LMFDB - Embedded newform 1.78.a.a.1.3

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			1.3
Root			$7.14285e8$ 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)

$f(q)$	$=$	$q-9.30224e10 q^{2} +3.16609e18 q^{3} -1.42463e23 q^{4} -6.28590e26 q^{5} -2.94518e29 q^{6} +2.92216e32 q^{7} +2.73094e34 q^{8} +4.54975e36 q^{9} +O(q^{10})$	\(q-9.30224e10 q^{2} +3.16609e18 q^{3} -1.42463e23 q^{4} -6.28590e26 q^{5} -2.94518e29 q^{6} +2.92216e32 q^{7} +2.73094e34 q^{8} +4.54975e36 q^{9} +5.84729e37 q^{10} +1.02571e40 q^{11} -4.51050e41 q^{12} -1.31031e43 q^{13} -2.71826e43 q^{14} -1.99017e45 q^{15} +1.89880e46 q^{16} +2.50974e47 q^{17} -4.23229e47 q^{18} -1.88236e49 q^{19} +8.95505e49 q^{20} +9.25183e50 q^{21} -9.54141e50 q^{22} -2.47189e52 q^{23} +8.64640e52 q^{24} -2.66619e53 q^{25} +1.21888e54 q^{26} -2.92753e54 q^{27} -4.16298e55 q^{28} +2.56733e56 q^{29} +1.85131e56 q^{30} -2.95180e57 q^{31} -5.89318e57 q^{32} +3.24750e58 q^{33} -2.33462e58 q^{34} -1.83684e59 q^{35} -6.48169e59 q^{36} -1.00772e60 q^{37} +1.75102e60 q^{38} -4.14855e61 q^{39} -1.71664e61 q^{40} -1.42253e62 q^{41} -8.60628e61 q^{42} -8.97221e62 q^{43} -1.46125e63 q^{44} -2.85993e63 q^{45} +2.29941e63 q^{46} +1.95430e64 q^{47} +6.01176e64 q^{48} -3.27912e64 q^{49} +2.48016e64 q^{50} +7.94607e65 q^{51} +1.86669e66 q^{52} -4.28657e66 q^{53} +2.72326e65 q^{54} -6.44752e66 q^{55} +7.98023e66 q^{56} -5.95974e67 q^{57} -2.38819e67 q^{58} -1.46325e68 q^{59} +2.83525e68 q^{60} +4.24026e68 q^{61} +2.74583e68 q^{62} +1.32951e69 q^{63} -2.32118e69 q^{64} +8.23645e69 q^{65} -3.02090e69 q^{66} +7.34532e69 q^{67} -3.57544e70 q^{68} -7.82624e70 q^{69} +1.70867e70 q^{70} -1.69374e71 q^{71} +1.24251e71 q^{72} +5.96260e71 q^{73} +9.37402e70 q^{74} -8.44142e71 q^{75} +2.68166e72 q^{76} +2.99729e72 q^{77} +3.85908e72 q^{78} -1.09737e73 q^{79} -1.19356e73 q^{80} -3.41760e73 q^{81} +1.32327e73 q^{82} +7.84532e73 q^{83} -1.31804e74 q^{84} -1.57760e74 q^{85} +8.34617e73 q^{86} +8.12840e74 q^{87} +2.80115e74 q^{88} +6.20669e74 q^{89} +2.66037e74 q^{90} -3.82892e75 q^{91} +3.52152e75 q^{92} -9.34567e75 q^{93} -1.81794e75 q^{94} +1.18323e76 q^{95} -1.86584e76 q^{96} -6.02484e75 q^{97} +3.05032e75 q^{98} +4.66673e76 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−9.30224e10	−0.239295	−0.119647	−	0.992816i	$-0.538176\pi$
$2$	−9.30224e10	−0.239295	−0.119647	+	0.992816i	$0.538176\pi$
$3$	3.16609e18	1.35318	0.676590	−	0.736360i	$-0.263457\pi$
$3$	3.16609e18	1.35318	0.676590	+	0.736360i	$0.263457\pi$
$4$	−1.42463e23	−0.942738
$5$	−6.28590e26	−0.772720	−0.386360	−	0.922348i	$-0.626268\pi$
$5$	−6.28590e26	−0.772720	−0.386360	+	0.922348i	$0.626268\pi$
$6$	−2.94518e29	−0.323809
$7$	2.92216e32	0.850021	0.425010	−	0.905189i	$-0.360270\pi$
$7$	2.92216e32	0.850021	0.425010	+	0.905189i	$0.360270\pi$
$8$	2.73094e34	0.464887
$9$	4.54975e36	0.831095
$10$	5.84729e37	0.184908
$11$	1.02571e40	0.826812	0.413406	−	0.910547i	$-0.364339\pi$
$11$	1.02571e40	0.826812	0.413406	+	0.910547i	$0.364339\pi$
$12$	−4.51050e41	−1.27569
$13$	−1.31031e43	−1.70041	−0.850205	−	0.526452i	$-0.823522\pi$
$13$	−1.31031e43	−1.70041	−0.850205	+	0.526452i	$0.823522\pi$
$14$	−2.71826e43	−0.203405
$15$	−1.99017e45	−1.04563
$16$	1.89880e46	0.831493
$17$	2.50974e47	1.06499	0.532495	−	0.846433i	$-0.321255\pi$
$17$	2.50974e47	1.06499	0.532495	+	0.846433i	$0.321255\pi$
$18$	−4.23229e47	−0.198877
$19$	−1.88236e49	−1.10329	−0.551645	−	0.834079i	$-0.686000\pi$
$19$	−1.88236e49	−1.10329	−0.551645	+	0.834079i	$0.686000\pi$
$20$	8.95505e49	0.728473
$21$	9.25183e50	1.15023
$22$	−9.54141e50	−0.197852
$23$	−2.47189e52	−0.925779	−0.462890	−	0.886416i	$-0.653187\pi$
$23$	−2.47189e52	−0.925779	−0.462890	+	0.886416i	$0.653187\pi$
$24$	8.64640e52	0.629075
$25$	−2.66619e53	−0.402904
$26$	1.21888e54	0.406899
$27$	−2.92753e54	−0.228558
$28$	−4.16298e55	−0.801347
$29$	2.56733e56	1.27985	0.639924	−	0.768438i	$-0.278966\pi$
$29$	2.56733e56	1.27985	0.639924	+	0.768438i	$0.278966\pi$
$30$	1.85131e56	0.250213
$31$	−2.95180e57	−1.12892	−0.564458	−	0.825462i	$-0.690915\pi$
$31$	−2.95180e57	−1.12892	−0.564458	+	0.825462i	$0.690915\pi$
$32$	−5.89318e57	−0.663858
$33$	3.24750e58	1.11882
$34$	−2.33462e58	−0.254846
$35$	−1.83684e59	−0.656828
$36$	−6.48169e59	−0.783505
$37$	−1.00772e60	−0.424201	−0.212101	−	0.977248i	$-0.568030\pi$
$37$	−1.00772e60	−0.424201	−0.212101	+	0.977248i	$0.568030\pi$
$38$	1.75102e60	0.264011
$39$	−4.14855e61	−2.30096
$40$	−1.71664e61	−0.359227
$41$	−1.42253e62	−1.15049	−0.575245	−	0.817981i	$-0.695093\pi$
$41$	−1.42253e62	−1.15049	−0.575245	+	0.817981i	$0.695093\pi$
$42$	−8.60628e61	−0.275244
$43$	−8.97221e62	−1.15975	−0.579874	−	0.814706i	$-0.696898\pi$
$43$	−8.97221e62	−1.15975	−0.579874	+	0.814706i	$0.696898\pi$
$44$	−1.46125e63	−0.779467
$45$	−2.85993e63	−0.642204
$46$	2.29941e63	0.221534
$47$	1.95430e64	0.822667	0.411334	−	0.911485i	$-0.365063\pi$
$47$	1.95430e64	0.822667	0.411334	+	0.911485i	$0.365063\pi$
$48$	6.01176e64	1.12516
$49$	−3.27912e64	−0.277465
$50$	2.48016e64	0.0964127
$51$	7.94607e65	1.44112
$52$	1.86669e66	1.60304
$53$	−4.28657e66	−1.76803	−0.884013	−	0.467462i	$-0.845168\pi$
$53$	−4.28657e66	−1.76803	−0.884013	+	0.467462i	$0.845168\pi$
$54$	2.72326e65	0.0546927
$55$	−6.44752e66	−0.638894
$56$	7.98023e66	0.395163
$57$	−5.95974e67	−1.49295
$58$	−2.38819e67	−0.306261
$59$	−1.46325e68	−0.971665	−0.485832	−	0.874052i	$-0.661483\pi$
$59$	−1.46325e68	−0.971665	−0.485832	+	0.874052i	$0.661483\pi$
$60$	2.83525e68	0.985754
$61$	4.24026e68	0.780178	0.390089	−	0.920777i	$-0.372444\pi$
$61$	4.24026e68	0.780178	0.390089	+	0.920777i	$0.372444\pi$
$62$	2.74583e68	0.270143
$63$	1.32951e69	0.706448
$64$	−2.32118e69	−0.672636
$65$	8.23645e69	1.31394
$66$	−3.02090e69	−0.267729
$67$	7.34532e69	0.364864	0.182432	−	0.983218i	$-0.441603\pi$
$67$	7.34532e69	0.364864	0.182432	+	0.983218i	$0.441603\pi$
$68$	−3.57544e70	−1.00401
$69$	−7.82624e70	−1.25275
$70$	1.70867e70	0.157175
$71$	−1.69374e71	−0.902404	−0.451202	−	0.892422i	$-0.649005\pi$
$71$	−1.69374e71	−0.902404	−0.451202	+	0.892422i	$0.649005\pi$
$72$	1.24251e71	0.386365
$73$	5.96260e71	1.09020	0.545099	−	0.838372i	$-0.316492\pi$
$73$	5.96260e71	1.09020	0.545099	+	0.838372i	$0.316492\pi$
$74$	9.37402e70	0.101509
$75$	−8.44142e71	−0.545201
$76$	2.68166e72	1.04011
$77$	2.99729e72	0.702807
$78$	3.85908e72	0.550607
$79$	−1.09737e73	−0.958763	−0.479381	−	0.877607i	$-0.659139\pi$
$79$	−1.09737e73	−0.958763	−0.479381	+	0.877607i	$0.659139\pi$
$80$	−1.19356e73	−0.642512
$81$	−3.41760e73	−1.14038
$82$	1.32327e73	0.275306
$83$	7.84532e73	1.02354	0.511769	−	0.859123i	$-0.328990\pi$
$83$	7.84532e73	1.02354	0.511769	+	0.859123i	$0.328990\pi$
$84$	−1.31804e74	−1.08437
$85$	−1.57760e74	−0.822939
$86$	8.34617e73	0.277522
$87$	8.12840e74	1.73186
$88$	2.80115e74	0.384374
$89$	6.20669e74	0.551245	0.275622	−	0.961266i	$-0.411116\pi$
$89$	6.20669e74	0.551245	0.275622	+	0.961266i	$0.411116\pi$
$90$	2.66037e74	0.153676
$91$	−3.82892e75	−1.44538
$92$	3.52152e75	0.872768
$93$	−9.34567e75	−1.52763
$94$	−1.81794e75	−0.196860
$95$	1.18323e76	0.852534
$96$	−1.86584e76	−0.898320
$97$	−6.02484e75	−0.194641	−0.0973204	−	0.995253i	$-0.531027\pi$
$97$	−6.02484e75	−0.194641	−0.0973204	+	0.995253i	$0.531027\pi$
$98$	3.05032e75	0.0663958
$99$	4.66673e76	0.687159
$100$	3.79833e76	0.379833
$101$	1.58938e77	1.08356	0.541782	−	0.840519i	$-0.317750\pi$
$101$	1.58938e77	1.08356	0.541782	+	0.840519i	$0.317750\pi$
$102$	−7.39163e76	−0.344853
$103$	1.78470e77	0.571916	0.285958	−	0.958242i	$-0.407688\pi$
$103$	1.78470e77	0.571916	0.285958	+	0.958242i	$0.407688\pi$
$104$	−3.57836e77	−0.790498
$105$	−5.81561e77	−0.888806
$106$	3.98747e77	0.423079
$107$	−1.13046e78	−0.835565	−0.417783	−	0.908547i	$-0.637193\pi$
$107$	−1.13046e78	−0.835565	−0.417783	+	0.908547i	$0.637193\pi$
$108$	4.17064e77	0.215471
$109$	−1.21387e78	−0.439798	−0.219899	−	0.975523i	$-0.570573\pi$
$109$	−1.21387e78	−0.439798	−0.219899	+	0.975523i	$0.570573\pi$
$110$	5.99763e77	0.152884
$111$	−3.19052e78	−0.574021
$112$	5.54858e78	0.706786
$113$	1.68437e79	1.52377	0.761883	−	0.647714i	$-0.224275\pi$
$113$	1.68437e79	1.52377	0.761883	+	0.647714i	$0.224275\pi$
$114$	5.54389e78	0.357255
$115$	1.55381e79	0.715368
$116$	−3.65748e79	−1.20656
$117$	−5.96156e79	−1.41320
$118$	1.36115e79	0.232514
$119$	7.33386e79	0.905263
$120$	−5.43504e79	−0.486099
$121$	−4.86910e79	−0.316382
$122$	−3.94439e79	−0.186692
$123$	−4.50386e80	−1.55682
$124$	4.20521e80	1.06427
$125$	5.83560e80	1.08405
$126$	−1.23674e80	−0.169049
$127$	1.18321e81	1.19294	0.596472	−	0.802634i	$-0.296569\pi$
$127$	1.18321e81	1.19294	0.596472	+	0.802634i	$0.296569\pi$
$128$	1.10647e81	0.824816
$129$	−2.84069e81	−1.56935
$130$	−7.66174e80	−0.314419
$131$	3.60297e81	1.10082	0.550410	−	0.834895i	$-0.314472\pi$
$131$	3.60297e81	1.10082	0.550410	+	0.834895i	$0.314472\pi$
$132$	−4.62647e81	−1.05476
$133$	−5.50056e81	−0.937819
$134$	−6.83280e80	−0.0873100
$135$	1.84022e81	0.176612
$136$	6.85394e81	0.495099
$137$	−1.51655e82	−0.826258	−0.413129	−	0.910673i	$-0.635564\pi$
$137$	−1.51655e82	−0.826258	−0.413129	+	0.910673i	$0.635564\pi$
$138$	7.28015e81	0.299775
$139$	1.52998e82	0.477107	0.238553	−	0.971129i	$-0.423327\pi$
$139$	1.52998e82	0.477107	0.238553	+	0.971129i	$0.423327\pi$
$140$	2.61681e82	0.619217
$141$	6.18750e82	1.11322
$142$	1.57556e82	0.215940
$143$	−1.34399e83	−1.40592
$144$	8.63904e82	0.691050
$145$	−1.61380e83	−0.988965
$146$	−5.54655e82	−0.260878
$147$	−1.03820e83	−0.375460
$148$	1.43562e83	0.399911
$149$	−1.34346e83	−0.288772	−0.144386	−	0.989521i	$-0.546121\pi$
$149$	−1.34346e83	−0.288772	−0.144386	+	0.989521i	$0.546121\pi$
$150$	7.85241e82	0.130464
$151$	−1.52629e83	−0.196347	−0.0981735	−	0.995169i	$-0.531300\pi$
$151$	−1.52629e83	−0.196347	−0.0981735	+	0.995169i	$0.531300\pi$
$152$	−5.14061e83	−0.512905
$153$	1.14187e84	0.885108
$154$	−2.78815e83	−0.168178
$155$	1.85547e84	0.872335
$156$	5.91013e84	2.16920
$157$	−4.25782e84	−1.22194	−0.610972	−	0.791652i	$-0.709221\pi$
$157$	−4.25782e84	−1.22194	−0.610972	+	0.791652i	$0.709221\pi$
$158$	1.02080e84	0.229427
$159$	−1.35717e85	−2.39246
$160$	3.70439e84	0.512977
$161$	−7.22326e84	−0.786932
$162$	3.17913e84	0.272886
$163$	5.90332e83	0.0399828	0.0199914	−	0.999800i	$-0.493636\pi$
$163$	5.90332e83	0.0399828	0.0199914	+	0.999800i	$0.493636\pi$
$164$	2.02657e85	1.08461
$165$	−2.04134e85	−0.864538
$166$	−7.29791e84	−0.244927
$167$	−1.39110e85	−0.370488	−0.185244	−	0.982693i	$-0.559308\pi$
$167$	−1.39110e85	−0.370488	−0.185244	+	0.982693i	$0.559308\pi$
$168$	2.52662e85	0.534727
$169$	1.12310e86	1.89139
$170$	1.46752e85	0.196925
$171$	−8.56428e85	−0.916939
$172$	1.27820e86	1.09334
$173$	−1.92359e86	−1.31625	−0.658123	−	0.752910i	$-0.728649\pi$
$173$	−1.92359e86	−1.31625	−0.658123	+	0.752910i	$0.728649\pi$
$174$	−7.56124e85	−0.414426
$175$	−7.79104e85	−0.342476
$176$	1.94761e86	0.687488
$177$	−4.63279e86	−1.31484
$178$	−5.77361e85	−0.131910
$179$	2.22679e86	0.410050	0.205025	−	0.978757i	$-0.434272\pi$
$179$	2.22679e86	0.410050	0.205025	+	0.978757i	$0.434272\pi$
$180$	4.07432e86	0.605430
$181$	−5.69718e86	−0.683967	−0.341983	−	0.939706i	$-0.611099\pi$
$181$	−5.69718e86	−0.683967	−0.341983	+	0.939706i	$0.611099\pi$
$182$	3.56176e86	0.345872
$183$	1.34251e87	1.05572
$184$	−6.75057e86	−0.430382
$185$	6.33440e86	0.327789
$186$	8.69356e86	0.365552
$187$	2.57427e87	0.880546
$188$	−2.78415e87	−0.775560
$189$	−8.55472e86	−0.194279
$190$	−1.10067e87	−0.204007
$191$	−8.05685e87	−1.22006	−0.610030	−	0.792379i	$-0.708842\pi$
$191$	−8.05685e87	−1.22006	−0.610030	+	0.792379i	$0.708842\pi$
$192$	−7.34907e87	−0.910197
$193$	−8.69825e86	−0.0882014	−0.0441007	−	0.999027i	$-0.514042\pi$
$193$	−8.69825e86	−0.0882014	−0.0441007	+	0.999027i	$0.514042\pi$
$194$	5.60445e86	0.0465765
$195$	2.60774e88	1.77800
$196$	4.67152e87	0.261577
$197$	−6.61271e87	−0.304390	−0.152195	−	0.988351i	$-0.548634\pi$
$197$	−6.61271e87	−0.304390	−0.152195	+	0.988351i	$0.548634\pi$
$198$	−4.34110e87	−0.164434
$199$	1.26482e88	0.394625	0.197313	−	0.980341i	$-0.436779\pi$
$199$	1.26482e88	0.394625	0.197313	+	0.980341i	$0.436779\pi$
$200$	−7.28120e87	−0.187305
$201$	2.32560e88	0.493727
$202$	−1.47848e88	−0.259291
$203$	7.50215e88	1.08790
$204$	−1.13202e89	−1.35860
$205$	8.94187e88	0.889006
$206$	−1.66017e88	−0.136856
$207$	−1.12465e89	−0.769411
$208$	−2.48800e89	−1.41388
$209$	−1.93076e89	−0.912213
$210$	5.40982e88	0.212686
$211$	4.21657e89	1.38065	0.690327	−	0.723497i	$-0.257466\pi$
$211$	4.21657e89	1.38065	0.690327	+	0.723497i	$0.257466\pi$
$212$	6.10675e89	1.66679
$213$	−5.36255e89	−1.22111
$214$	1.05158e89	0.199946
$215$	5.63984e89	0.896161
$216$	−7.99491e88	−0.106254
$217$	−8.62562e89	−0.959601
$218$	1.12918e89	0.105241
$219$	1.88781e90	1.47523
$220$	9.18529e89	0.602310
$221$	−3.28853e90	−1.81092
$222$	2.96790e89	0.137360
$223$	−2.14716e90	−0.835847	−0.417923	−	0.908482i	$-0.637242\pi$
$223$	−2.14716e90	−0.835847	−0.417923	+	0.908482i	$0.637242\pi$
$224$	−1.72208e90	−0.564293
$225$	−1.21305e90	−0.334851
$226$	−1.56685e90	−0.364629
$227$	3.19292e90	0.626893	0.313446	−	0.949606i	$-0.398516\pi$
$227$	3.19292e90	0.626893	0.313446	+	0.949606i	$0.398516\pi$
$228$	8.49039e90	1.40746
$229$	−2.81955e90	−0.394924	−0.197462	−	0.980311i	$-0.563270\pi$
$229$	−2.81955e90	−0.394924	−0.197462	+	0.980311i	$0.563270\pi$
$230$	−1.44539e90	−0.171184
$231$	9.48971e90	0.951024
$232$	7.01121e90	0.594984
$233$	−9.23794e90	−0.664312	−0.332156	−	0.943224i	$-0.607776\pi$
$233$	−9.23794e90	−0.664312	−0.332156	+	0.943224i	$0.607776\pi$
$234$	5.54559e90	0.338172
$235$	−1.22845e91	−0.635691
$236$	2.08459e91	0.916026
$237$	−3.47438e91	−1.29738
$238$	−6.82214e90	−0.216625
$239$	1.76667e91	0.477348	0.238674	−	0.971100i	$-0.423287\pi$
$239$	1.76667e91	0.477348	0.238674	+	0.971100i	$0.423287\pi$
$240$	−3.77893e91	−0.869434
$241$	4.41141e91	0.864812	0.432406	−	0.901679i	$-0.357665\pi$
$241$	4.41141e91	0.864812	0.432406	+	0.901679i	$0.357665\pi$
$242$	4.52936e90	0.0757086
$243$	−9.21779e91	−1.31458
$244$	−6.04078e91	−0.735503
$245$	2.06122e91	0.214403
$246$	4.18960e91	0.372538
$247$	2.46647e92	1.87604
$248$	−8.06117e91	−0.524818
$249$	2.48390e92	1.38503
$250$	−5.42842e91	−0.259408
$251$	1.39362e92	0.571093	0.285546	−	0.958365i	$-0.407825\pi$
$251$	1.39362e92	0.571093	0.285546	+	0.958365i	$0.407825\pi$
$252$	−1.89405e92	−0.665996
$253$	−2.53545e92	−0.765445
$254$	−1.10065e92	−0.285465
$255$	−4.99482e92	−1.11358
$256$	2.47840e92	0.475262
$257$	1.63172e92	0.269291	0.134645	−	0.990894i	$-0.457010\pi$
$257$	1.63172e92	0.269291	0.134645	+	0.990894i	$0.457010\pi$
$258$	2.64248e92	0.375537
$259$	−2.94471e92	−0.360580
$260$	−1.17339e93	−1.23870
$261$	1.16807e93	1.06368
$262$	−3.35157e92	−0.263420
$263$	−1.02277e93	−0.694196	−0.347098	−	0.937829i	$-0.612833\pi$
$263$	−1.02277e93	−0.694196	−0.347098	+	0.937829i	$0.612833\pi$
$264$	8.86871e92	0.520127
$265$	2.69449e93	1.36619
$266$	5.11676e92	0.224415
$267$	1.96510e93	0.745933
$268$	−1.04643e93	−0.343971
$269$	1.26205e93	0.359431	0.179715	−	0.983719i	$-0.442482\pi$
$269$	1.26205e93	0.359431	0.179715	+	0.983719i	$0.442482\pi$
$270$	−1.71181e92	−0.0422622
$271$	−7.39368e93	−1.58323	−0.791613	−	0.611023i	$-0.790758\pi$
$271$	−7.39368e93	−1.58323	−0.791613	+	0.611023i	$0.790758\pi$
$272$	4.76548e93	0.885532
$273$	−1.21227e94	−1.95586
$274$	1.41073e93	0.197719
$275$	−2.73474e93	−0.333126
$276$	1.11495e94	1.18101
$277$	4.96535e93	0.457593	0.228796	−	0.973474i	$-0.426521\pi$
$277$	4.96535e93	0.457593	0.228796	+	0.973474i	$0.426521\pi$
$278$	−1.42322e93	−0.114169
$279$	−1.34299e94	−0.938236
$280$	−5.01629e93	−0.305351
$281$	2.43013e93	0.128954	0.0644771	−	0.997919i	$-0.479462\pi$
$281$	2.43013e93	0.128954	0.0644771	+	0.997919i	$0.479462\pi$
$282$	−5.75577e93	−0.266387
$283$	2.16796e94	0.875536	0.437768	−	0.899088i	$-0.355769\pi$
$283$	2.16796e94	0.875536	0.437768	+	0.899088i	$0.355769\pi$
$284$	2.41295e94	0.850730
$285$	3.74623e94	1.15363
$286$	1.25022e94	0.336429
$287$	−4.15686e94	−0.977940
$288$	−2.68125e94	−0.551730
$289$	7.45296e93	0.134203
$290$	1.50119e94	0.236654
$291$	−1.90752e94	−0.263384
$292$	−8.49447e94	−1.02777
$293$	−1.11195e95	−1.17946	−0.589728	−	0.807602i	$-0.700765\pi$
$293$	−1.11195e95	−1.17946	−0.589728	+	0.807602i	$0.700765\pi$
$294$	9.65759e93	0.0898455
$295$	9.19785e94	0.750825
$296$	−2.75201e94	−0.197205
$297$	−3.00280e94	−0.188975
$298$	1.24972e94	0.0691015
$299$	3.23893e95	1.57420
$300$	1.20259e95	0.513982
$301$	−2.62182e95	−0.985811
$302$	1.41979e94	0.0469847
$303$	5.03213e95	1.46626
$304$	−3.57422e95	−0.917378
$305$	−2.66538e95	−0.602859
$306$	−1.06219e95	−0.211802
$307$	8.24790e95	1.45049	0.725247	−	0.688489i	$-0.241726\pi$
$307$	8.24790e95	1.45049	0.725247	+	0.688489i	$0.241726\pi$
$308$	−4.27002e95	−0.662563
$309$	5.65053e95	0.773906
$310$	−1.72600e95	−0.208745
$311$	−1.46922e96	−1.56968	−0.784841	−	0.619697i	$-0.787255\pi$
$311$	−1.46922e96	−1.56968	−0.784841	+	0.619697i	$0.787255\pi$
$312$	−1.13294e96	−1.06969
$313$	−6.25454e94	−0.0522081	−0.0261041	−	0.999659i	$-0.508310\pi$
$313$	−6.25454e94	−0.0522081	−0.0261041	+	0.999659i	$0.508310\pi$
$314$	3.96073e95	0.292404
$315$	−8.35716e95	−0.545887
$316$	1.56335e96	0.903862
$317$	4.81996e95	0.246753	0.123376	−	0.992360i	$-0.460628\pi$
$317$	4.81996e95	0.246753	0.123376	+	0.992360i	$0.460628\pi$
$318$	1.26247e96	0.572502
$319$	2.63334e96	1.05819
$320$	1.45907e96	0.519759
$321$	−3.57915e96	−1.13067
$322$	6.71925e95	0.188308
$323$	−4.72424e96	−1.17499
$324$	4.86880e96	1.07508
$325$	3.49353e96	0.685101
$326$	−5.49141e94	−0.00956767
$327$	−3.84324e96	−0.595126
$328$	−3.88483e96	−0.534847
$329$	5.71078e96	0.699284
$330$	1.89891e96	0.206879
$331$	−1.37471e97	−1.33301	−0.666507	−	0.745499i	$-0.732211\pi$
$331$	−1.37471e97	−1.33301	−0.666507	+	0.745499i	$0.732211\pi$
$332$	−1.11766e97	−0.964929
$333$	−4.58486e96	−0.352552
$334$	1.29404e96	0.0886558
$335$	−4.61720e96	−0.281938
$336$	1.75673e97	0.956409
$337$	1.45560e97	0.706789	0.353394	−	0.935474i	$-0.385027\pi$
$337$	1.45560e97	0.706789	0.353394	+	0.935474i	$0.385027\pi$
$338$	−1.04474e97	−0.452600
$339$	5.33289e97	2.06193
$340$	2.24749e97	0.775816
$341$	−3.02769e97	−0.933400
$342$	7.96670e96	0.219418
$343$	−4.41166e97	−1.08587
$344$	−2.45025e97	−0.539152
$345$	4.91949e97	0.968022
$346$	1.78937e97	0.314971
$347$	−6.68297e97	−1.05265	−0.526326	−	0.850283i	$-0.676431\pi$
$347$	−6.68297e97	−1.05265	−0.526326	+	0.850283i	$0.676431\pi$
$348$	−1.15799e98	−1.63270
$349$	1.39474e98	1.76082	0.880411	−	0.474211i	$-0.157267\pi$
$349$	1.39474e98	1.76082	0.880411	+	0.474211i	$0.157267\pi$
$350$	7.24742e96	0.0819527
$351$	3.83596e97	0.388643
$352$	−6.04470e97	−0.548886
$353$	−2.42214e98	−1.97185	−0.985925	−	0.167191i	$-0.946530\pi$
$353$	−2.42214e98	−1.97185	−0.985925	+	0.167191i	$0.946530\pi$
$354$	4.30953e97	0.314633
$355$	1.06467e98	0.697305
$356$	−8.84220e97	−0.519679
$357$	2.32197e98	1.22498
$358$	−2.07141e97	−0.0981228
$359$	2.62539e98	1.11701	0.558506	−	0.829501i	$-0.311375\pi$
$359$	2.62539e98	1.11701	0.558506	+	0.829501i	$0.311375\pi$
$360$	−7.81028e97	−0.298552
$361$	6.32387e97	0.217248
$362$	5.29966e97	0.163670
$363$	−1.54160e98	−0.428122
$364$	5.45478e98	1.36262
$365$	−3.74803e98	−0.842418
$366$	−1.24883e98	−0.252628
$367$	1.25612e98	0.228763	0.114382	−	0.993437i	$-0.463511\pi$
$367$	1.25612e98	0.228763	0.114382	+	0.993437i	$0.463511\pi$
$368$	−4.69361e98	−0.769779
$369$	−6.47215e98	−0.956166
$370$	−5.89241e97	−0.0784381
$371$	−1.25260e99	−1.50286
$372$	1.33141e99	1.44015
$373$	1.42579e98	0.139080	0.0695402	−	0.997579i	$-0.477847\pi$
$373$	1.42579e98	0.139080	0.0695402	+	0.997579i	$0.477847\pi$
$374$	−2.39465e98	−0.210710
$375$	1.84761e99	1.46692
$376$	5.33707e98	0.382447
$377$	−3.36398e99	−2.17627
$378$	7.95781e97	0.0464900
$379$	2.35241e99	1.24138	0.620688	−	0.784058i	$-0.286854\pi$
$379$	2.35241e99	1.24138	0.620688	+	0.784058i	$0.286854\pi$
$380$	−1.68566e99	−0.803716
$381$	3.74617e99	1.61427
$382$	7.49468e98	0.291953
$383$	−3.96319e98	−0.139602	−0.0698010	−	0.997561i	$-0.522236\pi$
$383$	−3.96319e98	−0.139602	−0.0698010	+	0.997561i	$0.522236\pi$
$384$	3.50320e99	1.11612
$385$	−1.88407e99	−0.543073
$386$	8.09132e97	0.0211061
$387$	−4.08213e99	−0.963862
$388$	8.58314e98	0.183495
$389$	−7.65552e99	−1.48223	−0.741114	−	0.671380i	$-0.765702\pi$
$389$	−7.65552e99	−1.48223	−0.741114	+	0.671380i	$0.765702\pi$
$390$	−2.42578e99	−0.425465
$391$	−6.20380e99	−0.985946
$392$	−8.95507e98	−0.128990
$393$	1.14073e100	1.48961
$394$	6.15131e98	0.0728388
$395$	6.89797e99	0.740855
$396$	−6.64834e99	−0.647811
$397$	1.70389e100	1.50663	0.753315	−	0.657660i	$-0.228454\pi$
$397$	1.70389e100	1.50663	0.753315	+	0.657660i	$0.228454\pi$
$398$	−1.17656e99	−0.0944317
$399$	−1.74153e100	−1.26904
$400$	−5.06255e99	−0.335012
$401$	7.36969e99	0.442987	0.221494	−	0.975162i	$-0.428907\pi$
$401$	7.36969e99	0.442987	0.221494	+	0.975162i	$0.428907\pi$
$402$	−2.16333e99	−0.118146
$403$	3.86776e100	1.91962
$404$	−2.26427e100	−1.02152
$405$	2.14827e100	0.881191
$406$	−6.97868e99	−0.260328
$407$	−1.03363e100	−0.350735
$408$	2.17002e100	0.669959
$409$	−1.37273e100	−0.385690	−0.192845	−	0.981229i	$-0.561771\pi$
$409$	−1.37273e100	−0.385690	−0.192845	+	0.981229i	$0.561771\pi$
$410$	−8.31794e99	−0.212734
$411$	−4.80155e100	−1.11808
$412$	−2.54253e100	−0.539167
$413$	−4.27586e100	−0.825935
$414$	1.04617e100	0.184116
$415$	−4.93149e100	−0.790909
$416$	7.72186e100	1.12883
$417$	4.84406e100	0.645611
$418$	1.79604e100	0.218288
$419$	−2.66119e100	−0.295009	−0.147505	−	0.989061i	$-0.547124\pi$
$419$	−2.66119e100	−0.295009	−0.147505	+	0.989061i	$0.547124\pi$
$420$	8.28506e100	0.837912
$421$	8.54928e100	0.788985	0.394493	−	0.918899i	$-0.370920\pi$
$421$	8.54928e100	0.788985	0.394493	+	0.918899i	$0.370920\pi$
$422$	−3.92236e100	−0.330383
$423$	8.89159e100	0.683715
$424$	−1.17063e101	−0.821932
$425$	−6.69145e100	−0.429088
$426$	4.98837e100	0.292206
$427$	1.23907e101	0.663167
$428$	1.61048e101	0.787719
$429$	−4.25521e101	−1.90246
$430$	−5.24632e100	−0.214447
$431$	3.11407e101	1.16400	0.582001	−	0.813188i	$-0.302270\pi$
$431$	3.11407e101	1.16400	0.582001	+	0.813188i	$0.302270\pi$
$432$	−5.55878e100	−0.190045
$433$	−4.91529e101	−1.53732	−0.768662	−	0.639655i	$-0.779077\pi$
$433$	−4.91529e101	−1.53732	−0.768662	+	0.639655i	$0.779077\pi$
$434$	8.02376e100	0.229627
$435$	−5.10943e101	−1.33825
$436$	1.72932e101	0.414615
$437$	4.65299e101	1.02140
$438$	−1.75609e101	−0.353015
$439$	1.30905e101	0.241031	0.120515	−	0.992711i	$-0.461545\pi$
$439$	1.30905e101	0.241031	0.120515	+	0.992711i	$0.461545\pi$
$440$	−1.76078e101	−0.297013
$441$	−1.49192e101	−0.230600
$442$	3.05907e101	0.433343
$443$	1.26166e102	1.63832	0.819159	−	0.573567i	$-0.194441\pi$
$443$	1.26166e102	1.63832	0.819159	+	0.573567i	$0.194441\pi$
$444$	4.54530e101	0.541151
$445$	−3.90146e101	−0.425958
$446$	1.99734e101	0.200014
$447$	−4.25353e101	−0.390760
$448$	−6.78286e101	−0.571754
$449$	1.59614e102	1.23477	0.617386	−	0.786661i	$-0.288192\pi$
$449$	1.59614e102	1.23477	0.617386	+	0.786661i	$0.288192\pi$
$450$	1.12841e101	0.0801281
$451$	−1.45910e102	−0.951238
$452$	−2.39960e102	−1.43651
$453$	−4.83237e101	−0.265693
$454$	−2.97014e101	−0.150012
$455$	2.40682e102	1.11688
$456$	−1.62757e102	−0.694052
$457$	2.43377e102	0.953906	0.476953	−	0.878929i	$-0.341741\pi$
$457$	2.43377e102	0.953906	0.476953	+	0.878929i	$0.341741\pi$
$458$	2.62281e101	0.0945032
$459$	−7.34735e101	−0.243412
$460$	−2.21359e102	−0.674405
$461$	−4.70609e101	−0.131879	−0.0659394	−	0.997824i	$-0.521004\pi$
$461$	−4.70609e101	−0.131879	−0.0659394	+	0.997824i	$0.521004\pi$
$462$	−8.82755e101	−0.227575
$463$	−7.21636e102	−1.71179	−0.855894	−	0.517152i	$-0.826992\pi$
$463$	−7.21636e102	−1.71179	−0.855894	+	0.517152i	$0.826992\pi$
$464$	4.87483e102	1.06419
$465$	5.87459e102	1.18043
$466$	8.59335e101	0.158966
$467$	7.94994e102	1.35414	0.677071	−	0.735918i	$-0.263249\pi$
$467$	7.94994e102	1.35414	0.677071	+	0.735918i	$0.263249\pi$
$468$	8.49299e102	1.33228
$469$	2.14642e102	0.310142
$470$	1.14274e102	0.152117
$471$	−1.34807e103	−1.65351
$472$	−3.99605e102	−0.451714
$473$	−9.20290e102	−0.958894
$474$	3.23196e102	0.310456
$475$	5.01874e102	0.444519
$476$	−1.04480e103	−0.853426
$477$	−1.95028e103	−1.46940
$478$	−1.64339e102	−0.114227
$479$	1.13714e103	0.729284	0.364642	−	0.931148i	$-0.381191\pi$
$479$	1.13714e103	0.729284	0.364642	+	0.931148i	$0.381191\pi$
$480$	1.17285e103	0.694150
$481$	1.32042e103	0.721316
$482$	−4.10360e102	−0.206945
$483$	−2.28695e103	−1.06486
$484$	6.93665e102	0.298266
$485$	3.78715e102	0.150403
$486$	8.57461e102	0.314571
$487$	3.75882e101	0.0127405	0.00637025	−	0.999980i	$-0.497972\pi$
$487$	3.75882e101	0.0127405	0.00637025	+	0.999980i	$0.497972\pi$
$488$	1.15799e103	0.362694
$489$	1.86905e102	0.0541039
$490$	−1.91740e102	−0.0513054
$491$	−1.77808e103	−0.439861	−0.219930	−	0.975516i	$-0.570583\pi$
$491$	−1.77808e103	−0.439861	−0.219930	+	0.975516i	$0.570583\pi$
$492$	6.41631e103	1.46767
$493$	6.44333e103	1.36303
$494$	−2.29437e103	−0.448927
$495$	−2.93346e103	−0.530982
$496$	−5.60486e103	−0.938685
$497$	−4.94938e103	−0.767062
$498$	−2.31059e103	−0.331430
$499$	8.72155e103	1.15804	0.579019	−	0.815314i	$-0.303436\pi$
$499$	8.72155e103	1.15804	0.579019	+	0.815314i	$0.303436\pi$
$500$	−8.31355e103	−1.02198
$501$	−4.40435e103	−0.501337
$502$	−1.29638e103	−0.136659
$503$	−3.42241e103	−0.334168	−0.167084	−	0.985943i	$-0.553435\pi$
$503$	−3.42241e103	−0.334168	−0.167084	+	0.985943i	$0.553435\pi$
$504$	3.63081e103	0.328418
$505$	−9.99068e103	−0.837292
$506$	2.35853e103	0.183167
$507$	3.55585e104	2.55939
$508$	−1.68564e104	−1.12463
$509$	−4.68928e102	−0.0290049	−0.0145025	−	0.999895i	$-0.504616\pi$
$509$	−4.68928e102	−0.0290049	−0.0145025	+	0.999895i	$0.504616\pi$
$510$	4.64630e103	0.266475
$511$	1.74237e104	0.926691
$512$	−1.90260e104	−0.938544
$513$	5.51068e103	0.252166
$514$	−1.51787e103	−0.0644398
$515$	−1.12185e104	−0.441931
$516$	4.04691e104	1.47949
$517$	2.00455e104	0.680191
$518$	2.73924e103	0.0862848
$519$	−6.09026e104	−1.78112
$520$	2.24932e104	0.610833
$521$	−1.10963e104	−0.279851	−0.139925	−	0.990162i	$-0.544686\pi$
$521$	−1.10963e104	−0.279851	−0.139925	+	0.990162i	$0.544686\pi$
$522$	−1.08657e104	−0.254532
$523$	1.45914e104	0.317527	0.158763	−	0.987317i	$-0.449249\pi$
$523$	1.45914e104	0.317527	0.158763	+	0.987317i	$0.449249\pi$
$524$	−5.13289e104	−1.03778
$525$	−2.46672e104	−0.463432
$526$	9.51407e103	0.166117
$527$	−7.40825e104	−1.20228
$528$	6.16633e104	0.930295
$529$	−1.01900e104	−0.142932
$530$	−2.50648e104	−0.326922
$531$	−6.65743e104	−0.807546
$532$	7.83624e104	0.884118
$533$	1.86395e105	1.95630
$534$	−1.82798e104	−0.178498
$535$	7.10597e104	0.645658
$536$	2.00596e104	0.169620
$537$	7.05022e104	0.554872
$538$	−1.17399e104	−0.0860098
$539$	−3.36343e104	−0.229411
$540$	−2.62162e104	−0.166498
$541$	−1.58201e105	−0.935655	−0.467827	−	0.883820i	$-0.654963\pi$
$541$	−1.58201e105	−0.935655	−0.467827	+	0.883820i	$0.654963\pi$
$542$	6.87778e104	0.378857
$543$	−1.80378e105	−0.925530
$544$	−1.47904e105	−0.707002
$545$	7.63029e104	0.339841
$546$	1.12769e105	0.468027
$547$	−8.47637e104	−0.327867	−0.163934	−	0.986471i	$-0.552418\pi$
$547$	−8.47637e104	−0.327867	−0.163934	+	0.986471i	$0.552418\pi$
$548$	2.16052e105	0.778945
$549$	1.92921e105	0.648402
$550$	2.54392e104	0.0797151
$551$	−4.83264e105	−1.41204
$552$	−2.13730e105	−0.582385
$553$	−3.20670e105	−0.814968
$554$	−4.61889e104	−0.109499
$555$	2.00553e105	0.443557
$556$	−2.17965e105	−0.449787
$557$	3.05650e105	0.588572	0.294286	−	0.955717i	$-0.404918\pi$
$557$	3.05650e105	0.588572	0.294286	+	0.955717i	$0.404918\pi$
$558$	1.24929e105	0.224515
$559$	1.17563e106	1.97205
$560$	−3.48778e105	−0.546148
$561$	8.15038e105	1.19154
$562$	−2.26056e104	−0.0308580
$563$	1.20860e106	1.54066	0.770332	−	0.637642i	$-0.220090\pi$
$563$	1.20860e106	1.54066	0.770332	+	0.637642i	$0.220090\pi$
$564$	−8.81488e105	−1.04947
$565$	−1.05878e106	−1.17745
$566$	−2.01669e105	−0.209511
$567$	−9.98677e105	−0.969343
$568$	−4.62550e105	−0.419515
$569$	1.35507e106	1.14852	0.574260	−	0.818673i	$-0.305290\pi$
$569$	1.35507e106	1.14852	0.574260	+	0.818673i	$0.305290\pi$
$570$	−3.48483e105	−0.276058
$571$	−7.87875e105	−0.583401	−0.291701	−	0.956510i	$-0.594221\pi$
$571$	−7.87875e105	−0.583401	−0.291701	+	0.956510i	$0.594221\pi$
$572$	1.91469e106	1.32541
$573$	−2.55088e106	−1.65096
$574$	3.86681e105	0.234016
$575$	6.59054e105	0.373000
$576$	−1.05608e106	−0.559024
$577$	−1.45275e106	−0.719321	−0.359661	−	0.933083i	$-0.617108\pi$
$577$	−1.45275e106	−0.719321	−0.359661	+	0.933083i	$0.617108\pi$
$578$	−6.93293e104	−0.0321140
$579$	−2.75395e105	−0.119352
$580$	2.29906e106	0.932335
$581$	2.29253e106	0.870029
$582$	1.77442e105	0.0630263
$583$	−4.39678e106	−1.46182
$584$	1.62835e106	0.506818
$585$	3.74738e106	1.09201
$586$	1.03436e106	0.282237
$587$	5.64378e105	0.144213	0.0721063	−	0.997397i	$-0.477028\pi$
$587$	5.64378e105	0.144213	0.0721063	+	0.997397i	$0.477028\pi$
$588$	1.47905e106	0.353960
$589$	5.55635e106	1.24552
$590$	−8.55606e105	−0.179668
$591$	−2.09365e106	−0.411894
$592$	−1.91345e106	−0.352721
$593$	−9.16283e106	−1.58279	−0.791396	−	0.611304i	$-0.790645\pi$
$593$	−9.16283e106	−1.58279	−0.791396	+	0.611304i	$0.790645\pi$
$594$	2.79328e105	0.0452206
$595$	−4.60999e106	−0.699515
$596$	1.91393e106	0.272236
$597$	4.00453e106	0.533999
$598$	−3.01293e106	−0.376698
$599$	−1.36149e107	−1.59618	−0.798090	−	0.602539i	$-0.794156\pi$
$599$	−1.36149e107	−1.59618	−0.798090	+	0.602539i	$0.794156\pi$
$600$	−2.30530e106	−0.253457
$601$	1.13574e107	1.17115	0.585573	−	0.810620i	$-0.300870\pi$
$601$	1.13574e107	1.17115	0.585573	+	0.810620i	$0.300870\pi$
$602$	2.43888e106	0.235899
$603$	3.34194e106	0.303237
$604$	2.17439e106	0.185104
$605$	3.06067e106	0.244475
$606$	−4.68101e106	−0.350868
$607$	−6.34971e106	−0.446673	−0.223336	−	0.974741i	$-0.571695\pi$
$607$	−6.34971e106	−0.446673	−0.223336	+	0.974741i	$0.571695\pi$
$608$	1.10931e107	0.732428
$609$	2.37525e107	1.47212
$610$	2.47940e106	0.144261
$611$	−2.56073e107	−1.39887
$612$	−1.62674e107	−0.834425
$613$	1.79869e107	0.866421	0.433211	−	0.901293i	$-0.357381\pi$
$613$	1.79869e107	0.866421	0.433211	+	0.901293i	$0.357381\pi$
$614$	−7.67239e106	−0.347095
$615$	2.83108e107	1.20299
$616$	8.18541e106	0.326726
$617$	1.50102e107	0.562869	0.281435	−	0.959580i	$-0.409190\pi$
$617$	1.50102e107	0.562869	0.281435	+	0.959580i	$0.409190\pi$
$618$	−5.25626e106	−0.185191
$619$	−2.73097e107	−0.904123	−0.452062	−	0.891987i	$-0.649311\pi$
$619$	−2.73097e107	−0.904123	−0.452062	+	0.891987i	$0.649311\pi$
$620$	−2.64335e107	−0.822384
$621$	7.23654e106	0.211595
$622$	1.36670e107	0.375616
$623$	1.81369e107	0.468569
$624$	−7.87725e107	−1.91323
$625$	−1.90386e107	−0.434765
$626$	5.81812e105	0.0124931
$627$	−6.11297e107	−1.23439
$628$	6.06580e107	1.15197
$629$	−2.52911e107	−0.451770
$630$	7.77403e106	0.130628
$631$	6.09609e107	0.963653	0.481827	−	0.876267i	$-0.339974\pi$
$631$	6.09609e107	0.963653	0.481827	+	0.876267i	$0.339974\pi$
$632$	−2.99685e107	−0.445716
$633$	1.33501e108	1.86827
$634$	−4.48365e106	−0.0590466
$635$	−7.43756e107	−0.921812
$636$	1.93346e108	2.25546
$637$	4.29665e107	0.471804
$638$	−2.44959e107	−0.253220
$639$	−7.70610e107	−0.749983
$640$	−6.95518e107	−0.637352
$641$	−1.65502e108	−1.42813	−0.714067	−	0.700077i	$-0.753149\pi$
$641$	−1.65502e108	−1.42813	−0.714067	+	0.700077i	$0.753149\pi$
$642$	3.32941e107	0.270563
$643$	−6.30287e107	−0.482409	−0.241205	−	0.970474i	$-0.577542\pi$
$643$	−6.30287e107	−0.482409	−0.241205	+	0.970474i	$0.577542\pi$
$644$	1.02904e108	0.741870
$645$	1.78563e108	1.21267
$646$	4.39460e107	0.281169
$647$	−5.18685e106	−0.0312672	−0.0156336	−	0.999878i	$-0.504977\pi$
$647$	−5.18685e106	−0.0312672	−0.0156336	+	0.999878i	$0.504977\pi$
$648$	−9.33325e107	−0.530145
$649$	−1.50087e108	−0.803384
$650$	−3.24976e107	−0.163941
$651$	−2.73095e108	−1.29851
$652$	−8.41002e106	−0.0376933
$653$	1.09909e108	0.464382	0.232191	−	0.972670i	$-0.425410\pi$
$653$	1.09909e108	0.464382	0.232191	+	0.972670i	$0.425410\pi$
$654$	3.57507e107	0.142410
$655$	−2.26479e108	−0.850625
$656$	−2.70109e108	−0.956624
$657$	2.71283e108	0.906059
$658$	−5.31231e107	−0.167335
$659$	5.75221e108	1.70902	0.854509	−	0.519437i	$-0.173858\pi$
$659$	5.75221e108	1.70902	0.854509	+	0.519437i	$0.173858\pi$
$660$	2.90815e108	0.815033
$661$	7.13198e108	1.88562	0.942809	−	0.333333i	$-0.108173\pi$
$661$	7.13198e108	1.88562	0.942809	+	0.333333i	$0.108173\pi$
$662$	1.27879e108	0.318983
$663$	−1.04118e109	−2.45050
$664$	2.14251e108	0.475829
$665$	3.45760e108	0.724671
$666$	4.26495e107	0.0843637
$667$	−6.34615e108	−1.18486
$668$	1.98180e108	0.349273
$669$	−6.79810e108	−1.13105
$670$	4.29503e107	0.0674662
$671$	4.34928e108	0.645060
$672$	−5.45227e108	−0.763590
$673$	9.25123e108	1.22354	0.611772	−	0.791034i	$-0.290457\pi$
$673$	9.25123e108	1.22354	0.611772	+	0.791034i	$0.290457\pi$
$674$	−1.35403e108	−0.169131
$675$	7.80537e107	0.0920870
$676$	−1.60000e109	−1.78309
$677$	6.77137e108	0.712874	0.356437	−	0.934319i	$-0.383991\pi$
$677$	6.77137e108	0.712874	0.356437	+	0.934319i	$0.383991\pi$
$678$	−4.96078e108	−0.493409
$679$	−1.76055e108	−0.165449
$680$	−4.30832e108	−0.382573
$681$	1.01091e109	0.848298
$682$	2.81643e108	0.223358
$683$	−2.17905e109	−1.63332	−0.816659	−	0.577120i	$-0.804176\pi$
$683$	−2.17905e109	−1.63332	−0.816659	+	0.577120i	$0.804176\pi$
$684$	1.22009e109	0.864433
$685$	9.53289e108	0.638466
$686$	4.10383e108	0.259843
$687$	−8.92696e108	−0.534403
$688$	−1.70364e109	−0.964324
$689$	5.61671e109	3.00637
$690$	−4.57623e108	−0.231642
$691$	−2.36466e109	−1.13204	−0.566022	−	0.824390i	$-0.691518\pi$
$691$	−2.36466e109	−1.13204	−0.566022	+	0.824390i	$0.691518\pi$
$692$	2.74039e109	1.24088
$693$	1.36369e109	0.584100
$694$	6.21666e108	0.251894
$695$	−9.61729e108	−0.368670
$696$	2.21982e109	0.805121
$697$	−3.57018e109	−1.22526
$698$	−1.29742e109	−0.421355
$699$	−2.92482e109	−0.898933
$700$	1.10993e109	0.322866
$701$	−5.34907e109	−1.47277	−0.736385	−	0.676563i	$-0.763469\pi$
$701$	−5.34907e109	−1.47277	−0.736385	+	0.676563i	$0.763469\pi$
$702$	−3.56830e108	−0.0930000
$703$	1.89689e109	0.468017
$704$	−2.38086e109	−0.556143
$705$	−3.88940e109	−0.860205
$706$	2.25314e109	0.471853
$707$	4.64442e109	0.921053
$708$	6.59999e109	1.23955
$709$	−3.24233e109	−0.576736	−0.288368	−	0.957520i	$-0.593113\pi$
$709$	−3.24233e109	−0.576736	−0.288368	+	0.957520i	$0.593113\pi$
$710$	−9.90381e108	−0.166861
$711$	−4.99277e109	−0.796823
$712$	1.69501e109	0.256266
$713$	7.29652e109	1.04513
$714$	−2.15995e109	−0.293132
$715$	8.44821e109	1.08638
$716$	−3.17234e109	−0.386570
$717$	5.59343e109	0.645938
$718$	−2.44220e109	−0.267295
$719$	−6.28521e109	−0.652014	−0.326007	−	0.945367i	$-0.605703\pi$
$719$	−6.28521e109	−0.652014	−0.326007	+	0.945367i	$0.605703\pi$
$720$	−5.43041e109	−0.533988
$721$	5.21518e109	0.486141
$722$	−5.88262e108	−0.0519862
$723$	1.39669e110	1.17025
$724$	8.11635e109	0.644802
$725$	−6.84499e109	−0.515656
$726$	1.43404e109	0.102447
$727$	−7.63794e109	−0.517489	−0.258745	−	0.965946i	$-0.583309\pi$
$727$	−7.63794e109	−0.517489	−0.258745	+	0.965946i	$0.583309\pi$
$728$	−1.04565e110	−0.671939
$729$	−1.04751e110	−0.638481
$730$	3.48651e109	0.201586
$731$	−2.25179e110	−1.23512
$732$	−1.91257e110	−0.995268
$733$	7.75582e109	0.382934	0.191467	−	0.981499i	$-0.438675\pi$
$733$	7.75582e109	0.382934	0.191467	+	0.981499i	$0.438675\pi$
$734$	−1.16847e109	−0.0547418
$735$	6.52602e109	0.290125
$736$	1.45673e110	0.614586
$737$	7.53418e109	0.301674
$738$	6.02055e109	0.228805
$739$	−9.81957e109	−0.354227	−0.177113	−	0.984190i	$-0.556676\pi$
$739$	−9.81957e109	−0.354227	−0.177113	+	0.984190i	$0.556676\pi$
$740$	−9.02415e109	−0.309019
$741$	7.80907e110	2.53862
$742$	1.16520e110	0.359626
$743$	−2.26801e110	−0.664623	−0.332312	−	0.943170i	$-0.607829\pi$
$743$	−2.26801e110	−0.664623	−0.332312	+	0.943170i	$0.607829\pi$
$744$	−2.55224e110	−0.710172
$745$	8.44488e109	0.223140
$746$	−1.32631e109	−0.0332812
$747$	3.56942e110	0.850658
$748$	−3.66737e110	−0.830124
$749$	−3.30339e110	−0.710248
$750$	−1.71869e110	−0.351025
$751$	1.28796e110	0.249899	0.124949	−	0.992163i	$-0.460123\pi$
$751$	1.28796e110	0.249899	0.124949	+	0.992163i	$0.460123\pi$
$752$	3.71082e110	0.684042
$753$	4.41234e110	0.772791
$754$	3.12926e110	0.520769
$755$	9.59409e109	0.151721
$756$	1.21873e110	0.183154
$757$	−1.08655e111	−1.55188	−0.775941	−	0.630806i	$-0.782724\pi$
$757$	−1.08655e111	−1.55188	−0.775941	+	0.630806i	$0.782724\pi$
$758$	−2.18827e110	−0.297054
$759$	−8.02746e110	−1.03579
$760$	3.23134e110	0.396332
$761$	−1.41251e111	−1.64696	−0.823478	−	0.567348i	$-0.807969\pi$
$761$	−1.41251e111	−1.64696	−0.823478	+	0.567348i	$0.807969\pi$
$762$	−3.48477e110	−0.386285
$763$	−3.54714e110	−0.373838
$764$	1.14780e111	1.15020
$765$	−7.17767e110	−0.683941
$766$	3.68665e109	0.0334060
$767$	1.91731e111	1.65223
$768$	7.84685e110	0.643114
$769$	1.33326e111	1.03932	0.519662	−	0.854372i	$-0.326058\pi$
$769$	1.33326e111	1.03932	0.519662	+	0.854372i	$0.326058\pi$
$770$	1.75260e110	0.129954
$771$	5.16619e110	0.364399
$772$	1.23917e110	0.0831508
$773$	−1.69555e111	−1.08243	−0.541214	−	0.840885i	$-0.682035\pi$
$773$	−1.69555e111	−1.08243	−0.541214	+	0.840885i	$0.682035\pi$
$774$	3.79730e110	0.230647
$775$	7.87006e110	0.454844
$776$	−1.64535e110	−0.0904859
$777$	−9.32322e110	−0.487929
$778$	7.12135e110	0.354689
$779$	2.67771e111	1.26932
$780$	−3.71505e111	−1.67619
$781$	−1.73729e111	−0.746118
$782$	5.77093e110	0.235931
$783$	−7.51594e110	−0.292520
$784$	−6.22638e110	−0.230710
$785$	2.67642e111	0.944220
$786$	−1.06114e111	−0.356455
$787$	−2.59992e111	−0.831635	−0.415817	−	0.909448i	$-0.636504\pi$
$787$	−2.59992e111	−0.831635	−0.415817	+	0.909448i	$0.636504\pi$
$788$	9.42064e110	0.286960
$789$	−3.23819e111	−0.939373
$790$	−6.41666e110	−0.177283
$791$	4.92201e111	1.29523
$792$	1.27445e111	0.319451
$793$	−5.55603e111	−1.32662
$794$	−1.58500e111	−0.360528
$795$	8.53102e111	1.84870
$796$	−1.80189e111	−0.372028
$797$	−6.71474e111	−1.32094	−0.660471	−	0.750852i	$-0.729643\pi$
$797$	−6.71474e111	−1.32094	−0.660471	+	0.750852i	$0.729643\pi$
$798$	1.62001e111	0.303674
$799$	4.90479e111	0.876132
$800$	1.57124e111	0.267471
$801$	2.82389e111	0.458137
$802$	−6.85547e110	−0.106004
$803$	6.11590e111	0.901388
$804$	−3.31311e111	−0.465455
$805$	4.54047e111	0.608078
$806$	−3.59788e111	−0.459354
$807$	3.99578e111	0.486375
$808$	4.34050e111	0.503735
$809$	9.36825e111	1.03667	0.518335	−	0.855178i	$-0.326552\pi$
$809$	9.36825e111	1.03667	0.518335	+	0.855178i	$0.326552\pi$
$810$	−1.99837e111	−0.210864
$811$	−1.71758e112	−1.72828	−0.864140	−	0.503251i	$-0.832137\pi$
$811$	−1.71758e112	−1.72828	−0.864140	+	0.503251i	$0.832137\pi$
$812$	−1.06877e112	−1.02560
$813$	−2.34091e112	−2.14239
$814$	9.61504e110	0.0839289
$815$	−3.71077e110	−0.0308955
$816$	1.50880e112	1.19828
$817$	1.68890e112	1.27954
$818$	1.27695e111	0.0922935
$819$	−1.74206e112	−1.20125
$820$	−1.27388e112	−0.838100
$821$	−2.58019e111	−0.161972	−0.0809862	−	0.996715i	$-0.525807\pi$
$821$	−2.58019e111	−0.161972	−0.0809862	+	0.996715i	$0.525807\pi$
$822$	4.46652e111	0.267549
$823$	2.09935e112	1.20003	0.600014	−	0.799989i	$-0.295162\pi$
$823$	2.09935e112	1.20003	0.600014	+	0.799989i	$0.295162\pi$
$824$	4.87391e111	0.265876
$825$	−8.65845e111	−0.450779
$826$	3.97750e111	0.197642
$827$	3.69477e111	0.175237	0.0876184	−	0.996154i	$-0.472074\pi$
$827$	3.69477e111	0.175237	0.0876184	+	0.996154i	$0.472074\pi$
$828$	1.60220e112	0.725353
$829$	−3.47099e112	−1.50004	−0.750022	−	0.661413i	$-0.769957\pi$
$829$	−3.47099e112	−1.50004	−0.750022	+	0.661413i	$0.769957\pi$
$830$	4.58739e111	0.189260
$831$	1.57208e112	0.619205
$832$	3.04146e112	1.14376
$833$	−8.22974e111	−0.295497
$834$	−4.50606e111	−0.154491
$835$	8.74432e111	0.286284
$836$	2.75061e112	0.859978
$837$	8.64148e111	0.258023
$838$	2.47550e111	0.0705942
$839$	−3.96449e112	−1.07982	−0.539911	−	0.841722i	$-0.681542\pi$
$839$	−3.96449e112	−1.07982	−0.539911	+	0.841722i	$0.681542\pi$
$840$	−1.58821e112	−0.413194
$841$	2.56729e112	0.638012
$842$	−7.95275e111	−0.188800
$843$	7.69400e111	0.174498
$844$	−6.00704e112	−1.30160
$845$	−7.05971e112	−1.46152
$846$	−8.27117e111	−0.163609
$847$	−1.42283e112	−0.268932
$848$	−8.13931e112	−1.47010
$849$	6.86398e112	1.18476
$850$	6.22455e111	0.102678
$851$	2.49096e112	0.392717
$852$	7.63962e112	1.15119
$853$	5.99655e112	0.863701	0.431850	−	0.901945i	$-0.357861\pi$
$853$	5.99655e112	0.863701	0.431850	+	0.901945i	$0.357861\pi$
$854$	−1.15261e112	−0.158692
$855$	5.38342e112	0.708537
$856$	−3.08722e112	−0.388443
$857$	−1.42482e110	−0.00171395	−0.000856975	−	1.00000i	$-0.500273\pi$
$857$	−1.42482e110	−0.00171395	−0.000856975		1.00000i	$0.500273\pi$
$858$	3.95830e112	0.455248
$859$	9.85045e112	1.08323	0.541613	−	0.840628i	$-0.317814\pi$
$859$	9.85045e112	1.08323	0.541613	+	0.840628i	$0.317814\pi$
$860$	−8.03466e112	−0.844845
$861$	−1.31610e113	−1.32333
$862$	−2.89678e112	−0.278539
$863$	−2.63878e112	−0.242654	−0.121327	−	0.992613i	$-0.538715\pi$
$863$	−2.63878e112	−0.242654	−0.121327	+	0.992613i	$0.538715\pi$
$864$	1.72525e112	0.151730
$865$	1.20915e113	1.01709
$866$	4.57232e112	0.367873
$867$	2.35968e112	0.181601
$868$	1.22883e113	0.904653
$869$	−1.12559e113	−0.792716
$870$	4.75292e112	0.320235
$871$	−9.62462e112	−0.620418
$872$	−3.31501e112	−0.204456
$873$	−2.74115e112	−0.161765
$874$	−4.32833e112	−0.244416
$875$	1.70526e113	0.921466
$876$	−2.68943e113	−1.39076
$877$	−1.13802e113	−0.563204	−0.281602	−	0.959531i	$-0.590866\pi$
$877$	−1.13802e113	−0.563204	−0.281602	+	0.959531i	$0.590866\pi$
$878$	−1.21771e112	−0.0576773
$879$	−3.52054e113	−1.59602
$880$	−1.22425e113	−0.531236
$881$	2.76289e113	1.14760	0.573801	−	0.818995i	$-0.305468\pi$
$881$	2.76289e113	1.14760	0.573801	+	0.818995i	$0.305468\pi$
$882$	1.38782e112	0.0551813
$883$	−1.75944e113	−0.669711	−0.334856	−	0.942269i	$-0.608688\pi$
$883$	−1.75944e113	−0.669711	−0.334856	+	0.942269i	$0.608688\pi$
$884$	4.68492e113	1.70722
$885$	2.91213e113	1.01600
$886$	−1.17362e113	−0.392041
$887$	2.09363e113	0.669637	0.334819	−	0.942283i	$-0.391325\pi$
$887$	2.09363e113	0.669637	0.334819	+	0.942283i	$0.391325\pi$
$888$	−8.71312e112	−0.266854
$889$	3.45754e113	1.01403
$890$	3.62923e112	0.101929
$891$	−3.50547e113	−0.942876
$892$	3.05889e113	0.787984
$893$	−3.67870e113	−0.907640
$894$	3.95674e112	0.0935067
$895$	−1.39974e113	−0.316854
$896$	3.23329e113	0.701111
$897$	1.02548e114	2.13018
$898$	−1.48477e113	−0.295474
$899$	−7.57823e113	−1.44484
$900$	1.72814e113	0.315677
$901$	−1.07582e114	−1.88293
$902$	1.35729e113	0.227626
$903$	−8.30094e113	−1.33398
$904$	4.59992e113	0.708379
$905$	3.58119e113	0.528515
$906$	4.49519e112	0.0635788
$907$	−4.90070e113	−0.664320	−0.332160	−	0.943223i	$-0.607777\pi$
$907$	−4.90070e113	−0.664320	−0.332160	+	0.943223i	$0.607777\pi$
$908$	−4.54872e113	−0.590996
$909$	7.23128e113	0.900546
$910$	−2.23888e113	−0.267262
$911$	6.10143e113	0.698191	0.349095	−	0.937087i	$-0.386489\pi$
$911$	6.10143e113	0.698191	0.349095	+	0.937087i	$0.386489\pi$
$912$	−1.13163e114	−1.24138
$913$	8.04703e113	0.846274
$914$	−2.26395e113	−0.228264
$915$	−8.43885e113	−0.815777
$916$	4.01680e113	0.372310
$917$	1.05285e114	0.935719
$918$	6.83468e112	0.0582472
$919$	−1.55226e114	−1.26858	−0.634289	−	0.773096i	$-0.718707\pi$
$919$	−1.55226e114	−1.26858	−0.634289	+	0.773096i	$0.718707\pi$
$920$	4.24334e113	0.332565
$921$	2.61136e114	1.96278
$922$	4.37772e112	0.0315579
$923$	2.21932e114	1.53446
$924$	−1.35193e114	−0.896567
$925$	2.68677e113	0.170912
$926$	6.71283e113	0.409621
$927$	8.11995e113	0.475317
$928$	−1.51297e114	−0.849638
$929$	−1.74661e114	−0.941000	−0.470500	−	0.882400i	$-0.655926\pi$
$929$	−1.74661e114	−0.941000	−0.470500	+	0.882400i	$0.655926\pi$
$930$	−5.46469e113	−0.282470
$931$	6.17249e113	0.306124
$932$	1.31606e114	0.626272
$933$	−4.65169e114	−2.12406
$934$	−7.39523e113	−0.324039
$935$	−1.61816e114	−0.680416
$936$	−1.62806e114	−0.656979
$937$	4.39609e114	1.70252	0.851260	−	0.524744i	$-0.175839\pi$
$937$	4.39609e114	1.70252	0.851260	+	0.524744i	$0.175839\pi$
$938$	−1.99665e113	−0.0742153
$939$	−1.98024e113	−0.0706470
$940$	1.75009e114	0.599291
$941$	−2.67179e114	−0.878216	−0.439108	−	0.898434i	$-0.644706\pi$
$941$	−2.67179e114	−0.878216	−0.439108	+	0.898434i	$0.644706\pi$
$942$	1.25400e114	0.395676
$943$	3.51634e114	1.06510
$944$	−2.77841e114	−0.807933
$945$	5.37741e113	0.150123
$946$	8.56076e113	0.229458
$947$	−2.07210e114	−0.533256	−0.266628	−	0.963799i	$-0.585910\pi$
$947$	−2.07210e114	−0.533256	−0.266628	+	0.963799i	$0.585910\pi$
$948$	4.94970e114	1.22309
$949$	−7.81282e114	−1.85378
$950$	−4.66855e113	−0.106371
$951$	1.52605e114	0.333901
$952$	2.00283e114	0.420845
$953$	1.88972e114	0.381347	0.190673	−	0.981654i	$-0.438933\pi$
$953$	1.88972e114	0.381347	0.190673	+	0.981654i	$0.438933\pi$
$954$	1.81420e114	0.351619
$955$	5.06446e114	0.942764
$956$	−2.51684e114	−0.450014
$957$	8.33739e114	1.43193
$958$	−1.05779e114	−0.174514
$959$	−4.43161e114	−0.702336
$960$	4.61955e114	0.703327
$961$	1.87634e114	0.274449
$962$	−1.22828e114	−0.172607
$963$	−5.14332e114	−0.694434
$964$	−6.28461e114	−0.815291
$965$	5.46763e113	0.0681550
$966$	2.12738e114	0.254815
$967$	−9.22508e114	−1.06182	−0.530910	−	0.847428i	$-0.678150\pi$
$967$	−9.22508e114	−1.06182	−0.530910	+	0.847428i	$0.678150\pi$
$968$	−1.32972e114	−0.147082
$969$	−1.49574e115	−1.58998
$970$	−3.52290e113	−0.0359906
$971$	−1.73859e115	−1.70709	−0.853547	−	0.521016i	$-0.825553\pi$
$971$	−1.73859e115	−1.70709	−0.853547	+	0.521016i	$0.825553\pi$
$972$	1.31319e115	1.23930
$973$	4.47084e114	0.405551
$974$	−3.49654e112	−0.00304873
$975$	1.10608e115	0.927065
$976$	8.05138e114	0.648713
$977$	1.27608e115	0.988409	0.494205	−	0.869346i	$-0.335459\pi$
$977$	1.27608e115	0.988409	0.494205	+	0.869346i	$0.335459\pi$
$978$	−1.73863e113	−0.0129468
$979$	6.36627e114	0.455776
$980$	−2.93647e114	−0.202126
$981$	−5.52282e114	−0.365514
$982$	1.65402e114	0.105256
$983$	5.16933e114	0.316318	0.158159	−	0.987414i	$-0.449444\pi$
$983$	5.16933e114	0.316318	0.158159	+	0.987414i	$0.449444\pi$
$984$	−1.22998e115	−0.723744
$985$	4.15669e114	0.235208
$986$	−5.99374e114	−0.326165
$987$	1.80809e115	0.946257
$988$	−3.51380e115	−1.76862
$989$	2.21783e115	1.07367
$990$	2.72877e114	0.127061
$991$	4.34886e115	1.94778	0.973889	−	0.227023i	$-0.0728993\pi$
$991$	4.34886e115	1.94778	0.973889	+	0.227023i	$0.0728993\pi$
$992$	1.73955e115	0.749440
$993$	−4.35247e115	−1.80381
$994$	4.60404e114	0.183554
$995$	−7.95052e114	−0.304935
$996$	−3.53863e115	−1.30572
$997$	8.08512e114	0.287027	0.143514	−	0.989648i	$-0.454160\pi$
$997$	8.08512e114	0.287027	0.143514	+	0.989648i	$0.454160\pi$
$998$	−8.11299e114	−0.277112
$999$	2.95012e114	0.0969547

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1.78.a.a.1.3	✓	6
3.2	odd	2		9.78.a.a.1.4		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1.78.a.a.1.3	✓	6	1.1	even	1	trivial
9.78.a.a.1.4		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)

\(f(q)\)	\(=\)	\(q-9.30224e10 q^{2} +3.16609e18 q^{3} -1.42463e23 q^{4} -6.28590e26 q^{5} -2.94518e29 q^{6} +2.92216e32 q^{7} +2.73094e34 q^{8} +4.54975e36 q^{9} +O(q^{10})\)	\(q-9.30224e10 q^{2} +3.16609e18 q^{3} -1.42463e23 q^{4} -6.28590e26 q^{5} -2.94518e29 q^{6} +2.92216e32 q^{7} +2.73094e34 q^{8} +4.54975e36 q^{9} +5.84729e37 q^{10} +1.02571e40 q^{11} -4.51050e41 q^{12} -1.31031e43 q^{13} -2.71826e43 q^{14} -1.99017e45 q^{15} +1.89880e46 q^{16} +2.50974e47 q^{17} -4.23229e47 q^{18} -1.88236e49 q^{19} +8.95505e49 q^{20} +9.25183e50 q^{21} -9.54141e50 q^{22} -2.47189e52 q^{23} +8.64640e52 q^{24} -2.66619e53 q^{25} +1.21888e54 q^{26} -2.92753e54 q^{27} -4.16298e55 q^{28} +2.56733e56 q^{29} +1.85131e56 q^{30} -2.95180e57 q^{31} -5.89318e57 q^{32} +3.24750e58 q^{33} -2.33462e58 q^{34} -1.83684e59 q^{35} -6.48169e59 q^{36} -1.00772e60 q^{37} +1.75102e60 q^{38} -4.14855e61 q^{39} -1.71664e61 q^{40} -1.42253e62 q^{41} -8.60628e61 q^{42} -8.97221e62 q^{43} -1.46125e63 q^{44} -2.85993e63 q^{45} +2.29941e63 q^{46} +1.95430e64 q^{47} +6.01176e64 q^{48} -3.27912e64 q^{49} +2.48016e64 q^{50} +7.94607e65 q^{51} +1.86669e66 q^{52} -4.28657e66 q^{53} +2.72326e65 q^{54} -6.44752e66 q^{55} +7.98023e66 q^{56} -5.95974e67 q^{57} -2.38819e67 q^{58} -1.46325e68 q^{59} +2.83525e68 q^{60} +4.24026e68 q^{61} +2.74583e68 q^{62} +1.32951e69 q^{63} -2.32118e69 q^{64} +8.23645e69 q^{65} -3.02090e69 q^{66} +7.34532e69 q^{67} -3.57544e70 q^{68} -7.82624e70 q^{69} +1.70867e70 q^{70} -1.69374e71 q^{71} +1.24251e71 q^{72} +5.96260e71 q^{73} +9.37402e70 q^{74} -8.44142e71 q^{75} +2.68166e72 q^{76} +2.99729e72 q^{77} +3.85908e72 q^{78} -1.09737e73 q^{79} -1.19356e73 q^{80} -3.41760e73 q^{81} +1.32327e73 q^{82} +7.84532e73 q^{83} -1.31804e74 q^{84} -1.57760e74 q^{85} +8.34617e73 q^{86} +8.12840e74 q^{87} +2.80115e74 q^{88} +6.20669e74 q^{89} +2.66037e74 q^{90} -3.82892e75 q^{91} +3.52152e75 q^{92} -9.34567e75 q^{93} -1.81794e75 q^{94} +1.18323e76 q^{95} -1.86584e76 q^{96} -6.02484e75 q^{97} +3.05032e75 q^{98} +4.66673e76 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 264721893120 q^{2} + 14\!\cdots\!80 q^{3}+ \cdots - 48\!\cdots\!42 q^{9}+O(q^{10}) \) 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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