LMFDB - Embedded newform 2.48.a.b.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2,48,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, 48, names="a")

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

chi := DirichletCharacter("2.1");

S:= CuspForms(chi, 48);

N := Newforms(S);

Level:	$ N $	$=$	$ 2 $
Weight:	$ k $	$=$	$ 48 $
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:	$27.9815325310$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\mathbb{Q}[x]/(x^{2} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x - 5897345978580 $ x^2 - x - 5897345978580
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{7}\cdot 3^{3}\cdot 5 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$-2.42844e6$ 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)

$f(q)$	$=$	$q-8.38861e6 q^{2} +2.70963e11 q^{3} +7.03687e13 q^{4} -1.02521e16 q^{5} -2.27300e18 q^{6} +1.08843e20 q^{7} -5.90296e20 q^{8} +4.68319e22 q^{9} +O(q^{10})$	\(q-8.38861e6 q^{2} +2.70963e11 q^{3} +7.03687e13 q^{4} -1.02521e16 q^{5} -2.27300e18 q^{6} +1.08843e20 q^{7} -5.90296e20 q^{8} +4.68319e22 q^{9} +8.60007e22 q^{10} +3.92772e24 q^{11} +1.90673e25 q^{12} -2.33551e26 q^{13} -9.13045e26 q^{14} -2.77793e27 q^{15} +4.95176e27 q^{16} +4.05682e28 q^{17} -3.92855e29 q^{18} -1.56322e29 q^{19} -7.21426e29 q^{20} +2.94925e31 q^{21} -3.29481e31 q^{22} +3.32892e31 q^{23} -1.59948e32 q^{24} -6.05438e32 q^{25} +1.95916e33 q^{26} +5.48512e33 q^{27} +7.65918e33 q^{28} +9.92617e32 q^{29} +2.33030e34 q^{30} +1.71111e35 q^{31} -4.15384e34 q^{32} +1.06427e36 q^{33} -3.40310e35 q^{34} -1.11587e36 q^{35} +3.29550e36 q^{36} +1.08691e37 q^{37} +1.31132e36 q^{38} -6.32835e37 q^{39} +6.05176e36 q^{40} -7.95054e37 q^{41} -2.47401e38 q^{42} +3.70345e38 q^{43} +2.76389e38 q^{44} -4.80124e38 q^{45} -2.79250e38 q^{46} -6.30322e38 q^{47} +1.34174e39 q^{48} +6.60357e39 q^{49} +5.07878e39 q^{50} +1.09925e40 q^{51} -1.64347e40 q^{52} +2.32864e40 q^{53} -4.60125e40 q^{54} -4.02673e40 q^{55} -6.42499e40 q^{56} -4.23574e40 q^{57} -8.32668e39 q^{58} -3.80182e41 q^{59} -1.95479e41 q^{60} +1.07627e42 q^{61} -1.43538e42 q^{62} +5.09735e42 q^{63} +3.48449e41 q^{64} +2.39438e42 q^{65} -8.92770e42 q^{66} -1.46013e42 q^{67} +2.85473e42 q^{68} +9.02012e42 q^{69} +9.36061e42 q^{70} -1.66419e43 q^{71} -2.76447e43 q^{72} -5.99210e42 q^{73} -9.11763e43 q^{74} -1.64051e44 q^{75} -1.10002e43 q^{76} +4.27507e44 q^{77} +5.30860e44 q^{78} -1.80688e44 q^{79} -5.07658e43 q^{80} +2.41058e44 q^{81} +6.66940e44 q^{82} -2.37314e45 q^{83} +2.07535e45 q^{84} -4.15908e44 q^{85} -3.10668e45 q^{86} +2.68962e44 q^{87} -2.31852e45 q^{88} +1.07890e45 q^{89} +4.02758e45 q^{90} -2.54205e46 q^{91} +2.34252e45 q^{92} +4.63646e46 q^{93} +5.28752e45 q^{94} +1.60263e45 q^{95} -1.12553e46 q^{96} -5.98242e45 q^{97} -5.53948e46 q^{98} +1.83943e47 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 16777216 q^{2} + 122289844824 q^{3} + 140737488355328 q^{4} + 18\!\cdots\!40 q^{5}+ \cdots + 42\!\cdots\!14 q^{9}+O(q^{10}) $ 2 * q - 16777216 * q^2 + 122289844824 * q^3 + 140737488355328 * q^4 + 18178497839194140 * q^5 - 1025841570609364992 * q^6 + 161018545456026827632 * q^7 - 1180591620717411303424 * q^8 + 42346678028148839299914 * q^9	$ 2 q - 16777216 q^{2} + 122289844824 q^{3} + 140737488355328 q^{4} + 18\!\cdots\!40 q^{5}+ \cdots + 19\!\cdots\!88 q^{99}+O(q^{100}) $ 2 * q - 16777216 * q^2 + 122289844824 * q^3 + 140737488355328 * q^4 + 18178497839194140 * q^5 - 1025841570609364992 * q^6 + 161018545456026827632 * q^7 - 1180591620717411303424 * q^8 + 42346678028148839299914 * q^9 - 152492292401846676357120 * q^10 + 1148414200601353937498184 * q^11 + 8605382805946284046811136 * q^12 - 91147460388086216079419636 * q^13 - 1350721458560790294488416256 * q^14 - 7004781615634981008503062320 * q^15 + 9903520314283042199192993792 * q^16 - 102841736272610788276309928988 * q^17 - 355229682080353578541972979712 * q^18 + 1021269902513170084335814340920 * q^19 + 1279198063980470244062747688960 * q^20 + 21735508585019662606113256728384 * q^21 - 9633596550478122450928766287872 * q^22 + 8761047668524985915668413593424 * q^23 - 72187183049023445925352269938688 * q^24 - 507682648872986273192302737941650 * q^25 + 764600315391183136893548193906688 * q^26 + 10104984547772788958914840573828080 * q^27 + 11330672833054713950667884512411648 * q^28 + 44866738270461738647546902365332460 * q^29 + 58760367099168526767776856602050560 * q^30 + 207627610718284877414441666427987904 * q^31 - 83076749736557242056487941267521536 * q^32 + 1477472372445089531927832872318579808 * q^33 + 862699011630313039420959680788168704 * q^34 + 367494533980940143565872352084574240 * q^35 + 2979882552936710671785822873395920896 * q^36 + 15454503825836181610788445034143257052 * q^37 - 8567032874381198674820086866756239360 * q^38 - 84454902625144773203023026649833922032 * q^39 - 10730691113091084533106717765591367680 * q^40 - 183644075219801436287443355635335693516 * q^41 - 182330661200364621894942514297775849472 * q^42 + 251792238934935641547265550793932228104 * q^43 + 80812465092113181816840656312573362176 * q^44 - 607642114901245348425108558238563820020 * q^45 - 73492994560570045052063379617105313792 * q^46 + 2877259596300283378159171629753736631712 * q^47 + 605549981222502470676977454425837666304 * q^48 + 4082466065158778742105339967177123972626 * q^49 + 4258750729797123635191136285919228723200 * q^50 + 32313595089705813278113192123424261680944 * q^51 - 6413932322493001991610313527791194210304 * q^52 + 36237003736012302609225684974144068811964 * q^53 - 84766754217323199643064702956338822512640 * q^54 - 119284580676988289643910520626568801967120 * q^55 - 95048572772745437884284221363892449705984 * q^56 - 217433238554190330563790441928328986980960 * q^57 - 376369479589501504512721125557046796615680 * q^58 + 216631413518842627379871131067900548684520 * q^59 - 492917685531021896992387081506814144020480 * q^60 + 2343345794410501150323838534047225181209004 * q^61 - 1741706636292290268957804678531150755397632 * q^62 + 4863331655836708395434595438453038464171824 * q^63 + 696898287454081973172991196020261297061888 * q^64 + 6442979197855565506819083799260229348557480 * q^65 - 12393936563271857608246074255394617126027264 * q^66 + 9679359518522646693994124509775830904939992 * q^67 - 7236843830554137004990977745937078295724032 * q^68 + 12666786020488197907659082189490927173898688 * q^69 - 3082767587708786335837825339675476146257920 * q^70 - 34699689890171309465034074226599979171319056 * q^71 - 24997066622625314635027928042352009195552768 * q^72 - 44919947676390510667705279890416107043412236 * q^73 - 129641774429439999749712836320974399252463616 * q^74 - 178584439183245940201476654984555123803179800 * q^75 + 71865480506297118253185179251166323545210880 * q^76 + 282496402053252599536812437150318196880350144 * q^77 + 708459071800510445649064585539010037029011456 * q^78 + 459051391676893300046865817924586171479631200 * q^79 + 90015561316804776443095277502181871651389440 * q^80 - 326533112556292583027849224141868597638781358 * q^81 + 1540518158541428086852337632629422081313865728 * q^82 - 1357110492338922730441331533770737425416063816 * q^83 + 1529500443190668270144889934978436873087614976 * q^84 - 4493133982253416774682211563698820690839841160 * q^85 - 2112186389867512602168524177514386240131039232 * q^86 - 6253923718333989640702287995671643099683866480 * q^87 - 677904091171421373894204064268903406536491008 * q^88 + 4559737044037194815580171398227946101567633620 * q^89 + 5097271506197505939761653052508482369130332160 * q^90 - 17990568925125012147062510675834829593464410976 * q^91 + 616503922114754364484099282763086572118081536 * q^92 + 40935592303229143353065306088384219268477064448 * q^93 - 24136202867601327548293052406725233138672336896 * q^94 + 35082243421784097273165847234698748298121392400 * q^95 - 5079721416882934005540658490016217254259064832 * q^96 + 53827580940974934190192198959367945947750881092 * q^97 - 34246207493919452626254791691381759573762244608 * q^98 + 196408474482694469089639477350277927611611498088 * 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 $

$2$	−8.38861e6	−0.707107
$2$	−8.38861e6	−0.707107
$3$	2.70963e11	1.66173	0.830864	−	0.556476i	$-0.187847\pi$
$3$	2.70963e11	1.66173	0.830864	+	0.556476i	$0.187847\pi$
$4$	7.03687e13	0.500000
$5$	−1.02521e16	−0.384607	−0.192303	−	0.981336i	$-0.561596\pi$
$5$	−1.02521e16	−0.384607	−0.192303	+	0.981336i	$0.561596\pi$
$6$	−2.27300e18	−1.17502
$7$	1.08843e20	1.50314	0.751568	−	0.659655i	$-0.229298\pi$
$7$	1.08843e20	1.50314	0.751568	+	0.659655i	$0.229298\pi$
$8$	−5.90296e20	−0.353553
$9$	4.68319e22	1.76134
$10$	8.60007e22	0.271958
$11$	3.92772e24	1.32255	0.661276	−	0.750143i	$-0.270015\pi$
$11$	3.92772e24	1.32255	0.661276	+	0.750143i	$0.270015\pi$
$12$	1.90673e25	0.830864
$13$	−2.33551e26	−1.55136	−0.775679	−	0.631128i	$-0.782592\pi$
$13$	−2.33551e26	−1.55136	−0.775679	+	0.631128i	$0.782592\pi$
$14$	−9.13045e26	−1.06288
$15$	−2.77793e27	−0.639112
$16$	4.95176e27	0.250000
$17$	4.05682e28	0.492760	0.246380	−	0.969173i	$-0.420759\pi$
$17$	4.05682e28	0.492760	0.246380	+	0.969173i	$0.420759\pi$
$18$	−3.92855e29	−1.24545
$19$	−1.56322e29	−0.139095	−0.0695473	−	0.997579i	$-0.522155\pi$
$19$	−1.56322e29	−0.139095	−0.0695473	+	0.997579i	$0.522155\pi$
$20$	−7.21426e29	−0.192303
$21$	2.94925e31	2.49780
$22$	−3.29481e31	−0.935185
$23$	3.32892e31	0.332429	0.166215	−	0.986090i	$-0.446846\pi$
$23$	3.32892e31	0.332429	0.166215	+	0.986090i	$0.446846\pi$
$24$	−1.59948e32	−0.587509
$25$	−6.05438e32	−0.852078
$26$	1.95916e33	1.09698
$27$	5.48512e33	1.26514
$28$	7.65918e33	0.751568
$29$	9.92617e32	0.0427001	0.0213500	−	0.999772i	$-0.493204\pi$
$29$	9.92617e32	0.0427001	0.0213500	+	0.999772i	$0.493204\pi$
$30$	2.33030e34	0.451920
$31$	1.71111e35	1.53560	0.767799	−	0.640690i	$-0.221352\pi$
$31$	1.71111e35	1.53560	0.767799	+	0.640690i	$0.221352\pi$
$32$	−4.15384e34	−0.176777
$33$	1.06427e36	2.19772
$34$	−3.40310e35	−0.348434
$35$	−1.11587e36	−0.578117
$36$	3.29550e36	0.880669
$37$	1.08691e37	1.52564	0.762819	−	0.646612i	$-0.223815\pi$
$37$	1.08691e37	1.52564	0.762819	+	0.646612i	$0.223815\pi$
$38$	1.31132e36	0.0983548
$39$	−6.32835e37	−2.57793
$40$	6.05176e36	0.135979
$41$	−7.95054e37	−0.999945	−0.499972	−	0.866041i	$-0.666656\pi$
$41$	−7.95054e37	−0.999945	−0.499972	+	0.866041i	$0.666656\pi$
$42$	−2.47401e38	−1.76621
$43$	3.70345e38	1.52089	0.760446	−	0.649402i	$-0.224981\pi$
$43$	3.70345e38	1.52089	0.760446	+	0.649402i	$0.224981\pi$
$44$	2.76389e38	0.661276
$45$	−4.80124e38	−0.677423
$46$	−2.79250e38	−0.235063
$47$	−6.30322e38	−0.320083	−0.160041	−	0.987110i	$-0.551163\pi$
$47$	−6.30322e38	−0.320083	−0.160041	+	0.987110i	$0.551163\pi$
$48$	1.34174e39	0.415432
$49$	6.60357e39	1.25942
$50$	5.07878e39	0.602510
$51$	1.09925e40	0.818833
$52$	−1.64347e40	−0.775679
$53$	2.32864e40	0.702456	0.351228	−	0.936290i	$-0.385764\pi$
$53$	2.32864e40	0.702456	0.351228	+	0.936290i	$0.385764\pi$
$54$	−4.60125e40	−0.894587
$55$	−4.02673e40	−0.508662
$56$	−6.42499e40	−0.531439
$57$	−4.23574e40	−0.231137
$58$	−8.32668e39	−0.0301935
$59$	−3.80182e41	−0.922507	−0.461253	−	0.887268i	$-0.652600\pi$
$59$	−3.80182e41	−0.922507	−0.461253	+	0.887268i	$0.652600\pi$
$60$	−1.95479e41	−0.319556
$61$	1.07627e42	1.19308	0.596541	−	0.802583i	$-0.296541\pi$
$61$	1.07627e42	1.19308	0.596541	+	0.802583i	$0.296541\pi$
$62$	−1.43538e42	−1.08583
$63$	5.09735e42	2.64753
$64$	3.48449e41	0.125000
$65$	2.39438e42	0.596663
$66$	−8.92770e42	−1.55402
$67$	−1.46013e42	−0.178498	−0.0892490	−	0.996009i	$-0.528447\pi$
$67$	−1.46013e42	−0.178498	−0.0892490	+	0.996009i	$0.528447\pi$
$68$	2.85473e42	0.246380
$69$	9.02012e42	0.552406
$70$	9.36061e42	0.408790
$71$	−1.66419e43	−0.520752	−0.260376	−	0.965507i	$-0.583847\pi$
$71$	−1.66419e43	−0.520752	−0.260376	+	0.965507i	$0.583847\pi$
$72$	−2.76447e43	−0.622727
$73$	−5.99210e42	−0.0976095	−0.0488047	−	0.998808i	$-0.515541\pi$
$73$	−5.99210e42	−0.0976095	−0.0488047	+	0.998808i	$0.515541\pi$
$74$	−9.11763e43	−1.07879
$75$	−1.64051e44	−1.41592
$76$	−1.10002e43	−0.0695473
$77$	4.27507e44	1.98798
$78$	5.30860e44	1.82287
$79$	−1.80688e44	−0.459931	−0.229966	−	0.973199i	$-0.573861\pi$
$79$	−1.80688e44	−0.459931	−0.229966	+	0.973199i	$0.573861\pi$
$80$	−5.07658e43	−0.0961517
$81$	2.41058e44	0.340975
$82$	6.66940e44	0.707068
$83$	−2.37314e45	−1.89229	−0.946144	−	0.323745i	$-0.895058\pi$
$83$	−2.37314e45	−1.89229	−0.946144	+	0.323745i	$0.895058\pi$
$84$	2.07535e45	1.24890
$85$	−4.15908e44	−0.189519
$86$	−3.10668e45	−1.07543
$87$	2.68962e44	0.0709559
$88$	−2.31852e45	−0.467592
$89$	1.07890e45	0.166846	0.0834232	−	0.996514i	$-0.473415\pi$
$89$	1.07890e45	0.166846	0.0834232	+	0.996514i	$0.473415\pi$
$90$	4.02758e45	0.479010
$91$	−2.54205e46	−2.33190
$92$	2.34252e45	0.166215
$93$	4.63646e46	2.55175
$94$	5.28752e45	0.226333
$95$	1.60263e45	0.0534967
$96$	−1.12553e46	−0.293755
$97$	−5.98242e45	−0.122389	−0.0611943	−	0.998126i	$-0.519491\pi$
$97$	−5.98242e45	−0.122389	−0.0611943	+	0.998126i	$0.519491\pi$
$98$	−5.53948e46	−0.890545
$99$	1.83943e47	2.32946
$100$	−4.26039e46	−0.426039
$101$	−6.21755e46	−0.492115	−0.246058	−	0.969255i	$-0.579135\pi$
$101$	−6.21755e46	−0.492115	−0.246058	+	0.969255i	$0.579135\pi$
$102$	−9.22114e46	−0.579003
$103$	1.44306e45	0.00720458	0.00360229	−	0.999994i	$-0.498853\pi$
$103$	1.44306e45	0.00720458	0.00360229	+	0.999994i	$0.498853\pi$
$104$	1.37864e47	0.548488
$105$	−3.02360e47	−0.960672
$106$	−1.95340e47	−0.496712
$107$	−8.78783e47	−1.79210	−0.896051	−	0.443951i	$-0.853577\pi$
$107$	−8.78783e47	−1.79210	−0.896051	+	0.443951i	$0.853577\pi$
$108$	3.85981e47	0.632569
$109$	−1.77433e45	−0.00234159	−0.00117080	−	0.999999i	$-0.500373\pi$
$109$	−1.77433e45	−0.00234159	−0.00117080	+	0.999999i	$0.500373\pi$
$110$	3.37787e47	0.359678
$111$	2.94511e48	2.53520
$112$	5.38967e47	0.375784
$113$	−6.05109e46	−0.0342365	−0.0171183	−	0.999853i	$-0.505449\pi$
$113$	−6.05109e46	−0.0342365	−0.0171183	+	0.999853i	$0.505449\pi$
$114$	3.55320e47	0.163439
$115$	−3.41283e47	−0.127854
$116$	6.98492e46	0.0213500
$117$	−1.09376e49	−2.73247
$118$	3.18920e48	0.652311
$119$	4.41558e48	0.740686
$120$	1.63980e48	0.225960
$121$	6.60724e48	0.749141
$122$	−9.02840e48	−0.843636
$123$	−2.15430e49	−1.66164
$124$	1.20409e49	0.767799
$125$	1.34915e49	0.712321
$126$	−4.27597e49	−1.87209
$127$	8.82915e48	0.321020	0.160510	−	0.987034i	$-0.448686\pi$
$127$	8.82915e48	0.321020	0.160510	+	0.987034i	$0.448686\pi$
$128$	−2.92300e48	−0.0883883
$129$	1.00350e50	2.52731
$130$	−2.00855e49	−0.421904
$131$	−1.59705e49	−0.280183	−0.140092	−	0.990139i	$-0.544740\pi$
$131$	−1.59705e49	−0.280183	−0.140092	+	0.990139i	$0.544740\pi$
$132$	7.48910e49	1.09886
$133$	−1.70146e49	−0.209078
$134$	1.22485e49	0.126217
$135$	−5.62339e49	−0.486580
$136$	−2.39472e49	−0.174217
$137$	−6.03702e49	−0.369734	−0.184867	−	0.982764i	$-0.559185\pi$
$137$	−6.03702e49	−0.369734	−0.184867	+	0.982764i	$0.559185\pi$
$138$	−7.56663e49	−0.390610
$139$	1.21646e50	0.529969	0.264985	−	0.964253i	$-0.414633\pi$
$139$	1.21646e50	0.529969	0.264985	+	0.964253i	$0.414633\pi$
$140$	−7.85225e49	−0.289058
$141$	−1.70794e50	−0.531891
$142$	1.39602e50	0.368227
$143$	−9.17321e50	−2.05175
$144$	2.31900e50	0.440335
$145$	−1.01764e49	−0.0164227
$146$	5.02654e49	0.0690203
$147$	1.78932e51	2.09281
$148$	7.64843e50	0.762819
$149$	−1.57670e51	−1.34237	−0.671185	−	0.741290i	$-0.734214\pi$
$149$	−1.57670e51	−1.34237	−0.671185	+	0.741290i	$0.734214\pi$
$150$	1.37616e51	1.00121
$151$	1.05031e51	0.653674	0.326837	−	0.945081i	$-0.394017\pi$
$151$	1.05031e51	0.653674	0.326837	+	0.945081i	$0.394017\pi$
$152$	9.22762e49	0.0491774
$153$	1.89988e51	0.867918
$154$	−3.58619e51	−1.40571
$155$	−1.75424e51	−0.590602
$156$	−4.45318e51	−1.28897
$157$	−3.24813e51	−0.809081	−0.404541	−	0.914520i	$-0.632569\pi$
$157$	−3.24813e51	−0.809081	−0.404541	+	0.914520i	$0.632569\pi$
$158$	1.51572e51	0.325221
$159$	6.30974e51	1.16729
$160$	4.25855e50	0.0679895
$161$	3.62331e51	0.499686
$162$	−2.02214e51	−0.241106
$163$	−4.29859e51	−0.443524	−0.221762	−	0.975101i	$-0.571181\pi$
$163$	−4.29859e51	−0.443524	−0.221762	+	0.975101i	$0.571181\pi$
$164$	−5.59469e51	−0.499972
$165$	−1.09109e52	−0.845258
$166$	1.99073e52	1.33805
$167$	−6.41790e50	−0.0374590	−0.0187295	−	0.999825i	$-0.505962\pi$
$167$	−6.41790e50	−0.0374590	−0.0187295	+	0.999825i	$0.505962\pi$
$168$	−1.74093e52	−0.883107
$169$	3.18818e52	1.40671
$170$	3.48889e51	0.134010
$171$	−7.32086e51	−0.244993
$172$	2.60607e52	0.760446
$173$	6.69399e52	1.70452	0.852259	−	0.523120i	$-0.175232\pi$
$173$	6.69399e52	1.70452	0.852259	+	0.523120i	$0.175232\pi$
$174$	−2.25622e51	−0.0501734
$175$	−6.58979e52	−1.28079
$176$	1.94491e52	0.330638
$177$	−1.03015e53	−1.53296
$178$	−9.05048e51	−0.117978
$179$	−1.38049e53	−1.57757	−0.788784	−	0.614671i	$-0.789289\pi$
$179$	−1.38049e53	−1.57757	−0.788784	+	0.614671i	$0.789289\pi$
$180$	−3.37858e52	−0.338711
$181$	−9.26435e52	−0.815396	−0.407698	−	0.913117i	$-0.633668\pi$
$181$	−9.26435e52	−0.815396	−0.407698	+	0.913117i	$0.633668\pi$
$182$	2.13242e53	1.64890
$183$	2.91629e53	1.98258
$184$	−1.96505e52	−0.117531
$185$	−1.11431e53	−0.586771
$186$	−3.88935e53	−1.80436
$187$	1.59340e53	0.651701
$188$	−4.43549e52	−0.160041
$189$	5.97020e53	1.90168
$190$	−1.34438e52	−0.0378279
$191$	3.78107e53	0.940439	0.470220	−	0.882549i	$-0.344175\pi$
$191$	3.78107e53	0.940439	0.470220	+	0.882549i	$0.344175\pi$
$192$	9.44167e52	0.207716
$193$	−6.95903e53	−1.35504	−0.677520	−	0.735504i	$-0.736945\pi$
$193$	−6.95903e53	−1.35504	−0.677520	+	0.735504i	$0.736945\pi$
$194$	5.01842e52	0.0865418
$195$	6.48787e53	0.991491
$196$	4.64685e53	0.629710
$197$	−7.80244e53	−0.938155	−0.469077	−	0.883157i	$-0.655413\pi$
$197$	−7.80244e53	−0.938155	−0.469077	+	0.883157i	$0.655413\pi$
$198$	−1.54302e54	−1.64718
$199$	−1.09549e54	−1.03887	−0.519434	−	0.854510i	$-0.673857\pi$
$199$	−1.09549e54	−1.03887	−0.519434	+	0.854510i	$0.673857\pi$
$200$	3.57387e53	0.301255
$201$	−3.95640e53	−0.296615
$202$	5.21566e53	0.347978
$203$	1.08040e53	0.0641841
$204$	7.73525e53	0.409417
$205$	8.15095e53	0.384585
$206$	−1.21052e52	−0.00509441
$207$	1.55900e54	0.585520
$208$	−1.15649e54	−0.387840
$209$	−6.13989e53	−0.183960
$210$	2.53638e54	0.679298
$211$	−1.93427e54	−0.463317	−0.231659	−	0.972797i	$-0.574415\pi$
$211$	−1.93427e54	−0.463317	−0.231659	+	0.972797i	$0.574415\pi$
$212$	1.63863e54	0.351228
$213$	−4.50932e54	−0.865348
$214$	7.37177e54	1.26721
$215$	−3.79681e54	−0.584945
$216$	−3.23784e54	−0.447294
$217$	1.86243e55	2.30822
$218$	1.48841e52	0.00165575
$219$	−1.62364e54	−0.162200
$220$	−2.83356e54	−0.254331
$221$	−9.47471e54	−0.764448
$222$	−2.47054e55	−1.79265
$223$	7.23600e54	0.472426	0.236213	−	0.971701i	$-0.424094\pi$
$223$	7.23600e54	0.472426	0.236213	+	0.971701i	$0.424094\pi$
$224$	−4.52118e54	−0.265720
$225$	−2.83538e55	−1.50080
$226$	5.07602e53	0.0242089
$227$	2.17948e55	0.937013	0.468507	−	0.883460i	$-0.344792\pi$
$227$	2.17948e55	0.937013	0.468507	+	0.883460i	$0.344792\pi$
$228$	−2.98064e54	−0.115569
$229$	−1.86932e55	−0.653957	−0.326979	−	0.945032i	$-0.606031\pi$
$229$	−1.86932e55	−0.653957	−0.326979	+	0.945032i	$0.606031\pi$
$230$	2.86289e54	0.0904067
$231$	1.15838e56	3.30347
$232$	−5.85938e53	−0.0150968
$233$	−5.14721e55	−1.19869	−0.599346	−	0.800490i	$-0.704573\pi$
$233$	−5.14721e55	−1.19869	−0.599346	+	0.800490i	$0.704573\pi$
$234$	9.17514e55	1.93215
$235$	6.46211e54	0.123106
$236$	−2.67530e55	−0.461253
$237$	−4.89597e55	−0.764281
$238$	−3.70406e55	−0.523744
$239$	−2.55198e55	−0.326984	−0.163492	−	0.986545i	$-0.552276\pi$
$239$	−2.55198e55	−0.326984	−0.163492	+	0.986545i	$0.552276\pi$
$240$	−1.37556e55	−0.159778
$241$	6.85848e55	0.722483	0.361241	−	0.932472i	$-0.382353\pi$
$241$	6.85848e55	0.722483	0.361241	+	0.932472i	$0.382353\pi$
$242$	−5.54255e55	−0.529723
$243$	−8.05253e55	−0.698529
$244$	7.57357e55	0.596541
$245$	−6.77003e55	−0.484382
$246$	1.80716e56	1.17495
$247$	3.65091e55	0.215786
$248$	−1.01006e56	−0.542916
$249$	−6.43031e56	−3.14447
$250$	−1.13175e56	−0.503687
$251$	4.26400e56	1.72776	0.863882	−	0.503694i	$-0.168026\pi$
$251$	4.26400e56	1.72776	0.863882	+	0.503694i	$0.168026\pi$
$252$	3.58694e56	1.32377
$253$	1.30751e56	0.439654
$254$	−7.40643e55	−0.226995
$255$	−1.12695e56	−0.314929
$256$	2.45199e55	0.0625000
$257$	5.48104e56	1.27478	0.637389	−	0.770543i	$-0.280015\pi$
$257$	5.48104e56	1.27478	0.637389	+	0.770543i	$0.280015\pi$
$258$	−8.41794e56	−1.78708
$259$	1.18303e57	2.29324
$260$	1.68489e56	0.298331
$261$	4.64862e55	0.0752093
$262$	1.33970e56	0.198119
$263$	−1.18349e57	−1.60032	−0.800158	−	0.599789i	$-0.795251\pi$
$263$	−1.18349e57	−1.60032	−0.800158	+	0.599789i	$0.795251\pi$
$264$	−6.28231e56	−0.777011
$265$	−2.38734e56	−0.270169
$266$	1.42729e56	0.147841
$267$	2.92342e56	0.277253
$268$	−1.02747e56	−0.0892490
$269$	−2.06922e55	−0.0164675	−0.00823375	−	0.999966i	$-0.502621\pi$
$269$	−2.06922e55	−0.0164675	−0.00823375	+	0.999966i	$0.502621\pi$
$270$	4.71724e56	0.344064
$271$	2.88469e57	1.92895	0.964473	−	0.264181i	$-0.0851015\pi$
$271$	2.88469e57	1.92895	0.964473	+	0.264181i	$0.0851015\pi$
$272$	2.00884e56	0.123190
$273$	−6.88799e57	−3.87499
$274$	5.06422e56	0.261441
$275$	−2.37799e57	−1.12692
$276$	6.34735e56	0.276203
$277$	−4.45744e55	−0.0178160	−0.00890801	−	0.999960i	$-0.502836\pi$
$277$	−4.45744e55	−0.0178160	−0.00890801	+	0.999960i	$0.502836\pi$
$278$	−1.02044e57	−0.374745
$279$	8.01345e57	2.70471
$280$	6.58695e56	0.204395
$281$	6.47805e56	0.184861	0.0924306	−	0.995719i	$-0.470536\pi$
$281$	6.47805e56	0.184861	0.0924306	+	0.995719i	$0.470536\pi$
$282$	1.43272e57	0.376104
$283$	4.33569e57	1.04731	0.523657	−	0.851929i	$-0.324567\pi$
$283$	4.33569e57	1.04731	0.523657	+	0.851929i	$0.324567\pi$
$284$	−1.17107e57	−0.260376
$285$	4.34252e56	0.0888970
$286$	7.69505e57	1.45081
$287$	−8.65364e57	−1.50305
$288$	−1.94532e57	−0.311364
$289$	−5.13219e57	−0.757187
$290$	8.53657e55	0.0116126
$291$	−1.62101e57	−0.203377
$292$	−4.21657e56	−0.0488047
$293$	−1.05782e58	−1.12986	−0.564929	−	0.825140i	$-0.691096\pi$
$293$	−1.05782e58	−1.12986	−0.564929	+	0.825140i	$0.691096\pi$
$294$	−1.50099e58	−1.47984
$295$	3.89766e57	0.354802
$296$	−6.41596e57	−0.539395
$297$	2.15440e58	1.67321
$298$	1.32263e58	0.949199
$299$	−7.77470e57	−0.515716
$300$	−1.15441e58	−0.707961
$301$	4.03097e58	2.28611
$302$	−8.81067e57	−0.462217
$303$	−1.68472e58	−0.817762
$304$	−7.74069e56	−0.0347737
$305$	−1.10340e58	−0.458867
$306$	−1.59374e58	−0.613710
$307$	2.06877e58	0.737837	0.368919	−	0.929462i	$-0.379728\pi$
$307$	2.06877e58	0.737837	0.368919	+	0.929462i	$0.379728\pi$
$308$	3.00831e58	0.993988
$309$	3.91015e56	0.0119721
$310$	1.47156e58	0.417618
$311$	−2.39439e58	−0.629978	−0.314989	−	0.949095i	$-0.602001\pi$
$311$	−2.39439e58	−0.629978	−0.314989	+	0.949095i	$0.602001\pi$
$312$	3.73560e58	0.911437
$313$	−9.48940e57	−0.214757	−0.107378	−	0.994218i	$-0.534246\pi$
$313$	−9.48940e57	−0.214757	−0.107378	+	0.994218i	$0.534246\pi$
$314$	2.72473e58	0.572107
$315$	−5.22584e58	−1.01826
$316$	−1.27148e58	−0.229966
$317$	9.13985e58	1.53478	0.767391	−	0.641180i	$-0.221555\pi$
$317$	9.13985e58	1.53478	0.767391	+	0.641180i	$0.221555\pi$
$318$	−5.29300e58	−0.825400
$319$	3.89872e57	0.0564731
$320$	−3.57233e57	−0.0480758
$321$	−2.38117e59	−2.97799
$322$	−3.03945e58	−0.353332
$323$	−6.34170e57	−0.0685403
$324$	1.69629e58	0.170488
$325$	1.41400e59	1.32188
$326$	3.60592e58	0.313619
$327$	−4.80776e56	−0.00389108
$328$	4.69317e58	0.353534
$329$	−6.86064e58	−0.481129
$330$	9.15275e58	0.597687
$331$	−1.08997e59	−0.662911	−0.331456	−	0.943471i	$-0.607540\pi$
$331$	−1.08997e59	−0.662911	−0.331456	+	0.943471i	$0.607540\pi$
$332$	−1.66995e59	−0.946144
$333$	5.09019e59	2.68717
$334$	5.38372e57	0.0264875
$335$	1.49694e58	0.0686516
$336$	1.46040e59	0.624451
$337$	−2.00408e59	−0.799120	−0.399560	−	0.916707i	$-0.630837\pi$
$337$	−2.00408e59	−0.799120	−0.399560	+	0.916707i	$0.630837\pi$
$338$	−2.67444e59	−0.994695
$339$	−1.63962e58	−0.0568918
$340$	−2.92669e58	−0.0947594
$341$	6.72076e59	2.03091
$342$	6.14118e58	0.173236
$343$	1.48052e59	0.389945
$344$	−2.18613e59	−0.537716
$345$	−9.24750e58	−0.212459
$346$	−5.61533e59	−1.20528
$347$	−8.91525e59	−1.78810	−0.894048	−	0.447971i	$-0.852147\pi$
$347$	−8.91525e59	−1.78810	−0.894048	+	0.447971i	$0.852147\pi$
$348$	1.89265e58	0.0354780
$349$	−2.64940e59	−0.464248	−0.232124	−	0.972686i	$-0.574567\pi$
$349$	−2.64940e59	−0.464248	−0.232124	+	0.972686i	$0.574567\pi$
$350$	5.52792e59	0.905655
$351$	−1.28105e60	−1.96268
$352$	−1.63151e59	−0.233796
$353$	6.11122e59	0.819261	0.409630	−	0.912252i	$-0.365658\pi$
$353$	6.11122e59	0.819261	0.409630	+	0.912252i	$0.365658\pi$
$354$	8.64154e59	1.08396
$355$	1.70614e59	0.200285
$356$	7.59209e58	0.0834232
$357$	1.19646e60	1.23082
$358$	1.15804e60	1.11551
$359$	−2.33703e59	−0.210836	−0.105418	−	0.994428i	$-0.533618\pi$
$359$	−2.33703e59	−0.210836	−0.105418	+	0.994428i	$0.533618\pi$
$360$	2.83415e59	0.239505
$361$	−1.23861e60	−0.980653
$362$	7.77150e59	0.576572
$363$	1.79031e60	1.24487
$364$	−1.78881e60	−1.16595
$365$	6.14315e58	0.0375413
$366$	−2.44636e60	−1.40189
$367$	7.93168e59	0.426298	0.213149	−	0.977020i	$-0.431628\pi$
$367$	7.93168e59	0.426298	0.213149	+	0.977020i	$0.431628\pi$
$368$	1.64840e59	0.0831073
$369$	−3.72339e60	−1.76124
$370$	9.34747e59	0.414910
$371$	2.53457e60	1.05589
$372$	3.26262e60	1.27587
$373$	−2.14688e60	−0.788224	−0.394112	−	0.919062i	$-0.628948\pi$
$373$	−2.14688e60	−0.788224	−0.394112	+	0.919062i	$0.628948\pi$
$374$	−1.33664e60	−0.460822
$375$	3.65570e60	1.18368
$376$	3.72076e59	0.113166
$377$	−2.31826e59	−0.0662431
$378$	−5.00816e60	−1.34469
$379$	−5.45651e60	−1.37687	−0.688436	−	0.725297i	$-0.741702\pi$
$379$	−5.45651e60	−1.37687	−0.688436	+	0.725297i	$0.741702\pi$
$380$	1.12775e59	0.0267484
$381$	2.39237e60	0.533447
$382$	−3.17179e60	−0.664991
$383$	−2.64466e60	−0.521434	−0.260717	−	0.965415i	$-0.583959\pi$
$383$	−2.64466e60	−0.521434	−0.260717	+	0.965415i	$0.583959\pi$
$384$	−7.92025e59	−0.146877
$385$	−4.38283e60	−0.764589
$386$	5.83766e60	0.958158
$387$	1.73440e61	2.67880
$388$	−4.20975e59	−0.0611943
$389$	8.47705e60	1.15992	0.579962	−	0.814644i	$-0.303068\pi$
$389$	8.47705e60	1.15992	0.579962	+	0.814644i	$0.303068\pi$
$390$	−5.44242e60	−0.701090
$391$	1.35048e60	0.163808
$392$	−3.89806e60	−0.445272
$393$	−4.32740e60	−0.465588
$394$	6.54516e60	0.663375
$395$	1.85243e60	0.176893
$396$	1.29438e61	1.16473
$397$	−1.01947e61	−0.864568	−0.432284	−	0.901738i	$-0.642292\pi$
$397$	−1.01947e61	−0.864568	−0.432284	+	0.901738i	$0.642292\pi$
$398$	9.18963e60	0.734591
$399$	−4.61033e60	−0.347431
$400$	−2.99798e60	−0.213019
$401$	−2.08710e61	−1.39846	−0.699230	−	0.714897i	$-0.746474\pi$
$401$	−2.08710e61	−1.39846	−0.699230	+	0.714897i	$0.746474\pi$
$402$	3.31887e60	0.209739
$403$	−3.99630e61	−2.38226
$404$	−4.37521e60	−0.246058
$405$	−2.47134e60	−0.131141
$406$	−9.06305e59	−0.0453850
$407$	4.26907e61	2.01774
$408$	−6.48880e60	−0.289501
$409$	2.90356e61	1.22302	0.611509	−	0.791238i	$-0.290563\pi$
$409$	2.90356e61	1.22302	0.611509	+	0.791238i	$0.290563\pi$
$410$	−6.83752e60	−0.271943
$411$	−1.63581e61	−0.614397
$412$	1.01546e59	0.00360229
$413$	−4.13804e61	−1.38665
$414$	−1.30778e61	−0.414025
$415$	2.43296e61	0.727787
$416$	9.70131e60	0.274244
$417$	3.29616e61	0.880664
$418$	5.15051e60	0.130079
$419$	4.51827e61	1.07880	0.539402	−	0.842048i	$-0.318650\pi$
$419$	4.51827e61	1.07880	0.539402	+	0.842048i	$0.318650\pi$
$420$	−2.12767e61	−0.480336
$421$	6.03083e61	1.28750	0.643751	−	0.765235i	$-0.277377\pi$
$421$	6.03083e61	1.28750	0.643751	+	0.765235i	$0.277377\pi$
$422$	1.62258e61	0.327615
$423$	−2.95192e61	−0.563775
$424$	−1.37459e61	−0.248356
$425$	−2.45615e61	−0.419870
$426$	3.78270e61	0.611894
$427$	1.17145e62	1.79336
$428$	−6.18389e61	−0.896051
$429$	−2.48560e62	−3.40945
$430$	3.18499e61	0.413619
$431$	−2.84185e61	−0.349450	−0.174725	−	0.984617i	$-0.555904\pi$
$431$	−2.84185e61	−0.349450	−0.174725	+	0.984617i	$0.555904\pi$
$432$	2.71610e61	0.316284
$433$	9.49921e61	1.04766	0.523832	−	0.851822i	$-0.324502\pi$
$433$	9.49921e61	1.04766	0.523832	+	0.851822i	$0.324502\pi$
$434$	−1.56232e62	−1.63215
$435$	−2.75742e60	−0.0272901
$436$	−1.24857e59	−0.00117080
$437$	−5.20383e60	−0.0462391
$438$	1.36200e61	0.114693
$439$	−8.51566e61	−0.679676	−0.339838	−	0.940484i	$-0.610372\pi$
$439$	−8.51566e61	−0.679676	−0.339838	+	0.940484i	$0.610372\pi$
$440$	2.37696e61	0.179839
$441$	3.09258e62	2.21827
$442$	7.94797e61	0.540546
$443$	−2.00324e62	−1.29195	−0.645974	−	0.763360i	$-0.723548\pi$
$443$	−2.00324e62	−1.29195	−0.645974	+	0.763360i	$0.723548\pi$
$444$	2.07244e62	1.26760
$445$	−1.10610e61	−0.0641702
$446$	−6.06999e61	−0.334056
$447$	−4.27227e62	−2.23065
$448$	3.79264e61	0.187892
$449$	1.70791e62	0.802927	0.401463	−	0.915875i	$-0.368502\pi$
$449$	1.70791e62	0.802927	0.401463	+	0.915875i	$0.368502\pi$
$450$	2.37849e62	1.06122
$451$	−3.12275e62	−1.32248
$452$	−4.25807e60	−0.0171183
$453$	2.84596e62	1.08623
$454$	−1.82828e62	−0.662568
$455$	2.60613e62	0.896866
$456$	2.50034e61	0.0817194
$457$	6.09529e62	1.89219	0.946093	−	0.323895i	$-0.104993\pi$
$457$	6.09529e62	1.89219	0.946093	+	0.323895i	$0.104993\pi$
$458$	1.56810e62	0.462418
$459$	2.22521e62	0.623409
$460$	−2.40157e61	−0.0639272
$461$	−6.69058e62	−1.69236	−0.846179	−	0.532898i	$-0.821103\pi$
$461$	−6.69058e62	−1.69236	−0.846179	+	0.532898i	$0.821103\pi$
$462$	−9.71723e62	−2.33591
$463$	4.30318e62	0.983187	0.491593	−	0.870825i	$-0.336415\pi$
$463$	4.30318e62	0.983187	0.491593	+	0.870825i	$0.336415\pi$
$464$	4.91520e60	0.0106750
$465$	−4.75334e62	−0.981419
$466$	4.31779e62	0.847604
$467$	−5.60104e62	−1.04550	−0.522748	−	0.852487i	$-0.675093\pi$
$467$	−5.60104e62	−1.04550	−0.522748	+	0.852487i	$0.675093\pi$
$468$	−7.69666e62	−1.36623
$469$	−1.58926e62	−0.268307
$470$	−5.42081e61	−0.0870491
$471$	−8.80123e62	−1.34447
$472$	2.24420e62	0.326155
$473$	1.45461e63	2.01146
$474$	4.10704e62	0.540428
$475$	9.46432e61	0.118519
$476$	3.10719e62	0.370343
$477$	1.09055e63	1.23726
$478$	2.14076e62	0.231213
$479$	1.45521e63	1.49638	0.748190	−	0.663484i	$-0.230923\pi$
$479$	1.45521e63	1.49638	0.748190	+	0.663484i	$0.230923\pi$
$480$	1.15391e62	0.112980
$481$	−2.53848e63	−2.36681
$482$	−5.75331e62	−0.510872
$483$	9.81782e62	0.830343
$484$	4.64943e62	0.374571
$485$	6.13322e61	0.0470715
$486$	6.75495e62	0.493935
$487$	−1.24716e62	−0.0868944	−0.0434472	−	0.999056i	$-0.513834\pi$
$487$	−1.24716e62	−0.0868944	−0.0434472	+	0.999056i	$0.513834\pi$
$488$	−6.35317e62	−0.421818
$489$	−1.16476e63	−0.737017
$490$	5.67911e62	0.342510
$491$	9.69339e62	0.557263	0.278632	−	0.960398i	$-0.410119\pi$
$491$	9.69339e62	0.557263	0.278632	+	0.960398i	$0.410119\pi$
$492$	−1.51595e63	−0.830818
$493$	4.02687e61	0.0210409
$494$	−3.06260e62	−0.152584
$495$	−1.88579e63	−0.895926
$496$	8.47300e62	0.383900
$497$	−1.81136e63	−0.782762
$498$	5.39413e63	2.22347
$499$	−3.24859e63	−1.27742	−0.638708	−	0.769449i	$-0.720531\pi$
$499$	−3.24859e63	−1.27742	−0.638708	+	0.769449i	$0.720531\pi$
$500$	9.49382e62	0.356161
$501$	−1.73901e62	−0.0622466
$502$	−3.57690e63	−1.22171
$503$	−2.69774e63	−0.879330	−0.439665	−	0.898162i	$-0.644903\pi$
$503$	−2.69774e63	−0.879330	−0.439665	+	0.898162i	$0.644903\pi$
$504$	−3.00894e63	−0.936044
$505$	6.37428e62	0.189271
$506$	−1.09682e63	−0.310883
$507$	8.63877e63	2.33757
$508$	6.21296e62	0.160510
$509$	6.02700e63	1.48673	0.743366	−	0.668884i	$-0.233228\pi$
$509$	6.02700e63	1.48673	0.743366	+	0.668884i	$0.233228\pi$
$510$	9.45358e62	0.222688
$511$	−6.52201e62	−0.146720
$512$	−2.05688e62	−0.0441942
$513$	−8.57445e62	−0.175974
$514$	−4.59783e63	−0.901404
$515$	−1.47943e61	−0.00277093
$516$	7.06148e63	1.26365
$517$	−2.47573e63	−0.423326
$518$	−9.92395e63	−1.62157
$519$	1.81382e64	2.83245
$520$	−1.41339e63	−0.210952
$521$	1.33678e63	0.190710	0.0953548	−	0.995443i	$-0.469601\pi$
$521$	1.33678e63	0.190710	0.0953548	+	0.995443i	$0.469601\pi$
$522$	−3.89954e62	−0.0531810
$523$	−8.20599e63	−1.06989	−0.534947	−	0.844885i	$-0.679669\pi$
$523$	−8.20599e63	−1.06989	−0.534947	+	0.844885i	$0.679669\pi$
$524$	−1.12382e63	−0.140092
$525$	−1.78559e64	−2.12832
$526$	9.92787e63	1.13159
$527$	6.94165e63	0.756682
$528$	5.26999e63	0.549430
$529$	−8.91969e63	−0.889491
$530$	2.00265e63	0.191039
$531$	−1.78047e64	−1.62485
$532$	−1.19730e63	−0.104539
$533$	1.85685e64	1.55127
$534$	−2.45234e63	−0.196048
$535$	9.00935e63	0.689255
$536$	8.61908e62	0.0631086
$537$	−3.74062e64	−2.62149
$538$	1.73579e62	0.0116443
$539$	2.59370e64	1.66565
$540$	−3.95711e63	−0.243290
$541$	−6.23992e62	−0.0367319	−0.0183660	−	0.999831i	$-0.505846\pi$
$541$	−6.23992e62	−0.0367319	−0.0183660	+	0.999831i	$0.505846\pi$
$542$	−2.41985e64	−1.36397
$543$	−2.51029e64	−1.35497
$544$	−1.68514e63	−0.0871085
$545$	1.81905e61	0.000900591 0
$546$	5.77807e64	2.74003
$547$	3.05397e64	1.38727	0.693636	−	0.720325i	$-0.256007\pi$
$547$	3.05397e64	1.38727	0.693636	+	0.720325i	$0.256007\pi$
$548$	−4.24817e63	−0.184867
$549$	5.04038e64	2.10142
$550$	1.99480e64	0.796850
$551$	−1.55168e62	−0.00593936
$552$	−5.32454e63	−0.195305
$553$	−1.96667e64	−0.691340
$554$	3.73917e62	0.0125978
$555$	−3.01935e64	−0.975053
$556$	8.56009e63	0.264985
$557$	3.06228e64	0.908758	0.454379	−	0.890809i	$-0.349861\pi$
$557$	3.06228e64	0.908758	0.454379	+	0.890809i	$0.349861\pi$
$558$	−6.72217e64	−1.91252
$559$	−8.64943e64	−2.35945
$560$	−5.52553e63	−0.144529
$561$	4.31753e64	1.08295
$562$	−5.43418e63	−0.130717
$563$	−1.53750e64	−0.354705	−0.177353	−	0.984147i	$-0.556753\pi$
$563$	−1.53750e64	−0.354705	−0.177353	+	0.984147i	$0.556753\pi$
$564$	−1.20185e64	−0.265945
$565$	6.20362e62	0.0131676
$566$	−3.63704e64	−0.740563
$567$	2.62376e64	0.512533
$568$	9.82363e63	0.184114
$569$	−9.13382e63	−0.164253	−0.0821266	−	0.996622i	$-0.526171\pi$
$569$	−9.13382e63	−0.164253	−0.0821266	+	0.996622i	$0.526171\pi$
$570$	−3.64277e63	−0.0628597
$571$	4.20849e64	0.696911	0.348456	−	0.937325i	$-0.386706\pi$
$571$	4.20849e64	0.696911	0.348456	+	0.937325i	$0.386706\pi$
$572$	−6.45507e64	−1.02588
$573$	1.02453e65	1.56275
$574$	7.25920e64	1.06282
$575$	−2.01545e64	−0.283255
$576$	1.63185e64	0.220167
$577$	1.16840e65	1.51342	0.756709	−	0.653752i	$-0.226806\pi$
$577$	1.16840e65	1.51342	0.756709	+	0.653752i	$0.226806\pi$
$578$	4.30519e64	0.535412
$579$	−1.88564e65	−2.25171
$580$	−7.16100e62	−0.00821137
$581$	−2.58300e65	−2.84437
$582$	1.35980e64	0.143809
$583$	9.14625e64	0.929035
$584$	3.53711e63	0.0345102
$585$	1.12133e65	1.05093
$586$	8.87366e64	0.798930
$587$	1.22823e65	1.06239	0.531197	−	0.847248i	$-0.321742\pi$
$587$	1.22823e65	1.06239	0.531197	+	0.847248i	$0.321742\pi$
$588$	1.25912e65	1.04641
$589$	−2.67484e64	−0.213594
$590$	−3.26959e64	−0.250883
$591$	−2.11417e65	−1.55896
$592$	5.38210e64	0.381410
$593$	2.18247e65	1.48649	0.743245	−	0.669019i	$-0.233286\pi$
$593$	2.18247e65	1.48649	0.743245	+	0.669019i	$0.233286\pi$
$594$	−1.80724e65	−1.18314
$595$	−4.52689e64	−0.284873
$596$	−1.10950e65	−0.671185
$597$	−2.96836e65	−1.72632
$598$	6.52189e64	0.364667
$599$	1.76834e65	0.950684	0.475342	−	0.879801i	$-0.342324\pi$
$599$	1.76834e65	0.950684	0.475342	+	0.879801i	$0.342324\pi$
$600$	9.68386e64	0.500604
$601$	−1.41803e65	−0.704912	−0.352456	−	0.935828i	$-0.614653\pi$
$601$	−1.41803e65	−0.704912	−0.352456	+	0.935828i	$0.614653\pi$
$602$	−3.38142e65	−1.61652
$603$	−6.83807e64	−0.314396
$604$	7.39093e64	0.326837
$605$	−6.77379e64	−0.288125
$606$	1.41325e65	0.578245
$607$	1.14990e65	0.452610	0.226305	−	0.974056i	$-0.427335\pi$
$607$	1.14990e65	0.452610	0.226305	+	0.974056i	$0.427335\pi$
$608$	6.49336e63	0.0245887
$609$	2.92748e64	0.106656
$610$	9.25599e64	0.324468
$611$	1.47212e65	0.496563
$612$	1.33692e65	0.433959
$613$	−9.28200e64	−0.289948	−0.144974	−	0.989435i	$-0.546310\pi$
$613$	−9.28200e64	−0.289948	−0.144974	+	0.989435i	$0.546310\pi$
$614$	−1.73541e65	−0.521730
$615$	2.20860e65	0.639076
$616$	−2.52355e65	−0.702855
$617$	5.27493e65	1.41421	0.707107	−	0.707107i	$-0.250000\pi$
$617$	5.27493e65	1.41421	0.707107	+	0.707107i	$0.250000\pi$
$618$	−3.28007e63	−0.00846552
$619$	−1.15047e65	−0.285854	−0.142927	−	0.989733i	$-0.545651\pi$
$619$	−1.15047e65	−0.285854	−0.142927	+	0.989733i	$0.545651\pi$
$620$	−1.23444e65	−0.295301
$621$	1.82595e65	0.420568
$622$	2.00856e65	0.445462
$623$	1.17431e65	0.250793
$624$	−3.13364e65	−0.644484
$625$	2.91873e65	0.578114
$626$	7.96029e64	0.151856
$627$	−1.66368e65	−0.305691
$628$	−2.28567e65	−0.404541
$629$	4.40938e65	0.751774
$630$	4.38375e65	0.720018
$631$	−4.57574e65	−0.724054	−0.362027	−	0.932168i	$-0.617915\pi$
$631$	−4.57574e65	−0.724054	−0.362027	+	0.932168i	$0.617915\pi$
$632$	1.06659e65	0.162610
$633$	−5.24114e65	−0.769907
$634$	−7.66706e65	−1.08525
$635$	−9.05172e64	−0.123466
$636$	4.44009e65	0.583646
$637$	−1.54227e66	−1.95381
$638$	−3.27049e64	−0.0399325
$639$	−7.79371e65	−0.917221
$640$	2.99669e64	0.0339948
$641$	−9.71867e65	−1.06278	−0.531390	−	0.847128i	$-0.678330\pi$
$641$	−9.71867e65	−1.06278	−0.531390	+	0.847128i	$0.678330\pi$
$642$	1.99747e66	2.10575
$643$	2.57162e65	0.261366	0.130683	−	0.991424i	$-0.458283\pi$
$643$	2.57162e65	0.261366	0.130683	+	0.991424i	$0.458283\pi$
$644$	2.54968e65	0.249843
$645$	−1.02879e66	−0.972019
$646$	5.31980e64	0.0484653
$647$	2.26973e66	1.99400	0.996998	−	0.0774314i	$-0.0246719\pi$
$647$	2.26973e66	1.99400	0.996998	+	0.0774314i	$0.0246719\pi$
$648$	−1.42295e65	−0.120553
$649$	−1.49325e66	−1.22006
$650$	−1.18615e66	−0.934709
$651$	5.04649e66	3.83563
$652$	−3.02487e65	−0.221762
$653$	1.60777e66	1.13701	0.568504	−	0.822681i	$-0.307522\pi$
$653$	1.60777e66	1.13701	0.568504	+	0.822681i	$0.307522\pi$
$654$	4.03304e63	0.00275141
$655$	1.63730e65	0.107760
$656$	−3.93692e65	−0.249986
$657$	−2.80622e65	−0.171923
$658$	5.75512e65	0.340209
$659$	−3.20448e66	−1.82789	−0.913946	−	0.405835i	$-0.866981\pi$
$659$	−3.20448e66	−1.82789	−0.913946	+	0.405835i	$0.866981\pi$
$660$	−7.67789e65	−0.422629
$661$	6.38586e65	0.339223	0.169611	−	0.985511i	$-0.445749\pi$
$661$	6.38586e65	0.339223	0.169611	+	0.985511i	$0.445749\pi$
$662$	9.14330e65	0.468749
$663$	−2.56729e66	−1.27030
$664$	1.40085e66	0.669025
$665$	1.74435e65	0.0804129
$666$	−4.26996e66	−1.90011
$667$	3.30434e64	0.0141948
$668$	−4.51619e64	−0.0187295
$669$	1.96068e66	0.785044
$670$	−1.25572e65	−0.0485440
$671$	4.22729e66	1.57791
$672$	−1.22507e66	−0.441554
$673$	−2.24978e66	−0.783043	−0.391521	−	0.920169i	$-0.628051\pi$
$673$	−2.24978e66	−0.783043	−0.391521	+	0.920169i	$0.628051\pi$
$674$	1.68114e66	0.565063
$675$	−3.32090e66	−1.07800
$676$	2.24348e66	0.703356
$677$	−4.79933e65	−0.145327	−0.0726636	−	0.997357i	$-0.523150\pi$
$677$	−4.79933e65	−0.145327	−0.0726636	+	0.997357i	$0.523150\pi$
$678$	1.37541e65	0.0402286
$679$	−6.51147e65	−0.183967
$680$	2.45509e65	0.0670050
$681$	5.90558e66	1.55706
$682$	−5.63778e66	−1.43607
$683$	−4.30311e66	−1.05900	−0.529500	−	0.848310i	$-0.677621\pi$
$683$	−4.30311e66	−1.05900	−0.529500	+	0.848310i	$0.677621\pi$
$684$	−5.15160e65	−0.122496
$685$	6.18920e65	0.142202
$686$	−1.24195e66	−0.275733
$687$	−5.06515e66	−1.08670
$688$	1.83386e66	0.380223
$689$	−5.43855e66	−1.08976
$690$	7.75737e65	0.150231
$691$	8.37771e66	1.56816	0.784081	−	0.620658i	$-0.213135\pi$
$691$	8.37771e66	1.56816	0.784081	+	0.620658i	$0.213135\pi$
$692$	4.71048e66	0.852259
$693$	2.00210e67	3.50150
$694$	7.47865e66	1.26437
$695$	−1.24713e66	−0.203830
$696$	−1.58767e65	−0.0250867
$697$	−3.22539e66	−0.492733
$698$	2.22248e66	0.328273
$699$	−1.39470e67	−1.99190
$700$	−4.63716e66	−0.640395
$701$	−1.18236e67	−1.57898	−0.789489	−	0.613765i	$-0.789654\pi$
$701$	−1.18236e67	−1.57898	−0.789489	+	0.613765i	$0.789654\pi$
$702$	1.07463e67	1.38783
$703$	−1.69907e66	−0.212208
$704$	1.36861e66	0.165319
$705$	1.75099e66	0.204569
$706$	−5.12646e66	−0.579305
$707$	−6.76740e66	−0.739717
$708$	−7.24905e66	−0.766478
$709$	8.35736e66	0.854836	0.427418	−	0.904054i	$-0.359423\pi$
$709$	8.35736e66	0.854836	0.427418	+	0.904054i	$0.359423\pi$
$710$	−1.43121e66	−0.141623
$711$	−8.46197e66	−0.810095
$712$	−6.36871e65	−0.0589891
$713$	5.69614e66	0.510478
$714$	−1.00366e67	−0.870320
$715$	9.40445e66	0.789117
$716$	−9.71436e66	−0.788784
$717$	−6.91492e66	−0.543359
$718$	1.96045e66	0.149084
$719$	1.29585e67	0.953731	0.476865	−	0.878976i	$-0.341773\pi$
$719$	1.29585e67	0.953731	0.476865	+	0.878976i	$0.341773\pi$
$720$	−2.37746e66	−0.169356
$721$	1.57067e65	0.0108295
$722$	1.03902e67	0.693426
$723$	1.85839e67	1.20057
$724$	−6.51921e66	−0.407698
$725$	−6.00968e65	−0.0363838
$726$	−1.50182e67	−0.880255
$727$	6.75407e66	0.383272	0.191636	−	0.981466i	$-0.438621\pi$
$727$	6.75407e66	0.383272	0.191636	+	0.981466i	$0.438621\pi$
$728$	1.50056e67	0.824452
$729$	−2.82288e67	−1.50174
$730$	−5.15325e65	−0.0265457
$731$	1.50242e67	0.749435
$732$	2.05216e67	0.991288
$733$	3.49174e67	1.63342	0.816711	−	0.577047i	$-0.195795\pi$
$733$	3.49174e67	1.63342	0.816711	+	0.577047i	$0.195795\pi$
$734$	−6.65358e66	−0.301438
$735$	−1.83443e67	−0.804910
$736$	−1.38278e66	−0.0587657
$737$	−5.73498e66	−0.236073
$738$	3.12341e67	1.24539
$739$	2.87820e66	0.111167	0.0555835	−	0.998454i	$-0.482298\pi$
$739$	2.87820e66	0.111167	0.0555835	+	0.998454i	$0.482298\pi$
$740$	−7.84123e66	−0.293385
$741$	9.89260e66	0.358577
$742$	−2.12615e67	−0.746626
$743$	−1.55726e66	−0.0529814	−0.0264907	−	0.999649i	$-0.508433\pi$
$743$	−1.55726e66	−0.0529814	−0.0264907	+	0.999649i	$0.508433\pi$
$744$	−2.73689e67	−0.902179
$745$	1.61645e67	0.516284
$746$	1.80093e67	0.557359
$747$	−1.11138e68	−3.33296
$748$	1.12126e67	0.325850
$749$	−9.56498e67	−2.69378
$750$	−3.06662e67	−0.836991
$751$	4.80070e67	1.26989	0.634946	−	0.772557i	$-0.281023\pi$
$751$	4.80070e67	1.26989	0.634946	+	0.772557i	$0.281023\pi$
$752$	−3.12120e66	−0.0800207
$753$	1.15538e68	2.87107
$754$	1.94470e66	0.0468410
$755$	−1.07679e67	−0.251407
$756$	4.20115e67	0.950838
$757$	−3.04494e67	−0.668076	−0.334038	−	0.942560i	$-0.608411\pi$
$757$	−3.04494e67	−0.668076	−0.334038	+	0.942560i	$0.608411\pi$
$758$	4.57725e67	0.973595
$759$	3.54285e67	0.730586
$760$	−9.46023e65	−0.0189140
$761$	−8.19495e67	−1.58857	−0.794286	−	0.607544i	$-0.792155\pi$
$761$	−8.19495e67	−1.58857	−0.794286	+	0.607544i	$0.792155\pi$
$762$	−2.00687e67	−0.377204
$763$	−1.93124e65	−0.00351973
$764$	2.66069e67	0.470220
$765$	−1.94778e67	−0.333807
$766$	2.21850e67	0.368709
$767$	8.87918e67	1.43114
$768$	6.64398e66	0.103858
$769$	−8.58726e67	−1.30192	−0.650962	−	0.759110i	$-0.725634\pi$
$769$	−8.58726e67	−1.30192	−0.650962	+	0.759110i	$0.725634\pi$
$770$	3.67659e67	0.540646
$771$	1.48516e68	2.11833
$772$	−4.89698e67	−0.677520
$773$	−5.74418e67	−0.770921	−0.385460	−	0.922724i	$-0.625957\pi$
$773$	−5.74418e67	−0.770921	−0.385460	+	0.922724i	$0.625957\pi$
$774$	−1.45492e68	−1.89420
$775$	−1.03597e68	−1.30845
$776$	3.53140e66	0.0432709
$777$	3.20556e68	3.81075
$778$	−7.11107e67	−0.820189
$779$	1.24284e67	0.139087
$780$	4.56543e67	0.495745
$781$	−6.53646e67	−0.688721
$782$	−1.13287e67	−0.115830
$783$	5.44463e66	0.0540215
$784$	3.26993e67	0.314855
$785$	3.33001e67	0.311178
$786$	3.63008e67	0.329221
$787$	1.78281e68	1.56928	0.784638	−	0.619954i	$-0.212849\pi$
$787$	1.78281e68	1.56928	0.784638	+	0.619954i	$0.212849\pi$
$788$	−5.49048e67	−0.469077
$789$	−3.20683e68	−2.65929
$790$	−1.55393e67	−0.125082
$791$	−6.58621e66	−0.0514622
$792$	−1.08581e68	−0.823589
$793$	−2.51363e68	−1.85090
$794$	8.55196e67	0.611342
$795$	−6.46880e67	−0.448948
$796$	−7.70882e67	−0.519434
$797$	7.67558e67	0.502158	0.251079	−	0.967967i	$-0.419215\pi$
$797$	7.67558e67	0.502158	0.251079	+	0.967967i	$0.419215\pi$
$798$	3.86742e67	0.245671
$799$	−2.55710e67	−0.157724
$800$	2.51489e67	0.150627
$801$	5.05270e67	0.293873
$802$	1.75078e68	0.988860
$803$	−2.35353e67	−0.129094
$804$	−2.78407e67	−0.148308
$805$	−3.71465e67	−0.192183
$806$	3.35234e68	1.68451
$807$	−5.60681e66	−0.0273645
$808$	3.67019e67	0.173989
$809$	1.39305e68	0.641472	0.320736	−	0.947169i	$-0.396070\pi$
$809$	1.39305e68	0.641472	0.320736	+	0.947169i	$0.396070\pi$
$810$	2.07311e67	0.0927310
$811$	6.57381e67	0.285645	0.142823	−	0.989748i	$-0.454382\pi$
$811$	6.57381e67	0.285645	0.142823	+	0.989748i	$0.454382\pi$
$812$	7.60263e66	0.0320920
$813$	7.81642e68	3.20538
$814$	−3.58115e68	−1.42675
$815$	4.40695e67	0.170582
$816$	5.44320e67	0.204708
$817$	−5.78931e67	−0.211548
$818$	−2.43568e68	−0.864804
$819$	−1.19049e69	−4.10727
$820$	5.73572e67	0.192293
$821$	2.60915e68	0.850030	0.425015	−	0.905186i	$-0.360269\pi$
$821$	2.60915e68	0.850030	0.425015	+	0.905186i	$0.360269\pi$
$822$	1.37221e68	0.434444
$823$	2.86763e68	0.882322	0.441161	−	0.897428i	$-0.354567\pi$
$823$	2.86763e68	0.882322	0.441161	+	0.897428i	$0.354567\pi$
$824$	−8.51831e65	−0.00254720
$825$	−6.44346e68	−1.87263
$826$	3.47124e68	0.980513
$827$	−2.35931e68	−0.647747	−0.323873	−	0.946100i	$-0.604985\pi$
$827$	−2.35931e68	−0.647747	−0.323873	+	0.946100i	$0.604985\pi$
$828$	1.09705e68	0.292760
$829$	8.80819e67	0.228484	0.114242	−	0.993453i	$-0.463556\pi$
$829$	8.80819e67	0.228484	0.114242	+	0.993453i	$0.463556\pi$
$830$	−2.04091e68	−0.514623
$831$	−1.20780e67	−0.0296054
$832$	−8.13805e67	−0.193920
$833$	2.67895e68	0.620592
$834$	−2.76502e68	−0.622724
$835$	6.57968e66	0.0144070
$836$	−4.32056e67	−0.0919799
$837$	9.38564e68	1.94274
$838$	−3.79020e68	−0.762830
$839$	−2.99608e68	−0.586337	−0.293168	−	0.956061i	$-0.594710\pi$
$839$	−2.99608e68	−0.586337	−0.293168	+	0.956061i	$0.594710\pi$
$840$	1.78482e68	0.339649
$841$	−5.39403e68	−0.998177
$842$	−5.05903e68	−0.910401
$843$	1.75531e68	0.307189
$844$	−1.36112e68	−0.231659
$845$	−3.26855e68	−0.541031
$846$	2.47625e68	0.398649
$847$	7.19155e68	1.12606
$848$	1.15309e68	0.175614
$849$	1.17481e69	1.74035
$850$	2.06037e68	0.296893
$851$	3.61822e68	0.507167
$852$	−3.17316e68	−0.432674
$853$	9.47738e68	1.25715	0.628573	−	0.777750i	$-0.283639\pi$
$853$	9.47738e68	1.25715	0.628573	+	0.777750i	$0.283639\pi$
$854$	−9.82683e68	−1.26810
$855$	7.50540e67	0.0942259
$856$	5.18742e68	0.633604
$857$	−9.55995e68	−1.13607	−0.568037	−	0.823003i	$-0.692297\pi$
$857$	−9.55995e68	−1.13607	−0.568037	+	0.823003i	$0.692297\pi$
$858$	2.08507e69	2.41085
$859$	−4.21759e68	−0.474488	−0.237244	−	0.971450i	$-0.576244\pi$
$859$	−4.21759e68	−0.474488	−0.237244	+	0.971450i	$0.576244\pi$
$860$	−2.67177e68	−0.292472
$861$	−2.34481e69	−2.49767
$862$	2.38391e68	0.247098
$863$	9.19093e68	0.927055	0.463528	−	0.886082i	$-0.346583\pi$
$863$	9.19093e68	0.927055	0.463528	+	0.886082i	$0.346583\pi$
$864$	−2.27843e68	−0.223647
$865$	−6.86273e68	−0.655569
$866$	−7.96851e68	−0.740810
$867$	−1.39063e69	−1.25824
$868$	1.31057e69	1.15411
$869$	−7.09693e68	−0.608283
$870$	2.31309e67	0.0192970
$871$	3.41014e68	0.276914
$872$	1.04738e66	0.000827877 0
$873$	−2.80168e68	−0.215568
$874$	4.36529e67	0.0326960
$875$	1.46847e69	1.07072
$876$	−1.14253e68	−0.0811002
$877$	1.86631e69	1.28971	0.644855	−	0.764305i	$-0.276918\pi$
$877$	1.86631e69	1.28971	0.644855	+	0.764305i	$0.276918\pi$
$878$	7.14346e68	0.480604
$879$	−2.86630e69	−1.87752
$880$	−1.99394e68	−0.127166
$881$	6.60423e68	0.410098	0.205049	−	0.978752i	$-0.434265\pi$
$881$	6.60423e68	0.410098	0.205049	+	0.978752i	$0.434265\pi$
$882$	−2.59424e69	−1.56855
$883$	−8.14396e68	−0.479467	−0.239734	−	0.970839i	$-0.577060\pi$
$883$	−8.14396e68	−0.479467	−0.239734	+	0.970839i	$0.577060\pi$
$884$	−6.66724e68	−0.382224
$885$	1.05612e69	0.589585
$886$	1.68044e69	0.913545
$887$	−1.87041e68	−0.0990221	−0.0495110	−	0.998774i	$-0.515766\pi$
$887$	−1.87041e68	−0.0990221	−0.0495110	+	0.998774i	$0.515766\pi$
$888$	−1.73849e69	−0.896327
$889$	9.60996e68	0.482537
$890$	9.27863e67	0.0453752
$891$	9.46807e68	0.450957
$892$	5.09188e68	0.236213
$893$	9.85332e67	0.0445218
$894$	3.58384e69	1.57731
$895$	1.41529e69	0.606743
$896$	−3.18150e68	−0.132860
$897$	−2.10665e69	−0.856980
$898$	−1.43270e69	−0.567755
$899$	1.69848e68	0.0655702
$900$	−1.99522e69	−0.750399
$901$	9.44686e68	0.346143
$902$	2.61955e69	0.935133
$903$	1.09224e70	3.79889
$904$	3.57193e67	0.0121044
$905$	9.49788e68	0.313607
$906$	−2.38736e69	−0.768079
$907$	−6.31631e69	−1.98012	−0.990062	−	0.140631i	$-0.955087\pi$
$907$	−6.31631e69	−1.98012	−0.990062	+	0.140631i	$0.955087\pi$
$908$	1.53367e69	0.468507
$909$	−2.91180e69	−0.866782
$910$	−2.18618e69	−0.634180
$911$	2.58489e69	0.730736	0.365368	−	0.930863i	$-0.380943\pi$
$911$	2.58489e69	0.730736	0.365368	+	0.930863i	$0.380943\pi$
$912$	−2.09744e68	−0.0577844
$913$	−9.32101e69	−2.50265
$914$	−5.11310e69	−1.33798
$915$	−2.98980e69	−0.762512
$916$	−1.31542e69	−0.326979
$917$	−1.73828e69	−0.421154
$918$	−1.86664e69	−0.440817
$919$	8.65693e68	0.199273	0.0996367	−	0.995024i	$-0.468232\pi$
$919$	8.65693e68	0.199273	0.0996367	+	0.995024i	$0.468232\pi$
$920$	2.01458e68	0.0452034
$921$	5.60559e69	1.22608
$922$	5.61247e69	1.19668
$923$	3.88672e69	0.807873
$924$	8.15140e69	1.65174
$925$	−6.58054e69	−1.29996
$926$	−3.60977e69	−0.695218
$927$	6.75811e67	0.0126897
$928$	−4.12317e67	−0.00754838
$929$	7.30808e69	1.30447	0.652235	−	0.758017i	$-0.273831\pi$
$929$	7.30808e69	1.30447	0.652235	+	0.758017i	$0.273831\pi$
$930$	3.98739e69	0.693968
$931$	−1.03228e69	−0.175179
$932$	−3.62203e69	−0.599346
$933$	−6.48789e69	−1.04685
$934$	4.69850e69	0.739277
$935$	−1.63357e69	−0.250648
$936$	6.45643e69	0.966073
$937$	8.40248e69	1.22610	0.613052	−	0.790043i	$-0.289942\pi$
$937$	8.40248e69	1.22610	0.613052	+	0.790043i	$0.289942\pi$
$938$	1.33316e69	0.189722
$939$	−2.57127e69	−0.356867
$940$	4.54730e68	0.0615530
$941$	−4.67075e69	−0.616638	−0.308319	−	0.951283i	$-0.599766\pi$
$941$	−4.67075e69	−0.616638	−0.308319	+	0.951283i	$0.599766\pi$
$942$	7.38300e69	0.950686
$943$	−2.64667e69	−0.332411
$944$	−1.88257e69	−0.230627
$945$	−6.12069e69	−0.731397
$946$	−1.22022e70	−1.42231
$947$	−1.91649e69	−0.217912	−0.108956	−	0.994047i	$-0.534751\pi$
$947$	−1.91649e69	−0.217912	−0.108956	+	0.994047i	$0.534751\pi$
$948$	−3.44523e69	−0.382140
$949$	1.39946e69	0.151427
$950$	−7.93925e68	−0.0838059
$951$	2.47656e70	2.55039
$952$	−2.60650e69	−0.261872
$953$	8.83831e69	0.866336	0.433168	−	0.901313i	$-0.357396\pi$
$953$	8.83831e69	0.866336	0.433168	+	0.901313i	$0.357396\pi$
$954$	−9.14817e69	−0.874878
$955$	−3.87638e69	−0.361699
$956$	−1.79580e69	−0.163492
$957$	1.05641e69	0.0938428
$958$	−1.22072e70	−1.05810
$959$	−6.57090e69	−0.555761
$960$	−9.67967e68	−0.0798889
$961$	1.68624e70	1.35806
$962$	2.12943e70	1.67359
$963$	−4.11551e70	−3.15650
$964$	4.82623e69	0.361241
$965$	7.13445e69	0.521157
$966$	−8.23578e69	−0.587141
$967$	−1.45957e70	−1.01556	−0.507778	−	0.861488i	$-0.669533\pi$
$967$	−1.45957e70	−1.01556	−0.507778	+	0.861488i	$0.669533\pi$
$968$	−3.90023e69	−0.264862
$969$	−1.71836e69	−0.113895
$970$	−5.14492e68	−0.0332846
$971$	−1.63771e70	−1.03415	−0.517077	−	0.855939i	$-0.672980\pi$
$971$	−1.63771e70	−1.03415	−0.517077	+	0.855939i	$0.672980\pi$
$972$	−5.66646e69	−0.349265
$973$	1.32404e70	0.796616
$974$	1.04619e69	0.0614436
$975$	3.83142e70	2.19660
$976$	5.32943e69	0.298270
$977$	2.81412e70	1.53752	0.768758	−	0.639540i	$-0.220875\pi$
$977$	2.81412e70	1.53752	0.768758	+	0.639540i	$0.220875\pi$
$978$	9.77070e69	0.521150
$979$	4.23762e69	0.220663
$980$	−4.76399e69	−0.242191
$981$	−8.30951e67	−0.00412433
$982$	−8.13140e69	−0.394045
$983$	−2.50839e70	−1.18683	−0.593414	−	0.804898i	$-0.702220\pi$
$983$	−2.50839e70	−1.18683	−0.593414	+	0.804898i	$0.702220\pi$
$984$	1.27167e70	0.587477
$985$	7.99913e69	0.360821
$986$	−3.37798e68	−0.0148782
$987$	−1.85898e70	−0.799505
$988$	2.56910e69	0.107893
$989$	1.23285e70	0.505588
$990$	1.58192e70	0.633515
$991$	1.15349e70	0.451111	0.225556	−	0.974230i	$-0.427580\pi$
$991$	1.15349e70	0.451111	0.225556	+	0.974230i	$0.427580\pi$
$992$	−7.10767e69	−0.271458
$993$	−2.95340e70	−1.10158
$994$	1.51948e70	0.553496
$995$	1.12310e70	0.399556
$996$	−4.52493e70	−1.57223
$997$	−1.95619e70	−0.663858	−0.331929	−	0.943304i	$-0.607699\pi$
$997$	−1.95619e70	−0.663858	−0.331929	+	0.943304i	$0.607699\pi$
$998$	2.72512e70	0.903270
$999$	5.96181e70	1.93014

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2.48.a.b.1.2	✓	2
4.3	odd	2		16.48.a.b.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2.48.a.b.1.2	✓	2	1.1	even	1	trivial
16.48.a.b.1.1		2	4.3	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 2 \)
Weight:	\( k \)	\(=\)	\( 48 \)
Character orbit:	\([\chi]\)	\(=\)	2.a (trivial)

\(f(q)\)	\(=\)	\(q-8.38861e6 q^{2} +2.70963e11 q^{3} +7.03687e13 q^{4} -1.02521e16 q^{5} -2.27300e18 q^{6} +1.08843e20 q^{7} -5.90296e20 q^{8} +4.68319e22 q^{9} +O(q^{10})\)	\(q-8.38861e6 q^{2} +2.70963e11 q^{3} +7.03687e13 q^{4} -1.02521e16 q^{5} -2.27300e18 q^{6} +1.08843e20 q^{7} -5.90296e20 q^{8} +4.68319e22 q^{9} +8.60007e22 q^{10} +3.92772e24 q^{11} +1.90673e25 q^{12} -2.33551e26 q^{13} -9.13045e26 q^{14} -2.77793e27 q^{15} +4.95176e27 q^{16} +4.05682e28 q^{17} -3.92855e29 q^{18} -1.56322e29 q^{19} -7.21426e29 q^{20} +2.94925e31 q^{21} -3.29481e31 q^{22} +3.32892e31 q^{23} -1.59948e32 q^{24} -6.05438e32 q^{25} +1.95916e33 q^{26} +5.48512e33 q^{27} +7.65918e33 q^{28} +9.92617e32 q^{29} +2.33030e34 q^{30} +1.71111e35 q^{31} -4.15384e34 q^{32} +1.06427e36 q^{33} -3.40310e35 q^{34} -1.11587e36 q^{35} +3.29550e36 q^{36} +1.08691e37 q^{37} +1.31132e36 q^{38} -6.32835e37 q^{39} +6.05176e36 q^{40} -7.95054e37 q^{41} -2.47401e38 q^{42} +3.70345e38 q^{43} +2.76389e38 q^{44} -4.80124e38 q^{45} -2.79250e38 q^{46} -6.30322e38 q^{47} +1.34174e39 q^{48} +6.60357e39 q^{49} +5.07878e39 q^{50} +1.09925e40 q^{51} -1.64347e40 q^{52} +2.32864e40 q^{53} -4.60125e40 q^{54} -4.02673e40 q^{55} -6.42499e40 q^{56} -4.23574e40 q^{57} -8.32668e39 q^{58} -3.80182e41 q^{59} -1.95479e41 q^{60} +1.07627e42 q^{61} -1.43538e42 q^{62} +5.09735e42 q^{63} +3.48449e41 q^{64} +2.39438e42 q^{65} -8.92770e42 q^{66} -1.46013e42 q^{67} +2.85473e42 q^{68} +9.02012e42 q^{69} +9.36061e42 q^{70} -1.66419e43 q^{71} -2.76447e43 q^{72} -5.99210e42 q^{73} -9.11763e43 q^{74} -1.64051e44 q^{75} -1.10002e43 q^{76} +4.27507e44 q^{77} +5.30860e44 q^{78} -1.80688e44 q^{79} -5.07658e43 q^{80} +2.41058e44 q^{81} +6.66940e44 q^{82} -2.37314e45 q^{83} +2.07535e45 q^{84} -4.15908e44 q^{85} -3.10668e45 q^{86} +2.68962e44 q^{87} -2.31852e45 q^{88} +1.07890e45 q^{89} +4.02758e45 q^{90} -2.54205e46 q^{91} +2.34252e45 q^{92} +4.63646e46 q^{93} +5.28752e45 q^{94} +1.60263e45 q^{95} -1.12553e46 q^{96} -5.98242e45 q^{97} -5.53948e46 q^{98} +1.83943e47 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 16777216 q^{2} + 122289844824 q^{3} + 140737488355328 q^{4} + 18\!\cdots\!40 q^{5}+ \cdots + 42\!\cdots\!14 q^{9}+O(q^{10}) \) 2 * q - 16777216 * q^2 + 122289844824 * q^3 + 140737488355328 * q^4 + 18178497839194140 * q^5 - 1025841570609364992 * q^6 + 161018545456026827632 * q^7 - 1180591620717411303424 * q^8 + 42346678028148839299914 * q^9	\( 2 q - 16777216 q^{2} + 122289844824 q^{3} + 140737488355328 q^{4} + 18\!\cdots\!40 q^{5}+ \cdots + 19\!\cdots\!88 q^{99}+O(q^{100}) \) 2 * q - 16777216 * q^2 + 122289844824 * q^3 + 140737488355328 * q^4 + 18178497839194140 * q^5 - 1025841570609364992 * q^6 + 161018545456026827632 * q^7 - 1180591620717411303424 * q^8 + 42346678028148839299914 * q^9 - 152492292401846676357120 * q^10 + 1148414200601353937498184 * q^11 + 8605382805946284046811136 * q^12 - 91147460388086216079419636 * q^13 - 1350721458560790294488416256 * q^14 - 7004781615634981008503062320 * q^15 + 9903520314283042199192993792 * q^16 - 102841736272610788276309928988 * q^17 - 355229682080353578541972979712 * q^18 + 1021269902513170084335814340920 * q^19 + 1279198063980470244062747688960 * q^20 + 21735508585019662606113256728384 * q^21 - 9633596550478122450928766287872 * q^22 + 8761047668524985915668413593424 * q^23 - 72187183049023445925352269938688 * q^24 - 507682648872986273192302737941650 * q^25 + 764600315391183136893548193906688 * q^26 + 10104984547772788958914840573828080 * q^27 + 11330672833054713950667884512411648 * q^28 + 44866738270461738647546902365332460 * q^29 + 58760367099168526767776856602050560 * q^30 + 207627610718284877414441666427987904 * q^31 - 83076749736557242056487941267521536 * q^32 + 1477472372445089531927832872318579808 * q^33 + 862699011630313039420959680788168704 * q^34 + 367494533980940143565872352084574240 * q^35 + 2979882552936710671785822873395920896 * q^36 + 15454503825836181610788445034143257052 * q^37 - 8567032874381198674820086866756239360 * q^38 - 84454902625144773203023026649833922032 * q^39 - 10730691113091084533106717765591367680 * q^40 - 183644075219801436287443355635335693516 * q^41 - 182330661200364621894942514297775849472 * q^42 + 251792238934935641547265550793932228104 * q^43 + 80812465092113181816840656312573362176 * q^44 - 607642114901245348425108558238563820020 * q^45 - 73492994560570045052063379617105313792 * q^46 + 2877259596300283378159171629753736631712 * q^47 + 605549981222502470676977454425837666304 * q^48 + 4082466065158778742105339967177123972626 * q^49 + 4258750729797123635191136285919228723200 * q^50 + 32313595089705813278113192123424261680944 * q^51 - 6413932322493001991610313527791194210304 * q^52 + 36237003736012302609225684974144068811964 * q^53 - 84766754217323199643064702956338822512640 * q^54 - 119284580676988289643910520626568801967120 * q^55 - 95048572772745437884284221363892449705984 * q^56 - 217433238554190330563790441928328986980960 * q^57 - 376369479589501504512721125557046796615680 * q^58 + 216631413518842627379871131067900548684520 * q^59 - 492917685531021896992387081506814144020480 * q^60 + 2343345794410501150323838534047225181209004 * q^61 - 1741706636292290268957804678531150755397632 * q^62 + 4863331655836708395434595438453038464171824 * q^63 + 696898287454081973172991196020261297061888 * q^64 + 6442979197855565506819083799260229348557480 * q^65 - 12393936563271857608246074255394617126027264 * q^66 + 9679359518522646693994124509775830904939992 * q^67 - 7236843830554137004990977745937078295724032 * q^68 + 12666786020488197907659082189490927173898688 * q^69 - 3082767587708786335837825339675476146257920 * q^70 - 34699689890171309465034074226599979171319056 * q^71 - 24997066622625314635027928042352009195552768 * q^72 - 44919947676390510667705279890416107043412236 * q^73 - 129641774429439999749712836320974399252463616 * q^74 - 178584439183245940201476654984555123803179800 * q^75 + 71865480506297118253185179251166323545210880 * q^76 + 282496402053252599536812437150318196880350144 * q^77 + 708459071800510445649064585539010037029011456 * q^78 + 459051391676893300046865817924586171479631200 * q^79 + 90015561316804776443095277502181871651389440 * q^80 - 326533112556292583027849224141868597638781358 * q^81 + 1540518158541428086852337632629422081313865728 * q^82 - 1357110492338922730441331533770737425416063816 * q^83 + 1529500443190668270144889934978436873087614976 * q^84 - 4493133982253416774682211563698820690839841160 * q^85 - 2112186389867512602168524177514386240131039232 * q^86 - 6253923718333989640702287995671643099683866480 * q^87 - 677904091171421373894204064268903406536491008 * q^88 + 4559737044037194815580171398227946101567633620 * q^89 + 5097271506197505939761653052508482369130332160 * q^90 - 17990568925125012147062510675834829593464410976 * q^91 + 616503922114754364484099282763086572118081536 * q^92 + 40935592303229143353065306088384219268477064448 * q^93 - 24136202867601327548293052406725233138672336896 * q^94 + 35082243421784097273165847234698748298121392400 * q^95 - 5079721416882934005540658490016217254259064832 * q^96 + 53827580940974934190192198959367945947750881092 * q^97 - 34246207493919452626254791691381759573762244608 * q^98 + 196408474482694469089639477350277927611611498088 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more