LMFDB - Embedded newform 384.2.v.a.109.14

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			109.14
Character	$\chi$	$=$	384.109
Dual form			384.2.v.a.229.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.143333 + 1.40693i) q^{2} +(0.881921 + 0.471397i) q^{3} +(-1.95891 - 0.403320i) q^{4} +(-0.269913 + 0.328889i) q^{5} +(-0.789631 + 1.17324i) q^{6} +(3.15893 + 2.11073i) q^{7} +(0.848221 - 2.69824i) q^{8} +(0.555570 + 0.831470i) q^{9} +O(q^{10})$	\(q+(-0.143333 + 1.40693i) q^{2} +(0.881921 + 0.471397i) q^{3} +(-1.95891 - 0.403320i) q^{4} +(-0.269913 + 0.328889i) q^{5} +(-0.789631 + 1.17324i) q^{6} +(3.15893 + 2.11073i) q^{7} +(0.848221 - 2.69824i) q^{8} +(0.555570 + 0.831470i) q^{9} +(-0.424037 - 0.426889i) q^{10} +(3.14204 + 0.953127i) q^{11} +(-1.53748 - 1.27912i) q^{12} +(-1.62061 + 1.33000i) q^{13} +(-3.42243 + 4.14186i) q^{14} +(-0.393079 + 0.162819i) q^{15} +(3.67467 + 1.58014i) q^{16} +(-2.65733 - 1.10070i) q^{17} +(-1.24945 + 0.662472i) q^{18} +(-0.0395911 + 0.401976i) q^{19} +(0.661383 - 0.535404i) q^{20} +(1.79094 + 3.35061i) q^{21} +(-1.79134 + 4.28402i) q^{22} +(-9.04551 - 1.79926i) q^{23} +(2.02001 - 1.97979i) q^{24} +(0.940136 + 4.72638i) q^{25} +(-1.63893 - 2.47071i) q^{26} +(0.0980171 + 0.995185i) q^{27} +(-5.33677 - 5.40879i) q^{28} +(1.40450 + 4.63000i) q^{29} +(-0.172733 - 0.576373i) q^{30} +(0.112693 - 0.112693i) q^{31} +(-2.74984 + 4.94352i) q^{32} +(2.32173 + 2.32173i) q^{33} +(1.92949 - 3.58091i) q^{34} +(-1.54683 + 0.469227i) q^{35} +(-0.752964 - 1.85285i) q^{36} +(8.95331 - 0.881825i) q^{37} +(-0.559877 - 0.113318i) q^{38} +(-2.05620 + 0.409004i) q^{39} +(0.658479 + 1.00726i) q^{40} +(2.48811 - 12.5086i) q^{41} +(-4.97078 + 2.03947i) q^{42} +(2.40162 - 1.28369i) q^{43} +(-5.77056 - 3.13434i) q^{44} +(-0.423417 - 0.0417029i) q^{45} +(3.82796 - 12.4685i) q^{46} +(2.88785 - 6.97189i) q^{47} +(2.49589 + 3.12578i) q^{48} +(2.84488 + 6.86815i) q^{49} +(-6.78445 + 0.645259i) q^{50} +(-1.82469 - 2.22339i) q^{51} +(3.71104 - 1.95172i) q^{52} +(-1.22324 + 4.03247i) q^{53} +(-1.41421 - 0.00473968i) q^{54} +(-1.16155 + 0.776122i) q^{55} +(8.37474 - 6.73320i) q^{56} +(-0.224406 + 0.335848i) q^{57} +(-6.71541 + 1.31240i) q^{58} +(-2.95652 - 2.42636i) q^{59} +(0.835675 - 0.160411i) q^{60} +(-2.79625 + 5.23141i) q^{61} +(0.142398 + 0.174704i) q^{62} +3.79921i q^{63} +(-6.56104 - 4.57741i) q^{64} -0.891983i q^{65} +(-3.59930 + 2.93373i) q^{66} +(6.18280 - 11.5672i) q^{67} +(4.76154 + 3.22793i) q^{68} +(-7.12926 - 5.85084i) q^{69} +(-0.438457 - 2.24354i) q^{70} +(-4.93625 + 7.38762i) q^{71} +(2.71475 - 0.793794i) q^{72} +(8.60941 - 5.75262i) q^{73} +(-0.0426412 + 12.7231i) q^{74} +(-1.39888 + 4.61148i) q^{75} +(0.239680 - 0.771466i) q^{76} +(7.91369 + 9.64286i) q^{77} +(-0.280718 - 2.95156i) q^{78} +(-3.45146 - 8.33255i) q^{79} +(-1.51153 + 0.782060i) q^{80} +(-0.382683 + 0.923880i) q^{81} +(17.2421 + 5.29349i) q^{82} +(3.02350 + 0.297789i) q^{83} +(-2.15692 - 7.28587i) q^{84} +(1.07926 - 0.576874i) q^{85} +(1.46184 + 3.56291i) q^{86} +(-0.943914 + 4.74537i) q^{87} +(5.23691 - 7.66953i) q^{88} +(5.02318 - 0.999172i) q^{89} +(0.119363 - 0.589741i) q^{90} +(-7.92665 + 0.780706i) q^{91} +(16.9937 + 7.17284i) q^{92} +(0.152509 - 0.0462631i) q^{93} +(9.39505 + 5.06231i) q^{94} +(-0.121519 - 0.121519i) q^{95} +(-4.75550 + 3.06352i) q^{96} +(7.81107 - 7.81107i) q^{97} +(-10.0708 + 3.01812i) q^{98} +(0.953127 + 3.14204i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 512 q+O(q^{10}) $ 512 * 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

Display 100 coefficients 10 coefficients

Character values

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

$n$	$127$	$133$	$257$
$\chi(n)$	$1$	$e\left(\frac{23}{32}\right)$	$1$

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 $

$2$	−0.143333	+	1.40693i	−0.101352	+	0.994851i
$2$	−0.143333	+	1.40693i	−0.101352	+	0.994851i
$3$	0.881921	+	0.471397i	0.509177	+	0.272161i
$3$	0.881921	+	0.471397i	0.509177	+	0.272161i
$4$	−1.95891	−	0.403320i	−0.979456	−	0.201660i
$5$	−0.269913	+	0.328889i	−0.120709	+	0.147084i	−0.829859	−	0.557974i	$-0.811579\pi$
$5$	−0.269913	+	0.328889i	−0.120709	+	0.147084i	0.709150	+	0.705058i	$0.249079\pi$
$6$	−0.789631	+	1.17324i	−0.322366	+	0.478971i
$7$	3.15893	+	2.11073i	1.19396	+	0.797781i	0.983692	−	0.179862i	$-0.0575650\pi$
$7$	3.15893	+	2.11073i	1.19396	+	0.797781i	0.210272	+	0.977643i	$0.432565\pi$
$8$	0.848221	−	2.69824i	0.299891	−	0.953973i
$9$	0.555570	+	0.831470i	0.185190	+	0.277157i
$10$	−0.424037	−	0.426889i	−0.134092	−	0.134994i
$11$	3.14204	+	0.953127i	0.947360	+	0.287379i	0.725907	−	0.687792i	$-0.241420\pi$
$11$	3.14204	+	0.953127i	0.947360	+	0.287379i	0.221453	+	0.975171i	$0.428920\pi$
$12$	−1.53748	−	1.27912i	−0.443833	−	0.369250i
$13$	−1.62061	+	1.33000i	−0.449475	+	0.368875i	−0.831728	−	0.555183i	$-0.812648\pi$
$13$	−1.62061	+	1.33000i	−0.449475	+	0.368875i	0.382253	+	0.924058i	$0.375148\pi$
$14$	−3.42243	+	4.14186i	−0.914684	+	1.10696i
$15$	−0.393079	+	0.162819i	−0.101493	+	0.0420396i
$16$	3.67467	+	1.58014i	0.918666	+	0.395034i
$17$	−2.65733	−	1.10070i	−0.644497	−	0.266959i	0.0364015	−	0.999337i	$-0.488410\pi$
$17$	−2.65733	−	1.10070i	−0.644497	−	0.266959i	−0.680898	+	0.732378i	$0.738410\pi$
$18$	−1.24945	+	0.662472i	−0.294499	+	0.156146i
$19$	−0.0395911	+	0.401976i	−0.00908283	+	0.0922195i	−0.998657	−	0.0518021i	$-0.983503\pi$
$19$	−0.0395911	+	0.401976i	−0.00908283	+	0.0922195i	0.989575	+	0.144022i	$0.0460035\pi$
$20$	0.661383	−	0.535404i	0.147890	−	0.119720i
$21$	1.79094	+	3.35061i	0.390815	+	0.731163i
$22$	−1.79134	+	4.28402i	−0.381916	+	0.913356i
$23$	−9.04551	−	1.79926i	−1.88612	−	0.375173i	−0.889473	−	0.456988i	$-0.848928\pi$
$23$	−9.04551	−	1.79926i	−1.88612	−	0.375173i	−0.996647	+	0.0818159i	$0.973928\pi$
$24$	2.02001	−	1.97979i	0.412332	−	0.404123i
$25$	0.940136	+	4.72638i	0.188027	+	0.945277i
$26$	−1.63893	−	2.47071i	−0.321420	−	0.484547i
$27$	0.0980171	+	0.995185i	0.0188634	+	0.191523i
$28$	−5.33677	−	5.40879i	−1.00855	−	1.02217i
$29$	1.40450	+	4.63000i	0.260808	+	0.859770i	0.985351	+	0.170540i	$0.0545512\pi$
$29$	1.40450	+	4.63000i	0.260808	+	0.859770i	−0.724542	+	0.689230i	$0.757949\pi$
$30$	−0.172733	−	0.576373i	−0.0315367	−	0.105231i
$31$	0.112693	−	0.112693i	0.0202402	−	0.0202402i	−0.696914	−	0.717154i	$-0.745444\pi$
$31$	0.112693	−	0.112693i	0.0202402	−	0.0202402i	0.717154	+	0.696914i	$0.245444\pi$
$32$	−2.74984	+	4.94352i	−0.486109	+	0.873898i
$33$	2.32173	+	2.32173i	0.404161	+	0.404161i
$34$	1.92949	−	3.58091i	0.330906	−	0.614121i
$35$	−1.54683	+	0.469227i	−0.261462	+	0.0793138i
$36$	−0.752964	−	1.85285i	−0.125494	−	0.308808i
$37$	8.95331	−	0.881825i	1.47192	−	0.144971i	0.669979	−	0.742380i	$-0.266303\pi$
$37$	8.95331	−	0.881825i	1.47192	−	0.144971i	0.801937	+	0.597409i	$0.203803\pi$
$38$	−0.559877	−	0.113318i	−0.0908241	−	0.0183827i
$39$	−2.05620	+	0.409004i	−0.329256	+	0.0654931i
$40$	0.658479	+	1.00726i	0.104115	+	0.159262i
$41$	2.48811	−	12.5086i	0.388577	−	1.95351i	0.105459	−	0.994424i	$-0.466369\pi$
$41$	2.48811	−	12.5086i	0.388577	−	1.95351i	0.283118	−	0.959085i	$-0.408631\pi$
$42$	−4.97078	+	2.03947i	−0.767007	+	0.314697i
$43$	2.40162	−	1.28369i	0.366244	−	0.195761i	−0.278001	−	0.960581i	$-0.589672\pi$
$43$	2.40162	−	1.28369i	0.366244	−	0.195761i	0.644245	+	0.764819i	$0.277172\pi$
$44$	−5.77056	−	3.13434i	−0.869945	−	0.472519i
$45$	−0.423417	−	0.0417029i	−0.0631193	−	0.00621671i
$46$	3.82796	−	12.4685i	0.564403	−	1.83838i
$47$	2.88785	−	6.97189i	0.421237	−	1.01696i	−0.560747	−	0.827987i	$-0.689486\pi$
$47$	2.88785	−	6.97189i	0.421237	−	1.01696i	0.981983	−	0.188968i	$-0.0605141\pi$
$48$	2.49589	+	3.12578i	0.360251	+	0.451168i
$49$	2.84488	+	6.86815i	0.406412	+	0.981165i
$50$	−6.78445	+	0.645259i	−0.959466	+	0.0912534i
$51$	−1.82469	−	2.22339i	−0.255507	−	0.311337i
$52$	3.71104	−	1.95172i	0.514628	−	0.270655i
$53$	−1.22324	+	4.03247i	−0.168024	+	0.553902i	−1.00000		0.000910499i	$-0.999710\pi$
$53$	−1.22324	+	4.03247i	−0.168024	+	0.553902i	0.831975	+	0.554813i	$0.187210\pi$
$54$	−1.41421	−	0.00473968i	−0.192449	−	0.000644989i
$55$	−1.16155	+	0.776122i	−0.156623	+	0.104652i
$56$	8.37474	−	6.73320i	1.11912	−	0.899762i
$57$	−0.224406	+	0.335848i	−0.0297233	+	0.0444841i
$58$	−6.71541	+	1.31240i	−0.881776	+	0.172326i
$59$	−2.95652	−	2.42636i	−0.384907	−	0.315885i	0.421964	−	0.906612i	$-0.361341\pi$
$59$	−2.95652	−	2.42636i	−0.384907	−	0.315885i	−0.806871	+	0.590728i	$0.798841\pi$
$60$	0.835675	−	0.160411i	0.107885	−	0.0207089i
$61$	−2.79625	+	5.23141i	−0.358023	+	0.669814i	−0.994868	−	0.101178i	$-0.967739\pi$
$61$	−2.79625	+	5.23141i	−0.358023	+	0.669814i	0.636845	+	0.770991i	$0.280239\pi$
$62$	0.142398	+	0.174704i	0.0180846	+	0.0221874i
$63$			3.79921i			0.478656i
$64$	−6.56104	−	4.57741i	−0.820130	−	0.572177i
$65$		−	0.891983i		−	0.110637i
$66$	−3.59930	+	2.93373i	−0.443043	+	0.361118i
$67$	6.18280	−	11.5672i	0.755349	−	1.41316i	−0.150086	−	0.988673i	$-0.547955\pi$
$67$	6.18280	−	11.5672i	0.755349	−	1.41316i	0.905435	−	0.424486i	$-0.139545\pi$
$68$	4.76154	+	3.22793i	0.577421	+	0.391444i
$69$	−7.12926	−	5.85084i	−0.858262	−	0.704358i
$70$	−0.438457	−	2.24354i	−0.0524056	−	0.268155i
$71$	−4.93625	+	7.38762i	−0.585825	+	0.876750i	−0.999432	−	0.0337061i	$-0.989269\pi$
$71$	−4.93625	+	7.38762i	−0.585825	+	0.876750i	0.413606	+	0.910456i	$0.364269\pi$
$72$	2.71475	−	0.793794i	0.319937	−	0.0935496i
$73$	8.60941	−	5.75262i	1.00766	−	0.673294i	0.0618694	−	0.998084i	$-0.480294\pi$
$73$	8.60941	−	5.75262i	1.00766	−	0.673294i	0.945786	+	0.324790i	$0.105294\pi$
$74$	−0.0426412	+	12.7231i	−0.00495694	+	1.47903i
$75$	−1.39888	+	4.61148i	−0.161528	+	0.532487i
$76$	0.239680	−	0.771466i	0.0274932	−	0.0884933i
$77$	7.91369	+	9.64286i	0.901849	+	1.09891i
$78$	−0.280718	−	2.95156i	−0.0317851	−	0.334198i
$79$	−3.45146	−	8.33255i	−0.388319	−	0.937485i	−0.990296	−	0.138972i	$-0.955620\pi$
$79$	−3.45146	−	8.33255i	−0.388319	−	0.937485i	0.601977	−	0.798513i	$-0.294380\pi$
$80$	−1.51153	+	0.782060i	−0.168994	+	0.0874370i
$81$	−0.382683	+	0.923880i	−0.0425204	+	0.102653i
$82$	17.2421	+	5.29349i	1.90407	+	0.584568i
$83$	3.02350	+	0.297789i	0.331872	+	0.0326865i	0.262581	−	0.964910i	$-0.415426\pi$
$83$	3.02350	+	0.297789i	0.331872	+	0.0326865i	0.0692910	+	0.997596i	$0.477926\pi$
$84$	−2.15692	−	7.28587i	−0.235339	−	0.794953i
$85$	1.07926	−	0.576874i	0.117062	−	0.0625708i
$86$	1.46184	+	3.56291i	0.157634	+	0.384199i
$87$	−0.943914	+	4.74537i	−0.101198	+	0.508758i
$88$	5.23691	−	7.66953i	0.558257	−	0.817574i
$89$	5.02318	−	0.999172i	0.532456	−	0.105912i	0.0784622	−	0.996917i	$-0.474999\pi$
$89$	5.02318	−	0.999172i	0.532456	−	0.105912i	0.453993	+	0.891005i	$0.349999\pi$
$90$	0.119363	−	0.589741i	0.0125820	−	0.0621642i
$91$	−7.92665	+	0.780706i	−0.830938	+	0.0818403i
$92$	16.9937	+	7.17284i	1.77171	+	0.747820i
$93$	0.152509	−	0.0462631i	0.0158145	−	0.00479726i
$94$	9.39505	+	5.06231i	0.969025	+	0.522138i
$95$	−0.121519	−	0.121519i	−0.0124676	−	0.0124676i
$96$	−4.75550	+	3.06352i	−0.485357	+	0.312670i
$97$	7.81107	−	7.81107i	0.793094	−	0.793094i	−0.188902	−	0.981996i	$-0.560493\pi$
$97$	7.81107	−	7.81107i	0.793094	−	0.793094i	0.981996	+	0.188902i	$0.0604928\pi$
$98$	−10.0708	+	3.01812i	−1.01730	+	0.304876i
$99$	0.953127	+	3.14204i	0.0957929	+	0.315787i
$100$	0.0646021	−	9.63774i	0.00646021	−	0.963774i
$101$	0.00385740	+	0.0391648i	0.000383826	+	0.00389705i	0.995375	−	0.0960684i	$-0.0306268\pi$
$101$	0.00385740	+	0.0391648i	0.000383826	+	0.00389705i	−0.994991	+	0.0999655i	$0.968127\pi$
$102$	3.38969	−	2.24852i	0.335630	−	0.222637i
$103$	−1.81125	−	9.10575i	−0.178467	−	0.897216i	−0.961410	−	0.275121i	$-0.911282\pi$
$103$	−1.81125	−	9.10575i	−0.178467	−	0.897216i	0.782942	−	0.622094i	$-0.213718\pi$
$104$	2.21402	+	5.50092i	0.217103	+	0.539409i
$105$	−1.58538	−	0.315351i	−0.154717	−	0.0307751i
$106$	−5.49808	−	2.29900i	−0.534021	−	0.223298i
$107$	−5.92358	−	11.0822i	−0.572654	−	1.07136i	−0.986921	−	0.161205i	$-0.948462\pi$
$107$	−5.92358	−	11.0822i	−0.572654	−	1.07136i	0.414267	−	0.910156i	$-0.364038\pi$
$108$	0.209371	−	1.98901i	0.0201467	−	0.191393i
$109$	−1.56627	+	15.9026i	−0.150021	+	1.52319i	0.565588	+	0.824688i	$0.308649\pi$
$109$	−1.56627	+	15.9026i	−0.150021	+	1.52319i	−0.715609	+	0.698501i	$0.753851\pi$
$110$	−0.925462	−	1.74546i	−0.0882394	−	0.166423i
$111$	8.31181	+	3.44286i	0.788922	+	0.326782i
$112$	8.27278	+	12.7478i	0.781704	+	1.20455i
$113$	1.07060	−	0.443459i	0.100714	−	0.0417171i	−0.331758	−	0.943365i	$-0.607642\pi$
$113$	1.07060	−	0.443459i	0.100714	−	0.0417171i	0.432472	+	0.901648i	$0.357642\pi$
$114$	−0.440350	−	0.363862i	−0.0412425	−	0.0340788i
$115$	3.03326	−	2.48933i	0.282853	−	0.232131i
$116$	−0.883910	−	9.63623i	−0.0820690	−	0.894701i
$117$	−2.00621	−	0.608578i	−0.185474	−	0.0562630i
$118$	3.83748	−	3.81185i	0.353269	−	0.350909i
$119$	−6.07104	−	9.08595i	−0.556531	−	0.832907i
$120$	0.105907	+	1.19873i	0.00966792	+	0.109429i
$121$	−0.182210	−	0.121749i	−0.0165646	−	0.0110681i
$122$	−6.95944	−	4.68396i	−0.630078	−	0.424066i
$123$	8.09081	−	9.85868i	0.729524	−	0.888927i
$124$	−0.266206	+	0.175304i	−0.0239060	+	0.0157428i
$125$	−3.68435	−	1.96933i	−0.329538	−	0.176142i
$126$	−5.34523	−	0.544554i	−0.476191	−	0.0485127i
$127$	−5.58603			−0.495680			−0.247840	−	0.968801i	$-0.579721\pi$
$127$	−5.58603			−0.495680			−0.247840	+	0.968801i	$0.579721\pi$
$128$	7.38052	−	8.57484i	0.652352	−	0.757916i
$129$	2.72317			0.239762
$130$	1.25496	+	0.127851i	0.110067	+	0.0112133i
$131$	13.9761	+	7.47039i	1.22110	+	0.652691i	0.950716	−	0.310062i	$-0.100350\pi$
$131$	13.9761	+	7.47039i	1.22110	+	0.652691i	0.270383	+	0.962753i	$0.412850\pi$
$132$	−3.61166	−	5.48446i	−0.314355	−	0.477361i
$133$	−0.973528	+	1.18625i	−0.0844156	+	0.102861i
$134$	15.3881	+	10.3567i	1.32933	+	0.894686i
$135$	−0.353762	−	0.236376i	−0.0304470	−	0.0203440i
$136$	−5.22396	+	6.23648i	−0.447951	+	0.534774i
$137$	−1.85059	−	2.76960i	−0.158107	−	0.236623i	0.743956	−	0.668229i	$-0.232947\pi$
$137$	−1.85059	−	2.76960i	−0.158107	−	0.236623i	−0.902062	+	0.431606i	$0.857947\pi$
$138$	9.25358	−	9.19176i	0.787717	−	0.782455i
$139$	−9.14388	−	2.77376i	−0.775574	−	0.235268i	−0.122405	−	0.992480i	$-0.539061\pi$
$139$	−9.14388	−	2.77376i	−0.775574	−	0.235268i	−0.653169	+	0.757213i	$0.726561\pi$
$140$	3.21936	−	0.295305i	0.272085	−	0.0249578i
$141$	5.83339	−	4.78734i	0.491260	−	0.403166i
$142$	−9.68635	−	8.00386i	−0.812860	−	0.671669i
$143$	−6.35966	+	2.63426i	−0.531821	+	0.220288i
$144$	0.727700	+	3.93325i	0.0606416	+	0.327771i
$145$	−1.90185	−	0.787773i	−0.157940	−	0.0654210i
$146$	6.85953	+	12.9374i	0.567699	+	1.07071i
$147$	−0.728663	+	7.39824i	−0.0600991	+	0.610196i
$148$	−17.8944	−	1.88364i	−1.47091	−	0.154834i
$149$	−7.86611	−	14.7165i	−0.644417	−	1.20562i	−0.965952	−	0.258722i	$-0.916699\pi$
$149$	−7.86611	−	14.7165i	−0.644417	−	1.20562i	0.321535	−	0.946898i	$-0.395801\pi$
$150$	−6.28752	−	2.62910i	−0.513374	−	0.214665i
$151$	−14.4338	−	2.87105i	−1.17460	−	0.233643i	−0.431055	−	0.902326i	$-0.641858\pi$
$151$	−14.4338	−	2.87105i	−1.17460	−	0.233643i	−0.743548	+	0.668683i	$0.766858\pi$
$152$	1.05105	+	0.447791i	0.0852511	+	0.0363206i
$153$	−0.561133	−	2.82101i	−0.0453649	−	0.228065i
$154$	−14.7011	+	9.75188i	−1.18465	+	0.785829i
$155$	0.00664627	+	0.0674807i	0.000533841	+	0.00542018i
$156$	4.19288	+	0.0281050i	0.335699	+	0.00225020i
$157$	6.42989	+	21.1965i	0.513161	+	1.69166i	0.704132	+	0.710069i	$0.251336\pi$
$157$	6.42989	+	21.1965i	0.513161	+	1.69166i	−0.190971	+	0.981596i	$0.561164\pi$
$158$	12.2180	−	3.66163i	0.972015	−	0.291304i
$159$	−2.97969	+	2.97969i	−0.236305	+	0.236305i
$160$	−0.883653	−	2.23871i	−0.0698589	−	0.176986i
$161$	−24.7764	−	24.7764i	−1.95265	−	1.95265i
$162$	−1.24498	−	0.670832i	−0.0978152	−	0.0527055i
$163$	10.3277	−	3.13286i	0.808924	−	0.245384i	0.141381	−	0.989955i	$-0.454846\pi$
$163$	10.3277	−	3.13286i	0.808924	−	0.245384i	0.667543	+	0.744571i	$0.267346\pi$
$164$	−9.91893	+	23.4997i	−0.774539	+	1.83501i
$165$	−1.39026	+	0.136928i	−0.108231	+	0.0106599i
$166$	−0.852336	+	4.21117i	−0.0661541	+	0.326850i
$167$	6.64785	−	1.32234i	0.514426	−	0.102326i	0.0689510	−	0.997620i	$-0.478035\pi$
$167$	6.64785	−	1.32234i	0.514426	−	0.102326i	0.445475	+	0.895294i	$0.353035\pi$
$168$	10.5599	−	1.99033i	0.814712	−	0.153557i
$169$	−1.67870	+	8.43941i	−0.129131	+	0.649185i
$170$	0.656929	+	1.60112i	0.0503842	+	0.122801i
$171$	−0.356226	+	0.190407i	−0.0272413	+	0.0145608i
$172$	−5.22230	+	1.54602i	−0.398197	+	0.117883i
$173$	4.16354	+	0.410073i	0.316548	+	0.0311773i	0.255044	−	0.966930i	$-0.417910\pi$
$173$	4.16354	+	0.410073i	0.316548	+	0.0311773i	0.0615045	+	0.998107i	$0.480410\pi$
$174$	−6.54112	−	2.00819i	−0.495881	−	0.152241i
$175$	−7.00630	+	16.9147i	−0.529626	+	1.27863i
$176$	10.0399	+	8.46727i	0.756784	+	0.638245i
$177$	−1.46364	−	3.53355i	−0.110014	−	0.265598i
$178$	0.685778	+	7.21048i	0.0514012	+	0.540448i
$179$	2.02540	+	2.46795i	0.151385	+	0.184463i	0.843181	−	0.537630i	$-0.180680\pi$
$179$	2.02540	+	2.46795i	0.151385	+	0.184463i	−0.691796	+	0.722093i	$0.743180\pi$
$180$	0.812617	+	0.252465i	0.0605689	+	0.0188176i
$181$	−1.02539	+	3.38027i	−0.0762169	+	0.251253i	−0.986767	−	0.162146i	$-0.948159\pi$
$181$	−1.02539	+	3.38027i	−0.0762169	+	0.251253i	0.910550	+	0.413399i	$0.135659\pi$
$182$	0.0377515	−	11.2641i	0.00279833	−	0.834954i
$183$	−4.93214	+	3.29555i	−0.364594	+	0.243614i
$184$	−12.5274	+	22.8808i	−0.923536	+	1.68680i
$185$	−2.12659	+	3.18267i	−0.156350	+	0.233994i
$186$	0.0432294	+	0.221201i	0.00316974	+	0.0162192i
$187$	−7.30032	−	5.99122i	−0.533852	−	0.438121i
$188$	−8.46895	+	12.4926i	−0.617662	+	0.911116i
$189$	−1.79094	+	3.35061i	−0.130272	+	0.243721i
$190$	0.188387	−	0.153552i	0.0136670	−	0.0111398i
$191$		−	11.1529i		−	0.806993i	−0.914981	−	0.403497i	$-0.867795\pi$
$191$		−	11.1529i		−	0.806993i	0.914981	−	0.403497i	$-0.132205\pi$
$192$	−3.62855	−	7.12977i	−0.261868	−	0.514547i
$193$			10.2421i			0.737242i	0.929580	+	0.368621i	$0.120170\pi$
$193$			10.2421i			0.737242i	−0.929580	+	0.368621i	$0.879830\pi$
$194$	9.87005	+	12.1092i	0.708629	+	0.869392i
$195$	0.420478	−	0.786659i	0.0301110	−	0.0563338i
$196$	−2.80281	−	14.6015i	−0.200201	−	1.04296i
$197$	0.884643	+	0.726007i	0.0630282	+	0.0517259i	0.665380	−	0.746505i	$-0.268270\pi$
$197$	0.884643	+	0.726007i	0.0630282	+	0.0517259i	−0.602352	+	0.798231i	$0.705770\pi$
$198$	−4.55725	+	0.890626i	−0.323869	+	0.0632940i
$199$	−5.43348	+	8.13178i	−0.385169	+	0.576447i	−0.972501	−	0.232900i	$-0.925179\pi$
$199$	−5.43348	+	8.13178i	−0.385169	+	0.576447i	0.587331	+	0.809347i	$0.300179\pi$
$200$	13.5504	+	1.47230i	0.958157	+	0.104107i
$201$	10.9055	−	7.28681i	0.769213	−	0.513972i
$202$	−0.0556551		0.000186527i	−0.00391588		1.31240e-5i
$203$	−5.33598	+	17.5904i	−0.374513	+	1.23460i
$204$	2.67766	+	5.09135i	0.187474	+	0.356466i
$205$	3.44236	+	4.19453i	0.240425	+	0.292959i
$206$	13.0708	−	1.24314i	0.910684	−	0.0866138i
$207$	−3.52938	−	8.52069i	−0.245309	−	0.592229i
$208$	−8.05676	+	2.32651i	−0.558636	+	0.161315i
$209$	−0.507531	+	1.22529i	−0.0351066	+	0.0847549i
$210$	0.670914	−	2.18532i	0.0462975	−	0.150801i
$211$	−2.96923	−	0.292443i	−0.204410	−	0.0201326i	−0.00470616	−	0.999989i	$-0.501498\pi$
$211$	−2.96923	−	0.292443i	−0.204410	−	0.0201326i	−0.199704	+	0.979856i	$0.563998\pi$
$212$	4.02259	−	7.40590i	0.276272	−	0.508639i
$213$	−7.83589	+	4.18837i	−0.536906	+	0.286982i
$214$	16.4410	−	6.74562i	1.12388	−	0.461121i
$215$	−0.226035	+	1.13635i	−0.0154154	+	0.0774987i
$216$	2.76839	+	0.579662i	0.188365	+	0.0394410i
$217$	0.593853	−	0.118125i	0.0403134	−	0.00801883i
$218$	−22.1493	−	4.48299i	−1.50014	−	0.303627i
$219$	10.3046	−	1.01491i	0.696320	−	0.0685815i
$220$	2.58840	−	1.05188i	0.174510	−	0.0709177i
$221$	5.77041	−	1.75043i	0.388160	−	0.117747i
$222$	−6.03523	+	11.2007i	−0.405058	+	0.751739i
$223$	−20.5203	−	20.5203i	−1.37414	−	1.37414i	−0.854209	−	0.519930i	$-0.825958\pi$
$223$	−20.5203	−	20.5203i	−1.37414	−	1.37414i	−0.519930	−	0.854209i	$-0.674042\pi$
$224$	−19.1210	+	9.81205i	−1.27758	+	0.655595i
$225$	−3.40753	+	3.40753i	−0.227169	+	0.227169i
$226$	0.470463	+	1.56983i	0.0312947	+	0.104424i
$227$	0.955512	+	3.14990i	0.0634196	+	0.209066i	0.982924	−	0.184014i	$-0.0589093\pi$
$227$	0.955512	+	3.14990i	0.0634196	+	0.209066i	−0.919504	+	0.393081i	$0.871409\pi$
$228$	0.575046	−	0.567388i	0.0380833	−	0.0375762i
$229$	−1.96159	−	19.9164i	−0.129626	−	1.31611i	−0.811375	−	0.584526i	$-0.801281\pi$
$229$	−1.96159	−	19.9164i	−0.129626	−	1.31611i	0.681750	−	0.731586i	$-0.261219\pi$
$230$	3.06755	+	4.62439i	0.202268	+	0.304923i
$231$	2.43364	+	12.2347i	0.160122	+	0.804986i
$232$	13.6842	+	0.137591i	0.898412	+	0.00903330i
$233$	−22.5847	−	4.49237i	−1.47957	−	0.294305i	−0.611698	−	0.791092i	$-0.709513\pi$
$233$	−22.5847	−	4.49237i	−1.47957	−	0.294305i	−0.867873	+	0.496787i	$0.834513\pi$
$234$	1.14378	−	2.73537i	0.0747715	−	0.178817i
$235$	1.51351	+	2.83159i	0.0987308	+	0.184712i
$236$	4.81297	+	5.94544i	0.313298	+	0.387015i
$237$	0.884025	−	8.97566i	0.0574236	−	0.583032i
$238$	13.6535	−	7.23921i	0.885024	−	0.469248i
$239$	−2.01090	−	0.832942i	−0.130074	−	0.0538786i	0.316697	−	0.948527i	$-0.397426\pi$
$239$	−2.01090	−	0.832942i	−0.130074	−	0.0538786i	−0.446771	+	0.894648i	$0.647426\pi$
$240$	−1.70171	−	0.0228143i	−0.109845	−	0.00147265i
$241$	−16.9808	+	7.03367i	−1.09383	+	0.453079i	−0.855340	−	0.518067i	$-0.826652\pi$
$241$	−16.9808	+	7.03367i	−1.09383	+	0.453079i	−0.238489	+	0.971145i	$0.576652\pi$
$242$	0.197409	−	0.238906i	0.0126899	−	0.0153575i
$243$	−0.773010	+	0.634393i	−0.0495886	+	0.0406963i
$244$	7.58754	−	9.12009i	0.485742	−	0.583854i
$245$	−3.02673	−	0.918149i	−0.193371	−	0.0586584i
$246$	12.7108	+	12.7963i	0.810411	+	0.815861i
$247$	−0.470464	−	0.704100i	−0.0299349	−	0.0448008i
$248$	−0.208484	−	0.399661i	−0.0132388	−	0.0253785i
$249$	2.52611	+	1.68789i	0.160086	+	0.106966i
$250$	3.29880	−	4.90136i	0.208634	−	0.309989i
$251$	−17.5873	+	21.4302i	−1.11010	+	1.35266i	−0.180724	+	0.983534i	$0.557844\pi$
$251$	−17.5873	+	21.4302i	−1.11010	+	1.35266i	−0.929378	+	0.369129i	$0.879656\pi$
$252$	1.53230	−	7.44232i	0.0965258	−	0.468822i
$253$	−26.7064	−	14.2749i	−1.67902	−	0.897454i
$254$	0.800664	−	7.85916i	0.0502381	−	0.493128i
$255$	1.22376			0.0766345
$256$	11.0063	+	11.6129i	0.687896	+	0.725809i
$257$	−12.9358			−0.806913			−0.403456	−	0.914999i	$-0.632191\pi$
$257$	−12.9358			−0.806913			−0.403456	+	0.914999i	$0.632191\pi$
$258$	−0.390321	+	3.83131i	−0.0243003	+	0.238527i
$259$	30.1442	+	16.1124i	1.87307	+	1.00118i
$260$	−0.359755	+	1.74732i	−0.0223110	+	0.108364i
$261$	−3.06941	+	3.74009i	−0.189992	+	0.231506i
$262$	−12.5136	+	18.5927i	−0.773091	+	1.14866i
$263$	2.97530	+	1.98803i	0.183465	+	0.122587i	0.643911	−	0.765100i	$-0.277311\pi$
$263$	2.97530	+	1.98803i	0.183465	+	0.122587i	−0.460446	+	0.887688i	$0.652311\pi$
$264$	8.23393	−	4.29525i	0.506764	−	0.264355i
$265$	−0.996070	−	1.49072i	−0.0611881	−	0.0915745i
$266$	−1.52943	−	1.53972i	−0.0937753	−	0.0944060i
$267$	4.90105	+	1.48672i	0.299939	+	0.0909856i
$268$	−16.7768	+	20.1655i	−1.02481	+	1.23180i
$269$	15.1414	−	12.4263i	0.923190	−	0.757643i	−0.0472754	−	0.998882i	$-0.515054\pi$
$269$	15.1414	−	12.4263i	0.923190	−	0.757643i	0.970466	+	0.241239i	$0.0775538\pi$
$270$	0.383271	−	0.463838i	0.0233251	−	0.0282283i
$271$	13.7844	−	5.70969i	0.837343	−	0.346839i	0.0775375	−	0.996989i	$-0.475294\pi$
$271$	13.7844	−	5.70969i	0.837343	−	0.346839i	0.759805	+	0.650151i	$0.225294\pi$
$272$	−8.02554	−	8.24365i	−0.486620	−	0.499845i
$273$	−7.35870	−	3.04807i	−0.445369	−	0.184478i
$274$	4.16189	−	2.20668i	0.251429	−	0.133310i
$275$	−1.55090	+	15.7465i	−0.0935228	+	0.949553i
$276$	11.6058	+	14.3366i	0.698589	+	0.862964i
$277$	9.62504	+	18.0072i	0.578312	+	1.08195i	0.985671	+	0.168678i	$0.0539499\pi$
$277$	9.62504	+	18.0072i	0.578312	+	1.08195i	−0.407359	+	0.913268i	$0.633550\pi$
$278$	5.21312	−	12.4672i	0.312662	−	0.747735i
$279$	0.156309	+	0.0310919i	0.00935800	+	0.00186142i
$280$	−0.0459676	+	4.57174i	−0.00274709	+	0.273214i
$281$	2.74857	+	13.8180i	0.163966	+	0.824313i	0.971964	+	0.235128i	$0.0755511\pi$
$281$	2.74857	+	13.8180i	0.163966	+	0.824313i	−0.807998	+	0.589185i	$0.799449\pi$
$282$	5.89933	+	8.89336i	0.351300	+	0.529592i
$283$	−1.92602	−	19.5552i	−0.114490	−	1.16244i	−0.865068	−	0.501654i	$-0.832725\pi$
$283$	−1.92602	−	19.5552i	−0.114490	−	1.16244i	0.750578	−	0.660781i	$-0.229775\pi$
$284$	12.6493	−	12.4808i	0.750595	−	0.740600i
$285$	−0.0498867	−	0.164454i	−0.00295503	−	0.00974144i
$286$	−2.79467	−	9.32518i	−0.165252	−	0.551409i
$287$	34.2620	−	34.2620i	2.02242	−	2.02242i
$288$	−5.63812	+	0.460058i	−0.332229	+	0.0271092i
$289$	−6.17096	−	6.17096i	−0.362998	−	0.362998i
$290$	1.38094	−	2.56286i	0.0810916	−	0.150496i
$291$	10.5709	−	3.20664i	0.619675	−	0.187976i
$292$	−19.1852	+	7.79653i	−1.12273	+	0.456258i
$293$	18.1607	−	1.78867i	1.06096	−	0.104495i	0.447549	−	0.894259i	$-0.352297\pi$
$293$	18.1607	−	1.78867i	1.06096	−	0.104495i	0.613411	+	0.789764i	$0.289797\pi$
$294$	−10.3044	−	2.08559i	−0.600963	−	0.121634i
$295$	1.59601	−	0.317465i	0.0929230	−	0.0184835i
$296$	5.21501	−	24.9062i	0.303116	−	1.44764i
$297$	−0.640564	+	3.22033i	−0.0371693	+	0.186863i
$298$	21.8325	−	8.95772i	1.26472	−	0.518907i
$299$	17.0522	−	9.11460i	0.986155	−	0.527111i
$300$	4.60017	−	8.46928i	0.265591	−	0.488974i
$301$	10.2961	+	1.01408i	0.593457	+	0.0584504i
$302$	6.10821	−	19.8958i	0.351488	−	1.14487i
$303$	−0.0150603	+	0.0363587i	−0.000865189	+	0.00208875i
$304$	−0.780660	+	1.41457i	−0.0447739	+	0.0811309i
$305$	−0.965814	−	2.33168i	−0.0553023	−	0.133512i
$306$	4.04939	−	0.385131i	0.231488	−	0.0220165i
$307$	13.5182	+	16.4720i	0.771525	+	0.940106i	0.999436	−	0.0335758i	$-0.0106895\pi$
$307$	13.5182	+	16.4720i	0.771525	+	0.940106i	−0.227911	+	0.973682i	$0.573190\pi$
$308$	−11.6131	−	22.0813i	−0.661715	−	1.25820i
$309$	2.69504	−	8.88437i	0.153316	−	0.505414i
$310$	−0.0958933		0.000321384i	−0.00544637		1.82534e-5i
$311$	3.96866	−	2.65177i	0.225042	−	0.150368i	−0.437938	−	0.899005i	$-0.644291\pi$
$311$	3.96866	−	2.65177i	0.225042	−	0.150368i	0.662981	+	0.748637i	$0.269291\pi$
$312$	−0.640520	+	5.89506i	−0.0362623	+	0.333742i
$313$	7.63271	−	11.4232i	0.431426	−	0.645675i	−0.550523	−	0.834820i	$-0.685572\pi$
$313$	7.63271	−	11.4232i	0.431426	−	0.645675i	0.981949	+	0.189145i	$0.0605716\pi$
$314$	−30.7436	+	6.00825i	−1.73496	+	0.339065i
$315$	−1.24952	−	1.02546i	−0.0704026	−	0.0577779i
$316$	3.40041	+	17.7148i	0.191288	+	0.996534i
$317$	−5.95078	+	11.1331i	−0.334229	+	0.625299i	−0.991757	−	0.128131i	$-0.959102\pi$
$317$	−5.95078	+	11.1331i	−0.334229	+	0.625299i	0.657528	+	0.753430i	$0.271602\pi$
$318$	−3.76513	−	4.61931i	−0.211138	−	0.259038i
$319$			15.8863i			0.889463i
$320$	3.27637	−	0.922357i	0.183155	−	0.0515613i
$321$		−	12.5660i		−	0.701367i
$322$	38.4100	−	31.3074i	2.14050	−	1.74469i
$323$	0.547662	−	1.02460i	0.0304727	−	0.0570104i
$324$	1.12226	−	1.65545i	0.0623479	−	0.0919697i
$325$	−7.80966	−	6.40922i	−0.433202	−	0.355520i
$326$	2.92742	+	14.9793i	0.162135	+	0.829629i
$327$	−8.87774	+	13.2865i	−0.490940	+	0.734744i
$328$	−31.6407	−	17.3235i	−1.74706	−	0.956532i
$329$	23.8383	−	15.9283i	1.31425	−	0.878153i
$330$	0.00662125	−	1.97562i	0.000364488	−	0.108754i
$331$	−2.22574	+	7.33728i	−0.122338	+	0.403294i	−0.996622	−	0.0821199i	$-0.973831\pi$
$331$	−2.22574	+	7.33728i	−0.122338	+	0.403294i	0.874285	+	0.485414i	$0.161331\pi$
$332$	−5.80266	−	1.80278i	−0.318462	−	0.0989403i
$333$	5.70741	+	6.95449i	0.312764	+	0.381104i
$334$	0.907583	+	9.54260i	0.0496607	+	0.522148i
$335$	2.13552	+	5.15559i	0.116676	+	0.281680i
$336$	1.28668	+	15.1423i	0.0701941	+	0.826080i
$337$	−1.18413	+	2.85873i	−0.0645034	+	0.155725i	−0.952844	−	0.303459i	$-0.901858\pi$
$337$	−1.18413	+	2.85873i	−0.0645034	+	0.155725i	0.888341	+	0.459184i	$0.151858\pi$
$338$	−11.6331	−	3.57147i	−0.632755	−	0.194262i
$339$	1.15323	+	0.113584i	0.0626351	+	0.00616902i
$340$	−2.34683	+	0.694760i	−0.127275	+	0.0376786i
$341$	0.461496	−	0.246675i	0.0249914	−	0.0133582i
$342$	−0.216830	−	0.528477i	−0.0117248	−	0.0285768i
$343$	−0.321702	+	1.61730i	−0.0173703	+	0.0873262i
$344$	−1.42661	−	7.56902i	−0.0769178	−	0.408094i
$345$	3.84856	−	0.765526i	0.207199	−	0.0412145i
$346$	−1.17372	+	5.79904i	−0.0630995	+	0.311758i
$347$	16.7671	−	1.65141i	0.900103	−	0.0886524i	0.362630	−	0.931933i	$-0.381879\pi$
$347$	16.7671	−	1.65141i	0.900103	−	0.0886524i	0.537473	+	0.843281i	$0.319379\pi$
$348$	3.76295	−	8.91507i	0.201715	−	0.477898i
$349$	−18.8176	+	5.70826i	−1.00728	+	0.305556i	−0.750470	−	0.660904i	$-0.770173\pi$
$349$	−18.8176	+	5.70826i	−1.00728	+	0.305556i	−0.256814	+	0.966461i	$0.582673\pi$
$350$	−22.7936	−	12.2818i	−1.21837	−	0.656491i
$351$	−1.48244	−	1.48244i	−0.0791267	−	0.0791267i
$352$	−13.3519	+	12.9118i	−0.711660	+	0.688200i
$353$	−10.7767	+	10.7767i	−0.573587	+	0.573587i	−0.933129	−	0.359542i	$-0.882933\pi$
$353$	−10.7767	+	10.7767i	−0.573587	+	0.573587i	0.359542	+	0.933129i	$0.382933\pi$
$354$	5.18125	−	1.55277i	0.275380	−	0.0825289i
$355$	−1.09736	−	3.61749i	−0.0582416	−	0.191997i
$356$	−10.2429	−	0.0686588i	−0.542875	−	0.00363891i
$357$	−1.07109	−	10.8750i	−0.0566881	−	0.575564i
$358$	−3.76255	+	2.49585i	−0.198857	+	0.131910i
$359$	5.33069	+	26.7992i	0.281343	+	1.41441i	0.820233	+	0.572030i	$0.193844\pi$
$359$	5.33069	+	26.7992i	0.281343	+	1.41441i	−0.538890	+	0.842376i	$0.681156\pi$
$360$	−0.471676	+	1.10711i	−0.0248595	+	0.0583498i
$361$	18.4749	+	3.67489i	0.972363	+	0.193415i
$362$	−4.60883	−	1.92716i	−0.242235	−	0.101289i
$363$	−0.103303	−	0.193266i	−0.00542200	−	0.0101438i
$364$	15.8425	+	1.66764i	0.830371	+	0.0874081i
$365$	−0.431811	+	4.38425i	−0.0226020	+	0.229482i
$366$	−3.92967	−	7.41155i	−0.205407	−	0.387408i
$367$	7.54307	+	3.12444i	0.393745	+	0.163095i	0.570767	−	0.821112i	$-0.306646\pi$
$367$	7.54307	+	3.12444i	0.393745	+	0.163095i	−0.177021	+	0.984207i	$0.556646\pi$
$368$	−30.3962	−	20.9048i	−1.58451	−	1.08974i
$369$	11.7828	−	4.88060i	0.613388	−	0.254074i
$370$	−4.17298	−	3.44815i	−0.216943	−	0.179261i
$371$	−12.3756	+	10.1564i	−0.642508	+	0.527293i
$372$	−0.317411	+	0.0291154i	−0.0164570	+	0.00150956i
$373$	−19.3119	−	5.85820i	−0.999932	−	0.303326i	−0.252451	−	0.967610i	$-0.581237\pi$
$373$	−19.3119	−	5.85820i	−0.999932	−	0.303326i	−0.747481	+	0.664283i	$0.768737\pi$
$374$	9.47561	−	9.41231i	0.489972	−	0.486699i
$375$	−2.32097	−	3.47358i	−0.119854	−	0.179375i
$376$	−16.3623	−	13.7058i	−0.843823	−	0.706824i
$377$	−8.43402	−	5.63543i	−0.434374	−	0.290240i
$378$	−4.45737	−	2.99998i	−0.229263	−	0.154302i
$379$	22.8078	−	27.7914i	1.17156	−	1.42755i	0.289014	−	0.957325i	$-0.406673\pi$
$379$	22.8078	−	27.7914i	1.17156	−	1.42755i	0.882546	−	0.470225i	$-0.155827\pi$
$380$	0.189034	+	0.287057i	0.00969726	+	0.0147257i
$381$	−4.92644	−	2.63324i	−0.252389	−	0.134905i
$382$	15.6913	+	1.59858i	0.802838	+	0.0817903i
$383$	27.8074			1.42089			0.710445	−	0.703753i	$-0.248494\pi$
$383$	27.8074			1.42089			0.710445	+	0.703753i	$0.248494\pi$
$384$	10.5512	−	4.08318i	0.538438	−	0.208369i
$385$	−5.30744			−0.270492
$386$	−14.4099	−	1.46803i	−0.733445	−	0.0747208i
$387$	2.40162	+	1.28369i	0.122081	+	0.0652538i
$388$	−18.4516	+	12.1508i	−0.936736	+	0.616865i
$389$	−8.46689	+	10.3169i	−0.429289	+	0.523090i	−0.942064	−	0.335433i	$-0.891117\pi$
$389$	−8.46689	+	10.3169i	−0.429289	+	0.523090i	0.512775	+	0.858523i	$0.328617\pi$
$390$	1.04651	+	0.704338i	0.0529919	+	0.0356655i
$391$	22.0565	+	14.7376i	1.11544	+	0.745315i
$392$	20.9450	−	1.85048i	1.05788	−	0.0934632i
$393$	8.80432	+	13.1766i	0.444119	+	0.664671i
$394$	−1.14824	+	1.14057i	−0.0578476	+	0.0574611i
$395$	3.67208	+	1.11391i	0.184762	+	0.0560471i
$396$	−0.599844	−	6.53939i	−0.0301433	−	0.328617i
$397$	−4.44839	+	3.65070i	−0.223258	+	0.183223i	−0.739373	−	0.673296i	$-0.764878\pi$
$397$	−4.44839	+	3.65070i	−0.223258	+	0.183223i	0.516115	+	0.856520i	$0.327378\pi$
$398$	−10.6621	−	8.81009i	−0.534441	−	0.441610i
$399$	−1.41777	+	0.587259i	−0.0709772	+	0.0293997i
$400$	−4.01364	+	18.8534i	−0.200682	+	0.942671i
$401$	24.7604	+	10.2561i	1.23648	+	0.512165i	0.902611	−	0.430456i	$-0.141647\pi$
$401$	24.7604	+	10.2561i	1.23648	+	0.512165i	0.333864	+	0.942621i	$0.391647\pi$
$402$	8.68892	+	16.3877i	0.433364	+	0.817344i
$403$	−0.0327495	+	0.332511i	−0.00163137	+	0.0165636i
$404$	0.00823966	−	0.0782762i	0.000409938	−	0.00389439i
$405$	−0.200563	−	0.375227i	−0.00996606	−	0.0186452i
$406$	−23.9836	−	10.0286i	−1.19029	−	0.497714i
$407$	28.9722	+	5.76292i	1.43610	+	0.285657i
$408$	−7.54698	+	3.03753i	−0.373631	+	0.150380i
$409$	−3.10828	−	15.6264i	−0.153694	−	0.772674i	−0.978337	−	0.207019i	$-0.933624\pi$
$409$	−3.10828	−	15.6264i	−0.153694	−	0.772674i	0.824642	−	0.565654i	$-0.191376\pi$
$410$	−6.39482	+	4.24195i	−0.315818	+	0.209495i
$411$	−0.326492	−	3.31493i	−0.0161047	−	0.163514i
$412$	−0.124461	+	18.5679i	−0.00613175	+	0.914773i
$413$	−4.21807	−	13.9051i	−0.207558	−	0.684226i
$414$	12.4939	−	3.74430i	0.614042	−	0.184022i
$415$	−0.914020	+	0.914020i	−0.0448675	+	0.0448675i
$416$	−2.11845	−	11.6688i	−0.103865	−	0.572109i
$417$	−6.75664	−	6.75664i	−0.330874	−	0.330874i
$418$	−1.65115	−	0.889685i	−0.0807603	−	0.0435159i
$419$	−29.1726	+	8.84940i	−1.42517	+	0.432322i	−0.906338	−	0.422553i	$-0.861134\pi$
$419$	−29.1726	+	8.84940i	−1.42517	+	0.432322i	−0.518835	+	0.854874i	$0.673634\pi$
$420$	2.97842	+	1.25716i	0.145332	+	0.0613431i
$421$	−18.6229	+	1.83420i	−0.907624	+	0.0893932i	−0.541045	−	0.840994i	$-0.681971\pi$
$421$	−18.6229	+	1.83420i	−0.907624	+	0.0893932i	−0.366579	+	0.930387i	$0.619471\pi$
$422$	0.837037	−	4.13558i	0.0407463	−	0.201317i
$423$	7.40132	−	1.47221i	0.359865	−	0.0715815i
$424$	9.84302	+	6.72102i	0.478019	+	0.326401i
$425$	2.70409	−	13.5944i	0.131167	−	0.659423i
$426$	−4.76960	−	11.6249i	−0.231088	−	0.563228i
$427$	−19.8753	+	10.6235i	−0.961831	+	0.514110i
$428$	7.13408	+	24.0982i	0.344839	+	1.16483i
$429$	−6.85050	−	0.674715i	−0.330745	−	0.0325756i
$430$	−1.56637	−	0.480893i	−0.0755372	−	0.0231907i
$431$	−12.8307	+	30.9760i	−0.618032	+	1.49206i	0.235953	+	0.971764i	$0.424179\pi$
$431$	−12.8307	+	30.9760i	−0.618032	+	1.49206i	−0.853985	+	0.520297i	$0.825821\pi$
$432$	−1.21235	+	3.81185i	−0.0583291	+	0.183398i
$433$	8.54133	+	20.6206i	0.410470	+	0.990962i	0.985012	+	0.172487i	$0.0551803\pi$
$433$	8.54133	+	20.6206i	0.410470	+	0.990962i	−0.574542	+	0.818475i	$0.694820\pi$
$434$	0.0810744	+	0.852441i	0.00389170	+	0.0409185i
$435$	−1.30593	−	1.59128i	−0.0626145	−	0.0762960i
$436$	9.48200	−	30.5200i	0.454105	−	1.46164i
$437$	1.08138	−	3.56484i	0.0517295	−	0.170529i
$438$	−0.0490768	+	14.6433i	−0.00234498	+	0.699685i
$439$	−18.6917	+	12.4894i	−0.892104	+	0.596085i	−0.914911	−	0.403655i	$-0.867740\pi$
$439$	−18.6917	+	12.4894i	−0.892104	+	0.596085i	0.0228072	+	0.999740i	$0.492740\pi$
$440$	1.10892	+	3.79247i	0.0528656	+	0.180799i
$441$	−4.13013	+	6.18117i	−0.196673	+	0.294342i
$442$	1.63565	+	8.36947i	0.0777999	+	0.398095i
$443$	−27.1196	−	22.2564i	−1.28849	−	1.05744i	−0.994833	−	0.101524i	$-0.967628\pi$
$443$	−27.1196	−	22.2564i	−1.28849	−	1.05744i	−0.293656	−	0.955911i	$-0.594872\pi$
$444$	−14.8935	−	10.0966i	−0.706815	−	0.479163i
$445$	−1.02720	+	1.92176i	−0.0486940	+	0.0911001i
$446$	31.8118	−	25.9294i	1.50633	−	1.22779i
$447$		−	16.6868i		−	0.789260i
$448$	−11.0642	−	28.3083i	−0.522734	−	1.33744i
$449$		−	23.1394i		−	1.09201i	−0.837781	−	0.546007i	$-0.816147\pi$
$449$		−	23.1394i		−	1.09201i	0.837781	−	0.546007i	$-0.183853\pi$
$450$	−4.30575	−	5.28258i	−0.202975	−	0.249023i
$451$	19.7400	−	36.9309i	0.929519	−	1.73901i
$452$	−2.27608	+	0.436901i	−0.107058	+	0.0205501i
$453$	−11.3760	−	9.33607i	−0.534492	−	0.438647i
$454$	−4.56865	+	0.892855i	−0.214418	+	0.0419037i
$455$	1.88274	−	2.81771i	0.0882640	−	0.132096i
$456$	0.715853	+	0.890376i	0.0335229	+	0.0416957i
$457$	8.37861	−	5.59841i	0.391935	−	0.261882i	−0.343952	−	0.938987i	$-0.611766\pi$
$457$	8.37861	−	5.59841i	0.391935	−	0.261882i	0.735887	+	0.677105i	$0.236766\pi$
$458$	28.3021	+	0.0948540i	1.32247	+	0.00443224i
$459$	0.834938	−	2.75242i	0.0389716	−	0.128472i
$460$	−6.94588	+	3.65300i	−0.323853	+	0.170322i
$461$	18.6673	+	22.7461i	0.869421	+	1.05939i	0.997709	+	0.0676555i	$0.0215519\pi$
$461$	18.6673	+	22.7461i	0.869421	+	1.05939i	−0.128288	+	0.991737i	$0.540948\pi$
$462$	−17.5622	+	1.67032i	−0.817070	+	0.0777103i
$463$	3.78041	+	9.12672i	0.175691	+	0.424155i	0.987054	−	0.160387i	$-0.0512743\pi$
$463$	3.78041	+	9.12672i	0.175691	+	0.424155i	−0.811364	+	0.584542i	$0.801274\pi$
$464$	−2.15498	+	19.2330i	−0.100043	+	0.892870i
$465$	−0.0259487	+	0.0626457i	−0.00120334	+	0.00290512i
$466$	9.55759	−	31.1312i	0.442747	−	1.44212i
$467$	−10.8221	−	1.06588i	−0.500785	−	0.0493231i	−0.155529	−	0.987831i	$-0.549708\pi$
$467$	−10.8221	−	1.06588i	−0.500785	−	0.0493231i	−0.345257	+	0.938508i	$0.612208\pi$
$468$	3.68454	+	2.00129i	0.170318	+	0.0925099i
$469$	43.9463	−	23.4898i	2.02925	−	1.08466i
$470$	−4.20078	+	1.72355i	−0.193768	+	0.0795014i
$471$	−4.32131	+	21.7247i	−0.199115	+	1.00102i
$472$	−9.05468	+	5.91934i	−0.416776	+	0.272460i
$473$	8.76951	−	1.74436i	0.403223	−	0.0802060i
$474$	12.5014	+	2.53027i	0.574209	+	0.116219i
$475$	−1.93711	+	0.190789i	−0.0888808	+	0.00875399i
$476$	8.22807	+	20.2471i	0.377133	+	0.928026i
$477$	−4.03247	+	1.22324i	−0.184634	+	0.0560082i
$478$	1.46012	−	2.70981i	0.0667844	−	0.123944i
$479$	−12.7438	−	12.7438i	−0.582279	−	0.582279i	0.353250	−	0.935529i	$-0.385077\pi$
$479$	−12.7438	−	12.7438i	−0.582279	−	0.582279i	−0.935529	+	0.353250i	$0.885077\pi$
$480$	0.276010	−	2.39092i	0.0125981	−	0.109130i
$481$	−13.3370	+	13.3370i	−0.608113	+	0.608113i
$482$	−7.46198	−	24.8990i	−0.339884	−	1.13412i
$483$	−10.1713	−	33.5303i	−0.462811	−	1.52568i
$484$	0.307830	+	0.311984i	0.0139923	+	0.0141811i
$485$	0.460672	+	4.67729i	0.0209181	+	0.212385i
$486$	−0.781750	−	1.17850i	−0.0354609	−	0.0534579i
$487$	−5.55902	−	27.9471i	−0.251903	−	1.26640i	−0.874948	−	0.484217i	$-0.839104\pi$
$487$	−5.55902	−	27.9471i	−0.251903	−	1.26640i	0.623044	−	0.782186i	$-0.285896\pi$
$488$	11.7438	+	11.9824i	0.531617	+	0.542416i
$489$	10.5850	+	2.10549i	0.478670	+	0.0952134i
$490$	1.72560	−	4.12680i	0.0779549	−	0.186430i
$491$	20.4957	+	38.3448i	0.924960	+	1.73048i	0.633202	+	0.773987i	$0.281740\pi$
$491$	20.4957	+	38.3448i	0.924960	+	1.73048i	0.291758	+	0.956492i	$0.405760\pi$
$492$	−19.8254	+	16.0491i	−0.893797	+	0.723549i
$493$	1.36404	−	13.8494i	0.0614335	−	0.623744i
$494$	1.05805	−	0.560990i	0.0476041	−	0.0252401i
$495$	−1.29064	−	0.534602i	−0.0580102	−	0.0240286i
$496$	0.592178	−	0.236038i	0.0265896	−	0.0105984i
$497$	−31.1866	+	12.9179i	−1.39891	+	0.579447i
$498$	−2.73683	+	3.31213i	−0.122640	+	0.148420i
$499$	−20.6071	+	16.9118i	−0.922501	+	0.757077i	−0.970331	−	0.241778i	$-0.922269\pi$
$499$	−20.6071	+	16.9118i	−0.922501	+	0.757077i	0.0478305	+	0.998855i	$0.484769\pi$
$500$	6.42304	+	5.34371i	0.287247	+	0.238978i
$501$	6.48623	+	1.96758i	0.289783	+	0.0879048i
$502$	−27.6300	−	27.8158i	−1.23319	−	1.24148i
$503$	−5.01185	−	7.50076i	−0.223467	−	0.334443i	0.702747	−	0.711440i	$-0.251957\pi$
$503$	−5.01185	−	7.50076i	−0.223467	−	0.334443i	−0.926214	+	0.376997i	$0.876957\pi$
$504$	10.2512	+	3.22257i	0.456625	+	0.143545i
$505$	−0.0139221	−	0.00930243i	−0.000619524	−	0.000413953i
$506$	23.9117	−	35.5280i	1.06300	−	1.57941i
$507$	−5.45879	+	6.65156i	−0.242434	+	0.295406i
$508$	10.9425	+	2.25296i	0.485497	+	0.0999588i
$509$	1.84518	+	0.986271i	0.0817863	+	0.0437157i	0.511783	−	0.859115i	$-0.328985\pi$
$509$	1.84518	+	0.986271i	0.0817863	+	0.0437157i	−0.429997	+	0.902831i	$0.641485\pi$
$510$	−0.175405	+	1.72174i	−0.00776706	+	0.0762399i
$511$	39.3388			1.74025
$512$	−17.9162	+	13.8206i	−0.791791	+	0.610792i
$513$	−0.403921			−0.0178335
$514$	1.85413	−	18.1998i	0.0817822	−	0.802758i
$515$	3.48366	+	1.86206i	0.153508	+	0.0820520i
$516$	−5.33445	−	1.09831i	−0.234836	−	0.0483504i
$517$	15.7188	−	19.1535i	0.691314	−	0.842368i
$518$	−26.9897	+	40.1014i	−1.18586	+	1.76195i
$519$	3.47861	+	2.32433i	0.152694	+	0.102027i
$520$	−2.40679	−	0.756598i	−0.105545	−	0.0331790i
$521$	21.2848	+	31.8549i	0.932502	+	1.39559i	0.918385	+	0.395688i	$0.129494\pi$
$521$	21.2848	+	31.8549i	0.932502	+	1.39559i	0.0141171	+	0.999900i	$0.495506\pi$
$522$	−4.82210	−	4.85453i	−0.211058	−	0.212477i
$523$	−35.5978	−	10.7985i	−1.55658	−	0.472184i	−0.609395	−	0.792867i	$-0.708588\pi$
$523$	−35.5978	−	10.7985i	−1.55658	−	0.472184i	−0.947187	+	0.320683i	$0.896088\pi$
$524$	−24.3650	−	20.2707i	−1.06439	−	0.885529i
$525$	−14.1525	+	11.6147i	−0.617667	+	0.506906i
$526$	−3.22348	+	3.90109i	−0.140550	+	0.170096i
$527$	−0.423503	+	0.175421i	−0.0184481	+	0.00764144i
$528$	4.86293	+	12.2002i	0.211632	+	0.530947i
$529$	57.3347	+	23.7488i	2.49281	+	1.03256i
$530$	2.24012	−	1.18773i	0.0973045	−	0.0515918i
$531$	0.374885	−	3.80627i	0.0162686	−	0.165178i
$532$	2.38549	−	1.93111i	0.103424	−	0.0837242i
$533$	12.6041	+	23.5806i	0.545944	+	1.02139i
$534$	−2.79419	+	6.68235i	−0.120917	+	0.289173i
$535$	5.24368	+	1.04303i	0.226704	+	0.0450943i
$536$	−25.9668	−	26.4942i	−1.12159	−	1.14438i
$537$	0.622856	+	3.13131i	0.0268782	+	0.135126i
$538$	15.3126	+	23.0841i	0.660174	+	0.995225i
$539$	2.39251	+	24.2915i	0.103053	+	1.04631i
$540$	0.597653	+	0.605719i	0.0257189	+	0.0260660i
$541$	−4.01093	−	13.2223i	−0.172444	−	0.568470i	−0.999975	−	0.00705104i	$-0.997756\pi$
$541$	−4.01093	−	13.2223i	−0.172444	−	0.568470i	0.827532	−	0.561419i	$-0.189744\pi$
$542$	6.05737	+	20.2121i	0.260186	+	0.868184i
$543$	−2.49776	+	2.49776i	−0.107189	+	0.107189i
$544$	12.7486	−	10.1098i	0.546591	−	0.433454i
$545$	−4.80743	−	4.80743i	−0.205928	−	0.205928i
$546$	5.34318	−	9.91629i	0.228667	−	0.424378i
$547$	−22.3276	+	6.77300i	−0.954659	+	0.289593i	−0.728923	−	0.684596i	$-0.759979\pi$
$547$	−22.3276	+	6.77300i	−0.954659	+	0.289593i	−0.225736	+	0.974188i	$0.572479\pi$
$548$	2.50810	+	6.17179i	0.107141	+	0.263646i
$549$	−5.90327	+	0.581422i	−0.251946	+	0.0248145i
$550$	−21.9320	−	4.43901i	−0.935184	−	0.189280i
$551$	−1.91675	+	0.381266i	−0.0816565	+	0.0162425i
$552$	−21.8342	+	14.2737i	−0.929324	+	0.607529i
$553$	6.68486	−	33.6071i	0.284269	−	1.42912i
$554$	−26.7144	+	10.9607i	−1.13499	+	0.465677i
$555$	−3.37578	+	1.80439i	−0.143294	+	0.0765923i
$556$	16.7933	+	9.12147i	0.712196	+	0.386836i
$557$	15.9371	+	1.56967i	0.675278	+	0.0665090i	0.429842	−	0.902904i	$-0.358569\pi$
$557$	15.9371	+	1.56967i	0.675278	+	0.0665090i	0.245435	+	0.969413i	$0.421069\pi$
$558$	−0.0661484	+	0.215460i	−0.00280029	+	0.00912115i
$559$	−2.18477	+	5.27451i	−0.0924061	+	0.223088i
$560$	−6.42554	−	0.719956i	−0.271528	−	0.0304237i
$561$	−3.61407	−	8.72513i	−0.152586	−	0.368375i
$562$	−19.8350	+	1.88647i	−0.836687	+	0.0795761i
$563$	−0.147032	−	0.179159i	−0.00619665	−	0.00755064i	0.769903	−	0.638161i	$-0.220305\pi$
$563$	−0.147032	−	0.179159i	−0.00619665	−	0.00755064i	−0.776100	+	0.630610i	$0.782805\pi$
$564$	−13.3579	+	7.02524i	−0.562470	+	0.295816i
$565$	−0.143121	+	0.471806i	−0.00602114	+	0.0198490i
$566$	27.7889	+	0.0931338i	1.16805	+	0.00391471i
$567$	−3.15893	+	2.11073i	−0.132663	+	0.0886424i
$568$	15.7466	+	19.5856i	0.660712	+	0.821791i
$569$	−17.3612	+	25.9828i	−0.727818	+	1.08926i	0.264360	+	0.964424i	$0.414839\pi$
$569$	−17.3612	+	25.9828i	−0.727818	+	1.08926i	−0.992178	+	0.124832i	$0.960161\pi$
$570$	0.238526	−	0.0466154i	0.00999077	−	0.00195250i
$571$	−6.45014	−	5.29349i	−0.269930	−	0.221526i	0.489684	−	0.871900i	$-0.337112\pi$
$571$	−6.45014	−	5.29349i	−0.269930	−	0.221526i	−0.759614	+	0.650374i	$0.774612\pi$
$572$	13.5205	−	2.59530i	0.565319	−	0.108515i
$573$	5.25743	−	9.83595i	0.219632	−	0.410903i
$574$	43.2933	+	53.1151i	1.80703	+	2.21698i
$575$		−	44.4441i		−	1.85345i
$576$	0.160860	−	7.99838i	0.00670248	−	0.333266i
$577$			38.5629i			1.60540i	0.596386	+	0.802698i	$0.296603\pi$
$577$			38.5629i			1.60540i	−0.596386	+	0.802698i	$0.703397\pi$
$578$	9.56663	−	7.79762i	0.397919	−	0.324338i
$579$	−4.82809	+	9.03271i	−0.200648	+	0.375387i
$580$	3.40783	+	2.31023i	0.141503	+	0.0959271i
$581$	8.92247	+	7.32248i	0.370167	+	0.303788i
$582$	2.99636	+	15.3321i	0.124203	+	0.635536i
$583$	−7.68691	+	11.5043i	−0.318359	+	0.476459i
$584$	−8.21931	−	28.1098i	−0.340117	−	1.16319i
$585$	0.741657	−	0.495559i	0.0306637	−	0.0204888i
$586$	−0.0864925	+	25.8073i	−0.00357297	+	1.06609i
$587$	−0.827259	+	2.72711i	−0.0341446	+	0.112560i	−0.972356	−	0.233502i	$-0.924981\pi$
$587$	−0.827259	+	2.72711i	−0.0341446	+	0.112560i	0.938212	+	0.346062i	$0.112481\pi$
$588$	4.41124	−	14.1986i	0.181917	−	0.585541i
$589$	0.0408381	+	0.0497614i	0.00168270	+	0.00205038i
$590$	0.217891	+	2.29097i	0.00897044	+	0.0943179i
$591$	0.437948	+	1.05730i	0.0180148	+	0.0434915i
$592$	34.2938	+	10.9070i	1.40947	+	0.448277i
$593$	−6.56242	+	15.8431i	−0.269486	+	0.650597i	−0.999459	−	0.0328785i	$-0.989533\pi$
$593$	−6.56242	+	15.8431i	−0.269486	+	0.650597i	0.729973	+	0.683476i	$0.239533\pi$
$594$	−4.43897	−	1.36281i	−0.182133	−	0.0559168i
$595$	4.62692	+	0.455712i	0.189685	+	0.0186824i
$596$	9.47357	+	32.0008i	0.388053	+	1.31080i
$597$	−8.62520	+	4.61027i	−0.353006	+	0.188686i
$598$	10.3795	+	25.2977i	0.424448	+	1.03450i
$599$	−7.58522	+	38.1335i	−0.309924	+	1.55809i	0.440880	+	0.897566i	$0.354666\pi$
$599$	−7.58522	+	38.1335i	−0.309924	+	1.55809i	−0.750804	+	0.660525i	$0.770334\pi$
$600$	11.2563	+	7.68606i	0.459538	+	0.313782i
$601$	−30.8904	+	6.14449i	−1.26005	+	0.250639i	−0.779540	−	0.626352i	$-0.784547\pi$
$601$	−30.8904	+	6.14449i	−1.26005	+	0.250639i	−0.480507	+	0.876991i	$0.659547\pi$
$602$	−2.90251	+	14.3405i	−0.118297	+	0.584477i
$603$	13.0528	−	1.28558i	0.531549	−	0.0523530i
$604$	27.1165	+	11.4456i	1.10335	+	0.465713i
$605$	0.0892227	−	0.0270654i	0.00362742	−	0.00110037i
$606$	−0.0489955	−	0.0264001i	−0.00199031	−	0.00107243i
$607$	20.0356	+	20.0356i	0.813220	+	0.813220i	0.985115	−	0.171895i	$-0.0549889\pi$
$607$	20.0356	+	20.0356i	0.813220	+	0.813220i	−0.171895	+	0.985115i	$0.554989\pi$
$608$	−1.87830	−	1.30109i	−0.0761753	−	0.0527662i
$609$	−12.9980	+	12.9980i	−0.526704	+	0.526704i
$610$	3.41895	−	1.02463i	0.138429	−	0.0414859i
$611$	4.59252	+	15.1395i	0.185794	+	0.612479i
$612$	−0.0385586	+	5.75241i	−0.00155864	+	0.232528i
$613$	−3.36465	−	34.1619i	−0.135897	−	1.37979i	−0.785193	−	0.619251i	$-0.787437\pi$
$613$	−3.36465	−	34.1619i	−0.135897	−	1.37979i	0.649296	−	0.760535i	$-0.275063\pi$
$614$	−25.1126	+	16.6582i	−1.01346	+	0.672271i
$615$	1.05860	+	5.32196i	0.0426870	+	0.214602i
$616$	32.7313	−	13.1738i	1.31878	−	0.530787i
$617$	−20.9394	−	4.16511i	−0.842989	−	0.167681i	−0.245338	−	0.969438i	$-0.578899\pi$
$617$	−20.9394	−	4.16511i	−0.842989	−	0.167681i	−0.597651	+	0.801757i	$0.703899\pi$
$618$	12.1134	+	5.06516i	0.487272	+	0.203751i
$619$	−4.31236	−	8.06785i	−0.173328	−	0.324274i	0.780225	−	0.625499i	$-0.215105\pi$
$619$	−4.31236	−	8.06785i	−0.173328	−	0.324274i	−0.953553	+	0.301225i	$0.902605\pi$
$620$	0.0141969	−	0.134869i	0.000570160	−	0.00541648i
$621$	0.903985	−	9.17832i	0.0362757	−	0.368313i
$622$	3.16202	+	5.96372i	0.126786	+	0.239123i
$623$	17.9769	+	7.44626i	0.720227	+	0.298328i
$624$	−8.20214	−	1.74613i	−0.328348	−	0.0699010i
$625$	−20.6186	+	8.54052i	−0.824745	+	0.341621i
$626$	14.9776	+	12.3760i	0.598624	+	0.494645i
$627$	−1.02520	+	0.841359i	−0.0409425	+	0.0336006i
$628$	−4.04660	−	44.1154i	−0.161477	−	1.76039i
$629$	−24.7625	−	7.51163i	−0.987347	−	0.299508i
$630$	1.62184	−	1.61101i	0.0646158	−	0.0641842i
$631$	−26.7942	−	40.1004i	−1.06666	−	1.59637i	−0.766227	−	0.642570i	$-0.777868\pi$
$631$	−26.7942	−	40.1004i	−1.06666	−	1.59637i	−0.300435	−	0.953802i	$-0.597132\pi$
$632$	−25.4109	+	2.24503i	−1.01079	+	0.0893024i
$633$	−2.48077	−	1.65760i	−0.0986017	−	0.0658835i
$634$	−14.8106	−	9.96809i	−0.588204	−	0.395884i
$635$	1.50774	−	1.83719i	0.0598328	−	0.0729065i
$636$	7.03872	−	4.63518i	0.279103	−	0.183797i
$637$	−13.7450	−	7.34688i	−0.544599	−	0.291094i
$638$	−22.3510	−	2.27704i	−0.884883	−	0.0901488i
$639$	−8.88502			−0.351486
$640$	0.828079	+	4.74183i	0.0327327	+	0.187437i
$641$	−21.6904			−0.856719			−0.428360	−	0.903608i	$-0.640908\pi$
$641$	−21.6904			−0.856719			−0.428360	+	0.903608i	$0.640908\pi$
$642$	17.6795	+	1.80113i	0.697756	+	0.0710849i
$643$	−7.31344	−	3.90911i	−0.288414	−	0.154160i	0.320845	−	0.947132i	$-0.396033\pi$
$643$	−7.31344	−	3.90911i	−0.288414	−	0.154160i	−0.609259	+	0.792971i	$0.708533\pi$
$644$	38.5419	+	58.5276i	1.51877	+	2.30631i
$645$	−0.735018	+	0.895622i	−0.0289413	+	0.0352651i
$646$	1.36305	+	0.917382i	0.0536284	+	0.0360939i
$647$	−0.287743	−	0.192264i	−0.0113123	−	0.00755867i	0.549901	−	0.835230i	$-0.314665\pi$
$647$	−0.287743	−	0.192264i	−0.0113123	−	0.00755867i	−0.561214	+	0.827671i	$0.689665\pi$
$648$	2.16825	+	1.81623i	0.0851770	+	0.0713481i
$649$	−6.97688	−	10.4416i	−0.273867	−	0.409870i
$650$	10.1367	−	10.0690i	0.397595	−	0.394939i
$651$	0.579415	+	0.175764i	0.0227091	+	0.00688872i
$652$	−21.4945	+	1.97164i	−0.841790	+	0.0772155i
$653$	8.68517	−	7.12774i	0.339877	−	0.278930i	−0.448935	−	0.893564i	$-0.648197\pi$
$653$	8.68517	−	7.12774i	0.339877	−	0.278930i	0.788812	+	0.614635i	$0.210697\pi$
$654$	−17.4207	−	14.3948i	−0.681202	−	0.562880i
$655$	−6.22926	+	2.58025i	−0.243397	+	0.100819i
$656$	28.9082	−	42.0332i	1.12868	−	1.64112i
$657$	9.56627	+	3.96248i	0.373216	+	0.154591i
$658$	18.9931	+	35.8219i	0.740429	+	1.39648i
$659$	2.31531	−	23.5077i	0.0901917	−	0.915731i	−0.838506	−	0.544893i	$-0.816570\pi$
$659$	2.31531	−	23.5077i	0.0901917	−	0.915731i	0.928697	−	0.370839i	$-0.120930\pi$
$660$	2.77862	+	0.292488i	0.108157	+	0.0113851i
$661$	14.8758	+	27.8307i	0.578602	+	1.08249i	0.985605	+	0.169062i	$0.0540738\pi$
$661$	14.8758	+	27.8307i	0.578602	+	1.08249i	−0.407003	+	0.913427i	$0.633426\pi$
$662$	−10.0040	−	4.18314i	−0.388818	−	0.162582i
$663$	5.91420	+	1.17641i	0.229688	+	0.0456879i
$664$	3.36810	−	7.90555i	0.130708	−	0.306795i
$665$	−0.127377	−	0.640366i	−0.00493946	−	0.0248323i
$666$	−10.6026	+	7.03312i	−0.410841	+	0.272528i
$667$	−4.37379	−	44.4078i	−0.169354	−	1.71948i
$668$	−13.5559	−	0.0908655i	−0.524493	−	0.00351569i
$669$	−8.42407	−	27.7705i	−0.325694	−	1.07367i
$670$	−7.55965	+	2.26556i	−0.292055	+	0.0875261i
$671$	−13.7721	+	13.7721i	−0.531667	+	0.531667i
$672$	−21.4886	−	0.360125i	−0.828940	−	0.0138921i
$673$	1.97620	+	1.97620i	0.0761770	+	0.0761770i	0.744169	−	0.667992i	$-0.232846\pi$
$673$	1.97620	+	1.97620i	0.0761770	+	0.0761770i	−0.667992	+	0.744169i	$0.732846\pi$
$674$	−3.85231	−	2.07573i	−0.148386	−	0.0799543i
$675$	−4.61148	+	1.39888i	−0.177496	+	0.0538428i
$676$	6.69221	−	15.8550i	0.257393	−	0.609808i
$677$	22.2756	−	2.19396i	0.856121	−	0.0843206i	0.339574	−	0.940579i	$-0.389717\pi$
$677$	22.2756	−	2.19396i	0.856121	−	0.0843206i	0.516547	+	0.856259i	$0.327217\pi$
$678$	−0.325101	+	1.60624i	−0.0124854	+	0.0616873i
$679$	41.1617	−	8.18757i	1.57964	−	0.314210i
$680$	−0.641100	−	3.40141i	−0.0245851	−	0.130438i
$681$	−0.642167	+	3.22839i	−0.0246079	+	0.123712i
$682$	0.280906	+	0.684649i	0.0107565	+	0.0262166i
$683$	−6.28900	+	3.36154i	−0.240642	+	0.128626i	−0.587310	−	0.809362i	$-0.699813\pi$
$683$	−6.28900	+	3.36154i	−0.240642	+	0.128626i	0.346668	+	0.937988i	$0.387313\pi$
$684$	0.774610	−	0.229317i	0.0296180	−	0.00876815i
$685$	1.41039	+	0.138911i	0.0538883	+	0.00530753i
$686$	−2.22933	−	0.684426i	−0.0851160	−	0.0261315i
$687$	7.65855	−	18.4894i	0.292192	−	0.705413i
$688$	10.8536	−	0.922255i	0.413788	−	0.0351607i
$689$	−3.38079	−	8.16194i	−0.128798	−	0.310945i
$690$	0.525416	+	5.52438i	0.0200022	+	0.210310i
$691$	4.57599	+	5.57587i	0.174079	+	0.212116i	0.852740	−	0.522336i	$-0.174939\pi$
$691$	4.57599	+	5.57587i	0.174079	+	0.212116i	−0.678661	+	0.734452i	$0.737439\pi$
$692$	−7.99062	−	2.48254i	−0.303758	−	0.0943719i
$693$	−3.62113	+	11.9373i	−0.137556	+	0.453460i
$694$	−0.0798550	+	23.8268i	−0.00303125	+	0.904453i
$695$	3.38031	−	2.25865i	0.128222	−	0.0856755i
$696$	12.0035	+	6.57203i	0.454993	+	0.249112i
$697$	−20.3799	+	30.5007i	−0.771944	+	1.15530i
$698$	−5.33394	−	27.2933i	−0.201893	−	1.03307i
$699$	−17.8002	−	14.6082i	−0.673266	−	0.552535i
$700$	20.5468	−	30.3086i	0.776594	−	1.14556i
$701$	−18.9683	+	35.4872i	−0.716424	+	1.34033i	0.215077	+	0.976597i	$0.431000\pi$
$701$	−18.9683	+	35.4872i	−0.716424	+	1.34033i	−0.931501	+	0.363738i	$0.881500\pi$
$702$	2.29817	−	1.87321i	0.0867389	−	0.0706996i
$703$			3.63393i			0.137056i
$704$	−16.2522	−	20.6359i	−0.612528	−	0.777745i
$705$			3.21070i			0.120922i
$706$	−13.6174	−	16.7068i	−0.512499	−	0.628767i
$707$	−0.0704812	+	0.131861i	−0.00265072	+	0.00495914i
$708$	1.44200	+	7.51223i	0.0541936	+	0.282327i
$709$	−24.2825	−	19.9281i	−0.911948	−	0.748416i	0.0562986	−	0.998414i	$-0.482070\pi$
$709$	−24.2825	−	19.9281i	−0.911948	−	0.748416i	−0.968246	+	0.249998i	$0.919570\pi$
$710$	5.24685	−	1.02540i	0.196911	−	0.0384824i
$711$	5.01074	−	7.49910i	0.187917	−	0.281238i
$712$	1.56475	−	14.4013i	0.0586416	−	0.539710i
$713$	−1.22213	+	0.816600i	−0.0457691	+	0.0305819i
$714$	15.4538	+	0.0517932i	0.578345	+	0.00193831i
$715$	0.850173	−	2.80264i	0.0317947	−	0.104813i
$716$	−2.97220	−	5.65138i	−0.111076	−	0.211202i
$717$	−1.38081	−	1.68252i	−0.0515673	−	0.0628349i
$718$	−38.4687	+	3.65870i	−1.43564	+	0.136541i
$719$	−15.3736	−	37.1151i	−0.573338	−	1.38416i	−0.898697	−	0.438570i	$-0.855485\pi$
$719$	−15.3736	−	37.1151i	−0.573338	−	1.38416i	0.325359	−	0.945591i	$-0.394515\pi$
$720$	−1.49002	−	0.822301i	−0.0555298	−	0.0306453i
$721$	13.4982	−	32.5875i	0.502698	−	1.21362i
$722$	−7.81838	+	25.4662i	−0.290970	+	0.947753i
$723$	−18.2914	−	1.80154i	−0.680263	−	0.0670001i
$724$	3.37198	−	6.20808i	0.125319	−	0.230722i
$725$	−20.5628	+	10.9910i	−0.763682	+	0.408196i
$726$	0.286719	−	0.117639i	0.0106411	−	0.00436598i
$727$	6.27828	−	31.5630i	0.232848	−	1.17061i	−0.670570	−	0.741847i	$-0.733950\pi$
$727$	6.27828	−	31.5630i	0.232848	−	1.17061i	0.903418	−	0.428761i	$-0.141050\pi$
$728$	−4.61701	+	22.0502i	−0.171118	+	0.817236i
$729$	−0.980785	+	0.195090i	−0.0363254	+	0.00722557i
$730$	−6.10645	−	1.23594i	−0.226010	−	0.0457441i
$731$	−7.79486	+	0.767727i	−0.288303	+	0.0283954i
$732$	10.9908	−	4.46646i	0.406231	−	0.165085i
$733$	42.6261	−	12.9305i	1.57443	−	0.477598i	0.622169	−	0.782883i	$-0.286252\pi$
$733$	42.6261	−	12.9305i	1.57443	−	0.477598i	0.952261	+	0.305285i	$0.0987517\pi$
$734$	−5.47705	+	10.1647i	−0.202162	+	0.375188i
$735$	−2.23653	−	2.23653i	−0.0824955	−	0.0824955i
$736$	33.7685	−	39.7689i	1.24472	−	1.46590i
$737$	30.4516	−	30.4516i	1.12170	−	1.12170i
$738$	5.17780	+	17.2771i	0.190597	+	0.635981i
$739$	13.2914	+	43.8159i	0.488933	+	1.61180i	0.760474	+	0.649368i	$0.224967\pi$
$739$	13.2914	+	43.8159i	0.488933	+	1.61180i	−0.271541	+	0.962427i	$0.587533\pi$
$740$	5.44943	−	5.37686i	0.200325	−	0.197657i
$741$	−0.0830022	−	0.842736i	−0.00304916	−	0.0309587i
$742$	−12.5155	−	18.8673i	−0.459458	−	0.692642i
$743$	−2.00497	−	10.0797i	−0.0735554	−	0.369788i	0.926422	−	0.376486i	$-0.122868\pi$
$743$	−2.00497	−	10.0797i	−0.0735554	−	0.369788i	−0.999978	+	0.00669844i	$0.997868\pi$
$744$	0.00453216	−	0.450748i	0.000166157	−	0.0165252i
$745$	6.96325	+	1.38508i	0.255114	+	0.0507453i
$746$	11.0101	−	26.3308i	0.403109	−	0.964040i
$747$	1.43216	+	2.67939i	0.0524001	+	0.0980337i
$748$	11.8843	+	14.6806i	0.434533	+	0.536777i
$749$	4.67944	−	47.5111i	0.170983	−	1.73602i
$750$	5.21976	−	2.76757i	0.190599	−	0.101057i
$751$	−32.2182	−	13.3452i	−1.17566	−	0.486973i	−0.292599	−	0.956235i	$-0.594520\pi$
$751$	−32.2182	−	13.3452i	−1.17566	−	0.486973i	−0.883059	+	0.469262i	$0.844520\pi$
$752$	21.6284	−	21.0562i	0.788708	−	0.767840i
$753$	−25.6128	+	10.6092i	−0.933381	+	0.386619i
$754$	9.13754	−	11.0583i	0.332770	−	0.402721i
$755$	4.84011	−	3.97218i	0.176150	−	0.144562i
$756$	4.85966	−	5.84122i	0.176744	−	0.212443i
$757$	−32.8254	−	9.95747i	−1.19306	−	0.361911i	−0.369549	−	0.929211i	$-0.620488\pi$
$757$	−32.8254	−	9.95747i	−1.19306	−	0.361911i	−0.823511	+	0.567301i	$0.807988\pi$
$758$	35.8315	+	36.0725i	1.30146	+	1.31021i
$759$	−16.8238	−	25.1786i	−0.610666	−	0.913927i
$760$	−0.430964	+	0.224814i	−0.0156327	+	0.00815485i
$761$	37.0025	+	24.7243i	1.34134	+	0.896254i	0.999060	−	0.0433450i	$-0.0138015\pi$
$761$	37.0025	+	24.7243i	1.34134	+	0.896254i	0.342278	+	0.939599i	$0.388801\pi$
$762$	4.41091	−	6.55373i	0.159790	−	0.237417i
$763$	−38.5137	+	46.9291i	−1.39429	+	1.69895i
$764$	−4.49817	+	21.8475i	−0.162738	+	0.790414i
$765$	1.07926	+	0.576874i	0.0390206	+	0.0208569i
$766$	−3.98572	+	39.1230i	−0.144010	+	1.41357i
$767$	8.01840			0.289528
$768$	4.23242	+	15.4301i	0.152724	+	0.556784i
$769$	30.9452			1.11591			0.557956	−	0.829870i

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)

\(f(q)\)	\(=\)	\(q+(-0.143333 + 1.40693i) q^{2} +(0.881921 + 0.471397i) q^{3} +(-1.95891 - 0.403320i) q^{4} +(-0.269913 + 0.328889i) q^{5} +(-0.789631 + 1.17324i) q^{6} +(3.15893 + 2.11073i) q^{7} +(0.848221 - 2.69824i) q^{8} +(0.555570 + 0.831470i) q^{9} +O(q^{10})\)	\(q+(-0.143333 + 1.40693i) q^{2} +(0.881921 + 0.471397i) q^{3} +(-1.95891 - 0.403320i) q^{4} +(-0.269913 + 0.328889i) q^{5} +(-0.789631 + 1.17324i) q^{6} +(3.15893 + 2.11073i) q^{7} +(0.848221 - 2.69824i) q^{8} +(0.555570 + 0.831470i) q^{9} +(-0.424037 - 0.426889i) q^{10} +(3.14204 + 0.953127i) q^{11} +(-1.53748 - 1.27912i) q^{12} +(-1.62061 + 1.33000i) q^{13} +(-3.42243 + 4.14186i) q^{14} +(-0.393079 + 0.162819i) q^{15} +(3.67467 + 1.58014i) q^{16} +(-2.65733 - 1.10070i) q^{17} +(-1.24945 + 0.662472i) q^{18} +(-0.0395911 + 0.401976i) q^{19} +(0.661383 - 0.535404i) q^{20} +(1.79094 + 3.35061i) q^{21} +(-1.79134 + 4.28402i) q^{22} +(-9.04551 - 1.79926i) q^{23} +(2.02001 - 1.97979i) q^{24} +(0.940136 + 4.72638i) q^{25} +(-1.63893 - 2.47071i) q^{26} +(0.0980171 + 0.995185i) q^{27} +(-5.33677 - 5.40879i) q^{28} +(1.40450 + 4.63000i) q^{29} +(-0.172733 - 0.576373i) q^{30} +(0.112693 - 0.112693i) q^{31} +(-2.74984 + 4.94352i) q^{32} +(2.32173 + 2.32173i) q^{33} +(1.92949 - 3.58091i) q^{34} +(-1.54683 + 0.469227i) q^{35} +(-0.752964 - 1.85285i) q^{36} +(8.95331 - 0.881825i) q^{37} +(-0.559877 - 0.113318i) q^{38} +(-2.05620 + 0.409004i) q^{39} +(0.658479 + 1.00726i) q^{40} +(2.48811 - 12.5086i) q^{41} +(-4.97078 + 2.03947i) q^{42} +(2.40162 - 1.28369i) q^{43} +(-5.77056 - 3.13434i) q^{44} +(-0.423417 - 0.0417029i) q^{45} +(3.82796 - 12.4685i) q^{46} +(2.88785 - 6.97189i) q^{47} +(2.49589 + 3.12578i) q^{48} +(2.84488 + 6.86815i) q^{49} +(-6.78445 + 0.645259i) q^{50} +(-1.82469 - 2.22339i) q^{51} +(3.71104 - 1.95172i) q^{52} +(-1.22324 + 4.03247i) q^{53} +(-1.41421 - 0.00473968i) q^{54} +(-1.16155 + 0.776122i) q^{55} +(8.37474 - 6.73320i) q^{56} +(-0.224406 + 0.335848i) q^{57} +(-6.71541 + 1.31240i) q^{58} +(-2.95652 - 2.42636i) q^{59} +(0.835675 - 0.160411i) q^{60} +(-2.79625 + 5.23141i) q^{61} +(0.142398 + 0.174704i) q^{62} +3.79921i q^{63} +(-6.56104 - 4.57741i) q^{64} -0.891983i q^{65} +(-3.59930 + 2.93373i) q^{66} +(6.18280 - 11.5672i) q^{67} +(4.76154 + 3.22793i) q^{68} +(-7.12926 - 5.85084i) q^{69} +(-0.438457 - 2.24354i) q^{70} +(-4.93625 + 7.38762i) q^{71} +(2.71475 - 0.793794i) q^{72} +(8.60941 - 5.75262i) q^{73} +(-0.0426412 + 12.7231i) q^{74} +(-1.39888 + 4.61148i) q^{75} +(0.239680 - 0.771466i) q^{76} +(7.91369 + 9.64286i) q^{77} +(-0.280718 - 2.95156i) q^{78} +(-3.45146 - 8.33255i) q^{79} +(-1.51153 + 0.782060i) q^{80} +(-0.382683 + 0.923880i) q^{81} +(17.2421 + 5.29349i) q^{82} +(3.02350 + 0.297789i) q^{83} +(-2.15692 - 7.28587i) q^{84} +(1.07926 - 0.576874i) q^{85} +(1.46184 + 3.56291i) q^{86} +(-0.943914 + 4.74537i) q^{87} +(5.23691 - 7.66953i) q^{88} +(5.02318 - 0.999172i) q^{89} +(0.119363 - 0.589741i) q^{90} +(-7.92665 + 0.780706i) q^{91} +(16.9937 + 7.17284i) q^{92} +(0.152509 - 0.0462631i) q^{93} +(9.39505 + 5.06231i) q^{94} +(-0.121519 - 0.121519i) q^{95} +(-4.75550 + 3.06352i) q^{96} +(7.81107 - 7.81107i) q^{97} +(-10.0708 + 3.01812i) q^{98} +(0.953127 + 3.14204i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 512 q+O(q^{10}) \) 512 * 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

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