.25683e134	0.204580
$707$	3.94464e134	0.177250
$708$	1.30495e135	0.548294
$709$	−1.61498e135	−0.634559	−0.317280	−	0.948332i	$-0.602769\pi$
$709$	−1.61498e135	−0.634559	−0.317280	+	0.948332i	$0.602769\pi$
$710$	2.76806e134	0.101719
$711$	−3.16258e135	−1.08702
$712$	−6.37447e134	−0.204948
$713$	−7.34899e134	−0.221042
$714$	−1.22889e135	−0.345818
$715$	1.32082e135	0.347782
$716$	−1.32633e135	−0.326801
$717$	−1.09946e136	−2.53525
$718$	−1.01862e135	−0.219837
$719$	4.50767e135	0.910604	0.455302	−	0.890337i	$-0.349531\pi$
$719$	4.50767e135	0.910604	0.455302	+	0.890337i	$0.349531\pi$
$720$	1.19320e136	2.25642
$721$	1.53777e136	2.72249
$722$	1.08276e135	0.179480
$723$	−3.02565e135	−0.469624
$724$	−5.76238e135	−0.837568
$725$	1.26444e136	1.72125
$726$	−1.02434e135	−0.130603
$727$	−1.43897e136	−1.71857	−0.859286	−	0.511496i	$-0.829092\pi$
$727$	−1.43897e136	−1.71857	−0.859286	+	0.511496i	$0.829092\pi$
$728$	1.54333e135	0.172671
$729$	−1.54121e136	−1.61549
$730$	4.74405e135	0.465922
$731$	9.89607e135	0.910725
$732$	1.23280e136	1.06320
$733$	7.32110e134	0.0591749	0.0295874	−	0.999562i	$-0.490581\pi$
$733$	7.32110e134	0.0591749	0.0295874	+	0.999562i	$0.490581\pi$
$734$	1.82077e135	0.137940
$735$	−4.82502e136	−3.42650
$736$	−1.26645e136	−0.843127
$737$	2.42284e136	1.51223
$738$	7.44455e134	0.0435674
$739$	−5.20564e134	−0.0285669	−0.0142834	−	0.999898i	$-0.504547\pi$
$739$	−5.20564e134	−0.0285669	−0.0142834	+	0.999898i	$0.504547\pi$
$740$	−5.88634e135	−0.302927
$741$	3.35247e135	0.161808
$742$	2.74398e135	0.124221
$743$	3.23626e136	1.37428	0.687138	−	0.726527i	$-0.258867\pi$
$743$	3.23626e136	1.37428	0.687138	+	0.726527i	$0.258867\pi$
$744$	2.49498e135	0.0993923
$745$	−5.35962e136	−2.00314
$746$	−7.41115e135	−0.259891
$747$	3.26649e136	1.07486
$748$	1.64503e136	0.507982
$749$	−1.51291e136	−0.438457
$750$	1.00790e136	0.274161
$751$	−6.60512e135	−0.168649	−0.0843245	−	0.996438i	$-0.526873\pi$
$751$	−6.60512e135	−0.168649	−0.0843245	+	0.996438i	$0.526873\pi$
$752$	−1.73988e136	−0.417036
$753$	2.94529e136	0.662777
$754$	−3.09686e135	−0.0654308
$755$	5.43650e136	1.07855
$756$	7.94245e136	1.47969
$757$	2.11730e136	0.370449	0.185224	−	0.982696i	$-0.440699\pi$
$757$	2.11730e136	0.370449	0.185224	+	0.982696i	$0.440699\pi$
$758$	−4.20831e135	−0.0691546
$759$	−1.18523e137	−1.82944
$760$	−1.56401e136	−0.226774
$761$	4.05975e136	0.553004	0.276502	−	0.961013i	$-0.410825\pi$
$761$	4.05975e136	0.553004	0.276502	+	0.961013i	$0.410825\pi$
$762$	−1.36859e136	−0.175151
$763$	8.12736e136	0.977313
$764$	−1.43787e137	−1.62475
$765$	−1.65204e137	−1.75429
$766$	−2.73036e136	−0.272492
$767$	1.05902e136	0.0993405
$768$	−1.11017e137	−0.978886
$769$	5.31974e136	0.440950	0.220475	−	0.975393i	$-0.429239\pi$
$769$	5.31974e136	0.440950	0.220475	+	0.975393i	$0.429239\pi$
$770$	−4.98029e136	−0.388102
$771$	4.16367e137	3.05065
$772$	−1.71104e137	−1.17879
$773$	2.65854e135	0.0172234	0.00861168	−	0.999963i	$-0.497259\pi$
$773$	2.65854e135	0.0172234	0.00861168	+	0.999963i	$0.497259\pi$
$774$	7.32995e136	0.446586
$775$	−4.04451e136	−0.231758
$776$	1.28841e137	0.694422
$777$	−9.72466e136	−0.493033
$778$	3.80797e135	0.0181619
$779$	1.03386e136	0.0463910
$780$	1.63988e137	0.692340
$781$	−6.12160e136	−0.243187
$782$	5.41697e136	0.202505
$783$	−3.25768e137	−1.14611
$784$	3.52237e137	1.16633
$785$	3.88743e137	1.21159
$786$	−1.58729e137	−0.465678
$787$	9.86766e136	0.272530	0.136265	−	0.990672i	$-0.456490\pi$
$787$	9.86766e136	0.272530	0.136265	+	0.990672i	$0.456490\pi$
$788$	2.87067e137	0.746428
$789$	−7.24362e137	−1.77336
$790$	9.46401e136	0.218167
$791$	−4.13990e137	−0.898683
$792$	2.49060e137	0.509164
$793$	1.00047e137	0.192632
$794$	−8.54607e136	−0.154986
$795$	5.95974e137	1.01810
$796$	−1.06691e138	−1.71695
$797$	−8.52625e137	−1.29267	−0.646335	−	0.763054i	$-0.723699\pi$
$797$	−8.52625e137	−1.29267	−0.646335	+	0.763054i	$0.723699\pi$
$798$	−1.26408e137	−0.180567
$799$	2.40895e137	0.324232
$800$	−6.96992e137	−0.884002
$801$	−6.92610e137	−0.827836
$802$	1.24943e137	0.140744
$803$	−1.04915e138	−1.11391
$804$	3.00811e138	3.01045
$805$	3.72286e138	3.51215
$806$	9.90577e135	0.00880996
$807$	−4.01921e137	−0.337014
$808$	5.90323e136	0.0466714
$809$	−7.10788e137	−0.529889	−0.264945	−	0.964264i	$-0.585354\pi$
$809$	−7.10788e137	−0.529889	−0.264945	+	0.964264i	$0.585354\pi$
$810$	−6.60577e135	−0.00464393
$811$	−2.16217e138	−1.43351	−0.716754	−	0.697326i	$-0.754373\pi$
$811$	−2.16217e138	−1.43351	−0.716754	+	0.697326i	$0.754373\pi$
$812$	−2.65077e138	−1.65752
$813$	3.26135e138	1.92352
$814$	−5.73450e136	−0.0319034
$815$	−2.60313e138	−1.36618
$816$	1.94848e138	0.964745
$817$	1.01795e138	0.475530
$818$	1.07993e137	0.0476007
$819$	1.67689e138	0.697459
$820$	5.05721e137	0.198497
$821$	1.08348e138	0.401347	0.200674	−	0.979658i	$-0.435687\pi$
$821$	1.08348e138	0.401347	0.200674	+	0.979658i	$0.435687\pi$
$822$	5.37843e137	0.188037
$823$	−4.74157e138	−1.56470	−0.782348	−	0.622841i	$-0.785978\pi$
$823$	−4.74157e138	−1.56470	−0.782348	+	0.622841i	$0.785978\pi$
$824$	2.30130e138	0.716854
$825$	−6.52291e138	−1.91813
$826$	−3.99316e137	−0.110857
$827$	4.18889e138	1.09796	0.548980	−	0.835835i	$-0.315016\pi$
$827$	4.18889e138	1.09796	0.548980	+	0.835835i	$0.315016\pi$
$828$	−9.10823e138	−2.25420
$829$	−1.36940e138	−0.320030	−0.160015	−	0.987115i	$-0.551154\pi$
$829$	−1.36940e138	−0.320030	−0.160015	+	0.987115i	$0.551154\pi$
$830$	−9.77497e137	−0.215728
$831$	5.25238e138	1.09473
$832$	−1.07918e138	−0.212440
$833$	−4.87688e138	−0.906785
$834$	1.40638e138	0.247011
$835$	1.77032e139	2.93727
$836$	1.69214e138	0.265240
$837$	1.04202e138	0.154318
$838$	−3.50447e137	−0.0490378
$839$	3.26844e138	0.432163	0.216081	−	0.976375i	$-0.430672\pi$
$839$	3.26844e138	0.432163	0.216081	+	0.976375i	$0.430672\pi$
$840$	−1.26391e139	−1.57925
$841$	2.40383e138	0.283854
$842$	1.46080e138	0.163029
$843$	1.63236e139	1.72190
$844$	9.44034e138	0.941286
$845$	−1.55082e139	−1.46173
$846$	1.78429e138	0.158991
$847$	−7.11553e138	−0.599439
$848$	−4.35075e138	−0.346546
$849$	−9.46614e138	−0.712948
$850$	2.98123e138	0.212323
$851$	4.28665e138	0.288711
$852$	−7.60036e138	−0.484121
$853$	−4.55262e138	−0.274273	−0.137136	−	0.990552i	$-0.543790\pi$
$853$	−4.55262e138	−0.274273	−0.137136	+	0.990552i	$0.543790\pi$
$854$	−3.77238e138	−0.214965
$855$	−1.69935e139	−0.915995
$856$	−2.26410e138	−0.115449
$857$	1.58178e139	0.763058	0.381529	−	0.924357i	$-0.375398\pi$
$857$	1.58178e139	0.763058	0.381529	+	0.924357i	$0.375398\pi$
$858$	1.59758e138	0.0729151
$859$	−3.21909e139	−1.39014	−0.695068	−	0.718944i	$-0.744626\pi$
$859$	−3.21909e139	−1.39014	−0.695068	+	0.718944i	$0.744626\pi$
$860$	4.97936e139	2.03469
$861$	8.35488e138	0.323065
$862$	−7.08799e138	−0.259375
$863$	−4.92675e138	−0.170627	−0.0853136	−	0.996354i	$-0.527189\pi$
$863$	−4.92675e138	−0.170627	−0.0853136	+	0.996354i	$0.527189\pi$
$864$	1.79571e139	0.588619
$865$	−7.00733e139	−2.17414
$866$	8.50203e137	0.0249703
$867$	3.12892e139	0.869937
$868$	8.47888e138	0.223178
$869$	−2.09298e139	−0.521585
$870$	2.53617e139	0.598430
$871$	2.44122e139	0.545437
$872$	1.21628e139	0.257335
$873$	1.39991e140	2.80494
$874$	5.57211e138	0.105737
$875$	7.00131e139	1.25834
$876$	−1.30259e140	−2.21750
$877$	−4.91052e139	−0.791858	−0.395929	−	0.918281i	$-0.629577\pi$
$877$	−4.91052e139	−0.791858	−0.395929	+	0.918281i	$0.629577\pi$
$878$	−2.36214e139	−0.360842
$879$	−1.39845e140	−2.02384
$880$	7.89654e139	1.08270
$881$	2.20729e139	0.286750	0.143375	−	0.989668i	$-0.454204\pi$
$881$	2.20729e139	0.286750	0.143375	+	0.989668i	$0.454204\pi$
$882$	−3.61227e139	−0.444654
$883$	−6.07035e139	−0.708077	−0.354038	−	0.935231i	$-0.615192\pi$
$883$	−6.07035e139	−0.708077	−0.354038	+	0.935231i	$0.615192\pi$
$884$	1.65751e139	0.183220
$885$	−8.67288e139	−0.908569
$886$	1.21328e139	0.120464
$887$	1.03147e140	0.970704	0.485352	−	0.874319i	$-0.338692\pi$
$887$	1.03147e140	0.970704	0.485352	+	0.874319i	$0.338692\pi$
$888$	−1.45532e139	−0.129820
$889$	−9.50685e139	−0.803902
$890$	2.07263e139	0.166149
$891$	1.46088e138	0.0111025
$892$	9.82954e139	0.708276
$893$	2.47794e139	0.169296
$894$	−6.48267e139	−0.419974
$895$	8.81499e139	0.541537
$896$	1.93245e140	1.12584
$897$	−1.19422e140	−0.659849
$898$	7.77456e138	0.0407427
$899$	−3.47770e139	−0.172865
$900$	−5.01271e140	−2.36349
$901$	6.02380e139	0.269428
$902$	4.92676e138	0.0209050
$903$	8.22627e140	3.31158
$904$	−6.19544e139	−0.236631
$905$	3.82977e140	1.38792
$906$	6.57566e139	0.226126
$907$	−2.25866e140	−0.737063	−0.368532	−	0.929615i	$-0.620139\pi$
$907$	−2.25866e140	−0.737063	−0.368532	+	0.929615i	$0.620139\pi$
$908$	−3.51779e140	−1.08941
$909$	6.41409e139	0.188517
$910$	−5.01808e139	−0.139982
$911$	−3.34653e139	−0.0886078	−0.0443039	−	0.999018i	$-0.514107\pi$
$911$	−3.34653e139	−0.0886078	−0.0443039	+	0.999018i	$0.514107\pi$
$912$	2.00428e140	0.503737
$913$	2.16175e140	0.515755
$914$	1.62509e139	0.0368072
$915$	−8.19335e140	−1.76181
$916$	−5.17690e140	−1.05690
$917$	−1.10261e141	−2.13736
$918$	−7.68077e139	−0.141377
$919$	4.84263e140	0.846436	0.423218	−	0.906028i	$-0.360900\pi$
$919$	4.84263e140	0.846436	0.423218	+	0.906028i	$0.360900\pi$
$920$	5.57134e140	0.924778
$921$	−8.14612e140	−1.28416
$922$	1.48699e140	0.222633
$923$	−6.16804e139	−0.0877135
$924$	1.36746e141	1.84712
$925$	2.35915e140	0.302708
$926$	−1.31614e140	−0.160428
$927$	2.50045e141	2.89555
$928$	−5.99313e140	−0.659364
$929$	−4.92815e140	−0.515154	−0.257577	−	0.966258i	$-0.582924\pi$
$929$	−4.92815e140	−0.515154	−0.257577	+	0.966258i	$0.582924\pi$
$930$	−8.11232e139	−0.0805759
$931$	−5.01655e140	−0.473473
$932$	8.35524e140	0.749382
$933$	−1.78761e141	−1.52369
$934$	5.58985e139	0.0452818
$935$	−1.09331e141	−0.841768
$936$	2.50950e140	0.183647
$937$	8.13367e140	0.565791	0.282896	−	0.959151i	$-0.408705\pi$
$937$	8.13367e140	0.565791	0.282896	+	0.959151i	$0.408705\pi$
$938$	−9.20489e140	−0.608672
$939$	3.24312e141	2.03867
$940$	1.21210e141	0.724379
$941$	3.07455e140	0.174692	0.0873462	−	0.996178i	$-0.472161\pi$
$941$	3.07455e140	0.174692	0.0873462	+	0.996178i	$0.472161\pi$
$942$	4.70200e140	0.254018
$943$	−3.68285e140	−0.189181
$944$	6.33139e140	0.309264
$945$	−5.27867e141	−2.45196
$946$	4.85092e140	0.214287
$947$	−3.15683e141	−1.32625	−0.663127	−	0.748507i	$-0.730771\pi$
$947$	−3.15683e141	−1.32625	−0.663127	+	0.748507i	$0.730771\pi$
$948$	−2.59857e141	−1.03834
$949$	−1.05711e141	−0.401769
$950$	3.06661e140	0.110863
$951$	6.12977e141	2.10799
$952$	−1.27749e141	−0.417931
$953$	−3.82327e141	−1.18993	−0.594966	−	0.803751i	$-0.702835\pi$
$953$	−3.82327e141	−1.18993	−0.594966	+	0.803751i	$0.702835\pi$
$954$	4.46179e140	0.132118
$955$	9.55631e141	2.69234
$956$	−5.59158e141	−1.49894
$957$	−5.60877e141	−1.43071
$958$	5.74952e140	0.139563
$959$	3.73610e141	0.863048
$960$	8.83795e141	1.94298
$961$	−4.66802e141	−0.976725
$962$	−5.77801e139	−0.0115070
$963$	−2.46003e141	−0.466328
$964$	−1.53877e141	−0.277660
$965$	1.13718e142	1.95336
$966$	4.50295e141	0.736348
$967$	5.82772e141	0.907280	0.453640	−	0.891185i	$-0.350125\pi$
$967$	5.82772e141	0.907280	0.453640	+	0.891185i	$0.350125\pi$
$968$	−1.06485e141	−0.157838
$969$	−2.77502e141	−0.391639
$970$	−4.18922e141	−0.562958
$971$	−1.36042e142	−1.74085	−0.870423	−	0.492305i	$-0.836155\pi$
$971$	−1.36042e142	−1.74085	−0.870423	+	0.492305i	$0.836155\pi$
$972$	−7.76909e141	−0.946723
$973$	9.76936e141	1.13372
$974$	2.36011e141	0.260845
$975$	−6.57240e141	−0.691839
$976$	5.98133e141	0.599696
$977$	4.48538e141	0.428359	0.214179	−	0.976794i	$-0.431292\pi$
$977$	4.48538e141	0.428359	0.214179	+	0.976794i	$0.431292\pi$
$978$	−3.14859e141	−0.286431
$979$	−4.58366e141	−0.397223
$980$	−2.45388e142	−2.02588
$981$	1.32153e142	1.03944
$982$	−3.35885e141	−0.251707
$983$	1.67273e142	1.19435	0.597177	−	0.802109i	$-0.296289\pi$
$983$	1.67273e142	1.19435	0.597177	+	0.802109i	$0.296289\pi$
$984$	1.25032e141	0.0850659
$985$	−1.90789e142	−1.23689
$986$	2.56343e141	0.158368
$987$	2.00248e142	1.17897
$988$	1.70498e141	0.0956675
$989$	−3.62615e142	−1.93920
$990$	−8.09808e141	−0.412772
$991$	−2.03424e142	−0.988332	−0.494166	−	0.869368i	$-0.664526\pi$
$991$	−2.03424e142	−0.988332	−0.494166	+	0.869368i	$0.664526\pi$
$992$	1.91700e141	0.0887803
$993$	2.48294e142	1.09617
$994$	2.32573e141	0.0978825
$995$	7.09087e142	2.84514
$996$	2.68395e142	1.02673
$997$	−6.28827e140	−0.0229357	−0.0114678	−	0.999934i	$-0.503650\pi$
$997$	−6.28827e140	−0.0229357	−0.0114678	+	0.999934i	$0.503650\pi$
$998$	−2.58451e141	−0.0898829
$999$	−6.07807e141	−0.201560

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1.96.a.a.1.4	✓	8	1.1	even	1	trivial
9.96.a.c.1.5		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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 1 \)
Weight:	\( k \)	\(=\)	\( 96 \)
Character orbit:	\([\chi]\)	\(=\)	1.a (trivial)

\(f(q)\)	\(=\)	\(q-4.08831e13 q^{2} -7.46060e22 q^{3} -3.79427e28 q^{4} +2.52173e33 q^{5} +3.05013e36 q^{6} +2.11876e40 q^{7} +3.17076e42 q^{8} +3.44515e45 q^{9} -1.03096e47 q^{10} +2.27998e49 q^{11} +2.83075e51 q^{12} +2.29728e52 q^{13} -8.66214e53 q^{14} -1.88136e56 q^{15} +1.37343e57 q^{16} -1.90158e58 q^{17} -1.40849e59 q^{18} -1.95604e60 q^{19} -9.56809e61 q^{20} -1.58072e63 q^{21} -9.32129e62 q^{22} +6.96784e64 q^{23} -2.36558e65 q^{24} +3.83474e66 q^{25} -9.39201e65 q^{26} -9.87975e67 q^{27} -8.03912e68 q^{28} +3.29733e69 q^{29} +7.69158e69 q^{30} -1.05470e70 q^{31} -1.81757e71 q^{32} -1.70100e72 q^{33} +7.77425e71 q^{34} +5.34292e73 q^{35} -1.30718e74 q^{36} +6.15205e73 q^{37} +7.99690e73 q^{38} -1.71391e75 q^{39} +7.99579e75 q^{40} -5.28549e75 q^{41} +6.46247e76 q^{42} -5.20413e77 q^{43} -8.65086e77 q^{44} +8.68773e78 q^{45} -2.84867e78 q^{46} -1.26681e79 q^{47} -1.02466e80 q^{48} +2.56465e80 q^{49} -1.56776e80 q^{50} +1.41869e81 q^{51} -8.71650e80 q^{52} -3.16779e81 q^{53} +4.03915e81 q^{54} +5.74949e82 q^{55} +6.71807e82 q^{56} +1.45932e83 q^{57} -1.34805e83 q^{58} +4.60990e83 q^{59} +7.13837e84 q^{60} +4.35502e84 q^{61} +4.31195e83 q^{62} +7.29944e85 q^{63} -4.69765e85 q^{64} +5.79311e85 q^{65} +6.95424e85 q^{66} +1.06266e87 q^{67} +7.21510e86 q^{68} -5.19842e87 q^{69} -2.18435e87 q^{70} -2.68493e87 q^{71} +1.09238e88 q^{72} -4.60158e88 q^{73} -2.51515e87 q^{74} -2.86095e89 q^{75} +7.42173e88 q^{76} +4.83073e89 q^{77} +7.00700e88 q^{78} -9.17980e89 q^{79} +3.46342e90 q^{80} +6.40740e88 q^{81} +2.16088e89 q^{82} +9.48142e90 q^{83} +5.99766e91 q^{84} -4.79526e91 q^{85} +2.12761e91 q^{86} -2.46001e92 q^{87} +7.22929e91 q^{88} -2.01039e92 q^{89} -3.55182e92 q^{90} +4.86738e92 q^{91} -2.64378e93 q^{92} +7.86870e92 q^{93} +5.17914e92 q^{94} -4.93259e93 q^{95} +1.35602e94 q^{96} +4.06342e94 q^{97} -1.04851e94 q^{98} +7.85489e94 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 5835659138280 q^{2} - 95\!\cdots\!80 q^{3} + 20\!\cdots\!84 q^{4} + 19\!\cdots\!60 q^{5} + 10\!\cdots\!76 q^{6} + 31\!\cdots\!00 q^{7} - 14\!\cdots\!60 q^{8} + 92\!\cdots\!36 q^{9} - 35\!\cdots\!40 q^{10}+ \cdots + 30\!\cdots\!72 q^{99}+O(q^{100}) \) 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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