LMFDB - Embedded newform 378.2.z.a.83.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [378,2,Mod(41,378)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(378, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([17, 9]))

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

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

chi := DirichletCharacter("378.41");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 378 = 2 \cdot 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	378.z (of order $18$, degree $6$, 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:	$3.01834519640$
Analytic rank:	$0$
Dimension:	$144$
Relative dimension:	$24$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			83.9
Character	$\chi$	$=$	378.83
Dual form			378.2.z.a.41.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.984808 - 0.173648i) q^{2} +(0.826027 - 1.52239i) q^{3} +(0.939693 + 0.342020i) q^{4} +(-1.99843 + 1.67688i) q^{5} +(-1.07784 + 1.35583i) q^{6} +(1.84005 + 1.90111i) q^{7} +(-0.866025 - 0.500000i) q^{8} +(-1.63536 - 2.51507i) q^{9} +O(q^{10})$	\(q+(-0.984808 - 0.173648i) q^{2} +(0.826027 - 1.52239i) q^{3} +(0.939693 + 0.342020i) q^{4} +(-1.99843 + 1.67688i) q^{5} +(-1.07784 + 1.35583i) q^{6} +(1.84005 + 1.90111i) q^{7} +(-0.866025 - 0.500000i) q^{8} +(-1.63536 - 2.51507i) q^{9} +(2.25926 - 1.30438i) q^{10} +(1.10056 - 1.31159i) q^{11} +(1.29690 - 1.14806i) q^{12} +(6.54906 - 1.15478i) q^{13} +(-1.48197 - 2.19175i) q^{14} +(0.902117 + 4.42755i) q^{15} +(0.766044 + 0.642788i) q^{16} +(3.19200 + 5.52870i) q^{17} +(1.17378 + 2.76084i) q^{18} +(-1.36673 - 0.789081i) q^{19} +(-2.45144 + 0.892251i) q^{20} +(4.41416 - 1.23092i) q^{21} +(-1.31159 + 1.10056i) q^{22} +(2.89352 - 7.94988i) q^{23} +(-1.47656 + 0.905418i) q^{24} +(0.313551 - 1.77824i) q^{25} -6.65009 q^{26} +(-5.17978 + 0.412142i) q^{27} +(1.07887 + 2.41579i) q^{28} +(3.93278 + 0.693456i) q^{29} +(-0.119576 - 4.51694i) q^{30} +(0.301809 - 0.829214i) q^{31} +(-0.642788 - 0.766044i) q^{32} +(-1.08767 - 2.75889i) q^{33} +(-2.18346 - 5.99900i) q^{34} +(-6.86515 - 0.713683i) q^{35} +(-0.676530 - 2.92272i) q^{36} +(-2.57189 - 4.45464i) q^{37} +(1.20894 + 1.01442i) q^{38} +(3.65167 - 10.9241i) q^{39} +(2.56913 - 0.453008i) q^{40} +(-0.142302 - 0.807035i) q^{41} +(-4.56085 + 0.445703i) q^{42} +(6.82048 + 5.72306i) q^{43} +(1.48277 - 0.856080i) q^{44} +(7.48564 + 2.28390i) q^{45} +(-4.23005 + 7.32665i) q^{46} +(-6.60763 + 2.40498i) q^{47} +(1.61135 - 0.635261i) q^{48} +(-0.228422 + 6.99627i) q^{49} +(-0.617575 + 1.69677i) q^{50} +(11.0535 - 0.292619i) q^{51} +(6.54906 + 1.15478i) q^{52} +6.75035i q^{53} +(5.17266 + 0.493579i) q^{54} +4.46663i q^{55} +(-0.642977 - 2.56643i) q^{56} +(-2.33024 + 1.42890i) q^{57} +(-3.75262 - 1.36584i) q^{58} +(0.690522 - 0.579417i) q^{59} +(-0.666598 + 4.46908i) q^{60} +(-1.46604 - 4.02791i) q^{61} +(-0.441216 + 0.764208i) q^{62} +(1.77228 - 7.73686i) q^{63} +(0.500000 + 0.866025i) q^{64} +(-11.1514 + 13.2897i) q^{65} +(0.592069 + 2.90584i) q^{66} +(-2.06631 - 11.7186i) q^{67} +(1.10857 + 6.28701i) q^{68} +(-9.71272 - 10.9719i) q^{69} +(6.63693 + 1.89496i) q^{70} +(2.69703 - 1.55713i) q^{71} +(0.158726 + 2.99580i) q^{72} +(1.04793 + 0.605023i) q^{73} +(1.75928 + 4.83357i) q^{74} +(-2.44817 - 1.94622i) q^{75} +(-1.01442 - 1.20894i) q^{76} +(4.51855 - 0.321120i) q^{77} +(-5.49315 + 10.1240i) q^{78} +(-1.88666 + 10.6998i) q^{79} -2.60877 q^{80} +(-3.65120 + 8.22610i) q^{81} +0.819485i q^{82} +(0.170323 - 0.965952i) q^{83} +(4.56896 + 0.353051i) q^{84} +(-15.6500 - 5.69613i) q^{85} +(-5.72306 - 6.82048i) q^{86} +(4.30430 - 5.41443i) q^{87} +(-1.60890 + 0.585593i) q^{88} +(-1.37986 + 2.38999i) q^{89} +(-6.97532 - 3.54907i) q^{90} +(14.2460 + 10.3256i) q^{91} +(5.43804 - 6.48081i) q^{92} +(-1.01309 - 1.14443i) q^{93} +(6.92487 - 1.22104i) q^{94} +(4.05451 - 0.714919i) q^{95} +(-1.69718 + 0.345802i) q^{96} +(-11.7988 + 14.0613i) q^{97} +(1.43984 - 6.85032i) q^{98} +(-5.09855 - 0.623055i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 144 q - 12 q^{9}+O(q^{10}) $ 144 * q - 12 * q^9	$ 144 q - 12 q^{9} + 12 q^{11} + 6 q^{14} + 12 q^{15} + 24 q^{21} - 60 q^{23} + 12 q^{29} - 72 q^{30} + 54 q^{35} - 12 q^{36} + 48 q^{39} + 24 q^{42} + 18 q^{49} - 60 q^{50} - 36 q^{51} + 6 q^{56} - 60 q^{57} - 36 q^{60} - 78 q^{63} + 72 q^{64} - 120 q^{65} + 36 q^{70} - 72 q^{71} - 24 q^{72} - 36 q^{74} + 66 q^{77} - 60 q^{78} - 72 q^{79} + 12 q^{84} - 72 q^{85} - 48 q^{86} - 18 q^{91} + 12 q^{92} + 24 q^{93} - 120 q^{95} + 36 q^{98} + 144 q^{99}+O(q^{100}) $ 144 * q - 12 * q^9 + 12 * q^11 + 6 * q^14 + 12 * q^15 + 24 * q^21 - 60 * q^23 + 12 * q^29 - 72 * q^30 + 54 * q^35 - 12 * q^36 + 48 * q^39 + 24 * q^42 + 18 * q^49 - 60 * q^50 - 36 * q^51 + 6 * q^56 - 60 * q^57 - 36 * q^60 - 78 * q^63 + 72 * q^64 - 120 * q^65 + 36 * q^70 - 72 * q^71 - 24 * q^72 - 36 * q^74 + 66 * q^77 - 60 * q^78 - 72 * q^79 + 12 * q^84 - 72 * q^85 - 48 * q^86 - 18 * q^91 + 12 * q^92 + 24 * q^93 - 120 * q^95 + 36 * q^98 + 144 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/378\mathbb{Z}\right)^\times$.

$n$	$29$	$325$
$\chi(n)$	$e\left(\frac{1}{18}\right)$	$-1$

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 $

$2$	−0.984808	−	0.173648i	−0.696364	−	0.122788i
$2$	−0.984808	−	0.173648i	−0.696364	−	0.122788i
$3$	0.826027	−	1.52239i	0.476907	−	0.878954i
$3$	0.826027	−	1.52239i	0.476907	−	0.878954i
$4$	0.939693	+	0.342020i	0.469846	+	0.171010i
$5$	−1.99843	+	1.67688i	−0.893726	+	0.749925i	−0.968954	−	0.247241i	$-0.920476\pi$
$5$	−1.99843	+	1.67688i	−0.893726	+	0.749925i	0.0752280	+	0.997166i	$0.476032\pi$
$6$	−1.07784	+	1.35583i	−0.440026	+	0.553514i
$7$	1.84005	+	1.90111i	0.695474	+	0.718551i
$7$	1.84005	+	1.90111i	0.695474	+	0.718551i
$8$	−0.866025	−	0.500000i	−0.306186	−	0.176777i
$9$	−1.63536	−	2.51507i	−0.545120	−	0.838358i
$10$	2.25926	−	1.30438i	0.714440	−	0.412482i
$11$	1.10056	−	1.31159i	0.331830	−	0.395459i	−0.574171	−	0.818735i	$-0.694676\pi$
$11$	1.10056	−	1.31159i	0.331830	−	0.395459i	0.906001	+	0.423276i	$0.139120\pi$
$12$	1.29690	−	1.14806i	0.374383	−	0.331417i
$13$	6.54906	−	1.15478i	1.81638	−	0.320277i	0.841039	−	0.540974i	$-0.181944\pi$
$13$	6.54906	−	1.15478i	1.81638	−	0.320277i	0.975342	+	0.220697i	$0.0708333\pi$
$14$	−1.48197	−	2.19175i	−0.396074	−	0.585769i
$15$	0.902117	+	4.42755i	0.232926	+	1.14319i
$16$	0.766044	+	0.642788i	0.191511	+	0.160697i
$17$	3.19200	+	5.52870i	0.774173	+	1.34091i	0.935258	+	0.353967i	$0.115167\pi$
$17$	3.19200	+	5.52870i	0.774173	+	1.34091i	−0.161085	+	0.986941i	$0.551499\pi$
$18$	1.17378	+	2.76084i	0.276662	+	0.650737i
$19$	−1.36673	−	0.789081i	−0.313549	−	0.181028i	0.334965	−	0.942231i	$-0.391276\pi$
$19$	−1.36673	−	0.789081i	−0.313549	−	0.181028i	−0.648513	+	0.761203i	$0.724609\pi$
$20$	−2.45144	+	0.892251i	−0.548159	+	0.199513i
$21$	4.41416	−	1.23092i	0.963250	−	0.268608i
$22$	−1.31159	+	1.10056i	−0.279632	+	0.234639i
$23$	2.89352	−	7.94988i	0.603341	−	1.65767i	−0.141114	−	0.989993i	$-0.545069\pi$
$23$	2.89352	−	7.94988i	0.603341	−	1.65767i	0.744455	−	0.667672i	$-0.232709\pi$
$24$	−1.47656	+	0.905418i	−0.301401	+	0.184818i
$25$	0.313551	−	1.77824i	0.0627102	−	0.355647i
$26$	−6.65009			−1.30419
$27$	−5.17978	+	0.412142i	−0.996849	+	0.0793167i
$28$	1.07887	+	2.41579i	0.203886	+	0.456542i
$29$	3.93278	+	0.693456i	0.730300	+	0.128772i	0.526420	−	0.850224i	$-0.323534\pi$
$29$	3.93278	+	0.693456i	0.730300	+	0.128772i	0.203879	+	0.978996i	$0.434645\pi$
$30$	−0.119576	−	4.51694i	−0.0218316	−	0.824676i
$31$	0.301809	−	0.829214i	0.0542065	−	0.148931i	−0.909634	−	0.415410i	$-0.863638\pi$
$31$	0.301809	−	0.829214i	0.0542065	−	0.148931i	0.963841	+	0.266479i	$0.0858603\pi$
$32$	−0.642788	−	0.766044i	−0.113630	−	0.135419i
$33$	−1.08767	−	2.75889i	−0.189339	−	0.480260i
$34$	−2.18346	−	5.99900i	−0.374460	−	1.02882i
$35$	−6.86515	−	0.713683i	−1.16042	−	0.120634i
$36$	−0.676530	−	2.92272i	−0.112755	−	0.487120i
$37$	−2.57189	−	4.45464i	−0.422816	−	0.732339i	0.573398	−	0.819277i	$-0.305625\pi$
$37$	−2.57189	−	4.45464i	−0.422816	−	0.732339i	−0.996214	+	0.0869382i	$0.972292\pi$
$38$	1.20894	+	1.01442i	0.196116	+	0.164561i
$39$	3.65167	−	10.9241i	0.584736	−	1.74926i
$40$	2.56913	−	0.453008i	0.406216	−	0.0716268i
$41$	−0.142302	−	0.807035i	−0.0222239	−	0.126038i	0.971677	−	0.236311i	$-0.0759385\pi$
$41$	−0.142302	−	0.807035i	−0.0222239	−	0.126038i	−0.993901	+	0.110273i	$0.964827\pi$
$42$	−4.56085	+	0.445703i	−0.703754	+	0.0687735i
$43$	6.82048	+	5.72306i	1.04011	+	0.872758i	0.992020	−	0.126084i	$-0.0402410\pi$
$43$	6.82048	+	5.72306i	1.04011	+	0.872758i	0.0480935	+	0.998843i	$0.484685\pi$
$44$	1.48277	−	0.856080i	0.223537	−	0.129059i
$45$	7.48564	+	2.28390i	1.11589	+	0.340463i
$46$	−4.23005	+	7.32665i	−0.623686	+	1.08026i
$47$	−6.60763	+	2.40498i	−0.963823	+	0.350803i	−0.775530	−	0.631310i	$-0.782517\pi$
$47$	−6.60763	+	2.40498i	−0.963823	+	0.350803i	−0.188292	+	0.982113i	$0.560295\pi$
$48$	1.61135	−	0.635261i	0.232578	−	0.0916920i
$49$	−0.228422	+	6.99627i	−0.0326318	+	0.999467i
$50$	−0.617575	+	1.69677i	−0.0873383	+	0.239960i
$51$	11.0535	−	0.292619i	1.54780	−	0.0409749i
$52$	6.54906	+	1.15478i	0.908191	+	0.160139i
$53$			6.75035i			0.927232i	0.886036	+	0.463616i	$0.153448\pi$
$53$			6.75035i			0.927232i	−0.886036	+	0.463616i	$0.846552\pi$
$54$	5.17266	+	0.493579i	0.703909	+	0.0671676i
$55$			4.46663i			0.602280i
$56$	−0.642977	−	2.56643i	−0.0859214	−	0.342954i
$57$	−2.33024	+	1.42890i	−0.308648	+	0.189262i
$58$	−3.75262	−	1.36584i	−0.492743	−	0.179344i
$59$	0.690522	−	0.579417i	0.0898983	−	0.0754336i	−0.596731	−	0.802441i	$-0.703534\pi$
$59$	0.690522	−	0.579417i	0.0898983	−	0.0754336i	0.686629	+	0.727008i	$0.259090\pi$
$60$	−0.666598	+	4.46908i	−0.0860574	+	0.576955i
$61$	−1.46604	−	4.02791i	−0.187707	−	0.515722i	0.809767	−	0.586752i	$-0.199594\pi$
$61$	−1.46604	−	4.02791i	−0.187707	−	0.515722i	−0.997474	+	0.0710302i	$0.977371\pi$
$62$	−0.441216	+	0.764208i	−0.0560344	+	0.0970545i
$63$	1.77228	−	7.73686i	0.223286	−	0.974753i
$64$	0.500000	+	0.866025i	0.0625000	+	0.108253i
$65$	−11.1514	+	13.2897i	−1.38316	+	1.64839i
$66$	0.592069	+	2.90584i	0.0728786	+	0.357685i
$67$	−2.06631	−	11.7186i	−0.252440	−	1.43166i	−0.802560	−	0.596572i	$-0.796529\pi$
$67$	−2.06631	−	11.7186i	−0.252440	−	1.43166i	0.550120	−	0.835086i	$-0.314582\pi$
$68$	1.10857	+	6.28701i	0.134434	+	0.762412i
$69$	−9.71272	−	10.9719i	−1.16927	−	1.32086i
$70$	6.63693	+	1.89496i	0.793265	+	0.226491i
$71$	2.69703	−	1.55713i	0.320079	−	0.184798i	−0.331349	−	0.943508i	$-0.607504\pi$
$71$	2.69703	−	1.55713i	0.320079	−	0.184798i	0.651428	+	0.758711i	$0.274170\pi$
$72$	0.158726	+	2.99580i	0.0187061	+	0.353058i
$73$	1.04793	+	0.605023i	0.122651	+	0.0708126i	0.560070	−	0.828445i	$-0.310774\pi$
$73$	1.04793	+	0.605023i	0.122651	+	0.0708126i	−0.437419	+	0.899258i	$0.644107\pi$
$74$	1.75928	+	4.83357i	0.204512	+	0.561891i
$75$	−2.44817	−	1.94622i	−0.282691	−	0.224730i
$76$	−1.01442	−	1.20894i	−0.116362	−	0.138675i
$77$	4.51855	−	0.321120i	0.514937	−	0.0365950i
$78$	−5.49315	+	10.1240i	−0.621977	+	1.14632i
$79$	−1.88666	+	10.6998i	−0.212266	+	1.20382i	0.673323	+	0.739349i	$0.264867\pi$
$79$	−1.88666	+	10.6998i	−0.212266	+	1.20382i	−0.885588	+	0.464471i	$0.846245\pi$
$80$	−2.60877			−0.291669
$81$	−3.65120	+	8.22610i	−0.405688	+	0.914011i
$82$			0.819485i			0.0904970i
$83$	0.170323	−	0.965952i	0.0186954	−	0.106027i	−0.974032	−	0.226410i	$-0.927301\pi$
$83$	0.170323	−	0.965952i	0.0186954	−	0.106027i	0.992728	+	0.120383i	$0.0384122\pi$
$84$	4.56896	+	0.353051i	0.498514	+	0.0385211i
$85$	−15.6500	−	5.69613i	−1.69748	−	0.617832i
$86$	−5.72306	−	6.82048i	−0.617133	−	0.735471i
$87$	4.30430	−	5.41443i	0.461469	−	0.580488i
$88$	−1.60890	+	0.585593i	−0.171510	+	0.0624244i
$89$	−1.37986	+	2.38999i	−0.146265	+	0.253339i	−0.929844	−	0.367953i	$-0.880059\pi$
$89$	−1.37986	+	2.38999i	−0.146265	+	0.253339i	0.783579	+	0.621292i	$0.213392\pi$
$90$	−6.97532	−	3.54907i	−0.735264	−	0.374105i
$91$	14.2460	+	10.3256i	1.49338	+	1.08242i
$92$	5.43804	−	6.48081i	0.566955	−	0.675671i
$93$	−1.01309	−	1.14443i	−0.105052	−	0.118671i
$94$	6.92487	−	1.22104i	0.714246	−	0.125941i
$95$	4.05451	−	0.714919i	0.415984	−	0.0733492i
$96$	−1.69718	+	0.345802i	−0.173218	+	0.0352933i
$97$	−11.7988	+	14.0613i	−1.19799	+	1.42770i	−0.321074	+	0.947054i	$0.604044\pi$
$97$	−11.7988	+	14.0613i	−1.19799	+	1.42770i	−0.876912	+	0.480650i	$0.840401\pi$
$98$	1.43984	−	6.85032i	0.145446	−	0.691987i
$99$	−5.09855	−	0.623055i	−0.512424	−	0.0626194i
$100$	0.902835	−	1.56376i	0.0902835	−	0.156376i
$101$	−1.77454	+	0.645878i	−0.176573	+	0.0642673i	−0.428794	−	0.903402i	$-0.641061\pi$
$101$	−1.77454	+	0.645878i	−0.176573	+	0.0642673i	0.252221	+	0.967670i	$0.418839\pi$
$102$	−10.9364	−	1.63125i	−1.08287	−	0.161518i
$103$	−11.5732	−	13.7924i	−1.14034	−	1.35900i	−0.923866	−	0.382717i	$-0.874989\pi$
$103$	−11.5732	−	13.7924i	−1.14034	−	1.35900i	−0.216475	−	0.976288i	$-0.569456\pi$
$104$	−6.24904	−	2.27446i	−0.612768	−	0.223029i
$105$	−6.75731	+	9.86194i	−0.659446	+	0.962427i
$106$	1.17219	−	6.64779i	0.113853	−	0.645691i
$107$			12.3862i			1.19742i	0.800967	+	0.598708i	$0.204319\pi$
$107$			12.3862i			1.19742i	−0.800967	+	0.598708i	$0.795681\pi$
$108$	−5.00836	−	1.38430i	−0.481930	−	0.133205i
$109$	−5.18562			−0.496692			−0.248346	−	0.968671i	$-0.579887\pi$
$109$	−5.18562			−0.496692			−0.248346	+	0.968671i	$0.579887\pi$
$110$	0.775622	−	4.39877i	0.0739526	−	0.419406i
$111$	−8.90617	+	0.235772i	−0.845336	+	0.0223785i
$112$	0.187552	+	2.63910i	0.0177220	+	0.249371i
$113$	−11.9051	−	14.1880i	−1.11994	−	1.33469i	−0.936098	−	0.351739i	$-0.885591\pi$
$113$	−11.9051	−	14.1880i	−1.11994	−	1.33469i	−0.183843	−	0.982956i	$-0.558854\pi$
$114$	2.54297	−	1.00254i	0.238171	−	0.0938969i
$115$	7.54853	+	20.7394i	0.703904	+	1.93396i
$116$	3.45843	+	1.99673i	0.321107	+	0.185391i
$117$	−13.6144	−	14.5829i	−1.25865	−	1.34819i
$118$	−0.780646	+	0.450706i	−0.0718643	+	0.0414909i
$119$	−4.63722	+	16.2414i	−0.425093	+	1.48885i
$120$	1.43252	−	4.28543i	0.130770	−	0.391204i
$121$	1.40108	+	7.94593i	0.127371	+	0.722357i
$122$	0.744328	+	4.22130i	0.0673883	+	0.382178i
$123$	−1.34617	−	0.449993i	−0.121380	−	0.0405745i
$124$	0.567216	−	0.675982i	0.0509375	−	0.0607049i
$125$	−4.16663	−	7.21682i	−0.372675	−	0.645492i
$126$	−3.08885	+	7.31157i	−0.275176	+	0.651366i
$127$	1.15030	−	1.99238i	0.102073	−	0.176796i	−0.810466	−	0.585786i	$-0.800786\pi$
$127$	1.15030	−	1.99238i	0.102073	−	0.176796i	0.912539	+	0.408991i	$0.134119\pi$
$128$	−0.342020	−	0.939693i	−0.0302306	−	0.0830579i
$129$	14.3466	−	5.65605i	1.26315	−	0.497987i
$130$	13.2897	−	11.1514i	1.16559	−	0.978044i
$131$	13.0034	+	4.73283i	1.13611	+	0.413510i	0.840506	−	0.541802i	$-0.182258\pi$
$131$	13.0034	+	4.73283i	1.13611	+	0.413510i	0.295602	+	0.955311i	$0.404480\pi$
$132$	−0.0784792	−	2.96451i	−0.00683073	−	0.258027i
$133$	−1.01472	−	4.05025i	−0.0879875	−	0.351201i
$134$			11.8994i			1.02795i
$135$	9.66033	−	9.50953i	0.831429	−	0.818450i
$136$		−	6.38400i		−	0.547423i
$137$	−9.76310	−	1.72150i	−0.834118	−	0.147078i	−0.259751	−	0.965676i	$-0.583641\pi$
$137$	−9.76310	−	1.72150i	−0.834118	−	0.147078i	−0.574367	+	0.818598i	$0.694752\pi$
$138$	7.65991	+	12.4918i	0.652055	+	1.06337i
$139$	−2.00774	+	5.51622i	−0.170294	+	0.467879i	−0.995254	−	0.0973121i	$-0.968976\pi$
$139$	−2.00774	+	5.51622i	−0.170294	+	0.467879i	0.824960	+	0.565191i	$0.191198\pi$
$140$	−6.20704	−	3.01866i	−0.524591	−	0.255124i
$141$	−1.79675	+	12.0460i	−0.151314	+	1.01446i
$142$	−2.92645	+	1.06514i	−0.245582	+	0.0893846i
$143$	5.69301	−	9.86057i	0.476073	−	0.824583i
$144$	0.363900	−	2.97785i	0.0303250	−	0.248154i
$145$	−9.02225	+	5.20900i	−0.749257	+	0.432584i
$146$	−0.926949	−	0.777803i	−0.0767148	−	0.0643714i
$147$	10.4624	+	6.12686i	0.862924	+	0.505335i
$148$	−0.893208	−	5.06563i	−0.0734212	−	0.416393i
$149$	2.92838	−	0.516353i	0.239903	−	0.0423013i	−0.0524040	−	0.998626i	$-0.516688\pi$
$149$	2.92838	−	0.516353i	0.239903	−	0.0423013i	0.292307	+	0.956325i	$0.405577\pi$
$150$	2.07302	+	2.34177i	0.169262	+	0.191205i
$151$	−1.27898	−	1.07319i	−0.104082	−	0.0873353i	0.589262	−	0.807942i	$-0.299419\pi$
$151$	−1.27898	−	1.07319i	−0.104082	−	0.0873353i	−0.693344	+	0.720607i	$0.743863\pi$
$152$	0.789081	+	1.36673i	0.0640029	+	0.110856i
$153$	8.68503	−	17.0695i	0.702143	−	1.37999i
$154$	−4.50567	−	0.468397i	−0.363077	−	0.0377445i
$155$	0.787350	+	2.16323i	0.0632415	+	0.173755i
$156$	7.16772	−	9.01636i	0.573877	−	0.721887i
$157$	−4.83620	−	5.76356i	−0.385971	−	0.459983i	0.537718	−	0.843125i	$-0.319286\pi$
$157$	−4.83620	−	5.76356i	−0.385971	−	0.459983i	−0.923689	+	0.383142i	$0.874842\pi$
$158$	3.71600	−	10.2096i	0.295629	−	0.812233i
$159$	10.2767	+	5.57597i	0.814994	+	0.442203i
$160$	2.56913	+	0.453008i	0.203108	+	0.0358134i
$161$	20.4378	−	9.12730i	1.61073	−	0.719332i
$162$	5.02417	−	7.46711i	0.394736	−	0.586671i
$163$	−7.10349			−0.556388			−0.278194	−	0.960525i	$-0.589736\pi$
$163$	−7.10349			−0.556388			−0.278194	+	0.960525i	$0.589736\pi$
$164$	0.142302	−	0.807035i	0.0111119	−	0.0630189i
$165$	6.79996	+	3.68955i	0.529376	+	0.287231i
$166$	−0.335471	+	0.921700i	−0.0260376	+	0.0715378i
$167$	9.09652	−	7.63288i	0.703910	−	0.590650i	−0.218973	−	0.975731i	$-0.570271\pi$
$167$	9.09652	−	7.63288i	0.703910	−	0.590650i	0.922883	+	0.385080i	$0.125826\pi$
$168$	−4.43824	−	1.14108i	−0.342417	−	0.0880361i
$169$	29.3406	−	10.6791i	2.25697	−	0.821470i
$170$	14.4231	+	8.32718i	1.10620	+	0.638666i
$171$	0.250495	+	4.72785i	0.0191559	+	0.361548i
$172$	4.45175	+	7.71066i	0.339443	+	0.587932i
$173$	4.23871	+	3.55670i	0.322263	+	0.270411i	0.789539	−	0.613701i	$-0.210320\pi$
$173$	4.23871	+	3.55670i	0.322263	+	0.270411i	−0.467275	+	0.884112i	$0.654764\pi$
$174$	−5.17911	+	4.58474i	−0.392627	+	0.347568i
$175$	3.95757	−	2.67595i	0.299164	−	0.202283i
$176$	1.68615	−	0.297313i	0.127098	−	0.0224108i
$177$	−0.311710	−	1.52986i	−0.0234296	−	0.114991i
$178$	1.77392	−	2.11407i	0.132961	−	0.158457i
$179$	16.3924	−	9.46415i	1.22522	−	0.707384i	0.259197	−	0.965824i	$-0.416542\pi$
$179$	16.3924	−	9.46415i	1.22522	−	0.707384i	0.966027	+	0.258441i	$0.0832087\pi$
$180$	6.25306	+	4.70640i	0.466076	+	0.350794i
$181$	−11.2216	−	6.47882i	−0.834099	−	0.481567i	0.0211554	−	0.999776i	$-0.493266\pi$
$181$	−11.2216	−	6.47882i	−0.834099	−	0.481567i	−0.855254	+	0.518209i	$0.826599\pi$
$182$	−12.2365	−	12.6425i	−0.907030	−	0.937127i
$183$	−7.34306	−	1.09527i	−0.542814	−	0.0809650i
$184$	−6.48081	+	5.43804i	−0.477771	+	0.400898i
$185$	12.6097	+	4.58954i	0.927081	+	0.337430i
$186$	0.798969	+	1.30296i	0.0585832	+	0.0955376i
$187$	10.7644	+	1.89805i	0.787168	+	0.138799i
$188$	−7.03170			−0.512839
$189$	−10.3146	−	9.08896i	−0.750276	−	0.661125i
$190$	−4.11706			−0.298683
$191$	1.21312	+	0.213906i	0.0877784	+	0.0154777i	0.217365	−	0.976090i	$-0.430254\pi$
$191$	1.21312	+	0.213906i	0.0877784	+	0.0154777i	−0.129586	+	0.991568i	$0.541365\pi$
$192$	1.73144	−	0.0458363i	0.124956	−	0.00330795i
$193$	−24.6718	−	8.97980i	−1.77591	−	0.646380i	−0.999877	−	0.0156930i	$-0.995005\pi$
$193$	−24.6718	−	8.97980i	−1.77591	−	0.646380i	−0.776037	−	0.630687i	$-0.782773\pi$
$194$	14.0613	−	11.7988i	1.00954	−	0.847104i
$195$	11.0208	+	27.9545i	0.789219	+	2.00187i
$196$	−2.60751	+	6.49622i	−0.186251	+	0.464016i
$197$	9.13794	+	5.27579i	0.651051	+	0.375884i	0.788859	−	0.614575i	$-0.210672\pi$
$197$	9.13794	+	5.27579i	0.651051	+	0.375884i	−0.137808	+	0.990459i	$0.544006\pi$
$198$	4.91290	+	1.49894i	0.349145	+	0.106525i
$199$	−5.90158	+	3.40728i	−0.418352	+	0.241536i	−0.694372	−	0.719616i	$-0.744318\pi$
$199$	−5.90158	+	3.40728i	−0.418352	+	0.241536i	0.276020	+	0.961152i	$0.410984\pi$
$200$	−1.16066	+	1.38322i	−0.0820712	+	0.0978086i
$201$	−19.5472	−	6.53416i	−1.37875	−	0.460884i
$202$	1.85973	−	0.327921i	0.130850	−	0.0230724i
$203$	5.91819	+	8.75264i	0.415376	+	0.614315i
$204$	10.4870	+	3.50556i	0.734237	+	0.245438i
$205$	1.63769	+	1.37418i	0.114381	+	0.0959770i
$206$	9.00235	+	15.5925i	0.627223	+	1.08638i
$207$	−24.7265	+	5.72350i	−1.71861	+	0.397811i
$208$	5.75914	+	3.32504i	0.399325	+	0.230550i
$209$	−2.53911	+	0.924161i	−0.175634	+	0.0639255i
$210$	8.36716	−	8.53872i	0.577389	−	0.589228i
$211$	0.224300	−	0.188210i	0.0154414	−	0.0129569i	−0.635034	−	0.772484i	$-0.719014\pi$
$211$	0.224300	−	0.188210i	0.0154414	−	0.0129569i	0.650476	+	0.759527i	$0.274570\pi$
$212$	−2.30875	+	6.34325i	−0.158566	+	0.435656i
$213$	−0.142746	−	5.39217i	−0.00978083	−	0.369466i
$214$	2.15084	−	12.1980i	0.147028	−	0.833838i
$215$	−23.2272			−1.58408
$216$	4.69189	+	2.23297i	0.319243	+	0.151934i
$217$	2.13177	−	0.952025i	0.144714	−	0.0646276i
$218$	5.10683	+	0.900473i	0.345878	+	0.0609877i
$219$	1.78670	−	1.09560i	0.120734	−	0.0740336i
$220$	−1.52768	+	4.19726i	−0.102996	+	0.282979i
$221$	27.2890	+	32.5218i	1.83566	+	2.18765i
$222$	8.81180	+	1.31435i	0.591410	+	0.0882134i
$223$	−5.80906	−	15.9603i	−0.389003	−	1.06878i	−0.967451	−	0.253058i	$-0.918564\pi$
$223$	−5.80906	−	15.9603i	−0.389003	−	1.06878i	0.578448	−	0.815719i	$-0.303659\pi$
$224$	0.273571	−	2.63157i	0.0182787	−	0.175829i
$225$	−4.98517	+	2.11945i	−0.332345	+	0.141297i
$226$	9.26056	+	16.0398i	0.616003	+	1.06695i
$227$	−20.3610	−	17.0849i	−1.35141	−	1.13397i	−0.978534	−	0.206085i	$-0.933928\pi$
$227$	−20.3610	−	17.0849i	−1.35141	−	1.13397i	−0.372874	−	0.927882i	$-0.621628\pi$
$228$	−2.67842	+	0.545732i	−0.177383	+	0.0361420i
$229$	0.678629	−	0.119661i	0.0448451	−	0.00790739i	−0.151181	−	0.988506i	$-0.548308\pi$
$229$	0.678629	−	0.119661i	0.0448451	−	0.00790739i	0.196026	+	0.980599i	$0.437196\pi$
$230$	−3.83249	−	21.7351i	−0.252707	−	1.43317i
$231$	3.24358	−	7.14427i	0.213412	−	0.470058i
$232$	−3.05916	−	2.56694i	−0.200844	−	0.168528i
$233$	−4.56619	+	2.63629i	−0.299141	+	0.172709i	−0.642057	−	0.766657i	$-0.721919\pi$
$233$	−4.56619	+	2.63629i	−0.299141	+	0.172709i	0.342916	+	0.939366i	$0.388585\pi$
$234$	10.8753	+	16.7255i	0.710940	+	1.09338i
$235$	9.17203	−	15.8864i	0.598318	−	1.03632i
$236$	0.847050	−	0.308301i	0.0551383	−	0.0200687i
$237$	14.7308	+	11.7105i	0.956871	+	0.760682i
$238$	7.38707	−	15.1894i	0.478832	−	0.984585i
$239$	7.71216	−	21.1890i	0.498858	−	1.37060i	−0.393522	−	0.919315i	$-0.628743\pi$
$239$	7.71216	−	21.1890i	0.498858	−	1.37060i	0.892380	−	0.451285i	$-0.149034\pi$
$240$	−2.15491	+	3.97157i	−0.139099	+	0.256364i
$241$	−23.0229	−	4.05955i	−1.48303	−	0.261499i	−0.627244	−	0.778823i	$-0.715817\pi$
$241$	−23.0229	−	4.05955i	−1.48303	−	0.261499i	−0.855790	+	0.517324i	$0.826928\pi$
$242$		−	8.06851i		−	0.518663i
$243$	9.50737	+	12.3535i	0.609898	+	0.792480i
$244$		−	4.28642i		−	0.274410i
$245$	−11.2754	−	14.3646i	−0.720362	−	0.917721i
$246$	1.24758	+	0.676917i	0.0795427	+	0.0431586i
$247$	−9.86199	−	3.58947i	−0.627503	−	0.228393i
$248$	−0.675982	+	0.567216i	−0.0429249	+	0.0360182i
$249$	−1.32987	−	1.05720i	−0.0842768	−	0.0669974i
$250$	2.85014	+	7.83071i	0.180259	+	0.495258i
$251$	−9.14058	+	15.8320i	−0.576949	+	0.999304i	0.418878	+	0.908042i	$0.362423\pi$
$251$	−9.14058	+	15.8320i	−0.576949	+	0.999304i	−0.995827	+	0.0912619i	$0.970910\pi$
$252$	4.31156	−	6.66412i	0.271603	−	0.419800i
$253$	−7.24251	−	12.5444i	−0.455333	−	0.788660i
$254$	−1.47880	+	1.76237i	−0.0927883	+	0.110581i
$255$	−21.5991	+	19.1203i	−1.35259	+	1.19736i
$256$	0.173648	+	0.984808i	0.0108530	+	0.0615505i
$257$	0.169038	+	0.958665i	0.0105443	+	0.0597999i	0.989626	−	0.143668i	$-0.0458898\pi$
$257$	0.169038	+	0.958665i	0.0105443	+	0.0597999i	−0.979082	+	0.203468i	$0.934779\pi$
$258$	−15.1108	+	3.07885i	−0.940760	+	0.191681i
$259$	3.73635	−	13.0862i	0.232165	−	0.813138i
$260$	−15.0243	+	8.67427i	−0.931766	+	0.537955i
$261$	−4.68742	−	11.0253i	−0.290144	−	0.682449i
$262$	−11.9840	−	6.91894i	−0.740371	−	0.427454i
$263$	7.50286	+	20.6139i	0.462646	+	1.27111i	0.923488	+	0.383628i	$0.125325\pi$
$263$	7.50286	+	20.6139i	0.462646	+	1.27111i	−0.460842	+	0.887482i	$0.652452\pi$
$264$	−0.437495	+	2.93310i	−0.0269259	+	0.180520i
$265$	−11.3195	−	13.4901i	−0.695354	−	0.828691i
$266$	0.295988	+	4.16492i	0.0181482	+	0.255368i
$267$	2.49871	+	4.07489i	0.152918	+	0.249379i
$268$	2.06631	−	11.7186i	0.126220	−	0.715829i
$269$	11.0618			0.674447			0.337224	−	0.941425i	$-0.390512\pi$
$269$	11.0618			0.674447			0.337224	+	0.941425i	$0.390512\pi$
$270$	−11.1649	+	7.68756i	−0.679473	+	0.467850i
$271$			5.87429i			0.356838i	0.983955	+	0.178419i	$0.0570982\pi$
$271$			5.87429i			0.356838i	−0.983955	+	0.178419i	$0.942902\pi$
$272$	−1.10857	+	6.28701i	−0.0672169	+	0.381206i
$273$	27.4872	−	13.1587i	1.66360	−	0.796401i
$274$	9.31584	+	3.39069i	0.562791	+	0.204839i
$275$	−1.98724	−	2.36830i	−0.119835	−	0.142814i
$276$	−5.37436	−	13.6322i	−0.323499	−	0.820559i
$277$	9.97230	−	3.62962i	0.599177	−	0.218083i	−0.0245838	−	0.999698i	$-0.507826\pi$
$277$	9.97230	−	3.62962i	0.599177	−	0.218083i	0.623761	+	0.781615i	$0.285604\pi$
$278$	2.93512	−	5.08377i	0.176037	−	0.304904i
$279$	−2.57910	+	0.596991i	−0.154407	+	0.0357409i
$280$	5.58856	+	4.05064i	0.333980	+	0.242072i
$281$	−0.941246	+	1.12173i	−0.0561500	+	0.0669170i	−0.793388	−	0.608716i	$-0.791685\pi$
$281$	−0.941246	+	1.12173i	−0.0561500	+	0.0669170i	0.737238	+	0.675633i	$0.236129\pi$
$282$	3.86122	−	11.5510i	0.229932	−	0.687851i
$283$	5.63290	−	0.993233i	0.334841	−	0.0590416i	−0.00369981	−	0.999993i	$-0.501178\pi$
$283$	5.63290	−	0.993233i	0.334841	−	0.0590416i	0.338541	+	0.940952i	$0.390067\pi$
$284$	3.06695	−	0.540786i	0.181990	−	0.0320898i
$285$	2.26074	−	6.76310i	0.133915	−	0.400611i
$286$	−7.31879	+	8.72219i	−0.432769	+	0.515754i
$287$	1.27242	−	1.75552i	0.0751085	−	0.103625i
$288$	−0.875469	+	2.86942i	−0.0515875	+	0.169082i
$289$	−11.8777	+	20.5728i	−0.698689	+	1.21016i
$290$	9.78971	−	3.56316i	0.574872	−	0.209236i
$291$	11.6606	+	29.5774i	0.683559	+	1.73386i
$292$	0.777803	+	0.926949i	0.0455175	+	0.0542456i
$293$	−19.9297	−	7.25381i	−1.16430	−	0.423772i	−0.313671	−	0.949532i	$-0.601559\pi$
$293$	−19.9297	−	7.25381i	−1.16430	−	0.423772i	−0.850633	+	0.525760i	$0.823781\pi$
$294$	−9.23953	−	7.85055i	−0.538860	−	0.457853i
$295$	−0.408347	+	2.31585i	−0.0237749	+	0.134834i
$296$			5.14378i			0.298976i
$297$	−5.16007	+	7.24734i	−0.299418	+	0.420533i
$298$	−2.97356			−0.172254
$299$	9.76950	−	55.4056i	0.564985	−	3.20419i
$300$	−1.63488	−	2.66617i	−0.0943901	−	0.153932i
$301$	1.66987	+	23.4972i	0.0962499	+	1.35436i
$302$	1.07319	+	1.27898i	0.0617554	+	0.0735972i
$303$	−0.482534	+	3.23505i	−0.0277208	+	0.185849i
$304$	−0.539763	−	1.48299i	−0.0309575	−	0.0850551i
$305$	9.68413	+	5.59113i	0.554511	+	0.320147i
$306$	−11.5172	+	15.3021i	−0.658393	+	0.874761i
$307$	9.39899	−	5.42651i	0.536429	−	0.309707i	−0.207202	−	0.978298i	$-0.566436\pi$
$307$	9.39899	−	5.42651i	0.536429	−	0.309707i	0.743630	+	0.668591i	$0.233102\pi$
$308$	4.35588	+	1.24368i	0.248199	+	0.0708654i
$309$	−30.5572	+	6.22606i	−1.73834	+	0.354188i
$310$	−0.399748	−	2.26709i	−0.0227042	−	0.128762i
$311$	−1.03703	−	5.88131i	−0.0588048	−	0.333499i	0.941186	−	0.337890i	$-0.109713\pi$
$311$	−1.03703	−	5.88131i	−0.0588048	−	0.333499i	−0.999990	+	0.00439151i	$0.998602\pi$
$312$	−8.62450	+	7.63472i	−0.488266	+	0.432231i
$313$	2.45451	−	2.92517i	0.138737	−	0.165340i	−0.692202	−	0.721704i	$-0.743359\pi$
$313$	2.45451	−	2.92517i	0.138737	−	0.165340i	0.830939	+	0.556363i	$0.187804\pi$
$314$	3.76190	+	6.51580i	0.212296	+	0.367708i
$315$	9.43203	+	18.4335i	0.531435	+	1.03861i
$316$	−5.43242	+	9.40923i	−0.305598	+	0.529311i
$317$	−6.10186	−	16.7647i	−0.342715	−	0.941601i	−0.984603	−	0.174803i	$-0.944071\pi$
$317$	−6.10186	−	16.7647i	−0.342715	−	0.941601i	0.641889	−	0.766798i	$-0.278151\pi$
$318$	−9.15230	−	7.27578i	−0.513235	−	0.408006i
$319$	5.23778	−	4.39502i	0.293259	−	0.246074i
$320$	−2.45144	−	0.892251i	−0.137040	−	0.0498784i
$321$	18.8566	+	10.2313i	1.05247	+	0.571056i
$322$	−21.7123	+	5.43965i	−1.20998	+	0.303140i
$323$		−	10.0750i		−	0.560587i
$324$	−6.24449	+	6.48123i	−0.346916	+	0.360068i
$325$		−	12.0079i		−	0.666076i
$326$	6.99557	+	1.23351i	0.387449	+	0.0683177i
$327$	−4.28346	+	7.89454i	−0.236876	+	0.436569i
$328$	−0.280280	+	0.770064i	−0.0154759	+	0.0425197i
$329$	−16.7305	−	8.13654i	−0.922383	−	0.448582i
$330$	−6.05597	−	4.81430i	−0.333370	−	0.265019i
$331$	19.6490	−	7.15164i	1.08000	−	0.393090i	0.260095	−	0.965583i	$-0.416246\pi$
$331$	19.6490	−	7.15164i	1.08000	−	0.393090i	0.819909	+	0.572493i	$0.194024\pi$
$332$	0.490426	−	0.849443i	0.0269156	−	0.0466193i
$333$	−6.99779	+	13.7534i	−0.383477	+	0.753684i
$334$	−10.2838	+	5.93733i	−0.562702	+	0.324876i
$335$	23.7801	+	19.9539i	1.29925	+	1.09020i
$336$	4.17266	+	1.89443i	0.227637	+	0.103350i
$337$	4.43907	+	25.1752i	0.241812	+	1.37138i	0.827782	+	0.561050i	$0.189602\pi$
$337$	4.43907	+	25.1752i	0.241812	+	1.37138i	−0.585970	+	0.810333i	$0.699286\pi$
$338$	−30.7493	+	5.42193i	−1.67254	+	0.294914i
$339$	−31.4337	+	6.40464i	−1.70724	+	0.347852i
$340$	−12.7580	−	10.7052i	−0.691899	−	0.580572i
$341$	−0.755432	−	1.30845i	−0.0409089	−	0.0708563i
$342$	0.574293	−	4.69952i	0.0310542	−	0.254121i
$343$	−13.7210	+	12.4392i	−0.740863	+	0.671656i
$344$	−3.04518	−	8.36655i	−0.164185	−	0.451094i
$345$	37.8088	+	5.63948i	2.03556	+	0.303619i
$346$	−3.55670	−	4.23871i	−0.191210	−	0.227875i
$347$	1.84812	−	5.07767i	0.0992124	−	0.272584i	−0.880150	−	0.474695i	$-0.842558\pi$
$347$	1.84812	−	5.07767i	0.0992124	−	0.272584i	0.979362	+	0.202112i	$0.0647804\pi$
$348$	5.89656	−	3.61574i	0.316089	−	0.193824i
$349$	−13.2466	−	2.33574i	−0.709076	−	0.125029i	−0.192533	−	0.981291i	$-0.561670\pi$
$349$	−13.2466	−	2.33574i	−0.709076	−	0.125029i	−0.516543	+	0.856261i	$0.672781\pi$
$350$	−4.36212	+	1.94807i	−0.233165	+	0.104129i
$351$	−33.4468	+	8.68062i	−1.78526	+	0.463337i
$352$	−1.71216			−0.0912584
$353$	−1.52656	+	8.65757i	−0.0812507	+	0.460796i	0.916852	+	0.399227i	$0.130721\pi$
$353$	−1.52656	+	8.65757i	−0.0812507	+	0.460796i	−0.998103	+	0.0615688i	$0.980390\pi$
$354$	0.0413174	+	1.56074i	0.00219600	+	0.0829527i
$355$	−2.77871	+	7.63443i	−0.147478	+	0.405193i
$356$	−2.11407	+	1.77392i	−0.112046	+	0.0940175i
$357$	20.8954	+	20.4755i	1.10590	+	1.08368i
$358$	−17.7868	+	6.47386i	−0.940060	+	0.342154i
$359$	−23.4946	−	13.5646i	−1.24000	−	0.715914i	−0.270905	−	0.962606i	$-0.587323\pi$
$359$	−23.4946	−	13.5646i	−1.24000	−	0.715914i	−0.969094	+	0.246692i	$0.920656\pi$
$360$	−5.34081	−	5.72073i	−0.281485	−	0.301509i
$361$	−8.25470	−	14.2976i	−0.434458	−	0.752503i
$362$	9.92613	+	8.32901i	0.521706	+	0.437763i
$363$	13.2542	+	4.43055i	0.695663	+	0.232544i
$364$	9.85525	+	14.5753i	0.516555	+	0.763954i
$365$	−3.10877	+	0.548160i	−0.162721	+	0.0286920i
$366$	7.04131	+	2.35374i	0.368055	+	0.123032i
$367$	14.0714	−	16.7696i	0.734521	−	0.875368i	−0.261434	−	0.965221i	$-0.584195\pi$
$367$	14.0714	−	16.7696i	0.734521	−	0.875368i	0.995955	+	0.0898533i	$0.0286398\pi$
$368$	7.32665	−	4.23005i	0.381928	−	0.220506i
$369$	−1.79704	+	1.67769i	−0.0935501	+	0.0873373i
$370$	−11.6211	−	6.70946i	−0.604154	−	0.348808i
$371$	−12.8331	+	12.4210i	−0.666263	+	0.644865i
$372$	−0.560574	−	1.42190i	−0.0290644	−	0.0737223i
$373$	3.63872	−	3.05325i	0.188406	−	0.158091i	−0.543706	−	0.839276i	$-0.682979\pi$
$373$	3.63872	−	3.05325i	0.188406	−	0.158091i	0.732112	+	0.681185i	$0.238535\pi$
$374$	−10.2712	−	3.73843i	−0.531113	−	0.193309i
$375$	−14.4286	+	0.381966i	−0.745089	+	0.0197247i
$376$	6.92487	+	1.22104i	0.357123	+	0.0629704i
$377$	26.5568			1.36775
$378$	8.57961	+	10.7420i	0.441287	+	0.552508i
$379$	25.0501			1.28674			0.643368	−	0.765557i	$-0.277537\pi$
$379$	25.0501			1.28674			0.643368	+	0.765557i	$0.277537\pi$
$380$	4.05451	+	0.714919i	0.207992	+	0.0366746i
$381$	−2.08301	−	3.39698i	−0.106716	−	0.174032i
$382$	−1.15755	−	0.421312i	−0.0592252	−	0.0215562i
$383$	−8.07952	+	6.77952i	−0.412844	+	0.346417i	−0.825433	−	0.564500i	$-0.809069\pi$
$383$	−8.07952	+	6.77952i	−0.412844	+	0.346417i	0.412589	+	0.910917i	$0.364625\pi$
$384$	−1.71310	−	0.255522i	−0.0874212	−	0.0130396i
$385$	−8.49154	+	8.21882i	−0.432769	+	0.418870i
$386$	22.7376	+	13.1276i	1.15732	+	0.668176i
$387$	3.23999	−	26.5133i	0.164698	−	1.34775i
$388$	−15.8965	+	9.17783i	−0.807021	+	0.465934i
$389$	−14.6938	+	17.5114i	−0.745007	+	0.887865i	−0.996802	−	0.0799161i	$-0.974535\pi$
$389$	−14.6938	+	17.5114i	−0.745007	+	0.887865i	0.251795	+	0.967781i	$0.418979\pi$
$390$	−5.99916	−	29.4436i	−0.303779	−	1.49093i
$391$	53.1887	−	9.37860i	2.68987	−	0.474296i
$392$	3.69596	−	5.94474i	0.186674	−	0.300255i
$393$	17.9464	−	15.8868i	0.905274	−	0.801381i
$394$	−8.08298	−	6.78242i	−0.407215	−	0.341694i
$395$	−14.1719	−	24.5465i	−0.713067	−	1.23507i
$396$	−4.57797	−	2.32929i	−0.230052	−	0.117051i
$397$	14.8355	+	8.56528i	0.744572	+	0.429879i	0.823729	−	0.566983i	$-0.191890\pi$
$397$	14.8355	+	8.56528i	0.744572	+	0.429879i	−0.0791571	+	0.996862i	$0.525223\pi$
$398$	6.40359	−	2.33072i	0.320983	−	0.116828i
$399$	−7.00425	−	1.80081i	−0.350651	−	0.0901531i
$400$	1.38322	−	1.16066i	0.0691612	−	0.0580331i
$401$	−7.32564	+	20.1270i	−0.365825	+	1.00510i	0.611107	+	0.791548i	$0.290724\pi$
$401$	−7.32564	+	20.1270i	−0.365825	+	1.00510i	−0.976932	+	0.213549i	$0.931498\pi$
$402$	18.1156	+	9.82922i	0.903522	+	0.490237i
$403$	1.01901	−	5.77909i	0.0507605	−	0.287877i
$404$	−1.88842			−0.0939525
$405$	−6.49755	−	22.5619i	−0.322866	−	1.12111i
$406$	−4.30840	−	9.64735i	−0.213822	−	0.478790i
$407$	−8.67318	−	1.52932i	−0.429913	−	0.0758053i
$408$	−9.71895	−	5.27335i	−0.481160	−	0.261070i
$409$	−4.78260	+	13.1401i	−0.236484	+	0.649735i	0.763508	+	0.645798i	$0.223475\pi$
$409$	−4.78260	+	13.1401i	−0.236484	+	0.649735i	−0.999992	+	0.00393670i	$0.998747\pi$
$410$	−1.37418	−	1.63769i	−0.0678660	−	0.0808795i
$411$	−10.6854	+	13.4413i	−0.527071	+	0.663009i
$412$	−6.15797	−	16.9189i	−0.303381	−	0.833533i
$413$	2.37213	+	0.246600i	0.116725	+	0.0121344i
$414$	25.3447	−	1.34284i	1.24563	−	0.0659969i
$415$	1.27941	+	2.21600i	0.0628037	+	0.108779i
$416$	−5.09426	−	4.27459i	−0.249767	−	0.209579i
$417$	6.73940	+	7.61311i	0.330030	+	0.372816i
$418$	2.66101	−	0.469209i	0.130154	−	0.0229497i
$419$	0.291638	+	1.65396i	0.0142475	+	0.0808014i	0.991102	−	0.133101i	$-0.0424936\pi$
$419$	0.291638	+	1.65396i	0.0142475	+	0.0808014i	−0.976855	+	0.213903i	$0.931382\pi$
$420$	−9.72277	+	6.95606i	−0.474423	+	0.339421i
$421$	22.7105	+	19.0564i	1.10684	+	0.928752i	0.997866	−	0.0652923i	$-0.0207980\pi$
$421$	22.7105	+	19.0564i	1.10684	+	0.928752i	0.108977	+	0.994044i	$0.465242\pi$
$422$	−0.253575	+	0.146401i	−0.0123438	+	0.00712671i
$423$	16.8546	+	12.6857i	0.819497	+	0.616799i
$424$	3.37517	−	5.84597i	0.163913	−	0.283906i
$425$	10.8322	−	3.94260i	0.525439	−	0.191244i
$426$	−0.795763	+	5.33504i	−0.0385549	+	0.258484i
$427$	4.95991	−	10.1987i	0.240027	−	0.493548i
$428$	−4.23632	+	11.6392i	−0.204770	+	0.562602i
$429$	−10.3091	−	16.8121i	−0.497728	−	0.811695i
$430$	22.8743	+	4.03336i	1.10310	+	0.194506i
$431$		−	4.02188i		−	0.193727i	−0.995298	−	0.0968635i	$-0.969119\pi$
$431$		−	4.02188i		−	0.193727i	0.995298	−	0.0968635i	$-0.0308810\pi$
$432$	−4.23286	−	3.01378i	−0.203654	−	0.145001i
$433$			13.4318i			0.645489i	0.946486	+	0.322744i	$0.104605\pi$
$433$			13.4318i			0.645489i	−0.946486	+	0.322744i	$0.895395\pi$
$434$	−2.26470	+	0.567383i	−0.108709	+	0.0272353i
$435$	0.477523	+	18.0382i	0.0228955	+	0.864864i
$436$	−4.87288	−	1.77358i	−0.233369	−	0.0849393i
$437$	−10.2278	+	8.58211i	−0.489260	+	0.410538i
$438$	−1.94981	+	0.768695i	−0.0931653	+	0.0367297i
$439$	−0.194851	−	0.535350i	−0.00929975	−	0.0255509i	0.934956	−	0.354764i	$-0.115439\pi$
$439$	−0.194851	−	0.535350i	−0.00929975	−	0.0255509i	−0.944256	+	0.329213i	$0.893217\pi$
$440$	2.23331	−	3.86821i	0.106469	−	0.184410i
$441$	17.9697	−	10.8669i	0.855700	−	0.517473i
$442$	−21.2271	−	36.7664i	−1.00967	−	1.74880i
$443$	20.8026	−	24.7916i	0.988360	−	1.17788i	0.00431031	−	0.999991i	$-0.498628\pi$
$443$	20.8026	−	24.7916i	0.988360	−	1.17788i	0.984050	−	0.177891i	$-0.0569276\pi$
$444$	−8.44970	−	2.82454i	−0.401005	−	0.134047i
$445$	−1.25018	−	7.09011i	−0.0592641	−	0.336103i
$446$	2.94934	+	16.7265i	0.139655	+	0.792023i
$447$	1.63283	−	4.88467i	0.0772303	−	0.231037i
$448$	−0.726382	+	2.54409i	−0.0343183	+	0.120197i
$449$	6.83982	−	3.94897i	0.322791	−	0.186364i	−0.329845	−	0.944035i	$-0.606996\pi$
$449$	6.83982	−	3.94897i	0.322791	−	0.186364i	0.652636	+	0.757672i	$0.273663\pi$
$450$	5.27747	−	1.22159i	0.248782	−	0.0575863i
$451$	−1.21511	−	0.701545i	−0.0572174	−	0.0330345i
$452$	−6.33459	−	17.4042i	−0.297954	−	0.818622i
$453$	−2.69030	+	1.06063i	−0.126401	+	0.0498326i
$454$	17.0849	+	20.3610i	0.801835	+	0.955590i
$455$	−45.7844	+	3.25376i	−2.14641	+	0.152539i
$456$	2.73250	−	0.0723372i	0.127961	−	0.00338750i
$457$	−4.40132	+	24.9611i	−0.205885	+	1.16763i	0.690156	+	0.723660i	$0.257542\pi$
$457$	−4.40132	+	24.9611i	−0.205885	+	1.16763i	−0.896041	+	0.443971i	$0.853569\pi$
$458$	−0.689098			−0.0321994
$459$	−18.8125	−	27.3219i	−0.878091	−	1.27528i
$460$			22.0704i			1.02904i
$461$	−6.86447	+	38.9304i	−0.319710	+	1.81317i	0.224790	+	0.974407i	$0.427830\pi$
$461$	−6.86447	+	38.9304i	−0.319710	+	1.81317i	−0.544500	+	0.838761i	$0.683281\pi$
$462$	−4.43489	+	6.47249i	−0.206330	+	0.301127i
$463$	9.30119	+	3.38536i	0.432263	+	0.157331i	0.548982	−	0.835834i	$-0.315016\pi$
$463$	9.30119	+	3.38536i	0.432263	+	0.157331i	−0.116719	+	0.993165i	$0.537238\pi$
$464$	2.56694	+	3.05916i	0.119167	+	0.142018i
$465$	3.94365	+	0.588227i	0.182883	+	0.0272784i
$466$	4.95461	−	1.80333i	0.229518	−	0.0835376i
$467$	−12.3433	+	21.3792i	−0.571180	+	0.989313i	0.425265	+	0.905069i	$0.360181\pi$
$467$	−12.3433	+	21.3792i	−0.571180	+	0.989313i	−0.996445	+	0.0842444i	$0.973152\pi$
$468$	−7.80572	−	18.3598i	−0.360819	−	0.848684i
$469$	18.4763	−	25.4911i	0.853154	−	1.17707i
$470$	−11.7913	+	14.0524i	−0.543894	+	0.648188i
$471$	−12.7692	+	2.60175i	−0.588376	+	0.119882i
$472$	−0.887718	+	0.156529i	−0.0408605	+	0.00720481i
$473$	15.0126	−	2.64713i	0.690281	−	0.121715i
$474$	−12.4735	−	14.0906i	−0.572928	−	0.647204i
$475$	−1.83171	+	2.18295i	−0.0840447	+	0.100161i
$476$	−9.91246	+	13.6759i	−0.454337	+	0.626835i
$477$	16.9776	−	11.0392i	0.777352	−	0.505452i
$478$	−11.2744	+	19.5279i	−0.515680	+	0.893184i
$479$	−3.12136	+	1.13608i	−0.142619	+	0.0519090i	−0.412343	−	0.911029i	$-0.635290\pi$
$479$	−3.12136	+	1.13608i	−0.142619	+	0.0519090i	0.269725	+	0.962938i	$0.413067\pi$
$480$	2.81183	−	3.53704i	0.128342	−	0.161443i
$481$	−21.9876	−	26.2038i	−1.00255	−	1.19479i
$482$	21.9682	+	7.99576i	1.00062	+	0.364197i
$483$	2.98685	−	38.6538i	0.135906	−	1.75881i
$484$	−1.40108	+	7.94593i	−0.0636855	+	0.361179i
$485$		−	47.8857i		−	2.17438i
$486$	−7.21777	−	13.8168i	−0.327405	−	0.626743i
$487$	−27.7371			−1.25689			−0.628445	−	0.777854i	$-0.716308\pi$
$487$	−27.7371			−1.25689			−0.628445	+	0.777854i	$0.716308\pi$
$488$	−0.744328	+	4.22130i	−0.0336942	+	0.191089i
$489$	−5.86767	+	10.8143i	−0.265345	+	0.489040i
$490$	8.60976	+	16.1043i	0.388949	+	0.727520i
$491$	6.47307	+	7.71430i	0.292125	+	0.348142i	0.892068	−	0.451902i	$-0.149254\pi$
$491$	6.47307	+	7.71430i	0.292125	+	0.348142i	−0.599942	+	0.800043i	$0.704810\pi$
$492$	−1.11108	−	0.883273i	−0.0500913	−	0.0398210i
$493$	8.71953	+	23.9567i	0.392708	+	1.07896i
$494$	9.08886	+	5.24745i	0.408927	+	0.236094i
$495$	11.2339	−	7.30454i	0.504926	−	0.328315i
$496$	0.764208	−	0.441216i	0.0343140	−	0.0198112i
$497$	7.92295	+	2.26215i	0.355393	+	0.101471i
$498$	1.12608	+	1.27207i	0.0504609	+	0.0570027i
$499$	2.56761	+	14.5616i	0.114942	+	0.651868i	0.986779	+	0.162072i	$0.0518176\pi$
$499$	2.56761	+	14.5616i	0.114942	+	0.651868i	−0.871837	+	0.489796i	$0.837071\pi$
$500$	−1.44706	−	8.20667i	−0.0647143	−	0.367013i
$501$	−4.10628	−	20.1534i	−0.183455	−	0.900389i
$502$	11.7509	−	14.0042i	0.524469	−	0.625037i
$503$	−4.12896	−	7.15158i	−0.184101	−	0.318873i	0.759172	−	0.650890i	$-0.225604\pi$
$503$	−4.12896	−	7.15158i	−0.184101	−	0.318873i	−0.943273	+	0.332017i	$0.892271\pi$
$504$	−5.40327	+	5.81418i	−0.240681	+	0.258984i
$505$	2.46323	−	4.26643i	0.109612	−	0.189854i
$506$	4.95417	+	13.6115i	0.220240	+	0.605104i
$507$	7.97833	−	53.4892i	0.354330	−	2.37554i
$508$	1.76237	−	1.47880i	0.0781924	−	0.0656112i
$509$	22.9263	+	8.34449i	1.01619	+	0.369863i	0.795807	−	0.605551i	$-0.207047\pi$
$509$	22.9263	+	8.34449i	1.01619	+	0.369863i	0.220383	+	0.975413i	$0.429269\pi$
$510$	24.5911	−	15.0792i	1.08891	−	0.667716i
$511$	0.778032	+	3.10550i	0.0344181	+	0.137379i
$512$		−	1.00000i		−	0.0441942i
$513$	7.40457	+	3.52398i	0.326920	+	0.155588i
$514$		−	0.973454i		−	0.0429372i
$515$	46.2565	+	8.15626i	2.03830	+	0.359408i
$516$	15.4159	−	0.408104i	0.678648	−	0.0179658i
$517$	−4.11771	+	11.3133i	−0.181097	+	0.497560i
$518$	−5.95198	+	12.2386i	−0.261515	+	0.537733i
$519$	8.91599	−	3.51506i	0.391368	−	0.154294i
$520$	16.3023	−	5.93355i	0.714903	−	0.260203i
$521$	−14.6429	+	25.3623i	−0.641518	+	1.11114i	0.343575	+	0.939125i	$0.388362\pi$
$521$	−14.6429	+	25.3623i	−0.641518	+	1.11114i	−0.985094	+	0.172017i	$0.944971\pi$
$522$	2.70169	+	11.6718i	0.118250	+	0.510859i
$523$	−24.7419	+	14.2847i	−1.08189	+	0.624628i	−0.931405	−	0.363985i	$-0.881416\pi$
$523$	−24.7419	+	14.2847i	−1.08189	+	0.624628i	−0.150482	+	0.988613i	$0.548083\pi$
$524$	10.6004	+	8.89482i	0.463082	+	0.388572i
$525$	−0.804793	−	8.23539i	−0.0351240	−	0.359422i
$526$	−3.80930	−	21.6036i	−0.166093	−	0.941963i
$527$	5.54785	−	0.978236i	0.241668	−	0.0426126i
$528$	0.940176	−	2.81257i	0.0409159	−	0.122401i
$529$	−37.2092	−	31.2222i	−1.61779	−	1.35749i
$530$	8.80504	+	15.2508i	0.382467	+	0.662452i
$531$	−2.58653	−	0.789159i	−0.112246	−	0.0342466i
$532$	0.431739	−	4.15304i	0.0187183	−	0.180057i
$533$	−1.86389	−	5.12099i	−0.0807340	−	0.221815i
$534$	−1.75315	−	4.44688i	−0.0758661	−	0.192435i
$535$	−20.7702	−	24.7529i	−0.897973	−	1.07016i
$536$	−4.06984	+	11.1818i	−0.175790	+	0.482979i
$537$	−0.867604	−	32.7733i	−0.0374399	−	1.41427i
$538$	−10.8937	−	1.92085i	−0.469661	−	0.0828139i
$539$	8.92485	+	7.99938i	0.384421	+	0.344558i
$540$	12.3302	−	5.63201i	0.530607	−	0.242363i
$541$	26.0907			1.12173			0.560864	−	0.827908i	$-0.310469\pi$
$541$	26.0907			1.12173			0.560864	+	0.827908i	$0.310469\pi$
$542$	1.02006	−	5.78505i	0.0438154	−	0.248489i
$543$	−19.1327	+	11.7321i	−0.821062	+	0.503472i
$544$	2.18346	−	5.99900i	0.0936149	−	0.257205i
$545$	10.3631	−	8.69567i	0.443906	−	0.372482i
$546$	−29.3546	+	8.18569i	−1.25626	+	0.350315i
$547$	−40.8376	+	14.8637i	−1.74609	+	0.635525i	−0.999555	−	0.0298202i	$-0.990507\pi$
$547$	−40.8376	+	14.8637i	−1.74609	+	0.635525i	−0.746536	+	0.665345i	$0.768284\pi$
$548$	−8.58553	−	4.95686i	−0.366756	−	0.211746i
$549$	−7.73300	+	10.2743i	−0.330036	+	0.438496i
$550$	1.54580	+	2.67740i	0.0659130	+	0.114165i
$551$	−4.82785	−	4.05105i	−0.205673	−	0.172581i
$552$	2.92552	+	14.3583i	0.124518	+	0.611130i
$553$	−23.8130	+	16.1014i	−1.01263	+	0.684701i
$554$	−10.4511	+	1.84281i	−0.444024	+	0.0782933i
$555$	17.4030	−	15.4058i	0.738717	−	0.653939i
$556$	−3.77331	+	4.49686i	−0.160024	+	0.190709i
$557$	−2.66929	+	1.54111i	−0.113101	+	0.0652990i	−0.555483	−	0.831528i	$-0.687467\pi$
$557$	−2.66929	+	1.54111i	−0.113101	+	0.0652990i	0.442382	+	0.896827i	$0.354133\pi$
$558$	2.64359	−	0.140065i	0.111912	−	0.00592942i
$559$	51.2765	+	29.6045i	2.16877	+	1.25214i
$560$	−4.80027	−	4.95955i	−0.202848	−	0.209579i
$561$	11.7812	−	14.8198i	0.497404	−	0.625691i
$562$	1.12173	−	0.941246i	0.0473175	−	0.0397041i
$563$	−7.80618	−	2.84122i	−0.328991	−	0.119743i	0.172243	−	0.985054i	$-0.444898\pi$
$563$	−7.80618	−	2.84122i	−0.328991	−	0.119743i	−0.501235	+	0.865311i	$0.667121\pi$
$564$	−5.80837	+	10.7050i	−0.244577	+	0.450762i
$565$	47.5832	+	8.39021i	2.00184	+	0.352979i
$566$	−5.71980			−0.240421
$567$	−22.3571	+	8.19513i	−0.938910	+	0.344163i
$568$	−3.11426			−0.130672
$569$	−14.6123	−	2.57654i	−0.612579	−	0.108014i	−0.141253	−	0.989973i	$-0.545113\pi$
$569$	−14.6123	−	2.57654i	−0.612579	−	0.108014i	−0.471326	+	0.881959i	$0.656224\pi$
$570$	−3.40080	+	6.26778i	−0.142444	+	0.262528i
$571$	18.9116	+	6.88326i	0.791425	+	0.288055i	0.705928	−	0.708283i	$-0.250530\pi$
$571$	18.9116	+	6.88326i	0.791425	+	0.288055i	0.0854969	+	0.996338i	$0.472752\pi$
$572$	8.72219	−	7.31879i	0.364693	−	0.306014i
$573$	1.32772	−	1.67015i	0.0554663	−	0.0697717i
$574$	−1.55793	+	1.50789i	−0.0650267	+	0.0629383i
$575$	−13.2295	−	7.63806i	−0.551709	−	0.318529i
$576$	1.36044	−	2.67380i	0.0566849	−	0.111408i
$577$	13.3663	−	7.71706i	0.556448	−	0.321265i	−0.195271	−	0.980749i	$-0.562558\pi$
$577$	13.3663	−	7.71706i	0.556448	−	0.321265i	0.751719	+	0.659484i	$0.229225\pi$
$578$	15.2697	−	18.1977i	0.635135	−	0.756925i
$579$	−34.0503	+	30.1426i	−1.41508	+	1.25268i
$580$	−10.2597	+	1.80907i	−0.426012	+	0.0751174i
$581$	2.14978	−	1.45360i	0.0891880	−	0.0603054i
$582$	−6.34743	−	31.1529i	−0.263109	−	1.29133i
$583$	8.85369	+	7.42913i	0.366682	+	0.307683i
$584$	−0.605023	−	1.04793i	−0.0250360	−	0.0433637i
$585$	51.6613	+	6.31313i	2.13593	+	0.261016i
$586$	18.3673	+	10.6044i	0.758745	+	0.438062i
$587$	−21.2817	+	7.74592i	−0.878391	+	0.319708i	−0.741560	−	0.670886i	$-0.765914\pi$
$587$	−21.2817	+	7.74592i	−0.878391	+	0.319708i	−0.136831	+	0.990594i	$0.543692\pi$
$588$	7.73592	+	9.33571i	0.319024	+	0.384998i
$589$	−1.06681	+	0.895158i	−0.0439571	+	0.0368844i
$590$	0.804286	−	2.20976i	0.0331119	−	0.0909743i
$591$	15.5800	−	9.55359i	0.640876	−	0.392982i
$592$	0.893208	−	5.06563i	0.0367106	−	0.208196i
$593$	−3.92178			−0.161048			−0.0805242	−	0.996753i	$-0.525659\pi$
$593$	−3.92178			−0.161048			−0.0805242	+	0.996753i	$0.525659\pi$
$594$	6.34017	−	6.24120i	0.260140	−	0.256079i
$595$	−17.9678	−	40.2335i	−0.736609	−	1.64941i
$596$	2.92838	+	0.516353i	0.119951	+	0.0211506i
$597$	0.312355	+	11.7990i	0.0127838	+	0.482902i
$598$	−19.2422	+	52.8674i	−0.786871	+	2.16191i
$599$	−6.18718	−	7.37360i	−0.252802	−	0.301277i	0.624687	−	0.780876i	$-0.285227\pi$
$599$	−6.18718	−	7.37360i	−0.252802	−	0.301277i	−0.877488	+	0.479599i	$0.840782\pi$
$600$	1.14707	+	2.90956i	0.0468290	+	0.118782i
$601$	−2.98399	−	8.19846i	−0.121720	−	0.334422i	0.863836	−	0.503773i	$-0.168055\pi$
$601$	−2.98399	−	8.19846i	−0.121720	−	0.334422i	−0.985556	+	0.169351i	$0.945833\pi$
$602$	2.43574	−	23.4302i	0.0992733	−	0.954943i
$603$	−26.0940	+	24.3611i	−1.06263	+	0.992060i
$604$	−0.834797	−	1.44591i	−0.0339674	−	0.0588333i
$605$	−16.1244	−	13.5299i	−0.655549	−	0.550071i
$606$	1.03696	−	3.10211i	0.0421238	−	0.126015i
$607$	20.4674	−	3.60895i	0.830745	−	0.146483i	0.257926	−	0.966165i	$-0.416961\pi$
$607$	20.4674	−	3.60895i	0.830745	−	0.146483i	0.572819	+	0.819682i	$0.305850\pi$
$608$	0.274045	+	1.55419i	0.0111140	+	0.0630305i
$609$	18.2135	−	1.77989i	0.738050	−	0.0721250i
$610$	−8.56611	−	7.18782i	−0.346832	−	0.291026i
$611$	−40.4966	+	23.3807i	−1.63832	+	0.945882i
$612$	13.9994	−	13.0697i	0.565892	−	0.528310i
$613$	14.4313	−	24.9958i	0.582875	−	1.00957i	−0.412262	−	0.911065i	$-0.635261\pi$
$613$	14.4313	−	24.9958i	0.582875	−	1.00957i	0.995137	−	0.0985035i	$-0.0314056\pi$
$614$	−10.1985	+	3.71195i	−0.411578	+	0.149802i
$615$	3.44482	−	1.35809i	0.138908	−	0.0547635i
$616$	−4.07374	−	1.98118i	−0.164136	−	0.0798240i
$617$	−5.76580	+	15.8414i	−0.232122	+	0.637751i	−0.999996	−	0.00285055i	$-0.999093\pi$
$617$	−5.76580	+	15.8414i	−0.232122	+	0.637751i	0.767874	+	0.640601i	$0.221315\pi$
$618$	31.1741	−	0.825269i	1.25401	−	0.0331972i
$619$	11.3516	+	2.00160i	0.456261	+	0.0804511i	0.397055	−	0.917795i	$-0.370032\pi$
$619$	11.3516	+	2.00160i	0.456261	+	0.0804511i	0.0592057	+	0.998246i	$0.481143\pi$
$620$			2.30206i			0.0924529i
$621$	−11.7113	+	42.3712i	−0.469959	+	1.70030i
$622$			5.97204i			0.239457i
$623$	−7.08266	+	1.77444i	−0.283761	+	0.0710915i
$624$	9.81923	−	6.02110i	0.393084	−	0.241037i
$625$	28.9124	+	10.5232i	1.15649	+	0.420930i
$626$	−2.92517	+	2.45451i	−0.116913	+	0.0981019i
$627$	−0.690437	+	4.62890i	−0.0275734	+	0.184861i
$628$	−2.57329	−	7.07006i	−0.102685	−	0.282126i
$629$	16.4189	−	28.4384i	0.654666	−	1.13391i
$630$	−6.08779	−	19.7913i	−0.242544	−	0.788505i
$631$	11.5880	+	20.0711i	0.461313	+	0.799017i	0.999027	−	0.0441100i	$-0.0140452\pi$
$631$	11.5880	+	20.0711i	0.461313	+	0.799017i	−0.537714	+	0.843127i	$0.680712\pi$
$632$	6.98379	−	8.32295i	0.277800	−	0.331069i
$633$	−0.101252	−	0.496939i	−0.00402440	−	0.0197516i
$634$	3.09800	+	17.5696i	0.123037	+	0.697779i
$635$	1.04219	+	5.91057i	0.0413582	+	0.234554i
$636$	7.74983	+	8.75453i	0.307301	+	0.347140i
$637$	6.58317	+	46.0828i	0.260835	+	1.82587i
$638$	−5.92139	+	3.41872i	−0.234430	+	0.135348i
$639$	−8.32692	−	4.23676i	−0.329408	−	0.167604i
$640$	2.25926	+	1.30438i	0.0893051	+	0.0515603i
$641$	−5.63020	−	15.4689i	−0.222380	−	0.610983i	0.777459	−	0.628933i	$-0.216508\pi$
$641$	−5.63020	−	15.4689i	−0.222380	−	0.610983i	−0.999839	+	0.0179503i	$0.994286\pi$
$642$	−16.7935	−	13.3503i	−0.662786	−	0.526894i
$643$	20.4845	+	24.4125i	0.807832	+	0.962736i	0.999826	−	0.0186599i	$-0.00593997\pi$
$643$	20.4845	+	24.4125i	0.807832	+	0.962736i	−0.191994	+	0.981396i	$0.561496\pi$
$644$	22.3270	−	1.58671i	0.879806	−	0.0625252i
$645$	−19.1863	+	35.3609i	−0.755458	+	1.39233i
$646$	−1.74950	+	9.92192i	−0.0688332	+	0.390373i
$647$	18.2647			0.718060			0.359030	−	0.933326i	$-0.383108\pi$
$647$	18.2647			0.718060			0.359030	+	0.933326i	$0.383108\pi$
$648$	7.27508	−	5.29842i	0.285792	−	0.208141i
$649$		−	1.54336i		−	0.0605823i
$650$	−2.08514	+	11.8254i	−0.0817860	+	0.463832i
$651$	0.311544	−	4.03179i	0.0122104	−	0.158018i
$652$	−6.67510	−	2.42954i	−0.261417	−	0.0951480i
$653$	8.08178	+	9.63149i	0.316264	+	0.376909i	0.900634	−	0.434578i	$-0.143103\pi$
$653$	8.08178	+	9.63149i	0.316264	+	0.376909i	−0.584370	+	0.811488i	$0.698658\pi$
$654$	5.58925	−	7.03079i	0.218557	−	0.274926i
$655$	−33.9227	+	12.3469i	−1.32547	+	0.482432i
$656$	0.409743	−	0.709695i	0.0159978	−	0.0277089i
$657$	−0.192066	−	3.62505i	−0.00749321	−	0.141427i
$658$	15.0634	+	10.9181i	0.587234	+	0.425634i
$659$	11.1909	−	13.3368i	0.435935	−	0.519527i	−0.502690	−	0.864467i	$-0.667656\pi$
$659$	11.1909	−	13.3368i	0.435935	−	0.519527i	0.938625	+	0.344940i	$0.112101\pi$
$660$	5.12797	+	5.79277i	0.199606	+	0.225483i
$661$	17.2877	−	3.04829i	0.672413	−	0.118565i	0.172991	−	0.984923i	$-0.444657\pi$
$661$	17.2877	−	3.04829i	0.672413	−	0.118565i	0.499422	+	0.866359i	$0.333546\pi$
$662$	−20.5923	+	3.63098i	−0.800343	+	0.141122i
$663$	72.0523	−	14.6807i	2.79828	−	0.570152i
$664$	−0.630480	+	0.751377i	−0.0244674	+	0.0291591i
$665$	8.81964	+	6.39257i	0.342011	+	0.247893i
$666$	9.27974	−	12.3293i	0.359583	−	0.477752i
$667$	16.8925	−	29.2587i	0.654080	−	1.13290i
$668$	11.1585	−	4.06137i	0.431737	−	0.157139i
$669$	−29.0962	−	4.33993i	−1.12492	−	0.167791i
$670$	−19.9539	−	23.7801i	−0.770887	−	0.918707i
$671$	−6.89643	−	2.51010i	−0.266234	−	0.0969012i
$672$	−3.78031	−	2.59023i	−0.145828	−	0.0999203i
$673$	5.35143	−	30.3495i	0.206283	−	1.16989i	−0.689126	−	0.724641i	$-0.742005\pi$
$673$	5.35143	−	30.3495i	0.206283	−	1.16989i	0.895409	−	0.445245i	$-0.146883\pi$
$674$		−	25.5636i		−	0.984673i
$675$	−0.891241	+	9.34011i	−0.0343039	+	0.359501i
$676$	31.2236			1.20091
$677$	3.20150	−	18.1566i	0.123044	−	0.697814i	−0.859407	−	0.511292i	$-0.829167\pi$
$677$	3.20150	−	18.1566i	0.123044	−	0.697814i	0.982451	−	0.186523i	$-0.0597218\pi$
$678$	32.0683	−	0.848940i	1.23157	−	0.0326033i
$679$	−48.4424	+	3.44265i	−1.85905	+	0.132117i
$680$	10.7052	+	12.7580i	0.410526	+	0.489246i
$681$	−42.8287	+	16.8849i	−1.64120	+	0.647030i
$682$	0.516746	+	1.41975i	0.0197872	+	0.0543649i
$683$	−3.63658	−	2.09958i	−0.139150	−	0.0803382i	0.428809	−	0.903395i	$-0.358933\pi$
$683$	−3.63658	−	2.09958i	−0.139150	−	0.0803382i	−0.567959	+	0.823057i	$0.692267\pi$
$684$	−1.38163	+	4.52840i	−0.0528280	+	0.173148i
$685$	22.3976	−	12.9313i	0.855770	−	0.494079i
$686$	15.6726	−	9.86764i	0.598382	−	0.376748i
$687$	0.378395	−	1.13198i	0.0144367	−	0.0431878i
$688$	1.54608	+	8.76824i	0.0589436	+	0.334286i
$689$	7.79513	+	44.2084i	0.296971	+	1.68421i
$690$	−36.2551	−	12.1192i	−1.38021	−	0.461371i
$691$	7.54937	−	8.99699i	0.287192	−	0.342262i	−0.603089	−	0.797674i	$-0.706064\pi$
$691$	7.54937	−	8.99699i	0.287192	−	0.342262i	0.890281	+	0.455412i	$0.150508\pi$
$692$	2.76662	+	4.79193i	0.105171	+	0.182162i
$693$	−8.19710	−	10.8394i	−0.311382	−	0.411753i
$694$	−2.70177	+	4.67961i	−0.102558	+	0.177635i
$695$	−5.23772	−	14.3905i	−0.198678	−	0.545864i
$696$	−6.43485	+	2.53688i	−0.243912	+	0.0961604i
$697$	4.00763	−	3.36280i	0.151800	−	0.127375i
$698$	12.6398	+	4.60051i	0.478423	+	0.174132i
$699$	0.241676	+	9.12918i	0.00914102	+	0.345297i
$700$	4.63413	−	1.16100i	0.175154	−	0.0438818i
$701$		−	18.0424i		−	0.681453i	−0.940162	−	0.340726i	$-0.889327\pi$
$701$		−	18.0424i		−	0.681453i	0.940162	−	0.340726i	$-0.110673\pi$
$702$	34.4460	−	2.74078i	1.30008	−	0.103444i
$703$			8.11772i			0.306165i
$704$	1.68615	+	0.297313i	0.0635491	+	0.0112054i
$705$	−16.6090	−	27.0861i	−0.625533	−	1.02012i
$706$	3.00674	−	8.26095i	0.113160	−	0.310905i
$707$	−4.49312	−	2.18514i	−0.168981	−	0.0821805i
$708$	0.230331	−	1.54421i	0.00865636	−	0.0580349i
$709$	−24.2443	+	8.82421i	−0.910514	+	0.331400i	−0.754458	−	0.656348i	$-0.772100\pi$
$709$	−24.2443	+	8.82421i	−0.910514	+	0.331400i	−0.156056	+	0.987748i	$0.549878\pi$
$710$	4.06220	−	7.03593i	0.152451	−	0.264054i
$711$	29.9961	−	12.7529i	1.12494	−	0.478271i
$712$	2.38999	−	1.37986i	0.0895688	−	0.0517126i
$713$	−5.71887	−	4.79870i	−0.214173	−	0.179713i
$714$	−17.0224	−	23.7929i	−0.637047	−	0.890427i
$715$	5.15795	+	29.2522i	0.192896	+	1.09397i
$716$	18.6407	−	3.28686i	0.696637	−	0.122836i
$717$	−25.8875	−	29.2436i	−0.966786	−	1.09212i
$718$	20.7822	+	17.4383i	0.775585	+	0.650793i
$719$	−17.8367	−	30.8941i	−0.665198	−	1.15216i	−0.979232	−	0.202744i	$-0.935014\pi$
$719$	−17.8367	−	30.8941i	−0.665198	−	1.15216i	0.314034	−	0.949412i	$-0.398319\pi$
$720$	4.26627	+	6.56124i	0.158995	+	0.244523i
$721$	4.92556	−	47.3806i	0.183437	−	1.76455i
$722$	5.64655	+	15.5138i	0.210143	+	0.577363i
$723$	−25.1977	+	31.6966i	−0.937114	+	1.17881i
$724$	−8.32901	−	9.92613i	−0.309545	−	0.368902i
$725$	2.46626	−	6.77599i	0.0915945	−	0.251654i
$726$	−12.2834	−	6.66480i	−0.455881	−	0.247354i
$727$	−17.0647	−	3.00897i	−0.632895	−	0.111596i	−0.152008	−	0.988379i	$-0.548574\pi$
$727$	−17.0647	−	3.00897i	−0.632895	−	0.111596i	−0.480886	+	0.876783i	$0.659685\pi$
$728$	−7.17455	−	16.0652i	−0.265906	−	0.595417i
$729$	26.6603	−	4.26961i	0.987418	−	0.158134i
$730$	3.15673			0.116836
$731$	−9.87015	+	55.9764i	−0.365061	+	2.07036i
$732$	−6.52561	−	3.54069i	−0.241194	−	0.130868i
$733$	−1.69293	+	4.65129i	−0.0625298	+	0.171799i	−0.967023	−	0.254689i	$-0.918027\pi$
$733$	−1.69293	+	4.65129i	−0.0625298	+	0.171799i	0.904493	+	0.426488i	$0.140249\pi$
$734$	−16.7696	+	14.0714i	−0.618979	+	0.519385i
$735$	−31.1824	+	5.30011i	−1.15018	+	0.195497i
$736$	−7.94988	+	2.89352i	−0.293037	+	0.106657i
$737$	−17.6441	−	10.1868i	−0.649930	−	0.375237i
$738$	2.06107	−	1.34015i	0.0758689	−	0.0493317i
$739$	10.0817	+	17.4621i	0.370863	+	0.642353i	0.989699	−	0.143167i	$-0.0457287\pi$
$739$	10.0817	+	17.4621i	0.370863	+	0.642353i	−0.618836	+	0.785520i	$0.712395\pi$
$740$	10.2795	+	8.62552i	0.377882	+	0.317080i
$741$	−13.6108	+	12.0488i	−0.500007	+	0.442625i
$742$	14.7951	−	10.0038i	0.543144	−	0.367252i
$743$	11.0456	−	1.94764i	0.405224	−	0.0714519i	0.0326787	−	0.999466i	$-0.489596\pi$
$743$	11.0456	−	1.94764i	0.405224	−	0.0714519i	0.372545	+	0.928014i	$0.378485\pi$
$744$	0.305147	+	1.49765i	0.0111872	+	0.0549063i
$745$	−4.98631	+	5.94246i	−0.182684	+	0.217715i
$746$	−4.11363	+	2.37500i	−0.150611	+	0.0869551i
$747$	−2.70798	+	1.15130i	−0.0990798	+	0.0421240i
$748$	9.46603	+	5.46521i	0.346112	+	0.199828i
$749$	−23.5475	+	22.7912i	−0.860405	+	0.832772i
$750$	14.2757	+	2.12933i	0.521275	+	0.0777523i
$751$	−1.24071	+	1.04108i	−0.0452740	+	0.0379894i	−0.665144	−	0.746715i	$-0.731630\pi$
$751$	−1.24071	+	1.04108i	−0.0452740	+	0.0379894i	0.619870	+	0.784705i	$0.287185\pi$
$752$	−6.60763	−	2.40498i	−0.240956	−	0.0877007i
$753$	16.5521	+	26.9932i	0.603192	+	0.983686i
$754$	−26.1534	−	4.61154i	−0.952449	−	0.167942i
$755$	4.35558			0.158516
$756$	−6.58394	−	12.0686i	−0.239455	−	0.438932i
$757$	25.8070			0.937972			0.468986	−	0.883206i	$-0.344619\pi$
$757$	25.8070			0.937972			0.468986	+	0.883206i	$0.344619\pi$
$758$	−24.6695	−	4.34990i	−0.896036	−	0.157995i
$759$	−25.0800	+	0.663941i	−0.910347	+	0.0240995i
$760$	−3.86877	−	1.40812i	−0.140335	−	0.0510777i
$761$	−28.5821	+	23.9832i	−1.03610	+	0.869391i	−0.991564	−	0.129617i	$-0.958625\pi$
$761$	−28.5821	+	23.9832i	−1.03610	+	0.869391i	−0.0445359	+	0.999008i	$0.514181\pi$
$762$	1.46149	+	3.70708i	0.0529441	+	0.134293i
$763$	−9.54180	−	9.85841i	−0.345436	−	0.356899i
$764$	1.06680	+	0.615918i	0.0385955	+	0.0222831i
$765$	11.2672	+	48.6761i	0.407365	+	1.75989i
$766$	9.13403	−	5.27353i	0.330026	−	0.190540i
$767$	3.85317	−	4.59203i	0.139130	−	0.165809i
$768$	1.64270	+	0.549117i	0.0592759	+	0.0198145i
$769$	24.6590	−	4.34804i	0.889226	−	0.156795i	0.289669	−	0.957127i	$-0.406455\pi$
$769$	24.6590	−	4.34804i	0.889226	−	0.156795i	0.599557	+	0.800332i	$0.295344\pi$

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:	\( N \)	\(=\)	\( 378 = 2 \cdot 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	378.z (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.984808 - 0.173648i) q^{2} +(0.826027 - 1.52239i) q^{3} +(0.939693 + 0.342020i) q^{4} +(-1.99843 + 1.67688i) q^{5} +(-1.07784 + 1.35583i) q^{6} +(1.84005 + 1.90111i) q^{7} +(-0.866025 - 0.500000i) q^{8} +(-1.63536 - 2.51507i) q^{9} +O(q^{10})\)	\(q+(-0.984808 - 0.173648i) q^{2} +(0.826027 - 1.52239i) q^{3} +(0.939693 + 0.342020i) q^{4} +(-1.99843 + 1.67688i) q^{5} +(-1.07784 + 1.35583i) q^{6} +(1.84005 + 1.90111i) q^{7} +(-0.866025 - 0.500000i) q^{8} +(-1.63536 - 2.51507i) q^{9} +(2.25926 - 1.30438i) q^{10} +(1.10056 - 1.31159i) q^{11} +(1.29690 - 1.14806i) q^{12} +(6.54906 - 1.15478i) q^{13} +(-1.48197 - 2.19175i) q^{14} +(0.902117 + 4.42755i) q^{15} +(0.766044 + 0.642788i) q^{16} +(3.19200 + 5.52870i) q^{17} +(1.17378 + 2.76084i) q^{18} +(-1.36673 - 0.789081i) q^{19} +(-2.45144 + 0.892251i) q^{20} +(4.41416 - 1.23092i) q^{21} +(-1.31159 + 1.10056i) q^{22} +(2.89352 - 7.94988i) q^{23} +(-1.47656 + 0.905418i) q^{24} +(0.313551 - 1.77824i) q^{25} -6.65009 q^{26} +(-5.17978 + 0.412142i) q^{27} +(1.07887 + 2.41579i) q^{28} +(3.93278 + 0.693456i) q^{29} +(-0.119576 - 4.51694i) q^{30} +(0.301809 - 0.829214i) q^{31} +(-0.642788 - 0.766044i) q^{32} +(-1.08767 - 2.75889i) q^{33} +(-2.18346 - 5.99900i) q^{34} +(-6.86515 - 0.713683i) q^{35} +(-0.676530 - 2.92272i) q^{36} +(-2.57189 - 4.45464i) q^{37} +(1.20894 + 1.01442i) q^{38} +(3.65167 - 10.9241i) q^{39} +(2.56913 - 0.453008i) q^{40} +(-0.142302 - 0.807035i) q^{41} +(-4.56085 + 0.445703i) q^{42} +(6.82048 + 5.72306i) q^{43} +(1.48277 - 0.856080i) q^{44} +(7.48564 + 2.28390i) q^{45} +(-4.23005 + 7.32665i) q^{46} +(-6.60763 + 2.40498i) q^{47} +(1.61135 - 0.635261i) q^{48} +(-0.228422 + 6.99627i) q^{49} +(-0.617575 + 1.69677i) q^{50} +(11.0535 - 0.292619i) q^{51} +(6.54906 + 1.15478i) q^{52} +6.75035i q^{53} +(5.17266 + 0.493579i) q^{54} +4.46663i q^{55} +(-0.642977 - 2.56643i) q^{56} +(-2.33024 + 1.42890i) q^{57} +(-3.75262 - 1.36584i) q^{58} +(0.690522 - 0.579417i) q^{59} +(-0.666598 + 4.46908i) q^{60} +(-1.46604 - 4.02791i) q^{61} +(-0.441216 + 0.764208i) q^{62} +(1.77228 - 7.73686i) q^{63} +(0.500000 + 0.866025i) q^{64} +(-11.1514 + 13.2897i) q^{65} +(0.592069 + 2.90584i) q^{66} +(-2.06631 - 11.7186i) q^{67} +(1.10857 + 6.28701i) q^{68} +(-9.71272 - 10.9719i) q^{69} +(6.63693 + 1.89496i) q^{70} +(2.69703 - 1.55713i) q^{71} +(0.158726 + 2.99580i) q^{72} +(1.04793 + 0.605023i) q^{73} +(1.75928 + 4.83357i) q^{74} +(-2.44817 - 1.94622i) q^{75} +(-1.01442 - 1.20894i) q^{76} +(4.51855 - 0.321120i) q^{77} +(-5.49315 + 10.1240i) q^{78} +(-1.88666 + 10.6998i) q^{79} -2.60877 q^{80} +(-3.65120 + 8.22610i) q^{81} +0.819485i q^{82} +(0.170323 - 0.965952i) q^{83} +(4.56896 + 0.353051i) q^{84} +(-15.6500 - 5.69613i) q^{85} +(-5.72306 - 6.82048i) q^{86} +(4.30430 - 5.41443i) q^{87} +(-1.60890 + 0.585593i) q^{88} +(-1.37986 + 2.38999i) q^{89} +(-6.97532 - 3.54907i) q^{90} +(14.2460 + 10.3256i) q^{91} +(5.43804 - 6.48081i) q^{92} +(-1.01309 - 1.14443i) q^{93} +(6.92487 - 1.22104i) q^{94} +(4.05451 - 0.714919i) q^{95} +(-1.69718 + 0.345802i) q^{96} +(-11.7988 + 14.0613i) q^{97} +(1.43984 - 6.85032i) q^{98} +(-5.09855 - 0.623055i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 144 q - 12 q^{9}+O(q^{10}) \) 144 * q - 12 * q^9	\( 144 q - 12 q^{9} + 12 q^{11} + 6 q^{14} + 12 q^{15} + 24 q^{21} - 60 q^{23} + 12 q^{29} - 72 q^{30} + 54 q^{35} - 12 q^{36} + 48 q^{39} + 24 q^{42} + 18 q^{49} - 60 q^{50} - 36 q^{51} + 6 q^{56} - 60 q^{57} - 36 q^{60} - 78 q^{63} + 72 q^{64} - 120 q^{65} + 36 q^{70} - 72 q^{71} - 24 q^{72} - 36 q^{74} + 66 q^{77} - 60 q^{78} - 72 q^{79} + 12 q^{84} - 72 q^{85} - 48 q^{86} - 18 q^{91} + 12 q^{92} + 24 q^{93} - 120 q^{95} + 36 q^{98} + 144 q^{99}+O(q^{100}) \) 144 * q - 12 * q^9 + 12 * q^11 + 6 * q^14 + 12 * q^15 + 24 * q^21 - 60 * q^23 + 12 * q^29 - 72 * q^30 + 54 * q^35 - 12 * q^36 + 48 * q^39 + 24 * q^42 + 18 * q^49 - 60 * q^50 - 36 * q^51 + 6 * q^56 - 60 * q^57 - 36 * q^60 - 78 * q^63 + 72 * q^64 - 120 * q^65 + 36 * q^70 - 72 * q^71 - 24 * q^72 - 36 * q^74 + 66 * q^77 - 60 * q^78 - 72 * q^79 + 12 * q^84 - 72 * q^85 - 48 * q^86 - 18 * q^91 + 12 * q^92 + 24 * q^93 - 120 * q^95 + 36 * q^98 + 144 * q^99

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