LMFDB - Embedded newform 100.11.b.h.51.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [100,11,Mod(51,100)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(100, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 0]))

N = Newforms(chi, 11, names="a")

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

chi := DirichletCharacter("100.51");

S:= CuspForms(chi, 11);

N := Newforms(S);

Level:	$ N $	$=$	$ 100 = 2^{2} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 11 $
Character orbit:	$[\chi]$	$=$	100.b (of order $2$, degree $1$, minimal)

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:	no
Analytic conductor:	$63.5357252674$
Analytic rank:	$0$
Dimension:	$24$
Twist minimal:	no (minimal twist has level 20)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			51.3
Character	$\chi$	$=$	100.51
Dual form			100.11.b.h.51.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-26.9619 - 17.2353i) q^{2} +146.443i q^{3} +(429.889 + 929.393i) q^{4} +(2523.99 - 3948.38i) q^{6} +13979.7i q^{7} +(4427.76 - 32467.5i) q^{8} +37603.5 q^{9} +O(q^{10})$	\(q+(-26.9619 - 17.2353i) q^{2} +146.443i q^{3} +(429.889 + 929.393i) q^{4} +(2523.99 - 3948.38i) q^{6} +13979.7i q^{7} +(4427.76 - 32467.5i) q^{8} +37603.5 q^{9} -88389.7i q^{11} +(-136103. + 62954.1i) q^{12} +249490. q^{13} +(240944. - 376918. i) q^{14} +(-678968. + 799071. i) q^{16} -410905. q^{17} +(-1.01386e6 - 648107. i) q^{18} -3.01950e6i q^{19} -2.04722e6 q^{21} +(-1.52342e6 + 2.38315e6i) q^{22} -4.53962e6i q^{23} +(4.75463e6 + 648414. i) q^{24} +(-6.72671e6 - 4.30003e6i) q^{26} +1.41541e7i q^{27} +(-1.29926e7 + 6.00970e6i) q^{28} -2.62491e7 q^{29} -3.62534e7i q^{31} +(3.20785e7 - 9.84227e6i) q^{32} +1.29440e7 q^{33} +(1.10788e7 + 7.08207e6i) q^{34} +(1.61653e7 + 3.49484e7i) q^{36} -8.29063e7 q^{37} +(-5.20419e7 + 8.14114e7i) q^{38} +3.65360e7i q^{39} +1.07285e8 q^{41} +(5.51970e7 + 3.52845e7i) q^{42} +1.58335e6i q^{43} +(8.21488e7 - 3.79977e7i) q^{44} +(-7.82418e7 + 1.22397e8i) q^{46} +4.34667e8i q^{47} +(-1.17018e8 - 9.94300e7i) q^{48} +8.70443e7 q^{49} -6.01741e7i q^{51} +(1.07253e8 + 2.31874e8i) q^{52} +3.42615e8 q^{53} +(2.43950e8 - 3.81621e8i) q^{54} +(4.53884e8 + 6.18986e7i) q^{56} +4.42184e8 q^{57} +(7.07725e8 + 4.52411e8i) q^{58} -8.22725e8i q^{59} -9.43238e8 q^{61} +(-6.24838e8 + 9.77460e8i) q^{62} +5.25684e8i q^{63} +(-1.03453e9 - 2.87516e8i) q^{64} +(-3.48996e8 - 2.23094e8i) q^{66} -1.13591e9i q^{67} +(-1.76643e8 - 3.81892e8i) q^{68} +6.64796e8 q^{69} -2.91342e9i q^{71} +(1.66499e8 - 1.22089e9i) q^{72} -2.08673e9 q^{73} +(2.23531e9 + 1.42892e9i) q^{74} +(2.80630e9 - 1.29805e9i) q^{76} +1.23566e9 q^{77} +(6.29709e8 - 9.85080e8i) q^{78} -5.83812e9i q^{79} +1.47685e8 q^{81} +(-2.89261e9 - 1.84909e9i) q^{82} -9.99337e8i q^{83} +(-8.80078e8 - 1.90267e9i) q^{84} +(2.72896e7 - 4.26902e7i) q^{86} -3.84399e9i q^{87} +(-2.86979e9 - 3.91368e8i) q^{88} +3.97301e9 q^{89} +3.48778e9i q^{91} +(4.21910e9 - 1.95153e9i) q^{92} +5.30905e9 q^{93} +(7.49163e9 - 1.17195e10i) q^{94} +(1.44133e9 + 4.69767e9i) q^{96} -6.44299e9 q^{97} +(-2.34688e9 - 1.50024e9i) q^{98} -3.32376e9i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 608 q^{4} - 19584 q^{6} - 597192 q^{9}+O(q^{10}) $ 24 * q - 608 * q^4 - 19584 * q^6 - 597192 * q^9	$ 24 q - 608 q^{4} - 19584 q^{6} - 597192 q^{9} + 1706016 q^{14} - 4733376 q^{16} - 13030368 q^{21} - 10190784 q^{24} - 9454368 q^{26} - 121656816 q^{29} + 335231168 q^{34} - 276632160 q^{36} + 892843248 q^{41} - 766329600 q^{44} + 433181216 q^{46} + 738102008 q^{49} - 139387968 q^{54} - 2629032384 q^{56} + 228563248 q^{61} + 1875284992 q^{64} - 1440259200 q^{66} + 943422432 q^{69} - 21045467232 q^{74} + 828422400 q^{76} - 5619065544 q^{81} + 28069573632 q^{84} + 8163556416 q^{86} - 4631088816 q^{89} - 63404384 q^{94} - 5617046784 q^{96}+O(q^{100}) $ 24 * q - 608 * q^4 - 19584 * q^6 - 597192 * q^9 + 1706016 * q^14 - 4733376 * q^16 - 13030368 * q^21 - 10190784 * q^24 - 9454368 * q^26 - 121656816 * q^29 + 335231168 * q^34 - 276632160 * q^36 + 892843248 * q^41 - 766329600 * q^44 + 433181216 * q^46 + 738102008 * q^49 - 139387968 * q^54 - 2629032384 * q^56 + 228563248 * q^61 + 1875284992 * q^64 - 1440259200 * q^66 + 943422432 * q^69 - 21045467232 * q^74 + 828422400 * q^76 - 5619065544 * q^81 + 28069573632 * q^84 + 8163556416 * q^86 - 4631088816 * q^89 - 63404384 * q^94 - 5617046784 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/100\mathbb{Z}\right)^\times$.

$n$	$51$	$77$
$\chi(n)$	$-1$	$1$

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 $

$2$	−26.9619	−	17.2353i	−0.842560	−	0.538603i
$2$	−26.9619	−	17.2353i	−0.842560	−	0.538603i
$3$			146.443i			0.602646i	0.953522	+	0.301323i	$0.0974282\pi$
$3$			146.443i			0.602646i	−0.953522	+	0.301323i	$0.902572\pi$
$4$	429.889	+	929.393i	0.419813	+	0.907611i
$5$		0			0
$5$		0			0
$6$	2523.99	−	3948.38i	0.324587	−	0.507765i
$7$			13979.7i			0.831776i	0.909416	+	0.415888i	$0.136529\pi$
$7$			13979.7i			0.831776i	−0.909416	+	0.415888i	$0.863471\pi$
$8$	4427.76	−	32467.5i	0.135124	−	0.990829i
$9$	37603.5			0.636818
$10$		0			0
$11$		−	88389.7i		−	0.548830i	−0.961611	−	0.274415i	$-0.911516\pi$
$11$		−	88389.7i		−	0.548830i	0.961611	−	0.274415i	$-0.0884843\pi$
$12$	−136103.	+	62954.1i	−0.546968	+	0.252999i
$13$	249490.			0.671948			0.335974	−	0.941871i	$-0.390935\pi$
$13$	249490.			0.671948			0.335974	+	0.941871i	$0.390935\pi$
$14$	240944.	−	376918.i	0.447997	−	0.700821i
$15$		0			0
$16$	−678968.	+	799071.i	−0.647514	+	0.762054i
$17$	−410905.			−0.289399			−0.144699	−	0.989476i	$-0.546221\pi$
$17$	−410905.			−0.289399			−0.144699	+	0.989476i	$0.546221\pi$
$18$	−1.01386e6	−	648107.i	−0.536557	−	0.342992i
$19$		−	3.01950e6i		−	1.21946i	−0.792610	−	0.609729i	$-0.791278\pi$
$19$		−	3.01950e6i		−	1.21946i	0.792610	−	0.609729i	$-0.208722\pi$
$20$		0			0
$21$	−2.04722e6			−0.501266
$22$	−1.52342e6	+	2.38315e6i	−0.295602	+	0.462422i
$23$		−	4.53962e6i		−	0.705311i	−0.935753	−	0.352655i	$-0.885279\pi$
$23$		−	4.53962e6i		−	0.705311i	0.935753	−	0.352655i	$-0.114721\pi$
$24$	4.75463e6	+	648414.i	0.597119	+	0.0814322i
$25$		0			0
$26$	−6.72671e6	−	4.30003e6i	−0.566156	−	0.361913i
$27$			1.41541e7i			0.986421i
$28$	−1.29926e7	+	6.00970e6i	−0.754929	+	0.349191i
$29$	−2.62491e7			−1.27975			−0.639874	−	0.768480i	$-0.721013\pi$
$29$	−2.62491e7			−1.27975			−0.639874	+	0.768480i	$0.721013\pi$
$30$		0			0
$31$		−	3.62534e7i		−	1.26631i	−0.774025	−	0.633155i	$-0.781760\pi$
$31$		−	3.62534e7i		−	1.26631i	0.774025	−	0.633155i	$-0.218240\pi$
$32$	3.20785e7	−	9.84227e6i	0.956014	−	0.293323i
$33$	1.29440e7			0.330750
$34$	1.10788e7	+	7.08207e6i	0.243836	+	0.155871i
$35$		0			0
$36$	1.61653e7	+	3.49484e7i	0.267345	+	0.577983i
$37$	−8.29063e7			−1.19558			−0.597791	−	0.801652i	$-0.703955\pi$
$37$	−8.29063e7			−1.19558			−0.597791	+	0.801652i	$0.703955\pi$
$38$	−5.20419e7	+	8.14114e7i	−0.656804	+	1.02747i
$39$			3.65360e7i			0.404947i
$40$		0			0
$41$	1.07285e8			0.926018			0.463009	−	0.886354i	$-0.346770\pi$
$41$	1.07285e8			0.926018			0.463009	+	0.886354i	$0.346770\pi$
$42$	5.51970e7	+	3.52845e7i	0.422347	+	0.269984i
$43$			1.58335e6i			0.0107705i	0.999985	+	0.00538525i	$0.00171419\pi$
$43$			1.58335e6i			0.0107705i	−0.999985	+	0.00538525i	$0.998286\pi$
$44$	8.21488e7	−	3.79977e7i	0.498124	−	0.230406i
$45$		0			0
$46$	−7.82418e7	+	1.22397e8i	−0.379883	+	0.594266i
$47$			4.34667e8i			1.89526i	0.319376	+	0.947628i	$0.396527\pi$
$47$			4.34667e8i			1.89526i	−0.319376	+	0.947628i	$0.603473\pi$
$48$	−1.17018e8	−	9.94300e7i	−0.459248	−	0.390221i
$49$	8.70443e7			0.308148
$50$		0			0
$51$		−	6.01741e7i		−	0.174405i
$52$	1.07253e8	+	2.31874e8i	0.282093	+	0.609867i
$53$	3.42615e8			0.819269			0.409635	−	0.912250i	$-0.365656\pi$
$53$	3.42615e8			0.819269			0.409635	+	0.912250i	$0.365656\pi$
$54$	2.43950e8	−	3.81621e8i	0.531290	−	0.831119i
$55$		0			0
$56$	4.53884e8	+	6.18986e7i	0.824148	+	0.112393i
$57$	4.42184e8			0.734901
$58$	7.07725e8	+	4.52411e8i	1.07826	+	0.689276i
$59$		−	8.22725e8i		−	1.15079i	−0.817877	−	0.575393i	$-0.804849\pi$
$59$		−	8.22725e8i		−	1.15079i	0.817877	−	0.575393i	$-0.195151\pi$
$60$		0			0
$61$	−9.43238e8			−1.11679			−0.558396	−	0.829575i	$-0.688583\pi$
$61$	−9.43238e8			−1.11679			−0.558396	+	0.829575i	$0.688583\pi$
$62$	−6.24838e8	+	9.77460e8i	−0.682039	+	1.06694i
$63$			5.25684e8i			0.529690i
$64$	−1.03453e9	−	2.87516e8i	−0.963483	−	0.267770i
$65$		0			0
$66$	−3.48996e8	−	2.23094e8i	−0.278677	−	0.178143i
$67$		−	1.13591e9i		−	0.841333i	−0.907215	−	0.420667i	$-0.861796\pi$
$67$		−	1.13591e9i		−	0.841333i	0.907215	−	0.420667i	$-0.138204\pi$
$68$	−1.76643e8	−	3.81892e8i	−0.121493	−	0.262661i
$69$	6.64796e8			0.425053
$70$		0			0
$71$		−	2.91342e9i		−	1.61477i	−0.590023	−	0.807386i	$-0.700882\pi$
$71$		−	2.91342e9i		−	1.61477i	0.590023	−	0.807386i	$-0.299118\pi$
$72$	1.66499e8	−	1.22089e9i	0.0860497	−	0.630978i
$73$	−2.08673e9			−1.00659			−0.503295	−	0.864114i	$-0.667879\pi$
$73$	−2.08673e9			−1.00659			−0.503295	+	0.864114i	$0.667879\pi$
$74$	2.23531e9	+	1.42892e9i	1.00735	+	0.643944i
$75$		0			0
$76$	2.80630e9	−	1.29805e9i	1.10679	−	0.511944i
$77$	1.23566e9			0.456504
$78$	6.29709e8	−	9.85080e8i	0.218106	−	0.341192i
$79$		−	5.83812e9i		−	1.89731i	−0.316318	−	0.948653i	$-0.602447\pi$
$79$		−	5.83812e9i		−	1.89731i	0.316318	−	0.948653i	$-0.397553\pi$
$80$		0			0
$81$	1.47685e8			0.0423556
$82$	−2.89261e9	−	1.84909e9i	−0.780225	−	0.498756i
$83$		−	9.99337e8i		−	0.253700i	−0.991922	−	0.126850i	$-0.959513\pi$
$83$		−	9.99337e8i		−	0.253700i	0.991922	−	0.126850i	$-0.0404868\pi$
$84$	−8.80078e8	−	1.90267e9i	−0.210438	−	0.454955i
$85$		0			0
$86$	2.72896e7	−	4.26902e7i	0.00580102	−	0.00907478i
$87$		−	3.84399e9i		−	0.771234i
$88$	−2.86979e9	−	3.91368e8i	−0.543797	−	0.0741604i
$89$	3.97301e9			0.711492			0.355746	−	0.934583i	$-0.384227\pi$
$89$	3.97301e9			0.711492			0.355746	+	0.934583i	$0.384227\pi$
$90$		0			0
$91$			3.48778e9i			0.558910i
$92$	4.21910e9	−	1.95153e9i	0.640148	−	0.296099i
$93$	5.30905e9			0.763136
$94$	7.49163e9	−	1.17195e10i	1.02079	−	1.59687i
$95$		0			0
$96$	1.44133e9	+	4.69767e9i	0.176770	+	0.576137i
$97$	−6.44299e9			−0.750290			−0.375145	−	0.926966i	$-0.622407\pi$
$97$	−6.44299e9			−0.750290			−0.375145	+	0.926966i	$0.622407\pi$
$98$	−2.34688e9	−	1.50024e9i	−0.259633	−	0.165970i
$99$		−	3.32376e9i		−	0.349505i
$100$		0			0
$101$	8.50355e9			0.809083			0.404542	−	0.914520i	$-0.367431\pi$
$101$	8.50355e9			0.809083			0.404542	+	0.914520i	$0.367431\pi$
$102$	−1.03712e9	+	1.62241e9i	−0.0939350	+	0.146946i
$103$		−	1.62785e10i		−	1.40420i	−0.712078	−	0.702100i	$-0.752246\pi$
$103$		−	1.62785e10i		−	1.40420i	0.712078	−	0.702100i	$-0.247754\pi$
$104$	1.10468e9	−	8.10030e9i	0.0907966	−	0.665785i
$105$		0			0
$106$	−9.23755e9	−	5.90507e9i	−0.690283	−	0.441261i
$107$			8.18368e8i			0.0583485i	0.999574	+	0.0291743i	$0.00928777\pi$
$107$			8.18368e8i			0.0583485i	−0.999574	+	0.0291743i	$0.990712\pi$
$108$	−1.31547e10	+	6.08467e9i	−0.895286	+	0.414113i
$109$	2.97062e9			0.193070			0.0965350	−	0.995330i	$-0.469224\pi$
$109$	2.97062e9			0.193070			0.0965350	+	0.995330i	$0.469224\pi$
$110$		0			0
$111$		−	1.21410e10i		−	0.720512i
$112$	−1.11707e10	−	9.49174e9i	−0.633858	−	0.538587i
$113$	2.00487e10			1.08816			0.544080	−	0.839033i	$-0.316879\pi$
$113$	2.00487e10			1.08816			0.544080	+	0.839033i	$0.316879\pi$
$114$	−1.19221e10	−	7.62117e9i	−0.619198	−	0.395820i
$115$		0			0
$116$	−1.12842e10	−	2.43957e10i	−0.537255	−	1.16151i
$117$	9.38168e9			0.427909
$118$	−1.41799e10	+	2.21822e10i	−0.619817	+	0.969605i
$119$		−	5.74431e9i		−	0.240715i
$120$		0			0
$121$	1.81247e10			0.698785
$122$	2.54315e10	+	1.62570e10i	0.940963	+	0.601507i
$123$			1.57111e10i			0.558061i
$124$	3.36936e10	−	1.55849e10i	1.14932	−	0.531614i
$125$		0			0
$126$	9.06032e9	−	1.41734e10i	0.285293	−	0.446296i
$127$			1.68474e10i			0.509936i	0.966950	+	0.254968i	$0.0820649\pi$
$127$			1.68474e10i			0.509936i	−0.966950	+	0.254968i	$0.917935\pi$
$128$	2.29375e10	+	2.55825e10i	0.667570	+	0.744547i
$129$	−2.31871e8			−0.00649079
$130$		0			0
$131$			6.87972e9i			0.178326i	0.996017	+	0.0891629i	$0.0284192\pi$
$131$			6.87972e9i			0.178326i	−0.996017	+	0.0891629i	$0.971581\pi$
$132$	5.56450e9	+	1.20301e10i	0.138853	+	0.300192i
$133$	4.22115e10			1.01432
$134$	−1.95777e10	+	3.06262e10i	−0.453145	+	0.708873i
$135$		0			0
$136$	−1.81939e9	+	1.33410e10i	−0.0391048	+	0.286745i
$137$	3.80906e10			0.789251			0.394626	−	0.918842i	$-0.370874\pi$
$137$	3.80906e10			0.789251			0.394626	+	0.918842i	$0.370874\pi$
$138$	−1.79242e10	−	1.14580e10i	−0.358132	−	0.228935i
$139$		−	1.89688e10i		−	0.365566i	−0.983153	−	0.182783i	$-0.941489\pi$
$139$		−	1.89688e10i		−	0.365566i	0.983153	−	0.182783i	$-0.0585107\pi$
$140$		0			0
$141$	−6.36540e10			−1.14217
$142$	−5.02137e10	+	7.85513e10i	−0.869722	+	1.36054i
$143$		−	2.20523e10i		−	0.368785i
$144$	−2.55315e10	+	3.00479e10i	−0.412349	+	0.485290i
$145$		0			0
$146$	5.62623e10	+	3.59655e10i	0.848112	+	0.542153i
$147$			1.27470e10i			0.185704i
$148$	−3.56405e10	−	7.70526e10i	−0.501921	−	1.08512i
$149$	2.46526e10			0.335685			0.167842	−	0.985814i	$-0.446320\pi$
$149$	2.46526e10			0.335685			0.167842	+	0.985814i	$0.446320\pi$
$150$		0			0
$151$			9.59561e10i			1.22233i	0.791504	+	0.611164i	$0.209299\pi$
$151$			9.59561e10i			1.22233i	−0.791504	+	0.611164i	$0.790701\pi$
$152$	−9.80354e10	−	1.33696e10i	−1.20827	−	0.164778i
$153$	−1.54514e10			−0.184294
$154$	−3.33157e10	−	2.12969e10i	−0.384632	−	0.245875i
$155$		0			0
$156$	−3.39563e10	+	1.57064e10i	−0.367534	+	0.170002i
$157$	4.22802e10			0.443240			0.221620	−	0.975133i	$-0.428866\pi$
$157$	4.22802e10			0.443240			0.221620	+	0.975133i	$0.428866\pi$
$158$	−1.00622e11	+	1.57407e11i	−1.02190	+	1.59859i
$159$			5.01735e10i			0.493729i
$160$		0			0
$161$	6.34624e10			0.586661
$162$	−3.98186e9	−	2.54539e9i	−0.0356871	−	0.0228129i
$163$		−	1.44588e11i		−	1.25659i	−0.777974	−	0.628297i	$-0.783752\pi$
$163$		−	1.44588e11i		−	1.25659i	0.777974	−	0.628297i	$-0.216248\pi$
$164$	4.61206e10	+	9.97099e10i	0.388754	+	0.840464i
$165$		0			0
$166$	−1.72239e10	+	2.69440e10i	−0.136644	+	0.213758i
$167$		−	2.16899e11i		−	1.66984i	−0.550368	−	0.834922i	$-0.685513\pi$
$167$		−	2.16899e11i		−	1.66984i	0.550368	−	0.834922i	$-0.314487\pi$
$168$	−9.06460e9	+	6.64681e10i	−0.0677333	+	0.496669i
$169$	−7.56134e10			−0.548486
$170$		0			0
$171$		−	1.13544e11i		−	0.776573i
$172$	−1.47156e9	+	6.80666e8i	−0.00977541	+	0.00452159i
$173$	2.64712e11			1.70821			0.854107	−	0.520097i	$-0.174104\pi$
$173$	2.64712e11			1.70821			0.854107	+	0.520097i	$0.174104\pi$
$174$	−6.62524e10	+	1.03641e11i	−0.415389	+	0.649811i
$175$		0			0
$176$	7.06296e10	+	6.00137e10i	0.418238	+	0.355375i
$177$	1.20482e11			0.693516
$178$	−1.07120e11	−	6.84761e10i	−0.599474	−	0.383212i
$179$			3.53056e11i			1.92122i	0.277892	+	0.960612i	$0.410364\pi$
$179$			3.53056e11i			1.92122i	−0.277892	+	0.960612i	$0.589636\pi$
$180$		0			0
$181$	−1.89345e11			−0.974678			−0.487339	−	0.873213i	$-0.662032\pi$
$181$	−1.89345e11			−0.974678			−0.487339	+	0.873213i	$0.662032\pi$
$182$	6.01129e10	−	9.40372e10i	0.301031	−	0.470915i
$183$		−	1.38130e11i		−	0.673030i
$184$	−1.47390e11	−	2.01004e10i	−0.698842	−	0.0953047i
$185$		0			0
$186$	−1.43142e11	−	9.15031e10i	−0.642988	−	0.411028i
$187$			3.63197e10i			0.158831i
$188$	−4.03977e11	+	1.86859e11i	−1.72015	+	0.795653i
$189$	−1.97869e11			−0.820482
$190$		0			0
$191$		−	1.77750e11i		−	0.699266i	−0.936887	−	0.349633i	$-0.886306\pi$
$191$		−	1.77750e11i		−	0.699266i	0.936887	−	0.349633i	$-0.113694\pi$
$192$	4.21047e10	−	1.51500e11i	0.161371	−	0.580639i
$193$	4.76572e11			1.77968			0.889841	−	0.456271i	$-0.150815\pi$
$193$	4.76572e11			1.77968			0.889841	+	0.456271i	$0.150815\pi$
$194$	1.73715e11	+	1.11047e11i	0.632164	+	0.404108i
$195$		0			0
$196$	3.74194e10	+	8.08984e10i	0.129365	+	0.279679i
$197$	−3.11485e11			−1.04980			−0.524900	−	0.851164i	$-0.675897\pi$
$197$	−3.11485e11			−1.04980			−0.524900	+	0.851164i	$0.675897\pi$
$198$	−5.72860e10	+	8.96149e10i	−0.188245	+	0.294479i
$199$		−	8.32510e10i		−	0.266762i	−0.991065	−	0.133381i	$-0.957417\pi$
$199$		−	8.32510e10i		−	0.266762i	0.991065	−	0.133381i	$-0.0425834\pi$
$200$		0			0
$201$	1.66345e11			0.507026
$202$	−2.29272e11	−	1.46561e11i	−0.681701	−	0.435775i
$203$		−	3.66953e11i		−	1.06446i
$204$	5.59254e10	−	2.58682e10i	0.158292	−	0.0732175i
$205$		0			0
$206$	−2.80565e11	+	4.38900e11i	−0.756307	+	1.18312i
$207$		−	1.70706e11i		−	0.449155i
$208$	−1.69395e11	+	1.99360e11i	−0.435096	+	0.512060i
$209$	−2.66892e11			−0.669275
$210$		0			0
$211$			4.08040e11i			0.975641i	0.872944	+	0.487820i	$0.162208\pi$
$211$			4.08040e11i			0.975641i	−0.872944	+	0.487820i	$0.837792\pi$
$212$	1.47286e11	+	3.18424e11i	0.343940	+	0.743578i
$213$	4.26650e11			0.973136
$214$	1.41048e10	−	2.20648e10i	0.0314267	−	0.0491621i
$215$		0			0
$216$	4.59547e11	+	6.26708e10i	0.977375	+	0.133290i
$217$	5.06810e11			1.05329
$218$	−8.00936e10	−	5.11996e10i	−0.162673	−	0.103988i
$219$		−	3.05587e11i		−	0.606617i
$220$		0			0
$221$	−1.02516e11			−0.194461
$222$	−2.09255e11	+	3.27346e11i	−0.388070	+	0.607074i
$223$		−	3.09347e11i		−	0.560947i	−0.959862	−	0.280473i	$-0.909509\pi$
$223$		−	3.09347e11i		−	0.560947i	0.959862	−	0.280473i	$-0.0904914\pi$
$224$	1.37592e11	+	4.48446e11i	0.243979	+	0.795189i
$225$		0			0
$226$	−5.40550e11	−	3.45545e11i	−0.916840	−	0.586087i
$227$			4.36504e11i			0.724200i	0.932139	+	0.362100i	$0.117940\pi$
$227$			4.36504e11i			0.724200i	−0.932139	+	0.362100i	$0.882060\pi$
$228$	1.90090e11	+	4.10963e11i	0.308521	+	0.667004i
$229$	8.85513e11			1.40610			0.703052	−	0.711138i	$-0.251820\pi$
$229$	8.85513e11			1.40610			0.703052	+	0.711138i	$0.251820\pi$
$230$		0			0
$231$			1.80953e11i			0.275110i
$232$	−1.16225e11	+	8.52241e11i	−0.172925	+	1.26801i
$233$	3.44547e10			0.0501729			0.0250864	−	0.999685i	$-0.492014\pi$
$233$	3.44547e10			0.0501729			0.0250864	+	0.999685i	$0.492014\pi$
$234$	−2.52948e11	−	1.61696e11i	−0.360539	−	0.230473i
$235$		0			0
$236$	7.64635e11	−	3.53680e11i	1.04447	−	0.483115i
$237$	8.54951e11			1.14340
$238$	−9.90049e10	+	1.54878e11i	−0.129650	+	0.202817i
$239$			3.54744e11i			0.454910i	0.973789	+	0.227455i	$0.0730404\pi$
$239$			3.54744e11i			0.454910i	−0.973789	+	0.227455i	$0.926960\pi$
$240$		0			0
$241$	5.46010e11			0.671608			0.335804	−	0.941932i	$-0.390992\pi$
$241$	5.46010e11			0.671608			0.335804	+	0.941932i	$0.390992\pi$
$242$	−4.88676e11	−	3.12385e11i	−0.588768	−	0.376368i
$243$			8.57411e11i			1.01195i
$244$	−4.05487e11	−	8.76639e11i	−0.468844	−	1.01361i
$245$		0			0
$246$	2.70786e11	−	4.23602e11i	0.300573	−	0.470199i
$247$		−	7.53333e11i		−	0.819412i
$248$	−1.17706e12	−	1.60521e11i	−1.25470	−	0.171109i
$249$	1.46346e11			0.152892
$250$		0			0
$251$		−	2.78449e11i		−	0.279497i	−0.990187	−	0.139748i	$-0.955371\pi$
$251$		−	2.78449e11i		−	0.279497i	0.990187	−	0.139748i	$-0.0446293\pi$
$252$	−4.88567e11	+	2.25986e11i	−0.480752	+	0.222371i
$253$	−4.01256e11			−0.387096
$254$	2.90371e11	−	4.54239e11i	0.274653	−	0.429651i
$255$		0			0
$256$	−1.77518e11	−	1.08509e12i	−0.161452	−	0.986881i
$257$	−1.03896e11			−0.0926688			−0.0463344	−	0.998926i	$-0.514754\pi$
$257$	−1.03896e11			−0.0926688			−0.0463344	+	0.998926i	$0.514754\pi$
$258$	6.25168e9	+	3.99636e9i	0.00546888	+	0.00349596i
$259$		−	1.15900e12i		−	0.994456i
$260$		0			0
$261$	−9.87057e11			−0.814966
$262$	1.18574e11	−	1.85490e11i	0.0960469	−	0.150250i
$263$		−	3.81998e11i		−	0.303586i	−0.988412	−	0.151793i	$-0.951495\pi$
$263$		−	3.81998e11i		−	0.303586i	0.988412	−	0.151793i	$-0.0485048\pi$
$264$	5.73131e10	−	4.20260e11i	0.0446924	−	0.327717i
$265$		0			0
$266$	−1.13810e12	−	7.27529e11i	−0.854621	−	0.546314i
$267$			5.81820e11i			0.428778i
$268$	1.05570e12	−	4.88313e11i	0.763603	−	0.353203i
$269$	9.64366e11			0.684668			0.342334	−	0.939578i	$-0.388782\pi$
$269$	9.64366e11			0.684668			0.342334	+	0.939578i	$0.388782\pi$
$270$		0			0
$271$		−	5.71457e10i		−	0.0390964i	−0.999809	−	0.0195482i	$-0.993777\pi$
$271$		−	5.71457e10i		−	0.0390964i	0.999809	−	0.0195482i	$-0.00622279\pi$
$272$	2.78991e11	−	3.28342e11i	0.187390	−	0.220537i
$273$	−5.10761e11			−0.336825
$274$	−1.02700e12	−	6.56504e11i	−0.664991	−	0.425093i
$275$		0			0
$276$	2.85788e11	+	6.17857e11i	0.178443	+	0.385782i
$277$	−1.80699e12			−1.10804			−0.554021	−	0.832503i	$-0.686907\pi$
$277$	−1.80699e12			−1.10804			−0.554021	+	0.832503i	$0.686907\pi$
$278$	−3.26933e11	+	5.11436e11i	−0.196895	+	0.308012i
$279$		−	1.36325e12i		−	0.806409i
$280$		0			0
$281$	1.67597e12			0.956612			0.478306	−	0.878193i	$-0.341251\pi$
$281$	1.67597e12			0.956612			0.478306	+	0.878193i	$0.341251\pi$
$282$	1.71623e12	+	1.09710e12i	0.962344	+	0.615175i
$283$		−	1.29146e12i		−	0.711459i	−0.934589	−	0.355730i	$-0.884232\pi$
$283$		−	1.29146e12i		−	0.711459i	0.934589	−	0.355730i	$-0.115768\pi$
$284$	2.70771e12	−	1.25245e12i	1.46558	−	0.677903i
$285$		0			0
$286$	−3.80078e11	+	5.94572e11i	−0.198629	+	0.310724i
$287$			1.49981e12i			0.770240i
$288$	1.20626e12	−	3.70104e11i	0.608807	−	0.186793i
$289$	−1.84715e12			−0.916248
$290$		0			0
$291$		−	9.43530e11i		−	0.452159i
$292$	−8.97063e11	−	1.93940e12i	−0.422580	−	0.913592i
$293$	3.77568e12			1.74847			0.874233	−	0.485507i	$-0.161365\pi$
$293$	3.77568e12			1.74847			0.874233	+	0.485507i	$0.161365\pi$
$294$	2.19699e11	−	3.43684e11i	0.100021	−	0.156467i
$295$		0			0
$296$	−3.67089e11	+	2.69176e12i	−0.161552	+	1.18462i
$297$	1.25107e12			0.541378
$298$	−6.64682e11	−	4.24896e11i	−0.282835	−	0.180801i
$299$		−	1.13259e12i		−	0.473932i
$300$		0			0
$301$	−2.21347e10			−0.00895864
$302$	1.65383e12	−	2.58716e12i	0.658350	−	1.02988i
$303$			1.24528e12i			0.487591i
$304$	2.41279e12	+	2.05014e12i	0.929292	+	0.789615i
$305$		0			0
$306$	4.16600e11	+	2.66310e11i	0.155279	+	0.0992615i
$307$		−	3.98468e12i		−	1.46117i	−0.682820	−	0.730587i	$-0.739246\pi$
$307$		−	3.98468e12i		−	1.46117i	0.682820	−	0.730587i	$-0.260754\pi$
$308$	5.31195e11	+	1.14841e12i	0.191646	+	0.414328i
$309$	2.38388e12			0.846236
$310$		0			0
$311$		−	1.39871e12i		−	0.480758i	−0.970679	−	0.240379i	$-0.922728\pi$
$311$		−	1.39871e12i		−	0.480758i	0.970679	−	0.240379i	$-0.0772717\pi$
$312$	1.18623e12	+	1.61772e11i	0.401233	+	0.0547182i
$313$	−5.82569e12			−1.93921			−0.969607	−	0.244667i	$-0.921321\pi$
$313$	−5.82569e12			−1.93921			−0.969607	+	0.244667i	$0.921321\pi$
$314$	−1.13995e12	−	7.28712e11i	−0.373456	−	0.238730i
$315$		0			0
$316$	5.42591e12	−	2.50974e12i	1.72202	−	0.796514i
$317$	−4.41493e12			−1.37920			−0.689600	−	0.724190i	$-0.742214\pi$
$317$	−4.41493e12			−1.37920			−0.689600	+	0.724190i	$0.742214\pi$
$318$	8.64756e11	−	1.35277e12i	0.265924	−	0.415996i
$319$			2.32015e12i			0.702364i
$320$		0			0
$321$	−1.19844e11			−0.0351635
$322$	−1.71107e12	−	1.09379e12i	−0.494297	−	0.315977i
$323$			1.24073e12i			0.352909i
$324$	6.34880e10	+	1.37257e11i	0.0177814	+	0.0384424i
$325$		0			0
$326$	−2.49202e12	+	3.89838e12i	−0.676806	+	1.05876i
$327$			4.35027e11i			0.116353i
$328$	4.75032e11	−	3.48327e12i	0.125128	−	0.917525i
$329$	−6.07650e12			−1.57643
$330$		0			0
$331$		−	1.01492e12i		−	0.255441i	−0.991810	−	0.127720i	$-0.959234\pi$
$331$		−	1.01492e12i		−	0.255441i	0.991810	−	0.127720i	$-0.0407660\pi$
$332$	9.28777e11	−	4.29603e11i	0.230261	−	0.106507i
$333$	−3.11757e12			−0.761368
$334$	−3.73833e12	+	5.84802e12i	−0.899383	+	1.40694i
$335$		0			0
$336$	1.39000e12	−	1.63588e12i	0.324577	−	0.381992i
$337$	2.73619e12			0.629503			0.314751	−	0.949174i	$-0.398079\pi$
$337$	2.73619e12			0.629503			0.314751	+	0.949174i	$0.398079\pi$
$338$	2.03868e12	+	1.30322e12i	0.462132	+	0.295416i
$339$			2.93598e12i			0.655775i
$340$		0			0
$341$	−3.20442e12			−0.694989
$342$	−1.95696e12	+	3.06135e12i	−0.418264	+	0.654309i
$343$			5.16576e12i			1.08809i
$344$	5.14075e10	+	7.01070e9i	0.0106717	+	0.00145536i
$345$		0			0
$346$	−7.13713e12	−	4.56238e12i	−1.43927	−	0.920050i
$347$			4.92030e12i			0.978013i	0.872280	+	0.489006i	$0.162641\pi$
$347$			4.92030e12i			0.978013i	−0.872280	+	0.489006i	$0.837359\pi$
$348$	3.57258e12	−	1.65249e12i	0.699980	−	0.323774i
$349$	4.17497e12			0.806355			0.403178	−	0.915122i	$-0.367906\pi$
$349$	4.17497e12			0.806355			0.403178	+	0.915122i	$0.367906\pi$
$350$		0			0
$351$			3.53129e12i			0.662824i
$352$	−8.69955e11	−	2.83541e12i	−0.160984	−	0.524689i
$353$	−6.96972e12			−1.27157			−0.635787	−	0.771864i	$-0.719324\pi$
$353$	−6.96972e12			−1.27157			−0.635787	+	0.771864i	$0.719324\pi$
$354$	−3.24843e12	−	2.07655e12i	−0.584328	−	0.373530i
$355$		0			0
$356$	1.70795e12	+	3.69249e12i	0.298694	+	0.645758i
$357$	8.41213e11			0.145066
$358$	6.08502e12	−	9.51905e12i	1.03478	−	1.61875i
$359$		−	6.96682e11i		−	0.116832i	−0.998292	−	0.0584161i	$-0.981395\pi$
$359$		−	6.96682e11i		−	0.116832i	0.998292	−	0.0584161i	$-0.0186050\pi$
$360$		0			0
$361$	−2.98629e12			−0.487076
$362$	5.10510e12	+	3.26342e12i	0.821224	+	0.524965i
$363$			2.65423e12i			0.421120i
$364$	−3.24152e12	+	1.49936e12i	−0.507273	+	0.234638i
$365$		0			0
$366$	−2.38072e12	+	3.72426e12i	−0.362496	+	0.567067i
$367$			3.80852e12i			0.572039i	0.958224	+	0.286020i	$0.0923322\pi$
$367$			3.80852e12i			0.572039i	−0.958224	+	0.286020i	$0.907668\pi$
$368$	3.62748e12	+	3.08226e12i	0.537485	+	0.456699i
$369$	4.03429e12			0.589705
$370$		0			0
$371$			4.78964e12i			0.681449i
$372$	2.28230e12	+	4.93419e12i	0.320375	+	0.692630i
$373$	−9.60132e12			−1.32980			−0.664901	−	0.746932i	$-0.731526\pi$
$373$	−9.60132e12			−1.32980			−0.664901	+	0.746932i	$0.731526\pi$
$374$	6.25982e11	−	9.79249e11i	0.0855468	−	0.133824i
$375$		0			0
$376$	1.41126e13	+	1.92460e12i	1.87787	+	0.256095i
$377$	−6.54887e12			−0.859924
$378$	5.33493e12	+	3.41033e12i	0.691305	+	0.441914i
$379$			6.23848e12i			0.797779i	0.916999	+	0.398890i	$0.130604\pi$
$379$			6.23848e12i			0.797779i	−0.916999	+	0.398890i	$0.869396\pi$
$380$		0			0
$381$	−2.46719e12			−0.307311
$382$	−3.06357e12	+	4.79248e12i	−0.376627	+	0.589173i
$383$			8.64559e12i			1.04906i	0.851392	+	0.524530i	$0.175759\pi$
$383$			8.64559e12i			1.04906i	−0.851392	+	0.524530i	$0.824241\pi$
$384$	−3.74637e12	+	3.35904e12i	−0.448698	+	0.402308i
$385$		0			0
$386$	−1.28493e13	−	8.21387e12i	−1.49949	−	0.958542i
$387$			5.95396e10i			0.00685884i
$388$	−2.76977e12	−	5.98807e12i	−0.314981	−	0.680971i
$389$	−8.65443e12			−0.971606			−0.485803	−	0.874068i	$-0.661473\pi$
$389$	−8.65443e12			−0.971606			−0.485803	+	0.874068i	$0.661473\pi$
$390$		0			0
$391$			1.86535e12i			0.204116i
$392$	3.85411e11	−	2.82611e12i	0.0416384	−	0.305322i
$393$	−1.00749e12			−0.107467
$394$	8.39823e12	+	5.36854e12i	0.884518	+	0.565425i
$395$		0			0
$396$	3.08908e12	−	1.42885e12i	0.317215	−	0.146727i
$397$	5.71458e11			0.0579471			0.0289736	−	0.999580i	$-0.490776\pi$
$397$	5.71458e11			0.0579471			0.0289736	+	0.999580i	$0.490776\pi$
$398$	−1.43486e12	+	2.24461e12i	−0.143679	+	0.224763i
$399$			6.18158e12i			0.611273i
$400$		0			0
$401$	1.44767e13			1.39620			0.698098	−	0.716002i	$-0.254030\pi$
$401$	1.44767e13			1.39620			0.698098	+	0.716002i	$0.254030\pi$
$402$	−4.48499e12	−	2.86701e12i	−0.427200	−	0.273086i
$403$		−	9.04484e12i		−	0.850894i
$404$	3.65558e12	+	7.90314e12i	0.339664	+	0.734333i
$405$		0			0
$406$	−6.32455e12	+	9.89376e12i	−0.573323	+	0.896874i
$407$			7.32807e12i			0.656171i
$408$	−1.95370e12	−	2.66436e11i	−0.172805	−	0.0235664i
$409$	−7.48900e12			−0.654346			−0.327173	−	0.944964i	$-0.606096\pi$
$409$	−7.48900e12			−0.654346			−0.327173	+	0.944964i	$0.606096\pi$
$410$		0			0
$411$			5.57810e12i			0.475639i
$412$	1.51292e13	−	6.99796e12i	1.27447	−	0.589502i
$413$	1.15014e13			0.957196
$414$	−2.94216e12	+	4.60255e12i	−0.241916	+	0.378440i
$415$		0			0
$416$	8.00325e12	−	2.45554e12i	0.642391	−	0.197097i
$417$	2.77785e12			0.220307
$418$	7.19593e12	+	4.59997e12i	0.563904	+	0.360474i
$419$			6.35022e12i			0.491721i	0.969305	+	0.245861i	$0.0790705\pi$
$419$			6.35022e12i			0.491721i	−0.969305	+	0.245861i	$0.920929\pi$
$420$		0			0
$421$	2.25594e12			0.170575			0.0852877	−	0.996356i	$-0.472819\pi$
$421$	2.25594e12			0.170575			0.0852877	+	0.996356i	$0.472819\pi$
$422$	7.03269e12	−	1.10015e13i	0.525483	−	0.822035i
$423$			1.63450e13i			1.20693i
$424$	1.51702e12	−	1.11238e13i	0.110703	−	0.811756i
$425$		0			0
$426$	−1.15033e13	−	7.35344e12i	−0.819925	−	0.524134i
$427$		−	1.31861e13i		−	0.928920i
$428$	−7.60586e11	+	3.51807e11i	−0.0529577	+	0.0244955i
$429$	3.22940e12			0.222247
$430$		0			0
$431$		−	1.04502e13i		−	0.702646i	−0.936254	−	0.351323i	$-0.885732\pi$
$431$		−	1.04502e13i		−	0.702646i	0.936254	−	0.351323i	$-0.114268\pi$
$432$	−1.13101e13	−	9.61015e12i	−0.751706	−	0.638722i
$433$	6.36111e12			0.417920			0.208960	−	0.977924i	$-0.432992\pi$
$433$	6.36111e12			0.417920			0.208960	+	0.977924i	$0.432992\pi$
$434$	−1.36646e13	−	8.73502e12i	−0.887456	−	0.567303i
$435$		0			0
$436$	1.27704e12	+	2.76088e12i	0.0810533	+	0.175232i
$437$	−1.37074e13			−0.860097
$438$	−5.26689e12	+	8.23922e12i	−0.326726	+	0.511111i
$439$		−	1.91298e13i		−	1.17324i	−0.809862	−	0.586620i	$-0.800458\pi$
$439$		−	1.91298e13i		−	1.17324i	0.809862	−	0.586620i	$-0.199542\pi$
$440$		0			0
$441$	3.27317e12			0.196235
$442$	2.76404e12	+	1.76690e12i	0.163845	+	0.104737i
$443$		−	1.80726e13i		−	1.05926i	−0.848229	−	0.529629i	$-0.822331\pi$
$443$		−	1.80726e13i		−	1.05926i	0.848229	−	0.529629i	$-0.177669\pi$
$444$	1.12838e13	−	5.21930e12i	0.653944	−	0.302480i
$445$		0			0
$446$	−5.33169e12	+	8.34058e12i	−0.302128	+	0.472631i
$447$			3.61020e12i			0.202299i
$448$	4.01938e12	−	1.44624e13i	0.222725	−	0.801402i
$449$	7.71297e12			0.422659			0.211329	−	0.977415i	$-0.432221\pi$
$449$	7.71297e12			0.422659			0.211329	+	0.977415i	$0.432221\pi$
$450$		0			0
$451$		−	9.48288e12i		−	0.508227i
$452$	8.61869e12	+	1.86331e13i	0.456824	+	0.987626i
$453$	−1.40521e13			−0.736631
$454$	7.52327e12	−	1.17690e13i	0.390056	−	0.610182i
$455$		0			0
$456$	1.95788e12	−	1.43566e13i	0.0993030	−	0.728161i
$457$	−5.55477e12			−0.278667			−0.139333	−	0.990246i	$-0.544496\pi$
$457$	−5.55477e12			−0.278667			−0.139333	+	0.990246i	$0.544496\pi$
$458$	−2.38751e13	−	1.52621e13i	−1.18473	−	0.757332i
$459$		−	5.81597e12i		−	0.285469i
$460$		0			0
$461$	−1.48116e13			−0.711372			−0.355686	−	0.934605i	$-0.615753\pi$
$461$	−1.48116e13			−0.711372			−0.355686	+	0.934605i	$0.615753\pi$
$462$	3.11879e12	−	4.87885e12i	0.148175	−	0.231797i
$463$		−	2.87422e13i		−	1.35087i	−0.737418	−	0.675436i	$-0.763955\pi$
$463$		−	2.87422e13i		−	1.35087i	0.737418	−	0.675436i	$-0.236045\pi$
$464$	1.78223e13	−	2.09749e13i	0.828654	−	0.975236i
$465$		0			0
$466$	−9.28965e11	−	5.93837e11i	−0.0422736	−	0.0270233i
$467$		−	1.93804e13i		−	0.872527i	−0.899819	−	0.436264i	$-0.856302\pi$
$467$		−	1.93804e13i		−	0.872527i	0.899819	−	0.436264i	$-0.143698\pi$
$468$	4.03308e12	+	8.71927e12i	0.179642	+	0.388374i
$469$	1.58796e13			0.699801
$470$		0			0
$471$			6.19163e12i			0.267117i
$472$	−2.67118e13	−	3.64282e12i	−1.14023	−	0.155499i
$473$	1.39952e11			0.00591117
$474$	−2.30511e13	−	1.47353e13i	−0.963386	−	0.615841i
$475$		0			0
$476$	5.33872e12	−	2.46941e12i	0.218475	−	0.101055i
$477$	1.28835e13			0.521726
$478$	6.11412e12	−	9.56457e12i	0.245016	−	0.383288i
$479$		−	1.28939e13i		−	0.511335i	−0.966765	−	0.255667i	$-0.917705\pi$
$479$		−	1.28939e13i		−	0.511335i	0.966765	−	0.255667i	$-0.0822952\pi$
$480$		0			0
$481$	−2.06843e13			−0.803369
$482$	−1.47215e13	−	9.41065e12i	−0.565869	−	0.361730i
$483$			9.29362e12i			0.353549i
$484$	7.79160e12	+	1.68450e13i	0.293359	+	0.634225i
$485$		0			0
$486$	1.47777e13	−	2.31174e13i	0.545038	−	0.852625i
$487$		−	1.59672e11i		−	0.00582886i	−0.999996	−	0.00291443i	$-0.999072\pi$
$487$		−	1.59672e11i		−	0.00582886i	0.999996	−	0.00291443i	$-0.000927693\pi$
$488$	−4.17643e12	+	3.06246e13i	−0.150906	+	1.10655i
$489$	2.11739e13			0.757281
$490$		0			0
$491$		−	4.18477e12i		−	0.146644i	−0.997308	−	0.0733219i	$-0.976640\pi$
$491$		−	4.18477e12i		−	0.146644i	0.997308	−	0.0733219i	$-0.0233601\pi$
$492$	−1.46018e13	+	6.75403e12i	−0.506502	+	0.234281i
$493$	1.07859e13			0.370357
$494$	−1.29839e13	+	2.03113e13i	−0.441338	+	0.690403i
$495$		0			0
$496$	2.89690e13	+	2.46149e13i	0.964996	+	0.819953i
$497$	4.07286e13			1.34313
$498$	−3.94576e12	−	2.52231e12i	−0.128820	−	0.0823479i
$499$		−	5.68728e13i		−	1.83824i	−0.393978	−	0.919120i	$-0.628902\pi$
$499$		−	5.68728e13i		−	1.83824i	0.393978	−	0.919120i	$-0.371098\pi$
$500$		0			0
$501$	3.17634e13			1.00632
$502$	−4.79915e12	+	7.50751e12i	−0.150538	+	0.235493i
$503$			4.10150e13i			1.27380i	0.770945	+	0.636902i	$0.219784\pi$
$503$			4.10150e13i			1.27380i	−0.770945	+	0.636902i	$0.780216\pi$
$504$	1.70676e13	+	2.32760e12i	0.524832	+	0.0715741i
$505$		0			0
$506$	1.08186e13	+	6.91577e12i	0.326151	+	0.208491i
$507$		−	1.10731e13i		−	0.330543i
$508$	−1.56579e13	+	7.24252e12i	−0.462823	+	0.214078i
$509$	−3.18969e13			−0.933599			−0.466799	−	0.884363i	$-0.654593\pi$
$509$	−3.18969e13			−0.933599			−0.466799	+	0.884363i	$0.654593\pi$
$510$		0			0
$511$		−	2.91718e13i		−	0.837258i
$512$	−1.39156e13	+	3.23156e13i	−0.395505	+	0.918464i
$513$	4.27382e13			1.20290
$514$	2.80124e12	+	1.79068e12i	0.0780790	+	0.0499117i
$515$		0			0
$516$	−9.96786e10	−	2.15499e11i	−0.00272492	−	0.00589111i
$517$	3.84201e13			1.04017
$518$	−1.99758e13	+	3.12489e13i	−0.535617	+	0.837888i
$519$			3.87651e13i			1.02945i
$520$		0			0
$521$	−1.50084e13			−0.390972			−0.195486	−	0.980707i	$-0.562628\pi$
$521$	−1.50084e13			−0.390972			−0.195486	+	0.980707i	$0.562628\pi$
$522$	2.66129e13	+	1.70122e13i	0.686658	+	0.438943i
$523$		−	4.78587e13i		−	1.22307i	−0.791216	−	0.611537i	$-0.790552\pi$
$523$		−	4.78587e13i		−	1.22307i	0.791216	−	0.611537i	$-0.209448\pi$
$524$	−6.39397e12	+	2.95751e12i	−0.161850	+	0.0748635i
$525$		0			0
$526$	−6.58385e12	+	1.02994e13i	−0.163513	+	0.255790i
$527$			1.48967e13i			0.366468i
$528$	−8.78858e12	+	1.03432e13i	−0.214165	+	0.252049i
$529$	2.08183e13			0.502536
$530$		0			0
$531$		−	3.09373e13i		−	0.732841i
$532$	1.81463e13	+	3.92311e13i	0.425823	+	0.920603i
$533$	2.67665e13			0.622236
$534$	1.00278e13	−	1.56870e13i	0.230941	−	0.361271i
$535$		0			0
$536$	−3.68800e13	−	5.02951e12i	−0.833617	−	0.113685i
$537$	−5.17025e13			−1.15782
$538$	−2.60011e13	−	1.66211e13i	−0.576874	−	0.368765i
$539$		−	7.69382e12i		−	0.169121i
$540$		0			0
$541$	5.80418e12			0.125243			0.0626217	−	0.998037i	$-0.480054\pi$
$541$	5.80418e12			0.125243			0.0626217	+	0.998037i	$0.480054\pi$
$542$	−9.84924e11	+	1.54076e12i	−0.0210575	+	0.0329411i
$543$		−	2.77282e13i		−	0.587385i
$544$	−1.31812e13	+	4.04424e12i	−0.276669	+	0.0848872i
$545$		0			0
$546$	1.37711e13	+	8.80311e12i	0.283795	+	0.181415i
$547$			5.03600e13i			1.02837i	0.857679	+	0.514185i	$0.171906\pi$
$547$			5.03600e13i			1.02837i	−0.857679	+	0.514185i	$0.828094\pi$
$548$	1.63747e13	+	3.54012e13i	0.331338	+	0.716333i
$549$	−3.54690e13			−0.711193
$550$		0			0
$551$			7.92590e13i			1.56060i
$552$	2.94355e12	−	2.15842e13i	0.0574350	−	0.421154i
$553$	8.16149e13			1.57813
$554$	4.87198e13	+	3.11440e13i	0.933591	+	0.596795i
$555$		0			0
$556$	1.76295e13	−	8.15448e12i	0.331792	−	0.153470i
$557$	3.19874e13			0.596627			0.298314	−	0.954468i	$-0.403576\pi$
$557$	3.19874e13			0.596627			0.298314	+	0.954468i	$0.403576\pi$
$558$	−2.34961e13	+	3.67559e13i	−0.434335	+	0.679448i
$559$			3.95030e11i			0.00723721i
$560$		0			0
$561$	−5.31877e12			−0.0957187
$562$	−4.51875e13	−	2.88859e13i	−0.806002	−	0.515234i
$563$		−	3.34105e13i		−	0.590665i	−0.955395	−	0.295332i	$-0.904570\pi$
$563$		−	3.34105e13i		−	0.590665i	0.955395	−	0.295332i	$-0.0954304\pi$
$564$	−2.73641e13	−	5.91596e13i	−0.479497	−	1.03664i
$565$		0			0
$566$	−2.22588e13	+	3.48203e13i	−0.383194	+	0.599447i
$567$			2.06458e12i			0.0352304i
$568$	−9.45914e13	−	1.28999e13i	−1.59996	−	0.218195i
$569$	3.53976e13			0.593488			0.296744	−	0.954957i	$-0.404099\pi$
$569$	3.53976e13			0.593488			0.296744	+	0.954957i	$0.404099\pi$
$570$		0			0
$571$			9.52378e12i			0.156902i	0.996918	+	0.0784511i	$0.0249974\pi$
$571$			9.52378e12i			0.156902i	−0.996918	+	0.0784511i	$0.975003\pi$
$572$	2.04953e13	−	9.48003e12i	0.334714	−	0.154821i
$573$	2.60302e13			0.421410
$574$	2.58496e13	−	4.04377e13i	0.414854	−	0.648973i
$575$		0			0
$576$	−3.89020e13	−	1.08116e13i	−0.613563	−	0.170521i
$577$	−7.27346e13			−1.13727			−0.568633	−	0.822592i	$-0.692527\pi$
$577$	−7.27346e13			−1.13727			−0.568633	+	0.822592i	$0.692527\pi$
$578$	4.98027e13	+	3.18362e13i	0.771994	+	0.493494i
$579$			6.97906e13i			1.07252i
$580$		0			0
$581$	1.39704e13			0.211022
$582$	−1.62620e13	+	2.54394e13i	−0.243534	+	0.380971i
$583$		−	3.02836e13i		−	0.449640i
$584$	−9.23955e12	+	6.77510e13i	−0.136015	+	0.997359i
$585$		0			0
$586$	−1.01800e14	−	6.50750e13i	−1.47319	−	0.941729i
$587$		−	3.06508e13i		−	0.439795i	−0.975523	−	0.219898i	$-0.929428\pi$
$587$		−	3.06508e13i		−	0.439795i	0.975523	−	0.219898i	$-0.0705724\pi$
$588$	−1.18470e13	+	5.47980e12i	−0.168547	+	0.0779611i
$589$	−1.09467e14			−1.54421
$590$		0			0
$591$		−	4.56148e13i		−	0.632657i
$592$	5.62907e13	−	6.62481e13i	0.774156	−	0.911097i
$593$	1.36696e13			0.186416			0.0932078	−	0.995647i	$-0.470288\pi$
$593$	1.36696e13			0.186416			0.0932078	+	0.995647i	$0.470288\pi$
$594$	−3.37313e13	−	2.15626e13i	−0.456143	−	0.291588i
$595$		0			0
$596$	1.05979e13	+	2.29120e13i	0.140925	+	0.304671i
$597$	1.21915e13			0.160763
$598$	−1.95205e13	+	3.05367e13i	−0.255261	+	0.399316i
$599$			9.08884e13i			1.17862i	0.807906	+	0.589311i	$0.200601\pi$
$599$			9.08884e13i			1.17862i	−0.807906	+	0.589311i	$0.799399\pi$
$600$		0			0
$601$	2.58195e13			0.329288			0.164644	−	0.986353i	$-0.447352\pi$
$601$	2.58195e13			0.329288			0.164644	+	0.986353i	$0.447352\pi$
$602$	5.96795e11	+	3.81499e11i	0.00754819	+	0.00482515i
$603$		−	4.27140e13i		−	0.535776i
$604$	−8.91810e13	+	4.12505e13i	−1.10940	+	0.513150i
$605$		0			0
$606$	2.14628e13	−	3.35752e13i	0.262618	−	0.410824i
$607$		−	1.20909e14i		−	1.46729i	−0.679532	−	0.733646i	$-0.737817\pi$
$607$		−	1.20909e14i		−	1.46729i	0.679532	−	0.733646i	$-0.262183\pi$
$608$	−2.97187e13	−	9.68609e13i	−0.357694	−	1.16582i
$609$	5.37377e13			0.641494
$610$		0			0
$611$			1.08445e14i			1.27351i
$612$	−6.64240e12	−	1.43605e13i	−0.0773692	−	0.167268i
$613$	−4.75439e13			−0.549278			−0.274639	−	0.961547i	$-0.588558\pi$
$613$	−4.75439e13			−0.549278			−0.274639	+	0.961547i	$0.588558\pi$
$614$	−6.86772e13	+	1.07435e14i	−0.786993	+	1.23113i
$615$		0			0
$616$	5.47119e12	−	4.01187e13i	0.0616848	−	0.452317i
$617$	1.10787e14			1.23898			0.619488	−	0.785006i	$-0.287340\pi$
$617$	1.10787e14			1.23898			0.619488	+	0.785006i	$0.287340\pi$
$618$	−6.42738e13	−	4.10868e13i	−0.713004	−	0.455785i
$619$			1.29963e14i			1.43010i	0.699071	+	0.715052i	$0.253597\pi$
$619$			1.29963e14i			1.43010i	−0.699071	+	0.715052i	$0.746403\pi$
$620$		0			0
$621$	6.42541e13			0.695734
$622$	−2.41072e13	+	3.77119e13i	−0.258938	+	0.405067i
$623$			5.55414e13i			0.591802i
$624$	−2.91948e13	−	2.48067e13i	−0.308591	−	0.262209i
$625$		0			0
$626$	1.57072e14	+	1.00408e14i	1.63390	+	1.04447i
$627$		−	3.90845e13i		−	0.403336i
$628$	1.81758e13	+	3.92949e13i	0.186078	+	0.402289i
$629$	3.40666e13			0.346000
$630$		0			0
$631$		−	1.72818e13i		−	0.172760i	−0.996262	−	0.0863798i	$-0.972470\pi$
$631$		−	1.72818e13i		−	0.172760i	0.996262	−	0.0863798i	$-0.0275299\pi$
$632$	−1.89549e14	−	2.58498e13i	−1.87991	−	0.256372i
$633$	−5.97545e13			−0.587966
$634$	1.19035e14	+	7.60926e13i	1.16206	+	0.742842i
$635$		0			0
$636$	−4.66309e13	+	2.15690e13i	−0.448114	+	0.207274i
$637$	2.17166e13			0.207060
$638$	3.99885e13	−	6.25556e13i	0.378296	−	0.591784i
$639$		−	1.09555e14i		−	1.02832i
$640$		0			0
$641$	−2.02056e14			−1.86716			−0.933580	−	0.358369i	$-0.883333\pi$
$641$	−2.02056e14			−1.86716			−0.933580	+	0.358369i	$0.883333\pi$
$642$	3.23123e12	+	2.06555e12i	0.0296273	+	0.0189392i
$643$			7.34393e13i			0.668150i	0.942547	+	0.334075i	$0.108424\pi$
$643$			7.34393e13i			0.668150i	−0.942547	+	0.334075i	$0.891576\pi$
$644$	2.72818e13	+	5.89815e13i	0.246288	+	0.532460i
$645$		0			0
$646$	2.13843e13	−	3.34523e13i	0.190078	−	0.297347i
$647$		−	2.94516e13i		−	0.259769i	−0.991529	−	0.129885i	$-0.958539\pi$
$647$		−	2.94516e13i		−	0.259769i	0.991529	−	0.129885i	$-0.0414607\pi$
$648$	6.53912e11	−	4.79495e12i	0.00572327	−	0.0419671i
$649$	−7.27204e13			−0.631586
$650$		0			0
$651$			7.42187e13i			0.634759i
$652$	1.34379e14	−	6.21569e13i	1.14050	−	0.527535i
$653$	−9.08012e13			−0.764761			−0.382381	−	0.924005i	$-0.624896\pi$
$653$	−9.08012e13			−0.764761			−0.382381	+	0.924005i	$0.624896\pi$
$654$	7.49781e12	−	1.17291e13i	0.0626680	−	0.0980342i
$655$		0			0
$656$	−7.28430e13	+	8.57283e13i	−0.599609	+	0.705675i
$657$	−7.84685e13			−0.641015
$658$	1.63834e14	+	1.04730e14i	1.32823	+	0.849070i
$659$		−	1.09885e14i		−	0.884119i	−0.896986	−	0.442060i	$-0.854248\pi$
$659$		−	1.09885e14i		−	0.884119i	0.896986	−	0.442060i	$-0.145752\pi$
$660$		0			0
$661$	9.98769e13			0.791512			0.395756	−	0.918356i	$-0.370483\pi$
$661$	9.98769e13			0.791512			0.395756	+	0.918356i	$0.370483\pi$
$662$	−1.74924e13	+	2.73640e13i	−0.137581	+	0.215224i
$663$		−	1.50128e13i		−	0.117191i
$664$	−3.24459e13	−	4.42482e12i	−0.251374	−	0.0342811i
$665$		0			0
$666$	8.40555e13	+	5.37322e13i	0.641498	+	0.410075i
$667$			1.19161e14i			0.902620i
$668$	2.01585e14	−	9.32426e13i	1.51557	−	0.701022i
$669$	4.53017e13			0.338052
$670$		0			0
$671$			8.33725e13i			0.612929i
$672$	−6.56718e13	+	2.01493e13i	−0.479217	+	0.147033i
$673$	−3.19718e13			−0.231575			−0.115787	−	0.993274i	$-0.536939\pi$
$673$	−3.19718e13			−0.231575			−0.115787	+	0.993274i	$0.536939\pi$
$674$	−7.37730e13	−	4.71591e13i	−0.530393	−	0.339052i
$675$		0			0
$676$	−3.25054e13	−	7.02746e13i	−0.230262	−	0.497812i
$677$	−1.90887e13			−0.134225			−0.0671123	−	0.997745i	$-0.521379\pi$
$677$	−1.90887e13			−0.134225			−0.0671123	+	0.997745i	$0.521379\pi$
$678$	5.06026e13	−	7.91597e13i	0.353203	−	0.552530i
$679$		−	9.00708e13i		−	0.624073i
$680$		0			0
$681$	−6.39229e13			−0.436436
$682$	8.63974e13	+	5.52292e13i	0.585570	+	0.374323i
$683$		−	9.20549e12i		−	0.0619360i	−0.999520	−	0.0309680i	$-0.990141\pi$
$683$		−	9.20549e12i		−	0.0619360i	0.999520	−	0.0309680i	$-0.00985900\pi$
$684$	1.05527e14	−	4.88111e13i	0.704825	−	0.326015i
$685$		0			0
$686$	8.90334e13	−	1.39279e14i	0.586047	−	0.916778i
$687$			1.29677e14i			0.847383i
$688$	−1.26521e12	−	1.07505e12i	−0.00820769	−	0.00697404i
$689$	8.54788e13			0.550506
$690$		0			0
$691$		−	2.89506e14i		−	1.83767i	−0.394645	−	0.918834i	$-0.629132\pi$
$691$		−	2.89506e14i		−	1.83767i	0.394645	−	0.918834i	$-0.370868\pi$
$692$	1.13796e14	+	2.46021e14i	0.717131	+	1.55039i
$693$	4.64650e13			0.290710
$694$	8.48029e13	−	1.32661e14i	0.526761	−	0.824034i
$695$		0			0
$696$	−1.24805e14	−	1.70203e13i	−0.764161	−	0.104213i
$697$	−4.40839e13			−0.267988
$698$	−1.12565e14	−	7.19569e13i	−0.679402	−	0.434306i
$699$			5.04565e12i			0.0302365i
$700$		0			0
$701$	−1.50130e14			−0.886903			−0.443451	−	0.896298i	$-0.646246\pi$
$701$	−1.50130e14			−0.886903			−0.443451	+	0.896298i	$0.646246\pi$
$702$	6.08629e13	−	9.52104e13i	0.356999	−	0.558469i
$703$			2.50335e14i			1.45796i
$704$	−2.54135e13	+	9.14419e13i	−0.146960	+	0.528789i
$705$		0			0
$706$	1.87917e14	+	1.20125e14i	1.07138	+	0.684874i
$707$			1.18877e14i			0.672976i
$708$	5.17939e13	+	1.11975e14i	0.291147	+	0.629442i
$709$	−5.68854e13			−0.317519			−0.158760	−	0.987317i	$-0.550749\pi$
$709$	−5.68854e13			−0.317519			−0.158760	+	0.987317i	$0.550749\pi$
$710$		0			0
$711$		−	2.19534e14i		−	1.20824i
$712$	1.75915e13	−	1.28994e14i	0.0961400	−	0.704967i
$713$	−1.64577e14			−0.893142
$714$	−2.26807e13	−	1.44986e13i	−0.122227	−	0.0781329i
$715$		0			0
$716$	−3.28128e14	+	1.51775e14i	−1.74372	+	0.806555i
$717$	−5.19497e13			−0.274149
$718$	−1.20075e13	+	1.87839e13i	−0.0629262	+	0.0984381i
$719$			4.60962e13i			0.239895i	0.992780	+	0.119947i	$0.0382725\pi$
$719$			4.60962e13i			0.239895i	−0.992780	+	0.119947i	$0.961727\pi$
$720$		0			0
$721$	2.27568e14			1.16798
$722$	8.05162e13	+	5.14697e13i	0.410390	+	0.262341i
$723$			7.99593e13i			0.404741i
$724$	−8.13973e13	−	1.75976e14i	−0.409183	−	0.884628i
$725$		0			0
$726$	4.57465e13	−	7.15632e13i	0.226817	−	0.354819i
$727$			1.49821e14i			0.737736i	0.929482	+	0.368868i	$0.120254\pi$
$727$			1.49821e14i			0.737736i	−0.929482	+	0.368868i	$0.879746\pi$
$728$	1.13239e14	+	1.54430e13i	0.553784	+	0.0755224i
$729$	−1.16841e14			−0.567490
$730$		0			0
$731$		−	6.50607e11i		−	0.00311697i
$732$	1.28378e14	−	5.93807e13i	0.610849	−	0.282547i
$733$	−9.25379e13			−0.437320			−0.218660	−	0.975801i	$-0.570169\pi$
$733$	−9.25379e13			−0.437320			−0.218660	+	0.975801i	$0.570169\pi$
$734$	6.56410e13	−	1.02685e14i	0.308102	−	0.481977i
$735$		0			0
$736$	−4.46802e13	−	1.45624e14i	−0.206884	−	0.674287i
$737$	−1.00402e14			−0.461749
$738$	−1.08772e14	−	6.95321e13i	−0.496862	−	0.317617i
$739$		−	4.85434e13i		−	0.220246i	−0.993918	−	0.110123i	$-0.964876\pi$
$739$		−	4.85434e13i		−	0.220246i	0.993918	−	0.110123i	$-0.0351245\pi$
$740$		0			0
$741$	1.10320e14			0.493815
$742$	8.25509e13	−	1.29138e14i	0.367031	−	0.574161i
$743$			4.13114e13i			0.182442i	0.995831	+	0.0912211i	$0.0290770\pi$
$743$			4.13114e13i			0.182442i	−0.995831	+	0.0912211i	$0.970923\pi$
$744$	2.35072e13	−	1.72371e14i	0.103118	−	0.756137i
$745$		0			0
$746$	2.58870e14	+	1.65482e14i	1.12044	+	0.716235i
$747$		−	3.75785e13i		−	0.161561i
$748$	−3.37553e13	+	1.56134e13i	−0.144157	+	0.0666792i
$749$	−1.14405e13			−0.0485329
$750$		0			0
$751$			8.29433e13i			0.347202i	0.984816	+	0.173601i	$0.0555403\pi$
$751$			8.29433e13i			0.347202i	−0.984816	+	0.173601i	$0.944460\pi$
$752$	−3.47330e14	−	2.95125e14i	−1.44429	−	1.22720i
$753$	4.07768e13			0.168437
$754$	1.76570e14	+	1.12872e14i	0.724537	+	0.463158i
$755$		0			0
$756$	−8.50617e13	−	1.83898e14i	−0.344449	−	0.744678i
$757$	−1.93514e14			−0.778455			−0.389228	−	0.921142i	$-0.627258\pi$
$757$	−1.93514e14			−0.778455			−0.389228	+	0.921142i	$0.627258\pi$
$758$	1.07522e14	−	1.68201e14i	0.429686	−	0.672176i
$759$		−	5.87611e13i		−	0.233282i
$760$		0			0
$761$	1.66032e14			0.650531			0.325265	−	0.945623i	$-0.394546\pi$
$761$	1.66032e14			0.650531			0.325265	+	0.945623i	$0.394546\pi$
$762$	6.65201e13	+	4.25227e13i	0.258927	+	0.165518i
$763$			4.15283e13i			0.160591i
$764$	1.65200e14	−	7.64127e13i	0.634661	−	0.293561i
$765$		0			0
$766$	1.49009e14	−	2.33102e14i	0.565028	−	0.883896i
$767$		−	2.05261e14i		−	0.773268i
$768$	1.58903e14	−	2.59962e13i	0.594739	−	0.0972981i
$769$	4.26640e14			1.58646			0.793232	−	0.608919i	$-0.208397\pi$
$769$	4.26640e14			1.58646			0.793232	+	0.608919i	$0.208397\pi$
$770$		0			0
$771$		−	1.52148e13i		−	0.0558464i
$772$	2.04873e14	+	4.42923e14i	0.747134	+	1.61526i
$773$	−4.17310e14			−1.51203			−0.756017	−	0.654552i	$-0.772857\pi$
$773$	−4.17310e14			−1.51203			−0.756017	+	0.654552i	$0.772857\pi$
$774$	1.02618e12	−	1.60530e12i	0.00369420	−	0.00577898i
$775$		0			0
$776$	−2.85280e13	+	2.09188e14i	−0.101382	+	0.743408i
$777$	1.69728e14			0.599305
$778$	2.33340e14	+	1.49162e14i	0.818636	+	0.523310i
$779$		−	3.23946e14i		−	1.12924i
$780$		0			0
$781$	−2.57516e14			−0.886236
$782$	3.21499e13	−	5.02935e13i	0.109938	−	0.171980i
$783$		−	3.71531e14i		−	1.26237i
$784$	−5.91003e13	+	6.95546e13i	−0.199530	+	0.234826i
$785$		0			0
$786$	2.71637e13	+	1.73643e13i	0.0905476	+	0.0578822i
$787$		−	1.87778e13i		−	0.0621974i	−0.999516	−	0.0310987i	$-0.990099\pi$
$787$		−	1.87778e13i		−	0.0621974i	0.999516	−	0.0310987i	$-0.00990061\pi$
$788$	−1.33904e14	−	2.89492e14i	−0.440719	−	0.952809i
$789$	5.59409e13			0.182955
$790$		0			0
$791$			2.80273e14i			0.905106i
$792$	−1.07914e14	−	1.47168e13i	−0.346300	−	0.0472267i
$793$	−2.35328e14			−0.750426
$794$	−1.54076e13	−	9.84926e12i	−0.0488239	−	0.0312105i
$795$		0			0
$796$	7.73729e13	−	3.57887e13i	0.242116	−	0.111990i
$797$	−2.33356e14			−0.725649			−0.362825	−	0.931857i	$-0.618188\pi$
$797$	−2.33356e14			−0.725649			−0.362825	+	0.931857i	$0.618188\pi$
$798$	1.06541e14	−	1.66667e14i	0.329234	−	0.515034i
$799$		−	1.78607e14i		−	0.548485i
$800$		0			0
$801$	1.49399e14			0.453091
$802$	−3.90318e14	−	2.49510e14i	−1.17638	−	0.751996i
$803$			1.84446e14i			0.552447i
$804$	7.15099e13	+	1.54600e14i	0.212856	+	0.460182i
$805$		0			0
$806$	−1.55891e14	+	2.43866e14i	−0.458294	+	0.716929i
$807$			1.41224e14i			0.412612i
$808$	3.76516e13	−	2.76089e14i	0.109327	−	0.801663i
$809$	−3.46851e14			−1.00092			−0.500461	−	0.865759i	$-0.666836\pi$
$809$	−3.46851e14			−1.00092			−0.500461	+	0.865759i	$0.666836\pi$
$810$		0			0
$811$			1.48396e14i			0.422978i	0.977380	+	0.211489i	$0.0678313\pi$
$811$			1.48396e14i			0.422978i	−0.977380	+	0.211489i	$0.932169\pi$
$812$	3.41044e14	−	1.57749e14i	0.966118	−	0.446876i
$813$	8.36859e12			0.0235613
$814$	1.26301e14	−	1.97579e14i	0.353416	−	0.552863i
$815$		0			0
$816$	4.80834e13	+	4.08562e13i	0.132906	+	0.112930i
$817$	4.78093e12			0.0131342
$818$	2.01918e14	+	1.29075e14i	0.551325	+	0.352433i
$819$			1.31153e14i			0.355924i
$820$		0			0
$821$	−4.15425e14			−1.11372			−0.556861	−	0.830605i	$-0.687995\pi$
$821$	−4.15425e14			−1.11372			−0.556861	+	0.830605i	$0.687995\pi$
$822$	9.61403e13	−	1.50396e14i	0.256181	−	0.400754i
$823$			4.98563e14i			1.32045i	0.751069	+	0.660224i	$0.229539\pi$
$823$			4.98563e14i			1.32045i	−0.751069	+	0.660224i	$0.770461\pi$
$824$	−5.28523e14	−	7.20774e13i	−1.39132	−	0.189742i
$825$		0			0
$826$	−3.10100e14	−	1.98230e14i	−0.806495	−	0.515549i
$827$		−	6.46871e14i		−	1.67221i	−0.548571	−	0.836104i	$-0.684828\pi$
$827$		−	6.46871e14i		−	1.67221i	0.548571	−	0.836104i	$-0.315172\pi$
$828$	1.58653e14	−	7.33844e13i	0.407658	−	0.188561i
$829$	1.71726e14			0.438596			0.219298	−	0.975658i	$-0.429623\pi$
$829$	1.71726e14			0.438596			0.219298	+	0.975658i	$0.429623\pi$
$830$		0			0
$831$		−	2.64620e14i		−	0.667756i
$832$	−2.58105e14	−	7.17323e13i	−0.647410	−	0.179928i
$833$	−3.57669e13			−0.0891778
$834$	−7.48961e13	−	4.78771e13i	−0.185622	−	0.118658i
$835$		0			0
$836$	−1.14734e14	−	2.48048e14i	−0.280970	−	0.607441i
$837$	5.13133e14			1.24912
$838$	1.09448e14	−	1.71214e14i	0.264843	−	0.414304i
$839$			3.56109e14i			0.856591i	0.903639	+	0.428295i	$0.140886\pi$
$839$			3.56109e14i			0.856591i	−0.903639	+	0.428295i	$0.859114\pi$
$840$		0			0
$841$	2.68307e14			0.637753
$842$	−6.08244e13	−	3.88818e13i	−0.143720	−	0.0918725i
$843$			2.45435e14i			0.576498i
$844$	−3.79229e14	+	1.75412e14i	−0.885502	+	0.409587i
$845$		0			0
$846$	2.81711e14	−	4.40693e14i	0.650058	−	1.01691i
$847$			2.53377e14i			0.581233i
$848$	−2.32624e14	+	2.73774e14i	−0.530488	+	0.624327i
$849$	1.89126e14			0.428758
$850$		0			0
$851$			3.76364e14i			0.843257i
$852$	1.83412e14	+	3.96525e14i	0.408535	+	0.883228i
$853$	3.78193e14			0.837468			0.418734	−	0.908109i	$-0.362474\pi$
$853$	3.78193e14			0.837468			0.418734	+	0.908109i	$0.362474\pi$
$854$	−2.27267e14	+	3.55524e14i	−0.500320	+	0.782671i
$855$		0			0
$856$	2.65703e13	+	3.62354e12i	0.0578134	+	0.00788431i
$857$	3.25573e14			0.704278			0.352139	−	0.935948i	$-0.385454\pi$
$857$	3.25573e14			0.704278			0.352139	+	0.935948i	$0.385454\pi$
$858$	−8.70709e13	−	5.56597e13i	−0.187256	−	0.119703i
$859$			1.71426e14i			0.366531i	0.983063	+	0.183266i	$0.0586668\pi$
$859$			1.71426e14i			0.366531i	−0.983063	+	0.183266i	$0.941333\pi$
$860$		0			0
$861$	−2.19636e14			−0.464182
$862$	−1.80112e14	+	2.81756e14i	−0.378447	+	0.592021i
$863$		−	7.32951e14i		−	1.53116i	−0.643340	−	0.765581i	$-0.722452\pi$
$863$		−	7.32951e14i		−	1.53116i	0.643340	−	0.765581i	$-0.277548\pi$
$864$	1.39308e14	+	4.54041e14i	0.289340	+	0.943032i
$865$		0			0
$866$	−1.71508e14	−	1.09636e14i	−0.352123	−	0.225093i
$867$		−	2.70502e14i		−	0.552173i
$868$	2.17872e14	+	4.71026e14i	0.442183	+	0.955974i
$869$	−5.16029e14			−1.04130
$870$		0			0
$871$		−	2.83397e14i		−	0.565332i
$872$	1.31532e13	−	9.64486e13i	0.0260885	−	0.191299i
$873$	−2.42279e14			−0.477798
$874$	3.69577e14	+	2.36251e14i	0.724683	+	0.463251i
$875$		0			0
$876$	2.84011e14	−	1.31369e14i	0.550572	−	0.254666i
$877$	−6.25010e14			−1.20473			−0.602364	−	0.798222i	$-0.705774\pi$
$877$	−6.25010e14			−1.20473			−0.602364	+	0.798222i	$0.705774\pi$
$878$	−3.29707e14	+	5.15775e14i	−0.631911	+	0.988524i
$879$			5.52922e14i			1.05371i
$880$		0			0
$881$	3.05476e14			0.575569			0.287784	−	0.957695i	$-0.407081\pi$
$881$	3.05476e14			0.575569			0.287784	+	0.957695i	$0.407081\pi$
$882$	−8.82509e13	−	5.64141e13i	−0.165339	−	0.105693i
$883$		−	3.59888e13i		−	0.0670446i	−0.999438	−	0.0335223i	$-0.989328\pi$
$883$		−	3.59888e13i		−	0.0670446i	0.999438	−	0.0335223i	$-0.0106725\pi$
$884$	−4.40707e13	−	9.52781e13i	−0.0816372	−	0.176495i
$885$		0			0
$886$	−3.11487e14	+	4.87272e14i	−0.570520	+	0.892488i
$887$			4.13812e14i			0.753677i	0.926279	+	0.376839i	$0.122989\pi$
$887$			4.13812e14i			0.753677i	−0.926279	+	0.376839i	$0.877011\pi$
$888$	−3.94189e14	−	5.37576e13i	−0.713904	−	0.0973588i
$889$	−2.35522e14			−0.424152
$890$		0			0
$891$		−	1.30538e13i		−	0.0232460i
$892$	2.87505e14	−	1.32985e14i	0.509121	−	0.235493i
$893$	1.31248e15			2.31118
$894$	6.22229e13	−	9.73379e13i	0.108959	−	0.170449i
$895$		0			0
$896$	−3.57634e14	+	3.20659e14i	−0.619297	+	0.555269i
$897$	1.65860e14			0.285613
$898$	−2.07956e14	−	1.32935e14i	−0.356115	−	0.227645i
$899$			9.51618e14i			1.62056i
$900$		0			0
$901$	−1.40782e14			−0.237096
$902$	−1.63440e14	+	2.55676e14i	−0.273733	+	0.428211i
$903$		−	3.24148e12i		−	0.00539888i
$904$	8.87706e13	−	6.50929e14i	0.147037	−	1.07818i
$905$		0			0
$906$	3.78871e14	+	2.42192e14i	0.620656	+	0.396752i
$907$			8.06692e14i			1.31423i	0.753791	+	0.657115i	$0.228223\pi$
$907$			8.06692e14i			1.31423i	−0.753791	+	0.657115i	$0.771777\pi$
$908$	−4.05684e14	+	1.87648e14i	−0.657292	+	0.304029i
$909$	3.19763e14			0.515239
$910$		0			0
$911$			8.50991e14i			1.35623i	0.734956	+	0.678115i	$0.237203\pi$
$911$			8.50991e14i			1.35623i	−0.734956	+	0.678115i	$0.762797\pi$
$912$	−3.00228e14	+	3.53336e14i	−0.475858	+	0.560034i
$913$	−8.83310e13			−0.139239
$914$	1.49767e14	+	9.57381e13i	0.234793	+	0.150091i
$915$		0			0
$916$	3.80672e14	+	8.22990e14i	0.590301	+	1.27620i
$917$	−9.61762e13			−0.148327
$918$	−1.00240e14	+	1.56810e14i	−0.153755	+	0.240525i
$919$		−	3.79956e14i		−	0.579637i	−0.957082	−	0.289819i	$-0.906405\pi$
$919$		−	3.79956e14i		−	0.579637i	0.957082	−	0.289819i	$-0.0935950\pi$
$920$		0			0
$921$	5.83529e14			0.880570
$922$	3.99349e14	+	2.55282e14i	0.599374	+	0.383147i
$923$		−	7.26868e14i		−	1.08504i
$924$	−1.68177e14	+	7.77898e13i	−0.249693	+	0.115495i
$925$		0			0
$926$	−4.95380e14	+	7.74943e14i	−0.727584	+	1.13819i
$927$		−	6.12130e14i		−	0.894221i
$928$	−8.42031e14	+	2.58351e14i	−1.22346	+	0.375379i
$929$	−3.47287e14			−0.501891			−0.250946	−	0.968001i	$-0.580742\pi$
$929$	−3.47287e14			−0.501891			−0.250946	+	0.968001i	$0.580742\pi$
$930$		0			0
$931$		−	2.62830e14i		−	0.375774i
$932$	1.48117e13	+	3.20220e13i	0.0210632	+	0.0455374i
$933$	2.04831e14			0.289726
$934$	−3.34027e14	+	5.22533e14i	−0.469946	+	0.735156i
$935$		0			0
$936$	4.15398e13	−	3.04599e14i	0.0578209	−	0.423984i
$937$	2.94468e14			0.407700			0.203850	−	0.979002i	$-0.434654\pi$
$937$	2.94468e14			0.407700			0.203850	+	0.979002i	$0.434654\pi$
$938$	−4.28144e14	−	2.73689e14i	−0.589624	−	0.376915i
$939$		−	8.53131e14i		−	1.16866i
$940$		0			0
$941$	−6.35492e14			−0.861315			−0.430657	−	0.902515i	$-0.641718\pi$
$941$	−6.35492e14			−0.861315			−0.430657	+	0.902515i	$0.641718\pi$
$942$	1.06715e14	−	1.66938e14i	0.143870	−	0.225062i
$943$		−	4.87033e14i		−	0.653131i
$944$	6.57416e14	+	5.58603e14i	0.876960	+	0.745150i
$945$		0			0
$946$	−3.77337e12	−	2.41212e12i	−0.00498051	−	0.00318378i
$947$			1.19083e15i			1.56351i	0.623589	+	0.781753i	$0.285674\pi$
$947$			1.19083e15i			1.56351i	−0.623589	+	0.781753i	$0.714326\pi$
$948$	3.67534e14	+	7.94586e14i	0.480016	+	1.03777i
$949$	−5.20618e14			−0.676376
$950$		0			0
$951$		−	6.46535e14i		−	0.831169i
$952$	−1.86503e14	−	2.54344e13i	−0.238507	−	0.0325265i
$953$	8.93473e14			1.13662			0.568312	−	0.822813i	$-0.307597\pi$
$953$	8.93473e14			1.13662			0.568312	+	0.822813i	$0.307597\pi$
$954$	−3.47364e14	−	2.22051e14i	−0.439585	−	0.281003i
$955$		0			0
$956$	−3.29696e14	+	1.52500e14i	−0.412881	+	0.190977i
$957$	−3.39769e14			−0.423277
$958$	−2.22229e14	+	3.47643e14i	−0.275406	+	0.430830i
$959$			5.32494e14i			0.656480i
$960$		0			0
$961$	−4.94679e14			−0.603541
$962$	5.57687e14	+	3.56500e14i	0.676886	+	0.432697i
$963$			3.07735e13i			0.0371574i
$964$	2.34724e14	+	5.07458e14i	0.281950	+	0.609558i
$965$		0			0
$966$	1.60178e14	−	2.50574e14i	0.190422	−	0.297886i
$967$		−	8.32138e14i		−	0.984154i	−0.870552	−	0.492077i	$-0.836238\pi$
$967$		−	8.32138e14i		−	0.984154i	0.870552	−	0.492077i	$-0.163762\pi$
$968$	8.02517e13	−	5.88463e14i	0.0944230	−	0.692376i
$969$	−1.81695e14			−0.212679
$970$		0			0
$971$		−	7.63526e14i		−	0.884561i	−0.896877	−	0.442281i	$-0.854170\pi$
$971$		−	7.63526e14i		−	0.884561i	0.896877	−	0.442281i	$-0.145830\pi$
$972$	−7.96872e14	+	3.68591e14i	−0.918454	+	0.424829i
$973$	2.65178e14			0.304069
$974$	−2.75199e12	+	4.30506e12i	−0.00313944	+	0.00491116i
$975$		0			0
$976$	6.40428e14	−	7.53714e14i	0.723138	−	0.851055i
$977$	−1.34095e14			−0.150640			−0.0753201	−	0.997159i	$-0.523998\pi$
$977$	−1.34095e14			−0.150640			−0.0753201	+	0.997159i	$0.523998\pi$
$978$	−5.70889e14	−	3.64939e14i	−0.638054	−	0.407874i
$979$		−	3.51173e14i		−	0.390488i
$980$		0			0
$981$	1.11706e14			0.122951
$982$	−7.21257e13	+	1.12829e14i	−0.0789829	+	0.123556i
$983$		−	8.02271e13i		−	0.0874084i	−0.999045	−	0.0437042i	$-0.986084\pi$
$983$		−	8.02271e13i		−	0.0874084i	0.999045	−	0.0437042i	$-0.0139159\pi$
$984$	5.10100e14	+	6.95650e13i	0.552943	+	0.0754076i
$985$		0			0
$986$	−2.90808e14	−	1.85898e14i	−0.312048	−	0.199476i
$987$		−	8.89861e14i		−	0.950028i
$988$	7.00143e14	−	3.23849e14i	0.743707	−	0.344000i
$989$	7.18783e12			0.00759655
$990$		0			0
$991$		−	3.38502e14i		−	0.354155i	−0.984197	−	0.177077i	$-0.943336\pi$
$991$		−	3.38502e14i		−	0.354155i	0.984197	−	0.177077i	$-0.0566643\pi$
$992$	−3.56816e14	−	1.16295e15i	−0.371437	−	1.21061i
$993$	1.48627e14			0.153940
$994$	−1.09812e15	−	7.01970e14i	−1.13167	−	0.723414i
$995$		0			0
$996$	6.29124e13	+	1.36013e14i	0.0641859	+	0.138766i
$997$	1.63118e15			1.65587			0.827934	−	0.560825i	$-0.189516\pi$
$997$	1.63118e15			1.65587			0.827934	+	0.560825i	$0.189516\pi$
$998$	−9.80220e14	+	1.53340e15i	−0.990082	+	1.54883i
$999$		−	1.17346e15i		−	1.17935i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	100.11.b.h.51.3		24
4.3	odd	2	inner	100.11.b.h.51.4		24
5.2	odd	4		20.11.d.d.19.15	yes	24
5.3	odd	4		20.11.d.d.19.10	yes	24
5.4	even	2	inner	100.11.b.h.51.22		24
20.3	even	4		20.11.d.d.19.16	yes	24
20.7	even	4		20.11.d.d.19.9	✓	24
20.19	odd	2	inner	100.11.b.h.51.21		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
20.11.d.d.19.9	✓	24	20.7	even	4
20.11.d.d.19.10	yes	24	5.3	odd	4
20.11.d.d.19.15	yes	24	5.2	odd	4
20.11.d.d.19.16	yes	24	20.3	even	4
100.11.b.h.51.3		24	1.1	even	1	trivial
100.11.b.h.51.4		24	4.3	odd	2	inner
100.11.b.h.51.21		24	20.19	odd	2	inner
100.11.b.h.51.22		24	5.4	even	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 100 = 2^{2} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 11 \)
Character orbit:	\([\chi]\)	\(=\)	100.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-26.9619 - 17.2353i) q^{2} +146.443i q^{3} +(429.889 + 929.393i) q^{4} +(2523.99 - 3948.38i) q^{6} +13979.7i q^{7} +(4427.76 - 32467.5i) q^{8} +37603.5 q^{9} +O(q^{10})\)	\(q+(-26.9619 - 17.2353i) q^{2} +146.443i q^{3} +(429.889 + 929.393i) q^{4} +(2523.99 - 3948.38i) q^{6} +13979.7i q^{7} +(4427.76 - 32467.5i) q^{8} +37603.5 q^{9} -88389.7i q^{11} +(-136103. + 62954.1i) q^{12} +249490. q^{13} +(240944. - 376918. i) q^{14} +(-678968. + 799071. i) q^{16} -410905. q^{17} +(-1.01386e6 - 648107. i) q^{18} -3.01950e6i q^{19} -2.04722e6 q^{21} +(-1.52342e6 + 2.38315e6i) q^{22} -4.53962e6i q^{23} +(4.75463e6 + 648414. i) q^{24} +(-6.72671e6 - 4.30003e6i) q^{26} +1.41541e7i q^{27} +(-1.29926e7 + 6.00970e6i) q^{28} -2.62491e7 q^{29} -3.62534e7i q^{31} +(3.20785e7 - 9.84227e6i) q^{32} +1.29440e7 q^{33} +(1.10788e7 + 7.08207e6i) q^{34} +(1.61653e7 + 3.49484e7i) q^{36} -8.29063e7 q^{37} +(-5.20419e7 + 8.14114e7i) q^{38} +3.65360e7i q^{39} +1.07285e8 q^{41} +(5.51970e7 + 3.52845e7i) q^{42} +1.58335e6i q^{43} +(8.21488e7 - 3.79977e7i) q^{44} +(-7.82418e7 + 1.22397e8i) q^{46} +4.34667e8i q^{47} +(-1.17018e8 - 9.94300e7i) q^{48} +8.70443e7 q^{49} -6.01741e7i q^{51} +(1.07253e8 + 2.31874e8i) q^{52} +3.42615e8 q^{53} +(2.43950e8 - 3.81621e8i) q^{54} +(4.53884e8 + 6.18986e7i) q^{56} +4.42184e8 q^{57} +(7.07725e8 + 4.52411e8i) q^{58} -8.22725e8i q^{59} -9.43238e8 q^{61} +(-6.24838e8 + 9.77460e8i) q^{62} +5.25684e8i q^{63} +(-1.03453e9 - 2.87516e8i) q^{64} +(-3.48996e8 - 2.23094e8i) q^{66} -1.13591e9i q^{67} +(-1.76643e8 - 3.81892e8i) q^{68} +6.64796e8 q^{69} -2.91342e9i q^{71} +(1.66499e8 - 1.22089e9i) q^{72} -2.08673e9 q^{73} +(2.23531e9 + 1.42892e9i) q^{74} +(2.80630e9 - 1.29805e9i) q^{76} +1.23566e9 q^{77} +(6.29709e8 - 9.85080e8i) q^{78} -5.83812e9i q^{79} +1.47685e8 q^{81} +(-2.89261e9 - 1.84909e9i) q^{82} -9.99337e8i q^{83} +(-8.80078e8 - 1.90267e9i) q^{84} +(2.72896e7 - 4.26902e7i) q^{86} -3.84399e9i q^{87} +(-2.86979e9 - 3.91368e8i) q^{88} +3.97301e9 q^{89} +3.48778e9i q^{91} +(4.21910e9 - 1.95153e9i) q^{92} +5.30905e9 q^{93} +(7.49163e9 - 1.17195e10i) q^{94} +(1.44133e9 + 4.69767e9i) q^{96} -6.44299e9 q^{97} +(-2.34688e9 - 1.50024e9i) q^{98} -3.32376e9i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 608 q^{4} - 19584 q^{6} - 597192 q^{9}+O(q^{10}) \) 24 * q - 608 * q^4 - 19584 * q^6 - 597192 * q^9	\( 24 q - 608 q^{4} - 19584 q^{6} - 597192 q^{9} + 1706016 q^{14} - 4733376 q^{16} - 13030368 q^{21} - 10190784 q^{24} - 9454368 q^{26} - 121656816 q^{29} + 335231168 q^{34} - 276632160 q^{36} + 892843248 q^{41} - 766329600 q^{44} + 433181216 q^{46} + 738102008 q^{49} - 139387968 q^{54} - 2629032384 q^{56} + 228563248 q^{61} + 1875284992 q^{64} - 1440259200 q^{66} + 943422432 q^{69} - 21045467232 q^{74} + 828422400 q^{76} - 5619065544 q^{81} + 28069573632 q^{84} + 8163556416 q^{86} - 4631088816 q^{89} - 63404384 q^{94} - 5617046784 q^{96}+O(q^{100}) \) 24 * q - 608 * q^4 - 19584 * q^6 - 597192 * q^9 + 1706016 * q^14 - 4733376 * q^16 - 13030368 * q^21 - 10190784 * q^24 - 9454368 * q^26 - 121656816 * q^29 + 335231168 * q^34 - 276632160 * q^36 + 892843248 * q^41 - 766329600 * q^44 + 433181216 * q^46 + 738102008 * q^49 - 139387968 * q^54 - 2629032384 * q^56 + 228563248 * q^61 + 1875284992 * q^64 - 1440259200 * q^66 + 943422432 * q^69 - 21045467232 * q^74 + 828422400 * q^76 - 5619065544 * q^81 + 28069573632 * q^84 + 8163556416 * q^86 - 4631088816 * q^89 - 63404384 * q^94 - 5617046784 * q^96

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