LMFDB - Embedded newform 1.78.a.a.1.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1,78,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, 78, names="a")

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

chi := DirichletCharacter("1.1");

S:= CuspForms(chi, 78);

N := Newforms(S);

Level:	$ N $	$=$	$ 1 $
Weight:	$ k $	$=$	$ 78 $
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:	$37.5479417817$
Analytic rank:	$1$
Dimension:	$6$
Coefficient field:	$\mathbb{Q}[x]/(x^{6} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} + \cdots - 44\!\cdots\!16 $ x^6 - 17761277524319496093x^4 - 5418653098480012458842128200x^3 + 63613941732383091007079230349679850008x^2 + 25593744940652395086700970560658253564764671200x - 44271959822073232588337476834309941911954845745332334416
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	multiple of $ 2^{64}\cdot 3^{20}\cdot 5^{8}\cdot 7^{3}\cdot 11^{2}\cdot 13^{2}\cdot 19 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.5
Root			$-1.61977e9$ 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)

$f(q)$	$=$	$q+3.55117e11 q^{2} +1.22969e18 q^{3} -2.50080e22 q^{4} +1.38608e27 q^{5} +4.36684e29 q^{6} -5.00002e32 q^{7} -6.25444e34 q^{8} -3.96226e36 q^{9} +O(q^{10})$	\(q+3.55117e11 q^{2} +1.22969e18 q^{3} -2.50080e22 q^{4} +1.38608e27 q^{5} +4.36684e29 q^{6} -5.00002e32 q^{7} -6.25444e34 q^{8} -3.96226e36 q^{9} +4.92219e38 q^{10} -1.21522e40 q^{11} -3.07521e40 q^{12} -3.54947e41 q^{13} -1.77559e44 q^{14} +1.70445e45 q^{15} -1.84315e46 q^{16} +1.84177e47 q^{17} -1.40706e48 q^{18} -2.35325e49 q^{19} -3.46629e49 q^{20} -6.14849e50 q^{21} -4.31545e51 q^{22} +1.55537e52 q^{23} -7.69104e52 q^{24} +1.25946e54 q^{25} -1.26048e53 q^{26} -1.16042e55 q^{27} +1.25040e55 q^{28} -2.36858e56 q^{29} +6.05278e56 q^{30} +1.62207e56 q^{31} +2.90613e57 q^{32} -1.49435e58 q^{33} +6.54042e58 q^{34} -6.93041e59 q^{35} +9.90880e58 q^{36} +1.28912e60 q^{37} -8.35677e60 q^{38} -4.36476e59 q^{39} -8.66914e61 q^{40} -1.91035e62 q^{41} -2.18343e62 q^{42} -3.74016e62 q^{43} +3.03902e62 q^{44} -5.49199e63 q^{45} +5.52339e63 q^{46} +6.85766e63 q^{47} -2.26650e64 q^{48} +1.31821e65 q^{49} +4.47257e65 q^{50} +2.26481e65 q^{51} +8.87651e63 q^{52} +5.42027e65 q^{53} -4.12084e66 q^{54} -1.68439e67 q^{55} +3.12724e67 q^{56} -2.89377e67 q^{57} -8.41123e67 q^{58} -7.28240e67 q^{59} -4.26248e67 q^{60} +5.56705e68 q^{61} +5.76023e67 q^{62} +1.98114e69 q^{63} +3.81730e69 q^{64} -4.91984e68 q^{65} -5.30667e69 q^{66} -1.72617e70 q^{67} -4.60588e69 q^{68} +1.91263e70 q^{69} -2.46110e71 q^{70} +2.59217e71 q^{71} +2.47817e71 q^{72} -9.27057e71 q^{73} +4.57789e71 q^{74} +1.54875e72 q^{75} +5.88499e71 q^{76} +6.07612e72 q^{77} -1.55000e71 q^{78} -6.11343e72 q^{79} -2.55474e73 q^{80} +7.42141e72 q^{81} -6.78397e73 q^{82} +1.75907e73 q^{83} +1.53761e73 q^{84} +2.55283e74 q^{85} -1.32819e74 q^{86} -2.91263e74 q^{87} +7.60052e74 q^{88} +1.53377e75 q^{89} -1.95030e75 q^{90} +1.77475e74 q^{91} -3.88967e74 q^{92} +1.99464e74 q^{93} +2.43527e75 q^{94} -3.26178e76 q^{95} +3.57364e75 q^{96} -4.42098e75 q^{97} +4.68117e76 q^{98} +4.81501e76 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 264721893120 q^{2} + 14\!\cdots\!80 q^{3}+ \cdots - 48\!\cdots\!42 q^{9}+O(q^{10}) $ 6 * q + 264721893120 * q^2 + 1441611375788089080 * q^3 + 414488718051562044137472 * q^4 - 262034655809276597802623100 * q^5 - 366806373876514422355130201088 * q^6 + 270857839709680313679329082207600 * q^7 - 21222715175771442181432808272035840 * q^8 - 4895011902698601362943838014820938642 * q^9	$ 6 q + 264721893120 q^{2} + 14\!\cdots\!80 q^{3}+ \cdots + 22\!\cdots\!76 q^{99}+O(q^{100}) $ 6 * q + 264721893120 * q^2 + 1441611375788089080 * q^3 + 414488718051562044137472 * q^4 - 262034655809276597802623100 * q^5 - 366806373876514422355130201088 * q^6 + 270857839709680313679329082207600 * q^7 - 21222715175771442181432808272035840 * q^8 - 4895011902698601362943838014820938642 * q^9 - 943981839595570481933588950406110963200 * q^10 - 18259523505888985403727472716999830396568 * q^11 + 464880745107061653664227300592441229475840 * q^12 + 2380194429688668511174277092390661204777460 * q^13 - 294635885851315312797761966406968268616083456 * q^14 - 205398878502504702020984224024402427189799600 * q^15 + 44678683808767880535489561508977888302859288576 * q^16 - 354360527898668112383938884095051354700497739540 * q^17 - 579271368199620858231236048886957435939670283520 * q^18 + 5609349588345922508653624528305080863470217945560 * q^19 - 203683258723050328883517820082887345024612662067200 * q^20 - 540436528239602082418470626392633746858753885327168 * q^21 + 6114758837406209570140637531269380807939078825354240 * q^22 - 47704848518150781083381010364499925248017731105789360 * q^23 + 54816594321451146263884987133438313725918160963502080 * q^24 + 1218179184124654235834607721614209488740550081397516250 * q^25 - 550866287661514215594856318864157268196554716662599168 * q^26 - 18043016639677384483149377528753631298041104958650825040 * q^27 + 27673374074418016612675778175139670616136146452210319360 * q^28 + 16280759001892520996902191080778000816917007177111344340 * q^29 - 1011764162094599483190536262352170796094588963959467571200 * q^30 + 1790157695657501252076176026171679301117057950393828071872 * q^31 + 2181738275733175796144863923114890278726253762313317253120 * q^32 - 43587817236406175039900898992317145479130853281029781929440 * q^33 - 194953896897775283488395124499645480734536214093757337125376 * q^34 - 154692900477132731635374066357063627778968619353419533615200 * q^35 - 3492826558014976862445701719551945606786728595490426565320704 * q^36 - 7407081044970614504852172741178628092123742757389002078546620 * q^37 - 23437112252897896880014527036750794366537612969976459081384960 * q^38 - 70639623729776089938517469701883961219469901500376562016990704 * q^39 - 405188969845671269189619479481322249890553020909404426600448000 * q^40 - 622334267497818741826318492502909006845617873220194725690266308 * q^41 - 1785314244915654620512096109946411089204707510656231457419632640 * q^42 - 2618736058252833489926178823787488683637632009899828264542685400 * q^43 - 10432822146524346418364354026489166880919966717673650220195414016 * q^44 - 4261664397684963408032474279116855329416026736411628094706748300 * q^45 + 15015668129695292865283752907788076308022505321300082329335498752 * q^46 + 10456714010948157967838849947567752123265493969429352826408225440 * q^47 + 195413572872589369177356962560292275025549393856976542715493744640 * q^48 + 471540371160970162947042524598603402842322365532951363545112427542 * q^49 + 1643157939326752820476079797938119435570111533434962615482069920000 * q^50 + 1437480019590559075427205620912951154862381268364307425321563068272 * q^51 + 2497724095217025746860726558921243156289473926034163020782517862400 * q^52 - 1351874258191312033682238211039504811418206289179811594973968454620 * q^53 - 5802743153283665491865673044971704841325735354018068579171943024640 * q^54 - 31869417904451543700720919226087498810908552969327767789062308093200 * q^55 - 108662999456853131644146391920304784213919375663746888603843313008640 * q^56 - 80192344792625061999550741265686291327620988057496835084561604104480 * q^57 - 198994309984504890955955717028136272430515707470032642085684388912640 * q^58 - 314181202100222481576760882531528728694115253385468703103388053744120 * q^59 + 31757517058237454003450287009369504103827834377957826095111285964800 * q^60 + 1205268428250020260156089514176723127199311484106453915524972341789332 * q^61 + 5847595327663334724128627418101253733235456067016746715116600210186240 * q^62 + 5797157259817187838172511312525532039665297350177795293712349527116720 * q^63 + 7434996765286658306744699729117001037072361082977441755818145446100992 * q^64 + 8871205916648888694302367444130318424721491973331706441245421034929400 * q^65 + 2619665127058305678398408811495791734563636436120923156834123240689664 * q^66 - 20237777137309439154263683707086560559031166786916812035021461385807240 * q^67 - 192282119728407192675118903436134256417865682110612543314367901015326720 * q^68 - 200313232582951000798678573547728345115884560145782233425701325968721344 * q^69 - 275296905202040079140538321149869121020079259159855285360874363784294400 * q^70 - 84566701931998894021025479230103599698793740396961643247253155987263248 * q^71 - 111057066523302390867411925011041674769499898042748718262699840917995520 * q^72 + 314847243747931153403355639258701372803638975422668152047464555954073340 * q^73 + 2440978652597431277933746515377916372937009497503279937672013012437072384 * q^74 + 5406848712313524713947990348797970278787563587939911155459007261158885000 * q^75 + 12583857788866874491493997574394644552563831648352611876045224548363960320 * q^76 + 3503704566884313110653172829033905566483467863121365108497302013892404800 * q^77 - 3205965675068953356081325009194962500817273160296149320647178104103475200 * q^78 - 4478934474840817947707335445643189482501134177625819638140993021754592160 * q^79 - 71161053770974020381924657869896203411328788664145358716969422377556377600 * q^80 - 62119692812757584111204435712960193411658364945985590227036022119327600874 * q^81 - 215870435463876846311226667757904584387222051304478591060278478661208783360 * q^82 - 148140974166416303075124558783351182994193920545724368826080939980520858280 * q^83 + 51356650106390838431654087814077196024066314243448648781044119034071875584 * q^84 + 491597676589966787491574950515749558236649703170109339586274361878505865800 * q^85 + 282408262347204426247008847369759267182197911237017110679724533137839752192 * q^86 + 1363181037080164755262169098102975505194220445144287377094744451132352801680 * q^87 + 2657681751590091680961785563694793344274050442909114832295757477808460267520 * q^88 + 244875270415762051982571278168423166555270869887140541520680077076967187420 * q^89 + 4978403011748231687089157306213454731057762280800383772471249777474918822400 * q^90 + 637560104295539679774601429928812188462565548465392346037583647743398360352 * q^91 - 20568828732565451743944414428223922568301505472542794858122155367508257341440 * q^92 - 14490478249669505799006967900921922007746327667753988409512015425992979344640 * q^93 - 17973701798427203443369711151367318601937605119380706693990709867752930471936 * q^94 - 32941519370397986858775692207480112776415936672941584218885058160279506566000 * q^95 - 18725276161952705842933385524361085962413728935875751155361188816688573841408 * q^96 - 12282501490438986599941765679523755451099259695347356745999502279014355079860 * q^97 + 34498422662482146891923464099753801985751726005296311870693615309501356240640 * q^98 + 225826616422430389876328344183536014760241704676820880296433754570070950840776 * 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 $

$2$	3.55117e11	0.913516	0.456758	−	0.889591i	$-0.349011\pi$
$2$	3.55117e11	0.913516	0.456758	+	0.889591i	$0.349011\pi$
$3$	1.22969e18	0.525567	0.262784	−	0.964855i	$-0.415359\pi$
$3$	1.22969e18	0.525567	0.262784	+	0.964855i	$0.415359\pi$
$4$	−2.50080e22	−0.165489
$5$	1.38608e27	1.70389	0.851946	−	0.523630i	$-0.175422\pi$
$5$	1.38608e27	1.70389	0.851946	+	0.523630i	$0.175422\pi$
$6$	4.36684e29	0.480114
$7$	−5.00002e32	−1.45445	−0.727223	−	0.686402i	$-0.759189\pi$
$7$	−5.00002e32	−1.45445	−0.727223	+	0.686402i	$0.759189\pi$
$8$	−6.25444e34	−1.06469
$9$	−3.96226e36	−0.723779
$10$	4.92219e38	1.55653
$11$	−1.21522e40	−0.979572	−0.489786	−	0.871843i	$-0.662925\pi$
$11$	−1.21522e40	−0.979572	−0.489786	+	0.871843i	$0.662925\pi$
$12$	−3.07521e40	−0.0869755
$13$	−3.54947e41	−0.0460622	−0.0230311	−	0.999735i	$-0.507332\pi$
$13$	−3.54947e41	−0.0460622	−0.0230311	+	0.999735i	$0.507332\pi$
$14$	−1.77559e44	−1.32866
$15$	1.70445e45	0.895510
$16$	−1.84315e46	−0.807125
$17$	1.84177e47	0.781540	0.390770	−	0.920488i	$-0.372209\pi$
$17$	1.84177e47	0.781540	0.390770	+	0.920488i	$0.372209\pi$
$18$	−1.40706e48	−0.661184
$19$	−2.35325e49	−1.37929	−0.689643	−	0.724150i	$-0.742232\pi$
$19$	−2.35325e49	−1.37929	−0.689643	+	0.724150i	$0.742232\pi$
$20$	−3.46629e49	−0.281975
$21$	−6.14849e50	−0.764408
$22$	−4.31545e51	−0.894855
$23$	1.55537e52	0.582523	0.291262	−	0.956643i	$-0.405925\pi$
$23$	1.55537e52	0.582523	0.291262	+	0.956643i	$0.405925\pi$
$24$	−7.69104e52	−0.559567
$25$	1.25946e54	1.90325
$26$	−1.26048e53	−0.0420786
$27$	−1.16042e55	−0.905962
$28$	1.25040e55	0.240694
$29$	−2.36858e56	−1.18077	−0.590386	−	0.807121i	$-0.701024\pi$
$29$	−2.36858e56	−1.18077	−0.590386	+	0.807121i	$0.701024\pi$
$30$	6.05278e56	0.818062
$31$	1.62207e56	0.0620360	0.0310180	−	0.999519i	$-0.490125\pi$
$31$	1.62207e56	0.0620360	0.0310180	+	0.999519i	$0.490125\pi$
$32$	2.90613e57	0.327371
$33$	−1.49435e58	−0.514831
$34$	6.54042e58	0.713949
$35$	−6.93041e59	−2.47822
$36$	9.90880e58	0.119777
$37$	1.28912e60	0.542661	0.271330	−	0.962486i	$-0.412536\pi$
$37$	1.28912e60	0.542661	0.271330	+	0.962486i	$0.412536\pi$
$38$	−8.35677e60	−1.26000
$39$	−4.36476e59	−0.0242088
$40$	−8.66914e61	−1.81412
$41$	−1.91035e62	−1.54502	−0.772511	−	0.635002i	$-0.780999\pi$
$41$	−1.91035e62	−1.54502	−0.772511	+	0.635002i	$0.780999\pi$
$42$	−2.18343e62	−0.698299
$43$	−3.74016e62	−0.483453	−0.241727	−	0.970344i	$-0.577714\pi$
$43$	−3.74016e62	−0.483453	−0.241727	+	0.970344i	$0.577714\pi$
$44$	3.03902e62	0.162108
$45$	−5.49199e63	−1.23324
$46$	5.52339e63	0.532144
$47$	6.85766e63	0.288675	0.144337	−	0.989529i	$-0.453895\pi$
$47$	6.85766e63	0.288675	0.144337	+	0.989529i	$0.453895\pi$
$48$	−2.26650e64	−0.424198
$49$	1.31821e65	1.11541
$50$	4.47257e65	1.73865
$51$	2.26481e65	0.410752
$52$	8.87651e63	0.00762278
$53$	5.42027e65	0.223563	0.111781	−	0.993733i	$-0.464344\pi$
$53$	5.42027e65	0.223563	0.111781	+	0.993733i	$0.464344\pi$
$54$	−4.12084e66	−0.827610
$55$	−1.68439e67	−1.66909
$56$	3.12724e67	1.54854
$57$	−2.89377e67	−0.724907
$58$	−8.41123e67	−1.07865
$59$	−7.28240e67	−0.483584	−0.241792	−	0.970328i	$-0.577735\pi$
$59$	−7.28240e67	−0.483584	−0.241792	+	0.970328i	$0.577735\pi$
$60$	−4.26248e67	−0.148197
$61$	5.56705e68	1.02430	0.512149	−	0.858897i	$-0.328849\pi$
$61$	5.56705e68	1.02430	0.512149	+	0.858897i	$0.328849\pi$
$62$	5.76023e67	0.0566709
$63$	1.98114e69	1.05270
$64$	3.81730e69	1.10618
$65$	−4.91984e68	−0.0784851
$66$	−5.30667e69	−0.470306
$67$	−1.72617e70	−0.857440	−0.428720	−	0.903437i	$-0.641035\pi$
$67$	−1.72617e70	−0.857440	−0.428720	+	0.903437i	$0.641035\pi$
$68$	−4.60588e69	−0.129336
$69$	1.91263e70	0.306155
$70$	−2.46110e71	−2.26389
$71$	2.59217e71	1.38107	0.690537	−	0.723297i	$-0.257374\pi$
$71$	2.59217e71	1.38107	0.690537	+	0.723297i	$0.257374\pi$
$72$	2.47817e71	0.770602
$73$	−9.27057e71	−1.69503	−0.847513	−	0.530775i	$-0.821901\pi$
$73$	−9.27057e71	−1.69503	−0.847513	+	0.530775i	$0.821901\pi$
$74$	4.57789e71	0.495729
$75$	1.54875e72	1.00028
$76$	5.88499e71	0.228256
$77$	6.07612e72	1.42473
$78$	−1.55000e71	−0.0221151
$79$	−6.11343e72	−0.534124	−0.267062	−	0.963679i	$-0.586053\pi$
$79$	−6.11343e72	−0.534124	−0.267062	+	0.963679i	$0.586053\pi$
$80$	−2.55474e73	−1.37525
$81$	7.42141e72	0.247636
$82$	−6.78397e73	−1.41140
$83$	1.75907e73	0.229496	0.114748	−	0.993395i	$-0.463394\pi$
$83$	1.75907e73	0.229496	0.114748	+	0.993395i	$0.463394\pi$
$84$	1.53761e73	0.126501
$85$	2.55283e74	1.33166
$86$	−1.32819e74	−0.441642
$87$	−2.91263e74	−0.620575
$88$	7.60052e74	1.04294
$89$	1.53377e75	1.36221	0.681105	−	0.732186i	$-0.261500\pi$
$89$	1.53377e75	1.36221	0.681105	+	0.732186i	$0.261500\pi$
$90$	−1.95030e75	−1.12659
$91$	1.77475e74	0.0669950
$92$	−3.88967e74	−0.0964011
$93$	1.99464e74	0.0326041
$94$	2.43527e75	0.263709
$95$	−3.26178e76	−2.35015
$96$	3.57364e75	0.172056
$97$	−4.42098e75	−0.142826	−0.0714129	−	0.997447i	$-0.522751\pi$
$97$	−4.42098e75	−0.142826	−0.0714129	+	0.997447i	$0.522751\pi$
$98$	4.68117e76	1.01895
$99$	4.81501e76	0.708994
$100$	−3.14966e76	−0.314966
$101$	2.30088e77	1.56863	0.784315	−	0.620363i	$-0.213015\pi$
$101$	2.30088e77	1.56863	0.784315	+	0.620363i	$0.213015\pi$
$102$	8.04271e76	0.375228
$103$	−3.89684e77	−1.24876	−0.624381	−	0.781120i	$-0.714649\pi$
$103$	−3.89684e77	−1.24876	−0.624381	+	0.781120i	$0.714649\pi$
$104$	2.22000e76	0.0490421
$105$	−8.52228e77	−1.30247
$106$	1.92483e77	0.204228
$107$	3.32283e77	0.245603	0.122801	−	0.992431i	$-0.460812\pi$
$107$	3.32283e77	0.245603	0.122801	+	0.992431i	$0.460812\pi$
$108$	2.90197e77	0.149926
$109$	2.75257e77	0.0997282	0.0498641	−	0.998756i	$-0.484121\pi$
$109$	2.75257e77	0.0997282	0.0498641	+	0.998756i	$0.484121\pi$
$110$	−5.98154e78	−1.52474
$111$	1.58523e78	0.285205
$112$	9.21577e78	1.17392
$113$	8.46092e78	0.765416	0.382708	−	0.923869i	$-0.374992\pi$
$113$	8.46092e78	0.765416	0.382708	+	0.923869i	$0.374992\pi$
$114$	−1.02763e79	−0.662214
$115$	2.15587e79	0.992557
$116$	5.92335e78	0.195404
$117$	1.40639e78	0.0333389
$118$	−2.58610e79	−0.441762
$119$	−9.20888e79	−1.13671
$120$	−1.06604e80	−0.953442
$121$	−6.22347e78	−0.0404386
$122$	1.97695e80	0.935713
$123$	−2.34914e80	−0.812012
$124$	−4.05646e78	−0.0102663
$125$	8.28485e80	1.53904
$126$	7.03535e80	0.961656
$127$	−9.08186e80	−0.915654	−0.457827	−	0.889041i	$-0.651372\pi$
$127$	−9.08186e80	−0.915654	−0.457827	+	0.889041i	$0.651372\pi$
$128$	9.16424e80	0.683145
$129$	−4.59925e80	−0.254087
$130$	−1.74712e80	−0.0716974
$131$	−5.17005e81	−1.57961	−0.789806	−	0.613357i	$-0.789819\pi$
$131$	−5.17005e81	−1.57961	−0.789806	+	0.613357i	$0.789819\pi$
$132$	3.73705e80	0.0851987
$133$	1.17663e82	2.00609
$134$	−6.12992e81	−0.783285
$135$	−1.60843e82	−1.54366
$136$	−1.15192e82	−0.832100
$137$	2.25136e82	1.22660	0.613299	−	0.789851i	$-0.289842\pi$
$137$	2.25136e82	1.22660	0.613299	+	0.789851i	$0.289842\pi$
$138$	6.79207e81	0.279677
$139$	2.63228e81	0.0820848	0.0410424	−	0.999157i	$-0.486932\pi$
$139$	2.63228e81	0.0820848	0.0410424	+	0.999157i	$0.486932\pi$
$140$	1.73315e82	0.410117
$141$	8.43281e81	0.151718
$142$	9.20522e82	1.26163
$143$	4.31339e81	0.0451213
$144$	7.30302e82	0.584180
$145$	−3.28304e83	−2.01191
$146$	−3.29213e83	−1.54843
$147$	1.62099e83	0.586223
$148$	−3.22384e82	−0.0898042
$149$	−1.17632e82	−0.0252846	−0.0126423	−	0.999920i	$-0.504024\pi$
$149$	−1.17632e82	−0.0252846	−0.0126423	+	0.999920i	$0.504024\pi$
$150$	5.49988e83	0.913776
$151$	−9.93271e83	−1.27778	−0.638889	−	0.769299i	$-0.720606\pi$
$151$	−9.93271e83	−1.27778	−0.638889	+	0.769299i	$0.720606\pi$
$152$	1.47183e84	1.46851
$153$	−7.29756e83	−0.565663
$154$	2.15773e84	1.30152
$155$	2.24831e83	0.105703
$156$	1.09154e82	0.00400628
$157$	−1.82442e84	−0.523586	−0.261793	−	0.965124i	$-0.584314\pi$
$157$	−1.82442e84	−0.523586	−0.261793	+	0.965124i	$0.584314\pi$
$158$	−2.17098e84	−0.487931
$159$	6.66526e83	0.117497
$160$	4.02812e84	0.557805
$161$	−7.77691e84	−0.847248
$162$	2.63547e84	0.226219
$163$	−1.27574e85	−0.864051	−0.432026	−	0.901861i	$-0.642201\pi$
$163$	−1.27574e85	−0.864051	−0.432026	+	0.901861i	$0.642201\pi$
$164$	4.77739e84	0.255684
$165$	−2.07128e85	−0.877216
$166$	6.24673e84	0.209648
$167$	3.65643e85	0.973808	0.486904	−	0.873456i	$-0.338126\pi$
$167$	3.65643e85	0.973808	0.486904	+	0.873456i	$0.338126\pi$
$168$	3.84554e85	0.813860
$169$	−5.92537e85	−0.997878
$170$	9.06553e85	1.21649
$171$	9.32418e85	0.998298
$172$	9.35338e84	0.0800061
$173$	−6.25309e85	−0.427877	−0.213939	−	0.976847i	$-0.568629\pi$
$173$	−6.25309e85	−0.427877	−0.213939	+	0.976847i	$0.568629\pi$
$174$	−1.03432e86	−0.566905
$175$	−6.29735e86	−2.76817
$176$	2.23983e86	0.790637
$177$	−8.95511e85	−0.254156
$178$	5.44666e86	1.24440
$179$	−4.15527e86	−0.765169	−0.382585	−	0.923920i	$-0.624966\pi$
$179$	−4.15527e86	−0.765169	−0.382585	+	0.923920i	$0.624966\pi$
$180$	1.37344e86	0.204088
$181$	5.77354e86	0.693134	0.346567	−	0.938025i	$-0.387347\pi$
$181$	5.77354e86	0.693134	0.346567	+	0.938025i	$0.387347\pi$
$182$	6.30241e85	0.0612010
$183$	6.84576e86	0.538337
$184$	−9.72800e86	−0.620208
$185$	1.78682e87	0.924635
$186$	7.08331e85	0.0297844
$187$	−2.23815e87	−0.765575
$188$	−1.71496e86	−0.0477724
$189$	5.80212e87	1.31767
$190$	−1.15831e88	−2.14690
$191$	5.51587e87	0.835275	0.417637	−	0.908614i	$-0.362858\pi$
$191$	5.51587e87	0.835275	0.417637	+	0.908614i	$0.362858\pi$
$192$	4.69410e87	0.581374
$193$	−1.79804e88	−1.82324	−0.911619	−	0.411036i	$-0.865167\pi$
$193$	−1.79804e88	−1.82324	−0.911619	+	0.411036i	$0.865167\pi$
$194$	−1.56996e87	−0.130474
$195$	−6.04989e86	−0.0412492
$196$	−3.29657e87	−0.184588
$197$	2.21485e88	1.01952	0.509759	−	0.860317i	$-0.329734\pi$
$197$	2.21485e88	1.01952	0.509759	+	0.860317i	$0.329734\pi$
$198$	1.70989e88	0.647677
$199$	5.55948e88	1.73456	0.867282	−	0.497817i	$-0.165865\pi$
$199$	5.55948e88	1.73456	0.867282	+	0.497817i	$0.165865\pi$
$200$	−7.87725e88	−2.02637
$201$	−2.12266e88	−0.450642
$202$	8.17079e88	1.43297
$203$	1.18430e89	1.71737
$204$	−5.66382e87	−0.0679748
$205$	−2.64789e89	−2.63255
$206$	−1.38383e89	−1.14076
$207$	−6.16279e88	−0.421618
$208$	6.54220e87	0.0371780
$209$	2.85971e89	1.35111
$210$	−3.02640e89	−1.18983
$211$	3.76303e89	1.23215	0.616075	−	0.787688i	$-0.288722\pi$
$211$	3.76303e89	1.23215	0.616075	+	0.787688i	$0.288722\pi$
$212$	−1.35550e88	−0.0369971
$213$	3.18757e89	0.725847
$214$	1.17999e89	0.224362
$215$	−5.18415e89	−0.823752
$216$	7.25777e89	0.964571
$217$	−8.11038e88	−0.0902280
$218$	9.77482e88	0.0911033
$219$	−1.14000e90	−0.890850
$220$	4.21231e89	0.276215
$221$	−6.53731e88	−0.0359995
$222$	5.62940e89	0.260539
$223$	4.14523e89	0.161366	0.0806829	−	0.996740i	$-0.474290\pi$
$223$	4.14523e89	0.161366	0.0806829	+	0.996740i	$0.474290\pi$
$224$	−1.45307e90	−0.476144
$225$	−4.99032e90	−1.37753
$226$	3.00461e90	0.699220
$227$	−5.33861e90	−1.04817	−0.524087	−	0.851665i	$-0.675593\pi$
$227$	−5.33861e90	−1.04817	−0.524087	+	0.851665i	$0.675593\pi$
$228$	7.23673e89	0.119964
$229$	2.84919e90	0.399075	0.199538	−	0.979890i	$-0.436056\pi$
$229$	2.84919e90	0.399075	0.199538	+	0.979890i	$0.436056\pi$
$230$	7.65584e90	0.906716
$231$	7.47176e90	0.748793
$232$	1.48142e91	1.25716
$233$	−1.67827e91	−1.20687	−0.603433	−	0.797414i	$-0.706201\pi$
$233$	−1.67827e91	−1.20687	−0.603433	+	0.797414i	$0.706201\pi$
$234$	4.99434e89	0.0304556
$235$	9.50524e90	0.491870
$236$	1.82118e90	0.0800278
$237$	−7.51764e90	−0.280718
$238$	−3.27022e91	−1.03840
$239$	5.93351e90	0.160322	0.0801609	−	0.996782i	$-0.474457\pi$
$239$	5.93351e90	0.160322	0.0801609	+	0.996782i	$0.474457\pi$
$240$	−3.14155e91	−0.722788
$241$	−6.22759e91	−1.22085	−0.610427	−	0.792073i	$-0.709002\pi$
$241$	−6.22759e91	−1.22085	−0.610427	+	0.792073i	$0.709002\pi$
$242$	−2.21006e90	−0.0369413
$243$	7.26520e91	1.03611
$244$	−1.39221e91	−0.169510
$245$	1.82714e92	1.90054
$246$	−8.34219e91	−0.741786
$247$	8.35279e90	0.0635330
$248$	−1.01451e91	−0.0660493
$249$	2.16311e91	0.120616
$250$	2.94209e92	1.40594
$251$	−1.57591e92	−0.645792	−0.322896	−	0.946434i	$-0.604656\pi$
$251$	−1.57591e92	−0.645792	−0.322896	+	0.946434i	$0.604656\pi$
$252$	−4.95442e91	−0.174210
$253$	−1.89012e92	−0.570623
$254$	−3.22512e92	−0.836464
$255$	3.13920e92	0.699877
$256$	−2.51416e92	−0.482120
$257$	4.23812e92	0.699437	0.349718	−	0.936855i	$-0.386277\pi$
$257$	4.23812e92	0.699437	0.349718	+	0.936855i	$0.386277\pi$
$258$	−1.63327e92	−0.232113
$259$	−6.44565e92	−0.789270
$260$	1.23035e91	0.0129884
$261$	9.38494e92	0.854618
$262$	−1.83597e93	−1.44300
$263$	−7.37246e92	−0.500399	−0.250199	−	0.968194i	$-0.580496\pi$
$263$	−7.37246e92	−0.500399	−0.250199	+	0.968194i	$0.580496\pi$
$264$	9.34630e92	0.548136
$265$	7.51290e92	0.380927
$266$	4.17840e93	1.83260
$267$	1.88606e93	0.715932
$268$	4.31680e92	0.141897
$269$	1.29982e93	0.370186	0.185093	−	0.982721i	$-0.440741\pi$
$269$	1.29982e93	0.370186	0.185093	+	0.982721i	$0.440741\pi$
$270$	−5.71180e93	−1.41016
$271$	−2.25909e93	−0.483745	−0.241872	−	0.970308i	$-0.577762\pi$
$271$	−2.25909e93	−0.483745	−0.241872	+	0.970308i	$0.577762\pi$
$272$	−3.39465e93	−0.630800
$273$	2.18239e92	0.0352104
$274$	7.99494e93	1.12052
$275$	−1.53053e94	−1.86437
$276$	−4.78310e92	−0.0506652
$277$	−9.02776e93	−0.831972	−0.415986	−	0.909371i	$-0.636563\pi$
$277$	−9.02776e93	−0.831972	−0.415986	+	0.909371i	$0.636563\pi$
$278$	9.34767e92	0.0749858
$279$	−6.42705e92	−0.0449004
$280$	4.33459e94	2.63854
$281$	−2.32819e93	−0.123545	−0.0617724	−	0.998090i	$-0.519675\pi$
$281$	−2.32819e93	−0.123545	−0.0617724	+	0.998090i	$0.519675\pi$
$282$	2.99463e93	0.138597
$283$	4.80654e93	0.194113	0.0970565	−	0.995279i	$-0.469057\pi$
$283$	4.80654e93	0.194113	0.0970565	+	0.995279i	$0.469057\pi$
$284$	−6.48249e93	−0.228552
$285$	−4.01099e94	−1.23516
$286$	1.53176e93	0.0412190
$287$	9.55179e94	2.24715
$288$	−1.15148e94	−0.236945
$289$	−2.16139e94	−0.389195
$290$	−1.16586e95	−1.83791
$291$	−5.43645e93	−0.0750646
$292$	2.31838e94	0.280508
$293$	6.39154e93	0.0677957	0.0338979	−	0.999425i	$-0.489208\pi$
$293$	6.39154e93	0.0677957	0.0338979	+	0.999425i	$0.489208\pi$
$294$	5.75640e94	0.535524
$295$	−1.00940e95	−0.823976
$296$	−8.06275e94	−0.577767
$297$	1.41016e95	0.887455
$298$	−4.17732e93	−0.0230978
$299$	−5.52076e93	−0.0268323
$300$	−3.87312e94	−0.165536
$301$	1.87009e95	0.703156
$302$	−3.52727e95	−1.16727
$303$	2.82937e95	0.824420
$304$	4.33738e95	1.11326
$305$	7.71636e95	1.74529
$306$	−2.59148e95	−0.516742
$307$	−6.99830e95	−1.23074	−0.615369	−	0.788239i	$-0.710993\pi$
$307$	−6.99830e95	−1.23074	−0.615369	+	0.788239i	$0.710993\pi$
$308$	−1.51951e95	−0.235777
$309$	−4.79192e95	−0.656308
$310$	7.98412e94	0.0965611
$311$	−3.45452e95	−0.369073	−0.184537	−	0.982826i	$-0.559078\pi$
$311$	−3.45452e95	−0.369073	−0.184537	+	0.982826i	$0.559078\pi$
$312$	2.72992e94	0.0257749
$313$	−2.17031e96	−1.81161	−0.905803	−	0.423698i	$-0.860732\pi$
$313$	−2.17031e96	−1.81161	−0.905803	+	0.423698i	$0.860732\pi$
$314$	−6.47882e95	−0.478304
$315$	2.74601e96	1.79368
$316$	1.52884e95	0.0883915
$317$	−8.25400e95	−0.422555	−0.211277	−	0.977426i	$-0.567762\pi$
$317$	−8.25400e95	−0.422555	−0.211277	+	0.977426i	$0.567762\pi$
$318$	2.36694e95	0.107336
$319$	2.87835e96	1.15665
$320$	5.29107e96	1.88482
$321$	4.08606e95	0.129081
$322$	−2.76171e96	−0.773975
$323$	−4.33414e96	−1.07797
$324$	−1.85594e95	−0.0409809
$325$	−4.47044e95	−0.0876679
$326$	−4.53037e96	−0.789325
$327$	3.38481e95	0.0524138
$328$	1.19482e97	1.64497
$329$	−3.42885e96	−0.419861
$330$	−7.35545e96	−0.801351
$331$	−6.03191e96	−0.584894	−0.292447	−	0.956282i	$-0.594469\pi$
$331$	−6.03191e96	−0.584894	−0.292447	+	0.956282i	$0.594469\pi$
$332$	−4.39906e95	−0.0379790
$333$	−5.10784e96	−0.392767
$334$	1.29846e97	0.889589
$335$	−2.39260e97	−1.46099
$336$	1.13326e97	0.616973
$337$	3.56760e97	1.73231	0.866153	−	0.499779i	$-0.166586\pi$
$337$	3.56760e97	1.73231	0.866153	+	0.499779i	$0.166586\pi$
$338$	−2.10420e97	−0.911578
$339$	1.04043e97	0.402277
$340$	−6.38411e96	−0.220375
$341$	−1.97117e96	−0.0607688
$342$	3.31117e97	0.911961
$343$	−6.81973e96	−0.167859
$344$	2.33926e97	0.514729
$345$	2.65105e97	0.521655
$346$	−2.22057e97	−0.390873
$347$	−5.46717e97	−0.861148	−0.430574	−	0.902555i	$-0.641689\pi$
$347$	−5.46717e97	−0.861148	−0.430574	+	0.902555i	$0.641689\pi$
$348$	7.28389e96	0.102698
$349$	5.43270e97	0.685862	0.342931	−	0.939361i	$-0.388580\pi$
$349$	5.43270e97	0.685862	0.342931	+	0.939361i	$0.388580\pi$
$350$	−2.23629e98	−2.52877
$351$	4.11888e96	0.0417306
$352$	−3.53158e97	−0.320684
$353$	−2.38809e97	−0.194413	−0.0972064	−	0.995264i	$-0.530991\pi$
$353$	−2.38809e97	−0.194413	−0.0972064	+	0.995264i	$0.530991\pi$
$354$	−3.18011e97	−0.232176
$355$	3.59295e98	2.35320
$356$	−3.83563e97	−0.225430
$357$	−1.13241e98	−0.597416
$358$	−1.47561e98	−0.698994
$359$	1.68745e98	0.717953	0.358976	−	0.933347i	$-0.383126\pi$
$359$	1.68745e98	0.717953	0.358976	+	0.933347i	$0.383126\pi$
$360$	3.43494e98	1.31302
$361$	2.62688e98	0.902427
$362$	2.05028e98	0.633189
$363$	−7.65296e96	−0.0212532
$364$	−4.43828e96	−0.0110869
$365$	−1.28497e99	−2.88814
$366$	2.43104e98	0.491780
$367$	−6.34065e98	−1.15476	−0.577378	−	0.816477i	$-0.695924\pi$
$367$	−6.34065e98	−1.15476	−0.577378	+	0.816477i	$0.695924\pi$
$368$	−2.86678e98	−0.470169
$369$	7.56930e98	1.11825
$370$	6.34531e98	0.844669
$371$	−2.71015e98	−0.325160
$372$	−4.98820e96	−0.00539561
$373$	−4.73429e98	−0.461812	−0.230906	−	0.972976i	$-0.574169\pi$
$373$	−4.73429e98	−0.461812	−0.230906	+	0.972976i	$0.574169\pi$
$374$	−7.94805e98	−0.699365
$375$	1.01878e99	0.808867
$376$	−4.28909e98	−0.307350
$377$	8.40723e97	0.0543890
$378$	2.06043e99	1.20371
$379$	−1.11320e99	−0.587442	−0.293721	−	0.955891i	$-0.594894\pi$
$379$	−1.11320e99	−0.587442	−0.293721	+	0.955891i	$0.594894\pi$
$380$	8.15705e98	0.388924
$381$	−1.11679e99	−0.481238
$382$	1.95878e99	0.763037
$383$	−2.29696e99	−0.809099	−0.404549	−	0.914516i	$-0.632572\pi$
$383$	−2.29696e99	−0.809099	−0.404549	+	0.914516i	$0.632572\pi$
$384$	1.12692e99	0.359038
$385$	8.42197e99	2.42759
$386$	−6.38514e99	−1.66556
$387$	1.48195e99	0.349914
$388$	1.10560e98	0.0236361
$389$	−8.49702e99	−1.64516	−0.822578	−	0.568653i	$-0.807465\pi$
$389$	−8.49702e99	−1.64516	−0.822578	+	0.568653i	$0.807465\pi$
$390$	−2.14842e98	−0.0376818
$391$	2.86464e99	0.455265
$392$	−8.24466e99	−1.18757
$393$	−6.35758e99	−0.830192
$394$	7.86531e99	0.931347
$395$	−8.47369e99	−0.910090
$396$	−1.20414e99	−0.117331
$397$	1.00797e100	0.891274	0.445637	−	0.895214i	$-0.352977\pi$
$397$	1.00797e100	0.891274	0.445637	+	0.895214i	$0.352977\pi$
$398$	1.97426e100	1.58455
$399$	1.44689e100	1.05434
$400$	−2.32138e100	−1.53616
$401$	1.83750e100	1.10451	0.552254	−	0.833676i	$-0.313768\pi$
$401$	1.83750e100	1.10451	0.552254	+	0.833676i	$0.313768\pi$
$402$	−7.53791e99	−0.411669
$403$	−5.75749e97	−0.00285752
$404$	−5.75402e99	−0.259591
$405$	1.02866e100	0.421944
$406$	4.20564e100	1.56884
$407$	−1.56657e100	−0.531575
$408$	−1.41651e100	−0.437324
$409$	−4.47587e100	−1.25757	−0.628783	−	0.777581i	$-0.716446\pi$
$409$	−4.47587e100	−1.25757	−0.628783	+	0.777581i	$0.716446\pi$
$410$	−9.40310e100	−2.40488
$411$	2.76847e100	0.644659
$412$	9.74520e99	0.206656
$413$	3.64122e100	0.703347
$414$	−2.18851e100	−0.385155
$415$	2.43820e100	0.391037
$416$	−1.03152e99	−0.0150795
$417$	3.23690e99	0.0431411
$418$	1.01553e101	1.23426
$419$	−5.40560e99	−0.0599245	−0.0299622	−	0.999551i	$-0.509539\pi$
$419$	−5.40560e99	−0.0599245	−0.0299622	+	0.999551i	$0.509539\pi$
$420$	2.13125e100	0.215544
$421$	−1.76535e101	−1.62918	−0.814591	−	0.580036i	$-0.803038\pi$
$421$	−1.76535e101	−1.62918	−0.814591	+	0.580036i	$0.803038\pi$
$422$	1.33631e101	1.12559
$423$	−2.71718e100	−0.208937
$424$	−3.39008e100	−0.238026
$425$	2.31964e101	1.48746
$426$	1.13196e101	0.663073
$427$	−2.78354e101	−1.48979
$428$	−8.30972e99	−0.0406445
$429$	5.30414e99	0.0237143
$430$	−1.84098e101	−0.752511
$431$	1.36461e101	0.510076	0.255038	−	0.966931i	$-0.417912\pi$
$431$	1.36461e101	0.510076	0.255038	+	0.966931i	$0.417912\pi$
$432$	2.13882e101	0.731224
$433$	−1.32905e101	−0.415680	−0.207840	−	0.978163i	$-0.566643\pi$
$433$	−1.32905e101	−0.415680	−0.207840	+	0.978163i	$0.566643\pi$
$434$	−2.88013e100	−0.0824247
$435$	−4.03713e101	−1.05739
$436$	−6.88361e99	−0.0165039
$437$	−3.66018e101	−0.803466
$438$	−4.04831e101	−0.813806
$439$	7.00628e100	0.129004	0.0645021	−	0.997918i	$-0.479454\pi$
$439$	7.00628e100	0.129004	0.0645021	+	0.997918i	$0.479454\pi$
$440$	1.05349e102	1.77706
$441$	−5.22308e101	−0.807311
$442$	−2.32151e100	−0.0328861
$443$	1.10308e102	1.43239	0.716196	−	0.697899i	$-0.245882\pi$
$443$	1.10308e102	1.43239	0.716196	+	0.697899i	$0.245882\pi$
$444$	−3.96433e100	−0.0471982
$445$	2.12592e102	2.32106
$446$	1.47204e101	0.147410
$447$	−1.44652e100	−0.0132887
$448$	−1.90866e102	−1.60888
$449$	−5.92001e101	−0.457972	−0.228986	−	0.973430i	$-0.573541\pi$
$449$	−5.92001e101	−0.457972	−0.228986	+	0.973430i	$0.573541\pi$
$450$	−1.77215e102	−1.25840
$451$	2.32149e102	1.51346
$452$	−2.11590e101	−0.126668
$453$	−1.22142e102	−0.671558
$454$	−1.89583e102	−0.957523
$455$	2.45993e101	0.114152
$456$	1.80989e102	0.771803
$457$	−3.61967e102	−1.41872	−0.709358	−	0.704848i	$-0.751015\pi$
$457$	−3.61967e102	−1.41872	−0.709358	+	0.704848i	$0.751015\pi$
$458$	1.01179e102	0.364562
$459$	−2.13722e102	−0.708045
$460$	−5.39139e101	−0.164257
$461$	4.52516e102	1.26808	0.634042	−	0.773299i	$-0.281395\pi$
$461$	4.52516e102	1.26808	0.634042	+	0.773299i	$0.281395\pi$
$462$	2.65335e102	0.684034
$463$	2.39146e102	0.567278	0.283639	−	0.958931i	$-0.408458\pi$
$463$	2.39146e102	0.567278	0.283639	+	0.958931i	$0.408458\pi$
$464$	4.36565e102	0.953030
$465$	2.76473e101	0.0555538
$466$	−5.95982e102	−1.10249
$467$	−6.43631e102	−1.09632	−0.548160	−	0.836374i	$-0.684671\pi$
$467$	−6.43631e102	−1.09632	−0.548160	+	0.836374i	$0.684671\pi$
$468$	−3.51710e100	−0.00551721
$469$	8.63089e102	1.24710
$470$	3.37547e102	0.449331
$471$	−2.24348e102	−0.275180
$472$	4.55474e102	0.514869
$473$	4.54512e102	0.473577
$474$	−2.66964e102	−0.256440
$475$	−2.96383e103	−2.62512
$476$	2.30295e102	0.188112
$477$	−2.14765e102	−0.161810
$478$	2.10709e102	0.146456
$479$	1.60919e103	1.03202	0.516011	−	0.856582i	$-0.327416\pi$
$479$	1.60919e103	1.03202	0.516011	+	0.856582i	$0.327416\pi$
$480$	4.95334e102	0.293164
$481$	−4.57571e101	−0.0249962
$482$	−2.21152e103	−1.11527
$483$	−9.56320e102	−0.445286
$484$	1.55636e101	0.00669213
$485$	−6.12782e102	−0.243360
$486$	2.57999e103	0.946504
$487$	1.82945e103	0.620091	0.310045	−	0.950722i	$-0.399656\pi$
$487$	1.82945e103	0.620091	0.310045	+	0.950722i	$0.399656\pi$
$488$	−3.48188e103	−1.09056
$489$	−1.56877e103	−0.454117
$490$	6.48847e103	1.73617
$491$	6.83702e103	1.69133	0.845667	−	0.533711i	$-0.179203\pi$
$491$	6.83702e103	1.69133	0.845667	+	0.533711i	$0.179203\pi$
$492$	5.87473e102	0.134379
$493$	−4.36238e103	−0.922821
$494$	2.96622e102	0.0580384
$495$	6.67398e103	1.20805
$496$	−2.98971e102	−0.0500708
$497$	−1.29609e104	−2.00870
$498$	7.68156e102	0.110184
$499$	−1.35568e104	−1.80005	−0.900027	−	0.435833i	$-0.856454\pi$
$499$	−1.35568e104	−1.80005	−0.900027	+	0.435833i	$0.856454\pi$
$500$	−2.07187e103	−0.254693
$501$	4.49629e103	0.511801
$502$	−5.59631e103	−0.589941
$503$	2.49984e103	0.244087	0.122043	−	0.992525i	$-0.461055\pi$
$503$	2.49984e103	0.244087	0.122043	+	0.992525i	$0.461055\pi$
$504$	−1.23909e104	−1.12080
$505$	3.18919e104	2.67278
$506$	−6.71213e103	−0.521274
$507$	−7.28639e103	−0.524452
$508$	2.27119e103	0.151530
$509$	−8.36592e103	−0.517463	−0.258732	−	0.965949i	$-0.583304\pi$
$509$	−8.36592e103	−0.517463	−0.258732	+	0.965949i	$0.583304\pi$
$510$	1.11478e104	0.639348
$511$	4.63531e104	2.46532
$512$	−2.27768e104	−1.12357
$513$	2.73075e104	1.24958
$514$	1.50503e104	0.638947
$515$	−5.40132e104	−2.12776
$516$	1.15018e103	0.0420486
$517$	−8.33356e103	−0.282778
$518$	−2.28896e104	−0.721011
$519$	−7.68937e103	−0.224878
$520$	3.07709e103	0.0835625
$521$	4.05242e104	1.02203	0.511013	−	0.859573i	$-0.329270\pi$
$521$	4.05242e104	1.02203	0.511013	+	0.859573i	$0.329270\pi$
$522$	3.33275e104	0.780707
$523$	−3.13697e104	−0.682645	−0.341322	−	0.939946i	$-0.610875\pi$
$523$	−3.13697e104	−0.682645	−0.341322	+	0.939946i	$0.610875\pi$
$524$	1.29293e104	0.261408
$525$	−7.74380e104	−1.45486
$526$	−2.61808e104	−0.457122
$527$	2.98747e103	0.0484836
$528$	2.75430e104	0.415533
$529$	−4.71005e104	−0.660667
$530$	2.66796e104	0.347983
$531$	2.88548e104	0.350008
$532$	−2.94251e104	−0.331986
$533$	6.78074e103	0.0711671
$534$	6.69771e104	0.654015
$535$	4.60570e104	0.418480
$536$	1.07962e105	0.912910
$537$	−5.10970e104	−0.402148
$538$	4.61588e104	0.338171
$539$	−1.60191e105	−1.09263
$540$	4.02235e104	0.255459
$541$	1.81610e105	1.07410	0.537052	−	0.843549i	$-0.319538\pi$
$541$	1.81610e105	1.07410	0.537052	+	0.843549i	$0.319538\pi$
$542$	−8.02241e104	−0.441909
$543$	7.09968e104	0.364288
$544$	5.35241e104	0.255854
$545$	3.81527e104	0.169926
$546$	7.75003e103	0.0321652
$547$	−4.98557e105	−1.92843	−0.964213	−	0.265130i	$-0.914585\pi$
$547$	−4.98557e105	−1.92843	−0.964213	+	0.265130i	$0.914585\pi$
$548$	−5.63018e104	−0.202988
$549$	−2.20581e105	−0.741366
$550$	−5.43515e105	−1.70313
$551$	5.57387e105	1.62862
$552$	−1.19624e105	−0.325961
$553$	3.05673e105	0.776854
$554$	−3.20591e105	−0.760020
$555$	2.19724e105	0.485958
$556$	−6.58280e103	−0.0135841
$557$	5.58006e105	1.07452	0.537259	−	0.843417i	$-0.319460\pi$
$557$	5.58006e105	1.07452	0.537259	+	0.843417i	$0.319460\pi$
$558$	−2.28235e104	−0.0410172
$559$	1.32756e104	0.0222689
$560$	1.27738e106	2.00023
$561$	−2.75224e105	−0.402361
$562$	−8.26778e104	−0.112860
$563$	−6.03774e105	−0.769665	−0.384832	−	0.922986i	$-0.625741\pi$
$563$	−6.03774e105	−0.769665	−0.384832	+	0.922986i	$0.625741\pi$
$564$	−2.10887e104	−0.0251076
$565$	1.17275e106	1.30419
$566$	1.70688e105	0.177325
$567$	−3.71072e105	−0.360173
$568$	−1.62126e106	−1.47042
$569$	−6.49632e105	−0.550611	−0.275306	−	0.961357i	$-0.588779\pi$
$569$	−6.49632e105	−0.550611	−0.275306	+	0.961357i	$0.588779\pi$
$570$	−1.42437e106	−1.12834
$571$	−1.11968e106	−0.829097	−0.414548	−	0.910027i	$-0.636060\pi$
$571$	−1.11968e106	−0.829097	−0.414548	+	0.910027i	$0.636060\pi$
$572$	−1.07869e104	−0.00746707
$573$	6.78282e105	0.438993
$574$	3.39200e106	2.05281
$575$	1.95894e106	1.10869
$576$	−1.51251e106	−0.800633
$577$	−7.15176e105	−0.354115	−0.177057	−	0.984201i	$-0.556658\pi$
$577$	−7.15176e105	−0.354115	−0.177057	+	0.984201i	$0.556658\pi$
$578$	−7.67547e105	−0.355536
$579$	−2.21104e106	−0.958234
$580$	8.21021e105	0.332948
$581$	−8.79537e105	−0.333790
$582$	−1.93057e105	−0.0685727
$583$	−6.58681e105	−0.218996
$584$	5.79823e106	1.80468
$585$	1.94937e105	0.0568059
$586$	2.26974e105	0.0619325
$587$	2.84881e106	0.727941	0.363970	−	0.931411i	$-0.381421\pi$
$587$	2.84881e106	0.727941	0.363970	+	0.931411i	$0.381421\pi$
$588$	−4.05377e105	−0.0970134
$589$	−3.81713e105	−0.0855654
$590$	−3.58454e106	−0.752715
$591$	2.72359e106	0.535826
$592$	−2.37604e106	−0.437995
$593$	4.11222e106	0.710346	0.355173	−	0.934801i	$-0.384422\pi$
$593$	4.11222e106	0.710346	0.355173	+	0.934801i	$0.384422\pi$
$594$	5.00772e106	0.810704
$595$	−1.27642e107	−1.93683
$596$	2.94174e104	0.00418431
$597$	6.83644e106	0.911630
$598$	−1.96051e105	−0.0245118
$599$	−1.58346e107	−1.85641	−0.928207	−	0.372065i	$-0.878650\pi$
$599$	−1.58346e107	−1.85641	−0.928207	+	0.372065i	$0.878650\pi$
$600$	−9.68659e106	−1.06500
$601$	−4.79616e106	−0.494568	−0.247284	−	0.968943i	$-0.579538\pi$
$601$	−4.79616e106	−0.494568	−0.247284	+	0.968943i	$0.579538\pi$
$602$	6.64099e106	0.642345
$603$	6.83953e106	0.620597
$604$	2.48397e106	0.211458
$605$	−8.62621e105	−0.0689030
$606$	1.00476e107	0.753121
$607$	−4.40237e106	−0.309686	−0.154843	−	0.987939i	$-0.549487\pi$
$607$	−4.40237e106	−0.309686	−0.154843	+	0.987939i	$0.549487\pi$
$608$	−6.83884e106	−0.451538
$609$	1.45632e107	0.902592
$610$	2.74021e107	1.59435
$611$	−2.43411e105	−0.0132970
$612$	1.82497e106	0.0936108
$613$	3.63980e107	1.75327	0.876637	−	0.481153i	$-0.159782\pi$
$613$	3.63980e107	1.75327	0.876637	+	0.481153i	$0.159782\pi$
$614$	−2.48521e107	−1.12430
$615$	−3.25609e107	−1.38358
$616$	−3.80028e107	−1.51690
$617$	3.74592e107	1.40469	0.702344	−	0.711838i	$-0.252137\pi$
$617$	3.74592e107	1.40469	0.702344	+	0.711838i	$0.252137\pi$
$618$	−1.70169e107	−0.599548
$619$	3.65307e107	1.20939	0.604697	−	0.796456i	$-0.293294\pi$
$619$	3.65307e107	1.20939	0.604697	+	0.796456i	$0.293294\pi$
$620$	−5.62257e105	−0.0174926
$621$	−1.80489e107	−0.527744
$622$	−1.22676e107	−0.337154
$623$	−7.66886e107	−1.98126
$624$	8.04490e105	0.0195395
$625$	3.14900e107	0.719105
$626$	−7.70711e107	−1.65493
$627$	3.51657e107	0.710098
$628$	4.56250e106	0.0866476
$629$	2.37427e107	0.424111
$630$	9.75153e107	1.63856
$631$	9.87906e106	0.156166	0.0780828	−	0.996947i	$-0.475120\pi$
$631$	9.87906e106	0.156166	0.0780828	+	0.996947i	$0.475120\pi$
$632$	3.82361e107	0.568678
$633$	4.62737e107	0.647577
$634$	−2.93113e107	−0.386010
$635$	−1.25881e108	−1.56018
$636$	−1.66685e106	−0.0194445
$637$	−4.67895e106	−0.0513783
$638$	1.02215e108	1.05662
$639$	−1.02708e108	−0.999593
$640$	1.27023e108	1.16401
$641$	−9.18114e107	−0.792251	−0.396125	−	0.918196i	$-0.629645\pi$
$641$	−9.18114e107	−0.792251	−0.396125	+	0.918196i	$0.629645\pi$
$642$	1.45103e107	0.117917
$643$	1.80765e108	1.38354	0.691771	−	0.722117i	$-0.256831\pi$
$643$	1.80765e108	1.38354	0.691771	+	0.722117i	$0.256831\pi$
$644$	1.94485e107	0.140210
$645$	−6.37491e107	−0.432937
$646$	−1.53912e108	−0.984740
$647$	−8.04409e107	−0.484911	−0.242456	−	0.970162i	$-0.577953\pi$
$647$	−8.04409e107	−0.484911	−0.242456	+	0.970162i	$0.577953\pi$
$648$	−4.64168e107	−0.263656
$649$	8.84972e107	0.473706
$650$	−1.58753e107	−0.0800860
$651$	−9.97327e106	−0.0474209
$652$	3.19037e107	0.142991
$653$	−1.47674e108	−0.623946	−0.311973	−	0.950091i	$-0.600990\pi$
$653$	−1.47674e108	−0.623946	−0.311973	+	0.950091i	$0.600990\pi$
$654$	1.20200e107	0.0478809
$655$	−7.16609e108	−2.69149
$656$	3.52106e108	1.24702
$657$	3.67324e108	1.22682
$658$	−1.21764e108	−0.383550
$659$	−4.30323e106	−0.0127851	−0.00639257	−	0.999980i	$-0.502035\pi$
$659$	−4.30323e106	−0.0127851	−0.00639257	+	0.999980i	$0.502035\pi$
$660$	5.17984e107	0.145169
$661$	6.31898e108	1.67067	0.835335	−	0.549742i	$-0.185274\pi$
$661$	6.31898e108	1.67067	0.835335	+	0.549742i	$0.185274\pi$
$662$	−2.14203e108	−0.534310
$663$	−8.03888e106	−0.0189201
$664$	−1.10020e108	−0.244343
$665$	1.63090e109	3.41817
$666$	−1.81388e108	−0.358798
$667$	−3.68404e108	−0.687827
$668$	−9.14399e107	−0.161154
$669$	5.09736e107	0.0848085
$670$	−8.49654e108	−1.33463
$671$	−6.76519e108	−1.00337
$672$	−1.78683e108	−0.250245
$673$	−8.35175e108	−1.10458	−0.552291	−	0.833652i	$-0.686246\pi$
$673$	−8.35175e108	−1.10458	−0.552291	+	0.833652i	$0.686246\pi$
$674$	1.26691e109	1.58249
$675$	−1.46151e109	−1.72427
$676$	1.48181e108	0.165138
$677$	1.06166e109	1.11769	0.558847	−	0.829271i	$-0.311244\pi$
$677$	1.06166e109	1.11769	0.558847	+	0.829271i	$0.311244\pi$
$678$	3.69475e108	0.367487
$679$	2.21050e108	0.207732
$680$	−1.59665e109	−1.41781
$681$	−6.56485e108	−0.550885
$682$	−6.99995e107	−0.0555132
$683$	5.56228e108	0.416923	0.208461	−	0.978031i	$-0.433154\pi$
$683$	5.56228e108	0.416923	0.208461	+	0.978031i	$0.433154\pi$
$684$	−2.33179e108	−0.165207
$685$	3.12055e109	2.08999
$686$	−2.42180e108	−0.153342
$687$	3.50362e108	0.209741
$688$	6.89366e108	0.390207
$689$	−1.92391e107	−0.0102978
$690$	9.41433e108	0.476540
$691$	5.59367e108	0.267789	0.133894	−	0.990996i	$-0.457252\pi$
$691$	5.59367e108	0.267789	0.133894	+	0.990996i	$0.457252\pi$
$692$	1.56377e108	0.0708089
$693$	−2.40752e109	−1.03119
$694$	−1.94148e109	−0.786673
$695$	3.64855e108	0.139864
$696$	1.82169e109	0.660721
$697$	−3.51842e109	−1.20750
$698$	1.92924e109	0.626546
$699$	−2.06376e109	−0.634289
$700$	1.57484e109	0.458101
$701$	4.17726e109	1.15013	0.575066	−	0.818107i	$-0.304977\pi$
$701$	4.17726e109	1.15013	0.575066	+	0.818107i	$0.304977\pi$
$702$	1.46268e108	0.0381216
$703$	−3.03363e109	−0.748484
$704$	−4.63886e109	−1.08359
$705$	1.16885e109	0.258511
$706$	−8.48051e108	−0.177599
$707$	−1.15044e110	−2.28149
$708$	2.23949e108	0.0420600
$709$	8.34146e109	1.48376	0.741878	−	0.670535i	$-0.233936\pi$
$709$	8.34146e109	1.48376	0.741878	+	0.670535i	$0.233936\pi$
$710$	1.27591e110	2.14969
$711$	2.42230e109	0.386588
$712$	−9.59285e109	−1.45033
$713$	2.52292e108	0.0361374
$714$	−4.02137e109	−0.545749
$715$	5.97869e108	0.0768818
$716$	1.03915e109	0.126627
$717$	7.29639e108	0.0842598
$718$	5.99243e109	0.655861
$719$	−6.23741e109	−0.647056	−0.323528	−	0.946219i	$-0.604869\pi$
$719$	−6.23741e109	−0.647056	−0.323528	+	0.946219i	$0.604869\pi$
$720$	1.01226e110	0.995380
$721$	1.94843e110	1.81626
$722$	9.32847e109	0.824382
$723$	−7.65801e109	−0.641640
$724$	−1.44384e109	−0.114706
$725$	−2.98315e110	−2.24730
$726$	−2.71769e108	−0.0194151
$727$	1.38483e110	0.938254	0.469127	−	0.883131i	$-0.344569\pi$
$727$	1.38483e110	0.938254	0.469127	+	0.883131i	$0.344569\pi$
$728$	−1.11000e109	−0.0713291
$729$	4.87119e109	0.296910
$730$	−4.56315e110	−2.63836
$731$	−6.88850e109	−0.377838
$732$	−1.71198e109	−0.0890888
$733$	−7.68264e109	−0.379321	−0.189661	−	0.981850i	$-0.560739\pi$
$733$	−7.68264e109	−0.379321	−0.189661	+	0.981850i	$0.560739\pi$
$734$	−2.25167e110	−1.05489
$735$	2.24682e110	0.998861
$736$	4.52012e109	0.190701
$737$	2.09768e110	0.839924
$738$	2.68798e110	1.02154
$739$	2.23268e110	0.805407	0.402703	−	0.915331i	$-0.368071\pi$
$739$	2.23268e110	0.805407	0.402703	+	0.915331i	$0.368071\pi$
$740$	−4.46848e109	−0.153017
$741$	1.02714e109	0.0333908
$742$	−9.62417e109	−0.297039
$743$	3.66496e110	1.07399	0.536995	−	0.843586i	$-0.319559\pi$
$743$	3.66496e110	1.07399	0.536995	+	0.843586i	$0.319559\pi$
$744$	−1.24754e109	−0.0347133
$745$	−1.63047e109	−0.0430822
$746$	−1.68123e110	−0.421873
$747$	−6.96987e109	−0.166105
$748$	5.59716e109	0.126694
$749$	−1.66142e110	−0.357215
$750$	3.61786e110	0.738913
$751$	1.89152e110	0.367006	0.183503	−	0.983019i	$-0.441256\pi$
$751$	1.89152e110	0.367006	0.183503	+	0.983019i	$0.441256\pi$
$752$	−1.26397e110	−0.232996
$753$	−1.93788e110	−0.339407
$754$	2.98555e109	0.0496852
$755$	−1.37675e111	−2.17719
$756$	−1.45099e110	−0.218060
$757$	2.44246e110	0.348848	0.174424	−	0.984671i	$-0.444194\pi$
$757$	2.44246e110	0.348848	0.174424	+	0.984671i	$0.444194\pi$
$758$	−3.95317e110	−0.536638
$759$	−2.32427e110	−0.299901
$760$	2.04006e111	2.50219
$761$	1.80796e110	0.210805	0.105402	−	0.994430i	$-0.466387\pi$
$761$	1.80796e110	0.210805	0.105402	+	0.994430i	$0.466387\pi$
$762$	−3.96590e110	−0.439618
$763$	−1.37629e110	−0.145049
$764$	−1.37941e110	−0.138229
$765$	−1.01150e111	−0.963828
$766$	−8.15690e110	−0.739125
$767$	2.58487e109	0.0222750
$768$	−3.09165e110	−0.253386
$769$	−8.54850e109	−0.0666386	−0.0333193	−	0.999445i	$-0.510608\pi$
$769$	−8.54850e109	−0.0666386	−0.0333193	+	0.999445i	$0.510608\pi$
$770$	2.99078e111	2.21764
$771$	5.21159e110	0.367601
$772$	4.49654e110	0.301725
$773$	−3.59274e110	−0.229359	−0.114679	−	0.993403i	$-0.536584\pi$
$773$	−3.59274e110	−0.229359	−0.114679	+	0.993403i	$0.536584\pi$
$774$	5.26264e110	0.319652
$775$	2.04294e110	0.118070
$776$	2.76508e110	0.152066
$777$	−7.92616e110	−0.414814
$778$	−3.01743e111	−1.50288
$779$	4.49553e111	2.13102
$780$	1.51295e109	0.00682628
$781$	−3.15005e111	−1.35286
$782$	1.01728e111	0.415892
$783$	2.74855e111	1.06973
$784$	−2.42965e111	−0.900276
$785$	−2.52879e111	−0.892134
$786$	−2.25768e111	−0.758393
$787$	4.19000e111	1.34025	0.670127	−	0.742247i	$-0.266240\pi$
$787$	4.19000e111	1.34025	0.670127	+	0.742247i	$0.266240\pi$
$788$	−5.53890e110	−0.168719
$789$	−9.06586e110	−0.262993
$790$	−3.00915e111	−0.831381
$791$	−4.23048e111	−1.11326
$792$	−3.01152e111	−0.754861
$793$	−1.97601e110	−0.0471815
$794$	3.57945e111	0.814193
$795$	9.23856e110	0.200203
$796$	−1.39031e111	−0.287051
$797$	6.85586e111	1.34870	0.674352	−	0.738410i	$-0.264423\pi$
$797$	6.85586e111	1.34870	0.674352	+	0.738410i	$0.264423\pi$
$798$	5.13815e111	0.963154
$799$	1.26302e111	0.225611
$800$	3.66016e111	0.623069
$801$	−6.07718e111	−0.985939
$802$	6.52526e111	1.00898
$803$	1.12658e112	1.66040
$804$	5.30834e110	0.0745762
$805$	−1.07794e112	−1.44362
$806$	−2.04458e109	−0.00261039
$807$	1.59838e111	0.194558
$808$	−1.43907e112	−1.67011
$809$	−4.63564e111	−0.512970	−0.256485	−	0.966548i	$-0.582564\pi$
$809$	−4.63564e111	−0.512970	−0.256485	+	0.966548i	$0.582564\pi$
$810$	3.65296e111	0.385453
$811$	1.20708e112	1.21460	0.607302	−	0.794471i	$-0.292252\pi$
$811$	1.20708e112	1.21460	0.607302	+	0.794471i	$0.292252\pi$
$812$	−2.96169e111	−0.284205
$813$	−2.77799e111	−0.254240
$814$	−5.56315e111	−0.485602
$815$	−1.76827e112	−1.47225
$816$	−4.17437e111	−0.331528
$817$	8.80152e111	0.666820
$818$	−1.58946e112	−1.14881
$819$	−7.03200e110	−0.0484896
$820$	6.62184e111	0.435657
$821$	1.07825e112	0.676876	0.338438	−	0.940989i	$-0.390102\pi$
$821$	1.07825e112	0.676876	0.338438	+	0.940989i	$0.390102\pi$
$822$	9.83131e111	0.588907
$823$	1.58016e112	0.903247	0.451623	−	0.892209i	$-0.350845\pi$
$823$	1.58016e112	0.903247	0.451623	+	0.892209i	$0.350845\pi$
$824$	2.43726e112	1.32955
$825$	−1.88208e112	−0.979851
$826$	1.29306e112	0.642519
$827$	−2.47076e112	−1.17184	−0.585921	−	0.810368i	$-0.699267\pi$
$827$	−2.47076e112	−1.17184	−0.585921	+	0.810368i	$0.699267\pi$
$828$	1.54119e111	0.0697731
$829$	−2.28727e112	−0.988480	−0.494240	−	0.869326i	$-0.664554\pi$
$829$	−2.28727e112	−0.988480	−0.494240	+	0.869326i	$0.664554\pi$
$830$	8.65845e111	0.357218
$831$	−1.11014e112	−0.437257
$832$	−1.35494e111	−0.0509533
$833$	2.42783e112	0.871738
$834$	1.14948e111	0.0394100
$835$	5.06809e112	1.65926
$836$	−7.15156e111	−0.223593
$837$	−1.88228e111	−0.0562023
$838$	−1.91962e111	−0.0547420
$839$	−3.57912e112	−0.974857	−0.487428	−	0.873163i	$-0.662065\pi$
$839$	−3.57912e112	−0.974857	−0.487428	+	0.873163i	$0.662065\pi$
$840$	5.33021e112	1.38673
$841$	1.58630e112	0.394222
$842$	−6.26904e112	−1.48828
$843$	−2.86295e111	−0.0649311
$844$	−9.41057e111	−0.203907
$845$	−8.21302e112	−1.70028
$846$	−9.64916e111	−0.190867
$847$	3.11175e111	0.0588157
$848$	−9.99035e111	−0.180443
$849$	5.91056e111	0.102019
$850$	8.23743e112	1.35882
$851$	2.00507e112	0.316112
$852$	−7.97146e111	−0.120120
$853$	−1.19743e113	−1.72469	−0.862344	−	0.506322i	$-0.831005\pi$
$853$	−1.19743e113	−1.72469	−0.862344	+	0.506322i	$0.831005\pi$
$854$	−9.88480e112	−1.36094
$855$	1.29240e113	1.70099
$856$	−2.07825e112	−0.261491
$857$	1.42922e113	1.71924	0.859621	−	0.510933i	$-0.170700\pi$
$857$	1.42922e113	1.71924	0.859621	+	0.510933i	$0.170700\pi$
$858$	1.88359e111	0.0216634
$859$	−3.84626e112	−0.422963	−0.211481	−	0.977382i	$-0.567829\pi$
$859$	−3.84626e112	−0.422963	−0.211481	+	0.977382i	$0.567829\pi$
$860$	1.29645e112	0.136322
$861$	1.17458e113	1.18103
$862$	4.84597e112	0.465962
$863$	1.23394e113	1.13469	0.567346	−	0.823480i	$-0.307970\pi$
$863$	1.23394e113	1.13469	0.567346	+	0.823480i	$0.307970\pi$
$864$	−3.37233e112	−0.296586
$865$	−8.66726e112	−0.729057
$866$	−4.71969e112	−0.379730
$867$	−2.65785e112	−0.204548
$868$	2.02824e111	0.0149317
$869$	7.42916e112	0.523213
$870$	−1.43365e113	−0.965945
$871$	6.12700e111	0.0394956
$872$	−1.72158e112	−0.106180
$873$	1.75171e112	0.103374
$874$	−1.29979e113	−0.733979
$875$	−4.14244e113	−2.23845
$876$	2.85089e112	0.147426
$877$	3.27320e111	0.0161990	0.00809950	−	0.999967i	$-0.497422\pi$
$877$	3.27320e111	0.0161990	0.00809950	+	0.999967i	$0.497422\pi$
$878$	2.48805e112	0.117847
$879$	7.85963e111	0.0356312
$880$	3.10457e113	1.34716
$881$	3.05403e113	1.26853	0.634266	−	0.773115i	$-0.281303\pi$
$881$	3.05403e113	1.26853	0.634266	+	0.773115i	$0.281303\pi$
$882$	−1.85480e113	−0.737492
$883$	−2.28296e113	−0.868982	−0.434491	−	0.900676i	$-0.643072\pi$
$883$	−2.28296e113	−0.868982	−0.434491	+	0.900676i	$0.643072\pi$
$884$	1.63485e111	0.00595751
$885$	−1.24125e113	−0.433054
$886$	3.91720e113	1.30851
$887$	−1.33597e113	−0.427306	−0.213653	−	0.976910i	$-0.568536\pi$
$887$	−1.33597e113	−0.427306	−0.213653	+	0.976910i	$0.568536\pi$
$888$	−9.91471e112	−0.303655
$889$	4.54095e113	1.33177
$890$	7.54948e113	2.12032
$891$	−9.01864e112	−0.242577
$892$	−1.03664e112	−0.0267042
$893$	−1.61378e113	−0.398164
$894$	−5.13682e111	−0.0121395
$895$	−5.75952e113	−1.30377
$896$	−4.58214e113	−0.993597
$897$	−6.78884e111	−0.0141022
$898$	−2.10229e113	−0.418364
$899$	−3.84201e112	−0.0732504
$900$	1.24798e113	0.227966
$901$	9.98287e112	0.174723
$902$	8.24401e113	1.38257
$903$	2.29963e113	0.369556
$904$	−5.29183e113	−0.814933
$905$	8.00257e113	1.18103
$906$	−4.33745e113	−0.613479
$907$	−9.27948e113	−1.25789	−0.628945	−	0.777450i	$-0.716513\pi$
$907$	−9.27948e113	−1.25789	−0.628945	+	0.777450i	$0.716513\pi$
$908$	1.33508e113	0.173461
$909$	−9.11667e113	−1.13534
$910$	8.73563e112	0.104280
$911$	−4.09760e113	−0.468891	−0.234446	−	0.972129i	$-0.575327\pi$
$911$	−4.09760e113	−0.468891	−0.234446	+	0.972129i	$0.575327\pi$
$912$	5.33364e113	0.585090
$913$	−2.13765e113	−0.224808
$914$	−1.28541e114	−1.29602
$915$	9.48875e113	0.917269
$916$	−7.12523e112	−0.0660425
$917$	2.58504e114	2.29746
$918$	−7.58963e113	−0.646811
$919$	1.03248e114	0.843787	0.421894	−	0.906645i	$-0.361366\pi$
$919$	1.03248e114	0.843787	0.421894	+	0.906645i	$0.361366\pi$
$920$	−1.34838e114	−1.05677
$921$	−8.60576e113	−0.646835
$922$	1.60696e114	1.15842
$923$	−9.20084e112	−0.0636154
$924$	−1.86854e113	−0.123917
$925$	1.62361e114	1.03282
$926$	8.49249e113	0.518217
$927$	1.54403e114	0.903828
$928$	−6.88341e113	−0.386551
$929$	5.72466e113	0.308422	0.154211	−	0.988038i	$-0.450717\pi$
$929$	5.72466e113	0.308422	0.154211	+	0.988038i	$0.450717\pi$
$930$	9.81802e112	0.0507493
$931$	−3.10207e114	−1.53847
$932$	4.19701e113	0.199723
$933$	−4.24799e113	−0.193973
$934$	−2.28564e114	−1.00151
$935$	−3.10225e114	−1.30446
$936$	−8.79621e112	−0.0354957
$937$	−1.10642e114	−0.428495	−0.214247	−	0.976779i	$-0.568730\pi$
$937$	−1.10642e114	−0.428495	−0.214247	+	0.976779i	$0.568730\pi$
$938$	3.06497e114	1.13925
$939$	−2.66881e114	−0.952121
$940$	−2.37707e113	−0.0813990
$941$	−4.65513e113	−0.153014	−0.0765070	−	0.997069i	$-0.524377\pi$
$941$	−4.65513e113	−0.153014	−0.0765070	+	0.997069i	$0.524377\pi$
$942$	−7.96695e113	−0.251381
$943$	−2.97131e114	−0.900011
$944$	1.34225e114	0.390313
$945$	8.04218e114	2.24517
$946$	1.61405e114	0.432620
$947$	6.01687e114	1.54845	0.774223	−	0.632912i	$-0.218141\pi$
$947$	6.01687e114	1.54845	0.774223	+	0.632912i	$0.218141\pi$
$948$	1.88001e113	0.0464557
$949$	3.29057e113	0.0780767
$950$	−1.05251e115	−2.39809
$951$	−1.01499e114	−0.222081
$952$	5.75964e114	1.21024
$953$	−2.03963e114	−0.411599	−0.205799	−	0.978594i	$-0.565979\pi$
$953$	−2.03963e114	−0.411599	−0.205799	+	0.978594i	$0.565979\pi$
$954$	−7.62666e113	−0.147816
$955$	7.64542e114	1.42322
$956$	−1.48385e113	−0.0265315
$957$	3.53948e114	0.607898
$958$	5.71449e114	0.942769
$959$	−1.12568e115	−1.78402
$960$	6.50639e114	0.990598
$961$	−6.81045e114	−0.996152
$962$	−1.62491e113	−0.0228344
$963$	−1.31659e114	−0.177762
$964$	1.55739e114	0.202038
$965$	−2.49222e115	−3.10660
$966$	−3.39605e114	−0.406776
$967$	1.47256e115	1.69494	0.847468	−	0.530846i	$-0.178126\pi$
$967$	1.47256e115	1.69494	0.847468	+	0.530846i	$0.178126\pi$
$968$	3.89244e113	0.0430547
$969$	−5.32965e114	−0.566544
$970$	−2.17609e114	−0.222313
$971$	1.63196e115	1.60239	0.801197	−	0.598401i	$-0.204197\pi$
$971$	1.63196e115	1.60239	0.801197	+	0.598401i	$0.204197\pi$
$972$	−1.81688e114	−0.171465
$973$	−1.31615e114	−0.119388
$974$	6.49668e114	0.566463
$975$	−5.49726e113	−0.0460753
$976$	−1.02609e115	−0.826737
$977$	1.23622e115	0.957539	0.478770	−	0.877941i	$-0.341083\pi$
$977$	1.23622e115	0.957539	0.478770	+	0.877941i	$0.341083\pi$
$978$	−5.57096e114	−0.414843
$979$	−1.86386e115	−1.33438
$980$	−4.56930e114	−0.314518
$981$	−1.09064e114	−0.0721812
$982$	2.42794e115	1.54506
$983$	−8.58711e114	−0.525456	−0.262728	−	0.964870i	$-0.584622\pi$
$983$	−8.58711e114	−0.525456	−0.262728	+	0.964870i	$0.584622\pi$
$984$	1.46926e115	0.864543
$985$	3.06996e115	1.73715
$986$	−1.54915e115	−0.843011
$987$	−4.21642e114	−0.220665
$988$	−2.08886e113	−0.0105140
$989$	−5.81735e114	−0.281623
$990$	2.37004e115	1.10357
$991$	−1.05038e115	−0.470447	−0.235223	−	0.971941i	$-0.575582\pi$
$991$	−1.05038e115	−0.470447	−0.235223	+	0.971941i	$0.575582\pi$
$992$	4.71394e113	0.0203088
$993$	−7.41739e114	−0.307401
$994$	−4.60263e115	−1.83498
$995$	7.70586e115	2.95551
$996$	−5.40950e113	−0.0199605
$997$	1.87016e115	0.663920	0.331960	−	0.943293i	$-0.392290\pi$
$997$	1.87016e115	0.663920	0.331960	+	0.943293i	$0.392290\pi$
$998$	−4.81424e115	−1.64438
$999$	−1.49592e115	−0.491630

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1.78.a.a.1.5	✓	6
3.2	odd	2		9.78.a.a.1.2		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1.78.a.a.1.5	✓	6	1.1	even	1	trivial
9.78.a.a.1.2		6	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:	\( k \)	\(=\)	\( 78 \)
Character orbit:	\([\chi]\)	\(=\)	1.a (trivial)

\(f(q)\)	\(=\)	\(q+3.55117e11 q^{2} +1.22969e18 q^{3} -2.50080e22 q^{4} +1.38608e27 q^{5} +4.36684e29 q^{6} -5.00002e32 q^{7} -6.25444e34 q^{8} -3.96226e36 q^{9} +O(q^{10})\)	\(q+3.55117e11 q^{2} +1.22969e18 q^{3} -2.50080e22 q^{4} +1.38608e27 q^{5} +4.36684e29 q^{6} -5.00002e32 q^{7} -6.25444e34 q^{8} -3.96226e36 q^{9} +4.92219e38 q^{10} -1.21522e40 q^{11} -3.07521e40 q^{12} -3.54947e41 q^{13} -1.77559e44 q^{14} +1.70445e45 q^{15} -1.84315e46 q^{16} +1.84177e47 q^{17} -1.40706e48 q^{18} -2.35325e49 q^{19} -3.46629e49 q^{20} -6.14849e50 q^{21} -4.31545e51 q^{22} +1.55537e52 q^{23} -7.69104e52 q^{24} +1.25946e54 q^{25} -1.26048e53 q^{26} -1.16042e55 q^{27} +1.25040e55 q^{28} -2.36858e56 q^{29} +6.05278e56 q^{30} +1.62207e56 q^{31} +2.90613e57 q^{32} -1.49435e58 q^{33} +6.54042e58 q^{34} -6.93041e59 q^{35} +9.90880e58 q^{36} +1.28912e60 q^{37} -8.35677e60 q^{38} -4.36476e59 q^{39} -8.66914e61 q^{40} -1.91035e62 q^{41} -2.18343e62 q^{42} -3.74016e62 q^{43} +3.03902e62 q^{44} -5.49199e63 q^{45} +5.52339e63 q^{46} +6.85766e63 q^{47} -2.26650e64 q^{48} +1.31821e65 q^{49} +4.47257e65 q^{50} +2.26481e65 q^{51} +8.87651e63 q^{52} +5.42027e65 q^{53} -4.12084e66 q^{54} -1.68439e67 q^{55} +3.12724e67 q^{56} -2.89377e67 q^{57} -8.41123e67 q^{58} -7.28240e67 q^{59} -4.26248e67 q^{60} +5.56705e68 q^{61} +5.76023e67 q^{62} +1.98114e69 q^{63} +3.81730e69 q^{64} -4.91984e68 q^{65} -5.30667e69 q^{66} -1.72617e70 q^{67} -4.60588e69 q^{68} +1.91263e70 q^{69} -2.46110e71 q^{70} +2.59217e71 q^{71} +2.47817e71 q^{72} -9.27057e71 q^{73} +4.57789e71 q^{74} +1.54875e72 q^{75} +5.88499e71 q^{76} +6.07612e72 q^{77} -1.55000e71 q^{78} -6.11343e72 q^{79} -2.55474e73 q^{80} +7.42141e72 q^{81} -6.78397e73 q^{82} +1.75907e73 q^{83} +1.53761e73 q^{84} +2.55283e74 q^{85} -1.32819e74 q^{86} -2.91263e74 q^{87} +7.60052e74 q^{88} +1.53377e75 q^{89} -1.95030e75 q^{90} +1.77475e74 q^{91} -3.88967e74 q^{92} +1.99464e74 q^{93} +2.43527e75 q^{94} -3.26178e76 q^{95} +3.57364e75 q^{96} -4.42098e75 q^{97} +4.68117e76 q^{98} +4.81501e76 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 264721893120 q^{2} + 14\!\cdots\!80 q^{3}+ \cdots - 48\!\cdots\!42 q^{9}+O(q^{10}) \) 6 * q + 264721893120 * q^2 + 1441611375788089080 * q^3 + 414488718051562044137472 * q^4 - 262034655809276597802623100 * q^5 - 366806373876514422355130201088 * q^6 + 270857839709680313679329082207600 * q^7 - 21222715175771442181432808272035840 * q^8 - 4895011902698601362943838014820938642 * q^9	\( 6 q + 264721893120 q^{2} + 14\!\cdots\!80 q^{3}+ \cdots + 22\!\cdots\!76 q^{99}+O(q^{100}) \) 6 * q + 264721893120 * q^2 + 1441611375788089080 * q^3 + 414488718051562044137472 * q^4 - 262034655809276597802623100 * q^5 - 366806373876514422355130201088 * q^6 + 270857839709680313679329082207600 * q^7 - 21222715175771442181432808272035840 * q^8 - 4895011902698601362943838014820938642 * q^9 - 943981839595570481933588950406110963200 * q^10 - 18259523505888985403727472716999830396568 * q^11 + 464880745107061653664227300592441229475840 * q^12 + 2380194429688668511174277092390661204777460 * q^13 - 294635885851315312797761966406968268616083456 * q^14 - 205398878502504702020984224024402427189799600 * q^15 + 44678683808767880535489561508977888302859288576 * q^16 - 354360527898668112383938884095051354700497739540 * q^17 - 579271368199620858231236048886957435939670283520 * q^18 + 5609349588345922508653624528305080863470217945560 * q^19 - 203683258723050328883517820082887345024612662067200 * q^20 - 540436528239602082418470626392633746858753885327168 * q^21 + 6114758837406209570140637531269380807939078825354240 * q^22 - 47704848518150781083381010364499925248017731105789360 * q^23 + 54816594321451146263884987133438313725918160963502080 * q^24 + 1218179184124654235834607721614209488740550081397516250 * q^25 - 550866287661514215594856318864157268196554716662599168 * q^26 - 18043016639677384483149377528753631298041104958650825040 * q^27 + 27673374074418016612675778175139670616136146452210319360 * q^28 + 16280759001892520996902191080778000816917007177111344340 * q^29 - 1011764162094599483190536262352170796094588963959467571200 * q^30 + 1790157695657501252076176026171679301117057950393828071872 * q^31 + 2181738275733175796144863923114890278726253762313317253120 * q^32 - 43587817236406175039900898992317145479130853281029781929440 * q^33 - 194953896897775283488395124499645480734536214093757337125376 * q^34 - 154692900477132731635374066357063627778968619353419533615200 * q^35 - 3492826558014976862445701719551945606786728595490426565320704 * q^36 - 7407081044970614504852172741178628092123742757389002078546620 * q^37 - 23437112252897896880014527036750794366537612969976459081384960 * q^38 - 70639623729776089938517469701883961219469901500376562016990704 * q^39 - 405188969845671269189619479481322249890553020909404426600448000 * q^40 - 622334267497818741826318492502909006845617873220194725690266308 * q^41 - 1785314244915654620512096109946411089204707510656231457419632640 * q^42 - 2618736058252833489926178823787488683637632009899828264542685400 * q^43 - 10432822146524346418364354026489166880919966717673650220195414016 * q^44 - 4261664397684963408032474279116855329416026736411628094706748300 * q^45 + 15015668129695292865283752907788076308022505321300082329335498752 * q^46 + 10456714010948157967838849947567752123265493969429352826408225440 * q^47 + 195413572872589369177356962560292275025549393856976542715493744640 * q^48 + 471540371160970162947042524598603402842322365532951363545112427542 * q^49 + 1643157939326752820476079797938119435570111533434962615482069920000 * q^50 + 1437480019590559075427205620912951154862381268364307425321563068272 * q^51 + 2497724095217025746860726558921243156289473926034163020782517862400 * q^52 - 1351874258191312033682238211039504811418206289179811594973968454620 * q^53 - 5802743153283665491865673044971704841325735354018068579171943024640 * q^54 - 31869417904451543700720919226087498810908552969327767789062308093200 * q^55 - 108662999456853131644146391920304784213919375663746888603843313008640 * q^56 - 80192344792625061999550741265686291327620988057496835084561604104480 * q^57 - 198994309984504890955955717028136272430515707470032642085684388912640 * q^58 - 314181202100222481576760882531528728694115253385468703103388053744120 * q^59 + 31757517058237454003450287009369504103827834377957826095111285964800 * q^60 + 1205268428250020260156089514176723127199311484106453915524972341789332 * q^61 + 5847595327663334724128627418101253733235456067016746715116600210186240 * q^62 + 5797157259817187838172511312525532039665297350177795293712349527116720 * q^63 + 7434996765286658306744699729117001037072361082977441755818145446100992 * q^64 + 8871205916648888694302367444130318424721491973331706441245421034929400 * q^65 + 2619665127058305678398408811495791734563636436120923156834123240689664 * q^66 - 20237777137309439154263683707086560559031166786916812035021461385807240 * q^67 - 192282119728407192675118903436134256417865682110612543314367901015326720 * q^68 - 200313232582951000798678573547728345115884560145782233425701325968721344 * q^69 - 275296905202040079140538321149869121020079259159855285360874363784294400 * q^70 - 84566701931998894021025479230103599698793740396961643247253155987263248 * q^71 - 111057066523302390867411925011041674769499898042748718262699840917995520 * q^72 + 314847243747931153403355639258701372803638975422668152047464555954073340 * q^73 + 2440978652597431277933746515377916372937009497503279937672013012437072384 * q^74 + 5406848712313524713947990348797970278787563587939911155459007261158885000 * q^75 + 12583857788866874491493997574394644552563831648352611876045224548363960320 * q^76 + 3503704566884313110653172829033905566483467863121365108497302013892404800 * q^77 - 3205965675068953356081325009194962500817273160296149320647178104103475200 * q^78 - 4478934474840817947707335445643189482501134177625819638140993021754592160 * q^79 - 71161053770974020381924657869896203411328788664145358716969422377556377600 * q^80 - 62119692812757584111204435712960193411658364945985590227036022119327600874 * q^81 - 215870435463876846311226667757904584387222051304478591060278478661208783360 * q^82 - 148140974166416303075124558783351182994193920545724368826080939980520858280 * q^83 + 51356650106390838431654087814077196024066314243448648781044119034071875584 * q^84 + 491597676589966787491574950515749558236649703170109339586274361878505865800 * q^85 + 282408262347204426247008847369759267182197911237017110679724533137839752192 * q^86 + 1363181037080164755262169098102975505194220445144287377094744451132352801680 * q^87 + 2657681751590091680961785563694793344274050442909114832295757477808460267520 * q^88 + 244875270415762051982571278168423166555270869887140541520680077076967187420 * q^89 + 4978403011748231687089157306213454731057762280800383772471249777474918822400 * q^90 + 637560104295539679774601429928812188462565548465392346037583647743398360352 * q^91 - 20568828732565451743944414428223922568301505472542794858122155367508257341440 * q^92 - 14490478249669505799006967900921922007746327667753988409512015425992979344640 * q^93 - 17973701798427203443369711151367318601937605119380706693990709867752930471936 * q^94 - 32941519370397986858775692207480112776415936672941584218885058160279506566000 * q^95 - 18725276161952705842933385524361085962413728935875751155361188816688573841408 * q^96 - 12282501490438986599941765679523755451099259695347356745999502279014355079860 * q^97 + 34498422662482146891923464099753801985751726005296311870693615309501356240640 * q^98 + 225826616422430389876328344183536014760241704676820880296433754570070950840776 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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