LMFDB - Embedded newform 20.20.e.b.3.19

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [20,20,Mod(3,20)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(20, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 3]))

N = Newforms(chi, 20, names="a")

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

chi := DirichletCharacter("20.3");

S:= CuspForms(chi, 20);

N := Newforms(S);

Level:	$ N $	$=$	$ 20 = 2^{2} \cdot 5 $
Weight:	$ k $	$=$	$ 20 $
Character orbit:	$[\chi]$	$=$	20.e (of order $4$, 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:	$45.7633393113$
Analytic rank:	$0$
Dimension:	$108$
Relative dimension:	$54$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			3.19
Character	$\chi$	$=$	20.3
Dual form			20.20.e.b.7.19

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-393.959 + 607.523i) q^{2} +(-40275.2 + 40275.2i) q^{3} +(-213881. - 478678. i) q^{4} +(-1.25692e6 - 4.18254e6i) q^{5} +(-8.60133e6 - 4.03349e7i) q^{6} +(-4.01530e7 - 4.01530e7i) q^{7} +(3.75068e8 + 5.86423e7i) q^{8} -2.08192e9i q^{9} +(3.03616e9 + 8.84143e8i) q^{10} -1.22429e10i q^{11} +(2.78929e10 + 1.06648e10i) q^{12} +(-4.37398e10 - 4.37398e10i) q^{13} +(4.02125e10 - 8.57524e9i) q^{14} +(2.19075e11 + 1.17830e11i) q^{15} +(-1.83388e11 + 2.04760e11i) q^{16} +(-3.10621e11 + 3.10621e11i) q^{17} +(1.26481e12 + 8.20190e11i) q^{18} +1.26212e12 q^{19} +(-1.73326e12 + 1.49622e12i) q^{20} +3.23434e12 q^{21} +(7.43782e12 + 4.82318e12i) q^{22} +(-2.76090e12 + 2.76090e12i) q^{23} +(-1.74678e13 + 1.27441e13i) q^{24} +(-1.59138e13 + 1.05142e13i) q^{25} +(4.38047e13 - 9.34125e12i) q^{26} +(3.70393e13 + 3.70393e13i) q^{27} +(-1.06324e13 + 2.78083e13i) q^{28} -1.11287e14i q^{29} +(-1.57891e14 + 8.66730e13i) q^{30} -2.25360e14i q^{31} +(-5.21490e13 - 1.92080e14i) q^{32} +(4.93083e14 + 4.93083e14i) q^{33} +(-6.63375e13 - 3.11082e14i) q^{34} +(-1.17473e14 + 2.18411e14i) q^{35} +(-9.96569e14 + 4.45282e14i) q^{36} +(-3.54771e14 + 3.54771e14i) q^{37} +(-4.97222e14 + 7.66765e14i) q^{38} +3.52326e15 q^{39} +(-2.26156e14 - 1.64245e15i) q^{40} -6.44728e14 q^{41} +(-1.27420e15 + 1.96494e15i) q^{42} +(3.10817e15 - 3.10817e15i) q^{43} +(-5.86039e15 + 2.61851e15i) q^{44} +(-8.70771e15 + 2.61680e15i) q^{45} +(-5.89628e14 - 2.76499e15i) q^{46} +(7.04277e14 + 7.04277e14i) q^{47} +(-8.60756e14 - 1.56327e16i) q^{48} -8.17437e15i q^{49} +(-1.18242e14 - 1.38102e16i) q^{50} -2.50206e16i q^{51} +(-1.15822e16 + 3.02924e16i) q^{52} +(-1.30980e16 - 1.30980e16i) q^{53} +(-3.70942e16 + 7.91027e15i) q^{54} +(-5.12063e16 + 1.53883e16i) q^{55} +(-1.27055e16 - 1.74148e16i) q^{56} +(-5.08320e16 + 5.08320e16i) q^{57} +(6.76091e16 + 4.38423e16i) q^{58} -4.00837e16 q^{59} +(9.54676e15 - 1.30068e17i) q^{60} +3.58022e16 q^{61} +(1.36911e17 + 8.87825e16i) q^{62} +(-8.35953e16 + 8.35953e16i) q^{63} +(1.37237e17 + 4.39898e16i) q^{64} +(-1.27966e17 + 2.37921e17i) q^{65} +(-4.93814e17 + 1.05305e17i) q^{66} +(-1.62605e16 - 1.62605e16i) q^{67} +(2.15123e17 + 8.22518e16i) q^{68} -2.22391e17i q^{69} +(-8.64101e16 - 1.57412e17i) q^{70} +1.01577e17i q^{71} +(1.22088e17 - 7.80862e17i) q^{72} +(-2.56630e17 - 2.56630e17i) q^{73} +(-7.57663e16 - 3.55297e17i) q^{74} +(2.17469e17 - 1.06439e18i) q^{75} +(-2.69942e17 - 6.04148e17i) q^{76} +(-4.91587e17 + 4.91587e17i) q^{77} +(-1.38802e18 + 2.14046e18i) q^{78} -2.61061e17 q^{79} +(1.08692e18 + 5.09662e17i) q^{80} -5.63798e17 q^{81} +(2.53996e17 - 3.91687e17i) q^{82} +(1.42688e18 - 1.42688e18i) q^{83} +(-6.91762e17 - 1.54821e18i) q^{84} +(1.68961e18 + 9.08760e17i) q^{85} +(6.63794e17 + 3.11278e18i) q^{86} +(4.48208e18 + 4.48208e18i) q^{87} +(7.17950e17 - 4.59191e18i) q^{88} +4.27003e17i q^{89} +(1.84071e18 - 6.32104e18i) q^{90} +3.51257e18i q^{91} +(1.91208e18 + 7.31079e17i) q^{92} +(9.07640e18 + 9.07640e18i) q^{93} +(-7.05320e17 + 1.50408e17i) q^{94} +(-1.58638e18 - 5.27886e18i) q^{95} +(9.83635e18 + 5.63573e18i) q^{96} +(1.00451e17 - 1.00451e17i) q^{97} +(4.96612e18 + 3.22037e18i) q^{98} -2.54886e19 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 108 q - 1026 q^{2} - 7131840 q^{5} - 50939608 q^{6} + 1332591828 q^{8} + 1805468790 q^{10} + 25565343280 q^{12} - 99498527404 q^{13} + 759936037048 q^{16} + 1103360788948 q^{17} - 2932289137902 q^{18} - 4821918866500 q^{20}+ \cdots + 66\!\cdots\!58 q^{98}+O(q^{100}) $ 108 * q - 1026 * q^2 - 7131840 * q^5 - 50939608 * q^6 + 1332591828 * q^8 + 1805468790 * q^10 + 25565343280 * q^12 - 99498527404 * q^13 + 759936037048 * q^16 + 1103360788948 * q^17 - 2932289137902 * q^18 - 4821918866500 * q^20 + 3306300862704 * q^21 + 26555173338440 * q^22 - 57672549609740 * q^25 - 151870176076556 * q^26 + 145347487073040 * q^28 + 265510366207880 * q^30 + 451426657209224 * q^32 - 229672757216560 * q^33 - 2556468817119620 * q^36 - 2904533279226852 * q^37 + 4500710811976960 * q^38 + 2246744304601900 * q^40 - 4721437306521104 * q^41 + 452761724453480 * q^42 - 970083854699780 * q^45 + 8478786115826952 * q^46 + 16046505545373280 * q^48 + 56844159661370 * q^50 - 101281742222079732 * q^52 - 27665397406960484 * q^53 - 10433774450699008 * q^56 + 83589162043122240 * q^57 - 22879145244078184 * q^58 + 145234473586307920 * q^60 - 6358689987281664 * q^61 - 371338823915128280 * q^62 - 91631698278804820 * q^65 + 331374884002311600 * q^66 - 694094458817479804 * q^68 - 165782163012631200 * q^70 - 215667461842637436 * q^72 + 1087298370549745276 * q^73 + 1949878275840327200 * q^76 - 1250723257104163920 * q^77 + 668342418678475560 * q^78 + 4071497833979030320 * q^80 - 12135903560578575228 * q^81 - 3459475352437471112 * q^82 + 14947305238413951060 * q^85 + 11624244909135363112 * q^86 - 5598373834541334880 * q^88 - 9907327634674956330 * q^90 + 27521624775955257680 * q^92 - 25916131489404857680 * q^93 - 50213774290767283648 * q^96 + 8468568053676169148 * q^97 + 66196294974841827558 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/20\mathbb{Z}\right)^\times$.

$n$	$11$	$17$
$\chi(n)$	$-1$	$e\left(\frac{3}{4}\right)$

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 $

$2$	−393.959	+	607.523i	−0.544084	+	0.839031i
$2$	−393.959	+	607.523i	−0.544084	+	0.839031i
$3$	−40275.2	+	40275.2i	−1.18137	+	1.18137i	−0.201979	+	0.979390i	$0.564737\pi$
$3$	−40275.2	+	40275.2i	−1.18137	+	1.18137i	−0.979390	+	0.201979i	$0.935263\pi$
$4$	−213881.	−	478678.i	−0.407945	−	0.913007i
$5$	−1.25692e6	−	4.18254e6i	−0.287801	−	0.957690i
$5$	−1.25692e6	−	4.18254e6i	−0.287801	−	0.957690i
$6$	−8.60133e6	−	4.03349e7i	−0.348441	−	1.63397i
$7$	−4.01530e7	−	4.01530e7i	−0.376086	−	0.376086i	0.493602	−	0.869688i	$-0.335680\pi$
$7$	−4.01530e7	−	4.01530e7i	−0.376086	−	0.376086i	−0.869688	+	0.493602i	$0.835680\pi$
$8$	3.75068e8	+	5.86423e7i	0.987997	+	0.154474i
$9$		−	2.08192e9i		−	1.79126i
$10$	3.03616e9	+	8.84143e8i	0.960119	+	0.279591i
$11$		−	1.22429e10i		−	1.56550i	−0.622338	−	0.782749i	$-0.713817\pi$
$11$		−	1.22429e10i		−	1.56550i	0.622338	−	0.782749i	$-0.286183\pi$
$12$	2.78929e10	+	1.06648e10i	1.56053	+	0.596664i
$13$	−4.37398e10	−	4.37398e10i	−1.14397	−	1.14397i	−0.987717	−	0.156255i	$-0.950058\pi$
$13$	−4.37398e10	−	4.37398e10i	−1.14397	−	1.14397i	−0.156255	−	0.987717i	$-0.549942\pi$
$14$	4.02125e10	−	8.57524e9i	0.520169	−	0.110925i
$15$	2.19075e11	+	1.17830e11i	1.47138	+	0.791387i
$16$	−1.83388e11	+	2.04760e11i	−0.667162	+	0.744913i
$17$	−3.10621e11	+	3.10621e11i	−0.635282	+	0.635282i	−0.949388	−	0.314106i	$-0.898295\pi$
$17$	−3.10621e11	+	3.10621e11i	−0.635282	+	0.635282i	0.314106	+	0.949388i	$0.398295\pi$
$18$	1.26481e12	+	8.20190e11i	1.50293	+	0.974599i
$19$	1.26212e12			0.897306			0.448653	−	0.893706i	$-0.351904\pi$
$19$	1.26212e12			0.897306			0.448653	+	0.893706i	$0.351904\pi$
$20$	−1.73326e12	+	1.49622e12i	−0.756971	+	0.653449i
$21$	3.23434e12			0.888591
$22$	7.43782e12	+	4.82318e12i	1.31350	+	0.851762i
$23$	−2.76090e12	+	2.76090e12i	−0.319621	+	0.319621i	−0.848622	−	0.529000i	$-0.822567\pi$
$23$	−2.76090e12	+	2.76090e12i	−0.319621	+	0.319621i	0.529000	+	0.848622i	$0.322567\pi$
$24$	−1.74678e13	+	1.27441e13i	−1.34968	+	0.984698i
$25$	−1.59138e13	+	1.05142e13i	−0.834342	+	0.551248i
$26$	4.38047e13	−	9.34125e12i	1.58224	−	0.337410i
$27$	3.70393e13	+	3.70393e13i	0.934776	+	0.934776i
$28$	−1.06324e13	+	2.78083e13i	−0.189946	+	0.496791i
$29$		−	1.11287e14i		−	1.42450i	−0.701927	−	0.712249i	$-0.747677\pi$
$29$		−	1.11287e14i		−	1.42450i	0.701927	−	0.712249i	$-0.252323\pi$
$30$	−1.57891e14	+	8.66730e13i	−1.46455	+	0.803955i
$31$		−	2.25360e14i		−	1.53088i	−0.643509	−	0.765438i	$-0.722522\pi$
$31$		−	2.25360e14i		−	1.53088i	0.643509	−	0.765438i	$-0.277478\pi$
$32$	−5.21490e13	−	1.92080e14i	−0.262012	−	0.965065i
$33$	4.93083e14	+	4.93083e14i	1.84943	+	1.84943i
$34$	−6.63375e13	−	3.11082e14i	−0.187374	−	0.878667i
$35$	−1.17473e14	+	2.18411e14i	−0.251936	+	0.468411i
$36$	−9.96569e14	+	4.45282e14i	−1.63544	+	0.730737i
$37$	−3.54771e14	+	3.54771e14i	−0.448778	+	0.448778i	−0.894948	−	0.446170i	$-0.852788\pi$
$37$	−3.54771e14	+	3.54771e14i	−0.448778	+	0.448778i	0.446170	+	0.894948i	$0.352788\pi$
$38$	−4.97222e14	+	7.66765e14i	−0.488210	+	0.752867i
$39$	3.52326e15			2.70290
$40$	−2.26156e14	−	1.64245e15i	−0.136408	−	0.990653i
$41$	−6.44728e14			−0.307560			−0.153780	−	0.988105i	$-0.549145\pi$
$41$	−6.44728e14			−0.307560			−0.153780	+	0.988105i	$0.549145\pi$
$42$	−1.27420e15	+	1.96494e15i	−0.483469	+	0.745555i
$43$	3.10817e15	−	3.10817e15i	0.943094	−	0.943094i	−0.0553716	−	0.998466i	$-0.517634\pi$
$43$	3.10817e15	−	3.10817e15i	0.943094	−	0.943094i	0.998466	+	0.0553716i	$0.0176344\pi$
$44$	−5.86039e15	+	2.61851e15i	−1.42931	+	0.638636i
$45$	−8.70771e15	+	2.61680e15i	−1.71548	+	0.515527i
$46$	−5.89628e14	−	2.76499e15i	−0.0942711	−	0.442073i
$47$	7.04277e14	+	7.04277e14i	0.0917939	+	0.0917939i	0.751513	−	0.659719i	$-0.229325\pi$
$47$	7.04277e14	+	7.04277e14i	0.0917939	+	0.0917939i	−0.659719	+	0.751513i	$0.729325\pi$
$48$	−8.60756e14	−	1.56327e16i	−0.0918520	−	1.66818i
$49$		−	8.17437e15i		−	0.717119i
$50$	−1.18242e14	−	1.38102e16i	−0.00856166	−	0.999963i
$51$		−	2.50206e16i		−	1.50100i
$52$	−1.15822e16	+	3.02924e16i	−0.577776	+	1.51113i
$53$	−1.30980e16	−	1.30980e16i	−0.545234	−	0.545234i	0.379825	−	0.925059i	$-0.375984\pi$
$53$	−1.30980e16	−	1.30980e16i	−0.545234	−	0.545234i	−0.925059	+	0.379825i	$0.875984\pi$
$54$	−3.70942e16	+	7.91027e15i	−1.29290	+	0.275709i
$55$	−5.12063e16	+	1.53883e16i	−1.49926	+	0.450551i
$56$	−1.27055e16	−	1.74148e16i	−0.313476	−	0.429667i
$57$	−5.08320e16	+	5.08320e16i	−1.06005	+	1.06005i
$58$	6.76091e16	+	4.38423e16i	1.19520	+	0.775046i
$59$	−4.00837e16			−0.602385			−0.301193	−	0.953563i	$-0.597385\pi$
$59$	−4.00837e16			−0.602385			−0.301193	+	0.953563i	$0.597385\pi$
$60$	9.54676e15	−	1.30068e17i	0.122298	−	1.66623i
$61$	3.58022e16			0.391992			0.195996	−	0.980605i	$-0.437206\pi$
$61$	3.58022e16			0.391992			0.195996	+	0.980605i	$0.437206\pi$
$62$	1.36911e17	+	8.87825e16i	1.28445	+	0.832926i
$63$	−8.35953e16	+	8.35953e16i	−0.673669	+	0.673669i
$64$	1.37237e17	+	4.39898e16i	0.952275	+	0.305240i
$65$	−1.27966e17	+	2.37921e17i	−0.766335	+	1.42481i
$66$	−4.93814e17	+	1.05305e17i	−2.55797	+	0.545483i
$67$	−1.62605e16	−	1.62605e16i	−0.0730168	−	0.0730168i	0.669655	−	0.742672i	$-0.266442\pi$
$67$	−1.62605e16	−	1.62605e16i	−0.0730168	−	0.0730168i	−0.742672	+	0.669655i	$0.766442\pi$
$68$	2.15123e17	+	8.22518e16i	0.839176	+	0.320856i
$69$		−	2.22391e17i		−	0.755181i
$70$	−8.64101e16	−	1.57412e17i	−0.255937	−	0.466237i
$71$			1.01577e17i			0.262930i	0.991321	+	0.131465i	$0.0419682\pi$
$71$			1.01577e17i			0.262930i	−0.991321	+	0.131465i	$0.958032\pi$
$72$	1.22088e17	−	7.80862e17i	0.276704	−	1.76976i
$73$	−2.56630e17	−	2.56630e17i	−0.510199	−	0.510199i	0.404388	−	0.914587i	$-0.367484\pi$
$73$	−2.56630e17	−	2.56630e17i	−0.510199	−	0.510199i	−0.914587	+	0.404388i	$0.867484\pi$
$74$	−7.57663e16	−	3.55297e17i	−0.132366	−	0.620712i
$75$	2.17469e17	−	1.06439e18i	0.334438	−	1.63689i
$76$	−2.69942e17	−	6.04148e17i	−0.366051	−	0.819246i
$77$	−4.91587e17	+	4.91587e17i	−0.588761	+	0.588761i
$78$	−1.38802e18	+	2.14046e18i	−1.47061	+	2.26782i
$79$	−2.61061e17			−0.245067			−0.122533	−	0.992464i	$-0.539102\pi$
$79$	−2.61061e17			−0.245067			−0.122533	+	0.992464i	$0.539102\pi$
$80$	1.08692e18	+	5.09662e17i	0.905405	+	0.424548i
$81$	−5.63798e17			−0.417365
$82$	2.53996e17	−	3.91687e17i	0.167338	−	0.258052i
$83$	1.42688e18	−	1.42688e18i	0.837813	−	0.837813i	−0.150758	−	0.988571i	$-0.548171\pi$
$83$	1.42688e18	−	1.42688e18i	0.837813	−	0.837813i	0.988571	+	0.150758i	$0.0481714\pi$
$84$	−6.91762e17	−	1.54821e18i	−0.362496	−	0.811290i
$85$	1.68961e18	+	9.08760e17i	0.791237	+	0.425569i
$86$	6.63794e17	+	3.11278e18i	0.278162	+	1.30441i
$87$	4.48208e18	+	4.48208e18i	1.68286	+	1.68286i
$88$	7.17950e17	−	4.59191e18i	0.241829	−	1.54671i
$89$			4.27003e17i			0.129189i	0.997912	+	0.0645946i	$0.0205754\pi$
$89$			4.27003e17i			0.129189i	−0.997912	+	0.0645946i	$0.979425\pi$
$90$	1.84071e18	−	6.32104e18i	0.500821	−	1.71983i
$91$			3.51257e18i			0.860462i
$92$	1.91208e18	+	7.31079e17i	0.422204	+	0.161428i
$93$	9.07640e18	+	9.07640e18i	1.80853	+	1.80853i
$94$	−7.05320e17	+	1.50408e17i	−0.126961	+	0.0270743i
$95$	−1.58638e18	−	5.27886e18i	−0.258245	−	0.859341i
$96$	9.83635e18	+	5.63573e18i	1.44963	+	0.830564i
$97$	1.00451e17	−	1.00451e17i	0.0134159	−	0.0134159i	−0.700367	−	0.713783i	$-0.746980\pi$
$97$	1.00451e17	−	1.00451e17i	0.0134159	−	0.0134159i	0.713783	+	0.700367i	$0.246980\pi$
$98$	4.96612e18	+	3.22037e18i	0.601685	+	0.390173i
$99$	−2.54886e19			−2.80422
$100$	8.43658e18	+	5.36881e18i	0.843658	+	0.536881i
$101$	−1.70283e19			−1.54924			−0.774621	−	0.632426i	$-0.782059\pi$
$101$	−1.70283e19			−1.54924			−0.774621	+	0.632426i	$0.782059\pi$
$102$	1.52006e19	+	9.85711e18i	1.25939	+	0.816672i
$103$	−6.59082e18	+	6.59082e18i	−0.497721	+	0.497721i	−0.910728	−	0.413007i	$-0.864479\pi$
$103$	−6.59082e18	+	6.59082e18i	−0.497721	+	0.497721i	0.413007	+	0.910728i	$0.364479\pi$
$104$	−1.38404e19	−	1.89704e19i	−0.953526	−	1.30695i
$105$	−4.06530e18	−	1.35278e19i	−0.255737	−	0.850995i
$106$	1.31174e19	−	2.79725e18i	0.754121	−	0.160815i
$107$	2.72688e18	+	2.72688e18i	0.143391	+	0.143391i	0.775158	−	0.631767i	$-0.217670\pi$
$107$	2.72688e18	+	2.72688e18i	0.143391	+	0.143391i	−0.631767	+	0.775158i	$0.717670\pi$
$108$	9.80794e18	−	2.56519e19i	0.472120	−	1.23479i
$109$			3.27288e19i			1.44337i	0.692219	+	0.721687i	$0.256633\pi$
$109$			3.27288e19i			1.44337i	−0.692219	+	0.721687i	$0.743367\pi$
$110$	1.08244e19	−	3.71713e19i	0.437698	−	1.50306i
$111$		−	2.85769e19i		−	1.06035i
$112$	1.55853e19	−	8.58145e17i	0.531061	−	0.0292408i
$113$	−4.94521e18	−	4.94521e18i	−0.154860	−	0.154860i	0.625425	−	0.780285i	$-0.284926\pi$
$113$	−4.94521e18	−	4.94521e18i	−0.154860	−	0.154860i	−0.780285	+	0.625425i	$0.784926\pi$
$114$	−1.08559e19	−	5.09073e19i	−0.312658	−	1.46617i
$115$	1.50178e19	+	8.07734e18i	0.398085	+	0.214111i
$116$	−5.32705e19	+	2.38020e19i	−1.30058	+	0.581116i
$117$	−9.10627e19	+	9.10627e19i	−2.04916	+	2.04916i
$118$	1.57914e19	−	2.43518e19i	0.327748	−	0.505419i
$119$	2.49447e19			0.477840
$120$	7.52583e19	+	5.70414e19i	1.33147	+	1.00918i
$121$	−8.87285e19			−1.45078
$122$	−1.41046e19	+	2.17507e19i	−0.213276	+	0.328893i
$123$	2.59665e19	−	2.59665e19i	0.363342	−	0.363342i
$124$	−1.07875e20	+	4.82001e19i	−1.39770	+	0.624513i
$125$	6.39785e19	+	5.33446e19i	0.768049	+	0.640391i
$126$	−1.78529e19	−	8.37192e19i	−0.198696	−	0.931761i
$127$	−6.48390e19	−	6.48390e19i	−0.669424	−	0.669424i	0.288159	−	0.957583i	$-0.406957\pi$
$127$	−6.48390e19	−	6.48390e19i	−0.669424	−	0.669424i	−0.957583	+	0.288159i	$0.906957\pi$
$128$	−8.07907e19	+	6.60447e19i	−0.774224	+	0.632912i
$129$			2.50365e20i			2.22828i
$130$	−9.41290e19	−	1.71474e20i	−0.778505	−	1.41819i
$131$			3.25752e19i			0.250501i	0.992125	+	0.125251i	$0.0399735\pi$
$131$			3.25752e19i			0.250501i	−0.992125	+	0.125251i	$0.960026\pi$
$132$	1.30567e20	−	3.41489e20i	0.934076	−	2.44301i
$133$	−5.06778e19	−	5.06778e19i	−0.337464	−	0.337464i
$134$	1.62846e19	−	3.47266e18i	0.100991	−	0.0215361i
$135$	1.08363e20	−	2.01474e20i	0.626197	−	1.16425i
$136$	−1.34720e20	+	9.82886e19i	−0.725791	+	0.529521i
$137$	7.71768e19	−	7.71768e19i	0.387830	−	0.387830i	−0.486083	−	0.873913i	$-0.661575\pi$
$137$	7.71768e19	−	7.71768e19i	0.387830	−	0.387830i	0.873913	+	0.486083i	$0.161575\pi$
$138$	1.35108e20	+	8.76130e19i	0.633620	+	0.410882i
$139$	4.32244e19			0.189273			0.0946363	−	0.995512i	$-0.469831\pi$
$139$	4.32244e19			0.189273			0.0946363	+	0.995512i	$0.469831\pi$
$140$	1.29674e20	+	9.51780e18i	0.530438	+	0.0389332i
$141$	−5.67297e19			−0.216885
$142$	−6.17104e19	−	4.00172e19i	−0.220607	−	0.143056i
$143$	−5.35500e20	+	5.35500e20i	−1.79088	+	1.79088i
$144$	4.26294e20	+	3.81799e20i	1.33434	+	1.19506i
$145$	−4.65460e20	+	1.39878e20i	−1.36423	+	0.409971i
$146$	2.57010e20	−	5.48069e19i	0.705664	−	0.150481i
$147$	3.29224e20	+	3.29224e20i	0.847183	+	0.847183i
$148$	2.45700e20	+	9.39426e19i	0.592814	+	0.226661i
$149$		−	4.40737e20i		−	0.997492i	−0.866748	−	0.498746i	$-0.833794\pi$
$149$		−	4.40737e20i		−	0.997492i	0.866748	−	0.498746i	$-0.166206\pi$
$150$	5.60969e20	+	5.51445e20i	1.19144	+	1.17121i
$151$		−	8.83899e20i		−	1.76247i	−0.472679	−	0.881235i	$-0.656713\pi$
$151$		−	8.83899e20i		−	1.76247i	0.472679	−	0.881235i	$-0.343287\pi$
$152$	4.73380e20	+	7.40135e19i	0.886535	+	0.138611i
$153$	6.46688e20	+	6.46688e20i	1.13796	+	1.13796i
$154$	−1.04985e20	−	4.92316e20i	−0.173653	−	0.814324i
$155$	−9.42576e20	+	2.83259e20i	−1.46611	+	0.440587i
$156$	−7.53556e20	−	1.68651e21i	−1.10264	−	2.46777i
$157$	4.77457e20	−	4.77457e20i	0.657487	−	0.657487i	−0.297298	−	0.954785i	$-0.596085\pi$
$157$	4.77457e20	−	4.77457e20i	0.657487	−	0.657487i	0.954785	+	0.297298i	$0.0960854\pi$
$158$	1.02847e20	−	1.58601e20i	0.133337	−	0.205619i
$159$	1.05505e21			1.28824
$160$	−7.37834e20	+	4.59544e20i	−0.848826	+	0.528673i
$161$	2.21716e20			0.240410
$162$	2.22113e20	−	3.42520e20i	0.227082	−	0.350182i
$163$	−1.08795e21	+	1.08795e21i	−1.04913	+	1.04913i	−0.0503979	+	0.998729i	$0.516049\pi$
$163$	−1.08795e21	+	1.08795e21i	−1.04913	+	1.04913i	−0.998729	+	0.0503979i	$0.983951\pi$
$164$	1.37895e20	+	3.08617e20i	0.125467	+	0.280804i
$165$	1.44258e21	−	2.68211e21i	1.23891	−	2.30345i
$166$	3.04731e20	+	1.42900e21i	0.247110	+	1.15879i
$167$	5.75231e20	+	5.75231e20i	0.440591	+	0.440591i	0.892211	−	0.451620i	$-0.149154\pi$
$167$	5.75231e20	+	5.75231e20i	0.440591	+	0.440591i	−0.451620	+	0.892211i	$0.649154\pi$
$168$	1.21310e21	+	1.89669e20i	0.877926	+	0.137265i
$169$			2.36442e21i			1.61734i
$170$	−1.21773e21	+	6.68463e20i	−0.787565	+	0.432327i
$171$		−	2.62762e21i		−	1.60731i
$172$	−2.15259e21	−	8.23038e20i	−1.24578	−	0.476321i
$173$	−1.27107e21	−	1.27107e21i	−0.696197	−	0.696197i	0.267391	−	0.963588i	$-0.413839\pi$
$173$	−1.27107e21	−	1.27107e21i	−0.696197	−	0.696197i	−0.963588	+	0.267391i	$0.913839\pi$
$174$	−4.48873e21	+	9.57212e20i	−2.32758	+	0.496353i
$175$	1.06116e21	+	2.16810e20i	0.521100	+	0.106468i
$176$	2.50685e21	+	2.24519e21i	1.16616	+	1.04444i
$177$	1.61438e21	−	1.61438e21i	0.711639	−	0.711639i
$178$	−2.59414e20	−	1.68222e20i	−0.108394	−	0.0702898i
$179$	4.81211e21			1.90648			0.953239	−	0.302216i	$-0.0977264\pi$
$179$	4.81211e21			1.90648			0.953239	+	0.302216i	$0.0977264\pi$
$180$	3.11501e21	+	3.60851e21i	1.17050	+	1.35594i
$181$	−1.95255e21			−0.696075			−0.348037	−	0.937481i	$-0.613152\pi$
$181$	−1.95255e21			−0.696075			−0.348037	+	0.937481i	$0.613152\pi$
$182$	−2.13397e21	−	1.38381e21i	−0.721954	−	0.468164i
$183$	−1.44194e21	+	1.44194e21i	−0.463087	+	0.463087i
$184$	−1.19743e21	+	8.73619e20i	−0.365158	+	0.266411i
$185$	1.92976e21	+	1.03793e21i	0.558949	+	0.300632i
$186$	−9.08986e21	+	1.93839e21i	−2.50140	+	0.533420i
$187$	3.80289e21	+	3.80289e21i	0.994532	+	0.994532i
$188$	1.86491e20	−	4.87753e20i	0.0463616	−	0.121255i
$189$		−	2.97448e21i		−	0.703111i
$190$	3.83199e21	+	1.11589e21i	0.861520	+	0.250878i
$191$			4.32831e20i			0.0925766i	0.998928	+	0.0462883i	$0.0147393\pi$
$191$			4.32831e20i			0.0925766i	−0.998928	+	0.0462883i	$0.985261\pi$
$192$	−7.29895e21	+	3.75556e21i	−1.48559	+	0.764387i
$193$	−3.60299e21	−	3.60299e21i	−0.698022	−	0.698022i	0.265962	−	0.963984i	$-0.414311\pi$
$193$	−3.60299e21	−	3.60299e21i	−0.698022	−	0.698022i	−0.963984	+	0.265962i	$0.914311\pi$
$194$	2.14526e19	+	1.00599e20i	0.00395698	+	0.0185558i
$195$	−4.42844e21	−	1.47362e22i	−0.777898	−	2.58855i
$196$	−3.91289e21	+	1.74834e21i	−0.654735	+	0.292545i
$197$	8.94625e20	−	8.94625e20i	0.142630	−	0.142630i	−0.632186	−	0.774817i	$-0.717842\pi$
$197$	8.94625e20	−	8.94625e20i	0.142630	−	0.142630i	0.774817	+	0.632186i	$0.217842\pi$
$198$	1.00415e22	−	1.54849e22i	1.52573	−	2.35283i
$199$	−1.05189e22			−1.52359			−0.761795	−	0.647818i	$-0.775682\pi$
$199$	−1.05189e22			−1.52359			−0.761795	+	0.647818i	$0.775682\pi$
$200$	−6.58534e21	+	3.01033e21i	−0.909480	+	0.415747i
$201$	1.30979e21			0.172520
$202$	6.70847e21	−	1.03451e22i	0.842918	−	1.29986i
$203$	−4.46849e21	+	4.46849e21i	−0.535733	+	0.535733i
$204$	−1.19768e22	+	5.35143e21i	−1.37043	+	0.612327i
$205$	8.10370e20	+	2.69660e21i	0.0885159	+	0.294547i
$206$	−1.40756e21	−	6.60059e21i	−0.146801	−	0.688406i
$207$	5.74796e21	+	5.74796e21i	0.572526	+	0.572526i
$208$	1.69775e22	−	9.34802e20i	1.61537	−	0.0889443i
$209$		−	1.54519e22i		−	1.40473i
$210$	9.81998e21	+	2.85962e21i	0.853154	+	0.248442i
$211$			1.30392e22i			1.08285i	0.840749	+	0.541426i	$0.182115\pi$
$211$			1.30392e22i			1.08285i	−0.840749	+	0.541426i	$0.817885\pi$
$212$	−3.46831e21	+	9.07111e21i	−0.275377	+	0.720227i
$213$	−4.09103e21	−	4.09103e21i	−0.310618	−	0.310618i
$214$	−2.73093e21	+	5.82364e20i	−0.198326	+	0.0422925i
$215$	−1.69068e22	−	9.09335e21i	−1.17462	−	0.631769i
$216$	1.17202e22	+	1.60644e22i	0.779157	+	1.06795i
$217$	−9.04887e21	+	9.04887e21i	−0.575741	+	0.575741i
$218$	−1.98835e22	−	1.28938e22i	−1.21104	−	0.785317i
$219$	2.06716e22			1.20547
$220$	1.83181e22	+	2.12201e22i	1.02297	+	1.18504i
$221$	2.71730e22			1.45349
$222$	1.73611e22	+	1.12581e22i	0.889662	+	0.576917i
$223$	−5.79930e21	+	5.79930e21i	−0.284760	+	0.284760i	−0.835004	−	0.550244i	$-0.814535\pi$
$223$	−5.79930e21	+	5.79930e21i	−0.284760	+	0.284760i	0.550244	+	0.835004i	$0.314535\pi$
$224$	−5.61863e21	+	9.80651e21i	−0.264408	+	0.461486i
$225$	2.18897e22	+	3.31312e22i	0.987431	+	1.49453i
$226$	4.95254e21	−	1.05612e21i	0.214189	−	0.0456754i
$227$	2.73873e22	+	2.73873e22i	1.13581	+	1.13581i	0.989194	+	0.146612i	$0.0468368\pi$
$227$	2.73873e22	+	2.73873e22i	1.13581	+	1.13581i	0.146612	+	0.989194i	$0.453163\pi$
$228$	3.52041e22	+	1.34602e22i	1.40027	+	0.535390i
$229$			2.55016e22i			0.973040i	0.873669	+	0.486520i	$0.161734\pi$
$229$			2.55016e22i			0.973040i	−0.873669	+	0.486520i	$0.838266\pi$
$230$	−1.08236e22	+	5.94150e21i	−0.396237	+	0.217511i
$231$		−	3.95975e22i		−	1.39109i
$232$	6.52610e21	−	4.17400e22i	0.220048	−	1.40740i
$233$	−2.01561e22	−	2.01561e22i	−0.652416	−	0.652416i	0.301158	−	0.953574i	$-0.402627\pi$
$233$	−2.01561e22	−	2.01561e22i	−0.652416	−	0.652416i	−0.953574	+	0.301158i	$0.902627\pi$
$234$	−1.94477e22	−	9.11977e22i	−0.604391	−	2.83422i
$235$	2.06045e21	−	3.83088e21i	0.0614918	−	0.114328i
$236$	8.57313e21	+	1.91872e22i	0.245740	+	0.549982i
$237$	1.05143e22	−	1.05143e22i	0.289514	−	0.289514i
$238$	−9.82721e21	+	1.51545e22i	−0.259985	+	0.400923i
$239$	5.27228e22			1.34035			0.670176	−	0.742203i	$-0.266219\pi$
$239$	5.27228e22			1.34035			0.670176	+	0.742203i	$0.266219\pi$
$240$	−6.43026e22	+	2.32492e22i	−1.57117	+	0.568069i
$241$	−3.84521e22			−0.903147			−0.451573	−	0.892234i	$-0.649137\pi$
$241$	−3.84521e22			−0.903147			−0.451573	+	0.892234i	$0.649137\pi$
$242$	3.49554e22	−	5.39046e22i	0.789347	−	1.21725i
$243$	−2.03423e22	+	2.03423e22i	−0.441714	+	0.441714i
$244$	−7.65740e21	−	1.71378e22i	−0.159911	−	0.357891i
$245$	−3.41896e22	+	1.02745e22i	−0.686778	+	0.206387i
$246$	5.54552e21	+	2.60050e22i	0.107166	+	0.502543i
$247$	−5.52048e22	−	5.52048e22i	−1.02649	−	1.02649i
$248$	1.32156e22	−	8.45253e22i	0.236481	−	1.51250i
$249$			1.14936e23i			1.97953i
$250$	−5.76130e22	+	1.78528e22i	−0.955191	+	0.295989i
$251$		−	9.95293e21i		−	0.158873i	−0.996840	−	0.0794366i	$-0.974688\pi$
$251$		−	9.95293e21i		−	0.158873i	0.996840	−	0.0794366i	$-0.0253121\pi$
$252$	5.78946e22	+	2.21358e22i	0.889884	+	0.340244i
$253$	3.38012e22	+	3.38012e22i	0.500366	+	0.500366i
$254$	6.49351e22	−	1.38473e22i	0.925890	−	0.197444i
$255$	−1.04650e23	+	3.14489e22i	−1.43750	+	0.431990i
$256$	−8.29546e21	−	7.51011e22i	−0.109789	−	0.993955i
$257$	3.81534e22	−	3.81534e22i	0.486596	−	0.486596i	−0.420634	−	0.907230i	$-0.638192\pi$
$257$	3.81534e22	−	3.81534e22i	0.486596	−	0.486596i	0.907230	+	0.420634i	$0.138192\pi$
$258$	−1.52102e23	−	9.86334e22i	−1.86960	−	1.21237i
$259$	2.84902e22			0.337558
$260$	1.41257e23	+	1.03680e22i	1.61348	+	0.118426i
$261$	−2.31689e23			−2.55165
$262$	−1.97902e22	−	1.28333e22i	−0.210178	−	0.136294i
$263$	1.27722e22	−	1.27722e22i	0.130823	−	0.130823i	−0.638663	−	0.769487i	$-0.720512\pi$
$263$	1.27722e22	−	1.27722e22i	0.130823	−	0.130823i	0.769487	+	0.638663i	$0.220512\pi$
$264$	1.56024e23	+	2.13855e23i	1.54154	+	2.11292i
$265$	−3.83197e22	+	7.12458e22i	−0.365247	+	0.679084i
$266$	5.07529e22	−	1.08230e22i	0.466751	−	0.0995337i
$267$	−1.71976e22	−	1.71976e22i	−0.152620	−	0.152620i
$268$	−4.30574e21	+	1.12613e22i	−0.0368780	+	0.0964517i
$269$		−	2.50597e22i		−	0.207171i	−0.994621	−	0.103585i	$-0.966969\pi$
$269$		−	2.50597e22i		−	0.207171i	0.994621	−	0.103585i	$-0.0330315\pi$
$270$	7.97094e22	+	1.45206e23i	0.636142	+	1.15885i
$271$		−	4.97376e22i		−	0.383245i	−0.981469	−	0.191622i	$-0.938625\pi$
$271$		−	4.97376e22i		−	0.383245i	0.981469	−	0.191622i	$-0.0613749\pi$
$272$	−6.63856e21	−	1.20567e23i	−0.0493934	−	0.897065i
$273$	−1.41469e23	−	1.41469e23i	−1.01652	−	1.01652i
$274$	1.64822e22	+	7.72912e22i	0.114389	+	0.536413i
$275$	1.28724e23	+	1.94830e23i	0.862977	+	1.30616i
$276$	−1.06454e23	+	4.75651e22i	−0.689485	+	0.308072i
$277$	−2.19887e22	+	2.19887e22i	−0.137608	+	0.137608i	−0.772555	−	0.634948i	$-0.781022\pi$
$277$	−2.19887e22	+	2.19887e22i	−0.137608	+	0.137608i	0.634948	+	0.772555i	$0.281022\pi$
$278$	−1.70286e22	+	2.62598e22i	−0.102980	+	0.158806i
$279$	−4.69181e23			−2.74221
$280$	−5.68683e22	+	7.50300e22i	−0.321269	+	0.423871i
$281$	2.12672e23			1.16145			0.580723	−	0.814101i	$-0.302770\pi$
$281$	2.12672e23			1.16145			0.580723	+	0.814101i	$0.302770\pi$
$282$	2.23492e22	−	3.44646e22i	0.118004	−	0.181973i
$283$	1.93802e23	−	1.93802e23i	0.989435	−	0.989435i	−0.0105099	−	0.999945i	$-0.503345\pi$
$283$	1.93802e23	−	1.93802e23i	0.989435	−	0.989435i	0.999945	+	0.0105099i	$0.00334547\pi$
$284$	4.86227e22	−	2.17253e22i	0.240057	−	0.107261i
$285$	2.76498e23	+	1.48715e23i	1.32028	+	0.710116i
$286$	−1.14364e23	−	5.36294e23i	−0.528215	−	2.47700i
$287$	2.58878e22	+	2.58878e22i	0.115669	+	0.115669i
$288$	−3.99894e23	+	1.08570e23i	−1.72869	+	0.469333i
$289$			4.61015e22i			0.192835i
$290$	9.83932e22	−	3.37884e23i	0.398276	−	1.36769i
$291$			8.09133e21i			0.0316983i
$292$	−6.79550e22	+	1.77731e23i	−0.257682	+	0.673948i
$293$	7.13493e22	+	7.13493e22i	0.261907	+	0.261907i	0.825829	−	0.563921i	$-0.190708\pi$
$293$	7.13493e22	+	7.13493e22i	0.261907	+	0.261907i	−0.563921	+	0.825829i	$0.690708\pi$
$294$	−3.29712e23	+	7.03104e22i	−1.17175	+	0.249873i
$295$	5.03820e22	+	1.67652e23i	0.173367	+	0.576898i
$296$	−1.53868e23	+	1.12259e23i	−0.512716	+	0.374067i
$297$	4.53467e23	−	4.53467e23i	1.46339	−	1.46339i
$298$	2.67758e23	+	1.73632e23i	0.836927	+	0.542720i
$299$	2.41522e23			0.731275
$300$	−5.56014e23	+	1.23555e23i	−1.63093	+	0.362417i
$301$	−2.49605e23			−0.709368
$302$	5.36989e23	+	3.48220e23i	1.47877	+	0.958932i
$303$	6.85819e23	−	6.85819e23i	1.83023	−	1.83023i
$304$	−2.31457e23	+	2.58431e23i	−0.598648	+	0.668414i
$305$	−4.50005e22	−	1.49744e23i	−0.112815	−	0.375407i
$306$	−6.47646e23	+	1.38109e23i	−1.57393	+	0.335637i
$307$	5.65688e23	+	5.65688e23i	1.33279	+	1.33279i	0.902862	+	0.429930i	$0.141462\pi$
$307$	5.65688e23	+	5.65688e23i	1.33279	+	1.33279i	0.429930	+	0.902862i	$0.358538\pi$
$308$	3.40453e23	+	1.30171e23i	0.777724	+	0.297361i
$309$		−	5.30893e23i		−	1.17598i
$310$	1.99250e23	−	6.84229e23i	0.428019	−	1.46982i
$311$			1.67445e23i			0.348858i	0.984670	+	0.174429i	$0.0558079\pi$
$311$			1.67445e23i			0.348858i	−0.984670	+	0.174429i	$0.944192\pi$
$312$	1.32146e24	+	2.06612e23i	2.67046	+	0.417529i
$313$	−2.54016e23	−	2.54016e23i	−0.497955	−	0.497955i	0.412846	−	0.910801i	$-0.364535\pi$
$313$	−2.54016e23	−	2.54016e23i	−0.497955	−	0.497955i	−0.910801	+	0.412846i	$0.864535\pi$
$314$	1.01968e23	+	4.78164e23i	0.193923	+	0.909380i
$315$	4.54713e23	+	2.44568e23i	0.839048	+	0.451284i
$316$	5.58359e22	+	1.24964e23i	0.0999738	+	0.223748i
$317$	5.58521e23	−	5.58521e23i	0.970457	−	0.970457i	−0.0291189	−	0.999576i	$-0.509270\pi$
$317$	5.58521e23	−	5.58521e23i	0.970457	−	0.970457i	0.999576	+	0.0291189i	$0.00927013\pi$
$318$	−4.15645e23	+	6.40964e23i	−0.700914	+	1.08088i
$319$	−1.36247e24			−2.23005
$320$	1.14929e22	−	6.29292e23i	0.0182602	−	0.999833i
$321$	−2.19651e23			−0.338794
$322$	−8.73472e22	+	1.34698e23i	−0.130803	+	0.201711i
$323$	−3.92040e23	+	3.92040e23i	−0.570042	+	0.570042i
$324$	1.20585e23	+	2.69878e23i	0.170262	+	0.381057i
$325$	1.15596e24	+	2.36177e23i	1.58507	+	0.323851i
$326$	−2.32348e23	−	1.08957e24i	−0.309436	−	1.45106i
$327$	−1.31816e24	−	1.31816e24i	−1.70516	−	1.70516i
$328$	−2.41817e23	−	3.78083e22i	−0.303868	−	0.0475101i
$329$		−	5.65576e22i		−	0.0690447i
$330$	1.06113e24	+	1.93304e24i	1.25859	+	2.29276i
$331$			1.16882e24i			1.34705i	0.739166	+	0.673524i	$0.235220\pi$
$331$			1.16882e24i			1.34705i	−0.739166	+	0.673524i	$0.764780\pi$
$332$	−9.88202e23	−	3.77836e23i	−1.10671	−	0.423147i
$333$	7.38604e23	+	7.38604e23i	0.803881	+	0.803881i
$334$	−5.76083e23	+	1.22849e23i	−0.609388	+	0.129951i
$335$	−4.75721e22	+	8.84483e22i	−0.0489132	+	0.0909418i
$336$	−5.93139e23	+	6.62263e23i	−0.592835	+	0.661923i
$337$	9.23141e23	−	9.23141e23i	0.896983	−	0.896983i	−0.0981853	−	0.995168i	$-0.531304\pi$
$337$	9.23141e23	−	9.23141e23i	0.896983	−	0.896983i	0.995168	+	0.0981853i	$0.0313038\pi$
$338$	−1.43644e24	−	9.31486e23i	−1.35700	−	0.879970i
$339$	3.98338e23			0.365894
$340$	7.36291e22	−	1.00315e24i	0.0657657	−	0.896013i
$341$	−2.75905e24			−2.39658
$342$	1.59634e24	+	1.03518e24i	1.34858	+	0.874513i
$343$	−7.85925e23	+	7.85925e23i	−0.645784	+	0.645784i
$344$	1.34805e24	−	9.83507e23i	1.07746	−	0.786090i
$345$	−9.30160e23	+	2.79527e23i	−0.723229	+	0.217342i
$346$	1.27296e24	−	2.71455e23i	0.962921	−	0.205341i
$347$	7.07405e23	+	7.07405e23i	0.520641	+	0.520641i	0.917765	−	0.397124i	$-0.129992\pi$
$347$	7.07405e23	+	7.07405e23i	0.520641	+	0.520641i	−0.397124	+	0.917765i	$0.629992\pi$
$348$	1.18685e24	−	3.10411e24i	0.849947	−	2.22297i
$349$			8.71502e23i			0.607333i	0.952778	+	0.303667i	$0.0982109\pi$
$349$			8.71502e23i			0.607333i	−0.952778	+	0.303667i	$0.901789\pi$
$350$	−5.49772e23	+	5.59268e23i	−0.372852	+	0.379292i
$351$		−	3.24019e24i		−	2.13871i
$352$	−2.35160e24	+	6.38453e23i	−1.51081	+	0.410179i
$353$	−1.95109e23	−	1.95109e23i	−0.122016	−	0.122016i	0.643462	−	0.765478i	$-0.277498\pi$
$353$	−1.95109e23	−	1.95109e23i	−0.122016	−	0.122016i	−0.765478	+	0.643462i	$0.777498\pi$
$354$	3.44773e23	+	1.61677e24i	0.209895	+	0.984278i
$355$	4.24850e23	−	1.27674e23i	0.251806	−	0.0756716i
$356$	2.04397e23	−	9.13277e22i	0.117951	−	0.0527021i
$357$	−1.00465e24	+	1.00465e24i	−0.564506	+	0.564506i
$358$	−1.89578e24	+	2.92347e24i	−1.03729	+	1.59959i
$359$	−5.00351e23			−0.266611			−0.133305	−	0.991075i	$-0.542559\pi$
$359$	−5.00351e23			−0.266611			−0.133305	+	0.991075i	$0.542559\pi$
$360$	−3.41944e24	+	4.70839e23i	−1.77452	+	0.244342i
$361$	−3.85480e23			−0.194843
$362$	7.69225e23	−	1.18622e24i	0.378723	−	0.584028i
$363$	3.57356e24	−	3.57356e24i	1.71391	−	1.71391i
$364$	1.68139e24	−	7.51270e23i	0.785608	−	0.351021i
$365$	−7.50802e23	+	1.39593e24i	−0.341777	+	0.635448i
$366$	−3.07947e23	−	1.44408e24i	−0.136586	−	0.640502i
$367$	2.71996e24	+	2.71996e24i	1.17553	+	1.17553i	0.980870	+	0.194662i	$0.0623609\pi$
$367$	2.71996e24	+	2.71996e24i	1.17553	+	1.17553i	0.194662	+	0.980870i	$0.437639\pi$
$368$	−5.90055e22	−	1.07164e24i	−0.0248507	−	0.451329i
$369$			1.34227e24i			0.550921i
$370$	−1.39081e24	+	7.63475e23i	−0.556355	+	0.305406i
$371$			1.05184e24i			0.410109i
$372$	2.40341e24	−	6.28594e24i	0.913420	−	2.38898i
$373$	−1.68512e24	−	1.68512e24i	−0.624305	−	0.624305i	0.322324	−	0.946629i	$-0.395536\pi$
$373$	−1.68512e24	−	1.68512e24i	−0.624305	−	0.624305i	−0.946629	+	0.322324i	$0.895536\pi$
$374$	−3.80853e24	+	8.12161e23i	−1.37555	+	0.293334i
$375$	−4.72521e24	+	4.28280e23i	−1.66389	+	0.150810i
$376$	2.22851e23	+	3.05452e23i	0.0765122	+	0.104872i
$377$	−4.86765e24	+	4.86765e24i	−1.62958	+	1.62958i
$378$	1.80707e24	+	1.17182e24i	0.589932	+	0.382552i
$379$	4.75737e24			1.51459			0.757294	−	0.653075i	$-0.226521\pi$
$379$	4.75737e24			1.51459			0.757294	+	0.653075i	$0.226521\pi$
$380$	−2.18758e24	+	1.88841e24i	−0.679234	+	0.586343i
$381$	5.22281e24			1.58167
$382$	−2.62955e23	−	1.70518e23i	−0.0776746	−	0.0503695i
$383$	−2.87573e24	+	2.87573e24i	−0.828628	+	0.828628i	−0.987327	−	0.158699i	$-0.949270\pi$
$383$	−2.87573e24	+	2.87573e24i	−0.828628	+	0.828628i	0.158699	+	0.987327i	$0.449270\pi$
$384$	5.93897e23	−	5.91382e24i	0.166942	−	1.66235i
$385$	2.67397e24	+	1.43820e24i	0.733296	+	0.394405i
$386$	3.60833e24	−	7.69470e23i	0.965445	−	0.205879i
$387$	−6.47096e24	−	6.47096e24i	−1.68933	−	1.68933i
$388$	−6.95679e22	−	2.65991e22i	−0.0177218	−	0.00677587i
$389$		−	3.80778e24i		−	0.946566i	−0.880910	−	0.473283i	$-0.843069\pi$
$389$		−	3.80778e24i		−	0.946566i	0.880910	−	0.473283i	$-0.156931\pi$
$390$	1.06972e25	+	3.11507e24i	2.59511	+	0.755707i
$391$		−	1.71518e24i		−	0.406099i
$392$	4.79364e23	−	3.06595e24i	0.110777	−	0.708512i
$393$	−1.31197e24	−	1.31197e24i	−0.295934	−	0.295934i
$394$	1.91060e23	+	8.95951e23i	0.0420683	+	0.197274i
$395$	3.28132e23	+	1.09190e24i	0.0705304	+	0.234698i
$396$	5.45152e24	+	1.22009e25i	1.14397	+	2.56027i
$397$	−3.90708e23	+	3.90708e23i	−0.0800465	+	0.0800465i	−0.745996	−	0.665950i	$-0.768026\pi$
$397$	−3.90708e23	+	3.90708e23i	−0.0800465	+	0.0800465i	0.665950	+	0.745996i	$0.268026\pi$
$398$	4.14404e24	−	6.39050e24i	0.828961	−	1.27834i
$399$	4.08211e24			0.797338
$400$	7.65512e23	−	5.18669e24i	0.146010	−	0.989283i
$401$	9.07597e24			1.69052			0.845262	−	0.534351i	$-0.179444\pi$
$401$	9.07597e24			1.69052			0.845262	+	0.534351i	$0.179444\pi$
$402$	−5.16003e23	+	7.95727e23i	−0.0938652	+	0.144749i
$403$	−9.85720e24	+	9.85720e24i	−1.75128	+	1.75128i
$404$	3.64203e24	+	8.15109e24i	0.632005	+	1.41447i
$405$	7.08648e23	+	2.35811e24i	0.120118	+	0.399706i
$406$	−9.54308e23	−	4.47511e24i	−0.158012	−	0.740980i
$407$	4.34341e24	+	4.34341e24i	0.702561	+	0.702561i
$408$	1.46727e24	−	9.38445e24i	0.231866	−	1.48299i
$409$			1.15544e25i			1.78393i	0.452106	+	0.891964i	$0.350673\pi$
$409$			1.15544e25i			1.78393i	−0.452106	+	0.891964i	$0.649327\pi$
$410$	−1.95750e24	−	5.70032e23i	−0.295294	−	0.0859909i
$411$			6.21662e24i			0.916341i
$412$	4.56453e24	+	1.74524e24i	0.657465	+	0.251380i
$413$	1.60948e24	+	1.60948e24i	0.226548	+	0.226548i
$414$	−5.75648e24	+	1.22756e24i	−0.791869	+	0.168865i
$415$	−7.76148e24	−	4.17453e24i	−1.04349	−	0.561242i
$416$	−6.12054e24	+	1.06825e25i	−0.804272	+	1.40374i
$417$	−1.74087e24	+	1.74087e24i	−0.223601	+	0.223601i
$418$	9.38740e24	+	6.08742e24i	1.17861	+	0.764291i
$419$	5.59223e24			0.686359			0.343180	−	0.939270i	$-0.388496\pi$
$419$	5.59223e24			0.686359			0.343180	+	0.939270i	$0.388496\pi$
$420$	−5.60595e24	+	4.83929e24i	−0.672638	+	0.580649i
$421$	−1.33301e25			−1.56369			−0.781847	−	0.623470i	$-0.785722\pi$
$421$	−1.33301e25			−1.56369			−0.781847	+	0.623470i	$0.785722\pi$
$422$	−7.92163e24	−	5.13692e24i	−0.908545	−	0.589162i
$423$	1.46625e24	−	1.46625e24i	0.164427	−	0.164427i
$424$	−4.14453e24	−	5.68072e24i	−0.454465	−	0.622914i
$425$	1.67723e24	−	8.20910e24i	0.179844	−	0.880239i
$426$	4.09709e24	−	8.73697e23i	0.429620	−	0.0916156i
$427$	−1.43757e24	−	1.43757e24i	−0.147422	−	0.147422i
$428$	7.22073e23	−	1.88853e24i	0.0724211	−	0.189412i
$429$		−	4.31348e25i		−	4.23139i
$430$	1.21850e25	−	6.68886e24i	1.16916	−	0.641803i
$431$		−	1.51693e25i		−	1.42374i	−0.702311	−	0.711870i	$-0.747848\pi$
$431$		−	1.51693e25i		−	1.42374i	0.702311	−	0.711870i	$-0.252152\pi$
$432$	−1.43767e25	+	7.91600e23i	−1.31997	+	0.0726792i
$433$	3.56847e24	+	3.56847e24i	0.320514	+	0.320514i	0.848964	−	0.528450i	$-0.177227\pi$
$433$	3.56847e24	+	3.56847e24i	0.320514	+	0.320514i	−0.528450	+	0.848964i	$0.677227\pi$
$434$	−1.93251e24	−	9.06228e24i	−0.169813	−	0.796315i
$435$	1.31129e25	−	2.43801e25i	1.12733	−	2.09598i
$436$	1.56666e25	−	7.00006e24i	1.31781	−	0.588817i
$437$	−3.48457e24	+	3.48457e24i	−0.286798	+	0.286798i
$438$	−8.14377e24	+	1.25585e25i	−0.655875	+	1.01142i
$439$	7.90582e24			0.623066			0.311533	−	0.950235i	$-0.399158\pi$
$439$	7.90582e24			0.623066			0.311533	+	0.950235i	$0.399158\pi$
$440$	−2.01082e25	+	2.76880e24i	−1.55086	+	0.213546i
$441$	−1.70184e25			−1.28455
$442$	−1.07051e25	+	1.65082e25i	−0.790820	+	1.21952i
$443$	−1.11541e25	+	1.11541e25i	−0.806494	+	0.806494i	−0.984101	−	0.177608i	$-0.943164\pi$
$443$	−1.11541e25	+	1.11541e25i	−0.806494	+	0.806494i	0.177608	+	0.984101i	$0.443164\pi$
$444$	−1.36792e25	+	6.11205e24i	−0.968102	+	0.432562i
$445$	1.78596e24	−	5.36708e23i	0.123723	−	0.0371807i
$446$	−1.23852e24	−	5.80790e24i	−0.0839891	−	0.393856i
$447$	1.77507e25	+	1.77507e25i	1.17841	+	1.17841i
$448$	−3.74417e24	−	7.27681e24i	−0.243341	−	0.472933i
$449$			5.20284e24i			0.331055i	0.986205	+	0.165528i	$0.0529327\pi$
$449$			5.20284e24i			0.331055i	−0.986205	+	0.165528i	$0.947067\pi$
$450$	−2.87517e25	+	2.46171e23i	−1.79120	+	0.0153362i
$451$			7.89331e24i			0.481484i
$452$	−1.30948e24	+	3.42485e24i	−0.0782139	+	0.204562i
$453$	3.55992e25	+	3.55992e25i	2.08213	+	2.08213i
$454$	−2.74279e25	+	5.84895e24i	−1.57095	+	0.335002i
$455$	1.46915e25	−	4.41501e24i	0.824056	−	0.247642i
$456$	−2.20464e25	+	1.60846e25i	−1.21108	+	0.883575i
$457$	−8.50179e24	+	8.50179e24i	−0.457411	+	0.457411i	−0.897805	−	0.440394i	$-0.854839\pi$
$457$	−8.50179e24	+	8.50179e24i	−0.457411	+	0.457411i	0.440394	+	0.897805i	$0.354839\pi$
$458$	−1.54928e25	−	1.00466e25i	−0.816410	−	0.529416i
$459$	−2.30104e25			−1.18769
$460$	6.54438e23	−	8.91627e24i	0.0330879	−	0.450800i
$461$	1.50528e25			0.745517			0.372758	−	0.927928i	$-0.378412\pi$
$461$	1.50528e25			0.745517			0.372758	+	0.927928i	$0.378412\pi$
$462$	2.40564e25	+	1.55998e25i	1.16717	+	0.756869i
$463$	1.78302e25	−	1.78302e25i	0.847495	−	0.847495i	−0.142325	−	0.989820i	$-0.545458\pi$
$463$	1.78302e25	−	1.78302e25i	0.847495	−	0.847495i	0.989820	+	0.142325i	$0.0454577\pi$
$464$	2.27870e25	+	2.04086e25i	1.06113	+	0.950370i
$465$	2.65541e25	−	4.93707e25i	1.21152	−	2.25251i
$466$	2.01859e25	−	4.30461e24i	0.902366	−	0.192428i
$467$	−3.82736e24	−	3.82736e24i	−0.167644	−	0.167644i	0.618299	−	0.785943i	$-0.287822\pi$
$467$	−3.82736e24	−	3.82736e24i	−0.167644	−	0.167644i	−0.785943	+	0.618299i	$0.787822\pi$
$468$	6.30663e25	+	2.41132e25i	2.70684	+	1.03495i
$469$			1.30581e24i			0.0549211i
$470$	1.51562e24	+	2.76098e24i	0.0624683	+	0.113798i
$471$			3.84593e25i			1.55347i
$472$	−1.50341e25	−	2.35060e24i	−0.595154	−	0.0930530i
$473$	−3.80529e25	−	3.80529e25i	−1.47641	−	1.47641i
$474$	2.24547e24	+	1.05299e25i	0.0853912	+	0.400432i
$475$	−2.00851e25	+	1.32702e25i	−0.748659	+	0.494638i
$476$	−5.33519e24	−	1.19405e25i	−0.194932	−	0.436271i
$477$	−2.72689e25	+	2.72689e25i	−0.976658	+	0.976658i
$478$	−2.07706e25	+	3.20303e25i	−0.729264	+	1.12460i
$479$	−1.26642e25			−0.435904			−0.217952	−	0.975959i	$-0.569938\pi$
$479$	−1.26642e25			−0.435904			−0.217952	+	0.975959i	$0.569938\pi$
$480$	1.12082e25	−	4.82246e25i	0.378219	−	1.62733i
$481$	3.10352e25			1.02678
$482$	1.51486e25	−	2.33605e25i	0.491388	−	0.757768i
$483$	−8.92967e24	+	8.92967e24i	−0.284013	+	0.284013i
$484$	1.89773e25	+	4.24724e25i	0.591839	+	1.32457i
$485$	−5.46396e23	−	2.93880e23i	−0.0167094	−	0.00898719i
$486$	−4.34439e24	−	2.03725e25i	−0.130282	−	0.610941i
$487$	−3.26676e25	−	3.26676e25i	−0.960711	−	0.960711i	0.0385459	−	0.999257i	$-0.487727\pi$
$487$	−3.26676e25	−	3.26676e25i	−0.960711	−	0.960711i	−0.999257	+	0.0385459i	$0.987727\pi$
$488$	1.34283e25	+	2.09953e24i	0.387286	+	0.0605526i
$489$		−	8.76350e25i		−	2.47881i
$490$	7.22731e24	−	2.48187e25i	0.200500	−	0.688520i
$491$		−	6.86788e25i		−	1.86874i	−0.356305	−	0.934370i	$-0.615964\pi$
$491$		−	6.86788e25i		−	1.86874i	0.356305	−	0.934370i	$-0.384036\pi$
$492$	−1.79833e25	−	6.87588e24i	−0.479957	−	0.183510i
$493$	3.45679e25	+	3.45679e25i	0.904957	+	0.904957i
$494$	5.52866e25	−	1.17898e25i	1.41976	−	0.302760i
$495$	3.20371e25	+	1.06607e26i	0.807056	+	2.68557i
$496$	4.61447e25	+	4.13283e25i	1.14037	+	1.02134i
$497$	4.07862e24	−	4.07862e24i	0.0988843	−	0.0988843i
$498$	−6.98263e25	−	4.52801e25i	−1.66089	−	1.07703i
$499$	1.45462e25			0.339464			0.169732	−	0.985490i	$-0.445710\pi$
$499$	1.45462e25			0.339464			0.169732	+	0.985490i	$0.445710\pi$
$500$	1.18512e25	−	4.20345e25i	0.271360	−	0.962478i
$501$	−4.63350e25			−1.04100
$502$	6.04663e24	+	3.92105e24i	0.133299	+	0.0864404i
$503$	−6.67399e24	+	6.67399e24i	−0.144374	+	0.144374i	−0.775600	−	0.631225i	$-0.782552\pi$
$503$	−6.67399e24	+	6.67399e24i	−0.144374	+	0.144374i	0.631225	+	0.775600i	$0.282552\pi$
$504$	−3.62562e25	+	2.64517e25i	−0.769647	+	0.561518i
$505$	2.14032e25	+	7.12217e25i	0.445873	+	1.48369i
$506$	−3.38513e25	+	7.21873e24i	−0.692064	+	0.147581i
$507$	−9.52276e25	−	9.52276e25i	−1.91068	−	1.91068i
$508$	−1.71692e25	+	4.49049e25i	−0.338100	+	0.884276i
$509$		−	7.67112e24i		−	0.148265i	−0.997248	−	0.0741327i	$-0.976381\pi$
$509$		−	7.67112e24i		−	0.148265i	0.997248	−	0.0741327i	$-0.0236188\pi$
$510$	2.21218e25	−	7.59668e25i	0.419667	−	1.44114i
$511$			2.06089e25i			0.383757i
$512$	4.88937e25	+	2.45471e25i	0.893693	+	0.448678i
$513$	4.67480e25	+	4.67480e25i	0.838780	+	0.838780i
$514$	8.14819e24	+	3.82100e25i	0.143520	+	0.673018i
$515$	3.58505e25	+	1.92823e25i	0.619907	+	0.333418i
$516$	1.19844e26	−	5.35481e25i	2.03444	−	0.909017i
$517$	8.62236e24	−	8.62236e24i	0.143703	−	0.143703i
$518$	−1.12240e25	+	1.73085e25i	−0.183660	+	0.283221i
$519$	1.02385e26			1.64493
$520$	−6.19483e25	+	8.17324e25i	−0.977232	+	1.28932i
$521$	−4.12704e25			−0.639264			−0.319632	−	0.947542i	$-0.603559\pi$
$521$	−4.12704e25			−0.639264			−0.319632	+	0.947542i	$0.603559\pi$
$522$	9.12761e25	−	1.40757e26i	1.38831	−	2.14091i
$523$	4.72074e25	−	4.72074e25i	0.705089	−	0.705089i	−0.260409	−	0.965498i	$-0.583858\pi$
$523$	4.72074e25	−	4.72074e25i	0.705089	−	0.705089i	0.965498	+	0.260409i	$0.0838575\pi$
$524$	1.55931e25	−	6.96721e24i	0.228709	−	0.102191i
$525$	−5.14706e25	+	3.40065e25i	−0.741389	+	0.489834i
$526$	2.72768e24	+	1.27911e25i	0.0385859	+	0.180944i
$527$	7.00015e25	+	7.00015e25i	0.972538	+	0.972538i
$528$	−1.91389e26	+	1.05381e25i	−2.61153	+	0.143794i
$529$			5.93704e25i			0.795685i
$530$	−2.81871e25	−	5.13480e25i	−0.371047	−	0.675932i
$531$			8.34511e25i			1.07903i
$532$	−1.34194e25	+	3.50974e25i	−0.170440	+	0.445773i
$533$	2.82003e25	+	2.82003e25i	0.351840	+	0.351840i
$534$	1.72231e25	−	3.67280e24i	0.211091	−	0.0450148i
$535$	7.97783e24	−	1.48328e25i	0.0960559	−	0.178592i
$536$	−5.14524e24	−	7.05235e24i	−0.0608612	−	0.0834196i
$537$	−1.93809e26	+	1.93809e26i	−2.25225	+	2.25225i
$538$	1.52243e25	+	9.87248e24i	0.173823	+	0.112718i
$539$	−1.00078e26			−1.12265
$540$	−1.19618e26	−	8.77974e24i	−1.31843	−	0.0967700i
$541$	−1.67689e25			−0.181606			−0.0908029	−	0.995869i	$-0.528943\pi$
$541$	−1.67689e25			−0.181606			−0.0908029	+	0.995869i	$0.528943\pi$
$542$	3.02167e25	+	1.95946e25i	0.321554	+	0.208517i
$543$	7.86393e25	−	7.86393e25i	0.822321	−	0.822321i
$544$	7.58626e25	+	4.34654e25i	0.779539	+	0.446636i
$545$	1.36890e26	−	4.11375e25i	1.38231	−	0.415404i
$546$	1.41679e26	−	3.02128e25i	1.40597	−	0.299820i
$547$	−7.59100e25	−	7.59100e25i	−0.740319	−	0.740319i	0.232320	−	0.972639i	$-0.425368\pi$
$547$	−7.59100e25	−	7.59100e25i	−0.740319	−	0.740319i	−0.972639	+	0.232320i	$0.925368\pi$
$548$	−5.34495e25	−	2.04363e25i	−0.512305	−	0.195878i
$549$		−	7.45373e25i		−	0.702161i
$550$	−1.69076e26	+	1.44762e24i	−1.56544	+	0.0134033i
$551$		−	1.40457e26i		−	1.27821i
$552$	1.30415e25	−	8.34119e25i	0.116656	−	0.746116i
$553$	1.04824e25	+	1.04824e25i	0.0921661	+	0.0921661i
$554$	−4.69600e24	−	2.20213e25i	−0.0405869	−	0.190327i
$555$	−1.19524e26	+	3.59188e25i	−1.01548	+	0.305168i
$556$	−9.24485e24	−	2.06906e25i	−0.0772128	−	0.172807i
$557$	4.99266e25	−	4.99266e25i	0.409928	−	0.409928i	−0.471786	−	0.881713i	$-0.656390\pi$
$557$	4.99266e25	−	4.99266e25i	0.409928	−	0.409928i	0.881713	+	0.471786i	$0.156390\pi$
$558$	1.84838e26	−	2.85038e26i	1.49199	−	2.30079i
$559$	−2.71902e26			−2.15775
$560$	−2.31787e25	−	6.41076e25i	−0.180843	−	0.500176i
$561$	−3.06324e26			−2.34982
$562$	−8.37839e25	+	1.29203e26i	−0.631925	+	0.974490i
$563$	2.07757e25	−	2.07757e25i	0.154072	−	0.154072i	−0.625862	−	0.779934i	$-0.715253\pi$
$563$	2.07757e25	−	2.07757e25i	0.154072	−	0.154072i	0.779934	+	0.625862i	$0.215253\pi$
$564$	1.21334e25	+	2.71553e25i	0.0884770	+	0.198017i
$565$	−1.44678e25	+	2.68992e25i	−0.103739	+	0.192877i
$566$	4.13891e25	+	1.94089e26i	0.291830	+	1.36850i
$567$	2.26382e25	+	2.26382e25i	0.156965	+	0.156965i
$568$	−5.95671e24	+	3.80983e25i	−0.0406160	+	0.259774i
$569$		−	2.36882e26i		−	1.58842i	−0.607644	−	0.794210i	$-0.707885\pi$
$569$		−	2.36882e26i		−	1.58842i	0.607644	−	0.794210i	$-0.292115\pi$
$570$	−1.99277e26	+	1.09391e26i	−1.31415	+	0.721394i
$571$			1.35004e26i			0.875593i	0.899074	+	0.437797i	$0.144241\pi$
$571$			1.35004e26i			0.875593i	−0.899074	+	0.437797i	$0.855759\pi$
$572$	3.70866e26	+	1.41799e26i	2.36567	+	0.904507i
$573$	−1.74323e25	−	1.74323e25i	−0.109367	−	0.109367i
$574$	−2.59261e25	+	5.52869e24i	−0.159983	+	0.0341161i
$575$	1.49077e25	−	7.29650e25i	0.0904828	−	0.442864i
$576$	9.15831e25	−	2.85717e26i	0.546766	−	1.70578i
$577$	−2.19056e26	+	2.19056e26i	−1.28643	+	1.28643i	−0.349485	+	0.936942i	$0.613643\pi$
$577$	−2.19056e26	+	2.19056e26i	−1.28643	+	1.28643i	−0.936942	+	0.349485i	$0.886357\pi$
$578$	−2.80077e25	−	1.81621e25i	−0.161794	−	0.104918i
$579$	2.90222e26			1.64924
$580$	1.66509e26	+	1.92889e26i	0.930836	+	1.07830i
$581$	−1.14587e26			−0.630178
$582$	−4.91567e24	−	3.18765e24i	−0.0265959	−	0.0172466i
$583$	−1.60356e26	+	1.60356e26i	−0.853562	+	0.853562i
$584$	−8.12043e25	−	1.11303e26i	−0.425263	−	0.582888i
$585$	4.95332e26	+	2.66415e26i	2.55221	+	1.37271i
$586$	−7.14551e25	+	1.52377e25i	−0.362248	+	0.0772486i
$587$	1.23314e26	+	1.23314e26i	0.615106	+	0.615106i	0.944272	−	0.329166i	$-0.106768\pi$
$587$	1.23314e26	+	1.23314e26i	0.615106	+	0.615106i	−0.329166	+	0.944272i	$0.606768\pi$
$588$	8.71778e25	−	2.28007e26i	0.427880	−	1.11909i
$589$		−	2.84430e26i		−	1.37366i
$590$	−1.21701e26	−	3.54398e25i	−0.578361	−	0.168421i
$591$			7.20624e25i			0.336998i
$592$	−7.58212e24	−	1.37704e26i	−0.0348927	−	0.633708i
$593$	−1.10097e26	−	1.10097e26i	−0.498602	−	0.498602i	0.412400	−	0.911003i	$-0.364690\pi$
$593$	−1.10097e26	−	1.10097e26i	−0.498602	−	0.498602i	−0.911003	+	0.412400i	$0.864690\pi$
$594$	9.68443e25	+	4.54139e26i	0.431621	+	2.02403i
$595$	−3.13535e25	−	1.04332e26i	−0.137523	−	0.457623i
$596$	−2.10971e26	+	9.42650e25i	−0.910717	+	0.406922i
$597$	4.23653e26	−	4.23653e26i	1.79992	−	1.79992i
$598$	−9.51498e25	+	1.46730e26i	−0.397875	+	0.613562i
$599$	1.65256e26			0.680146			0.340073	−	0.940399i	$-0.389548\pi$
$599$	1.65256e26			0.680146			0.340073	+	0.940399i	$0.389548\pi$
$600$	1.43984e26	−	3.86467e26i	0.583282	−	1.56558i
$601$	3.78697e26			1.51003			0.755014	−	0.655709i	$-0.227630\pi$
$601$	3.78697e26			1.51003			0.755014	+	0.655709i	$0.227630\pi$
$602$	9.83342e25	−	1.51641e26i	0.385956	−	0.595182i
$603$	−3.38530e25	+	3.38530e25i	−0.130792	+	0.130792i
$604$	−4.23103e26	+	1.89049e26i	−1.60915	+	0.718990i
$605$	1.11524e26	+	3.71111e26i	0.417536	+	1.38940i
$606$	1.46466e26	+	6.86836e26i	0.539818	+	2.53141i
$607$	−1.08502e26	−	1.08502e26i	−0.393681	−	0.393681i	0.482317	−	0.875997i	$-0.339796\pi$
$607$	−1.08502e26	−	1.08502e26i	−0.393681	−	0.393681i	−0.875997	+	0.482317i	$0.839796\pi$
$608$	−6.58182e25	−	2.42427e26i	−0.235105	−	0.865958i
$609$		−	3.59938e26i		−	1.26580i
$610$	1.08701e26	+	3.16543e25i	0.376359	+	0.109597i
$611$		−	6.16099e25i		−	0.210019i
$612$	1.71242e26	−	4.47869e26i	0.574739	−	1.50319i
$613$	2.47370e26	+	2.47370e26i	0.817471	+	0.817471i	0.985741	−	0.168270i	$-0.0538179\pi$
$613$	2.47370e26	+	2.47370e26i	0.817471	+	0.817471i	−0.168270	+	0.985741i	$0.553818\pi$
$614$	−5.66527e26	+	1.20811e26i	−1.84340	+	0.393102i
$615$	−1.41244e26	−	7.59683e25i	−0.452539	−	0.243399i
$616$	−2.13207e26	+	1.55551e26i	−0.672642	+	0.490745i
$617$	1.43940e26	−	1.43940e26i	0.447169	−	0.447169i	−0.447243	−	0.894412i	$-0.647594\pi$
$617$	1.43940e26	−	1.43940e26i	0.447169	−	0.447169i	0.894412	+	0.447243i	$0.147594\pi$
$618$	3.22530e26	+	2.09150e26i	0.986687	+	0.639835i
$619$	3.26531e26			0.983702			0.491851	−	0.870679i	$-0.336320\pi$
$619$	3.26531e26			0.983702			0.491851	+	0.870679i	$0.336320\pi$
$620$	3.37188e26	+	3.90607e26i	1.00035	+	1.15883i
$621$	−2.04523e26			−0.597548
$622$	−1.01727e26	−	6.59665e25i	−0.292702	−	0.189808i
$623$	1.71455e25	−	1.71455e25i	0.0485862	−	0.0485862i
$624$	−6.46124e26	+	7.21422e26i	−1.80328	+	2.01343i
$625$	1.42700e26	−	3.34642e26i	0.392252	−	0.919858i
$626$	2.54393e26	−	5.42487e25i	0.688729	−	0.146870i
$627$	6.22329e26	+	6.22329e26i	1.65950	+	1.65950i
$628$	−3.30667e26	−	1.26429e26i	−0.868509	−	0.332072i
$629$		−	2.20399e26i		−	0.570201i
$630$	−3.27719e26	+	1.79899e26i	−0.835154	+	0.458451i
$631$		−	4.94705e26i		−	1.24184i	−0.783872	−	0.620922i	$-0.786758\pi$
$631$		−	4.94705e26i		−	1.24184i	0.783872	−	0.620922i	$-0.213242\pi$
$632$	−9.79157e25	−	1.53092e25i	−0.242125	−	0.0378565i
$633$	−5.25157e26	−	5.25157e26i	−1.27925	−	1.27925i
$634$	1.19280e26	+	5.59349e26i	0.286233	+	1.34225i
$635$	−1.89695e26	+	3.52689e26i	−0.448440	+	0.833761i
$636$	−2.25654e26	−	5.05027e26i	−0.525533	−	1.17618i
$637$	−3.57545e26	+	3.57545e26i	−0.820364	+	0.820364i
$638$	5.36755e26	−	8.27729e26i	1.21333	−	1.87108i
$639$	2.11475e26			0.470978
$640$	3.77782e26	+	2.54898e26i	0.828956	+	0.559314i
$641$	−2.79875e26			−0.605080			−0.302540	−	0.953137i	$-0.597835\pi$
$641$	−2.79875e26			−0.605080			−0.302540	+	0.953137i	$0.597835\pi$
$642$	8.65337e25	−	1.33443e26i	0.184333	−	0.284259i
$643$	−1.31228e24	+	1.31228e24i	−0.00275436	+	0.00275436i	−0.708483	−	0.705728i	$-0.750620\pi$
$643$	−1.31228e24	+	1.31228e24i	−0.00275436	+	0.00275436i	0.705728	+	0.708483i	$0.250620\pi$
$644$	−4.74208e25	−	1.06131e26i	−0.0980739	−	0.219496i
$645$	1.04716e27	−	3.14688e26i	2.13401	−	0.641302i
$646$	−8.37257e25	−	3.92621e26i	−0.168132	−	0.788433i
$647$	−2.19197e26	−	2.19197e26i	−0.433754	−	0.433754i	0.456149	−	0.889903i	$-0.349228\pi$
$647$	−2.19197e26	−	2.19197e26i	−0.433754	−	0.433754i	−0.889903	+	0.456149i	$0.849228\pi$
$648$	−2.11463e26	−	3.30624e25i	−0.412355	−	0.0644722i
$649$			4.90740e26i			0.943032i
$650$	−5.98883e26	+	6.09226e26i	−1.13414	+	1.15372i
$651$		−	7.28890e26i		−	1.36032i
$652$	7.53472e26	+	2.88088e26i	1.38585	+	0.529874i
$653$	2.57141e25	+	2.57141e25i	0.0466118	+	0.0466118i	0.730029	−	0.683417i	$-0.239507\pi$
$653$	2.57141e25	+	2.57141e25i	0.0466118	+	0.0466118i	−0.683417	+	0.730029i	$0.739507\pi$
$654$	1.32011e27	−	2.81512e26i	2.35843	−	0.502930i
$655$	1.36247e26	−	4.09444e25i	0.239903	−	0.0720944i
$656$	1.18235e26	−	1.32014e26i	0.205192	−	0.229105i
$657$	−5.34282e26	+	5.34282e26i	−0.913902	+	0.913902i
$658$	3.43601e25	+	2.22814e25i	0.0579306	+	0.0375661i
$659$	−3.64222e26			−0.605278			−0.302639	−	0.953105i	$-0.597868\pi$
$659$	−3.64222e26			−0.605278			−0.302639	+	0.953105i	$0.597868\pi$
$660$	−1.59241e27	−	1.16880e26i	−2.60847	−	0.191457i
$661$	−7.89558e26			−1.27488			−0.637441	−	0.770499i	$-0.720007\pi$
$661$	−7.89558e26			−1.27488			−0.637441	+	0.770499i	$0.720007\pi$
$662$	−7.10087e26	−	4.60468e26i	−1.13021	−	0.732907i
$663$	−1.09440e27	+	1.09440e27i	−1.71711	+	1.71711i
$664$	6.18855e26	−	4.51503e26i	0.957177	−	0.698336i
$665$	−1.48264e26	+	2.75660e26i	−0.226063	+	0.420308i
$666$	−7.39699e26	+	1.57739e26i	−1.11186	+	0.237102i
$667$	3.07250e26	+	3.07250e26i	0.455299	+	0.455299i
$668$	1.52320e26	−	3.98381e26i	0.222526	−	0.581999i
$669$		−	4.67136e26i		−	0.672814i
$670$	−3.49929e25	−	6.37461e25i	−0.0496900	−	0.0905197i
$671$		−	4.38322e26i		−	0.613662i
$672$	−1.68668e26	−	6.21250e26i	−0.232822	−	0.857548i
$673$	5.69599e26	+	5.69599e26i	0.775222	+	0.775222i	0.979014	−	0.203792i	$-0.0653266\pi$
$673$	5.69599e26	+	5.69599e26i	0.775222	+	0.775222i	−0.203792	+	0.979014i	$0.565327\pi$
$674$	1.97150e26	+	9.24510e26i	0.264562	+	1.24063i
$675$	−9.78876e26	−	1.99997e26i	−1.29522	−	0.264629i
$676$	1.13180e27	−	5.05704e26i	1.47664	−	0.659786i
$677$	4.66771e26	−	4.66771e26i	0.600497	−	0.600497i	−0.339947	−	0.940445i	$-0.610409\pi$
$677$	4.66771e26	−	4.66771e26i	0.600497	−	0.600497i	0.940445	+	0.339947i	$0.110409\pi$
$678$	−1.56929e26	+	2.42000e26i	−0.199077	+	0.306996i
$679$	−8.06678e24			−0.0100911
$680$	5.80428e26	+	4.39930e26i	0.716001	+	0.542686i
$681$	−2.20606e27			−2.68361
$682$	1.08695e27	−	1.67618e27i	1.30394	−	2.01081i
$683$	2.30923e26	−	2.30923e26i	0.273193	−	0.273193i	−0.557191	−	0.830384i	$-0.688121\pi$
$683$	2.30923e26	−	2.30923e26i	0.273193	−	0.273193i	0.830384	+	0.557191i	$0.188121\pi$
$684$	−1.25779e27	+	5.61998e26i	−1.46749	+	0.655695i
$685$	−4.19800e26	−	2.25790e26i	−0.483039	−	0.259803i
$686$	−1.67845e26	−	7.87090e26i	−0.190472	−	0.893193i
$687$	−1.02708e27	−	1.02708e27i	−1.14952	−	1.14952i
$688$	6.64275e25	+	1.20643e27i	0.0733260	+	1.33172i
$689$			1.14580e27i			1.24746i
$690$	1.96626e26	−	6.75216e26i	0.211142	−	0.725064i
$691$		−	1.29406e26i		−	0.137060i	−0.997649	−	0.0685302i	$-0.978169\pi$
$691$		−	1.29406e26i		−	0.137060i	0.997649	−	0.0685302i	$-0.0218310\pi$
$692$	−3.36577e26	+	8.80293e26i	−0.351623	+	0.919643i
$693$	1.02344e27	+	1.02344e27i	1.05463	+	1.05463i
$694$	−7.08454e26	+	1.51076e26i	−0.720106	+	0.153561i
$695$	−5.43294e25	−	1.80788e26i	−0.0544728	−	0.181265i
$696$	1.41825e27	+	1.94393e27i	1.40270	+	1.92261i
$697$	2.00266e26	−	2.00266e26i	0.195387	−	0.195387i
$698$	−5.29458e26	−	3.43336e26i	−0.509571	−	0.330440i
$699$	1.62358e27			1.54149
$700$	−1.23180e26	−	5.54328e26i	−0.115375	−	0.519201i
$701$	4.41307e26			0.407774			0.203887	−	0.978994i	$-0.434642\pi$
$701$	4.41307e26			0.407774			0.203887	+	0.978994i	$0.434642\pi$
$702$	1.96849e27	+	1.27650e27i	1.79445	+	1.16364i
$703$	−4.47763e26	+	4.47763e26i	−0.402691	+	0.402691i
$704$	5.38560e26	−	1.68018e27i	0.477853	−	1.49078i
$705$	7.13046e25	+	2.37274e26i	0.0624196	+	0.207708i
$706$	1.95398e26	−	4.16683e25i	0.168763	−	0.0359883i
$707$	6.83739e26	+	6.83739e26i	0.582647	+	0.582647i
$708$	−1.11805e27	−	4.27484e26i	−0.940040	−	0.359422i
$709$		−	6.44226e26i		−	0.534440i	−0.963636	−	0.267220i	$-0.913895\pi$
$709$		−	6.44226e26i		−	0.534440i	0.963636	−	0.267220i	$-0.0861050\pi$
$710$	−8.98086e25	+	3.08404e26i	−0.0735129	+	0.252445i
$711$			5.43508e26i			0.438980i
$712$	−2.50405e25	+	1.60155e26i	−0.0199564	+	0.127639i
$713$	6.22195e26	+	6.22195e26i	0.489301	+	0.489301i
$714$	−2.14558e26	−	1.00614e27i	−0.166499	−	0.780776i
$715$	2.91283e27	+	1.56667e27i	2.23053	+	1.19969i
$716$	−1.02922e27	−	2.30345e27i	−0.777738	−	1.74063i
$717$	−2.12342e27	+	2.12342e27i	−1.58345	+	1.58345i
$718$	1.97118e26	−	3.03975e26i	0.145059	−	0.223694i
$719$	−2.94255e26			−0.213698			−0.106849	−	0.994275i	$-0.534076\pi$
$719$	−2.94255e26			−0.213698			−0.106849	+	0.994275i	$0.534076\pi$
$720$	1.06107e27	−	2.26288e27i	0.760479	−	1.62182i
$721$	5.29283e26			0.374371
$722$	1.51863e26	−	2.34188e26i	0.106011	−	0.163479i
$723$	1.54867e27	−	1.54867e27i	1.06695	−	1.06695i
$724$	4.17613e26	+	9.34644e26i	0.283960	+	0.635521i
$725$	1.17009e27	+	1.77099e27i	0.785251	+	1.18852i
$726$	7.63183e26	+	3.57885e27i	0.505511	+	2.37053i
$727$	−5.26319e26	−	5.26319e26i	−0.344090	−	0.344090i	0.513813	−	0.857902i	$-0.328233\pi$
$727$	−5.26319e26	−	5.26319e26i	−0.344090	−	0.344090i	−0.857902	+	0.513813i	$0.828233\pi$
$728$	−2.05985e26	+	1.31745e27i	−0.132919	+	0.850134i
$729$		−	2.29386e27i		−	1.46102i
$730$	−5.52272e26	−	1.00607e27i	−0.347205	−	0.632499i
$731$			1.93093e27i			1.19826i
$732$	9.98629e26	+	3.81823e26i	0.611715	+	0.233887i
$733$	−1.53271e27	−	1.53271e27i	−0.926769	−	0.926769i	0.0707270	−	0.997496i	$-0.477468\pi$
$733$	−1.53271e27	−	1.53271e27i	−0.926769	−	0.926769i	−0.997496	+	0.0707270i	$0.977468\pi$
$734$	−2.72399e27	+	5.80885e26i	−1.62590	+	0.346719i
$735$	9.63186e26	−	1.79080e27i	0.567519	−	1.05516i
$736$	6.74290e26	+	3.86334e26i	0.392200	+	0.224710i
$737$	−1.99075e26	+	1.99075e26i	−0.114308	+	0.114308i
$738$	−8.15460e26	−	5.28800e26i	−0.462240	−	0.299748i
$739$	−2.82633e27			−1.58161			−0.790807	−	0.612065i	$-0.790339\pi$
$739$	−2.82633e27			−1.58161			−0.790807	+	0.612065i	$0.790339\pi$
$740$	8.40943e25	−	1.14573e27i	0.0464585	−	0.632966i
$741$	4.44676e27			2.42533
$742$	−6.39020e26	−	4.14384e26i	−0.344094	−	0.223134i
$743$	8.21577e26	−	8.21577e26i	0.436772	−	0.436772i	−0.454152	−	0.890924i	$-0.650058\pi$
$743$	8.21577e26	−	8.21577e26i	0.436772	−	0.436772i	0.890924	+	0.454152i	$0.150058\pi$
$744$	2.87201e27	+	3.93653e27i	1.50745	+	2.06619i
$745$	−1.84340e27	+	5.53970e26i	−0.955289	+	0.287079i
$746$	1.68762e27	−	3.59881e26i	0.863486	−	0.184137i
$747$	−2.97066e27	−	2.97066e27i	−1.50074	−	1.50074i
$748$	1.00700e27	−	2.63373e27i	0.502300	−	1.31373i
$749$		−	2.18985e26i		−	0.107854i
$750$	1.60135e27	−	3.03940e27i	0.778760	−	1.47811i
$751$			1.93337e27i			0.928400i	0.885730	+	0.464200i	$0.153658\pi$
$751$			1.93337e27i			0.928400i	−0.885730	+	0.464200i	$0.846342\pi$
$752$	−2.73364e26	+	1.50517e25i	−0.129620	+	0.00713701i
$753$	4.00856e26	+	4.00856e26i	0.187688	+	0.187688i
$754$	−1.03956e27	−	4.87487e27i	−0.480640	−	2.25390i
$755$	−3.69694e27	+	1.11099e27i	−1.68790	+	0.507240i
$756$	−1.42382e27	+	6.36184e26i	−0.641945	+	0.286831i
$757$	−5.24895e26	+	5.24895e26i	−0.233702	+	0.233702i	−0.814236	−	0.580534i	$-0.802844\pi$
$757$	−5.24895e26	+	5.24895e26i	−0.233702	+	0.233702i	0.580534	+	0.814236i	$0.302844\pi$
$758$	−1.87421e27	+	2.89021e27i	−0.824063	+	1.27078i
$759$	−2.72270e27			−1.18223
$760$	−2.85435e26	−	2.07296e27i	−0.122399	−	0.888918i
$761$	−1.41037e27			−0.597283			−0.298642	−	0.954365i	$-0.596534\pi$
$761$	−1.41037e27			−0.597283			−0.298642	+	0.954365i	$0.596534\pi$
$762$	−2.05757e27	+	3.17298e27i	−0.860563	+	1.32707i
$763$	1.31416e27	−	1.31416e27i	0.542832	−	0.542832i
$764$	2.07187e26	−	9.25741e25i	0.0845230	−	0.0377661i
$765$	1.89196e27	−	3.51763e27i	0.762306	−	1.41732i
$766$	−6.14153e26	−	2.87999e27i	−0.244401	−	1.14609i
$767$	1.75326e27	+	1.75326e27i	0.689111	+	0.689111i
$768$	3.35881e27	+	2.69061e27i	1.30393	+	1.04453i
$769$		−	4.49480e27i		−	1.72349i	−0.507338	−	0.861747i	$-0.669371\pi$
$769$		−	4.49480e27i		−	1.72349i	0.507338	−	0.861747i	$-0.330629\pi$
$770$	−1.92717e27	+	1.05791e27i	−0.729893	+	0.400669i
$771$			3.07327e27i			1.14970i
$772$	−9.54065e26	+	2.49529e27i	−0.352544	+	0.922053i
$773$	8.90548e26	+	8.90548e26i	0.325052	+	0.325052i	0.850701	−	0.525650i	$-0.176178\pi$
$773$	8.90548e26	+	8.90548e26i	0.325052	+	0.325052i	−0.525650	+	0.850701i	$0.676178\pi$
$774$	6.48056e27	−	1.38197e27i	2.33654	−	0.498262i
$775$	2.36948e27	+	3.58633e27i	0.843892	+	1.27727i
$776$	4.35665e25	−	3.17852e25i	0.0153273	−	0.0111825i
$777$	−1.14745e27	+	1.14745e27i	−0.398780	+	0.398780i
$778$	2.31332e27	+	1.50011e27i	0.794198	+	0.515011i
$779$	−8.13722e26			−0.275975
$780$	−6.10673e27	+	5.27158e27i	−2.04602	+	1.76621i
$781$	1.24359e27			0.411617
$782$	1.04201e27	+	6.75713e26i	0.340729	+	0.220952i
$783$	4.12198e27	−	4.12198e27i	1.33159	−	1.33159i
$784$	1.67378e27	+	1.49908e27i	0.534191	+	0.478435i
$785$	−2.59711e27	−	1.39686e27i	−0.818894	−	0.440444i
$786$	1.31392e27	−	2.80190e26i	0.409311	−	0.0872848i
$787$	−3.29500e26	−	3.29500e26i	−0.101413	−	0.101413i	0.654580	−	0.755993i	$-0.272846\pi$
$787$	−3.29500e26	−	3.29500e26i	−0.101413	−	0.101413i	−0.755993	+	0.654580i	$0.772846\pi$
$788$	−6.19581e26	−	2.36895e26i	−0.188408	−	0.0720371i
$789$			1.02880e27i			0.309102i
$790$	−7.92624e26	−	2.30815e26i	−0.235293	−	0.0685184i
$791$			3.97130e26i			0.116481i
$792$	−9.55998e27	−	1.49471e27i	−2.77056	−	0.433180i
$793$	−1.56598e27	−	1.56598e27i	−0.448427	−	0.448427i
$794$	−8.34411e25	−	3.91287e26i	−0.0236094	−	0.110713i
$795$	−1.32610e27	−	4.41277e27i	−0.370758	−	1.23374i
$796$	2.24980e27	+	5.03519e27i	0.621541	+	1.39105i
$797$	−2.53523e26	+	2.53523e26i	−0.0692092	+	0.0692092i	−0.740864	−	0.671655i	$-0.765584\pi$
$797$	−2.53523e26	+	2.53523e26i	−0.0692092	+	0.0692092i	0.671655	+	0.740864i	$0.265584\pi$
$798$	−1.60819e27	+	2.47998e27i	−0.433819	+	0.668991i
$799$	−4.37526e26			−0.116630
$800$	2.84946e27	+	2.50841e27i	0.750597	+	0.660760i
$801$	8.88986e26			0.231412
$802$	−3.57556e27	+	5.51386e27i	−0.919788	+	1.41840i
$803$	−3.14188e27	+	3.14188e27i	−0.798715	+	0.798715i
$804$	−2.80138e26	−	6.26967e26i	−0.0703785	−	0.157512i
$805$	−2.78679e26	−	9.27338e26i	−0.0691901	−	0.230238i
$806$	−2.10514e27	−	9.87180e27i	−0.516534	−	2.42222i
$807$	1.00928e27	+	1.00928e27i	0.244745	+	0.244745i
$808$	−6.38679e27	−	9.98581e26i	−1.53065	−	0.239318i
$809$			4.18850e27i			0.992082i	0.868299	+	0.496041i	$0.165214\pi$
$809$			4.18850e27i			0.992082i	−0.868299	+	0.496041i	$0.834786\pi$
$810$	−1.71178e27	−	4.98478e26i	−0.400720	−	0.116691i
$811$		−	5.39338e27i		−	1.24785i	−0.781484	−	0.623925i	$-0.785537\pi$
$811$		−	5.39338e27i		−	1.24785i	0.781484	−	0.623925i	$-0.214463\pi$
$812$	3.09469e27	+	1.18325e27i	0.707677	+	0.270578i
$813$	2.00319e27	+	2.00319e27i	0.452754	+	0.452754i
$814$	−4.34985e27	+	9.27596e26i	−0.971723	+	0.207218i
$815$	5.91788e27	+	3.18294e27i	1.30668	+	0.702800i
$816$	5.12323e27	+	4.58849e27i	1.11812	+	1.00141i
$817$	3.92288e27	−	3.92288e27i	0.846244	−	0.846244i
$818$	−7.01959e27	−	4.55198e27i	−1.49677	−	0.970607i
$819$	7.31288e27			1.54132
$820$	1.11748e27	−	9.64657e26i	0.232814	−	0.200975i
$821$	7.75463e27			1.59699			0.798493	−	0.602003i	$-0.205631\pi$
$821$	7.75463e27			1.59699			0.798493	+	0.602003i	$0.205631\pi$
$822$	−3.77674e27	−	2.44909e27i	−0.768838	−	0.498566i
$823$	2.94825e25	−	2.94825e25i	0.00593289	−	0.00593289i	−0.704134	−	0.710067i	$-0.748665\pi$
$823$	2.94825e25	−	2.94825e25i	0.00593289	−	0.00593289i	0.710067	+	0.704134i	$0.248665\pi$
$824$	−2.85851e27	+	2.08551e27i	−0.568632	+	0.414862i
$825$	−1.30312e28	−	2.66245e27i	−2.56255	−	0.523562i
$826$	−1.61187e27	+	3.43728e26i	−0.313342	+	0.0668196i
$827$	−5.20345e27	−	5.20345e27i	−0.999976	−	0.999976i	2.44023e−5	−	1.00000i	$-0.499992\pi$
$827$	−5.20345e27	−	5.20345e27i	−0.999976	−	0.999976i	−1.00000		2.44023e-5i	$0.999992\pi$
$828$	1.52205e27	−	3.98080e27i	0.289161	−	0.756279i
$829$		−	4.40067e27i		−	0.826515i	−0.910614	−	0.413257i	$-0.864391\pi$
$829$		−	4.40067e27i		−	0.826515i	0.910614	−	0.413257i	$-0.135609\pi$
$830$	5.59383e27	−	3.07068e27i	1.03864	−	0.570156i
$831$		−	1.77120e27i		−	0.325131i
$832$	−4.07863e27	−	7.92684e27i	−0.740190	−	1.43856i
$833$	2.53913e27	+	2.53913e27i	0.455573	+	0.455573i
$834$	−3.71787e26	−	1.74345e27i	−0.0659503	−	0.309266i
$835$	1.68291e27	−	3.12894e27i	0.295147	−	0.548752i
$836$	−7.39650e27	+	3.30487e27i	−1.28253	+	0.573052i
$837$	8.34717e27	−	8.34717e27i	1.43103	−	1.43103i
$838$	−2.20311e27	+	3.39741e27i	−0.373437	+	0.575876i
$839$	1.04922e28			1.75845			0.879223	−	0.476411i	$-0.158063\pi$
$839$	1.04922e28			1.75845			0.879223	+	0.476411i	$0.158063\pi$
$840$	−7.31465e26	−	5.31223e27i	−0.121211	−	0.880286i
$841$	−6.28143e27			−1.02919
$842$	5.25149e27	−	8.09831e27i	0.850782	−	1.31199i
$843$	−8.56538e27	+	8.56538e27i	−1.37210	+	1.37210i
$844$	6.24160e27	−	2.78884e27i	0.988650	−	0.441743i
$845$	9.88930e27	−	2.97189e27i	1.54891	−	0.465472i
$846$	3.13137e26	+	1.46842e27i	0.0484972	+	0.227422i
$847$	3.56272e27	+	3.56272e27i	0.545618	+	0.545618i
$848$	5.08395e27	−	2.79928e26i	0.769911	−	0.0423922i
$849$			1.56108e28i			2.33778i
$850$	4.32646e27	+	4.25300e27i	0.640697	+	0.629819i
$851$		−	1.95897e27i		−	0.286878i
$852$	−1.08330e27	+	2.83328e27i	−0.156881	+	0.410311i
$853$	−6.25866e27	−	6.25866e27i	−0.896325	−	0.896325i	0.0987835	−	0.995109i	$-0.468505\pi$
$853$	−6.25866e27	−	6.25866e27i	−0.896325	−	0.896325i	−0.995109	+	0.0987835i	$0.968505\pi$
$854$	1.43970e27	−	3.07013e26i	0.203902	−	0.0434817i
$855$	−1.09901e28	+	3.30271e27i	−1.53931	+	0.462585i
$856$	8.62857e26	+	1.18268e27i	0.119519	+	0.163820i
$857$	−4.79894e27	+	4.79894e27i	−0.657397	+	0.657397i	−0.954763	−	0.297366i	$-0.903892\pi$
$857$	−4.79894e27	+	4.79894e27i	−0.657397	+	0.657397i	0.297366	+	0.954763i	$0.403892\pi$
$858$	2.62054e28	+	1.69933e28i	3.55027	+	2.30223i
$859$	4.01166e26			0.0537513			0.0268756	−	0.999639i	$-0.491444\pi$
$859$	4.01166e26			0.0537513			0.0268756	+	0.999639i	$0.491444\pi$
$860$	−7.36756e26	+	1.00378e28i	−0.0976312	+	1.33016i
$861$	−2.08527e27			−0.273295
$862$	9.21568e27	+	5.97607e27i	1.19456	+	0.774635i
$863$	−8.62748e27	+	8.62748e27i	−1.10607	+	1.10607i	−0.112404	+	0.993663i	$0.535855\pi$
$863$	−8.62748e27	+	8.62748e27i	−1.10607	+	1.10607i	−0.993663	+	0.112404i	$0.964145\pi$
$864$	5.18293e27	−	9.04606e27i	0.657196	−	1.14704i
$865$	−3.71868e27	+	6.91394e27i	−0.466375	+	0.867107i
$866$	−3.57376e27	+	7.62097e26i	−0.443308	+	0.0945344i
$867$	−1.85674e27	−	1.85674e27i	−0.227809	−	0.227809i
$868$	6.26688e27	+	2.39612e27i	0.760525	+	0.290785i
$869$			3.19613e27i			0.383652i
$870$	9.64554e27	+	1.75711e28i	1.14523	+	2.08625i
$871$			1.42246e27i			0.167058i
$872$	−1.91930e27	+	1.22756e28i	−0.222964	+	1.42605i
$873$	−2.09130e26	−	2.09130e26i	−0.0240315	−	0.0240315i
$874$	−7.44179e26	−	3.48974e27i	−0.0845900	−	0.396674i
$875$	−4.26981e26	−	4.71087e27i	−0.0480100	−	0.529694i
$876$	−4.42126e27	−	9.89506e27i	−0.491764	−	1.10060i
$877$	4.16802e27	−	4.16802e27i	0.458600	−	0.458600i	−0.439596	−	0.898196i	$-0.644878\pi$
$877$	4.16802e27	−	4.16802e27i	0.458600	−	0.458600i	0.898196	+	0.439596i	$0.144878\pi$
$878$	−3.11457e27	+	4.80297e27i	−0.339000	+	0.522771i
$879$	−5.74721e27			−0.618818
$880$	6.23972e27	−	1.33070e28i	0.664629	−	1.41741i
$881$	1.77084e28			1.86599			0.932993	−	0.359894i	$-0.117187\pi$
$881$	1.77084e28			1.86599			0.932993	+	0.359894i	$0.117187\pi$
$882$	6.70454e27	−	1.03391e28i	0.698904	−	1.07778i
$883$	−4.57375e25	+	4.57375e25i	−0.00471678	+	0.00471678i	−0.709461	−	0.704744i	$-0.751062\pi$
$883$	−4.57375e25	+	4.57375e25i	−0.00471678	+	0.00471678i	0.704744	+	0.709461i	$0.251062\pi$
$884$	−5.81178e27	−	1.30071e28i	−0.592943	−	1.32704i
$885$	−8.78135e27	−	4.72307e27i	−0.886340	−	0.476720i
$886$	−2.38212e27	−	1.11707e28i	−0.237872	−	1.11547i
$887$	1.07049e28	+	1.07049e28i	1.05757	+	1.05757i	0.998238	+	0.0593339i	$0.0188977\pi$
$887$	1.07049e28	+	1.07049e28i	1.05757	+	1.05757i	0.0593339	+	0.998238i	$0.481102\pi$
$888$	1.67582e27	−	1.07183e28i	0.163796	−	1.04762i
$889$			5.20696e27i			0.503521i
$890$	−3.77532e26	+	1.29645e27i	−0.0361201	+	0.124037i
$891$			6.90250e27i			0.653384i
$892$	4.01636e27	+	1.53564e27i	0.376155	+	0.143822i
$893$	8.88879e26	+	8.88879e26i	0.0823671	+	0.0823671i
$894$	−1.77771e28	+	3.79092e27i	−1.62987	+	0.347567i
$895$	−6.04843e27	−	2.01269e28i	−0.548686	−	1.82582i
$896$	5.89588e27	+	5.92096e26i	0.529203	+	0.0531454i
$897$	−9.72735e27	+	9.72735e27i	−0.863905	+	0.863905i
$898$	−3.16085e27	−	2.04971e27i	−0.277765	−	0.180122i
$899$	−2.50795e28			−2.18073
$900$	1.11774e28	−	1.75643e28i	0.961696	−	1.51122i
$901$	8.13700e27			0.692754
$902$	−4.79537e27	−	3.10964e27i	−0.403980	−	0.261968i
$903$	1.00529e28	−	1.00529e28i	0.838025	−	0.838025i
$904$	−1.56479e27	−	2.14479e27i	−0.129079	−	0.176923i
$905$	2.45419e27	+	8.16662e27i	0.200331	+	0.666624i
$906$	−3.56520e28	+	7.60271e27i	−2.87982	+	0.614116i
$907$	9.51712e27	+	9.51712e27i	0.760740	+	0.760740i	0.976456	−	0.215716i	$-0.0692085\pi$
$907$	9.51712e27	+	9.51712e27i	0.760740	+	0.760740i	−0.215716	+	0.976456i	$0.569208\pi$
$908$	7.25211e27	−	1.89673e28i	0.573652	−	1.50034i
$909$			3.54516e28i			2.77510i
$910$	−3.10562e27	+	1.06647e28i	−0.240577	+	0.826146i
$911$		−	1.96550e28i		−	1.50677i	−0.657578	−	0.753387i	$-0.728419\pi$
$911$		−	1.96550e28i		−	1.50677i	0.657578	−	0.753387i	$-0.271581\pi$
$912$	−1.08638e27	−	1.97303e28i	−0.0824193	−	1.49687i
$913$	−1.74691e28	−	1.74691e28i	−1.31159	−	1.31159i
$914$	−1.81568e27	−	8.51439e27i	−0.134912	−	0.632652i
$915$	7.84338e27	+	4.21858e27i	0.576770	+	0.310217i
$916$	1.22071e28	−	5.45430e27i	0.888392	−	0.396947i
$917$	1.30799e27	−	1.30799e27i	0.0942099	−	0.0942099i
$918$	9.06516e27	−	1.39793e28i	0.646204	−	0.996510i
$919$	−5.04679e27			−0.356055			−0.178028	−	0.984025i	$-0.556972\pi$
$919$	−5.04679e27			−0.356055			−0.178028	+	0.984025i	$0.556972\pi$
$920$	5.15902e27	+	3.91023e27i	0.360232	+	0.273035i
$921$	−4.55664e28			−3.14904
$922$	−5.93017e27	+	9.14490e27i	−0.405624	+	0.625511i
$923$	4.44296e27	−	4.44296e27i	0.300785	−	0.300785i
$924$	−1.89545e28	+	8.46914e27i	−1.27007	+	0.567487i
$925$	1.91562e27	−	9.37590e27i	0.127046	−	0.621822i
$926$	3.80789e27	+	1.78566e28i	0.249966	+	1.17218i
$927$	1.37216e28	+	1.37216e28i	0.891550	+	0.891550i
$928$	−2.13759e28	+	5.80348e27i	−1.37473	+	0.373235i
$929$		−	1.28456e27i		−	0.0817720i	−0.999164	−	0.0408860i	$-0.986982\pi$
$929$		−	1.28456e27i		−	0.0817720i	0.999164	−	0.0408860i	$-0.0130180\pi$
$930$	1.95326e28	+	3.55823e28i	1.23076	+	2.24205i
$931$		−	1.03170e28i		−	0.643475i
$932$	−5.33728e27	+	1.39593e28i	−0.329510	+	0.861810i
$933$	−6.74388e27	−	6.74388e27i	−0.412130	−	0.412130i
$934$	3.83303e27	−	8.17386e26i	0.231871	−	0.0494461i
$935$	1.11258e28	−	2.06857e28i	0.666226	−	1.23868i
$936$	−3.94949e28	+	2.88146e28i	−2.34110	+	1.70802i
$937$	−2.02734e27	+	2.02734e27i	−0.118960	+	0.118960i	−0.764081	−	0.645121i	$-0.776807\pi$
$937$	−2.02734e27	+	2.02734e27i	−0.118960	+	0.118960i	0.645121	+	0.764081i	$0.276807\pi$
$938$	−7.93313e26	−	5.14438e26i	−0.0460805	−	0.0298817i
$939$	2.04611e28			1.17654
$940$	−2.27445e27	−	1.66941e26i	−0.129468	−	0.00950270i
$941$	1.29214e28			0.728131			0.364066	−	0.931373i	$-0.381388\pi$
$941$	1.29214e28			0.728131			0.364066	+	0.931373i	$0.381388\pi$
$942$	−2.33649e28	−	1.51514e28i	−1.30341	−	0.845218i
$943$	1.78003e27	−	1.78003e27i	0.0983026	−	0.0983026i
$944$	7.35088e27	−	8.20755e27i	0.401888	−	0.448724i
$945$	−1.24409e28	+	3.73868e27i	−0.673363	+	0.202356i
$946$	3.81093e28	−	8.12674e27i	2.04205	−	0.435462i
$947$	−4.58094e27	−	4.58094e27i	−0.243013	−	0.243013i	0.575082	−	0.818096i	$-0.304970\pi$
$947$	−4.58094e27	−	4.58094e27i	−0.243013	−	0.243013i	−0.818096	+	0.575082i	$0.804970\pi$
$948$	−7.28176e27	−	2.78416e27i	−0.382434	−	0.146223i
$949$			2.24499e28i			1.16731i
$950$	−1.49236e26	−	1.74301e28i	−0.00768242	−	0.897273i
$951$			4.49890e28i			2.29294i
$952$	9.35598e27	+	1.46282e27i	0.472105	+	0.0738141i
$953$	1.80360e28	+	1.80360e28i	0.901066	+	0.901066i	0.995528	−	0.0944623i	$-0.0301132\pi$
$953$	1.80360e28	+	1.80360e28i	0.901066	+	0.901066i	−0.0944623	+	0.995528i	$0.530113\pi$
$954$	−5.82365e27	−	2.73093e28i	−0.288062	−	1.35083i
$955$	1.81033e27	−	5.44033e26i	0.0886597	−	0.0266436i
$956$	−1.12764e28	−	2.52373e28i	−0.546789	−	1.22375i
$957$	5.48735e28	−	5.48735e28i	2.63451	−	2.63451i
$958$	4.98918e27	−	7.69380e27i	0.237168	−	0.365737i
$959$	−6.19776e27			−0.291714
$960$	2.48820e28	+	2.58077e28i	1.15960	+	1.20274i
$961$	−2.91163e28			−1.34358
$962$	−1.22266e28	+	1.88546e28i	−0.558654	+	0.861499i
$963$	5.67715e27	−	5.67715e27i	0.256851	−	0.256851i
$964$	8.22416e27	+	1.84062e28i	0.368434	+	0.824579i
$965$	−1.05410e28	+	1.95983e28i	−0.467598	+	0.869380i
$966$	−1.90706e27	−	8.94290e27i	−0.0837685	−	0.392822i
$967$	−1.52800e28	−	1.52800e28i	−0.664618	−	0.664618i	0.291847	−	0.956465i	$-0.405730\pi$
$967$	−1.52800e28	−	1.52800e28i	−0.664618	−	0.664618i	−0.956465	+	0.291847i	$0.905730\pi$
$968$	−3.32793e28	−	5.20324e27i	−1.43337	−	0.224109i
$969$		−	3.15790e28i		−	1.34686i
$970$	3.93797e26	−	2.16172e26i	0.0166319	−	0.00912993i
$971$		−	1.91032e28i		−	0.798957i	−0.916742	−	0.399479i	$-0.869191\pi$
$971$		−	1.91032e28i		−	0.798957i	0.916742	−	0.399479i	$-0.130809\pi$
$972$	1.40883e28	+	5.38660e27i	0.583482	+	0.223093i
$973$	−1.73559e27	−	1.73559e27i	−0.0711827	−	0.0711827i
$974$	3.27161e28	−	6.97663e27i	1.32877	−	0.283358i
$975$	−5.60684e28	+	3.70443e28i	−2.25515	+	1.48997i
$976$	−6.56571e27	+	7.33087e27i	−0.261522	+	0.291999i
$977$	2.63248e28	−	2.63248e28i	1.03841	−	1.03841i	0.0391742	−	0.999232i	$-0.487527\pi$
$977$	2.63248e28	−	2.63248e28i	1.03841	−	1.03841i	0.999232	−	0.0391742i	$-0.0124727\pi$
$978$	5.32403e28	+	3.45246e28i	2.07980	+	1.34868i
$979$	5.22774e27			0.202245
$980$	1.22307e28	+	1.41683e28i	0.468601	+	0.542838i
$981$	6.81388e28			2.58547
$982$	4.17240e28	+	2.70566e28i	1.56793	+	1.01675i
$983$	−3.02300e28	+	3.02300e28i	−1.12507	+	1.12507i	−0.134103	+	0.990967i	$0.542815\pi$
$983$	−3.02300e28	+	3.02300e28i	−1.12507	+	1.12507i	−0.990967	+	0.134103i	$0.957185\pi$
$984$	1.12620e28	−	8.21648e27i	0.415107	−	0.302853i
$985$	−4.86627e27	−	2.61734e27i	−0.177645	−	0.0955466i
$986$	−3.46192e28	+	7.38247e27i	−1.25166	+	0.266914i
$987$	2.27787e27	+	2.27787e27i	0.0815672	+	0.0815672i
$988$	−1.46181e28	+	3.82326e28i	−0.518442	+	1.35595i
$989$			1.71627e28i			0.602866i
$990$	−7.73877e28	−	2.25356e28i	−2.69239	−	0.784034i
$991$		−	3.83190e28i		−	1.32043i	−0.751078	−	0.660214i	$-0.770466\pi$
$991$		−	3.83190e28i		−	1.32043i	0.751078	−	0.660214i	$-0.229534\pi$
$992$	−4.32870e28	+	1.17523e28i	−1.47739	+	0.401108i
$993$	−4.70746e28	−	4.70746e28i	−1.59136	−	1.59136i
$994$	8.71046e26	+	4.08466e27i	0.0291656	+	0.136768i
$995$	1.32215e28	+	4.39959e28i	0.438490	+	1.45913i
$996$	5.50174e28	−	2.45826e28i	1.80733	−	0.807540i
$997$	1.32495e28	−	1.32495e28i	0.431117	−	0.431117i	−0.457891	−	0.889008i	$-0.651395\pi$
$997$	1.32495e28	−	1.32495e28i	0.431117	−	0.431117i	0.889008	+	0.457891i	$0.151395\pi$
$998$	−5.73060e27	+	8.83713e27i	−0.184697	+	0.284821i
$999$	−2.62810e28			−0.839014

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	20.20.e.b.3.19	yes	108
4.3	odd	2	inner	20.20.e.b.3.10	✓	108
5.2	odd	4	inner	20.20.e.b.7.10	yes	108
20.7	even	4	inner	20.20.e.b.7.19	yes	108

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
20.20.e.b.3.10	✓	108	4.3	odd	2	inner
20.20.e.b.3.19	yes	108	1.1	even	1	trivial
20.20.e.b.7.10	yes	108	5.2	odd	4	inner
20.20.e.b.7.19	yes	108	20.7	even	4	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 20 = 2^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 20 \)
Character orbit:	\([\chi]\)	\(=\)	20.e (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-393.959 + 607.523i) q^{2} +(-40275.2 + 40275.2i) q^{3} +(-213881. - 478678. i) q^{4} +(-1.25692e6 - 4.18254e6i) q^{5} +(-8.60133e6 - 4.03349e7i) q^{6} +(-4.01530e7 - 4.01530e7i) q^{7} +(3.75068e8 + 5.86423e7i) q^{8} -2.08192e9i q^{9} +(3.03616e9 + 8.84143e8i) q^{10} -1.22429e10i q^{11} +(2.78929e10 + 1.06648e10i) q^{12} +(-4.37398e10 - 4.37398e10i) q^{13} +(4.02125e10 - 8.57524e9i) q^{14} +(2.19075e11 + 1.17830e11i) q^{15} +(-1.83388e11 + 2.04760e11i) q^{16} +(-3.10621e11 + 3.10621e11i) q^{17} +(1.26481e12 + 8.20190e11i) q^{18} +1.26212e12 q^{19} +(-1.73326e12 + 1.49622e12i) q^{20} +3.23434e12 q^{21} +(7.43782e12 + 4.82318e12i) q^{22} +(-2.76090e12 + 2.76090e12i) q^{23} +(-1.74678e13 + 1.27441e13i) q^{24} +(-1.59138e13 + 1.05142e13i) q^{25} +(4.38047e13 - 9.34125e12i) q^{26} +(3.70393e13 + 3.70393e13i) q^{27} +(-1.06324e13 + 2.78083e13i) q^{28} -1.11287e14i q^{29} +(-1.57891e14 + 8.66730e13i) q^{30} -2.25360e14i q^{31} +(-5.21490e13 - 1.92080e14i) q^{32} +(4.93083e14 + 4.93083e14i) q^{33} +(-6.63375e13 - 3.11082e14i) q^{34} +(-1.17473e14 + 2.18411e14i) q^{35} +(-9.96569e14 + 4.45282e14i) q^{36} +(-3.54771e14 + 3.54771e14i) q^{37} +(-4.97222e14 + 7.66765e14i) q^{38} +3.52326e15 q^{39} +(-2.26156e14 - 1.64245e15i) q^{40} -6.44728e14 q^{41} +(-1.27420e15 + 1.96494e15i) q^{42} +(3.10817e15 - 3.10817e15i) q^{43} +(-5.86039e15 + 2.61851e15i) q^{44} +(-8.70771e15 + 2.61680e15i) q^{45} +(-5.89628e14 - 2.76499e15i) q^{46} +(7.04277e14 + 7.04277e14i) q^{47} +(-8.60756e14 - 1.56327e16i) q^{48} -8.17437e15i q^{49} +(-1.18242e14 - 1.38102e16i) q^{50} -2.50206e16i q^{51} +(-1.15822e16 + 3.02924e16i) q^{52} +(-1.30980e16 - 1.30980e16i) q^{53} +(-3.70942e16 + 7.91027e15i) q^{54} +(-5.12063e16 + 1.53883e16i) q^{55} +(-1.27055e16 - 1.74148e16i) q^{56} +(-5.08320e16 + 5.08320e16i) q^{57} +(6.76091e16 + 4.38423e16i) q^{58} -4.00837e16 q^{59} +(9.54676e15 - 1.30068e17i) q^{60} +3.58022e16 q^{61} +(1.36911e17 + 8.87825e16i) q^{62} +(-8.35953e16 + 8.35953e16i) q^{63} +(1.37237e17 + 4.39898e16i) q^{64} +(-1.27966e17 + 2.37921e17i) q^{65} +(-4.93814e17 + 1.05305e17i) q^{66} +(-1.62605e16 - 1.62605e16i) q^{67} +(2.15123e17 + 8.22518e16i) q^{68} -2.22391e17i q^{69} +(-8.64101e16 - 1.57412e17i) q^{70} +1.01577e17i q^{71} +(1.22088e17 - 7.80862e17i) q^{72} +(-2.56630e17 - 2.56630e17i) q^{73} +(-7.57663e16 - 3.55297e17i) q^{74} +(2.17469e17 - 1.06439e18i) q^{75} +(-2.69942e17 - 6.04148e17i) q^{76} +(-4.91587e17 + 4.91587e17i) q^{77} +(-1.38802e18 + 2.14046e18i) q^{78} -2.61061e17 q^{79} +(1.08692e18 + 5.09662e17i) q^{80} -5.63798e17 q^{81} +(2.53996e17 - 3.91687e17i) q^{82} +(1.42688e18 - 1.42688e18i) q^{83} +(-6.91762e17 - 1.54821e18i) q^{84} +(1.68961e18 + 9.08760e17i) q^{85} +(6.63794e17 + 3.11278e18i) q^{86} +(4.48208e18 + 4.48208e18i) q^{87} +(7.17950e17 - 4.59191e18i) q^{88} +4.27003e17i q^{89} +(1.84071e18 - 6.32104e18i) q^{90} +3.51257e18i q^{91} +(1.91208e18 + 7.31079e17i) q^{92} +(9.07640e18 + 9.07640e18i) q^{93} +(-7.05320e17 + 1.50408e17i) q^{94} +(-1.58638e18 - 5.27886e18i) q^{95} +(9.83635e18 + 5.63573e18i) q^{96} +(1.00451e17 - 1.00451e17i) q^{97} +(4.96612e18 + 3.22037e18i) q^{98} -2.54886e19 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 108 q - 1026 q^{2} - 7131840 q^{5} - 50939608 q^{6} + 1332591828 q^{8} + 1805468790 q^{10} + 25565343280 q^{12} - 99498527404 q^{13} + 759936037048 q^{16} + 1103360788948 q^{17} - 2932289137902 q^{18} - 4821918866500 q^{20}+ \cdots + 66\!\cdots\!58 q^{98}+O(q^{100}) \) 108 * q - 1026 * q^2 - 7131840 * q^5 - 50939608 * q^6 + 1332591828 * q^8 + 1805468790 * q^10 + 25565343280 * q^12 - 99498527404 * q^13 + 759936037048 * q^16 + 1103360788948 * q^17 - 2932289137902 * q^18 - 4821918866500 * q^20 + 3306300862704 * q^21 + 26555173338440 * q^22 - 57672549609740 * q^25 - 151870176076556 * q^26 + 145347487073040 * q^28 + 265510366207880 * q^30 + 451426657209224 * q^32 - 229672757216560 * q^33 - 2556468817119620 * q^36 - 2904533279226852 * q^37 + 4500710811976960 * q^38 + 2246744304601900 * q^40 - 4721437306521104 * q^41 + 452761724453480 * q^42 - 970083854699780 * q^45 + 8478786115826952 * q^46 + 16046505545373280 * q^48 + 56844159661370 * q^50 - 101281742222079732 * q^52 - 27665397406960484 * q^53 - 10433774450699008 * q^56 + 83589162043122240 * q^57 - 22879145244078184 * q^58 + 145234473586307920 * q^60 - 6358689987281664 * q^61 - 371338823915128280 * q^62 - 91631698278804820 * q^65 + 331374884002311600 * q^66 - 694094458817479804 * q^68 - 165782163012631200 * q^70 - 215667461842637436 * q^72 + 1087298370549745276 * q^73 + 1949878275840327200 * q^76 - 1250723257104163920 * q^77 + 668342418678475560 * q^78 + 4071497833979030320 * q^80 - 12135903560578575228 * q^81 - 3459475352437471112 * q^82 + 14947305238413951060 * q^85 + 11624244909135363112 * q^86 - 5598373834541334880 * q^88 - 9907327634674956330 * q^90 + 27521624775955257680 * q^92 - 25916131489404857680 * q^93 - 50213774290767283648 * q^96 + 8468568053676169148 * q^97 + 66196294974841827558 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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