LMFDB - Embedded newform 14.44.a.c.1.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [14,44,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, 44, 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, 44); N := Newforms(S);

Level:	$ N $	$=$	$ 14 = 2 \cdot 7 $
Weight:	$ k $	$=$	$ 44 $
Character orbit:	$[\chi]$	$=$	14.a (trivial)

Newform invariants

comment:select newform

sage:traces = [6,-12582912] 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:	$163.954553484$
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 - 62\!\cdots\!00 $ x^6 - 2x^5 - 360496203267315887351x^4 - 952860912928483967880089117728x^3 + 32792619888459994993089725317686944598056x^2 + 99957779832029512128255479571165284652232622514080*x - 627476474282264898098501008230652404216507948253146502508400
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{33}\cdot 3^{11}\cdot 5^{3}\cdot 7^{6} $
Twist minimal:	yes
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Root			$-9.84461e9$ 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)

$f(q)$	$=$	\(q-2.09715e6 q^{2} +2.06706e10 q^{3} +4.39805e12 q^{4} -3.66872e14 q^{5} -4.33493e16 q^{6} -5.58546e17 q^{7} -9.22337e18 q^{8} +9.90153e19 q^{9} +7.69386e20 q^{10} +1.87548e22 q^{11} +9.09101e22 q^{12} -1.38064e24 q^{13} +1.17136e24 q^{14} -7.58344e24 q^{15} +1.93428e25 q^{16} +3.48300e26 q^{17} -2.07650e26 q^{18} +3.24082e27 q^{19} -1.61352e27 q^{20} -1.15455e28 q^{21} -3.93318e28 q^{22} -4.93948e28 q^{23} -1.90652e29 q^{24} -1.00227e30 q^{25} +2.89540e30 q^{26} -4.73856e30 q^{27} -2.45651e30 q^{28} -1.66224e31 q^{29} +1.59036e31 q^{30} -1.58604e32 q^{31} -4.05648e31 q^{32} +3.87673e32 q^{33} -7.30438e32 q^{34} +2.04915e32 q^{35} +4.35474e32 q^{36} +5.14914e33 q^{37} -6.79650e33 q^{38} -2.85385e34 q^{39} +3.38379e33 q^{40} +9.41346e34 q^{41} +2.42126e34 q^{42} +2.84250e34 q^{43} +8.24847e34 q^{44} -3.63259e34 q^{45} +1.03589e35 q^{46} -3.54783e35 q^{47} +3.99827e35 q^{48} +3.11973e35 q^{49} +2.10192e36 q^{50} +7.19956e36 q^{51} -6.07210e36 q^{52} -9.79738e34 q^{53} +9.93747e36 q^{54} -6.88062e36 q^{55} +5.15168e36 q^{56} +6.69897e37 q^{57} +3.48596e37 q^{58} +8.41451e37 q^{59} -3.33523e37 q^{60} -2.30721e38 q^{61} +3.32618e38 q^{62} -5.53046e37 q^{63} +8.50706e37 q^{64} +5.06516e38 q^{65} -8.13010e38 q^{66} +1.89971e39 q^{67} +1.53184e39 q^{68} -1.02102e39 q^{69} -4.29737e38 q^{70} +7.16921e39 q^{71} -9.13255e38 q^{72} +4.88777e39 q^{73} -1.07985e40 q^{74} -2.07176e40 q^{75} +1.42533e40 q^{76} -1.04754e40 q^{77} +5.98496e40 q^{78} -3.32784e40 q^{79} -7.09633e39 q^{80} -1.30451e41 q^{81} -1.97415e41 q^{82} -2.22244e41 q^{83} -5.07775e40 q^{84} -1.27781e41 q^{85} -5.96116e40 q^{86} -3.43593e41 q^{87} -1.72983e41 q^{88} +2.06614e41 q^{89} +7.61809e40 q^{90} +7.71149e41 q^{91} -2.17241e41 q^{92} -3.27844e42 q^{93} +7.44033e41 q^{94} -1.18897e42 q^{95} -8.38498e41 q^{96} +9.44705e42 q^{97} -6.54256e41 q^{98} +1.85702e42 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 12582912 q^{2} + 5888073464 q^{3} + 26388279066624 q^{4} + 11\!\cdots\!36 q^{5} - 12\!\cdots\!28 q^{6} - 33\!\cdots\!42 q^{7} - 55\!\cdots\!48 q^{8} + 92\!\cdots\!42 q^{9} - 23\!\cdots\!72 q^{10}+ \cdots - 32\!\cdots\!68 q^{99}+O(q^{100}) $ 6 * q - 12582912 * q^2 + 5888073464 * q^3 + 26388279066624 * q^4 + 1101555913947636 * q^5 - 12348185041174528 * q^6 - 3351275184499704042 * q^7 - 55340232221128654848 * q^8 + 920206056624214792942 * q^9 - 2310130188047112732672 * q^10 + 12364443308352069449256 * q^11 + 25896020955469243744256 * q^12 + 2673480309226397380134852 * q^13 + 7028133455723923331088384 * q^14 + 2596751366800458111241088 * q^15 + 116056878683004400771792896 * q^16 - 151523956294392739202437236 * q^17 - 1929811972061585301447901184 * q^18 + 2924396698591999816313232888 * q^19 + 4844694144123378561548550144 * q^20 - 3288759080735735247592290248 * q^21 - 25930117012997159149646118912 * q^22 - 138189734932452843094441090944 * q^23 - 54307892138804235456753958912 * q^24 - 543783005857111577200118310054 * q^25 - 5606694577454757718544565141504 * q^26 - 18238081241455439895784620403120 * q^27 - 14739064132938337261638666682368 * q^28 + 15447844631699667206917310415204 * q^29 - 5445782322388314328905470181376 * q^30 + 292785585487600534640913741920928 * q^31 - 243388915243820045087367015432192 * q^32 + 1256563034943030983841204584125696 * q^33 + 317768767990698321803869654351872 * q^34 - 615269499791933990825610314257452 * q^35 + 4047109036832897738102068863827968 * q^36 + 13132693042122798744929986162932564 * q^37 - 6132904385245609598780928977534976 * q^38 - 11796100190350809899368491556833120 * q^39 - 10160060013736631597108665031589888 * q^40 + 38981092234624183196209759743431868 * q^41 + 6897027683683108645958666678173696 * q^42 + 430991577964570312120449205257671880 * q^43 + 54379396754041018304998657568538624 * q^44 + 1263061387411010892502511029097132932 * q^45 + 289804878993063344801193322755391488 * q^46 - 784780034728411639235800111087185504 * q^47 + 113891904614677579996602478440218624 * q^48 + 1871840893707254227807981930931856294 * q^49 + 1140395618299253258348382514166366208 * q^50 - 4129766731791997339074126003018671024 * q^51 + 11758090746498400058961171875635396608 * q^52 - 5122212740431365179538885282523396620 * q^53 + 38248028551680758688324508247643914240 * q^54 + 19027704776584231317971437400261902992 * q^55 + 30910057824519899864920053110261415936 * q^56 - 64661904785167221488182671806938840784 * q^57 - 32396478265058220482321051371865899008 * q^58 - 225588768299241350012896084475002479768 * q^59 + 11420633288961298171492764601813041152 * q^60 - 289339159435618635377414484178126783836 * q^61 - 614015876176492436423261535696957997056 * q^62 - 513977287031843422506703993072885078594 * q^63 + 510423550381407695195061911147652317184 * q^64 + 2969906390398104707050197163877586869448 * q^65 - 2635203681856847313824549876008371617792 * q^66 + 343125170025663033658904147138490807384 * q^67 - 666409407329228966967628853363337068544 * q^68 - 4357220448246785465479348340754665191232 * q^69 + 1290313662027653952727910321765643976704 * q^70 + 635590344686651753765595281077318128528 * q^71 - 8487402810812185157256229921914550747136 * q^72 - 9478833007778008309161031802868345211524 * q^73 - 27541253478673911633527410341566352457728 * q^74 + 55503132748045488211550409222557144224168 * q^75 + 12861632697326600661302622767095429988352 * q^76 - 6906108671572285429766593587660322848792 * q^77 + 24738215106394581682080430805395691274240 * q^78 + 13951895275060241802227058786665972744064 * q^79 + 21307190177927804427139631088328796798976 * q^80 - 212409481320219330710102337846447562488314 * q^81 - 81749275542026575038297690065457628839936 * q^82 - 502154910435404229689941892541408044858856 * q^83 - 14464115400891398663089509741465322913792 * q^84 - 1000746630485747513730682155323702476554936 * q^85 - 903854849711554559204024291704537098485760 * q^86 - 2690709214665092528127861704935698013155472 * q^87 - 114041860661530629620364544717175912398848 * q^88 - 856940390846180859846255318363956366936580 * q^89 - 2648831714731776315233426009693110522609664 * q^90 - 1493261369426503449082730790844060674911964 * q^91 - 607764881590060779676512179203114769842176 * q^92 - 4154098765617263344275692549676994999091040 * q^93 + 1645803019390757926046636674566713254084608 * q^94 + 2655639101562245253717328091596898746886880 * q^95 - 238848635546480316245034880865861367758848 * q^96 - 213479928900084648762297914406854395008372 * q^97 - 3925534873919955618355964922417604290674688 * q^98 - 32120028965593175956683290170081167190685368 * 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 $

$2$	−2.09715e6	−0.707107
$2$	−2.09715e6	−0.707107
$3$	2.06706e10	1.14089	0.570447	−	0.821334i	$-0.306770\pi$
$3$	2.06706e10	1.14089	0.570447	+	0.821334i	$0.306770\pi$
$4$	4.39805e12	0.500000
$5$	−3.66872e14	−0.344080	−0.172040	−	0.985090i	$-0.555036\pi$
$5$	−3.66872e14	−0.344080	−0.172040	+	0.985090i	$0.555036\pi$
$6$	−4.33493e16	−0.806734
$7$	−5.58546e17	−0.377964
$7$	−5.58546e17	−0.377964
$8$	−9.22337e18	−0.353553
$9$	9.90153e19	0.301640
$10$	7.69386e20	0.243301
$11$	1.87548e22	0.764136	0.382068	−	0.924134i	$-0.375212\pi$
$11$	1.87548e22	0.764136	0.382068	+	0.924134i	$0.375212\pi$
$12$	9.09101e22	0.570447
$13$	−1.38064e24	−1.54988	−0.774938	−	0.632037i	$-0.782219\pi$
$13$	−1.38064e24	−1.54988	−0.774938	+	0.632037i	$0.782219\pi$
$14$	1.17136e24	0.267261
$15$	−7.58344e24	−0.392559
$16$	1.93428e25	0.250000
$17$	3.48300e26	1.22265	0.611324	−	0.791380i	$-0.290637\pi$
$17$	3.48300e26	1.22265	0.611324	+	0.791380i	$0.290637\pi$
$18$	−2.07650e26	−0.213291
$19$	3.24082e27	1.04101	0.520503	−	0.853860i	$-0.325745\pi$
$19$	3.24082e27	1.04101	0.520503	+	0.853860i	$0.325745\pi$
$20$	−1.61352e27	−0.172040
$21$	−1.15455e28	−0.431217
$22$	−3.93318e28	−0.540326
$23$	−4.93948e28	−0.260936	−0.130468	−	0.991453i	$-0.541648\pi$
$23$	−4.93948e28	−0.260936	−0.130468	+	0.991453i	$0.541648\pi$
$24$	−1.90652e29	−0.403367
$25$	−1.00227e30	−0.881609
$26$	2.89540e30	1.09593
$27$	−4.73856e30	−0.796755
$28$	−2.45651e30	−0.188982
$29$	−1.66224e31	−0.601362	−0.300681	−	0.953725i	$-0.597214\pi$
$29$	−1.66224e31	−0.601362	−0.300681	+	0.953725i	$0.597214\pi$
$30$	1.59036e31	0.277581
$31$	−1.58604e32	−1.36785	−0.683926	−	0.729552i	$-0.739729\pi$
$31$	−1.58604e32	−1.36785	−0.683926	+	0.729552i	$0.739729\pi$
$32$	−4.05648e31	−0.176777
$33$	3.87673e32	0.871798
$34$	−7.30438e32	−0.864543
$35$	2.04915e32	0.130050
$36$	4.35474e32	0.150820
$37$	5.14914e33	0.989459	0.494730	−	0.869047i	$-0.335267\pi$
$37$	5.14914e33	0.989459	0.494730	+	0.869047i	$0.335267\pi$
$38$	−6.79650e33	−0.736102
$39$	−2.85385e34	−1.76825
$40$	3.38379e33	0.121651
$41$	9.41346e34	1.99020	0.995100	−	0.0988783i	$-0.0315254\pi$
$41$	9.41346e34	1.99020	0.995100	+	0.0988783i	$0.0315254\pi$
$42$	2.42126e34	0.304917
$43$	2.84250e34	0.215839	0.107919	−	0.994160i	$-0.465581\pi$
$43$	2.84250e34	0.215839	0.107919	+	0.994160i	$0.465581\pi$
$44$	8.24847e34	0.382068
$45$	−3.63259e34	−0.103788
$46$	1.03589e35	0.184509
$47$	−3.54783e35	−0.397978	−0.198989	−	0.980002i	$-0.563766\pi$
$47$	−3.54783e35	−0.397978	−0.198989	+	0.980002i	$0.563766\pi$
$48$	3.99827e35	0.285224
$49$	3.11973e35	0.142857
$50$	2.10192e36	0.623392
$51$	7.19956e36	1.39491
$52$	−6.07210e36	−0.774938
$53$	−9.79738e34	−0.00830192	−0.00415096	−	0.999991i	$-0.501321\pi$
$53$	−9.79738e34	−0.00830192	−0.00415096	+	0.999991i	$0.501321\pi$
$54$	9.93747e36	0.563391
$55$	−6.88062e36	−0.262924
$56$	5.15168e36	0.133631
$57$	6.69897e37	1.18768
$58$	3.48596e37	0.425227
$59$	8.41451e37	0.710740	0.355370	−	0.934726i	$-0.384355\pi$
$59$	8.41451e37	0.710740	0.355370	+	0.934726i	$0.384355\pi$
$60$	−3.33523e37	−0.196279
$61$	−2.30721e38	−0.951689	−0.475844	−	0.879530i	$-0.657857\pi$
$61$	−2.30721e38	−0.951689	−0.475844	+	0.879530i	$0.657857\pi$
$62$	3.32618e38	0.967217
$63$	−5.53046e37	−0.114009
$64$	8.50706e37	0.125000
$65$	5.06516e38	0.533281
$66$	−8.13010e38	−0.616455
$67$	1.89971e39	1.04251	0.521255	−	0.853401i	$-0.325464\pi$
$67$	1.89971e39	1.04251	0.521255	+	0.853401i	$0.325464\pi$
$68$	1.53184e39	0.611324
$69$	−1.02102e39	−0.297700
$70$	−4.29737e38	−0.0919592
$71$	7.16921e39	1.13088	0.565440	−	0.824789i	$-0.308706\pi$
$71$	7.16921e39	1.13088	0.565440	+	0.824789i	$0.308706\pi$
$72$	−9.13255e38	−0.106646
$73$	4.88777e39	0.424296	0.212148	−	0.977238i	$-0.431954\pi$
$73$	4.88777e39	0.424296	0.212148	+	0.977238i	$0.431954\pi$
$74$	−1.07985e40	−0.699653
$75$	−2.07176e40	−1.00582
$76$	1.42533e40	0.520503
$77$	−1.04754e40	−0.288816
$78$	5.98496e40	1.25034
$79$	−3.32784e40	−0.528664	−0.264332	−	0.964432i	$-0.585152\pi$
$79$	−3.32784e40	−0.528664	−0.264332	+	0.964432i	$0.585152\pi$
$80$	−7.09633e39	−0.0860199
$81$	−1.30451e41	−1.21065
$82$	−1.97415e41	−1.40728
$83$	−2.22244e41	−1.22082	−0.610410	−	0.792086i	$-0.708995\pi$
$83$	−2.22244e41	−1.22082	−0.610410	+	0.792086i	$0.708995\pi$
$84$	−5.07775e40	−0.215609
$85$	−1.27781e41	−0.420688
$86$	−5.96116e40	−0.152621
$87$	−3.43593e41	−0.686090
$88$	−1.72983e41	−0.270163
$89$	2.06614e41	0.253089	0.126545	−	0.991961i	$-0.459611\pi$
$89$	2.06614e41	0.253089	0.126545	+	0.991961i	$0.459611\pi$
$90$	7.61809e40	0.0733892
$91$	7.71149e41	0.585798
$92$	−2.17241e41	−0.130468
$93$	−3.27844e42	−1.56057
$94$	7.44033e41	0.281413
$95$	−1.18897e42	−0.358189
$96$	−8.38498e41	−0.201684
$97$	9.44705e42	1.81846	0.909230	−	0.416293i	$-0.136671\pi$
$97$	9.44705e42	1.81846	0.909230	+	0.416293i	$0.136671\pi$
$98$	−6.54256e41	−0.101015
$99$	1.85702e42	0.230494
$100$	−4.40805e42	−0.440805
$101$	6.25547e42	0.505068	0.252534	−	0.967588i	$-0.418736\pi$
$101$	6.25547e42	0.505068	0.252534	+	0.967588i	$0.418736\pi$
$102$	−1.50986e43	−0.986352
$103$	−3.11542e43	−1.65012	−0.825061	−	0.565044i	$-0.808859\pi$
$103$	−3.11542e43	−1.65012	−0.825061	+	0.565044i	$0.808859\pi$
$104$	1.27341e43	0.547964
$105$	4.23570e42	0.148373
$106$	2.05466e41	0.00587034
$107$	8.09367e43	1.88971	0.944853	−	0.327493i	$-0.106204\pi$
$107$	8.09367e43	1.88971	0.944853	+	0.327493i	$0.106204\pi$
$108$	−2.08404e43	−0.398378
$109$	−9.40999e43	−1.47543	−0.737716	−	0.675111i	$-0.764096\pi$
$109$	−9.40999e43	−1.47543	−0.737716	+	0.675111i	$0.764096\pi$
$110$	1.44297e43	0.185915
$111$	1.06436e44	1.12887
$112$	−1.08038e43	−0.0944911
$113$	−6.16833e43	−0.445637	−0.222819	−	0.974860i	$-0.571526\pi$
$113$	−6.16833e43	−0.445637	−0.222819	+	0.974860i	$0.571526\pi$
$114$	−1.40487e44	−0.839814
$115$	1.81216e43	0.0897826
$116$	−7.31059e43	−0.300681
$117$	−1.36704e44	−0.467504
$118$	−1.76465e44	−0.502569
$119$	−1.94541e44	−0.462118
$120$	6.99449e43	0.138790
$121$	−2.50657e44	−0.416096
$122$	4.83856e44	0.672946
$123$	1.94582e45	2.27061
$124$	−6.97550e44	−0.683926
$125$	7.84790e44	0.647423
$126$	1.15982e44	0.0806166
$127$	2.58644e45	1.51678	0.758389	−	0.651802i	$-0.225987\pi$
$127$	2.58644e45	1.51678	0.758389	+	0.651802i	$0.225987\pi$
$128$	−1.78406e44	−0.0883883
$129$	5.87561e44	0.246249
$130$	−1.06224e45	−0.377087
$131$	5.13813e45	1.54693	0.773467	−	0.633836i	$-0.218521\pi$
$131$	5.13813e45	1.54693	0.773467	+	0.633836i	$0.218521\pi$
$132$	1.70500e45	0.435899
$133$	−1.81015e45	−0.393463
$134$	−3.98399e45	−0.737165
$135$	1.73844e45	0.274147
$136$	−3.21250e45	−0.432271
$137$	1.10601e46	1.27135	0.635677	−	0.771955i	$-0.280721\pi$
$137$	1.10601e46	1.27135	0.635677	+	0.771955i	$0.280721\pi$
$138$	2.14123e45	0.210506
$139$	−5.83939e45	−0.491529	−0.245765	−	0.969330i	$-0.579039\pi$
$139$	−5.83939e45	−0.491529	−0.245765	+	0.969330i	$0.579039\pi$
$140$	9.01224e44	0.0650249
$141$	−7.33356e45	−0.454050
$142$	−1.50349e46	−0.799653
$143$	−2.58936e46	−1.18432
$144$	1.91523e45	0.0754099
$145$	6.09827e45	0.206916
$146$	−1.02504e46	−0.300023
$147$	6.44867e45	0.162985
$148$	2.26462e46	0.494730
$149$	2.88506e46	0.545318	0.272659	−	0.962111i	$-0.412097\pi$
$149$	2.88506e46	0.545318	0.272659	+	0.962111i	$0.412097\pi$
$150$	4.34479e46	0.711224
$151$	−9.60073e46	−1.36239	−0.681193	−	0.732104i	$-0.738538\pi$
$151$	−9.60073e46	−1.36239	−0.681193	+	0.732104i	$0.738538\pi$
$152$	−2.98913e46	−0.368051
$153$	3.44870e46	0.368799
$154$	2.19686e46	0.204224
$155$	5.81875e46	0.470650
$156$	−1.25514e47	−0.884123
$157$	−4.10743e46	−0.252190	−0.126095	−	0.992018i	$-0.540244\pi$
$157$	−4.10743e46	−0.252190	−0.126095	+	0.992018i	$0.540244\pi$
$158$	6.97899e46	0.373822
$159$	−2.02517e45	−0.00947161
$160$	1.48821e46	0.0608253
$161$	2.75893e46	0.0986244
$162$	2.73576e47	0.856061
$163$	2.47830e47	0.679393	0.339696	−	0.940535i	$-0.389676\pi$
$163$	2.47830e47	0.679393	0.339696	+	0.940535i	$0.389676\pi$
$164$	4.14008e47	0.995100
$165$	−1.42226e47	−0.299968
$166$	4.66080e47	0.863250
$167$	3.25854e47	0.530420	0.265210	−	0.964191i	$-0.414559\pi$
$167$	3.25854e47	0.530420	0.265210	+	0.964191i	$0.414559\pi$
$168$	1.06488e47	0.152458
$169$	1.11262e48	1.40212
$170$	2.67977e47	0.297472
$171$	3.20891e47	0.314008
$172$	1.25015e47	0.107919
$173$	2.31190e47	0.176188	0.0880942	−	0.996112i	$-0.471922\pi$
$173$	2.31190e47	0.176188	0.0880942	+	0.996112i	$0.471922\pi$
$174$	7.20568e47	0.485139
$175$	5.59816e47	0.333217
$176$	3.62771e47	0.191034
$177$	1.73933e48	0.810879
$178$	−4.33300e47	−0.178961
$179$	1.62191e48	0.593864	0.296932	−	0.954899i	$-0.404036\pi$
$179$	1.62191e48	0.593864	0.296932	+	0.954899i	$0.404036\pi$
$180$	−1.59763e47	−0.0518940
$181$	5.77250e48	1.66446	0.832232	−	0.554428i	$-0.187063\pi$
$181$	5.77250e48	1.66446	0.832232	+	0.554428i	$0.187063\pi$
$182$	−1.61722e48	−0.414222
$183$	−4.76913e48	−1.08578
$184$	4.55587e47	0.0922546
$185$	−1.88907e48	−0.340453
$186$	6.87539e48	1.10349
$187$	6.53231e48	0.934270
$188$	−1.56035e48	−0.198989
$189$	2.64670e48	0.301145
$190$	2.49344e48	0.253278
$191$	4.86122e48	0.441090	0.220545	−	0.975377i	$-0.429216\pi$
$191$	4.86122e48	0.441090	0.220545	+	0.975377i	$0.429216\pi$
$192$	1.75846e48	0.142612
$193$	−1.17519e48	−0.0852363	−0.0426182	−	0.999091i	$-0.513570\pi$
$193$	−1.17519e48	−0.0852363	−0.0426182	+	0.999091i	$0.513570\pi$
$194$	−1.98119e49	−1.28585
$195$	1.04700e49	0.608417
$196$	1.37207e48	0.0714286
$197$	2.24013e49	1.04532	0.522660	−	0.852541i	$-0.324940\pi$
$197$	2.24013e49	1.04532	0.522660	+	0.852541i	$0.324940\pi$
$198$	−3.89445e48	−0.162984
$199$	3.80988e49	1.43077	0.715385	−	0.698730i	$-0.246251\pi$
$199$	3.80988e49	1.43077	0.715385	+	0.698730i	$0.246251\pi$
$200$	9.24434e48	0.311696
$201$	3.92681e49	1.18939
$202$	−1.31187e49	−0.357137
$203$	9.28435e48	0.227293
$204$	3.16640e49	0.697456
$205$	−3.45353e49	−0.684787
$206$	6.53351e49	1.16681
$207$	−4.89085e48	−0.0787085
$208$	−2.67054e49	−0.387469
$209$	6.07811e49	0.795470
$210$	−8.88291e48	−0.104916
$211$	−5.01520e49	−0.534829	−0.267415	−	0.963582i	$-0.586169\pi$
$211$	−5.01520e49	−0.534829	−0.267415	+	0.963582i	$0.586169\pi$
$212$	−4.30893e47	−0.00415096
$213$	1.48192e50	1.29021
$214$	−1.69737e50	−1.33622
$215$	−1.04283e49	−0.0742657
$216$	4.37055e49	0.281696
$217$	8.85878e49	0.516999
$218$	1.97342e50	1.04329
$219$	1.01033e50	0.484077
$220$	−3.02613e49	−0.131462
$221$	−4.80875e50	−1.89495
$222$	−2.23212e50	−0.798231
$223$	1.82003e50	0.590914	0.295457	−	0.955356i	$-0.404528\pi$
$223$	1.82003e50	0.590914	0.295457	+	0.955356i	$0.404528\pi$
$224$	2.26573e49	0.0668153
$225$	−9.92404e49	−0.265928
$226$	1.29359e50	0.315113
$227$	−4.60937e50	−1.02114	−0.510570	−	0.859836i	$-0.670566\pi$
$227$	−4.60937e50	−1.02114	−0.510570	+	0.859836i	$0.670566\pi$
$228$	2.94624e50	0.593838
$229$	4.00777e50	0.735259	0.367630	−	0.929972i	$-0.380169\pi$
$229$	4.00777e50	0.735259	0.367630	+	0.929972i	$0.380169\pi$
$230$	−3.80037e49	−0.0634859
$231$	−2.16533e50	−0.329509
$232$	1.53314e50	0.212613
$233$	−4.41260e50	−0.557882	−0.278941	−	0.960308i	$-0.589983\pi$
$233$	−4.41260e50	−0.557882	−0.278941	+	0.960308i	$0.589983\pi$
$234$	2.86689e50	0.330575
$235$	1.30160e50	0.136936
$236$	3.70074e50	0.355370
$237$	−6.87883e50	−0.603150
$238$	4.07983e50	0.326767
$239$	1.20215e49	0.00879844	0.00439922	−	0.999990i	$-0.498600\pi$
$239$	1.20215e49	0.00879844	0.00439922	+	0.999990i	$0.498600\pi$
$240$	−1.46685e50	−0.0981396
$241$	5.77573e49	0.0353379	0.0176689	−	0.999844i	$-0.494376\pi$
$241$	5.77573e49	0.0353379	0.0176689	+	0.999844i	$0.494376\pi$
$242$	5.25665e50	0.294224
$243$	−1.14103e51	−0.584472
$244$	−1.01472e51	−0.475844
$245$	−1.14454e50	−0.0491542
$246$	−4.08067e51	−1.60556
$247$	−4.47440e51	−1.61343
$248$	1.46287e51	0.483608
$249$	−4.59392e51	−1.39283
$250$	−1.64582e51	−0.457798
$251$	1.73429e51	0.442729	0.221364	−	0.975191i	$-0.428949\pi$
$251$	1.73429e51	0.442729	0.221364	+	0.975191i	$0.428949\pi$
$252$	−2.43232e50	−0.0570045
$253$	−9.26393e50	−0.199390
$254$	−5.42416e51	−1.07252
$255$	−2.64131e51	−0.479961
$256$	3.74144e50	0.0625000
$257$	−7.25467e51	−1.11444	−0.557218	−	0.830366i	$-0.688131\pi$
$257$	−7.25467e51	−1.11444	−0.557218	+	0.830366i	$0.688131\pi$
$258$	−1.23221e51	−0.174124
$259$	−2.87603e51	−0.373980
$260$	2.22768e51	0.266641
$261$	−1.64587e51	−0.181394
$262$	−1.07754e52	−1.09385
$263$	5.06186e51	0.473436	0.236718	−	0.971578i	$-0.423928\pi$
$263$	5.06186e51	0.473436	0.236718	+	0.971578i	$0.423928\pi$
$264$	−3.57565e51	−0.308227
$265$	3.59438e49	0.00285652
$266$	3.79616e51	0.278220
$267$	4.27082e51	0.288748
$268$	8.35503e51	0.521255
$269$	2.47334e52	1.42433	0.712164	−	0.702013i	$-0.247715\pi$
$269$	2.47334e52	1.42433	0.712164	+	0.702013i	$0.247715\pi$
$270$	−3.64578e51	−0.193851
$271$	2.98646e52	1.46662	0.733308	−	0.679896i	$-0.237975\pi$
$271$	2.98646e52	1.46662	0.733308	+	0.679896i	$0.237975\pi$
$272$	6.73710e51	0.305662
$273$	1.59401e52	0.668334
$274$	−2.31947e52	−0.898983
$275$	−1.87975e52	−0.673669
$276$	−4.49049e51	−0.148850
$277$	1.63760e52	0.502219	0.251110	−	0.967959i	$-0.419205\pi$
$277$	1.63760e52	0.502219	0.251110	+	0.967959i	$0.419205\pi$
$278$	1.22461e52	0.347564
$279$	−1.57043e52	−0.412598
$280$	−1.89000e51	−0.0459796
$281$	3.42545e52	0.771847	0.385924	−	0.922531i	$-0.373883\pi$
$281$	3.42545e52	0.771847	0.385924	+	0.922531i	$0.373883\pi$
$282$	1.53796e52	0.321062
$283$	2.24301e52	0.433934	0.216967	−	0.976179i	$-0.430384\pi$
$283$	2.24301e52	0.433934	0.216967	+	0.976179i	$0.430384\pi$
$284$	3.15305e52	0.565440
$285$	−2.45766e52	−0.408656
$286$	5.43028e52	0.837438
$287$	−5.25785e52	−0.752225
$288$	−4.01654e51	−0.0533228
$289$	4.01600e52	0.494869
$290$	−1.27890e52	−0.146312
$291$	1.95276e53	2.07467
$292$	2.14966e52	0.212148
$293$	−1.67562e53	−1.53646	−0.768231	−	0.640172i	$-0.778863\pi$
$293$	−1.67562e53	−1.53646	−0.768231	+	0.640172i	$0.778863\pi$
$294$	−1.35238e52	−0.115248
$295$	−3.08705e52	−0.244551
$296$	−4.74925e52	−0.349827
$297$	−8.88709e52	−0.608830
$298$	−6.05041e52	−0.385598
$299$	6.81963e52	0.404418
$300$	−9.11168e52	−0.502911
$301$	−1.58767e52	−0.0815793
$302$	2.01342e53	0.963352
$303$	1.29304e53	0.576230
$304$	6.26866e52	0.260251
$305$	8.46448e52	0.327457
$306$	−7.23245e52	−0.260780
$307$	4.97448e53	1.67214	0.836071	−	0.548622i	$-0.184847\pi$
$307$	4.97448e53	1.67214	0.836071	+	0.548622i	$0.184847\pi$
$308$	−4.60715e52	−0.144408
$309$	−6.43975e53	−1.88261
$310$	−1.22028e53	−0.332800
$311$	3.08611e53	0.785350	0.392675	−	0.919677i	$-0.371550\pi$
$311$	3.08611e53	0.785350	0.392675	+	0.919677i	$0.371550\pi$
$312$	2.63221e53	0.625169
$313$	6.55098e53	1.45246	0.726228	−	0.687454i	$-0.241272\pi$
$313$	6.55098e53	1.45246	0.726228	+	0.687454i	$0.241272\pi$
$314$	8.61391e52	0.178325
$315$	2.02897e52	0.0392282
$316$	−1.46360e53	−0.264332
$317$	−1.96912e53	−0.332275	−0.166137	−	0.986103i	$-0.553130\pi$
$317$	−1.96912e53	−0.332275	−0.166137	+	0.986103i	$0.553130\pi$
$318$	4.24710e51	0.00669744
$319$	−3.11750e53	−0.459522
$320$	−3.12100e52	−0.0430100
$321$	1.67301e54	2.15596
$322$	−5.78589e52	−0.0697379
$323$	1.12878e54	1.27278
$324$	−5.73730e53	−0.605327
$325$	1.38378e54	1.36639
$326$	−5.19738e53	−0.480403
$327$	−1.94510e54	−1.68331
$328$	−8.68239e53	−0.703642
$329$	1.98162e53	0.150421
$330$	2.98270e53	0.212109
$331$	3.06072e53	0.203949	0.101975	−	0.994787i	$-0.467484\pi$
$331$	3.06072e53	0.203949	0.101975	+	0.994787i	$0.467484\pi$
$332$	−9.77441e53	−0.610410
$333$	5.09844e53	0.298460
$334$	−6.83366e53	−0.375063
$335$	−6.96951e53	−0.358706
$336$	−2.23322e53	−0.107804
$337$	−1.17538e54	−0.532275	−0.266137	−	0.963935i	$-0.585747\pi$
$337$	−1.17538e54	−0.532275	−0.266137	+	0.963935i	$0.585747\pi$
$338$	−2.33334e54	−0.991447
$339$	−1.27503e54	−0.508425
$340$	−5.61988e53	−0.210344
$341$	−2.97460e54	−1.04522
$342$	−6.72957e53	−0.222037
$343$	−1.74251e53	−0.0539949
$344$	−2.62175e53	−0.0763105
$345$	3.74583e53	0.102432
$346$	−4.84840e53	−0.124584
$347$	−8.58145e53	−0.207242	−0.103621	−	0.994617i	$-0.533043\pi$
$347$	−8.58145e53	−0.207242	−0.103621	+	0.994617i	$0.533043\pi$
$348$	−1.51114e54	−0.343045
$349$	1.02482e54	0.218727	0.109363	−	0.994002i	$-0.465119\pi$
$349$	1.02482e54	0.218727	0.109363	+	0.994002i	$0.465119\pi$
$350$	−1.17402e54	−0.235620
$351$	6.54222e54	1.23487
$352$	−7.60787e53	−0.135081
$353$	−3.04715e54	−0.509023	−0.254512	−	0.967070i	$-0.581915\pi$
$353$	−3.04715e54	−0.509023	−0.254512	+	0.967070i	$0.581915\pi$
$354$	−3.64763e54	−0.573378
$355$	−2.63018e54	−0.389113
$356$	9.08697e53	0.126545
$357$	−4.02128e54	−0.527227
$358$	−3.40140e54	−0.419925
$359$	−3.69837e52	−0.00430011	−0.00215006	−	0.999998i	$-0.500684\pi$
$359$	−3.69837e52	−0.00430011	−0.00215006	+	0.999998i	$0.500684\pi$
$360$	3.35047e53	0.0366946
$361$	8.11129e53	0.0836922
$362$	−1.21058e55	−1.17695
$363$	−5.18121e54	−0.474722
$364$	3.39155e54	0.292899
$365$	−1.79318e54	−0.145992
$366$	1.00016e55	0.767760
$367$	1.02989e55	0.745541	0.372771	−	0.927924i	$-0.378408\pi$
$367$	1.02989e55	0.745541	0.372771	+	0.927924i	$0.378408\pi$
$368$	−9.55435e53	−0.0652339
$369$	9.32077e54	0.600323
$370$	3.96168e54	0.240737
$371$	5.47228e52	0.00313783
$372$	−1.44187e55	−0.780287
$373$	−2.97486e55	−1.51959	−0.759796	−	0.650161i	$-0.774701\pi$
$373$	−2.97486e55	−1.51959	−0.759796	+	0.650161i	$0.774701\pi$
$374$	−1.36992e55	−0.660628
$375$	1.62221e55	0.738642
$376$	3.27229e54	0.140706
$377$	2.29494e55	0.932036
$378$	−5.55053e54	−0.212942
$379$	5.02500e55	1.82135	0.910675	−	0.413123i	$-0.135562\pi$
$379$	5.02500e55	1.82135	0.910675	+	0.413123i	$0.135562\pi$
$380$	−5.22913e54	−0.179094
$381$	5.34632e55	1.73048
$382$	−1.01947e55	−0.311898
$383$	4.98480e54	0.144170	0.0720848	−	0.997399i	$-0.477035\pi$
$383$	4.98480e54	0.144170	0.0720848	+	0.997399i	$0.477035\pi$
$384$	−3.68775e54	−0.100842
$385$	3.84314e54	0.0993758
$386$	2.46454e54	0.0602712
$387$	2.81451e54	0.0651055
$388$	4.15486e55	0.909230
$389$	6.53476e54	0.135305	0.0676524	−	0.997709i	$-0.478449\pi$
$389$	6.53476e54	0.135305	0.0676524	+	0.997709i	$0.478449\pi$
$390$	−2.19571e55	−0.430216
$391$	−1.72042e55	−0.319032
$392$	−2.87745e54	−0.0505076
$393$	1.06208e56	1.76489
$394$	−4.69789e55	−0.739153
$395$	1.22089e55	0.181903
$396$	8.16724e54	0.115247
$397$	−5.26489e55	−0.703709	−0.351854	−	0.936055i	$-0.614449\pi$
$397$	−5.26489e55	−0.703709	−0.351854	+	0.936055i	$0.614449\pi$
$398$	−7.98989e55	−1.01171
$399$	−3.74168e55	−0.448900
$400$	−1.93868e55	−0.220402
$401$	1.46043e56	1.57354	0.786770	−	0.617246i	$-0.211752\pi$
$401$	1.46043e56	1.57354	0.786770	+	0.617246i	$0.211752\pi$
$402$	−8.23513e55	−0.841027
$403$	2.18975e56	2.12000
$404$	2.75118e55	0.252534
$405$	4.78588e55	0.416561
$406$	−1.94707e55	−0.160721
$407$	9.65714e55	0.756082
$408$	−6.64042e55	−0.493176
$409$	7.46368e55	0.525899	0.262949	−	0.964810i	$-0.415305\pi$
$409$	7.46368e55	0.525899	0.262949	+	0.964810i	$0.415305\pi$
$410$	7.24258e55	0.484218
$411$	2.28618e56	1.45048
$412$	−1.37018e56	−0.825061
$413$	−4.69989e55	−0.268634
$414$	1.02568e55	0.0556553
$415$	8.15351e55	0.420059
$416$	5.60053e55	0.273982
$417$	−1.20704e56	−0.560783
$418$	−1.27467e56	−0.562482
$419$	−4.53948e56	−1.90285	−0.951424	−	0.307883i	$-0.900379\pi$
$419$	−4.53948e56	−1.90285	−0.951424	+	0.307883i	$0.900379\pi$
$420$	1.86288e55	0.0741866
$421$	1.29970e56	0.491788	0.245894	−	0.969297i	$-0.420919\pi$
$421$	1.29970e56	0.491788	0.245894	+	0.969297i	$0.420919\pi$
$422$	1.05176e56	0.378181
$423$	−3.51289e55	−0.120046
$424$	9.03648e53	0.00293517
$425$	−3.49092e56	−1.07790
$426$	−3.10780e56	−0.912319
$427$	1.28868e56	0.359705
$428$	3.55964e56	0.944853
$429$	−5.35236e56	−1.35118
$430$	2.18698e55	0.0525138
$431$	1.28068e56	0.292535	0.146268	−	0.989245i	$-0.453274\pi$
$431$	1.28068e56	0.292535	0.146268	+	0.989245i	$0.453274\pi$
$432$	−9.16570e55	−0.199189
$433$	−5.03861e56	−1.04189	−0.520943	−	0.853591i	$-0.674420\pi$
$433$	−5.03861e56	−1.04189	−0.520943	+	0.853591i	$0.674420\pi$
$434$	−1.85782e56	−0.365574
$435$	1.26055e56	0.236070
$436$	−4.13856e56	−0.737716
$437$	−1.60080e56	−0.271635
$438$	−2.11881e56	−0.342294
$439$	−6.67116e56	−1.02616	−0.513079	−	0.858341i	$-0.671495\pi$
$439$	−6.67116e56	−1.02616	−0.513079	+	0.858341i	$0.671495\pi$
$440$	6.34625e55	0.0929576
$441$	3.08901e55	0.0430914
$442$	1.00847e57	1.33993
$443$	−7.20830e56	−0.912331	−0.456166	−	0.889895i	$-0.650778\pi$
$443$	−7.20830e56	−0.912331	−0.456166	+	0.889895i	$0.650778\pi$
$444$	4.68109e56	0.564434
$445$	−7.58007e55	−0.0870829
$446$	−3.81688e56	−0.417839
$447$	5.96358e56	0.622151
$448$	−4.75158e55	−0.0472456
$449$	1.18545e57	1.12353	0.561767	−	0.827296i	$-0.310122\pi$
$449$	1.18545e57	1.12353	0.561767	+	0.827296i	$0.310122\pi$
$450$	2.08122e56	0.188040
$451$	1.76548e57	1.52078
$452$	−2.71286e56	−0.222819
$453$	−1.98453e57	−1.55434
$454$	9.66654e56	0.722055
$455$	−2.82913e56	−0.201561
$456$	−6.17871e56	−0.419907
$457$	4.60969e56	0.298864	0.149432	−	0.988772i	$-0.452256\pi$
$457$	4.60969e56	0.298864	0.149432	+	0.988772i	$0.452256\pi$
$458$	−8.40491e56	−0.519907
$459$	−1.65044e57	−0.974152
$460$	7.96995e55	0.0448913
$461$	−2.91635e57	−1.56772	−0.783861	−	0.620936i	$-0.786753\pi$
$461$	−2.91635e57	−1.56772	−0.783861	+	0.620936i	$0.786753\pi$
$462$	4.54103e56	0.232998
$463$	2.73355e57	1.33886	0.669432	−	0.742873i	$-0.266538\pi$
$463$	2.73355e57	1.33886	0.669432	+	0.742873i	$0.266538\pi$
$464$	−3.21523e56	−0.150340
$465$	1.20277e57	0.536962
$466$	9.25389e56	0.394482
$467$	9.00737e56	0.366678	0.183339	−	0.983050i	$-0.441309\pi$
$467$	9.00737e56	0.366678	0.183339	+	0.983050i	$0.441309\pi$
$468$	−6.01231e56	−0.233752
$469$	−1.06108e57	−0.394031
$470$	−2.72965e56	−0.0968284
$471$	−8.49029e56	−0.287722
$472$	−7.76102e56	−0.251284
$473$	5.33107e56	0.164930
$474$	1.44260e57	0.426491
$475$	−3.24819e57	−0.917760
$476$	−8.55602e56	−0.231059
$477$	−9.70090e54	−0.00250419
$478$	−2.52110e55	−0.00622143
$479$	1.39825e57	0.329892	0.164946	−	0.986303i	$-0.447255\pi$
$479$	1.39825e57	0.329892	0.164946	+	0.986303i	$0.447255\pi$
$480$	3.07621e56	0.0693952
$481$	−7.10909e57	−1.53354
$482$	−1.21126e56	−0.0249876
$483$	5.70286e56	0.112520
$484$	−1.10240e57	−0.208048
$485$	−3.46585e57	−0.625695
$486$	2.39292e57	0.413284
$487$	−3.33071e57	−0.550382	−0.275191	−	0.961390i	$-0.588741\pi$
$487$	−3.33071e57	−0.550382	−0.275191	+	0.961390i	$0.588741\pi$
$488$	2.12802e57	0.336473
$489$	5.12279e57	0.775115
$490$	2.40028e56	0.0347573
$491$	1.03954e58	1.44075	0.720375	−	0.693585i	$-0.243970\pi$
$491$	1.03954e58	1.44075	0.720375	+	0.693585i	$0.243970\pi$
$492$	8.55779e57	1.13530
$493$	−5.78957e57	−0.735254
$494$	9.38349e57	1.14087
$495$	−6.81287e56	−0.0793082
$496$	−3.06786e57	−0.341963
$497$	−4.00433e57	−0.427432
$498$	9.63414e57	0.984877
$499$	1.49044e58	1.45933	0.729665	−	0.683805i	$-0.239676\pi$
$499$	1.49044e58	1.45933	0.729665	+	0.683805i	$0.239676\pi$
$500$	3.45155e57	0.323712
$501$	6.73560e57	0.605153
$502$	−3.63708e57	−0.313056
$503$	4.84460e57	0.399527	0.199763	−	0.979844i	$-0.435983\pi$
$503$	4.84460e57	0.399527	0.199763	+	0.979844i	$0.435983\pi$
$504$	5.10095e56	0.0403083
$505$	−2.29495e57	−0.173784
$506$	1.94279e57	0.140990
$507$	2.29986e58	1.59967
$508$	1.13753e58	0.758389
$509$	−6.54767e57	−0.418460	−0.209230	−	0.977866i	$-0.567096\pi$
$509$	−6.54767e57	−0.418460	−0.209230	+	0.977866i	$0.567096\pi$
$510$	5.53923e57	0.339384
$511$	−2.73004e57	−0.160369
$512$	−7.84638e56	−0.0441942
$513$	−1.53568e58	−0.829427
$514$	1.52141e58	0.788026
$515$	1.14296e58	0.567773
$516$	2.58412e57	0.123125
$517$	−6.65390e57	−0.304109
$518$	6.03148e57	0.264444
$519$	4.77882e57	0.201012
$520$	−4.67179e57	−0.188543
$521$	−3.64719e58	−1.41237	−0.706183	−	0.708029i	$-0.749585\pi$
$521$	−3.64719e58	−1.41237	−0.706183	+	0.708029i	$0.749585\pi$
$522$	3.45163e57	0.128265
$523$	−1.19708e58	−0.426910	−0.213455	−	0.976953i	$-0.568472\pi$
$523$	−1.19708e58	−0.426910	−0.213455	+	0.976953i	$0.568472\pi$
$524$	2.25977e58	0.773467
$525$	1.15717e58	0.380165
$526$	−1.06155e58	−0.334770
$527$	−5.52419e58	−1.67240
$528$	7.49869e57	0.217950
$529$	−3.33943e58	−0.931913
$530$	−7.53796e55	−0.00201987
$531$	8.33165e57	0.214387
$532$	−7.96112e57	−0.196732
$533$	−1.29966e59	−3.08456
$534$	−8.95656e57	−0.204176
$535$	−2.96934e58	−0.650210
$536$	−1.75218e58	−0.368583
$537$	3.35258e58	0.677536
$538$	−5.18697e58	−1.00715
$539$	5.85101e57	0.109162
$540$	7.64575e57	0.137074
$541$	7.03759e58	1.21250	0.606252	−	0.795273i	$-0.292672\pi$
$541$	7.03759e58	1.21250	0.606252	+	0.795273i	$0.292672\pi$
$542$	−6.26305e58	−1.03705
$543$	1.19321e59	1.89898
$544$	−1.41287e58	−0.216136
$545$	3.45226e58	0.507666
$546$	−3.34288e58	−0.472583
$547$	−1.00937e59	−1.37190	−0.685948	−	0.727650i	$-0.740612\pi$
$547$	−1.00937e59	−1.37190	−0.685948	+	0.727650i	$0.740612\pi$
$548$	4.86428e58	0.635677
$549$	−2.28449e58	−0.287067
$550$	3.94212e58	0.476356
$551$	−5.38701e58	−0.626021
$552$	9.41724e57	0.105253
$553$	1.85875e58	0.199816
$554$	−3.43430e58	−0.355123
$555$	−3.90482e58	−0.388421
$556$	−2.56819e58	−0.245765
$557$	−1.75260e59	−1.61360	−0.806802	−	0.590822i	$-0.798804\pi$
$557$	−1.75260e59	−1.61360	−0.806802	+	0.590822i	$0.798804\pi$
$558$	3.29342e58	0.291751
$559$	−3.92446e58	−0.334523
$560$	3.96363e57	0.0325125
$561$	1.35027e59	1.06590
$562$	−7.18368e58	−0.545779
$563$	1.88748e59	1.38023	0.690114	−	0.723700i	$-0.257560\pi$
$563$	1.88748e59	1.38023	0.690114	+	0.723700i	$0.257560\pi$
$564$	−3.22533e58	−0.227025
$565$	2.26299e58	0.153335
$566$	−4.70394e58	−0.306838
$567$	7.28629e58	0.457584
$568$	−6.61243e58	−0.399826
$569$	2.38127e59	1.38642	0.693211	−	0.720735i	$-0.256195\pi$
$569$	2.38127e59	1.38642	0.693211	+	0.720735i	$0.256195\pi$
$570$	5.15409e58	0.288963
$571$	−7.10372e58	−0.383539	−0.191770	−	0.981440i	$-0.561423\pi$
$571$	−7.10372e58	−0.383539	−0.191770	+	0.981440i	$0.561423\pi$
$572$	−1.13881e59	−0.592158
$573$	1.00484e59	0.503237
$574$	1.10265e59	0.531903
$575$	4.95072e58	0.230043
$576$	8.42329e57	0.0377049
$577$	−1.65236e59	−0.712566	−0.356283	−	0.934378i	$-0.615956\pi$
$577$	−1.65236e59	−0.712566	−0.356283	+	0.934378i	$0.615956\pi$
$578$	−8.42217e58	−0.349925
$579$	−2.42918e58	−0.0972456
$580$	2.68205e58	0.103458
$581$	1.24134e59	0.461427
$582$	−4.09523e59	−1.46701
$583$	−1.83748e57	−0.00634380
$584$	−4.50817e58	−0.150011
$585$	5.01528e58	0.160859
$586$	3.51403e59	1.08644
$587$	4.61453e59	1.37534	0.687668	−	0.726026i	$-0.258635\pi$
$587$	4.61453e59	1.37534	0.687668	+	0.726026i	$0.258635\pi$
$588$	2.83615e58	0.0814924
$589$	−5.14009e59	−1.42394
$590$	6.47400e58	0.172924
$591$	4.63047e59	1.19260
$592$	9.95989e58	0.247365
$593$	−3.31627e59	−0.794280	−0.397140	−	0.917758i	$-0.629997\pi$
$593$	−3.31627e59	−0.794280	−0.397140	+	0.917758i	$0.629997\pi$
$594$	1.86376e59	0.430507
$595$	7.13717e58	0.159005
$596$	1.26886e59	0.272659
$597$	7.87523e59	1.63236
$598$	−1.43018e59	−0.285967
$599$	−1.90049e59	−0.366598	−0.183299	−	0.983057i	$-0.558678\pi$
$599$	−1.90049e59	−0.366598	−0.183299	+	0.983057i	$0.558678\pi$
$600$	1.91086e59	0.355612
$601$	−1.24909e59	−0.224281	−0.112141	−	0.993692i	$-0.535771\pi$
$601$	−1.24909e59	−0.224281	−0.112141	+	0.993692i	$0.535771\pi$
$602$	3.32958e58	0.0576853
$603$	1.88101e59	0.314462
$604$	−4.22245e59	−0.681193
$605$	9.19588e58	0.143170
$606$	−2.71170e59	−0.407456
$607$	3.67382e59	0.532795	0.266398	−	0.963863i	$-0.414167\pi$
$607$	3.67382e59	0.532795	0.266398	+	0.963863i	$0.414167\pi$
$608$	−1.31463e59	−0.184025
$609$	1.91913e59	0.259318
$610$	−1.77513e59	−0.231547
$611$	4.89826e59	0.616816
$612$	1.51676e59	0.184400
$613$	1.60293e60	1.88155	0.940774	−	0.339035i	$-0.110101\pi$
$613$	1.60293e60	1.88155	0.940774	+	0.339035i	$0.110101\pi$
$614$	−1.04322e60	−1.18238
$615$	−7.13865e59	−0.781270
$616$	9.66189e58	0.102112
$617$	−5.57012e59	−0.568504	−0.284252	−	0.958750i	$-0.591745\pi$
$617$	−5.57012e59	−0.568504	−0.284252	+	0.958750i	$0.591745\pi$
$618$	1.35051e60	1.33121
$619$	−4.32518e59	−0.411771	−0.205885	−	0.978576i	$-0.566007\pi$
$619$	−4.32518e59	−0.411771	−0.205885	+	0.978576i	$0.566007\pi$
$620$	2.55911e59	0.235325
$621$	2.34060e59	0.207902
$622$	−6.47205e59	−0.555326
$623$	−1.15403e59	−0.0956588
$624$	−5.52015e59	−0.442061
$625$	8.51536e59	0.658844
$626$	−1.37384e60	−1.02704
$627$	1.25638e60	0.907547
$628$	−1.80647e59	−0.126095
$629$	1.79345e60	1.20976
$630$	−4.25505e58	−0.0277385
$631$	−7.08414e59	−0.446330	−0.223165	−	0.974781i	$-0.571639\pi$
$631$	−7.08414e59	−0.446330	−0.223165	+	0.974781i	$0.571639\pi$
$632$	3.06939e59	0.186911
$633$	−1.03667e60	−0.610184
$634$	4.12954e59	0.234954
$635$	−9.48891e59	−0.521893
$636$	−8.90680e57	−0.00473581
$637$	−4.30722e59	−0.221411
$638$	6.53786e59	0.324931
$639$	7.09861e59	0.341118
$640$	6.54521e58	0.0304126
$641$	−1.47369e60	−0.662153	−0.331076	−	0.943604i	$-0.607412\pi$
$641$	−1.47369e60	−0.662153	−0.331076	+	0.943604i	$0.607412\pi$
$642$	−3.50855e60	−1.52449
$643$	−3.70803e60	−1.55814	−0.779072	−	0.626934i	$-0.784309\pi$
$643$	−3.70803e60	−1.55814	−0.779072	+	0.626934i	$0.784309\pi$
$644$	1.21339e59	0.0493122
$645$	−2.15560e59	−0.0847293
$646$	−2.36722e60	−0.899994
$647$	−3.86925e59	−0.142293	−0.0711467	−	0.997466i	$-0.522666\pi$
$647$	−3.86925e59	−0.142293	−0.0711467	+	0.997466i	$0.522666\pi$
$648$	1.20320e60	0.428031
$649$	1.57813e60	0.543102
$650$	−2.90199e60	−0.966180
$651$	1.83116e60	0.589841
$652$	1.08997e60	0.339696
$653$	5.48528e59	0.165412	0.0827058	−	0.996574i	$-0.473644\pi$
$653$	5.48528e59	0.165412	0.0827058	+	0.996574i	$0.473644\pi$
$654$	4.07916e60	1.19028
$655$	−1.88503e60	−0.532269
$656$	1.82083e60	0.497550
$657$	4.83964e59	0.127984
$658$	−4.15577e59	−0.106364
$659$	−1.39153e60	−0.344712	−0.172356	−	0.985035i	$-0.555138\pi$
$659$	−1.39153e60	−0.344712	−0.172356	+	0.985035i	$0.555138\pi$
$660$	−6.25518e59	−0.149984
$661$	1.52924e60	0.354932	0.177466	−	0.984127i	$-0.443210\pi$
$661$	1.52924e60	0.354932	0.177466	+	0.984127i	$0.443210\pi$
$662$	−6.41880e59	−0.144214
$663$	−9.93997e60	−2.16194
$664$	2.04984e60	0.431625
$665$	6.64092e59	0.135383
$666$	−1.06922e60	−0.211043
$667$	8.21059e59	0.156917
$668$	1.43312e60	0.265210
$669$	3.76211e60	0.674170
$670$	1.46161e60	0.253644
$671$	−4.32713e60	−0.727220
$672$	4.68339e59	0.0762292
$673$	−2.93034e60	−0.461949	−0.230974	−	0.972960i	$-0.574191\pi$
$673$	−2.93034e60	−0.461949	−0.230974	+	0.972960i	$0.574191\pi$
$674$	2.46495e60	0.376375
$675$	4.74933e60	0.702427
$676$	4.89337e60	0.701059
$677$	−1.36592e61	−1.89570	−0.947849	−	0.318719i	$-0.896748\pi$
$677$	−1.36592e61	−1.89570	−0.947849	+	0.318719i	$0.896748\pi$
$678$	2.67393e60	0.359511
$679$	−5.27661e60	−0.687314
$680$	1.17858e60	0.148736
$681$	−9.52782e60	−1.16501
$682$	6.23819e60	0.739085
$683$	−3.03155e59	−0.0348032	−0.0174016	−	0.999849i	$-0.505539\pi$
$683$	−3.03155e59	−0.0348032	−0.0174016	+	0.999849i	$0.505539\pi$
$684$	1.41129e60	0.157004
$685$	−4.05763e60	−0.437447
$686$	3.65432e59	0.0381802
$687$	8.28430e60	0.838853
$688$	5.49820e59	0.0539597
$689$	1.35266e59	0.0128670
$690$	−7.85558e59	−0.0724307
$691$	−2.14721e61	−1.91909	−0.959546	−	0.281553i	$-0.909151\pi$
$691$	−2.14721e61	−1.91909	−0.959546	+	0.281553i	$0.909151\pi$
$692$	1.01678e60	0.0880942
$693$	−1.03723e60	−0.0871184
$694$	1.79966e60	0.146542
$695$	2.14231e60	0.169125
$696$	3.16909e60	0.242569
$697$	3.27871e61	2.43331
$698$	−2.14921e60	−0.154663
$699$	−9.12109e60	−0.636484
$700$	2.46210e60	0.166608
$701$	9.40948e59	0.0617488	0.0308744	−	0.999523i	$-0.490171\pi$
$701$	9.40948e59	0.0617488	0.0308744	+	0.999523i	$0.490171\pi$
$702$	−1.37200e61	−0.873187
$703$	1.66875e61	1.03003
$704$	1.59549e60	0.0955170
$705$	2.69048e60	0.156229
$706$	6.39034e60	0.359934
$707$	−3.49396e60	−0.190898
$708$	7.64964e60	0.405439
$709$	1.53584e61	0.789681	0.394841	−	0.918750i	$-0.370800\pi$
$709$	1.53584e61	0.789681	0.394841	+	0.918750i	$0.370800\pi$
$710$	5.51588e60	0.275144
$711$	−3.29507e60	−0.159466
$712$	−1.90568e60	−0.0894806
$713$	7.83424e60	0.356921
$714$	8.43324e60	0.372806
$715$	9.49963e60	0.407499
$716$	7.13325e60	0.296932
$717$	2.48492e59	0.0100381
$718$	7.75605e58	0.00304064
$719$	−2.98425e61	−1.13544	−0.567720	−	0.823222i	$-0.692174\pi$
$719$	−2.98425e61	−1.13544	−0.567720	+	0.823222i	$0.692174\pi$
$720$	−7.02645e59	−0.0259470
$721$	1.74010e61	0.623687
$722$	−1.70106e60	−0.0591793
$723$	1.19388e60	0.0403168
$724$	2.53877e61	0.832232
$725$	1.66601e61	0.530166
$726$	1.08658e61	0.335679
$727$	4.38325e61	1.31464	0.657320	−	0.753612i	$-0.271690\pi$
$727$	4.38325e61	1.31464	0.657320	+	0.753612i	$0.271690\pi$
$728$	−7.11259e60	−0.207111
$729$	1.92357e61	0.543833
$730$	3.76058e60	0.103232
$731$	9.90044e60	0.263895
$732$	−2.09748e61	−0.542888
$733$	1.34759e61	0.338706	0.169353	−	0.985555i	$-0.445832\pi$
$733$	1.34759e61	0.338706	0.169353	+	0.985555i	$0.445832\pi$
$734$	−2.15984e61	−0.527177
$735$	−2.36583e60	−0.0560798
$736$	2.00369e60	0.0461273
$737$	3.56288e61	0.796619
$738$	−1.95471e61	−0.424492
$739$	−5.28176e61	−1.11410	−0.557049	−	0.830480i	$-0.688066\pi$
$739$	−5.28176e61	−1.11410	−0.557049	+	0.830480i	$0.688066\pi$
$740$	−8.30824e60	−0.170226
$741$	−9.24883e61	−1.84075
$742$	−1.14762e59	−0.00221878
$743$	8.11706e61	1.52454	0.762271	−	0.647258i	$-0.224084\pi$
$743$	8.11706e61	1.52454	0.762271	+	0.647258i	$0.224084\pi$
$744$	3.02383e61	0.551746
$745$	−1.05845e61	−0.187633
$746$	6.23874e61	1.07451
$747$	−2.20056e61	−0.368248
$748$	2.87294e61	0.467135
$749$	−4.52069e61	−0.714242
$750$	−3.40201e61	−0.522299
$751$	−2.88556e61	−0.430498	−0.215249	−	0.976559i	$-0.569056\pi$
$751$	−2.88556e61	−0.430498	−0.215249	+	0.976559i	$0.569056\pi$
$752$	−6.86250e60	−0.0994944
$753$	3.58488e61	0.505107
$754$	−4.81284e61	−0.659049
$755$	3.52224e61	0.468769
$756$	1.16403e61	0.150573
$757$	−1.57431e62	−1.97938	−0.989690	−	0.143224i	$-0.954253\pi$
$757$	−1.57431e62	−1.97938	−0.989690	+	0.143224i	$0.954253\pi$
$758$	−1.05382e62	−1.28789
$759$	−1.91491e61	−0.227483
$760$	1.09663e61	0.126639
$761$	−6.37765e61	−0.715963	−0.357981	−	0.933729i	$-0.616535\pi$
$761$	−6.37765e61	−0.715963	−0.357981	+	0.933729i	$0.616535\pi$
$762$	−1.12120e62	−1.22364
$763$	5.25591e61	0.557661
$764$	2.13799e61	0.220545
$765$	−1.26523e61	−0.126896
$766$	−1.04539e61	−0.101943
$767$	−1.16174e62	−1.10156
$768$	7.73378e60	0.0713059
$769$	−8.43935e61	−0.756646	−0.378323	−	0.925674i	$-0.623499\pi$
$769$	−8.43935e61	−0.756646	−0.378323	+	0.925674i	$0.623499\pi$
$770$	−8.05965e60	−0.0702693
$771$	−1.49958e62	−1.27145
$772$	−5.16852e60	−0.0426182
$773$	−2.28687e62	−1.83393	−0.916966	−	0.398965i	$-0.869369\pi$
$773$	−2.28687e62	−1.83393	−0.916966	+	0.398965i	$0.869369\pi$
$774$	−5.90246e60	−0.0460365
$775$	1.58965e62	1.20591
$776$	−8.71337e61	−0.642923
$777$	−5.94492e61	−0.426672
$778$	−1.37044e61	−0.0956749
$779$	3.05074e62	2.07181
$780$	4.60474e61	0.304209
$781$	1.34457e62	0.864146
$782$	3.60799e61	0.225590
$783$	7.87659e61	0.479138
$784$	6.03444e60	0.0357143
$785$	1.50690e61	0.0867734
$786$	−2.22734e62	−1.24796
$787$	−6.62818e61	−0.361358	−0.180679	−	0.983542i	$-0.557830\pi$
$787$	−6.62818e61	−0.361358	−0.180679	+	0.983542i	$0.557830\pi$
$788$	9.85219e61	0.522660
$789$	1.04632e62	0.540141
$790$	−2.56039e61	−0.128625
$791$	3.44530e61	0.168435
$792$	−1.71280e61	−0.0814918
$793$	3.18541e62	1.47500
$794$	1.10413e62	0.497597
$795$	7.42978e59	0.00325899
$796$	1.67560e62	0.715385
$797$	3.24845e62	1.34997	0.674983	−	0.737834i	$-0.264151\pi$
$797$	3.24845e62	1.34997	0.674983	+	0.737834i	$0.264151\pi$
$798$	7.84687e61	0.317420
$799$	−1.23571e62	−0.486587
$800$	4.06570e61	0.155848
$801$	2.04579e61	0.0763418
$802$	−3.06275e62	−1.11266
$803$	9.16693e61	0.324220
$804$	1.72703e62	0.594696
$805$	−1.01217e61	−0.0339346
$806$	−4.59224e62	−1.49907
$807$	5.11254e62	1.62501
$808$	−5.76965e61	−0.178569
$809$	−5.06218e62	−1.52561	−0.762806	−	0.646627i	$-0.776179\pi$
$809$	−5.06218e62	−1.52561	−0.762806	+	0.646627i	$0.776179\pi$
$810$	−1.00367e62	−0.294553
$811$	6.33281e62	1.80987	0.904937	−	0.425546i	$-0.139918\pi$
$811$	6.33281e62	1.80987	0.904937	+	0.425546i	$0.139918\pi$
$812$	4.08330e61	0.113647
$813$	6.17318e62	1.67325
$814$	−2.02525e62	−0.534630
$815$	−9.09219e61	−0.233765
$816$	1.39260e62	0.348728
$817$	9.21205e61	0.224689
$818$	−1.56525e62	−0.371867
$819$	7.63555e61	0.176700
$820$	−1.51888e62	−0.342394
$821$	−8.68631e62	−1.90747	−0.953735	−	0.300649i	$-0.902797\pi$
$821$	−8.68631e62	−1.90747	−0.953735	+	0.300649i	$0.902797\pi$
$822$	−4.79447e62	−1.02564
$823$	−6.68844e62	−1.39389	−0.696945	−	0.717125i	$-0.745458\pi$
$823$	−6.68844e62	−1.39389	−0.696945	+	0.717125i	$0.745458\pi$
$824$	2.87347e62	0.583406
$825$	−3.88555e62	−0.768585
$826$	9.85638e61	0.189953
$827$	2.87051e62	0.539001	0.269501	−	0.963000i	$-0.413141\pi$
$827$	2.87051e62	0.539001	0.269501	+	0.963000i	$0.413141\pi$
$828$	−2.15102e61	−0.0393542
$829$	4.01819e62	0.716321	0.358161	−	0.933660i	$-0.383404\pi$
$829$	4.01819e62	0.716321	0.358161	+	0.933660i	$0.383404\pi$
$830$	−1.70992e62	−0.297027
$831$	3.38502e62	0.572979
$832$	−1.17452e62	−0.193735
$833$	1.08660e62	0.174664
$834$	2.53134e62	0.396533
$835$	−1.19547e62	−0.182507
$836$	2.67318e62	0.397735
$837$	7.51556e62	1.08984
$838$	9.51997e62	1.34552
$839$	1.79352e62	0.247073	0.123536	−	0.992340i	$-0.460576\pi$
$839$	1.79352e62	0.247073	0.123536	+	0.992340i	$0.460576\pi$
$840$	−3.90674e61	−0.0524578
$841$	−4.87733e62	−0.638364
$842$	−2.72567e62	−0.347746
$843$	7.08059e62	0.880596
$844$	−2.20571e62	−0.267415
$845$	−4.08190e62	−0.482440
$846$	7.36707e61	0.0848852
$847$	1.40003e62	0.157270
$848$	−1.89509e60	−0.00207548
$849$	4.63644e62	0.495073
$850$	7.32099e62	0.762189
$851$	−2.54341e62	−0.258185
$852$	6.51753e62	0.645107
$853$	1.47682e63	1.42535	0.712676	−	0.701493i	$-0.247483\pi$
$853$	1.47682e63	1.42535	0.712676	+	0.701493i	$0.247483\pi$
$854$	−2.70256e62	−0.254350
$855$	−1.17726e62	−0.108044
$856$	−7.46510e62	−0.668112
$857$	−2.12969e63	−1.85878	−0.929391	−	0.369098i	$-0.879667\pi$
$857$	−2.12969e63	−1.85878	−0.929391	+	0.369098i	$0.879667\pi$
$858$	1.12247e63	0.955429
$859$	1.28077e62	0.106321	0.0531603	−	0.998586i	$-0.483071\pi$
$859$	1.28077e62	0.106321	0.0531603	+	0.998586i	$0.483071\pi$
$860$	−4.58643e61	−0.0371328
$861$	−1.08683e63	−0.858209
$862$	−2.68578e62	−0.206854
$863$	−9.62637e62	−0.723154	−0.361577	−	0.932342i	$-0.617761\pi$
$863$	−9.62637e62	−0.723154	−0.361577	+	0.932342i	$0.617761\pi$
$864$	1.92219e62	0.140848
$865$	−8.48170e61	−0.0606229
$866$	1.05667e63	0.736725
$867$	8.30130e62	0.564593
$868$	3.89613e62	0.258500
$869$	−6.24131e62	−0.403971
$870$	−2.64356e62	−0.166926
$871$	−2.62281e63	−1.61576
$872$	8.67918e62	0.521644
$873$	9.35402e62	0.548520
$874$	3.35712e62	0.192075
$875$	−4.38341e62	−0.244703
$876$	4.44347e62	0.242038
$877$	3.01221e63	1.60101	0.800504	−	0.599327i	$-0.204565\pi$
$877$	3.01221e63	1.60101	0.800504	+	0.599327i	$0.204565\pi$
$878$	1.39904e63	0.725603
$879$	−3.46360e63	−1.75294
$880$	−1.33091e62	−0.0657309
$881$	−1.23291e63	−0.594223	−0.297112	−	0.954843i	$-0.596023\pi$
$881$	−1.23291e63	−0.594223	−0.297112	+	0.954843i	$0.596023\pi$
$882$	−6.47813e61	−0.0304702
$883$	3.53664e62	0.162344	0.0811720	−	0.996700i	$-0.474134\pi$
$883$	3.53664e62	0.162344	0.0811720	+	0.996700i	$0.474134\pi$
$884$	−2.11491e63	−0.947477
$885$	−6.38110e62	−0.279007
$886$	1.51169e63	0.645116
$887$	−2.79600e63	−1.16461	−0.582304	−	0.812971i	$-0.697849\pi$
$887$	−2.79600e63	−1.16461	−0.582304	+	0.812971i	$0.697849\pi$
$888$	−9.81696e62	−0.399115
$889$	−1.44464e63	−0.573288
$890$	1.58966e62	0.0615769
$891$	−2.44659e63	−0.925104
$892$	8.00458e62	0.295457
$893$	−1.14979e63	−0.414297
$894$	−1.25065e63	−0.439927
$895$	−5.95034e62	−0.204337
$896$	9.96479e61	0.0334077
$897$	1.40966e63	0.461398
$898$	−2.48606e63	−0.794458
$899$	2.63638e63	0.822573
$900$	−4.36464e62	−0.132964
$901$	−3.41243e61	−0.0101503
$902$	−3.70248e63	−1.07536
$903$	−3.28180e62	−0.0930734
$904$	5.68928e62	0.157557
$905$	−2.11777e63	−0.572708
$906$	4.16185e63	1.09908
$907$	−5.54261e63	−1.42941	−0.714706	−	0.699425i	$-0.753440\pi$
$907$	−5.54261e63	−1.42941	−0.714706	+	0.699425i	$0.753440\pi$
$908$	−2.02722e63	−0.510570
$909$	6.19387e62	0.152349
$910$	5.93311e62	0.142525
$911$	5.94792e63	1.39547	0.697734	−	0.716357i	$-0.254192\pi$
$911$	5.94792e63	1.39547	0.697734	+	0.716357i	$0.254192\pi$
$912$	1.29577e63	0.296919
$913$	−4.16816e63	−0.932873
$914$	−9.66721e62	−0.211328
$915$	1.74966e63	0.373594
$916$	1.76264e63	0.367630
$917$	−2.86988e63	−0.584686
$918$	3.46122e63	0.688829
$919$	8.09148e63	1.57306	0.786528	−	0.617554i	$-0.211876\pi$
$919$	8.09148e63	1.57306	0.786528	+	0.617554i	$0.211876\pi$
$920$	−1.67142e62	−0.0317429
$921$	1.02825e64	1.90774
$922$	6.11602e63	1.10855
$923$	−9.89806e63	−1.75272
$924$	−9.52323e62	−0.164754
$925$	−5.16085e63	−0.872316
$926$	−5.73268e63	−0.946720
$927$	−3.08474e63	−0.497742
$928$	6.74283e62	0.106307
$929$	−4.69455e62	−0.0723197	−0.0361598	−	0.999346i	$-0.511513\pi$
$929$	−4.69455e62	−0.0723197	−0.0361598	+	0.999346i	$0.511513\pi$
$930$	−2.52239e63	−0.379689
$931$	1.01105e63	0.148715
$932$	−1.94068e63	−0.278941
$933$	6.37917e63	0.896001
$934$	−1.88898e63	−0.259281
$935$	−2.39652e63	−0.321463
$936$	1.26087e63	0.165288
$937$	1.10223e64	1.41212	0.706061	−	0.708151i	$-0.250471\pi$
$937$	1.10223e64	1.41212	0.706061	+	0.708151i	$0.250471\pi$
$938$	2.22524e63	0.278622
$939$	1.35412e64	1.65710
$940$	5.72449e62	0.0684680
$941$	7.10273e63	0.830326	0.415163	−	0.909747i	$-0.363725\pi$
$941$	7.10273e63	0.830326	0.415163	+	0.909747i	$0.363725\pi$
$942$	1.78054e63	0.203450
$943$	−4.64977e63	−0.519314
$944$	1.62760e63	0.177685
$945$	−9.70999e62	−0.103618
$946$	−1.11801e63	−0.116623
$947$	−1.52477e64	−1.55482	−0.777408	−	0.628997i	$-0.783466\pi$
$947$	−1.52477e64	−1.55482	−0.777408	+	0.628997i	$0.783466\pi$
$948$	−3.02534e63	−0.301575
$949$	−6.74823e63	−0.657607
$950$	6.81195e63	0.648954
$951$	−4.07028e63	−0.379090
$952$	1.79433e63	0.163383
$953$	1.47199e64	1.31041	0.655206	−	0.755450i	$-0.272582\pi$
$953$	1.47199e64	1.31041	0.655206	+	0.755450i	$0.272582\pi$
$954$	2.03443e61	0.00177073
$955$	−1.78344e63	−0.151770
$956$	5.28713e61	0.00439922
$957$	−6.44404e63	−0.524266
$958$	−2.93234e63	−0.233269
$959$	−6.17757e63	−0.480527
$960$	−6.45128e62	−0.0490698
$961$	1.17106e64	0.871017
$962$	1.49089e64	1.08438
$963$	8.01397e63	0.570010
$964$	2.54019e62	0.0176689
$965$	4.31143e62	0.0293281
$966$	−1.19598e63	−0.0795636
$967$	4.38850e63	0.285527	0.142764	−	0.989757i	$-0.454401\pi$
$967$	4.38850e63	0.285527	0.142764	+	0.989757i	$0.454401\pi$
$968$	2.31190e63	0.147112
$969$	2.33325e64	1.45211
$970$	7.26842e63	0.442433
$971$	5.34892e63	0.318459	0.159229	−	0.987242i	$-0.449099\pi$
$971$	5.34892e63	0.318459	0.159229	+	0.987242i	$0.449099\pi$
$972$	−5.01832e63	−0.292236
$973$	3.26157e63	0.185781
$974$	6.98501e63	0.389179
$975$	2.86034e64	1.55890
$976$	−4.46279e63	−0.237922
$977$	−1.15112e64	−0.600324	−0.300162	−	0.953888i	$-0.597041\pi$
$977$	−1.15112e64	−0.600324	−0.300162	+	0.953888i	$0.597041\pi$
$978$	−1.07433e64	−0.548089
$979$	3.87501e63	0.193395
$980$	−5.03375e62	−0.0245771
$981$	−9.31732e63	−0.445049
$982$	−2.18007e64	−1.01876
$983$	1.21385e63	0.0554965	0.0277483	−	0.999615i	$-0.491166\pi$
$983$	1.21385e63	0.0554965	0.0277483	+	0.999615i	$0.491166\pi$
$984$	−1.79470e64	−0.802781
$985$	−8.21840e63	−0.359673
$986$	1.21416e64	0.519903
$987$	4.09613e63	0.171615
$988$	−1.96786e64	−0.806715
$989$	−1.40405e63	−0.0563200
$990$	1.42876e63	0.0560794
$991$	6.90479e63	0.265196	0.132598	−	0.991170i	$-0.457668\pi$
$991$	6.90479e63	0.265196	0.132598	+	0.991170i	$0.457668\pi$
$992$	6.43376e63	0.241804
$993$	6.32669e63	0.232684
$994$	8.39769e63	0.302240
$995$	−1.39774e64	−0.492299
$996$	−2.02043e64	−0.696413
$997$	2.20463e64	0.743688	0.371844	−	0.928295i	$-0.378726\pi$
$997$	2.20463e64	0.743688	0.371844	+	0.928295i	$0.378726\pi$
$998$	−3.12568e64	−1.03190
$999$	−2.43995e64	−0.788357

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	14.44.a.c.1.4	✓	6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
14.44.a.c.1.4	✓	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:	\( k \)	\(=\)	\( 44 \)
Character orbit:	\([\chi]\)	\(=\)	14.a (trivial)

\(f(q)\)	\(=\)	\(q-2.09715e6 q^{2} +2.06706e10 q^{3} +4.39805e12 q^{4} -3.66872e14 q^{5} -4.33493e16 q^{6} -5.58546e17 q^{7} -9.22337e18 q^{8} +9.90153e19 q^{9} +7.69386e20 q^{10} +1.87548e22 q^{11} +9.09101e22 q^{12} -1.38064e24 q^{13} +1.17136e24 q^{14} -7.58344e24 q^{15} +1.93428e25 q^{16} +3.48300e26 q^{17} -2.07650e26 q^{18} +3.24082e27 q^{19} -1.61352e27 q^{20} -1.15455e28 q^{21} -3.93318e28 q^{22} -4.93948e28 q^{23} -1.90652e29 q^{24} -1.00227e30 q^{25} +2.89540e30 q^{26} -4.73856e30 q^{27} -2.45651e30 q^{28} -1.66224e31 q^{29} +1.59036e31 q^{30} -1.58604e32 q^{31} -4.05648e31 q^{32} +3.87673e32 q^{33} -7.30438e32 q^{34} +2.04915e32 q^{35} +4.35474e32 q^{36} +5.14914e33 q^{37} -6.79650e33 q^{38} -2.85385e34 q^{39} +3.38379e33 q^{40} +9.41346e34 q^{41} +2.42126e34 q^{42} +2.84250e34 q^{43} +8.24847e34 q^{44} -3.63259e34 q^{45} +1.03589e35 q^{46} -3.54783e35 q^{47} +3.99827e35 q^{48} +3.11973e35 q^{49} +2.10192e36 q^{50} +7.19956e36 q^{51} -6.07210e36 q^{52} -9.79738e34 q^{53} +9.93747e36 q^{54} -6.88062e36 q^{55} +5.15168e36 q^{56} +6.69897e37 q^{57} +3.48596e37 q^{58} +8.41451e37 q^{59} -3.33523e37 q^{60} -2.30721e38 q^{61} +3.32618e38 q^{62} -5.53046e37 q^{63} +8.50706e37 q^{64} +5.06516e38 q^{65} -8.13010e38 q^{66} +1.89971e39 q^{67} +1.53184e39 q^{68} -1.02102e39 q^{69} -4.29737e38 q^{70} +7.16921e39 q^{71} -9.13255e38 q^{72} +4.88777e39 q^{73} -1.07985e40 q^{74} -2.07176e40 q^{75} +1.42533e40 q^{76} -1.04754e40 q^{77} +5.98496e40 q^{78} -3.32784e40 q^{79} -7.09633e39 q^{80} -1.30451e41 q^{81} -1.97415e41 q^{82} -2.22244e41 q^{83} -5.07775e40 q^{84} -1.27781e41 q^{85} -5.96116e40 q^{86} -3.43593e41 q^{87} -1.72983e41 q^{88} +2.06614e41 q^{89} +7.61809e40 q^{90} +7.71149e41 q^{91} -2.17241e41 q^{92} -3.27844e42 q^{93} +7.44033e41 q^{94} -1.18897e42 q^{95} -8.38498e41 q^{96} +9.44705e42 q^{97} -6.54256e41 q^{98} +1.85702e42 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 12582912 q^{2} + 5888073464 q^{3} + 26388279066624 q^{4} + 11\!\cdots\!36 q^{5} - 12\!\cdots\!28 q^{6} - 33\!\cdots\!42 q^{7} - 55\!\cdots\!48 q^{8} + 92\!\cdots\!42 q^{9} - 23\!\cdots\!72 q^{10}+ \cdots - 32\!\cdots\!68 q^{99}+O(q^{100}) \) 6 * q - 12582912 * q^2 + 5888073464 * q^3 + 26388279066624 * q^4 + 1101555913947636 * q^5 - 12348185041174528 * q^6 - 3351275184499704042 * q^7 - 55340232221128654848 * q^8 + 920206056624214792942 * q^9 - 2310130188047112732672 * q^10 + 12364443308352069449256 * q^11 + 25896020955469243744256 * q^12 + 2673480309226397380134852 * q^13 + 7028133455723923331088384 * q^14 + 2596751366800458111241088 * q^15 + 116056878683004400771792896 * q^16 - 151523956294392739202437236 * q^17 - 1929811972061585301447901184 * q^18 + 2924396698591999816313232888 * q^19 + 4844694144123378561548550144 * q^20 - 3288759080735735247592290248 * q^21 - 25930117012997159149646118912 * q^22 - 138189734932452843094441090944 * q^23 - 54307892138804235456753958912 * q^24 - 543783005857111577200118310054 * q^25 - 5606694577454757718544565141504 * q^26 - 18238081241455439895784620403120 * q^27 - 14739064132938337261638666682368 * q^28 + 15447844631699667206917310415204 * q^29 - 5445782322388314328905470181376 * q^30 + 292785585487600534640913741920928 * q^31 - 243388915243820045087367015432192 * q^32 + 1256563034943030983841204584125696 * q^33 + 317768767990698321803869654351872 * q^34 - 615269499791933990825610314257452 * q^35 + 4047109036832897738102068863827968 * q^36 + 13132693042122798744929986162932564 * q^37 - 6132904385245609598780928977534976 * q^38 - 11796100190350809899368491556833120 * q^39 - 10160060013736631597108665031589888 * q^40 + 38981092234624183196209759743431868 * q^41 + 6897027683683108645958666678173696 * q^42 + 430991577964570312120449205257671880 * q^43 + 54379396754041018304998657568538624 * q^44 + 1263061387411010892502511029097132932 * q^45 + 289804878993063344801193322755391488 * q^46 - 784780034728411639235800111087185504 * q^47 + 113891904614677579996602478440218624 * q^48 + 1871840893707254227807981930931856294 * q^49 + 1140395618299253258348382514166366208 * q^50 - 4129766731791997339074126003018671024 * q^51 + 11758090746498400058961171875635396608 * q^52 - 5122212740431365179538885282523396620 * q^53 + 38248028551680758688324508247643914240 * q^54 + 19027704776584231317971437400261902992 * q^55 + 30910057824519899864920053110261415936 * q^56 - 64661904785167221488182671806938840784 * q^57 - 32396478265058220482321051371865899008 * q^58 - 225588768299241350012896084475002479768 * q^59 + 11420633288961298171492764601813041152 * q^60 - 289339159435618635377414484178126783836 * q^61 - 614015876176492436423261535696957997056 * q^62 - 513977287031843422506703993072885078594 * q^63 + 510423550381407695195061911147652317184 * q^64 + 2969906390398104707050197163877586869448 * q^65 - 2635203681856847313824549876008371617792 * q^66 + 343125170025663033658904147138490807384 * q^67 - 666409407329228966967628853363337068544 * q^68 - 4357220448246785465479348340754665191232 * q^69 + 1290313662027653952727910321765643976704 * q^70 + 635590344686651753765595281077318128528 * q^71 - 8487402810812185157256229921914550747136 * q^72 - 9478833007778008309161031802868345211524 * q^73 - 27541253478673911633527410341566352457728 * q^74 + 55503132748045488211550409222557144224168 * q^75 + 12861632697326600661302622767095429988352 * q^76 - 6906108671572285429766593587660322848792 * q^77 + 24738215106394581682080430805395691274240 * q^78 + 13951895275060241802227058786665972744064 * q^79 + 21307190177927804427139631088328796798976 * q^80 - 212409481320219330710102337846447562488314 * q^81 - 81749275542026575038297690065457628839936 * q^82 - 502154910435404229689941892541408044858856 * q^83 - 14464115400891398663089509741465322913792 * q^84 - 1000746630485747513730682155323702476554936 * q^85 - 903854849711554559204024291704537098485760 * q^86 - 2690709214665092528127861704935698013155472 * q^87 - 114041860661530629620364544717175912398848 * q^88 - 856940390846180859846255318363956366936580 * q^89 - 2648831714731776315233426009693110522609664 * q^90 - 1493261369426503449082730790844060674911964 * q^91 - 607764881590060779676512179203114769842176 * q^92 - 4154098765617263344275692549676994999091040 * q^93 + 1645803019390757926046636674566713254084608 * q^94 + 2655639101562245253717328091596898746886880 * q^95 - 238848635546480316245034880865861367758848 * q^96 - 213479928900084648762297914406854395008372 * q^97 - 3925534873919955618355964922417604290674688 * q^98 - 32120028965593175956683290170081167190685368 * q^99

Introduction

L-functions

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