LMFDB - Embedded newform 2.76.a.b.1.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [2,76,Mod(1,2)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("2.1"); S:= CuspForms(chi, 76); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(2, base_ring=CyclotomicField(1)) chi = DirichletCharacter(H, H._module([])) N = Newforms(chi, 76, names="a")

Level:	$ N $	$=$	$ 2 $
Weight:	$ k $	$=$	$ 76 $
Character orbit:	$[\chi]$	$=$	2.a (trivial)

Newform invariants

comment:select newform

sage:traces = [3,412316860416] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$71.2456785644$
Analytic rank:	$1$
Dimension:	$3$
Coefficient field:	$\mathbb{Q}[x]/(x^{3} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - x^{2} - 69170275937846809816619130x + 194820240227429941309097792198860377672 $ x^3 - x^2 - 69170275937846809816619130*x + 194820240227429941309097792198860377672
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{24}\cdot 3^{8}\cdot 5^{3}\cdot 7\cdot 11 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$6.10323e12$ of defining polynomial
Character	$\chi$	$=$	2.1

$q$-expansion

comment:q-expansion

sage:f.q_expansion() # note that sage often uses an isomorphic number field

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+1.37439e11 q^{2} +7.85531e17 q^{3} +1.88895e22 q^{4} +1.02529e26 q^{5} +1.07962e29 q^{6} -9.01778e31 q^{7} +2.59615e33 q^{8} +8.79144e33 q^{9} +1.40915e37 q^{10} +1.29798e39 q^{11} +1.48383e40 q^{12} -8.54396e41 q^{13} -1.23939e43 q^{14} +8.05398e43 q^{15} +3.56812e44 q^{16} -1.96919e46 q^{17} +1.20829e45 q^{18} +1.45015e47 q^{19} +1.93672e48 q^{20} -7.08374e49 q^{21} +1.78393e50 q^{22} -9.62630e50 q^{23} +2.03935e51 q^{24} -1.59575e52 q^{25} -1.17427e53 q^{26} -4.70906e53 q^{27} -1.70341e54 q^{28} +6.83539e54 q^{29} +1.10693e55 q^{30} -2.27798e55 q^{31} +4.90399e55 q^{32} +1.01960e57 q^{33} -2.70643e57 q^{34} -9.24586e57 q^{35} +1.66066e56 q^{36} -6.31677e58 q^{37} +1.99307e58 q^{38} -6.71154e59 q^{39} +2.66181e59 q^{40} +3.47026e60 q^{41} -9.73582e60 q^{42} -1.32858e61 q^{43} +2.45182e61 q^{44} +9.01379e59 q^{45} -1.32303e62 q^{46} +4.14273e62 q^{47} +2.80287e62 q^{48} +5.72018e63 q^{49} -2.19319e63 q^{50} -1.54686e64 q^{51} -1.61391e64 q^{52} +1.50768e64 q^{53} -6.47209e64 q^{54} +1.33081e65 q^{55} -2.34115e65 q^{56} +1.13913e65 q^{57} +9.39448e65 q^{58} -1.88385e66 q^{59} +1.52135e66 q^{60} +2.68011e66 q^{61} -3.13083e66 q^{62} -7.92793e65 q^{63} +6.73999e66 q^{64} -8.76006e67 q^{65} +1.40133e68 q^{66} -3.70871e68 q^{67} -3.71969e68 q^{68} -7.56175e68 q^{69} -1.27074e69 q^{70} +2.25253e69 q^{71} +2.28239e67 q^{72} -2.96144e69 q^{73} -8.68170e69 q^{74} -1.25351e70 q^{75} +2.73925e69 q^{76} -1.17049e71 q^{77} -9.22428e70 q^{78} -2.41694e71 q^{79} +3.65836e70 q^{80} -3.75259e71 q^{81} +4.76949e71 q^{82} +9.02951e70 q^{83} -1.33808e72 q^{84} -2.01899e72 q^{85} -1.82599e72 q^{86} +5.36941e72 q^{87} +3.36975e72 q^{88} -1.80794e73 q^{89} +1.23885e71 q^{90} +7.70476e73 q^{91} -1.81836e73 q^{92} -1.78942e73 q^{93} +5.69372e73 q^{94} +1.48682e73 q^{95} +3.85223e73 q^{96} +5.17925e74 q^{97} +7.86175e74 q^{98} +1.14111e73 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q + 412316860416 q^{2} + 45\!\cdots\!16 q^{3} + 56\!\cdots\!52 q^{4} - 19\!\cdots\!90 q^{5} + 62\!\cdots\!52 q^{6} - 37\!\cdots\!52 q^{7} + 77\!\cdots\!44 q^{8} - 26\!\cdots\!69 q^{9} - 26\!\cdots\!80 q^{10}+ \cdots + 90\!\cdots\!32 q^{99}+O(q^{100}) $ 3 * q + 412316860416 * q^2 + 458242166228809716 * q^3 + 56668397794435742564352 * q^4 - 195317864575755505617919590 * q^5 + 62980323763229868263265533952 * q^6 - 37066282910854192405810923152952 * q^7 + 7788445287802241442795744493830144 * q^8 - 267707440809547675110176979472664769 * q^9 - 26844282901677657955869085139447316480 * q^10 + 1089522657174857887018090027503932523516 * q^11 + 8655949787346045808675641167610164281344 * q^12 - 200775423127509346148989234344235815084894 * q^13 - 5094351132364878073838383209647937467449344 * q^14 + 227412712084025466854308442890234618066471320 * q^15 + 1070435769529469910793714477087121352287059968 * q^16 - 13964607281546105485967748168451725560455001322 * q^17 - 36793430501531616932833386355429072282444627968 * q^18 - 2115042489507394854414232114360954083096137041020 * q^19 - 3689450148712880782538621821803706361489978818560 * q^20 - 23475337414840802232472405760772442593547635795744 * q^21 + 149742853786145100102091508112420182396543069847552 * q^22 + 116856323604290944270046589717244430012820187772376 * q^23 + 1189664680079021484261752060374941122097914333626368 * q^24 - 13677553808937057350680884197678632002550617150091275 * q^25 - 27594364037542869748616073758866330620848742196051968 * q^26 - 516713355711438316758259090904905946273936306702420280 * q^27 - 700162288251126990917226530398508899089535904532922368 * q^28 - 4685039575774269774425123141334628221923373816078325710 * q^29 + 31255365155057708293452376285127724875601442352702423040 * q^30 + 19810012207866372881154886539183629090472506922981842976 * q^31 + 147119571923125330402401314606429681627398955729625808896 * q^32 - 1585737135797838535515313355184995617533368424120408715248 * q^33 - 1919281010423167596108725289416449927581488049844056489984 * q^34 - 10950361456133471021484484744548030403192620947333255249040 * q^35 - 5056850582775269524368615136432015920023032065710301904896 * q^36 - 45940866101102779827043188076640168610273759105645032828742 * q^37 - 290689226306709889595769861380263351240178400483683535421440 * q^38 - 1672442610320761978222551615006671064699371016431534859756168 * q^39 - 507074167326213102558408594609883473733971611438333370040320 * q^40 + 362400026981966097502505178180515117776287761483498293835886 * q^41 - 3226425806697805780315928702878708500394384523546861311623168 * q^42 - 28702095070206583225102323926867241705153753782220140424278244 * q^43 + 20580501114278495451172137233349227993712236430421745461100544 * q^44 + 9961130143898573860468040684586213478623455196227513865892770 * q^45 + 16060610822759118429081878247420630852583154150749888390889472 * q^46 + 1440358153753731871262284486476744104832092319767060853177135408 * q^47 + 163506268612662399058739321695071667754754719127516276584349696 * q^48 + 5851233763188937006285451636437763810170039730055265549739289339 * q^49 - 1879828681557276602996825630764573554207164455816279985278156800 * q^50 - 13135245964480362237443576676736477680682849131997768459350096984 * q^51 - 3792540515045284536585400897736149761666199151832909532046032896 * q^52 - 66482008582006413625317152148536776263636987496863720447690376374 * q^53 - 71016542853985356275136369066600386726479663823165462612709212160 * q^54 - 128059259461243668378349058265162253832978578499704027402037026680 * q^55 - 96229572157795694756236063714724658200144668345173751227740061696 * q^56 + 541881412323488933705214064356590630418338964926058970501983678960 * q^57 - 643906936269318481901990434969760448175344664257252092764351365120 * q^58 - 371683568940617616838543919579672241129155497105032841329863886420 * q^59 + 4295704677296346435618749666499505584755003623529158533656220794880 * q^60 + 13573422560821853027615494323023031372615121991355370424474791441746 * q^61 + 2722667346116698414806449036684297903429556557482899404279274012672 * q^62 - 26481097073687004346685625189284323701988206005717909402281686334104 * q^63 + 20219960000362979846000261315264723005227858316905429360827707686912 * q^64 - 283941175814397704527430731718044717252185233543246078490644938760580 * q^65 - 217942052425741676080857771766770822630692530250118815940593168941056 * q^66 - 413223374254023917043840598633408380930841273575662432347998564181452 * q^67 - 263783973491242878272445183305337195628289905571041296782650610024448 * q^68 - 1061510208317927203185294055302976167343619039092488023800560677951328 * q^69 - 1505006218671110292743666411175830556253632030634267830651108332666880 * q^70 - 5329648930387886406281280512948717239625311590459101731821120548966904 * q^71 - 695008251960906352791957665913154768123208777247522230138074312998912 * q^72 - 6126925276337568901196002641779188883652596184658648256377551348614514 * q^73 - 6314064558532847004538848933399893303713650078903283999497384282292224 * q^74 - 42136550820801138510743282158837727891370079859020453164369744977721300 * q^75 - 39952023049179578917555270866261904430205672681056363719959756071239680 * q^76 - 289482613480384241434628541067945562255609470975872005377156987184398944 * q^77 - 229858762104465432520515948676020321430825554794999067063574019017015296 * q^78 - 622218748753103295378700837548188457771583126386550471357575046848039600 * q^79 - 69691742890000545248481882996952684737865058410241963042196499243991040 * q^80 - 813867571538426179661468949362446700360464407612291411834932342915810277 * q^81 + 49807880446625983057728224587390886889047813755413555702301720357896192 * q^82 - 1533020732833757587948568401531575056248575332031888360930290411083590204 * q^83 - 443436586327599794605333578455416130045154708181833960219813479549239296 * q^84 - 2509870850873749953965285441354116293863644192517282543162006812905493740 * q^85 - 3944785908903043165302934000623779163435604708680697900633683916297863168 * q^86 + 7656197026313956905810590821633236160642701737759808104389066992317050680 * q^87 + 2828562535075766291163811017077083352954935971317797639765224852729888768 * q^88 - 9273679405251457383346320465116747436209848620322393707782099041195555170 * q^89 + 1369047302375812757496022463791847621861188325322189908140671263771197440 * q^90 + 37855086806940858491220205001548043782409020136053538320652371512227893296 * q^91 + 2207353543601090116438321996125612987761063814335917584464651090902646784 * q^92 + 116428442792693075708882307667561815114456133894684752952005955774351769472 * q^93 + 197961317276774976800780611445304646234068226708873622478004936714355736576 * q^94 + 357878094222078480931183160357756124777870531843559815899687819400578887800 * q^95 + 22472130444236041454277970229425795116251176548939137972399120951921344512 * q^96 + 1302609856697415284410811597650709289615858746443991563079136355124529279078 * q^97 + 804187444932719779552005159010876080129685530867457081879222689193166635008 * q^98 + 904093342516791279625791645893932380898957972599927163310277116835911049132 * q^99

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	1.37439e11	0.707107
$2$	1.37439e11	0.707107
$3$	7.85531e17	1.00720	0.503600	−	0.863937i	$-0.332008\pi$
$3$	7.85531e17	1.00720	0.503600	+	0.863937i	$0.332008\pi$
$4$	1.88895e22	0.500000
$5$	1.02529e26	0.630191	0.315096	−	0.949060i	$-0.397963\pi$
$5$	1.02529e26	0.630191	0.315096	+	0.949060i	$0.397963\pi$
$6$	1.07962e29	0.712198
$7$	−9.01778e31	−1.83621	−0.918107	−	0.396332i	$-0.870283\pi$
$7$	−9.01778e31	−1.83621	−0.918107	+	0.396332i	$0.870283\pi$
$8$	2.59615e33	0.353553
$9$	8.79144e33	0.0144533
$10$	1.40915e37	0.445613
$11$	1.29798e39	1.15091	0.575457	−	0.817832i	$-0.304824\pi$
$11$	1.29798e39	1.15091	0.575457	+	0.817832i	$0.304824\pi$
$12$	1.48383e40	0.503600
$13$	−8.54396e41	−1.44140	−0.720699	−	0.693249i	$-0.756179\pi$
$13$	−8.54396e41	−1.44140	−0.720699	+	0.693249i	$0.756179\pi$
$14$	−1.23939e43	−1.29840
$15$	8.05398e43	0.634729
$16$	3.56812e44	0.250000
$17$	−1.96919e46	−1.42054	−0.710269	−	0.703931i	$-0.751427\pi$
$17$	−1.96919e46	−1.42054	−0.710269	+	0.703931i	$0.751427\pi$
$18$	1.20829e45	0.0102200
$19$	1.45015e47	0.161492	0.0807462	−	0.996735i	$-0.474270\pi$
$19$	1.45015e47	0.161492	0.0807462	+	0.996735i	$0.474270\pi$
$20$	1.93672e48	0.315096
$21$	−7.08374e49	−1.84944
$22$	1.78393e50	0.813819
$23$	−9.62630e50	−0.829212	−0.414606	−	0.910001i	$-0.636081\pi$
$23$	−9.62630e50	−0.829212	−0.414606	+	0.910001i	$0.636081\pi$
$24$	2.03935e51	0.356099
$25$	−1.59575e52	−0.602859
$26$	−1.17427e53	−1.01922
$27$	−4.70906e53	−0.992643
$28$	−1.70341e54	−0.918107
$29$	6.83539e54	0.988185	0.494092	−	0.869409i	$-0.335500\pi$
$29$	6.83539e54	0.988185	0.494092	+	0.869409i	$0.335500\pi$
$30$	1.10693e55	0.448821
$31$	−2.27798e55	−0.270076	−0.135038	−	0.990840i	$-0.543116\pi$
$31$	−2.27798e55	−0.270076	−0.135038	+	0.990840i	$0.543116\pi$
$32$	4.90399e55	0.176777
$33$	1.01960e57	1.15920
$34$	−2.70643e57	−1.00447
$35$	−9.24586e57	−1.15717
$36$	1.66066e56	0.00722663
$37$	−6.31677e58	−0.983853	−0.491927	−	0.870637i	$-0.663707\pi$
$37$	−6.31677e58	−0.983853	−0.491927	+	0.870637i	$0.663707\pi$
$38$	1.99307e58	0.114192
$39$	−6.71154e59	−1.45178
$40$	2.66181e59	0.222806
$41$	3.47026e60	1.15071	0.575357	−	0.817903i	$-0.304863\pi$
$41$	3.47026e60	1.15071	0.575357	+	0.817903i	$0.304863\pi$
$42$	−9.73582e60	−1.30775
$43$	−1.32858e61	−0.738450	−0.369225	−	0.929340i	$-0.620377\pi$
$43$	−1.32858e61	−0.738450	−0.369225	+	0.929340i	$0.620377\pi$
$44$	2.45182e61	0.575457
$45$	9.01379e59	0.00910832
$46$	−1.32303e62	−0.586341
$47$	4.14273e62	0.819628	0.409814	−	0.912169i	$-0.365594\pi$
$47$	4.14273e62	0.819628	0.409814	+	0.912169i	$0.365594\pi$
$48$	2.80287e62	0.251800
$49$	5.72018e63	2.37168
$50$	−2.19319e63	−0.426286
$51$	−1.54686e64	−1.43077
$52$	−1.61391e64	−0.720699
$53$	1.50768e64	0.329582	0.164791	−	0.986328i	$-0.447305\pi$
$53$	1.50768e64	0.329582	0.164791	+	0.986328i	$0.447305\pi$
$54$	−6.47209e64	−0.701905
$55$	1.33081e65	0.725296
$56$	−2.34115e65	−0.649200
$57$	1.13913e65	0.162655
$58$	9.39448e65	0.698752
$59$	−1.88385e66	−0.738066	−0.369033	−	0.929416i	$-0.620311\pi$
$59$	−1.88385e66	−0.738066	−0.369033	+	0.929416i	$0.620311\pi$
$60$	1.52135e66	0.317365
$61$	2.68011e66	0.300804	0.150402	−	0.988625i	$-0.451943\pi$
$61$	2.68011e66	0.300804	0.150402	+	0.988625i	$0.451943\pi$
$62$	−3.13083e66	−0.190973
$63$	−7.92793e65	−0.0265393
$64$	6.73999e66	0.125000
$65$	−8.76006e67	−0.908356
$66$	1.40133e68	0.819679
$67$	−3.70871e68	−1.23429	−0.617146	−	0.786849i	$-0.711711\pi$
$67$	−3.70871e68	−1.23429	−0.617146	+	0.786849i	$0.711711\pi$
$68$	−3.71969e68	−0.710269
$69$	−7.56175e68	−0.835182
$70$	−1.27074e69	−0.818240
$71$	2.25253e69	0.852083	0.426041	−	0.904704i	$-0.359908\pi$
$71$	2.25253e69	0.852083	0.426041	+	0.904704i	$0.359908\pi$
$72$	2.28239e67	0.00511000
$73$	−2.96144e69	−0.395271	−0.197636	−	0.980276i	$-0.563326\pi$
$73$	−2.96144e69	−0.395271	−0.197636	+	0.980276i	$0.563326\pi$
$74$	−8.68170e69	−0.695689
$75$	−1.25351e70	−0.607200
$76$	2.73925e69	0.0807462
$77$	−1.17049e71	−2.11333
$78$	−9.22428e70	−1.02656
$79$	−2.41694e71	−1.66821	−0.834103	−	0.551608i	$-0.814014\pi$
$79$	−2.41694e71	−1.66821	−0.834103	+	0.551608i	$0.814014\pi$
$80$	3.65836e70	0.157548
$81$	−3.75259e71	−1.01424
$82$	4.76949e71	0.813677
$83$	9.02951e70	0.0977768	0.0488884	−	0.998804i	$-0.484432\pi$
$83$	9.02951e70	0.0977768	0.0488884	+	0.998804i	$0.484432\pi$
$84$	−1.33808e72	−0.924718
$85$	−2.01899e72	−0.895210
$86$	−1.82599e72	−0.522163
$87$	5.36941e72	0.995301
$88$	3.36975e72	0.406910
$89$	−1.80794e73	−1.42909	−0.714545	−	0.699590i	$-0.753366\pi$
$89$	−1.80794e73	−1.42909	−0.714545	+	0.699590i	$0.753366\pi$
$90$	1.23885e71	0.00644055
$91$	7.70476e73	2.64671
$92$	−1.81836e73	−0.414606
$93$	−1.78942e73	−0.272021
$94$	5.69372e73	0.579565
$95$	1.48682e73	0.101771
$96$	3.85223e73	0.178050
$97$	5.17925e74	1.62303	0.811516	−	0.584331i	$-0.198643\pi$
$97$	5.17925e74	1.62303	0.811516	+	0.584331i	$0.198643\pi$
$98$	7.86175e74	1.67703
$99$	1.14111e73	0.0166345
$100$	−3.01429e74	−0.301429
$101$	−7.35239e74	−0.506264	−0.253132	−	0.967432i	$-0.581461\pi$
$101$	−7.35239e74	−0.506264	−0.253132	+	0.967432i	$0.581461\pi$
$102$	−2.12598e75	−1.01170
$103$	2.79143e75	0.921363	0.460681	−	0.887566i	$-0.347605\pi$
$103$	2.79143e75	0.921363	0.460681	+	0.887566i	$0.347605\pi$
$104$	−2.21814e75	−0.509611
$105$	−7.26291e75	−1.16550
$106$	2.07214e75	0.233050
$107$	−2.24267e76	−1.77367	−0.886835	−	0.462086i	$-0.847101\pi$
$107$	−2.24267e76	−1.77367	−0.886835	+	0.462086i	$0.847101\pi$
$108$	−8.89517e75	−0.496322
$109$	3.99273e76	1.57680	0.788399	−	0.615164i	$-0.210910\pi$
$109$	3.99273e76	1.57680	0.788399	+	0.615164i	$0.210910\pi$
$110$	1.82905e76	0.512862
$111$	−4.96201e76	−0.990938
$112$	−3.21765e76	−0.459054
$113$	−8.24272e76	−0.842615	−0.421307	−	0.906918i	$-0.638429\pi$
$113$	−8.24272e76	−0.842615	−0.421307	+	0.906918i	$0.638429\pi$
$114$	1.56562e76	0.115015
$115$	−9.86977e76	−0.522562
$116$	1.29117e77	0.494092
$117$	−7.51137e75	−0.0208329
$118$	−2.58914e77	−0.521891
$119$	1.77577e78	2.60841
$120$	2.09093e77	0.224411
$121$	4.12862e77	0.324604
$122$	3.68352e77	0.212701
$123$	2.72599e78	1.15900
$124$	−4.30298e77	−0.135038
$125$	−4.35004e78	−1.01011
$126$	−1.08961e77	−0.0187661
$127$	5.25547e78	0.672933	0.336467	−	0.941695i	$-0.390768\pi$
$127$	5.25547e78	0.672933	0.336467	+	0.941695i	$0.390768\pi$
$128$	9.26337e77	0.0883883
$129$	−1.04364e79	−0.743767
$130$	−1.20397e79	−0.642305
$131$	−2.32241e79	−0.929534	−0.464767	−	0.885433i	$-0.653862\pi$
$131$	−2.32241e79	−0.929534	−0.464767	+	0.885433i	$0.653862\pi$
$132$	1.92598e79	0.579601
$133$	−1.30771e79	−0.296535
$134$	−5.09721e79	−0.872776
$135$	−4.82816e79	−0.625555
$136$	−5.11230e79	−0.502236
$137$	1.23025e80	0.918273	0.459137	−	0.888366i	$-0.348159\pi$
$137$	1.23025e80	0.918273	0.459137	+	0.888366i	$0.348159\pi$
$138$	−1.03928e80	−0.590563
$139$	3.79063e80	1.64307	0.821536	−	0.570156i	$-0.193117\pi$
$139$	3.79063e80	1.64307	0.821536	+	0.570156i	$0.193117\pi$
$140$	−1.74649e80	−0.578583
$141$	3.25424e80	0.825530
$142$	3.09585e80	0.602514
$143$	−1.10899e81	−1.65892
$144$	3.13689e78	0.00361331
$145$	7.00827e80	0.622746
$146$	−4.07017e80	−0.279499
$147$	4.49337e81	2.38876
$148$	−1.19320e81	−0.491927
$149$	2.96376e81	0.949199	0.474600	−	0.880202i	$-0.342593\pi$
$149$	2.96376e81	0.949199	0.474600	+	0.880202i	$0.342593\pi$
$150$	−1.72282e81	−0.429355
$151$	1.22543e81	0.238041	0.119021	−	0.992892i	$-0.462025\pi$
$151$	1.22543e81	0.238041	0.119021	+	0.992892i	$0.462025\pi$
$152$	3.76480e80	0.0570962
$153$	−1.73120e80	−0.0205314
$154$	−1.60871e82	−1.49435
$155$	−2.33559e81	−0.170200
$156$	−1.26777e82	−0.725888
$157$	−1.69000e82	−0.761463	−0.380731	−	0.924686i	$-0.624328\pi$
$157$	−1.69000e82	−0.761463	−0.380731	+	0.924686i	$0.624328\pi$
$158$	−3.32182e82	−1.17960
$159$	1.18433e82	0.331956
$160$	5.02802e81	0.111403
$161$	8.68079e82	1.52261
$162$	−5.15752e82	−0.717179
$163$	−4.91000e82	−0.542058	−0.271029	−	0.962571i	$-0.587364\pi$
$163$	−4.91000e82	−0.542058	−0.271029	+	0.962571i	$0.587364\pi$
$164$	6.55513e82	0.575357
$165$	1.04539e83	0.730519
$166$	1.24101e82	0.0691386
$167$	2.21709e83	0.986087	0.493044	−	0.870005i	$-0.335884\pi$
$167$	2.21709e83	0.986087	0.493044	+	0.870005i	$0.335884\pi$
$168$	−1.83905e83	−0.653874
$169$	3.78634e83	1.07763
$170$	−2.77488e83	−0.633009
$171$	1.27489e81	0.00233409
$172$	−2.50962e83	−0.369225
$173$	1.61653e83	0.191362	0.0956810	−	0.995412i	$-0.469497\pi$
$173$	1.61653e83	0.191362	0.0956810	+	0.995412i	$0.469497\pi$
$174$	7.37965e83	0.703784
$175$	1.43902e84	1.10698
$176$	4.63135e83	0.287729
$177$	−1.47982e84	−0.743380
$178$	−2.48482e84	−1.01052
$179$	−3.73094e84	−1.22979	−0.614893	−	0.788611i	$-0.710801\pi$
$179$	−3.73094e84	−1.22979	−0.614893	+	0.788611i	$0.710801\pi$
$180$	1.70266e82	0.00455416
$181$	−7.18396e84	−1.56105	−0.780526	−	0.625123i	$-0.785049\pi$
$181$	−7.18396e84	−1.56105	−0.780526	+	0.625123i	$0.785049\pi$
$182$	1.05893e85	1.87151
$183$	2.10531e84	0.302970
$184$	−2.49913e84	−0.293171
$185$	−6.47653e84	−0.620016
$186$	−2.45936e84	−0.192348
$187$	−2.55597e85	−1.63492
$188$	7.82539e84	0.409814
$189$	4.24653e85	1.82271
$190$	2.04348e84	0.0719630
$191$	−3.04594e85	−0.880988	−0.440494	−	0.897756i	$-0.645197\pi$
$191$	−3.04594e85	−0.880988	−0.440494	+	0.897756i	$0.645197\pi$
$192$	5.29447e84	0.125900
$193$	7.27211e85	1.42318	0.711592	−	0.702592i	$-0.247974\pi$
$193$	7.27211e85	1.42318	0.711592	+	0.702592i	$0.247974\pi$
$194$	7.11831e85	1.14766
$195$	−6.88129e85	−0.914897
$196$	1.08051e86	1.18584
$197$	3.98372e85	0.361248	0.180624	−	0.983552i	$-0.442188\pi$
$197$	3.98372e85	0.361248	0.180624	+	0.983552i	$0.442188\pi$
$198$	1.56833e84	0.0117623
$199$	5.61638e85	0.348712	0.174356	−	0.984683i	$-0.444216\pi$
$199$	5.61638e85	0.348712	0.174356	+	0.984683i	$0.444216\pi$
$200$	−4.14281e85	−0.213143
$201$	−2.91330e86	−1.24318
$202$	−1.01051e86	−0.357983
$203$	−6.16400e86	−1.81452
$204$	−2.92193e86	−0.715383
$205$	3.55803e86	0.725170
$206$	3.83651e86	0.651502
$207$	−8.46290e84	−0.0119848
$208$	−3.04859e86	−0.360349
$209$	1.88226e86	0.185864
$210$	−9.98207e86	−0.824132
$211$	1.55868e87	1.07687	0.538436	−	0.842666i	$-0.319015\pi$
$211$	1.55868e87	1.07687	0.538436	+	0.842666i	$0.319015\pi$
$212$	2.84793e86	0.164791
$213$	1.76943e87	0.858218
$214$	−3.08230e87	−1.25417
$215$	−1.36218e87	−0.465365
$216$	−1.22254e87	−0.350952
$217$	2.05423e87	0.495917
$218$	5.48756e87	1.11496
$219$	−2.32630e87	−0.398118
$220$	2.51383e87	0.362648
$221$	1.68247e88	2.04756
$222$	−6.81974e87	−0.700699
$223$	4.75168e87	0.412491	0.206246	−	0.978500i	$-0.433875\pi$
$223$	4.75168e87	0.412491	0.206246	+	0.978500i	$0.433875\pi$
$224$	−4.42231e87	−0.324600
$225$	−1.40290e86	−0.00871327
$226$	−1.13287e88	−0.595818
$227$	−6.13164e87	−0.273280	−0.136640	−	0.990621i	$-0.543630\pi$
$227$	−6.13164e87	−0.273280	−0.136640	+	0.990621i	$0.543630\pi$
$228$	2.15177e87	0.0813276
$229$	2.03715e88	0.653420	0.326710	−	0.945125i	$-0.394060\pi$
$229$	2.03715e88	0.653420	0.326710	+	0.945125i	$0.394060\pi$
$230$	−1.35649e88	−0.369507
$231$	−9.19457e88	−2.12854
$232$	1.77457e88	0.349376
$233$	−4.65710e88	−0.780312	−0.390156	−	0.920749i	$-0.627579\pi$
$233$	−4.65710e88	−0.780312	−0.390156	+	0.920749i	$0.627579\pi$
$234$	−1.03235e87	−0.0147311
$235$	4.24751e88	0.516523
$236$	−3.55848e88	−0.369033
$237$	−1.89858e89	−1.68022
$238$	2.44060e89	1.84442
$239$	1.90246e89	1.22855	0.614276	−	0.789091i	$-0.289448\pi$
$239$	1.90246e89	1.22855	0.614276	+	0.789091i	$0.289448\pi$
$240$	2.87376e88	0.158682
$241$	−1.84010e89	−0.869364	−0.434682	−	0.900584i	$-0.643139\pi$
$241$	−1.84010e89	−0.869364	−0.434682	+	0.900584i	$0.643139\pi$
$242$	5.67433e88	0.229529
$243$	−8.34060e87	−0.0289043
$244$	5.06259e88	0.150402
$245$	5.86485e89	1.49461
$246$	3.74658e89	0.819536
$247$	−1.23900e89	−0.232775
$248$	−5.91397e88	−0.0954863
$249$	7.09296e88	0.0984808
$250$	−5.97865e89	−0.714254
$251$	3.38690e89	0.348367	0.174184	−	0.984713i	$-0.444271\pi$
$251$	3.38690e89	0.348367	0.174184	+	0.984713i	$0.444271\pi$
$252$	−1.49754e88	−0.0132696
$253$	−1.24948e90	−0.954351
$254$	7.22307e89	0.475836
$255$	−1.58598e90	−0.901656
$256$	1.27315e89	0.0625000
$257$	−3.97231e90	−1.68481	−0.842405	−	0.538845i	$-0.818861\pi$
$257$	−3.97231e90	−1.68481	−0.842405	+	0.538845i	$0.818861\pi$
$258$	−1.43437e90	−0.525923
$259$	5.69633e90	1.80657
$260$	−1.65473e90	−0.454178
$261$	6.00929e88	0.0142825
$262$	−3.19189e90	−0.657280
$263$	8.11187e90	1.44804	0.724020	−	0.689779i	$-0.242292\pi$
$263$	8.11187e90	1.44804	0.724020	+	0.689779i	$0.242292\pi$
$264$	2.64704e90	0.409840
$265$	1.54581e90	0.207700
$266$	−1.79730e90	−0.209682
$267$	−1.42019e91	−1.43938
$268$	−7.00555e90	−0.617146
$269$	7.31405e89	0.0560335	0.0280167	−	0.999607i	$-0.491081\pi$
$269$	7.31405e89	0.0560335	0.0280167	+	0.999607i	$0.491081\pi$
$270$	−6.63578e90	−0.442334
$271$	2.83610e91	1.64578	0.822892	−	0.568198i	$-0.192359\pi$
$271$	2.83610e91	1.64578	0.822892	+	0.568198i	$0.192359\pi$
$272$	−7.02630e90	−0.355134
$273$	6.05233e91	2.66577
$274$	1.69084e91	0.649317
$275$	−2.07126e91	−0.693839
$276$	−1.42837e91	−0.417591
$277$	−1.73164e91	−0.442044	−0.221022	−	0.975269i	$-0.570939\pi$
$277$	−1.73164e91	−0.442044	−0.221022	+	0.975269i	$0.570939\pi$
$278$	5.20981e91	1.16183
$279$	−2.00267e89	−0.00390348
$280$	−2.40036e91	−0.409120
$281$	−8.47169e91	−1.26323	−0.631616	−	0.775281i	$-0.717608\pi$
$281$	−8.47169e91	−1.26323	−0.631616	+	0.775281i	$0.717608\pi$
$282$	4.47259e91	0.583738
$283$	−1.28047e92	−1.46346	−0.731728	−	0.681597i	$-0.761286\pi$
$283$	−1.28047e92	−1.46346	−0.731728	+	0.681597i	$0.761286\pi$
$284$	4.25490e91	0.426041
$285$	1.16795e91	0.102504
$286$	−1.52419e92	−1.17304
$287$	−3.12940e92	−2.11296
$288$	4.31131e89	0.00255500
$289$	1.95607e92	1.01793
$290$	9.63209e91	0.440348
$291$	4.06846e92	1.63472
$292$	−5.59400e91	−0.197636
$293$	−2.04899e92	−0.636801	−0.318400	−	0.947956i	$-0.603146\pi$
$293$	−2.04899e92	−0.636801	−0.318400	+	0.947956i	$0.603146\pi$
$294$	6.17565e92	1.68911
$295$	−1.93149e92	−0.465123
$296$	−1.63993e92	−0.347845
$297$	−6.11228e92	−1.14245
$298$	4.07335e92	0.671185
$299$	8.22467e92	1.19522
$300$	−2.36782e92	−0.303600
$301$	1.19809e93	1.35595
$302$	1.68422e92	0.168321
$303$	−5.77553e92	−0.509910
$304$	5.17430e91	0.0403731
$305$	2.74790e92	0.189564
$306$	−2.37934e91	−0.0145179
$307$	−2.23813e93	−1.20836	−0.604181	−	0.796847i	$-0.706500\pi$
$307$	−2.23813e93	−1.20836	−0.604181	+	0.796847i	$0.706500\pi$
$308$	−2.21100e93	−1.05666
$309$	2.19275e93	0.927997
$310$	−3.21001e92	−0.120349
$311$	1.49082e93	0.495349	0.247675	−	0.968843i	$-0.420334\pi$
$311$	1.49082e93	0.495349	0.247675	+	0.968843i	$0.420334\pi$
$312$	−1.74242e93	−0.513280
$313$	−2.24659e93	−0.586965	−0.293482	−	0.955964i	$-0.594814\pi$
$313$	−2.24659e93	−0.586965	−0.293482	+	0.955964i	$0.594814\pi$
$314$	−2.32271e93	−0.538435
$315$	−8.12844e91	−0.0167248
$316$	−4.56547e93	−0.834103
$317$	3.45883e93	0.561316	0.280658	−	0.959808i	$-0.409447\pi$
$317$	3.45883e93	0.561316	0.280658	+	0.959808i	$0.409447\pi$
$318$	1.62773e93	0.234728
$319$	8.87221e93	1.13732
$320$	6.91046e92	0.0787739
$321$	−1.76168e94	−1.78644
$322$	1.19308e94	1.07665
$323$	−2.85561e93	−0.229406
$324$	−7.08844e93	−0.507122
$325$	1.36341e94	0.868959
$326$	−6.74825e93	−0.383293
$327$	3.13641e94	1.58815
$328$	9.00931e93	0.406839
$329$	−3.73582e94	−1.50501
$330$	1.43678e94	0.516555
$331$	3.53434e94	1.13438	0.567190	−	0.823587i	$-0.308031\pi$
$331$	3.53434e94	1.13438	0.567190	+	0.823587i	$0.308031\pi$
$332$	1.70563e93	0.0488884
$333$	−5.55335e92	−0.0142199
$334$	3.04714e94	0.697269
$335$	−3.80251e94	−0.777840
$336$	−2.52756e94	−0.462359
$337$	2.91131e94	0.476395	0.238198	−	0.971217i	$-0.423443\pi$
$337$	2.91131e94	0.476395	0.238198	+	0.971217i	$0.423443\pi$
$338$	5.20390e94	0.761997
$339$	−6.47491e94	−0.848682
$340$	−3.81377e94	−0.447605
$341$	−2.95677e94	−0.310834
$342$	1.75219e92	0.00165045
$343$	−2.98337e95	−2.51870
$344$	−3.44920e94	−0.261082
$345$	−7.75300e94	−0.526325
$346$	2.22175e94	0.135313
$347$	−8.29680e94	−0.453477	−0.226738	−	0.973956i	$-0.572806\pi$
$347$	−8.29680e94	−0.453477	−0.226738	+	0.973956i	$0.572806\pi$
$348$	1.01425e95	0.497650
$349$	2.84562e95	1.25379	0.626894	−	0.779105i	$-0.284326\pi$
$349$	2.84562e95	1.25379	0.626894	+	0.779105i	$0.284326\pi$
$350$	1.97777e95	0.782752
$351$	4.02341e95	1.43079
$352$	6.36528e94	0.203455
$353$	−1.91592e95	−0.550588	−0.275294	−	0.961360i	$-0.588775\pi$
$353$	−1.91592e95	−0.550588	−0.275294	+	0.961360i	$0.588775\pi$
$354$	−2.03385e95	−0.525649
$355$	2.30950e95	0.536975
$356$	−3.41511e95	−0.714545
$357$	1.39492e96	2.62719
$358$	−5.12776e95	−0.869590
$359$	−9.46701e94	−0.144601	−0.0723005	−	0.997383i	$-0.523034\pi$
$359$	−9.46701e94	−0.144601	−0.0723005	+	0.997383i	$0.523034\pi$
$360$	2.34011e93	0.00322028
$361$	−7.85314e95	−0.973920
$362$	−9.87356e95	−1.10383
$363$	3.24316e95	0.326941
$364$	1.45539e96	1.32336
$365$	−3.03634e95	−0.249097
$366$	2.89352e95	0.214232
$367$	2.71050e95	0.181164	0.0905820	−	0.995889i	$-0.471127\pi$
$367$	2.71050e95	0.181164	0.0905820	+	0.995889i	$0.471127\pi$
$368$	−3.43478e95	−0.207303
$369$	3.05086e94	0.0166316
$370$	−8.90128e95	−0.438417
$371$	−1.35959e96	−0.605184
$372$	−3.38012e95	−0.136010
$373$	1.92238e96	0.699453	0.349726	−	0.936852i	$-0.386275\pi$
$373$	1.92238e96	0.699453	0.349726	+	0.936852i	$0.386275\pi$
$374$	−3.51290e96	−1.15606
$375$	−3.41709e96	−1.01738
$376$	1.07551e96	0.289782
$377$	−5.84013e96	−1.42437
$378$	5.83639e96	1.28885
$379$	3.63371e96	0.726742	0.363371	−	0.931645i	$-0.381626\pi$
$379$	3.63371e96	0.726742	0.363371	+	0.931645i	$0.381626\pi$
$380$	2.80853e95	0.0508856
$381$	4.12833e96	0.677779
$382$	−4.18631e96	−0.622953
$383$	5.44163e96	0.734133	0.367066	−	0.930195i	$-0.380362\pi$
$383$	5.44163e96	0.734133	0.367066	+	0.930195i	$0.380362\pi$
$384$	7.27666e95	0.0890248
$385$	−1.20010e97	−1.33180
$386$	9.99471e96	1.00634
$387$	−1.16801e95	−0.0106730
$388$	9.78333e96	0.811516
$389$	8.15340e96	0.614086	0.307043	−	0.951696i	$-0.400661\pi$
$389$	8.15340e96	0.614086	0.307043	+	0.951696i	$0.400661\pi$
$390$	−9.45758e96	−0.646930
$391$	1.89560e97	1.17793
$392$	1.48504e97	0.838516
$393$	−1.82432e97	−0.936227
$394$	5.47518e96	0.255441
$395$	−2.47807e97	−1.05129
$396$	2.15550e95	0.00831723
$397$	−7.76359e96	−0.272533	−0.136266	−	0.990672i	$-0.543510\pi$
$397$	−7.76359e96	−0.272533	−0.136266	+	0.990672i	$0.543510\pi$
$398$	7.71910e96	0.246576
$399$	−1.02725e97	−0.298670
$400$	−5.69384e96	−0.150715
$401$	2.43424e97	0.586746	0.293373	−	0.955998i	$-0.405222\pi$
$401$	2.43424e97	0.586746	0.293373	+	0.955998i	$0.405222\pi$
$402$	−4.00401e97	−0.879060
$403$	1.94630e97	0.389287
$404$	−1.38883e97	−0.253132
$405$	−3.84750e97	−0.639168
$406$	−8.47174e97	−1.28306
$407$	−8.19905e97	−1.13233
$408$	−4.01587e97	−0.505852
$409$	3.16223e97	0.363386	0.181693	−	0.983355i	$-0.441842\pi$
$409$	3.16223e97	0.363386	0.181693	+	0.983355i	$0.441842\pi$
$410$	4.89012e97	0.512773
$411$	9.66399e97	0.924885
$412$	5.27286e97	0.460681
$413$	1.69881e98	1.35525
$414$	−1.16313e96	−0.00847454
$415$	9.25789e96	0.0616181
$416$	−4.18995e97	−0.254805
$417$	2.97766e98	1.65490
$418$	2.58697e97	0.131426
$419$	3.68532e97	0.171179	0.0855894	−	0.996330i	$-0.472723\pi$
$419$	3.68532e97	0.171179	0.0855894	+	0.996330i	$0.472723\pi$
$420$	−1.37192e98	−0.582749
$421$	−3.63097e98	−1.41073	−0.705365	−	0.708844i	$-0.749217\pi$
$421$	−3.63097e98	−1.41073	−0.705365	+	0.708844i	$0.749217\pi$
$422$	2.14223e98	0.761463
$423$	3.64205e96	0.0118463
$424$	3.91416e97	0.116525
$425$	3.14234e98	0.856383
$426$	2.43188e98	0.606852
$427$	−2.41687e98	−0.552341
$428$	−4.23627e98	−0.886835
$429$	−8.71146e98	−1.67087
$430$	−1.87217e98	−0.329063
$431$	4.57047e97	0.0736314	0.0368157	−	0.999322i	$-0.488279\pi$
$431$	4.57047e97	0.0736314	0.0368157	+	0.999322i	$0.488279\pi$
$432$	−1.68025e98	−0.248161
$433$	2.97308e98	0.402633	0.201317	−	0.979526i	$-0.435478\pi$
$433$	2.97308e98	0.402633	0.201317	+	0.979526i	$0.435478\pi$
$434$	2.82331e98	0.350666
$435$	5.50521e98	0.627230
$436$	7.54205e98	0.788399
$437$	−1.39595e98	−0.133911
$438$	−3.19724e98	−0.281512
$439$	−2.21989e99	−1.79437	−0.897186	−	0.441654i	$-0.854392\pi$
$439$	−2.21989e99	−1.79437	−0.897186	+	0.441654i	$0.854392\pi$
$440$	3.45498e98	0.256431
$441$	5.02886e97	0.0342785
$442$	2.31236e99	1.44784
$443$	−2.49037e99	−1.43260	−0.716298	−	0.697795i	$-0.754165\pi$
$443$	−2.49037e99	−1.43260	−0.716298	+	0.697795i	$0.754165\pi$
$444$	−9.37298e98	−0.495469
$445$	−1.85367e99	−0.900600
$446$	6.53066e98	0.291675
$447$	2.32812e99	0.956034
$448$	−6.07797e98	−0.229527
$449$	3.33297e99	1.15769	0.578847	−	0.815436i	$-0.303503\pi$
$449$	3.33297e99	1.15769	0.578847	+	0.815436i	$0.303503\pi$
$450$	−1.92813e97	−0.00616121
$451$	4.50433e99	1.32437
$452$	−1.55701e99	−0.421307
$453$	9.62612e98	0.239755
$454$	−8.42727e98	−0.193238
$455$	7.89963e99	1.66794
$456$	2.95736e98	0.0575073
$457$	−6.20869e99	−1.11210	−0.556048	−	0.831150i	$-0.687683\pi$
$457$	−6.20869e99	−1.11210	−0.556048	+	0.831150i	$0.687683\pi$
$458$	2.79984e99	0.462038
$459$	9.27303e99	1.41009
$460$	−1.86435e99	−0.261281
$461$	−1.08181e100	−1.39754	−0.698770	−	0.715346i	$-0.746269\pi$
$461$	−1.08181e100	−1.39754	−0.698770	+	0.715346i	$0.746269\pi$
$462$	−1.26369e100	−1.50511
$463$	−6.44809e99	−0.708181	−0.354090	−	0.935211i	$-0.615209\pi$
$463$	−6.44809e99	−0.708181	−0.354090	+	0.935211i	$0.615209\pi$
$464$	2.43895e99	0.247046
$465$	−1.83468e99	−0.171425
$466$	−6.40066e99	−0.551764
$467$	−1.11112e100	−0.883852	−0.441926	−	0.897052i	$-0.645705\pi$
$467$	−1.11112e100	−0.883852	−0.441926	+	0.897052i	$0.645705\pi$
$468$	−1.41886e98	−0.0104164
$469$	3.34443e100	2.26642
$470$	5.83773e99	0.365237
$471$	−1.32754e100	−0.766946
$472$	−4.89074e99	−0.260946
$473$	−1.72447e100	−0.849893
$474$	−2.60939e100	−1.18809
$475$	−2.31408e99	−0.0973571
$476$	3.35434e100	1.30421
$477$	1.32547e98	0.00476354
$478$	2.61472e100	0.868717
$479$	−3.33540e100	−1.02463	−0.512314	−	0.858798i	$-0.671212\pi$
$479$	−3.33540e100	−1.02463	−0.512314	+	0.858798i	$0.671212\pi$
$480$	3.94966e99	0.112205
$481$	5.39702e100	1.41812
$482$	−2.52901e100	−0.614733
$483$	6.81902e100	1.53357
$484$	7.79874e99	0.162302
$485$	5.31024e100	1.02282
$486$	−1.14632e99	−0.0204384
$487$	−6.07920e100	−1.00348	−0.501742	−	0.865017i	$-0.667307\pi$
$487$	−6.07920e100	−1.00348	−0.501742	+	0.865017i	$0.667307\pi$
$488$	6.95797e99	0.106350
$489$	−3.85695e100	−0.545961
$490$	8.06059e100	1.05685
$491$	−7.16627e99	−0.0870437	−0.0435218	−	0.999052i	$-0.513858\pi$
$491$	−7.16627e99	−0.0870437	−0.0435218	+	0.999052i	$0.513858\pi$
$492$	5.14926e100	0.579500
$493$	−1.34602e101	−1.40375
$494$	−1.70287e100	−0.164597
$495$	1.16997e99	0.0104829
$496$	−8.12809e99	−0.0675190
$497$	−2.03128e101	−1.56461
$498$	9.74848e99	0.0696365
$499$	−8.00208e100	−0.530191	−0.265096	−	0.964222i	$-0.585403\pi$
$499$	−8.00208e100	−0.530191	−0.265096	+	0.964222i	$0.585403\pi$
$500$	−8.21699e100	−0.505054
$501$	1.74159e101	0.993188
$502$	4.65492e100	0.246333
$503$	4.71638e100	0.231638	0.115819	−	0.993270i	$-0.463051\pi$
$503$	4.71638e100	0.231638	0.115819	+	0.993270i	$0.463051\pi$
$504$	−2.05821e99	−0.00938305
$505$	−7.53835e100	−0.319043
$506$	−1.71727e101	−0.674828
$507$	2.97428e101	1.08539
$508$	9.92730e100	0.336467
$509$	−1.25156e101	−0.394035	−0.197018	−	0.980400i	$-0.563126\pi$
$509$	−1.25156e101	−0.394035	−0.197018	+	0.980400i	$0.563126\pi$
$510$	−2.17976e101	−0.637567
$511$	2.67056e101	0.725803
$512$	1.74980e100	0.0441942
$513$	−6.82883e100	−0.160304
$514$	−5.45950e101	−1.19134
$515$	2.86203e101	0.580635
$516$	−1.97138e101	−0.371884
$517$	5.37719e101	0.943322
$518$	7.82897e101	1.27743
$519$	1.26984e101	0.192740
$520$	−2.27424e101	−0.321152
$521$	−2.07385e101	−0.272498	−0.136249	−	0.990675i	$-0.543505\pi$
$521$	−2.07385e101	−0.272498	−0.136249	+	0.990675i	$0.543505\pi$
$522$	8.25910e99	0.0100992
$523$	−1.75255e101	−0.199460	−0.0997302	−	0.995015i	$-0.531798\pi$
$523$	−1.75255e101	−0.199460	−0.0997302	+	0.995015i	$0.531798\pi$
$524$	−4.38691e101	−0.464767
$525$	1.13039e102	1.11495
$526$	1.11489e102	1.02392
$527$	4.48576e101	0.383653
$528$	3.63807e101	0.289800
$529$	−4.21027e101	−0.312408
$530$	2.12455e101	0.146866
$531$	−1.65617e100	−0.0106675
$532$	−2.47020e101	−0.148267
$533$	−2.96498e102	−1.65864
$534$	−1.95190e102	−1.01779
$535$	−2.29939e102	−1.11775
$536$	−9.62836e101	−0.436388
$537$	−2.93077e102	−1.23864
$538$	1.00524e101	0.0396216
$539$	7.42469e102	2.72960
$540$	−9.12014e101	−0.312778
$541$	−4.29564e102	−1.37445	−0.687227	−	0.726443i	$-0.741172\pi$
$541$	−4.29564e102	−1.37445	−0.687227	+	0.726443i	$0.741172\pi$
$542$	3.89790e102	1.16374
$543$	−5.64322e102	−1.57229
$544$	−9.65687e101	−0.251118
$545$	4.09371e102	0.993685
$546$	8.31825e102	1.88499
$547$	−2.65894e102	−0.562579	−0.281290	−	0.959623i	$-0.590762\pi$
$547$	−2.65894e102	−0.562579	−0.281290	+	0.959623i	$0.590762\pi$
$548$	2.32388e102	0.459137
$549$	2.35620e100	0.00434760
$550$	−2.84672e102	−0.490618
$551$	9.91232e101	0.159584
$552$	−1.96314e102	−0.295282
$553$	2.17954e103	3.06318
$554$	−2.37994e102	−0.312572
$555$	−5.08752e102	−0.624480
$556$	7.16030e102	0.821536
$557$	−1.00502e103	−1.07797	−0.538983	−	0.842317i	$-0.681191\pi$
$557$	−1.00502e103	−1.07797	−0.538983	+	0.842317i	$0.681191\pi$
$558$	−2.75245e100	−0.00276017
$559$	1.13514e103	1.06440
$560$	−3.29903e102	−0.289292
$561$	−2.00779e103	−1.64669
$562$	−1.16434e103	−0.893240
$563$	4.01911e102	0.288446	0.144223	−	0.989545i	$-0.453932\pi$
$563$	4.01911e102	0.288446	0.144223	+	0.989545i	$0.453932\pi$
$564$	6.14709e102	0.412765
$565$	−8.45120e102	−0.531008
$566$	−1.75987e103	−1.03482
$567$	3.38400e103	1.86237
$568$	5.84789e102	0.301257
$569$	2.07254e103	0.999522	0.499761	−	0.866163i	$-0.333421\pi$
$569$	2.07254e103	0.999522	0.499761	+	0.866163i	$0.333421\pi$
$570$	1.60521e102	0.0724812
$571$	−2.07815e103	−0.878662	−0.439331	−	0.898325i	$-0.644785\pi$
$571$	−2.07815e103	−0.878662	−0.439331	+	0.898325i	$0.644785\pi$
$572$	−2.09482e103	−0.829462
$573$	−2.39268e103	−0.887332
$574$	−4.30102e103	−1.49409
$575$	1.53612e103	0.499897
$576$	5.92542e100	0.00180666
$577$	−6.16474e103	−1.76125	−0.880626	−	0.473812i	$-0.842878\pi$
$577$	−6.16474e103	−1.76125	−0.880626	+	0.473812i	$0.842878\pi$
$578$	2.68841e103	0.719782
$579$	5.71246e103	1.43343
$580$	1.32382e103	0.311373
$581$	−8.14262e102	−0.179539
$582$	5.59165e103	1.15592
$583$	1.95694e103	0.379321
$584$	−7.68833e102	−0.139750
$585$	−7.70135e101	−0.0131287
$586$	−2.81611e103	−0.450286
$587$	1.34972e103	0.202449	0.101224	−	0.994864i	$-0.467724\pi$
$587$	1.34972e103	0.202449	0.101224	+	0.994864i	$0.467724\pi$
$588$	8.48774e103	1.19438
$589$	−3.30340e102	−0.0436152
$590$	−2.65462e103	−0.328891
$591$	3.12933e103	0.363849
$592$	−2.25390e103	−0.245963
$593$	−1.15614e104	−1.18429	−0.592147	−	0.805830i	$-0.701720\pi$
$593$	−1.15614e104	−1.18429	−0.592147	+	0.805830i	$0.701720\pi$
$594$	−8.40065e103	−0.807832
$595$	1.82068e104	1.64380
$596$	5.59838e103	0.474600
$597$	4.41184e103	0.351223
$598$	1.13039e104	0.845150
$599$	−9.38440e103	−0.659023	−0.329512	−	0.944151i	$-0.606884\pi$
$599$	−9.38440e103	−0.659023	−0.329512	+	0.944151i	$0.606884\pi$
$600$	−3.25431e103	−0.214678
$601$	−2.55768e104	−1.58509	−0.792544	−	0.609815i	$-0.791244\pi$
$601$	−2.55768e104	−1.58509	−0.792544	+	0.609815i	$0.791244\pi$
$602$	1.64664e104	0.958803
$603$	−3.26049e102	−0.0178395
$604$	2.31477e103	0.119021
$605$	4.23304e103	0.204562
$606$	−7.93783e103	−0.360561
$607$	2.20623e104	0.942051	0.471025	−	0.882120i	$-0.343884\pi$
$607$	2.20623e104	0.942051	0.471025	+	0.882120i	$0.343884\pi$
$608$	7.11150e102	0.0285481
$609$	−4.84201e104	−1.82758
$610$	3.77668e103	0.134042
$611$	−3.53953e104	−1.18141
$612$	−3.27014e102	−0.0102657
$613$	−2.87547e104	−0.849065	−0.424533	−	0.905413i	$-0.639562\pi$
$613$	−2.87547e104	−0.849065	−0.424533	+	0.905413i	$0.639562\pi$
$614$	−3.07607e104	−0.854441
$615$	2.79494e104	0.730392
$616$	−3.03877e104	−0.747173
$617$	3.40731e103	0.0788348	0.0394174	−	0.999223i	$-0.487450\pi$
$617$	3.40731e103	0.0788348	0.0394174	+	0.999223i	$0.487450\pi$
$618$	3.01370e104	0.656193
$619$	1.30427e104	0.267282	0.133641	−	0.991030i	$-0.457333\pi$
$619$	1.30427e104	0.267282	0.133641	+	0.991030i	$0.457333\pi$
$620$	−4.41181e103	−0.0850998
$621$	4.53308e104	0.823111
$622$	2.04897e104	0.350265
$623$	1.63036e105	2.62411
$624$	−2.39476e104	−0.362944
$625$	−2.36137e103	−0.0337026
$626$	−3.08770e104	−0.415047
$627$	1.47858e104	0.187202
$628$	−3.19231e104	−0.380731
$629$	1.24389e105	1.39760
$630$	−1.11716e103	−0.0118262
$631$	−5.65015e104	−0.563585	−0.281792	−	0.959475i	$-0.590929\pi$
$631$	−5.65015e104	−0.563585	−0.281792	+	0.959475i	$0.590929\pi$
$632$	−6.27473e104	−0.589800
$633$	1.22439e105	1.08463
$634$	4.75378e104	0.396910
$635$	5.38839e104	0.424077
$636$	2.23713e104	0.165978
$637$	−4.88730e105	−3.41854
$638$	1.21939e105	0.804204
$639$	1.98029e103	0.0123154
$640$	9.49766e103	0.0557016
$641$	−3.19604e105	−1.76781	−0.883905	−	0.467666i	$-0.845095\pi$
$641$	−3.19604e105	−1.76781	−0.883905	+	0.467666i	$0.845095\pi$
$642$	−2.42124e105	−1.26320
$643$	2.49801e105	1.22937	0.614685	−	0.788773i	$-0.289283\pi$
$643$	2.49801e105	1.22937	0.614685	+	0.788773i	$0.289283\pi$
$644$	1.63975e105	0.761305
$645$	−1.07004e105	−0.468716
$646$	−3.92472e104	−0.162214
$647$	2.98625e105	1.16471	0.582353	−	0.812936i	$-0.302132\pi$
$647$	2.98625e105	1.16471	0.582353	+	0.812936i	$0.302132\pi$
$648$	−9.74227e104	−0.358590
$649$	−2.44520e105	−0.849450
$650$	1.87385e105	0.614447
$651$	1.61366e105	0.499488
$652$	−9.27472e104	−0.271029
$653$	−3.29496e105	−0.909086	−0.454543	−	0.890725i	$-0.650197\pi$
$653$	−3.29496e105	−0.909086	−0.454543	+	0.890725i	$0.650197\pi$
$654$	4.31065e105	1.12299
$655$	−2.38115e105	−0.585784
$656$	1.23823e105	0.287678
$657$	−2.60353e103	−0.00571296
$658$	−5.13448e105	−1.06420
$659$	4.12976e105	0.808577	0.404289	−	0.914632i	$-0.367519\pi$
$659$	4.12976e105	0.808577	0.404289	+	0.914632i	$0.367519\pi$
$660$	1.97469e105	0.365259
$661$	−8.43736e105	−1.47452	−0.737262	−	0.675607i	$-0.763882\pi$
$661$	−8.43736e105	−1.47452	−0.737262	+	0.675607i	$0.763882\pi$
$662$	4.85756e105	0.802127
$663$	1.32163e106	2.06230
$664$	2.34419e104	0.0345693
$665$	−1.34079e105	−0.186874
$666$	−7.63246e103	−0.0100550
$667$	−6.57995e105	−0.819414
$668$	4.18796e105	0.493044
$669$	3.73259e105	0.415462
$670$	−5.22613e105	−0.550016
$671$	3.47874e105	0.346200
$672$	−3.47386e105	−0.326937
$673$	1.44679e106	1.28778	0.643889	−	0.765119i	$-0.277320\pi$
$673$	1.44679e106	1.28778	0.643889	+	0.765119i	$0.277320\pi$
$674$	4.00127e105	0.336862
$675$	7.51450e105	0.598424
$676$	7.15219e105	0.538813
$677$	−4.48584e105	−0.319719	−0.159860	−	0.987140i	$-0.551104\pi$
$677$	−4.48584e105	−0.319719	−0.159860	+	0.987140i	$0.551104\pi$
$678$	−8.89905e105	−0.600109
$679$	−4.67054e106	−2.98023
$680$	−5.24161e105	−0.316505
$681$	−4.81659e105	−0.275247
$682$	−4.06376e105	−0.219793
$683$	2.90525e106	1.48733	0.743665	−	0.668552i	$-0.233086\pi$
$683$	2.90525e106	1.48733	0.743665	+	0.668552i	$0.233086\pi$
$684$	2.40819e103	0.00116705
$685$	1.26137e106	0.578688
$686$	−4.10031e106	−1.78099
$687$	1.60024e106	0.658125
$688$	−4.74054e105	−0.184613
$689$	−1.28816e106	−0.475059
$690$	−1.06556e106	−0.372168
$691$	4.99324e105	0.165179	0.0825897	−	0.996584i	$-0.473681\pi$
$691$	4.99324e105	0.165179	0.0825897	+	0.996584i	$0.473681\pi$
$692$	3.05354e105	0.0956810
$693$	−1.02903e105	−0.0305444
$694$	−1.14030e106	−0.320657
$695$	3.88651e106	1.03545
$696$	1.39398e106	0.351892
$697$	−6.83359e106	−1.63463
$698$	3.91100e106	0.886562
$699$	−3.65829e106	−0.785930
$700$	2.71823e106	0.553489
$701$	5.51946e106	1.06530	0.532649	−	0.846336i	$-0.321197\pi$
$701$	5.51946e106	1.06530	0.532649	+	0.846336i	$0.321197\pi$
$702$	5.52973e106	1.01172
$703$	−9.16024e105	−0.158885
$704$	8.74838e105	0.143864
$705$	3.33655e106	0.520242
$706$	−2.63323e106	−0.389325
$707$	6.63023e106	0.929610
$708$	−2.79530e106	−0.371690
$709$	−2.59978e106	−0.327871	−0.163935	−	0.986471i	$-0.552419\pi$
$709$	−2.59978e106	−0.327871	−0.163935	+	0.986471i	$0.552419\pi$
$710$	3.17415e106	0.379699
$711$	−2.12484e105	−0.0241110
$712$	−4.69369e106	−0.505259
$713$	2.19285e106	0.223950
$714$	1.91717e107	1.85771
$715$	−1.13704e107	−1.04544
$716$	−7.04754e106	−0.614893
$717$	1.49444e107	1.23740
$718$	−1.30114e106	−0.102248
$719$	−1.49504e107	−1.11512	−0.557559	−	0.830138i	$-0.688262\pi$
$719$	−1.49504e107	−1.11512	−0.557559	+	0.830138i	$0.688262\pi$
$720$	3.21623e104	0.00227708
$721$	−2.51725e107	−1.69182
$722$	−1.07933e107	−0.688666
$723$	−1.44545e107	−0.875624
$724$	−1.35701e107	−0.780526
$725$	−1.09076e107	−0.595736
$726$	4.45736e106	0.231182
$727$	−1.99131e107	−0.980842	−0.490421	−	0.871486i	$-0.663157\pi$
$727$	−1.99131e107	−0.980842	−0.490421	+	0.871486i	$0.663157\pi$
$728$	2.00027e107	0.935755
$729$	2.21706e107	0.985132
$730$	−4.17311e106	−0.176138
$731$	2.61623e107	1.04900
$732$	3.97682e106	0.151485
$733$	3.73602e107	1.35211	0.676053	−	0.736853i	$-0.263689\pi$
$733$	3.73602e107	1.35211	0.676053	+	0.736853i	$0.263689\pi$
$734$	3.72528e106	0.128102
$735$	4.60702e107	1.50538
$736$	−4.72072e106	−0.146585
$737$	−4.81384e107	−1.42056
$738$	4.19306e105	0.0117603
$739$	2.19613e106	0.0585452	0.0292726	−	0.999571i	$-0.490681\pi$
$739$	2.19613e106	0.0585452	0.0292726	+	0.999571i	$0.490681\pi$
$740$	−1.22338e107	−0.310008
$741$	−9.73273e106	−0.234451
$742$	−1.86861e107	−0.427930
$743$	−1.99376e106	−0.0434102	−0.0217051	−	0.999764i	$-0.506909\pi$
$743$	−1.99376e106	−0.0434102	−0.0217051	+	0.999764i	$0.506909\pi$
$744$	−4.64560e106	−0.0961738
$745$	3.03872e107	0.598177
$746$	2.64210e107	0.494588
$747$	7.93823e104	0.00141319
$748$	−4.82809e107	−0.817458
$749$	2.02239e108	3.25684
$750$	−4.69641e107	−0.719397
$751$	−1.17537e108	−1.71268	−0.856341	−	0.516411i	$-0.827268\pi$
$751$	−1.17537e108	−1.71268	−0.856341	+	0.516411i	$0.827268\pi$
$752$	1.47818e107	0.204907
$753$	2.66051e107	0.350876
$754$	−8.02661e107	−1.00718
$755$	1.25642e107	0.150012
$756$	8.02147e107	0.911353
$757$	1.40392e107	0.151791	0.0758954	−	0.997116i	$-0.475818\pi$
$757$	1.40392e107	0.151791	0.0758954	+	0.997116i	$0.475818\pi$
$758$	4.99413e107	0.513884
$759$	−9.81501e107	−0.961223
$760$	3.86002e106	0.0359815
$761$	1.06409e108	0.944173	0.472087	−	0.881552i	$-0.343501\pi$
$761$	1.06409e108	0.944173	0.472087	+	0.881552i	$0.343501\pi$
$762$	5.67394e107	0.479262
$763$	−3.60056e108	−2.89534
$764$	−5.75362e107	−0.440494
$765$	−1.77498e106	−0.0129387
$766$	7.47892e107	0.519110
$767$	1.60955e108	1.06385
$768$	1.00010e107	0.0629500
$769$	−9.70747e107	−0.581927	−0.290963	−	0.956734i	$-0.593976\pi$
$769$	−9.70747e107	−0.581927	−0.290963	+	0.956734i	$0.593976\pi$
$770$	−1.64940e108	−0.941724
$771$	−3.12037e108	−1.69694
$772$	1.37366e108	0.711592
$773$	−2.69431e108	−1.32958	−0.664792	−	0.747028i	$-0.731480\pi$
$773$	−2.69431e108	−1.32958	−0.664792	+	0.747028i	$0.731480\pi$
$774$	−1.60531e106	−0.00754696
$775$	3.63509e107	0.162818
$776$	1.34461e108	0.573828
$777$	4.47464e108	1.81957
$778$	1.12060e108	0.434224
$779$	5.03239e107	0.185831
$780$	−1.29984e108	−0.457448
$781$	2.92374e108	0.980674
$782$	2.60529e108	0.832919
$783$	−3.21883e108	−0.980915
$784$	2.04103e108	0.592921
$785$	−1.73274e108	−0.479867
$786$	−2.50733e108	−0.662012
$787$	2.65570e108	0.668538	0.334269	−	0.942478i	$-0.391511\pi$
$787$	2.65570e108	0.668538	0.334269	+	0.942478i	$0.391511\pi$
$788$	7.52503e107	0.180624
$789$	6.37212e108	1.45847
$790$	−3.40583e108	−0.743374
$791$	7.43311e108	1.54722
$792$	2.96250e106	0.00588117
$793$	−2.28988e108	−0.433579
$794$	−1.06702e108	−0.192710
$795$	1.21428e108	0.209196
$796$	1.06090e108	0.174356
$797$	−9.86207e108	−1.54626	−0.773128	−	0.634250i	$-0.781309\pi$
$797$	−9.86207e108	−1.54626	−0.773128	+	0.634250i	$0.781309\pi$
$798$	−1.41184e108	−0.211191
$799$	−8.15781e108	−1.16431
$800$	−7.82555e107	−0.106571
$801$	−1.58944e107	−0.0206550
$802$	3.34560e108	0.414892
$803$	−3.84389e108	−0.454923
$804$	−5.50308e108	−0.621590
$805$	8.90034e108	0.959536
$806$	2.67497e108	0.275267
$807$	5.74541e107	0.0564370
$808$	−1.90879e108	−0.178991
$809$	−1.63082e109	−1.45994	−0.729971	−	0.683478i	$-0.760467\pi$
$809$	−1.63082e109	−1.45994	−0.729971	+	0.683478i	$0.760467\pi$
$810$	−5.28796e108	−0.451960
$811$	7.78650e108	0.635419	0.317710	−	0.948188i	$-0.397086\pi$
$811$	7.78650e108	0.635419	0.317710	+	0.948188i	$0.397086\pi$
$812$	−1.16435e109	−0.907260
$813$	2.22784e109	1.65763
$814$	−1.12687e109	−0.800679
$815$	−5.03418e108	−0.341600
$816$	−5.51937e108	−0.357691
$817$	−1.92664e108	−0.119254
$818$	4.34613e108	0.256953
$819$	6.77359e107	0.0382536
$820$	6.72093e108	0.362585
$821$	1.82914e109	0.942713	0.471356	−	0.881943i	$-0.343765\pi$
$821$	1.82914e109	0.942713	0.471356	+	0.881943i	$0.343765\pi$
$822$	1.32821e109	0.653993
$823$	1.30030e109	0.611714	0.305857	−	0.952077i	$-0.401057\pi$
$823$	1.30030e109	0.611714	0.305857	+	0.952077i	$0.401057\pi$
$824$	7.24696e108	0.325751
$825$	−1.62704e109	−0.698835
$826$	2.33483e109	0.958304
$827$	3.46207e108	0.135793	0.0678967	−	0.997692i	$-0.478371\pi$
$827$	3.46207e108	0.135793	0.0678967	+	0.997692i	$0.478371\pi$
$828$	−1.59860e107	−0.00599240
$829$	4.09855e109	1.46837	0.734186	−	0.678949i	$-0.237564\pi$
$829$	4.09855e109	1.46837	0.734186	+	0.678949i	$0.237564\pi$
$830$	1.27239e108	0.0435706
$831$	−1.36025e109	−0.445227
$832$	−5.75862e108	−0.180175
$833$	−1.12641e110	−3.36906
$834$	4.09246e109	1.17019
$835$	2.27316e109	0.621424
$836$	3.55550e108	0.0929319
$837$	1.07271e109	0.268089
$838$	5.06507e108	0.121042
$839$	1.09826e109	0.250975	0.125488	−	0.992095i	$-0.459950\pi$
$839$	1.09826e109	0.250975	0.125488	+	0.992095i	$0.459950\pi$
$840$	−1.88556e109	−0.412066
$841$	−1.12394e108	−0.0234906
$842$	−4.99037e109	−0.997537
$843$	−6.65477e109	−1.27233
$844$	2.94426e109	0.538436
$845$	3.88210e109	0.679111
$846$	5.00560e107	0.00837660
$847$	−3.72310e109	−0.596042
$848$	5.37958e108	0.0823956
$849$	−1.00585e110	−1.47399
$850$	4.31880e109	0.605554
$851$	6.08071e109	0.815822
$852$	3.34236e109	0.429109
$853$	1.00491e110	1.23464	0.617318	−	0.786714i	$-0.288219\pi$
$853$	1.00491e110	1.23464	0.617318	+	0.786714i	$0.288219\pi$
$854$	−3.32172e109	−0.390564
$855$	1.30713e107	0.00147092
$856$	−5.82229e109	−0.627087
$857$	2.60565e109	0.268618	0.134309	−	0.990939i	$-0.457119\pi$
$857$	2.60565e109	0.268618	0.134309	+	0.990939i	$0.457119\pi$
$858$	−1.19729e110	−1.18148
$859$	2.42705e109	0.229263	0.114632	−	0.993408i	$-0.463431\pi$
$859$	2.42705e109	0.229263	0.114632	+	0.993408i	$0.463431\pi$
$860$	−2.57309e109	−0.232682
$861$	−2.45824e110	−2.12817
$862$	6.28160e108	0.0520653
$863$	1.83690e110	1.45774	0.728871	−	0.684651i	$-0.240046\pi$
$863$	1.83690e110	1.45774	0.728871	+	0.684651i	$0.240046\pi$
$864$	−2.30932e109	−0.175476
$865$	1.65742e109	0.120595
$866$	4.08616e109	0.284705
$867$	1.53656e110	1.02526
$868$	3.88033e109	0.247959
$869$	−3.13714e110	−1.91996
$870$	7.56630e109	0.443518
$871$	3.16871e110	1.77910
$872$	1.03657e110	0.557482
$873$	4.55330e108	0.0234581
$874$	−1.91859e109	−0.0946896
$875$	3.92277e110	1.85477
$876$	−4.39426e109	−0.199059
$877$	3.43961e110	1.49288	0.746439	−	0.665454i	$-0.231762\pi$
$877$	3.43961e110	1.49288	0.746439	+	0.665454i	$0.231762\pi$
$878$	−3.05100e110	−1.26881
$879$	−1.60954e110	−0.641386
$880$	4.74849e109	0.181324
$881$	−2.59777e110	−0.950614	−0.475307	−	0.879820i	$-0.657663\pi$
$881$	−2.59777e110	−0.950614	−0.475307	+	0.879820i	$0.657663\pi$
$882$	6.91161e108	0.0242386
$883$	3.56875e110	1.19947	0.599736	−	0.800198i	$-0.295272\pi$
$883$	3.56875e110	1.19947	0.599736	+	0.800198i	$0.295272\pi$
$884$	3.17809e110	1.02378
$885$	−1.51725e110	−0.468472
$886$	−3.42273e110	−1.01300
$887$	−5.32736e110	−1.51139	−0.755694	−	0.654925i	$-0.772700\pi$
$887$	−5.32736e110	−1.51139	−0.755694	+	0.654925i	$0.772700\pi$
$888$	−1.28821e110	−0.350349
$889$	−4.73927e110	−1.23565
$890$	−2.54766e110	−0.636820
$891$	−4.87079e110	−1.16731
$892$	8.97567e109	0.206246
$893$	6.00757e109	0.132364
$894$	3.19974e110	0.676018
$895$	−3.82530e110	−0.775000
$896$	−8.35350e109	−0.162300
$897$	6.46073e110	1.20383
$898$	4.58080e110	0.818613
$899$	−1.55709e110	−0.266885
$900$	−2.65000e108	−0.00435664
$901$	−2.96890e110	−0.468184
$902$	6.19071e110	0.936473
$903$	9.41133e110	1.36572
$904$	−2.13993e110	−0.297909
$905$	−7.36566e110	−0.983761
$906$	1.32300e110	0.169533
$907$	−8.50638e110	−1.04585	−0.522927	−	0.852377i	$-0.675160\pi$
$907$	−8.50638e110	−1.04585	−0.522927	+	0.852377i	$0.675160\pi$
$908$	−1.15823e110	−0.136640
$909$	−6.46381e108	−0.00731717
$910$	1.08572e111	1.17941
$911$	5.63353e110	0.587275	0.293637	−	0.955917i	$-0.405134\pi$
$911$	5.63353e110	0.587275	0.293637	+	0.955917i	$0.405134\pi$
$912$	4.06457e109	0.0406638
$913$	1.17201e110	0.112533
$914$	−8.53316e110	−0.786371
$915$	2.15856e110	0.190929
$916$	3.84807e110	0.326710
$917$	2.09430e111	1.70682
$918$	1.27448e111	0.997082
$919$	1.89082e111	1.42010	0.710051	−	0.704151i	$-0.248672\pi$
$919$	1.89082e111	1.42010	0.710051	+	0.704151i	$0.248672\pi$
$920$	−2.56234e110	−0.184754
$921$	−1.75812e111	−1.21706
$922$	−1.48682e111	−0.988210
$923$	−1.92455e111	−1.22819
$924$	−1.73681e111	−1.06427
$925$	1.00800e111	0.593125
$926$	−8.86219e110	−0.500759
$927$	2.45407e109	0.0133167
$928$	3.35206e110	0.174688
$929$	1.54585e111	0.773711	0.386856	−	0.922140i	$-0.373561\pi$
$929$	1.54585e111	0.773711	0.386856	+	0.922140i	$0.373561\pi$
$930$	−2.52156e110	−0.121216
$931$	8.29510e110	0.383009
$932$	−8.79700e110	−0.390156
$933$	1.17109e111	0.498916
$934$	−1.52712e111	−0.624978
$935$	−2.62062e111	−1.03031
$936$	−1.95006e109	−0.00736554
$937$	−2.08081e111	−0.755088	−0.377544	−	0.925992i	$-0.623231\pi$
$937$	−2.08081e111	−0.755088	−0.377544	+	0.925992i	$0.623231\pi$
$938$	4.59655e111	1.60260
$939$	−1.76477e111	−0.591191
$940$	8.02332e110	0.258261
$941$	−2.40159e111	−0.742827	−0.371413	−	0.928468i	$-0.621127\pi$
$941$	−2.40159e111	−0.742827	−0.371413	+	0.928468i	$0.621127\pi$
$942$	−1.82456e111	−0.542312
$943$	−3.34057e111	−0.954185
$944$	−6.72179e110	−0.184516
$945$	4.35393e111	1.14865
$946$	−2.37010e111	−0.600965
$947$	4.27840e111	1.04270	0.521348	−	0.853344i	$-0.325429\pi$
$947$	4.27840e111	1.04270	0.521348	+	0.853344i	$0.325429\pi$
$948$	−3.58632e111	−0.840109
$949$	2.53024e111	0.569743
$950$	−3.18044e110	−0.0688419
$951$	2.71702e111	0.565358
$952$	4.61017e111	0.922212
$953$	3.13699e111	0.603295	0.301648	−	0.953419i	$-0.402463\pi$
$953$	3.13699e111	0.603295	0.301648	+	0.953419i	$0.402463\pi$
$954$	1.82171e109	0.00336833
$955$	−3.12298e111	−0.555191
$956$	3.59364e111	0.614276
$957$	6.96939e111	1.14551
$958$	−4.58414e111	−0.724522
$959$	−1.10941e112	−1.68615
$960$	5.42837e110	0.0793412
$961$	−6.59530e111	−0.927059
$962$	7.41761e111	1.00276
$963$	−1.97162e110	−0.0256353
$964$	−3.47584e111	−0.434682
$965$	7.45604e111	0.896879
$966$	9.37199e111	1.08440
$967$	6.44471e111	0.717316	0.358658	−	0.933469i	$-0.383234\pi$
$967$	6.44471e111	0.717316	0.358658	+	0.933469i	$0.383234\pi$
$968$	1.07185e111	0.114765
$969$	−2.24317e111	−0.231058
$970$	7.29835e111	0.723243
$971$	5.03724e111	0.480255	0.240127	−	0.970741i	$-0.422811\pi$
$971$	5.03724e111	0.480255	0.240127	+	0.970741i	$0.422811\pi$
$972$	−1.57549e110	−0.0144521
$973$	−3.41831e112	−3.01703
$974$	−8.35520e111	−0.709571
$975$	1.07100e112	0.875216
$976$	9.56296e110	0.0752011
$977$	2.60852e112	1.97400	0.987000	−	0.160719i	$-0.0513813\pi$
$977$	2.60852e112	1.97400	0.987000	+	0.160719i	$0.0513813\pi$
$978$	−5.30095e111	−0.386053
$979$	−2.34668e112	−1.64476
$980$	1.10784e112	0.747307
$981$	3.51018e110	0.0227899
$982$	−9.84925e110	−0.0615492
$983$	−2.65720e112	−1.59833	−0.799166	−	0.601110i	$-0.794725\pi$
$983$	−2.65720e112	−1.59833	−0.799166	+	0.601110i	$0.794725\pi$
$984$	7.07709e111	0.409768
$985$	4.08448e111	0.227655
$986$	−1.84995e112	−0.992603
$987$	−2.93460e112	−1.51585
$988$	−2.34041e111	−0.116387
$989$	1.27893e112	0.612331
$990$	1.60800e110	0.00741252
$991$	−2.01124e112	−0.892690	−0.446345	−	0.894861i	$-0.647275\pi$
$991$	−2.01124e112	−0.892690	−0.446345	+	0.894861i	$0.647275\pi$
$992$	−1.11712e111	−0.0477431
$993$	2.77633e112	1.14255
$994$	−2.79177e112	−1.10634
$995$	5.75843e111	0.219755
$996$	1.33982e111	0.0492404
$997$	1.51098e112	0.534797	0.267398	−	0.963586i	$-0.413836\pi$
$997$	1.51098e112	0.534797	0.267398	+	0.963586i	$0.413836\pi$
$998$	−1.09980e112	−0.374902
$999$	2.97461e112	0.976615

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2.76.a.b.1.3	✓	3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2.76.a.b.1.3	✓	3	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 2 \)
Weight:	\( k \)	\(=\)	\( 76 \)
Character orbit:	\([\chi]\)	\(=\)	2.a (trivial)

\(f(q)\)	\(=\)	\(q+1.37439e11 q^{2} +7.85531e17 q^{3} +1.88895e22 q^{4} +1.02529e26 q^{5} +1.07962e29 q^{6} -9.01778e31 q^{7} +2.59615e33 q^{8} +8.79144e33 q^{9} +1.40915e37 q^{10} +1.29798e39 q^{11} +1.48383e40 q^{12} -8.54396e41 q^{13} -1.23939e43 q^{14} +8.05398e43 q^{15} +3.56812e44 q^{16} -1.96919e46 q^{17} +1.20829e45 q^{18} +1.45015e47 q^{19} +1.93672e48 q^{20} -7.08374e49 q^{21} +1.78393e50 q^{22} -9.62630e50 q^{23} +2.03935e51 q^{24} -1.59575e52 q^{25} -1.17427e53 q^{26} -4.70906e53 q^{27} -1.70341e54 q^{28} +6.83539e54 q^{29} +1.10693e55 q^{30} -2.27798e55 q^{31} +4.90399e55 q^{32} +1.01960e57 q^{33} -2.70643e57 q^{34} -9.24586e57 q^{35} +1.66066e56 q^{36} -6.31677e58 q^{37} +1.99307e58 q^{38} -6.71154e59 q^{39} +2.66181e59 q^{40} +3.47026e60 q^{41} -9.73582e60 q^{42} -1.32858e61 q^{43} +2.45182e61 q^{44} +9.01379e59 q^{45} -1.32303e62 q^{46} +4.14273e62 q^{47} +2.80287e62 q^{48} +5.72018e63 q^{49} -2.19319e63 q^{50} -1.54686e64 q^{51} -1.61391e64 q^{52} +1.50768e64 q^{53} -6.47209e64 q^{54} +1.33081e65 q^{55} -2.34115e65 q^{56} +1.13913e65 q^{57} +9.39448e65 q^{58} -1.88385e66 q^{59} +1.52135e66 q^{60} +2.68011e66 q^{61} -3.13083e66 q^{62} -7.92793e65 q^{63} +6.73999e66 q^{64} -8.76006e67 q^{65} +1.40133e68 q^{66} -3.70871e68 q^{67} -3.71969e68 q^{68} -7.56175e68 q^{69} -1.27074e69 q^{70} +2.25253e69 q^{71} +2.28239e67 q^{72} -2.96144e69 q^{73} -8.68170e69 q^{74} -1.25351e70 q^{75} +2.73925e69 q^{76} -1.17049e71 q^{77} -9.22428e70 q^{78} -2.41694e71 q^{79} +3.65836e70 q^{80} -3.75259e71 q^{81} +4.76949e71 q^{82} +9.02951e70 q^{83} -1.33808e72 q^{84} -2.01899e72 q^{85} -1.82599e72 q^{86} +5.36941e72 q^{87} +3.36975e72 q^{88} -1.80794e73 q^{89} +1.23885e71 q^{90} +7.70476e73 q^{91} -1.81836e73 q^{92} -1.78942e73 q^{93} +5.69372e73 q^{94} +1.48682e73 q^{95} +3.85223e73 q^{96} +5.17925e74 q^{97} +7.86175e74 q^{98} +1.14111e73 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q + 412316860416 q^{2} + 45\!\cdots\!16 q^{3} + 56\!\cdots\!52 q^{4} - 19\!\cdots\!90 q^{5} + 62\!\cdots\!52 q^{6} - 37\!\cdots\!52 q^{7} + 77\!\cdots\!44 q^{8} - 26\!\cdots\!69 q^{9} - 26\!\cdots\!80 q^{10}+ \cdots + 90\!\cdots\!32 q^{99}+O(q^{100}) \) 3 * q + 412316860416 * q^2 + 458242166228809716 * q^3 + 56668397794435742564352 * q^4 - 195317864575755505617919590 * q^5 + 62980323763229868263265533952 * q^6 - 37066282910854192405810923152952 * q^7 + 7788445287802241442795744493830144 * q^8 - 267707440809547675110176979472664769 * q^9 - 26844282901677657955869085139447316480 * q^10 + 1089522657174857887018090027503932523516 * q^11 + 8655949787346045808675641167610164281344 * q^12 - 200775423127509346148989234344235815084894 * q^13 - 5094351132364878073838383209647937467449344 * q^14 + 227412712084025466854308442890234618066471320 * q^15 + 1070435769529469910793714477087121352287059968 * q^16 - 13964607281546105485967748168451725560455001322 * q^17 - 36793430501531616932833386355429072282444627968 * q^18 - 2115042489507394854414232114360954083096137041020 * q^19 - 3689450148712880782538621821803706361489978818560 * q^20 - 23475337414840802232472405760772442593547635795744 * q^21 + 149742853786145100102091508112420182396543069847552 * q^22 + 116856323604290944270046589717244430012820187772376 * q^23 + 1189664680079021484261752060374941122097914333626368 * q^24 - 13677553808937057350680884197678632002550617150091275 * q^25 - 27594364037542869748616073758866330620848742196051968 * q^26 - 516713355711438316758259090904905946273936306702420280 * q^27 - 700162288251126990917226530398508899089535904532922368 * q^28 - 4685039575774269774425123141334628221923373816078325710 * q^29 + 31255365155057708293452376285127724875601442352702423040 * q^30 + 19810012207866372881154886539183629090472506922981842976 * q^31 + 147119571923125330402401314606429681627398955729625808896 * q^32 - 1585737135797838535515313355184995617533368424120408715248 * q^33 - 1919281010423167596108725289416449927581488049844056489984 * q^34 - 10950361456133471021484484744548030403192620947333255249040 * q^35 - 5056850582775269524368615136432015920023032065710301904896 * q^36 - 45940866101102779827043188076640168610273759105645032828742 * q^37 - 290689226306709889595769861380263351240178400483683535421440 * q^38 - 1672442610320761978222551615006671064699371016431534859756168 * q^39 - 507074167326213102558408594609883473733971611438333370040320 * q^40 + 362400026981966097502505178180515117776287761483498293835886 * q^41 - 3226425806697805780315928702878708500394384523546861311623168 * q^42 - 28702095070206583225102323926867241705153753782220140424278244 * q^43 + 20580501114278495451172137233349227993712236430421745461100544 * q^44 + 9961130143898573860468040684586213478623455196227513865892770 * q^45 + 16060610822759118429081878247420630852583154150749888390889472 * q^46 + 1440358153753731871262284486476744104832092319767060853177135408 * q^47 + 163506268612662399058739321695071667754754719127516276584349696 * q^48 + 5851233763188937006285451636437763810170039730055265549739289339 * q^49 - 1879828681557276602996825630764573554207164455816279985278156800 * q^50 - 13135245964480362237443576676736477680682849131997768459350096984 * q^51 - 3792540515045284536585400897736149761666199151832909532046032896 * q^52 - 66482008582006413625317152148536776263636987496863720447690376374 * q^53 - 71016542853985356275136369066600386726479663823165462612709212160 * q^54 - 128059259461243668378349058265162253832978578499704027402037026680 * q^55 - 96229572157795694756236063714724658200144668345173751227740061696 * q^56 + 541881412323488933705214064356590630418338964926058970501983678960 * q^57 - 643906936269318481901990434969760448175344664257252092764351365120 * q^58 - 371683568940617616838543919579672241129155497105032841329863886420 * q^59 + 4295704677296346435618749666499505584755003623529158533656220794880 * q^60 + 13573422560821853027615494323023031372615121991355370424474791441746 * q^61 + 2722667346116698414806449036684297903429556557482899404279274012672 * q^62 - 26481097073687004346685625189284323701988206005717909402281686334104 * q^63 + 20219960000362979846000261315264723005227858316905429360827707686912 * q^64 - 283941175814397704527430731718044717252185233543246078490644938760580 * q^65 - 217942052425741676080857771766770822630692530250118815940593168941056 * q^66 - 413223374254023917043840598633408380930841273575662432347998564181452 * q^67 - 263783973491242878272445183305337195628289905571041296782650610024448 * q^68 - 1061510208317927203185294055302976167343619039092488023800560677951328 * q^69 - 1505006218671110292743666411175830556253632030634267830651108332666880 * q^70 - 5329648930387886406281280512948717239625311590459101731821120548966904 * q^71 - 695008251960906352791957665913154768123208777247522230138074312998912 * q^72 - 6126925276337568901196002641779188883652596184658648256377551348614514 * q^73 - 6314064558532847004538848933399893303713650078903283999497384282292224 * q^74 - 42136550820801138510743282158837727891370079859020453164369744977721300 * q^75 - 39952023049179578917555270866261904430205672681056363719959756071239680 * q^76 - 289482613480384241434628541067945562255609470975872005377156987184398944 * q^77 - 229858762104465432520515948676020321430825554794999067063574019017015296 * q^78 - 622218748753103295378700837548188457771583126386550471357575046848039600 * q^79 - 69691742890000545248481882996952684737865058410241963042196499243991040 * q^80 - 813867571538426179661468949362446700360464407612291411834932342915810277 * q^81 + 49807880446625983057728224587390886889047813755413555702301720357896192 * q^82 - 1533020732833757587948568401531575056248575332031888360930290411083590204 * q^83 - 443436586327599794605333578455416130045154708181833960219813479549239296 * q^84 - 2509870850873749953965285441354116293863644192517282543162006812905493740 * q^85 - 3944785908903043165302934000623779163435604708680697900633683916297863168 * q^86 + 7656197026313956905810590821633236160642701737759808104389066992317050680 * q^87 + 2828562535075766291163811017077083352954935971317797639765224852729888768 * q^88 - 9273679405251457383346320465116747436209848620322393707782099041195555170 * q^89 + 1369047302375812757496022463791847621861188325322189908140671263771197440 * q^90 + 37855086806940858491220205001548043782409020136053538320652371512227893296 * q^91 + 2207353543601090116438321996125612987761063814335917584464651090902646784 * q^92 + 116428442792693075708882307667561815114456133894684752952005955774351769472 * q^93 + 197961317276774976800780611445304646234068226708873622478004936714355736576 * q^94 + 357878094222078480931183160357756124777870531843559815899687819400578887800 * q^95 + 22472130444236041454277970229425795116251176548939137972399120951921344512 * q^96 + 1302609856697415284410811597650709289615858746443991563079136355124529279078 * q^97 + 804187444932719779552005159010876080129685530867457081879222689193166635008 * q^98 + 904093342516791279625791645893932380898957972599927163310277116835911049132 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more