LMFDB - Embedded newform 1.68.a.a.1.1

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			1.1
Root			$7.63188e8$ 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)

$f(q)$	$=$	$q-1.72055e10 q^{2} -1.09955e16 q^{3} +1.48456e20 q^{4} +4.93311e23 q^{5} +1.89183e26 q^{6} +1.79351e28 q^{7} -1.51842e28 q^{8} +2.81916e31 q^{9} +O(q^{10})$	\(q-1.72055e10 q^{2} -1.09955e16 q^{3} +1.48456e20 q^{4} +4.93311e23 q^{5} +1.89183e26 q^{6} +1.79351e28 q^{7} -1.51842e28 q^{8} +2.81916e31 q^{9} -8.48767e33 q^{10} +5.33040e34 q^{11} -1.63235e36 q^{12} +2.30226e37 q^{13} -3.08583e38 q^{14} -5.42420e39 q^{15} -2.16471e40 q^{16} -1.47145e40 q^{17} -4.85052e41 q^{18} +5.15198e42 q^{19} +7.32351e43 q^{20} -1.97206e44 q^{21} -9.17124e44 q^{22} -8.82286e44 q^{23} +1.66958e44 q^{24} +1.75593e47 q^{25} -3.96116e47 q^{26} +7.09406e47 q^{27} +2.66258e48 q^{28} -1.08736e49 q^{29} +9.33262e49 q^{30} +8.83737e49 q^{31} +3.74690e50 q^{32} -5.86105e50 q^{33} +2.53171e50 q^{34} +8.84758e51 q^{35} +4.18523e51 q^{36} -4.39811e52 q^{37} -8.86426e52 q^{38} -2.53145e53 q^{39} -7.49053e51 q^{40} -2.89577e53 q^{41} +3.39303e54 q^{42} -3.62794e54 q^{43} +7.91333e54 q^{44} +1.39072e55 q^{45} +1.51802e55 q^{46} -8.12174e54 q^{47} +2.38020e56 q^{48} -9.67096e55 q^{49} -3.02117e57 q^{50} +1.61793e56 q^{51} +3.41786e57 q^{52} +7.18898e57 q^{53} -1.22057e58 q^{54} +2.62954e58 q^{55} -2.72330e56 q^{56} -5.66486e58 q^{57} +1.87086e59 q^{58} +5.28583e58 q^{59} -8.05257e59 q^{60} +5.02401e59 q^{61} -1.52052e60 q^{62} +5.05620e59 q^{63} -3.25220e60 q^{64} +1.13573e61 q^{65} +1.00842e61 q^{66} -3.52159e60 q^{67} -2.18446e60 q^{68} +9.70118e60 q^{69} -1.52227e62 q^{70} +1.01640e62 q^{71} -4.28067e59 q^{72} -1.36139e62 q^{73} +7.56719e62 q^{74} -1.93073e63 q^{75} +7.64845e62 q^{76} +9.56014e62 q^{77} +4.35550e63 q^{78} +4.98511e63 q^{79} -1.06787e64 q^{80} -1.04139e64 q^{81} +4.98233e63 q^{82} -4.78696e63 q^{83} -2.92764e64 q^{84} -7.25882e63 q^{85} +6.24207e64 q^{86} +1.19560e65 q^{87} -8.09379e62 q^{88} -1.28002e64 q^{89} -2.39281e65 q^{90} +4.12913e65 q^{91} -1.30981e65 q^{92} -9.71713e65 q^{93} +1.39739e65 q^{94} +2.54153e66 q^{95} -4.11990e66 q^{96} -4.06660e66 q^{97} +1.66394e66 q^{98} +1.50273e66 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−1.72055e10	−1.41633	−0.708163	−	0.706049i	$-0.750476\pi$
$2$	−1.72055e10	−1.41633	−0.708163	+	0.706049i	$0.750476\pi$
$3$	−1.09955e16	−1.14197	−0.570983	−	0.820962i	$-0.693438\pi$
$3$	−1.09955e16	−1.14197	−0.570983	+	0.820962i	$0.693438\pi$
$4$	1.48456e20	1.00598
$5$	4.93311e23	1.89507	0.947535	−	0.319652i	$-0.103566\pi$
$5$	4.93311e23	1.89507	0.947535	+	0.319652i	$0.103566\pi$
$6$	1.89183e26	1.61740
$7$	1.79351e28	0.876839	0.438419	−	0.898771i	$-0.355538\pi$
$7$	1.79351e28	0.876839	0.438419	+	0.898771i	$0.355538\pi$
$8$	−1.51842e28	−0.00846988
$9$	2.81916e31	0.304086
$10$	−8.48767e33	−2.68404
$11$	5.33040e34	0.691998	0.345999	−	0.938235i	$-0.387540\pi$
$11$	5.33040e34	0.691998	0.345999	+	0.938235i	$0.387540\pi$
$12$	−1.63235e36	−1.14879
$13$	2.30226e37	1.10931	0.554654	−	0.832081i	$-0.312851\pi$
$13$	2.30226e37	1.10931	0.554654	+	0.832081i	$0.312851\pi$
$14$	−3.08583e38	−1.24189
$15$	−5.42420e39	−2.16410
$16$	−2.16471e40	−0.993984
$17$	−1.47145e40	−0.0886557	−0.0443279	−	0.999017i	$-0.514115\pi$
$17$	−1.47145e40	−0.0886557	−0.0443279	+	0.999017i	$0.514115\pi$
$18$	−4.85052e41	−0.430684
$19$	5.15198e42	0.747702	0.373851	−	0.927489i	$-0.378037\pi$
$19$	5.15198e42	0.747702	0.373851	+	0.927489i	$0.378037\pi$
$20$	7.32351e43	1.90640
$21$	−1.97206e44	−1.00132
$22$	−9.17124e44	−0.980096
$23$	−8.82286e44	−0.212680	−0.106340	−	0.994330i	$-0.533913\pi$
$23$	−8.82286e44	−0.212680	−0.106340	+	0.994330i	$0.533913\pi$
$24$	1.66958e44	0.00967232
$25$	1.75593e47	2.59129
$26$	−3.96116e47	−1.57114
$27$	7.09406e47	0.794710
$28$	2.66258e48	0.882082
$29$	−1.08736e49	−1.11183	−0.555916	−	0.831238i	$-0.687633\pi$
$29$	−1.08736e49	−1.11183	−0.555916	+	0.831238i	$0.687633\pi$
$30$	9.33262e49	3.06508
$31$	8.83737e49	0.967623	0.483812	−	0.875172i	$-0.339252\pi$
$31$	8.83737e49	0.967623	0.483812	+	0.875172i	$0.339252\pi$
$32$	3.74690e50	1.41628
$33$	−5.86105e50	−0.790238
$34$	2.53171e50	0.125565
$35$	8.84758e51	1.66167
$36$	4.18523e51	0.305904
$37$	−4.39811e52	−1.28383	−0.641917	−	0.766774i	$-0.721860\pi$
$37$	−4.39811e52	−1.28383	−0.641917	+	0.766774i	$0.721860\pi$
$38$	−8.86426e52	−1.05899
$39$	−2.53145e53	−1.26679
$40$	−7.49053e51	−0.0160510
$41$	−2.89577e53	−0.271335	−0.135667	−	0.990754i	$-0.543318\pi$
$41$	−2.89577e53	−0.271335	−0.135667	+	0.990754i	$0.543318\pi$
$42$	3.39303e54	1.41820
$43$	−3.62794e54	−0.689393	−0.344697	−	0.938714i	$-0.612018\pi$
$43$	−3.62794e54	−0.689393	−0.344697	+	0.938714i	$0.612018\pi$
$44$	7.91333e54	0.696137
$45$	1.39072e55	0.576263
$46$	1.51802e55	0.301224
$47$	−8.12174e54	−0.0784099	−0.0392049	−	0.999231i	$-0.512483\pi$
$47$	−8.12174e54	−0.0784099	−0.0392049	+	0.999231i	$0.512483\pi$
$48$	2.38020e56	1.13510
$49$	−9.67096e55	−0.231154
$50$	−3.02117e57	−3.67011
$51$	1.61793e56	0.101242
$52$	3.41786e57	1.11594
$53$	7.18898e57	1.24001	0.620005	−	0.784598i	$-0.287130\pi$
$53$	7.18898e57	1.24001	0.620005	+	0.784598i	$0.287130\pi$
$54$	−1.22057e58	−1.12557
$55$	2.62954e58	1.31139
$56$	−2.72330e56	−0.00742672
$57$	−5.66486e58	−0.853850
$58$	1.87086e59	1.57472
$59$	5.28583e58	0.250941	0.125470	−	0.992097i	$-0.459956\pi$
$59$	5.28583e58	0.250941	0.125470	+	0.992097i	$0.459956\pi$
$60$	−8.05257e59	−2.17705
$61$	5.02401e59	0.780731	0.390366	−	0.920660i	$-0.372349\pi$
$61$	5.02401e59	0.780731	0.390366	+	0.920660i	$0.372349\pi$
$62$	−1.52052e60	−1.37047
$63$	5.05620e59	0.266634
$64$	−3.25220e60	−1.01192
$65$	1.13573e61	2.10222
$66$	1.00842e61	1.11924
$67$	−3.52159e60	−0.236174	−0.118087	−	0.993003i	$-0.537676\pi$
$67$	−3.52159e60	−0.236174	−0.118087	+	0.993003i	$0.537676\pi$
$68$	−2.18446e60	−0.0891859
$69$	9.70118e60	0.242873
$70$	−1.52227e62	−2.35347
$71$	1.01640e62	0.977033	0.488516	−	0.872555i	$-0.337538\pi$
$71$	1.01640e62	0.977033	0.488516	+	0.872555i	$0.337538\pi$
$72$	−4.28067e59	−0.00257557
$73$	−1.36139e62	−0.516019	−0.258010	−	0.966142i	$-0.583067\pi$
$73$	−1.36139e62	−0.516019	−0.258010	+	0.966142i	$0.583067\pi$
$74$	7.56719e62	1.81833
$75$	−1.93073e63	−2.95916
$76$	7.64845e62	0.752173
$77$	9.56014e62	0.606771
$78$	4.35550e63	1.79419
$79$	4.98511e63	1.34019	0.670096	−	0.742274i	$-0.266253\pi$
$79$	4.98511e63	1.34019	0.670096	+	0.742274i	$0.266253\pi$
$80$	−1.06787e64	−1.88367
$81$	−1.04139e64	−1.21162
$82$	4.98233e63	0.384298
$83$	−4.78696e63	−0.246005	−0.123002	−	0.992406i	$-0.539252\pi$
$83$	−4.78696e63	−0.246005	−0.123002	+	0.992406i	$0.539252\pi$
$84$	−2.92764e64	−1.00731
$85$	−7.25882e63	−0.168009
$86$	6.24207e64	0.976406
$87$	1.19560e65	1.26967
$88$	−8.09379e62	−0.00586115
$89$	−1.28002e64	−0.0634823	−0.0317411	−	0.999496i	$-0.510105\pi$
$89$	−1.28002e64	−0.0634823	−0.0317411	+	0.999496i	$0.510105\pi$
$90$	−2.39281e65	−0.816177
$91$	4.12913e65	0.972684
$92$	−1.30981e65	−0.213952
$93$	−9.71713e65	−1.10499
$94$	1.39739e65	0.111054
$95$	2.54153e66	1.41695
$96$	−4.11990e66	−1.61734
$97$	−4.06660e66	−1.12818	−0.564090	−	0.825713i	$-0.690773\pi$
$97$	−4.06660e66	−1.12818	−0.564090	+	0.825713i	$0.690773\pi$
$98$	1.66394e66	0.327389
$99$	1.50273e66	0.210427
$100$	2.60679e67	2.60679
$101$	−1.05153e66	−0.0753450	−0.0376725	−	0.999290i	$-0.511994\pi$
$101$	−1.05153e66	−0.0753450	−0.0376725	+	0.999290i	$0.511994\pi$
$102$	−2.78374e66	−0.143391
$103$	−2.37836e66	−0.0883548	−0.0441774	−	0.999024i	$-0.514067\pi$
$103$	−2.37836e66	−0.0883548	−0.0441774	+	0.999024i	$0.514067\pi$
$104$	−3.49580e65	−0.00939571
$105$	−9.72836e67	−1.89757
$106$	−1.23690e68	−1.75626
$107$	1.67319e68	1.73455	0.867277	−	0.497827i	$-0.165868\pi$
$107$	1.67319e68	1.73455	0.867277	+	0.497827i	$0.165868\pi$
$108$	1.05316e68	0.799463
$109$	1.41616e68	0.789450	0.394725	−	0.918799i	$-0.370840\pi$
$109$	1.41616e68	0.789450	0.394725	+	0.918799i	$0.370840\pi$
$110$	−4.52427e68	−1.85735
$111$	4.83595e68	1.46609
$112$	−3.88242e68	−0.871564
$113$	4.00544e68	0.667609	0.333804	−	0.942642i	$-0.391668\pi$
$113$	4.00544e68	0.667609	0.333804	+	0.942642i	$0.391668\pi$
$114$	9.74670e68	1.20933
$115$	−4.35241e68	−0.403044
$116$	−1.61425e69	−1.11848
$117$	6.49044e68	0.337325
$118$	−9.09456e68	−0.355414
$119$	−2.63906e68	−0.0777368
$120$	8.23621e67	0.0183297
$121$	−3.09217e69	−0.521138
$122$	−8.64409e69	−1.10577
$123$	3.18405e69	0.309855
$124$	1.31196e70	0.973410
$125$	5.31937e70	3.01561
$126$	−8.69946e69	−0.377641
$127$	−4.86585e70	−1.62082	−0.810408	−	0.585866i	$-0.800754\pi$
$127$	−4.86585e70	−1.62082	−0.810408	+	0.585866i	$0.800754\pi$
$128$	6.61353e68	0.0169395
$129$	3.98910e70	0.787263
$130$	−1.95408e71	−2.97742
$131$	8.62495e70	1.01664	0.508321	−	0.861168i	$-0.330266\pi$
$131$	8.62495e70	1.01664	0.508321	+	0.861168i	$0.330266\pi$
$132$	−8.70110e70	−0.794964
$133$	9.24013e70	0.655614
$134$	6.05908e70	0.334500
$135$	3.49958e71	1.50603
$136$	2.23428e68	0.000750903 0
$137$	−6.03931e71	−1.58799	−0.793997	−	0.607922i	$-0.792003\pi$
$137$	−6.03931e71	−1.58799	−0.793997	+	0.607922i	$0.792003\pi$
$138$	−1.66914e71	−0.343988
$139$	3.74979e71	0.606752	0.303376	−	0.952871i	$-0.401886\pi$
$139$	3.74979e71	0.606752	0.303376	+	0.952871i	$0.401886\pi$
$140$	1.31348e72	1.67161
$141$	8.93026e70	0.0895414
$142$	−1.74877e72	−1.38380
$143$	1.22720e72	0.767639
$144$	−6.10265e71	−0.302256
$145$	−5.36405e72	−2.10700
$146$	2.34234e72	0.730851
$147$	1.06337e72	0.263970
$148$	−6.52928e72	−1.29151
$149$	−1.44128e72	−0.227514	−0.113757	−	0.993509i	$-0.536289\pi$
$149$	−1.44128e72	−0.227514	−0.113757	+	0.993509i	$0.536289\pi$
$150$	3.32192e73	4.19114
$151$	−1.20935e73	−1.22130	−0.610651	−	0.791900i	$-0.709092\pi$
$151$	−1.20935e73	−1.22130	−0.610651	+	0.791900i	$0.709092\pi$
$152$	−7.82287e70	−0.00633295
$153$	−4.14826e71	−0.0269589
$154$	−1.64487e73	−0.859386
$155$	4.35957e73	1.83371
$156$	−3.75810e73	−1.27437
$157$	−1.14455e73	−0.313327	−0.156664	−	0.987652i	$-0.550074\pi$
$157$	−1.14455e73	−0.313327	−0.156664	+	0.987652i	$0.550074\pi$
$158$	−8.57714e73	−1.89815
$159$	−7.90464e73	−1.41605
$160$	1.84839e74	2.68394
$161$	−1.58239e73	−0.186486
$162$	1.79177e74	1.71605
$163$	−2.51517e73	−0.196012	−0.0980061	−	0.995186i	$-0.531246\pi$
$163$	−2.51517e73	−0.196012	−0.0980061	+	0.995186i	$0.531246\pi$
$164$	−4.29896e73	−0.272957
$165$	−2.89132e74	−1.49756
$166$	8.23621e73	0.348423
$167$	2.64467e74	0.914893	0.457446	−	0.889237i	$-0.348764\pi$
$167$	2.64467e74	0.914893	0.457446	+	0.889237i	$0.348764\pi$
$168$	2.99441e72	0.00848106
$169$	9.93110e73	0.230565
$170$	1.24892e74	0.237955
$171$	1.45243e74	0.227365
$172$	−5.38591e74	−0.693516
$173$	−1.12766e75	−1.19573	−0.597864	−	0.801598i	$-0.703984\pi$
$173$	−1.12766e75	−1.19573	−0.597864	+	0.801598i	$0.703984\pi$
$174$	−2.05710e75	−1.79827
$175$	3.14927e75	2.27214
$176$	−1.15388e75	−0.687835
$177$	−5.81204e74	−0.286566
$178$	2.20235e74	0.0899116
$179$	5.82360e75	1.97068	0.985338	−	0.170612i	$-0.0545746\pi$
$179$	5.82360e75	1.97068	0.985338	+	0.170612i	$0.0545746\pi$
$180$	2.06462e75	0.579710
$181$	5.77923e75	1.34784	0.673919	−	0.738805i	$-0.264609\pi$
$181$	5.77923e75	1.34784	0.673919	+	0.738805i	$0.264609\pi$
$182$	−7.10439e75	−1.37764
$183$	−5.52416e75	−0.891568
$184$	1.33968e73	0.00180138
$185$	−2.16964e76	−2.43295
$186$	1.67188e76	1.56503
$187$	−7.84342e74	−0.0613496
$188$	−1.20572e75	−0.0788788
$189$	1.27233e76	0.696833
$190$	−4.37283e76	−2.00686
$191$	2.42687e76	0.934177	0.467089	−	0.884210i	$-0.345303\pi$
$191$	2.42687e76	0.934177	0.467089	+	0.884210i	$0.345303\pi$
$192$	3.57596e76	1.15558
$193$	1.12591e76	0.305726	0.152863	−	0.988247i	$-0.451151\pi$
$193$	1.12591e76	0.305726	0.152863	+	0.988247i	$0.451151\pi$
$194$	6.99680e76	1.59787
$195$	−1.24879e77	−2.40066
$196$	−1.43572e76	−0.232536
$197$	9.92756e76	1.35589	0.677944	−	0.735113i	$-0.262871\pi$
$197$	9.92756e76	1.35589	0.677944	+	0.735113i	$0.262871\pi$
$198$	−2.58552e76	−0.298033
$199$	−4.94327e76	−0.481323	−0.240661	−	0.970609i	$-0.577364\pi$
$199$	−4.94327e76	−0.481323	−0.240661	+	0.970609i	$0.577364\pi$
$200$	−2.66623e75	−0.0219479
$201$	3.87216e76	0.269703
$202$	1.80921e76	0.106713
$203$	−1.95019e77	−0.974898
$204$	2.40193e76	0.101847
$205$	−1.42852e77	−0.514198
$206$	4.09209e76	0.125139
$207$	−2.48731e76	−0.0646730
$208$	−4.98372e77	−1.10263
$209$	2.74621e77	0.517409
$210$	1.67382e78	2.68758
$211$	7.97263e77	1.09179	0.545895	−	0.837853i	$-0.316190\pi$
$211$	7.97263e77	1.09179	0.545895	+	0.837853i	$0.316190\pi$
$212$	1.06725e78	1.24743
$213$	−1.11758e78	−1.11574
$214$	−2.87881e78	−2.45669
$215$	−1.78970e78	−1.30645
$216$	−1.07718e76	−0.00673110
$217$	1.58499e78	0.848450
$218$	−2.43658e78	−1.11812
$219$	1.49691e78	0.589276
$220$	3.90373e78	1.31923
$221$	−3.38766e77	−0.0983465
$222$	−8.32050e78	−2.07647
$223$	7.26198e78	1.55899	0.779493	−	0.626411i	$-0.215477\pi$
$223$	7.26198e78	1.55899	0.779493	+	0.626411i	$0.215477\pi$
$224$	6.72011e78	1.24185
$225$	4.95024e78	0.787974
$226$	−6.89157e78	−0.945552
$227$	−6.69941e78	−0.792812	−0.396406	−	0.918075i	$-0.629743\pi$
$227$	−6.69941e78	−0.792812	−0.396406	+	0.918075i	$0.629743\pi$
$228$	−8.40985e78	−0.858956
$229$	1.52622e79	1.34626	0.673131	−	0.739523i	$-0.264949\pi$
$229$	1.52622e79	1.34626	0.673131	+	0.739523i	$0.264949\pi$
$230$	7.48856e78	0.570841
$231$	−1.05119e79	−0.692912
$232$	1.65107e77	0.00941709
$233$	−3.84717e78	−0.189985	−0.0949923	−	0.995478i	$-0.530283\pi$
$233$	−3.84717e78	−0.189985	−0.0949923	+	0.995478i	$0.530283\pi$
$234$	−1.11672e79	−0.477762
$235$	−4.00654e78	−0.148592
$236$	7.84716e78	0.252441
$237$	−5.48138e79	−1.53045
$238$	4.54065e78	0.110101
$239$	3.15386e79	0.664526	0.332263	−	0.943187i	$-0.392188\pi$
$239$	3.15386e79	0.664526	0.332263	+	0.943187i	$0.392188\pi$
$240$	1.17418e80	2.15109
$241$	−1.13954e80	−1.81618	−0.908091	−	0.418773i	$-0.862460\pi$
$241$	−1.13954e80	−1.81618	−0.908091	+	0.418773i	$0.862460\pi$
$242$	5.32024e79	0.738102
$243$	4.87375e79	0.588915
$244$	7.45848e79	0.785400
$245$	−4.77079e79	−0.438052
$246$	−5.47832e79	−0.438856
$247$	1.18612e80	0.829432
$248$	−1.34188e78	−0.00819566
$249$	5.26350e79	0.280929
$250$	−9.15226e80	−4.27108
$251$	8.37200e78	0.0341790	0.0170895	−	0.999854i	$-0.494560\pi$
$251$	8.37200e78	0.0341790	0.0170895	+	0.999854i	$0.494560\pi$
$252$	7.50625e79	0.268229
$253$	−4.70294e79	−0.147174
$254$	8.37195e80	2.29560
$255$	7.98144e79	0.191860
$256$	4.68561e80	0.987933
$257$	3.71814e80	0.687964	0.343982	−	0.938976i	$-0.388224\pi$
$257$	3.71814e80	0.687964	0.343982	+	0.938976i	$0.388224\pi$
$258$	−6.86347e80	−1.11502
$259$	−7.88806e80	−1.12571
$260$	1.68606e81	2.11479
$261$	−3.06544e80	−0.338092
$262$	−1.48397e81	−1.43990
$263$	−1.23154e81	−1.05179	−0.525897	−	0.850548i	$-0.676270\pi$
$263$	−1.23154e81	−1.05179	−0.525897	+	0.850548i	$0.676270\pi$
$264$	8.89953e78	0.00669323
$265$	3.54640e81	2.34991
$266$	−1.58981e81	−0.928564
$267$	1.40745e80	0.0724946
$268$	−5.22803e80	−0.237587
$269$	2.94340e81	1.18072	0.590361	−	0.807139i	$-0.298985\pi$
$269$	2.94340e81	1.18072	0.590361	+	0.807139i	$0.298985\pi$
$270$	−6.02121e81	−2.13303
$271$	−2.56265e81	−0.802081	−0.401041	−	0.916060i	$-0.631351\pi$
$271$	−2.56265e81	−0.802081	−0.401041	+	0.916060i	$0.631351\pi$
$272$	3.18526e80	0.0881224
$273$	−4.54019e81	−1.11077
$274$	1.03910e82	2.24912
$275$	9.35980e81	1.79317
$276$	1.44020e81	0.244326
$277$	−3.12521e81	−0.469686	−0.234843	−	0.972033i	$-0.575458\pi$
$277$	−3.12521e81	−0.469686	−0.234843	+	0.972033i	$0.575458\pi$
$278$	−6.45171e81	−0.859359
$279$	2.49140e81	0.294240
$280$	−1.34343e80	−0.0140742
$281$	1.11908e82	1.04040	0.520199	−	0.854045i	$-0.325858\pi$
$281$	1.11908e82	1.04040	0.520199	+	0.854045i	$0.325858\pi$
$282$	−1.53650e81	−0.126820
$283$	−2.21997e82	−1.62743	−0.813713	−	0.581267i	$-0.802557\pi$
$283$	−2.21997e82	−1.62743	−0.813713	+	0.581267i	$0.802557\pi$
$284$	1.50891e82	0.982876
$285$	−2.79454e82	−1.61811
$286$	−2.11146e82	−1.08723
$287$	−5.19360e81	−0.237917
$288$	1.05631e82	0.430669
$289$	−2.73307e82	−0.992140
$290$	9.22913e82	2.98420
$291$	4.47143e82	1.28834
$292$	−2.02107e82	−0.519105
$293$	−1.80269e82	−0.412909	−0.206455	−	0.978456i	$-0.566193\pi$
$293$	−1.80269e82	−0.412909	−0.206455	+	0.978456i	$0.566193\pi$
$294$	−1.82959e82	−0.373867
$295$	2.60756e82	0.475550
$296$	6.67818e80	0.0108739
$297$	3.78142e82	0.549938
$298$	2.47980e82	0.322234
$299$	−2.03125e82	−0.235928
$300$	−2.86629e83	−2.97686
$301$	−6.50675e82	−0.604487
$302$	2.08075e83	1.72976
$303$	1.15621e82	0.0860414
$304$	−1.11525e83	−0.743204
$305$	2.47840e83	1.47954
$306$	7.13729e81	0.0381826
$307$	−1.00209e83	−0.480587	−0.240294	−	0.970700i	$-0.577244\pi$
$307$	−1.00209e83	−0.480587	−0.240294	+	0.970700i	$0.577244\pi$
$308$	1.41926e83	0.610400
$309$	2.61512e82	0.100898
$310$	−7.50087e83	−2.59714
$311$	2.45800e83	0.764028	0.382014	−	0.924157i	$-0.375231\pi$
$311$	2.45800e83	0.764028	0.382014	+	0.924157i	$0.375231\pi$
$312$	3.84381e81	0.0107296
$313$	5.45376e83	1.36761	0.683803	−	0.729667i	$-0.260325\pi$
$313$	5.45376e83	1.36761	0.683803	+	0.729667i	$0.260325\pi$
$314$	1.96927e83	0.443774
$315$	2.49428e83	0.505290
$316$	7.40072e83	1.34821
$317$	−1.09174e84	−1.78910	−0.894550	−	0.446969i	$-0.852503\pi$
$317$	−1.09174e84	−1.78910	−0.894550	+	0.446969i	$0.852503\pi$
$318$	1.36004e84	2.00559
$319$	−5.79605e83	−0.769386
$320$	−1.60434e84	−1.91767
$321$	−1.83975e84	−1.98080
$322$	2.72259e83	0.264125
$323$	−7.58088e82	−0.0662880
$324$	−1.54601e84	−1.21886
$325$	4.04260e84	2.87454
$326$	4.32749e83	0.277617
$327$	−1.55714e84	−0.901524
$328$	4.39700e81	0.00229817
$329$	−1.45664e83	−0.0687528
$330$	4.97466e84	2.12103
$331$	2.14161e84	0.825093	0.412547	−	0.910937i	$-0.364639\pi$
$331$	2.14161e84	0.825093	0.412547	+	0.910937i	$0.364639\pi$
$332$	−7.10655e83	−0.247476
$333$	−1.23990e84	−0.390395
$334$	−4.55030e84	−1.29579
$335$	−1.73724e84	−0.447567
$336$	4.26892e84	0.995296
$337$	−1.76405e84	−0.372313	−0.186157	−	0.982520i	$-0.559603\pi$
$337$	−1.76405e84	−0.372313	−0.186157	+	0.982520i	$0.559603\pi$
$338$	−1.70870e84	−0.326555
$339$	−4.40418e84	−0.762386
$340$	−1.07762e84	−0.169013
$341$	4.71067e84	0.669594
$342$	−2.49898e84	−0.322024
$343$	−9.23815e84	−1.07952
$344$	5.50874e82	0.00583908
$345$	4.78569e84	0.460262
$346$	1.94019e85	1.69354
$347$	5.12606e84	0.406206	0.203103	−	0.979157i	$-0.434897\pi$
$347$	5.12606e84	0.406206	0.203103	+	0.979157i	$0.434897\pi$
$348$	1.77495e85	1.27727
$349$	−1.40759e85	−0.920078	−0.460039	−	0.887899i	$-0.652165\pi$
$349$	−1.40759e85	−0.920078	−0.460039	+	0.887899i	$0.652165\pi$
$350$	−5.41849e85	−3.21810
$351$	1.63324e85	0.881579
$352$	1.99725e85	0.980060
$353$	−4.27961e84	−0.190964	−0.0954820	−	0.995431i	$-0.530439\pi$
$353$	−4.27961e84	−0.190964	−0.0954820	+	0.995431i	$0.530439\pi$
$354$	9.99992e84	0.405870
$355$	5.01400e85	1.85155
$356$	−1.90028e84	−0.0638619
$357$	2.90178e84	0.0887727
$358$	−1.00198e86	−2.79112
$359$	3.75174e85	0.951849	0.475925	−	0.879486i	$-0.342114\pi$
$359$	3.75174e85	0.951849	0.475925	+	0.879486i	$0.342114\pi$
$360$	−2.11170e83	−0.00488088
$361$	−2.09350e85	−0.440942
$362$	−9.94348e85	−1.90898
$363$	3.39999e85	0.595122
$364$	6.12996e85	0.978501
$365$	−6.71587e85	−0.977892
$366$	9.50461e85	1.26275
$367$	−1.08913e86	−1.32058	−0.660291	−	0.751010i	$-0.729567\pi$
$367$	−1.08913e86	−1.32058	−0.660291	+	0.751010i	$0.729567\pi$
$368$	1.90989e85	0.211401
$369$	−8.16365e84	−0.0825090
$370$	3.73297e86	3.44586
$371$	1.28935e86	1.08729
$372$	−1.44257e86	−1.11160
$373$	1.78512e86	1.25725	0.628625	−	0.777708i	$-0.283618\pi$
$373$	1.78512e86	1.25725	0.628625	+	0.777708i	$0.283618\pi$
$374$	1.34950e85	0.0868911
$375$	−5.84891e86	−3.44372
$376$	1.23322e83	0.000664123 0
$377$	−2.50338e86	−1.23337
$378$	−2.18911e86	−0.986943
$379$	−7.64909e83	−0.00315643	−0.00157821	−	0.999999i	$-0.500502\pi$
$379$	−7.64909e83	−0.00315643	−0.00157821	+	0.999999i	$0.500502\pi$
$380$	3.77306e86	1.42542
$381$	5.35024e86	1.85092
$382$	−4.17557e86	−1.32310
$383$	−2.98598e85	−0.0866817	−0.0433409	−	0.999060i	$-0.513800\pi$
$383$	−2.98598e85	−0.0866817	−0.0433409	+	0.999060i	$0.513800\pi$
$384$	−7.27191e84	−0.0193443
$385$	4.71612e86	1.14987
$386$	−1.93718e86	−0.433008
$387$	−1.02278e86	−0.209635
$388$	−6.03713e86	−1.13493
$389$	−3.82483e86	−0.659631	−0.329815	−	0.944045i	$-0.606987\pi$
$389$	−3.82483e86	−0.659631	−0.329815	+	0.944045i	$0.606987\pi$
$390$	2.14861e87	3.40012
$391$	1.29824e85	0.0188553
$392$	1.46846e84	0.00195784
$393$	−9.48356e86	−1.16097
$394$	−1.70809e87	−1.92038
$395$	2.45921e87	2.53976
$396$	2.23089e86	0.211685
$397$	−8.84606e86	−0.771380	−0.385690	−	0.922629i	$-0.626036\pi$
$397$	−8.84606e86	−0.771380	−0.385690	+	0.922629i	$0.626036\pi$
$398$	8.50516e86	0.681710
$399$	−1.01600e87	−0.748689
$400$	−3.80106e87	−2.57570
$401$	3.03362e87	1.89071	0.945356	−	0.326041i	$-0.105715\pi$
$401$	3.03362e87	1.89071	0.945356	+	0.326041i	$0.105715\pi$
$402$	−6.66227e86	−0.381987
$403$	2.03459e87	1.07339
$404$	−1.56106e86	−0.0757955
$405$	−5.13729e87	−2.29610
$406$	3.35540e87	1.38077
$407$	−2.34437e87	−0.888410
$408$	−2.45670e84	−0.000857506 0
$409$	5.25302e86	0.168919	0.0844594	−	0.996427i	$-0.473084\pi$
$409$	5.25302e86	0.168919	0.0844594	+	0.996427i	$0.473084\pi$
$410$	2.45784e87	0.728272
$411$	6.64053e87	1.81343
$412$	−3.53082e86	−0.0888831
$413$	9.48020e86	0.220034
$414$	4.27954e86	0.0915980
$415$	−2.36146e87	−0.466196
$416$	8.62634e87	1.57109
$417$	−4.12308e87	−0.692890
$418$	−4.72501e87	−0.732819
$419$	−5.17945e87	−0.741504	−0.370752	−	0.928732i	$-0.620900\pi$
$419$	−5.17945e87	−0.741504	−0.370752	+	0.928732i	$0.620900\pi$
$420$	−1.44424e88	−1.90892
$421$	6.80858e87	0.831010	0.415505	−	0.909591i	$-0.363605\pi$
$421$	6.80858e87	0.831010	0.415505	+	0.909591i	$0.363605\pi$
$422$	−1.37173e88	−1.54633
$423$	−2.28965e86	−0.0238433
$424$	−1.09159e86	−0.0105027
$425$	−2.58376e87	−0.229733
$426$	1.92286e88	1.58025
$427$	9.01063e87	0.684575
$428$	2.48395e88	1.74493
$429$	−1.34937e88	−0.876618
$430$	3.07928e88	1.85036
$431$	−2.41768e88	−1.34404	−0.672018	−	0.740535i	$-0.734572\pi$
$431$	−2.41768e88	−1.34404	−0.672018	+	0.740535i	$0.734572\pi$
$432$	−1.53566e88	−0.789929
$433$	−1.54829e88	−0.737066	−0.368533	−	0.929615i	$-0.620140\pi$
$433$	−1.54829e88	−0.737066	−0.368533	+	0.929615i	$0.620140\pi$
$434$	−2.72706e88	−1.20168
$435$	5.89804e88	2.40612
$436$	2.10238e88	0.794171
$437$	−4.54552e87	−0.159021
$438$	−2.57552e88	−0.834607
$439$	−4.85118e88	−1.45642	−0.728208	−	0.685356i	$-0.759647\pi$
$439$	−4.85118e88	−1.45642	−0.728208	+	0.685356i	$0.759647\pi$
$440$	−3.99275e86	−0.0111073
$441$	−2.72640e87	−0.0702905
$442$	5.82865e87	0.139291
$443$	4.06798e88	0.901267	0.450634	−	0.892709i	$-0.351198\pi$
$443$	4.06798e88	0.901267	0.450634	+	0.892709i	$0.351198\pi$
$444$	7.17927e88	1.47486
$445$	−6.31449e87	−0.120303
$446$	−1.24946e89	−2.20803
$447$	1.58476e88	0.259813
$448$	−5.83286e88	−0.887295
$449$	1.75617e88	0.247921	0.123961	−	0.992287i	$-0.460440\pi$
$449$	1.75617e88	0.247921	0.123961	+	0.992287i	$0.460440\pi$
$450$	−8.51715e88	−1.11603
$451$	−1.54356e88	−0.187763
$452$	5.94633e88	0.671601
$453$	1.32974e89	1.39469
$454$	1.15267e89	1.12288
$455$	2.03694e89	1.84331
$456$	8.60164e86	0.00723201
$457$	1.71391e88	0.133905	0.0669524	−	0.997756i	$-0.478672\pi$
$457$	1.71391e88	0.133905	0.0669524	+	0.997756i	$0.478672\pi$
$458$	−2.62595e89	−1.90675
$459$	−1.04386e88	−0.0704556
$460$	−6.46144e88	−0.405454
$461$	−2.85185e89	−1.66397	−0.831984	−	0.554799i	$-0.812795\pi$
$461$	−2.85185e89	−1.66397	−0.831984	+	0.554799i	$0.812795\pi$
$462$	1.80862e89	0.981389
$463$	1.68560e89	0.850731	0.425366	−	0.905022i	$-0.360145\pi$
$463$	1.68560e89	0.850731	0.425366	+	0.905022i	$0.360145\pi$
$464$	2.35381e89	1.10514
$465$	−4.79356e89	−2.09404
$466$	6.61927e88	0.269080
$467$	−4.95124e89	−1.87326	−0.936631	−	0.350317i	$-0.886074\pi$
$467$	−4.95124e89	−1.87326	−0.936631	+	0.350317i	$0.886074\pi$
$468$	9.63548e88	0.339342
$469$	−6.31601e88	−0.207087
$470$	6.89347e88	0.210455
$471$	1.25850e89	0.357809
$472$	−8.02611e86	−0.00212544
$473$	−1.93384e89	−0.477059
$474$	9.43100e89	2.16762
$475$	9.04650e89	1.93751
$476$	−3.91786e88	−0.0782016
$477$	2.02669e89	0.377069
$478$	−5.42638e89	−0.941186
$479$	6.60213e89	1.06769	0.533844	−	0.845583i	$-0.320747\pi$
$479$	6.60213e89	1.06769	0.533844	+	0.845583i	$0.320747\pi$
$480$	−2.03239e90	−3.06497
$481$	−1.01256e90	−1.42417
$482$	1.96064e90	2.57231
$483$	1.73992e89	0.212961
$484$	−4.59052e89	−0.524255
$485$	−2.00610e90	−2.13798
$486$	−8.38554e89	−0.834096
$487$	2.04394e90	1.89779	0.948896	−	0.315588i	$-0.102202\pi$
$487$	2.04394e90	1.89779	0.948896	+	0.315588i	$0.102202\pi$
$488$	−7.62857e87	−0.00661270
$489$	2.76556e89	0.223839
$490$	8.20839e89	0.620425
$491$	−1.82715e89	−0.128986	−0.0644932	−	0.997918i	$-0.520543\pi$
$491$	−1.82715e89	−0.128986	−0.0644932	+	0.997918i	$0.520543\pi$
$492$	4.72693e89	0.311708
$493$	1.59999e89	0.0985703
$494$	−2.04078e90	−1.17475
$495$	7.41311e89	0.398773
$496$	−1.91303e90	−0.961802
$497$	1.82292e90	0.856700
$498$	−9.05613e89	−0.397887
$499$	−2.98431e90	−1.22596	−0.612979	−	0.790100i	$-0.710029\pi$
$499$	−2.98431e90	−1.22596	−0.612979	+	0.790100i	$0.710029\pi$
$500$	7.89695e90	3.03364
$501$	−2.90795e90	−1.04478
$502$	−1.44045e89	−0.0484086
$503$	6.14610e90	1.93229	0.966145	−	0.258000i	$-0.0830634\pi$
$503$	6.14610e90	1.93229	0.966145	+	0.258000i	$0.0830634\pi$
$504$	−7.67743e87	−0.00225836
$505$	−5.18729e89	−0.142784
$506$	8.09166e89	0.208447
$507$	−1.09197e90	−0.263297
$508$	−7.22366e90	−1.63051
$509$	4.35588e89	0.0920515	0.0460257	−	0.998940i	$-0.485344\pi$
$509$	4.35588e89	0.0920515	0.0460257	+	0.998940i	$0.485344\pi$
$510$	−1.37325e90	−0.271737
$511$	−2.44166e90	−0.452466
$512$	−8.15944e90	−1.41617
$513$	3.65485e90	0.594207
$514$	−6.39725e90	−0.974381
$515$	−1.17327e90	−0.167438
$516$	5.92208e90	0.791971
$517$	−4.32921e89	−0.0542595
$518$	1.35718e91	1.59438
$519$	1.23991e91	1.36548
$520$	−1.72451e89	−0.0178055
$521$	−1.44636e91	−1.40028	−0.700139	−	0.714007i	$-0.746878\pi$
$521$	−1.44636e91	−1.40028	−0.700139	+	0.714007i	$0.746878\pi$
$522$	5.27425e90	0.478849
$523$	1.71161e91	1.45747	0.728733	−	0.684798i	$-0.240110\pi$
$523$	1.71161e91	1.45747	0.728733	+	0.684798i	$0.240110\pi$
$524$	1.28043e91	1.02272
$525$	−3.46278e91	−2.59471
$526$	2.11893e91	1.48968
$527$	−1.30037e90	−0.0857853
$528$	1.26874e91	0.785484
$529$	−1.64309e91	−0.954767
$530$	−6.10177e91	−3.32824
$531$	1.49016e90	0.0763074
$532$	1.37176e91	0.659535
$533$	−6.66682e90	−0.300994
$534$	−2.42159e90	−0.102676
$535$	8.25400e91	3.28710
$536$	5.34725e88	0.00200037
$537$	−6.40335e91	−2.25044
$538$	−5.06427e91	−1.67229
$539$	−5.15501e90	−0.159958
$540$	5.19535e91	1.51504
$541$	2.45133e91	0.671883	0.335941	−	0.941883i	$-0.390946\pi$
$541$	2.45133e91	0.671883	0.335941	+	0.941883i	$0.390946\pi$
$542$	4.40918e91	1.13601
$543$	−6.35456e91	−1.53919
$544$	−5.51338e90	−0.125561
$545$	6.98606e91	1.49606
$546$	7.81163e91	1.57322
$547$	2.28762e91	0.433319	0.216660	−	0.976247i	$-0.430484\pi$
$547$	2.28762e91	0.433319	0.216660	+	0.976247i	$0.430484\pi$
$548$	−8.96575e91	−1.59749
$549$	1.41635e91	0.237409
$550$	−1.61040e92	−2.53971
$551$	−5.60204e91	−0.831320
$552$	−1.47305e89	−0.00205711
$553$	8.94085e91	1.17513
$554$	5.37710e91	0.665229
$555$	2.38562e92	2.77835
$556$	5.56681e91	0.610380
$557$	−1.43839e92	−1.48500	−0.742499	−	0.669847i	$-0.766360\pi$
$557$	−1.43839e92	−1.48500	−0.742499	+	0.669847i	$0.766360\pi$
$558$	−4.28658e91	−0.416740
$559$	−8.35247e91	−0.764750
$560$	−1.91524e92	−1.65167
$561$	8.62424e90	0.0700591
$562$	−1.92544e92	−1.47354
$563$	−1.11672e92	−0.805216	−0.402608	−	0.915372i	$-0.631896\pi$
$563$	−1.11672e92	−0.805216	−0.402608	+	0.915372i	$0.631896\pi$
$564$	1.32576e91	0.0900769
$565$	1.97592e92	1.26517
$566$	3.81958e92	2.30497
$567$	−1.86775e92	−1.06239
$568$	−1.54332e90	−0.00827535
$569$	−3.93668e91	−0.199007	−0.0995036	−	0.995037i	$-0.531725\pi$
$569$	−3.93668e91	−0.199007	−0.0995036	+	0.995037i	$0.531725\pi$
$570$	4.80815e92	2.29177
$571$	1.48833e92	0.668943	0.334471	−	0.942406i	$-0.391442\pi$
$571$	1.48833e92	0.668943	0.334471	+	0.942406i	$0.391442\pi$
$572$	1.82185e92	0.772230
$573$	−2.66847e92	−1.06680
$574$	8.93587e91	0.336968
$575$	−1.54923e92	−0.551116
$576$	−9.16848e91	−0.307712
$577$	−3.49967e92	−1.10825	−0.554124	−	0.832434i	$-0.686947\pi$
$577$	−3.49967e92	−1.10825	−0.554124	+	0.832434i	$0.686947\pi$
$578$	4.70239e92	1.40519
$579$	−1.23799e92	−0.349129
$580$	−7.96328e92	−2.11960
$581$	−8.58546e91	−0.215706
$582$	−7.69333e92	−1.82471
$583$	3.83201e92	0.858085
$584$	2.06716e90	0.00437062
$585$	3.20180e92	0.639254
$586$	3.10162e92	0.584814
$587$	4.67398e92	0.832359	0.416180	−	0.909282i	$-0.363369\pi$
$587$	4.67398e92	0.832359	0.416180	+	0.909282i	$0.363369\pi$
$588$	1.57864e92	0.265548
$589$	4.55300e92	0.723494
$590$	−4.48644e92	−0.673534
$591$	−1.09159e93	−1.54838
$592$	9.52062e92	1.27611
$593$	1.07249e93	1.35851	0.679253	−	0.733904i	$-0.262304\pi$
$593$	1.07249e93	1.35851	0.679253	+	0.733904i	$0.262304\pi$
$594$	−6.50614e92	−0.778892
$595$	−1.30188e92	−0.147317
$596$	−2.13967e92	−0.228875
$597$	5.43538e92	0.549654
$598$	3.49488e92	0.334151
$599$	−1.28809e93	−1.16452	−0.582259	−	0.813003i	$-0.697831\pi$
$599$	−1.28809e93	−1.16452	−0.582259	+	0.813003i	$0.697831\pi$
$600$	2.93166e91	0.0250638
$601$	7.69849e92	0.622459	0.311230	−	0.950335i	$-0.399259\pi$
$601$	7.69849e92	0.622459	0.311230	+	0.950335i	$0.399259\pi$
$602$	1.11952e93	0.856151
$603$	−9.92793e91	−0.0718172
$604$	−1.79535e93	−1.22861
$605$	−1.52540e93	−0.987593
$606$	−1.98931e92	−0.121863
$607$	5.65104e92	0.327572	0.163786	−	0.986496i	$-0.447629\pi$
$607$	5.65104e92	0.327572	0.163786	+	0.986496i	$0.447629\pi$
$608$	1.93040e93	1.05895
$609$	2.14433e93	1.11330
$610$	−4.26422e93	−2.09551
$611$	−1.86984e92	−0.0869807
$612$	−6.15835e91	−0.0271201
$613$	−3.50864e93	−1.46289	−0.731447	−	0.681898i	$-0.761155\pi$
$613$	−3.50864e93	−1.46289	−0.731447	+	0.681898i	$0.761155\pi$
$614$	1.72415e93	0.680669
$615$	1.57072e93	0.587197
$616$	−1.45163e91	−0.00513928
$617$	2.70034e93	0.905451	0.452725	−	0.891650i	$-0.350452\pi$
$617$	2.70034e93	0.905451	0.452725	+	0.891650i	$0.350452\pi$
$618$	−4.49946e92	−0.142905
$619$	−2.68678e93	−0.808342	−0.404171	−	0.914683i	$-0.632440\pi$
$619$	−2.68678e93	−0.808342	−0.404171	+	0.914683i	$0.632440\pi$
$620$	6.47206e93	1.84468
$621$	−6.25899e92	−0.169019
$622$	−4.22912e93	−1.08211
$623$	−2.29574e92	−0.0556637
$624$	5.47985e93	1.25917
$625$	1.43424e94	3.12349
$626$	−9.38349e93	−1.93698
$627$	−3.01960e93	−0.590863
$628$	−1.69917e93	−0.315201
$629$	6.47160e92	0.113819
$630$	−4.29153e93	−0.715656
$631$	−3.83662e93	−0.606688	−0.303344	−	0.952881i	$-0.598103\pi$
$631$	−3.83662e93	−0.606688	−0.303344	+	0.952881i	$0.598103\pi$
$632$	−7.56949e91	−0.0113513
$633$	−8.76631e93	−1.24679
$634$	1.87840e94	2.53395
$635$	−2.40037e94	−3.07156
$636$	−1.17350e94	−1.42452
$637$	−2.22651e93	−0.256421
$638$	9.97242e93	1.08970
$639$	2.86539e93	0.297102
$640$	3.26253e92	0.0321015
$641$	1.07467e94	1.00353	0.501765	−	0.865004i	$-0.332684\pi$
$641$	1.07467e94	1.00353	0.501765	+	0.865004i	$0.332684\pi$
$642$	3.16539e94	2.80546
$643$	−4.05930e93	−0.341494	−0.170747	−	0.985315i	$-0.554618\pi$
$643$	−4.05930e93	−0.341494	−0.170747	+	0.985315i	$0.554618\pi$
$644$	−2.34916e93	−0.187601
$645$	1.96787e94	1.49192
$646$	1.30433e93	0.0938855
$647$	−1.63125e93	−0.111488	−0.0557438	−	0.998445i	$-0.517753\pi$
$647$	−1.63125e93	−0.111488	−0.0557438	+	0.998445i	$0.517753\pi$
$648$	1.58127e92	0.0102623
$649$	2.81756e93	0.173650
$650$	−6.95551e94	−4.07129
$651$	−1.74278e94	−0.968900
$652$	−3.73394e93	−0.197184
$653$	5.05458e93	0.253568	0.126784	−	0.991930i	$-0.459535\pi$
$653$	5.05458e93	0.253568	0.126784	+	0.991930i	$0.459535\pi$
$654$	2.67914e94	1.27685
$655$	4.25478e94	1.92661
$656$	6.26850e93	0.269702
$657$	−3.83797e93	−0.156914
$658$	2.50623e93	0.0973765
$659$	7.75623e93	0.286411	0.143205	−	0.989693i	$-0.454259\pi$
$659$	7.75623e93	0.286411	0.143205	+	0.989693i	$0.454259\pi$
$660$	−4.29235e94	−1.50651
$661$	−2.70603e94	−0.902784	−0.451392	−	0.892326i	$-0.649072\pi$
$661$	−2.70603e94	−0.902784	−0.451392	+	0.892326i	$0.649072\pi$
$662$	−3.68476e94	−1.16860
$663$	3.72490e93	0.112308
$664$	7.26861e91	0.00208363
$665$	4.55826e94	1.24243
$666$	2.13331e94	0.552927
$667$	9.59361e93	0.236465
$668$	3.92619e94	0.920364
$669$	−7.98491e94	−1.78031
$670$	2.98901e94	0.633901
$671$	2.67800e94	0.540265
$672$	−7.38910e94	−1.41814
$673$	−1.46662e94	−0.267801	−0.133900	−	0.990995i	$-0.542750\pi$
$673$	−1.46662e94	−0.267801	−0.133900	+	0.990995i	$0.542750\pi$
$674$	3.03514e94	0.527317
$675$	1.24567e95	2.05933
$676$	1.47434e94	0.231943
$677$	−1.64408e94	−0.246152	−0.123076	−	0.992397i	$-0.539276\pi$
$677$	−1.64408e94	−0.246152	−0.123076	+	0.992397i	$0.539276\pi$
$678$	7.57762e94	1.07979
$679$	−7.29349e94	−0.989232
$680$	1.10219e92	0.00142301
$681$	7.36634e94	0.905364
$682$	−8.10497e94	−0.948363
$683$	−9.12704e94	−1.01680	−0.508401	−	0.861120i	$-0.669763\pi$
$683$	−9.12704e94	−1.01680	−0.508401	+	0.861120i	$0.669763\pi$
$684$	2.15622e94	0.228725
$685$	−2.97926e95	−3.00936
$686$	1.58947e95	1.52896
$687$	−1.67816e95	−1.53739
$688$	7.85343e94	0.685246
$689$	1.65509e95	1.37555
$690$	−8.23404e94	−0.651881
$691$	9.94852e94	0.750315	0.375158	−	0.926961i	$-0.377589\pi$
$691$	9.94852e94	0.750315	0.375158	+	0.926961i	$0.377589\pi$
$692$	−1.67408e95	−1.20288
$693$	2.69516e94	0.184510
$694$	−8.81965e94	−0.575320
$695$	1.84981e95	1.14984
$696$	−1.81543e93	−0.0107540
$697$	4.26099e93	0.0240554
$698$	2.42183e95	1.30313
$699$	4.23016e94	0.216956
$700$	4.67530e95	2.28573
$701$	1.03900e95	0.484243	0.242121	−	0.970246i	$-0.422157\pi$
$701$	1.03900e95	0.484243	0.242121	+	0.970246i	$0.422157\pi$
$702$	−2.81007e95	−1.24860
$703$	−2.26590e95	−0.959925
$704$	−1.73355e95	−0.700250
$705$	4.40539e94	0.169687
$706$	7.36329e94	0.270467
$707$	−1.88592e94	−0.0660654
$708$	−8.62835e94	−0.288279
$709$	−1.34893e95	−0.429874	−0.214937	−	0.976628i	$-0.568955\pi$
$709$	−1.34893e95	−0.429874	−0.214937	+	0.976628i	$0.568955\pi$
$710$	−8.62685e95	−2.62239
$711$	1.40538e95	0.407533
$712$	1.94361e92	0.000537687 0
$713$	−7.79709e94	−0.205794
$714$	−4.99267e94	−0.125731
$715$	6.05390e95	1.45473
$716$	8.64552e95	1.98246
$717$	−3.46782e95	−0.758866
$718$	−6.45506e95	−1.34813
$719$	4.02663e95	0.802645	0.401322	−	0.915937i	$-0.368551\pi$
$719$	4.02663e95	0.802645	0.401322	+	0.915937i	$0.368551\pi$
$720$	−3.01050e95	−0.572797
$721$	−4.26561e94	−0.0774729
$722$	3.60197e95	0.624517
$723$	1.25298e96	2.07402
$724$	8.57965e95	1.35590
$725$	−1.90932e96	−2.88108
$726$	−5.84987e95	−0.842887
$727$	−6.99986e95	−0.963133	−0.481567	−	0.876410i	$-0.659932\pi$
$727$	−6.99986e95	−0.963133	−0.481567	+	0.876410i	$0.659932\pi$
$728$	−6.26976e93	−0.00823852
$729$	4.29575e95	0.539097
$730$	1.15550e96	1.38501
$731$	5.33834e94	0.0611186
$732$	−8.20097e95	−0.896900
$733$	5.32830e94	0.0556679	0.0278340	−	0.999613i	$-0.491139\pi$
$733$	5.32830e94	0.0556679	0.0278340	+	0.999613i	$0.491139\pi$
$734$	1.87390e96	1.87037
$735$	5.24572e95	0.500241
$736$	−3.30584e95	−0.301214
$737$	−1.87715e95	−0.163432
$738$	1.40460e95	0.116860
$739$	8.51506e95	0.677016	0.338508	−	0.940963i	$-0.390078\pi$
$739$	8.51506e95	0.677016	0.338508	+	0.940963i	$0.390078\pi$
$740$	−3.22096e96	−2.44750
$741$	−1.30420e96	−0.947183
$742$	−2.21840e96	−1.53996
$743$	1.89590e96	1.25803	0.629013	−	0.777395i	$-0.283459\pi$
$743$	1.89590e96	1.25803	0.629013	+	0.777395i	$0.283459\pi$
$744$	1.47547e94	0.00935916
$745$	−7.10998e95	−0.431155
$746$	−3.07140e96	−1.78068
$747$	−1.34952e95	−0.0748065
$748$	−1.16441e95	−0.0617165
$749$	3.00088e96	1.52092
$750$	1.00634e97	4.87743
$751$	−4.17131e96	−1.93346	−0.966728	−	0.255806i	$-0.917659\pi$
$751$	−4.17131e96	−1.93346	−0.966728	+	0.255806i	$0.917659\pi$
$752$	1.75812e95	0.0779382
$753$	−9.20543e94	−0.0390312
$754$	4.30720e96	1.74685
$755$	−5.96584e96	−2.31445
$756$	1.88885e96	0.701000
$757$	8.46751e95	0.300638	0.150319	−	0.988638i	$-0.451970\pi$
$757$	8.46751e95	0.300638	0.150319	+	0.988638i	$0.451970\pi$
$758$	1.31607e94	0.00447053
$759$	5.17112e95	0.168068
$760$	−3.85910e94	−0.0120014
$761$	3.16557e95	0.0942033	0.0471016	−	0.998890i	$-0.485002\pi$
$761$	3.16557e95	0.0942033	0.0471016	+	0.998890i	$0.485002\pi$
$762$	−9.20538e96	−2.62150
$763$	2.53990e96	0.692220
$764$	3.60285e96	0.939764
$765$	−2.04638e95	−0.0510890
$766$	5.13753e95	0.122770
$767$	1.21694e96	0.278370
$768$	−5.15206e96	−1.12819
$769$	−5.10943e96	−1.07113	−0.535563	−	0.844496i	$-0.679900\pi$
$769$	−5.10943e96	−1.07113	−0.535563	+	0.844496i	$0.679900\pi$
$770$	−8.11433e96	−1.62860
$771$	−4.08828e96	−0.785631
$772$	1.67148e96	0.307555
$773$	4.84034e96	0.852831	0.426416	−	0.904527i	$-0.359776\pi$
$773$	4.84034e96	0.852831	0.426416	+	0.904527i	$0.359776\pi$
$774$	1.75974e96	0.296911
$775$	1.55178e97	2.50739
$776$	6.17481e94	0.00955555
$777$	8.67332e96	1.28553
$778$	6.58083e96	0.934253
$779$	−1.49190e96	−0.202877
$780$	−1.85391e97	−2.41502
$781$	5.41781e96	0.676105
$782$	−2.23369e95	−0.0267053
$783$	−7.71378e96	−0.883585
$784$	2.09348e96	0.229763
$785$	−5.64621e96	−0.593777
$786$	1.63170e97	1.64431
$787$	−8.19889e96	−0.791775	−0.395887	−	0.918299i	$-0.629563\pi$
$787$	−8.19889e96	−0.791775	−0.395887	+	0.918299i	$0.629563\pi$
$788$	1.47381e97	1.36400
$789$	1.35414e97	1.20111
$790$	−4.23120e97	−3.59713
$791$	7.18380e96	0.585385
$792$	−2.28177e94	−0.00178229
$793$	1.15666e97	0.866071
$794$	1.52201e97	1.09253
$795$	−3.89944e97	−2.68351
$796$	−7.33861e96	−0.484201
$797$	−1.17038e97	−0.740413	−0.370206	−	0.928949i	$-0.620713\pi$
$797$	−1.17038e97	−0.740413	−0.370206	+	0.928949i	$0.620713\pi$
$798$	1.74808e97	1.06039
$799$	1.19507e95	0.00695148
$800$	6.57928e97	3.66998
$801$	−3.60859e95	−0.0193040
$802$	−5.21951e97	−2.67786
$803$	−7.25674e96	−0.357084
$804$	5.74848e96	0.271316
$805$	−7.80610e96	−0.353404
$806$	−3.50063e97	−1.52027
$807$	−3.23641e97	−1.34834
$808$	1.59666e94	0.000638163 0
$809$	6.68432e96	0.256319	0.128160	−	0.991754i	$-0.459093\pi$
$809$	6.68432e96	0.256319	0.128160	+	0.991754i	$0.459093\pi$
$810$	8.83898e97	3.25203
$811$	4.48195e97	1.58223	0.791113	−	0.611670i	$-0.209502\pi$
$811$	4.48195e97	1.58223	0.791113	+	0.611670i	$0.209502\pi$
$812$	−2.89518e97	−0.980728
$813$	2.81776e97	0.915949
$814$	4.03362e97	1.25828
$815$	−1.24076e97	−0.371457
$816$	−3.50235e96	−0.100633
$817$	−1.86911e97	−0.515461
$818$	−9.03810e96	−0.239244
$819$	1.16407e97	0.295779
$820$	−2.12072e97	−0.517273
$821$	5.60928e97	1.31344	0.656721	−	0.754133i	$-0.271943\pi$
$821$	5.60928e97	1.31344	0.656721	+	0.754133i	$0.271943\pi$
$822$	−1.14254e98	−2.56841
$823$	−1.05963e97	−0.228696	−0.114348	−	0.993441i	$-0.536478\pi$
$823$	−1.05963e97	−0.228696	−0.114348	+	0.993441i	$0.536478\pi$
$824$	3.61134e94	0.000748354 0
$825$	−1.02916e98	−2.04774
$826$	−1.63112e97	−0.311641
$827$	−1.39147e97	−0.255292	−0.127646	−	0.991820i	$-0.540742\pi$
$827$	−1.39147e97	−0.255292	−0.127646	+	0.991820i	$0.540742\pi$
$828$	−3.69257e96	−0.0650597
$829$	4.21519e97	0.713247	0.356624	−	0.934248i	$-0.383928\pi$
$829$	4.21519e97	0.713247	0.356624	+	0.934248i	$0.383928\pi$
$830$	4.06301e97	0.660286
$831$	3.43633e97	0.536365
$832$	−7.48741e97	−1.12254
$833$	1.42303e96	0.0204931
$834$	7.09398e97	0.981358
$835$	1.30465e98	1.73379
$836$	4.07693e97	0.520503
$837$	6.26928e97	0.768980
$838$	8.91151e97	1.05021
$839$	−1.62194e98	−1.83657	−0.918287	−	0.395915i	$-0.870427\pi$
$839$	−1.62194e98	−1.83657	−0.918287	+	0.395915i	$0.870427\pi$
$840$	1.47717e96	0.0160722
$841$	2.25889e97	0.236172
$842$	−1.17145e98	−1.17698
$843$	−1.23048e98	−1.18810
$844$	1.18359e98	1.09832
$845$	4.89911e97	0.436936
$846$	3.93946e96	0.0337699
$847$	−5.54584e97	−0.456954
$848$	−1.55620e98	−1.23255
$849$	2.44097e98	1.85847
$850$	4.44549e97	0.325376
$851$	3.88039e97	0.273046
$852$	−1.65912e98	−1.12241
$853$	−5.59225e97	−0.363742	−0.181871	−	0.983322i	$-0.558215\pi$
$853$	−5.59225e97	−0.363742	−0.181871	+	0.983322i	$0.558215\pi$
$854$	−1.55033e98	−0.969582
$855$	7.16497e97	0.430873
$856$	−2.54060e96	−0.0146915
$857$	−1.87727e98	−1.04393	−0.521963	−	0.852968i	$-0.674800\pi$
$857$	−1.87727e98	−1.04393	−0.521963	+	0.852968i	$0.674800\pi$
$858$	2.32166e98	1.24158
$859$	−7.06967e97	−0.363603	−0.181802	−	0.983335i	$-0.558193\pi$
$859$	−7.06967e97	−0.363603	−0.181802	+	0.983335i	$0.558193\pi$
$860$	−2.65693e98	−1.31426
$861$	5.71063e97	0.271693
$862$	4.15975e98	1.90359
$863$	−8.77573e97	−0.386297	−0.193149	−	0.981170i	$-0.561870\pi$
$863$	−8.77573e97	−0.386297	−0.193149	+	0.981170i	$0.561870\pi$
$864$	2.65807e98	1.12553
$865$	−5.56285e98	−2.26599
$866$	2.66391e98	1.04393
$867$	3.00515e98	1.13299
$868$	2.35302e98	0.853523
$869$	2.65726e98	0.927411
$870$	−1.01479e99	−3.40785
$871$	−8.10762e97	−0.261990
$872$	−2.15032e96	−0.00668655
$873$	−1.14644e98	−0.343063
$874$	7.82081e97	0.225226
$875$	9.54035e98	2.64420
$876$	2.22226e98	0.592800
$877$	−5.28961e98	−1.35812	−0.679058	−	0.734084i	$-0.737612\pi$
$877$	−5.28961e98	−1.35812	−0.679058	+	0.734084i	$0.737612\pi$
$878$	8.34671e98	2.06276
$879$	1.98214e98	0.471528
$880$	−5.69219e98	−1.30350
$881$	−4.98423e98	−1.09877	−0.549383	−	0.835571i	$-0.685137\pi$
$881$	−4.98423e98	−1.09877	−0.549383	+	0.835571i	$0.685137\pi$
$882$	4.69091e97	0.0995543
$883$	6.32680e97	0.129271	0.0646355	−	0.997909i	$-0.479412\pi$
$883$	6.32680e97	0.129271	0.0646355	+	0.997909i	$0.479412\pi$
$884$	−5.02920e97	−0.0989346
$885$	−2.86714e98	−0.543062
$886$	−6.99917e98	−1.27649
$887$	−3.93382e98	−0.690834	−0.345417	−	0.938449i	$-0.612263\pi$
$887$	−3.93382e98	−0.690834	−0.345417	+	0.938449i	$0.612263\pi$
$888$	−7.34300e96	−0.0124176
$889$	−8.72695e98	−1.42119
$890$	1.08644e98	0.170389
$891$	−5.55103e98	−0.838437
$892$	1.07809e99	1.56831
$893$	−4.18430e97	−0.0586272
$894$	−2.72666e98	−0.367980
$895$	2.87285e99	3.73457
$896$	1.18614e97	0.0148532
$897$	2.23346e98	0.269421
$898$	−3.02158e98	−0.351138
$899$	−9.60938e98	−1.07584
$900$	7.34895e98	0.792686
$901$	−1.05782e98	−0.109934
$902$	2.65578e98	0.265934
$903$	7.15450e98	0.690303
$904$	−6.08194e96	−0.00565457
$905$	2.85096e99	2.55425
$906$	−2.28789e99	−1.97533
$907$	2.18119e98	0.181488	0.0907442	−	0.995874i	$-0.471075\pi$
$907$	2.18119e98	0.181488	0.0907442	+	0.995874i	$0.471075\pi$
$908$	−9.94571e98	−0.797553
$909$	−2.96442e97	−0.0229113
$910$	−3.50467e99	−2.61072
$911$	−1.64375e99	−1.18024	−0.590120	−	0.807316i	$-0.700920\pi$
$911$	−1.64375e99	−1.18024	−0.590120	+	0.807316i	$0.700920\pi$
$912$	1.22628e99	0.848713
$913$	−2.55164e98	−0.170235
$914$	−2.94888e98	−0.189653
$915$	−2.72512e99	−1.68958
$916$	2.26578e99	1.35431
$917$	1.54689e99	0.891431
$918$	1.79601e98	0.0997881
$919$	1.01573e99	0.544136	0.272068	−	0.962278i	$-0.412292\pi$
$919$	1.01573e99	0.544136	0.272068	+	0.962278i	$0.412292\pi$
$920$	6.60879e96	0.00341373
$921$	1.10185e99	0.548814
$922$	4.90675e99	2.35672
$923$	2.34001e99	1.08383
$924$	−1.56055e99	−0.697055
$925$	−7.72276e99	−3.32678
$926$	−2.90017e99	−1.20491
$927$	−6.70497e97	−0.0268674
$928$	−4.07422e99	−1.57466
$929$	2.75267e99	1.02619	0.513095	−	0.858332i	$-0.328499\pi$
$929$	2.75267e99	1.02619	0.513095	+	0.858332i	$0.328499\pi$
$930$	8.24758e99	2.96584
$931$	−4.98246e98	−0.172834
$932$	−5.71138e98	−0.191121
$933$	−2.70270e99	−0.872493
$934$	8.51888e99	2.65315
$935$	−3.86924e98	−0.116262
$936$	−9.85522e96	−0.00285710
$937$	−2.08417e99	−0.582984	−0.291492	−	0.956573i	$-0.594152\pi$
$937$	−2.08417e99	−0.582984	−0.291492	+	0.956573i	$0.594152\pi$
$938$	1.08670e99	0.293303
$939$	−5.99669e99	−1.56176
$940$	−5.94797e98	−0.149481
$941$	2.96805e99	0.719812	0.359906	−	0.932989i	$-0.382809\pi$
$941$	2.96805e99	0.719812	0.359906	+	0.932989i	$0.382809\pi$
$942$	−2.16531e99	−0.506774
$943$	2.55490e98	0.0577075
$944$	−1.14423e99	−0.249431
$945$	6.27653e99	1.32055
$946$	3.32727e99	0.675671
$947$	−4.39465e99	−0.861391	−0.430696	−	0.902497i	$-0.641732\pi$
$947$	−4.39465e99	−0.861391	−0.430696	+	0.902497i	$0.641732\pi$
$948$	−8.13746e99	−1.53961
$949$	−3.13427e99	−0.572424
$950$	−1.55650e100	−2.74415
$951$	1.20042e100	2.04309
$952$	4.00721e96	0.000658421 0
$953$	−2.21477e99	−0.351330	−0.175665	−	0.984450i	$-0.556208\pi$
$953$	−2.21477e99	−0.351330	−0.175665	+	0.984450i	$0.556208\pi$
$954$	−3.48703e99	−0.534053
$955$	1.19720e100	1.77033
$956$	4.68210e99	0.668500
$957$	6.37305e99	0.878613
$958$	−1.13593e100	−1.51219
$959$	−1.08316e100	−1.39241
$960$	1.76406e100	2.18991
$961$	−5.31385e98	−0.0637053
$962$	1.74216e100	2.01708
$963$	4.71698e99	0.527453
$964$	−1.69172e100	−1.82704
$965$	5.55422e99	0.579373
$966$	−2.99362e99	−0.301622
$967$	−8.50453e99	−0.827681	−0.413841	−	0.910349i	$-0.635813\pi$
$967$	−8.50453e99	−0.827681	−0.413841	+	0.910349i	$0.635813\pi$
$968$	4.69521e97	0.00441398
$969$	8.33556e98	0.0756987
$970$	3.45160e100	3.02808
$971$	−6.28247e98	−0.0532459	−0.0266229	−	0.999646i	$-0.508475\pi$
$971$	−6.28247e98	−0.0532459	−0.0266229	+	0.999646i	$0.508475\pi$
$972$	7.23539e99	0.592437
$973$	6.72529e99	0.532024
$974$	−3.51671e100	−2.68789
$975$	−4.44504e100	−3.28263
$976$	−1.08755e100	−0.776034
$977$	4.93122e99	0.340006	0.170003	−	0.985444i	$-0.445622\pi$
$977$	4.93122e99	0.340006	0.170003	+	0.985444i	$0.445622\pi$
$978$	−4.75829e99	−0.317029
$979$	−6.82304e98	−0.0439296
$980$	−7.08254e99	−0.440672
$981$	3.99238e99	0.240060
$982$	3.14371e99	0.182687
$983$	3.40156e99	0.191045	0.0955223	−	0.995427i	$-0.469548\pi$
$983$	3.40156e99	0.191045	0.0955223	+	0.995427i	$0.469548\pi$
$984$	−4.83472e97	−0.00262443
$985$	4.89737e100	2.56950
$986$	−2.75287e99	−0.139608
$987$	1.60165e99	0.0785134
$988$	1.76087e100	0.834392
$989$	3.20088e99	0.146620
$990$	−1.27546e100	−0.564793
$991$	2.76108e100	1.18198	0.590992	−	0.806678i	$-0.298737\pi$
$991$	2.76108e100	1.18198	0.590992	+	0.806678i	$0.298737\pi$
$992$	3.31127e100	1.37042
$993$	−2.35481e100	−0.942228
$994$	−3.13643e100	−1.21337
$995$	−2.43857e100	−0.912140
$996$	7.81401e99	0.282609
$997$	−5.66901e100	−1.98253	−0.991263	−	0.131897i	$-0.957893\pi$
$997$	−5.66901e100	−1.98253	−0.991263	+	0.131897i	$0.957893\pi$
$998$	5.13466e100	1.73636
$999$	−3.12005e100	−1.02028

Twists

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

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

\(f(q)\)	\(=\)	\(q-1.72055e10 q^{2} -1.09955e16 q^{3} +1.48456e20 q^{4} +4.93311e23 q^{5} +1.89183e26 q^{6} +1.79351e28 q^{7} -1.51842e28 q^{8} +2.81916e31 q^{9} +O(q^{10})\)	\(q-1.72055e10 q^{2} -1.09955e16 q^{3} +1.48456e20 q^{4} +4.93311e23 q^{5} +1.89183e26 q^{6} +1.79351e28 q^{7} -1.51842e28 q^{8} +2.81916e31 q^{9} -8.48767e33 q^{10} +5.33040e34 q^{11} -1.63235e36 q^{12} +2.30226e37 q^{13} -3.08583e38 q^{14} -5.42420e39 q^{15} -2.16471e40 q^{16} -1.47145e40 q^{17} -4.85052e41 q^{18} +5.15198e42 q^{19} +7.32351e43 q^{20} -1.97206e44 q^{21} -9.17124e44 q^{22} -8.82286e44 q^{23} +1.66958e44 q^{24} +1.75593e47 q^{25} -3.96116e47 q^{26} +7.09406e47 q^{27} +2.66258e48 q^{28} -1.08736e49 q^{29} +9.33262e49 q^{30} +8.83737e49 q^{31} +3.74690e50 q^{32} -5.86105e50 q^{33} +2.53171e50 q^{34} +8.84758e51 q^{35} +4.18523e51 q^{36} -4.39811e52 q^{37} -8.86426e52 q^{38} -2.53145e53 q^{39} -7.49053e51 q^{40} -2.89577e53 q^{41} +3.39303e54 q^{42} -3.62794e54 q^{43} +7.91333e54 q^{44} +1.39072e55 q^{45} +1.51802e55 q^{46} -8.12174e54 q^{47} +2.38020e56 q^{48} -9.67096e55 q^{49} -3.02117e57 q^{50} +1.61793e56 q^{51} +3.41786e57 q^{52} +7.18898e57 q^{53} -1.22057e58 q^{54} +2.62954e58 q^{55} -2.72330e56 q^{56} -5.66486e58 q^{57} +1.87086e59 q^{58} +5.28583e58 q^{59} -8.05257e59 q^{60} +5.02401e59 q^{61} -1.52052e60 q^{62} +5.05620e59 q^{63} -3.25220e60 q^{64} +1.13573e61 q^{65} +1.00842e61 q^{66} -3.52159e60 q^{67} -2.18446e60 q^{68} +9.70118e60 q^{69} -1.52227e62 q^{70} +1.01640e62 q^{71} -4.28067e59 q^{72} -1.36139e62 q^{73} +7.56719e62 q^{74} -1.93073e63 q^{75} +7.64845e62 q^{76} +9.56014e62 q^{77} +4.35550e63 q^{78} +4.98511e63 q^{79} -1.06787e64 q^{80} -1.04139e64 q^{81} +4.98233e63 q^{82} -4.78696e63 q^{83} -2.92764e64 q^{84} -7.25882e63 q^{85} +6.24207e64 q^{86} +1.19560e65 q^{87} -8.09379e62 q^{88} -1.28002e64 q^{89} -2.39281e65 q^{90} +4.12913e65 q^{91} -1.30981e65 q^{92} -9.71713e65 q^{93} +1.39739e65 q^{94} +2.54153e66 q^{95} -4.11990e66 q^{96} -4.06660e66 q^{97} +1.66394e66 q^{98} +1.50273e66 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 5 q + 5554901256 q^{2} + 34\!\cdots\!72 q^{3}+ \cdots + 27\!\cdots\!85 q^{9}+O(q^{10}) \) 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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