LMFDB - Embedded newform 14.42.a.d.1.5

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [14,42,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, 42, 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, 42); N := Newforms(S);

Level:	$ N $	$=$	$ 14 = 2 \cdot 7 $
Weight:	$ k $	$=$	$ 42 $
Character orbit:	$[\chi]$	$=$	14.a (trivial)

Newform invariants

comment:select newform

sage:traces = [6,-6291456] 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:	$149.060338639$
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 - 10\!\cdots\!00 $ x^6 - 2x^5 - 33654200525555939939x^4 - 16229167658884781405401882060x^3 + 279927803735169134573552725517816429300x^2 + 296535382703829983152824934477895853926294108000*x - 106166339617512040934955672225996483835623594378260760000
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{30}\cdot 3^{10}\cdot 5^{3}\cdot 7^{6} $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.5
Root			$4.00095e9$ 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)

$f(q)$	$=$	\(q-1.04858e6 q^{2} +7.61188e9 q^{3} +1.09951e12 q^{4} -9.47383e13 q^{5} -7.98164e15 q^{6} +7.97923e16 q^{7} -1.15292e18 q^{8} +2.14677e19 q^{9} +9.93403e19 q^{10} -3.99797e21 q^{11} +8.36935e21 q^{12} +3.88838e22 q^{13} -8.36683e22 q^{14} -7.21136e23 q^{15} +1.20893e24 q^{16} -7.69424e24 q^{17} -2.25105e25 q^{18} +1.23400e26 q^{19} -1.04166e26 q^{20} +6.07369e26 q^{21} +4.19218e27 q^{22} -8.27721e27 q^{23} -8.77590e27 q^{24} -3.64994e28 q^{25} -4.07726e28 q^{26} -1.14218e29 q^{27} +8.77325e28 q^{28} +4.08980e29 q^{29} +7.56166e29 q^{30} -1.50954e30 q^{31} -1.26765e30 q^{32} -3.04321e31 q^{33} +8.06800e30 q^{34} -7.55938e30 q^{35} +2.36040e31 q^{36} +2.18213e32 q^{37} -1.29395e32 q^{38} +2.95979e32 q^{39} +1.09226e32 q^{40} +1.19847e33 q^{41} -6.36873e32 q^{42} +2.44113e33 q^{43} -4.39582e33 q^{44} -2.03382e33 q^{45} +8.67928e33 q^{46} +1.60527e34 q^{47} +9.20220e33 q^{48} +6.36681e33 q^{49} +3.82724e34 q^{50} -5.85677e34 q^{51} +4.27532e34 q^{52} +2.41936e35 q^{53} +1.19767e35 q^{54} +3.78761e35 q^{55} -9.19942e34 q^{56} +9.39310e35 q^{57} -4.28847e35 q^{58} -1.11558e36 q^{59} -7.92898e35 q^{60} +1.61612e36 q^{61} +1.58287e36 q^{62} +1.71296e36 q^{63} +1.32923e36 q^{64} -3.68379e36 q^{65} +3.19104e37 q^{66} +3.72091e37 q^{67} -8.45991e36 q^{68} -6.30051e37 q^{69} +7.92658e36 q^{70} -1.14501e38 q^{71} -2.47506e37 q^{72} +3.90033e37 q^{73} -2.28813e38 q^{74} -2.77829e38 q^{75} +1.35680e38 q^{76} -3.19007e38 q^{77} -3.10356e38 q^{78} -3.74054e38 q^{79} -1.14532e38 q^{80} -1.65241e39 q^{81} -1.25669e39 q^{82} -4.95162e38 q^{83} +6.67810e38 q^{84} +7.28939e38 q^{85} -2.55971e39 q^{86} +3.11311e39 q^{87} +4.60935e39 q^{88} +4.38732e39 q^{89} +2.13261e39 q^{90} +3.10263e39 q^{91} -9.10089e39 q^{92} -1.14904e40 q^{93} -1.68325e40 q^{94} -1.16907e40 q^{95} -9.64921e39 q^{96} +8.52599e40 q^{97} -6.67608e39 q^{98} -8.58274e40 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 6291456 q^{2} - 2340113048 q^{3} + 6597069766656 q^{4} - 178161928499100 q^{5} + 24\!\cdots\!48 q^{6} + 47\!\cdots\!06 q^{7} - 69\!\cdots\!56 q^{8} + 51\!\cdots\!58 q^{9} + 18\!\cdots\!00 q^{10} + 14\!\cdots\!48 q^{11}+ \cdots - 48\!\cdots\!84 q^{99}+O(q^{100}) $ 6 * q - 6291456 * q^2 - 2340113048 * q^3 + 6597069766656 * q^4 - 178161928499100 * q^5 + 2453786379419648 * q^6 + 478753597785672006 * q^7 - 6917529027641081856 * q^8 + 51308314120992776158 * q^9 + 186816322337872281600 * q^10 + 1436248344978714407448 * q^11 - 2572981506586336821248 * q^12 + 34301876705702636440116 * q^13 - 502009532551708809363456 * q^14 + 656926621499476771816800 * q^15 + 7253554917687775048237056 * q^16 + 30276052253972503691396460 * q^17 - 53800666787734121252651008 * q^18 + 61818651164394150562143048 * q^19 - 195891112011756765551001600 * q^20 - 186722923492532494781489048 * q^21 - 1506015544584400438504194048 * q^22 + 10773306728112038743730630400 * q^23 + 2697966656250274718676942848 * q^24 - 2052708525720541417377953910 * q^25 - 35968124668558847707831074816 * q^26 + 244827393668175182742514248976 * q^27 + 526395147604940616487095238656 * q^28 + 1858263976358013274666185585588 * q^29 - 688837489065435355484572876800 * q^30 - 3026665292350546396080823084800 * q^31 - 7605903601369376408980219232256 * q^32 - 4896034938196446312177112267680 * q^33 - 31746741768261472030709734440960 * q^34 - 14215944042896296003236077699100 * q^35 + 56414087977615093926619783364608 * q^36 + 36388638978207164300560818509508 * q^37 - 64821553963355760819849708699648 * q^38 + 1349472180986220352912856250575552 * q^39 + 205406718668839862194407053721600 * q^40 + 3928217707909089189820717743560988 * q^41 + 195793176224105753247994659995648 * q^42 + 4279178185760899188404399696028024 * q^43 + 1579171755678132274204973778075648 * q^44 + 9771204462083328418570928249843700 * q^45 - 11296630875736809137746089502310400 * q^46 - 5329487100372894471454831212332544 * q^47 - 2829023084544288063411394023784448 * q^48 + 38200834565454167914448610835344006 * q^49 + 2152420895065942437268505399132160 * q^50 + 137264354577108170962850174657040432 * q^51 + 37715312292458762294086677106262016 * q^52 + 89882484295477272450372378995983908 * q^53 - 256720129143000460419414621134258176 * q^54 - 688920073150979141025746602426354800 * q^55 - 551965318294998211873572376968953856 * q^56 - 4296631731665940403373896952488068976 * q^57 - 1948531007273580127496370216593522688 * q^58 - 2098674926749446087055800157350918120 * q^59 + 722298458934277943312591488863436800 * q^60 - 4154432586061843368860666149845842316 * q^61 + 3173688585591766537816845146967244800 * q^62 + 4094006663623781812762810246927472158 * q^63 + 7975367974709495237422842361682067456 * q^64 - 641510480348272181759116614056928600 * q^65 + 5133864731354276888237427673194823680 * q^66 - 908094220382585683627028817656747352 * q^67 + 33288871496396541296073490501164072960 * q^68 + 26819934334947518038863842406109202400 * q^69 + 14906497740724026477889273409411481600 * q^70 - 215878036680020205164533780979567075952 * q^71 - 59154458715215724729199265961327198208 * q^72 - 366319328063377168243687845513023714436 * q^73 - 38156253505212555513624860829425860608 * q^74 - 659900775570837083521758503011572720680 * q^75 + 67970325768679730257434728149442101248 * q^76 + 114601510412046088219176694376128583448 * q^77 - 1415024141649806992775951155803510013952 * q^78 - 708002425286449904990404275469758062304 * q^79 - 215384555434897427340362570763180441600 * q^80 - 3611254295706029330226546538084588140986 * q^81 - 4119034811288481106305448928672206553088 * q^82 - 7105924773159166013413745618032255980600 * q^83 - 205304025552367914317769248599596597248 * q^84 - 4868319246825467861790604801633358487000 * q^85 - 4487043545312420627380331815662281293824 * q^86 - 16737524180679527763204021080859713384112 * q^87 - 1655881602881953227556754584319450677248 * q^88 - 17070846531385954927672654485955438871364 * q^89 - 10245850490033488179831429660508107571200 * q^90 + 2737024480609278648170478684774439432116 * q^91 + 11845376017156600378421243545974629990400 * q^92 - 30355715547120221823292802943319787274208 * q^93 + 5588372265760608193300221093302809657344 * q^94 - 77620172449655779402892509820789510740800 * q^95 + 2966445709899111400379665899883801346048 * q^96 - 48291725996003567390264085027900911661204 * q^97 - 40056478305305669575060866555281676435456 * q^98 - 4885293233811587121115440246715559440584 * 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 $

$2$	−1.04858e6	−0.707107
$2$	−1.04858e6	−0.707107
$3$	7.61188e9	1.26039	0.630197	−	0.776435i	$-0.282974\pi$
$3$	7.61188e9	1.26039	0.630197	+	0.776435i	$0.282974\pi$
$4$	1.09951e12	0.500000
$5$	−9.47383e13	−0.444263	−0.222132	−	0.975017i	$-0.571301\pi$
$5$	−9.47383e13	−0.444263	−0.222132	+	0.975017i	$0.571301\pi$
$6$	−7.98164e15	−0.891233
$7$	7.97923e16	0.377964
$7$	7.97923e16	0.377964
$8$	−1.15292e18	−0.353553
$9$	2.14677e19	0.588592
$10$	9.93403e19	0.314142
$11$	−3.99797e21	−1.79180	−0.895901	−	0.444254i	$-0.853469\pi$
$11$	−3.99797e21	−1.79180	−0.895901	+	0.444254i	$0.853469\pi$
$12$	8.36935e21	0.630197
$13$	3.88838e22	0.567453	0.283727	−	0.958905i	$-0.408429\pi$
$13$	3.88838e22	0.567453	0.283727	+	0.958905i	$0.408429\pi$
$14$	−8.36683e22	−0.267261
$15$	−7.21136e23	−0.559947
$16$	1.20893e24	0.250000
$17$	−7.69424e24	−0.459159	−0.229579	−	0.973290i	$-0.573735\pi$
$17$	−7.69424e24	−0.459159	−0.229579	+	0.973290i	$0.573735\pi$
$18$	−2.25105e25	−0.416198
$19$	1.23400e26	0.753127	0.376563	−	0.926391i	$-0.377106\pi$
$19$	1.23400e26	0.753127	0.376563	+	0.926391i	$0.377106\pi$
$20$	−1.04166e26	−0.222132
$21$	6.07369e26	0.476384
$22$	4.19218e27	1.26700
$23$	−8.27721e27	−1.00569	−0.502844	−	0.864377i	$-0.667713\pi$
$23$	−8.27721e27	−1.00569	−0.502844	+	0.864377i	$0.667713\pi$
$24$	−8.77590e27	−0.445616
$25$	−3.64994e28	−0.802630
$26$	−4.07726e28	−0.401250
$27$	−1.14218e29	−0.518536
$28$	8.77325e28	0.188982
$29$	4.08980e29	0.429085	0.214543	−	0.976715i	$-0.431174\pi$
$29$	4.08980e29	0.429085	0.214543	+	0.976715i	$0.431174\pi$
$30$	7.56166e29	0.395942
$31$	−1.50954e30	−0.403580	−0.201790	−	0.979429i	$-0.564676\pi$
$31$	−1.50954e30	−0.403580	−0.201790	+	0.979429i	$0.564676\pi$
$32$	−1.26765e30	−0.176777
$33$	−3.04321e31	−2.25838
$34$	8.06800e30	0.324674
$35$	−7.55938e30	−0.167916
$36$	2.36040e31	0.294296
$37$	2.18213e32	1.55148	0.775739	−	0.631054i	$-0.217377\pi$
$37$	2.18213e32	1.55148	0.775739	+	0.631054i	$0.217377\pi$
$38$	−1.29395e32	−0.532541
$39$	2.95979e32	0.715215
$40$	1.09226e32	0.157071
$41$	1.19847e33	1.03886	0.519431	−	0.854512i	$-0.326144\pi$
$41$	1.19847e33	1.03886	0.519431	+	0.854512i	$0.326144\pi$
$42$	−6.36873e32	−0.336854
$43$	2.44113e33	0.797055	0.398527	−	0.917156i	$-0.369521\pi$
$43$	2.44113e33	0.797055	0.398527	+	0.917156i	$0.369521\pi$
$44$	−4.39582e33	−0.895901
$45$	−2.03382e33	−0.261490
$46$	8.67928e33	0.711129
$47$	1.60527e34	0.846335	0.423168	−	0.906051i	$-0.360918\pi$
$47$	1.60527e34	0.846335	0.423168	+	0.906051i	$0.360918\pi$
$48$	9.20220e33	0.315098
$49$	6.36681e33	0.142857
$50$	3.82724e34	0.567545
$51$	−5.85677e34	−0.578721
$52$	4.27532e34	0.283727
$53$	2.41936e35	1.08654	0.543270	−	0.839558i	$-0.317186\pi$
$53$	2.41936e35	1.08654	0.543270	+	0.839558i	$0.317186\pi$
$54$	1.19767e35	0.366660
$55$	3.78761e35	0.796032
$56$	−9.19942e34	−0.133631
$57$	9.39310e35	0.949236
$58$	−4.28847e35	−0.303409
$59$	−1.11558e36	−0.555946	−0.277973	−	0.960589i	$-0.589663\pi$
$59$	−1.11558e36	−0.555946	−0.277973	+	0.960589i	$0.589663\pi$
$60$	−7.92898e35	−0.279973
$61$	1.61612e36	0.406642	0.203321	−	0.979112i	$-0.434827\pi$
$61$	1.61612e36	0.406642	0.203321	+	0.979112i	$0.434827\pi$
$62$	1.58287e36	0.285374
$63$	1.71296e36	0.222467
$64$	1.32923e36	0.125000
$65$	−3.68379e36	−0.252099
$66$	3.19104e37	1.59691
$67$	3.72091e37	1.36809	0.684047	−	0.729438i	$-0.260218\pi$
$67$	3.72091e37	1.36809	0.684047	+	0.729438i	$0.260218\pi$
$68$	−8.45991e36	−0.229579
$69$	−6.30051e37	−1.26756
$70$	7.92658e36	0.118734
$71$	−1.14501e38	−1.28237	−0.641183	−	0.767388i	$-0.721556\pi$
$71$	−1.14501e38	−1.28237	−0.641183	+	0.767388i	$0.721556\pi$
$72$	−2.47506e37	−0.208099
$73$	3.90033e37	0.247162	0.123581	−	0.992334i	$-0.460562\pi$
$73$	3.90033e37	0.247162	0.123581	+	0.992334i	$0.460562\pi$
$74$	−2.28813e38	−1.09706
$75$	−2.77829e38	−1.01163
$76$	1.35680e38	0.376563
$77$	−3.19007e38	−0.677237
$78$	−3.10356e38	−0.505733
$79$	−3.74054e38	−0.469439	−0.234719	−	0.972063i	$-0.575417\pi$
$79$	−3.74054e38	−0.469439	−0.234719	+	0.972063i	$0.575417\pi$
$80$	−1.14532e38	−0.111066
$81$	−1.65241e39	−1.24215
$82$	−1.25669e39	−0.734587
$83$	−4.95162e38	−0.225760	−0.112880	−	0.993609i	$-0.536008\pi$
$83$	−4.95162e38	−0.225760	−0.112880	+	0.993609i	$0.536008\pi$
$84$	6.67810e38	0.238192
$85$	7.28939e38	0.203987
$86$	−2.55971e39	−0.563603
$87$	3.11311e39	0.540816
$88$	4.60935e39	0.633498
$89$	4.38732e39	0.478304	0.239152	−	0.970982i	$-0.423131\pi$
$89$	4.38732e39	0.478304	0.239152	+	0.970982i	$0.423131\pi$
$90$	2.13261e39	0.184901
$91$	3.10263e39	0.214477
$92$	−9.10089e39	−0.502844
$93$	−1.14904e40	−0.508670
$94$	−1.68325e40	−0.598450
$95$	−1.16907e40	−0.334586
$96$	−9.64921e39	−0.222808
$97$	8.52599e40	1.59193	0.795966	−	0.605342i	$-0.206964\pi$
$97$	8.52599e40	1.59193	0.795966	+	0.605342i	$0.206964\pi$
$98$	−6.67608e39	−0.101015
$99$	−8.58274e40	−1.05464
$100$	−4.01315e40	−0.401315
$101$	2.13845e41	1.74386	0.871930	−	0.489631i	$-0.162868\pi$
$101$	2.13845e41	1.74386	0.871930	+	0.489631i	$0.162868\pi$
$102$	6.14126e40	0.409218
$103$	−6.42609e40	−0.350577	−0.175289	−	0.984517i	$-0.556086\pi$
$103$	−6.42609e40	−0.350577	−0.175289	+	0.984517i	$0.556086\pi$
$104$	−4.48300e40	−0.200625
$105$	−5.75411e40	−0.211640
$106$	−2.53689e41	−0.768300
$107$	−7.80930e41	−1.95094	−0.975472	−	0.220125i	$-0.929353\pi$
$107$	−7.80930e41	−1.95094	−0.975472	+	0.220125i	$0.929353\pi$
$108$	−1.25584e41	−0.259268
$109$	6.42300e41	1.09773	0.548864	−	0.835912i	$-0.315061\pi$
$109$	6.42300e41	1.09773	0.548864	+	0.835912i	$0.315061\pi$
$110$	−3.97160e41	−0.562879
$111$	1.66101e42	1.95547
$112$	9.64629e40	0.0944911
$113$	−2.82320e41	−0.230480	−0.115240	−	0.993338i	$-0.536764\pi$
$113$	−2.82320e41	−0.230480	−0.115240	+	0.993338i	$0.536764\pi$
$114$	−9.84938e41	−0.671211
$115$	7.84169e41	0.446790
$116$	4.49679e41	0.214543
$117$	8.34747e41	0.333999
$118$	1.16977e42	0.393113
$119$	−6.13941e41	−0.173546
$120$	8.31414e41	0.197971
$121$	1.10053e43	2.21055
$122$	−1.69463e42	−0.287539
$123$	9.12261e42	1.30938
$124$	−1.65976e42	−0.201790
$125$	7.76609e42	0.800842
$126$	−1.79617e42	−0.157308
$127$	−1.50717e43	−1.12250	−0.561251	−	0.827646i	$-0.689680\pi$
$127$	−1.50717e43	−1.12250	−0.561251	+	0.827646i	$0.689680\pi$
$128$	−1.39380e42	−0.0883883
$129$	1.85816e43	1.00460
$130$	3.86273e42	0.178261
$131$	−2.07505e43	−0.818401	−0.409201	−	0.912444i	$-0.634192\pi$
$131$	−2.07505e43	−0.818401	−0.409201	+	0.912444i	$0.634192\pi$
$132$	−3.34605e43	−1.12919
$133$	9.84641e42	0.284655
$134$	−3.90166e43	−0.967389
$135$	1.08208e43	0.230366
$136$	8.87086e42	0.162337
$137$	−8.91677e43	−1.40422	−0.702112	−	0.712067i	$-0.747759\pi$
$137$	−8.91677e43	−1.40422	−0.702112	+	0.712067i	$0.747759\pi$
$138$	6.60657e43	0.896302
$139$	−4.88064e43	−0.571049	−0.285524	−	0.958371i	$-0.592168\pi$
$139$	−4.88064e43	−0.571049	−0.285524	+	0.958371i	$0.592168\pi$
$140$	−8.31163e42	−0.0839578
$141$	1.22191e44	1.06672
$142$	1.20063e44	0.906770
$143$	−1.55457e44	−1.01676
$144$	2.59529e43	0.147148
$145$	−3.87461e43	−0.190627
$146$	−4.08979e43	−0.174770
$147$	4.84634e43	0.180056
$148$	2.39928e44	0.775739
$149$	2.66733e44	0.751205	0.375602	−	0.926781i	$-0.377436\pi$
$149$	2.66733e44	0.751205	0.375602	+	0.926781i	$0.377436\pi$
$150$	2.91325e44	0.715331
$151$	3.10084e44	0.664434	0.332217	−	0.943203i	$-0.392203\pi$
$151$	3.10084e44	0.664434	0.332217	+	0.943203i	$0.392203\pi$
$152$	−1.42271e44	−0.266271
$153$	−1.65178e44	−0.270257
$154$	3.34504e44	0.478879
$155$	1.43011e44	0.179296
$156$	3.25432e44	0.357607
$157$	1.25525e45	1.21001	0.605004	−	0.796222i	$-0.293171\pi$
$157$	1.25525e45	1.21001	0.605004	+	0.796222i	$0.293171\pi$
$158$	3.92224e44	0.331943
$159$	1.84159e45	1.36947
$160$	1.20095e44	0.0785354
$161$	−6.60457e44	−0.380114
$162$	1.73268e45	0.878334
$163$	1.68291e45	0.751994	0.375997	−	0.926621i	$-0.377300\pi$
$163$	1.68291e45	0.751994	0.375997	+	0.926621i	$0.377300\pi$
$164$	1.31773e45	0.519431
$165$	2.88308e45	1.00331
$166$	5.19215e44	0.159636
$167$	3.12246e45	0.848808	0.424404	−	0.905473i	$-0.360484\pi$
$167$	3.12246e45	0.848808	0.424404	+	0.905473i	$0.360484\pi$
$168$	−7.00249e44	−0.168427
$169$	−3.18350e45	−0.677997
$170$	−7.64348e44	−0.144241
$171$	2.64913e45	0.443285
$172$	2.68405e45	0.398527
$173$	1.00726e46	1.32799	0.663995	−	0.747737i	$-0.268860\pi$
$173$	1.00726e46	1.32799	0.663995	+	0.747737i	$0.268860\pi$
$174$	−3.26433e45	−0.382415
$175$	−2.91237e45	−0.303366
$176$	−4.83325e45	−0.447950
$177$	−8.49163e45	−0.700711
$178$	−4.60044e45	−0.338212
$179$	1.67923e46	1.10059	0.550293	−	0.834972i	$-0.314516\pi$
$179$	1.67923e46	1.10059	0.550293	+	0.834972i	$0.314516\pi$
$180$	−2.23620e45	−0.130745
$181$	3.02497e46	1.57874	0.789370	−	0.613918i	$-0.210408\pi$
$181$	3.02497e46	1.57874	0.789370	+	0.613918i	$0.210408\pi$
$182$	−3.25334e45	−0.151658
$183$	1.23017e46	0.512529
$184$	9.54297e45	0.355564
$185$	−2.06731e46	−0.689265
$186$	1.20486e46	0.359684
$187$	3.07614e46	0.822722
$188$	1.76502e46	0.423168
$189$	−9.11374e45	−0.195988
$190$	1.22586e46	0.236588
$191$	8.12526e46	1.40816	0.704082	−	0.710118i	$-0.251359\pi$
$191$	8.12526e46	1.40816	0.704082	+	0.710118i	$0.251359\pi$
$192$	1.01179e46	0.157549
$193$	4.62754e46	0.647776	0.323888	−	0.946095i	$-0.395010\pi$
$193$	4.62754e46	0.647776	0.323888	+	0.946095i	$0.395010\pi$
$194$	−8.94015e46	−1.12567
$195$	−2.80405e46	−0.317744
$196$	7.00038e45	0.0714286
$197$	6.33379e46	0.582246	0.291123	−	0.956686i	$-0.405971\pi$
$197$	6.33379e46	0.582246	0.291123	+	0.956686i	$0.405971\pi$
$198$	8.99966e46	0.745744
$199$	−1.18620e47	−0.886483	−0.443242	−	0.896402i	$-0.646172\pi$
$199$	−1.18620e47	−0.886483	−0.443242	+	0.896402i	$0.646172\pi$
$200$	4.20809e46	0.283773
$201$	2.83231e47	1.72434
$202$	−2.24233e47	−1.23309
$203$	3.26335e46	0.162179
$204$	−6.43958e46	−0.289360
$205$	−1.13541e47	−0.461528
$206$	6.73825e46	0.247896
$207$	−1.77693e47	−0.591940
$208$	4.70077e46	0.141863
$209$	−4.93352e47	−1.34945
$210$	6.03362e46	0.149652
$211$	7.44008e46	0.167412	0.0837061	−	0.996490i	$-0.473324\pi$
$211$	7.44008e46	0.167412	0.0837061	+	0.996490i	$0.473324\pi$
$212$	2.66012e47	0.543270
$213$	−8.71566e47	−1.61629
$214$	8.18864e47	1.37953
$215$	−2.31269e47	−0.354102
$216$	1.31685e47	0.183330
$217$	−1.20450e47	−0.152539
$218$	−6.73500e47	−0.776211
$219$	2.96888e47	0.311522
$220$	4.16452e47	0.398016
$221$	−2.99182e47	−0.260551
$222$	−1.74170e48	−1.38273
$223$	2.43341e47	0.176183	0.0880917	−	0.996112i	$-0.471923\pi$
$223$	2.43341e47	0.176183	0.0880917	+	0.996112i	$0.471923\pi$
$224$	−1.01149e47	−0.0668153
$225$	−7.83559e47	−0.472422
$226$	2.96034e47	0.162974
$227$	−1.17660e47	−0.0591696	−0.0295848	−	0.999562i	$-0.509419\pi$
$227$	−1.17660e47	−0.0591696	−0.0295848	+	0.999562i	$0.509419\pi$
$228$	1.03278e48	0.474618
$229$	1.08318e48	0.455067	0.227533	−	0.973770i	$-0.426934\pi$
$229$	1.08318e48	0.455067	0.227533	+	0.973770i	$0.426934\pi$
$230$	−8.22260e47	−0.315928
$231$	−2.42825e48	−0.853586
$232$	−4.71522e47	−0.151704
$233$	−2.81188e48	−0.828325	−0.414163	−	0.910203i	$-0.635926\pi$
$233$	−2.81188e48	−0.828325	−0.414163	+	0.910203i	$0.635926\pi$
$234$	−8.75296e47	−0.236173
$235$	−1.52081e48	−0.375996
$236$	−1.22659e48	−0.277973
$237$	−2.84725e48	−0.591678
$238$	6.43764e47	0.122715
$239$	−5.56423e47	−0.0973303	−0.0486651	−	0.998815i	$-0.515497\pi$
$239$	−5.56423e47	−0.0973303	−0.0486651	+	0.998815i	$0.515497\pi$
$240$	−8.71800e47	−0.139987
$241$	−9.29447e48	−1.37049	−0.685244	−	0.728313i	$-0.740305\pi$
$241$	−9.29447e48	−1.37049	−0.685244	+	0.728313i	$0.740305\pi$
$242$	−1.15399e49	−1.56310
$243$	−8.41205e48	−1.04706
$244$	1.77694e48	0.203321
$245$	−6.03180e47	−0.0634662
$246$	−9.56575e48	−0.925868
$247$	4.79828e48	0.427364
$248$	1.74038e48	0.142687
$249$	−3.76911e48	−0.284546
$250$	−8.14333e48	−0.566281
$251$	2.88601e49	1.84921	0.924606	−	0.380925i	$-0.124395\pi$
$251$	2.88601e49	1.84921	0.924606	+	0.380925i	$0.124395\pi$
$252$	1.88342e48	0.111234
$253$	3.30921e49	1.80199
$254$	1.58039e49	0.793729
$255$	5.54860e48	0.257104
$256$	1.46150e48	0.0625000
$257$	4.04251e49	1.59596	0.797980	−	0.602684i	$-0.205902\pi$
$257$	4.04251e49	1.59596	0.797980	+	0.602684i	$0.205902\pi$
$258$	−1.94842e49	−0.710361
$259$	1.74117e49	0.586404
$260$	−4.05036e48	−0.126049
$261$	8.77988e48	0.252556
$262$	2.17584e49	0.578697
$263$	−4.20638e49	−1.03470	−0.517351	−	0.855773i	$-0.673082\pi$
$263$	−4.20638e49	−1.03470	−0.517351	+	0.855773i	$0.673082\pi$
$264$	3.50858e49	0.798456
$265$	−2.29206e49	−0.482710
$266$	−1.03247e49	−0.201282
$267$	3.33957e49	0.602851
$268$	4.09119e49	0.684047
$269$	5.31394e49	0.823181	0.411590	−	0.911369i	$-0.364973\pi$
$269$	5.31394e49	0.823181	0.411590	+	0.911369i	$0.364973\pi$
$270$	−1.13465e49	−0.162894
$271$	−5.28970e49	−0.703981	−0.351990	−	0.936004i	$-0.614495\pi$
$271$	−5.28970e49	−0.703981	−0.351990	+	0.936004i	$0.614495\pi$
$272$	−9.30177e48	−0.114790
$273$	2.36168e49	0.270326
$274$	9.34992e49	0.992936
$275$	1.45924e50	1.43815
$276$	−6.92749e49	−0.633782
$277$	−1.22897e49	−0.104401	−0.0522005	−	0.998637i	$-0.516623\pi$
$277$	−1.22897e49	−0.104401	−0.0522005	+	0.998637i	$0.516623\pi$
$278$	5.11772e49	0.403792
$279$	−3.24064e49	−0.237544
$280$	8.71537e48	0.0593672
$281$	−4.31503e49	−0.273215	−0.136607	−	0.990625i	$-0.543620\pi$
$281$	−4.31503e49	−0.273215	−0.136607	+	0.990625i	$0.543620\pi$
$282$	−1.28127e50	−0.754282
$283$	−1.40208e50	−0.767626	−0.383813	−	0.923411i	$-0.625389\pi$
$283$	−1.40208e50	−0.767626	−0.383813	+	0.923411i	$0.625389\pi$
$284$	−1.25895e50	−0.641183
$285$	−8.89886e49	−0.421711
$286$	1.63008e50	0.718961
$287$	9.56286e49	0.392653
$288$	−2.72136e49	−0.104049
$289$	−2.21604e50	−0.789173
$290$	4.06282e49	0.134793
$291$	6.48988e50	2.00646
$292$	4.28846e49	0.123581
$293$	9.10915e49	0.244732	0.122366	−	0.992485i	$-0.460952\pi$
$293$	9.10915e49	0.244732	0.122366	+	0.992485i	$0.460952\pi$
$294$	−5.08175e49	−0.127319
$295$	1.05688e50	0.246986
$296$	−2.51583e50	−0.548530
$297$	4.56642e50	0.929113
$298$	−2.79690e50	−0.531182
$299$	−3.21850e50	−0.570681
$300$	−3.05476e50	−0.505815
$301$	1.94784e50	0.301258
$302$	−3.25147e50	−0.469826
$303$	1.62776e51	2.19795
$304$	1.49182e50	0.188282
$305$	−1.53108e50	−0.180656
$306$	1.73202e50	0.191101
$307$	9.86179e50	1.01770	0.508849	−	0.860856i	$-0.330071\pi$
$307$	9.86179e50	1.01770	0.508849	+	0.860856i	$0.330071\pi$
$308$	−3.50752e50	−0.338619
$309$	−4.89147e50	−0.441866
$310$	−1.49958e50	−0.126781
$311$	−9.35571e50	−0.740438	−0.370219	−	0.928944i	$-0.620717\pi$
$311$	−9.35571e50	−0.740438	−0.370219	+	0.928944i	$0.620717\pi$
$312$	−3.41241e50	−0.252867
$313$	2.47338e51	1.71645	0.858225	−	0.513274i	$-0.171567\pi$
$313$	2.47338e51	1.71645	0.858225	+	0.513274i	$0.171567\pi$
$314$	−1.31623e51	−0.855605
$315$	−1.62283e50	−0.0988339
$316$	−4.11277e50	−0.234719
$317$	−7.17879e50	−0.384004	−0.192002	−	0.981394i	$-0.561498\pi$
$317$	−7.17879e50	−0.384004	−0.192002	+	0.981394i	$0.561498\pi$
$318$	−1.93105e51	−0.968361
$319$	−1.63509e51	−0.768835
$320$	−1.25929e50	−0.0555329
$321$	−5.94435e51	−2.45896
$322$	6.92540e50	0.268781
$323$	−9.49473e50	−0.345805
$324$	−1.81684e51	−0.621076
$325$	−1.41924e51	−0.455455
$326$	−1.76466e51	−0.531740
$327$	4.88911e51	1.38357
$328$	−1.38174e51	−0.367293
$329$	1.28088e51	0.319885
$330$	−3.02313e51	−0.709450
$331$	−6.60580e50	−0.145697	−0.0728487	−	0.997343i	$-0.523209\pi$
$331$	−6.60580e50	−0.145697	−0.0728487	+	0.997343i	$0.523209\pi$
$332$	−5.44436e50	−0.112880
$333$	4.68454e51	0.913188
$334$	−3.27414e51	−0.600198
$335$	−3.52513e51	−0.607794
$336$	7.34264e50	0.119096
$337$	−3.44162e51	−0.525230	−0.262615	−	0.964901i	$-0.584585\pi$
$337$	−3.44162e51	−0.525230	−0.262615	+	0.964901i	$0.584585\pi$
$338$	3.33814e51	0.479416
$339$	−2.14899e51	−0.290496
$340$	8.01477e50	0.101994
$341$	6.03510e51	0.723135
$342$	−2.77781e51	−0.313450
$343$	5.08022e50	0.0539949
$344$	−2.81443e51	−0.281801
$345$	5.96900e51	0.563132
$346$	−1.05618e52	−0.939031
$347$	−7.87615e51	−0.660024	−0.330012	−	0.943977i	$-0.607053\pi$
$347$	−7.87615e51	−0.660024	−0.330012	+	0.943977i	$0.607053\pi$
$348$	3.42290e51	0.270408
$349$	2.15217e52	1.60308	0.801540	−	0.597941i	$-0.204014\pi$
$349$	2.15217e52	1.60308	0.801540	+	0.597941i	$0.204014\pi$
$350$	3.05384e51	0.214512
$351$	−4.44124e51	−0.294245
$352$	5.06803e51	0.316749
$353$	1.13342e52	0.668360	0.334180	−	0.942509i	$-0.391541\pi$
$353$	1.13342e52	0.668360	0.334180	+	0.942509i	$0.391541\pi$
$354$	8.90412e51	0.495478
$355$	1.08476e52	0.569708
$356$	4.82391e51	0.239152
$357$	−4.67325e51	−0.218736
$358$	−1.76080e52	−0.778232
$359$	−2.95132e51	−0.123191	−0.0615956	−	0.998101i	$-0.519619\pi$
$359$	−2.95132e51	−0.123191	−0.0615956	+	0.998101i	$0.519619\pi$
$360$	2.34483e51	0.0924507
$361$	−1.16194e52	−0.432800
$362$	−3.17191e52	−1.11634
$363$	8.37709e52	2.78617
$364$	3.41138e51	0.107239
$365$	−3.69510e51	−0.109805
$366$	−1.28993e52	−0.362413
$367$	3.32424e52	0.883157	0.441578	−	0.897223i	$-0.354419\pi$
$367$	3.32424e52	0.883157	0.441578	+	0.897223i	$0.354419\pi$
$368$	−1.00065e52	−0.251422
$369$	2.57284e52	0.611467
$370$	2.16774e52	0.487384
$371$	1.93047e52	0.410674
$372$	−1.26339e52	−0.254335
$373$	8.84932e52	1.68608	0.843041	−	0.537849i	$-0.180763\pi$
$373$	8.84932e52	1.68608	0.843041	+	0.537849i	$0.180763\pi$
$374$	−3.22556e52	−0.581752
$375$	5.91145e52	1.00938
$376$	−1.85075e52	−0.299225
$377$	1.59027e52	0.243486
$378$	9.55645e51	0.138584
$379$	−1.93310e52	−0.265553	−0.132777	−	0.991146i	$-0.542389\pi$
$379$	−1.93310e52	−0.265553	−0.132777	+	0.991146i	$0.542389\pi$
$380$	−1.28541e52	−0.167293
$381$	−1.14724e53	−1.41479
$382$	−8.51996e52	−0.995723
$383$	1.07301e53	1.18859	0.594293	−	0.804249i	$-0.297432\pi$
$383$	1.07301e53	1.18859	0.594293	+	0.804249i	$0.297432\pi$
$384$	−1.06094e52	−0.111404
$385$	3.02222e52	0.300872
$386$	−4.85232e52	−0.458047
$387$	5.24056e52	0.469140
$388$	9.37443e52	0.795966
$389$	−1.19912e53	−0.965818	−0.482909	−	0.875670i	$-0.660420\pi$
$389$	−1.19912e53	−0.965818	−0.482909	+	0.875670i	$0.660420\pi$
$390$	2.94026e52	0.224679
$391$	6.36869e52	0.461771
$392$	−7.34043e51	−0.0505076
$393$	−1.57950e53	−1.03151
$394$	−6.64146e52	−0.411710
$395$	3.54372e52	0.208554
$396$	−9.43683e52	−0.527321
$397$	2.39613e53	1.27146	0.635732	−	0.771909i	$-0.280698\pi$
$397$	2.39613e53	1.27146	0.635732	+	0.771909i	$0.280698\pi$
$398$	1.24382e53	0.626838
$399$	7.49497e52	0.358778
$400$	−4.41251e52	−0.200658
$401$	1.28235e53	0.554047	0.277024	−	0.960863i	$-0.410652\pi$
$401$	1.28235e53	0.554047	0.277024	+	0.960863i	$0.410652\pi$
$402$	−2.96990e53	−1.21929
$403$	−5.86967e52	−0.229013
$404$	2.35125e53	0.871930
$405$	1.56546e53	0.551842
$406$	−3.42187e52	−0.114678
$407$	−8.72411e53	−2.77994
$408$	6.75239e52	0.204609
$409$	−6.34815e53	−1.82945	−0.914723	−	0.404082i	$-0.867591\pi$
$409$	−6.34815e53	−1.82945	−0.914723	+	0.404082i	$0.867591\pi$
$410$	1.19056e53	0.326350
$411$	−6.78734e53	−1.76987
$412$	−7.06556e52	−0.175289
$413$	−8.90143e52	−0.210128
$414$	1.86325e53	0.418565
$415$	4.69108e52	0.100297
$416$	−4.92911e52	−0.100313
$417$	−3.71508e53	−0.719746
$418$	5.17317e53	0.954208
$419$	2.81463e53	0.494350	0.247175	−	0.968971i	$-0.420498\pi$
$419$	2.81463e53	0.494350	0.247175	+	0.968971i	$0.420498\pi$
$420$	−6.32671e52	−0.105820
$421$	−8.69714e53	−1.38546	−0.692729	−	0.721198i	$-0.743592\pi$
$421$	−8.69714e53	−1.38546	−0.692729	+	0.721198i	$0.743592\pi$
$422$	−7.80149e52	−0.118378
$423$	3.44615e53	0.498147
$424$	−2.78934e53	−0.384150
$425$	2.80835e53	0.368535
$426$	9.13903e53	1.14289
$427$	1.28954e53	0.153696
$428$	−8.58642e53	−0.975472
$429$	−1.18332e54	−1.28152
$430$	2.42503e53	0.250388
$431$	1.95195e54	1.92169	0.960846	−	0.277083i	$-0.0893678\pi$
$431$	1.95195e54	1.92169	0.960846	+	0.277083i	$0.0893678\pi$
$432$	−1.38081e53	−0.129634
$433$	−1.72839e53	−0.154753	−0.0773767	−	0.997002i	$-0.524654\pi$
$433$	−1.72839e53	−0.154753	−0.0773767	+	0.997002i	$0.524654\pi$
$434$	1.26301e53	0.107861
$435$	−2.94930e53	−0.240265
$436$	7.06216e53	0.548864
$437$	−1.02141e54	−0.757411
$438$	−3.11310e53	−0.220279
$439$	1.74242e54	1.17660	0.588302	−	0.808641i	$-0.299797\pi$
$439$	1.74242e54	1.17660	0.588302	+	0.808641i	$0.299797\pi$
$440$	−4.36682e53	−0.281440
$441$	1.36681e53	0.0840846
$442$	3.13715e53	0.184238
$443$	2.26513e54	1.27004	0.635018	−	0.772497i	$-0.280993\pi$
$443$	2.26513e54	1.27004	0.635018	+	0.772497i	$0.280993\pi$
$444$	1.82630e54	0.977737
$445$	−4.15647e53	−0.212493
$446$	−2.55161e53	−0.124581
$447$	2.03034e54	0.946814
$448$	1.06062e53	0.0472456
$449$	−2.96283e54	−1.26083	−0.630415	−	0.776259i	$-0.717115\pi$
$449$	−2.96283e54	−1.26083	−0.630415	+	0.776259i	$0.717115\pi$
$450$	8.21621e53	0.334053
$451$	−4.79145e54	−1.86144
$452$	−3.10414e53	−0.115240
$453$	2.36032e54	0.837449
$454$	1.23375e53	0.0418392
$455$	−2.93938e53	−0.0952843
$456$	−1.08295e54	−0.335606
$457$	−5.74123e54	−1.70107	−0.850536	−	0.525916i	$-0.823723\pi$
$457$	−5.74123e54	−1.70107	−0.850536	+	0.525916i	$0.823723\pi$
$458$	−1.13580e54	−0.321781
$459$	8.78823e53	0.238090
$460$	8.62202e53	0.223395
$461$	−6.22598e54	−1.54290	−0.771452	−	0.636287i	$-0.780469\pi$
$461$	−6.22598e54	−1.54290	−0.771452	+	0.636287i	$0.780469\pi$
$462$	2.54620e54	0.603576
$463$	5.31009e54	1.20418	0.602091	−	0.798428i	$-0.294335\pi$
$463$	5.31009e54	1.20418	0.602091	+	0.798428i	$0.294335\pi$
$464$	4.94427e53	0.107271
$465$	1.08858e54	0.225983
$466$	2.94847e54	0.585714
$467$	2.75884e54	0.524483	0.262241	−	0.965002i	$-0.415538\pi$
$467$	2.75884e54	0.524483	0.262241	+	0.965002i	$0.415538\pi$
$468$	9.17814e53	0.166999
$469$	2.96900e54	0.517091
$470$	1.59468e54	0.265869
$471$	9.55483e54	1.52509
$472$	1.28617e54	0.196557
$473$	−9.75959e54	−1.42816
$474$	2.98556e54	0.418379
$475$	−4.50404e54	−0.604482
$476$	−6.75035e53	−0.0867729
$477$	5.19383e54	0.639530
$478$	5.83451e53	0.0688229
$479$	8.63620e54	0.975989	0.487994	−	0.872847i	$-0.337729\pi$
$479$	8.63620e54	0.975989	0.487994	+	0.872847i	$0.337729\pi$
$480$	9.14149e53	0.0989855
$481$	8.48496e54	0.880392
$482$	9.74596e54	0.969082
$483$	−5.02732e54	−0.479094
$484$	1.21004e55	1.10528
$485$	−8.07738e54	−0.707237
$486$	8.82068e54	0.740386
$487$	−2.29291e55	−1.84520	−0.922601	−	0.385755i	$-0.873941\pi$
$487$	−2.29291e55	−1.84520	−0.922601	+	0.385755i	$0.873941\pi$
$488$	−1.86326e54	−0.143770
$489$	1.28101e55	0.947809
$490$	6.32480e53	0.0448774
$491$	4.38594e54	0.298464	0.149232	−	0.988802i	$-0.452320\pi$
$491$	4.38594e54	0.298464	0.149232	+	0.988802i	$0.452320\pi$
$492$	1.00304e55	0.654688
$493$	−3.14679e54	−0.197018
$494$	−5.03136e54	−0.302192
$495$	8.13114e54	0.468538
$496$	−1.82492e54	−0.100895
$497$	−9.13627e54	−0.484689
$498$	3.95220e54	0.201204
$499$	−1.33110e55	−0.650356	−0.325178	−	0.945653i	$-0.605424\pi$
$499$	−1.33110e55	−0.650356	−0.325178	+	0.945653i	$0.605424\pi$
$500$	8.53890e54	0.400421
$501$	2.37678e55	1.06983
$502$	−3.02620e55	−1.30759
$503$	−3.85944e54	−0.160096	−0.0800481	−	0.996791i	$-0.525507\pi$
$503$	−3.85944e54	−0.160096	−0.0800481	+	0.996791i	$0.525507\pi$
$504$	−1.97491e54	−0.0786540
$505$	−2.02593e55	−0.774733
$506$	−3.46996e55	−1.27420
$507$	−2.42324e55	−0.854543
$508$	−1.65716e55	−0.561251
$509$	−6.09223e55	−1.98181	−0.990905	−	0.134566i	$-0.957036\pi$
$509$	−6.09223e55	−1.98181	−0.990905	+	0.134566i	$0.957036\pi$
$510$	−5.81813e54	−0.181800
$511$	3.11216e54	0.0934186
$512$	−1.53250e54	−0.0441942
$513$	−1.40946e55	−0.390523
$514$	−4.23888e55	−1.12851
$515$	6.08797e54	0.155749
$516$	2.04307e55	0.502301
$517$	−6.41784e55	−1.51647
$518$	−1.82575e55	−0.414650
$519$	7.66712e55	1.67379
$520$	4.24712e54	0.0891303
$521$	2.22216e55	0.448335	0.224168	−	0.974551i	$-0.428034\pi$
$521$	2.22216e55	0.448335	0.224168	+	0.974551i	$0.428034\pi$
$522$	−9.20637e54	−0.178584
$523$	−3.12455e55	−0.582778	−0.291389	−	0.956605i	$-0.594117\pi$
$523$	−3.12455e55	−0.582778	−0.291389	+	0.956605i	$0.594117\pi$
$524$	−2.28154e55	−0.409201
$525$	−2.21686e55	−0.382360
$526$	4.41071e55	0.731645
$527$	1.16148e55	0.185307
$528$	−3.67902e55	−0.564594
$529$	7.72823e53	0.0114088
$530$	2.40340e55	0.341327
$531$	−2.39489e55	−0.327226
$532$	1.08262e55	0.142328
$533$	4.66011e55	0.589506
$534$	−3.50180e55	−0.426280
$535$	7.39839e55	0.866732
$536$	−4.28992e55	−0.483694
$537$	1.27821e56	1.38717
$538$	−5.57207e55	−0.582077
$539$	−2.54543e55	−0.255972
$540$	1.18976e55	0.115183
$541$	4.98038e55	0.464214	0.232107	−	0.972690i	$-0.425438\pi$
$541$	4.98038e55	0.464214	0.232107	+	0.972690i	$0.425438\pi$
$542$	5.54666e55	0.497790
$543$	2.30257e56	1.98983
$544$	9.75361e54	0.0811686
$545$	−6.08504e55	−0.487680
$546$	−2.47640e55	−0.191149
$547$	1.49701e56	1.11297	0.556486	−	0.830857i	$-0.312149\pi$
$547$	1.49701e56	1.11297	0.556486	+	0.830857i	$0.312149\pi$
$548$	−9.80410e55	−0.702112
$549$	3.46944e55	0.239346
$550$	−1.53012e56	−1.01693
$551$	5.04684e55	0.323155
$552$	7.26400e55	0.448151
$553$	−2.98466e55	−0.177431
$554$	1.28866e55	0.0738227
$555$	−1.57361e56	−0.868745
$556$	−5.36632e55	−0.285524
$557$	4.33820e55	0.222474	0.111237	−	0.993794i	$-0.464519\pi$
$557$	4.33820e55	0.222474	0.111237	+	0.993794i	$0.464519\pi$
$558$	3.39806e55	0.167969
$559$	9.49206e55	0.452291
$560$	−9.13873e54	−0.0419789
$561$	2.34152e56	1.03695
$562$	4.52464e55	0.193192
$563$	−2.41126e56	−0.992711	−0.496355	−	0.868119i	$-0.665329\pi$
$563$	−2.41126e56	−0.992711	−0.496355	+	0.868119i	$0.665329\pi$
$564$	1.34351e56	0.533358
$565$	2.67465e55	0.102394
$566$	1.47018e56	0.542794
$567$	−1.31849e56	−0.469489
$568$	1.32010e56	0.453385
$569$	−5.22175e55	−0.172987	−0.0864937	−	0.996252i	$-0.527566\pi$
$569$	−5.22175e55	−0.172987	−0.0864937	+	0.996252i	$0.527566\pi$
$570$	9.33113e55	0.298195
$571$	−2.96562e56	−0.914273	−0.457136	−	0.889397i	$-0.651125\pi$
$571$	−2.96562e56	−0.914273	−0.457136	+	0.889397i	$0.651125\pi$
$572$	−1.70926e56	−0.508382
$573$	6.18485e56	1.77484
$574$	−1.00274e56	−0.277648
$575$	3.02113e56	0.807196
$576$	2.85355e55	0.0735741
$577$	3.98880e56	0.992518	0.496259	−	0.868175i	$-0.334707\pi$
$577$	3.98880e56	0.992518	0.496259	+	0.868175i	$0.334707\pi$
$578$	2.32369e56	0.558030
$579$	3.52243e56	0.816453
$580$	−4.26018e55	−0.0953133
$581$	−3.95101e55	−0.0853291
$582$	−6.80514e56	−1.41878
$583$	−9.67256e56	−1.94687
$584$	−4.49677e55	−0.0873851
$585$	−7.90825e55	−0.148383
$586$	−9.55163e55	−0.173052
$587$	4.02140e55	0.0703552	0.0351776	−	0.999381i	$-0.488800\pi$
$587$	4.02140e55	0.0703552	0.0351776	+	0.999381i	$0.488800\pi$
$588$	5.32860e55	0.0900281
$589$	−1.86278e56	−0.303947
$590$	−1.10822e56	−0.174646
$591$	4.82121e56	0.733859
$592$	2.63804e56	0.387870
$593$	1.34324e57	1.90780	0.953898	−	0.300130i	$-0.0970300\pi$
$593$	1.34324e57	1.90780	0.953898	+	0.300130i	$0.0970300\pi$
$594$	−4.78824e56	−0.656982
$595$	5.81637e55	0.0771000
$596$	2.93276e56	0.375602
$597$	−9.02923e56	−1.11732
$598$	3.37484e56	0.403533
$599$	−1.19938e57	−1.38582	−0.692912	−	0.721022i	$-0.743673\pi$
$599$	−1.19938e57	−1.38582	−0.692912	+	0.721022i	$0.743673\pi$
$600$	3.20315e56	0.357665
$601$	2.75563e56	0.297368	0.148684	−	0.988885i	$-0.452496\pi$
$601$	2.75563e56	0.297368	0.148684	+	0.988885i	$0.452496\pi$
$602$	−2.04245e56	−0.213022
$603$	7.98796e56	0.805250
$604$	3.40941e56	0.332217
$605$	−1.04262e57	−0.982068
$606$	−1.70684e57	−1.55419
$607$	1.95537e56	0.172132	0.0860658	−	0.996289i	$-0.472570\pi$
$607$	1.95537e56	0.172132	0.0860658	+	0.996289i	$0.472570\pi$
$608$	−1.56429e56	−0.133135
$609$	2.48402e56	0.204409
$610$	1.60546e56	0.127743
$611$	6.24191e56	0.480256
$612$	−1.81615e56	−0.135129
$613$	−1.11336e56	−0.0801118	−0.0400559	−	0.999197i	$-0.512754\pi$
$613$	−1.11336e56	−0.0801118	−0.0400559	+	0.999197i	$0.512754\pi$
$614$	−1.03408e57	−0.719622
$615$	−8.64260e56	−0.581707
$616$	3.67791e56	0.239440
$617$	−1.19973e57	−0.755507	−0.377754	−	0.925906i	$-0.623303\pi$
$617$	−1.19973e57	−0.755507	−0.377754	+	0.925906i	$0.623303\pi$
$618$	5.12907e56	0.312446
$619$	−1.93940e57	−1.14290	−0.571451	−	0.820636i	$-0.693619\pi$
$619$	−1.93940e57	−1.14290	−0.571451	+	0.820636i	$0.693619\pi$
$620$	1.57242e56	0.0896479
$621$	9.45409e56	0.521485
$622$	9.81018e56	0.523569
$623$	3.50074e56	0.180782
$624$	3.57817e56	0.178804
$625$	9.24055e56	0.446846
$626$	−2.59352e57	−1.21371
$627$	−3.75534e57	−1.70084
$628$	1.38016e57	0.605004
$629$	−1.67899e57	−0.712375
$630$	1.70166e56	0.0698861
$631$	−4.03284e57	−1.60328	−0.801640	−	0.597807i	$-0.796039\pi$
$631$	−4.03284e57	−1.60328	−0.801640	+	0.597807i	$0.796039\pi$
$632$	4.31255e56	0.165972
$633$	5.66330e56	0.211005
$634$	7.52750e56	0.271532
$635$	1.42787e57	0.498686
$636$	2.02485e57	0.684734
$637$	2.47566e56	0.0810648
$638$	1.71452e57	0.543649
$639$	−2.45807e57	−0.754791
$640$	1.32046e56	0.0392677
$641$	−3.36578e57	−0.969383	−0.484692	−	0.874685i	$-0.661068\pi$
$641$	−3.36578e57	−0.969383	−0.484692	+	0.874685i	$0.661068\pi$
$642$	6.23310e57	1.73875
$643$	5.64556e57	1.52539	0.762697	−	0.646756i	$-0.223875\pi$
$643$	5.64556e57	1.52539	0.762697	+	0.646756i	$0.223875\pi$
$644$	−7.26181e56	−0.190057
$645$	−1.76039e57	−0.446308
$646$	9.95595e56	0.244521
$647$	−5.52219e57	−1.31393	−0.656967	−	0.753920i	$-0.728161\pi$
$647$	−5.52219e57	−1.31393	−0.656967	+	0.753920i	$0.728161\pi$
$648$	1.90510e57	0.439167
$649$	4.46004e57	0.996146
$650$	1.48818e57	0.322055
$651$	−9.16848e56	−0.192259
$652$	1.85038e57	0.375997
$653$	1.57869e57	0.310869	0.155435	−	0.987846i	$-0.450322\pi$
$653$	1.57869e57	0.310869	0.155435	+	0.987846i	$0.450322\pi$
$654$	−5.12660e57	−0.978331
$655$	1.96586e57	0.363585
$656$	1.44886e57	0.259716
$657$	8.37312e56	0.145478
$658$	−1.34310e57	−0.226193
$659$	−1.98097e57	−0.323391	−0.161695	−	0.986841i	$-0.551696\pi$
$659$	−1.98097e57	−0.323391	−0.161695	+	0.986841i	$0.551696\pi$
$660$	3.16998e57	0.501657
$661$	−2.01251e57	−0.308750	−0.154375	−	0.988012i	$-0.549336\pi$
$661$	−2.01251e57	−0.308750	−0.154375	+	0.988012i	$0.549336\pi$
$662$	6.92669e56	0.103024
$663$	−2.27733e57	−0.328397
$664$	5.70883e56	0.0798181
$665$	−9.32831e56	−0.126462
$666$	−4.91210e57	−0.645722
$667$	−3.38522e57	−0.431526
$668$	3.43318e57	0.424404
$669$	1.85228e57	0.222061
$670$	3.69637e57	0.429775
$671$	−6.46121e57	−0.728622
$672$	−7.69932e56	−0.0842136
$673$	−1.38763e56	−0.0147219	−0.00736095	−	0.999973i	$-0.502343\pi$
$673$	−1.38763e56	−0.0147219	−0.00736095	+	0.999973i	$0.502343\pi$
$674$	3.60880e57	0.371394
$675$	4.16890e57	0.416192
$676$	−3.50030e57	−0.338998
$677$	1.32919e58	1.24888	0.624440	−	0.781073i	$-0.285327\pi$
$677$	1.32919e58	1.24888	0.624440	+	0.781073i	$0.285327\pi$
$678$	2.25337e57	0.205411
$679$	6.80308e57	0.601694
$680$	−8.40410e56	−0.0721204
$681$	−8.95613e56	−0.0745770
$682$	−6.32826e57	−0.511334
$683$	8.57042e57	0.672013	0.336007	−	0.941860i	$-0.390924\pi$
$683$	8.57042e57	0.672013	0.336007	+	0.941860i	$0.390924\pi$
$684$	2.91275e57	0.221642
$685$	8.44760e57	0.623845
$686$	−5.32700e56	−0.0381802
$687$	8.24507e57	0.573563
$688$	2.95115e57	0.199264
$689$	9.40741e57	0.616561
$690$	−6.25895e57	−0.398194
$691$	2.19872e58	1.35791	0.678955	−	0.734180i	$-0.262433\pi$
$691$	2.19872e58	1.35791	0.678955	+	0.734180i	$0.262433\pi$
$692$	1.10749e58	0.663995
$693$	−6.84837e57	−0.398617
$694$	8.25874e57	0.466707
$695$	4.62383e57	0.253696
$696$	−3.58917e57	−0.191207
$697$	−9.22132e57	−0.477003
$698$	−2.25671e58	−1.13355
$699$	−2.14037e58	−1.04402
$700$	−3.20218e57	−0.151683
$701$	−2.62291e57	−0.120660	−0.0603302	−	0.998178i	$-0.519215\pi$
$701$	−2.62291e57	−0.120660	−0.0603302	+	0.998178i	$0.519215\pi$
$702$	4.65698e57	0.208062
$703$	2.69276e58	1.16846
$704$	−5.31422e57	−0.223975
$705$	−1.15762e58	−0.473903
$706$	−1.18848e58	−0.472602
$707$	1.70632e58	0.659117
$708$	−9.33665e57	−0.350356
$709$	−1.50669e58	−0.549259	−0.274629	−	0.961550i	$-0.588555\pi$
$709$	−1.50669e58	−0.549259	−0.274629	+	0.961550i	$0.588555\pi$
$710$	−1.13745e58	−0.402844
$711$	−8.03009e57	−0.276308
$712$	−5.05823e57	−0.169106
$713$	1.24948e58	0.405876
$714$	4.90025e57	0.154670
$715$	1.47277e58	0.451711
$716$	1.84634e58	0.550293
$717$	−4.23542e57	−0.122674
$718$	3.09468e57	0.0871094
$719$	2.48651e57	0.0680218	0.0340109	−	0.999421i	$-0.489172\pi$
$719$	2.48651e57	0.0680218	0.0340109	+	0.999421i	$0.489172\pi$
$720$	−2.45873e57	−0.0653725
$721$	−5.12753e57	−0.132506
$722$	1.21839e58	0.306036
$723$	−7.07484e58	−1.72736
$724$	3.32599e58	0.789370
$725$	−1.49275e58	−0.344397
$726$	−8.78401e58	−1.97012
$727$	−5.23971e57	−0.114249	−0.0571244	−	0.998367i	$-0.518193\pi$
$727$	−5.23971e57	−0.114249	−0.0571244	+	0.998367i	$0.518193\pi$
$728$	−3.57709e57	−0.0758291
$729$	−3.76325e57	−0.0775620
$730$	3.87460e57	0.0776440
$731$	−1.87827e58	−0.365975
$732$	1.35259e58	0.256264
$733$	−5.87774e58	−1.08288	−0.541438	−	0.840741i	$-0.682120\pi$
$733$	−5.87774e58	−1.08288	−0.541438	+	0.840741i	$0.682120\pi$
$734$	−3.48572e58	−0.624486
$735$	−4.59133e57	−0.0799924
$736$	1.04926e58	0.177782
$737$	−1.48761e59	−2.45135
$738$	−2.69782e58	−0.432372
$739$	5.31386e58	0.828322	0.414161	−	0.910204i	$-0.364075\pi$
$739$	5.31386e58	0.828322	0.414161	+	0.910204i	$0.364075\pi$
$740$	−2.27304e58	−0.344632
$741$	3.65240e58	0.538647
$742$	−2.02424e58	−0.290390
$743$	3.34215e58	0.466397	0.233199	−	0.972429i	$-0.425081\pi$
$743$	3.34215e58	0.466397	0.233199	+	0.972429i	$0.425081\pi$
$744$	1.32476e58	0.179842
$745$	−2.52698e58	−0.333733
$746$	−9.27918e58	−1.19224
$747$	−1.06300e58	−0.132880
$748$	3.38225e58	0.411361
$749$	−6.23122e58	−0.737387
$750$	−6.19861e58	−0.713737
$751$	4.32824e58	0.484946	0.242473	−	0.970158i	$-0.422041\pi$
$751$	4.32824e58	0.484946	0.242473	+	0.970158i	$0.422041\pi$
$752$	1.94065e58	0.211584
$753$	2.19680e59	2.33073
$754$	−1.66752e58	−0.172170
$755$	−2.93768e58	−0.295184
$756$	−1.00207e58	−0.0979940
$757$	−4.13773e58	−0.393819	−0.196909	−	0.980422i	$-0.563090\pi$
$757$	−4.13773e58	−0.393819	−0.196909	+	0.980422i	$0.563090\pi$
$758$	2.02701e58	0.187774
$759$	2.51893e59	2.27122
$760$	1.34785e58	0.118294
$761$	2.71850e57	0.0232244	0.0116122	−	0.999933i	$-0.496304\pi$
$761$	2.71850e57	0.0232244	0.0116122	+	0.999933i	$0.496304\pi$
$762$	1.20297e59	1.00041
$763$	5.12506e58	0.414902
$764$	8.93382e58	0.704082
$765$	1.56487e58	0.120065
$766$	−1.12514e59	−0.840457
$767$	−4.33778e58	−0.315474
$768$	1.11248e58	0.0787746
$769$	−2.45267e59	−1.69102	−0.845509	−	0.533961i	$-0.820703\pi$
$769$	−2.45267e59	−1.69102	−0.845509	+	0.533961i	$0.820703\pi$
$770$	−3.16903e58	−0.212748
$771$	3.07711e59	2.01154
$772$	5.08803e58	0.323888
$773$	3.01359e59	1.86812	0.934060	−	0.357115i	$-0.116240\pi$
$773$	3.01359e59	1.86812	0.934060	+	0.357115i	$0.116240\pi$
$774$	−5.49512e58	−0.331732
$775$	5.50973e58	0.323926
$776$	−9.82980e58	−0.562833
$777$	1.32536e59	0.739100
$778$	1.25737e59	0.682937
$779$	1.47892e59	0.782395
$780$	−3.08309e58	−0.158872
$781$	4.57771e59	2.29775
$782$	−6.67805e58	−0.326521
$783$	−4.67130e58	−0.222496
$784$	7.69700e57	0.0357143
$785$	−1.18920e59	−0.537562
$786$	1.65623e59	0.729386
$787$	−2.02677e59	−0.869604	−0.434802	−	0.900526i	$-0.643182\pi$
$787$	−2.02677e59	−0.869604	−0.434802	+	0.900526i	$0.643182\pi$
$788$	6.96408e58	0.291123
$789$	−3.20184e59	−1.30413
$790$	−3.71586e58	−0.147470
$791$	−2.25269e58	−0.0871133
$792$	9.89523e58	0.372872
$793$	6.28409e58	0.230750
$794$	−2.51252e59	−0.899062
$795$	−1.74469e59	−0.608405
$796$	−1.30424e59	−0.443242
$797$	−5.14384e59	−1.70370	−0.851848	−	0.523790i	$-0.824518\pi$
$797$	−5.14384e59	−1.70370	−0.851848	+	0.523790i	$0.824518\pi$
$798$	−7.85904e58	−0.253694
$799$	−1.23514e59	−0.388602
$800$	4.62685e58	0.141886
$801$	9.41858e58	0.281526
$802$	−1.34464e59	−0.391770
$803$	−1.55934e59	−0.442866
$804$	3.11416e59	0.862169
$805$	6.25706e58	0.168871
$806$	6.15479e58	0.161937
$807$	4.04491e59	1.03753
$808$	−2.46547e59	−0.616547
$809$	1.96341e59	0.478703	0.239352	−	0.970933i	$-0.423065\pi$
$809$	1.96341e59	0.478703	0.239352	+	0.970933i	$0.423065\pi$
$810$	−1.64151e59	−0.390211
$811$	−5.57625e59	−1.29245	−0.646226	−	0.763146i	$-0.723654\pi$
$811$	−5.57625e59	−1.29245	−0.646226	+	0.763146i	$0.723654\pi$
$812$	3.58809e58	0.0810894
$813$	−4.02646e59	−0.887293
$814$	9.14789e59	1.96572
$815$	−1.59436e59	−0.334083
$816$	−7.08039e58	−0.144680
$817$	3.01237e59	0.600283
$818$	6.65652e59	1.29361
$819$	6.66064e58	0.126240
$820$	−1.24840e59	−0.230764
$821$	−9.79282e59	−1.76552	−0.882761	−	0.469822i	$-0.844318\pi$
$821$	−9.79282e59	−1.76552	−0.882761	+	0.469822i	$0.844318\pi$
$822$	7.11704e59	1.25149
$823$	2.47404e59	0.424337	0.212168	−	0.977233i	$-0.431947\pi$
$823$	2.47404e59	0.424337	0.212168	+	0.977233i	$0.431947\pi$
$824$	7.40878e58	0.123948
$825$	1.11075e60	1.81264
$826$	9.33383e58	0.148583
$827$	−1.16997e60	−1.81682	−0.908408	−	0.418084i	$-0.862702\pi$
$827$	−1.16997e60	−1.81682	−0.908408	+	0.418084i	$0.862702\pi$
$828$	−1.95375e59	−0.295970
$829$	4.96485e59	0.733733	0.366867	−	0.930274i	$-0.380431\pi$
$829$	4.96485e59	0.733733	0.366867	+	0.930274i	$0.380431\pi$
$830$	−4.91895e58	−0.0709205
$831$	−9.35474e58	−0.131586
$832$	5.16855e58	0.0709317
$833$	−4.89877e58	−0.0655941
$834$	3.89555e59	0.508937
$835$	−2.95817e59	−0.377094
$836$	−5.42446e59	−0.674727
$837$	1.72417e59	0.209271
$838$	−2.95136e59	−0.349558
$839$	−9.66153e59	−1.11667	−0.558336	−	0.829615i	$-0.688560\pi$
$839$	−9.66153e59	−1.11667	−0.558336	+	0.829615i	$0.688560\pi$
$840$	6.63404e58	0.0748260
$841$	−7.41221e59	−0.815886
$842$	9.11961e59	0.979667
$843$	−3.28455e59	−0.344358
$844$	8.18045e58	0.0837061
$845$	3.01599e59	0.301209
$846$	−3.61356e59	−0.352243
$847$	8.78136e59	0.835511
$848$	2.92483e59	0.271635
$849$	−1.06724e60	−0.967511
$850$	−2.94477e59	−0.260593
$851$	−1.80620e60	−1.56030
$852$	−9.58297e59	−0.808143
$853$	2.01671e60	1.66031	0.830153	−	0.557535i	$-0.188253\pi$
$853$	2.01671e60	1.66031	0.830153	+	0.557535i	$0.188253\pi$
$854$	−1.35218e59	−0.108680
$855$	−2.50974e59	−0.196935
$856$	9.00351e59	0.689763
$857$	−2.04824e60	−1.53205	−0.766027	−	0.642808i	$-0.777769\pi$
$857$	−2.04824e60	−1.53205	−0.766027	+	0.642808i	$0.777769\pi$
$858$	1.24080e60	0.906174
$859$	−3.52658e59	−0.251474	−0.125737	−	0.992064i	$-0.540130\pi$
$859$	−3.52658e59	−0.251474	−0.125737	+	0.992064i	$0.540130\pi$
$860$	−2.54283e59	−0.177051
$861$	7.27914e59	0.494897
$862$	−2.04676e60	−1.35884
$863$	−2.94062e60	−1.90642	−0.953208	−	0.302314i	$-0.902241\pi$
$863$	−2.94062e60	−1.90642	−0.953208	+	0.302314i	$0.902241\pi$
$864$	1.44789e59	0.0916650
$865$	−9.54257e59	−0.589977
$866$	1.81235e59	0.109427
$867$	−1.68683e60	−0.994669
$868$	−1.32436e59	−0.0762695
$869$	1.49546e60	0.841141
$870$	3.09257e59	0.169893
$871$	1.44683e60	0.776330
$872$	−7.40521e59	−0.388105
$873$	1.83034e60	0.936999
$874$	1.07103e60	0.535570
$875$	6.19674e59	0.302690
$876$	3.26432e59	0.155761
$877$	1.00651e58	0.00469167	0.00234584	−	0.999997i	$-0.499253\pi$
$877$	1.00651e58	0.00469167	0.00234584	+	0.999997i	$0.499253\pi$
$878$	−1.82706e60	−0.831985
$879$	6.93377e59	0.308459
$880$	4.57894e59	0.199008
$881$	2.23485e60	0.948947	0.474474	−	0.880270i	$-0.342638\pi$
$881$	2.23485e60	0.948947	0.474474	+	0.880270i	$0.342638\pi$
$882$	−1.43320e59	−0.0594568
$883$	−1.44046e60	−0.583855	−0.291928	−	0.956440i	$-0.594297\pi$
$883$	−1.44046e60	−0.583855	−0.291928	+	0.956440i	$0.594297\pi$
$884$	−3.28954e59	−0.130276
$885$	8.04482e59	0.311300
$886$	−2.37516e60	−0.898051
$887$	4.32167e60	1.59668	0.798340	−	0.602208i	$-0.205712\pi$
$887$	4.32167e60	1.59668	0.798340	+	0.602208i	$0.205712\pi$
$888$	−1.91502e60	−0.691364
$889$	−1.20261e60	−0.424266
$890$	4.35837e59	0.150255
$891$	6.60629e60	2.22569
$892$	2.67556e59	0.0880917
$893$	1.98091e60	0.637398
$894$	−2.12897e60	−0.669499
$895$	−1.59088e60	−0.488950
$896$	−1.11214e59	−0.0334077
$897$	−2.44988e60	−0.719283
$898$	3.10675e60	0.891541
$899$	−6.17372e59	−0.173170
$900$	−8.61532e59	−0.236211
$901$	−1.86152e60	−0.498895
$902$	5.02420e60	1.31623
$903$	1.48267e60	0.379704
$904$	3.25493e59	0.0814870
$905$	−2.86580e60	−0.701376
$906$	−2.47498e60	−0.592166
$907$	5.37020e60	1.25615	0.628074	−	0.778154i	$-0.283843\pi$
$907$	5.37020e60	1.25615	0.628074	+	0.778154i	$0.283843\pi$
$908$	−1.29368e59	−0.0295848
$909$	4.59077e60	1.02642
$910$	3.08216e59	0.0673762
$911$	4.41100e60	0.942780	0.471390	−	0.881925i	$-0.343752\pi$
$911$	4.41100e60	0.942780	0.471390	+	0.881925i	$0.343752\pi$
$912$	1.13556e60	0.237309
$913$	1.97964e60	0.404516
$914$	6.02012e60	1.20284
$915$	−1.16544e60	−0.227698
$916$	1.19097e60	0.227533
$917$	−1.65573e60	−0.309327
$918$	−9.21513e59	−0.168355
$919$	−7.37898e60	−1.31834	−0.659171	−	0.751993i	$-0.729093\pi$
$919$	−7.37898e60	−1.31834	−0.659171	+	0.751993i	$0.729093\pi$
$920$	−9.04085e59	−0.157964
$921$	7.50668e60	1.28270
$922$	6.52842e60	1.09100
$923$	−4.45223e60	−0.727683
$924$	−2.66989e60	−0.426793
$925$	−7.96465e60	−1.24526
$926$	−5.56804e60	−0.851485
$927$	−1.37954e60	−0.206347
$928$	−5.18444e59	−0.0758522
$929$	5.17816e60	0.741060	0.370530	−	0.928820i	$-0.379176\pi$
$929$	5.17816e60	0.741060	0.370530	+	0.928820i	$0.379176\pi$
$930$	−1.14146e60	−0.159794
$931$	7.85667e59	0.107590
$932$	−3.09170e60	−0.414163
$933$	−7.12146e60	−0.933244
$934$	−2.89286e60	−0.370865
$935$	−2.91428e60	−0.365505
$936$	−9.62398e59	−0.118086
$937$	1.30339e61	1.56463	0.782316	−	0.622882i	$-0.214038\pi$
$937$	1.30339e61	1.56463	0.782316	+	0.622882i	$0.214038\pi$
$938$	−3.11322e60	−0.365639
$939$	1.88270e61	2.16340
$940$	−1.67214e60	−0.187998
$941$	8.50936e59	0.0936073	0.0468036	−	0.998904i	$-0.485096\pi$
$941$	8.50936e59	0.0936073	0.0468036	+	0.998904i	$0.485096\pi$
$942$	−1.00190e61	−1.07840
$943$	−9.91999e60	−1.04477
$944$	−1.34865e60	−0.138987
$945$	8.63420e59	0.0870702
$946$	1.02337e61	1.00986
$947$	1.49866e61	1.44720	0.723602	−	0.690218i	$-0.242485\pi$
$947$	1.49866e61	1.44720	0.723602	+	0.690218i	$0.242485\pi$
$948$	−3.13059e60	−0.295839
$949$	1.51660e60	0.140253
$950$	4.72283e60	0.427434
$951$	−5.46441e60	−0.483997
$952$	7.07826e59	0.0613577
$953$	1.92071e61	1.62951	0.814754	−	0.579806i	$-0.196872\pi$
$953$	1.92071e61	1.62951	0.814754	+	0.579806i	$0.196872\pi$
$954$	−5.44612e60	−0.452216
$955$	−7.69773e60	−0.625596
$956$	−6.11793e59	−0.0486651
$957$	−1.24461e61	−0.969035
$958$	−9.05572e60	−0.690128
$959$	−7.11490e60	−0.530747
$960$	−9.58555e59	−0.0699933
$961$	−1.17117e61	−0.837123
$962$	−8.89713e60	−0.622531
$963$	−1.67648e61	−1.14831
$964$	−1.02194e61	−0.685244
$965$	−4.38405e60	−0.287783
$966$	5.27153e60	0.338771
$967$	1.11663e61	0.702534	0.351267	−	0.936275i	$-0.385751\pi$
$967$	1.11663e61	0.702534	0.351267	+	0.936275i	$0.385751\pi$
$968$	−1.26882e61	−0.781549
$969$	−7.22728e60	−0.435850
$970$	8.46974e60	0.500092
$971$	3.12771e61	1.80814	0.904071	−	0.427382i	$-0.140564\pi$
$971$	3.12771e61	1.80814	0.904071	+	0.427382i	$0.140564\pi$
$972$	−9.24915e60	−0.523532
$973$	−3.89437e60	−0.215836
$974$	2.40429e61	1.30476
$975$	−1.08031e61	−0.574053
$976$	1.95377e60	0.101660
$977$	−2.82155e61	−1.43764	−0.718819	−	0.695197i	$-0.755317\pi$
$977$	−2.82155e61	−1.43764	−0.718819	+	0.695197i	$0.755317\pi$
$978$	−1.34324e61	−0.670202
$979$	−1.75404e61	−0.857026
$980$	−6.63204e59	−0.0317331
$981$	1.37887e61	0.646114
$982$	−4.59899e60	−0.211046
$983$	−1.07369e61	−0.482539	−0.241269	−	0.970458i	$-0.577564\pi$
$983$	−1.07369e61	−0.482539	−0.241269	+	0.970458i	$0.577564\pi$
$984$	−1.05177e61	−0.462934
$985$	−6.00052e60	−0.258670
$986$	3.29965e60	0.139313
$987$	9.74993e60	0.403181
$988$	5.27577e60	0.213682
$989$	−2.02058e61	−0.801588
$990$	−8.52612e60	−0.331307
$991$	1.90258e61	0.724156	0.362078	−	0.932148i	$-0.382067\pi$
$991$	1.90258e61	0.724156	0.362078	+	0.932148i	$0.382067\pi$
$992$	1.91357e60	0.0713435
$993$	−5.02826e60	−0.183636
$994$	9.58008e60	0.342727
$995$	1.12379e61	0.393832
$996$	−4.14418e60	−0.142273
$997$	−2.21774e61	−0.745865	−0.372932	−	0.927859i	$-0.621648\pi$
$997$	−2.21774e61	−0.745865	−0.372932	+	0.927859i	$0.621648\pi$
$998$	1.39576e61	0.459871
$999$	−2.49239e61	−0.804497

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	14.42.a.d.1.5	✓	6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
14.42.a.d.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:	\( k \)	\(=\)	\( 42 \)
Character orbit:	\([\chi]\)	\(=\)	14.a (trivial)

\(f(q)\)	\(=\)	\(q-1.04858e6 q^{2} +7.61188e9 q^{3} +1.09951e12 q^{4} -9.47383e13 q^{5} -7.98164e15 q^{6} +7.97923e16 q^{7} -1.15292e18 q^{8} +2.14677e19 q^{9} +9.93403e19 q^{10} -3.99797e21 q^{11} +8.36935e21 q^{12} +3.88838e22 q^{13} -8.36683e22 q^{14} -7.21136e23 q^{15} +1.20893e24 q^{16} -7.69424e24 q^{17} -2.25105e25 q^{18} +1.23400e26 q^{19} -1.04166e26 q^{20} +6.07369e26 q^{21} +4.19218e27 q^{22} -8.27721e27 q^{23} -8.77590e27 q^{24} -3.64994e28 q^{25} -4.07726e28 q^{26} -1.14218e29 q^{27} +8.77325e28 q^{28} +4.08980e29 q^{29} +7.56166e29 q^{30} -1.50954e30 q^{31} -1.26765e30 q^{32} -3.04321e31 q^{33} +8.06800e30 q^{34} -7.55938e30 q^{35} +2.36040e31 q^{36} +2.18213e32 q^{37} -1.29395e32 q^{38} +2.95979e32 q^{39} +1.09226e32 q^{40} +1.19847e33 q^{41} -6.36873e32 q^{42} +2.44113e33 q^{43} -4.39582e33 q^{44} -2.03382e33 q^{45} +8.67928e33 q^{46} +1.60527e34 q^{47} +9.20220e33 q^{48} +6.36681e33 q^{49} +3.82724e34 q^{50} -5.85677e34 q^{51} +4.27532e34 q^{52} +2.41936e35 q^{53} +1.19767e35 q^{54} +3.78761e35 q^{55} -9.19942e34 q^{56} +9.39310e35 q^{57} -4.28847e35 q^{58} -1.11558e36 q^{59} -7.92898e35 q^{60} +1.61612e36 q^{61} +1.58287e36 q^{62} +1.71296e36 q^{63} +1.32923e36 q^{64} -3.68379e36 q^{65} +3.19104e37 q^{66} +3.72091e37 q^{67} -8.45991e36 q^{68} -6.30051e37 q^{69} +7.92658e36 q^{70} -1.14501e38 q^{71} -2.47506e37 q^{72} +3.90033e37 q^{73} -2.28813e38 q^{74} -2.77829e38 q^{75} +1.35680e38 q^{76} -3.19007e38 q^{77} -3.10356e38 q^{78} -3.74054e38 q^{79} -1.14532e38 q^{80} -1.65241e39 q^{81} -1.25669e39 q^{82} -4.95162e38 q^{83} +6.67810e38 q^{84} +7.28939e38 q^{85} -2.55971e39 q^{86} +3.11311e39 q^{87} +4.60935e39 q^{88} +4.38732e39 q^{89} +2.13261e39 q^{90} +3.10263e39 q^{91} -9.10089e39 q^{92} -1.14904e40 q^{93} -1.68325e40 q^{94} -1.16907e40 q^{95} -9.64921e39 q^{96} +8.52599e40 q^{97} -6.67608e39 q^{98} -8.58274e40 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 6291456 q^{2} - 2340113048 q^{3} + 6597069766656 q^{4} - 178161928499100 q^{5} + 24\!\cdots\!48 q^{6} + 47\!\cdots\!06 q^{7} - 69\!\cdots\!56 q^{8} + 51\!\cdots\!58 q^{9} + 18\!\cdots\!00 q^{10} + 14\!\cdots\!48 q^{11}+ \cdots - 48\!\cdots\!84 q^{99}+O(q^{100}) \) 6 * q - 6291456 * q^2 - 2340113048 * q^3 + 6597069766656 * q^4 - 178161928499100 * q^5 + 2453786379419648 * q^6 + 478753597785672006 * q^7 - 6917529027641081856 * q^8 + 51308314120992776158 * q^9 + 186816322337872281600 * q^10 + 1436248344978714407448 * q^11 - 2572981506586336821248 * q^12 + 34301876705702636440116 * q^13 - 502009532551708809363456 * q^14 + 656926621499476771816800 * q^15 + 7253554917687775048237056 * q^16 + 30276052253972503691396460 * q^17 - 53800666787734121252651008 * q^18 + 61818651164394150562143048 * q^19 - 195891112011756765551001600 * q^20 - 186722923492532494781489048 * q^21 - 1506015544584400438504194048 * q^22 + 10773306728112038743730630400 * q^23 + 2697966656250274718676942848 * q^24 - 2052708525720541417377953910 * q^25 - 35968124668558847707831074816 * q^26 + 244827393668175182742514248976 * q^27 + 526395147604940616487095238656 * q^28 + 1858263976358013274666185585588 * q^29 - 688837489065435355484572876800 * q^30 - 3026665292350546396080823084800 * q^31 - 7605903601369376408980219232256 * q^32 - 4896034938196446312177112267680 * q^33 - 31746741768261472030709734440960 * q^34 - 14215944042896296003236077699100 * q^35 + 56414087977615093926619783364608 * q^36 + 36388638978207164300560818509508 * q^37 - 64821553963355760819849708699648 * q^38 + 1349472180986220352912856250575552 * q^39 + 205406718668839862194407053721600 * q^40 + 3928217707909089189820717743560988 * q^41 + 195793176224105753247994659995648 * q^42 + 4279178185760899188404399696028024 * q^43 + 1579171755678132274204973778075648 * q^44 + 9771204462083328418570928249843700 * q^45 - 11296630875736809137746089502310400 * q^46 - 5329487100372894471454831212332544 * q^47 - 2829023084544288063411394023784448 * q^48 + 38200834565454167914448610835344006 * q^49 + 2152420895065942437268505399132160 * q^50 + 137264354577108170962850174657040432 * q^51 + 37715312292458762294086677106262016 * q^52 + 89882484295477272450372378995983908 * q^53 - 256720129143000460419414621134258176 * q^54 - 688920073150979141025746602426354800 * q^55 - 551965318294998211873572376968953856 * q^56 - 4296631731665940403373896952488068976 * q^57 - 1948531007273580127496370216593522688 * q^58 - 2098674926749446087055800157350918120 * q^59 + 722298458934277943312591488863436800 * q^60 - 4154432586061843368860666149845842316 * q^61 + 3173688585591766537816845146967244800 * q^62 + 4094006663623781812762810246927472158 * q^63 + 7975367974709495237422842361682067456 * q^64 - 641510480348272181759116614056928600 * q^65 + 5133864731354276888237427673194823680 * q^66 - 908094220382585683627028817656747352 * q^67 + 33288871496396541296073490501164072960 * q^68 + 26819934334947518038863842406109202400 * q^69 + 14906497740724026477889273409411481600 * q^70 - 215878036680020205164533780979567075952 * q^71 - 59154458715215724729199265961327198208 * q^72 - 366319328063377168243687845513023714436 * q^73 - 38156253505212555513624860829425860608 * q^74 - 659900775570837083521758503011572720680 * q^75 + 67970325768679730257434728149442101248 * q^76 + 114601510412046088219176694376128583448 * q^77 - 1415024141649806992775951155803510013952 * q^78 - 708002425286449904990404275469758062304 * q^79 - 215384555434897427340362570763180441600 * q^80 - 3611254295706029330226546538084588140986 * q^81 - 4119034811288481106305448928672206553088 * q^82 - 7105924773159166013413745618032255980600 * q^83 - 205304025552367914317769248599596597248 * q^84 - 4868319246825467861790604801633358487000 * q^85 - 4487043545312420627380331815662281293824 * q^86 - 16737524180679527763204021080859713384112 * q^87 - 1655881602881953227556754584319450677248 * q^88 - 17070846531385954927672654485955438871364 * q^89 - 10245850490033488179831429660508107571200 * q^90 + 2737024480609278648170478684774439432116 * q^91 + 11845376017156600378421243545974629990400 * q^92 - 30355715547120221823292802943319787274208 * q^93 + 5588372265760608193300221093302809657344 * q^94 - 77620172449655779402892509820789510740800 * q^95 + 2966445709899111400379665899883801346048 * q^96 - 48291725996003567390264085027900911661204 * q^97 - 40056478305305669575060866555281676435456 * q^98 - 4885293233811587121115440246715559440584 * q^99

Introduction

L-functions

Modular forms

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