LMFDB - Embedded newform 21.11.f.a.10.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [21,11,Mod(10,21)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(21, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("21.10");

S:= CuspForms(chi, 11);

N := Newforms(S);

Level:	$ N $	$=$	$ 21 = 3 \cdot 7 $
Weight:	$ k $	$=$	$ 11 $
Character orbit:	$[\chi]$	$=$	21.f (of order $6$, degree $2$, 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:	$13.3425023061$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - x^{11} + 3773 x^{10} + 44516 x^{9} + 11068388 x^{8} + 100480832 x^{7} + 11177140432 x^{6} + \cdots + 30\!\cdots\!00 $ x^12 - x^11 + 3773x^10 + 44516x^9 + 11068388x^8 + 100480832x^7 + 11177140432x^6 + 67553728512x^5 + 8140577253696x^4 + 32158758551040x^3 + 2022248850888960x^2 - 9516227338368000x + 300517801880601600
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{10}\cdot 3^{7}\cdot 7^{7} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			10.1
Root			$28.0722 + 48.6225i$ of defining polynomial
Character	$\chi$	$=$	21.10
Dual form			21.11.f.a.19.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-27.0722 - 46.8904i) q^{2} +(-121.500 - 70.1481i) q^{3} +(-953.808 + 1652.04i) q^{4} +(-1899.28 + 1096.55i) q^{5} +7596.25i q^{6} +(16751.6 - 1363.71i) q^{7} +47842.8 q^{8} +(9841.50 + 17046.0i) q^{9} +O(q^{10})$	\(q+(-27.0722 - 46.8904i) q^{2} +(-121.500 - 70.1481i) q^{3} +(-953.808 + 1652.04i) q^{4} +(-1899.28 + 1096.55i) q^{5} +7596.25i q^{6} +(16751.6 - 1363.71i) q^{7} +47842.8 q^{8} +(9841.50 + 17046.0i) q^{9} +(102836. + 59372.1i) q^{10} +(-37291.0 + 64590.0i) q^{11} +(231775. - 133816. i) q^{12} +192289. i q^{13} +(-517447. - 748570. i) q^{14} +307684. q^{15} +(-318511. - 551677. i) q^{16} +(-1.62873e6 - 940350. i) q^{17} +(532862. - 922944. i) q^{18} +(2.28273e6 - 1.31793e6i) q^{19} -4.18360e6i q^{20} +(-2.13098e6 - 1.00940e6i) q^{21} +4.03820e6 q^{22} +(-1.71647e6 - 2.97301e6i) q^{23} +(-5.81290e6 - 3.35608e6i) q^{24} +(-2.47796e6 + 4.29195e6i) q^{25} +(9.01650e6 - 5.20568e6i) q^{26} -2.76145e6i q^{27} +(-1.37249e7 + 2.89751e7i) q^{28} +3.62803e7 q^{29} +(-8.32968e6 - 1.44274e7i) q^{30} +(3.29414e7 + 1.90187e7i) q^{31} +(7.24994e6 - 1.25573e7i) q^{32} +(9.06172e6 - 5.23179e6i) q^{33} +1.01829e8i q^{34} +(-3.03206e7 + 2.09590e7i) q^{35} -3.75476e7 q^{36} +(-3.81864e7 - 6.61408e7i) q^{37} +(-1.23597e8 - 7.13587e7i) q^{38} +(1.34887e7 - 2.33631e7i) q^{39} +(-9.08671e7 + 5.24621e7i) q^{40} +5.67989e7i q^{41} +(1.03590e7 + 1.27249e8i) q^{42} +1.45433e8 q^{43} +(-7.11369e7 - 1.23213e8i) q^{44} +(-3.73836e7 - 2.15834e7i) q^{45} +(-9.29371e7 + 1.60972e8i) q^{46} +(3.81967e8 - 2.20529e8i) q^{47} +8.93717e7i q^{48} +(2.78756e8 - 4.56884e7i) q^{49} +2.68335e8 q^{50} +(1.31927e8 + 2.28505e8i) q^{51} +(-3.17669e8 - 1.83407e8i) q^{52} +(-2.06890e8 + 3.58343e8i) q^{53} +(-1.29485e8 + 7.47585e7i) q^{54} -1.63566e8i q^{55} +(8.01443e8 - 6.52435e7i) q^{56} -3.69802e8 q^{57} +(-9.82188e8 - 1.70120e9i) q^{58} +(6.76207e8 + 3.90408e8i) q^{59} +(-2.93471e8 + 5.08307e8i) q^{60} +(1.59327e8 - 9.19872e7i) q^{61} -2.05951e9i q^{62} +(1.88106e8 + 2.72126e8i) q^{63} -1.43740e9 q^{64} +(-2.10855e8 - 3.65211e8i) q^{65} +(-4.90641e8 - 2.83272e8i) q^{66} +(-6.18123e8 + 1.07062e9i) q^{67} +(3.10700e9 - 1.79383e9i) q^{68} +4.81628e8i q^{69} +(1.80362e9 + 8.54340e8i) q^{70} -2.72270e9 q^{71} +(4.70845e8 + 8.15527e8i) q^{72} +(-7.93899e7 - 4.58358e7i) q^{73} +(-2.06758e9 + 3.58115e9i) q^{74} +(6.02144e8 - 3.47648e8i) q^{75} +5.02822e9i q^{76} +(-5.36602e8 + 1.13284e9i) q^{77} -1.46067e9 q^{78} +(2.25652e9 + 3.90841e9i) q^{79} +(1.20989e9 + 6.98528e8i) q^{80} +(-1.93710e8 + 3.35516e8i) q^{81} +(2.66332e9 - 1.53767e9i) q^{82} -8.61953e8i q^{83} +(3.70012e9 - 2.55769e9i) q^{84} +4.12457e9 q^{85} +(-3.93720e9 - 6.81942e9i) q^{86} +(-4.40806e9 - 2.54499e9i) q^{87} +(-1.78411e9 + 3.09016e9i) q^{88} +(3.55326e9 - 2.05148e9i) q^{89} +2.33724e9i q^{90} +(2.62225e8 + 3.22114e9i) q^{91} +6.54872e9 q^{92} +(-2.66825e9 - 4.62155e9i) q^{93} +(-2.06814e10 - 1.19404e10i) q^{94} +(-2.89036e9 + 5.00626e9i) q^{95} +(-1.76174e9 + 1.01714e9i) q^{96} +9.12562e9i q^{97} +(-9.68888e9 - 1.18341e10i) q^{98} -1.46800e9 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 11 q^{2} - 1458 q^{3} - 1421 q^{4} - 1287 q^{5} + 20090 q^{7} + 99310 q^{8} + 118098 q^{9}+O(q^{10}) $ 12 * q + 11 * q^2 - 1458 * q^3 - 1421 * q^4 - 1287 * q^5 + 20090 * q^7 + 99310 * q^8 + 118098 * q^9	\( 12 q + 11 q^{2} - 1458 q^{3} - 1421 q^{4} - 1287 q^{5} + 20090 q^{7} + 99310 q^{8} + 118098 q^{9} + 359661 q^{10} + 236165 q^{11} + 345303 q^{12} + 223832 q^{14} + 208494 q^{15} + 1350895 q^{16} - 2038782 q^{17} - 216513 q^{18} + 1012389 q^{19} - 5131917 q^{21} + 29162074 q^{22} - 4341928 q^{23} - 12066165 q^{24} + 12365439 q^{25} + 4398486 q^{26} + 37097165 q^{28} + 95444234 q^{29} - 29132541 q^{30} + 9658932 q^{31} - 49606359 q^{32} - 57388095 q^{33} - 77592186 q^{35} - 55939086 q^{36} - 87545045 q^{37} - 319584648 q^{38} + 1789695 q^{39} - 607773201 q^{40} - 180831609 q^{42} + 700816306 q^{43} + 133692537 q^{44} - 25332021 q^{45} - 74981552 q^{46} - 181842702 q^{47} + 333171090 q^{49} + 3398506976 q^{50} + 165141342 q^{51} - 1573473588 q^{52} - 695152867 q^{53} + 52612659 q^{54} + 1977142699 q^{56} - 164007018 q^{57} - 1023653321 q^{58} + 1373785545 q^{59} + 35593425 q^{60} - 2524633584 q^{61} + 851624361 q^{63} - 482439838 q^{64} + 2692260666 q^{65} - 3543191991 q^{66} - 2255105709 q^{67} + 4313617758 q^{68} - 650925555 q^{70} - 3878911780 q^{71} + 977359365 q^{72} - 1888675383 q^{73} - 445804820 q^{74} - 3004801677 q^{75} - 7759715803 q^{77} - 712554732 q^{78} + 8260659900 q^{79} - 5477579577 q^{80} - 2324522934 q^{81} + 14912212206 q^{82} + 665315532 q^{84} + 15563062356 q^{85} - 257575928 q^{86} - 11596474431 q^{87} - 10015831801 q^{88} + 9451951530 q^{89} - 3182715375 q^{91} + 20533179072 q^{92} - 782373492 q^{93} - 54481927140 q^{94} - 33375267288 q^{95} + 12054345237 q^{96} - 3841749499 q^{98} + 9296871390 q^{99}+O(q^{100}) \) 12 * q + 11 * q^2 - 1458 * q^3 - 1421 * q^4 - 1287 * q^5 + 20090 * q^7 + 99310 * q^8 + 118098 * q^9 + 359661 * q^10 + 236165 * q^11 + 345303 * q^12 + 223832 * q^14 + 208494 * q^15 + 1350895 * q^16 - 2038782 * q^17 - 216513 * q^18 + 1012389 * q^19 - 5131917 * q^21 + 29162074 * q^22 - 4341928 * q^23 - 12066165 * q^24 + 12365439 * q^25 + 4398486 * q^26 + 37097165 * q^28 + 95444234 * q^29 - 29132541 * q^30 + 9658932 * q^31 - 49606359 * q^32 - 57388095 * q^33 - 77592186 * q^35 - 55939086 * q^36 - 87545045 * q^37 - 319584648 * q^38 + 1789695 * q^39 - 607773201 * q^40 - 180831609 * q^42 + 700816306 * q^43 + 133692537 * q^44 - 25332021 * q^45 - 74981552 * q^46 - 181842702 * q^47 + 333171090 * q^49 + 3398506976 * q^50 + 165141342 * q^51 - 1573473588 * q^52 - 695152867 * q^53 + 52612659 * q^54 + 1977142699 * q^56 - 164007018 * q^57 - 1023653321 * q^58 + 1373785545 * q^59 + 35593425 * q^60 - 2524633584 * q^61 + 851624361 * q^63 - 482439838 * q^64 + 2692260666 * q^65 - 3543191991 * q^66 - 2255105709 * q^67 + 4313617758 * q^68 - 650925555 * q^70 - 3878911780 * q^71 + 977359365 * q^72 - 1888675383 * q^73 - 445804820 * q^74 - 3004801677 * q^75 - 7759715803 * q^77 - 712554732 * q^78 + 8260659900 * q^79 - 5477579577 * q^80 - 2324522934 * q^81 + 14912212206 * q^82 + 665315532 * q^84 + 15563062356 * q^85 - 257575928 * q^86 - 11596474431 * q^87 - 10015831801 * q^88 + 9451951530 * q^89 - 3182715375 * q^91 + 20533179072 * q^92 - 782373492 * q^93 - 54481927140 * q^94 - 33375267288 * q^95 + 12054345237 * q^96 - 3841749499 * q^98 + 9296871390 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/21\mathbb{Z}\right)^\times$.

$n$	$8$	$10$
$\chi(n)$	$1$	$e\left(\frac{1}{6}\right)$

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 $

$2$	−27.0722	−	46.8904i	−0.846006	−	1.46533i	−0.884745	−	0.466076i	$-0.845667\pi$
$2$	−27.0722	−	46.8904i	−0.846006	−	1.46533i	0.0387384	−	0.999249i	$-0.487666\pi$
$3$	−121.500	−	70.1481i	−0.500000	−	0.288675i
$3$	−121.500	−	70.1481i	−0.500000	−	0.288675i
$4$	−953.808	+	1652.04i	−0.931453	+	1.61332i
$5$	−1899.28	+	1096.55i	−0.607771	+	0.350897i	−0.772093	−	0.635510i	$-0.780790\pi$
$5$	−1899.28	+	1096.55i	−0.607771	+	0.350897i	0.164322	+	0.986407i	$0.447457\pi$
$6$			7596.25i			0.976884i
$7$	16751.6	−	1363.71i	0.996703	−	0.0811391i
$7$	16751.6	−	1363.71i	0.996703	−	0.0811391i
$8$	47842.8			1.46005
$9$	9841.50	+	17046.0i	0.166667	+	0.288675i
$10$	102836.	+	59372.1i	1.02836	+	0.593721i
$11$	−37291.0	+	64590.0i	−0.231548	+	0.401053i	−0.958264	−	0.285885i	$-0.907712\pi$
$11$	−37291.0	+	64590.0i	−0.231548	+	0.401053i	0.726716	+	0.686938i	$0.241046\pi$
$12$	231775.	−	133816.i	0.931453	−	0.537774i
$13$			192289.i			0.517890i	0.965892	+	0.258945i	$0.0833748\pi$
$13$			192289.i			0.517890i	−0.965892	+	0.258945i	$0.916625\pi$
$14$	−517447.	−	748570.i	−0.962112	−	1.39185i
$15$	307684.			0.405181
$16$	−318511.	−	551677.i	−0.303756	−	0.526120i
$17$	−1.62873e6	−	940350.i	−1.14711	−	0.662285i	−0.198930	−	0.980014i	$-0.563747\pi$
$17$	−1.62873e6	−	940350.i	−1.14711	−	0.662285i	−0.948182	+	0.317729i	$0.897080\pi$
$18$	532862.	−	922944.i	0.282002	−	0.488442i
$19$	2.28273e6	−	1.31793e6i	0.921905	−	0.532262i	0.0376625	−	0.999291i	$-0.488009\pi$
$19$	2.28273e6	−	1.31793e6i	0.921905	−	0.532262i	0.884242	+	0.467029i	$0.154675\pi$
$20$		−	4.18360e6i		−	1.30737i
$21$	−2.13098e6	−	1.00940e6i	−0.521774	−	0.247154i
$22$	4.03820e6			0.783564
$23$	−1.71647e6	−	2.97301e6i	−0.266684	−	0.461910i	0.701320	−	0.712847i	$-0.252595\pi$
$23$	−1.71647e6	−	2.97301e6i	−0.266684	−	0.461910i	−0.968003	+	0.250937i	$0.919261\pi$
$24$	−5.81290e6	−	3.35608e6i	−0.730023	−	0.421479i
$25$	−2.47796e6	+	4.29195e6i	−0.253743	+	0.439496i
$26$	9.01650e6	−	5.20568e6i	0.758877	−	0.438138i
$27$		−	2.76145e6i		−	0.192450i
$28$	−1.37249e7	+	2.89751e7i	−0.797478	+	1.68358i
$29$	3.62803e7			1.76881			0.884405	−	0.466720i	$-0.154565\pi$
$29$	3.62803e7			1.76881			0.884405	+	0.466720i	$0.154565\pi$
$30$	−8.32968e6	−	1.44274e7i	−0.342785	−	0.593721i
$31$	3.29414e7	+	1.90187e7i	1.15062	+	0.664313i	0.949039	−	0.315158i	$-0.102058\pi$
$31$	3.29414e7	+	1.90187e7i	1.15062	+	0.664313i	0.201584	+	0.979471i	$0.435391\pi$
$32$	7.24994e6	−	1.25573e7i	0.216065	−	0.374236i
$33$	9.06172e6	−	5.23179e6i	0.231548	−	0.133684i
$34$			1.01829e8i			2.24119i
$35$	−3.03206e7	+	2.09590e7i	−0.577295	+	0.399054i
$36$	−3.75476e7			−0.620968
$37$	−3.81864e7	−	6.61408e7i	−0.550681	−	0.953807i	−0.998226	−	0.0595455i	$-0.981035\pi$
$37$	−3.81864e7	−	6.61408e7i	−0.550681	−	0.953807i	0.447545	−	0.894261i	$-0.352298\pi$
$38$	−1.23597e8	−	7.13587e7i	−1.55987	−	0.900594i
$39$	1.34887e7	−	2.33631e7i	0.149502	−	0.258945i
$40$	−9.08671e7	+	5.24621e7i	−0.887374	+	0.512326i
$41$			5.67989e7i			0.490254i	0.969491	+	0.245127i	$0.0788296\pi$
$41$			5.67989e7i			0.490254i	−0.969491	+	0.245127i	$0.921170\pi$
$42$	1.03590e7	+	1.27249e8i	0.0792635	+	0.973663i
$43$	1.45433e8			0.989285			0.494642	−	0.869097i	$-0.335299\pi$
$43$	1.45433e8			0.989285			0.494642	+	0.869097i	$0.335299\pi$
$44$	−7.11369e7	−	1.23213e8i	−0.431352	−	0.747123i
$45$	−3.73836e7	−	2.15834e7i	−0.202590	−	0.116966i
$46$	−9.29371e7	+	1.60972e8i	−0.451232	+	0.781557i
$47$	3.81967e8	−	2.20529e8i	1.66547	−	0.961560i	0.695437	−	0.718587i	$-0.255211\pi$
$47$	3.81967e8	−	2.20529e8i	1.66547	−	0.961560i	0.970033	−	0.242973i	$-0.0781226\pi$
$48$			8.93717e7i			0.350747i
$49$	2.78756e8	−	4.56884e7i	0.986833	−	0.161743i
$50$	2.68335e8			0.858673
$51$	1.31927e8	+	2.28505e8i	0.382370	+	0.662285i
$52$	−3.17669e8	−	1.83407e8i	−0.835524	−	0.482390i
$53$	−2.06890e8	+	3.58343e8i	−0.494720	+	0.856880i	−0.999981	−	0.00608623i	$-0.998063\pi$
$53$	−2.06890e8	+	3.58343e8i	−0.494720	+	0.856880i	0.505262	+	0.862966i	$0.331396\pi$
$54$	−1.29485e8	+	7.47585e7i	−0.282002	+	0.162814i
$55$		−	1.63566e8i		−	0.324998i
$56$	8.01443e8	−	6.52435e7i	1.45523	−	0.118467i
$57$	−3.69802e8			−0.614603
$58$	−9.82188e8	−	1.70120e9i	−1.49642	−	2.59188i
$59$	6.76207e8	+	3.90408e8i	0.945844	+	0.546083i	0.891787	−	0.452455i	$-0.149452\pi$
$59$	6.76207e8	+	3.90408e8i	0.945844	+	0.546083i	0.0540564	+	0.998538i	$0.482785\pi$
$60$	−2.93471e8	+	5.08307e8i	−0.377407	+	0.653687i
$61$	1.59327e8	−	9.19872e7i	0.188642	−	0.108913i	−0.402705	−	0.915330i	$-0.631930\pi$
$61$	1.59327e8	−	9.19872e7i	0.188642	−	0.108913i	0.591347	+	0.806417i	$0.298596\pi$
$62$		−	2.05951e9i		−	2.24805i
$63$	1.88106e8	+	2.72126e8i	0.189540	+	0.274200i
$64$	−1.43740e9			−1.33868
$65$	−2.10855e8	−	3.65211e8i	−0.181726	−	0.314758i
$66$	−4.90641e8	−	2.83272e8i	−0.391782	−	0.226195i
$67$	−6.18123e8	+	1.07062e9i	−0.457826	+	0.792978i	−0.998846	−	0.0480318i	$-0.984705\pi$
$67$	−6.18123e8	+	1.07062e9i	−0.457826	+	0.792978i	0.541020	+	0.841010i	$0.318038\pi$
$68$	3.10700e9	−	1.79383e9i	2.13696	−	1.23377i
$69$			4.81628e8i			0.307940i
$70$	1.80362e9	+	8.54340e8i	1.07314	+	0.508324i
$71$	−2.72270e9			−1.50907			−0.754533	−	0.656263i	$-0.772136\pi$
$71$	−2.72270e9			−1.50907			−0.754533	+	0.656263i	$0.772136\pi$
$72$	4.70845e8	+	8.15527e8i	0.243341	+	0.421479i
$73$	−7.93899e7	−	4.58358e7i	−0.0382958	−	0.0221101i	0.480730	−	0.876869i	$-0.340372\pi$
$73$	−7.93899e7	−	4.58358e7i	−0.0382958	−	0.0221101i	−0.519026	+	0.854759i	$0.673705\pi$
$74$	−2.06758e9	+	3.58115e9i	−0.931759	+	1.61385i
$75$	6.02144e8	−	3.47648e8i	0.253743	−	0.146499i
$76$			5.02822e9i			1.98311i
$77$	−5.36602e8	+	1.13284e9i	−0.198243	+	0.418518i
$78$	−1.46067e9			−0.505918
$79$	2.25652e9	+	3.90841e9i	0.733338	+	1.27018i	0.955449	+	0.295157i	$0.0953720\pi$
$79$	2.25652e9	+	3.90841e9i	0.733338	+	1.27018i	−0.222111	+	0.975021i	$0.571295\pi$
$80$	1.20989e9	+	6.98528e8i	0.369228	+	0.213174i
$81$	−1.93710e8	+	3.35516e8i	−0.0555556	+	0.0962250i
$82$	2.66332e9	−	1.53767e9i	0.718381	−	0.414757i
$83$		−	8.61953e8i		−	0.218823i	−0.993997	−	0.109412i	$-0.965103\pi$
$83$		−	8.61953e8i		−	0.218823i	0.993997	−	0.109412i	$-0.0348966\pi$
$84$	3.70012e9	−	2.55769e9i	0.884747	−	0.611579i
$85$	4.12457e9			0.929575
$86$	−3.93720e9	−	6.81942e9i	−0.836941	−	1.44962i
$87$	−4.40806e9	−	2.54499e9i	−0.884405	−	0.510611i
$88$	−1.78411e9	+	3.09016e9i	−0.338071	+	0.585556i
$89$	3.55326e9	−	2.05148e9i	0.636322	−	0.367381i	−0.146874	−	0.989155i	$-0.546921\pi$
$89$	3.55326e9	−	2.05148e9i	0.636322	−	0.367381i	0.783196	+	0.621774i	$0.213588\pi$
$90$			2.33724e9i			0.395814i
$91$	2.62225e8	+	3.22114e9i	0.0420211	+	0.516182i
$92$	6.54872e9			0.993613
$93$	−2.66825e9	−	4.62155e9i	−0.383541	−	0.664313i
$94$	−2.06814e10	−	1.19404e10i	−2.81800	−	1.62697i
$95$	−2.89036e9	+	5.00626e9i	−0.373538	+	0.646987i
$96$	−1.76174e9	+	1.01714e9i	−0.216065	+	0.124745i
$97$			9.12562e9i			1.06268i	0.847158	+	0.531342i	$0.178312\pi$
$97$			9.12562e9i			1.06268i	−0.847158	+	0.531342i	$0.821688\pi$
$98$	−9.68888e9	−	1.18341e10i	−1.07187	−	1.30920i
$99$	−1.46800e9			−0.154365
$100$	−4.72699e9	−	8.18739e9i	−0.472699	−	0.818739i
$101$	1.02145e10	+	5.89736e9i	0.971877	+	0.561113i	0.899808	−	0.436286i	$-0.143706\pi$
$101$	1.02145e10	+	5.89736e9i	0.971877	+	0.561113i	0.0720690	+	0.997400i	$0.477040\pi$
$102$	7.14313e9	−	1.23723e10i	0.646975	−	1.12059i
$103$	1.23325e10	−	7.12019e9i	1.06381	−	0.614194i	0.137330	−	0.990525i	$-0.456148\pi$
$103$	1.23325e10	−	7.12019e9i	1.06381	−	0.614194i	0.926485	+	0.376332i	$0.122815\pi$
$104$			9.19964e9i			0.756143i
$105$	5.15419e9	−	4.19590e8i	0.403845	−	0.0328760i
$106$	2.24038e10			1.67414
$107$	3.86448e9	+	6.69347e9i	0.275532	+	0.477235i	0.970269	−	0.242028i	$-0.0778127\pi$
$107$	3.86448e9	+	6.69347e9i	0.275532	+	0.477235i	−0.694737	+	0.719264i	$0.744479\pi$
$108$	4.56203e9	+	2.63389e9i	0.310484	+	0.179258i
$109$	1.36326e10	−	2.36123e10i	0.886023	−	1.53464i	0.0414873	−	0.999139i	$-0.486790\pi$
$109$	1.36326e10	−	2.36123e10i	0.886023	−	1.53464i	0.844536	−	0.535499i	$-0.179876\pi$
$110$	−7.66969e9	+	4.42810e9i	−0.476227	+	0.274950i
$111$			1.07148e10i			0.635871i
$112$	−6.08789e9	−	8.80711e9i	−0.345443	−	0.499739i
$113$	−4.76049e8			−0.0258380			−0.0129190	−	0.999917i	$-0.504112\pi$
$113$	−4.76049e8			−0.0258380			−0.0129190	+	0.999917i	$0.504112\pi$
$114$	1.00113e10	+	1.73402e10i	0.519958	+	0.900594i
$115$	6.52012e9	+	3.76439e9i	0.324165	+	0.187157i
$116$	−3.46044e10	+	5.99367e10i	−1.64756	+	2.85366i
$117$	−3.27775e9	+	1.89241e9i	−0.149502	+	0.0863150i
$118$		−	4.22768e10i		−	1.84796i
$119$	−2.85662e10	−	1.35312e10i	−1.19707	−	0.567026i
$120$	1.47205e10			0.591583
$121$	1.01875e10	+	1.76452e10i	0.392771	+	0.680299i
$122$	−8.62664e9	−	4.98059e9i	−0.319185	−	0.184282i
$123$	3.98433e9	−	6.90107e9i	0.141524	−	0.245127i
$124$	−6.28395e10	+	3.62804e10i	−2.14350	+	1.23755i
$125$		−	3.22859e10i		−	1.05794i
$126$	7.66766e9	−	1.61874e10i	0.241440	−	0.509713i
$127$	1.10936e10			0.335780			0.167890	−	0.985806i	$-0.446305\pi$
$127$	1.10936e10			0.335780			0.167890	+	0.985806i	$0.446305\pi$
$128$	3.14896e10	+	5.45415e10i	0.916467	+	1.58737i
$129$	−1.76701e10	−	1.02019e10i	−0.494642	−	0.285582i
$130$	−1.14166e10	+	1.97741e10i	−0.307482	+	0.532575i
$131$	−1.86619e10	+	1.07744e10i	−0.483726	+	0.279279i	−0.721968	−	0.691927i	$-0.756762\pi$
$131$	−1.86619e10	+	1.07744e10i	−0.483726	+	0.279279i	0.238242	+	0.971206i	$0.423429\pi$
$132$			1.99605e10i			0.498082i
$133$	3.64420e10	−	2.51904e10i	0.875678	−	0.605309i
$134$	6.69357e10			1.54929
$135$	3.02807e9	+	5.24477e9i	0.0675301	+	0.116966i
$136$	−7.79232e10	−	4.49890e10i	−1.67484	−	0.966967i
$137$	−1.15405e10	+	1.99888e10i	−0.239124	+	0.414174i	−0.960463	−	0.278407i	$-0.910193\pi$
$137$	−1.15405e10	+	1.99888e10i	−0.239124	+	0.414174i	0.721339	+	0.692582i	$0.243527\pi$
$138$	2.25837e10	−	1.30387e10i	0.451232	−	0.260519i
$139$		−	4.66682e10i		−	0.899388i	−0.893183	−	0.449694i	$-0.851533\pi$
$139$		−	4.66682e10i		−	0.899388i	0.893183	−	0.449694i	$-0.148467\pi$
$140$	−5.70520e9	−	7.00819e10i	−0.106079	−	1.30306i
$141$	−6.18787e10			−1.11031
$142$	7.37095e10	+	1.27669e11i	1.27668	+	2.21127i
$143$	−1.24199e10	−	7.17065e9i	−0.207701	−	0.119916i
$144$	6.26925e9	−	1.08587e10i	0.101252	−	0.175373i
$145$	−6.89066e10	+	3.97833e10i	−1.07503	+	0.620670i
$146$			4.96350e9i			0.0748211i
$147$	−3.70738e10	−	1.40030e10i	−0.540108	−	0.204003i
$148$	1.45690e11			2.05173
$149$	2.14741e10	+	3.71942e10i	0.292404	+	0.506459i	0.974378	−	0.224918i	$-0.0722114\pi$
$149$	2.14741e10	+	3.71942e10i	0.292404	+	0.506459i	−0.681974	+	0.731377i	$0.738878\pi$
$150$	−3.26027e10	−	1.88232e10i	−0.429336	−	0.247877i
$151$	−4.75499e10	+	8.23589e10i	−0.605711	+	1.04912i	0.386228	+	0.922403i	$0.373778\pi$
$151$	−4.75499e10	+	8.23589e10i	−0.605711	+	1.04912i	−0.991939	+	0.126718i	$0.959556\pi$
$152$	1.09212e11	−	6.30536e10i	1.34602	−	0.777127i
$153$		−	3.70178e10i		−	0.441523i
$154$	6.76462e10	−	5.50692e9i	0.780980	−	0.0635777i
$155$	−8.34200e10			−0.932421
$156$	2.57312e10	+	4.45678e10i	0.278508	+	0.482390i
$157$	2.73879e10	+	1.58124e10i	0.287118	+	0.165768i	0.636642	−	0.771160i	$-0.280323\pi$
$157$	2.73879e10	+	1.58124e10i	0.287118	+	0.165768i	−0.349523	+	0.936928i	$0.613656\pi$
$158$	1.22178e11	−	2.11619e11i	1.24082	−	2.14916i
$159$	5.02742e10	−	2.90258e10i	0.494720	−	0.285627i
$160$			3.17997e10i			0.303266i
$161$	−3.28079e10	−	4.74619e10i	−0.303283	−	0.438748i
$162$	2.09766e10			0.188001
$163$	−8.66044e10	−	1.50003e11i	−0.752666	−	1.30366i	−0.946526	−	0.322626i	$-0.895434\pi$
$163$	−8.66044e10	−	1.50003e11i	−0.752666	−	1.30366i	0.193861	−	0.981029i	$-0.437899\pi$
$164$	−9.38343e10	−	5.41752e10i	−0.790938	−	0.456648i
$165$	−1.14739e10	+	1.98733e10i	−0.0938187	+	0.162499i
$166$	−4.04173e10	+	2.33350e10i	−0.320647	+	0.185126i
$167$			5.24799e10i			0.404027i	0.979383	+	0.202013i	$0.0647485\pi$
$167$			5.24799e10i			0.404027i	−0.979383	+	0.202013i	$0.935252\pi$
$168$	−1.01952e11	−	4.82926e10i	−0.761815	−	0.360856i
$169$	1.00883e11			0.731790
$170$	−1.11661e11	−	1.93403e11i	−0.786426	−	1.36213i
$171$	4.49309e10	+	2.59409e10i	0.307302	+	0.177421i
$172$	−1.38715e11	+	2.40262e11i	−0.921472	+	1.59604i
$173$	−1.62529e10	+	9.38363e9i	−0.104882	+	0.0605537i	−0.551524	−	0.834159i	$-0.685953\pi$
$173$	−1.62529e10	+	9.38363e9i	−0.104882	+	0.0605537i	0.446641	+	0.894713i	$0.352620\pi$
$174$			2.75594e11i			1.72792i
$175$	−3.56568e10	+	7.52762e10i	−0.217246	+	0.458635i
$176$	4.75104e10			0.281336
$177$	−5.47727e10	−	9.48692e10i	−0.315281	−	0.546083i
$178$	−1.92389e11	−	1.11076e11i	−1.07666	−	0.621613i
$179$	−9.94163e9	+	1.72194e10i	−0.0540994	+	0.0937029i	−0.891807	−	0.452416i	$-0.850562\pi$
$179$	−9.94163e9	+	1.72194e10i	−0.0540994	+	0.0937029i	0.837707	+	0.546119i	$0.183895\pi$
$180$	7.13135e10	−	4.11729e10i	0.377407	−	0.217896i
$181$		−	2.54943e11i		−	1.31235i	−0.754607	−	0.656176i	$-0.772173\pi$
$181$		−	2.54943e11i		−	1.31235i	0.754607	−	0.656176i	$-0.227827\pi$
$182$	1.43942e11	−	9.94993e10i	0.720825	−	0.498268i
$183$	−2.58109e10			−0.125761
$184$	−8.21206e10	−	1.42237e11i	−0.389371	−	0.674410i
$185$	1.45054e11	+	8.37467e10i	0.669375	+	0.386464i
$186$	−1.44471e11	+	2.50231e11i	−0.648956	+	1.12403i
$187$	1.21474e11	−	7.01332e10i	0.531223	−	0.306701i
$188$			8.41369e11i			3.58259i
$189$	−3.76580e9	−	4.62586e10i	−0.0156152	−	0.191816i
$190$	3.12994e11			1.26406
$191$	1.20830e11	+	2.09285e11i	0.475346	+	0.823323i	0.999601	−	0.0282379i	$-0.00898960\pi$
$191$	1.20830e11	+	2.09285e11i	0.475346	+	0.823323i	−0.524255	+	0.851561i	$0.675656\pi$
$192$	1.74644e11	+	1.00831e11i	0.669340	+	0.386444i
$193$	−1.48133e11	+	2.56574e11i	−0.553180	+	0.958135i	0.444863	+	0.895599i	$0.353252\pi$
$193$	−1.48133e11	+	2.56574e11i	−0.553180	+	0.958135i	−0.998043	+	0.0625365i	$0.980081\pi$
$194$	4.27904e11	−	2.47051e11i	1.55718	−	0.899036i
$195$			5.91642e10i			0.209839i
$196$	−1.90400e11	+	5.04095e11i	−0.658244	+	1.74274i
$197$	5.16897e10			0.174210			0.0871049	−	0.996199i	$-0.472238\pi$
$197$	5.16897e10			0.174210			0.0871049	+	0.996199i	$0.472238\pi$
$198$	3.97419e10	+	6.88351e10i	0.130594	+	0.226195i
$199$	−1.50791e11	−	8.70591e10i	−0.483181	−	0.278964i	0.238560	−	0.971128i	$-0.423324\pi$
$199$	−1.50791e11	−	8.70591e10i	−0.483181	−	0.278964i	−0.721741	+	0.692163i	$0.756658\pi$
$200$	−1.18553e11	+	2.05339e11i	−0.370477	+	0.641684i
$201$	1.50204e11	−	8.67202e10i	0.457826	−	0.264326i
$202$		−	6.38618e11i		−	1.89882i
$203$	6.07753e11	−	4.94757e10i	1.76298	−	0.143520i
$204$	−5.03334e11			−1.42464
$205$	−6.22830e10	−	1.07877e11i	−0.172028	−	0.297962i
$206$	−6.67737e11	−	3.85518e11i	−1.79999	−	1.03922i
$207$	3.37852e10	−	5.85177e10i	0.0888946	−	0.153970i
$208$	1.06081e11	−	6.12461e10i	0.272472	−	0.157312i
$209$			1.96588e11i			0.492977i
$210$	−1.59210e11	−	2.30323e11i	−0.389829	−	0.563951i
$211$	−4.02881e11			−0.963306			−0.481653	−	0.876362i	$-0.659963\pi$
$211$	−4.02881e11			−0.963306			−0.481653	+	0.876362i	$0.659963\pi$
$212$	−3.94666e11	−	6.83581e11i	−0.921616	−	1.59629i
$213$	3.30808e11	+	1.90992e11i	0.754533	+	0.435630i
$214$	2.09240e11	−	3.62414e11i	0.466203	−	0.807488i
$215$	−2.76219e11	+	1.59475e11i	−0.601258	+	0.347137i
$216$		−	1.32115e11i		−	0.280986i
$217$	5.77756e11	+	2.73671e11i	1.20073	+	0.568762i
$218$	−1.47625e12			−2.99833
$219$	6.43058e9	+	1.11381e10i	0.0127653	+	0.0221101i
$220$	2.70218e11	+	1.56011e11i	0.524326	+	0.302720i
$221$	1.80819e11	−	3.13187e11i	0.342991	−	0.594077i
$222$	5.02422e11	−	2.90073e11i	0.931759	−	0.537951i
$223$		−	9.51145e11i		−	1.72474i	−0.506283	−	0.862368i	$-0.668981\pi$
$223$		−	9.51145e11i		−	1.72474i	0.506283	−	0.862368i	$-0.331019\pi$
$224$	1.04324e11	−	2.20241e11i	0.184987	−	0.390533i
$225$	−9.75473e10			−0.169162
$226$	1.28877e10	+	2.23221e10i	0.0218591	+	0.0378611i
$227$	4.73039e11	+	2.73109e11i	0.784816	+	0.453114i	0.838134	−	0.545464i	$-0.183646\pi$
$227$	4.73039e11	+	2.73109e11i	0.784816	+	0.453114i	−0.0533181	+	0.998578i	$0.516980\pi$
$228$	3.52720e11	−	6.10929e11i	0.572474	−	0.991554i
$229$	−1.63252e11	+	9.42534e10i	−0.259227	+	0.149665i	−0.623982	−	0.781439i	$-0.714486\pi$
$229$	−1.63252e11	+	9.42534e10i	−0.259227	+	0.149665i	0.364755	+	0.931104i	$0.381153\pi$
$230$		−	4.07642e11i		−	0.633343i
$231$	1.44664e11	−	9.99982e10i	0.219937	−	0.152031i
$232$	1.73575e12			2.58255
$233$	5.54460e11	+	9.60352e11i	0.807403	+	1.39846i	0.914657	+	0.404231i	$0.132461\pi$
$233$	5.54460e11	+	9.60352e11i	0.807403	+	1.39846i	−0.107254	+	0.994232i	$0.534206\pi$
$234$	1.77472e11	+	1.02463e11i	0.252959	+	0.146046i
$235$	−4.83643e11	+	8.37694e11i	−0.674816	+	1.16882i
$236$	−1.28994e12	+	7.44748e11i	−1.76202	+	1.01730i
$237$		−	6.33163e11i		−	0.846786i
$238$	1.38865e11	+	1.70580e12i	0.181848	+	2.23380i
$239$	−4.29375e11			−0.550613			−0.275307	−	0.961356i	$-0.588779\pi$
$239$	−4.29375e11			−0.550613			−0.275307	+	0.961356i	$0.588779\pi$
$240$	−9.80007e10	−	1.69742e11i	−0.123076	−	0.213174i
$241$	−4.60909e11	−	2.66106e11i	−0.566930	−	0.327317i	0.188992	−	0.981979i	$-0.439478\pi$
$241$	−4.60909e11	−	2.66106e11i	−0.566930	−	0.327317i	−0.755922	+	0.654661i	$0.772811\pi$
$242$	5.51594e11	−	9.55390e11i	0.664574	−	1.15108i
$243$	4.70716e10	−	2.71768e10i	0.0555556	−	0.0320750i
$244$			3.50952e11i			0.405788i
$245$	−4.79337e11	+	3.92446e11i	−0.543013	+	0.444579i
$246$	−4.31459e11			−0.478921
$247$	2.53424e11	+	4.38943e11i	0.275653	+	0.477445i
$248$	1.57601e12	+	9.09908e11i	1.67996	+	0.969928i
$249$	−6.04643e10	+	1.04727e11i	−0.0631688	+	0.109412i
$250$	−1.51390e12	+	8.74050e11i	−1.55023	+	0.895027i
$251$			2.75628e11i			0.276665i	0.990386	+	0.138333i	$0.0441743\pi$
$251$			2.75628e11i			0.276665i	−0.990386	+	0.138333i	$0.955826\pi$
$252$	−6.28982e11	+	5.12039e10i	−0.618921	+	0.0503848i
$253$	2.56035e11			0.247000
$254$	−3.00329e11	−	5.20185e11i	−0.284072	−	0.492027i
$255$	−5.01135e11	−	2.89331e11i	−0.464787	−	0.268345i
$256$	9.69036e11	−	1.67842e12i	0.881333	−	1.52651i
$257$	1.00002e12	−	5.77364e11i	0.891959	−	0.514973i	0.0173760	−	0.999849i	$-0.494469\pi$
$257$	1.00002e12	−	5.77364e11i	0.891959	−	0.514973i	0.874583	+	0.484876i	$0.161135\pi$
$258$			1.10475e12i			0.966416i
$259$	−7.29879e11	−	1.05589e12i	−0.626256	−	0.905980i
$260$	8.04459e11			0.677076
$261$	3.57053e11	+	6.18434e11i	0.294802	+	0.510611i
$262$	1.01044e12	+	5.83376e11i	0.818470	+	0.472544i
$263$	−1.09614e12	+	1.89857e12i	−0.871140	+	1.50886i	−0.0103210	+	0.999947i	$0.503285\pi$
$263$	−1.09614e12	+	1.89857e12i	−0.871140	+	1.50886i	−0.860819	+	0.508912i	$0.830048\pi$
$264$	4.33538e11	−	2.50303e11i	0.338071	−	0.195185i
$265$		−	9.07461e11i		−	0.694382i
$266$	−2.16776e12	−	1.02682e12i	−1.62780	−	0.771057i
$267$	−5.75628e11			−0.424215
$268$	−1.17914e12	−	2.04233e12i	−0.852887	−	1.47724i
$269$	1.29703e12	+	7.48842e11i	0.920851	+	0.531654i	0.883907	−	0.467664i	$-0.154904\pi$
$269$	1.29703e12	+	7.48842e11i	0.920851	+	0.531654i	0.0369446	+	0.999317i	$0.488237\pi$
$270$	1.63953e11	−	2.83975e11i	0.114262	−	0.197907i
$271$	−2.18819e12	+	1.26335e12i	−1.49706	+	0.864325i	−0.999994	−	0.00339002i	$-0.998921\pi$
$271$	−2.18819e12	+	1.26335e12i	−1.49706	+	0.864325i	−0.497061	+	0.867715i	$0.665588\pi$
$272$			1.19805e12i			0.804691i
$273$	1.94097e11	−	4.09763e11i	0.127998	−	0.270222i
$274$	1.24971e12			0.809200
$275$	−1.84811e11	−	3.20103e11i	−0.117507	−	0.203529i
$276$	−7.95670e11	−	4.59380e11i	−0.496807	−	0.286831i
$277$	1.24822e12	−	2.16198e12i	0.765407	−	1.32572i	−0.174624	−	0.984635i	$-0.555871\pi$
$277$	1.24822e12	−	2.16198e12i	0.765407	−	1.32572i	0.940031	−	0.341089i	$-0.110796\pi$
$278$	−2.18829e12	+	1.26341e12i	−1.31790	+	0.760888i
$279$			7.48691e11i			0.442875i
$280$	−1.45062e12	+	1.00274e12i	−0.842878	+	0.582637i
$281$	−1.22244e12			−0.697743			−0.348872	−	0.937171i	$-0.613435\pi$
$281$	−1.22244e12			−0.697743			−0.348872	+	0.937171i	$0.613435\pi$
$282$	1.67519e12	+	2.90152e12i	0.939332	+	1.62697i
$283$	−6.41093e11	−	3.70135e11i	−0.353174	−	0.203905i	0.312908	−	0.949783i	$-0.398697\pi$
$283$	−6.41093e11	−	3.70135e11i	−0.353174	−	0.203905i	−0.666082	+	0.745878i	$0.732030\pi$
$284$	2.59693e12	−	4.49802e12i	1.40562	−	2.43461i
$285$	7.02359e11	−	4.05507e11i	0.373538	−	0.215662i
$286$			7.76501e11i			0.405800i
$287$	7.74570e10	+	9.51472e11i	0.0397787	+	0.488637i
$288$	2.85401e11			0.144043
$289$	7.60520e11	+	1.31726e12i	0.377243	+	0.653404i
$290$	3.73091e12	+	2.15404e12i	1.81897	+	1.05018i
$291$	6.40145e11	−	1.10876e12i	0.306770	−	0.531342i
$292$	1.51445e11	−	8.74371e10i	0.0713415	−	0.0411890i
$293$		−	2.53524e12i		−	1.17403i	−0.809574	−	0.587017i	$-0.800302\pi$
$293$		−	2.53524e12i		−	1.17403i	0.809574	−	0.587017i	$-0.199698\pi$
$294$	3.47061e11	+	2.11750e12i	0.158004	+	0.964021i
$295$	−1.71241e12			−0.766475
$296$	−1.82694e12	−	3.16436e12i	−0.804020	−	1.39260i
$297$	1.78362e11	+	1.02977e11i	0.0771827	+	0.0445614i
$298$	1.16270e12	−	2.01386e12i	0.494751	−	0.856935i
$299$	5.71677e11	−	3.30058e11i	0.239218	−	0.138113i
$300$			1.32636e12i			0.545826i
$301$	2.43624e12	−	1.98328e11i	0.986023	−	0.0802697i
$302$	5.14913e12			2.04974
$303$	−8.27376e11	−	1.43306e12i	−0.323959	−	0.561113i
$304$	−1.45415e12	−	8.39552e11i	−0.560068	−	0.323355i
$305$	−2.01738e11	+	3.49420e11i	−0.0764342	+	0.132388i
$306$	−1.73578e12	+	1.00215e12i	−0.646975	+	0.373531i
$307$		−	2.20110e12i		−	0.807138i	−0.914949	−	0.403569i	$-0.867770\pi$
$307$		−	2.20110e12i		−	0.807138i	0.914949	−	0.403569i	$-0.132230\pi$
$308$	−1.35968e12	−	1.96700e12i	−0.490551	−	0.709661i
$309$	−1.99787e12			−0.709210
$310$	2.25836e12	+	3.91160e12i	0.788834	+	1.36630i
$311$	4.58713e11	+	2.64838e11i	0.157666	+	0.0910287i	0.576757	−	0.816916i	$-0.304318\pi$
$311$	4.58713e11	+	2.64838e11i	0.157666	+	0.0910287i	−0.419091	+	0.907944i	$0.637651\pi$
$312$	6.45337e11	−	1.11776e12i	0.218280	−	0.378072i
$313$	3.71628e12	−	2.14560e12i	1.23705	−	0.714211i	0.268560	−	0.963263i	$-0.413452\pi$
$313$	3.71628e12	−	2.14560e12i	1.23705	−	0.714211i	0.968490	+	0.249052i	$0.0801190\pi$
$314$		−	1.71231e12i		−	0.560962i
$315$	−6.55668e11	−	3.10577e11i	−0.211413	−	0.100142i
$316$	−8.60915e12			−2.73228
$317$	−1.32350e9	−	2.29237e9i	−0.000413454	−	0.000716124i	0.865819	−	0.500358i	$-0.166798\pi$
$317$	−1.32350e9	−	2.29237e9i	−0.000413454	−	0.000716124i	−0.866232	+	0.499642i	$0.833465\pi$
$318$	−2.72206e12	−	1.57158e12i	−0.837072	−	0.483284i
$319$	−1.35293e12	+	2.34334e12i	−0.409564	+	0.709386i
$320$	2.73003e12	−	1.57618e12i	0.813611	−	0.469739i
$321$		−	1.08434e12i		−	0.318157i
$322$	−1.33733e12	+	2.82327e12i	−0.386329	+	0.815593i
$323$	−4.95727e12			−1.41004
$324$	−3.69525e11	−	6.40035e11i	−0.103495	−	0.179258i
$325$	−8.25294e11	−	4.76484e11i	−0.227610	−	0.131411i
$326$	−4.68914e12	+	8.12184e12i	−1.27352	+	2.20580i
$327$	−3.31271e12	+	1.91260e12i	−0.886023	+	0.511546i
$328$			2.71742e12i			0.715793i
$329$	6.09782e12	−	4.21510e12i	1.58196	−	1.09352i
$330$	1.24249e12			0.317485
$331$	2.64923e12	+	4.58861e12i	0.666777	+	1.15489i	0.978800	+	0.204817i	$0.0656598\pi$
$331$	2.64923e12	+	4.58861e12i	0.666777	+	1.15489i	−0.312024	+	0.950074i	$0.601007\pi$
$332$	1.42398e12	+	8.22137e11i	0.353032	+	0.203823i
$333$	7.51623e11	−	1.30185e12i	0.183560	−	0.317936i
$334$	2.46080e12	−	1.42075e12i	0.592031	−	0.341809i
$335$		−	2.71121e12i		−	0.642599i
$336$	1.21877e11	+	1.49712e12i	0.0284593	+	0.349590i
$337$	−5.21043e11			−0.119874			−0.0599368	−	0.998202i	$-0.519090\pi$
$337$	−5.21043e11			−0.119874			−0.0599368	+	0.998202i	$0.519090\pi$
$338$	−2.73114e12	−	4.73047e12i	−0.619099	−	1.07231i
$339$	5.78399e10	+	3.33939e10i	0.0129190	+	0.00745879i
$340$	−3.93405e12	+	6.81397e12i	−0.865855	+	1.49970i
$341$	−2.45684e12	+	1.41845e12i	−0.532849	+	0.307641i
$342$		−	2.80911e12i		−	0.600396i
$343$	4.60730e12	−	1.14549e12i	0.970455	−	0.241281i
$344$	6.95793e12			1.44440
$345$	−5.28130e11	−	9.14748e11i	−0.108055	−	0.187157i
$346$	8.80005e11	+	5.08071e11i	0.177462	+	0.102458i
$347$	−2.95893e12	+	5.12502e12i	−0.588149	+	1.01870i	0.406325	+	0.913729i	$0.366810\pi$
$347$	−2.95893e12	+	5.12502e12i	−0.588149	+	1.01870i	−0.994475	+	0.104976i	$0.966523\pi$
$348$	8.40888e12	−	4.85487e12i	1.64756	−	0.951221i
$349$			7.48505e12i			1.44567i	0.691023	+	0.722833i	$0.257160\pi$
$349$			7.48505e12i			1.44567i	−0.691023	+	0.722833i	$0.742840\pi$
$350$	4.49504e12	−	3.65930e11i	0.855841	−	0.0696720i
$351$	5.30996e11			0.0996679
$352$	5.40715e11	+	9.36547e11i	0.100059	+	0.173307i
$353$	−3.96765e11	−	2.29072e11i	−0.0723869	−	0.0417926i	0.463370	−	0.886165i	$-0.346640\pi$
$353$	−3.96765e11	−	2.29072e11i	−0.0723869	−	0.0417926i	−0.535757	+	0.844372i	$0.679974\pi$
$354$	−2.96564e12	+	5.13663e12i	−0.533460	+	0.923979i
$355$	5.17118e12	−	2.98558e12i	0.917166	−	0.529526i
$356$			7.82685e12i			1.36879i
$357$	2.52161e12	+	3.64791e12i	0.434847	+	0.629076i
$358$	1.07657e12			0.183074
$359$	−4.02917e12	−	6.97873e12i	−0.675684	−	1.17032i	−0.976269	−	0.216564i	$-0.930515\pi$
$359$	−4.02917e12	−	6.97873e12i	−0.675684	−	1.17032i	0.300585	−	0.953755i	$-0.402818\pi$
$360$	−1.78854e12	−	1.03261e12i	−0.295791	−	0.170775i
$361$	4.08363e11	−	7.07305e11i	0.0666055	−	0.115364i
$362$	−1.19544e13	+	6.90187e12i	−1.92302	+	1.11026i
$363$		−	2.85853e12i		−	0.453533i
$364$	−5.57158e12	−	2.63914e12i	−0.871910	−	0.413006i
$365$	2.01045e11			0.0310334
$366$	6.98758e11	+	1.21028e12i	0.106395	+	0.184282i
$367$	1.26635e12	+	7.31128e11i	0.190206	+	0.109815i	0.592079	−	0.805880i	$-0.298307\pi$
$367$	1.26635e12	+	7.31128e11i	0.190206	+	0.109815i	−0.401873	+	0.915695i	$0.631641\pi$
$368$	−1.09343e12	+	1.89387e12i	−0.162013	+	0.280615i
$369$	−9.68193e11	+	5.58986e11i	−0.141524	+	0.0817089i
$370$		−	9.06883e12i		−	1.30780i
$371$	−2.97705e12	+	6.28496e12i	−0.423562	+	0.894196i
$372$	1.01800e13			1.42900
$373$	−5.01492e12	−	8.68610e12i	−0.694576	−	1.20304i	−0.970323	−	0.241811i	$-0.922259\pi$
$373$	−5.01492e12	−	8.68610e12i	−0.694576	−	1.20304i	0.275747	−	0.961230i	$-0.411075\pi$
$374$	−6.57715e12	−	3.79732e12i	−0.898835	−	0.518943i
$375$	−2.26479e12	+	3.92273e12i	−0.305402	+	0.528972i
$376$	1.82744e13	−	1.05507e13i	2.43166	−	1.40392i
$377$			6.97630e12i			0.916049i
$378$	−2.06714e12	+	1.42890e12i	−0.267862	+	0.185159i
$379$	−8.75591e12			−1.11971			−0.559855	−	0.828591i	$-0.689143\pi$
$379$	−8.75591e12			−1.11971			−0.559855	+	0.828591i	$0.689143\pi$
$380$	−5.51370e12	−	9.55002e12i	−0.695866	−	1.20527i
$381$	−1.34788e12	−	7.78197e11i	−0.167890	−	0.0969314i
$382$	6.54229e12	−	1.13316e13i	0.804291	−	1.39307i
$383$	−1.31559e12	+	7.59555e11i	−0.159634	+	0.0921648i	−0.577689	−	0.816257i	$-0.696045\pi$
$383$	−1.31559e12	+	7.59555e11i	−0.159634	+	0.0921648i	0.418055	+	0.908422i	$0.362712\pi$
$384$		−	8.83573e12i		−	1.05824i
$385$	−2.23056e11	−	2.73999e12i	−0.0263700	−	0.323926i
$386$	1.60412e13			1.87197
$387$	1.43128e12	+	2.47905e12i	0.164881	+	0.285582i
$388$	−1.50759e13	−	8.70409e12i	−1.71445	−	0.989839i
$389$	2.97433e12	−	5.15168e12i	0.333919	−	0.578364i	−0.649358	−	0.760483i	$-0.724962\pi$
$389$	2.97433e12	−	5.15168e12i	0.333919	−	0.578364i	0.983276	+	0.182119i	$0.0582956\pi$
$390$	2.77423e12	−	1.60170e12i	0.307482	−	0.177525i
$391$			6.45632e12i			0.706483i
$392$	1.33365e13	−	2.18586e12i	1.44082	−	0.236153i
$393$	3.02323e12			0.322484
$394$	−1.39935e12	−	2.42375e12i	−0.147383	−	0.255274i
$395$	−8.57155e12	−	4.94879e12i	−0.891403	−	0.514652i
$396$	1.40019e12	−	2.42520e12i	0.143784	−	0.249041i
$397$	2.62723e12	−	1.51683e12i	0.266407	−	0.153810i	−0.360847	−	0.932625i	$-0.617512\pi$
$397$	2.62723e12	−	1.51683e12i	0.266407	−	0.153810i	0.627254	+	0.778815i	$0.284179\pi$
$398$			9.42752e12i			0.944022i
$399$	−6.19477e12	+	5.04301e11i	−0.612577	+	0.0498684i
$400$	3.15703e12			0.308304
$401$	4.11372e12	+	7.12517e12i	0.396746	+	0.687184i	0.993322	−	0.115372i	$-0.0368060\pi$
$401$	4.11372e12	+	7.12517e12i	0.396746	+	0.687184i	−0.596576	+	0.802556i	$0.703473\pi$
$402$	−8.13269e12	−	4.69541e12i	−0.774647	−	0.447243i
$403$	−3.65709e12	+	6.33426e12i	−0.344041	+	0.595896i
$404$	−1.94854e13	+	1.12499e13i	−1.81051	+	1.04530i
$405$		−	8.49654e11i		−	0.0779770i
$406$	−1.87731e13	−	2.71584e13i	−1.70179	−	2.46192i
$407$	5.69604e12			0.510036
$408$	6.31178e12	+	1.09323e13i	0.558279	+	0.966967i
$409$	5.39988e12	+	3.11762e12i	0.471810	+	0.272400i	0.716997	−	0.697076i	$-0.245516\pi$
$409$	5.39988e12	+	3.11762e12i	0.471810	+	0.272400i	−0.245187	+	0.969476i	$0.578849\pi$
$410$	−3.37227e12	+	5.84095e12i	−0.291074	+	0.504155i
$411$	2.80435e12	−	1.61909e12i	0.239124	−	0.138058i
$412$			2.71652e13i			2.28837i
$413$	1.18599e13	+	5.61781e12i	0.987034	+	0.467538i
$414$	−3.65856e12			−0.300821
$415$	9.45176e11	+	1.63709e12i	0.0767843	+	0.132994i
$416$	2.41462e12	+	1.39408e12i	0.193813	+	0.111898i
$417$	−3.27368e12	+	5.67019e12i	−0.259631	+	0.449694i
$418$	9.21811e12	−	5.32208e12i	0.722371	−	0.417061i
$419$			2.13990e11i			0.0165700i	0.999966	+	0.00828500i	$0.00263723\pi$
$419$			2.13990e11i			0.0165700i	−0.999966	+	0.00828500i	$0.997363\pi$
$420$	−4.22293e12	+	8.91516e12i	−0.323123	+	0.682154i
$421$	1.48740e13			1.12465			0.562326	−	0.826915i	$-0.309906\pi$
$421$	1.48740e13			1.12465			0.562326	+	0.826915i	$0.309906\pi$
$422$	1.09069e13	+	1.88912e13i	0.814963	+	1.41156i
$423$	7.51826e12	+	4.34067e12i	0.555157	+	0.320520i
$424$	−9.89818e12	+	1.71442e13i	−0.722314	+	1.25108i
$425$	8.07187e12	−	4.66030e12i	0.582143	−	0.336100i
$426$		−	2.06823e13i		−	1.47418i
$427$	2.54353e12	−	1.75821e12i	0.179183	−	0.123860i
$428$	−1.47439e13			−1.02658
$429$	1.00601e12	+	1.74247e12i	0.0692337	+	0.119916i
$430$	1.49557e13	+	8.63468e12i	1.01734	+	0.587360i
$431$	8.32876e12	−	1.44258e13i	0.560008	−	0.969962i	−0.437487	−	0.899225i	$-0.644131\pi$
$431$	8.32876e12	−	1.44258e13i	0.560008	−	0.969962i	0.997495	−	0.0707373i	$-0.0225352\pi$
$432$	−1.52343e12	+	8.79551e11i	−0.101252	+	0.0584578i
$433$			4.75638e12i			0.312491i	0.987718	+	0.156245i	$0.0499391\pi$
$433$			4.75638e12i			0.312491i	−0.987718	+	0.156245i	$0.950061\pi$
$434$	−2.80857e12	−	3.45001e13i	−0.182405	−	2.24064i
$435$	1.11629e13			0.716687
$436$	2.60057e13	+	4.50432e13i	1.65058	+	2.85888i
$437$	−7.83646e12	−	4.52438e12i	−0.491714	−	0.283891i
$438$	3.48180e11	−	6.03066e11i	0.0215990	−	0.0374105i
$439$	−6.36528e12	+	3.67500e12i	−0.390387	+	0.225390i	−0.682328	−	0.731047i	$-0.739032\pi$
$439$	−6.36528e12	+	3.67500e12i	−0.390387	+	0.225390i	0.291941	+	0.956436i	$0.405699\pi$
$440$		−	7.82547e12i		−	0.474512i
$441$	3.52218e12	+	4.30202e12i	0.211163	+	0.257917i
$442$	−1.95807e13			−1.16069
$443$	−6.46814e12	−	1.12031e13i	−0.379106	−	0.656631i	0.611826	−	0.790992i	$-0.290435\pi$
$443$	−6.46814e12	−	1.12031e13i	−0.379106	−	0.656631i	−0.990932	+	0.134361i	$0.957102\pi$
$444$	−1.77013e13	−	1.02199e13i	−1.02587	−	0.592284i
$445$	−4.49910e12	+	7.79267e12i	−0.257825	+	0.446567i
$446$	−4.45996e13	+	2.57496e13i	−2.52730	+	1.45914i
$447$		−	6.02547e12i		−	0.337639i
$448$	−2.40787e13	+	1.96019e12i	−1.33427	+	0.108619i
$449$	−8.74407e11			−0.0479162			−0.0239581	−	0.999713i	$-0.507627\pi$
$449$	−8.74407e11			−0.0479162			−0.0239581	+	0.999713i	$0.507627\pi$
$450$	2.64082e12	+	4.57404e12i	0.143112	+	0.247877i
$451$	−3.66864e12	−	2.11809e12i	−0.196618	−	0.113517i
$452$	4.54059e11	−	7.86453e11i	0.0240669	−	0.0416851i
$453$	1.15546e13	−	6.67107e12i	0.605711	−	0.349707i
$454$		−	2.95747e13i		−	1.53335i
$455$	−4.03019e12	−	5.83032e12i	−0.206666	−	0.298975i
$456$	−1.76924e13			−0.897349
$457$	3.29965e12	+	5.71516e12i	0.165534	+	0.286713i	0.936845	−	0.349746i	$-0.113732\pi$
$457$	3.29965e12	+	5.71516e12i	0.165534	+	0.286713i	−0.771311	+	0.636458i	$0.780399\pi$
$458$	8.83916e12	+	5.10329e12i	0.438615	+	0.253235i
$459$	−2.59673e12	+	4.49767e12i	−0.127457	+	0.220762i
$460$	−1.24379e13	+	7.18101e12i	−0.603889	+	0.348656i
$461$		−	3.86873e13i		−	1.85808i	−0.369983	−	0.929038i	$-0.620637\pi$
$461$		−	3.86873e13i		−	1.85808i	0.369983	−	0.929038i	$-0.379363\pi$
$462$	−8.60532e12	−	4.07616e12i	−0.408843	−	0.193661i
$463$	−1.02593e13			−0.482186			−0.241093	−	0.970502i	$-0.577506\pi$
$463$	−1.02593e13			−0.482186			−0.241093	+	0.970502i	$0.577506\pi$
$464$	−1.15557e13	−	2.00150e13i	−0.537286	−	0.930607i
$465$	1.01355e13	+	5.85175e12i	0.466210	+	0.269167i
$466$	3.00209e13	−	5.19977e13i	1.36614	−	2.36622i
$467$	5.14190e12	−	2.96868e12i	0.231494	−	0.133653i	−0.379767	−	0.925082i	$-0.623996\pi$
$467$	5.14190e12	−	2.96868e12i	0.231494	−	0.133653i	0.611261	+	0.791429i	$0.290663\pi$
$468$		−	7.21998e12i		−	0.321593i
$469$	−8.89452e12	+	1.87775e13i	−0.391975	+	0.827511i
$470$	5.23731e13			2.28359
$471$	−2.21842e12	−	3.84242e12i	−0.0957061	−	0.165768i
$472$	3.23516e13	+	1.86782e13i	1.38098	+	0.797307i
$473$	−5.42335e12	+	9.39352e12i	−0.229067	+	0.396755i
$474$	−2.96893e13	+	1.71411e13i	−1.24082	+	0.716386i
$475$			1.30631e13i			0.540231i
$476$	4.96009e13	−	3.42865e13i	2.02981	−	1.40310i
$477$	−8.14442e12			−0.329813
$478$	1.16241e13	+	2.01336e13i	0.465822	+	0.806828i
$479$	3.74283e13	+	2.16092e13i	1.48430	+	0.856962i	0.999841	−	0.0178507i	$-0.00568234\pi$
$479$	3.74283e13	+	2.16092e13i	1.48430	+	0.856962i	0.484461	+	0.874813i	$0.339016\pi$
$480$	2.23069e12	−	3.86367e12i	0.0875454	−	0.151633i
$481$	1.27181e13	−	7.34282e12i	0.493967	−	0.285192i
$482$			2.88163e13i			1.10765i
$483$	6.56798e11	+	8.06802e12i	0.0249860	+	0.306924i
$484$	−3.88675e13			−1.46339
$485$	−1.00067e13	−	1.73321e13i	−0.372892	−	0.645868i
$486$	−2.54866e12	−	1.47147e12i	−0.0940007	−	0.0542713i
$487$	5.44991e12	−	9.43953e12i	0.198950	−	0.344592i	−0.749238	−	0.662301i	$-0.769580\pi$
$487$	5.44991e12	−	9.43953e12i	0.198950	−	0.344592i	0.948188	+	0.317709i	$0.102913\pi$
$488$	7.62263e12	−	4.40093e12i	0.275426	−	0.159018i
$489$			2.43005e13i			0.869103i
$490$	3.13786e13	+	1.18519e13i	1.11085	+	0.419574i
$491$	2.76727e13			0.969716			0.484858	−	0.874593i	$-0.338871\pi$
$491$	2.76727e13			0.969716			0.484858	+	0.874593i	$0.338871\pi$
$492$	7.60057e12	+	1.31646e13i	0.263646	+	0.456648i
$493$	−5.90910e13	−	3.41162e13i	−2.02902	−	1.17146i
$494$	1.37215e13	−	2.37663e13i	0.466408	−	0.807843i
$495$	2.78815e12	−	1.60974e12i	0.0938187	−	0.0541663i
$496$		−	2.42307e13i		−	0.807155i
$497$	−4.56095e13	+	3.71296e12i	−1.50409	+	0.122444i
$498$	6.54761e12			0.213765
$499$	−2.25565e13	−	3.90690e13i	−0.729069	−	1.26279i	−0.957277	−	0.289173i	$-0.906620\pi$
$499$	−2.25565e13	−	3.90690e13i	−0.729069	−	1.26279i	0.228207	−	0.973613i	$-0.426714\pi$
$500$	5.33377e13	+	3.07945e13i	1.70681	+	0.985425i
$501$	3.68136e12	−	6.37630e12i	0.116633	−	0.202013i
$502$	1.29243e13	−	7.46186e12i	0.405405	−	0.234061i
$503$			2.82834e13i			0.878400i	0.898389	+	0.439200i	$0.144738\pi$
$503$			2.82834e13i			0.878400i	−0.898389	+	0.439200i	$0.855262\pi$
$504$	8.99954e12	+	1.30193e13i	0.276737	+	0.400345i
$505$	−2.58670e13			−0.787571
$506$	−6.93144e12	−	1.20056e13i	−0.208964	−	0.361936i
$507$	−1.22573e13	−	7.07678e12i	−0.365895	−	0.211250i
$508$	−1.05812e13	+	1.83272e13i	−0.312763	+	0.541722i
$509$	−2.38810e12	+	1.37877e12i	−0.0698979	+	0.0403556i	−0.534542	−	0.845142i	$-0.679516\pi$
$509$	−2.38810e12	+	1.37877e12i	−0.0698979	+	0.0403556i	0.464644	+	0.885498i	$0.346182\pi$
$510$			3.13313e13i			0.908086i
$511$	−1.39241e12	−	6.59558e11i	−0.0399635	−	0.0189299i
$512$	−4.04451e13			−1.14952
$513$	−3.63940e12	−	6.30363e12i	−0.102434	−	0.177421i
$514$	−5.41457e13	−	3.12610e13i	−1.50921	−	0.871340i
$515$	−1.56153e13	+	2.70465e13i	−0.431037	+	0.746578i
$516$	3.37078e13	−	1.94612e13i	0.921472	−	0.532012i
$517$			3.28950e13i			0.890589i
$518$	−2.97516e13	+	6.28095e13i	−0.797740	+	1.68413i
$519$	2.63298e12			0.0699214
$520$	−1.00879e13	−	1.74727e13i	−0.265328	−	0.459562i
$521$	−4.56520e13	−	2.63572e13i	−1.18925	−	0.686611i	−0.231110	−	0.972928i	$-0.574236\pi$
$521$	−4.56520e13	−	2.63572e13i	−1.18925	−	0.686611i	−0.958135	+	0.286316i	$0.907569\pi$
$522$	1.93324e13	−	3.34847e13i	0.498808	−	0.863961i
$523$	1.40704e13	−	8.12354e12i	0.359582	−	0.207605i	−0.309316	−	0.950959i	$-0.600100\pi$
$523$	1.40704e13	−	8.12354e12i	0.359582	−	0.207605i	0.668897	+	0.743355i	$0.266767\pi$
$524$		−	4.11070e13i		−	1.04054i
$525$	9.61278e12	−	6.64480e12i	0.241020	−	0.166604i
$526$	1.18700e14			2.94796
$527$	−3.57685e13	−	6.19528e13i	−0.879929	−	1.52408i
$528$	−5.77251e12	−	3.33276e12i	−0.140668	−	0.0812147i
$529$	1.48207e13	−	2.56703e13i	0.357760	−	0.619658i
$530$	−4.25512e13	+	2.45670e13i	−1.01750	+	0.587452i
$531$			1.53688e13i			0.364055i
$532$	6.85701e12	+	8.42306e13i	0.160908	+	1.97657i
$533$	−1.09218e13			−0.253897
$534$	1.55835e13	+	2.69914e13i	0.358888	+	0.621613i
$535$	−1.46795e13	−	8.47520e12i	−0.334921	−	0.193366i
$536$	−2.95727e13	+	5.12215e13i	−0.668448	+	1.15779i
$537$	2.41582e12	−	1.39477e12i	0.0540994	−	0.0312343i
$538$		−	8.10912e13i		−	1.79913i
$539$	−7.44408e12	+	1.97086e13i	−0.163632	+	0.433223i
$540$	−1.15528e13			−0.251604
$541$	−1.22431e13	−	2.12056e13i	−0.264182	−	0.457577i	0.703167	−	0.711025i	$-0.251769\pi$
$541$	−1.22431e13	−	2.12056e13i	−0.264182	−	0.457577i	−0.967349	+	0.253448i	$0.918435\pi$
$542$	1.18478e14	+	6.84033e13i	2.53304	+	1.46245i
$543$	−1.78838e13	+	3.09756e13i	−0.378844	+	0.656176i
$544$	−2.36164e13	+	1.36350e13i	−0.495701	+	0.286193i
$545$			5.97953e13i			1.24361i
$546$	−2.44686e13	+	1.99193e12i	−0.504250	+	0.0410498i
$547$	9.78966e12			0.199908			0.0999542	−	0.994992i	$-0.468130\pi$
$547$	9.78966e12			0.199908			0.0999542	+	0.994992i	$0.468130\pi$
$548$	−2.20149e13	−	3.81309e13i	−0.445465	−	0.771568i
$549$	3.13602e12	+	1.81058e12i	0.0628807	+	0.0363042i
$550$	−1.00065e13	+	1.73318e13i	−0.198824	+	0.344373i
$551$	8.28181e13	−	4.78150e13i	1.63067	−	0.941470i
$552$			2.30424e13i			0.449607i
$553$	4.31302e13	+	6.23948e13i	0.833981	+	1.20649i
$554$	−1.35168e14			−2.59016
$555$	−1.17493e13	−	2.03505e13i	−0.223125	−	0.386464i
$556$	7.70979e13	+	4.45125e13i	1.45100	+	0.837737i
$557$	−1.66211e13	+	2.87885e13i	−0.310015	+	0.536962i	−0.978365	−	0.206885i	$-0.933667\pi$
$557$	−1.66211e13	+	2.87885e13i	−0.310015	+	0.536962i	0.668350	+	0.743847i	$0.267001\pi$
$558$	3.51064e13	−	2.02687e13i	0.648956	−	0.374675i
$559$			2.79652e13i			0.512340i
$560$	2.12201e13	+	1.00515e13i	0.385307	+	0.182512i
$561$	−1.96788e13			−0.354148
$562$	3.30941e13	+	5.73207e13i	0.590295	+	1.02242i
$563$	4.43583e13	+	2.56103e13i	0.784211	+	0.452765i	0.837921	−	0.545792i	$-0.183771\pi$
$563$	4.43583e13	+	2.56103e13i	0.784211	+	0.452765i	−0.0537095	+	0.998557i	$0.517104\pi$
$564$	5.90204e13	−	1.02226e14i	1.03420	−	1.79129i
$565$	9.04152e11	−	5.22012e11i	0.0157036	−	0.00906648i
$566$			4.00815e13i			0.690020i
$567$	−2.78741e12	+	5.88459e12i	−0.0475648	+	0.100415i
$568$	−1.30262e14			−2.20331
$569$	−3.59257e13	−	6.22251e13i	−0.602343	−	1.04329i	−0.992465	−	0.122526i	$-0.960901\pi$
$569$	−3.59257e13	−	6.22251e13i	−0.602343	−	1.04329i	0.390122	−	0.920763i	$-0.372433\pi$
$570$	−3.80288e13	−	2.19559e13i	−0.632031	−	0.364903i
$571$	−3.98661e12	+	6.90500e12i	−0.0656784	+	0.113758i	−0.896995	−	0.442041i	$-0.854254\pi$
$571$	−3.98661e12	+	6.90500e12i	−0.0656784	+	0.113758i	0.831316	+	0.555800i	$0.187588\pi$
$572$	2.36924e13	−	1.36788e13i	0.386928	−	0.223393i
$573$		−	3.39041e13i		−	0.548882i
$574$	4.25180e13	−	2.93904e13i	0.682359	−	0.471679i
$575$	1.70134e13			0.270677
$576$	−1.41461e13	−	2.45018e13i	−0.223113	−	0.386444i
$577$	5.57318e13	+	3.21767e13i	0.871412	+	0.503110i	0.867817	−	0.496883i	$-0.165522\pi$
$577$	5.57318e13	+	3.21767e13i	0.871412	+	0.503110i	0.00359495	+	0.999994i	$0.498856\pi$
$578$	4.11779e13	−	7.13222e13i	0.638300	−	1.10557i
$579$	3.59964e13	−	2.07825e13i	0.553180	−	0.319378i
$580$		−	1.51782e14i		−	2.31250i
$581$	−1.17545e12	−	1.44391e13i	−0.0177551	−	0.218102i
$582$	−6.93205e13			−1.03812
$583$	−1.54303e13	−	2.67260e13i	−0.229103	−	0.396818i
$584$	−3.79824e12	−	2.19291e12i	−0.0559137	−	0.0322818i
$585$	4.15025e12	−	7.18845e12i	0.0605753	−	0.104919i
$586$	−1.18878e14	+	6.86345e13i	−1.72034	+	0.993241i
$587$		−	5.01333e13i		−	0.719343i	−0.933079	−	0.359672i	$-0.882889\pi$
$587$		−	5.01333e13i		−	0.719343i	0.933079	−	0.359672i	$-0.117111\pi$
$588$	5.84949e13	−	4.78913e13i	0.832207	−	0.681350i
$589$	1.00262e14			1.41435
$590$	4.63587e13	+	8.02957e13i	0.648443	+	1.12314i
$591$	−6.28030e12	−	3.62593e12i	−0.0871049	−	0.0502901i
$592$	−2.43256e13	+	4.21331e13i	−0.334545	+	0.579449i
$593$	4.86966e13	−	2.81150e13i	0.664088	−	0.383411i	−0.129745	−	0.991547i	$-0.541416\pi$
$593$	4.86966e13	−	2.81150e13i	0.664088	−	0.383411i	0.793833	+	0.608136i	$0.208083\pi$
$594$		−	1.11513e13i		−	0.150797i
$595$	6.90931e13	−	5.62470e12i	0.926510	−	0.0754249i
$596$	−8.19286e13			−1.08944
$597$	1.22141e13	+	2.11554e13i	0.161060	+	0.278964i
$598$	−3.09531e13	−	1.78708e13i	−0.404760	−	0.233689i
$599$	−2.69111e13	+	4.66114e13i	−0.348978	+	0.604447i	−0.986068	−	0.166342i	$-0.946804\pi$
$599$	−2.69111e13	+	4.66114e13i	−0.348978	+	0.604447i	0.637090	+	0.770789i	$0.280138\pi$
$600$	2.88083e13	−	1.66325e13i	0.370477	−	0.213895i
$601$			3.68433e13i			0.469879i	0.972010	+	0.234940i	$0.0754892\pi$
$601$			3.68433e13i			0.469879i	−0.972010	+	0.234940i	$0.924511\pi$
$602$	−7.52539e13	−	1.08867e14i	−0.951802	−	1.37694i
$603$	−2.43330e13			−0.305217
$604$	−9.07070e13	−	1.57109e14i	−1.12838	−	1.95441i
$605$	−3.86978e13	−	2.23422e13i	−0.477430	−	0.275644i
$606$	−4.47978e13	+	7.75921e13i	−0.548143	+	0.949411i
$607$	1.33970e13	−	7.73475e12i	0.162579	−	0.0938648i	−0.416503	−	0.909134i	$-0.636745\pi$
$607$	1.33970e13	−	7.73475e12i	0.162579	−	0.0938648i	0.579082	+	0.815269i	$0.303411\pi$
$608$		−	3.82197e13i		−	0.460013i
$609$	−7.73126e13	−	3.66214e13i	−0.922919	−	0.437168i
$610$	2.18459e13			0.258655
$611$	4.24053e13	+	7.34480e13i	0.497982	+	0.862530i
$612$	6.11550e13	+	3.53079e13i	0.712320	+	0.411258i
$613$	2.35205e13	−	4.07388e13i	0.271735	−	0.470658i	−0.697572	−	0.716515i	$-0.745736\pi$
$613$	2.35205e13	−	4.07388e13i	0.271735	−	0.470658i	0.969306	+	0.245857i	$0.0790694\pi$
$614$	−1.03210e14	+	5.95886e13i	−1.18272	+	0.682843i
$615$			1.74761e13i			0.198641i
$616$	−2.56726e13	+	5.41982e13i	−0.289445	+	0.611056i
$617$	−5.03438e13			−0.563015			−0.281507	−	0.959559i	$-0.590834\pi$
$617$	−5.03438e13			−0.563015			−0.281507	+	0.959559i	$0.590834\pi$
$618$	5.40867e13	+	9.36809e13i	0.599996	+	1.03922i
$619$	5.19455e13	+	2.99907e13i	0.571603	+	0.330015i	0.757789	−	0.652499i	$-0.226279\pi$
$619$	5.19455e13	+	2.99907e13i	0.571603	+	0.330015i	−0.186186	+	0.982514i	$0.559613\pi$
$620$	7.95667e13	−	1.37813e14i	0.868506	−	1.50430i
$621$	−8.20981e12	+	4.73994e12i	−0.0888946	+	0.0513233i
$622$		−	2.86790e13i		−	0.308043i
$623$	5.67251e13	−	3.92111e13i	0.604415	−	0.417800i
$624$	−1.71852e13			−0.181648
$625$	1.12043e13	+	1.94065e13i	0.117486	+	0.203492i
$626$	−2.01216e14	−	1.16172e14i	−2.09310	−	1.20845i
$627$	1.37903e13	−	2.38855e13i	0.142310	−	0.246488i
$628$	−5.22456e13	+	3.01640e13i	−0.534874	+	0.308810i
$629$			1.43634e14i			1.45883i
$630$	3.18731e12	+	3.91525e13i	0.0321160	+	0.394509i
$631$	6.95431e13			0.695196			0.347598	−	0.937644i	$-0.386997\pi$
$631$	6.95431e13			0.695196			0.347598	+	0.937644i	$0.386997\pi$
$632$	1.07958e14	+	1.86989e14i	1.07071	+	1.85452i
$633$	4.89500e13	+	2.82613e13i	0.481653	+	0.278082i
$634$	−7.16601e10	+	1.24119e11i	−0.000699569	+	0.00121169i
$635$	−2.10700e13	+	1.21647e13i	−0.204077	+	0.117824i
$636$			1.10740e14i			1.06419i
$637$	8.78538e12	+	5.36016e13i	0.0837651	+	0.511071i
$638$	1.46507e14			1.38598
$639$	−2.67954e13	−	4.64111e13i	−0.251511	−	0.435630i
$640$	−1.19615e14	−	6.90599e13i	−1.11400	−	0.643170i
$641$	−5.84889e13	+	1.01306e14i	−0.540485	+	0.936147i	0.458391	+	0.888750i	$0.348426\pi$
$641$	−5.84889e13	+	1.01306e14i	−0.540485	+	0.936147i	−0.998876	+	0.0473966i	$0.984908\pi$
$642$	−5.08453e13	+	2.93555e13i	−0.466203	+	0.269163i
$643$		−	3.58951e13i		−	0.326573i	−0.986579	−	0.163287i	$-0.947791\pi$
$643$		−	3.58951e13i		−	0.326573i	0.986579	−	0.163287i	$-0.0522095\pi$
$644$	1.09701e14	−	8.93053e12i	0.990337	−	0.0806209i
$645$	4.47475e13			0.400839
$646$	1.34204e14	+	2.32449e14i	1.19290	+	2.06616i
$647$	1.42856e14	+	8.24778e13i	1.26002	+	0.727471i	0.973078	−	0.230478i	$-0.0740290\pi$
$647$	1.42856e14	+	8.24778e13i	1.26002	+	0.727471i	0.286939	+	0.957949i	$0.407362\pi$
$648$	−9.26764e12	+	1.60520e13i	−0.0811137	+	0.140493i
$649$	−5.04329e13	+	2.91174e13i	−0.438016	+	0.252889i
$650$			5.15979e13i			0.444698i
$651$	−5.09999e13	−	7.37795e13i	−0.436178	−	0.631002i
$652$	3.30416e14			2.80429
$653$	−9.22472e12	−	1.59777e13i	−0.0776940	−	0.134570i	0.824561	−	0.565774i	$-0.191422\pi$
$653$	−9.22472e12	−	1.59777e13i	−0.0776940	−	0.134570i	−0.902255	+	0.431204i	$0.858089\pi$
$654$	1.79365e14	+	1.03556e14i	1.49916	+	0.865542i
$655$	2.36295e13	−	4.09275e13i	0.195996	−	0.339475i
$656$	3.13347e13	−	1.80911e13i	0.257932	−	0.148917i
$657$		−	1.80437e12i		−	0.0147401i
$658$	−3.62729e14	−	1.71817e14i	−2.94072	−	1.39296i
$659$	2.14033e13			0.172208			0.0861040	−	0.996286i	$-0.472558\pi$
$659$	2.14033e13			0.172208			0.0861040	+	0.996286i	$0.472558\pi$
$660$	−2.18877e13	−	3.79106e13i	−0.174775	−	0.302720i
$661$	−1.83712e14	−	1.06066e14i	−1.45590	−	0.840562i	−0.457090	−	0.889421i	$-0.651108\pi$
$661$	−1.83712e14	−	1.06066e14i	−1.45590	−	0.840562i	−0.998806	+	0.0488589i	$0.984442\pi$
$662$	1.43441e14	−	2.48447e14i	1.12819	−	1.95409i
$663$	−4.39390e13	+	2.53682e13i	−0.342991	+	0.198026i
$664$		−	4.12382e13i		−	0.319492i
$665$	−4.15911e13	+	8.78044e13i	−0.319810	+	0.675162i
$666$	−8.13923e13			−0.621172
$667$	−6.22740e13	−	1.07862e14i	−0.471713	−	0.817031i
$668$	−8.66990e13	−	5.00557e13i	−0.651826	−	0.376332i
$669$	−6.67210e13	+	1.15564e14i	−0.497888	+	0.862368i
$670$	−1.27130e14	+	7.33985e13i	−0.941616	+	0.543642i
$671$			1.37212e13i			0.100874i
$672$	−2.81248e13	+	1.94412e13i	−0.205231	+	0.141865i
$673$	−2.23003e14			−1.61523			−0.807616	−	0.589709i	$-0.799242\pi$
$673$	−2.23003e14			−1.61523			−0.807616	+	0.589709i	$0.799242\pi$
$674$	1.41058e13	+	2.44319e13i	0.101414	+	0.175654i
$675$	1.18520e13	+	6.84276e12i	0.0845810	+	0.0488329i
$676$	−9.62234e13	+	1.66664e14i	−0.681628	+	1.18061i
$677$	−5.23975e13	+	3.02517e13i	−0.368440	+	0.212719i	−0.672777	−	0.739845i	$-0.734899\pi$
$677$	−5.23975e13	+	3.02517e13i	−0.368440	+	0.212719i	0.304337	+	0.952565i	$0.401565\pi$
$678$		−	3.61618e12i		−	0.0252407i
$679$	1.24447e13	+	1.52869e14i	0.0862252	+	1.05918i
$680$	1.97331e14			1.35722
$681$	−3.83162e13	−	6.63656e13i	−0.261605	−	0.453114i
$682$	1.33024e14	+	7.68014e13i	0.901587	+	0.520532i
$683$	6.76682e13	−	1.17205e14i	0.455283	−	0.788572i	−0.543422	−	0.839460i	$-0.682872\pi$
$683$	6.76682e13	−	1.17205e14i	0.455283	−	0.788572i	0.998704	+	0.0508873i	$0.0162049\pi$
$684$	−8.57109e13	+	4.94852e13i	−0.572474	+	0.330518i
$685$		−	5.06191e13i		−	0.335631i
$686$	−1.78442e14	−	1.85027e14i	−1.17457	−	1.21791i
$687$	2.64468e13			0.172818
$688$	−4.63221e13	−	8.02321e13i	−0.300501	−	0.520483i
$689$	−6.89054e13	−	3.97826e13i	−0.443769	−	0.256210i
$690$	−2.85953e13	+	4.95284e13i	−0.182830	+	0.316672i
$691$	1.19099e14	−	6.87620e13i	0.755995	−	0.436474i	−0.0718609	−	0.997415i	$-0.522894\pi$
$691$	1.19099e14	−	6.87620e13i	0.755995	−	0.436474i	0.827856	+	0.560941i	$0.189560\pi$
$692$		−	3.58007e13i		−	0.225612i
$693$	−2.45913e13	+	2.00192e12i	−0.153856	+	0.0125251i
$694$	3.20419e14			1.99031
$695$	5.11741e13	+	8.86362e13i	0.315592	+	0.546622i
$696$	−2.10894e14	−	1.21760e14i	−1.29127	−	0.745517i
$697$	5.34109e13	−	9.25103e13i	0.324688	−	0.562375i
$698$	3.50977e14	−	2.02637e14i	2.11837	−	1.22304i
$699$		−	1.55577e14i		−	0.932308i
$700$	−9.03498e13	−	1.30706e14i	−0.537572	−	0.777685i
$701$	−1.18390e14			−0.699401			−0.349701	−	0.936862i	$-0.613717\pi$
$701$	−1.18390e14			−0.699401			−0.349701	+	0.936862i	$0.613717\pi$
$702$	−1.43752e13	−	2.48986e13i	−0.0843197	−	0.146046i
$703$	−1.74338e14	−	1.00654e14i	−1.01535	−	0.586213i
$704$	5.36020e13	−	9.28414e13i	0.309969	−	0.536882i
$705$	1.17525e14	−	6.78532e13i	0.674816	−	0.389605i
$706$			2.48060e13i			0.141427i
$707$	1.79152e14	+	8.48605e13i	1.01420	+	0.480406i
$708$	2.08971e14			1.17468
$709$	1.21126e14	+	2.09797e14i	0.676093	+	1.17103i	0.976148	+	0.217106i	$0.0696616\pi$
$709$	1.21126e14	+	2.09797e14i	0.676093	+	1.17103i	−0.300055	+	0.953922i	$0.597005\pi$
$710$	−2.79990e14	−	1.61653e14i	−1.55186	−	0.895964i
$711$	−4.44151e13	+	7.69293e13i	−0.244446	+	0.423393i
$712$	1.69998e14	−	9.81484e13i	0.929060	−	0.536393i
$713$		−	1.30580e14i		−	0.708646i
$714$	1.02787e14	−	2.16996e14i	0.553918	−	1.16939i
$715$	3.14520e13			0.168313
$716$	−1.89648e13	−	3.28480e13i	−0.100782	−	0.174560i
$717$	5.21690e13	+	3.01198e13i	0.275307	+	0.158948i
$718$	−2.18157e14	+	3.77859e14i	−1.14327	+	1.98019i
$719$	−6.69744e13	+	3.86677e13i	−0.348549	+	0.201235i	−0.664046	−	0.747692i	$-0.731162\pi$
$719$	−6.69744e13	+	3.86677e13i	−0.348549	+	0.201235i	0.315497	+	0.948927i	$0.397829\pi$
$720$			2.74982e13i			0.142116i
$721$	1.96880e14	−	1.36092e14i	1.01047	−	0.698485i
$722$	−4.42211e13			−0.225395
$723$	3.73336e13	+	6.46637e13i	0.188977	+	0.327317i
$724$	4.21177e14	+	2.43167e14i	2.11725	+	1.22239i
$725$	−8.99012e13	+	1.55713e14i	−0.448823	+	0.777385i
$726$	−1.34037e14	+	7.73866e13i	−0.664574	+	0.383692i
$727$			2.85202e14i			1.40437i	0.711997	+	0.702183i	$0.247791\pi$
$727$			2.85202e14i			1.40437i	−0.711997	+	0.702183i	$0.752209\pi$
$728$	1.25456e13	+	1.54109e14i	0.0613528	+	0.753650i
$729$	−7.62560e12			−0.0370370
$730$	−5.44274e12	−	9.42710e12i	−0.0262545	−	0.0454741i
$731$	−2.36872e14	−	1.36758e14i	−1.13482	−	0.655188i
$732$	2.46186e13	−	4.26407e13i	0.117141	−	0.202894i
$733$	−2.01654e14	+	1.16425e14i	−0.952985	+	0.550206i	−0.894007	−	0.448053i	$-0.852118\pi$
$733$	−2.01654e14	+	1.16425e14i	−0.952985	+	0.550206i	−0.0589782	+	0.998259i	$0.518784\pi$
$734$		−	7.91730e13i		−	0.371618i
$735$	8.57687e13	−	1.40576e13i	0.399846	−	0.0655352i
$736$	−4.97772e13			−0.230484
$737$	−4.61009e13	−	7.98490e13i	−0.212017	−	0.367225i
$738$	5.24222e13	+	3.02660e13i	0.239460	+	0.138252i
$739$	3.02144e13	−	5.23329e13i	0.137086	−	0.237439i	−0.789307	−	0.613999i	$-0.789560\pi$
$739$	3.02144e13	−	5.23329e13i	0.137086	−	0.237439i	0.926392	+	0.376560i	$0.122893\pi$
$740$	−2.76706e14	+	1.59757e14i	−1.24698	+	0.719946i
$741$		−	7.11088e13i		−	0.318297i
$742$	3.75300e14	−	3.05522e13i	1.66862	−	0.135839i
$743$	1.58976e14			0.702083			0.351041	−	0.936360i	$-0.385828\pi$
$743$	1.58976e14			0.702083			0.351041	+	0.936360i	$0.385828\pi$
$744$	−1.27657e14	−	2.21108e14i	−0.559988	−	0.969928i
$745$	−8.15708e13	−	4.70949e13i	−0.355430	−	0.205207i
$746$	−2.71530e14	+	4.70304e14i	−1.17523	+	2.03556i
$747$	1.46928e13	−	8.48291e12i	0.0631688	−	0.0364705i
$748$			2.67574e14i			1.14271i
$749$	7.38641e13	+	1.06856e14i	0.313346	+	0.453305i
$750$	2.45252e14			1.03349
$751$	−2.85233e13	−	4.94038e13i	−0.119399	−	0.206805i	0.800131	−	0.599826i	$-0.204763\pi$
$751$	−2.85233e13	−	4.94038e13i	−0.119399	−	0.206805i	−0.919530	+	0.393021i	$0.871430\pi$
$752$	−2.43321e14	−	1.40482e14i	−1.01179	−	0.584158i
$753$	1.93348e13	−	3.34888e13i	0.0798664	−	0.138333i
$754$	3.27122e14	−	1.88864e14i	1.34231	−	0.774983i
$755$		−	2.08564e14i		−	0.850168i
$756$	8.00131e13	+	3.79006e13i	0.324005	+	0.153475i
$757$	−4.48101e14			−1.80259			−0.901294	−	0.433209i	$-0.857381\pi$
$757$	−4.48101e14			−1.80259			−0.901294	+	0.433209i	$0.857381\pi$
$758$	2.37042e14	+	4.10568e14i	0.947281	+	1.64074i
$759$	−3.11083e13	−	1.79604e13i	−0.123500	−	0.0713028i
$760$	−1.38283e14	+	2.39513e14i	−0.545383	+	0.944631i
$761$	3.66197e14	−	2.11424e14i	1.43480	−	0.828383i	0.437320	−	0.899306i	$-0.355928\pi$
$761$	3.66197e14	−	2.11424e14i	1.43480	−	0.828383i	0.997482	+	0.0709230i	$0.0225944\pi$
$762$			8.42700e13i			0.328018i
$763$	1.96167e14	−	4.14134e14i	0.758583	−	1.60147i
$764$	−4.60996e14			−1.77105
$765$	4.05920e13	+	7.03074e13i	0.154929	+	0.268345i
$766$	7.12317e13	+	4.11256e13i	0.270103	+	0.155944i
$767$	−7.50711e13	+	1.30027e14i	−0.282811	+	0.489843i
$768$	−2.35476e14	+	1.35952e14i	−0.881333	+	0.508838i
$769$		−	3.48246e14i		−	1.29495i	−0.762086	−	0.647476i	$-0.775824\pi$
$769$		−	3.48246e14i		−	1.29495i	0.762086	−	0.647476i	$-0.224176\pi$
$770$	−1.22441e14	+	8.46368e13i	−0.452348	+	0.312684i
$771$	−1.62004e14			−0.594639
$772$	−2.82581e14	−	4.89445e14i	−1.03052	−	1.78491i
$773$	3.80211e14	+	2.19515e14i	1.37761	+	0.795366i	0.991872	−	0.127241i	$-0.0406121\pi$
$773$	3.80211e14	+	2.19515e14i	1.37761	+	0.795366i	0.385742	+	0.922607i	$0.373945\pi$
$774$	7.74958e13	−	1.34227e14i	0.278980	−	0.483208i
$775$	−1.63255e14	+	9.42552e13i	−0.583925	+	0.337129i
$776$			4.36595e14i			1.55157i
$777$	1.46118e13	+	1.79490e14i	0.0515940	+	0.633775i
$778$	−3.22086e14			−1.12999
$779$	7.48572e13	+	1.29656e14i	0.260943	+	0.451967i
$780$	−9.77418e13	−	5.64313e13i	−0.338538	−	0.195455i
$781$	1.01532e14	−	1.75859e14i	0.349421	−	0.605215i
$782$	3.02740e14	−	1.74787e14i	1.03523	−	0.597689i
$783$		−	1.00186e14i		−	0.340408i
$784$	−1.13992e14	−	1.39231e14i	−0.384852	−	0.470062i
$785$	−6.93566e13			−0.232669
$786$	−8.18454e13	−	1.41760e14i	−0.272823	−	0.472544i
$787$	−2.17814e14	−	1.25755e14i	−0.721461	−	0.416536i	0.0938290	−	0.995588i	$-0.470089\pi$
$787$	−2.17814e14	−	1.25755e14i	−0.721461	−	0.416536i	−0.815290	+	0.579052i	$0.803423\pi$
$788$	−4.93020e13	+	8.53936e13i	−0.162268	+	0.281057i
$789$	2.66362e14	−	1.53784e14i	0.871140	−	0.502953i
$790$			5.35898e14i			1.74159i
$791$	−7.97457e12	+	6.49190e11i	−0.0257528	+	0.00209647i
$792$	−7.02332e13			−0.225381
$793$	1.76881e13	+	3.06367e13i	0.0564047	+	0.0976959i
$794$	−1.42250e14	−	8.21281e13i	−0.450765	−	0.260249i
$795$	−6.36566e13	+	1.10257e14i	−0.200451	+	0.347191i
$796$	2.87651e14	−	1.66075e14i	0.900120	−	0.519684i
$797$		−	5.11256e14i		−	1.58982i	−0.606729	−	0.794908i	$-0.707519\pi$
$797$		−	5.11256e14i		−	1.58982i	0.606729	−	0.794908i	$-0.292481\pi$
$798$	1.91353e14	+	2.76823e14i	0.591317	+	0.855435i
$799$	−8.29498e14			−2.54731
$800$	3.59301e13	+	6.22328e13i	0.109650	+	0.189919i
$801$	6.99388e13	+	4.03792e13i	0.212107	+	0.122460i
$802$	2.22735e14	−	3.85788e14i	0.671299	−	1.16272i
$803$	5.92106e12	−	3.41853e12i	0.0177346	−	0.0102391i
$804$			3.30858e14i			0.984829i
$805$	1.14356e14	+	5.41680e13i	0.338282	+	0.160237i
$806$	3.96021e14			1.16424
$807$	−1.05060e14	−	1.81969e14i	−0.306950	−	0.531654i
$808$	4.88691e14	+	2.82146e14i	1.41899	+	0.819252i
$809$	−2.76910e14	+	4.79622e14i	−0.799090	+	1.38406i	0.121119	+	0.992638i	$0.461352\pi$
$809$	−2.76910e14	+	4.79622e14i	−0.799090	+	1.38406i	−0.920209	+	0.391427i	$0.871982\pi$
$810$	−3.98406e13	+	2.30020e13i	−0.114262	+	0.0659691i
$811$			5.20694e14i			1.48415i	0.670316	+	0.742075i	$0.266158\pi$
$811$			5.20694e14i			1.48415i	−0.670316	+	0.742075i	$0.733842\pi$
$812$	−4.97943e14	+	1.05122e15i	−1.41059	+	2.97794i
$813$	3.54486e14			0.998037
$814$	−1.54204e14	−	2.67090e14i	−0.431494	−	0.747369i
$815$	3.28973e14	+	1.89933e14i	0.914897	+	0.528216i
$816$	8.40407e13	−	1.45563e14i	0.232294	−	0.402346i
$817$	3.31984e14	−	1.91671e14i	0.912026	−	0.526558i
$818$		−	3.37603e14i		−	0.921807i
$819$	−5.23268e13	+	3.61708e13i	−0.142005	+	0.0981608i
$820$	2.37624e14			0.640945
$821$	−6.30154e13	−	1.09146e14i	−0.168940	−	0.292612i	0.769108	−	0.639119i	$-0.220701\pi$
$821$	−6.30154e13	−	1.09146e14i	−0.168940	−	0.292612i	−0.938047	+	0.346507i	$0.887368\pi$
$822$	−1.51840e14	−	8.76647e13i	−0.404600	−	0.233596i
$823$	9.72642e13	−	1.68466e14i	0.257605	−	0.446184i	−0.707995	−	0.706217i	$-0.750400\pi$
$823$	9.72642e13	−	1.68466e14i	0.257605	−	0.446184i	0.965600	+	0.260033i	$0.0837335\pi$
$824$	5.90023e14	−	3.40650e14i	1.55322	−	0.896751i
$825$			5.18566e13i			0.135686i
$826$	−5.76531e13	−	7.08204e14i	−0.149942	−	1.84187i
$827$	2.59580e14			0.671033			0.335516	−	0.942034i	$-0.391089\pi$
$827$	2.59580e14			0.671033			0.335516	+	0.942034i	$0.391089\pi$
$828$	6.44492e13	+	1.11629e14i	0.165602	+	0.286831i
$829$	2.48995e14	+	1.43757e14i	0.635942	+	0.367161i	0.783050	−	0.621959i	$-0.213663\pi$
$829$	2.48995e14	+	1.43757e14i	0.635942	+	0.367161i	−0.147108	+	0.989120i	$0.546996\pi$
$830$	5.11760e13	−	8.86394e13i	0.129920	−	0.225028i
$831$	−3.03318e14	+	1.75120e14i	−0.765407	+	0.441908i
$832$		−	2.76395e14i		−	0.693289i
$833$	−4.96982e14	−	1.87714e14i	−1.23913	−	0.468027i
$834$	3.54503e14			0.878598
$835$	−5.75469e13	−	9.96742e13i	−0.141772	−	0.245556i
$836$	−3.24772e14	−	1.87507e14i	−0.795331	−	0.459184i
$837$	5.25192e13	−	9.09659e13i	0.127847	−	0.221438i
$838$	1.00341e13	−	5.79317e12i	0.0242804	−	0.0140183i
$839$			3.26191e13i			0.0784624i	0.999230	+	0.0392312i	$0.0124909\pi$
$839$			3.26191e13i			0.0784624i	−0.999230	+	0.0392312i	$0.987509\pi$
$840$	2.46591e14	−	2.00744e13i	0.589632	−	0.0480005i
$841$	8.95555e14			2.12869
$842$	−4.02673e14	−	6.97450e14i	−0.951463	−	1.64798i
$843$	1.48526e14	+	8.57517e13i	0.348872	+	0.201421i
$844$	3.84271e14	−	6.65576e14i	0.897274	−	1.55412i
$845$	−1.91606e14	+	1.10624e14i	−0.444761	+	0.256783i
$846$		−	4.70046e14i		−	1.08465i
$847$	1.94719e14	+	2.81693e14i	0.446675	+	0.646187i
$848$	2.63586e14			0.601096
$849$	5.19286e13	+	8.99429e13i	0.117725	+	0.203905i
$850$	−4.37047e14	−	2.52329e14i	−0.984993	−	0.568686i
$851$	−1.31091e14	+	2.27057e14i	−0.293715	+	0.508730i
$852$	−6.31054e14	+	3.64339e14i	−1.40562	+	0.811537i
$853$			6.31200e14i			1.39773i	0.715256	+	0.698863i	$0.246310\pi$
$853$			6.31200e14i			1.39773i	−0.715256	+	0.698863i	$0.753690\pi$
$854$	−1.51302e14	−	7.16686e13i	−0.333085	−	0.157776i
$855$	−1.13782e14			−0.249025
$856$	1.84887e14	+	3.20235e14i	0.402289	+	0.696786i
$857$	−4.39558e14	−	2.53779e14i	−0.950850	−	0.548974i	−0.0575054	−	0.998345i	$-0.518315\pi$
$857$	−4.39558e14	−	2.53779e14i	−0.950850	−	0.548974i	−0.893345	+	0.449371i	$0.851648\pi$
$858$	5.44700e13	−	9.43449e13i	0.117144	−	0.202900i
$859$	−7.95017e14	+	4.59003e14i	−1.69985	+	0.981409i	−0.753962	+	0.656918i	$0.771860\pi$
$859$	−7.95017e14	+	4.59003e14i	−1.69985	+	0.981409i	−0.945889	+	0.324491i	$0.894807\pi$
$860$		−	6.08434e14i		−	1.29337i
$861$	5.73329e13	−	1.21037e14i	0.121168	−	0.255802i
$862$	−9.01911e14			−1.89508
$863$	5.67402e13	+	9.82769e13i	0.118532	+	0.205304i	0.919186	−	0.393823i	$-0.128848\pi$
$863$	5.67402e13	+	9.82769e13i	0.118532	+	0.205304i	−0.800654	+	0.599127i	$0.795514\pi$
$864$	−3.46762e13	−	2.00203e13i	−0.0720217	−	0.0415817i
$865$	2.05793e13	−	3.56444e13i	0.0424962	−	0.0736055i
$866$	2.23029e14	−	1.28766e14i	0.457901	−	0.264369i
$867$		−	2.13396e14i		−	0.435603i
$868$	−1.00318e15	+	6.93448e14i	−2.03602	+	1.40739i
$869$	−3.36592e14			−0.679212
$870$	−3.02204e14	−	5.23432e14i	−0.606322	−	1.05018i
$871$	−2.05868e14	−	1.18858e14i	−0.410675	−	0.237103i
$872$	6.52220e14	−	1.12968e15i	1.29364	−	2.24064i
$873$	−1.55555e14	+	8.98098e13i	−0.306770	+	0.177114i
$874$			4.89940e14i			0.960695i
$875$	−4.40284e13	−	5.40840e14i	−0.0858406	−	1.05446i
$876$	−2.45342e13			−0.0475610
$877$	2.85732e14	+	4.94902e14i	0.550758	+	0.953940i	0.998220	+	0.0596374i	$0.0189944\pi$
$877$	2.85732e14	+	4.94902e14i	0.550758	+	0.953940i	−0.447463	+	0.894303i	$0.647672\pi$
$878$	3.44644e14	+	1.98980e14i	0.660539	+	0.381362i
$879$	−1.77842e14	+	3.08032e14i	−0.338915	+	0.587017i
$880$	−9.02357e13	+	5.20976e13i	−0.170988	+	0.0987199i
$881$		−	5.51809e14i		−	1.03970i	−0.854257	−	0.519851i	$-0.825987\pi$
$881$		−	5.51809e14i		−	1.03970i	0.854257	−	0.519851i	$-0.174013\pi$
$882$	1.06371e14	−	2.81622e14i	0.199287	−	0.527622i
$883$	−6.94820e14			−1.29440			−0.647200	−	0.762320i	$-0.724060\pi$
$883$	−6.94820e14			−1.29440			−0.647200	+	0.762320i	$0.724060\pi$
$884$	3.44933e14	+	5.97441e14i	0.638959	+	1.10671i
$885$	2.08058e14	+	1.20122e14i	0.383238	+	0.221262i
$886$	−3.50213e14	+	6.06587e14i	−0.641452	+	1.11103i
$887$	−3.95183e14	+	2.28159e14i	−0.719748	+	0.415547i	−0.814660	−	0.579939i	$-0.803076\pi$
$887$	−3.95183e14	+	2.28159e14i	−0.719748	+	0.415547i	0.0949118	+	0.995486i	$0.469743\pi$
$888$			5.12626e14i			0.928402i
$889$	1.85836e14	−	1.51284e13i	0.334673	−	0.0272449i
$890$	4.87202e14			0.872487
$891$	−1.44473e13	−	2.50235e13i	−0.0257276	−	0.0445614i
$892$	1.57133e15	+	9.07209e14i	2.78256	+	1.60651i
$893$	5.81285e14	−	1.00681e15i	1.02360	−	1.77293i
$894$	−2.82537e14	+	1.63123e14i	−0.494751	+	0.285645i
$895$		−	4.36061e13i		−	0.0759332i
$896$	6.01879e14	+	8.70714e14i	1.04224	+	1.50777i
$897$	−9.26116e13			−0.159479
$898$	2.36721e13	+	4.10013e13i	0.0405374	+	0.0702128i
$899$	1.19512e15	+	6.90005e14i	2.03523	+	1.17504i
$900$	9.30414e13	−	1.61152e14i	0.157566	−	0.272913i
$901$	6.73936e14	−	3.89097e14i	1.13500	−	0.655291i
$902$			2.29365e14i			0.384145i
$903$	−3.09915e14	−	1.46800e14i	−0.516183	−	0.244505i
$904$	−2.27755e13			−0.0377247
$905$	2.79559e14	+	4.84210e14i	0.460500	+	0.797610i
$906$	−6.25619e14	−	3.61201e14i	−1.02487	−	0.591709i
$907$	2.77416e14	−	4.80499e14i	0.451955	−	0.782809i	−0.546552	−	0.837425i	$-0.684060\pi$
$907$	2.77416e14	−	4.80499e14i	0.451955	−	0.782809i	0.998507	+	0.0546156i	$0.0173933\pi$
$908$	−9.02377e14	+	5.20988e14i	−1.46204	+	0.844108i
$909$			2.32155e14i			0.374076i
$910$	−1.64280e14	+	3.46817e14i	−0.263256	+	0.555768i
$911$	1.90788e14			0.304060			0.152030	−	0.988376i	$-0.451419\pi$
$911$	1.90788e14			0.304060			0.152030	+	0.988376i	$0.451419\pi$
$912$	1.17786e14	+	2.04011e14i	0.186689	+	0.323355i
$913$	5.56735e13	+	3.21431e13i	0.0877596	+	0.0506680i
$914$	1.78657e14	−	3.09444e14i	0.280085	−	0.485122i
$915$	4.90222e13	−	2.83030e13i	0.0764342	−	0.0441293i
$916$		−	3.59598e14i		−	0.557622i
$917$	−2.97923e14	+	2.05938e14i	−0.459470	+	0.317607i
$918$	2.81197e14			0.431317
$919$	6.49831e14	+	1.12554e15i	0.991341	+	1.71705i	0.609393	+	0.792868i	$0.291413\pi$
$919$	6.49831e14	+	1.12554e15i	0.991341	+	1.71705i	0.381948	+	0.924184i	$0.375253\pi$
$920$	3.11941e14	+	1.80099e14i	0.473296	+	0.273258i
$921$	−1.54403e14	+	2.67433e14i	−0.233001	+	0.403569i
$922$	−1.81406e15	+	1.04735e15i	−2.72269	+	1.57194i
$923$		−	5.23545e14i		−	0.781529i
$924$	2.72202e13	+	3.34369e14i	0.0404140	+	0.496440i
$925$	3.78497e14			0.558926
$926$	2.77743e14	+	4.81064e14i	0.407932	+	0.706559i
$927$	2.42741e14	+	1.40147e14i	0.354605	+	0.204731i
$928$	2.63030e14	−	4.55582e14i	0.382178	−	0.661952i
$929$	−6.64232e14	+	3.83494e14i	−0.959933	+	0.554218i	−0.896153	−	0.443746i	$-0.853649\pi$
$929$	−6.64232e14	+	3.83494e14i	−0.959933	+	0.554218i	−0.0637808	+	0.997964i	$0.520316\pi$
$930$		−	6.33679e14i		−	0.910866i
$931$	5.76109e14	−	4.71676e14i	0.823676	−	0.674365i
$932$	−2.11539e15			−3.00823
$933$	−3.71557e13	−	6.43556e13i	−0.0525554	−	0.0910287i
$934$	−2.78405e14	−	1.60737e14i	−0.391690	−	0.226143i
$935$	−1.53810e14	+	2.66406e14i	−0.215241	+	0.372808i
$936$	−1.56817e14	+	9.05382e13i	−0.218280	+	0.126024i
$937$			1.36869e14i			0.189500i	0.995501	+	0.0947498i	$0.0302051\pi$
$937$			1.36869e14i			0.189500i	−0.995501	+	0.0947498i	$0.969795\pi$
$938$	1.12128e15	−	9.12806e13i	1.54419	−	0.125708i
$939$	−6.02038e14			−0.824700
$940$	−9.22605e14	−	1.59800e15i	−1.25712	−	2.17739i
$941$	−5.72546e14	−	3.30559e14i	−0.776000	−	0.448024i	0.0590105	−	0.998257i	$-0.481205\pi$
$941$	−5.72546e14	−	3.30559e14i	−0.776000	−	0.448024i	−0.835011	+	0.550233i	$0.814539\pi$
$942$	−1.20115e14	+	2.08045e14i	−0.161936	+	0.280481i
$943$	1.68864e14	−	9.74935e13i	0.226453	−	0.130743i
$944$		−	4.97397e14i		−	0.663503i
$945$	5.78773e13	+	8.37289e13i	0.0767979	+	0.111101i
$946$	5.87288e14			0.775168
$947$	−4.31695e14	−	7.47718e14i	−0.566797	−	0.981721i	−0.996880	−	0.0789318i	$-0.974849\pi$
$947$	−4.31695e14	−	7.47718e14i	−0.566797	−	0.981721i	0.430083	−	0.902789i	$-0.358484\pi$
$948$	1.04601e15	+	6.03915e14i	1.36614	+	0.788741i
$949$	8.81371e12	−	1.52658e13i	0.0114506	−	0.0198330i
$950$	6.12536e14	−	3.53648e14i	0.791614	−	0.457039i
$951$			3.71364e11i			0.000477416i
$952$	−1.36669e15	−	6.47372e14i	−1.74777	−	0.827884i
$953$	3.29329e14			0.418954			0.209477	−	0.977814i	$-0.432824\pi$
$953$	3.29329e14			0.418954			0.209477	+	0.977814i	$0.432824\pi$
$954$	2.20487e14	+	3.81895e14i	0.279024	+	0.483284i
$955$	−4.58983e14	−	2.64994e14i	−0.577803	−	0.333595i
$956$	4.09541e14	−	7.09345e14i	0.512870	−	0.888318i
$957$	3.28762e14	−	1.89811e14i	0.409564	−	0.236462i
$958$		−	2.34004e15i		−	2.89998i
$959$	−1.66063e14	+	3.50581e14i	−0.204729	+	0.432211i
$960$	−4.42264e14			−0.542407
$961$	3.13609e14	+	5.43186e14i	0.382623	+	0.662722i
$962$	−6.88615e14	−	3.97572e14i	−0.835798	−	0.482548i
$963$	−7.60645e13	+	1.31748e14i	−0.0918440	+	0.159078i
$964$	8.79236e14	−	5.07627e14i	1.05614	−	0.609761i
$965$		−	6.49743e14i		−	0.776435i
$966$	3.60532e14	−	2.49217e14i	0.428606	−	0.296273i
$967$	8.65551e14			1.02367			0.511835	−	0.859084i	$-0.328966\pi$
$967$	8.65551e14			1.02367			0.511835	+	0.859084i	$0.328966\pi$
$968$	4.87397e14	+	8.44197e14i	0.573464	+	0.993269i
$969$	6.02309e14	+	3.47743e14i	0.705018	+	0.407042i
$970$	−5.41808e14	+	9.38439e14i	−0.630938	+	1.09282i
$971$	1.90592e14	−	1.10038e14i	0.220804	−	0.127482i	−0.385518	−	0.922700i	$-0.625977\pi$
$971$	1.90592e14	−	1.10038e14i	0.220804	−	0.127482i	0.606323	+	0.795219i	$0.292644\pi$
$972$			1.03686e14i			0.119505i
$973$	−6.36417e13	−	7.81766e14i	−0.0729756	−	0.896423i
$974$	−5.90164e14			−0.673253
$975$	6.68488e13	+	1.15786e14i	0.0758701	+	0.131411i
$976$	−1.01494e14	−	5.85979e13i	−0.114602	−	0.0661657i
$977$	1.09397e14	−	1.89482e14i	0.122895	−	0.212860i	−0.798013	−	0.602640i	$-0.794115\pi$
$977$	1.09397e14	−	1.89482e14i	0.122895	−	0.212860i	0.920908	+	0.389780i	$0.127449\pi$
$978$	1.13946e15	−	6.57869e14i	1.27352	−	0.735267i
$979$			3.06007e14i			0.340265i
$980$	−1.91142e14	−	1.16620e15i	−0.211459	−	1.29016i
$981$	5.36660e14			0.590682
$982$	−7.49162e14	−	1.29759e15i	−0.820386	−	1.42095i
$983$	−7.45341e14	−	4.30323e14i	−0.812059	−	0.468842i	0.0356115	−	0.999366i	$-0.488662\pi$
$983$	−7.45341e14	−	4.30323e14i	−0.812059	−	0.468842i	−0.847670	+	0.530523i	$0.821995\pi$
$984$	1.90622e14	−	3.30166e14i	0.206632	−	0.357897i
$985$	−9.81734e13	+	5.66804e13i	−0.105880	+	0.0611297i
$986$			3.69440e15i			3.96424i
$987$	−1.03657e15	+	8.43843e13i	−1.10665	+	0.0900899i
$988$	−9.66870e14			−1.02703
$989$	−2.49631e14	−	4.32374e14i	−0.263826	−	0.456960i
$990$	−1.50962e14	−	8.71582e13i	−0.158742	−	0.0916500i
$991$	1.24024e13	−	2.14815e13i	0.0129759	−	0.0224749i	−0.859465	−	0.511195i	$-0.829203\pi$
$991$	1.24024e13	−	2.14815e13i	0.0129759	−	0.0224749i	0.872440	+	0.488720i	$0.162536\pi$
$992$	4.77646e14	−	2.75769e14i	0.497219	−	0.287069i
$993$		−	7.43355e14i		−	0.769927i
$994$	1.40885e15	+	2.03813e15i	1.45189	+	2.10039i
$995$	3.81859e14			0.391551
$996$	−1.15343e14	−	1.99779e14i	−0.117677	−	0.203823i
$997$	5.89228e14	+	3.40191e14i	0.598146	+	0.345340i	0.768312	−	0.640076i	$-0.221097\pi$
$997$	5.89228e14	+	3.40191e14i	0.598146	+	0.345340i	−0.170166	+	0.985415i	$0.554430\pi$
$998$	−1.22131e15	+	2.11537e15i	−1.23359	+	2.13665i
$999$	−1.82644e14	+	1.05450e14i	−0.183560	+	0.105979i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	21.11.f.a.10.1	✓	12
3.2	odd	2		63.11.m.b.10.6		12
7.3	odd	6		147.11.d.a.97.11		12
7.4	even	3		147.11.d.a.97.12		12
7.5	odd	6	inner	21.11.f.a.19.1	yes	12
21.5	even	6		63.11.m.b.19.6		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
21.11.f.a.10.1	✓	12	1.1	even	1	trivial
21.11.f.a.19.1	yes	12	7.5	odd	6	inner
63.11.m.b.10.6		12	3.2	odd	2
63.11.m.b.19.6		12	21.5	even	6
147.11.d.a.97.11		12	7.3	odd	6
147.11.d.a.97.12		12	7.4	even	3

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:	\( N \)	\(=\)	\( 21 = 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 11 \)
Character orbit:	\([\chi]\)	\(=\)	21.f (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-27.0722 - 46.8904i) q^{2} +(-121.500 - 70.1481i) q^{3} +(-953.808 + 1652.04i) q^{4} +(-1899.28 + 1096.55i) q^{5} +7596.25i q^{6} +(16751.6 - 1363.71i) q^{7} +47842.8 q^{8} +(9841.50 + 17046.0i) q^{9} +O(q^{10})\)	\(q+(-27.0722 - 46.8904i) q^{2} +(-121.500 - 70.1481i) q^{3} +(-953.808 + 1652.04i) q^{4} +(-1899.28 + 1096.55i) q^{5} +7596.25i q^{6} +(16751.6 - 1363.71i) q^{7} +47842.8 q^{8} +(9841.50 + 17046.0i) q^{9} +(102836. + 59372.1i) q^{10} +(-37291.0 + 64590.0i) q^{11} +(231775. - 133816. i) q^{12} +192289. i q^{13} +(-517447. - 748570. i) q^{14} +307684. q^{15} +(-318511. - 551677. i) q^{16} +(-1.62873e6 - 940350. i) q^{17} +(532862. - 922944. i) q^{18} +(2.28273e6 - 1.31793e6i) q^{19} -4.18360e6i q^{20} +(-2.13098e6 - 1.00940e6i) q^{21} +4.03820e6 q^{22} +(-1.71647e6 - 2.97301e6i) q^{23} +(-5.81290e6 - 3.35608e6i) q^{24} +(-2.47796e6 + 4.29195e6i) q^{25} +(9.01650e6 - 5.20568e6i) q^{26} -2.76145e6i q^{27} +(-1.37249e7 + 2.89751e7i) q^{28} +3.62803e7 q^{29} +(-8.32968e6 - 1.44274e7i) q^{30} +(3.29414e7 + 1.90187e7i) q^{31} +(7.24994e6 - 1.25573e7i) q^{32} +(9.06172e6 - 5.23179e6i) q^{33} +1.01829e8i q^{34} +(-3.03206e7 + 2.09590e7i) q^{35} -3.75476e7 q^{36} +(-3.81864e7 - 6.61408e7i) q^{37} +(-1.23597e8 - 7.13587e7i) q^{38} +(1.34887e7 - 2.33631e7i) q^{39} +(-9.08671e7 + 5.24621e7i) q^{40} +5.67989e7i q^{41} +(1.03590e7 + 1.27249e8i) q^{42} +1.45433e8 q^{43} +(-7.11369e7 - 1.23213e8i) q^{44} +(-3.73836e7 - 2.15834e7i) q^{45} +(-9.29371e7 + 1.60972e8i) q^{46} +(3.81967e8 - 2.20529e8i) q^{47} +8.93717e7i q^{48} +(2.78756e8 - 4.56884e7i) q^{49} +2.68335e8 q^{50} +(1.31927e8 + 2.28505e8i) q^{51} +(-3.17669e8 - 1.83407e8i) q^{52} +(-2.06890e8 + 3.58343e8i) q^{53} +(-1.29485e8 + 7.47585e7i) q^{54} -1.63566e8i q^{55} +(8.01443e8 - 6.52435e7i) q^{56} -3.69802e8 q^{57} +(-9.82188e8 - 1.70120e9i) q^{58} +(6.76207e8 + 3.90408e8i) q^{59} +(-2.93471e8 + 5.08307e8i) q^{60} +(1.59327e8 - 9.19872e7i) q^{61} -2.05951e9i q^{62} +(1.88106e8 + 2.72126e8i) q^{63} -1.43740e9 q^{64} +(-2.10855e8 - 3.65211e8i) q^{65} +(-4.90641e8 - 2.83272e8i) q^{66} +(-6.18123e8 + 1.07062e9i) q^{67} +(3.10700e9 - 1.79383e9i) q^{68} +4.81628e8i q^{69} +(1.80362e9 + 8.54340e8i) q^{70} -2.72270e9 q^{71} +(4.70845e8 + 8.15527e8i) q^{72} +(-7.93899e7 - 4.58358e7i) q^{73} +(-2.06758e9 + 3.58115e9i) q^{74} +(6.02144e8 - 3.47648e8i) q^{75} +5.02822e9i q^{76} +(-5.36602e8 + 1.13284e9i) q^{77} -1.46067e9 q^{78} +(2.25652e9 + 3.90841e9i) q^{79} +(1.20989e9 + 6.98528e8i) q^{80} +(-1.93710e8 + 3.35516e8i) q^{81} +(2.66332e9 - 1.53767e9i) q^{82} -8.61953e8i q^{83} +(3.70012e9 - 2.55769e9i) q^{84} +4.12457e9 q^{85} +(-3.93720e9 - 6.81942e9i) q^{86} +(-4.40806e9 - 2.54499e9i) q^{87} +(-1.78411e9 + 3.09016e9i) q^{88} +(3.55326e9 - 2.05148e9i) q^{89} +2.33724e9i q^{90} +(2.62225e8 + 3.22114e9i) q^{91} +6.54872e9 q^{92} +(-2.66825e9 - 4.62155e9i) q^{93} +(-2.06814e10 - 1.19404e10i) q^{94} +(-2.89036e9 + 5.00626e9i) q^{95} +(-1.76174e9 + 1.01714e9i) q^{96} +9.12562e9i q^{97} +(-9.68888e9 - 1.18341e10i) q^{98} -1.46800e9 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 11 q^{2} - 1458 q^{3} - 1421 q^{4} - 1287 q^{5} + 20090 q^{7} + 99310 q^{8} + 118098 q^{9}+O(q^{10}) \) 12 * q + 11 * q^2 - 1458 * q^3 - 1421 * q^4 - 1287 * q^5 + 20090 * q^7 + 99310 * q^8 + 118098 * q^9	\( 12 q + 11 q^{2} - 1458 q^{3} - 1421 q^{4} - 1287 q^{5} + 20090 q^{7} + 99310 q^{8} + 118098 q^{9} + 359661 q^{10} + 236165 q^{11} + 345303 q^{12} + 223832 q^{14} + 208494 q^{15} + 1350895 q^{16} - 2038782 q^{17} - 216513 q^{18} + 1012389 q^{19} - 5131917 q^{21} + 29162074 q^{22} - 4341928 q^{23} - 12066165 q^{24} + 12365439 q^{25} + 4398486 q^{26} + 37097165 q^{28} + 95444234 q^{29} - 29132541 q^{30} + 9658932 q^{31} - 49606359 q^{32} - 57388095 q^{33} - 77592186 q^{35} - 55939086 q^{36} - 87545045 q^{37} - 319584648 q^{38} + 1789695 q^{39} - 607773201 q^{40} - 180831609 q^{42} + 700816306 q^{43} + 133692537 q^{44} - 25332021 q^{45} - 74981552 q^{46} - 181842702 q^{47} + 333171090 q^{49} + 3398506976 q^{50} + 165141342 q^{51} - 1573473588 q^{52} - 695152867 q^{53} + 52612659 q^{54} + 1977142699 q^{56} - 164007018 q^{57} - 1023653321 q^{58} + 1373785545 q^{59} + 35593425 q^{60} - 2524633584 q^{61} + 851624361 q^{63} - 482439838 q^{64} + 2692260666 q^{65} - 3543191991 q^{66} - 2255105709 q^{67} + 4313617758 q^{68} - 650925555 q^{70} - 3878911780 q^{71} + 977359365 q^{72} - 1888675383 q^{73} - 445804820 q^{74} - 3004801677 q^{75} - 7759715803 q^{77} - 712554732 q^{78} + 8260659900 q^{79} - 5477579577 q^{80} - 2324522934 q^{81} + 14912212206 q^{82} + 665315532 q^{84} + 15563062356 q^{85} - 257575928 q^{86} - 11596474431 q^{87} - 10015831801 q^{88} + 9451951530 q^{89} - 3182715375 q^{91} + 20533179072 q^{92} - 782373492 q^{93} - 54481927140 q^{94} - 33375267288 q^{95} + 12054345237 q^{96} - 3841749499 q^{98} + 9296871390 q^{99}+O(q^{100}) \) 12 * q + 11 * q^2 - 1458 * q^3 - 1421 * q^4 - 1287 * q^5 + 20090 * q^7 + 99310 * q^8 + 118098 * q^9 + 359661 * q^10 + 236165 * q^11 + 345303 * q^12 + 223832 * q^14 + 208494 * q^15 + 1350895 * q^16 - 2038782 * q^17 - 216513 * q^18 + 1012389 * q^19 - 5131917 * q^21 + 29162074 * q^22 - 4341928 * q^23 - 12066165 * q^24 + 12365439 * q^25 + 4398486 * q^26 + 37097165 * q^28 + 95444234 * q^29 - 29132541 * q^30 + 9658932 * q^31 - 49606359 * q^32 - 57388095 * q^33 - 77592186 * q^35 - 55939086 * q^36 - 87545045 * q^37 - 319584648 * q^38 + 1789695 * q^39 - 607773201 * q^40 - 180831609 * q^42 + 700816306 * q^43 + 133692537 * q^44 - 25332021 * q^45 - 74981552 * q^46 - 181842702 * q^47 + 333171090 * q^49 + 3398506976 * q^50 + 165141342 * q^51 - 1573473588 * q^52 - 695152867 * q^53 + 52612659 * q^54 + 1977142699 * q^56 - 164007018 * q^57 - 1023653321 * q^58 + 1373785545 * q^59 + 35593425 * q^60 - 2524633584 * q^61 + 851624361 * q^63 - 482439838 * q^64 + 2692260666 * q^65 - 3543191991 * q^66 - 2255105709 * q^67 + 4313617758 * q^68 - 650925555 * q^70 - 3878911780 * q^71 + 977359365 * q^72 - 1888675383 * q^73 - 445804820 * q^74 - 3004801677 * q^75 - 7759715803 * q^77 - 712554732 * q^78 + 8260659900 * q^79 - 5477579577 * q^80 - 2324522934 * q^81 + 14912212206 * q^82 + 665315532 * q^84 + 15563062356 * q^85 - 257575928 * q^86 - 11596474431 * q^87 - 10015831801 * q^88 + 9451951530 * q^89 - 3182715375 * q^91 + 20533179072 * q^92 - 782373492 * q^93 - 54481927140 * q^94 - 33375267288 * q^95 + 12054345237 * q^96 - 3841749499 * q^98 + 9296871390 * q^99

Introduction

L-functions

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