LMFDB - Embedded newform 164.3.c.a.83.19

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [164,3,Mod(83,164)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(164, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("164.83");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 164 = 2^{2} \cdot 41 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	164.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:	$4.46867633551$
Analytic rank:	$0$
Dimension:	$40$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			83.19
Character	$\chi$	$=$	164.83
Dual form			164.3.c.a.83.20

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.387677 - 1.96207i) q^{2} -0.338353i q^{3} +(-3.69941 + 1.52129i) q^{4} -3.21167 q^{5} +(-0.663871 + 0.131171i) q^{6} +12.6392i q^{7} +(4.41906 + 6.66873i) q^{8} +8.88552 q^{9} +O(q^{10})$	\(q+(-0.387677 - 1.96207i) q^{2} -0.338353i q^{3} +(-3.69941 + 1.52129i) q^{4} -3.21167 q^{5} +(-0.663871 + 0.131171i) q^{6} +12.6392i q^{7} +(4.41906 + 6.66873i) q^{8} +8.88552 q^{9} +(1.24509 + 6.30151i) q^{10} -2.51931i q^{11} +(0.514734 + 1.25171i) q^{12} +6.94325 q^{13} +(24.7989 - 4.89991i) q^{14} +1.08668i q^{15} +(11.3713 - 11.2558i) q^{16} -13.6375 q^{17} +(-3.44471 - 17.4340i) q^{18} +27.4606i q^{19} +(11.8813 - 4.88590i) q^{20} +4.27649 q^{21} +(-4.94306 + 0.976678i) q^{22} +9.25078i q^{23} +(2.25638 - 1.49520i) q^{24} -14.6852 q^{25} +(-2.69174 - 13.6231i) q^{26} -6.05161i q^{27} +(-19.2279 - 46.7575i) q^{28} +27.8728 q^{29} +(2.13213 - 0.421279i) q^{30} +51.3520i q^{31} +(-26.4930 - 17.9477i) q^{32} -0.852416 q^{33} +(5.28696 + 26.7578i) q^{34} -40.5928i q^{35} +(-32.8712 + 13.5175i) q^{36} +47.9059 q^{37} +(53.8796 - 10.6458i) q^{38} -2.34927i q^{39} +(-14.1926 - 21.4177i) q^{40} -6.40312 q^{41} +(-1.65790 - 8.39077i) q^{42} -7.63380i q^{43} +(3.83262 + 9.31998i) q^{44} -28.5373 q^{45} +(18.1506 - 3.58631i) q^{46} +23.1623i q^{47} +(-3.80843 - 3.84752i) q^{48} -110.748 q^{49} +(5.69310 + 28.8133i) q^{50} +4.61430i q^{51} +(-25.6860 + 10.5627i) q^{52} -55.7920 q^{53} +(-11.8737 + 2.34607i) q^{54} +8.09120i q^{55} +(-84.2871 + 55.8532i) q^{56} +9.29138 q^{57} +(-10.8056 - 54.6883i) q^{58} -12.8091i q^{59} +(-1.65316 - 4.02007i) q^{60} +19.2743 q^{61} +(100.756 - 19.9080i) q^{62} +112.305i q^{63} +(-24.9438 + 58.9390i) q^{64} -22.2994 q^{65} +(0.330462 + 1.67250i) q^{66} -47.8688i q^{67} +(50.4509 - 20.7467i) q^{68} +3.13003 q^{69} +(-79.6458 + 15.7369i) q^{70} -112.687i q^{71} +(39.2656 + 59.2551i) q^{72} -73.1553 q^{73} +(-18.5720 - 93.9946i) q^{74} +4.96877i q^{75} +(-41.7757 - 101.588i) q^{76} +31.8420 q^{77} +(-4.60942 + 0.910756i) q^{78} -69.2886i q^{79} +(-36.5209 + 36.1499i) q^{80} +77.9221 q^{81} +(2.48234 + 12.5634i) q^{82} +7.27874i q^{83} +(-15.8205 + 6.50581i) q^{84} +43.7993 q^{85} +(-14.9780 + 2.95945i) q^{86} -9.43085i q^{87} +(16.8006 - 11.1330i) q^{88} +128.198 q^{89} +(11.0633 + 55.9922i) q^{90} +87.7568i q^{91} +(-14.0732 - 34.2225i) q^{92} +17.3751 q^{93} +(45.4460 - 8.97948i) q^{94} -88.1945i q^{95} +(-6.07265 + 8.96399i) q^{96} +2.67485 q^{97} +(42.9345 + 217.296i) q^{98} -22.3854i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q - 2 q^{2} - 2 q^{4} + 12 q^{6} + 10 q^{8} - 120 q^{9}+O(q^{10}) $ 40 * q - 2 * q^2 - 2 * q^4 + 12 * q^6 + 10 * q^8 - 120 * q^9	$ 40 q - 2 q^{2} - 2 q^{4} + 12 q^{6} + 10 q^{8} - 120 q^{9} - 20 q^{10} + 10 q^{12} - 16 q^{13} + 36 q^{14} - 42 q^{16} - 34 q^{18} + 8 q^{20} + 48 q^{21} - 38 q^{22} + 52 q^{24} + 216 q^{25} + 54 q^{26} - 54 q^{28} - 32 q^{29} + 66 q^{30} - 2 q^{32} - 48 q^{33} - 124 q^{34} - 70 q^{36} + 16 q^{37} - 140 q^{38} + 16 q^{40} + 88 q^{42} + 100 q^{44} - 48 q^{45} + 196 q^{46} + 78 q^{48} - 152 q^{49} + 198 q^{50} + 26 q^{52} - 32 q^{53} - 74 q^{54} + 96 q^{56} - 112 q^{57} + 38 q^{58} - 102 q^{60} + 96 q^{61} - 112 q^{62} + 70 q^{64} - 96 q^{65} - 528 q^{66} - 148 q^{68} - 80 q^{69} - 82 q^{70} - 458 q^{72} + 128 q^{73} + 372 q^{74} - 50 q^{76} + 192 q^{77} + 144 q^{78} - 100 q^{80} + 520 q^{81} + 344 q^{84} - 176 q^{85} - 460 q^{86} + 66 q^{88} + 16 q^{89} + 80 q^{90} + 572 q^{92} + 32 q^{93} + 262 q^{94} - 304 q^{96} - 304 q^{97} + 174 q^{98}+O(q^{100}) $ 40 * q - 2 * q^2 - 2 * q^4 + 12 * q^6 + 10 * q^8 - 120 * q^9 - 20 * q^10 + 10 * q^12 - 16 * q^13 + 36 * q^14 - 42 * q^16 - 34 * q^18 + 8 * q^20 + 48 * q^21 - 38 * q^22 + 52 * q^24 + 216 * q^25 + 54 * q^26 - 54 * q^28 - 32 * q^29 + 66 * q^30 - 2 * q^32 - 48 * q^33 - 124 * q^34 - 70 * q^36 + 16 * q^37 - 140 * q^38 + 16 * q^40 + 88 * q^42 + 100 * q^44 - 48 * q^45 + 196 * q^46 + 78 * q^48 - 152 * q^49 + 198 * q^50 + 26 * q^52 - 32 * q^53 - 74 * q^54 + 96 * q^56 - 112 * q^57 + 38 * q^58 - 102 * q^60 + 96 * q^61 - 112 * q^62 + 70 * q^64 - 96 * q^65 - 528 * q^66 - 148 * q^68 - 80 * q^69 - 82 * q^70 - 458 * q^72 + 128 * q^73 + 372 * q^74 - 50 * q^76 + 192 * q^77 + 144 * q^78 - 100 * q^80 + 520 * q^81 + 344 * q^84 - 176 * q^85 - 460 * q^86 + 66 * q^88 + 16 * q^89 + 80 * q^90 + 572 * q^92 + 32 * q^93 + 262 * q^94 - 304 * q^96 - 304 * q^97 + 174 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/164\mathbb{Z}\right)^\times$.

$n$	$83$	$129$
$\chi(n)$	$-1$	$1$

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 $

$2$	−0.387677	−	1.96207i	−0.193838	−	0.981033i
$2$	−0.387677	−	1.96207i	−0.193838	−	0.981033i
$3$		−	0.338353i		−	0.112784i	−0.998409	−	0.0563921i	$-0.982040\pi$
$3$		−	0.338353i		−	0.112784i	0.998409	−	0.0563921i	$-0.0179597\pi$
$4$	−3.69941	+	1.52129i	−0.924853	+	0.380324i
$5$	−3.21167			−0.642334			−0.321167	−	0.947023i	$-0.604075\pi$
$5$	−3.21167			−0.642334			−0.321167	+	0.947023i	$0.604075\pi$
$6$	−0.663871	+	0.131171i	−0.110645	+	0.0218619i
$7$			12.6392i			1.80559i	0.430067	+	0.902797i	$0.358490\pi$
$7$			12.6392i			1.80559i	−0.430067	+	0.902797i	$0.641510\pi$
$8$	4.41906	+	6.66873i	0.552382	+	0.833591i
$9$	8.88552			0.987280
$10$	1.24509	+	6.30151i	0.124509	+	0.630151i
$11$		−	2.51931i		−	0.229028i	−0.993422	−	0.114514i	$-0.963469\pi$
$11$		−	2.51931i		−	0.229028i	0.993422	−	0.114514i	$-0.0365311\pi$
$12$	0.514734	+	1.25171i	0.0428945	+	0.104309i
$13$	6.94325			0.534096			0.267048	−	0.963683i	$-0.413952\pi$
$13$	6.94325			0.534096			0.267048	+	0.963683i	$0.413952\pi$
$14$	24.7989	−	4.89991i	1.77135	−	0.349993i
$15$			1.08668i			0.0724452i
$16$	11.3713	−	11.2558i	0.710708	−	0.703487i
$17$	−13.6375			−0.802208			−0.401104	−	0.916032i	$-0.631373\pi$
$17$	−13.6375			−0.802208			−0.401104	+	0.916032i	$0.631373\pi$
$18$	−3.44471	−	17.4340i	−0.191373	−	0.968554i
$19$			27.4606i			1.44530i	0.691216	+	0.722648i	$0.257075\pi$
$19$			27.4606i			1.44530i	−0.691216	+	0.722648i	$0.742925\pi$
$20$	11.8813	−	4.88590i	0.594065	−	0.244295i
$21$	4.27649			0.203643
$22$	−4.94306	+	0.976678i	−0.224685	+	0.0443945i
$23$			9.25078i			0.402208i	0.979570	+	0.201104i	$0.0644529\pi$
$23$			9.25078i			0.402208i	−0.979570	+	0.201104i	$0.935547\pi$
$24$	2.25638	−	1.49520i	0.0940159	−	0.0623000i
$25$	−14.6852			−0.587407
$26$	−2.69174	−	13.6231i	−0.103528	−	0.523966i
$27$		−	6.05161i		−	0.224134i
$28$	−19.2279	−	46.7575i	−0.686710	−	1.66991i
$29$	27.8728			0.961132			0.480566	−	0.876959i	$-0.340431\pi$
$29$	27.8728			0.961132			0.480566	+	0.876959i	$0.340431\pi$
$30$	2.13213	−	0.421279i	0.0710711	−	0.0140426i
$31$			51.3520i			1.65652i	0.560347	+	0.828258i	$0.310668\pi$
$31$			51.3520i			1.65652i	−0.560347	+	0.828258i	$0.689332\pi$
$32$	−26.4930	−	17.9477i	−0.827907	−	0.560865i
$33$	−0.852416			−0.0258308
$34$	5.28696	+	26.7578i	0.155499	+	0.786993i
$35$		−	40.5928i		−	1.15979i
$36$	−32.8712	+	13.5175i	−0.913089	+	0.375486i
$37$	47.9059			1.29475			0.647377	−	0.762170i	$-0.275866\pi$
$37$	47.9059			1.29475			0.647377	+	0.762170i	$0.275866\pi$
$38$	53.8796	−	10.6458i	1.41788	−	0.280154i
$39$		−	2.34927i		−	0.0602376i
$40$	−14.1926	−	21.4177i	−0.354814	−	0.535444i
$41$	−6.40312			−0.156174
$41$	−6.40312			−0.156174
$42$	−1.65790	−	8.39077i	−0.0394737	−	0.199780i
$43$		−	7.63380i		−	0.177530i	−0.996053	−	0.0887651i	$-0.971708\pi$
$43$		−	7.63380i		−	0.177530i	0.996053	−	0.0887651i	$-0.0282920\pi$
$44$	3.83262	+	9.31998i	0.0871049	+	0.211818i
$45$	−28.5373			−0.634163
$46$	18.1506	−	3.58631i	0.394579	−	0.0779633i
$47$			23.1623i			0.492815i	0.969166	+	0.246408i	$0.0792502\pi$
$47$			23.1623i			0.492815i	−0.969166	+	0.246408i	$0.920750\pi$
$48$	−3.80843	−	3.84752i	−0.0793423	−	0.0801566i
$49$	−110.748			−2.26017
$50$	5.69310	+	28.8133i	0.113862	+	0.576266i
$51$			4.61430i			0.0904765i
$52$	−25.6860	+	10.5627i	−0.493961	+	0.203129i
$53$	−55.7920			−1.05268			−0.526340	−	0.850274i	$-0.676436\pi$
$53$	−55.7920			−1.05268			−0.526340	+	0.850274i	$0.676436\pi$
$54$	−11.8737	+	2.34607i	−0.219883	+	0.0434457i
$55$			8.09120i			0.147113i
$56$	−84.2871	+	55.8532i	−1.50513	+	0.997378i
$57$	9.29138			0.163007
$58$	−10.8056	−	54.6883i	−0.186304	−	0.942903i
$59$		−	12.8091i		−	0.217103i	−0.994091	−	0.108551i	$-0.965379\pi$
$59$		−	12.8091i		−	0.217103i	0.994091	−	0.108551i	$-0.0346212\pi$
$60$	−1.65316	−	4.02007i	−0.0275526	−	0.0670011i
$61$	19.2743			0.315973			0.157986	−	0.987441i	$-0.449500\pi$
$61$	19.2743			0.315973			0.157986	+	0.987441i	$0.449500\pi$
$62$	100.756	−	19.9080i	1.62510	−	0.321096i
$63$			112.305i			1.78263i
$64$	−24.9438	+	58.9390i	−0.389748	+	0.920922i
$65$	−22.2994			−0.343068
$66$	0.330462	+	1.67250i	0.00500700	+	0.0253409i
$67$		−	47.8688i		−	0.714459i	−0.934017	−	0.357230i	$-0.883721\pi$
$67$		−	47.8688i		−	0.714459i	0.934017	−	0.357230i	$-0.116279\pi$
$68$	50.4509	−	20.7467i	0.741925	−	0.305099i
$69$	3.13003			0.0453627
$70$	−79.6458	+	15.7369i	−1.13780	+	0.224813i
$71$		−	112.687i		−	1.58714i	−0.608478	−	0.793571i	$-0.708219\pi$
$71$		−	112.687i		−	1.58714i	0.608478	−	0.793571i	$-0.291781\pi$
$72$	39.2656	+	59.2551i	0.545356	+	0.822987i
$73$	−73.1553			−1.00213			−0.501064	−	0.865410i	$-0.667058\pi$
$73$	−73.1553			−1.00213			−0.501064	+	0.865410i	$0.667058\pi$
$74$	−18.5720	−	93.9946i	−0.250973	−	1.27020i
$75$			4.96877i			0.0662503i
$76$	−41.7757	−	101.588i	−0.549680	−	1.33669i
$77$	31.8420			0.413532
$78$	−4.60942	+	0.910756i	−0.0590952	+	0.0116764i
$79$		−	69.2886i		−	0.877071i	−0.898714	−	0.438535i	$-0.855497\pi$
$79$		−	69.2886i		−	0.877071i	0.898714	−	0.438535i	$-0.144503\pi$
$80$	−36.5209	+	36.1499i	−0.456512	+	0.451874i
$81$	77.9221			0.962001
$82$	2.48234	+	12.5634i	0.0302725	+	0.153212i
$83$			7.27874i			0.0876957i	0.999038	+	0.0438478i	$0.0139617\pi$
$83$			7.27874i			0.0876957i	−0.999038	+	0.0438478i	$0.986038\pi$
$84$	−15.8205	+	6.50581i	−0.188340	+	0.0774501i
$85$	43.7993			0.515286
$86$	−14.9780	+	2.95945i	−0.174163	+	0.0344122i
$87$		−	9.43085i		−	0.108401i
$88$	16.8006	−	11.1330i	0.190916	−	0.126511i
$89$	128.198			1.44043			0.720216	−	0.693750i	$-0.244043\pi$
$89$	128.198			1.44043			0.720216	+	0.693750i	$0.244043\pi$
$90$	11.0633	+	55.9922i	0.122925	+	0.622135i
$91$			87.7568i			0.964361i
$92$	−14.0732	−	34.2225i	−0.152969	−	0.371983i
$93$	17.3751			0.186829
$94$	45.4460	−	8.97948i	0.483468	−	0.0955264i
$95$		−	88.1945i		−	0.928363i
$96$	−6.07265	+	8.96399i	−0.0632568	+	0.0933749i
$97$	2.67485			0.0275757			0.0137879	−	0.999905i	$-0.495611\pi$
$97$	2.67485			0.0275757			0.0137879	+	0.999905i	$0.495611\pi$
$98$	42.9345	+	217.296i	0.438107	+	2.21730i
$99$		−	22.3854i		−	0.226115i
$100$	54.3265	−	22.3405i	0.543265	−	0.223405i
$101$	165.367			1.63729			0.818647	−	0.574297i	$-0.194725\pi$
$101$	165.367			1.63729			0.818647	+	0.574297i	$0.194725\pi$
$102$	9.05356	−	1.78886i	0.0887604	−	0.0175378i
$103$		−	186.868i		−	1.81425i	−0.420863	−	0.907124i	$-0.638273\pi$
$103$		−	186.868i		−	1.81425i	0.420863	−	0.907124i	$-0.361727\pi$
$104$	30.6826	+	46.3027i	0.295025	+	0.445218i
$105$	−13.7347			−0.130807
$106$	21.6293	+	109.468i	0.204050	+	1.03271i
$107$			81.0677i			0.757642i	0.925470	+	0.378821i	$0.123670\pi$
$107$			81.0677i			0.757642i	−0.925470	+	0.378821i	$0.876330\pi$
$108$	9.20629	+	22.3874i	0.0852434	+	0.207291i
$109$	−116.879			−1.07228			−0.536141	−	0.844129i	$-0.680118\pi$
$109$	−116.879			−1.07228			−0.536141	+	0.844129i	$0.680118\pi$
$110$	15.8755	−	3.13677i	0.144323	−	0.0285161i
$111$		−	16.2091i		−	0.146028i
$112$	142.264	+	143.724i	1.27021	+	1.28325i
$113$	−136.569			−1.20857			−0.604287	−	0.796767i	$-0.706542\pi$
$113$	−136.569			−1.20857			−0.604287	+	0.796767i	$0.706542\pi$
$114$	−3.60205	−	18.2303i	−0.0315969	−	0.159915i
$115$		−	29.7104i		−	0.258352i
$116$	−103.113	+	42.4028i	−0.888906	+	0.365541i
$117$	61.6944			0.527302
$118$	−25.1323	+	4.96578i	−0.212985	+	0.0420829i
$119$		−	172.367i		−	1.44846i
$120$	−7.24675	+	4.80209i	−0.0603896	+	0.0400174i
$121$	114.653			0.947546
$122$	−7.47221	−	37.8175i	−0.0612476	−	0.309980i
$123$			2.16651i			0.0176139i
$124$	−78.1215	−	189.972i	−0.630012	−	1.53203i
$125$	127.456			1.01965
$126$	220.351	−	43.5382i	1.74882	−	0.345541i
$127$			149.003i			1.17325i	0.809859	+	0.586625i	$0.199544\pi$
$127$			149.003i			1.17325i	−0.809859	+	0.586625i	$0.800456\pi$
$128$	125.312	+	26.0922i	0.979003	+	0.203845i
$129$	−2.58292			−0.0200226
$130$	8.64497	+	43.7530i	0.0664997	+	0.336561i
$131$		−	79.3803i		−	0.605956i	−0.952998	−	0.302978i	$-0.902019\pi$
$131$		−	79.3803i		−	0.605956i	0.952998	−	0.302978i	$-0.0979809\pi$
$132$	3.15344	−	1.29678i	0.0238897	−	0.00982407i
$133$	−347.079			−2.60962
$134$	−93.9218	+	18.5576i	−0.700909	+	0.138490i
$135$			19.4358i			0.143969i
$136$	−60.2651	−	90.9450i	−0.443126	−	0.668714i
$137$	153.247			1.11859			0.559297	−	0.828968i	$-0.311071\pi$
$137$	153.247			1.11859			0.559297	+	0.828968i	$0.311071\pi$
$138$	−1.21344	−	6.14132i	−0.00879303	−	0.0445023i
$139$			58.3468i			0.419761i	0.977727	+	0.209880i	$0.0673075\pi$
$139$			58.3468i			0.419761i	−0.977727	+	0.209880i	$0.932693\pi$
$140$	61.7536	+	150.170i	0.441097	+	1.07264i
$141$	7.83703			0.0555818
$142$	−221.100	+	43.6861i	−1.55704	+	0.307649i
$143$		−	17.4922i		−	0.122323i
$144$	101.040	−	100.014i	0.701667	−	0.694539i
$145$	−89.5183			−0.617368
$146$	28.3606	+	143.536i	0.194251	+	0.983121i
$147$			37.4720i			0.254911i
$148$	−177.224	+	72.8790i	−1.19746	+	0.492426i
$149$	290.460			1.94940			0.974699	−	0.223520i	$-0.0717548\pi$
$149$	290.460			1.94940			0.974699	+	0.223520i	$0.0717548\pi$
$150$	9.74906	−	1.92628i	0.0649937	−	0.0128418i
$151$			99.4186i			0.658401i	0.944260	+	0.329201i	$0.106779\pi$
$151$			99.4186i			0.658401i	−0.944260	+	0.329201i	$0.893221\pi$
$152$	−183.127	+	121.350i	−1.20479	+	0.798356i
$153$	−121.177			−0.792004
$154$	−12.3444	−	62.4761i	−0.0801584	−	0.405689i
$155$		−	164.926i		−	1.06404i
$156$	3.57393	+	8.69092i	0.0229098	+	0.0557110i
$157$	175.583			1.11836			0.559182	−	0.829045i	$-0.311115\pi$
$157$	175.583			1.11836			0.559182	+	0.829045i	$0.311115\pi$
$158$	−135.949	+	26.8616i	−0.860436	+	0.170010i
$159$			18.8774i			0.118726i
$160$	85.0868	+	57.6421i	0.531793	+	0.360263i
$161$	−116.922			−0.726224
$162$	−30.2086	−	152.888i	−0.186473	−	0.943755i
$163$		−	12.0272i		−	0.0737868i	−0.999319	−	0.0368934i	$-0.988254\pi$
$163$		−	12.0272i		−	0.0737868i	0.999319	−	0.0368934i	$-0.0117462\pi$
$164$	23.6878	−	9.74104i	0.144438	−	0.0593966i
$165$	2.73768			0.0165920
$166$	14.2814	−	2.82180i	0.0860324	−	0.0169988i
$167$			294.672i			1.76450i	0.470779	+	0.882251i	$0.343973\pi$
$167$			294.672i			1.76450i	−0.470779	+	0.882251i	$0.656027\pi$
$168$	18.8981	+	28.5188i	0.112489	+	0.169755i
$169$	−120.791			−0.714741
$170$	−16.9800	−	85.9371i	−0.0998821	−	0.505512i
$171$			244.002i			1.42691i
$172$	11.6133	+	28.2406i	0.0675190	+	0.164189i
$173$	−110.381			−0.638038			−0.319019	−	0.947748i	$-0.603353\pi$
$173$	−110.381			−0.638038			−0.319019	+	0.947748i	$0.603353\pi$
$174$	−18.5040	+	3.65612i	−0.106345	+	0.0210122i
$175$		−	185.608i		−	1.06062i
$176$	−28.3569	−	28.6479i	−0.161119	−	0.162772i
$177$	−4.33399			−0.0244858
$178$	−49.6995	−	251.534i	−0.279211	−	1.41311i
$179$		−	193.730i		−	1.08229i	−0.840928	−	0.541147i	$-0.817990\pi$
$179$		−	193.730i		−	1.08229i	0.840928	−	0.541147i	$-0.182010\pi$
$180$	105.571	−	43.4137i	0.586508	−	0.241187i
$181$	−42.5373			−0.235012			−0.117506	−	0.993072i	$-0.537490\pi$
$181$	−42.5373			−0.235012			−0.117506	+	0.993072i	$0.537490\pi$
$182$	172.185	−	34.0213i	0.946070	−	0.186930i
$183$		−	6.52152i		−	0.0356367i
$184$	−61.6909	+	40.8797i	−0.335277	+	0.222172i
$185$	−153.858			−0.831665
$186$	−6.73592	−	34.0911i	−0.0362146	−	0.183285i
$187$			34.3572i			0.183728i
$188$	−35.2367	−	85.6869i	−0.187429	−	0.455782i
$189$	76.4873			0.404695
$190$	−173.043	+	34.1909i	−0.910755	+	0.179952i
$191$			68.8755i			0.360605i	0.983611	+	0.180302i	$0.0577076\pi$
$191$			68.8755i			0.360605i	−0.983611	+	0.180302i	$0.942292\pi$
$192$	19.9422	+	8.43982i	0.103865	+	0.0439574i
$193$	1.68325			0.00872148			0.00436074	−	0.999990i	$-0.498612\pi$
$193$	1.68325			0.00872148			0.00436074	+	0.999990i	$0.498612\pi$
$194$	−1.03698	−	5.24823i	−0.00534524	−	0.0270527i
$195$			7.54507i			0.0386927i
$196$	409.704	−	168.481i	2.09033	−	0.859596i
$197$	−48.1790			−0.244564			−0.122282	−	0.992495i	$-0.539021\pi$
$197$	−48.1790			−0.244564			−0.122282	+	0.992495i	$0.539021\pi$
$198$	−43.9216	+	8.67829i	−0.221826	+	0.0438298i
$199$		−	219.235i		−	1.10168i	−0.834611	−	0.550841i	$-0.814307\pi$
$199$		−	219.235i		−	1.10168i	0.834611	−	0.550841i	$-0.185693\pi$
$200$	−64.8947	−	97.9314i	−0.324473	−	0.489657i
$201$	−16.1965			−0.0805798
$202$	−64.1088	−	324.461i	−0.317370	−	1.60624i
$203$			352.289i			1.73541i
$204$	−7.01971	−	17.0702i	−0.0344103	−	0.0836775i
$205$	20.5647			0.100316
$206$	−366.647	+	72.4442i	−1.77984	+	0.351671i
$207$			82.1980i			0.397092i
$208$	78.9540	−	78.1518i	0.379586	−	0.375730i
$209$	69.1819			0.331014
$210$	5.32462	+	26.9484i	0.0253553	+	0.128326i
$211$		−	196.200i		−	0.929859i	−0.885348	−	0.464930i	$-0.846080\pi$
$211$		−	196.200i		−	0.929859i	0.885348	−	0.464930i	$-0.153920\pi$
$212$	206.398	−	84.8761i	0.973574	−	0.400359i
$213$	−38.1280			−0.179005
$214$	159.060	−	31.4280i	0.743272	−	0.146860i
$215$			24.5172i			0.114034i
$216$	40.3566	−	26.7424i	0.186836	−	0.123808i
$217$	−649.046			−2.99100
$218$	45.3111	+	229.324i	0.207849	+	1.05194i
$219$			24.7523i			0.113024i
$220$	−12.3091	−	29.9327i	−0.0559505	−	0.136058i
$221$	−94.6889			−0.428456
$222$	−31.8033	+	6.28389i	−0.143258	+	0.0283058i
$223$			211.288i			0.947479i	0.880665	+	0.473739i	$0.157096\pi$
$223$			211.288i			0.947479i	−0.880665	+	0.473739i	$0.842904\pi$
$224$	226.844	−	334.850i	1.01269	−	1.49486i
$225$	−130.485			−0.579935
$226$	52.9445	+	267.957i	0.234268	+	1.18565i
$227$		−	131.171i		−	0.577847i	−0.957352	−	0.288924i	$-0.906703\pi$
$227$		−	131.171i		−	0.577847i	0.957352	−	0.288924i	$-0.0932973\pi$
$228$	−34.3727	+	14.1349i	−0.150757	+	0.0619953i
$229$	386.696			1.68863			0.844314	−	0.535848i	$-0.180008\pi$
$229$	386.696			1.68863			0.844314	+	0.535848i	$0.180008\pi$
$230$	−58.2939	+	11.5180i	−0.253452	+	0.0500785i
$231$		−	10.7738i		−	0.0466399i
$232$	123.172	+	185.876i	0.530912	+	0.801191i
$233$	−41.6555			−0.178779			−0.0893895	−	0.995997i	$-0.528492\pi$
$233$	−41.6555			−0.178779			−0.0893895	+	0.995997i	$0.528492\pi$
$234$	−23.9175	−	121.049i	−0.102211	−	0.517301i
$235$		−	74.3897i		−	0.316552i
$236$	19.4864	+	47.3861i	0.0825694	+	0.200788i
$237$	−23.4440			−0.0989198
$238$	−338.196	+	66.8227i	−1.42099	+	0.280767i
$239$		−	61.3922i		−	0.256871i	−0.991718	−	0.128436i	$-0.959004\pi$
$239$		−	61.3922i		−	0.256871i	0.991718	−	0.128436i	$-0.0409955\pi$
$240$	12.2314	+	12.3570i	0.0509643	+	0.0514873i
$241$	195.666			0.811891			0.405945	−	0.913897i	$-0.366942\pi$
$241$	195.666			0.811891			0.405945	+	0.913897i	$0.366942\pi$
$242$	−44.4483	−	224.957i	−0.183671	−	0.929574i
$243$		−	80.8297i		−	0.332632i
$244$	−71.3037	+	29.3219i	−0.292228	+	0.120172i
$245$	355.687			1.45178
$246$	4.25085	−	0.839907i	0.0172799	−	0.00341426i
$247$			190.666i			0.771927i
$248$	−342.453	+	226.928i	−1.38086	+	0.915030i
$249$	2.46278			0.00989069
$250$	−49.4116	−	250.077i	−0.197646	−	1.00031i
$251$		−	221.433i		−	0.882203i	−0.897457	−	0.441102i	$-0.854588\pi$
$251$		−	221.433i		−	0.882203i	0.897457	−	0.441102i	$-0.145412\pi$
$252$	−170.850	−	415.464i	−0.677975	−	1.64867i
$253$	23.3056			0.0921170
$254$	292.353	−	57.7649i	1.15100	−	0.227421i
$255$		−	14.8196i		−	0.0581161i
$256$	2.61401	−	255.987i	0.0102110	−	0.999948i
$257$	−13.1202			−0.0510513			−0.0255257	−	0.999674i	$-0.508126\pi$
$257$	−13.1202			−0.0510513			−0.0255257	+	0.999674i	$0.508126\pi$
$258$	1.00134	+	5.06786i	0.00388115	+	0.0196429i
$259$			605.490i			2.33780i
$260$	82.4948	−	33.9240i	0.317288	−	0.130477i
$261$	247.664			0.948906
$262$	−155.749	+	30.7739i	−0.594463	+	0.117458i
$263$			169.700i			0.645246i	0.946527	+	0.322623i	$0.104565\pi$
$263$			169.700i			0.645246i	−0.946527	+	0.322623i	$0.895435\pi$
$264$	−3.76688	−	5.68453i	−0.0142685	−	0.0215323i
$265$	179.186			0.676172
$266$	134.554	+	680.993i	0.505844	+	2.56012i
$267$		−	43.3763i		−	0.162458i
$268$	72.8225	+	177.086i	0.271726	+	0.660770i
$269$	−430.271			−1.59952			−0.799761	−	0.600319i	$-0.795040\pi$
$269$	−430.271			−1.59952			−0.799761	+	0.600319i	$0.795040\pi$
$270$	38.1343	−	7.53480i	0.141238	−	0.0279067i
$271$			99.5194i			0.367230i	0.982998	+	0.183615i	$0.0587800\pi$
$271$			99.5194i			0.367230i	−0.982998	+	0.183615i	$0.941220\pi$
$272$	−155.077	+	153.501i	−0.570136	+	0.564343i
$273$	29.6928			0.108765
$274$	−59.4104	−	300.681i	−0.216826	−	1.09738i
$275$			36.9966i			0.134533i
$276$	−11.5793	+	4.76169i	−0.0419539	+	0.0172525i
$277$	480.856			1.73594			0.867972	−	0.496613i	$-0.165423\pi$
$277$	480.856			1.73594			0.867972	+	0.496613i	$0.165423\pi$
$278$	114.480	−	22.6197i	0.411800	−	0.0813657i
$279$			456.289i			1.63544i
$280$	270.702	−	179.382i	0.966794	−	0.640650i
$281$	−111.854			−0.398059			−0.199029	−	0.979994i	$-0.563779\pi$
$281$	−111.854			−0.398059			−0.199029	+	0.979994i	$0.563779\pi$
$282$	−3.03823	−	15.3768i	−0.0107739	−	0.0545276i
$283$			244.529i			0.864061i	0.901859	+	0.432031i	$0.142203\pi$
$283$			244.529i			0.864061i	−0.901859	+	0.432031i	$0.857797\pi$
$284$	171.430	+	416.876i	0.603628	+	1.46787i
$285$	−29.8408			−0.104705
$286$	−34.3209	+	6.78132i	−0.120003	+	0.0237109i
$287$		−	80.9301i		−	0.281986i
$288$	−235.404	−	159.475i	−0.817376	−	0.553731i
$289$	−103.017			−0.356462
$290$	34.7042	+	175.641i	0.119669	+	0.605658i
$291$		−	0.905042i		−	0.00311011i
$292$	270.632	−	111.291i	0.926821	−	0.381133i
$293$	−30.1836			−0.103016			−0.0515078	−	0.998673i	$-0.516403\pi$
$293$	−30.1836			−0.103016			−0.0515078	+	0.998673i	$0.516403\pi$
$294$	73.5226	−	14.5270i	0.250077	−	0.0494116i
$295$			41.1385i			0.139453i
$296$	211.699	+	319.471i	0.715199	+	1.07930i
$297$	−15.2459			−0.0513330
$298$	−112.605	−	569.903i	−0.377868	−	1.91243i
$299$			64.2305i			0.214818i
$300$	−7.55896	−	18.3815i	−0.0251965	−	0.0612718i
$301$	96.4848			0.320547
$302$	195.066	−	38.5422i	0.645914	−	0.127623i
$303$		−	55.9523i		−	0.184661i
$304$	309.091	+	312.264i	1.01675	+	1.02718i
$305$	−61.9028			−0.202960
$306$	46.9773	+	237.757i	0.153521	+	0.776982i
$307$			156.325i			0.509201i	0.967046	+	0.254600i	$0.0819439\pi$
$307$			156.325i			0.509201i	−0.967046	+	0.254600i	$0.918056\pi$
$308$	−117.797	+	48.4411i	−0.382457	+	0.157276i
$309$	−63.2271			−0.204619
$310$	−323.595	+	63.9378i	−1.04386	+	0.206251i
$311$			181.273i			0.582871i	0.956590	+	0.291436i	$0.0941329\pi$
$311$			181.273i			0.582871i	−0.956590	+	0.291436i	$0.905867\pi$
$312$	15.6666	−	10.3816i	0.0502136	−	0.0332742i
$313$	176.012			0.562338			0.281169	−	0.959658i	$-0.409278\pi$
$313$	176.012			0.562338			0.281169	+	0.959658i	$0.409278\pi$
$314$	−68.0695	−	344.506i	−0.216782	−	1.09715i
$315$		−	360.688i		−	1.14504i
$316$	105.408	+	256.327i	0.333571	+	0.811162i
$317$	−444.226			−1.40134			−0.700671	−	0.713484i	$-0.747116\pi$
$317$	−444.226			−1.40134			−0.700671	+	0.713484i	$0.747116\pi$
$318$	37.0387	−	7.31832i	0.116474	−	0.0230136i
$319$		−	70.2204i		−	0.220127i
$320$	80.1114	−	189.293i	0.250348	−	0.591539i
$321$	27.4295			0.0854501
$322$	45.3279	+	229.409i	0.140770	+	0.712450i
$323$		−	374.495i		−	1.15943i
$324$	−288.266	+	118.542i	−0.889710	+	0.365872i
$325$	−101.963			−0.313732
$326$	−23.5983	+	4.66268i	−0.0723873	+	0.0143027i
$327$			39.5462i			0.120936i
$328$	−28.2958	−	42.7007i	−0.0862676	−	0.130185i
$329$	−292.752			−0.889824
$330$	−1.06133	−	5.37151i	−0.00321616	−	0.0162773i
$331$		−	369.398i		−	1.11601i	−0.829838	−	0.558004i	$-0.811567\pi$
$331$		−	369.398i		−	1.11601i	0.829838	−	0.558004i	$-0.188433\pi$
$332$	−11.0731	−	26.9271i	−0.0333528	−	0.0811057i
$333$	425.669			1.27828
$334$	578.166	−	114.237i	1.73104	−	0.342028i
$335$			153.739i			0.458922i
$336$	48.6294	−	48.1353i	0.144730	−	0.143260i
$337$	423.304			1.25610			0.628048	−	0.778175i	$-0.283854\pi$
$337$	423.304			1.25610			0.628048	+	0.778175i	$0.283854\pi$
$338$	46.8279	+	237.001i	0.138544	+	0.701185i
$339$			46.2085i			0.136308i
$340$	−162.032	+	66.6316i	−0.476564	+	0.195975i
$341$	129.372			0.379389
$342$	478.748	−	94.5938i	1.39985	−	0.276590i
$343$		−	780.446i		−	2.27535i
$344$	50.9077	−	33.7342i	0.147988	−	0.0980646i
$345$	−10.0526			−0.0291380
$346$	42.7920	+	216.574i	0.123676	+	0.625937i
$347$		−	496.592i		−	1.43110i	−0.698560	−	0.715551i	$-0.746176\pi$
$347$		−	496.592i		−	1.43110i	0.698560	−	0.715551i	$-0.253824\pi$
$348$	14.3471	+	34.8886i	0.0412273	+	0.100255i
$349$	274.484			0.786487			0.393243	−	0.919434i	$-0.371353\pi$
$349$	274.484			0.786487			0.393243	+	0.919434i	$0.371353\pi$
$350$	−364.176	+	71.9560i	−1.04050	+	0.205589i
$351$		−	42.0179i		−	0.119709i
$352$	−45.2158	+	66.7442i	−0.128454	+	0.189614i
$353$	−205.449			−0.582007			−0.291004	−	0.956722i	$-0.593989\pi$
$353$	−205.449			−0.582007			−0.291004	+	0.956722i	$0.593989\pi$
$354$	1.68018	+	8.50357i	0.00474628	+	0.0240214i
$355$			361.914i			1.01948i
$356$	−474.259	+	195.028i	−1.33219	+	0.547830i
$357$	−58.3209			−0.163364
$358$	−380.112	+	75.1048i	−1.06177	+	0.209790i
$359$		−	614.015i		−	1.71035i	−0.518341	−	0.855174i	$-0.673450\pi$
$359$		−	614.015i		−	1.71035i	0.518341	−	0.855174i	$-0.326550\pi$
$360$	−126.108	−	190.308i	−0.350301	−	0.528633i
$361$	−393.086			−1.08888
$362$	16.4907	+	83.4609i	0.0455544	+	0.230555i
$363$		−	38.7932i		−	0.106868i
$364$	−133.504	−	324.649i	−0.366769	−	0.891893i
$365$	234.951			0.643701
$366$	−12.7957	+	2.52824i	−0.0349608	+	0.00690776i
$367$			50.5875i			0.137841i	0.997622	+	0.0689203i	$0.0219554\pi$
$367$			50.5875i			0.137841i	−0.997622	+	0.0689203i	$0.978045\pi$
$368$	104.125	+	105.194i	0.282948	+	0.285852i
$369$	−56.8951			−0.154187
$370$	59.6471	+	301.880i	0.161208	+	0.815891i
$371$		−	705.164i		−	1.90071i
$372$	−64.2777	+	26.4326i	−0.172789	+	0.0710555i
$373$	212.367			0.569348			0.284674	−	0.958624i	$-0.408115\pi$
$373$	212.367			0.569348			0.284674	+	0.958624i	$0.408115\pi$
$374$	67.4112	−	13.3195i	0.180244	−	0.0356136i
$375$		−	43.1250i		−	0.115000i
$376$	−154.463	+	102.356i	−0.410806	+	0.272222i
$377$	193.528			0.513337
$378$	−29.6523	−	150.073i	−0.0784453	−	0.397019i
$379$			365.890i			0.965410i	0.875783	+	0.482705i	$0.160346\pi$
$379$			365.890i			0.965410i	−0.875783	+	0.482705i	$0.839654\pi$
$380$	134.170	+	326.268i	0.353078	+	0.858600i
$381$	50.4155			0.132324
$382$	135.138	−	26.7014i	0.353765	−	0.0698990i
$383$		−	278.552i		−	0.727290i	−0.931538	−	0.363645i	$-0.881532\pi$
$383$		−	278.552i		−	0.727290i	0.931538	−	0.363645i	$-0.118468\pi$
$384$	8.82838	−	42.3998i	0.0229906	−	0.110416i
$385$	−102.266			−0.265626
$386$	−0.652555	−	3.30264i	−0.00169056	−	0.00855606i
$387$		−	67.8303i		−	0.175272i
$388$	−9.89537	+	4.06923i	−0.0255035	+	0.0104877i
$389$	179.577			0.461638			0.230819	−	0.972997i	$-0.425860\pi$
$389$	179.577			0.461638			0.230819	+	0.972997i	$0.425860\pi$
$390$	14.8039	−	2.92505i	0.0379588	−	0.00750012i
$391$		−	126.158i		−	0.322654i
$392$	−489.403	−	738.550i	−1.24848	−	1.88406i
$393$	−26.8585			−0.0683423
$394$	18.6779	+	94.5305i	0.0474058	+	0.239925i
$395$			222.532i			0.563372i
$396$	34.0548	+	82.8128i	0.0859969	+	0.209123i
$397$	−489.789			−1.23373			−0.616863	−	0.787071i	$-0.711597\pi$
$397$	−489.789			−1.23373			−0.616863	+	0.787071i	$0.711597\pi$
$398$	−430.153	+	84.9921i	−1.08079	+	0.213548i
$399$			117.435i			0.294324i
$400$	−166.990	+	165.293i	−0.417475	+	0.413233i
$401$	580.558			1.44777			0.723887	−	0.689918i	$-0.242354\pi$
$401$	580.558			1.44777			0.723887	+	0.689918i	$0.242354\pi$
$402$	6.27902	+	31.7787i	0.0156194	+	0.0790515i
$403$			356.550i			0.884739i
$404$	−611.760	+	251.572i	−1.51426	+	0.622702i
$405$	−250.260			−0.617926
$406$	691.215	−	136.574i	1.70250	−	0.336390i
$407$		−	120.690i		−	0.296535i
$408$	−30.7715	+	20.3909i	−0.0754204	+	0.0499776i
$409$	−109.775			−0.268399			−0.134199	−	0.990954i	$-0.542846\pi$
$409$	−109.775			−0.268399			−0.134199	+	0.990954i	$0.542846\pi$
$410$	−7.97246	−	40.3494i	−0.0194450	−	0.0984131i
$411$		−	51.8517i		−	0.126160i
$412$	284.281	+	691.300i	0.690002	+	1.67791i
$413$	161.896			0.392000
$414$	161.278	−	31.8662i	0.389560	−	0.0769716i
$415$		−	23.3769i		−	0.0563299i
$416$	−183.948	−	124.615i	−0.442182	−	0.299556i
$417$	19.7418			0.0473424
$418$	−26.8202	−	135.740i	−0.0641632	−	0.324736i
$419$			418.143i			0.997955i	0.866615	+	0.498977i	$0.166291\pi$
$419$			418.143i			0.997955i	−0.866615	+	0.498977i	$0.833709\pi$
$420$	50.8103	−	20.8945i	0.120977	−	0.0497488i
$421$	23.3921			0.0555633			0.0277816	−	0.999614i	$-0.491156\pi$
$421$	23.3921			0.0555633			0.0277816	+	0.999614i	$0.491156\pi$
$422$	−384.958	+	76.0623i	−0.912223	+	0.180242i
$423$			205.809i			0.486546i
$424$	−246.548	−	372.062i	−0.581481	−	0.877504i
$425$	200.270			0.471223
$426$	14.7813	+	74.8097i	0.0346980	+	0.175610i
$427$			243.611i			0.570518i
$428$	−123.328	−	299.903i	−0.288149	−	0.700708i
$429$	−5.91854			−0.0137961
$430$	48.1045	−	9.50476i	0.111871	−	0.0221041i
$431$		−	505.552i		−	1.17297i	−0.809958	−	0.586487i	$-0.800510\pi$
$431$		−	505.552i		−	1.17297i	0.809958	−	0.586487i	$-0.199490\pi$
$432$	−68.1157	−	68.8149i	−0.157675	−	0.159294i
$433$	−479.198			−1.10669			−0.553346	−	0.832951i	$-0.686649\pi$
$433$	−479.198			−1.10669			−0.553346	+	0.832951i	$0.686649\pi$
$434$	251.620	+	1273.47i	0.579769	+	2.93427i
$435$			30.2888i			0.0696293i
$436$	432.383	−	177.807i	0.991703	−	0.407814i
$437$	−254.032			−0.581309
$438$	48.5657	−	9.59589i	0.110881	−	0.0219084i
$439$		−	23.1559i		−	0.0527469i	−0.999652	−	0.0263734i	$-0.991604\pi$
$439$		−	23.1559i		−	0.0527469i	0.999652	−	0.0263734i	$-0.00839590\pi$
$440$	−53.9580	+	35.7555i	−0.122632	+	0.0812625i
$441$	−984.056			−2.23142
$442$	36.7087	+	185.786i	0.0830513	+	0.420330i
$443$		−	770.344i		−	1.73893i	−0.493999	−	0.869463i	$-0.664465\pi$
$443$		−	770.344i		−	1.73893i	0.493999	−	0.869463i	$-0.335535\pi$
$444$	24.6588	+	59.9641i	0.0555379	+	0.135054i
$445$	−411.731			−0.925238
$446$	414.561	−	81.9113i	0.929508	−	0.183658i
$447$		−	98.2781i		−	0.219861i
$448$	−744.939	−	315.269i	−1.66281	−	0.703726i
$449$	−674.407			−1.50202			−0.751010	−	0.660291i	$-0.770433\pi$
$449$	−674.407			−1.50202			−0.751010	+	0.660291i	$0.770433\pi$
$450$	50.5861	+	256.021i	0.112414	+	0.568936i
$451$			16.1315i			0.0357682i
$452$	505.225	−	207.762i	1.11775	−	0.459649i
$453$	33.6385			0.0742573
$454$	−257.367	+	50.8520i	−0.566887	+	0.112009i
$455$		−	281.846i		−	0.619442i
$456$	41.0592	+	61.9617i	0.0900420	+	0.135881i
$457$	−89.6787			−0.196233			−0.0981167	−	0.995175i	$-0.531282\pi$
$457$	−89.6787			−0.196233			−0.0981167	+	0.995175i	$0.531282\pi$
$458$	−149.913	−	758.723i	−0.327321	−	1.65660i
$459$			82.5291i			0.179802i
$460$	45.1984	+	109.911i	0.0982573	+	0.238937i
$461$	236.550			0.513124			0.256562	−	0.966528i	$-0.417410\pi$
$461$	236.550			0.513124			0.256562	+	0.966528i	$0.417410\pi$
$462$	−21.1390	+	4.17676i	−0.0457553	+	0.00904060i
$463$		−	62.7110i		−	0.135445i	−0.997704	−	0.0677224i	$-0.978427\pi$
$463$		−	62.7110i		−	0.135445i	0.997704	−	0.0677224i	$-0.0215732\pi$
$464$	316.951	−	313.731i	0.683084	−	0.676144i
$465$	−55.8031			−0.120007
$466$	16.1489	+	81.7309i	0.0346542	+	0.175388i
$467$			114.770i			0.245761i	0.992421	+	0.122880i	$0.0392131\pi$
$467$			114.770i			0.245761i	−0.992421	+	0.122880i	$0.960787\pi$
$468$	−228.233	+	93.8553i	−0.487677	+	0.200546i
$469$	605.021			1.29002
$470$	−145.958	+	28.8391i	−0.310548	+	0.0613599i
$471$		−	59.4091i		−	0.126134i
$472$	85.4202	−	56.6040i	0.180975	−	0.119924i
$473$	−19.2319			−0.0406595
$474$	9.08868	+	45.9987i	0.0191744	+	0.0970436i
$475$		−	403.264i		−	0.848977i
$476$	262.221	+	637.657i	0.550885	+	1.33962i
$477$	−495.741			−1.03929
$478$	−120.456	+	23.8003i	−0.251999	+	0.0497915i
$479$			83.0607i			0.173404i	0.996234	+	0.0867022i	$0.0276329\pi$
$479$			83.0607i			0.173404i	−0.996234	+	0.0867022i	$0.972367\pi$
$480$	19.5033	−	28.7894i	0.0406320	−	0.0599779i
$481$	332.623			0.691523
$482$	−75.8550	−	383.909i	−0.157376	−	0.796492i
$483$			39.5609i			0.0819066i
$484$	−424.149	+	174.421i	−0.876341	+	0.360374i
$485$	−8.59073			−0.0177128
$486$	−158.593	+	31.3358i	−0.326324	+	0.0644769i
$487$			696.604i			1.43040i	0.698921	+	0.715199i	$0.253664\pi$
$487$			696.604i			1.43040i	−0.698921	+	0.715199i	$0.746336\pi$
$488$	85.1744	+	128.535i	0.174538	+	0.263392i
$489$	−4.06945			−0.00832199
$490$	−137.891	−	697.882i	−0.281411	−	1.42425i
$491$			607.298i			1.23686i	0.785840	+	0.618430i	$0.212231\pi$
$491$			607.298i			1.23686i	−0.785840	+	0.618430i	$0.787769\pi$
$492$	−3.29591	−	8.01483i	−0.00669900	−	0.0162903i
$493$	−380.117			−0.771028
$494$	374.100	−	73.9168i	0.757287	−	0.149629i
$495$			71.8945i			0.145241i
$496$	578.008	+	583.940i	1.16534	+	1.17730i
$497$	1424.27			2.86573
$498$	−0.954763	−	4.83214i	−0.00191720	−	0.00970310i
$499$			415.498i			0.832662i	0.909213	+	0.416331i	$0.136684\pi$
$499$			415.498i			0.832662i	−0.909213	+	0.416331i	$0.863316\pi$
$500$	−471.511	+	193.898i	−0.943023	+	0.387795i
$501$	99.7030			0.199008
$502$	−434.466	+	85.8444i	−0.865471	+	0.171005i
$503$			518.510i			1.03083i	0.856939	+	0.515417i	$0.172363\pi$
$503$			518.510i			1.03083i	−0.856939	+	0.515417i	$0.827637\pi$
$504$	−748.934	+	496.284i	−1.48598	+	0.984691i
$505$	−531.103			−1.05169
$506$	−9.03504	−	45.7272i	−0.0178558	−	0.0903699i
$507$			40.8701i			0.0806115i
$508$	−226.677	−	551.223i	−0.446215	−	1.08508i
$509$	907.204			1.78233			0.891163	−	0.453682i	$-0.149890\pi$
$509$	907.204			1.78233			0.891163	+	0.453682i	$0.149890\pi$
$510$	−29.0771	+	5.74521i	−0.0570138	+	0.0112651i
$511$		−	924.622i		−	1.80944i
$512$	−503.276	+	94.1112i	−0.982962	+	0.183811i
$513$	166.181			0.323940
$514$	5.08639	+	25.7427i	0.00989570	+	0.0500831i
$515$			600.157i			1.16535i
$516$	9.55528	−	3.92938i	0.0185180	−	0.00761507i
$517$	58.3531			0.112869
$518$	1188.01	−	234.734i	2.29346	−	0.453155i
$519$			37.3476i			0.0719607i
$520$	−98.5425	−	148.709i	−0.189505	−	0.285978i
$521$	−347.383			−0.666761			−0.333381	−	0.942792i	$-0.608189\pi$
$521$	−347.383			−0.666761			−0.333381	+	0.942792i	$0.608189\pi$
$522$	−96.0137	−	485.934i	−0.183934	−	0.930909i
$523$			220.921i			0.422411i	0.977442	+	0.211205i	$0.0677389\pi$
$523$			220.921i			0.422411i	−0.977442	+	0.211205i	$0.932261\pi$
$524$	120.761	+	293.660i	0.230460	+	0.560421i
$525$	−62.8011			−0.119621
$526$	332.962	−	65.7886i	0.633008	−	0.125073i
$527$		−	700.315i		−	1.32887i
$528$	−9.69310	+	9.59463i	−0.0183581	+	0.0181716i
$529$	443.423			0.838229
$530$	−69.4660	−	351.574i	−0.131068	−	0.663347i
$531$		−	113.815i		−	0.214341i
$532$	1283.99	−	528.010i	2.41351	−	0.992500i
$533$	−44.4585			−0.0834118
$534$	−85.1072	+	16.8160i	−0.159377	+	0.0314906i
$535$		−	260.363i		−	0.486659i
$536$	319.224	−	211.535i	0.595567	−	0.394655i
$537$	−65.5492			−0.122066
$538$	166.806	+	844.221i	0.310048	+	1.56918i
$539$			279.010i			0.517643i
$540$	−29.5676	−	71.9010i	−0.0547547	−	0.133150i
$541$	872.588			1.61292			0.806458	−	0.591291i	$-0.201382\pi$
$541$	872.588			1.61292			0.806458	+	0.591291i	$0.201382\pi$
$542$	195.264	−	38.5814i	0.360265	−	0.0711833i
$543$			14.3926i			0.0265057i
$544$	361.300	+	244.762i	0.664154	+	0.449931i
$545$	375.376			0.688763
$546$	−11.5112	−	58.2592i	−0.0210828	−	0.106702i
$547$			786.807i			1.43840i	0.694801	+	0.719202i	$0.255493\pi$
$547$			786.807i			1.43840i	−0.694801	+	0.719202i	$0.744507\pi$
$548$	−566.925	+	233.134i	−1.03454	+	0.425428i
$549$	171.262			0.311953
$550$	72.5897	−	14.3427i	0.131981	−	0.0260776i
$551$			765.405i			1.38912i
$552$	13.8318	+	20.8733i	0.0250576	+	0.0378139i
$553$	875.749			1.58363
$554$	−186.417	−	943.472i	−0.336492	−	1.70302i
$555$			52.0583i			0.0937987i
$556$	−88.7626	−	215.849i	−0.159645	−	0.388217i
$557$	−647.208			−1.16195			−0.580977	−	0.813920i	$-0.697329\pi$
$557$	−647.208			−1.16195			−0.580977	+	0.813920i	$0.697329\pi$
$558$	895.270	−	176.893i	1.60443	−	0.317012i
$559$		−	53.0034i		−	0.0948182i
$560$	−456.904	−	461.594i	−0.815901	−	0.824275i
$561$	11.6249			0.0207217
$562$	43.3634	+	219.466i	0.0771590	+	0.390509i
$563$		−	627.550i		−	1.11465i	−0.830293	−	0.557327i	$-0.811827\pi$
$563$		−	627.550i		−	1.11465i	0.830293	−	0.557327i	$-0.188173\pi$
$564$	−28.9924	+	11.9224i	−0.0514050	+	0.0211391i
$565$	438.614			0.776308
$566$	479.783	−	94.7983i	0.847673	−	0.167488i
$567$			984.869i			1.73698i
$568$	751.479	−	497.971i	1.32303	−	0.876709i
$569$	−532.412			−0.935697			−0.467848	−	0.883809i	$-0.654971\pi$
$569$	−532.412			−0.935697			−0.467848	+	0.883809i	$0.654971\pi$
$570$	11.5686	+	58.5497i	0.0202958	+	0.102719i
$571$		−	912.367i		−	1.59784i	−0.601437	−	0.798920i	$-0.705405\pi$
$571$		−	912.367i		−	1.59784i	0.601437	−	0.798920i	$-0.294595\pi$
$572$	26.6108	+	64.7110i	0.0465224	+	0.113131i
$573$	23.3042			0.0406705
$574$	−158.790	+	31.3747i	−0.276638	+	0.0546598i
$575$		−	135.849i		−	0.236260i
$576$	−221.639	+	523.703i	−0.384790	+	0.909207i
$577$	866.267			1.50133			0.750665	−	0.660683i	$-0.229733\pi$
$577$	866.267			1.50133			0.750665	+	0.660683i	$0.229733\pi$
$578$	39.9375	+	202.127i	0.0690960	+	0.349701i
$579$		−	0.569531i		−	0.000983645i
$580$	331.165	−	136.184i	0.570975	−	0.234800i
$581$	−91.9972			−0.158343
$582$	−1.77575	+	0.350864i	−0.00305112	+	0.000602858i
$583$			140.558i			0.241093i
$584$	−323.278	−	487.853i	−0.553558	−	0.835364i
$585$	−198.142			−0.338704
$586$	11.7015	+	59.2222i	0.0199684	+	0.101062i
$587$		−	650.528i		−	1.10822i	−0.832442	−	0.554112i	$-0.813058\pi$
$587$		−	650.528i		−	1.10822i	0.832442	−	0.554112i	$-0.186942\pi$
$588$	−57.0059	−	138.624i	−0.0969489	−	0.235756i
$589$	−1410.16			−2.39416
$590$	80.7165	−	15.9484i	0.136808	−	0.0270312i
$591$			16.3015i			0.0275829i
$592$	544.754	−	539.219i	0.920192	−	0.910843i
$593$	−708.833			−1.19533			−0.597667	−	0.801745i	$-0.703905\pi$
$593$	−708.833			−1.19533			−0.597667	+	0.801745i	$0.703905\pi$
$594$	5.91048	+	29.9135i	0.00995031	+	0.0503594i
$595$			553.586i			0.930397i
$596$	−1074.53	+	441.876i	−1.80291	+	0.741403i
$597$	−74.1786			−0.124252
$598$	126.025	−	24.9007i	0.210743	−	0.0416399i
$599$			489.228i			0.816741i	0.912816	+	0.408371i	$0.133903\pi$
$599$			489.228i			0.816741i	−0.912816	+	0.408371i	$0.866097\pi$
$600$	−33.1354	+	21.9573i	−0.0552256	+	0.0365955i
$601$	502.627			0.836317			0.418159	−	0.908374i	$-0.362676\pi$
$601$	502.627			0.836317			0.418159	+	0.908374i	$0.362676\pi$
$602$	−37.4049	−	189.310i	−0.0621344	−	0.314468i
$603$		−	425.339i		−	0.705371i
$604$	−151.245	−	367.790i	−0.250406	−	0.608925i
$605$	−368.228			−0.608641
$606$	−109.782	+	21.6914i	−0.181159	+	0.0357944i
$607$			514.148i			0.847031i	0.905889	+	0.423516i	$0.139204\pi$
$607$			514.148i			0.847031i	−0.905889	+	0.423516i	$0.860796\pi$
$608$	492.855	−	727.515i	0.810617	−	1.19657i
$609$	119.198			0.195727
$610$	23.9983	+	121.457i	0.0393414	+	0.199111i
$611$			160.822i			0.263211i
$612$	448.282	−	184.345i	0.732488	−	0.301218i
$613$	−530.228			−0.864972			−0.432486	−	0.901641i	$-0.642363\pi$
$613$	−530.228			−0.864972			−0.432486	+	0.901641i	$0.642363\pi$
$614$	306.719	−	60.6034i	0.499543	−	0.0987026i
$615$		−	6.95813i		−	0.0113140i
$616$	140.712	+	212.346i	0.228428	+	0.344717i
$617$	271.869			0.440631			0.220316	−	0.975429i	$-0.429291\pi$
$617$	271.869			0.440631			0.220316	+	0.975429i	$0.429291\pi$
$618$	24.5117	+	124.056i	0.0396629	+	0.200738i
$619$			1073.14i			1.73367i	0.498593	+	0.866836i	$0.333850\pi$
$619$			1073.14i			1.73367i	−0.498593	+	0.866836i	$0.666150\pi$
$620$	250.901	+	610.128i	0.404678	+	0.984078i
$621$	55.9821			0.0901484
$622$	355.670	−	70.2753i	0.571816	−	0.112983i
$623$			1620.32i			2.60083i
$624$	−26.4429	−	26.7143i	−0.0423764	−	0.0428114i
$625$	−42.2161			−0.0675458
$626$	−68.2357	−	345.347i	−0.109003	−	0.551673i
$627$		−	23.4079i		−	0.0373332i
$628$	−649.555	+	267.114i	−1.03432	+	0.425340i
$629$	−653.319			−1.03866
$630$	−707.694	+	139.830i	−1.12332	+	0.221953i
$631$			260.101i			0.412205i	0.978530	+	0.206102i	$0.0660780\pi$
$631$			260.101i			0.412205i	−0.978530	+	0.206102i	$0.933922\pi$
$632$	462.067	−	306.190i	0.731118	−	0.484478i
$633$	−66.3849			−0.104873
$634$	172.216	+	871.600i	0.271634	+	1.37476i
$635$		−	478.548i		−	0.753618i
$636$	−28.7181	−	69.8352i	−0.0451542	−	0.109804i
$637$	−768.953			−1.20715
$638$	−137.777	+	27.2228i	−0.215951	+	0.0426689i
$639$		−	1001.28i		−	1.56695i
$640$	−402.462	−	83.7996i	−0.628847	−	0.130937i
$641$	−192.709			−0.300639			−0.150319	−	0.988638i	$-0.548030\pi$
$641$	−192.709			−0.300639			−0.150319	+	0.988638i	$0.548030\pi$
$642$	−10.6338	−	53.8185i	−0.0165635	−	0.0838294i
$643$		−	938.021i		−	1.45882i	−0.684077	−	0.729410i	$-0.739795\pi$
$643$		−	938.021i		−	1.45882i	0.684077	−	0.729410i	$-0.260205\pi$
$644$	432.543	−	177.873i	0.671651	−	0.276200i
$645$	8.29548			0.0128612
$646$	−734.785	+	145.183i	−1.13744	+	0.224742i
$647$			992.203i			1.53354i	0.641919	+	0.766772i	$0.278138\pi$
$647$			992.203i			1.53354i	−0.641919	+	0.766772i	$0.721862\pi$
$648$	344.342	+	519.641i	0.531392	+	0.801915i
$649$	−32.2701			−0.0497227
$650$	39.5286	+	200.058i	0.0608133	+	0.307782i
$651$			219.607i			0.337337i
$652$	18.2970	+	44.4938i	0.0280629	+	0.0682420i
$653$	−169.351			−0.259344			−0.129672	−	0.991557i	$-0.541392\pi$
$653$	−169.351			−0.259344			−0.129672	+	0.991557i	$0.541392\pi$
$654$	77.5924	−	15.3311i	0.118643	−	0.0234421i
$655$			254.943i			0.389226i
$656$	−72.8120	+	72.0723i	−0.110994	+	0.109866i
$657$	−650.023			−0.989380
$658$	113.493	+	574.399i	0.172482	+	0.872947i
$659$		−	998.374i		−	1.51498i	−0.652845	−	0.757492i	$-0.726425\pi$
$659$		−	998.374i		−	1.51498i	0.652845	−	0.757492i	$-0.273575\pi$
$660$	−10.1278	+	4.16482i	−0.0153452	+	0.00631033i
$661$	463.666			0.701461			0.350731	−	0.936476i	$-0.385933\pi$
$661$	463.666			0.701461			0.350731	+	0.936476i	$0.385933\pi$
$662$	−724.785	+	143.207i	−1.09484	+	0.216325i
$663$			32.0382i			0.0483231i
$664$	−48.5399	+	32.1652i	−0.0731023	+	0.0484416i
$665$	1114.70			1.67625
$666$	−165.022	−	835.191i	−0.247780	−	1.25404i
$667$			257.845i			0.386575i
$668$	−448.283	−	1090.11i	−0.671082	−	1.63191i
$669$	71.4898			0.106861
$670$	301.646	−	59.6009i	0.450217	−	0.0889566i
$671$		−	48.5581i		−	0.0723667i
$672$	−113.297	−	76.7532i	−0.168597	−	0.114216i
$673$	−6.15330			−0.00914309			−0.00457154	−	0.999990i	$-0.501455\pi$
$673$	−6.15330			−0.00914309			−0.00457154	+	0.999990i	$0.501455\pi$
$674$	−164.105	−	830.551i	−0.243479	−	1.23227i
$675$			88.8690i			0.131658i
$676$	446.857	−	183.759i	0.661031	−	0.271833i
$677$	995.712			1.47077			0.735385	−	0.677649i	$-0.237001\pi$
$677$	995.712			1.47077			0.735385	+	0.677649i	$0.237001\pi$
$678$	90.6641	−	17.9139i	0.133723	−	0.0264217i
$679$			33.8078i			0.0497906i
$680$	193.552	+	292.085i	0.284635	+	0.429537i
$681$	−44.3822			−0.0651721
$682$	−50.1544	−	253.836i	−0.0735402	−	0.372194i
$683$		−	65.4415i		−	0.0958148i	−0.998852	−	0.0479074i	$-0.984745\pi$
$683$		−	65.4415i		−	0.0958148i	0.998852	−	0.0479074i	$-0.0152552\pi$
$684$	−371.199	−	902.664i	−0.542688	−	1.31968i
$685$	−492.180			−0.718511
$686$	−1531.29	+	302.561i	−2.23220	+	0.441051i
$687$		−	130.840i		−	0.190451i
$688$	−85.9245	−	86.8064i	−0.124890	−	0.126172i
$689$	−387.378			−0.562232
$690$	3.89716	+	19.7239i	0.00564806	+	0.0285854i
$691$		−	568.274i		−	0.822394i	−0.911547	−	0.411197i	$-0.865111\pi$
$691$		−	568.274i		−	0.822394i	0.911547	−	0.411197i	$-0.134889\pi$
$692$	408.344	−	167.921i	0.590092	−	0.242661i
$693$	282.933			0.408272
$694$	−974.348	+	192.517i	−1.40396	+	0.277402i
$695$		−	187.391i		−	0.269627i
$696$	62.8917	−	41.6755i	0.0903617	−	0.0598785i
$697$	87.3229			0.125284
$698$	−106.411	−	538.556i	−0.152451	−	0.771570i
$699$			14.0943i			0.0201634i
$700$	282.365	+	686.642i	0.403378	+	0.980917i
$701$	−65.6040			−0.0935864			−0.0467932	−	0.998905i	$-0.514900\pi$
$701$	−65.6040			−0.0935864			−0.0467932	+	0.998905i	$0.514900\pi$
$702$	−82.4419	+	16.2893i	−0.117439	+	0.0232042i
$703$			1315.53i			1.87130i
$704$	148.486	+	62.8413i	0.210917	+	0.0892633i
$705$	−25.1700			−0.0357021
$706$	79.6476	+	403.104i	0.112815	+	0.570969i
$707$			2090.10i			2.95629i
$708$	16.0332	−	6.59327i	0.0226458	−	0.00931253i
$709$	−194.518			−0.274356			−0.137178	−	0.990546i	$-0.543803\pi$
$709$	−194.518			−0.274356			−0.137178	+	0.990546i	$0.543803\pi$
$710$	710.099	−	140.305i	1.00014	−	0.197613i
$711$		−	615.665i		−	0.865914i
$712$	566.516	+	854.920i	0.795669	+	1.20073i
$713$	−475.046			−0.666264
$714$	22.6096	+	114.429i	0.0316661	+	0.160265i
$715$			56.1792i			0.0785724i
$716$	294.721	+	716.689i	0.411622	+	1.00096i
$717$	−20.7722			−0.0289710
$718$	−1204.74	+	238.039i	−1.67791	+	0.331531i
$719$		−	235.719i		−	0.327843i	−0.986473	−	0.163922i	$-0.947586\pi$
$719$		−	235.719i		−	0.327843i	0.986473	−	0.163922i	$-0.0524144\pi$
$720$	−324.507	+	321.211i	−0.450705	+	0.446126i
$721$	2361.85			3.27580
$722$	152.390	+	771.262i	0.211067	+	1.06823i
$723$		−	66.2040i		−	0.0915685i
$724$	157.363	−	64.7117i	0.217352	−	0.0893808i
$725$	−409.317			−0.564576
$726$	−76.1148	+	15.0392i	−0.104841	+	0.0207152i
$727$		−	542.829i		−	0.746670i	−0.927697	−	0.373335i	$-0.878214\pi$
$727$		−	542.829i		−	0.746670i	0.927697	−	0.373335i	$-0.121786\pi$
$728$	−585.226	+	387.803i	−0.803883	+	0.532696i
$729$	673.950			0.924485
$730$	−91.0849	−	460.989i	−0.124774	−	0.631492i
$731$			104.106i			0.142416i
$732$	9.92116	+	24.1258i	0.0135535	+	0.0329588i
$733$	−722.302			−0.985405			−0.492702	−	0.870198i	$-0.663991\pi$
$733$	−722.302			−0.985405			−0.492702	+	0.870198i	$0.663991\pi$
$734$	99.2561	−	19.6116i	0.135226	−	0.0267188i
$735$		−	120.348i		−	0.163738i
$736$	166.030	−	245.081i	0.225584	−	0.332991i
$737$	−120.596			−0.163632
$738$	22.0569	+	111.632i	0.0298874	+	0.151263i
$739$		−	1364.64i		−	1.84660i	−0.384075	−	0.923302i	$-0.625480\pi$
$739$		−	1364.64i		−	1.84660i	0.384075	−	0.923302i	$-0.374520\pi$
$740$	569.184	−	234.063i	0.769168	−	0.316302i
$741$	64.5124			0.0870613
$742$	−1383.58	+	273.376i	−1.86466	+	0.368431i
$743$		−	643.055i		−	0.865484i	−0.901518	−	0.432742i	$-0.857546\pi$
$743$		−	643.055i		−	0.865484i	0.901518	−	0.432742i	$-0.142454\pi$
$744$	76.7815	+	115.870i	0.103201	+	0.155739i
$745$	−932.863			−1.25216
$746$	−82.3297	−	416.678i	−0.110361	−	0.558550i
$747$			64.6754i			0.0865802i
$748$	−52.2675	−	127.102i	−0.0698763	−	0.169922i
$749$	−1024.63			−1.36799
$750$	−84.6141	+	16.7185i	−0.112819	+	0.0222914i
$751$		−	561.060i		−	0.747084i	−0.927613	−	0.373542i	$-0.878143\pi$
$751$		−	561.060i		−	0.747084i	0.927613	−	0.373542i	$-0.121857\pi$
$752$	260.710	+	263.386i	0.346689	+	0.350247i
$753$	−74.9225			−0.0994986
$754$	−75.0263	−	379.715i	−0.0995044	−	0.503601i
$755$		−	319.300i		−	0.422913i
$756$	−282.958	+	116.360i	−0.374283	+	0.153915i
$757$	−1103.14			−1.45725			−0.728625	−	0.684913i	$-0.759840\pi$
$757$	−1103.14			−1.45725			−0.728625	+	0.684913i	$0.759840\pi$
$758$	717.901	−	141.847i	0.947099	−	0.187133i
$759$		−	7.88552i		−	0.0103893i
$760$	588.145	−	389.737i	0.773875	−	0.512811i
$761$	−669.229			−0.879408			−0.439704	−	0.898143i	$-0.644917\pi$
$761$	−669.229			−0.879408			−0.439704	+	0.898143i	$0.644917\pi$
$762$	−19.5449	−	98.9185i	−0.0256495	−	0.129814i
$763$		−	1477.25i		−	1.93611i
$764$	−104.780	−	254.799i	−0.137146	−	0.333506i
$765$	389.179			0.508731
$766$	−546.538	+	107.988i	−0.713495	+	0.140977i
$767$		−	88.9366i		−	0.115954i
$768$	−86.6138	−	0.884457i	−0.112778	−	0.00115164i
$769$	1298.11			1.68805			0.844027	−	0.536301i	$-0.180179\pi$
$769$	1298.11			1.68805			0.844027	+	0.536301i	$0.180179\pi$
$770$	39.6461	+	200.653i	0.0514885	+	0.260588i
$771$			4.43925i			0.00575778i
$772$	−6.22702	+	2.56071i	−0.00806609	+	0.00331698i
$773$	−1339.58			−1.73296			−0.866482	−	0.499208i	$-0.833624\pi$
$773$	−1339.58			−1.73296			−0.866482	+	0.499208i	$0.833624\pi$
$774$	−133.088	+	26.2962i	−0.171948	+	0.0339744i
$775$		−	754.113i		−	0.973049i
$776$	11.8203	+	17.8378i	0.0152324	+	0.0229869i
$777$	204.869			0.263667
$778$	−69.6178	−	352.342i	−0.0894831	−	0.452882i
$779$		−	175.834i		−	0.225717i
$780$	−11.4783	−	27.9123i	−0.0147157	−	0.0357851i
$781$	−283.894			−0.363501
$782$	−247.530	+	48.9085i	−0.316535	+	0.0625428i
$783$		−	168.676i		−	0.215422i
$784$	−1259.35	+	1246.56i	−1.60632	+	1.59000i
$785$	−563.915			−0.718363
$786$	10.4124	+	52.6982i	0.0132474	+	0.0670461i
$787$		−	729.788i		−	0.927304i	−0.886017	−	0.463652i	$-0.846539\pi$
$787$		−	729.788i		−	0.927304i	0.886017	−	0.463652i	$-0.153461\pi$
$788$	178.234	−	73.2945i	0.226186	−	0.0930134i
$789$	57.4184			0.0727736
$790$	436.623	−	86.2705i	0.552687	−	0.109203i
$791$		−	1726.12i		−	2.18219i
$792$	149.282	−	98.9224i	0.188487	−	0.124902i
$793$	133.827			0.168760
$794$	189.880	+	960.999i	0.239143	+	1.21033i
$795$		−	60.6279i		−	0.0762615i
$796$	333.520	+	811.039i	0.418995	+	1.01889i
$797$	290.191			0.364104			0.182052	−	0.983289i	$-0.441726\pi$
$797$	290.191			0.364104			0.182052	+	0.983289i	$0.441726\pi$
$798$	230.416	−	45.5269i	0.288742	−	0.0570512i
$799$		−	315.877i		−	0.395340i
$800$	389.055	+	263.565i	0.486319	+	0.329456i
$801$	1139.11			1.42211
$802$	−225.069	−	1139.09i	−0.280634	−	1.42032i
$803$			184.301i			0.229516i
$804$	59.9177	−	24.6397i	0.0745245	−	0.0306464i
$805$	375.515			0.466478
$806$	699.575	−	138.226i	0.867959	−	0.171496i
$807$			145.583i			0.180401i
$808$	730.765	+	1102.79i	0.904412	+	1.36483i
$809$	267.269			0.330369			0.165185	−	0.986263i	$-0.447178\pi$
$809$	267.269			0.330369			0.165185	+	0.986263i	$0.447178\pi$
$810$	97.0199	+	491.027i	0.119778	+	0.606206i
$811$		−	230.688i		−	0.284448i	−0.989834	−	0.142224i	$-0.954575\pi$
$811$		−	230.688i		−	0.284448i	0.989834	−	0.142224i	$-0.0454254\pi$
$812$	−535.935	−	1303.26i	−0.660019	−	1.60500i
$813$	33.6727			0.0414178
$814$	−236.802	+	46.7887i	−0.290911	+	0.0574799i
$815$			38.6276i			0.0473958i
$816$	51.9376	+	52.4707i	0.0636491	+	0.0643023i
$817$	209.629			0.256584
$818$	42.5573	+	215.386i	0.0520260	+	0.263308i
$819$			779.765i			0.952094i
$820$	−76.0774	+	31.2850i	−0.0927773	+	0.0381524i
$821$	−741.726			−0.903442			−0.451721	−	0.892159i	$-0.649190\pi$
$821$	−741.726			−0.903442			−0.451721	+	0.892159i	$0.649190\pi$
$822$	−101.736	+	20.1017i	−0.123767	+	0.0244546i
$823$			620.679i			0.754166i	0.926179	+	0.377083i	$0.123073\pi$
$823$			620.679i			0.754166i	−0.926179	+	0.377083i	$0.876927\pi$
$824$	1246.17	−	825.779i	1.51234	−	1.00216i
$825$	12.5179			0.0151732
$826$	−62.7632	−	317.651i	−0.0759846	−	0.384565i
$827$			152.037i			0.183841i	0.995766	+	0.0919206i	$0.0293006\pi$
$827$			152.037i			0.183841i	−0.995766	+	0.0919206i	$0.970699\pi$
$828$	−125.047	−	304.084i	−0.151023	−	0.367252i
$829$	−554.184			−0.668498			−0.334249	−	0.942485i	$-0.608483\pi$
$829$	−554.184			−0.668498			−0.334249	+	0.942485i	$0.608483\pi$
$830$	−45.8671	+	9.06268i	−0.0552615	+	0.0109189i
$831$		−	162.699i		−	0.195787i
$832$	−173.191	+	409.228i	−0.208163	+	0.491861i
$833$	1510.33			1.81313
$834$	−7.65343	−	38.7347i	−0.00917677	−	0.0464445i
$835$		−	946.389i		−	1.13340i
$836$	−255.933	+	105.246i	−0.306139	+	0.125892i
$837$	310.763			0.371281
$838$	820.425	−	162.104i	0.979027	−	0.193442i
$839$			24.5679i			0.0292823i	0.999893	+	0.0146412i	$0.00466059\pi$
$839$			24.5679i			0.0292823i	−0.999893	+	0.0146412i	$0.995339\pi$
$840$	−60.6944	−	91.5929i	−0.0722552	−	0.109039i
$841$	−64.1057			−0.0762256
$842$	−9.06858	−	45.8969i	−0.0107703	−	0.0545094i
$843$			37.8463i			0.0448947i
$844$	298.479	+	725.826i	0.353648	+	0.859984i
$845$	387.942			0.459103
$846$	403.811	−	79.7874i	0.477318	−	0.0943113i
$847$			1449.12i			1.71088i
$848$	−634.429	+	627.984i	−0.748147	+	0.740547i
$849$	82.7372			0.0974525
$850$	−77.6399	−	392.943i	−0.0913410	−	0.462285i
$851$			443.167i			0.520760i
$852$	141.051	−	58.0039i	0.165553	−	0.0680797i
$853$	997.329			1.16920			0.584601	−	0.811321i	$-0.301251\pi$
$853$	997.329			1.16920			0.584601	+	0.811321i	$0.301251\pi$
$854$	477.982	−	94.4424i	0.559698	−	0.110588i
$855$		−	783.654i		−	0.916554i
$856$	−540.618	+	358.243i	−0.631563	+	0.418508i
$857$	−238.889			−0.278750			−0.139375	−	0.990240i	$-0.544509\pi$
$857$	−238.889			−0.278750			−0.139375	+	0.990240i	$0.544509\pi$
$858$	2.29448	+	11.6126i	0.00267422	+	0.0135345i
$859$			1589.97i			1.85095i	0.378806	+	0.925476i	$0.376335\pi$
$859$			1589.97i			1.85095i	−0.378806	+	0.925476i	$0.623665\pi$
$860$	−37.2980	−	90.6994i	−0.0433697	−	0.105464i
$861$	−27.3829			−0.0318036
$862$	−991.927	+	195.991i	−1.15073	+	0.227367i
$863$		−	693.887i		−	0.804040i	−0.915631	−	0.402020i	$-0.868308\pi$
$863$		−	693.887i		−	0.804040i	0.915631	−	0.402020i	$-0.131692\pi$
$864$	−108.612	+	160.326i	−0.125709	+	0.185562i
$865$	354.506			0.409834
$866$	185.774	+	940.218i	0.214519	+	1.08570i
$867$			34.8562i			0.0402033i
$868$	2401.09	−	987.390i	2.76623	−	1.13755i
$869$	−174.560			−0.200874
$870$	59.4286	−	11.7422i	0.0683087	−	0.0134968i
$871$		−	332.365i		−	0.381590i
$872$	−516.494	−	779.432i	−0.592309	−	0.893844i
$873$	23.7674			0.0272250
$874$	98.4823	+	498.428i	0.112680	+	0.570284i
$875$			1610.93i			1.84107i
$876$	−37.6556	−	91.5690i	−0.0429858	−	0.104531i
$877$	1156.87			1.31912			0.659561	−	0.751651i	$-0.270742\pi$
$877$	1156.87			1.31912			0.659561	+	0.751651i	$0.270742\pi$
$878$	−45.4334	+	8.97699i	−0.0517464	+	0.0102244i
$879$			10.2127i			0.0116185i
$880$	91.0729	+	92.0077i	0.103492	+	0.104554i
$881$	487.877			0.553776			0.276888	−	0.960902i	$-0.410697\pi$
$881$	487.877			0.553776			0.276888	+	0.960902i	$0.410697\pi$
$882$	381.495	+	1930.78i	0.432534	+	2.18910i
$883$		−	538.939i		−	0.610350i	−0.952296	−	0.305175i	$-0.901285\pi$
$883$		−	538.939i		−	0.610350i	0.952296	−	0.305175i	$-0.0987149\pi$
$884$	350.293	−	144.050i	0.396259	−	0.162952i
$885$	13.9193			0.0157281
$886$	−1511.47	+	298.644i	−1.70594	+	0.337070i
$887$			1569.14i			1.76904i	0.466499	+	0.884522i	$0.345515\pi$
$887$			1569.14i			1.76904i	−0.466499	+	0.884522i	$0.654485\pi$
$888$	108.094	−	71.6289i	0.121728	−	0.0806632i
$889$	−1883.27			−2.11841
$890$	159.618	+	807.844i	0.179347	+	0.907690i
$891$		−	196.310i		−	0.220326i
$892$	−321.431	−	781.641i	−0.360349	−	0.876279i
$893$	−636.052			−0.712264
$894$	−192.828	+	38.1001i	−0.215691	+	0.0426176i
$895$			622.198i			0.695194i
$896$	−329.784	+	1583.84i	−0.368062	+	1.76768i
$897$	21.7326			0.0242281
$898$	261.452	+	1323.23i	0.291149	+	1.47353i
$899$			1431.33i			1.59213i
$900$	482.719	−	198.507i	0.536355	−	0.220563i
$901$	760.866			0.844468
$902$	31.6510	−	6.25379i	0.0350898	−	0.00693325i
$903$		−	32.6459i		−	0.0361527i
$904$	−603.506	−	910.740i	−0.667595	−	1.00746i
$905$	136.616			0.150956
$906$	−13.0409	−	66.0011i	−0.0143939	−	0.0728489i
$907$		−	158.223i		−	0.174447i	−0.996189	−	0.0872234i	$-0.972201\pi$
$907$		−	158.223i		−	0.174447i	0.996189	−	0.0872234i	$-0.0277994\pi$
$908$	199.550	+	485.257i	0.219769	+	0.534424i
$909$	1469.37			1.61647
$910$	−553.001	+	109.265i	−0.607693	+	0.120072i
$911$			491.226i			0.539216i	0.962970	+	0.269608i	$0.0868941\pi$
$911$			491.226i			0.539216i	−0.962970	+	0.269608i	$0.913106\pi$
$912$	105.655	−	104.582i	0.115850	−	0.114673i
$913$	18.3374			0.0200848
$914$	34.7663	+	175.956i	0.0380376	+	0.192512i
$915$			20.9450i			0.0228907i
$916$	−1430.55	+	588.279i	−1.56173	+	0.642226i
$917$	1003.30			1.09411
$918$	161.928	−	31.9946i	0.176392	−	0.0348525i
$919$		−	1475.09i		−	1.60510i	−0.596585	−	0.802550i	$-0.703476\pi$
$919$		−	1475.09i		−	1.60510i	0.596585	−	0.802550i	$-0.296524\pi$
$920$	198.131	−	131.292i	0.215360	−	0.142709i
$921$	52.8929			0.0574298
$922$	−91.7050	−	464.127i	−0.0994631	−	0.503392i
$923$		−	782.415i		−	0.847687i
$924$	16.3902	+	39.8568i	0.0177383	+	0.0431351i
$925$	−703.507			−0.760548
$926$	−123.043	+	24.3116i	−0.132876	+	0.0262544i
$927$		−	1660.41i		−	1.79117i
$928$	−738.435	−	500.253i	−0.795728	−	0.539066i
$929$	398.102			0.428527			0.214264	−	0.976776i	$-0.431265\pi$
$929$	398.102			0.428527			0.214264	+	0.976776i	$0.431265\pi$
$930$	21.6335	+	109.489i	0.0232619	+	0.117730i
$931$		−	3041.22i		−	3.26661i
$932$	154.101	−	63.3703i	0.165344	−	0.0679939i
$933$	61.3342			0.0657387
$934$	225.187	−	44.4937i	0.241099	−	0.0476378i
$935$		−	110.344i		−	0.118015i
$936$	272.631	+	411.423i	0.291273	+	0.439554i
$937$	664.066			0.708715			0.354358	−	0.935110i	$-0.384700\pi$
$937$	664.066			0.708715			0.354358	+	0.935110i	$0.384700\pi$
$938$	−234.552	−	1187.09i	−0.250056	−	1.26556i
$939$		−	59.5541i		−	0.0634229i
$940$	113.169	+	275.198i	0.120392	+	0.292764i
$941$	418.937			0.445204			0.222602	−	0.974909i	$-0.428545\pi$
$941$	418.937			0.445204			0.222602	+	0.974909i	$0.428545\pi$
$942$	−116.565	+	23.0315i	−0.123742	+	0.0244496i
$943$		−	59.2339i		−	0.0628143i
$944$	−144.176	−	145.656i	−0.152729	−	0.154297i
$945$	−245.652			−0.259949
$946$	7.45577	+	37.7343i	0.00788136	+	0.0398883i
$947$		−	24.8290i		−	0.0262186i	−0.999914	−	0.0131093i	$-0.995827\pi$
$947$		−	24.8290i		−	0.0262186i	0.999914	−	0.0131093i	$-0.00417294\pi$
$948$	86.7290	−	35.6652i	0.0914863	−	0.0376215i
$949$	−507.936			−0.535233
$950$	−791.231	+	156.336i	−0.832875	+	0.164564i
$951$			150.305i			0.158049i
$952$	1149.47	−	761.700i	1.20743	−	0.800105i
$953$	−703.766			−0.738474			−0.369237	−	0.929335i	$-0.620381\pi$
$953$	−703.766			−0.738474			−0.369237	+	0.929335i	$0.620381\pi$
$954$	192.187	+	972.677i	0.201454	+	1.01958i
$955$		−	221.205i		−	0.231629i
$956$	93.3956	+	227.115i	0.0976942	+	0.237568i
$957$	−23.7593			−0.0248268
$958$	162.971	−	32.2007i	0.170116	−	0.0336124i
$959$			1936.92i			2.01973i
$960$	−64.0477	−	27.1059i	−0.0667163	−	0.0282353i
$961$	−1676.03			−1.74405
$962$	−128.950	−	652.628i	−0.134044	−	0.678408i
$963$			720.328i			0.748005i
$964$	−723.848	+	297.665i	−0.750880	+	0.308781i
$965$	−5.40603			−0.00560210
$966$	77.6211	−	15.3368i	0.0803531	−	0.0158766i
$967$		−	1241.20i		−	1.28355i	−0.766892	−	0.641776i	$-0.778198\pi$
$967$		−	1241.20i		−	1.28355i	0.766892	−	0.641776i	$-0.221802\pi$
$968$	506.659	+	764.590i	0.523408	+	0.789866i
$969$	−126.712			−0.130765
$970$	3.33042	+	16.8556i	0.00343343	+	0.0173769i
$971$			1118.18i			1.15157i	0.817601	+	0.575786i	$0.195304\pi$
$971$			1118.18i			1.15157i	−0.817601	+	0.575786i	$0.804696\pi$
$972$	122.966	+	299.022i	0.126508	+	0.307636i
$973$	−737.454			−0.757918
$974$	1366.78	−	270.057i	1.40327	−	0.277266i
$975$			34.4994i			0.0353840i
$976$	219.175	−	216.948i	0.224564	−	0.222283i
$977$	598.892			0.612990			0.306495	−	0.951872i	$-0.400844\pi$
$977$	598.892			0.612990			0.306495	+	0.951872i	$0.400844\pi$
$978$	1.57763	+	7.98454i	0.00161312	+	0.00816415i
$979$		−	322.972i		−	0.329900i
$980$	−1315.83	+	541.105i	−1.34269	+	0.552148i
$981$	−1038.53			−1.05864
$982$	1191.56	−	235.435i	1.21340	−	0.239751i
$983$		−	326.764i		−	0.332415i	−0.986091	−	0.166207i	$-0.946848\pi$
$983$		−	326.764i		−	0.332415i	0.986091	−	0.166207i	$-0.0531521\pi$
$984$	−14.4479	+	9.57396i	−0.0146828	+	0.00972963i
$985$	154.735			0.157092
$986$	147.362	+	745.815i	0.149455	+	0.756404i
$987$			99.0534i			0.100358i
$988$	−290.059	−	705.353i	−0.293582	−	0.713920i
$989$	70.6186			0.0714040
$990$	141.062	−	27.8718i	0.142487	−	0.0281533i
$991$			1547.42i			1.56147i	0.624861	+	0.780736i	$0.285156\pi$
$991$			1547.42i			1.56147i	−0.624861	+	0.780736i	$0.714844\pi$
$992$	921.650	−	1360.47i	0.929082	−	1.37144i
$993$	−124.987			−0.125868
$994$	−552.156	−	2794.51i	−0.555489	−	2.81138i
$995$			704.109i			0.707647i
$996$	−9.11085	+	3.74662i	−0.00914744	+	0.00376167i
$997$	−1042.55			−1.04568			−0.522841	−	0.852430i	$-0.675128\pi$
$997$	−1042.55			−1.04568			−0.522841	+	0.852430i	$0.675128\pi$
$998$	815.235	−	161.079i	0.816869	−	0.161402i
$999$		−	289.908i		−	0.290198i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	164.3.c.a.83.19	✓	40
4.3	odd	2	inner	164.3.c.a.83.20	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
164.3.c.a.83.19	✓	40	1.1	even	1	trivial
164.3.c.a.83.20	yes	40	4.3	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:	\( N \)	\(=\)	\( 164 = 2^{2} \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	164.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.387677 - 1.96207i) q^{2} -0.338353i q^{3} +(-3.69941 + 1.52129i) q^{4} -3.21167 q^{5} +(-0.663871 + 0.131171i) q^{6} +12.6392i q^{7} +(4.41906 + 6.66873i) q^{8} +8.88552 q^{9} +O(q^{10})\)	\(q+(-0.387677 - 1.96207i) q^{2} -0.338353i q^{3} +(-3.69941 + 1.52129i) q^{4} -3.21167 q^{5} +(-0.663871 + 0.131171i) q^{6} +12.6392i q^{7} +(4.41906 + 6.66873i) q^{8} +8.88552 q^{9} +(1.24509 + 6.30151i) q^{10} -2.51931i q^{11} +(0.514734 + 1.25171i) q^{12} +6.94325 q^{13} +(24.7989 - 4.89991i) q^{14} +1.08668i q^{15} +(11.3713 - 11.2558i) q^{16} -13.6375 q^{17} +(-3.44471 - 17.4340i) q^{18} +27.4606i q^{19} +(11.8813 - 4.88590i) q^{20} +4.27649 q^{21} +(-4.94306 + 0.976678i) q^{22} +9.25078i q^{23} +(2.25638 - 1.49520i) q^{24} -14.6852 q^{25} +(-2.69174 - 13.6231i) q^{26} -6.05161i q^{27} +(-19.2279 - 46.7575i) q^{28} +27.8728 q^{29} +(2.13213 - 0.421279i) q^{30} +51.3520i q^{31} +(-26.4930 - 17.9477i) q^{32} -0.852416 q^{33} +(5.28696 + 26.7578i) q^{34} -40.5928i q^{35} +(-32.8712 + 13.5175i) q^{36} +47.9059 q^{37} +(53.8796 - 10.6458i) q^{38} -2.34927i q^{39} +(-14.1926 - 21.4177i) q^{40} -6.40312 q^{41} +(-1.65790 - 8.39077i) q^{42} -7.63380i q^{43} +(3.83262 + 9.31998i) q^{44} -28.5373 q^{45} +(18.1506 - 3.58631i) q^{46} +23.1623i q^{47} +(-3.80843 - 3.84752i) q^{48} -110.748 q^{49} +(5.69310 + 28.8133i) q^{50} +4.61430i q^{51} +(-25.6860 + 10.5627i) q^{52} -55.7920 q^{53} +(-11.8737 + 2.34607i) q^{54} +8.09120i q^{55} +(-84.2871 + 55.8532i) q^{56} +9.29138 q^{57} +(-10.8056 - 54.6883i) q^{58} -12.8091i q^{59} +(-1.65316 - 4.02007i) q^{60} +19.2743 q^{61} +(100.756 - 19.9080i) q^{62} +112.305i q^{63} +(-24.9438 + 58.9390i) q^{64} -22.2994 q^{65} +(0.330462 + 1.67250i) q^{66} -47.8688i q^{67} +(50.4509 - 20.7467i) q^{68} +3.13003 q^{69} +(-79.6458 + 15.7369i) q^{70} -112.687i q^{71} +(39.2656 + 59.2551i) q^{72} -73.1553 q^{73} +(-18.5720 - 93.9946i) q^{74} +4.96877i q^{75} +(-41.7757 - 101.588i) q^{76} +31.8420 q^{77} +(-4.60942 + 0.910756i) q^{78} -69.2886i q^{79} +(-36.5209 + 36.1499i) q^{80} +77.9221 q^{81} +(2.48234 + 12.5634i) q^{82} +7.27874i q^{83} +(-15.8205 + 6.50581i) q^{84} +43.7993 q^{85} +(-14.9780 + 2.95945i) q^{86} -9.43085i q^{87} +(16.8006 - 11.1330i) q^{88} +128.198 q^{89} +(11.0633 + 55.9922i) q^{90} +87.7568i q^{91} +(-14.0732 - 34.2225i) q^{92} +17.3751 q^{93} +(45.4460 - 8.97948i) q^{94} -88.1945i q^{95} +(-6.07265 + 8.96399i) q^{96} +2.67485 q^{97} +(42.9345 + 217.296i) q^{98} -22.3854i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q - 2 q^{2} - 2 q^{4} + 12 q^{6} + 10 q^{8} - 120 q^{9}+O(q^{10}) \) 40 * q - 2 * q^2 - 2 * q^4 + 12 * q^6 + 10 * q^8 - 120 * q^9	\( 40 q - 2 q^{2} - 2 q^{4} + 12 q^{6} + 10 q^{8} - 120 q^{9} - 20 q^{10} + 10 q^{12} - 16 q^{13} + 36 q^{14} - 42 q^{16} - 34 q^{18} + 8 q^{20} + 48 q^{21} - 38 q^{22} + 52 q^{24} + 216 q^{25} + 54 q^{26} - 54 q^{28} - 32 q^{29} + 66 q^{30} - 2 q^{32} - 48 q^{33} - 124 q^{34} - 70 q^{36} + 16 q^{37} - 140 q^{38} + 16 q^{40} + 88 q^{42} + 100 q^{44} - 48 q^{45} + 196 q^{46} + 78 q^{48} - 152 q^{49} + 198 q^{50} + 26 q^{52} - 32 q^{53} - 74 q^{54} + 96 q^{56} - 112 q^{57} + 38 q^{58} - 102 q^{60} + 96 q^{61} - 112 q^{62} + 70 q^{64} - 96 q^{65} - 528 q^{66} - 148 q^{68} - 80 q^{69} - 82 q^{70} - 458 q^{72} + 128 q^{73} + 372 q^{74} - 50 q^{76} + 192 q^{77} + 144 q^{78} - 100 q^{80} + 520 q^{81} + 344 q^{84} - 176 q^{85} - 460 q^{86} + 66 q^{88} + 16 q^{89} + 80 q^{90} + 572 q^{92} + 32 q^{93} + 262 q^{94} - 304 q^{96} - 304 q^{97} + 174 q^{98}+O(q^{100}) \) 40 * q - 2 * q^2 - 2 * q^4 + 12 * q^6 + 10 * q^8 - 120 * q^9 - 20 * q^10 + 10 * q^12 - 16 * q^13 + 36 * q^14 - 42 * q^16 - 34 * q^18 + 8 * q^20 + 48 * q^21 - 38 * q^22 + 52 * q^24 + 216 * q^25 + 54 * q^26 - 54 * q^28 - 32 * q^29 + 66 * q^30 - 2 * q^32 - 48 * q^33 - 124 * q^34 - 70 * q^36 + 16 * q^37 - 140 * q^38 + 16 * q^40 + 88 * q^42 + 100 * q^44 - 48 * q^45 + 196 * q^46 + 78 * q^48 - 152 * q^49 + 198 * q^50 + 26 * q^52 - 32 * q^53 - 74 * q^54 + 96 * q^56 - 112 * q^57 + 38 * q^58 - 102 * q^60 + 96 * q^61 - 112 * q^62 + 70 * q^64 - 96 * q^65 - 528 * q^66 - 148 * q^68 - 80 * q^69 - 82 * q^70 - 458 * q^72 + 128 * q^73 + 372 * q^74 - 50 * q^76 + 192 * q^77 + 144 * q^78 - 100 * q^80 + 520 * q^81 + 344 * q^84 - 176 * q^85 - 460 * q^86 + 66 * q^88 + 16 * q^89 + 80 * q^90 + 572 * q^92 + 32 * q^93 + 262 * q^94 - 304 * q^96 - 304 * q^97 + 174 * q^98

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