LMFDB - Embedded newform 2.76.a.b.1.1

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			1.1
Root			$-9.47292e12$ 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)

$f(q)$	$=$	\(q+1.37439e11 q^{2} -8.29405e17 q^{3} +1.88895e22 q^{4} -2.22623e26 q^{5} -1.13993e29 q^{6} -1.55415e31 q^{7} +2.59615e33 q^{8} +7.96464e34 q^{9} -3.05970e37 q^{10} +1.87805e39 q^{11} -1.56670e40 q^{12} +9.98468e41 q^{13} -2.13601e42 q^{14} +1.84644e44 q^{15} +3.56812e44 q^{16} +4.07379e44 q^{17} +1.09465e46 q^{18} -1.17368e48 q^{19} -4.20522e48 q^{20} +1.28902e49 q^{21} +2.58118e50 q^{22} +6.36387e50 q^{23} -2.15326e51 q^{24} +2.30910e52 q^{25} +1.37228e53 q^{26} +4.38441e53 q^{27} -2.93571e53 q^{28} -6.06178e54 q^{29} +2.53773e55 q^{30} -8.48184e55 q^{31} +4.90399e55 q^{32} -1.55767e57 q^{33} +5.59898e55 q^{34} +3.45990e57 q^{35} +1.50448e57 q^{36} +4.74204e58 q^{37} -1.61309e59 q^{38} -8.28135e59 q^{39} -5.77961e59 q^{40} -1.53555e60 q^{41} +1.77162e60 q^{42} -7.65577e60 q^{43} +3.54754e61 q^{44} -1.77311e61 q^{45} +8.74644e61 q^{46} +5.36288e62 q^{47} -2.95942e62 q^{48} -2.17033e63 q^{49} +3.17361e63 q^{50} -3.37882e62 q^{51} +1.88605e64 q^{52} -3.23526e64 q^{53} +6.02588e64 q^{54} -4.18097e65 q^{55} -4.03481e64 q^{56} +9.73456e65 q^{57} -8.33125e65 q^{58} -1.88381e66 q^{59} +3.48783e66 q^{60} +1.66500e67 q^{61} -1.16574e67 q^{62} -1.23783e66 q^{63} +6.73999e66 q^{64} -2.22282e68 q^{65} -2.14084e68 q^{66} +4.39869e68 q^{67} +7.69517e66 q^{68} -5.27823e68 q^{69} +4.75524e68 q^{70} -4.24492e69 q^{71} +2.06774e68 q^{72} -8.11635e69 q^{73} +6.51741e69 q^{74} -1.91518e70 q^{75} -2.21702e70 q^{76} -2.91878e70 q^{77} -1.13818e71 q^{78} -1.61362e71 q^{79} -7.94344e70 q^{80} -4.12091e71 q^{81} -2.11045e71 q^{82} -6.54865e71 q^{83} +2.43490e71 q^{84} -9.06918e70 q^{85} -1.05220e72 q^{86} +5.02767e72 q^{87} +4.87571e72 q^{88} -1.38399e73 q^{89} -2.43694e72 q^{90} -1.55177e73 q^{91} +1.20210e73 q^{92} +7.03488e73 q^{93} +7.37069e73 q^{94} +2.61288e74 q^{95} -4.06739e73 q^{96} +5.00488e74 q^{97} -2.98287e74 q^{98} +1.49580e74 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	−8.29405e17	−1.06346	−0.531728	−	0.846915i	$-0.678457\pi$
$3$	−8.29405e17	−1.06346	−0.531728	+	0.846915i	$0.678457\pi$
$4$	1.88895e22	0.500000
$5$	−2.22623e26	−1.36834	−0.684170	−	0.729322i	$-0.739835\pi$
$5$	−2.22623e26	−1.36834	−0.684170	+	0.729322i	$0.739835\pi$
$6$	−1.13993e29	−0.751977
$7$	−1.55415e31	−0.316459	−0.158229	−	0.987402i	$-0.550579\pi$
$7$	−1.55415e31	−0.316459	−0.158229	+	0.987402i	$0.550579\pi$
$8$	2.59615e33	0.353553
$9$	7.96464e34	0.130940
$10$	−3.05970e37	−0.967563
$11$	1.87805e39	1.66526	0.832631	−	0.553829i	$-0.186834\pi$
$11$	1.87805e39	1.66526	0.832631	+	0.553829i	$0.186834\pi$
$12$	−1.56670e40	−0.531728
$13$	9.98468e41	1.68445	0.842226	−	0.539125i	$-0.181245\pi$
$13$	9.98468e41	1.68445	0.842226	+	0.539125i	$0.181245\pi$
$14$	−2.13601e42	−0.223770
$15$	1.84644e44	1.45517
$16$	3.56812e44	0.250000
$17$	4.07379e44	0.0293876	0.0146938	−	0.999892i	$-0.495323\pi$
$17$	4.07379e44	0.0293876	0.0146938	+	0.999892i	$0.495323\pi$
$18$	1.09465e46	0.0925886
$19$	−1.17368e48	−1.30704	−0.653521	−	0.756908i	$-0.726709\pi$
$19$	−1.17368e48	−1.30704	−0.653521	+	0.756908i	$0.726709\pi$
$20$	−4.20522e48	−0.684170
$21$	1.28902e49	0.336540
$22$	2.58118e50	1.17752
$23$	6.36387e50	0.548185	0.274093	−	0.961703i	$-0.411622\pi$
$23$	6.36387e50	0.548185	0.274093	+	0.961703i	$0.411622\pi$
$24$	−2.15326e51	−0.375989
$25$	2.30910e52	0.872355
$26$	1.37228e53	1.19109
$27$	4.38441e53	0.924208
$28$	−2.93571e53	−0.158229
$29$	−6.06178e54	−0.876345	−0.438173	−	0.898891i	$-0.644374\pi$
$29$	−6.06178e54	−0.876345	−0.438173	+	0.898891i	$0.644374\pi$
$30$	2.53773e55	1.02896
$31$	−8.48184e55	−1.00560	−0.502802	−	0.864402i	$-0.667697\pi$
$31$	−8.48184e55	−1.00560	−0.502802	+	0.864402i	$0.667697\pi$
$32$	4.90399e55	0.176777
$33$	−1.55767e57	−1.77093
$34$	5.59898e55	0.0207802
$35$	3.45990e57	0.433023
$36$	1.50448e57	0.0654700
$37$	4.74204e58	0.738585	0.369293	−	0.929313i	$-0.379600\pi$
$37$	4.74204e58	0.738585	0.369293	+	0.929313i	$0.379600\pi$
$38$	−1.61309e59	−0.924218
$39$	−8.28135e59	−1.79134
$40$	−5.77961e59	−0.483781
$41$	−1.53555e60	−0.509179	−0.254590	−	0.967049i	$-0.581940\pi$
$41$	−1.53555e60	−0.509179	−0.254590	+	0.967049i	$0.581940\pi$
$42$	1.77162e60	0.237970
$43$	−7.65577e60	−0.425522	−0.212761	−	0.977104i	$-0.568246\pi$
$43$	−7.65577e60	−0.425522	−0.212761	+	0.977104i	$0.568246\pi$
$44$	3.54754e61	0.832631
$45$	−1.77311e61	−0.179170
$46$	8.74644e61	0.387626
$47$	5.36288e62	1.06103	0.530516	−	0.847675i	$-0.321998\pi$
$47$	5.36288e62	1.06103	0.530516	+	0.847675i	$0.321998\pi$
$48$	−2.95942e62	−0.265864
$49$	−2.17033e63	−0.899854
$50$	3.17361e63	0.616848
$51$	−3.37882e62	−0.0312524
$52$	1.88605e64	0.842226
$53$	−3.23526e64	−0.707236	−0.353618	−	0.935390i	$-0.615049\pi$
$53$	−3.23526e64	−0.707236	−0.353618	+	0.935390i	$0.615049\pi$
$54$	6.02588e64	0.653513
$55$	−4.18097e65	−2.27864
$56$	−4.03481e64	−0.111885
$57$	9.73456e65	1.38998
$58$	−8.33125e65	−0.619670
$59$	−1.88381e66	−0.738052	−0.369026	−	0.929419i	$-0.620309\pi$
$59$	−1.88381e66	−0.738052	−0.369026	+	0.929419i	$0.620309\pi$
$60$	3.48783e66	0.727585
$61$	1.66500e67	1.86873	0.934363	−	0.356322i	$-0.115969\pi$
$61$	1.66500e67	1.86873	0.934363	+	0.356322i	$0.115969\pi$
$62$	−1.16574e67	−0.711069
$63$	−1.23783e66	−0.0414371
$64$	6.73999e66	0.125000
$65$	−2.22282e68	−2.30490
$66$	−2.14084e68	−1.25224
$67$	4.39869e68	1.46392	0.731962	−	0.681345i	$-0.238605\pi$
$67$	4.39869e68	1.46392	0.731962	+	0.681345i	$0.238605\pi$
$68$	7.69517e66	0.0146938
$69$	−5.27823e68	−0.582971
$70$	4.75524e68	0.306194
$71$	−4.24492e69	−1.60576	−0.802881	−	0.596139i	$-0.796701\pi$
$71$	−4.24492e69	−1.60576	−0.802881	+	0.596139i	$0.796701\pi$
$72$	2.06774e68	0.0462943
$73$	−8.11635e69	−1.08331	−0.541656	−	0.840600i	$-0.682203\pi$
$73$	−8.11635e69	−1.08331	−0.541656	+	0.840600i	$0.682203\pi$
$74$	6.51741e69	0.522259
$75$	−1.91518e70	−0.927712
$76$	−2.21702e70	−0.653521
$77$	−2.91878e70	−0.526987
$78$	−1.13818e71	−1.26667
$79$	−1.61362e71	−1.11375	−0.556873	−	0.830598i	$-0.687999\pi$
$79$	−1.61362e71	−1.11375	−0.556873	+	0.830598i	$0.687999\pi$
$80$	−7.94344e70	−0.342085
$81$	−4.12091e71	−1.11379
$82$	−2.11045e71	−0.360044
$83$	−6.54865e71	−0.709126	−0.354563	−	0.935032i	$-0.615370\pi$
$83$	−6.54865e71	−0.709126	−0.354563	+	0.935032i	$0.615370\pi$
$84$	2.43490e71	0.168270
$85$	−9.06918e70	−0.0402122
$86$	−1.05220e72	−0.300890
$87$	5.02767e72	0.931955
$88$	4.87571e72	0.588759
$89$	−1.38399e73	−1.09398	−0.546988	−	0.837140i	$-0.684226\pi$
$89$	−1.38399e73	−1.09398	−0.546988	+	0.837140i	$0.684226\pi$
$90$	−2.43694e72	−0.126693
$91$	−1.55177e73	−0.533060
$92$	1.20210e73	0.274093
$93$	7.03488e73	1.06942
$94$	7.37069e73	0.750263
$95$	2.61288e74	1.78848
$96$	−4.06739e73	−0.187994
$97$	5.00488e74	1.56839	0.784194	−	0.620515i	$-0.213076\pi$
$97$	5.00488e74	1.56839	0.784194	+	0.620515i	$0.213076\pi$
$98$	−2.98287e74	−0.636293
$99$	1.49580e74	0.218049
$100$	4.36177e74	0.436177
$101$	−7.09691e74	−0.488672	−0.244336	−	0.969691i	$-0.578570\pi$
$101$	−7.09691e74	−0.488672	−0.244336	+	0.969691i	$0.578570\pi$
$102$	−4.64382e73	−0.0220988
$103$	−3.41071e75	−1.12577	−0.562884	−	0.826536i	$-0.690308\pi$
$103$	−3.41071e75	−1.12577	−0.562884	+	0.826536i	$0.690308\pi$
$104$	2.59217e75	0.595543
$105$	−2.86966e75	−0.460502
$106$	−4.44651e75	−0.500091
$107$	−6.22448e75	−0.492279	−0.246139	−	0.969234i	$-0.579162\pi$
$107$	−6.22448e75	−0.492279	−0.246139	+	0.969234i	$0.579162\pi$
$108$	8.28191e75	0.462104
$109$	−9.85092e75	−0.389030	−0.194515	−	0.980900i	$-0.562313\pi$
$109$	−9.85092e75	−0.389030	−0.194515	+	0.980900i	$0.562313\pi$
$110$	−5.74628e76	−1.61124
$111$	−3.93307e76	−0.785454
$112$	−5.54540e75	−0.0791147
$113$	1.23536e77	1.26285	0.631424	−	0.775438i	$-0.282471\pi$
$113$	1.23536e77	1.26285	0.631424	+	0.775438i	$0.282471\pi$
$114$	1.33791e77	0.982866
$115$	−1.41674e77	−0.750104
$116$	−1.14504e77	−0.438173
$117$	7.95244e76	0.220562
$118$	−2.58909e77	−0.521881
$119$	−6.33129e75	−0.00929997
$120$	4.79364e77	0.514480
$121$	2.25519e78	1.77309
$122$	2.28836e78	1.32139
$123$	1.27360e78	0.541490
$124$	−1.60217e78	−0.502802
$125$	7.52184e77	0.174662
$126$	−1.70126e77	−0.0293005
$127$	−6.94705e78	−0.889530	−0.444765	−	0.895647i	$-0.646713\pi$
$127$	−6.94705e78	−0.889530	−0.444765	+	0.895647i	$0.646713\pi$
$128$	9.26337e77	0.0883883
$129$	6.34974e78	0.452524
$130$	−3.05501e79	−1.62981
$131$	−1.92359e79	−0.769909	−0.384955	−	0.922935i	$-0.625783\pi$
$131$	−1.92359e79	−0.769909	−0.384955	+	0.922935i	$0.625783\pi$
$132$	−2.94235e79	−0.885466
$133$	1.82408e79	0.413625
$134$	6.04552e79	1.03515
$135$	−9.76068e79	−1.26463
$136$	1.05762e78	0.0103901
$137$	1.46819e80	1.09587	0.547937	−	0.836520i	$-0.315414\pi$
$137$	1.46819e80	1.09587	0.547937	+	0.836520i	$0.315414\pi$
$138$	−7.25434e79	−0.412223
$139$	−4.54534e79	−0.197021	−0.0985103	−	0.995136i	$-0.531408\pi$
$139$	−4.54534e79	−0.197021	−0.0985103	+	0.995136i	$0.531408\pi$
$140$	6.53556e79	0.216512
$141$	−4.44800e80	−1.12836
$142$	−5.83417e80	−1.13545
$143$	1.87518e81	2.80505
$144$	2.84188e79	0.0327350
$145$	1.34949e81	1.19914
$146$	−1.11550e81	−0.766018
$147$	1.80008e81	0.956955
$148$	8.95746e80	0.369293
$149$	2.15905e81	0.691477	0.345739	−	0.938331i	$-0.387628\pi$
$149$	2.15905e81	0.691477	0.345739	+	0.938331i	$0.387628\pi$
$150$	−2.63221e81	−0.655991
$151$	−3.16567e81	−0.614937	−0.307468	−	0.951558i	$-0.599482\pi$
$151$	−3.16567e81	−0.614937	−0.307468	+	0.951558i	$0.599482\pi$
$152$	−3.04705e81	−0.462109
$153$	3.24463e79	0.00384801
$154$	−4.01155e81	−0.372636
$155$	1.88825e82	1.37601
$156$	−1.56430e82	−0.895670
$157$	−4.16545e82	−1.87683	−0.938414	−	0.345512i	$-0.887705\pi$
$157$	−4.16545e82	−1.87683	−0.938414	+	0.345512i	$0.887705\pi$
$158$	−2.21775e82	−0.787537
$159$	2.68334e82	0.752115
$160$	−1.09174e82	−0.241891
$161$	−9.89043e81	−0.173478
$162$	−5.66374e82	−0.787572
$163$	6.27900e82	0.693195	0.346597	−	0.938014i	$-0.387337\pi$
$163$	6.27900e82	0.693195	0.346597	+	0.938014i	$0.387337\pi$
$164$	−2.90058e82	−0.254590
$165$	3.46772e83	2.42324
$166$	−9.00040e82	−0.501428
$167$	−4.12831e82	−0.183614	−0.0918068	−	0.995777i	$-0.529264\pi$
$167$	−4.12831e82	−0.183614	−0.0918068	+	0.995777i	$0.529264\pi$
$168$	3.34649e82	0.118985
$169$	6.45579e83	1.83738
$170$	−1.24646e82	−0.0284343
$171$	−9.34794e82	−0.171144
$172$	−1.44613e83	−0.212761
$173$	−1.45822e84	−1.72621	−0.863106	−	0.505023i	$-0.831484\pi$
$173$	−1.45822e84	−1.72621	−0.863106	+	0.505023i	$0.831484\pi$
$174$	6.90998e83	0.658992
$175$	−3.58870e83	−0.276064
$176$	6.70112e83	0.416315
$177$	1.56244e84	0.784886
$178$	−1.90214e84	−0.773558
$179$	3.62514e84	1.19491	0.597456	−	0.801902i	$-0.296178\pi$
$179$	3.62514e84	1.19491	0.597456	+	0.801902i	$0.296178\pi$
$180$	−3.34931e83	−0.0895852
$181$	−4.64230e84	−1.00876	−0.504378	−	0.863483i	$-0.668278\pi$
$181$	−4.64230e84	−1.00876	−0.504378	+	0.863483i	$0.668278\pi$
$182$	−2.13274e84	−0.376930
$183$	−1.38096e85	−1.98731
$184$	1.65216e84	0.193813
$185$	−1.05569e85	−1.01064
$186$	9.66867e84	0.756191
$187$	7.65080e83	0.0489380
$188$	1.01302e85	0.530516
$189$	−6.81404e84	−0.292474
$190$	3.59111e85	1.26465
$191$	2.99797e85	0.867114	0.433557	−	0.901126i	$-0.357258\pi$
$191$	2.99797e85	0.867114	0.433557	+	0.901126i	$0.357258\pi$
$192$	−5.59018e84	−0.132932
$193$	−7.54317e85	−1.47623	−0.738117	−	0.674673i	$-0.764285\pi$
$193$	−7.54317e85	−1.47623	−0.738117	+	0.674673i	$0.764285\pi$
$194$	6.87866e85	1.10902
$195$	1.84361e86	2.45116
$196$	−4.09963e85	−0.449927
$197$	−1.05701e85	−0.0958509	−0.0479254	−	0.998851i	$-0.515261\pi$
$197$	−1.05701e85	−0.0958509	−0.0479254	+	0.998851i	$0.515261\pi$
$198$	2.05582e85	0.154184
$199$	−1.54616e86	−0.959986	−0.479993	−	0.877272i	$-0.659361\pi$
$199$	−1.54616e86	−0.959986	−0.479993	+	0.877272i	$0.659361\pi$
$200$	5.99478e85	0.308424
$201$	−3.64830e86	−1.55682
$202$	−9.75392e85	−0.345544
$203$	9.42093e85	0.277327
$204$	−6.38242e84	−0.0156262
$205$	3.41849e86	0.696730
$206$	−4.68764e86	−0.796038
$207$	5.06860e85	0.0717794
$208$	3.56265e86	0.421113
$209$	−2.20423e87	−2.17657
$210$	−3.94403e86	−0.325624
$211$	8.71904e86	0.602388	0.301194	−	0.953563i	$-0.402615\pi$
$211$	8.71904e86	0.602388	0.301194	+	0.953563i	$0.402615\pi$
$212$	−6.11124e86	−0.353618
$213$	3.52076e87	1.70766
$214$	−8.55486e86	−0.348094
$215$	1.70435e87	0.582259
$216$	1.13826e87	0.326757
$217$	1.31821e87	0.318232
$218$	−1.35390e87	−0.275086
$219$	6.73175e87	1.15206
$220$	−7.89763e87	−1.13932
$221$	4.06755e86	0.0495020
$222$	−5.40558e87	−0.555400
$223$	1.26884e88	1.10147	0.550737	−	0.834679i	$-0.314347\pi$
$223$	1.26884e88	1.10147	0.550737	+	0.834679i	$0.314347\pi$
$224$	−7.62154e86	−0.0559426
$225$	1.83912e87	0.114226
$226$	1.69786e88	0.892969
$227$	−1.10095e88	−0.490678	−0.245339	−	0.969437i	$-0.578899\pi$
$227$	−1.10095e88	−0.490678	−0.245339	+	0.969437i	$0.578899\pi$
$228$	1.83881e88	0.694991
$229$	−4.27548e88	−1.37137	−0.685684	−	0.727900i	$-0.740497\pi$
$229$	−4.27548e88	−1.37137	−0.685684	+	0.727900i	$0.740497\pi$
$230$	−1.94715e88	−0.530404
$231$	2.42085e88	0.560427
$232$	−1.57373e88	−0.309835
$233$	−1.08994e89	−1.82624	−0.913119	−	0.407693i	$-0.866333\pi$
$233$	−1.08994e89	−1.82624	−0.913119	+	0.407693i	$0.866333\pi$
$234$	1.09298e88	0.155961
$235$	−1.19390e89	−1.45185
$236$	−3.55842e88	−0.369026
$237$	1.33835e89	1.18442
$238$	−8.70166e86	−0.00657607
$239$	1.86707e89	1.20570	0.602849	−	0.797855i	$-0.294032\pi$
$239$	1.86707e89	1.20570	0.602849	+	0.797855i	$0.294032\pi$
$240$	6.58833e88	0.363793
$241$	−1.73191e89	−0.818252	−0.409126	−	0.912478i	$-0.634166\pi$
$241$	−1.73191e89	−0.818252	−0.409126	+	0.912478i	$0.634166\pi$
$242$	3.09951e89	1.25377
$243$	7.51018e88	0.260265
$244$	3.14510e89	0.934363
$245$	4.83164e89	1.23131
$246$	1.75042e89	0.382891
$247$	−1.17188e90	−2.20165
$248$	−2.20201e89	−0.355534
$249$	5.43149e89	0.754125
$250$	1.03379e89	0.123505
$251$	−1.23851e90	−1.27390	−0.636951	−	0.770904i	$-0.719805\pi$
$251$	−1.23851e90	−1.27390	−0.636951	+	0.770904i	$0.719805\pi$
$252$	−2.33819e88	−0.0207186
$253$	1.19517e90	0.912872
$254$	−9.54795e89	−0.628993
$255$	7.52203e88	0.0427640
$256$	1.27315e89	0.0625000
$257$	−4.72488e89	−0.200401	−0.100200	−	0.994967i	$-0.531948\pi$
$257$	−4.72488e89	−0.200401	−0.100200	+	0.994967i	$0.531948\pi$
$258$	8.72702e89	0.319983
$259$	−7.36986e89	−0.233732
$260$	−4.19878e90	−1.15245
$261$	−4.82799e89	−0.114749
$262$	−2.64377e90	−0.544408
$263$	−3.66064e89	−0.0653456	−0.0326728	−	0.999466i	$-0.510402\pi$
$263$	−3.66064e89	−0.0653456	−0.0326728	+	0.999466i	$0.510402\pi$
$264$	−4.04394e90	−0.626119
$265$	7.20242e90	0.967739
$266$	2.50699e90	0.292477
$267$	1.14789e91	1.16340
$268$	8.30890e90	0.731962
$269$	−4.34444e90	−0.332830	−0.166415	−	0.986056i	$-0.553219\pi$
$269$	−4.34444e90	−0.332830	−0.166415	+	0.986056i	$0.553219\pi$
$270$	−1.34150e91	−0.894229
$271$	−1.48592e90	−0.0862275	−0.0431138	−	0.999070i	$-0.513728\pi$
$271$	−1.48592e90	−0.0862275	−0.0431138	+	0.999070i	$0.513728\pi$
$272$	1.45358e89	0.00734690
$273$	1.28705e91	0.566886
$274$	2.01786e91	0.774899
$275$	4.33662e91	1.45270
$276$	−9.97029e90	−0.291486
$277$	−2.88571e91	−0.736651	−0.368325	−	0.929697i	$-0.620069\pi$
$277$	−2.88571e91	−0.736651	−0.368325	+	0.929697i	$0.620069\pi$
$278$	−6.24707e90	−0.139315
$279$	−6.75548e90	−0.131674
$280$	8.98240e90	0.153097
$281$	3.86862e91	0.576858	0.288429	−	0.957501i	$-0.406867\pi$
$281$	3.86862e91	0.576858	0.288429	+	0.957501i	$0.406867\pi$
$282$	−6.11329e91	−0.797872
$283$	−6.68958e91	−0.764553	−0.382277	−	0.924048i	$-0.624860\pi$
$283$	−6.68958e91	−0.764553	−0.382277	+	0.924048i	$0.624860\pi$
$284$	−8.01842e91	−0.802881
$285$	−2.16713e92	−1.90197
$286$	2.57722e92	1.98347
$287$	2.38649e91	0.161134
$288$	3.90585e90	0.0231471
$289$	−1.91997e92	−0.999136
$290$	1.85472e92	0.847919
$291$	−4.15108e92	−1.66791
$292$	−1.53314e92	−0.541656
$293$	6.91610e91	0.214944	0.107472	−	0.994208i	$-0.465724\pi$
$293$	6.91610e91	0.214944	0.107472	+	0.994208i	$0.465724\pi$
$294$	2.47401e92	0.676670
$295$	4.19379e92	1.00991
$296$	1.23110e92	0.261129
$297$	8.23415e92	1.53905
$298$	2.96738e92	0.488948
$299$	6.35412e92	0.923391
$300$	−3.61768e92	−0.463856
$301$	1.18982e92	0.134660
$302$	−4.35087e92	−0.434826
$303$	5.88622e92	0.519682
$304$	−4.18783e92	−0.326761
$305$	−3.70667e93	−2.55705
$306$	4.45938e90	0.00272096
$307$	−3.60397e92	−0.194577	−0.0972886	−	0.995256i	$-0.531017\pi$
$307$	−3.60397e92	−0.194577	−0.0972886	+	0.995256i	$0.531017\pi$
$308$	−5.51343e92	−0.263493
$309$	2.82886e93	1.19721
$310$	2.59519e93	0.972984
$311$	9.54657e92	0.317200	0.158600	−	0.987343i	$-0.449302\pi$
$311$	9.54657e92	0.317200	0.158600	+	0.987343i	$0.449302\pi$
$312$	−2.14996e93	−0.633335
$313$	−1.85955e92	−0.0485843	−0.0242922	−	0.999705i	$-0.507733\pi$
$313$	−1.85955e92	−0.0485843	−0.0242922	+	0.999705i	$0.507733\pi$
$314$	−5.72495e93	−1.32712
$315$	2.75568e92	0.0567001
$316$	−3.04805e93	−0.556873
$317$	3.74074e93	0.607065	0.303532	−	0.952821i	$-0.401834\pi$
$317$	3.74074e93	0.607065	0.303532	+	0.952821i	$0.401834\pi$
$318$	3.68796e93	0.531825
$319$	−1.13843e94	−1.45934
$320$	−1.50047e93	−0.171043
$321$	5.16261e93	0.523517
$322$	−1.35933e93	−0.122668
$323$	−4.78133e92	−0.0384108
$324$	−7.78418e93	−0.556897
$325$	2.30557e94	1.46944
$326$	8.62979e93	0.490163
$327$	8.17041e93	0.413717
$328$	−3.98653e93	−0.180022
$329$	−8.33474e93	−0.335773
$330$	4.76600e94	1.71349
$331$	2.81699e94	0.904140	0.452070	−	0.891983i	$-0.350686\pi$
$331$	2.81699e94	0.904140	0.452070	+	0.891983i	$0.350686\pi$
$332$	−1.23701e94	−0.354563
$333$	3.77687e93	0.0967104
$334$	−5.67391e93	−0.129834
$335$	−9.79249e94	−2.00315
$336$	4.59939e93	0.0841351
$337$	7.42858e93	0.121558	0.0607791	−	0.998151i	$-0.480641\pi$
$337$	7.42858e93	0.121558	0.0607791	+	0.998151i	$0.480641\pi$
$338$	8.87277e94	1.29922
$339$	−1.02461e95	−1.34298
$340$	−1.71312e93	−0.0201061
$341$	−1.59294e95	−1.67459
$342$	−1.28477e94	−0.121017
$343$	7.12143e94	0.601226
$344$	−1.98755e94	−0.150445
$345$	1.17505e95	0.797703
$346$	−2.00416e95	−1.22062
$347$	−7.85535e93	−0.0429349	−0.0214674	−	0.999770i	$-0.506834\pi$
$347$	−7.85535e93	−0.0429349	−0.0214674	+	0.999770i	$0.506834\pi$
$348$	9.49700e94	0.465977
$349$	−2.08330e95	−0.917908	−0.458954	−	0.888460i	$-0.651776\pi$
$349$	−2.08330e95	−0.917908	−0.458954	+	0.888460i	$0.651776\pi$
$350$	−4.93227e94	−0.195207
$351$	4.37769e95	1.55678
$352$	9.20995e94	0.294379
$353$	−4.56945e95	−1.31314	−0.656572	−	0.754264i	$-0.727994\pi$
$353$	−4.56945e95	−1.31314	−0.656572	+	0.754264i	$0.727994\pi$
$354$	2.14740e95	0.554998
$355$	9.45014e95	2.19723
$356$	−2.61429e95	−0.546988
$357$	5.25121e93	0.00989011
$358$	4.98235e95	0.844930
$359$	3.68523e95	0.562889	0.281445	−	0.959578i	$-0.409186\pi$
$359$	3.68523e95	0.562889	0.281445	+	0.959578i	$0.409186\pi$
$360$	−4.60326e94	−0.0633463
$361$	5.71181e95	0.708360
$362$	−6.38032e95	−0.713298
$363$	−1.87047e96	−1.88561
$364$	−2.93121e95	−0.266530
$365$	1.80688e96	1.48234
$366$	−1.89798e96	−1.40524
$367$	−8.46585e94	−0.0565839	−0.0282920	−	0.999600i	$-0.509007\pi$
$367$	−8.46585e94	−0.0565839	−0.0282920	+	0.999600i	$0.509007\pi$
$368$	2.27070e95	0.137046
$369$	−1.22301e95	−0.0666719
$370$	−1.45092e96	−0.714628
$371$	5.02809e95	0.223811
$372$	1.32885e96	0.534708
$373$	−3.70126e95	−0.134669	−0.0673345	−	0.997730i	$-0.521449\pi$
$373$	−3.70126e95	−0.134669	−0.0673345	+	0.997730i	$0.521449\pi$
$374$	1.05152e95	0.0346044
$375$	−6.23865e95	−0.185745
$376$	1.39228e96	0.375132
$377$	−6.05249e96	−1.47616
$378$	−9.36514e95	−0.206810
$379$	−1.73905e96	−0.347809	−0.173904	−	0.984763i	$-0.555638\pi$
$379$	−1.73905e96	−0.347809	−0.173904	+	0.984763i	$0.555638\pi$
$380$	4.93558e96	0.894239
$381$	5.76192e96	0.945977
$382$	4.12038e96	0.613143
$383$	−8.53437e96	−1.15138	−0.575689	−	0.817669i	$-0.695266\pi$
$383$	−8.53437e96	−1.15138	−0.575689	+	0.817669i	$0.695266\pi$
$384$	−7.68309e95	−0.0939972
$385$	6.49787e96	0.721097
$386$	−1.03673e97	−1.04385
$387$	−6.09755e95	−0.0557179
$388$	9.45395e96	0.784194
$389$	9.40337e94	0.00708229	0.00354114	−	0.999994i	$-0.498873\pi$
$389$	9.40337e94	0.00708229	0.00354114	+	0.999994i	$0.498873\pi$
$390$	2.53384e97	1.73323
$391$	2.59251e95	0.0161099
$392$	−5.63449e96	−0.318146
$393$	1.59544e97	0.818765
$394$	−1.45275e96	−0.0677768
$395$	3.59229e97	1.52398
$396$	2.82549e96	0.109025
$397$	−3.95671e97	−1.38896	−0.694481	−	0.719511i	$-0.744366\pi$
$397$	−3.95671e97	−1.38896	−0.694481	+	0.719511i	$0.744366\pi$
$398$	−2.12503e97	−0.678812
$399$	−1.51290e97	−0.439872
$400$	8.23916e96	0.218089
$401$	−7.69863e97	−1.85566	−0.927832	−	0.372999i	$-0.878330\pi$
$401$	−7.69863e97	−1.85566	−0.927832	+	0.372999i	$0.878330\pi$
$402$	−5.01419e97	−1.10084
$403$	−8.46885e97	−1.69389
$404$	−1.34057e97	−0.244336
$405$	9.17408e97	1.52405
$406$	1.29480e97	0.196100
$407$	8.90581e97	1.22994
$408$	−8.77193e95	−0.0110494
$409$	7.46400e97	0.857724	0.428862	−	0.903370i	$-0.358915\pi$
$409$	7.46400e97	0.857724	0.428862	+	0.903370i	$0.358915\pi$
$410$	4.69834e97	0.492663
$411$	−1.21772e98	−1.16541
$412$	−6.44265e97	−0.562884
$413$	2.92773e97	0.233563
$414$	6.96623e96	0.0507557
$415$	1.45788e98	0.970326
$416$	4.89647e97	0.297772
$417$	3.76993e97	0.209523
$418$	−3.02948e98	−1.53907
$419$	4.15685e98	1.93081	0.965403	−	0.260764i	$-0.0839743\pi$
$419$	4.15685e98	1.93081	0.965403	+	0.260764i	$0.0839743\pi$
$420$	−5.42063e97	−0.230251
$421$	5.18566e97	0.201477	0.100738	−	0.994913i	$-0.467879\pi$
$421$	5.18566e97	0.201477	0.100738	+	0.994913i	$0.467879\pi$
$422$	1.19834e98	0.425953
$423$	4.27135e97	0.138932
$424$	−8.39922e97	−0.250046
$425$	9.40681e96	0.0256364
$426$	4.83889e98	1.20750
$427$	−2.58767e98	−0.591375
$428$	−1.17577e98	−0.246139
$429$	−1.55528e99	−2.98305
$430$	2.34244e98	0.411719
$431$	2.19728e98	0.353987	0.176993	−	0.984212i	$-0.443363\pi$
$431$	2.19728e98	0.353987	0.176993	+	0.984212i	$0.443363\pi$
$432$	1.56441e98	0.231052
$433$	5.89966e98	0.798970	0.399485	−	0.916740i	$-0.369189\pi$
$433$	5.89966e98	0.798970	0.399485	+	0.916740i	$0.369189\pi$
$434$	1.81173e98	0.225024
$435$	−1.11927e99	−1.27523
$436$	−1.86079e98	−0.194515
$437$	−7.46915e98	−0.716501
$438$	9.25204e98	0.814626
$439$	−1.28246e98	−0.103664	−0.0518318	−	0.998656i	$-0.516506\pi$
$439$	−1.28246e98	−0.103664	−0.0518318	+	0.998656i	$0.516506\pi$
$440$	−1.08544e99	−0.805622
$441$	−1.72859e98	−0.117827
$442$	5.59040e97	0.0350032
$443$	1.16361e99	0.669372	0.334686	−	0.942330i	$-0.391370\pi$
$443$	1.16361e99	0.669372	0.334686	+	0.942330i	$0.391370\pi$
$444$	−7.42937e98	−0.392727
$445$	3.08108e99	1.49693
$446$	1.74388e99	0.778859
$447$	−1.79073e99	−0.735356
$448$	−1.04750e98	−0.0395574
$449$	−6.16043e98	−0.213980	−0.106990	−	0.994260i	$-0.534121\pi$
$449$	−6.16043e98	−0.213980	−0.106990	+	0.994260i	$0.534121\pi$
$450$	2.52767e98	0.0807701
$451$	−2.88385e99	−0.847916
$452$	2.33353e99	0.631424
$453$	2.62563e99	0.653958
$454$	−1.51313e99	−0.346961
$455$	3.45460e99	0.729407
$456$	2.52724e99	0.491433
$457$	4.54761e99	0.814565	0.407282	−	0.913302i	$-0.366477\pi$
$457$	4.54761e99	0.814565	0.407282	+	0.913302i	$0.366477\pi$
$458$	−5.87617e99	−0.969703
$459$	1.78611e98	0.0271602
$460$	−2.67615e99	−0.375052
$461$	1.15281e100	1.48927	0.744637	−	0.667470i	$-0.232623\pi$
$461$	1.15281e100	1.48927	0.744637	+	0.667470i	$0.232623\pi$
$462$	3.32720e99	0.396282
$463$	−2.73824e99	−0.300735	−0.150368	−	0.988630i	$-0.548046\pi$
$463$	−2.73824e99	−0.300735	−0.150368	+	0.988630i	$0.548046\pi$
$464$	−2.16291e99	−0.219086
$465$	−1.56612e100	−1.46332
$466$	−1.49801e100	−1.29135
$467$	−1.35563e100	−1.07835	−0.539174	−	0.842195i	$-0.681263\pi$
$467$	−1.35563e100	−1.07835	−0.539174	+	0.842195i	$0.681263\pi$
$468$	1.50217e99	0.110281
$469$	−6.83624e99	−0.463272
$470$	−1.64088e100	−1.02662
$471$	3.45484e100	1.99593
$472$	−4.89065e99	−0.260941
$473$	−1.43780e100	−0.708605
$474$	1.83941e100	0.837512
$475$	−2.71015e100	−1.14020
$476$	−1.19595e98	−0.00464998
$477$	−2.57677e99	−0.0926055
$478$	2.56608e100	0.852557
$479$	6.35771e100	1.95307	0.976537	−	0.215349i	$-0.0690888\pi$
$479$	6.35771e100	1.95307	0.976537	+	0.215349i	$0.0690888\pi$
$480$	9.05493e99	0.257240
$481$	4.73478e100	1.24411
$482$	−2.38032e100	−0.578592
$483$	8.20317e99	0.184486
$484$	4.25994e100	0.886547
$485$	−1.11420e101	−2.14609
$486$	1.03219e100	0.184035
$487$	3.48960e100	0.576023	0.288011	−	0.957627i	$-0.407006\pi$
$487$	3.48960e100	0.576023	0.288011	+	0.957627i	$0.407006\pi$
$488$	4.32259e100	0.660695
$489$	−5.20784e100	−0.737182
$490$	6.64055e100	0.870665
$491$	−6.33059e100	−0.768932	−0.384466	−	0.923139i	$-0.625614\pi$
$491$	−6.33059e100	−0.768932	−0.384466	+	0.923139i	$0.625614\pi$
$492$	2.40576e100	0.270745
$493$	−2.46944e99	−0.0257537
$494$	−1.61062e101	−1.55680
$495$	−3.33000e100	−0.298366
$496$	−3.02642e100	−0.251401
$497$	6.59725e100	0.508158
$498$	7.46498e100	0.533247
$499$	−3.51910e100	−0.233164	−0.116582	−	0.993181i	$-0.537194\pi$
$499$	−3.51910e100	−0.233164	−0.116582	+	0.993181i	$0.537194\pi$
$500$	1.42083e100	0.0873310
$501$	3.42404e100	0.195265
$502$	−1.70220e101	−0.900785
$503$	3.58969e100	0.176302	0.0881511	−	0.996107i	$-0.471904\pi$
$503$	3.58969e100	0.176302	0.0881511	+	0.996107i	$0.471904\pi$
$504$	−3.21358e99	−0.0146502
$505$	1.57993e101	0.668670
$506$	1.64263e101	0.645498
$507$	−5.35447e101	−1.95397
$508$	−1.31226e101	−0.444765
$509$	−7.46958e99	−0.0235168	−0.0117584	−	0.999931i	$-0.503743\pi$
$509$	−7.46958e99	−0.0235168	−0.0117584	+	0.999931i	$0.503743\pi$
$510$	1.03382e100	0.0302387
$511$	1.26141e101	0.342824
$512$	1.74980e100	0.0441942
$513$	−5.14589e101	−1.20798
$514$	−6.49383e100	−0.141705
$515$	7.59301e101	1.54043
$516$	1.19943e101	0.226262
$517$	1.00718e102	1.76690
$518$	−1.01291e101	−0.165273
$519$	1.20946e102	1.83575
$520$	−5.77076e101	−0.814906
$521$	3.09674e101	0.406902	0.203451	−	0.979085i	$-0.434784\pi$
$521$	3.09674e101	0.406902	0.203451	+	0.979085i	$0.434784\pi$
$522$	−6.63554e100	−0.0811395
$523$	−9.52389e101	−1.08393	−0.541965	−	0.840401i	$-0.682319\pi$
$523$	−9.52389e101	−1.08393	−0.541965	+	0.840401i	$0.682319\pi$
$524$	−3.63356e101	−0.384955
$525$	2.97649e101	0.293583
$526$	−5.03115e100	−0.0462064
$527$	−3.45532e100	−0.0295523
$528$	−5.55794e101	−0.442733
$529$	−9.42694e101	−0.699493
$530$	9.89894e101	0.684295
$531$	−1.50039e101	−0.0966405
$532$	3.44559e101	0.206813
$533$	−1.53320e102	−0.857687
$534$	1.57765e102	0.822646
$535$	1.38571e102	0.673605
$536$	1.14197e102	0.517575
$537$	−3.00671e102	−1.27074
$538$	−5.97095e101	−0.235347
$539$	−4.07599e102	−1.49849
$540$	−1.84374e102	−0.632315
$541$	−4.46468e102	−1.42854	−0.714271	−	0.699869i	$-0.753242\pi$
$541$	−4.46468e102	−1.42854	−0.714271	+	0.699869i	$0.753242\pi$
$542$	−2.04223e101	−0.0609721
$543$	3.85035e102	1.07277
$544$	1.99778e100	0.00519504
$545$	2.19304e102	0.532325
$546$	1.76891e102	0.400849
$547$	−1.26733e102	−0.268142	−0.134071	−	0.990972i	$-0.542805\pi$
$547$	−1.26733e102	−0.268142	−0.134071	+	0.990972i	$0.542805\pi$
$548$	2.77333e102	0.547937
$549$	1.32611e102	0.244691
$550$	5.96021e102	1.02721
$551$	7.11459e102	1.14542
$552$	−1.37031e102	−0.206112
$553$	2.50782e102	0.352455
$554$	−3.96609e102	−0.520891
$555$	8.75591e102	1.07477
$556$	−8.58591e101	−0.0985103
$557$	−4.72421e101	−0.0506710	−0.0253355	−	0.999679i	$-0.508065\pi$
$557$	−4.72421e101	−0.0506710	−0.0253355	+	0.999679i	$0.508065\pi$
$558$	−9.28467e101	−0.0931073
$559$	−7.64405e102	−0.716771
$560$	1.23453e102	0.108256
$561$	−6.34561e101	−0.0520435
$562$	5.31699e102	0.407900
$563$	1.10218e103	0.791024	0.395512	−	0.918461i	$-0.370567\pi$
$563$	1.10218e103	0.791024	0.395512	+	0.918461i	$0.370567\pi$
$564$	−8.40204e102	−0.564181
$565$	−2.75019e103	−1.72801
$566$	−9.19409e102	−0.540621
$567$	6.40453e102	0.352470
$568$	−1.10204e103	−0.567723
$569$	−5.86938e102	−0.283062	−0.141531	−	0.989934i	$-0.545203\pi$
$569$	−5.86938e102	−0.283062	−0.141531	+	0.989934i	$0.545203\pi$
$570$	−2.97849e103	−1.34490
$571$	1.45096e103	0.613481	0.306740	−	0.951793i	$-0.400762\pi$
$571$	1.45096e103	0.613481	0.306740	+	0.951793i	$0.400762\pi$
$572$	3.54211e103	1.40253
$573$	−2.48653e103	−0.922139
$574$	3.27996e102	0.113939
$575$	1.46948e103	0.478212
$576$	5.36816e101	0.0163675
$577$	7.89017e102	0.225420	0.112710	−	0.993628i	$-0.464047\pi$
$577$	7.89017e102	0.225420	0.112710	+	0.993628i	$0.464047\pi$
$578$	−2.63878e103	−0.706496
$579$	6.25635e103	1.56991
$580$	2.54911e103	0.599569
$581$	1.01776e103	0.224409
$582$	−5.70519e103	−1.17939
$583$	−6.07600e103	−1.17773
$584$	−2.10713e103	−0.383009
$585$	−1.77039e103	−0.301804
$586$	9.50541e102	0.151988
$587$	−3.76809e102	−0.0565187	−0.0282594	−	0.999601i	$-0.508996\pi$
$587$	−3.76809e102	−0.0565187	−0.0282594	+	0.999601i	$0.508996\pi$
$588$	3.40025e103	0.478478
$589$	9.95497e103	1.31437
$590$	5.76390e103	0.714111
$591$	8.76691e102	0.101933
$592$	1.69202e103	0.184646
$593$	−1.26288e104	−1.29363	−0.646814	−	0.762648i	$-0.723899\pi$
$593$	−1.26288e104	−1.29363	−0.646814	+	0.762648i	$0.723899\pi$
$594$	1.13169e104	1.08827
$595$	1.40949e102	0.0127255
$596$	4.07833e103	0.345739
$597$	1.28240e104	1.02090
$598$	8.73304e103	0.652936
$599$	−3.24607e103	−0.227957	−0.113978	−	0.993483i	$-0.536359\pi$
$599$	−3.24607e103	−0.227957	−0.113978	+	0.993483i	$0.536359\pi$
$600$	−4.97210e103	−0.327996
$601$	−2.30066e104	−1.42580	−0.712902	−	0.701264i	$-0.752620\pi$
$601$	−2.30066e104	−1.42580	−0.712902	+	0.701264i	$0.752620\pi$
$602$	1.63528e103	0.0952192
$603$	3.50340e103	0.191686
$604$	−5.97979e103	−0.307468
$605$	−5.02056e104	−2.42620
$606$	8.08995e103	0.367471
$607$	3.30878e104	1.41284	0.706419	−	0.707794i	$-0.250310\pi$
$607$	3.30878e104	1.41284	0.706419	+	0.707794i	$0.250310\pi$
$608$	−5.75571e103	−0.231055
$609$	−7.81377e103	−0.294925
$610$	−5.09441e104	−1.80811
$611$	5.35467e104	1.78726
$612$	6.12893e101	0.00192401
$613$	−5.93336e104	−1.75199	−0.875997	−	0.482316i	$-0.839796\pi$
$613$	−5.93336e104	−1.75199	−0.875997	+	0.482316i	$0.839796\pi$
$614$	−4.95326e103	−0.137587
$615$	−2.83532e104	−0.740942
$616$	−7.57759e103	−0.186318
$617$	7.08431e103	0.163910	0.0819548	−	0.996636i	$-0.473884\pi$
$617$	7.08431e103	0.163910	0.0819548	+	0.996636i	$0.473884\pi$
$618$	3.88796e104	0.846552
$619$	6.67201e104	1.36728	0.683640	−	0.729820i	$-0.260396\pi$
$619$	6.67201e104	1.36728	0.683640	+	0.729820i	$0.260396\pi$
$620$	3.56680e104	0.688003
$621$	2.79018e104	0.506637
$622$	1.31207e104	0.224294
$623$	2.15093e104	0.346199
$624$	−2.95488e104	−0.447835
$625$	−7.78668e104	−1.11135
$626$	−2.55575e103	−0.0343543
$627$	1.82820e105	2.31468
$628$	−7.86831e104	−0.938414
$629$	1.93181e103	0.0217053
$630$	3.78738e103	0.0400930
$631$	8.55168e104	0.853003	0.426502	−	0.904487i	$-0.359746\pi$
$631$	8.55168e104	0.853003	0.426502	+	0.904487i	$0.359746\pi$
$632$	−4.18920e104	−0.393769
$633$	−7.23162e104	−0.640614
$634$	5.14123e104	0.429260
$635$	1.54657e105	1.21718
$636$	5.06869e104	0.376057
$637$	−2.16700e105	−1.51576
$638$	−1.56465e105	−1.03191
$639$	−3.38093e104	−0.210258
$640$	−2.06223e104	−0.120945
$641$	2.71307e105	1.50067	0.750335	−	0.661058i	$-0.229892\pi$
$641$	2.71307e105	1.50067	0.750335	+	0.661058i	$0.229892\pi$
$642$	7.09544e104	0.370183
$643$	−3.18845e105	−1.56917	−0.784583	−	0.620024i	$-0.787123\pi$
$643$	−3.18845e105	−1.56917	−0.784583	+	0.620024i	$0.787123\pi$
$644$	−1.86825e104	−0.0867391
$645$	−1.41360e105	−0.619207
$646$	−6.57140e103	−0.0271606
$647$	−2.76536e105	−1.07855	−0.539276	−	0.842129i	$-0.681302\pi$
$647$	−2.76536e105	−1.07855	−0.539276	+	0.842129i	$0.681302\pi$
$648$	−1.06985e105	−0.393786
$649$	−3.53790e105	−1.22905
$650$	3.16875e105	1.03905
$651$	−1.09333e105	−0.338426
$652$	1.18607e105	0.346597
$653$	2.47810e105	0.683714	0.341857	−	0.939752i	$-0.388944\pi$
$653$	2.47810e105	0.683714	0.341857	+	0.939752i	$0.388944\pi$
$654$	1.12293e105	0.292542
$655$	4.28235e105	1.05350
$656$	−5.47904e104	−0.127295
$657$	−6.46439e104	−0.141849
$658$	−1.14552e105	−0.237427
$659$	6.68906e105	1.30967	0.654835	−	0.755772i	$-0.272738\pi$
$659$	6.68906e105	1.30967	0.654835	+	0.755772i	$0.272738\pi$
$660$	6.55034e105	1.21162
$661$	−6.13773e105	−1.07264	−0.536319	−	0.844015i	$-0.680186\pi$
$661$	−6.13773e105	−1.07264	−0.536319	+	0.844015i	$0.680186\pi$
$662$	3.87164e105	0.639323
$663$	−3.37365e104	−0.0526432
$664$	−1.70013e105	−0.250714
$665$	−4.06081e105	−0.565980
$666$	5.19089e104	0.0683846
$667$	−3.85764e105	−0.480400
$668$	−7.79816e104	−0.0918068
$669$	−1.05238e106	−1.17137
$670$	−1.34587e106	−1.41644
$671$	3.12696e106	3.11192
$672$	6.32135e104	0.0594925
$673$	−3.50520e105	−0.311995	−0.155997	−	0.987757i	$-0.549859\pi$
$673$	−3.50520e105	−0.311995	−0.155997	+	0.987757i	$0.549859\pi$
$674$	1.02098e105	0.0859546
$675$	1.01240e106	0.806237
$676$	1.21946e106	0.918688
$677$	1.71047e106	1.21911	0.609553	−	0.792745i	$-0.291349\pi$
$677$	1.71047e106	1.21911	0.609553	+	0.792745i	$0.291349\pi$
$678$	−1.40822e106	−0.949633
$679$	−7.77835e105	−0.496331
$680$	−2.35449e104	−0.0142172
$681$	9.13130e105	0.521814
$682$	−2.18931e106	−1.18412
$683$	−3.84199e106	−1.96689	−0.983444	−	0.181210i	$-0.941999\pi$
$683$	−3.84199e106	−1.96689	−0.983444	+	0.181210i	$0.941999\pi$
$684$	−1.76578e105	−0.0855721
$685$	−3.26852e106	−1.49953
$686$	9.78761e105	0.425131
$687$	3.54610e106	1.45839
$688$	−2.73167e105	−0.106381
$689$	−3.23031e106	−1.19130
$690$	1.61498e106	0.564061
$691$	−1.12187e105	−0.0371121	−0.0185561	−	0.999828i	$-0.505907\pi$
$691$	−1.12187e105	−0.0371121	−0.0185561	+	0.999828i	$0.505907\pi$
$692$	−2.75450e106	−0.863106
$693$	−2.32471e105	−0.0690036
$694$	−1.07963e105	−0.0303595
$695$	1.01190e106	0.269591
$696$	1.30526e106	0.329496
$697$	−6.25553e104	−0.0149636
$698$	−2.86327e106	−0.649059
$699$	9.04006e106	1.94213
$700$	−6.77886e105	−0.138032
$701$	2.83921e106	0.547988	0.273994	−	0.961731i	$-0.411655\pi$
$701$	2.83921e106	0.547988	0.273994	+	0.961731i	$0.411655\pi$
$702$	6.01665e106	1.10081
$703$	−5.56564e106	−0.965362
$704$	1.26581e106	0.208158
$705$	9.90226e106	1.54398
$706$	−6.28020e106	−0.928533
$707$	1.10297e106	0.154645
$708$	2.95137e106	0.392443
$709$	4.94736e106	0.623935	0.311968	−	0.950093i	$-0.399012\pi$
$709$	4.94736e106	0.623935	0.311968	+	0.950093i	$0.399012\pi$
$710$	1.29882e107	1.55368
$711$	−1.28519e106	−0.145834
$712$	−3.59305e106	−0.386779
$713$	−5.39773e106	−0.551257
$714$	7.21721e104	0.00699337
$715$	−4.17457e107	−3.83826
$716$	6.84769e106	0.597456
$717$	−1.54856e107	−1.28221
$718$	5.06494e106	0.398023
$719$	7.68470e106	0.573183	0.286592	−	0.958053i	$-0.407478\pi$
$719$	7.68470e106	0.573183	0.286592	+	0.958053i	$0.407478\pi$
$720$	−6.32667e105	−0.0447926
$721$	5.30077e106	0.356259
$722$	7.85025e106	0.500886
$723$	1.43646e107	0.870176
$724$	−8.76905e106	−0.504378
$725$	−1.39973e107	−0.764484
$726$	−2.57075e107	−1.33333
$727$	3.98650e106	0.196359	0.0981795	−	0.995169i	$-0.468698\pi$
$727$	3.98650e106	0.196359	0.0981795	+	0.995169i	$0.468698\pi$
$728$	−4.02863e106	−0.188465
$729$	1.88372e107	0.837014
$730$	2.48336e107	1.04817
$731$	−3.11880e105	−0.0125051
$732$	−2.60856e107	−0.993655
$733$	−1.11549e107	−0.403707	−0.201853	−	0.979416i	$-0.564696\pi$
$733$	−1.11549e107	−0.403707	−0.201853	+	0.979416i	$0.564696\pi$
$734$	−1.16354e106	−0.0400109
$735$	−4.00738e107	−1.30944
$736$	3.12083e106	0.0969064
$737$	8.26098e107	2.43782
$738$	−1.68090e106	−0.0471442
$739$	−4.22593e107	−1.12656	−0.563282	−	0.826265i	$-0.690462\pi$
$739$	−4.22593e107	−1.12656	−0.563282	+	0.826265i	$0.690462\pi$
$740$	−1.99413e107	−0.505318
$741$	9.71965e107	2.34136
$742$	6.91056e106	0.158258
$743$	5.42936e107	1.18214	0.591069	−	0.806621i	$-0.298706\pi$
$743$	5.42936e107	1.18214	0.591069	+	0.806621i	$0.298706\pi$
$744$	1.82636e107	0.378095
$745$	−4.80654e107	−0.946176
$746$	−5.08697e106	−0.0952254
$747$	−5.21577e106	−0.0928529
$748$	1.44519e106	0.0244690
$749$	9.67379e106	0.155786
$750$	−8.57434e106	−0.131342
$751$	−7.98494e107	−1.16352	−0.581760	−	0.813360i	$-0.697636\pi$
$751$	−7.98494e107	−1.16352	−0.581760	+	0.813360i	$0.697636\pi$
$752$	1.91354e107	0.265258
$753$	1.02723e108	1.35474
$754$	−8.31848e107	−1.04380
$755$	7.04750e107	0.841443
$756$	−1.28714e107	−0.146237
$757$	−2.06338e107	−0.223092	−0.111546	−	0.993759i	$-0.535580\pi$
$757$	−2.06338e107	−0.223092	−0.111546	+	0.993759i	$0.535580\pi$
$758$	−2.39013e107	−0.245938
$759$	−9.91280e107	−0.970800
$760$	6.78342e107	0.632323
$761$	−1.47887e108	−1.31221	−0.656106	−	0.754669i	$-0.727798\pi$
$761$	−1.47887e108	−1.31221	−0.656106	+	0.754669i	$0.727798\pi$
$762$	7.91912e107	0.668907
$763$	1.53098e107	0.123112
$764$	5.66301e107	0.433557
$765$	−7.22328e105	−0.00526539
$766$	−1.17296e108	−0.814147
$767$	−1.88092e108	−1.24321
$768$	−1.05596e107	−0.0664660
$769$	7.93316e107	0.475564	0.237782	−	0.971319i	$-0.423580\pi$
$769$	7.93316e107	0.475564	0.237782	+	0.971319i	$0.423580\pi$
$770$	8.93061e107	0.509893
$771$	3.91884e107	0.213117
$772$	−1.42487e108	−0.738117
$773$	1.03986e108	0.513149	0.256574	−	0.966524i	$-0.417406\pi$
$773$	1.03986e108	0.513149	0.256574	+	0.966524i	$0.417406\pi$
$774$	−8.38041e106	−0.0393985
$775$	−1.95855e108	−0.877243
$776$	1.29934e108	0.554509
$777$	6.11260e107	0.248564
$778$	1.29239e106	0.00500793
$779$	1.80225e108	0.665519
$780$	3.48249e108	1.22558
$781$	−7.97218e108	−2.67401
$782$	3.56312e106	0.0113914
$783$	−2.65773e108	−0.809925
$784$	−7.74398e107	−0.224963
$785$	9.27322e108	2.56814
$786$	2.19275e108	0.578954
$787$	2.02195e108	0.509000	0.254500	−	0.967073i	$-0.418089\pi$
$787$	2.02195e108	0.509000	0.254500	+	0.967073i	$0.418089\pi$
$788$	−1.99664e107	−0.0479254
$789$	3.03616e107	0.0694923
$790$	4.93720e108	1.07762
$791$	−1.91994e108	−0.399640
$792$	3.88333e107	0.0770921
$793$	1.66245e109	3.14778
$794$	−5.43807e108	−0.982145
$795$	−5.97373e108	−1.02915
$796$	−2.92062e108	−0.479993
$797$	−3.29051e108	−0.515913	−0.257956	−	0.966157i	$-0.583049\pi$
$797$	−3.29051e108	−0.515913	−0.257956	+	0.966157i	$0.583049\pi$
$798$	−2.07931e108	−0.311037
$799$	2.18473e107	0.0311812
$800$	1.13238e108	0.154212
$801$	−1.10230e108	−0.143245
$802$	−1.05809e109	−1.31215
$803$	−1.52429e109	−1.80400
$804$	−6.89144e108	−0.778410
$805$	2.20183e108	0.237377
$806$	−1.16395e109	−1.19776
$807$	3.60330e108	0.353951
$808$	−1.84246e108	−0.172772
$809$	−2.09693e108	−0.187722	−0.0938608	−	0.995585i	$-0.529921\pi$
$809$	−2.09693e108	−0.187722	−0.0938608	+	0.995585i	$0.529921\pi$
$810$	1.26088e109	1.07767
$811$	1.16218e109	0.948402	0.474201	−	0.880416i	$-0.342737\pi$
$811$	1.16218e109	0.948402	0.474201	+	0.880416i	$0.342737\pi$
$812$	1.77956e108	0.138664
$813$	1.23243e108	0.0916993
$814$	1.22401e109	0.869697
$815$	−1.39785e109	−0.948526
$816$	−1.20560e107	−0.00781311
$817$	8.98543e108	0.556175
$818$	1.02584e109	0.606503
$819$	−1.23593e108	−0.0697988
$820$	6.45735e108	0.348365
$821$	3.65373e108	0.188308	0.0941539	−	0.995558i	$-0.469985\pi$
$821$	3.65373e108	0.188308	0.0941539	+	0.995558i	$0.469985\pi$
$822$	−1.67363e109	−0.824072
$823$	3.56139e109	1.67543	0.837714	−	0.546109i	$-0.183892\pi$
$823$	3.56139e109	1.67543	0.837714	+	0.546109i	$0.183892\pi$
$824$	−8.85471e108	−0.398019
$825$	−3.59682e109	−1.54488
$826$	4.02384e108	0.165154
$827$	1.71189e109	0.671459	0.335729	−	0.941958i	$-0.391017\pi$
$827$	1.71189e109	0.671459	0.335729	+	0.941958i	$0.391017\pi$
$828$	9.57431e107	0.0358897
$829$	−2.00028e109	−0.716633	−0.358316	−	0.933600i	$-0.616649\pi$
$829$	−2.00028e109	−0.716633	−0.358316	+	0.933600i	$0.616649\pi$
$830$	2.00369e109	0.686124
$831$	2.39342e109	0.783396
$832$	6.72966e108	0.210556
$833$	−8.84145e107	−0.0264445
$834$	5.18136e108	0.148155
$835$	9.19056e108	0.251246
$836$	−4.16368e109	−1.08828
$837$	−3.71878e109	−0.929386
$838$	5.71313e109	1.36529
$839$	4.00565e109	0.915377	0.457688	−	0.889113i	$-0.348678\pi$
$839$	4.00565e109	0.915377	0.457688	+	0.889113i	$0.348678\pi$
$840$	−7.45005e108	−0.162812
$841$	−1.11013e109	−0.232019
$842$	7.12711e108	0.142466
$843$	−3.20865e109	−0.613463
$844$	1.64698e109	0.301194
$845$	−1.43720e110	−2.51415
$846$	5.87049e108	0.0982395
$847$	−3.50491e109	−0.561112
$848$	−1.15438e109	−0.176809
$849$	5.54838e109	0.813069
$850$	1.29286e108	0.0181277
$851$	3.01777e109	0.404882
$852$	6.65052e109	0.853829
$853$	−1.40330e109	−0.172410	−0.0862048	−	0.996277i	$-0.527474\pi$
$853$	−1.40330e109	−0.172410	−0.0862048	+	0.996277i	$0.527474\pi$
$854$	−3.55646e109	−0.418165
$855$	2.08106e109	0.234183
$856$	−1.61597e109	−0.174047
$857$	4.46969e109	0.460783	0.230391	−	0.973098i	$-0.425999\pi$
$857$	4.46969e109	0.460783	0.230391	+	0.973098i	$0.425999\pi$
$858$	−2.13756e110	−2.10933
$859$	−1.18479e110	−1.11917	−0.559587	−	0.828772i	$-0.689040\pi$
$859$	−1.18479e110	−1.11917	−0.559587	+	0.828772i	$0.689040\pi$
$860$	3.21942e109	0.291129
$861$	−1.97936e109	−0.171359
$862$	3.01991e109	0.250307
$863$	1.46698e109	0.116418	0.0582089	−	0.998304i	$-0.481461\pi$
$863$	1.46698e109	0.116418	0.0582089	+	0.998304i	$0.481461\pi$
$864$	2.15011e109	0.163378
$865$	3.24633e110	2.36204
$866$	8.10843e109	0.564957
$867$	1.59243e110	1.06254
$868$	2.49002e109	0.159116
$869$	−3.03047e110	−1.85468
$870$	−1.53832e110	−0.901725
$871$	4.39196e110	2.46591
$872$	−2.55745e109	−0.137543
$873$	3.98621e109	0.205365
$874$	−1.02655e110	−0.506643
$875$	−1.16901e109	−0.0552733
$876$	1.27159e110	0.576028
$877$	1.25090e110	0.542922	0.271461	−	0.962449i	$-0.412493\pi$
$877$	1.25090e110	0.542922	0.271461	+	0.962449i	$0.412493\pi$
$878$	−1.76261e109	−0.0733012
$879$	−5.73625e109	−0.228584
$880$	−1.49182e110	−0.569661
$881$	−2.80953e110	−1.02810	−0.514052	−	0.857759i	$-0.671856\pi$
$881$	−2.80953e110	−1.02810	−0.514052	+	0.857759i	$0.671856\pi$
$882$	−2.37575e109	−0.0833162
$883$	1.39779e110	0.469804	0.234902	−	0.972019i	$-0.424523\pi$
$883$	1.39779e110	0.469804	0.234902	+	0.972019i	$0.424523\pi$
$884$	7.68338e108	0.0247510
$885$	−3.47835e110	−1.07399
$886$	1.59925e110	0.473318
$887$	5.30801e110	1.50590	0.752949	−	0.658079i	$-0.228631\pi$
$887$	5.30801e110	1.50590	0.752949	+	0.658079i	$0.228631\pi$
$888$	−1.02108e110	−0.277700
$889$	1.07968e110	0.281500
$890$	4.23460e110	1.05849
$891$	−7.73929e110	−1.85476
$892$	2.39677e110	0.550737
$893$	−6.29431e110	−1.38681
$894$	−2.46116e110	−0.519975
$895$	−8.07038e110	−1.63505
$896$	−1.43967e109	−0.0279713
$897$	−5.27014e110	−0.981987
$898$	−8.46683e109	−0.151307
$899$	5.14150e110	0.881255
$900$	3.47400e109	0.0571131
$901$	−1.31798e109	−0.0207840
$902$	−3.96354e110	−0.599567
$903$	−9.86847e109	−0.143205
$904$	3.20717e110	0.446484
$905$	1.03348e111	1.38032
$906$	3.60863e110	0.462418
$907$	1.22817e111	1.51003	0.755017	−	0.655705i	$-0.227629\pi$
$907$	1.22817e111	1.51003	0.755017	+	0.655705i	$0.227629\pi$
$908$	−2.07963e110	−0.245339
$909$	−5.65244e109	−0.0639868
$910$	4.74796e110	0.515768
$911$	−1.04727e110	−0.109174	−0.0545869	−	0.998509i	$-0.517384\pi$
$911$	−1.04727e110	−0.109174	−0.0545869	+	0.998509i	$0.517384\pi$
$912$	3.47341e110	0.347496
$913$	−1.22987e111	−1.18088
$914$	6.25018e110	0.575984
$915$	3.07433e111	2.71932
$916$	−8.07614e110	−0.685684
$917$	2.98956e110	0.243645
$918$	2.45482e109	0.0192052
$919$	−1.55586e111	−1.16853	−0.584265	−	0.811563i	$-0.698617\pi$
$919$	−1.55586e111	−1.16853	−0.584265	+	0.811563i	$0.698617\pi$
$920$	−3.67807e110	−0.265202
$921$	2.98915e110	0.206924
$922$	1.58442e111	1.05308
$923$	−4.23841e111	−2.70483
$924$	4.57286e110	0.280214
$925$	1.09499e111	0.644309
$926$	−3.76341e110	−0.212652
$927$	−2.71651e110	−0.147408
$928$	−2.97269e110	−0.154917
$929$	5.14453e110	0.257488	0.128744	−	0.991678i	$-0.458906\pi$
$929$	5.14453e110	0.257488	0.128744	+	0.991678i	$0.458906\pi$
$930$	−2.15246e111	−1.03473
$931$	2.54727e111	1.17615
$932$	−2.05885e111	−0.913119
$933$	−7.91798e110	−0.337328
$934$	−1.86317e111	−0.762507
$935$	−1.70324e110	−0.0669639
$936$	2.06457e110	0.0779804
$937$	1.80393e111	0.654613	0.327306	−	0.944918i	$-0.393859\pi$
$937$	1.80393e111	0.654613	0.327306	+	0.944918i	$0.393859\pi$
$938$	−9.39566e110	−0.327583
$939$	1.54232e110	0.0516673
$940$	−2.25521e111	−0.725927
$941$	3.50968e111	1.08557	0.542783	−	0.839873i	$-0.317370\pi$
$941$	3.50968e111	1.08557	0.542783	+	0.839873i	$0.317370\pi$
$942$	4.74830e111	1.41133
$943$	−9.77207e110	−0.279125
$944$	−6.72166e110	−0.184513
$945$	1.51696e111	0.400204
$946$	−1.97609e111	−0.501060
$947$	−8.18908e109	−0.0199577	−0.00997886	−	0.999950i	$-0.503176\pi$
$947$	−8.18908e109	−0.0199577	−0.00997886	+	0.999950i	$0.503176\pi$
$948$	2.52807e111	0.592210
$949$	−8.10392e111	−1.82479
$950$	−3.72480e111	−0.806246
$951$	−3.10259e111	−0.645587
$952$	−1.64370e109	−0.00328804
$953$	3.51442e111	0.675880	0.337940	−	0.941168i	$-0.390270\pi$
$953$	3.51442e111	0.675880	0.337940	+	0.941168i	$0.390270\pi$
$954$	−3.54149e110	−0.0654820
$955$	−6.67417e111	−1.18651
$956$	3.52679e111	0.602849
$957$	9.44224e111	1.55195
$958$	8.73797e111	1.38103
$959$	−2.28179e111	−0.346799
$960$	1.24450e111	0.181896
$961$	7.99453e109	0.0112374
$962$	6.50743e111	0.879719
$963$	−4.95758e110	−0.0644590
$964$	−3.27149e111	−0.409126
$965$	1.67928e112	2.01999
$966$	1.12744e111	0.130452
$967$	−9.06620e110	−0.100910	−0.0504548	−	0.998726i	$-0.516067\pi$
$967$	−9.06620e110	−0.100910	−0.0504548	+	0.998726i	$0.516067\pi$
$968$	5.85481e111	0.626884
$969$	3.96566e110	0.0408483
$970$	−1.53134e112	−1.51751
$971$	−6.33234e111	−0.603731	−0.301865	−	0.953351i	$-0.597609\pi$
$971$	−6.33234e111	−0.603731	−0.301865	+	0.953351i	$0.597609\pi$
$972$	1.41863e111	0.130132
$973$	7.06416e110	0.0623489
$974$	4.79607e111	0.407309
$975$	−1.91225e112	−1.56268
$976$	5.94092e111	0.467182
$977$	−8.44572e111	−0.639132	−0.319566	−	0.947564i	$-0.603537\pi$
$977$	−8.44572e111	−0.639132	−0.319566	+	0.947564i	$0.603537\pi$
$978$	−7.15759e111	−0.521267
$979$	−2.59921e112	−1.82176
$980$	9.12670e111	0.615653
$981$	−7.84591e110	−0.0509396
$982$	−8.70069e111	−0.543717
$983$	2.68399e112	1.61445	0.807223	−	0.590246i	$-0.200969\pi$
$983$	2.68399e112	1.61445	0.807223	+	0.590246i	$0.200969\pi$
$984$	3.30645e111	0.191446
$985$	2.35315e111	0.131157
$986$	−3.39397e110	−0.0182106
$987$	6.91288e111	0.357080
$988$	−2.21362e112	−1.10082
$989$	−4.87204e111	−0.233265
$990$	−4.57671e111	−0.210976
$991$	−1.66221e112	−0.737773	−0.368886	−	0.929475i	$-0.620261\pi$
$991$	−1.66221e112	−0.737773	−0.368886	+	0.929475i	$0.620261\pi$
$992$	−4.15948e111	−0.177767
$993$	−2.33643e112	−0.961513
$994$	9.06719e111	0.359322
$995$	3.44211e112	1.31359
$996$	1.02598e112	0.377062
$997$	2.22959e112	0.789143	0.394572	−	0.918865i	$-0.370893\pi$
$997$	2.22959e112	0.789143	0.394572	+	0.918865i	$0.370893\pi$
$998$	−4.83662e111	−0.164872
$999$	2.07910e112	0.682606

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2.76.a.b.1.1	✓	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)

\(f(q)\)	\(=\)	\(q+1.37439e11 q^{2} -8.29405e17 q^{3} +1.88895e22 q^{4} -2.22623e26 q^{5} -1.13993e29 q^{6} -1.55415e31 q^{7} +2.59615e33 q^{8} +7.96464e34 q^{9} -3.05970e37 q^{10} +1.87805e39 q^{11} -1.56670e40 q^{12} +9.98468e41 q^{13} -2.13601e42 q^{14} +1.84644e44 q^{15} +3.56812e44 q^{16} +4.07379e44 q^{17} +1.09465e46 q^{18} -1.17368e48 q^{19} -4.20522e48 q^{20} +1.28902e49 q^{21} +2.58118e50 q^{22} +6.36387e50 q^{23} -2.15326e51 q^{24} +2.30910e52 q^{25} +1.37228e53 q^{26} +4.38441e53 q^{27} -2.93571e53 q^{28} -6.06178e54 q^{29} +2.53773e55 q^{30} -8.48184e55 q^{31} +4.90399e55 q^{32} -1.55767e57 q^{33} +5.59898e55 q^{34} +3.45990e57 q^{35} +1.50448e57 q^{36} +4.74204e58 q^{37} -1.61309e59 q^{38} -8.28135e59 q^{39} -5.77961e59 q^{40} -1.53555e60 q^{41} +1.77162e60 q^{42} -7.65577e60 q^{43} +3.54754e61 q^{44} -1.77311e61 q^{45} +8.74644e61 q^{46} +5.36288e62 q^{47} -2.95942e62 q^{48} -2.17033e63 q^{49} +3.17361e63 q^{50} -3.37882e62 q^{51} +1.88605e64 q^{52} -3.23526e64 q^{53} +6.02588e64 q^{54} -4.18097e65 q^{55} -4.03481e64 q^{56} +9.73456e65 q^{57} -8.33125e65 q^{58} -1.88381e66 q^{59} +3.48783e66 q^{60} +1.66500e67 q^{61} -1.16574e67 q^{62} -1.23783e66 q^{63} +6.73999e66 q^{64} -2.22282e68 q^{65} -2.14084e68 q^{66} +4.39869e68 q^{67} +7.69517e66 q^{68} -5.27823e68 q^{69} +4.75524e68 q^{70} -4.24492e69 q^{71} +2.06774e68 q^{72} -8.11635e69 q^{73} +6.51741e69 q^{74} -1.91518e70 q^{75} -2.21702e70 q^{76} -2.91878e70 q^{77} -1.13818e71 q^{78} -1.61362e71 q^{79} -7.94344e70 q^{80} -4.12091e71 q^{81} -2.11045e71 q^{82} -6.54865e71 q^{83} +2.43490e71 q^{84} -9.06918e70 q^{85} -1.05220e72 q^{86} +5.02767e72 q^{87} +4.87571e72 q^{88} -1.38399e73 q^{89} -2.43694e72 q^{90} -1.55177e73 q^{91} +1.20210e73 q^{92} +7.03488e73 q^{93} +7.37069e73 q^{94} +2.61288e74 q^{95} -4.06739e73 q^{96} +5.00488e74 q^{97} -2.98287e74 q^{98} +1.49580e74 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q + 412316860416 q^{2} + 45\!\cdots\!16 q^{3} + 56\!\cdots\!52 q^{4} - 19\!\cdots\!90 q^{5} + 62\!\cdots\!52 q^{6} - 37\!\cdots\!52 q^{7} + 77\!\cdots\!44 q^{8} - 26\!\cdots\!69 q^{9} - 26\!\cdots\!80 q^{10}+ \cdots + 90\!\cdots\!32 q^{99}+O(q^{100}) \) 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

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