LMFDB - Embedded newform 570.2.c.f.569.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [570,2,Mod(569,570)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(570, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("570.569");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 570 = 2 \cdot 3 \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	570.c (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$4.55147291521$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	8.0.1499238400.2
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 4x^{7} + 16x^{6} - 34x^{5} + 59x^{4} - 66x^{3} + 54x^{2} - 26x + 5 $ x^8 - 4x^7 + 16x^6 - 34x^5 + 59x^4 - 66x^3 + 54x^2 - 26*x + 5
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			569.7
Root			$0.500000 - 0.0845405i$ of defining polynomial
Character	$\chi$	$=$	570.569
Dual form			570.2.c.f.569.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000i q^{2} +(0.500000 + 1.65831i) q^{3} -1.00000 q^{4} +(-0.584541 - 2.15831i) q^{5} +(-1.65831 + 0.500000i) q^{6} +4.86140i q^{7} -1.00000i q^{8} +(-2.50000 + 1.65831i) q^{9} +O(q^{10})$	\(q+1.00000i q^{2} +(0.500000 + 1.65831i) q^{3} -1.00000 q^{4} +(-0.584541 - 2.15831i) q^{5} +(-1.65831 + 0.500000i) q^{6} +4.86140i q^{7} -1.00000i q^{8} +(-2.50000 + 1.65831i) q^{9} +(2.15831 - 0.584541i) q^{10} +2.31662i q^{11} +(-0.500000 - 1.65831i) q^{12} +3.31662 q^{13} -4.86140 q^{14} +(3.28689 - 2.04851i) q^{15} +1.00000 q^{16} -4.86140 q^{17} +(-1.65831 - 2.50000i) q^{18} +(2.31662 - 3.69232i) q^{19} +(0.584541 + 2.15831i) q^{20} +(-8.06173 + 2.43070i) q^{21} -2.31662 q^{22} -6.03049 q^{23} +(1.65831 - 0.500000i) q^{24} +(-4.31662 + 2.52324i) q^{25} +3.31662i q^{26} +(-4.00000 - 3.31662i) q^{27} -4.86140i q^{28} -1.35416 q^{29} +(2.04851 + 3.28689i) q^{30} +8.55373i q^{31} +1.00000i q^{32} +(-3.84169 + 1.15831i) q^{33} -4.86140i q^{34} +(10.4924 - 2.84169i) q^{35} +(2.50000 - 1.65831i) q^{36} +2.00000 q^{37} +(3.69232 + 2.31662i) q^{38} +(1.65831 + 5.50000i) q^{39} +(-2.15831 + 0.584541i) q^{40} -3.50724 q^{41} +(-2.43070 - 8.06173i) q^{42} +1.16908i q^{43} -2.31662i q^{44} +(5.04051 + 4.42643i) q^{45} -6.03049i q^{46} +5.04648 q^{47} +(0.500000 + 1.65831i) q^{48} -16.6332 q^{49} +(-2.52324 - 4.31662i) q^{50} +(-2.43070 - 8.06173i) q^{51} -3.31662 q^{52} +1.00000i q^{53} +(3.31662 - 4.00000i) q^{54} +(5.00000 - 1.35416i) q^{55} +4.86140 q^{56} +(7.28134 + 1.99553i) q^{57} -1.35416i q^{58} +9.90789 q^{59} +(-3.28689 + 2.04851i) q^{60} +4.31662 q^{61} -8.55373 q^{62} +(-8.06173 - 12.1535i) q^{63} -1.00000 q^{64} +(-1.93870 - 7.15831i) q^{65} +(-1.15831 - 3.84169i) q^{66} +7.00000 q^{67} +4.86140 q^{68} +(-3.01524 - 10.0004i) q^{69} +(2.84169 + 10.4924i) q^{70} +10.8919 q^{71} +(1.65831 + 2.50000i) q^{72} +11.0770i q^{73} +2.00000i q^{74} +(-6.34264 - 5.89669i) q^{75} +(-2.31662 + 3.69232i) q^{76} -11.2620 q^{77} +(-5.50000 + 1.65831i) q^{78} -4.67632i q^{79} +(-0.584541 - 2.15831i) q^{80} +(3.50000 - 8.29156i) q^{81} -3.50724i q^{82} +9.72281 q^{83} +(8.06173 - 2.43070i) q^{84} +(2.84169 + 10.4924i) q^{85} -1.16908 q^{86} +(-0.677081 - 2.24562i) q^{87} +2.31662 q^{88} +8.55373 q^{89} +(-4.42643 + 5.04051i) q^{90} +16.1235i q^{91} +6.03049 q^{92} +(-14.1848 + 4.27686i) q^{93} +5.04648i q^{94} +(-9.32335 - 2.84169i) q^{95} +(-1.65831 + 0.500000i) q^{96} +16.6332 q^{97} -16.6332i q^{98} +(-3.84169 - 5.79156i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 4 q^{3} - 8 q^{4} - 20 q^{9}+O(q^{10}) $ 8 * q + 4 * q^3 - 8 * q^4 - 20 * q^9	$ 8 q + 4 q^{3} - 8 q^{4} - 20 q^{9} + 4 q^{10} - 4 q^{12} + 22 q^{15} + 8 q^{16} - 8 q^{19} + 8 q^{22} - 8 q^{25} - 32 q^{27} + 2 q^{30} - 44 q^{33} + 20 q^{36} + 16 q^{37} - 4 q^{40} + 22 q^{45} + 4 q^{48} - 80 q^{49} + 40 q^{55} - 4 q^{57} - 22 q^{60} + 8 q^{61} - 8 q^{64} + 4 q^{66} + 56 q^{67} + 36 q^{70} - 4 q^{75} + 8 q^{76} - 44 q^{78} + 28 q^{81} + 36 q^{85} - 8 q^{88} - 10 q^{90} + 80 q^{97} - 44 q^{99}+O(q^{100}) $ 8 * q + 4 * q^3 - 8 * q^4 - 20 * q^9 + 4 * q^10 - 4 * q^12 + 22 * q^15 + 8 * q^16 - 8 * q^19 + 8 * q^22 - 8 * q^25 - 32 * q^27 + 2 * q^30 - 44 * q^33 + 20 * q^36 + 16 * q^37 - 4 * q^40 + 22 * q^45 + 4 * q^48 - 80 * q^49 + 40 * q^55 - 4 * q^57 - 22 * q^60 + 8 * q^61 - 8 * q^64 + 4 * q^66 + 56 * q^67 + 36 * q^70 - 4 * q^75 + 8 * q^76 - 44 * q^78 + 28 * q^81 + 36 * q^85 - 8 * q^88 - 10 * q^90 + 80 * q^97 - 44 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/570\mathbb{Z}\right)^\times$.

$n$	$191$	$211$	$457$
$\chi(n)$	$-1$	$-1$	$-1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$			1.00000i			0.707107i
$2$			1.00000i			0.707107i
$3$	0.500000	+	1.65831i	0.288675	+	0.957427i
$3$	0.500000	+	1.65831i	0.288675	+	0.957427i
$4$	−1.00000			−0.500000
$5$	−0.584541	−	2.15831i	−0.261414	−	0.965227i
$5$	−0.584541	−	2.15831i	−0.261414	−	0.965227i
$6$	−1.65831	+	0.500000i	−0.677003	+	0.204124i
$7$			4.86140i			1.83744i	0.394912	+	0.918719i	$0.370775\pi$
$7$			4.86140i			1.83744i	−0.394912	+	0.918719i	$0.629225\pi$
$8$		−	1.00000i		−	0.353553i
$9$	−2.50000	+	1.65831i	−0.833333	+	0.552771i
$10$	2.15831	−	0.584541i	0.682518	−	0.184848i
$11$			2.31662i			0.698489i	0.937032	+	0.349244i	$0.113562\pi$
$11$			2.31662i			0.698489i	−0.937032	+	0.349244i	$0.886438\pi$
$12$	−0.500000	−	1.65831i	−0.144338	−	0.478714i
$13$	3.31662			0.919866			0.459933	−	0.887954i	$-0.347873\pi$
$13$	3.31662			0.919866			0.459933	+	0.887954i	$0.347873\pi$
$14$	−4.86140			−1.29926
$15$	3.28689	−	2.04851i	0.848670	−	0.528922i
$16$	1.00000			0.250000
$17$	−4.86140			−1.17906			−0.589532	−	0.807745i	$-0.700688\pi$
$17$	−4.86140			−1.17906			−0.589532	+	0.807745i	$0.700688\pi$
$18$	−1.65831	−	2.50000i	−0.390868	−	0.589256i
$19$	2.31662	−	3.69232i	0.531470	−	0.847077i
$19$	2.31662	−	3.69232i	0.531470	−	0.847077i
$20$	0.584541	+	2.15831i	0.130707	+	0.482613i
$21$	−8.06173	+	2.43070i	−1.75921	+	0.530423i
$22$	−2.31662			−0.493906
$23$	−6.03049			−1.25744			−0.628722	−	0.777631i	$-0.716421\pi$
$23$	−6.03049			−1.25744			−0.628722	+	0.777631i	$0.716421\pi$
$24$	1.65831	−	0.500000i	0.338502	−	0.102062i
$25$	−4.31662	+	2.52324i	−0.863325	+	0.504648i
$26$			3.31662i			0.650444i
$27$	−4.00000	−	3.31662i	−0.769800	−	0.638285i
$28$		−	4.86140i		−	0.918719i
$29$	−1.35416			−0.251461			−0.125731	−	0.992064i	$-0.540128\pi$
$29$	−1.35416			−0.251461			−0.125731	+	0.992064i	$0.540128\pi$
$30$	2.04851	+	3.28689i	0.374004	+	0.600101i
$31$			8.55373i			1.53629i	0.640273	+	0.768147i	$0.278821\pi$
$31$			8.55373i			1.53629i	−0.640273	+	0.768147i	$0.721179\pi$
$32$			1.00000i			0.176777i
$33$	−3.84169	+	1.15831i	−0.668752	+	0.201636i
$34$		−	4.86140i		−	0.833724i
$35$	10.4924	−	2.84169i	1.77354	−	0.480333i
$36$	2.50000	−	1.65831i	0.416667	−	0.276385i
$37$	2.00000			0.328798			0.164399	−	0.986394i	$-0.447432\pi$
$37$	2.00000			0.328798			0.164399	+	0.986394i	$0.447432\pi$
$38$	3.69232	+	2.31662i	0.598974	+	0.375806i
$39$	1.65831	+	5.50000i	0.265543	+	0.880705i
$40$	−2.15831	+	0.584541i	−0.341259	+	0.0924240i
$41$	−3.50724			−0.547739			−0.273870	−	0.961767i	$-0.588304\pi$
$41$	−3.50724			−0.547739			−0.273870	+	0.961767i	$0.588304\pi$
$42$	−2.43070	−	8.06173i	−0.375065	−	1.24395i
$43$			1.16908i			0.178283i	0.996019	+	0.0891416i	$0.0284124\pi$
$43$			1.16908i			0.178283i	−0.996019	+	0.0891416i	$0.971588\pi$
$44$		−	2.31662i		−	0.349244i
$45$	5.04051	+	4.42643i	0.751394	+	0.659853i
$46$		−	6.03049i		−	0.889147i
$47$	5.04648			0.736105			0.368053	−	0.929805i	$-0.380025\pi$
$47$	5.04648			0.736105			0.368053	+	0.929805i	$0.380025\pi$
$48$	0.500000	+	1.65831i	0.0721688	+	0.239357i
$49$	−16.6332			−2.37618
$50$	−2.52324	−	4.31662i	−0.356840	−	0.610463i
$51$	−2.43070	−	8.06173i	−0.340366	−	1.12887i
$52$	−3.31662			−0.459933
$53$			1.00000i			0.137361i	0.997639	+	0.0686803i	$0.0218788\pi$
$53$			1.00000i			0.137361i	−0.997639	+	0.0686803i	$0.978121\pi$
$54$	3.31662	−	4.00000i	0.451335	−	0.544331i
$55$	5.00000	−	1.35416i	0.674200	−	0.182595i
$56$	4.86140			0.649632
$57$	7.28134	+	1.99553i	0.964437	+	0.264314i
$58$		−	1.35416i		−	0.177810i
$59$	9.90789			1.28990			0.644949	−	0.764226i	$-0.276879\pi$
$59$	9.90789			1.28990			0.644949	+	0.764226i	$0.276879\pi$
$60$	−3.28689	+	2.04851i	−0.424335	+	0.264461i
$61$	4.31662			0.552687			0.276344	−	0.961059i	$-0.410877\pi$
$61$	4.31662			0.552687			0.276344	+	0.961059i	$0.410877\pi$
$62$	−8.55373			−1.08632
$63$	−8.06173	−	12.1535i	−1.01568	−	1.53120i
$64$	−1.00000			−0.125000
$65$	−1.93870	−	7.15831i	−0.240466	−	0.887879i
$66$	−1.15831	−	3.84169i	−0.142578	−	0.472879i
$67$	7.00000			0.855186			0.427593	−	0.903971i	$-0.359362\pi$
$67$	7.00000			0.855186			0.427593	+	0.903971i	$0.359362\pi$
$68$	4.86140			0.589532
$69$	−3.01524	−	10.0004i	−0.362993	−	1.20391i
$70$	2.84169	+	10.4924i	0.339647	+	1.25409i
$71$	10.8919			1.29263			0.646315	−	0.763071i	$-0.276309\pi$
$71$	10.8919			1.29263			0.646315	+	0.763071i	$0.276309\pi$
$72$	1.65831	+	2.50000i	0.195434	+	0.294628i
$73$			11.0770i			1.29646i	0.761444	+	0.648231i	$0.224491\pi$
$73$			11.0770i			1.29646i	−0.761444	+	0.648231i	$0.775509\pi$
$74$			2.00000i			0.232495i
$75$	−6.34264	−	5.89669i	−0.732385	−	0.680891i
$76$	−2.31662	+	3.69232i	−0.265735	+	0.423539i
$77$	−11.2620			−1.28343
$78$	−5.50000	+	1.65831i	−0.622752	+	0.187767i
$79$		−	4.67632i		−	0.526128i	−0.964778	−	0.263064i	$-0.915267\pi$
$79$		−	4.67632i		−	0.526128i	0.964778	−	0.263064i	$-0.0847330\pi$
$80$	−0.584541	−	2.15831i	−0.0653536	−	0.241307i
$81$	3.50000	−	8.29156i	0.388889	−	0.921285i
$82$		−	3.50724i		−	0.387310i
$83$	9.72281			1.06722			0.533608	−	0.845732i	$-0.320836\pi$
$83$	9.72281			1.06722			0.533608	+	0.845732i	$0.320836\pi$
$84$	8.06173	−	2.43070i	0.879606	−	0.265211i
$85$	2.84169	+	10.4924i	0.308224	+	1.13806i
$86$	−1.16908			−0.126065
$87$	−0.677081	−	2.24562i	−0.0725907	−	0.240756i
$88$	2.31662			0.246953
$89$	8.55373			0.906693			0.453347	−	0.891334i	$-0.350230\pi$
$89$	8.55373			0.906693			0.453347	+	0.891334i	$0.350230\pi$
$90$	−4.42643	+	5.04051i	−0.466587	+	0.531316i
$91$			16.1235i			1.69020i
$92$	6.03049			0.628722
$93$	−14.1848	+	4.27686i	−1.47089	+	0.443490i
$94$			5.04648i			0.520505i
$95$	−9.32335	−	2.84169i	−0.956555	−	0.291551i
$96$	−1.65831	+	0.500000i	−0.169251	+	0.0510310i
$97$	16.6332			1.68885			0.844425	−	0.535673i	$-0.179942\pi$
$97$	16.6332			1.68885			0.844425	+	0.535673i	$0.179942\pi$
$98$		−	16.6332i		−	1.68021i
$99$	−3.84169	−	5.79156i	−0.386104	−	0.582074i
$100$	4.31662	−	2.52324i	0.431662	−	0.252324i
$101$			7.68338i			0.764524i	0.924054	+	0.382262i	$0.124855\pi$
$101$			7.68338i			0.764524i	−0.924054	+	0.382262i	$0.875145\pi$
$102$	8.06173	−	2.43070i	0.798230	−	0.240675i
$103$	−15.5831			−1.53545			−0.767725	−	0.640779i	$-0.778612\pi$
$103$	−15.5831			−1.53545			−0.767725	+	0.640779i	$0.778612\pi$
$104$		−	3.31662i		−	0.325222i
$105$	9.95862	+	15.9789i	0.971862	+	1.55938i
$106$	−1.00000			−0.0971286
$107$			19.9499i			1.92863i	0.264763	+	0.964314i	$0.414706\pi$
$107$			19.9499i			1.92863i	−0.264763	+	0.964314i	$0.585294\pi$
$108$	4.00000	+	3.31662i	0.384900	+	0.319142i
$109$		−	17.2925i		−	1.65632i	−0.560489	−	0.828162i	$-0.689387\pi$
$109$		−	17.2925i		−	1.65632i	0.560489	−	0.828162i	$-0.310613\pi$
$110$	1.35416	+	5.00000i	0.129114	+	0.476731i
$111$	1.00000	+	3.31662i	0.0949158	+	0.314800i
$112$			4.86140i			0.459360i
$113$			8.31662i			0.782362i	0.920314	+	0.391181i	$0.127933\pi$
$113$			8.31662i			0.782362i	−0.920314	+	0.391181i	$0.872067\pi$
$114$	−1.99553	+	7.28134i	−0.186898	+	0.681960i
$115$	3.52506	+	13.0157i	0.328714	+	1.21372i
$116$	1.35416			0.125731
$117$	−8.29156	+	5.50000i	−0.766555	+	0.508475i
$118$			9.90789i			0.912095i
$119$		−	23.6332i		−	2.16646i
$120$	−2.04851	−	3.28689i	−0.187002	−	0.300050i
$121$	5.63325			0.512114
$122$			4.31662i			0.390809i
$123$	−1.75362	−	5.81610i	−0.158119	−	0.524420i
$124$		−	8.55373i		−	0.768147i
$125$	7.96919	+	7.84169i	0.712786	+	0.701382i
$126$	12.1535	−	8.06173i	1.08272	−	0.718196i
$127$	−3.36675			−0.298751			−0.149375	−	0.988781i	$-0.547726\pi$
$127$	−3.36675			−0.298751			−0.149375	+	0.988781i	$0.547726\pi$
$128$		−	1.00000i		−	0.0883883i
$129$	−1.93870	+	0.584541i	−0.170693	+	0.0514659i
$130$	7.15831	−	1.93870i	0.627826	−	0.170035i
$131$			10.0000i			0.873704i	0.899533	+	0.436852i	$0.143907\pi$
$131$			10.0000i			0.873704i	−0.899533	+	0.436852i	$0.856093\pi$
$132$	3.84169	−	1.15831i	0.334376	−	0.100818i
$133$	17.9499	+	11.2620i	1.55645	+	0.976544i
$134$			7.00000i			0.604708i
$135$	−4.82015	+	10.5720i	−0.414852	+	0.909889i
$136$			4.86140i			0.416862i
$137$	−4.86140			−0.415338			−0.207669	−	0.978199i	$-0.566588\pi$
$137$	−4.86140			−0.415338			−0.207669	+	0.978199i	$0.566588\pi$
$138$	10.0004	−	3.01524i	0.851293	−	0.256674i
$139$	−10.0000			−0.848189			−0.424094	−	0.905618i	$-0.639408\pi$
$139$	−10.0000			−0.848189			−0.424094	+	0.905618i	$0.639408\pi$
$140$	−10.4924	+	2.84169i	−0.886772	+	0.240166i
$141$	2.52324	+	8.36865i	0.212495	+	0.704767i
$142$			10.8919i			0.914027i
$143$			7.68338i			0.642516i
$144$	−2.50000	+	1.65831i	−0.208333	+	0.138193i
$145$	0.791562	+	2.92270i	0.0657356	+	0.242717i
$146$	−11.0770			−0.916736
$147$	−8.31662	−	27.5831i	−0.685944	−	2.27502i
$148$	−2.00000			−0.164399
$149$		−	4.00000i		−	0.327693i	−0.986486	−	0.163846i	$-0.947610\pi$
$149$		−	4.00000i		−	0.327693i	0.986486	−	0.163846i	$-0.0523901\pi$
$150$	5.89669	−	6.34264i	0.481463	−	0.517874i
$151$			2.70832i			0.220400i	0.993909	+	0.110200i	$0.0351492\pi$
$151$			2.70832i			0.220400i	−0.993909	+	0.110200i	$0.964851\pi$
$152$	−3.69232	−	2.31662i	−0.299487	−	0.187903i
$153$	12.1535	−	8.06173i	0.982553	−	0.651752i
$154$		−	11.2620i		−	0.907522i
$155$	18.4616	−	5.00000i	1.48287	−	0.401610i
$156$	−1.65831	−	5.50000i	−0.132771	−	0.440352i
$157$		−	2.33816i		−	0.186606i	−0.995638	−	0.0933028i	$-0.970258\pi$
$157$		−	2.33816i		−	0.186606i	0.995638	−	0.0933028i	$-0.0297425\pi$
$158$	4.67632			0.372028
$159$	−1.65831	+	0.500000i	−0.131513	+	0.0396526i
$160$	2.15831	−	0.584541i	0.170630	−	0.0462120i
$161$		−	29.3166i		−	2.31047i
$162$	8.29156	+	3.50000i	0.651447	+	0.274986i
$163$		−	15.9384i		−	1.24839i	−0.781269	−	0.624195i	$-0.785427\pi$
$163$		−	15.9384i		−	1.24839i	0.781269	−	0.624195i	$-0.214573\pi$
$164$	3.50724			0.273870
$165$	4.74562	+	7.61448i	0.369446	+	0.592787i
$166$			9.72281i			0.754636i
$167$		−	5.05013i		−	0.390790i	−0.980725	−	0.195395i	$-0.937401\pi$
$167$		−	5.05013i		−	0.390790i	0.980725	−	0.195395i	$-0.0625990\pi$
$168$	2.43070	+	8.06173i	0.187533	+	0.621976i
$169$	−2.00000			−0.153846
$170$	−10.4924	+	2.84169i	−0.804733	+	0.217947i
$171$	0.331463	+	13.0725i	0.0253476	+	0.999679i
$172$		−	1.16908i		−	0.0891416i
$173$		−	13.2665i		−	1.00863i	−0.863519	−	0.504317i	$-0.831744\pi$
$173$		−	13.2665i		−	1.00863i	0.863519	−	0.504317i	$-0.168256\pi$
$174$	2.24562	−	0.677081i	0.170240	−	0.0513293i
$175$	−12.2665	−	20.9849i	−0.927260	−	1.58631i
$176$			2.31662i			0.174622i
$177$	4.95394	+	16.4304i	0.372361	+	1.23498i
$178$			8.55373i			0.641129i
$179$	2.70832			0.202429			0.101215	−	0.994865i	$-0.467727\pi$
$179$	2.70832			0.202429			0.101215	+	0.994865i	$0.467727\pi$
$180$	−5.04051	−	4.42643i	−0.375697	−	0.329927i
$181$		−	2.70832i		−	0.201308i	−0.994921	−	0.100654i	$-0.967906\pi$
$181$		−	2.70832i		−	0.201308i	0.994921	−	0.100654i	$-0.0320935\pi$
$182$	−16.1235			−1.19515
$183$	2.15831	+	7.15831i	0.159547	+	0.529158i
$184$			6.03049i			0.444573i
$185$	−1.16908	−	4.31662i	−0.0859525	−	0.317365i
$186$	−4.27686	−	14.1848i	−0.313595	−	1.04008i
$187$		−	11.2620i		−	0.823563i
$188$	−5.04648			−0.368053
$189$	16.1235	−	19.4456i	1.17281	−	1.41446i
$190$	2.84169	−	9.32335i	0.206158	−	0.676387i
$191$			5.00000i			0.361787i	0.983503	+	0.180894i	$0.0578990\pi$
$191$			5.00000i			0.361787i	−0.983503	+	0.180894i	$0.942101\pi$
$192$	−0.500000	−	1.65831i	−0.0360844	−	0.119678i
$193$	6.00000			0.431889			0.215945	−	0.976406i	$-0.430717\pi$
$193$	6.00000			0.431889			0.215945	+	0.976406i	$0.430717\pi$
$194$			16.6332i			1.19420i
$195$	10.9014	−	6.79413i	0.780663	−	0.486538i
$196$	16.6332			1.18809
$197$	−6.21557			−0.442841			−0.221420	−	0.975178i	$-0.571069\pi$
$197$	−6.21557			−0.442841			−0.221420	+	0.975178i	$0.571069\pi$
$198$	5.79156	−	3.84169i	0.411588	−	0.273017i
$199$	21.2164			1.50399			0.751994	−	0.659169i	$-0.229092\pi$
$199$	21.2164			1.50399			0.751994	+	0.659169i	$0.229092\pi$
$200$	2.52324	+	4.31662i	0.178420	+	0.305231i
$201$	3.50000	+	11.6082i	0.246871	+	0.818778i
$202$	−7.68338			−0.540600
$203$		−	6.58312i		−	0.462045i
$204$	2.43070	+	8.06173i	0.170183	+	0.564434i
$205$	2.05013	+	7.56973i	0.143187	+	0.528693i
$206$		−	15.5831i		−	1.08573i
$207$	15.0762	−	10.0004i	1.04787	−	0.695078i
$208$	3.31662			0.229967
$209$	8.55373	+	5.36675i	0.591674	+	0.371226i
$210$	−15.9789	+	9.95862i	−1.10265	+	0.687210i
$211$		−	18.4616i		−	1.27095i	−0.772121	−	0.635475i	$-0.780804\pi$
$211$		−	18.4616i		−	1.27095i	0.772121	−	0.635475i	$-0.219196\pi$
$212$		−	1.00000i		−	0.0686803i
$213$	5.44594	+	18.0622i	0.373150	+	1.23760i
$214$	−19.9499			−1.36375
$215$	2.52324	−	0.683375i	0.172084	−	0.0466058i
$216$	−3.31662	+	4.00000i	−0.225668	+	0.272166i
$217$	−41.5831			−2.82285
$218$	17.2925			1.17120
$219$	−18.3691	+	5.53848i	−1.24127	+	0.374256i
$220$	−5.00000	+	1.35416i	−0.337100	+	0.0912975i
$221$	−16.1235			−1.08458
$222$	−3.31662	+	1.00000i	−0.222597	+	0.0671156i
$223$	−23.2665			−1.55804			−0.779020	−	0.626999i	$-0.784283\pi$
$223$	−23.2665			−1.55804			−0.779020	+	0.626999i	$0.784283\pi$
$224$	−4.86140			−0.324816
$225$	6.60724	−	13.4664i	0.440483	−	0.897761i
$226$	−8.31662			−0.553214
$227$		−	0.0501256i		−	0.00332695i	−0.999999	−	0.00166348i	$-0.999470\pi$
$227$		−	0.0501256i		−	0.00332695i	0.999999	−	0.00166348i	$-0.000529502\pi$
$228$	−7.28134	−	1.99553i	−0.482218	−	0.132157i
$229$		0			0			−	1.00000i	$-0.5\pi$
$229$		0			0				1.00000i	$0.5\pi$
$230$	−13.0157	+	3.52506i	−0.858228	+	0.232436i
$231$	−5.63102	−	18.6760i	−0.370494	−	1.22879i
$232$			1.35416i			0.0889050i
$233$	15.1395			0.991818			0.495909	−	0.868374i	$-0.334835\pi$
$233$	15.1395			0.991818			0.495909	+	0.868374i	$0.334835\pi$
$234$	−5.50000	−	8.29156i	−0.359546	−	0.542036i
$235$	−2.94987	−	10.8919i	−0.192429	−	0.710509i
$236$	−9.90789			−0.644949
$237$	7.75481	−	2.33816i	0.503729	−	0.151880i
$238$	23.6332			1.53192
$239$			6.36675i			0.411831i	0.978570	+	0.205915i	$0.0660172\pi$
$239$			6.36675i			0.411831i	−0.978570	+	0.205915i	$0.933983\pi$
$240$	3.28689	−	2.04851i	0.212168	−	0.132231i
$241$			17.1075i			1.10199i	0.834509	+	0.550994i	$0.185751\pi$
$241$			17.1075i			1.10199i	−0.834509	+	0.550994i	$0.814249\pi$
$242$			5.63325i			0.362119i
$243$	15.5000	+	1.65831i	0.994325	+	0.106381i
$244$	−4.31662			−0.276344
$245$	9.72281	+	35.8997i	0.621167	+	2.29355i
$246$	5.81610	−	1.75362i	0.370821	−	0.111807i
$247$	7.68338	−	12.2461i	0.488881	−	0.779198i
$248$	8.55373			0.543162
$249$	4.86140	+	16.1235i	0.308079	+	1.02178i
$250$	−7.84169	+	7.96919i	−0.495952	+	0.504016i
$251$			1.58312i			0.0999259i	0.998751	+	0.0499629i	$0.0159103\pi$
$251$			1.58312i			0.0999259i	−0.998751	+	0.0499629i	$0.984090\pi$
$252$	8.06173	+	12.1535i	0.507841	+	0.765599i
$253$		−	13.9704i		−	0.878310i
$254$		−	3.36675i		−	0.211249i
$255$	−15.9789	+	9.95862i	−1.00064	+	0.623633i
$256$	1.00000			0.0625000
$257$			14.9499i			0.932548i	0.884640	+	0.466274i	$0.154404\pi$
$257$			14.9499i			0.932548i	−0.884640	+	0.466274i	$0.845596\pi$
$258$	−0.584541	−	1.93870i	−0.0363919	−	0.120698i
$259$			9.72281i			0.604146i
$260$	1.93870	+	7.15831i	0.120233	+	0.443940i
$261$	3.38540	−	2.24562i	0.209551	−	0.139001i
$262$	−10.0000			−0.617802
$263$	−21.7838			−1.34325			−0.671623	−	0.740893i	$-0.734402\pi$
$263$	−21.7838			−1.34325			−0.671623	+	0.740893i	$0.734402\pi$
$264$	1.15831	+	3.84169i	0.0712892	+	0.236440i
$265$	2.15831	−	0.584541i	0.132584	−	0.0359080i
$266$	−11.2620	+	17.9499i	−0.690521	+	1.10058i
$267$	4.27686	+	14.1848i	0.261740	+	0.868093i
$268$	−7.00000			−0.427593
$269$	−14.3991			−0.877931			−0.438965	−	0.898504i	$-0.644655\pi$
$269$	−14.3991			−0.877931			−0.438965	+	0.898504i	$0.644655\pi$
$270$	−10.5720	−	4.82015i	−0.643388	−	0.293345i
$271$	9.31662			0.565945			0.282972	−	0.959128i	$-0.408680\pi$
$271$	9.31662			0.565945			0.282972	+	0.959128i	$0.408680\pi$
$272$	−4.86140			−0.294766
$273$	−26.7377	+	8.06173i	−1.61824	+	0.487918i
$274$		−	4.86140i		−	0.293688i
$275$	−5.84541	−	10.0000i	−0.352491	−	0.603023i
$276$	3.01524	+	10.0004i	0.181496	+	0.601955i
$277$			12.0610i			0.724673i	0.932047	+	0.362337i	$0.118021\pi$
$277$			12.0610i			0.724673i	−0.932047	+	0.362337i	$0.881979\pi$
$278$		−	10.0000i		−	0.599760i
$279$	−14.1848	−	21.3843i	−0.849219	−	1.28025i
$280$	−2.84169	−	10.4924i	−0.169823	−	0.627043i
$281$	13.6002			0.811321			0.405660	−	0.914024i	$-0.367042\pi$
$281$	13.6002			0.811321			0.405660	+	0.914024i	$0.367042\pi$
$282$	−8.36865	+	2.52324i	−0.498346	+	0.150257i
$283$			15.1395i			0.899947i	0.893042	+	0.449974i	$0.148567\pi$
$283$			15.1395i			0.899947i	−0.893042	+	0.449974i	$0.851433\pi$
$284$	−10.8919			−0.646315
$285$	0.0507319	−	16.8819i	0.00300510	−	0.999995i
$286$	−7.68338			−0.454328
$287$		−	17.0501i		−	1.00644i
$288$	−1.65831	−	2.50000i	−0.0977170	−	0.147314i
$289$	6.63325			0.390191
$290$	−2.92270	+	0.791562i	−0.171627	+	0.0464821i
$291$	8.31662	+	27.5831i	0.487529	+	1.61695i
$292$		−	11.0770i		−	0.648231i
$293$		−	8.26650i		−	0.482934i	−0.970409	−	0.241467i	$-0.922371\pi$
$293$		−	8.26650i		−	0.482934i	0.970409	−	0.241467i	$-0.0776286\pi$
$294$	27.5831	−	8.31662i	1.60868	−	0.485035i
$295$	−5.79156	−	21.3843i	−0.337198	−	1.24504i
$296$		−	2.00000i		−	0.116248i
$297$	7.68338	−	9.26650i	0.445835	−	0.537697i
$298$	4.00000			0.231714
$299$	−20.0009			−1.15668
$300$	6.34264	+	5.89669i	0.366192	+	0.340446i
$301$	−5.68338			−0.327584
$302$	−2.70832			−0.155846
$303$	−12.7414	+	3.84169i	−0.731976	+	0.220699i
$304$	2.31662	−	3.69232i	0.132868	−	0.211769i
$305$	−2.52324	−	9.31662i	−0.144480	−	0.533468i
$306$	8.06173	+	12.1535i	0.460858	+	0.694770i
$307$	2.00000			0.114146			0.0570730	−	0.998370i	$-0.481823\pi$
$307$	2.00000			0.114146			0.0570730	+	0.998370i	$0.481823\pi$
$308$	11.2620			0.641715
$309$	−7.79156	−	25.8417i	−0.443246	−	1.47008i
$310$	5.00000	+	18.4616i	0.283981	+	1.04855i
$311$		−	18.8997i		−	1.07171i	−0.844311	−	0.535853i	$-0.819990\pi$
$311$		−	18.8997i		−	1.07171i	0.844311	−	0.535853i	$-0.180010\pi$
$312$	5.50000	−	1.65831i	0.311376	−	0.0938835i
$313$		−	28.5546i		−	1.61400i	−0.590551	−	0.807000i	$-0.701090\pi$
$313$		−	28.5546i		−	1.61400i	0.590551	−	0.807000i	$-0.298910\pi$
$314$	2.33816			0.131950
$315$	−21.5187	+	24.5039i	−1.21244	+	1.38064i
$316$			4.67632i			0.263064i
$317$		−	17.0000i		−	0.954815i	−0.878682	−	0.477408i	$-0.841577\pi$
$317$		−	17.0000i		−	0.954815i	0.878682	−	0.477408i	$-0.158423\pi$
$318$	−0.500000	−	1.65831i	−0.0280386	−	0.0929935i
$319$		−	3.13708i		−	0.175643i
$320$	0.584541	+	2.15831i	0.0326768	+	0.120653i
$321$	−33.0831	+	9.97494i	−1.84652	+	0.556747i
$322$	29.3166			1.63375
$323$	−11.2620	+	17.9499i	−0.626637	+	0.998758i
$324$	−3.50000	+	8.29156i	−0.194444	+	0.460642i
$325$	−14.3166	+	8.36865i	−0.794143	+	0.464209i
$326$	15.9384			0.882745
$327$	28.6764	−	8.64627i	1.58581	−	0.478140i
$328$			3.50724i			0.193655i
$329$			24.5330i			1.35255i
$330$	−7.61448	+	4.74562i	−0.419163	+	0.261238i
$331$		−	15.7533i		−	0.865879i	−0.901423	−	0.432940i	$-0.857476\pi$
$331$		−	15.7533i		−	0.865879i	0.901423	−	0.432940i	$-0.142524\pi$
$332$	−9.72281			−0.533608
$333$	−5.00000	+	3.31662i	−0.273998	+	0.181750i
$334$	5.05013			0.276331
$335$	−4.09178	−	15.1082i	−0.223558	−	0.825448i
$336$	−8.06173	+	2.43070i	−0.439803	+	0.132606i
$337$	18.2164			0.992309			0.496155	−	0.868234i	$-0.334745\pi$
$337$	18.2164			0.992309			0.496155	+	0.868234i	$0.334745\pi$
$338$		−	2.00000i		−	0.108786i
$339$	−13.7916	+	4.15831i	−0.749055	+	0.225849i
$340$	−2.84169	−	10.4924i	−0.154112	−	0.569032i
$341$	−19.8158			−1.07308
$342$	−13.0725	+	0.331463i	−0.706880	+	0.0179235i
$343$		−	46.8311i		−	2.52864i
$344$	1.16908			0.0630326
$345$	−19.8215	+	12.3535i	−1.06715	+	0.665090i
$346$	13.2665			0.713211
$347$	24.8623			1.33468			0.667338	−	0.744755i	$-0.267434\pi$
$347$	24.8623			1.33468			0.667338	+	0.744755i	$0.267434\pi$
$348$	0.677081	+	2.24562i	0.0362953	+	0.120378i
$349$	−4.63325			−0.248012			−0.124006	−	0.992281i	$-0.539574\pi$
$349$	−4.63325			−0.248012			−0.124006	+	0.992281i	$0.539574\pi$
$350$	20.9849	−	12.2665i	1.12169	−	0.655672i
$351$	−13.2665	−	11.0000i	−0.708113	−	0.587137i
$352$	−2.31662			−0.123477
$353$	−20.0009			−1.06454			−0.532269	−	0.846575i	$-0.678661\pi$
$353$	−20.0009			−1.06454			−0.532269	+	0.846575i	$0.678661\pi$
$354$	−16.4304	+	4.95394i	−0.873265	+	0.263299i
$355$	−6.36675	−	23.5081i	−0.337912	−	1.24768i
$356$	−8.55373			−0.453347
$357$	39.1913	−	11.8166i	2.07422	−	0.625402i
$358$			2.70832i			0.143139i
$359$			34.8997i			1.84194i	0.389636	+	0.920969i	$0.372601\pi$
$359$			34.8997i			1.84194i	−0.389636	+	0.920969i	$0.627399\pi$
$360$	4.42643	−	5.04051i	0.233293	−	0.265658i
$361$	−8.26650	−	17.1075i	−0.435079	−	0.900392i
$362$	2.70832			0.142346
$363$	2.81662	+	9.34169i	0.147834	+	0.490311i
$364$		−	16.1235i		−	0.845099i
$365$	23.9076	−	6.47494i	1.25138	−	0.338914i
$366$	−7.15831	+	2.15831i	−0.374171	+	0.112817i
$367$		−	2.33816i		−	0.122051i	−0.998136	−	0.0610255i	$-0.980563\pi$
$367$		−	2.33816i		−	0.122051i	0.998136	−	0.0610255i	$-0.0194371\pi$
$368$	−6.03049			−0.314361
$369$	8.76811	−	5.81610i	0.456449	−	0.302774i
$370$	4.31662	−	1.16908i	0.224411	−	0.0607776i
$371$	−4.86140			−0.252392
$372$	14.1848	−	4.27686i	0.735445	−	0.221745i
$373$	−16.6834			−0.863832			−0.431916	−	0.901914i	$-0.642162\pi$
$373$	−16.6834			−0.863832			−0.431916	+	0.901914i	$0.642162\pi$
$374$	11.2620			0.582347
$375$	−9.01937	+	17.1362i	−0.465758	+	0.884912i
$376$		−	5.04648i		−	0.260253i
$377$	−4.49124			−0.231311
$378$	19.4456	+	16.1235i	1.00017	+	0.829301i
$379$			22.7678i			1.16950i	0.811213	+	0.584751i	$0.198808\pi$
$379$			22.7678i			1.16950i	−0.811213	+	0.584751i	$0.801192\pi$
$380$	9.32335	+	2.84169i	0.478278	+	0.145775i
$381$	−1.68338	−	5.58312i	−0.0862419	−	0.286032i
$382$	−5.00000			−0.255822
$383$		−	25.5831i		−	1.30724i	−0.756824	−	0.653618i	$-0.773250\pi$
$383$		−	25.5831i		−	1.30724i	0.756824	−	0.653618i	$-0.226750\pi$
$384$	1.65831	−	0.500000i	0.0846254	−	0.0255155i
$385$	6.58312	+	24.3070i	0.335507	+	1.23880i
$386$			6.00000i			0.305392i
$387$	−1.93870	−	2.92270i	−0.0985497	−	0.148569i
$388$	−16.6332			−0.844425
$389$		−	30.2164i		−	1.53203i	−0.642822	−	0.766015i	$-0.722237\pi$
$389$		−	30.2164i		−	1.53203i	0.642822	−	0.766015i	$-0.277763\pi$
$390$	6.79413	+	10.9014i	0.344034	+	0.552012i
$391$	29.3166			1.48261
$392$			16.6332i			0.840106i
$393$	−16.5831	+	5.00000i	−0.836508	+	0.252217i
$394$		−	6.21557i		−	0.313136i
$395$	−10.0930	+	2.73350i	−0.507832	+	0.137537i
$396$	3.84169	+	5.79156i	0.193052	+	0.291037i
$397$		−	16.7373i		−	0.840021i	−0.907519	−	0.420010i	$-0.862026\pi$
$397$		−	16.7373i		−	0.840021i	0.907519	−	0.420010i	$-0.137974\pi$
$398$			21.2164i			1.06348i
$399$	−9.70106	+	35.3975i	−0.485660	+	1.77209i
$400$	−4.31662	+	2.52324i	−0.215831	+	0.126162i
$401$	−8.92389			−0.445638			−0.222819	−	0.974860i	$-0.571526\pi$
$401$	−8.92389			−0.445638			−0.222819	+	0.974860i	$0.571526\pi$
$402$	−11.6082	+	3.50000i	−0.578964	+	0.174564i
$403$			28.3695i			1.41319i
$404$		−	7.68338i		−	0.382262i
$405$	−19.9417	−	2.70734i	−0.990910	−	0.134529i
$406$	6.58312			0.326715
$407$			4.63325i			0.229662i
$408$	−8.06173	+	2.43070i	−0.399115	+	0.120338i
$409$			1.16908i			0.0578073i	0.999582	+	0.0289037i	$0.00920160\pi$
$409$			1.16908i			0.0578073i	−0.999582	+	0.0289037i	$0.990798\pi$
$410$	−7.56973	+	2.05013i	−0.373842	+	0.101248i
$411$	−2.43070	−	8.06173i	−0.119898	−	0.397656i
$412$	15.5831			0.767725
$413$			48.1662i			2.37011i
$414$	10.0004	+	15.0762i	0.491494	+	0.740955i
$415$	−5.68338	−	20.9849i	−0.278986	−	1.03011i
$416$			3.31662i			0.162611i
$417$	−5.00000	−	16.5831i	−0.244851	−	0.812079i
$418$	−5.36675	+	8.55373i	−0.262496	+	0.418376i
$419$			22.9499i			1.12117i	0.828095	+	0.560587i	$0.189425\pi$
$419$			22.9499i			1.12117i	−0.828095	+	0.560587i	$0.810575\pi$
$420$	−9.95862	−	15.9789i	−0.485931	−	0.779690i
$421$			24.3070i			1.18465i	0.805699	+	0.592326i	$0.201790\pi$
$421$			24.3070i			1.18465i	−0.805699	+	0.592326i	$0.798210\pi$
$422$	18.4616			0.898697
$423$	−12.6162	+	8.36865i	−0.613421	+	0.406898i
$424$	1.00000			0.0485643
$425$	20.9849	−	12.2665i	1.01792	−	0.595013i
$426$	−18.0622	+	5.44594i	−0.875114	+	0.263857i
$427$			20.9849i			1.01553i
$428$		−	19.9499i		−	0.964314i
$429$	−12.7414	+	3.84169i	−0.615162	+	0.185478i
$430$	0.683375	+	2.52324i	0.0329553	+	0.121682i
$431$	33.4160			1.60959			0.804796	−	0.593552i	$-0.202275\pi$
$431$	33.4160			1.60959			0.804796	+	0.593552i	$0.202275\pi$
$432$	−4.00000	−	3.31662i	−0.192450	−	0.159571i
$433$	8.31662			0.399671			0.199836	−	0.979829i	$-0.435959\pi$
$433$	8.31662			0.399671			0.199836	+	0.979829i	$0.435959\pi$
$434$		−	41.5831i		−	1.99605i
$435$	−4.45097	+	2.77401i	−0.213408	+	0.133004i
$436$			17.2925i			0.828162i
$437$	−13.9704	+	22.2665i	−0.668293	+	1.06515i
$438$	−5.53848	−	18.3691i	−0.264639	−	0.877708i
$439$			1.16908i			0.0557972i	0.999611	+	0.0278986i	$0.00888155\pi$
$439$			1.16908i			0.0557972i	−0.999611	+	0.0278986i	$0.991118\pi$
$440$	−1.35416	−	5.00000i	−0.0645571	−	0.238366i
$441$	41.5831	−	27.5831i	1.98015	−	1.31348i
$442$		−	16.1235i		−	0.766914i
$443$	3.87740			0.184221			0.0921105	−	0.995749i	$-0.470639\pi$
$443$	3.87740			0.184221			0.0921105	+	0.995749i	$0.470639\pi$
$444$	−1.00000	−	3.31662i	−0.0474579	−	0.157400i
$445$	−5.00000	−	18.4616i	−0.237023	−	0.875164i
$446$		−	23.2665i		−	1.10170i
$447$	6.63325	−	2.00000i	0.313742	−	0.0945968i
$448$		−	4.86140i		−	0.229680i
$449$	31.5066			1.48689			0.743444	−	0.668798i	$-0.233191\pi$
$449$	31.5066			1.48689			0.743444	+	0.668798i	$0.233191\pi$
$450$	13.4664	+	6.60724i	0.634813	+	0.311468i
$451$		−	8.12497i		−	0.382590i
$452$		−	8.31662i		−	0.391181i
$453$	−4.49124	+	1.35416i	−0.211017	+	0.0636240i
$454$	0.0501256			0.00235251
$455$	34.7994	−	9.42481i	1.63142	−	0.441842i
$456$	1.99553	−	7.28134i	0.0934491	−	0.340980i
$457$			18.8318i			0.880913i	0.897774	+	0.440457i	$0.145183\pi$
$457$			18.8318i			0.880913i	−0.897774	+	0.440457i	$0.854817\pi$
$458$		0			0
$459$	19.4456	+	16.1235i	0.907644	+	0.752578i
$460$	−3.52506	−	13.0157i	−0.164357	−	0.606859i
$461$			11.5831i			0.539480i	0.962933	+	0.269740i	$0.0869377\pi$
$461$			11.5831i			0.539480i	−0.962933	+	0.269740i	$0.913062\pi$
$462$	18.6760	−	5.63102i	0.868886	−	0.261979i
$463$		−	4.67632i		−	0.217327i	−0.994079	−	0.108664i	$-0.965343\pi$
$463$		−	4.67632i		−	0.217327i	0.994079	−	0.108664i	$-0.0346571\pi$
$464$	−1.35416			−0.0628653
$465$	17.5224	+	28.1151i	0.812580	+	1.30381i
$466$			15.1395i			0.701322i
$467$	8.18357			0.378690			0.189345	−	0.981911i	$-0.439363\pi$
$467$	8.18357			0.378690			0.189345	+	0.981911i	$0.439363\pi$
$468$	8.29156	−	5.50000i	0.383278	−	0.254238i
$469$			34.0298i			1.57135i
$470$	10.8919	−	2.94987i	0.502405	−	0.136068i
$471$	3.87740	−	1.16908i	0.178661	−	0.0538684i
$472$		−	9.90789i		−	0.456048i
$473$	−2.70832			−0.124529
$474$	2.33816	+	7.75481i	0.107395	+	0.356190i
$475$	−0.683375	+	21.7838i	−0.0313554	+	0.999508i
$476$			23.6332i			1.08323i
$477$	−1.65831	−	2.50000i	−0.0759289	−	0.114467i
$478$	−6.36675			−0.291208
$479$		−	14.0000i		−	0.639676i	−0.947472	−	0.319838i	$-0.896371\pi$
$479$		−	14.0000i		−	0.639676i	0.947472	−	0.319838i	$-0.103629\pi$
$480$	2.04851	+	3.28689i	0.0935011	+	0.150025i
$481$	6.63325			0.302450
$482$	−17.1075			−0.779223
$483$	48.6161	−	14.6583i	2.21211	−	0.666976i
$484$	−5.63325			−0.256057
$485$	−9.72281	−	35.8997i	−0.441490	−	1.63012i
$486$	−1.65831	+	15.5000i	−0.0752226	+	0.703094i
$487$	−16.5330			−0.749182			−0.374591	−	0.927190i	$-0.622217\pi$
$487$	−16.5330			−0.749182			−0.374591	+	0.927190i	$0.622217\pi$
$488$		−	4.31662i		−	0.195404i
$489$	26.4308	−	7.96919i	1.19524	−	0.360379i
$490$	−35.8997	+	9.72281i	−1.62179	+	0.439232i
$491$		−	41.5831i		−	1.87662i	−0.345795	−	0.938310i	$-0.612391\pi$
$491$		−	41.5831i		−	1.87662i	0.345795	−	0.938310i	$-0.387609\pi$
$492$	1.75362	+	5.81610i	0.0790594	+	0.262210i
$493$	6.58312			0.296489
$494$	12.2461	+	7.68338i	0.550976	+	0.345691i
$495$	−10.2544	+	11.6770i	−0.460900	+	0.524841i
$496$			8.55373i			0.384074i
$497$			52.9499i			2.37513i
$498$	−16.1235	+	4.86140i	−0.722509	+	0.217845i
$499$	41.5831			1.86152			0.930758	−	0.365635i	$-0.119148\pi$
$499$	41.5831			1.86152			0.930758	+	0.365635i	$0.119148\pi$
$500$	−7.96919	−	7.84169i	−0.356393	−	0.350691i
$501$	8.37469	−	2.52506i	0.374153	−	0.112811i
$502$	−1.58312			−0.0706583
$503$	13.7853			0.614656			0.307328	−	0.951604i	$-0.400565\pi$
$503$	13.7853			0.614656			0.307328	+	0.951604i	$0.400565\pi$
$504$	−12.1535	+	8.06173i	−0.541360	+	0.359098i
$505$	16.5831	−	4.49124i	0.737939	−	0.199858i
$506$	13.9704			0.621059
$507$	−1.00000	−	3.31662i	−0.0444116	−	0.147296i
$508$	3.36675			0.149375
$509$	−17.1075			−0.758275			−0.379137	−	0.925340i	$-0.623779\pi$
$509$	−17.1075			−0.758275			−0.379137	+	0.925340i	$0.623779\pi$
$510$	−9.95862	−	15.9789i	−0.440975	−	0.707557i
$511$	−53.8496			−2.38217
$512$			1.00000i			0.0441942i
$513$	−21.5125	+	7.08592i	−0.949802	+	0.312851i
$514$	−14.9499			−0.659411
$515$	9.10897	+	33.6332i	0.401389	+	1.48206i
$516$	1.93870	−	0.584541i	0.0853466	−	0.0257330i
$517$			11.6908i			0.514161i
$518$	−9.72281			−0.427196
$519$	22.0000	−	6.63325i	0.965693	−	0.291167i
$520$	−7.15831	+	1.93870i	−0.313913	+	0.0850177i
$521$	41.9697			1.83873			0.919363	−	0.393410i	$-0.128705\pi$
$521$	41.9697			1.83873			0.919363	+	0.393410i	$0.128705\pi$
$522$	2.24562	+	3.38540i	0.0982882	+	0.148175i
$523$	−29.0000			−1.26808			−0.634041	−	0.773300i	$-0.718605\pi$
$523$	−29.0000			−1.26808			−0.634041	+	0.773300i	$0.718605\pi$
$524$		−	10.0000i		−	0.436852i
$525$	28.6662	−	30.8341i	1.25110	−	1.34571i
$526$		−	21.7838i		−	0.949818i
$527$		−	41.5831i		−	1.81139i
$528$	−3.84169	+	1.15831i	−0.167188	+	0.0504091i
$529$	13.3668			0.581163
$530$	0.584541	+	2.15831i	0.0253908	+	0.0937511i
$531$	−24.7697	+	16.4304i	−1.07491	+	0.713017i
$532$	−17.9499	−	11.2620i	−0.778226	−	0.488272i
$533$	−11.6322			−0.503847
$534$	−14.1848	+	4.27686i	−0.613834	+	0.185078i
$535$	43.0581	−	11.6615i	1.86156	−	0.504171i
$536$		−	7.00000i		−	0.302354i
$537$	1.35416	+	4.49124i	0.0584364	+	0.193811i
$538$		−	14.3991i		−	0.620791i
$539$		−	38.5330i		−	1.65973i
$540$	4.82015	−	10.5720i	0.207426	−	0.454944i
$541$	−28.8496			−1.24034			−0.620171	−	0.784467i	$-0.712937\pi$
$541$	−28.8496			−1.24034			−0.620171	+	0.784467i	$0.712937\pi$
$542$			9.31662i			0.400183i
$543$	4.49124	−	1.35416i	0.192738	−	0.0581126i
$544$		−	4.86140i		−	0.208431i
$545$	−37.3227	+	10.1082i	−1.59873	+	0.432987i
$546$	−8.06173	−	26.7377i	−0.345010	−	1.14427i
$547$	12.0000			0.513083			0.256541	−	0.966533i	$-0.417417\pi$
$547$	12.0000			0.513083			0.256541	+	0.966533i	$0.417417\pi$
$548$	4.86140			0.207669
$549$	−10.7916	+	7.15831i	−0.460573	+	0.305509i
$550$	10.0000	−	5.84541i	0.426401	−	0.249249i
$551$	−3.13708	+	5.00000i	−0.133644	+	0.213007i
$552$	−10.0004	+	3.01524i	−0.425646	+	0.128337i
$553$	22.7335			0.966727
$554$	−12.0610			−0.512422
$555$	6.57377	−	4.09701i	0.279041	−	0.173909i
$556$	10.0000			0.424094
$557$	−34.5851			−1.46542			−0.732708	−	0.680543i	$-0.761744\pi$
$557$	−34.5851			−1.46542			−0.732708	+	0.680543i	$0.761744\pi$
$558$	21.3843	−	14.1848i	0.905270	−	0.600488i
$559$			3.87740i			0.163997i
$560$	10.4924	−	2.84169i	0.443386	−	0.120083i
$561$	18.6760	−	5.63102i	0.788501	−	0.237742i
$562$			13.6002i			0.573690i
$563$			9.89975i			0.417225i	0.977998	+	0.208612i	$0.0668947\pi$
$563$			9.89975i			0.417225i	−0.977998	+	0.208612i	$0.933105\pi$
$564$	−2.52324	−	8.36865i	−0.106248	−	0.352384i
$565$	17.9499	−	4.86140i	0.755157	−	0.204521i
$566$	−15.1395			−0.636359
$567$	40.3086	+	17.0149i	1.69280	+	0.714559i
$568$		−	10.8919i		−	0.457014i
$569$	−17.1075			−0.717182			−0.358591	−	0.933495i	$-0.616743\pi$
$569$	−17.1075			−0.717182			−0.358591	+	0.933495i	$0.616743\pi$
$570$	16.8819	+	0.0507319i	0.707104	+	0.00212493i
$571$	−25.6834			−1.07482			−0.537408	−	0.843322i	$-0.680596\pi$
$571$	−25.6834			−1.07482			−0.537408	+	0.843322i	$0.680596\pi$
$572$		−	7.68338i		−	0.321258i
$573$	−8.29156	+	2.50000i	−0.346385	+	0.104439i
$574$	17.0501			0.711658
$575$	26.0313	−	15.2164i	1.08558	−	0.634567i
$576$	2.50000	−	1.65831i	0.104167	−	0.0690963i
$577$		−	6.40065i		−	0.266462i	−0.991085	−	0.133231i	$-0.957465\pi$
$577$		−	6.40065i		−	0.266462i	0.991085	−	0.133231i	$-0.0425353\pi$
$578$			6.63325i			0.275907i
$579$	3.00000	+	9.94987i	0.124676	+	0.413503i
$580$	−0.791562	−	2.92270i	−0.0328678	−	0.121359i
$581$			47.2665i			1.96094i
$582$	−27.5831	+	8.31662i	−1.14336	+	0.344735i
$583$	−2.31662			−0.0959448
$584$	11.0770			0.458368
$585$	16.7175	+	14.6808i	0.691182	+	0.606977i
$586$	8.26650			0.341486
$587$	−26.0313			−1.07443			−0.537214	−	0.843446i	$-0.680523\pi$
$587$	−26.0313			−1.07443			−0.537214	+	0.843446i	$0.680523\pi$
$588$	8.31662	+	27.5831i	0.342972	+	1.13751i
$589$	31.5831	+	19.8158i	1.30136	+	0.816495i
$590$	21.3843	−	5.79156i	0.880378	−	0.238435i
$591$	−3.10778	−	10.3073i	−0.127837	−	0.423988i
$592$	2.00000			0.0821995
$593$	−21.7838			−0.894553			−0.447276	−	0.894396i	$-0.647606\pi$
$593$	−21.7838			−0.894553			−0.447276	+	0.894396i	$0.647606\pi$
$594$	9.26650	+	7.68338i	0.380209	+	0.315253i
$595$	−51.0079	+	13.8146i	−2.09112	+	0.566343i
$596$			4.00000i			0.163846i
$597$	10.6082	+	35.1834i	0.434164	+	1.43996i
$598$		−	20.0009i		−	0.817896i
$599$	48.1853			1.96880			0.984399	−	0.175953i	$-0.0563007\pi$
$599$	48.1853			1.96880			0.984399	+	0.175953i	$0.0563007\pi$
$600$	−5.89669	+	6.34264i	−0.240731	+	0.258937i
$601$		−	22.9529i		−	0.936267i	−0.883658	−	0.468133i	$-0.844927\pi$
$601$		−	22.9529i		−	0.936267i	0.883658	−	0.468133i	$-0.155073\pi$
$602$		−	5.68338i		−	0.231637i
$603$	−17.5000	+	11.6082i	−0.712655	+	0.472722i
$604$		−	2.70832i		−	0.110200i
$605$	−3.29286	−	12.1583i	−0.133874	−	0.494306i
$606$	−3.84169	−	12.7414i	−0.156058	−	0.517585i
$607$	−23.3668			−0.948427			−0.474214	−	0.880410i	$-0.657268\pi$
$607$	−23.3668			−0.948427			−0.474214	+	0.880410i	$0.657268\pi$
$608$	3.69232	+	2.31662i	0.149743	+	0.0939515i
$609$	10.9169	−	3.29156i	0.442374	−	0.133381i
$610$	9.31662	−	2.52324i	0.377219	−	0.102163i
$611$	16.7373			0.677118
$612$	−12.1535	+	8.06173i	−0.491277	+	0.325876i
$613$		−	13.2301i		−	0.534357i	−0.963647	−	0.267178i	$-0.913909\pi$
$613$		−	13.2301i		−	0.534357i	0.963647	−	0.267178i	$-0.0860913\pi$
$614$			2.00000i			0.0807134i
$615$	−11.5279	+	7.18461i	−0.464850	+	0.289712i
$616$			11.2620i			0.453761i
$617$	−17.4776			−0.703622			−0.351811	−	0.936071i	$-0.614434\pi$
$617$	−17.4776			−0.703622			−0.351811	+	0.936071i	$0.614434\pi$
$618$	25.8417	−	7.79156i	1.03951	−	0.313423i
$619$	−31.5831			−1.26943			−0.634716	−	0.772745i	$-0.718883\pi$
$619$	−31.5831			−1.26943			−0.634716	+	0.772745i	$0.718883\pi$
$620$	−18.4616	+	5.00000i	−0.741436	+	0.200805i
$621$	24.1219	+	20.0009i	0.967980	+	0.802607i
$622$	18.8997			0.757811
$623$			41.5831i			1.66599i
$624$	1.65831	+	5.50000i	0.0663856	+	0.220176i
$625$	12.2665	−	21.7838i	0.490660	−	0.871351i
$626$	28.5546			1.14127
$627$	−4.62289	+	16.8681i	−0.184620	+	0.673648i
$628$			2.33816i			0.0933028i
$629$	−9.72281			−0.387674
$630$	−24.5039	−	21.5187i	−0.976260	−	0.857324i
$631$	15.8997			0.632959			0.316480	−	0.948599i	$-0.397499\pi$
$631$	15.8997			0.632959			0.316480	+	0.948599i	$0.397499\pi$
$632$	−4.67632			−0.186014
$633$	30.6151	−	9.23081i	1.21684	−	0.366892i
$634$	17.0000			0.675156
$635$	1.96800	+	7.26650i	0.0780978	+	0.288362i
$636$	1.65831	−	0.500000i	0.0657564	−	0.0198263i
$637$	−55.1662			−2.18577
$638$	3.13708			0.124198
$639$	−27.2297	+	18.0622i	−1.07719	+	0.714528i
$640$	−2.15831	+	0.584541i	−0.0853148	+	0.0231060i
$641$	−23.3230			−0.921204			−0.460602	−	0.887607i	$-0.652366\pi$
$641$	−23.3230			−0.921204			−0.460602	+	0.887607i	$0.652366\pi$
$642$	−9.97494	−	33.0831i	−0.393679	−	1.30569i
$643$			46.6460i			1.83954i	0.392458	+	0.919770i	$0.371625\pi$
$643$			46.6460i			1.83954i	−0.392458	+	0.919770i	$0.628375\pi$
$644$			29.3166i			1.15524i
$645$	2.39487	+	3.84264i	0.0942979	+	0.151304i
$646$	−17.9499	−	11.2620i	−0.706228	−	0.443099i
$647$	3.69232			0.145160			0.0725801	−	0.997363i	$-0.476877\pi$
$647$	3.69232			0.145160			0.0725801	+	0.997363i	$0.476877\pi$
$648$	−8.29156	−	3.50000i	−0.325723	−	0.137493i
$649$			22.9529i			0.900979i
$650$	−8.36865	−	14.3166i	−0.328245	−	0.561544i
$651$	−20.7916	−	68.9578i	−0.814886	−	2.70267i
$652$			15.9384i			0.624195i
$653$	26.8303			1.04995			0.524975	−	0.851118i	$-0.324075\pi$
$653$	26.8303			1.04995			0.524975	+	0.851118i	$0.324075\pi$
$654$	8.64627	+	28.6764i	0.338096	+	1.12134i
$655$	21.5831	−	5.84541i	0.843322	−	0.228399i
$656$	−3.50724			−0.136935
$657$	−18.3691	−	27.6924i	−0.716646	−	1.08038i
$658$	−24.5330			−0.956396
$659$	−12.6162			−0.491458			−0.245729	−	0.969339i	$-0.579027\pi$
$659$	−12.6162			−0.491458			−0.245729	+	0.969339i	$0.579027\pi$
$660$	−4.74562	−	7.61448i	−0.184723	−	0.296393i
$661$		−	21.5987i		−	0.840092i	−0.907503	−	0.420046i	$-0.862014\pi$
$661$		−	21.5987i		−	0.840092i	0.907503	−	0.420046i	$-0.137986\pi$
$662$	15.7533			0.612269
$663$	−8.06173	−	26.7377i	−0.313092	−	1.03841i
$664$		−	9.72281i		−	0.377318i
$665$	13.8146	−	45.3246i	0.535707	−	1.75761i
$666$	−3.31662	−	5.00000i	−0.128517	−	0.193746i
$667$	8.16625			0.316198
$668$			5.05013i			0.195395i
$669$	−11.6332	−	38.5831i	−0.449767	−	1.49171i
$670$	15.1082	−	4.09178i	0.583680	−	0.158079i
$671$			10.0000i			0.386046i
$672$	−2.43070	−	8.06173i	−0.0937664	−	0.310988i
$673$	−13.2665			−0.511386			−0.255693	−	0.966758i	$-0.582304\pi$
$673$	−13.2665			−0.511386			−0.255693	+	0.966758i	$0.582304\pi$
$674$			18.2164i			0.701668i
$675$	25.6351	+	4.22366i	0.986697	+	0.162569i
$676$	2.00000			0.0769231
$677$		−	20.1662i		−	0.775052i	−0.921859	−	0.387526i	$-0.873330\pi$
$677$		−	20.1662i		−	0.775052i	0.921859	−	0.387526i	$-0.126670\pi$
$678$	−4.15831	−	13.7916i	−0.159699	−	0.529662i
$679$			80.8609i			3.10316i
$680$	10.4924	−	2.84169i	0.402366	−	0.108974i
$681$	0.0831240	−	0.0250628i	0.00318532	−	0.000960409i
$682$		−	19.8158i		−	0.758785i
$683$		−	24.0000i		−	0.918334i	−0.888350	−	0.459167i	$-0.848148\pi$
$683$		−	24.0000i		−	0.918334i	0.888350	−	0.459167i	$-0.151852\pi$
$684$	−0.331463	−	13.0725i	−0.0126738	−	0.499839i
$685$	2.84169	+	10.4924i	0.108575	+	0.400895i
$686$	46.8311			1.78802
$687$		0			0
$688$			1.16908i			0.0445708i
$689$			3.31662i			0.126353i
$690$	−12.3535	−	19.8215i	−0.470289	−	0.754592i
$691$	25.8997			0.985273			0.492636	−	0.870235i	$-0.336033\pi$
$691$	25.8997			0.985273			0.492636	+	0.870235i	$0.336033\pi$
$692$			13.2665i			0.504317i
$693$	28.1551	−	18.6760i	1.06952	−	0.709442i
$694$			24.8623i			0.943758i
$695$	5.84541	+	21.5831i	0.221729	+	0.818695i
$696$	−2.24562	+	0.677081i	−0.0851201	+	0.0256647i
$697$	17.0501			0.645820
$698$		−	4.63325i		−	0.175371i
$699$	7.56973	+	25.1059i	0.286313	+	0.949594i
$700$	12.2665	+	20.9849i	0.463630	+	0.793153i
$701$			10.7335i			0.405399i	0.979241	+	0.202699i	$0.0649714\pi$
$701$			10.7335i			0.405399i	−0.979241	+	0.202699i	$0.935029\pi$
$702$	11.0000	−	13.2665i	0.415168	−	0.500712i
$703$	4.63325	−	7.38465i	0.174746	−	0.278517i
$704$		−	2.31662i		−	0.0873111i
$705$	16.5872	−	10.3378i	0.624711	−	0.389342i
$706$		−	20.0009i		−	0.752742i
$707$	−37.3520			−1.40477
$708$	−4.95394	−	16.4304i	−0.186181	−	0.617491i
$709$	15.3668			0.577110			0.288555	−	0.957463i	$-0.406825\pi$
$709$	15.3668			0.577110			0.288555	+	0.957463i	$0.406825\pi$
$710$	23.5081	−	6.36675i	0.882243	−	0.238940i
$711$	7.75481	+	11.6908i	0.290828	+	0.438440i
$712$		−	8.55373i		−	0.320564i
$713$		−	51.5831i		−	1.93180i
$714$	11.8166	+	39.1913i	0.442226	+	1.46670i
$715$	16.5831	−	4.49124i	0.620174	−	0.167963i
$716$	−2.70832			−0.101215
$717$	−10.5581	+	3.18338i	−0.394298	+	0.118885i
$718$	−34.8997			−1.30245
$719$			4.89975i			0.182730i	0.995817	+	0.0913649i	$0.0291230\pi$
$719$			4.89975i			0.182730i	−0.995817	+	0.0913649i	$0.970877\pi$
$720$	5.04051	+	4.42643i	0.187849	+	0.164963i
$721$		−	75.7559i		−	2.82130i
$722$	17.1075	−	8.26650i	0.636674	−	0.307647i
$723$	−28.3695	+	8.55373i	−1.05507	+	0.318117i
$724$			2.70832i			0.100654i
$725$	5.84541	−	3.41688i	0.217093	−	0.126900i
$726$	−9.34169	+	2.81662i	−0.346703	+	0.104535i
$727$			7.56973i			0.280746i	0.990099	+	0.140373i	$0.0448301\pi$
$727$			7.56973i			0.280746i	−0.990099	+	0.140373i	$0.955170\pi$
$728$	16.1235			0.597575
$729$	5.00000	+	26.5330i	0.185185	+	0.982704i
$730$	6.47494	+	23.9076i	0.239648	+	0.884858i
$731$		−	5.68338i		−	0.210207i
$732$	−2.15831	−	7.15831i	−0.0797735	−	0.264579i
$733$			9.72281i			0.359120i	0.983747	+	0.179560i	$0.0574674\pi$
$733$			9.72281i			0.359120i	−0.983747	+	0.179560i	$0.942533\pi$
$734$	2.33816			0.0863031
$735$	−54.6716	+	34.0733i	−2.01659	+	1.25681i
$736$		−	6.03049i		−	0.222287i
$737$			16.2164i			0.597338i
$738$	5.81610	+	8.76811i	0.214094	+	0.322759i
$739$	36.2164			1.33224			0.666120	−	0.745844i	$-0.267954\pi$
$739$	36.2164			1.33224			0.666120	+	0.745844i	$0.267954\pi$
$740$	1.16908	+	4.31662i	0.0429763	+	0.158682i
$741$	24.1495	+	6.61841i	0.887153	+	0.243133i
$742$		−	4.86140i		−	0.178468i
$743$		−	14.8496i		−	0.544780i	−0.962187	−	0.272390i	$-0.912186\pi$
$743$		−	14.8496i		−	0.544780i	0.962187	−	0.272390i	$-0.0878141\pi$
$744$	4.27686	+	14.1848i	0.156797	+	0.520038i
$745$	−8.63325	+	2.33816i	−0.316298	+	0.0856636i
$746$		−	16.6834i		−	0.610822i
$747$	−24.3070	+	16.1235i	−0.889347	+	0.589926i
$748$			11.2620i			0.411781i
$749$	−96.9844			−3.54373
$750$	−17.1362	−	9.01937i	−0.625727	−	0.329341i
$751$		−	22.9529i		−	0.837562i	−0.908087	−	0.418781i	$-0.862458\pi$
$751$		−	22.9529i		−	0.837562i	0.908087	−	0.418781i	$-0.137542\pi$
$752$	5.04648			0.184026
$753$	−2.62531	+	0.791562i	−0.0956718	+	0.0288461i
$754$		−	4.49124i		−	0.163561i
$755$	5.84541	−	1.58312i	0.212736	−	0.0576158i
$756$	−16.1235	+	19.4456i	−0.586404	+	0.707230i
$757$		−	19.4456i		−	0.706763i	−0.935479	−	0.353381i	$-0.885032\pi$
$757$		−	19.4456i		−	0.706763i	0.935479	−	0.353381i	$-0.114968\pi$
$758$	−22.7678			−0.826963
$759$	23.1672	−	6.98519i	0.840918	−	0.253546i
$760$	−2.84169	+	9.32335i	−0.103079	+	0.338193i
$761$			17.3166i			0.627727i	0.949468	+	0.313864i	$0.101623\pi$
$761$			17.3166i			0.627727i	−0.949468	+	0.313864i	$0.898377\pi$
$762$	5.58312	−	1.68338i	0.202255	−	0.0609822i
$763$	84.0660			3.04339
$764$		−	5.00000i		−	0.180894i
$765$	−24.5039	−	21.5187i	−0.885942	−	0.778009i
$766$	25.5831			0.924356
$767$	32.8607			1.18653
$768$	0.500000	+	1.65831i	0.0180422	+	0.0598392i
$769$	18.1662			0.655092			0.327546	−	0.944835i	$-0.393778\pi$
$769$	18.1662			0.655092			0.327546	+	0.944835i	$0.393778\pi$
$770$	−24.3070	+	6.58312i	−0.875964	+	0.237239i
$771$	−24.7916	+	7.47494i	−0.892846	+	0.269203i
$772$	−6.00000			−0.215945
$773$		−	42.1662i		−	1.51661i	−0.651897	−	0.758307i	$-0.726027\pi$
$773$		−	42.1662i		−	1.51661i	0.651897	−	0.758307i	$-0.273973\pi$
$774$	2.92270	−	1.93870i	0.105054	−	0.0696852i
$775$	−21.5831	−	36.9232i	−0.775289	−	1.32632i
$776$		−	16.6332i		−	0.597099i
$777$	−16.1235	+	4.86140i	−0.578426	+	0.174402i
$778$	30.2164			1.08331
$779$	−8.12497	+	12.9499i	−0.291107	+	0.463977i
$780$	−10.9014	+	6.79413i	−0.390332	+	0.243269i
$781$			25.2324i			0.902887i
$782$			29.3166i			1.04836i
$783$	5.41664	+	4.49124i	0.193575	+	0.160504i
$784$	−16.6332			−0.594045
$785$	−5.04648	+	1.36675i	−0.180117	+	0.0487814i
$786$	−5.00000	−	16.5831i	−0.178344	−	0.591500i
$787$	21.6332			0.771142			0.385571	−	0.922678i	$-0.374004\pi$
$787$	21.6332			0.771142			0.385571	+	0.922678i	$0.374004\pi$
$788$	6.21557			0.221420
$789$	−10.8919	−	36.1243i	−0.387762	−	1.28606i
$790$	−2.73350	−	10.0930i	−0.0972536	−	0.359092i
$791$	−40.4305			−1.43754
$792$	−5.79156	+	3.84169i	−0.205794	+	0.136508i
$793$	14.3166			0.508398
$794$	16.7373			0.593984
$795$	2.04851	+	3.28689i	0.0726531	+	0.116574i
$796$	−21.2164			−0.751994
$797$			18.3668i			0.650584i	0.945614	+	0.325292i	$0.105463\pi$
$797$			18.3668i			0.650584i	−0.945614	+	0.325292i	$0.894537\pi$
$798$	−35.3975	−	9.70106i	−1.25306	−	0.343414i
$799$	−24.5330			−0.867915
$800$	−2.52324	−	4.31662i	−0.0892101	−	0.152616i
$801$	−21.3843	+	14.1848i	−0.755578	+	0.501194i
$802$		−	8.92389i		−	0.315113i
$803$	−25.6612			−0.905563
$804$	−3.50000	−	11.6082i	−0.123435	−	0.409389i
$805$	−63.2744	+	17.1368i	−2.23013	+	0.603991i
$806$	−28.3695			−0.999273
$807$	−7.19957	−	23.8783i	−0.253437	−	0.840555i
$808$	7.68338			0.270300
$809$			17.9499i			0.631084i	0.948912	+	0.315542i	$0.102186\pi$
$809$			17.9499i			0.631084i	−0.948912	+	0.315542i	$0.897814\pi$
$810$	2.70734	−	19.9417i	0.0951262	−	0.700679i
$811$		−	6.77081i		−	0.237755i	−0.992909	−	0.118878i	$-0.962070\pi$
$811$		−	6.77081i		−	0.237755i	0.992909	−	0.118878i	$-0.0379296\pi$
$812$			6.58312i			0.231022i
$813$	4.65831	+	15.4499i	0.163374	+	0.541851i
$814$	−4.63325			−0.162395
$815$	−34.4000	+	9.31662i	−1.20498	+	0.326347i
$816$	−2.43070	−	8.06173i	−0.0850916	−	0.282217i
$817$	4.31662	+	2.70832i	0.151020	+	0.0947522i
$818$	−1.16908			−0.0408760
$819$	−26.7377	−	40.3086i	−0.934292	−	1.40850i
$820$	−2.05013	−	7.56973i	−0.0715935	−	0.264346i
$821$			30.0000i			1.04701i	0.852023	+	0.523504i	$0.175375\pi$
$821$			30.0000i			1.04701i	−0.852023	+	0.523504i	$0.824625\pi$
$822$	8.06173	−	2.43070i	0.281185	−	0.0847805i
$823$			16.9224i			0.589877i	0.955516	+	0.294938i	$0.0952991\pi$
$823$			16.9224i			0.589877i	−0.955516	+	0.294938i	$0.904701\pi$
$824$			15.5831i			0.542864i
$825$	13.6604	−	14.6935i	0.475595	−	0.511562i
$826$	−48.1662			−1.67592
$827$			24.5831i			0.854839i	0.904053	+	0.427419i	$0.140577\pi$
$827$			24.5831i			0.854839i	−0.904053	+	0.427419i	$0.859423\pi$
$828$	−15.0762	+	10.0004i	−0.523935	+	0.347539i
$829$		−	28.9833i		−	1.00663i	−0.864102	−	0.503317i	$-0.832113\pi$
$829$		−	28.9833i		−	1.00663i	0.864102	−	0.503317i	$-0.167887\pi$
$830$	20.9849	−	5.68338i	0.728395	−	0.197273i
$831$	−20.0009	+	6.03049i	−0.693822	+	0.209195i
$832$	−3.31662			−0.114983
$833$	80.8609			2.80167
$834$	16.5831	−	5.00000i	0.574227	−	0.173136i
$835$	−10.8997	+	2.95200i	−0.377201	+	0.102158i
$836$	−8.55373	−	5.36675i	−0.295837	−	0.185613i
$837$	28.3695	−	34.2149i	0.980593	−	1.18264i
$838$	−22.9499			−0.792790
$839$	−36.9232			−1.27473			−0.637366	−	0.770561i	$-0.719976\pi$
$839$	−36.9232			−1.27473			−0.637366	+	0.770561i	$0.719976\pi$
$840$	15.9789	−	9.95862i	0.551324	−	0.343605i
$841$	−27.1662			−0.936767
$842$	−24.3070			−0.837675
$843$	6.80011	+	22.5534i	0.234208	+	0.776780i
$844$			18.4616i			0.635475i
$845$	1.16908	+	4.31662i	0.0402176	+	0.148496i
$846$	−8.36865	−	12.6162i	−0.287720	−	0.433754i
$847$			27.3855i			0.940977i
$848$			1.00000i			0.0343401i
$849$	−25.1059	+	7.56973i	−0.861634	+	0.259792i
$850$	12.2665	+	20.9849i	0.420737	+	0.719775i
$851$	−12.0610			−0.413445
$852$	−5.44594	−	18.0622i	−0.186575	−	0.618799i
$853$			38.5211i			1.31894i	0.751732	+	0.659468i	$0.229218\pi$
$853$			38.5211i			1.31894i	−0.751732	+	0.659468i	$0.770782\pi$
$854$	−20.9849			−0.718087
$855$	28.0208	−	8.35680i	0.958290	−	0.285797i
$856$	19.9499			0.681873
$857$		−	12.0000i		−	0.409912i	−0.978771	−	0.204956i	$-0.934295\pi$
$857$		−	12.0000i		−	0.409912i	0.978771	−	0.204956i	$-0.0657052\pi$
$858$	−3.84169	−	12.7414i	−0.131153	−	0.434985i
$859$	−16.9499			−0.578322			−0.289161	−	0.957280i	$-0.593376\pi$
$859$	−16.9499			−0.578322			−0.289161	+	0.957280i	$0.593376\pi$
$860$	−2.52324	+	0.683375i	−0.0860418	+	0.0233029i
$861$	28.2744	−	8.52506i	0.963590	−	0.290533i
$862$			33.4160i			1.13815i
$863$			18.3166i			0.623505i	0.950163	+	0.311753i	$0.100916\pi$
$863$			18.3166i			0.623505i	−0.950163	+	0.311753i	$0.899084\pi$
$864$	3.31662	−	4.00000i	0.112834	−	0.136083i
$865$	−28.6332	+	7.75481i	−0.973560	+	0.263671i
$866$			8.31662i			0.282610i
$867$	3.31662	+	11.0000i	0.112638	+	0.373580i
$868$	41.5831			1.41142
$869$	10.8333			0.367494
$870$	−2.77401	−	4.45097i	−0.0940477	−	0.150902i
$871$	23.2164			0.786657
$872$	−17.2925			−0.585599
$873$	−41.5831	+	27.5831i	−1.40738	+	0.933547i
$874$	−22.2665	−	13.9704i	−0.753176	−	0.472555i
$875$	−38.1216	+	38.7414i	−1.28875	+	1.30970i
$876$	18.3691	−	5.53848i	0.620634	−	0.187128i
$877$	0.0501256			0.00169262			0.000846311	−	1.00000i	$-0.499731\pi$
$877$	0.0501256			0.00169262			0.000846311		1.00000i	$0.499731\pi$
$878$	−1.16908			−0.0394546
$879$	13.7084	−	4.13325i	0.462374	−	0.139411i
$880$	5.00000	−	1.35416i	0.168550	−	0.0456488i
$881$			23.8997i			0.805203i	0.915375	+	0.402601i	$0.131894\pi$
$881$			23.8997i			0.805203i	−0.915375	+	0.402601i	$0.868106\pi$
$882$	27.5831	+	41.5831i	0.928772	+	1.40018i
$883$			46.6460i			1.56976i	0.619645	+	0.784882i	$0.287277\pi$
$883$			46.6460i			1.56976i	−0.619645	+	0.784882i	$0.712723\pi$
$884$	16.1235			0.542290
$885$	32.5661	−	20.2964i	1.09470	−	0.682255i
$886$			3.87740i			0.130264i
$887$		−	0.416876i		−	0.0139973i	−0.999976	−	0.00699866i	$-0.997772\pi$
$887$		−	0.416876i		−	0.0139973i	0.999976	−	0.00699866i	$-0.00222776\pi$
$888$	3.31662	−	1.00000i	0.111299	−	0.0335578i
$889$		−	16.3671i		−	0.548936i
$890$	18.4616	−	5.00000i	0.618835	−	0.167600i
$891$	19.2084	+	8.10819i	0.643507	+	0.271634i
$892$	23.2665			0.779020
$893$	11.6908	−	18.6332i	0.391218	−	0.623538i
$894$	2.00000	+	6.63325i	0.0668900	+	0.221849i
$895$	−1.58312	−	5.84541i	−0.0529180	−	0.195390i
$896$	4.86140			0.162408
$897$	−10.0004	−	33.1677i	−0.333905	−	1.10744i
$898$			31.5066i			1.05139i
$899$		−	11.5831i		−	0.386319i
$900$	−6.60724	+	13.4664i	−0.220241	+	0.448881i
$901$		−	4.86140i		−	0.161957i
$902$	8.12497			0.270532
$903$	−2.84169	−	9.42481i	−0.0945654	−	0.313638i
$904$	8.31662			0.276607
$905$	−5.84541	+	1.58312i	−0.194308	+	0.0526248i
$906$	−1.35416	−	4.49124i	−0.0449890	−	0.149212i
$907$	60.1662			1.99779			0.998894	−	0.0470245i	$-0.0149739\pi$
$907$	60.1662			1.99779			0.998894	+	0.0470245i	$0.0149739\pi$
$908$			0.0501256i			0.00166348i
$909$	−12.7414	−	19.2084i	−0.422607	−	0.637104i
$910$	9.42481	+	34.7994i	0.312429	+	1.15359i
$911$	−0.370160			−0.0122639			−0.00613197	−	0.999981i	$-0.501952\pi$
$911$	−0.370160			−0.0122639			−0.00613197	+	0.999981i	$0.501952\pi$
$912$	7.28134	+	1.99553i	0.241109	+	0.0660785i
$913$			22.5241i			0.745439i
$914$	−18.8318			−0.622900
$915$	14.1883	−	8.84264i	0.469049	−	0.292329i
$916$		0			0
$917$	−48.6140			−1.60538
$918$	−16.1235	+	19.4456i	−0.532153	+	0.641801i
$919$	1.94987			0.0643204			0.0321602	−	0.999483i	$-0.489761\pi$
$919$	1.94987			0.0643204			0.0321602	+	0.999483i	$0.489761\pi$
$920$	13.0157	−	3.52506i	0.429114	−	0.116218i
$921$	1.00000	+	3.31662i	0.0329511	+	0.109287i
$922$	−11.5831			−0.381470
$923$	36.1243			1.18905
$924$	5.63102	+	18.6760i	0.185247	+	0.614395i
$925$	−8.63325	+	5.04648i	−0.283859	+	0.165927i
$926$	4.67632			0.153674
$927$	38.9578	−	25.8417i	1.27954	−	0.848752i
$928$		−	1.35416i		−	0.0444525i
$929$			37.9499i			1.24509i	0.782582	+	0.622547i	$0.213902\pi$
$929$			37.9499i			1.24509i	−0.782582	+	0.622547i	$0.786098\pi$
$930$	−28.1151	+	17.5224i	−0.921931	+	0.574581i
$931$	−38.5330	+	61.4153i	−1.26287	+	2.01281i
$932$	−15.1395			−0.495909
$933$	31.3417	−	9.44987i	1.02608	−	0.309375i
$934$			8.18357i			0.267774i
$935$	−24.3070	+	6.58312i	−0.794925	+	0.215291i
$936$	5.50000	+	8.29156i	0.179773	+	0.271018i
$937$		−	55.0147i		−	1.79725i	−0.438716	−	0.898626i	$-0.644567\pi$
$937$		−	55.0147i		−	1.79725i	0.438716	−	0.898626i	$-0.355433\pi$
$938$	−34.0298			−1.11111
$939$	47.3524	−	14.2773i	1.54529	−	0.465922i
$940$	2.94987	+	10.8919i	0.0962143	+	0.355254i
$941$	−13.4151			−0.437321			−0.218660	−	0.975801i	$-0.570169\pi$
$941$	−13.4151			−0.437321			−0.218660	+	0.975801i	$0.570169\pi$
$942$	1.16908	+	3.87740i	0.0380907	+	0.126333i
$943$	21.1504			0.688751
$944$	9.90789			0.322474
$945$	−51.3945	−	23.4327i	−1.67186	−	0.762266i
$946$		−	2.70832i		−	0.0880551i
$947$	−17.4776			−0.567946			−0.283973	−	0.958832i	$-0.591653\pi$
$947$	−17.4776			−0.567946			−0.283973	+	0.958832i	$0.591653\pi$
$948$	−7.75481	+	2.33816i	−0.251864	+	0.0759400i
$949$			36.7382i			1.19257i
$950$	−21.7838	−	0.683375i	−0.706759	−	0.0221716i
$951$	28.1913	−	8.50000i	0.914166	−	0.275631i
$952$	−23.6332			−0.765958
$953$		−	35.5831i		−	1.15265i	−0.817220	−	0.576325i	$-0.804486\pi$
$953$		−	35.5831i		−	1.15265i	0.817220	−	0.576325i	$-0.195514\pi$
$954$	2.50000	−	1.65831i	0.0809405	−	0.0536898i
$955$	10.7916	−	2.92270i	0.349207	−	0.0945764i
$956$		−	6.36675i		−	0.205915i
$957$	5.20226	−	1.56854i	0.168165	−	0.0507037i
$958$	14.0000			0.452319
$959$		−	23.6332i		−	0.763157i
$960$	−3.28689	+	2.04851i	−0.106084	+	0.0661153i
$961$	−42.1662			−1.36020
$962$			6.63325i			0.213865i
$963$	−33.0831	−	49.8747i	−1.06609	−	1.60719i
$964$		−	17.1075i		−	0.550994i
$965$	−3.50724	−	12.9499i	−0.112902	−	0.416871i
$966$	14.6583	+	48.6161i	0.471623	+	1.56420i
$967$			26.4601i			0.850900i	0.904982	+	0.425450i	$0.139884\pi$
$967$			26.4601i			0.850900i	−0.904982	+	0.425450i	$0.860116\pi$
$968$		−	5.63325i		−	0.181059i
$969$	−35.3975	−	9.70106i	−1.13713	−	0.311643i
$970$	35.8997	−	9.72281i	1.15267	−	0.312181i
$971$	−48.9842			−1.57198			−0.785989	−	0.618241i	$-0.787846\pi$
$971$	−48.9842			−1.57198			−0.785989	+	0.618241i	$0.787846\pi$
$972$	−15.5000	−	1.65831i	−0.497163	−	0.0531904i
$973$		−	48.6140i		−	1.55849i
$974$		−	16.5330i		−	0.529751i
$975$	−21.0361	−	19.5571i	−0.673696	−	0.626329i
$976$	4.31662			0.138172
$977$		−	3.58312i		−	0.114634i	−0.998356	−	0.0573171i	$-0.981745\pi$
$977$		−	3.58312i		−	0.114634i	0.998356	−	0.0573171i	$-0.0182546\pi$
$978$	7.96919	+	26.4308i	0.254826	+	0.845164i
$979$			19.8158i			0.633315i
$980$	−9.72281	−	35.8997i	−0.310584	−	1.14678i
$981$	28.6764	+	43.2313i	0.915568	+	1.38027i
$982$	41.5831			1.32697
$983$			39.1662i			1.24921i	0.780941	+	0.624605i	$0.214740\pi$
$983$			39.1662i			1.24921i	−0.780941	+	0.624605i	$0.785260\pi$
$984$	−5.81610	+	1.75362i	−0.185411	+	0.0559034i
$985$	3.63325	+	13.4151i	0.115765	+	0.427442i
$986$			6.58312i			0.209649i
$987$	−40.6834	+	12.2665i	−1.29497	+	0.390447i
$988$	−7.68338	+	12.2461i	−0.244441	+	0.389599i
$989$		−	7.05013i		−	0.224181i
$990$	−11.6770	−	10.2544i	−0.371118	−	0.325906i
$991$			13.9704i			0.443783i	0.975071	+	0.221892i	$0.0712232\pi$
$991$			13.9704i			0.443783i	−0.975071	+	0.221892i	$0.928777\pi$
$992$	−8.55373			−0.271581
$993$	26.1239	−	7.87665i	0.829016	−	0.249958i
$994$	−52.9499			−1.67947
$995$	−12.4018	−	45.7916i	−0.393164	−	1.45169i
$996$	−4.86140	−	16.1235i	−0.154039	−	0.510891i
$997$			17.9064i			0.567101i	0.958957	+	0.283550i	$0.0915123\pi$
$997$			17.9064i			0.567101i	−0.958957	+	0.283550i	$0.908488\pi$
$998$			41.5831i			1.31629i
$999$	−8.00000	−	6.63325i	−0.253109	−	0.209867i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	570.2.c.f.569.7	yes	8
3.2	odd	2	inner	570.2.c.f.569.2	yes	8
5.4	even	2		570.2.c.c.569.2	yes	8
15.14	odd	2		570.2.c.c.569.7	yes	8
19.18	odd	2		570.2.c.c.569.1	✓	8
57.56	even	2		570.2.c.c.569.8	yes	8
95.94	odd	2	inner	570.2.c.f.569.8	yes	8
285.284	even	2	inner	570.2.c.f.569.1	yes	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
570.2.c.c.569.1	✓	8	19.18	odd	2
570.2.c.c.569.2	yes	8	5.4	even	2
570.2.c.c.569.7	yes	8	15.14	odd	2
570.2.c.c.569.8	yes	8	57.56	even	2
570.2.c.f.569.1	yes	8	285.284	even	2	inner
570.2.c.f.569.2	yes	8	3.2	odd	2	inner
570.2.c.f.569.7	yes	8	1.1	even	1	trivial
570.2.c.f.569.8	yes	8	95.94	odd	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 570 = 2 \cdot 3 \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	570.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+1.00000i q^{2} +(0.500000 + 1.65831i) q^{3} -1.00000 q^{4} +(-0.584541 - 2.15831i) q^{5} +(-1.65831 + 0.500000i) q^{6} +4.86140i q^{7} -1.00000i q^{8} +(-2.50000 + 1.65831i) q^{9} +O(q^{10})\)	\(q+1.00000i q^{2} +(0.500000 + 1.65831i) q^{3} -1.00000 q^{4} +(-0.584541 - 2.15831i) q^{5} +(-1.65831 + 0.500000i) q^{6} +4.86140i q^{7} -1.00000i q^{8} +(-2.50000 + 1.65831i) q^{9} +(2.15831 - 0.584541i) q^{10} +2.31662i q^{11} +(-0.500000 - 1.65831i) q^{12} +3.31662 q^{13} -4.86140 q^{14} +(3.28689 - 2.04851i) q^{15} +1.00000 q^{16} -4.86140 q^{17} +(-1.65831 - 2.50000i) q^{18} +(2.31662 - 3.69232i) q^{19} +(0.584541 + 2.15831i) q^{20} +(-8.06173 + 2.43070i) q^{21} -2.31662 q^{22} -6.03049 q^{23} +(1.65831 - 0.500000i) q^{24} +(-4.31662 + 2.52324i) q^{25} +3.31662i q^{26} +(-4.00000 - 3.31662i) q^{27} -4.86140i q^{28} -1.35416 q^{29} +(2.04851 + 3.28689i) q^{30} +8.55373i q^{31} +1.00000i q^{32} +(-3.84169 + 1.15831i) q^{33} -4.86140i q^{34} +(10.4924 - 2.84169i) q^{35} +(2.50000 - 1.65831i) q^{36} +2.00000 q^{37} +(3.69232 + 2.31662i) q^{38} +(1.65831 + 5.50000i) q^{39} +(-2.15831 + 0.584541i) q^{40} -3.50724 q^{41} +(-2.43070 - 8.06173i) q^{42} +1.16908i q^{43} -2.31662i q^{44} +(5.04051 + 4.42643i) q^{45} -6.03049i q^{46} +5.04648 q^{47} +(0.500000 + 1.65831i) q^{48} -16.6332 q^{49} +(-2.52324 - 4.31662i) q^{50} +(-2.43070 - 8.06173i) q^{51} -3.31662 q^{52} +1.00000i q^{53} +(3.31662 - 4.00000i) q^{54} +(5.00000 - 1.35416i) q^{55} +4.86140 q^{56} +(7.28134 + 1.99553i) q^{57} -1.35416i q^{58} +9.90789 q^{59} +(-3.28689 + 2.04851i) q^{60} +4.31662 q^{61} -8.55373 q^{62} +(-8.06173 - 12.1535i) q^{63} -1.00000 q^{64} +(-1.93870 - 7.15831i) q^{65} +(-1.15831 - 3.84169i) q^{66} +7.00000 q^{67} +4.86140 q^{68} +(-3.01524 - 10.0004i) q^{69} +(2.84169 + 10.4924i) q^{70} +10.8919 q^{71} +(1.65831 + 2.50000i) q^{72} +11.0770i q^{73} +2.00000i q^{74} +(-6.34264 - 5.89669i) q^{75} +(-2.31662 + 3.69232i) q^{76} -11.2620 q^{77} +(-5.50000 + 1.65831i) q^{78} -4.67632i q^{79} +(-0.584541 - 2.15831i) q^{80} +(3.50000 - 8.29156i) q^{81} -3.50724i q^{82} +9.72281 q^{83} +(8.06173 - 2.43070i) q^{84} +(2.84169 + 10.4924i) q^{85} -1.16908 q^{86} +(-0.677081 - 2.24562i) q^{87} +2.31662 q^{88} +8.55373 q^{89} +(-4.42643 + 5.04051i) q^{90} +16.1235i q^{91} +6.03049 q^{92} +(-14.1848 + 4.27686i) q^{93} +5.04648i q^{94} +(-9.32335 - 2.84169i) q^{95} +(-1.65831 + 0.500000i) q^{96} +16.6332 q^{97} -16.6332i q^{98} +(-3.84169 - 5.79156i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 4 q^{3} - 8 q^{4} - 20 q^{9}+O(q^{10}) \) 8 * q + 4 * q^3 - 8 * q^4 - 20 * q^9	\( 8 q + 4 q^{3} - 8 q^{4} - 20 q^{9} + 4 q^{10} - 4 q^{12} + 22 q^{15} + 8 q^{16} - 8 q^{19} + 8 q^{22} - 8 q^{25} - 32 q^{27} + 2 q^{30} - 44 q^{33} + 20 q^{36} + 16 q^{37} - 4 q^{40} + 22 q^{45} + 4 q^{48} - 80 q^{49} + 40 q^{55} - 4 q^{57} - 22 q^{60} + 8 q^{61} - 8 q^{64} + 4 q^{66} + 56 q^{67} + 36 q^{70} - 4 q^{75} + 8 q^{76} - 44 q^{78} + 28 q^{81} + 36 q^{85} - 8 q^{88} - 10 q^{90} + 80 q^{97} - 44 q^{99}+O(q^{100}) \) 8 * q + 4 * q^3 - 8 * q^4 - 20 * q^9 + 4 * q^10 - 4 * q^12 + 22 * q^15 + 8 * q^16 - 8 * q^19 + 8 * q^22 - 8 * q^25 - 32 * q^27 + 2 * q^30 - 44 * q^33 + 20 * q^36 + 16 * q^37 - 4 * q^40 + 22 * q^45 + 4 * q^48 - 80 * q^49 + 40 * q^55 - 4 * q^57 - 22 * q^60 + 8 * q^61 - 8 * q^64 + 4 * q^66 + 56 * q^67 + 36 * q^70 - 4 * q^75 + 8 * q^76 - 44 * q^78 + 28 * q^81 + 36 * q^85 - 8 * q^88 - 10 * q^90 + 80 * q^97 - 44 * q^99

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