LMFDB - Embedded newform 14.50.a.c.1.5

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [14,50,Mod(1,14)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(14, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0])) N = Newforms(chi, 50, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("14.1"); S:= CuspForms(chi, 50); N := Newforms(S);

Level:	$ N $	$=$	$ 14 = 2 \cdot 7 $
Weight:	$ k $	$=$	$ 50 $
Character orbit:	$[\chi]$	$=$	14.a (trivial)

Newform invariants

comment:select newform

sage:traces = [6,100663296] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$212.892687139$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	$\mathbb{Q}[x]/(x^{6} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 2 x^{5} + \cdots + 43\!\cdots\!00 $ x^6 - 2x^5 - 203175676558619318376719x^4 - 3419566010670394893004208592324880x^3 + 8387437890222708849465217967834896594930824800x^2 + 749992190970225444044098070740580209503030746947751072000*x + 4378820497185396601931374665584549576641809046609939862188736160000
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{36}\cdot 3^{12}\cdot 5^{6}\cdot 7^{6} $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.5
Root			$-1.52153e11$ of defining polynomial
Character	$\chi$	$=$	14.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+1.67772e7 q^{2} +4.04355e11 q^{3} +2.81475e14 q^{4} +2.21202e17 q^{5} +6.78395e18 q^{6} -1.91581e20 q^{7} +4.72237e21 q^{8} -7.57966e22 q^{9} +3.71115e24 q^{10} +5.62954e25 q^{11} +1.13816e26 q^{12} -1.96258e27 q^{13} -3.21420e27 q^{14} +8.94441e28 q^{15} +7.92282e28 q^{16} +2.82188e29 q^{17} -1.27166e30 q^{18} +4.97367e29 q^{19} +6.22628e31 q^{20} -7.74668e31 q^{21} +9.44480e32 q^{22} +3.40504e33 q^{23} +1.90951e33 q^{24} +3.11668e34 q^{25} -3.29266e34 q^{26} -1.27411e35 q^{27} -5.39253e34 q^{28} -1.03033e36 q^{29} +1.50062e36 q^{30} -1.55199e36 q^{31} +1.32923e36 q^{32} +2.27633e37 q^{33} +4.73434e36 q^{34} -4.23782e37 q^{35} -2.13348e37 q^{36} +2.95756e38 q^{37} +8.34443e36 q^{38} -7.93577e38 q^{39} +1.04460e39 q^{40} +3.46561e39 q^{41} -1.29968e39 q^{42} +1.20947e40 q^{43} +1.58457e40 q^{44} -1.67664e40 q^{45} +5.71271e40 q^{46} +1.51872e41 q^{47} +3.20363e40 q^{48} +3.67034e40 q^{49} +5.22892e41 q^{50} +1.14104e41 q^{51} -5.52416e41 q^{52} -1.44509e42 q^{53} -2.13759e42 q^{54} +1.24527e43 q^{55} -9.04717e41 q^{56} +2.01113e41 q^{57} -1.72861e43 q^{58} -4.08343e42 q^{59} +2.51763e43 q^{60} +5.03042e43 q^{61} -2.60381e43 q^{62} +1.45212e43 q^{63} +2.23007e43 q^{64} -4.34126e44 q^{65} +3.81905e44 q^{66} -4.20396e44 q^{67} +7.94290e43 q^{68} +1.37684e45 q^{69} -7.10988e44 q^{70} +1.58873e44 q^{71} -3.57939e44 q^{72} +5.96797e45 q^{73} +4.96196e45 q^{74} +1.26024e46 q^{75} +1.39996e44 q^{76} -1.07851e46 q^{77} -1.33140e46 q^{78} +4.05103e46 q^{79} +1.75254e46 q^{80} -3.33810e46 q^{81} +5.81433e46 q^{82} -1.14810e47 q^{83} -2.18050e46 q^{84} +6.24207e46 q^{85} +2.02916e47 q^{86} -4.16619e47 q^{87} +2.65847e47 q^{88} +2.24417e47 q^{89} -2.81293e47 q^{90} +3.75993e47 q^{91} +9.58434e47 q^{92} -6.27556e47 q^{93} +2.54800e48 q^{94} +1.10019e47 q^{95} +5.37480e47 q^{96} +2.25892e48 q^{97} +6.15780e47 q^{98} -4.26700e48 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 100663296 q^{2} + 600288540488 q^{3} + 16\!\cdots\!36 q^{4} + 23\!\cdots\!44 q^{5} + 10\!\cdots\!08 q^{6} - 11\!\cdots\!06 q^{7} + 28\!\cdots\!76 q^{8} + 24\!\cdots\!58 q^{9} + 39\!\cdots\!04 q^{10}+ \cdots - 23\!\cdots\!84 q^{99}+O(q^{100}) $ 6 * q + 100663296 * q^2 + 600288540488 * q^3 + 1688849860263936 * q^4 + 237495319633852644 * q^5 + 10071170506091921408 * q^6 - 1149487388283398486406 * q^7 + 28334198897217871282176 * q^8 + 249667159058784905352958 * q^9 + 3984510276486186720559104 * q^10 + 22232534037385203892080408 * q^11 + 168966202953533481317040128 * q^12 + 2632998893516569086205448724 * q^13 - 19285198202506445620506525696 * q^14 + 149072300431744884273809122880 * q^15 + 475368975085586025561263702016 * q^16 - 1409004291529529137192771562100 * q^17 + 4188719855635591054646132604928 * q^18 + 18105270833681321619211508609928 * q^19 + 66848989562828475627151728574464 * q^20 - 115004017770334038187527674767688 * q^21 + 373000025772563640901473694384128 * q^22 + 5618913122903377817563359905020800 * q^23 + 2834782483651269179287946708123648 * q^24 + 5996249800897839089131003669066986 * q^25 + 44174391164288479138191433619472384 * q^26 + 124497907324429451768320951590293744 * q^27 - 323551935846262379567492011011342336 * q^28 - 483091083860359843452294275052160332 * q^29 + 2501018183960277180356698797328302080 * q^30 + 6486298240062882259192167116430562080 * q^31 + 7975367974709495237422842361682067456 * q^32 - 62373898779937118804633162567140460480 * q^33 - 23639169343917880712976762136009113600 * q^34 - 45499645782574701040199480904673526244 * q^35 + 70275057781487128411465970277519720448 * q^36 - 175145361056063681116535719938063892668 * q^37 + 303756039515171607970981229634621800448 * q^38 - 81396995084096796106565511444255620448 * q^39 + 1121539937277318906547460015067154612224 * q^40 + 835550088847864742420204150305371241308 * q^41 - 1929447247000732550824400305555251396608 * q^42 + 17308185468083461647372224162326046585976 * q^43 + 6257902000391867077150458889000502427648 * q^44 + 103167727297878364026250185422148990648148 * q^45 + 94269719148184516774869082812273446092800 * q^46 + 184831957187272343600261999594531459533344 * q^47 + 47559758041233811695056608118679397203968 * q^48 + 220220209303764752647381266192201961132806 * q^49 + 100600378099620040331594100852729342590976 * q^50 - 1771571524511561271442105788532936222457168 * q^51 + 741123302231759300812931531183549992402944 * q^52 + 2351347648887961413461306710918084645940772 * q^53 + 2088728282729934989078702562155901646536704 * q^54 + 3085506887527435207314999234586652419171056 * q^55 - 5428300714910886734677800047011668821016576 * q^56 + 31386997170933042757613940977962373909990896 * q^57 - 8104923461599370931325326748113505156595712 * q^58 + 30944438467849109083090742506105243891298520 * q^59 + 41960122292229305674715292769717146909409280 * q^60 + 150150609374563344118041131116366350036061044 * q^61 + 108822026613954829245034973220452689017569280 * q^62 - 47831541767769749048424100541375377399148158 * q^63 + 133804471191183738849214309635890169035882496 * q^64 + 752748549799322853557360453473881793779240456 * q^65 - 1046460372593141508602992369152030007812423680 * q^66 - 128785963396634280403104719488486831723130328 * q^67 - 396599450143488570983845141336446276835737600 * q^68 + 683944728096651671392678575425131612212016000 * q^69 - 763357385217744795486851374225583159277256704 * q^70 + 280171533474803716136746628126132726863354608 * q^71 + 1179019823812490354578901459995528294215712768 * q^72 + 6359164269014273149745068623217940032230909276 * q^73 - 2938451553835568487847240945116404549091852288 * q^74 + 21669926216235979931654849241861968650694269720 * q^75 + 5096180686250569343996473821525651024424992768 * q^76 - 4259336247592613144486630846481598632941155608 * q^77 - 1365614968276830113187808603650748503470112768 * q^78 - 67602995067772997355679612466712542986464262464 * q^79 + 18816317780328031196030550924144907434678288384 * q^80 - 16854545541923284876477831491790840658294025626 * q^81 + 14018204319419817922368127793769679275612438528 * q^82 - 45613436384448178087860777699340468946504675160 * q^83 - 32370753223536642163411941996766452615194083328 * q^84 - 55477811327569765203281837835132224387734181592 * q^85 + 290383166166097342085679637171763145998981922816 * q^86 - 384172046681295864425179771398097404272715681328 * q^87 + 104990173567406438596641913279881453337174867968 * q^88 + 802941729082063189409562013460525749819175687196 * q^89 + 1730867245105601654995029030867444800285958995968 * q^90 - 504433170243573172459186088471907935721940674324 * q^91 + 1581583440408427645787601974063399056163261644800 * q^92 + 5393326286497522306808749269007443718265926441248 * q^93 + 3100965669433620559407813223789366715386171490304 * q^94 + 6309934171256595954343099570284482000731174337760 * q^95 + 797920333565516565311290846634437881640767193088 * q^96 + 2208884359814234277165695356094087258476148891724 * q^97 + 3694682019054470868351687337260069817548690948096 * q^98 - 23361740711649209489147347130820123162443505968584 * q^99

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	1.67772e7	0.707107
$2$	1.67772e7	0.707107
$3$	4.04355e11	0.826593	0.413297	−	0.910596i	$-0.364377\pi$
$3$	4.04355e11	0.826593	0.413297	+	0.910596i	$0.364377\pi$
$4$	2.81475e14	0.500000
$5$	2.21202e17	1.65968	0.829839	−	0.558002i	$-0.188432\pi$
$5$	2.21202e17	1.65968	0.829839	+	0.558002i	$0.188432\pi$
$6$	6.78395e18	0.584490
$7$	−1.91581e20	−0.377964
$7$	−1.91581e20	−0.377964
$8$	4.72237e21	0.353553
$9$	−7.57966e22	−0.316744
$10$	3.71115e24	1.17357
$11$	5.62954e25	1.72326	0.861632	−	0.507533i	$-0.169443\pi$
$11$	5.62954e25	1.72326	0.861632	+	0.507533i	$0.169443\pi$
$12$	1.13816e26	0.413297
$13$	−1.96258e27	−1.00280	−0.501400	−	0.865215i	$-0.667182\pi$
$13$	−1.96258e27	−1.00280	−0.501400	+	0.865215i	$0.667182\pi$
$14$	−3.21420e27	−0.267261
$15$	8.94441e28	1.37188
$16$	7.92282e28	0.250000
$17$	2.82188e29	0.201623	0.100812	−	0.994906i	$-0.467856\pi$
$17$	2.82188e29	0.201623	0.100812	+	0.994906i	$0.467856\pi$
$18$	−1.27166e30	−0.223972
$19$	4.97367e29	0.0232924	0.0116462	−	0.999932i	$-0.496293\pi$
$19$	4.97367e29	0.0232924	0.0116462	+	0.999932i	$0.496293\pi$
$20$	6.22628e31	0.829839
$21$	−7.74668e31	−0.312423
$22$	9.44480e32	1.21853
$23$	3.40504e33	1.47839	0.739197	−	0.673489i	$-0.235205\pi$
$23$	3.40504e33	1.47839	0.739197	+	0.673489i	$0.235205\pi$
$24$	1.90951e33	0.292245
$25$	3.11668e34	1.75453
$26$	−3.29266e34	−0.709087
$27$	−1.27411e35	−1.08841
$28$	−5.39253e34	−0.188982
$29$	−1.03033e36	−1.52836	−0.764179	−	0.645004i	$-0.776856\pi$
$29$	−1.03033e36	−1.52836	−0.764179	+	0.645004i	$0.776856\pi$
$30$	1.50062e36	0.970065
$31$	−1.55199e36	−0.449291	−0.224646	−	0.974441i	$-0.572122\pi$
$31$	−1.55199e36	−0.449291	−0.224646	+	0.974441i	$0.572122\pi$
$32$	1.32923e36	0.176777
$33$	2.27633e37	1.42444
$34$	4.73434e36	0.142569
$35$	−4.23782e37	−0.627300
$36$	−2.13348e37	−0.158372
$37$	2.95756e38	1.12199	0.560997	−	0.827818i	$-0.310418\pi$
$37$	2.95756e38	1.12199	0.560997	+	0.827818i	$0.310418\pi$
$38$	8.34443e36	0.0164702
$39$	−7.93577e38	−0.828908
$40$	1.04460e39	0.586785
$41$	3.46561e39	1.06310	0.531552	−	0.847026i	$-0.321609\pi$
$41$	3.46561e39	1.06310	0.531552	+	0.847026i	$0.321609\pi$
$42$	−1.29968e39	−0.220916
$43$	1.20947e40	1.15510	0.577550	−	0.816355i	$-0.304009\pi$
$43$	1.20947e40	1.15510	0.577550	+	0.816355i	$0.304009\pi$
$44$	1.58457e40	0.861632
$45$	−1.67664e40	−0.525693
$46$	5.71271e40	1.04538
$47$	1.51872e41	1.64090	0.820449	−	0.571720i	$-0.193724\pi$
$47$	1.51872e41	1.64090	0.820449	+	0.571720i	$0.193724\pi$
$48$	3.20363e40	0.206648
$49$	3.67034e40	0.142857
$50$	5.22892e41	1.24064
$51$	1.14104e41	0.166660
$52$	−5.52416e41	−0.501400
$53$	−1.44509e42	−0.822502	−0.411251	−	0.911522i	$-0.634908\pi$
$53$	−1.44509e42	−0.822502	−0.411251	+	0.911522i	$0.634908\pi$
$54$	−2.13759e42	−0.769623
$55$	1.24527e43	2.86007
$56$	−9.04717e41	−0.133631
$57$	2.01113e41	0.0192533
$58$	−1.72861e43	−1.08071
$59$	−4.08343e42	−0.167939	−0.0839695	−	0.996468i	$-0.526760\pi$
$59$	−4.08343e42	−0.167939	−0.0839695	+	0.996468i	$0.526760\pi$
$60$	2.51763e43	0.685940
$61$	5.03042e43	0.914163	0.457081	−	0.889425i	$-0.348895\pi$
$61$	5.03042e43	0.914163	0.457081	+	0.889425i	$0.348895\pi$
$62$	−2.60381e43	−0.317697
$63$	1.45212e43	0.119718
$64$	2.23007e43	0.125000
$65$	−4.34126e44	−1.66433
$66$	3.81905e44	1.00723
$67$	−4.20396e44	−0.767054	−0.383527	−	0.923530i	$-0.625291\pi$
$67$	−4.20396e44	−0.767054	−0.383527	+	0.923530i	$0.625291\pi$
$68$	7.94290e43	0.100812
$69$	1.37684e45	1.22203
$70$	−7.10988e44	−0.443568
$71$	1.58873e44	0.0700198	0.0350099	−	0.999387i	$-0.488854\pi$
$71$	1.58873e44	0.0700198	0.0350099	+	0.999387i	$0.488854\pi$
$72$	−3.57939e44	−0.111986
$73$	5.96797e45	1.33173	0.665866	−	0.746071i	$-0.268062\pi$
$73$	5.96797e45	1.33173	0.665866	+	0.746071i	$0.268062\pi$
$74$	4.96196e45	0.793370
$75$	1.26024e46	1.45029
$76$	1.39996e44	0.0116462
$77$	−1.07851e46	−0.651333
$78$	−1.33140e46	−0.586126
$79$	4.05103e46	1.30527	0.652637	−	0.757670i	$-0.273663\pi$
$79$	4.05103e46	1.30527	0.652637	+	0.757670i	$0.273663\pi$
$80$	1.75254e46	0.414920
$81$	−3.33810e46	−0.582930
$82$	5.81433e46	0.751728
$83$	−1.14810e47	−1.10298	−0.551489	−	0.834182i	$-0.685940\pi$
$83$	−1.14810e47	−1.10298	−0.551489	+	0.834182i	$0.685940\pi$
$84$	−2.18050e46	−0.156211
$85$	6.24207e46	0.334630
$86$	2.02916e47	0.816779
$87$	−4.16619e47	−1.26333
$88$	2.65847e47	0.609266
$89$	2.24417e47	0.389942	0.194971	−	0.980809i	$-0.437539\pi$
$89$	2.24417e47	0.389942	0.194971	+	0.980809i	$0.437539\pi$
$90$	−2.81293e47	−0.371721
$91$	3.75993e47	0.379023
$92$	9.58434e47	0.739197
$93$	−6.27556e47	−0.371381
$94$	2.54800e48	1.16029
$95$	1.10019e47	0.0386579
$96$	5.37480e47	0.146122
$97$	2.25892e48	0.476423	0.238211	−	0.971213i	$-0.423439\pi$
$97$	2.25892e48	0.476423	0.238211	+	0.971213i	$0.423439\pi$
$98$	6.15780e47	0.101015
$99$	−4.26700e48	−0.545833
$100$	8.77267e48	0.877267
$101$	1.31891e49	1.03358	0.516788	−	0.856114i	$-0.327128\pi$
$101$	1.31891e49	1.03358	0.516788	+	0.856114i	$0.327128\pi$
$102$	1.91435e48	0.117847
$103$	−3.95803e49	−1.91852	−0.959261	−	0.282522i	$-0.908829\pi$
$103$	−3.95803e49	−1.91852	−0.959261	+	0.282522i	$0.908829\pi$
$104$	−9.26801e48	−0.354543
$105$	−1.71358e49	−0.518522
$106$	−2.42446e49	−0.581597
$107$	−4.93899e49	−0.941317	−0.470659	−	0.882315i	$-0.655984\pi$
$107$	−4.93899e49	−0.941317	−0.470659	+	0.882315i	$0.655984\pi$
$108$	−3.58629e49	−0.544206
$109$	−1.44996e50	−1.75553	−0.877765	−	0.479092i	$-0.840966\pi$
$109$	−1.44996e50	−1.75553	−0.877765	+	0.479092i	$0.840966\pi$
$110$	2.08921e50	2.02237
$111$	1.19590e50	0.927433
$112$	−1.51786e49	−0.0944911
$113$	1.27983e50	0.640810	0.320405	−	0.947281i	$-0.396181\pi$
$113$	1.27983e50	0.640810	0.320405	+	0.947281i	$0.396181\pi$
$114$	3.37411e48	0.0136142
$115$	7.53202e50	2.45366
$116$	−2.90012e50	−0.764179
$117$	1.48757e50	0.317631
$118$	−6.85087e49	−0.118751
$119$	−5.40620e49	−0.0762064
$120$	4.22388e50	0.485033
$121$	2.10198e51	1.96964
$122$	8.43965e50	0.646411
$123$	1.40134e51	0.878754
$124$	−4.36847e50	−0.224646
$125$	2.96482e51	1.25228
$126$	2.43625e50	0.0846533
$127$	−1.82857e51	−0.523505	−0.261753	−	0.965135i	$-0.584300\pi$
$127$	−1.82857e51	−0.523505	−0.261753	+	0.965135i	$0.584300\pi$
$128$	3.74144e50	0.0883883
$129$	4.89057e51	0.954798
$130$	−7.28343e51	−1.17686
$131$	−1.28682e52	−1.72334	−0.861670	−	0.507469i	$-0.830581\pi$
$131$	−1.28682e52	−1.72334	−0.861670	+	0.507469i	$0.830581\pi$
$132$	6.40730e51	0.712219
$133$	−9.52862e49	−0.00880369
$134$	−7.05307e51	−0.542389
$135$	−2.81835e52	−1.80641
$136$	1.33260e51	0.0712846
$137$	3.79116e52	1.69480	0.847399	−	0.530956i	$-0.178167\pi$
$137$	3.79116e52	1.69480	0.847399	+	0.530956i	$0.178167\pi$
$138$	2.30996e52	0.864106
$139$	3.99595e52	1.25244	0.626220	−	0.779646i	$-0.284601\pi$
$139$	3.99595e52	1.25244	0.626220	+	0.779646i	$0.284601\pi$
$140$	−1.19284e52	−0.313650
$141$	6.14103e52	1.35635
$142$	2.66545e51	0.0495115
$143$	−1.10484e53	−1.72809
$144$	−6.00522e51	−0.0791859
$145$	−2.27911e53	−2.53658
$146$	1.00126e53	0.941677
$147$	1.48412e52	0.118085
$148$	8.32478e52	0.560997
$149$	−1.38308e53	−0.790287	−0.395143	−	0.918619i	$-0.629305\pi$
$149$	−1.38308e53	−0.790287	−0.395143	+	0.918619i	$0.629305\pi$
$150$	2.11434e53	1.02551
$151$	−2.78255e53	−1.14685	−0.573426	−	0.819258i	$-0.694386\pi$
$151$	−2.78255e53	−1.14685	−0.573426	+	0.819258i	$0.694386\pi$
$152$	2.34875e51	0.00823510
$153$	−2.13889e52	−0.0638629
$154$	−1.80945e53	−0.460562
$155$	−3.43304e53	−0.745679
$156$	−2.23372e53	−0.414454
$157$	3.98818e53	0.632751	0.316376	−	0.948634i	$-0.397534\pi$
$157$	3.98818e53	0.632751	0.316376	+	0.948634i	$0.397534\pi$
$158$	6.79650e53	0.922969
$159$	−5.84330e53	−0.679874
$160$	2.94028e53	0.293393
$161$	−6.52342e53	−0.558781
$162$	−5.60040e53	−0.412193
$163$	−1.71077e54	−1.08292	−0.541459	−	0.840727i	$-0.682128\pi$
$163$	−1.71077e54	−1.08292	−0.541459	+	0.840727i	$0.682128\pi$
$164$	9.75483e53	0.531552
$165$	5.03529e54	2.36411
$166$	−1.92620e54	−0.779924
$167$	1.85130e54	0.647028	0.323514	−	0.946223i	$-0.395136\pi$
$167$	1.85130e54	0.647028	0.323514	+	0.946223i	$0.395136\pi$
$168$	−3.65827e53	−0.110458
$169$	2.14827e52	0.00560874
$170$	1.04725e54	0.236619
$171$	−3.76987e52	−0.00737771
$172$	3.40437e54	0.577550
$173$	7.36516e53	0.108406	0.0542029	−	0.998530i	$-0.482738\pi$
$173$	7.36516e53	0.108406	0.0542029	+	0.998530i	$0.482738\pi$
$174$	−6.98970e54	−0.893310
$175$	−5.97097e54	−0.663152
$176$	4.46018e54	0.430816
$177$	−1.65116e54	−0.138817
$178$	3.76509e54	0.275731
$179$	−1.45263e55	−0.927376	−0.463688	−	0.885998i	$-0.653474\pi$
$179$	−1.45263e55	−0.927376	−0.463688	+	0.885998i	$0.653474\pi$
$180$	−4.71931e54	−0.262846
$181$	−2.68101e55	−1.30368	−0.651842	−	0.758354i	$-0.726004\pi$
$181$	−2.68101e55	−1.30368	−0.651842	+	0.758354i	$0.726004\pi$
$182$	6.30811e54	0.268010
$183$	2.03407e55	0.755640
$184$	1.60798e55	0.522691
$185$	6.54218e55	1.86215
$186$	−1.05286e55	−0.262606
$187$	1.58859e55	0.347450
$188$	4.27483e55	0.820449
$189$	2.44095e55	0.411381
$190$	1.84581e54	0.0273352
$191$	4.89183e55	0.637022	0.318511	−	0.947919i	$-0.396817\pi$
$191$	4.89183e55	0.637022	0.318511	+	0.947919i	$0.396817\pi$
$192$	9.01741e54	0.103324
$193$	2.39777e55	0.241910	0.120955	−	0.992658i	$-0.461404\pi$
$193$	2.39777e55	0.241910	0.120955	+	0.992658i	$0.461404\pi$
$194$	3.78983e55	0.336882
$195$	−1.75541e56	−1.37572
$196$	1.03311e55	0.0714286
$197$	1.92776e56	1.17660	0.588301	−	0.808642i	$-0.299797\pi$
$197$	1.92776e56	1.17660	0.588301	+	0.808642i	$0.299797\pi$
$198$	−7.15883e55	−0.385962
$199$	1.75771e55	0.0837618	0.0418809	−	0.999123i	$-0.486665\pi$
$199$	1.75771e55	0.0837618	0.0418809	+	0.999123i	$0.486665\pi$
$200$	1.47181e56	0.620322
$201$	−1.69989e56	−0.634041
$202$	2.21277e56	0.730848
$203$	1.97392e56	0.577665
$204$	3.21175e55	0.0833302
$205$	7.66601e56	1.76441
$206$	−6.64047e56	−1.35660
$207$	−2.58090e56	−0.468272
$208$	−1.55491e56	−0.250700
$209$	2.79995e55	0.0401389
$210$	−2.87491e56	−0.366650
$211$	−2.76088e55	−0.0313421	−0.0156710	−	0.999877i	$-0.504988\pi$
$211$	−2.76088e55	−0.0313421	−0.0156710	+	0.999877i	$0.504988\pi$
$212$	−4.06757e56	−0.411251
$213$	6.42411e55	0.0578779
$214$	−8.28626e56	−0.665612
$215$	2.67538e57	1.91709
$216$	−6.01679e56	−0.384812
$217$	2.97333e56	0.169816
$218$	−2.43264e57	−1.24135
$219$	2.41318e57	1.10080
$220$	3.50511e57	1.43003
$221$	−5.53816e56	−0.202188
$222$	2.00639e57	0.655794
$223$	1.22320e56	0.0358120	0.0179060	−	0.999840i	$-0.494300\pi$
$223$	1.22320e56	0.0358120	0.0179060	+	0.999840i	$0.494300\pi$
$224$	−2.54655e56	−0.0668153
$225$	−2.36234e57	−0.555738
$226$	2.14719e57	0.453121
$227$	9.96756e56	0.188780	0.0943899	−	0.995535i	$-0.469910\pi$
$227$	9.96756e56	0.188780	0.0943899	+	0.995535i	$0.469910\pi$
$228$	5.66082e55	0.00962666
$229$	7.75813e56	0.118519	0.0592595	−	0.998243i	$-0.481126\pi$
$229$	7.75813e56	0.118519	0.0592595	+	0.998243i	$0.481126\pi$
$230$	1.26366e58	1.73500
$231$	−4.36102e57	−0.538387
$232$	−4.86559e57	−0.540356
$233$	2.81706e57	0.281563	0.140781	−	0.990041i	$-0.455039\pi$
$233$	2.81706e57	0.281563	0.140781	+	0.990041i	$0.455039\pi$
$234$	2.49572e57	0.224599
$235$	3.35945e58	2.72336
$236$	−1.14938e57	−0.0839695
$237$	1.63805e58	1.07893
$238$	−9.07010e56	−0.0538861
$239$	1.18544e58	0.635520	0.317760	−	0.948171i	$-0.397069\pi$
$239$	1.18544e58	0.635520	0.317760	+	0.948171i	$0.397069\pi$
$240$	7.08649e57	0.342970
$241$	1.60775e58	0.702752	0.351376	−	0.936234i	$-0.385714\pi$
$241$	1.60775e58	0.702752	0.351376	+	0.936234i	$0.385714\pi$
$242$	3.52653e58	1.39275
$243$	1.69915e58	0.606566
$244$	1.41594e58	0.457081
$245$	8.11886e57	0.237097
$246$	2.35105e58	0.621373
$247$	−9.76121e56	−0.0233576
$248$	−7.32908e57	−0.158848
$249$	−4.64240e58	−0.911715
$250$	4.97414e58	0.885499
$251$	−3.02944e58	−0.489053	−0.244526	−	0.969643i	$-0.578632\pi$
$251$	−3.02944e58	−0.489053	−0.244526	+	0.969643i	$0.578632\pi$
$252$	4.08735e57	0.0598589
$253$	1.91688e59	2.54766
$254$	−3.06783e58	−0.370174
$255$	2.52401e58	0.276603
$256$	6.27710e57	0.0625000
$257$	−4.22546e58	−0.382395	−0.191197	−	0.981552i	$-0.561237\pi$
$257$	−4.22546e58	−0.382395	−0.191197	+	0.981552i	$0.561237\pi$
$258$	8.20501e58	0.675144
$259$	−5.66612e58	−0.424074
$260$	−1.22196e59	−0.832163
$261$	7.80954e58	0.484098
$262$	−2.15893e59	−1.21859
$263$	1.95052e59	1.00285	0.501423	−	0.865202i	$-0.332810\pi$
$263$	1.95052e59	1.00285	0.501423	+	0.865202i	$0.332810\pi$
$264$	1.07497e59	0.503615
$265$	−3.19657e59	−1.36509
$266$	−1.59864e57	−0.00622515
$267$	9.07440e58	0.322323
$268$	−1.18331e59	−0.383527
$269$	1.83448e59	0.542728	0.271364	−	0.962477i	$-0.412525\pi$
$269$	1.83448e59	0.542728	0.271364	+	0.962477i	$0.412525\pi$
$270$	−4.72840e59	−1.27733
$271$	−5.98119e59	−1.47584	−0.737921	−	0.674887i	$-0.764192\pi$
$271$	−5.98119e59	−1.47584	−0.737921	+	0.674887i	$0.764192\pi$
$272$	2.23573e58	0.0504058
$273$	1.52035e59	0.313298
$274$	6.36051e59	1.19840
$275$	1.75455e60	3.02353
$276$	3.87547e59	0.611015
$277$	8.36571e59	1.20711	0.603557	−	0.797320i	$-0.293750\pi$
$277$	8.36571e59	1.20711	0.603557	+	0.797320i	$0.293750\pi$
$278$	6.70409e59	0.885609
$279$	1.17636e59	0.142310
$280$	−2.00125e59	−0.221784
$281$	−1.00107e60	−1.01662	−0.508311	−	0.861174i	$-0.669730\pi$
$281$	−1.00107e60	−1.01662	−0.508311	+	0.861174i	$0.669730\pi$
$282$	1.03029e60	0.959087
$283$	−8.95120e59	−0.764036	−0.382018	−	0.924155i	$-0.624771\pi$
$283$	−8.95120e59	−0.764036	−0.382018	+	0.924155i	$0.624771\pi$
$284$	4.47188e58	0.0350099
$285$	4.44866e58	0.0319543
$286$	−1.85361e60	−1.22194
$287$	−6.63946e59	−0.401815
$288$	−1.00751e59	−0.0559929
$289$	−1.87920e60	−0.959348
$290$	−3.82371e60	−1.79364
$291$	9.13403e59	0.393808
$292$	1.67984e60	0.665866
$293$	2.02943e60	0.739805	0.369902	−	0.929071i	$-0.379391\pi$
$293$	2.02943e60	0.739805	0.369902	+	0.929071i	$0.379391\pi$
$294$	2.48994e59	0.0834985
$295$	−9.03264e59	−0.278725
$296$	1.39667e60	0.396685
$297$	−7.17262e60	−1.87562
$298$	−2.32043e60	−0.558817
$299$	−6.68265e60	−1.48253
$300$	3.54727e60	0.725143
$301$	−2.31713e60	−0.436587
$302$	−4.66834e60	−0.810946
$303$	5.33308e60	0.854346
$304$	3.94055e58	0.00582309
$305$	1.11274e61	1.51722
$306$	−3.58846e59	−0.0451579
$307$	1.11873e61	1.29968	0.649840	−	0.760071i	$-0.274836\pi$
$307$	1.11873e61	1.29968	0.649840	+	0.760071i	$0.274836\pi$
$308$	−3.03575e60	−0.325666
$309$	−1.60045e61	−1.58584
$310$	−5.75968e60	−0.527275
$311$	1.01512e61	0.858789	0.429395	−	0.903117i	$-0.358727\pi$
$311$	1.01512e61	0.858789	0.429395	+	0.903117i	$0.358727\pi$
$312$	−3.74756e60	−0.293063
$313$	−2.14333e61	−1.54972	−0.774859	−	0.632135i	$-0.782179\pi$
$313$	−2.14333e61	−1.54972	−0.774859	+	0.632135i	$0.782179\pi$
$314$	6.69105e60	0.447423
$315$	3.21212e60	0.198693
$316$	1.14026e61	0.652637
$317$	1.80985e61	0.958720	0.479360	−	0.877618i	$-0.340869\pi$
$317$	1.80985e61	0.958720	0.479360	+	0.877618i	$0.340869\pi$
$318$	−9.80343e60	−0.480744
$319$	−5.80028e61	−2.63377
$320$	4.93297e60	0.207460
$321$	−1.99711e61	−0.778086
$322$	−1.09445e61	−0.395118
$323$	1.40351e59	0.00469629
$324$	−9.39591e60	−0.291465
$325$	−6.11672e61	−1.75945
$326$	−2.87020e61	−0.765738
$327$	−5.86300e61	−1.45111
$328$	1.63659e61	0.375864
$329$	−2.90959e61	−0.620201
$330$	8.44781e61	1.67168
$331$	1.03361e62	1.89919	0.949596	−	0.313475i	$-0.101493\pi$
$331$	1.03361e62	1.89919	0.949596	+	0.313475i	$0.101493\pi$
$332$	−3.23162e61	−0.551489
$333$	−2.24173e61	−0.355385
$334$	3.10597e61	0.457518
$335$	−9.29924e61	−1.27306
$336$	−6.13755e60	−0.0781057
$337$	−4.47543e61	−0.529545	−0.264772	−	0.964311i	$-0.585297\pi$
$337$	−4.47543e61	−0.529545	−0.264772	+	0.964311i	$0.585297\pi$
$338$	3.60421e59	0.00396598
$339$	5.17504e61	0.529689
$340$	1.75699e61	0.167315
$341$	−8.73700e61	−0.774248
$342$	−6.32480e59	−0.00521683
$343$	−7.03168e60	−0.0539949
$344$	5.71158e61	0.408389
$345$	3.04561e62	2.02818
$346$	1.23567e61	0.0766545
$347$	1.64103e61	0.0948517	0.0474259	−	0.998875i	$-0.484898\pi$
$347$	1.64103e61	0.0948517	0.0474259	+	0.998875i	$0.484898\pi$
$348$	−1.17268e62	−0.631665
$349$	3.38513e62	1.69962	0.849810	−	0.527089i	$-0.176717\pi$
$349$	3.38513e62	1.69962	0.849810	+	0.527089i	$0.176717\pi$
$350$	−1.00176e62	−0.468919
$351$	2.50053e62	1.09146
$352$	7.48294e61	0.304633
$353$	−3.26938e62	−1.24161	−0.620806	−	0.783964i	$-0.713194\pi$
$353$	−3.26938e62	−1.24161	−0.620806	+	0.783964i	$0.713194\pi$
$354$	−2.77018e61	−0.0981586
$355$	3.51431e61	0.116210
$356$	6.31677e61	0.194971
$357$	−2.18602e61	−0.0629917
$358$	−2.43711e62	−0.655754
$359$	6.21356e62	1.56144	0.780722	−	0.624879i	$-0.214852\pi$
$359$	6.21356e62	1.56144	0.780722	+	0.624879i	$0.214852\pi$
$360$	−7.91769e61	−0.185861
$361$	−4.55712e62	−0.999457
$362$	−4.49798e62	−0.921844
$363$	8.49945e62	1.62809
$364$	1.05833e62	0.189511
$365$	1.32013e63	2.21025
$366$	3.41261e62	0.534319
$367$	−3.24990e61	−0.0475939	−0.0237970	−	0.999717i	$-0.507576\pi$
$367$	−3.24990e61	−0.0475939	−0.0237970	+	0.999717i	$0.507576\pi$
$368$	2.69775e62	0.369599
$369$	−2.62681e62	−0.336731
$370$	1.09759e63	1.31674
$371$	2.76853e62	0.310876
$372$	−1.76641e62	−0.185691
$373$	−7.60603e62	−0.748672	−0.374336	−	0.927293i	$-0.622129\pi$
$373$	−7.60603e62	−0.748672	−0.374336	+	0.927293i	$0.622129\pi$
$374$	2.66521e62	0.245684
$375$	1.19884e63	1.03513
$376$	7.17197e62	0.580145
$377$	2.02210e63	1.53264
$378$	4.09523e62	0.290890
$379$	−2.77522e63	−1.84772	−0.923862	−	0.382725i	$-0.874986\pi$
$379$	−2.77522e63	−1.84772	−0.923862	+	0.382725i	$0.874986\pi$
$380$	3.09675e61	0.0193289
$381$	−7.39392e62	−0.432726
$382$	8.20714e62	0.450442
$383$	7.91849e62	0.407636	0.203818	−	0.979009i	$-0.434665\pi$
$383$	7.91849e62	0.407636	0.203818	+	0.979009i	$0.434665\pi$
$384$	1.51287e62	0.0730612
$385$	−2.38569e63	−1.08100
$386$	4.02279e62	0.171056
$387$	−9.16740e62	−0.365871
$388$	6.35828e62	0.238211
$389$	−5.03940e63	−1.77261	−0.886305	−	0.463102i	$-0.846736\pi$
$389$	−5.03940e63	−1.77261	−0.886305	+	0.463102i	$0.846736\pi$
$390$	−2.94509e63	−0.972782
$391$	9.60863e62	0.298079
$392$	1.73327e62	0.0505076
$393$	−5.20332e63	−1.42450
$394$	3.23424e63	0.831983
$395$	8.96097e63	2.16634
$396$	−1.20105e63	−0.272917
$397$	−6.85734e63	−1.46483	−0.732417	−	0.680856i	$-0.761608\pi$
$397$	−6.85734e63	−1.46483	−0.732417	+	0.680856i	$0.761608\pi$
$398$	2.94894e62	0.0592285
$399$	−3.85294e61	−0.00727707
$400$	2.46929e63	0.438634
$401$	−4.02197e63	−0.672050	−0.336025	−	0.941853i	$-0.609083\pi$
$401$	−4.02197e63	−0.672050	−0.336025	+	0.941853i	$0.609083\pi$
$402$	−2.85194e63	−0.448335
$403$	3.04590e63	0.450550
$404$	3.71241e63	0.516788
$405$	−7.38394e63	−0.967476
$406$	3.31169e63	0.408471
$407$	1.66497e64	1.93349
$408$	5.38842e62	0.0589234
$409$	−7.84713e63	−0.808146	−0.404073	−	0.914727i	$-0.632406\pi$
$409$	−7.84713e63	−0.808146	−0.404073	+	0.914727i	$0.632406\pi$
$410$	1.28614e64	1.24763
$411$	1.53297e64	1.40091
$412$	−1.11409e64	−0.959261
$413$	7.82309e62	0.0634749
$414$	−4.33004e63	−0.331118
$415$	−2.53963e64	−1.83059
$416$	−2.60871e63	−0.177272
$417$	1.61578e64	1.03526
$418$	4.69753e62	0.0283825
$419$	−1.01718e64	−0.579637	−0.289818	−	0.957082i	$-0.593595\pi$
$419$	−1.01718e64	−0.579637	−0.289818	+	0.957082i	$0.593595\pi$
$420$	−4.82330e63	−0.259261
$421$	2.80793e63	0.142389	0.0711944	−	0.997462i	$-0.477319\pi$
$421$	2.80793e63	0.142389	0.0711944	+	0.997462i	$0.477319\pi$
$422$	−4.63199e62	−0.0221622
$423$	−1.15114e64	−0.519744
$424$	−6.82426e63	−0.290798
$425$	8.79491e63	0.353755
$426$	1.07779e63	0.0409258
$427$	−9.63734e63	−0.345521
$428$	−1.39020e64	−0.470659
$429$	−4.46747e64	−1.42843
$430$	4.48855e64	1.35559
$431$	−2.19225e64	−0.625456	−0.312728	−	0.949843i	$-0.601243\pi$
$431$	−2.19225e64	−0.625456	−0.312728	+	0.949843i	$0.601243\pi$
$432$	−1.00945e64	−0.272103
$433$	−4.35722e64	−1.10983	−0.554915	−	0.831907i	$-0.687249\pi$
$433$	−4.35722e64	−1.10983	−0.554915	+	0.831907i	$0.687249\pi$
$434$	4.98841e63	0.120078
$435$	−9.21569e64	−2.09672
$436$	−4.08129e64	−0.877765
$437$	1.69356e63	0.0344353
$438$	4.04864e64	0.778384
$439$	−7.10673e63	−0.129208	−0.0646040	−	0.997911i	$-0.520578\pi$
$439$	−7.10673e63	−0.129208	−0.0646040	+	0.997911i	$0.520578\pi$
$440$	5.88060e64	1.01119
$441$	−2.78199e63	−0.0452491
$442$	−9.29150e63	−0.142968
$443$	−7.01150e64	−1.02075	−0.510375	−	0.859952i	$-0.670493\pi$
$443$	−7.01150e64	−1.02075	−0.510375	+	0.859952i	$0.670493\pi$
$444$	3.36616e64	0.463717
$445$	4.96414e64	0.647179
$446$	2.05219e63	0.0253229
$447$	−5.59256e64	−0.653246
$448$	−4.27240e63	−0.0472456
$449$	−7.22798e64	−0.756801	−0.378401	−	0.925642i	$-0.623526\pi$
$449$	−7.22798e64	−0.756801	−0.378401	+	0.925642i	$0.623526\pi$
$450$	−3.96334e64	−0.392966
$451$	1.95098e65	1.83201
$452$	3.60239e64	0.320405
$453$	−1.12514e65	−0.947980
$454$	1.67228e64	0.133487
$455$	8.31704e64	0.629056
$456$	9.49728e62	0.00680708
$457$	−1.87095e65	−1.27091	−0.635456	−	0.772137i	$-0.719188\pi$
$457$	−1.87095e65	−1.27091	−0.635456	+	0.772137i	$0.719188\pi$
$458$	1.30160e64	0.0838056
$459$	−3.59538e64	−0.219449
$460$	2.12008e65	1.22683
$461$	2.44591e65	1.34205	0.671024	−	0.741435i	$-0.265855\pi$
$461$	2.44591e65	1.34205	0.671024	+	0.741435i	$0.265855\pi$
$462$	−7.31658e64	−0.380697
$463$	−1.93583e65	−0.955283	−0.477642	−	0.878555i	$-0.658508\pi$
$463$	−1.93583e65	−0.955283	−0.477642	+	0.878555i	$0.658508\pi$
$464$	−8.16311e64	−0.382090
$465$	−1.38817e65	−0.616374
$466$	4.72623e64	0.199095
$467$	3.35588e64	0.134135	0.0670677	−	0.997748i	$-0.478636\pi$
$467$	3.35588e64	0.134135	0.0670677	+	0.997748i	$0.478636\pi$
$468$	4.18713e64	0.158815
$469$	8.05399e64	0.289919
$470$	5.63622e65	1.92571
$471$	1.61264e65	0.523028
$472$	−1.92835e64	−0.0593754
$473$	6.80878e65	1.99054
$474$	2.74820e65	0.762919
$475$	1.55013e64	0.0408673
$476$	−1.52171e64	−0.0381032
$477$	1.09533e65	0.260522
$478$	1.98883e65	0.449381
$479$	9.46852e63	0.0203265	0.0101632	−	0.999948i	$-0.496765\pi$
$479$	9.46852e63	0.0203265	0.0101632	+	0.999948i	$0.496765\pi$
$480$	1.18892e65	0.242516
$481$	−5.80443e65	−1.12514
$482$	2.69737e65	0.496921
$483$	−2.63778e65	−0.461884
$484$	5.91654e65	0.984820
$485$	4.99677e65	0.790709
$486$	2.85070e65	0.428907
$487$	−1.08068e66	−1.54610	−0.773049	−	0.634347i	$-0.781269\pi$
$487$	−1.08068e66	−1.54610	−0.773049	+	0.634347i	$0.781269\pi$
$488$	2.37555e65	0.323205
$489$	−6.91758e65	−0.895132
$490$	1.36212e65	0.167653
$491$	1.51931e66	1.77890	0.889448	−	0.457036i	$-0.151089\pi$
$491$	1.51931e66	1.77890	0.889448	+	0.457036i	$0.151089\pi$
$492$	3.94441e65	0.439377
$493$	−2.90747e65	−0.308153
$494$	−1.63766e64	−0.0165163
$495$	−9.43868e65	−0.905908
$496$	−1.22962e65	−0.112323
$497$	−3.04371e64	−0.0264650
$498$	−7.78866e65	−0.644680
$499$	−6.07377e65	−0.478624	−0.239312	−	0.970943i	$-0.576922\pi$
$499$	−6.07377e65	−0.478624	−0.239312	+	0.970943i	$0.576922\pi$
$500$	8.34523e65	0.626142
$501$	7.48582e65	0.534829
$502$	−5.08255e65	−0.345813
$503$	−2.81314e66	−1.82295	−0.911477	−	0.411350i	$-0.865057\pi$
$503$	−2.81314e66	−1.82295	−0.911477	+	0.411350i	$0.865057\pi$
$504$	6.85744e64	0.0423267
$505$	2.91746e66	1.71540
$506$	3.21599e66	1.80147
$507$	8.68665e63	0.00463615
$508$	−5.14697e65	−0.261753
$509$	−2.59182e66	−1.25609	−0.628043	−	0.778179i	$-0.716144\pi$
$509$	−2.59182e66	−1.25609	−0.628043	+	0.778179i	$0.716144\pi$
$510$	4.23459e65	0.195588
$511$	−1.14335e66	−0.503347
$512$	1.05312e65	0.0441942
$513$	−6.33698e64	−0.0253517
$514$	−7.08914e65	−0.270394
$515$	−8.75524e66	−3.18413
$516$	1.37657e66	0.477399
$517$	8.54971e66	2.82770
$518$	−9.50618e65	−0.299866
$519$	2.97814e65	0.0896076
$520$	−2.05010e66	−0.588428
$521$	1.69545e66	0.464261	0.232130	−	0.972685i	$-0.425430\pi$
$521$	1.69545e66	0.464261	0.232130	+	0.972685i	$0.425430\pi$
$522$	1.31022e66	0.342309
$523$	−2.92996e66	−0.730416	−0.365208	−	0.930926i	$-0.619002\pi$
$523$	−2.92996e66	−0.730416	−0.365208	+	0.930926i	$0.619002\pi$
$524$	−3.62208e66	−0.861670
$525$	−2.41439e66	−0.548157
$526$	3.27243e66	0.709120
$527$	−4.37954e65	−0.0905876
$528$	1.80349e66	0.356110
$529$	6.28956e66	1.18565
$530$	−5.36296e66	−0.965264
$531$	3.09510e65	0.0531936
$532$	−2.68207e64	−0.00440185
$533$	−6.80153e66	−1.06608
$534$	1.52243e66	0.227917
$535$	−1.09252e67	−1.56228
$536$	−1.98526e66	−0.271194
$537$	−5.87378e66	−0.766563
$538$	3.07775e66	0.383767
$539$	2.06623e66	0.246181
$540$	−7.93294e66	−0.903207
$541$	−4.00248e66	−0.435508	−0.217754	−	0.976004i	$-0.569873\pi$
$541$	−4.00248e66	−0.435508	−0.217754	+	0.976004i	$0.569873\pi$
$542$	−1.00348e67	−1.04358
$543$	−1.08408e67	−1.07762
$544$	3.75093e65	0.0356423
$545$	−3.20735e67	−2.91362
$546$	2.55072e66	0.221535
$547$	2.06656e67	1.71616	0.858080	−	0.513517i	$-0.171658\pi$
$547$	2.06656e67	1.71616	0.858080	+	0.513517i	$0.171658\pi$
$548$	1.06712e67	0.847399
$549$	−3.81289e66	−0.289555
$550$	2.94364e67	2.13796
$551$	−5.12452e65	−0.0355991
$552$	6.50196e66	0.432053
$553$	−7.76102e66	−0.493347
$554$	1.40353e67	0.853558
$555$	2.64536e67	1.53924
$556$	1.12476e67	0.626220
$557$	−6.27794e66	−0.334476	−0.167238	−	0.985917i	$-0.553485\pi$
$557$	−6.27794e66	−0.334476	−0.167238	+	0.985917i	$0.553485\pi$
$558$	1.97360e66	0.100629
$559$	−2.37369e67	−1.15833
$560$	−3.35754e66	−0.156825
$561$	6.42354e66	0.287200
$562$	−1.67952e67	−0.718860
$563$	4.79486e66	0.196481	0.0982404	−	0.995163i	$-0.468679\pi$
$563$	4.79486e66	0.196481	0.0982404	+	0.995163i	$0.468679\pi$
$564$	1.72855e67	0.678177
$565$	2.83100e67	1.06354
$566$	−1.50176e67	−0.540255
$567$	6.39517e66	0.220327
$568$	7.50257e65	0.0247557
$569$	−3.67096e67	−1.16019	−0.580095	−	0.814549i	$-0.696985\pi$
$569$	−3.67096e67	−1.16019	−0.580095	+	0.814549i	$0.696985\pi$
$570$	7.46361e65	0.0225951
$571$	−5.53197e66	−0.160433	−0.0802167	−	0.996777i	$-0.525561\pi$
$571$	−5.53197e66	−0.160433	−0.0802167	+	0.996777i	$0.525561\pi$
$572$	−3.10985e67	−0.864045
$573$	1.97804e67	0.526558
$574$	−1.11392e67	−0.284126
$575$	1.06124e68	2.59389
$576$	−1.69032e66	−0.0395930
$577$	6.73056e67	1.51093	0.755464	−	0.655190i	$-0.227411\pi$
$577$	6.73056e67	1.51093	0.755464	+	0.655190i	$0.227411\pi$
$578$	−3.15278e67	−0.678362
$579$	9.69550e66	0.199961
$580$	−6.41513e67	−1.26829
$581$	2.19955e67	0.416887
$582$	1.53244e67	0.278464
$583$	−8.13520e67	−1.41739
$584$	2.81830e67	0.470838
$585$	3.29053e67	0.527165
$586$	3.40482e67	0.523121
$587$	−8.12357e67	−1.19705	−0.598527	−	0.801103i	$-0.704247\pi$
$587$	−8.12357e67	−1.19705	−0.598527	+	0.801103i	$0.704247\pi$
$588$	4.17742e66	0.0590424
$589$	−7.71910e65	−0.0104651
$590$	−1.51543e67	−0.197088
$591$	7.79497e67	0.972571
$592$	2.34322e67	0.280499
$593$	−1.37601e68	−1.58045	−0.790225	−	0.612817i	$-0.790036\pi$
$593$	−1.37601e68	−1.58045	−0.790225	+	0.612817i	$0.790036\pi$
$594$	−1.20337e68	−1.32626
$595$	−1.19586e67	−0.126478
$596$	−3.89303e67	−0.395143
$597$	7.10737e66	0.0692369
$598$	−1.12116e68	−1.04831
$599$	1.22268e68	1.09738	0.548688	−	0.836027i	$-0.315128\pi$
$599$	1.22268e68	1.09738	0.548688	+	0.836027i	$0.315128\pi$
$600$	5.95133e67	0.512754
$601$	1.72865e68	1.42982	0.714910	−	0.699216i	$-0.246468\pi$
$601$	1.72865e68	1.42982	0.714910	+	0.699216i	$0.246468\pi$
$602$	−3.88749e67	−0.308713
$603$	3.18646e67	0.242959
$604$	−7.83217e67	−0.573426
$605$	4.64962e68	3.26897
$606$	8.94743e67	0.604114
$607$	2.45667e68	1.59303	0.796514	−	0.604620i	$-0.206675\pi$
$607$	2.45667e68	1.59303	0.796514	+	0.604620i	$0.206675\pi$
$608$	6.61114e65	0.00411755
$609$	7.98163e67	0.477494
$610$	1.86687e68	1.07283
$611$	−2.98061e68	−1.64549
$612$	−6.02044e66	−0.0319315
$613$	−1.05071e67	−0.0535427	−0.0267713	−	0.999642i	$-0.508523\pi$
$613$	−1.05071e67	−0.0535427	−0.0267713	+	0.999642i	$0.508523\pi$
$614$	1.87692e68	0.919013
$615$	3.09979e68	1.45845
$616$	−5.09314e67	−0.230281
$617$	2.63133e67	0.114337	0.0571687	−	0.998365i	$-0.481793\pi$
$617$	2.63133e67	0.114337	0.0571687	+	0.998365i	$0.481793\pi$
$618$	−2.68510e68	−1.12136
$619$	−9.19896e67	−0.369248	−0.184624	−	0.982809i	$-0.559107\pi$
$619$	−9.19896e67	−0.369248	−0.184624	+	0.982809i	$0.559107\pi$
$620$	−9.66315e67	−0.372840
$621$	−4.33838e68	−1.60910
$622$	1.70308e68	0.607256
$623$	−4.29940e67	−0.147384
$624$	−6.28737e67	−0.207227
$625$	1.02191e68	0.323856
$626$	−3.59591e68	−1.09582
$627$	1.13217e67	0.0331786
$628$	1.12257e68	0.316376
$629$	8.34588e67	0.226220
$630$	5.38904e67	0.140497
$631$	−1.36432e68	−0.342135	−0.171068	−	0.985259i	$-0.554722\pi$
$631$	−1.36432e68	−0.342135	−0.171068	+	0.985259i	$0.554722\pi$
$632$	1.91305e68	0.461484
$633$	−1.11638e67	−0.0259071
$634$	3.03643e68	0.677917
$635$	−4.04484e68	−0.868850
$636$	−1.64474e68	−0.339937
$637$	−7.20332e67	−0.143257
$638$	−9.73125e68	−1.86235
$639$	−1.20420e67	−0.0221783
$640$	8.27615e67	0.146696
$641$	−5.70938e68	−0.974019	−0.487010	−	0.873397i	$-0.661912\pi$
$641$	−5.70938e68	−0.974019	−0.487010	+	0.873397i	$0.661912\pi$
$642$	−3.35059e68	−0.550190
$643$	−2.67877e68	−0.423415	−0.211707	−	0.977333i	$-0.567902\pi$
$643$	−2.67877e68	−0.423415	−0.211707	+	0.977333i	$0.567902\pi$
$644$	−1.83618e68	−0.279390
$645$	1.08180e69	1.58466
$646$	2.35470e66	0.00332078
$647$	9.40638e68	1.27723	0.638613	−	0.769528i	$-0.279508\pi$
$647$	9.40638e68	1.27723	0.638613	+	0.769528i	$0.279508\pi$
$648$	−1.57637e68	−0.206097
$649$	−2.29878e68	−0.289403
$650$	−1.02622e69	−1.24412
$651$	1.20228e68	0.140369
$652$	−4.81539e68	−0.541459
$653$	1.67210e69	1.81087	0.905437	−	0.424481i	$-0.139543\pi$
$653$	1.67210e69	1.81087	0.905437	+	0.424481i	$0.139543\pi$
$654$	−9.83648e68	−1.02609
$655$	−2.84647e69	−2.86019
$656$	2.74574e68	0.265776
$657$	−4.52352e68	−0.421818
$658$	−4.88148e68	−0.438548
$659$	3.62381e68	0.313670	0.156835	−	0.987625i	$-0.449871\pi$
$659$	3.62381e68	0.313670	0.156835	+	0.987625i	$0.449871\pi$
$660$	1.41731e69	1.18206
$661$	−1.40562e69	−1.12962	−0.564811	−	0.825220i	$-0.691051\pi$
$661$	−1.40562e69	−1.12962	−0.564811	+	0.825220i	$0.691051\pi$
$662$	1.73410e69	1.34293
$663$	−2.23938e68	−0.167127
$664$	−5.42176e68	−0.389962
$665$	−2.10775e67	−0.0146113
$666$	−3.76099e68	−0.251295
$667$	−3.50831e69	−2.25952
$668$	5.21095e68	0.323514
$669$	4.94607e67	0.0296020
$670$	−1.56015e69	−0.900191
$671$	2.83189e69	1.57534
$672$	−1.02971e68	−0.0552291
$673$	2.27495e69	1.17653	0.588264	−	0.808669i	$-0.299811\pi$
$673$	2.27495e69	1.17653	0.588264	+	0.808669i	$0.299811\pi$
$674$	−7.50853e68	−0.374445
$675$	−3.97098e69	−1.90966
$676$	6.04685e66	0.00280437
$677$	−3.97025e68	−0.177581	−0.0887904	−	0.996050i	$-0.528300\pi$
$677$	−3.97025e68	−0.177581	−0.0887904	+	0.996050i	$0.528300\pi$
$678$	8.68228e68	0.374547
$679$	−4.32766e68	−0.180071
$680$	2.94773e68	0.118310
$681$	4.03043e68	0.156044
$682$	−1.46583e69	−0.547476
$683$	−1.53957e69	−0.554743	−0.277372	−	0.960763i	$-0.589463\pi$
$683$	−1.53957e69	−0.554743	−0.277372	+	0.960763i	$0.589463\pi$
$684$	−1.06112e67	−0.00368886
$685$	8.38612e69	2.81282
$686$	−1.17972e68	−0.0381802
$687$	3.13704e68	0.0979670
$688$	9.58244e68	0.288775
$689$	2.83611e69	0.824805
$690$	5.10968e69	1.43414
$691$	2.33614e68	0.0632829	0.0316414	−	0.999499i	$-0.489927\pi$
$691$	2.33614e68	0.0632829	0.0316414	+	0.999499i	$0.489927\pi$
$692$	2.07311e68	0.0542029
$693$	8.17476e68	0.206306
$694$	2.75320e68	0.0670703
$695$	8.83912e69	2.07865
$696$	−1.96743e69	−0.446655
$697$	9.77956e68	0.214346
$698$	5.67930e69	1.20181
$699$	1.13909e69	0.232738
$700$	−1.68068e69	−0.331576
$701$	−1.68766e69	−0.321509	−0.160754	−	0.986994i	$-0.551393\pi$
$701$	−1.68766e69	−0.321509	−0.160754	+	0.986994i	$0.551393\pi$
$702$	4.19519e69	0.771778
$703$	1.47099e68	0.0261339
$704$	1.25543e69	0.215408
$705$	1.35841e70	2.25111
$706$	−5.48512e69	−0.877952
$707$	−2.52679e69	−0.390655
$708$	−4.64759e68	−0.0694086
$709$	−8.24952e69	−1.19013	−0.595067	−	0.803676i	$-0.702875\pi$
$709$	−8.24952e69	−1.19013	−0.595067	+	0.803676i	$0.702875\pi$
$710$	5.89603e68	0.0821731
$711$	−3.07054e69	−0.413438
$712$	1.05978e69	0.137865
$713$	−5.28460e69	−0.664230
$714$	−3.66754e68	−0.0445419
$715$	−2.44393e70	−2.86807
$716$	−4.08879e69	−0.463688
$717$	4.79337e69	0.525317
$718$	1.04246e70	1.10411
$719$	−4.85357e69	−0.496825	−0.248413	−	0.968654i	$-0.579909\pi$
$719$	−4.85357e69	−0.496825	−0.248413	+	0.968654i	$0.579909\pi$
$720$	−1.32837e69	−0.131423
$721$	7.58284e69	0.725133
$722$	−7.64558e69	−0.706723
$723$	6.50103e69	0.580890
$724$	−7.54636e69	−0.651842
$725$	−3.21121e70	−2.68156
$726$	1.42597e70	1.15123
$727$	1.47435e70	1.15082	0.575410	−	0.817865i	$-0.304842\pi$
$727$	1.47435e70	1.15082	0.575410	+	0.817865i	$0.304842\pi$
$728$	1.77558e69	0.134005
$729$	1.48586e70	1.08431
$730$	2.21481e70	1.56288
$731$	3.41300e69	0.232895
$732$	5.72541e69	0.377820
$733$	1.10214e70	0.703379	0.351689	−	0.936117i	$-0.385607\pi$
$733$	1.10214e70	0.703379	0.351689	+	0.936117i	$0.385607\pi$
$734$	−5.45243e68	−0.0336540
$735$	3.28290e69	0.195983
$736$	4.52608e69	0.261346
$737$	−2.36663e70	−1.32184
$738$	−4.40706e69	−0.238105
$739$	−1.56036e70	−0.815525	−0.407762	−	0.913088i	$-0.633691\pi$
$739$	−1.56036e70	−0.815525	−0.407762	+	0.913088i	$0.633691\pi$
$740$	1.84146e70	0.931075
$741$	−3.94699e68	−0.0193072
$742$	4.64482e69	0.219823
$743$	7.97622e69	0.365234	0.182617	−	0.983184i	$-0.441543\pi$
$743$	7.97622e69	0.365234	0.182617	+	0.983184i	$0.441543\pi$
$744$	−2.96355e69	−0.131303
$745$	−3.05941e70	−1.31162
$746$	−1.27608e70	−0.529391
$747$	8.70222e69	0.349362
$748$	4.47148e69	0.173725
$749$	9.46219e69	0.355784
$750$	2.01132e70	0.731947
$751$	−4.56512e70	−1.60796	−0.803978	−	0.594659i	$-0.797287\pi$
$751$	−4.56512e70	−1.60796	−0.803978	+	0.594659i	$0.797287\pi$
$752$	1.20326e70	0.410224
$753$	−1.22497e70	−0.404248
$754$	3.39252e70	1.08374
$755$	−6.15505e70	−1.90341
$756$	6.87065e69	0.205690
$757$	−2.50927e70	−0.727276	−0.363638	−	0.931540i	$-0.618465\pi$
$757$	−2.50927e70	−0.727276	−0.363638	+	0.931540i	$0.618465\pi$
$758$	−4.65605e70	−1.30654
$759$	7.75100e70	2.10588
$760$	5.19548e68	0.0136676
$761$	−8.03268e69	−0.204615	−0.102307	−	0.994753i	$-0.532623\pi$
$761$	−8.03268e69	−0.204615	−0.102307	+	0.994753i	$0.532623\pi$
$762$	−1.24049e70	−0.305983
$763$	2.77786e70	0.663528
$764$	1.37693e70	0.318511
$765$	−4.73127e69	−0.105992
$766$	1.32850e70	0.288242
$767$	8.01405e69	0.168409
$768$	2.53818e69	0.0516621
$769$	−4.78343e70	−0.943070	−0.471535	−	0.881847i	$-0.656300\pi$
$769$	−4.78343e70	−0.943070	−0.471535	+	0.881847i	$0.656300\pi$
$770$	−4.00253e70	−0.764385
$771$	−1.70858e70	−0.316085
$772$	6.74912e69	0.120955
$773$	−1.04179e71	−1.80876	−0.904380	−	0.426728i	$-0.859666\pi$
$773$	−1.04179e71	−1.80876	−0.904380	+	0.426728i	$0.859666\pi$
$774$	−1.53803e70	−0.258710
$775$	−4.83706e70	−0.788297
$776$	1.06674e70	0.168441
$777$	−2.29112e70	−0.350537
$778$	−8.45470e70	−1.25342
$779$	1.72368e69	0.0247622
$780$	−4.94104e70	−0.687861
$781$	8.94382e69	0.120663
$782$	1.61206e70	0.210773
$783$	1.31275e71	1.66348
$784$	2.90794e69	0.0357143
$785$	8.82193e70	1.05016
$786$	−8.72972e70	−1.00727
$787$	8.21032e70	0.918289	0.459144	−	0.888362i	$-0.348156\pi$
$787$	8.21032e70	0.918289	0.459144	+	0.888362i	$0.348156\pi$
$788$	5.42615e70	0.588301
$789$	7.88702e70	0.828946
$790$	1.50340e71	1.53183
$791$	−2.45191e70	−0.242203
$792$	−2.01503e70	−0.192981
$793$	−9.87259e70	−0.916723
$794$	−1.15047e71	−1.03579
$795$	−1.29255e71	−1.12837
$796$	4.94750e69	0.0418809
$797$	2.08175e69	0.0170883	0.00854417	−	0.999963i	$-0.497280\pi$
$797$	2.08175e69	0.0170883	0.00854417	+	0.999963i	$0.497280\pi$
$798$	−6.46416e68	−0.00514567
$799$	4.28566e70	0.330843
$800$	4.14278e70	0.310161
$801$	−1.70100e70	−0.123512
$802$	−6.74775e70	−0.475211
$803$	3.35969e71	2.29493
$804$	−4.78477e70	−0.317021
$805$	−1.44299e71	−0.927396
$806$	5.11018e70	0.318587
$807$	7.41781e70	0.448615
$808$	6.22838e70	0.365424
$809$	1.91632e69	0.0109076	0.00545380	−	0.999985i	$-0.498264\pi$
$809$	1.91632e69	0.0109076	0.00545380	+	0.999985i	$0.498264\pi$
$810$	−1.23882e71	−0.684109
$811$	−9.80519e70	−0.525346	−0.262673	−	0.964885i	$-0.584604\pi$
$811$	−9.80519e70	−0.525346	−0.262673	+	0.964885i	$0.584604\pi$
$812$	5.55609e70	0.288833
$813$	−2.41852e71	−1.21992
$814$	2.79335e71	1.36719
$815$	−3.78426e71	−1.79730
$816$	9.04027e69	0.0416651
$817$	6.01553e69	0.0269050
$818$	−1.31653e71	−0.571446
$819$	−2.84990e70	−0.120053
$820$	2.15779e71	0.882205
$821$	7.67512e70	0.304564	0.152282	−	0.988337i	$-0.451338\pi$
$821$	7.67512e70	0.304564	0.152282	+	0.988337i	$0.451338\pi$
$822$	2.57190e71	0.990592
$823$	−8.64979e70	−0.323378	−0.161689	−	0.986842i	$-0.551694\pi$
$823$	−8.64979e70	−0.323378	−0.161689	+	0.986842i	$0.551694\pi$
$824$	−1.86912e71	−0.678300
$825$	7.09459e71	2.49923
$826$	1.31250e70	0.0448836
$827$	4.98625e71	1.65535	0.827674	−	0.561210i	$-0.189664\pi$
$827$	4.98625e71	1.65535	0.827674	+	0.561210i	$0.189664\pi$
$828$	−7.26460e70	−0.234136
$829$	−2.09310e71	−0.654942	−0.327471	−	0.944861i	$-0.606196\pi$
$829$	−2.09310e71	−0.654942	−0.327471	+	0.944861i	$0.606196\pi$
$830$	−4.26078e71	−1.29442
$831$	3.38271e71	0.997792
$832$	−4.37669e70	−0.125350
$833$	1.03573e70	0.0288033
$834$	2.71083e71	0.732038
$835$	4.09511e71	1.07386
$836$	7.88115e69	0.0200695
$837$	1.97740e71	0.489014
$838$	−1.70655e71	−0.409865
$839$	2.45639e70	0.0572967	0.0286484	−	0.999590i	$-0.490880\pi$
$839$	2.45639e70	0.0572967	0.0286484	+	0.999590i	$0.490880\pi$
$840$	−8.09216e70	−0.183325
$841$	6.07113e71	1.33588
$842$	4.71093e70	0.100684
$843$	−4.04787e71	−0.840332
$844$	−7.77119e69	−0.0156710
$845$	4.75203e69	0.00930871
$846$	−1.93129e71	−0.367514
$847$	−4.02700e71	−0.744454
$848$	−1.14492e71	−0.205625
$849$	−3.61946e71	−0.631547
$850$	1.47554e71	0.250143
$851$	1.00706e72	1.65875
$852$	1.80823e70	0.0289389
$853$	−2.38410e71	−0.370743	−0.185372	−	0.982668i	$-0.559349\pi$
$853$	−2.38410e71	−0.370743	−0.185372	+	0.982668i	$0.559349\pi$
$854$	−1.61688e71	−0.244320
$855$	−8.33903e69	−0.0122446
$856$	−2.33237e71	−0.332806
$857$	8.17297e71	1.13331	0.566656	−	0.823954i	$-0.308237\pi$
$857$	8.17297e71	1.13331	0.566656	+	0.823954i	$0.308237\pi$
$858$	−7.49517e71	−1.01005
$859$	1.07270e72	1.40491	0.702454	−	0.711730i	$-0.252088\pi$
$859$	1.07270e72	1.40491	0.702454	+	0.711730i	$0.252088\pi$
$860$	7.53053e71	0.958547
$861$	−2.68470e71	−0.332138
$862$	−3.67798e71	−0.442264
$863$	−1.77461e71	−0.207415	−0.103707	−	0.994608i	$-0.533071\pi$
$863$	−1.77461e71	−0.207415	−0.103707	+	0.994608i	$0.533071\pi$
$864$	−1.69358e71	−0.192406
$865$	1.62919e71	0.179919
$866$	−7.31020e71	−0.784768
$867$	−7.59864e71	−0.792991
$868$	8.36917e70	0.0849081
$869$	2.28054e72	2.24933
$870$	−1.54614e72	−1.48261
$871$	8.25059e71	0.769202
$872$	−6.84726e71	−0.620673
$873$	−1.71218e71	−0.150904
$874$	2.84131e70	0.0243494
$875$	−5.68004e71	−0.473319
$876$	6.79249e71	0.550400
$877$	−6.23171e71	−0.491040	−0.245520	−	0.969392i	$-0.578959\pi$
$877$	−6.23171e71	−0.491040	−0.245520	+	0.969392i	$0.578959\pi$
$878$	−1.19231e71	−0.0913638
$879$	8.20609e71	0.611518
$880$	9.86601e71	0.715016
$881$	−9.84259e70	−0.0693744	−0.0346872	−	0.999398i	$-0.511043\pi$
$881$	−9.84259e70	−0.0693744	−0.0346872	+	0.999398i	$0.511043\pi$
$882$	−4.66740e70	−0.0319960
$883$	−1.57148e72	−1.04779	−0.523893	−	0.851784i	$-0.675521\pi$
$883$	−1.57148e72	−1.04779	−0.523893	+	0.851784i	$0.675521\pi$
$884$	−1.55885e71	−0.101094
$885$	−3.65239e71	−0.230392
$886$	−1.17633e72	−0.721779
$887$	−3.00798e71	−0.179534	−0.0897670	−	0.995963i	$-0.528612\pi$
$887$	−3.00798e71	−0.179534	−0.0897670	+	0.995963i	$0.528612\pi$
$888$	5.64749e71	0.327897
$889$	3.50320e71	0.197866
$890$	8.32845e71	0.457624
$891$	−1.87919e72	−1.00454
$892$	3.44301e70	0.0179060
$893$	7.55363e70	0.0382204
$894$	−9.38276e71	−0.461914
$895$	−3.21325e72	−1.53915
$896$	−7.16790e70	−0.0334077
$897$	−2.70216e72	−1.22545
$898$	−1.21265e72	−0.535139
$899$	1.59906e72	0.686678
$900$	−6.64938e71	−0.277869
$901$	−4.07788e71	−0.165836
$902$	3.27320e72	1.29543
$903$	−9.36941e71	−0.360880
$904$	6.04381e71	0.226561
$905$	−5.93044e72	−2.16370
$906$	−1.88766e72	−0.670323
$907$	−4.79903e72	−1.65873	−0.829364	−	0.558709i	$-0.811297\pi$
$907$	−4.79903e72	−1.65873	−0.829364	+	0.558709i	$0.811297\pi$
$908$	2.80562e71	0.0943899
$909$	−9.99690e71	−0.327378
$910$	1.39537e72	0.444810
$911$	9.93139e71	0.308184	0.154092	−	0.988057i	$-0.450755\pi$
$911$	9.93139e71	0.308184	0.154092	+	0.988057i	$0.450755\pi$
$912$	1.59338e70	0.00481333
$913$	−6.46328e72	−1.90072
$914$	−3.13894e72	−0.898671
$915$	4.49942e72	1.25412
$916$	2.18372e71	0.0592595
$917$	2.46531e72	0.651361
$918$	−6.03204e71	−0.155174
$919$	−2.23015e72	−0.558604	−0.279302	−	0.960203i	$-0.590103\pi$
$919$	−2.23015e72	−0.558604	−0.279302	+	0.960203i	$0.590103\pi$
$920$	3.55690e72	0.867500
$921$	4.52365e72	1.07431
$922$	4.10356e72	0.948972
$923$	−3.11801e71	−0.0702159
$924$	−1.22752e72	−0.269194
$925$	9.21775e72	1.96858
$926$	−3.24778e72	−0.675487
$927$	3.00005e72	0.607680
$928$	−1.36954e72	−0.270178
$929$	9.18253e72	1.76432	0.882160	−	0.470950i	$-0.156089\pi$
$929$	9.18253e72	1.76432	0.882160	+	0.470950i	$0.156089\pi$
$930$	−2.32896e72	−0.435842
$931$	1.82550e70	0.00332748
$932$	7.92931e71	0.140781
$933$	4.10467e72	0.709869
$934$	5.63024e71	0.0948480
$935$	3.51399e72	0.576656
$936$	7.02483e71	0.112299
$937$	−1.09047e73	−1.69823	−0.849113	−	0.528211i	$-0.822863\pi$
$937$	−1.09047e73	−1.69823	−0.849113	+	0.528211i	$0.822863\pi$
$938$	1.35124e72	0.205004
$939$	−8.66665e72	−1.28099
$940$	9.45601e72	1.36168
$941$	−3.21159e72	−0.450582	−0.225291	−	0.974292i	$-0.572333\pi$
$941$	−3.21159e72	−0.450582	−0.225291	+	0.974292i	$0.572333\pi$
$942$	2.70556e72	0.369837
$943$	1.18005e73	1.57169
$944$	−3.23523e71	−0.0419847
$945$	5.39942e72	0.682760
$946$	1.14232e73	1.40753
$947$	1.28424e73	1.54196	0.770979	−	0.636860i	$-0.219767\pi$
$947$	1.28424e73	1.54196	0.770979	+	0.636860i	$0.219767\pi$
$948$	4.61071e72	0.539466
$949$	−1.17126e73	−1.33546
$950$	2.60069e71	0.0288975
$951$	7.31823e72	0.792471
$952$	−2.55301e71	−0.0269430
$953$	−6.15950e72	−0.633533	−0.316767	−	0.948504i	$-0.602597\pi$
$953$	−6.15950e72	−0.633533	−0.316767	+	0.948504i	$0.602597\pi$
$954$	1.83766e72	0.184217
$955$	1.08208e73	1.05725
$956$	3.33670e72	0.317760
$957$	−2.34537e73	−2.17705
$958$	1.58855e71	0.0143730
$959$	−7.26315e72	−0.640574
$960$	1.99467e72	0.171485
$961$	−9.52359e72	−0.798137
$962$	−9.73822e72	−0.795592
$963$	3.74359e72	0.298156
$964$	4.52543e72	0.351376
$965$	5.30392e72	0.401493
$966$	−4.42545e72	−0.326601
$967$	−1.55997e73	−1.12245	−0.561226	−	0.827663i	$-0.689670\pi$
$967$	−1.55997e73	−1.12245	−0.561226	+	0.827663i	$0.689670\pi$
$968$	9.92631e72	0.696373
$969$	5.67517e70	0.00388192
$970$	8.38319e72	0.559116
$971$	4.27353e72	0.277917	0.138959	−	0.990298i	$-0.455624\pi$
$971$	4.27353e72	0.277917	0.138959	+	0.990298i	$0.455624\pi$
$972$	4.78268e72	0.303283
$973$	−7.65548e72	−0.473378
$974$	−1.81308e73	−1.09326
$975$	−2.47333e73	−1.45435
$976$	3.98551e72	0.228541
$977$	8.21910e71	0.0459629	0.0229814	−	0.999736i	$-0.492684\pi$
$977$	8.21910e71	0.0459629	0.0229814	+	0.999736i	$0.492684\pi$
$978$	−1.16058e73	−0.632954
$979$	1.26336e73	0.671973
$980$	2.28526e72	0.118548
$981$	1.09902e73	0.556053
$982$	2.54898e73	1.25787
$983$	−2.13732e73	−1.02874	−0.514372	−	0.857567i	$-0.671975\pi$
$983$	−2.13732e73	−1.02874	−0.514372	+	0.857567i	$0.671975\pi$
$984$	6.61763e72	0.310686
$985$	4.26423e73	1.95278
$986$	−4.87793e72	−0.217897
$987$	−1.17651e73	−0.512654
$988$	−2.74754e71	−0.0116788
$989$	4.11831e73	1.70769
$990$	−1.58355e73	−0.640574
$991$	−5.50676e72	−0.217316	−0.108658	−	0.994079i	$-0.534655\pi$
$991$	−5.50676e72	−0.217316	−0.108658	+	0.994079i	$0.534655\pi$
$992$	−2.06295e72	−0.0794242
$993$	4.17943e73	1.56986
$994$	−5.10650e71	−0.0187136
$995$	3.88808e72	0.139018
$996$	−1.30672e73	−0.455857
$997$	−4.60641e73	−1.56794	−0.783972	−	0.620796i	$-0.786810\pi$
$997$	−4.60641e73	−1.56794	−0.783972	+	0.620796i	$0.786810\pi$
$998$	−1.01901e73	−0.338439
$999$	−3.76824e73	−1.22119

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	14.50.a.c.1.5	✓	6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
14.50.a.c.1.5	✓	6	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 14 = 2 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 50 \)
Character orbit:	\([\chi]\)	\(=\)	14.a (trivial)

\(f(q)\)	\(=\)	\(q+1.67772e7 q^{2} +4.04355e11 q^{3} +2.81475e14 q^{4} +2.21202e17 q^{5} +6.78395e18 q^{6} -1.91581e20 q^{7} +4.72237e21 q^{8} -7.57966e22 q^{9} +3.71115e24 q^{10} +5.62954e25 q^{11} +1.13816e26 q^{12} -1.96258e27 q^{13} -3.21420e27 q^{14} +8.94441e28 q^{15} +7.92282e28 q^{16} +2.82188e29 q^{17} -1.27166e30 q^{18} +4.97367e29 q^{19} +6.22628e31 q^{20} -7.74668e31 q^{21} +9.44480e32 q^{22} +3.40504e33 q^{23} +1.90951e33 q^{24} +3.11668e34 q^{25} -3.29266e34 q^{26} -1.27411e35 q^{27} -5.39253e34 q^{28} -1.03033e36 q^{29} +1.50062e36 q^{30} -1.55199e36 q^{31} +1.32923e36 q^{32} +2.27633e37 q^{33} +4.73434e36 q^{34} -4.23782e37 q^{35} -2.13348e37 q^{36} +2.95756e38 q^{37} +8.34443e36 q^{38} -7.93577e38 q^{39} +1.04460e39 q^{40} +3.46561e39 q^{41} -1.29968e39 q^{42} +1.20947e40 q^{43} +1.58457e40 q^{44} -1.67664e40 q^{45} +5.71271e40 q^{46} +1.51872e41 q^{47} +3.20363e40 q^{48} +3.67034e40 q^{49} +5.22892e41 q^{50} +1.14104e41 q^{51} -5.52416e41 q^{52} -1.44509e42 q^{53} -2.13759e42 q^{54} +1.24527e43 q^{55} -9.04717e41 q^{56} +2.01113e41 q^{57} -1.72861e43 q^{58} -4.08343e42 q^{59} +2.51763e43 q^{60} +5.03042e43 q^{61} -2.60381e43 q^{62} +1.45212e43 q^{63} +2.23007e43 q^{64} -4.34126e44 q^{65} +3.81905e44 q^{66} -4.20396e44 q^{67} +7.94290e43 q^{68} +1.37684e45 q^{69} -7.10988e44 q^{70} +1.58873e44 q^{71} -3.57939e44 q^{72} +5.96797e45 q^{73} +4.96196e45 q^{74} +1.26024e46 q^{75} +1.39996e44 q^{76} -1.07851e46 q^{77} -1.33140e46 q^{78} +4.05103e46 q^{79} +1.75254e46 q^{80} -3.33810e46 q^{81} +5.81433e46 q^{82} -1.14810e47 q^{83} -2.18050e46 q^{84} +6.24207e46 q^{85} +2.02916e47 q^{86} -4.16619e47 q^{87} +2.65847e47 q^{88} +2.24417e47 q^{89} -2.81293e47 q^{90} +3.75993e47 q^{91} +9.58434e47 q^{92} -6.27556e47 q^{93} +2.54800e48 q^{94} +1.10019e47 q^{95} +5.37480e47 q^{96} +2.25892e48 q^{97} +6.15780e47 q^{98} -4.26700e48 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 100663296 q^{2} + 600288540488 q^{3} + 16\!\cdots\!36 q^{4} + 23\!\cdots\!44 q^{5} + 10\!\cdots\!08 q^{6} - 11\!\cdots\!06 q^{7} + 28\!\cdots\!76 q^{8} + 24\!\cdots\!58 q^{9} + 39\!\cdots\!04 q^{10}+ \cdots - 23\!\cdots\!84 q^{99}+O(q^{100}) \) 6 * q + 100663296 * q^2 + 600288540488 * q^3 + 1688849860263936 * q^4 + 237495319633852644 * q^5 + 10071170506091921408 * q^6 - 1149487388283398486406 * q^7 + 28334198897217871282176 * q^8 + 249667159058784905352958 * q^9 + 3984510276486186720559104 * q^10 + 22232534037385203892080408 * q^11 + 168966202953533481317040128 * q^12 + 2632998893516569086205448724 * q^13 - 19285198202506445620506525696 * q^14 + 149072300431744884273809122880 * q^15 + 475368975085586025561263702016 * q^16 - 1409004291529529137192771562100 * q^17 + 4188719855635591054646132604928 * q^18 + 18105270833681321619211508609928 * q^19 + 66848989562828475627151728574464 * q^20 - 115004017770334038187527674767688 * q^21 + 373000025772563640901473694384128 * q^22 + 5618913122903377817563359905020800 * q^23 + 2834782483651269179287946708123648 * q^24 + 5996249800897839089131003669066986 * q^25 + 44174391164288479138191433619472384 * q^26 + 124497907324429451768320951590293744 * q^27 - 323551935846262379567492011011342336 * q^28 - 483091083860359843452294275052160332 * q^29 + 2501018183960277180356698797328302080 * q^30 + 6486298240062882259192167116430562080 * q^31 + 7975367974709495237422842361682067456 * q^32 - 62373898779937118804633162567140460480 * q^33 - 23639169343917880712976762136009113600 * q^34 - 45499645782574701040199480904673526244 * q^35 + 70275057781487128411465970277519720448 * q^36 - 175145361056063681116535719938063892668 * q^37 + 303756039515171607970981229634621800448 * q^38 - 81396995084096796106565511444255620448 * q^39 + 1121539937277318906547460015067154612224 * q^40 + 835550088847864742420204150305371241308 * q^41 - 1929447247000732550824400305555251396608 * q^42 + 17308185468083461647372224162326046585976 * q^43 + 6257902000391867077150458889000502427648 * q^44 + 103167727297878364026250185422148990648148 * q^45 + 94269719148184516774869082812273446092800 * q^46 + 184831957187272343600261999594531459533344 * q^47 + 47559758041233811695056608118679397203968 * q^48 + 220220209303764752647381266192201961132806 * q^49 + 100600378099620040331594100852729342590976 * q^50 - 1771571524511561271442105788532936222457168 * q^51 + 741123302231759300812931531183549992402944 * q^52 + 2351347648887961413461306710918084645940772 * q^53 + 2088728282729934989078702562155901646536704 * q^54 + 3085506887527435207314999234586652419171056 * q^55 - 5428300714910886734677800047011668821016576 * q^56 + 31386997170933042757613940977962373909990896 * q^57 - 8104923461599370931325326748113505156595712 * q^58 + 30944438467849109083090742506105243891298520 * q^59 + 41960122292229305674715292769717146909409280 * q^60 + 150150609374563344118041131116366350036061044 * q^61 + 108822026613954829245034973220452689017569280 * q^62 - 47831541767769749048424100541375377399148158 * q^63 + 133804471191183738849214309635890169035882496 * q^64 + 752748549799322853557360453473881793779240456 * q^65 - 1046460372593141508602992369152030007812423680 * q^66 - 128785963396634280403104719488486831723130328 * q^67 - 396599450143488570983845141336446276835737600 * q^68 + 683944728096651671392678575425131612212016000 * q^69 - 763357385217744795486851374225583159277256704 * q^70 + 280171533474803716136746628126132726863354608 * q^71 + 1179019823812490354578901459995528294215712768 * q^72 + 6359164269014273149745068623217940032230909276 * q^73 - 2938451553835568487847240945116404549091852288 * q^74 + 21669926216235979931654849241861968650694269720 * q^75 + 5096180686250569343996473821525651024424992768 * q^76 - 4259336247592613144486630846481598632941155608 * q^77 - 1365614968276830113187808603650748503470112768 * q^78 - 67602995067772997355679612466712542986464262464 * q^79 + 18816317780328031196030550924144907434678288384 * q^80 - 16854545541923284876477831491790840658294025626 * q^81 + 14018204319419817922368127793769679275612438528 * q^82 - 45613436384448178087860777699340468946504675160 * q^83 - 32370753223536642163411941996766452615194083328 * q^84 - 55477811327569765203281837835132224387734181592 * q^85 + 290383166166097342085679637171763145998981922816 * q^86 - 384172046681295864425179771398097404272715681328 * q^87 + 104990173567406438596641913279881453337174867968 * q^88 + 802941729082063189409562013460525749819175687196 * q^89 + 1730867245105601654995029030867444800285958995968 * q^90 - 504433170243573172459186088471907935721940674324 * q^91 + 1581583440408427645787601974063399056163261644800 * q^92 + 5393326286497522306808749269007443718265926441248 * q^93 + 3100965669433620559407813223789366715386171490304 * q^94 + 6309934171256595954343099570284482000731174337760 * q^95 + 797920333565516565311290846634437881640767193088 * q^96 + 2208884359814234277165695356094087258476148891724 * q^97 + 3694682019054470868351687337260069817548690948096 * q^98 - 23361740711649209489147347130820123162443505968584 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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