LMFDB - Embedded newform 1.68.a.a.1.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1,68,Mod(1,1)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1, base_ring=CyclotomicField(1))

chi = DirichletCharacter(H, H._module([]))

N = Newforms(chi, 68, names="a")

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

chi := DirichletCharacter("1.1");

S:= CuspForms(chi, 68);

N := Newforms(S);

Level:	$ N $	$=$	$ 1 $
Weight:	$ k $	$=$	$ 68 $
Character orbit:	$[\chi]$	$=$	1.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	yes
Analytic conductor:	$28.4290351930$
Analytic rank:	$0$
Dimension:	$5$
Coefficient field:	$\mathbb{Q}[x]/(x^{5} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{5} - x^{4} + \cdots + 20\!\cdots\!00 $ x^5 - x^4 - 939384011925257456x^3 + 31046449413968483513911200x^2 + 156793504704482691874379743265203200*x + 20916736226052669578405116700517591609696000
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{40}\cdot 3^{15}\cdot 5^{4}\cdot 7^{2}\cdot 11\cdot 13\cdot 17 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.5
Root			$-8.99335e8$ of defining polynomial
Character	$\chi$	$=$	1.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.26950e10 q^{2} -1.28429e15 q^{3} +3.67490e20 q^{4} -1.61198e23 q^{5} -2.91471e25 q^{6} +2.93806e28 q^{7} +4.99099e30 q^{8} -9.10601e31 q^{9} +O(q^{10})$	\(q+2.26950e10 q^{2} -1.28429e15 q^{3} +3.67490e20 q^{4} -1.61198e23 q^{5} -2.91471e25 q^{6} +2.93806e28 q^{7} +4.99099e30 q^{8} -9.10601e31 q^{9} -3.65838e33 q^{10} +1.03989e35 q^{11} -4.71965e35 q^{12} -9.30624e35 q^{13} +6.66794e38 q^{14} +2.07025e38 q^{15} +5.90387e40 q^{16} +2.52116e41 q^{17} -2.06661e42 q^{18} -4.10720e41 q^{19} -5.92385e43 q^{20} -3.77334e43 q^{21} +2.36002e45 q^{22} -7.28152e44 q^{23} -6.40990e45 q^{24} -4.17779e46 q^{25} -2.11205e46 q^{26} +2.36014e47 q^{27} +1.07971e49 q^{28} -8.66841e48 q^{29} +4.69844e48 q^{30} +5.42697e49 q^{31} +6.03344e50 q^{32} -1.33552e50 q^{33} +5.72177e51 q^{34} -4.73609e51 q^{35} -3.34636e52 q^{36} +2.44090e52 q^{37} -9.32129e51 q^{38} +1.19520e51 q^{39} -8.04536e53 q^{40} +8.84851e52 q^{41} -8.56360e53 q^{42} -3.35174e54 q^{43} +3.82147e55 q^{44} +1.46787e55 q^{45} -1.65254e55 q^{46} -1.34362e56 q^{47} -7.58230e55 q^{48} +4.44845e56 q^{49} -9.48151e56 q^{50} -3.23791e56 q^{51} -3.41995e56 q^{52} -3.87432e57 q^{53} +5.35634e57 q^{54} -1.67627e58 q^{55} +1.46639e59 q^{56} +5.27485e56 q^{57} -1.96730e59 q^{58} -2.62052e59 q^{59} +7.60797e58 q^{60} -4.77635e59 q^{61} +1.23165e60 q^{62} -2.67540e60 q^{63} +4.98032e60 q^{64} +1.50015e59 q^{65} -3.03096e60 q^{66} -2.36430e61 q^{67} +9.26500e61 q^{68} +9.35162e59 q^{69} -1.07486e62 q^{70} +2.36087e61 q^{71} -4.54480e62 q^{72} +7.86035e61 q^{73} +5.53962e62 q^{74} +5.36551e61 q^{75} -1.50935e62 q^{76} +3.05525e63 q^{77} +2.71250e61 q^{78} -2.74602e63 q^{79} -9.51690e63 q^{80} +8.13902e63 q^{81} +2.00817e63 q^{82} +9.16622e63 q^{83} -1.38666e64 q^{84} -4.06405e64 q^{85} -7.60679e64 q^{86} +1.11328e64 q^{87} +5.19006e65 q^{88} -3.36134e65 q^{89} +3.33133e65 q^{90} -2.73423e64 q^{91} -2.67588e65 q^{92} -6.96983e64 q^{93} -3.04935e66 q^{94} +6.62071e64 q^{95} -7.74871e65 q^{96} +6.50306e66 q^{97} +1.00958e67 q^{98} -9.46921e66 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 5 q + 5554901256 q^{2} + 34\!\cdots\!72 q^{3}+ \cdots + 27\!\cdots\!85 q^{9}+O(q^{10}) $ 5 * q + 5554901256 * q^2 + 3443360269119372 * q^3 + 350472004382296600640 * q^4 + 330744836907160597528950 * q^5 + 146648871573834733762548960 * q^6 + 33632726520317603069152899256 * q^7 + 3261706912683890613885787783680 * q^8 + 27806018581845734541016911293385 * q^9	$ 5 q + 5554901256 q^{2} + 34\!\cdots\!72 q^{3}+ \cdots + 16\!\cdots\!20 q^{99}+O(q^{100}) $ 5 * q + 5554901256 * q^2 + 3443360269119372 * q^3 + 350472004382296600640 * q^4 + 330744836907160597528950 * q^5 + 146648871573834733762548960 * q^6 + 33632726520317603069152899256 * q^7 + 3261706912683890613885787783680 * q^8 + 27806018581845734541016911293385 * q^9 - 5287067006725590176865792208438800 * q^10 + 203006981551281631527218766884109060 * q^11 - 2089518810401181456110201520986913024 * q^12 + 177822884499813229570219072356766702 * q^13 + 290753425875732621001638220329334092480 * q^14 - 933024301033068664231979455289562936600 * q^15 + 18266362102387359184851236859301091348480 * q^16 + 75241497376497768433807587544150344102906 * q^17 - 1011568566626978308983328666525487111002968 * q^18 + 3998884102997801557241177083441346393295100 * q^19 - 15074831378020267075078660994426474705846400 * q^20 - 175719863949295325296418063144372762630915040 * q^21 + 1841247880573095918698534631505063585473750432 * q^22 - 419660874260151197180020017656265233426170968 * q^23 - 13019747846573945420584224979196286639928166400 * q^24 + 175279270003539476977813620578789764300129011875 * q^25 + 21416337629300654169124097666599354769371062960 * q^26 + 1886613800166950113417786970194782722207999659320 * q^27 + 14982728306233364463143494158089725946900023694848 * q^28 + 18733547497571939101380180097730717676662894233950 * q^29 + 183881202860964913168534714290880945912096094414400 * q^30 + 365849822471060800690376948081970588059264217288160 * q^31 + 1591165751988992347021834813546084975107380979204096 * q^32 + 2437038903031213839498705428654461423996034595356784 * q^33 + 7817592154883765712044327776251337623941567500782480 * q^34 + 4524513410554564733118320802153390591800073874285200 * q^35 - 38131548457864843751915538710226876689225094472585920 * q^36 - 56389392588768330454829645685931746748224606527380394 * q^37 - 311451303114725973135630000941921262878276604287141280 * q^38 - 717177850582388225418943791249053833224228521090828280 * q^39 - 1886768345048751997029226502271137564956948018338432000 * q^40 + 113555410342193387626817165052765483601006465327103010 * q^41 + 2805540126450529847390961864461873572829871059166350592 * q^42 + 6508304671085340439704487085091235272293711787089861092 * q^43 + 49369449025916528958230735645862721892607029455332199680 * q^44 + 99011086960300194550392336618799141939148872728728967150 * q^45 + 79552980744915855625545425031873854934595203714399466560 * q^46 - 128023594814179612806658270243785955024442659789917751344 * q^47 - 198512903890152994486195174416803543869354744423782432768 * q^48 - 771329931628098140389185999842408514636676231229111640435 * q^49 - 3919481096957516748709549462396523762064894577356951885000 * q^50 - 3397415009313164473667296477133432796692029796730856284840 * q^51 + 672997930141532412373441872733517069231734104886640838016 * q^52 + 1046765637663599376128164919371991945530174947374966490822 * q^53 + 19066352042639687223500180230679796188217876586398799185600 * q^54 + 66942753107037791618627925698973654692865254681839842449400 * q^55 + 164746697572073652525116376573879338548073684495562965299200 * q^56 - 9288557942524759644038647059781434529266663439727382990960 * q^57 - 61137956327686914952144218440883774026433838412764071303120 * q^58 - 305790738450157663862297559072875409310668010528073986627500 * q^59 - 1346157500908637758724100110370785768539984220742218248588800 * q^60 - 1137073938560830615075915586814815057732339483683661907261890 * q^61 - 2197846158587850633685459639420082896328263471188214086352128 * q^62 - 2062780018748959038039139080074136999529046449885010133153768 * q^63 + 6319522016046144185339524760669817745425888834305772325437440 * q^64 + 17054811715744261908524663200762497384422620874171150779332900 * q^65 + 27998862803339055552343423092993933514291039899414979026779520 * q^66 - 11903044989154510038048691316368615691989662189985228212145844 * q^67 + 81678078346863753465296539273887923556029130514802676363013248 * q^68 + 3593002077831059525793506029116145162632074080747869594484320 * q^69 - 262230520857255225386866306600227822969034558447869634844476800 * q^70 - 112169920751076079402369696382938772997794660792753351047772040 * q^71 - 747723581155501189674233444839980291686130221322311676193789440 * q^72 - 304061800126793465330511223999919410949872771539142074085150718 * q^73 + 921008183492866283853128598587548033201480125306857491530532080 * q^74 + 21623812027928499471467875193108522496460255319651250940492500 * q^75 + 2076567511595431334156222539483464646991367936386801535927366400 * q^76 + 5018131462902473316385236580394702266689060843204393245422638432 * q^77 + 6187393864780941106550100388692932558738785969110711253222726464 * q^78 + 2994504004186984867153587379277397704940492543518650040519815600 * q^79 - 15198313539268031787508043655897930060910106707913153957798092800 * q^80 - 11195187555119704986426983039082721262159900559267345597680888595 * q^81 - 17699192859543411700126655967680257958811789647196784631772687408 * q^82 - 47352447490969920981134910324833485175129837165394254819464203588 * q^83 - 52124143836539534782259645807914007868879894236203487647926097920 * q^84 - 39334683419450918052255554891934302881190270223971152032299949300 * q^85 + 49699285824187070765304255878405188987409992188766856866277888160 * q^86 + 357574798440063707158439877351651513807909832776407769090038489160 * q^87 + 430257938373980762031490456670953174964896424231159472833711400960 * q^88 - 11988583288945008097106276879882407358382120120051430459779195150 * q^89 + 477054381540878916877701150770415125576892082956059127548575220400 * q^90 + 232376792470844928685229521265495056030669651812230900159714321360 * q^91 - 986292139147147043544160128863480288571347084605459783959415954944 * q^92 - 1849280210034321990512094428557344731461785100166176155774311127936 * q^93 - 4927754861315037106505826725122767884474273389521981763161929704320 * q^94 - 2022377488008256909110920831467942087293430657450319294506545963000 * q^95 - 2242556165580376632567217570505477297218451346654758522676359331840 * q^96 + 2897556354128426205551279700626881901316694084191208635967319112106 * q^97 + 12426885478574475523720488645206508880013087100212747539199689691208 * q^98 + 16175146031966622867876651602334534091105243319832315048256094545620 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	2.26950e10	1.86821	0.934105	−	0.356999i	$-0.116200\pi$
$2$	2.26950e10	1.86821	0.934105	+	0.356999i	$0.116200\pi$
$3$	−1.28429e15	−0.133384	−0.0666918	−	0.997774i	$-0.521244\pi$
$3$	−1.28429e15	−0.133384	−0.0666918	+	0.997774i	$0.521244\pi$
$4$	3.67490e20	2.49021
$5$	−1.61198e23	−0.619247	−0.309623	−	0.950859i	$-0.600203\pi$
$5$	−1.61198e23	−0.619247	−0.309623	+	0.950859i	$0.600203\pi$
$6$	−2.91471e25	−0.249189
$7$	2.93806e28	1.43641	0.718203	−	0.695834i	$-0.244965\pi$
$7$	2.93806e28	1.43641	0.718203	+	0.695834i	$0.244965\pi$
$8$	4.99099e30	2.78402
$9$	−9.10601e31	−0.982209
$10$	−3.65838e33	−1.15688
$11$	1.03989e35	1.34999	0.674995	−	0.737822i	$-0.264146\pi$
$11$	1.03989e35	1.34999	0.674995	+	0.737822i	$0.264146\pi$
$12$	−4.71965e35	−0.332153
$13$	−9.30624e35	−0.0448407	−0.0224203	−	0.999749i	$-0.507137\pi$
$13$	−9.30624e35	−0.0448407	−0.0224203	+	0.999749i	$0.507137\pi$
$14$	6.66794e38	2.68351
$15$	2.07025e38	0.0825974
$16$	5.90387e40	2.71092
$17$	2.52116e41	1.51901	0.759506	−	0.650500i	$-0.225441\pi$
$17$	2.52116e41	1.51901	0.759506	+	0.650500i	$0.225441\pi$
$18$	−2.06661e42	−1.83497
$19$	−4.10720e41	−0.0596074	−0.0298037	−	0.999556i	$-0.509488\pi$
$19$	−4.10720e41	−0.0596074	−0.0298037	+	0.999556i	$0.509488\pi$
$20$	−5.92385e43	−1.54205
$21$	−3.77334e43	−0.191593
$22$	2.36002e45	2.52207
$23$	−7.28152e44	−0.175525	−0.0877626	−	0.996141i	$-0.527972\pi$
$23$	−7.28152e44	−0.175525	−0.0877626	+	0.996141i	$0.527972\pi$
$24$	−6.40990e45	−0.371342
$25$	−4.17779e46	−0.616533
$26$	−2.11205e46	−0.0837718
$27$	2.36014e47	0.264394
$28$	1.07971e49	3.57695
$29$	−8.66841e48	−0.886353	−0.443176	−	0.896434i	$-0.646148\pi$
$29$	−8.66841e48	−0.886353	−0.443176	+	0.896434i	$0.646148\pi$
$30$	4.69844e48	0.154309
$31$	5.42697e49	0.594211	0.297106	−	0.954845i	$-0.403979\pi$
$31$	5.42697e49	0.594211	0.297106	+	0.954845i	$0.403979\pi$
$32$	6.03344e50	2.28056
$33$	−1.33552e50	−0.180067
$34$	5.72177e51	2.83783
$35$	−4.73609e51	−0.889490
$36$	−3.34636e52	−2.44590
$37$	2.44090e52	0.712511	0.356255	−	0.934389i	$-0.384053\pi$
$37$	2.44090e52	0.712511	0.356255	+	0.934389i	$0.384053\pi$
$38$	−9.32129e51	−0.111359
$39$	1.19520e51	0.00598101
$40$	−8.04536e53	−1.72399
$41$	8.84851e52	0.0829108	0.0414554	−	0.999140i	$-0.486801\pi$
$41$	8.84851e52	0.0829108	0.0414554	+	0.999140i	$0.486801\pi$
$42$	−8.56360e53	−0.357936
$43$	−3.35174e54	−0.636909	−0.318455	−	0.947938i	$-0.603164\pi$
$43$	−3.35174e54	−0.636909	−0.318455	+	0.947938i	$0.603164\pi$
$44$	3.82147e55	3.36176
$45$	1.46787e55	0.608230
$46$	−1.65254e55	−0.327918
$47$	−1.34362e56	−1.29718	−0.648588	−	0.761140i	$-0.724640\pi$
$47$	−1.34362e56	−1.29718	−0.648588	+	0.761140i	$0.724640\pi$
$48$	−7.58230e55	−0.361593
$49$	4.44845e56	1.06326
$50$	−9.48151e56	−1.15181
$51$	−3.23791e56	−0.202611
$52$	−3.41995e56	−0.111663
$53$	−3.87432e57	−0.668273	−0.334136	−	0.942525i	$-0.608445\pi$
$53$	−3.87432e57	−0.668273	−0.334136	+	0.942525i	$0.608445\pi$
$54$	5.35634e57	0.493944
$55$	−1.67627e58	−0.835977
$56$	1.46639e59	3.99898
$57$	5.27485e56	0.00795064
$58$	−1.96730e59	−1.65589
$59$	−2.62052e59	−1.24407	−0.622035	−	0.782989i	$-0.713694\pi$
$59$	−2.62052e59	−1.24407	−0.622035	+	0.782989i	$0.713694\pi$
$60$	7.60797e58	0.205685
$61$	−4.77635e59	−0.742244	−0.371122	−	0.928584i	$-0.621027\pi$
$61$	−4.77635e59	−0.742244	−0.371122	+	0.928584i	$0.621027\pi$
$62$	1.23165e60	1.11011
$63$	−2.67540e60	−1.41085
$64$	4.98032e60	1.54963
$65$	1.50015e59	0.0277674
$66$	−3.03096e60	−0.336402
$67$	−2.36430e61	−1.58561	−0.792805	−	0.609476i	$-0.791380\pi$
$67$	−2.36430e61	−1.58561	−0.792805	+	0.609476i	$0.791380\pi$
$68$	9.26500e61	3.78265
$69$	9.35162e59	0.0234122
$70$	−1.07486e62	−1.66175
$71$	2.36087e61	0.226943	0.113471	−	0.993541i	$-0.463803\pi$
$71$	2.36087e61	0.226943	0.113471	+	0.993541i	$0.463803\pi$
$72$	−4.54480e62	−2.73449
$73$	7.86035e61	0.297938	0.148969	−	0.988842i	$-0.452404\pi$
$73$	7.86035e61	0.297938	0.148969	+	0.988842i	$0.452404\pi$
$74$	5.53962e62	1.33112
$75$	5.36551e61	0.0822354
$76$	−1.50935e62	−0.148435
$77$	3.05525e63	1.93913
$78$	2.71250e61	0.0111738
$79$	−2.74602e63	−0.738237	−0.369118	−	0.929382i	$-0.620340\pi$
$79$	−2.74602e63	−0.738237	−0.369118	+	0.929382i	$0.620340\pi$
$80$	−9.51690e63	−1.67873
$81$	8.13902e63	0.946943
$82$	2.00817e63	0.154895
$83$	9.16622e63	0.471058	0.235529	−	0.971867i	$-0.424318\pi$
$83$	9.16622e63	0.471058	0.235529	+	0.971867i	$0.424318\pi$
$84$	−1.38666e64	−0.477106
$85$	−4.06405e64	−0.940643
$86$	−7.60679e64	−1.18988
$87$	1.11328e64	0.118225
$88$	5.19006e65	3.75840
$89$	−3.36134e65	−1.66704	−0.833521	−	0.552488i	$-0.813679\pi$
$89$	−3.36134e65	−1.66704	−0.833521	+	0.552488i	$0.813679\pi$
$90$	3.33133e65	1.13630
$91$	−2.73423e64	−0.0644094
$92$	−2.67588e65	−0.437094
$93$	−6.96983e64	−0.0792580
$94$	−3.04935e66	−2.42340
$95$	6.62071e64	0.0369117
$96$	−7.74871e65	−0.304189
$97$	6.50306e66	1.80412	0.902059	−	0.431614i	$-0.142056\pi$
$97$	6.50306e66	1.80412	0.902059	+	0.431614i	$0.142056\pi$
$98$	1.00958e67	1.98639
$99$	−9.46921e66	−1.32597
$100$	−1.53530e67	−1.53530
$101$	1.99950e67	1.43270	0.716352	−	0.697739i	$-0.245811\pi$
$101$	1.99950e67	1.43270	0.716352	+	0.697739i	$0.245811\pi$
$102$	−7.34844e66	−0.378520
$103$	2.01461e67	0.748417	0.374209	−	0.927345i	$-0.377914\pi$
$103$	2.01461e67	0.748417	0.374209	+	0.927345i	$0.377914\pi$
$104$	−4.64474e66	−0.124837
$105$	6.08254e66	0.118643
$106$	−8.79277e67	−1.24847
$107$	−3.65427e67	−0.378830	−0.189415	−	0.981897i	$-0.560659\pi$
$107$	−3.65427e67	−0.378830	−0.189415	+	0.981897i	$0.560659\pi$
$108$	8.67327e67	0.658396
$109$	−5.60552e67	−0.312484	−0.156242	−	0.987719i	$-0.549938\pi$
$109$	−5.60552e67	−0.312484	−0.156242	+	0.987719i	$0.549938\pi$
$110$	−3.80430e68	−1.56178
$111$	−3.13483e67	−0.0950373
$112$	1.73460e69	3.89399
$113$	−9.31318e66	−0.0155228	−0.00776140	−	0.999970i	$-0.502471\pi$
$113$	−9.31318e66	−0.0155228	−0.00776140	+	0.999970i	$0.502471\pi$
$114$	1.19713e67	0.0148535
$115$	1.17376e68	0.108693
$116$	−3.18555e69	−2.20720
$117$	8.47427e67	0.0440429
$118$	−5.94727e69	−2.32418
$119$	7.40733e69	2.18192
$120$	1.03326e69	0.229953
$121$	4.88014e69	0.822474
$122$	−1.08399e70	−1.38667
$123$	−1.13641e68	−0.0110589
$124$	1.99436e70	1.47971
$125$	1.76577e70	1.00103
$126$	−6.07183e70	−2.63576
$127$	2.79868e70	0.932243	0.466121	−	0.884721i	$-0.345651\pi$
$127$	2.79868e70	0.932243	0.466121	+	0.884721i	$0.345651\pi$
$128$	2.39907e70	0.614480
$129$	4.30463e69	0.0849533
$130$	3.40458e69	0.0518754
$131$	−2.72280e70	−0.320943	−0.160471	−	0.987040i	$-0.551301\pi$
$131$	−2.72280e70	−0.320943	−0.160471	+	0.987040i	$0.551301\pi$
$132$	−4.90790e70	−0.448403
$133$	−1.20672e70	−0.0856204
$134$	−5.36578e71	−2.96225
$135$	−3.80449e70	−0.163725
$136$	1.25831e72	4.22896
$137$	3.57817e70	0.0940853	0.0470427	−	0.998893i	$-0.485020\pi$
$137$	3.57817e70	0.0940853	0.0470427	+	0.998893i	$0.485020\pi$
$138$	2.12235e70	0.0437389
$139$	7.45641e71	1.20652	0.603259	−	0.797545i	$-0.293869\pi$
$139$	7.45641e71	1.20652	0.603259	+	0.797545i	$0.293869\pi$
$140$	−1.74047e72	−2.21501
$141$	1.72561e71	0.173022
$142$	5.35799e71	0.423977
$143$	−9.67743e70	−0.0605345
$144$	−5.37607e72	−2.66269
$145$	1.39733e72	0.548871
$146$	1.78391e72	0.556611
$147$	−5.71311e71	−0.141822
$148$	8.97004e72	1.77430
$149$	1.30102e72	0.205373	0.102686	−	0.994714i	$-0.467256\pi$
$149$	1.30102e72	0.205373	0.102686	+	0.994714i	$0.467256\pi$
$150$	1.21770e72	0.153633
$151$	−1.36349e73	−1.37697	−0.688486	−	0.725250i	$-0.741724\pi$
$151$	−1.36349e73	−1.37697	−0.688486	+	0.725250i	$0.741724\pi$
$152$	−2.04990e72	−0.165948
$153$	−2.29577e73	−1.49199
$154$	6.93390e73	3.62271
$155$	−8.74816e72	−0.367963
$156$	4.39222e71	0.0148940
$157$	−1.66635e73	−0.456171	−0.228085	−	0.973641i	$-0.573247\pi$
$157$	−1.66635e73	−0.456171	−0.228085	+	0.973641i	$0.573247\pi$
$158$	−6.23209e73	−1.37918
$159$	4.97576e72	0.0891366
$160$	−9.72577e73	−1.41223
$161$	−2.13936e73	−0.252125
$162$	1.84715e74	1.76909
$163$	−9.35739e70	−0.000729239 0	−0.000364620	−	1.00000i	$-0.500116\pi$
$163$	−9.35739e70	−0.000729239 0	−0.000364620		1.00000i	$0.500116\pi$
$164$	3.25174e73	0.206465
$165$	2.15283e73	0.111506
$166$	2.08027e74	0.880035
$167$	4.79288e74	1.65804	0.829019	−	0.559220i	$-0.188899\pi$
$167$	4.79288e74	1.65804	0.829019	+	0.559220i	$0.188899\pi$
$168$	−1.88327e74	−0.533398
$169$	−4.29863e74	−0.997989
$170$	−9.22337e74	−1.75732
$171$	3.74002e73	0.0585469
$172$	−1.23173e75	−1.58604
$173$	1.22221e75	1.29599	0.647995	−	0.761645i	$-0.275608\pi$
$173$	1.22221e75	1.29599	0.647995	+	0.761645i	$0.275608\pi$
$174$	2.52659e74	0.220869
$175$	−1.22746e75	−0.885592
$176$	6.13935e75	3.65972
$177$	3.36552e74	0.165939
$178$	−7.62856e75	−3.11438
$179$	−1.85195e75	−0.626689	−0.313344	−	0.949640i	$-0.601449\pi$
$179$	−1.85195e75	−0.626689	−0.313344	+	0.949640i	$0.601449\pi$
$180$	5.39426e75	1.51462
$181$	4.04550e75	0.943497	0.471748	−	0.881733i	$-0.343623\pi$
$181$	4.04550e75	0.943497	0.471748	+	0.881733i	$0.343623\pi$
$182$	−6.20535e74	−0.120330
$183$	6.13424e74	0.0990032
$184$	−3.63420e75	−0.488666
$185$	−3.93467e75	−0.441220
$186$	−1.58180e75	−0.148071
$187$	2.62172e76	2.05065
$188$	−4.93767e76	−3.23024
$189$	6.93425e75	0.379777
$190$	1.50257e75	0.0689587
$191$	8.00578e74	0.0308167	0.0154083	−	0.999881i	$-0.495095\pi$
$191$	8.00578e74	0.0308167	0.0154083	+	0.999881i	$0.495095\pi$
$192$	−6.39620e75	−0.206695
$193$	−5.34503e76	−1.45138	−0.725688	−	0.688024i	$-0.758478\pi$
$193$	−5.34503e76	−1.45138	−0.725688	+	0.688024i	$0.758478\pi$
$194$	1.47587e77	3.37047
$195$	−1.92663e74	−0.00370372
$196$	1.63476e77	2.64774
$197$	2.95191e75	0.0403166	0.0201583	−	0.999797i	$-0.493583\pi$
$197$	2.95191e75	0.0403166	0.0201583	+	0.999797i	$0.493583\pi$
$198$	−2.14904e77	−2.47719
$199$	−1.57308e77	−1.53170	−0.765850	−	0.643019i	$-0.777682\pi$
$199$	−1.57308e77	−1.53170	−0.765850	+	0.643019i	$0.777682\pi$
$200$	−2.08513e77	−1.71644
$201$	3.03645e76	0.211494
$202$	4.53788e77	2.67659
$203$	−2.54684e77	−1.27316
$204$	−1.18990e77	−0.504544
$205$	−1.42636e76	−0.0513422
$206$	4.57216e77	1.39820
$207$	6.63056e76	0.172402
$208$	−5.49428e76	−0.121560
$209$	−4.27102e76	−0.0804694
$210$	1.38043e77	0.221651
$211$	9.28985e77	1.27217	0.636087	−	0.771618i	$-0.280552\pi$
$211$	9.28985e77	1.27217	0.636087	+	0.771618i	$0.280552\pi$
$212$	−1.42377e78	−1.66414
$213$	−3.03205e76	−0.0302705
$214$	−8.29337e77	−0.707734
$215$	5.40294e77	0.394404
$216$	1.17794e78	0.736078
$217$	1.59448e78	0.853528
$218$	−1.27217e78	−0.583786
$219$	−1.00950e77	−0.0397401
$220$	−6.16013e78	−2.08176
$221$	−2.34625e77	−0.0681135
$222$	−7.11450e77	−0.177550
$223$	−6.42241e78	−1.37875	−0.689374	−	0.724406i	$-0.742114\pi$
$223$	−6.42241e78	−1.37875	−0.689374	+	0.724406i	$0.742114\pi$
$224$	1.77266e79	3.27580
$225$	3.80430e78	0.605565
$226$	−2.11363e77	−0.0289999
$227$	1.17887e79	1.39509	0.697543	−	0.716543i	$-0.254277\pi$
$227$	1.17887e79	1.39509	0.697543	+	0.716543i	$0.254277\pi$
$228$	1.93845e77	0.0197988
$229$	−1.55534e79	−1.37194	−0.685972	−	0.727628i	$-0.740623\pi$
$229$	−1.55534e79	−1.37194	−0.685972	+	0.727628i	$0.740623\pi$
$230$	2.66386e78	0.203062
$231$	−3.92384e78	−0.258649
$232$	−4.32640e79	−2.46762
$233$	1.81926e79	0.898403	0.449201	−	0.893431i	$-0.351709\pi$
$233$	1.81926e79	0.898403	0.449201	+	0.893431i	$0.351709\pi$
$234$	1.92324e78	0.0822814
$235$	2.16589e79	0.803272
$236$	−9.63014e79	−3.09799
$237$	3.52669e78	0.0984687
$238$	1.68109e80	4.07628
$239$	−2.13612e79	−0.450087	−0.225043	−	0.974349i	$-0.572252\pi$
$239$	−2.13612e79	−0.450087	−0.225043	+	0.974349i	$0.572252\pi$
$240$	1.22225e79	0.223915
$241$	−3.27834e79	−0.522497	−0.261248	−	0.965272i	$-0.584134\pi$
$241$	−3.27834e79	−0.522497	−0.261248	+	0.965272i	$0.584134\pi$
$242$	1.10755e80	1.53655
$243$	−3.23336e79	−0.390701
$244$	−1.75526e80	−1.84834
$245$	−7.17080e79	−0.658421
$246$	−2.57908e78	−0.0206604
$247$	3.82226e77	0.00267283
$248$	2.70860e80	1.65430
$249$	−1.17721e79	−0.0628314
$250$	4.00742e80	1.87014
$251$	−2.97257e80	−1.21356	−0.606782	−	0.794868i	$-0.707540\pi$
$251$	−2.97257e80	−1.21356	−0.606782	+	0.794868i	$0.707540\pi$
$252$	−9.83183e80	−3.51331
$253$	−7.57195e79	−0.236957
$254$	6.35161e80	1.74162
$255$	5.21943e79	0.125466
$256$	−1.90498e80	−0.401653
$257$	2.91395e80	0.539166	0.269583	−	0.962977i	$-0.413114\pi$
$257$	2.91395e80	0.539166	0.269583	+	0.962977i	$0.413114\pi$
$258$	9.76935e79	0.158710
$259$	7.17151e80	1.02345
$260$	5.51288e79	0.0691467
$261$	7.89346e80	0.870583
$262$	−6.17940e80	−0.599588
$263$	8.50029e79	0.0725966	0.0362983	−	0.999341i	$-0.488443\pi$
$263$	8.50029e79	0.0725966	0.0362983	+	0.999341i	$0.488443\pi$
$264$	−6.66556e80	−0.501309
$265$	6.24531e80	0.413826
$266$	−2.73866e80	−0.159957
$267$	4.31694e80	0.222356
$268$	−8.68855e81	−3.94850
$269$	−1.19177e81	−0.478070	−0.239035	−	0.971011i	$-0.576831\pi$
$269$	−1.19177e81	−0.478070	−0.239035	+	0.971011i	$0.576831\pi$
$270$	−8.63430e80	−0.305873
$271$	3.56294e81	1.11516	0.557580	−	0.830123i	$-0.311730\pi$
$271$	3.56294e81	1.11516	0.557580	+	0.830123i	$0.311730\pi$
$272$	1.48846e82	4.11793
$273$	3.51156e79	0.00859115
$274$	8.12066e80	0.175771
$275$	−4.34443e81	−0.832314
$276$	3.43662e80	0.0583012
$277$	−1.14305e82	−1.71787	−0.858937	−	0.512081i	$-0.828875\pi$
$277$	−1.14305e82	−1.71787	−0.858937	+	0.512081i	$0.828875\pi$
$278$	1.69223e82	2.25403
$279$	−4.94180e81	−0.583640
$280$	−2.36378e82	−2.47636
$281$	1.56122e82	1.45145	0.725727	−	0.687983i	$-0.241504\pi$
$281$	1.56122e82	1.45145	0.725727	+	0.687983i	$0.241504\pi$
$282$	3.91626e81	0.323241
$283$	−9.49072e81	−0.695751	−0.347875	−	0.937541i	$-0.613097\pi$
$283$	−9.49072e81	−0.695751	−0.347875	+	0.937541i	$0.613097\pi$
$284$	8.67594e81	0.565135
$285$	−8.50294e79	−0.00492341
$286$	−2.19629e81	−0.113091
$287$	2.59975e81	0.119094
$288$	−5.49405e82	−2.23998
$289$	3.60152e82	1.30740
$290$	3.17124e82	1.02541
$291$	−8.35184e81	−0.240640
$292$	2.88860e82	0.741928
$293$	−8.72184e82	−1.99776	−0.998879	−	0.0473268i	$-0.984930\pi$
$293$	−8.72184e82	−1.99776	−0.998879	+	0.0473268i	$0.984930\pi$
$294$	−1.29659e82	−0.264952
$295$	4.22422e82	0.770387
$296$	1.21825e83	1.98364
$297$	2.45428e82	0.356930
$298$	2.95266e82	0.383679
$299$	6.77636e80	0.00787067
$300$	1.97177e82	0.204783
$301$	−9.84764e82	−0.914860
$302$	−3.09445e83	−2.57247
$303$	−2.56795e82	−0.191099
$304$	−2.42484e82	−0.161591
$305$	7.69937e82	0.459632
$306$	−5.21025e83	−2.78734
$307$	1.53054e83	0.734021	0.367010	−	0.930217i	$-0.380381\pi$
$307$	1.53054e83	0.734021	0.367010	+	0.930217i	$0.380381\pi$
$308$	1.12277e84	4.82884
$309$	−2.58735e82	−0.0998266
$310$	−1.98540e83	−0.687433
$311$	−5.46579e82	−0.169895	−0.0849473	−	0.996385i	$-0.527072\pi$
$311$	−5.46579e82	−0.169895	−0.0849473	+	0.996385i	$0.527072\pi$
$312$	5.96521e81	0.0166512
$313$	3.36258e83	0.843214	0.421607	−	0.906779i	$-0.361466\pi$
$313$	3.36258e83	0.843214	0.421607	+	0.906779i	$0.361466\pi$
$314$	−3.78178e83	−0.852222
$315$	4.31269e83	0.873664
$316$	−1.00913e84	−1.83836
$317$	6.50933e83	1.06672	0.533360	−	0.845888i	$-0.320929\pi$
$317$	6.50933e83	1.06672	0.533360	+	0.845888i	$0.320929\pi$
$318$	1.12925e83	0.166526
$319$	−9.01416e83	−1.19657
$320$	−8.02817e83	−0.959604
$321$	4.69316e82	0.0505297
$322$	−4.85528e83	−0.471023
$323$	−1.03549e83	−0.0905443
$324$	2.99100e84	2.35808
$325$	3.88796e82	0.0276458
$326$	−2.12366e81	−0.00136237
$327$	7.19914e82	0.0416803
$328$	4.41628e83	0.230825
$329$	−3.94765e84	−1.86327
$330$	4.88584e83	0.208316
$331$	−2.75141e84	−1.06003	−0.530014	−	0.847989i	$-0.677813\pi$
$331$	−2.75141e84	−1.06003	−0.530014	+	0.847989i	$0.677813\pi$
$332$	3.36849e84	1.17303
$333$	−2.22268e84	−0.699835
$334$	1.08774e85	3.09756
$335$	3.81119e84	0.981883
$336$	−2.22773e84	−0.519394
$337$	8.52892e83	0.180008	0.0900041	−	0.995941i	$-0.471312\pi$
$337$	8.52892e83	0.180008	0.0900041	+	0.995941i	$0.471312\pi$
$338$	−9.75576e84	−1.86445
$339$	1.19609e82	0.00207049
$340$	−1.49350e85	−2.34240
$341$	5.64343e84	0.802180
$342$	8.48797e83	0.109378
$343$	7.77614e83	0.0908681
$344$	−1.67285e85	−1.77317
$345$	−1.50746e83	−0.0144979
$346$	2.77381e85	2.42118
$347$	1.21189e84	0.0960340	0.0480170	−	0.998847i	$-0.484710\pi$
$347$	1.21189e84	0.0960340	0.0480170	+	0.998847i	$0.484710\pi$
$348$	4.09118e84	0.294404
$349$	1.49172e85	0.975067	0.487534	−	0.873104i	$-0.337897\pi$
$349$	1.49172e85	0.975067	0.487534	+	0.873104i	$0.337897\pi$
$350$	−2.78573e85	−1.65447
$351$	−2.19640e83	−0.0118556
$352$	6.27409e85	3.07873
$353$	3.26597e84	0.145734	0.0728668	−	0.997342i	$-0.476785\pi$
$353$	3.26597e84	0.145734	0.0728668	+	0.997342i	$0.476785\pi$
$354$	7.63804e84	0.310008
$355$	−3.80566e84	−0.140534
$356$	−1.23526e86	−4.15128
$357$	−9.51318e84	−0.291032
$358$	−4.20300e85	−1.17079
$359$	2.09151e85	0.530636	0.265318	−	0.964161i	$-0.414523\pi$
$359$	2.09151e85	0.530636	0.265318	+	0.964161i	$0.414523\pi$
$360$	7.32611e85	1.69332
$361$	−4.73092e85	−0.996447
$362$	9.18128e85	1.76265
$363$	−6.26754e84	−0.109705
$364$	−1.00480e85	−0.160393
$365$	−1.26707e85	−0.184497
$366$	1.39217e85	0.184959
$367$	7.55910e85	0.916552	0.458276	−	0.888810i	$-0.348467\pi$
$367$	7.55910e85	0.916552	0.458276	+	0.888810i	$0.348467\pi$
$368$	−4.29892e85	−0.475836
$369$	−8.05746e84	−0.0814357
$370$	−8.92974e85	−0.824292
$371$	−1.13830e86	−0.959911
$372$	−2.56134e85	−0.197369
$373$	1.75561e86	1.23647	0.618233	−	0.785995i	$-0.287849\pi$
$373$	1.75561e86	1.23647	0.618233	+	0.785995i	$0.287849\pi$
$374$	5.94999e86	3.83105
$375$	−2.26777e85	−0.133521
$376$	−6.70600e86	−3.61136
$377$	8.06703e84	0.0397446
$378$	1.57373e86	0.709503
$379$	−2.06583e86	−0.852475	−0.426237	−	0.904611i	$-0.640161\pi$
$379$	−2.06583e86	−0.852475	−0.426237	+	0.904611i	$0.640161\pi$
$380$	2.43304e85	0.0919177
$381$	−3.59433e85	−0.124346
$382$	1.81691e85	0.0575720
$383$	1.50230e86	0.436111	0.218055	−	0.975936i	$-0.430029\pi$
$383$	1.50230e86	0.436111	0.218055	+	0.975936i	$0.430029\pi$
$384$	−3.08110e85	−0.0819616
$385$	−4.92500e86	−1.20080
$386$	−1.21305e87	−2.71147
$387$	3.05210e86	0.625578
$388$	2.38981e87	4.49263
$389$	−6.44644e86	−1.11175	−0.555876	−	0.831265i	$-0.687617\pi$
$389$	−6.44644e86	−1.11175	−0.555876	+	0.831265i	$0.687617\pi$
$390$	−4.37248e84	−0.00691933
$391$	−1.83579e86	−0.266625
$392$	2.22022e87	2.96014
$393$	3.49688e85	0.0428085
$394$	6.69936e85	0.0753199
$395$	4.42652e86	0.457151
$396$	−3.47984e87	−3.30195
$397$	1.17131e87	1.02139	0.510694	−	0.859762i	$-0.329388\pi$
$397$	1.17131e87	1.02139	0.510694	+	0.859762i	$0.329388\pi$
$398$	−3.57012e87	−2.86154
$399$	1.54978e85	0.0114203
$400$	−2.46651e87	−1.67138
$401$	2.38898e87	1.48894	0.744469	−	0.667657i	$-0.232703\pi$
$401$	2.38898e87	1.48894	0.744469	+	0.667657i	$0.232703\pi$
$402$	6.89123e86	0.395116
$403$	−5.05047e85	−0.0266448
$404$	7.34797e87	3.56773
$405$	−1.31199e87	−0.586391
$406$	−5.78005e87	−2.37853
$407$	2.53825e87	0.961883
$408$	−1.61604e87	−0.564074
$409$	2.85528e87	0.918159	0.459079	−	0.888395i	$-0.348179\pi$
$409$	2.85528e87	0.918159	0.459079	+	0.888395i	$0.348179\pi$
$410$	−3.23713e86	−0.0959181
$411$	−4.59542e85	−0.0125494
$412$	7.40348e87	1.86371
$413$	−7.69926e87	−1.78699
$414$	1.50481e87	0.322084
$415$	−1.47757e87	−0.291701
$416$	−5.61486e86	−0.102262
$417$	−9.57622e86	−0.160930
$418$	−9.69308e86	−0.150334
$419$	−3.71561e87	−0.531937	−0.265969	−	0.963982i	$-0.585692\pi$
$419$	−3.71561e87	−0.531937	−0.265969	+	0.963982i	$0.585692\pi$
$420$	2.23527e87	0.295446
$421$	−8.25851e87	−1.00798	−0.503990	−	0.863710i	$-0.668135\pi$
$421$	−8.25851e87	−1.00798	−0.503990	+	0.863710i	$0.668135\pi$
$422$	2.10833e88	2.37669
$423$	1.22350e88	1.27410
$424$	−1.93367e88	−1.86048
$425$	−1.05329e88	−0.936522
$426$	−6.88123e86	−0.0565516
$427$	−1.40332e88	−1.06616
$428$	−1.34291e88	−0.943365
$429$	1.24287e86	0.00807431
$430$	1.22620e88	0.736830
$431$	2.02458e88	1.12550	0.562750	−	0.826627i	$-0.309743\pi$
$431$	2.02458e88	1.12550	0.562750	+	0.826627i	$0.309743\pi$
$432$	1.39340e88	0.716752
$433$	2.20914e88	1.05167	0.525835	−	0.850587i	$-0.323753\pi$
$433$	2.20914e88	1.05167	0.525835	+	0.850587i	$0.323753\pi$
$434$	3.61867e88	1.59457
$435$	−1.79458e87	−0.0732104
$436$	−2.05997e88	−0.778151
$437$	2.99067e86	0.0104626
$438$	−2.29106e87	−0.0742428
$439$	4.98644e86	0.0149703	0.00748513	−	0.999972i	$-0.497617\pi$
$439$	4.98644e86	0.0149703	0.00748513	+	0.999972i	$0.497617\pi$
$440$	−8.36626e88	−2.32738
$441$	−4.05076e88	−1.04434
$442$	−5.32482e87	−0.127250
$443$	4.20816e88	0.932324	0.466162	−	0.884699i	$-0.345636\pi$
$443$	4.20816e88	0.932324	0.466162	+	0.884699i	$0.345636\pi$
$444$	−1.15202e88	−0.236662
$445$	5.41840e88	1.03231
$446$	−1.45757e89	−2.57579
$447$	−1.67089e87	−0.0273933
$448$	1.46325e89	2.22590
$449$	−5.36803e88	−0.757814	−0.378907	−	0.925435i	$-0.623700\pi$
$449$	−5.36803e88	−0.757814	−0.378907	+	0.925435i	$0.623700\pi$
$450$	8.63386e88	1.13132
$451$	9.20144e87	0.111929
$452$	−3.42250e87	−0.0386550
$453$	1.75112e88	0.183665
$454$	2.67546e89	2.60631
$455$	4.40752e87	0.0398853
$456$	2.63267e87	0.0221347
$457$	−2.47901e89	−1.93680	−0.968401	−	0.249399i	$-0.919767\pi$
$457$	−2.47901e89	−1.93680	−0.968401	+	0.249399i	$0.919767\pi$
$458$	−3.52984e89	−2.56308
$459$	5.95029e88	0.401618
$460$	4.31347e88	0.270669
$461$	1.39269e89	0.812593	0.406297	−	0.913741i	$-0.366820\pi$
$461$	1.39269e89	0.812593	0.406297	+	0.913741i	$0.366820\pi$
$462$	−8.90517e88	−0.483210
$463$	2.69968e89	1.36254	0.681271	−	0.732032i	$-0.261428\pi$
$463$	2.69968e89	1.36254	0.681271	+	0.732032i	$0.261428\pi$
$464$	−5.11772e89	−2.40283
$465$	1.12352e88	0.0490803
$466$	4.12881e89	1.67840
$467$	3.76688e89	1.42517	0.712584	−	0.701586i	$-0.247525\pi$
$467$	3.76688e89	1.42517	0.712584	+	0.701586i	$0.247525\pi$
$468$	3.11421e88	0.109676
$469$	−6.94646e89	−2.27758
$470$	4.91549e89	1.50068
$471$	2.14008e88	0.0608457
$472$	−1.30790e90	−3.46352
$473$	−3.48543e89	−0.859822
$474$	8.00383e88	0.183960
$475$	1.71590e88	0.0367499
$476$	2.72212e90	5.43343
$477$	3.52796e89	0.656383
$478$	−4.84793e89	−0.840857
$479$	−6.97444e89	−1.12790	−0.563949	−	0.825810i	$-0.690718\pi$
$479$	−6.97444e89	−1.12790	−0.563949	+	0.825810i	$0.690718\pi$
$480$	1.24907e89	0.188368
$481$	−2.27156e88	−0.0319495
$482$	−7.44020e89	−0.976133
$483$	2.74757e88	0.0336294
$484$	1.79340e90	2.04813
$485$	−1.04828e90	−1.11719
$486$	−7.33812e89	−0.729911
$487$	2.50021e89	0.232143	0.116072	−	0.993241i	$-0.462970\pi$
$487$	2.50021e89	0.232143	0.116072	+	0.993241i	$0.462970\pi$
$488$	−2.38387e90	−2.06642
$489$	1.20176e86	9.72686e−5 0
$490$	−1.62741e90	−1.23007
$491$	2.37132e90	1.67402	0.837009	−	0.547189i	$-0.184302\pi$
$491$	2.37132e90	1.67402	0.837009	+	0.547189i	$0.184302\pi$
$492$	−4.17619e88	−0.0275390
$493$	−2.18544e90	−1.34638
$494$	8.67462e87	0.00499341
$495$	1.52641e90	0.821104
$496$	3.20401e90	1.61086
$497$	6.93638e89	0.325982
$498$	−2.67168e89	−0.117382
$499$	3.70263e90	1.52104	0.760522	−	0.649312i	$-0.224943\pi$
$499$	3.70263e90	1.52104	0.760522	+	0.649312i	$0.224943\pi$
$500$	6.48902e90	2.49278
$501$	−6.15546e89	−0.221155
$502$	−6.74626e90	−2.26719
$503$	3.39121e90	1.06617	0.533086	−	0.846061i	$-0.321032\pi$
$503$	3.39121e90	1.06617	0.533086	+	0.846061i	$0.321032\pi$
$504$	−1.33529e91	−3.92783
$505$	−3.22316e90	−0.887197
$506$	−1.71846e90	−0.442686
$507$	5.52071e89	0.133115
$508$	1.02849e91	2.32148
$509$	−6.34938e89	−0.134179	−0.0670897	−	0.997747i	$-0.521371\pi$
$509$	−6.34938e89	−0.134179	−0.0670897	+	0.997747i	$0.521371\pi$
$510$	1.18455e90	0.234398
$511$	2.30942e90	0.427960
$512$	−7.86374e90	−1.36485
$513$	−9.69356e88	−0.0157598
$514$	6.61321e90	1.00727
$515$	−3.24750e90	−0.463455
$516$	1.58191e90	0.211551
$517$	−1.39721e91	−1.75117
$518$	1.62758e91	1.91203
$519$	−1.56968e90	−0.172864
$520$	7.48721e89	0.0773051
$521$	−6.72297e90	−0.650874	−0.325437	−	0.945564i	$-0.605511\pi$
$521$	−6.72297e90	−0.650874	−0.325437	+	0.945564i	$0.605511\pi$
$522$	1.79142e91	1.62643
$523$	−3.61652e90	−0.307953	−0.153977	−	0.988075i	$-0.549208\pi$
$523$	−3.61652e90	−0.307953	−0.153977	+	0.988075i	$0.549208\pi$
$524$	−1.00060e91	−0.799214
$525$	1.57642e90	0.118123
$526$	1.92914e90	0.135626
$527$	1.36823e91	0.902614
$528$	−7.88473e90	−0.488147
$529$	−1.66792e91	−0.969191
$530$	1.41738e91	0.773113
$531$	2.38625e91	1.22194
$532$	−4.43458e90	−0.213212
$533$	−8.23464e88	−0.00371777
$534$	9.79731e90	0.415408
$535$	5.89060e90	0.234589
$536$	−1.18002e92	−4.41437
$537$	2.37844e90	0.0835900
$538$	−2.70473e91	−0.893135
$539$	4.62588e91	1.43539
$540$	−1.39811e91	−0.407710
$541$	−5.31972e91	−1.45808	−0.729039	−	0.684472i	$-0.760033\pi$
$541$	−5.31972e91	−1.45808	−0.729039	+	0.684472i	$0.760033\pi$
$542$	8.08610e91	2.08335
$543$	−5.19562e90	−0.125847
$544$	1.52113e92	3.46419
$545$	9.03597e90	0.193505
$546$	7.96949e89	0.0160501
$547$	−1.75688e90	−0.0332788	−0.0166394	−	0.999862i	$-0.505297\pi$
$547$	−1.75688e90	−0.0332788	−0.0166394	+	0.999862i	$0.505297\pi$
$548$	1.31494e91	0.234292
$549$	4.34935e91	0.729039
$550$	−9.85968e91	−1.55494
$551$	3.56029e90	0.0528331
$552$	4.66738e90	0.0651800
$553$	−8.06798e91	−1.06041
$554$	−2.59414e92	−3.20935
$555$	5.05327e90	0.0588515
$556$	2.74015e92	3.00448
$557$	4.64449e91	0.479500	0.239750	−	0.970835i	$-0.422935\pi$
$557$	4.64449e91	0.479500	0.239750	+	0.970835i	$0.422935\pi$
$558$	−1.12154e92	−1.09036
$559$	3.11921e90	0.0285594
$560$	−2.79613e92	−2.41134
$561$	−3.36705e91	−0.273523
$562$	3.54320e92	2.71162
$563$	8.66238e90	0.0624606	0.0312303	−	0.999512i	$-0.490057\pi$
$563$	8.66238e90	0.0624606	0.0312303	+	0.999512i	$0.490057\pi$
$564$	6.34142e91	0.430860
$565$	1.50126e90	0.00961245
$566$	−2.15392e92	−1.29981
$567$	2.39130e92	1.36019
$568$	1.17831e92	0.631813
$569$	1.65010e92	0.834162	0.417081	−	0.908869i	$-0.363053\pi$
$569$	1.65010e92	0.834162	0.417081	+	0.908869i	$0.363053\pi$
$570$	−1.92974e90	−0.00919796
$571$	−3.09486e92	−1.39101	−0.695507	−	0.718519i	$-0.744820\pi$
$571$	−3.09486e92	−1.39101	−0.695507	+	0.718519i	$0.744820\pi$
$572$	−3.55636e91	−0.150743
$573$	−1.02818e90	−0.00411044
$574$	5.90014e91	0.222492
$575$	3.04207e91	0.108217
$576$	−4.53508e92	−1.52206
$577$	−4.88740e92	−1.54771	−0.773853	−	0.633366i	$-0.781673\pi$
$577$	−4.88740e92	−1.54771	−0.773853	+	0.633366i	$0.781673\pi$
$578$	8.17365e92	2.44249
$579$	6.86459e91	0.193590
$580$	5.13504e92	1.36680
$581$	2.69309e92	0.676630
$582$	−1.89545e92	−0.449565
$583$	−4.02885e92	−0.902162
$584$	3.92310e92	0.829466
$585$	−1.36603e91	−0.0272734
$586$	−1.97942e93	−3.73223
$587$	−4.93586e92	−0.878995	−0.439498	−	0.898244i	$-0.644843\pi$
$587$	−4.93586e92	−0.878995	−0.439498	+	0.898244i	$0.644843\pi$
$588$	−2.09951e92	−0.353165
$589$	−2.22896e91	−0.0354194
$590$	9.58687e92	1.43924
$591$	−3.79112e90	−0.00537758
$592$	1.44107e93	1.93156
$593$	8.91235e92	1.12891	0.564456	−	0.825463i	$-0.309086\pi$
$593$	8.91235e92	1.12891	0.564456	+	0.825463i	$0.309086\pi$
$594$	5.56999e92	0.666819
$595$	−1.19404e93	−1.35115
$596$	4.78110e92	0.511420
$597$	2.02030e92	0.204304
$598$	1.53790e91	0.0147041
$599$	1.27437e92	0.115212	0.0576059	−	0.998339i	$-0.481653\pi$
$599$	1.27437e92	0.115212	0.0576059	+	0.998339i	$0.481653\pi$
$600$	2.67792e92	0.228945
$601$	1.93861e93	1.56746	0.783728	−	0.621104i	$-0.213316\pi$
$601$	1.93861e93	1.56746	0.783728	+	0.621104i	$0.213316\pi$
$602$	−2.23492e93	−1.70915
$603$	2.15293e93	1.55740
$604$	−5.01069e93	−3.42894
$605$	−7.86668e92	−0.509315
$606$	−5.82797e92	−0.357013
$607$	4.21833e92	0.244523	0.122261	−	0.992498i	$-0.460985\pi$
$607$	4.21833e92	0.244523	0.122261	+	0.992498i	$0.460985\pi$
$608$	−2.47805e92	−0.135938
$609$	3.27089e92	0.169819
$610$	1.74737e93	0.858690
$611$	1.25041e92	0.0581662
$612$	−8.43671e93	−3.71536
$613$	−8.48939e92	−0.353957	−0.176979	−	0.984215i	$-0.556632\pi$
$613$	−8.48939e92	−0.353957	−0.176979	+	0.984215i	$0.556632\pi$
$614$	3.47356e93	1.37130
$615$	1.83187e91	0.00684821
$616$	1.52487e94	5.39859
$617$	5.31064e93	1.78071	0.890357	−	0.455263i	$-0.150455\pi$
$617$	5.31064e93	1.78071	0.890357	+	0.455263i	$0.150455\pi$
$618$	−5.87200e92	−0.186497
$619$	−5.93673e93	−1.78612	−0.893060	−	0.449937i	$-0.851446\pi$
$619$	−5.93673e93	−1.78612	−0.893060	+	0.449937i	$0.851446\pi$
$620$	−3.21486e93	−0.916305
$621$	−1.71854e92	−0.0464079
$622$	−1.24046e93	−0.317399
$623$	−9.87582e93	−2.39455
$624$	7.05628e91	0.0162141
$625$	−1.53972e91	−0.00335322
$626$	7.63139e93	1.57530
$627$	5.48524e91	0.0107333
$628$	−6.12366e93	−1.13596
$629$	6.15389e93	1.08231
$630$	9.78766e93	1.63219
$631$	−4.19002e93	−0.662572	−0.331286	−	0.943530i	$-0.607482\pi$
$631$	−4.19002e93	−0.662572	−0.331286	+	0.943530i	$0.607482\pi$
$632$	−1.37053e94	−2.05527
$633$	−1.19309e93	−0.169687
$634$	1.47729e94	1.99286
$635$	−4.51141e93	−0.577288
$636$	1.82854e93	0.221969
$637$	−4.13983e92	−0.0476773
$638$	−2.04576e94	−2.23544
$639$	−2.14981e93	−0.222905
$640$	−3.86724e93	−0.380515
$641$	1.17710e94	1.09919	0.549593	−	0.835433i	$-0.314783\pi$
$641$	1.17710e94	1.09919	0.549593	+	0.835433i	$0.314783\pi$
$642$	1.06511e93	0.0944000
$643$	2.15010e94	1.80880	0.904400	−	0.426686i	$-0.140319\pi$
$643$	2.15010e94	1.80880	0.904400	+	0.426686i	$0.140319\pi$
$644$	−7.86192e93	−0.627845
$645$	−6.93896e92	−0.0526070
$646$	−2.35004e93	−0.169156
$647$	−5.59785e93	−0.382585	−0.191292	−	0.981533i	$-0.561268\pi$
$647$	−5.59785e93	−0.382585	−0.191292	+	0.981533i	$0.561268\pi$
$648$	4.06218e94	2.63631
$649$	−2.72504e94	−1.67948
$650$	8.82372e92	0.0516481
$651$	−2.04778e93	−0.113847
$652$	−3.43875e91	−0.00181596
$653$	3.65193e94	1.83202	0.916012	−	0.401150i	$-0.131389\pi$
$653$	3.65193e94	1.83202	0.916012	+	0.401150i	$0.131389\pi$
$654$	1.63384e93	0.0778675
$655$	4.38909e93	0.198743
$656$	5.22405e93	0.224765
$657$	−7.15764e93	−0.292638
$658$	−8.95919e94	−3.48098
$659$	−2.31946e94	−0.856497	−0.428249	−	0.903661i	$-0.640869\pi$
$659$	−2.31946e94	−0.856497	−0.428249	+	0.903661i	$0.640869\pi$
$660$	7.91142e93	0.277672
$661$	1.29957e94	0.433563	0.216782	−	0.976220i	$-0.430444\pi$
$661$	1.29957e94	0.433563	0.216782	+	0.976220i	$0.430444\pi$
$662$	−6.24433e94	−1.98035
$663$	3.01328e92	0.00908522
$664$	4.57485e94	1.31143
$665$	1.94521e93	0.0530201
$666$	−5.04438e94	−1.30744
$667$	6.31192e93	0.155577
$668$	1.76133e95	4.12886
$669$	8.24826e93	0.183902
$670$	8.64951e94	1.83436
$671$	−4.96686e94	−1.00202
$672$	−2.27662e94	−0.436938
$673$	3.32902e94	0.607872	0.303936	−	0.952693i	$-0.401699\pi$
$673$	3.32902e94	0.607872	0.303936	+	0.952693i	$0.401699\pi$
$674$	1.93564e94	0.336293
$675$	−9.86018e93	−0.163008
$676$	−1.57970e95	−2.48520
$677$	−7.15153e94	−1.07073	−0.535364	−	0.844622i	$-0.679825\pi$
$677$	−7.15153e94	−1.07073	−0.535364	+	0.844622i	$0.679825\pi$
$678$	2.71452e92	0.00386811
$679$	1.91064e95	2.59144
$680$	−2.02836e95	−2.61877
$681$	−1.51402e94	−0.186082
$682$	1.28078e95	1.49864
$683$	−4.63147e94	−0.515971	−0.257985	−	0.966149i	$-0.583059\pi$
$683$	−4.63147e94	−0.515971	−0.257985	+	0.966149i	$0.583059\pi$
$684$	1.37442e94	0.145794
$685$	−5.76793e93	−0.0582620
$686$	1.76480e94	0.169761
$687$	1.99751e94	0.182995
$688$	−1.97883e95	−1.72661
$689$	3.60554e93	0.0299658
$690$	−3.42118e93	−0.0270852
$691$	3.93163e94	0.296523	0.148261	−	0.988948i	$-0.452632\pi$
$691$	3.93163e94	0.296523	0.148261	+	0.988948i	$0.452632\pi$
$692$	4.49150e95	3.22728
$693$	−2.78211e95	−1.90463
$694$	2.75038e94	0.179412
$695$	−1.20196e95	−0.747132
$696$	5.55636e94	0.329140
$697$	2.23085e94	0.125942
$698$	3.38545e95	1.82163
$699$	−2.33646e94	−0.119832
$700$	−4.51080e95	−2.20531
$701$	−2.12972e95	−0.992588	−0.496294	−	0.868154i	$-0.665306\pi$
$701$	−2.12972e95	−0.992588	−0.496294	+	0.868154i	$0.665306\pi$
$702$	−4.98474e93	−0.0221488
$703$	−1.00252e94	−0.0424709
$704$	5.17897e95	2.09199
$705$	−2.78164e94	−0.107143
$706$	7.41213e94	0.272261
$707$	5.87467e95	2.05794
$708$	1.23679e95	0.413221
$709$	−4.82912e94	−0.153893	−0.0769466	−	0.997035i	$-0.524517\pi$
$709$	−4.82912e94	−0.153893	−0.0769466	+	0.997035i	$0.524517\pi$
$710$	−8.63695e94	−0.262546
$711$	2.50052e95	0.725103
$712$	−1.67764e96	−4.64108
$713$	−3.95166e94	−0.104299
$714$	−2.15902e95	−0.543709
$715$	1.55998e94	0.0374858
$716$	−6.80571e95	−1.56059
$717$	2.74341e94	0.0600342
$718$	4.74669e95	0.991339
$719$	−3.57892e93	−0.00713401	−0.00356700	−	0.999994i	$-0.501135\pi$
$719$	−3.57892e93	−0.00713401	−0.00356700	+	0.999994i	$0.501135\pi$
$720$	8.66610e95	1.64886
$721$	5.91905e95	1.07503
$722$	−1.07368e96	−1.86157
$723$	4.21036e94	0.0696925
$724$	1.48668e96	2.34950
$725$	3.62148e95	0.546466
$726$	−1.42242e95	−0.204951
$727$	1.13472e96	1.56129	0.780646	−	0.624973i	$-0.214890\pi$
$727$	1.13472e96	1.56129	0.780646	+	0.624973i	$0.214890\pi$
$728$	−1.36465e95	−0.179317
$729$	−7.13038e95	−0.894830
$730$	−2.87562e95	−0.344680
$731$	−8.45028e95	−0.967473
$732$	2.25427e95	0.246538
$733$	−7.88530e95	−0.823826	−0.411913	−	0.911223i	$-0.635139\pi$
$733$	−7.88530e95	−0.823826	−0.411913	+	0.911223i	$0.635139\pi$
$734$	1.71554e96	1.71231
$735$	9.20941e94	0.0878225
$736$	−4.39326e95	−0.400295
$737$	−2.45860e96	−2.14056
$738$	−1.82864e95	−0.152139
$739$	8.22688e95	0.654104	0.327052	−	0.945006i	$-0.393945\pi$
$739$	8.22688e95	0.654104	0.327052	+	0.945006i	$0.393945\pi$
$740$	−1.44595e96	−1.09873
$741$	−4.90890e92	−0.000356512 0
$742$	−2.58337e96	−1.79331
$743$	1.18799e96	0.788293	0.394147	−	0.919048i	$-0.371040\pi$
$743$	1.18799e96	0.788293	0.394147	+	0.919048i	$0.371040\pi$
$744$	−3.47863e95	−0.220656
$745$	−2.09721e95	−0.127176
$746$	3.98436e96	2.30998
$747$	−8.34676e95	−0.462677
$748$	9.63454e96	5.10655
$749$	−1.07365e96	−0.544153
$750$	−5.14670e95	−0.249446
$751$	−2.90797e96	−1.34788	−0.673941	−	0.738785i	$-0.735400\pi$
$751$	−2.90797e96	−1.34788	−0.673941	+	0.738785i	$0.735400\pi$
$752$	−7.93257e96	−3.51654
$753$	3.81766e95	0.161870
$754$	1.83081e95	0.0742513
$755$	2.19792e96	0.852685
$756$	2.54826e96	0.945724
$757$	1.73071e96	0.614487	0.307244	−	0.951631i	$-0.400593\pi$
$757$	1.73071e96	0.614487	0.307244	+	0.951631i	$0.400593\pi$
$758$	−4.68841e96	−1.59260
$759$	9.72461e94	0.0316062
$760$	3.30439e95	0.102763
$761$	3.70707e96	1.10318	0.551588	−	0.834117i	$-0.314022\pi$
$761$	3.70707e96	1.10318	0.551588	+	0.834117i	$0.314022\pi$
$762$	−8.15734e95	−0.232304
$763$	−1.64694e96	−0.448854
$764$	2.94204e95	0.0767399
$765$	3.70073e96	0.923908
$766$	3.40947e96	0.814746
$767$	2.43872e95	0.0557849
$768$	2.44655e95	0.0535739
$769$	−9.72162e95	−0.203801	−0.101900	−	0.994795i	$-0.532492\pi$
$769$	−9.72162e95	−0.203801	−0.101900	+	0.994795i	$0.532492\pi$
$770$	−1.11773e97	−2.24335
$771$	−3.74237e95	−0.0719158
$772$	−1.96424e97	−3.61423
$773$	−7.27011e95	−0.128094	−0.0640469	−	0.997947i	$-0.520401\pi$
$773$	−7.27011e95	−0.128094	−0.0640469	+	0.997947i	$0.520401\pi$
$774$	6.92675e96	1.16871
$775$	−2.26728e96	−0.366351
$776$	3.24567e97	5.02270
$777$	−9.21033e95	−0.136512
$778$	−1.46302e97	−2.07699
$779$	−3.63426e94	−0.00494209
$780$	−7.08016e94	−0.00922303
$781$	2.45503e96	0.306371
$782$	−4.16632e96	−0.498111
$783$	−2.04587e96	−0.234346
$784$	2.62631e97	2.88242
$785$	2.68611e96	0.282482
$786$	7.93617e95	0.0799752
$787$	−1.49904e96	−0.144764	−0.0723820	−	0.997377i	$-0.523060\pi$
$787$	−1.49904e96	−0.144764	−0.0723820	+	0.997377i	$0.523060\pi$
$788$	1.08480e96	0.100397
$789$	−1.09169e95	−0.00968320
$790$	1.00460e97	0.854053
$791$	−2.73627e95	−0.0222970
$792$	−4.72607e97	−3.69153
$793$	4.44499e95	0.0332827
$794$	2.65830e97	1.90817
$795$	−8.02082e95	−0.0551976
$796$	−5.78092e97	−3.81425
$797$	1.40542e97	0.889107	0.444553	−	0.895752i	$-0.353362\pi$
$797$	1.40542e97	0.889107	0.444553	+	0.895752i	$0.353362\pi$
$798$	3.51724e95	0.0213356
$799$	−3.38748e97	−1.97043
$800$	−2.52065e97	−1.40604
$801$	3.06083e97	1.63738
$802$	5.42180e97	2.78165
$803$	8.17387e96	0.402214
$804$	1.11587e97	0.526664
$805$	3.44860e96	0.156128
$806$	−1.14621e96	−0.0497781
$807$	1.53058e96	0.0637667
$808$	9.97951e97	3.98867
$809$	−1.72375e97	−0.660996	−0.330498	−	0.943807i	$-0.607217\pi$
$809$	−1.72375e97	−0.660996	−0.330498	+	0.943807i	$0.607217\pi$
$810$	−2.97757e97	−1.09550
$811$	−3.10291e97	−1.09540	−0.547698	−	0.836676i	$-0.684496\pi$
$811$	−3.10291e97	−1.09540	−0.547698	+	0.836676i	$0.684496\pi$
$812$	−9.35936e97	−3.17044
$813$	−4.57586e96	−0.148744
$814$	5.76057e97	1.79700
$815$	1.50839e94	0.000451579 0
$816$	−1.91162e97	−0.549264
$817$	1.37663e96	0.0379645
$818$	6.48006e97	1.71531
$819$	2.48980e96	0.0632635
$820$	−5.24173e96	−0.127853
$821$	−4.71160e97	−1.10325	−0.551623	−	0.834094i	$-0.685991\pi$
$821$	−4.71160e97	−1.10325	−0.551623	+	0.834094i	$0.685991\pi$
$822$	−1.04293e96	−0.0234450
$823$	−3.28396e97	−0.708766	−0.354383	−	0.935100i	$-0.615309\pi$
$823$	−3.28396e97	−0.708766	−0.354383	+	0.935100i	$0.615309\pi$
$824$	1.00549e98	2.08361
$825$	5.57952e96	0.111017
$826$	−1.74735e98	−3.33847
$827$	1.14554e97	0.210172	0.105086	−	0.994463i	$-0.466488\pi$
$827$	1.14554e97	0.210172	0.105086	+	0.994463i	$0.466488\pi$
$828$	2.43666e97	0.429318
$829$	5.31404e97	0.899183	0.449591	−	0.893234i	$-0.351570\pi$
$829$	5.31404e97	0.899183	0.449591	+	0.893234i	$0.351570\pi$
$830$	−3.35336e97	−0.544959
$831$	1.46801e97	0.229136
$832$	−4.63481e96	−0.0694865
$833$	1.12152e98	1.61511
$834$	−2.17332e97	−0.300650
$835$	−7.72601e97	−1.02673
$836$	−1.56955e97	−0.200385
$837$	1.28084e97	0.157106
$838$	−8.43258e97	−0.993770
$839$	8.20510e97	0.929091	0.464545	−	0.885549i	$-0.346218\pi$
$839$	8.20510e97	0.929091	0.464545	+	0.885549i	$0.346218\pi$
$840$	3.03579e97	0.330305
$841$	−2.05045e97	−0.214379
$842$	−1.87427e98	−1.88312
$843$	−2.00507e97	−0.193600
$844$	3.41392e98	3.16797
$845$	6.92930e97	0.618002
$846$	2.77674e98	2.38028
$847$	1.43382e98	1.18141
$848$	−2.28735e98	−1.81164
$849$	1.21889e97	0.0928017
$850$	−2.39044e98	−1.74962
$851$	−1.77734e97	−0.125064
$852$	−1.11425e97	−0.0753797
$853$	−2.75788e97	−0.179384	−0.0896918	−	0.995970i	$-0.528588\pi$
$853$	−2.75788e97	−0.179384	−0.0896918	+	0.995970i	$0.528588\pi$
$854$	−3.18484e98	−1.99182
$855$	−6.02882e96	−0.0362550
$856$	−1.82384e98	−1.05467
$857$	−2.49466e98	−1.38725	−0.693624	−	0.720337i	$-0.743987\pi$
$857$	−2.49466e98	−1.38725	−0.693624	+	0.720337i	$0.743987\pi$
$858$	2.82069e96	0.0150845
$859$	−5.28515e97	−0.271823	−0.135912	−	0.990721i	$-0.543396\pi$
$859$	−5.28515e97	−0.271823	−0.135912	+	0.990721i	$0.543396\pi$
$860$	1.98552e98	0.982148
$861$	−3.33884e96	−0.0158851
$862$	4.59478e98	2.10267
$863$	−1.41322e96	−0.00622084	−0.00311042	−	0.999995i	$-0.500990\pi$
$863$	−1.41322e96	−0.00622084	−0.00311042	+	0.999995i	$0.500990\pi$
$864$	1.42398e98	0.602965
$865$	−1.97018e98	−0.802537
$866$	5.01365e98	1.96474
$867$	−4.62541e97	−0.174385
$868$	5.85955e98	2.12546
$869$	−2.85554e98	−0.996613
$870$	−4.07280e97	−0.136772
$871$	2.20027e97	0.0710998
$872$	−2.79771e98	−0.869962
$873$	−5.92169e98	−1.77202
$874$	6.78732e96	0.0195463
$875$	5.18794e98	1.43789
$876$	−3.70981e97	−0.0989610
$877$	4.90704e98	1.25989	0.629946	−	0.776639i	$-0.283077\pi$
$877$	4.90704e98	1.25989	0.629946	+	0.776639i	$0.283077\pi$
$878$	1.13167e97	0.0279676
$879$	1.12014e98	0.266468
$880$	−9.89649e98	−2.26627
$881$	−1.83004e98	−0.403430	−0.201715	−	0.979444i	$-0.564651\pi$
$881$	−1.83004e98	−0.403430	−0.201715	+	0.979444i	$0.564651\pi$
$882$	−9.19320e98	−1.95105
$883$	1.47514e98	0.301404	0.150702	−	0.988579i	$-0.451847\pi$
$883$	1.47514e98	0.301404	0.150702	+	0.988579i	$0.451847\pi$
$884$	−8.62223e97	−0.169617
$885$	−5.42514e97	−0.102757
$886$	9.55042e98	1.74178
$887$	−4.64176e98	−0.815157	−0.407579	−	0.913170i	$-0.633627\pi$
$887$	−4.64176e98	−0.815157	−0.407579	+	0.913170i	$0.633627\pi$
$888$	−1.56459e98	−0.264586
$889$	8.22271e98	1.33908
$890$	1.22971e99	1.92857
$891$	8.46365e98	1.27836
$892$	−2.36017e99	−3.43337
$893$	5.51852e97	0.0773212
$894$	−3.79208e97	−0.0511765
$895$	2.98530e98	0.388075
$896$	7.04861e98	0.882643
$897$	−8.70284e95	−0.00104982
$898$	−1.21828e99	−1.41576
$899$	−4.70432e98	−0.526681
$900$	1.39804e99	1.50798
$901$	−9.76777e98	−1.01511
$902$	2.08827e98	0.209106
$903$	1.26473e98	0.122027
$904$	−4.64820e97	−0.0432158
$905$	−6.52126e98	−0.584257
$906$	3.97418e98	0.343125
$907$	8.33172e98	0.693251	0.346626	−	0.938004i	$-0.387327\pi$
$907$	8.33172e98	0.693251	0.346626	+	0.938004i	$0.387327\pi$
$908$	4.33224e99	3.47405
$909$	−1.82075e99	−1.40721
$910$	1.00029e98	0.0745141
$911$	1.45347e99	1.04362	0.521809	−	0.853062i	$-0.325257\pi$
$911$	1.45347e99	1.04362	0.521809	+	0.853062i	$0.325257\pi$
$912$	3.11420e97	0.0215536
$913$	9.53182e98	0.635924
$914$	−5.62611e99	−3.61835
$915$	−9.88826e97	−0.0613074
$916$	−5.71571e99	−3.41643
$917$	−7.99977e98	−0.461004
$918$	1.35042e99	0.750306
$919$	1.11251e99	0.595984	0.297992	−	0.954568i	$-0.403683\pi$
$919$	1.11251e99	0.595984	0.297992	+	0.954568i	$0.403683\pi$
$920$	5.85825e98	0.302605
$921$	−1.96566e98	−0.0979063
$922$	3.16071e99	1.51809
$923$	−2.19708e97	−0.0101763
$924$	−1.44197e99	−0.644089
$925$	−1.01976e99	−0.439287
$926$	6.12694e99	2.54551
$927$	−1.83450e99	−0.735102
$928$	−5.23003e99	−2.02138
$929$	3.66789e99	1.36738	0.683692	−	0.729771i	$-0.260373\pi$
$929$	3.66789e99	1.36738	0.683692	+	0.729771i	$0.260373\pi$
$930$	2.54983e98	0.0916923
$931$	−1.82707e98	−0.0633782
$932$	6.68559e99	2.23721
$933$	7.01968e97	0.0226612
$934$	8.54894e99	2.66251
$935$	−4.22615e99	−1.26986
$936$	4.22950e98	0.122616
$937$	1.86027e98	0.0520354	0.0260177	−	0.999661i	$-0.491717\pi$
$937$	1.86027e98	0.0520354	0.0260177	+	0.999661i	$0.491717\pi$
$938$	−1.57650e100	−4.25499
$939$	−4.31854e98	−0.112471
$940$	7.95941e99	2.00031
$941$	4.09124e99	0.992208	0.496104	−	0.868263i	$-0.334763\pi$
$941$	4.09124e99	0.992208	0.496104	+	0.868263i	$0.334763\pi$
$942$	4.85692e98	0.113672
$943$	−6.44306e97	−0.0145529
$944$	−1.54712e100	−3.37258
$945$	−1.11778e99	−0.235176
$946$	−7.91019e99	−1.60633
$947$	−4.63796e99	−0.909082	−0.454541	−	0.890726i	$-0.650197\pi$
$947$	−4.63796e99	−0.909082	−0.454541	+	0.890726i	$0.650197\pi$
$948$	1.29602e99	0.245207
$949$	−7.31504e97	−0.0133598
$950$	3.89424e98	0.0686566
$951$	−8.35989e98	−0.142283
$952$	3.69699e100	6.07450
$953$	−2.75137e99	−0.436452	−0.218226	−	0.975898i	$-0.570027\pi$
$953$	−2.75137e99	−0.436452	−0.218226	+	0.975898i	$0.570027\pi$
$954$	8.00670e99	1.22626
$955$	−1.29051e98	−0.0190831
$956$	−7.85003e99	−1.12081
$957$	1.15768e99	0.159602
$958$	−1.58285e100	−2.10715
$959$	1.05129e99	0.135145
$960$	1.03105e99	0.127995
$961$	−5.39609e99	−0.646913
$962$	−5.15530e98	−0.0596883
$963$	3.32758e99	0.372090
$964$	−1.20476e100	−1.30112
$965$	8.61606e99	0.898760
$966$	6.23560e98	0.0628268
$967$	4.36496e99	0.424809	0.212404	−	0.977182i	$-0.431871\pi$
$967$	4.36496e99	0.424809	0.212404	+	0.977182i	$0.431871\pi$
$968$	2.43567e100	2.28978
$969$	1.32987e98	0.0120771
$970$	−2.37907e100	−2.08715
$971$	6.33150e99	0.536614	0.268307	−	0.963333i	$-0.413536\pi$
$971$	6.33150e99	0.536614	0.268307	+	0.963333i	$0.413536\pi$
$972$	−1.18823e100	−0.972926
$973$	2.19074e100	1.73305
$974$	5.67423e99	0.433692
$975$	−4.99328e97	−0.00368749
$976$	−2.81990e100	−2.01217
$977$	1.58929e100	1.09581	0.547905	−	0.836540i	$-0.315425\pi$
$977$	1.58929e100	1.09581	0.547905	+	0.836540i	$0.315425\pi$
$978$	2.72741e96	0.000181718 0
$979$	−3.49541e100	−2.25049
$980$	−2.63519e100	−1.63960
$981$	5.10439e99	0.306925
$982$	5.38171e100	3.12742
$983$	4.62180e97	0.00259578	0.00129789	−	0.999999i	$-0.499587\pi$
$983$	4.62180e97	0.00259578	0.00129789	+	0.999999i	$0.499587\pi$
$984$	−5.67181e98	−0.0307883
$985$	−4.75841e98	−0.0249659
$986$	−4.95987e100	−2.51532
$987$	5.06994e99	0.248530
$988$	1.40464e98	0.00665591
$989$	2.44058e99	0.111794
$990$	3.46420e100	1.53399
$991$	−4.58345e100	−1.96212	−0.981059	−	0.193708i	$-0.937948\pi$
$991$	−4.58345e100	−1.96212	−0.981059	+	0.193708i	$0.937948\pi$
$992$	3.27433e100	1.35513
$993$	3.53362e99	0.141390
$994$	1.57421e100	0.609003
$995$	2.53578e100	0.948501
$996$	−4.32613e99	−0.156463
$997$	−4.49091e100	−1.57053	−0.785266	−	0.619159i	$-0.787474\pi$
$997$	−4.49091e100	−1.57053	−0.785266	+	0.619159i	$0.787474\pi$
$998$	8.40312e100	2.84163
$999$	5.76086e99	0.188384

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1.68.a.a.1.5	✓	5
3.2	odd	2		9.68.a.a.1.1		5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1.68.a.a.1.5	✓	5	1.1	even	1	trivial
9.68.a.a.1.1		5	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1 \)
Weight:	\( k \)	\(=\)	\( 68 \)
Character orbit:	\([\chi]\)	\(=\)	1.a (trivial)

\(f(q)\)	\(=\)	\(q+2.26950e10 q^{2} -1.28429e15 q^{3} +3.67490e20 q^{4} -1.61198e23 q^{5} -2.91471e25 q^{6} +2.93806e28 q^{7} +4.99099e30 q^{8} -9.10601e31 q^{9} +O(q^{10})\)	\(q+2.26950e10 q^{2} -1.28429e15 q^{3} +3.67490e20 q^{4} -1.61198e23 q^{5} -2.91471e25 q^{6} +2.93806e28 q^{7} +4.99099e30 q^{8} -9.10601e31 q^{9} -3.65838e33 q^{10} +1.03989e35 q^{11} -4.71965e35 q^{12} -9.30624e35 q^{13} +6.66794e38 q^{14} +2.07025e38 q^{15} +5.90387e40 q^{16} +2.52116e41 q^{17} -2.06661e42 q^{18} -4.10720e41 q^{19} -5.92385e43 q^{20} -3.77334e43 q^{21} +2.36002e45 q^{22} -7.28152e44 q^{23} -6.40990e45 q^{24} -4.17779e46 q^{25} -2.11205e46 q^{26} +2.36014e47 q^{27} +1.07971e49 q^{28} -8.66841e48 q^{29} +4.69844e48 q^{30} +5.42697e49 q^{31} +6.03344e50 q^{32} -1.33552e50 q^{33} +5.72177e51 q^{34} -4.73609e51 q^{35} -3.34636e52 q^{36} +2.44090e52 q^{37} -9.32129e51 q^{38} +1.19520e51 q^{39} -8.04536e53 q^{40} +8.84851e52 q^{41} -8.56360e53 q^{42} -3.35174e54 q^{43} +3.82147e55 q^{44} +1.46787e55 q^{45} -1.65254e55 q^{46} -1.34362e56 q^{47} -7.58230e55 q^{48} +4.44845e56 q^{49} -9.48151e56 q^{50} -3.23791e56 q^{51} -3.41995e56 q^{52} -3.87432e57 q^{53} +5.35634e57 q^{54} -1.67627e58 q^{55} +1.46639e59 q^{56} +5.27485e56 q^{57} -1.96730e59 q^{58} -2.62052e59 q^{59} +7.60797e58 q^{60} -4.77635e59 q^{61} +1.23165e60 q^{62} -2.67540e60 q^{63} +4.98032e60 q^{64} +1.50015e59 q^{65} -3.03096e60 q^{66} -2.36430e61 q^{67} +9.26500e61 q^{68} +9.35162e59 q^{69} -1.07486e62 q^{70} +2.36087e61 q^{71} -4.54480e62 q^{72} +7.86035e61 q^{73} +5.53962e62 q^{74} +5.36551e61 q^{75} -1.50935e62 q^{76} +3.05525e63 q^{77} +2.71250e61 q^{78} -2.74602e63 q^{79} -9.51690e63 q^{80} +8.13902e63 q^{81} +2.00817e63 q^{82} +9.16622e63 q^{83} -1.38666e64 q^{84} -4.06405e64 q^{85} -7.60679e64 q^{86} +1.11328e64 q^{87} +5.19006e65 q^{88} -3.36134e65 q^{89} +3.33133e65 q^{90} -2.73423e64 q^{91} -2.67588e65 q^{92} -6.96983e64 q^{93} -3.04935e66 q^{94} +6.62071e64 q^{95} -7.74871e65 q^{96} +6.50306e66 q^{97} +1.00958e67 q^{98} -9.46921e66 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 5 q + 5554901256 q^{2} + 34\!\cdots\!72 q^{3}+ \cdots + 27\!\cdots\!85 q^{9}+O(q^{10}) \) 5 * q + 5554901256 * q^2 + 3443360269119372 * q^3 + 350472004382296600640 * q^4 + 330744836907160597528950 * q^5 + 146648871573834733762548960 * q^6 + 33632726520317603069152899256 * q^7 + 3261706912683890613885787783680 * q^8 + 27806018581845734541016911293385 * q^9	\( 5 q + 5554901256 q^{2} + 34\!\cdots\!72 q^{3}+ \cdots + 16\!\cdots\!20 q^{99}+O(q^{100}) \) 5 * q + 5554901256 * q^2 + 3443360269119372 * q^3 + 350472004382296600640 * q^4 + 330744836907160597528950 * q^5 + 146648871573834733762548960 * q^6 + 33632726520317603069152899256 * q^7 + 3261706912683890613885787783680 * q^8 + 27806018581845734541016911293385 * q^9 - 5287067006725590176865792208438800 * q^10 + 203006981551281631527218766884109060 * q^11 - 2089518810401181456110201520986913024 * q^12 + 177822884499813229570219072356766702 * q^13 + 290753425875732621001638220329334092480 * q^14 - 933024301033068664231979455289562936600 * q^15 + 18266362102387359184851236859301091348480 * q^16 + 75241497376497768433807587544150344102906 * q^17 - 1011568566626978308983328666525487111002968 * q^18 + 3998884102997801557241177083441346393295100 * q^19 - 15074831378020267075078660994426474705846400 * q^20 - 175719863949295325296418063144372762630915040 * q^21 + 1841247880573095918698534631505063585473750432 * q^22 - 419660874260151197180020017656265233426170968 * q^23 - 13019747846573945420584224979196286639928166400 * q^24 + 175279270003539476977813620578789764300129011875 * q^25 + 21416337629300654169124097666599354769371062960 * q^26 + 1886613800166950113417786970194782722207999659320 * q^27 + 14982728306233364463143494158089725946900023694848 * q^28 + 18733547497571939101380180097730717676662894233950 * q^29 + 183881202860964913168534714290880945912096094414400 * q^30 + 365849822471060800690376948081970588059264217288160 * q^31 + 1591165751988992347021834813546084975107380979204096 * q^32 + 2437038903031213839498705428654461423996034595356784 * q^33 + 7817592154883765712044327776251337623941567500782480 * q^34 + 4524513410554564733118320802153390591800073874285200 * q^35 - 38131548457864843751915538710226876689225094472585920 * q^36 - 56389392588768330454829645685931746748224606527380394 * q^37 - 311451303114725973135630000941921262878276604287141280 * q^38 - 717177850582388225418943791249053833224228521090828280 * q^39 - 1886768345048751997029226502271137564956948018338432000 * q^40 + 113555410342193387626817165052765483601006465327103010 * q^41 + 2805540126450529847390961864461873572829871059166350592 * q^42 + 6508304671085340439704487085091235272293711787089861092 * q^43 + 49369449025916528958230735645862721892607029455332199680 * q^44 + 99011086960300194550392336618799141939148872728728967150 * q^45 + 79552980744915855625545425031873854934595203714399466560 * q^46 - 128023594814179612806658270243785955024442659789917751344 * q^47 - 198512903890152994486195174416803543869354744423782432768 * q^48 - 771329931628098140389185999842408514636676231229111640435 * q^49 - 3919481096957516748709549462396523762064894577356951885000 * q^50 - 3397415009313164473667296477133432796692029796730856284840 * q^51 + 672997930141532412373441872733517069231734104886640838016 * q^52 + 1046765637663599376128164919371991945530174947374966490822 * q^53 + 19066352042639687223500180230679796188217876586398799185600 * q^54 + 66942753107037791618627925698973654692865254681839842449400 * q^55 + 164746697572073652525116376573879338548073684495562965299200 * q^56 - 9288557942524759644038647059781434529266663439727382990960 * q^57 - 61137956327686914952144218440883774026433838412764071303120 * q^58 - 305790738450157663862297559072875409310668010528073986627500 * q^59 - 1346157500908637758724100110370785768539984220742218248588800 * q^60 - 1137073938560830615075915586814815057732339483683661907261890 * q^61 - 2197846158587850633685459639420082896328263471188214086352128 * q^62 - 2062780018748959038039139080074136999529046449885010133153768 * q^63 + 6319522016046144185339524760669817745425888834305772325437440 * q^64 + 17054811715744261908524663200762497384422620874171150779332900 * q^65 + 27998862803339055552343423092993933514291039899414979026779520 * q^66 - 11903044989154510038048691316368615691989662189985228212145844 * q^67 + 81678078346863753465296539273887923556029130514802676363013248 * q^68 + 3593002077831059525793506029116145162632074080747869594484320 * q^69 - 262230520857255225386866306600227822969034558447869634844476800 * q^70 - 112169920751076079402369696382938772997794660792753351047772040 * q^71 - 747723581155501189674233444839980291686130221322311676193789440 * q^72 - 304061800126793465330511223999919410949872771539142074085150718 * q^73 + 921008183492866283853128598587548033201480125306857491530532080 * q^74 + 21623812027928499471467875193108522496460255319651250940492500 * q^75 + 2076567511595431334156222539483464646991367936386801535927366400 * q^76 + 5018131462902473316385236580394702266689060843204393245422638432 * q^77 + 6187393864780941106550100388692932558738785969110711253222726464 * q^78 + 2994504004186984867153587379277397704940492543518650040519815600 * q^79 - 15198313539268031787508043655897930060910106707913153957798092800 * q^80 - 11195187555119704986426983039082721262159900559267345597680888595 * q^81 - 17699192859543411700126655967680257958811789647196784631772687408 * q^82 - 47352447490969920981134910324833485175129837165394254819464203588 * q^83 - 52124143836539534782259645807914007868879894236203487647926097920 * q^84 - 39334683419450918052255554891934302881190270223971152032299949300 * q^85 + 49699285824187070765304255878405188987409992188766856866277888160 * q^86 + 357574798440063707158439877351651513807909832776407769090038489160 * q^87 + 430257938373980762031490456670953174964896424231159472833711400960 * q^88 - 11988583288945008097106276879882407358382120120051430459779195150 * q^89 + 477054381540878916877701150770415125576892082956059127548575220400 * q^90 + 232376792470844928685229521265495056030669651812230900159714321360 * q^91 - 986292139147147043544160128863480288571347084605459783959415954944 * q^92 - 1849280210034321990512094428557344731461785100166176155774311127936 * q^93 - 4927754861315037106505826725122767884474273389521981763161929704320 * q^94 - 2022377488008256909110920831467942087293430657450319294506545963000 * q^95 - 2242556165580376632567217570505477297218451346654758522676359331840 * q^96 + 2897556354128426205551279700626881901316694084191208635967319112106 * q^97 + 12426885478574475523720488645206508880013087100212747539199689691208 * q^98 + 16175146031966622867876651602334534091105243319832315048256094545620 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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