LMFDB - Embedded newform 668.2.b.b.667.1

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			667.1
Character	$\chi$	$=$	668.667
Dual form			668.2.b.b.667.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.37801 - 0.317929i) q^{2} +2.42728i q^{3} +(1.79784 + 0.876221i) q^{4} -2.41022i q^{5} +(0.771702 - 3.34482i) q^{6} +1.33262i q^{7} +(-2.19887 - 1.77903i) q^{8} -2.89167 q^{9} +O(q^{10})$	\(q+(-1.37801 - 0.317929i) q^{2} +2.42728i q^{3} +(1.79784 + 0.876221i) q^{4} -2.41022i q^{5} +(0.771702 - 3.34482i) q^{6} +1.33262i q^{7} +(-2.19887 - 1.77903i) q^{8} -2.89167 q^{9} +(-0.766278 + 3.32131i) q^{10} -1.75356i q^{11} +(-2.12683 + 4.36386i) q^{12} -3.38725i q^{13} +(0.423677 - 1.83636i) q^{14} +5.85026 q^{15} +(2.46447 + 3.15062i) q^{16} -7.79385i q^{17} +(3.98476 + 0.919346i) q^{18} -2.81770i q^{19} +(2.11188 - 4.33319i) q^{20} -3.23463 q^{21} +(-0.557509 + 2.41644i) q^{22} -1.74193 q^{23} +(4.31820 - 5.33727i) q^{24} -0.809143 q^{25} +(-1.07691 + 4.66768i) q^{26} +0.262949i q^{27} +(-1.16767 + 2.39583i) q^{28} -4.79436 q^{29} +(-8.06174 - 1.85997i) q^{30} -4.24209i q^{31} +(-2.39440 - 5.12512i) q^{32} +4.25639 q^{33} +(-2.47789 + 10.7400i) q^{34} +3.21189 q^{35} +(-5.19876 - 2.53374i) q^{36} +4.05644i q^{37} +(-0.895828 + 3.88282i) q^{38} +8.22180 q^{39} +(-4.28785 + 5.29976i) q^{40} +1.69380i q^{41} +(4.45736 + 1.02838i) q^{42} -3.20921 q^{43} +(1.53651 - 3.15263i) q^{44} +6.96955i q^{45} +(2.40041 + 0.553812i) q^{46} -8.39180i q^{47} +(-7.64741 + 5.98195i) q^{48} +5.22414 q^{49} +(1.11501 + 0.257250i) q^{50} +18.9178 q^{51} +(2.96798 - 6.08974i) q^{52} -4.10219i q^{53} +(0.0835992 - 0.362347i) q^{54} -4.22647 q^{55} +(2.37076 - 2.93025i) q^{56} +6.83932 q^{57} +(6.60670 + 1.52427i) q^{58} +8.58911 q^{59} +(10.5178 + 5.12612i) q^{60} +6.73113 q^{61} +(-1.34868 + 5.84566i) q^{62} -3.85348i q^{63} +(1.67010 + 7.82373i) q^{64} -8.16401 q^{65} +(-5.86536 - 1.35323i) q^{66} +3.95347 q^{67} +(6.82914 - 14.0121i) q^{68} -4.22815i q^{69} +(-4.42603 - 1.02115i) q^{70} +15.7078 q^{71} +(6.35842 + 5.14437i) q^{72} +4.79094i q^{73} +(1.28966 - 5.58983i) q^{74} -1.96401i q^{75} +(2.46892 - 5.06577i) q^{76} +2.33683 q^{77} +(-11.3297 - 2.61395i) q^{78} -10.8000 q^{79} +(7.59366 - 5.93991i) q^{80} -9.31326 q^{81} +(0.538508 - 2.33408i) q^{82} -8.54578 q^{83} +(-5.81535 - 2.83425i) q^{84} -18.7849 q^{85} +(4.42233 + 1.02030i) q^{86} -11.6372i q^{87} +(-3.11965 + 3.85587i) q^{88} +5.23960 q^{89} +(2.21582 - 9.60413i) q^{90} +4.51390 q^{91} +(-3.13172 - 1.52632i) q^{92} +10.2967 q^{93} +(-2.66800 + 11.5640i) q^{94} -6.79126 q^{95} +(12.4401 - 5.81188i) q^{96} -6.14079 q^{97} +(-7.19893 - 1.66091i) q^{98} +5.07073i 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 $

$2$	−1.37801	−	0.317929i	−0.974403	−	0.224810i
$2$	−1.37801	−	0.317929i	−0.974403	−	0.224810i
$3$			2.42728i			1.40139i	0.713462	+	0.700694i	$0.247126\pi$
$3$			2.42728i			1.40139i	−0.713462	+	0.700694i	$0.752874\pi$
$4$	1.79784	+	0.876221i	0.898921	+	0.438111i
$5$		−	2.41022i		−	1.07788i	−0.842344	−	0.538941i	$-0.818825\pi$
$5$		−	2.41022i		−	1.07788i	0.842344	−	0.538941i	$-0.181175\pi$
$6$	0.771702	−	3.34482i	0.315046	−	1.36552i
$7$			1.33262i			0.503681i	0.967769	+	0.251841i	$0.0810359\pi$
$7$			1.33262i			0.503681i	−0.967769	+	0.251841i	$0.918964\pi$
$8$	−2.19887	−	1.77903i	−0.777419	−	0.628983i
$9$	−2.89167			−0.963890
$10$	−0.766278	+	3.32131i	−0.242318	+	1.05029i
$11$		−	1.75356i		−	0.528720i	−0.964424	−	0.264360i	$-0.914839\pi$
$11$		−	1.75356i		−	0.528720i	0.964424	−	0.264360i	$-0.0851607\pi$
$12$	−2.12683	+	4.36386i	−0.613963	+	1.25974i
$13$		−	3.38725i		−	0.939455i	−0.882812	−	0.469727i	$-0.844352\pi$
$13$		−	3.38725i		−	0.939455i	0.882812	−	0.469727i	$-0.155648\pi$
$14$	0.423677	−	1.83636i	0.113233	−	0.490788i
$15$	5.85026			1.51053
$16$	2.46447	+	3.15062i	0.616118	+	0.787654i
$17$		−	7.79385i		−	1.89029i	−0.326657	−	0.945143i	$-0.605922\pi$
$17$		−	7.79385i		−	1.89029i	0.326657	−	0.945143i	$-0.394078\pi$
$18$	3.98476	+	0.919346i	0.939217	+	0.216692i
$19$		−	2.81770i		−	0.646424i	−0.946327	−	0.323212i	$-0.895237\pi$
$19$		−	2.81770i		−	0.646424i	0.946327	−	0.323212i	$-0.104763\pi$
$20$	2.11188	−	4.33319i	0.472231	−	0.968930i
$21$	−3.23463			−0.705853
$22$	−0.557509	+	2.41644i	−0.118861	+	0.515186i
$23$	−1.74193			−0.363218			−0.181609	−	0.983371i	$-0.558131\pi$
$23$	−1.74193			−0.363218			−0.181609	+	0.983371i	$0.558131\pi$
$24$	4.31820	−	5.33727i	0.881449	−	1.08947i
$25$	−0.809143			−0.161829
$26$	−1.07691	+	4.66768i	−0.211199	+	0.915407i
$27$			0.262949i			0.0506046i
$28$	−1.16767	+	2.39583i	−0.220668	+	0.452770i
$29$	−4.79436			−0.890291			−0.445145	−	0.895458i	$-0.646848\pi$
$29$	−4.79436			−0.890291			−0.445145	+	0.895458i	$0.646848\pi$
$30$	−8.06174	−	1.85997i	−1.47187	−	0.339582i
$31$		−	4.24209i		−	0.761902i	−0.924595	−	0.380951i	$-0.875597\pi$
$31$		−	4.24209i		−	0.761902i	0.924595	−	0.380951i	$-0.124403\pi$
$32$	−2.39440	−	5.12512i	−0.423275	−	0.906001i
$33$	4.25639			0.740942
$34$	−2.47789	+	10.7400i	−0.424955	+	1.84190i
$35$	3.21189			0.542909
$36$	−5.19876	−	2.53374i	−0.866461	−	0.422290i
$37$			4.05644i			0.666875i	0.942772	+	0.333438i	$0.108209\pi$
$37$			4.05644i			0.666875i	−0.942772	+	0.333438i	$0.891791\pi$
$38$	−0.895828	+	3.88282i	−0.145322	+	0.629877i
$39$	8.22180			1.31654
$40$	−4.28785	+	5.29976i	−0.677969	+	0.837966i
$41$			1.69380i			0.264527i	0.991215	+	0.132263i	$0.0422245\pi$
$41$			1.69380i			0.264527i	−0.991215	+	0.132263i	$0.957776\pi$
$42$	4.45736	+	1.02838i	0.687785	+	0.158683i
$43$	−3.20921			−0.489400			−0.244700	−	0.969599i	$-0.578689\pi$
$43$	−3.20921			−0.489400			−0.244700	+	0.969599i	$0.578689\pi$
$44$	1.53651	−	3.15263i	0.231638	−	0.475277i
$45$			6.96955i			1.03896i
$46$	2.40041	+	0.553812i	0.353921	+	0.0816551i
$47$		−	8.39180i		−	1.22407i	−0.790831	−	0.612035i	$-0.790351\pi$
$47$		−	8.39180i		−	1.22407i	0.790831	−	0.612035i	$-0.209649\pi$
$48$	−7.64741	+	5.98195i	−1.10381	+	0.863421i
$49$	5.22414			0.746305
$50$	1.11501	+	0.257250i	0.157686	+	0.0363807i
$51$	18.9178			2.64902
$52$	2.96798	−	6.08974i	0.411585	−	0.844496i
$53$		−	4.10219i		−	0.563479i	−0.959491	−	0.281739i	$-0.909089\pi$
$53$		−	4.10219i		−	0.563479i	0.959491	−	0.281739i	$-0.0909114\pi$
$54$	0.0835992	−	0.362347i	0.0113764	−	0.0493092i
$55$	−4.22647			−0.569897
$56$	2.37076	−	2.93025i	0.316807	−	0.391572i
$57$	6.83932			0.905891
$58$	6.60670	+	1.52427i	0.867502	+	0.200146i
$59$	8.58911			1.11821			0.559103	−	0.829098i	$-0.311146\pi$
$59$	8.58911			1.11821			0.559103	+	0.829098i	$0.311146\pi$
$60$	10.5178	+	5.12612i	1.35785	+	0.661780i
$61$	6.73113			0.861833			0.430916	−	0.902392i	$-0.358190\pi$
$61$	6.73113			0.861833			0.430916	+	0.902392i	$0.358190\pi$
$62$	−1.34868	+	5.84566i	−0.171283	+	0.742399i
$63$		−	3.85348i		−	0.485493i
$64$	1.67010	+	7.82373i	0.208762	+	0.977966i
$65$	−8.16401			−1.01262
$66$	−5.86536	−	1.35323i	−0.721975	−	0.166571i
$67$	3.95347			0.482993			0.241497	−	0.970402i	$-0.422362\pi$
$67$	3.95347			0.482993			0.241497	+	0.970402i	$0.422362\pi$
$68$	6.82914	−	14.0121i	0.828154	−	1.69922i
$69$		−	4.22815i		−	0.509010i
$70$	−4.42603	−	1.02115i	−0.529012	−	0.122051i
$71$	15.7078			1.86418			0.932088	−	0.362232i	$-0.117985\pi$
$71$	15.7078			1.86418			0.932088	+	0.362232i	$0.117985\pi$
$72$	6.35842	+	5.14437i	0.749347	+	0.606270i
$73$			4.79094i			0.560737i	0.959892	+	0.280369i	$0.0904567\pi$
$73$			4.79094i			0.560737i	−0.959892	+	0.280369i	$0.909543\pi$
$74$	1.28966	−	5.58983i	0.149920	−	0.649805i
$75$		−	1.96401i		−	0.226785i
$76$	2.46892	−	5.06577i	0.283205	−	0.581084i
$77$	2.33683			0.266306
$78$	−11.3297	−	2.61395i	−1.28284	−	0.295971i
$79$	−10.8000			−1.21509			−0.607547	−	0.794283i	$-0.707847\pi$
$79$	−10.8000			−1.21509			−0.607547	+	0.794283i	$0.707847\pi$
$80$	7.59366	−	5.93991i	0.848997	−	0.664102i
$81$	−9.31326			−1.03481
$82$	0.538508	−	2.33408i	0.0594682	−	0.257756i
$83$	−8.54578			−0.938022			−0.469011	−	0.883192i	$-0.655389\pi$
$83$	−8.54578			−0.938022			−0.469011	+	0.883192i	$0.655389\pi$
$84$	−5.81535	−	2.83425i	−0.634506	−	0.309242i
$85$	−18.7849			−2.03750
$86$	4.42233	+	1.02030i	0.476873	+	0.110022i
$87$		−	11.6372i		−	1.24764i
$88$	−3.11965	+	3.85587i	−0.332555	+	0.411037i
$89$	5.23960			0.555397			0.277698	−	0.960668i	$-0.410428\pi$
$89$	5.23960			0.555397			0.277698	+	0.960668i	$0.410428\pi$
$90$	2.21582	−	9.60413i	0.233568	−	1.01236i
$91$	4.51390			0.473186
$92$	−3.13172	−	1.52632i	−0.326505	−	0.159130i
$93$	10.2967			1.06772
$94$	−2.66800	+	11.5640i	−0.275183	+	1.19274i
$95$	−6.79126			−0.696768
$96$	12.4401	−	5.81188i	1.26966	−	0.593172i
$97$	−6.14079			−0.623503			−0.311751	−	0.950164i	$-0.600916\pi$
$97$	−6.14079			−0.623503			−0.311751	+	0.950164i	$0.600916\pi$
$98$	−7.19893	−	1.66091i	−0.727202	−	0.167777i
$99$			5.07073i			0.509627i
$100$	−1.45471	−	0.708988i	−0.145471	−	0.0708988i
$101$		−	3.14837i		−	0.313275i	−0.987656	−	0.156637i	$-0.949935\pi$
$101$		−	3.14837i		−	0.313275i	0.987656	−	0.156637i	$-0.0500654\pi$
$102$	−26.0690	−	6.01453i	−2.58122	−	0.595527i
$103$	2.57624			0.253845			0.126922	−	0.991913i	$-0.459490\pi$
$103$	2.57624			0.253845			0.126922	+	0.991913i	$0.459490\pi$
$104$	−6.02603	+	7.44814i	−0.590901	+	0.730350i
$105$			7.79615i			0.760826i
$106$	−1.30421	+	5.65287i	−0.126676	+	0.549055i
$107$			8.85374i			0.855923i	0.903797	+	0.427962i	$0.140768\pi$
$107$			8.85374i			0.855923i	−0.903797	+	0.427962i	$0.859232\pi$
$108$	−0.230402	+	0.472741i	−0.0221704	+	0.0454895i
$109$		−	18.6724i		−	1.78849i	−0.447573	−	0.894247i	$-0.647712\pi$
$109$		−	18.6724i		−	1.78849i	0.447573	−	0.894247i	$-0.352288\pi$
$110$	5.82413	+	1.34372i	0.555309	+	0.128119i
$111$	−9.84611			−0.934551
$112$	−4.19856	+	3.28419i	−0.396727	+	0.310327i
$113$			10.6351i			1.00046i	0.865892	+	0.500232i	$0.166752\pi$
$113$			10.6351i			1.00046i	−0.865892	+	0.500232i	$0.833248\pi$
$114$	−9.42468	−	2.17442i	−0.882702	−	0.203653i
$115$			4.19844i			0.391506i
$116$	−8.61951	−	4.20092i	−0.800301	−	0.390046i
$117$			9.79481i			0.905531i
$118$	−11.8359	−	2.73073i	−1.08958	−	0.251384i
$119$	10.3862			0.952102
$120$	−12.8640	−	10.4078i	−1.17432	−	0.950097i
$121$	7.92501			0.720456
$122$	−9.27558	−	2.14002i	−0.839772	−	0.193748i
$123$	−4.11131			−0.370705
$124$	3.71701	−	7.62661i	0.333797	−	0.684890i
$125$		−	10.1009i		−	0.903450i
$126$	−1.22513	+	5.31015i	−0.109144	+	0.473066i
$127$			5.98940i			0.531473i	0.964046	+	0.265736i	$0.0856151\pi$
$127$			5.98940i			0.531473i	−0.964046	+	0.265736i	$0.914385\pi$
$128$	0.185979	−	11.3122i	0.0164383	−	0.999865i
$129$		−	7.78964i		−	0.685839i
$130$	11.2501	+	2.59558i	0.986700	+	0.227647i
$131$	5.65233			0.493846			0.246923	−	0.969035i	$-0.420580\pi$
$131$	5.65233			0.493846			0.246923	+	0.969035i	$0.420580\pi$
$132$	7.65231	+	3.72954i	0.666048	+	0.324614i
$133$	3.75490			0.325592
$134$	−5.44793	−	1.25692i	−0.470630	−	0.108582i
$135$	0.633764			0.0545457
$136$	−13.8655	+	17.1377i	−1.18896	+	1.46954i
$137$	6.26038			0.534861			0.267430	−	0.963577i	$-0.413825\pi$
$137$	6.26038			0.534861			0.267430	+	0.963577i	$0.413825\pi$
$138$	−1.34425	+	5.82645i	−0.114430	+	0.495981i
$139$	−22.6698			−1.92283			−0.961414	−	0.275106i	$-0.911287\pi$
$139$	−22.6698			−1.92283			−0.961414	+	0.275106i	$0.911287\pi$
$140$	5.77447	+	2.81433i	0.488032	+	0.237854i
$141$	20.3692			1.71540
$142$	−21.6456	−	4.99398i	−1.81646	−	0.419085i
$143$	−5.93977			−0.496708
$144$	−7.12644	−	9.11054i	−0.593870	−	0.759211i
$145$			11.5555i			0.959628i
$146$	1.52318	−	6.60198i	0.126059	−	0.546384i
$147$			12.6804i			1.04586i
$148$	−3.55434	+	7.29284i	−0.292165	+	0.599468i
$149$			7.10237i			0.581849i	0.956746	+	0.290924i	$0.0939628\pi$
$149$			7.10237i			0.581849i	−0.956746	+	0.290924i	$0.906037\pi$
$150$	−0.624417	+	2.70644i	−0.0509834	+	0.220980i
$151$	11.1871			0.910397			0.455198	−	0.890390i	$-0.349568\pi$
$151$	11.1871			0.910397			0.455198	+	0.890390i	$0.349568\pi$
$152$	−5.01277	+	6.19576i	−0.406589	+	0.502542i
$153$			22.5372i			1.82203i
$154$	−3.22018	−	0.742946i	−0.259489	−	0.0598683i
$155$	−10.2244			−0.821240
$156$	14.7815	+	7.20411i	1.18347	+	0.576791i
$157$	−19.3371			−1.54326			−0.771632	−	0.636069i	$-0.780559\pi$
$157$	−19.3371			−1.54326			−0.771632	+	0.636069i	$0.780559\pi$
$158$	14.8825	+	3.43364i	1.18399	+	0.273165i
$159$	9.95714			0.789653
$160$	−12.3526	+	5.77103i	−0.976562	+	0.456240i
$161$		−	2.32133i		−	0.182946i
$162$	12.8338	+	2.96096i	1.00832	+	0.232635i
$163$	−9.60580			−0.752384			−0.376192	−	0.926542i	$-0.622767\pi$
$163$	−9.60580			−0.752384			−0.376192	+	0.926542i	$0.622767\pi$
$164$	−1.48414	+	3.04518i	−0.115892	+	0.237789i
$165$		−	10.2588i		−	0.798647i
$166$	11.7762	+	2.71695i	0.914011	+	0.210877i
$167$	−12.0214	−	4.74181i	−0.930248	−	0.366932i
$167$	−12.0214	−	4.74181i	−0.930248	−	0.366932i
$168$	7.11254	+	5.75450i	0.548744	+	0.443969i
$169$	1.52652			0.117425
$170$	25.8858	+	5.97225i	1.98535	+	0.458051i
$171$			8.14784i			0.623081i
$172$	−5.76965	−	2.81198i	−0.439932	−	0.214411i
$173$	−8.27669			−0.629265			−0.314632	−	0.949214i	$-0.601881\pi$
$173$	−8.27669			−0.629265			−0.314632	+	0.949214i	$0.601881\pi$
$174$	−3.69982	+	16.0363i	−0.280483	+	1.21571i
$175$		−	1.07828i		−	0.0815100i
$176$	5.52481	−	4.32161i	0.416448	−	0.325754i
$177$			20.8481i			1.56704i
$178$	−7.22024	−	1.66582i	−0.541180	−	0.124859i
$179$			20.9456i			1.56555i	0.622307	+	0.782773i	$0.286195\pi$
$179$			20.9456i			1.56555i	−0.622307	+	0.782773i	$0.713805\pi$
$180$	−6.10687	+	12.5301i	−0.455179	+	0.933942i
$181$	6.37568			0.473900			0.236950	−	0.971522i	$-0.423852\pi$
$181$	6.37568			0.473900			0.236950	+	0.971522i	$0.423852\pi$
$182$	−6.22022	−	1.43510i	−0.461074	−	0.106377i
$183$			16.3383i			1.20776i
$184$	3.83029	+	3.09896i	0.282373	+	0.228458i
$185$	9.77690			0.718812
$186$	−14.1890	−	3.27363i	−1.04039	−	0.240034i
$187$	−13.6670			−0.999431
$188$	7.35307	−	15.0871i	0.536278	−	1.10034i
$189$	−0.350410			−0.0254886
$190$	9.35844	+	2.15914i	0.678933	+	0.156640i
$191$		−	10.7219i		−	0.775810i	−0.921699	−	0.387905i	$-0.873199\pi$
$191$		−	10.7219i		−	0.775810i	0.921699	−	0.387905i	$-0.126801\pi$
$192$	−18.9904	+	4.05378i	−1.37051	+	0.292557i
$193$			0.527991i			0.0380056i	0.999819	+	0.0190028i	$0.00604914\pi$
$193$			0.527991i			0.0380056i	−0.999819	+	0.0190028i	$0.993951\pi$
$194$	8.46209	+	1.95234i	0.607543	+	0.140170i
$195$		−	19.8163i		−	1.41908i
$196$	9.39217	+	4.57750i	0.670869	+	0.326964i
$197$		−	17.0565i		−	1.21522i	−0.794235	−	0.607611i	$-0.792128\pi$
$197$		−	17.0565i		−	1.21522i	0.794235	−	0.607611i	$-0.207872\pi$
$198$	1.61213	−	6.98753i	0.114569	−	0.496582i
$199$		−	24.2104i		−	1.71623i	−0.513458	−	0.858115i	$-0.671636\pi$
$199$		−	24.2104i		−	1.71623i	0.513458	−	0.858115i	$-0.328364\pi$
$200$	1.77920	+	1.43949i	0.125809	+	0.101787i
$201$			9.59616i			0.676861i
$202$	−1.00096	+	4.33850i	−0.0704273	+	0.305256i
$203$		−	6.38904i		−	0.448423i
$204$	34.0113	+	16.5762i	2.38126	+	1.16057i
$205$	4.08242			0.285128
$206$	−3.55010	−	0.819062i	−0.247347	−	0.0570668i
$207$	5.03710			0.350102
$208$	10.6719	−	8.34779i	0.739965	−	0.578815i
$209$	−4.94101			−0.341777
$210$	2.47862	−	10.7432i	0.171041	−	0.741351i
$211$			16.8603i			1.16071i	0.814362	+	0.580357i	$0.197087\pi$
$211$			16.8603i			1.16071i	−0.814362	+	0.580357i	$0.802913\pi$
$212$	3.59443	−	7.37509i	0.246866	−	0.506523i
$213$			38.1272i			2.61243i
$214$	2.81486	−	12.2006i	0.192420	−	0.834014i
$215$			7.73489i			0.527515i
$216$	0.467795	−	0.578192i	0.0318294	−	0.0393410i
$217$	5.65307			0.383756
$218$	−5.93651	+	25.7309i	−0.402071	+	1.74271i
$219$	−11.6289			−0.785811
$220$	−7.59853	−	3.70332i	−0.512293	−	0.249678i
$221$	−26.3997			−1.77584
$222$	13.5681	+	3.13036i	0.910629	+	0.210096i
$223$			19.3608i			1.29650i	0.761428	+	0.648249i	$0.224498\pi$
$223$			19.3608i			1.29650i	−0.761428	+	0.648249i	$0.775502\pi$
$224$	6.82981	−	3.19082i	0.456336	−	0.213196i
$225$	2.33977			0.155985
$226$	3.38120	−	14.6553i	0.224914	−	0.974854i
$227$	−21.5014			−1.42710			−0.713549	−	0.700605i	$-0.752913\pi$
$227$	−21.5014			−1.42710			−0.713549	+	0.700605i	$0.752913\pi$
$228$	12.2960	+	5.99276i	0.814324	+	0.396880i
$229$	7.83862			0.517991			0.258995	−	0.965879i	$-0.416609\pi$
$229$	7.83862			0.517991			0.258995	+	0.965879i	$0.416609\pi$
$230$	1.33481	−	5.78550i	0.0880145	−	0.381485i
$231$			5.67213i			0.373198i
$232$	10.5422	+	8.52932i	0.692129	+	0.559977i
$233$	0.796677			0.0521920			0.0260960	−	0.999659i	$-0.491692\pi$
$233$	0.796677			0.0521920			0.0260960	+	0.999659i	$0.491692\pi$
$234$	3.11406	−	13.4974i	0.203572	−	0.882352i
$235$	−20.2260			−1.31940
$236$	15.4419	+	7.52596i	1.00518	+	0.489898i
$237$		−	26.2146i		−	1.70282i
$238$	−14.3123	−	3.30208i	−0.927730	−	0.214042i
$239$			14.4068i			0.931898i	0.884812	+	0.465949i	$0.154287\pi$
$239$			14.4068i			0.931898i	−0.884812	+	0.465949i	$0.845713\pi$
$240$	14.4178	+	18.4319i	0.930665	+	1.18978i
$241$		−	10.4474i		−	0.672976i	−0.941688	−	0.336488i	$-0.890761\pi$
$241$		−	10.4474i		−	0.672976i	0.941688	−	0.336488i	$-0.109239\pi$
$242$	−10.9208	−	2.51959i	−0.702014	−	0.161966i
$243$		−	21.8170i		−	1.39956i
$244$	12.1015	+	5.89796i	0.774719	+	0.377578i
$245$		−	12.5913i		−	0.804428i
$246$	5.66545	+	1.30711i	0.361216	+	0.0833381i
$247$	−9.54425			−0.607286
$248$	−7.54681	+	9.32782i	−0.479223	+	0.592317i
$249$		−	20.7430i		−	1.31453i
$250$	−3.21136	+	13.9191i	−0.203104	+	0.880324i
$251$			12.2603i			0.773864i	0.922108	+	0.386932i	$0.126465\pi$
$251$			12.2603i			0.773864i	−0.922108	+	0.386932i	$0.873535\pi$
$252$	3.37650	−	6.92795i	0.212700	−	0.436420i
$253$			3.05459i			0.192041i
$254$	1.90420	−	8.25347i	0.119480	−	0.517869i
$255$		−	45.5960i		−	2.85533i
$256$	−3.85275	+	15.5292i	−0.240797	+	0.970575i
$257$		−	15.2461i		−	0.951025i	−0.879709	−	0.475512i	$-0.842263\pi$
$257$		−	15.2461i		−	0.951025i	0.879709	−	0.475512i	$-0.157737\pi$
$258$	−2.47655	+	10.7342i	−0.154183	+	0.668284i
$259$	−5.40568			−0.335892
$260$	−14.6776	−	7.15348i	−0.910266	−	0.443640i
$261$	13.8637			0.858142
$262$	−7.78899	−	1.79704i	−0.481205	−	0.111022i
$263$			13.8114i			0.851650i	0.904806	+	0.425825i	$0.140016\pi$
$263$			13.8114i			0.851650i	−0.904806	+	0.425825i	$0.859984\pi$
$264$	−9.35926	−	7.57224i	−0.576022	−	0.466039i
$265$	−9.88716			−0.607363
$266$	−5.17431	−	1.19379i	−0.317257	−	0.0731962i
$267$			12.7180i			0.778327i
$268$	7.10771	+	3.46411i	0.434173	+	0.211604i
$269$		−	9.61889i		−	0.586474i	−0.956040	−	0.293237i	$-0.905267\pi$
$269$		−	9.61889i		−	0.586474i	0.956040	−	0.293237i	$-0.0947325\pi$
$270$	−0.873336	−	0.201492i	−0.0531495	−	0.0122624i
$271$	21.4750			1.30451			0.652256	−	0.757999i	$-0.273823\pi$
$271$	21.4750			1.30451			0.652256	+	0.757999i	$0.273823\pi$
$272$	24.5554	−	19.2077i	1.48889	−	1.16464i
$273$			10.9565i			0.663117i
$274$	−8.62689	−	1.99036i	−0.521170	−	0.120242i
$275$			1.41888i			0.0855619i
$276$	3.70480	−	7.60155i	0.223003	−	0.457560i
$277$		−	31.2285i		−	1.87634i	−0.346173	−	0.938171i	$-0.612519\pi$
$277$		−	31.2285i		−	1.87634i	0.346173	−	0.938171i	$-0.387481\pi$
$278$	31.2393	+	7.20739i	1.87361	+	0.432271i
$279$			12.2667i			0.734389i
$280$	−7.06255	−	5.71406i	−0.422068	−	0.341480i
$281$	4.84868			0.289248			0.144624	−	0.989487i	$-0.453803\pi$
$281$	4.84868			0.289248			0.144624	+	0.989487i	$0.453803\pi$
$282$	−28.0690	−	6.47596i	−1.67149	−	0.385638i
$283$		−	17.1678i		−	1.02052i	−0.860021	−	0.510259i	$-0.829549\pi$
$283$		−	17.1678i		−	1.02052i	0.860021	−	0.510259i	$-0.170451\pi$
$284$	28.2402	+	13.7635i	1.67575	+	0.816715i
$285$		−	16.4843i		−	0.976443i
$286$	8.18508	+	1.88842i	0.483994	+	0.111665i
$287$	−2.25718			−0.133237
$288$	6.92382	+	14.8201i	0.407990	+	0.873285i
$289$	−43.7441			−2.57318
$290$	3.67381	−	15.9236i	0.215734	−	0.935064i
$291$		−	14.9054i		−	0.873769i
$292$	−4.19792	+	8.61335i	−0.245665	+	0.504058i
$293$	3.46159			0.202228			0.101114	−	0.994875i	$-0.467759\pi$
$293$	3.46159			0.202228			0.101114	+	0.994875i	$0.467759\pi$
$294$	4.03148	−	17.4738i	0.235120	−	1.01909i
$295$		−	20.7016i		−	1.20529i
$296$	7.21654	−	8.91961i	0.419453	−	0.518442i
$297$	0.461098			0.0267556
$298$	2.25805	−	9.78716i	0.130805	−	0.566955i
$299$			5.90037i			0.341227i
$300$	1.72091	−	3.53098i	0.0993568	−	0.203861i
$301$		−	4.27664i		−	0.246502i
$302$	−15.4160	−	3.55672i	−0.887093	−	0.204666i
$303$	7.64197			0.439020
$304$	8.87747	−	6.94413i	0.509158	−	0.398273i
$305$		−	16.2235i		−	0.928953i
$306$	7.16524	−	31.0566i	0.409610	−	1.77539i
$307$	23.6634			1.35054			0.675270	−	0.737570i	$-0.264027\pi$
$307$	23.6634			1.35054			0.675270	+	0.737570i	$0.264027\pi$
$308$	4.20125	+	2.04758i	0.239388	+	0.116672i
$309$			6.25325i			0.355735i
$310$	14.0893	+	3.25062i	0.800218	+	0.184623i
$311$		−	16.1751i		−	0.917206i	−0.888641	−	0.458603i	$-0.848350\pi$
$311$		−	16.1751i		−	0.917206i	0.888641	−	0.458603i	$-0.151650\pi$
$312$	−18.0787	−	14.6268i	−1.02350	−	0.828081i
$313$			25.6675i			1.45081i	0.688321	+	0.725406i	$0.258348\pi$
$313$			25.6675i			1.45081i	−0.688321	+	0.725406i	$0.741652\pi$
$314$	26.6467	+	6.14781i	1.50376	+	0.346941i
$315$	−9.28773			−0.523304
$316$	−19.4167	−	9.46319i	−1.09227	−	0.532346i
$317$	−23.8975			−1.34222			−0.671109	−	0.741358i	$-0.734182\pi$
$317$	−23.8975			−1.34222			−0.671109	+	0.741358i	$0.734182\pi$
$318$	−13.7211	−	3.16567i	−0.769440	−	0.177522i
$319$			8.40722i			0.470714i
$320$	18.8569	−	4.02529i	1.05413	−	0.225021i
$321$	−21.4905			−1.19948
$322$	−0.738018	+	3.19882i	−0.0411281	+	0.178263i
$323$	−21.9607			−1.22193
$324$	−16.7438	−	8.16047i	−0.930209	−	0.453360i
$325$			2.74077i			0.152031i
$326$	13.2369	+	3.05396i	0.733125	+	0.169143i
$327$	45.3231			2.50638
$328$	3.01332	−	3.72445i	0.166383	−	0.205648i
$329$	11.1830			0.616541
$330$	−3.26158	+	14.1368i	−0.179544	+	0.778204i
$331$	−12.3751			−0.680196			−0.340098	−	0.940390i	$-0.610460\pi$
$331$	−12.3751			−0.680196			−0.340098	+	0.940390i	$0.610460\pi$
$332$	−15.3640	−	7.48800i	−0.843207	−	0.410957i
$333$		−	11.7299i		−	0.642794i
$334$	15.0582	+	10.3562i	0.823946	+	0.566669i
$335$		−	9.52872i		−	0.520609i
$336$	−7.97165	−	10.1911i	−0.434889	−	0.555968i
$337$	28.0776			1.52949			0.764743	−	0.644336i	$-0.222866\pi$
$337$	28.0776			1.52949			0.764743	+	0.644336i	$0.222866\pi$
$338$	−2.10357	−	0.485326i	−0.114419	−	0.0263983i
$339$	−25.8142			−1.40204
$340$	−33.7722	−	16.4597i	−1.83156	−	0.892652i
$341$	−7.43878			−0.402832
$342$	2.59044	−	11.2278i	0.140075	−	0.607132i
$343$			16.2901i			0.879581i
$344$	7.05665	+	5.70928i	0.380469	+	0.307824i
$345$	−10.1908			−0.548652
$346$	11.4054	+	2.63140i	0.613157	+	0.141465i
$347$	1.59573			0.0856631			0.0428315	−	0.999082i	$-0.486362\pi$
$347$	1.59573			0.0856631			0.0428315	+	0.999082i	$0.486362\pi$
$348$	10.1968	−	20.9219i	0.546606	−	1.12153i
$349$			27.1281i			1.45214i	0.687623	+	0.726068i	$0.258654\pi$
$349$			27.1281i			1.45214i	−0.687623	+	0.726068i	$0.741346\pi$
$350$	−0.342815	+	1.48588i	−0.0183243	+	0.0794236i
$351$	0.890675			0.0475407
$352$	−8.98723	+	4.19874i	−0.479021	+	0.223794i
$353$	31.9383			1.69990			0.849951	−	0.526862i	$-0.176632\pi$
$353$	31.9383			1.69990			0.849951	+	0.526862i	$0.176632\pi$
$354$	6.62823	−	28.7290i	0.352286	−	1.52693i
$355$		−	37.8592i		−	2.00936i
$356$	9.41998	+	4.59105i	0.499258	+	0.243325i
$357$			25.2102i			1.33426i
$358$	6.65921	−	28.8633i	0.351950	−	1.52547i
$359$			33.6791i			1.77751i	0.458378	+	0.888757i	$0.348431\pi$
$359$			33.6791i			1.77751i	−0.458378	+	0.888757i	$0.651569\pi$
$360$	12.3990	−	15.3252i	0.653487	−	0.807707i
$361$	11.0606			0.582136
$362$	−8.78577	−	2.02701i	−0.461770	−	0.106537i
$363$			19.2362i			1.00964i
$364$	8.11529	+	3.95518i	0.425357	+	0.207308i
$365$	11.5472			0.604408
$366$	5.19442	−	22.5144i	0.271517	−	1.17685i
$367$			1.83413i			0.0957409i	0.998854	+	0.0478704i	$0.0152435\pi$
$367$			1.83413i			0.0957409i	−0.998854	+	0.0478704i	$0.984757\pi$
$368$	−4.29295	−	5.48816i	−0.223785	−	0.286090i
$369$		−	4.89790i		−	0.254975i
$370$	−13.4727	−	3.10836i	−0.700413	−	0.161596i
$371$	5.46664			0.283814
$372$	18.5119	+	9.02221i	0.959796	+	0.467780i
$373$		−	14.2163i		−	0.736092i	−0.929808	−	0.368046i	$-0.880027\pi$
$373$		−	14.2163i		−	0.736092i	0.929808	−	0.368046i	$-0.119973\pi$
$374$	18.8333	+	4.34514i	0.973848	+	0.224682i
$375$	24.5176			1.26608
$376$	−14.9293	+	18.4525i	−0.769918	+	0.951615i
$377$			16.2397i			0.836388i
$378$	0.482870	+	0.111406i	0.0248361	+	0.00573009i
$379$	19.2639			0.989519			0.494759	−	0.869030i	$-0.335256\pi$
$379$	19.2639			0.989519			0.494759	+	0.869030i	$0.335256\pi$
$380$	−12.2096	−	5.95064i	−0.626340	−	0.305262i
$381$	−14.5379			−0.744800
$382$	−3.40881	+	14.7749i	−0.174410	+	0.755951i
$383$			4.66477i			0.238359i	0.992873	+	0.119179i	$0.0380263\pi$
$383$			4.66477i			0.238359i	−0.992873	+	0.119179i	$0.961974\pi$
$384$	27.4578	+	0.451422i	1.40120	+	0.0230365i
$385$		−	5.63226i		−	0.287047i
$386$	0.167864	−	0.727578i	0.00854403	−	0.0370327i
$387$	9.27997			0.471728
$388$	−11.0402	−	5.38069i	−0.560480	−	0.273163i
$389$			21.9586i			1.11335i	0.830731	+	0.556674i	$0.187923\pi$
$389$			21.9586i			1.11335i	−0.830731	+	0.556674i	$0.812077\pi$
$390$	−6.30018	+	27.3071i	−0.319022	+	1.38275i
$391$			13.5764i			0.686586i
$392$	−11.4872	−	9.29390i	−0.580192	−	0.469413i
$393$			13.7198i			0.692071i
$394$	−5.42275	+	23.5040i	−0.273194	+	1.18412i
$395$			26.0303i			1.30973i
$396$	−4.44308	+	9.11637i	−0.223273	+	0.458115i
$397$	8.81195			0.442259			0.221130	−	0.975244i	$-0.429026\pi$
$397$	8.81195			0.442259			0.221130	+	0.975244i	$0.429026\pi$
$398$	−7.69719	+	33.3623i	−0.385825	+	1.67230i
$399$			9.11419i			0.456280i
$400$	−1.99411	−	2.54930i	−0.0997055	−	0.127465i
$401$			7.05403i			0.352261i	0.984367	+	0.176131i	$0.0563581\pi$
$401$			7.05403i			0.352261i	−0.984367	+	0.176131i	$0.943642\pi$
$402$	3.05090	−	13.2236i	0.152165	−	0.659535i
$403$	−14.3690			−0.715772
$404$	2.75867	−	5.66028i	0.137249	−	0.281609i
$405$			22.4470i			1.11540i
$406$	−2.03126	+	8.80419i	−0.100810	+	0.436944i
$407$	7.11323			0.352590
$408$	−41.5979	−	33.6554i	−2.05940	−	1.66619i
$409$	30.2831			1.49740			0.748701	−	0.662908i	$-0.230678\pi$
$409$	30.2831			1.49740			0.748701	+	0.662908i	$0.230678\pi$
$410$	−5.62563	−	1.29792i	−0.277830	−	0.0640997i
$411$			15.1957i			0.749548i
$412$	4.63168	+	2.25736i	0.228186	+	0.111212i
$413$			11.4460i			0.563220i
$414$	−6.94119	−	1.60144i	−0.341141	−	0.0787065i
$415$			20.5972i			1.01108i
$416$	−17.3601	+	8.11045i	−0.851147	+	0.397647i
$417$		−	55.0259i		−	2.69463i
$418$	6.80878	+	1.57089i	0.333028	+	0.0768348i
$419$		−	25.2748i		−	1.23476i	−0.786667	−	0.617378i	$-0.788195\pi$
$419$		−	25.2748i		−	1.23476i	0.786667	−	0.617378i	$-0.211805\pi$
$420$	−6.83115	+	14.0162i	−0.333326	+	0.683923i
$421$	−27.1662			−1.32400			−0.662000	−	0.749504i	$-0.730292\pi$
$421$	−27.1662			−1.32400			−0.662000	+	0.749504i	$0.730292\pi$
$422$	5.36040	−	23.2338i	0.260940	−	1.13100i
$423$			24.2663i			1.17987i
$424$	−7.29792	+	9.02020i	−0.354418	+	0.438059i
$425$			6.30633i			0.305902i
$426$	12.1218	−	52.5398i	0.587301	−	2.54556i
$427$			8.97000i			0.434089i
$428$	−7.75784	+	15.9176i	−0.374989	+	0.769408i
$429$		−	14.4175i		−	0.696081i
$430$	2.45915	−	10.6588i	0.118591	−	0.514012i
$431$		−	28.9628i		−	1.39509i	−0.716542	−	0.697544i	$-0.754276\pi$
$431$		−	28.9628i		−	1.39509i	0.716542	−	0.697544i	$-0.245724\pi$
$432$	−0.828451	+	0.648031i	−0.0398589	+	0.0311784i
$433$	33.2695			1.59883			0.799415	−	0.600779i	$-0.205143\pi$
$433$	33.2695			1.59883			0.799415	+	0.600779i	$0.205143\pi$
$434$	−7.79001	−	1.79728i	−0.373933	−	0.0862721i
$435$	−28.0483			−1.34481
$436$	16.3612	−	33.5701i	0.783559	−	1.60772i
$437$			4.90824i			0.234793i
$438$	16.0248	+	3.69718i	0.765696	+	0.176658i
$439$	−4.81189			−0.229659			−0.114829	−	0.993385i	$-0.536632\pi$
$439$	−4.81189			−0.229659			−0.114829	+	0.993385i	$0.536632\pi$
$440$	9.29348	+	7.51902i	0.443049	+	0.358455i
$441$	−15.1065			−0.719356
$442$	36.3792	+	8.39324i	1.73038	+	0.399226i
$443$	−12.4071			−0.589481			−0.294740	−	0.955577i	$-0.595233\pi$
$443$	−12.4071			−0.589481			−0.294740	+	0.955577i	$0.595233\pi$
$444$	−17.7017	−	8.62737i	−0.840088	−	0.409437i
$445$		−	12.6286i		−	0.598652i
$446$	6.15538	−	26.6795i	0.291466	−	1.26331i
$447$	−17.2394			−0.815396
$448$	−10.4260	+	2.22560i	−0.492583	+	0.105149i
$449$	11.5721			0.546120			0.273060	−	0.961997i	$-0.411964\pi$
$449$	11.5721			0.546120			0.273060	+	0.961997i	$0.411964\pi$
$450$	−3.22424	−	0.743882i	−0.151992	−	0.0350669i
$451$	2.97018			0.139860
$452$	−9.31867	+	19.1202i	−0.438314	+	0.899337i
$453$			27.1543i			1.27582i
$454$	29.6292	+	6.83592i	1.39057	+	0.320826i
$455$		−	10.8795i		−	0.510038i
$456$	−15.0388	−	12.1674i	−0.704257	−	0.569789i
$457$			39.6983i			1.85701i	0.371321	+	0.928504i	$0.378905\pi$
$457$			39.6983i			1.85701i	−0.371321	+	0.928504i	$0.621095\pi$
$458$	−10.8017	−	2.49213i	−0.504731	−	0.116449i
$459$	2.04939			0.0956571
$460$	−3.67876	+	7.54813i	−0.171523	+	0.351933i
$461$	9.56033			0.445269			0.222635	−	0.974902i	$-0.428534\pi$
$461$	9.56033			0.445269			0.222635	+	0.974902i	$0.428534\pi$
$462$	1.80333	−	7.81627i	0.0838987	−	0.363646i
$463$	2.30890			0.107304			0.0536518	−	0.998560i	$-0.482914\pi$
$463$	2.30890			0.107304			0.0536518	+	0.998560i	$0.482914\pi$
$464$	−11.8156	−	15.1052i	−0.548524	−	0.701241i
$465$		−	24.8173i		−	1.15088i
$466$	−1.09783	−	0.253287i	−0.0508561	−	0.0117333i
$467$			6.66058i			0.308215i	0.988054	+	0.154107i	$0.0492502\pi$
$467$			6.66058i			0.308215i	−0.988054	+	0.154107i	$0.950750\pi$
$468$	−8.58242	+	17.6095i	−0.396723	+	0.814001i
$469$			5.26845i			0.243275i
$470$	27.8718	+	6.43045i	1.28563	+	0.296615i
$471$		−	46.9364i		−	2.16271i
$472$	−18.8864	−	15.2803i	−0.869315	−	0.703332i
$473$			5.62756i			0.258755i
$474$	−8.33438	+	36.1240i	−0.382811	+	1.65923i
$475$			2.27992i			0.104610i
$476$	18.6728	+	9.10061i	0.855864	+	0.417126i
$477$			11.8622i			0.543131i
$478$	4.58034	−	19.8527i	0.209500	−	0.908044i
$479$	−17.9664			−0.820905			−0.410452	−	0.911882i	$-0.634629\pi$
$479$	−17.9664			−0.820905			−0.410452	+	0.911882i	$0.634629\pi$
$480$	−14.0079	−	29.9833i	−0.639369	−	1.36854i
$481$	13.7402			0.626499
$482$	−3.32153	+	14.3967i	−0.151292	+	0.655750i
$483$	5.63450			0.256379
$484$	14.2479	+	6.94406i	0.647633	+	0.315639i
$485$			14.8006i			0.672062i
$486$	−6.93626	+	30.0641i	−0.314635	+	1.36374i
$487$	31.3864			1.42226			0.711128	−	0.703063i	$-0.248185\pi$
$487$	31.3864			1.42226			0.711128	+	0.703063i	$0.248185\pi$
$488$	−14.8009	−	11.9749i	−0.670005	−	0.542078i
$489$		−	23.3159i		−	1.05438i
$490$	−4.00314	+	17.3510i	−0.180843	+	0.783837i
$491$		−	30.8628i		−	1.39282i	−0.717644	−	0.696410i	$-0.754779\pi$
$491$		−	30.8628i		−	1.39282i	0.717644	−	0.696410i	$-0.245221\pi$
$492$	−7.39149	−	3.60242i	−0.333234	−	0.162410i
$493$			37.3665i			1.68290i
$494$	13.1521	+	3.03439i	0.591741	+	0.136524i
$495$	12.2216			0.549318
$496$	13.3652	−	10.4545i	0.600115	−	0.469421i
$497$			20.9325i			0.938950i
$498$	−6.59480	+	28.5841i	−0.295520	+	1.28088i
$499$	27.6722			1.23878			0.619390	−	0.785084i	$-0.287380\pi$
$499$	27.6722			1.23878			0.619390	+	0.785084i	$0.287380\pi$
$500$	8.85060	−	18.1598i	0.395811	−	0.812130i
$501$	11.5097	−	29.1794i	0.514215	−	1.30364i
$502$	3.89791	−	16.8949i	0.173972	−	0.754055i
$503$		−	18.7732i		−	0.837056i	−0.908204	−	0.418528i	$-0.862546\pi$
$503$		−	18.7732i		−	0.837056i	0.908204	−	0.418528i	$-0.137454\pi$
$504$	−6.85547	+	8.47332i	−0.305367	+	0.377432i
$505$	−7.58826			−0.337673
$506$	0.971145	−	4.20927i	0.0431726	−	0.187125i
$507$			3.70529i			0.164558i
$508$	−5.24804	+	10.7680i	−0.232844	+	0.477752i
$509$	17.6311			0.781484			0.390742	−	0.920500i	$-0.372218\pi$
$509$	17.6311			0.781484			0.390742	+	0.920500i	$0.372218\pi$
$510$	−14.4963	+	62.8319i	−0.641907	+	2.78225i
$511$	−6.38448			−0.282433
$512$	10.2463	−	20.1746i	0.452828	−	0.891598i
$513$	0.740911			0.0327120
$514$	−4.84718	+	21.0093i	−0.213800	+	0.926681i
$515$		−	6.20930i		−	0.273614i
$516$	6.82545	−	14.0045i	0.300474	−	0.616515i
$517$	−14.7156			−0.647189
$518$	7.44910	+	1.71862i	0.327295	+	0.0755120i
$519$		−	20.0898i		−	0.881845i
$520$	17.9516	+	14.5240i	0.787231	+	0.636921i
$521$			32.1800i			1.40983i	0.709291	+	0.704916i	$0.249015\pi$
$521$			32.1800i			1.40983i	−0.709291	+	0.704916i	$0.750985\pi$
$522$	−19.1044	−	4.40768i	−0.836176	−	0.192919i
$523$			26.9149i			1.17691i	0.808531	+	0.588454i	$0.200263\pi$
$523$			26.9149i			1.17691i	−0.808531	+	0.588454i	$0.799737\pi$
$524$	10.1620	+	4.95269i	0.443929	+	0.216359i
$525$	2.61727			0.114227
$526$	4.39106	−	19.0323i	0.191459	−	0.829850i
$527$	−33.0622			−1.44021
$528$	10.4897	+	13.4102i	0.456508	+	0.583606i
$529$	−19.9657			−0.868072
$530$	13.6246	+	3.14342i	0.591817	+	0.136541i
$531$	−24.8369			−1.07783
$532$	6.75073	+	3.29013i	0.292681	+	0.142645i
$533$	5.73732			0.248511
$534$	4.04341	−	17.5255i	0.174975	−	0.758403i
$535$	21.3394			0.922584
$536$	−8.69318	−	7.03335i	−0.375488	−	0.303794i
$537$	−50.8407			−2.19394
$538$	−3.05813	+	13.2550i	−0.131845	+	0.571462i
$539$		−	9.16086i		−	0.394586i
$540$	1.13941	+	0.555318i	0.0490323	+	0.0238971i
$541$		−	7.83732i		−	0.336953i	−0.985706	−	0.168476i	$-0.946115\pi$
$541$		−	7.83732i		−	0.336953i	0.985706	−	0.168476i	$-0.0538847\pi$
$542$	−29.5928	−	6.82752i	−1.27112	−	0.293267i
$543$			15.4755i			0.664119i
$544$	−39.9444	+	18.6616i	−1.71260	+	0.800110i
$545$	−45.0046			−1.92779
$546$	3.48339	−	15.0982i	0.149075	−	0.646143i
$547$	36.5761			1.56388			0.781941	−	0.623353i	$-0.214230\pi$
$547$	36.5761			1.56388			0.781941	+	0.623353i	$0.214230\pi$
$548$	11.2552	+	5.48548i	0.480798	+	0.234328i
$549$	−19.4642			−0.830711
$550$	0.451105	−	1.95524i	0.0192352	−	0.0833718i
$551$			13.5091i			0.575505i
$552$	−7.52202	+	9.29718i	−0.320158	+	0.395714i
$553$		−	14.3922i		−	0.612021i
$554$	−9.92847	+	43.0334i	−0.421820	+	1.82831i
$555$			23.7312i			1.00734i
$556$	−40.7567	−	19.8638i	−1.72847	−	0.842411i
$557$	−16.5524			−0.701347			−0.350674	−	0.936498i	$-0.614047\pi$
$557$	−16.5524			−0.701347			−0.350674	+	0.936498i	$0.614047\pi$
$558$	3.89995	−	16.9037i	0.165098	−	0.715591i
$559$			10.8704i			0.459769i
$560$	7.91562	+	10.1194i	0.334496	+	0.427624i
$561$		−	33.1736i		−	1.40059i
$562$	−6.68154	−	1.54154i	−0.281844	−	0.0650258i
$563$			4.72297i			0.199050i	0.995035	+	0.0995248i	$0.0317323\pi$
$563$			4.72297i			0.199050i	−0.995035	+	0.0995248i	$0.968268\pi$
$564$	36.6206	+	17.8479i	1.54201	+	0.751534i
$565$	25.6328			1.07838
$566$	−5.45814	+	23.6574i	−0.229423	+	0.994396i
$567$		−	12.4110i		−	0.521213i
$568$	−34.5395	−	27.9447i	−1.44925	−	1.17253i
$569$			22.8034i			0.955970i	0.878368	+	0.477985i	$0.158633\pi$
$569$			22.8034i			0.955970i	−0.878368	+	0.477985i	$0.841367\pi$
$570$	−5.24082	+	22.7155i	−0.219514	+	0.951448i
$571$	3.00335			0.125686			0.0628431	−	0.998023i	$-0.479983\pi$
$571$	3.00335			0.125686			0.0628431	+	0.998023i	$0.479983\pi$
$572$	−10.6788	−	5.20455i	−0.446501	−	0.217613i
$573$	26.0250			1.08721
$574$	3.11043	+	0.717624i	0.129827	+	0.0299530i
$575$	1.40947			0.0587791
$576$	−4.82936	−	22.6236i	−0.201223	−	0.942652i
$577$	23.9603			0.997479			0.498740	−	0.866752i	$-0.333796\pi$
$577$	23.9603			0.997479			0.498740	+	0.866752i	$0.333796\pi$
$578$	60.2799	+	13.9075i	2.50731	+	0.578476i
$579$	−1.28158			−0.0532606
$580$	−10.1251	+	20.7749i	−0.420423	+	0.862630i
$581$		−	11.3882i		−	0.472464i
$582$	−4.73886	+	20.5398i	−0.196432	+	0.851403i
$583$	−7.19345			−0.297922
$584$	8.52323	−	10.5347i	0.352694	−	0.435928i
$585$	23.6076			0.976055
$586$	−4.77011	−	1.10054i	−0.197052	−	0.0454629i
$587$	−22.5948			−0.932587			−0.466293	−	0.884630i	$-0.654411\pi$
$587$	−22.5948			−0.932587			−0.466293	+	0.884630i	$0.654411\pi$
$588$	−11.1109	+	22.7974i	−0.458204	+	0.940149i
$589$	−11.9529			−0.492511
$590$	−6.58164	+	28.5271i	−0.270962	+	1.17444i
$591$	41.4007			1.70300
$592$	−12.7803	+	9.99699i	−0.525267	+	0.410874i
$593$		−	0.425255i		−	0.0174631i	−0.999962	−	0.00873156i	$-0.997221\pi$
$593$		−	0.425255i		−	0.0174631i	0.999962	−	0.00873156i	$-0.00277938\pi$
$594$	−0.635400	−	0.146597i	−0.0260708	−	0.00601493i
$595$		−	25.0330i		−	1.02625i
$596$	−6.22325	+	12.7689i	−0.254914	+	0.523036i
$597$	58.7653			2.40510
$598$	1.87590	−	8.13079i	0.0767112	−	0.332493i
$599$		−	25.2241i		−	1.03063i	−0.857001	−	0.515314i	$-0.827675\pi$
$599$		−	25.2241i		−	1.03063i	0.857001	−	0.515314i	$-0.172325\pi$
$600$	−3.49404	+	4.31862i	−0.142644	+	0.176307i
$601$	−16.6767			−0.680255			−0.340128	−	0.940379i	$-0.610470\pi$
$601$	−16.6767			−0.680255			−0.340128	+	0.940379i	$0.610470\pi$
$602$	−1.35967	+	5.89327i	−0.0554160	+	0.240192i
$603$	−11.4321			−0.465552
$604$	20.1127	+	9.80241i	0.818375	+	0.398854i
$605$		−	19.1010i		−	0.776566i
$606$	−10.5307	−	2.42961i	−0.427782	−	0.0986960i
$607$	1.33269			0.0540922			0.0270461	−	0.999634i	$-0.491390\pi$
$607$	1.33269			0.0540922			0.0270461	+	0.999634i	$0.491390\pi$
$608$	−14.4410	+	6.74670i	−0.585661	+	0.273615i
$609$	15.5080			0.628415
$610$	−5.15792	+	22.3562i	−0.208838	+	0.905175i
$611$	−28.4251			−1.14996
$612$	−19.7476	+	40.5184i	−0.798249	+	1.63786i
$613$	8.59307			0.347071			0.173535	−	0.984828i	$-0.444481\pi$
$613$	8.59307			0.347071			0.173535	+	0.984828i	$0.444481\pi$
$614$	−32.6085	−	7.52328i	−1.31597	−	0.303615i
$615$			9.90915i			0.399576i
$616$	−5.13839	−	4.15729i	−0.207032	−	0.167502i
$617$	−32.7499			−1.31846			−0.659231	−	0.751940i	$-0.729118\pi$
$617$	−32.7499			−1.31846			−0.659231	+	0.751940i	$0.729118\pi$
$618$	1.98809	−	8.61706i	0.0799727	−	0.346629i
$619$	−4.51522			−0.181482			−0.0907411	−	0.995875i	$-0.528924\pi$
$619$	−4.51522			−0.181482			−0.0907411	+	0.995875i	$0.528924\pi$
$620$	−18.3818	−	8.95880i	−0.738230	−	0.359794i
$621$		−	0.458040i		−	0.0183805i
$622$	−5.14254	+	22.2895i	−0.206197	+	0.893728i
$623$			6.98237i			0.279743i
$624$	20.2624	+	25.9037i	0.811145	+	1.03698i
$625$	−28.3910			−1.13564
$626$	8.16044	−	35.3701i	0.326157	−	1.41368i
$627$		−	11.9932i		−	0.478962i
$628$	−34.7650	−	16.9435i	−1.38727	−	0.676121i
$629$	31.6153			1.26058
$630$	12.7986	+	2.95284i	0.509909	+	0.117644i
$631$			12.8752i			0.512555i	0.966603	+	0.256278i	$0.0824961\pi$
$631$			12.8752i			0.512555i	−0.966603	+	0.256278i	$0.917504\pi$
$632$	23.7478	+	19.2135i	0.944638	+	0.764274i
$633$	−40.9247			−1.62661
$634$	32.9311	+	7.59772i	1.30786	+	0.301744i
$635$	14.4357			0.572865
$636$	17.9014	+	8.72466i	0.709836	+	0.345955i
$637$		−	17.6955i		−	0.701120i
$638$	2.67290	−	11.5853i	0.105821	−	0.458665i
$639$	−45.4218			−1.79686
$640$	−27.2648	−	0.448249i	−1.07774	−	0.0177186i
$641$		−	10.4661i		−	0.413388i	−0.978406	−	0.206694i	$-0.933730\pi$
$641$		−	10.4661i		−	0.413388i	0.978406	−	0.206694i	$-0.0662704\pi$
$642$	29.6142	+	6.83245i	1.16878	+	0.269655i
$643$	8.30877			0.327666			0.163833	−	0.986488i	$-0.447614\pi$
$643$	8.30877			0.327666			0.163833	+	0.986488i	$0.447614\pi$
$644$	2.03400	−	4.17338i	0.0801507	−	0.164454i
$645$	−18.7747			−0.739254
$646$	30.2621	+	6.98194i	1.19065	+	0.274701i
$647$	43.7513			1.72004			0.860021	−	0.510259i	$-0.170450\pi$
$647$	43.7513			1.72004			0.860021	+	0.510259i	$0.170450\pi$
$648$	20.4787	+	16.5686i	0.804479	+	0.650875i
$649$		−	15.0616i		−	0.591218i
$650$	0.871371	−	3.77682i	0.0341780	−	0.148139i
$651$			13.7216i			0.537791i
$652$	−17.2697	−	8.41681i	−0.676334	−	0.329628i
$653$	17.8511			0.698569			0.349285	−	0.937017i	$-0.386425\pi$
$653$	17.8511			0.698569			0.349285	+	0.937017i	$0.386425\pi$
$654$	−62.4559	−	14.4096i	−2.44222	−	0.563458i
$655$		−	13.6233i		−	0.532308i
$656$	−5.33650	+	4.17432i	−0.208355	+	0.162980i
$657$		−	13.8538i		−	0.540489i
$658$	−15.4104	−	3.55541i	−0.600759	−	0.138604i
$659$	−36.9383			−1.43891			−0.719456	−	0.694538i	$-0.755609\pi$
$659$	−36.9383			−1.43891			−0.719456	+	0.694538i	$0.755609\pi$
$660$	8.98899	−	18.4437i	0.349896	−	0.717921i
$661$			35.0188i			1.36207i	0.732250	+	0.681036i	$0.238470\pi$
$661$			35.0188i			1.36207i	−0.732250	+	0.681036i	$0.761530\pi$
$662$	17.0530	+	3.93440i	0.662785	+	0.152915i
$663$		−	64.0794i		−	2.48864i
$664$	18.7911	+	15.2032i	0.729236	+	0.589999i
$665$		−	9.05013i		−	0.350949i
$666$	−3.72927	+	16.1639i	−0.144506	+	0.626340i
$667$	8.35146			0.323370
$668$	−17.4578	−	19.0585i	−0.675462	−	0.737395i
$669$	−46.9941			−1.81690
$670$	−3.02946	+	13.1307i	−0.117038	+	0.507283i
$671$		−	11.8035i		−	0.455668i
$672$	7.74500	+	16.5778i	0.298770	+	0.639504i
$673$		−	18.2642i		−	0.704034i	−0.935994	−	0.352017i	$-0.885496\pi$
$673$		−	18.2642i		−	0.704034i	0.935994	−	0.352017i	$-0.114504\pi$
$674$	−38.6913	−	8.92669i	−1.49033	−	0.343843i
$675$		−	0.212763i		−	0.00818926i
$676$	2.74445	+	1.33757i	0.105556	+	0.0514451i
$677$	34.7912			1.33714			0.668568	−	0.743651i	$-0.266908\pi$
$677$	34.7912			1.33714			0.668568	+	0.743651i	$0.266908\pi$
$678$	35.5724	+	8.20710i	1.36615	+	0.315192i
$679$		−	8.18331i		−	0.314047i
$680$	41.3055	+	33.4188i	1.58400	+	1.28155i
$681$		−	52.1898i		−	1.99992i
$682$	10.2507	+	2.36500i	0.392521	+	0.0905607i
$683$	−39.9792			−1.52976			−0.764881	−	0.644171i	$-0.777202\pi$
$683$	−39.9792			−1.52976			−0.764881	+	0.644171i	$0.777202\pi$
$684$	−7.13931	+	14.6485i	−0.272978	+	0.560101i
$685$		−	15.0889i		−	0.576517i
$686$	5.17909	−	22.4479i	0.197739	−	0.857066i
$687$			19.0265i			0.725906i
$688$	−7.90901	−	10.1110i	−0.301528	−	0.385478i
$689$	−13.8951			−0.529363
$690$	14.0430	+	3.23994i	0.534608	+	0.123342i
$691$	3.29276			0.125262			0.0626312	−	0.998037i	$-0.480051\pi$
$691$	3.29276			0.125262			0.0626312	+	0.998037i	$0.480051\pi$
$692$	−14.8802	−	7.25221i	−0.565659	−	0.275688i
$693$	−6.75733			−0.256690
$694$	−2.19893	−	0.507328i	−0.0834703	−	0.0192579i
$695$			54.6391i			2.07258i
$696$	−20.7030	+	25.5888i	−0.784746	+	0.969942i
$697$	13.2012			0.500031
$698$	8.62482	−	37.3829i	0.326454	−	1.41496i
$699$			1.93375i			0.0731413i
$700$	0.944808	−	1.93857i	0.0357104	−	0.0732711i
$701$	5.41283			0.204440			0.102220	−	0.994762i	$-0.467405\pi$
$701$	5.41283			0.204440			0.102220	+	0.994762i	$0.467405\pi$
$702$	−1.22736	−	0.283172i	−0.0463238	−	0.0106876i
$703$	11.4298			0.431084
$704$	13.7194	−	2.92862i	0.517070	−	0.110377i
$705$		−	49.0942i		−	1.84899i
$706$	−44.0113	−	10.1541i	−1.65639	−	0.382155i
$707$	4.19557			0.157791
$708$	−18.2676	+	37.4816i	−0.686538	+	1.40865i
$709$		−	9.99067i		−	0.375208i	−0.982245	−	0.187604i	$-0.939928\pi$
$709$		−	9.99067i		−	0.375208i	0.982245	−	0.187604i	$-0.0600721\pi$
$710$	−12.0366	+	52.1706i	−0.451724	+	1.95793i
$711$	31.2300			1.17122
$712$	−11.5212	−	9.32142i	−0.431776	−	0.349335i
$713$			7.38944i			0.276737i
$714$	8.01505	−	34.7400i	0.299956	−	1.30011i
$715$			14.3161i			0.535393i
$716$	−18.3530	+	37.6568i	−0.685882	+	1.40730i
$717$	−34.9693			−1.30595
$718$	10.7076	−	46.4102i	0.399603	−	1.73201i
$719$	−14.0459			−0.523824			−0.261912	−	0.965092i	$-0.584353\pi$
$719$	−14.0459			−0.523824			−0.261912	+	0.965092i	$0.584353\pi$
$720$	−21.9584	+	17.1763i	−0.818340	+	0.640121i
$721$			3.43314i			0.127857i
$722$	−15.2416	−	3.51649i	−0.567235	−	0.130870i
$723$	25.3587			0.943101
$724$	11.4625	+	5.58651i	0.425999	+	0.207621i
$725$	3.87932			0.144074
$726$	6.11575	−	26.5077i	0.226977	−	0.983794i
$727$	−39.4803			−1.46424			−0.732121	−	0.681174i	$-0.761470\pi$
$727$	−39.4803			−1.46424			−0.732121	+	0.681174i	$0.761470\pi$
$728$	−9.92551	−	8.03038i	−0.367864	−	0.297626i
$729$	25.0161			0.926522
$730$	−15.9122	−	3.67119i	−0.588937	−	0.135877i
$731$			25.0121i			0.925106i
$732$	−14.3160	+	29.3737i	−0.529134	+	1.08568i
$733$	−46.6179			−1.72187			−0.860935	−	0.508715i	$-0.830121\pi$
$733$	−46.6179			−1.72187			−0.860935	+	0.508715i	$0.830121\pi$
$734$	0.583124	−	2.52746i	0.0215235	−	0.0932902i
$735$	30.5626			1.12732
$736$	4.17089	+	8.92762i	0.153741	+	0.329076i
$737$		−	6.93266i		−	0.255368i
$738$	−1.55719	+	6.74937i	−0.0573208	+	0.248448i
$739$	−8.54028			−0.314159			−0.157080	−	0.987586i	$-0.550208\pi$
$739$	−8.54028			−0.314159			−0.157080	+	0.987586i	$0.550208\pi$
$740$	17.5773	+	8.56673i	0.646155	+	0.314919i
$741$		−	23.1665i		−	0.851043i
$742$	−7.53310	−	1.73800i	−0.276549	−	0.0638041i
$743$			33.5292i			1.23007i	0.788501	+	0.615034i	$0.210858\pi$
$743$			33.5292i			1.23007i	−0.788501	+	0.615034i	$0.789142\pi$
$744$	−22.6412	−	18.3182i	−0.830067	−	0.671577i
$745$	17.1182			0.627164
$746$	−4.51978	+	19.5903i	−0.165481	+	0.717250i
$747$	24.7116			0.904149
$748$	−24.5711	−	11.9753i	−0.898410	−	0.437861i
$749$	−11.7986			−0.431113
$750$	−33.7856	−	7.79486i	−1.23368	−	0.284628i
$751$	15.0822			0.550358			0.275179	−	0.961393i	$-0.411263\pi$
$751$	15.0822			0.550358			0.275179	+	0.961393i	$0.411263\pi$
$752$	26.4393	−	20.6813i	0.964143	−	0.754171i
$753$	−29.7592			−1.08448
$754$	5.16308	−	22.3785i	0.188028	−	0.814979i
$755$		−	26.9634i		−	0.981300i
$756$	−0.629982	−	0.307037i	−0.0229122	−	0.0111668i
$757$	11.5054			0.418172			0.209086	−	0.977897i	$-0.432951\pi$
$757$	11.5054			0.418172			0.209086	+	0.977897i	$0.432951\pi$
$758$	−26.5459	−	6.12455i	−0.964190	−	0.222454i
$759$	−7.41434			−0.269124
$760$	14.9331	+	12.0819i	0.541681	+	0.438255i
$761$	22.6906			0.822533			0.411266	−	0.911515i	$-0.365087\pi$
$761$	22.6906			0.822533			0.411266	+	0.911515i	$0.365087\pi$
$762$	20.0334	+	4.62203i	0.725735	+	0.167438i
$763$	24.8832			0.900831
$764$	9.39476	−	19.2763i	0.339890	−	0.697392i
$765$	54.3196			1.96393
$766$	1.48307	−	6.42811i	0.0535854	−	0.232257i
$767$		−	29.0935i		−	1.05050i
$768$	−37.6937	−	9.35170i	−1.36015	−	0.337450i
$769$		−	32.8378i		−	1.18416i	−0.805878	−	0.592081i	$-0.798306\pi$
$769$		−	32.8378i		−	1.18416i	0.805878	−	0.592081i	$-0.201694\pi$
$770$	−1.79066	+	7.76133i	−0.0645309	+	0.279699i
$771$	37.0065			1.33276
$772$	−0.462637	+	0.949244i	−0.0166507	+	0.0341640i
$773$			27.3665i			0.984304i	0.870509	+	0.492152i	$0.163790\pi$
$773$			27.3665i			0.984304i	−0.870509	+	0.492152i	$0.836210\pi$
$774$	−12.7879	−	2.95037i	−0.459653	−	0.106049i
$775$			3.43246i			0.123297i
$776$	13.5028	+	10.9247i	0.484723	+	0.392172i
$777$		−	13.1211i		−	0.470716i
$778$	6.98129	−	30.2593i	0.250291	−	1.08485i
$779$	4.77260			0.170996
$780$	17.3635	−	35.6266i	0.621712	−	1.27564i
$781$		−	27.5447i		−	0.985626i
$782$	4.31632	−	18.7084i	0.154351	−	0.669012i
$783$		−	1.26067i		−	0.0450528i
$784$	12.8747	+	16.4592i	0.459812	+	0.587830i
$785$			46.6065i			1.66346i
$786$	4.36191	−	18.9060i	0.155584	−	0.674356i
$787$	20.0766			0.715652			0.357826	−	0.933788i	$-0.383518\pi$
$787$	20.0766			0.715652			0.357826	+	0.933788i	$0.383518\pi$
$788$	14.9452	−	30.6648i	0.532402	−	1.09239i
$789$	−33.5242			−1.19349
$790$	8.27580	−	35.8702i	0.294440	−	1.27620i
$791$	−14.1725			−0.503915
$792$	9.02099	−	11.1499i	0.320547	−	0.396194i
$793$		−	22.8000i		−	0.809653i
$794$	−12.1430	−	2.80158i	−0.430938	−	0.0994242i
$795$		−	23.9989i		−	0.851152i
$796$	21.2137	−	43.5265i	0.751899	−	1.54276i
$797$			41.2578i			1.46143i	0.682685	+	0.730713i	$0.260812\pi$
$797$			41.2578i			1.46143i	−0.682685	+	0.730713i	$0.739188\pi$
$798$	2.89767	−	12.5595i	0.102576	−	0.444601i
$799$	−65.4044			−2.31384
$800$	1.93741	+	4.14695i	0.0684979	+	0.146617i
$801$	−15.1512			−0.535341
$802$	2.24268	−	9.72054i	0.0791918	−	0.343244i
$803$	8.40122			0.296473
$804$	−8.40836	+	17.2524i	−0.296540	+	0.608445i
$805$	−5.59490			−0.197194
$806$	19.8007	+	4.56833i	0.697450	+	0.160913i
$807$	23.3477			0.821878
$808$	−5.60106	+	6.92288i	−0.197045	+	0.243546i
$809$	−34.2548			−1.20434			−0.602168	−	0.798370i	$-0.705696\pi$
$809$	−34.2548			−1.20434			−0.602168	+	0.798370i	$0.705696\pi$
$810$	7.13654	−	30.9322i	0.250753	−	1.08685i
$811$	46.2469			1.62395			0.811975	−	0.583692i	$-0.198393\pi$
$811$	46.2469			1.62395			0.811975	+	0.583692i	$0.198393\pi$
$812$	5.59821	−	11.4865i	0.196459	−	0.403097i
$813$			52.1257i			1.82813i
$814$	−9.80213	−	2.26150i	−0.343565	−	0.0792657i
$815$			23.1521i			0.810981i
$816$	46.6224	+	59.6028i	1.63211	+	2.08651i
$817$			9.04258i			0.316360i
$818$	−41.7305	−	9.62788i	−1.45907	−	0.336631i
$819$	−13.0527			−0.456099
$820$	7.33954	+	3.57710i	0.256308	+	0.124918i
$821$			37.4083i			1.30556i	0.757548	+	0.652779i	$0.226397\pi$
$821$			37.4083i			1.30556i	−0.757548	+	0.652779i	$0.773603\pi$
$822$	4.83115	−	20.9399i	0.168506	−	0.730361i
$823$	34.2261			1.19305			0.596523	−	0.802596i	$-0.296548\pi$
$823$	34.2261			1.19305			0.596523	+	0.802596i	$0.296548\pi$
$824$	−5.66483	−	4.58321i	−0.197344	−	0.159664i
$825$	−3.44402			−0.119905
$826$	3.63901	−	15.7727i	0.126617	−	0.548803i
$827$	−32.2401			−1.12110			−0.560549	−	0.828121i	$-0.689410\pi$
$827$	−32.2401			−1.12110			−0.560549	+	0.828121i	$0.689410\pi$
$828$	9.05590	+	4.41361i	0.314714	+	0.153384i
$829$			40.9754i			1.42313i	0.702618	+	0.711567i	$0.252014\pi$
$829$			40.9754i			1.42313i	−0.702618	+	0.711567i	$0.747986\pi$
$830$	6.54845	−	28.3832i	0.227300	−	0.985195i
$831$	75.8003			2.62948
$832$	26.5010	−	5.65703i	0.918755	−	0.196122i
$833$		−	40.7161i		−	1.41073i
$834$	−17.4943	+	75.8264i	−0.605779	+	2.62565i
$835$	−11.4288	+	28.9743i	−0.395510	+	1.00270i
$836$	−8.88316	−	4.32942i	−0.307230	−	0.149736i
$837$	1.11545			0.0385557
$838$	−8.03560	+	34.8290i	−0.277585	+	1.20315i
$839$			39.6990i			1.37056i	0.728279	+	0.685281i	$0.240320\pi$
$839$			39.6990i			1.37056i	−0.728279	+	0.685281i	$0.759680\pi$
$840$	13.8696	−	17.1427i	0.478546	−	0.591481i
$841$	−6.01409			−0.207382
$842$	37.4354	+	8.63693i	1.29011	+	0.297648i
$843$			11.7691i			0.405349i
$844$	−14.7734	+	30.3122i	−0.508521	+	1.04339i
$845$		−	3.67925i		−	0.126570i
$846$	7.71496	−	33.4393i	0.265246	−	1.14967i
$847$			10.5610i			0.362880i
$848$	12.9244	−	10.1097i	0.443826	−	0.347170i
$849$	41.6709			1.43014
$850$	2.00497	−	8.69021i	0.0687698	−	0.298072i
$851$		−	7.06606i		−	0.242221i
$852$	−33.4079	+	68.5467i	−1.14454	+	2.34837i
$853$	32.0879			1.09867			0.549335	−	0.835602i	$-0.314881\pi$
$853$	32.0879			1.09867			0.549335	+	0.835602i	$0.314881\pi$
$854$	2.85183	−	12.3608i	0.0975875	−	0.422977i
$855$	19.6381			0.671608
$856$	15.7511	−	19.4683i	0.538361	−	0.665412i
$857$	22.7280			0.776373			0.388186	−	0.921581i	$-0.373102\pi$
$857$	22.7280			0.776373			0.388186	+	0.921581i	$0.373102\pi$
$858$	−4.58373	+	19.8674i	−0.156486	+	0.678263i
$859$		−	26.8303i		−	0.915439i	−0.889097	−	0.457720i	$-0.848666\pi$
$859$		−	26.8303i		−	0.915439i	0.889097	−	0.457720i	$-0.151334\pi$
$860$	−6.77748	+	13.9061i	−0.231110	+	0.474194i
$861$		−	5.47880i		−	0.186717i
$862$	−9.20811	+	39.9111i	−0.313629	+	1.35938i
$863$		−	28.3875i		−	0.966323i	−0.875531	−	0.483161i	$-0.839488\pi$
$863$		−	28.3875i		−	0.966323i	0.875531	−	0.483161i	$-0.160512\pi$
$864$	1.34765	−	0.629606i	0.0458478	−	0.0214196i
$865$			19.9486i			0.678273i
$866$	−45.8458	−	10.5773i	−1.55790	−	0.359433i
$867$		−	106.179i		−	3.60602i
$868$	10.1633	+	4.95334i	0.344966	+	0.168127i
$869$			18.9385i			0.642445i
$870$	38.6509	+	8.91736i	1.31039	+	0.302327i
$871$		−	13.3914i		−	0.453750i
$872$	−33.2188	+	41.0583i	−1.12493	+	1.39041i
$873$	17.7571			0.600988
$874$	1.56047	−	6.76362i	0.0527838	−	0.228783i
$875$	13.4606			0.455051
$876$	−20.9070	−	10.1895i	−0.706382	−	0.344272i
$877$	11.1144			0.375306			0.187653	−	0.982235i	$-0.439912\pi$
$877$	11.1144			0.375306			0.187653	+	0.982235i	$0.439912\pi$
$878$	6.63085	+	1.52984i	0.223780	+	0.0516296i
$879$			8.40223i			0.283400i
$880$	−10.4160	−	13.3160i	−0.351124	−	0.448882i
$881$		−	8.06649i		−	0.271767i	−0.990725	−	0.135883i	$-0.956613\pi$
$881$		−	8.06649i		−	0.271767i	0.990725	−	0.135883i	$-0.0433873\pi$
$882$	20.8169	+	4.80279i	0.700942	+	0.161718i
$883$			17.4684i			0.587859i	0.955827	+	0.293930i	$0.0949632\pi$
$883$			17.4684i			0.587859i	−0.955827	+	0.293930i	$0.905037\pi$
$884$	−47.4625	−	23.1320i	−1.59634	−	0.778013i
$885$	50.2485			1.68909
$886$	17.0972	+	3.94459i	0.574392	+	0.132521i
$887$	31.9504			1.07279			0.536394	−	0.843967i	$-0.319786\pi$
$887$	31.9504			1.07279			0.536394	+	0.843967i	$0.319786\pi$
$888$	21.6503	+	17.5165i	0.726538	+	0.587816i
$889$	−7.98156			−0.267693
$890$	−4.01499	+	17.4023i	−0.134583	+	0.583328i
$891$			16.3314i			0.547122i
$892$	−16.9644	+	34.8077i	−0.568010	+	1.16545i
$893$	−23.6455			−0.791267
$894$	23.7561	+	5.48091i	0.794524	+	0.183309i
$895$	50.4834			1.68747
$896$	15.0748	+	0.247838i	0.503613	+	0.00827969i
$897$	−14.3218			−0.478192
$898$	−15.9465	−	3.67910i	−0.532141	−	0.122773i
$899$			20.3381i			0.678314i
$900$	4.20654	+	2.05016i	0.140218	+	0.0683386i
$901$	−31.9718			−1.06514
$902$	−4.09295	−	0.944308i	−0.136280	−	0.0314420i
$903$	10.3806			0.345444
$904$	18.9201	−	23.3852i	0.629274	−	0.777779i
$905$		−	15.3668i		−	0.510808i
$906$	8.63314	−	37.4190i	0.286817	−	1.24316i
$907$			24.6309i			0.817854i	0.912567	+	0.408927i	$0.134097\pi$
$907$			24.6309i			0.817854i	−0.912567	+	0.408927i	$0.865903\pi$
$908$	−38.6561	−	18.8400i	−1.28285	−	0.625227i
$909$			9.10406i			0.301963i
$910$	−3.45891	+	14.9921i	−0.114662	+	0.496983i
$911$		−	18.0719i		−	0.598749i	−0.954136	−	0.299374i	$-0.903222\pi$
$911$		−	18.0719i		−	0.598749i	0.954136	−	0.299374i	$-0.0967780\pi$
$912$	16.8553	+	21.5481i	0.558136	+	0.713528i
$913$			14.9856i			0.495951i
$914$	12.6213	−	54.7048i	0.417474	−	1.80947i
$915$	39.3788			1.30182
$916$	14.0926	+	6.86837i	0.465633	+	0.226937i
$917$			7.53238i			0.248741i
$918$	−2.82408	−	0.651559i	−0.0932085	−	0.0215047i
$919$		−	9.92878i		−	0.327520i	−0.986500	−	0.163760i	$-0.947638\pi$
$919$		−	9.92878i		−	0.327520i	0.986500	−	0.163760i	$-0.0523623\pi$
$920$	7.46915	−	9.23184i	0.246251	−	0.304365i
$921$			57.4376i			1.89263i
$922$	−13.1743	−	3.03951i	−0.433871	−	0.100101i
$923$		−	53.2064i		−	1.75131i
$924$	−4.97004	+	10.1976i	−0.163502	+	0.335476i
$925$		−	3.28224i		−	0.107919i
$926$	−3.18169	−	0.734066i	−0.104557	−	0.0241229i
$927$	−7.44964			−0.244678
$928$	11.4796	+	24.5717i	0.376838	+	0.806605i
$929$	−3.09413			−0.101515			−0.0507575	−	0.998711i	$-0.516164\pi$
$929$	−3.09413			−0.101515			−0.0507575	+	0.998711i	$0.516164\pi$
$930$	−7.89015	+	34.1986i	−0.258728	+	1.12142i
$931$		−	14.7200i		−	0.482429i
$932$	1.43230	+	0.698065i	0.0469165	+	0.0228659i
$933$	39.2614			1.28536
$934$	2.11759	−	9.17836i	0.0692897	−	0.300325i
$935$			32.9405i			1.07727i
$936$	17.4253	−	21.5376i	0.569563	−	0.703977i
$937$			27.6784i			0.904215i	0.891964	+	0.452107i	$0.149328\pi$
$937$			27.6784i			0.904215i	−0.891964	+	0.452107i	$0.850672\pi$
$938$	1.67500	−	7.26000i	0.0546905	−	0.237047i
$939$	−62.3021			−2.03315
$940$	−36.3632	−	17.7225i	−1.18604	−	0.578044i
$941$		−	23.3136i		−	0.760003i	−0.924986	−	0.380001i	$-0.875923\pi$
$941$		−	23.3136i		−	0.760003i	0.924986	−	0.380001i	$-0.124077\pi$
$942$	−14.9224	+	64.6789i	−0.486199	+	2.10735i
$943$		−	2.95048i		−	0.0960809i
$944$	21.1676	+	27.0610i	0.688947	+	0.880760i
$945$			0.844564i			0.0274737i
$946$	1.78916	−	7.75485i	0.0581708	−	0.252132i
$947$			48.5217i			1.57674i	0.615199	+	0.788372i	$0.289076\pi$
$947$			48.5217i			1.57674i	−0.615199	+	0.788372i	$0.710924\pi$
$948$	22.9698	−	47.1297i	0.746024	−	1.53070i
$949$	16.2281			0.526787
$950$	0.724852	−	3.14176i	0.0235173	−	0.101932i
$951$		−	58.0059i		−	1.88097i
$952$	−22.8380	−	18.4774i	−0.740182	−	0.598855i
$953$			6.37328i			0.206451i	0.994658	+	0.103225i	$0.0329163\pi$
$953$			6.37328i			0.206451i	−0.994658	+	0.103225i	$0.967084\pi$
$954$	3.77133	−	16.3462i	0.122101	−	0.529229i
$955$	−25.8421			−0.836231
$956$	−12.6235	+	25.9011i	−0.408274	+	0.837702i
$957$	−20.4067			−0.659653
$958$	24.7579	+	5.71204i	0.799892	+	0.184547i
$959$			8.34269i			0.269399i
$960$	9.77049	+	45.7709i	0.315341	+	1.47725i
$961$	13.0047			0.419506
$962$	−18.9342	−	4.36841i	−0.610462	−	0.140843i
$963$		−	25.6021i		−	0.825016i
$964$	9.15423	−	18.7828i	0.294838	−	0.604952i
$965$	1.27257			0.0409655
$966$	−7.76442	−	1.79137i	−0.249816	−	0.0576365i
$967$		−	53.6806i		−	1.72625i	−0.504989	−	0.863126i	$-0.668503\pi$
$967$		−	53.6806i		−	1.72625i	0.504989	−	0.863126i	$-0.331497\pi$
$968$	−17.4261	−	14.0988i	−0.560096	−	0.453154i
$969$		−	53.3047i		−	1.71239i
$970$	4.70555	−	20.3955i	0.151086	−	0.654859i
$971$	−50.7330			−1.62810			−0.814050	−	0.580795i	$-0.802742\pi$
$971$	−50.7330			−1.62810			−0.814050	+	0.580795i	$0.802742\pi$
$972$	19.1165	−	39.2235i	0.613163	−	1.25809i
$973$		−	30.2101i		−	0.968492i
$974$	−43.2509	−	9.97866i	−1.38585	−	0.319737i
$975$	−6.65261			−0.213054
$976$	16.5887	+	21.2072i	0.530991	+	0.678826i
$977$			40.1001i			1.28292i	0.767158	+	0.641458i	$0.221670\pi$
$977$			40.1001i			1.28292i	−0.767158	+	0.641458i	$0.778330\pi$
$978$	−7.41281	+	32.1297i	−0.237036	+	1.02739i
$979$		−	9.18798i		−	0.293649i
$980$	11.0328	−	22.6372i	0.352429	−	0.723118i
$981$			53.9945i			1.72391i
$982$	−9.81220	+	42.5294i	−0.313120	+	1.35717i
$983$	18.9948			0.605840			0.302920	−	0.953016i	$-0.402038\pi$
$983$	18.9948			0.605840			0.302920	+	0.953016i	$0.402038\pi$
$984$	9.04026	+	7.31416i	0.288193	+	0.233167i
$985$	−41.1098			−1.30987
$986$	11.8799	−	51.4916i	0.378333	−	1.63983i
$987$			27.1443i			0.864013i
$988$	−17.1590	−	8.36287i	−0.545902	−	0.266058i
$989$	5.59023			0.177759
$990$	−16.8415	−	3.88559i	−0.535257	−	0.123492i
$991$	−15.8889			−0.504727			−0.252363	−	0.967633i	$-0.581208\pi$
$991$	−15.8889			−0.504727			−0.252363	+	0.967633i	$0.581208\pi$
$992$	−21.7412	+	10.1573i	−0.690284	+	0.322494i
$993$		−	30.0378i		−	0.953220i
$994$	6.65505	−	28.8452i	0.211085	−	0.914916i
$995$	−58.3523			−1.84989
$996$	18.1754	−	37.2926i	0.575911	−	1.18166i
$997$	14.0715			0.445647			0.222824	−	0.974859i	$-0.428473\pi$
$997$	14.0715			0.445647			0.222824	+	0.974859i	$0.428473\pi$
$998$	−38.1327	−	8.79781i	−1.20707	−	0.278490i
$999$	−1.06664			−0.0337469

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	668.2.b.b.667.1	✓	60
4.3	odd	2	inner	668.2.b.b.667.3	yes	60
167.166	odd	2	inner	668.2.b.b.667.2	yes	60
668.667	even	2	inner	668.2.b.b.667.4	yes	60

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
668.2.b.b.667.1	✓	60	1.1	even	1	trivial
668.2.b.b.667.2	yes	60	167.166	odd	2	inner
668.2.b.b.667.3	yes	60	4.3	odd	2	inner
668.2.b.b.667.4	yes	60	668.667	even	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)

\(f(q)\)	\(=\)	\(q+(-1.37801 - 0.317929i) q^{2} +2.42728i q^{3} +(1.79784 + 0.876221i) q^{4} -2.41022i q^{5} +(0.771702 - 3.34482i) q^{6} +1.33262i q^{7} +(-2.19887 - 1.77903i) q^{8} -2.89167 q^{9} +O(q^{10})\)	\(q+(-1.37801 - 0.317929i) q^{2} +2.42728i q^{3} +(1.79784 + 0.876221i) q^{4} -2.41022i q^{5} +(0.771702 - 3.34482i) q^{6} +1.33262i q^{7} +(-2.19887 - 1.77903i) q^{8} -2.89167 q^{9} +(-0.766278 + 3.32131i) q^{10} -1.75356i q^{11} +(-2.12683 + 4.36386i) q^{12} -3.38725i q^{13} +(0.423677 - 1.83636i) q^{14} +5.85026 q^{15} +(2.46447 + 3.15062i) q^{16} -7.79385i q^{17} +(3.98476 + 0.919346i) q^{18} -2.81770i q^{19} +(2.11188 - 4.33319i) q^{20} -3.23463 q^{21} +(-0.557509 + 2.41644i) q^{22} -1.74193 q^{23} +(4.31820 - 5.33727i) q^{24} -0.809143 q^{25} +(-1.07691 + 4.66768i) q^{26} +0.262949i q^{27} +(-1.16767 + 2.39583i) q^{28} -4.79436 q^{29} +(-8.06174 - 1.85997i) q^{30} -4.24209i q^{31} +(-2.39440 - 5.12512i) q^{32} +4.25639 q^{33} +(-2.47789 + 10.7400i) q^{34} +3.21189 q^{35} +(-5.19876 - 2.53374i) q^{36} +4.05644i q^{37} +(-0.895828 + 3.88282i) q^{38} +8.22180 q^{39} +(-4.28785 + 5.29976i) q^{40} +1.69380i q^{41} +(4.45736 + 1.02838i) q^{42} -3.20921 q^{43} +(1.53651 - 3.15263i) q^{44} +6.96955i q^{45} +(2.40041 + 0.553812i) q^{46} -8.39180i q^{47} +(-7.64741 + 5.98195i) q^{48} +5.22414 q^{49} +(1.11501 + 0.257250i) q^{50} +18.9178 q^{51} +(2.96798 - 6.08974i) q^{52} -4.10219i q^{53} +(0.0835992 - 0.362347i) q^{54} -4.22647 q^{55} +(2.37076 - 2.93025i) q^{56} +6.83932 q^{57} +(6.60670 + 1.52427i) q^{58} +8.58911 q^{59} +(10.5178 + 5.12612i) q^{60} +6.73113 q^{61} +(-1.34868 + 5.84566i) q^{62} -3.85348i q^{63} +(1.67010 + 7.82373i) q^{64} -8.16401 q^{65} +(-5.86536 - 1.35323i) q^{66} +3.95347 q^{67} +(6.82914 - 14.0121i) q^{68} -4.22815i q^{69} +(-4.42603 - 1.02115i) q^{70} +15.7078 q^{71} +(6.35842 + 5.14437i) q^{72} +4.79094i q^{73} +(1.28966 - 5.58983i) q^{74} -1.96401i q^{75} +(2.46892 - 5.06577i) q^{76} +2.33683 q^{77} +(-11.3297 - 2.61395i) q^{78} -10.8000 q^{79} +(7.59366 - 5.93991i) q^{80} -9.31326 q^{81} +(0.538508 - 2.33408i) q^{82} -8.54578 q^{83} +(-5.81535 - 2.83425i) q^{84} -18.7849 q^{85} +(4.42233 + 1.02030i) q^{86} -11.6372i q^{87} +(-3.11965 + 3.85587i) q^{88} +5.23960 q^{89} +(2.21582 - 9.60413i) q^{90} +4.51390 q^{91} +(-3.13172 - 1.52632i) q^{92} +10.2967 q^{93} +(-2.66800 + 11.5640i) q^{94} -6.79126 q^{95} +(12.4401 - 5.81188i) q^{96} -6.14079 q^{97} +(-7.19893 - 1.66091i) q^{98} +5.07073i 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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