LMFDB - Embedded newform 384.2.v.a.229.27

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [384,2,Mod(13,384)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(384, base_ring=CyclotomicField(32))

chi = DirichletCharacter(H, H._module([0, 15, 0]))

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

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

chi := DirichletCharacter("384.13");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 384 = 2^{7} \cdot 3 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	384.v (of order $32$, degree $16$, 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:	$3.06625543762$
Analytic rank:	$0$
Dimension:	$512$
Relative dimension:	$32$ over $\Q(\zeta_{32})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{32}]$

Embedding invariants

Embedding label			229.27
Character	$\chi$	$=$	384.229
Dual form			384.2.v.a.109.27

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.19522 + 0.755950i) q^{2} +(0.881921 - 0.471397i) q^{3} +(0.857080 + 1.80705i) q^{4} +(0.324989 + 0.396000i) q^{5} +(1.41044 + 0.103268i) q^{6} +(-2.62499 + 1.75396i) q^{7} +(-0.341641 + 2.80772i) q^{8} +(0.555570 - 0.831470i) q^{9} +(0.0890756 + 0.718981i) q^{10} +(2.66741 - 0.809151i) q^{11} +(1.60771 + 1.18965i) q^{12} +(3.50927 + 2.87998i) q^{13} +(-4.46333 + 0.112002i) q^{14} +(0.473288 + 0.196042i) q^{15} +(-2.53083 + 3.09756i) q^{16} +(-1.24239 + 0.514614i) q^{17} +(1.29258 - 0.573802i) q^{18} +(-0.508900 - 5.16694i) q^{19} +(-0.437049 + 0.926674i) q^{20} +(-1.48822 + 2.78427i) q^{21} +(3.79981 + 1.04932i) q^{22} +(0.610074 - 0.121351i) q^{23} +(1.02225 + 2.63723i) q^{24} +(0.924253 - 4.64653i) q^{25} +(2.01721 + 6.09502i) q^{26} +(0.0980171 - 0.995185i) q^{27} +(-5.41931 - 3.24019i) q^{28} +(1.53679 - 5.06611i) q^{29} +(0.417483 + 0.592095i) q^{30} +(-4.71383 - 4.71383i) q^{31} +(-5.36649 + 1.78908i) q^{32} +(1.97102 - 1.97102i) q^{33} +(-1.87394 - 0.324108i) q^{34} +(-1.54766 - 0.469478i) q^{35} +(1.97867 + 0.291305i) q^{36} +(-0.337930 - 0.0332832i) q^{37} +(3.29771 - 6.56031i) q^{38} +(4.45251 + 0.885659i) q^{39} +(-1.22289 + 0.777188i) q^{40} +(-0.532960 - 2.67937i) q^{41} +(-3.88351 + 2.20278i) q^{42} +(-4.98592 - 2.66503i) q^{43} +(3.74836 + 4.12663i) q^{44} +(0.509817 - 0.0502126i) q^{45} +(0.820906 + 0.316144i) q^{46} +(2.42698 + 5.85925i) q^{47} +(-0.771809 + 3.92483i) q^{48} +(1.13540 - 2.74110i) q^{49} +(4.61723 - 4.85492i) q^{50} +(-0.853101 + 1.03951i) q^{51} +(-2.19653 + 8.80978i) q^{52} +(3.19382 + 10.5286i) q^{53} +(0.869461 - 1.11536i) q^{54} +(1.18730 + 0.793332i) q^{55} +(-4.02783 - 7.96945i) q^{56} +(-2.88449 - 4.31694i) q^{57} +(5.66652 - 4.89336i) q^{58} +(-10.5526 + 8.66027i) q^{59} +(0.0513882 + 1.02328i) q^{60} +(-1.48249 - 2.77355i) q^{61} +(-2.07062 - 9.19746i) q^{62} +3.15705i q^{63} +(-7.76656 - 1.91846i) q^{64} +2.32563i q^{65} +(3.84578 - 0.865800i) q^{66} +(-5.88175 - 11.0040i) q^{67} +(-1.99476 - 1.80399i) q^{68} +(0.480833 - 0.394609i) q^{69} +(-1.49489 - 1.73108i) q^{70} +(-4.98217 - 7.45634i) q^{71} +(2.14473 + 1.84395i) q^{72} +(6.36198 + 4.25094i) q^{73} +(-0.378739 - 0.295239i) q^{74} +(-1.37524 - 4.53357i) q^{75} +(8.90074 - 5.34809i) q^{76} +(-5.58271 + 6.80255i) q^{77} +(4.65219 + 4.42443i) q^{78} +(3.81862 - 9.21898i) q^{79} +(-2.04913 + 0.00446587i) q^{80} +(-0.382683 - 0.923880i) q^{81} +(1.38847 - 3.60532i) q^{82} +(12.4261 - 1.22386i) q^{83} +(-6.30682 - 0.302946i) q^{84} +(-0.607550 - 0.324742i) q^{85} +(-3.94462 - 6.95439i) q^{86} +(-1.03282 - 5.19235i) q^{87} +(1.36057 + 7.76578i) q^{88} +(12.3634 + 2.45923i) q^{89} +(0.647299 + 0.325381i) q^{90} +(-14.2632 - 1.40480i) q^{91} +(0.742170 + 0.998424i) q^{92} +(-6.37931 - 1.93514i) q^{93} +(-1.52853 + 8.83774i) q^{94} +(1.88073 - 1.88073i) q^{95} +(-3.88945 + 4.10757i) q^{96} +(-4.31715 - 4.31715i) q^{97} +(3.42919 - 2.41790i) q^{98} +(0.809151 - 2.66741i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 512 q - 96 q^{50} - 96 q^{52} - 32 q^{54} - 224 q^{56} - 192 q^{60} - 192 q^{62} - 192 q^{64} - 192 q^{66} - 192 q^{68} - 192 q^{70} - 224 q^{74} - 32 q^{76} - 96 q^{78} - 96 q^{80}+O(q^{100}) $ 512 * q - 96 * q^50 - 96 * q^52 - 32 * q^54 - 224 * q^56 - 192 * q^60 - 192 * q^62 - 192 * q^64 - 192 * q^66 - 192 * q^68 - 192 * q^70 - 224 * q^74 - 32 * q^76 - 96 * q^78 - 96 * q^80

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/384\mathbb{Z}\right)^\times$.

$n$	$127$	$133$	$257$
$\chi(n)$	$1$	$e\left(\frac{9}{32}\right)$	$1$

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 $

$2$	1.19522	+	0.755950i	0.845145	+	0.534537i
$2$	1.19522	+	0.755950i	0.845145	+	0.534537i
$3$	0.881921	−	0.471397i	0.509177	−	0.272161i
$3$	0.881921	−	0.471397i	0.509177	−	0.272161i
$4$	0.857080	+	1.80705i	0.428540	+	0.903523i
$5$	0.324989	+	0.396000i	0.145340	+	0.177097i	0.840592	−	0.541669i	$-0.182207\pi$
$5$	0.324989	+	0.396000i	0.145340	+	0.177097i	−0.695252	+	0.718766i	$0.744707\pi$
$6$	1.41044	+	0.103268i	0.575809	+	0.0421588i
$7$	−2.62499	+	1.75396i	−0.992153	+	0.662935i	−0.941932	−	0.335803i	$-0.890992\pi$
$7$	−2.62499	+	1.75396i	−0.992153	+	0.662935i	−0.0502204	+	0.998738i	$0.515992\pi$
$8$	−0.341641	+	2.80772i	−0.120788	+	0.992678i
$9$	0.555570	−	0.831470i	0.185190	−	0.277157i
$10$	0.0890756	+	0.718981i	0.0281682	+	0.227362i
$11$	2.66741	−	0.809151i	0.804255	−	0.243968i	0.138717	−	0.990332i	$-0.455702\pi$
$11$	2.66741	−	0.809151i	0.804255	−	0.243968i	0.665538	+	0.746364i	$0.268202\pi$
$12$	1.60771	+	1.18965i	0.464107	+	0.343422i
$13$	3.50927	+	2.87998i	0.973295	+	0.798763i	0.979547	−	0.201218i	$-0.0644899\pi$
$13$	3.50927	+	2.87998i	0.973295	+	0.798763i	−0.00625145	+	0.999980i	$0.501990\pi$
$14$	−4.46333	+	0.112002i	−1.19288	+	0.0299338i
$15$	0.473288	+	0.196042i	0.122202	+	0.0506179i
$16$	−2.53083	+	3.09756i	−0.632707	+	0.774391i
$17$	−1.24239	+	0.514614i	−0.301323	+	0.124812i	−0.528222	−	0.849106i	$-0.677141\pi$
$17$	−1.24239	+	0.514614i	−0.301323	+	0.124812i	0.226899	+	0.973918i	$0.427141\pi$
$18$	1.29258	−	0.573802i	0.304663	−	0.135246i
$19$	−0.508900	−	5.16694i	−0.116750	−	1.18538i	−0.857820	−	0.513951i	$-0.828181\pi$
$19$	−0.508900	−	5.16694i	−0.116750	−	1.18538i	0.741070	−	0.671428i	$-0.234319\pi$
$20$	−0.437049	+	0.926674i	−0.0977272	+	0.207211i
$21$	−1.48822	+	2.78427i	−0.324757	+	0.607577i
$22$	3.79981	+	1.04932i	0.810122	+	0.223716i
$23$	0.610074	−	0.121351i	0.127209	−	0.0253035i	−0.131075	−	0.991372i	$-0.541843\pi$
$23$	0.610074	−	0.121351i	0.127209	−	0.0253035i	0.258284	+	0.966069i	$0.416843\pi$
$24$	1.02225	+	2.63723i	0.208666	+	0.538323i
$25$	0.924253	−	4.64653i	0.184851	−	0.929307i
$26$	2.01721	+	6.09502i	0.395607	+	1.19533i
$27$	0.0980171	−	0.995185i	0.0188634	−	0.191523i
$28$	−5.41931	−	3.24019i	−1.02415	−	0.612338i
$29$	1.53679	−	5.06611i	0.285374	−	0.940753i	−0.690668	−	0.723172i	$-0.742683\pi$
$29$	1.53679	−	5.06611i	0.285374	−	0.940753i	0.976042	−	0.217581i	$-0.0698166\pi$
$30$	0.417483	+	0.592095i	0.0762216	+	0.108101i
$31$	−4.71383	−	4.71383i	−0.846629	−	0.846629i	0.143082	−	0.989711i	$-0.454299\pi$
$31$	−4.71383	−	4.71383i	−0.846629	−	0.846629i	−0.989711	+	0.143082i	$0.954299\pi$
$32$	−5.36649	+	1.78908i	−0.948670	+	0.316267i
$33$	1.97102	−	1.97102i	0.343110	−	0.343110i
$34$	−1.87394	−	0.324108i	−0.321378	−	0.0555841i
$35$	−1.54766	−	0.469478i	−0.261603	−	0.0793563i
$36$	1.97867	+	0.291305i	0.329779	+	0.0485508i
$37$	−0.337930	−	0.0332832i	−0.0555553	−	0.00547172i	0.0702013	−	0.997533i	$-0.477636\pi$
$37$	−0.337930	−	0.0332832i	−0.0555553	−	0.00547172i	−0.125757	+	0.992061i	$0.540136\pi$
$38$	3.29771	−	6.56031i	0.534958	−	1.06422i
$39$	4.45251	+	0.885659i	0.712972	+	0.141819i
$40$	−1.22289	+	0.777188i	−0.193355	+	0.122884i
$41$	−0.532960	−	2.67937i	−0.0832344	−	0.418447i	−0.999827	−	0.0186240i	$-0.994071\pi$
$41$	−0.532960	−	2.67937i	−0.0832344	−	0.418447i	0.916592	−	0.399823i	$-0.130929\pi$
$42$	−3.88351	+	2.20278i	−0.599239	+	0.339896i
$43$	−4.98592	−	2.66503i	−0.760346	−	0.406413i	0.0451764	−	0.998979i	$-0.485615\pi$
$43$	−4.98592	−	2.66503i	−0.760346	−	0.406413i	−0.805522	+	0.592566i	$0.798115\pi$
$44$	3.74836	+	4.12663i	0.565086	+	0.622113i
$45$	0.509817	−	0.0502126i	0.0759990	−	0.00748525i
$46$	0.820906	+	0.316144i	0.121036	+	0.0466130i
$47$	2.42698	+	5.85925i	0.354012	+	0.854660i	0.996117	+	0.0880431i	$0.0280613\pi$
$47$	2.42698	+	5.85925i	0.354012	+	0.854660i	−0.642105	+	0.766617i	$0.721939\pi$
$48$	−0.771809	+	3.92483i	−0.111401	+	0.566501i
$49$	1.13540	−	2.74110i	0.162200	−	0.391586i
$50$	4.61723	−	4.85492i	0.652975	−	0.686589i
$51$	−0.853101	+	1.03951i	−0.119458	+	0.145560i
$52$	−2.19653	+	8.80978i	−0.304604	+	1.22170i
$53$	3.19382	+	10.5286i	0.438706	+	1.44622i	0.846129	+	0.532979i	$0.178927\pi$
$53$	3.19382	+	10.5286i	0.438706	+	1.44622i	−0.407423	+	0.913240i	$0.633573\pi$
$54$	0.869461	−	1.11536i	0.118319	−	0.151782i
$55$	1.18730	+	0.793332i	0.160096	+	0.106973i
$56$	−4.02783	−	7.96945i	−0.538241	−	1.06496i
$57$	−2.88449	−	4.31694i	−0.382060	−	0.571793i
$58$	5.66652	−	4.89336i	0.744050	−	0.642530i
$59$	−10.5526	+	8.66027i	−1.37383	+	1.12747i	−0.395956	+	0.918270i	$0.629587\pi$
$59$	−10.5526	+	8.66027i	−1.37383	+	1.12747i	−0.977872	+	0.209202i	$0.932913\pi$
$60$	0.0513882	+	1.02328i	0.00663419	+	0.132105i
$61$	−1.48249	−	2.77355i	−0.189814	−	0.355117i	0.768955	−	0.639302i	$-0.220777\pi$
$61$	−1.48249	−	2.77355i	−0.189814	−	0.355117i	−0.958769	+	0.284186i	$0.908277\pi$
$62$	−2.07062	−	9.19746i	−0.262969	−	1.16808i
$63$			3.15705i			0.397751i
$64$	−7.76656	−	1.91846i	−0.970820	−	0.239808i
$65$			2.32563i			0.288459i
$66$	3.84578	−	0.865800i	0.473383	−	0.106573i
$67$	−5.88175	−	11.0040i	−0.718571	−	1.34435i	−0.930219	−	0.367005i	$-0.880383\pi$
$67$	−5.88175	−	11.0040i	−0.718571	−	1.34435i	0.211648	−	0.977346i	$-0.432117\pi$
$68$	−1.99476	−	1.80399i	−0.241900	−	0.218765i
$69$	0.480833	−	0.394609i	0.0578855	−	0.0475054i
$70$	−1.49489	−	1.73108i	−0.178673	−	0.206904i
$71$	−4.98217	−	7.45634i	−0.591275	−	0.884905i	0.408335	−	0.912832i	$-0.366109\pi$
$71$	−4.98217	−	7.45634i	−0.591275	−	0.884905i	−0.999610	+	0.0279270i	$0.991109\pi$
$72$	2.14473	+	1.84395i	0.252758	+	0.217311i
$73$	6.36198	+	4.25094i	0.744614	+	0.497535i	0.869069	−	0.494690i	$-0.164718\pi$
$73$	6.36198	+	4.25094i	0.744614	+	0.497535i	−0.124456	+	0.992225i	$0.539718\pi$
$74$	−0.378739	−	0.295239i	−0.0440275	−	0.0343208i
$75$	−1.37524	−	4.53357i	−0.158799	−	0.523491i
$76$	8.90074	−	5.34809i	1.02098	−	0.613468i
$77$	−5.58271	+	6.80255i	−0.636209	+	0.775223i
$78$	4.65219	+	4.42443i	0.526757	+	0.500968i
$79$	3.81862	−	9.21898i	0.429629	−	1.03722i	−0.549777	−	0.835312i	$-0.685287\pi$
$79$	3.81862	−	9.21898i	0.429629	−	1.03722i	0.979405	−	0.201904i	$-0.0647129\pi$
$80$	−2.04913	+	0.00446587i	−0.229100	+	0.000499299i
$81$	−0.382683	−	0.923880i	−0.0425204	−	0.102653i
$82$	1.38847	−	3.60532i	0.153331	−	0.398141i
$83$	12.4261	−	1.22386i	1.36394	−	0.134337i	0.610586	−	0.791950i	$-0.290934\pi$
$83$	12.4261	−	1.22386i	1.36394	−	0.134337i	0.753356	+	0.657613i	$0.228434\pi$
$84$	−6.30682	−	0.302946i	−0.688131	−	0.0330541i
$85$	−0.607550	−	0.324742i	−0.0658980	−	0.0352232i
$86$	−3.94462	−	6.95439i	−0.425359	−	0.749911i
$87$	−1.03282	−	5.19235i	−0.110730	−	0.556678i
$88$	1.36057	+	7.76578i	0.145037	+	0.827835i
$89$	12.3634	+	2.45923i	1.31051	+	0.260678i	0.800419	−	0.599440i	$-0.204610\pi$
$89$	12.3634	+	2.45923i	1.31051	+	0.260678i	0.510095	+	0.860118i	$0.329610\pi$
$90$	0.647299	+	0.325381i	0.0682313	+	0.0342982i
$91$	−14.2632	−	1.40480i	−1.49519	−	0.147263i
$92$	0.742170	+	0.998424i	0.0773765	+	0.104093i
$93$	−6.37931	−	1.93514i	−0.661504	−	0.200665i
$94$	−1.52853	+	8.83774i	−0.157656	+	0.911544i
$95$	1.88073	−	1.88073i	0.192958	−	0.192958i
$96$	−3.88945	+	4.10757i	−0.396966	+	0.419227i
$97$	−4.31715	−	4.31715i	−0.438340	−	0.438340i	0.453113	−	0.891453i	$-0.350313\pi$
$97$	−4.31715	−	4.31715i	−0.438340	−	0.438340i	−0.891453	+	0.453113i	$0.850313\pi$
$98$	3.42919	−	2.41790i	0.346400	−	0.244245i
$99$	0.809151	−	2.66741i	0.0813227	−	0.268085i
$100$	9.18866	−	2.31228i	0.918866	−	0.231228i
$101$	−0.514166	+	5.22042i	−0.0511615	+	0.519451i	0.935114	+	0.354346i	$0.115296\pi$
$101$	−0.514166	+	5.22042i	−0.0511615	+	0.519451i	−0.986276	+	0.165105i	$0.947204\pi$
$102$	−1.80545	+	0.597532i	−0.178767	+	0.0591645i
$103$	−0.878928	+	4.41867i	−0.0866033	+	0.435384i	0.913019	+	0.407916i	$0.133744\pi$
$103$	−0.878928	+	4.41867i	−0.0866033	+	0.435384i	−0.999623	+	0.0274681i	$0.991256\pi$
$104$	−9.28508	+	8.86911i	−0.910477	+	0.869688i
$105$	−1.58623	+	0.315520i	−0.154800	+	0.0307916i
$106$	−4.14181	+	14.9983i	−0.402288	+	1.45677i
$107$	0.0238305	−	0.0445837i	0.00230378	−	0.00431007i	−0.880767	−	0.473550i	$-0.842972\pi$
$107$	0.0238305	−	0.0445837i	0.00230378	−	0.00431007i	0.883071	+	0.469240i	$0.155472\pi$
$108$	1.88235	−	0.675831i	0.181129	−	0.0650319i
$109$	0.418707	+	4.25120i	0.0401048	+	0.407191i	0.994189	+	0.107652i	$0.0343331\pi$
$109$	0.418707	+	4.25120i	0.0401048	+	0.407191i	−0.954084	+	0.299540i	$0.903167\pi$
$110$	0.819366	+	1.84574i	0.0781235	+	0.175985i
$111$	−0.313717	+	0.129946i	−0.0297767	+	0.0123339i
$112$	1.21039	−	12.5700i	0.114371	−	1.18776i
$113$	16.4197	+	6.80124i	1.54463	+	0.639807i	0.982335	−	0.187129i	$-0.0599181\pi$
$113$	16.4197	+	6.80124i	1.54463	+	0.639807i	0.562296	+	0.826936i	$0.309918\pi$
$114$	−0.184194	−	7.34021i	−0.0172513	−	0.687473i
$115$	0.246323	+	0.202152i	0.0229697	+	0.0188508i
$116$	10.4718	−	1.56502i	0.972286	−	0.145308i
$117$	4.34426	−	1.31782i	0.401627	−	0.121832i
$118$	−19.1593	+	2.37368i	−1.76376	+	0.218515i
$119$	2.35864	−	3.52995i	0.216216	−	0.323590i
$120$	−0.712126	+	1.26188i	−0.0650079	+	0.115194i
$121$	−2.68580	+	1.79459i	−0.244164	+	0.163145i
$122$	0.324766	−	4.43568i	0.0294029	−	0.401588i
$123$	−1.73308	−	2.11176i	−0.156266	−	0.190411i
$124$	4.47798	−	12.5582i	0.402134	−	1.12776i
$125$	4.39937	−	2.35151i	0.393492	−	0.210326i
$126$	−2.38657	+	3.77335i	−0.212612	+	0.336157i
$127$	10.8650			0.964109			0.482054	−	0.876141i	$-0.339891\pi$
$127$	10.8650			0.964109			0.482054	+	0.876141i	$0.339891\pi$
$128$	−7.83246	−	8.16411i	−0.692298	−	0.721612i
$129$	−5.65347			−0.497761
$130$	−1.75806	+	2.77963i	−0.154192	+	0.243790i
$131$	−2.32166	+	1.24095i	−0.202845	+	0.108423i	−0.569692	−	0.821859i	$-0.692937\pi$
$131$	−2.32166	+	1.24095i	−0.202845	+	0.108423i	0.366847	+	0.930281i	$0.380437\pi$
$132$	5.25104	+	1.87240i	0.457044	+	0.162971i
$133$	10.3985	+	12.6706i	0.901662	+	1.09868i
$134$	1.28850	−	17.5984i	0.111309	−	1.52027i
$135$	0.425948	−	0.284609i	0.0366598	−	0.0244953i
$136$	−1.02044	−	3.66409i	−0.0875020	−	0.314193i
$137$	1.40646	−	2.10492i	0.120162	−	0.179836i	−0.766512	−	0.642230i	$-0.778010\pi$
$137$	1.40646	−	2.10492i	0.120162	−	0.179836i	0.886674	+	0.462394i	$0.153010\pi$
$138$	0.873004	−	0.108158i	0.0743150	−	0.00920699i
$139$	−10.5798	+	3.20933i	−0.897363	+	0.272212i	−0.705080	−	0.709128i	$-0.749089\pi$
$139$	−10.5798	+	3.20933i	−0.897363	+	0.272212i	−0.192283	+	0.981340i	$0.561589\pi$
$140$	−0.478102	−	3.19908i	−0.0404070	−	0.270371i
$141$	4.90244	+	4.02333i	0.412860	+	0.338825i
$142$	−0.318144	−	12.6782i	−0.0266981	−	1.06393i
$143$	11.6910	+	4.84257i	0.977650	+	0.404956i
$144$	1.16948	+	3.82522i	0.0974565	+	0.318768i
$145$	2.50562	−	1.03786i	0.208081	−	0.0861898i
$146$	4.39044	+	9.89013i	0.363356	+	0.818513i
$147$	−0.290812	−	2.95266i	−0.0239858	−	0.243531i
$148$	−0.229489	−	0.639181i	−0.0188639	−	0.0525404i
$149$	−3.91105	+	7.31705i	−0.320405	+	0.599436i	−0.989633	−	0.143621i	$-0.954125\pi$
$149$	−3.91105	+	7.31705i	−0.320405	+	0.599436i	0.669227	+	0.743058i	$0.266625\pi$
$150$	1.78344	−	6.45820i	0.145617	−	0.527310i
$151$	−23.0443	+	4.58380i	−1.87532	+	0.373025i	−0.994874	−	0.101119i	$-0.967758\pi$
$151$	−23.0443	+	4.58380i	−1.87532	+	0.373025i	−0.880447	+	0.474144i	$0.842758\pi$
$152$	14.6812	+	0.336392i	1.19080	+	0.0272850i
$153$	−0.262348	+	1.31891i	−0.0212096	+	0.106628i
$154$	−11.8149	+	3.91027i	−0.952074	+	0.315098i
$155$	0.334735	−	3.39862i	0.0268866	−	0.272984i
$156$	2.21573	+	8.80497i	0.177400	+	0.704962i
$157$	3.42177	−	11.2801i	0.273087	−	0.900247i	−0.707923	−	0.706290i	$-0.750368\pi$
$157$	3.42177	−	11.2801i	0.273087	−	0.900247i	0.981010	−	0.193957i	$-0.0621324\pi$
$158$	11.5332	−	8.13197i	0.917529	−	0.646945i
$159$	7.77986	+	7.77986i	0.616983	+	0.616983i
$160$	−2.45253	−	1.54370i	−0.193889	−	0.122040i
$161$	−1.38859	+	1.38859i	−0.109436	+	0.109436i
$162$	0.241017	−	1.39352i	0.0189361	−	0.109486i
$163$	−6.22873	−	1.88946i	−0.487871	−	0.147994i	0.0367592	−	0.999324i	$-0.488297\pi$
$163$	−6.22873	−	1.88946i	−0.487871	−	0.147994i	−0.524631	+	0.851330i	$0.675797\pi$
$164$	4.38496	−	3.25952i	0.342408	−	0.254526i
$165$	1.42108	+	0.139964i	0.110631	+	0.0108962i
$166$	15.7771	+	7.93073i	1.22454	+	0.615544i
$167$	1.63266	+	0.324756i	0.126339	+	0.0251304i	0.257855	−	0.966184i	$-0.416984\pi$
$167$	1.63266	+	0.324756i	0.126339	+	0.0251304i	−0.131516	+	0.991314i	$0.541984\pi$
$168$	−7.30900	−	5.12973i	−0.563902	−	0.395767i
$169$	1.48449	+	7.46302i	0.114191	+	0.574078i
$170$	−0.480664	−	0.847414i	−0.0368653	−	0.0649937i
$171$	−4.57889	−	2.44747i	−0.350156	−	0.187162i
$172$	0.542499	−	11.2939i	0.0413652	−	0.861154i
$173$	−24.9561	+	2.45796i	−1.89738	+	0.186875i	−0.978298	−	0.207201i	$-0.933565\pi$
$173$	−24.9561	+	2.45796i	−1.89738	+	0.186875i	−0.919078	+	0.394076i	$0.871065\pi$
$174$	2.69071	−	6.98674i	0.203982	−	0.529663i
$175$	5.72369	+	13.8182i	0.432670	+	1.04456i
$176$	−4.24437	+	10.3103i	−0.319931	+	0.777169i
$177$	−5.22411	+	12.6121i	−0.392668	+	0.947986i
$178$	12.9178	+	12.2854i	0.968233	+	0.920829i
$179$	−2.07261	+	2.52548i	−0.154914	+	0.188763i	−0.844684	−	0.535265i	$-0.820212\pi$
$179$	−2.07261	+	2.52548i	−0.154914	+	0.188763i	0.689770	+	0.724029i	$0.257712\pi$
$180$	0.527690	+	0.878226i	0.0393317	+	0.0654591i
$181$	4.29826	+	14.1695i	0.319487	+	1.05321i	0.958757	+	0.284226i	$0.0917368\pi$
$181$	4.29826	+	14.1695i	0.319487	+	1.05321i	−0.639270	+	0.768983i	$0.720763\pi$
$182$	−15.9856	−	12.4613i	−1.18493	−	0.923691i
$183$	−2.61488	−	1.74721i	−0.193298	−	0.129157i
$184$	0.132294	+	1.75437i	0.00975284	+	0.129334i
$185$	−0.0966434	−	0.144637i	−0.00710537	−	0.0106339i
$186$	−6.16178	−	7.13535i	−0.451804	−	0.523189i
$187$	−2.89756	+	2.37797i	−0.211891	+	0.173894i
$188$	−8.50782	+	9.40751i	−0.620496	+	0.686113i
$189$	1.48822	+	2.78427i	0.108252	+	0.202526i
$190$	3.66961	−	0.826138i	0.266221	−	0.0599344i
$191$			4.55766i			0.329781i	0.986312	+	0.164890i	$0.0527270\pi$
$191$			4.55766i			0.329781i	−0.986312	+	0.164890i	$0.947273\pi$
$192$	−7.75385	+	1.96920i	−0.559586	+	0.142115i
$193$		−	26.9836i		−	1.94232i	−0.238424	−	0.971161i	$-0.576631\pi$
$193$		−	26.9836i		−	1.94232i	0.238424	−	0.971161i	$-0.423369\pi$
$194$	−1.89638	−	8.42347i	−0.136152	−	0.604770i
$195$	1.09630	+	2.05103i	0.0785074	+	0.146877i
$196$	5.92643	−	0.297621i	0.423316	−	0.0212586i
$197$	−10.8509	+	8.90507i	−0.773092	+	0.634460i	−0.935927	−	0.352193i	$-0.885436\pi$
$197$	−10.8509	+	8.90507i	−0.773092	+	0.634460i	0.162836	+	0.986653i	$0.447936\pi$
$198$	2.98354	−	2.57646i	0.212031	−	0.183101i
$199$	13.9364	+	20.8573i	0.987924	+	1.47853i	0.874524	+	0.484983i	$0.161174\pi$
$199$	13.9364	+	20.8573i	0.987924	+	1.47853i	0.113400	+	0.993549i	$0.463826\pi$
$200$	12.7304	+	4.18249i	0.900175	+	0.295747i
$201$	−10.3745	−	6.93201i	−0.731760	−	0.488946i
$202$	−4.56091	+	5.85084i	−0.320905	+	0.411664i
$203$	4.85171	+	15.9940i	0.340523	+	1.12256i
$204$	−2.60961	−	0.650652i	−0.182709	−	0.0455548i
$205$	0.887826	−	1.08182i	0.0620085	−	0.0755575i
$206$	−4.39080	+	4.61684i	−0.305922	+	0.321670i
$207$	0.238039	−	0.574677i	0.0165449	−	0.0399428i
$208$	−17.8023	+	3.58144i	−1.23437	+	0.248328i
$209$	−5.53828	−	13.3706i	−0.383091	−	0.924864i
$210$	−2.13440	−	0.821993i	−0.147288	−	0.0567229i
$211$	5.25265	−	0.517340i	0.361607	−	0.0356152i	0.0844176	−	0.996430i	$-0.473097\pi$
$211$	5.25265	−	0.517340i	0.361607	−	0.0356152i	0.277189	+	0.960815i	$0.410597\pi$
$212$	−16.2883	+	14.7953i	−1.11869	+	1.01614i
$213$	−7.90878	−	4.22733i	−0.541900	−	0.289652i
$214$	0.0621857	−	0.0352725i	0.00425092	−	0.00241118i
$215$	−0.565017	−	2.84053i	−0.0385338	−	0.193723i
$216$	2.76071	+	0.615200i	0.187843	+	0.0418591i
$217$	20.6416	+	4.10588i	1.40125	+	0.278725i
$218$	−2.71325	+	5.39762i	−0.183765	+	0.365573i
$219$	7.61465	+	0.749977i	0.514550	+	0.0506788i
$220$	−0.415972	+	2.82546i	−0.0280448	+	0.190493i
$221$	−5.84194	−	1.77213i	−0.392972	−	0.119207i
$222$	−0.473192	−	0.0818411i	−0.0317586	−	0.00549281i
$223$	−11.9760	+	11.9760i	−0.801973	+	0.801973i	−0.983404	−	0.181431i	$-0.941927\pi$
$223$	−11.9760	+	11.9760i	−0.801973	+	0.801973i	0.181431	+	0.983404i	$0.441927\pi$
$224$	10.9490	−	14.1089i	0.731561	−	0.942692i
$225$	−3.34996	−	3.34996i	−0.223331	−	0.223331i
$226$	14.4836	+	20.5414i	0.963437	+	1.36639i
$227$	−7.70283	+	25.3928i	−0.511255	+	1.68538i	0.197812	+	0.980240i	$0.436616\pi$
$227$	−7.70283	+	25.3928i	−0.511255	+	1.68538i	−0.709067	+	0.705141i	$0.750884\pi$
$228$	5.32868	−	8.91237i	0.352900	−	0.590236i
$229$	−1.38909	+	14.1037i	−0.0917937	+	0.931998i	0.833443	+	0.552606i	$0.186367\pi$
$229$	−1.38909	+	14.1037i	−0.0917937	+	0.931998i	−0.925236	+	0.379391i	$0.876133\pi$
$230$	0.141592	+	0.427823i	0.00933630	+	0.0282098i
$231$	−1.71681	+	8.63099i	−0.112958	+	0.567877i
$232$	13.6992	+	6.04566i	0.899395	+	0.396917i
$233$	20.2852	−	4.03498i	1.32893	−	0.264340i	0.520967	−	0.853577i	$-0.325571\pi$
$233$	20.2852	−	4.03498i	1.32893	−	0.264340i	0.807961	+	0.589236i	$0.200571\pi$
$234$	6.18853	+	1.70897i	0.404557	+	0.111719i
$235$	−1.53152	+	2.86528i	−0.0999056	+	0.186910i
$236$	−24.6939	−	11.6464i	−1.60744	−	0.758118i
$237$	−0.978069	−	9.93050i	−0.0635324	−	0.645055i
$238$	5.48755	−	2.43604i	0.355705	−	0.157905i
$239$	20.0048	−	8.28626i	1.29400	−	0.535994i	0.373828	−	0.927498i	$-0.378045\pi$
$239$	20.0048	−	8.28626i	1.29400	−	0.535994i	0.920176	+	0.391504i	$0.128045\pi$
$240$	−1.80507	+	0.969891i	−0.116516	+	0.0626062i
$241$	−0.884074	−	0.366195i	−0.0569482	−	0.0235887i	0.354028	−	0.935235i	$-0.384812\pi$
$241$	−0.884074	−	0.366195i	−0.0569482	−	0.0235887i	−0.410976	+	0.911646i	$0.634812\pi$
$242$	−4.56673	+	0.114597i	−0.293561	+	0.00736655i
$243$	−0.773010	−	0.634393i	−0.0495886	−	0.0406963i
$244$	3.74132	−	5.05609i	0.239513	−	0.323683i
$245$	1.45447	−	0.441209i	0.0929228	−	0.0281878i
$246$	−0.475015	−	3.83412i	−0.0302859	−	0.244455i
$247$	13.0948	−	19.5978i	0.833204	−	1.24698i
$248$	14.8455	−	11.6247i	0.942693	−	0.738167i
$249$	10.3819	−	6.93698i	0.657928	−	0.439613i
$250$	7.03582	+	0.515139i	0.444984	+	0.0325803i
$251$	5.17411	+	6.30467i	0.326587	+	0.397947i	0.910257	−	0.414044i	$-0.135884\pi$
$251$	5.17411	+	6.30467i	0.326587	+	0.397947i	−0.583670	+	0.811991i	$0.698384\pi$
$252$	−5.70493	+	2.70584i	−0.359377	+	0.170452i
$253$	1.52913	−	0.817336i	0.0961355	−	0.0513855i
$254$	12.9860	+	8.21336i	0.814812	+	0.515352i
$255$	−0.688893			−0.0431402
$256$	−3.18982	−	15.6788i	−0.199363	−	0.979926i
$257$	−28.5654			−1.78186			−0.890931	−	0.454139i	$-0.849947\pi$
$257$	−28.5654			−1.78186			−0.890931	+	0.454139i	$0.849947\pi$
$258$	−6.75712	−	4.27374i	−0.420680	−	0.266072i
$259$	0.945440	−	0.505348i	0.0587468	−	0.0314008i
$260$	−4.20253	+	1.99325i	−0.260630	+	0.123616i
$261$	−3.35852	−	4.09237i	−0.207887	−	0.253311i
$262$	−3.71299	−	0.271852i	−0.229389	−	0.0167951i
$263$	4.19063	−	2.80009i	0.258405	−	0.172661i	−0.419619	−	0.907700i	$-0.637836\pi$
$263$	4.19063	−	2.80009i	0.258405	−	0.172661i	0.678024	+	0.735039i	$0.262836\pi$
$264$	4.86068	+	6.20744i	0.299154	+	0.382042i
$265$	−3.13138	+	4.68645i	−0.192359	+	0.287886i
$266$	2.85010	+	23.0048i	0.174751	+	1.41051i
$267$	12.0628	−	3.65921i	0.738231	−	0.223940i
$268$	14.8436	−	20.0599i	0.906716	−	1.22535i
$269$	−5.61490	−	4.60803i	−0.342347	−	0.280957i	0.447471	−	0.894299i	$-0.352325\pi$
$269$	−5.61490	−	4.60803i	−0.342347	−	0.280957i	−0.789818	+	0.613342i	$0.789825\pi$
$270$	0.724250	−	0.0181742i	0.0440765	−	0.00110605i
$271$	14.4400	+	5.98123i	0.877166	+	0.363334i	0.775397	−	0.631474i	$-0.217550\pi$
$271$	14.4400	+	5.98123i	0.877166	+	0.363334i	0.101769	+	0.994808i	$0.467550\pi$
$272$	1.55022	−	5.15077i	0.0939959	−	0.312312i
$273$	−13.2412	+	5.48468i	−0.801394	+	0.331948i
$274$	3.27224	−	1.45262i	0.197683	−	0.0877559i
$275$	−1.29438	−	13.1421i	−0.0780542	−	0.792498i
$276$	1.12519	+	0.530675i	0.0677284	+	0.0319429i
$277$	3.08508	−	5.77178i	0.185365	−	0.346793i	−0.772025	−	0.635592i	$-0.780756\pi$
$277$	3.08508	−	5.77178i	0.185365	−	0.346793i	0.957390	+	0.288799i	$0.0932560\pi$
$278$	−15.0712	−	4.16192i	−0.903909	−	0.249615i
$279$	−6.53827	+	1.30054i	−0.391436	+	0.0778615i
$280$	1.84691	−	4.18501i	0.110374	−	0.250102i
$281$	2.15600	−	10.8389i	0.128616	−	0.646596i	−0.861661	−	0.507485i	$-0.830575\pi$
$281$	2.15600	−	10.8389i	0.128616	−	0.646596i	0.990277	−	0.139112i	$-0.0444247\pi$
$282$	2.81804	+	8.51474i	0.167812	+	0.507045i
$283$	0.275637	−	2.79859i	0.0163849	−	0.166359i	−0.983510	−	0.180853i	$-0.942114\pi$
$283$	0.275637	−	2.79859i	0.0163849	−	0.166359i	0.999895	+	0.0144948i	$0.00461402\pi$
$284$	9.20383	−	15.3937i	0.546147	−	0.913447i
$285$	0.772084	−	2.54522i	0.0457343	−	0.150766i
$286$	10.3125	+	14.6257i	0.609792	+	0.864837i
$287$	6.09853	+	6.09853i	0.359985	+	0.359985i
$288$	−1.49390	+	5.45603i	−0.0880287	+	0.321500i
$289$	−10.7421	+	10.7421i	−0.631889	+	0.631889i
$290$	3.77933	+	0.653655i	0.221930	+	0.0383839i
$291$	−5.84248	−	1.77230i	−0.342492	−	0.103894i
$292$	−2.22892	+	15.1398i	−0.130438	+	0.885989i
$293$	−17.0643	−	1.68068i	−0.996905	−	0.0981865i	−0.413616	−	0.910451i	$-0.635734\pi$
$293$	−17.0643	−	1.68068i	−0.996905	−	0.0981865i	−0.583289	+	0.812265i	$0.698234\pi$
$294$	1.88448	−	3.74891i	0.109905	−	0.218641i
$295$	−6.85894	−	1.36433i	−0.399343	−	0.0794343i
$296$	0.208900	−	0.937441i	0.0121421	−	0.0544877i
$297$	−0.543802	−	2.73388i	−0.0315546	−	0.158636i
$298$	−10.2059	+	5.78890i	−0.591210	+	0.335342i
$299$	2.49040	+	1.33115i	0.144024	+	0.0769822i
$300$	7.01367	−	6.37076i	0.404934	−	0.367816i
$301$	17.7623	−	1.74944i	1.02380	−	0.100836i
$302$	−31.0081	−	11.9417i	−1.78431	−	0.687169i
$303$	2.00743	+	4.84637i	0.115324	+	0.278417i
$304$	17.2929	+	11.5003i	0.991815	+	0.659587i
$305$	0.616533	−	1.48844i	0.0353026	−	0.0852279i
$306$	−1.31059	+	1.37806i	−0.0749216	+	0.0787785i
$307$	15.3043	−	18.6483i	0.873461	−	1.06432i	−0.123942	−	0.992289i	$-0.539554\pi$
$307$	15.3043	−	18.6483i	0.873461	−	1.06432i	0.997403	−	0.0720258i	$-0.0229464\pi$
$308$	−17.0774	−	4.25788i	−0.973072	−	0.242615i
$309$	1.30780	+	4.31124i	0.0743982	+	0.245258i
$310$	2.96927	−	3.80904i	0.168643	−	0.216339i
$311$	−5.62710	−	3.75991i	−0.319084	−	0.213205i	0.385705	−	0.922622i	$-0.373958\pi$
$311$	−5.62710	−	3.75991i	−0.319084	−	0.213205i	−0.704789	+	0.709417i	$0.748958\pi$
$312$	−4.00784	+	12.1988i	−0.226899	+	0.690622i
$313$	11.6843	+	17.4868i	0.660434	+	0.988410i	0.998875	+	0.0474219i	$0.0151005\pi$
$313$	11.6843	+	17.4868i	0.660434	+	0.988410i	−0.338441	+	0.940988i	$0.609899\pi$
$314$	12.6169	−	10.8954i	0.712014	−	0.614864i
$315$	−1.25019	+	1.02601i	−0.0704404	+	0.0578089i
$316$	19.9320	−	1.00097i	1.12126	−	0.0563089i
$317$	0.0828413	+	0.154985i	0.00465283	+	0.00870483i	0.884237	−	0.467039i	$-0.154679\pi$
$317$	0.0828413	+	0.154985i	0.00465283	+	0.00870483i	−0.879584	+	0.475743i	$0.842179\pi$
$318$	3.41743	+	15.1798i	0.191640	+	0.851241i
$319$		−	14.7569i		−	0.826228i
$320$	−1.76434	−	3.69904i	−0.0986294	−	0.206783i
$321$		−	0.0505530i		−	0.00282159i
$322$	−2.70937	+	0.609961i	−0.150987	+	0.0339918i
$323$	3.29123	+	6.15746i	0.183129	+	0.342610i
$324$	1.34150	−	1.48336i	0.0745279	−	0.0824092i
$325$	16.6254	−	13.6441i	0.922210	−	0.756838i
$326$	−6.01633	−	6.96692i	−0.333214	−	0.385862i
$327$	2.37327	+	3.55185i	0.131242	+	0.196418i
$328$	7.70500	−	0.581019i	0.425437	−	0.0320814i
$329$	−16.6477	−	11.1236i	−0.917818	−	0.613266i
$330$	1.59269	+	1.24156i	0.0876749	+	0.0683454i
$331$	8.00761	+	26.3976i	0.440138	+	1.45094i	0.844110	+	0.536169i	$0.180129\pi$
$331$	8.00761	+	26.3976i	0.440138	+	1.45094i	−0.403972	+	0.914771i	$0.632371\pi$
$332$	12.8617	+	21.4056i	0.705880	+	1.17478i
$333$	−0.215418	+	0.262487i	−0.0118048	+	0.0143842i
$334$	1.70588	+	1.62236i	0.0933416	+	0.0887717i
$335$	2.44608	−	5.90536i	0.133644	−	0.322644i
$336$	−4.85801	−	11.6564i	−0.265026	−	0.635907i
$337$	1.67342	+	4.04000i	0.0911571	+	0.220073i	0.962882	−	0.269923i	$-0.0869983\pi$
$337$	1.67342	+	4.04000i	0.0911571	+	0.220073i	−0.871725	+	0.489996i	$0.836998\pi$
$338$	−3.86738	+	10.0421i	−0.210358	+	0.546219i
$339$	17.6869	−	1.74201i	0.960622	−	0.0946130i
$340$	0.0661052	−	1.37620i	0.00358506	−	0.0746349i
$341$	−16.3879	−	8.75953i	−0.887456	−	0.474355i
$342$	−3.62259	−	6.38666i	−0.195887	−	0.345351i
$343$	−2.48399	−	12.4879i	−0.134123	−	0.674282i
$344$	9.18605	−	13.0886i	0.495278	−	0.705689i
$345$	0.312531	+	0.0621663i	0.0168261	+	0.00334692i
$346$	−31.6860	−	15.9278i	−1.70345	−	0.856281i
$347$	−21.7729	−	2.14445i	−1.16883	−	0.115120i	−0.505080	−	0.863072i	$-0.668537\pi$
$347$	−21.7729	−	2.14445i	−1.16883	−	0.115120i	−0.663752	+	0.747953i	$0.731037\pi$
$348$	8.49760	−	6.31661i	0.455519	−	0.338606i
$349$	−21.7312	−	6.59209i	−1.16324	−	0.352866i	−0.351109	−	0.936335i	$-0.614195\pi$
$349$	−21.7312	−	6.59209i	−1.16324	−	0.352866i	−0.812136	+	0.583468i	$0.801695\pi$
$350$	−3.60483	+	20.8426i	−0.192686	+	1.11408i
$351$	3.21008	−	3.21008i	0.171341	−	0.171341i
$352$	−12.8670	+	9.11451i	−0.685814	+	0.485805i
$353$	2.66637	+	2.66637i	0.141917	+	0.141917i	0.774496	−	0.632579i	$-0.218004\pi$
$353$	2.66637	+	2.66637i	0.141917	+	0.141917i	−0.632579	+	0.774496i	$0.718004\pi$
$354$	−15.7781	+	11.1250i	−0.838595	+	0.591289i
$355$	1.33356	−	4.39617i	0.0707782	−	0.233325i
$356$	6.15246	+	24.4489i	0.326080	+	1.29579i
$357$	0.416126	−	4.22500i	0.0220237	−	0.223611i
$358$	−4.38635	+	1.45171i	−0.231826	+	0.0767250i
$359$	2.48458	−	12.4908i	0.131131	−	0.659240i	−0.858172	−	0.513363i	$-0.828400\pi$
$359$	2.48458	−	12.4908i	0.131131	−	0.659240i	0.989303	−	0.145877i	$-0.0466004\pi$
$360$	−0.0331915	+	1.44858i	−0.00174934	+	0.0763467i
$361$	−7.80341	+	1.55219i	−0.410706	+	0.0816945i
$362$	−5.57406	+	20.1849i	−0.292966	+	1.06089i
$363$	−1.52270	+	2.84877i	−0.0799209	+	0.149521i
$364$	−9.68613	−	26.9782i	−0.507691	−	1.41404i
$365$	0.384201	+	3.90086i	0.0201100	+	0.204180i
$366$	−1.80455	−	4.06501i	−0.0943252	−	0.212482i
$367$	−28.1644	+	11.6661i	−1.47017	+	0.608964i	−0.966898	−	0.255164i	$-0.917871\pi$
$367$	−28.1644	+	11.6661i	−1.47017	+	0.608964i	−0.503272	+	0.864128i	$0.667871\pi$
$368$	−1.16810	+	2.19686i	−0.0608914	+	0.114519i
$369$	−2.52391	−	1.04544i	−0.131390	−	0.0544234i
$370$	−0.00617132	−	0.245930i	−0.000320832	−	0.0127853i
$371$	−26.8506	−	22.0357i	−1.39401	−	1.14404i
$372$	−1.97069	−	13.1863i	−0.102175	−	0.683677i
$373$	28.9290	−	8.77552i	1.49789	−	0.454379i	0.568250	−	0.822856i	$-0.307621\pi$
$373$	28.9290	−	8.77552i	1.49789	−	0.454379i	0.929637	+	0.368477i	$0.120121\pi$
$374$	−5.26083	+	0.651772i	−0.272031	+	0.0337023i
$375$	2.77140	−	4.14770i	0.143115	−	0.214186i
$376$	−17.2803	+	4.81252i	−0.891163	+	0.248187i
$377$	19.9833	−	13.3524i	1.02919	−	0.687684i
$378$	−0.326021	+	4.45282i	−0.0167687	+	0.229028i
$379$	6.23718	+	7.60003i	0.320382	+	0.390387i	0.908152	−	0.418642i	$-0.137494\pi$
$379$	6.23718	+	7.60003i	0.320382	+	0.390387i	−0.587769	+	0.809029i	$0.699994\pi$
$380$	5.01049	+	1.78662i	0.257033	+	0.0916519i
$381$	9.58203	−	5.12170i	0.490902	−	0.262393i
$382$	−3.44536	+	5.44738i	−0.176280	+	0.278712i
$383$	−13.4199			−0.685724			−0.342862	−	0.939386i	$-0.611396\pi$
$383$	−13.4199			−0.685724			−0.342862	+	0.939386i	$0.611396\pi$
$384$	−10.7561	−	3.50791i	−0.548897	−	0.179012i
$385$	−4.50813			−0.229756
$386$	20.3982	−	32.2512i	1.03824	−	1.64154i
$387$	−4.98592	+	2.66503i	−0.253449	+	0.135471i
$388$	4.10114	−	11.5014i	0.208204	−	0.583896i
$389$	−17.6572	−	21.5153i	−0.895255	−	1.09087i	−0.995391	−	0.0958975i	$-0.969428\pi$
$389$	−17.6572	−	21.5153i	−0.895255	−	1.09087i	0.100136	−	0.994974i	$-0.468072\pi$
$390$	−0.240162	+	3.28016i	−0.0121611	+	0.166097i
$391$	−0.695499	+	0.464718i	−0.0351729	+	0.0235018i
$392$	7.30835	+	4.12436i	0.369127	+	0.208312i
$393$	−1.46254	+	2.18885i	−0.0737755	+	0.110413i
$394$	−19.7009	+	2.44077i	−0.992517	+	0.122964i
$395$	4.89173	−	1.48389i	0.246130	−	0.0746626i
$396$	5.51364	−	0.824013i	0.277071	−	0.0414082i
$397$	−27.6849	−	22.7204i	−1.38947	−	1.14031i	−0.972907	−	0.231199i	$-0.925735\pi$
$397$	−27.6849	−	22.7204i	−1.38947	−	1.14031i	−0.416561	−	0.909108i	$-0.636765\pi$
$398$	0.889930	+	35.4641i	0.0446082	+	1.77766i
$399$	15.1435	+	6.27265i	0.758124	+	0.314025i
$400$	12.0538	+	14.6225i	0.602691	+	0.731126i
$401$	5.65403	−	2.34198i	0.282349	−	0.116953i	−0.237015	−	0.971506i	$-0.576169\pi$
$401$	5.65403	−	2.34198i	0.282349	−	0.116953i	0.519364	+	0.854553i	$0.326169\pi$
$402$	−7.15950	−	16.1278i	−0.357083	−	0.804384i
$403$	−2.96635	−	30.1178i	−0.147764	−	1.50028i
$404$	−9.87422	+	3.54519i	−0.491261	+	0.176380i
$405$	0.241489	−	0.451794i	0.0119997	−	0.0224498i
$406$	−6.29178	+	22.7839i	−0.312256	+	1.13074i
$407$	−0.928330	+	0.184656i	−0.0460156	+	0.00915307i
$408$	−2.62719	−	2.75040i	−0.130065	−	0.136165i
$409$	5.72045	−	28.7587i	0.282858	−	1.42202i	−0.534146	−	0.845392i	$-0.679367\pi$
$409$	5.72045	−	28.7587i	0.282858	−	1.42202i	0.817004	−	0.576632i	$-0.195633\pi$
$410$	1.87894	−	0.621855i	0.0927944	−	0.0307112i
$411$	0.248137	−	2.51938i	0.0122397	−	0.124272i
$412$	−8.73805	+	2.19889i	−0.430493	+	0.108331i
$413$	12.5106	−	41.2419i	0.615607	−	2.02938i
$414$	0.718935	−	0.506918i	0.0353337	−	0.0249136i
$415$	4.52300	+	4.52300i	0.222025	+	0.222025i
$416$	−23.9849	−	9.17703i	−1.17596	−	0.449941i
$417$	−7.81764	+	7.81764i	−0.382831	+	0.382831i
$418$	3.48806	−	20.1674i	0.170607	−	0.986420i
$419$	33.9739	+	10.3059i	1.65974	+	0.503475i	0.974413	−	0.224764i	$-0.0721612\pi$
$419$	33.9739	+	10.3059i	1.65974	+	0.503475i	0.685323	+	0.728240i	$0.259661\pi$
$420$	−1.92968	−	2.59596i	−0.0941589	−	0.126670i
$421$	−26.4049	−	2.60066i	−1.28690	−	0.126748i	−0.568675	−	0.822562i	$-0.692544\pi$
$421$	−26.4049	−	2.60066i	−1.28690	−	0.126748i	−0.718222	+	0.695814i	$0.755044\pi$
$422$	6.66913	+	3.35240i	0.324648	+	0.163192i
$423$	6.22015	+	1.23726i	0.302434	+	0.0601579i
$424$	−30.6526	+	5.37035i	−1.48862	+	0.260807i
$425$	1.24289	+	6.24843i	0.0602890	+	0.303093i
$426$	−6.25704	−	11.0312i	−0.303155	−	0.534464i
$427$	8.75623	+	4.68030i	0.423744	+	0.226496i
$428$	0.100989	+	0.00485099i	0.00488151	+	0.000234481i
$429$	12.5933	−	1.24033i	0.608011	−	0.0598838i
$430$	1.47198	−	3.82217i	0.0709853	−	0.184322i
$431$	−1.12918	−	2.72609i	−0.0543909	−	0.131311i	0.894348	−	0.447372i	$-0.147640\pi$
$431$	−1.12918	−	2.72609i	−0.0543909	−	0.131311i	−0.948739	+	0.316060i	$0.897640\pi$
$432$	2.83458	+	2.82226i	0.136379	+	0.135786i
$433$	−2.96487	+	7.15783i	−0.142483	+	0.343984i	−0.978970	−	0.204002i	$-0.934605\pi$
$433$	−2.96487	+	7.15783i	−0.142483	+	0.343984i	0.836488	+	0.547986i	$0.184605\pi$
$434$	21.5674	+	20.5114i	1.03527	+	0.984581i
$435$	1.72052	−	2.09645i	0.0824924	−	0.100517i
$436$	−7.32325	+	4.40024i	−0.350720	+	0.210733i
$437$	−0.937482	−	3.09046i	−0.0448458	−	0.147837i
$438$	8.53420	+	6.65267i	0.407780	+	0.317877i
$439$	−3.74565	−	2.50276i	−0.178770	−	0.119450i	0.462966	−	0.886376i	$-0.346785\pi$
$439$	−3.74565	−	2.50276i	−0.178770	−	0.119450i	−0.641736	+	0.766926i	$0.721785\pi$
$440$	−2.63308	+	3.06258i	−0.125527	+	0.146003i
$441$	−1.64835	−	2.46693i	−0.0784928	−	0.117473i
$442$	−5.64274	−	6.53430i	−0.268398	−	0.310805i
$443$	20.8921	−	17.1457i	0.992611	−	0.814615i	0.00993601	−	0.999951i	$-0.496837\pi$
$443$	20.8921	−	17.1457i	0.992611	−	0.814615i	0.982675	+	0.185336i	$0.0593372\pi$
$444$	−0.503699	−	0.455527i	−0.0239045	−	0.0216184i
$445$	3.04411	+	5.69512i	0.144304	+	0.269975i
$446$	−23.3672	+	5.26065i	−1.10647	+	0.249099i
$447$			8.29672i			0.392421i
$448$	23.7521	−	8.58631i	1.12218	−	0.405665i
$449$		−	4.25577i		−	0.200842i	−0.994945	−	0.100421i	$-0.967981\pi$
$449$		−	4.25577i		−	0.200842i	0.994945	−	0.100421i	$-0.0320190\pi$
$450$	−1.47152	−	6.53633i	−0.0693683	−	0.308126i
$451$	−3.58964	−	6.71574i	−0.169030	−	0.316232i
$452$	1.78280	+	35.5003i	0.0838557	+	1.66979i
$453$	−18.1625	+	14.9056i	−0.853349	+	0.700325i
$454$	−28.4022	+	24.5269i	−1.33298	+	1.15111i
$455$	−4.07907	−	6.10476i	−0.191230	−	0.286196i
$456$	13.1062	−	6.62399i	0.613755	−	0.310197i
$457$	−27.2769	−	18.2258i	−1.27596	−	0.852568i	−0.281692	−	0.959505i	$-0.590896\pi$
$457$	−27.2769	−	18.2258i	−1.27596	−	0.852568i	−0.994266	+	0.106937i	$0.965896\pi$
$458$	−12.3219	+	15.8069i	−0.575766	+	0.738606i
$459$	0.390360	+	1.28685i	0.0182205	+	0.0600648i
$460$	−0.154179	+	0.618377i	−0.00718865	+	0.0288320i
$461$	−15.3259	+	18.6747i	−0.713800	+	0.869768i	−0.995978	−	0.0895938i	$-0.971443\pi$
$461$	−15.3259	+	18.6747i	−0.713800	+	0.869768i	0.282178	+	0.959362i	$0.408943\pi$
$462$	−8.57655	+	9.01807i	−0.399017	+	0.419558i
$463$	2.88236	−	6.95864i	0.133955	−	0.323395i	−0.842642	−	0.538474i	$-0.819001\pi$
$463$	2.88236	−	6.95864i	0.133955	−	0.323395i	0.976597	+	0.215079i	$0.0690009\pi$
$464$	11.8033	+	17.5818i	0.547953	+	0.816213i
$465$	−1.30689	−	3.15511i	−0.0606056	−	0.146315i
$466$	27.2954	+	10.5119i	1.26444	+	0.486956i
$467$	−0.780109	+	0.0768340i	−0.0360991	+	0.00355545i	−0.116051	−	0.993243i	$-0.537023\pi$
$467$	−0.780109	+	0.0768340i	−0.0360991	+	0.00355545i	0.0799515	+	0.996799i	$0.474523\pi$
$468$	6.10473	+	6.72080i	0.282191	+	0.310669i
$469$	34.7401	+	18.5690i	1.60415	+	0.857436i
$470$	−3.99651	+	2.26687i	−0.184345	+	0.104563i
$471$	−2.29965	−	11.5611i	−0.105962	−	0.532709i
$472$	−20.7104	−	32.5874i	−0.953274	−	1.49995i
$473$	−15.4559	−	3.07437i	−0.710664	−	0.141360i
$474$	6.33795	−	12.6085i	0.291112	−	0.579125i
$475$	−24.4787	−	2.41095i	−1.12316	−	0.110622i
$476$	8.40033	+	1.23672i	0.385029	+	0.0566849i
$477$	10.5286	+	3.19382i	0.482073	+	0.146235i
$478$	30.1741	+	5.21876i	1.38013	+	0.238701i
$479$	9.72626	−	9.72626i	0.444404	−	0.444404i	−0.449085	−	0.893489i	$-0.648250\pi$
$479$	9.72626	−	9.72626i	0.444404	−	0.444404i	0.893489	+	0.449085i	$0.148250\pi$
$480$	−2.89063	−	0.205310i	−0.131939	−	0.00937106i
$481$	−1.09003	−	1.09003i	−0.0497011	−	0.0497011i
$482$	−0.779833	−	1.10600i	−0.0355204	−	0.0503768i
$483$	−0.570051	+	1.87921i	−0.0259382	+	0.0855069i
$484$	−5.54486	−	3.31525i	−0.252039	−	0.150693i
$485$	0.306566	−	3.11262i	0.0139205	−	0.141337i
$486$	−0.444345	−	1.34259i	−0.0201559	−	0.0609013i
$487$	−2.79710	+	14.0620i	−0.126749	+	0.637210i	0.864220	+	0.503115i	$0.167813\pi$
$487$	−2.79710	+	14.0620i	−0.126749	+	0.637210i	−0.990968	+	0.134095i	$0.957187\pi$
$488$	8.29383	−	3.21487i	0.375444	−	0.145530i
$489$	−6.38393	+	1.26984i	−0.288691	+	0.0574243i
$490$	2.07194	+	0.572168i	0.0936007	+	0.0258479i
$491$	−5.22346	+	9.77240i	−0.235731	+	0.441022i	−0.971774	−	0.235913i	$-0.924192\pi$
$491$	−5.22346	+	9.77240i	−0.235731	+	0.441022i	0.736043	+	0.676935i	$0.236692\pi$
$492$	2.33066	−	4.94169i	0.105074	−	0.222789i
$493$	0.697804	+	7.08492i	0.0314275	+	0.319089i
$494$	30.4661	−	13.5246i	1.37073	−	0.608499i
$495$	1.31926	−	0.546456i	0.0592964	−	0.0245614i
$496$	26.5313	−	2.67150i	1.19129	−	0.119954i
$497$	26.1563	+	10.8343i	1.17327	+	0.485984i
$498$	17.6526	−	0.442972i	0.791034	−	0.0198500i
$499$	31.2569	+	25.6519i	1.39925	+	1.14834i	0.969414	+	0.245431i	$0.0789295\pi$
$499$	31.2569	+	25.6519i	1.39925	+	1.14834i	0.429839	+	0.902906i	$0.358570\pi$
$500$	8.01990	+	5.93443i	0.358661	+	0.265396i
$501$	1.59297	−	0.483221i	0.0711684	−	0.0215887i
$502$	1.41816	+	11.4468i	0.0632956	+	0.510896i
$503$	12.7105	−	19.0226i	0.566734	−	0.848177i	−0.431819	−	0.901960i	$-0.642128\pi$
$503$	12.7105	−	19.0226i	0.566734	−	0.848177i	0.998553	+	0.0537832i	$0.0171280\pi$
$504$	−8.86410	−	1.07858i	−0.394838	−	0.0480436i
$505$	−2.23439	+	1.49297i	−0.0994289	+	0.0664363i
$506$	2.44550	+	0.179051i	0.108716	+	0.00795981i
$507$	4.82724	+	5.88201i	0.214385	+	0.261229i
$508$	9.31213	+	19.6335i	0.413159	+	0.871094i
$509$	7.81886	−	4.17927i	0.346565	−	0.185243i	−0.288925	−	0.957352i	$-0.593298\pi$
$509$	7.81886	−	4.17927i	0.346565	−	0.185243i	0.635490	+	0.772109i	$0.280798\pi$
$510$	−0.823376	−	0.520769i	−0.0364597	−	0.0230600i
$511$	−24.1561			−1.06860
$512$	8.03988	−	21.1509i	0.355316	−	0.934746i
$513$	−5.19194			−0.229230
$514$	−34.1418	−	21.5940i	−1.50593	−	0.952471i
$515$	−2.03544	+	1.08796i	−0.0896921	+	0.0479414i
$516$	−4.84548	−	10.2161i	−0.213310	−	0.449738i
$517$	11.2148	+	13.6653i	0.493226	+	0.600997i
$518$	1.51202	+	0.110705i	0.0664344	+	0.00486411i
$519$	−20.8506	+	13.9319i	−0.915241	+	0.611544i
$520$	−6.52972	−	0.794531i	−0.286347	−	0.0348425i
$521$	7.33901	−	10.9836i	0.321528	−	0.481201i	−0.635134	−	0.772402i	$-0.719055\pi$
$521$	7.33901	−	10.9836i	0.321528	−	0.481201i	0.956662	+	0.291202i	$0.0940550\pi$
$522$	−0.920531	−	7.43014i	−0.0402905	−	0.325208i
$523$	−8.65277	+	2.62479i	−0.378359	+	0.114774i	−0.473735	−	0.880667i	$-0.657095\pi$
$523$	−8.65277	+	2.62479i	−0.378359	+	0.114774i	0.0953760	+	0.995441i	$0.469595\pi$
$524$	−4.23231	−	3.13175i	−0.184889	−	0.136811i
$525$	11.5617	+	9.48844i	0.504594	+	0.414110i
$526$	7.12543	−	0.178804i	0.310683	−	0.00779623i
$527$	8.28220	+	3.43060i	0.360778	+	0.149439i
$528$	1.11705	+	11.0937i	0.0486132	+	0.482790i
$529$	−20.8918	+	8.65365i	−0.908338	+	0.376246i
$530$	−7.28540	+	3.23414i	−0.316457	+	0.140482i
$531$	1.33806	+	13.5855i	0.0580668	+	0.589562i
$532$	−13.9840	+	29.6502i	−0.606283	+	1.28550i
$533$	5.84624	−	10.9375i	0.253229	−	0.473757i
$534$	17.1838	+	4.74532i	0.743616	+	0.205350i
$535$	0.0253998	−	0.00505234i	0.00109813	−	0.000218432i
$536$	32.9055	−	12.7549i	1.42130	−	0.550928i
$537$	−0.637374	+	3.20430i	−0.0275047	+	0.138276i
$538$	−3.22758	−	9.75218i	−0.139151	−	0.420446i
$539$	0.810620	−	8.23037i	0.0349159	−	0.354507i
$540$	0.879374	+	0.525775i	0.0378422	+	0.0226257i
$541$	4.66301	−	15.3719i	0.200479	−	0.660890i	−0.797837	−	0.602873i	$-0.794022\pi$
$541$	4.66301	−	15.3719i	0.200479	−	0.660890i	0.998316	−	0.0580163i	$-0.0184775\pi$
$542$	12.7374	+	18.0648i	0.547117	+	0.775948i
$543$	10.4702	+	10.4702i	0.449318	+	0.449318i
$544$	5.74657	−	4.98440i	0.246382	−	0.213704i
$545$	−1.54740	+	1.54740i	−0.0662835	+	0.0662835i
$546$	−19.9722	−	3.45430i	−0.854733	−	0.147830i
$547$	22.6028	+	6.85648i	0.966425	+	0.293162i	0.733770	−	0.679398i	$-0.237759\pi$
$547$	22.6028	+	6.85648i	0.966425	+	0.293162i	0.232654	+	0.972559i	$0.425259\pi$
$548$	5.00914	+	0.737458i	0.213980	+	0.0315026i
$549$	−3.12975	−	0.308254i	−0.133575	−	0.0131559i
$550$	8.38769	−	16.6861i	0.357652	−	0.711498i
$551$	−26.9584	−	5.36235i	−1.14847	−	0.228444i
$552$	0.943679	+	1.48486i	0.0401657	+	0.0631997i
$553$	6.14588	+	30.8974i	0.261349	+	1.31389i
$554$	8.05052	−	4.56636i	0.342034	−	0.194006i
$555$	−0.153413	−	0.0820011i	−0.00651203	−	0.00348075i
$556$	−14.8671	−	16.3674i	−0.630506	−	0.694134i
$557$	37.4089	−	3.68445i	1.58507	−	0.156115i	0.733251	−	0.679958i	$-0.238002\pi$
$557$	37.4089	−	3.68445i	1.58507	−	0.156115i	0.851815	+	0.523843i	$0.175502\pi$
$558$	−8.79779	−	3.38817i	−0.372440	−	0.143433i
$559$	−9.82168	−	23.7116i	−0.415413	−	1.00290i
$560$	5.37111	−	3.60582i	0.226971	−	0.152374i
$561$	−1.43445	+	3.46308i	−0.0605627	+	0.146211i
$562$	10.7706	−	11.3250i	0.454329	−	0.477718i
$563$	11.8537	−	14.4438i	0.499576	−	0.608735i	−0.460779	−	0.887515i	$-0.652430\pi$
$563$	11.8537	−	14.4438i	0.499576	−	0.608735i	0.960355	+	0.278780i	$0.0899300\pi$
$564$	−3.06856	+	12.3072i	−0.129209	+	0.518228i
$565$	2.64292	+	8.71252i	0.111188	+	0.366539i
$566$	2.44504	−	3.13655i	0.102772	−	0.131839i
$567$	2.62499	+	1.75396i	0.110239	+	0.0736595i
$568$	22.6374	−	11.4411i	0.949845	−	0.480059i
$569$	14.0434	+	21.0174i	0.588730	+	0.881097i	0.999531	−	0.0306281i	$-0.00975075\pi$
$569$	14.0434	+	21.0174i	0.588730	+	0.881097i	−0.410801	+	0.911725i	$0.634751\pi$
$570$	2.84686	−	2.45843i	0.119242	−	0.102972i
$571$	−28.1903	+	23.1352i	−1.17973	+	0.968178i	−0.999880	−	0.0155166i	$-0.995061\pi$
$571$	−28.1903	+	23.1352i	−1.17973	+	0.968178i	−0.179848	+	0.983694i	$0.557561\pi$
$572$	1.26937	+	25.2766i	0.0530752	+	1.05687i
$573$	2.14846	+	4.01949i	0.0897534	+	0.167917i
$574$	2.67887	+	11.8992i	0.111814	+	0.496665i
$575$		−	2.94689i		−	0.122894i
$576$	−5.91001	+	5.39182i	−0.246251	+	0.224659i
$577$			17.5319i			0.729863i	0.931034	+	0.364931i	$0.118908\pi$
$577$			17.5319i			0.729863i	−0.931034	+	0.364931i	$0.881092\pi$
$578$	−20.9596	+	4.71864i	−0.871806	+	0.196270i
$579$	−12.7200	−	23.7974i	−0.528624	−	0.988987i
$580$	4.02298	+	3.63824i	0.167045	+	0.151070i
$581$	−30.4718	+	25.0075i	−1.26418	+	1.03749i
$582$	−5.64325	−	6.53489i	−0.233920	−	0.270880i
$583$	17.0385	+	25.4999i	0.705662	+	1.05610i
$584$	−14.1090	+	16.4104i	−0.583833	+	0.679065i
$585$	1.93369	+	1.29205i	0.0799484	+	0.0534198i
$586$	−19.1250	−	14.9085i	−0.790045	−	0.615865i
$587$	11.7741	+	38.8141i	0.485970	+	1.60203i	0.766541	+	0.642195i	$0.221976\pi$
$587$	11.7741	+	38.8141i	0.485970	+	1.60203i	−0.280571	+	0.959833i	$0.590524\pi$
$588$	5.08635	−	3.05618i	0.209757	−	0.126035i
$589$	−21.9572	+	26.7550i	−0.904732	+	1.10242i
$590$	−7.16655	−	6.81568i	−0.295042	−	0.280597i
$591$	−5.37178	+	12.9686i	−0.220966	+	0.533458i
$592$	0.958340	−	0.962526i	0.0393875	−	0.0395596i
$593$	5.67732	+	13.7063i	0.233139	+	0.562848i	0.996543	−	0.0830729i	$-0.0264734\pi$
$593$	5.67732	+	13.7063i	0.233139	+	0.562848i	−0.763404	+	0.645921i	$0.776473\pi$
$594$	1.41671	−	3.67866i	0.0581285	−	0.150937i
$595$	2.16440	−	0.213174i	0.0887316	−	0.00873930i
$596$	−16.5743	−	0.796141i	−0.678911	−	0.0326112i
$597$	22.1228	+	11.8249i	0.905427	+	0.483961i
$598$	1.97029	+	3.47363i	0.0805710	+	0.142047i
$599$	−6.64640	−	33.4137i	−0.271564	−	1.36525i	−0.840030	−	0.542539i	$-0.817463\pi$
$599$	−6.64640	−	33.4137i	−0.271564	−	1.36525i	0.568466	−	0.822707i	$-0.307537\pi$
$600$	13.1988	−	2.31244i	0.538840	−	0.0944051i
$601$	0.0821398	+	0.0163386i	0.00335055	+	0.000666467i	0.196765	−	0.980451i	$-0.436956\pi$
$601$	0.0821398	+	0.0163386i	0.00335055	+	0.000666467i	−0.193415	+	0.981117i	$0.561956\pi$
$602$	22.5523	+	11.3365i	0.919164	+	0.462041i
$603$	−12.4172	−	1.22299i	−0.505668	−	0.0498039i
$604$	−28.0340	−	37.7135i	−1.14069	−	1.53454i
$605$	−1.58352	−	0.480354i	−0.0643791	−	0.0195292i
$606$	−1.26430	+	7.30998i	−0.0513587	+	0.296948i
$607$	−16.0416	+	16.0416i	−0.651108	+	0.651108i	−0.953260	−	0.302152i	$-0.902295\pi$
$607$	−16.0416	+	16.0416i	−0.651108	+	0.651108i	0.302152	+	0.953260i	$0.402295\pi$
$608$	11.9751	+	26.8179i	0.485653	+	1.08761i
$609$	11.8183	+	11.8183i	0.478903	+	0.478903i
$610$	1.86208	−	1.31294i	0.0753933	−	0.0531594i
$611$	−8.35760	+	27.5513i	−0.338112	+	1.11461i
$612$	−2.60819	+	0.656338i	−0.105430	+	0.0265309i
$613$	3.83137	−	38.9006i	0.154748	−	1.57118i	−0.533561	−	0.845762i	$-0.679146\pi$
$613$	3.83137	−	38.9006i	0.154748	−	1.57118i	0.688308	−	0.725418i	$-0.258354\pi$
$614$	32.3891	−	10.7195i	1.30712	−	0.432603i
$615$	0.273027	−	1.37260i	0.0110095	−	0.0553485i
$616$	−17.1924	−	17.9987i	−0.692700	−	0.725189i
$617$	19.1306	−	3.80531i	0.770169	−	0.153196i	0.205661	−	0.978623i	$-0.434066\pi$
$617$	19.1306	−	3.80531i	0.770169	−	0.153196i	0.564508	+	0.825427i	$0.309066\pi$
$618$	−1.69598	+	6.14149i	−0.0682223	+	0.247047i
$619$	22.8012	−	42.6580i	0.916457	−	1.71457i	0.251231	−	0.967927i	$-0.419165\pi$
$619$	22.8012	−	42.6580i	0.916457	−	1.71457i	0.665225	−	0.746643i	$-0.268335\pi$
$620$	6.42836	−	2.30801i	0.258169	−	0.0926919i
$621$	−0.0609692	−	0.619031i	−0.00244661	−	0.0248409i
$622$	−3.88329	−	8.74770i	−0.155706	−	0.350751i
$623$	−36.7671	+	15.2294i	−1.47304	+	0.610154i
$624$	−14.0119	+	11.5505i	−0.560926	+	0.462389i
$625$	−19.5238	−	8.08700i	−0.780950	−	0.323480i
$626$	0.746118	+	29.7332i	0.0298209	+	1.18838i
$627$	−11.1872	−	9.18109i	−0.446773	−	0.366657i
$628$	23.3163	−	3.48462i	0.930422	−	0.139051i
$629$	0.436968	−	0.132553i	0.0174230	−	0.00528522i
$630$	−2.26986	+	0.281216i	−0.0904333	+	0.0112039i
$631$	2.38620	−	3.57120i	0.0949930	−	0.142167i	−0.780929	−	0.624620i	$-0.785254\pi$
$631$	2.38620	−	3.57120i	0.0949930	−	0.142167i	0.875922	+	0.482453i	$0.160254\pi$
$632$	24.5797	+	13.8712i	0.977727	+	0.551767i
$633$	4.38855	−	2.93233i	0.174429	−	0.116550i
$634$	−0.0181478	+	0.247864i	−0.000720741	+	0.00984395i
$635$	3.53099	+	4.30253i	0.140123	+	0.170741i
$636$	−7.39060	+	20.7265i	−0.293057	+	0.821860i
$637$	11.8787	−	6.34932i	0.470653	−	0.251569i
$638$	11.1555	−	17.6377i	0.441650	−	0.698282i
$639$	−8.96767			−0.354755
$640$	0.687527	−	5.75490i	0.0271769	−	0.227482i
$641$	−12.7492			−0.503563			−0.251781	−	0.967784i	$-0.581016\pi$
$641$	−12.7492			−0.503563			−0.251781	+	0.967784i	$0.581016\pi$
$642$	0.0382155	−	0.0604217i	0.00150825	−	0.00238465i
$643$	6.21912	−	3.32419i	0.245258	−	0.131093i	−0.344188	−	0.938901i	$-0.611846\pi$
$643$	6.21912	−	3.32419i	0.245258	−	0.131093i	0.589446	+	0.807807i	$0.299346\pi$
$644$	−3.69938	−	1.31912i	−0.145776	−	0.0519804i
$645$	−1.83732	−	2.23878i	−0.0723443	−	0.0881518i
$646$	−0.721000	+	9.84749i	−0.0283674	+	0.387444i
$647$	−23.5938	+	15.7649i	−0.927567	+	0.619781i	−0.924898	−	0.380216i	$-0.875850\pi$
$647$	−23.5938	+	15.7649i	−0.927567	+	0.619781i	−0.00266938	+	0.999996i	$0.500850\pi$
$648$	2.72473	−	0.758832i	0.107038	−	0.0298097i
$649$	−21.1406	+	31.6392i	−0.829841	+	1.24195i
$650$	30.1852	−	3.73968i	1.18396	−	0.146682i
$651$	20.1398	−	6.10934i	0.789340	−	0.239444i
$652$	−1.92417	−	12.8750i	−0.0753563	−	0.504224i
$653$	19.0736	+	15.6533i	0.746407	+	0.612560i	0.928764	−	0.370672i	$-0.120873\pi$
$653$	19.0736	+	15.6533i	0.746407	+	0.612560i	−0.182357	+	0.983232i	$0.558373\pi$
$654$	0.151549	+	6.03930i	0.00592603	+	0.236155i
$655$	−1.24593	−	0.516083i	−0.0486827	−	0.0201650i
$656$	9.64836	+	5.13015i	0.376705	+	0.200299i
$657$	7.06906	−	2.92810i	0.275790	−	0.114236i
$658$	−11.4887	−	25.8800i	−0.447875	−	1.00891i
$659$	2.41273	+	24.4969i	0.0939866	+	0.954262i	0.920342	+	0.391114i	$0.127910\pi$
$659$	2.41273	+	24.4969i	0.0939866	+	0.954262i	−0.826356	+	0.563148i	$0.809590\pi$
$660$	0.965059	+	2.68792i	0.0375649	+	0.104627i
$661$	−3.26950	+	6.11680i	−0.127169	+	0.237916i	−0.937446	−	0.348131i	$-0.886817\pi$
$661$	−3.26950	+	6.11680i	−0.127169	+	0.237916i	0.810277	+	0.586047i	$0.199317\pi$
$662$	−10.3844	+	37.6041i	−0.403601	+	1.46153i
$663$	−5.98751	+	1.19099i	−0.232536	+	0.0462542i
$664$	−0.808998	+	35.3071i	−0.0313952	+	1.37018i
$665$	−1.63816	+	8.23560i	−0.0635253	+	0.319363i
$666$	−0.455898	+	0.150884i	−0.0176657	+	0.00584663i
$667$	0.322775	−	3.27719i	0.0124979	−	0.126893i
$668$	0.812470	+	3.22863i	0.0314354	+	0.124919i
$669$	−4.91645	+	16.2074i	−0.190081	+	0.626612i
$670$	7.38774	−	5.20906i	0.285413	−	0.201244i
$671$	−6.19864	−	6.19864i	−0.239296	−	0.239296i
$672$	3.00525	−	17.6043i	0.115930	−	0.679100i
$673$	34.9869	−	34.9869i	1.34865	−	1.34865i	0.461510	−	0.887135i	$-0.347308\pi$
$673$	34.9869	−	34.9869i	1.34865	−	1.34865i	0.887135	−	0.461510i	$-0.152692\pi$
$674$	−1.05394	+	6.09369i	−0.0405961	+	0.234720i
$675$	−4.53357	−	1.37524i	−0.174497	−	0.0529331i
$676$	−12.2137	+	9.07894i	−0.469757	+	0.349190i
$677$	36.2258	+	3.56793i	1.39227	+	0.137127i	0.766181	−	0.642625i	$-0.222155\pi$
$677$	36.2258	+	3.56793i	1.39227	+	0.137127i	0.626089	+	0.779752i	$0.284655\pi$
$678$	22.4566	+	11.2884i	0.862439	+	0.433527i
$679$	18.9046	+	3.76036i	0.725491	+	0.144309i
$680$	1.11935	−	1.59488i	0.0429250	−	0.0611610i
$681$	5.17681	+	26.0256i	0.198376	+	0.997302i
$682$	−12.9653	−	22.8580i	−0.496469	−	0.875277i
$683$	34.4762	+	18.4279i	1.31919	+	0.705124i	0.972511	−	0.232859i	$-0.0748080\pi$
$683$	34.4762	+	18.4279i	1.31919	+	0.705124i	0.346683	+	0.937982i	$0.387308\pi$
$684$	0.498211	−	10.3719i	0.0190496	−	0.396581i
$685$	1.29063	−	0.127116i	0.0493126	−	0.00485687i
$686$	6.47130	−	16.8035i	0.247076	−	0.641560i
$687$	5.42336	+	13.0932i	0.206914	+	0.499535i
$688$	20.8736	−	8.69948i	0.795799	−	0.331664i
$689$	−19.1143	+	46.1459i	−0.728195	+	1.75802i
$690$	0.326547	+	0.310560i	0.0124314	+	0.0118228i
$691$	14.8207	−	18.0591i	0.563807	−	0.687000i	−0.410594	−	0.911818i	$-0.634679\pi$
$691$	14.8207	−	18.0591i	0.563807	−	0.687000i	0.974401	+	0.224818i	$0.0721787\pi$
$692$	−25.8310	−	42.9901i	−0.981947	−	1.63424i
$693$	2.55453	+	8.42115i	0.0970385	+	0.319893i
$694$	−24.4023	−	19.0223i	−0.926297	−	0.722077i
$695$	−4.70920	−	3.14659i	−0.178630	−	0.119357i
$696$	14.9315	−	1.12596i	0.565977	−	0.0426792i
$697$	2.04098	+	3.05455i	0.0773078	+	0.115699i
$698$	−20.9902	−	24.3067i	−0.794490	−	0.920021i
$699$	15.9879	−	13.1209i	0.604717	−	0.496278i
$700$	−20.0645	+	22.1863i	−0.758366	+	0.838562i
$701$	−7.48686	−	14.0069i	−0.282775	−	0.529034i	0.699930	−	0.714211i	$-0.253214\pi$
$701$	−7.48686	−	14.0069i	−0.282775	−	0.529034i	−0.982705	+	0.185177i	$0.940714\pi$
$702$	6.26340	−	1.41008i	0.236397	−	0.0532200i
$703$			1.76300i			0.0664929i
$704$	−22.2690	+	1.16699i	−0.839293	+	0.0439826i
$705$			3.24891i			0.122361i
$706$	1.17125	+	5.20254i	0.0440804	+	0.195800i
$707$	−7.80673	−	14.6054i	−0.293602	−	0.549291i
$708$	−27.2682	+	1.36939i	−1.02480	+	0.0514647i
$709$	−4.77677	+	3.92019i	−0.179395	+	0.147226i	−0.719806	−	0.694176i	$-0.755769\pi$
$709$	−4.77677	+	3.92019i	−0.179395	+	0.147226i	0.540410	+	0.841402i	$0.318269\pi$
$710$	4.91718	−	4.24626i	0.184539	−	0.159359i
$711$	−5.54378	−	8.29686i	−0.207908	−	0.311156i
$712$	−11.1286	+	33.8727i	−0.417064	+	1.26943i
$713$	−3.44782	−	2.30376i	−0.129122	−	0.0862764i
$714$	3.69125	−	4.73521i	0.138141	−	0.177211i
$715$	1.88179	+	6.20342i	0.0703749	+	0.231995i
$716$	−6.34005	−	1.58076i	−0.236939	−	0.0590758i
$717$	13.7366	−	16.7380i	0.513001	−	0.625093i
$718$	12.4120	−	13.0510i	0.463213	−	0.487059i
$719$	19.4885	−	47.0494i	0.726798	−	1.75465i	0.0738157	−	0.997272i	$-0.476482\pi$
$719$	19.4885	−	47.0494i	0.726798	−	1.75465i	0.652982	−	0.757373i	$-0.273518\pi$
$720$	−1.13472	+	1.70627i	−0.0422886	+	0.0635889i
$721$	−5.44300	−	13.1406i	−0.202708	−	0.489380i
$722$	−10.5001	−	4.04378i	−0.390775	−	0.150494i
$723$	−0.952307	+	0.0937940i	−0.0354167	+	0.00348824i
$724$	−21.9209	+	19.9115i	−0.814685	+	0.740006i
$725$	−22.1195	−	11.8231i	−0.821497	−	0.439099i
$726$	−3.97348	+	2.25381i	−0.147470	+	0.0836466i
$727$	6.76966	+	34.0334i	0.251073	+	1.26223i	0.876292	+	0.481780i	$0.160010\pi$
$727$	6.76966	+	34.0334i	0.251073	+	1.26223i	−0.625219	+	0.780449i	$0.714990\pi$
$728$	8.81715	−	39.5670i	0.326785	−	1.46645i
$729$	−0.980785	−	0.195090i	−0.0363254	−	0.00722557i
$730$	−2.48965	+	4.95280i	−0.0921461	+	0.183311i
$731$	7.56590	+	0.745176i	0.279835	+	0.0275613i
$732$	0.916124	−	6.22271i	0.0338609	−	0.229998i
$733$	−41.9839	−	12.7357i	−1.55071	−	0.470403i	−0.605221	−	0.796057i	$-0.706915\pi$
$733$	−41.9839	−	12.7357i	−1.55071	−	0.470403i	−0.945489	+	0.325655i	$0.894415\pi$
$734$	−42.4815	−	7.34740i	−1.56802	−	0.271197i
$735$	1.07474	−	1.07474i	0.0396426	−	0.0396426i
$736$	−3.05685	+	1.74270i	−0.112677	+	0.0642368i
$737$	−24.5930	−	24.5930i	−0.905893	−	0.905893i
$738$	−2.22632	−	3.15748i	−0.0819520	−	0.116228i
$739$	−2.96378	+	9.77027i	−0.109024	+	0.359405i	−0.994428	−	0.105418i	$-0.966382\pi$
$739$	−2.96378	+	9.77027i	−0.109024	+	0.359405i	0.885404	+	0.464823i	$0.153882\pi$
$740$	0.178535	−	0.298605i	0.00656307	−	0.0109769i
$741$	2.31027	−	23.4566i	0.0848699	−	0.861699i
$742$	−15.4343	−	46.6351i	−0.566612	−	1.71203i
$743$	5.60811	−	28.1939i	0.205742	−	1.03433i	−0.730483	−	0.682931i	$-0.760705\pi$
$743$	5.60811	−	28.1939i	0.205742	−	1.03433i	0.936225	−	0.351402i	$-0.114295\pi$
$744$	7.61277	−	17.2502i	0.279098	−	0.632422i
$745$	−4.16861	+	0.829187i	−0.152726	+	0.0303791i
$746$	41.2102	+	11.3802i	1.50881	+	0.416660i
$747$	5.88597	−	11.0119i	0.215356	−	0.402903i
$748$	−6.78053	−	3.19792i	−0.247921	−	0.116927i
$749$	0.0156434	+	0.158830i	0.000571596	+	0.00580351i
$750$	6.44788	−	2.86235i	0.235443	−	0.104518i
$751$	22.1887	−	9.19086i	0.809677	−	0.335379i	0.0608517	−	0.998147i	$-0.480618\pi$
$751$	22.1887	−	9.19086i	0.809677	−	0.335379i	0.748825	+	0.662768i	$0.230618\pi$
$752$	−24.2917	−	7.31103i	−0.885827	−	0.266606i
$753$	7.53515	+	3.12116i	0.274596	+	0.113741i
$754$	33.9781	−	0.852640i	1.23741	−	0.0310513i
$755$	−9.30435	−	7.63588i	−0.338620	−	0.277898i
$756$	−3.75577	+	5.07562i	−0.136596	+	0.184599i
$757$	45.6122	−	13.8363i	1.65780	−	0.502889i	0.683847	−	0.729626i	$-0.260306\pi$
$757$	45.6122	−	13.8363i	1.65780	−	0.502889i	0.973956	+	0.226737i	$0.0728056\pi$
$758$	1.70954	+	13.7987i	0.0620931	+	0.501190i
$759$	0.963281	−	1.44165i	0.0349649	−	0.0523287i
$760$	4.63801	+	5.92308i	0.168238	+	0.214853i
$761$	−12.8222	+	8.56755i	−0.464806	+	0.310573i	−0.765830	−	0.643043i	$-0.777672\pi$
$761$	−12.8222	+	8.56755i	−0.464806	+	0.310573i	0.301024	+	0.953617i	$0.402672\pi$
$762$	15.3243	+	1.12200i	0.555142	+	0.0406457i
$763$	−8.55555	−	10.4250i	−0.309732	−	0.377409i
$764$	−8.23590	+	3.90628i	−0.297964	+	0.141324i
$765$	−0.607550	+	0.324742i	−0.0219660	+	0.0117411i
$766$	−16.0397	−	10.1448i	−0.579536	−	0.366545i
$767$	−61.9732			−2.23772
$768$	−10.2041	−	12.3238i	−0.368209	−	0.444697i
$769$	−22.5471			−0.813071			−0.406535	−	0.913635i	$-0.633263\pi$
$769$	−22.5471			−0.813071			−0.406535	+

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:	\( N \)	\(=\)	\( 384 = 2^{7} \cdot 3 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	384.v (of order \(32\), degree \(16\), minimal)

\(f(q)\)	\(=\)	\(q+(1.19522 + 0.755950i) q^{2} +(0.881921 - 0.471397i) q^{3} +(0.857080 + 1.80705i) q^{4} +(0.324989 + 0.396000i) q^{5} +(1.41044 + 0.103268i) q^{6} +(-2.62499 + 1.75396i) q^{7} +(-0.341641 + 2.80772i) q^{8} +(0.555570 - 0.831470i) q^{9} +(0.0890756 + 0.718981i) q^{10} +(2.66741 - 0.809151i) q^{11} +(1.60771 + 1.18965i) q^{12} +(3.50927 + 2.87998i) q^{13} +(-4.46333 + 0.112002i) q^{14} +(0.473288 + 0.196042i) q^{15} +(-2.53083 + 3.09756i) q^{16} +(-1.24239 + 0.514614i) q^{17} +(1.29258 - 0.573802i) q^{18} +(-0.508900 - 5.16694i) q^{19} +(-0.437049 + 0.926674i) q^{20} +(-1.48822 + 2.78427i) q^{21} +(3.79981 + 1.04932i) q^{22} +(0.610074 - 0.121351i) q^{23} +(1.02225 + 2.63723i) q^{24} +(0.924253 - 4.64653i) q^{25} +(2.01721 + 6.09502i) q^{26} +(0.0980171 - 0.995185i) q^{27} +(-5.41931 - 3.24019i) q^{28} +(1.53679 - 5.06611i) q^{29} +(0.417483 + 0.592095i) q^{30} +(-4.71383 - 4.71383i) q^{31} +(-5.36649 + 1.78908i) q^{32} +(1.97102 - 1.97102i) q^{33} +(-1.87394 - 0.324108i) q^{34} +(-1.54766 - 0.469478i) q^{35} +(1.97867 + 0.291305i) q^{36} +(-0.337930 - 0.0332832i) q^{37} +(3.29771 - 6.56031i) q^{38} +(4.45251 + 0.885659i) q^{39} +(-1.22289 + 0.777188i) q^{40} +(-0.532960 - 2.67937i) q^{41} +(-3.88351 + 2.20278i) q^{42} +(-4.98592 - 2.66503i) q^{43} +(3.74836 + 4.12663i) q^{44} +(0.509817 - 0.0502126i) q^{45} +(0.820906 + 0.316144i) q^{46} +(2.42698 + 5.85925i) q^{47} +(-0.771809 + 3.92483i) q^{48} +(1.13540 - 2.74110i) q^{49} +(4.61723 - 4.85492i) q^{50} +(-0.853101 + 1.03951i) q^{51} +(-2.19653 + 8.80978i) q^{52} +(3.19382 + 10.5286i) q^{53} +(0.869461 - 1.11536i) q^{54} +(1.18730 + 0.793332i) q^{55} +(-4.02783 - 7.96945i) q^{56} +(-2.88449 - 4.31694i) q^{57} +(5.66652 - 4.89336i) q^{58} +(-10.5526 + 8.66027i) q^{59} +(0.0513882 + 1.02328i) q^{60} +(-1.48249 - 2.77355i) q^{61} +(-2.07062 - 9.19746i) q^{62} +3.15705i q^{63} +(-7.76656 - 1.91846i) q^{64} +2.32563i q^{65} +(3.84578 - 0.865800i) q^{66} +(-5.88175 - 11.0040i) q^{67} +(-1.99476 - 1.80399i) q^{68} +(0.480833 - 0.394609i) q^{69} +(-1.49489 - 1.73108i) q^{70} +(-4.98217 - 7.45634i) q^{71} +(2.14473 + 1.84395i) q^{72} +(6.36198 + 4.25094i) q^{73} +(-0.378739 - 0.295239i) q^{74} +(-1.37524 - 4.53357i) q^{75} +(8.90074 - 5.34809i) q^{76} +(-5.58271 + 6.80255i) q^{77} +(4.65219 + 4.42443i) q^{78} +(3.81862 - 9.21898i) q^{79} +(-2.04913 + 0.00446587i) q^{80} +(-0.382683 - 0.923880i) q^{81} +(1.38847 - 3.60532i) q^{82} +(12.4261 - 1.22386i) q^{83} +(-6.30682 - 0.302946i) q^{84} +(-0.607550 - 0.324742i) q^{85} +(-3.94462 - 6.95439i) q^{86} +(-1.03282 - 5.19235i) q^{87} +(1.36057 + 7.76578i) q^{88} +(12.3634 + 2.45923i) q^{89} +(0.647299 + 0.325381i) q^{90} +(-14.2632 - 1.40480i) q^{91} +(0.742170 + 0.998424i) q^{92} +(-6.37931 - 1.93514i) q^{93} +(-1.52853 + 8.83774i) q^{94} +(1.88073 - 1.88073i) q^{95} +(-3.88945 + 4.10757i) q^{96} +(-4.31715 - 4.31715i) q^{97} +(3.42919 - 2.41790i) q^{98} +(0.809151 - 2.66741i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 512 q - 96 q^{50} - 96 q^{52} - 32 q^{54} - 224 q^{56} - 192 q^{60} - 192 q^{62} - 192 q^{64} - 192 q^{66} - 192 q^{68} - 192 q^{70} - 224 q^{74} - 32 q^{76} - 96 q^{78} - 96 q^{80}+O(q^{100}) \) 512 * q - 96 * q^50 - 96 * q^52 - 32 * q^54 - 224 * q^56 - 192 * q^60 - 192 * q^62 - 192 * q^64 - 192 * q^66 - 192 * q^68 - 192 * q^70 - 224 * q^74 - 32 * q^76 - 96 * q^78 - 96 * q^80

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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