LMFDB - Embedded newform 2.66.a.b.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2,66,Mod(1,2)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2, base_ring=CyclotomicField(1))

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

N = Newforms(chi, 66, names="a")

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

chi := DirichletCharacter("2.1");

S:= CuspForms(chi, 66);

N := Newforms(S);

Level:	$ N $	$=$	$ 2 $
Weight:	$ k $	$=$	$ 66 $
Character orbit:	$[\chi]$	$=$	2.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:	$53.5144712945$
Analytic rank:	$0$
Dimension:	$3$
Coefficient field:	$\mathbb{Q}[x]/(x^{3} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - x^{2} - 4862367805520722608042x + 130125819203569060903952569933488 $ x^3 - x^2 - 4862367805520722608042*x + 130125819203569060903952569933488
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{22}\cdot 3^{8}\cdot 5^{3}\cdot 7\cdot 11\cdot 13 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$4.20131e10$ of defining polynomial
Character	$\chi$	$=$	2.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+4.29497e9 q^{2} -2.64736e15 q^{3} +1.84467e19 q^{4} -6.66845e22 q^{5} -1.13703e25 q^{6} +1.54537e27 q^{7} +7.92282e28 q^{8} -3.29254e30 q^{9} +O(q^{10})$	\(q+4.29497e9 q^{2} -2.64736e15 q^{3} +1.84467e19 q^{4} -6.66845e22 q^{5} -1.13703e25 q^{6} +1.54537e27 q^{7} +7.92282e28 q^{8} -3.29254e30 q^{9} -2.86408e32 q^{10} -6.12279e33 q^{11} -4.88352e34 q^{12} -1.65799e35 q^{13} +6.63732e36 q^{14} +1.76538e38 q^{15} +3.40282e38 q^{16} -1.55625e40 q^{17} -1.41414e40 q^{18} -7.97496e40 q^{19} -1.23011e42 q^{20} -4.09115e42 q^{21} -2.62972e43 q^{22} +2.69892e44 q^{23} -2.09745e44 q^{24} +1.73632e45 q^{25} -7.12103e44 q^{26} +3.59871e46 q^{27} +2.85071e46 q^{28} -3.43367e47 q^{29} +7.58224e47 q^{30} +4.83078e48 q^{31} +1.46150e48 q^{32} +1.62092e49 q^{33} -6.68402e49 q^{34} -1.03052e50 q^{35} -6.07367e49 q^{36} -4.98691e49 q^{37} -3.42522e50 q^{38} +4.38930e50 q^{39} -5.28329e51 q^{40} +3.20492e52 q^{41} -1.75714e52 q^{42} +4.40775e52 q^{43} -1.12945e53 q^{44} +2.19562e53 q^{45} +1.15918e54 q^{46} -1.74273e54 q^{47} -9.00850e53 q^{48} -6.15015e54 q^{49} +7.45743e54 q^{50} +4.11994e55 q^{51} -3.05846e54 q^{52} +1.18591e56 q^{53} +1.54564e56 q^{54} +4.08295e56 q^{55} +1.22437e56 q^{56} +2.11126e56 q^{57} -1.47475e57 q^{58} +5.94000e57 q^{59} +3.25655e57 q^{60} +1.70767e58 q^{61} +2.07481e58 q^{62} -5.08820e57 q^{63} +6.27710e57 q^{64} +1.10562e58 q^{65} +6.96180e58 q^{66} +2.38391e59 q^{67} -2.87077e59 q^{68} -7.14502e59 q^{69} -4.42606e59 q^{70} -7.47480e59 q^{71} -2.60862e59 q^{72} -2.25552e60 q^{73} -2.14186e59 q^{74} -4.59666e60 q^{75} -1.47112e60 q^{76} -9.46198e60 q^{77} +1.88519e60 q^{78} -7.12014e60 q^{79} -2.26916e61 q^{80} -6.13542e61 q^{81} +1.37650e62 q^{82} +2.80557e62 q^{83} -7.54684e61 q^{84} +1.03777e63 q^{85} +1.89311e62 q^{86} +9.09015e62 q^{87} -4.85097e62 q^{88} -3.82247e63 q^{89} +9.43010e62 q^{90} -2.56221e62 q^{91} +4.97863e63 q^{92} -1.27888e64 q^{93} -7.48496e63 q^{94} +5.31806e63 q^{95} -3.86912e63 q^{96} -2.41196e64 q^{97} -2.64147e64 q^{98} +2.01595e64 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q + 12884901888 q^{2} + 29\!\cdots\!12 q^{3}+ \cdots + 85\!\cdots\!19 q^{9}+O(q^{10}) $ 3 * q + 12884901888 * q^2 + 2984558598211212 * q^3 + 55340232221128654848 * q^4 + 3918092878575519628050 * q^5 + 12818581572312759640522752 * q^6 + 4292799991821220115501533464 * q^7 + 237684487542793012780631851008 * q^8 + 8506531680020675520627594612519 * q^9	$ 3 q + 12884901888 q^{2} + 29\!\cdots\!12 q^{3}+ \cdots - 11\!\cdots\!32 q^{99}+O(q^{100}) $ 3 * q + 12884901888 * q^2 + 2984558598211212 * q^3 + 55340232221128654848 * q^4 + 3918092878575519628050 * q^5 + 12818581572312759640522752 * q^6 + 4292799991821220115501533464 * q^7 + 237684487542793012780631851008 * q^8 + 8506531680020675520627594612519 * q^9 + 16828080776172355868680834252800 * q^10 - 196390756437727241578921135931484 * q^11 + 55055388634191561739553936183918592 * q^12 + 594291588159789125437621076340076842 * q^13 + 18437435573141207874896428865729593344 * q^14 + 223941641190704507876888119858515088200 * q^15 + 1020847100762815390390123822295304634368 * q^16 - 4543147667338787792770556318133924095946 * q^17 + 36535275368076737964923292255914897178624 * q^18 - 76776862412732416183497479026519297722180 * q^19 + 72276056588106564515257853777772596428800 * q^20 + 26265549620028199801130322543173760738908256 * q^21 - 843491876136739963149757681788894276747264 * q^22 - 246585175089558483596492707518472201143440568 * q^23 + 236461093652422865070549025538001393766367232 * q^24 + 193546046773561655726447442157501687259788125 * q^25 + 2552462935434195116011024210920949410516959232 * q^26 + 104360942861770930686026372969796096727969655160 * q^27 + 79188182808748503812617821365498978591859277824 * q^28 + 531967266741361557870395008315736313563375166810 * q^29 + 961822025126642360531008869043250450941555507200 * q^30 + 6029738539523787679291490893311596271283256878176 * q^31 + 4384504911992708754611054498148849058967797628928 * q^32 + 2499511318103852899572045391368179633250062699664 * q^33 - 19512670652118780922233564618111375740234436182016 * q^34 - 213108430526997938381296997393828498022497121759600 * q^35 + 156917812856243951977707135387804545941392750280704 * q^36 - 1620332873097169620543940609594653833354625777112206 * q^37 - 329754113152177381507182807317346300429650393825280 * q^38 - 8058443520000240583429939491235801869291744868819032 * q^39 + 310423299329763037155946574982683353386702392524800 * q^40 + 36703565948034838377558864834222924936123775941865086 * q^41 + 112809676629486344743608439156862850418939754264395776 * q^42 + 198917478867600910841699694521456326480823486676005892 * q^43 - 3622770022448980965784454393608075694631072137478144 * q^44 - 216645431861240266977838791183480248608297455718819350 * q^45 - 1059075262688087558126288639094331419796211044479664128 * q^46 - 1550246333207342372432412618727579166713397594577369456 * q^47 + 1015592664013549396640628797450384791428965526166044672 * q^48 + 11478891131098122565712354085801141363063646718069629611 * q^49 + 831273941162533628784702886329321427845609852764160000 * q^50 + 57291625837763827945225305750991869614936958866433005016 * q^51 + 10962744831942027583350274961369683759440818354805276672 * q^52 + 388195149550139617029551617840486557495245907961121867682 * q^53 + 448226836571030795939966116098772631235082277392597647360 * q^54 + 895742624805791195861557775792485861196137895636425392600 * q^55 + 340110655393244246564124854911588175773439730088258043904 * q^56 + 1787627119006620995570153951692449536429396987788043658480 * q^57 + 2284782013196656381564957967317735508914297564827494645760 * q^58 + 9942474367718630997051455369033666316253859457002364589620 * q^59 + 4130994142491419196768924286426707496331233310792692531200 * q^60 + 30901057913347435136984168017635112365997774001894406985146 * q^61 + 25897529830685471496604689837855131122717132244132976132096 * q^62 + 138514635870008809143798247361228813659466120862088577199672 * q^63 + 18831305206160042291507368269622999248307066333392103538688 * q^64 + 135257076450309235113689373768740271196683349960342621544700 * q^65 + 10735319367237900935256707351753852219862293485006350188544 * q^66 + 17100824266138937068734192820846019367859612644204005842764 * q^67 - 83806282308469157168381879308291088089874694774757823348736 * q^68 - 2698212859345134110276706952535684126822641673823538886031072 * q^69 - 915293739615344190407093781869490631239425810211611974041600 * q^70 - 2069639192653675666961611875517343804017024313729705648459304 * q^71 + 673956874377416123142046667556464802058411395147118499856384 * q^72 - 1495815738901851328847860331660544347506225395356711624209698 * q^73 - 6959276698586061750400954649175342030699151683015510092414976 * q^74 - 19630994079897599350490393185253943873910057323490546919647500 * q^75 - 1416283131710085324764265346521471853851939190193097938042880 * q^76 - 42888418275967578631586680891050882789238717944468360701613792 * q^77 - 34610751375064155217963549622116647652943710894353552582377472 * q^78 + 6108958390094940959359012430413819561677141119540814251420400 * q^79 + 1333257918537750964014423391473836769119497617178970868940800 * q^80 + 199173830104428424071020062682585715958512675590259821728258923 * q^81 + 157640615393388866300261024777871924174114506678342141614227456 * q^82 + 205502582077300871012959214620783777968329728364540523725320572 * q^83 + 484513871795979359952379751208331756506686143559856395120541696 * q^84 + 1563497203971321203580713284666021364588991577456628214456792900 * q^85 + 854344066339117026044912021022845292527435646422137054043308032 * q^86 + 2751581088715129276210795138032395912793526337910098768398145640 * q^87 - 15559678767347559076570726605750196549932937615885444394778624 * q^88 - 1130441655406023955699836505406122255346035459613687451813849330 * q^89 - 930485044671823356668126364893220803234587086552337279981977600 * q^90 - 13758542132769965346791751406178617412263818701689332035952867504 * q^91 - 4548693617247945110936908742766500507009973420754158766824357888 * q^92 - 16692928740948609788490018454765087545603973049886739588798586496 * q^93 - 6658257301869454276672264167812669654284974473754868755229310976 * q^94 - 8930271988344088631293827502889147672196124499832288756967215000 * q^95 + 4361937277995710759452032949925210861803188041994594131915046912 * q^96 - 74357502639901786600354059238491465614418207375045893147311856346 * q^97 + 49301462002410884986734171741687880113831225020606791430078201856 * q^98 - 116077555785702594445847201289530245195179661533809750801608233132 * 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 $

$2$	4.29497e9	0.707107
$2$	4.29497e9	0.707107
$3$	−2.64736e15	−0.824844	−0.412422	−	0.910993i	$-0.635317\pi$
$3$	−2.64736e15	−0.824844	−0.412422	+	0.910993i	$0.635317\pi$
$4$	1.84467e19	0.500000
$5$	−6.66845e22	−1.28085	−0.640427	−	0.768019i	$-0.721243\pi$
$5$	−6.66845e22	−1.28085	−0.640427	+	0.768019i	$0.721243\pi$
$6$	−1.13703e25	−0.583253
$7$	1.54537e27	0.528867	0.264433	−	0.964404i	$-0.414815\pi$
$7$	1.54537e27	0.528867	0.264433	+	0.964404i	$0.414815\pi$
$8$	7.92282e28	0.353553
$9$	−3.29254e30	−0.319632
$10$	−2.86408e32	−0.905701
$11$	−6.12279e33	−0.874353	−0.437177	−	0.899376i	$-0.644022\pi$
$11$	−6.12279e33	−0.874353	−0.437177	+	0.899376i	$0.644022\pi$
$12$	−4.88352e34	−0.412422
$13$	−1.65799e35	−0.103854	−0.0519271	−	0.998651i	$-0.516536\pi$
$13$	−1.65799e35	−0.103854	−0.0519271	+	0.998651i	$0.516536\pi$
$14$	6.63732e36	0.373965
$15$	1.76538e38	1.05651
$16$	3.40282e38	0.250000
$17$	−1.55625e40	−1.59400	−0.797000	−	0.603980i	$-0.793581\pi$
$17$	−1.55625e40	−1.59400	−0.797000	+	0.603980i	$0.793581\pi$
$18$	−1.41414e40	−0.226014
$19$	−7.97496e40	−0.219906	−0.109953	−	0.993937i	$-0.535070\pi$
$19$	−7.97496e40	−0.219906	−0.109953	+	0.993937i	$0.535070\pi$
$20$	−1.23011e42	−0.640427
$21$	−4.09115e42	−0.436233
$22$	−2.62972e43	−0.618261
$23$	2.69892e44	1.49636	0.748180	−	0.663496i	$-0.230928\pi$
$23$	2.69892e44	1.49636	0.748180	+	0.663496i	$0.230928\pi$
$24$	−2.09745e44	−0.291627
$25$	1.73632e45	0.640588
$26$	−7.12103e44	−0.0734360
$27$	3.59871e46	1.08849
$28$	2.85071e46	0.264433
$29$	−3.43367e47	−1.01818	−0.509089	−	0.860714i	$-0.670017\pi$
$29$	−3.43367e47	−1.01818	−0.509089	+	0.860714i	$0.670017\pi$
$30$	7.58224e47	0.747062
$31$	4.83078e48	1.63969	0.819846	−	0.572584i	$-0.194059\pi$
$31$	4.83078e48	1.63969	0.819846	+	0.572584i	$0.194059\pi$
$32$	1.46150e48	0.176777
$33$	1.62092e49	0.721205
$34$	−6.68402e49	−1.12713
$35$	−1.03052e50	−0.677402
$36$	−6.07367e49	−0.159816
$37$	−4.98691e49	−0.0538612	−0.0269306	−	0.999637i	$-0.508573\pi$
$37$	−4.98691e49	−0.0538612	−0.0269306	+	0.999637i	$0.508573\pi$
$38$	−3.42522e50	−0.155497
$39$	4.38930e50	0.0856635
$40$	−5.28329e51	−0.452850
$41$	3.20492e52	1.23124	0.615618	−	0.788044i	$-0.288906\pi$
$41$	3.20492e52	1.23124	0.615618	+	0.788044i	$0.288906\pi$
$42$	−1.75714e52	−0.308463
$43$	4.40775e52	0.360157	0.180079	−	0.983652i	$-0.442365\pi$
$43$	4.40775e52	0.360157	0.180079	+	0.983652i	$0.442365\pi$
$44$	−1.12945e53	−0.437177
$45$	2.19562e53	0.409402
$46$	1.15918e54	1.05809
$47$	−1.74273e54	−0.790768	−0.395384	−	0.918516i	$-0.629389\pi$
$47$	−1.74273e54	−0.790768	−0.395384	+	0.918516i	$0.629389\pi$
$48$	−9.00850e53	−0.206211
$49$	−6.15015e54	−0.720300
$50$	7.45743e54	0.452964
$51$	4.11994e55	1.31480
$52$	−3.05846e54	−0.0519271
$53$	1.18591e56	1.08414	0.542069	−	0.840334i	$-0.317641\pi$
$53$	1.18591e56	1.08414	0.542069	+	0.840334i	$0.317641\pi$
$54$	1.54564e56	0.769679
$55$	4.08295e56	1.11992
$56$	1.22437e56	0.186983
$57$	2.11126e56	0.181388
$58$	−1.47475e57	−0.719960
$59$	5.94000e57	1.66378	0.831890	−	0.554940i	$-0.187259\pi$
$59$	5.94000e57	1.66378	0.831890	+	0.554940i	$0.187259\pi$
$60$	3.25655e57	0.528253
$61$	1.70767e58	1.61877	0.809383	−	0.587281i	$-0.199802\pi$
$61$	1.70767e58	1.61877	0.809383	+	0.587281i	$0.199802\pi$
$62$	2.07481e58	1.15944
$63$	−5.08820e57	−0.169043
$64$	6.27710e57	0.125000
$65$	1.10562e58	0.133022
$66$	6.96180e58	0.509969
$67$	2.38391e59	1.07117	0.535586	−	0.844480i	$-0.320091\pi$
$67$	2.38391e59	1.07117	0.535586	+	0.844480i	$0.320091\pi$
$68$	−2.87077e59	−0.797000
$69$	−7.14502e59	−1.23426
$70$	−4.42606e59	−0.478995
$71$	−7.47480e59	−0.510156	−0.255078	−	0.966920i	$-0.582101\pi$
$71$	−7.47480e59	−0.510156	−0.255078	+	0.966920i	$0.582101\pi$
$72$	−2.60862e59	−0.113007
$73$	−2.25552e60	−0.624099	−0.312050	−	0.950066i	$-0.601016\pi$
$73$	−2.25552e60	−0.624099	−0.312050	+	0.950066i	$0.601016\pi$
$74$	−2.14186e59	−0.0380856
$75$	−4.59666e60	−0.528386
$76$	−1.47112e60	−0.109953
$77$	−9.46198e60	−0.462416
$78$	1.88519e60	0.0605733
$79$	−7.12014e60	−0.151220	−0.0756098	−	0.997137i	$-0.524090\pi$
$79$	−7.12014e60	−0.151220	−0.0756098	+	0.997137i	$0.524090\pi$
$80$	−2.26916e61	−0.320214
$81$	−6.13542e61	−0.578204
$82$	1.37650e62	0.870616
$83$	2.80557e62	1.19670	0.598348	−	0.801237i	$-0.295824\pi$
$83$	2.80557e62	1.19670	0.598348	+	0.801237i	$0.295824\pi$
$84$	−7.54684e61	−0.218116
$85$	1.03777e63	2.04168
$86$	1.89311e62	0.254669
$87$	9.09015e62	0.839838
$88$	−4.85097e62	−0.309131
$89$	−3.82247e63	−1.68721	−0.843604	−	0.536967i	$-0.819570\pi$
$89$	−3.82247e63	−1.68721	−0.843604	+	0.536967i	$0.819570\pi$
$90$	9.43010e62	0.289491
$91$	−2.56221e62	−0.0549250
$92$	4.97863e63	0.748180
$93$	−1.27888e64	−1.35249
$94$	−7.48496e63	−0.559158
$95$	5.31806e63	0.281667
$96$	−3.86912e63	−0.145813
$97$	−2.41196e64	−0.649066	−0.324533	−	0.945874i	$-0.605207\pi$
$97$	−2.41196e64	−0.649066	−0.324533	+	0.945874i	$0.605207\pi$
$98$	−2.64147e64	−0.509329
$99$	2.01595e64	0.279471
$100$	3.20294e64	0.320294
$101$	−2.17762e65	−1.57593	−0.787966	−	0.615719i	$-0.788866\pi$
$101$	−2.17762e65	−1.57593	−0.787966	+	0.615719i	$0.788866\pi$
$102$	1.76950e65	0.929705
$103$	3.09823e65	1.18551	0.592754	−	0.805384i	$-0.298041\pi$
$103$	3.09823e65	1.18551	0.592754	+	0.805384i	$0.298041\pi$
$104$	−1.31360e64	−0.0367180
$105$	2.72816e65	0.558751
$106$	5.09342e65	0.766601
$107$	−1.14216e66	−1.26693	−0.633466	−	0.773771i	$-0.718368\pi$
$107$	−1.14216e66	−1.26693	−0.633466	+	0.773771i	$0.718368\pi$
$108$	6.63845e65	0.544245
$109$	1.88483e66	1.14528	0.572639	−	0.819808i	$-0.305920\pi$
$109$	1.88483e66	1.14528	0.572639	+	0.819808i	$0.305920\pi$
$110$	1.75361e66	0.791902
$111$	1.32021e65	0.0444271
$112$	5.25862e65	0.132217
$113$	−9.72623e66	−1.83187	−0.915936	−	0.401324i	$-0.868550\pi$
$113$	−9.72623e66	−1.83187	−0.915936	+	0.401324i	$0.868550\pi$
$114$	9.06778e65	0.128261
$115$	−1.79976e67	−1.91662
$116$	−6.33400e66	−0.509089
$117$	5.45901e65	0.0331951
$118$	2.55121e67	1.17647
$119$	−2.40498e67	−0.843014
$120$	1.39868e67	0.373531
$121$	−1.15486e67	−0.235507
$122$	7.33438e67	1.14464
$123$	−8.48457e67	−1.01558
$124$	8.91122e67	0.819846
$125$	6.49632e67	0.460354
$126$	−2.18537e67	−0.119531
$127$	9.77757e67	0.413628	0.206814	−	0.978380i	$-0.433690\pi$
$127$	9.77757e67	0.413628	0.206814	+	0.978380i	$0.433690\pi$
$128$	2.69599e67	0.0883883
$129$	−1.16689e68	−0.297074
$130$	4.74862e67	0.0940608
$131$	5.38570e68	0.831620	0.415810	−	0.909451i	$-0.363498\pi$
$131$	5.38570e68	0.831620	0.415810	+	0.909451i	$0.363498\pi$
$132$	2.99007e68	0.360603
$133$	−1.23243e68	−0.116301
$134$	1.02388e69	0.757434
$135$	−2.39978e69	−1.39420
$136$	−1.23298e69	−0.563564
$137$	−3.19295e69	−1.15020	−0.575100	−	0.818083i	$-0.695037\pi$
$137$	−3.19295e69	−1.15020	−0.575100	+	0.818083i	$0.695037\pi$
$138$	−3.06876e69	−0.872756
$139$	2.26921e69	0.510381	0.255190	−	0.966891i	$-0.417862\pi$
$139$	2.26921e69	0.510381	0.255190	+	0.966891i	$0.417862\pi$
$140$	−1.90098e69	−0.338701
$141$	4.61363e69	0.652261
$142$	−3.21040e69	−0.360735
$143$	1.01515e69	0.0908052
$144$	−1.12039e69	−0.0799079
$145$	2.28972e70	1.30414
$146$	−9.68739e69	−0.441305
$147$	1.62817e70	0.594135
$148$	−9.19923e68	−0.0269306
$149$	6.18237e70	1.45412	0.727062	−	0.686572i	$-0.240885\pi$
$149$	6.18237e70	1.45412	0.727062	+	0.686572i	$0.240885\pi$
$150$	−1.97425e70	−0.373625
$151$	1.59596e70	0.243372	0.121686	−	0.992569i	$-0.461170\pi$
$151$	1.59596e70	0.243372	0.121686	+	0.992569i	$0.461170\pi$
$152$	−6.31841e69	−0.0777484
$153$	5.12401e70	0.509493
$154$	−4.06389e70	−0.326978
$155$	−3.22138e71	−2.10021
$156$	8.09684e69	0.0428318
$157$	1.19213e71	0.512372	0.256186	−	0.966627i	$-0.417534\pi$
$157$	1.19213e71	0.512372	0.256186	+	0.966627i	$0.417534\pi$
$158$	−3.05808e70	−0.106928
$159$	−3.13952e71	−0.894244
$160$	−9.74595e70	−0.226425
$161$	4.17084e71	0.791375
$162$	−2.63514e71	−0.408852
$163$	−9.30929e69	−0.0118255	−0.00591275	−	0.999983i	$-0.501882\pi$
$163$	−9.30929e69	−0.0118255	−0.00591275	+	0.999983i	$0.501882\pi$
$164$	5.91203e71	0.615618
$165$	−1.08090e72	−0.923759
$166$	1.20498e72	0.846191
$167$	−1.16536e71	−0.0673249	−0.0336625	−	0.999433i	$-0.510717\pi$
$167$	−1.16536e71	−0.0673249	−0.0336625	+	0.999433i	$0.510717\pi$
$168$	−3.24134e71	−0.154232
$169$	−2.52121e72	−0.989214
$170$	4.45721e72	1.44369
$171$	2.62579e71	0.0702888
$172$	8.13086e71	0.180079
$173$	8.87455e72	1.62798	0.813988	−	0.580881i	$-0.197292\pi$
$173$	8.87455e72	1.62798	0.813988	+	0.580881i	$0.197292\pi$
$174$	3.90419e72	0.593855
$175$	2.68326e72	0.338786
$176$	−2.08348e72	−0.218588
$177$	−1.57253e73	−1.37236
$178$	−1.64174e73	−1.19304
$179$	−1.60076e73	−0.969621	−0.484811	−	0.874619i	$-0.661111\pi$
$179$	−1.60076e73	−0.969621	−0.484811	+	0.874619i	$0.661111\pi$
$180$	4.05020e72	0.204701
$181$	1.05786e73	0.446556	0.223278	−	0.974755i	$-0.428324\pi$
$181$	1.05786e73	0.446556	0.223278	+	0.974755i	$0.428324\pi$
$182$	−1.10046e72	−0.0388379
$183$	−4.52081e73	−1.33523
$184$	2.13831e73	0.529043
$185$	3.32550e72	0.0689883
$186$	−5.49275e73	−0.956356
$187$	9.52856e73	1.39372
$188$	−3.21477e73	−0.395384
$189$	5.56134e73	0.575667
$190$	2.28409e73	0.199169
$191$	1.66121e74	1.22135	0.610675	−	0.791882i	$-0.290898\pi$
$191$	1.66121e74	1.22135	0.610675	+	0.791882i	$0.290898\pi$
$192$	−1.66177e73	−0.103106
$193$	1.19341e74	0.625426	0.312713	−	0.949848i	$-0.398762\pi$
$193$	1.19341e74	0.625426	0.312713	+	0.949848i	$0.398762\pi$
$194$	−1.03593e74	−0.458959
$195$	−2.92699e73	−0.109723
$196$	−1.13450e74	−0.360150
$197$	−2.25185e74	−0.605882	−0.302941	−	0.953009i	$-0.597968\pi$
$197$	−2.25185e74	−0.605882	−0.302941	+	0.953009i	$0.597968\pi$
$198$	8.65846e73	0.197616
$199$	8.37447e74	1.62268	0.811339	−	0.584576i	$-0.198739\pi$
$199$	8.37447e74	1.62268	0.811339	+	0.584576i	$0.198739\pi$
$200$	1.37565e74	0.226482
$201$	−6.31108e74	−0.883551
$202$	−9.35280e74	−1.11435
$203$	−5.30629e74	−0.538480
$204$	7.59995e74	0.657401
$205$	−2.13718e75	−1.57704
$206$	1.33068e75	0.838280
$207$	−8.88632e74	−0.478284
$208$	−5.64186e73	−0.0259635
$209$	4.88290e74	0.192275
$210$	1.17174e75	0.395097
$211$	−7.84387e74	−0.226647	−0.113324	−	0.993558i	$-0.536150\pi$
$211$	−7.84387e74	−0.226647	−0.113324	+	0.993558i	$0.536150\pi$
$212$	2.18761e75	0.542069
$213$	1.97885e75	0.420799
$214$	−4.90553e75	−0.895856
$215$	−2.93928e75	−0.461309
$216$	2.85119e75	0.384840
$217$	7.46535e75	0.867179
$218$	8.09528e75	0.809833
$219$	5.97117e75	0.514785
$220$	7.53171e75	0.559960
$221$	2.58025e75	0.165543
$222$	5.67028e74	0.0314147
$223$	−1.39501e76	−0.667835	−0.333917	−	0.942602i	$-0.608371\pi$
$223$	−1.39501e76	−0.667835	−0.333917	+	0.942602i	$0.608371\pi$
$224$	2.25856e75	0.0934913
$225$	−5.71690e75	−0.204752
$226$	−4.17738e76	−1.29533
$227$	−5.42125e76	−1.45633	−0.728163	−	0.685404i	$-0.759626\pi$
$227$	−5.42125e76	−1.45633	−0.728163	+	0.685404i	$0.759626\pi$
$228$	3.89458e75	0.0906940
$229$	3.71253e76	0.749924	0.374962	−	0.927040i	$-0.377656\pi$
$229$	3.71253e76	0.749924	0.374962	+	0.927040i	$0.377656\pi$
$230$	−7.72993e76	−1.35525
$231$	2.50492e76	0.381422
$232$	−2.72043e76	−0.359980
$233$	3.10737e76	0.357541	0.178771	−	0.983891i	$-0.442788\pi$
$233$	3.10737e76	0.357541	0.178771	+	0.983891i	$0.442788\pi$
$234$	2.34463e75	0.0234725
$235$	1.16213e77	1.01286
$236$	1.09574e77	0.831890
$237$	1.88496e76	0.124733
$238$	−1.03293e77	−0.596101
$239$	2.21096e77	1.11339	0.556696	−	0.830716i	$-0.312069\pi$
$239$	2.21096e77	1.11339	0.556696	+	0.830716i	$0.312069\pi$
$240$	6.00727e76	0.264126
$241$	−2.03086e77	−0.780056	−0.390028	−	0.920803i	$-0.627535\pi$
$241$	−2.03086e77	−0.780056	−0.390028	+	0.920803i	$0.627535\pi$
$242$	−4.96007e76	−0.166528
$243$	−2.08279e77	−0.611563
$244$	3.15009e77	0.809383
$245$	4.10120e77	0.922599
$246$	−3.64409e77	−0.718123
$247$	1.32224e76	0.0228381
$248$	3.82734e77	0.579719
$249$	−7.42736e77	−0.987087
$250$	2.79015e77	0.325519
$251$	3.55818e77	0.364613	0.182306	−	0.983242i	$-0.441644\pi$
$251$	3.55818e77	0.364613	0.182306	+	0.983242i	$0.441644\pi$
$252$	−9.38607e76	−0.0845213
$253$	−1.65249e78	−1.30835
$254$	4.19943e77	0.292479
$255$	−2.74736e78	−1.68407
$256$	1.15792e77	0.0625000
$257$	1.47187e78	0.699913	0.349956	−	0.936766i	$-0.386196\pi$
$257$	1.47187e78	0.699913	0.349956	+	0.936766i	$0.386196\pi$
$258$	−5.01175e77	−0.210063
$259$	−7.70663e76	−0.0284854
$260$	2.03952e77	0.0665110
$261$	1.13055e78	0.325442
$262$	2.31314e78	0.588044
$263$	1.82032e78	0.408870	0.204435	−	0.978880i	$-0.434464\pi$
$263$	1.82032e78	0.408870	0.204435	+	0.978880i	$0.434464\pi$
$264$	1.28423e78	0.254985
$265$	−7.90815e78	−1.38862
$266$	−5.29323e77	−0.0822371
$267$	1.01194e79	1.39168
$268$	4.39755e78	0.535586
$269$	1.47383e79	1.59037	0.795186	−	0.606365i	$-0.207373\pi$
$269$	1.47383e79	1.59037	0.795186	+	0.606365i	$0.207373\pi$
$270$	−1.03070e79	−0.985847
$271$	8.90901e78	0.755662	0.377831	−	0.925875i	$-0.376670\pi$
$271$	8.90901e78	0.755662	0.377831	+	0.925875i	$0.376670\pi$
$272$	−5.29563e78	−0.398500
$273$	6.78310e77	0.0453046
$274$	−1.37136e79	−0.813314
$275$	−1.06311e79	−0.560100
$276$	−1.31802e79	−0.617132
$277$	−1.07006e79	−0.445469	−0.222734	−	0.974879i	$-0.571498\pi$
$277$	−1.07006e79	−0.445469	−0.222734	+	0.974879i	$0.571498\pi$
$278$	9.74620e78	0.360894
$279$	−1.59056e79	−0.524098
$280$	−8.16464e78	−0.239498
$281$	5.08380e78	0.132811	0.0664054	−	0.997793i	$-0.478847\pi$
$281$	5.08380e78	0.132811	0.0664054	+	0.997793i	$0.478847\pi$
$282$	1.98154e79	0.461218
$283$	−5.34486e79	−1.10886	−0.554430	−	0.832230i	$-0.687064\pi$
$283$	−5.34486e79	−1.10886	−0.554430	+	0.832230i	$0.687064\pi$
$284$	−1.37886e79	−0.255078
$285$	−1.40788e79	−0.232332
$286$	4.36005e78	0.0642090
$287$	4.95279e79	0.651161
$288$	−4.81206e78	−0.0565034
$289$	1.46871e80	1.54083
$290$	9.83429e79	0.922164
$291$	6.38533e79	0.535378
$292$	−4.16070e79	−0.312050
$293$	9.79243e79	0.657193	0.328597	−	0.944470i	$-0.393424\pi$
$293$	9.79243e79	0.657193	0.328597	+	0.944470i	$0.393424\pi$
$294$	6.99292e79	0.420117
$295$	−3.96106e80	−2.13106
$296$	−3.95104e78	−0.0190428
$297$	−2.20341e80	−0.951725
$298$	2.65531e80	1.02822
$299$	−4.47480e79	−0.155403
$300$	−8.47934e79	−0.264193
$301$	6.81160e79	0.190475
$302$	6.85457e79	0.172090
$303$	5.76494e80	1.29990
$304$	−2.71374e79	−0.0549764
$305$	−1.13875e81	−2.07340
$306$	2.20074e80	0.360266
$307$	5.47778e80	0.806506	0.403253	−	0.915089i	$-0.367880\pi$
$307$	5.47778e80	0.806506	0.403253	+	0.915089i	$0.367880\pi$
$308$	−1.74543e80	−0.231208
$309$	−8.20213e80	−0.977859
$310$	−1.38357e81	−1.48507
$311$	−1.86230e80	−0.180027	−0.0900135	−	0.995941i	$-0.528691\pi$
$311$	−1.86230e80	−0.180027	−0.0900135	+	0.995941i	$0.528691\pi$
$312$	3.47756e79	0.0302866
$313$	9.86701e80	0.774452	0.387226	−	0.921985i	$-0.373433\pi$
$313$	9.86701e80	0.774452	0.387226	+	0.921985i	$0.373433\pi$
$314$	5.12017e80	0.362302
$315$	3.39304e80	0.216519
$316$	−1.31343e80	−0.0756098
$317$	1.84631e81	0.959135	0.479567	−	0.877505i	$-0.340794\pi$
$317$	1.84631e81	0.959135	0.479567	+	0.877505i	$0.340794\pi$
$318$	−1.34841e81	−0.632326
$319$	2.10236e81	0.890246
$320$	−4.18585e80	−0.160107
$321$	3.02370e81	1.04502
$322$	1.79136e81	0.559587
$323$	1.24110e81	0.350530
$324$	−1.13178e81	−0.289102
$325$	−2.87880e80	−0.0665278
$326$	−3.99831e79	−0.00836189
$327$	−4.98982e81	−0.944675
$328$	2.53920e81	0.435308
$329$	−2.69316e81	−0.418211
$330$	−4.64244e81	−0.653196
$331$	−7.07685e81	−0.902465	−0.451232	−	0.892406i	$-0.649015\pi$
$331$	−7.07685e81	−0.902465	−0.451232	+	0.892406i	$0.649015\pi$
$332$	5.17537e81	0.598348
$333$	1.64196e80	0.0172157
$334$	−5.00520e80	−0.0476059
$335$	−1.58970e82	−1.37202
$336$	−1.39215e81	−0.109058
$337$	3.19845e81	0.227493	0.113746	−	0.993510i	$-0.463715\pi$
$337$	3.19845e81	0.227493	0.113746	+	0.993510i	$0.463715\pi$
$338$	−1.08285e82	−0.699480
$339$	2.57488e82	1.51101
$340$	1.91436e82	1.02084
$341$	−2.95779e82	−1.43367
$342$	1.12777e81	0.0497017
$343$	−2.26991e82	−0.909810
$344$	3.49218e81	0.127335
$345$	4.76462e82	1.58091
$346$	3.81159e82	1.15115
$347$	1.11675e82	0.307079	0.153539	−	0.988143i	$-0.450933\pi$
$347$	1.11675e82	0.307079	0.153539	+	0.988143i	$0.450933\pi$
$348$	1.67684e82	0.419919
$349$	−1.43046e82	−0.326325	−0.163163	−	0.986599i	$-0.552170\pi$
$349$	−1.43046e82	−0.326325	−0.163163	+	0.986599i	$0.552170\pi$
$350$	1.15245e82	0.239558
$351$	−5.96664e81	−0.113044
$352$	−8.94846e81	−0.154565
$353$	−1.38312e82	−0.217862	−0.108931	−	0.994049i	$-0.534743\pi$
$353$	−1.38312e82	−0.217862	−0.108931	+	0.994049i	$0.534743\pi$
$354$	−6.75397e82	−0.970405
$355$	4.98453e82	0.653436
$356$	−7.05120e82	−0.843604
$357$	6.36684e82	0.695355
$358$	−6.87520e82	−0.685626
$359$	1.40088e82	0.127595	0.0637974	−	0.997963i	$-0.479679\pi$
$359$	1.40088e82	0.127595	0.0637974	+	0.997963i	$0.479679\pi$
$360$	1.73955e82	0.144745
$361$	−1.25158e83	−0.951641
$362$	4.54348e82	0.315762
$363$	3.05732e82	0.194256
$364$	−4.72645e81	−0.0274625
$365$	1.50408e83	0.799381
$366$	−1.94167e83	−0.944150
$367$	−2.21776e83	−0.986889	−0.493444	−	0.869777i	$-0.664262\pi$
$367$	−2.21776e83	−0.986889	−0.493444	+	0.869777i	$0.664262\pi$
$368$	9.18396e82	0.374090
$369$	−1.05523e83	−0.393542
$370$	1.42829e82	0.0487821
$371$	1.83266e83	0.573364
$372$	−2.35912e83	−0.676246
$373$	2.09267e83	0.549748	0.274874	−	0.961480i	$-0.411364\pi$
$373$	2.09267e83	0.549748	0.274874	+	0.961480i	$0.411364\pi$
$374$	4.09249e83	0.985508
$375$	−1.71981e83	−0.379720
$376$	−1.38073e83	−0.279579
$377$	5.69300e82	0.105742
$378$	2.38858e83	0.407058
$379$	8.47361e83	1.32524	0.662620	−	0.748956i	$-0.269445\pi$
$379$	8.47361e83	1.32524	0.662620	+	0.748956i	$0.269445\pi$
$380$	9.81009e82	0.140834
$381$	−2.58847e83	−0.341179
$382$	7.13484e83	0.863624
$383$	−5.17075e83	−0.574902	−0.287451	−	0.957795i	$-0.592808\pi$
$383$	−5.17075e83	−0.574902	−0.287451	+	0.957795i	$0.592808\pi$
$384$	−7.13727e82	−0.0729066
$385$	6.30967e83	0.592288
$386$	5.12564e83	0.442243
$387$	−1.45127e83	−0.115118
$388$	−4.44928e83	−0.324533
$389$	−1.56077e84	−1.04707	−0.523535	−	0.852004i	$-0.675387\pi$
$389$	−1.56077e84	−1.04707	−0.523535	+	0.852004i	$0.675387\pi$
$390$	−1.25713e83	−0.0775855
$391$	−4.20019e84	−2.38520
$392$	−4.87265e83	−0.254664
$393$	−1.42579e84	−0.685957
$394$	−9.67164e83	−0.428423
$395$	4.74803e83	0.193690
$396$	3.71878e83	0.139735
$397$	3.61989e84	1.25315	0.626576	−	0.779360i	$-0.284456\pi$
$397$	3.61989e84	1.25315	0.626576	+	0.779360i	$0.284456\pi$
$398$	3.59681e84	1.14741
$399$	3.26268e83	0.0959301
$400$	5.90838e83	0.160147
$401$	3.93219e84	0.982748	0.491374	−	0.870949i	$-0.336495\pi$
$401$	3.93219e84	0.982748	0.491374	+	0.870949i	$0.336495\pi$
$402$	−2.71059e84	−0.624765
$403$	−8.00941e83	−0.170289
$404$	−4.01700e84	−0.787966
$405$	4.09137e84	0.740595
$406$	−2.27903e84	−0.380763
$407$	3.05338e83	0.0470937
$408$	3.26415e84	0.464853
$409$	7.43836e84	0.978295	0.489148	−	0.872201i	$-0.337308\pi$
$409$	7.43836e84	0.978295	0.489148	+	0.872201i	$0.337308\pi$
$410$	−9.17914e84	−1.11513
$411$	8.45288e84	0.948736
$412$	5.71523e84	0.592754
$413$	9.17950e84	0.879918
$414$	−3.81665e84	−0.338198
$415$	−1.87088e85	−1.53279
$416$	−2.42316e83	−0.0183590
$417$	−6.00742e84	−0.420985
$418$	2.09719e84	0.135959
$419$	−7.89407e84	−0.473527	−0.236764	−	0.971567i	$-0.576087\pi$
$419$	−7.89407e84	−0.473527	−0.236764	+	0.971567i	$0.576087\pi$
$420$	5.03257e84	0.279375
$421$	−1.71906e85	−0.883329	−0.441665	−	0.897180i	$-0.645612\pi$
$421$	−1.71906e85	−0.883329	−0.441665	+	0.897180i	$0.645612\pi$
$422$	−3.36892e84	−0.160264
$423$	5.73801e84	0.252755
$424$	9.39571e84	0.383300
$425$	−2.70214e85	−1.02110
$426$	8.49908e84	0.297550
$427$	2.63898e85	0.856112
$428$	−2.10691e85	−0.633466
$429$	−2.68748e84	−0.0749002
$430$	−1.26241e85	−0.326195
$431$	−3.29777e85	−0.790150	−0.395075	−	0.918649i	$-0.629281\pi$
$431$	−3.29777e85	−0.790150	−0.395075	+	0.918649i	$0.629281\pi$
$432$	1.22458e85	0.272123
$433$	7.33117e85	1.51118	0.755591	−	0.655044i	$-0.227350\pi$
$433$	7.33117e85	1.51118	0.755591	+	0.655044i	$0.227350\pi$
$434$	3.20634e85	0.613188
$435$	−6.06172e85	−1.07571
$436$	3.47689e85	0.572639
$437$	−2.15238e85	−0.329058
$438$	2.56460e85	0.364008
$439$	3.41001e85	0.449426	0.224713	−	0.974425i	$-0.427856\pi$
$439$	3.41001e85	0.449426	0.224713	+	0.974425i	$0.427856\pi$
$440$	3.23485e85	0.395951
$441$	2.02496e85	0.230231
$442$	1.10821e85	0.117057
$443$	−1.07834e86	−1.05836	−0.529179	−	0.848510i	$-0.677500\pi$
$443$	−1.07834e86	−1.05836	−0.529179	+	0.848510i	$0.677500\pi$
$444$	2.43537e84	0.0222135
$445$	2.54899e86	2.16107
$446$	−5.99152e85	−0.472230
$447$	−1.63669e86	−1.19943
$448$	9.70045e84	0.0661084
$449$	2.64815e86	1.67856	0.839278	−	0.543702i	$-0.182978\pi$
$449$	2.64815e86	1.67856	0.839278	+	0.543702i	$0.182978\pi$
$450$	−2.45539e85	−0.144782
$451$	−1.96230e86	−1.07654
$452$	−1.79417e86	−0.915936
$453$	−4.22507e85	−0.200744
$454$	−2.32841e86	−1.02978
$455$	1.70860e85	0.0703510
$456$	1.67271e85	0.0641303
$457$	−1.70742e86	−0.609626	−0.304813	−	0.952412i	$-0.598594\pi$
$457$	−1.70742e86	−0.609626	−0.304813	+	0.952412i	$0.598594\pi$
$458$	1.59452e86	0.530276
$459$	−5.60048e86	−1.73505
$460$	−3.31998e86	−0.958309
$461$	3.04624e86	0.819377	0.409689	−	0.912225i	$-0.365637\pi$
$461$	3.04624e86	0.819377	0.409689	+	0.912225i	$0.365637\pi$
$462$	1.07586e86	0.269706
$463$	6.73656e86	1.57418	0.787092	−	0.616835i	$-0.211585\pi$
$463$	6.73656e86	1.57418	0.787092	+	0.616835i	$0.211585\pi$
$464$	−1.16842e86	−0.254544
$465$	8.52816e86	1.73234
$466$	1.33461e86	0.252820
$467$	−2.87718e86	−0.508356	−0.254178	−	0.967157i	$-0.581805\pi$
$467$	−2.87718e86	−0.508356	−0.254178	+	0.967157i	$0.581805\pi$
$468$	1.00701e85	0.0165975
$469$	3.68403e86	0.566508
$470$	4.99131e86	0.716200
$471$	−3.15600e86	−0.422627
$472$	4.70615e86	0.588235
$473$	−2.69877e86	−0.314904
$474$	8.09582e85	0.0881993
$475$	−1.38471e86	−0.140869
$476$	−4.43640e86	−0.421507
$477$	−3.90464e86	−0.346525
$478$	9.49598e86	0.787287
$479$	−1.35846e87	−1.05231	−0.526155	−	0.850389i	$-0.676367\pi$
$479$	−1.35846e87	−1.05231	−0.526155	+	0.850389i	$0.676367\pi$
$480$	2.58010e86	0.186766
$481$	8.26827e84	0.00559371
$482$	−8.72247e86	−0.551583
$483$	−1.10417e87	−0.652761
$484$	−2.13033e86	−0.117753
$485$	1.60840e87	0.831359
$486$	−8.94550e86	−0.432440
$487$	−1.17478e87	−0.531209	−0.265604	−	0.964082i	$-0.585571\pi$
$487$	−1.17478e87	−0.531209	−0.265604	+	0.964082i	$0.585571\pi$
$488$	1.35296e87	0.572320
$489$	2.46450e85	0.00975419
$490$	1.76145e87	0.652376
$491$	−4.64482e87	−1.60998	−0.804990	−	0.593289i	$-0.797829\pi$
$491$	−4.64482e87	−1.60998	−0.804990	+	0.593289i	$0.797829\pi$
$492$	−1.56513e87	−0.507789
$493$	5.34363e87	1.62297
$494$	5.67899e85	0.0161490
$495$	−1.34433e87	−0.357962
$496$	1.64383e87	0.409923
$497$	−1.15513e87	−0.269805
$498$	−3.19003e87	−0.697976
$499$	−3.53381e87	−0.724396	−0.362198	−	0.932101i	$-0.617974\pi$
$499$	−3.53381e87	−0.724396	−0.362198	+	0.932101i	$0.617974\pi$
$500$	1.19836e87	0.230177
$501$	3.08513e86	0.0555326
$502$	1.52823e87	0.257820
$503$	8.33066e87	1.31741	0.658704	−	0.752402i	$-0.271105\pi$
$503$	8.33066e87	1.31741	0.658704	+	0.752402i	$0.271105\pi$
$504$	−4.03129e86	−0.0597656
$505$	1.45213e88	2.01854
$506$	−7.09740e87	−0.925141
$507$	6.67454e87	0.815948
$508$	1.80364e87	0.206814
$509$	5.85185e87	0.629456	0.314728	−	0.949182i	$-0.398087\pi$
$509$	5.85185e87	0.629456	0.314728	+	0.949182i	$0.398087\pi$
$510$	−1.17998e88	−1.19082
$511$	−3.48562e87	−0.330066
$512$	4.97323e86	0.0441942
$513$	−2.86996e87	−0.239365
$514$	6.32165e87	0.494913
$515$	−2.06604e88	−1.51846
$516$	−2.15253e87	−0.148537
$517$	1.06704e88	0.691411
$518$	−3.30997e86	−0.0201422
$519$	−2.34941e88	−1.34283
$520$	8.75966e86	0.0470304
$521$	−2.04181e88	−1.02989	−0.514943	−	0.857225i	$-0.672187\pi$
$521$	−2.04181e88	−1.02989	−0.514943	+	0.857225i	$0.672187\pi$
$522$	4.85568e87	0.230122
$523$	3.35982e88	1.49627	0.748136	−	0.663545i	$-0.230949\pi$
$523$	3.35982e88	1.49627	0.748136	+	0.663545i	$0.230949\pi$
$524$	9.93486e87	0.415810
$525$	−7.10354e87	−0.279446
$526$	7.81821e87	0.289115
$527$	−7.51788e88	−2.61367
$528$	5.51571e87	0.180301
$529$	4.03100e88	1.23909
$530$	−3.39652e88	−0.981904
$531$	−1.95577e88	−0.531797
$532$	−2.27343e87	−0.0581504
$533$	−5.31373e87	−0.127869
$534$	4.34627e88	0.984069
$535$	7.61642e88	1.62275
$536$	1.88873e88	0.378717
$537$	4.23778e88	0.799786
$538$	6.33006e88	1.12456
$539$	3.76561e88	0.629796
$540$	−4.42682e88	−0.697099
$541$	−2.41461e88	−0.358044	−0.179022	−	0.983845i	$-0.557293\pi$
$541$	−2.41461e88	−0.358044	−0.179022	+	0.983845i	$0.557293\pi$
$542$	3.82639e88	0.534333
$543$	−2.80054e88	−0.368339
$544$	−2.27446e88	−0.281782
$545$	−1.25689e89	−1.46693
$546$	2.91332e87	0.0320352
$547$	8.02189e88	0.831168	0.415584	−	0.909555i	$-0.363577\pi$
$547$	8.02189e88	0.831168	0.415584	+	0.909555i	$0.363577\pi$
$548$	−5.88995e88	−0.575100
$549$	−5.62257e88	−0.517409
$550$	−4.56603e88	−0.396051
$551$	2.73834e88	0.223903
$552$	−5.66087e88	−0.436378
$553$	−1.10033e88	−0.0799750
$554$	−4.59589e88	−0.314994
$555$	−8.80379e87	−0.0569046
$556$	4.18596e88	0.255190
$557$	−1.21614e88	−0.0699342	−0.0349671	−	0.999388i	$-0.511133\pi$
$557$	−1.21614e88	−0.0699342	−0.0349671	+	0.999388i	$0.511133\pi$
$558$	−6.83139e88	−0.370593
$559$	−7.30802e87	−0.0374038
$560$	−3.50669e88	−0.169350
$561$	−2.52255e89	−1.14960
$562$	2.18348e88	0.0939114
$563$	3.89598e89	1.58159	0.790794	−	0.612082i	$-0.209668\pi$
$563$	3.89598e89	1.58159	0.790794	+	0.612082i	$0.209668\pi$
$564$	8.51064e88	0.326130
$565$	6.48589e89	2.34636
$566$	−2.29560e89	−0.784083
$567$	−9.48149e88	−0.305793
$568$	−5.92214e88	−0.180367
$569$	−4.49304e89	−1.29238	−0.646192	−	0.763175i	$-0.723640\pi$
$569$	−4.49304e89	−1.29238	−0.646192	+	0.763175i	$0.723640\pi$
$570$	−6.04681e88	−0.164283
$571$	2.99057e89	0.767504	0.383752	−	0.923436i	$-0.374632\pi$
$571$	2.99057e89	0.767504	0.383752	+	0.923436i	$0.374632\pi$
$572$	1.87263e88	0.0454026
$573$	−4.39782e89	−1.00742
$574$	2.12721e89	0.460440
$575$	4.68619e89	0.958550
$576$	−2.06676e88	−0.0399540
$577$	−8.41119e88	−0.153689	−0.0768446	−	0.997043i	$-0.524485\pi$
$577$	−8.41119e88	−0.153689	−0.0768446	+	0.997043i	$0.524485\pi$
$578$	6.30806e89	1.08953
$579$	−3.15937e89	−0.515879
$580$	4.22380e89	0.652069
$581$	4.33565e89	0.632892
$582$	2.74248e89	0.378570
$583$	−7.26104e89	−0.947919
$584$	−1.78701e89	−0.220652
$585$	−3.64032e88	−0.0425181
$586$	4.20582e89	0.464706
$587$	−9.47291e89	−0.990250	−0.495125	−	0.868822i	$-0.664878\pi$
$587$	−9.47291e89	−0.990250	−0.495125	+	0.868822i	$0.664878\pi$
$588$	3.00344e89	0.297068
$589$	−3.85253e89	−0.360578
$590$	−1.70126e90	−1.50689
$591$	5.96147e89	0.499758
$592$	−1.69696e88	−0.0134653
$593$	−2.20695e90	−1.65774	−0.828868	−	0.559444i	$-0.811015\pi$
$593$	−2.20695e90	−1.65774	−0.828868	+	0.559444i	$0.811015\pi$
$594$	−9.46359e89	−0.672971
$595$	1.60375e90	1.07978
$596$	1.14045e90	0.727062
$597$	−2.21702e90	−1.33846
$598$	−1.92191e89	−0.109887
$599$	3.17481e90	1.71928	0.859638	−	0.510904i	$-0.170689\pi$
$599$	3.17481e90	1.71928	0.859638	+	0.510904i	$0.170689\pi$
$600$	−3.64185e89	−0.186813
$601$	−9.84905e89	−0.478602	−0.239301	−	0.970945i	$-0.576918\pi$
$601$	−9.84905e89	−0.478602	−0.239301	+	0.970945i	$0.576918\pi$
$602$	2.92556e89	0.134686
$603$	−7.84914e89	−0.342381
$604$	2.94402e89	0.121686
$605$	7.70110e89	0.301650
$606$	2.47602e90	0.919167
$607$	5.52518e90	1.94408	0.972039	−	0.234819i	$-0.0754498\pi$
$607$	5.52518e90	1.94408	0.972039	+	0.234819i	$0.0754498\pi$
$608$	−1.16554e89	−0.0388742
$609$	1.40477e90	0.444162
$610$	−4.89090e90	−1.46612
$611$	2.88943e89	0.0821246
$612$	9.45212e89	0.254746
$613$	3.96374e89	0.101307	0.0506535	−	0.998716i	$-0.483870\pi$
$613$	3.96374e89	0.101307	0.0506535	+	0.998716i	$0.483870\pi$
$614$	2.35269e90	0.570286
$615$	5.65789e90	1.30081
$616$	−7.49655e89	−0.163489
$617$	−7.93279e90	−1.64119	−0.820594	−	0.571512i	$-0.806357\pi$
$617$	−7.93279e90	−1.64119	−0.820594	+	0.571512i	$0.806357\pi$
$618$	−3.52279e90	−0.691451
$619$	−1.02366e89	−0.0190638	−0.00953189	−	0.999955i	$-0.503034\pi$
$619$	−1.02366e89	−0.0190638	−0.00953189	+	0.999955i	$0.503034\pi$
$620$	−5.94240e90	−1.05010
$621$	9.71265e90	1.62877
$622$	−7.99853e89	−0.127298
$623$	−5.90713e90	−0.892308
$624$	1.49360e89	0.0214159
$625$	−9.03834e90	−1.23023
$626$	4.23785e90	0.547621
$627$	−1.29268e90	−0.158597
$628$	2.19910e90	0.256186
$629$	7.76086e89	0.0858547
$630$	1.45730e90	0.153102
$631$	−1.48054e91	−1.47729	−0.738647	−	0.674092i	$-0.764535\pi$
$631$	−1.48054e91	−1.47729	−0.738647	+	0.674092i	$0.764535\pi$
$632$	−5.64115e89	−0.0534642
$633$	2.07655e90	0.186949
$634$	7.92986e90	0.678211
$635$	−6.52012e90	−0.529797
$636$	−5.79139e90	−0.447122
$637$	1.01969e90	0.0748061
$638$	9.02958e90	0.629499
$639$	2.46111e90	0.163062
$640$	−1.79781e90	−0.113213
$641$	2.01149e91	1.20401	0.602006	−	0.798491i	$-0.294368\pi$
$641$	2.01149e91	1.20401	0.602006	+	0.798491i	$0.294368\pi$
$642$	1.29867e91	0.738942
$643$	−3.20161e90	−0.173186	−0.0865928	−	0.996244i	$-0.527598\pi$
$643$	−3.20161e90	−0.173186	−0.0865928	+	0.996244i	$0.527598\pi$
$644$	7.69384e90	0.395687
$645$	7.78134e90	0.380508
$646$	5.33048e90	0.247862
$647$	2.08730e91	0.922988	0.461494	−	0.887143i	$-0.347314\pi$
$647$	2.08730e91	0.922988	0.461494	+	0.887143i	$0.347314\pi$
$648$	−4.86098e90	−0.204426
$649$	−3.63693e91	−1.45473
$650$	−1.23644e90	−0.0470422
$651$	−1.97635e91	−0.715288
$652$	−1.71726e89	−0.00591275
$653$	2.78230e91	0.911435	0.455717	−	0.890125i	$-0.349383\pi$
$653$	2.78230e91	0.911435	0.455717	+	0.890125i	$0.349383\pi$
$654$	−2.14311e91	−0.667986
$655$	−3.59143e91	−1.06518
$656$	1.09058e91	0.307809
$657$	7.42640e90	0.199482
$658$	−1.15670e91	−0.295720
$659$	6.98319e91	1.69933	0.849666	−	0.527322i	$-0.176804\pi$
$659$	6.98319e91	1.69933	0.849666	+	0.527322i	$0.176804\pi$
$660$	−1.99391e91	−0.461880
$661$	2.46067e91	0.542633	0.271316	−	0.962490i	$-0.412541\pi$
$661$	2.46067e91	0.542633	0.271316	+	0.962490i	$0.412541\pi$
$662$	−3.03949e91	−0.638139
$663$	−6.83084e90	−0.136548
$664$	2.22280e91	0.423096
$665$	8.21838e90	0.148964
$666$	7.05218e89	0.0121734
$667$	−9.26721e91	−1.52356
$668$	−2.14972e90	−0.0336625
$669$	3.69309e91	0.550860
$670$	−6.82772e91	−0.970162
$671$	−1.04557e92	−1.41537
$672$	−5.97922e90	−0.0771158
$673$	−4.44681e91	−0.546461	−0.273230	−	0.961949i	$-0.588092\pi$
$673$	−4.44681e91	−0.546461	−0.273230	+	0.961949i	$0.588092\pi$
$674$	1.37372e91	0.160862
$675$	6.24851e91	0.697275
$676$	−4.65080e91	−0.494607
$677$	6.73549e91	0.682712	0.341356	−	0.939934i	$-0.389114\pi$
$677$	6.73549e91	0.682712	0.341356	+	0.939934i	$0.389114\pi$
$678$	1.10590e92	1.06844
$679$	−3.72737e91	−0.343270
$680$	8.22210e91	0.721843
$681$	1.43520e92	1.20124
$682$	−1.27036e92	−1.01376
$683$	1.39262e92	1.05965	0.529823	−	0.848108i	$-0.322258\pi$
$683$	1.39262e92	1.05965	0.529823	+	0.848108i	$0.322258\pi$
$684$	4.84373e90	0.0351444
$685$	2.12920e92	1.47324
$686$	−9.74921e91	−0.643333
$687$	−9.82841e91	−0.618570
$688$	1.49988e91	0.0900393
$689$	−1.96622e91	−0.112592
$690$	2.04639e92	1.11787
$691$	−1.63458e92	−0.851860	−0.425930	−	0.904756i	$-0.640053\pi$
$691$	−1.63458e92	−0.851860	−0.425930	+	0.904756i	$0.640053\pi$
$692$	1.63707e92	0.813988
$693$	3.11540e91	0.147803
$694$	4.79642e91	0.217137
$695$	−1.51321e92	−0.653724
$696$	7.20196e91	0.296928
$697$	−4.98764e92	−1.96259
$698$	−6.14380e91	−0.230747
$699$	−8.22633e91	−0.294916
$700$	4.94973e91	0.169393
$701$	−1.85854e92	−0.607205	−0.303603	−	0.952799i	$-0.598189\pi$
$701$	−1.85854e92	−0.607205	−0.303603	+	0.952799i	$0.598189\pi$
$702$	−2.56265e91	−0.0799344
$703$	3.97704e90	0.0118444
$704$	−3.84334e91	−0.109294
$705$	−3.07657e92	−0.835451
$706$	−5.94046e91	−0.154052
$707$	−3.36523e92	−0.833458
$708$	−2.90081e92	−0.686180
$709$	7.92773e92	1.79121	0.895604	−	0.444851i	$-0.146744\pi$
$709$	7.92773e92	1.79121	0.895604	+	0.444851i	$0.146744\pi$
$710$	2.14084e92	0.462049
$711$	2.34434e91	0.0483346
$712$	−3.02847e92	−0.596518
$713$	1.30379e93	2.45357
$714$	2.73454e92	0.491690
$715$	−6.76951e91	−0.116308
$716$	−2.95288e92	−0.484811
$717$	−5.85319e92	−0.918375
$718$	6.01675e91	0.0902231
$719$	−1.85714e92	−0.266169	−0.133084	−	0.991105i	$-0.542488\pi$
$719$	−1.85714e92	−0.266169	−0.133084	+	0.991105i	$0.542488\pi$
$720$	7.47129e91	0.102350
$721$	4.78792e92	0.626976
$722$	−5.37548e92	−0.672912
$723$	5.37641e92	0.643425
$724$	1.95141e92	0.223278
$725$	−5.96194e92	−0.652233
$726$	1.31311e92	0.137360
$727$	1.59787e93	1.59835	0.799175	−	0.601098i	$-0.205270\pi$
$727$	1.59787e93	1.59835	0.799175	+	0.601098i	$0.205270\pi$
$728$	−2.03000e91	−0.0194189
$729$	1.18340e93	1.08265
$730$	6.45999e92	0.565247
$731$	−6.85954e92	−0.574090
$732$	−8.33943e92	−0.667615
$733$	−6.86013e92	−0.525355	−0.262678	−	0.964884i	$-0.584606\pi$
$733$	−6.86013e92	−0.525355	−0.262678	+	0.964884i	$0.584606\pi$
$734$	−9.52522e92	−0.697836
$735$	−1.08573e93	−0.761001
$736$	3.94448e92	0.264521
$737$	−1.45962e93	−0.936583
$738$	−4.53219e92	−0.278276
$739$	1.45255e93	0.853470	0.426735	−	0.904377i	$-0.359664\pi$
$739$	1.45255e93	0.853470	0.426735	+	0.904377i	$0.359664\pi$
$740$	6.13446e91	0.0344942
$741$	−3.50045e91	−0.0188379
$742$	7.87123e92	0.405430
$743$	1.26412e93	0.623233	0.311617	−	0.950208i	$-0.399130\pi$
$743$	1.26412e93	0.623233	0.311617	+	0.950208i	$0.399130\pi$
$744$	−1.01323e93	−0.478178
$745$	−4.12268e93	−1.86252
$746$	8.98794e92	0.388730
$747$	−9.23747e92	−0.382502
$748$	1.75771e93	0.696859
$749$	−1.76506e93	−0.670038
$750$	−7.38652e92	−0.268503
$751$	3.87525e93	1.34897	0.674484	−	0.738289i	$-0.264366\pi$
$751$	3.87525e93	1.34897	0.674484	+	0.738289i	$0.264366\pi$
$752$	−5.93020e92	−0.197692
$753$	−9.41978e92	−0.300749
$754$	2.44512e92	0.0747708
$755$	−1.06425e93	−0.311724
$756$	1.02589e93	0.287833
$757$	−5.04865e93	−1.35693	−0.678467	−	0.734631i	$-0.737356\pi$
$757$	−5.04865e93	−1.35693	−0.678467	+	0.734631i	$0.737356\pi$
$758$	3.63939e93	0.937086
$759$	4.37474e93	1.07918
$760$	4.21340e92	0.0995844
$761$	2.32191e93	0.525828	0.262914	−	0.964819i	$-0.415316\pi$
$761$	2.32191e93	0.525828	0.262914	+	0.964819i	$0.415316\pi$
$762$	−1.11174e93	−0.241250
$763$	2.91276e93	0.605699
$764$	3.06439e93	0.610675
$765$	−3.41692e93	−0.652586
$766$	−2.22082e93	−0.406517
$767$	−9.84848e92	−0.172790
$768$	−3.06543e92	−0.0515528
$769$	7.49527e93	1.20832	0.604159	−	0.796864i	$-0.293509\pi$
$769$	7.49527e93	1.20832	0.604159	+	0.796864i	$0.293509\pi$
$770$	2.70998e93	0.418811
$771$	−3.89658e93	−0.577319
$772$	2.20145e93	0.312713
$773$	−5.85877e92	−0.0797945	−0.0398973	−	0.999204i	$-0.512703\pi$
$773$	−5.85877e92	−0.0797945	−0.0398973	+	0.999204i	$0.512703\pi$
$774$	−6.23316e92	−0.0814004
$775$	8.38778e93	1.05037
$776$	−1.91095e93	−0.229479
$777$	2.04022e92	0.0234960
$778$	−6.70344e93	−0.740391
$779$	−2.55591e93	−0.270756
$780$	−5.39934e92	−0.0548613
$781$	4.57666e93	0.446056
$782$	−1.80397e94	−1.68659
$783$	−1.23568e94	−1.10828
$784$	−2.09279e93	−0.180075
$785$	−7.94967e93	−0.656274
$786$	−6.12371e93	−0.485045
$787$	1.11409e94	0.846726	0.423363	−	0.905960i	$-0.360850\pi$
$787$	1.11409e94	0.846726	0.423363	+	0.905960i	$0.360850\pi$
$788$	−4.15394e93	−0.302941
$789$	−4.81904e93	−0.337254
$790$	2.03926e93	0.136960
$791$	−1.50306e94	−0.968817
$792$	1.59720e93	0.0988079
$793$	−2.83130e93	−0.168116
$794$	1.55473e94	0.886112
$795$	2.09357e94	1.14540
$796$	1.54482e94	0.811339
$797$	4.32846e93	0.218242	0.109121	−	0.994028i	$-0.465196\pi$
$797$	4.32846e93	0.218242	0.109121	+	0.994028i	$0.465196\pi$
$798$	1.40131e93	0.0678328
$799$	2.71211e94	1.26048
$800$	2.53763e93	0.113241
$801$	1.25856e94	0.539285
$802$	1.68886e94	0.694908
$803$	1.38101e94	0.545683
$804$	−1.16419e94	−0.441775
$805$	−2.78130e94	−1.01364
$806$	−3.44001e93	−0.120412
$807$	−3.90176e94	−1.31181
$808$	−1.72529e94	−0.557176
$809$	2.26406e94	0.702361	0.351180	−	0.936308i	$-0.385780\pi$
$809$	2.26406e94	0.702361	0.351180	+	0.936308i	$0.385780\pi$
$810$	1.75723e94	0.523680
$811$	8.52845e93	0.244170	0.122085	−	0.992520i	$-0.461042\pi$
$811$	8.52845e93	0.244170	0.122085	+	0.992520i	$0.461042\pi$
$812$	−9.78838e93	−0.269240
$813$	−2.35853e94	−0.623303
$814$	1.31142e93	0.0333003
$815$	6.20785e92	0.0151467
$816$	1.40194e94	0.328700
$817$	−3.51516e93	−0.0792006
$818$	3.19475e94	0.691759
$819$	8.43620e92	0.0175558
$820$	−3.94241e94	−0.788518
$821$	−3.16309e94	−0.608077	−0.304038	−	0.952660i	$-0.598335\pi$
$821$	−3.16309e94	−0.608077	−0.304038	+	0.952660i	$0.598335\pi$
$822$	3.63048e94	0.670858
$823$	−6.31437e94	−1.12159	−0.560796	−	0.827954i	$-0.689505\pi$
$823$	−6.31437e94	−1.12159	−0.560796	+	0.827954i	$0.689505\pi$
$824$	2.45467e94	0.419140
$825$	2.81444e94	0.461996
$826$	3.94257e94	0.622196
$827$	−7.47676e94	−1.13445	−0.567223	−	0.823564i	$-0.691982\pi$
$827$	−7.47676e94	−1.13445	−0.567223	+	0.823564i	$0.691982\pi$
$828$	−1.63924e94	−0.239142
$829$	−6.64757e94	−0.932482	−0.466241	−	0.884658i	$-0.654392\pi$
$829$	−6.64757e94	−0.932482	−0.466241	+	0.884658i	$0.654392\pi$
$830$	−8.03538e94	−1.08385
$831$	2.83284e94	0.367442
$832$	−1.04074e93	−0.0129818
$833$	9.57115e94	1.14816
$834$	−2.58017e94	−0.297681
$835$	7.77117e93	0.0862334
$836$	9.00736e93	0.0961376
$837$	1.73846e95	1.78479
$838$	−3.39048e94	−0.334834
$839$	−7.98624e94	−0.758715	−0.379357	−	0.925250i	$-0.623855\pi$
$839$	−7.98624e94	−0.758715	−0.379357	+	0.925250i	$0.623855\pi$
$840$	2.16147e94	0.197548
$841$	4.17214e93	0.0366850
$842$	−7.38330e94	−0.624608
$843$	−1.34587e94	−0.109548
$844$	−1.44694e94	−0.113324
$845$	1.68125e95	1.26704
$846$	2.46446e94	0.178725
$847$	−1.78468e94	−0.124552
$848$	4.03543e94	0.271034
$849$	1.41498e95	0.914637
$850$	−1.16056e95	−0.722025
$851$	−1.34593e94	−0.0805957
$852$	3.65033e94	0.210400
$853$	1.62211e95	0.899987	0.449993	−	0.893032i	$-0.351426\pi$
$853$	1.62211e95	0.899987	0.449993	+	0.893032i	$0.351426\pi$
$854$	1.13343e95	0.605363
$855$	−1.75099e94	−0.0900298
$856$	−9.04910e94	−0.447928
$857$	9.29313e94	0.442879	0.221440	−	0.975174i	$-0.428924\pi$
$857$	9.29313e94	0.442879	0.221440	+	0.975174i	$0.428924\pi$
$858$	−1.15426e94	−0.0529624
$859$	−1.44218e95	−0.637151	−0.318576	−	0.947897i	$-0.603204\pi$
$859$	−1.44218e95	−0.637151	−0.318576	+	0.947897i	$0.603204\pi$
$860$	−5.42202e94	−0.230654
$861$	−1.31118e95	−0.537106
$862$	−1.41638e95	−0.558720
$863$	1.10405e95	0.419411	0.209705	−	0.977765i	$-0.432749\pi$
$863$	1.10405e95	0.419411	0.209705	+	0.977765i	$0.432749\pi$
$864$	5.25952e94	0.192420
$865$	−5.91795e95	−2.08520
$866$	3.14871e95	1.06857
$867$	−3.88820e95	−1.27095
$868$	1.37711e95	0.433590
$869$	4.35951e94	0.132219
$870$	−2.60349e95	−0.760642
$871$	−3.95251e94	−0.111246
$872$	1.49331e95	0.404917
$873$	7.94148e94	0.207462
$874$	−9.24440e94	−0.232679
$875$	1.00392e95	0.243466
$876$	1.10149e95	0.257392
$877$	−9.63427e94	−0.216936	−0.108468	−	0.994100i	$-0.534595\pi$
$877$	−9.63427e94	−0.216936	−0.108468	+	0.994100i	$0.534595\pi$
$878$	1.46459e95	0.317792
$879$	−2.59241e95	−0.542082
$880$	1.38936e95	0.279980
$881$	−2.72686e95	−0.529597	−0.264799	−	0.964304i	$-0.585305\pi$
$881$	−2.72686e95	−0.529597	−0.264799	+	0.964304i	$0.585305\pi$
$882$	8.69715e94	0.162798
$883$	−4.32461e95	−0.780233	−0.390116	−	0.920766i	$-0.627565\pi$
$883$	−4.32461e95	−0.780233	−0.390116	+	0.920766i	$0.627565\pi$
$884$	4.75971e94	0.0827717
$885$	1.04863e96	1.75779
$886$	−4.63142e95	−0.748372
$887$	8.37366e95	1.30436	0.652180	−	0.758064i	$-0.273854\pi$
$887$	8.37366e95	1.30436	0.652180	+	0.758064i	$0.273854\pi$
$888$	1.04598e94	0.0157073
$889$	1.51100e95	0.218754
$890$	1.09478e96	1.52811
$891$	3.75659e95	0.505554
$892$	−2.57334e95	−0.333917
$893$	1.38982e95	0.173894
$894$	−7.02955e95	−0.848122
$895$	1.06746e96	1.24194
$896$	4.16631e94	0.0467457
$897$	1.18464e95	0.128183
$898$	1.13737e96	1.18692
$899$	−1.65873e96	−1.66950
$900$	−1.05458e95	−0.102376
$901$	−1.84556e96	−1.72811
$902$	−8.42803e95	−0.761226
$903$	−1.80328e95	−0.157112
$904$	−7.70591e95	−0.647665
$905$	−7.05430e95	−0.571973
$906$	−1.81465e95	−0.141947
$907$	2.17375e96	1.64049	0.820245	−	0.572012i	$-0.193837\pi$
$907$	2.17375e96	1.64049	0.820245	+	0.572012i	$0.193837\pi$
$908$	−1.00004e96	−0.728163
$909$	7.16990e95	0.503718
$910$	7.33838e94	0.0497457
$911$	−1.50608e96	−0.985148	−0.492574	−	0.870270i	$-0.663944\pi$
$911$	−1.50608e96	−0.985148	−0.492574	+	0.870270i	$0.663944\pi$
$912$	7.18424e94	0.0453470
$913$	−1.71779e96	−1.04633
$914$	−7.33330e95	−0.431070
$915$	3.01468e96	1.71024
$916$	6.84841e95	0.374962
$917$	8.32290e95	0.439816
$918$	−2.40539e96	−1.22687
$919$	2.74310e96	1.35048	0.675239	−	0.737599i	$-0.264040\pi$
$919$	2.74310e96	1.35048	0.675239	+	0.737599i	$0.264040\pi$
$920$	−1.42592e96	−0.677627
$921$	−1.45016e96	−0.665242
$922$	1.30835e96	0.579387
$923$	1.23932e95	0.0529818
$924$	4.62077e95	0.190711
$925$	−8.65887e94	−0.0345028
$926$	2.89333e96	1.11312
$927$	−1.02011e96	−0.378926
$928$	−5.01831e95	−0.179990
$929$	−1.35433e96	−0.469043	−0.234522	−	0.972111i	$-0.575352\pi$
$929$	−1.35433e96	−0.469043	−0.234522	+	0.972111i	$0.575352\pi$
$930$	3.66282e96	1.22495
$931$	4.90472e95	0.158398
$932$	5.73209e95	0.178771
$933$	4.93018e95	0.148494
$934$	−1.23574e96	−0.359462
$935$	−6.35407e96	−1.78515
$936$	4.32508e94	0.0117362
$937$	3.03086e96	0.794382	0.397191	−	0.917736i	$-0.369985\pi$
$937$	3.03086e96	0.794382	0.397191	+	0.917736i	$0.369985\pi$
$938$	1.58228e96	0.400582
$939$	−2.61215e96	−0.638803
$940$	2.14375e96	0.506430
$941$	−2.51931e95	−0.0574936	−0.0287468	−	0.999587i	$-0.509152\pi$
$941$	−2.51931e95	−0.0574936	−0.0287468	+	0.999587i	$0.509152\pi$
$942$	−1.35549e96	−0.298843
$943$	8.64983e96	1.84237
$944$	2.02128e96	0.415945
$945$	−3.70856e96	−0.737345
$946$	−1.15911e96	−0.222671
$947$	9.78174e96	1.81569	0.907845	−	0.419306i	$-0.137726\pi$
$947$	9.78174e96	1.81569	0.907845	+	0.419306i	$0.137726\pi$
$948$	3.47713e95	0.0623663
$949$	3.73964e95	0.0648153
$950$	−5.94727e95	−0.0996094
$951$	−4.88786e96	−0.791137
$952$	−1.90542e96	−0.298050
$953$	−1.15361e97	−1.74398	−0.871989	−	0.489526i	$-0.837170\pi$
$953$	−1.15361e97	−1.74398	−0.871989	+	0.489526i	$0.837170\pi$
$954$	−1.67703e96	−0.245030
$955$	−1.10777e97	−1.56437
$956$	4.07849e96	0.556696
$957$	−5.56571e96	−0.734315
$958$	−5.83455e96	−0.744095
$959$	−4.93429e96	−0.608303
$960$	1.10815e96	0.132063
$961$	1.46567e97	1.68859
$962$	3.55119e94	0.00395535
$963$	3.76060e96	0.404951
$964$	−3.74627e96	−0.390028
$965$	−7.95817e96	−0.801079
$966$	−4.74238e96	−0.461572
$967$	1.60897e97	1.51421	0.757107	−	0.653291i	$-0.226612\pi$
$967$	1.60897e97	1.51421	0.757107	+	0.653291i	$0.226612\pi$
$968$	−9.14971e95	−0.0832642
$969$	−3.28564e96	−0.289132
$970$	6.90804e96	0.587860
$971$	1.33190e97	1.09609	0.548046	−	0.836448i	$-0.315372\pi$
$971$	1.33190e97	1.09609	0.548046	+	0.836448i	$0.315372\pi$
$972$	−3.84206e96	−0.305781
$973$	3.50678e96	0.269924
$974$	−5.04564e96	−0.375621
$975$	7.62123e95	0.0548751
$976$	5.81090e96	0.404692
$977$	4.56057e96	0.307217	0.153609	−	0.988132i	$-0.450910\pi$
$977$	4.56057e96	0.307217	0.153609	+	0.988132i	$0.450910\pi$
$978$	1.05850e95	0.00689726
$979$	2.34041e97	1.47521
$980$	7.56538e96	0.461300
$981$	−6.20588e96	−0.366067
$982$	−1.99493e97	−1.13843
$983$	−1.50638e97	−0.831659	−0.415829	−	0.909443i	$-0.636509\pi$
$983$	−1.50638e97	−0.831659	−0.415829	+	0.909443i	$0.636509\pi$
$984$	−6.72217e96	−0.359061
$985$	1.50164e97	0.776046
$986$	2.29507e97	1.14762
$987$	7.12976e96	0.344959
$988$	2.43911e95	0.0114191
$989$	1.18962e97	0.538924
$990$	−5.77385e96	−0.253117
$991$	−2.30819e97	−0.979215	−0.489608	−	0.871943i	$-0.662860\pi$
$991$	−2.30819e97	−0.979215	−0.489608	+	0.871943i	$0.662860\pi$
$992$	7.06020e96	0.289859
$993$	1.87350e97	0.744393
$994$	−4.96126e96	−0.190781
$995$	−5.58447e97	−2.07841
$996$	−1.37011e97	−0.493544
$997$	−2.08033e96	−0.0725336	−0.0362668	−	0.999342i	$-0.511547\pi$
$997$	−2.08033e96	−0.0725336	−0.0362668	+	0.999342i	$0.511547\pi$
$998$	−1.51776e97	−0.512225
$999$	−1.79465e96	−0.0586274

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2.66.a.b.1.1	✓	3

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

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 2 \)
Weight:	\( k \)	\(=\)	\( 66 \)
Character orbit:	\([\chi]\)	\(=\)	2.a (trivial)

\(f(q)\)	\(=\)	\(q+4.29497e9 q^{2} -2.64736e15 q^{3} +1.84467e19 q^{4} -6.66845e22 q^{5} -1.13703e25 q^{6} +1.54537e27 q^{7} +7.92282e28 q^{8} -3.29254e30 q^{9} +O(q^{10})\)	\(q+4.29497e9 q^{2} -2.64736e15 q^{3} +1.84467e19 q^{4} -6.66845e22 q^{5} -1.13703e25 q^{6} +1.54537e27 q^{7} +7.92282e28 q^{8} -3.29254e30 q^{9} -2.86408e32 q^{10} -6.12279e33 q^{11} -4.88352e34 q^{12} -1.65799e35 q^{13} +6.63732e36 q^{14} +1.76538e38 q^{15} +3.40282e38 q^{16} -1.55625e40 q^{17} -1.41414e40 q^{18} -7.97496e40 q^{19} -1.23011e42 q^{20} -4.09115e42 q^{21} -2.62972e43 q^{22} +2.69892e44 q^{23} -2.09745e44 q^{24} +1.73632e45 q^{25} -7.12103e44 q^{26} +3.59871e46 q^{27} +2.85071e46 q^{28} -3.43367e47 q^{29} +7.58224e47 q^{30} +4.83078e48 q^{31} +1.46150e48 q^{32} +1.62092e49 q^{33} -6.68402e49 q^{34} -1.03052e50 q^{35} -6.07367e49 q^{36} -4.98691e49 q^{37} -3.42522e50 q^{38} +4.38930e50 q^{39} -5.28329e51 q^{40} +3.20492e52 q^{41} -1.75714e52 q^{42} +4.40775e52 q^{43} -1.12945e53 q^{44} +2.19562e53 q^{45} +1.15918e54 q^{46} -1.74273e54 q^{47} -9.00850e53 q^{48} -6.15015e54 q^{49} +7.45743e54 q^{50} +4.11994e55 q^{51} -3.05846e54 q^{52} +1.18591e56 q^{53} +1.54564e56 q^{54} +4.08295e56 q^{55} +1.22437e56 q^{56} +2.11126e56 q^{57} -1.47475e57 q^{58} +5.94000e57 q^{59} +3.25655e57 q^{60} +1.70767e58 q^{61} +2.07481e58 q^{62} -5.08820e57 q^{63} +6.27710e57 q^{64} +1.10562e58 q^{65} +6.96180e58 q^{66} +2.38391e59 q^{67} -2.87077e59 q^{68} -7.14502e59 q^{69} -4.42606e59 q^{70} -7.47480e59 q^{71} -2.60862e59 q^{72} -2.25552e60 q^{73} -2.14186e59 q^{74} -4.59666e60 q^{75} -1.47112e60 q^{76} -9.46198e60 q^{77} +1.88519e60 q^{78} -7.12014e60 q^{79} -2.26916e61 q^{80} -6.13542e61 q^{81} +1.37650e62 q^{82} +2.80557e62 q^{83} -7.54684e61 q^{84} +1.03777e63 q^{85} +1.89311e62 q^{86} +9.09015e62 q^{87} -4.85097e62 q^{88} -3.82247e63 q^{89} +9.43010e62 q^{90} -2.56221e62 q^{91} +4.97863e63 q^{92} -1.27888e64 q^{93} -7.48496e63 q^{94} +5.31806e63 q^{95} -3.86912e63 q^{96} -2.41196e64 q^{97} -2.64147e64 q^{98} +2.01595e64 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q + 12884901888 q^{2} + 29\!\cdots\!12 q^{3}+ \cdots + 85\!\cdots\!19 q^{9}+O(q^{10}) \) 3 * q + 12884901888 * q^2 + 2984558598211212 * q^3 + 55340232221128654848 * q^4 + 3918092878575519628050 * q^5 + 12818581572312759640522752 * q^6 + 4292799991821220115501533464 * q^7 + 237684487542793012780631851008 * q^8 + 8506531680020675520627594612519 * q^9	\( 3 q + 12884901888 q^{2} + 29\!\cdots\!12 q^{3}+ \cdots - 11\!\cdots\!32 q^{99}+O(q^{100}) \) 3 * q + 12884901888 * q^2 + 2984558598211212 * q^3 + 55340232221128654848 * q^4 + 3918092878575519628050 * q^5 + 12818581572312759640522752 * q^6 + 4292799991821220115501533464 * q^7 + 237684487542793012780631851008 * q^8 + 8506531680020675520627594612519 * q^9 + 16828080776172355868680834252800 * q^10 - 196390756437727241578921135931484 * q^11 + 55055388634191561739553936183918592 * q^12 + 594291588159789125437621076340076842 * q^13 + 18437435573141207874896428865729593344 * q^14 + 223941641190704507876888119858515088200 * q^15 + 1020847100762815390390123822295304634368 * q^16 - 4543147667338787792770556318133924095946 * q^17 + 36535275368076737964923292255914897178624 * q^18 - 76776862412732416183497479026519297722180 * q^19 + 72276056588106564515257853777772596428800 * q^20 + 26265549620028199801130322543173760738908256 * q^21 - 843491876136739963149757681788894276747264 * q^22 - 246585175089558483596492707518472201143440568 * q^23 + 236461093652422865070549025538001393766367232 * q^24 + 193546046773561655726447442157501687259788125 * q^25 + 2552462935434195116011024210920949410516959232 * q^26 + 104360942861770930686026372969796096727969655160 * q^27 + 79188182808748503812617821365498978591859277824 * q^28 + 531967266741361557870395008315736313563375166810 * q^29 + 961822025126642360531008869043250450941555507200 * q^30 + 6029738539523787679291490893311596271283256878176 * q^31 + 4384504911992708754611054498148849058967797628928 * q^32 + 2499511318103852899572045391368179633250062699664 * q^33 - 19512670652118780922233564618111375740234436182016 * q^34 - 213108430526997938381296997393828498022497121759600 * q^35 + 156917812856243951977707135387804545941392750280704 * q^36 - 1620332873097169620543940609594653833354625777112206 * q^37 - 329754113152177381507182807317346300429650393825280 * q^38 - 8058443520000240583429939491235801869291744868819032 * q^39 + 310423299329763037155946574982683353386702392524800 * q^40 + 36703565948034838377558864834222924936123775941865086 * q^41 + 112809676629486344743608439156862850418939754264395776 * q^42 + 198917478867600910841699694521456326480823486676005892 * q^43 - 3622770022448980965784454393608075694631072137478144 * q^44 - 216645431861240266977838791183480248608297455718819350 * q^45 - 1059075262688087558126288639094331419796211044479664128 * q^46 - 1550246333207342372432412618727579166713397594577369456 * q^47 + 1015592664013549396640628797450384791428965526166044672 * q^48 + 11478891131098122565712354085801141363063646718069629611 * q^49 + 831273941162533628784702886329321427845609852764160000 * q^50 + 57291625837763827945225305750991869614936958866433005016 * q^51 + 10962744831942027583350274961369683759440818354805276672 * q^52 + 388195149550139617029551617840486557495245907961121867682 * q^53 + 448226836571030795939966116098772631235082277392597647360 * q^54 + 895742624805791195861557775792485861196137895636425392600 * q^55 + 340110655393244246564124854911588175773439730088258043904 * q^56 + 1787627119006620995570153951692449536429396987788043658480 * q^57 + 2284782013196656381564957967317735508914297564827494645760 * q^58 + 9942474367718630997051455369033666316253859457002364589620 * q^59 + 4130994142491419196768924286426707496331233310792692531200 * q^60 + 30901057913347435136984168017635112365997774001894406985146 * q^61 + 25897529830685471496604689837855131122717132244132976132096 * q^62 + 138514635870008809143798247361228813659466120862088577199672 * q^63 + 18831305206160042291507368269622999248307066333392103538688 * q^64 + 135257076450309235113689373768740271196683349960342621544700 * q^65 + 10735319367237900935256707351753852219862293485006350188544 * q^66 + 17100824266138937068734192820846019367859612644204005842764 * q^67 - 83806282308469157168381879308291088089874694774757823348736 * q^68 - 2698212859345134110276706952535684126822641673823538886031072 * q^69 - 915293739615344190407093781869490631239425810211611974041600 * q^70 - 2069639192653675666961611875517343804017024313729705648459304 * q^71 + 673956874377416123142046667556464802058411395147118499856384 * q^72 - 1495815738901851328847860331660544347506225395356711624209698 * q^73 - 6959276698586061750400954649175342030699151683015510092414976 * q^74 - 19630994079897599350490393185253943873910057323490546919647500 * q^75 - 1416283131710085324764265346521471853851939190193097938042880 * q^76 - 42888418275967578631586680891050882789238717944468360701613792 * q^77 - 34610751375064155217963549622116647652943710894353552582377472 * q^78 + 6108958390094940959359012430413819561677141119540814251420400 * q^79 + 1333257918537750964014423391473836769119497617178970868940800 * q^80 + 199173830104428424071020062682585715958512675590259821728258923 * q^81 + 157640615393388866300261024777871924174114506678342141614227456 * q^82 + 205502582077300871012959214620783777968329728364540523725320572 * q^83 + 484513871795979359952379751208331756506686143559856395120541696 * q^84 + 1563497203971321203580713284666021364588991577456628214456792900 * q^85 + 854344066339117026044912021022845292527435646422137054043308032 * q^86 + 2751581088715129276210795138032395912793526337910098768398145640 * q^87 - 15559678767347559076570726605750196549932937615885444394778624 * q^88 - 1130441655406023955699836505406122255346035459613687451813849330 * q^89 - 930485044671823356668126364893220803234587086552337279981977600 * q^90 - 13758542132769965346791751406178617412263818701689332035952867504 * q^91 - 4548693617247945110936908742766500507009973420754158766824357888 * q^92 - 16692928740948609788490018454765087545603973049886739588798586496 * q^93 - 6658257301869454276672264167812669654284974473754868755229310976 * q^94 - 8930271988344088631293827502889147672196124499832288756967215000 * q^95 + 4361937277995710759452032949925210861803188041994594131915046912 * q^96 - 74357502639901786600354059238491465614418207375045893147311856346 * q^97 + 49301462002410884986734171741687880113831225020606791430078201856 * q^98 - 116077555785702594445847201289530245195179661533809750801608233132 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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