LMFDB - Embedded newform 189.2.be.a.20.20

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [189,2,Mod(20,189)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(189, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([7, 9]))

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

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

chi := DirichletCharacter("189.20");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 189 = 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	189.be (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:	$1.50917259820$
Analytic rank:	$0$
Dimension:	$132$
Relative dimension:	$22$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			20.20
Character	$\chi$	$=$	189.20
Dual form			189.2.be.a.104.20

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.735125 + 2.01974i) q^{2} +(1.28358 - 1.16294i) q^{3} +(-2.00685 + 1.68395i) q^{4} +(-0.0677816 - 0.384409i) q^{5} +(3.29242 + 1.73760i) q^{6} +(2.64076 + 0.162359i) q^{7} +(-1.15362 - 0.666045i) q^{8} +(0.295160 - 2.98544i) q^{9} +O(q^{10})$	\(q+(0.735125 + 2.01974i) q^{2} +(1.28358 - 1.16294i) q^{3} +(-2.00685 + 1.68395i) q^{4} +(-0.0677816 - 0.384409i) q^{5} +(3.29242 + 1.73760i) q^{6} +(2.64076 + 0.162359i) q^{7} +(-1.15362 - 0.666045i) q^{8} +(0.295160 - 2.98544i) q^{9} +(0.726578 - 0.419490i) q^{10} +(-4.77807 - 0.842503i) q^{11} +(-0.617633 + 4.49533i) q^{12} +(-1.96127 + 5.38855i) q^{13} +(1.61337 + 5.45301i) q^{14} +(-0.534046 - 0.414594i) q^{15} +(-0.412653 + 2.34027i) q^{16} +(-3.57147 - 6.18597i) q^{17} +(6.24680 - 1.59853i) q^{18} +(-0.398672 - 0.230173i) q^{19} +(0.783352 + 0.657311i) q^{20} +(3.57845 - 2.86264i) q^{21} +(-1.81084 - 10.2698i) q^{22} +(0.358944 + 0.427773i) q^{23} +(-2.25534 + 0.486668i) q^{24} +(4.55529 - 1.65799i) q^{25} -12.3252 q^{26} +(-3.09302 - 4.17531i) q^{27} +(-5.57303 + 4.12109i) q^{28} +(1.73522 + 4.76747i) q^{29} +(0.444781 - 1.38341i) q^{30} +(-2.14159 - 2.55225i) q^{31} +(-7.65380 + 1.34957i) q^{32} +(-7.11282 + 4.47517i) q^{33} +(9.86858 - 11.7609i) q^{34} +(-0.116583 - 1.02614i) q^{35} +(4.43500 + 6.48838i) q^{36} +(-1.07348 - 1.85933i) q^{37} +(0.171817 - 0.974420i) q^{38} +(3.74909 + 9.19747i) q^{39} +(-0.177839 + 0.488609i) q^{40} +(-0.917771 - 0.334041i) q^{41} +(8.41240 + 5.12314i) q^{42} +(1.16047 - 6.58138i) q^{43} +(11.0076 - 6.35525i) q^{44} +(-1.16764 + 0.0888961i) q^{45} +(-0.600121 + 1.03944i) q^{46} +(2.83834 + 2.38165i) q^{47} +(2.19191 + 3.48382i) q^{48} +(6.94728 + 0.857502i) q^{49} +(6.69741 + 7.98167i) q^{50} +(-11.7782 - 3.78680i) q^{51} +(-5.13806 - 14.1167i) q^{52} -3.13310i q^{53} +(6.15929 - 9.31647i) q^{54} +1.89384i q^{55} +(-2.93831 - 1.94617i) q^{56} +(-0.779405 + 0.168184i) q^{57} +(-8.35346 + 7.00938i) q^{58} +(0.715255 + 4.05641i) q^{59} +(1.76991 - 0.0672771i) q^{60} +(-7.89549 + 9.40948i) q^{61} +(3.58054 - 6.20168i) q^{62} +(1.26416 - 7.83594i) q^{63} +(-5.97591 - 10.3506i) q^{64} +(2.20434 + 0.388685i) q^{65} +(-14.2675 - 11.0762i) q^{66} +(6.30401 + 2.29447i) q^{67} +(17.5843 + 6.40016i) q^{68} +(0.958206 + 0.131652i) q^{69} +(1.98683 - 0.989808i) q^{70} +(6.08593 - 3.51371i) q^{71} +(-2.32894 + 3.24749i) q^{72} +(6.55906 + 3.78687i) q^{73} +(2.96621 - 3.53499i) q^{74} +(3.91895 - 7.42567i) q^{75} +(1.18768 - 0.209419i) q^{76} +(-12.4810 - 3.00061i) q^{77} +(-15.8205 + 14.3335i) q^{78} +(-0.818714 + 0.297987i) q^{79} +0.927591 q^{80} +(-8.82576 - 1.76237i) q^{81} -2.09922i q^{82} +(-6.78293 + 2.46878i) q^{83} +(-2.36088 + 11.7708i) q^{84} +(-2.13586 + 1.79220i) q^{85} +(14.1458 - 2.49428i) q^{86} +(7.77156 + 4.10149i) q^{87} +(4.95095 + 4.15434i) q^{88} +(-2.65800 + 4.60379i) q^{89} +(-1.03791 - 2.29297i) q^{90} +(-6.05413 + 13.9115i) q^{91} +(-1.44070 - 0.254033i) q^{92} +(-5.71701 - 0.785485i) q^{93} +(-2.72378 + 7.48351i) q^{94} +(-0.0614580 + 0.168854i) q^{95} +(-8.25481 + 10.6332i) q^{96} +(-10.7873 - 1.90209i) q^{97} +(3.37519 + 14.6621i) q^{98} +(-3.92554 + 14.0160i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 132 q - 12 q^{2} - 12 q^{4} - 6 q^{7} - 18 q^{8} - 6 q^{9}+O(q^{10}) $ 132 * q - 12 * q^2 - 12 * q^4 - 6 * q^7 - 18 * q^8 - 6 * q^9	$ 132 q - 12 q^{2} - 12 q^{4} - 6 q^{7} - 18 q^{8} - 6 q^{9} - 18 q^{11} + 3 q^{14} - 24 q^{15} - 24 q^{16} - 12 q^{18} - 12 q^{21} - 12 q^{22} + 12 q^{23} - 12 q^{25} - 12 q^{28} - 48 q^{29} + 42 q^{30} - 6 q^{32} - 36 q^{35} - 36 q^{36} - 6 q^{37} - 18 q^{39} - 12 q^{43} - 18 q^{44} - 6 q^{46} - 24 q^{49} + 18 q^{50} + 24 q^{51} + 57 q^{56} - 12 q^{58} - 6 q^{60} + 21 q^{63} + 18 q^{64} + 78 q^{65} - 12 q^{67} - 69 q^{70} + 18 q^{71} + 114 q^{72} - 6 q^{74} - 57 q^{77} + 12 q^{78} + 24 q^{79} - 42 q^{81} - 48 q^{84} + 54 q^{85} - 42 q^{86} - 72 q^{88} + 6 q^{91} - 120 q^{92} - 60 q^{93} + 126 q^{95} + 126 q^{98} - 192 q^{99}+O(q^{100}) $ 132 * q - 12 * q^2 - 12 * q^4 - 6 * q^7 - 18 * q^8 - 6 * q^9 - 18 * q^11 + 3 * q^14 - 24 * q^15 - 24 * q^16 - 12 * q^18 - 12 * q^21 - 12 * q^22 + 12 * q^23 - 12 * q^25 - 12 * q^28 - 48 * q^29 + 42 * q^30 - 6 * q^32 - 36 * q^35 - 36 * q^36 - 6 * q^37 - 18 * q^39 - 12 * q^43 - 18 * q^44 - 6 * q^46 - 24 * q^49 + 18 * q^50 + 24 * q^51 + 57 * q^56 - 12 * q^58 - 6 * q^60 + 21 * q^63 + 18 * q^64 + 78 * q^65 - 12 * q^67 - 69 * q^70 + 18 * q^71 + 114 * q^72 - 6 * q^74 - 57 * q^77 + 12 * q^78 + 24 * q^79 - 42 * q^81 - 48 * q^84 + 54 * q^85 - 42 * q^86 - 72 * q^88 + 6 * q^91 - 120 * q^92 - 60 * q^93 + 126 * q^95 + 126 * q^98 - 192 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/189\mathbb{Z}\right)^\times$.

$n$	$29$	$136$
$\chi(n)$	$e\left(\frac{7}{18}\right)$	$-1$

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 $

$2$	0.735125	+	2.01974i	0.519812	+	1.42817i	0.870728	+	0.491765i	$0.163648\pi$
$2$	0.735125	+	2.01974i	0.519812	+	1.42817i	−0.350916	+	0.936407i	$0.614130\pi$
$3$	1.28358	−	1.16294i	0.741076	−	0.671421i
$3$	1.28358	−	1.16294i	0.741076	−	0.671421i
$4$	−2.00685	+	1.68395i	−1.00343	+	0.841975i
$5$	−0.0677816	−	0.384409i	−0.0303129	−	0.171913i	0.965893	−	0.258942i	$-0.0833738\pi$
$5$	−0.0677816	−	0.384409i	−0.0303129	−	0.171913i	−0.996206	+	0.0870291i	$0.972263\pi$
$6$	3.29242	+	1.73760i	1.34413	+	0.709371i
$7$	2.64076	+	0.162359i	0.998115	+	0.0613658i
$7$	2.64076	+	0.162359i	0.998115	+	0.0613658i
$8$	−1.15362	−	0.666045i	−0.407868	−	0.235483i
$9$	0.295160	−	2.98544i	0.0983867	−	0.995148i
$10$	0.726578	−	0.419490i	0.229764	−	0.132654i
$11$	−4.77807	−	0.842503i	−1.44064	−	0.254024i	−0.601909	−	0.798565i	$-0.705593\pi$
$11$	−4.77807	−	0.842503i	−1.44064	−	0.254024i	−0.838734	+	0.544541i	$0.816704\pi$
$12$	−0.617633	+	4.49533i	−0.178295	+	1.29769i
$13$	−1.96127	+	5.38855i	−0.543959	+	1.49451i	0.297783	+	0.954634i	$0.403753\pi$
$13$	−1.96127	+	5.38855i	−0.543959	+	1.49451i	−0.841742	+	0.539881i	$0.818469\pi$
$14$	1.61337	+	5.45301i	0.431192	+	1.45738i
$15$	−0.534046	−	0.414594i	−0.137890	−	0.107048i
$16$	−0.412653	+	2.34027i	−0.103163	+	0.585068i
$17$	−3.57147	−	6.18597i	−0.866209	−	1.50032i	−0.865841	−	0.500319i	$-0.833216\pi$
$17$	−3.57147	−	6.18597i	−0.866209	−	1.50032i	−0.000368279	−	1.00000i	$-0.500117\pi$
$18$	6.24680	−	1.59853i	1.47239	−	0.376777i
$19$	−0.398672	−	0.230173i	−0.0914616	−	0.0528054i	0.453572	−	0.891220i	$-0.350150\pi$
$19$	−0.398672	−	0.230173i	−0.0914616	−	0.0528054i	−0.545033	+	0.838414i	$0.683483\pi$
$20$	0.783352	+	0.657311i	0.175163	+	0.146979i
$21$	3.57845	−	2.86264i	0.780881	−	0.624679i
$22$	−1.81084	−	10.2698i	−0.386073	−	2.18953i
$23$	0.358944	+	0.427773i	0.0748450	+	0.0891968i	0.802168	−	0.597099i	$-0.203680\pi$
$23$	0.358944	+	0.427773i	0.0748450	+	0.0891968i	−0.727323	+	0.686296i	$0.759236\pi$
$24$	−2.25534	+	0.486668i	−0.460369	+	0.0993407i
$25$	4.55529	−	1.65799i	0.911057	−	0.331598i
$26$	−12.3252			−2.41718
$27$	−3.09302	−	4.17531i	−0.595252	−	0.803539i
$28$	−5.57303	+	4.12109i	−1.05320	+	0.778812i
$29$	1.73522	+	4.76747i	0.322222	+	0.885298i	0.990016	+	0.140952i	$0.0450163\pi$
$29$	1.73522	+	4.76747i	0.322222	+	0.885298i	−0.667794	+	0.744346i	$0.732761\pi$
$30$	0.444781	−	1.38341i	0.0812056	−	0.252575i
$31$	−2.14159	−	2.55225i	−0.384641	−	0.458398i	0.538632	−	0.842541i	$-0.318941\pi$
$31$	−2.14159	−	2.55225i	−0.384641	−	0.458398i	−0.923273	+	0.384143i	$0.874497\pi$
$32$	−7.65380	+	1.34957i	−1.35301	+	0.238573i
$33$	−7.11282	+	4.47517i	−1.23818	+	0.779027i
$34$	9.86858	−	11.7609i	1.69245	−	2.01698i
$35$	−0.116583	−	1.02614i	−0.0197062	−	0.173449i
$36$	4.43500	+	6.48838i	0.739166	+	1.08140i
$37$	−1.07348	−	1.85933i	−0.176479	−	0.305671i	0.764193	−	0.644988i	$-0.223138\pi$
$37$	−1.07348	−	1.85933i	−0.176479	−	0.305671i	−0.940672	+	0.339317i	$0.889804\pi$
$38$	0.171817	−	0.974420i	0.0278723	−	0.158072i
$39$	3.74909	+	9.19747i	0.600334	+	1.47277i
$40$	−0.177839	+	0.488609i	−0.0281188	+	0.0772558i
$41$	−0.917771	−	0.334041i	−0.143332	−	0.0521685i	0.269358	−	0.963040i	$-0.413188\pi$
$41$	−0.917771	−	0.334041i	−0.143332	−	0.0521685i	−0.412690	+	0.910872i	$0.635411\pi$
$42$	8.41240	+	5.12314i	1.29806	+	0.790517i
$43$	1.16047	−	6.58138i	0.176971	−	1.00365i	−0.758874	−	0.651238i	$-0.774250\pi$
$43$	1.16047	−	6.58138i	0.176971	−	1.00365i	0.935845	−	0.352413i	$-0.114639\pi$
$44$	11.0076	−	6.35525i	1.65946	−	0.958090i
$45$	−1.16764	+	0.0888961i	−0.174061	+	0.0132519i
$46$	−0.600121	+	1.03944i	−0.0884830	+	0.153257i
$47$	2.83834	+	2.38165i	0.414014	+	0.347399i	0.825880	−	0.563845i	$-0.190679\pi$
$47$	2.83834	+	2.38165i	0.414014	+	0.347399i	−0.411867	+	0.911244i	$0.635123\pi$
$48$	2.19191	+	3.48382i	0.316376	+	0.502846i
$49$	6.94728	+	0.857502i	0.992468	+	0.122500i
$50$	6.69741	+	7.98167i	0.947157	+	1.12878i
$51$	−11.7782	−	3.78680i	−1.64927	−	0.530258i
$52$	−5.13806	−	14.1167i	−0.712521	−	1.95763i
$53$		−	3.13310i		−	0.430364i	−0.976574	−	0.215182i	$-0.930966\pi$
$53$		−	3.13310i		−	0.430364i	0.976574	−	0.215182i	$-0.0690345\pi$
$54$	6.15929	−	9.31647i	0.838173	−	1.26781i
$55$			1.89384i			0.255365i
$56$	−2.93831	−	1.94617i	−0.392648	−	0.260068i
$57$	−0.779405	+	0.168184i	−0.103235	+	0.0222765i
$58$	−8.35346	+	7.00938i	−1.09686	+	0.920377i
$59$	0.715255	+	4.05641i	0.0931183	+	0.528100i	0.995308	+	0.0967600i	$0.0308479\pi$
$59$	0.715255	+	4.05641i	0.0931183	+	0.528100i	−0.902189	+	0.431340i	$0.858041\pi$
$60$	1.76991	−	0.0672771i	0.228494	−	0.00868544i
$61$	−7.89549	+	9.40948i	−1.01091	+	1.20476i	−0.0322101	+	0.999481i	$0.510255\pi$
$61$	−7.89549	+	9.40948i	−1.01091	+	1.20476i	−0.978704	+	0.205279i	$0.934190\pi$
$62$	3.58054	−	6.20168i	0.454730	−	0.787615i
$63$	1.26416	−	7.83594i	0.159269	−	0.987235i
$64$	−5.97591	−	10.3506i	−0.746989	−	1.29382i
$65$	2.20434	+	0.388685i	0.273415	+	0.0482104i
$66$	−14.2675	−	11.0762i	−1.75621	−	1.36339i
$67$	6.30401	+	2.29447i	0.770158	+	0.280314i	0.697062	−	0.717011i	$-0.254490\pi$
$67$	6.30401	+	2.29447i	0.770158	+	0.280314i	0.0730953	+	0.997325i	$0.476712\pi$
$68$	17.5843	+	6.40016i	2.13241	+	0.776133i
$69$	0.958206	+	0.131652i	0.115354	+	0.0158491i
$70$	1.98683	−	0.989808i	0.237471	−	0.118305i
$71$	6.08593	−	3.51371i	0.722267	−	0.417001i	−0.0933194	−	0.995636i	$-0.529748\pi$
$71$	6.08593	−	3.51371i	0.722267	−	0.417001i	0.815587	+	0.578635i	$0.196414\pi$
$72$	−2.32894	+	3.24749i	−0.274469	+	0.382720i
$73$	6.55906	+	3.78687i	0.767680	+	0.443220i	0.832046	−	0.554706i	$-0.187169\pi$
$73$	6.55906	+	3.78687i	0.767680	+	0.443220i	−0.0643665	+	0.997926i	$0.520503\pi$
$74$	2.96621	−	3.53499i	0.344815	−	0.410935i
$75$	3.91895	−	7.42567i	0.452521	−	0.857443i
$76$	1.18768	−	0.209419i	0.136236	−	0.0240221i
$77$	−12.4810	−	3.00061i	−1.42234	−	0.341952i
$78$	−15.8205	+	14.3335i	−1.79131	+	1.62295i
$79$	−0.818714	+	0.297987i	−0.0921125	+	0.0335262i	−0.387665	−	0.921800i	$-0.626718\pi$
$79$	−0.818714	+	0.297987i	−0.0921125	+	0.0335262i	0.295553	+	0.955326i	$0.404496\pi$
$80$	0.927591			0.103708
$81$	−8.82576	−	1.76237i	−0.980640	−	0.195819i
$82$		−	2.09922i		−	0.231820i
$83$	−6.78293	+	2.46878i	−0.744523	+	0.270984i	−0.686299	−	0.727319i	$-0.740766\pi$
$83$	−6.78293	+	2.46878i	−0.744523	+	0.270984i	−0.0582238	+	0.998304i	$0.518544\pi$
$84$	−2.36088	+	11.7708i	−0.257593	+	1.28430i
$85$	−2.13586	+	1.79220i	−0.231667	+	0.194391i
$86$	14.1458	−	2.49428i	1.52538	−	0.268965i
$87$	7.77156	+	4.10149i	0.833199	+	0.439726i
$88$	4.95095	+	4.15434i	0.527773	+	0.442854i
$89$	−2.65800	+	4.60379i	−0.281748	+	0.488001i	−0.971815	−	0.235744i	$-0.924247\pi$
$89$	−2.65800	+	4.60379i	−0.281748	+	0.488001i	0.690068	+	0.723745i	$0.257581\pi$
$90$	−1.03791	−	2.29297i	−0.109405	−	0.241701i
$91$	−6.05413	+	13.9115i	−0.634646	+	1.45832i
$92$	−1.44070	−	0.254033i	−0.150203	−	0.0264848i
$93$	−5.71701	−	0.785485i	−0.592826	−	0.0814510i
$94$	−2.72378	+	7.48351i	−0.280936	+	0.771865i
$95$	−0.0614580	+	0.168854i	−0.00630546	+	0.0173241i
$96$	−8.25481	+	10.6332i	−0.842503	+	1.08524i
$97$	−10.7873	−	1.90209i	−1.09528	−	0.193128i	−0.403318	−	0.915060i	$-0.632143\pi$
$97$	−10.7873	−	1.90209i	−1.09528	−	0.193128i	−0.691964	+	0.721932i	$0.743254\pi$
$98$	3.37519	+	14.6621i	0.340946	+	1.48109i
$99$	−3.92554	+	14.0160i	−0.394532	+	1.40866i
$100$	−6.34982	+	10.9982i	−0.634982	+	1.09982i
$101$	10.5964	+	8.89141i	1.05438	+	0.884728i	0.993547	−	0.113420i	$-0.0361806\pi$
$101$	10.5964	+	8.89141i	1.05438	+	0.884728i	0.0608307	+	0.998148i	$0.480625\pi$
$102$	−1.01007	−	26.5726i	−0.100012	−	2.63108i
$103$	12.0281	−	2.12089i	1.18517	−	0.208977i	0.453890	−	0.891058i	$-0.350036\pi$
$103$	12.0281	−	2.12089i	1.18517	−	0.208977i	0.731277	+	0.682080i	$0.238925\pi$
$104$	5.85159	−	4.91006i	0.573795	−	0.481471i
$105$	−1.34298	−	1.18155i	−0.131061	−	0.115308i
$106$	6.32804	−	2.30322i	0.614634	−	0.223708i
$107$			5.57017i			0.538489i	0.963072	+	0.269244i	$0.0867739\pi$
$107$			5.57017i			0.538489i	−0.963072	+	0.269244i	$0.913226\pi$
$108$	13.2383	+	3.17075i	1.27385	+	0.305106i
$109$	−3.73204			−0.357464			−0.178732	−	0.983898i	$-0.557200\pi$
$109$	−3.73204			−0.357464			−0.178732	+	0.983898i	$0.557200\pi$
$110$	−3.82506	+	1.39221i	−0.364705	+	0.132742i
$111$	−3.54018	−	1.13820i	−0.336019	−	0.108034i
$112$	−1.46968	+	6.11311i	−0.138872	+	0.577635i
$113$	−9.56433	+	1.68645i	−0.899737	+	0.158648i	−0.604340	−	0.796727i	$-0.706563\pi$
$113$	−9.56433	+	1.68645i	−0.899737	+	0.158648i	−0.295397	+	0.955375i	$0.595452\pi$
$114$	−0.912648	−	1.45056i	−0.0854773	−	0.135857i
$115$	0.140110	−	0.166976i	0.0130653	−	0.0155706i
$116$	−11.5105	−	6.64560i	−1.06872	−	0.617028i
$117$	15.5083	+	7.44575i	1.43375	+	0.688360i
$118$	−7.66710	+	4.42660i	−0.705814	+	0.407502i
$119$	−8.42708	−	16.9156i	−0.772509	−	1.55065i
$120$	0.339950	+	0.833984i	0.0310330	+	0.0761320i
$121$	11.7835	+	4.28886i	1.07123	+	0.389896i
$122$	−24.8089	−	9.02969i	−2.24609	−	0.817510i
$123$	−1.56650	+	0.638540i	−0.141247	+	0.0575752i
$124$	8.59572	+	1.51566i	0.771919	+	0.136110i
$125$	−1.92196	−	3.32893i	−0.171905	−	0.297748i
$126$	16.7559	−	3.20712i	1.49273	−	0.285713i
$127$	5.60501	−	9.70817i	0.497365	−	0.861461i	−0.502631	−	0.864501i	$-0.667634\pi$
$127$	5.60501	−	9.70817i	0.497365	−	0.861461i	0.999995	+	0.00304049i	$0.000967819\pi$
$128$	6.52112	−	7.77157i	0.576391	−	0.686916i
$129$	−6.16416	−	9.79729i	−0.542724	−	0.862603i
$130$	0.835425	+	4.73793i	0.0732716	+	0.415544i
$131$	16.2722	−	13.6540i	1.42171	−	1.19296i	0.471295	−	0.881976i	$-0.343787\pi$
$131$	16.2722	−	13.6540i	1.42171	−	1.19296i	0.950416	−	0.310982i	$-0.100658\pi$
$132$	6.73842	−	20.9586i	0.586504	−	1.82422i
$133$	−1.01543	−	0.672562i	−0.0880488	−	0.0583185i
$134$			14.4192i			1.24563i
$135$	−1.39538	+	1.47199i	−0.120095	+	0.126689i
$136$			9.51505i			0.815909i
$137$	−0.365575	−	1.00441i	−0.0312332	−	0.0858125i	0.923096	−	0.384570i	$-0.125650\pi$
$137$	−0.365575	−	1.00441i	−0.0312332	−	0.0858125i	−0.954329	+	0.298757i	$0.903428\pi$
$138$	0.438498	+	2.03211i	0.0373274	+	0.172984i
$139$	3.73504	+	4.45125i	0.316802	+	0.377550i	0.900821	−	0.434190i	$-0.142965\pi$
$139$	3.73504	+	4.45125i	0.316802	+	0.377550i	−0.584020	+	0.811740i	$0.698521\pi$
$140$	1.96193	+	1.86299i	0.165813	+	0.157451i
$141$	6.41294	−	0.243766i	0.540067	−	0.0205288i
$142$	11.5707	+	9.70898i	0.970993	+	0.814760i
$143$	13.9110	−	24.0945i	1.16329	−	2.01488i
$144$	6.86496	+	1.92271i	0.572080	+	0.160226i
$145$	1.71504	−	0.990180i	0.142427	−	0.0822300i
$146$	−2.82677	+	16.0314i	−0.233945	+	1.32677i
$147$	9.91462	−	6.97857i	0.817744	−	0.575583i
$148$	5.28533	+	1.92370i	0.434452	+	0.158127i
$149$	0.464232	−	1.27547i	0.0380314	−	0.104490i	−0.919223	−	0.393736i	$-0.871182\pi$
$149$	0.464232	−	1.27547i	0.0380314	−	0.104490i	0.957255	+	0.289246i	$0.0934045\pi$
$150$	17.8788	+	2.45645i	1.45980	+	0.200569i
$151$	−2.48969	+	14.1197i	−0.202608	+	1.14905i	0.698552	+	0.715559i	$0.253828\pi$
$151$	−2.48969	+	14.1197i	−0.202608	+	1.14905i	−0.901160	+	0.433487i	$0.857283\pi$
$152$	0.306612	+	0.531067i	0.0248695	+	0.0430752i
$153$	−19.5220	+	8.83658i	−1.57826	+	0.714395i
$154$	−3.11462	−	27.4142i	−0.250983	−	2.20910i
$155$	−0.835946	+	0.996242i	−0.0671448	+	0.0800201i
$156$	−23.0119	−	12.1447i	−1.84243	−	0.972354i
$157$	1.93067	−	0.340430i	0.154085	−	0.0271693i	−0.0960737	−	0.995374i	$-0.530628\pi$
$157$	1.93067	−	0.340430i	0.154085	−	0.0271693i	0.250158	+	0.968205i	$0.419517\pi$
$158$	−1.20371	−	1.43453i	−0.0957624	−	0.114125i
$159$	−3.64359	−	4.02158i	−0.288956	−	0.318932i
$160$	1.03757	+	2.85071i	0.0820274	+	0.225369i
$161$	0.878434	+	1.18792i	0.0692303	+	0.0936216i
$162$	−2.92851	−	19.1213i	−0.230086	−	1.50231i
$163$	14.8246			1.16115			0.580575	−	0.814207i	$-0.302828\pi$
$163$	14.8246			1.16115			0.580575	+	0.814207i	$0.302828\pi$
$164$	2.40434	−	0.875109i	0.187748	−	0.0683345i
$165$	2.20241	+	2.43089i	0.171458	+	0.189245i
$166$	−9.97260	−	11.8849i	−0.774024	−	0.922446i
$167$	0.656828	+	3.72506i	0.0508269	+	0.288254i	0.999618	−	0.0276516i	$-0.00880290\pi$
$167$	0.656828	+	3.72506i	0.0508269	+	0.288254i	−0.948791	+	0.315905i	$0.897692\pi$
$168$	−6.03483	+	0.919002i	−0.465597	+	0.0709026i
$169$	−15.2313	−	12.7806i	−1.17164	−	0.983121i
$170$	−5.18990	−	2.99639i	−0.398048	−	0.229813i
$171$	−0.804842	+	1.12228i	−0.0615478	+	0.0858225i
$172$	8.75381	+	15.1620i	0.667472	+	1.15609i
$173$	−2.67149	+	15.1508i	−0.203110	+	1.15189i	0.697277	+	0.716802i	$0.254395\pi$
$173$	−2.67149	+	15.1508i	−0.203110	+	1.15189i	−0.900387	+	0.435090i	$0.856716\pi$
$174$	−2.57088	+	18.7116i	−0.194898	+	1.41853i
$175$	12.2986	−	3.63877i	0.929689	−	0.275065i
$176$	3.94337	−	10.8343i	0.297243	−	0.816669i
$177$	5.63544	+	4.37494i	0.423585	+	0.328841i
$178$	−11.2524	−	1.98411i	−0.843405	−	0.148715i
$179$	14.0113	−	8.08943i	1.04725	−	0.604632i	0.125374	−	0.992109i	$-0.459987\pi$
$179$	14.0113	−	8.08943i	1.04725	−	0.604632i	0.921879	+	0.387477i	$0.126653\pi$
$180$	2.19358	−	2.14464i	0.163500	−	0.159852i
$181$	−15.8886	−	9.17326i	−1.18099	−	0.681843i	−0.224744	−	0.974418i	$-0.572155\pi$
$181$	−15.8886	−	9.17326i	−1.18099	−	0.681843i	−0.956243	+	0.292575i	$0.905488\pi$
$182$	−32.5481	−	2.00111i	−2.41262	−	0.148332i
$183$	0.808119	+	21.2598i	0.0597379	+	1.57157i
$184$	−0.129170	−	0.732562i	−0.00952257	−	0.0540052i
$185$	−0.641978	+	0.538684i	−0.0471992	+	0.0396048i
$186$	−2.61624	−	12.1243i	−0.191832	−	0.888997i
$187$	11.8531	+	32.5660i	0.866781	+	2.38146i
$188$	−9.70670			−0.707934
$189$	−7.49004	−	11.5282i	−0.544820	−	0.838553i
$190$	−0.386222			−0.0280195
$191$	−6.87241	−	18.8818i	−0.497270	−	1.36624i	−0.893903	−	0.448261i	$-0.852044\pi$
$191$	−6.87241	−	18.8818i	−0.497270	−	1.36624i	0.396633	−	0.917977i	$-0.370179\pi$
$192$	−19.7076	−	6.33621i	−1.42228	−	0.457277i
$193$	−16.4758	+	13.8249i	−1.18596	+	0.995136i	−0.186037	+	0.982543i	$0.559564\pi$
$193$	−16.4758	+	13.8249i	−1.18596	+	0.995136i	−0.999921	+	0.0125936i	$0.995991\pi$
$194$	−4.08827	−	23.1858i	−0.293521	−	1.66464i
$195$	3.28147	−	2.06460i	0.234991	−	0.147849i
$196$	−15.3862	+	9.97799i	−1.09901	+	0.712713i
$197$	2.96839	+	1.71380i	0.211489	+	0.122103i	0.602003	−	0.798494i	$-0.294369\pi$
$197$	2.96839	+	1.71380i	0.211489	+	0.122103i	−0.390514	+	0.920597i	$0.627703\pi$
$198$	−31.1944	+	2.37494i	−2.21689	+	0.168779i
$199$	9.32690	−	5.38489i	0.661166	−	0.381725i	−0.131555	−	0.991309i	$-0.541997\pi$
$199$	9.32690	−	5.38489i	0.661166	−	0.381725i	0.792721	+	0.609584i	$0.208664\pi$
$200$	−6.35938	−	1.12133i	−0.449676	−	0.0792901i
$201$	10.7600	−	4.38602i	0.758954	−	0.309366i
$202$	−10.1687	+	27.9382i	−0.715466	+	1.96573i
$203$	3.80826	+	12.8715i	0.267288	+	0.903403i
$204$	30.0138	−	12.2343i	2.10139	−	0.856571i
$205$	−0.0662004	+	0.375441i	−0.00462364	+	0.0262219i
$206$	13.1258	+	22.7346i	0.914520	+	1.58399i
$207$	1.38304	−	0.945346i	0.0961278	−	0.0657061i
$208$	−11.8014	−	6.81351i	−0.818276	−	0.472432i
$209$	1.71096	+	1.43567i	0.118350	+	0.0993072i
$210$	1.39917	−	3.58105i	0.0965521	−	0.247116i
$211$	0.0518221	+	0.293898i	0.00356758	+	0.0202327i	0.986540	−	0.163523i	$-0.0522857\pi$
$211$	0.0518221	+	0.293898i	0.00356758	+	0.0202327i	−0.982972	+	0.183755i	$0.941175\pi$
$212$	5.27598	+	6.28767i	0.362356	+	0.431839i
$213$	3.72556	−	11.5877i	0.255271	−	0.793975i
$214$	−11.2503	+	4.09477i	−0.769054	+	0.279913i
$215$	−2.60860			−0.177905
$216$	0.787234	+	6.87683i	0.0535645	+	0.467909i
$217$	−5.24106	−	7.08760i	−0.355786	−	0.481138i
$218$	−2.74352	−	7.53775i	−0.185814	−	0.510521i
$219$	12.8230	−	2.76701i	0.866496	−	0.186977i
$220$	−3.18913	−	3.80065i	−0.215011	−	0.256240i
$221$	40.3380	−	7.11269i	2.71343	−	0.478451i
$222$	−0.303598	−	7.98696i	−0.0203761	−	0.536050i
$223$	1.84202	−	2.19524i	0.123351	−	0.147004i	−0.700835	−	0.713324i	$-0.747189\pi$
$223$	1.84202	−	2.19524i	0.123351	−	0.147004i	0.824185	+	0.566320i	$0.191633\pi$
$224$	−20.4310	+	2.32124i	−1.36510	+	0.155094i
$225$	−3.60529	−	14.0889i	−0.240353	−	0.939262i
$226$	−10.4372	−	18.0777i	−0.694270	−	1.20251i
$227$	−4.81038	+	27.2810i	−0.319276	+	1.81070i	0.227897	+	0.973685i	$0.426815\pi$
$227$	−4.81038	+	27.2810i	−0.319276	+	1.81070i	−0.547173	+	0.837019i	$0.684296\pi$
$228$	1.28094	−	1.65000i	0.0848322	−	0.109274i
$229$	8.06759	−	22.1655i	0.533121	−	1.46474i	−0.322216	−	0.946666i	$-0.604428\pi$
$229$	8.06759	−	22.1655i	0.533121	−	1.46474i	0.855337	−	0.518072i	$-0.173350\pi$
$230$	0.440247	+	0.160237i	0.0290290	+	0.0105657i
$231$	−19.5099	+	10.6630i	−1.28365	+	0.701577i
$232$	1.17356	−	6.65561i	0.0770482	−	0.436962i
$233$	7.45007	−	4.30130i	0.488070	−	0.281787i	−0.235703	−	0.971825i	$-0.575739\pi$
$233$	7.45007	−	4.30130i	0.488070	−	0.281787i	0.723774	+	0.690038i	$0.242406\pi$
$234$	−3.63792	+	36.7963i	−0.237818	+	2.40545i
$235$	0.723139	−	1.25251i	0.0471724	−	0.0817049i
$236$	−8.26621	−	6.93617i	−0.538084	−	0.451506i
$237$	−0.704345	+	1.33460i	−0.0457521	+	0.0866918i
$238$	27.9701	−	29.4556i	1.81303	−	1.90932i
$239$	8.52364	+	10.1581i	0.551348	+	0.657071i	0.967692	−	0.252136i	$-0.0811331\pi$
$239$	8.52364	+	10.1581i	0.551348	+	0.657071i	−0.416344	+	0.909207i	$0.636689\pi$
$240$	1.19064	−	1.07873i	0.0768554	−	0.0696317i
$241$	−3.73945	−	10.2740i	−0.240879	−	0.661809i	−0.999942	−	0.0107919i	$-0.996565\pi$
$241$	−3.73945	−	10.2740i	−0.240879	−	0.661809i	0.759063	−	0.651017i	$-0.225657\pi$
$242$			26.9525i			1.73258i
$243$	−13.3781	+	8.00165i	−0.858206	+	0.513306i
$244$		−	32.1790i		−	2.06005i
$245$	−0.141267	−	2.72872i	−0.00902520	−	0.174331i
$246$	−2.44126	−	2.69452i	−0.155649	−	0.171796i
$247$	2.02220	−	1.69683i	0.128670	−	0.107967i
$248$	0.770678	+	4.37073i	0.0489381	+	0.277542i
$249$	−5.83540	+	11.0570i	−0.369803	+	0.700708i
$250$	5.31069	−	6.32903i	0.335877	−	0.400283i
$251$	5.12956	−	8.88466i	0.323775	−	0.560795i	−0.657489	−	0.753464i	$-0.728381\pi$
$251$	5.12956	−	8.88466i	0.323775	−	0.560795i	0.981264	+	0.192670i	$0.0617146\pi$
$252$	10.6583	+	17.8544i	0.671412	+	1.12472i
$253$	−1.35466	−	2.34634i	−0.0851667	−	0.147513i
$254$	23.7284	+	4.18395i	1.48885	+	0.262524i
$255$	−0.657337	+	4.78430i	−0.0411640	+	0.299605i
$256$	−1.97169	−	0.717638i	−0.123231	−	0.0448524i
$257$	−1.27159	−	0.462822i	−0.0793198	−	0.0288700i	0.302055	−	0.953290i	$-0.402327\pi$
$257$	−1.27159	−	0.462822i	−0.0793198	−	0.0288700i	−0.381375	+	0.924420i	$0.624549\pi$
$258$	15.2566	−	19.6522i	0.949831	−	1.22349i
$259$	−2.53294	−	5.08433i	−0.157389	−	0.315925i
$260$	−5.07832	+	2.93197i	−0.314944	+	0.181833i
$261$	14.7452	−	3.77323i	0.912705	−	0.233557i
$262$	39.5397	+	22.8283i	2.44277	+	1.41033i
$263$	4.58008	−	5.45832i	0.282420	−	0.336575i	−0.606121	−	0.795372i	$-0.707275\pi$
$263$	4.58008	−	5.45832i	0.282420	−	0.336575i	0.888541	+	0.458798i	$0.151720\pi$
$264$	11.1862	−	0.425206i	0.688462	−	0.0261696i
$265$	−1.20439	+	0.212366i	−0.0739851	+	0.0130456i
$266$	0.611933	−	2.54532i	0.0375200	−	0.156064i
$267$	1.94216	+	9.00042i	0.118858	+	0.550817i
$268$	−16.5150	+	6.01097i	−1.00881	+	0.367178i
$269$	6.69363			0.408118			0.204059	−	0.978959i	$-0.434587\pi$
$269$	6.69363			0.408118			0.204059	+	0.978959i	$0.434587\pi$
$270$	−3.99882	−	1.73620i	−0.243360	−	0.105662i
$271$		−	15.0044i		−	0.911450i	−0.890121	−	0.455725i	$-0.849380\pi$
$271$		−	15.0044i		−	0.911450i	0.890121	−	0.455725i	$-0.150620\pi$
$272$	15.9506	−	5.80556i	0.967150	−	0.352014i
$273$	8.40717	+	24.8971i	0.508825	+	1.50684i
$274$	1.75990	−	1.47673i	0.106320	−	0.0892128i
$275$	−23.1624	+	4.08415i	−1.39674	+	0.246283i
$276$	−2.14467	+	1.34936i	−0.129094	+	0.0812222i
$277$	−19.7269	−	16.5529i	−1.18528	−	0.994566i	−0.999929	−	0.0118925i	$-0.996214\pi$
$277$	−19.7269	−	16.5529i	−1.18528	−	0.994566i	−0.185348	−	0.982673i	$-0.559341\pi$
$278$	−6.24464	+	10.8160i	−0.374529	+	0.648703i
$279$	−8.25171	+	5.64028i	−0.494017	+	0.337675i
$280$	−0.548961	+	1.26143i	−0.0328067	+	0.0753847i
$281$	−7.95320	−	1.40236i	−0.474448	−	0.0836580i	−0.0686892	−	0.997638i	$-0.521882\pi$
$281$	−7.95320	−	1.40236i	−0.474448	−	0.0836580i	−0.405759	+	0.913980i	$0.632993\pi$
$282$	5.20666	+	12.7733i	0.310052	+	0.760637i
$283$	−2.15839	+	5.93013i	−0.128303	+	0.352510i	−0.987166	−	0.159695i	$-0.948949\pi$
$283$	−2.15839	+	5.93013i	−0.128303	+	0.352510i	0.858863	+	0.512205i	$0.171171\pi$
$284$	−6.29665	+	17.2999i	−0.373638	+	1.02656i
$285$	0.117481	+	0.288210i	0.00695895	+	0.0170721i
$286$	58.8909	+	10.3841i	3.48229	+	0.614022i
$287$	−2.36938	−	1.03113i	−0.139860	−	0.0608659i
$288$	1.76997	+	23.2483i	0.104297	+	1.36992i
$289$	−17.0108	+	29.4636i	−1.00064	+	1.73316i
$290$	3.26068	+	2.73603i	0.191474	+	0.160665i
$291$	−16.0583	+	10.1034i	−0.941357	+	0.592273i
$292$	−19.5400	+	3.44542i	−1.14349	+	0.201628i
$293$	−6.25563	+	5.24910i	−0.365458	+	0.306656i	−0.806962	−	0.590604i	$-0.798890\pi$
$293$	−6.25563	+	5.24910i	−0.365458	+	0.306656i	0.441504	+	0.897259i	$0.354445\pi$
$294$	21.3834	+	14.8948i	1.24710	+	0.868684i
$295$	1.51084	−	0.549900i	0.0879644	−	0.0320164i
$296$			2.85995i			0.166231i
$297$	11.2610	+	22.5558i	0.653427	+	1.30882i
$298$	2.91738			0.168999
$299$	−3.00906	+	1.09521i	−0.174018	+	0.0633375i
$300$	4.63971	+	21.5015i	0.267874	+	1.24139i
$301$	4.13308	−	17.1915i	0.238227	−	0.990899i
$302$	−30.3484	+	5.35124i	−1.74635	+	0.307929i
$303$	23.9414	−	0.910054i	1.37540	−	0.0522812i
$304$	0.703182	−	0.838020i	0.0403303	−	0.0480637i
$305$	4.15225	+	2.39730i	0.237757	+	0.137269i
$306$	−32.1987	−	32.9335i	−1.84068	−	1.88268i
$307$	20.0345	−	11.5669i	1.14343	−	0.660159i	0.196151	−	0.980574i	$-0.437156\pi$
$307$	20.0345	−	11.5669i	1.14343	−	0.660159i	0.947277	+	0.320415i	$0.103822\pi$
$308$	30.1004	−	14.9955i	1.71513	−	0.854451i
$309$	12.9726	−	16.7103i	0.737987	−	0.950615i
$310$	−2.62668	−	0.956032i	−0.149185	−	0.0542990i
$311$	−22.1526	−	8.06290i	−1.25616	−	0.457205i	−0.373682	−	0.927557i	$-0.621905\pi$
$311$	−22.1526	−	8.06290i	−1.25616	−	0.457205i	−0.882479	+	0.470352i	$0.844127\pi$
$312$	1.80090	−	13.1075i	0.101956	−	0.742065i
$313$	−11.7748	−	2.07621i	−0.665550	−	0.117354i	−0.169341	−	0.985557i	$-0.554164\pi$
$313$	−11.7748	−	2.07621i	−0.665550	−	0.117354i	−0.496209	+	0.868203i	$0.665275\pi$
$314$	2.10687	+	3.64920i	0.118897	+	0.205936i
$315$	−3.09789	+	0.0451778i	−0.174546	+	0.00254548i
$316$	1.14124	−	1.97669i	0.0641999	−	0.111197i
$317$	−18.1039	+	21.5754i	−1.01682	+	1.21179i	−0.0396733	+	0.999213i	$0.512632\pi$
$317$	−18.1039	+	21.5754i	−1.01682	+	1.21179i	−0.977143	+	0.212582i	$0.931813\pi$
$318$	5.44406	−	10.3155i	0.305288	−	0.578463i
$319$	−4.27439	−	24.2413i	−0.239320	−	1.35725i
$320$	−3.57380	+	2.99877i	−0.199781	+	0.167636i
$321$	6.47775	+	7.14976i	0.361553	+	0.399061i
$322$	−1.75354	+	2.64748i	−0.0977210	+	0.147538i
$323$			3.28823i			0.182962i
$324$	20.6797	−	11.3253i	1.14887	−	0.629184i
$325$			27.7982i			1.54196i
$326$	10.8979	+	29.9418i	0.603580	+	1.65832i
$327$	−4.79037	+	4.34012i	−0.264908	+	0.240009i
$328$	0.836276	+	0.996635i	0.0461756	+	0.0550300i
$329$	7.10870	+	6.75020i	0.391915	+	0.372150i
$330$	−3.29073	+	6.23531i	−0.181149	+	0.343243i
$331$	−11.5569	−	9.69739i	−0.635224	−	0.533017i	0.267323	−	0.963607i	$-0.413861\pi$
$331$	−11.5569	−	9.69739i	−0.635224	−	0.533017i	−0.902547	+	0.430590i	$0.858305\pi$
$332$	9.45503	−	16.3766i	0.518912	−	0.898782i
$333$	−5.86776	+	2.65602i	−0.321551	+	0.145549i
$334$	−7.04080	+	4.06501i	−0.385255	+	0.222427i
$335$	0.454719	−	2.57884i	0.0248440	−	0.140897i
$336$	5.22270	+	9.55582i	0.284922	+	0.521313i
$337$	−15.3260	−	5.57821i	−0.834860	−	0.303864i	−0.111008	−	0.993819i	$-0.535408\pi$
$337$	−15.3260	−	5.57821i	−0.834860	−	0.303864i	−0.723852	+	0.689955i	$0.757630\pi$
$338$	14.6165	−	40.1586i	0.795034	−	2.18434i
$339$	−10.3154	+	13.2874i	−0.560253	+	0.721672i
$340$	1.26838	−	7.19337i	0.0687878	−	0.390115i
$341$	8.08240	+	13.9991i	0.437687	+	0.758096i
$342$	−2.85836	−	0.800559i	−0.154563	−	0.0432893i
$343$	18.2069	+	3.39241i	0.983081	+	0.183173i
$344$	−5.72225	+	6.81951i	−0.308523	+	0.367683i
$345$	−0.0143405	−	0.377266i	−0.000772067	−	0.0203113i
$346$	−32.5645	+	5.74200i	−1.75068	+	0.308692i
$347$	−23.3846	−	27.8687i	−1.25535	−	1.49607i	−0.792802	−	0.609480i	$-0.791378\pi$
$347$	−23.3846	−	27.8687i	−1.25535	−	1.49607i	−0.462552	−	0.886592i	$-0.653066\pi$
$348$	−22.5031	+	4.85583i	−1.20629	+	0.260300i
$349$	−2.98415	−	8.19888i	−0.159738	−	0.438876i	0.833843	−	0.552002i	$-0.186136\pi$
$349$	−2.98415	−	8.19888i	−0.159738	−	0.438876i	−0.993581	+	0.113126i	$0.963914\pi$
$350$	16.3904	+	22.1651i	0.876104	+	1.18477i
$351$	28.5651	−	8.47796i	1.52469	−	0.452520i
$352$	37.7074			2.00981
$353$	8.54968	−	3.11183i	0.455053	−	0.165626i	−0.104316	−	0.994544i	$-0.533265\pi$
$353$	8.54968	−	3.11183i	0.455053	−	0.165626i	0.559370	+	0.828918i	$0.311043\pi$
$354$	−4.69349	+	14.5982i	−0.249456	+	0.775888i
$355$	−1.76322	−	2.10132i	−0.0935818	−	0.111526i
$356$	−2.41834	−	13.7151i	−0.128172	−	0.726897i
$357$	−30.4885	−	11.9123i	−1.61362	−	0.630468i
$358$	26.6386	+	22.3524i	1.40789	+	1.18136i
$359$	−0.444525	−	0.256647i	−0.0234611	−	0.0135453i	0.488224	−	0.872719i	$-0.337645\pi$
$359$	−0.444525	−	0.256647i	−0.0234611	−	0.0135453i	−0.511685	+	0.859173i	$0.670978\pi$
$360$	1.40622	+	0.675146i	0.0741145	+	0.0355833i
$361$	−9.39404	−	16.2710i	−0.494423	−	0.856366i
$362$	6.84752	−	38.8342i	0.359898	−	2.04108i
$363$	20.1128	−	8.19841i	1.05565	−	0.430305i
$364$	−11.2764	−	38.1131i	−0.591046	−	1.99767i
$365$	1.01112	−	2.77804i	0.0529246	−	0.145409i
$366$	−42.3451	+	17.2608i	−2.21342	+	0.902236i
$367$	−30.6284	−	5.40061i	−1.59879	−	0.281910i	−0.697977	−	0.716120i	$-0.745916\pi$
$367$	−30.6284	−	5.40061i	−1.59879	−	0.281910i	−0.900812	+	0.434210i	$0.857028\pi$
$368$	−1.14922	+	0.663505i	−0.0599075	+	0.0345876i
$369$	−1.26815	+	2.64136i	−0.0660174	+	0.137504i
$370$	−1.55994	−	0.900630i	−0.0810972	−	0.0468215i
$371$	0.508685	−	8.27377i	0.0264096	−	0.429553i
$372$	12.7959	−	8.05080i	0.663437	−	0.417415i
$373$	4.53556	+	25.7224i	0.234842	+	1.33186i	0.842945	+	0.537999i	$0.180820\pi$
$373$	4.53556	+	25.7224i	0.234842	+	1.33186i	−0.608103	+	0.793858i	$0.708069\pi$
$374$	−57.0614	+	47.8802i	−2.95057	+	2.47583i
$375$	−6.33832	−	2.03783i	−0.327309	−	0.105233i
$376$	−1.68809	−	4.63799i	−0.0870565	−	0.239186i
$377$	−29.0930			−1.49837
$378$	17.7778	−	23.6026i	0.914394	−	1.21399i
$379$	−28.5024			−1.46407			−0.732035	−	0.681267i	$-0.761429\pi$
$379$	−28.5024			−1.46407			−0.732035	+	0.681267i	$0.761429\pi$
$380$	−0.161005	−	0.442358i	−0.00825940	−	0.0226925i
$381$	−4.09549	−	18.9795i	−0.209818	−	0.972349i
$382$	33.0842	−	27.7610i	1.69274	−	1.42037i
$383$	2.37420	+	13.4648i	0.121316	+	0.688017i	0.983428	+	0.181299i	$0.0580303\pi$
$383$	2.37420	+	13.4648i	0.121316	+	0.688017i	−0.862112	+	0.506718i	$0.830859\pi$
$384$	−0.667450	−	17.5591i	−0.0340607	−	0.896058i
$385$	−0.307481	+	5.00118i	−0.0156707	+	0.254884i
$386$	−40.0345	−	23.1139i	−2.03770	−	1.17647i
$387$	−19.3058	−	5.40709i	−0.981370	−	0.274858i
$388$	24.8515	−	14.3480i	1.26164	−	0.728410i
$389$	24.7405	+	4.36241i	1.25439	+	0.221183i	0.761073	−	0.648666i	$-0.224673\pi$
$389$	24.7405	+	4.36241i	1.25439	+	0.221183i	0.493318	+	0.869849i	$0.335784\pi$
$390$	6.58225	+	5.10997i	0.333305	+	0.258754i
$391$	1.36423	−	3.74820i	0.0689922	−	0.189554i
$392$	−7.44341	−	5.61644i	−0.375949	−	0.283673i
$393$	5.00797	−	36.4496i	0.252619	−	1.83864i
$394$	−1.27929	+	7.25523i	−0.0644498	+	0.365513i
$395$	0.170043	+	0.294523i	0.00855578	+	0.0148190i
$396$	−15.7242	−	34.7385i	−0.790173	−	1.74567i
$397$	−6.75634	−	3.90078i	−0.339091	−	0.195774i	0.320779	−	0.947154i	$-0.396055\pi$
$397$	−6.75634	−	3.90078i	−0.339091	−	0.195774i	−0.659870	+	0.751380i	$0.729389\pi$
$398$	17.7325	+	14.8794i	0.888851	+	0.745834i
$399$	−2.08553	+	0.317591i	−0.104407	+	0.0158994i
$400$	2.00039	+	11.3448i	0.100020	+	0.567240i
$401$	0.935778	+	1.11522i	0.0467305	+	0.0556913i	0.788903	−	0.614517i	$-0.210649\pi$
$401$	0.935778	+	1.11522i	0.0467305	+	0.0556913i	−0.742173	+	0.670208i	$0.766205\pi$
$402$	16.7686	+	18.5082i	0.836342	+	0.923105i
$403$	17.9532	−	6.53442i	0.894311	−	0.325503i
$404$	−36.2380			−1.80291
$405$	−0.0792456	+	3.51215i	−0.00393775	+	0.174520i
$406$	−23.1975	+	17.1539i	−1.15128	+	0.851333i
$407$	3.56269	+	9.78840i	0.176596	+	0.485193i
$408$	11.0654	+	12.2133i	0.547819	+	0.604650i
$409$	6.16526	+	7.34748i	0.304853	+	0.363309i	0.896621	−	0.442799i	$-0.146014\pi$
$409$	6.16526	+	7.34748i	0.304853	+	0.363309i	−0.591768	+	0.806108i	$0.701570\pi$
$410$	−0.806959	+	0.142289i	−0.0398529	+	0.00702714i
$411$	−1.63731	−	0.864101i	−0.0807625	−	0.0426229i
$412$	−20.5672	+	24.5111i	−1.01328	+	1.20757i
$413$	1.23023	+	10.8282i	0.0605355	+	0.532819i
$414$	2.92606	+	2.09843i	0.143808	+	0.103132i
$415$	1.40878	+	2.44008i	0.0691543	+	0.119779i
$416$	7.73895	−	43.8898i	0.379433	−	2.15187i
$417$	9.97074	+	1.36992i	0.488269	+	0.0670855i
$418$	−1.64190	+	4.51109i	−0.0803081	+	0.220645i
$419$	20.7203	+	7.54159i	1.01225	+	0.368431i	0.794298	−	0.607528i	$-0.207839\pi$
$419$	20.7203	+	7.54159i	1.01225	+	0.368431i	0.217956	+	0.975959i	$0.430061\pi$
$420$	4.68483	+	0.109697i	0.228596	+	0.00535264i
$421$	−4.79615	+	27.2003i	−0.233750	+	1.32566i	0.611481	+	0.791259i	$0.290574\pi$
$421$	−4.79615	+	27.2003i	−0.233750	+	1.32566i	−0.845230	+	0.534402i	$0.820537\pi$
$422$	−0.555501	+	0.320719i	−0.0270414	+	0.0156123i
$423$	7.94804	−	7.77073i	0.386447	−	0.377826i
$424$	−2.08678	+	3.61442i	−0.101343	+	0.175532i
$425$	−26.5254	−	22.2574i	−1.28667	−	1.07964i
$426$	26.1429	−	0.993734i	1.26663	−	0.0481466i
$427$	−22.3778	+	23.5663i	−1.08294	+	1.14045i
$428$	−9.37988	−	11.1785i	−0.453394	−	0.540334i
$429$	−10.1645	−	47.1048i	−0.490747	−	2.27424i
$430$	−1.91765	−	5.26869i	−0.0924771	−	0.254079i
$431$		−	13.9378i		−	0.671358i	−0.941976	−	0.335679i	$-0.891034\pi$
$431$		−	13.9378i		−	0.671358i	0.941976	−	0.335679i	$-0.108966\pi$
$432$	11.0477	−	5.51555i	0.531534	−	0.265367i
$433$			20.8489i			1.00193i	0.865467	+	0.500966i	$0.167022\pi$
$433$			20.8489i			1.00193i	−0.865467	+	0.500966i	$0.832978\pi$
$434$	10.4623	−	15.7959i	0.502205	−	0.758225i
$435$	1.04988	−	3.26546i	0.0503379	−	0.156567i
$436$	7.48965	−	6.28456i	0.358689	−	0.300976i
$437$	−0.0446390	−	0.253160i	−0.00213537	−	0.0121103i
$438$	15.0151	+	23.8650i	0.717451	+	1.14031i
$439$	−2.39592	+	2.85534i	−0.114351	+	0.136278i	−0.820183	−	0.572101i	$-0.806129\pi$
$439$	−2.39592	+	2.85534i	−0.114351	+	0.136278i	0.705833	+	0.708379i	$0.250573\pi$
$440$	1.26138	−	2.18478i	0.0601340	−	0.104155i
$441$	4.61059	−	20.4876i	0.219552	−	0.975601i
$442$	44.0193	+	76.2437i	2.09378	+	3.62654i
$443$	5.16917	+	0.911464i	0.245595	+	0.0433050i	0.295090	−	0.955469i	$-0.404650\pi$
$443$	5.16917	+	0.911464i	0.245595	+	0.0433050i	−0.0494956	+	0.998774i	$0.515761\pi$
$444$	9.02130	−	3.67727i	0.428132	−	0.174516i
$445$	1.94990	+	0.709706i	0.0924342	+	0.0336433i
$446$	5.78792	+	2.10663i	0.274066	+	0.0997519i
$447$	−0.887407	−	2.17704i	−0.0419729	−	0.102970i
$448$	−14.1005	−	28.3037i	−0.666185	−	1.33722i
$449$	−22.4516	+	12.9624i	−1.05956	+	0.611735i	−0.925310	−	0.379212i	$-0.876195\pi$
$449$	−22.4516	+	12.9624i	−1.05956	+	0.611735i	−0.134247	+	0.990948i	$0.542862\pi$
$450$	25.8056	−	17.6389i	1.21649	−	0.831505i
$451$	4.10375	+	2.36930i	0.193238	+	0.111566i
$452$	16.3543	−	19.4903i	0.769242	−	0.916747i
$453$	13.2246	+	21.0191i	0.621346	+	0.987565i
$454$	−58.6368	+	10.3392i	−2.75196	+	0.485245i
$455$	5.75804	+	1.38432i	0.269941	+	0.0648979i
$456$	1.01116	+	0.325098i	0.0473518	+	0.0152241i
$457$	19.4951	−	7.09562i	0.911940	−	0.331919i	0.156913	−	0.987612i	$-0.449846\pi$
$457$	19.4951	−	7.09562i	0.911940	−	0.331919i	0.755027	+	0.655693i	$0.227624\pi$
$458$	50.6993			2.36902
$459$	−14.7817	+	34.0453i	−0.689952	+	1.58910i
$460$			0.571034i			0.0266246i
$461$	−0.166492	+	0.0605983i	−0.00775433	+	0.00282234i	−0.345894	−	0.938273i	$-0.612424\pi$
$461$	−0.166492	+	0.0605983i	−0.00775433	+	0.00282234i	0.338140	+	0.941096i	$0.390202\pi$
$462$	−35.8788	−	31.5662i	−1.66923	−	1.46859i
$463$	22.1677	−	18.6009i	1.03022	−	0.864457i	0.0393425	−	0.999226i	$-0.487474\pi$
$463$	22.1677	−	18.6009i	1.03022	−	0.864457i	0.990877	+	0.134769i	$0.0430292\pi$
$464$	−11.8732	+	2.09357i	−0.551201	+	0.0971916i
$465$	0.0855608	+	2.25091i	0.00396779	+	0.104383i
$466$	14.1642	+	11.8852i	0.656146	+	0.550572i
$467$	4.43621	−	7.68373i	0.205283	−	0.355561i	−0.744940	−	0.667132i	$-0.767522\pi$
$467$	4.43621	−	7.68373i	0.205283	−	0.355561i	0.950223	+	0.311571i	$0.100855\pi$
$468$	−43.6612	+	11.1727i	−2.01824	+	0.516459i
$469$	16.2749	+	7.08267i	0.751504	+	0.327047i
$470$	3.06135	+	0.539798i	0.141209	+	0.0248990i
$471$	2.08228	−	2.68222i	0.0959463	−	0.123590i
$472$	1.87662	−	5.15597i	0.0863784	−	0.237323i
$473$	−11.0897	+	30.4686i	−0.509903	+	1.40095i
$474$	−3.21333	−	0.441494i	−0.147593	−	0.0202785i
$475$	−2.19769	−	0.387512i	−0.100837	−	0.0177803i
$476$	45.3969	+	19.7563i	2.08076	+	0.905527i
$477$	−9.35369	−	0.924766i	−0.428276	−	0.0423421i
$478$	−14.2507	+	24.6830i	−0.651813	+	1.12897i
$479$	−4.86205	−	4.07975i	−0.222153	−	0.186408i	0.524918	−	0.851153i	$-0.324096\pi$
$479$	−4.86205	−	4.07975i	−0.222153	−	0.186408i	−0.747071	+	0.664744i	$0.768540\pi$
$480$	4.64700	+	2.45249i	0.212106	+	0.111940i
$481$	12.1245	−	2.13787i	0.552828	−	0.0974784i
$482$	18.0019	−	15.1054i	0.819966	−	0.688033i
$483$	2.50902	+	0.503235i	0.114164	+	0.0228980i
$484$	−30.8701	+	11.2358i	−1.40318	+	0.510717i
$485$			4.27565i			0.194147i
$486$	−25.9958	−	21.1381i	−1.17920	−	0.958843i
$487$	5.19850			0.235566			0.117783	−	0.993039i	$-0.462421\pi$
$487$	5.19850			0.235566			0.117783	+	0.993039i	$0.462421\pi$
$488$	15.3756	−	5.59625i	0.696019	−	0.253330i
$489$	19.0285	−	17.2400i	0.860500	−	0.779621i
$490$	5.40745	−	2.29127i	0.244284	−	0.103509i
$491$	−13.4965	+	2.37981i	−0.609091	+	0.107399i	−0.469682	−	0.882836i	$-0.655631\pi$
$491$	−13.4965	+	2.37981i	−0.609091	+	0.107399i	−0.139409	+	0.990235i	$0.544520\pi$
$492$	2.06847	−	3.91937i	0.0932539	−	0.176699i
$493$	23.2942	−	27.7609i	1.04912	−	1.25029i
$494$	4.91373	+	2.83694i	0.221079	+	0.127640i
$495$	5.65395	+	0.558986i	0.254126	+	0.0251245i
$496$	6.85670	−	3.95872i	0.307875	−	0.177752i
$497$	16.6420	−	8.29079i	0.746496	−	0.371893i
$498$	−26.6220	−	3.65772i	−1.19296	−	0.163906i
$499$	−32.4000	−	11.7926i	−1.45042	−	0.527911i	−0.507714	−	0.861526i	$-0.669509\pi$
$499$	−32.4000	−	11.7926i	−1.45042	−	0.527911i	−0.942709	+	0.333615i	$0.891732\pi$
$500$	9.46283	+	3.44419i	0.423191	+	0.154029i
$501$	5.17510	+	4.01757i	0.231206	+	0.179492i
$502$	21.7156	+	3.82904i	0.969213	+	0.170898i
$503$	−19.0162	−	32.9370i	−0.847891	−	1.46859i	−0.883087	−	0.469209i	$-0.844539\pi$
$503$	−19.0162	−	32.9370i	−0.847891	−	1.46859i	0.0351966	−	0.999380i	$-0.488794\pi$
$504$	−6.67745	+	8.19774i	−0.297437	+	0.365156i
$505$	2.69969	−	4.67601i	0.120135	−	0.208080i
$506$	3.74315	−	4.46092i	0.166403	−	0.198312i
$507$	−34.4136	+	1.30812i	−1.52836	+	0.0580955i
$508$	5.09963	+	28.9214i	0.226259	+	1.28318i
$509$	2.43971	−	2.04716i	0.108138	−	0.0907387i	−0.587115	−	0.809503i	$-0.699737\pi$
$509$	2.43971	−	2.04716i	0.108138	−	0.0907387i	0.695254	+	0.718765i	$0.255292\pi$
$510$	−10.1463	+	2.18941i	−0.449285	+	0.0969489i
$511$	16.7061	+	11.0652i	0.739034	+	0.489494i
$512$		−	24.8000i		−	1.09601i
$513$	0.272054	+	2.37651i	0.0120115	+	0.104926i
$514$		−	2.90852i		−	0.128289i
$515$	−1.63057	−	4.47996i	−0.0718516	−	0.197411i
$516$	28.8687	+	9.28159i	1.27087	+	0.408599i
$517$	−11.5552	−	13.7710i	−0.508198	−	0.605647i
$518$	8.40700	−	8.85350i	0.369383	−	0.389000i
$519$	14.1903	+	22.5540i	0.622885	+	0.990011i
$520$	−2.28410	−	1.91659i	−0.100164	−	0.0840479i
$521$	−13.0875	+	22.6683i	−0.573375	+	0.993115i	0.422841	+	0.906204i	$0.361033\pi$
$521$	−13.0875	+	22.6683i	−0.573375	+	0.993115i	−0.996216	+	0.0869113i	$0.972300\pi$
$522$	18.4605	+	27.0077i	0.807995	+	1.18209i
$523$	−14.0356	+	8.10349i	−0.613736	+	0.354341i	−0.774426	−	0.632664i	$-0.781961\pi$
$523$	−14.0356	+	8.10349i	−0.613736	+	0.354341i	0.160690	+	0.987005i	$0.448628\pi$
$524$	−9.66329	+	54.8032i	−0.422143	+	2.39409i
$525$	11.5546	−	18.9732i	0.504286	−	0.828057i
$526$	14.3913	+	5.23801i	0.627492	+	0.228388i
$527$	−8.13951	+	22.3631i	−0.354563	+	0.974153i
$528$	−7.53799	−	18.4926i	−0.328049	−	0.804789i
$529$	3.93976	−	22.3435i	0.171294	−	0.971456i
$530$	−1.31430	−	2.27644i	−0.0570897	−	0.0988822i
$531$	12.3213	−	0.938063i	0.534699	−	0.0407084i
$532$	3.17038	−	0.360198i	0.137453	−	0.0156166i
$533$	3.60000	−	4.29031i	0.155933	−	0.185834i
$534$	−16.7508	+	10.5391i	−0.724878	+	0.456071i
$535$	2.14122	−	0.377555i	0.0925731	−	0.0163231i
$536$	−5.74424	−	6.84572i	−0.248113	−	0.295690i
$537$	8.57715	−	26.6777i	0.370131	−	1.15123i
$538$	4.92065	+	13.5194i	0.212144	+	0.582862i
$539$	−32.4722	−	9.95031i	−1.39867	−	0.428590i
$540$	0.321554	−	5.30382i	0.0138375	−	0.228240i
$541$	9.50292			0.408562			0.204281	−	0.978912i	$-0.434514\pi$
$541$	9.50292			0.408562			0.204281	+	0.978912i	$0.434514\pi$
$542$	30.3049	−	11.0301i	1.30171	−	0.473783i
$543$	−31.0622	+	6.70274i	−1.33300	+	0.287642i
$544$	35.6838	+	42.5263i	1.52993	+	1.82330i
$545$	0.252964	+	1.43463i	0.0108358	+	0.0614527i
$546$	−44.1053	+	35.2827i	−1.88753	+	1.50996i
$547$	−7.11504	−	5.97023i	−0.304217	−	0.255269i	0.477880	−	0.878425i	$-0.341405\pi$
$547$	−7.11504	−	5.97023i	−0.304217	−	0.255269i	−0.782097	+	0.623157i	$0.785850\pi$
$548$	2.42503	+	1.40009i	0.103592	+	0.0598090i
$549$	25.7610	+	26.3488i	1.09945	+	1.12454i
$550$	−25.2762	−	43.7796i	−1.07778	−	1.86677i
$551$	0.405563	−	2.30006i	0.0172775	−	0.0979858i
$552$	−1.01772	−	0.790085i	−0.0433172	−	0.0336283i
$553$	−2.21041	+	0.653990i	−0.0939963	+	0.0278105i
$554$	18.9307	−	52.0117i	0.804289	−	2.20977i
$555$	−0.197577	+	1.43802i	−0.00838666	+	0.0610407i
$556$	−14.9913	−	2.64338i	−0.635775	−	0.112104i
$557$	10.3816	−	5.99382i	0.439882	−	0.253966i	−0.263665	−	0.964614i	$-0.584931\pi$
$557$	10.3816	−	5.99382i	0.439882	−	0.253966i	0.703548	+	0.710648i	$0.251598\pi$
$558$	−17.4580	−	12.5200i	−0.739054	−	0.530014i
$559$	33.1881	+	19.1611i	1.40371	+	0.810430i
$560$	2.44955	+	0.150602i	0.103512	+	0.00636412i
$561$	53.0865	+	28.0168i	2.24131	+	1.18287i
$562$	−3.01419	−	17.0943i	−0.127146	−	0.721080i
$563$	−0.0744631	+	0.0624819i	−0.00313824	+	0.00263330i	−0.644355	−	0.764726i	$-0.722874\pi$
$563$	−0.0744631	+	0.0624819i	−0.00313824	+	0.00263330i	0.641217	+	0.767359i	$0.278430\pi$
$564$	−12.4593	+	11.2883i	−0.524633	+	0.475322i
$565$	1.29657	+	3.56230i	0.0545472	+	0.149867i
$566$	−13.5640			−0.570138
$567$	−23.0206	−	6.08694i	−0.966775	−	0.255628i
$568$	−9.36117			−0.392786
$569$	6.26646	+	17.2169i	0.262704	+	0.721772i	0.998983	+	0.0450941i	$0.0143588\pi$
$569$	6.26646	+	17.2169i	0.262704	+	0.721772i	−0.736279	+	0.676678i	$0.763419\pi$
$570$	−0.495747	+	0.449151i	−0.0207645	+	0.0188129i
$571$	11.0847	−	9.30116i	0.463880	−	0.389241i	−0.380676	−	0.924708i	$-0.624309\pi$
$571$	11.0847	−	9.30116i	0.463880	−	0.389241i	0.844556	+	0.535467i	$0.179864\pi$
$572$	12.6567	+	71.7795i	0.529201	+	3.00125i
$573$	−30.7796	−	16.2441i	−1.28584	−	0.678608i
$574$	0.340827	−	5.54355i	0.0142258	−	0.231383i
$575$	2.34434	+	1.35350i	0.0977655	+	0.0564450i
$576$	−32.6650	+	14.7857i	−1.36104	+	0.616070i
$577$	−21.6982	+	12.5275i	−0.903309	+	0.521526i	−0.878272	−	0.478161i	$-0.841304\pi$
$577$	−21.6982	+	12.5275i	−0.903309	+	0.521526i	−0.0250367	+	0.999687i	$0.507970\pi$
$578$	−72.0140	−	12.6980i	−2.99539	−	0.528168i
$579$	−5.07064	+	36.9057i	−0.210729	+	1.53375i
$580$	−1.77442	+	4.87519i	−0.0736790	+	0.202431i
$581$	−18.3129	+	5.41821i	−0.759749	+	0.224785i
$582$	−32.2112	−	25.0064i	−1.33520	−	1.03655i
$583$	−2.63964	+	14.9702i	−0.109323	+	0.620001i
$584$	−5.04446	−	8.73726i	−0.208741	−	0.361550i
$585$	1.81103	−	6.46622i	0.0748770	−	0.267345i
$586$	−15.2005	−	8.77601i	−0.627927	−	0.362534i
$587$	21.3062	+	17.8781i	0.879402	+	0.737906i	0.966056	−	0.258332i	$-0.0831729\pi$
$587$	21.3062	+	17.8781i	0.879402	+	0.737906i	−0.0866537	+	0.996238i	$0.527617\pi$
$588$	−8.14562	+	30.7007i	−0.335920	+	1.26607i
$589$	0.266333	+	1.51045i	0.0109741	+	0.0622369i
$590$	2.22131	+	2.64726i	0.0914500	+	0.108986i
$591$	5.80320	−	1.25224i	0.238712	−	0.0515104i
$592$	4.79431	−	1.74498i	0.197045	−	0.0717184i
$593$	43.7366			1.79605			0.898023	−	0.439949i	$-0.145004\pi$
$593$	43.7366			1.79605			0.898023	+	0.439949i	$0.145004\pi$
$594$	−37.2787	+	39.3256i	−1.52956	+	1.61355i
$595$	−5.93129	+	4.38600i	−0.243159	+	0.179809i
$596$	1.21618	+	3.34142i	0.0498165	+	0.136870i
$597$	5.70955	−	17.7585i	0.233676	−	0.726808i
$598$	−4.42407	−	5.27240i	−0.180914	−	0.215605i
$599$	9.06627	−	1.59863i	0.370438	−	0.0653181i	0.0146695	−	0.999892i	$-0.495330\pi$
$599$	9.06627	−	1.59863i	0.370438	−	0.0653181i	0.355768	+	0.934574i	$0.384219\pi$
$600$	−9.46682	+	5.95624i	−0.386481	+	0.243162i
$601$	25.8812	−	30.8440i	1.05571	−	1.25815i	0.0907219	−	0.995876i	$-0.471083\pi$
$601$	25.8812	−	30.8440i	1.05571	−	1.25815i	0.964993	−	0.262276i	$-0.0844730\pi$
$602$	37.7606	−	4.29012i	1.53901	−	0.174852i
$603$	8.71072	−	18.1430i	0.354728	−	0.738842i
$604$	−18.7804	−	32.5287i	−0.764166	−	1.32357i
$605$	0.849967	−	4.82040i	0.0345561	−	0.195977i
$606$	19.4380	+	47.6865i	0.789616	+	1.93713i
$607$	−0.602537	+	1.65546i	−0.0244562	+	0.0671930i	−0.951320	−	0.308205i	$-0.900272\pi$
$607$	−0.602537	+	1.65546i	−0.0244562	+	0.0671930i	0.926864	+	0.375398i	$0.122494\pi$
$608$	3.36199	+	1.22367i	0.136347	+	0.0496262i
$609$	19.8570	+	12.0929i	0.804644	+	0.490027i
$610$	−1.78951	+	10.1488i	−0.0724550	+	0.410913i
$611$	−18.4004	+	10.6235i	−0.744399	+	0.429779i
$612$	24.2975	−	50.6079i	0.982168	−	2.04570i
$613$	−11.2627	+	19.5075i	−0.454895	+	0.787901i	−0.998682	−	0.0513222i	$-0.983656\pi$
$613$	−11.2627	+	19.5075i	−0.454895	+	0.787901i	0.543787	+	0.839223i	$0.316990\pi$
$614$	38.0900	+	31.9613i	1.53719	+	1.28985i
$615$	0.351640	+	0.558896i	0.0141795	+	0.0225369i
$616$	12.3998	+	11.7745i	0.499603	+	0.474407i
$617$	12.7802	+	15.2309i	0.514513	+	0.613173i	0.959274	−	0.282476i	$-0.0911558\pi$
$617$	12.7802	+	15.2309i	0.514513	+	0.613173i	−0.444761	+	0.895649i	$0.646711\pi$
$618$	43.2869	+	13.9172i	1.74126	+	0.559832i
$619$	−1.43450	−	3.94126i	−0.0576575	−	0.158413i	0.907520	−	0.420009i	$-0.137973\pi$
$619$	−1.43450	−	3.94126i	−0.0576575	−	0.158413i	−0.965177	+	0.261597i	$0.915751\pi$
$620$		−	3.40700i		−	0.136829i
$621$	0.675864	−	2.82181i	0.0271215	−	0.113235i
$622$		−	50.6698i		−	2.03167i
$623$	−7.76662	+	11.7260i	−0.311163	+	0.469792i
$624$	−23.0717	+	4.97852i	−0.923606	+	0.199300i
$625$	17.4181	−	14.6155i	0.696725	−	0.584622i
$626$	−4.46253	−	25.3083i	−0.178359	−	1.01152i
$627$	3.86575	−	0.146943i	0.154383	−	0.00586836i
$628$	−3.30131	+	3.93435i	−0.131737	+	0.156998i
$629$	−7.66783	+	13.2811i	−0.305736	+	0.529551i
$630$	−2.36858	−	6.22372i	−0.0943666	−	0.247959i
$631$	7.09781	+	12.2938i	0.282559	+	0.489407i	0.972014	−	0.234921i	$-0.0754833\pi$
$631$	7.09781	+	12.2938i	0.282559	+	0.489407i	−0.689455	+	0.724328i	$0.742150\pi$
$632$	1.14296	+	0.201535i	0.0454645	+	0.00801663i
$633$	0.408302	+	0.316976i	0.0162285	+	0.0125986i
$634$	−56.8853	−	20.7046i	−2.25920	−	0.822283i
$635$	−4.11182	−	1.49658i	−0.163173	−	0.0593900i
$636$	14.0843	+	1.93510i	0.558479	+	0.0767319i
$637$	−18.2462	+	35.7540i	−0.722940	+	1.41662i
$638$	45.8188	−	26.4535i	1.81399	−	1.04730i
$639$	−8.69367	−	19.2063i	−0.343916	−	0.759790i
$640$	−3.42947	−	1.98001i	−0.135562	−	0.0782666i
$641$	16.7592	−	19.9729i	0.661949	−	0.788881i	−0.325715	−	0.945468i	$-0.605605\pi$
$641$	16.7592	−	19.9729i	0.661949	−	0.788881i	0.987664	+	0.156588i	$0.0500493\pi$
$642$	−9.67871	+	18.3393i	−0.381988	+	0.723796i
$643$	−35.5086	+	6.26113i	−1.40032	+	0.246915i	−0.822277	−	0.569088i	$-0.807296\pi$
$643$	−35.5086	+	6.26113i	−1.40032	+	0.246915i	−0.578048	+	0.816003i	$0.696185\pi$
$644$	−3.76329	−	0.904752i	−0.148295	−	0.0356522i
$645$	−3.34835	+	3.03363i	−0.131841	+	0.119449i
$646$	−6.64138	+	2.41726i	−0.261301	+	0.0951059i
$647$	−14.1360			−0.555744			−0.277872	−	0.960618i	$-0.589629\pi$
$647$	−14.1360			−0.555744			−0.277872	+	0.960618i	$0.589629\pi$
$648$	9.00779	+	7.91147i	0.353860	+	0.310792i
$649$		−	19.9844i		−	0.784458i
$650$	−56.1451	+	20.4351i	−2.20219	+	0.801532i
$651$	−14.9698	−	3.00249i	−0.586711	−	0.117677i
$652$	−29.7507	+	24.9638i	−1.16513	+	0.977659i
$653$	33.8858	−	5.97498i	1.32605	−	0.233819i	0.534629	−	0.845087i	$-0.320451\pi$
$653$	33.8858	−	5.97498i	1.32605	−	0.233819i	0.791424	+	0.611268i	$0.209340\pi$
$654$	−12.2874	−	6.48478i	−0.480477	−	0.253575i
$655$	−6.35168	−	5.32969i	−0.248181	−	0.208248i
$656$	1.16047	−	2.00999i	0.0453087	−	0.0784770i
$657$	13.2415	−	18.4640i	0.516599	−	0.720348i
$658$	−8.40786	+	19.3200i	−0.327773	+	0.753171i
$659$	−38.1009	−	6.71821i	−1.48420	−	0.261704i	−0.627944	−	0.778258i	$-0.716104\pi$
$659$	−38.1009	−	6.71821i	−1.48420	−	0.261704i	−0.856255	+	0.516554i	$0.827215\pi$
$660$	−8.51342	−	1.16970i	−0.331385	−	0.0455304i
$661$	10.2109	−	28.0542i	0.397158	−	1.09118i	−0.566504	−	0.824059i	$-0.691704\pi$
$661$	10.2109	−	28.0542i	0.397158	−	1.09118i	0.963662	−	0.267124i	$-0.0860733\pi$
$662$	11.0904	−	30.4707i	0.431042	−	1.18428i
$663$	43.5055	−	56.0403i	1.68962	−	2.17642i
$664$	9.46927	+	1.66969i	0.367479	+	0.0647964i
$665$	−0.189711	+	0.435927i	−0.00735668	+	0.0169045i
$666$	−9.67802	−	9.89885i	−0.375016	−	0.383573i
$667$	−1.41655	+	2.45353i	−0.0548490	+	0.0950013i
$668$	−7.59097	−	6.36958i	−0.293703	−	0.246446i
$669$	−0.188535	−	4.95992i	−0.00728917	−	0.191761i
$670$	5.54286	−	0.977356i	0.214139	−	0.0377586i
$671$	45.6527	−	38.3072i	1.76240	−	1.47883i
$672$	−23.5254	+	26.7395i	−0.907512	+	1.03150i
$673$	20.3275	−	7.39859i	0.783566	−	0.285195i	0.0809075	−	0.996722i	$-0.474218\pi$
$673$	20.3275	−	7.39859i	0.783566	−	0.285195i	0.702659	+	0.711527i	$0.251996\pi$
$674$		−	35.0552i		−	1.35028i
$675$	−21.0122	−	13.8916i	−0.808760	−	0.534686i
$676$	52.0888			2.00342
$677$	−7.25316	+	2.63993i	−0.278761	+	0.101461i	−0.477618	−	0.878568i	$-0.658500\pi$
$677$	−7.25316	+	2.63993i	−0.278761	+	0.101461i	0.198856	+	0.980029i	$0.436277\pi$
$678$	−34.4202	−	11.0664i	−1.32190	−	0.425004i
$679$	−28.1778	−	6.77437i	−1.08137	−	0.259976i
$680$	3.65767	−	0.644945i	0.140265	−	0.0247325i
$681$	25.5516	+	40.6116i	0.979138	+	1.55624i
$682$	−22.3330	+	26.6155i	−0.855176	+	1.01916i
$683$	7.78254	+	4.49325i	0.297791	+	0.171930i	0.641450	−	0.767165i	$-0.278333\pi$
$683$	7.78254	+	4.49325i	0.297791	+	0.171930i	−0.343659	+	0.939094i	$0.611667\pi$
$684$	−0.274655	−	3.60755i	−0.0105017	−	0.137938i
$685$	−0.361325	+	0.208611i	−0.0138055	+	0.00797061i
$686$	6.53257	+	39.2671i	0.249415	+	1.49922i
$687$	−15.4217	−	37.8333i	−0.588374	−	1.44343i
$688$	14.9234	+	5.43166i	0.568947	+	0.207080i
$689$	16.8828	+	6.14485i	0.643185	+	0.234100i
$690$	0.751438	−	0.306302i	0.0286067	−	0.0116607i
$691$	34.0362	+	6.00150i	1.29480	+	0.228308i	0.778253	−	0.627951i	$-0.216106\pi$
$691$	34.0362	+	6.00150i	1.29480	+	0.228308i	0.516546	+	0.856259i	$0.327217\pi$
$692$	−20.1518	−	34.9040i	−0.766058	−	1.32685i
$693$	−12.6421	+	36.3756i	−0.480232	+	1.38180i
$694$	39.0970	−	67.7179i	1.48410	−	2.57054i
$695$	1.45793	−	1.73749i	0.0553025	−	0.0659069i
$696$	−6.23368	−	9.90779i	−0.236287	−	0.375554i
$697$	1.21142	+	6.87033i	0.0458860	+	0.260232i
$698$	14.3659	−	12.0544i	0.543757	−	0.456266i
$699$	4.56063	−	14.1850i	0.172499	−	0.536527i
$700$	−18.5540	+	28.0128i	−0.701277	+	1.05878i
$701$			23.2192i			0.876977i	0.898737	+	0.438488i	$0.144486\pi$
$701$			23.2192i			0.876977i	−0.898737	+	0.438488i	$0.855514\pi$
$702$	38.1222	+	51.4618i	1.43883	+	1.94230i
$703$			0.988348i			0.0372763i
$704$	19.8329	+	54.4906i	0.747482	+	2.05369i
$705$	−0.528385	−	2.44867i	−0.0199001	−	0.0922221i
$706$	12.5702	+	14.9805i	0.473085	+	0.563800i
$707$	26.5389	+	25.2005i	0.998099	+	0.947763i
$708$	−18.6767	+	0.709931i	−0.701912	+	0.0266809i
$709$	27.0985	+	22.7383i	1.01770	+	0.853955i	0.989337	−	0.145643i	$-0.0465250\pi$
$709$	27.0985	+	22.7383i	1.01770	+	0.853955i	0.0283665	+	0.999598i	$0.490969\pi$
$710$	2.94793	−	5.10597i	0.110634	−	0.191624i
$711$	0.647973	+	2.53218i	0.0243009	+	0.0949641i
$712$	6.13267	−	3.54070i	0.229831	−	0.132693i
$713$	0.323071	−	1.83223i	0.0120991	−	0.0686175i
$714$	1.64694	−	70.3360i	0.0616351	−	2.63226i
$715$	−10.2050	−	3.71433i	−0.381647	−	0.138908i
$716$	−14.4964	+	39.8286i	−0.541757	+	1.48847i
$717$	22.7540	+	3.12627i	0.849762	+	0.116753i
$718$	0.191578	−	1.08649i	0.00714963	−	0.0405476i
$719$	16.5681	+	28.6967i	0.617884	+	1.07021i	0.989871	+	0.141969i	$0.0453433\pi$
$719$	16.5681	+	28.6967i	0.617884	+	1.07021i	−0.371987	+	0.928238i	$0.621323\pi$
$720$	0.273788	−	2.76927i	0.0102035	−	0.103205i
$721$	32.1078	−	3.64789i	1.19576	−	0.135854i
$722$	25.9573	−	30.9347i	0.966031	−	1.15127i
$723$	−16.7479	−	8.83883i	−0.622862	−	0.328720i
$724$	47.3333	−	8.34614i	1.75913	−	0.310182i
$725$	15.8088	+	18.8402i	0.587126	+	0.699709i
$726$	31.3441	+	34.5958i	1.16329	+	1.28397i
$727$	2.36915	+	6.50919i	0.0878670	+	0.241413i	0.975841	−	0.218480i	$-0.0701100\pi$
$727$	2.36915	+	6.50919i	0.0878670	+	0.241413i	−0.887974	+	0.459893i	$0.847888\pi$
$728$	16.2499	−	12.0163i	0.602260	−	0.445353i
$729$	−7.86647	+	25.8286i	−0.291351	+	0.956616i
$730$	6.35422			0.235180
$731$	−44.8568	+	16.3266i	−1.65909	+	0.603859i
$732$	−37.4222	−	41.3044i	−1.38316	−	1.52665i
$733$	18.5983	+	22.1646i	0.686943	+	0.818666i	0.990982	−	0.133993i	$-0.0427800\pi$
$733$	18.5983	+	22.1646i	0.686943	+	0.818666i	−0.304040	+	0.952659i	$0.598336\pi$
$734$	−11.6079	−	65.8315i	−0.428454	−	2.42989i
$735$	−3.35465	−	3.33824i	−0.123738	−	0.123133i
$736$	−3.32460	−	2.78967i	−0.122546	−	0.102828i
$737$	−28.1879	−	16.2743i	−1.03832	−	0.599472i
$738$	−6.26711	−	0.619607i	−0.230696	−	0.0228080i
$739$	8.46122	+	14.6553i	0.311251	+	0.539103i	0.978633	−	0.205613i	$-0.0659187\pi$
$739$	8.46122	+	14.6553i	0.311251	+	0.539103i	−0.667382	+	0.744715i	$0.732585\pi$
$740$	0.381240	−	2.16212i	0.0140147	−	0.0794811i
$741$	0.622357	−	4.52971i	0.0228629	−	0.166403i
$742$	17.0848	−	5.05485i	0.627204	−	0.185569i
$743$	−4.26829	+	11.7270i	−0.156588	+	0.430223i	−0.993034	−	0.117827i	$-0.962407\pi$
$743$	−4.26829	+	11.7270i	−0.156588	+	0.430223i	0.836446	+	0.548049i	$0.184629\pi$
$744$	6.07211	+	4.71394i	0.222614	+	0.172821i
$745$	−0.521767	−	0.0920016i	−0.0191161	−	0.00337068i
$746$	−48.6184	+	28.0699i	−1.78005	+	1.02771i
$747$	5.36837	+	20.9787i	0.196418	+	0.767572i
$748$	−78.6268	−	45.3952i	−2.87488	−	1.65981i
$749$	−0.904365	+	14.7095i	−0.0330448	+	0.537474i
$750$	−0.543560	−	14.2998i	−0.0198480	−	0.522155i
$751$	−2.59871	−	14.7380i	−0.0948283	−	0.537798i	−0.994800	−	0.101849i	$-0.967524\pi$
$751$	−2.59871	−	14.7380i	−0.0948283	−	0.537798i	0.899972	−	0.435949i	$-0.143587\pi$
$752$	−6.74495	+	5.65969i	−0.245963	+	0.206388i
$753$	−3.74808	−	17.3695i	−0.136588	−	0.632981i
$754$	−21.3870	−	58.7603i	−0.778869	−	2.13992i
$755$	5.59649			0.203677
$756$	34.4443	+	10.5226i	1.25273	+	0.382701i
$757$	−48.2688			−1.75436			−0.877180	−	0.480162i	$-0.840578\pi$
$757$	−48.2688			−1.75436			−0.877180	+	0.480162i	$0.840578\pi$
$758$	−20.9528	−	57.5674i	−0.761041	−	2.09094i
$759$	−4.46746	−	1.43633i	−0.162158	−	0.0521356i
$760$	0.183364	−	0.153861i	0.00665132	−	0.00558112i
$761$	−7.10296	−	40.2829i	−0.257482	−	1.46025i	−0.789620	−	0.613596i	$-0.789722\pi$
$761$	−7.10296	−	40.2829i	−0.257482	−	1.46025i	0.532138	−	0.846657i	$-0.321389\pi$
$762$	35.3229	−	22.2241i	1.27962	−	0.805095i
$763$	−9.85543	−	0.605928i	−0.356791	−	0.0219361i
$764$	45.5879	+	26.3202i	1.64931	+	0.952231i
$765$	4.72009	+	6.90548i	0.170655	+	0.249668i
$766$	−25.4500	+	14.6936i	−0.919545	+	0.530900i
$767$	−23.2610	−	4.10154i	−0.839905	−	0.148098i
$768$	−3.36539	+	1.37181i	−0.121438	+	0.0495008i
$769$	−7.22183	+	19.8418i	−0.260426	+	0.715514i	0.738713	+	0.674020i	$0.235434\pi$
$769$	−7.22183	+	19.8418i	−0.260426	+	0.715514i	−0.999139	+	0.0414940i	$0.986788\pi$
$770$	−10.3271	+	3.05546i	−0.372164	+	0.110111i
$771$	−2.17043	+	0.884712i	−0.0781660	+	0.0318621i
$772$	9.78421	−	55.4890i	0.352141	−	1.99709i
$773$	−0.539761	−	0.934893i	−0.0194138	−	0.0336258i	0.856155	−	0.516719i	$-0.172847\pi$
$773$	−0.539761	−	0.934893i	−0.0194138	−	0.0336258i	−0.875569	+	0.483093i	$0.839513\pi$
$774$	−3.27127	−	42.9676i	−0.117583	−	1.54444i
$775$	−13.9872	−	8.07550i	−0.502434	−	0.290080i
$776$	11.1776	+	9.37910i	0.401252	+	0.336690i
$777$	−9.16398	−	3.58051i	−0.328756	−	0.128450i
$778$	9.37640	+	53.1762i	0.336160	+	1.90646i
$779$	0.289002	+	0.344420i	0.0103546	+	0.0123401i
$780$	−3.10874	+	9.66918i	−0.111311	+	0.346212i
$781$	−32.0393	+	11.6614i	−1.14646	+	0.417276i
$782$	8.57326			0.306579
$783$	14.5386	−	21.9910i	0.519568	−	0.785893i
$784$	−4.87361	+	15.9047i	−0.174057	+	0.568024i
$785$	−0.261728	−	0.719093i	−0.00934149	−	0.0256655i
$786$	77.3002	−	16.6802i	2.75721	−	0.594964i
$787$	22.2373	+	26.5014i	0.792674	+	0.944673i	0.999431	−	0.0337197i	$-0.0107354\pi$
$787$	22.2373	+	26.5014i	0.792674	+	0.944673i	−0.206757	+	0.978392i	$0.566291\pi$
$788$	−8.84307	+	1.55927i	−0.315021	+	0.0555467i
$789$	−0.468780	−	12.3325i	−0.0166890	−	0.439050i
$790$	−0.469856	+	0.559953i	−0.0167167	+	0.0199222i
$791$	−25.5310	+	2.90067i	−0.907776	+	0.103136i
$792$	13.8639	−	13.5546i	0.492632	−	0.481642i
$793$	−35.2182	−	60.9998i	−1.25064	−	2.16616i
$794$	2.91180	−	16.5136i	0.103336	−	0.586046i
$795$	−1.29896	+	1.67322i	−0.0460695	+	0.0593429i
$796$	−9.64984	+	26.5127i	−0.342029	+	0.939718i
$797$	−13.7273	−	4.99634i	−0.486247	−	0.176980i	0.0872509	−	0.996186i	$-0.472192\pi$
$797$	−13.7273	−	4.99634i	−0.486247	−	0.176980i	−0.573498	+	0.819207i	$0.694414\pi$
$798$	−2.17458	−	3.97876i	−0.0769792	−	0.140847i
$799$	4.59576	−	26.0639i	0.162586	−	0.922073i
$800$	−32.6277	+	18.8376i	−1.15356	+	0.666010i
$801$	12.9598	+	9.29417i	0.457913	+	0.328393i
$802$	−1.56453	+	2.70985i	−0.0552456	+	0.0956882i
$803$	−28.1492	−	23.6200i	−0.993364	−	0.833531i
$804$	−14.2080	+	26.9215i	−0.501076	+	0.949446i
$805$	0.397107	−	0.418197i	0.0139962	−	0.0147395i
$806$	26.3957	+	31.4571i	0.929747	+	1.10803i
$807$	8.59181	−	7.78426i	0.302446	−	0.274019i
$808$	−6.30214	−	17.3150i	−0.221709	−	0.609140i
$809$			19.4950i			0.685407i	0.939444	+	0.342704i	$0.111343\pi$
$809$			19.4950i			0.685407i	−0.939444	+	0.342704i	$0.888657\pi$
$810$	−7.15190	+	2.42182i	−0.251292	+	0.0850940i
$811$		−	8.74742i		−	0.307163i	−0.988136	−	0.153582i	$-0.950919\pi$
$811$		−	8.74742i		−	0.307163i	0.988136	−	0.153582i	$-0.0490808\pi$
$812$	−29.3176	−	19.4183i	−1.02885	−	0.681449i
$813$	−17.4491	−	19.2593i	−0.611967	−	0.675453i
$814$	−17.1510	+	14.3914i	−0.601143	+	0.504419i
$815$	−1.00483	−	5.69869i	−0.0351978	−	0.199617i
$816$	13.7225	−	26.0015i	0.480382	−	0.910234i
$817$	−1.97751	+	2.35670i	−0.0691842	+	0.0824505i
$818$	−10.3078	+	17.8535i	−0.360402	+	0.624235i
$819$	39.7450	+	22.1804i	1.38880	+	0.775046i
$820$	−0.499369	−	0.864933i	−0.0174387	−	0.0302048i
$821$	−14.8604	−	2.62030i	−0.518633	−	0.0914490i	−0.0917964	−	0.995778i	$-0.529261\pi$
$821$	−14.8604	−	2.62030i	−0.518633	−	0.0914490i	−0.426836	+	0.904329i	$0.640372\pi$
$822$	0.541631	−	3.94216i	0.0188916	−	0.137499i
$823$	45.4998	+	16.5606i	1.58602	+	0.577265i	0.976503	−	0.215505i	$-0.0691396\pi$
$823$	45.4998	+	16.5606i	1.58602	+	0.577265i	0.609521	+	0.792770i	$0.291362\pi$
$824$	−15.2886	−	5.56458i	−0.532602	−	0.193851i
$825$	−24.9812	+	32.1787i	−0.869732	+	1.12032i
$826$	−20.9657	+	10.4448i	−0.729490	+	0.363421i
$827$	1.87534	−	1.08273i	0.0652119	−	0.0376501i	−0.467040	−	0.884236i	$-0.654679\pi$
$827$	1.87534	−	1.08273i	0.0652119	−	0.0376501i	0.532251	+	0.846586i	$0.321346\pi$
$828$	−1.18364	+	4.22614i	−0.0411343	+	0.146868i
$829$	−34.8737	−	20.1344i	−1.21121	−	0.699295i	−0.248191	−	0.968711i	$-0.579836\pi$
$829$	−34.8737	−	20.1344i	−1.21121	−	0.699295i	−0.963024	+	0.269416i	$0.913169\pi$
$830$	−3.89269	+	4.63913i	−0.135117	+	0.161027i
$831$	−44.5711	+	1.69422i	−1.54615	+	0.0587718i
$832$	67.4950	−	11.9012i	2.33997	−	0.412600i
$833$	−19.5075	−	46.0382i	−0.675896	−	1.59513i
$834$	4.56285	+	21.1454i	0.157999	+	0.732204i
$835$	1.38742	−	0.504981i	0.0480138	−	0.0174756i
$836$	−5.85124			−0.202369
$837$	−4.03246	+	16.8360i	−0.139382	+	0.581936i
$838$			47.3937i			1.63719i
$839$	8.35277	−	3.04016i	0.288370	−	0.104958i	−0.193785	−	0.981044i	$-0.562076\pi$
$839$	8.35277	−	3.04016i	0.288370	−	0.104958i	0.482155	+	0.876086i	$0.339854\pi$
$840$	0.762323	+	2.25755i	0.0263026	+	0.0778929i
$841$	2.49746	−	2.09562i	0.0861194	−	0.0722628i
$842$	−58.4633	+	10.3087i	−2.01478	+	0.355260i
$843$	−11.8394	+	7.44902i	−0.407772	+	0.256558i
$844$	−0.598908	−	0.502543i	−0.0206153	−	0.0172983i
$845$	−3.88056	+	6.72133i	−0.133495	+	0.231221i
$846$	21.5377	+	10.3405i	0.740480	+	0.355514i
$847$	30.4212	+	13.2390i	1.04529	+	0.454898i
$848$	7.33230	+	1.29288i	0.251792	+	0.0443978i
$849$	4.12589	+	10.1219i	0.141600	+	0.347382i
$850$	25.4547	−	69.9363i	0.873091	−	2.39880i
$851$	0.410049	−	1.12660i	0.0140563	−	0.0386194i
$852$	12.0364	+	29.5284i	0.412361	+	1.01163i
$853$	7.05528	+	1.24404i	0.241568	+	0.0425950i	0.293121	−	0.956075i	$-0.405306\pi$
$853$	7.05528	+	1.24404i	0.241568	+	0.0425950i	−0.0515532	+	0.998670i	$0.516417\pi$
$854$	−64.0484	−	27.8732i	−2.19169	−	0.953802i
$855$	0.485966	+	0.233319i	0.0166197	+	0.00797933i
$856$	3.70998	−	6.42588i	0.126805	−	0.219632i
$857$	−27.4777	−	23.0565i	−0.938619	−	0.787595i	0.0387252	−	0.999250i	$-0.487670\pi$
$857$	−27.4777	−	23.0565i	−0.938619	−	0.787595i	−0.977344	+	0.211655i	$0.932115\pi$
$858$	87.6673	−	55.1576i	2.99291	−	1.88305i
$859$	−4.46217	+	0.786801i	−0.152247	+	0.0268453i	−0.249252	−	0.968439i	$-0.580185\pi$
$859$	−4.46217	+	0.786801i	−0.152247	+	0.0268453i	0.0970050	+	0.995284i	$0.469074\pi$
$860$	5.23507	−	4.39275i	0.178514	−	0.149791i
$861$	−4.24044	+	1.43190i	−0.144514	+	0.0487990i
$862$	28.1506	−	10.2460i	0.958815	−	0.348980i
$863$			33.0683i			1.12566i	0.826573	+	0.562830i	$0.190287\pi$
$863$			33.0683i			1.12566i	−0.826573	+	0.562830i	$0.809713\pi$
$864$	29.3082	+	27.7828i	0.997086	+	0.945189i
$865$	6.00516			0.204182
$866$	−42.1093	+	15.3265i	−1.43093	+	0.520817i
$867$	12.4295	+	57.6015i	0.422129	+	1.95625i
$868$	22.4532	+	5.39808i	0.762111	+	0.183223i
$869$	4.16293	−	0.734037i	0.141218	−	0.0249005i
$870$	7.36718	−	0.280039i	0.249771	−	0.00949420i
$871$	−24.7278	+	29.4694i	−0.837868	+	0.998532i
$872$	4.30537	+	2.48571i	0.145798	+	0.0841766i
$873$	−8.86255	+	31.6434i	−0.299952	+	1.07097i
$874$	0.478503	−	0.276264i	0.0161856	−	0.00934476i
$875$	−4.53496	−	9.10296i	−0.153310	−	0.307736i
$876$	−21.0743	+	27.1462i	−0.712036	+	0.917186i
$877$	−12.0002	−	4.36773i	−0.405219	−	0.147488i	0.131366	−	0.991334i	$-0.458064\pi$
$877$	−12.0002	−	4.36773i	−0.405219	−	0.147488i	−0.536585	+	0.843846i	$0.680286\pi$
$878$	−7.52835	−	2.74009i	−0.254069	−	0.0924737i
$879$	−1.92525	+	14.0125i	−0.0649369	+	0.472631i
$880$	−4.43210	−	0.781499i	−0.149406	−	0.0263443i
$881$	8.46605	+	14.6636i	0.285229	+	0.494030i	0.972665	−	0.232215i	$-0.0745972\pi$
$881$	8.46605	+	14.6636i	0.285229	+	0.494030i	−0.687436	+	0.726245i	$0.741264\pi$
$882$	44.7690	−	5.74878i	1.50745	−	0.193572i
$883$	4.01408	−	6.95260i	0.135085	−	0.233973i	−0.790545	−	0.612404i	$-0.790203\pi$
$883$	4.01408	−	6.95260i	0.135085	−	0.233973i	0.925630	+	0.378430i	$0.123536\pi$
$884$	−68.9751	+	82.2013i	−2.31988	+	2.76473i
$885$	1.29979	−	2.46285i	0.0436918	−	0.0827878i
$886$	1.95907	+	11.1104i	0.0658161	+	0.373262i
$887$	−23.0852	+	19.3708i	−0.775125	+	0.650408i	−0.942016	−	0.335568i	$-0.891072\pi$
$887$	−23.0852	+	19.3708i	−0.775125	+	0.650408i	0.166891	+	0.985975i	$0.446627\pi$
$888$	3.32594	+	3.67098i	0.111611	+	0.123190i
$889$	16.3777	−	24.7270i	0.549291	−	0.829316i
$890$			4.46002i			0.149500i
$891$	40.6853	+	15.8565i	1.36301	+	0.531211i
$892$			7.50739i			0.251366i
$893$	−0.583374	−	1.60281i	−0.0195218	−	0.0536358i
$894$	3.74469	−	3.39273i	0.125241	−	0.113470i
$895$	−4.05935	−	4.83775i	−0.135689	−	0.161708i
$896$	18.4825	−	19.4641i	0.617458	−	0.650251i
$897$	−2.58872	+	4.90513i	−0.0864347	+	0.163778i
$898$	−42.6855	−	35.8174i	−1.42443	−	1.19524i
$899$	8.45166	−	14.6387i	0.281879	−	0.488228i
$900$	30.9603	+	22.2033i	1.03201	+	0.740109i
$901$	−19.3813	+	11.1898i	−0.645683	+	0.372785i
$902$	−1.76860	+	10.0302i	−0.0588880	+	0.333970i
$903$	−14.6874	−	26.8731i	−0.488767	−	0.894282i
$904$	12.1569	+	4.42475i	0.404332	+	0.147165i
$905$	−2.44933	+	6.72947i	−0.0814184	+	0.223695i
$906$	−32.7315	+	42.1620i	−1.08743	+	1.40074i
$907$	−4.40531	+	24.9838i	−0.146276	+	0.829572i	0.820058	+	0.572281i	$0.193941\pi$
$907$	−4.40531	+	24.9838i	−0.146276	+	0.829572i	−0.966334	+	0.257292i	$0.917170\pi$
$908$	−36.2861	−	62.8494i	−1.20420	−	2.08573i
$909$	29.6724	−	29.0105i	0.984172	−	0.962217i
$910$	1.43692	+	12.6474i	0.0476334	+	0.419257i
$911$	−0.815474	+	0.971845i	−0.0270179	+	0.0321986i	−0.779384	−	0.626546i	$-0.784468\pi$
$911$	−0.815474	+	0.971845i	−0.0270179	+	0.0321986i	0.752366	+	0.658745i	$0.228912\pi$
$912$	−0.0719721	−	1.89342i	−0.00238323	−	0.0626975i
$913$	34.4893	−	6.08139i	1.14143	−	0.201265i
$914$	28.6626	+	34.1588i	0.948075	+	1.12987i
$915$	8.11766	−	1.75167i	0.268362	−	0.0579084i
$916$	21.1352	+	58.0683i	0.698325	+	1.91863i
$917$	45.1880	−	33.4151i	1.49224	−	1.10346i
$918$	−79.6292	−	4.82767i	−2.62816	−	0.159337i
$919$	38.7081			1.27686			0.638430	−	0.769680i	$-0.279584\pi$
$919$	38.7081			1.27686			0.638430	+	0.769680i	$0.279584\pi$
$920$	−0.272848	+	0.0993084i	−0.00899552	+	0.00327410i
$921$	12.2643	−	38.1459i	0.404123	−	1.25695i
$922$	−0.244786	−	0.291724i	−0.00806159	−	0.00960743i
$923$	6.99766	+	39.6857i	0.230331	+	1.30627i
$924$	21.1974	−	54.2528i	0.697343	−	1.78479i
$925$	−7.97276	−	6.68994i	−0.262143	−	0.219964i
$926$	53.8650	+	31.0990i	1.77011	+	1.02198i
$927$	−2.78156	−	36.5353i	−0.0913583	−	1.19998i
$928$	−19.7151	−	34.1475i	−0.647179	−	1.12095i
$929$	−6.02005	+	34.1414i	−0.197512	+	1.12014i	0.711285	+	0.702904i	$0.248114\pi$
$929$	−6.02005	+	34.1414i	−0.197512	+	1.12014i	−0.908796	+	0.417240i	$0.862998\pi$
$930$	−4.48335	+	1.82751i	−0.147015	+	0.0599265i
$931$	−2.57231	−	1.94094i	−0.0843041	−	0.0636118i
$932$	−7.70802	+	21.1776i	−0.252485	+	0.693696i
$933$	−37.8113	+	15.4127i	−1.23789	+	0.504589i
$934$	18.7803	+	3.31148i	0.614511	+	0.108355i
$935$	11.7152	−	6.76379i	0.383129	−	0.221200i
$936$	−12.9316	−	18.9188i	−0.422682	−	0.618382i
$937$	24.7426	+	14.2852i	0.808307	+	0.466676i	0.846367	−	0.532599i	$-0.178785\pi$
$937$	24.7426	+	14.2852i	0.808307	+	0.466676i	−0.0380609	+	0.999275i	$0.512118\pi$
$938$	−2.34108	+	38.0777i	−0.0764390	+	1.24328i
$939$	−17.5284	+	11.0283i	−0.572018	+	0.359896i
$940$	0.657936	+	3.73134i	0.0214595	+	0.121703i
$941$	37.2620	−	31.2666i	1.21471	−	1.01926i	0.215623	−	0.976477i	$-0.430822\pi$
$941$	37.2620	−	31.2666i	1.21471	−	1.01926i	0.999084	−	0.0427842i	$-0.0136228\pi$
$942$	6.94812	+	2.23389i	0.226382	+	0.0727842i
$943$	−0.186535	−	0.512500i	−0.00607440	−	0.0166893i
$944$	−9.78827			−0.318581
$945$	−3.92385	+	3.66063i	−0.127643	+	0.119080i
$946$	−69.6909			−2.26585
$947$	−6.23321	−	17.1256i	−0.202552	−	0.556508i	0.796275	−	0.604935i	$-0.206801\pi$
$947$	−6.23321	−	17.1256i	−0.202552	−	0.556508i	−0.998827	+	0.0484279i	$0.984579\pi$
$948$	−0.833886	−	3.86443i	−0.0270834	−	0.125511i
$949$	−33.2698	+	27.9167i	−1.07999	+	0.906215i
$950$	−0.832904	−	4.72363i	−0.0270230	−	0.153255i
$951$	1.85297	+	48.7474i	0.0600867	+	1.58074i
$952$	−1.54485	+	25.1270i	−0.0500689	+	0.814371i
$953$	28.1743	+	16.2665i	0.912656	+	0.526922i	0.881285	−	0.472586i	$-0.156679\pi$
$953$	28.1743	+	16.2665i	0.912656	+	0.526922i	0.0313712	+	0.999508i	$0.490013\pi$
$954$	−5.00835	−	19.5718i	−0.162151	−	0.633662i
$955$	−6.79250	+	3.92165i	−0.219800	+	0.126902i
$956$	−34.2114	−	6.03239i	−1.10647	−	0.195101i
$957$	−33.6776	−	26.1448i	−1.08864	−	0.845141i
$958$	4.66581	−	12.8192i	0.150746	−	0.414170i
$959$	−0.802324	−	2.71176i	−0.0259084	−	0.0875675i
$960$	−1.09988	+	8.00526i	−0.0354984	+	0.258369i
$961$	3.45553	−	19.5973i	0.111469	−	0.632170i
$962$	13.2309	+	22.9167i	0.426582	+	0.738863i
$963$	16.6294	+	1.64409i	0.535876	+	0.0529801i
$964$	24.8055	+	14.3215i	0.798931	+	0.461263i
$965$	6.43116	+	5.39639i	0.207026	+	0.173716i
$966$	0.828041	+	5.43751i	0.0266418	+	0.174949i
$967$	0.197163	+	1.11816i	0.00634032	+	0.0359577i	0.987814	−	0.155640i	$-0.0497441\pi$
$967$	0.197163	+	1.11816i	0.00634032	+	0.0359577i	−0.981473	+	0.191598i	$0.938633\pi$
$968$	−10.7372	−	12.7961i	−0.345107	−	0.411282i
$969$	3.82400	+	4.22071i	0.122845	+	0.135589i
$970$	−8.63569	+	3.14314i	−0.277275	+	0.100920i
$971$	37.6895			1.20951			0.604757	−	0.796410i	$-0.293270\pi$
$971$	37.6895			1.20951			0.604757	+	0.796410i	$0.293270\pi$
$972$	13.3735	−	38.5862i	0.428955	−	1.23765i
$973$	9.14066	+	12.3611i	0.293036	+	0.396279i
$974$	3.82155	+	10.4996i	0.122450	+	0.336429i
$975$	32.3275	+	35.6812i	1.03531	+	1.14271i
$976$	−18.7626	−	22.3604i	−0.600578	−	0.715741i
$977$	−29.2666	+	5.16050i	−0.936323	+	0.165099i	−0.620933	−	0.783863i	$-0.713246\pi$
$977$	−29.2666	+	5.16050i	−0.936323	+	0.165099i	−0.315390	+	0.948962i	$0.602135\pi$
$978$	48.8088	+	25.7591i	1.56073	+	0.823686i
$979$	16.5788	−	19.7579i	0.529862	−	0.631465i
$980$	4.87852	+	5.23825i	0.155839	+	0.167330i
$981$	−1.10155	+	11.1418i	−0.0351698	+	0.355730i
$982$	−14.7282	−	25.5101i	−0.469997	−	0.814059i
$983$	−0.460838	+	2.61354i	−0.0146984	+	0.0833590i	−0.991275	−	0.131813i	$-0.957920\pi$
$983$	−0.460838	+	2.61354i	−0.0146984	+	0.0833590i	0.976576	+	0.215172i	$0.0690312\pi$
$984$	2.23245	+	0.306726i	0.0711680	+	0.00977808i
$985$	0.457597	−	1.25724i	0.0145803	−	0.0400589i
$986$	73.1940	+	26.6404i	2.33097	+	0.848404i
$987$	16.9746	+	0.397466i	0.540309	+	0.0126515i
$988$	−1.20089	+	6.81058i	−0.0382054	+	0.216673i
$989$	3.23188	−	1.86593i	0.102768	−	0.0593330i
$990$	3.02736	+	11.8304i	0.0962157	+	0.375996i
$991$	−16.1884	+	28.0391i	−0.514242	+	0.890693i	0.485622	+	0.874169i	$0.338593\pi$
$991$	−16.1884	+	28.0391i	−0.514242	+	0.890693i	−0.999863	+	0.0165236i	$0.994740\pi$
$992$	19.8358	+	16.6442i	0.629786	+	0.528453i
$993$	−26.1116	+	0.992547i	−0.828628	+	0.0314975i
$994$	28.9792	+	27.5177i	0.919164	+	0.872810i
$995$	−2.70219	−	3.22034i	−0.0856652	−	0.102092i
$996$	−6.90863	−	32.0163i	−0.218908	−	1.01447i
$997$	−3.04666	−	8.37063i	−0.0964887	−	0.265100i	0.882053	−	0.471151i	$-0.156161\pi$
$997$	−3.04666	−	8.37063i	−0.0964887	−	0.265100i	−0.978541	+	0.206050i	$0.933939\pi$
$998$		−	74.1087i		−	2.34587i
$999$	−4.44297	+	10.2331i	−0.140569	+	0.323759i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	189.2.be.a.20.20	yes	132
3.2	odd	2		567.2.be.a.62.4		132
7.6	odd	2	inner	189.2.be.a.20.19	✓	132
21.20	even	2		567.2.be.a.62.3		132
27.4	even	9		567.2.be.a.503.3		132
27.23	odd	18	inner	189.2.be.a.104.19	yes	132
189.104	even	18	inner	189.2.be.a.104.20	yes	132
189.139	odd	18		567.2.be.a.503.4		132

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
189.2.be.a.20.19	✓	132	7.6	odd	2	inner
189.2.be.a.20.20	yes	132	1.1	even	1	trivial
189.2.be.a.104.19	yes	132	27.23	odd	18	inner
189.2.be.a.104.20	yes	132	189.104	even	18	inner
567.2.be.a.62.3		132	21.20	even	2
567.2.be.a.62.4		132	3.2	odd	2
567.2.be.a.503.3		132	27.4	even	9
567.2.be.a.503.4		132	189.139	odd	18

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:	\( N \)	\(=\)	\( 189 = 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	189.be (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(0.735125 + 2.01974i) q^{2} +(1.28358 - 1.16294i) q^{3} +(-2.00685 + 1.68395i) q^{4} +(-0.0677816 - 0.384409i) q^{5} +(3.29242 + 1.73760i) q^{6} +(2.64076 + 0.162359i) q^{7} +(-1.15362 - 0.666045i) q^{8} +(0.295160 - 2.98544i) q^{9} +O(q^{10})\)	\(q+(0.735125 + 2.01974i) q^{2} +(1.28358 - 1.16294i) q^{3} +(-2.00685 + 1.68395i) q^{4} +(-0.0677816 - 0.384409i) q^{5} +(3.29242 + 1.73760i) q^{6} +(2.64076 + 0.162359i) q^{7} +(-1.15362 - 0.666045i) q^{8} +(0.295160 - 2.98544i) q^{9} +(0.726578 - 0.419490i) q^{10} +(-4.77807 - 0.842503i) q^{11} +(-0.617633 + 4.49533i) q^{12} +(-1.96127 + 5.38855i) q^{13} +(1.61337 + 5.45301i) q^{14} +(-0.534046 - 0.414594i) q^{15} +(-0.412653 + 2.34027i) q^{16} +(-3.57147 - 6.18597i) q^{17} +(6.24680 - 1.59853i) q^{18} +(-0.398672 - 0.230173i) q^{19} +(0.783352 + 0.657311i) q^{20} +(3.57845 - 2.86264i) q^{21} +(-1.81084 - 10.2698i) q^{22} +(0.358944 + 0.427773i) q^{23} +(-2.25534 + 0.486668i) q^{24} +(4.55529 - 1.65799i) q^{25} -12.3252 q^{26} +(-3.09302 - 4.17531i) q^{27} +(-5.57303 + 4.12109i) q^{28} +(1.73522 + 4.76747i) q^{29} +(0.444781 - 1.38341i) q^{30} +(-2.14159 - 2.55225i) q^{31} +(-7.65380 + 1.34957i) q^{32} +(-7.11282 + 4.47517i) q^{33} +(9.86858 - 11.7609i) q^{34} +(-0.116583 - 1.02614i) q^{35} +(4.43500 + 6.48838i) q^{36} +(-1.07348 - 1.85933i) q^{37} +(0.171817 - 0.974420i) q^{38} +(3.74909 + 9.19747i) q^{39} +(-0.177839 + 0.488609i) q^{40} +(-0.917771 - 0.334041i) q^{41} +(8.41240 + 5.12314i) q^{42} +(1.16047 - 6.58138i) q^{43} +(11.0076 - 6.35525i) q^{44} +(-1.16764 + 0.0888961i) q^{45} +(-0.600121 + 1.03944i) q^{46} +(2.83834 + 2.38165i) q^{47} +(2.19191 + 3.48382i) q^{48} +(6.94728 + 0.857502i) q^{49} +(6.69741 + 7.98167i) q^{50} +(-11.7782 - 3.78680i) q^{51} +(-5.13806 - 14.1167i) q^{52} -3.13310i q^{53} +(6.15929 - 9.31647i) q^{54} +1.89384i q^{55} +(-2.93831 - 1.94617i) q^{56} +(-0.779405 + 0.168184i) q^{57} +(-8.35346 + 7.00938i) q^{58} +(0.715255 + 4.05641i) q^{59} +(1.76991 - 0.0672771i) q^{60} +(-7.89549 + 9.40948i) q^{61} +(3.58054 - 6.20168i) q^{62} +(1.26416 - 7.83594i) q^{63} +(-5.97591 - 10.3506i) q^{64} +(2.20434 + 0.388685i) q^{65} +(-14.2675 - 11.0762i) q^{66} +(6.30401 + 2.29447i) q^{67} +(17.5843 + 6.40016i) q^{68} +(0.958206 + 0.131652i) q^{69} +(1.98683 - 0.989808i) q^{70} +(6.08593 - 3.51371i) q^{71} +(-2.32894 + 3.24749i) q^{72} +(6.55906 + 3.78687i) q^{73} +(2.96621 - 3.53499i) q^{74} +(3.91895 - 7.42567i) q^{75} +(1.18768 - 0.209419i) q^{76} +(-12.4810 - 3.00061i) q^{77} +(-15.8205 + 14.3335i) q^{78} +(-0.818714 + 0.297987i) q^{79} +0.927591 q^{80} +(-8.82576 - 1.76237i) q^{81} -2.09922i q^{82} +(-6.78293 + 2.46878i) q^{83} +(-2.36088 + 11.7708i) q^{84} +(-2.13586 + 1.79220i) q^{85} +(14.1458 - 2.49428i) q^{86} +(7.77156 + 4.10149i) q^{87} +(4.95095 + 4.15434i) q^{88} +(-2.65800 + 4.60379i) q^{89} +(-1.03791 - 2.29297i) q^{90} +(-6.05413 + 13.9115i) q^{91} +(-1.44070 - 0.254033i) q^{92} +(-5.71701 - 0.785485i) q^{93} +(-2.72378 + 7.48351i) q^{94} +(-0.0614580 + 0.168854i) q^{95} +(-8.25481 + 10.6332i) q^{96} +(-10.7873 - 1.90209i) q^{97} +(3.37519 + 14.6621i) q^{98} +(-3.92554 + 14.0160i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 132 q - 12 q^{2} - 12 q^{4} - 6 q^{7} - 18 q^{8} - 6 q^{9}+O(q^{10}) \) 132 * q - 12 * q^2 - 12 * q^4 - 6 * q^7 - 18 * q^8 - 6 * q^9	\( 132 q - 12 q^{2} - 12 q^{4} - 6 q^{7} - 18 q^{8} - 6 q^{9} - 18 q^{11} + 3 q^{14} - 24 q^{15} - 24 q^{16} - 12 q^{18} - 12 q^{21} - 12 q^{22} + 12 q^{23} - 12 q^{25} - 12 q^{28} - 48 q^{29} + 42 q^{30} - 6 q^{32} - 36 q^{35} - 36 q^{36} - 6 q^{37} - 18 q^{39} - 12 q^{43} - 18 q^{44} - 6 q^{46} - 24 q^{49} + 18 q^{50} + 24 q^{51} + 57 q^{56} - 12 q^{58} - 6 q^{60} + 21 q^{63} + 18 q^{64} + 78 q^{65} - 12 q^{67} - 69 q^{70} + 18 q^{71} + 114 q^{72} - 6 q^{74} - 57 q^{77} + 12 q^{78} + 24 q^{79} - 42 q^{81} - 48 q^{84} + 54 q^{85} - 42 q^{86} - 72 q^{88} + 6 q^{91} - 120 q^{92} - 60 q^{93} + 126 q^{95} + 126 q^{98} - 192 q^{99}+O(q^{100}) \) 132 * q - 12 * q^2 - 12 * q^4 - 6 * q^7 - 18 * q^8 - 6 * q^9 - 18 * q^11 + 3 * q^14 - 24 * q^15 - 24 * q^16 - 12 * q^18 - 12 * q^21 - 12 * q^22 + 12 * q^23 - 12 * q^25 - 12 * q^28 - 48 * q^29 + 42 * q^30 - 6 * q^32 - 36 * q^35 - 36 * q^36 - 6 * q^37 - 18 * q^39 - 12 * q^43 - 18 * q^44 - 6 * q^46 - 24 * q^49 + 18 * q^50 + 24 * q^51 + 57 * q^56 - 12 * q^58 - 6 * q^60 + 21 * q^63 + 18 * q^64 + 78 * q^65 - 12 * q^67 - 69 * q^70 + 18 * q^71 + 114 * q^72 - 6 * q^74 - 57 * q^77 + 12 * q^78 + 24 * q^79 - 42 * q^81 - 48 * q^84 + 54 * q^85 - 42 * q^86 - 72 * q^88 + 6 * q^91 - 120 * q^92 - 60 * q^93 + 126 * q^95 + 126 * q^98 - 192 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more