LMFDB - Embedded newform 23.18.a.a.1.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [23,18,Mod(1,23)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(23, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0]))

N = Newforms(chi, 18, names="a")

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

chi := DirichletCharacter("23.1");

S:= CuspForms(chi, 18);

N := Newforms(S);

Level:	$ N $	$=$	$ 23 $
Weight:	$ k $	$=$	$ 18 $
Character orbit:	$[\chi]$	$=$	23.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	yes
Analytic conductor:	$42.1410800892$
Analytic rank:	$1$
Dimension:	$14$
Coefficient field:	$\mathbb{Q}[x]/(x^{14} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{14} - 327680 x^{12} - 2885829 x^{11} + 40317445636 x^{10} + 536194434472 x^{9} + \cdots + 12\!\cdots\!92 $ x^14 - 327680x^12 - 2885829x^11 + 40317445636x^10 + 536194434472x^9 - 2300019484636976x^8 - 30461644509683376x^7 + 60510672631444445504x^6 + 637677963007481584640x^5 - 633979316201323448274944x^4 - 10096979557697212773105664x^3 + 2069146574976541180680732672x^2 + 62007390478567900843052367872x + 124088176545413917176959598592
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	multiple of $ 2^{33}\cdot 3^{12} $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.5
Root			$120.434$ of defining polynomial
Character	$\chi$	$=$	23.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-240.868 q^{2} -3749.07 q^{3} -73054.7 q^{4} +725316. q^{5} +903030. q^{6} -1.21078e7 q^{7} +4.91676e7 q^{8} -1.15085e8 q^{9} +O(q^{10})$	\(q-240.868 q^{2} -3749.07 q^{3} -73054.7 q^{4} +725316. q^{5} +903030. q^{6} -1.21078e7 q^{7} +4.91676e7 q^{8} -1.15085e8 q^{9} -1.74705e8 q^{10} +2.04526e8 q^{11} +2.73887e8 q^{12} +4.29941e8 q^{13} +2.91639e9 q^{14} -2.71926e9 q^{15} -2.26746e9 q^{16} +2.77767e10 q^{17} +2.77202e10 q^{18} +7.24724e10 q^{19} -5.29877e10 q^{20} +4.53931e10 q^{21} -4.92638e10 q^{22} -7.83110e10 q^{23} -1.84332e11 q^{24} -2.36856e11 q^{25} -1.03559e11 q^{26} +9.15615e11 q^{27} +8.84534e11 q^{28} +3.36022e12 q^{29} +6.54982e11 q^{30} +3.72356e12 q^{31} -5.89833e12 q^{32} -7.66782e11 q^{33} -6.69052e12 q^{34} -8.78201e12 q^{35} +8.40747e12 q^{36} -7.49011e11 q^{37} -1.74563e13 q^{38} -1.61188e12 q^{39} +3.56620e13 q^{40} -6.28604e13 q^{41} -1.09337e13 q^{42} -6.85390e13 q^{43} -1.49416e13 q^{44} -8.34728e13 q^{45} +1.88626e13 q^{46} -1.78619e14 q^{47} +8.50088e12 q^{48} -8.60308e13 q^{49} +5.70509e13 q^{50} -1.04137e14 q^{51} -3.14092e13 q^{52} -3.64188e14 q^{53} -2.20542e14 q^{54} +1.48346e14 q^{55} -5.95313e14 q^{56} -2.71704e14 q^{57} -8.09370e14 q^{58} -9.51304e14 q^{59} +1.98655e14 q^{60} -2.09516e14 q^{61} -8.96885e14 q^{62} +1.39343e15 q^{63} +1.71792e15 q^{64} +3.11843e14 q^{65} +1.84693e14 q^{66} +3.63986e15 q^{67} -2.02922e15 q^{68} +2.93593e14 q^{69} +2.11530e15 q^{70} -9.01826e15 q^{71} -5.65843e15 q^{72} -2.95286e14 q^{73} +1.80413e14 q^{74} +8.87987e14 q^{75} -5.29444e15 q^{76} -2.47637e15 q^{77} +3.88250e14 q^{78} -1.30379e15 q^{79} -1.64463e15 q^{80} +1.14293e16 q^{81} +1.51410e16 q^{82} +1.28978e16 q^{83} -3.31618e15 q^{84} +2.01469e16 q^{85} +1.65088e16 q^{86} -1.25977e16 q^{87} +1.00560e16 q^{88} +9.13793e15 q^{89} +2.01059e16 q^{90} -5.20566e15 q^{91} +5.72098e15 q^{92} -1.39599e16 q^{93} +4.30237e16 q^{94} +5.25654e16 q^{95} +2.21132e16 q^{96} +8.55512e16 q^{97} +2.07221e16 q^{98} -2.35378e16 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 14 q - 10640 q^{3} + 786432 q^{4} - 363048 q^{5} - 2333030 q^{6} - 39649066 q^{7} - 69259896 q^{8} + 796129528 q^{9}+O(q^{10}) $ 14 * q - 10640 * q^3 + 786432 * q^4 - 363048 * q^5 - 2333030 * q^6 - 39649066 * q^7 - 69259896 * q^8 + 796129528 * q^9	\( 14 q - 10640 q^{3} + 786432 q^{4} - 363048 q^{5} - 2333030 q^{6} - 39649066 q^{7} - 69259896 q^{8} + 796129528 q^{9} - 312719540 q^{10} - 45399620 q^{11} - 8621310628 q^{12} - 10510197306 q^{13} - 12286634640 q^{14} - 16443659490 q^{15} + 65383333632 q^{16} - 35705720330 q^{17} + 27658188862 q^{18} - 84895273414 q^{19} + 331348024336 q^{20} + 185190266362 q^{21} + 270540900120 q^{22} - 1096353793934 q^{23} + 1697198124384 q^{24} + 525715171346 q^{25} + 4272672484934 q^{26} - 3706093330604 q^{27} - 9883598189096 q^{28} - 4114009788386 q^{29} - 14194804268004 q^{30} + 3718266369468 q^{31} - 29197309605632 q^{32} - 16110579243626 q^{33} - 31423174598564 q^{34} + 13804822380504 q^{35} + 51950006703548 q^{36} - 58067881808868 q^{37} - 76590705469880 q^{38} + 69866971570764 q^{39} - 129282722434320 q^{40} - 74370388815170 q^{41} - 430581394397552 q^{42} - 127444248270174 q^{43} - 563872902913048 q^{44} - 602432292081270 q^{45} - 749727107945564 q^{47} - 17\!\cdots\!72 q^{48}+ \cdots + 35\!\cdots\!38 q^{99}+O(q^{100}) \) 14 * q - 10640 * q^3 + 786432 * q^4 - 363048 * q^5 - 2333030 * q^6 - 39649066 * q^7 - 69259896 * q^8 + 796129528 * q^9 - 312719540 * q^10 - 45399620 * q^11 - 8621310628 * q^12 - 10510197306 * q^13 - 12286634640 * q^14 - 16443659490 * q^15 + 65383333632 * q^16 - 35705720330 * q^17 + 27658188862 * q^18 - 84895273414 * q^19 + 331348024336 * q^20 + 185190266362 * q^21 + 270540900120 * q^22 - 1096353793934 * q^23 + 1697198124384 * q^24 + 525715171346 * q^25 + 4272672484934 * q^26 - 3706093330604 * q^27 - 9883598189096 * q^28 - 4114009788386 * q^29 - 14194804268004 * q^30 + 3718266369468 * q^31 - 29197309605632 * q^32 - 16110579243626 * q^33 - 31423174598564 * q^34 + 13804822380504 * q^35 + 51950006703548 * q^36 - 58067881808868 * q^37 - 76590705469880 * q^38 + 69866971570764 * q^39 - 129282722434320 * q^40 - 74370388815170 * q^41 - 430581394397552 * q^42 - 127444248270174 * q^43 - 563872902913048 * q^44 - 602432292081270 * q^45 - 749727107945564 * q^47 - 1762369490938672 * q^48 - 560241909258462 * q^49 - 1212733967351616 * q^50 - 2013927378521294 * q^51 - 3438555393950964 * q^52 - 1954645162253818 * q^53 - 2748549190422938 * q^54 - 2426218557075404 * q^55 - 1321001371084560 * q^56 - 2335835167092904 * q^57 - 340295461037046 * q^58 - 1561709417167508 * q^59 - 7486616247365616 * q^60 - 679115861109266 * q^61 - 12552327168177062 * q^62 - 10591353756704576 * q^63 - 6775416249353536 * q^64 - 6252697705990982 * q^65 - 20881430274671372 * q^66 - 7577612038827396 * q^67 + 2901964856169680 * q^68 + 833228883389840 * q^69 - 10700966230255240 * q^70 + 25039332312392368 * q^71 - 7954969753997256 * q^72 - 18720848443128734 * q^73 - 6297551300657404 * q^74 + 22553223201966436 * q^75 + 34141945529937952 * q^76 + 35092380107507048 * q^77 + 27963841408286022 * q^78 + 965348846593408 * q^79 + 36943919850262880 * q^80 + 51275234750545798 * q^81 + 106728632435914846 * q^82 + 65089411455584544 * q^83 + 189770883431502392 * q^84 + 20919534362994588 * q^85 + 86205449672049764 * q^86 + 130649890213719716 * q^87 + 164304846335490592 * q^88 - 61322357257717500 * q^89 + 237420523836214152 * q^90 + 181977537844157150 * q^91 - 61586264776507392 * q^92 - 71304974484877430 * q^93 - 14005510384703054 * q^94 + 123323286964112684 * q^95 + 566787465801380768 * q^96 - 67350702995984898 * q^97 + 134333537201072600 * q^98 + 353912447692290838 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−240.868	−0.665310	−0.332655	−	0.943049i	$-0.607944\pi$
$2$	−240.868	−0.665310	−0.332655	+	0.943049i	$0.607944\pi$
$3$	−3749.07	−0.329908	−0.164954	−	0.986301i	$-0.552748\pi$
$3$	−3749.07	−0.329908	−0.164954	+	0.986301i	$0.552748\pi$
$4$	−73054.7	−0.557363
$5$	725316.	0.830391	0.415195	−	0.909732i	$-0.363713\pi$
$5$	725316.	0.830391	0.415195	+	0.909732i	$0.363713\pi$
$6$	903030.	0.219491
$7$	−1.21078e7	−0.793840	−0.396920	−	0.917853i	$-0.629921\pi$
$7$	−1.21078e7	−0.793840	−0.396920	+	0.917853i	$0.629921\pi$
$8$	4.91676e7	1.03613
$9$	−1.15085e8	−0.891161
$10$	−1.74705e8	−0.552467
$11$	2.04526e8	0.287681	0.143840	−	0.989601i	$-0.454055\pi$
$11$	2.04526e8	0.287681	0.143840	+	0.989601i	$0.454055\pi$
$12$	2.73887e8	0.183878
$13$	4.29941e8	0.146181	0.0730904	−	0.997325i	$-0.476714\pi$
$13$	4.29941e8	0.146181	0.0730904	+	0.997325i	$0.476714\pi$
$14$	2.91639e9	0.528150
$15$	−2.71926e9	−0.273952
$16$	−2.26746e9	−0.131984
$17$	2.77767e10	0.965752	0.482876	−	0.875689i	$-0.339592\pi$
$17$	2.77767e10	0.965752	0.482876	+	0.875689i	$0.339592\pi$
$18$	2.77202e10	0.592898
$19$	7.24724e10	0.978964	0.489482	−	0.872013i	$-0.337186\pi$
$19$	7.24724e10	0.978964	0.489482	+	0.872013i	$0.337186\pi$
$20$	−5.29877e10	−0.462829
$21$	4.53931e10	0.261894
$22$	−4.92638e10	−0.191397
$23$	−7.83110e10	−0.208514
$23$	−7.83110e10	−0.208514
$24$	−1.84332e11	−0.341827
$25$	−2.36856e11	−0.310451
$26$	−1.03559e11	−0.0972556
$27$	9.15615e11	0.623909
$28$	8.84534e11	0.442457
$29$	3.36022e12	1.24734	0.623670	−	0.781687i	$-0.285641\pi$
$29$	3.36022e12	1.24734	0.623670	+	0.781687i	$0.285641\pi$
$30$	6.54982e11	0.182263
$31$	3.72356e12	0.784122	0.392061	−	0.919939i	$-0.371762\pi$
$31$	3.72356e12	0.784122	0.392061	+	0.919939i	$0.371762\pi$
$32$	−5.89833e12	−0.948319
$33$	−7.66782e11	−0.0949081
$34$	−6.69052e12	−0.642524
$35$	−8.78201e12	−0.659198
$36$	8.40747e12	0.496700
$37$	−7.49011e11	−0.0350569	−0.0175285	−	0.999846i	$-0.505580\pi$
$37$	−7.49011e11	−0.0350569	−0.0175285	+	0.999846i	$0.505580\pi$
$38$	−1.74563e13	−0.651315
$39$	−1.61188e12	−0.0482262
$40$	3.56620e13	0.860392
$41$	−6.28604e13	−1.22946	−0.614730	−	0.788738i	$-0.710735\pi$
$41$	−6.28604e13	−1.22946	−0.614730	+	0.788738i	$0.710735\pi$
$42$	−1.09337e13	−0.174241
$43$	−6.85390e13	−0.894244	−0.447122	−	0.894473i	$-0.647551\pi$
$43$	−6.85390e13	−0.894244	−0.447122	+	0.894473i	$0.647551\pi$
$44$	−1.49416e13	−0.160343
$45$	−8.34728e13	−0.740012
$46$	1.88626e13	0.138727
$47$	−1.78619e14	−1.09420	−0.547100	−	0.837067i	$-0.684268\pi$
$47$	−1.78619e14	−1.09420	−0.547100	+	0.837067i	$0.684268\pi$
$48$	8.50088e12	0.0435425
$49$	−8.60308e13	−0.369817
$50$	5.70509e13	0.206546
$51$	−1.04137e14	−0.318609
$52$	−3.14092e13	−0.0814758
$53$	−3.64188e14	−0.803491	−0.401746	−	0.915751i	$-0.631596\pi$
$53$	−3.64188e14	−0.803491	−0.401746	+	0.915751i	$0.631596\pi$
$54$	−2.20542e14	−0.415093
$55$	1.48346e14	0.238887
$56$	−5.95313e14	−0.822521
$57$	−2.71704e14	−0.322968
$58$	−8.09370e14	−0.829868
$59$	−9.51304e14	−0.843485	−0.421743	−	0.906716i	$-0.638581\pi$
$59$	−9.51304e14	−0.843485	−0.421743	+	0.906716i	$0.638581\pi$
$60$	1.98655e14	0.152691
$61$	−2.09516e14	−0.139931	−0.0699655	−	0.997549i	$-0.522289\pi$
$61$	−2.09516e14	−0.139931	−0.0699655	+	0.997549i	$0.522289\pi$
$62$	−8.96885e14	−0.521684
$63$	1.39343e15	0.707439
$64$	1.71792e15	0.762910
$65$	3.11843e14	0.121387
$66$	1.84693e14	0.0631433
$67$	3.63986e15	1.09509	0.547543	−	0.836777i	$-0.315563\pi$
$67$	3.63986e15	1.09509	0.547543	+	0.836777i	$0.315563\pi$
$68$	−2.02922e15	−0.538274
$69$	2.93593e14	0.0687905
$70$	2.11530e15	0.438571
$71$	−9.01826e15	−1.65740	−0.828699	−	0.559695i	$-0.810918\pi$
$71$	−9.01826e15	−1.65740	−0.828699	+	0.559695i	$0.810918\pi$
$72$	−5.65843e15	−0.923357
$73$	−2.95286e14	−0.0428548	−0.0214274	−	0.999770i	$-0.506821\pi$
$73$	−2.95286e14	−0.0428548	−0.0214274	+	0.999770i	$0.506821\pi$
$74$	1.80413e14	0.0233237
$75$	8.87987e14	0.102420
$76$	−5.29444e15	−0.545638
$77$	−2.47637e15	−0.228373
$78$	3.88250e14	0.0320854
$79$	−1.30379e15	−0.0966890	−0.0483445	−	0.998831i	$-0.515395\pi$
$79$	−1.30379e15	−0.0966890	−0.0483445	+	0.998831i	$0.515395\pi$
$80$	−1.64463e15	−0.109598
$81$	1.14293e16	0.685329
$82$	1.51410e16	0.817971
$83$	1.28978e16	0.628566	0.314283	−	0.949329i	$-0.398236\pi$
$83$	1.28978e16	0.628566	0.314283	+	0.949329i	$0.398236\pi$
$84$	−3.31618e15	−0.145970
$85$	2.01469e16	0.801951
$86$	1.65088e16	0.594949
$87$	−1.25977e16	−0.411507
$88$	1.00560e16	0.298074
$89$	9.13793e15	0.246055	0.123028	−	0.992403i	$-0.460740\pi$
$89$	9.13793e15	0.246055	0.123028	+	0.992403i	$0.460740\pi$
$90$	2.01059e16	0.492337
$91$	−5.20566e15	−0.116044
$92$	5.72098e15	0.116218
$93$	−1.39599e16	−0.258688
$94$	4.30237e16	0.727982
$95$	5.25654e16	0.812923
$96$	2.21132e16	0.312858
$97$	8.55512e16	1.10832	0.554162	−	0.832409i	$-0.313039\pi$
$97$	8.55512e16	1.10832	0.554162	+	0.832409i	$0.313039\pi$
$98$	2.07221e16	0.246043
$99$	−2.35378e16	−0.256370
$100$	1.73034e16	0.173034
$101$	−6.72575e16	−0.618029	−0.309014	−	0.951057i	$-0.599999\pi$
$101$	−6.72575e16	−0.618029	−0.309014	+	0.951057i	$0.599999\pi$
$102$	2.50832e16	0.211974
$103$	−5.29933e16	−0.412197	−0.206098	−	0.978531i	$-0.566077\pi$
$103$	−5.29933e16	−0.412197	−0.206098	+	0.978531i	$0.566077\pi$
$104$	2.11392e16	0.151462
$105$	3.29243e16	0.217474
$106$	8.77213e16	0.534571
$107$	−1.73351e17	−0.975357	−0.487679	−	0.873023i	$-0.662156\pi$
$107$	−1.73351e17	−0.975357	−0.487679	+	0.873023i	$0.662156\pi$
$108$	−6.68900e16	−0.347743
$109$	−2.26491e17	−1.08874	−0.544372	−	0.838844i	$-0.683232\pi$
$109$	−2.26491e17	−1.08874	−0.544372	+	0.838844i	$0.683232\pi$
$110$	−3.57318e16	−0.158934
$111$	2.80809e15	0.0115655
$112$	2.74541e16	0.104774
$113$	−1.35866e17	−0.480776	−0.240388	−	0.970677i	$-0.577275\pi$
$113$	−1.35866e17	−0.480776	−0.240388	+	0.970677i	$0.577275\pi$
$114$	6.54447e16	0.214874
$115$	−5.68002e16	−0.173148
$116$	−2.45480e17	−0.695221
$117$	−4.94796e16	−0.130271
$118$	2.29139e17	0.561179
$119$	−3.36316e17	−0.766653
$120$	−1.33699e17	−0.283850
$121$	−4.63616e17	−0.917240
$122$	5.04657e16	0.0930975
$123$	2.35668e17	0.405608
$124$	−2.72023e17	−0.437040
$125$	−7.25168e17	−1.08819
$126$	−3.35632e17	−0.470666
$127$	1.11899e17	0.146722	0.0733612	−	0.997305i	$-0.476627\pi$
$127$	1.11899e17	0.146722	0.0733612	+	0.997305i	$0.476627\pi$
$128$	3.59314e17	0.440747
$129$	2.56957e17	0.295018
$130$	−7.51130e16	−0.0807601
$131$	1.54202e18	1.55340	0.776702	−	0.629869i	$-0.216891\pi$
$131$	1.54202e18	1.55340	0.776702	+	0.629869i	$0.216891\pi$
$132$	5.60170e16	0.0528983
$133$	−8.77483e17	−0.777141
$134$	−8.76725e17	−0.728572
$135$	6.64111e17	0.518088
$136$	1.36571e18	1.00064
$137$	−1.66209e18	−1.14427	−0.572137	−	0.820158i	$-0.693885\pi$
$137$	−1.66209e18	−1.14427	−0.572137	+	0.820158i	$0.693885\pi$
$138$	−7.07171e16	−0.0457670
$139$	−2.49028e18	−1.51573	−0.757865	−	0.652412i	$-0.773757\pi$
$139$	−2.49028e18	−1.51573	−0.757865	+	0.652412i	$0.773757\pi$
$140$	6.41567e17	0.367412
$141$	6.69656e17	0.360985
$142$	2.17221e18	1.10268
$143$	8.79342e16	0.0420534
$144$	2.60950e17	0.117619
$145$	2.43722e18	1.03578
$146$	7.11250e16	0.0285117
$147$	3.22535e17	0.122006
$148$	5.47188e16	0.0195394
$149$	−2.52545e18	−0.851640	−0.425820	−	0.904808i	$-0.640014\pi$
$149$	−2.52545e18	−0.851640	−0.425820	+	0.904808i	$0.640014\pi$
$150$	−2.13888e17	−0.0681412
$151$	5.29488e18	1.59423	0.797116	−	0.603826i	$-0.206358\pi$
$151$	5.29488e18	1.59423	0.797116	+	0.603826i	$0.206358\pi$
$152$	3.56329e18	1.01433
$153$	−3.19668e18	−0.860640
$154$	5.96478e17	0.151939
$155$	2.70076e18	0.651127
$156$	1.17755e17	0.0268795
$157$	1.21176e18	0.261982	0.130991	−	0.991384i	$-0.458184\pi$
$157$	1.21176e18	0.261982	0.130991	+	0.991384i	$0.458184\pi$
$158$	3.14041e17	0.0643281
$159$	1.36537e18	0.265078
$160$	−4.27816e18	−0.787475
$161$	9.48177e17	0.165527
$162$	−2.75296e18	−0.455956
$163$	−2.28216e18	−0.358717	−0.179359	−	0.983784i	$-0.557402\pi$
$163$	−2.28216e18	−0.358717	−0.179359	+	0.983784i	$0.557402\pi$
$164$	4.59224e18	0.685255
$165$	−5.56160e17	−0.0788108
$166$	−3.10666e18	−0.418191
$167$	8.68868e18	1.11138	0.555692	−	0.831388i	$-0.312454\pi$
$167$	8.68868e18	1.11138	0.555692	+	0.831388i	$0.312454\pi$
$168$	2.23187e18	0.271356
$169$	−8.46557e18	−0.978631
$170$	−4.85275e18	−0.533546
$171$	−8.34046e18	−0.872415
$172$	5.00709e18	0.498418
$173$	8.08324e18	0.765938	0.382969	−	0.923761i	$-0.374902\pi$
$173$	8.08324e18	0.765938	0.382969	+	0.923761i	$0.374902\pi$
$174$	3.03438e18	0.273780
$175$	2.86781e18	0.246449
$176$	−4.63756e17	−0.0379692
$177$	3.56650e18	0.278272
$178$	−2.20103e18	−0.163703
$179$	−1.20973e19	−0.857900	−0.428950	−	0.903328i	$-0.641116\pi$
$179$	−1.20973e19	−0.857900	−0.428950	+	0.903328i	$0.641116\pi$
$180$	6.09808e18	0.412455
$181$	−6.17261e18	−0.398291	−0.199146	−	0.979970i	$-0.563817\pi$
$181$	−6.17261e18	−0.398291	−0.199146	+	0.979970i	$0.563817\pi$
$182$	1.25388e18	0.0772054
$183$	7.85490e17	0.0461643
$184$	−3.85036e18	−0.216048
$185$	−5.43270e17	−0.0291109
$186$	3.36248e18	0.172108
$187$	5.68107e18	0.277828
$188$	1.30490e19	0.609866
$189$	−1.10861e19	−0.495284
$190$	−1.26613e19	−0.540845
$191$	2.42959e19	0.992543	0.496272	−	0.868167i	$-0.334702\pi$
$191$	2.42959e19	0.992543	0.496272	+	0.868167i	$0.334702\pi$
$192$	−6.44059e18	−0.251690
$193$	−3.91626e19	−1.46431	−0.732157	−	0.681136i	$-0.761486\pi$
$193$	−3.91626e19	−1.46431	−0.732157	+	0.681136i	$0.761486\pi$
$194$	−2.06065e19	−0.737378
$195$	−1.16912e18	−0.0400466
$196$	6.28495e18	0.206123
$197$	9.72433e16	0.00305420	0.00152710	−	0.999999i	$-0.499514\pi$
$197$	9.72433e16	0.00305420	0.00152710	+	0.999999i	$0.499514\pi$
$198$	5.66950e18	0.170565
$199$	−4.68558e19	−1.35056	−0.675278	−	0.737563i	$-0.735976\pi$
$199$	−4.68558e19	−1.35056	−0.675278	+	0.737563i	$0.735976\pi$
$200$	−1.16456e19	−0.321668
$201$	−1.36461e19	−0.361278
$202$	1.62002e19	0.411181
$203$	−4.06850e19	−0.990190
$204$	7.60768e18	0.177581
$205$	−4.55937e19	−1.02093
$206$	1.27644e19	0.274239
$207$	9.01239e18	0.185820
$208$	−9.74876e17	−0.0192935
$209$	1.48225e19	0.281629
$210$	−7.93042e18	−0.144688
$211$	3.24597e19	0.568779	0.284390	−	0.958709i	$-0.408209\pi$
$211$	3.24597e19	0.568779	0.284390	+	0.958709i	$0.408209\pi$
$212$	2.66057e19	0.447836
$213$	3.38101e19	0.546788
$214$	4.17546e19	0.648915
$215$	−4.97125e19	−0.742572
$216$	4.50186e19	0.646450
$217$	−4.50842e19	−0.622468
$218$	5.45544e19	0.724352
$219$	1.10705e18	0.0141381
$220$	−1.08374e19	−0.133147
$221$	1.19424e19	0.141174
$222$	−6.76379e17	−0.00769467
$223$	−1.09544e20	−1.19950	−0.599748	−	0.800189i	$-0.704733\pi$
$223$	−1.09544e20	−1.19950	−0.599748	+	0.800189i	$0.704733\pi$
$224$	7.14160e19	0.752814
$225$	2.72584e19	0.276662
$226$	3.27257e19	0.319865
$227$	1.57840e18	0.0148593	0.00742965	−	0.999972i	$-0.497635\pi$
$227$	1.57840e18	0.0148593	0.00742965	+	0.999972i	$0.497635\pi$
$228$	1.98492e19	0.180010
$229$	1.39739e20	1.22100	0.610502	−	0.792015i	$-0.290968\pi$
$229$	1.39739e20	1.22100	0.610502	+	0.792015i	$0.290968\pi$
$230$	1.36814e19	0.115197
$231$	9.28407e18	0.0753419
$232$	1.65214e20	1.29241
$233$	−1.63310e20	−1.23165	−0.615827	−	0.787882i	$-0.711178\pi$
$233$	−1.63310e20	−1.23165	−0.615827	+	0.787882i	$0.711178\pi$
$234$	1.19181e19	0.0866703
$235$	−1.29555e20	−0.908613
$236$	6.94972e19	0.470127
$237$	4.88799e18	0.0318984
$238$	8.10078e19	0.510061
$239$	1.86882e20	1.13549	0.567747	−	0.823203i	$-0.307815\pi$
$239$	1.86882e20	1.13549	0.567747	+	0.823203i	$0.307815\pi$
$240$	6.16582e18	0.0361573
$241$	1.95578e20	1.10707	0.553534	−	0.832826i	$-0.313279\pi$
$241$	1.95578e20	1.10707	0.553534	+	0.832826i	$0.313279\pi$
$242$	1.11670e20	0.610249
$243$	−1.61092e20	−0.850004
$244$	1.53061e19	0.0779924
$245$	−6.23996e19	−0.307093
$246$	−5.67648e19	−0.269855
$247$	3.11588e19	0.143106
$248$	1.83078e20	0.812451
$249$	−4.83546e19	−0.207369
$250$	1.74670e20	0.723981
$251$	1.53897e20	0.616601	0.308300	−	0.951289i	$-0.400240\pi$
$251$	1.53897e20	0.616601	0.308300	+	0.951289i	$0.400240\pi$
$252$	−1.01796e20	−0.394300
$253$	−1.60166e19	−0.0599856
$254$	−2.69530e19	−0.0976158
$255$	−7.55322e19	−0.264570
$256$	−3.11718e20	−1.05614
$257$	−3.77561e20	−1.23753	−0.618765	−	0.785576i	$-0.712367\pi$
$257$	−3.77561e20	−1.23753	−0.618765	+	0.785576i	$0.712367\pi$
$258$	−6.18928e19	−0.196278
$259$	9.06890e18	0.0278296
$260$	−2.27816e19	−0.0676567
$261$	−3.86710e20	−1.11158
$262$	−3.71423e20	−1.03349
$263$	4.07812e20	1.09859	0.549295	−	0.835628i	$-0.314896\pi$
$263$	4.07812e20	1.09859	0.549295	+	0.835628i	$0.314896\pi$
$264$	−3.77008e19	−0.0983370
$265$	−2.64152e20	−0.667212
$266$	2.11358e20	0.517040
$267$	−3.42587e19	−0.0811756
$268$	−2.65909e20	−0.610361
$269$	−6.25888e20	−1.39188	−0.695940	−	0.718100i	$-0.745012\pi$
$269$	−6.25888e20	−1.39188	−0.695940	+	0.718100i	$0.745012\pi$
$270$	−1.59963e20	−0.344689
$271$	−4.21658e20	−0.880485	−0.440242	−	0.897879i	$-0.645107\pi$
$271$	−4.21658e20	−0.880485	−0.440242	+	0.897879i	$0.645107\pi$
$272$	−6.29828e19	−0.127464
$273$	1.95164e19	0.0382839
$274$	4.00344e20	0.761296
$275$	−4.84432e19	−0.0893109
$276$	−2.14483e19	−0.0383413
$277$	−2.31217e20	−0.400813	−0.200406	−	0.979713i	$-0.564226\pi$
$277$	−2.31217e20	−0.400813	−0.200406	+	0.979713i	$0.564226\pi$
$278$	5.99827e20	1.00843
$279$	−4.28524e20	−0.698779
$280$	−4.31790e20	−0.683014
$281$	9.31287e20	1.42916	0.714578	−	0.699556i	$-0.246619\pi$
$281$	9.31287e20	1.42916	0.714578	+	0.699556i	$0.246619\pi$
$282$	−1.61299e20	−0.240167
$283$	−4.17098e19	−0.0602633	−0.0301317	−	0.999546i	$-0.509593\pi$
$283$	−4.17098e19	−0.0602633	−0.0301317	+	0.999546i	$0.509593\pi$
$284$	6.58826e20	0.923772
$285$	−1.97071e20	−0.268189
$286$	−2.11805e19	−0.0279786
$287$	7.61103e20	0.975995
$288$	6.78807e20	0.845105
$289$	−5.56931e19	−0.0673240
$290$	−5.87049e20	−0.689115
$291$	−3.20737e20	−0.365644
$292$	2.15720e19	0.0238857
$293$	3.58362e20	0.385432	0.192716	−	0.981255i	$-0.438270\pi$
$293$	3.58362e20	0.385432	0.192716	+	0.981255i	$0.438270\pi$
$294$	−7.76884e19	−0.0811716
$295$	−6.89997e20	−0.700422
$296$	−3.68270e19	−0.0363235
$297$	1.87267e20	0.179487
$298$	6.08301e20	0.566605
$299$	−3.36691e19	−0.0304808
$300$	−6.48716e19	−0.0570853
$301$	8.29859e20	0.709887
$302$	−1.27537e21	−1.06066
$303$	2.52153e20	0.203893
$304$	−1.64329e20	−0.129207
$305$	−1.51966e20	−0.116197
$306$	7.69977e20	0.572592
$307$	4.97471e20	0.359825	0.179913	−	0.983683i	$-0.442418\pi$
$307$	4.97471e20	0.359825	0.179913	+	0.983683i	$0.442418\pi$
$308$	1.80910e20	0.127286
$309$	1.98675e20	0.135987
$310$	−6.50526e20	−0.433202
$311$	−2.40131e20	−0.155591	−0.0777955	−	0.996969i	$-0.524788\pi$
$311$	−2.40131e20	−0.155591	−0.0777955	+	0.996969i	$0.524788\pi$
$312$	−7.92521e19	−0.0499685
$313$	1.96632e21	1.20650	0.603251	−	0.797552i	$-0.293872\pi$
$313$	1.96632e21	1.20650	0.603251	+	0.797552i	$0.293872\pi$
$314$	−2.91875e20	−0.174299
$315$	1.01067e21	0.587451
$316$	9.52479e19	0.0538908
$317$	−1.95106e21	−1.07465	−0.537326	−	0.843375i	$-0.680566\pi$
$317$	−1.95106e21	−1.07465	−0.537326	+	0.843375i	$0.680566\pi$
$318$	−3.28873e20	−0.176359
$319$	6.87253e20	0.358836
$320$	1.24604e21	0.633513
$321$	6.49904e20	0.321778
$322$	−2.28385e20	−0.110127
$323$	2.01305e21	0.945436
$324$	−8.34967e20	−0.381977
$325$	−1.01834e20	−0.0453820
$326$	5.49700e20	0.238658
$327$	8.49129e20	0.359185
$328$	−3.09069e21	−1.27388
$329$	2.16269e21	0.868620
$330$	1.33961e20	0.0524336
$331$	−2.14480e21	−0.818179	−0.409090	−	0.912494i	$-0.634154\pi$
$331$	−2.14480e21	−0.818179	−0.409090	+	0.912494i	$0.634154\pi$
$332$	−9.42242e20	−0.350339
$333$	8.61997e19	0.0312413
$334$	−2.09282e21	−0.739414
$335$	2.64005e21	0.909350
$336$	−1.02927e20	−0.0345658
$337$	3.12133e21	1.02208	0.511040	−	0.859557i	$-0.329260\pi$
$337$	3.12133e21	1.02208	0.511040	+	0.859557i	$0.329260\pi$
$338$	2.03908e21	0.651093
$339$	5.09369e20	0.158612
$340$	−1.47183e21	−0.446978
$341$	7.61565e20	0.225577
$342$	2.00895e21	0.580426
$343$	3.85830e21	1.08742
$344$	−3.36989e21	−0.926552
$345$	2.12948e20	0.0571230
$346$	−1.94699e21	−0.509586
$347$	−2.95269e20	−0.0754080	−0.0377040	−	0.999289i	$-0.512004\pi$
$347$	−2.95269e20	−0.0754080	−0.0377040	+	0.999289i	$0.512004\pi$
$348$	9.20321e20	0.229359
$349$	−7.11356e20	−0.173010	−0.0865049	−	0.996251i	$-0.527570\pi$
$349$	−7.11356e20	−0.173010	−0.0865049	+	0.996251i	$0.527570\pi$
$350$	−6.90763e20	−0.163965
$351$	3.93661e20	0.0912035
$352$	−1.20636e21	−0.272813
$353$	−6.58820e21	−1.45439	−0.727197	−	0.686429i	$-0.759177\pi$
$353$	−6.58820e21	−1.45439	−0.727197	+	0.686429i	$0.759177\pi$
$354$	−8.59056e20	−0.185137
$355$	−6.54109e21	−1.37629
$356$	−6.67569e20	−0.137142
$357$	1.26087e21	0.252925
$358$	2.91384e21	0.570769
$359$	−6.81224e21	−1.30313	−0.651564	−	0.758594i	$-0.725887\pi$
$359$	−6.81224e21	−1.30313	−0.651564	+	0.758594i	$0.725887\pi$
$360$	−4.10415e21	−0.766747
$361$	−2.28143e20	−0.0416291
$362$	1.48678e21	0.264987
$363$	1.73813e21	0.302604
$364$	3.80297e20	0.0646788
$365$	−2.14176e20	−0.0355862
$366$	−1.89199e20	−0.0307136
$367$	2.49474e21	0.395699	0.197849	−	0.980232i	$-0.436604\pi$
$367$	2.49474e21	0.395699	0.197849	+	0.980232i	$0.436604\pi$
$368$	1.77567e20	0.0275205
$369$	7.23427e21	1.09565
$370$	1.30856e20	0.0193678
$371$	4.40953e21	0.637844
$372$	1.01983e21	0.144183
$373$	−3.45963e21	−0.478084	−0.239042	−	0.971009i	$-0.576833\pi$
$373$	−3.45963e21	−0.478084	−0.239042	+	0.971009i	$0.576833\pi$
$374$	−1.36839e21	−0.184842
$375$	2.71870e21	0.359001
$376$	−8.78227e21	−1.13373
$377$	1.44470e21	0.182337
$378$	2.67029e21	0.329517
$379$	−4.94430e21	−0.596584	−0.298292	−	0.954475i	$-0.596417\pi$
$379$	−4.94430e21	−0.596584	−0.298292	+	0.954475i	$0.596417\pi$
$380$	−3.84015e21	−0.453093
$381$	−4.19519e20	−0.0484048
$382$	−5.85210e21	−0.660349
$383$	−3.13187e21	−0.345632	−0.172816	−	0.984954i	$-0.555287\pi$
$383$	−3.13187e21	−0.345632	−0.172816	+	0.984954i	$0.555287\pi$
$384$	−1.34709e21	−0.145406
$385$	−1.79615e21	−0.189639
$386$	9.43301e21	0.974222
$387$	7.88779e21	0.796915
$388$	−6.24991e21	−0.617738
$389$	−1.35692e22	−1.31215	−0.656075	−	0.754696i	$-0.727785\pi$
$389$	−1.35692e22	−1.31215	−0.656075	+	0.754696i	$0.727785\pi$
$390$	2.81604e20	0.0266434
$391$	−2.17522e21	−0.201373
$392$	−4.22993e21	−0.383179
$393$	−5.78114e21	−0.512480
$394$	−2.34228e19	−0.00203199
$395$	−9.45659e20	−0.0802896
$396$	1.71955e21	0.142891
$397$	−2.09917e21	−0.170737	−0.0853687	−	0.996349i	$-0.527207\pi$
$397$	−2.09917e21	−0.170737	−0.0853687	+	0.996349i	$0.527207\pi$
$398$	1.12861e22	0.898538
$399$	3.28974e21	0.256385
$400$	5.37062e20	0.0409746
$401$	1.95526e21	0.146042	0.0730208	−	0.997330i	$-0.476736\pi$
$401$	1.95526e21	0.146042	0.0730208	+	0.997330i	$0.476736\pi$
$402$	3.28690e21	0.240362
$403$	1.60091e21	0.114624
$404$	4.91347e21	0.344466
$405$	8.28989e21	0.569090
$406$	9.79972e21	0.658783
$407$	−1.53192e20	−0.0100852
$408$	−5.12015e21	−0.330120
$409$	1.82089e22	1.14983	0.574917	−	0.818212i	$-0.305034\pi$
$409$	1.82089e22	1.14983	0.574917	+	0.818212i	$0.305034\pi$
$410$	1.09820e22	0.679236
$411$	6.23129e21	0.377505
$412$	3.87141e21	0.229743
$413$	1.15182e22	0.669593
$414$	−2.17080e21	−0.123628
$415$	9.35496e21	0.521955
$416$	−2.53593e21	−0.138626
$417$	9.33621e21	0.500051
$418$	−3.57026e21	−0.187371
$419$	4.56779e21	0.234902	0.117451	−	0.993079i	$-0.462528\pi$
$419$	4.56779e21	0.234902	0.117451	+	0.993079i	$0.462528\pi$
$420$	−2.40528e21	−0.121212
$421$	−3.30467e22	−1.63204	−0.816019	−	0.578024i	$-0.803824\pi$
$421$	−3.30467e22	−1.63204	−0.816019	+	0.578024i	$0.803824\pi$
$422$	−7.81850e21	−0.378414
$423$	2.05563e22	0.975108
$424$	−1.79063e22	−0.832521
$425$	−6.57908e21	−0.299819
$426$	−8.14376e21	−0.363784
$427$	2.53679e21	0.111083
$428$	1.26641e22	0.543628
$429$	−3.29671e20	−0.0138737
$430$	1.19741e22	0.494040
$431$	3.18523e22	1.28850	0.644249	−	0.764816i	$-0.277170\pi$
$431$	3.18523e22	1.28850	0.644249	+	0.764816i	$0.277170\pi$
$432$	−2.07612e21	−0.0823458
$433$	3.33487e21	0.129698	0.0648489	−	0.997895i	$-0.479343\pi$
$433$	3.33487e21	0.129698	0.0648489	+	0.997895i	$0.479343\pi$
$434$	1.08593e22	0.414134
$435$	−9.13732e21	−0.341712
$436$	1.65462e22	0.606825
$437$	−5.67538e21	−0.204128
$438$	−2.66652e20	−0.00940623
$439$	8.02240e21	0.277559	0.138780	−	0.990323i	$-0.455682\pi$
$439$	8.02240e21	0.277559	0.138780	+	0.990323i	$0.455682\pi$
$440$	7.29382e21	0.247518
$441$	9.90083e21	0.329567
$442$	−2.87653e21	−0.0939247
$443$	−4.05437e22	−1.29865	−0.649324	−	0.760512i	$-0.724948\pi$
$443$	−4.05437e22	−1.29865	−0.649324	+	0.760512i	$0.724948\pi$
$444$	−2.05144e20	−0.00644620
$445$	6.62789e21	0.204322
$446$	2.63857e22	0.798037
$447$	9.46810e21	0.280963
$448$	−2.08003e22	−0.605628
$449$	4.10092e21	0.117162	0.0585811	−	0.998283i	$-0.481342\pi$
$449$	4.10092e21	0.117162	0.0585811	+	0.998283i	$0.481342\pi$
$450$	−6.56568e21	−0.184066
$451$	−1.28566e22	−0.353692
$452$	9.92561e21	0.267967
$453$	−1.98508e22	−0.525950
$454$	−3.80187e20	−0.00988603
$455$	−3.77575e21	−0.0963621
$456$	−1.33590e22	−0.334636
$457$	−4.99225e22	−1.22746	−0.613732	−	0.789515i	$-0.710332\pi$
$457$	−4.99225e22	−1.22746	−0.613732	+	0.789515i	$0.710332\pi$
$458$	−3.36587e22	−0.812346
$459$	2.54328e22	0.602541
$460$	4.14952e21	0.0965065
$461$	−4.25639e22	−0.971815	−0.485907	−	0.874010i	$-0.661511\pi$
$461$	−4.25639e22	−0.971815	−0.485907	+	0.874010i	$0.661511\pi$
$462$	−2.23623e21	−0.0501257
$463$	−7.17987e22	−1.58008	−0.790038	−	0.613058i	$-0.789939\pi$
$463$	−7.17987e22	−1.58008	−0.790038	+	0.613058i	$0.789939\pi$
$464$	−7.61919e21	−0.164629
$465$	−1.01253e22	−0.214812
$466$	3.93362e22	0.819431
$467$	−7.18268e22	−1.46924	−0.734621	−	0.678478i	$-0.762640\pi$
$467$	−7.18268e22	−1.46924	−0.734621	+	0.678478i	$0.762640\pi$
$468$	3.61472e21	0.0726080
$469$	−4.40708e22	−0.869324
$470$	3.12058e22	0.604509
$471$	−4.54299e21	−0.0864298
$472$	−4.67733e22	−0.873959
$473$	−1.40180e22	−0.257257
$474$	−1.17736e21	−0.0212223
$475$	−1.71655e22	−0.303921
$476$	2.45695e22	0.427304
$477$	4.19125e22	0.716040
$478$	−4.50138e22	−0.755455
$479$	9.73166e22	1.60448	0.802241	−	0.597000i	$-0.203641\pi$
$479$	9.73166e22	1.60448	0.802241	+	0.597000i	$0.203641\pi$
$480$	1.60391e22	0.259794
$481$	−3.22031e20	−0.00512465
$482$	−4.71084e22	−0.736544
$483$	−3.55478e21	−0.0546087
$484$	3.38693e22	0.511235
$485$	6.20517e22	0.920341
$486$	3.88019e22	0.565516
$487$	−1.03288e23	−1.47929	−0.739646	−	0.672996i	$-0.765007\pi$
$487$	−1.03288e23	−1.47929	−0.739646	+	0.672996i	$0.765007\pi$
$488$	−1.03014e22	−0.144987
$489$	8.55599e21	0.118344
$490$	1.50301e22	0.204312
$491$	8.37980e20	0.0111954	0.00559772	−	0.999984i	$-0.498218\pi$
$491$	8.37980e20	0.0111954	0.00559772	+	0.999984i	$0.498218\pi$
$492$	−1.72166e22	−0.226071
$493$	9.33360e22	1.20462
$494$	−7.50517e21	−0.0952097
$495$	−1.70724e22	−0.212887
$496$	−8.44303e21	−0.103491
$497$	1.09192e23	1.31571
$498$	1.16471e22	0.137964
$499$	−7.97873e22	−0.929136	−0.464568	−	0.885537i	$-0.653790\pi$
$499$	−7.97873e22	−0.929136	−0.464568	+	0.885537i	$0.653790\pi$
$500$	5.29769e22	0.606515
$501$	−3.25744e22	−0.366654
$502$	−3.70689e22	−0.410230
$503$	−2.98934e22	−0.325272	−0.162636	−	0.986686i	$-0.552000\pi$
$503$	−2.98934e22	−0.325272	−0.162636	+	0.986686i	$0.552000\pi$
$504$	6.85114e22	0.732998
$505$	−4.87829e22	−0.513205
$506$	3.85789e21	0.0399090
$507$	3.17380e22	0.322858
$508$	−8.17478e21	−0.0817776
$509$	1.36386e23	1.34174	0.670871	−	0.741574i	$-0.265920\pi$
$509$	1.36386e23	1.34174	0.670871	+	0.741574i	$0.265920\pi$
$510$	1.81933e22	0.176021
$511$	3.57528e21	0.0340198
$512$	2.79869e22	0.261915
$513$	6.63568e22	0.610784
$514$	9.09423e22	0.823341
$515$	−3.84369e22	−0.342284
$516$	−1.87719e22	−0.164432
$517$	−3.65323e22	−0.314780
$518$	−2.18441e21	−0.0185153
$519$	−3.03046e22	−0.252689
$520$	1.53326e22	0.125773
$521$	7.94043e21	0.0640801	0.0320401	−	0.999487i	$-0.489800\pi$
$521$	7.94043e21	0.0640801	0.0320401	+	0.999487i	$0.489800\pi$
$522$	9.31461e22	0.739546
$523$	−2.29864e22	−0.179559	−0.0897796	−	0.995962i	$-0.528616\pi$
$523$	−2.29864e22	−0.179559	−0.0897796	+	0.995962i	$0.528616\pi$
$524$	−1.12652e23	−0.865809
$525$	−1.07516e22	−0.0813054
$526$	−9.82288e22	−0.730903
$527$	1.03428e23	0.757267
$528$	1.73865e21	0.0125263
$529$	6.13261e21	0.0434783
$530$	6.36257e22	0.443902
$531$	1.09481e23	0.751681
$532$	6.41043e22	0.433150
$533$	−2.70263e22	−0.179723
$534$	8.25183e21	0.0540069
$535$	−1.25734e23	−0.809928
$536$	1.78963e23	1.13465
$537$	4.53535e22	0.283028
$538$	1.50756e23	0.926032
$539$	−1.75955e22	−0.106389
$540$	−4.85164e22	−0.288763
$541$	−3.08356e23	−1.80666	−0.903329	−	0.428949i	$-0.858884\pi$
$541$	−3.08356e23	−1.80666	−0.903329	+	0.428949i	$0.858884\pi$
$542$	1.01564e23	0.585795
$543$	2.31415e22	0.131399
$544$	−1.63836e23	−0.915840
$545$	−1.64278e23	−0.904082
$546$	−4.70086e21	−0.0254707
$547$	−2.35554e23	−1.25660	−0.628302	−	0.777969i	$-0.716250\pi$
$547$	−2.35554e23	−1.25660	−0.628302	+	0.777969i	$0.716250\pi$
$548$	1.21423e23	0.637775
$549$	2.41121e22	0.124701
$550$	1.16684e22	0.0594194
$551$	2.43523e23	1.22110
$552$	1.44353e22	0.0712758
$553$	1.57861e22	0.0767556
$554$	5.56927e22	0.266665
$555$	2.03676e21	0.00960392
$556$	1.81926e23	0.844811
$557$	−1.38996e23	−0.635673	−0.317836	−	0.948146i	$-0.602956\pi$
$557$	−1.38996e23	−0.635673	−0.317836	+	0.948146i	$0.602956\pi$
$558$	1.03218e23	0.464904
$559$	−2.94677e22	−0.130721
$560$	1.99129e22	0.0870034
$561$	−2.12987e22	−0.0916577
$562$	−2.24317e23	−0.950831
$563$	3.08573e23	1.28836	0.644179	−	0.764875i	$-0.277199\pi$
$563$	3.08573e23	1.28836	0.644179	+	0.764875i	$0.277199\pi$
$564$	−4.89215e22	−0.201200
$565$	−9.85455e22	−0.399232
$566$	1.00465e22	0.0400938
$567$	−1.38385e23	−0.544042
$568$	−4.43406e23	−1.71728
$569$	2.57697e22	0.0983231	0.0491616	−	0.998791i	$-0.484345\pi$
$569$	2.57697e22	0.0983231	0.0491616	+	0.998791i	$0.484345\pi$
$570$	4.74681e22	0.178429
$571$	1.18613e23	0.439265	0.219632	−	0.975583i	$-0.429514\pi$
$571$	1.18613e23	0.439265	0.219632	+	0.975583i	$0.429514\pi$
$572$	−6.42400e21	−0.0234390
$573$	−9.10870e22	−0.327448
$574$	−1.83325e23	−0.649339
$575$	1.85484e22	0.0647336
$576$	−1.97706e23	−0.679875
$577$	−4.59593e21	−0.0155732	−0.00778662	−	0.999970i	$-0.502479\pi$
$577$	−4.59593e21	−0.0155732	−0.00778662	+	0.999970i	$0.502479\pi$
$578$	1.34147e22	0.0447913
$579$	1.46823e23	0.483088
$580$	−1.78051e23	−0.577305
$581$	−1.56164e23	−0.498981
$582$	7.72553e22	0.243267
$583$	−7.44860e22	−0.231149
$584$	−1.45185e22	−0.0444031
$585$	−3.58884e22	−0.108176
$586$	−8.63179e22	−0.256431
$587$	3.50290e23	1.02566	0.512831	−	0.858490i	$-0.328597\pi$
$587$	3.50290e23	1.02566	0.512831	+	0.858490i	$0.328597\pi$
$588$	−2.35627e22	−0.0680014
$589$	2.69855e23	0.767627
$590$	1.66198e23	0.465998
$591$	−3.64572e20	−0.00100760
$592$	1.69836e21	0.00462694
$593$	−1.00414e23	−0.269669	−0.134835	−	0.990868i	$-0.543050\pi$
$593$	−1.00414e23	−0.269669	−0.134835	+	0.990868i	$0.543050\pi$
$594$	−4.51067e22	−0.119414
$595$	−2.43936e23	−0.636621
$596$	1.84496e23	0.474673
$597$	1.75666e23	0.445559
$598$	8.10981e21	0.0202792
$599$	2.34873e23	0.579035	0.289517	−	0.957173i	$-0.406505\pi$
$599$	2.34873e23	0.579035	0.289517	+	0.957173i	$0.406505\pi$
$600$	4.36602e22	0.106121
$601$	2.66477e23	0.638596	0.319298	−	0.947654i	$-0.396553\pi$
$601$	2.66477e23	0.638596	0.319298	+	0.947654i	$0.396553\pi$
$602$	−1.99886e23	−0.472295
$603$	−4.18892e23	−0.975899
$604$	−3.86815e23	−0.888566
$605$	−3.36268e23	−0.761667
$606$	−6.07355e22	−0.135652
$607$	3.09862e23	0.682440	0.341220	−	0.939983i	$-0.389160\pi$
$607$	3.09862e23	0.682440	0.341220	+	0.939983i	$0.389160\pi$
$608$	−4.27466e23	−0.928370
$609$	1.52531e23	0.326671
$610$	3.66036e22	0.0773073
$611$	−7.67958e22	−0.159951
$612$	2.33532e23	0.479689
$613$	−9.39464e23	−1.90312	−0.951560	−	0.307464i	$-0.900520\pi$
$613$	−9.39464e23	−1.90312	−0.951560	+	0.307464i	$0.900520\pi$
$614$	−1.19825e23	−0.239395
$615$	1.70934e23	0.336813
$616$	−1.21757e23	−0.236623
$617$	5.58491e23	1.07051	0.535257	−	0.844689i	$-0.320215\pi$
$617$	5.58491e23	1.07051	0.535257	+	0.844689i	$0.320215\pi$
$618$	−4.78545e22	−0.0904734
$619$	3.61799e23	0.674678	0.337339	−	0.941383i	$-0.390473\pi$
$619$	3.61799e23	0.674678	0.337339	+	0.941383i	$0.390473\pi$
$620$	−1.97303e23	−0.362914
$621$	−7.17027e22	−0.130094
$622$	5.78398e22	0.103516
$623$	−1.10641e23	−0.195329
$624$	3.65488e21	0.00636508
$625$	−3.45270e23	−0.593169
$626$	−4.73624e23	−0.802697
$627$	−5.55705e22	−0.0929117
$628$	−8.85251e22	−0.146019
$629$	−2.08051e22	−0.0338563
$630$	−2.43439e23	−0.390837
$631$	1.20672e24	1.91143	0.955713	−	0.294300i	$-0.0950864\pi$
$631$	1.20672e24	1.91143	0.955713	+	0.294300i	$0.0950864\pi$
$632$	−6.41041e22	−0.100182
$633$	−1.21694e23	−0.187645
$634$	4.69949e23	0.714976
$635$	8.11625e22	0.121837
$636$	−9.97464e22	−0.147745
$637$	−3.69882e22	−0.0540602
$638$	−1.65537e23	−0.238737
$639$	1.03786e24	1.47701
$640$	2.60617e23	0.365993
$641$	5.24116e23	0.726331	0.363165	−	0.931725i	$-0.381696\pi$
$641$	5.24116e23	0.726331	0.363165	+	0.931725i	$0.381696\pi$
$642$	−1.56541e23	−0.214082
$643$	1.14724e24	1.54832	0.774158	−	0.632993i	$-0.218174\pi$
$643$	1.14724e24	1.54832	0.774158	+	0.632993i	$0.218174\pi$
$644$	−6.92687e22	−0.0922587
$645$	1.86375e23	0.244980
$646$	−4.84878e23	−0.629008
$647$	6.89456e23	0.882714	0.441357	−	0.897332i	$-0.354497\pi$
$647$	6.89456e23	0.882714	0.441357	+	0.897332i	$0.354497\pi$
$648$	5.61953e23	0.710089
$649$	−1.94567e23	−0.242654
$650$	2.45285e22	0.0301931
$651$	1.69024e23	0.205357
$652$	1.66723e23	0.199936
$653$	−7.81548e23	−0.925110	−0.462555	−	0.886591i	$-0.653067\pi$
$653$	−7.81548e23	−0.925110	−0.462555	+	0.886591i	$0.653067\pi$
$654$	−2.04528e23	−0.238969
$655$	1.11845e24	1.28993
$656$	1.42534e23	0.162269
$657$	3.39829e22	0.0381905
$658$	−5.20923e23	−0.577901
$659$	−1.46662e23	−0.160617	−0.0803085	−	0.996770i	$-0.525591\pi$
$659$	−1.46662e23	−0.160617	−0.0803085	+	0.996770i	$0.525591\pi$
$660$	4.06300e22	0.0439262
$661$	1.74712e24	1.86470	0.932351	−	0.361555i	$-0.117754\pi$
$661$	1.74712e24	1.86470	0.932351	+	0.361555i	$0.117754\pi$
$662$	5.16613e23	0.544343
$663$	−4.47727e22	−0.0465745
$664$	6.34151e23	0.651275
$665$	−6.36453e23	−0.645331
$666$	−2.07627e22	−0.0207852
$667$	−2.63142e23	−0.260089
$668$	−6.34749e23	−0.619444
$669$	4.10689e23	0.395723
$670$	−6.35903e23	−0.604999
$671$	−4.28515e22	−0.0402555
$672$	−2.67743e23	−0.248359
$673$	−9.16976e23	−0.839905	−0.419952	−	0.907546i	$-0.637953\pi$
$673$	−9.16976e23	−0.839905	−0.419952	+	0.907546i	$0.637953\pi$
$674$	−7.51828e23	−0.680000
$675$	−2.16869e23	−0.193693
$676$	6.18449e23	0.545453
$677$	1.65287e24	1.43958	0.719789	−	0.694192i	$-0.244238\pi$
$677$	1.65287e24	1.43958	0.719789	+	0.694192i	$0.244238\pi$
$678$	−1.22691e23	−0.105526
$679$	−1.03584e24	−0.879832
$680$	9.90575e23	0.830925
$681$	−5.91754e21	−0.00490220
$682$	−1.83436e23	−0.150078
$683$	−1.18810e24	−0.960016	−0.480008	−	0.877264i	$-0.659366\pi$
$683$	−1.18810e24	−0.960016	−0.480008	+	0.877264i	$0.659366\pi$
$684$	6.09309e23	0.486251
$685$	−1.20554e24	−0.950194
$686$	−9.29340e23	−0.723469
$687$	−5.23892e23	−0.402819
$688$	1.55410e23	0.118026
$689$	−1.56580e23	−0.117455
$690$	−5.12923e22	−0.0380045
$691$	1.06336e24	0.778245	0.389123	−	0.921186i	$-0.372778\pi$
$691$	1.06336e24	0.778245	0.389123	+	0.921186i	$0.372778\pi$
$692$	−5.90518e23	−0.426905
$693$	2.84992e23	0.203517
$694$	7.11208e22	0.0501697
$695$	−1.80624e24	−1.25865
$696$	−6.19398e23	−0.426375
$697$	−1.74606e24	−1.18735
$698$	1.71343e23	0.115105
$699$	6.12262e23	0.406332
$700$	−2.09507e23	−0.137361
$701$	−1.29294e24	−0.837479	−0.418739	−	0.908106i	$-0.637528\pi$
$701$	−1.29294e24	−0.837479	−0.418739	+	0.908106i	$0.637528\pi$
$702$	−9.48202e22	−0.0606786
$703$	−5.42826e22	−0.0343195
$704$	3.51359e23	0.219474
$705$	4.85712e23	0.299759
$706$	1.58689e24	0.967622
$707$	8.14342e23	0.490616
$708$	−2.60550e23	−0.155099
$709$	−2.75748e24	−1.62188	−0.810940	−	0.585129i	$-0.801044\pi$
$709$	−2.75748e24	−1.62188	−0.810940	+	0.585129i	$0.801044\pi$
$710$	1.57554e24	0.915658
$711$	1.50046e23	0.0861654
$712$	4.49290e23	0.254945
$713$	−2.91595e23	−0.163501
$714$	−3.03704e23	−0.168273
$715$	6.37801e22	0.0349208
$716$	8.83762e23	0.478162
$717$	−7.00632e23	−0.374608
$718$	1.64085e24	0.866984
$719$	−2.81588e24	−1.47034	−0.735171	−	0.677882i	$-0.762898\pi$
$719$	−2.81588e24	−1.47034	−0.735171	+	0.677882i	$0.762898\pi$
$720$	1.89272e23	0.0976696
$721$	6.41634e23	0.327218
$722$	5.49524e22	0.0276962
$723$	−7.33234e23	−0.365230
$724$	4.50938e23	0.221993
$725$	−7.95888e23	−0.387239
$726$	−4.18659e23	−0.201326
$727$	−7.94543e23	−0.377637	−0.188819	−	0.982012i	$-0.560466\pi$
$727$	−7.94543e23	−0.377637	−0.188819	+	0.982012i	$0.560466\pi$
$728$	−2.55949e23	−0.120237
$729$	−8.72043e23	−0.404906
$730$	5.15881e22	0.0236758
$731$	−1.90379e24	−0.863617
$732$	−5.73837e22	−0.0257303
$733$	−9.97013e23	−0.441893	−0.220946	−	0.975286i	$-0.570915\pi$
$733$	−9.97013e23	−0.441893	−0.220946	+	0.975286i	$0.570915\pi$
$734$	−6.00904e23	−0.263262
$735$	2.33940e23	0.101312
$736$	4.61904e23	0.197738
$737$	7.44446e23	0.315035
$738$	−1.74250e24	−0.728944
$739$	2.65907e24	1.09965	0.549823	−	0.835281i	$-0.314695\pi$
$739$	2.65907e24	1.09965	0.549823	+	0.835281i	$0.314695\pi$
$740$	3.96884e22	0.0162253
$741$	−1.16817e23	−0.0472117
$742$	−1.06211e24	−0.424364
$743$	7.82074e23	0.308918	0.154459	−	0.987999i	$-0.450637\pi$
$743$	7.82074e23	0.308918	0.154459	+	0.987999i	$0.450637\pi$
$744$	−6.86372e23	−0.268034
$745$	−1.83175e24	−0.707194
$746$	8.33313e23	0.318074
$747$	−1.48433e24	−0.560153
$748$	−4.15028e23	−0.154851
$749$	2.09890e24	0.774278
$750$	−6.54848e23	−0.238847
$751$	2.07442e24	0.748095	0.374047	−	0.927410i	$-0.377970\pi$
$751$	2.07442e24	0.748095	0.374047	+	0.927410i	$0.377970\pi$
$752$	4.05013e23	0.144417
$753$	−5.76971e23	−0.203421
$754$	−3.47981e23	−0.121311
$755$	3.84046e24	1.32384
$756$	8.09893e23	0.276053
$757$	3.91989e24	1.32117	0.660585	−	0.750751i	$-0.270308\pi$
$757$	3.91989e24	1.32117	0.660585	+	0.750751i	$0.270308\pi$
$758$	1.19092e24	0.396913
$759$	6.00474e22	0.0197897
$760$	2.58451e24	0.842293
$761$	6.53785e23	0.210700	0.105350	−	0.994435i	$-0.466404\pi$
$761$	6.53785e23	0.210700	0.105350	+	0.994435i	$0.466404\pi$
$762$	1.01049e23	0.0322042
$763$	2.74231e24	0.864288
$764$	−1.77493e24	−0.553207
$765$	−2.31860e24	−0.714667
$766$	7.54366e23	0.229952
$767$	−4.09005e23	−0.123301
$768$	1.16865e24	0.348430
$769$	4.86042e24	1.43318	0.716588	−	0.697496i	$-0.245703\pi$
$769$	4.86042e24	1.43318	0.716588	+	0.697496i	$0.245703\pi$
$770$	4.32635e23	0.126168
$771$	1.41550e24	0.408271
$772$	2.86101e24	0.816154
$773$	−6.07517e24	−1.71409	−0.857043	−	0.515246i	$-0.827701\pi$
$773$	−6.07517e24	−1.71409	−0.857043	+	0.515246i	$0.827701\pi$
$774$	−1.89991e24	−0.530195
$775$	−8.81945e23	−0.243432
$776$	4.20634e24	1.14837
$777$	−3.39999e22	−0.00918120
$778$	3.26839e24	0.872986
$779$	−4.55564e24	−1.20360
$780$	8.54098e22	0.0223205
$781$	−1.84447e24	−0.476802
$782$	5.23942e23	0.133976
$783$	3.07667e24	0.778227
$784$	1.95072e23	0.0488099
$785$	8.78913e23	0.217547
$786$	1.39249e24	0.340958
$787$	4.16529e24	1.00893	0.504464	−	0.863433i	$-0.331690\pi$
$787$	4.16529e24	1.00893	0.504464	+	0.863433i	$0.331690\pi$
$788$	−7.10408e21	−0.00170229
$789$	−1.52891e24	−0.362434
$790$	2.27779e23	0.0534175
$791$	1.64504e24	0.381659
$792$	−1.15730e24	−0.265632
$793$	−9.00796e22	−0.0204552
$794$	5.05623e23	0.113593
$795$	9.90323e23	0.220118
$796$	3.42304e24	0.752750
$797$	−8.87188e24	−1.93028	−0.965139	−	0.261736i	$-0.915705\pi$
$797$	−8.87188e24	−1.93028	−0.965139	+	0.261736i	$0.915705\pi$
$798$	−7.92394e23	−0.170575
$799$	−4.96146e24	−1.05672
$800$	1.39705e24	0.294407
$801$	−1.05164e24	−0.219275
$802$	−4.70959e23	−0.0971630
$803$	−6.03938e22	−0.0123285
$804$	9.96909e23	0.201363
$805$	6.87728e23	0.137452
$806$	−3.85608e23	−0.0762602
$807$	2.34649e24	0.459192
$808$	−3.30688e24	−0.640358
$809$	−1.30713e24	−0.250470	−0.125235	−	0.992127i	$-0.539968\pi$
$809$	−1.30713e24	−0.250470	−0.125235	+	0.992127i	$0.539968\pi$
$810$	−1.99677e24	−0.378621
$811$	1.60807e24	0.301736	0.150868	−	0.988554i	$-0.451793\pi$
$811$	1.60807e24	0.301736	0.150868	+	0.988554i	$0.451793\pi$
$812$	2.97223e24	0.551895
$813$	1.58083e24	0.290479
$814$	3.68991e22	0.00670978
$815$	−1.65529e24	−0.297875
$816$	2.36127e23	0.0420512
$817$	−4.96718e24	−0.875433
$818$	−4.38594e24	−0.764996
$819$	5.99091e23	0.103414
$820$	3.33083e24	0.569029
$821$	−1.56079e24	−0.263892	−0.131946	−	0.991257i	$-0.542123\pi$
$821$	−1.56079e24	−0.263892	−0.131946	+	0.991257i	$0.542123\pi$
$822$	−1.50092e24	−0.251157
$823$	1.01109e23	0.0167452	0.00837258	−	0.999965i	$-0.497335\pi$
$823$	1.01109e23	0.0167452	0.00837258	+	0.999965i	$0.497335\pi$
$824$	−2.60555e24	−0.427089
$825$	1.81617e23	0.0294644
$826$	−2.77437e24	−0.445487
$827$	−2.45558e24	−0.390262	−0.195131	−	0.980777i	$-0.562513\pi$
$827$	−2.45558e24	−0.390262	−0.195131	+	0.980777i	$0.562513\pi$
$828$	−6.58397e23	−0.103569
$829$	−2.42682e24	−0.377854	−0.188927	−	0.981991i	$-0.560501\pi$
$829$	−2.42682e24	−0.377854	−0.188927	+	0.981991i	$0.560501\pi$
$830$	−2.25331e24	−0.347262
$831$	8.66847e23	0.132231
$832$	7.38604e23	0.111523
$833$	−2.38966e24	−0.357152
$834$	−2.24879e24	−0.332689
$835$	6.30204e24	0.922882
$836$	−1.08285e24	−0.156970
$837$	3.40934e24	0.489220
$838$	−1.10023e24	−0.156283
$839$	−2.75341e24	−0.387163	−0.193581	−	0.981084i	$-0.562010\pi$
$839$	−2.75341e24	−0.387163	−0.193581	+	0.981084i	$0.562010\pi$
$840$	1.61881e24	0.225331
$841$	4.03395e24	0.555859
$842$	7.95989e24	1.08581
$843$	−3.49146e24	−0.471490
$844$	−2.37133e24	−0.317016
$845$	−6.14021e24	−0.812646
$846$	−4.95136e24	−0.648749
$847$	5.61339e24	0.728142
$848$	8.25784e23	0.106048
$849$	1.56373e23	0.0198813
$850$	1.58469e24	0.199472
$851$	5.86558e22	0.00730987
$852$	−2.46998e24	−0.304760
$853$	−1.47533e24	−0.180228	−0.0901138	−	0.995931i	$-0.528723\pi$
$853$	−1.47533e24	−0.180228	−0.0901138	+	0.995931i	$0.528723\pi$
$854$	−6.11031e23	−0.0739046
$855$	−6.04947e24	−0.724445
$856$	−8.52324e24	−1.01060
$857$	4.52466e24	0.531189	0.265594	−	0.964085i	$-0.414432\pi$
$857$	4.52466e24	0.531189	0.265594	+	0.964085i	$0.414432\pi$
$858$	7.94072e22	0.00923034
$859$	8.67756e24	0.998748	0.499374	−	0.866387i	$-0.333563\pi$
$859$	8.67756e24	0.998748	0.499374	+	0.866387i	$0.333563\pi$
$860$	3.63173e24	0.413882
$861$	−2.85343e24	−0.321988
$862$	−7.67219e24	−0.857250
$863$	9.39613e24	1.03958	0.519789	−	0.854295i	$-0.326010\pi$
$863$	9.39613e24	1.03958	0.519789	+	0.854295i	$0.326010\pi$
$864$	−5.40060e24	−0.591664
$865$	5.86291e24	0.636028
$866$	−8.03264e23	−0.0862892
$867$	2.08797e23	0.0222107
$868$	3.29361e24	0.346940
$869$	−2.66659e23	−0.0278156
$870$	2.20089e24	0.227344
$871$	1.56492e24	0.160081
$872$	−1.11360e25	−1.12808
$873$	−9.84563e24	−0.987694
$874$	1.36702e24	0.135808
$875$	8.78021e24	0.863846
$876$	−8.08750e22	−0.00788006
$877$	−1.11678e25	−1.07764	−0.538818	−	0.842422i	$-0.681129\pi$
$877$	−1.11678e25	−1.07764	−0.538818	+	0.842422i	$0.681129\pi$
$878$	−1.93234e24	−0.184663
$879$	−1.34352e24	−0.127157
$880$	−3.36370e23	−0.0315293
$881$	8.30663e24	0.771134	0.385567	−	0.922680i	$-0.374006\pi$
$881$	8.30663e24	0.771134	0.385567	+	0.922680i	$0.374006\pi$
$882$	−2.38479e24	−0.219264
$883$	1.10243e25	1.00389	0.501945	−	0.864900i	$-0.332618\pi$
$883$	1.10243e25	1.00389	0.501945	+	0.864900i	$0.332618\pi$
$884$	−8.72445e23	−0.0786854
$885$	2.58684e24	0.231075
$886$	9.76567e24	0.864003
$887$	−2.52327e24	−0.221112	−0.110556	−	0.993870i	$-0.535263\pi$
$887$	−2.52327e24	−0.221112	−0.110556	+	0.993870i	$0.535263\pi$
$888$	1.38067e23	0.0119834
$889$	−1.35486e24	−0.116474
$890$	−1.59645e24	−0.135938
$891$	2.33760e24	0.197156
$892$	8.00273e24	0.668555
$893$	−1.29450e25	−1.07118
$894$	−2.28056e24	−0.186927
$895$	−8.77435e24	−0.712392
$896$	−4.35052e24	−0.349883
$897$	1.26228e23	0.0100559
$898$	−9.87780e23	−0.0779491
$899$	1.25120e25	0.978067
$900$	−1.99136e24	−0.154201
$901$	−1.01160e25	−0.775973
$902$	3.09674e24	0.235315
$903$	−3.11120e24	−0.234197
$904$	−6.68018e24	−0.498146
$905$	−4.47710e24	−0.330738
$906$	4.78143e24	0.349920
$907$	1.20327e25	0.872369	0.436184	−	0.899857i	$-0.356330\pi$
$907$	1.20327e25	0.872369	0.436184	+	0.899857i	$0.356330\pi$
$908$	−1.15310e23	−0.00828202
$909$	7.74030e24	0.550763
$910$	9.09456e23	0.0641106
$911$	2.22835e25	1.55624	0.778122	−	0.628113i	$-0.216172\pi$
$911$	2.22835e25	1.55624	0.778122	+	0.628113i	$0.216172\pi$
$912$	6.16079e23	0.0426265
$913$	2.63793e24	0.180826
$914$	1.20247e25	0.816643
$915$	5.69729e23	0.0383344
$916$	−1.02086e25	−0.680542
$917$	−1.86705e25	−1.23315
$918$	−6.12595e24	−0.400876
$919$	1.63163e25	1.05789	0.528943	−	0.848657i	$-0.322589\pi$
$919$	1.63163e25	1.05789	0.528943	+	0.848657i	$0.322589\pi$
$920$	−2.79273e24	−0.179404
$921$	−1.86505e24	−0.118709
$922$	1.02523e25	0.646558
$923$	−3.87732e24	−0.242280
$924$	−6.78245e23	−0.0419928
$925$	1.77407e23	0.0108835
$926$	1.72940e25	1.05124
$927$	6.09872e24	0.367334
$928$	−1.98197e25	−1.18288
$929$	−6.74051e24	−0.398620	−0.199310	−	0.979936i	$-0.563870\pi$
$929$	−6.74051e24	−0.398620	−0.199310	+	0.979936i	$0.563870\pi$
$930$	2.43886e24	0.142917
$931$	−6.23486e24	−0.362038
$932$	1.19306e25	0.686478
$933$	9.00266e23	0.0513307
$934$	1.73008e25	0.977500
$935$	4.12057e24	0.230706
$936$	−2.43279e24	−0.134977
$937$	4.64505e24	0.255390	0.127695	−	0.991813i	$-0.459242\pi$
$937$	4.64505e24	0.255390	0.127695	+	0.991813i	$0.459242\pi$
$938$	1.06152e25	0.578370
$939$	−7.37187e24	−0.398034
$940$	9.46463e24	0.506427
$941$	5.53201e24	0.293340	0.146670	−	0.989185i	$-0.453144\pi$
$941$	5.53201e24	0.293340	0.146670	+	0.989185i	$0.453144\pi$
$942$	1.09426e24	0.0575026
$943$	4.92266e24	0.256360
$944$	2.15705e24	0.111326
$945$	−8.04094e24	−0.411279
$946$	3.37649e24	0.171155
$947$	−1.07016e25	−0.537617	−0.268809	−	0.963194i	$-0.586630\pi$
$947$	−1.07016e25	−0.537617	−0.268809	+	0.963194i	$0.586630\pi$
$948$	−3.57091e23	−0.0177790
$949$	−1.26956e23	−0.00626455
$950$	4.13461e24	0.202201
$951$	7.31467e24	0.354536
$952$	−1.65358e25	−0.794351
$953$	3.09336e25	1.47279	0.736394	−	0.676553i	$-0.236527\pi$
$953$	3.09336e25	1.47279	0.736394	+	0.676553i	$0.236527\pi$
$954$	−1.00954e25	−0.476388
$955$	1.76222e25	0.824199
$956$	−1.36526e25	−0.632882
$957$	−2.57656e24	−0.118383
$958$	−2.34404e25	−1.06748
$959$	2.01243e25	0.908370
$960$	−4.67147e24	−0.209001
$961$	−8.68524e24	−0.385153
$962$	7.75668e22	0.00340948
$963$	1.99500e25	0.869200
$964$	−1.42879e25	−0.617039
$965$	−2.84053e25	−1.21595
$966$	8.56232e23	0.0363317
$967$	8.77797e24	0.369206	0.184603	−	0.982813i	$-0.440900\pi$
$967$	8.77797e24	0.369206	0.184603	+	0.982813i	$0.440900\pi$
$968$	−2.27949e25	−0.950379
$969$	−7.54704e24	−0.311907
$970$	−1.49463e25	−0.612312
$971$	3.70303e25	1.50381	0.751906	−	0.659271i	$-0.229135\pi$
$971$	3.70303e25	1.50381	0.751906	+	0.659271i	$0.229135\pi$
$972$	1.17685e25	0.473761
$973$	3.01519e25	1.20325
$974$	2.48788e25	0.984188
$975$	3.81782e23	0.0149719
$976$	4.75071e23	0.0184686
$977$	−4.85355e25	−1.87049	−0.935246	−	0.353998i	$-0.884822\pi$
$977$	−4.85355e25	−1.87049	−0.935246	+	0.353998i	$0.884822\pi$
$978$	−2.06086e24	−0.0787351
$979$	1.86895e24	0.0707854
$980$	4.55858e24	0.171162
$981$	2.60656e25	0.970245
$982$	−2.01843e23	−0.00744843
$983$	−3.15000e25	−1.15241	−0.576203	−	0.817307i	$-0.695466\pi$
$983$	−3.15000e25	−1.15241	−0.576203	+	0.817307i	$0.695466\pi$
$984$	1.15872e25	0.420262
$985$	7.05322e22	0.00253617
$986$	−2.24817e25	−0.801446
$987$	−8.10808e24	−0.286564
$988$	−2.27630e24	−0.0797619
$989$	5.36736e24	0.186463
$990$	4.11218e24	0.141636
$991$	−1.59158e25	−0.543502	−0.271751	−	0.962368i	$-0.587603\pi$
$991$	−1.59158e25	−0.543502	−0.271751	+	0.962368i	$0.587603\pi$
$992$	−2.19628e25	−0.743597
$993$	8.04099e24	0.269924
$994$	−2.63007e25	−0.875354
$995$	−3.39853e25	−1.12149
$996$	3.53253e24	0.115580
$997$	−4.55299e25	−1.47702	−0.738512	−	0.674241i	$-0.764471\pi$
$997$	−4.55299e25	−1.47702	−0.738512	+	0.674241i	$0.764471\pi$
$998$	1.92182e25	0.618163
$999$	−6.85806e23	−0.0218723

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	23.18.a.a.1.5	✓	14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
23.18.a.a.1.5	✓	14	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 23 \)
Weight:	\( k \)	\(=\)	\( 18 \)
Character orbit:	\([\chi]\)	\(=\)	23.a (trivial)

\(f(q)\)	\(=\)	\(q-240.868 q^{2} -3749.07 q^{3} -73054.7 q^{4} +725316. q^{5} +903030. q^{6} -1.21078e7 q^{7} +4.91676e7 q^{8} -1.15085e8 q^{9} +O(q^{10})\)	\(q-240.868 q^{2} -3749.07 q^{3} -73054.7 q^{4} +725316. q^{5} +903030. q^{6} -1.21078e7 q^{7} +4.91676e7 q^{8} -1.15085e8 q^{9} -1.74705e8 q^{10} +2.04526e8 q^{11} +2.73887e8 q^{12} +4.29941e8 q^{13} +2.91639e9 q^{14} -2.71926e9 q^{15} -2.26746e9 q^{16} +2.77767e10 q^{17} +2.77202e10 q^{18} +7.24724e10 q^{19} -5.29877e10 q^{20} +4.53931e10 q^{21} -4.92638e10 q^{22} -7.83110e10 q^{23} -1.84332e11 q^{24} -2.36856e11 q^{25} -1.03559e11 q^{26} +9.15615e11 q^{27} +8.84534e11 q^{28} +3.36022e12 q^{29} +6.54982e11 q^{30} +3.72356e12 q^{31} -5.89833e12 q^{32} -7.66782e11 q^{33} -6.69052e12 q^{34} -8.78201e12 q^{35} +8.40747e12 q^{36} -7.49011e11 q^{37} -1.74563e13 q^{38} -1.61188e12 q^{39} +3.56620e13 q^{40} -6.28604e13 q^{41} -1.09337e13 q^{42} -6.85390e13 q^{43} -1.49416e13 q^{44} -8.34728e13 q^{45} +1.88626e13 q^{46} -1.78619e14 q^{47} +8.50088e12 q^{48} -8.60308e13 q^{49} +5.70509e13 q^{50} -1.04137e14 q^{51} -3.14092e13 q^{52} -3.64188e14 q^{53} -2.20542e14 q^{54} +1.48346e14 q^{55} -5.95313e14 q^{56} -2.71704e14 q^{57} -8.09370e14 q^{58} -9.51304e14 q^{59} +1.98655e14 q^{60} -2.09516e14 q^{61} -8.96885e14 q^{62} +1.39343e15 q^{63} +1.71792e15 q^{64} +3.11843e14 q^{65} +1.84693e14 q^{66} +3.63986e15 q^{67} -2.02922e15 q^{68} +2.93593e14 q^{69} +2.11530e15 q^{70} -9.01826e15 q^{71} -5.65843e15 q^{72} -2.95286e14 q^{73} +1.80413e14 q^{74} +8.87987e14 q^{75} -5.29444e15 q^{76} -2.47637e15 q^{77} +3.88250e14 q^{78} -1.30379e15 q^{79} -1.64463e15 q^{80} +1.14293e16 q^{81} +1.51410e16 q^{82} +1.28978e16 q^{83} -3.31618e15 q^{84} +2.01469e16 q^{85} +1.65088e16 q^{86} -1.25977e16 q^{87} +1.00560e16 q^{88} +9.13793e15 q^{89} +2.01059e16 q^{90} -5.20566e15 q^{91} +5.72098e15 q^{92} -1.39599e16 q^{93} +4.30237e16 q^{94} +5.25654e16 q^{95} +2.21132e16 q^{96} +8.55512e16 q^{97} +2.07221e16 q^{98} -2.35378e16 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q - 10640 q^{3} + 786432 q^{4} - 363048 q^{5} - 2333030 q^{6} - 39649066 q^{7} - 69259896 q^{8} + 796129528 q^{9}+O(q^{10}) \) 14 * q - 10640 * q^3 + 786432 * q^4 - 363048 * q^5 - 2333030 * q^6 - 39649066 * q^7 - 69259896 * q^8 + 796129528 * q^9	\( 14 q - 10640 q^{3} + 786432 q^{4} - 363048 q^{5} - 2333030 q^{6} - 39649066 q^{7} - 69259896 q^{8} + 796129528 q^{9} - 312719540 q^{10} - 45399620 q^{11} - 8621310628 q^{12} - 10510197306 q^{13} - 12286634640 q^{14} - 16443659490 q^{15} + 65383333632 q^{16} - 35705720330 q^{17} + 27658188862 q^{18} - 84895273414 q^{19} + 331348024336 q^{20} + 185190266362 q^{21} + 270540900120 q^{22} - 1096353793934 q^{23} + 1697198124384 q^{24} + 525715171346 q^{25} + 4272672484934 q^{26} - 3706093330604 q^{27} - 9883598189096 q^{28} - 4114009788386 q^{29} - 14194804268004 q^{30} + 3718266369468 q^{31} - 29197309605632 q^{32} - 16110579243626 q^{33} - 31423174598564 q^{34} + 13804822380504 q^{35} + 51950006703548 q^{36} - 58067881808868 q^{37} - 76590705469880 q^{38} + 69866971570764 q^{39} - 129282722434320 q^{40} - 74370388815170 q^{41} - 430581394397552 q^{42} - 127444248270174 q^{43} - 563872902913048 q^{44} - 602432292081270 q^{45} - 749727107945564 q^{47} - 17\!\cdots\!72 q^{48}+ \cdots + 35\!\cdots\!38 q^{99}+O(q^{100}) \) 14 * q - 10640 * q^3 + 786432 * q^4 - 363048 * q^5 - 2333030 * q^6 - 39649066 * q^7 - 69259896 * q^8 + 796129528 * q^9 - 312719540 * q^10 - 45399620 * q^11 - 8621310628 * q^12 - 10510197306 * q^13 - 12286634640 * q^14 - 16443659490 * q^15 + 65383333632 * q^16 - 35705720330 * q^17 + 27658188862 * q^18 - 84895273414 * q^19 + 331348024336 * q^20 + 185190266362 * q^21 + 270540900120 * q^22 - 1096353793934 * q^23 + 1697198124384 * q^24 + 525715171346 * q^25 + 4272672484934 * q^26 - 3706093330604 * q^27 - 9883598189096 * q^28 - 4114009788386 * q^29 - 14194804268004 * q^30 + 3718266369468 * q^31 - 29197309605632 * q^32 - 16110579243626 * q^33 - 31423174598564 * q^34 + 13804822380504 * q^35 + 51950006703548 * q^36 - 58067881808868 * q^37 - 76590705469880 * q^38 + 69866971570764 * q^39 - 129282722434320 * q^40 - 74370388815170 * q^41 - 430581394397552 * q^42 - 127444248270174 * q^43 - 563872902913048 * q^44 - 602432292081270 * q^45 - 749727107945564 * q^47 - 1762369490938672 * q^48 - 560241909258462 * q^49 - 1212733967351616 * q^50 - 2013927378521294 * q^51 - 3438555393950964 * q^52 - 1954645162253818 * q^53 - 2748549190422938 * q^54 - 2426218557075404 * q^55 - 1321001371084560 * q^56 - 2335835167092904 * q^57 - 340295461037046 * q^58 - 1561709417167508 * q^59 - 7486616247365616 * q^60 - 679115861109266 * q^61 - 12552327168177062 * q^62 - 10591353756704576 * q^63 - 6775416249353536 * q^64 - 6252697705990982 * q^65 - 20881430274671372 * q^66 - 7577612038827396 * q^67 + 2901964856169680 * q^68 + 833228883389840 * q^69 - 10700966230255240 * q^70 + 25039332312392368 * q^71 - 7954969753997256 * q^72 - 18720848443128734 * q^73 - 6297551300657404 * q^74 + 22553223201966436 * q^75 + 34141945529937952 * q^76 + 35092380107507048 * q^77 + 27963841408286022 * q^78 + 965348846593408 * q^79 + 36943919850262880 * q^80 + 51275234750545798 * q^81 + 106728632435914846 * q^82 + 65089411455584544 * q^83 + 189770883431502392 * q^84 + 20919534362994588 * q^85 + 86205449672049764 * q^86 + 130649890213719716 * q^87 + 164304846335490592 * q^88 - 61322357257717500 * q^89 + 237420523836214152 * q^90 + 181977537844157150 * q^91 - 61586264776507392 * q^92 - 71304974484877430 * q^93 - 14005510384703054 * q^94 + 123323286964112684 * q^95 + 566787465801380768 * q^96 - 67350702995984898 * q^97 + 134333537201072600 * q^98 + 353912447692290838 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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