LMFDB - Embedded newform 384.2.v.a.229.14

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			229.14
Character	$\chi$	$=$	384.229
Dual form			384.2.v.a.109.14

$q$-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 $\left(\mathbb{Z}/384\mathbb{Z}\right)^\times$.

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

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 $

$2$	−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	0.709150	−	0.705058i	$-0.249079\pi$
$5$	−0.269913	−	0.328889i	−0.120709	−	0.147084i	−0.829859	+	0.557974i	$0.811579\pi$
$6$	−0.789631	−	1.17324i	−0.322366	−	0.478971i
$7$	3.15893	−	2.11073i	1.19396	−	0.797781i	0.210272	−	0.977643i	$-0.432565\pi$
$7$	3.15893	−	2.11073i	1.19396	−	0.797781i	0.983692	+	0.179862i	$0.0575650\pi$
$8$	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	0.221453	−	0.975171i	$-0.428920\pi$
$11$	3.14204	−	0.953127i	0.947360	−	0.287379i	0.725907	+	0.687792i	$0.241420\pi$
$12$	−1.53748	+	1.27912i	−0.443833	+	0.369250i
$13$	−1.62061	−	1.33000i	−0.449475	−	0.368875i	0.382253	−	0.924058i	$-0.375148\pi$
$13$	−1.62061	−	1.33000i	−0.449475	−	0.368875i	−0.831728	+	0.555183i	$0.812648\pi$
$14$	−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	−0.680898	−	0.732378i	$-0.738410\pi$
$17$	−2.65733	+	1.10070i	−0.644497	+	0.266959i	0.0364015	+	0.999337i	$0.488410\pi$
$18$	−1.24945	−	0.662472i	−0.294499	−	0.156146i
$19$	−0.0395911	−	0.401976i	−0.00908283	−	0.0922195i	0.989575	−	0.144022i	$-0.0460035\pi$
$19$	−0.0395911	−	0.401976i	−0.00908283	−	0.0922195i	−0.998657	+	0.0518021i	$0.983503\pi$
$20$	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	−0.996647	−	0.0818159i	$-0.973928\pi$
$23$	−9.04551	+	1.79926i	−1.88612	+	0.375173i	−0.889473	+	0.456988i	$0.848928\pi$
$24$	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	−0.724542	−	0.689230i	$-0.757949\pi$
$29$	1.40450	−	4.63000i	0.260808	−	0.859770i	0.985351	−	0.170540i	$-0.0545512\pi$
$30$	−0.172733	+	0.576373i	−0.0315367	+	0.105231i
$31$	0.112693	+	0.112693i	0.0202402	+	0.0202402i	0.717154	−	0.696914i	$-0.245444\pi$
$31$	0.112693	+	0.112693i	0.0202402	+	0.0202402i	−0.696914	+	0.717154i	$0.745444\pi$
$32$	−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	0.801937	−	0.597409i	$-0.203803\pi$
$37$	8.95331	+	0.881825i	1.47192	+	0.144971i	0.669979	+	0.742380i	$0.266303\pi$
$38$	−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	0.283118	+	0.959085i	$0.408631\pi$
$41$	2.48811	+	12.5086i	0.388577	+	1.95351i	0.105459	+	0.994424i	$0.466369\pi$
$42$	−4.97078	−	2.03947i	−0.767007	−	0.314697i
$43$	2.40162	+	1.28369i	0.366244	+	0.195761i	0.644245	−	0.764819i	$-0.277172\pi$
$43$	2.40162	+	1.28369i	0.366244	+	0.195761i	−0.278001	+	0.960581i	$0.589672\pi$
$44$	−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	0.981983	+	0.188968i	$0.0605141\pi$
$47$	2.88785	+	6.97189i	0.421237	+	1.01696i	−0.560747	+	0.827987i	$0.689486\pi$
$48$	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	0.831975	−	0.554813i	$-0.187210\pi$
$53$	−1.22324	−	4.03247i	−0.168024	−	0.553902i	−1.00000		0.000910499i	$0.999710\pi$
$54$	−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	−0.806871	−	0.590728i	$-0.798841\pi$
$59$	−2.95652	+	2.42636i	−0.384907	+	0.315885i	0.421964	+	0.906612i	$0.361341\pi$
$60$	0.835675	+	0.160411i	0.107885	+	0.0207089i
$61$	−2.79625	−	5.23141i	−0.358023	−	0.669814i	0.636845	−	0.770991i	$-0.280239\pi$
$61$	−2.79625	−	5.23141i	−0.358023	−	0.669814i	−0.994868	+	0.101178i	$0.967739\pi$
$62$	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	0.905435	+	0.424486i	$0.139545\pi$
$67$	6.18280	+	11.5672i	0.755349	+	1.41316i	−0.150086	+	0.988673i	$0.547955\pi$
$68$	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	0.413606	−	0.910456i	$-0.364269\pi$
$71$	−4.93625	−	7.38762i	−0.585825	−	0.876750i	−0.999432	+	0.0337061i	$0.989269\pi$
$72$	2.71475	+	0.793794i	0.319937	+	0.0935496i
$73$	8.60941	+	5.75262i	1.00766	+	0.673294i	0.945786	−	0.324790i	$-0.105294\pi$
$73$	8.60941	+	5.75262i	1.00766	+	0.673294i	0.0618694	+	0.998084i	$0.480294\pi$
$74$	−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	0.601977	+	0.798513i	$0.294380\pi$
$79$	−3.45146	+	8.33255i	−0.388319	+	0.937485i	−0.990296	+	0.138972i	$0.955620\pi$
$80$	−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	0.0692910	−	0.997596i	$-0.477926\pi$
$83$	3.02350	−	0.297789i	0.331872	−	0.0326865i	0.262581	+	0.964910i	$0.415426\pi$
$84$	−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	0.453993	−	0.891005i	$-0.349999\pi$
$89$	5.02318	+	0.999172i	0.532456	+	0.105912i	0.0784622	+	0.996917i	$0.474999\pi$
$90$	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	0.981996	−	0.188902i	$-0.0604928\pi$
$97$	7.81107	+	7.81107i	0.793094	+	0.793094i	−0.188902	+	0.981996i	$0.560493\pi$
$98$	−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	−0.994991	−	0.0999655i	$-0.968127\pi$
$101$	0.00385740	−	0.0391648i	0.000383826	−	0.00389705i	0.995375	+	0.0960684i	$0.0306268\pi$
$102$	3.38969	+	2.24852i	0.335630	+	0.222637i
$103$	−1.81125	+	9.10575i	−0.178467	+	0.897216i	0.782942	+	0.622094i	$0.213718\pi$
$103$	−1.81125	+	9.10575i	−0.178467	+	0.897216i	−0.961410	+	0.275121i	$0.911282\pi$
$104$	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	0.414267	+	0.910156i	$0.364038\pi$
$107$	−5.92358	+	11.0822i	−0.572654	+	1.07136i	−0.986921	+	0.161205i	$0.948462\pi$
$108$	0.209371	+	1.98901i	0.0201467	+	0.191393i
$109$	−1.56627	−	15.9026i	−0.150021	−	1.52319i	−0.715609	−	0.698501i	$-0.753851\pi$
$109$	−1.56627	−	15.9026i	−0.150021	−	1.52319i	0.565588	−	0.824688i	$-0.308649\pi$
$110$	−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	0.432472	−	0.901648i	$-0.357642\pi$
$113$	1.07060	+	0.443459i	0.100714	+	0.0417171i	−0.331758	+	0.943365i	$0.607642\pi$
$114$	−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	0.270383	−	0.962753i	$-0.412850\pi$
$131$	13.9761	−	7.47039i	1.22110	−	0.652691i	0.950716	+	0.310062i	$0.100350\pi$
$132$	−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	−0.902062	−	0.431606i	$-0.857947\pi$
$137$	−1.85059	+	2.76960i	−0.158107	+	0.236623i	0.743956	+	0.668229i	$0.232947\pi$
$138$	9.25358	+	9.19176i	0.787717	+	0.782455i
$139$	−9.14388	+	2.77376i	−0.775574	+	0.235268i	−0.653169	−	0.757213i	$-0.726561\pi$
$139$	−9.14388	+	2.77376i	−0.775574	+	0.235268i	−0.122405	+	0.992480i	$0.539061\pi$
$140$	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	0.321535	+	0.946898i	$0.395801\pi$
$149$	−7.86611	+	14.7165i	−0.644417	+	1.20562i	−0.965952	+	0.258722i	$0.916699\pi$
$150$	−6.28752	+	2.62910i	−0.513374	+	0.214665i
$151$	−14.4338	+	2.87105i	−1.17460	+	0.233643i	−0.743548	−	0.668683i	$-0.766858\pi$
$151$	−14.4338	+	2.87105i	−1.17460	+	0.233643i	−0.431055	+	0.902326i	$0.641858\pi$
$152$	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	−0.190971	−	0.981596i	$-0.561164\pi$
$157$	6.42989	−	21.1965i	0.513161	−	1.69166i	0.704132	−	0.710069i	$-0.251336\pi$
$158$	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	0.667543	−	0.744571i	$-0.267346\pi$
$163$	10.3277	+	3.13286i	0.808924	+	0.245384i	0.141381	+	0.989955i	$0.454846\pi$
$164$	−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	0.445475	−	0.895294i	$-0.353035\pi$
$167$	6.64785	+	1.32234i	0.514426	+	0.102326i	0.0689510	+	0.997620i	$0.478035\pi$
$168$	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	0.0615045	−	0.998107i	$-0.480410\pi$
$173$	4.16354	−	0.410073i	0.316548	−	0.0311773i	0.255044	+	0.966930i	$0.417910\pi$
$174$	−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	−0.691796	−	0.722093i	$-0.743180\pi$
$179$	2.02540	−	2.46795i	0.151385	−	0.184463i	0.843181	+	0.537630i	$0.180680\pi$
$180$	0.812617	−	0.252465i	0.0605689	−	0.0188176i
$181$	−1.02539	−	3.38027i	−0.0762169	−	0.251253i	0.910550	−	0.413399i	$-0.135659\pi$
$181$	−1.02539	−	3.38027i	−0.0762169	−	0.251253i	−0.986767	+	0.162146i	$0.948159\pi$
$182$	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	$0.132205\pi$
$191$			11.1529i			0.806993i	−0.914981	+	0.403497i	$0.867795\pi$
$192$	−3.62855	+	7.12977i	−0.261868	+	0.514547i
$193$		−	10.2421i		−	0.737242i	−0.929580	−	0.368621i	$-0.879830\pi$
$193$		−	10.2421i		−	0.737242i	0.929580	−	0.368621i	$-0.120170\pi$
$194$	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	−0.602352	−	0.798231i	$-0.705770\pi$
$197$	0.884643	−	0.726007i	0.0630282	−	0.0517259i	0.665380	+	0.746505i	$0.268270\pi$
$198$	−4.55725	−	0.890626i	−0.323869	−	0.0632940i
$199$	−5.43348	−	8.13178i	−0.385169	−	0.576447i	0.587331	−	0.809347i	$-0.300179\pi$
$199$	−5.43348	−	8.13178i	−0.385169	−	0.576447i	−0.972501	+	0.232900i	$0.925179\pi$
$200$	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	−0.199704	−	0.979856i	$-0.563998\pi$
$211$	−2.96923	+	0.292443i	−0.204410	+	0.0201326i	−0.00470616	+	0.999989i	$0.501498\pi$
$212$	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	−0.519930	+	0.854209i	$0.674042\pi$
$223$	−20.5203	+	20.5203i	−1.37414	+	1.37414i	−0.854209	+	0.519930i	$0.825958\pi$
$224$	−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	−0.919504	−	0.393081i	$-0.871409\pi$
$227$	0.955512	−	3.14990i	0.0634196	−	0.209066i	0.982924	+	0.184014i	$0.0589093\pi$
$228$	0.575046	+	0.567388i	0.0380833	+	0.0375762i
$229$	−1.96159	+	19.9164i	−0.129626	+	1.31611i	0.681750	+	0.731586i	$0.261219\pi$
$229$	−1.96159	+	19.9164i	−0.129626	+	1.31611i	−0.811375	+	0.584526i	$0.801281\pi$
$230$	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	−0.867873	−	0.496787i	$-0.834513\pi$
$233$	−22.5847	+	4.49237i	−1.47957	+	0.294305i	−0.611698	+	0.791092i	$0.709513\pi$
$234$	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	−0.446771	−	0.894648i	$-0.647426\pi$
$239$	−2.01090	+	0.832942i	−0.130074	+	0.0538786i	0.316697	+	0.948527i	$0.397426\pi$
$240$	−1.70171	+	0.0228143i	−0.109845	+	0.00147265i
$241$	−16.9808	−	7.03367i	−1.09383	−	0.453079i	−0.238489	−	0.971145i	$-0.576652\pi$
$241$	−16.9808	−	7.03367i	−1.09383	−	0.453079i	−0.855340	+	0.518067i	$0.826652\pi$
$242$	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	−0.929378	−	0.369129i	$-0.879656\pi$
$251$	−17.5873	−	21.4302i	−1.11010	−	1.35266i	−0.180724	−	0.983534i	$-0.557844\pi$
$252$	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	−0.460446	−	0.887688i	$-0.652311\pi$
$263$	2.97530	−	1.98803i	0.183465	−	0.122587i	0.643911	+	0.765100i	$0.277311\pi$
$264$	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	0.970466	−	0.241239i	$-0.0775538\pi$
$269$	15.1414	+	12.4263i	0.923190	+	0.757643i	−0.0472754	+	0.998882i	$0.515054\pi$
$270$	0.383271	+	0.463838i	0.0233251	+	0.0282283i
$271$	13.7844	+	5.70969i	0.837343	+	0.346839i	0.759805	−	0.650151i	$-0.225294\pi$
$271$	13.7844	+	5.70969i	0.837343	+	0.346839i	0.0775375	+	0.996989i	$0.475294\pi$
$272$	−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	−0.407359	−	0.913268i	$-0.633550\pi$
$277$	9.62504	−	18.0072i	0.578312	−	1.08195i	0.985671	−	0.168678i	$-0.0539499\pi$
$278$	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	−0.807998	−	0.589185i	$-0.799449\pi$
$281$	2.74857	−	13.8180i	0.163966	−	0.824313i	0.971964	−	0.235128i	$-0.0755511\pi$
$282$	5.89933	−	8.89336i	0.351300	−	0.529592i
$283$	−1.92602	+	19.5552i	−0.114490	+	1.16244i	0.750578	+	0.660781i	$0.229775\pi$
$283$	−1.92602	+	19.5552i	−0.114490	+	1.16244i	−0.865068	+	0.501654i	$0.832725\pi$
$284$	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	0.613411	−	0.789764i	$-0.289797\pi$
$293$	18.1607	+	1.78867i	1.06096	+	0.104495i	0.447549	+	0.894259i	$0.352297\pi$
$294$	−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	−0.227911	−	0.973682i	$-0.573190\pi$
$307$	13.5182	−	16.4720i	0.771525	−	0.940106i	0.999436	+	0.0335758i	$0.0106895\pi$
$308$	−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	0.662981	−	0.748637i	$-0.269291\pi$
$311$	3.96866	+	2.65177i	0.225042	+	0.150368i	−0.437938	+	0.899005i	$0.644291\pi$
$312$	−0.640520	−	5.89506i	−0.0362623	−	0.333742i
$313$	7.63271	+	11.4232i	0.431426	+	0.645675i	0.981949	−	0.189145i	$-0.0605716\pi$
$313$	7.63271	+	11.4232i	0.431426	+	0.645675i	−0.550523	+	0.834820i	$0.685572\pi$
$314$	−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	0.657528	−	0.753430i	$-0.271602\pi$
$317$	−5.95078	−	11.1331i	−0.334229	−	0.625299i	−0.991757	+	0.128131i	$0.959102\pi$
$318$	−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	0.874285	−	0.485414i	$-0.161331\pi$
$331$	−2.22574	−	7.33728i	−0.122338	−	0.403294i	−0.996622	+	0.0821199i	$0.973831\pi$
$332$	−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	0.888341	−	0.459184i	$-0.151858\pi$
$337$	−1.18413	−	2.85873i	−0.0645034	−	0.155725i	−0.952844	+	0.303459i	$0.901858\pi$
$338$	−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	0.537473	−	0.843281i	$-0.319379\pi$
$347$	16.7671	+	1.65141i	0.900103	+	0.0886524i	0.362630	+	0.931933i	$0.381879\pi$
$348$	3.76295	+	8.91507i	0.201715	+	0.477898i
$349$	−18.8176	−	5.70826i	−1.00728	−	0.305556i	−0.256814	−	0.966461i	$-0.582673\pi$
$349$	−18.8176	−	5.70826i	−1.00728	−	0.305556i	−0.750470	+	0.660904i	$0.770173\pi$
$350$	−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	0.359542	−	0.933129i	$-0.382933\pi$
$353$	−10.7767	−	10.7767i	−0.573587	−	0.573587i	−0.933129	+	0.359542i	$0.882933\pi$
$354$	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	−0.538890	−	0.842376i	$-0.681156\pi$
$359$	5.33069	−	26.7992i	0.281343	−	1.41441i	0.820233	−	0.572030i	$-0.193844\pi$
$360$	−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	−0.177021	−	0.984207i	$-0.556646\pi$
$367$	7.54307	−	3.12444i	0.393745	−	0.163095i	0.570767	+	0.821112i	$0.306646\pi$
$368$	−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	−0.747481	−	0.664283i	$-0.768737\pi$
$373$	−19.3119	+	5.85820i	−0.999932	+	0.303326i	−0.252451	+	0.967610i	$0.581237\pi$
$374$	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	0.882546	+	0.470225i	$0.155827\pi$
$379$	22.8078	+	27.7914i	1.17156	+	1.42755i	0.289014	+	0.957325i	$0.406673\pi$
$380$	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	0.512775	−	0.858523i	$-0.328617\pi$
$389$	−8.46689	−	10.3169i	−0.429289	−	0.523090i	−0.942064	+	0.335433i	$0.891117\pi$
$390$	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	0.516115	−	0.856520i	$-0.327378\pi$
$397$	−4.44839	−	3.65070i	−0.223258	−	0.183223i	−0.739373	+	0.673296i	$0.764878\pi$
$398$	−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	0.333864	−	0.942621i	$-0.391647\pi$
$401$	24.7604	−	10.2561i	1.23648	−	0.512165i	0.902611	+	0.430456i	$0.141647\pi$
$402$	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	0.824642	+	0.565654i	$0.191376\pi$
$409$	−3.10828	+	15.6264i	−0.153694	+	0.772674i	−0.978337	+	0.207019i	$0.933624\pi$
$410$	−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	−0.518835	−	0.854874i	$-0.673634\pi$
$419$	−29.1726	−	8.84940i	−1.42517	−	0.432322i	−0.906338	+	0.422553i	$0.861134\pi$
$420$	2.97842	−	1.25716i	0.145332	−	0.0613431i
$421$	−18.6229	−	1.83420i	−0.907624	−	0.0893932i	−0.366579	−	0.930387i	$-0.619471\pi$
$421$	−18.6229	−	1.83420i	−0.907624	−	0.0893932i	−0.541045	+	0.840994i	$0.681971\pi$
$422$	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	−0.853985	−	0.520297i	$-0.825821\pi$
$431$	−12.8307	−	30.9760i	−0.618032	−	1.49206i	0.235953	−	0.971764i	$-0.424179\pi$
$432$	−1.21235	−	3.81185i	−0.0583291	−	0.183398i
$433$	8.54133	−	20.6206i	0.410470	−	0.990962i	−0.574542	−	0.818475i	$-0.694820\pi$
$433$	8.54133	−	20.6206i	0.410470	−	0.990962i	0.985012	−	0.172487i	$-0.0551803\pi$
$434$	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	0.0228072	−	0.999740i	$-0.492740\pi$
$439$	−18.6917	−	12.4894i	−0.892104	−	0.596085i	−0.914911	+	0.403655i	$0.867740\pi$
$440$	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	−0.293656	+	0.955911i	$0.594872\pi$
$443$	−27.1196	+	22.2564i	−1.28849	+	1.05744i	−0.994833	+	0.101524i	$0.967628\pi$
$444$	−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	$0.183853\pi$
$449$			23.1394i			1.09201i	−0.837781	+	0.546007i	$0.816147\pi$
$450$	−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	0.735887	−	0.677105i	$-0.236766\pi$
$457$	8.37861	+	5.59841i	0.391935	+	0.261882i	−0.343952	+	0.938987i	$0.611766\pi$
$458$	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	−0.128288	−	0.991737i	$-0.540948\pi$
$461$	18.6673	−	22.7461i	0.869421	−	1.05939i	0.997709	−	0.0676555i	$-0.0215519\pi$
$462$	−17.5622	−	1.67032i	−0.817070	−	0.0777103i
$463$	3.78041	−	9.12672i	0.175691	−	0.424155i	−0.811364	−	0.584542i	$-0.801274\pi$
$463$	3.78041	−	9.12672i	0.175691	−	0.424155i	0.987054	+	0.160387i	$0.0512743\pi$
$464$	−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	−0.345257	−	0.938508i	$-0.612208\pi$
$467$	−10.8221	+	1.06588i	−0.500785	+	0.0493231i	−0.155529	+	0.987831i	$0.549708\pi$
$468$	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	−0.935529	−	0.353250i	$-0.885077\pi$
$479$	−12.7438	+	12.7438i	−0.582279	+	0.582279i	0.353250	+	0.935529i	$0.385077\pi$
$480$	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	0.623044	+	0.782186i	$0.285896\pi$
$487$	−5.55902	+	27.9471i	−0.251903	+	1.26640i	−0.874948	+	0.484217i	$0.839104\pi$
$488$	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	0.291758	−	0.956492i	$-0.405760\pi$
$491$	20.4957	−	38.3448i	0.924960	−	1.73048i	0.633202	−	0.773987i	$-0.281740\pi$
$492$	−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	0.0478305	−	0.998855i	$-0.484769\pi$
$499$	−20.6071	−	16.9118i	−0.922501	−	0.757077i	−0.970331	+	0.241778i	$0.922269\pi$
$500$	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	−0.926214	−	0.376997i	$-0.876957\pi$
$503$	−5.01185	+	7.50076i	−0.223467	+	0.334443i	0.702747	+	0.711440i	$0.251957\pi$
$504$	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	−0.429997	−	0.902831i	$-0.641485\pi$
$509$	1.84518	−	0.986271i	0.0817863	−	0.0437157i	0.511783	+	0.859115i	$0.328985\pi$
$510$	−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	0.0141171	−	0.999900i	$-0.495506\pi$
$521$	21.2848	−	31.8549i	0.932502	−	1.39559i	0.918385	−	0.395688i	$-0.129494\pi$
$522$	−4.82210	+	4.85453i	−0.211058	+	0.212477i
$523$	−35.5978	+	10.7985i	−1.55658	+	0.472184i	−0.947187	−	0.320683i	$-0.896088\pi$
$523$	−35.5978	+	10.7985i	−1.55658	+	0.472184i	−0.609395	+	0.792867i	$0.708588\pi$
$524$	−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	0.827532	+	0.561419i	$0.189744\pi$
$541$	−4.01093	+	13.2223i	−0.172444	+	0.568470i	−0.999975	+	0.00705104i	$0.997756\pi$
$542$	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	−0.225736	−	0.974188i	$-0.572479\pi$
$547$	−22.3276	−	6.77300i	−0.954659	−	0.289593i	−0.728923	+	0.684596i	$0.759979\pi$
$548$	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	0.245435	−	0.969413i	$-0.421069\pi$
$557$	15.9371	−	1.56967i	0.675278	−	0.0665090i	0.429842	+	0.902904i	$0.358569\pi$
$558$	−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	−0.776100	−	0.630610i	$-0.782805\pi$
$563$	−0.147032	+	0.179159i	−0.00619665	+	0.00755064i	0.769903	+	0.638161i	$0.220305\pi$
$564$	−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	−0.992178	−	0.124832i	$-0.960161\pi$
$569$	−17.3612	−	25.9828i	−0.727818	−	1.08926i	0.264360	−	0.964424i	$-0.414839\pi$
$570$	0.238526	+	0.0466154i	0.00999077	+	0.00195250i
$571$	−6.45014	+	5.29349i	−0.269930	+	0.221526i	−0.759614	−	0.650374i	$-0.774612\pi$
$571$	−6.45014	+	5.29349i	−0.269930	+	0.221526i	0.489684	+	0.871900i	$0.337112\pi$
$572$	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	$-0.703397\pi$
$577$		−	38.5629i		−	1.60540i	0.596386	−	0.802698i	$-0.296603\pi$
$578$	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	0.938212	−	0.346062i	$-0.112481\pi$
$587$	−0.827259	−	2.72711i	−0.0341446	−	0.112560i	−0.972356	+	0.233502i	$0.924981\pi$
$588$	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	0.729973	−	0.683476i	$-0.239533\pi$
$593$	−6.56242	−	15.8431i	−0.269486	−	0.650597i	−0.999459	+	0.0328785i	$0.989533\pi$
$594$	−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	−0.750804	−	0.660525i	$-0.770334\pi$
$599$	−7.58522	−	38.1335i	−0.309924	−	1.55809i	0.440880	−	0.897566i	$-0.354666\pi$
$600$	11.2563	−	7.68606i	0.459538	−	0.313782i
$601$	−30.8904	−	6.14449i	−1.26005	−	0.250639i	−0.480507	−	0.876991i	$-0.659547\pi$
$601$	−30.8904	−	6.14449i	−1.26005	−	0.250639i	−0.779540	+	0.626352i	$0.784547\pi$
$602$	−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	−0.171895	−	0.985115i	$-0.554989\pi$
$607$	20.0356	−	20.0356i	0.813220	−	0.813220i	0.985115	+	0.171895i	$0.0549889\pi$
$608$	−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	0.649296	+	0.760535i	$0.275063\pi$
$613$	−3.36465	+	34.1619i	−0.135897	+	1.37979i	−0.785193	+	0.619251i	$0.787437\pi$
$614$	−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	−0.597651	−	0.801757i	$-0.703899\pi$
$617$	−20.9394	+	4.16511i	−0.842989	+	0.167681i	−0.245338	+	0.969438i	$0.578899\pi$
$618$	12.1134	−	5.06516i	0.487272	−	0.203751i
$619$	−4.31236	+	8.06785i	−0.173328	+	0.324274i	−0.953553	−	0.301225i	$-0.902605\pi$
$619$	−4.31236	+	8.06785i	−0.173328	+	0.324274i	0.780225	+	0.625499i	$0.215105\pi$
$620$	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	−0.300435	+	0.953802i	$0.597132\pi$
$631$	−26.7942	+	40.1004i	−1.06666	+	1.59637i	−0.766227	+	0.642570i	$0.777868\pi$
$632$	−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	−0.609259	−	0.792971i	$-0.708533\pi$
$643$	−7.31344	+	3.90911i	−0.288414	+	0.154160i	0.320845	+	0.947132i	$0.396033\pi$
$644$	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	−0.561214	−	0.827671i	$-0.689665\pi$
$647$	−0.287743	+	0.192264i	−0.0113123	+	0.00755867i	0.549901	+	0.835230i	$0.314665\pi$
$648$	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	0.788812	−	0.614635i	$-0.210697\pi$
$653$	8.68517	+	7.12774i	0.339877	+	0.278930i	−0.448935	+	0.893564i	$0.648197\pi$
$654$	−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	0.928697	+	0.370839i	$0.120930\pi$
$659$	2.31531	+	23.5077i	0.0901917	+	0.915731i	−0.838506	+	0.544893i	$0.816570\pi$
$660$	2.77862	−	0.292488i	0.108157	−	0.0113851i
$661$	14.8758	−	27.8307i	0.578602	−	1.08249i	−0.407003	−	0.913427i	$-0.633426\pi$
$661$	14.8758	−	27.8307i	0.578602	−	1.08249i	0.985605	−	0.169062i	$-0.0540738\pi$
$662$	−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	−0.667992	−	0.744169i	$-0.732846\pi$
$673$	1.97620	−	1.97620i	0.0761770	−	0.0761770i	0.744169	+	0.667992i	$0.232846\pi$
$674$	−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	0.516547	−	0.856259i	$-0.327217\pi$
$677$	22.2756	+	2.19396i	0.856121	+	0.0843206i	0.339574	+	0.940579i	$0.389717\pi$
$678$	−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	0.346668	−	0.937988i	$-0.387313\pi$
$683$	−6.28900	−	3.36154i	−0.240642	−	0.128626i	−0.587310	+	0.809362i	$0.699813\pi$
$684$	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	−0.678661	−	0.734452i	$-0.737439\pi$
$691$	4.57599	−	5.57587i	0.174079	−	0.212116i	0.852740	+	0.522336i	$0.174939\pi$
$692$	−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	−0.931501	−	0.363738i	$-0.881500\pi$
$701$	−18.9683	−	35.4872i	−0.716424	−	1.34033i	0.215077	−	0.976597i	$-0.431000\pi$
$702$	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	−0.968246	−	0.249998i	$-0.919570\pi$
$709$	−24.2825	+	19.9281i	−0.911948	+	0.748416i	0.0562986	+	0.998414i	$0.482070\pi$
$710$	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	0.325359	+	0.945591i	$0.394515\pi$
$719$	−15.3736	+	37.1151i	−0.573338	+	1.38416i	−0.898697	+	0.438570i	$0.855485\pi$
$720$	−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	0.903418	+	0.428761i	$0.141050\pi$
$727$	6.27828	+	31.5630i	0.232848	+	1.17061i	−0.670570	+	0.741847i	$0.733950\pi$
$728$	−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	0.952261	−	0.305285i	$-0.0987517\pi$
$733$	42.6261	+	12.9305i	1.57443	+	0.477598i	0.622169	+	0.782883i	$0.286252\pi$
$734$	−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	−0.271541	−	0.962427i	$-0.587533\pi$
$739$	13.2914	−	43.8159i	0.488933	−	1.61180i	0.760474	−	0.649368i	$-0.224967\pi$
$740$	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	−0.999978	−	0.00669844i	$-0.997868\pi$
$743$	−2.00497	+	10.0797i	−0.0735554	+	0.369788i	0.926422	+	0.376486i	$0.122868\pi$
$744$	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	−0.883059	−	0.469262i	$-0.844520\pi$
$751$	−32.2182	+	13.3452i	−1.17566	+	0.486973i	−0.292599	+	0.956235i	$0.594520\pi$
$752$	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	−0.823511	−	0.567301i	$-0.807988\pi$
$757$	−32.8254	+	9.95747i	−1.19306	+	0.361911i	−0.369549	+	0.929211i	$0.620488\pi$
$758$	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	0.342278	−	0.939599i	$-0.388801\pi$
$761$	37.0025	−	24.7243i	1.34134	−	0.896254i	0.999060	+	0.0433450i	$0.0138015\pi$
$762$	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	$-0.311586\pi$
$769$	30.9452			1.11591			0.557956	+	0.829870i	$0.311586\pi$
$770$	0.760733	+	7.46720i	0.0274149	+	0.269099i
$771$	−11.4084	+	6.09789i	−0.410862	+	0.219610i
$772$	4.13084	+	20.0633i	0.148672	+	0.722095i
$773$	8.13468	+	9.91214i	0.292584	+	0.356515i	0.898469	−	0.439038i	$-0.144681\pi$
$773$	8.13468	+	9.91214i	0.292584	+	0.356515i	−0.605884	+	0.795553i	$0.707181\pi$
$774$	−2.15030	−	3.19492i	−0.0772910	−	0.114839i
$775$	0.638576	−	0.426683i	0.0229383	−	0.0153269i
$776$	−14.4507	+	27.7017i	−0.518749	+	0.994433i
$777$	18.9895	−	28.4198i	0.681244	−	1.01955i
$778$	−13.3016	+	13.3911i	−0.476887	+	0.480094i
$779$	4.92963	−	1.49539i	0.176622	−	0.0535778i
$780$	−1.14095	−	1.37141i	−0.0408527	−	0.0491043i
$781$	−22.5512	−	18.5073i	−0.806947	−	0.662244i
$782$	−23.8963	−	28.9195i	−0.854529	−	1.03416i
$783$	−4.47005	−	1.85155i	−0.159746	−	0.0661691i
$784$	−0.398627	−	29.7335i	−0.0142367	−	1.06191i
$785$	−8.70681	+	3.60648i	−0.310759	+	0.128721i
$786$	−19.8005	−	10.4984i	−0.706261	−	0.374466i
$787$	2.70489	+	27.4632i	0.0964189	+	0.978958i	0.914698	+	0.404137i	$0.132428\pi$
$787$	2.70489	+	27.4632i	0.0964189	+	0.978958i	−0.818279	+	0.574821i	$0.805072\pi$
$788$	−1.44012	+	1.77898i	−0.0513023	+	0.0633735i
$789$	1.68683	−	3.15583i	0.0600526	−	0.112351i
$790$	−2.09353	−	5.00670i	−0.0744845	−	0.178131i
$791$	4.31799	−	0.858902i	0.153530	−	0.0305390i
$792$	9.28645	−	0.0933728i	0.329980	−	0.00331786i
$793$	−2.42615	+	12.1971i	−0.0861549	+	0.433130i
$794$	−4.49868	+	6.78184i	−0.159652	+	0.240679i
$795$	−0.175733	+	1.78425i	−0.00623260	+	0.0632807i
$796$	13.9234	+	13.7380i	0.493503	+	0.486931i
$797$	2.80392	−	9.24329i	0.0993200	−	0.327414i	−0.893173	−	0.449712i	$-0.851526\pi$
$797$	2.80392	−	9.24329i	0.0993200	−	0.327414i	0.992493	+	0.122298i	$0.0390265\pi$
$798$	−0.623019	+	2.07888i	−0.0220546	+	0.0735914i
$799$	−15.3479	−	15.3479i	−0.542971	−	0.542971i
$800$	−25.9502	+	8.34924i	−0.917477	+	0.295190i
$801$	3.62151	−	3.62151i	0.127960	−	0.127960i
$802$	−17.9786	−	33.3661i	−0.634847	−	1.17820i
$803$	32.5341	+	9.86911i	1.14810	+	0.348273i
$804$	−24.3018	−	9.87581i	−0.857058	−	0.348293i
$805$	14.8362	+	1.46123i	0.522906	+	0.0515017i
$806$	−0.463127	+	0.0937363i	−0.0163129	+	0.00330172i
$807$	19.2113	+	3.82136i	0.676269	+	0.134518i
$808$	0.108948	−	0.0228122i	0.00383278	−	0.000802531i
$809$	−7.02701	−	35.3272i	−0.247057	−	1.24204i	−0.882656	−	0.470019i	$-0.844247\pi$
$809$	−7.02701	−	35.3272i	−0.247057	−	1.24204i	0.635600	−	0.772019i	$-0.280753\pi$
$810$	0.556666	+	0.228396i	0.0195593	+	0.00802502i
$811$	45.7874	+	24.4739i	1.60781	+	0.859394i	0.997750	+	0.0670418i	$0.0213561\pi$
$811$	45.7874	+	24.4739i	1.60781	+	0.859394i	0.610063	+	0.792353i	$0.291144\pi$
$812$	17.5473	+	32.3059i	0.615789	+	1.13371i
$813$	14.8483	−	1.46243i	0.520752	−	0.0512896i
$814$	−12.2607	−	39.9358i	−0.429737	−	1.39975i
$815$	−1.75720	−	4.24226i	−0.0615520	−	0.148600i
$816$	−3.19186	+	11.0535i	−0.111737	+	0.386949i
$817$	0.420931	−	1.01622i	0.0147265	−	0.0355529i
$818$	22.4307	+	2.13335i	0.784272	+	0.0745910i
$819$	−5.05294	+	6.15703i	−0.176564	+	0.215144i
$820$	−5.05154	+	9.60509i	−0.176408	+	0.335424i
$821$	3.95128	+	13.0256i	0.137901	+	0.454598i	0.998504	−	0.0546781i	$-0.0174133\pi$
$821$	3.95128	+	13.0256i	0.137901	+	0.454598i	−0.860603	+	0.509276i	$0.829913\pi$
$822$	4.71068	−	0.0157877i	0.164304	−	0.000550661i
$823$	13.1380	+	8.77855i	0.457963	+	0.306001i	0.763069	−	0.646317i	$-0.223692\pi$
$823$	13.1380	+	8.77855i	0.457963	+	0.306001i	−0.305106	+	0.952319i	$0.598692\pi$
$824$	−26.1059	+	2.83650i	−0.909441	+	0.0988141i
$825$	−8.79064	−	13.1561i	−0.306051	−	0.458038i
$826$	20.1681	+	3.94147i	0.701739	+	0.137141i
$827$	−42.1018	+	34.5521i	−1.46402	+	1.20149i	−0.528154	+	0.849149i	$0.677116\pi$
$827$	−42.1018	+	34.5521i	−1.46402	+	1.20149i	−0.935870	+	0.352345i	$0.885384\pi$
$828$	3.47719	−	18.1147i	0.120841	−	0.629531i
$829$	7.29868	+	13.6549i	0.253494	+	0.474254i	0.976191	−	0.216911i	$-0.0695981\pi$
$829$	7.29868	+	13.6549i	0.253494	+	0.474254i	−0.722698	+	0.691164i	$0.757098\pi$
$830$	−1.15495	+	1.41697i	−0.0400890	+	0.0491838i
$831$		−	20.4181i		−	0.708297i
$832$	16.7208	+	1.30798i	0.579690	+	0.0453462i
$833$			21.3823i			0.740853i
$834$	10.4746	+	8.53767i	0.362705	+	0.295635i
$835$	−1.35944	−	2.54332i	−0.0470452	−	0.0880154i
$836$	1.48839	+	2.19553i	0.0514771	+	0.0759341i
$837$	0.123196	−	0.101104i	0.00425827	−	0.00349468i
$838$	−8.26910	+	42.3122i	−0.285651	+	1.46165i
$839$	22.1757	+	33.1883i	0.765592	+	1.14579i	0.985402	+	0.170246i	$0.0544563\pi$
$839$	22.1757	+	33.1883i	0.765592	+	1.14579i	−0.219810	+	0.975543i	$0.570544\pi$
$840$	−2.19564	−	4.01025i	−0.0757569	−	0.138367i
$841$	4.64829	+	3.10589i	0.160286	+	0.107100i
$842$	0.0886937	+	26.4640i	0.00305659	+	0.912011i
$843$	−4.08974	−	13.4821i	−0.140858	−	0.464347i
$844$	5.69850	−	1.77042i	0.196151	−	0.0609404i
$845$	−2.32253	+	2.83001i	−0.0798975	+	0.0973554i
$846$	1.01045	−	10.6242i	0.0347400	−	0.365266i
$847$	−0.318610	+	0.769193i	−0.0109476	+	0.0264298i
$848$	−10.8668	−	12.8851i	−0.373169	−	0.442476i
$849$	7.51966	+	18.1541i	0.258074	+	0.623046i
$850$	18.7387	−	5.75299i	0.642734	−	0.197326i
$851$	−82.5740	+	8.13283i	−2.83060	+	0.278790i
$852$	17.0391	+	5.04427i	0.583749	+	0.172814i
$853$	−1.35615	−	0.724879i	−0.0464338	−	0.0248194i	0.448016	−	0.894025i	$-0.352131\pi$
$853$	−1.35615	−	0.724879i	−0.0464338	−	0.0248194i	−0.494450	+	0.869206i	$0.664631\pi$
$854$	−12.0978	+	29.4858i	−0.413979	+	1.00898i
$855$	0.0335271	+	0.168552i	0.00114660	+	0.00576436i
$856$	−34.9271	−	6.58308i	−1.19378	−	0.225005i
$857$	16.5794	+	3.29784i	0.566341	+	0.112652i	0.469953	−	0.882692i	$-0.344271\pi$
$857$	16.5794	+	3.29784i	0.566341	+	0.112652i	0.0963882	+	0.995344i	$0.469271\pi$
$858$	1.93118	+	9.54147i	0.0659295	+	0.325740i
$859$	−16.0897	−	1.58470i	−0.548975	−	0.0540693i	−0.180272	−	0.983617i	$-0.557698\pi$
$859$	−16.0897	−	1.58470i	−0.548975	−	0.0540693i	−0.368703	+	0.929547i	$0.620198\pi$
$860$	0.901096	+	2.13485i	0.0307271	+	0.0727978i
$861$	46.3673	+	14.0654i	1.58019	+	0.479347i
$862$	−41.7420	+	22.4918i	−1.42174	+	0.766073i
$863$	−20.9331	+	20.9331i	−0.712571	+	0.712571i	−0.967072	−	0.254502i	$-0.918089\pi$
$863$	−20.9331	+	20.9331i	−0.712571	+	0.712571i	0.254502	+	0.967072i	$0.418089\pi$
$864$	−5.18924	+	2.25205i	−0.176542	+	0.0766164i
$865$	−1.25866	−	1.25866i	−0.0427958	−	0.0427958i
$866$	−30.2360	−	9.06145i	−1.02746	−	0.307920i
$867$	−2.53333	+	8.35128i	−0.0860365	+	0.283624i
$868$	−1.21095	+	0.00811702i	−0.0411022	+	0.000275510i
$869$	−2.90263	+	29.4709i	−0.0984649	+	0.999731i
$870$	2.42600	+	1.60927i	0.0822493	+	0.0545594i
$871$	5.36446	−	26.9690i	0.181768	−	0.913808i
$872$	41.5804	−	17.7150i	1.40809	−	0.599907i
$873$	10.8343	−	2.15507i	0.366684	−	0.0729381i
$874$	4.86049	−	2.03239i	0.164408	−	0.0687467i
$875$	−7.48189	+	13.9976i	−0.252934	+	0.473206i
$876$	−20.5951	+	2.16792i	−0.695844	+	0.0732473i
$877$	0.589433	+	5.98461i	0.0199037	+	0.202086i	0.999994	+	0.00353239i	$0.00112440\pi$
$877$	0.589433	+	5.98461i	0.0199037	+	0.202086i	−0.980090	+	0.198554i	$0.936376\pi$
$878$	−14.8925	+	28.0880i	−0.502599	+	0.947925i
$879$	16.8595	−	6.98343i	0.568657	−	0.235545i
$880$	−5.49469	−	1.01658i	−0.185226	−	0.0342691i
$881$	−12.1936	−	5.05076i	−0.410813	−	0.170164i	0.167699	−	0.985838i	$-0.446366\pi$
$881$	−12.1936	−	5.05076i	−0.410813	−	0.170164i	−0.578512	+	0.815674i	$0.696366\pi$
$882$	−8.10450	+	6.69677i	−0.272893	+	0.225492i
$883$	−10.1086	−	8.29591i	−0.340181	−	0.279179i	0.448755	−	0.893655i	$-0.351868\pi$
$883$	−10.1086	−	8.29591i	−0.340181	−	0.279179i	−0.788936	+	0.614475i	$0.789368\pi$
$884$	−12.0097	−	1.10162i	−0.403930	−	0.0370516i
$885$	1.55720	−	0.472373i	0.0523448	−	0.0158786i
$886$	35.2004	+	34.9653i	1.18258	+	1.17468i
$887$	−4.71490	+	7.05634i	−0.158311	+	0.236929i	−0.902143	−	0.431438i	$-0.858006\pi$
$887$	−4.71490	+	7.05634i	−0.158311	+	0.236929i	0.743832	+	0.668367i	$0.233006\pi$
$888$	16.3399	+	19.5070i	0.548332	+	0.654611i
$889$	−17.6459	+	11.7906i	−0.591824	+	0.395444i
$890$	−2.55655	+	1.72065i	−0.0856958	+	0.0576764i
$891$	−2.08298	−	2.53812i	−0.0697825	−	0.0850302i
$892$	31.9212	−	48.4736i	1.06880	−	1.62302i
$893$	2.68820	−	1.43687i	0.0899571	−	0.0480831i
$894$	23.4772	−	2.39178i	0.785195	−	0.0799930i
$895$	−1.35836			−0.0454051
$896$	41.4137	+	11.5090i	1.38354	+	0.384490i
$897$	19.3353			0.645587
$898$	32.5555	−	3.31664i	1.08639	−	0.110678i
$899$	0.680045	−	0.363491i	0.0226808	−	0.0121231i
$900$	8.04938	+	5.30073i	0.268313	+	0.176691i
$901$	7.68909	+	9.36918i	0.256161	+	0.312133i
$902$	49.1298	−	33.0662i	1.63584	−	1.10098i
$903$	8.60231	−	5.74788i	0.286267	−	0.191277i
$904$	−0.288452	+	3.26490i	−0.00959376	+	0.108589i
$905$	−0.834968	+	1.24962i	−0.0277553	+	0.0415387i
$906$	14.7658	+	14.6671i	0.490560	+	0.487282i
$907$	5.03913	−	1.52860i	0.167322	−	0.0507565i	−0.205512	−	0.978655i	$-0.565886\pi$
$907$	5.03913	−	1.52860i	0.167322	−	0.0507565i	0.372834	+	0.927898i	$0.378386\pi$
$908$	−0.601345	+	6.55576i	−0.0199563	+	0.217560i
$909$	−0.0304213	−	0.0249661i	−0.00100901	−	0.000828074i
$910$	3.69447	−	3.05275i	0.122470	−	0.101198i
$911$	7.74261	+	3.20709i	0.256524	+	0.106256i	0.507240	−	0.861805i	$-0.330666\pi$
$911$	7.74261	+	3.20709i	0.256524	+	0.106256i	−0.250716	+	0.968061i	$0.580666\pi$
$912$	−1.35530	−	0.879535i	−0.0448786	−	0.0291243i
$913$	9.21612	−	3.81744i	0.305009	−	0.126339i
$914$	6.67564	−	12.5906i	0.220811	−	0.416459i
$915$	0.247375	+	2.51164i	0.00817797	+	0.0830323i
$916$	−4.19009	−	39.8056i	−0.138444	−	1.31521i
$917$	28.3816	−	53.0983i	0.937244	−	1.75346i
$918$	3.75279	−	1.56921i	0.123861	−	0.0517918i
$919$	2.93398	−	0.583605i	0.0967831	−	0.0192514i	−0.146461	−	0.989216i	$-0.546788\pi$
$919$	2.93398	−	0.583605i	0.0967831	−	0.0192514i	0.243244	+	0.969965i	$0.421788\pi$
$920$	−4.14395	+	10.2960i	−0.136622	+	0.339448i
$921$	4.15716	−	20.8994i	0.136983	−	0.688660i
$922$	−34.6779	−	23.0033i	−1.14205	−	0.757572i
$923$	−1.82580	+	18.5376i	−0.0600968	+	0.610173i
$924$	0.167229	+	24.9483i	0.00550144	+	0.820738i
$925$	12.5852	−	41.4878i	0.413798	−	1.36411i
$926$	−13.3825	−	4.01062i	−0.439777	−	0.131797i
$927$	6.56488	+	6.56488i	0.215619	+	0.215619i
$928$	−26.7507	+	5.78864i	−0.878133	+	0.190022i
$929$	−4.23160	+	4.23160i	−0.138834	+	0.138834i	−0.773108	−	0.634274i	$-0.781299\pi$
$929$	−4.23160	+	4.23160i	−0.138834	+	0.138834i	0.634274	+	0.773108i	$0.281299\pi$
$930$	−0.0844188	+	0.0454872i	−0.00276820	+	0.00149158i
$931$	−2.87346	−	0.871655i	−0.0941739	−	0.0285673i
$932$	42.4295	−	17.9090i	1.38982	−	0.586629i
$933$	4.75008	+	0.467843i	0.155511	+	0.0153165i
$934$	3.05078	+	15.0731i	0.0998246	+	0.493208i
$935$	3.94090	+	0.783893i	0.128881	+	0.0256361i
$936$	−3.34380	−	4.89704i	−0.109296	−	0.160065i
$937$	5.95913	+	29.9586i	0.194676	+	0.978703i	0.947323	+	0.320279i	$0.103777\pi$
$937$	5.95913	+	29.9586i	0.194676	+	0.978703i	−0.752647	+	0.658424i	$0.771223\pi$
$938$	26.7495	−	65.1963i	0.873403	−	2.12873i
$939$	12.1163	+	6.47629i	0.395400	+	0.211346i
$940$	−1.82280	+	6.15726i	−0.0594533	+	0.200828i
$941$	37.7501	−	3.71806i	1.23062	−	0.121205i	0.538273	−	0.842771i	$-0.319077\pi$
$941$	37.7501	−	3.71806i	1.23062	−	0.121205i	0.692346	+	0.721565i	$0.256577\pi$
$942$	−29.9457	+	9.19365i	−0.975685	+	0.299545i
$943$	−45.0124	−	108.670i	−1.46581	−	3.53877i
$944$	−7.03026	+	13.5878i	−0.228816	+	0.442244i
$945$	−0.618583	+	1.49339i	−0.0201225	+	0.0485800i
$946$	1.19724	−	12.5881i	0.0389256	−	0.409275i
$947$	−4.54448	+	5.53746i	−0.147676	+	0.179943i	−0.841594	−	0.540110i	$-0.818383\pi$
$947$	−4.54448	+	5.53746i	−0.147676	+	0.179943i	0.693919	+	0.720053i	$0.255883\pi$
$948$	−5.35179	−	17.2260i	−0.173818	−	0.559474i
$949$	−6.30149	−	20.7732i	−0.204555	−	0.674327i
$950$	0.00922571	+	2.75273i	0.000299322	+	0.0893103i
$951$	−10.4962	−	7.01337i	−0.340364	−	0.227424i
$952$	−29.6657	−	8.67425i	−0.961470	−	0.281134i
$953$	−13.6626	−	20.4475i	−0.442575	−	0.662360i	0.541380	−	0.840778i	$-0.317902\pi$
$953$	−13.6626	−	20.4475i	−0.442575	−	0.662360i	−0.983955	+	0.178418i	$0.942902\pi$
$954$	−1.14302	+	5.84874i	−0.0370067	+	0.189360i
$955$	3.66806	−	3.01030i	0.118696	−	0.0974110i
$956$	3.60323	−	2.44270i	0.116537	−	0.0790025i
$957$	−7.48876	−	14.0105i	−0.242077	−	0.452895i
$958$	19.7563	+	16.1030i	0.638296	+	0.520266i
$959$			12.6551i			0.408654i
$960$	3.32430	−	0.731025i	0.107291	−	0.0235937i
$961$		−	30.9746i		−	0.999181i
$962$	−16.8526	+	20.6758i	−0.543348	+	0.666615i
$963$	5.92358	+	11.0822i	0.190885	+	0.357120i
$964$	36.1007	+	6.92965i	1.16272	+	0.223189i
$965$	−3.36851	+	2.76447i	−0.108436	+	0.0889914i
$966$	48.6328	+	9.50433i	1.56473	+	0.305797i
$967$	7.77263	+	11.6326i	0.249951	+	0.374078i	0.935135	−	0.354292i	$-0.115278\pi$
$967$	7.77263	+	11.6326i	0.249951	+	0.374078i	−0.685184	+	0.728370i	$0.740278\pi$
$968$	−0.483063	−	0.388377i	−0.0155262	−	0.0124829i
$969$	0.965989	+	0.645453i	0.0310320	+	0.0207349i
$970$	−6.64665	+	0.0222761i	−0.213411	+	0.000715243i
$971$	−1.96373	−	6.47355i	−0.0630191	−	0.207746i	0.919777	−	0.392443i	$-0.128370\pi$
$971$	−1.96373	−	6.47355i	−0.0630191	−	0.207746i	−0.982796	+	0.184696i	$0.940870\pi$
$972$	1.77012	+	0.930949i	0.0567767	+	0.0298602i
$973$	−23.0302	+	28.0624i	−0.738315	+	0.899639i
$974$	40.1164	+	3.81541i	1.28541	+	0.122254i
$975$	−3.86622	+	9.33388i	−0.123818	+	0.298923i
$976$	−18.5416	−	14.8052i	−0.593503	−	0.473904i
$977$	−11.2731	−	27.2157i	−0.360658	−	0.870706i	−0.995204	−	0.0978209i	$-0.968813\pi$
$977$	−11.2731	−	27.2157i	−0.360658	−	0.870706i	0.634546	−	0.772885i	$-0.281187\pi$
$978$	−4.47946	−	14.5906i	−0.143237	−	0.466555i
$979$	16.7353	−	1.64829i	0.534864	−	0.0526795i
$980$	5.55879	−	3.01931i	0.177569	−	0.0964485i
$981$	−14.0927	−	7.53269i	−0.449944	−	0.240500i
$982$	−56.8863	−	23.3400i	−1.81531	−	0.744810i
$983$	−2.42839	−	12.2083i	−0.0774535	−	0.389385i	−0.999994	−	0.00348462i	$-0.998891\pi$
$983$	−2.42839	−	12.2083i	−0.0774535	−	0.389385i	0.922540	−	0.385900i	$-0.126109\pi$
$984$	−19.7383	+	30.1933i	−0.629235	+	0.962528i
$985$	−0.477552	−	0.0949911i	−0.0152161	−	0.00302667i
$986$	19.2896	−	3.90419i	0.614306	−	0.124335i
$987$	28.5320	+	2.81016i	0.908185	+	0.0894484i
$988$	0.637620	−	1.56902i	0.0202854	−	0.0499171i
$989$	−24.0336	−	7.29052i	−0.764224	−	0.231825i
$990$	0.937141	+	1.73922i	0.0297843	+	0.0552761i
$991$	26.6433	−	26.6433i	0.846351	−	0.846351i	−0.143324	−	0.989676i	$-0.545779\pi$
$991$	26.6433	−	26.6433i	0.846351	−	0.846351i	0.989676	+	0.143324i	$0.0457792\pi$
$992$	0.247211	−	0.866986i	0.00784895	−	0.0275268i
$993$	−5.42170	−	5.42170i	−0.172052	−	0.172052i
$994$	−13.7045	+	45.7289i	−0.434681	+	1.45043i
$995$	−1.20789	+	3.98189i	−0.0382928	+	0.126234i
$996$	−4.26767	+	4.32526i	−0.135226	+	0.137051i
$997$	0.682979	−	6.93440i	0.0216302	−	0.219615i	−0.978293	−	0.207226i	$-0.933556\pi$
$997$	0.682979	−	6.93440i	0.0216302	−	0.219615i	0.999923	−	0.0123887i	$-0.00394355\pi$
$998$	−20.8401	+	31.4168i	−0.659681	+	0.994482i
$999$	1.75516	−	8.82377i	0.0555307	−	0.279172i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	384.2.v.a.229.14	yes	512
128.109	even	32	inner	384.2.v.a.109.14	✓	512

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
384.2.v.a.109.14	✓	512	128.109	even	32	inner
384.2.v.a.229.14	yes	512	1.1	even	1	trivial

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

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more