LMFDB - Embedded newform 21.11.f.a.19.6

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			19.6
Root			$-22.8056 + 39.5005i$ of defining polynomial
Character	$\chi$	$=$	21.19
Dual form			21.11.f.a.10.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(23.8056 - 41.2326i) q^{2} +(-121.500 + 70.1481i) q^{3} +(-621.416 - 1076.32i) q^{4} +(4637.22 + 2677.30i) q^{5} +6679.68i q^{6} +(-5755.42 + 15790.8i) q^{7} -10418.9 q^{8} +(9841.50 - 17046.0i) q^{9} +O(q^{10})$	\(q+(23.8056 - 41.2326i) q^{2} +(-121.500 + 70.1481i) q^{3} +(-621.416 - 1076.32i) q^{4} +(4637.22 + 2677.30i) q^{5} +6679.68i q^{6} +(-5755.42 + 15790.8i) q^{7} -10418.9 q^{8} +(9841.50 - 17046.0i) q^{9} +(220784. - 127470. i) q^{10} +(116835. + 202364. i) q^{11} +(151004. + 87182.3i) q^{12} -320679. i q^{13} +(514085. + 613221. i) q^{14} -751229. q^{15} +(388302. - 672558. i) q^{16} +(590383. - 340858. i) q^{17} +(-468566. - 811581. i) q^{18} +(-1.45200e6 - 838310. i) q^{19} -6.65487e6i q^{20} +(-408413. - 2.32232e6i) q^{21} +1.11253e7 q^{22} +(-3.23715e6 + 5.60690e6i) q^{23} +(1.26590e6 - 730866. i) q^{24} +(9.45304e6 + 1.63732e7i) q^{25} +(-1.32224e7 - 7.63397e6i) q^{26} +2.76145e6i q^{27} +(2.05726e7 - 3.61798e6i) q^{28} +3.89328e7 q^{29} +(-1.78835e7 + 3.09751e7i) q^{30} +(8.51944e6 - 4.91870e6i) q^{31} +(-2.38220e7 - 4.12609e7i) q^{32} +(-2.83909e7 - 1.63915e7i) q^{33} -3.24573e7i q^{34} +(-6.89659e7 + 5.78165e7i) q^{35} -2.44627e7 q^{36} +(-3.50223e7 + 6.06603e7i) q^{37} +(-6.91314e7 + 3.99130e7i) q^{38} +(2.24950e7 + 3.89625e7i) q^{39} +(-4.83147e7 - 2.78945e7i) q^{40} -1.03480e6i q^{41} +(-1.05478e8 - 3.84443e7i) q^{42} -7.79910e7 q^{43} +(1.45206e8 - 2.51504e8i) q^{44} +(9.12743e7 - 5.26973e7i) q^{45} +(1.54125e8 + 2.66952e8i) q^{46} +(-9.76660e6 - 5.63875e6i) q^{47} +1.08954e8i q^{48} +(-2.16226e8 - 1.81766e8i) q^{49} +9.00143e8 q^{50} +(-4.78210e7 + 8.28285e7i) q^{51} +(-3.45155e8 + 1.99275e8i) q^{52} +(-2.05978e8 - 3.56765e8i) q^{53} +(1.13862e8 + 6.57380e7i) q^{54} +1.25121e9i q^{55} +(5.99652e7 - 1.64523e8i) q^{56} +2.35223e8 q^{57} +(9.26821e8 - 1.60530e9i) q^{58} +(7.52579e8 - 4.34502e8i) q^{59} +(4.66826e8 + 8.08567e8i) q^{60} +(-1.35409e9 - 7.81782e8i) q^{61} -4.68371e8i q^{62} +(2.12528e8 + 2.53512e8i) q^{63} -1.47315e9 q^{64} +(8.58554e8 - 1.48706e9i) q^{65} +(-1.35172e9 + 7.80419e8i) q^{66} +(-2.66373e8 - 4.61372e8i) q^{67} +(-7.33747e8 - 4.23629e8i) q^{68} -9.08319e8i q^{69} +(7.42147e8 + 4.22000e9i) q^{70} -5.77691e8 q^{71} +(-1.02538e8 + 1.77600e8i) q^{72} +(6.26346e8 - 3.61621e8i) q^{73} +(1.66745e9 + 2.88812e9i) q^{74} +(-2.29709e9 - 1.32623e9i) q^{75} +2.08376e9i q^{76} +(-3.86793e9 + 6.80230e8i) q^{77} +2.14203e9 q^{78} +(5.84483e8 - 1.01235e9i) q^{79} +(3.60128e9 - 2.07920e9i) q^{80} +(-1.93710e8 - 3.35516e8i) q^{81} +(-4.26675e7 - 2.46341e7i) q^{82} +6.01623e8i q^{83} +(-2.24577e9 + 1.88271e9i) q^{84} +3.65031e9 q^{85} +(-1.85663e9 + 3.21577e9i) q^{86} +(-4.73034e9 + 2.73106e9i) q^{87} +(-1.21729e9 - 2.10841e9i) q^{88} +(-7.28042e9 - 4.20335e9i) q^{89} -5.01797e9i q^{90} +(5.06379e9 + 1.84564e9i) q^{91} +8.04647e9 q^{92} +(-6.90074e8 + 1.19524e9i) q^{93} +(-4.65000e8 + 2.68468e8i) q^{94} +(-4.48881e9 - 7.77485e9i) q^{95} +(5.78875e9 + 3.34214e9i) q^{96} -4.45744e9i q^{97} +(-1.26421e10 + 4.58848e9i) q^{98} +4.59932e9 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 $\left(\mathbb{Z}/21\mathbb{Z}\right)^\times$.

$n$	$8$	$10$
$\chi(n)$	$1$	$e\left(\frac{5}{6}\right)$

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 $

$2$	23.8056	−	41.2326i	0.743926	−	1.28852i	−0.206769	−	0.978390i	$-0.566295\pi$
$2$	23.8056	−	41.2326i	0.743926	−	1.28852i	0.950695	−	0.310128i	$-0.100372\pi$
$3$	−121.500	+	70.1481i	−0.500000	+	0.288675i
$3$	−121.500	+	70.1481i	−0.500000	+	0.288675i
$4$	−621.416	−	1076.32i	−0.606852	−	1.05110i
$5$	4637.22	+	2677.30i	1.48391	+	0.856736i	0.999833	−	0.0182900i	$-0.00582221\pi$
$5$	4637.22	+	2677.30i	1.48391	+	0.856736i	0.484077	+	0.875026i	$0.339156\pi$
$6$			6679.68i			0.859012i
$7$	−5755.42	+	15790.8i	−0.342442	+	0.939539i
$7$	−5755.42	+	15790.8i	−0.342442	+	0.939539i
$8$	−10418.9			−0.317960
$9$	9841.50	−	17046.0i	0.166667	−	0.288675i
$10$	220784.	−	127470.i	2.20784	−	1.27470i
$11$	116835.	+	202364.i	0.725452	+	1.25652i	0.958788	+	0.284124i	$0.0917027\pi$
$11$	116835.	+	202364.i	0.725452	+	1.25652i	−0.233335	+	0.972396i	$0.574964\pi$
$12$	151004.	+	87182.3i	0.606852	+	0.350366i
$13$		−	320679.i		−	0.863682i	−0.901950	−	0.431841i	$-0.857864\pi$
$13$		−	320679.i		−	0.863682i	0.901950	−	0.431841i	$-0.142136\pi$
$14$	514085.	+	613221.i	0.955861	+	1.14019i
$15$	−751229.			−0.989273
$16$	388302.	−	672558.i	0.370313	−	0.641402i
$17$	590383.	−	340858.i	0.415805	−	0.240065i	−0.277476	−	0.960733i	$-0.589498\pi$
$17$	590383.	−	340858.i	0.415805	−	0.240065i	0.693281	+	0.720668i	$0.256165\pi$
$18$	−468566.	−	811581.i	−0.247975	−	0.429506i
$19$	−1.45200e6	−	838310.i	−0.586405	−	0.338561i	0.177270	−	0.984162i	$-0.443273\pi$
$19$	−1.45200e6	−	838310.i	−0.586405	−	0.338561i	−0.763675	+	0.645601i	$0.776607\pi$
$20$		−	6.65487e6i		−	2.07965i
$21$	−408413.	−	2.32232e6i	−0.100001	−	0.568624i
$22$	1.11253e7			2.15873
$23$	−3.23715e6	+	5.60690e6i	−0.502948	+	0.871132i	0.497046	+	0.867724i	$0.334418\pi$
$23$	−3.23715e6	+	5.60690e6i	−0.502948	+	0.871132i	−0.999994	+	0.00340778i	$0.998915\pi$
$24$	1.26590e6	−	730866.i	0.158980	−	0.0917870i
$25$	9.45304e6	+	1.63732e7i	0.967992	+	1.67661i
$26$	−1.32224e7	−	7.63397e6i	−1.11287	−	0.642516i
$27$			2.76145e6i			0.192450i
$28$	2.05726e7	−	3.61798e6i	1.19536	−	0.210221i
$29$	3.89328e7			1.89813			0.949065	−	0.315080i	$-0.102031\pi$
$29$	3.89328e7			1.89813			0.949065	+	0.315080i	$0.102031\pi$
$30$	−1.78835e7	+	3.09751e7i	−0.735946	+	1.27470i
$31$	8.51944e6	−	4.91870e6i	0.297579	−	0.171807i	−0.343776	−	0.939052i	$-0.611706\pi$
$31$	8.51944e6	−	4.91870e6i	0.297579	−	0.171807i	0.641355	+	0.767244i	$0.278373\pi$
$32$	−2.38220e7	−	4.12609e7i	−0.709951	−	1.22967i
$33$	−2.83909e7	−	1.63915e7i	−0.725452	−	0.418840i
$34$		−	3.24573e7i		−	0.714362i
$35$	−6.89659e7	+	5.78165e7i	−1.31309	+	1.10081i
$36$	−2.44627e7			−0.404568
$37$	−3.50223e7	+	6.06603e7i	−0.505051	+	0.874775i	0.494932	+	0.868932i	$0.335193\pi$
$37$	−3.50223e7	+	6.06603e7i	−0.505051	+	0.874775i	−0.999983	+	0.00584267i	$0.998140\pi$
$38$	−6.91314e7	+	3.99130e7i	−0.872483	+	0.503728i
$39$	2.24950e7	+	3.89625e7i	0.249324	+	0.431841i
$40$	−4.83147e7	−	2.78945e7i	−0.471823	−	0.272407i
$41$		−	1.03480e6i		−	0.00893176i	−0.999990	−	0.00446588i	$-0.998578\pi$
$41$		−	1.03480e6i		−	0.00893176i	0.999990	−	0.00446588i	$-0.00142154\pi$
$42$	−1.05478e8	−	3.84443e7i	−0.807075	−	0.294162i
$43$	−7.79910e7			−0.530521			−0.265260	−	0.964177i	$-0.585458\pi$
$43$	−7.79910e7			−0.530521			−0.265260	+	0.964177i	$0.585458\pi$
$44$	1.45206e8	−	2.51504e8i	0.880484	−	1.52504i
$45$	9.12743e7	−	5.26973e7i	0.494636	−	0.285579i
$46$	1.54125e8	+	2.66952e8i	0.748313	+	1.29612i
$47$	−9.76660e6	−	5.63875e6i	−0.0425848	−	0.0245863i	0.478556	−	0.878057i	$-0.341160\pi$
$47$	−9.76660e6	−	5.63875e6i	−0.0425848	−	0.0245863i	−0.521141	+	0.853470i	$0.674494\pi$
$48$			1.08954e8i			0.427601i
$49$	−2.16226e8	−	1.81766e8i	−0.765467	−	0.643475i
$50$	9.00143e8			2.88046
$51$	−4.78210e7	+	8.28285e7i	−0.138602	+	0.240065i
$52$	−3.45155e8	+	1.99275e8i	−0.907815	+	0.524127i
$53$	−2.05978e8	−	3.56765e8i	−0.492540	−	0.853105i	0.507423	−	0.861697i	$-0.330598\pi$
$53$	−2.05978e8	−	3.56765e8i	−0.492540	−	0.853105i	−0.999963	+	0.00859220i	$0.997265\pi$
$54$	1.13862e8	+	6.57380e7i	0.247975	+	0.143169i
$55$			1.25121e9i			2.48608i
$56$	5.99652e7	−	1.64523e8i	0.108883	−	0.298735i
$57$	2.35223e8			0.390936
$58$	9.26821e8	−	1.60530e9i	1.41207	−	2.44577i
$59$	7.52579e8	−	4.34502e8i	1.05267	−	0.607759i	0.129274	−	0.991609i	$-0.458735\pi$
$59$	7.52579e8	−	4.34502e8i	1.05267	−	0.607759i	0.923395	+	0.383850i	$0.125402\pi$
$60$	4.66826e8	+	8.08567e8i	0.600342	+	1.03982i
$61$	−1.35409e9	−	7.81782e8i	−1.60323	−	0.925628i	−0.990835	−	0.135079i	$-0.956871\pi$
$61$	−1.35409e9	−	7.81782e8i	−1.60323	−	0.925628i	−0.612399	−	0.790549i	$-0.709796\pi$
$62$		−	4.68371e8i		−	0.511248i
$63$	2.12528e8	+	2.53512e8i	0.214148	+	0.255444i
$64$	−1.47315e9			−1.37198
$65$	8.58554e8	−	1.48706e9i	0.739947	−	1.28163i
$66$	−1.35172e9	+	7.80419e8i	−1.07937	+	0.623172i
$67$	−2.66373e8	−	4.61372e8i	−0.197295	−	0.341726i	0.750355	−	0.661035i	$-0.229882\pi$
$67$	−2.66373e8	−	4.61372e8i	−0.197295	−	0.341726i	−0.947651	+	0.319309i	$0.896549\pi$
$68$	−7.33747e8	−	4.23629e8i	−0.504664	−	0.291368i
$69$		−	9.08319e8i		−	0.580755i
$70$	7.42147e8	+	4.22000e9i	0.441570	+	2.51086i
$71$	−5.77691e8			−0.320187			−0.160094	−	0.987102i	$-0.551180\pi$
$71$	−5.77691e8			−0.320187			−0.160094	+	0.987102i	$0.551180\pi$
$72$	−1.02538e8	+	1.77600e8i	−0.0529933	+	0.0917870i
$73$	6.26346e8	−	3.61621e8i	0.302134	−	0.174437i	−0.341267	−	0.939966i	$-0.610856\pi$
$73$	6.26346e8	−	3.61621e8i	0.302134	−	0.174437i	0.643401	+	0.765529i	$0.277523\pi$
$74$	1.66745e9	+	2.88812e9i	0.751442	+	1.30154i
$75$	−2.29709e9	−	1.32623e9i	−0.967992	−	0.558870i
$76$			2.08376e9i			0.821825i
$77$	−3.86793e9	+	6.80230e8i	−1.42898	+	0.251306i
$78$	2.14203e9			0.741913
$79$	5.84483e8	−	1.01235e9i	0.189949	−	0.329001i	−0.755284	−	0.655397i	$-0.772501\pi$
$79$	5.84483e8	−	1.01235e9i	0.189949	−	0.329001i	0.945233	+	0.326397i	$0.105834\pi$
$80$	3.60128e9	−	2.07920e9i	1.09902	−	0.634521i
$81$	−1.93710e8	−	3.35516e8i	−0.0555556	−	0.0962250i
$82$	−4.26675e7	−	2.46341e7i	−0.0115087	−	0.00664457i
$83$			6.01623e8i			0.152733i	0.997080	+	0.0763667i	$0.0243320\pi$
$83$			6.01623e8i			0.152733i	−0.997080	+	0.0763667i	$0.975668\pi$
$84$	−2.24577e9	+	1.88271e9i	−0.536994	+	0.450181i
$85$	3.65031e9			0.822689
$86$	−1.85663e9	+	3.21577e9i	−0.394668	+	0.683586i
$87$	−4.73034e9	+	2.73106e9i	−0.949065	+	0.547943i
$88$	−1.21729e9	−	2.10841e9i	−0.230665	−	0.399523i
$89$	−7.28042e9	−	4.20335e9i	−1.30379	−	0.752741i	−0.322734	−	0.946490i	$-0.604602\pi$
$89$	−7.28042e9	−	4.20335e9i	−1.30379	−	0.752741i	−0.981051	+	0.193749i	$0.937935\pi$
$90$		−	5.01797e9i		−	0.849797i
$91$	5.06379e9	+	1.84564e9i	0.811463	+	0.295761i
$92$	8.04647e9			1.22086
$93$	−6.90074e8	+	1.19524e9i	−0.0991930	+	0.171807i
$94$	−4.65000e8	+	2.68468e8i	−0.0633598	+	0.0365808i
$95$	−4.48881e9	−	7.77485e9i	−0.580114	−	1.00479i
$96$	5.78875e9	+	3.34214e9i	0.709951	+	0.409891i
$97$		−	4.45744e9i		−	0.519071i	−0.965734	−	0.259536i	$-0.916431\pi$
$97$		−	4.45744e9i		−	0.519071i	0.965734	−	0.259536i	$-0.0835695\pi$
$98$	−1.26421e10	+	4.58848e9i	−1.39858	+	0.507620i
$99$	4.59932e9			0.483635
$100$	1.17486e10	−	2.03491e10i	1.17486	−	2.03491i
$101$	−4.37531e9	+	2.52609e9i	−0.416296	+	0.240348i	−0.693491	−	0.720465i	$-0.743928\pi$
$101$	−4.37531e9	+	2.52609e9i	−0.416296	+	0.240348i	0.277196	+	0.960814i	$0.410595\pi$
$102$	2.27682e9	+	3.94357e9i	0.206219	+	0.357181i
$103$	5.78873e9	+	3.34213e9i	0.499341	+	0.288295i	0.728441	−	0.685108i	$-0.240245\pi$
$103$	5.78873e9	+	3.34213e9i	0.499341	+	0.288295i	−0.229100	+	0.973403i	$0.573578\pi$
$104$			3.34113e9i			0.274616i
$105$	4.32364e9	−	1.18625e10i	0.338768	−	0.929461i
$106$	−1.96138e10			−1.46565
$107$	−3.49517e9	+	6.05382e9i	−0.249201	+	0.431629i	−0.963304	−	0.268411i	$-0.913501\pi$
$107$	−3.49517e9	+	6.05382e9i	−0.249201	+	0.431629i	0.714103	+	0.700040i	$0.246835\pi$
$108$	2.97222e9	−	1.71601e9i	0.202284	−	0.116789i
$109$	6.96014e9	+	1.20553e10i	0.452362	+	0.783513i	0.998532	−	0.0541607i	$-0.0172483\pi$
$109$	6.96014e9	+	1.20553e10i	0.452362	+	0.783513i	−0.546171	+	0.837674i	$0.683915\pi$
$110$	5.15905e10	+	2.97858e10i	3.20336	+	1.84946i
$111$		−	9.82697e9i		−	0.583183i
$112$	8.38542e9	+	1.00025e10i	0.475811	+	0.567567i
$113$	3.00952e10			1.63345			0.816725	−	0.577028i	$-0.195787\pi$
$113$	3.00952e10			1.63345			0.816725	+	0.577028i	$0.195787\pi$
$114$	5.59964e9	−	9.69886e9i	0.290828	−	0.503728i
$115$	−3.00227e10	+	1.73336e10i	−1.49266	+	0.861787i
$116$	−2.41935e10	−	4.19044e10i	−1.15188	−	1.99512i
$117$	−5.46629e9	−	3.15596e9i	−0.249324	−	0.143947i
$118$		−	4.13743e10i		−	1.80851i
$119$	1.98453e9	+	1.12844e10i	0.0831615	+	0.472873i
$120$	7.82698e9			0.314549
$121$	−1.43320e10	+	2.48238e10i	−0.552562	+	0.957066i
$122$	−6.44697e10	+	3.72216e10i	−2.38538	+	1.37720i
$123$	7.25892e7	+	1.25728e8i	0.00257838	+	0.00446588i
$124$	−1.05882e10	−	6.11312e9i	−0.361173	−	0.208523i
$125$			4.89435e10i			1.60378i
$126$	1.55123e10	−	2.72806e9i	0.488455	−	0.0859017i
$127$	−5.23288e9			−0.158388			−0.0791940	−	0.996859i	$-0.525235\pi$
$127$	−5.23288e9			−0.158388			−0.0791940	+	0.996859i	$0.525235\pi$
$128$	−1.06755e10	+	1.84906e10i	−0.310699	+	0.538147i
$129$	9.47591e9	−	5.47092e9i	0.265260	−	0.153148i
$130$	−4.08768e10	−	7.08008e10i	−1.10093	−	1.90687i
$131$	−4.48326e10	−	2.58841e10i	−1.16208	−	0.670929i	−0.210281	−	0.977641i	$-0.567438\pi$
$131$	−4.48326e10	−	2.58841e10i	−1.16208	−	0.670929i	−0.951802	+	0.306712i	$0.900771\pi$
$132$			4.07437e10i			1.01670i
$133$	2.15945e10	−	1.81034e10i	0.518901	−	0.435013i
$134$	−2.53648e10			−0.587093
$135$	−7.39322e9	+	1.28054e10i	−0.164879	+	0.285579i
$136$	−6.15114e9	+	3.55136e9i	−0.132209	+	0.0763310i
$137$	−4.33233e10	−	7.50381e10i	−0.897673	−	1.55482i	−0.830461	−	0.557077i	$-0.811923\pi$
$137$	−4.33233e10	−	7.50381e10i	−0.897673	−	1.55482i	−0.0672124	−	0.997739i	$-0.521411\pi$
$138$	−3.74523e10	−	2.16231e10i	−0.748313	−	0.432039i
$139$			1.62051e10i			0.312305i	0.987733	+	0.156152i	$0.0499091\pi$
$139$			1.62051e10i			0.312305i	−0.987733	+	0.156152i	$0.950091\pi$
$140$	1.05086e11	+	3.83016e10i	1.95391	+	0.712158i
$141$	1.58219e9			0.0283898
$142$	−1.37523e10	+	2.38197e10i	−0.238196	+	0.412567i
$143$	6.48939e10	−	3.74665e10i	1.08523	−	0.626560i
$144$	−7.64294e9	−	1.32380e10i	−0.123438	−	0.213801i
$145$	1.80540e11	+	1.04235e11i	2.81665	+	1.62620i
$146$		−	3.44345e10i		−	0.519074i
$147$	3.90219e10	+	6.91674e9i	0.568489	+	0.100766i
$148$	8.70536e10			1.22597
$149$	−4.44083e9	+	7.69175e9i	−0.0604690	+	0.104735i	−0.894675	−	0.446717i	$-0.852593\pi$
$149$	−4.44083e9	+	7.69175e9i	−0.0604690	+	0.104735i	0.834206	+	0.551453i	$0.185926\pi$
$150$	−1.09367e11	+	6.31433e10i	−1.44023	+	0.831516i
$151$	−4.77294e9	−	8.26697e9i	−0.0607996	−	0.105308i	0.834023	−	0.551729i	$-0.186032\pi$
$151$	−4.77294e9	−	8.26697e9i	−0.0607996	−	0.105308i	−0.894823	+	0.446421i	$0.852698\pi$
$152$	1.51282e10	+	8.73427e9i	0.186453	+	0.107649i
$153$		−	1.34182e10i		−	0.160043i
$154$	−6.40308e10	+	1.75678e11i	−0.739240	+	2.02821i
$155$	5.26753e10			0.588774
$156$	2.79576e10	−	4.84239e10i	0.302605	−	0.524127i
$157$	4.29488e10	−	2.47965e10i	0.450249	−	0.259951i	−0.257686	−	0.966229i	$-0.582960\pi$
$157$	4.29488e10	−	2.47965e10i	0.450249	−	0.259951i	0.707935	+	0.706277i	$0.249627\pi$
$158$	−2.78280e10	−	4.81995e10i	−0.282616	−	0.489505i
$159$	5.00527e10	+	2.88979e10i	0.492540	+	0.284368i
$160$		−	2.55115e11i		−	2.43296i
$161$	−6.99065e10	−	8.33874e10i	−0.646232	−	0.770852i
$162$	−1.84456e10			−0.165317
$163$	2.09616e10	−	3.63065e10i	0.182174	−	0.315534i	−0.760447	−	0.649400i	$-0.775020\pi$
$163$	2.09616e10	−	3.63065e10i	0.182174	−	0.315534i	0.942620	+	0.333866i	$0.108353\pi$
$164$	−1.11378e9	+	6.43042e8i	−0.00938816	+	0.00542026i
$165$	−8.77697e10	−	1.52022e11i	−0.717670	−	1.24304i
$166$	2.48065e10	+	1.43220e10i	0.196800	+	0.113622i
$167$			2.86900e10i			0.220876i	0.993883	+	0.110438i	$0.0352254\pi$
$167$			2.86900e10i			0.220876i	−0.993883	+	0.110438i	$0.964775\pi$
$168$	4.25521e9	+	2.41960e10i	0.0317962	+	0.180799i
$169$	3.50233e10			0.254053
$170$	8.68980e10	−	1.50512e11i	0.612019	−	1.06005i
$171$	−2.85796e10	+	1.65005e10i	−0.195468	+	0.112854i
$172$	4.84649e10	+	8.39437e10i	0.321948	+	0.557630i
$173$	−1.28445e11	−	7.41579e10i	−0.828872	−	0.478549i	0.0245945	−	0.999698i	$-0.492171\pi$
$173$	−1.28445e11	−	7.41579e10i	−0.828872	−	0.478549i	−0.853466	+	0.521148i	$0.825504\pi$
$174$			2.60059e11i			1.63052i
$175$	−3.12952e11	+	5.50371e10i	−1.90672	+	0.335324i
$176$	1.81469e11			1.07458
$177$	−6.09589e10	+	1.05584e11i	−0.350890	+	0.607759i
$178$	−3.46630e11	+	2.00127e11i	−1.93984	+	1.11997i
$179$	1.82101e11	+	3.15407e11i	0.990937	+	1.71635i	0.611799	+	0.791014i	$0.290446\pi$
$179$	1.82101e11	+	3.15407e11i	0.990937	+	1.71635i	0.379138	+	0.925340i	$0.376220\pi$
$180$	−1.13439e11	−	6.54939e10i	−0.600342	−	0.346608i
$181$		−	2.53268e11i		−	1.30373i	−0.758336	−	0.651864i	$-0.773987\pi$
$181$		−	2.53268e11i		−	1.30373i	0.758336	−	0.651864i	$-0.226013\pi$
$182$	1.96647e11	−	1.64856e11i	0.984762	−	0.825561i
$183$	2.19362e11			1.06882
$184$	3.37275e10	−	5.84178e10i	0.159917	−	0.276985i
$185$	−3.24812e11	+	1.87530e11i	−1.49890	+	0.865391i
$186$	3.28553e10	+	5.69071e10i	0.147585	+	0.255624i
$187$	1.37955e11	+	7.96481e10i	0.603293	+	0.348311i
$188$			1.40160e10i			0.0596810i
$189$	−4.36056e10	−	1.58933e10i	−0.180814	−	0.0659030i
$190$	−4.27436e11			−1.72625
$191$	1.86193e11	−	3.22496e11i	0.732481	−	1.26869i	−0.223339	−	0.974741i	$-0.571696\pi$
$191$	1.86193e11	−	3.22496e11i	0.732481	−	1.26869i	0.955820	−	0.293953i	$-0.0949710\pi$
$192$	1.78988e11	−	1.03339e11i	0.685989	−	0.396056i
$193$	6.20777e10	+	1.07522e11i	0.231819	+	0.401522i	0.958343	−	0.285618i	$-0.0921990\pi$
$193$	6.20777e10	+	1.07522e11i	0.231819	+	0.401522i	−0.726525	+	0.687141i	$0.758866\pi$
$194$	−1.83792e11	−	1.06112e11i	−0.668832	−	0.386151i
$195$			2.40904e11i			0.854418i
$196$	−6.12729e10	+	3.45681e11i	−0.211830	+	1.19508i
$197$	8.65004e10			0.291532			0.145766	−	0.989319i	$-0.453435\pi$
$197$	8.65004e10			0.291532			0.145766	+	0.989319i	$0.453435\pi$
$198$	1.09490e11	−	1.89642e11i	0.359789	−	0.623172i
$199$	3.12588e11	−	1.80473e11i	1.00163	−	0.578290i	0.0928982	−	0.995676i	$-0.470387\pi$
$199$	3.12588e11	−	1.80473e11i	1.00163	−	0.578290i	0.908729	+	0.417386i	$0.137054\pi$
$200$	−9.84903e10	−	1.70590e11i	−0.307782	−	0.533094i
$201$	6.47288e10	+	3.73712e10i	0.197295	+	0.113909i
$202$			2.40540e11i			0.715206i
$203$	−2.24075e11	+	6.14782e11i	−0.649999	+	1.78337i
$204$	1.18867e11			0.336442
$205$	2.77047e9	−	4.79859e9i	0.00765216	−	0.0132539i
$206$	2.75609e11	−	1.59123e11i	0.742946	−	0.428940i
$207$	6.37168e10	+	1.10361e11i	0.167649	+	0.290377i
$208$	−2.15676e11	−	1.24520e11i	−0.553967	−	0.319833i
$209$		−	3.91775e11i		−	0.982439i
$210$	−3.86196e11	−	4.60670e11i	−0.945608	−	1.12796i
$211$	−6.13642e11			−1.46725			−0.733623	−	0.679557i	$-0.762172\pi$
$211$	−6.13642e11			−1.46725			−0.733623	+	0.679557i	$0.762172\pi$
$212$	−2.55996e11	+	4.43399e11i	−0.597798	+	1.03542i
$213$	7.01895e10	−	4.05239e10i	0.160094	−	0.0924301i
$214$	1.66410e11	+	2.88230e11i	0.370774	+	0.642200i
$215$	−3.61661e11	−	2.08805e11i	−0.787245	−	0.454516i
$216$		−	2.87713e10i		−	0.0611914i
$217$	2.86374e10	+	1.62838e11i	0.0595162	+	0.338421i
$218$	6.62763e11			1.34609
$219$	−5.07340e10	+	8.78739e10i	−0.100711	+	0.174437i
$220$	1.34670e12	−	7.77520e11i	2.61312	−	1.50868i
$221$	−1.09306e11	−	1.89324e11i	−0.207340	−	0.359123i
$222$	−4.05191e11	−	2.33937e11i	−0.751442	−	0.433845i
$223$		−	6.85710e11i		−	1.24342i	−0.783249	−	0.621708i	$-0.786439\pi$
$223$		−	6.85710e11i		−	1.24342i	0.783249	−	0.621708i	$-0.213561\pi$
$224$	7.88650e11	−	1.38695e11i	1.39844	−	0.245936i
$225$	3.72128e11			0.645328
$226$	7.16436e11	−	1.24090e12i	1.21517	−	2.10473i
$227$	−7.09705e11	+	4.09748e11i	−1.17747	+	0.679811i	−0.955427	−	0.295227i	$-0.904605\pi$
$227$	−7.09705e11	+	4.09748e11i	−1.17747	+	0.679811i	−0.222039	+	0.975038i	$0.571271\pi$
$228$	−1.46172e11	−	2.53177e11i	−0.237240	−	0.410913i
$229$	8.91456e10	+	5.14682e10i	0.141554	+	0.0817263i	0.569104	−	0.822265i	$-0.307290\pi$
$229$	8.91456e10	+	5.14682e10i	0.141554	+	0.0817263i	−0.427550	+	0.903992i	$0.640623\pi$
$230$			1.65055e12i			2.56442i
$231$	4.22236e11	−	3.53976e11i	0.641942	−	0.538162i
$232$	−4.05637e11			−0.603529
$233$	−5.33118e11	+	9.23388e11i	−0.776326	+	1.34464i	0.157721	+	0.987484i	$0.449585\pi$
$233$	−5.33118e11	+	9.23388e11i	−0.776326	+	1.34464i	−0.934046	+	0.357152i	$0.883748\pi$
$234$	−2.60257e11	+	1.50259e11i	−0.370957	+	0.214172i
$235$	−3.01932e10	−	5.22962e10i	−0.0421280	−	0.0729678i
$236$	−9.35329e11	−	5.40013e11i	−1.27763	−	0.737639i
$237$			1.64001e11i			0.219334i
$238$	5.12529e11	+	1.86806e11i	0.671171	+	0.244627i
$239$	4.62962e10			0.0593685			0.0296842	−	0.999559i	$-0.490550\pi$
$239$	4.62962e10			0.0593685			0.0296842	+	0.999559i	$0.490550\pi$
$240$	−2.91704e11	+	5.05246e11i	−0.366341	+	0.634521i
$241$	1.03859e12	−	5.99632e11i	1.27750	−	0.737563i	0.301110	−	0.953590i	$-0.402643\pi$
$241$	1.03859e12	−	5.99632e11i	1.27750	−	0.737563i	0.976388	+	0.216026i	$0.0693096\pi$
$242$	6.82367e11	+	1.18189e12i	0.822131	+	1.42397i
$243$	4.70716e10	+	2.71768e10i	0.0555556	+	0.0320750i
$244$			1.94325e12i			2.24688i
$245$	−5.16044e11	−	1.42179e12i	−0.584596	−	1.61066i
$246$	6.91213e9			0.00767249
$247$	−2.68829e11	+	4.65625e11i	−0.292409	+	0.506467i
$248$	−8.87632e10	+	5.12474e10i	−0.0946181	+	0.0546278i
$249$	−4.22027e10	−	7.30972e10i	−0.0440903	−	0.0763667i
$250$	2.01807e12	+	1.16513e12i	2.06650	+	1.19309i
$251$		−	1.08944e12i		−	1.09354i	−0.837283	−	0.546769i	$-0.815857\pi$
$251$		−	1.08944e12i		−	1.09354i	0.837283	−	0.546769i	$-0.184143\pi$
$252$	1.40793e11	−	3.86286e11i	0.138541	−	0.380107i
$253$	−1.51285e12			−1.45946
$254$	−1.24572e11	+	2.15765e11i	−0.117829	+	0.204086i
$255$	−4.43513e11	+	2.56062e11i	−0.411344	+	0.237490i
$256$	−2.45977e11	−	4.26045e11i	−0.223715	−	0.387486i
$257$	1.73048e9	+	9.99095e8i	0.00154348	+	0.000891130i	0.500772	−	0.865579i	$-0.333050\pi$
$257$	1.73048e9	+	9.99095e8i	0.00154348	+	0.000891130i	−0.499228	+	0.866471i	$0.666383\pi$
$258$		−	5.20955e11i		−	0.455724i
$259$	−7.56309e11	−	9.02156e11i	−0.648934	−	0.774075i
$260$	−2.13408e12			−1.79615
$261$	3.83157e11	−	6.63648e11i	0.316355	−	0.547943i
$262$	−2.13454e12	+	1.23237e12i	−1.72901	+	0.998243i
$263$	9.47595e10	+	1.64128e11i	0.0753085	+	0.130438i	0.901220	−	0.433361i	$-0.142673\pi$
$263$	9.47595e10	+	1.64128e11i	0.0753085	+	0.130438i	−0.825912	+	0.563799i	$0.809339\pi$
$264$	2.95802e11	+	1.70781e11i	0.230665	+	0.133174i
$265$		−	2.20586e12i		−	1.68791i
$266$	−2.32380e11	−	1.32136e12i	−0.174498	−	0.992230i
$267$	1.17943e12			0.869190
$268$	−3.31058e11	+	5.73409e11i	−0.239458	+	0.414754i
$269$	1.52984e12	−	8.83253e11i	1.08614	−	0.627081i	0.153591	−	0.988135i	$-0.450916\pi$
$269$	1.52984e12	−	8.83253e11i	1.08614	−	0.627081i	0.932545	+	0.361054i	$0.117583\pi$
$270$	3.52001e11	+	6.09683e11i	0.245315	+	0.424899i
$271$	9.21627e11	+	5.32102e11i	0.630534	+	0.364039i	0.780959	−	0.624582i	$-0.214731\pi$
$271$	9.21627e11	+	5.32102e11i	0.630534	+	0.364039i	−0.150425	+	0.988621i	$0.548064\pi$
$272$		−	5.29423e11i		−	0.355597i
$273$	−7.44719e11	+	1.30969e11i	−0.491111	+	0.0863688i
$274$	−4.12535e12			−2.67121
$275$	−2.20889e12	+	3.82591e12i	−1.40446	+	2.43260i
$276$	−9.77646e11	+	5.64444e11i	−0.610430	+	0.352432i
$277$	6.14882e11	+	1.06501e12i	0.377045	+	0.653061i	0.990631	−	0.136567i	$-0.0436069\pi$
$277$	6.14882e11	+	1.06501e12i	0.377045	+	0.653061i	−0.613586	+	0.789628i	$0.710274\pi$
$278$	6.68179e11	+	3.85774e11i	0.402410	+	0.232332i
$279$		−	1.93629e11i		−	0.114538i
$280$	7.18549e11	−	6.02385e11i	0.417509	−	0.350013i
$281$	2.28008e12			1.30142			0.650710	−	0.759326i	$-0.274471\pi$
$281$	2.28008e12			1.30142			0.650710	+	0.759326i	$0.274471\pi$
$282$	3.76650e10	−	6.52377e10i	0.0211199	−	0.0365808i
$283$	−7.29889e11	+	4.21402e11i	−0.402091	+	0.232147i	−0.687386	−	0.726292i	$-0.741242\pi$
$283$	−7.29889e11	+	4.21402e11i	−0.402091	+	0.232147i	0.285295	+	0.958440i	$0.407909\pi$
$284$	3.58987e11	+	6.21784e11i	0.194306	+	0.336548i
$285$	1.09078e12	+	6.29763e11i	0.580114	+	0.334929i
$286$		−	3.56766e12i		−	1.86446i
$287$	1.63404e10	+	5.95571e9i	0.00839174	+	0.00305861i
$288$	−9.37778e11			−0.473301
$289$	−7.75629e11	+	1.34343e12i	−0.384738	+	0.666385i
$290$	8.59574e12	−	4.96275e12i	4.19076	−	2.41954i
$291$	3.12681e11	+	5.41579e11i	0.149843	+	0.259536i
$292$	−7.78443e11	−	4.49435e11i	−0.366702	−	0.211715i
$293$			1.92926e12i			0.893413i	0.894681	+	0.446707i	$0.147403\pi$
$293$			1.92926e12i			0.893413i	−0.894681	+	0.446707i	$0.852597\pi$
$294$	1.21414e12	−	1.44432e12i	0.552753	−	0.657545i
$295$	4.65316e12			2.08275
$296$	3.64893e11	−	6.32014e11i	0.160586	−	0.278143i
$297$	−5.58817e11	+	3.22633e11i	−0.241817	+	0.139613i
$298$	2.11434e11	+	3.66214e11i	0.0899690	+	0.155831i
$299$	1.79802e12	+	1.03809e12i	0.752381	+	0.434388i
$300$			3.29655e12i			1.35661i
$301$	4.48871e11	−	1.23154e12i	0.181673	−	0.498445i
$302$	−4.54491e11			−0.180922
$303$	3.54400e11	−	6.13839e11i	0.138765	−	0.240348i
$304$	−1.12763e12	+	6.51035e11i	−0.434307	+	0.250747i
$305$	−4.18613e12	−	7.25058e12i	−1.58604	−	2.74710i
$306$	−5.53267e11	−	3.19429e11i	−0.206219	−	0.119060i
$307$			3.65080e12i			1.33874i	0.742929	+	0.669370i	$0.233436\pi$
$307$			3.65080e12i			1.33874i	−0.742929	+	0.669370i	$0.766564\pi$
$308$	3.13574e12	+	3.74044e12i	1.13132	+	1.34949i
$309$	−9.37775e11			−0.332894
$310$	1.25397e12	−	2.17194e12i	0.438004	−	0.758646i
$311$	−3.33228e12	+	1.92390e12i	−1.14536	+	0.661271i	−0.947751	−	0.319011i	$-0.896649\pi$
$311$	−3.33228e12	+	1.92390e12i	−1.14536	+	0.661271i	−0.197604	+	0.980282i	$0.563316\pi$
$312$	−2.34373e11	−	4.05947e11i	−0.0792749	−	0.137308i
$313$	−1.79244e12	−	1.03487e12i	−0.596655	−	0.344479i	0.171069	−	0.985259i	$-0.445278\pi$
$313$	−1.79244e12	−	1.03487e12i	−0.596655	−	0.344479i	−0.767725	+	0.640780i	$0.778611\pi$
$314$		−	2.36119e12i		−	0.773539i
$315$	3.06812e11	+	1.74459e12i	0.0989279	+	0.562524i
$316$	−1.45283e12			−0.461083
$317$	6.13455e11	−	1.06253e12i	0.191640	−	0.331930i	−0.754154	−	0.656698i	$-0.771953\pi$
$317$	6.13455e11	−	1.06253e12i	0.191640	−	0.331930i	0.945794	+	0.324768i	$0.105286\pi$
$318$	2.38307e12	−	1.37587e12i	0.732827	−	0.423098i
$319$	4.54871e12	+	7.87860e12i	1.37700	+	2.38504i
$320$	−6.83132e12	−	3.94406e12i	−2.03589	−	1.17542i
$321$		−	9.80718e11i		−	0.287753i
$322$	−5.10244e12	+	8.97338e11i	−1.47400	+	0.259225i
$323$	−1.14298e12			−0.325106
$324$	−2.40749e11	+	4.16990e11i	−0.0674280	+	0.116789i
$325$	5.25053e12	−	3.03139e12i	1.44806	−	0.836037i
$326$	−9.98006e11	−	1.72860e12i	−0.271047	−	0.469468i
$327$	−1.69131e12	−	9.76481e11i	−0.452362	−	0.261171i
$328$			1.07815e10i			0.00283994i
$329$	1.45251e11	−	1.21769e11i	0.0376826	−	0.0315907i
$330$	−8.35766e12			−2.13557
$331$	−3.03103e12	+	5.24990e12i	−0.762870	+	1.32133i	0.178495	+	0.983941i	$0.442877\pi$
$331$	−3.03103e12	+	5.24990e12i	−0.762870	+	1.32133i	−0.941365	+	0.337389i	$0.890456\pi$
$332$	6.47542e11	−	3.73858e11i	0.160538	−	0.0926865i
$333$	6.89343e11	+	1.19398e12i	0.168350	+	0.291592i
$334$	1.18296e12	+	6.82984e11i	0.284603	+	0.164315i
$335$		−	2.85265e12i		−	0.676120i
$336$	−1.72048e12	−	6.27079e11i	−0.401748	−	0.146429i
$337$	1.50869e12			0.347098			0.173549	−	0.984825i	$-0.444477\pi$
$337$	1.50869e12			0.347098			0.173549	+	0.984825i	$0.444477\pi$
$338$	8.33752e11	−	1.44410e12i	0.188996	−	0.327351i
$339$	−3.65657e12	+	2.11112e12i	−0.816725	+	0.471536i
$340$	−2.26836e12	−	3.92892e12i	−0.499250	−	0.864727i
$341$	1.99073e12	+	1.14935e12i	0.431759	+	0.249276i
$342$			1.57122e12i			0.335819i
$343$	4.11470e12	−	2.36824e12i	0.866698	−	0.498834i
$344$	8.12581e11			0.168684
$345$	2.43184e12	−	4.21207e12i	0.497553	−	0.861787i
$346$	−6.11544e12	+	3.53075e12i	−1.23324	+	0.712011i
$347$	3.17710e12	+	5.50290e12i	0.631515	+	1.09382i	0.987242	+	0.159226i	$0.0508999\pi$
$347$	3.17710e12	+	5.50290e12i	0.631515	+	1.09382i	−0.355727	+	0.934590i	$0.615767\pi$
$348$	5.87902e12	+	3.39425e12i	1.15188	+	0.665041i
$349$		−	1.09629e12i		−	0.211737i	−0.994380	−	0.105868i	$-0.966238\pi$
$349$		−	1.09629e12i		−	0.211737i	0.994380	−	0.105868i	$-0.0337623\pi$
$350$	−5.18070e12	+	1.42140e13i	−0.986389	+	2.70630i
$351$	8.85539e11			0.166216
$352$	5.56648e12	−	9.64143e12i	1.03007	−	1.78414i
$353$	−5.16044e12	+	2.97938e12i	−0.941485	+	0.543567i	−0.890426	−	0.455129i	$-0.849593\pi$
$353$	−5.16044e12	+	2.97938e12i	−0.941485	+	0.543567i	−0.0510597	+	0.998696i	$0.516260\pi$
$354$	2.90233e12	+	5.02698e12i	0.522072	+	0.904255i
$355$	−2.67888e12	−	1.54665e12i	−0.475129	−	0.274316i
$356$			1.04481e13i			1.82721i
$357$	−1.03270e12	−	1.23185e12i	−0.178087	−	0.212430i
$358$	1.73401e13			2.94874
$359$	1.79199e12	−	3.10382e12i	0.300514	−	0.520505i	−0.675739	−	0.737141i	$-0.736175\pi$
$359$	1.79199e12	−	3.10382e12i	0.300514	−	0.520505i	0.976252	+	0.216636i	$0.0695085\pi$
$360$	−9.50978e11	+	5.49048e11i	−0.157274	+	0.0908024i
$361$	−1.66001e12	−	2.87521e12i	−0.270753	−	0.468958i
$362$	−1.04429e13	−	6.02920e12i	−1.67988	−	0.969877i
$363$		−	4.02146e12i		−	0.638044i
$364$	−1.16021e12	−	6.59720e12i	−0.181564	−	1.03241i
$365$	3.87267e12			0.597787
$366$	5.22205e12	−	9.04485e12i	0.795125	−	1.37720i
$367$	−1.08123e13	+	6.24247e12i	−1.62400	+	0.937619i	−0.638169	+	0.769896i	$0.720308\pi$
$367$	−1.08123e13	+	6.24247e12i	−1.62400	+	0.937619i	−0.985834	+	0.167723i	$0.946359\pi$
$368$	2.51398e12	+	4.35434e12i	0.372497	+	0.645184i
$369$	−1.76392e10	−	1.01840e10i	−0.00257838	−	0.00148863i
$370$			1.78571e13i			2.57515i
$371$	6.81910e12	−	1.19924e12i	0.970192	−	0.170622i
$372$	1.71529e12			0.240782
$373$	3.07522e12	−	5.32644e12i	0.425924	−	0.737722i	−0.570582	−	0.821240i	$-0.693282\pi$
$373$	3.07522e12	−	5.32644e12i	0.425924	−	0.737722i	0.996506	+	0.0835187i	$0.0266158\pi$
$374$	6.56819e12	−	3.79215e12i	0.897611	−	0.518236i
$375$	−3.43329e12	−	5.94663e12i	−0.462971	−	0.801890i
$376$	1.01757e11	+	5.87496e10i	0.0135402	+	0.00781746i
$377$		−	1.24850e13i		−	1.63938i
$378$	−1.69338e12	+	1.41962e12i	−0.219430	+	0.183956i
$379$	2.23649e12			0.286003			0.143001	−	0.989722i	$-0.454325\pi$
$379$	2.23649e12			0.286003			0.143001	+	0.989722i	$0.454325\pi$
$380$	−5.57884e12	+	9.66284e12i	−0.704087	+	1.21951i
$381$	6.35795e11	−	3.67076e11i	0.0791940	−	0.0457227i
$382$	−8.86488e12	−	1.53544e13i	−1.08982	−	1.88763i
$383$	−3.98201e12	−	2.29901e12i	−0.483179	−	0.278964i	0.238561	−	0.971127i	$-0.423324\pi$
$383$	−3.98201e12	−	2.29901e12i	−0.483179	−	0.278964i	−0.721740	+	0.692164i	$0.756658\pi$
$384$		−	2.99547e12i		−	0.358764i
$385$	−1.97576e13	−	7.20122e12i	−2.33577	−	0.851339i
$386$	5.91119e12			0.689824
$387$	−7.67549e11	+	1.32943e12i	−0.0884201	+	0.153148i
$388$	−4.79765e12	+	2.76993e12i	−0.545595	+	0.314999i
$389$	2.12104e12	+	3.67376e12i	0.238123	+	0.412441i	0.960176	−	0.279397i	$-0.0901345\pi$
$389$	2.12104e12	+	3.67376e12i	0.238123	+	0.412441i	−0.722053	+	0.691838i	$0.756801\pi$
$390$	9.93307e12	+	5.73486e12i	1.10093	+	0.635624i
$391$			4.41363e12i			0.482961i
$392$	2.25283e12	+	1.89380e12i	0.243388	+	0.204599i
$393$	7.26288e12			0.774722
$394$	2.05920e12	−	3.56663e12i	0.216879	−	0.375645i
$395$	5.42075e12	−	3.12967e12i	0.563733	−	0.325472i
$396$	−2.85809e12	−	4.95036e12i	−0.293495	−	0.508348i
$397$	2.75236e12	+	1.58907e12i	0.279095	+	0.161136i	0.633014	−	0.774141i	$-0.281818\pi$
$397$	2.75236e12	+	1.58907e12i	0.279095	+	0.161136i	−0.353919	+	0.935276i	$0.615151\pi$
$398$		−	1.71851e13i		−	1.72082i
$399$	−1.35381e12	+	3.71437e12i	−0.133873	+	0.367300i
$400$	1.46825e13			1.43384
$401$	−5.17146e12	+	8.95723e12i	−0.498759	+	0.863877i	−0.999999	−	0.00143192i	$-0.999544\pi$
$401$	−5.17146e12	+	8.95723e12i	−0.498759	+	0.863877i	0.501240	+	0.865309i	$0.332878\pi$
$402$	3.08182e12	−	1.77929e12i	0.293546	−	0.169479i
$403$	−1.57732e12	−	2.73201e12i	−0.148387	−	0.257014i
$404$	5.43778e12	+	3.13950e12i	0.505260	+	0.291712i
$405$		−	2.07448e12i		−	0.190386i
$406$	2.00148e13	+	2.38745e13i	1.81435	+	2.16423i
$407$	−1.63673e13			−1.46556
$408$	4.98243e11	−	8.62982e11i	0.0440697	−	0.0763310i
$409$	4.21907e12	−	2.43588e12i	0.368638	−	0.212834i	−0.304225	−	0.952600i	$-0.598397\pi$
$409$	4.21907e12	−	2.43588e12i	0.368638	−	0.212834i	0.672863	+	0.739767i	$0.265064\pi$
$410$	−1.31906e11	−	2.28467e11i	−0.0113853	−	0.0197199i
$411$	1.05276e13	+	6.07809e12i	0.897673	+	0.518272i
$412$		−	8.30741e12i		−	0.699809i
$413$	2.52973e12	+	1.43846e13i	0.210535	+	1.19715i
$414$	6.06727e12			0.498875
$415$	−1.61072e12	+	2.78986e12i	−0.130852	+	0.226642i
$416$	−1.32315e13	+	7.63923e12i	−1.06205	+	0.613173i
$417$	−1.13676e12	−	1.96892e12i	−0.0901546	−	0.156152i
$418$	−1.61539e13	−	9.32646e12i	−1.26589	−	0.730862i
$419$		−	1.90902e13i		−	1.47823i	−0.673581	−	0.739114i	$-0.735245\pi$
$419$		−	1.90902e13i		−	1.47823i	0.673581	−	0.739114i	$-0.264755\pi$
$420$	−1.54547e13	+	2.71793e12i	−1.18254	+	0.207966i
$421$	−1.23392e13			−0.932992			−0.466496	−	0.884523i	$-0.654484\pi$
$421$	−1.23392e13			−0.932992			−0.466496	+	0.884523i	$0.654484\pi$
$422$	−1.46081e13	+	2.53020e13i	−1.09152	+	1.89057i
$423$	−1.92236e11	+	1.10988e11i	−0.0141949	+	0.00819544i
$424$	2.14607e12	+	3.71710e12i	0.156608	+	0.271253i
$425$	1.11618e13	+	6.44429e12i	0.804991	+	0.464762i
$426$		−	3.85879e12i		−	0.275045i
$427$	2.01383e13	−	1.68827e13i	1.41868	−	1.18933i
$428$	8.68783e12			0.604912
$429$	−5.25640e12	+	9.10436e12i	−0.361745	+	0.626560i
$430$	−1.72192e13	+	9.94149e12i	−1.17130	+	0.676253i
$431$	−2.45198e12	−	4.24696e12i	−0.164866	−	0.285556i	0.771742	−	0.635936i	$-0.219386\pi$
$431$	−2.45198e12	−	4.24696e12i	−0.164866	−	0.285556i	−0.936608	+	0.350380i	$0.886052\pi$
$432$	1.85724e12	+	1.07228e12i	0.123438	+	0.0712669i
$433$			2.91525e13i			1.91530i	0.287939	+	0.957649i	$0.407030\pi$
$433$			2.91525e13i			1.91530i	−0.287939	+	0.957649i	$0.592970\pi$
$434$	7.39597e12	+	2.69567e12i	0.480337	+	0.175073i
$435$	−2.92475e13			−1.87777
$436$	8.65029e12	−	1.49827e13i	0.549033	−	0.950953i
$437$	9.40065e12	−	5.42747e12i	0.589862	−	0.340557i
$438$	2.41551e12	+	4.18379e12i	0.149844	+	0.259537i
$439$	1.47458e13	+	8.51350e12i	0.904370	+	0.522138i	0.878615	−	0.477530i	$-0.158468\pi$
$439$	1.47458e13	+	8.51350e12i	0.904370	+	0.522138i	0.0257544	+	0.999668i	$0.491801\pi$
$440$		−	1.30362e13i		−	0.790474i
$441$	−5.22636e12	+	1.89693e12i	−0.313333	+	0.113726i
$442$	−1.04084e13			−0.616982
$443$	−4.69834e12	+	8.13776e12i	−0.275376	+	0.476965i	−0.970230	−	0.242186i	$-0.922136\pi$
$443$	−4.69834e12	+	8.13776e12i	−0.275376	+	0.476965i	0.694854	+	0.719151i	$0.255469\pi$
$444$	−1.05770e13	+	6.10664e12i	−0.612983	+	0.353906i
$445$	−2.25072e13	−	3.89837e13i	−1.28980	−	2.23400i
$446$	−2.82736e13	−	1.63238e13i	−1.60216	−	0.925009i
$447$		−	1.24606e12i		−	0.0698236i
$448$	8.47860e12	−	2.32623e13i	0.469823	−	1.28903i
$449$	7.36934e12			0.403828			0.201914	−	0.979403i	$-0.435284\pi$
$449$	7.36934e12			0.403828			0.201914	+	0.979403i	$0.435284\pi$
$450$	8.85875e12	−	1.53438e13i	0.480076	−	0.831516i
$451$	2.09406e11	−	1.20901e11i	0.0112229	−	0.00647957i
$452$	−1.87017e13	−	3.23923e13i	−0.991262	−	1.71692i
$453$	1.15982e12	+	6.69624e11i	0.0607996	+	0.0351027i
$454$			3.90173e13i			2.02292i
$455$	1.85406e13	+	2.21159e13i	0.950749	+	1.13409i
$456$	−2.45077e12			−0.124302
$457$	−4.95021e12	+	8.57402e12i	−0.248338	+	0.430134i	−0.963065	−	0.269270i	$-0.913218\pi$
$457$	−4.95021e12	+	8.57402e12i	−0.248338	+	0.430134i	0.714727	+	0.699404i	$0.246551\pi$
$458$	4.24433e12	−	2.45047e12i	0.210612	−	0.121597i
$459$	9.41261e11	+	1.63031e12i	0.0462005	+	0.0800216i
$460$	3.73132e13	+	2.15428e13i	1.81165	+	1.04595i
$461$			1.65820e13i			0.796404i	0.917298	+	0.398202i	$0.130366\pi$
$461$			1.65820e13i			0.796404i	−0.917298	+	0.398202i	$0.869634\pi$
$462$	−4.54372e12	−	2.58365e13i	−0.215875	−	1.22751i
$463$	−2.68551e13			−1.26218			−0.631092	−	0.775708i	$-0.717393\pi$
$463$	−2.68551e13			−1.26218			−0.631092	+	0.775708i	$0.717393\pi$
$464$	1.51177e13	−	2.61846e13i	0.702903	−	1.21746i
$465$	−6.40005e12	+	3.69507e12i	−0.294387	+	0.169964i
$466$	2.53824e13	+	4.39637e13i	1.15506	+	2.00062i
$467$	3.24694e12	+	1.87462e12i	0.146180	+	0.0843973i	0.571306	−	0.820737i	$-0.306437\pi$
$467$	3.24694e12	+	1.87462e12i	0.146180	+	0.0843973i	−0.425126	+	0.905134i	$0.639770\pi$
$468$			7.84467e12i			0.349418i
$469$	8.81855e12	−	1.55087e12i	0.388627	−	0.0683456i
$470$	−2.87508e12			−0.125360
$471$	−3.47885e12	+	6.02555e12i	−0.150083	+	0.259951i
$472$	−7.84104e12	+	4.52703e12i	−0.334706	+	0.193243i
$473$	−9.11207e12	−	1.57826e13i	−0.384868	−	0.666610i
$474$	6.76220e12	+	3.90416e12i	0.282616	+	0.163168i
$475$		−	3.16983e13i		−	1.31090i
$476$	1.09125e13	−	9.14832e12i	0.446569	−	0.374375i
$477$	−8.10854e12			−0.328360
$478$	1.10211e12	−	1.90891e12i	0.0441657	−	0.0764973i
$479$	−3.36179e12	+	1.94093e12i	−0.133319	+	0.0769720i	−0.565176	−	0.824970i	$-0.691192\pi$
$479$	−3.36179e12	+	1.94093e12i	−0.133319	+	0.0769720i	0.431857	+	0.901942i	$0.357859\pi$
$480$	1.78958e13	+	3.09964e13i	0.702336	+	1.21648i
$481$	1.94525e13	+	1.12309e13i	0.755527	+	0.436204i
$482$		−	5.70984e13i		−	2.19477i
$483$	1.43431e13	+	5.22775e12i	0.545642	+	0.198875i
$484$	3.56247e13			1.34129
$485$	1.19339e13	−	2.06701e13i	0.444707	−	0.770255i
$486$	2.24114e12	−	1.29392e12i	0.0826584	−	0.0477229i
$487$	−2.12761e12	−	3.68513e12i	−0.0776689	−	0.134527i	0.824575	−	0.565753i	$-0.191414\pi$
$487$	−2.12761e12	−	3.68513e12i	−0.0776689	−	0.134527i	−0.902244	+	0.431226i	$0.858081\pi$
$488$	1.41081e13	+	8.14531e12i	0.509764	+	0.294312i
$489$			5.88165e12i			0.210356i
$490$	−7.09087e13	−	1.25688e13i	−2.51026	−	0.444951i
$491$	4.09925e13			1.43647			0.718236	−	0.695800i	$-0.244950\pi$
$491$	4.09925e13			1.43647			0.718236	+	0.695800i	$0.244950\pi$
$492$	9.02163e10	−	1.56259e11i	0.00312939	−	0.00542026i
$493$	2.29853e13	−	1.32706e13i	0.789251	−	0.455675i
$494$	1.27993e13	+	2.21690e13i	0.435061	+	0.753548i
$495$	2.13280e13	+	1.23138e13i	0.717670	+	0.414347i
$496$		−	7.63976e12i		−	0.254490i
$497$	3.32486e12	−	9.12223e12i	0.109646	−	0.300829i
$498$	−4.01865e12			−0.131200
$499$	−6.07611e12	+	1.05241e13i	−0.196391	+	0.340160i	−0.947356	−	0.320183i	$-0.896256\pi$
$499$	−6.07611e12	+	1.05241e13i	−0.196391	+	0.340160i	0.750964	+	0.660343i	$0.229589\pi$
$500$	5.26791e13	−	3.04143e13i	1.68573	−	0.973257i
$501$	−2.01255e12	−	3.48584e12i	−0.0637614	−	0.110438i
$502$	−4.49203e13	−	2.59348e13i	−1.40904	−	0.813512i
$503$			3.12824e13i			0.971539i	0.874087	+	0.485769i	$0.161461\pi$
$503$			3.12824e13i			0.971539i	−0.874087	+	0.485769i	$0.838539\pi$
$504$	−2.21431e12	−	2.64132e12i	−0.0680904	−	0.0812210i
$505$	−2.70523e13			−0.823660
$506$	−3.60143e13	+	6.23785e13i	−1.08573	+	1.88054i
$507$	−4.25533e12	+	2.45682e12i	−0.127026	+	0.0733387i
$508$	3.25180e12	+	5.63228e12i	0.0961180	+	0.166481i
$509$	1.39937e12	+	8.07928e11i	0.0409586	+	0.0236474i	0.520339	−	0.853960i	$-0.325805\pi$
$509$	1.39937e12	+	8.07928e11i	0.0409586	+	0.0236474i	−0.479381	+	0.877607i	$0.659139\pi$
$510$			2.43829e13i			0.706699i
$511$	2.10541e12	+	1.19718e13i	0.0604273	+	0.343602i
$512$	−4.52861e13			−1.28711
$513$	2.31495e12	−	4.00961e12i	0.0651561	−	0.112854i
$514$	8.23905e10	−	4.75682e10i	0.00229647	−	0.00132587i
$515$	1.78957e13	+	3.09963e13i	0.493985	+	0.855607i
$516$	−1.17770e13	−	6.79944e12i	−0.321948	−	0.185877i
$517$		−	2.63521e12i		−	0.0713448i
$518$	−5.52026e13	+	9.70817e12i	−1.48017	+	0.260309i
$519$	2.08081e13			0.552581
$520$	−8.94519e12	+	1.54935e13i	−0.235273	+	0.407506i
$521$	3.59418e13	−	2.07510e13i	0.936291	−	0.540568i	0.0474956	−	0.998871i	$-0.484876\pi$
$521$	3.59418e13	−	2.07510e13i	0.936291	−	0.540568i	0.888796	+	0.458303i	$0.151543\pi$
$522$	−1.82426e13	−	3.15971e13i	−0.470690	−	0.815258i
$523$	−4.56925e13	−	2.63806e13i	−1.16771	−	0.674180i	−0.214574	−	0.976708i	$-0.568836\pi$
$523$	−4.56925e13	−	2.63806e13i	−1.16771	−	0.674180i	−0.953141	+	0.302528i	$0.902170\pi$
$524$			6.43392e13i			1.62862i
$525$	3.41629e13	−	2.86400e13i	0.856561	−	0.718085i
$526$	9.02324e12			0.224096
$527$	3.35315e12	−	5.80783e12i	0.0824898	−	0.142877i
$528$	−2.20484e13	+	1.27297e13i	−0.537290	+	0.310204i
$529$	−2.44998e11	−	4.24349e11i	−0.00591403	−	0.0102434i
$530$	−9.09533e13	−	5.25119e13i	−2.17490	−	1.25568i
$531$		−	1.71046e13i		−	0.405173i
$532$	−3.29043e13	−	1.19929e13i	−0.772137	−	0.281427i
$533$	−3.31839e11			−0.00771421
$534$	2.80770e13	−	4.86308e13i	0.646613	−	1.11997i
$535$	−3.24158e13	+	1.87152e13i	−0.739584	+	0.426999i
$536$	2.77532e12	+	4.80699e12i	0.0627320	+	0.108655i
$537$	−4.42504e13	−	2.55480e13i	−0.990937	−	0.572118i
$538$		−	8.41056e13i		−	1.86601i
$539$	1.15201e13	−	6.49928e13i	0.253229	−	1.42864i
$540$	1.83771e13			0.400228
$541$	−1.25112e13	+	2.16700e13i	−0.269967	+	0.467597i	−0.968853	−	0.247636i	$-0.920346\pi$
$541$	−1.25112e13	+	2.16700e13i	−0.269967	+	0.467597i	0.698886	+	0.715233i	$0.253680\pi$
$542$	4.38798e13	−	2.53340e13i	0.938142	−	0.541636i
$543$	1.77662e13	+	3.07720e13i	0.376354	+	0.651864i
$544$	−2.81282e13	−	1.62398e13i	−0.590402	−	0.340869i
$545$			7.45375e13i			1.55022i
$546$	−1.23283e13	+	3.38245e13i	−0.254062	+	0.697057i
$547$	5.61071e12			0.114573			0.0572863	−	0.998358i	$-0.481755\pi$
$547$	5.61071e12			0.114573			0.0572863	+	0.998358i	$0.481755\pi$
$548$	−5.38436e13	+	9.32598e13i	−1.08951	+	1.88709i
$549$	−2.66525e13	+	1.53878e13i	−0.534411	+	0.308543i
$550$	1.05168e14	+	1.82156e14i	2.08963	+	3.61935i
$551$	−5.65303e13	−	3.26378e13i	−1.11307	−	0.642633i
$552$			9.46368e12i			0.184657i
$553$	1.26220e13	+	1.50560e13i	0.244063	+	0.291128i
$554$	5.85507e13			1.12197
$555$	2.63097e13	−	4.55698e13i	0.499634	−	0.865391i
$556$	1.74420e13	−	1.00701e13i	0.328263	−	0.189523i
$557$	−6.97311e12	−	1.20778e13i	−0.130062	−	0.225274i	0.793638	−	0.608390i	$-0.208184\pi$
$557$	−6.97311e12	−	1.20778e13i	−0.130062	−	0.225274i	−0.923700	+	0.383116i	$0.874851\pi$
$558$	−7.98384e12	−	4.60947e12i	−0.147585	−	0.0852080i
$559$			2.50101e13i			0.458202i
$560$	1.21054e13	+	6.88339e13i	0.219806	+	1.24986i
$561$	−2.23486e13			−0.402195
$562$	5.42787e13	−	9.40134e13i	0.968161	−	1.67690i
$563$	4.86307e13	−	2.80769e13i	0.859742	−	0.496372i	−0.00418378	−	0.999991i	$-0.501332\pi$
$563$	4.86307e13	−	2.80769e13i	0.859742	−	0.496372i	0.863926	+	0.503619i	$0.167998\pi$
$564$	−9.83198e11	−	1.70295e12i	−0.0172284	−	0.0298405i
$565$	1.39558e14	+	8.05740e13i	2.42389	+	1.39943i
$566$			4.01269e13i			0.690802i
$567$	6.41296e12	−	1.12781e12i	0.109432	−	0.0192451i
$568$	6.01891e12			0.101807
$569$	−3.27912e13	+	5.67960e13i	−0.549789	+	0.952263i	0.448499	+	0.893783i	$0.351959\pi$
$569$	−3.27912e13	+	5.67960e13i	−0.549789	+	0.952263i	−0.998289	+	0.0584796i	$0.981375\pi$
$570$	5.19335e13	−	2.99838e13i	0.863124	−	0.498325i
$571$	−2.43831e13	−	4.22328e13i	−0.401706	−	0.695775i	0.592226	−	0.805772i	$-0.298249\pi$
$571$	−2.43831e13	−	4.22328e13i	−0.401706	−	0.695775i	−0.993932	+	0.109997i	$0.964916\pi$
$572$	−8.06522e13	−	4.65646e13i	−1.31715	−	0.760459i
$573$			5.22443e13i			0.845796i
$574$	6.34562e11	−	5.31975e11i	0.0101839	−	0.00853753i
$575$	−1.22404e14			−1.94740
$576$	−1.44980e13	+	2.51113e13i	−0.228663	+	0.396056i
$577$	3.46921e13	−	2.00295e13i	0.542440	−	0.313178i	−0.203627	−	0.979048i	$-0.565273\pi$
$577$	3.46921e13	−	2.00295e13i	0.542440	−	0.313178i	0.746067	+	0.665871i	$0.231940\pi$
$578$	3.69287e13	+	6.39623e13i	0.572433	+	0.991483i
$579$	−1.50849e13	−	8.70925e12i	−0.231819	−	0.133841i
$580$		−	2.59093e14i		−	3.94744i
$581$	−9.50013e12	−	3.46259e12i	−0.143499	−	0.0523023i
$582$	2.97743e13			0.445888
$583$	4.81309e13	−	8.33651e13i	0.714629	−	1.23777i
$584$	−6.52584e12	+	3.76769e12i	−0.0960665	+	0.0554640i
$585$	−1.68989e13	−	2.92698e13i	−0.246649	−	0.427209i
$586$	7.95483e13	+	4.59272e13i	1.15118	+	0.664633i
$587$		−	4.47535e13i		−	0.642150i	−0.947054	−	0.321075i	$-0.895956\pi$
$587$		−	4.47535e13i		−	0.642150i	0.947054	−	0.321075i	$-0.104044\pi$
$588$	−1.68042e13	−	4.62984e13i	−0.239073	−	0.658688i
$589$	−1.64936e13			−0.232669
$590$	1.10771e14	−	1.91862e14i	1.54942	−	2.68367i
$591$	−1.05098e13	+	6.06783e12i	−0.145766	+	0.0841582i
$592$	2.71984e13	+	4.71090e13i	0.374055	+	0.647882i
$593$	7.51190e13	+	4.33700e13i	1.02442	+	0.591447i	0.915380	−	0.402591i	$-0.131890\pi$
$593$	7.51190e13	+	4.33700e13i	1.02442	+	0.591447i	0.109036	+	0.994038i	$0.465224\pi$
$594$			3.07220e13i			0.415448i
$595$	−2.10091e13	+	5.76415e13i	−0.281723	+	0.772948i
$596$	1.10384e13			0.146783
$597$	−2.53196e13	+	4.38548e13i	−0.333876	+	0.578290i
$598$	8.56059e13	−	4.94246e13i	1.11943	−	0.646305i
$599$	−2.11393e13	−	3.66143e13i	−0.274129	−	0.474806i	0.695786	−	0.718249i	$-0.255056\pi$
$599$	−2.11393e13	−	3.66143e13i	−0.274129	−	0.474806i	−0.969915	+	0.243443i	$0.921723\pi$
$600$	2.39331e13	+	1.38178e13i	0.307782	+	0.177698i
$601$			1.03632e14i			1.32167i	0.750533	+	0.660833i	$0.229797\pi$
$601$			1.03632e14i			1.32167i	−0.750533	+	0.660833i	$0.770203\pi$
$602$	−4.00940e13	−	4.78258e13i	−0.507104	−	0.604895i
$603$	−1.04861e13			−0.131530
$604$	−5.93196e12	+	1.02745e13i	−0.0737927	+	0.127813i
$605$	−1.32922e14	+	7.67423e13i	−1.63990	+	0.946799i
$606$	−1.68734e13	−	2.92256e13i	−0.206462	−	0.357603i
$607$	−4.65959e13	−	2.69022e13i	−0.565463	−	0.326470i	0.189872	−	0.981809i	$-0.439193\pi$
$607$	−4.65959e13	−	2.69022e13i	−0.565463	−	0.326470i	−0.755335	+	0.655339i	$0.772526\pi$
$608$			7.98810e13i			0.961447i
$609$	−1.59007e13	−	9.04144e13i	−0.189814	−	1.07932i
$610$	−3.98614e14			−4.71957
$611$	−1.80823e12	+	3.13195e12i	−0.0212348	+	0.0367797i
$612$	−1.44424e13	+	8.33829e12i	−0.168221	+	0.0971226i
$613$	−2.42811e13	−	4.20561e13i	−0.280522	−	0.485878i	0.690992	−	0.722863i	$-0.257174\pi$
$613$	−2.42811e13	−	4.20561e13i	−0.280522	−	0.485878i	−0.971513	+	0.236985i	$0.923841\pi$
$614$	1.50532e14	+	8.69096e13i	1.72499	+	0.995923i
$615$			7.77372e11i			0.00883595i
$616$	4.02996e13	−	7.08725e12i	0.454356	−	0.0799051i
$617$	−4.73364e13			−0.529382			−0.264691	−	0.964333i	$-0.585270\pi$
$617$	−4.73364e13			−0.529382			−0.264691	+	0.964333i	$0.585270\pi$
$618$	−2.23243e13	+	3.86669e13i	−0.247649	+	0.428940i
$619$	1.05922e14	−	6.11539e13i	1.16555	−	0.672932i	0.212924	−	0.977069i	$-0.431701\pi$
$619$	1.05922e14	−	6.11539e13i	1.16555	−	0.672932i	0.952628	+	0.304137i	$0.0983680\pi$
$620$	−3.27333e13	−	5.66957e13i	−0.357299	−	0.618859i
$621$	−1.54832e13	−	8.93922e12i	−0.167649	−	0.0967925i
$622$			1.83198e14i			1.96775i
$623$	1.08276e14	−	9.07718e13i	1.15370	−	0.967187i
$624$	3.49394e13			0.369312
$625$	−3.87214e13	+	6.70675e13i	−0.406024	+	0.703254i
$626$	−8.53404e13	+	4.92713e13i	−0.887734	+	0.512534i
$627$	2.74823e13	+	4.76007e13i	0.283606	+	0.491220i
$628$	−5.33782e13	−	3.08179e13i	−0.546469	−	0.315504i
$629$			4.77504e13i			0.484980i
$630$	7.92379e13	+	2.88805e13i	0.798418	+	0.291006i
$631$	1.38094e14			1.38047			0.690235	−	0.723585i	$-0.257507\pi$
$631$	1.38094e14			1.38047			0.690235	+	0.723585i	$0.257507\pi$
$632$	−6.08967e12	+	1.05476e13i	−0.0603960	+	0.104609i
$633$	7.45575e13	−	4.30458e13i	0.733623	−	0.423557i
$634$	−2.92074e13	−	5.05886e13i	−0.285132	−	0.493863i
$635$	−2.42660e13	−	1.40100e13i	−0.235033	−	0.135697i
$636$		−	7.18306e13i		−	0.690278i
$637$	−5.82885e13	+	6.93390e13i	−0.555758	+	0.661121i
$638$	4.33140e14			4.09755
$639$	−5.68535e12	+	9.84732e12i	−0.0533646	+	0.0924301i
$640$	−9.90096e13	+	5.71632e13i	−0.922099	+	0.532374i
$641$	−7.99815e13	−	1.38532e14i	−0.739093	−	1.28015i	−0.952904	−	0.303272i	$-0.901921\pi$
$641$	−7.99815e13	−	1.38532e14i	−0.739093	−	1.28015i	0.213811	−	0.976875i	$-0.431412\pi$
$642$	−4.04375e13	−	2.33466e13i	−0.370774	−	0.214067i
$643$			3.92234e13i			0.356853i	0.983953	+	0.178427i	$0.0571008\pi$
$643$			3.92234e13i			0.356853i	−0.983953	+	0.178427i	$0.942899\pi$
$644$	−4.63108e13	+	1.27060e14i	−0.418074	+	1.14705i
$645$	5.85892e13			0.524830
$646$	−2.72093e13	+	4.71279e13i	−0.241855	+	0.418905i
$647$	−8.00601e13	+	4.62227e13i	−0.706146	+	0.407694i	−0.809632	−	0.586937i	$-0.800334\pi$
$647$	−8.00601e13	+	4.62227e13i	−0.706146	+	0.407694i	0.103486	+	0.994631i	$0.467000\pi$
$648$	2.01825e12	+	3.49571e12i	0.0176644	+	0.0305957i
$649$	1.75855e14	+	1.01530e14i	1.52732	+	0.881800i
$650$		−	2.88657e14i		−	2.48780i
$651$	−1.49022e13	−	1.77760e13i	−0.127452	−	0.152030i
$652$	−5.21034e13			−0.442210
$653$	−5.84412e13	+	1.01223e14i	−0.492213	+	0.852538i	−0.999960	−	0.00896860i	$-0.997145\pi$
$653$	−5.84412e13	+	1.01223e14i	−0.492213	+	0.852538i	0.507747	+	0.861506i	$0.330479\pi$
$654$	−8.05256e13	+	4.64915e13i	−0.673047	+	0.388584i
$655$	−1.38599e14	−	2.40060e14i	−1.14962	−	1.99120i
$656$	−6.95964e11	−	4.01815e11i	−0.00572885	−	0.00330755i
$657$		−	1.42356e13i		−	0.116292i
$658$	−1.56306e12	−	8.88789e12i	−0.0126720	−	0.0720558i
$659$	−1.09799e14			−0.883425			−0.441713	−	0.897157i	$-0.645629\pi$
$659$	−1.09799e14			−0.883425			−0.441713	+	0.897157i	$0.645629\pi$
$660$	−1.09083e14	+	1.88937e14i	−0.871039	+	1.50868i
$661$	−1.00729e14	+	5.81560e13i	−0.798267	+	0.460880i	−0.842865	−	0.538125i	$-0.819133\pi$
$661$	−1.00729e14	+	5.81560e13i	−0.798267	+	0.460880i	0.0445978	+	0.999005i	$0.485799\pi$
$662$	1.44311e14	+	2.49954e14i	1.13504	+	1.96594i
$663$	2.65614e13	+	1.53352e13i	0.207340	+	0.119708i
$664$		−	6.26825e12i		−	0.0485630i
$665$	1.48606e14	−	2.61346e13i	1.14269	−	0.200959i
$666$	6.56410e13			0.500961
$667$	−1.26031e14	+	2.18293e14i	−0.954662	+	1.65352i
$668$	3.08798e13	−	1.78284e13i	0.232162	−	0.134039i
$669$	4.81012e13	+	8.33138e13i	0.358943	+	0.621708i
$670$	−1.17622e14	−	6.79090e13i	−0.871193	−	0.502983i
$671$		−	3.65357e14i		−	2.68600i
$672$	−8.60918e13	+	7.21738e13i	−0.628225	+	0.526663i
$673$	−2.40567e14			−1.74245			−0.871227	−	0.490881i	$-0.836675\pi$
$673$	−2.40567e14			−1.74245			−0.871227	+	0.490881i	$0.836675\pi$
$674$	3.59154e13	−	6.22073e13i	0.258215	−	0.447241i
$675$	−4.52136e13	+	2.61041e13i	−0.322664	+	0.186290i
$676$	−2.17641e13	−	3.76965e13i	−0.154172	−	0.267034i
$677$	4.10013e13	+	2.36721e13i	0.288306	+	0.166454i	0.637178	−	0.770717i	$-0.280102\pi$
$677$	4.10013e13	+	2.36721e13i	0.288306	+	0.166454i	−0.348871	+	0.937171i	$0.613435\pi$
$678$			2.01026e14i			1.40315i
$679$	7.03867e13	+	2.56544e13i	0.487688	+	0.177752i
$680$	−3.80322e13			−0.261582
$681$	5.74861e13	−	9.95689e13i	0.392489	−	0.679811i
$682$	9.47813e13	−	5.47220e13i	0.642393	−	0.370886i
$683$	−5.04788e13	−	8.74318e13i	−0.339629	−	0.588255i	0.644734	−	0.764407i	$-0.276968\pi$
$683$	−5.04788e13	−	8.74318e13i	−0.339629	−	0.588255i	−0.984363	+	0.176152i	$0.943635\pi$
$684$	3.55197e13	+	2.05073e13i	0.237240	+	0.136971i
$685$		−	4.63957e14i		−	3.07627i
$686$	3.04332e11	−	2.26037e14i	0.00200321	−	1.48785i
$687$	−1.44416e13			−0.0943694
$688$	−3.02841e13	+	5.24535e13i	−0.196459	+	0.340277i
$689$	−1.14407e14	+	6.60529e13i	−0.736812	+	0.425399i
$690$	−1.15783e14	−	2.00542e14i	−0.740286	−	1.28221i
$691$	1.08881e14	+	6.28623e13i	0.691131	+	0.399025i	0.804036	−	0.594581i	$-0.202682\pi$
$691$	1.08881e14	+	6.28623e13i	0.691131	+	0.399025i	−0.112905	+	0.993606i	$0.536015\pi$
$692$			1.84332e14i			1.16163i
$693$	−2.64710e13	+	7.26271e13i	−0.165617	+	0.454394i
$694$	3.02532e14			1.87920
$695$	−4.33860e13	+	7.51467e13i	−0.267563	+	0.463432i
$696$	4.92849e13	−	2.84547e13i	0.301764	−	0.174224i
$697$	−3.52720e11	−	6.10929e11i	−0.00214420	−	0.00371387i
$698$	−4.52027e13	−	2.60978e13i	−0.272827	−	0.157517i
$699$		−	1.49589e14i		−	0.896424i
$700$	2.53711e14	+	3.02637e14i	1.50956	+	1.80066i
$701$	1.05463e14			0.623033			0.311516	−	0.950241i	$-0.399163\pi$
$701$	1.05463e14			0.623033			0.311516	+	0.950241i	$0.399163\pi$
$702$	2.10808e13	−	3.65131e13i	0.123652	−	0.214172i
$703$	1.01704e14	−	5.87190e13i	0.592329	−	0.341981i
$704$	−1.72115e14	−	2.98112e14i	−0.995305	−	1.72392i
$705$	7.33696e12	+	4.23599e12i	0.0421280	+	0.0243226i
$706$			2.83704e14i			1.61749i
$707$	−1.47073e13	−	8.36285e13i	−0.0832597	−	0.473431i
$708$	1.51523e14			0.851752
$709$	1.45894e14	−	2.52695e14i	0.814340	−	1.41048i	−0.0954614	−	0.995433i	$-0.530433\pi$
$709$	1.45894e14	−	2.52695e14i	0.814340	−	1.41048i	0.909801	−	0.415045i	$-0.136234\pi$
$710$	−1.27545e14	+	7.36381e13i	−0.706922	+	0.408141i
$711$	−1.15044e13	−	1.99262e13i	−0.0633162	−	0.109667i
$712$	7.58539e13	+	4.37943e13i	0.414551	+	0.239341i
$713$			6.36902e13i			0.345641i
$714$	−7.53763e13	+	1.32560e13i	−0.406203	+	0.0714367i
$715$	4.01236e14			2.14719
$716$	2.26321e14	−	3.91999e14i	1.20270	−	2.08314i
$717$	−5.62499e12	+	3.24759e12i	−0.0296842	+	0.0171382i
$718$	−8.53191e13	−	1.47777e14i	−0.447120	−	0.774435i
$719$	1.12130e14	+	6.47381e13i	0.583547	+	0.336911i	0.762542	−	0.646939i	$-0.223951\pi$
$719$	1.12130e14	+	6.47381e13i	0.583547	+	0.336911i	−0.178995	+	0.983850i	$0.557284\pi$
$720$		−	8.18498e13i		−	0.423014i
$721$	−8.60916e13	+	7.21736e13i	−0.441860	+	0.370426i
$722$	−1.58070e14			−0.805681
$723$	−8.41260e13	+	1.45710e14i	−0.425832	+	0.737563i
$724$	−2.72598e14	+	1.57385e14i	−1.37035	+	0.791170i
$725$	3.68034e14	+	6.37453e14i	1.83737	+	3.18243i
$726$	−1.65815e14	−	9.57334e13i	−0.822131	−	0.474658i
$727$			3.81436e14i			1.87823i	0.343597	+	0.939117i	$0.388355\pi$
$727$			3.81436e14i			1.87823i	−0.343597	+	0.939117i	$0.611645\pi$
$728$	−5.27592e13	−	1.92296e13i	−0.258013	−	0.0940401i
$729$	−7.62560e12			−0.0370370
$730$	9.21914e13	−	1.59680e14i	0.444709	−	0.770259i
$731$	−4.60446e13	+	2.65839e13i	−0.220593	+	0.127359i
$732$	−1.36315e14	−	2.36105e14i	−0.648617	−	1.12344i
$733$	−1.98056e14	−	1.14348e14i	−0.935985	−	0.540391i	−0.0472857	−	0.998881i	$-0.515057\pi$
$733$	−1.98056e14	−	1.14348e14i	−0.935985	−	0.540391i	−0.888700	+	0.458490i	$0.848390\pi$
$734$			5.94424e14i			2.79008i
$735$	1.62435e14	+	1.36548e14i	0.757256	+	0.636572i
$736$	3.08462e14			1.42828
$737$	6.22434e13	−	1.07809e14i	0.286257	−	0.495811i
$738$	−8.39824e11	+	4.84873e11i	−0.00383625	+	0.00221486i
$739$	8.39356e13	+	1.45381e14i	0.380824	+	0.659606i	0.991180	−	0.132521i	$-0.0423072\pi$
$739$	8.39356e13	+	1.45381e14i	0.380824	+	0.659606i	−0.610357	+	0.792127i	$0.708974\pi$
$740$	4.03687e14	+	2.33069e14i	1.81922	+	1.05033i
$741$		−	7.54312e13i		−	0.337645i
$742$	1.12885e14	−	3.09718e14i	0.501902	−	1.37704i
$743$	−1.95483e14			−0.863309			−0.431654	−	0.902039i	$-0.642070\pi$
$743$	−1.95483e14			−0.863309			−0.431654	+	0.902039i	$0.642070\pi$
$744$	7.18982e12	−	1.24531e13i	0.0315394	−	0.0546278i
$745$	−4.11862e13	+	2.37789e13i	−0.179461	+	0.103612i
$746$	−1.46415e14	−	2.53598e14i	−0.633712	−	1.09762i
$747$	1.02553e13	+	5.92087e12i	0.0440903	+	0.0254556i
$748$		−	1.97979e14i		−	0.845494i
$749$	−7.54786e13	−	9.00340e13i	−0.320195	−	0.381942i
$750$	−3.26927e14			−1.37767
$751$	2.22473e13	−	3.85335e13i	0.0931274	−	0.161301i	−0.815698	−	0.578478i	$-0.803647\pi$
$751$	2.22473e13	−	3.85335e13i	0.0931274	−	0.161301i	0.908826	+	0.417176i	$0.136980\pi$
$752$	−7.58478e12	+	4.37907e12i	−0.0315394	+	0.0182093i
$753$	7.64220e13	+	1.32367e14i	0.315677	+	0.546769i
$754$	−5.14787e14	−	2.97212e14i	−2.11237	−	1.21958i
$755$		−	5.11143e13i		−	0.208357i
$756$	9.99087e12	+	5.68101e13i	0.0404571	+	0.230047i
$757$	−6.32190e13			−0.254313			−0.127156	−	0.991883i	$-0.540585\pi$
$757$	−6.32190e13			−0.254313			−0.127156	+	0.991883i	$0.540585\pi$
$758$	5.32410e13	−	9.22161e13i	0.212765	−	0.368520i
$759$	1.83811e14	−	1.06123e14i	0.729730	−	0.421310i
$760$	4.67685e13	+	8.10054e13i	0.184453	+	0.319482i
$761$	−2.15144e14	−	1.24213e14i	−0.842956	−	0.486681i	0.0153116	−	0.999883i	$-0.495126\pi$
$761$	−2.15144e14	−	1.24213e14i	−0.842956	−	0.486681i	−0.858268	+	0.513202i	$0.828459\pi$
$762$		−	3.49539e13i		−	0.136057i
$763$	−2.30422e14	+	4.05230e13i	−0.891049	+	0.156704i
$764$	−4.62813e14			−1.77803
$765$	3.59246e13	−	6.22232e13i	0.137115	−	0.237490i
$766$	−1.89588e14	+	1.09459e14i	−0.718899	+	0.415057i
$767$	−1.39336e14	−	2.41336e14i	−0.524911	−	0.909172i
$768$	5.97725e13	+	3.45096e13i	0.223715	+	0.129162i
$769$		−	5.71340e13i		−	0.212453i	−0.994342	−	0.106227i	$-0.966123\pi$
$769$		−	5.71340e13i		−	0.212453i	0.994342	−	0.106227i	$-0.0338769\pi$
$770$	−7.67267e14	+	6.43227e14i	−2.83461	+	2.37635i
$771$	−2.80338e11			−0.00102899
$772$	7.71521e13	−	1.33631e14i	0.281359	−	0.487329i
$773$	−2.30365e14	+	1.33001e14i	−0.834677	+	0.481901i	−0.855451	−	0.517883i	$-0.826720\pi$
$773$	−2.30365e14	+	1.33001e14i	−0.834677	+	0.481901i	0.0207746	+	0.999784i	$0.493387\pi$
$774$	3.65440e13	+	6.32960e13i	0.131556	+	0.227862i
$775$	1.61069e14	+	9.29933e13i	0.576108	+	0.332616i
$776$			4.64416e13i			0.165044i
$777$	1.55176e14	+	5.65584e13i	0.547923	+	0.199706i
$778$	2.01971e14			0.708584
$779$	−8.67484e11	+	1.50253e12i	−0.00302395	+	0.00523763i
$780$	2.59290e14	−	1.49701e14i	0.898077	−	0.518505i
$781$	−6.74945e13	−	1.16904e14i	−0.232281	−	0.402322i
$782$	1.81985e14	+	1.05069e14i	0.622304	+	0.359287i
$783$			1.07511e14i			0.365295i
$784$	−2.06209e14	+	7.48443e13i	−0.696189	+	0.252685i
$785$	2.65551e14			0.890839
$786$	1.72897e14	−	2.99467e14i	0.576336	−	0.998243i
$787$	1.31239e14	−	7.57709e13i	0.434700	−	0.250974i	−0.266647	−	0.963794i	$-0.585916\pi$
$787$	1.31239e14	−	7.57709e13i	0.434700	−	0.250974i	0.701347	+	0.712820i	$0.252582\pi$
$788$	−5.37528e13	−	9.31025e13i	−0.176917	−	0.306429i
$789$	−2.30266e13	−	1.32944e13i	−0.0753085	−	0.0434794i
$790$		−	2.98015e14i		−	0.968507i
$791$	−1.73211e14	+	4.75229e14i	−0.559361	+	1.53469i
$792$	−4.79199e13			−0.153776
$793$	−2.50701e14	+	4.34227e14i	−0.799448	+	1.38469i
$794$	1.31043e14	−	7.56578e13i	0.415252	−	0.239746i
$795$	1.54737e14	+	2.68012e14i	0.487257	+	0.843954i
$796$	−3.88494e14	−	2.24297e14i	−1.21568	−	0.701873i
$797$			1.11268e14i			0.346001i	0.984922	+	0.173000i	$0.0553461\pi$
$797$			1.11268e14i			0.346001i	−0.984922	+	0.173000i	$0.944654\pi$
$798$	1.20925e14	+	1.44244e14i	0.373681	+	0.445742i
$799$	−7.68805e12			−0.0236093
$800$	4.50381e14	−	7.80083e14i	1.37445	−	2.38062i
$801$	−1.43300e14	+	8.27345e13i	−0.434595	+	0.250914i
$802$	2.46220e14	+	4.26465e14i	0.742080	+	1.28532i
$803$	1.46358e14	+	8.44999e13i	0.438368	+	0.253092i
$804$		−	9.28922e13i		−	0.276503i
$805$	−1.00919e14	−	5.73846e14i	−0.298534	−	1.69752i
$806$	−1.50197e14			−0.441556
$807$	−1.23917e14	+	2.14630e14i	−0.362045	+	0.627081i
$808$	4.55859e13	−	2.63190e13i	0.132365	−	0.0764211i
$809$	2.78688e14	+	4.82701e14i	0.804220	+	1.39295i	0.916816	+	0.399309i	$0.130750\pi$
$809$	2.78688e14	+	4.82701e14i	0.804220	+	1.39295i	−0.112596	+	0.993641i	$0.535917\pi$
$810$	−8.55362e13	−	4.93843e13i	−0.245315	−	0.141633i
$811$			6.84842e13i			0.195203i	0.995226	+	0.0976015i	$0.0311170\pi$
$811$			6.84842e13i			0.195203i	−0.995226	+	0.0976015i	$0.968883\pi$
$812$	8.00949e14	−	1.40858e14i	2.26895	−	0.399027i
$813$	−1.49304e14			−0.420356
$814$	−3.89633e14	+	6.74865e14i	−1.09027	+	1.88840i
$815$	1.94407e14	−	1.12241e14i	0.540658	−	0.312149i
$816$	3.71380e13	+	6.43249e13i	0.102652	+	0.177799i
$817$	1.13243e14	+	6.53807e13i	0.311100	+	0.179614i
$818$		−	2.31951e14i		−	0.633330i
$819$	8.12961e13	−	6.81534e13i	0.220623	−	0.184956i
$820$	−6.88646e12			−0.0185749
$821$	4.46196e13	−	7.72834e13i	0.119622	−	0.207191i	−0.799996	−	0.600005i	$-0.795165\pi$
$821$	4.46196e13	−	7.72834e13i	0.119622	−	0.207191i	0.919618	+	0.392814i	$0.128499\pi$
$822$	5.01230e14	−	2.89385e14i	1.33561	−	0.771112i
$823$	−2.42887e14	−	4.20693e14i	−0.643289	−	1.11421i	−0.984694	−	0.174293i	$-0.944236\pi$
$823$	−2.42887e14	−	4.20693e14i	−0.643289	−	1.11421i	0.341405	−	0.939916i	$-0.389097\pi$
$824$	−6.03122e13	−	3.48213e13i	−0.158770	−	0.0916661i
$825$		−	6.19797e14i		−	1.62173i
$826$	6.53335e14	+	2.38127e14i	1.69917	+	0.619310i
$827$	4.33517e14			1.12067			0.560336	−	0.828265i	$-0.310672\pi$
$827$	4.33517e14			1.12067			0.560336	+	0.828265i	$0.310672\pi$
$828$	7.91893e13	−	1.37160e14i	0.203477	−	0.352432i
$829$	2.15587e14	−	1.24469e14i	0.550618	−	0.317899i	−0.198753	−	0.980050i	$-0.563689\pi$
$829$	2.15587e14	−	1.24469e14i	0.550618	−	0.317899i	0.749371	+	0.662150i	$0.230356\pi$
$830$	7.66886e13	+	1.32829e14i	0.194689	+	0.337210i
$831$	−1.49416e14	−	8.62656e13i	−0.377045	−	0.217687i
$832$			4.72409e14i			1.18495i
$833$	−1.89612e14	−	3.36093e13i	−0.472761	−	0.0837980i
$834$	−1.08245e14			−0.268274
$835$	−7.68117e13	+	1.33042e14i	−0.189232	+	0.327760i
$836$	−4.21677e14	+	2.43456e14i	−1.03264	+	0.596195i
$837$	1.35827e13	+	2.35260e13i	0.0330643	+	0.0572691i
$838$	−7.87140e14	−	4.54455e14i	−1.90472	−	1.09969i
$839$		−	1.56856e14i		−	0.377303i	−0.982044	−	0.188651i	$-0.939588\pi$
$839$		−	1.56856e14i		−	0.377303i	0.982044	−	0.188651i	$-0.0604116\pi$
$840$	−4.50476e13	+	1.23595e14i	−0.107715	+	0.295531i
$841$	1.09506e15			2.60290
$842$	−2.93743e14	+	5.08778e14i	−0.694077	+	1.20218i
$843$	−2.77029e14	+	1.59943e14i	−0.650710	+	0.375688i
$844$	3.81327e14	+	6.60478e14i	0.890401	+	1.54222i
$845$	1.62411e14	+	9.37679e13i	0.376991	+	0.217656i
$846$			1.05685e13i			0.0243872i
$847$	−3.09502e14	−	3.69186e14i	−0.709980	−	0.846893i
$848$	−3.19927e14			−0.729577
$849$	5.91210e13	−	1.02401e14i	0.134030	−	0.232147i
$850$	5.31429e14	−	3.06821e14i	1.19771	−	0.691497i
$851$	−2.26744e14	−	3.92733e14i	−0.508029	−	0.879933i
$852$	−8.72338e13	−	5.03645e13i	−0.194306	−	0.112183i
$853$		−	2.31078e14i		−	0.511697i	−0.966717	−	0.255849i	$-0.917645\pi$
$853$		−	2.31078e14i		−	0.511697i	0.966717	−	0.255849i	$-0.0823548\pi$
$854$	−2.16710e14	−	1.23226e15i	−0.477078	−	2.71276i
$855$	−1.76707e14			−0.386743
$856$	3.64159e13	−	6.30741e13i	0.0792359	−	0.137241i
$857$	2.06111e14	−	1.18998e14i	0.445858	−	0.257416i	−0.260222	−	0.965549i	$-0.583796\pi$
$857$	2.06111e14	−	1.18998e14i	0.445858	−	0.257416i	0.706079	+	0.708133i	$0.250462\pi$
$858$	2.50264e14	+	4.33470e14i	0.538223	+	0.932229i
$859$	−3.72715e14	−	2.15187e14i	−0.796913	−	0.460098i	0.0454778	−	0.998965i	$-0.485519\pi$
$859$	−3.72715e14	−	2.15187e14i	−0.796913	−	0.460098i	−0.842390	+	0.538868i	$0.818852\pi$
$860$			5.19020e14i			1.10330i
$861$	−2.40314e12	+	4.22626e11i	−0.00507882	+	0.000893182i
$862$	−2.33484e14			−0.490592
$863$	−1.42404e14	+	2.46651e14i	−0.297487	+	0.515263i	−0.975560	−	0.219731i	$-0.929482\pi$
$863$	−1.42404e14	+	2.46651e14i	−0.297487	+	0.515263i	0.678073	+	0.734994i	$0.262815\pi$
$864$	1.13940e14	−	6.57833e13i	0.236650	−	0.136630i
$865$	−3.97085e14	−	6.87772e14i	−0.819980	−	1.42025i
$866$	1.20203e15	+	6.93994e14i	2.46789	+	1.42484i
$867$		−	2.17635e14i		−	0.444257i
$868$	1.57471e14	−	1.32013e14i	0.319596	−	0.267929i
$869$	2.73152e14			0.551195
$870$	−6.96255e14	+	1.20595e15i	−1.39692	+	2.41954i
$871$	−1.47953e14	+	8.54204e13i	−0.295142	+	0.170401i
$872$	−7.25171e13	−	1.25603e14i	−0.143833	−	0.249126i
$873$	−7.59814e13	−	4.38679e13i	−0.149843	−	0.0865119i
$874$		−	5.16817e14i		−	1.01340i
$875$	−7.72858e14	−	2.81690e14i	−1.50681	−	0.549201i
$876$	1.26108e14			0.244468
$877$	−9.62396e12	+	1.66692e13i	−0.0185505	+	0.0321304i	−0.875152	−	0.483849i	$-0.839238\pi$
$877$	−9.62396e12	+	1.66692e13i	−0.0185505	+	0.0321304i	0.856601	+	0.515979i	$0.172572\pi$
$878$	7.02067e14	−	4.05338e14i	1.34557	−	0.776864i
$879$	−1.35334e14	−	2.34405e14i	−0.257906	−	0.446707i
$880$	8.41510e14	+	4.85846e14i	1.59458	+	0.920630i
$881$		−	4.68704e14i		−	0.883119i	−0.897232	−	0.441559i	$-0.854425\pi$
$881$		−	4.68704e14i		−	0.883119i	0.897232	−	0.441559i	$-0.145575\pi$
$882$	−4.62016e13	+	2.60654e14i	−0.0865593	+	0.488339i
$883$	−7.38558e13			−0.137588			−0.0687941	−	0.997631i	$-0.521915\pi$
$883$	−7.38558e13			−0.137588			−0.0687941	+	0.997631i	$0.521915\pi$
$884$	−1.35849e14	+	2.35298e14i	−0.251649	+	0.435869i
$885$	−5.65359e14	+	3.26410e14i	−1.04138	+	0.601239i
$886$	2.23694e14	+	3.87449e14i	0.409718	+	0.709653i
$887$	−5.25532e14	−	3.03416e14i	−0.957152	−	0.552612i	−0.0618569	−	0.998085i	$-0.519702\pi$
$887$	−5.25532e14	−	3.03416e14i	−0.957152	−	0.552612i	−0.895295	+	0.445473i	$0.853036\pi$
$888$			1.02386e14i			0.185429i
$889$	3.01174e13	−	8.26315e13i	0.0542387	−	0.148812i
$890$	−2.14320e15			−3.83806
$891$	4.52642e13	−	7.83999e13i	0.0806058	−	0.139613i
$892$	−7.38047e14	+	4.26111e14i	−1.30695	+	0.754569i
$893$	9.45404e12	+	1.63749e13i	0.0166479	+	0.0288351i
$894$	−5.13784e13	−	2.96633e13i	−0.0899690	−	0.0519436i
$895$			1.95015e15i			3.39588i
$896$	−2.30539e14	−	2.74997e14i	−0.399213	−	0.476198i
$897$	−2.91279e14			−0.501588
$898$	1.75432e14	−	3.03857e14i	0.300418	−	0.520340i
$899$	3.31686e14	−	1.91499e14i	0.564844	−	0.326113i
$900$	−2.31247e14	−	4.00531e14i	−0.391618	−	0.678303i
$901$	−2.43212e14	−	1.40419e14i	−0.409601	−	0.236483i
$902$		−	1.15125e13i		−	0.0192813i
$903$	3.18525e13	+	1.81120e14i	0.0530524	+	0.301667i
$904$	−3.13559e14			−0.519371
$905$	6.78073e14	−	1.17446e15i	1.11695	−	1.93461i
$906$	5.52207e13	−	3.18817e13i	0.0904608	−	0.0522276i
$907$	4.96633e14	+	8.60194e14i	0.809095	+	1.40139i	0.913492	+	0.406858i	$0.133375\pi$
$907$	4.96633e14	+	8.60194e14i	0.809095	+	1.40139i	−0.104397	+	0.994536i	$0.533291\pi$
$908$	8.82045e14	+	5.09249e14i	1.42910	+	0.825089i
$909$			9.94419e13i			0.160232i
$910$	1.35327e15	−	2.37991e14i	2.16858	−	0.381377i
$911$	−5.60473e14			−0.893230			−0.446615	−	0.894726i	$-0.647371\pi$
$911$	−5.60473e14			−0.893230			−0.446615	+	0.894726i	$0.647371\pi$
$912$	9.13376e13	−	1.58201e14i	0.144769	−	0.250747i
$913$	−1.21747e14	+	7.02905e13i	−0.191913	+	0.110801i
$914$	2.35686e14	+	4.08220e14i	0.369490	+	0.639976i
$915$	1.01723e15	+	5.87297e14i	1.58604	+	0.915698i
$916$		−	1.27933e14i		−	0.198383i
$917$	6.66762e14	−	5.58970e14i	1.02831	−	0.862068i
$918$	8.96293e13			0.137479
$919$	−3.16524e14	+	5.48235e14i	−0.482868	+	0.836352i	−0.999807	−	0.0196704i	$-0.993738\pi$
$919$	−3.16524e14	+	5.48235e14i	−0.482868	+	0.836352i	0.516938	+	0.856023i	$0.327072\pi$
$920$	3.12804e14	−	1.80597e14i	0.474605	−	0.274014i
$921$	−2.56096e14	−	4.43572e14i	−0.386461	−	0.669370i
$922$	6.83720e14	+	3.94746e14i	1.02618	+	0.592466i
$923$			1.85254e14i			0.276540i
$924$	−6.43377e14	−	2.34497e14i	−0.955225	−	0.348159i
$925$	−1.32427e15			−1.95554
$926$	−6.39304e14	+	1.10731e15i	−0.938971	+	1.62635i
$927$	1.13940e14	−	6.57831e13i	0.166447	−	0.0960983i
$928$	−9.27459e14	−	1.60641e15i	−1.34758	−	2.33408i
$929$	−2.54458e14	−	1.46911e14i	−0.367737	−	0.212313i	0.304733	−	0.952438i	$-0.401433\pi$
$929$	−2.54458e14	−	1.46911e14i	−0.367737	−	0.212313i	−0.672469	+	0.740125i	$0.734766\pi$
$930$			3.51854e14i			0.505764i
$931$	1.61582e14	+	4.45187e14i	0.231018	+	0.636494i
$932$	1.32515e15			1.88446
$933$	2.69915e14	−	4.67507e14i	0.381785	−	0.661271i
$934$	1.54591e14	−	8.92530e13i	0.217495	−	0.125571i
$935$	4.26484e14	+	7.38691e14i	0.596821	+	1.03372i
$936$	5.69527e13	+	3.28817e13i	0.0792749	+	0.0457694i
$937$			5.72007e14i			0.791960i	0.918259	+	0.395980i	$0.129595\pi$
$937$			5.72007e14i			0.791960i	−0.918259	+	0.395980i	$0.870405\pi$
$938$	1.45985e14	−	4.00531e14i	0.201045	−	0.551597i
$939$	2.90376e14			0.397770
$940$	−3.75251e13	+	6.49955e13i	−0.0511309	+	0.0885612i
$941$	−1.11334e15	+	6.42788e14i	−1.50897	+	0.871203i	−0.509023	+	0.860753i	$0.669993\pi$
$941$	−1.11334e15	+	6.42788e14i	−1.50897	+	0.871203i	−0.999945	+	0.0104504i	$0.996673\pi$
$942$	1.65633e14	+	2.86884e14i	0.223301	+	0.386769i
$943$	5.80203e12	+	3.34980e12i	0.00778075	+	0.00449222i
$944$		−	6.74871e14i		−	0.900245i
$945$	−1.59657e14	−	1.90446e14i	−0.211851	−	0.252704i
$946$	−8.67674e14			−1.14525
$947$	2.43687e13	−	4.22078e13i	0.0319950	−	0.0554169i	−0.849585	−	0.527452i	$-0.823147\pi$
$947$	2.43687e13	−	4.22078e13i	0.0319950	−	0.0554169i	0.881580	+	0.472036i	$0.156481\pi$
$948$	1.76519e14	−	1.01913e14i	0.230542	−	0.133103i
$949$	−1.15964e14	−	2.00856e14i	−0.150658	−	0.260948i
$950$	−1.30700e15	−	7.54599e14i	−1.68911	−	0.975210i
$951$			1.72131e14i			0.221287i
$952$	−2.06766e13	−	1.17571e14i	−0.0264420	−	0.150355i
$953$	5.12931e14			0.652521			0.326260	−	0.945280i	$-0.394211\pi$
$953$	5.12931e14			0.652521			0.326260	+	0.945280i	$0.394211\pi$
$954$	−1.93029e14	+	3.34336e14i	−0.244276	+	0.423098i
$955$	1.72683e15	−	9.96988e14i	2.17387	−	1.25508i
$956$	−2.87692e13	−	4.98297e13i	−0.0360279	−	0.0624021i
$957$	−1.10534e15	−	6.38167e14i	−1.37700	−	0.795013i
$958$			1.84820e14i			0.229046i
$959$	1.43426e15	−	2.52235e14i	1.76821	−	0.310965i
$960$	1.10667e15			1.35726
$961$	−3.61427e14	+	6.26010e14i	−0.440964	+	0.763773i
$962$	9.26159e14	−	5.34718e14i	1.12411	−	0.649007i
$963$	6.87955e13	+	1.19157e14i	0.0830670	+	0.143876i
$964$	−1.29080e15	−	7.45242e14i	−1.55050	−	0.895184i
$965$			6.64802e14i			0.794430i
$966$	5.57000e14	−	4.66953e14i	0.662171	−	0.555121i
$967$	−8.95789e14			−1.05943			−0.529716	−	0.848175i	$-0.677702\pi$
$967$	−8.95789e14			−1.05943			−0.529716	+	0.848175i	$0.677702\pi$
$968$	1.49324e14	−	2.58637e14i	0.175692	−	0.304308i
$969$	1.38872e14	−	8.01777e13i	0.162553	−	0.0938501i
$970$	−5.68188e14	−	9.84131e14i	−0.661658	−	1.14603i
$971$	2.23313e14	+	1.28930e14i	0.258713	+	0.149368i	0.623747	−	0.781626i	$-0.285609\pi$
$971$	2.23313e14	+	1.28930e14i	0.258713	+	0.149368i	−0.365034	+	0.930994i	$0.618943\pi$
$972$		−	6.75524e13i		−	0.0778591i
$973$	−2.55893e14	−	9.32674e13i	−0.293423	−	0.106946i
$974$	−2.02596e14			−0.231120
$975$	−4.25293e14	+	7.36629e14i	−0.482686	+	0.836037i
$976$	−1.05159e15	+	6.07134e14i	−1.18740	+	0.685545i
$977$	4.85092e14	+	8.40205e14i	0.544944	+	0.943870i	0.998610	+	0.0526988i	$0.0167823\pi$
$977$	4.85092e14	+	8.40205e14i	0.544944	+	0.943870i	−0.453667	+	0.891171i	$0.649884\pi$
$978$	2.42515e14	+	1.40016e14i	0.271047	+	0.156489i
$979$		−	1.96439e15i		−	2.18431i
$980$	−1.20963e15	+	1.43895e15i	−1.33820	+	1.59190i
$981$	2.73993e14			0.301574
$982$	9.75853e14	−	1.69023e15i	1.06863	−	1.85092i
$983$	−1.25370e15	+	7.23825e14i	−1.36593	+	0.788617i	−0.990405	−	0.138197i	$-0.955869\pi$
$983$	−1.25370e15	+	7.23825e14i	−1.36593	+	0.788617i	−0.375520	+	0.926814i	$0.622536\pi$
$984$	−7.56300e11	−	1.30995e12i	−0.000819820	−	0.00141997i
$985$	4.01121e14	+	2.31587e14i	0.432608	+	0.249766i
$986$		−	1.26366e15i		−	1.35595i
$987$	−9.10617e12	+	2.49841e13i	−0.00972187	+	0.0266734i
$988$	6.68218e14			0.709796
$989$	2.52469e14	−	4.37288e14i	0.266825	−	0.462154i
$990$	1.01546e15	−	5.86273e14i	1.06779	−	0.616487i
$991$	7.27136e14	+	1.25944e15i	0.760759	+	1.31767i	0.942460	+	0.334319i	$0.108506\pi$
$991$	7.27136e14	+	1.25944e15i	0.760759	+	1.31767i	−0.181701	+	0.983354i	$0.558160\pi$
$992$	−4.05900e14	−	2.34347e14i	−0.422533	−	0.243950i
$993$		−	8.50484e14i		−	0.880886i
$994$	−2.96983e14	−	3.54253e14i	−0.306055	−	0.365074i
$995$	1.93272e15			1.98177
$996$	−5.24509e13	+	9.08476e13i	−0.0535126	+	0.0926865i
$997$	1.66109e15	−	9.59031e14i	1.68623	−	0.973547i	0.728872	−	0.684650i	$-0.240045\pi$
$997$	1.66109e15	−	9.59031e14i	1.68623	−	0.973547i	0.957360	−	0.288897i	$-0.0932884\pi$
$998$	2.89291e14	+	5.01067e14i	0.292201	+	0.506108i
$999$	−1.67510e14	−	9.67122e13i	−0.168350	−	0.0971972i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	21.11.f.a.19.6	yes	12
3.2	odd	2		63.11.m.b.19.1		12
7.2	even	3		147.11.d.a.97.1		12
7.3	odd	6	inner	21.11.f.a.10.6	✓	12
7.5	odd	6		147.11.d.a.97.2		12
21.17	even	6		63.11.m.b.10.1		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
21.11.f.a.10.6	✓	12	7.3	odd	6	inner
21.11.f.a.19.6	yes	12	1.1	even	1	trivial
63.11.m.b.10.1		12	21.17	even	6
63.11.m.b.19.1		12	3.2	odd	2
147.11.d.a.97.1		12	7.2	even	3
147.11.d.a.97.2		12	7.5	odd	6

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)

\(f(q)\)	\(=\)	\(q+(23.8056 - 41.2326i) q^{2} +(-121.500 + 70.1481i) q^{3} +(-621.416 - 1076.32i) q^{4} +(4637.22 + 2677.30i) q^{5} +6679.68i q^{6} +(-5755.42 + 15790.8i) q^{7} -10418.9 q^{8} +(9841.50 - 17046.0i) q^{9} +O(q^{10})\)	\(q+(23.8056 - 41.2326i) q^{2} +(-121.500 + 70.1481i) q^{3} +(-621.416 - 1076.32i) q^{4} +(4637.22 + 2677.30i) q^{5} +6679.68i q^{6} +(-5755.42 + 15790.8i) q^{7} -10418.9 q^{8} +(9841.50 - 17046.0i) q^{9} +(220784. - 127470. i) q^{10} +(116835. + 202364. i) q^{11} +(151004. + 87182.3i) q^{12} -320679. i q^{13} +(514085. + 613221. i) q^{14} -751229. q^{15} +(388302. - 672558. i) q^{16} +(590383. - 340858. i) q^{17} +(-468566. - 811581. i) q^{18} +(-1.45200e6 - 838310. i) q^{19} -6.65487e6i q^{20} +(-408413. - 2.32232e6i) q^{21} +1.11253e7 q^{22} +(-3.23715e6 + 5.60690e6i) q^{23} +(1.26590e6 - 730866. i) q^{24} +(9.45304e6 + 1.63732e7i) q^{25} +(-1.32224e7 - 7.63397e6i) q^{26} +2.76145e6i q^{27} +(2.05726e7 - 3.61798e6i) q^{28} +3.89328e7 q^{29} +(-1.78835e7 + 3.09751e7i) q^{30} +(8.51944e6 - 4.91870e6i) q^{31} +(-2.38220e7 - 4.12609e7i) q^{32} +(-2.83909e7 - 1.63915e7i) q^{33} -3.24573e7i q^{34} +(-6.89659e7 + 5.78165e7i) q^{35} -2.44627e7 q^{36} +(-3.50223e7 + 6.06603e7i) q^{37} +(-6.91314e7 + 3.99130e7i) q^{38} +(2.24950e7 + 3.89625e7i) q^{39} +(-4.83147e7 - 2.78945e7i) q^{40} -1.03480e6i q^{41} +(-1.05478e8 - 3.84443e7i) q^{42} -7.79910e7 q^{43} +(1.45206e8 - 2.51504e8i) q^{44} +(9.12743e7 - 5.26973e7i) q^{45} +(1.54125e8 + 2.66952e8i) q^{46} +(-9.76660e6 - 5.63875e6i) q^{47} +1.08954e8i q^{48} +(-2.16226e8 - 1.81766e8i) q^{49} +9.00143e8 q^{50} +(-4.78210e7 + 8.28285e7i) q^{51} +(-3.45155e8 + 1.99275e8i) q^{52} +(-2.05978e8 - 3.56765e8i) q^{53} +(1.13862e8 + 6.57380e7i) q^{54} +1.25121e9i q^{55} +(5.99652e7 - 1.64523e8i) q^{56} +2.35223e8 q^{57} +(9.26821e8 - 1.60530e9i) q^{58} +(7.52579e8 - 4.34502e8i) q^{59} +(4.66826e8 + 8.08567e8i) q^{60} +(-1.35409e9 - 7.81782e8i) q^{61} -4.68371e8i q^{62} +(2.12528e8 + 2.53512e8i) q^{63} -1.47315e9 q^{64} +(8.58554e8 - 1.48706e9i) q^{65} +(-1.35172e9 + 7.80419e8i) q^{66} +(-2.66373e8 - 4.61372e8i) q^{67} +(-7.33747e8 - 4.23629e8i) q^{68} -9.08319e8i q^{69} +(7.42147e8 + 4.22000e9i) q^{70} -5.77691e8 q^{71} +(-1.02538e8 + 1.77600e8i) q^{72} +(6.26346e8 - 3.61621e8i) q^{73} +(1.66745e9 + 2.88812e9i) q^{74} +(-2.29709e9 - 1.32623e9i) q^{75} +2.08376e9i q^{76} +(-3.86793e9 + 6.80230e8i) q^{77} +2.14203e9 q^{78} +(5.84483e8 - 1.01235e9i) q^{79} +(3.60128e9 - 2.07920e9i) q^{80} +(-1.93710e8 - 3.35516e8i) q^{81} +(-4.26675e7 - 2.46341e7i) q^{82} +6.01623e8i q^{83} +(-2.24577e9 + 1.88271e9i) q^{84} +3.65031e9 q^{85} +(-1.85663e9 + 3.21577e9i) q^{86} +(-4.73034e9 + 2.73106e9i) q^{87} +(-1.21729e9 - 2.10841e9i) q^{88} +(-7.28042e9 - 4.20335e9i) q^{89} -5.01797e9i q^{90} +(5.06379e9 + 1.84564e9i) q^{91} +8.04647e9 q^{92} +(-6.90074e8 + 1.19524e9i) q^{93} +(-4.65000e8 + 2.68468e8i) q^{94} +(-4.48881e9 - 7.77485e9i) q^{95} +(5.78875e9 + 3.34214e9i) q^{96} -4.45744e9i q^{97} +(-1.26421e10 + 4.58848e9i) q^{98} +4.59932e9 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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