LMFDB - Embedded newform 2.48.a.b.1.1

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			1.1
Root			$2.42845e6$ 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)

$f(q)$	$=$	$q-8.38861e6 q^{2} -1.48673e11 q^{3} +7.03687e13 q^{4} +2.84306e16 q^{5} +1.24716e18 q^{6} +5.21750e19 q^{7} -5.90296e20 q^{8} -4.48523e21 q^{9} +O(q^{10})$	\(q-8.38861e6 q^{2} -1.48673e11 q^{3} +7.03687e13 q^{4} +2.84306e16 q^{5} +1.24716e18 q^{6} +5.21750e19 q^{7} -5.90296e20 q^{8} -4.48523e21 q^{9} -2.38493e23 q^{10} -2.77931e24 q^{11} -1.04619e25 q^{12} +1.42403e26 q^{13} -4.37676e26 q^{14} -4.22685e27 q^{15} +4.95176e27 q^{16} -1.43410e29 q^{17} +3.76248e28 q^{18} +1.17759e30 q^{19} +2.00062e30 q^{20} -7.75701e30 q^{21} +2.33145e31 q^{22} -2.45281e31 q^{23} +8.77609e31 q^{24} +9.77550e31 q^{25} -1.19456e33 q^{26} +4.61986e33 q^{27} +3.67149e33 q^{28} +4.38741e34 q^{29} +3.54574e34 q^{30} +3.65168e34 q^{31} -4.15384e34 q^{32} +4.13207e35 q^{33} +1.20301e36 q^{34} +1.48337e36 q^{35} -3.15620e35 q^{36} +4.58544e36 q^{37} -9.87836e36 q^{38} -2.11715e37 q^{39} -1.67825e37 q^{40} -1.04139e38 q^{41} +6.50705e37 q^{42} -1.18553e38 q^{43} -1.95576e38 q^{44} -1.27518e38 q^{45} +2.05757e38 q^{46} +3.50758e39 q^{47} -7.36192e38 q^{48} -2.52110e39 q^{49} -8.20028e38 q^{50} +2.13211e40 q^{51} +1.00207e40 q^{52} +1.29506e40 q^{53} -3.87542e40 q^{54} -7.90173e40 q^{55} -3.07987e40 q^{56} -1.75076e41 q^{57} -3.68043e41 q^{58} +5.96814e41 q^{59} -2.97438e41 q^{60} +1.26708e42 q^{61} -3.06325e41 q^{62} -2.34017e41 q^{63} +3.48449e41 q^{64} +4.04860e42 q^{65} -3.46623e42 q^{66} +1.11395e43 q^{67} -1.00916e43 q^{68} +3.64666e42 q^{69} -1.24434e43 q^{70} -1.80578e43 q^{71} +2.64761e42 q^{72} -3.89278e43 q^{73} -3.84654e43 q^{74} -1.45335e43 q^{75} +8.28657e43 q^{76} -1.45010e44 q^{77} +1.77599e44 q^{78} +6.39740e44 q^{79} +1.40781e44 q^{80} -5.67591e44 q^{81} +8.73579e44 q^{82} +1.01602e45 q^{83} -5.45851e44 q^{84} -4.07723e45 q^{85} +9.94495e44 q^{86} -6.52289e45 q^{87} +1.64061e45 q^{88} +3.48084e45 q^{89} +1.06970e45 q^{90} +7.42989e45 q^{91} -1.72601e45 q^{92} -5.42905e45 q^{93} -2.94237e46 q^{94} +3.34796e46 q^{95} +6.17562e45 q^{96} +5.98100e46 q^{97} +2.11485e46 q^{98} +1.24658e46 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	−1.48673e11	−0.911763	−0.455881	−	0.890041i	$-0.650676\pi$
$3$	−1.48673e11	−0.911763	−0.455881	+	0.890041i	$0.650676\pi$
$4$	7.03687e13	0.500000
$5$	2.84306e16	1.06657	0.533286	−	0.845935i	$-0.320957\pi$
$5$	2.84306e16	1.06657	0.533286	+	0.845935i	$0.320957\pi$
$6$	1.24716e18	0.644714
$7$	5.21750e19	0.720541	0.360271	−	0.932848i	$-0.382684\pi$
$7$	5.21750e19	0.720541	0.360271	+	0.932848i	$0.382684\pi$
$8$	−5.90296e20	−0.353553
$9$	−4.48523e21	−0.168689
$10$	−2.38493e23	−0.754181
$11$	−2.77931e24	−0.935854	−0.467927	−	0.883767i	$-0.654999\pi$
$11$	−2.77931e24	−0.935854	−0.467927	+	0.883767i	$0.654999\pi$
$12$	−1.04619e25	−0.455881
$13$	1.42403e26	0.945912	0.472956	−	0.881086i	$-0.343187\pi$
$13$	1.42403e26	0.945912	0.472956	+	0.881086i	$0.343187\pi$
$14$	−4.37676e26	−0.509500
$15$	−4.22685e27	−0.972462
$16$	4.95176e27	0.250000
$17$	−1.43410e29	−1.74193	−0.870963	−	0.491349i	$-0.836504\pi$
$17$	−1.43410e29	−1.74193	−0.870963	+	0.491349i	$0.836504\pi$
$18$	3.76248e28	0.119281
$19$	1.17759e30	1.04782	0.523908	−	0.851775i	$-0.324473\pi$
$19$	1.17759e30	1.04782	0.523908	+	0.851775i	$0.324473\pi$
$20$	2.00062e30	0.533286
$21$	−7.75701e30	−0.656963
$22$	2.33145e31	0.661749
$23$	−2.45281e31	−0.244940	−0.122470	−	0.992472i	$-0.539082\pi$
$23$	−2.45281e31	−0.244940	−0.122470	+	0.992472i	$0.539082\pi$
$24$	8.77609e31	0.322357
$25$	9.77550e31	0.137578
$26$	−1.19456e33	−0.668860
$27$	4.61986e33	1.06557
$28$	3.67149e33	0.360271
$29$	4.38741e34	1.88736	0.943682	−	0.330855i	$-0.107337\pi$
$29$	4.38741e34	1.88736	0.943682	+	0.330855i	$0.107337\pi$
$30$	3.54574e34	0.687634
$31$	3.65168e34	0.327712	0.163856	−	0.986484i	$-0.447607\pi$
$31$	3.65168e34	0.327712	0.163856	+	0.986484i	$0.447607\pi$
$32$	−4.15384e34	−0.176777
$33$	4.13207e35	0.853277
$34$	1.20301e36	1.23173
$35$	1.48337e36	0.768510
$36$	−3.15620e35	−0.0843443
$37$	4.58544e36	0.643636	0.321818	−	0.946802i	$-0.395706\pi$
$37$	4.58544e36	0.643636	0.321818	+	0.946802i	$0.395706\pi$
$38$	−9.87836e36	−0.740918
$39$	−2.11715e37	−0.862447
$40$	−1.67825e37	−0.377090
$41$	−1.04139e38	−1.30976	−0.654880	−	0.755733i	$-0.727281\pi$
$41$	−1.04139e38	−1.30976	−0.654880	+	0.755733i	$0.727281\pi$
$42$	6.50705e37	0.464543
$43$	−1.18553e38	−0.486860	−0.243430	−	0.969918i	$-0.578273\pi$
$43$	−1.18553e38	−0.486860	−0.243430	+	0.969918i	$0.578273\pi$
$44$	−1.95576e38	−0.467927
$45$	−1.27518e38	−0.179919
$46$	2.05757e38	0.173199
$47$	3.50758e39	1.78118	0.890591	−	0.454806i	$-0.150291\pi$
$47$	3.50758e39	1.78118	0.890591	+	0.454806i	$0.150291\pi$
$48$	−7.36192e38	−0.227941
$49$	−2.52110e39	−0.480820
$50$	−8.20028e38	−0.0972823
$51$	2.13211e40	1.58822
$52$	1.00207e40	0.472956
$53$	1.29506e40	0.390667	0.195334	−	0.980737i	$-0.437421\pi$
$53$	1.29506e40	0.390667	0.195334	+	0.980737i	$0.437421\pi$
$54$	−3.87542e40	−0.753470
$55$	−7.90173e40	−0.998157
$56$	−3.07987e40	−0.254750
$57$	−1.75076e41	−0.955360
$58$	−3.68043e41	−1.33457
$59$	5.96814e41	1.44816	0.724080	−	0.689716i	$-0.242265\pi$
$59$	5.96814e41	1.44816	0.724080	+	0.689716i	$0.242265\pi$
$60$	−2.97438e41	−0.486231
$61$	1.26708e42	1.40460	0.702298	−	0.711883i	$-0.252157\pi$
$61$	1.26708e42	1.40460	0.702298	+	0.711883i	$0.252157\pi$
$62$	−3.06325e41	−0.231727
$63$	−2.34017e41	−0.121547
$64$	3.48449e41	0.125000
$65$	4.04860e42	1.00888
$66$	−3.46623e42	−0.603358
$67$	1.11395e43	1.36178	0.680891	−	0.732385i	$-0.261593\pi$
$67$	1.11395e43	1.36178	0.680891	+	0.732385i	$0.261593\pi$
$68$	−1.00916e43	−0.870963
$69$	3.64666e42	0.223327
$70$	−1.24434e43	−0.543419
$71$	−1.80578e43	−0.565059	−0.282530	−	0.959259i	$-0.591174\pi$
$71$	−1.80578e43	−0.565059	−0.282530	+	0.959259i	$0.591174\pi$
$72$	2.64761e42	0.0596404
$73$	−3.89278e43	−0.634122	−0.317061	−	0.948405i	$-0.602696\pi$
$73$	−3.89278e43	−0.634122	−0.317061	+	0.948405i	$0.602696\pi$
$74$	−3.84654e43	−0.455119
$75$	−1.45335e43	−0.125438
$76$	8.28657e43	0.523908
$77$	−1.45010e44	−0.674322
$78$	1.77599e44	0.609842
$79$	6.39740e44	1.62842	0.814210	−	0.580570i	$-0.197170\pi$
$79$	6.39740e44	1.62842	0.814210	+	0.580570i	$0.197170\pi$
$80$	1.40781e44	0.266643
$81$	−5.67591e44	−0.802856
$82$	8.73579e44	0.926140
$83$	1.01602e45	0.810157	0.405078	−	0.914282i	$-0.367244\pi$
$83$	1.01602e45	0.810157	0.405078	+	0.914282i	$0.367244\pi$
$84$	−5.45851e44	−0.328481
$85$	−4.07723e45	−1.85789
$86$	9.94495e44	0.344262
$87$	−6.52289e45	−1.72083
$88$	1.64061e45	0.330875
$89$	3.48084e45	0.538293	0.269146	−	0.963099i	$-0.413258\pi$
$89$	3.48084e45	0.538293	0.269146	+	0.963099i	$0.413258\pi$
$90$	1.06970e45	0.127222
$91$	7.42989e45	0.681568
$92$	−1.72601e45	−0.122470
$93$	−5.42905e45	−0.298796
$94$	−2.94237e46	−1.25949
$95$	3.34796e46	1.11757
$96$	6.17562e45	0.161178
$97$	5.98100e46	1.22360	0.611798	−	0.791014i	$-0.290447\pi$
$97$	5.98100e46	1.22360	0.611798	+	0.791014i	$0.290447\pi$
$98$	2.11485e46	0.339991
$99$	1.24658e46	0.157868
$100$	6.87889e45	0.0687889
$101$	−7.17475e46	−0.567877	−0.283939	−	0.958842i	$-0.591641\pi$
$101$	−7.17475e46	−0.567877	−0.283939	+	0.958842i	$0.591641\pi$
$102$	−1.78855e47	−1.12304
$103$	8.90072e46	0.444376	0.222188	−	0.975004i	$-0.428680\pi$
$103$	8.90072e46	0.444376	0.222188	+	0.975004i	$0.428680\pi$
$104$	−8.40599e46	−0.334430
$105$	−2.20536e47	−0.700699
$106$	−1.08638e47	−0.276244
$107$	−5.20104e47	−1.06065	−0.530325	−	0.847795i	$-0.677930\pi$
$107$	−5.20104e47	−1.06065	−0.530325	+	0.847795i	$0.677930\pi$
$108$	3.25094e47	0.532783
$109$	9.03483e47	1.19233	0.596166	−	0.802861i	$-0.296690\pi$
$109$	9.03483e47	1.19233	0.596166	+	0.802861i	$0.296690\pi$
$110$	6.62845e47	0.705804
$111$	−6.81730e47	−0.586843
$112$	2.58358e47	0.180135
$113$	8.97141e47	0.507595	0.253797	−	0.967257i	$-0.418320\pi$
$113$	8.97141e47	0.507595	0.253797	+	0.967257i	$0.418320\pi$
$114$	1.46864e48	0.675542
$115$	−6.97349e47	−0.261247
$116$	3.08737e48	0.943682
$117$	−6.38711e47	−0.159565
$118$	−5.00644e48	−1.02400
$119$	−7.48242e48	−1.25513
$120$	2.49509e48	0.343817
$121$	−1.09521e48	−0.124176
$122$	−1.06290e49	−0.993200
$123$	1.54826e49	1.19419
$124$	2.56964e48	0.163856
$125$	−1.74219e49	−0.919836
$126$	1.96308e48	0.0859468
$127$	1.79907e49	0.654123	0.327062	−	0.945003i	$-0.393942\pi$
$127$	1.79907e49	0.654123	0.327062	+	0.945003i	$0.393942\pi$
$128$	−2.92300e48	−0.0883883
$129$	1.76256e49	0.443901
$130$	−3.39621e49	−0.713388
$131$	3.54474e49	0.621883	0.310941	−	0.950429i	$-0.399356\pi$
$131$	3.54474e49	0.621883	0.310941	+	0.950429i	$0.399356\pi$
$132$	2.90769e49	0.426639
$133$	6.14409e49	0.754995
$134$	−9.34448e49	−0.962925
$135$	1.31345e50	1.13650
$136$	8.46543e49	0.615864
$137$	−1.37395e50	−0.841467	−0.420733	−	0.907184i	$-0.638227\pi$
$137$	−1.37395e50	−0.841467	−0.420733	+	0.907184i	$0.638227\pi$
$138$	−3.05904e49	−0.157916
$139$	−3.51383e50	−1.53085	−0.765425	−	0.643525i	$-0.777471\pi$
$139$	−3.51383e50	−1.53085	−0.765425	+	0.643525i	$0.777471\pi$
$140$	1.04383e50	0.384255
$141$	−5.21482e50	−1.62401
$142$	1.51480e50	0.399557
$143$	−3.95782e50	−0.885235
$144$	−2.22098e49	−0.0421722
$145$	1.24737e51	2.01301
$146$	3.26550e50	0.448392
$147$	3.74819e50	0.438394
$148$	3.22672e50	0.321818
$149$	−2.50856e50	−0.213573	−0.106787	−	0.994282i	$-0.534056\pi$
$149$	−2.50856e50	−0.213573	−0.106787	+	0.994282i	$0.534056\pi$
$150$	1.21916e50	0.0886983
$151$	−3.64159e50	−0.226638	−0.113319	−	0.993559i	$-0.536148\pi$
$151$	−3.64159e50	−0.226638	−0.113319	+	0.993559i	$0.536148\pi$
$152$	−6.95128e50	−0.370459
$153$	6.43226e50	0.293843
$154$	1.21644e51	0.476818
$155$	1.03819e51	0.349529
$156$	−1.48981e51	−0.431223
$157$	−1.27736e51	−0.318179	−0.159090	−	0.987264i	$-0.550856\pi$
$157$	−1.27736e51	−0.318179	−0.159090	+	0.987264i	$0.550856\pi$
$158$	−5.36652e51	−1.15147
$159$	−1.92540e51	−0.356196
$160$	−1.18096e51	−0.188545
$161$	−1.27976e51	−0.176490
$162$	4.76130e51	0.567705
$163$	4.90188e51	0.505771	0.252886	−	0.967496i	$-0.418620\pi$
$163$	4.90188e51	0.505771	0.252886	+	0.967496i	$0.418620\pi$
$164$	−7.32811e51	−0.654880
$165$	1.17477e52	0.910082
$166$	−8.52303e51	−0.572867
$167$	3.29109e51	0.192089	0.0960445	−	0.995377i	$-0.469381\pi$
$167$	3.29109e51	0.192089	0.0960445	+	0.995377i	$0.469381\pi$
$168$	4.57893e51	0.232271
$169$	−2.38542e51	−0.105251
$170$	3.42023e52	1.31373
$171$	−5.28177e51	−0.176755
$172$	−8.34243e51	−0.243430
$173$	−1.72672e52	−0.439681	−0.219841	−	0.975536i	$-0.570554\pi$
$173$	−1.72672e52	−0.439681	−0.219841	+	0.975536i	$0.570554\pi$
$174$	5.47179e52	1.21681
$175$	5.10037e51	0.0991306
$176$	−1.37625e52	−0.233964
$177$	−8.87299e52	−1.32038
$178$	−2.91994e52	−0.380630
$179$	4.97567e52	0.568598	0.284299	−	0.958736i	$-0.408239\pi$
$179$	4.97567e52	0.568598	0.284299	+	0.958736i	$0.408239\pi$
$180$	−8.97326e51	−0.0899594
$181$	−8.38189e52	−0.737727	−0.368863	−	0.929484i	$-0.620253\pi$
$181$	−8.38189e52	−0.737727	−0.368863	+	0.929484i	$0.620253\pi$
$182$	−6.23264e52	−0.481942
$183$	−1.88380e53	−1.28066
$184$	1.44789e52	0.0865995
$185$	1.30367e53	0.686485
$186$	4.55421e52	0.211280
$187$	3.98580e53	1.63019
$188$	2.46824e53	0.890591
$189$	2.41042e53	0.767785
$190$	−2.80847e53	−0.790243
$191$	2.46535e52	0.0613190	0.0306595	−	0.999530i	$-0.490239\pi$
$191$	2.46535e52	0.0613190	0.0306595	+	0.999530i	$0.490239\pi$
$192$	−5.18049e52	−0.113970
$193$	3.57651e53	0.696407	0.348204	−	0.937419i	$-0.386792\pi$
$193$	3.57651e53	0.696407	0.348204	+	0.937419i	$0.386792\pi$
$194$	−5.01723e53	−0.865213
$195$	−6.01917e53	−0.919863
$196$	−1.77407e53	−0.240410
$197$	7.55663e53	0.908599	0.454299	−	0.890849i	$-0.349890\pi$
$197$	7.55663e53	0.908599	0.454299	+	0.890849i	$0.349890\pi$
$198$	−1.04571e53	−0.111630
$199$	−9.30125e53	−0.882052	−0.441026	−	0.897494i	$-0.645385\pi$
$199$	−9.30125e53	−0.882052	−0.441026	+	0.897494i	$0.645385\pi$
$200$	−5.77043e52	−0.0486411
$201$	−1.65614e54	−1.24162
$202$	6.01862e53	0.401550
$203$	2.28913e54	1.35992
$204$	1.50034e54	0.794111
$205$	−2.96072e54	−1.39695
$206$	−7.46647e53	−0.314221
$207$	1.10014e53	0.0413186
$208$	7.05146e53	0.236478
$209$	−3.27289e54	−0.980604
$210$	1.84999e54	0.495469
$211$	6.30159e54	1.50943	0.754715	−	0.656053i	$-0.227775\pi$
$211$	6.30159e54	1.50943	0.754715	+	0.656053i	$0.227775\pi$
$212$	9.11318e53	0.195334
$213$	2.68471e54	0.515200
$214$	4.36295e54	0.749992
$215$	−3.37053e54	−0.519272
$216$	−2.72709e54	−0.376735
$217$	1.90526e54	0.236130
$218$	−7.57896e54	−0.843106
$219$	5.78751e54	0.578169
$220$	−5.56035e54	−0.499079
$221$	−2.04220e55	−1.64771
$222$	5.71876e54	0.414961
$223$	7.17665e54	0.468552	0.234276	−	0.972170i	$-0.424728\pi$
$223$	7.17665e54	0.468552	0.234276	+	0.972170i	$0.424728\pi$
$224$	−2.16727e54	−0.127375
$225$	−4.38454e53	−0.0232078
$226$	−7.52576e54	−0.358924
$227$	−8.35266e54	−0.359101	−0.179551	−	0.983749i	$-0.557464\pi$
$227$	−8.35266e54	−0.359101	−0.179551	+	0.983749i	$0.557464\pi$
$228$	−1.23199e55	−0.477680
$229$	9.94929e54	0.348063	0.174032	−	0.984740i	$-0.444321\pi$
$229$	9.94929e54	0.348063	0.174032	+	0.984740i	$0.444321\pi$
$230$	5.84979e54	0.184729
$231$	2.15591e55	0.614822
$232$	−2.58987e55	−0.667284
$233$	5.19501e55	1.20982	0.604912	−	0.796292i	$-0.293208\pi$
$233$	5.19501e55	1.20982	0.604912	+	0.796292i	$0.293208\pi$
$234$	5.35789e54	0.112829
$235$	9.97226e55	1.89976
$236$	4.19970e55	0.724080
$237$	−9.51118e55	−1.48473
$238$	6.27671e55	0.887510
$239$	−5.60025e55	−0.717558	−0.358779	−	0.933423i	$-0.616807\pi$
$239$	−5.60025e55	−0.717558	−0.358779	+	0.933423i	$0.616807\pi$
$240$	−2.09304e55	−0.243115
$241$	−1.72627e56	−1.81848	−0.909239	−	0.416275i	$-0.863335\pi$
$241$	−1.72627e56	−1.81848	−0.909239	+	0.416275i	$0.863335\pi$
$242$	9.18725e54	0.0878060
$243$	−3.84514e55	−0.333553
$244$	8.91626e55	0.702298
$245$	−7.16764e55	−0.512830
$246$	−1.29877e56	−0.844420
$247$	1.67693e56	0.991142
$248$	−2.15557e55	−0.115864
$249$	−1.51055e56	−0.738671
$250$	1.46146e56	0.650422
$251$	6.29528e55	0.255084	0.127542	−	0.991833i	$-0.459291\pi$
$251$	6.29528e55	0.255084	0.127542	+	0.991833i	$0.459291\pi$
$252$	−1.64675e55	−0.0607736
$253$	6.81712e55	0.229228
$254$	−1.50917e56	−0.462535
$255$	6.06172e56	1.69396
$256$	2.45199e55	0.0625000
$257$	−4.95551e56	−1.15255	−0.576276	−	0.817255i	$-0.695495\pi$
$257$	−4.95551e56	−1.15255	−0.576276	+	0.817255i	$0.695495\pi$
$258$	−1.47854e56	−0.313885
$259$	2.39245e56	0.463766
$260$	2.84895e56	0.504442
$261$	−1.96786e56	−0.318377
$262$	−2.97354e56	−0.439737
$263$	1.41594e57	1.91463	0.957317	−	0.289041i	$-0.0933365\pi$
$263$	1.41594e57	1.91463	0.957317	+	0.289041i	$0.0933365\pi$
$264$	−2.43914e56	−0.301679
$265$	3.68193e56	0.416675
$266$	−5.15404e56	−0.533862
$267$	−5.17505e56	−0.490795
$268$	7.83872e56	0.680891
$269$	−2.34338e57	−1.86494	−0.932468	−	0.361254i	$-0.882349\pi$
$269$	−2.34338e57	−1.86494	−0.932468	+	0.361254i	$0.882349\pi$
$270$	−1.10180e57	−0.803630
$271$	2.70087e56	0.180603	0.0903016	−	0.995914i	$-0.471217\pi$
$271$	2.70087e56	0.180603	0.0903016	+	0.995914i	$0.471217\pi$
$272$	−7.10131e56	−0.435481
$273$	−1.10462e57	−0.621429
$274$	1.15255e57	0.595007
$275$	−2.71691e56	−0.128753
$276$	2.56611e56	0.111664
$277$	1.64716e57	0.658357	0.329179	−	0.944268i	$-0.393228\pi$
$277$	1.64716e57	0.658357	0.329179	+	0.944268i	$0.393228\pi$
$278$	2.94761e57	1.08247
$279$	−1.63786e56	−0.0552813
$280$	−8.75625e56	−0.271709
$281$	−1.90241e57	−0.542882	−0.271441	−	0.962455i	$-0.587500\pi$
$281$	−1.90241e57	−0.542882	−0.271441	+	0.962455i	$0.587500\pi$
$282$	4.37451e57	1.14835
$283$	6.53457e57	1.57847	0.789235	−	0.614092i	$-0.210478\pi$
$283$	6.53457e57	1.57847	0.789235	+	0.614092i	$0.210478\pi$
$284$	−1.27071e57	−0.282530
$285$	−4.97751e57	−1.01896
$286$	3.32006e57	0.625956
$287$	−5.43344e57	−0.943736
$288$	1.86309e56	0.0298202
$289$	1.37884e58	2.03430
$290$	−1.04637e58	−1.42341
$291$	−8.89212e57	−1.11563
$292$	−2.73930e57	−0.317061
$293$	−7.60826e57	−0.812636	−0.406318	−	0.913732i	$-0.633188\pi$
$293$	−7.60826e57	−0.812636	−0.406318	+	0.913732i	$0.633188\pi$
$294$	−3.14421e57	−0.309991
$295$	1.69678e58	1.54457
$296$	−2.70676e57	−0.227560
$297$	−1.28400e58	−0.997215
$298$	2.10433e57	0.151019
$299$	−3.49288e57	−0.231692
$300$	−1.02270e57	−0.0627192
$301$	−6.18551e57	−0.350803
$302$	3.05479e57	0.160257
$303$	1.06669e58	0.517769
$304$	5.83115e57	0.261954
$305$	3.60237e58	1.49810
$306$	−5.39577e57	−0.207778
$307$	4.61796e58	1.64702	0.823509	−	0.567303i	$-0.192013\pi$
$307$	4.61796e58	1.64702	0.823509	+	0.567303i	$0.192013\pi$
$308$	−1.02042e58	−0.337161
$309$	−1.32330e58	−0.405165
$310$	−8.70899e57	−0.247154
$311$	−6.49416e58	−1.70865	−0.854326	−	0.519737i	$-0.826030\pi$
$311$	−6.49416e58	−1.70865	−0.854326	+	0.519737i	$0.826030\pi$
$312$	1.24974e58	0.304921
$313$	−8.01419e57	−0.181371	−0.0906854	−	0.995880i	$-0.528906\pi$
$313$	−8.01419e57	−0.181371	−0.0906854	+	0.995880i	$0.528906\pi$
$314$	1.07153e58	0.224987
$315$	−6.65324e57	−0.129639
$316$	4.50177e58	0.814210
$317$	3.99300e58	0.670512	0.335256	−	0.942127i	$-0.391177\pi$
$317$	3.99300e58	0.670512	0.335256	+	0.942127i	$0.391177\pi$
$318$	1.61514e58	0.251869
$319$	−1.21940e59	−1.76630
$320$	9.90661e57	0.133322
$321$	7.73253e58	0.967060
$322$	1.07354e58	0.124797
$323$	−1.68878e59	−1.82522
$324$	−3.99407e58	−0.401428
$325$	1.39206e58	0.130137
$326$	−4.11200e58	−0.357634
$327$	−1.34323e59	−1.08712
$328$	6.14726e58	0.463070
$329$	1.83008e59	1.28341
$330$	−9.85470e58	−0.643525
$331$	1.90654e59	1.15954	0.579772	−	0.814778i	$-0.303141\pi$
$331$	1.90654e59	1.15954	0.579772	+	0.814778i	$0.303141\pi$
$332$	7.14964e58	0.405078
$333$	−2.05667e58	−0.108574
$334$	−2.76077e58	−0.135827
$335$	3.16702e59	1.45244
$336$	−3.84108e58	−0.164241
$337$	3.28004e59	1.30791	0.653953	−	0.756535i	$-0.273109\pi$
$337$	3.28004e59	1.30791	0.653953	+	0.756535i	$0.273109\pi$
$338$	2.00104e58	0.0744240
$339$	−1.33380e59	−0.462806
$340$	−2.86909e59	−0.928945
$341$	−1.01491e59	−0.306691
$342$	4.43067e58	0.124984
$343$	−4.05110e59	−1.06699
$344$	6.99814e58	0.172131
$345$	1.03677e59	0.238195
$346$	1.44848e59	0.310901
$347$	−4.54665e59	−0.911904	−0.455952	−	0.890004i	$-0.650701\pi$
$347$	−4.54665e59	−0.911904	−0.455952	+	0.890004i	$0.650701\pi$
$348$	−4.59007e59	−0.860414
$349$	−7.41259e59	−1.29889	−0.649445	−	0.760408i	$-0.724999\pi$
$349$	−7.41259e59	−1.29889	−0.649445	+	0.760408i	$0.724999\pi$
$350$	−4.27850e58	−0.0700959
$351$	6.57883e59	1.00793
$352$	1.15448e59	0.165437
$353$	3.28761e59	0.440732	0.220366	−	0.975417i	$-0.429275\pi$
$353$	3.28761e59	0.440732	0.220366	+	0.975417i	$0.429275\pi$
$354$	7.44321e59	0.933648
$355$	−5.13394e59	−0.602677
$356$	2.44942e59	0.269146
$357$	1.11243e60	1.14438
$358$	−4.17390e59	−0.402060
$359$	−7.17218e59	−0.647041	−0.323520	−	0.946221i	$-0.604866\pi$
$359$	−7.17218e59	−0.647041	−0.323520	+	0.946221i	$0.604866\pi$
$360$	7.52732e58	0.0636109
$361$	1.23677e59	0.0979192
$362$	7.03124e59	0.521652
$363$	1.62827e59	0.113219
$364$	5.22832e59	0.340784
$365$	−1.10674e60	−0.676338
$366$	1.58024e60	0.905563
$367$	3.67201e59	0.197356	0.0986781	−	0.995119i	$-0.468539\pi$
$367$	3.67201e59	0.197356	0.0986781	+	0.995119i	$0.468539\pi$
$368$	−1.21457e59	−0.0612351
$369$	4.67086e59	0.220941
$370$	−1.09359e60	−0.485418
$371$	6.75698e59	0.281492
$372$	−3.82035e59	−0.149398
$373$	−4.89584e60	−1.79750	−0.898751	−	0.438459i	$-0.855524\pi$
$373$	−4.89584e60	−1.79750	−0.898751	+	0.438459i	$0.855524\pi$
$374$	−3.34353e60	−1.15272
$375$	2.59016e60	0.838672
$376$	−2.07051e60	−0.629743
$377$	6.24781e60	1.78528
$378$	−2.02200e60	−0.542906
$379$	−2.57969e60	−0.650949	−0.325474	−	0.945551i	$-0.605524\pi$
$379$	−2.57969e60	−0.650949	−0.325474	+	0.945551i	$0.605524\pi$
$380$	2.35592e60	0.558786
$381$	−2.67472e60	−0.596405
$382$	−2.06809e59	−0.0433591
$383$	4.89711e60	0.965536	0.482768	−	0.875748i	$-0.339631\pi$
$383$	4.89711e60	0.965536	0.482768	+	0.875748i	$0.339631\pi$
$384$	4.34571e59	0.0805892
$385$	−4.12273e60	−0.719213
$386$	−3.00020e60	−0.492434
$387$	5.31738e59	0.0821277
$388$	4.20875e60	0.611798
$389$	2.56595e60	0.351102	0.175551	−	0.984470i	$-0.443829\pi$
$389$	2.56595e60	0.351102	0.175551	+	0.984470i	$0.443829\pi$
$390$	5.04924e60	0.650441
$391$	3.51758e60	0.426668
$392$	1.48820e60	0.169996
$393$	−5.27006e60	−0.567009
$394$	−6.33896e60	−0.642476
$395$	1.81882e61	1.73683
$396$	8.77205e59	0.0789340
$397$	−2.88569e59	−0.0244722	−0.0122361	−	0.999925i	$-0.503895\pi$
$397$	−2.88569e59	−0.0244722	−0.0122361	+	0.999925i	$0.503895\pi$
$398$	7.80245e60	0.623705
$399$	−9.13459e60	−0.688376
$400$	4.84059e59	0.0343945
$401$	−2.91481e61	−1.95307	−0.976534	−	0.215364i	$-0.930906\pi$
$401$	−2.91481e61	−1.95307	−0.976534	+	0.215364i	$0.930906\pi$
$402$	1.38927e61	0.877959
$403$	5.20010e60	0.309987
$404$	−5.04878e60	−0.283939
$405$	−1.61369e61	−0.856304
$406$	−1.92027e61	−0.961611
$407$	−1.27443e61	−0.602350
$408$	−1.25858e61	−0.561521
$409$	−2.80914e61	−1.18325	−0.591624	−	0.806214i	$-0.701513\pi$
$409$	−2.80914e61	−1.18325	−0.591624	+	0.806214i	$0.701513\pi$
$410$	2.48363e61	0.987796
$411$	2.04269e61	0.767218
$412$	6.26333e60	0.222188
$413$	3.11388e61	1.04346
$414$	−9.22867e59	−0.0292167
$415$	2.88862e61	0.864091
$416$	−5.91519e60	−0.167215
$417$	5.22411e61	1.39577
$418$	2.74550e61	0.693391
$419$	−1.11614e61	−0.266494	−0.133247	−	0.991083i	$-0.542540\pi$
$419$	−1.11614e61	−0.266494	−0.133247	+	0.991083i	$0.542540\pi$
$420$	−1.55189e61	−0.350349
$421$	8.47504e60	0.180931	0.0904654	−	0.995900i	$-0.471165\pi$
$421$	8.47504e60	0.180931	0.0904654	+	0.995900i	$0.471165\pi$
$422$	−5.28616e61	−1.06733
$423$	−1.57323e61	−0.300465
$424$	−7.64469e60	−0.138122
$425$	−1.40190e61	−0.239650
$426$	−2.25209e61	−0.364301
$427$	6.61098e61	1.01207
$428$	−3.65991e61	−0.530325
$429$	5.88419e61	0.807125
$430$	2.82741e61	0.367181
$431$	−8.27219e61	−1.01720	−0.508598	−	0.861004i	$-0.669836\pi$
$431$	−8.27219e61	−1.01720	−0.508598	+	0.861004i	$0.669836\pi$
$432$	2.28765e61	0.266392
$433$	1.10514e61	0.121885	0.0609426	−	0.998141i	$-0.480589\pi$
$433$	1.10514e61	0.121885	0.0609426	+	0.998141i	$0.480589\pi$
$434$	−1.59825e61	−0.166969
$435$	−1.85449e62	−1.83539
$436$	6.35770e61	0.596166
$437$	−2.88841e61	−0.256652
$438$	−4.85491e61	−0.408827
$439$	−1.05593e61	−0.0842786	−0.0421393	−	0.999112i	$-0.513417\pi$
$439$	−1.05593e61	−0.0842786	−0.0421393	+	0.999112i	$0.513417\pi$
$440$	4.66436e61	0.352902
$441$	1.13077e61	0.0811089
$442$	1.71312e62	1.16510
$443$	−9.55558e61	−0.616268	−0.308134	−	0.951343i	$-0.599704\pi$
$443$	−9.55558e61	−0.616268	−0.308134	+	0.951343i	$0.599704\pi$
$444$	−4.79725e61	−0.293422
$445$	9.89622e61	0.574128
$446$	−6.02021e61	−0.331316
$447$	3.72954e61	0.194728
$448$	1.81804e61	0.0900677
$449$	−8.44757e61	−0.397139	−0.198570	−	0.980087i	$-0.563630\pi$
$449$	−8.44757e61	−0.397139	−0.198570	+	0.980087i	$0.563630\pi$
$450$	3.67801e60	0.0164104
$451$	2.89433e62	1.22574
$452$	6.31307e61	0.253797
$453$	5.41405e61	0.206640
$454$	7.00672e61	0.253923
$455$	2.11236e62	0.726942
$456$	1.03347e62	0.337771
$457$	−1.07944e62	−0.335096	−0.167548	−	0.985864i	$-0.553585\pi$
$457$	−1.07944e62	−0.335096	−0.167548	+	0.985864i	$0.553585\pi$
$458$	−8.34607e61	−0.246118
$459$	−6.62534e62	−1.85614
$460$	−4.90716e61	−0.130623
$461$	5.28262e62	1.33622	0.668110	−	0.744063i	$-0.267104\pi$
$461$	5.28262e62	1.33622	0.668110	+	0.744063i	$0.267104\pi$
$462$	−1.80851e62	−0.434744
$463$	−2.87182e62	−0.656150	−0.328075	−	0.944652i	$-0.606400\pi$
$463$	−2.87182e62	−0.656150	−0.328075	+	0.944652i	$0.606400\pi$
$464$	2.17254e62	0.471841
$465$	−1.54351e62	−0.318687
$466$	−4.35789e62	−0.855475
$467$	−3.39411e62	−0.633548	−0.316774	−	0.948501i	$-0.602600\pi$
$467$	−3.39411e62	−0.633548	−0.316774	+	0.948501i	$0.602600\pi$
$468$	−4.49453e61	−0.0797823
$469$	5.81203e62	0.981220
$470$	−8.36533e62	−1.34333
$471$	1.89909e62	0.290104
$472$	−3.52297e62	−0.512002
$473$	3.29495e62	0.455630
$474$	7.97856e62	1.04986
$475$	1.15115e62	0.144156
$476$	−5.26528e62	−0.627565
$477$	−5.80864e61	−0.0659011
$478$	4.69783e62	0.507390
$479$	−3.41865e62	−0.351536	−0.175768	−	0.984432i	$-0.556241\pi$
$479$	−3.41865e62	−0.351536	−0.175768	+	0.984432i	$0.556241\pi$
$480$	1.75577e62	0.171909
$481$	6.52980e62	0.608823
$482$	1.44810e63	1.28586
$483$	1.90265e62	0.160917
$484$	−7.70682e61	−0.0620882
$485$	1.70043e63	1.30505
$486$	3.22554e62	0.235858
$487$	−7.68487e62	−0.535434	−0.267717	−	0.963498i	$-0.586269\pi$
$487$	−7.68487e62	−0.535434	−0.267717	+	0.963498i	$0.586269\pi$
$488$	−7.47950e62	−0.496600
$489$	−7.28776e62	−0.461143
$490$	6.01265e62	0.362625
$491$	−3.02686e62	−0.174011	−0.0870056	−	0.996208i	$-0.527730\pi$
$491$	−3.02686e62	−0.174011	−0.0870056	+	0.996208i	$0.527730\pi$
$492$	1.08949e63	0.597095
$493$	−6.29198e63	−3.28765
$494$	−1.40671e63	−0.700843
$495$	3.54411e62	0.168378
$496$	1.80822e62	0.0819280
$497$	−9.42167e62	−0.407149
$498$	1.26714e63	0.522319
$499$	2.90194e63	1.14111	0.570553	−	0.821261i	$-0.306729\pi$
$499$	2.90194e63	1.14111	0.570553	+	0.821261i	$0.306729\pi$
$500$	−1.22596e63	−0.459918
$501$	−4.89295e62	−0.175140
$502$	−5.28086e62	−0.180371
$503$	4.14260e63	1.35028	0.675142	−	0.737687i	$-0.264082\pi$
$503$	4.14260e63	1.35028	0.675142	+	0.737687i	$0.264082\pi$
$504$	1.38139e62	0.0429734
$505$	−2.03982e63	−0.605683
$506$	−5.71861e62	−0.162089
$507$	3.54647e62	0.0959643
$508$	1.26598e63	0.327062
$509$	3.09549e63	0.763592	0.381796	−	0.924247i	$-0.375306\pi$
$509$	3.09549e63	0.763592	0.381796	+	0.924247i	$0.375306\pi$
$510$	−5.08494e63	−1.19781
$511$	−2.03106e63	−0.456911
$512$	−2.05688e62	−0.0441942
$513$	5.44031e63	1.11652
$514$	4.15699e63	0.814977
$515$	2.53053e63	0.473959
$516$	1.24029e63	0.221950
$517$	−9.74864e63	−1.66693
$518$	−2.00694e63	−0.327932
$519$	2.56716e63	0.400885
$520$	−2.38987e63	−0.356694
$521$	6.69938e63	0.955759	0.477879	−	0.878425i	$-0.341406\pi$
$521$	6.69938e63	0.955759	0.477879	+	0.878425i	$0.341406\pi$
$522$	1.65076e63	0.225126
$523$	1.22198e64	1.59322	0.796609	−	0.604495i	$-0.206625\pi$
$523$	1.22198e64	1.59322	0.796609	+	0.604495i	$0.206625\pi$
$524$	2.49439e63	0.310941
$525$	−7.58286e62	−0.0903835
$526$	−1.18778e64	−1.35385
$527$	−5.23686e63	−0.570850
$528$	2.04610e63	0.213319
$529$	−9.42623e63	−0.940004
$530$	−3.08863e63	−0.294634
$531$	−2.67685e63	−0.244288
$532$	4.32352e63	0.377498
$533$	−1.48297e64	−1.23892
$534$	4.34115e63	0.347045
$535$	−1.47869e64	−1.13126
$536$	−6.57559e63	−0.481462
$537$	−7.39747e63	−0.518427
$538$	1.96577e64	1.31871
$539$	7.00692e63	0.449978
$540$	9.24261e63	0.568252
$541$	6.50385e63	0.382855	0.191428	−	0.981507i	$-0.438688\pi$
$541$	6.50385e63	0.382855	0.191428	+	0.981507i	$0.438688\pi$
$542$	−2.26565e63	−0.127706
$543$	1.24616e64	0.672632
$544$	5.95701e63	0.307932
$545$	2.56865e64	1.27171
$546$	9.26624e63	0.439416
$547$	−4.28727e64	−1.94750	−0.973752	−	0.227611i	$-0.926909\pi$
$547$	−4.28727e64	−1.94750	−0.973752	+	0.227611i	$0.926909\pi$
$548$	−9.66830e63	−0.420733
$549$	−5.68313e63	−0.236939
$550$	2.27911e63	0.0910420
$551$	5.16658e64	1.97761
$552$	−2.15261e63	−0.0789582
$553$	3.33784e64	1.17334
$554$	−1.38174e64	−0.465529
$555$	−1.93820e64	−0.625911
$556$	−2.47264e64	−0.765425
$557$	2.42365e64	0.719237	0.359619	−	0.933099i	$-0.382907\pi$
$557$	2.42365e64	0.719237	0.359619	+	0.933099i	$0.382907\pi$
$558$	1.37394e63	0.0390898
$559$	−1.68823e64	−0.460526
$560$	7.34528e63	0.192127
$561$	−5.92580e64	−1.48635
$562$	1.59586e64	0.383875
$563$	−2.37308e64	−0.547476	−0.273738	−	0.961804i	$-0.588260\pi$
$563$	−2.37308e64	−0.547476	−0.273738	+	0.961804i	$0.588260\pi$
$564$	−3.66960e64	−0.812007
$565$	2.55062e64	0.541387
$566$	−5.48160e64	−1.11615
$567$	−2.96141e64	−0.578491
$568$	1.06595e64	0.199779
$569$	−1.16381e64	−0.209288	−0.104644	−	0.994510i	$-0.533370\pi$
$569$	−1.16381e64	−0.209288	−0.104644	+	0.994510i	$0.533370\pi$
$570$	4.17544e64	0.720514
$571$	7.57518e64	1.25442	0.627212	−	0.778849i	$-0.284196\pi$
$571$	7.57518e64	1.25442	0.627212	+	0.778849i	$0.284196\pi$
$572$	−2.78507e64	−0.442618
$573$	−3.66531e63	−0.0559084
$574$	4.55790e64	0.667322
$575$	−2.39775e63	−0.0336984
$576$	−1.56287e63	−0.0210861
$577$	1.00315e65	1.29937	0.649686	−	0.760203i	$-0.274900\pi$
$577$	1.00315e65	1.29937	0.649686	+	0.760203i	$0.274900\pi$
$578$	−1.15666e65	−1.43847
$579$	−5.31730e64	−0.634958
$580$	8.77756e64	1.00651
$581$	5.30111e64	0.583752
$582$	7.45925e64	0.788869
$583$	−3.59937e64	−0.365608
$584$	2.29789e64	0.224196
$585$	−1.81589e64	−0.170187
$586$	6.38227e64	0.574621
$587$	−2.23472e64	−0.193298	−0.0966491	−	0.995319i	$-0.530812\pi$
$587$	−2.23472e64	−0.193298	−0.0966491	+	0.995319i	$0.530812\pi$
$588$	2.63756e64	0.219197
$589$	4.30018e64	0.343382
$590$	−1.42336e65	−1.09217
$591$	−1.12347e65	−0.828426
$592$	2.27060e64	0.160909
$593$	−6.37130e64	−0.433953	−0.216977	−	0.976177i	$-0.569620\pi$
$593$	−6.37130e64	−0.433953	−0.216977	+	0.976177i	$0.569620\pi$
$594$	1.07710e65	0.705138
$595$	−2.12729e65	−1.33869
$596$	−1.76524e64	−0.106787
$597$	1.38284e65	0.804222
$598$	2.93004e64	0.163831
$599$	−2.52571e64	−0.135785	−0.0678927	−	0.997693i	$-0.521628\pi$
$599$	−2.52571e64	−0.135785	−0.0678927	+	0.997693i	$0.521628\pi$
$600$	8.57906e63	0.0443492
$601$	6.82578e64	0.339314	0.169657	−	0.985503i	$-0.445734\pi$
$601$	6.82578e64	0.339314	0.169657	+	0.985503i	$0.445734\pi$
$602$	5.18878e64	0.248055
$603$	−4.99632e64	−0.229717
$604$	−2.56254e64	−0.113319
$605$	−3.11373e64	−0.132443
$606$	−8.94804e64	−0.366118
$607$	−1.24624e65	−0.490532	−0.245266	−	0.969456i	$-0.578875\pi$
$607$	−1.24624e65	−0.490532	−0.245266	+	0.969456i	$0.578875\pi$
$608$	−4.89153e64	−0.185230
$609$	−3.40332e65	−1.23993
$610$	−3.02189e65	−1.05932
$611$	4.99490e65	1.68484
$612$	4.52630e64	0.146921
$613$	1.92574e65	0.601556	0.300778	−	0.953694i	$-0.402754\pi$
$613$	1.92574e65	0.601556	0.300778	+	0.953694i	$0.402754\pi$
$614$	−3.87383e65	−1.16462
$615$	4.40179e65	1.27369
$616$	8.55991e64	0.238409
$617$	3.65173e65	0.979034	0.489517	−	0.871994i	$-0.337173\pi$
$617$	3.65173e65	0.979034	0.489517	+	0.871994i	$0.337173\pi$
$618$	1.11006e65	0.286495
$619$	2.51959e65	0.626035	0.313018	−	0.949747i	$-0.398660\pi$
$619$	2.51959e65	0.626035	0.313018	+	0.949747i	$0.398660\pi$
$620$	7.30563e64	0.174764
$621$	−1.13317e65	−0.261000
$622$	5.44770e65	1.20820
$623$	1.81613e65	0.387862
$624$	−1.04836e65	−0.215612
$625$	−5.64774e65	−1.11865
$626$	6.72279e64	0.128249
$627$	4.86589e65	0.894078
$628$	−8.98863e64	−0.159090
$629$	−6.57597e65	−1.12117
$630$	5.58114e64	0.0916685
$631$	−7.41146e65	−1.17277	−0.586386	−	0.810032i	$-0.699450\pi$
$631$	−7.41146e65	−1.17277	−0.586386	+	0.810032i	$0.699450\pi$
$632$	−3.77636e65	−0.575734
$633$	−9.36875e65	−1.37624
$634$	−3.34957e65	−0.474123
$635$	5.11485e65	0.697670
$636$	−1.35488e65	−0.178098
$637$	−3.59013e65	−0.454813
$638$	1.02290e66	1.24896
$639$	8.09935e64	0.0953191
$640$	−8.31027e64	−0.0942726
$641$	6.30821e65	0.689831	0.344915	−	0.938634i	$-0.387908\pi$
$641$	6.30821e65	0.689831	0.344915	+	0.938634i	$0.387908\pi$
$642$	−6.48652e65	−0.683815
$643$	−9.53122e65	−0.968703	−0.484352	−	0.874873i	$-0.660944\pi$
$643$	−9.53122e65	−0.968703	−0.484352	+	0.874873i	$0.660944\pi$
$644$	−9.00548e64	−0.0882448
$645$	5.01106e65	0.473453
$646$	1.41665e66	1.29062
$647$	7.88156e65	0.692407	0.346204	−	0.938159i	$-0.387471\pi$
$647$	7.88156e65	0.692407	0.346204	+	0.938159i	$0.387471\pi$
$648$	3.35046e65	0.283852
$649$	−1.65873e66	−1.35527
$650$	−1.16774e65	−0.0920204
$651$	−2.83261e65	−0.215295
$652$	3.44939e65	0.252886
$653$	2.02259e66	1.43037	0.715185	−	0.698935i	$-0.246342\pi$
$653$	2.02259e66	1.43037	0.715185	+	0.698935i	$0.246342\pi$
$654$	1.12679e66	0.768713
$655$	1.00779e66	0.663283
$656$	−5.15670e65	−0.327440
$657$	1.74600e65	0.106969
$658$	−1.53518e66	−0.907511
$659$	−1.00776e66	−0.574844	−0.287422	−	0.957804i	$-0.592798\pi$
$659$	−1.00776e66	−0.574844	−0.287422	+	0.957804i	$0.592798\pi$
$660$	8.26672e65	0.455041
$661$	−1.17727e66	−0.625379	−0.312689	−	0.949855i	$-0.601230\pi$
$661$	−1.17727e66	−0.625379	−0.312689	+	0.949855i	$0.601230\pi$
$662$	−1.59932e66	−0.819922
$663$	3.03620e66	1.50232
$664$	−5.99755e65	−0.286434
$665$	1.74680e66	0.805257
$666$	1.72526e65	0.0767735
$667$	−1.07615e66	−0.462291
$668$	2.31590e65	0.0960445
$669$	−1.06697e66	−0.427208
$670$	−2.65669e66	−1.02703
$671$	−3.52159e66	−1.31450
$672$	3.22213e65	0.116136
$673$	3.29510e66	1.14687	0.573435	−	0.819251i	$-0.305610\pi$
$673$	3.29510e66	1.14687	0.573435	+	0.819251i	$0.305610\pi$
$674$	−2.75150e66	−0.924830
$675$	4.51615e65	0.146598
$676$	−1.67859e65	−0.0526257
$677$	−4.94748e66	−1.49813	−0.749067	−	0.662494i	$-0.769498\pi$
$677$	−4.94748e66	−1.49813	−0.749067	+	0.662494i	$0.769498\pi$
$678$	1.11888e66	0.327253
$679$	3.12059e66	0.881651
$680$	2.40677e66	0.656863
$681$	1.24181e66	0.327415
$682$	8.51370e65	0.216863
$683$	2.44018e66	0.600531	0.300266	−	0.953856i	$-0.402925\pi$
$683$	2.44018e66	0.600531	0.300266	+	0.953856i	$0.402925\pi$
$684$	−3.71672e65	−0.0883774
$685$	−3.90621e66	−0.897485
$686$	3.39831e66	0.754477
$687$	−1.47919e66	−0.317351
$688$	−5.87046e65	−0.121715
$689$	1.84421e66	0.369537
$690$	−8.69704e65	−0.168429
$691$	−6.35166e65	−0.118892	−0.0594461	−	0.998232i	$-0.518933\pi$
$691$	−6.35166e65	−0.118892	−0.0594461	+	0.998232i	$0.518933\pi$
$692$	−1.21507e66	−0.219841
$693$	6.50405e65	0.113750
$694$	3.81401e66	0.644813
$695$	−9.99002e66	−1.63276
$696$	3.85043e66	0.608404
$697$	1.49345e67	2.28150
$698$	6.21813e66	0.918454
$699$	−7.72357e66	−1.10307
$700$	3.58907e65	0.0495653
$701$	9.25129e66	1.23546	0.617731	−	0.786390i	$-0.288052\pi$
$701$	9.25129e66	1.23546	0.617731	+	0.786390i	$0.288052\pi$
$702$	−5.51872e66	−0.712715
$703$	5.39977e66	0.674412
$704$	−9.68447e65	−0.116982
$705$	−1.48260e67	−1.73213
$706$	−2.75785e66	−0.311645
$707$	−3.74343e66	−0.409179
$708$	−6.24381e66	−0.660189
$709$	−5.37433e65	−0.0549715	−0.0274858	−	0.999622i	$-0.508750\pi$
$709$	−5.37433e65	−0.0549715	−0.0274858	+	0.999622i	$0.508750\pi$
$710$	4.30666e66	0.426157
$711$	−2.86938e66	−0.274696
$712$	−2.05472e66	−0.190315
$713$	−8.95688e65	−0.0802699
$714$	−9.33175e66	−0.809199
$715$	−1.12523e67	−0.944168
$716$	3.50132e66	0.284299
$717$	8.32605e66	0.654243
$718$	6.01646e66	0.457527
$719$	−1.66065e67	−1.22222	−0.611109	−	0.791546i	$-0.709276\pi$
$719$	−1.66065e67	−1.22222	−0.611109	+	0.791546i	$0.709276\pi$
$720$	−6.31437e65	−0.0449797
$721$	4.64396e66	0.320191
$722$	−1.03747e66	−0.0692394
$723$	2.56649e67	1.65802
$724$	−5.89823e66	−0.368863
$725$	4.28891e66	0.259659
$726$	−1.36589e66	−0.0800583
$727$	1.40648e67	0.798133	0.399066	−	0.916922i	$-0.369334\pi$
$727$	1.40648e67	0.798133	0.399066	+	0.916922i	$0.369334\pi$
$728$	−4.38583e66	−0.240971
$729$	2.08082e67	1.10698
$730$	9.28402e66	0.478243
$731$	1.70017e67	0.848074
$732$	−1.32560e67	−0.640329
$733$	1.94974e67	0.912082	0.456041	−	0.889959i	$-0.349267\pi$
$733$	1.94974e67	0.912082	0.456041	+	0.889959i	$0.349267\pi$
$734$	−3.08030e66	−0.139552
$735$	1.06563e67	0.467579
$736$	1.01886e66	0.0432997
$737$	−3.09601e67	−1.27443
$738$	−3.91820e66	−0.156229
$739$	−2.30620e67	−0.890742	−0.445371	−	0.895346i	$-0.646928\pi$
$739$	−2.30620e67	−0.890742	−0.445371	+	0.895346i	$0.646928\pi$
$740$	9.17374e66	0.343242
$741$	−2.49313e67	−0.903686
$742$	−5.66817e66	−0.199045
$743$	−5.16074e67	−1.75580	−0.877899	−	0.478846i	$-0.841055\pi$
$743$	−5.16074e67	−1.75580	−0.877899	+	0.478846i	$0.841055\pi$
$744$	3.20474e66	0.105640
$745$	−7.13198e66	−0.227791
$746$	4.10693e67	1.27103
$747$	−4.55711e66	−0.136664
$748$	2.80476e67	0.815094
$749$	−2.71365e67	−0.764242
$750$	−2.17279e67	−0.593031
$751$	6.94354e67	1.83672	0.918359	−	0.395749i	$-0.129515\pi$
$751$	6.94354e67	1.83672	0.918359	+	0.395749i	$0.129515\pi$
$752$	1.73687e67	0.445295
$753$	−9.35937e66	−0.232576
$754$	−5.24104e67	−1.26238
$755$	−1.03532e67	−0.241726
$756$	1.69618e67	0.383892
$757$	−2.69181e67	−0.590597	−0.295299	−	0.955405i	$-0.595419\pi$
$757$	−2.69181e67	−0.590597	−0.295299	+	0.955405i	$0.595419\pi$
$758$	2.16400e67	0.460290
$759$	−1.01352e67	−0.209002
$760$	−1.97629e67	−0.395122
$761$	−4.78143e67	−0.926869	−0.463434	−	0.886131i	$-0.653383\pi$
$761$	−4.78143e67	−0.926869	−0.463434	+	0.886131i	$0.653383\pi$
$762$	2.24372e67	0.421722
$763$	4.71393e67	0.859125
$764$	1.73484e66	0.0306595
$765$	1.82873e67	0.313405
$766$	−4.10799e67	−0.682737
$767$	8.49881e67	1.36983
$768$	−3.64544e66	−0.0569852
$769$	−4.73313e67	−0.717595	−0.358797	−	0.933416i	$-0.616813\pi$
$769$	−4.73313e67	−0.717595	−0.358797	+	0.933416i	$0.616813\pi$
$770$	3.45840e67	0.508561
$771$	7.36750e67	1.05085
$772$	2.51675e67	0.348204
$773$	7.92001e67	1.06294	0.531469	−	0.847078i	$-0.321640\pi$
$773$	7.92001e67	1.06294	0.531469	+	0.847078i	$0.321640\pi$
$774$	−4.46054e66	−0.0580731
$775$	3.56969e66	0.0450859
$776$	−3.53056e67	−0.432607
$777$	−3.55693e67	−0.422845
$778$	−2.15248e67	−0.248266
$779$	−1.22633e68	−1.37239
$780$	−4.23561e67	−0.459931
$781$	5.01882e67	0.528813
$782$	−2.95076e67	−0.301700
$783$	2.02692e68	2.01111
$784$	−1.24839e67	−0.120205
$785$	−3.63161e67	−0.339361
$786$	4.42084e67	0.400936
$787$	−1.54384e68	−1.35892	−0.679462	−	0.733711i	$-0.737787\pi$
$787$	−1.54384e68	−1.35892	−0.679462	+	0.733711i	$0.737787\pi$
$788$	5.31751e67	0.454299
$789$	−2.10512e68	−1.74569
$790$	−1.52573e68	−1.22812
$791$	4.68084e67	0.365743
$792$	−7.35853e66	−0.0558148
$793$	1.80436e68	1.32862
$794$	2.42069e66	0.0173044
$795$	−5.47403e67	−0.379909
$796$	−6.54517e67	−0.441026
$797$	2.49717e68	1.63372	0.816861	−	0.576835i	$-0.195712\pi$
$797$	2.49717e68	1.63372	0.816861	+	0.576835i	$0.195712\pi$
$798$	7.66265e67	0.486756
$799$	−5.03022e68	−3.10268
$800$	−4.06058e66	−0.0243206
$801$	−1.56123e67	−0.0908038
$802$	2.44512e68	1.38103
$803$	1.08192e68	0.593446
$804$	−1.16540e68	−0.620811
$805$	−3.63842e67	−0.188239
$806$	−4.36216e67	−0.219194
$807$	3.48396e68	1.70038
$808$	4.23522e67	0.200775
$809$	−1.17695e68	−0.541962	−0.270981	−	0.962585i	$-0.587348\pi$
$809$	−1.17695e68	−0.541962	−0.270981	+	0.962585i	$0.587348\pi$
$810$	1.35366e68	0.605498
$811$	4.92587e67	0.214039	0.107020	−	0.994257i	$-0.465869\pi$
$811$	4.92587e67	0.214039	0.107020	+	0.994257i	$0.465869\pi$
$812$	1.61084e68	0.679962
$813$	−4.01546e67	−0.164667
$814$	1.06907e68	0.425925
$815$	1.39363e68	0.539442
$816$	1.05577e68	0.397056
$817$	−1.39607e68	−0.510140
$818$	2.35648e68	0.836683
$819$	−3.33248e67	−0.114973
$820$	−2.08342e68	−0.698477
$821$	−9.68202e67	−0.315429	−0.157715	−	0.987485i	$-0.550413\pi$
$821$	−9.68202e67	−0.315429	−0.157715	+	0.987485i	$0.550413\pi$
$822$	−1.71353e68	−0.542505
$823$	−3.39626e67	−0.104497	−0.0522486	−	0.998634i	$-0.516639\pi$
$823$	−3.39626e67	−0.104497	−0.0522486	+	0.998634i	$0.516639\pi$
$824$	−5.25406e67	−0.157111
$825$	4.03930e67	0.117392
$826$	−2.61211e68	−0.737837
$827$	−4.85290e68	−1.33236	−0.666181	−	0.745790i	$-0.732072\pi$
$827$	−4.85290e68	−1.33236	−0.666181	+	0.745790i	$0.732072\pi$
$828$	7.74157e66	0.0206593
$829$	6.15189e67	0.159579	0.0797897	−	0.996812i	$-0.474575\pi$
$829$	6.15189e67	0.159579	0.0797897	+	0.996812i	$0.474575\pi$
$830$	−2.42315e68	−0.611005
$831$	−2.44888e68	−0.600266
$832$	4.96202e67	0.118239
$833$	3.61551e68	0.837553
$834$	−4.38230e68	−0.986960
$835$	9.35676e67	0.204877
$836$	−2.30309e68	−0.490302
$837$	1.68702e68	0.349199
$838$	9.36282e67	0.188440
$839$	−3.74895e68	−0.733675	−0.366838	−	0.930285i	$-0.619560\pi$
$839$	−3.74895e68	−0.733675	−0.366838	+	0.930285i	$0.619560\pi$
$840$	1.30182e68	0.247734
$841$	1.38455e69	2.56214
$842$	−7.10938e67	−0.127937
$843$	2.82836e68	0.494979
$844$	4.43435e68	0.754715
$845$	−6.78189e67	−0.112258
$846$	1.31972e68	0.212461
$847$	−5.71424e67	−0.0894743
$848$	6.41283e67	0.0976668
$849$	−9.71513e68	−1.43919
$850$	1.17600e68	0.169458
$851$	−1.12472e68	−0.157652
$852$	1.88919e68	0.257600
$853$	8.40714e67	0.111518	0.0557592	−	0.998444i	$-0.482242\pi$
$853$	8.40714e67	0.111518	0.0557592	+	0.998444i	$0.482242\pi$
$854$	−5.54569e68	−0.715641
$855$	−1.50164e68	−0.188522
$856$	3.07015e68	0.374996
$857$	1.39713e69	1.66031	0.830153	−	0.557536i	$-0.188253\pi$
$857$	1.39713e69	1.66031	0.830153	+	0.557536i	$0.188253\pi$
$858$	−4.93602e68	−0.570723
$859$	−4.05890e68	−0.456634	−0.228317	−	0.973587i	$-0.573322\pi$
$859$	−4.05890e68	−0.456634	−0.228317	+	0.973587i	$0.573322\pi$
$860$	−2.37180e68	−0.259636
$861$	8.07805e68	0.860463
$862$	6.93922e68	0.719267
$863$	3.10515e68	0.313205	0.156603	−	0.987662i	$-0.449946\pi$
$863$	3.10515e68	0.313205	0.156603	+	0.987662i	$0.449946\pi$
$864$	−1.91902e68	−0.188367
$865$	−4.90916e68	−0.468952
$866$	−9.27057e67	−0.0861858
$867$	−2.04996e69	−1.85480
$868$	1.34071e68	0.118065
$869$	−1.77803e69	−1.52396
$870$	1.55566e69	1.29782
$871$	1.58630e69	1.28812
$872$	−5.33322e68	−0.421553
$873$	−2.68262e68	−0.206407
$874$	2.42298e68	0.181481
$875$	−9.08989e68	−0.662780
$876$	4.07260e68	0.289085
$877$	−1.45608e69	−1.00622	−0.503111	−	0.864222i	$-0.667811\pi$
$877$	−1.45608e69	−1.00622	−0.503111	+	0.864222i	$0.667811\pi$
$878$	8.85775e67	0.0595940
$879$	1.13114e69	0.740932
$880$	−3.91275e68	−0.249539
$881$	−1.00945e69	−0.626834	−0.313417	−	0.949616i	$-0.601474\pi$
$881$	−1.00945e69	−0.626834	−0.313417	+	0.949616i	$0.601474\pi$
$882$	−9.48561e67	−0.0573526
$883$	2.76740e66	0.00162928	0.000814640	−	1.00000i	$-0.499741\pi$
$883$	2.76740e66	0.00162928	0.000814640		1.00000i	$0.499741\pi$
$884$	−1.43707e69	−0.823853
$885$	−2.52264e69	−1.40828
$886$	8.01580e68	0.435767
$887$	2.60603e69	1.37967	0.689834	−	0.723967i	$-0.257683\pi$
$887$	2.60603e69	1.37967	0.689834	+	0.723967i	$0.257683\pi$
$888$	4.02422e68	0.207480
$889$	9.38664e68	0.471323
$890$	−8.30155e68	−0.405970
$891$	1.57751e69	0.751356
$892$	5.05012e68	0.234276
$893$	4.13050e69	1.86635
$894$	−3.12857e68	−0.137694
$895$	1.41461e69	0.606452
$896$	−1.52508e68	−0.0636875
$897$	5.19296e68	0.211248
$898$	7.08634e68	0.280820
$899$	1.60214e69	0.618512
$900$	−3.08534e67	−0.0116039
$901$	−1.85724e69	−0.680513
$902$	−2.42794e69	−0.866732
$903$	9.19617e68	0.319849
$904$	−5.29579e68	−0.179462
$905$	−2.38302e69	−0.786839
$906$	−4.54163e68	−0.146117
$907$	−2.18961e69	−0.686430	−0.343215	−	0.939257i	$-0.611516\pi$
$907$	−2.18961e69	−0.686430	−0.343215	+	0.939257i	$0.611516\pi$
$908$	−5.87766e68	−0.179551
$909$	3.21804e68	0.0957944
$910$	−1.77198e69	−0.514026
$911$	4.80229e69	1.35758	0.678792	−	0.734331i	$-0.262504\pi$
$911$	4.80229e69	1.35758	0.678792	+	0.734331i	$0.262504\pi$
$912$	−8.66933e68	−0.238840
$913$	−2.82384e69	−0.758189
$914$	9.05502e68	0.236948
$915$	−5.35574e69	−1.36592
$916$	7.00119e68	0.174032
$917$	1.84947e69	0.448092
$918$	5.55774e69	1.31249
$919$	−1.06530e69	−0.245221	−0.122611	−	0.992455i	$-0.539127\pi$
$919$	−1.06530e69	−0.245221	−0.122611	+	0.992455i	$0.539127\pi$
$920$	4.11642e68	0.0923647
$921$	−6.86565e69	−1.50169
$922$	−4.43139e69	−0.944850
$923$	−2.57149e69	−0.534496
$924$	1.51709e69	0.307411
$925$	4.48249e68	0.0885501
$926$	2.40905e69	0.463968
$927$	−3.99218e68	−0.0749612
$928$	−1.82246e69	−0.333642
$929$	2.63253e69	0.469899	0.234950	−	0.972008i	$-0.424507\pi$
$929$	2.63253e69	0.469899	0.234950	+	0.972008i	$0.424507\pi$
$930$	1.29479e69	0.225346
$931$	−2.96883e69	−0.503811
$932$	3.65567e69	0.604912
$933$	9.65505e69	1.55789
$934$	2.84719e69	0.447986
$935$	1.13319e70	1.73871
$936$	3.77028e68	0.0564146
$937$	−2.94388e69	−0.429576	−0.214788	−	0.976661i	$-0.568906\pi$
$937$	−2.94388e69	−0.429576	−0.214788	+	0.976661i	$0.568906\pi$
$938$	−4.87549e69	−0.693827
$939$	1.19149e69	0.165367
$940$	7.01735e69	0.949880
$941$	−6.13459e69	−0.809896	−0.404948	−	0.914340i	$-0.632710\pi$
$941$	−6.13459e69	−0.809896	−0.404948	+	0.914340i	$0.632710\pi$
$942$	−1.59307e69	−0.205135
$943$	2.55433e69	0.320813
$944$	2.95528e69	0.362040
$945$	6.85295e69	0.818899
$946$	−2.76401e69	−0.322179
$947$	−1.26712e70	−1.44077	−0.720384	−	0.693575i	$-0.756035\pi$
$947$	−1.26712e70	−1.44077	−0.720384	+	0.693575i	$0.756035\pi$
$948$	−6.69290e69	−0.742367
$949$	−5.54344e69	−0.599824
$950$	−9.65658e68	−0.101934
$951$	−5.93650e69	−0.611348
$952$	4.41684e69	0.443755
$953$	−3.67798e69	−0.360517	−0.180258	−	0.983619i	$-0.557693\pi$
$953$	−3.67798e69	−0.360517	−0.180258	+	0.983619i	$0.557693\pi$
$954$	4.87264e68	0.0465991
$955$	7.00914e68	0.0654012
$956$	−3.94083e69	−0.358779
$957$	1.81291e70	1.61044
$958$	2.86777e69	0.248574
$959$	−7.16858e69	−0.606311
$960$	−1.47284e69	−0.121558
$961$	−1.10830e70	−0.892605
$962$	−5.47760e69	−0.430503
$963$	2.33279e69	0.178919
$964$	−1.21475e70	−0.909239
$965$	1.01682e70	0.742769
$966$	−1.59606e69	−0.113785
$967$	1.17076e70	0.814604	0.407302	−	0.913294i	$-0.366470\pi$
$967$	1.17076e70	0.814604	0.407302	+	0.913294i	$0.366470\pi$
$968$	6.46495e68	0.0439030
$969$	2.51076e70	1.66417
$970$	−1.42643e70	−0.922813
$971$	−6.44897e69	−0.407229	−0.203614	−	0.979051i	$-0.565269\pi$
$971$	−6.44897e69	−0.407229	−0.203614	+	0.979051i	$0.565269\pi$
$972$	−2.70578e69	−0.166777
$973$	−1.83334e70	−1.10304
$974$	6.44654e69	0.378609
$975$	−2.06961e69	−0.118654
$976$	6.27426e69	0.351149
$977$	1.07014e70	0.584680	0.292340	−	0.956314i	$-0.405566\pi$
$977$	1.07014e70	0.584680	0.292340	+	0.956314i	$0.405566\pi$
$978$	6.11342e69	0.326078
$979$	−9.67431e69	−0.503763
$980$	−5.04378e69	−0.256415
$981$	−4.05233e69	−0.201133
$982$	2.53911e69	0.123045
$983$	1.67060e69	0.0790432	0.0395216	−	0.999219i	$-0.487417\pi$
$983$	1.67060e69	0.0790432	0.0395216	+	0.999219i	$0.487417\pi$
$984$	−9.13930e69	−0.422210
$985$	2.14839e70	0.969087
$986$	5.27810e70	2.32472
$987$	−2.72083e70	−1.17017
$988$	1.18003e70	0.495571
$989$	2.90788e69	0.119252
$990$	−2.97301e69	−0.119061
$991$	4.20628e70	1.64500	0.822502	−	0.568762i	$-0.192577\pi$
$991$	4.20628e70	1.64500	0.822502	+	0.568762i	$0.192577\pi$
$992$	−1.51685e69	−0.0579319
$993$	−2.83450e70	−1.05723
$994$	7.90347e69	0.287898
$995$	−2.64440e70	−0.940772
$996$	−1.06296e70	−0.369335
$997$	2.11611e70	0.718128	0.359064	−	0.933313i	$-0.383096\pi$
$997$	2.11611e70	0.718128	0.359064	+	0.933313i	$0.383096\pi$
$998$	−2.43432e70	−0.806883
$999$	2.11841e70	0.685837

Twists

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

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

\(f(q)\)	\(=\)	\(q-8.38861e6 q^{2} -1.48673e11 q^{3} +7.03687e13 q^{4} +2.84306e16 q^{5} +1.24716e18 q^{6} +5.21750e19 q^{7} -5.90296e20 q^{8} -4.48523e21 q^{9} +O(q^{10})\)	\(q-8.38861e6 q^{2} -1.48673e11 q^{3} +7.03687e13 q^{4} +2.84306e16 q^{5} +1.24716e18 q^{6} +5.21750e19 q^{7} -5.90296e20 q^{8} -4.48523e21 q^{9} -2.38493e23 q^{10} -2.77931e24 q^{11} -1.04619e25 q^{12} +1.42403e26 q^{13} -4.37676e26 q^{14} -4.22685e27 q^{15} +4.95176e27 q^{16} -1.43410e29 q^{17} +3.76248e28 q^{18} +1.17759e30 q^{19} +2.00062e30 q^{20} -7.75701e30 q^{21} +2.33145e31 q^{22} -2.45281e31 q^{23} +8.77609e31 q^{24} +9.77550e31 q^{25} -1.19456e33 q^{26} +4.61986e33 q^{27} +3.67149e33 q^{28} +4.38741e34 q^{29} +3.54574e34 q^{30} +3.65168e34 q^{31} -4.15384e34 q^{32} +4.13207e35 q^{33} +1.20301e36 q^{34} +1.48337e36 q^{35} -3.15620e35 q^{36} +4.58544e36 q^{37} -9.87836e36 q^{38} -2.11715e37 q^{39} -1.67825e37 q^{40} -1.04139e38 q^{41} +6.50705e37 q^{42} -1.18553e38 q^{43} -1.95576e38 q^{44} -1.27518e38 q^{45} +2.05757e38 q^{46} +3.50758e39 q^{47} -7.36192e38 q^{48} -2.52110e39 q^{49} -8.20028e38 q^{50} +2.13211e40 q^{51} +1.00207e40 q^{52} +1.29506e40 q^{53} -3.87542e40 q^{54} -7.90173e40 q^{55} -3.07987e40 q^{56} -1.75076e41 q^{57} -3.68043e41 q^{58} +5.96814e41 q^{59} -2.97438e41 q^{60} +1.26708e42 q^{61} -3.06325e41 q^{62} -2.34017e41 q^{63} +3.48449e41 q^{64} +4.04860e42 q^{65} -3.46623e42 q^{66} +1.11395e43 q^{67} -1.00916e43 q^{68} +3.64666e42 q^{69} -1.24434e43 q^{70} -1.80578e43 q^{71} +2.64761e42 q^{72} -3.89278e43 q^{73} -3.84654e43 q^{74} -1.45335e43 q^{75} +8.28657e43 q^{76} -1.45010e44 q^{77} +1.77599e44 q^{78} +6.39740e44 q^{79} +1.40781e44 q^{80} -5.67591e44 q^{81} +8.73579e44 q^{82} +1.01602e45 q^{83} -5.45851e44 q^{84} -4.07723e45 q^{85} +9.94495e44 q^{86} -6.52289e45 q^{87} +1.64061e45 q^{88} +3.48084e45 q^{89} +1.06970e45 q^{90} +7.42989e45 q^{91} -1.72601e45 q^{92} -5.42905e45 q^{93} -2.94237e46 q^{94} +3.34796e46 q^{95} +6.17562e45 q^{96} +5.98100e46 q^{97} +2.11485e46 q^{98} +1.24658e46 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 16777216 q^{2} + 122289844824 q^{3} + 140737488355328 q^{4} + 18\!\cdots\!40 q^{5}+ \cdots + 42\!\cdots\!14 q^{9}+O(q^{10}) \) 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

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Fields

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