LMFDB - Embedded newform 384.2.v.a.349.7

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			349.7
Character	$\chi$	$=$	384.349
Dual form			384.2.v.a.373.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.12120 + 0.861919i) q^{2} +(-0.995185 - 0.0980171i) q^{3} +(0.514192 - 1.93277i) q^{4} +(-0.309446 - 0.578933i) q^{5} +(1.20029 - 0.747871i) q^{6} +(0.348403 + 1.75154i) q^{7} +(1.08938 + 2.61022i) q^{8} +(0.980785 + 0.195090i) q^{9} +O(q^{10})$	\(q+(-1.12120 + 0.861919i) q^{2} +(-0.995185 - 0.0980171i) q^{3} +(0.514192 - 1.93277i) q^{4} +(-0.309446 - 0.578933i) q^{5} +(1.20029 - 0.747871i) q^{6} +(0.348403 + 1.75154i) q^{7} +(1.08938 + 2.61022i) q^{8} +(0.980785 + 0.195090i) q^{9} +(0.845945 + 0.382384i) q^{10} +(-4.36582 - 3.58294i) q^{11} +(-0.701160 + 1.87307i) q^{12} +(2.90909 + 1.55494i) q^{13} +(-1.90032 - 1.66354i) q^{14} +(0.251211 + 0.606476i) q^{15} +(-3.47121 - 1.98763i) q^{16} +(1.84909 - 4.46410i) q^{17} +(-1.26781 + 0.626622i) q^{18} +(1.74472 - 0.529256i) q^{19} +(-1.27806 + 0.300406i) q^{20} +(-0.175045 - 1.77726i) q^{21} +(7.98317 + 0.254215i) q^{22} +(3.47326 - 2.32076i) q^{23} +(-0.828288 - 2.70443i) q^{24} +(2.53844 - 3.79905i) q^{25} +(-4.60192 + 0.763996i) q^{26} +(-0.956940 - 0.290285i) q^{27} +(3.56448 + 0.227244i) q^{28} +(-1.30664 - 1.59214i) q^{29} +(-0.804391 - 0.463460i) q^{30} +(4.13304 - 4.13304i) q^{31} +(5.60511 - 0.763369i) q^{32} +(3.99361 + 3.99361i) q^{33} +(1.77449 + 6.59893i) q^{34} +(0.906213 - 0.743710i) q^{35} +(0.881377 - 1.79532i) q^{36} +(0.415677 - 1.37031i) q^{37} +(-1.50001 + 2.09721i) q^{38} +(-2.74267 - 1.83260i) q^{39} +(1.17404 - 1.43840i) q^{40} +(5.11516 + 7.65538i) q^{41} +(1.72811 + 1.84179i) q^{42} +(-1.57554 + 0.155177i) q^{43} +(-9.16986 + 6.59582i) q^{44} +(-0.190556 - 0.628179i) q^{45} +(-1.89392 + 5.59571i) q^{46} +(-0.431738 - 0.178832i) q^{47} +(3.25968 + 2.31830i) q^{48} +(3.52064 - 1.45830i) q^{49} +(0.428363 + 6.44744i) q^{50} +(-2.27775 + 4.26136i) q^{51} +(4.50118 - 4.82307i) q^{52} +(7.00630 - 8.53721i) q^{53} +(1.32313 - 0.499337i) q^{54} +(-0.723293 + 3.63624i) q^{55} +(-4.19237 + 2.81750i) q^{56} +(-1.78820 + 0.355695i) q^{57} +(2.83730 + 0.658898i) q^{58} +(-9.21337 + 4.92465i) q^{59} +(1.30135 - 0.173688i) q^{60} +(1.11029 - 11.2730i) q^{61} +(-1.07163 + 8.19632i) q^{62} +1.78586i q^{63} +(-5.62650 + 5.68704i) q^{64} -2.16534i q^{65} +(-7.91981 - 1.03548i) q^{66} +(0.433064 - 4.39697i) q^{67} +(-7.67731 - 5.86928i) q^{68} +(-3.68401 + 1.96914i) q^{69} +(-0.375031 + 1.61493i) q^{70} +(-7.09985 + 1.41225i) q^{71} +(0.559219 + 2.77259i) q^{72} +(-0.260710 + 1.31068i) q^{73} +(0.715033 + 1.89467i) q^{74} +(-2.89859 + 3.53195i) q^{75} +(-0.125809 - 3.64429i) q^{76} +(4.75459 - 8.89522i) q^{77} +(4.65464 - 0.309251i) q^{78} +(-4.15370 + 1.72052i) q^{79} +(-0.0765507 + 2.62466i) q^{80} +(0.923880 + 0.382683i) q^{81} +(-12.3334 - 4.17438i) q^{82} +(-3.07586 - 10.1398i) q^{83} +(-3.52504 - 0.575529i) q^{84} +(-3.15661 + 0.310899i) q^{85} +(1.63275 - 1.53198i) q^{86} +(1.14429 + 1.71255i) q^{87} +(4.59622 - 15.2989i) q^{88} +(-0.956283 - 0.638968i) q^{89} +(0.755091 + 0.540072i) q^{90} +(-1.71001 + 5.63714i) q^{91} +(-2.69957 - 7.90633i) q^{92} +(-4.51825 + 3.70803i) q^{93} +(0.638205 - 0.171617i) q^{94} +(-0.846302 - 0.846302i) q^{95} +(-5.65294 + 0.210296i) q^{96} +(-12.6937 + 12.6937i) q^{97} +(-2.69042 + 4.66956i) q^{98} +(-3.58294 - 4.36582i) 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 $\left(\mathbb{Z}/384\mathbb{Z}\right)^\times$.

$n$	$127$	$133$	$257$
$\chi(n)$	$1$	$e\left(\frac{11}{32}\right)$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−1.12120	+	0.861919i	−0.792810	+	0.609469i
$2$	−1.12120	+	0.861919i	−0.792810	+	0.609469i
$3$	−0.995185	−	0.0980171i	−0.574570	−	0.0565902i
$3$	−0.995185	−	0.0980171i	−0.574570	−	0.0565902i
$4$	0.514192	−	1.93277i	0.257096	−	0.966386i
$5$	−0.309446	−	0.578933i	−0.138388	−	0.258907i	0.803174	−	0.595744i	$-0.203143\pi$
$5$	−0.309446	−	0.578933i	−0.138388	−	0.258907i	−0.941563	+	0.336837i	$0.890643\pi$
$6$	1.20029	−	0.747871i	0.490015	−	0.305317i
$7$	0.348403	+	1.75154i	0.131684	+	0.662021i	0.989082	+	0.147366i	$0.0470797\pi$
$7$	0.348403	+	1.75154i	0.131684	+	0.662021i	−0.857398	+	0.514654i	$0.827920\pi$
$8$	1.08938	+	2.61022i	0.385154	+	0.922852i
$9$	0.980785	+	0.195090i	0.326928	+	0.0650301i
$10$	0.845945	+	0.382384i	0.267511	+	0.120920i
$11$	−4.36582	−	3.58294i	−1.31634	−	1.08030i	−0.990881	−	0.134741i	$-0.956980\pi$
$11$	−4.36582	−	3.58294i	−1.31634	−	1.08030i	−0.325463	−	0.945555i	$-0.605520\pi$
$12$	−0.701160	+	1.87307i	−0.202408	+	0.540707i
$13$	2.90909	+	1.55494i	0.806837	+	0.431263i	0.822606	−	0.568612i	$-0.192519\pi$
$13$	2.90909	+	1.55494i	0.806837	+	0.431263i	−0.0157685	+	0.999876i	$0.505019\pi$
$14$	−1.90032	−	1.66354i	−0.507881	−	0.444599i
$15$	0.251211	+	0.606476i	0.0648623	+	0.156591i
$16$	−3.47121	−	1.98763i	−0.867804	−	0.496907i
$17$	1.84909	−	4.46410i	0.448471	−	1.08270i	−0.524424	−	0.851457i	$-0.675719\pi$
$17$	1.84909	−	4.46410i	0.448471	−	1.08270i	0.972895	−	0.231247i	$-0.0742806\pi$
$18$	−1.26781	+	0.626622i	−0.298826	+	0.147696i
$19$	1.74472	−	0.529256i	0.400267	−	0.121420i	−0.0837317	−	0.996488i	$-0.526684\pi$
$19$	1.74472	−	0.529256i	0.400267	−	0.121420i	0.483999	+	0.875069i	$0.339184\pi$
$20$	−1.27806	+	0.300406i	−0.285783	+	0.0671729i
$21$	−0.175045	−	1.77726i	−0.0381978	−	0.387829i
$22$	7.98317	+	0.254215i	1.70202	+	0.0541988i
$23$	3.47326	−	2.32076i	0.724224	−	0.483911i	−0.138004	−	0.990432i	$-0.544069\pi$
$23$	3.47326	−	2.32076i	0.724224	−	0.483911i	0.862228	+	0.506520i	$0.169069\pi$
$24$	−0.828288	−	2.70443i	−0.169073	−	0.552039i
$25$	2.53844	−	3.79905i	0.507689	−	0.759810i
$26$	−4.60192	+	0.763996i	−0.902510	+	0.149832i
$27$	−0.956940	−	0.290285i	−0.184163	−	0.0558653i
$28$	3.56448	+	0.227244i	0.673623	+	0.0429450i
$29$	−1.30664	−	1.59214i	−0.242636	−	0.295653i	0.637426	−	0.770512i	$-0.279999\pi$
$29$	−1.30664	−	1.59214i	−0.242636	−	0.295653i	−0.880062	+	0.474859i	$0.842499\pi$
$30$	−0.804391	−	0.463460i	−0.146861	−	0.0846157i
$31$	4.13304	−	4.13304i	0.742316	−	0.742316i	−0.230707	−	0.973023i	$-0.574104\pi$
$31$	4.13304	−	4.13304i	0.742316	−	0.742316i	0.973023	+	0.230707i	$0.0741040\pi$
$32$	5.60511	−	0.763369i	0.990853	−	0.134946i
$33$	3.99361	+	3.99361i	0.695198	+	0.695198i
$34$	1.77449	+	6.59893i	0.304322	+	1.13171i
$35$	0.906213	−	0.743710i	0.153178	−	0.125710i
$36$	0.881377	−	1.79532i	0.146896	−	0.299220i
$37$	0.415677	−	1.37031i	0.0683370	−	0.225277i	−0.916120	−	0.400905i	$-0.868696\pi$
$37$	0.415677	−	1.37031i	0.0683370	−	0.225277i	0.984457	+	0.175628i	$0.0561957\pi$
$38$	−1.50001	+	2.09721i	−0.243334	+	0.340213i
$39$	−2.74267	−	1.83260i	−0.439179	−	0.293450i
$40$	1.17404	−	1.43840i	0.185632	−	0.227431i
$41$	5.11516	+	7.65538i	0.798854	+	1.19557i	0.977350	+	0.211629i	$0.0678767\pi$
$41$	5.11516	+	7.65538i	0.798854	+	1.19557i	−0.178496	+	0.983941i	$0.557123\pi$
$42$	1.72811	+	1.84179i	0.266653	+	0.284195i
$43$	−1.57554	+	0.155177i	−0.240268	+	0.0236643i	−0.217434	−	0.976075i	$-0.569769\pi$
$43$	−1.57554	+	0.155177i	−0.240268	+	0.0236643i	−0.0228337	+	0.999739i	$0.507269\pi$
$44$	−9.16986	+	6.59582i	−1.38241	+	0.994357i
$45$	−0.190556	−	0.628179i	−0.0284064	−	0.0936434i
$46$	−1.89392	+	5.59571i	−0.279244	+	0.825042i
$47$	−0.431738	−	0.178832i	−0.0629755	−	0.0260853i	0.350973	−	0.936385i	$-0.385851\pi$
$47$	−0.431738	−	0.178832i	−0.0629755	−	0.0260853i	−0.413949	+	0.910300i	$0.635851\pi$
$48$	3.25968	+	2.31830i	0.470494	+	0.334617i
$49$	3.52064	−	1.45830i	0.502949	−	0.208328i
$50$	0.428363	+	6.44744i	0.0605796	+	0.911806i
$51$	−2.27775	+	4.26136i	−0.318948	+	0.596710i
$52$	4.50118	−	4.82307i	0.624201	−	0.668840i
$53$	7.00630	−	8.53721i	0.962390	−	1.17268i	−0.0225442	−	0.999746i	$-0.507177\pi$
$53$	7.00630	−	8.53721i	0.962390	−	1.17268i	0.984934	−	0.172930i	$-0.0553233\pi$
$54$	1.32313	−	0.499337i	0.180055	−	0.0679512i
$55$	−0.723293	+	3.63624i	−0.0975289	+	0.490311i
$56$	−4.19237	+	2.81750i	−0.560229	+	0.376505i
$57$	−1.78820	+	0.355695i	−0.236853	+	0.0471130i
$58$	2.83730	+	0.658898i	0.372556	+	0.0865175i
$59$	−9.21337	+	4.92465i	−1.19948	+	0.641135i	−0.945357	−	0.326037i	$-0.894287\pi$
$59$	−9.21337	+	4.92465i	−1.19948	+	0.641135i	−0.254122	+	0.967172i	$0.581787\pi$
$60$	1.30135	−	0.173688i	0.168004	−	0.0224230i
$61$	1.11029	−	11.2730i	0.142159	−	1.44336i	−0.614173	−	0.789171i	$-0.710510\pi$
$61$	1.11029	−	11.2730i	0.142159	−	1.44336i	0.756331	−	0.654189i	$-0.226990\pi$
$62$	−1.07163	+	8.19632i	−0.136097	+	1.04093i
$63$			1.78586i			0.224997i
$64$	−5.62650	+	5.68704i	−0.703313	+	0.710880i
$65$		−	2.16534i		−	0.268577i
$66$	−7.91981	−	1.03548i	−0.974861	−	0.127459i
$67$	0.433064	−	4.39697i	0.0529072	−	0.537176i	−0.931802	−	0.362968i	$-0.881763\pi$
$67$	0.433064	−	4.39697i	0.0529072	−	0.537176i	0.984709	−	0.174208i	$-0.0557365\pi$
$68$	−7.67731	−	5.86928i	−0.931010	−	0.711754i
$69$	−3.68401	+	1.96914i	−0.443502	+	0.237057i
$70$	−0.375031	+	1.61493i	−0.0448248	+	0.193021i
$71$	−7.09985	+	1.41225i	−0.842597	+	0.167603i	−0.597473	−	0.801889i	$-0.703829\pi$
$71$	−7.09985	+	1.41225i	−0.842597	+	0.167603i	−0.245124	+	0.969492i	$0.578829\pi$
$72$	0.559219	+	2.77259i	0.0659046	+	0.326753i
$73$	−0.260710	+	1.31068i	−0.0305139	+	0.153403i	−0.993038	−	0.117791i	$-0.962419\pi$
$73$	−0.260710	+	1.31068i	−0.0305139	+	0.153403i	0.962525	+	0.271195i	$0.0874187\pi$
$74$	0.715033	+	1.89467i	0.0831209	+	0.220251i
$75$	−2.89859	+	3.53195i	−0.334701	+	0.407834i
$76$	−0.125809	−	3.64429i	−0.0144313	−	0.418029i
$77$	4.75459	−	8.89522i	0.541836	−	1.01370i
$78$	4.65464	−	0.309251i	0.527034	−	0.0350157i
$79$	−4.15370	+	1.72052i	−0.467327	+	0.193573i	−0.603905	−	0.797056i	$-0.706390\pi$
$79$	−4.15370	+	1.72052i	−0.467327	+	0.193573i	0.136578	+	0.990629i	$0.456390\pi$
$80$	−0.0765507	+	2.62466i	−0.00855863	+	0.293446i
$81$	0.923880	+	0.382683i	0.102653	+	0.0425204i
$82$	−12.3334	−	4.17438i	−1.36200	−	0.460983i
$83$	−3.07586	−	10.1398i	−0.337620	−	1.11298i	−0.947303	−	0.320338i	$-0.896203\pi$
$83$	−3.07586	−	10.1398i	−0.337620	−	1.11298i	0.609684	−	0.792645i	$-0.291297\pi$
$84$	−3.52504	−	0.575529i	−0.384613	−	0.0627954i
$85$	−3.15661	+	0.310899i	−0.342382	+	0.0337217i
$86$	1.63275	−	1.53198i	0.176064	−	0.165197i
$87$	1.14429	+	1.71255i	0.122680	+	0.183604i
$88$	4.59622	−	15.2989i	0.489958	−	1.63087i
$89$	−0.956283	−	0.638968i	−0.101366	−	0.0677304i	0.503854	−	0.863789i	$-0.331915\pi$
$89$	−0.956283	−	0.638968i	−0.101366	−	0.0677304i	−0.605220	+	0.796058i	$0.706915\pi$
$90$	0.755091	+	0.540072i	0.0795936	+	0.0569286i
$91$	−1.71001	+	5.63714i	−0.179258	+	0.590933i
$92$	−2.69957	−	7.90633i	−0.281450	−	0.824292i
$93$	−4.51825	+	3.70803i	−0.468520	+	0.384505i
$94$	0.638205	−	0.171617i	0.0658258	−	0.0177009i
$95$	−0.846302	−	0.846302i	−0.0868288	−	0.0868288i
$96$	−5.65294	+	0.210296i	−0.576951	+	0.0214633i
$97$	−12.6937	+	12.6937i	−1.28885	+	1.28885i	−0.353363	+	0.935486i	$0.614962\pi$
$97$	−12.6937	+	12.6937i	−1.28885	+	1.28885i	−0.935486	+	0.353363i	$0.885038\pi$
$98$	−2.69042	+	4.66956i	−0.271774	+	0.471697i
$99$	−3.58294	−	4.36582i	−0.360099	−	0.438781i
$100$	−6.03745	−	6.85967i	−0.603745	−	0.685967i
$101$	17.3749	+	5.27063i	1.72887	+	0.524447i	0.988950	−	0.148247i	$-0.0473631\pi$
$101$	17.3749	+	5.27063i	1.72887	+	0.524447i	0.739920	+	0.672694i	$0.234863\pi$
$102$	−1.11913	−	6.74109i	−0.110811	−	0.667467i
$103$	−1.82135	+	2.72585i	−0.179463	+	0.268586i	−0.910285	−	0.413983i	$-0.864137\pi$
$103$	−1.82135	+	2.72585i	−0.179463	+	0.268586i	0.730821	+	0.682569i	$0.239137\pi$
$104$	−0.889637	+	9.28730i	−0.0872360	+	0.910694i
$105$	−0.974746	+	0.651304i	−0.0951254	+	0.0635608i
$106$	−0.497108	+	15.6108i	−0.0482834	+	1.51626i
$107$	1.45556	+	14.7786i	0.140714	+	1.42870i	0.763249	+	0.646105i	$0.223603\pi$
$107$	1.45556	+	14.7786i	0.140714	+	1.42870i	−0.622534	+	0.782593i	$0.713897\pi$
$108$	−1.05310	+	1.70029i	−0.101335	+	0.163610i
$109$	−15.0863	+	4.57639i	−1.44501	+	0.438339i	−0.912847	−	0.408303i	$-0.866121\pi$
$109$	−15.0863	+	4.57639i	−1.44501	+	0.438339i	−0.532163	+	0.846642i	$0.678621\pi$
$110$	−2.32319	−	4.70038i	−0.221507	−	0.448164i
$111$	−0.547989	+	1.32296i	−0.0520128	+	0.125570i
$112$	2.27203	−	6.77247i	0.214687	−	0.639939i
$113$	−1.34775	−	3.25375i	−0.126785	−	0.306087i	0.847723	−	0.530440i	$-0.177973\pi$
$113$	−1.34775	−	3.25375i	−0.126785	−	0.306087i	−0.974508	+	0.224353i	$0.927973\pi$
$114$	1.69835	−	1.94009i	0.159065	−	0.181706i
$115$	−2.41835	−	1.29263i	−0.225512	−	0.120539i
$116$	−3.74910	+	1.70676i	−0.348096	+	0.158469i
$117$	2.54984	+	2.09260i	0.235733	+	0.193461i
$118$	6.08541	−	13.4627i	0.560208	−	1.23934i
$119$	8.46329	+	1.68345i	0.775829	+	0.154322i
$120$	−1.30937	+	1.31640i	−0.119529	+	0.120170i
$121$	4.07696	+	20.4963i	0.370633	+	1.86330i
$122$	8.47155	+	13.5963i	0.766978	+	1.23095i
$123$	−4.34017	−	8.11989i	−0.391340	−	0.732146i
$124$	−5.86305	−	10.1134i	−0.526517	−	0.908210i
$125$	−6.25133	−	0.615702i	−0.559136	−	0.0550701i
$126$	−1.53926	−	2.00231i	−0.137128	−	0.178380i
$127$	18.1979			1.61480			0.807402	−	0.590002i	$-0.200873\pi$
$127$	18.1979			1.61480			0.807402	+	0.590002i	$0.200873\pi$
$128$	1.40668	−	11.2259i	0.124334	−	0.992240i
$129$	1.58317			0.139390
$130$	1.86635	+	2.42779i	0.163690	+	0.212931i
$131$	1.85702	+	0.182900i	0.162248	+	0.0159801i	0.178815	−	0.983883i	$-0.442774\pi$
$131$	1.85702	+	0.182900i	0.162248	+	0.0159801i	−0.0165668	+	0.999863i	$0.505274\pi$
$132$	9.77221	−	5.66525i	0.850562	−	0.493097i
$133$	1.53488	+	2.87156i	0.133091	+	0.248996i
$134$	3.30428	+	5.30317i	0.285446	+	0.458124i
$135$	0.128066	+	0.643832i	0.0110222	+	0.0554122i
$136$	13.6667	−	0.0365647i	1.17191	−	0.00313540i
$137$	−4.47928	−	0.890985i	−0.382691	−	0.0761220i	−3.91458e−6	−	1.00000i	$-0.500001\pi$
$137$	−4.47928	−	0.890985i	−0.382691	−	0.0761220i	−0.382687	+	0.923878i	$0.625001\pi$
$138$	2.43328	−	5.38312i	0.207134	−	0.458242i
$139$	−4.73339	−	3.88459i	−0.401481	−	0.329487i	0.411889	−	0.911234i	$-0.364869\pi$
$139$	−4.73339	−	3.88459i	−0.401481	−	0.329487i	−0.813370	+	0.581747i	$0.802369\pi$
$140$	−0.971454	−	2.13391i	−0.0821029	−	0.180348i
$141$	0.412131	+	0.220289i	0.0347077	+	0.0185516i
$142$	6.74313	−	7.70291i	0.565871	−	0.646414i
$143$	−7.12931	−	17.2117i	−0.596183	−	1.43931i
$144$	−3.01675	−	2.62664i	−0.251396	−	0.218887i
$145$	−0.517409	+	1.24914i	−0.0429685	+	0.103735i
$146$	−0.837391	−	1.69425i	−0.0693029	−	0.140217i
$147$	−3.64663	+	1.10619i	−0.300769	+	0.0912372i
$148$	−2.43475	−	1.50801i	−0.200135	−	0.123958i
$149$	1.20198	+	12.2040i	0.0984704	+	0.999787i	0.909758	+	0.415139i	$0.136267\pi$
$149$	1.20198	+	12.2040i	0.0984704	+	0.999787i	−0.811287	+	0.584647i	$0.801233\pi$
$150$	0.205660	−	6.45838i	0.0167921	−	0.527325i
$151$	−2.46077	+	1.64423i	−0.200255	+	0.133806i	−0.651655	−	0.758516i	$-0.725925\pi$
$151$	−2.46077	+	1.64423i	−0.200255	+	0.133806i	0.451400	+	0.892322i	$0.350925\pi$
$152$	3.28214	+	3.97755i	0.266217	+	0.322622i
$153$	2.68447	−	4.01759i	0.217026	−	0.324803i
$154$	2.33609	+	14.0714i	0.188248	+	1.13391i
$155$	−3.67171	−	1.11380i	−0.294918	−	0.0894625i
$156$	−4.95225	+	4.35866i	−0.396497	+	0.348972i
$157$	−9.73158	−	11.8580i	−0.776664	−	0.946368i	0.222930	−	0.974834i	$-0.428438\pi$
$157$	−9.73158	−	11.8580i	−0.776664	−	0.946368i	−0.999595	+	0.0284661i	$0.990938\pi$
$158$	3.17419	−	5.50920i	0.252525	−	0.438288i
$159$	−7.80936	+	7.80936i	−0.619323	+	0.619323i
$160$	−2.17642	−	3.00876i	−0.172061	−	0.237863i
$161$	5.27500	+	5.27500i	0.415728	+	0.415728i
$162$	−1.36570	+	0.367244i	−0.107299	+	0.0288534i
$163$	14.3152	−	11.7482i	1.12126	−	0.920191i	0.123860	−	0.992300i	$-0.460473\pi$
$163$	14.3152	−	11.7482i	1.12126	−	0.920191i	0.997397	+	0.0721084i	$0.0229728\pi$
$164$	17.4263	−	5.95011i	1.36076	−	0.464625i
$165$	1.07622	−	3.54784i	0.0837840	−	0.276199i
$166$	12.1883	+	8.71758i	0.945997	+	0.676616i
$167$	15.2580	+	10.1951i	1.18070	+	0.788920i	0.981579	−	0.191054i	$-0.0611907\pi$
$167$	15.2580	+	10.1951i	1.18070	+	0.788920i	0.199123	+	0.979975i	$0.436191\pi$
$168$	4.44834	−	2.39301i	0.343197	−	0.184625i
$169$	−1.17744	−	1.76216i	−0.0905722	−	0.135551i
$170$	3.27123	−	3.06932i	0.250892	−	0.235406i
$171$	1.81445	−	0.178708i	0.138755	−	0.0136661i
$172$	−0.510208	+	3.12496i	−0.0389030	+	0.238276i
$173$	−1.88658	−	6.21923i	−0.143434	−	0.472839i	0.855559	−	0.517706i	$-0.173214\pi$
$173$	−1.88658	−	6.21923i	−0.143434	−	0.472839i	−0.998993	+	0.0448666i	$0.985714\pi$
$174$	−2.75905	−	0.933829i	−0.209163	−	0.0707934i
$175$	7.53860	+	3.12259i	0.569864	+	0.236046i
$176$	8.03314	+	21.1148i	0.605521	+	1.59159i
$177$	9.65171	−	3.99787i	0.725467	−	0.300498i
$178$	1.62293	−	0.107826i	0.121643	−	0.00808189i
$179$	−6.60521	+	12.3575i	−0.493696	+	0.923641i	0.504489	+	0.863418i	$0.331681\pi$
$179$	−6.60521	+	12.3575i	−0.493696	+	0.923641i	−0.998185	+	0.0602227i	$0.980819\pi$
$180$	−1.31211	+	0.0452970i	−0.0977988	+	0.00337624i
$181$	−7.51956	+	9.16261i	−0.558925	+	0.681052i	−0.973427	−	0.228996i	$-0.926456\pi$
$181$	−7.51956	+	9.16261i	−0.558925	+	0.681052i	0.414503	+	0.910048i	$0.363956\pi$
$182$	−2.94149	−	7.79427i	−0.218038	−	0.577750i
$183$	−2.20989	+	11.1099i	−0.163360	+	0.821267i
$184$	9.84138	+	6.53778i	0.725516	+	0.481972i
$185$	−0.921944	+	0.183386i	−0.0677827	+	0.0134828i
$186$	1.86985	−	8.05182i	0.137104	−	0.590388i
$187$	−24.0674	+	12.8643i	−1.75998	+	0.940730i
$188$	−0.567638	+	0.742498i	−0.0413992	+	0.0541522i
$189$	0.175045	−	1.77726i	0.0127326	−	0.129276i
$190$	1.67832	+	0.219432i	0.121758	+	0.0159193i
$191$		−	10.6900i		−	0.773499i	−0.922185	−	0.386750i	$-0.873598\pi$
$191$		−	10.6900i		−	0.773499i	0.922185	−	0.386750i	$-0.126402\pi$
$192$	6.15684	−	5.10816i	0.444332	−	0.368650i
$193$			9.90954i			0.713304i	0.934237	+	0.356652i	$0.116082\pi$
$193$			9.90954i			0.713304i	−0.934237	+	0.356652i	$0.883918\pi$
$194$	3.29127	−	25.1731i	0.236299	−	1.80733i
$195$	−0.212240	+	2.15491i	−0.0151989	+	0.154317i
$196$	−1.00827	−	7.55445i	−0.0720195	−	0.539603i
$197$	16.3320	−	8.72961i	1.16360	−	0.621959i	0.227533	−	0.973770i	$-0.426934\pi$
$197$	16.3320	−	8.72961i	1.16360	−	0.621959i	0.936071	+	0.351812i	$0.114434\pi$
$198$	7.78018	+	1.80677i	0.552913	+	0.128401i
$199$	11.2942	−	2.24655i	0.800624	−	0.159254i	0.222212	−	0.974998i	$-0.428672\pi$
$199$	11.2942	−	2.24655i	0.800624	−	0.159254i	0.578412	+	0.815744i	$0.303672\pi$
$200$	12.6817	+	2.48729i	0.896731	+	0.175878i
$201$	−0.861958	+	4.33335i	−0.0607978	+	0.305651i
$202$	−24.0237	+	9.06634i	−1.69030	+	0.637906i
$203$	2.33346	−	2.84333i	0.163777	−	0.199563i
$204$	7.06505	+	6.59352i	0.494652	+	0.461639i
$205$	2.84908	−	5.33026i	0.198989	−	0.372282i
$206$	−0.307353	−	4.62609i	−0.0214143	−	0.322315i
$207$	3.85928	−	1.59857i	0.268238	−	0.111108i
$208$	−7.00743	−	11.1797i	−0.485878	−	0.775175i
$209$	−9.51344	−	3.94060i	−0.658059	−	0.272577i
$210$	0.531516	−	1.57040i	0.0366781	−	0.108368i
$211$	4.49890	+	14.8309i	0.309717	+	1.02100i	0.964256	+	0.264972i	$0.0853628\pi$
$211$	4.49890	+	14.8309i	0.309717	+	1.02100i	−0.654539	+	0.756028i	$0.727137\pi$
$212$	−12.8979	−	17.9313i	−0.885831	−	1.23153i
$213$	7.20409	−	0.709541i	0.493616	−	0.0486169i
$214$	−14.3699	−	15.3152i	−0.982306	−	1.04692i
$215$	0.577383	+	0.864115i	0.0393772	+	0.0589321i
$216$	−0.284764	−	2.81406i	−0.0193758	−	0.191472i
$217$	8.67916	+	5.79923i	0.589180	+	0.393677i
$218$	12.9704	−	18.1343i	0.878465	−	1.22821i
$219$	0.387924	−	1.27881i	0.0262135	−	0.0864143i
$220$	6.65611	+	3.26769i	0.448755	+	0.220307i
$221$	12.3206	−	10.1113i	0.828774	−	0.680157i
$222$	−0.525880	−	1.95563i	−0.0352947	−	0.131253i
$223$	3.89198	+	3.89198i	0.260626	+	0.260626i	0.825308	−	0.564682i	$-0.191001\pi$
$223$	3.89198	+	3.89198i	0.260626	+	0.260626i	−0.564682	+	0.825308i	$0.691001\pi$
$224$	3.28991	+	9.55162i	0.219816	+	0.638195i
$225$	3.23083	−	3.23083i	0.215388	−	0.215388i
$226$	4.31557	+	2.48646i	0.287067	+	0.165397i
$227$	13.9367	+	16.9819i	0.925010	+	1.12713i	0.991599	+	0.129348i	$0.0412883\pi$
$227$	13.9367	+	16.9819i	0.925010	+	1.12713i	−0.0665892	+	0.997780i	$0.521212\pi$
$228$	−0.232000	+	3.63908i	−0.0153646	+	0.241004i
$229$	−5.00438	−	1.51806i	−0.330699	−	0.100316i	0.120569	−	0.992705i	$-0.461528\pi$
$229$	−5.00438	−	1.51806i	−0.330699	−	0.100316i	−0.451268	+	0.892389i	$0.649028\pi$
$230$	3.82560	−	0.635115i	0.252253	−	0.0418783i
$231$	−5.60358	+	8.38636i	−0.368689	+	0.551782i
$232$	2.73241	−	5.14505i	0.179392	−	0.337789i
$233$	−17.7710	+	11.8742i	−1.16422	+	0.777906i	−0.978813	−	0.204756i	$-0.934360\pi$
$233$	−17.7710	+	11.8742i	−1.16422	+	0.777906i	−0.185406	+	0.982662i	$0.559360\pi$
$234$	−4.66254	−	0.148473i	−0.304800	−	0.00970600i
$235$	0.0300681	+	0.305286i	0.00196143	+	0.0199147i
$236$	4.78079	+	20.3396i	0.311203	+	1.32399i
$237$	4.30234	−	1.30510i	0.279467	−	0.0847753i
$238$	−10.9401	+	5.40718i	−0.709139	+	0.350495i
$239$	11.6236	−	28.0619i	0.751869	−	1.81517i	0.203187	−	0.979140i	$-0.434870\pi$
$239$	11.6236	−	28.0619i	0.751869	−	1.81517i	0.548682	−	0.836031i	$-0.315130\pi$
$240$	0.333444	−	2.60452i	0.0215237	−	0.168121i
$241$	−8.54527	−	20.6301i	−0.550449	−	1.32890i	−0.917142	−	0.398560i	$-0.869510\pi$
$241$	−8.54527	−	20.6301i	−0.550449	−	1.32890i	0.366693	−	0.930342i	$-0.380490\pi$
$242$	−22.2372	−	19.4665i	−1.42946	−	1.25135i
$243$	−0.881921	−	0.471397i	−0.0565753	−	0.0302401i
$244$	−21.2172	−	7.94243i	−1.35829	−	0.508462i
$245$	−1.93371	−	1.58695i	−0.123540	−	0.101387i
$246$	11.8649	+	5.36317i	0.756478	+	0.341943i
$247$	5.89853	+	1.17329i	0.375314	+	0.0746547i
$248$	15.2906	+	6.28570i	0.970954	+	0.399142i
$249$	2.06718	+	10.3924i	0.131002	+	0.658593i
$250$	7.53969	−	4.69781i	0.476852	−	0.297116i
$251$	−5.85765	−	10.9589i	−0.369731	−	0.691719i	0.626409	−	0.779495i	$-0.284524\pi$
$251$	−5.85765	−	10.9589i	−0.369731	−	0.691719i	−0.996140	+	0.0877759i	$0.972024\pi$
$252$	3.45165	+	0.918272i	0.217434	+	0.0578457i
$253$	−23.4787	−	2.31245i	−1.47610	−	0.145383i
$254$	−20.4035	+	15.6851i	−1.28023	+	0.984172i
$255$	3.17188			0.198631
$256$	8.09865	+	13.7990i	0.506166	+	0.862436i
$257$	10.1005			0.630053			0.315027	−	0.949083i	$-0.397987\pi$
$257$	10.1005			0.630053			0.315027	+	0.949083i	$0.397987\pi$
$258$	−1.77505	+	1.36456i	−0.110510	+	0.0849539i
$259$	2.54497	+	0.250658i	0.158137	+	0.0155751i
$260$	−4.18511	−	1.11340i	−0.259549	−	0.0690501i
$261$	−0.970918	−	1.81646i	−0.0600983	−	0.112436i
$262$	−2.23974	+	1.39553i	−0.138371	+	0.0862161i
$263$	−1.87812	−	9.44193i	−0.115810	−	0.582214i	−0.994492	−	0.104808i	$-0.966577\pi$
$263$	−1.87812	−	9.44193i	−0.115810	−	0.582214i	0.878683	−	0.477406i	$-0.158423\pi$
$264$	−6.07364	+	14.7748i	−0.373807	+	0.909323i
$265$	−7.11054	−	1.41437i	−0.436797	−	0.0868844i
$266$	−4.19597	−	1.89666i	−0.257271	−	0.116292i
$267$	0.889048	+	0.729623i	0.0544089	+	0.0446522i
$268$	−8.27567	−	3.09790i	−0.505517	−	0.189234i
$269$	9.55295	+	5.10616i	0.582454	+	0.311328i	0.736180	−	0.676785i	$-0.236627\pi$
$269$	9.55295	+	5.10616i	0.582454	+	0.311328i	−0.153727	+	0.988113i	$0.549127\pi$
$270$	−0.698519	−	0.611483i	−0.0425105	−	0.0372137i
$271$	−8.20977	−	19.8201i	−0.498708	−	1.20399i	−0.950180	−	0.311702i	$-0.899101\pi$
$271$	−8.20977	−	19.8201i	−0.498708	−	1.20399i	0.451472	−	0.892285i	$-0.350899\pi$
$272$	−15.2916	+	11.8205i	−0.927188	+	0.716726i
$273$	2.25431	−	5.44239i	0.136437	−	0.329388i
$274$	5.79014	−	2.86180i	0.349795	−	0.172888i
$275$	−24.6941	+	7.49089i	−1.48911	+	0.451717i
$276$	1.91162	+	8.13286i	0.115066	+	0.489541i
$277$	0.593719	+	6.02813i	0.0356731	+	0.362195i	0.996405	+	0.0847171i	$0.0269987\pi$
$277$	0.593719	+	6.02813i	0.0356731	+	0.362195i	−0.960732	+	0.277478i	$0.910501\pi$
$278$	8.65530	+	0.275618i	0.519110	+	0.0165305i
$279$	4.85994	−	3.24731i	0.290957	−	0.194411i
$280$	2.92846	+	1.55523i	0.175009	+	0.0929430i
$281$	−12.3179	+	18.4350i	−0.734823	+	1.09974i	0.256275	+	0.966604i	$0.417505\pi$
$281$	−12.3179	+	18.4350i	−0.734823	+	1.09974i	−0.991098	+	0.133136i	$0.957495\pi$
$282$	−0.651953	+	0.108235i	−0.0388232	+	0.00644532i
$283$	5.01999	+	1.52280i	0.298408	+	0.0905209i	0.435938	−	0.899977i	$-0.356417\pi$
$283$	5.01999	+	1.52280i	0.298408	+	0.0905209i	−0.137531	+	0.990498i	$0.543917\pi$
$284$	−0.921130	+	14.4486i	−0.0546590	+	0.857364i
$285$	0.759275	+	0.925179i	0.0449756	+	0.0548029i
$286$	22.8285	+	13.1529i	1.34988	+	0.777747i
$287$	−11.6266	+	11.6266i	−0.686295	+	0.686295i
$288$	5.64634	+	0.344802i	0.332714	+	0.0203176i
$289$	−4.48826	−	4.48826i	−0.264015	−	0.264015i
$290$	−0.496533	−	1.84650i	−0.0291574	−	0.108430i
$291$	13.8768	−	11.3884i	0.813471	−	0.667598i
$292$	2.39919	+	1.17783i	0.140402	+	0.0689275i
$293$	4.02108	−	13.2557i	0.234914	−	0.774408i	−0.757647	−	0.652664i	$-0.773651\pi$
$293$	4.02108	−	13.2557i	0.234914	−	0.774408i	0.992562	−	0.121744i	$-0.0388487\pi$
$294$	3.13516	−	4.38336i	0.182846	−	0.255643i
$295$	5.70208	+	3.81001i	0.331988	+	0.221827i
$296$	4.02963	−	0.407772i	0.234217	−	0.0237013i
$297$	3.13776	+	4.69599i	0.182071	+	0.272489i
$298$	−11.8665	−	12.6471i	−0.687407	−	0.732626i
$299$	13.7127	−	1.35058i	0.793024	−	0.0781061i
$300$	5.33601	+	7.41842i	0.308075	+	0.428303i
$301$	−0.820724	−	2.70557i	−0.0473058	−	0.155946i
$302$	1.34183	−	3.96450i	0.0772134	−	0.228131i
$303$	−16.7747	−	6.94829i	−0.963679	−	0.399169i
$304$	−7.10828	−	1.63070i	−0.407688	−	0.0935273i
$305$	−6.86989	+	2.84560i	−0.393369	+	0.162939i
$306$	0.453004	+	6.81832i	0.0258965	+	0.389777i
$307$	13.0491	−	24.4132i	0.744753	−	1.39334i	−0.168400	−	0.985719i	$-0.553860\pi$
$307$	13.0491	−	24.4132i	0.744753	−	1.39334i	0.913153	−	0.407617i	$-0.133640\pi$
$308$	−14.7477	−	13.7634i	−0.840326	−	0.784242i
$309$	2.07976	−	2.53420i	0.118314	−	0.144166i
$310$	5.07673	−	1.91592i	0.288339	−	0.108817i
$311$	4.44946	−	22.3690i	0.252306	−	1.26843i	−0.621987	−	0.783028i	$-0.713674\pi$
$311$	4.44946	−	22.3690i	0.252306	−	1.26843i	0.874293	−	0.485399i	$-0.161326\pi$
$312$	1.79567	−	9.15538i	0.101660	−	0.518321i
$313$	−15.7720	+	3.13725i	−0.891487	+	0.177328i	−0.619522	−	0.784979i	$-0.712673\pi$
$313$	−15.7720	+	3.13725i	−0.891487	+	0.177328i	−0.271965	+	0.962307i	$0.587673\pi$
$314$	21.1317	+	4.90735i	1.19253	+	0.276938i
$315$	1.03389	−	0.552626i	0.0582532	−	0.0311370i
$316$	1.18957	+	8.91282i	0.0669187	+	0.501386i
$317$	−2.56558	+	26.0488i	−0.144097	+	1.46304i	0.602687	+	0.797978i	$0.294097\pi$
$317$	−2.56558	+	26.0488i	−0.144097	+	1.46304i	−0.746784	+	0.665066i	$0.768403\pi$
$318$	2.02484	−	15.4869i	0.113547	−	0.868463i
$319$			11.6326i			0.651300i
$320$	5.03352	+	1.49754i	0.281382	+	0.0837148i
$321$		−	14.8501i		−	0.828850i
$322$	−10.4610	−	1.36772i	−0.582967	−	0.0762201i
$323$	0.863501	−	8.76727i	0.0480465	−	0.487824i
$324$	1.21469	−	1.58888i	0.0674828	−	0.0882709i
$325$	13.2919	−	7.10466i	0.737301	−	0.394095i
$326$	−5.92428	+	25.5107i	−0.328116	+	1.41291i
$327$	15.4623	−	3.07564i	0.855065	−	0.170083i
$328$	−14.4099	+	21.6913i	−0.795652	+	1.19770i
$329$	0.162812	−	0.818513i	0.00897614	−	0.0451261i
$330$	1.85128	+	4.90546i	0.101910	+	0.270037i
$331$	−5.24205	+	6.38746i	−0.288129	+	0.351087i	−0.896879	−	0.442276i	$-0.854171\pi$
$331$	−5.24205	+	6.38746i	−0.288129	+	0.351087i	0.608750	+	0.793362i	$0.291671\pi$
$332$	−21.1794	+	0.731162i	−1.16237	+	0.0401277i
$333$	0.675024	−	1.26288i	0.0369911	−	0.0692054i
$334$	−25.8947	+	1.72042i	−1.41689	+	0.0941373i
$335$	−2.67956	+	1.10991i	−0.146400	+	0.0606409i
$336$	−2.92491	+	6.51716i	−0.159567	+	0.355540i
$337$	−6.92907	−	2.87011i	−0.377450	−	0.156345i	0.185889	−	0.982571i	$-0.440484\pi$
$337$	−6.92907	−	2.87011i	−0.377450	−	0.156345i	−0.563339	+	0.826226i	$0.690484\pi$
$338$	2.83899	+	0.960883i	0.154421	+	0.0522652i
$339$	1.02233	+	3.37018i	0.0555256	+	0.183043i
$340$	−1.02221	+	6.26087i	−0.0554369	+	0.339543i
$341$	−32.8525	+	3.23569i	−1.77906	+	0.175222i
$342$	−1.88034	+	1.76428i	−0.101677	+	0.0954013i
$343$	10.7261	+	16.0527i	0.579152	+	0.866763i
$344$	−2.12141	−	3.94347i	−0.114379	−	0.212618i
$345$	2.28000	+	1.52345i	0.122751	+	0.0820198i
$346$	7.47571	+	5.34693i	0.401897	+	0.287453i
$347$	−5.52449	+	18.2118i	−0.296570	+	0.977661i	0.674381	+	0.738384i	$0.264411\pi$
$347$	−5.52449	+	18.2118i	−0.296570	+	0.977661i	−0.970951	+	0.239278i	$0.923089\pi$
$348$	3.89834	−	1.33107i	0.208973	−	0.0713528i
$349$	−10.4502	+	8.57623i	−0.559384	+	0.459075i	−0.871104	−	0.491099i	$-0.836595\pi$
$349$	−10.4502	+	8.57623i	−0.559384	+	0.459075i	0.311719	+	0.950174i	$0.399095\pi$
$350$	−11.1437	+	2.99660i	−0.595657	+	0.160175i
$351$	−2.33245	−	2.33245i	−0.124497	−	0.124497i
$352$	−27.2060	−	16.7500i	−1.45008	−	0.892779i
$353$	8.21627	−	8.21627i	0.437308	−	0.437308i	−0.453797	−	0.891105i	$-0.649931\pi$
$353$	8.21627	−	8.21627i	0.437308	−	0.437308i	0.891105	+	0.453797i	$0.149931\pi$
$354$	−7.37569	+	12.8014i	−0.392013	+	0.680387i
$355$	3.01462	+	3.67332i	0.159999	+	0.194960i
$356$	−1.72669	+	1.51972i	−0.0915145	+	0.0805452i
$357$	−8.25753	−	2.50489i	−0.437035	−	0.132573i
$358$	−3.24536	−	19.5484i	−0.171523	−	1.03316i
$359$	−10.5173	+	15.7403i	−0.555084	+	0.830742i	−0.997826	−	0.0659074i	$-0.979006\pi$
$359$	−10.5173	+	15.7403i	−0.555084	+	0.830742i	0.442742	+	0.896649i	$0.354006\pi$
$360$	1.43210	−	1.18172i	0.0754782	−	0.0622820i
$361$	−13.0340	+	8.70902i	−0.685998	+	0.458370i
$362$	0.533525	−	16.7544i	0.0280414	−	0.880592i
$363$	−2.04834	−	20.7972i	−0.107510	−	1.09157i
$364$	10.0160	+	6.20363i	0.524983	+	0.325159i
$365$	0.839472	−	0.254651i	0.0439399	−	0.0133290i
$366$	−7.09809	−	14.3612i	−0.371023	−	0.750672i
$367$	−7.40459	+	17.8763i	−0.386517	+	0.933134i	0.604155	+	0.796866i	$0.293511\pi$
$367$	−7.40459	+	17.8763i	−0.386517	+	0.933134i	−0.990672	+	0.136267i	$0.956489\pi$
$368$	−16.6692	+	1.15229i	−0.868944	+	0.0600674i
$369$	3.52338	+	8.50620i	0.183420	+	0.442815i
$370$	0.875623	−	1.00025i	0.0455215	−	0.0520007i
$371$	17.3943	+	9.29744i	0.903067	+	0.482699i
$372$	4.84353	+	10.6394i	0.251125	+	0.551626i
$373$	4.01245	+	3.29294i	0.207757	+	0.170502i	0.732518	−	0.680748i	$-0.238345\pi$
$373$	4.01245	+	3.29294i	0.207757	+	0.170502i	−0.524761	+	0.851250i	$0.675845\pi$
$374$	15.8965	−	35.1676i	0.821986	−	1.81847i
$375$	6.16088	+	1.22547i	0.318146	+	0.0632832i
$376$	−0.00353630	−	1.32175i	−0.000182370	−	0.0681640i
$377$	−1.32544	−	6.66343i	−0.0682635	−	0.343184i
$378$	1.33559	+	2.14354i	0.0686954	+	0.110252i
$379$	−6.24631	−	11.6860i	−0.320852	−	0.600271i	0.668853	−	0.743394i	$-0.266785\pi$
$379$	−6.24631	−	11.6860i	−0.320852	−	0.600271i	−0.989705	+	0.143123i	$0.954285\pi$
$380$	−2.07087	+	1.20055i	−0.106233	+	0.0615868i
$381$	−18.1103	−	1.78371i	−0.927818	−	0.0913821i
$382$	9.21389	+	11.9856i	0.471424	+	0.613238i
$383$	8.09281			0.413523			0.206762	−	0.978391i	$-0.433708\pi$
$383$	8.09281			0.413523			0.206762	+	0.978391i	$0.433708\pi$
$384$	−2.50024	+	11.0340i	−0.127590	+	0.563076i
$385$	−6.62103			−0.337439
$386$	−8.54122	−	11.1106i	−0.434736	−	0.565515i
$387$	−1.57554	−	0.155177i	−0.0800894	−	0.00788811i
$388$	18.0070	+	31.0610i	0.914168	+	1.57688i
$389$	1.37154	+	2.56597i	0.0695399	+	0.130100i	0.914289	−	0.405063i	$-0.132750\pi$
$389$	1.37154	+	2.56597i	0.0695399	+	0.130100i	−0.844749	+	0.535163i	$0.820250\pi$
$390$	−1.61940	−	2.59903i	−0.0820013	−	0.131607i
$391$	−3.93772	−	19.7963i	−0.199139	−	1.00114i
$392$	7.64180	+	7.60102i	0.385969	+	0.383909i
$393$	−1.83015	−	0.364039i	−0.0923187	−	0.0183633i
$394$	−10.7872	+	23.8645i	−0.543452	+	1.20228i
$395$	2.28141	+	1.87230i	0.114790	+	0.0942059i
$396$	−10.2804	+	4.68013i	−0.516612	+	0.235185i
$397$	−2.82957	−	1.51244i	−0.142012	−	0.0759070i	0.398860	−	0.917012i	$-0.369406\pi$
$397$	−2.82957	−	1.51244i	−0.142012	−	0.0759070i	−0.540872	+	0.841105i	$0.681906\pi$
$398$	−10.7267	+	12.2535i	−0.537682	+	0.614213i
$399$	−1.24603	−	3.00818i	−0.0623795	−	0.150597i
$400$	−16.3626	+	8.14183i	−0.818130	+	0.407092i
$401$	3.82644	−	9.23784i	0.191083	−	0.461316i	−0.799081	−	0.601223i	$-0.794680\pi$
$401$	3.82644	−	9.23784i	0.191083	−	0.461316i	0.990165	+	0.139907i	$0.0446804\pi$
$402$	−2.76857	−	5.60151i	−0.138084	−	0.279378i
$403$	18.4500	−	5.59676i	0.919062	−	0.278794i
$404$	19.1210	−	30.8717i	0.951304	−	1.53592i
$405$	−0.0643429	−	0.653284i	−0.00319722	−	0.0324619i
$406$	−0.165563	+	5.19921i	−0.00821675	+	0.258032i
$407$	−6.72449	+	4.49316i	−0.333320	+	0.222718i
$408$	−13.6044	−	1.30318i	−0.673520	−	0.0645169i
$409$	21.8315	−	32.6732i	1.07950	−	1.61558i	0.342737	−	0.939431i	$-0.388646\pi$
$409$	21.8315	−	32.6732i	1.07950	−	1.61558i	0.736762	−	0.676153i	$-0.236354\pi$
$410$	1.39985	+	8.43198i	0.0691338	+	0.416426i
$411$	4.37038	+	1.32574i	0.215575	+	0.0653940i
$412$	4.33192	+	4.92187i	0.213418	+	0.242483i
$413$	−11.8357	−	14.4218i	−0.582397	−	0.709653i
$414$	−2.94920	+	5.11870i	−0.144945	+	0.251570i
$415$	−4.91843	+	4.91843i	−0.241436	+	0.241436i
$416$	17.4928	+	6.49491i	0.857654	+	0.318439i
$417$	4.32984	+	4.32984i	0.212033	+	0.212033i
$418$	14.0630	−	3.78161i	0.687843	−	0.184964i
$419$	−13.3591	+	10.9635i	−0.652635	+	0.535604i	−0.901415	−	0.432956i	$-0.857471\pi$
$419$	−13.3591	+	10.9635i	−0.652635	+	0.535604i	0.248780	+	0.968560i	$0.419971\pi$
$420$	0.757616	+	2.21886i	0.0369679	+	0.108269i
$421$	−6.44263	+	21.2385i	−0.313995	+	1.03510i	0.647910	+	0.761717i	$0.275643\pi$
$421$	−6.44263	+	21.2385i	−0.313995	+	1.03510i	−0.961905	+	0.273385i	$0.911857\pi$
$422$	−17.8272	−	12.7508i	−0.867815	−	0.620697i
$423$	−0.388554	−	0.259624i	−0.0188922	−	0.0126233i
$424$	29.9165	+	8.98774i	1.45287	+	0.436483i
$425$	−12.2655	−	18.3567i	−0.594966	−	0.890429i
$426$	−7.46568	+	7.00488i	−0.361713	+	0.339387i
$427$	20.1320	−	1.98283i	0.974254	−	0.0959556i
$428$	29.3120	+	4.78574i	1.41685	+	0.231328i
$429$	5.40794	+	17.8276i	0.261098	+	0.860725i
$430$	−1.39216	−	0.471191i	−0.0671359	−	0.0227228i
$431$	−16.8299	−	6.97117i	−0.810667	−	0.335789i	−0.0614471	−	0.998110i	$-0.519572\pi$
$431$	−16.8299	−	6.97117i	−0.810667	−	0.335789i	−0.749220	+	0.662321i	$0.769572\pi$
$432$	2.74477	+	2.90968i	0.132058	+	0.139992i
$433$	32.3317	−	13.3922i	1.55376	−	0.643590i	0.569772	−	0.821803i	$-0.307031\pi$
$433$	32.3317	−	13.3922i	1.55376	−	0.643590i	0.983992	+	0.178212i	$0.0570313\pi$
$434$	−14.7296	+	0.978620i	−0.707041	+	0.0469752i
$435$	0.637354	−	1.19241i	0.0305588	−	0.0571715i
$436$	1.08785	+	31.5116i	0.0520987	+	1.50913i
$437$	4.83160	−	5.88733i	0.231127	−	0.281629i
$438$	0.667293	+	1.76817i	0.0318845	+	0.0844864i
$439$	3.18364	−	16.0052i	0.151947	−	0.763888i	−0.827386	−	0.561633i	$-0.810173\pi$
$439$	3.18364	−	16.0052i	0.151947	−	0.763888i	0.979333	−	0.202255i	$-0.0648268\pi$
$440$	−10.2793	+	2.07329i	−0.490048	+	0.0988403i
$441$	3.73750	−	0.743434i	0.177976	−	0.0354016i
$442$	−5.09881	+	21.9561i	−0.242526	+	1.04435i
$443$	13.6606	−	7.30176i	0.649036	−	0.346917i	−0.113805	−	0.993503i	$-0.536304\pi$
$443$	13.6606	−	7.30176i	0.649036	−	0.346917i	0.762841	+	0.646586i	$0.223804\pi$
$444$	2.27521	+	1.73939i	0.107977	+	0.0825480i
$445$	−0.0740015	+	0.751350i	−0.00350801	+	0.0356174i
$446$	−7.71826	−	1.00913i	−0.365470	−	0.0477836i
$447$		−	12.2630i		−	0.580020i
$448$	−11.9214	−	7.87367i	−0.563232	−	0.371996i
$449$			18.3027i			0.863757i	0.901932	+	0.431878i	$0.142149\pi$
$449$			18.3027i			0.863757i	−0.901932	+	0.431878i	$0.857851\pi$
$450$	−0.837702	+	6.40712i	−0.0394896	+	0.302035i
$451$	5.09686	−	51.7493i	0.240002	−	2.43678i
$452$	−6.98176	+	0.931837i	−0.328394	+	0.0438299i
$453$	2.61008	−	1.39512i	0.122632	−	0.0655484i
$454$	−30.2629	−	7.02786i	−1.42031	−	0.329834i
$455$	3.79268	−	0.754412i	0.177804	−	0.0353674i
$456$	−2.87647	−	4.28011i	−0.134703	−	0.200434i
$457$	−3.88396	+	19.5260i	−0.181684	+	0.913386i	0.777128	+	0.629343i	$0.216676\pi$
$457$	−3.88396	+	19.5260i	−0.181684	+	0.913386i	−0.958811	+	0.284043i	$0.908324\pi$
$458$	6.91937	−	2.61132i	0.323321	−	0.122019i
$459$	−3.06533	+	3.73512i	−0.143077	+	0.174340i
$460$	−3.74186	+	4.00945i	−0.174465	+	0.186942i
$461$	−1.30112	+	2.43422i	−0.0605991	+	0.113373i	−0.910397	−	0.413735i	$-0.864224\pi$
$461$	−1.30112	+	2.43422i	−0.0605991	+	0.113373i	0.849798	+	0.527108i	$0.176724\pi$
$462$	−0.945605	−	14.2326i	−0.0439935	−	0.662162i
$463$	35.5653	−	14.7316i	1.65286	−	0.684637i	0.655360	−	0.755317i	$-0.272517\pi$
$463$	35.5653	−	14.7316i	1.65286	−	0.684637i	0.997499	+	0.0706803i	$0.0225170\pi$
$464$	1.37103	+	8.12377i	0.0636483	+	0.377136i
$465$	3.54485	+	1.46833i	0.164389	+	0.0680920i
$466$	9.69031	−	28.6306i	0.448895	−	1.32629i
$467$	10.4399	+	34.4156i	0.483099	+	1.59256i	0.772275	+	0.635288i	$0.219119\pi$
$467$	10.4399	+	34.4156i	0.483099	+	1.59256i	−0.289176	+	0.957276i	$0.593381\pi$
$468$	5.35563	−	3.85226i	0.247564	−	0.178071i
$469$	7.85236	−	0.773390i	0.362588	−	0.0357118i
$470$	−0.296845	−	0.316372i	−0.0136924	−	0.0145931i
$471$	8.52243	+	12.7547i	0.392693	+	0.587707i
$472$	−22.8913	−	18.6841i	−1.05366	−	0.860007i
$473$	7.43453	+	4.96759i	0.341840	+	0.228410i
$474$	−3.69890	+	5.17155i	−0.169896	+	0.237537i
$475$	2.41821	−	7.97179i	0.110955	−	0.365771i
$476$	7.60548	−	15.4920i	0.348597	−	0.710074i
$477$	8.53721	−	7.00630i	0.390892	−	0.320797i
$478$	11.1546	+	41.4817i	0.510201	+	1.89733i
$479$	17.8185	+	17.8185i	0.814149	+	0.814149i	0.985253	−	0.171104i	$-0.0547334\pi$
$479$	17.8185	+	17.8185i	0.814149	+	0.814149i	−0.171104	+	0.985253i	$0.554733\pi$
$480$	1.87103	+	3.20760i	0.0854004	+	0.146406i
$481$	3.33999	−	3.33999i	0.152290	−	0.152290i
$482$	27.3625	+	15.7652i	1.24633	+	0.718085i
$483$	−4.73256	−	5.76664i	−0.215339	−	0.262391i
$484$	41.7109	+	2.65917i	1.89595	+	0.120871i
$485$	11.2768	+	3.42078i	0.512054	+	0.155330i
$486$	1.39512	−	0.231613i	0.0632839	−	0.0105062i
$487$	−21.0882	+	31.5607i	−0.955597	+	1.43015i	−0.0535253	+	0.998566i	$0.517046\pi$
$487$	−21.0882	+	31.5607i	−0.955597	+	1.43015i	−0.902072	+	0.431586i	$0.857954\pi$
$488$	30.6346	−	9.38247i	1.38676	−	0.424724i
$489$	−15.3978	+	10.2885i	−0.696314	+	0.465262i
$490$	3.53590	+	0.112597i	0.159736	+	0.00508660i
$491$	0.112807	+	1.14535i	0.00509090	+	0.0516888i	0.997395	−	0.0721397i	$-0.0229827\pi$
$491$	0.112807	+	1.14535i	0.00509090	+	0.0516888i	−0.992304	+	0.123828i	$0.960483\pi$
$492$	−17.9256	+	4.21338i	−0.808147	+	0.189954i
$493$	−9.52357	+	2.88894i	−0.428920	+	0.130111i
$494$	−7.62473	+	3.76856i	−0.343053	+	0.169555i
$495$	−1.41879	+	3.42526i	−0.0637699	+	0.153954i
$496$	−22.5616	+	6.13171i	−1.01305	+	0.275322i
$497$	−4.94722	−	11.9437i	−0.221913	−	0.535746i
$498$	−11.2752	−	9.87027i	−0.505252	−	0.442297i
$499$	9.03308	+	4.82828i	0.404376	+	0.216144i	0.661029	−	0.750360i	$-0.270120\pi$
$499$	9.03308	+	4.82828i	0.404376	+	0.216144i	−0.256653	+	0.966504i	$0.582620\pi$
$500$	−4.40439	+	11.7658i	−0.196970	+	0.526183i
$501$	−14.1853	−	11.6416i	−0.633751	−	0.520106i
$502$	16.0133	+	7.23832i	0.714708	+	0.323062i
$503$	10.3099	+	2.05077i	0.459695	+	0.0914391i	0.419505	−	0.907753i	$-0.362204\pi$
$503$	10.3099	+	2.05077i	0.459695	+	0.0914391i	0.0401903	+	0.999192i	$0.487204\pi$
$504$	−4.66148	+	1.94548i	−0.207639	+	0.0866584i
$505$	−2.32526	−	11.6899i	−0.103473	−	0.520194i
$506$	28.3176	−	17.6440i	1.25887	−	0.784373i
$507$	0.999047	+	1.86908i	0.0443692	+	0.0830090i
$508$	9.35721	−	35.1724i	0.415159	−	1.56052i
$509$	3.66610	+	0.361080i	0.162497	+	0.0160046i	0.178938	−	0.983860i	$-0.442734\pi$
$509$	3.66610	+	0.361080i	0.162497	+	0.0160046i	−0.0164414	+	0.999865i	$0.505234\pi$
$510$	−3.55632	+	2.73391i	−0.157477	+	0.121059i
$511$	−2.38654			−0.105574
$512$	−20.9738	−	8.49107i	−0.926921	−	0.375256i
$513$	−1.82323			−0.0804977
$514$	−11.3247	+	8.70583i	−0.499512	+	0.383998i
$515$	2.14169	+	0.210938i	0.0943743	+	0.00929506i
$516$	0.814051	−	3.05990i	0.0358366	−	0.134705i
$517$	1.24415	+	2.32764i	0.0547176	+	0.102369i
$518$	−3.06947	+	1.91252i	−0.134865	+	0.0840313i
$519$	1.26791	+	6.37420i	0.0556549	+	0.279796i
$520$	5.65202	−	2.35888i	0.247857	−	0.103444i
$521$	−13.6783	−	2.72078i	−0.599256	−	0.119199i	−0.113864	−	0.993496i	$-0.536323\pi$
$521$	−13.6783	−	2.72078i	−0.599256	−	0.119199i	−0.485392	+	0.874297i	$0.661323\pi$
$522$	2.65424	+	1.19977i	0.116173	+	0.0525124i
$523$	8.65256	+	7.10097i	0.378350	+	0.310504i	0.804278	−	0.594253i	$-0.202552\pi$
$523$	8.65256	+	7.10097i	0.378350	+	0.310504i	−0.425928	+	0.904757i	$0.640052\pi$
$524$	1.30837	−	3.49514i	0.0571562	−	0.152686i
$525$	−7.19623	−	3.84647i	−0.314069	−	0.167874i
$526$	10.2439	+	8.96753i	0.446656	+	0.391003i
$527$	−10.8079	−	26.0927i	−0.470802	−	1.13662i
$528$	−5.92485	−	21.8005i	−0.257846	−	0.948744i
$529$	−2.12411	+	5.12806i	−0.0923526	+	0.222959i
$530$	9.19144	−	4.54291i	0.399251	−	0.197331i
$531$	−9.99709	+	3.03259i	−0.433837	+	0.131603i
$532$	6.33930	−	1.49004i	0.274843	−	0.0646016i
$533$	2.97680	+	30.2240i	0.128940	+	1.30915i
$534$	−1.62568	−	0.0517679i	−0.0703500	−	0.00224022i
$535$	8.10538	−	5.41584i	0.350426	−	0.234147i
$536$	11.9488	−	3.65958i	0.516111	−	0.158070i
$537$	7.78465	−	11.6505i	0.335932	−	0.502758i
$538$	−15.1119	+	2.50883i	−0.651520	+	0.108163i
$539$	−20.5955	−	6.24757i	−0.887110	−	0.269102i
$540$	1.31023	+	0.0835303i	0.0563833	+	0.00359457i
$541$	−25.4510	−	31.0121i	−1.09422	−	1.33332i	−0.938408	−	0.345529i	$-0.887699\pi$
$541$	−25.4510	−	31.0121i	−1.09422	−	1.33332i	−0.155816	−	0.987786i	$-0.549801\pi$
$542$	26.2882	+	15.1462i	1.12917	+	0.650586i
$543$	8.38145	−	8.38145i	0.359682	−	0.359682i
$544$	6.95661	−	26.4333i	0.298262	−	1.13332i
$545$	7.31783	+	7.31783i	0.313462	+	0.313462i
$546$	2.16336	+	8.04506i	0.0925832	+	0.344297i
$547$	27.8980	−	22.8953i	1.19283	−	0.978933i	0.192836	−	0.981231i	$-0.438231\pi$
$547$	27.8980	−	22.8953i	1.19283	−	0.978933i	0.999997	+	0.00229756i	$0.000731336\pi$
$548$	−4.02528	+	8.19930i	−0.171951	+	0.350257i
$549$	3.28821	−	10.8398i	0.140338	−	0.462631i
$550$	21.2306	−	29.6832i	0.905276	−	1.26569i
$551$	−3.12237	−	2.08630i	−0.133017	−	0.0888794i
$552$	−9.15318	−	7.47093i	−0.389585	−	0.317984i
$553$	−4.46072	−	6.67594i	−0.189689	−	0.283890i
$554$	−5.86144	−	6.24702i	−0.249029	−	0.265411i
$555$	0.935480	−	0.0921367i	0.0397089	−	0.00391099i
$556$	−9.94190	+	7.15114i	−0.421631	+	0.303276i
$557$	10.6538	+	35.1208i	0.451416	+	1.48812i	0.827464	+	0.561518i	$0.189783\pi$
$557$	10.6538	+	35.1208i	0.451416	+	1.48812i	−0.376049	+	0.926600i	$0.622717\pi$
$558$	−2.65006	+	7.82977i	−0.112186	+	0.331460i
$559$	−4.82469	−	1.99845i	−0.204063	−	0.0845256i
$560$	−4.62388	+	0.780360i	−0.195395	+	0.0329762i
$561$	25.2124	−	10.4433i	1.06447	−	0.440918i
$562$	−2.07864	−	31.2864i	−0.0876822	−	1.31974i
$563$	10.3496	−	19.3627i	0.436183	−	0.816041i	−0.563768	−	0.825933i	$-0.690649\pi$
$563$	10.3496	−	19.3627i	0.436183	−	0.816041i	0.999951	+	0.00989218i	$0.00314883\pi$
$564$	0.637682	−	0.683284i	0.0268512	−	0.0287715i
$565$	−1.46665	+	1.78712i	−0.0617023	+	0.0751845i
$566$	−6.94096	+	2.61946i	−0.291750	+	0.110104i
$567$	−0.348403	+	1.75154i	−0.0146316	+	0.0735578i
$568$	−11.4207	−	16.9937i	−0.479202	−	0.713040i
$569$	−20.3496	+	4.04778i	−0.853098	+	0.169692i	−0.602223	−	0.798328i	$-0.705718\pi$
$569$	−20.3496	+	4.04778i	−0.853098	+	0.169692i	−0.250875	+	0.968020i	$0.580718\pi$
$570$	−1.64873	−	0.382880i	−0.0690577	−	0.0160371i
$571$	9.28205	−	4.96136i	0.388442	−	0.207626i	−0.265603	−	0.964083i	$-0.585571\pi$
$571$	9.28205	−	4.96136i	0.388442	−	0.207626i	0.654044	+	0.756456i	$0.273071\pi$
$572$	−36.9321	+	4.92923i	−1.54421	+	0.206102i
$573$	−1.04780	+	10.6385i	−0.0437725	+	0.444430i
$574$	3.01458	−	23.0569i	0.125826	−	0.962377i
$575$		−	19.0862i		−	0.795949i
$576$	−6.62788	+	4.48009i	−0.276162	+	0.186670i
$577$		−	19.8089i		−	0.824654i	−0.911036	−	0.412327i	$-0.864716\pi$
$577$		−	19.8089i		−	0.824654i	0.911036	−	0.412327i	$-0.135284\pi$
$578$	8.90077	+	1.16373i	0.370223	+	0.0484049i
$579$	0.971304	−	9.86182i	0.0403660	−	0.409843i
$580$	2.14825	+	1.64233i	0.0892011	+	0.0681940i
$581$	16.6886	−	8.92022i	0.692358	−	0.370073i
$582$	−5.74282	+	24.7293i	−0.238048	+	1.02506i
$583$	−61.1765	+	12.1688i	−2.53367	+	0.503979i
$584$	−3.70518	+	0.747316i	−0.153321	+	0.0309242i
$585$	0.422437	−	2.12373i	0.0174656	−	0.0878056i
$586$	6.91692	+	18.3282i	0.285735	+	0.757132i
$587$	−19.3413	+	23.5674i	−0.798300	+	0.972731i	−0.999977	−	0.00672072i	$-0.997861\pi$
$587$	−19.3413	+	23.5674i	−0.798300	+	0.972731i	0.201677	+	0.979452i	$0.435361\pi$
$588$	0.262953	+	7.61690i	0.0108440	+	0.314116i
$589$	5.02358	−	9.39845i	0.206993	−	0.387257i
$590$	−9.67711	+	0.642939i	−0.398400	+	0.0264694i
$591$	−17.1090	+	7.08676i	−0.703769	+	0.291510i
$592$	−4.16656	+	3.93041i	−0.171245	+	0.161539i
$593$	−29.4005	−	12.1781i	−1.20733	−	0.500093i	−0.313971	−	0.949433i	$-0.601659\pi$
$593$	−29.4005	−	12.1781i	−1.20733	−	0.500093i	−0.893361	+	0.449339i	$0.851659\pi$
$594$	−7.56562	−	2.56066i	−0.310421	−	0.105065i
$595$	−1.64433	−	5.42062i	−0.0674108	−	0.222224i
$596$	24.2055	+	3.95201i	0.991496	+	0.161881i
$597$	−11.4600	+	1.12871i	−0.469027	+	0.0461951i
$598$	−14.2106	+	13.3335i	−0.581115	+	0.545247i
$599$	−5.74712	−	8.60118i	−0.234821	−	0.351435i	0.695280	−	0.718739i	$-0.255281\pi$
$599$	−5.74712	−	8.60118i	−0.234821	−	0.351435i	−0.930101	+	0.367305i	$0.880281\pi$
$600$	−12.3768	−	3.71834i	−0.505282	−	0.151801i
$601$	8.06530	+	5.38906i	0.328990	+	0.219824i	0.709085	−	0.705123i	$-0.249108\pi$
$601$	8.06530	+	5.38906i	0.328990	+	0.219824i	−0.380094	+	0.924948i	$0.624108\pi$
$602$	3.25218	+	2.32609i	0.132549	+	0.0948043i
$603$	1.28255	−	4.22800i	0.0522295	−	0.172177i
$604$	1.91262	+	5.60156i	0.0778235	+	0.227924i
$605$	10.6044	−	8.70277i	0.431128	−	0.353818i
$606$	24.7967	−	6.66795i	1.00730	−	0.270867i
$607$	4.99071	+	4.99071i	0.202567	+	0.202567i	0.801099	−	0.598532i	$-0.204249\pi$
$607$	4.99071	+	4.99071i	0.202567	+	0.202567i	−0.598532	+	0.801099i	$0.704249\pi$
$608$	9.37536	−	4.29841i	0.380221	−	0.174324i
$609$	−2.60092	+	2.60092i	−0.105395	+	0.105395i
$610$	5.24986	−	9.11178i	0.212561	−	0.368925i
$611$	−0.977894	−	1.19157i	−0.0395613	−	0.0482056i
$612$	−6.38475	−	7.25427i	−0.258088	−	0.293236i
$613$	30.5680	+	9.27269i	1.23463	+	0.374520i	0.839122	−	0.543943i	$-0.183069\pi$
$613$	30.5680	+	9.27269i	1.23463	+	0.374520i	0.395506	+	0.918463i	$0.370569\pi$
$614$	6.41148	+	38.6194i	0.258746	+	1.55855i
$615$	−3.35782	+	5.02533i	−0.135400	+	0.202641i
$616$	28.3980	+	2.72027i	1.14419	+	0.109603i
$617$	−17.4544	+	11.6627i	−0.702689	+	0.469522i	−0.854878	−	0.518830i	$-0.826368\pi$
$617$	−17.4544	+	11.6627i	−0.702689	+	0.469522i	0.152189	+	0.988351i	$0.451368\pi$
$618$	−0.147562	+	4.63394i	−0.00593583	+	0.186404i
$619$	2.08021	+	21.1207i	0.0836105	+	0.848912i	0.941933	+	0.335801i	$0.109007\pi$
$619$	2.08021	+	21.1207i	0.0836105	+	0.848912i	−0.858322	+	0.513111i	$0.828493\pi$
$620$	−4.04068	+	6.52386i	−0.162278	+	0.262005i
$621$	−3.99738	+	1.21259i	−0.160409	+	0.0486596i
$622$	14.2915	+	28.9152i	0.573036	+	1.15939i
$623$	0.786007	−	1.89759i	0.0314907	−	0.0760252i
$624$	5.87789	+	11.8128i	0.235304	+	0.472889i
$625$	−7.16456	−	17.2968i	−0.286582	−	0.691871i
$626$	14.9796	−	17.1117i	0.598704	−	0.683921i
$627$	9.08139	+	4.85410i	0.362676	+	0.193854i
$628$	−27.9226	+	12.7117i	−1.11423	+	0.507250i
$629$	−5.34856	−	4.38945i	−0.213261	−	0.175019i
$630$	−0.682882	+	1.51074i	−0.0272067	+	0.0601892i
$631$	20.5578	+	4.08921i	0.818395	+	0.162789i	0.586497	−	0.809951i	$-0.300506\pi$
$631$	20.5578	+	4.08921i	0.818395	+	0.162789i	0.231898	+	0.972740i	$0.425506\pi$
$632$	−9.01588	−	8.96777i	−0.358633	−	0.356719i
$633$	−3.02356	−	15.2004i	−0.120176	−	0.604164i
$634$	−19.5754	−	31.4173i	−0.777438	−	1.24774i
$635$	−5.63127	−	10.5354i	−0.223470	−	0.418083i
$636$	11.0782	+	19.1092i	0.439279	+	0.757730i
$637$	12.5094	+	1.23207i	0.495642	+	0.0488165i
$638$	−10.0263	−	13.0425i	−0.396947	−	0.516357i
$639$	−7.23894			−0.286368
$640$	−6.93435	+	2.65944i	−0.274104	+	0.105124i
$641$	−17.8452			−0.704844			−0.352422	−	0.935841i	$-0.614642\pi$
$641$	−17.8452			−0.704844			−0.352422	+	0.935841i	$0.614642\pi$
$642$	12.7996	+	16.6499i	0.505158	+	0.657121i
$643$	−31.0249	−	3.05569i	−1.22350	−	0.120505i	−0.534441	−	0.845206i	$-0.679478\pi$
$643$	−31.0249	−	3.05569i	−1.22350	−	0.120505i	−0.689063	+	0.724701i	$0.741978\pi$
$644$	12.9077	−	7.48301i	0.508636	−	0.294872i
$645$	−0.489905	−	0.916547i	−0.0192900	−	0.0360890i
$646$	6.58852	+	10.5742i	0.259222	+	0.416035i
$647$	2.69554	+	13.5514i	0.105972	+	0.532760i	0.996904	+	0.0786228i	$0.0250523\pi$
$647$	2.69554	+	13.5514i	0.105972	+	0.532760i	−0.890932	+	0.454137i	$0.849948\pi$
$648$	0.00756734	+	2.82842i	0.000297273	+	0.111111i
$649$	57.8686	+	11.5108i	2.27154	+	0.451838i
$650$	−8.77925	+	19.4223i	−0.344351	+	0.761805i
$651$	−8.06894	−	6.62201i	−0.316247	−	0.259537i
$652$	−15.3458	−	33.7089i	−0.600990	−	1.32014i
$653$	40.1772	+	21.4751i	1.57225	+	0.840387i	0.999791	+	0.0204565i	$0.00651196\pi$
$653$	40.1772	+	21.4751i	1.57225	+	0.840387i	0.572463	+	0.819931i	$0.305988\pi$
$654$	−14.6854	+	16.7756i	−0.574244	+	0.655979i
$655$	−0.468759	−	1.13169i	−0.0183159	−	0.0442186i
$656$	−2.53976	−	36.7405i	−0.0991609	−	1.43448i
$657$	−0.511402	+	1.23463i	−0.0199517	+	0.0481676i
$658$	0.522946	+	1.05805i	0.0203866	+	0.0412471i
$659$	20.9548	−	6.35657i	0.816283	−	0.247617i	0.145584	−	0.989346i	$-0.453494\pi$
$659$	20.9548	−	6.35657i	0.816283	−	0.247617i	0.670700	+	0.741729i	$0.265994\pi$
$660$	−6.30377	−	3.90436i	−0.245374	−	0.151977i
$661$	2.89768	+	29.4206i	0.112707	+	1.14433i	0.870614	+	0.491967i	$0.163722\pi$
$661$	2.89768	+	29.4206i	0.112707	+	1.14433i	−0.757907	+	0.652363i	$0.773778\pi$
$662$	0.371932	−	11.6799i	0.0144555	−	0.453951i
$663$	−13.2524	+	8.85494i	−0.514679	+	0.343897i
$664$	23.1162	−	19.0747i	0.897083	−	0.740243i
$665$	1.18748	−	1.77719i	0.0460485	−	0.0689164i
$666$	0.331662	+	1.99776i	0.0128516	+	0.0774117i
$667$	−8.23325	−	2.49753i	−0.318793	−	0.0967047i
$668$	27.5503	−	24.2481i	1.06595	−	0.938186i
$669$	−3.49176	−	4.25472i	−0.134999	−	0.164497i
$670$	2.04768	−	3.55400i	0.0791088	−	0.137303i
$671$	−45.2378	+	45.2378i	−1.74639	+	1.74639i
$672$	−2.33785	−	9.82810i	−0.0901844	−	0.379127i
$673$	10.1634	+	10.1634i	0.391772	+	0.391772i	0.875319	−	0.483547i	$-0.160652\pi$
$673$	10.1634	+	10.1634i	0.391772	+	0.391772i	−0.483547	+	0.875319i	$0.660652\pi$
$674$	10.2427	−	2.75432i	0.394534	−	0.106092i
$675$	−3.53195	+	2.89859i	−0.135945	+	0.111567i
$676$	−4.01128	+	1.36963i	−0.154280	+	0.0526781i
$677$	−0.398526	+	1.31377i	−0.0153166	+	0.0504921i	−0.964266	−	0.264938i	$-0.914649\pi$
$677$	−0.398526	+	1.31377i	−0.0153166	+	0.0504921i	0.948949	+	0.315430i	$0.102149\pi$
$678$	−4.05107	−	2.89749i	−0.155580	−	0.111277i
$679$	−26.6561	−	17.8110i	−1.02297	−	0.683524i
$680$	−4.25026	−	7.90076i	−0.162990	−	0.302980i
$681$	−12.2051	−	18.2662i	−0.467699	−	0.699961i
$682$	34.0454	−	31.9441i	1.30367	−	1.22320i
$683$	42.3808	−	4.17415i	1.62166	−	0.159719i	0.753998	−	0.656877i	$-0.228123\pi$
$683$	42.3808	−	4.17415i	1.62166	−	0.159719i	0.867660	+	0.497158i	$0.165623\pi$
$684$	0.587575	−	3.59881i	0.0224665	−	0.137604i
$685$	0.870276	+	2.86892i	0.0332515	+	0.109616i
$686$	−25.8622	−	8.75332i	−0.987423	−	0.334203i
$687$	4.83149	+	2.00127i	0.184333	+	0.0763531i
$688$	5.77748	+	2.59294i	0.220264	+	0.0988550i
$689$	33.6569	−	13.9411i	1.28222	−	0.531115i
$690$	−3.86944	+	0.257082i	−0.147307	+	0.00978695i
$691$	−16.1976	+	30.3036i	−0.616187	+	1.15280i	0.359399	+	0.933184i	$0.382982\pi$
$691$	−16.1976	+	30.3036i	−0.616187	+	1.15280i	−0.975585	+	0.219620i	$0.929518\pi$
$692$	−12.9904	+	0.448458i	−0.493821	+	0.0170478i
$693$	6.39861	−	7.79673i	0.243063	−	0.296173i
$694$	−9.50303	−	25.1808i	−0.360730	−	0.955850i
$695$	−0.784190	+	3.94239i	−0.0297460	+	0.149543i
$696$	−3.22356	+	4.85245i	−0.122189	+	0.183932i
$697$	43.6328	−	8.67910i	1.65271	−	0.328744i
$698$	4.32474	−	18.6229i	0.163694	−	0.704886i
$699$	18.8493	−	10.0752i	0.712947	−	0.381078i
$700$	9.91154	−	12.9648i	0.374621	−	0.490023i
$701$	−3.36068	+	34.1216i	−0.126931	+	1.28875i	0.694935	+	0.719073i	$0.255433\pi$
$701$	−3.36068	+	34.1216i	−0.126931	+	1.28875i	−0.821866	+	0.569681i	$0.807067\pi$
$702$	4.62554	+	0.604767i	0.174580	+	0.0228255i
$703$		−	2.61080i		−	0.0984684i
$704$	44.9406	−	4.66920i	1.69376	−	0.175977i
$705$		−	0.306764i		−	0.0115534i
$706$	−2.13035	+	16.2939i	−0.0801767	+	0.613228i
$707$	−3.17824	+	32.2692i	−0.119530	+	1.21361i
$708$	−2.76414	−	20.7102i	−0.103883	−	0.778338i
$709$	−26.9193	+	14.3887i	−1.01098	+	0.540379i	−0.891769	−	0.452491i	$-0.850536\pi$
$709$	−26.9193	+	14.3887i	−1.01098	+	0.540379i	−0.119208	+	0.992869i	$0.538036\pi$
$710$	−6.54610	−	1.52018i	−0.245671	−	0.0570515i
$711$	−4.40954	+	0.877112i	−0.165371	+	0.0328943i
$712$	0.626092	−	3.19219i	0.0234638	−	0.119632i
$713$	4.76333	−	23.9469i	0.178388	−	0.896818i
$714$	11.4174	−	4.30883i	0.427285	−	0.161254i
$715$	−7.75827	+	9.45348i	−0.290143	+	0.353540i
$716$	20.4878	+	19.1205i	0.765666	+	0.714566i
$717$	−14.3182	+	26.7874i	−0.534722	+	1.00039i
$718$	−1.77480	−	26.7132i	−0.0662350	−	0.996927i
$719$	2.28259	−	0.945478i	0.0851261	−	0.0352604i	−0.339714	−	0.940529i	$-0.610330\pi$
$719$	2.28259	−	0.945478i	0.0851261	−	0.0352604i	0.424840	+	0.905268i	$0.360330\pi$
$720$	−0.587126	+	2.55930i	−0.0218809	+	0.0953794i
$721$	−5.40900	−	2.24048i	−0.201442	−	0.0834399i
$722$	7.10726	−	20.9988i	0.264505	−	0.781495i
$723$	6.48202	+	21.3683i	0.241069	+	0.794697i
$724$	13.8427	+	19.2449i	0.514462	+	0.715232i
$725$	−9.36544	+	0.922416i	−0.347824	+	0.0342577i
$726$	20.2221	+	21.5523i	0.750512	+	0.799882i
$727$	−7.03020	−	10.5214i	−0.260736	−	0.390218i	0.677886	−	0.735167i	$-0.262896\pi$
$727$	−7.03020	−	10.5214i	−0.260736	−	0.390218i	−0.938622	+	0.344949i	$0.887896\pi$
$728$	−16.5770	+	1.67749i	−0.614386	+	0.0621719i
$729$	0.831470	+	0.555570i	0.0307952	+	0.0205767i
$730$	−0.721729	+	1.00907i	−0.0267124	+	0.0373474i
$731$	−2.22060	+	7.32033i	−0.0821317	+	0.270752i
$732$	20.3366	+	9.98384i	0.751662	+	0.369013i
$733$	6.96857	−	5.71896i	0.257390	−	0.211234i	−0.496845	−	0.867839i	$-0.665508\pi$
$733$	6.96857	−	5.71896i	0.257390	−	0.211234i	0.754235	+	0.656605i	$0.228008\pi$
$734$	−7.10584	−	26.4251i	−0.262282	−	0.975368i
$735$	1.76885	+	1.76885i	0.0652449	+	0.0652449i
$736$	17.6964	−	15.6595i	0.652298	−	0.577216i
$737$	−17.6448	+	17.6448i	−0.649953	+	0.649953i
$738$	−11.2821	−	6.50030i	−0.415299	−	0.239280i
$739$	21.5134	+	26.2141i	0.791383	+	0.964302i	0.999906	−	0.0137149i	$-0.00436572\pi$
$739$	21.5134	+	26.2141i	0.791383	+	0.964302i	−0.208523	+	0.978017i	$0.566866\pi$
$740$	−0.119612	+	1.87620i	−0.00439704	+	0.0689706i
$741$	−5.75512	−	1.74580i	−0.211420	−	0.0641335i
$742$	−27.5162	+	4.56815i	−1.01015	+	0.167702i
$743$	−20.5592	+	30.7690i	−0.754244	+	1.12881i	0.233444	+	0.972370i	$0.425000\pi$
$743$	−20.5592	+	30.7690i	−0.754244	+	1.12881i	−0.987688	+	0.156436i	$0.950000\pi$
$744$	−14.6009	−	7.75417i	−0.535294	−	0.284282i
$745$	6.69332	−	4.47233i	0.245224	−	0.163854i
$746$	−7.33702	−	0.233639i	−0.268627	−	0.00855413i
$747$	−1.03859	−	10.5450i	−0.0380001	−	0.385821i
$748$	12.4885	+	53.1315i	0.456624	+	1.94268i
$749$	−25.3781	+	7.69838i	−0.927297	+	0.281293i
$750$	−7.96385	+	3.93617i	−0.290799	+	0.143729i
$751$	−13.8639	+	33.4705i	−0.505902	+	1.22136i	0.440320	+	0.897841i	$0.354865\pi$
$751$	−13.8639	+	33.4705i	−0.505902	+	1.22136i	−0.946223	+	0.323516i	$0.895135\pi$
$752$	1.14320	+	1.47890i	0.0416884	+	0.0539299i
$753$	4.75528	+	11.4803i	0.173292	+	0.418364i
$754$	7.22942	+	6.32863i	0.263280	+	0.230475i
$755$	1.71338	+	0.915819i	0.0623561	+	0.0333301i
$756$	−3.34503	−	1.25217i	−0.121657	−	0.0455410i
$757$	35.7357	+	29.3275i	1.29884	+	1.06593i	0.993518	+	0.113676i	$0.0362627\pi$
$757$	35.7357	+	29.3275i	1.29884	+	1.06593i	0.305318	+	0.952251i	$0.401237\pi$
$758$	17.0758	+	7.71860i	0.620221	+	0.280352i
$759$	23.1390	+	4.60264i	0.839893	+	0.167065i
$760$	1.28709	−	3.13098i	0.0466877	−	0.113573i
$761$	10.2637	+	51.5992i	0.372059	+	1.87047i	0.481456	+	0.876470i	$0.340108\pi$
$761$	10.2637	+	51.5992i	0.372059	+	1.87047i	−0.109397	+	0.993998i	$0.534892\pi$
$762$	21.8427	−	13.6097i	0.791278	−	0.493027i
$763$	−13.2719	−	24.8299i	−0.480474	−	0.898904i
$764$	−20.6613	−	5.49669i	−0.747499	−	0.198863i
$765$	−3.15661	−	0.310899i	−0.114127	−	0.0112406i
$766$	−9.07368	+	6.97535i	−0.327846	+	0.252030i
$767$	−34.4601			−1.24428
$768$	−6.70712	−	14.5263i	−0.242022	−	0.524174i
$769$	−8.97933			−0.323803			−0.161902	−	0.986807i	$-0.551763\pi$
$769$	−8.97933			−0.323803			−0.161902	+	0.986807i	$0.551763\pi$
$770$	7.42351	−	5.70679i	0.267525	−	0.205658i
$771$	−10.0519	−	0.990024i	−0.362010	−	0.0356548i
$772$	19.1529	+	5.09540i	0.689327	+	0.183387i
$773$	−11.7266	−	21.9389i	−0.421776	−	0.789088i	0.577858	−	0.816137i	$-0.303889\pi$
$773$	−11.7266	−	21.9389i	−0.421776	−	0.789088i	−0.999634	+	0.0270496i	$0.991389\pi$
$774$	1.90025	−	1.18401i	0.0683032	−	0.0425582i
$775$	−5.21014	−	26.1931i	−0.187154	−	0.940885i
$776$	−46.9616	−	19.3051i	−1.68582	−	0.693012i
$777$	−2.50815	−	0.498901i	−0.0899792	−	0.0178980i
$778$	−3.74943	−	1.69482i	−0.134424	−	0.0607622i
$779$	12.9762	+	10.6493i	0.464921	+	0.381551i
$780$	4.05582	+	1.51825i	0.145222	+	0.0543621i
$781$	36.0567	+	19.2727i	1.29021	+	0.689631i
$782$	21.4778	+	18.8016i	0.768044	+	0.672345i
$783$	0.788198	+	1.90288i	0.0281679	+	0.0680033i
$784$	−15.1195	−	1.93567i	−0.539981	−	0.0691311i
$785$	−3.85356	+	9.30333i	−0.137540	+	0.332050i
$786$	2.36574	−	1.16928i	0.0843830	−	0.0417067i
$787$	−51.8076	+	15.7157i	−1.84674	+	0.560203i	−0.847157	+	0.531343i	$0.821688\pi$
$787$	−51.8076	+	15.7157i	−1.84674	+	0.560203i	−0.999583	+	0.0288594i	$0.990812\pi$
$788$	−8.47459	−	36.0546i	−0.301895	−	1.28439i
$789$	0.943602	+	9.58055i	0.0335931	+	0.341077i
$790$	−4.17170	−	0.132843i	−0.148422	−	0.00472634i
$791$	5.22952	−	3.49425i	0.185940	−	0.124241i
$792$	7.49257	−	14.1083i	0.266237	−	0.501316i
$793$	20.7588	−	31.0678i	0.737167	−	1.10325i
$794$	4.47612	−	0.743112i	0.158852	−	0.0263720i
$795$	6.93767	+	2.10452i	0.246054	+	0.0746396i
$796$	1.46530	−	22.9843i	0.0519362	−	0.814655i
$797$	5.77010	+	7.03088i	0.204387	+	0.249047i	0.865109	−	0.501585i	$-0.167249\pi$
$797$	5.77010	+	7.03088i	0.204387	+	0.249047i	−0.660721	+	0.750631i	$0.729749\pi$
$798$	3.98986	+	2.29880i	0.141239	+	0.0813768i
$799$	−1.59665	+	1.59665i	−0.0564853	+	0.0564853i
$800$	11.3282	−	23.2319i	0.400512	−	0.821371i
$801$	−0.813252	−	0.813252i	−0.0287348	−	0.0287348i
$802$	3.67206	+	13.6556i	0.129665	+	0.482195i
$803$	5.83430	−	4.78808i	0.205888	−	0.168968i
$804$	7.93217	+	3.89414i	0.279746	+	0.137336i
$805$	1.42154	−	4.68620i	0.0501028	−	0.165167i
$806$	−15.8623	+	22.1775i	−0.558725	+	0.781170i
$807$	−9.00646	−	6.01793i	−0.317043	−	0.211841i
$808$	5.17040	+	51.0941i	0.181894	+	1.79749i
$809$	−26.5333	−	39.7099i	−0.932861	−	1.39612i	−0.918150	−	0.396233i	$-0.870317\pi$
$809$	−26.5333	−	39.7099i	−0.932861	−	1.39612i	−0.0147109	−	0.999892i	$-0.504683\pi$
$810$	0.635219	+	0.677006i	0.0223193	+	0.0237876i
$811$	−17.9958	+	1.77243i	−0.631919	+	0.0622386i	−0.408905	−	0.912577i	$-0.634089\pi$
$811$	−17.9958	+	1.77243i	−0.631919	+	0.0622386i	−0.223014	+	0.974815i	$0.571589\pi$
$812$	−4.29567	−	5.97207i	−0.150748	−	0.209579i
$813$	6.22752	+	20.5294i	0.218409	+	0.719997i
$814$	3.66678	−	10.8337i	0.128520	−	0.379721i
$815$	−11.2312	−	4.65213i	−0.393413	−	0.162957i
$816$	16.3766	−	10.2648i	0.573294	−	0.359340i
$817$	−2.66676	+	1.10461i	−0.0932981	+	0.0386454i
$818$	3.68407	+	55.4502i	0.128810	+	1.93877i
$819$	−2.77690	+	5.19522i	−0.0970329	+	0.181536i
$820$	−8.83720	−	8.24740i	−0.308609	−	0.288012i
$821$	7.01063	−	8.54248i	0.244673	−	0.298135i	−0.636165	−	0.771553i	$-0.719480\pi$
$821$	7.01063	−	8.54248i	0.244673	−	0.298135i	0.880838	+	0.473419i	$0.156980\pi$
$822$	−6.04277	+	2.28049i	−0.210766	+	0.0795412i
$823$	−3.01908	+	15.1779i	−0.105238	+	0.529069i	0.891818	+	0.452395i	$0.149430\pi$
$823$	−3.01908	+	15.1779i	−0.105238	+	0.529069i	−0.997056	+	0.0766745i	$0.975570\pi$
$824$	−9.09921	−	1.78465i	−0.316986	−	0.0621713i
$825$	25.3095	−	5.03437i	0.881163	−	0.175274i
$826$	25.7007	+	5.96840i	0.894241	+	0.207667i
$827$	−26.9525	+	14.4064i	−0.937231	+	0.500960i	−0.867958	−	0.496637i	$-0.834568\pi$
$827$	−26.9525	+	14.4064i	−0.937231	+	0.500960i	−0.0692727	+	0.997598i	$0.522068\pi$
$828$	−1.10525	−	8.28107i	−0.0384102	−	0.287787i
$829$	2.06234	−	20.9393i	0.0716279	−	0.727250i	−0.890560	−	0.454865i	$-0.849687\pi$
$829$	2.06234	−	20.9393i	0.0716279	−	0.727250i	0.962188	−	0.272385i	$-0.0878125\pi$
$830$	1.27527	−	9.75384i	0.0442652	−	0.338561i
$831$		−	6.05730i		−	0.210125i
$832$	−25.2110	+	7.79524i	−0.874036	+	0.270251i
$833$		−	18.4130i		−	0.637974i
$834$	−8.58660	−	1.12266i	−0.297330	−	0.0388745i
$835$	1.18074	−	11.9882i	0.0408610	−	0.414869i
$836$	−12.5080	+	16.3611i	−0.432598	+	0.565860i
$837$	−5.15483	+	2.75531i	−0.178177	+	0.0952376i
$838$	5.52859	−	23.8068i	0.190982	−	0.822393i
$839$	33.1504	−	6.59402i	1.14448	−	0.227651i	0.413797	−	0.910369i	$-0.364202\pi$
$839$	33.1504	−	6.59402i	1.14448	−	0.227651i	0.730682	+	0.682718i	$0.239202\pi$
$840$	−2.76192	−	1.83478i	−0.0952951	−	0.0633060i
$841$	4.83001	−	24.2821i	0.166552	−	0.837313i
$842$	−11.0824	−	29.3657i	−0.381924	−	1.01201i
$843$	14.0655	−	17.1389i	0.484442	−	0.590294i
$844$	30.9780	−	1.06943i	1.06631	−	0.0368114i
$845$	−0.655819	+	1.22695i	−0.0225609	+	0.0422084i
$846$	0.659423	−	0.0438115i	0.0226714	−	0.00150627i
$847$	−34.4796	+	14.2819i	−1.18473	+	0.490733i
$848$	−41.2892	+	15.7085i	−1.41788	+	0.539433i
$849$	−4.84656	−	2.00751i	−0.166333	−	0.0688976i
$850$	29.5741	+	10.0097i	1.01438	+	0.343328i
$851$	−1.73639	−	5.72411i	−0.0595227	−	0.196220i
$852$	2.33290	−	14.2887i	0.0799239	−	0.489523i
$853$	−37.8549	+	3.72838i	−1.29613	+	0.127657i	−0.722449	−	0.691425i	$-0.756983\pi$
$853$	−37.8549	+	3.72838i	−1.29613	+	0.127657i	−0.573677	+	0.819082i	$0.694483\pi$
$854$	−20.8630	+	19.5753i	−0.713916	+	0.669852i
$855$	−0.664935	−	0.995146i	−0.0227403	−	0.0340333i
$856$	−36.9897	+	19.8988i	−1.26428	+	0.680127i
$857$	−11.5934	−	7.74647i	−0.396023	−	0.264614i	0.341574	−	0.939855i	$-0.389040\pi$
$857$	−11.5934	−	7.74647i	−0.396023	−	0.264614i	−0.737598	+	0.675240i	$0.764040\pi$
$858$	−21.4294	−	15.3272i	−0.731586	−	0.523260i
$859$	−8.92215	+	29.4124i	−0.304420	+	1.00354i	0.662629	+	0.748947i	$0.269440\pi$
$859$	−8.92215	+	29.4124i	−0.304420	+	1.00354i	−0.967049	+	0.254590i	$0.918060\pi$
$860$	1.96702	−	0.671629i	0.0670749	−	0.0229024i
$861$	12.7102	−	10.4310i	0.433162	−	0.355487i
$862$	24.8783	−	6.68991i	0.847358	−	0.227859i
$863$	−19.7786	−	19.7786i	−0.673272	−	0.673272i	0.285197	−	0.958469i	$-0.407941\pi$
$863$	−19.7786	−	19.7786i	−0.673272	−	0.673272i	−0.958469	+	0.285197i	$0.907941\pi$
$864$	−5.58535	−	0.896579i	−0.190017	−	0.0305022i
$865$	−3.01672	+	3.01672i	−0.102572	+	0.102572i
$866$	−24.7074	+	42.8828i	−0.839592	+	1.45722i
$867$	4.02672	+	4.90657i	0.136755	+	0.166636i
$868$	15.6713	−	13.7929i	0.531920	−	0.468162i
$869$	24.2988	+	7.37096i	0.824280	+	0.250043i
$870$	0.313154	+	1.88628i	0.0106169	+	0.0639508i
$871$	8.09686	−	12.1178i	0.274352	−	0.410596i
$872$	−28.3802	−	34.3933i	−0.961073	−	1.16470i
$873$	−14.9262	+	9.97337i	−0.505176	+	0.337548i
$874$	−0.342810	+	10.7653i	−0.0115957	+	0.364143i
$875$	−1.09956	−	11.1640i	−0.0371718	−	0.377411i
$876$	−2.27219	−	1.40732i	−0.0767702	−	0.0475491i
$877$	25.4505	−	7.72034i	0.859403	−	0.260697i	0.170329	−	0.985387i	$-0.445517\pi$
$877$	25.4505	−	7.72034i	0.859403	−	0.260697i	0.689075	+	0.724690i	$0.258017\pi$
$878$	10.2257	+	20.6891i	0.345101	+	0.698225i
$879$	−5.30101	+	12.7978i	−0.178799	+	0.431658i
$880$	9.73821	−	11.1845i	0.328275	−	0.377031i
$881$	−21.8908	−	52.8492i	−0.737521	−	1.78053i	−0.615698	−	0.787983i	$-0.711126\pi$
$881$	−21.8908	−	52.8492i	−0.737521	−	1.78053i	−0.121824	−	0.992552i	$-0.538874\pi$
$882$	−3.54971	+	4.05496i	−0.119525	+	0.136538i
$883$	−24.7472	−	13.2276i	−0.832808	−	0.445145i	−0.000860558	−	1.00000i	$-0.500274\pi$
$883$	−24.7472	−	13.2276i	−0.832808	−	0.445145i	−0.831947	+	0.554854i	$0.812774\pi$
$884$	−13.2076	−	29.0120i	−0.444220	−	0.975781i
$885$	−5.30118	−	4.35057i	−0.178197	−	0.146243i
$886$	−9.02281	+	19.9611i	−0.303127	+	0.670606i
$887$	−20.9062	−	4.15850i	−0.701962	−	0.139629i	−0.168810	−	0.985649i	$-0.553992\pi$
$887$	−20.9062	−	4.15850i	−0.701962	−	0.139629i	−0.533152	+	0.846020i	$0.678992\pi$
$888$	−4.05019	+	0.0108362i	−0.135916	+	0.000363638i
$889$	6.34021	+	31.8744i	0.212644	+	1.06903i
$890$	−0.564632	−	0.906199i	−0.0189265	−	0.0303758i
$891$	−2.66236	−	4.98093i	−0.0891925	−	0.166867i
$892$	9.52353	−	5.52108i	0.318871	−	0.184860i
$893$	−0.847913	−	0.0835121i	−0.0283743	−	0.00279463i
$894$	10.5697	+	13.7493i	0.353504	+	0.459846i
$895$	9.19810			0.307459
$896$	20.1528	−	1.44728i	0.673256	−	0.0483504i
$897$	−13.7790			−0.460068
$898$	−15.7754	−	20.5210i	−0.526433	−	0.684795i
$899$	−11.9808	−	1.18000i	−0.399581	−	0.0393552i
$900$	−4.58319	−	7.90572i	−0.152773	−	0.263524i
$901$	−25.1557	−	47.0629i	−0.838057	−	1.56789i
$902$	38.8891	+	62.4145i	1.29486	+	2.07818i
$903$	0.551580	+	2.77298i	0.0183554	+	0.0922791i
$904$	7.02480	−	7.06249i	0.233641	−	0.234895i
$905$	7.63144	+	1.51799i	0.253678	+	0.0504596i
$906$	−1.72395	+	3.81389i	−0.0572745	+	0.126708i
$907$	−0.0676077	−	0.0554842i	−0.00224488	−	0.00184232i	0.633270	−	0.773931i	$-0.281712\pi$
$907$	−0.0676077	−	0.0554842i	−0.00224488	−	0.00184232i	−0.635515	+	0.772088i	$0.719212\pi$
$908$	39.9883	−	18.2045i	1.32706	−	0.604137i
$909$	16.0128	+	8.55904i	0.531112	+	0.283885i
$910$	−3.60213	+	4.11483i	−0.119409	+	0.136405i
$911$	4.92176	+	11.8822i	0.163065	+	0.393674i	0.984200	−	0.177060i	$-0.0566587\pi$
$911$	4.92176	+	11.8822i	0.163065	+	0.393674i	−0.821135	+	0.570734i	$0.806659\pi$
$912$	6.91421	+	2.31959i	0.228952	+	0.0768091i
$913$	−22.9014	+	55.2890i	−0.757927	+	1.82980i
$914$	−12.4751	−	25.2402i	−0.412640	−	0.834872i
$915$	7.11572	−	2.15853i	0.235239	−	0.0713588i
$916$	−5.50728	+	8.89175i	−0.181966	+	0.293792i
$917$	0.326633	+	3.31636i	0.0107864	+	0.109516i
$918$	0.217490	−	6.82989i	0.00717824	−	0.225420i
$919$	−11.3803	+	7.60404i	−0.375400	+	0.250834i	−0.728929	−	0.684589i	$-0.759982\pi$
$919$	−11.3803	+	7.60404i	−0.375400	+	0.250834i	0.353529	+	0.935424i	$0.384982\pi$
$920$	0.739561	−	7.72059i	0.0243826	−	0.254540i
$921$	−15.3792	+	23.0166i	−0.506762	+	0.758423i
$922$	−0.639284	−	3.85072i	−0.0210537	−	0.126817i
$923$	−22.8501	−	6.93150i	−0.752120	−	0.228153i
$924$	13.3276	+	15.1426i	0.438446	+	0.498156i
$925$	−4.15068	−	5.05762i	−0.136474	−	0.166294i
$926$	−27.1784	+	47.1715i	−0.893139	+	1.55015i
$927$	−2.31814	+	2.31814i	−0.0761378	+	0.0761378i
$928$	−8.53923	−	7.92668i	−0.280314	−	0.260206i
$929$	27.8245	+	27.8245i	0.912894	+	0.912894i	0.996499	−	0.0836051i	$-0.0266434\pi$
$929$	27.8245	+	27.8245i	0.912894	+	0.912894i	−0.0836051	+	0.996499i	$0.526643\pi$
$930$	−5.24008	+	1.40908i	−0.171829	+	0.0462057i
$931$	5.37074	−	4.40765i	0.176019	−	0.144455i
$932$	13.8124	+	40.4530i	0.452442	+	1.32508i
$933$	−6.62058	+	21.8251i	−0.216748	+	0.714522i
$934$	−41.3687	−	29.5886i	−1.35362	−	0.968167i
$935$	14.8951	+	9.95260i	0.487122	+	0.325485i
$936$	−2.68440	+	8.93528i	−0.0877425	+	0.292059i
$937$	8.77166	+	13.1277i	0.286558	+	0.428864i	0.946622	−	0.322345i	$-0.104471\pi$
$937$	8.77166	+	13.1277i	0.286558	+	0.428864i	−0.660065	+	0.751209i	$0.729471\pi$
$938$	−8.13749	+	7.63523i	−0.265699	+	0.249299i
$939$	16.0036	−	1.57621i	0.522257	−	0.0514378i
$940$	0.605510	+	0.0988609i	0.0197495	+	0.00322449i
$941$	−5.98028	−	19.7143i	−0.194952	−	0.642669i	−0.998852	−	0.0479051i	$-0.984745\pi$
$941$	−5.98028	−	19.7143i	−0.194952	−	0.642669i	0.803900	−	0.594764i	$-0.202755\pi$
$942$	−20.5489	−	6.95498i	−0.669520	−	0.226606i
$943$	35.5325	+	14.7181i	1.15710	+	0.479286i
$944$	41.7700	+	1.21826i	1.35950	+	0.0396510i
$945$	−1.08308	+	0.448626i	−0.0352326	+	0.0145938i
$946$	−12.6173	+	0.838281i	−0.410223	+	0.0272549i
$947$	8.10741	−	15.1679i	0.263455	−	0.492890i	−0.715060	−	0.699063i	$-0.753601\pi$
$947$	8.10741	−	15.1679i	0.263455	−	0.492890i	0.978516	+	0.206172i	$0.0661008\pi$
$948$	−0.310235	−	8.98651i	−0.0100759	−	0.291868i
$949$	−2.79646	+	3.40750i	−0.0907770	+	0.110612i
$950$	4.15972	+	11.0223i	0.134959	+	0.357610i
$951$	5.10645	−	25.6718i	0.165588	−	0.832467i
$952$	4.82555	+	23.9250i	0.156397	+	0.775413i
$953$	−4.66600	+	0.928125i	−0.151147	+	0.0300649i	−0.270084	−	0.962837i	$-0.587051\pi$
$953$	−4.66600	+	0.928125i	−0.151147	+	0.0300649i	0.118937	+	0.992902i	$0.462051\pi$
$954$	−3.53307	+	15.2139i	−0.114387	+	0.492567i
$955$	−6.18878	+	3.30797i	−0.200264	+	0.107043i
$956$	−48.2604	−	36.8950i	−1.56085	−	1.19327i
$957$	1.14019	−	11.5766i	0.0368572	−	0.374217i
$958$	−35.3363	−	4.62006i	−1.14166	−	0.149267i
$959$		−	8.15607i		−	0.263373i
$960$	−4.86249	−	1.98369i	−0.156936	−	0.0640235i
$961$		−	3.16404i		−	0.102066i
$962$	−0.866006	+	6.62361i	−0.0279211	+	0.213554i
$963$	−1.45556	+	14.7786i	−0.0469048	+	0.476233i
$964$	−44.2672	+	5.90823i	−1.42575	+	0.190291i
$965$	5.73696	−	3.06647i	0.184679	−	0.0987130i
$966$	10.2765	+	2.38649i	0.330642	+	0.0767840i
$967$	−32.7389	+	6.51216i	−1.05281	+	0.209417i	−0.691015	−	0.722840i	$-0.742836\pi$
$967$	−32.7389	+	6.51216i	−1.05281	+	0.209417i	−0.361796	+	0.932257i	$0.617836\pi$
$968$	−49.0584	+	32.9700i	−1.57680	+	1.05969i
$969$	−1.71869	+	8.64042i	−0.0552122	+	0.277570i
$970$	−15.5920	+	5.88430i	−0.500630	+	0.188934i
$971$	13.2798	−	16.1814i	0.426168	−	0.519287i	−0.515017	−	0.857180i	$-0.672214\pi$
$971$	13.2798	−	16.1814i	0.426168	−	0.519287i	0.941184	+	0.337893i	$0.109714\pi$
$972$	−1.36458	+	1.46216i	−0.0437689	+	0.0468989i
$973$	5.15490	−	9.64414i	0.165258	−	0.309177i
$974$	−3.55863	−	53.5623i	−0.114026	−	1.71625i
$975$	−13.9243	+	5.76761i	−0.445933	+	0.184711i
$976$	−26.2606	+	36.9242i	−0.840582	+	1.18191i
$977$	11.7056	+	4.84862i	0.374496	+	0.155121i	0.561989	−	0.827145i	$-0.310036\pi$
$977$	11.7056	+	4.84862i	0.374496	+	0.155121i	−0.187493	+	0.982266i	$0.560036\pi$
$978$	8.39624	−	24.8072i	0.268482	−	0.793246i
$979$	1.88558	+	6.21592i	0.0602633	+	0.198662i
$980$	−4.06151	+	2.92142i	−0.129740	+	0.0933212i
$981$	−15.6893	+	1.54526i	−0.500920	+	0.0493363i
$982$	−1.11367	−	1.18694i	−0.0355388	−	0.0378766i
$983$	−22.4771	−	33.6394i	−0.716909	−	1.07293i	−0.993708	−	0.112002i	$-0.964274\pi$
$983$	−22.4771	−	33.6394i	−0.716909	−	1.07293i	0.276799	−	0.960928i	$-0.410726\pi$
$984$	16.4666	−	20.1744i	0.524936	−	0.643138i
$985$	−10.1077	−	6.75376i	−0.322059	−	0.215193i
$986$	8.18781	−	11.4476i	0.260753	−	0.364567i
$987$	−0.242257	+	0.798614i	−0.00771112	+	0.0254202i
$988$	5.30068	−	10.7972i	0.168637	−	0.343505i
$989$	−5.11214	+	4.19542i	−0.162557	+	0.133407i
$990$	−1.36155	−	5.06330i	−0.0432728	−	0.160922i
$991$	16.3357	+	16.3357i	0.518920	+	0.518920i	0.917245	−	0.398324i	$-0.130408\pi$
$991$	16.3357	+	16.3357i	0.518920	+	0.518920i	−0.398324	+	0.917245i	$0.630408\pi$
$992$	20.0111	−	26.3212i	0.635354	−	0.835698i
$993$	5.84289	−	5.84289i	0.185419	−	0.185419i
$994$	15.8413	+	9.12715i	0.502456	+	0.289496i
$995$	−4.79555	−	5.84339i	−0.152029	−	0.185248i
$996$	21.1491	+	1.34831i	0.670135	+	0.0427227i
$997$	31.8640	+	9.66584i	1.00914	+	0.306120i	0.751225	−	0.660047i	$-0.229464\pi$
$997$	31.8640	+	9.66584i	1.00914	+	0.306120i	0.257918	+	0.966167i	$0.416964\pi$
$998$	−14.2895	+	2.37230i	−0.452326	+	0.0750938i
$999$	−0.795557	+	1.19064i	−0.0251703	+	0.0376700i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	384.2.v.a.349.7	✓	512
128.117	even	32	inner	384.2.v.a.373.7	yes	512

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
384.2.v.a.349.7	✓	512	1.1	even	1	trivial
384.2.v.a.373.7	yes	512	128.117	even	32	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+(-1.12120 + 0.861919i) q^{2} +(-0.995185 - 0.0980171i) q^{3} +(0.514192 - 1.93277i) q^{4} +(-0.309446 - 0.578933i) q^{5} +(1.20029 - 0.747871i) q^{6} +(0.348403 + 1.75154i) q^{7} +(1.08938 + 2.61022i) q^{8} +(0.980785 + 0.195090i) q^{9} +O(q^{10})\)	\(q+(-1.12120 + 0.861919i) q^{2} +(-0.995185 - 0.0980171i) q^{3} +(0.514192 - 1.93277i) q^{4} +(-0.309446 - 0.578933i) q^{5} +(1.20029 - 0.747871i) q^{6} +(0.348403 + 1.75154i) q^{7} +(1.08938 + 2.61022i) q^{8} +(0.980785 + 0.195090i) q^{9} +(0.845945 + 0.382384i) q^{10} +(-4.36582 - 3.58294i) q^{11} +(-0.701160 + 1.87307i) q^{12} +(2.90909 + 1.55494i) q^{13} +(-1.90032 - 1.66354i) q^{14} +(0.251211 + 0.606476i) q^{15} +(-3.47121 - 1.98763i) q^{16} +(1.84909 - 4.46410i) q^{17} +(-1.26781 + 0.626622i) q^{18} +(1.74472 - 0.529256i) q^{19} +(-1.27806 + 0.300406i) q^{20} +(-0.175045 - 1.77726i) q^{21} +(7.98317 + 0.254215i) q^{22} +(3.47326 - 2.32076i) q^{23} +(-0.828288 - 2.70443i) q^{24} +(2.53844 - 3.79905i) q^{25} +(-4.60192 + 0.763996i) q^{26} +(-0.956940 - 0.290285i) q^{27} +(3.56448 + 0.227244i) q^{28} +(-1.30664 - 1.59214i) q^{29} +(-0.804391 - 0.463460i) q^{30} +(4.13304 - 4.13304i) q^{31} +(5.60511 - 0.763369i) q^{32} +(3.99361 + 3.99361i) q^{33} +(1.77449 + 6.59893i) q^{34} +(0.906213 - 0.743710i) q^{35} +(0.881377 - 1.79532i) q^{36} +(0.415677 - 1.37031i) q^{37} +(-1.50001 + 2.09721i) q^{38} +(-2.74267 - 1.83260i) q^{39} +(1.17404 - 1.43840i) q^{40} +(5.11516 + 7.65538i) q^{41} +(1.72811 + 1.84179i) q^{42} +(-1.57554 + 0.155177i) q^{43} +(-9.16986 + 6.59582i) q^{44} +(-0.190556 - 0.628179i) q^{45} +(-1.89392 + 5.59571i) q^{46} +(-0.431738 - 0.178832i) q^{47} +(3.25968 + 2.31830i) q^{48} +(3.52064 - 1.45830i) q^{49} +(0.428363 + 6.44744i) q^{50} +(-2.27775 + 4.26136i) q^{51} +(4.50118 - 4.82307i) q^{52} +(7.00630 - 8.53721i) q^{53} +(1.32313 - 0.499337i) q^{54} +(-0.723293 + 3.63624i) q^{55} +(-4.19237 + 2.81750i) q^{56} +(-1.78820 + 0.355695i) q^{57} +(2.83730 + 0.658898i) q^{58} +(-9.21337 + 4.92465i) q^{59} +(1.30135 - 0.173688i) q^{60} +(1.11029 - 11.2730i) q^{61} +(-1.07163 + 8.19632i) q^{62} +1.78586i q^{63} +(-5.62650 + 5.68704i) q^{64} -2.16534i q^{65} +(-7.91981 - 1.03548i) q^{66} +(0.433064 - 4.39697i) q^{67} +(-7.67731 - 5.86928i) q^{68} +(-3.68401 + 1.96914i) q^{69} +(-0.375031 + 1.61493i) q^{70} +(-7.09985 + 1.41225i) q^{71} +(0.559219 + 2.77259i) q^{72} +(-0.260710 + 1.31068i) q^{73} +(0.715033 + 1.89467i) q^{74} +(-2.89859 + 3.53195i) q^{75} +(-0.125809 - 3.64429i) q^{76} +(4.75459 - 8.89522i) q^{77} +(4.65464 - 0.309251i) q^{78} +(-4.15370 + 1.72052i) q^{79} +(-0.0765507 + 2.62466i) q^{80} +(0.923880 + 0.382683i) q^{81} +(-12.3334 - 4.17438i) q^{82} +(-3.07586 - 10.1398i) q^{83} +(-3.52504 - 0.575529i) q^{84} +(-3.15661 + 0.310899i) q^{85} +(1.63275 - 1.53198i) q^{86} +(1.14429 + 1.71255i) q^{87} +(4.59622 - 15.2989i) q^{88} +(-0.956283 - 0.638968i) q^{89} +(0.755091 + 0.540072i) q^{90} +(-1.71001 + 5.63714i) q^{91} +(-2.69957 - 7.90633i) q^{92} +(-4.51825 + 3.70803i) q^{93} +(0.638205 - 0.171617i) q^{94} +(-0.846302 - 0.846302i) q^{95} +(-5.65294 + 0.210296i) q^{96} +(-12.6937 + 12.6937i) q^{97} +(-2.69042 + 4.66956i) q^{98} +(-3.58294 - 4.36582i) 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

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