LMFDB - Embedded newform 668.2.b.b.667.19

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [668,2,Mod(667,668)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(668, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([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("668.667");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 668 = 2^{2} \cdot 167 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	668.b (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:	$5.33400685502$
Analytic rank:	$0$
Dimension:	$60$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			667.19
Character	$\chi$	$=$	668.667
Dual form			668.2.b.b.667.18

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.844041 + 1.13472i) q^{2} -0.873998i q^{3} +(-0.575190 - 1.91550i) q^{4} -2.77771i q^{5} +(0.991745 + 0.737690i) q^{6} +1.63351i q^{7} +(2.65905 + 0.964083i) q^{8} +2.23613 q^{9} +O(q^{10})$	\(q+(-0.844041 + 1.13472i) q^{2} -0.873998i q^{3} +(-0.575190 - 1.91550i) q^{4} -2.77771i q^{5} +(0.991745 + 0.737690i) q^{6} +1.63351i q^{7} +(2.65905 + 0.964083i) q^{8} +2.23613 q^{9} +(3.15193 + 2.34450i) q^{10} -3.15593i q^{11} +(-1.67415 + 0.502715i) q^{12} -2.07866i q^{13} +(-1.85358 - 1.37875i) q^{14} -2.42771 q^{15} +(-3.33831 + 2.20356i) q^{16} -0.279012i q^{17} +(-1.88738 + 2.53738i) q^{18} +2.74636i q^{19} +(-5.32071 + 1.59771i) q^{20} +1.42768 q^{21} +(3.58111 + 2.66374i) q^{22} -0.694696 q^{23} +(0.842606 - 2.32400i) q^{24} -2.71565 q^{25} +(2.35870 + 1.75447i) q^{26} -4.57636i q^{27} +(3.12900 - 0.939579i) q^{28} -4.60310 q^{29} +(2.04909 - 2.75478i) q^{30} +1.16126i q^{31} +(0.317247 - 5.64795i) q^{32} -2.75828 q^{33} +(0.316601 + 0.235498i) q^{34} +4.53741 q^{35} +(-1.28620 - 4.28331i) q^{36} -10.9009i q^{37} +(-3.11636 - 2.31804i) q^{38} -1.81674 q^{39} +(2.67794 - 7.38606i) q^{40} -10.0194i q^{41} +(-1.20502 + 1.62002i) q^{42} -10.3215 q^{43} +(-6.04521 + 1.81526i) q^{44} -6.21131i q^{45} +(0.586352 - 0.788287i) q^{46} +5.71650i q^{47} +(1.92590 + 2.91768i) q^{48} +4.33164 q^{49} +(2.29212 - 3.08151i) q^{50} -0.243856 q^{51} +(-3.98168 + 1.19562i) q^{52} -6.87169i q^{53} +(5.19290 + 3.86264i) q^{54} -8.76626 q^{55} +(-1.57484 + 4.34358i) q^{56} +2.40031 q^{57} +(3.88521 - 5.22325i) q^{58} +10.1359 q^{59} +(1.39639 + 4.65029i) q^{60} -4.53341 q^{61} +(-1.31770 - 0.980147i) q^{62} +3.65274i q^{63} +(6.14109 + 5.12709i) q^{64} -5.77391 q^{65} +(2.32810 - 3.12988i) q^{66} +2.66474 q^{67} +(-0.534449 + 0.160485i) q^{68} +0.607162i q^{69} +(-3.82976 + 5.14870i) q^{70} +4.93203 q^{71} +(5.94598 + 2.15581i) q^{72} +6.69774i q^{73} +(12.3695 + 9.20077i) q^{74} +2.37347i q^{75} +(5.26067 - 1.57968i) q^{76} +5.15525 q^{77} +(1.53341 - 2.06150i) q^{78} -2.61458 q^{79} +(6.12084 + 9.27285i) q^{80} +2.70865 q^{81} +(11.3692 + 8.45674i) q^{82} -1.43717 q^{83} +(-0.821189 - 2.73473i) q^{84} -0.775014 q^{85} +(8.71177 - 11.7120i) q^{86} +4.02310i q^{87} +(3.04258 - 8.39179i) q^{88} +1.88661 q^{89} +(7.04811 + 5.24260i) q^{90} +3.39551 q^{91} +(0.399582 + 1.33069i) q^{92} +1.01493 q^{93} +(-6.48664 - 4.82496i) q^{94} +7.62859 q^{95} +(-4.93630 - 0.277273i) q^{96} -7.93437 q^{97} +(-3.65609 + 4.91521i) q^{98} -7.05707i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 60 q - 2 q^{2} + 2 q^{4} - 8 q^{6} - 8 q^{8} - 16 q^{9}+O(q^{10}) $ 60 * q - 2 * q^2 + 2 * q^4 - 8 * q^6 - 8 * q^8 - 16 * q^9	$ 60 q - 2 q^{2} + 2 q^{4} - 8 q^{6} - 8 q^{8} - 16 q^{9} + 18 q^{12} + 10 q^{14} + 10 q^{16} - 20 q^{18} + 20 q^{22} + 10 q^{24} - 188 q^{25} + 4 q^{29} + 18 q^{32} + 8 q^{33} + 30 q^{36} - 36 q^{38} + 14 q^{42} + 28 q^{44} - 28 q^{48} + 72 q^{49} - 40 q^{50} - 74 q^{54} + 50 q^{56} + 8 q^{57} - 22 q^{58} + 36 q^{61} + 104 q^{62} + 8 q^{64} + 24 q^{65} + 24 q^{66} + 90 q^{72} - 36 q^{76} - 84 q^{81} - 110 q^{84} - 16 q^{85} - 20 q^{88} + 28 q^{89} + 72 q^{93} + 90 q^{94} + 2 q^{96} - 4 q^{97} - 114 q^{98}+O(q^{100}) $ 60 * q - 2 * q^2 + 2 * q^4 - 8 * q^6 - 8 * q^8 - 16 * q^9 + 18 * q^12 + 10 * q^14 + 10 * q^16 - 20 * q^18 + 20 * q^22 + 10 * q^24 - 188 * q^25 + 4 * q^29 + 18 * q^32 + 8 * q^33 + 30 * q^36 - 36 * q^38 + 14 * q^42 + 28 * q^44 - 28 * q^48 + 72 * q^49 - 40 * q^50 - 74 * q^54 + 50 * q^56 + 8 * q^57 - 22 * q^58 + 36 * q^61 + 104 * q^62 + 8 * q^64 + 24 * q^65 + 24 * q^66 + 90 * q^72 - 36 * q^76 - 84 * q^81 - 110 * q^84 - 16 * q^85 - 20 * q^88 + 28 * q^89 + 72 * q^93 + 90 * q^94 + 2 * q^96 - 4 * q^97 - 114 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/668\mathbb{Z}\right)^\times$.

$n$	$5$	$335$
$\chi(n)$	$-1$	$-1$

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 $

$2$	−0.844041	+	1.13472i	−0.596827	+	0.802370i
$2$	−0.844041	+	1.13472i	−0.596827	+	0.802370i
$3$		−	0.873998i		−	0.504603i	−0.967649	−	0.252301i	$-0.918813\pi$
$3$		−	0.873998i		−	0.504603i	0.967649	−	0.252301i	$-0.0811874\pi$
$4$	−0.575190	−	1.91550i	−0.287595	−	0.957752i
$5$		−	2.77771i		−	1.24223i	−0.783720	−	0.621114i	$-0.786680\pi$
$5$		−	2.77771i		−	1.24223i	0.783720	−	0.621114i	$-0.213320\pi$
$6$	0.991745	+	0.737690i	0.404878	+	0.301161i
$7$			1.63351i			0.617409i	0.951158	+	0.308704i	$0.0998954\pi$
$7$			1.63351i			0.617409i	−0.951158	+	0.308704i	$0.900105\pi$
$8$	2.65905	+	0.964083i	0.940116	+	0.340855i
$9$	2.23613			0.745376
$10$	3.15193	+	2.34450i	0.996726	+	0.741395i
$11$		−	3.15593i		−	0.951550i	−0.879567	−	0.475775i	$-0.842168\pi$
$11$		−	3.15593i		−	0.951550i	0.879567	−	0.475775i	$-0.157832\pi$
$12$	−1.67415	+	0.502715i	−0.483284	+	0.145121i
$13$		−	2.07866i		−	0.576517i	−0.957553	−	0.288258i	$-0.906924\pi$
$13$		−	2.07866i		−	0.576517i	0.957553	−	0.288258i	$-0.0930762\pi$
$14$	−1.85358	−	1.37875i	−0.495390	−	0.368486i
$15$	−2.42771			−0.626832
$16$	−3.33831	+	2.20356i	−0.834578	+	0.550889i
$17$		−	0.279012i		−	0.0676704i	−0.999427	−	0.0338352i	$-0.989228\pi$
$17$		−	0.279012i		−	0.0676704i	0.999427	−	0.0338352i	$-0.0107721\pi$
$18$	−1.88738	+	2.53738i	−0.444861	+	0.598067i
$19$			2.74636i			0.630059i	0.949082	+	0.315029i	$0.102014\pi$
$19$			2.74636i			0.630059i	−0.949082	+	0.315029i	$0.897986\pi$
$20$	−5.32071	+	1.59771i	−1.18975	+	0.357259i
$21$	1.42768			0.311546
$22$	3.58111	+	2.66374i	0.763495	+	0.567911i
$23$	−0.694696			−0.144854			−0.0724271	−	0.997374i	$-0.523074\pi$
$23$	−0.694696			−0.144854			−0.0724271	+	0.997374i	$0.523074\pi$
$24$	0.842606	−	2.32400i	0.171996	−	0.474385i
$25$	−2.71565			−0.543130
$26$	2.35870	+	1.75447i	0.462580	+	0.344081i
$27$		−	4.57636i		−	0.880722i
$28$	3.12900	−	0.939579i	0.591325	−	0.177564i
$29$	−4.60310			−0.854775			−0.427388	−	0.904069i	$-0.640566\pi$
$29$	−4.60310			−0.854775			−0.427388	+	0.904069i	$0.640566\pi$
$30$	2.04909	−	2.75478i	0.374110	−	0.502951i
$31$			1.16126i			0.208568i	0.994548	+	0.104284i	$0.0332550\pi$
$31$			1.16126i			0.208568i	−0.994548	+	0.104284i	$0.966745\pi$
$32$	0.317247	−	5.64795i	0.0560818	−	0.998426i
$33$	−2.75828			−0.480155
$34$	0.316601	+	0.235498i	0.0542967	+	0.0403875i
$35$	4.53741			0.766963
$36$	−1.28620	−	4.28331i	−0.214366	−	0.713886i
$37$		−	10.9009i		−	1.79209i	−0.443963	−	0.896045i	$-0.646428\pi$
$37$		−	10.9009i		−	1.79209i	0.443963	−	0.896045i	$-0.353572\pi$
$38$	−3.11636	−	2.31804i	−0.505540	−	0.376036i
$39$	−1.81674			−0.290912
$40$	2.67794	−	7.38606i	0.423419	−	1.16784i
$41$		−	10.0194i		−	1.56476i	−0.622802	−	0.782380i	$-0.714006\pi$
$41$		−	10.0194i		−	1.56476i	0.622802	−	0.782380i	$-0.285994\pi$
$42$	−1.20502	+	1.62002i	−0.185939	+	0.249975i
$43$	−10.3215			−1.57401			−0.787007	−	0.616944i	$-0.788371\pi$
$43$	−10.3215			−1.57401			−0.787007	+	0.616944i	$0.788371\pi$
$44$	−6.04521	+	1.81526i	−0.911349	+	0.273661i
$45$		−	6.21131i		−	0.925927i
$46$	0.586352	−	0.788287i	0.0864528	−	0.116227i
$47$			5.71650i			0.833837i	0.908944	+	0.416918i	$0.136890\pi$
$47$			5.71650i			0.833837i	−0.908944	+	0.416918i	$0.863110\pi$
$48$	1.92590	+	2.91768i	0.277980	+	0.421130i
$49$	4.33164			0.618806
$50$	2.29212	−	3.08151i	0.324155	−	0.435791i
$51$	−0.243856			−0.0341467
$52$	−3.98168	+	1.19562i	−0.552160	+	0.165803i
$53$		−	6.87169i		−	0.943899i	−0.881626	−	0.471949i	$-0.843551\pi$
$53$		−	6.87169i		−	0.943899i	0.881626	−	0.471949i	$-0.156449\pi$
$54$	5.19290	+	3.86264i	0.706664	+	0.525638i
$55$	−8.76626			−1.18204
$56$	−1.57484	+	4.34358i	−0.210447	+	0.580436i
$57$	2.40031			0.317929
$58$	3.88521	−	5.22325i	0.510153	−	0.685846i
$59$	10.1359			1.31959			0.659793	−	0.751448i	$-0.270644\pi$
$59$	10.1359			1.31959			0.659793	+	0.751448i	$0.270644\pi$
$60$	1.39639	+	4.65029i	0.180274	+	0.600349i
$61$	−4.53341			−0.580443			−0.290222	−	0.956959i	$-0.593729\pi$
$61$	−4.53341			−0.580443			−0.290222	+	0.956959i	$0.593729\pi$
$62$	−1.31770	−	0.980147i	−0.167348	−	0.124479i
$63$			3.65274i			0.460202i
$64$	6.14109	+	5.12709i	0.767636	+	0.640886i
$65$	−5.77391			−0.716165
$66$	2.32810	−	3.12988i	0.286569	−	0.385262i
$67$	2.66474			0.325550			0.162775	−	0.986663i	$-0.447956\pi$
$67$	2.66474			0.325550			0.162775	+	0.986663i	$0.447956\pi$
$68$	−0.534449	+	0.160485i	−0.0648114	+	0.0194617i
$69$			0.607162i			0.0730938i
$70$	−3.82976	+	5.14870i	−0.457744	+	0.615388i
$71$	4.93203			0.585324			0.292662	−	0.956216i	$-0.405459\pi$
$71$	4.93203			0.585324			0.292662	+	0.956216i	$0.405459\pi$
$72$	5.94598	+	2.15581i	0.700740	+	0.254065i
$73$			6.69774i			0.783911i	0.919984	+	0.391956i	$0.128201\pi$
$73$			6.69774i			0.783911i	−0.919984	+	0.391956i	$0.871799\pi$
$74$	12.3695	+	9.20077i	1.43792	+	1.06957i
$75$			2.37347i			0.274065i
$76$	5.26067	−	1.57968i	0.603440	−	0.181202i
$77$	5.15525			0.587495
$78$	1.53341	−	2.06150i	0.173624	−	0.233419i
$79$	−2.61458			−0.294163			−0.147082	−	0.989124i	$-0.546988\pi$
$79$	−2.61458			−0.294163			−0.147082	+	0.989124i	$0.546988\pi$
$80$	6.12084	+	9.27285i	0.684330	+	1.03674i
$81$	2.70865			0.300962
$82$	11.3692	+	8.45674i	1.25552	+	0.933891i
$83$	−1.43717			−0.157750			−0.0788752	−	0.996885i	$-0.525133\pi$
$83$	−1.43717			−0.157750			−0.0788752	+	0.996885i	$0.525133\pi$
$84$	−0.821189	−	2.73473i	−0.0895991	−	0.298384i
$85$	−0.775014			−0.0840620
$86$	8.71177	−	11.7120i	0.939415	−	1.26294i
$87$			4.02310i			0.431322i
$88$	3.04258	−	8.39179i	0.324340	−	0.894567i
$89$	1.88661			0.199980			0.0999902	−	0.994988i	$-0.468119\pi$
$89$	1.88661			0.199980			0.0999902	+	0.994988i	$0.468119\pi$
$90$	7.04811	+	5.24260i	0.742936	+	0.552618i
$91$	3.39551			0.355946
$92$	0.399582	+	1.33069i	0.0416593	+	0.138734i
$93$	1.01493			0.105244
$94$	−6.48664	−	4.82496i	−0.669045	−	0.497656i
$95$	7.62859			0.782677
$96$	−4.93630	−	0.277273i	−0.503809	−	0.0282990i
$97$	−7.93437			−0.805614			−0.402807	−	0.915285i	$-0.631965\pi$
$97$	−7.93437			−0.805614			−0.402807	+	0.915285i	$0.631965\pi$
$98$	−3.65609	+	4.91521i	−0.369320	+	0.496512i
$99$		−	7.05707i		−	0.709263i
$100$	1.56202	+	5.20184i	0.156202	+	0.520184i
$101$			3.57853i			0.356077i	0.984024	+	0.178038i	$0.0569751\pi$
$101$			3.57853i			0.356077i	−0.984024	+	0.178038i	$0.943025\pi$
$102$	0.205824	−	0.276709i	0.0203796	−	0.0273983i
$103$	−18.5624			−1.82901			−0.914506	−	0.404573i	$-0.867420\pi$
$103$	−18.5624			−1.82901			−0.914506	+	0.404573i	$0.867420\pi$
$104$	2.00400	−	5.52726i	0.196508	−	0.541993i
$105$		−	3.96569i		−	0.387011i
$106$	7.79746	+	5.79998i	0.757356	+	0.563344i
$107$		−	15.9116i		−	1.53823i	−0.639110	−	0.769115i	$-0.720697\pi$
$107$		−	15.9116i		−	1.53823i	0.639110	−	0.769115i	$-0.279303\pi$
$108$	−8.76604	+	2.63228i	−0.843513	+	0.253291i
$109$			9.84244i			0.942734i	0.881937	+	0.471367i	$0.156239\pi$
$109$			9.84244i			0.942734i	−0.881937	+	0.471367i	$0.843761\pi$
$110$	7.39908	−	9.94727i	0.705475	−	0.948435i
$111$	−9.52732			−0.904294
$112$	−3.59953	−	5.45317i	−0.340124	−	0.515276i
$113$			16.5755i			1.55929i	0.626223	+	0.779644i	$0.284600\pi$
$113$			16.5755i			1.55929i	−0.626223	+	0.779644i	$0.715400\pi$
$114$	−2.02596	+	2.72369i	−0.189749	+	0.255097i
$115$			1.92966i			0.179942i
$116$	2.64766	+	8.81727i	0.245829	+	0.818663i
$117$		−	4.64815i		−	0.429722i
$118$	−8.55514	+	11.5015i	−0.787564	+	1.05880i
$119$	0.455769			0.0417803
$120$	−6.45540	−	2.34051i	−0.589294	−	0.213659i
$121$	1.04008			0.0945527
$122$	3.82638	−	5.14416i	0.346424	−	0.465730i
$123$	−8.75689			−0.789582
$124$	2.22439	−	0.667943i	0.199756	−	0.0599830i
$125$		−	6.34525i		−	0.567536i
$126$	−4.14484	−	3.08306i	−0.369252	−	0.274661i
$127$			8.37380i			0.743054i	0.928422	+	0.371527i	$0.121166\pi$
$127$			8.37380i			0.743054i	−0.928422	+	0.371527i	$0.878834\pi$
$128$	−11.0012	+	2.64096i	−0.972374	+	0.233430i
$129$			9.02097i			0.794252i
$130$	4.87341	−	6.55178i	0.427427	−	0.574629i
$131$	11.9309			1.04240			0.521202	−	0.853433i	$-0.325484\pi$
$131$	11.9309			1.04240			0.521202	+	0.853433i	$0.325484\pi$
$132$	1.58653	+	5.28349i	0.138090	+	0.459869i
$133$	−4.48621			−0.389004
$134$	−2.24915	+	3.02374i	−0.194297	+	0.261211i
$135$	−12.7118			−1.09406
$136$	0.268991	−	0.741907i	0.0230658	−	0.0636180i
$137$	9.54510			0.815493			0.407746	−	0.913095i	$-0.366315\pi$
$137$	9.54510			0.815493			0.407746	+	0.913095i	$0.366315\pi$
$138$	−0.688961	−	0.512470i	−0.0586482	−	0.0436243i
$139$	4.77800			0.405265			0.202632	−	0.979255i	$-0.435050\pi$
$139$	4.77800			0.405265			0.202632	+	0.979255i	$0.435050\pi$
$140$	−2.60987	−	8.69143i	−0.220575	−	0.734560i
$141$	4.99620			0.420756
$142$	−4.16283	+	5.59648i	−0.349337	+	0.469646i
$143$	−6.56012			−0.548584
$144$	−7.46490	+	4.92744i	−0.622075	+	0.410620i
$145$			12.7861i			1.06183i
$146$	−7.60008	−	5.65317i	−0.628987	−	0.467859i
$147$		−	3.78585i		−	0.312251i
$148$	−20.8806	+	6.27006i	−1.71638	+	0.515396i
$149$		−	0.842992i		−	0.0690606i	−0.999404	−	0.0345303i	$-0.989006\pi$
$149$		−	0.842992i		−	0.0690606i	0.999404	−	0.0345303i	$-0.0109935\pi$
$150$	−2.69323	−	2.00331i	−0.219902	−	0.163569i
$151$	6.35135			0.516865			0.258433	−	0.966029i	$-0.416794\pi$
$151$	6.35135			0.516865			0.258433	+	0.966029i	$0.416794\pi$
$152$	−2.64772	+	7.30271i	−0.214759	+	0.592328i
$153$		−	0.623907i		−	0.0504399i
$154$	−4.35124	+	5.84978i	−0.350633	+	0.471389i
$155$	3.22563			0.259089
$156$	1.04497	+	3.47998i	0.0836648	+	0.278621i
$157$	2.38522			0.190362			0.0951808	−	0.995460i	$-0.469657\pi$
$157$	2.38522			0.190362			0.0951808	+	0.995460i	$0.469657\pi$
$158$	2.20681	−	2.96682i	0.175565	−	0.236028i
$159$	−6.00584			−0.476294
$160$	−15.6883	−	0.881218i	−1.24027	−	0.0696664i
$161$		−	1.13479i		−	0.0894342i
$162$	−2.28622	+	3.07357i	−0.179622	+	0.241483i
$163$	−14.5956			−1.14322			−0.571608	−	0.820527i	$-0.693680\pi$
$163$	−14.5956			−1.14322			−0.571608	+	0.820527i	$0.693680\pi$
$164$	−19.1921	+	5.76303i	−1.49865	+	0.450017i
$165$			7.66169i			0.596462i
$166$	1.21303	−	1.63079i	0.0941497	−	0.126574i
$167$	12.9058	+	0.663871i	0.998680	+	0.0513718i
$167$	12.9058	+	0.663871i	0.998680	+	0.0513718i
$168$	3.79628	+	1.37641i	0.292890	+	0.106192i
$169$	8.67917			0.667629
$170$	0.654143	−	0.879425i	0.0501705	−	0.0674488i
$171$			6.14122i			0.469631i
$172$	5.93683	+	19.7709i	0.452679	+	1.50752i
$173$	19.3519			1.47130			0.735648	−	0.677364i	$-0.236878\pi$
$173$	19.3519			1.47130			0.735648	+	0.677364i	$0.236878\pi$
$174$	−4.56510	−	3.39566i	−0.346080	−	0.257425i
$175$		−	4.43604i		−	0.335333i
$176$	6.95428	+	10.5355i	0.524199	+	0.794143i
$177$		−	8.85878i		−	0.665866i
$178$	−1.59238	+	2.14078i	−0.119354	+	0.160458i
$179$		−	1.38802i		−	0.103745i	−0.998654	−	0.0518727i	$-0.983481\pi$
$179$		−	1.38802i		−	0.103745i	0.998654	−	0.0518727i	$-0.0165190\pi$
$180$	−11.8978	+	3.57268i	−0.886809	+	0.266292i
$181$	7.39104			0.549372			0.274686	−	0.961534i	$-0.411426\pi$
$181$	7.39104			0.549372			0.274686	+	0.961534i	$0.411426\pi$
$182$	−2.86595	+	3.85296i	−0.212438	+	0.285601i
$183$			3.96219i			0.292893i
$184$	−1.84723	−	0.669745i	−0.136180	−	0.0493742i
$185$	−30.2794			−2.22618
$186$	−0.856646	+	1.15167i	−0.0628124	+	0.0844445i
$187$	−0.880544			−0.0643917
$188$	10.9500	−	3.28807i	0.798609	−	0.239807i
$189$	7.47554			0.543765
$190$	−6.43884	+	8.65633i	−0.467123	+	0.627996i
$191$		−	16.9379i		−	1.22558i	−0.790244	−	0.612792i	$-0.790046\pi$
$191$		−	16.9379i		−	1.22558i	0.790244	−	0.612792i	$-0.209954\pi$
$192$	4.48106	−	5.36730i	0.323393	−	0.387351i
$193$			6.65820i			0.479268i	0.970863	+	0.239634i	$0.0770274\pi$
$193$			6.65820i			0.479268i	−0.970863	+	0.239634i	$0.922973\pi$
$194$	6.69694	−	9.00331i	0.480812	−	0.646400i
$195$			5.04638i			0.361379i
$196$	−2.49152	−	8.29728i	−0.177966	−	0.592663i
$197$			20.3273i			1.44826i	0.689663	+	0.724131i	$0.257759\pi$
$197$			20.3273i			1.44826i	−0.689663	+	0.724131i	$0.742241\pi$
$198$	8.00782	+	5.95646i	0.569091	+	0.423307i
$199$		−	24.9502i		−	1.76867i	−0.466850	−	0.884336i	$-0.654611\pi$
$199$		−	24.9502i		−	1.76867i	0.466850	−	0.884336i	$-0.345389\pi$
$200$	−7.22105	−	2.61811i	−0.510605	−	0.185129i
$201$		−	2.32898i		−	0.164273i
$202$	−4.06063	−	3.02042i	−0.285705	−	0.212516i
$203$		−	7.51922i		−	0.527746i
$204$	0.140263	+	0.467107i	0.00982041	+	0.0327040i
$205$	−27.8308			−1.94379
$206$	15.6675	−	21.0632i	1.09160	−	1.46754i
$207$	−1.55343			−0.107971
$208$	4.58045	+	6.93922i	0.317597	+	0.481148i
$209$	8.66734			0.599532
$210$	4.49995	+	3.34720i	0.310526	+	0.230979i
$211$			12.8077i			0.881718i	0.897576	+	0.440859i	$0.145326\pi$
$211$			12.8077i			0.881718i	−0.897576	+	0.440859i	$0.854674\pi$
$212$	−13.1627	+	3.95252i	−0.904021	+	0.271461i
$213$		−	4.31058i		−	0.295356i
$214$	18.0552	+	13.4300i	1.23423	+	0.918057i
$215$			28.6701i			1.95529i
$216$	4.41199	−	12.1688i	0.300198	−	0.827980i
$217$	−1.89692			−0.128772
$218$	−11.1684	−	8.30742i	−0.756422	−	0.562649i
$219$	5.85381			0.395564
$220$	5.04226	+	16.7918i	0.339949	+	1.13210i
$221$	−0.579971			−0.0390131
$222$	8.04145	−	10.8109i	0.539707	−	0.725578i
$223$			19.1543i			1.28266i	0.767263	+	0.641332i	$0.221618\pi$
$223$			19.1543i			1.28266i	−0.767263	+	0.641332i	$0.778382\pi$
$224$	9.22599	+	0.518226i	0.616437	+	0.0346254i
$225$	−6.07255			−0.404836
$226$	−18.8085	−	13.9904i	−1.25113	−	0.930625i
$227$	11.0480			0.733283			0.366641	−	0.930362i	$-0.380508\pi$
$227$	11.0480			0.733283			0.366641	+	0.930362i	$0.380508\pi$
$228$	−1.38064	−	4.59781i	−0.0914349	−	0.304498i
$229$	−6.56811			−0.434033			−0.217017	−	0.976168i	$-0.569633\pi$
$229$	−6.56811			−0.434033			−0.217017	+	0.976168i	$0.569633\pi$
$230$	−2.18963	−	1.62871i	−0.144380	−	0.107394i
$231$		−	4.50568i		−	0.296452i
$232$	−12.2399	−	4.43778i	−0.803588	−	0.291354i
$233$	24.5471			1.60813			0.804066	−	0.594541i	$-0.202666\pi$
$233$	24.5471			1.60813			0.804066	+	0.594541i	$0.202666\pi$
$234$	5.27436	+	3.92323i	0.344796	+	0.256470i
$235$	15.8787			1.03582
$236$	−5.83008	−	19.4154i	−0.379506	−	1.26384i
$237$			2.28514i			0.148436i
$238$	−0.384688	+	0.517171i	−0.0249356	+	0.0335232i
$239$			11.0648i			0.715719i	0.933775	+	0.357860i	$0.116493\pi$
$239$			11.0648i			0.715719i	−0.933775	+	0.357860i	$0.883507\pi$
$240$	8.10445	−	5.34959i	0.523140	−	0.345315i
$241$			8.45153i			0.544411i	0.962239	+	0.272205i	$0.0877530\pi$
$241$			8.45153i			0.544411i	−0.962239	+	0.272205i	$0.912247\pi$
$242$	−0.877870	+	1.18020i	−0.0564316	+	0.0758662i
$243$		−	16.0964i		−	1.03259i
$244$	2.60757	+	8.68376i	0.166933	+	0.555921i
$245$		−	12.0320i		−	0.768699i
$246$	7.39117	−	9.93664i	0.471244	−	0.633537i
$247$	5.70876			0.363239
$248$	−1.11955	+	3.08784i	−0.0710913	+	0.196078i
$249$			1.25609i			0.0796012i
$250$	7.20010	+	5.35565i	0.455374	+	0.338721i
$251$			16.9683i			1.07103i	0.844525	+	0.535516i	$0.179883\pi$
$251$			16.9683i			1.07103i	−0.844525	+	0.535516i	$0.820117\pi$
$252$	6.99684	−	2.10102i	0.440759	−	0.132352i
$253$			2.19241i			0.137836i
$254$	−9.50193	−	7.06783i	−0.596204	−	0.443475i
$255$			0.677360i			0.0424179i
$256$	6.28867	−	14.7123i	0.393042	−	0.919521i
$257$		−	16.1976i		−	1.01038i	−0.863009	−	0.505189i	$-0.831423\pi$
$257$		−	16.1976i		−	1.01038i	0.863009	−	0.505189i	$-0.168577\pi$
$258$	−10.2363	−	7.61407i	−0.637284	−	0.474031i
$259$	17.8067			1.10645
$260$	3.32109	+	11.0599i	0.205965	+	0.685909i
$261$	−10.2931			−0.637129
$262$	−10.0701	+	13.5382i	−0.622135	+	0.836394i
$263$		−	11.7622i		−	0.725291i	−0.931927	−	0.362646i	$-0.881874\pi$
$263$		−	11.7622i		−	0.725291i	0.931927	−	0.362646i	$-0.118126\pi$
$264$	−7.33440	−	2.65921i	−0.451401	−	0.163663i
$265$	−19.0875			−1.17254
$266$	3.78655	−	5.09061i	0.232168	−	0.312125i
$267$		−	1.64889i		−	0.100911i
$268$	−1.53273	−	5.10432i	−0.0936265	−	0.311796i
$269$			24.2418i			1.47805i	0.673678	+	0.739025i	$0.264714\pi$
$269$			24.2418i			1.47805i	−0.673678	+	0.739025i	$0.735286\pi$
$270$	10.7293	−	14.4244i	0.652963	−	0.877838i
$271$	−2.28837			−0.139009			−0.0695043	−	0.997582i	$-0.522142\pi$
$271$	−2.28837			−0.139009			−0.0695043	+	0.997582i	$0.522142\pi$
$272$	0.614819	+	0.931430i	0.0372789	+	0.0564762i
$273$		−	2.96767i		−	0.179612i
$274$	−8.05645	+	10.8310i	−0.486708	+	0.654327i
$275$			8.57042i			0.516816i
$276$	1.16302	−	0.349234i	0.0700057	−	0.0210214i
$277$			27.8625i			1.67409i	0.547132	+	0.837046i	$0.315720\pi$
$277$			27.8625i			1.67409i	−0.547132	+	0.837046i	$0.684280\pi$
$278$	−4.03283	+	5.42170i	−0.241873	+	0.325172i
$279$			2.59672i			0.155461i
$280$	12.0652	+	4.37444i	0.721034	+	0.261423i
$281$	6.24618			0.372616			0.186308	−	0.982491i	$-0.440348\pi$
$281$	6.24618			0.372616			0.186308	+	0.982491i	$0.440348\pi$
$282$	−4.21700	+	5.66930i	−0.251119	+	0.337602i
$283$			2.57303i			0.152951i	0.997071	+	0.0764753i	$0.0243666\pi$
$283$			2.57303i			0.152951i	−0.997071	+	0.0764753i	$0.975633\pi$
$284$	−2.83685	−	9.44732i	−0.168336	−	0.560595i
$285$		−	6.66737i		−	0.394941i
$286$	5.53701	−	7.44391i	0.327410	−	0.440168i
$287$	16.3667			0.966096
$288$	0.709404	−	12.6295i	0.0418021	−	0.744203i
$289$	16.9222			0.995421
$290$	−14.5086	−	10.7920i	−0.851977	−	0.633726i
$291$			6.93462i			0.406515i
$292$	12.8295	−	3.85247i	0.750793	−	0.225449i
$293$	−17.2986			−1.01059			−0.505296	−	0.862946i	$-0.668617\pi$
$293$	−17.2986			−1.01059			−0.505296	+	0.862946i	$0.668617\pi$
$294$	4.29588	+	3.19541i	0.250541	+	0.186360i
$295$		−	28.1546i		−	1.63923i
$296$	10.5093	−	28.9859i	0.610843	−	1.68477i
$297$	−14.4427			−0.838051
$298$	0.956562	+	0.711520i	0.0554122	+	0.0412173i
$299$			1.44404i			0.0835108i
$300$	4.54640	−	1.36520i	0.262486	−	0.0788197i
$301$		−	16.8603i		−	0.971811i
$302$	−5.36080	+	7.20701i	−0.308479	+	0.414717i
$303$	3.12762			0.179677
$304$	−6.05177	−	9.16822i	−0.347093	−	0.525833i
$305$			12.5925i			0.721043i
$306$	0.707961	+	0.526603i	0.0404714	+	0.0301039i
$307$	2.60420			0.148629			0.0743147	−	0.997235i	$-0.476323\pi$
$307$	2.60420			0.148629			0.0743147	+	0.997235i	$0.476323\pi$
$308$	−2.96525	−	9.87490i	−0.168961	−	0.562675i
$309$			16.2235i			0.922924i
$310$	−2.72256	+	3.66019i	−0.154631	+	0.207885i
$311$		−	18.4367i		−	1.04545i	−0.852502	−	0.522725i	$-0.824916\pi$
$311$		−	18.4367i		−	1.04545i	0.852502	−	0.522725i	$-0.175084\pi$
$312$	−4.83081	−	1.75149i	−0.273491	−	0.0991587i
$313$		−	6.01499i		−	0.339987i	−0.985445	−	0.169994i	$-0.945625\pi$
$313$		−	6.01499i		−	0.339987i	0.985445	−	0.169994i	$-0.0543747\pi$
$314$	−2.01323	+	2.70657i	−0.113613	+	0.152740i
$315$	10.1462			0.571676
$316$	1.50388	+	5.00824i	0.0845999	+	0.281736i
$317$	8.25897			0.463870			0.231935	−	0.972731i	$-0.425494\pi$
$317$	8.25897			0.463870			0.231935	+	0.972731i	$0.425494\pi$
$318$	5.06917	−	6.81496i	0.284265	−	0.382164i
$319$			14.5271i			0.813361i
$320$	14.2415	−	17.0581i	0.796127	−	0.953579i
$321$	−13.9067			−0.776195
$322$	1.28767	+	0.957812i	0.0717593	+	0.0533767i
$323$	0.766269			0.0426363
$324$	−1.55799	−	5.18844i	−0.0865550	−	0.288247i
$325$			5.64492i			0.313124i
$326$	12.3193	−	16.5620i	0.682302	−	0.917282i
$327$	8.60227			0.475706
$328$	9.65949	−	26.6419i	0.533356	−	1.47106i
$329$	−9.33795			−0.514818
$330$	−8.69389	−	6.46678i	−0.478583	−	0.355984i
$331$	3.79728			0.208717			0.104359	−	0.994540i	$-0.466721\pi$
$331$	3.79728			0.208717			0.104359	+	0.994540i	$0.466721\pi$
$332$	0.826648	+	2.75291i	0.0453682	+	0.151086i
$333$		−	24.3757i		−	1.33578i
$334$	−11.6463	+	14.0841i	−0.637258	+	0.770650i
$335$		−	7.40187i		−	0.404407i
$336$	−4.76606	+	3.14598i	−0.260010	+	0.171627i
$337$	20.7278			1.12911			0.564557	−	0.825394i	$-0.309047\pi$
$337$	20.7278			1.12911			0.564557	+	0.825394i	$0.309047\pi$
$338$	−7.32557	+	9.84845i	−0.398459	+	0.535685i
$339$	14.4869			0.786821
$340$	0.445780	+	1.48454i	0.0241758	+	0.0805106i
$341$	3.66485			0.198463
$342$	−6.96858	−	5.18344i	−0.376818	−	0.280288i
$343$			18.5104i			0.999465i
$344$	−27.4454	−	9.95079i	−1.47976	−	0.536511i
$345$	1.68652			0.0907991
$346$	−16.3338	+	21.9590i	−0.878110	+	1.18052i
$347$	28.3724			1.52311			0.761556	−	0.648099i	$-0.224436\pi$
$347$	28.3724			1.52311			0.761556	+	0.648099i	$0.224436\pi$
$348$	7.70627	−	2.31405i	0.413099	−	0.124046i
$349$		−	10.7870i		−	0.577415i	−0.957417	−	0.288707i	$-0.906775\pi$
$349$		−	10.7870i		−	0.577415i	0.957417	−	0.288707i	$-0.0932254\pi$
$350$	5.03368	+	3.74420i	0.269061	+	0.200136i
$351$	−9.51271			−0.507751
$352$	−17.8246	−	1.00121i	−0.950052	−	0.0533647i
$353$	−7.38629			−0.393132			−0.196566	−	0.980491i	$-0.562979\pi$
$353$	−7.38629			−0.393132			−0.196566	+	0.980491i	$0.562979\pi$
$354$	10.0523	+	7.47717i	0.534271	+	0.397407i
$355$		−	13.6997i		−	0.727106i
$356$	−1.08516	−	3.61381i	−0.0575134	−	0.191532i
$357$		−	0.398341i		−	0.0210824i
$358$	1.57502	+	1.17155i	0.0832422	+	0.0619181i
$359$		−	12.7263i		−	0.671670i	−0.941921	−	0.335835i	$-0.890982\pi$
$359$		−	12.7263i		−	0.671670i	0.941921	−	0.335835i	$-0.109018\pi$
$360$	5.98822	−	16.5162i	0.315607	−	0.870479i
$361$	11.4575			0.603026
$362$	−6.23834	+	8.38678i	−0.327880	+	0.440799i
$363$		−	0.909027i		−	0.0477115i
$364$	−1.95306	−	6.50412i	−0.102368	−	0.340909i
$365$	18.6044			0.973796
$366$	−4.49598	−	3.34425i	−0.235009	−	0.174807i
$367$		−	6.84284i		−	0.357194i	−0.983922	−	0.178597i	$-0.942844\pi$
$367$		−	6.84284i		−	0.357194i	0.983922	−	0.178597i	$-0.0571558\pi$
$368$	2.31911	−	1.53080i	0.120892	−	0.0797986i
$369$		−	22.4046i		−	1.16633i
$370$	25.5570	−	34.3587i	1.32865	−	1.78622i
$371$	11.2250			0.582771
$372$	−0.583780	−	1.94411i	−0.0302676	−	0.100797i
$373$			11.2373i			0.581847i	0.956746	+	0.290923i	$0.0939624\pi$
$373$			11.2373i			0.581847i	−0.956746	+	0.290923i	$0.906038\pi$
$374$	0.743215	−	0.999173i	0.0384307	−	0.0516660i
$375$	−5.54573			−0.286380
$376$	−5.51118	+	15.2004i	−0.284217	+	0.783903i
$377$			9.56829i			0.492792i
$378$	−6.30966	+	8.48266i	−0.324534	+	0.436301i
$379$	21.4840			1.10356			0.551779	−	0.833991i	$-0.313949\pi$
$379$	21.4840			1.10356			0.551779	+	0.833991i	$0.313949\pi$
$380$	−4.38789	−	14.6126i	−0.225094	−	0.749610i
$381$	7.31868			0.374947
$382$	19.2198	+	14.2963i	0.983371	+	0.731461i
$383$		−	14.2491i		−	0.728095i	−0.931380	−	0.364048i	$-0.881395\pi$
$383$		−	14.2491i		−	0.728095i	0.931380	−	0.364048i	$-0.118605\pi$
$384$	2.30819	+	9.61498i	0.117789	+	0.490662i
$385$		−	14.3198i		−	0.729803i
$386$	−7.55521	−	5.61979i	−0.384550	−	0.286040i
$387$	−23.0802			−1.17323
$388$	4.56377	+	15.1983i	0.231690	+	0.771578i
$389$		−	2.86181i		−	0.145099i	−0.997365	−	0.0725497i	$-0.976886\pi$
$389$		−	2.86181i		−	0.145099i	0.997365	−	0.0725497i	$-0.0231136\pi$
$390$	−5.72624	−	4.25935i	−0.289960	−	0.215681i
$391$			0.193829i			0.00980233i
$392$	11.5181	+	4.17606i	0.581750	+	0.210923i
$393$		−	10.4275i		−	0.526000i
$394$	−23.0659	−	17.1571i	−1.16204	−	0.864362i
$395$			7.26254i			0.365418i
$396$	−13.5179	+	4.05916i	−0.679298	+	0.203980i
$397$	5.69569			0.285858			0.142929	−	0.989733i	$-0.454348\pi$
$397$	5.69569			0.285858			0.142929	+	0.989733i	$0.454348\pi$
$398$	28.3115	+	21.0590i	1.41913	+	1.05559i
$399$			3.92094i			0.196292i
$400$	9.06570	−	5.98409i	0.453285	−	0.299205i
$401$		−	8.69202i		−	0.434059i	−0.976165	−	0.217029i	$-0.930363\pi$
$401$		−	8.69202i		−	0.434059i	0.976165	−	0.217029i	$-0.0696367\pi$
$402$	2.64274	+	1.96575i	0.131808	+	0.0980428i
$403$	2.41386			0.120243
$404$	6.85468	−	2.05833i	0.341033	−	0.102406i
$405$		−	7.52385i		−	0.373863i
$406$	8.53223	+	6.34653i	0.423447	+	0.314973i
$407$	−34.4024			−1.70526
$408$	−0.648425	−	0.235097i	−0.0321018	−	0.0116391i
$409$	5.00654			0.247557			0.123779	−	0.992310i	$-0.460499\pi$
$409$	5.00654			0.247557			0.123779	+	0.992310i	$0.460499\pi$
$410$	23.4903	−	31.5802i	1.16011	−	1.55964i
$411$		−	8.34239i		−	0.411500i
$412$	10.6769	+	35.5564i	0.526014	+	1.75174i
$413$			16.5571i			0.814724i
$414$	1.31116	−	1.76271i	0.0644399	−	0.0866325i
$415$			3.99205i			0.195962i
$416$	−11.7402	−	0.659448i	−0.575609	−	0.0323321i
$417$		−	4.17596i		−	0.204498i
$418$	−7.31559	+	9.83503i	−0.357817	+	0.481047i
$419$			23.0549i			1.12631i	0.826352	+	0.563154i	$0.190412\pi$
$419$			23.0549i			1.12631i	−0.826352	+	0.563154i	$0.809588\pi$
$420$	−7.59629	+	2.28102i	−0.370661	+	0.111303i
$421$	26.9243			1.31221			0.656106	−	0.754669i	$-0.272203\pi$
$421$	26.9243			1.31221			0.656106	+	0.754669i	$0.272203\pi$
$422$	−14.5332	−	10.8102i	−0.707464	−	0.526233i
$423$			12.7828i			0.621522i
$424$	6.62488	−	18.2722i	0.321732	−	0.887374i
$425$			0.757700i			0.0367538i
$426$	4.89131	+	3.63831i	0.236985	+	0.176277i
$427$		−	7.40537i		−	0.358371i
$428$	−30.4787	+	9.15218i	−1.47324	+	0.442387i
$429$			5.73352i			0.276817i
$430$	−32.5326	−	24.1987i	−1.56886	−	1.16697i
$431$			6.01325i			0.289648i	0.989457	+	0.144824i	$0.0462616\pi$
$431$			6.01325i			0.289648i	−0.989457	+	0.144824i	$0.953738\pi$
$432$	10.0843	+	15.2773i	0.485180	+	0.735031i
$433$	−9.95207			−0.478266			−0.239133	−	0.970987i	$-0.576863\pi$
$433$	−9.95207			−0.478266			−0.239133	+	0.970987i	$0.576863\pi$
$434$	1.60108	−	2.15248i	0.0768543	−	0.103322i
$435$	11.1750			0.535800
$436$	18.8532	−	5.66127i	0.902906	−	0.271126i
$437$		−	1.90789i		−	0.0912666i
$438$	−4.94085	+	6.64245i	−0.236083	+	0.317388i
$439$	10.4082			0.496754			0.248377	−	0.968663i	$-0.420103\pi$
$439$	10.4082			0.496754			0.248377	+	0.968663i	$0.420103\pi$
$440$	−23.3099	−	8.45140i	−1.11126	−	0.402905i
$441$	9.68611			0.461243
$442$	0.489520	−	0.658107i	0.0232841	−	0.0313029i
$443$	−4.44348			−0.211116			−0.105558	−	0.994413i	$-0.533663\pi$
$443$	−4.44348			−0.211116			−0.105558	+	0.994413i	$0.533663\pi$
$444$	5.48002	+	18.2496i	0.260070	+	0.866089i
$445$		−	5.24045i		−	0.248421i
$446$	−21.7348	−	16.1670i	−1.02917	−	0.765529i
$447$	−0.736773			−0.0348482
$448$	−8.37515	+	10.0315i	−0.395689	+	0.473945i
$449$	15.8641			0.748673			0.374336	−	0.927293i	$-0.377871\pi$
$449$	15.8641			0.748673			0.374336	+	0.927293i	$0.377871\pi$
$450$	5.12548	−	6.89065i	0.241617	−	0.324829i
$451$	−31.6204			−1.48895
$452$	31.7504	−	9.53404i	1.49341	−	0.448443i
$453$		−	5.55106i		−	0.260812i
$454$	−9.32498	+	12.5364i	−0.437643	+	0.588364i
$455$		−	9.43174i		−	0.442167i
$456$	6.38255	+	2.31410i	0.298891	+	0.108368i
$457$			13.3386i			0.623952i	0.950090	+	0.311976i	$0.100991\pi$
$457$			13.3386i			0.623952i	−0.950090	+	0.311976i	$0.899009\pi$
$458$	5.54375	−	7.45298i	0.259043	−	0.348255i
$459$	−1.27686			−0.0595988
$460$	3.69627	−	1.10992i	0.172340	−	0.0517504i
$461$	−24.3222			−1.13280			−0.566399	−	0.824131i	$-0.691664\pi$
$461$	−24.3222			−1.13280			−0.566399	+	0.824131i	$0.691664\pi$
$462$	5.11269	+	3.80298i	0.237864	+	0.176930i
$463$	−3.83061			−0.178024			−0.0890119	−	0.996031i	$-0.528371\pi$
$463$	−3.83061			−0.178024			−0.0890119	+	0.996031i	$0.528371\pi$
$464$	15.3666	−	10.1432i	0.713377	−	0.470887i
$465$		−	2.81919i		−	0.130737i
$466$	−20.7187	+	27.8541i	−0.959776	+	1.29032i
$467$			20.8758i			0.966015i	0.875616	+	0.483008i	$0.160456\pi$
$467$			20.8758i			0.966015i	−0.875616	+	0.483008i	$0.839544\pi$
$468$	−8.90355	+	2.67357i	−0.411567	+	0.123586i
$469$			4.35288i			0.200997i
$470$	−13.4023	+	18.0180i	−0.618203	+	0.831107i
$471$		−	2.08468i		−	0.0960570i
$472$	26.9519	+	9.77188i	1.24056	+	0.449787i
$473$			32.5740i			1.49775i
$474$	−2.59300	−	1.92875i	−0.119100	−	0.0885904i
$475$		−	7.45816i		−	0.342204i
$476$	−0.262154	−	0.873028i	−0.0120158	−	0.0400152i
$477$		−	15.3660i		−	0.703560i
$478$	−12.5554	−	9.33910i	−0.574272	−	0.427161i
$479$	−24.8006			−1.13317			−0.566584	−	0.824004i	$-0.691735\pi$
$479$	−24.8006			−1.13317			−0.566584	+	0.824004i	$0.691735\pi$
$480$	−0.770183	+	13.7116i	−0.0351539	+	0.625845i
$481$	−22.6592			−1.03317
$482$	−9.59014	−	7.13344i	−0.436819	−	0.324919i
$483$	−0.991806			−0.0451287
$484$	−0.598243	−	1.99228i	−0.0271929	−	0.0905580i
$485$			22.0394i			1.00076i
$486$	18.2650	+	13.5861i	0.828517	+	0.616276i
$487$	−26.2545			−1.18971			−0.594853	−	0.803835i	$-0.702790\pi$
$487$	−26.2545			−1.18971			−0.594853	+	0.803835i	$0.702790\pi$
$488$	−12.0546	−	4.37058i	−0.545684	−	0.197847i
$489$			12.7565i			0.576870i
$490$	13.6530	+	10.1555i	0.616781	+	0.458780i
$491$		−	26.8124i		−	1.21002i	−0.796216	−	0.605012i	$-0.793168\pi$
$491$		−	26.8124i		−	1.21002i	0.796216	−	0.605012i	$-0.206832\pi$
$492$	5.03687	+	16.7739i	0.227080	+	0.756224i
$493$			1.28432i			0.0578430i
$494$	−4.81842	+	6.47785i	−0.216791	+	0.291452i
$495$	−19.6025			−0.881066
$496$	−2.55889	−	3.87663i	−0.114898	−	0.174066i
$497$			8.05652i			0.361384i
$498$	−1.42531	−	1.06019i	−0.0638696	−	0.0475082i
$499$	12.7442			0.570511			0.285255	−	0.958452i	$-0.407922\pi$
$499$	12.7442			0.570511			0.285255	+	0.958452i	$0.407922\pi$
$500$	−12.1544	+	3.64972i	−0.543559	+	0.163221i
$501$	0.580221	−	11.2796i	0.0259224	−	0.503936i
$502$	−19.2543	−	14.3220i	−0.859363	−	0.639220i
$503$		−	16.6611i		−	0.742883i	−0.928456	−	0.371441i	$-0.878864\pi$
$503$		−	16.6611i		−	0.742883i	0.928456	−	0.371441i	$-0.121136\pi$
$504$	−3.52154	+	9.71281i	−0.156862	+	0.432643i
$505$	9.94010			0.442328
$506$	−2.48778	−	1.85049i	−0.110595	−	0.0822642i
$507$		−	7.58557i		−	0.336887i
$508$	16.0400	−	4.81652i	0.711662	−	0.213699i
$509$	−41.3013			−1.83065			−0.915324	−	0.402718i	$-0.868066\pi$
$509$	−41.3013			−1.83065			−0.915324	+	0.402718i	$0.868066\pi$
$510$	−0.768616	−	0.571720i	−0.0340349	−	0.0253162i
$511$	−10.9408			−0.483994
$512$	11.3865	+	19.5537i	0.503218	+	0.864160i
$513$	12.5684			0.554906
$514$	18.3798	+	13.6714i	0.810697	+	0.603021i
$515$			51.5610i			2.27205i
$516$	17.2797	−	5.18877i	0.760697	−	0.228423i
$517$	18.0409			0.793437
$518$	−15.0296	+	20.2056i	−0.660361	+	0.887784i
$519$		−	16.9135i		−	0.742420i
$520$	−15.3531	−	5.56653i	−0.673278	−	0.244108i
$521$			5.85970i			0.256718i	0.991728	+	0.128359i	$0.0409710\pi$
$521$			5.85970i			0.256718i	−0.991728	+	0.128359i	$0.959029\pi$
$522$	8.68783	−	11.6798i	0.380256	−	0.511213i
$523$		−	33.1581i		−	1.44990i	−0.688800	−	0.724951i	$-0.741862\pi$
$523$		−	33.1581i		−	1.44990i	0.688800	−	0.724951i	$-0.258138\pi$
$524$	−6.86251	−	22.8536i	−0.299790	−	0.998365i
$525$	−3.87709			−0.169210
$526$	13.3469	+	9.92782i	0.581952	+	0.432873i
$527$	0.324004			0.0141139
$528$	9.20800	−	6.07803i	0.400727	−	0.264512i
$529$	−22.5174			−0.979017
$530$	16.1107	−	21.6590i	0.699802	−	0.940809i
$531$	22.6652			0.983587
$532$	2.58042	+	8.59336i	0.111876	+	0.372569i
$533$	−20.8268			−0.902110
$534$	1.87104	+	1.39173i	0.0809677	+	0.0602262i
$535$	−44.1977			−1.91083
$536$	7.08568	+	2.56903i	0.306055	+	0.110965i
$537$	−1.21313			−0.0523502
$538$	−27.5077	−	20.4611i	−1.18594	−	0.882141i
$539$		−	13.6704i		−	0.588825i
$540$	7.31169	+	24.3495i	0.314645	+	1.04784i
$541$		−	12.3723i		−	0.531927i	−0.963983	−	0.265964i	$-0.914310\pi$
$541$		−	12.3723i		−	0.531927i	0.963983	−	0.265964i	$-0.0856901\pi$
$542$	1.93148	−	2.59667i	0.0829641	−	0.111536i
$543$		−	6.45975i		−	0.277214i
$544$	−1.57585	−	0.0885157i	−0.0675639	−	0.00379508i
$545$	27.3394			1.17109
$546$	3.36748	+	2.50483i	0.144115	+	0.107197i
$547$	−12.7033			−0.543153			−0.271576	−	0.962417i	$-0.587545\pi$
$547$	−12.7033			−0.543153			−0.271576	+	0.962417i	$0.587545\pi$
$548$	−5.49025	−	18.2837i	−0.234532	−	0.781040i
$549$	−10.1373			−0.432649
$550$	−9.72504	−	7.23378i	−0.414677	−	0.308450i
$551$		−	12.6418i		−	0.538559i
$552$	−0.585355	+	1.61448i	−0.0249144	+	0.0687166i
$553$		−	4.27095i		−	0.181619i
$554$	−31.6162	−	23.5171i	−1.34324	−	0.999144i
$555$			26.4641i			1.12334i
$556$	−2.74826	−	9.15228i	−0.116552	−	0.388143i
$557$	−37.9279			−1.60706			−0.803528	−	0.595267i	$-0.797046\pi$
$557$	−37.9279			−1.60706			−0.803528	+	0.595267i	$0.797046\pi$
$558$	−2.94655	−	2.19174i	−0.124738	−	0.0927835i
$559$			21.4549i			0.907446i
$560$	−15.1473	+	9.99845i	−0.640090	+	0.422511i
$561$			0.769593i			0.0324923i
$562$	−5.27203	+	7.08768i	−0.222387	+	0.298976i
$563$			39.5032i			1.66486i	0.554128	+	0.832431i	$0.313052\pi$
$563$			39.5032i			1.66486i	−0.554128	+	0.832431i	$0.686948\pi$
$564$	−2.87377	−	9.57025i	−0.121007	−	0.402980i
$565$	46.0418			1.93699
$566$	−2.91967	−	2.17174i	−0.122723	−	0.0912850i
$567$			4.42462i			0.185816i
$568$	13.1145	+	4.75489i	0.550273	+	0.199511i
$569$			8.46777i			0.354987i	0.984122	+	0.177494i	$0.0567989\pi$
$569$			8.46777i			0.354987i	−0.984122	+	0.177494i	$0.943201\pi$
$570$	7.56561	+	5.62753i	0.316889	+	0.235711i
$571$	41.2116			1.72465			0.862325	−	0.506355i	$-0.169007\pi$
$571$	41.2116			1.72465			0.862325	+	0.506355i	$0.169007\pi$
$572$	3.77331	+	12.5659i	0.157770	+	0.525408i
$573$	−14.8037			−0.618433
$574$	−13.8142	+	18.5717i	−0.576592	+	0.775167i
$575$	1.88655			0.0786747
$576$	13.7323	+	11.4648i	0.572178	+	0.477701i
$577$	12.9428			0.538817			0.269408	−	0.963026i	$-0.413172\pi$
$577$	12.9428			0.538817			0.269408	+	0.963026i	$0.413172\pi$
$578$	−14.2830	+	19.2019i	−0.594094	+	0.798696i
$579$	5.81925			0.241840
$580$	24.4918	−	7.35442i	1.01697	−	0.305376i
$581$		−	2.34764i		−	0.0973964i
$582$	−7.86887	−	5.85311i	−0.326175	−	0.242619i
$583$	−21.6866			−0.898167
$584$	−6.45718	+	17.8096i	−0.267200	+	0.736967i
$585$	−12.9112			−0.533812
$586$	14.6007	−	19.6291i	0.603149	−	0.810869i
$587$	−36.5401			−1.50817			−0.754085	−	0.656776i	$-0.771920\pi$
$587$	−36.5401			−1.50817			−0.754085	+	0.656776i	$0.771920\pi$
$588$	−7.25181	+	2.17758i	−0.299059	+	0.0898019i
$589$	−3.18923			−0.131410
$590$	31.9477	+	23.7637i	1.31527	+	0.978334i
$591$	17.7660			0.730797
$592$	24.0207	+	36.3905i	0.987244	+	1.49564i
$593$			10.4247i			0.428090i	0.976824	+	0.214045i	$0.0686639\pi$
$593$			10.4247i			0.428090i	−0.976824	+	0.214045i	$0.931336\pi$
$594$	12.1902	−	16.3885i	0.500171	−	0.672427i
$595$		−	1.26599i		−	0.0519006i
$596$	−1.61476	+	0.484881i	−0.0661430	+	0.0198615i
$597$	−21.8064			−0.892477
$598$	−1.63858	−	1.21883i	−0.0670066	−	0.0498415i
$599$			10.4964i			0.428872i	0.976738	+	0.214436i	$0.0687913\pi$
$599$			10.4964i			0.428872i	−0.976738	+	0.214436i	$0.931209\pi$
$600$	−2.28822	+	6.31118i	−0.0934164	+	0.257653i
$601$	20.0554			0.818076			0.409038	−	0.912517i	$-0.365864\pi$
$601$	20.0554			0.818076			0.409038	+	0.912517i	$0.365864\pi$
$602$	19.1317	+	14.2308i	0.779752	+	0.580003i
$603$	5.95870			0.242657
$604$	−3.65323	−	12.1660i	−0.148648	−	0.495029i
$605$		−	2.88904i		−	0.117456i
$606$	−2.63984	+	3.54898i	−0.107236	+	0.144168i
$607$	−5.59687			−0.227170			−0.113585	−	0.993528i	$-0.536233\pi$
$607$	−5.59687			−0.227170			−0.113585	+	0.993528i	$0.536233\pi$
$608$	15.5113	+	0.871275i	0.629067	+	0.0353349i
$609$	−6.57178			−0.266302
$610$	−14.2890	−	10.6286i	−0.578543	−	0.430338i
$611$	11.8827			0.480721
$612$	−1.19510	+	0.358865i	−0.0483089	+	0.0145063i
$613$	5.19519			0.209832			0.104916	−	0.994481i	$-0.466543\pi$
$613$	5.19519			0.209832			0.104916	+	0.994481i	$0.466543\pi$
$614$	−2.19805	+	2.95504i	−0.0887060	+	0.119256i
$615$			24.3241i			0.980841i
$616$	13.7081	+	4.97009i	0.552314	+	0.200251i
$617$	−36.0575			−1.45162			−0.725810	−	0.687895i	$-0.758535\pi$
$617$	−36.0575			−1.45162			−0.725810	+	0.687895i	$0.758535\pi$
$618$	−18.4092	−	13.6933i	−0.740526	−	0.550826i
$619$	−0.781264			−0.0314017			−0.0157008	−	0.999877i	$-0.504998\pi$
$619$	−0.781264			−0.0314017			−0.0157008	+	0.999877i	$0.504998\pi$
$620$	−1.85535	−	6.17870i	−0.0745126	−	0.248143i
$621$			3.17918i			0.127576i
$622$	20.9205	+	15.5613i	0.838837	+	0.623952i
$623$			3.08180i			0.123470i
$624$	6.06486	−	4.00330i	0.242789	−	0.160260i
$625$	−31.2035			−1.24814
$626$	6.82534	+	5.07690i	0.272796	+	0.202914i
$627$		−	7.57523i		−	0.302526i
$628$	−1.37196	−	4.56891i	−0.0547470	−	0.182319i
$629$	−3.04147			−0.121271
$630$	−8.56384	+	11.5132i	−0.341191	+	0.458695i
$631$			9.50345i			0.378326i	0.981946	+	0.189163i	$0.0605775\pi$
$631$			9.50345i			0.378326i	−0.981946	+	0.189163i	$0.939422\pi$
$632$	−6.95230	−	2.52067i	−0.276548	−	0.100267i
$633$	11.1939			0.444917
$634$	−6.97091	+	9.37164i	−0.276850	+	0.372195i
$635$	23.2599			0.923043
$636$	3.45450	+	11.5042i	0.136980	+	0.456171i
$637$		−	9.00402i		−	0.356752i
$638$	−16.4842	−	12.2615i	−0.652617	−	0.485436i
$639$	11.0286			0.436287
$640$	7.33580	+	30.5580i	0.289973	+	1.20791i
$641$		−	40.9611i		−	1.61787i	−0.587900	−	0.808934i	$-0.700045\pi$
$641$		−	40.9611i		−	1.61787i	0.587900	−	0.808934i	$-0.299955\pi$
$642$	11.7378	−	15.7802i	0.463254	−	0.622796i
$643$	−25.6117			−1.01003			−0.505013	−	0.863112i	$-0.668512\pi$
$643$	−25.6117			−1.01003			−0.505013	+	0.863112i	$0.668512\pi$
$644$	−2.17370	+	0.652721i	−0.0856558	+	0.0257208i
$645$	25.0576			0.986642
$646$	−0.646762	+	0.869502i	−0.0254465	+	0.0342101i
$647$	−46.8891			−1.84340			−0.921700	−	0.387903i	$-0.873199\pi$
$647$	−46.8891			−1.84340			−0.921700	+	0.387903i	$0.873199\pi$
$648$	7.20245	+	2.61137i	0.282939	+	0.102584i
$649$		−	31.9883i		−	1.25565i
$650$	−6.40541	−	4.76454i	−0.251241	−	0.186881i
$651$			1.65791i			0.0649785i
$652$	8.39524	+	27.9579i	0.328783	+	1.09492i
$653$	49.0760			1.92049			0.960247	−	0.279151i	$-0.0900532\pi$
$653$	49.0760			1.92049			0.960247	+	0.279151i	$0.0900532\pi$
$654$	−7.26066	+	9.76118i	−0.283914	+	0.381692i
$655$		−	33.1404i		−	1.29490i
$656$	22.0782	+	33.4477i	0.862009	+	1.30591i
$657$			14.9770i			0.584309i
$658$	7.88162	−	10.5960i	0.307257	−	0.413075i
$659$	34.5451			1.34569			0.672843	−	0.739785i	$-0.265073\pi$
$659$	34.5451			1.34569			0.672843	+	0.739785i	$0.265073\pi$
$660$	14.6760	−	4.40693i	0.571262	−	0.171539i
$661$		−	33.2526i		−	1.29338i	−0.762754	−	0.646689i	$-0.776153\pi$
$661$		−	33.2526i		−	1.29338i	0.762754	−	0.646689i	$-0.223847\pi$
$662$	−3.20506	+	4.30885i	−0.124568	+	0.167468i
$663$			0.506894i			0.0196861i
$664$	−3.82152	−	1.38555i	−0.148304	−	0.0537700i
$665$			12.4614i			0.483232i
$666$	27.6597	+	20.5741i	1.07179	+	0.797230i
$667$	3.19776			0.123818
$668$	−6.15163	−	25.1029i	−0.238014	−	0.971262i
$669$	16.7408			0.647236
$670$	8.39906	+	6.24748i	0.324484	+	0.241361i
$671$			14.3071i			0.552321i
$672$	0.452928	−	8.06349i	0.0174721	−	0.311056i
$673$			40.0511i			1.54386i	0.635710	+	0.771928i	$0.280707\pi$
$673$			40.0511i			1.54386i	−0.635710	+	0.771928i	$0.719293\pi$
$674$	−17.4951	+	23.5203i	−0.673886	+	0.905967i
$675$			12.4278i			0.478347i
$676$	−4.99217	−	16.6250i	−0.192007	−	0.639423i
$677$	15.5968			0.599434			0.299717	−	0.954028i	$-0.403108\pi$
$677$	15.5968			0.599434			0.299717	+	0.954028i	$0.403108\pi$
$678$	−12.2275	+	16.4386i	−0.469596	+	0.631321i
$679$		−	12.9609i		−	0.497393i
$680$	−2.06080	−	0.747178i	−0.0790281	−	0.0286530i
$681$		−	9.65594i		−	0.370017i
$682$	−3.09328	+	4.15858i	−0.118448	+	0.159240i
$683$	46.4099			1.77583			0.887913	−	0.460012i	$-0.152155\pi$
$683$	46.4099			1.77583			0.887913	+	0.460012i	$0.152155\pi$
$684$	11.7635	−	3.53237i	0.449790	−	0.135063i
$685$		−	26.5135i		−	1.01303i
$686$	−21.0041	−	15.6235i	−0.801941	−	0.596508i
$687$			5.74051i			0.219014i
$688$	34.4564	−	22.7440i	1.31364	−	0.867108i
$689$	−14.2839			−0.544173
$690$	−1.42349	+	1.91373i	−0.0541914	+	0.0728545i
$691$	−29.8372			−1.13506			−0.567531	−	0.823352i	$-0.692101\pi$
$691$	−29.8372			−1.13506			−0.567531	+	0.823352i	$0.692101\pi$
$692$	−11.1310	−	37.0686i	−0.423138	−	1.40914i
$693$	11.5278			0.437905
$694$	−23.9475	+	32.1948i	−0.909034	+	1.22210i
$695$		−	13.2719i		−	0.503431i
$696$	−3.87860	+	10.6976i	−0.147018	+	0.405493i
$697$	−2.79552			−0.105888
$698$	12.2402	+	9.10466i	0.463300	+	0.344617i
$699$		−	21.4541i		−	0.811467i
$700$	−8.49726	+	2.55157i	−0.321166	+	0.0964402i
$701$	−28.6895			−1.08359			−0.541793	−	0.840512i	$-0.682255\pi$
$701$	−28.6895			−1.08359			−0.541793	+	0.840512i	$0.682255\pi$
$702$	8.02911	−	10.7943i	0.303039	−	0.407404i
$703$	29.9377			1.12912
$704$	16.1808	−	19.3809i	0.609835	−	0.730444i
$705$		−	13.8780i		−	0.522675i
$706$	6.23433	−	8.38138i	0.234632	−	0.315438i
$707$	−5.84556			−0.219845
$708$	−16.9690	+	5.09548i	−0.637735	+	0.191500i
$709$			26.1828i			0.983315i	0.870789	+	0.491658i	$0.163609\pi$
$709$			26.1828i			0.983315i	−0.870789	+	0.491658i	$0.836391\pi$
$710$	15.5454	+	11.5631i	0.583408	+	0.433957i
$711$	−5.84654			−0.219262
$712$	5.01659	+	1.81885i	0.188005	+	0.0681643i
$713$		−	0.806719i		−	0.0302119i
$714$	0.452007	+	0.336216i	0.0169159	+	0.0125826i
$715$			18.2221i			0.681467i
$716$	−2.65876	+	0.798375i	−0.0993624	+	0.0298367i
$717$	9.67057			0.361154
$718$	14.4409	+	10.7415i	0.538928	+	0.400871i
$719$	−41.8358			−1.56021			−0.780106	−	0.625647i	$-0.784835\pi$
$719$	−41.8358			−1.56021			−0.780106	+	0.625647i	$0.784835\pi$
$720$	13.6870	+	20.7353i	0.510083	+	0.772759i
$721$		−	30.3219i		−	1.12925i
$722$	−9.67059	+	13.0011i	−0.359902	+	0.483850i
$723$	7.38662			0.274711
$724$	−4.25125	−	14.1576i	−0.157996	−	0.526162i
$725$	12.5004			0.464254
$726$	1.03149	+	0.767256i	0.0382823	+	0.0284755i
$727$	−24.0262			−0.891084			−0.445542	−	0.895261i	$-0.646989\pi$
$727$	−24.0262			−0.891084			−0.445542	+	0.895261i	$0.646989\pi$
$728$	9.02884	+	3.27356i	0.334631	+	0.121326i
$729$	−5.94229			−0.220085
$730$	−15.7028	+	21.1108i	−0.581188	+	0.781345i
$731$			2.87982i			0.106514i
$732$	7.58959	−	2.27901i	0.280519	−	0.0842346i
$733$	1.01312			0.0374203			0.0187101	−	0.999825i	$-0.494044\pi$
$733$	1.01312			0.0374203			0.0187101	+	0.999825i	$0.494044\pi$
$734$	7.76473	+	5.77564i	0.286601	+	0.213183i
$735$	−10.5160			−0.387887
$736$	−0.220390	+	3.92361i	−0.00812368	+	0.144626i
$737$		−	8.40975i		−	0.309777i
$738$	25.4229	+	18.9104i	0.935832	+	0.696100i
$739$	−30.2972			−1.11450			−0.557250	−	0.830345i	$-0.688143\pi$
$739$	−30.2972			−1.11450			−0.557250	+	0.830345i	$0.688143\pi$
$740$	17.4164	+	58.0003i	0.640240	+	2.13213i
$741$		−	4.98944i		−	0.183292i
$742$	−9.47433	+	12.7372i	−0.347814	+	0.467598i
$743$		−	35.4226i		−	1.29953i	−0.760136	−	0.649764i	$-0.774868\pi$
$743$		−	35.4226i		−	1.29953i	0.760136	−	0.649764i	$-0.225132\pi$
$744$	2.69876	+	0.978481i	0.0989414	+	0.0358729i
$745$	−2.34159			−0.0857891
$746$	−12.7512	−	9.48476i	−0.466856	−	0.347262i
$747$	−3.21371			−0.117583
$748$	0.506480	+	1.68669i	0.0185187	+	0.0616713i
$749$	25.9917			0.949717
$750$	4.68082	−	6.29287i	0.170920	−	0.229783i
$751$	52.2429			1.90637			0.953186	−	0.302385i	$-0.0977829\pi$
$751$	52.2429			1.90637			0.953186	+	0.302385i	$0.0977829\pi$
$752$	−12.5966	−	19.0835i	−0.459352	−	0.695902i
$753$	14.8303			0.540445
$754$	−10.8574	−	8.07603i	−0.395402	−	0.294112i
$755$		−	17.6422i		−	0.642064i
$756$	−4.29985	−	14.3194i	−0.156384	−	0.520792i
$757$	−11.2082			−0.407368			−0.203684	−	0.979037i	$-0.565292\pi$
$757$	−11.2082			−0.407368			−0.203684	+	0.979037i	$0.565292\pi$
$758$	−18.1334	+	24.3783i	−0.658633	+	0.885461i
$759$	1.91616			0.0695524
$760$	20.2848	+	7.35459i	0.735807	+	0.266779i
$761$	−18.3854			−0.666472			−0.333236	−	0.942843i	$-0.608141\pi$
$761$	−18.3854			−0.666472			−0.333236	+	0.942843i	$0.608141\pi$
$762$	−6.17726	+	8.30467i	−0.223779	+	0.300846i
$763$	−16.0777			−0.582053
$764$	−32.4446	+	9.74251i	−1.17381	+	0.352472i
$765$	−1.73303			−0.0626578
$766$	16.1688	+	12.0268i	0.584202	+	0.434547i
$767$		−	21.0692i		−	0.760763i
$768$	−12.8585	−	5.49628i	−0.463993	−	0.198330i
$769$		−	15.9829i		−	0.576357i	−0.957577	−	0.288178i	$-0.906950\pi$
$769$		−	15.9829i		−	0.576357i	0.957577	−	0.288178i	$-0.0930496\pi$
$770$	16.2490	+	12.0865i	0.585572	+	0.435566i
$771$	−14.1567			−0.509839
$772$	12.7538	−	3.82973i	0.459020	−	0.137835i
$773$			53.5380i			1.92563i	0.270165	+	0.962814i	$0.412922\pi$
$773$			53.5380i			1.92563i	−0.270165	+	0.962814i	$0.587078\pi$
$774$	19.4806	−	26.1896i	0.700217	−	0.941367i
$775$		−	3.15357i		−	0.113279i
$776$	−21.0979	−	7.64940i	−0.757370	−	0.274597i
$777$		−	15.5630i		−	0.558319i
$778$	3.24736	+	2.41548i	0.116423	+	0.0865992i
$779$	27.5168			0.985891
$780$	9.66637	−	2.90263i	0.346111	−	0.103931i
$781$		−	15.5652i		−	0.556965i
$782$	−0.219942	−	0.163599i	−0.00786510	−	0.00585030i
$783$			21.0655i			0.752819i
$784$	−14.4604	+	9.54503i	−0.516442	+	0.340894i
$785$		−	6.62545i		−	0.236473i
$786$	11.8324	+	8.80127i	0.422047	+	0.313931i
$787$	−34.7572			−1.23896			−0.619480	−	0.785013i	$-0.712656\pi$
$787$	−34.7572			−1.23896			−0.619480	+	0.785013i	$0.712656\pi$
$788$	38.9371	−	11.6921i	1.38708	−	0.416513i
$789$	−10.2802			−0.365984
$790$	−8.24096	−	6.12988i	−0.293200	−	0.218091i
$791$	−27.0762			−0.962718
$792$	6.80361	−	18.7651i	0.241756	−	0.666789i
$793$			9.42342i			0.334635i
$794$	−4.80740	+	6.46303i	−0.170608	+	0.229364i
$795$			16.6825i			0.591666i
$796$	−47.7922	+	14.3511i	−1.69395	+	0.508661i
$797$		−	15.8189i		−	0.560333i	−0.959951	−	0.280167i	$-0.909610\pi$
$797$		−	15.8189i		−	0.560333i	0.959951	−	0.280167i	$-0.0903897\pi$
$798$	−4.44918	−	3.30943i	−0.157499	−	0.117153i
$799$	1.59497			0.0564260
$800$	−0.861532	+	15.3379i	−0.0304597	+	0.542276i
$801$	4.21871			0.149061
$802$	9.86303	+	7.33642i	0.348276	+	0.259058i
$803$	21.1376			0.745931
$804$	−4.46117	+	1.33960i	−0.157333	+	0.0472442i
$805$	−3.15212			−0.111098
$806$	−2.03739	+	2.73906i	−0.0717641	+	0.0964792i
$807$	21.1873			0.745828
$808$	−3.45000	+	9.51548i	−0.121370	+	0.334753i
$809$	22.7398			0.799488			0.399744	−	0.916627i	$-0.369099\pi$
$809$	22.7398			0.799488			0.399744	+	0.916627i	$0.369099\pi$
$810$	8.53748	+	6.35043i	0.299976	+	0.223132i
$811$	22.4207			0.787297			0.393648	−	0.919261i	$-0.371213\pi$
$811$	22.4207			0.787297			0.393648	+	0.919261i	$0.371213\pi$
$812$	−14.4031	+	4.32498i	−0.505450	+	0.151777i
$813$			2.00003i			0.0701441i
$814$	29.0370	−	39.0372i	1.01775	−	1.36825i
$815$			40.5423i			1.42013i
$816$	0.814067	−	0.537351i	0.0284981	−	0.0188110i
$817$		−	28.3466i		−	0.991722i
$818$	−4.22572	+	5.68103i	−0.147749	+	0.198633i
$819$	7.59280			0.265314
$820$	16.0080	+	53.3100i	0.559024	+	1.86167i
$821$		−	17.1972i		−	0.600186i	−0.953910	−	0.300093i	$-0.902982\pi$
$821$		−	17.1972i		−	0.600186i	0.953910	−	0.300093i	$-0.0970177\pi$
$822$	9.46630	+	7.04132i	0.330175	+	0.245594i
$823$	9.06897			0.316124			0.158062	−	0.987429i	$-0.449475\pi$
$823$	9.06897			0.316124			0.158062	+	0.987429i	$0.449475\pi$
$824$	−49.3584	−	17.8957i	−1.71948	−	0.623427i
$825$	7.49052			0.260787
$826$	−18.7878	−	13.9749i	−0.653710	−	0.486249i
$827$	−11.5947			−0.403188			−0.201594	−	0.979469i	$-0.564612\pi$
$827$	−11.5947			−0.403188			−0.201594	+	0.979469i	$0.564612\pi$
$828$	0.893517	+	2.97560i	0.0310519	+	0.103409i
$829$			25.0722i			0.870793i	0.900239	+	0.435397i	$0.143392\pi$
$829$			25.0722i			0.870793i	−0.900239	+	0.435397i	$0.856608\pi$
$830$	−4.52986	−	3.36945i	−0.157234	−	0.116955i
$831$	24.3517			0.844752
$832$	10.6575	−	12.7652i	0.369482	−	0.442555i
$833$		−	1.20858i		−	0.0418749i
$834$	4.73856	+	3.52468i	0.164083	+	0.122050i
$835$	1.84404	−	35.8485i	0.0638155	−	1.24059i
$836$	−4.98537	−	16.6023i	−0.172423	−	0.574204i
$837$	5.31433			0.183690
$838$	−26.1610	−	19.4593i	−0.903715	−	0.672211i
$839$		−	45.4847i		−	1.57031i	−0.619302	−	0.785153i	$-0.712584\pi$
$839$		−	45.4847i		−	1.57031i	0.619302	−	0.785153i	$-0.287416\pi$
$840$	3.82325	−	10.5450i	0.131915	−	0.363836i
$841$	−7.81143			−0.269360
$842$	−22.7252	+	30.5516i	−0.783163	+	1.05288i
$843$		−	5.45914i		−	0.188023i
$844$	24.5332	−	7.36686i	0.844467	−	0.253578i
$845$		−	24.1082i		−	0.829347i
$846$	−14.5050	−	10.7892i	−0.498690	−	0.370941i
$847$			1.69898i			0.0583777i
$848$	15.1422	+	22.9398i	0.519984	+	0.787757i
$849$	2.24882			0.0771792
$850$	−0.859779	−	0.639530i	−0.0294902	−	0.0219357i
$851$			7.57278i			0.259592i
$852$	−8.25694	+	2.47940i	−0.282878	+	0.0849429i
$853$	−44.1922			−1.51311			−0.756556	−	0.653928i	$-0.773120\pi$
$853$	−44.1922			−1.51311			−0.756556	+	0.653928i	$0.773120\pi$
$854$	8.40304	+	6.25043i	0.287546	+	0.213885i
$855$	17.0585			0.583389
$856$	15.3401	−	42.3097i	0.524313	−	1.44611i
$857$	40.3105			1.37698			0.688491	−	0.725245i	$-0.258273\pi$
$857$	40.3105			1.37698			0.688491	+	0.725245i	$0.258273\pi$
$858$	−6.50596	−	4.83933i	−0.222110	−	0.165212i
$859$		−	25.3676i		−	0.865530i	−0.901507	−	0.432765i	$-0.857538\pi$
$859$		−	25.3676i		−	0.865530i	0.901507	−	0.432765i	$-0.142462\pi$
$860$	54.9177	−	16.4908i	1.87268	−	0.562330i
$861$		−	14.3045i		−	0.487495i
$862$	−6.82337	−	5.07543i	−0.232405	−	0.172870i
$863$		−	14.4599i		−	0.492219i	−0.969242	−	0.246110i	$-0.920848\pi$
$863$		−	14.4599i		−	0.492219i	0.969242	−	0.246110i	$-0.0791524\pi$
$864$	−25.8471	−	1.45184i	−0.879335	−	0.0493925i
$865$		−	53.7539i		−	1.82769i
$866$	8.39995	−	11.2928i	0.285442	−	0.383746i
$867$		−	14.7899i		−	0.502292i
$868$	1.09109	+	3.63356i	0.0370340	+	0.123331i
$869$			8.25145i			0.279911i
$870$	−9.43215	+	12.6805i	−0.319780	+	0.429910i
$871$		−	5.53909i		−	0.187685i
$872$	−9.48893	+	26.1715i	−0.321336	+	0.886280i
$873$	−17.7423			−0.600485
$874$	2.16492	+	1.61033i	0.0732296	+	0.0544704i
$875$	10.3650			0.350402
$876$	−3.36705	−	11.2130i	−0.113762	−	0.378852i
$877$	35.2305			1.18965			0.594825	−	0.803855i	$-0.297221\pi$
$877$	35.2305			1.18965			0.594825	+	0.803855i	$0.297221\pi$
$878$	−8.78491	+	11.8104i	−0.296476	+	0.398581i
$879$			15.1189i			0.509948i
$880$	29.2645	−	19.3170i	0.986507	−	0.651174i
$881$			30.1992i			1.01744i	0.860933	+	0.508719i	$0.169881\pi$
$881$			30.1992i			1.01744i	−0.860933	+	0.508719i	$0.830119\pi$
$882$	−8.17548	+	10.9910i	−0.275283	+	0.370088i
$883$			27.6019i			0.928878i	0.885605	+	0.464439i	$0.153744\pi$
$883$			27.6019i			0.928878i	−0.885605	+	0.464439i	$0.846256\pi$
$884$	0.333594	+	1.11094i	0.0112200	+	0.0373649i
$885$	−24.6071			−0.827158
$886$	3.75048	−	5.04211i	0.126000	−	0.169393i
$887$	−22.4487			−0.753753			−0.376877	−	0.926263i	$-0.623002\pi$
$887$	−22.4487			−0.753753			−0.376877	+	0.926263i	$0.623002\pi$
$888$	−25.3336	−	9.18513i	−0.850141	−	0.308233i
$889$	−13.6787			−0.458768
$890$	5.94646	+	4.42316i	0.199326	+	0.148265i
$891$		−	8.54834i		−	0.286380i
$892$	36.6901	−	11.0173i	1.22847	−	0.368888i
$893$	−15.6996			−0.525366
$894$	0.621867	−	0.836033i	0.0207983	−	0.0279611i
$895$	−3.85551			−0.128875
$896$	−4.31403	−	17.9705i	−0.144122	−	0.600352i
$897$	1.26208			0.0421398
$898$	−13.3899	+	18.0013i	−0.446828	+	0.600712i
$899$		−	5.34538i		−	0.178278i
$900$	3.49287	+	11.6320i	0.116429	+	0.387733i
$901$	−1.91728			−0.0638740
$902$	26.6889	−	35.8804i	0.888644	−	1.19469i
$903$	−14.7358			−0.490378
$904$	−15.9801	+	44.0750i	−0.531491	+	1.46591i
$905$		−	20.5301i		−	0.682445i
$906$	6.29891	+	4.68532i	0.209267	+	0.155659i
$907$			38.6856i			1.28453i	0.766481	+	0.642267i	$0.222006\pi$
$907$			38.6856i			1.28453i	−0.766481	+	0.642267i	$0.777994\pi$
$908$	−6.35471	−	21.1625i	−0.210888	−	0.702303i
$909$			8.00204i			0.265411i
$910$	10.7024	+	7.96077i	0.354781	+	0.263897i
$911$			6.47174i			0.214418i	0.994236	+	0.107209i	$0.0341915\pi$
$911$			6.47174i			0.214418i	−0.994236	+	0.107209i	$0.965809\pi$
$912$	−8.01300	+	5.28923i	−0.265337	+	0.175144i
$913$			4.53563i			0.150107i
$914$	−15.1356	−	11.2583i	−0.500640	−	0.372391i
$915$	11.0058			0.363840
$916$	3.77791	+	12.5812i	0.124826	+	0.415696i
$917$			19.4892i			0.643590i
$918$	1.07772	−	1.44888i	0.0355702	−	0.0478203i
$919$			53.4502i			1.76316i	0.472035	+	0.881580i	$0.343520\pi$
$919$			53.4502i			1.76316i	−0.472035	+	0.881580i	$0.656480\pi$
$920$	−1.86035	+	5.13106i	−0.0613340	+	0.169166i
$921$		−	2.27606i		−	0.0749988i
$922$	20.5289	−	27.5990i	0.676085	−	0.908924i
$923$		−	10.2520i		−	0.337449i
$924$	−8.63064	+	2.59162i	−0.283927	+	0.0852580i
$925$			29.6029i			0.973339i
$926$	3.23320	−	4.34668i	0.106249	−	0.142841i
$927$	−41.5080			−1.36330
$928$	−1.46032	+	25.9981i	−0.0479374	+	0.853430i
$929$	−24.2509			−0.795645			−0.397823	−	0.917462i	$-0.630234\pi$
$929$	−24.2509			−0.795645			−0.397823	+	0.917462i	$0.630234\pi$
$930$	3.19900	+	2.37951i	0.104899	+	0.0780273i
$931$			11.8963i			0.389884i
$932$	−14.1192	−	47.0200i	−0.462490	−	1.54019i
$933$	−16.1136			−0.527537
$934$	−23.6882	−	17.6200i	−0.775102	−	0.576544i
$935$			2.44589i			0.0799892i
$936$	4.48120	−	12.3597i	0.146473	−	0.403988i
$937$		−	34.8644i		−	1.13897i	−0.822002	−	0.569485i	$-0.807143\pi$
$937$		−	34.8644i		−	1.13897i	0.822002	−	0.569485i	$-0.192857\pi$
$938$	−4.93931	−	3.67401i	−0.161274	−	0.119961i
$939$	−5.25709			−0.171558
$940$	−9.13329	−	30.4158i	−0.297895	−	0.992054i
$941$			18.6185i			0.606945i	0.952840	+	0.303472i	$0.0981460\pi$
$941$			18.6185i			0.606945i	−0.952840	+	0.303472i	$0.901854\pi$
$942$	2.36553	+	1.75956i	0.0770732	+	0.0573294i
$943$			6.96040i			0.226662i
$944$	−33.8369	+	22.3351i	−1.10130	+	0.726946i
$945$		−	20.7648i		−	0.675480i
$946$	−36.9624	−	27.4938i	−1.20175	−	0.893900i
$947$		−	32.6577i		−	1.06123i	−0.847612	−	0.530616i	$-0.821961\pi$
$947$		−	32.6577i		−	1.06123i	0.847612	−	0.530616i	$-0.178039\pi$
$948$	4.37719	−	1.31439i	0.142165	−	0.0426893i
$949$	13.9223			0.451938
$950$	8.46295	+	6.29500i	0.274574	+	0.204237i
$951$		−	7.21832i		−	0.234070i
$952$	1.21191	+	0.439399i	0.0392783	+	0.0142410i
$953$			47.6779i			1.54444i	0.635355	+	0.772220i	$0.280854\pi$
$953$			47.6779i			1.54444i	−0.635355	+	0.772220i	$0.719146\pi$
$954$	17.4361	+	12.9695i	0.564515	+	0.419903i
$955$	−47.0485			−1.52245
$956$	21.1946	−	6.36433i	0.685482	−	0.205837i
$957$	12.6966			0.410424
$958$	20.9327	−	28.1418i	0.676306	−	0.909220i
$959$			15.5920i			0.503493i
$960$	−14.9088	−	12.4471i	−0.481178	−	0.401728i
$961$	29.6515			0.956500
$962$	19.1253	−	25.7119i	0.616624	−	0.828985i
$963$		−	35.5803i		−	1.14656i
$964$	16.1889	−	4.86123i	0.521411	−	0.156570i
$965$	18.4945			0.595360
$966$	0.837125	−	1.12542i	0.0269341	−	0.0362099i
$967$			41.7636i			1.34303i	0.740993	+	0.671513i	$0.234355\pi$
$967$			41.7636i			1.34303i	−0.740993	+	0.671513i	$0.765645\pi$
$968$	2.76562	+	1.00272i	0.0888905	+	0.0322287i
$969$		−	0.669717i		−	0.0215144i
$970$	−25.0086	−	18.6021i	−0.802976	−	0.597278i
$971$	27.0131			0.866890			0.433445	−	0.901180i	$-0.357298\pi$
$971$	27.0131			0.866890			0.433445	+	0.901180i	$0.357298\pi$
$972$	−30.8328	+	9.25851i	−0.988963	+	0.296967i
$973$			7.80491i			0.250214i
$974$	22.1599	−	29.7916i	0.710049	−	0.954584i
$975$	4.93364			0.158003
$976$	15.1339	−	9.98962i	0.484425	−	0.319760i
$977$		−	31.8169i		−	1.01791i	−0.860792	−	0.508956i	$-0.830031\pi$
$977$		−	31.8169i		−	1.01791i	0.860792	−	0.508956i	$-0.169969\pi$
$978$	−14.4751	−	10.7670i	−0.462863	−	0.344291i
$979$		−	5.95402i		−	0.190291i
$980$	−23.0474	+	6.92071i	−0.736223	+	0.221074i
$981$			22.0090i			0.702692i
$982$	30.4246	+	22.6307i	0.970887	+	0.722175i
$983$	−35.7866			−1.14141			−0.570707	−	0.821154i	$-0.693331\pi$
$983$	−35.7866			−1.14141			−0.570707	+	0.821154i	$0.693331\pi$
$984$	−23.2850	−	8.44237i	−0.742299	−	0.269133i
$985$	56.4633			1.79907
$986$	−1.45735	−	1.08402i	−0.0464114	−	0.0345222i
$987$			8.16135i			0.259779i
$988$	−3.28362	−	10.9351i	−0.104466	−	0.347893i
$989$	7.17031			0.228002
$990$	16.5453	−	22.2434i	0.525844	−	0.706941i
$991$	14.8548			0.471879			0.235939	−	0.971768i	$-0.424183\pi$
$991$	14.8548			0.471879			0.235939	+	0.971768i	$0.424183\pi$
$992$	6.55872	+	0.368405i	0.208239	+	0.0116969i
$993$		−	3.31881i		−	0.105319i
$994$	−9.14191	−	6.80003i	−0.289964	−	0.215684i
$995$	−69.3043			−2.19709
$996$	2.40604	−	0.722488i	0.0762383	−	0.0228929i
$997$	−59.2698			−1.87709			−0.938546	−	0.345153i	$-0.887827\pi$
$997$	−59.2698			−1.87709			−0.938546	+	0.345153i	$0.887827\pi$
$998$	−10.7567	+	14.4612i	−0.340496	+	0.457761i
$999$	−49.8863			−1.57833

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	668.2.b.b.667.19	yes	60
4.3	odd	2	inner	668.2.b.b.667.17	✓	60
167.166	odd	2	inner	668.2.b.b.667.20	yes	60
668.667	even	2	inner	668.2.b.b.667.18	yes	60

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
668.2.b.b.667.17	✓	60	4.3	odd	2	inner
668.2.b.b.667.18	yes	60	668.667	even	2	inner
668.2.b.b.667.19	yes	60	1.1	even	1	trivial
668.2.b.b.667.20	yes	60	167.166	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:	\( N \)	\(=\)	\( 668 = 2^{2} \cdot 167 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	668.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.844041 + 1.13472i) q^{2} -0.873998i q^{3} +(-0.575190 - 1.91550i) q^{4} -2.77771i q^{5} +(0.991745 + 0.737690i) q^{6} +1.63351i q^{7} +(2.65905 + 0.964083i) q^{8} +2.23613 q^{9} +O(q^{10})\)	\(q+(-0.844041 + 1.13472i) q^{2} -0.873998i q^{3} +(-0.575190 - 1.91550i) q^{4} -2.77771i q^{5} +(0.991745 + 0.737690i) q^{6} +1.63351i q^{7} +(2.65905 + 0.964083i) q^{8} +2.23613 q^{9} +(3.15193 + 2.34450i) q^{10} -3.15593i q^{11} +(-1.67415 + 0.502715i) q^{12} -2.07866i q^{13} +(-1.85358 - 1.37875i) q^{14} -2.42771 q^{15} +(-3.33831 + 2.20356i) q^{16} -0.279012i q^{17} +(-1.88738 + 2.53738i) q^{18} +2.74636i q^{19} +(-5.32071 + 1.59771i) q^{20} +1.42768 q^{21} +(3.58111 + 2.66374i) q^{22} -0.694696 q^{23} +(0.842606 - 2.32400i) q^{24} -2.71565 q^{25} +(2.35870 + 1.75447i) q^{26} -4.57636i q^{27} +(3.12900 - 0.939579i) q^{28} -4.60310 q^{29} +(2.04909 - 2.75478i) q^{30} +1.16126i q^{31} +(0.317247 - 5.64795i) q^{32} -2.75828 q^{33} +(0.316601 + 0.235498i) q^{34} +4.53741 q^{35} +(-1.28620 - 4.28331i) q^{36} -10.9009i q^{37} +(-3.11636 - 2.31804i) q^{38} -1.81674 q^{39} +(2.67794 - 7.38606i) q^{40} -10.0194i q^{41} +(-1.20502 + 1.62002i) q^{42} -10.3215 q^{43} +(-6.04521 + 1.81526i) q^{44} -6.21131i q^{45} +(0.586352 - 0.788287i) q^{46} +5.71650i q^{47} +(1.92590 + 2.91768i) q^{48} +4.33164 q^{49} +(2.29212 - 3.08151i) q^{50} -0.243856 q^{51} +(-3.98168 + 1.19562i) q^{52} -6.87169i q^{53} +(5.19290 + 3.86264i) q^{54} -8.76626 q^{55} +(-1.57484 + 4.34358i) q^{56} +2.40031 q^{57} +(3.88521 - 5.22325i) q^{58} +10.1359 q^{59} +(1.39639 + 4.65029i) q^{60} -4.53341 q^{61} +(-1.31770 - 0.980147i) q^{62} +3.65274i q^{63} +(6.14109 + 5.12709i) q^{64} -5.77391 q^{65} +(2.32810 - 3.12988i) q^{66} +2.66474 q^{67} +(-0.534449 + 0.160485i) q^{68} +0.607162i q^{69} +(-3.82976 + 5.14870i) q^{70} +4.93203 q^{71} +(5.94598 + 2.15581i) q^{72} +6.69774i q^{73} +(12.3695 + 9.20077i) q^{74} +2.37347i q^{75} +(5.26067 - 1.57968i) q^{76} +5.15525 q^{77} +(1.53341 - 2.06150i) q^{78} -2.61458 q^{79} +(6.12084 + 9.27285i) q^{80} +2.70865 q^{81} +(11.3692 + 8.45674i) q^{82} -1.43717 q^{83} +(-0.821189 - 2.73473i) q^{84} -0.775014 q^{85} +(8.71177 - 11.7120i) q^{86} +4.02310i q^{87} +(3.04258 - 8.39179i) q^{88} +1.88661 q^{89} +(7.04811 + 5.24260i) q^{90} +3.39551 q^{91} +(0.399582 + 1.33069i) q^{92} +1.01493 q^{93} +(-6.48664 - 4.82496i) q^{94} +7.62859 q^{95} +(-4.93630 - 0.277273i) q^{96} -7.93437 q^{97} +(-3.65609 + 4.91521i) q^{98} -7.05707i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 60 q - 2 q^{2} + 2 q^{4} - 8 q^{6} - 8 q^{8} - 16 q^{9}+O(q^{10}) \) 60 * q - 2 * q^2 + 2 * q^4 - 8 * q^6 - 8 * q^8 - 16 * q^9	\( 60 q - 2 q^{2} + 2 q^{4} - 8 q^{6} - 8 q^{8} - 16 q^{9} + 18 q^{12} + 10 q^{14} + 10 q^{16} - 20 q^{18} + 20 q^{22} + 10 q^{24} - 188 q^{25} + 4 q^{29} + 18 q^{32} + 8 q^{33} + 30 q^{36} - 36 q^{38} + 14 q^{42} + 28 q^{44} - 28 q^{48} + 72 q^{49} - 40 q^{50} - 74 q^{54} + 50 q^{56} + 8 q^{57} - 22 q^{58} + 36 q^{61} + 104 q^{62} + 8 q^{64} + 24 q^{65} + 24 q^{66} + 90 q^{72} - 36 q^{76} - 84 q^{81} - 110 q^{84} - 16 q^{85} - 20 q^{88} + 28 q^{89} + 72 q^{93} + 90 q^{94} + 2 q^{96} - 4 q^{97} - 114 q^{98}+O(q^{100}) \) 60 * q - 2 * q^2 + 2 * q^4 - 8 * q^6 - 8 * q^8 - 16 * q^9 + 18 * q^12 + 10 * q^14 + 10 * q^16 - 20 * q^18 + 20 * q^22 + 10 * q^24 - 188 * q^25 + 4 * q^29 + 18 * q^32 + 8 * q^33 + 30 * q^36 - 36 * q^38 + 14 * q^42 + 28 * q^44 - 28 * q^48 + 72 * q^49 - 40 * q^50 - 74 * q^54 + 50 * q^56 + 8 * q^57 - 22 * q^58 + 36 * q^61 + 104 * q^62 + 8 * q^64 + 24 * q^65 + 24 * q^66 + 90 * q^72 - 36 * q^76 - 84 * q^81 - 110 * q^84 - 16 * q^85 - 20 * q^88 + 28 * q^89 + 72 * q^93 + 90 * q^94 + 2 * q^96 - 4 * q^97 - 114 * q^98

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