LMFDB - Embedded newform 21.11.f.a.10.3

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			10.3
Root			$5.98749 + 10.3706i$ of defining polynomial
Character	$\chi$	$=$	21.10
Dual form			21.11.f.a.19.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-4.98749 - 8.63859i) q^{2} +(-121.500 - 70.1481i) q^{3} +(462.250 - 800.640i) q^{4} +(2618.43 - 1511.75i) q^{5} +1399.45i q^{6} +(13450.1 + 10078.2i) q^{7} -19436.3 q^{8} +(9841.50 + 17046.0i) q^{9} +O(q^{10})$	\(q+(-4.98749 - 8.63859i) q^{2} +(-121.500 - 70.1481i) q^{3} +(462.250 - 800.640i) q^{4} +(2618.43 - 1511.75i) q^{5} +1399.45i q^{6} +(13450.1 + 10078.2i) q^{7} -19436.3 q^{8} +(9841.50 + 17046.0i) q^{9} +(-26118.8 - 15079.7i) q^{10} +(64150.2 - 111111. i) q^{11} +(-112327. + 64851.9i) q^{12} -412465. i q^{13} +(19979.2 - 166455. i) q^{14} -424185. q^{15} +(-376406. - 651954. i) q^{16} +(9963.42 + 5752.38i) q^{17} +(98168.8 - 170033. i) q^{18} +(-1.36514e6 + 788164. i) q^{19} -2.79523e6i q^{20} +(-927220. - 2.16800e6i) q^{21} -1.27979e6 q^{22} +(-4.66415e6 - 8.07854e6i) q^{23} +(2.36150e6 + 1.36342e6i) q^{24} +(-312035. + 540460. i) q^{25} +(-3.56312e6 + 2.05717e6i) q^{26} -2.76145e6i q^{27} +(1.42863e7 - 6.11004e6i) q^{28} -2.68723e6 q^{29} +(2.11562e6 + 3.66436e6i) q^{30} +(6.30236e6 + 3.63867e6i) q^{31} +(-1.37060e7 + 2.37395e7i) q^{32} +(-1.55885e7 + 9.00002e6i) q^{33} -114760. i q^{34} +(5.04538e7 + 6.05587e6i) q^{35} +1.81969e7 q^{36} +(5.42745e7 + 9.40062e7i) q^{37} +(1.36172e7 + 7.86192e6i) q^{38} +(-2.89337e7 + 5.01146e7i) q^{39} +(-5.08924e7 + 2.93828e7i) q^{40} -1.33775e8i q^{41} +(-1.41040e7 + 1.88228e7i) q^{42} -1.04778e6 q^{43} +(-5.93068e7 - 1.02722e8i) q^{44} +(5.15385e7 + 2.97558e7i) q^{45} +(-4.65248e7 + 8.05833e7i) q^{46} +(1.04162e8 - 6.01378e7i) q^{47} +1.05617e8i q^{48} +(7.93348e7 + 2.71106e8i) q^{49} +6.22509e6 q^{50} +(-807037. - 1.39783e6i) q^{51} +(-3.30236e8 - 1.90662e8i) q^{52} +(2.92480e8 - 5.06591e8i) q^{53} +(-2.38550e7 + 1.37727e7i) q^{54} -3.87916e8i q^{55} +(-2.61419e8 - 1.95883e8i) q^{56} +2.21153e8 q^{57} +(1.34026e7 + 2.32139e7i) q^{58} +(-8.72496e8 - 5.03736e8i) q^{59} +(-1.96080e8 + 3.39620e8i) q^{60} +(6.53699e8 - 3.77413e8i) q^{61} -7.25914e7i q^{62} +(-3.94238e7 + 3.28455e8i) q^{63} -4.97445e8 q^{64} +(-6.23545e8 - 1.08001e9i) q^{65} +(1.55495e8 + 8.97751e7i) q^{66} +(-1.06451e9 + 1.84378e9i) q^{67} +(9.21117e6 - 5.31807e6i) q^{68} +1.30872e9i q^{69} +(-1.99324e8 - 4.66054e8i) q^{70} +2.55897e9 q^{71} +(-1.91282e8 - 3.31310e8i) q^{72} +(2.13767e9 + 1.23418e9i) q^{73} +(5.41387e8 - 9.37710e8i) q^{74} +(7.58245e7 - 4.37773e7i) q^{75} +1.45731e9i q^{76} +(1.98263e9 - 8.47940e8i) q^{77} +5.77225e8 q^{78} +(1.03562e9 + 1.79375e9i) q^{79} +(-1.97118e9 - 1.13806e9i) q^{80} +(-1.93710e8 + 3.35516e8i) q^{81} +(-1.15563e9 + 6.67204e8i) q^{82} +5.24033e9i q^{83} +(-2.16440e9 - 2.59788e8i) q^{84} +3.47847e7 q^{85} +(5.22580e6 + 9.05136e6i) q^{86} +(3.26499e8 + 1.88504e8i) q^{87} +(-1.24684e9 + 2.15959e9i) q^{88} +(3.07035e9 - 1.77267e9i) q^{89} -5.93627e8i q^{90} +(4.15691e9 - 5.54770e9i) q^{91} -8.62400e9 q^{92} +(-5.10491e8 - 8.84197e8i) q^{93} +(-1.03901e9 - 5.99874e8i) q^{94} +(-2.38301e9 + 4.12750e9i) q^{95} +(3.33056e9 - 1.92290e9i) q^{96} -1.54240e10i q^{97} +(1.94629e9 - 2.03748e9i) q^{98} +2.52534e9 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 $

$2$	−4.98749	−	8.63859i	−0.155859	−	0.269956i	0.777512	−	0.628868i	$-0.216481\pi$
$2$	−4.98749	−	8.63859i	−0.155859	−	0.269956i	−0.933372	+	0.358912i	$0.883148\pi$
$3$	−121.500	−	70.1481i	−0.500000	−	0.288675i
$3$	−121.500	−	70.1481i	−0.500000	−	0.288675i
$4$	462.250	−	800.640i	0.451416	−	0.781875i
$5$	2618.43	−	1511.75i	0.837897	−	0.483760i	−0.0186518	−	0.999826i	$-0.505937\pi$
$5$	2618.43	−	1511.75i	0.837897	−	0.483760i	0.856549	+	0.516066i	$0.172604\pi$
$6$			1399.45i			0.179971i
$7$	13450.1	+	10078.2i	0.800267	+	0.599643i
$7$	13450.1	+	10078.2i	0.800267	+	0.599643i
$8$	−19436.3			−0.593147
$9$	9841.50	+	17046.0i	0.166667	+	0.288675i
$10$	−26118.8	−	15079.7i	−0.261188	−	0.150797i
$11$	64150.2	−	111111.i	0.398322	−	0.689914i	−0.595197	−	0.803580i	$-0.702926\pi$
$11$	64150.2	−	111111.i	0.398322	−	0.689914i	0.993519	+	0.113666i	$0.0362593\pi$
$12$	−112327.	+	64851.9i	−0.451416	+	0.260625i
$13$		−	412465.i		−	1.11089i	−0.831553	−	0.555445i	$-0.812548\pi$
$13$		−	412465.i		−	1.11089i	0.831553	−	0.555445i	$-0.187452\pi$
$14$	19979.2	−	166455.i	0.0371483	−	0.309497i
$15$	−424185.			−0.558598
$16$	−376406.	−	651954.i	−0.358968	−	0.621752i
$17$	9963.42	+	5752.38i	0.00701720	+	0.00405138i	0.503504	−	0.863993i	$-0.332044\pi$
$17$	9963.42	+	5752.38i	0.00701720	+	0.00405138i	−0.496487	+	0.868044i	$0.665377\pi$
$18$	98168.8	−	170033.i	0.0519530	−	0.0899853i
$19$	−1.36514e6	+	788164.i	−0.551327	+	0.318309i	−0.749657	−	0.661827i	$-0.769781\pi$
$19$	−1.36514e6	+	788164.i	−0.551327	+	0.318309i	0.198330	+	0.980135i	$0.436448\pi$
$20$		−	2.79523e6i		−	0.873508i
$21$	−927220.	−	2.16800e6i	−0.227032	−	0.530839i
$22$	−1.27979e6			−0.248329
$23$	−4.66415e6	−	8.07854e6i	−0.724658	−	1.25514i	−0.959115	−	0.283018i	$-0.908664\pi$
$23$	−4.66415e6	−	8.07854e6i	−0.724658	−	1.25514i	0.234457	−	0.972127i	$-0.424669\pi$
$24$	2.36150e6	+	1.36342e6i	0.296574	+	0.171227i
$25$	−312035.	+	540460.i	−0.0319524	+	0.0553432i
$26$	−3.56312e6	+	2.05717e6i	−0.299891	+	0.173142i
$27$		−	2.76145e6i		−	0.192450i
$28$	1.42863e7	−	6.11004e6i	0.830100	−	0.355021i
$29$	−2.68723e6			−0.131013			−0.0655067	−	0.997852i	$-0.520866\pi$
$29$	−2.68723e6			−0.131013			−0.0655067	+	0.997852i	$0.520866\pi$
$30$	2.11562e6	+	3.66436e6i	0.0870626	+	0.150797i
$31$	6.30236e6	+	3.63867e6i	0.220138	+	0.127097i	0.606014	−	0.795454i	$-0.292767\pi$
$31$	6.30236e6	+	3.63867e6i	0.220138	+	0.127097i	−0.385876	+	0.922551i	$0.626101\pi$
$32$	−1.37060e7	+	2.37395e7i	−0.408471	+	0.707492i
$33$	−1.55885e7	+	9.00002e6i	−0.398322	+	0.229971i
$34$		−	114760.i		−	0.00252578i
$35$	5.04538e7	+	6.05587e6i	0.960625	+	0.115302i
$36$	1.81969e7			0.300944
$37$	5.42745e7	+	9.40062e7i	0.782685	+	1.35565i	0.930372	+	0.366617i	$0.119484\pi$
$37$	5.42745e7	+	9.40062e7i	0.782685	+	1.35565i	−0.147687	+	0.989034i	$0.547183\pi$
$38$	1.36172e7	+	7.86192e6i	0.171859	+	0.0992226i
$39$	−2.89337e7	+	5.01146e7i	−0.320686	+	0.555445i
$40$	−5.08924e7	+	2.93828e7i	−0.496996	+	0.286941i
$41$		−	1.33775e8i		−	1.15467i	−0.816508	−	0.577334i	$-0.804093\pi$
$41$		−	1.33775e8i		−	1.15467i	0.816508	−	0.577334i	$-0.195907\pi$
$42$	−1.41040e7	+	1.88228e7i	−0.107918	+	0.144025i
$43$	−1.04778e6			−0.00712736			−0.00356368	−	0.999994i	$-0.501134\pi$
$43$	−1.04778e6			−0.00712736			−0.00356368	+	0.999994i	$0.501134\pi$
$44$	−5.93068e7	−	1.02722e8i	−0.359618	−	0.622877i
$45$	5.15385e7	+	2.97558e7i	0.279299	+	0.161253i
$46$	−4.65248e7	+	8.05833e7i	−0.225889	+	0.391251i
$47$	1.04162e8	−	6.01378e7i	0.454171	−	0.262216i	−0.255419	−	0.966830i	$-0.582214\pi$
$47$	1.04162e8	−	6.01378e7i	0.454171	−	0.262216i	0.709590	+	0.704615i	$0.248880\pi$
$48$			1.05617e8i			0.414501i
$49$	7.93348e7	+	2.71106e8i	0.280856	+	0.959750i
$50$	6.22509e6			0.0199203
$51$	−807037.	−	1.39783e6i	−0.00233907	−	0.00405138i
$52$	−3.30236e8	−	1.90662e8i	−0.868577	−	0.501473i
$53$	2.92480e8	−	5.06591e8i	0.699387	−	1.21137i	−0.269292	−	0.963058i	$-0.586790\pi$
$53$	2.92480e8	−	5.06591e8i	0.699387	−	1.21137i	0.968679	−	0.248315i	$-0.0798769\pi$
$54$	−2.38550e7	+	1.37727e7i	−0.0519530	+	0.0299951i
$55$		−	3.87916e8i		−	0.770769i
$56$	−2.61419e8	−	1.95883e8i	−0.474676	−	0.355677i
$57$	2.21153e8			0.367551
$58$	1.34026e7	+	2.32139e7i	0.0204196	+	0.0353678i
$59$	−8.72496e8	−	5.03736e8i	−1.22040	−	0.704600i	−0.255399	−	0.966836i	$-0.582207\pi$
$59$	−8.72496e8	−	5.03736e8i	−1.22040	−	0.704600i	−0.965004	+	0.262236i	$0.915540\pi$
$60$	−1.96080e8	+	3.39620e8i	−0.252160	+	0.436754i
$61$	6.53699e8	−	3.77413e8i	0.773978	−	0.446856i	−0.0603138	−	0.998179i	$-0.519210\pi$
$61$	6.53699e8	−	3.77413e8i	0.773978	−	0.446856i	0.834292	+	0.551323i	$0.185877\pi$
$62$		−	7.25914e7i		−	0.0792367i
$63$	−3.94238e7	+	3.28455e8i	−0.0397242	+	0.330958i
$64$	−4.97445e8			−0.463281
$65$	−6.23545e8	−	1.08001e9i	−0.537404	−	0.930811i
$66$	1.55495e8	+	8.97751e7i	0.124164	+	0.0716863i
$67$	−1.06451e9	+	1.84378e9i	−0.788451	+	1.36564i	0.138464	+	0.990367i	$0.455783\pi$
$67$	−1.06451e9	+	1.84378e9i	−0.788451	+	1.36564i	−0.926915	+	0.375270i	$0.877550\pi$
$68$	9.21117e6	−	5.31807e6i	0.00633535	−	0.00365771i
$69$			1.30872e9i			0.836763i
$70$	−1.99324e8	−	4.66054e8i	−0.118596	−	0.277297i
$71$	2.55897e9			1.41832			0.709158	−	0.705050i	$-0.249075\pi$
$71$	2.55897e9			1.41832			0.709158	+	0.705050i	$0.249075\pi$
$72$	−1.91282e8	−	3.31310e8i	−0.0988579	−	0.171227i
$73$	2.13767e9	+	1.23418e9i	1.03116	+	0.595340i	0.917316	−	0.398159i	$-0.130351\pi$
$73$	2.13767e9	+	1.23418e9i	1.03116	+	0.595340i	0.113842	+	0.993499i	$0.463684\pi$
$74$	5.41387e8	−	9.37710e8i	0.243977	−	0.422581i
$75$	7.58245e7	−	4.37773e7i	0.0319524	−	0.0184477i
$76$			1.45731e9i			0.574758i
$77$	1.98263e9	−	8.47940e8i	0.732467	−	0.313265i
$78$	5.77225e8			0.199927
$79$	1.03562e9	+	1.79375e9i	0.336563	+	0.582944i	0.983784	−	0.179359i	$-0.0574022\pi$
$79$	1.03562e9	+	1.79375e9i	0.336563	+	0.582944i	−0.647221	+	0.762302i	$0.724069\pi$
$80$	−1.97118e9	−	1.13806e9i	−0.601557	−	0.347309i
$81$	−1.93710e8	+	3.35516e8i	−0.0555556	+	0.0962250i
$82$	−1.15563e9	+	6.67204e8i	−0.311710	+	0.179966i
$83$			5.24033e9i			1.33036i	0.746684	+	0.665179i	$0.231645\pi$
$83$			5.24033e9i			1.33036i	−0.746684	+	0.665179i	$0.768355\pi$
$84$	−2.16440e9	−	2.59788e8i	−0.517535	−	0.0621187i
$85$	3.47847e7			0.00783958
$86$	5.22580e6	+	9.05136e6i	0.00111086	+	0.00192407i
$87$	3.26499e8	+	1.88504e8i	0.0655067	+	0.0378203i
$88$	−1.24684e9	+	2.15959e9i	−0.236264	+	0.409221i
$89$	3.07035e9	−	1.77267e9i	0.549842	−	0.317451i	−0.199216	−	0.979956i	$-0.563840\pi$
$89$	3.07035e9	−	1.77267e9i	0.549842	−	0.317451i	0.749058	+	0.662504i	$0.230506\pi$
$90$		−	5.93627e8i		−	0.100531i
$91$	4.15691e9	−	5.54770e9i	0.666137	−	0.889009i
$92$	−8.62400e9			−1.30849
$93$	−5.10491e8	−	8.84197e8i	−0.0733793	−	0.127097i
$94$	−1.03901e9	−	5.99874e8i	−0.141573	−	0.0817374i
$95$	−2.38301e9	+	4.12750e9i	−0.307970	+	0.533420i
$96$	3.33056e9	−	1.92290e9i	0.408471	−	0.235831i
$97$		−	1.54240e10i		−	1.79614i	−0.439855	−	0.898069i	$-0.644970\pi$
$97$		−	1.54240e10i		−	1.79614i	0.439855	−	0.898069i	$-0.355030\pi$
$98$	1.94629e9	−	2.03748e9i	0.215316	−	0.225404i
$99$	2.52534e9			0.265548
$100$	2.88476e8	+	4.99656e8i	0.0288476	+	0.0499656i
$101$	−1.14939e10	−	6.63603e9i	−1.09361	−	0.631395i	−0.159074	−	0.987267i	$-0.550851\pi$
$101$	−1.14939e10	−	6.63603e9i	−1.09361	−	0.631395i	−0.934535	+	0.355871i	$0.884184\pi$
$102$	−8.05018e6	+	1.39433e7i	−0.000729129	+	0.00126289i
$103$	4.06620e9	−	2.34762e9i	0.350754	−	0.202508i	−0.314263	−	0.949336i	$-0.601758\pi$
$103$	4.06620e9	−	2.34762e9i	0.350754	−	0.202508i	0.665017	+	0.746828i	$0.268424\pi$
$104$			8.01678e9i			0.658921i
$105$	−5.70533e9	−	4.27503e9i	−0.447028	−	0.334960i
$106$	−5.83498e9			−0.436023
$107$	9.94798e9	+	1.72304e10i	0.709277	+	1.22850i	0.965126	+	0.261787i	$0.0843119\pi$
$107$	9.94798e9	+	1.72304e10i	0.709277	+	1.22850i	−0.255848	+	0.966717i	$0.582355\pi$
$108$	−2.21093e9	−	1.27648e9i	−0.150472	−	0.0868750i
$109$	−7.07685e9	+	1.22575e10i	−0.459947	+	0.796652i	−0.998958	−	0.0456474i	$-0.985465\pi$
$109$	−7.07685e9	+	1.22575e10i	−0.459947	+	0.796652i	0.539011	+	0.842299i	$0.318798\pi$
$110$	−3.35105e9	+	1.93473e9i	−0.208074	+	0.120131i
$111$		−	1.52290e10i		−	0.903767i
$112$	1.50783e9	−	1.25623e10i	0.0855584	−	0.712821i
$113$	2.84684e10			1.54515			0.772576	−	0.634923i	$-0.218968\pi$
$113$	2.84684e10			1.54515			0.772576	+	0.634923i	$0.218968\pi$
$114$	−1.10300e9	−	1.91045e9i	−0.0572862	−	0.0992226i
$115$	−2.44255e10	−	1.41020e10i	−1.21438	−	0.701121i
$116$	−1.24217e9	+	2.15151e9i	−0.0591415	+	0.102436i
$117$	7.03088e9	−	4.05928e9i	0.320686	−	0.185148i
$118$			1.00495e10i			0.439273i
$119$	7.60352e7	+	1.77783e8i	0.00318625	+	0.00745000i
$120$	8.24457e9			0.331331
$121$	4.73822e9	+	8.20684e9i	0.182679	+	0.316409i
$122$	−6.52064e9	−	3.76469e9i	−0.241263	−	0.139293i
$123$	−9.38409e9	+	1.62537e10i	−0.333324	+	0.577334i
$124$	5.82653e9	−	3.36395e9i	0.198748	−	0.114747i
$125$			3.14132e10i			1.02935i
$126$	3.03401e9	−	1.29760e9i	0.0955354	−	0.0408590i
$127$	6.04397e10			1.82938			0.914690	−	0.404156i	$-0.132435\pi$
$127$	6.04397e10			1.82938			0.914690	+	0.404156i	$0.132435\pi$
$128$	1.65159e10	+	2.86065e10i	0.480677	+	0.832558i
$129$	1.27305e8	+	7.34999e7i	0.00356368	+	0.00205749i
$130$	−6.21985e9	+	1.07731e10i	−0.167519	+	0.290151i
$131$	−3.50875e10	+	2.02578e10i	−0.909485	+	0.525091i	−0.880265	−	0.474482i	$-0.842635\pi$
$131$	−3.50875e10	+	2.02578e10i	−0.909485	+	0.525091i	−0.0292195	+	0.999573i	$0.509302\pi$
$132$			1.66410e10i			0.415251i
$133$	−2.63045e10	−	3.15728e9i	−0.632080	−	0.0758673i
$134$	2.12369e10			0.491549
$135$	−4.17462e9	−	7.23065e9i	−0.0930997	−	0.161253i
$136$	−1.93651e8	−	1.11805e8i	−0.00416223	−	0.00240307i
$137$	−2.05412e10	+	3.55783e10i	−0.425620	+	0.737196i	−0.996478	−	0.0838531i	$-0.973277\pi$
$137$	−2.05412e10	+	3.55783e10i	−0.425620	+	0.737196i	0.570858	+	0.821049i	$0.306611\pi$
$138$	1.13055e10	−	6.52725e9i	0.225889	−	0.130417i
$139$		−	1.44964e10i		−	0.279374i	−0.990196	−	0.139687i	$-0.955390\pi$
$139$		−	1.44964e10i		−	0.279374i	0.990196	−	0.139687i	$-0.0446097\pi$
$140$	2.81709e10	−	3.75960e10i	0.523793	−	0.699040i
$141$	−1.68742e10			−0.302780
$142$	−1.27628e10	−	2.21059e10i	−0.221057	−	0.382883i
$143$	−4.58296e10	−	2.64597e10i	−0.766419	−	0.442492i
$144$	7.40879e9	−	1.28324e10i	0.119656	−	0.207251i
$145$	−7.03633e9	+	4.06243e9i	−0.109776	+	0.0633790i
$146$		−	2.46219e10i		−	0.371156i
$147$	9.37835e9	−	3.85045e10i	0.136628	−	0.560951i
$148$	1.00354e11			1.41327
$149$	−3.11245e10	−	5.39092e10i	−0.423810	−	0.734060i	0.572499	−	0.819906i	$-0.305974\pi$
$149$	−3.11245e10	−	5.39092e10i	−0.423810	−	0.734060i	−0.996308	+	0.0858454i	$0.972641\pi$
$150$	−7.56348e8	−	4.36678e8i	−0.00996014	−	0.00575049i
$151$	−3.75661e10	+	6.50664e10i	−0.478533	+	0.828843i	−0.999697	−	0.0246135i	$-0.992164\pi$
$151$	−3.75661e10	+	6.50664e10i	−0.478533	+	0.828843i	0.521164	+	0.853456i	$0.325498\pi$
$152$	2.65332e10	−	1.53189e10i	0.327018	−	0.188804i
$153$			2.26448e8i			0.00270092i
$154$	−1.72134e10	−	1.28980e10i	−0.198729	−	0.148909i
$155$	2.20031e10			0.245937
$156$	2.67492e10	+	4.63309e10i	0.289526	+	0.501473i
$157$	−1.13212e11	−	6.53630e10i	−1.18685	−	0.685226i	−0.229258	−	0.973366i	$-0.573630\pi$
$157$	−1.13212e11	−	6.53630e10i	−1.18685	−	0.685226i	−0.957588	+	0.288140i	$0.906963\pi$
$158$	1.03303e10	−	1.78926e10i	0.104913	−	0.181714i
$159$	−7.10728e10	+	4.10339e10i	−0.699387	+	0.403791i
$160$			8.28802e10i			0.790407i
$161$	1.86840e10	−	1.55663e11i	0.172719	−	1.43899i
$162$	3.86451e9			0.0346354
$163$	3.85196e10	+	6.67180e10i	0.334768	+	0.579835i	0.983440	−	0.181233i	$-0.0580087\pi$
$163$	3.85196e10	+	6.67180e10i	0.334768	+	0.579835i	−0.648672	+	0.761068i	$0.724675\pi$
$164$	−1.07106e11	−	6.18377e10i	−0.902806	−	0.521236i
$165$	−2.72116e10	+	4.71318e10i	−0.222502	+	0.385385i
$166$	4.52691e10	−	2.61361e10i	0.359138	−	0.207348i
$167$		−	7.63953e10i		−	0.588145i	−0.955783	−	0.294072i	$-0.904989\pi$
$167$		−	7.63953e10i		−	0.588145i	0.955783	−	0.294072i	$-0.0950106\pi$
$168$	1.80217e10	+	4.21378e10i	0.134663	+	0.314866i
$169$	−3.22693e10			−0.234075
$170$	−1.73488e8	−	3.00490e8i	−0.00122187	−	0.00211634i
$171$	−2.68700e10	−	1.55134e10i	−0.183776	−	0.106103i
$172$	−4.84337e8	+	8.38896e8i	−0.00321740	+	0.00557270i
$173$	2.25539e11	−	1.30215e11i	1.45543	−	0.840293i	0.456648	−	0.889647i	$-0.349050\pi$
$173$	2.25539e11	−	1.30215e11i	1.45543	−	0.840293i	0.998781	+	0.0493546i	$0.0157164\pi$
$174$		−	3.76065e9i		−	0.0235785i
$175$	−9.64377e9	+	4.12449e9i	−0.0587566	+	0.0251293i
$176$	−9.65860e10			−0.571940
$177$	7.06722e10	+	1.22408e11i	0.406801	+	0.704600i
$178$	−3.06267e10	−	1.76823e10i	−0.171396	−	0.0989554i
$179$	−1.17737e11	+	2.03926e11i	−0.640689	+	1.10971i	0.344590	+	0.938753i	$0.388018\pi$
$179$	−1.17737e11	+	2.03926e11i	−0.640689	+	1.10971i	−0.985279	+	0.170953i	$0.945316\pi$
$180$	4.76473e10	−	2.75092e10i	0.252160	−	0.145585i
$181$			3.11578e10i			0.160389i	0.996779	+	0.0801943i	$0.0255541\pi$
$181$			3.11578e10i			0.160389i	−0.996779	+	0.0801943i	$0.974446\pi$
$182$	−6.86569e10	−	8.24075e9i	−0.343817	−	0.0412676i
$183$	−1.05899e11			−0.515985
$184$	9.06535e10	+	1.57017e11i	0.429829	+	0.744486i
$185$	2.84228e11	+	1.64099e11i	1.31162	+	0.757264i
$186$	−5.09214e9	+	8.81985e9i	−0.0228737	+	0.0396184i
$187$	1.27831e9	−	7.38033e8i	0.00559021	−	0.00322751i
$188$		−	1.11195e11i		−	0.473473i
$189$	2.78304e10	−	3.71417e10i	0.115401	−	0.154012i
$190$	4.75410e10			0.192000
$191$	6.07916e10	+	1.05294e11i	0.239154	+	0.414226i	0.960472	−	0.278378i	$-0.0897967\pi$
$191$	6.07916e10	+	1.05294e11i	0.239154	+	0.414226i	−0.721318	+	0.692604i	$0.756463\pi$
$192$	6.04395e10	+	3.48948e10i	0.231641	+	0.133738i
$193$	−1.81272e10	+	3.13973e10i	−0.0676932	+	0.117248i	−0.897886	−	0.440229i	$-0.854897\pi$
$193$	−1.81272e10	+	3.13973e10i	−0.0676932	+	0.117248i	0.830192	+	0.557477i	$0.188231\pi$
$194$	−1.33242e11	+	7.69273e10i	−0.484878	+	0.279944i
$195$			1.74962e11i			0.620541i
$196$	2.53731e11	+	6.17999e10i	0.877188	+	0.213652i
$197$	4.78287e10			0.161197			0.0805986	−	0.996747i	$-0.474317\pi$
$197$	4.78287e10			0.161197			0.0805986	+	0.996747i	$0.474317\pi$
$198$	−1.25951e10	−	2.18153e10i	−0.0413881	−	0.0716863i
$199$	−3.86413e10	−	2.23095e10i	−0.123819	−	0.0714867i	0.436811	−	0.899553i	$-0.356108\pi$
$199$	−3.86413e10	−	2.23095e10i	−0.123819	−	0.0714867i	−0.560630	+	0.828066i	$0.689441\pi$
$200$	6.06479e9	−	1.05045e10i	0.0189525	−	0.0328266i
$201$	2.58675e11	−	1.49346e11i	0.788451	−	0.455213i
$202$			1.32389e11i			0.393635i
$203$	−3.61435e10	−	2.70825e10i	−0.104846	−	0.0785612i
$204$	−1.49221e9			−0.00422357
$205$	−2.02235e11	−	3.50281e11i	−0.558582	−	0.967493i
$206$	−4.05603e10	−	2.34175e10i	−0.109336	−	0.0631254i
$207$	9.18044e10	−	1.59010e11i	0.241553	−	0.418381i
$208$	−2.68908e11	+	1.55254e11i	−0.690697	+	0.398774i
$209$			2.02243e11i			0.507158i
$210$	−8.47490e9	+	7.06077e10i	−0.0207510	+	0.172884i
$211$	−5.00549e10			−0.119684			−0.0598418	−	0.998208i	$-0.519060\pi$
$211$	−5.00549e10			−0.119684			−0.0598418	+	0.998208i	$0.519060\pi$
$212$	−2.70398e11	−	4.68343e11i	−0.631429	−	1.09367i
$213$	−3.10914e11	−	1.79507e11i	−0.709158	−	0.409432i
$214$	9.92309e10	−	1.71873e11i	0.221095	−	0.382947i
$215$	−2.74354e9	+	1.58398e9i	−0.00597199	+	0.00344793i
$216$			5.36722e10i			0.114151i
$217$	4.80961e10	+	1.12457e11i	0.0999566	+	0.233716i
$218$	1.41183e11			0.286748
$219$	−1.73151e11	−	2.99906e11i	−0.343719	−	0.595340i
$220$	−3.10581e11	−	1.79314e11i	−0.602646	−	0.347938i
$221$	2.37266e9	−	4.10957e9i	0.00450064	−	0.00779533i
$222$	−1.31557e11	+	7.59545e10i	−0.243977	+	0.140860i
$223$		−	6.48917e11i		−	1.17670i	−0.808607	−	0.588349i	$-0.799778\pi$
$223$		−	6.48917e11i		−	1.17670i	0.808607	−	0.588349i	$-0.200222\pi$
$224$	−4.23598e11	+	1.81167e11i	−0.751129	+	0.321246i
$225$	−1.22836e10			−0.0213016
$226$	−1.41986e11	−	2.45927e11i	−0.240826	−	0.417123i
$227$	8.15884e11	+	4.71051e11i	1.35363	+	0.781517i	0.988756	−	0.149540i	$-0.0477793\pi$
$227$	8.15884e11	+	4.71051e11i	1.35363	+	0.781517i	0.364872	+	0.931058i	$0.381113\pi$
$228$	1.02228e11	−	1.77064e11i	0.165918	−	0.287379i
$229$	1.19655e11	−	6.90828e10i	0.190000	−	0.109696i	−0.401983	−	0.915647i	$-0.631679\pi$
$229$	1.19655e11	−	6.90828e10i	0.190000	−	0.109696i	0.591982	+	0.805951i	$0.298345\pi$
$230$			2.81335e11i			0.437104i
$231$	−3.00371e11	−	3.60529e10i	−0.456665	−	0.0548126i
$232$	5.22297e10			0.0777102
$233$	−9.98703e9	−	1.72980e10i	−0.0145431	−	0.0251894i	0.858662	−	0.512542i	$-0.171296\pi$
$233$	−9.98703e9	−	1.72980e10i	−0.0145431	−	0.0251894i	−0.873205	+	0.487352i	$0.837963\pi$
$234$	−7.01329e10	−	4.04912e10i	−0.0999637	−	0.0577141i
$235$	1.81827e11	−	3.14933e11i	0.253699	−	0.439419i
$236$	−8.06622e11	+	4.65704e11i	−1.10182	+	0.636135i
$237$		−	2.90588e11i		−	0.388629i
$238$	1.15657e9	−	1.54353e9i	0.00151457	−	0.00202130i
$239$	1.69366e11			0.217188			0.108594	−	0.994086i	$-0.465365\pi$
$239$	1.69366e11			0.217188			0.108594	+	0.994086i	$0.465365\pi$
$240$	1.59666e11	+	2.76549e11i	0.200519	+	0.347309i
$241$	9.39337e11	+	5.42326e11i	1.15541	+	0.667076i	0.950200	−	0.311642i	$-0.100879\pi$
$241$	9.39337e11	+	5.42326e11i	1.15541	+	0.667076i	0.205210	+	0.978718i	$0.434212\pi$
$242$	4.72637e10	−	8.18631e10i	0.0569443	−	0.0986305i
$243$	4.70716e10	−	2.71768e10i	0.0555556	−	0.0320750i
$244$		−	6.97837e11i		−	0.806872i
$245$	6.17577e11	+	5.89936e11i	0.699617	+	0.668305i
$246$	1.87212e11			0.207806
$247$	3.25090e11	+	5.63073e11i	0.353606	+	0.612463i
$248$	−1.22494e11	−	7.07221e10i	−0.130574	−	0.0753871i
$249$	3.67599e11	−	6.36701e11i	0.384041	−	0.665179i
$250$	2.71366e11	−	1.56673e11i	0.277879	−	0.160433i
$251$			1.12257e12i			1.12679i	0.826187	+	0.563396i	$0.190505\pi$
$251$			1.12257e12i			1.12679i	−0.826187	+	0.563396i	$0.809495\pi$
$252$	2.44750e11	+	1.83392e11i	0.240836	+	0.180459i
$253$	−1.19682e12			−1.15459
$254$	−3.01443e11	−	5.22114e11i	−0.285126	−	0.493852i
$255$	−4.22634e9	−	2.44008e9i	−0.00391979	−	0.00226309i
$256$	−8.99453e10	+	1.55790e11i	−0.0818048	+	0.141690i
$257$	−7.09038e10	+	4.09363e10i	−0.0632417	+	0.0365126i	−0.531287	−	0.847192i	$-0.678292\pi$
$257$	−7.09038e10	+	4.09363e10i	−0.0632417	+	0.0365126i	0.468046	+	0.883704i	$0.344958\pi$
$258$		−	1.46632e9i		−	0.00128271i
$259$	−2.17417e11	+	1.81138e12i	−0.186549	+	1.55422i
$260$	−1.15293e12			−0.970371
$261$	−2.64464e10	−	4.58065e10i	−0.0218356	−	0.0378203i
$262$	3.49997e11	+	2.02071e11i	0.283503	+	0.163681i
$263$	2.24009e11	−	3.87995e11i	0.178027	−	0.308352i	−0.763178	−	0.646189i	$-0.776362\pi$
$263$	2.24009e11	−	3.87995e11i	0.178027	−	0.308352i	0.941205	+	0.337837i	$0.109695\pi$
$264$	3.02982e11	−	1.74927e11i	0.236264	−	0.136407i
$265$		−	1.76863e12i		−	1.35334i
$266$	1.03919e11	+	2.42981e11i	0.0780347	+	0.182458i
$267$	−4.97397e11			−0.366561
$268$	9.84137e11	+	1.70458e12i	0.711839	+	1.23294i
$269$	1.59562e12	+	9.21229e11i	1.13284	+	0.654043i	0.944647	−	0.328090i	$-0.106405\pi$
$269$	1.59562e12	+	9.21229e11i	1.13284	+	0.654043i	0.188189	+	0.982133i	$0.439738\pi$
$270$	−4.16418e10	+	7.21257e10i	−0.0290209	+	0.0502656i
$271$	−1.26902e12	+	7.32669e11i	−0.868205	+	0.501258i	−0.866751	−	0.498741i	$-0.833796\pi$
$271$	−1.26902e12	+	7.32669e11i	−0.868205	+	0.501258i	−0.00145345	+	0.999999i	$0.500463\pi$
$272$		−	8.66092e9i		−	0.00581727i
$273$	−8.94225e11	+	3.82446e11i	−0.589703	+	0.252207i
$274$	4.09796e11			0.265347
$275$	4.00342e10	+	6.93413e10i	0.0254547	+	0.0440888i
$276$	1.04782e12	+	6.04957e11i	0.654244	+	0.377728i
$277$	9.50093e11	−	1.64561e12i	0.582596	−	1.00909i	−0.412575	−	0.910924i	$-0.635370\pi$
$277$	9.50093e11	−	1.64561e12i	0.582596	−	1.00909i	0.995170	−	0.0981615i	$-0.0312962\pi$
$278$	−1.25229e11	+	7.23007e10i	−0.0754187	+	0.0435430i
$279$			1.43240e11i			0.0847312i
$280$	−9.80633e11	−	1.17703e11i	−0.569792	−	0.0683910i
$281$	−6.78471e11			−0.387258			−0.193629	−	0.981075i	$-0.562026\pi$
$281$	−6.78471e11			−0.387258			−0.193629	+	0.981075i	$0.562026\pi$
$282$	8.41600e10	+	1.45769e11i	0.0471911	+	0.0817374i
$283$	−4.97216e11	−	2.87068e11i	−0.273913	−	0.158144i	0.356752	−	0.934199i	$-0.383884\pi$
$283$	−4.97216e11	−	2.87068e11i	−0.273913	−	0.158144i	−0.630665	+	0.776056i	$0.717218\pi$
$284$	1.18288e12	−	2.04881e12i	0.640250	−	1.10895i
$285$	5.79072e11	−	3.34327e11i	0.307970	−	0.177807i
$286$			5.27871e11i			0.275866i
$287$	1.34822e12	−	1.79929e12i	0.692389	−	0.924043i
$288$	−5.39550e11			−0.272314
$289$	−1.00793e12	−	1.74579e12i	−0.499967	−	0.865969i
$290$	7.01873e10	+	4.05226e10i	0.0342191	+	0.0197564i
$291$	−1.08197e12	+	1.87402e12i	−0.518500	+	0.898069i
$292$	1.97627e12	−	1.14100e12i	0.930963	−	0.537491i
$293$		−	2.62808e12i		−	1.21703i	−0.793542	−	0.608515i	$-0.791766\pi$
$293$		−	2.62808e12i		−	1.21703i	0.793542	−	0.608515i	$-0.208234\pi$
$294$	−3.79399e11	+	1.11025e11i	−0.172727	+	0.0505458i
$295$	−3.04609e12			−1.36343
$296$	−1.05489e12	−	1.82713e12i	−0.464248	−	0.804101i
$297$	−3.06828e11	−	1.77147e11i	−0.132774	−	0.0766571i
$298$	−3.10466e11	+	5.37744e11i	−0.132109	+	0.228820i
$299$	−3.33212e12	+	1.92380e12i	−1.39433	+	0.805015i
$300$		−	8.09442e10i		−	0.0333104i
$301$	−1.40928e10	−	1.05598e10i	−0.00570379	−	0.00427387i
$302$	7.49443e11			0.298335
$303$	9.31009e11	+	1.61255e12i	0.364536	+	0.631395i
$304$	1.02769e12	+	5.93339e11i	0.395818	+	0.228526i
$305$	1.14111e12	−	1.97646e12i	0.432343	−	0.748839i
$306$	1.95619e9	−	1.12941e9i	0.000729129	−	0.000420963i
$307$			3.80832e12i			1.39650i	0.715852	+	0.698252i	$0.246038\pi$
$307$			3.80832e12i			1.39650i	−0.715852	+	0.698252i	$0.753962\pi$
$308$	2.37575e11	−	1.97933e12i	0.0857132	−	0.714110i
$309$	−6.58724e11			−0.233836
$310$	−1.09740e11	−	1.90075e11i	−0.0383316	−	0.0663922i
$311$	−9.71444e11	−	5.60864e11i	−0.333900	−	0.192777i	0.323671	−	0.946170i	$-0.395083\pi$
$311$	−9.71444e11	−	5.60864e11i	−0.333900	−	0.192777i	−0.657571	+	0.753392i	$0.728416\pi$
$312$	5.62362e11	−	9.74039e11i	0.190214	−	0.329461i
$313$	6.12183e11	−	3.53444e11i	0.203779	−	0.117652i	−0.394638	−	0.918837i	$-0.629130\pi$
$313$	6.12183e11	−	3.53444e11i	0.203779	−	0.117652i	0.598417	+	0.801185i	$0.295797\pi$
$314$			1.30399e12i			0.427195i
$315$	3.93313e11	+	9.19634e11i	0.126819	+	0.296526i
$316$	1.91487e12			0.607719
$317$	−2.01443e12	−	3.48909e12i	−0.629297	−	1.08997i	−0.987693	−	0.156405i	$-0.950010\pi$
$317$	−2.01443e12	−	3.48909e12i	−0.629297	−	1.08997i	0.358396	−	0.933570i	$-0.383324\pi$
$318$	7.08950e11	+	4.09312e11i	0.218012	+	0.125869i
$319$	−1.72387e11	+	2.98582e11i	−0.0521855	+	0.0903879i
$320$	−1.30252e12	+	7.52012e11i	−0.388182	+	0.224117i
$321$		−	2.79133e12i		−	0.819003i
$322$	−1.43790e12	+	6.14967e11i	−0.415383	+	0.177653i
$323$	−1.81353e10			−0.00515836
$324$	1.79085e11	+	3.10184e11i	0.0501573	+	0.0868750i
$325$	2.22921e11	+	1.28704e11i	0.0614801	+	0.0354956i
$326$	3.84233e11	−	6.65511e11i	0.104353	−	0.180745i
$327$	1.71968e12	−	9.92855e11i	0.459947	−	0.265551i
$328$			2.60009e12i			0.684888i
$329$	2.00707e12	+	2.40904e11i	0.520694	+	0.0624978i
$330$	5.42870e11			0.138716
$331$	−3.29813e11	−	5.71253e11i	−0.0830095	−	0.143777i	0.821532	−	0.570163i	$-0.193120\pi$
$331$	−3.29813e11	−	5.71253e11i	−0.0830095	−	0.143777i	−0.904541	+	0.426386i	$0.859787\pi$
$332$	4.19562e12	+	2.42234e12i	1.04017	+	0.600545i
$333$	−1.06828e12	+	1.85032e12i	−0.260895	+	0.451884i
$334$	−6.59947e11	+	3.81021e11i	−0.158773	+	0.0916677i
$335$			6.43708e12i			1.52569i
$336$	−1.06442e12	+	1.42055e12i	−0.248553	+	0.331712i
$337$	5.71471e12			1.31476			0.657378	−	0.753561i	$-0.271666\pi$
$337$	5.71471e12			1.31476			0.657378	+	0.753561i	$0.271666\pi$
$338$	1.60943e11	+	2.78761e11i	0.0364828	+	0.0631901i
$339$	−3.45891e12	−	1.99700e12i	−0.772576	−	0.446047i
$340$	1.60792e10	−	2.78500e10i	0.00353891	−	0.00612958i
$341$	8.08596e11	−	4.66843e11i	0.175372	−	0.101251i
$342$			3.09492e11i			0.0661484i
$343$	−1.66520e12	+	4.44595e12i	−0.350748	+	0.936470i
$344$	2.03650e10			0.00422757
$345$	1.97846e12	+	3.42680e12i	0.404792	+	0.701121i
$346$	−2.24975e12	−	1.29889e12i	−0.453684	−	0.261935i
$347$	−3.42343e12	+	5.92956e12i	−0.680478	+	1.17862i	0.294357	+	0.955696i	$0.404895\pi$
$347$	−3.42343e12	+	5.92956e12i	−0.680478	+	1.17862i	−0.974835	+	0.222927i	$0.928439\pi$
$348$	3.01848e11	−	1.74272e11i	0.0591415	−	0.0341454i
$349$		−	4.59451e12i		−	0.887385i	−0.896179	−	0.443693i	$-0.853668\pi$
$349$		−	4.59451e12i		−	0.887385i	0.896179	−	0.443693i	$-0.146332\pi$
$350$	8.37280e10	+	6.27377e10i	0.0159416	+	0.0119451i
$351$	−1.13900e12			−0.213791
$352$	1.75849e12	+	3.04579e12i	0.325406	+	0.563620i
$353$	−2.23817e12	−	1.29221e12i	−0.408338	−	0.235754i	0.281737	−	0.959492i	$-0.409089\pi$
$353$	−2.23817e12	−	1.29221e12i	−0.408338	−	0.235754i	−0.690076	+	0.723737i	$0.742423\pi$
$354$	7.04954e11	−	1.22102e12i	0.126807	−	0.219637i
$355$	6.70047e12	−	3.86852e12i	1.18840	−	0.686124i
$356$		−	3.27766e12i		−	0.573210i
$357$	3.23288e9	−	2.69344e10i	0.000557505	−	0.00464479i
$358$	2.34885e12			0.399429
$359$	−2.05030e12	−	3.55123e12i	−0.343832	−	0.595534i	0.641309	−	0.767283i	$-0.278392\pi$
$359$	−2.05030e12	−	3.55123e12i	−0.343832	−	0.595534i	−0.985141	+	0.171749i	$0.945058\pi$
$360$	−1.00172e12	−	5.78341e11i	−0.165665	−	0.0956470i
$361$	−1.82313e12	+	3.15775e12i	−0.297359	+	0.515041i
$362$	2.69159e11	−	1.55399e11i	0.0432978	−	0.0249980i
$363$		−	1.32951e12i		−	0.210939i
$364$	−2.52018e12	−	5.89261e12i	−0.394389	−	0.922149i
$365$	7.46310e12			1.15201
$366$	5.28172e11	+	9.14820e11i	0.0804210	+	0.139293i
$367$	−5.18102e12	−	2.99126e12i	−0.778189	−	0.449287i	0.0575992	−	0.998340i	$-0.481655\pi$
$367$	−5.18102e12	−	2.99126e12i	−0.778189	−	0.449287i	−0.835788	+	0.549052i	$0.814989\pi$
$368$	−3.51122e12	+	6.08162e12i	−0.520259	+	0.901114i
$369$	2.28033e12	−	1.31655e12i	0.333324	−	0.192445i
$370$		−	3.27377e12i		−	0.472106i
$371$	9.03942e12	−	3.86602e12i	1.28609	−	0.550040i
$372$	−9.43898e11			−0.132498
$373$	2.47018e12	+	4.27848e12i	0.342125	+	0.592577i	0.984827	−	0.173539i	$-0.0555202\pi$
$373$	2.47018e12	+	4.27848e12i	0.342125	+	0.592577i	−0.642702	+	0.766116i	$0.722187\pi$
$374$	−1.27511e10	−	7.36186e9i	−0.00174257	−	0.00100607i
$375$	2.20358e12	−	3.81671e12i	0.297148	−	0.514675i
$376$	−2.02451e12	+	1.16885e12i	−0.269390	+	0.155532i
$377$			1.10839e12i			0.145541i
$378$	−4.59656e11	−	5.51716e10i	−0.0595627	−	0.00714919i
$379$	−1.17364e13			−1.50086			−0.750429	−	0.660951i	$-0.770153\pi$
$379$	−1.17364e13			−1.50086			−0.750429	+	0.660951i	$0.770153\pi$
$380$	2.20309e12	+	3.81587e12i	0.278045	+	0.481588i
$381$	−7.34343e12	−	4.23973e12i	−0.914690	−	0.528096i
$382$	6.06396e11	−	1.05031e12i	0.0745486	−	0.129122i
$383$	−1.06732e13	+	6.16216e12i	−1.29509	+	0.747721i	−0.979552	−	0.201192i	$-0.935518\pi$
$383$	−1.06732e13	+	6.16216e12i	−1.29509	+	0.747721i	−0.315538	+	0.948913i	$0.602185\pi$
$384$		−	4.63425e12i		−	0.555038i
$385$	3.90950e12	−	5.21751e12i	0.462187	−	0.616822i
$386$	3.61638e11			0.0422024
$387$	−1.03117e10	−	1.78605e10i	−0.00118789	−	0.00205749i
$388$	−1.23491e13	−	7.12976e12i	−1.40436	−	0.810805i
$389$	−7.34044e12	+	1.27140e13i	−0.824089	+	1.42736i	0.0785243	+	0.996912i	$0.474979\pi$
$389$	−7.34044e12	+	1.27140e13i	−0.824089	+	1.42736i	−0.902613	+	0.430452i	$0.858354\pi$
$390$	1.51142e12	−	8.72621e11i	0.167519	−	0.0967169i
$391$		−	1.07320e11i		−	0.0117435i
$392$	−1.54197e12	−	5.26928e12i	−0.166589	−	0.569273i
$393$	5.68417e12			0.606323
$394$	−2.38545e11	−	4.13172e11i	−0.0251240	−	0.0435161i
$395$	5.42341e12	+	3.13121e12i	0.564010	+	0.325631i
$396$	1.16734e12	−	2.02189e12i	0.119873	−	0.207626i
$397$	1.25703e13	−	7.25744e12i	1.27465	−	0.735921i	0.298792	−	0.954318i	$-0.403416\pi$
$397$	1.25703e13	−	7.25744e12i	1.27465	−	0.735921i	0.975860	+	0.218397i	$0.0700828\pi$
$398$			4.45075e11i			0.0445674i
$399$	2.97452e12	+	2.22882e12i	0.294139	+	0.220400i
$400$	4.69807e11			0.0458796
$401$	−6.56173e12	−	1.13652e13i	−0.632843	−	1.09612i	−0.986968	−	0.160918i	$-0.948554\pi$
$401$	−6.56173e12	−	1.13652e13i	−0.632843	−	1.09612i	0.354124	−	0.935198i	$-0.384779\pi$
$402$	−2.58028e12	−	1.48973e12i	−0.245775	−	0.141898i
$403$	1.50083e12	−	2.59951e12i	0.141190	−	0.244549i
$404$	−1.06261e13	+	6.13501e12i	−0.987345	+	0.570044i
$405$			1.17137e12i			0.107502i
$406$	−5.36889e10	+	4.47303e11i	−0.00486692	+	0.0405482i
$407$	1.39269e13			1.24704
$408$	1.56858e10	+	2.71685e10i	0.00138741	+	0.00240307i
$409$	−5.37212e11	−	3.10160e11i	−0.0469385	−	0.0271000i	0.476347	−	0.879257i	$-0.341961\pi$
$409$	−5.37212e11	−	3.10160e11i	−0.0469385	−	0.0271000i	−0.523286	+	0.852157i	$0.675294\pi$
$410$	−2.01729e12	+	3.49405e12i	−0.174120	+	0.301585i
$411$	4.99150e12	−	2.88185e12i	0.425620	−	0.245732i
$412$		−	4.34075e12i		−	0.365661i
$413$	−6.65840e12	−	1.55685e13i	−0.554140	−	1.29568i
$414$	−1.83149e12			−0.150593
$415$	7.92208e12	+	1.37214e13i	0.643574	+	1.11470i
$416$	9.79172e12	+	5.65325e12i	0.785945	+	0.453766i
$417$	−1.01689e12	+	1.76131e12i	−0.0806484	+	0.139687i
$418$	1.74710e12	−	1.00869e12i	0.136910	−	0.0790451i
$419$			1.31418e13i			1.01762i	0.860879	+	0.508809i	$0.169914\pi$
$419$			1.31418e13i			1.01762i	−0.860879	+	0.508809i	$0.830086\pi$
$420$	−6.06005e12	+	2.59179e12i	−0.463692	+	0.198314i
$421$	−5.16333e12			−0.390409			−0.195204	−	0.980763i	$-0.562537\pi$
$421$	−5.16333e12			−0.390409			−0.195204	+	0.980763i	$0.562537\pi$
$422$	2.49649e11	+	4.32404e11i	0.0186538	+	0.0323093i
$423$	2.05022e12	+	1.18369e12i	0.151390	+	0.0874052i
$424$	−5.68472e12	+	9.84623e12i	−0.414840	+	0.718523i
$425$	−6.21787e9	+	3.58989e9i	−0.000448432	+	0.000258903i
$426$			3.58115e12i			0.255255i
$427$	1.25960e13	+	1.51187e12i	0.887344	+	0.106506i
$428$	1.83938e13			1.28072
$429$	3.71220e12	+	6.42972e12i	0.255473	+	0.442492i
$430$	2.73668e10	+	1.58002e10i	0.00186158	+	0.00107478i
$431$	−4.26812e12	+	7.39260e12i	−0.286979	+	0.497062i	−0.973087	−	0.230437i	$-0.925984\pi$
$431$	−4.26812e12	+	7.39260e12i	−0.286979	+	0.497062i	0.686108	+	0.727500i	$0.259318\pi$
$432$	−1.80034e12	+	1.03942e12i	−0.119656	+	0.0690835i
$433$			1.74406e13i			1.14583i	0.819613	+	0.572917i	$0.194188\pi$
$433$			1.74406e13i			1.14583i	−0.819613	+	0.572917i	$0.805812\pi$
$434$	7.31591e11	−	9.76361e11i	0.0475138	−	0.0634106i
$435$	1.13989e12			0.0731838
$436$	6.54255e12	+	1.13320e13i	0.415255	+	0.719242i
$437$	1.27344e13	+	7.35222e12i	0.799047	+	0.461330i
$438$	−1.72718e12	+	2.99156e12i	−0.107144	+	0.185578i
$439$	4.73895e12	−	2.73604e12i	0.290643	−	0.167803i	−0.347589	−	0.937647i	$-0.612999\pi$
$439$	4.73895e12	−	2.73604e12i	0.290643	−	0.167803i	0.638232	+	0.769844i	$0.279666\pi$
$440$			7.53964e12i			0.457180i
$441$	−3.84049e12	+	4.02043e12i	−0.230247	+	0.241034i
$442$	−4.73345e10			−0.00280586
$443$	−1.55918e13	−	2.70058e13i	−0.913857	−	1.58285i	−0.808566	−	0.588405i	$-0.799756\pi$
$443$	−1.55918e13	−	2.70058e13i	−0.913857	−	1.58285i	−0.105290	−	0.994442i	$-0.533577\pi$
$444$	−1.21930e13	−	7.03960e12i	−0.706633	−	0.407975i
$445$	5.35966e12	−	9.28321e12i	0.307141	−	0.531983i
$446$	−5.60573e12	+	3.23647e12i	−0.317656	+	0.183399i
$447$			8.73330e12i			0.489374i
$448$	−6.69068e12	−	5.01335e12i	−0.370749	−	0.277804i
$449$	−8.64636e12			−0.473807			−0.236903	−	0.971533i	$-0.576133\pi$
$449$	−8.64636e12			−0.473807			−0.236903	+	0.971533i	$0.576133\pi$
$450$	6.12642e10	+	1.06113e11i	0.00332005	+	0.00575049i
$451$	−1.48640e13	−	8.58172e12i	−0.796622	−	0.459930i
$452$	1.31595e13	−	2.27930e13i	0.697506	−	1.20812i
$453$	9.12857e12	−	5.27038e12i	0.478533	−	0.276281i
$454$		−	9.39745e12i		−	0.487226i
$455$	2.49784e12	−	2.08105e13i	0.128088	−	1.06715i
$456$	−4.29838e12			−0.218012
$457$	1.02058e13	+	1.76769e13i	0.511994	+	0.886799i	0.999903	+	0.0139047i	$0.00442616\pi$
$457$	1.02058e13	+	1.76769e13i	0.511994	+	0.886799i	−0.487910	+	0.872894i	$0.662241\pi$
$458$	−1.19356e12	−	6.89100e11i	−0.0592264	−	0.0341944i
$459$	1.58849e10	−	2.75135e10i	0.000779689	−	0.00135046i
$460$	−2.25813e13	+	1.30373e13i	−1.09638	+	0.632994i
$461$		−	8.10372e12i		−	0.389206i	−0.980882	−	0.194603i	$-0.937658\pi$
$461$		−	8.10372e12i		−	0.389206i	0.980882	−	0.194603i	$-0.0623419\pi$
$462$	1.18665e12	+	2.77459e12i	0.0563784	+	0.131822i
$463$	3.61486e12			0.169897			0.0849487	−	0.996385i	$-0.472927\pi$
$463$	3.61486e12			0.169897			0.0849487	+	0.996385i	$0.472927\pi$
$464$	1.01149e12	+	1.75195e12i	0.0470296	+	0.0814577i
$465$	−2.67337e12	−	1.54347e12i	−0.122969	−	0.0709960i
$466$	−9.96204e10	+	1.72548e11i	−0.00453335	+	0.00785199i
$467$	1.13671e13	−	6.56281e12i	0.511760	−	0.295465i	−0.221797	−	0.975093i	$-0.571192\pi$
$467$	1.13671e13	−	6.56281e12i	0.511760	−	0.295465i	0.733557	+	0.679628i	$0.237859\pi$
$468$		−	7.50560e12i		−	0.334315i
$469$	−3.28997e13	+	1.40707e13i	−1.44987	+	0.620086i
$470$	−3.62744e12			−0.158165
$471$	9.17018e12	+	1.58832e13i	0.395615	+	0.685226i
$472$	1.69581e13	+	9.79074e12i	0.723879	+	0.417932i
$473$	−6.72154e10	+	1.16420e11i	−0.00283898	+	0.00491727i
$474$	−2.51027e12	+	1.44930e12i	−0.104913	+	0.0605714i
$475$		−	9.83739e11i		−	0.0406829i
$476$	1.77488e11	+	2.13035e10i	0.00726330	+	0.000871799i
$477$	1.15138e13			0.466258
$478$	−8.44711e11	−	1.46308e12i	−0.0338508	−	0.0586313i
$479$	−2.88138e13	−	1.66356e13i	−1.14267	−	0.659724i	−0.195583	−	0.980687i	$-0.562660\pi$
$479$	−2.88138e13	−	1.66356e13i	−1.14267	−	0.659724i	−0.947092	+	0.320964i	$0.895993\pi$
$480$	5.81389e12	−	1.00699e13i	0.228171	−	0.395204i
$481$	3.87743e13	−	2.23864e13i	1.50598	−	0.869477i
$482$		−	1.08194e13i		−	0.415880i
$483$	−1.31896e13	+	1.76025e13i	−0.501759	+	0.669634i
$484$	8.76096e12			0.329857
$485$	−2.33173e13	−	4.03868e13i	−0.868900	−	1.50498i
$486$	−4.69538e11	−	2.71088e11i	−0.0173177	−	0.00999837i
$487$	−9.48350e12	+	1.64259e13i	−0.346198	+	0.599632i	−0.985571	−	0.169265i	$-0.945861\pi$
$487$	−9.48350e12	+	1.64259e13i	−0.346198	+	0.599632i	0.639373	+	0.768897i	$0.279194\pi$
$488$	−1.27055e13	+	7.33550e12i	−0.459083	+	0.265052i
$489$		−	1.08083e13i		−	0.386557i
$490$	2.01606e12	−	8.27729e12i	0.0713711	−	0.293027i
$491$	−2.06563e13			−0.723845			−0.361922	−	0.932208i	$-0.617879\pi$
$491$	−2.06563e13			−0.723845			−0.361922	+	0.932208i	$0.617879\pi$
$492$	8.67559e12	+	1.50266e13i	0.300935	+	0.521236i
$493$	−2.67740e10	−	1.54580e10i	−0.000919346	−	0.000530785i
$494$	3.24277e12	−	5.61664e12i	0.110225	−	0.190916i
$495$	6.61241e12	−	3.81768e12i	0.222502	−	0.128462i
$496$		−	5.47847e12i		−	0.182495i
$497$	3.44183e13	+	2.57898e13i	1.13503	+	0.850483i
$498$	−7.33359e12			−0.239425
$499$	−2.15147e13	−	3.72645e13i	−0.695396	−	1.20446i	−0.970047	−	0.242917i	$-0.921896\pi$
$499$	−2.15147e13	−	3.72645e13i	−0.695396	−	1.20446i	0.274651	−	0.961544i	$-0.411438\pi$
$500$	2.51507e13	+	1.45208e13i	0.804823	+	0.464665i
$501$	−5.35898e12	+	9.28202e12i	−0.169783	+	0.294072i
$502$	9.69739e12	−	5.59879e12i	0.304184	−	0.175621i
$503$		−	1.78178e13i		−	0.553368i	−0.960961	−	0.276684i	$-0.910764\pi$
$503$		−	1.78178e13i		−	0.553368i	0.960961	−	0.276684i	$-0.0892356\pi$
$504$	7.66250e11	−	6.38393e12i	0.0235623	−	0.196307i
$505$	−4.01281e13			−1.22178
$506$	5.96915e12	+	1.03389e13i	0.179953	+	0.311688i
$507$	3.92072e12	+	2.26363e12i	0.117038	+	0.0675718i
$508$	2.79383e13	−	4.83905e13i	0.825811	−	1.43035i
$509$	−5.38768e13	+	3.11058e13i	−1.57693	+	0.910442i	−0.581648	+	0.813441i	$0.697592\pi$
$509$	−5.38768e13	+	3.11058e13i	−1.57693	+	0.910442i	−0.995284	+	0.0970016i	$0.969075\pi$
$510$			4.86794e10i			0.00141089i
$511$	1.63135e13	+	3.81437e13i	0.468211	+	1.09476i
$512$	3.56191e13			1.01235
$513$	2.17647e12	+	3.76976e12i	0.0612585	+	0.106103i
$514$	7.07264e11	+	4.08339e11i	0.0197136	+	0.0113817i
$515$	7.09803e12	−	1.22942e13i	0.195930	−	0.339361i
$516$	1.17694e11	−	6.79506e10i	0.00321740	−	0.00185757i
$517$		−	1.54314e13i		−	0.417785i
$518$	1.67321e13	−	7.15608e12i	0.448645	−	0.191879i
$519$	−3.65373e13			−0.970286
$520$	1.21194e13	+	2.09914e13i	0.318760	+	0.552108i
$521$	4.58124e13	+	2.64498e13i	1.19342	+	0.689023i	0.959081	−	0.283132i	$-0.0913733\pi$
$521$	4.58124e13	+	2.64498e13i	1.19342	+	0.689023i	0.234341	+	0.972154i	$0.424707\pi$
$522$	−2.63802e11	+	4.56919e11i	−0.00680654	+	0.0117893i
$523$	−5.37806e13	+	3.10503e13i	−1.37441	+	0.793518i	−0.991480	−	0.130258i	$-0.958419\pi$
$523$	−5.37806e13	+	3.10503e13i	−1.37441	+	0.793518i	−0.382933	+	0.923776i	$0.625086\pi$
$524$			3.74566e13i			0.948138i
$525$	1.46104e12	+	1.75366e11i	0.0366325	+	0.00439693i
$526$	−4.46897e12			−0.110989
$527$	4.18620e10	+	7.25072e10i	0.00102983	+	0.00178373i
$528$	1.17352e13	+	6.77532e12i	0.285970	+	0.165105i
$529$	−2.27953e13	+	3.94826e13i	−0.550258	+	0.953075i
$530$	−1.52785e13	+	8.82103e12i	−0.365343	+	0.210931i
$531$		−	1.98301e13i		−	0.469733i
$532$	−1.46871e13	+	1.96010e13i	−0.344650	+	0.459960i
$533$	−5.51778e13			−1.28271
$534$	2.48076e12	+	4.29681e12i	0.0571319	+	0.0989554i
$535$	5.20961e13	+	3.00777e13i	1.18860	+	0.686240i
$536$	2.06900e13	−	3.58362e13i	0.467668	−	0.810024i
$537$	2.86100e13	−	1.65180e13i	0.640689	−	0.369902i
$538$		−	1.83785e13i		−	0.407754i
$539$	3.52123e13	+	8.57647e12i	0.774016	+	0.188523i
$540$	−7.71887e12			−0.168107
$541$	−2.31919e13	−	4.01696e13i	−0.500438	−	0.866784i	−1.00000		0.000505659i	$-0.999839\pi$
$541$	−2.31919e13	−	4.01696e13i	−0.500438	−	0.866784i	0.499562	−	0.866278i	$-0.333494\pi$
$542$	1.26585e13	+	7.30836e12i	0.270635	+	0.156251i
$543$	2.18566e12	−	3.78567e12i	0.0463002	−	0.0801943i
$544$	−2.73117e11	+	1.57684e11i	−0.00573264	+	0.00330974i
$545$			4.27937e13i			0.890016i
$546$	7.76374e12	+	5.81740e12i	0.159995	+	0.119885i
$547$	7.56927e13			1.54567			0.772836	−	0.634606i	$-0.218838\pi$
$547$	7.56927e13			1.54567			0.772836	+	0.634606i	$0.218838\pi$
$548$	1.89903e13	+	3.28922e13i	0.384263	+	0.665564i
$549$	1.28668e13	+	7.42863e12i	0.257993	+	0.148952i
$550$	3.99341e11	−	6.91678e11i	0.00793469	−	0.0137433i
$551$	3.66845e12	−	2.11798e12i	0.0722311	−	0.0417027i
$552$		−	2.54367e13i		−	0.496324i
$553$	−4.14857e12	+	3.45633e13i	−0.0802181	+	0.668329i
$554$	−1.89543e13			−0.363211
$555$	−2.30224e13	−	3.98761e13i	−0.437206	−	0.757264i
$556$	−1.16064e13	−	6.70096e12i	−0.218436	−	0.126114i
$557$	−2.35451e13	+	4.07813e13i	−0.439162	+	0.760651i	−0.997625	−	0.0688786i	$-0.978058\pi$
$557$	−2.35451e13	+	4.07813e13i	−0.439162	+	0.760651i	0.558463	+	0.829529i	$0.311391\pi$
$558$	1.23739e12	−	7.14408e11i	0.0228737	−	0.0132061i
$559$			4.32174e11i			0.00791771i
$560$	−1.50430e13	−	3.51730e13i	−0.273145	−	0.638660i
$561$	−2.07086e11			−0.00372681
$562$	3.38387e12	+	5.86104e12i	0.0603576	+	0.104542i
$563$	4.45461e13	+	2.57187e13i	0.787531	+	0.454681i	0.839093	−	0.543988i	$-0.183086\pi$
$563$	4.45461e13	+	2.57187e13i	0.787531	+	0.454681i	−0.0515615	+	0.998670i	$0.516420\pi$
$564$	−7.80010e12	+	1.35102e13i	−0.136680	+	0.236737i
$565$	7.45425e13	−	4.30371e13i	1.29468	−	0.747482i
$566$			5.72699e12i			0.0985926i
$567$	−5.98682e12	+	2.56047e12i	−0.102160	+	0.0436923i
$568$	−4.97367e13			−0.841270
$569$	−3.00702e13	−	5.20830e13i	−0.504167	−	0.873243i	−0.999988	−	0.00481837i	$-0.998466\pi$
$569$	−3.00702e13	−	5.20830e13i	−0.504167	−	0.873243i	0.495821	−	0.868425i	$-0.334867\pi$
$570$	−5.77624e12	−	3.33491e12i	−0.0959999	−	0.0554255i
$571$	5.35807e13	−	9.28044e13i	0.882729	−	1.52893i	0.0344352	−	0.999407i	$-0.489037\pi$
$571$	5.35807e13	−	9.28044e13i	0.882729	−	1.52893i	0.848294	−	0.529525i	$-0.177630\pi$
$572$	−4.23695e13	+	2.44620e13i	−0.691947	+	0.399496i
$573$		−	1.70577e13i		−	0.276151i
$574$	−2.22676e13	−	2.67273e12i	−0.357366	−	0.0428939i
$575$	5.82151e12			0.0926182
$576$	−4.89560e12	−	8.47943e12i	−0.0772136	−	0.133738i
$577$	−6.53979e13	−	3.77575e13i	−1.02255	−	0.590370i	−0.107709	−	0.994182i	$-0.534351\pi$
$577$	−6.53979e13	−	3.77575e13i	−1.02255	−	0.590370i	−0.914842	+	0.403813i	$0.867685\pi$
$578$	−1.00541e13	+	1.74142e13i	−0.155849	+	0.269938i
$579$	4.40492e12	−	2.54318e12i	0.0676932	−	0.0390827i
$580$			7.51142e12i			0.114441i
$581$	−5.28132e13	+	7.04830e13i	−0.797740	+	1.06464i
$582$	2.15852e13			0.323252
$583$	−3.75254e13	−	6.49958e13i	−0.557163	−	0.965034i
$584$	−4.15482e13	−	2.39879e13i	−0.611629	−	0.353124i
$585$	1.22732e13	−	2.12579e13i	0.179135	−	0.310270i
$586$	−2.27029e13	+	1.31076e13i	−0.328544	+	0.189685i
$587$			4.05589e13i			0.581964i	0.956729	+	0.290982i	$0.0939820\pi$
$587$			4.05589e13i			0.581964i	−0.956729	+	0.290982i	$0.906018\pi$
$588$	−2.64931e13	−	2.53074e13i	−0.376918	−	0.360048i
$589$	−1.14715e13			−0.161824
$590$	1.51924e13	+	2.63139e13i	0.212503	+	0.368066i
$591$	−5.81119e12	−	3.35509e12i	−0.0805986	−	0.0465336i
$592$	4.08585e13	−	7.07689e13i	0.561919	−	0.973272i
$593$	2.22468e13	−	1.28442e13i	0.303384	−	0.175159i	−0.340578	−	0.940216i	$-0.610623\pi$
$593$	2.22468e13	−	1.28442e13i	0.303384	−	0.175159i	0.643962	+	0.765057i	$0.277289\pi$
$594$			3.53409e12i			0.0477909i
$595$	4.67857e11	+	3.50567e11i	0.00627376	+	0.00470095i
$596$	−5.75492e13			−0.765258
$597$	3.12994e12	+	5.42122e12i	0.0412729	+	0.0714867i
$598$	3.32378e13	+	1.91899e13i	0.434637	+	0.250938i
$599$	3.67055e13	−	6.35759e13i	0.475990	−	0.824438i	−0.523632	−	0.851945i	$-0.675423\pi$
$599$	3.67055e13	−	6.35759e13i	0.475990	−	0.824438i	0.999622	+	0.0275063i	$0.00875665\pi$
$600$	−1.47374e12	+	8.50867e11i	−0.0189525	+	0.0109422i
$601$		−	8.21156e12i		−	0.104726i	−0.998628	−	0.0523628i	$-0.983325\pi$
$601$		−	8.21156e12i		−	0.104726i	0.998628	−	0.0523628i	$-0.0166752\pi$
$602$	−2.09339e10	+	1.74408e11i	−0.000264769	+	0.00220589i
$603$	−4.19054e13			−0.525634
$604$	3.47299e13	+	6.01539e13i	0.432034	+	0.748306i
$605$	2.48134e13	+	1.43260e13i	0.306132	+	0.176745i
$606$	9.28680e12	−	1.60852e13i	0.113633	−	0.196817i
$607$	6.16257e13	−	3.55796e13i	0.747856	−	0.431775i	−0.0770625	−	0.997026i	$-0.524554\pi$
$607$	6.16257e13	−	3.55796e13i	0.747856	−	0.431775i	0.824919	+	0.565251i	$0.191221\pi$
$608$		−	4.32103e13i		−	0.520079i
$609$	2.49166e12	+	5.82592e12i	0.0297442	+	0.0695470i
$610$	−2.27651e13			−0.269538
$611$	−2.48048e13	−	4.29631e13i	−0.291292	−	0.504533i
$612$	1.81304e11	+	1.04676e11i	0.00211178	+	0.00121924i
$613$	−5.85887e13	+	1.01479e14i	−0.676880	+	1.17239i	0.299035	+	0.954242i	$0.403335\pi$
$613$	−5.85887e13	+	1.01479e14i	−0.676880	+	1.17239i	−0.975916	+	0.218149i	$0.929998\pi$
$614$	3.28986e13	−	1.89940e13i	0.376994	−	0.217658i
$615$			5.67456e13i			0.644995i
$616$	−3.85349e13	+	1.64808e13i	−0.434461	+	0.185812i
$617$	2.79508e13			0.312586			0.156293	−	0.987711i	$-0.450046\pi$
$617$	2.79508e13			0.312586			0.156293	+	0.987711i	$0.450046\pi$
$618$	3.28538e12	+	5.69045e12i	0.0364455	+	0.0631254i
$619$	−3.59569e13	−	2.07598e13i	−0.395667	−	0.228438i	0.288946	−	0.957345i	$-0.406695\pi$
$619$	−3.59569e13	−	2.07598e13i	−0.395667	−	0.228438i	−0.684613	+	0.728907i	$0.740029\pi$
$620$	1.01709e13	−	1.76165e13i	0.111020	−	0.192292i
$621$	−2.23085e13	+	1.28798e13i	−0.241553	+	0.139460i
$622$			1.11892e13i			0.120184i
$623$	5.91618e13	+	7.10107e12i	0.630378	+	0.0756630i
$624$	4.35632e13			0.460465
$625$	4.44418e13	+	7.69754e13i	0.466006	+	0.807146i
$626$	−6.10651e12	−	3.52560e12i	−0.0635216	−	0.0366742i
$627$	1.41870e13	−	2.45726e13i	0.146404	−	0.253579i
$628$	−1.04665e14	+	6.04281e13i	−1.07152	+	0.618644i
$629$			1.24883e12i			0.0126838i
$630$	5.98269e12	−	7.98434e12i	0.0602829	−	0.0804519i
$631$	−2.19182e13			−0.219108			−0.109554	−	0.993981i	$-0.534942\pi$
$631$	−2.19182e13			−0.219108			−0.109554	+	0.993981i	$0.534942\pi$
$632$	−2.01286e13	−	3.48638e13i	−0.199631	−	0.345772i
$633$	6.08167e12	+	3.51126e12i	0.0598418	+	0.0345497i
$634$	−2.00939e13	+	3.48036e13i	−0.196163	+	0.339765i
$635$	1.58257e14	−	9.13698e13i	1.53283	−	0.884981i
$636$			7.58716e13i			0.729111i
$637$	1.11822e14	−	3.27229e13i	1.06618	−	0.312000i
$638$	3.43911e12			0.0325343
$639$	2.51841e13	+	4.36201e13i	0.236386	+	0.409432i
$640$	8.64916e13	+	4.99360e13i	0.805516	+	0.465065i
$641$	−2.20470e13	+	3.81864e13i	−0.203732	+	0.352873i	−0.949728	−	0.313077i	$-0.898640\pi$
$641$	−2.20470e13	+	3.81864e13i	−0.203732	+	0.352873i	0.745996	+	0.665950i	$0.231974\pi$
$642$	−2.41131e13	+	1.39217e13i	−0.221095	+	0.127649i
$643$		−	3.12425e13i		−	0.284244i	−0.989849	−	0.142122i	$-0.954608\pi$
$643$		−	3.12425e13i		−	0.284244i	0.989849	−	0.142122i	$-0.0453925\pi$
$644$	−1.15994e14	−	8.69145e13i	−1.04714	−	0.784626i
$645$	4.44454e11			0.00398133
$646$	9.04495e10	+	1.56663e11i	0.000803977	+	0.00139253i
$647$	4.06767e12	+	2.34847e12i	0.0358776	+	0.0207140i	0.517832	−	0.855483i	$-0.326739\pi$
$647$	4.06767e12	+	2.34847e12i	0.0358776	+	0.0207140i	−0.481954	+	0.876197i	$0.660073\pi$
$648$	3.76500e12	−	6.52117e12i	0.0329526	−	0.0570756i
$649$	−1.11942e14	+	6.46295e13i	−0.972227	+	0.561316i
$650$		−	2.56763e12i		−	0.0221292i
$651$	2.04496e12	−	1.70374e13i	0.0174896	−	0.145713i
$652$	7.12228e13			0.604479
$653$	9.53892e13	+	1.65219e14i	0.803403	+	1.39153i	0.917364	+	0.398050i	$0.130313\pi$
$653$	9.53892e13	+	1.65219e14i	0.803403	+	1.39153i	−0.113961	+	0.993485i	$0.536354\pi$
$654$	−1.71537e13	−	9.90371e12i	−0.143374	−	0.0827769i
$655$	−6.12493e13	+	1.06087e14i	−0.508036	+	0.879945i
$656$	−8.72154e13	+	5.03539e13i	−0.717917	+	0.414489i
$657$			4.85848e13i			0.396893i
$658$	−7.92916e12	−	1.85397e13i	−0.0642832	−	0.150305i
$659$	1.46637e14			1.17982			0.589912	−	0.807468i	$-0.299162\pi$
$659$	1.46637e14			1.17982			0.589912	+	0.807468i	$0.299162\pi$
$660$	2.51571e13	+	4.35734e13i	0.200882	+	0.347938i
$661$	−3.75214e12	−	2.16630e12i	−0.0297352	−	0.0171677i	0.485059	−	0.874482i	$-0.338798\pi$
$661$	−3.75214e12	−	2.16630e12i	−0.0297352	−	0.0171677i	−0.514794	+	0.857314i	$0.672132\pi$
$662$	−3.28988e12	+	5.69824e12i	−0.0258756	+	0.0448178i
$663$	−5.76556e11	+	3.32875e11i	−0.00450064	+	0.00259844i
$664$		−	1.01852e14i		−	0.789098i
$665$	−7.36495e13	+	3.14988e13i	−0.566320	+	0.242206i
$666$	2.13123e13			0.162652
$667$	1.25337e13	+	2.17089e13i	0.0949398	+	0.164441i
$668$	−6.11651e13	−	3.53137e13i	−0.459856	−	0.265498i
$669$	−4.55203e13	+	7.88434e13i	−0.339683	+	0.588349i
$670$	5.56073e13	−	3.21049e13i	0.411868	−	0.237792i
$671$		−	9.68445e13i		−	0.711971i
$672$	6.41757e13	+	7.70288e12i	0.468300	+	0.0562091i
$673$	5.48259e13			0.397110			0.198555	−	0.980090i	$-0.436375\pi$
$673$	5.48259e13			0.397110			0.198555	+	0.980090i	$0.436375\pi$
$674$	−2.85021e13	−	4.93671e13i	−0.204917	−	0.354926i
$675$	1.49245e12	+	8.61669e11i	0.0106508	+	0.00614924i
$676$	−1.49165e13	+	2.58361e13i	−0.105665	+	0.183018i
$677$	9.10736e13	−	5.25814e13i	0.640397	−	0.369733i	−0.144370	−	0.989524i	$-0.546116\pi$
$677$	9.10736e13	−	5.25814e13i	0.640397	−	0.369733i	0.784767	+	0.619790i	$0.212782\pi$
$678$			3.98402e13i			0.278082i
$679$	1.55447e14	−	2.07455e14i	1.07704	−	1.43739i
$680$	−6.76083e11			−0.00465003
$681$	−6.60866e13	−	1.14465e14i	−0.451209	−	0.781517i
$682$	−8.06573e12	−	4.65675e12i	−0.0546666	−	0.0315618i
$683$	−4.88974e13	+	8.46928e13i	−0.328990	+	0.569827i	−0.982312	−	0.187253i	$-0.940042\pi$
$683$	−4.88974e13	+	8.46928e13i	−0.328990	+	0.569827i	0.653322	+	0.757080i	$0.273375\pi$
$684$	−2.48413e13	+	1.43422e13i	−0.165918	+	0.0957930i
$685$			1.24212e14i			0.823592i
$686$	4.67119e13	−	7.78918e12i	0.307473	−	0.0512709i
$687$	−1.93841e13			−0.126667
$688$	3.94391e11	+	6.83105e11i	0.00255850	+	0.00443145i
$689$	−2.08951e14	−	1.20638e14i	−1.34570	−	0.776942i
$690$	1.97351e13	−	3.41823e13i	0.126181	−	0.218552i
$691$	−1.65078e14	+	9.53079e13i	−1.04785	+	0.604977i	−0.922047	−	0.387078i	$-0.873484\pi$
$691$	−1.65078e14	+	9.53079e13i	−1.04785	+	0.604977i	−0.125804	+	0.992055i	$0.540151\pi$
$692$		−	2.40768e14i		−	1.51729i
$693$	3.39660e13	+	2.54509e13i	0.212510	+	0.159234i
$694$	6.82973e13			0.424235
$695$	−2.19149e13	−	3.79578e13i	−0.135150	−	0.234087i
$696$	−6.34591e12	−	3.66382e12i	−0.0388551	−	0.0224330i
$697$	7.69527e11	−	1.33286e12i	0.00467800	−	0.00810253i
$698$	−3.96901e13	+	2.29151e13i	−0.239555	+	0.138307i
$699$			2.80228e12i			0.0167929i
$700$	−1.15560e12	+	9.62774e12i	−0.00687570	+	0.0572841i
$701$	−3.35607e13			−0.198262			−0.0991312	−	0.995074i	$-0.531606\pi$
$701$	−3.35607e13			−0.198262			−0.0991312	+	0.995074i	$0.531606\pi$
$702$	5.68076e12	+	9.83937e12i	0.0333212	+	0.0577141i
$703$	−1.48185e14	−	8.55544e13i	−0.863031	−	0.498271i
$704$	−3.19112e13	+	5.52718e13i	−0.184535	+	0.319624i
$705$	−4.41839e13	+	2.55096e13i	−0.253699	+	0.146473i
$706$			2.57796e13i			0.146978i
$707$	−8.77153e13	−	2.05093e14i	−0.496567	−	1.16106i
$708$	1.30673e14			0.734546
$709$	−3.54511e13	−	6.14031e13i	−0.197878	−	0.342735i	0.749962	−	0.661481i	$-0.230072\pi$
$709$	−3.54511e13	−	6.14031e13i	−0.197878	−	0.342735i	−0.947840	+	0.318746i	$0.896738\pi$
$710$	−6.68371e13	−	3.85884e13i	−0.370447	−	0.213878i
$711$	−2.03842e13	+	3.53064e13i	−0.112188	+	0.194315i
$712$	−5.96761e13	+	3.44540e13i	−0.326137	+	0.188295i
$713$		−	6.78852e13i		−	0.368407i
$714$	−2.48799e11	+	1.06408e11i	−0.00134078	+	0.000573431i
$715$	−1.60002e14			−0.856240
$716$	1.08848e14	+	1.88530e14i	0.578434	+	1.00188i
$717$	−2.05780e13	−	1.18807e13i	−0.108594	−	0.0626969i
$718$	−2.04517e13	+	3.54234e13i	−0.107179	+	0.185639i
$719$	1.97086e14	−	1.13788e14i	1.02568	−	0.592176i	0.109935	−	0.993939i	$-0.464936\pi$
$719$	1.97086e14	−	1.13788e14i	1.02568	−	0.592176i	0.915744	+	0.401763i	$0.131602\pi$
$720$		−	4.48010e13i		−	0.231539i
$721$	7.83506e13	+	9.40426e12i	0.402129	+	0.0482668i
$722$	3.63714e13			0.185385
$723$	−7.60863e13	−	1.31785e14i	−0.385137	−	0.667076i
$724$	2.49462e13	+	1.44027e13i	0.125404	+	0.0724019i
$725$	8.38511e11	−	1.45234e12i	0.00418619	−	0.00725069i
$726$	−1.14851e13	+	6.63091e12i	−0.0569443	+	0.0328768i
$727$			8.06988e13i			0.397370i	0.980063	+	0.198685i	$0.0636671\pi$
$727$			8.06988e13i			0.397370i	−0.980063	+	0.198685i	$0.936333\pi$
$728$	−8.07948e13	+	1.07826e14i	−0.395118	+	0.527313i
$729$	−7.62560e12			−0.0370370
$730$	−3.72221e13	−	6.44706e13i	−0.179551	−	0.310991i
$731$	−1.04395e10	−	6.02724e9i	−5.00141e−5	−	2.88756e-5i
$732$	−4.89519e13	+	8.47872e13i	−0.232924	+	0.403436i
$733$	2.94920e14	−	1.70272e14i	1.39375	−	0.804682i	0.400022	−	0.916505i	$-0.369002\pi$
$733$	2.94920e14	−	1.70272e14i	1.39375	−	0.804682i	0.993728	+	0.111823i	$0.0356691\pi$
$734$			5.96756e13i			0.280102i
$735$	−3.36527e13	−	1.14999e14i	−0.156886	−	0.536114i
$736$	2.55707e14			1.18401
$737$	1.36577e14	+	2.36558e14i	0.628115	+	1.08793i
$738$	−2.27463e13	−	1.31326e13i	−0.103903	−	0.0599885i
$739$	−5.63048e13	+	9.75229e13i	−0.255460	+	0.442470i	−0.965020	−	0.262175i	$-0.915560\pi$
$739$	−5.63048e13	+	9.75229e13i	−0.255460	+	0.442470i	0.709560	+	0.704645i	$0.248894\pi$
$740$	2.62768e14	−	1.51709e14i	1.18417	−	0.683682i
$741$		−	9.12178e13i		−	0.408309i
$742$	−7.84810e13	−	5.88061e13i	−0.348935	−	0.261458i
$743$	7.32927e13			0.323681			0.161840	−	0.986817i	$-0.448257\pi$
$743$	7.32927e13			0.323681			0.161840	+	0.986817i	$0.448257\pi$
$744$	9.92204e12	+	1.71855e13i	0.0435248	+	0.0753871i
$745$	−1.62995e14	−	9.41050e13i	−0.710218	−	0.410045i
$746$	2.46400e13	−	4.26777e13i	0.106646	−	0.184717i
$747$	−8.93266e13	+	5.15728e13i	−0.384041	+	0.221726i
$748$		−	1.36462e12i		−	0.00582780i
$749$	−3.98503e13	+	3.32008e14i	−0.169053	+	1.40845i
$750$	−4.39613e13			−0.185253
$751$	−2.40829e13	−	4.17127e13i	−0.100811	−	0.174610i	0.811208	−	0.584758i	$-0.198810\pi$
$751$	−2.40829e13	−	4.17127e13i	−0.100811	−	0.174610i	−0.912019	+	0.410148i	$0.865477\pi$
$752$	−7.84142e13	−	4.52724e13i	−0.326066	−	0.188254i
$753$	7.87459e13	−	1.36392e14i	0.325277	−	0.563396i
$754$	9.57493e12	−	5.52809e12i	0.0392897	−	0.0226839i
$755$			2.27162e14i			0.925980i
$756$	−1.68726e13	−	3.94509e13i	−0.0683238	−	0.159753i
$757$	8.48880e13			0.341481			0.170741	−	0.985316i	$-0.445384\pi$
$757$	8.48880e13			0.341481			0.170741	+	0.985316i	$0.445384\pi$
$758$	5.85353e13	+	1.01386e14i	0.233923	+	0.405166i
$759$	1.45414e14	+	8.39548e13i	0.577295	+	0.333301i
$760$	4.63168e13	−	8.02231e13i	0.182672	−	0.316396i
$761$	−1.18973e14	+	6.86888e13i	−0.466147	+	0.269130i	−0.714626	−	0.699507i	$-0.753403\pi$
$761$	−1.18973e14	+	6.86888e13i	−0.466147	+	0.269130i	0.248478	+	0.968638i	$0.420070\pi$
$762$			8.45825e13i			0.329235i
$763$	−2.18718e14	+	9.35422e13i	−0.845787	+	0.361730i
$764$	1.12404e14			0.431831
$765$	3.42333e11	+	5.92938e11i	0.00130660	+	0.00226309i
$766$	1.06465e14	+	6.14675e13i	0.403703	+	0.233078i
$767$	−2.07774e14	+	3.59874e14i	−0.782733	+	1.35573i
$768$	2.18567e13	−	1.26190e13i	0.0818048	−	0.0472300i
$769$			3.98914e14i			1.48336i	0.670752	+	0.741682i	$0.265971\pi$
$769$			3.98914e14i			1.48336i	−0.670752	+	0.741682i	$0.734029\pi$
$770$	−6.45705e13	−	7.75027e12i	−0.238551	−	0.0286328i
$771$	1.14864e13			0.0421612
$772$	1.67586e13	+	2.90268e13i	0.0611156	+	0.105855i
$773$	−2.72758e14	−	1.57477e14i	−0.988279	−	0.570583i	−0.0835198	−	0.996506i	$-0.526616\pi$
$773$	−2.72758e14	−	1.57477e14i	−0.988279	−	0.570583i	−0.904760	+	0.425923i	$0.859950\pi$
$774$	−1.02859e11	+	1.78158e11i	−0.000370288	+	0.000641357i
$775$	−3.93312e12	+	2.27079e12i	−0.0140679	+	0.00812209i
$776$			2.99786e14i			1.06537i
$777$	1.53481e14	−	2.04832e14i	0.541938	−	0.723255i
$778$	1.46442e14			0.513767
$779$	1.05437e14	+	1.82622e14i	0.367541	+	0.636599i
$780$	1.40081e14	+	8.08761e13i	0.485185	+	0.280122i
$781$	1.64158e14	−	2.84330e14i	0.564947	−	0.978516i
$782$	−9.27092e11	+	5.35257e11i	−0.00317022	+	0.00183033i
$783$			7.42066e12i			0.0252135i
$784$	1.46886e14	−	1.53768e14i	0.495908	−	0.519143i
$785$	−3.95250e14			−1.32594
$786$	−2.83497e13	−	4.91032e13i	−0.0945010	−	0.163681i
$787$	−5.17501e13	−	2.98779e13i	−0.171411	−	0.0989639i	0.411840	−	0.911256i	$-0.364886\pi$
$787$	−5.17501e13	−	2.98779e13i	−0.171411	−	0.0989639i	−0.583251	+	0.812292i	$0.698220\pi$
$788$	2.21088e13	−	3.82936e13i	0.0727670	−	0.126036i
$789$	−5.44341e13	+	3.14276e13i	−0.178027	+	0.102784i
$790$		−	6.24674e13i		−	0.203010i
$791$	3.82903e14	+	2.86910e14i	1.23653	+	0.926539i
$792$	−4.90831e13			−0.157509
$793$	−1.55670e14	−	2.69628e14i	−0.496408	−	0.859804i
$794$	−1.25388e14	−	7.23929e13i	−0.397332	−	0.229400i
$795$	−1.24066e14	+	2.14889e14i	−0.390676	+	0.676671i
$796$	−3.57238e13	+	2.06252e13i	−0.111787	+	0.0645405i
$797$		−	1.01368e14i		−	0.315216i	−0.987502	−	0.157608i	$-0.949622\pi$
$797$		−	1.01368e14i		−	0.315216i	0.987502	−	0.157608i	$-0.0503782\pi$
$798$	4.41846e12	−	3.68119e13i	0.0136539	−	0.113756i
$799$	1.38374e12			0.00424934
$800$	−8.55350e12	−	1.48151e13i	−0.0261032	−	0.0452121i
$801$	6.04337e13	+	3.48914e13i	0.183281	+	0.105817i
$802$	−6.54531e13	+	1.13368e14i	−0.197269	+	0.341680i
$803$	2.74263e14	−	1.58346e14i	0.821467	−	0.474274i
$804$		−	2.76141e14i		−	0.821961i
$805$	−1.86401e14	−	4.35839e14i	−0.551404	−	1.28928i
$806$	−2.99414e13			−0.0880233
$807$	−1.29245e14	−	2.23859e14i	−0.377612	−	0.654043i
$808$	2.23399e14	+	1.28980e14i	0.648671	+	0.374510i
$809$	1.18093e14	−	2.04543e14i	0.340786	−	0.590259i	−0.643793	−	0.765200i	$-0.722640\pi$
$809$	1.18093e14	−	2.04543e14i	0.340786	−	0.590259i	0.984579	+	0.174941i	$0.0559735\pi$
$810$	1.01189e13	−	5.84218e12i	0.0290209	−	0.0167552i
$811$		−	1.63155e14i		−	0.465046i	−0.972591	−	0.232523i	$-0.925302\pi$
$811$		−	1.63155e14i		−	0.465046i	0.972591	−	0.232523i	$-0.0746981\pi$
$812$	−3.83907e13	+	1.64191e13i	−0.108754	+	0.0465124i
$813$	2.05581e14			0.578803
$814$	−6.94602e13	−	1.20309e14i	−0.194363	−	0.336647i
$815$	2.01722e14	+	1.16464e14i	0.561003	+	0.323895i
$816$	−6.07546e11	+	1.05230e12i	−0.00167930	+	0.00290864i
$817$	1.43037e12	−	8.25824e11i	0.00392950	−	0.00226870i
$818$			6.18768e12i			0.0168951i
$819$	1.35476e14	+	1.62609e13i	0.367658	+	0.0441292i
$820$	−3.73933e14			−1.00861
$821$	1.17781e14	+	2.04002e14i	0.315761	+	0.546914i	0.979599	−	0.200963i	$-0.0644070\pi$
$821$	1.17781e14	+	2.04002e14i	0.315761	+	0.546914i	−0.663838	+	0.747876i	$0.731074\pi$
$822$	−4.97902e13	−	2.87464e13i	−0.132674	−	0.0765991i
$823$	−2.09783e14	+	3.63355e14i	−0.555612	+	0.962348i	0.442244	+	0.896895i	$0.354183\pi$
$823$	−2.09783e14	+	3.63355e14i	−0.555612	+	0.962348i	−0.997856	+	0.0654532i	$0.979151\pi$
$824$	−7.90317e13	+	4.56290e13i	−0.208049	+	0.120117i
$825$		−	1.12333e13i		−	0.0293925i
$826$	−1.01281e14	+	1.35167e14i	−0.263407	+	0.351536i
$827$	−2.98977e14			−0.772876			−0.386438	−	0.922315i	$-0.626295\pi$
$827$	−2.98977e14			−0.772876			−0.386438	+	0.922315i	$0.626295\pi$
$828$	−8.48731e13	−	1.47005e14i	−0.218081	−	0.377728i
$829$	4.75001e14	+	2.74242e14i	1.21317	+	0.700424i	0.963449	−	0.267894i	$-0.0863276\pi$
$829$	4.75001e14	+	2.74242e14i	1.21317	+	0.700424i	0.249722	+	0.968318i	$0.419661\pi$
$830$	7.90226e13	−	1.36871e14i	0.200614	−	0.347473i
$831$	−2.30873e14	+	1.33294e14i	−0.582596	+	0.336362i
$832$			2.05179e14i			0.514654i
$833$	−7.69057e11	+	3.15750e12i	−0.00191749	+	0.00787261i
$834$	2.02870e13			0.0502792
$835$	−1.15491e14	−	2.00036e14i	−0.284521	−	0.492805i
$836$	1.61924e14	+	9.34870e13i	0.396534	+	0.228939i
$837$	1.00480e13	−	1.74037e13i	0.0244598	−	0.0423656i
$838$	1.13527e14	−	6.55447e13i	0.274712	−	0.158605i
$839$		−	7.68229e14i		−	1.84791i	−0.382500	−	0.923956i	$-0.624937\pi$
$839$		−	7.68229e14i		−	1.84791i	0.382500	−	0.923956i	$-0.375063\pi$
$840$	1.10890e14	+	8.30905e13i	0.265153	+	0.198680i
$841$	−4.13486e14			−0.982836
$842$	2.57521e13	+	4.46039e13i	0.0608487	+	0.105393i
$843$	8.24343e13	+	4.75934e13i	0.193629	+	0.111792i
$844$	−2.31379e13	+	4.00760e13i	−0.0540271	+	0.0935776i
$845$	−8.44948e13	+	4.87831e13i	−0.196131	+	0.113236i
$846$		−	2.36146e13i		−	0.0544916i
$847$	−1.89807e13	+	1.58135e14i	−0.0435406	+	0.362754i
$848$	−4.40365e14			−1.00423
$849$	4.02745e13	+	6.97574e13i	0.0913044	+	0.158144i
$850$	6.20231e10	+	3.58091e10i	0.000139785	+	8.07046e-5i
$851$	5.06288e14	−	8.76917e14i	1.13436	−	1.96477i
$852$	−2.87440e14	+	1.65954e14i	−0.640250	+	0.369649i
$853$		−	3.41880e14i		−	0.757057i	−0.925590	−	0.378529i	$-0.876430\pi$
$853$		−	3.41880e14i		−	0.757057i	0.925590	−	0.378529i	$-0.123570\pi$
$854$	−4.97619e13	−	1.16352e14i	−0.109549	−	0.256144i
$855$	−9.38097e13			−0.205313
$856$	−1.93351e14	−	3.34895e14i	−0.420706	−	0.728684i
$857$	−5.88193e14	−	3.39593e14i	−1.27238	−	0.734607i	−0.296942	−	0.954895i	$-0.595967\pi$
$857$	−5.88193e14	−	3.39593e14i	−1.27238	−	0.734607i	−0.975435	+	0.220288i	$0.929300\pi$
$858$	3.70291e13	−	6.41363e13i	0.0796355	−	0.137933i
$859$	−4.71016e14	+	2.71941e14i	−1.00709	+	0.581445i	−0.910339	−	0.413863i	$-0.864179\pi$
$859$	−4.71016e14	+	2.71941e14i	−1.00709	+	0.581445i	−0.0967535	+	0.995308i	$0.530846\pi$
$860$			2.92879e12i			0.00622580i
$861$	−2.90025e14	+	1.24039e14i	−0.612943	+	0.262146i
$862$	8.51488e13			0.178913
$863$	1.00392e14	+	1.73884e14i	0.209722	+	0.363249i	0.951627	−	0.307256i	$-0.0994107\pi$
$863$	1.00392e14	+	1.73884e14i	0.209722	+	0.363249i	−0.741905	+	0.670505i	$0.766077\pi$
$864$	6.55554e13	+	3.78484e13i	0.136157	+	0.0786102i
$865$	3.93705e14	−	6.81917e14i	0.813000	−	1.40816i
$866$	1.50662e14	−	8.69848e13i	0.309325	−	0.178589i
$867$			2.82818e14i			0.577312i
$868$	1.12270e14	+	1.34755e13i	0.227858	+	0.0273494i
$869$	2.65742e14			0.536242
$870$	−5.68517e12	−	9.84700e12i	−0.0114064	−	0.0197564i
$871$	7.60496e14	+	4.39073e14i	1.51707	+	0.875882i
$872$	1.37548e14	−	2.38239e14i	0.272816	−	0.472532i
$873$	2.62918e14	−	1.51796e14i	0.518500	−	0.299356i
$874$		−	1.46677e14i		−	0.287610i
$875$	−3.16589e14	+	4.22511e14i	−0.617242	+	0.823755i
$876$	−3.20156e14			−0.620642
$877$	1.60064e14	+	2.77239e14i	0.308529	+	0.534387i	0.978041	−	0.208414i	$-0.0668301\pi$
$877$	1.60064e14	+	2.77239e14i	0.308529	+	0.534387i	−0.669512	+	0.742801i	$0.733497\pi$
$878$	−4.72710e13	−	2.72919e13i	−0.0905987	−	0.0523072i
$879$	−1.84355e14	+	3.19312e14i	−0.351326	+	0.608515i
$880$	−2.52903e14	+	1.46014e14i	−0.479227	+	0.276682i
$881$		−	2.16265e14i		−	0.407481i	−0.979025	−	0.203740i	$-0.934690\pi$
$881$		−	2.16265e14i		−	0.407481i	0.979025	−	0.203740i	$-0.0653098\pi$
$882$	5.38852e13	+	1.31245e13i	0.100955	+	0.0245890i
$883$	5.31153e14			0.989501			0.494751	−	0.869035i	$-0.335259\pi$
$883$	5.31153e14			0.989501			0.494751	+	0.869035i	$0.335259\pi$
$884$	−2.19352e12	−	3.79929e12i	−0.00406332	−	0.00703787i
$885$	3.70100e14	+	2.13677e14i	0.681715	+	0.393588i
$886$	−1.55528e14	+	2.69383e14i	−0.284866	+	0.493402i
$887$	−4.03159e14	+	2.32764e14i	−0.734274	+	0.423933i	−0.819984	−	0.572387i	$-0.806018\pi$
$887$	−4.03159e14	+	2.32764e14i	−0.734274	+	0.423933i	0.0857096	+	0.996320i	$0.472684\pi$
$888$			2.95995e14i			0.536067i
$889$	8.12920e14	+	6.09124e14i	1.46399	+	1.09698i
$890$	−1.06925e14			−0.191483
$891$	2.48531e13	+	4.30468e13i	0.0442580	+	0.0766571i
$892$	−5.19549e14	−	2.99962e14i	−0.920031	−	0.531180i
$893$	−9.47969e13	+	1.64193e14i	−0.166931	+	0.289133i
$894$	7.54433e13	−	4.35572e13i	0.132109	−	0.0762733i
$895$			7.11955e14i			1.23976i
$896$	−6.61607e13	+	5.51211e14i	−0.114567	+	0.954504i
$897$	5.39803e14			0.929551
$898$	4.31236e13	+	7.46923e13i	0.0738471	+	0.127907i
$899$	−1.69359e13	−	9.77796e12i	−0.0288410	−	0.0166514i
$900$	−5.67808e12	+	9.83472e12i	−0.00961588	+	0.0166552i
$901$	5.82821e12	−	3.36492e12i	0.00981547	−	0.00566697i
$902$			1.71205e14i			0.286737i
$903$	9.71524e11	+	2.27159e12i	0.00161814	+	0.00378348i
$904$	−5.53319e14			−0.916502
$905$	4.71028e13	+	8.15844e13i	0.0775896	+	0.134389i
$906$	−9.10573e13	−	5.25720e13i	−0.149167	−	0.0861218i
$907$	7.01954e12	−	1.21582e13i	0.0114360	−	0.0198077i	−0.860251	−	0.509871i	$-0.829693\pi$
$907$	7.01954e12	−	1.21582e13i	0.0114360	−	0.0198077i	0.871687	+	0.490063i	$0.163026\pi$
$908$	7.54285e14	−	4.35487e14i	1.22210	−	0.705579i
$909$		−	2.61234e14i		−	0.420930i
$910$	−1.92231e14	+	8.22142e13i	−0.308047	+	0.131747i
$911$	4.82962e14			0.769700			0.384850	−	0.922979i	$-0.374253\pi$
$911$	4.82962e14			0.769700			0.384850	+	0.922979i	$0.374253\pi$
$912$	−8.32431e13	−	1.44181e14i	−0.131939	−	0.228526i
$913$	5.82261e14	+	3.36168e14i	0.917833	+	0.529911i
$914$	1.01802e14	−	1.76327e14i	0.159598	−	0.276431i
$915$	−2.77290e14	+	1.60093e14i	−0.432343	+	0.249613i
$916$		−	1.27734e14i		−	0.198075i
$917$	−6.76091e14	−	8.11499e13i	−1.04270	−	0.125153i
$918$	−3.16903e11			−0.000486086
$919$	4.54725e14	+	7.87607e14i	0.693700	+	1.20152i	0.970617	+	0.240630i	$0.0773539\pi$
$919$	4.54725e14	+	7.87607e14i	0.693700	+	1.20152i	−0.276917	+	0.960894i	$0.589313\pi$
$920$	4.74740e14	+	2.74091e14i	0.720305	+	0.415868i
$921$	2.67147e14	−	4.62711e14i	0.403136	−	0.698252i
$922$	−7.00047e13	+	4.04173e13i	−0.105069	+	0.0606614i
$923$		−	1.05549e15i		−	1.57559i
$924$	−1.67712e14	+	2.23823e14i	−0.249002	+	0.332312i
$925$	−6.77422e13			−0.100035
$926$	−1.80291e13	−	3.12273e13i	−0.0264800	−	0.0458648i
$927$	8.00350e13	+	4.62082e13i	0.116918	+	0.0675026i
$928$	3.68312e13	−	6.37936e13i	0.0535151	−	0.0926909i
$929$	3.40644e14	−	1.96671e14i	0.492292	−	0.284225i	−0.233233	−	0.972421i	$-0.574930\pi$
$929$	3.40644e14	−	1.96671e14i	0.492292	−	0.284225i	0.725525	+	0.688196i	$0.241597\pi$
$930$			3.07922e13i			0.0442615i
$931$	−3.21979e14	−	3.07568e14i	−0.460340	−	0.439737i
$932$	−1.84660e13			−0.0262599
$933$	7.86870e13	+	1.36290e14i	0.111300	+	0.192777i
$934$	−1.13387e14	−	6.54639e13i	−0.159525	−	0.0921017i
$935$	2.23144e12	−	3.86497e12i	0.00312268	−	0.00540864i
$936$	−1.36654e14	+	7.88972e13i	−0.190214	+	0.109820i
$937$		−	4.47271e14i		−	0.619259i	−0.950857	−	0.309630i	$-0.899795\pi$
$937$		−	4.47271e14i		−	0.619259i	0.950857	−	0.309630i	$-0.100205\pi$
$938$	2.85638e14	+	2.14030e14i	0.393371	+	0.294754i
$939$	−9.91736e13			−0.135853
$940$	−1.68099e14	−	2.91156e14i	−0.229047	−	0.396722i
$941$	−1.32505e14	−	7.65019e13i	−0.179591	−	0.103687i	0.407509	−	0.913201i	$-0.366397\pi$
$941$	−1.32505e14	−	7.65019e13i	−0.179591	−	0.103687i	−0.587101	+	0.809514i	$0.699731\pi$
$942$	9.14724e13	−	1.58435e14i	0.123321	−	0.213597i
$943$	−1.08071e15	+	6.23948e14i	−1.44928	+	0.836739i
$944$			7.58436e14i			1.01172i
$945$	1.67230e13	−	1.39326e14i	0.0221899	−	0.184872i
$946$	1.34094e12			0.00176993
$947$	−6.65886e14	−	1.15335e15i	−0.874279	−	1.51429i	−0.857529	−	0.514435i	$-0.828002\pi$
$947$	−6.65886e14	−	1.15335e15i	−0.874279	−	1.51429i	−0.0167493	−	0.999860i	$-0.505332\pi$
$948$	−2.32656e14	−	1.34324e14i	−0.303860	−	0.175433i
$949$	5.09057e14	−	8.81713e14i	0.661357	−	1.14550i
$950$	−8.49811e12	+	4.90639e12i	−0.0109826	+	0.00634080i
$951$			5.65233e14i			0.726650i
$952$	−1.47784e12	−	3.45544e12i	−0.00188992	−	0.00441895i
$953$	−1.06833e14			−0.135907			−0.0679533	−	0.997689i	$-0.521647\pi$
$953$	−1.06833e14			−0.135907			−0.0679533	+	0.997689i	$0.521647\pi$
$954$	−5.74249e13	−	9.94629e13i	−0.0726706	−	0.125869i
$955$	3.18357e14	+	1.83804e14i	0.400772	+	0.231386i
$956$	7.82894e13	−	1.35601e14i	0.0980422	−	0.169814i
$957$	4.18899e13	−	2.41852e13i	0.0521855	−	0.0301293i
$958$			3.31881e14i			0.411296i
$959$	−6.34846e14	+	2.71514e14i	−0.782664	+	0.334733i
$960$	2.11009e14			0.258788
$961$	−3.83334e14	−	6.63954e14i	−0.467693	−	0.810068i
$962$	−3.86773e14	−	2.23304e14i	−0.469441	−	0.271032i
$963$	−1.95806e14	+	3.39146e14i	−0.236426	+	0.409501i
$964$	8.68416e14	−	5.01380e14i	1.04314	−	0.602258i
$965$			1.09615e14i			0.130989i
$966$	2.17843e14	+	2.61473e13i	0.258975	+	0.0310843i
$967$	−1.51674e15			−1.79382			−0.896910	−	0.442213i	$-0.854194\pi$
$967$	−1.51674e15			−1.79382			−0.896910	+	0.442213i	$0.854194\pi$
$968$	−9.20932e13	−	1.59510e14i	−0.108355	−	0.187677i
$969$	2.20344e12	+	1.27215e12i	0.00257918	+	0.00148909i
$970$	−2.32590e14	+	4.02857e14i	−0.270852	+	0.469129i
$971$	−3.83624e13	+	2.21485e13i	−0.0444436	+	0.0256595i	−0.522057	−	0.852910i	$-0.674835\pi$
$971$	−3.83624e13	+	2.21485e13i	−0.0444436	+	0.0256595i	0.477614	+	0.878570i	$0.341502\pi$
$972$		−	5.02499e13i		−	0.0579167i
$973$	1.46098e14	−	1.94978e14i	0.167525	−	0.223574i
$974$	1.89196e14			0.215832
$975$	−1.80566e13	−	3.12750e13i	−0.0204934	−	0.0354956i
$976$	−4.92112e14	−	2.84121e14i	−0.555667	−	0.320815i
$977$	−3.94083e14	+	6.82572e14i	−0.442705	+	0.766788i	−0.997889	−	0.0649394i	$-0.979315\pi$
$977$	−3.94083e14	+	6.82572e14i	−0.442705	+	0.766788i	0.555184	+	0.831728i	$0.312648\pi$
$978$	−9.33686e13	+	5.39064e13i	−0.104353	+	0.0602484i
$979$		−	4.54868e14i		−	0.505792i
$980$	7.57801e14	−	2.21759e14i	0.838349	−	0.245330i
$981$	−2.78587e14			−0.306631
$982$	1.03023e14	+	1.78441e14i	0.112818	+	0.195406i
$983$	1.28113e15	+	7.39662e14i	1.39581	+	0.805872i	0.993950	−	0.109829i	$-0.0350304\pi$
$983$	1.28113e15	+	7.39662e14i	1.39581	+	0.805872i	0.401860	+	0.915701i	$0.368364\pi$
$984$	1.82392e14	−	3.15911e14i	0.197710	−	0.342444i
$985$	1.25236e14	−	7.23050e13i	0.135067	−	0.0779807i
$986$			3.08386e11i			0.000330911i
$987$	−2.26960e14	−	1.70062e14i	−0.242305	−	0.181560i
$988$	6.01092e14			0.638493
$989$	4.88701e12	+	8.46455e12i	0.00516490	+	0.00894586i
$990$	−6.59587e13	−	3.80813e13i	−0.0693579	−	0.0400438i
$991$	6.18623e14	−	1.07149e15i	0.647229	−	1.12103i	−0.336553	−	0.941664i	$-0.609261\pi$
$991$	6.18623e14	−	1.07149e15i	0.647229	−	1.12103i	0.983782	−	0.179368i	$-0.0574054\pi$
$992$	−1.72760e14	+	9.97433e13i	−0.179840	+	0.103831i
$993$			9.25429e13i			0.0958511i
$994$	5.11262e13	−	4.25952e14i	0.0526880	−	0.438964i
$995$	−1.34906e14			−0.138330
$996$	−3.39845e14	−	5.88630e14i	−0.346725	−	0.600545i
$997$	−1.07736e15	−	6.22014e14i	−1.09367	−	0.631428i	−0.159116	−	0.987260i	$-0.550864\pi$
$997$	−1.07736e15	−	6.22014e14i	−1.09367	−	0.631428i	−0.934550	+	0.355832i	$0.884198\pi$
$998$	−2.14609e14	+	3.71713e14i	−0.216768	+	0.375453i
$999$	2.59593e14	−	1.49876e14i	0.260895	−	0.150628i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	21.11.f.a.10.3	✓	12
3.2	odd	2		63.11.m.b.10.4		12
7.3	odd	6		147.11.d.a.97.7		12
7.4	even	3		147.11.d.a.97.8		12
7.5	odd	6	inner	21.11.f.a.19.3	yes	12
21.5	even	6		63.11.m.b.19.4		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
21.11.f.a.10.3	✓	12	1.1	even	1	trivial
21.11.f.a.19.3	yes	12	7.5	odd	6	inner
63.11.m.b.10.4		12	3.2	odd	2
63.11.m.b.19.4		12	21.5	even	6
147.11.d.a.97.7		12	7.3	odd	6
147.11.d.a.97.8		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)

\(f(q)\)	\(=\)	\(q+(-4.98749 - 8.63859i) q^{2} +(-121.500 - 70.1481i) q^{3} +(462.250 - 800.640i) q^{4} +(2618.43 - 1511.75i) q^{5} +1399.45i q^{6} +(13450.1 + 10078.2i) q^{7} -19436.3 q^{8} +(9841.50 + 17046.0i) q^{9} +O(q^{10})\)	\(q+(-4.98749 - 8.63859i) q^{2} +(-121.500 - 70.1481i) q^{3} +(462.250 - 800.640i) q^{4} +(2618.43 - 1511.75i) q^{5} +1399.45i q^{6} +(13450.1 + 10078.2i) q^{7} -19436.3 q^{8} +(9841.50 + 17046.0i) q^{9} +(-26118.8 - 15079.7i) q^{10} +(64150.2 - 111111. i) q^{11} +(-112327. + 64851.9i) q^{12} -412465. i q^{13} +(19979.2 - 166455. i) q^{14} -424185. q^{15} +(-376406. - 651954. i) q^{16} +(9963.42 + 5752.38i) q^{17} +(98168.8 - 170033. i) q^{18} +(-1.36514e6 + 788164. i) q^{19} -2.79523e6i q^{20} +(-927220. - 2.16800e6i) q^{21} -1.27979e6 q^{22} +(-4.66415e6 - 8.07854e6i) q^{23} +(2.36150e6 + 1.36342e6i) q^{24} +(-312035. + 540460. i) q^{25} +(-3.56312e6 + 2.05717e6i) q^{26} -2.76145e6i q^{27} +(1.42863e7 - 6.11004e6i) q^{28} -2.68723e6 q^{29} +(2.11562e6 + 3.66436e6i) q^{30} +(6.30236e6 + 3.63867e6i) q^{31} +(-1.37060e7 + 2.37395e7i) q^{32} +(-1.55885e7 + 9.00002e6i) q^{33} -114760. i q^{34} +(5.04538e7 + 6.05587e6i) q^{35} +1.81969e7 q^{36} +(5.42745e7 + 9.40062e7i) q^{37} +(1.36172e7 + 7.86192e6i) q^{38} +(-2.89337e7 + 5.01146e7i) q^{39} +(-5.08924e7 + 2.93828e7i) q^{40} -1.33775e8i q^{41} +(-1.41040e7 + 1.88228e7i) q^{42} -1.04778e6 q^{43} +(-5.93068e7 - 1.02722e8i) q^{44} +(5.15385e7 + 2.97558e7i) q^{45} +(-4.65248e7 + 8.05833e7i) q^{46} +(1.04162e8 - 6.01378e7i) q^{47} +1.05617e8i q^{48} +(7.93348e7 + 2.71106e8i) q^{49} +6.22509e6 q^{50} +(-807037. - 1.39783e6i) q^{51} +(-3.30236e8 - 1.90662e8i) q^{52} +(2.92480e8 - 5.06591e8i) q^{53} +(-2.38550e7 + 1.37727e7i) q^{54} -3.87916e8i q^{55} +(-2.61419e8 - 1.95883e8i) q^{56} +2.21153e8 q^{57} +(1.34026e7 + 2.32139e7i) q^{58} +(-8.72496e8 - 5.03736e8i) q^{59} +(-1.96080e8 + 3.39620e8i) q^{60} +(6.53699e8 - 3.77413e8i) q^{61} -7.25914e7i q^{62} +(-3.94238e7 + 3.28455e8i) q^{63} -4.97445e8 q^{64} +(-6.23545e8 - 1.08001e9i) q^{65} +(1.55495e8 + 8.97751e7i) q^{66} +(-1.06451e9 + 1.84378e9i) q^{67} +(9.21117e6 - 5.31807e6i) q^{68} +1.30872e9i q^{69} +(-1.99324e8 - 4.66054e8i) q^{70} +2.55897e9 q^{71} +(-1.91282e8 - 3.31310e8i) q^{72} +(2.13767e9 + 1.23418e9i) q^{73} +(5.41387e8 - 9.37710e8i) q^{74} +(7.58245e7 - 4.37773e7i) q^{75} +1.45731e9i q^{76} +(1.98263e9 - 8.47940e8i) q^{77} +5.77225e8 q^{78} +(1.03562e9 + 1.79375e9i) q^{79} +(-1.97118e9 - 1.13806e9i) q^{80} +(-1.93710e8 + 3.35516e8i) q^{81} +(-1.15563e9 + 6.67204e8i) q^{82} +5.24033e9i q^{83} +(-2.16440e9 - 2.59788e8i) q^{84} +3.47847e7 q^{85} +(5.22580e6 + 9.05136e6i) q^{86} +(3.26499e8 + 1.88504e8i) q^{87} +(-1.24684e9 + 2.15959e9i) q^{88} +(3.07035e9 - 1.77267e9i) q^{89} -5.93627e8i q^{90} +(4.15691e9 - 5.54770e9i) q^{91} -8.62400e9 q^{92} +(-5.10491e8 - 8.84197e8i) q^{93} +(-1.03901e9 - 5.99874e8i) q^{94} +(-2.38301e9 + 4.12750e9i) q^{95} +(3.33056e9 - 1.92290e9i) q^{96} -1.54240e10i q^{97} +(1.94629e9 - 2.03748e9i) q^{98} +2.52534e9 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

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