LMFDB - Embedded newform 2.66.a.b.1.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [2,66,Mod(1,2)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(2, base_ring=CyclotomicField(1)) chi = DirichletCharacter(H, H._module([])) N = Newforms(chi, 66, names="a")

magma://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:traces = [3] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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			1.3
Root			$3.84791e10$ 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)

$f(q)$	$=$	\(q+4.29497e9 q^{2} +5.69189e15 q^{3} +1.84467e19 q^{4} +8.97760e21 q^{5} +2.44465e25 q^{6} +5.30637e27 q^{7} +7.92282e28 q^{8} +2.20965e31 q^{9} +3.85585e31 q^{10} -2.32174e33 q^{11} +1.04997e35 q^{12} -1.46940e36 q^{13} +2.27907e37 q^{14} +5.10995e37 q^{15} +3.40282e38 q^{16} +2.91263e39 q^{17} +9.49039e40 q^{18} +2.74117e41 q^{19} +1.65607e41 q^{20} +3.02032e43 q^{21} -9.97178e42 q^{22} -3.50267e44 q^{23} +4.50958e44 q^{24} -2.62991e45 q^{25} -6.31103e45 q^{26} +6.71385e46 q^{27} +9.78852e46 q^{28} +3.29469e47 q^{29} +2.19471e47 q^{30} -6.66257e47 q^{31} +1.46150e48 q^{32} -1.32151e49 q^{33} +1.25097e49 q^{34} +4.76384e49 q^{35} +4.07609e50 q^{36} -1.78528e51 q^{37} +1.17732e51 q^{38} -8.36367e51 q^{39} +7.11278e50 q^{40} +1.18784e52 q^{41} +1.29722e53 q^{42} -2.18004e52 q^{43} -4.28285e52 q^{44} +1.98374e53 q^{45} -1.50438e54 q^{46} -1.89566e54 q^{47} +1.93685e54 q^{48} +1.96192e55 q^{49} -1.12954e55 q^{50} +1.65784e55 q^{51} -2.71057e55 q^{52} +8.64760e55 q^{53} +2.88358e56 q^{54} -2.08436e55 q^{55} +4.20414e56 q^{56} +1.56024e57 q^{57} +1.41506e57 q^{58} +8.99708e56 q^{59} +9.42619e56 q^{60} -4.97059e56 q^{61} -2.86155e57 q^{62} +1.17252e59 q^{63} +6.27710e57 q^{64} -1.31917e58 q^{65} -5.67583e58 q^{66} +1.70781e59 q^{67} +5.37286e58 q^{68} -1.99368e60 q^{69} +2.04605e59 q^{70} -8.12672e58 q^{71} +1.75067e60 q^{72} +2.82381e60 q^{73} -7.66773e60 q^{74} -1.49691e61 q^{75} +5.05656e60 q^{76} -1.23200e61 q^{77} -3.59217e61 q^{78} +4.27954e61 q^{79} +3.05492e60 q^{80} +1.54527e62 q^{81} +5.10173e61 q^{82} -2.84429e62 q^{83} +5.57151e62 q^{84} +2.61484e61 q^{85} -9.36321e61 q^{86} +1.87530e63 q^{87} -1.83947e62 q^{88} +1.66021e63 q^{89} +8.52009e62 q^{90} -7.79719e63 q^{91} -6.46128e63 q^{92} -3.79226e63 q^{93} -8.14180e63 q^{94} +2.46091e63 q^{95} +8.31870e63 q^{96} -3.26740e64 q^{97} +8.42638e64 q^{98} -5.13023e64 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q + 12884901888 q^{2} + 29\!\cdots\!12 q^{3} + 55\!\cdots\!48 q^{4} + 39\!\cdots\!50 q^{5} + 12\!\cdots\!52 q^{6} + 42\!\cdots\!64 q^{7} + 23\!\cdots\!08 q^{8} + 85\!\cdots\!19 q^{9} + 16\!\cdots\!00 q^{10}+ \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

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
$3$	5.69189e15	1.77344	0.886718	−	0.462311i	$-0.152980\pi$
$3$	5.69189e15	1.77344	0.886718	+	0.462311i	$0.152980\pi$
$4$	1.84467e19	0.500000
$5$	8.97760e21	0.172439	0.0862194	−	0.996276i	$-0.472521\pi$
$5$	8.97760e21	0.172439	0.0862194	+	0.996276i	$0.472521\pi$
$6$	2.44465e25	1.25401
$7$	5.30637e27	1.81598	0.907990	−	0.418992i	$-0.137617\pi$
$7$	5.30637e27	1.81598	0.907990	+	0.418992i	$0.137617\pi$
$8$	7.92282e28	0.353553
$9$	2.20965e31	2.14508
$10$	3.85585e31	0.121933
$11$	−2.32174e33	−0.331551	−0.165776	−	0.986163i	$-0.553013\pi$
$11$	−2.32174e33	−0.331551	−0.165776	+	0.986163i	$0.553013\pi$
$12$	1.04997e35	0.886718
$13$	−1.46940e36	−0.920411	−0.460205	−	0.887812i	$-0.652224\pi$
$13$	−1.46940e36	−0.920411	−0.460205	+	0.887812i	$0.652224\pi$
$14$	2.27907e37	1.28409
$15$	5.10995e37	0.305809
$16$	3.40282e38	0.250000
$17$	2.91263e39	0.298329	0.149165	−	0.988812i	$-0.452342\pi$
$17$	2.91263e39	0.298329	0.149165	+	0.988812i	$0.452342\pi$
$18$	9.49039e40	1.51680
$19$	2.74117e41	0.755863	0.377932	−	0.925833i	$-0.376635\pi$
$19$	2.74117e41	0.755863	0.377932	+	0.925833i	$0.376635\pi$
$20$	1.65607e41	0.0862194
$21$	3.02032e43	3.22052
$22$	−9.97178e42	−0.234442
$23$	−3.50267e44	−1.94198	−0.970989	−	0.239125i	$-0.923139\pi$
$23$	−3.50267e44	−1.94198	−0.970989	+	0.239125i	$0.923139\pi$
$24$	4.50958e44	0.627004
$25$	−2.62991e45	−0.970265
$26$	−6.31103e45	−0.650829
$27$	6.71385e46	2.03072
$28$	9.78852e46	0.907990
$29$	3.29469e47	0.976967	0.488483	−	0.872573i	$-0.337550\pi$
$29$	3.29469e47	0.976967	0.488483	+	0.872573i	$0.337550\pi$
$30$	2.19471e47	0.216240
$31$	−6.66257e47	−0.226145	−0.113072	−	0.993587i	$-0.536069\pi$
$31$	−6.66257e47	−0.226145	−0.113072	+	0.993587i	$0.536069\pi$
$32$	1.46150e48	0.176777
$33$	−1.32151e49	−0.587985
$34$	1.25097e49	0.210951
$35$	4.76384e49	0.313145
$36$	4.07609e50	1.07254
$37$	−1.78528e51	−1.92820	−0.964098	−	0.265548i	$-0.914447\pi$
$37$	−1.78528e51	−1.92820	−0.964098	+	0.265548i	$0.914447\pi$
$38$	1.17732e51	0.534476
$39$	−8.36367e51	−1.63229
$40$	7.11278e50	0.0609663
$41$	1.18784e52	0.456334	0.228167	−	0.973622i	$-0.426727\pi$
$41$	1.18784e52	0.456334	0.228167	+	0.973622i	$0.426727\pi$
$42$	1.29722e53	2.27725
$43$	−2.18004e52	−0.178131	−0.0890656	−	0.996026i	$-0.528388\pi$
$43$	−2.18004e52	−0.178131	−0.0890656	+	0.996026i	$0.528388\pi$
$44$	−4.28285e52	−0.165776
$45$	1.98374e53	0.369894
$46$	−1.50438e54	−1.37319
$47$	−1.89566e54	−0.860162	−0.430081	−	0.902790i	$-0.641515\pi$
$47$	−1.89566e54	−0.860162	−0.430081	+	0.902790i	$0.641515\pi$
$48$	1.93685e54	0.443359
$49$	1.96192e55	2.29778
$50$	−1.12954e55	−0.686081
$51$	1.65784e55	0.529068
$52$	−2.71057e55	−0.460205
$53$	8.64760e55	0.790551	0.395275	−	0.918563i	$-0.370649\pi$
$53$	8.64760e55	0.790551	0.395275	+	0.918563i	$0.370649\pi$
$54$	2.88358e56	1.43593
$55$	−2.08436e55	−0.0571723
$56$	4.20414e56	0.642046
$57$	1.56024e57	1.34048
$58$	1.41506e57	0.690820
$59$	8.99708e56	0.252006	0.126003	−	0.992030i	$-0.459785\pi$
$59$	8.99708e56	0.252006	0.126003	+	0.992030i	$0.459785\pi$
$60$	9.42619e56	0.152905
$61$	−4.97059e56	−0.0471181	−0.0235591	−	0.999722i	$-0.507500\pi$
$61$	−4.97059e56	−0.0471181	−0.0235591	+	0.999722i	$0.507500\pi$
$62$	−2.86155e57	−0.159908
$63$	1.17252e59	3.89541
$64$	6.27710e57	0.125000
$65$	−1.31917e58	−0.158715
$66$	−5.67583e58	−0.415768
$67$	1.70781e59	0.767376	0.383688	−	0.923463i	$-0.374654\pi$
$67$	1.70781e59	0.767376	0.383688	+	0.923463i	$0.374654\pi$
$68$	5.37286e58	0.149165
$69$	−1.99368e60	−3.44397
$70$	2.04605e59	0.221427
$71$	−8.12672e58	−0.0554650	−0.0277325	−	0.999615i	$-0.508829\pi$
$71$	−8.12672e58	−0.0554650	−0.0277325	+	0.999615i	$0.508829\pi$
$72$	1.75067e60	0.758399
$73$	2.82381e60	0.781345	0.390673	−	0.920530i	$-0.372242\pi$
$73$	2.82381e60	0.781345	0.390673	+	0.920530i	$0.372242\pi$
$74$	−7.66773e60	−1.36344
$75$	−1.49691e61	−1.72070
$76$	5.05656e60	0.377932
$77$	−1.23200e61	−0.602090
$78$	−3.59217e61	−1.15420
$79$	4.27954e61	0.908902	0.454451	−	0.890772i	$-0.349836\pi$
$79$	4.27954e61	0.908902	0.454451	+	0.890772i	$0.349836\pi$
$80$	3.05492e60	0.0431097
$81$	1.54527e62	1.45627
$82$	5.10173e61	0.322677
$83$	−2.84429e62	−1.21321	−0.606604	−	0.795004i	$-0.707469\pi$
$83$	−2.84429e62	−1.21321	−0.606604	+	0.795004i	$0.707469\pi$
$84$	5.57151e62	1.61026
$85$	2.61484e61	0.0514435
$86$	−9.36321e61	−0.125958
$87$	1.87530e63	1.73259
$88$	−1.83947e62	−0.117221
$89$	1.66021e63	0.732802	0.366401	−	0.930457i	$-0.380590\pi$
$89$	1.66021e63	0.732802	0.366401	+	0.930457i	$0.380590\pi$
$90$	8.52009e62	0.261555
$91$	−7.79719e63	−1.67145
$92$	−6.46128e63	−0.970989
$93$	−3.79226e63	−0.401053
$94$	−8.14180e63	−0.608226
$95$	2.46091e63	0.130340
$96$	8.31870e63	0.313502
$97$	−3.26740e64	−0.879267	−0.439634	−	0.898177i	$-0.644892\pi$
$97$	−3.26740e64	−0.879267	−0.439634	+	0.898177i	$0.644892\pi$
$98$	8.42638e64	1.62478
$99$	−5.13023e64	−0.711202
$100$	−4.85132e64	−0.485132
$101$	−1.61191e65	−1.16653	−0.583264	−	0.812283i	$-0.698225\pi$
$101$	−1.61191e65	−1.16653	−0.583264	+	0.812283i	$0.698225\pi$
$102$	7.12036e64	0.374107
$103$	2.11435e65	0.809035	0.404518	−	0.914530i	$-0.367439\pi$
$103$	2.11435e65	0.809035	0.404518	+	0.914530i	$0.367439\pi$
$104$	−1.16418e65	−0.325414
$105$	2.71152e65	0.555343
$106$	3.71411e65	0.559004
$107$	9.86617e65	1.09440	0.547200	−	0.837002i	$-0.315694\pi$
$107$	9.86617e65	1.09440	0.547200	+	0.837002i	$0.315694\pi$
$108$	1.23849e66	1.01536
$109$	2.20993e66	1.34282	0.671409	−	0.741087i	$-0.265689\pi$
$109$	2.20993e66	1.34282	0.671409	+	0.741087i	$0.265689\pi$
$110$	−8.95226e64	−0.0404269
$111$	−1.01616e67	−3.41953
$112$	1.80566e66	0.453995
$113$	−5.21878e66	−0.982922	−0.491461	−	0.870899i	$-0.663537\pi$
$113$	−5.21878e66	−0.982922	−0.491461	+	0.870899i	$0.663537\pi$
$114$	6.70118e66	0.947859
$115$	−3.14455e66	−0.334872
$116$	6.07763e66	0.488483
$117$	−3.24687e67	−1.97435
$118$	3.86422e66	0.178195
$119$	1.54555e67	0.541760
$120$	4.04852e66	0.108120
$121$	−4.36466e67	−0.890074
$122$	−2.13485e66	−0.0333176
$123$	6.76105e67	0.809279
$124$	−1.22903e67	−0.113072
$125$	−4.79441e67	−0.339750
$126$	5.03595e68	2.75447
$127$	−1.52520e67	−0.0645219	−0.0322609	−	0.999479i	$-0.510271\pi$
$127$	−1.52520e67	−0.0645219	−0.0322609	+	0.999479i	$0.510271\pi$
$128$	2.69599e67	0.0883883
$129$	−1.24086e68	−0.315904
$130$	−5.66579e67	−0.112228
$131$	−9.37591e68	−1.44776	−0.723880	−	0.689926i	$-0.757643\pi$
$131$	−9.37591e68	−1.44776	−0.723880	+	0.689926i	$0.757643\pi$
$132$	−2.43775e68	−0.293992
$133$	1.45456e69	1.37263
$134$	7.33498e68	0.542617
$135$	6.02743e68	0.350174
$136$	2.30763e68	0.105475
$137$	−3.37510e69	−1.21582	−0.607908	−	0.794008i	$-0.707991\pi$
$137$	−3.37510e69	−1.21582	−0.607908	+	0.794008i	$0.707991\pi$
$138$	−8.56278e69	−2.43526
$139$	4.30456e69	0.968160	0.484080	−	0.875024i	$-0.339154\pi$
$139$	4.30456e69	0.968160	0.484080	+	0.875024i	$0.339154\pi$
$140$	8.78774e68	0.156573
$141$	−1.07899e70	−1.52544
$142$	−3.49040e68	−0.0392197
$143$	3.41156e69	0.305163
$144$	7.51906e69	0.536269
$145$	2.95784e69	0.168467
$146$	1.21282e70	0.552495
$147$	1.11670e71	4.07497
$148$	−3.29327e70	−0.964098
$149$	−2.48674e70	−0.584894	−0.292447	−	0.956282i	$-0.594469\pi$
$149$	−2.48674e70	−0.584894	−0.292447	+	0.956282i	$0.594469\pi$
$150$	−6.42920e70	−1.21672
$151$	−2.23228e70	−0.340406	−0.170203	−	0.985409i	$-0.554442\pi$
$151$	−2.23228e70	−0.340406	−0.170203	+	0.985409i	$0.554442\pi$
$152$	2.17178e70	0.267238
$153$	6.43591e70	0.639939
$154$	−5.29139e70	−0.425742
$155$	−5.98138e69	−0.0389961
$156$	−1.54283e71	−0.816145
$157$	−1.51090e71	−0.649379	−0.324690	−	0.945821i	$-0.605260\pi$
$157$	−1.51090e71	−0.649379	−0.324690	+	0.945821i	$0.605260\pi$
$158$	1.83805e71	0.642690
$159$	4.92211e71	1.40199
$160$	1.31208e70	0.0304832
$161$	−1.85864e72	−3.52659
$162$	6.63690e71	1.02974
$163$	−5.12887e70	−0.0651515	−0.0325757	−	0.999469i	$-0.510371\pi$
$163$	−5.12887e70	−0.0651515	−0.0325757	+	0.999469i	$0.510371\pi$
$164$	2.19118e71	0.228167
$165$	−1.18639e71	−0.101391
$166$	−1.22161e72	−0.857867
$167$	2.11811e72	1.22367	0.611833	−	0.790987i	$-0.290433\pi$
$167$	2.11811e72	1.22367	0.611833	+	0.790987i	$0.290433\pi$
$168$	2.39295e72	1.13863
$169$	−3.89552e71	−0.152844
$170$	1.12307e71	0.0363761
$171$	6.05703e72	1.62138
$172$	−4.02147e71	−0.0890656
$173$	−5.72260e72	−1.04977	−0.524886	−	0.851173i	$-0.675892\pi$
$173$	−5.72260e72	−1.04977	−0.524886	+	0.851173i	$0.675892\pi$
$174$	8.05436e72	1.22512
$175$	−1.39553e73	−1.76198
$176$	−7.90046e71	−0.0828878
$177$	5.12103e72	0.446917
$178$	7.13053e72	0.518169
$179$	−1.12057e72	−0.0678760	−0.0339380	−	0.999424i	$-0.510805\pi$
$179$	−1.12057e72	−0.0678760	−0.0339380	+	0.999424i	$0.510805\pi$
$180$	3.65935e72	0.184947
$181$	−2.09131e73	−0.882803	−0.441402	−	0.897310i	$-0.645519\pi$
$181$	−2.09131e73	−0.882803	−0.441402	+	0.897310i	$0.645519\pi$
$182$	−3.34887e73	−1.18189
$183$	−2.82920e72	−0.0835610
$184$	−2.77510e73	−0.686593
$185$	−1.60275e73	−0.332496
$186$	−1.62876e73	−0.283587
$187$	−6.76237e72	−0.0989114
$188$	−3.49688e73	−0.430081
$189$	3.56262e74	3.68774
$190$	1.05695e73	0.0921644
$191$	6.14516e72	0.0451803	0.0225901	−	0.999745i	$-0.492809\pi$
$191$	6.14516e72	0.0451803	0.0225901	+	0.999745i	$0.492809\pi$
$192$	3.57286e73	0.221679
$193$	7.80236e73	0.408897	0.204448	−	0.978877i	$-0.434460\pi$
$193$	7.80236e73	0.408897	0.204448	+	0.978877i	$0.434460\pi$
$194$	−1.40334e74	−0.621736
$195$	−7.50857e73	−0.281470
$196$	3.61910e74	1.14889
$197$	−3.22186e74	−0.866871	−0.433435	−	0.901185i	$-0.642699\pi$
$197$	−3.22186e74	−0.866871	−0.433435	+	0.901185i	$0.642699\pi$
$198$	−2.20342e74	−0.502896
$199$	−7.02681e74	−1.36155	−0.680775	−	0.732493i	$-0.738357\pi$
$199$	−7.02681e74	−1.36155	−0.680775	+	0.732493i	$0.738357\pi$
$200$	−2.08363e74	−0.343040
$201$	9.72066e74	1.36089
$202$	−6.92308e74	−0.824860
$203$	1.74828e75	1.77415
$204$	3.05817e74	0.264534
$205$	1.06639e74	0.0786896
$206$	9.08107e74	0.572074
$207$	−7.73968e75	−4.16569
$208$	−5.00012e74	−0.230103
$209$	−6.36427e74	−0.250607
$210$	1.16459e75	0.392687
$211$	3.67552e75	1.06204	0.531018	−	0.847361i	$-0.321810\pi$
$211$	3.67552e75	1.06204	0.531018	+	0.847361i	$0.321810\pi$
$212$	1.59520e75	0.395275
$213$	−4.62564e74	−0.0983636
$214$	4.23749e75	0.773858
$215$	−1.95715e74	−0.0307167
$216$	5.31926e75	0.717967
$217$	−3.53540e75	−0.410674
$218$	9.49157e75	0.949516
$219$	1.60728e76	1.38567
$220$	−3.84497e74	−0.0285861
$221$	−4.27983e75	−0.274585
$222$	−4.36439e76	−2.41797
$223$	2.74243e76	1.31289	0.656443	−	0.754376i	$-0.272060\pi$
$223$	2.74243e76	1.31289	0.656443	+	0.754376i	$0.272060\pi$
$224$	7.75526e75	0.321023
$225$	−5.81118e76	−2.08129
$226$	−2.24145e76	−0.695031
$227$	3.88821e76	1.04450	0.522252	−	0.852792i	$-0.325092\pi$
$227$	3.88821e76	1.04450	0.522252	+	0.852792i	$0.325092\pi$
$228$	2.87814e76	0.670238
$229$	−2.55453e76	−0.516009	−0.258004	−	0.966144i	$-0.583065\pi$
$229$	−2.55453e76	−0.516009	−0.258004	+	0.966144i	$0.583065\pi$
$230$	−1.35058e76	−0.236790
$231$	−7.01240e76	−1.06777
$232$	2.61032e76	0.345410
$233$	4.94054e76	0.568469	0.284234	−	0.958755i	$-0.408261\pi$
$233$	4.94054e76	0.568469	0.284234	+	0.958755i	$0.408261\pi$
$234$	−1.39452e77	−1.39608
$235$	−1.70185e76	−0.148325
$236$	1.65967e76	0.126003
$237$	2.43587e77	1.61188
$238$	6.63808e76	0.383082
$239$	1.99210e77	1.00318	0.501591	−	0.865105i	$-0.332748\pi$
$239$	1.99210e77	1.00318	0.501591	+	0.865105i	$0.332748\pi$
$240$	1.73882e76	0.0764523
$241$	9.09862e75	0.0349479	0.0174740	−	0.999847i	$-0.494438\pi$
$241$	9.09862e75	0.0349479	0.0174740	+	0.999847i	$0.494438\pi$
$242$	−1.87461e77	−0.629377
$243$	1.87955e77	0.551888
$244$	−9.16912e75	−0.0235591
$245$	1.76133e77	0.396227
$246$	2.90385e77	0.572246
$247$	−4.02788e77	−0.695705
$248$	−5.27863e76	−0.0799542
$249$	−1.61894e78	−2.15155
$250$	−2.05918e77	−0.240240
$251$	−1.08437e78	−1.11117	−0.555585	−	0.831460i	$-0.687506\pi$
$251$	−1.08437e78	−1.11117	−0.555585	+	0.831460i	$0.687506\pi$
$252$	2.16292e78	1.94771
$253$	8.13227e77	0.643865
$254$	−6.55070e76	−0.0456238
$255$	1.48834e77	0.0912318
$256$	1.15792e77	0.0625000
$257$	9.52048e77	0.452723	0.226361	−	0.974043i	$-0.427317\pi$
$257$	9.52048e77	0.452723	0.226361	+	0.974043i	$0.427317\pi$
$258$	−5.32943e77	−0.223378
$259$	−9.47337e78	−3.50156
$260$	−2.43344e77	−0.0793573
$261$	7.28013e78	2.09567
$262$	−4.02692e78	−1.02372
$263$	3.36688e78	0.756252	0.378126	−	0.925754i	$-0.376569\pi$
$263$	3.36688e78	0.756252	0.378126	+	0.925754i	$0.376569\pi$
$264$	−1.04701e78	−0.207884
$265$	7.76346e77	0.136322
$266$	6.24730e78	0.970598
$267$	9.44971e78	1.29958
$268$	3.15035e78	0.383688
$269$	6.19433e78	0.668413	0.334207	−	0.942500i	$-0.391532\pi$
$269$	6.19433e78	0.668413	0.334207	+	0.942500i	$0.391532\pi$
$270$	2.58876e78	0.247611
$271$	1.47194e79	1.24850	0.624249	−	0.781226i	$-0.285405\pi$
$271$	1.47194e79	1.24850	0.624249	+	0.781226i	$0.285405\pi$
$272$	9.91117e77	0.0745823
$273$	−4.43807e79	−2.96420
$274$	−1.44959e79	−0.859711
$275$	6.10595e78	0.321693
$276$	−3.67769e79	−1.72199
$277$	7.58919e78	0.315939	0.157969	−	0.987444i	$-0.449505\pi$
$277$	7.58919e78	0.315939	0.157969	+	0.987444i	$0.449505\pi$
$278$	1.84879e79	0.684593
$279$	−1.47220e79	−0.485097
$280$	3.77430e78	0.110714
$281$	−2.23104e78	−0.0582842	−0.0291421	−	0.999575i	$-0.509278\pi$
$281$	−2.23104e78	−0.0582842	−0.0291421	+	0.999575i	$0.509278\pi$
$282$	−4.63422e79	−1.07865
$283$	5.16588e79	1.07173	0.535864	−	0.844304i	$-0.319986\pi$
$283$	5.16588e79	1.07173	0.535864	+	0.844304i	$0.319986\pi$
$284$	−1.49911e78	−0.0277325
$285$	1.40072e79	0.231150
$286$	1.46526e79	0.215783
$287$	6.30311e79	0.828693
$288$	3.22941e79	0.379199
$289$	−8.68357e79	−0.911000
$290$	1.27038e79	0.119124
$291$	−1.85977e80	−1.55932
$292$	5.20902e79	0.390673
$293$	9.09899e79	0.610655	0.305327	−	0.952247i	$-0.401234\pi$
$293$	9.09899e79	0.610655	0.305327	+	0.952247i	$0.401234\pi$
$294$	4.79620e80	2.88144
$295$	8.07721e78	0.0434556
$296$	−1.41445e80	−0.681720
$297$	−1.55878e80	−0.673287
$298$	−1.06805e80	−0.413582
$299$	5.14683e80	1.78742
$300$	−2.76132e80	−0.860351
$301$	−1.15681e80	−0.323483
$302$	−9.58756e79	−0.240704
$303$	−9.17479e80	−2.06876
$304$	9.32770e79	0.188966
$305$	−4.46239e78	−0.00812499
$306$	2.76420e80	0.452505
$307$	−1.71322e80	−0.252242	−0.126121	−	0.992015i	$-0.540253\pi$
$307$	−1.71322e80	−0.252242	−0.126121	+	0.992015i	$0.540253\pi$
$308$	−2.27264e80	−0.301045
$309$	1.20347e81	1.43477
$310$	−2.56898e79	−0.0275744
$311$	−1.47283e81	−1.42377	−0.711884	−	0.702297i	$-0.752158\pi$
$311$	−1.47283e81	−1.42377	−0.711884	+	0.702297i	$0.752158\pi$
$312$	−6.62638e80	−0.577102
$313$	1.01559e81	0.797125	0.398563	−	0.917141i	$-0.369509\pi$
$313$	1.01559e81	0.797125	0.398563	+	0.917141i	$0.369509\pi$
$314$	−6.48929e80	−0.459180
$315$	1.05264e81	0.671720
$316$	7.89436e80	0.454451
$317$	−9.07031e80	−0.471190	−0.235595	−	0.971851i	$-0.575704\pi$
$317$	−9.07031e80	−0.471190	−0.235595	+	0.971851i	$0.575704\pi$
$318$	2.11403e81	0.991357
$319$	−7.64941e80	−0.323915
$320$	5.63533e79	0.0215548
$321$	5.61572e81	1.94085
$322$	−7.98281e81	−2.49368
$323$	7.98401e80	0.225496
$324$	2.85053e81	0.728136
$325$	3.86439e81	0.893042
$326$	−2.20283e80	−0.0460691
$327$	1.25787e82	2.38140
$328$	9.41104e80	0.161338
$329$	−1.00591e82	−1.56204
$330$	−5.09553e80	−0.0716945
$331$	−1.00183e82	−1.27757	−0.638784	−	0.769387i	$-0.720562\pi$
$331$	−1.00183e82	−1.27757	−0.638784	+	0.769387i	$0.720562\pi$
$332$	−5.24678e81	−0.606604
$333$	−3.94486e82	−4.13612
$334$	9.09720e81	0.865262
$335$	1.53320e81	0.132325
$336$	1.02776e82	0.805131
$337$	2.55002e82	1.81373	0.906864	−	0.421424i	$-0.138470\pi$
$337$	2.55002e82	1.81373	0.906864	+	0.421424i	$0.138470\pi$
$338$	−1.67312e81	−0.108077
$339$	−2.97047e82	−1.74315
$340$	4.82354e80	0.0257218
$341$	1.54687e81	0.0749786
$342$	2.60147e82	1.14649
$343$	5.87992e82	2.35675
$344$	−1.72721e81	−0.0629789
$345$	−1.78984e82	−0.593874
$346$	−2.45784e82	−0.742301
$347$	4.89783e82	1.34678	0.673388	−	0.739289i	$-0.264838\pi$
$347$	4.89783e82	1.34678	0.673388	+	0.739289i	$0.264838\pi$
$348$	3.45932e82	0.866294
$349$	−1.82843e82	−0.417110	−0.208555	−	0.978011i	$-0.566876\pi$
$349$	−1.82843e82	−0.417110	−0.208555	+	0.978011i	$0.566876\pi$
$350$	−5.99374e82	−1.24591
$351$	−9.86535e82	−1.86909
$352$	−3.39322e81	−0.0586105
$353$	7.47308e82	1.17712	0.588561	−	0.808452i	$-0.299694\pi$
$353$	7.47308e82	1.17712	0.588561	+	0.808452i	$0.299694\pi$
$354$	2.19947e82	0.316018
$355$	−7.29584e80	−0.00956431
$356$	3.06254e82	0.366401
$357$	8.79709e82	0.960776
$358$	−4.81282e81	−0.0479956
$359$	1.54524e82	0.140743	0.0703714	−	0.997521i	$-0.477582\pi$
$359$	1.54524e82	0.140743	0.0703714	+	0.997521i	$0.477582\pi$
$360$	1.57168e82	0.130777
$361$	−5.63777e82	−0.428671
$362$	−8.98209e82	−0.624236
$363$	−2.48432e83	−1.57849
$364$	−1.43833e83	−0.835724
$365$	2.53511e82	0.134734
$366$	−1.21513e82	−0.0590866
$367$	−8.31838e82	−0.370162	−0.185081	−	0.982723i	$-0.559255\pi$
$367$	−8.31838e82	−0.370162	−0.185081	+	0.982723i	$0.559255\pi$
$368$	−1.19190e83	−0.485494
$369$	2.62471e83	0.978870
$370$	−6.88378e82	−0.235110
$371$	4.58873e83	1.43562
$372$	−6.99548e82	−0.200527
$373$	4.55055e83	1.19544	0.597718	−	0.801706i	$-0.296074\pi$
$373$	4.55055e83	1.19544	0.597718	+	0.801706i	$0.296074\pi$
$374$	−2.90441e82	−0.0699409
$375$	−2.72892e83	−0.602525
$376$	−1.50190e83	−0.304113
$377$	−4.84123e83	−0.899211
$378$	1.53013e84	2.60763
$379$	1.58011e83	0.247123	0.123561	−	0.992337i	$-0.460568\pi$
$379$	1.58011e83	0.247123	0.123561	+	0.992337i	$0.460568\pi$
$380$	4.53957e82	0.0651701
$381$	−8.68129e82	−0.114425
$382$	2.63933e82	0.0319473
$383$	−1.03903e84	−1.15523	−0.577613	−	0.816310i	$-0.696016\pi$
$383$	−1.03903e84	−1.15523	−0.577613	+	0.816310i	$0.696016\pi$
$384$	1.53453e83	0.156751
$385$	−1.10604e83	−0.103824
$386$	3.35109e83	0.289134
$387$	−4.81714e83	−0.382105
$388$	−6.02729e83	−0.439634
$389$	2.14998e84	1.44236	0.721178	−	0.692750i	$-0.243601\pi$
$389$	2.14998e84	1.44236	0.721178	+	0.692750i	$0.243601\pi$
$390$	−3.22490e83	−0.199029
$391$	−1.02020e84	−0.579349
$392$	1.55439e84	0.812389
$393$	−5.33666e84	−2.56751
$394$	−1.38378e84	−0.612970
$395$	3.84200e83	0.156730
$396$	−9.46361e83	−0.355601
$397$	−2.17837e84	−0.754121	−0.377060	−	0.926189i	$-0.623065\pi$
$397$	−2.17837e84	−0.754121	−0.377060	+	0.926189i	$0.623065\pi$
$398$	−3.01799e84	−0.962761
$399$	8.27921e84	2.43428
$400$	−8.94911e83	−0.242566
$401$	9.71673e83	0.242844	0.121422	−	0.992601i	$-0.461255\pi$
$401$	9.71673e83	0.242844	0.121422	+	0.992601i	$0.461255\pi$
$402$	4.17499e84	0.962296
$403$	9.78999e83	0.208146
$404$	−2.97344e84	−0.583264
$405$	1.38729e84	0.251118
$406$	7.50882e84	1.25451
$407$	4.14496e84	0.639296
$408$	1.31347e84	0.187054
$409$	1.14593e85	1.50713	0.753564	−	0.657374i	$-0.228333\pi$
$409$	1.14593e85	1.50713	0.753564	+	0.657374i	$0.228333\pi$
$410$	4.58013e83	0.0556420
$411$	−1.92107e85	−2.15617
$412$	3.90029e84	0.404518
$413$	4.77418e84	0.457638
$414$	−3.32417e85	−2.94559
$415$	−2.55348e84	−0.209204
$416$	−2.14753e84	−0.162707
$417$	2.45010e85	1.71697
$418$	−2.73343e84	−0.177206
$419$	−1.45063e85	−0.870163	−0.435081	−	0.900391i	$-0.643280\pi$
$419$	−1.45063e85	−0.870163	−0.435081	+	0.900391i	$0.643280\pi$
$420$	5.00188e84	0.277672
$421$	1.57997e85	0.811857	0.405929	−	0.913905i	$-0.366948\pi$
$421$	1.57997e85	0.811857	0.405929	+	0.913905i	$0.366948\pi$
$422$	1.57862e85	0.750972
$423$	−4.18875e85	−1.84511
$424$	6.85133e84	0.279502
$425$	−7.65996e84	−0.289458
$426$	−1.98670e84	−0.0695535
$427$	−2.63758e84	−0.0855656
$428$	1.81999e85	0.547200
$429$	1.94182e85	0.541188
$430$	−8.40591e83	−0.0217200
$431$	−4.68317e85	−1.12209	−0.561046	−	0.827784i	$-0.689601\pi$
$431$	−4.68317e85	−1.12209	−0.561046	+	0.827784i	$0.689601\pi$
$432$	2.28461e85	0.507679
$433$	−6.52893e85	−1.34582	−0.672908	−	0.739726i	$-0.734955\pi$
$433$	−6.52893e85	−1.34582	−0.672908	+	0.739726i	$0.734955\pi$
$434$	−1.51844e85	−0.290390
$435$	1.68357e85	0.298765
$436$	4.07660e85	0.671409
$437$	−9.60139e85	−1.46787
$438$	6.90323e85	0.979814
$439$	7.75117e85	1.02158	0.510788	−	0.859707i	$-0.329354\pi$
$439$	7.75117e85	1.02158	0.510788	+	0.859707i	$0.329354\pi$
$440$	−1.65140e84	−0.0202135
$441$	4.33516e86	4.92891
$442$	−1.83817e85	−0.194161
$443$	−9.85191e85	−0.966940	−0.483470	−	0.875361i	$-0.660624\pi$
$443$	−9.85191e85	−0.966940	−0.483470	+	0.875361i	$0.660624\pi$
$444$	−1.87449e86	−1.70977
$445$	1.49047e85	0.126364
$446$	1.17786e86	0.928350
$447$	−1.41543e86	−1.03727
$448$	3.33086e85	0.226997
$449$	−1.36456e86	−0.864939	−0.432469	−	0.901649i	$-0.642358\pi$
$449$	−1.36456e86	−0.864939	−0.432469	+	0.901649i	$0.642358\pi$
$450$	−2.49588e86	−1.47170
$451$	−2.75785e85	−0.151298
$452$	−9.62694e85	−0.491461
$453$	−1.27059e86	−0.603689
$454$	1.66997e86	0.738575
$455$	−7.00000e85	−0.288222
$456$	1.23615e86	0.473930
$457$	−2.23657e85	−0.0798558	−0.0399279	−	0.999203i	$-0.512713\pi$
$457$	−2.23657e85	−0.0798558	−0.0399279	+	0.999203i	$0.512713\pi$
$458$	−1.09716e86	−0.364873
$459$	1.95550e86	0.605822
$460$	−5.80068e85	−0.167436
$461$	3.57063e86	0.960428	0.480214	−	0.877151i	$-0.340559\pi$
$461$	3.57063e86	0.960428	0.480214	+	0.877151i	$0.340559\pi$
$462$	−3.01180e86	−0.755026
$463$	−4.15876e86	−0.971812	−0.485906	−	0.874011i	$-0.661510\pi$
$463$	−4.15876e86	−0.971812	−0.485906	+	0.874011i	$0.661510\pi$
$464$	1.12113e86	0.244242
$465$	−3.40454e85	−0.0691571
$466$	2.12194e86	0.401968
$467$	1.07360e87	1.89689	0.948447	−	0.316937i	$-0.102654\pi$
$467$	1.07360e87	1.89689	0.948447	+	0.316937i	$0.102654\pi$
$468$	−5.98942e86	−0.987175
$469$	9.06226e86	1.39354
$470$	−7.30938e85	−0.104882
$471$	−8.59990e86	−1.15163
$472$	7.12822e85	0.0890976
$473$	5.06148e85	0.0590596
$474$	1.04620e87	1.13977
$475$	−7.20902e86	−0.733388
$476$	2.85104e86	0.270880
$477$	1.91082e87	1.69579
$478$	8.55602e86	0.709357
$479$	−1.75484e87	−1.35936	−0.679679	−	0.733509i	$-0.737881\pi$
$479$	−1.75484e87	−1.35936	−0.679679	+	0.733509i	$0.737881\pi$
$480$	7.46819e85	0.0540599
$481$	2.62330e87	1.77473
$482$	3.90783e85	0.0247119
$483$	−1.05792e88	−6.25418
$484$	−8.05138e86	−0.445037
$485$	−2.93334e86	−0.151620
$486$	8.07263e86	0.390244
$487$	3.32055e87	1.50148	0.750739	−	0.660599i	$-0.229698\pi$
$487$	3.32055e87	1.50148	0.750739	+	0.660599i	$0.229698\pi$
$488$	−3.93811e85	−0.0166588
$489$	−2.91929e86	−0.115542
$490$	7.56487e86	0.280175
$491$	2.59897e87	0.900850	0.450425	−	0.892814i	$-0.351272\pi$
$491$	2.59897e87	0.900850	0.450425	+	0.892814i	$0.351272\pi$
$492$	1.24719e87	0.404639
$493$	9.59623e86	0.291458
$494$	−1.72996e87	−0.491938
$495$	−4.60571e86	−0.122639
$496$	−2.26715e86	−0.0565362
$497$	−4.31233e86	−0.100723
$498$	−6.95327e87	−1.52137
$499$	5.11644e87	1.04882	0.524409	−	0.851466i	$-0.324286\pi$
$499$	5.11644e87	1.04882	0.524409	+	0.851466i	$0.324286\pi$
$500$	−8.84412e86	−0.169875
$501$	1.20560e88	2.17009
$502$	−4.65732e87	−0.785716
$503$	−8.80885e87	−1.39303	−0.696514	−	0.717543i	$-0.745267\pi$
$503$	−8.80885e87	−1.39303	−0.696514	+	0.717543i	$0.745267\pi$
$504$	9.28968e87	1.37724
$505$	−1.44710e87	−0.201155
$506$	3.49278e87	0.455281
$507$	−2.21729e87	−0.271059
$508$	−2.81350e86	−0.0322609
$509$	−8.67295e87	−0.932908	−0.466454	−	0.884546i	$-0.654469\pi$
$509$	−8.67295e87	−0.932908	−0.466454	+	0.884546i	$0.654469\pi$
$510$	6.39237e86	0.0645106
$511$	1.49842e88	1.41891
$512$	4.97323e86	0.0441942
$513$	1.84038e88	1.53495
$514$	4.08901e87	0.320123
$515$	1.89818e87	0.139509
$516$	−2.28897e87	−0.157952
$517$	4.40123e87	0.285188
$518$	−4.06878e88	−2.47598
$519$	−3.25724e88	−1.86170
$520$	−1.04515e87	−0.0561141
$521$	−8.28543e87	−0.417916	−0.208958	−	0.977925i	$-0.567007\pi$
$521$	−8.28543e87	−0.417916	−0.208958	+	0.977925i	$0.567007\pi$
$522$	3.12679e88	1.48186
$523$	−5.89576e86	−0.0262564	−0.0131282	−	0.999914i	$-0.504179\pi$
$523$	−5.89576e86	−0.0262564	−0.0131282	+	0.999914i	$0.504179\pi$
$524$	−1.72955e88	−0.723880
$525$	−7.94318e88	−3.12476
$526$	1.44607e88	0.534751
$527$	−1.94056e87	−0.0674656
$528$	−4.49685e87	−0.146996
$529$	9.01549e88	2.77128
$530$	3.33438e87	0.0963939
$531$	1.98804e88	0.540572
$532$	2.68320e88	0.686316
$533$	−1.74541e88	−0.420015
$534$	4.05862e88	0.918940
$535$	8.85745e87	0.188717
$536$	1.35307e88	0.271308
$537$	−6.37817e87	−0.120374
$538$	2.66044e88	0.472640
$539$	−4.55506e88	−0.761832
$540$	1.11186e88	0.175087
$541$	5.57539e88	0.826731	0.413366	−	0.910565i	$-0.364353\pi$
$541$	5.57539e88	0.826731	0.413366	+	0.910565i	$0.364353\pi$
$542$	6.32193e88	0.882821
$543$	−1.19035e89	−1.56559
$544$	4.25682e87	0.0527376
$545$	1.98399e88	0.231554
$546$	−1.90614e89	−2.09601
$547$	7.07942e88	0.733516	0.366758	−	0.930316i	$-0.380468\pi$
$547$	7.07942e88	0.733516	0.366758	+	0.930316i	$0.380468\pi$
$548$	−6.22595e88	−0.607908
$549$	−1.09833e88	−0.101072
$550$	2.62249e88	0.227471
$551$	9.03130e88	0.738454
$552$	−1.57956e89	−1.21763
$553$	2.27088e89	1.65055
$554$	3.25953e88	0.223402
$555$	−9.12270e88	−0.589660
$556$	7.94050e88	0.484080
$557$	−3.02981e89	−1.74229	−0.871146	−	0.491024i	$-0.836623\pi$
$557$	−3.02981e89	−1.74229	−0.871146	+	0.491024i	$0.836623\pi$
$558$	−6.32303e88	−0.343016
$559$	3.20336e88	0.163954
$560$	1.62105e88	0.0782863
$561$	−3.84906e88	−0.175413
$562$	−9.58222e87	−0.0412132
$563$	−1.71058e89	−0.694419	−0.347209	−	0.937788i	$-0.612871\pi$
$563$	−1.71058e89	−0.694419	−0.347209	+	0.937788i	$0.612871\pi$
$564$	−1.99038e89	−0.762721
$565$	−4.68521e88	−0.169494
$566$	2.21873e89	0.757827
$567$	8.19979e89	2.64456
$568$	−6.43865e87	−0.0196098
$569$	−3.16278e89	−0.909747	−0.454874	−	0.890556i	$-0.650316\pi$
$569$	−3.16278e89	−0.909747	−0.454874	+	0.890556i	$0.650316\pi$
$570$	6.01605e88	0.163448
$571$	5.85264e88	0.150203	0.0751014	−	0.997176i	$-0.476072\pi$
$571$	5.85264e88	0.150203	0.0751014	+	0.997176i	$0.476072\pi$
$572$	6.29323e88	0.152582
$573$	3.49776e88	0.0801244
$574$	2.70717e89	0.585974
$575$	9.21169e89	1.88423
$576$	1.38702e89	0.268134
$577$	−4.96515e89	−0.907232	−0.453616	−	0.891197i	$-0.649866\pi$
$577$	−4.96515e89	−0.907232	−0.453616	+	0.891197i	$0.649866\pi$
$578$	−3.72956e89	−0.644174
$579$	4.44102e89	0.725152
$580$	5.45625e88	0.0842335
$581$	−1.50928e90	−2.20316
$582$	−7.98764e89	−1.10261
$583$	−2.00774e89	−0.262108
$584$	2.23726e89	0.276247
$585$	−2.91491e89	−0.340455
$586$	3.90799e89	0.431798
$587$	1.11789e90	1.16859	0.584293	−	0.811543i	$-0.301372\pi$
$587$	1.11789e90	1.16859	0.584293	+	0.811543i	$0.301372\pi$
$588$	2.05995e90	2.03748
$589$	−1.82632e89	−0.170935
$590$	3.46914e88	0.0307278
$591$	−1.83385e90	−1.53734
$592$	−6.07500e89	−0.482049
$593$	−2.22286e89	−0.166969	−0.0834843	−	0.996509i	$-0.526605\pi$
$593$	−2.22286e89	−0.166969	−0.0834843	+	0.996509i	$0.526605\pi$
$594$	−6.69491e89	−0.476086
$595$	1.38753e89	0.0934204
$596$	−4.58723e89	−0.292447
$597$	−3.99958e90	−2.41462
$598$	2.21055e90	1.26389
$599$	−1.31948e90	−0.714549	−0.357275	−	0.933999i	$-0.616294\pi$
$599$	−1.31948e90	−0.714549	−0.357275	+	0.933999i	$0.616294\pi$
$600$	−1.18598e90	−0.608360
$601$	3.59225e90	1.74561	0.872803	−	0.488072i	$-0.162300\pi$
$601$	3.59225e90	1.74561	0.872803	+	0.488072i	$0.162300\pi$
$602$	−4.96846e89	−0.228737
$603$	3.77367e90	1.64608
$604$	−4.11783e89	−0.170203
$605$	−3.91842e89	−0.153483
$606$	−3.94054e90	−1.46284
$607$	−8.43740e88	−0.0296877	−0.0148438	−	0.999890i	$-0.504725\pi$
$607$	−8.43740e88	−0.0296877	−0.0148438	+	0.999890i	$0.504725\pi$
$608$	4.00622e89	0.133619
$609$	9.95104e90	3.14634
$610$	−1.91658e88	−0.00574524
$611$	2.78549e90	0.791702
$612$	1.18722e90	0.319969
$613$	3.45526e90	0.883111	0.441556	−	0.897234i	$-0.354427\pi$
$613$	3.45526e90	0.883111	0.441556	+	0.897234i	$0.354427\pi$
$614$	−7.35824e89	−0.178362
$615$	6.06980e89	0.139551
$616$	−9.76090e89	−0.212871
$617$	−4.93363e90	−1.02070	−0.510351	−	0.859966i	$-0.670485\pi$
$617$	−4.93363e90	−1.02070	−0.510351	+	0.859966i	$0.670485\pi$
$618$	5.16884e90	1.01454
$619$	−6.19575e90	−1.15385	−0.576923	−	0.816798i	$-0.695747\pi$
$619$	−6.19575e90	−1.15385	−0.576923	+	0.816798i	$0.695747\pi$
$620$	−1.10337e89	−0.0194981
$621$	−2.35164e91	−3.94361
$622$	−6.32575e90	−1.00676
$623$	8.80966e90	1.33075
$624$	−2.84601e90	−0.408072
$625$	6.69796e90	0.911679
$626$	4.36192e90	0.563653
$627$	−3.62247e90	−0.444436
$628$	−2.78713e90	−0.324690
$629$	−5.19987e90	−0.575237
$630$	4.52107e90	0.474978
$631$	−6.36353e89	−0.0634956	−0.0317478	−	0.999496i	$-0.510107\pi$
$631$	−6.36353e89	−0.0634956	−0.0317478	+	0.999496i	$0.510107\pi$
$632$	3.39060e90	0.321345
$633$	2.09206e91	1.88345
$634$	−3.89567e90	−0.333182
$635$	−1.36927e89	−0.0111261
$636$	9.07970e90	0.700995
$637$	−2.88285e91	−2.11490
$638$	−3.28539e90	−0.229042
$639$	−1.79572e90	−0.118977
$640$	2.42035e89	0.0152416
$641$	2.26994e91	1.35871	0.679357	−	0.733808i	$-0.262259\pi$
$641$	2.26994e91	1.35871	0.679357	+	0.733808i	$0.262259\pi$
$642$	2.41193e91	1.37239
$643$	−1.14475e90	−0.0619234	−0.0309617	−	0.999521i	$-0.509857\pi$
$643$	−1.14475e90	−0.0619234	−0.0309617	+	0.999521i	$0.509857\pi$
$644$	−3.42859e91	−1.76330
$645$	−1.11399e90	−0.0544741
$646$	3.42911e90	0.159450
$647$	1.43147e91	0.632983	0.316492	−	0.948595i	$-0.397495\pi$
$647$	1.43147e91	0.632983	0.316492	+	0.948595i	$0.397495\pi$
$648$	1.22429e91	0.514870
$649$	−2.08888e90	−0.0835529
$650$	1.65974e91	0.631476
$651$	−2.01231e91	−0.728304
$652$	−9.46109e89	−0.0325757
$653$	−3.65589e91	−1.19761	−0.598804	−	0.800896i	$-0.704357\pi$
$653$	−3.65589e91	−1.19761	−0.598804	+	0.800896i	$0.704357\pi$
$654$	5.40250e91	1.68391
$655$	−8.41731e90	−0.249650
$656$	4.04201e90	0.114083
$657$	6.23965e91	1.67604
$658$	−4.32034e91	−1.10453
$659$	6.82976e91	1.66199	0.830996	−	0.556278i	$-0.187771\pi$
$659$	6.82976e91	1.66199	0.830996	+	0.556278i	$0.187771\pi$
$660$	−2.18851e90	−0.0506957
$661$	−6.45046e91	−1.42247	−0.711235	−	0.702954i	$-0.751864\pi$
$661$	−6.45046e91	−1.42247	−0.711235	+	0.702954i	$0.751864\pi$
$662$	−4.30282e91	−0.903376
$663$	−2.43603e91	−0.486960
$664$	−2.25348e91	−0.428934
$665$	1.30585e91	0.236695
$666$	−1.69430e92	−2.92468
$667$	−1.15402e92	−1.89725
$668$	3.90722e91	0.611833
$669$	1.56096e92	2.32832
$670$	6.58505e90	0.0935682
$671$	1.15404e90	0.0156221
$672$	4.41421e91	0.569314
$673$	1.08533e92	1.33374	0.666870	−	0.745174i	$-0.267633\pi$
$673$	1.08533e92	1.33374	0.666870	+	0.745174i	$0.267633\pi$
$674$	1.09523e92	1.28250
$675$	−1.76568e92	−1.97033
$676$	−7.18598e90	−0.0764219
$677$	1.17420e92	1.19017	0.595087	−	0.803661i	$-0.297117\pi$
$677$	1.17420e92	1.19017	0.595087	+	0.803661i	$0.297117\pi$
$678$	−1.27581e92	−1.23259
$679$	−1.73380e92	−1.59673
$680$	2.07169e90	0.0181880
$681$	2.21313e92	1.85236
$682$	6.64377e90	0.0530178
$683$	6.85366e91	0.521495	0.260747	−	0.965407i	$-0.416031\pi$
$683$	6.85366e91	0.521495	0.260747	+	0.965407i	$0.416031\pi$
$684$	1.11732e92	0.810692
$685$	−3.03002e91	−0.209654
$686$	2.52541e92	1.66647
$687$	−1.45401e92	−0.915109
$688$	−7.41830e90	−0.0445328
$689$	−1.27068e92	−0.727631
$690$	−7.68732e91	−0.419933
$691$	2.46496e92	1.28462	0.642308	−	0.766447i	$-0.277977\pi$
$691$	2.46496e92	1.28462	0.642308	+	0.766447i	$0.277977\pi$
$692$	−1.05563e92	−0.524886
$693$	−2.72229e92	−1.29153
$694$	2.10360e92	0.952315
$695$	3.86446e91	0.166948
$696$	1.48577e92	0.612562
$697$	3.45974e91	0.136138
$698$	−7.85303e91	−0.294942
$699$	2.81210e92	1.00814
$700$	−2.57429e92	−0.880991
$701$	1.34120e90	0.00438184	0.00219092	−	0.999998i	$-0.499303\pi$
$701$	1.34120e90	0.00438184	0.00219092	+	0.999998i	$0.499303\pi$
$702$	−4.23714e92	−1.32165
$703$	−4.89376e92	−1.45745
$704$	−1.45738e91	−0.0414439
$705$	−9.68673e91	−0.263045
$706$	3.20966e92	0.832352
$707$	−8.55336e92	−2.11839
$708$	9.44664e91	0.223458
$709$	−7.78630e92	−1.75925	−0.879627	−	0.475665i	$-0.842208\pi$
$709$	−7.78630e92	−1.75925	−0.879627	+	0.475665i	$0.842208\pi$
$710$	−3.13354e90	−0.00676299
$711$	9.45630e92	1.94966
$712$	1.31535e92	0.259085
$713$	2.33367e92	0.439168
$714$	3.77832e92	0.679371
$715$	3.06276e91	0.0526220
$716$	−2.06709e91	−0.0339380
$717$	1.13388e93	1.77908
$718$	6.63675e91	0.0995202
$719$	3.66023e92	0.524589	0.262294	−	0.964988i	$-0.415521\pi$
$719$	3.66023e92	0.524589	0.262294	+	0.964988i	$0.415521\pi$
$720$	6.75031e91	0.0924735
$721$	1.12195e93	1.46919
$722$	−2.42141e92	−0.303116
$723$	5.17883e91	0.0619779
$724$	−3.85778e92	−0.441402
$725$	−8.66474e92	−0.947917
$726$	−1.06701e93	−1.11616
$727$	6.64158e92	0.664359	0.332180	−	0.943216i	$-0.392216\pi$
$727$	6.64158e92	0.664359	0.332180	+	0.943216i	$0.392216\pi$
$728$	−6.17757e92	−0.590946
$729$	−5.21974e92	−0.477534
$730$	1.08882e92	0.0952715
$731$	−6.34966e91	−0.0531417
$732$	−5.21896e91	−0.0417805
$733$	−2.54774e92	−0.195108	−0.0975540	−	0.995230i	$-0.531102\pi$
$733$	−2.54774e92	−0.195108	−0.0975540	+	0.995230i	$0.531102\pi$
$734$	−3.57272e92	−0.261744
$735$	1.00253e93	0.702683
$736$	−5.11915e92	−0.343296
$737$	−3.96508e92	−0.254424
$738$	1.12731e93	0.692166
$739$	3.17995e93	1.86843	0.934214	−	0.356713i	$-0.116103\pi$
$739$	3.17995e93	1.86843	0.934214	+	0.356713i	$0.116103\pi$
$740$	−2.95656e92	−0.166248
$741$	−2.29262e93	−1.23379
$742$	1.97085e93	1.01514
$743$	−2.89059e93	−1.42512	−0.712559	−	0.701613i	$-0.752464\pi$
$743$	−2.89059e93	−1.42512	−0.712559	+	0.701613i	$0.752464\pi$
$744$	−3.00454e92	−0.141794
$745$	−2.23250e92	−0.100858
$746$	1.95445e93	0.845302
$747$	−6.28488e93	−2.60242
$748$	−1.24744e92	−0.0494557
$749$	5.23535e93	1.98741
$750$	−1.17206e93	−0.426049
$751$	−1.81741e93	−0.632638	−0.316319	−	0.948653i	$-0.602447\pi$
$751$	−1.81741e93	−0.632638	−0.316319	+	0.948653i	$0.602447\pi$
$752$	−6.45060e92	−0.215041
$753$	−6.17210e93	−1.97059
$754$	−2.07929e93	−0.635838
$755$	−2.00405e92	−0.0586992
$756$	6.57187e93	1.84387
$757$	2.17655e93	0.584997	0.292498	−	0.956266i	$-0.405513\pi$
$757$	2.17655e93	0.584997	0.292498	+	0.956266i	$0.405513\pi$
$758$	6.78652e92	0.174742
$759$	4.62880e93	1.14185
$760$	1.94973e92	0.0460822
$761$	−1.56556e93	−0.354541	−0.177271	−	0.984162i	$-0.556727\pi$
$761$	−1.56556e93	−0.354541	−0.177271	+	0.984162i	$0.556727\pi$
$762$	−3.72858e92	−0.0809110
$763$	1.17267e94	2.43853
$764$	1.13358e92	0.0225901
$765$	5.77790e92	0.110350
$766$	−4.46259e93	−0.816869
$767$	−1.32203e93	−0.231949
$768$	6.59076e92	0.110840
$769$	1.67026e93	0.269263	0.134632	−	0.990896i	$-0.457015\pi$
$769$	1.67026e93	0.269263	0.134632	+	0.990896i	$0.457015\pi$
$770$	−4.75040e92	−0.0734144
$771$	5.41895e93	0.802874
$772$	1.43928e93	0.204448
$773$	8.36386e93	1.13913	0.569565	−	0.821946i	$-0.307112\pi$
$773$	8.36386e93	1.13913	0.569565	+	0.821946i	$0.307112\pi$
$774$	−2.06894e93	−0.270189
$775$	1.75219e93	0.219420
$776$	−2.58870e93	−0.310868
$777$	−5.39213e94	−6.20980
$778$	9.23409e93	1.01990
$779$	3.25607e93	0.344926
$780$	−1.38509e93	−0.140735
$781$	1.88681e92	0.0183895
$782$	−4.38172e93	−0.409661
$783$	2.21201e94	1.98394
$784$	6.67607e93	0.574445
$785$	−1.35643e93	−0.111978
$786$	−2.29208e94	−1.81550
$787$	1.17315e94	0.891608	0.445804	−	0.895131i	$-0.352918\pi$
$787$	1.17315e94	0.891608	0.445804	+	0.895131i	$0.352918\pi$
$788$	−5.94328e93	−0.433435
$789$	1.91639e94	1.34116
$790$	1.65013e93	0.110825
$791$	−2.76927e94	−1.78497
$792$	−4.06459e93	−0.251448
$793$	7.30379e92	0.0433680
$794$	−9.35604e93	−0.533244
$795$	4.41888e93	0.241758
$796$	−1.29622e94	−0.680775
$797$	1.47465e94	0.743523	0.371762	−	0.928328i	$-0.378754\pi$
$797$	1.47465e94	0.743523	0.371762	+	0.928328i	$0.378754\pi$
$798$	3.55589e94	1.72129
$799$	−5.52136e93	−0.256611
$800$	−3.84362e93	−0.171520
$801$	3.66848e94	1.57192
$802$	4.17331e93	0.171717
$803$	−6.55615e93	−0.259056
$804$	1.79314e94	0.680446
$805$	−1.66862e94	−0.608121
$806$	4.20477e93	0.147181
$807$	3.52574e94	1.18539
$808$	−1.27708e94	−0.412430
$809$	−4.60643e94	−1.42902	−0.714508	−	0.699627i	$-0.753350\pi$
$809$	−4.60643e94	−1.42902	−0.714508	+	0.699627i	$0.753350\pi$
$810$	5.95834e93	0.177567
$811$	−5.13493e94	−1.47013	−0.735067	−	0.677995i	$-0.762849\pi$
$811$	−5.13493e94	−1.47013	−0.735067	+	0.677995i	$0.762849\pi$
$812$	3.22502e94	0.887076
$813$	8.37811e94	2.21413
$814$	1.78025e94	0.452050
$815$	−4.60449e92	−0.0112346
$816$	5.64133e93	0.132267
$817$	−5.97586e93	−0.134643
$818$	4.92173e94	1.06570
$819$	−1.72291e95	−3.58538
$820$	1.96715e93	0.0393448
$821$	−8.87475e94	−1.70610	−0.853048	−	0.521833i	$-0.825249\pi$
$821$	−8.87475e94	−1.70610	−0.853048	+	0.521833i	$0.825249\pi$
$822$	−8.25092e94	−1.52464
$823$	−1.31924e91	−0.000234330 0	−0.000117165	−	1.00000i	$-0.500037\pi$
$823$	−1.31924e91	−0.000234330 0	−0.000117165		1.00000i	$0.500037\pi$
$824$	1.67516e94	0.286037
$825$	3.47544e94	0.570501
$826$	2.05049e94	0.323599
$827$	6.22659e94	0.944760	0.472380	−	0.881395i	$-0.343395\pi$
$827$	6.22659e94	0.944760	0.472380	+	0.881395i	$0.343395\pi$
$828$	−1.42772e95	−2.08284
$829$	1.32545e95	1.85927	0.929633	−	0.368487i	$-0.120124\pi$
$829$	1.32545e95	1.85927	0.929633	+	0.368487i	$0.120124\pi$
$830$	−1.09671e94	−0.147930
$831$	4.31968e94	0.560297
$832$	−9.22359e93	−0.115051
$833$	5.71435e94	0.685495
$834$	1.05231e95	1.21408
$835$	1.90155e94	0.211007
$836$	−1.17400e94	−0.125304
$837$	−4.47315e94	−0.459236
$838$	−6.23040e94	−0.615298
$839$	−1.09266e95	−1.03806	−0.519030	−	0.854756i	$-0.673707\pi$
$839$	−1.09266e95	−1.03806	−0.519030	+	0.854756i	$0.673707\pi$
$840$	2.14829e94	0.196343
$841$	−5.17872e93	−0.0455357
$842$	6.78590e94	0.574070
$843$	−1.26988e94	−0.103363
$844$	6.78014e94	0.531018
$845$	−3.49724e93	−0.0263562
$846$	−1.79906e95	−1.30469
$847$	−2.31605e95	−1.61636
$848$	2.94262e94	0.197638
$849$	2.94036e95	1.90064
$850$	−3.28993e94	−0.204678
$851$	6.25325e95	3.74451
$852$	−8.53279e93	−0.0491818
$853$	−2.86943e95	−1.59203	−0.796017	−	0.605275i	$-0.793063\pi$
$853$	−2.86943e95	−1.59203	−0.796017	+	0.605275i	$0.793063\pi$
$854$	−1.13283e94	−0.0605040
$855$	5.43775e94	0.279589
$856$	7.81679e94	0.386929
$857$	−1.20587e93	−0.00574676	−0.00287338	−	0.999996i	$-0.500915\pi$
$857$	−1.20587e93	−0.00574676	−0.00287338	+	0.999996i	$0.500915\pi$
$858$	8.34007e94	0.382677
$859$	−1.83240e95	−0.809548	−0.404774	−	0.914417i	$-0.632650\pi$
$859$	−1.83240e95	−0.809548	−0.404774	+	0.914417i	$0.632650\pi$
$860$	−3.61031e93	−0.0153584
$861$	3.58766e95	1.46963
$862$	−2.01141e95	−0.793439
$863$	−1.65941e95	−0.630381	−0.315191	−	0.949028i	$-0.602068\pi$
$863$	−1.65941e95	−0.630381	−0.315191	+	0.949028i	$0.602068\pi$
$864$	9.81231e94	0.358984
$865$	−5.13752e94	−0.181021
$866$	−2.80416e95	−0.951635
$867$	−4.94259e95	−1.61560
$868$	−6.52166e94	−0.205337
$869$	−9.93597e94	−0.301347
$870$	7.23088e94	0.211259
$871$	−2.50946e95	−0.706301
$872$	1.75089e95	0.474758
$873$	−7.21982e95	−1.88609
$874$	−4.12377e95	−1.03794
$875$	−2.54409e95	−0.616979
$876$	2.96491e95	0.692833
$877$	1.48207e95	0.333719	0.166859	−	0.985981i	$-0.446637\pi$
$877$	1.48207e95	0.333719	0.166859	+	0.985981i	$0.446637\pi$
$878$	3.32910e95	0.722363
$879$	5.17904e95	1.08296
$880$	−7.09271e93	−0.0142931
$881$	7.47412e95	1.45159	0.725794	−	0.687912i	$-0.241473\pi$
$881$	7.47412e95	1.45159	0.725794	+	0.687912i	$0.241473\pi$
$882$	1.86194e96	3.48527
$883$	5.01949e94	0.0905601	0.0452800	−	0.998974i	$-0.485582\pi$
$883$	5.01949e94	0.0905601	0.0452800	+	0.998974i	$0.485582\pi$
$884$	−7.89489e94	−0.137293
$885$	4.59746e94	0.0770658
$886$	−4.23136e95	−0.683730
$887$	−6.49378e94	−0.101153	−0.0505766	−	0.998720i	$-0.516106\pi$
$887$	−6.49378e94	−0.101153	−0.0505766	+	0.998720i	$0.516106\pi$
$888$	−8.05087e95	−1.20899
$889$	−8.09329e94	−0.117170
$890$	6.40150e94	0.0893525
$891$	−3.58772e95	−0.482829
$892$	5.05888e95	0.656443
$893$	−5.19632e95	−0.650165
$894$	−6.07921e95	−0.733462
$895$	−1.00600e94	−0.0117045
$896$	1.43059e95	0.160511
$897$	2.92952e96	3.16987
$898$	−5.86073e95	−0.611604
$899$	−2.19511e95	−0.220936
$900$	−1.07197e96	−1.04065
$901$	2.51873e95	0.235844
$902$	−1.18449e95	−0.106984
$903$	−6.58443e95	−0.573676
$904$	−4.13474e95	−0.347516
$905$	−1.87749e95	−0.152229
$906$	−5.45713e95	−0.426872
$907$	6.33080e95	0.477773	0.238886	−	0.971048i	$-0.423218\pi$
$907$	6.33080e95	0.477773	0.238886	+	0.971048i	$0.423218\pi$
$908$	7.17249e95	0.522252
$909$	−3.56175e96	−2.50229
$910$	−3.00648e95	−0.203804
$911$	2.64509e96	1.73019	0.865095	−	0.501608i	$-0.167258\pi$
$911$	2.64509e96	1.73019	0.865095	+	0.501608i	$0.167258\pi$
$912$	5.30922e95	0.335119
$913$	6.60368e95	0.402241
$914$	−9.60600e94	−0.0564666
$915$	−2.53994e94	−0.0144092
$916$	−4.71227e95	−0.258004
$917$	−4.97520e96	−2.62910
$918$	8.39880e95	0.428381
$919$	2.77233e95	0.136487	0.0682434	−	0.997669i	$-0.478261\pi$
$919$	2.77233e95	0.136487	0.0682434	+	0.997669i	$0.478261\pi$
$920$	−2.49137e95	−0.118395
$921$	−9.75148e95	−0.447335
$922$	1.53357e96	0.679125
$923$	1.19414e95	0.0510506
$924$	−1.29356e96	−0.533884
$925$	4.69513e96	1.87086
$926$	−1.78618e96	−0.687175
$927$	4.67198e96	1.73544
$928$	4.81520e95	0.172705
$929$	−1.60427e96	−0.555605	−0.277802	−	0.960638i	$-0.589606\pi$
$929$	−1.60427e96	−0.555605	−0.277802	+	0.960638i	$0.589606\pi$
$930$	−1.46224e95	−0.0489015
$931$	5.37795e96	1.73681
$932$	9.11368e95	0.284234
$933$	−8.38317e96	−2.52496
$934$	4.61107e96	1.34131
$935$	−6.07098e94	−0.0170562
$936$	−2.57243e96	−0.698038
$937$	−6.51536e94	−0.0170766	−0.00853830	−	0.999964i	$-0.502718\pi$
$937$	−6.51536e94	−0.0170766	−0.00853830	+	0.999964i	$0.502718\pi$
$938$	3.89221e96	0.985381
$939$	5.78061e96	1.41365
$940$	−3.13935e95	−0.0741626
$941$	−1.98209e96	−0.452336	−0.226168	−	0.974088i	$-0.572620\pi$
$941$	−1.98209e96	−0.452336	−0.226168	+	0.974088i	$0.572620\pi$
$942$	−3.69363e96	−0.814327
$943$	−4.16061e96	−0.886190
$944$	3.06155e95	0.0630015
$945$	3.19837e96	0.635910
$946$	2.17389e95	0.0417615
$947$	−8.35493e96	−1.55085	−0.775423	−	0.631442i	$-0.782463\pi$
$947$	−8.35493e96	−1.55085	−0.775423	+	0.631442i	$0.782463\pi$
$948$	4.49338e96	0.805939
$949$	−4.14932e96	−0.719159
$950$	−3.09625e96	−0.518583
$951$	−5.16272e96	−0.835625
$952$	1.22451e96	0.191541
$953$	1.12245e97	1.69687	0.848435	−	0.529300i	$-0.177545\pi$
$953$	1.12245e97	1.69687	0.848435	+	0.529300i	$0.177545\pi$
$954$	8.20690e96	1.19910
$955$	5.51688e94	0.00779083
$956$	3.67478e96	0.501591
$957$	−4.35396e96	−0.574442
$958$	−7.53699e96	−0.961212
$959$	−1.79095e97	−2.20790
$960$	3.20757e95	0.0382261
$961$	−8.23591e96	−0.948859
$962$	1.12670e97	1.25492
$963$	2.18008e97	2.34757
$964$	1.67840e95	0.0174740
$965$	7.00465e95	0.0705096
$966$	−4.54373e97	−4.42238
$967$	1.34440e97	1.26523	0.632615	−	0.774466i	$-0.281981\pi$
$967$	1.34440e97	1.26523	0.632615	+	0.774466i	$0.281981\pi$
$968$	−3.45804e96	−0.314689
$969$	4.54441e96	0.399903
$970$	−1.25986e96	−0.107211
$971$	−1.89806e97	−1.56201	−0.781006	−	0.624524i	$-0.785293\pi$
$971$	−1.89806e97	−1.56201	−0.781006	+	0.624524i	$0.785293\pi$
$972$	3.46717e96	0.275944
$973$	2.28415e97	1.75816
$974$	1.42617e97	1.06170
$975$	2.19957e97	1.58375
$976$	−1.69140e95	−0.0117795
$977$	−1.74539e97	−1.17576	−0.587882	−	0.808947i	$-0.700038\pi$
$977$	−1.74539e97	−1.17576	−0.587882	+	0.808947i	$0.700038\pi$
$978$	−1.25383e96	−0.0817005
$979$	−3.85456e96	−0.242961
$980$	3.24909e96	0.198113
$981$	4.88318e97	2.88045
$982$	1.11625e97	0.636997
$983$	1.63070e97	0.900293	0.450146	−	0.892955i	$-0.351372\pi$
$983$	1.63070e97	0.900293	0.450146	+	0.892955i	$0.351372\pi$
$984$	5.35666e96	0.286123
$985$	−2.89246e96	−0.149482
$986$	4.12155e96	0.206092
$987$	−5.72551e97	−2.77017
$988$	−7.43012e96	−0.347852
$989$	7.63596e96	0.345927
$990$	−1.97814e96	−0.0867188
$991$	3.17629e97	1.34749	0.673747	−	0.738962i	$-0.264684\pi$
$991$	3.17629e97	1.34749	0.673747	+	0.738962i	$0.264684\pi$
$992$	−9.73735e95	−0.0399771
$993$	−5.70230e97	−2.26568
$994$	−1.85213e96	−0.0712221
$995$	−6.30839e96	−0.234784
$996$	−2.98641e97	−1.07577
$997$	6.25056e96	0.217935	0.108967	−	0.994045i	$-0.465246\pi$
$997$	6.25056e96	0.217935	0.108967	+	0.994045i	$0.465246\pi$
$998$	2.19749e97	0.741627
$999$	−1.19861e98	−3.91562

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2.66.a.b.1.3	✓	3

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

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+4.29497e9 q^{2} +5.69189e15 q^{3} +1.84467e19 q^{4} +8.97760e21 q^{5} +2.44465e25 q^{6} +5.30637e27 q^{7} +7.92282e28 q^{8} +2.20965e31 q^{9} +3.85585e31 q^{10} -2.32174e33 q^{11} +1.04997e35 q^{12} -1.46940e36 q^{13} +2.27907e37 q^{14} +5.10995e37 q^{15} +3.40282e38 q^{16} +2.91263e39 q^{17} +9.49039e40 q^{18} +2.74117e41 q^{19} +1.65607e41 q^{20} +3.02032e43 q^{21} -9.97178e42 q^{22} -3.50267e44 q^{23} +4.50958e44 q^{24} -2.62991e45 q^{25} -6.31103e45 q^{26} +6.71385e46 q^{27} +9.78852e46 q^{28} +3.29469e47 q^{29} +2.19471e47 q^{30} -6.66257e47 q^{31} +1.46150e48 q^{32} -1.32151e49 q^{33} +1.25097e49 q^{34} +4.76384e49 q^{35} +4.07609e50 q^{36} -1.78528e51 q^{37} +1.17732e51 q^{38} -8.36367e51 q^{39} +7.11278e50 q^{40} +1.18784e52 q^{41} +1.29722e53 q^{42} -2.18004e52 q^{43} -4.28285e52 q^{44} +1.98374e53 q^{45} -1.50438e54 q^{46} -1.89566e54 q^{47} +1.93685e54 q^{48} +1.96192e55 q^{49} -1.12954e55 q^{50} +1.65784e55 q^{51} -2.71057e55 q^{52} +8.64760e55 q^{53} +2.88358e56 q^{54} -2.08436e55 q^{55} +4.20414e56 q^{56} +1.56024e57 q^{57} +1.41506e57 q^{58} +8.99708e56 q^{59} +9.42619e56 q^{60} -4.97059e56 q^{61} -2.86155e57 q^{62} +1.17252e59 q^{63} +6.27710e57 q^{64} -1.31917e58 q^{65} -5.67583e58 q^{66} +1.70781e59 q^{67} +5.37286e58 q^{68} -1.99368e60 q^{69} +2.04605e59 q^{70} -8.12672e58 q^{71} +1.75067e60 q^{72} +2.82381e60 q^{73} -7.66773e60 q^{74} -1.49691e61 q^{75} +5.05656e60 q^{76} -1.23200e61 q^{77} -3.59217e61 q^{78} +4.27954e61 q^{79} +3.05492e60 q^{80} +1.54527e62 q^{81} +5.10173e61 q^{82} -2.84429e62 q^{83} +5.57151e62 q^{84} +2.61484e61 q^{85} -9.36321e61 q^{86} +1.87530e63 q^{87} -1.83947e62 q^{88} +1.66021e63 q^{89} +8.52009e62 q^{90} -7.79719e63 q^{91} -6.46128e63 q^{92} -3.79226e63 q^{93} -8.14180e63 q^{94} +2.46091e63 q^{95} +8.31870e63 q^{96} -3.26740e64 q^{97} +8.42638e64 q^{98} -5.13023e64 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q + 12884901888 q^{2} + 29\!\cdots\!12 q^{3} + 55\!\cdots\!48 q^{4} + 39\!\cdots\!50 q^{5} + 12\!\cdots\!52 q^{6} + 42\!\cdots\!64 q^{7} + 23\!\cdots\!08 q^{8} + 85\!\cdots\!19 q^{9} + 16\!\cdots\!00 q^{10}+ \cdots - 11\!\cdots\!32 q^{99}+O(q^{100}) \) 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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