LMFDB - Embedded newform 23.25.b.c.22.19

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [23,25,Mod(22,23)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(23, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([1])) N = Newforms(chi, 25, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("23.22"); S:= CuspForms(chi, 25); N := Newforms(S);

Level:	$ N $	$=$	$ 23 $
Weight:	$ k $	$=$	$ 25 $
Character orbit:	$[\chi]$	$=$	23.b (of order $2$, degree $1$, minimal)

Newform invariants

comment:select newform

sage:traces = [44] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$83.9424450193$
Analytic rank:	$0$
Dimension:	$44$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			22.19
Character	$\chi$	$=$	23.22
Dual form			23.25.b.c.22.20

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-1213.58 q^{2} +142839. q^{3} -1.53044e7 q^{4} -1.97797e8i q^{5} -1.73346e8 q^{6} -6.84832e9i q^{7} +3.89336e10 q^{8} -2.62027e11 q^{9} +2.40042e11i q^{10} +1.27147e12i q^{11} -2.18607e12 q^{12} +2.21048e13 q^{13} +8.31097e12i q^{14} -2.82532e13i q^{15} +2.09517e14 q^{16} -4.78477e13i q^{17} +3.17989e14 q^{18} +1.36683e15i q^{19} +3.02718e15i q^{20} -9.78208e14i q^{21} -1.54302e15i q^{22} +(5.32499e15 + 2.12578e16i) q^{23} +5.56124e15 q^{24} +2.04808e16 q^{25} -2.68258e16 q^{26} -7.77696e16 q^{27} +1.04810e17i q^{28} +5.15564e16 q^{29} +3.42875e16i q^{30} +2.06135e16 q^{31} -9.07462e17 q^{32} +1.81615e17i q^{33} +5.80669e16i q^{34} -1.35458e18 q^{35} +4.01017e18 q^{36} -9.91030e18i q^{37} -1.65876e18i q^{38} +3.15742e18 q^{39} -7.70096e18i q^{40} +1.69211e19 q^{41} +1.18713e18i q^{42} +6.15831e19i q^{43} -1.94591e19i q^{44} +5.18282e19i q^{45} +(-6.46229e18 - 2.57980e19i) q^{46} -2.09678e20 q^{47} +2.99272e19 q^{48} +1.44682e20 q^{49} -2.48550e19 q^{50} -6.83453e18i q^{51} -3.38301e20 q^{52} +8.75928e20i q^{53} +9.43794e19 q^{54} +2.51493e20 q^{55} -2.66630e20i q^{56} +1.95237e20i q^{57} -6.25676e19 q^{58} +1.74453e21 q^{59} +4.32400e20i q^{60} -4.45480e21i q^{61} -2.50160e19 q^{62} +1.79444e21i q^{63} -2.41384e21 q^{64} -4.37227e21i q^{65} -2.20404e20i q^{66} -3.08611e21i q^{67} +7.32283e20i q^{68} +(7.60617e20 + 3.03645e21i) q^{69} +1.64389e21 q^{70} -1.51440e22 q^{71} -1.02016e22 q^{72} +3.28331e22 q^{73} +1.20269e22i q^{74} +2.92546e21 q^{75} -2.09186e22i q^{76} +8.70742e21 q^{77} -3.83178e21 q^{78} -5.89628e22i q^{79} -4.14420e22i q^{80} +6.28955e22 q^{81} -2.05351e22 q^{82} -7.31440e22i q^{83} +1.49709e22i q^{84} -9.46416e21 q^{85} -7.47359e22i q^{86} +7.36427e21 q^{87} +4.95028e22i q^{88} -1.90199e23i q^{89} -6.28975e22i q^{90} -1.51381e23i q^{91} +(-8.14960e22 - 3.25339e23i) q^{92} +2.94441e21 q^{93} +2.54460e23 q^{94} +2.70356e23 q^{95} -1.29621e23 q^{96} -7.53162e23i q^{97} -1.75582e23 q^{98} -3.33158e23i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 44 q - 4232 q^{2} - 434562 q^{3} + 317760360 q^{4} - 8460029520 q^{6} - 198307023760 q^{8} + 4220041988298 q^{9} - 67439597688792 q^{12} + 5771152551358 q^{13} + 18\!\cdots\!92 q^{16} + 18\!\cdots\!68 q^{18}+ \cdots - 20\!\cdots\!92 q^{98}+O(q^{100}) $ 44 * q - 4232 * q^2 - 434562 * q^3 + 317760360 * q^4 - 8460029520 * q^6 - 198307023760 * q^8 + 4220041988298 * q^9 - 67439597688792 * q^12 + 5771152551358 * q^13 + 1801550792530192 * q^16 + 1842830558165568 * q^18 - 117204213263210644 * q^23 - 186493005437450784 * q^24 - 689533084157602612 * q^25 - 548650296251047576 * q^26 + 824037505793640630 * q^27 - 1583078054945709602 * q^29 - 77249813729122274 * q^31 - 2838716832733708512 * q^32 + 3418569899175948192 * q^35 + 71181245116739335248 * q^36 + 47106572467817156310 * q^39 - 9150679195666184738 * q^41 - 153049487518536134480 * q^46 + 22735751396127769438 * q^47 - 1317482931964495330032 * q^48 - 1842110772006482246836 * q^49 + 284936617115007894520 * q^50 + 207129175371045152568 * q^52 - 381774025126375304544 * q^54 - 5430040696094013021792 * q^55 - 2168901871328366220760 * q^58 + 16048018791948427185304 * q^59 + 14054450375064171442400 * q^62 + 20310379126091866412192 * q^64 + 24476879859710435470878 * q^69 - 118028399895318845638416 * q^70 - 68204988047209908888578 * q^71 - 106777935582637627887744 * q^72 - 7319375899831086678722 * q^73 + 12913295383070041819998 * q^75 + 111116199573084838704480 * q^77 - 422583593213386075404144 * q^78 - 331350288185757013618680 * q^81 + 1000764218021118649437320 * q^82 - 113385735487939722862944 * q^85 - 248828610584854760185290 * q^87 - 4238455111972177116774696 * q^92 + 4492289396741153284965270 * q^93 - 1602622056539190351258592 * q^94 - 1668692394291208047471936 * q^95 - 12092663288748189077973504 * q^96 - 2067304853876486831513192 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/23\mathbb{Z}\right)^\times$.

$n$	$5$
$\chi(n)$	$-1$

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 $

$2$	−1213.58			−0.296283			−0.148142	−	0.988966i	$-0.547329\pi$
$2$	−1213.58			−0.296283			−0.148142	+	0.988966i	$0.547329\pi$
$3$	142839.			0.268777			0.134388	−	0.990929i	$-0.457093\pi$
$3$	142839.			0.268777			0.134388	+	0.990929i	$0.457093\pi$
$4$	−1.53044e7			−0.912216
$5$		−	1.97797e8i		−	0.810178i	−0.914277	−	0.405089i	$-0.867240\pi$
$5$		−	1.97797e8i		−	0.810178i	0.914277	−	0.405089i	$-0.132760\pi$
$6$	−1.73346e8			−0.0796342
$7$		−	6.84832e9i		−	0.494775i	−0.968917	−	0.247387i	$-0.920428\pi$
$7$		−	6.84832e9i		−	0.494775i	0.968917	−	0.247387i	$-0.0795721\pi$
$8$	3.89336e10			0.566558
$9$	−2.62027e11			−0.927759
$10$			2.40042e11i			0.240042i
$11$			1.27147e12i			0.405129i	0.979269	+	0.202564i	$0.0649275\pi$
$11$			1.27147e12i			0.405129i	−0.979269	+	0.202564i	$0.935072\pi$
$12$	−2.18607e12			−0.245183
$13$	2.21048e13			0.948780			0.474390	−	0.880315i	$-0.342669\pi$
$13$	2.21048e13			0.948780			0.474390	+	0.880315i	$0.342669\pi$
$14$			8.31097e12i			0.146594i
$15$		−	2.82532e13i		−	0.217757i
$16$	2.09517e14			0.744354
$17$		−	4.78477e13i		−	0.0821248i	−0.999157	−	0.0410624i	$-0.986926\pi$
$17$		−	4.78477e13i		−	0.0821248i	0.999157	−	0.0410624i	$-0.0130742\pi$
$18$	3.17989e14			0.274880
$19$			1.36683e15i			0.617550i	0.951135	+	0.308775i	$0.0999190\pi$
$19$			1.36683e15i			0.617550i	−0.951135	+	0.308775i	$0.900081\pi$
$20$			3.02718e15i			0.739058i
$21$		−	9.78208e14i		−	0.132984i
$22$		−	1.54302e15i		−	0.120033i
$23$	5.32499e15	+	2.12578e16i	0.242988	+	0.970029i
$23$	5.32499e15	+	2.12578e16i	0.242988	+	0.970029i
$24$	5.56124e15			0.152278
$25$	2.04808e16			0.343611
$26$	−2.68258e16			−0.281108
$27$	−7.77696e16			−0.518137
$28$			1.04810e17i			0.451342i
$29$	5.15564e16			0.145716			0.0728579	−	0.997342i	$-0.476788\pi$
$29$	5.15564e16			0.145716			0.0728579	+	0.997342i	$0.476788\pi$
$30$			3.42875e16i			0.0645179i
$31$	2.06135e16			0.0261704			0.0130852	−	0.999914i	$-0.495835\pi$
$31$	2.06135e16			0.0261704			0.0130852	+	0.999914i	$0.495835\pi$
$32$	−9.07462e17			−0.787098
$33$			1.81615e17i			0.108889i
$34$			5.80669e16i			0.0243322i
$35$	−1.35458e18			−0.400856
$36$	4.01017e18			0.846317
$37$		−	9.91030e18i		−	1.50545i	−0.658336	−	0.752724i	$-0.728739\pi$
$37$		−	9.91030e18i		−	1.50545i	0.658336	−	0.752724i	$-0.271261\pi$
$38$		−	1.65876e18i		−	0.182970i
$39$	3.15742e18			0.255010
$40$		−	7.70096e18i		−	0.459013i
$41$	1.69211e19			0.749935			0.374967	−	0.927038i	$-0.377654\pi$
$41$	1.69211e19			0.749935			0.374967	+	0.927038i	$0.377654\pi$
$42$			1.18713e18i			0.0394010i
$43$			6.15831e19i			1.54113i	0.637359	+	0.770567i	$0.280027\pi$
$43$			6.15831e19i			1.54113i	−0.637359	+	0.770567i	$0.719973\pi$
$44$		−	1.94591e19i		−	0.369565i
$45$			5.18282e19i			0.751650i
$46$	−6.46229e18	−	2.57980e19i	−0.0719933	−	0.287404i
$47$	−2.09678e20			−1.80459			−0.902293	−	0.431123i	$-0.858118\pi$
$47$	−2.09678e20			−1.80459			−0.902293	+	0.431123i	$0.858118\pi$
$48$	2.99272e19			0.200065
$49$	1.44682e20			0.755198
$50$	−2.48550e19			−0.101806
$51$		−	6.83453e18i		−	0.0220733i
$52$	−3.38301e20			−0.865493
$53$			8.75928e20i			1.78303i	0.452994	+	0.891513i	$0.350356\pi$
$53$			8.75928e20i			1.78303i	−0.452994	+	0.891513i	$0.649644\pi$
$54$	9.43794e19			0.153515
$55$	2.51493e20			0.328226
$56$		−	2.66630e20i		−	0.280319i
$57$			1.95237e20i			0.165983i
$58$	−6.25676e19			−0.0431732
$59$	1.74453e21			0.980513			0.490256	−	0.871578i	$-0.336903\pi$
$59$	1.74453e21			0.980513			0.490256	+	0.871578i	$0.336903\pi$
$60$			4.32400e20i			0.198642i
$61$		−	4.45480e21i		−	1.67830i	−0.543897	−	0.839152i	$-0.683052\pi$
$61$		−	4.45480e21i		−	1.67830i	0.543897	−	0.839152i	$-0.316948\pi$
$62$	−2.50160e19			−0.00775386
$63$			1.79444e21i			0.459032i
$64$	−2.41384e21			−0.511150
$65$		−	4.37227e21i		−	0.768681i
$66$		−	2.20404e20i		−	0.0322621i
$67$		−	3.08611e21i		−	0.377150i	−0.982059	−	0.188575i	$-0.939613\pi$
$67$		−	3.08611e21i		−	0.377150i	0.982059	−	0.188575i	$-0.0603868\pi$
$68$			7.32283e20i			0.0749156i
$69$	7.60617e20	+	3.03645e21i	0.0653096	+	0.260722i
$70$	1.64389e21			0.118767
$71$	−1.51440e22			−0.922870			−0.461435	−	0.887174i	$-0.652665\pi$
$71$	−1.51440e22			−0.922870			−0.461435	+	0.887174i	$0.652665\pi$
$72$	−1.02016e22			−0.525629
$73$	3.28331e22			1.43363			0.716816	−	0.697262i	$-0.245599\pi$
$73$	3.28331e22			1.43363			0.716816	+	0.697262i	$0.245599\pi$
$74$			1.20269e22i			0.446040i
$75$	2.92546e21			0.0923547
$76$		−	2.09186e22i		−	0.563339i
$77$	8.70742e21			0.200448
$78$	−3.83178e21			−0.0755553
$79$		−	5.89628e22i		−	0.997823i	−0.866653	−	0.498911i	$-0.833733\pi$
$79$		−	5.89628e22i		−	0.997823i	0.866653	−	0.498911i	$-0.166267\pi$
$80$		−	4.14420e22i		−	0.603060i
$81$	6.28955e22			0.788496
$82$	−2.05351e22			−0.222193
$83$		−	7.31440e22i		−	0.684292i	−0.939647	−	0.342146i	$-0.888846\pi$
$83$		−	7.31440e22i		−	0.684292i	0.939647	−	0.342146i	$-0.111154\pi$
$84$			1.49709e22i			0.121310i
$85$	−9.46416e21			−0.0665358
$86$		−	7.47359e22i		−	0.456612i
$87$	7.36427e21			0.0391650
$88$			4.95028e22i			0.229529i
$89$		−	1.90199e23i		−	0.770066i	−0.922903	−	0.385033i	$-0.874190\pi$
$89$		−	1.90199e23i		−	0.770066i	0.922903	−	0.385033i	$-0.125810\pi$
$90$		−	6.28975e22i		−	0.222702i
$91$		−	1.51381e23i		−	0.469433i
$92$	−8.14960e22	−	3.25339e23i	−0.221658	−	0.884876i
$93$	2.94441e21			0.00703400
$94$	2.54460e23			0.534669
$95$	2.70356e23			0.500326
$96$	−1.29621e23			−0.211554
$97$		−	7.53162e23i		−	1.08550i	−0.839896	−	0.542748i	$-0.817384\pi$
$97$		−	7.53162e23i		−	1.08550i	0.839896	−	0.542748i	$-0.182616\pi$
$98$	−1.75582e23			−0.223753
$99$		−	3.33158e23i		−	0.375862i
$100$	−3.13447e23			−0.313447
$101$	7.69996e23			0.683332			0.341666	−	0.939821i	$-0.389009\pi$
$101$	7.69996e23			0.683332			0.341666	+	0.939821i	$0.389009\pi$
$102$			8.29423e21i			0.00653994i
$103$			1.13112e24i			0.793342i	0.917961	+	0.396671i	$0.129835\pi$
$103$			1.13112e24i			0.793342i	−0.917961	+	0.396671i	$0.870165\pi$
$104$	8.60617e23			0.537539
$105$	−1.93487e23			−0.107741
$106$		−	1.06301e24i		−	0.528281i
$107$		−	3.28637e24i		−	1.45919i	−0.683882	−	0.729593i	$-0.739710\pi$
$107$		−	3.28637e24i		−	1.45919i	0.683882	−	0.729593i	$-0.260290\pi$
$108$	1.19022e24			0.472653
$109$		−	1.96995e24i		−	0.700384i	−0.936678	−	0.350192i	$-0.886116\pi$
$109$		−	1.96995e24i		−	0.700384i	0.936678	−	0.350192i	$-0.113884\pi$
$110$	−3.05206e23			−0.0972481
$111$		−	1.41558e24i		−	0.404630i
$112$		−	1.43484e24i		−	0.368288i
$113$		−	7.13214e24i		−	1.64543i	−0.568456	−	0.822714i	$-0.692459\pi$
$113$		−	7.13214e24i		−	1.64543i	0.568456	−	0.822714i	$-0.307541\pi$
$114$		−	2.36935e23i		−	0.0491781i
$115$	4.20474e24	−	1.05327e24i	0.785897	−	0.196864i
$116$	−7.89042e23			−0.132924
$117$	−5.79203e24			−0.880239
$118$	−2.11712e24			−0.290510
$119$	−3.27677e23			−0.0406333
$120$		−	1.10000e24i		−	0.123372i
$121$	8.23310e24			0.835871
$122$			5.40625e24i			0.497254i
$123$	2.41700e24			0.201565
$124$	−3.15477e23			−0.0238731
$125$		−	1.58407e25i		−	1.08856i
$126$		−	2.17769e24i		−	0.136004i
$127$	−4.88388e24			−0.277409			−0.138704	−	0.990334i	$-0.544294\pi$
$127$	−4.88388e24			−0.277409			−0.138704	+	0.990334i	$0.544294\pi$
$128$	1.81541e25			0.938543
$129$			8.79648e24i			0.414221i
$130$			5.30608e24i			0.227748i
$131$	−1.41943e25			−0.555725			−0.277862	−	0.960621i	$-0.589626\pi$
$131$	−1.41943e25			−0.555725			−0.277862	+	0.960621i	$0.589626\pi$
$132$		−	2.77952e24i		−	0.0993305i
$133$	9.36051e24			0.305548
$134$			3.74523e24i			0.111743i
$135$			1.53826e25i			0.419784i
$136$		−	1.86288e24i		−	0.0465285i
$137$			6.38517e24i			0.146058i	0.997330	+	0.0730290i	$0.0232666\pi$
$137$			6.38517e24i			0.146058i	−0.997330	+	0.0730290i	$0.976733\pi$
$138$	−9.23067e23	−	3.68496e24i	−0.0193501	−	0.0772475i
$139$	−4.77175e25			−0.917276			−0.458638	−	0.888623i	$-0.651663\pi$
$139$	−4.77175e25			−0.917276			−0.458638	+	0.888623i	$0.651663\pi$
$140$	2.07311e25			0.365667
$141$	−2.99502e25			−0.485031
$142$	1.83784e25			0.273431
$143$			2.81055e25i			0.384378i
$144$	−5.48990e25			−0.690581
$145$		−	1.01977e25i		−	0.118056i
$146$	−3.98455e25			−0.424761
$147$	2.06662e25			0.202980
$148$			1.51672e26i			1.37329i
$149$			1.66762e26i			1.39272i	0.717694	+	0.696359i	$0.245198\pi$
$149$			1.66762e26i			1.39272i	−0.717694	+	0.696359i	$0.754802\pi$
$150$	−3.55027e24			−0.0273632
$151$	1.24611e26			0.886818			0.443409	−	0.896319i	$-0.353769\pi$
$151$	1.24611e26			0.886818			0.443409	+	0.896319i	$0.353769\pi$
$152$			5.32157e25i			0.349878i
$153$			1.25374e25i			0.0761920i
$154$	−1.05671e25			−0.0593893
$155$		−	4.07729e24i		−	0.0212027i
$156$	−4.83226e25			−0.232624
$157$			2.45163e26i			1.09310i	0.837427	+	0.546549i	$0.184059\pi$
$157$			2.45163e26i			1.09310i	−0.837427	+	0.546549i	$0.815941\pi$
$158$			7.15560e25i			0.295638i
$159$			1.25117e26i			0.479236i
$160$			1.79494e26i			0.637690i
$161$	1.45580e26	−	3.64673e25i	0.479946	−	0.120224i
$162$	−7.63285e25			−0.233618
$163$	−4.58499e26			−1.30343			−0.651714	−	0.758465i	$-0.725950\pi$
$163$	−4.58499e26			−1.30343			−0.651714	+	0.758465i	$0.725950\pi$
$164$	−2.58969e26			−0.684103
$165$	3.59230e25			0.0882197
$166$			8.87659e25i			0.202744i
$167$	2.15069e26			0.457067			0.228534	−	0.973536i	$-0.426607\pi$
$167$	2.15069e26			0.457067			0.228534	+	0.973536i	$0.426607\pi$
$168$		−	3.80851e25i		−	0.0753432i
$169$	−5.41803e25			−0.0998162
$170$	1.14855e25			0.0197134
$171$		−	3.58146e26i		−	0.572937i
$172$		−	9.42496e26i		−	1.40585i
$173$	2.99134e26			0.416210			0.208105	−	0.978106i	$-0.433270\pi$
$173$	2.99134e26			0.416210			0.208105	+	0.978106i	$0.433270\pi$
$174$	−8.93711e24			−0.0116040
$175$		−	1.40259e26i		−	0.170010i
$176$			2.66394e26i			0.301559i
$177$	2.49186e26			0.263539
$178$			2.30821e26i			0.228158i
$179$	7.94438e26			0.734216			0.367108	−	0.930178i	$-0.380348\pi$
$179$	7.94438e26			0.734216			0.367108	+	0.930178i	$0.380348\pi$
$180$		−	7.93202e26i		−	0.685668i
$181$			2.15339e26i			0.174173i	0.996201	+	0.0870863i	$0.0277556\pi$
$181$			2.15339e26i			0.174173i	−0.996201	+	0.0870863i	$0.972244\pi$
$182$			1.83712e26i			0.139085i
$183$		−	6.36320e26i		−	0.451089i
$184$	2.07321e26	+	8.27643e26i	0.137667	+	0.549578i
$185$	−1.96023e27			−1.21968
$186$	−3.57326e24			−0.00208406
$187$	6.08368e25			0.0332711
$188$	3.20900e27			1.64617
$189$			5.32591e26i			0.256361i
$190$	−3.28098e26			−0.148238
$191$		−	3.34395e27i		−	1.41860i	−0.704908	−	0.709298i	$-0.749012\pi$
$191$		−	3.34395e27i		−	1.41860i	0.704908	−	0.709298i	$-0.250988\pi$
$192$	−3.44790e26			−0.137385
$193$	−3.12624e27			−1.17040			−0.585200	−	0.810889i	$-0.698984\pi$
$193$	−3.12624e27			−1.17040			−0.585200	+	0.810889i	$0.698984\pi$
$194$			9.14021e26i			0.321614i
$195$		−	6.24530e26i		−	0.206604i
$196$	−2.21427e27			−0.688904
$197$	4.27484e27			1.25119			0.625597	−	0.780146i	$-0.284855\pi$
$197$	4.27484e27			1.25119			0.625597	+	0.780146i	$0.284855\pi$
$198$			4.04313e26i			0.111362i
$199$		−	2.46159e27i		−	0.638231i	−0.947716	−	0.319116i	$-0.896614\pi$
$199$		−	2.46159e27i		−	0.638231i	0.947716	−	0.319116i	$-0.103386\pi$
$200$	7.97391e26			0.194675
$201$		−	4.40817e26i		−	0.101369i
$202$	−9.34449e26			−0.202460
$203$		−	3.53075e26i		−	0.0720965i
$204$			1.04599e26i			0.0201356i
$205$		−	3.34696e27i		−	0.607581i
$206$		−	1.37270e27i		−	0.235054i
$207$	−1.39529e27	−	5.57011e27i	−0.225434	−	0.899953i
$208$	4.63133e27			0.706229
$209$	−1.73788e27			−0.250187
$210$	2.34812e26			0.0319218
$211$	4.33655e27			0.556872			0.278436	−	0.960455i	$-0.410184\pi$
$211$	4.33655e27			0.556872			0.278436	+	0.960455i	$0.410184\pi$
$212$		−	1.34056e28i		−	1.62651i
$213$	−2.16316e27			−0.248046
$214$			3.98826e27i			0.432333i
$215$	1.21810e28			1.24859
$216$	−3.02785e27			−0.293555
$217$		−	1.41168e26i		−	0.0129485i
$218$			2.39068e27i			0.207512i
$219$	4.68985e27			0.385327
$220$	−3.84896e27			−0.299413
$221$		−	1.05766e27i		−	0.0779184i
$222$			1.71791e27i			0.119885i
$223$	−1.49491e28			−0.988456			−0.494228	−	0.869332i	$-0.664549\pi$
$223$	−1.49491e28			−0.988456			−0.494228	+	0.869332i	$0.664549\pi$
$224$			6.21459e27i			0.389436i
$225$	−5.36651e27			−0.318788
$226$			8.65541e27i			0.487513i
$227$			5.28683e27i			0.282413i	0.989980	+	0.141207i	$0.0450982\pi$
$227$			5.28683e27i			0.282413i	−0.989980	+	0.141207i	$0.954902\pi$
$228$		−	2.98800e27i		−	0.151413i
$229$			1.44312e28i			0.693868i	0.937890	+	0.346934i	$0.112777\pi$
$229$			1.44312e28i			0.693868i	−0.937890	+	0.346934i	$0.887223\pi$
$230$	−5.10278e27	+	1.27822e27i	−0.232848	+	0.0583274i
$231$	1.24376e27			0.0538757
$232$	2.00727e27			0.0825564
$233$	4.99122e27			0.194956			0.0974778	−	0.995238i	$-0.468923\pi$
$233$	4.99122e27			0.194956			0.0974778	+	0.995238i	$0.468923\pi$
$234$	7.02908e27			0.260800
$235$			4.14737e28i			1.46204i
$236$	−2.66990e28			−0.894439
$237$		−	8.42220e27i		−	0.268192i
$238$	3.97661e26			0.0120390
$239$	−8.84057e27			−0.254510			−0.127255	−	0.991870i	$-0.540617\pi$
$239$	−8.84057e27			−0.254510			−0.127255	+	0.991870i	$0.540617\pi$
$240$		−	5.91953e27i		−	0.162089i
$241$			1.11978e28i			0.291695i	0.989307	+	0.145848i	$0.0465909\pi$
$241$			1.11978e28i			0.291695i	−0.989307	+	0.145848i	$0.953409\pi$
$242$	−9.99151e27			−0.247655
$243$	3.09484e28			0.730067
$244$			6.81783e28i			1.53098i
$245$		−	2.86177e28i		−	0.611845i
$246$	−2.93322e27			−0.0597204
$247$			3.02135e28i			0.585919i
$248$	8.02555e26			0.0148271
$249$		−	1.04478e28i		−	0.183922i
$250$			1.92239e28i			0.322524i
$251$			1.89179e28i			0.302544i	0.988492	+	0.151272i	$0.0483369\pi$
$251$			1.89179e28i			0.302544i	−0.988492	+	0.151272i	$0.951663\pi$
$252$		−	2.74629e28i		−	0.418736i
$253$	−2.70286e28	+	6.77055e27i	−0.392987	+	0.0984414i
$254$	5.92697e27			0.0821917
$255$	−1.35185e27			−0.0178833
$256$	1.84661e28			0.233075
$257$	2.57645e28			0.310330			0.155165	−	0.987889i	$-0.450409\pi$
$257$	2.57645e28			0.310330			0.155165	+	0.987889i	$0.450409\pi$
$258$		−	1.06752e28i		−	0.122727i
$259$	−6.78689e28			−0.744858
$260$			6.69151e28i			0.701203i
$261$	−1.35091e28			−0.135189
$262$	1.72259e28			0.164652
$263$			4.25008e28i			0.388086i	0.980993	+	0.194043i	$0.0621601\pi$
$263$			4.25008e28i			0.388086i	−0.980993	+	0.194043i	$0.937840\pi$
$264$			7.07093e27i			0.0616921i
$265$	1.73256e29			1.44457
$266$	−1.13597e28			−0.0905289
$267$		−	2.71678e28i		−	0.206976i
$268$			4.72312e28i			0.344042i
$269$	−2.65534e29			−1.84966			−0.924831	−	0.380377i	$-0.875794\pi$
$269$	−2.65534e29			−1.84966			−0.924831	+	0.380377i	$0.875794\pi$
$270$		−	1.86680e28i		−	0.124375i
$271$	−1.30488e29			−0.831650			−0.415825	−	0.909445i	$-0.636507\pi$
$271$	−1.30488e29			−0.831650			−0.415825	+	0.909445i	$0.636507\pi$
$272$		−	1.00249e28i		−	0.0611300i
$273$		−	2.16231e28i		−	0.126173i
$274$		−	7.74890e27i		−	0.0432746i
$275$			2.60407e28i			0.139207i
$276$	−1.16408e28	−	4.64712e28i	−0.0595764	−	0.237834i
$277$	2.32708e29			1.14039			0.570196	−	0.821509i	$-0.306867\pi$
$277$	2.32708e29			1.14039			0.570196	+	0.821509i	$0.306867\pi$
$278$	5.79089e28			0.271774
$279$	−5.40127e27			−0.0242798
$280$	−5.27387e28			−0.227108
$281$		−	1.92977e29i		−	0.796214i	−0.917339	−	0.398107i	$-0.869667\pi$
$281$		−	1.92977e29i		−	0.796214i	0.917339	−	0.398107i	$-0.130333\pi$
$282$	3.63468e28			0.143707
$283$		−	4.31081e29i		−	1.63351i	−0.576986	−	0.816754i	$-0.695771\pi$
$283$		−	4.31081e29i		−	1.63351i	0.576986	−	0.816754i	$-0.304229\pi$
$284$	2.31771e29			0.841857
$285$	3.86174e28			0.134476
$286$		−	3.41082e28i		−	0.113885i
$287$		−	1.15881e29i		−	0.371049i
$288$	2.37779e29			0.730237
$289$	3.37159e29			0.993256
$290$			1.23757e28i			0.0349780i
$291$		−	1.07581e29i		−	0.291756i
$292$	−5.02493e29			−1.30778
$293$		−	3.23912e29i		−	0.809125i	−0.914510	−	0.404562i	$-0.867424\pi$
$293$		−	3.23912e29i		−	0.809125i	0.914510	−	0.404562i	$-0.132576\pi$
$294$	−2.50800e28			−0.0601395
$295$		−	3.45063e29i		−	0.794390i
$296$		−	3.85843e29i		−	0.852924i
$297$		−	9.88815e28i		−	0.209912i
$298$		−	2.02379e29i		−	0.412639i
$299$	1.17708e29	+	4.69899e29i	0.230542	+	0.920345i
$300$	−4.47725e28			−0.0842474
$301$	4.21741e29			0.762514
$302$	−1.51226e29			−0.262750
$303$	1.09985e29			0.183664
$304$			2.86375e29i			0.459676i
$305$	−8.81149e29			−1.35973
$306$		−	1.52151e28i		−	0.0225744i
$307$	−4.04646e29			−0.577318			−0.288659	−	0.957432i	$-0.593209\pi$
$307$	−4.04646e29			−0.577318			−0.288659	+	0.957432i	$0.593209\pi$
$308$	−1.33262e29			−0.182851
$309$			1.61568e29i			0.213232i
$310$			4.94810e27i			0.00628201i
$311$	7.51635e28			0.0918084			0.0459042	−	0.998946i	$-0.485383\pi$
$311$	7.51635e28			0.0918084			0.0459042	+	0.998946i	$0.485383\pi$
$312$	1.22930e29			0.144478
$313$			1.52874e29i			0.172903i	0.996256	+	0.0864516i	$0.0275528\pi$
$313$			1.52874e29i			0.172903i	−0.996256	+	0.0864516i	$0.972447\pi$
$314$		−	2.97524e29i		−	0.323867i
$315$	3.54936e29			0.371898
$316$			9.02394e29i			0.910230i
$317$	1.07646e30			1.04541			0.522707	−	0.852512i	$-0.324922\pi$
$317$	1.07646e30			1.04541			0.522707	+	0.852512i	$0.324922\pi$
$318$		−	1.51839e29i		−	0.141990i
$319$			6.55522e28i			0.0590336i
$320$			4.77451e29i			0.414123i
$321$		−	4.69421e29i		−	0.392195i
$322$	−1.76673e29	+	4.42558e28i	−0.142200	+	0.0356205i
$323$	6.53998e28			0.0507162
$324$	−9.62581e29			−0.719278
$325$	4.52723e29			0.326011
$326$	5.56424e29			0.386184
$327$		−	2.81385e29i		−	0.188247i
$328$	6.58801e29			0.424882
$329$			1.43594e30i			0.892864i
$330$	−4.35954e28			−0.0261380
$331$	−1.86399e30			−1.07772			−0.538861	−	0.842395i	$-0.681145\pi$
$331$	−1.86399e30			−1.07772			−0.538861	+	0.842395i	$0.681145\pi$
$332$			1.11943e30i			0.624222i
$333$			2.59676e30i			1.39669i
$334$	−2.61003e29			−0.135421
$335$	−6.10425e29			−0.305559
$336$		−	2.04951e29i		−	0.0989873i
$337$			6.82671e28i			0.0318165i	0.999873	+	0.0159083i	$0.00506397\pi$
$337$			6.82671e28i			0.0318165i	−0.999873	+	0.0159083i	$0.994936\pi$
$338$	6.57520e28			0.0295739
$339$		−	1.01875e30i		−	0.442253i
$340$	1.44844e29			0.0606950
$341$			2.62093e28i			0.0106024i
$342$			4.34638e29i			0.169752i
$343$		−	2.30284e30i		−	0.868428i
$344$			2.39765e30i			0.873142i
$345$	6.00602e29	−	1.50448e29i	0.211231	−	0.0529124i
$346$	−3.63022e29			−0.123316
$347$	−3.35105e30			−1.09958			−0.549791	−	0.835302i	$-0.685293\pi$
$347$	−3.35105e30			−1.09958			−0.549791	+	0.835302i	$0.685293\pi$
$348$	−1.12706e29			−0.0357270
$349$	4.52748e29			0.138660			0.0693301	−	0.997594i	$-0.477914\pi$
$349$	4.52748e29			0.138660			0.0693301	+	0.997594i	$0.477914\pi$
$350$			1.70215e29i			0.0503712i
$351$	−1.71908e30			−0.491598
$352$		−	1.15381e30i		−	0.318876i
$353$	3.33239e30			0.890141			0.445070	−	0.895496i	$-0.353179\pi$
$353$	3.33239e30			0.890141			0.445070	+	0.895496i	$0.353179\pi$
$354$	−3.02407e29			−0.0780823
$355$			2.99545e30i			0.747690i
$356$			2.91089e30i			0.702467i
$357$	−4.68051e28			−0.0109213
$358$	−9.64112e29			−0.217536
$359$			6.34204e30i			1.38387i	0.721960	+	0.691935i	$0.243242\pi$
$359$			6.34204e30i			1.38387i	−0.721960	+	0.691935i	$0.756758\pi$
$360$			2.01786e30i			0.425854i
$361$	3.03053e30			0.618632
$362$		−	2.61330e29i		−	0.0516044i
$363$	1.17601e30			0.224663
$364$			2.31680e30i			0.428224i
$365$		−	6.49431e30i		−	1.16150i
$366$			7.72224e29i			0.133650i
$367$		−	9.52719e30i		−	1.59578i	−0.602805	−	0.797888i	$-0.705950\pi$
$367$		−	9.52719e30i		−	1.59578i	0.602805	−	0.797888i	$-0.294050\pi$
$368$	1.11568e30	+	4.45388e30i	0.180869	+	0.722045i
$369$	−4.43379e30			−0.695759
$370$	2.37889e30			0.361372
$371$	5.99864e30			0.882197
$372$	−4.50625e28			−0.00641653
$373$		−	3.38315e30i		−	0.466461i	−0.972422	−	0.233230i	$-0.925070\pi$
$373$		−	3.38315e30i		−	0.466461i	0.972422	−	0.233230i	$-0.0749296\pi$
$374$	−7.38302e28			−0.00985768
$375$		−	2.26267e30i		−	0.292581i
$376$	−8.16350e30			−1.02240
$377$	1.13964e30			0.138252
$378$		−	6.46341e29i		−	0.0759556i
$379$		−	1.25362e31i		−	1.42723i	−0.700537	−	0.713616i	$-0.747056\pi$
$379$		−	1.25362e31i		−	1.42723i	0.700537	−	0.713616i	$-0.252944\pi$
$380$	−4.13765e30			−0.456405
$381$	−6.97609e29			−0.0745611
$382$			4.05814e30i			0.420307i
$383$		−	1.47792e30i		−	0.148342i	−0.997246	−	0.0741710i	$-0.976369\pi$
$383$		−	1.47792e30i		−	0.148342i	0.997246	−	0.0741710i	$-0.0236311\pi$
$384$	2.59311e30			0.252259
$385$		−	1.72231e30i		−	0.162398i
$386$	3.79393e30			0.346770
$387$		−	1.61364e31i		−	1.42980i
$388$			1.15267e31i			0.990206i
$389$		−	7.33614e30i		−	0.611043i	−0.952185	−	0.305522i	$-0.901169\pi$
$389$		−	7.33614e30i		−	0.611043i	0.952185	−	0.305522i	$-0.0988309\pi$
$390$			7.57916e29i			0.0612133i
$391$	1.01714e30	−	2.54789e29i	0.0796635	−	0.0199553i
$392$	5.63298e30			0.427863
$393$	−2.02751e30			−0.149366
$394$	−5.18785e30			−0.370708
$395$	−1.16627e31			−0.808414
$396$			5.09880e30i			0.342867i
$397$	1.95177e31			1.27334			0.636668	−	0.771138i	$-0.280312\pi$
$397$	1.95177e31			1.27334			0.636668	+	0.771138i	$0.280312\pi$
$398$			2.98733e30i			0.189097i
$399$	1.33705e30			0.0821243
$400$	4.29108e30			0.255768
$401$		−	6.33891e30i		−	0.366675i	−0.983050	−	0.183338i	$-0.941310\pi$
$401$		−	6.33891e30i		−	0.366675i	0.983050	−	0.183338i	$-0.0586902\pi$
$402$			5.34966e29i			0.0300340i
$403$	4.55655e29			0.0248300
$404$	−1.17844e31			−0.623347
$405$		−	1.24406e31i		−	0.638822i
$406$			4.28483e29i			0.0213610i
$407$	1.26006e31			0.609900
$408$		−	2.66093e29i		−	0.0125058i
$409$	1.80953e31			0.825823			0.412911	−	0.910771i	$-0.364512\pi$
$409$	1.80953e31			0.825823			0.412911	+	0.910771i	$0.364512\pi$
$410$			4.06179e30i			0.180016i
$411$			9.12052e29i			0.0392570i
$412$		−	1.73111e31i		−	0.723699i
$413$		−	1.19471e31i		−	0.485133i
$414$	1.69329e30	+	6.75976e30i	0.0667925	+	0.266641i
$415$	−1.44677e31			−0.554399
$416$	−2.00592e31			−0.746783
$417$	−6.81592e30			−0.246543
$418$	2.10905e30			0.0741263
$419$		−	4.14884e31i		−	1.41696i	−0.705730	−	0.708481i	$-0.749381\pi$
$419$		−	4.14884e31i		−	1.41696i	0.705730	−	0.708481i	$-0.250619\pi$
$420$	2.96121e30			0.0982829
$421$		−	2.29365e31i		−	0.739846i	−0.929062	−	0.369923i	$-0.879384\pi$
$421$		−	2.29365e31i		−	0.739846i	0.929062	−	0.369923i	$-0.120616\pi$
$422$	−5.26274e30			−0.164992
$423$	5.49411e31			1.67422
$424$			3.41030e31i			1.01019i
$425$		−	9.79960e29i		−	0.0282190i
$426$	2.62516e30			0.0734920
$427$	−3.05079e31			−0.830383
$428$			5.02960e31i			1.33109i
$429$			4.01456e30i			0.103312i
$430$	−1.47826e31			−0.369938
$431$			4.50665e30i			0.109680i	0.998495	+	0.0548399i	$0.0174649\pi$
$431$			4.50665e30i			0.109680i	−0.998495	+	0.0548399i	$0.982535\pi$
$432$	−1.62941e31			−0.385678
$433$		−	8.56845e30i		−	0.197264i	−0.995124	−	0.0986319i	$-0.968553\pi$
$433$		−	8.56845e30i		−	0.197264i	0.995124	−	0.0986319i	$-0.0314466\pi$
$434$			1.71318e29i			0.00383642i
$435$		−	1.45663e30i		−	0.0317307i
$436$			3.01489e31i			0.638902i
$437$	−2.90559e31	+	7.27837e30i	−0.599041	+	0.150057i
$438$	−5.69150e30			−0.114166
$439$	6.42516e31			1.25403			0.627017	−	0.779005i	$-0.284275\pi$
$439$	6.42516e31			1.25403			0.627017	+	0.779005i	$0.284275\pi$
$440$	9.79152e30			0.185959
$441$	−3.79104e31			−0.700641
$442$			1.28356e30i			0.0230859i
$443$	−2.82886e31			−0.495183			−0.247592	−	0.968864i	$-0.579639\pi$
$443$	−2.82886e31			−0.495183			−0.247592	+	0.968864i	$0.579639\pi$
$444$			2.16646e31i			0.369110i
$445$	−3.76209e31			−0.623891
$446$	1.81419e31			0.292863
$447$			2.38202e31i			0.374330i
$448$			1.65307e31i			0.252904i
$449$	4.88889e31			0.728206			0.364103	−	0.931359i	$-0.381376\pi$
$449$	4.88889e31			0.728206			0.364103	+	0.931359i	$0.381376\pi$
$450$	6.51268e30			0.0944516
$451$			2.15147e31i			0.303820i
$452$			1.09154e32i			1.50099i
$453$	1.77994e31			0.238356
$454$		−	6.41598e30i		−	0.0836744i
$455$	−2.99427e31			−0.380324
$456$			7.60128e30i			0.0940391i
$457$			1.52304e32i			1.83534i	0.397346	+	0.917669i	$0.369931\pi$
$457$			1.52304e32i			1.83534i	−0.397346	+	0.917669i	$0.630069\pi$
$458$		−	1.75134e31i		−	0.205582i
$459$			3.72110e30i			0.0425519i
$460$	−6.43513e31	+	1.61197e31i	−0.716908	+	0.179582i
$461$	1.91122e31			0.207443			0.103722	−	0.994606i	$-0.466925\pi$
$461$	1.91122e31			0.207443			0.103722	+	0.994606i	$0.466925\pi$
$462$	−1.50940e30			−0.0159625
$463$	−7.01519e31			−0.722883			−0.361441	−	0.932395i	$-0.617715\pi$
$463$	−7.01519e31			−0.722883			−0.361441	+	0.932395i	$0.617715\pi$
$464$	1.08019e31			0.108464
$465$		−	5.82396e29i		−	0.00569880i
$466$	−6.05723e30			−0.0577621
$467$			8.79547e31i			0.817441i	0.912660	+	0.408721i	$0.134025\pi$
$467$			8.79547e31i			0.817441i	−0.912660	+	0.408721i	$0.865975\pi$
$468$	8.86439e31			0.802968
$469$	−2.11347e31			−0.186604
$470$		−	5.03315e31i		−	0.433177i
$471$			3.50188e31i			0.293799i
$472$	6.79206e31			0.555517
$473$	−7.83009e31			−0.624357
$474$			1.02210e31i			0.0794608i
$475$			2.79938e31i			0.212197i
$476$	5.01491e30			0.0370664
$477$		−	2.29516e32i		−	1.65422i
$478$	1.07287e31			0.0754072
$479$		−	1.87722e32i		−	1.28674i	−0.765557	−	0.643368i	$-0.777536\pi$
$479$		−	1.87722e32i		−	1.28674i	0.765557	−	0.643368i	$-0.222464\pi$
$480$			2.56387e31i			0.171396i
$481$		−	2.19065e32i		−	1.42834i
$482$		−	1.35894e31i		−	0.0864245i
$483$	2.07946e31	−	5.20895e30i	0.128998	−	0.0323135i
$484$	−1.26003e32			−0.762495
$485$	−1.48974e32			−0.879445
$486$	−3.75582e31			−0.216307
$487$	3.29697e32			1.85254			0.926270	−	0.376861i	$-0.122997\pi$
$487$	3.29697e32			1.85254			0.926270	+	0.376861i	$0.122997\pi$
$488$		−	1.73441e32i		−	0.950856i
$489$	−6.54916e31			−0.350331
$490$			3.47298e31i			0.181280i
$491$	2.26325e32			1.15280			0.576401	−	0.817167i	$-0.304456\pi$
$491$	2.26325e32			1.15280			0.576401	+	0.817167i	$0.304456\pi$
$492$	−3.69909e31			−0.183871
$493$		−	2.46686e30i		−	0.0119669i
$494$		−	3.66664e31i		−	0.173598i
$495$	−6.58978e31			−0.304515
$496$	4.31887e30			0.0194801
$497$			1.03711e32i			0.456613i
$498$			1.26792e31i			0.0544930i
$499$	1.09590e32			0.459796			0.229898	−	0.973215i	$-0.426161\pi$
$499$	1.09590e32			0.459796			0.229898	+	0.973215i	$0.426161\pi$
$500$			2.42433e32i			0.993006i
$501$	3.07202e31			0.122849
$502$		−	2.29584e31i		−	0.0896388i
$503$		−	1.39551e32i		−	0.532008i	−0.963972	−	0.266004i	$-0.914297\pi$
$503$		−	1.39551e32i		−	0.532008i	0.963972	−	0.266004i	$-0.0857034\pi$
$504$			6.98640e31i			0.260068i
$505$		−	1.52303e32i		−	0.553621i
$506$	3.28013e31	−	8.21659e30i	0.116435	−	0.0291666i
$507$	−7.73907e30			−0.0268283
$508$	7.47451e31			0.253057
$509$	5.29450e31			0.175070			0.0875350	−	0.996161i	$-0.472101\pi$
$509$	5.29450e31			0.175070			0.0875350	+	0.996161i	$0.472101\pi$
$510$	1.64058e30			0.00529852
$511$		−	2.24852e32i		−	0.709325i
$512$	−3.26985e32			−1.00760
$513$		−	1.06298e32i		−	0.319976i
$514$	−3.12672e31			−0.0919458
$515$	2.23732e32			0.642749
$516$		−	1.34625e32i		−	0.377859i
$517$		−	2.66598e32i		−	0.731090i
$518$	8.23642e31			0.220689
$519$	4.27280e31			0.111868
$520$		−	1.70228e32i		−	0.435503i
$521$			7.04983e32i			1.76249i	0.472662	+	0.881244i	$0.343293\pi$
$521$			7.04983e32i			1.76249i	−0.472662	+	0.881244i	$0.656707\pi$
$522$	1.63944e31			0.0400543
$523$		−	7.69688e32i		−	1.83778i	−0.394509	−	0.918892i	$-0.629085\pi$
$523$		−	7.69688e32i		−	1.83778i	0.394509	−	0.918892i	$-0.370915\pi$
$524$	2.17237e32			0.506941
$525$		−	2.00345e31i		−	0.0456948i
$526$		−	5.15779e31i		−	0.114983i
$527$		−	9.86307e29i		−	0.00214924i
$528$			3.80515e31i			0.0810522i
$529$	−4.23540e32	+	2.26395e32i	−0.881914	+	0.471411i
$530$	−2.10260e32			−0.428002
$531$	−4.57112e32			−0.909679
$532$	−1.43257e32			−0.278726
$533$	3.74038e32			0.711523
$534$			3.29703e31i			0.0613236i
$535$	−6.50035e32			−1.18220
$536$		−	1.20153e32i		−	0.213677i
$537$	1.13477e32			0.197340
$538$	3.22246e32			0.548025
$539$			1.83958e32i			0.305952i
$540$		−	2.35423e32i		−	0.382933i
$541$	9.42773e32			1.49982			0.749911	−	0.661538i	$-0.230096\pi$
$541$	9.42773e32			1.49982			0.749911	+	0.661538i	$0.230096\pi$
$542$	1.58358e32			0.246404
$543$			3.07588e31i			0.0468136i
$544$			4.34200e31i			0.0646403i
$545$	−3.89650e32			−0.567436
$546$			2.62412e31i			0.0373829i
$547$	6.54411e32			0.912017			0.456008	−	0.889976i	$-0.349279\pi$
$547$	6.54411e32			0.912017			0.456008	+	0.889976i	$0.349279\pi$
$548$		−	9.77215e31i		−	0.133237i
$549$			1.16728e33i			1.55706i
$550$		−	3.16024e31i		−	0.0412446i
$551$			7.04689e31i			0.0899867i
$552$	2.96135e31	+	1.18220e32i	0.0370017	+	0.147714i
$553$	−4.03797e32			−0.493698
$554$	−2.82409e32			−0.337879
$555$	−2.79998e32			−0.327822
$556$	7.30290e32			0.836754
$557$		−	3.54272e32i		−	0.397259i	−0.980075	−	0.198630i	$-0.936351\pi$
$557$		−	3.54272e32i		−	0.397259i	0.980075	−	0.198630i	$-0.0636491\pi$
$558$	6.55486e30			0.00719371
$559$			1.36128e33i			1.46220i
$560$	−2.83808e32			−0.298379
$561$	8.68988e30			0.00894251
$562$			2.34193e32i			0.235905i
$563$			5.90081e32i			0.581850i	0.956746	+	0.290925i	$0.0939630\pi$
$563$			5.90081e32i			0.581850i	−0.956746	+	0.290925i	$0.906037\pi$
$564$	4.58371e32			0.442453
$565$	−1.41072e33			−1.33309
$566$			5.23150e32i			0.483982i
$567$		−	4.30729e32i		−	0.390128i
$568$	−5.89610e32			−0.522860
$569$			2.05714e33i			1.78615i	0.449911	+	0.893073i	$0.351456\pi$
$569$			2.05714e33i			1.78615i	−0.449911	+	0.893073i	$0.648544\pi$
$570$	−4.68652e31			−0.0398430
$571$		−	4.18816e32i		−	0.348650i	−0.984688	−	0.174325i	$-0.944226\pi$
$571$		−	4.18816e32i		−	0.348650i	0.984688	−	0.174325i	$-0.0557744\pi$
$572$		−	4.30139e32i		−	0.350636i
$573$		−	4.77646e32i		−	0.381286i
$574$			1.40631e32i			0.109936i
$575$	1.09060e32	+	4.35377e32i	0.0834933	+	0.333313i
$576$	6.32490e32			0.474224
$577$	−6.83508e32			−0.501919			−0.250960	−	0.967998i	$-0.580746\pi$
$577$	−6.83508e32			−0.501919			−0.250960	+	0.967998i	$0.580746\pi$
$578$	−4.09169e32			−0.294285
$579$	−4.46549e32			−0.314577
$580$			1.56070e32i			0.107692i
$581$	−5.00914e32			−0.338571
$582$			1.30558e32i			0.0864425i
$583$	−1.11371e33			−0.722355
$584$	1.27831e33			0.812236
$585$			1.14565e33i			0.713151i
$586$			3.93092e32i			0.239730i
$587$	−2.47853e32			−0.148094			−0.0740469	−	0.997255i	$-0.523591\pi$
$587$	−2.47853e32			−0.148094			−0.0740469	+	0.997255i	$0.523591\pi$
$588$	−3.16285e32			−0.185161
$589$			2.81751e31i			0.0161615i
$590$			4.18760e32i			0.235365i
$591$	6.10614e32			0.336292
$592$		−	2.07638e33i		−	1.12059i
$593$	2.91239e33			1.54026			0.770129	−	0.637889i	$-0.220192\pi$
$593$	2.91239e33			1.54026			0.770129	+	0.637889i	$0.220192\pi$
$594$			1.20000e32i			0.0621935i
$595$			6.48136e31i			0.0329202i
$596$		−	2.55221e33i		−	1.27046i
$597$		−	3.51611e32i		−	0.171542i
$598$	−1.42847e32	−	5.70259e32i	−0.0683058	−	0.272683i
$599$	−8.62686e32			−0.404325			−0.202163	−	0.979352i	$-0.564797\pi$
$599$	−8.62686e32			−0.404325			−0.202163	+	0.979352i	$0.564797\pi$
$600$	1.13899e32			0.0523243
$601$	2.90463e33			1.30797			0.653985	−	0.756507i	$-0.273096\pi$
$601$	2.90463e33			1.30797			0.653985	+	0.756507i	$0.273096\pi$
$602$	−5.11815e32			−0.225920
$603$			8.08643e32i			0.349904i
$604$	−1.90711e33			−0.808970
$605$		−	1.62849e33i		−	0.677205i
$606$	−1.33476e32			−0.0544166
$607$	3.74668e33			1.49755			0.748776	−	0.662823i	$-0.230642\pi$
$607$	3.74668e33			1.49755			0.748776	+	0.662823i	$0.230642\pi$
$608$		−	1.24035e33i		−	0.486072i
$609$		−	5.04329e31i		−	0.0193779i
$610$	1.06934e33			0.402864
$611$	−4.63487e33			−1.71216
$612$		−	1.91878e32i		−	0.0695036i
$613$		−	8.91527e32i		−	0.316671i	−0.987385	−	0.158336i	$-0.949387\pi$
$613$		−	8.91527e32i		−	0.316671i	0.987385	−	0.158336i	$-0.0506128\pi$
$614$	4.91069e32			0.171050
$615$		−	4.78077e32i		−	0.163304i
$616$	3.39011e32			0.113565
$617$			3.47885e33i			1.14291i	0.820632	+	0.571457i	$0.193622\pi$
$617$			3.47885e33i			1.14291i	−0.820632	+	0.571457i	$0.806378\pi$
$618$		−	1.96075e32i		−	0.0631771i
$619$			3.87781e33i			1.22546i	0.790293	+	0.612729i	$0.209928\pi$
$619$			3.87781e33i			1.22546i	−0.790293	+	0.612729i	$0.790072\pi$
$620$			6.24006e31i			0.0193414i
$621$	−4.14122e32	−	1.65321e33i	−0.125901	−	0.502608i
$622$	−9.12167e31			−0.0272013
$623$	−1.30254e33			−0.381010
$624$	6.61534e32			0.189818
$625$	−1.91250e33			−0.538321
$626$		−	1.85525e32i		−	0.0512283i
$627$	−2.48238e32			−0.0672445
$628$		−	3.75208e33i		−	0.997141i
$629$	−4.74185e32			−0.123635
$630$	−4.30742e32			−0.110187
$631$		−	6.60078e32i		−	0.165670i	−0.996563	−	0.0828348i	$-0.973603\pi$
$631$		−	6.60078e32i		−	0.165670i	0.996563	−	0.0828348i	$-0.0263974\pi$
$632$		−	2.29563e33i		−	0.565324i
$633$	6.19429e32			0.149674
$634$	−1.30637e33			−0.309739
$635$			9.66019e32i			0.224751i
$636$		−	1.91484e33i		−	0.437167i
$637$	3.19815e33			0.716517
$638$		−	7.95527e31i		−	0.0174907i
$639$	3.96813e33			0.856201
$640$		−	3.59083e33i		−	0.760388i
$641$		−	4.06809e33i		−	0.845463i	−0.906255	−	0.422731i	$-0.861071\pi$
$641$		−	4.06809e33i		−	0.845463i	0.906255	−	0.422731i	$-0.138929\pi$
$642$			5.69679e32i			0.116201i
$643$		−	2.38172e33i		−	0.476825i	−0.971164	−	0.238412i	$-0.923373\pi$
$643$		−	2.38172e33i		−	0.476825i	0.971164	−	0.238412i	$-0.0766270\pi$
$644$	−2.22803e33	+	5.58111e32i	−0.437815	+	0.109671i
$645$	1.73992e33			0.335593
$646$	−7.93678e31			−0.0150264
$647$	−5.26703e33			−0.978847			−0.489423	−	0.872046i	$-0.662793\pi$
$647$	−5.26703e33			−0.978847			−0.489423	+	0.872046i	$0.662793\pi$
$648$	2.44875e33			0.446729
$649$			2.21811e33i			0.397234i
$650$	−5.49415e32			−0.0965917
$651$		−	2.01642e31i		−	0.00348025i
$652$	7.01707e33			1.18901
$653$	5.26239e33			0.875437			0.437719	−	0.899112i	$-0.355787\pi$
$653$	5.26239e33			0.875437			0.437719	+	0.899112i	$0.355787\pi$
$654$			3.41483e32i			0.0557745i
$655$			2.80761e33i			0.450236i
$656$	3.54527e33			0.558217
$657$	−8.60314e33			−1.33006
$658$		−	1.74262e33i		−	0.264541i
$659$		−	7.02936e33i		−	1.04783i	−0.851771	−	0.523915i	$-0.824471\pi$
$659$		−	7.02936e33i		−	1.04783i	0.851771	−	0.523915i	$-0.175529\pi$
$660$	−5.49782e32			−0.0804754
$661$			6.72454e33i			0.966596i	0.875456	+	0.483298i	$0.160561\pi$
$661$			6.72454e33i			0.966596i	−0.875456	+	0.483298i	$0.839439\pi$
$662$	2.26209e33			0.319311
$663$		−	1.51076e32i		−	0.0209427i
$664$		−	2.84776e33i		−	0.387691i
$665$		−	1.85149e33i		−	0.247549i
$666$		−	3.15137e33i		−	0.413817i
$667$	2.74537e32	+	1.09598e33i	0.0354072	+	0.141349i
$668$	−3.29151e33			−0.416944
$669$	−2.13532e33			−0.265674
$670$	7.40798e32			0.0905320
$671$	5.66414e33			0.679929
$672$			8.87687e32i			0.104672i
$673$	−9.11866e33			−1.05621			−0.528105	−	0.849179i	$-0.677097\pi$
$673$	−9.11866e33			−1.05621			−0.528105	+	0.849179i	$0.677097\pi$
$674$		−	8.28474e31i		−	0.00942671i
$675$	−1.59278e33			−0.178038
$676$	8.29200e32			0.0910540
$677$		−	1.42511e33i		−	0.153739i	−0.997041	−	0.0768697i	$-0.975507\pi$
$677$		−	1.42511e33i		−	0.153739i	0.997041	−	0.0768697i	$-0.0244925\pi$
$678$			1.23633e33i			0.131032i
$679$	−5.15790e33			−0.537076
$680$	−3.68474e32			−0.0376964
$681$			7.55166e32i			0.0759062i
$682$		−	3.18070e31i		−	0.00314131i
$683$	1.24170e34			1.20495			0.602473	−	0.798139i	$-0.294182\pi$
$683$	1.24170e34			1.20495			0.602473	+	0.798139i	$0.294182\pi$
$684$			5.48123e33i			0.522643i
$685$	1.26297e33			0.118333
$686$			2.79467e33i			0.257301i
$687$			2.06134e33i			0.186496i
$688$			1.29027e34i			1.14715i
$689$			1.93622e34i			1.69170i
$690$	−7.28877e32	+	1.82580e32i	−0.0625842	+	0.0156771i
$691$	−2.27630e34			−1.92085			−0.960425	−	0.278539i	$-0.910150\pi$
$691$	−2.27630e34			−1.92085			−0.960425	+	0.278539i	$0.910150\pi$
$692$	−4.57808e33			−0.379674
$693$	−2.28157e33			−0.185967
$694$	4.06676e33			0.325788
$695$			9.43840e33i			0.743157i
$696$	2.86717e32			0.0221893
$697$		−	8.09639e32i		−	0.0615883i
$698$	−5.49445e32			−0.0410827
$699$	7.12941e32			0.0523996
$700$			2.14659e33i			0.155086i
$701$			4.24110e33i			0.301205i	0.988594	+	0.150602i	$0.0481213\pi$
$701$			4.24110e33i			0.301205i	−0.988594	+	0.150602i	$0.951879\pi$
$702$	2.08623e33			0.145652
$703$	1.35457e34			0.929690
$704$		−	3.06912e33i		−	0.207082i
$705$			5.92406e33i			0.392962i
$706$	−4.04411e33			−0.263734
$707$		−	5.27318e33i		−	0.338096i
$708$	−3.81366e33			−0.240405
$709$			9.36367e33i			0.580352i	0.956973	+	0.290176i	$0.0937138\pi$
$709$			9.36367e33i			0.580352i	−0.956973	+	0.290176i	$0.906286\pi$
$710$		−	3.63521e33i		−	0.221528i
$711$			1.54498e34i			0.925739i
$712$		−	7.40513e33i		−	0.436287i
$713$	1.09766e32	+	4.38197e32i	0.00635909	+	0.0253861i
$714$	5.68015e31			0.00323580
$715$	5.55919e33			0.311415
$716$	−1.21584e34			−0.669763
$717$	−1.26278e33			−0.0684065
$718$		−	7.69655e33i		−	0.410018i
$719$	1.30145e34			0.681836			0.340918	−	0.940093i	$-0.389262\pi$
$719$	1.30145e34			0.681836			0.340918	+	0.940093i	$0.389262\pi$
$720$			1.08589e34i			0.559494i
$721$	7.74625e33			0.392526
$722$	−3.67778e33			−0.183290
$723$			1.59949e33i			0.0784009i
$724$		−	3.29564e33i		−	0.158883i
$725$	1.05592e33			0.0500695
$726$	−1.42718e33			−0.0665639
$727$		−	1.35053e34i		−	0.619571i	−0.950806	−	0.309785i	$-0.899743\pi$
$727$		−	1.35053e34i		−	0.619571i	0.950806	−	0.309785i	$-0.100257\pi$
$728$		−	5.89379e33i		−	0.265961i
$729$	−1.33429e34			−0.592271
$730$			7.88134e33i			0.344133i
$731$	2.94661e33			0.126565
$732$			9.73853e33i			0.411491i
$733$		−	1.64865e34i		−	0.685298i	−0.939463	−	0.342649i	$-0.888676\pi$
$733$		−	1.64865e34i		−	0.685298i	0.939463	−	0.342649i	$-0.111324\pi$
$734$			1.15620e34i			0.472802i
$735$		−	4.08772e33i		−	0.164450i
$736$	−4.83223e33	−	1.92907e34i	−0.191255	−	0.763508i
$737$	3.92389e33			0.152794
$738$	5.38075e33			0.206142
$739$	−2.05312e34			−0.773893			−0.386946	−	0.922102i	$-0.626470\pi$
$739$	−2.05312e34			−0.773893			−0.386946	+	0.922102i	$0.626470\pi$
$740$	3.00003e34			1.11261
$741$			4.31567e33i			0.157482i
$742$	−7.27981e33			−0.261380
$743$		−	7.63497e33i		−	0.269738i	−0.990863	−	0.134869i	$-0.956939\pi$
$743$		−	7.63497e33i		−	0.269738i	0.990863	−	0.134869i	$-0.0430613\pi$
$744$	1.14636e32			0.00398517
$745$	3.29852e34			1.12835
$746$			4.10571e33i			0.138205i
$747$			1.91657e34i			0.634858i
$748$	−9.31074e32			−0.0303504
$749$	−2.25061e34			−0.721968
$750$			2.74593e33i			0.0866869i
$751$		−	5.39179e34i		−	1.67515i	−0.546322	−	0.837575i	$-0.683973\pi$
$751$		−	5.39179e34i		−	1.67515i	0.546322	−	0.837575i	$-0.316027\pi$
$752$	−4.39310e34			−1.34325
$753$			2.70222e33i			0.0813169i
$754$	−1.38304e33			−0.0409618
$755$		−	2.46478e34i		−	0.718481i
$756$		−	8.15102e33i		−	0.233857i
$757$		−	5.16966e34i		−	1.45986i	−0.683522	−	0.729930i	$-0.739553\pi$
$757$		−	5.16966e34i		−	1.45986i	0.683522	−	0.729930i	$-0.260447\pi$
$758$			1.52136e34i			0.422865i
$759$	−3.86074e33	+	9.67099e32i	−0.105626	+	0.0264588i
$760$	1.05259e34			0.283464
$761$	2.57540e34			0.682699			0.341349	−	0.939937i	$-0.389116\pi$
$761$	2.57540e34			0.682699			0.341349	+	0.939937i	$0.389116\pi$
$762$	8.46602e32			0.0220912
$763$	−1.34908e34			−0.346533
$764$			5.11773e34i			1.29407i
$765$	2.47986e33			0.0617291
$766$			1.79356e33i			0.0439513i
$767$	3.85623e34			0.930291
$768$	2.63769e33			0.0626453
$769$		−	7.15399e34i		−	1.67275i	−0.548155	−	0.836377i	$-0.684670\pi$
$769$		−	7.15399e34i		−	1.67275i	0.548155	−	0.836377i	$-0.315330\pi$
$770$			2.09015e33i			0.0481159i
$771$	3.68018e33			0.0834097
$772$	4.78454e34			1.06766
$773$		−	6.86816e34i		−	1.50899i	−0.656305	−	0.754495i	$-0.727882\pi$
$773$		−	6.86816e34i		−	1.50899i	0.656305	−	0.754495i	$-0.272118\pi$
$774$			1.95828e34i			0.423626i
$775$	4.22180e32			0.00899243
$776$		−	2.93233e34i		−	0.614996i
$777$	−9.69433e33			−0.200201
$778$			8.90297e33i			0.181042i
$779$			2.31284e34i			0.463122i
$780$			9.55809e33i			0.188467i
$781$		−	1.92551e34i		−	0.373881i
$782$	−1.23438e33	+	3.09206e32i	−0.0236030	+	0.00591244i
$783$	−4.00952e33			−0.0755007
$784$	3.03133e34			0.562135
$785$	4.84926e34			0.885604
$786$	2.46054e33			0.0442547
$787$		−	4.17202e34i		−	0.739008i	−0.929229	−	0.369504i	$-0.879528\pi$
$787$		−	4.17202e34i		−	0.739008i	0.929229	−	0.369504i	$-0.120472\pi$
$788$	−6.54240e34			−1.14136
$789$			6.07077e33i			0.104308i
$790$	1.41536e34			0.239520
$791$	−4.88432e34			−0.814116
$792$		−	1.29710e34i		−	0.212947i
$793$		−	9.84724e34i		−	1.59234i
$794$	−2.36863e34			−0.377269
$795$	2.47478e34			0.388267
$796$			3.76732e34i			0.582205i
$797$			7.04181e34i			1.07198i	0.844226	+	0.535988i	$0.180061\pi$
$797$			7.04181e34i			1.07198i	−0.844226	+	0.535988i	$0.819939\pi$
$798$	−1.62261e33			−0.0243321
$799$			1.00326e34i			0.148201i
$800$	−1.85856e34			−0.270455
$801$			4.98372e34i			0.714436i
$802$			7.69275e33i			0.108640i
$803$			4.17462e34i			0.580805i
$804$			6.74646e33i			0.0924706i
$805$	−7.21313e33	−	2.87954e34i	−0.0974032	−	0.388842i
$806$	−5.52973e32			−0.00735671
$807$	−3.79286e34			−0.497147
$808$	2.99787e34			0.387147
$809$	−7.27114e34			−0.925167			−0.462583	−	0.886576i	$-0.653077\pi$
$809$	−7.27114e34			−0.925167			−0.462583	+	0.886576i	$0.653077\pi$
$810$			1.50976e34i			0.189272i
$811$	8.57949e34			1.05977			0.529885	−	0.848070i	$-0.322235\pi$
$811$	8.57949e34			1.05977			0.529885	+	0.848070i	$0.322235\pi$
$812$			5.40361e33i			0.0657676i
$813$	−1.86389e34			−0.223528
$814$	−1.52918e34			−0.180703
$815$			9.06899e34i			1.05601i
$816$		−	1.43195e33i		−	0.0164303i
$817$	−8.41738e34			−0.951727
$818$	−2.19601e34			−0.244678
$819$			3.96657e34i			0.435520i
$820$			5.12234e34i			0.554245i
$821$	−4.58370e34			−0.488763			−0.244381	−	0.969679i	$-0.578585\pi$
$821$	−4.58370e34			−0.488763			−0.244381	+	0.969679i	$0.578585\pi$
$822$		−	1.10685e33i		−	0.0116312i
$823$	5.91700e34			0.612778			0.306389	−	0.951906i	$-0.400879\pi$
$823$	5.91700e34			0.612778			0.306389	+	0.951906i	$0.400879\pi$
$824$			4.40384e34i			0.449474i
$825$			3.71963e33i			0.0374155i
$826$			1.44987e34i			0.143737i
$827$		−	1.50059e34i		−	0.146621i	−0.997309	−	0.0733104i	$-0.976644\pi$
$827$		−	1.50059e34i		−	0.146621i	0.997309	−	0.0733104i	$-0.0233564\pi$
$828$	2.13541e34	+	8.52475e34i	0.205645	+	0.820952i
$829$	1.23552e35			1.17272			0.586362	−	0.810049i	$-0.300560\pi$
$829$	1.23552e35			1.17272			0.586362	+	0.810049i	$0.300560\pi$
$830$	1.75577e34			0.164259
$831$	3.32398e34			0.306511
$832$	−5.33573e34			−0.484969
$833$		−	6.92269e33i		−	0.0620205i
$834$	8.27165e33			0.0730465
$835$		−	4.25401e34i		−	0.370306i
$836$	2.65973e34			0.228225
$837$	−1.60310e33			−0.0135599
$838$			5.03494e34i			0.419823i
$839$			8.55405e34i			0.703118i	0.936166	+	0.351559i	$0.114348\pi$
$839$			8.55405e34i			0.703118i	−0.936166	+	0.351559i	$0.885652\pi$
$840$	−7.53314e33			−0.0610415
$841$	−1.22527e35			−0.978767
$842$			2.78352e34i			0.219204i
$843$		−	2.75647e34i		−	0.214004i
$844$	−6.63685e34			−0.507987
$845$			1.07167e34i			0.0808690i
$846$	−6.66752e34			−0.496044
$847$		−	5.63830e34i		−	0.413568i
$848$			1.83522e35i			1.32720i
$849$		−	6.15752e34i		−	0.439049i
$850$			1.18926e33i			0.00836082i
$851$	2.10671e35	−	5.27722e34i	1.46033	−	0.365806i
$852$	3.31059e34			0.226272
$853$	1.94173e35			1.30858			0.654291	−	0.756243i	$-0.272967\pi$
$853$	1.94173e35			1.30858			0.654291	+	0.756243i	$0.272967\pi$
$854$	3.70237e34			0.246029
$855$	−7.08404e34			−0.464182
$856$		−	1.27950e35i		−	0.826713i
$857$	5.31180e34			0.338432			0.169216	−	0.985579i	$-0.445876\pi$
$857$	5.31180e34			0.338432			0.169216	+	0.985579i	$0.445876\pi$
$858$		−	4.87198e33i		−	0.0306096i
$859$	−1.11138e35			−0.688564			−0.344282	−	0.938866i	$-0.611878\pi$
$859$	−1.11138e35			−0.688564			−0.344282	+	0.938866i	$0.611878\pi$
$860$	−1.86423e35			−1.13899
$861$		−	1.65524e34i		−	0.0997294i
$862$		−	5.46917e33i		−	0.0324963i
$863$	−2.71590e35			−1.59142			−0.795708	−	0.605680i	$-0.792901\pi$
$863$	−2.71590e35			−1.59142			−0.795708	+	0.605680i	$0.792901\pi$
$864$	7.05730e34			0.407825
$865$		−	5.91680e34i		−	0.337204i
$866$			1.03985e34i			0.0584460i
$867$	4.81595e34			0.266964
$868$			2.16049e33i			0.0118118i
$869$	7.49693e34			0.404246
$870$			1.76774e33i			0.00940127i
$871$		−	6.82177e34i		−	0.357832i
$872$		−	7.66971e34i		−	0.396808i
$873$			1.97349e35i			1.00708i
$874$	3.52616e34	−	8.83286e33i	0.177486	−	0.0444595i
$875$	−1.08482e35			−0.538595
$876$	−7.17756e34			−0.351502
$877$	−1.41519e35			−0.683628			−0.341814	−	0.939768i	$-0.611041\pi$
$877$	−1.41519e35			−0.683628			−0.341814	+	0.939768i	$0.611041\pi$
$878$	−7.79743e34			−0.371550
$879$		−	4.62673e34i		−	0.217474i
$880$	5.26921e34			0.244317
$881$			3.71287e35i			1.69824i	0.528199	+	0.849120i	$0.322867\pi$
$881$			3.71287e35i			1.69824i	−0.528199	+	0.849120i	$0.677133\pi$
$882$	4.60072e34			0.207588
$883$	−1.09213e35			−0.486123			−0.243062	−	0.970011i	$-0.578152\pi$
$883$	−1.09213e35			−0.486123			−0.243062	+	0.970011i	$0.578152\pi$
$884$			1.61869e34i			0.0710784i
$885$		−	4.92884e34i		−	0.213514i
$886$	3.43303e34			0.146715
$887$	4.00908e35			1.69029			0.845145	−	0.534537i	$-0.179514\pi$
$887$	4.00908e35			1.69029			0.845145	+	0.534537i	$0.179514\pi$
$888$		−	5.51135e34i		−	0.229246i
$889$			3.34464e34i			0.137255i
$890$	4.56558e34			0.184849
$891$			7.99696e34i			0.319442i
$892$	2.28788e35			0.901686
$893$		−	2.86594e35i		−	1.11442i
$894$		−	2.89076e34i		−	0.110908i
$895$		−	1.57138e35i		−	0.594846i
$896$		−	1.24325e35i		−	0.464368i
$897$	1.68133e34	+	6.71200e34i	0.0619644	+	0.247367i
$898$	−5.93305e34			−0.215756
$899$	1.06275e33			0.00381344
$900$	8.21315e34			0.290804
$901$	4.19112e34			0.146431
$902$		−	2.61097e34i		−	0.0900169i
$903$	6.02411e34			0.204946
$904$		−	2.77680e35i		−	0.932230i
$905$	4.25935e34			0.141111
$906$	−2.16009e34			−0.0706210
$907$		−	1.48093e35i		−	0.477801i	−0.971044	−	0.238900i	$-0.923213\pi$
$907$		−	1.48093e35i		−	0.477801i	0.971044	−	0.238900i	$-0.0767869\pi$
$908$		−	8.09121e34i		−	0.257622i
$909$	−2.01759e35			−0.633967
$910$	3.63378e34			0.112684
$911$			6.01697e35i			1.84144i	0.390225	+	0.920720i	$0.372397\pi$
$911$			6.01697e35i			1.84144i	−0.390225	+	0.920720i	$0.627603\pi$
$912$			4.09055e34i			0.123550i
$913$	9.30002e34			0.277226
$914$		−	1.84832e35i		−	0.543780i
$915$	−1.25863e35			−0.365463
$916$		−	2.20862e35i		−	0.632958i
$917$			9.72074e34i			0.274959i
$918$		−	4.51584e33i		−	0.0126074i
$919$		−	4.70407e35i		−	1.29625i	−0.761535	−	0.648124i	$-0.775554\pi$
$919$		−	4.70407e35i		−	1.29625i	0.761535	−	0.648124i	$-0.224446\pi$
$920$	1.63706e35	−	4.10076e34i	0.445256	−	0.111535i
$921$	−5.77993e34			−0.155170
$922$	−2.31941e34			−0.0614620
$923$	−3.34755e35			−0.875601
$924$	−1.90351e34			−0.0491463
$925$		−	2.02971e35i		−	0.517289i
$926$	8.51348e34			0.214178
$927$		−	2.96382e35i		−	0.736030i
$928$	−4.67855e34			−0.114693
$929$	1.10644e35			0.267756			0.133878	−	0.990998i	$-0.457257\pi$
$929$	1.10644e35			0.267756			0.133878	+	0.990998i	$0.457257\pi$
$930$			7.06783e32i			0.00168846i
$931$			1.97756e35i			0.466372i
$932$	−7.63879e34			−0.177842
$933$	1.07363e34			0.0246760
$934$		−	1.06740e35i		−	0.242194i
$935$		−	1.20334e34i		−	0.0269555i
$936$	−2.25505e35			−0.498707
$937$		−	6.73987e35i		−	1.47155i	−0.677224	−	0.735777i	$-0.736817\pi$
$937$		−	6.73987e35i		−	1.47155i	0.677224	−	0.735777i	$-0.263183\pi$
$938$	2.56486e34			0.0552878
$939$			2.18364e34i			0.0464724i
$940$		−	6.34732e35i		−	1.33369i
$941$		−	1.12839e35i		−	0.234090i	−0.993127	−	0.117045i	$-0.962658\pi$
$941$		−	1.12839e35i		−	0.234090i	0.993127	−	0.117045i	$-0.0373421\pi$
$942$		−	4.24981e34i		−	0.0870479i
$943$	9.01049e34	+	3.59707e35i	0.182225	+	0.727459i
$944$	3.65508e35			0.729849
$945$	1.05345e35			0.207698
$946$	9.50242e34			0.184987
$947$	−2.27923e35			−0.438116			−0.219058	−	0.975712i	$-0.570298\pi$
$947$	−2.27923e35			−0.438116			−0.219058	+	0.975712i	$0.570298\pi$
$948$			1.28897e35i			0.244649i
$949$	7.25768e35			1.36020
$950$		−	3.39727e34i		−	0.0628704i
$951$	1.53761e35			0.280983
$952$	−1.27576e34			−0.0230211
$953$			8.30697e35i			1.48023i	0.672483	+	0.740113i	$0.265228\pi$
$953$			8.30697e35i			1.48023i	−0.672483	+	0.740113i	$0.734772\pi$
$954$			2.78536e35i			0.490118i
$955$	−6.61424e35			−1.14932
$956$	1.35300e35			0.232168
$957$			9.36342e33i			0.0158669i
$958$			2.27815e35i			0.381239i
$959$	4.37277e34			0.0722659
$960$			6.81987e34i			0.111307i
$961$	−6.19988e35			−0.999315
$962$			2.65852e35i			0.423194i
$963$			8.61115e35i			1.35377i
$964$		−	1.71377e35i		−	0.266089i
$965$			6.18362e35i			0.948234i
$966$	−2.52358e34	+	6.32146e33i	−0.0382201	+	0.00957397i
$967$	1.17440e35			0.175670			0.0878349	−	0.996135i	$-0.472005\pi$
$967$	1.17440e35			0.175670			0.0878349	+	0.996135i	$0.472005\pi$
$968$	3.20544e35			0.473569
$969$	9.34165e33			0.0136313
$970$	1.80791e35			0.260565
$971$		−	2.46321e35i		−	0.350647i	−0.984511	−	0.175324i	$-0.943903\pi$
$971$		−	2.46321e35i		−	0.350647i	0.984511	−	0.175324i	$-0.0560972\pi$
$972$	−4.73648e35			−0.665979
$973$			3.26785e35i			0.453845i
$974$	−4.00113e35			−0.548877
$975$	6.46666e34			0.0876243
$976$		−	9.33358e35i		−	1.24925i
$977$			1.96607e35i			0.259935i	0.991518	+	0.129967i	$0.0414873\pi$
$977$			1.96607e35i			0.259935i	−0.991518	+	0.129967i	$0.958513\pi$
$978$	7.94791e34			0.103797
$979$	2.41832e35			0.311976
$980$			4.37978e35i			0.558135i
$981$			5.16178e35i			0.649788i
$982$	−2.74663e35			−0.341556
$983$			1.06276e36i			1.30554i	0.757555	+	0.652772i	$0.226394\pi$
$983$			1.06276e36i			1.30554i	−0.757555	+	0.652772i	$0.773606\pi$
$984$	9.41025e34			0.114198
$985$		−	8.45552e35i		−	1.01369i
$986$			2.99372e33i			0.00354559i
$987$			2.05108e35i			0.239981i
$988$		−	4.62401e35i		−	0.534485i
$989$	−1.30912e36	+	3.27930e35i	−1.49494	+	0.374477i
$990$	7.99721e34			0.0902228
$991$	5.53394e35			0.616808			0.308404	−	0.951255i	$-0.400205\pi$
$991$	5.53394e35			0.616808			0.308404	+	0.951255i	$0.400205\pi$
$992$	−1.87059e34			−0.0205987
$993$	−2.66250e35			−0.289667
$994$		−	1.25861e35i		−	0.135287i
$995$	−4.86896e35			−0.517081
$996$			1.59898e35i			0.167777i
$997$	1.42803e36			1.48046			0.740230	−	0.672354i	$-0.234717\pi$
$997$	1.42803e36			1.48046			0.740230	+	0.672354i	$0.234717\pi$
$998$	−1.32996e35			−0.136230
$999$			7.70720e35i			0.780029i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	23.25.b.c.22.19	✓	44
23.22	odd	2	inner	23.25.b.c.22.20	yes	44

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
23.25.b.c.22.19	✓	44	1.1	even	1	trivial
23.25.b.c.22.20	yes	44	23.22	odd	2	inner

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:	\( N \)	\(=\)	\( 23 \)
Weight:	\( k \)	\(=\)	\( 25 \)
Character orbit:	\([\chi]\)	\(=\)	23.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-1213.58 q^{2} +142839. q^{3} -1.53044e7 q^{4} -1.97797e8i q^{5} -1.73346e8 q^{6} -6.84832e9i q^{7} +3.89336e10 q^{8} -2.62027e11 q^{9} +2.40042e11i q^{10} +1.27147e12i q^{11} -2.18607e12 q^{12} +2.21048e13 q^{13} +8.31097e12i q^{14} -2.82532e13i q^{15} +2.09517e14 q^{16} -4.78477e13i q^{17} +3.17989e14 q^{18} +1.36683e15i q^{19} +3.02718e15i q^{20} -9.78208e14i q^{21} -1.54302e15i q^{22} +(5.32499e15 + 2.12578e16i) q^{23} +5.56124e15 q^{24} +2.04808e16 q^{25} -2.68258e16 q^{26} -7.77696e16 q^{27} +1.04810e17i q^{28} +5.15564e16 q^{29} +3.42875e16i q^{30} +2.06135e16 q^{31} -9.07462e17 q^{32} +1.81615e17i q^{33} +5.80669e16i q^{34} -1.35458e18 q^{35} +4.01017e18 q^{36} -9.91030e18i q^{37} -1.65876e18i q^{38} +3.15742e18 q^{39} -7.70096e18i q^{40} +1.69211e19 q^{41} +1.18713e18i q^{42} +6.15831e19i q^{43} -1.94591e19i q^{44} +5.18282e19i q^{45} +(-6.46229e18 - 2.57980e19i) q^{46} -2.09678e20 q^{47} +2.99272e19 q^{48} +1.44682e20 q^{49} -2.48550e19 q^{50} -6.83453e18i q^{51} -3.38301e20 q^{52} +8.75928e20i q^{53} +9.43794e19 q^{54} +2.51493e20 q^{55} -2.66630e20i q^{56} +1.95237e20i q^{57} -6.25676e19 q^{58} +1.74453e21 q^{59} +4.32400e20i q^{60} -4.45480e21i q^{61} -2.50160e19 q^{62} +1.79444e21i q^{63} -2.41384e21 q^{64} -4.37227e21i q^{65} -2.20404e20i q^{66} -3.08611e21i q^{67} +7.32283e20i q^{68} +(7.60617e20 + 3.03645e21i) q^{69} +1.64389e21 q^{70} -1.51440e22 q^{71} -1.02016e22 q^{72} +3.28331e22 q^{73} +1.20269e22i q^{74} +2.92546e21 q^{75} -2.09186e22i q^{76} +8.70742e21 q^{77} -3.83178e21 q^{78} -5.89628e22i q^{79} -4.14420e22i q^{80} +6.28955e22 q^{81} -2.05351e22 q^{82} -7.31440e22i q^{83} +1.49709e22i q^{84} -9.46416e21 q^{85} -7.47359e22i q^{86} +7.36427e21 q^{87} +4.95028e22i q^{88} -1.90199e23i q^{89} -6.28975e22i q^{90} -1.51381e23i q^{91} +(-8.14960e22 - 3.25339e23i) q^{92} +2.94441e21 q^{93} +2.54460e23 q^{94} +2.70356e23 q^{95} -1.29621e23 q^{96} -7.53162e23i q^{97} -1.75582e23 q^{98} -3.33158e23i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 44 q - 4232 q^{2} - 434562 q^{3} + 317760360 q^{4} - 8460029520 q^{6} - 198307023760 q^{8} + 4220041988298 q^{9} - 67439597688792 q^{12} + 5771152551358 q^{13} + 18\!\cdots\!92 q^{16} + 18\!\cdots\!68 q^{18}+ \cdots - 20\!\cdots\!92 q^{98}+O(q^{100}) \) 44 * q - 4232 * q^2 - 434562 * q^3 + 317760360 * q^4 - 8460029520 * q^6 - 198307023760 * q^8 + 4220041988298 * q^9 - 67439597688792 * q^12 + 5771152551358 * q^13 + 1801550792530192 * q^16 + 1842830558165568 * q^18 - 117204213263210644 * q^23 - 186493005437450784 * q^24 - 689533084157602612 * q^25 - 548650296251047576 * q^26 + 824037505793640630 * q^27 - 1583078054945709602 * q^29 - 77249813729122274 * q^31 - 2838716832733708512 * q^32 + 3418569899175948192 * q^35 + 71181245116739335248 * q^36 + 47106572467817156310 * q^39 - 9150679195666184738 * q^41 - 153049487518536134480 * q^46 + 22735751396127769438 * q^47 - 1317482931964495330032 * q^48 - 1842110772006482246836 * q^49 + 284936617115007894520 * q^50 + 207129175371045152568 * q^52 - 381774025126375304544 * q^54 - 5430040696094013021792 * q^55 - 2168901871328366220760 * q^58 + 16048018791948427185304 * q^59 + 14054450375064171442400 * q^62 + 20310379126091866412192 * q^64 + 24476879859710435470878 * q^69 - 118028399895318845638416 * q^70 - 68204988047209908888578 * q^71 - 106777935582637627887744 * q^72 - 7319375899831086678722 * q^73 + 12913295383070041819998 * q^75 + 111116199573084838704480 * q^77 - 422583593213386075404144 * q^78 - 331350288185757013618680 * q^81 + 1000764218021118649437320 * q^82 - 113385735487939722862944 * q^85 - 248828610584854760185290 * q^87 - 4238455111972177116774696 * q^92 + 4492289396741153284965270 * q^93 - 1602622056539190351258592 * q^94 - 1668692394291208047471936 * q^95 - 12092663288748189077973504 * q^96 - 2067304853876486831513192 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more