LMFDB - Embedded newform 384.2.v.a.325.20

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			325.20
Character	$\chi$	$=$	384.325
Dual form			384.2.v.a.13.20

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.320440 + 1.37743i) q^{2} +(0.290285 - 0.956940i) q^{3} +(-1.79464 + 0.882769i) q^{4} +(-0.362380 + 3.67931i) q^{5} +(1.41114 + 0.0932050i) q^{6} +(1.08924 + 1.63016i) q^{7} +(-1.79103 - 2.18911i) q^{8} +(-0.831470 - 0.555570i) q^{9} +O(q^{10})$	\(q+(0.320440 + 1.37743i) q^{2} +(0.290285 - 0.956940i) q^{3} +(-1.79464 + 0.882769i) q^{4} +(-0.362380 + 3.67931i) q^{5} +(1.41114 + 0.0932050i) q^{6} +(1.08924 + 1.63016i) q^{7} +(-1.79103 - 2.18911i) q^{8} +(-0.831470 - 0.555570i) q^{9} +(-5.18411 + 0.679844i) q^{10} +(-2.84568 - 1.52105i) q^{11} +(0.323802 + 1.97361i) q^{12} +(-0.240556 + 0.0236927i) q^{13} +(-1.89640 + 2.02272i) q^{14} +(3.41568 + 1.41482i) q^{15} +(2.44144 - 3.16850i) q^{16} +(-5.94374 + 2.46198i) q^{17} +(0.498824 - 1.32332i) q^{18} +(6.47447 + 5.31346i) q^{19} +(-2.59764 - 6.92291i) q^{20} +(1.87615 - 0.569125i) q^{21} +(1.18327 - 4.40713i) q^{22} +(-0.594348 - 2.98799i) q^{23} +(-2.61476 + 1.07844i) q^{24} +(-8.50205 - 1.69116i) q^{25} +(-0.109719 - 0.323758i) q^{26} +(-0.773010 + 0.634393i) q^{27} +(-3.39384 - 1.96400i) q^{28} +(2.49129 + 4.66087i) q^{29} +(-0.854298 + 5.15824i) q^{30} +(0.818174 + 0.818174i) q^{31} +(5.14673 + 2.34760i) q^{32} +(-2.28161 + 2.28161i) q^{33} +(-5.29582 - 7.39818i) q^{34} +(-6.39257 + 3.41690i) q^{35} +(1.98263 + 0.263050i) q^{36} +(3.95276 + 4.81646i) q^{37} +(-5.24425 + 10.6208i) q^{38} +(-0.0471573 + 0.237076i) q^{39} +(8.70345 - 5.79645i) q^{40} +(-2.42653 + 0.482668i) q^{41} +(1.38513 + 2.40190i) q^{42} +(-0.861566 - 2.84020i) q^{43} +(6.44969 + 0.217648i) q^{44} +(2.34542 - 2.85790i) q^{45} +(3.92530 - 1.77615i) q^{46} +(3.72788 + 8.99989i) q^{47} +(-2.32335 - 3.25608i) q^{48} +(1.20780 - 2.91590i) q^{49} +(-0.394938 - 12.2529i) q^{50} +(0.630589 + 6.40248i) q^{51} +(0.410796 - 0.254876i) q^{52} +(5.77121 - 10.7972i) q^{53} +(-1.12154 - 0.861484i) q^{54} +(6.62761 - 9.91892i) q^{55} +(1.61775 - 5.30413i) q^{56} +(6.96410 - 4.65326i) q^{57} +(-5.62172 + 4.92511i) q^{58} +(4.74257 + 0.467102i) q^{59} +(-7.37887 + 0.476169i) q^{60} +(-4.34322 - 1.31750i) q^{61} +(-0.864803 + 1.38916i) q^{62} -1.96058i q^{63} +(-1.58444 + 7.84153i) q^{64} -0.893666i q^{65} +(-3.87388 - 2.41164i) q^{66} +(13.4450 + 4.07849i) q^{67} +(8.49349 - 9.66531i) q^{68} +(-3.03186 - 0.298612i) q^{69} +(-6.75499 - 7.71042i) q^{70} +(10.9379 - 7.30845i) q^{71} +(0.272979 + 2.81522i) q^{72} +(3.83429 - 5.73842i) q^{73} +(-5.36772 + 6.98805i) q^{74} +(-4.08636 + 7.64504i) q^{75} +(-16.3099 - 3.82026i) q^{76} +(-0.620071 - 6.29569i) q^{77} +(-0.341667 + 0.0110127i) q^{78} +(0.484546 - 1.16980i) q^{79} +(10.7732 + 10.1310i) q^{80} +(0.382683 + 0.923880i) q^{81} +(-1.44240 - 3.18772i) q^{82} +(-4.93831 + 6.01734i) q^{83} +(-2.86461 + 2.67758i) q^{84} +(-6.90448 - 22.7610i) q^{85} +(3.63611 - 2.09686i) q^{86} +(5.18336 - 1.03103i) q^{87} +(1.76695 + 8.95375i) q^{88} +(-2.97495 + 14.9561i) q^{89} +(4.68814 + 2.31487i) q^{90} +(-0.300646 - 0.366338i) q^{91} +(3.70434 + 4.83768i) q^{92} +(1.02045 - 0.545440i) q^{93} +(-11.2022 + 8.01883i) q^{94} +(-21.8961 + 21.8961i) q^{95} +(3.74053 - 4.24364i) q^{96} +(-7.36441 - 7.36441i) q^{97} +(4.40348 + 0.729296i) q^{98} +(1.52105 + 2.84568i) 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 $\left(\mathbb{Z}/384\mathbb{Z}\right)^\times$.

$n$	$127$	$133$	$257$
$\chi(n)$	$1$	$e\left(\frac{17}{32}\right)$	$1$

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 $

$2$	0.320440	+	1.37743i	0.226586	+	0.973991i
$2$	0.320440	+	1.37743i	0.226586	+	0.973991i
$3$	0.290285	−	0.956940i	0.167596	−	0.552490i
$3$	0.290285	−	0.956940i	0.167596	−	0.552490i
$4$	−1.79464	+	0.882769i	−0.897318	+	0.441385i
$5$	−0.362380	+	3.67931i	−0.162061	+	1.64544i	0.478905	+	0.877867i	$0.341034\pi$
$5$	−0.362380	+	3.67931i	−0.162061	+	1.64544i	−0.640966	+	0.767569i	$0.721466\pi$
$6$	1.41114	+	0.0932050i	0.576095	+	0.0380508i
$7$	1.08924	+	1.63016i	0.411693	+	0.616142i	0.978138	−	0.207957i	$-0.0666815\pi$
$7$	1.08924	+	1.63016i	0.411693	+	0.616142i	−0.566445	+	0.824100i	$0.691682\pi$
$8$	−1.79103	−	2.18911i	−0.633224	−	0.773969i
$9$	−0.831470	−	0.555570i	−0.277157	−	0.185190i
$10$	−5.18411	+	0.679844i	−1.63936	+	0.214986i
$11$	−2.84568	−	1.52105i	−0.858004	−	0.458613i	−0.0171361	−	0.999853i	$-0.505455\pi$
$11$	−2.84568	−	1.52105i	−0.858004	−	0.458613i	−0.840868	+	0.541240i	$0.817955\pi$
$12$	0.323802	+	1.97361i	0.0934737	+	0.569733i
$13$	−0.240556	+	0.0236927i	−0.0667183	+	0.00657118i	−0.131321	−	0.991340i	$-0.541922\pi$
$13$	−0.240556	+	0.0236927i	−0.0667183	+	0.00657118i	0.0646029	+	0.997911i	$0.479422\pi$
$14$	−1.89640	+	2.02272i	−0.506834	+	0.540594i
$15$	3.41568	+	1.41482i	0.881926	+	0.365306i
$16$	2.44144	−	3.16850i	0.610359	−	0.792125i
$17$	−5.94374	+	2.46198i	−1.44157	+	0.597117i	−0.960178	−	0.279389i	$-0.909868\pi$
$17$	−5.94374	+	2.46198i	−1.44157	+	0.597117i	−0.481391	+	0.876506i	$0.659868\pi$
$18$	0.498824	−	1.32332i	0.117574	−	0.311909i
$19$	6.47447	+	5.31346i	1.48534	+	1.21899i	0.918656	+	0.395059i	$0.129276\pi$
$19$	6.47447	+	5.31346i	1.48534	+	1.21899i	0.566689	+	0.823932i	$0.308224\pi$
$20$	−2.59764	−	6.92291i	−0.580850	−	1.54801i
$21$	1.87615	−	0.569125i	0.409410	−	0.124193i
$22$	1.18327	−	4.40713i	0.252273	−	0.939603i
$23$	−0.594348	−	2.98799i	−0.123930	−	0.623039i	−0.991963	−	0.126531i	$-0.959616\pi$
$23$	−0.594348	−	2.98799i	−0.123930	−	0.623039i	0.868033	−	0.496507i	$-0.165384\pi$
$24$	−2.61476	+	1.07844i	−0.533735	+	0.220136i
$25$	−8.50205	−	1.69116i	−1.70041	−	0.338233i
$26$	−0.109719	−	0.323758i	−0.0215177	−	0.0634941i
$27$	−0.773010	+	0.634393i	−0.148766	+	0.122089i
$28$	−3.39384	−	1.96400i	−0.641375	−	0.371161i
$29$	2.49129	+	4.66087i	0.462621	+	0.865502i	0.999758	+	0.0220074i	$0.00700573\pi$
$29$	2.49129	+	4.66087i	0.462621	+	0.865502i	−0.537137	+	0.843495i	$0.680494\pi$
$30$	−0.854298	+	5.15824i	−0.155973	+	0.941761i
$31$	0.818174	+	0.818174i	0.146948	+	0.146948i	0.776753	−	0.629805i	$-0.216865\pi$
$31$	0.818174	+	0.818174i	0.146948	+	0.146948i	−0.629805	+	0.776753i	$0.716865\pi$
$32$	5.14673	+	2.34760i	0.909821	+	0.415000i
$33$	−2.28161	+	2.28161i	−0.397177	+	0.397177i
$34$	−5.29582	−	7.39818i	−0.908226	−	1.26878i
$35$	−6.39257	+	3.41690i	−1.08054	+	0.577562i
$36$	1.98263	+	0.263050i	0.330438	+	0.0438417i
$37$	3.95276	+	4.81646i	0.649831	+	0.791821i	0.988843	−	0.148961i	$-0.0475929\pi$
$37$	3.95276	+	4.81646i	0.649831	+	0.791821i	−0.339013	+	0.940782i	$0.610093\pi$
$38$	−5.24425	+	10.6208i	−0.850729	+	1.72292i
$39$	−0.0471573	+	0.237076i	−0.00755121	+	0.0379625i
$40$	8.70345	−	5.79645i	1.37614	−	0.916499i
$41$	−2.42653	+	0.482668i	−0.378961	+	0.0753800i	−0.380895	−	0.924618i	$-0.624384\pi$
$41$	−2.42653	+	0.482668i	−0.378961	+	0.0753800i	0.00193451	+	0.999998i	$0.499384\pi$
$42$	1.38513	+	2.40190i	0.213730	+	0.370622i
$43$	−0.861566	−	2.84020i	−0.131388	−	0.433127i	0.866419	−	0.499317i	$-0.166416\pi$
$43$	−0.861566	−	2.84020i	−0.131388	−	0.433127i	−0.997807	+	0.0661900i	$0.978916\pi$
$44$	6.44969	+	0.217648i	0.972327	+	0.0328116i
$45$	2.34542	−	2.85790i	0.349635	−	0.426031i
$46$	3.92530	−	1.77615i	0.578753	−	0.261878i
$47$	3.72788	+	8.99989i	0.543767	+	1.31277i	0.922047	+	0.387078i	$0.126516\pi$
$47$	3.72788	+	8.99989i	0.543767	+	1.31277i	−0.378280	+	0.925691i	$0.623484\pi$
$48$	−2.32335	−	3.25608i	−0.335347	−	0.469974i
$49$	1.20780	−	2.91590i	0.172543	−	0.416556i
$50$	−0.394938	−	12.2529i	−0.0558527	−	1.73282i
$51$	0.630589	+	6.40248i	0.0883002	+	0.896527i
$52$	0.410796	−	0.254876i	0.0569671	−	0.0353449i
$53$	5.77121	−	10.7972i	0.792737	−	1.48311i	−0.0810041	−	0.996714i	$-0.525813\pi$
$53$	5.77121	−	10.7972i	0.792737	−	1.48311i	0.873741	−	0.486392i	$-0.161687\pi$
$54$	−1.12154	−	0.861484i	−0.152622	−	0.117233i
$55$	6.62761	−	9.91892i	0.893667	−	1.33747i
$56$	1.61775	−	5.30413i	0.216181	−	0.708794i
$57$	6.96410	−	4.65326i	0.922418	−	0.616340i
$58$	−5.62172	+	4.92511i	−0.738169	+	0.646699i
$59$	4.74257	+	0.467102i	0.617429	+	0.0608115i	0.401897	−	0.915685i	$-0.368351\pi$
$59$	4.74257	+	0.467102i	0.617429	+	0.0608115i	0.215533	+	0.976497i	$0.430851\pi$
$60$	−7.37887	+	0.476169i	−0.952608	+	0.0614732i
$61$	−4.34322	−	1.31750i	−0.556093	−	0.168689i	−0.000285186	−	1.00000i	$-0.500091\pi$
$61$	−4.34322	−	1.31750i	−0.556093	−	0.168689i	−0.555807	+	0.831311i	$0.687591\pi$
$62$	−0.864803	+	1.38916i	−0.109830	+	0.176423i
$63$		−	1.96058i		−	0.247009i
$64$	−1.58444	+	7.84153i	−0.198055	+	0.980191i
$65$		−	0.893666i		−	0.110846i
$66$	−3.87388	−	2.41164i	−0.476841	−	0.296852i
$67$	13.4450	+	4.07849i	1.64257	+	0.498267i	0.970272	−	0.242017i	$-0.0778091\pi$
$67$	13.4450	+	4.07849i	1.64257	+	0.498267i	0.672294	+	0.740284i	$0.265309\pi$
$68$	8.49349	−	9.66531i	1.02999	−	1.17209i
$69$	−3.03186	−	0.298612i	−0.364993	−	0.0359486i
$70$	−6.75499	−	7.71042i	−0.807375	−	0.921572i
$71$	10.9379	−	7.30845i	1.29809	−	0.867353i	0.301793	−	0.953374i	$-0.402415\pi$
$71$	10.9379	−	7.30845i	1.29809	−	0.867353i	0.996293	+	0.0860202i	$0.0274150\pi$
$72$	0.272979	+	2.81522i	0.0321709	+	0.331777i
$73$	3.83429	−	5.73842i	0.448770	−	0.671631i	−0.536253	−	0.844057i	$-0.680161\pi$
$73$	3.83429	−	5.73842i	0.448770	−	0.671631i	0.985022	+	0.172426i	$0.0551606\pi$
$74$	−5.36772	+	6.98805i	−0.623984	+	0.812344i
$75$	−4.08636	+	7.64504i	−0.471852	+	0.882773i
$76$	−16.3099	−	3.82026i	−1.87087	−	0.438214i
$77$	−0.620071	−	6.29569i	−0.0706637	−	0.717460i
$78$	−0.341667	+	0.0110127i	−0.0386861	+	0.00124694i
$79$	0.484546	−	1.16980i	0.0545156	−	0.131612i	−0.894275	−	0.447518i	$-0.852308\pi$
$79$	0.484546	−	1.16980i	0.0545156	−	0.131612i	0.948791	+	0.315905i	$0.102308\pi$
$80$	10.7732	+	10.1310i	1.20447	+	1.13268i
$81$	0.382683	+	0.923880i	0.0425204	+	0.102653i
$82$	−1.44240	−	3.18772i	−0.159287	−	0.352025i
$83$	−4.93831	+	6.01734i	−0.542049	+	0.660489i	−0.969941	−	0.243341i	$-0.921757\pi$
$83$	−4.93831	+	6.01734i	−0.542049	+	0.660489i	0.427891	+	0.903830i	$0.359257\pi$
$84$	−2.86461	+	2.67758i	−0.312554	+	0.292148i
$85$	−6.90448	−	22.7610i	−0.748896	−	2.46878i
$86$	3.63611	−	2.09686i	0.392091	−	0.226111i
$87$	5.18336	−	1.03103i	0.555714	−	0.110538i
$88$	1.76695	+	8.95375i	0.188357	+	0.954473i
$89$	−2.97495	+	14.9561i	−0.315345	+	1.58534i	0.419918	+	0.907562i	$0.362059\pi$
$89$	−2.97495	+	14.9561i	−0.315345	+	1.58534i	−0.735263	+	0.677782i	$0.762941\pi$
$90$	4.68814	+	2.31487i	0.494173	+	0.244009i
$91$	−0.300646	−	0.366338i	−0.0315163	−	0.0384027i
$92$	3.70434	+	4.83768i	0.386204	+	0.504363i
$93$	1.02045	−	0.545440i	0.105815	−	0.0565595i
$94$	−11.2022	+	8.01883i	−1.15542	+	0.827079i
$95$	−21.8961	+	21.8961i	−2.24649	+	2.24649i
$96$	3.74053	−	4.24364i	0.381766	−	0.433114i
$97$	−7.36441	−	7.36441i	−0.747742	−	0.747742i	0.226312	−	0.974055i	$-0.427333\pi$
$97$	−7.36441	−	7.36441i	−0.747742	−	0.747742i	−0.974055	+	0.226312i	$0.927333\pi$
$98$	4.40348	+	0.729296i	0.444818	+	0.0736700i
$99$	1.52105	+	2.84568i	0.152871	+	0.286001i
$100$	16.7510	−	4.47033i	1.67510	−	0.447033i
$101$	1.22638	−	1.00646i	0.122029	−	0.100147i	−0.571399	−	0.820672i	$-0.693599\pi$
$101$	1.22638	−	1.00646i	0.122029	−	0.100147i	0.693429	+	0.720525i	$0.256099\pi$
$102$	−8.61691	+	2.92021i	−0.853201	+	0.289144i
$103$	−8.77570	−	1.74560i	−0.864696	−	0.171999i	−0.257235	−	0.966349i	$-0.582812\pi$
$103$	−8.77570	−	1.74560i	−0.864696	−	0.171999i	−0.607460	+	0.794350i	$0.707812\pi$
$104$	0.482709	+	0.484171i	0.0473335	+	0.0474769i
$105$	1.41411	+	7.10919i	0.138003	+	0.693786i
$106$	16.7217	+	4.48960i	1.62415	+	0.436068i
$107$	10.8713	−	3.29776i	1.05097	−	0.318807i	0.282881	−	0.959155i	$-0.408710\pi$
$107$	10.8713	−	3.29776i	1.05097	−	0.318807i	0.768085	+	0.640348i	$0.221210\pi$
$108$	0.827249	−	1.82089i	0.0796021	−	0.175216i
$109$	11.6520	+	9.56253i	1.11606	+	0.915924i	0.997034	−	0.0769676i	$-0.0245238\pi$
$109$	11.6520	+	9.56253i	1.11606	+	0.915924i	0.119023	+	0.992892i	$0.462024\pi$
$110$	15.7864	+	5.95066i	1.50517	+	0.567373i
$111$	5.75649	−	2.38442i	0.546382	−	0.226319i
$112$	7.82446	+	0.528682i	0.739342	+	0.0499558i
$113$	3.45189	+	1.42982i	0.324727	+	0.134506i	0.539091	−	0.842248i	$-0.318768\pi$
$113$	3.45189	+	1.42982i	0.324727	+	0.134506i	−0.214364	+	0.976754i	$0.568768\pi$
$114$	8.64113	+	8.10148i	0.809316	+	0.758773i
$115$	11.2091	−	1.10400i	1.04525	−	0.102949i
$116$	−8.58543	−	6.16534i	−0.797137	−	0.572437i
$117$	0.213178	+	0.113946i	0.0197083	+	0.0105343i
$118$	0.876308	+	6.68224i	0.0806707	+	0.615150i
$119$	−10.4876	−	7.00757i	−0.961393	−	0.642382i
$120$	−3.02038	−	10.0113i	−0.275722	−	0.913903i
$121$	−0.326975	−	0.489353i	−0.0297250	−	0.0444866i
$122$	0.423025	−	6.40467i	0.0382989	−	0.579852i
$123$	−0.242502	+	2.46216i	−0.0218656	+	0.222005i
$124$	−2.19058	−	0.746066i	−0.196720	−	0.0669987i
$125$	3.93721	−	12.9792i	0.352155	−	1.16090i
$126$	2.70056	−	0.628248i	0.240585	−	0.0559687i
$127$	−5.11999			−0.454326			−0.227163	−	0.973857i	$-0.572945\pi$
$127$	−5.11999			−0.454326			−0.227163	+	0.973857i	$0.572945\pi$
$128$	−11.3089	+	0.330289i	−0.999574	+	0.0291937i
$129$	−2.96800			−0.261318
$130$	1.23096	−	0.286367i	0.107963	−	0.0251160i
$131$	−1.80021	+	5.93448i	−0.157285	+	0.518498i	−0.999796	−	0.0201800i	$-0.993576\pi$
$131$	−1.80021	+	5.93448i	−0.157285	+	0.518498i	0.842512	+	0.538678i	$0.181076\pi$
$132$	2.08052	−	6.10879i	0.181086	−	0.531702i
$133$	−1.60955	+	16.3420i	−0.139566	+	1.41703i
$134$	−1.30953	+	19.8265i	−0.113126	+	1.71275i
$135$	−2.05400	−	3.07403i	−0.176780	−	0.264571i
$136$	16.0350	+	8.60205i	1.37499	+	0.737620i
$137$	−9.70929	−	6.48754i	−0.829521	−	0.554268i	0.0667529	−	0.997770i	$-0.478736\pi$
$137$	−9.70929	−	6.48754i	−0.829521	−	0.554268i	−0.896274	+	0.443501i	$0.853736\pi$
$138$	−0.560212	−	4.27186i	−0.0476884	−	0.363645i
$139$	−4.55213	−	2.43317i	−0.386107	−	0.206378i	0.266911	−	0.963721i	$-0.413997\pi$
$139$	−4.55213	−	2.43317i	−0.386107	−	0.206378i	−0.653017	+	0.757343i	$0.726497\pi$
$140$	8.45601	−	11.7753i	0.714663	−	0.995191i
$141$	9.69451	−	0.954826i	0.816425	−	0.0804108i
$142$	13.5718	+	12.7242i	1.13892	+	1.06779i
$143$	0.720584	+	0.298475i	0.0602582	+	0.0249598i
$144$	−3.79030	+	1.27812i	−0.315859	+	0.106510i
$145$	−18.0516	+	7.47721i	−1.49910	+	0.620948i
$146$	9.13294	+	3.44265i	0.755848	+	0.284916i
$147$	−2.43973	−	2.00224i	−0.201226	−	0.165142i
$148$	−11.3456	−	5.15441i	−0.932602	−	0.423690i
$149$	−6.51869	+	1.97742i	−0.534032	+	0.161997i	−0.545771	−	0.837934i	$-0.683763\pi$
$149$	−6.51869	+	1.97742i	−0.534032	+	0.161997i	0.0117392	+	0.999931i	$0.496263\pi$
$150$	−11.8399	−	3.17890i	−0.966728	−	0.259556i
$151$	−1.91585	−	9.63165i	−0.155910	−	0.783812i	−0.977037	−	0.213068i	$-0.931655\pi$
$151$	−1.91585	−	9.63165i	−0.155910	−	0.783812i	0.821127	−	0.570745i	$-0.193345\pi$
$152$	0.0358098	−	23.6899i	0.00290456	−	1.92150i
$153$	6.30984	+	1.25511i	0.510120	+	0.101469i
$154$	8.47318	−	2.87150i	0.682789	−	0.231392i
$155$	−3.30680	+	2.71382i	−0.265609	+	0.217980i
$156$	−0.124653	−	0.467094i	−0.00998023	−	0.0373974i
$157$	0.847269	+	1.58513i	0.0676195	+	0.126507i	0.913460	−	0.406929i	$-0.133400\pi$
$157$	0.847269	+	1.58513i	0.0676195	+	0.126507i	−0.845840	+	0.533436i	$0.820900\pi$
$158$	1.76658	+	0.292578i	0.140542	+	0.0232763i
$159$	−8.65696	−	8.65696i	−0.686541	−	0.686541i
$160$	−10.5026	+	18.0857i	−0.830304	+	1.42980i
$161$	4.22351	−	4.22351i	0.332859	−	0.332859i
$162$	−1.14995	+	0.823169i	−0.0903489	+	0.0646742i
$163$	8.73846	−	4.67081i	0.684449	−	0.365846i	−0.0922338	−	0.995737i	$-0.529401\pi$
$163$	8.73846	−	4.67081i	0.684449	−	0.365846i	0.776683	+	0.629892i	$0.216901\pi$
$164$	3.92866	−	3.00828i	0.306777	−	0.234907i
$165$	−7.56792	−	9.22154i	−0.589162	−	0.717896i
$166$	−9.87091	−	4.87398i	−0.766131	−	0.378294i
$167$	−2.71605	+	13.6545i	−0.210174	+	1.05662i	0.721248	+	0.692677i	$0.243569\pi$
$167$	−2.71605	+	13.6545i	−0.210174	+	1.05662i	−0.931422	+	0.363941i	$0.881431\pi$
$168$	−4.60612	−	3.08780i	−0.355370	−	0.238229i
$169$	−12.6929	+	2.52478i	−0.976377	+	0.194213i
$170$	29.1393	−	16.8040i	2.23488	−	1.28881i
$171$	−2.43132	−	8.01500i	−0.185928	−	0.612922i
$172$	4.05344	+	4.33657i	0.309072	+	0.330660i
$173$	5.48915	−	6.68855i	0.417332	−	0.508521i	−0.521332	−	0.853354i	$-0.674565\pi$
$173$	5.48915	−	6.68855i	0.417332	−	0.508521i	0.938664	+	0.344833i	$0.112065\pi$
$174$	3.08114	+	6.80934i	0.233580	+	0.516215i
$175$	−6.50389	−	15.7018i	−0.491648	−	1.18694i
$176$	−11.7670	+	5.30299i	−0.886969	+	0.399728i
$177$	1.82368	−	4.40276i	0.137076	−	0.330932i
$178$	−21.5543	+	0.694743i	−1.61556	+	0.0520732i
$179$	−0.852121	−	8.65173i	−0.0636905	−	0.646661i	−0.973041	−	0.230631i	$-0.925921\pi$
$179$	−0.852121	−	8.65173i	−0.0636905	−	0.646661i	0.909351	−	0.416030i	$-0.136579\pi$
$180$	−1.68631	+	7.19936i	−0.125690	+	0.536609i
$181$	−10.1793	+	19.0442i	−0.756624	+	1.41554i	0.147848	+	0.989010i	$0.452765\pi$
$181$	−10.1793	+	19.0442i	−0.756624	+	1.41554i	−0.904472	+	0.426534i	$0.859735\pi$
$182$	0.408267	−	0.531509i	0.0302627	−	0.0393981i
$183$	−2.52154	+	3.77375i	−0.186398	+	0.278964i
$184$	−5.47655	+	6.65267i	−0.403737	+	0.490441i
$185$	−19.1536	+	12.7980i	−1.40820	+	0.940931i
$186$	1.07830	+	1.23082i	0.0790648	+	0.0902478i
$187$	20.6588	+	2.03471i	1.51072	+	0.148793i
$188$	−14.6350	−	12.8607i	−1.06737	−	0.937961i
$189$	−1.87615	−	0.569125i	−0.136470	−	0.0413978i
$190$	−37.1767	−	23.1439i	−2.69708	−	1.67904i
$191$		−	14.4920i		−	1.04860i	−0.851533	−	0.524301i	$-0.824327\pi$
$191$		−	14.4920i		−	1.04860i	0.851533	−	0.524301i	$-0.175673\pi$
$192$	7.04394	+	3.79249i	0.508352	+	0.273699i
$193$			12.3156i			0.886496i	0.896399	+	0.443248i	$0.146174\pi$
$193$			12.3156i			0.886496i	−0.896399	+	0.443248i	$0.853826\pi$
$194$	7.78412	−	12.5038i	0.558867	−	0.897722i
$195$	−0.855186	−	0.259418i	−0.0612411	−	0.0185773i
$196$	0.406495	+	6.29918i	0.0290354	+	0.449942i
$197$	−12.5851	−	1.23952i	−0.896651	−	0.0883124i	−0.360818	−	0.932636i	$-0.617502\pi$
$197$	−12.5851	−	1.23952i	−0.896651	−	0.0883124i	−0.535833	+	0.844324i	$0.680002\pi$
$198$	−3.43232	+	3.00701i	−0.243924	+	0.213699i
$199$	8.24583	−	5.50969i	0.584531	−	0.390571i	−0.227851	−	0.973696i	$-0.573170\pi$
$199$	8.24583	−	5.50969i	0.584531	−	0.390571i	0.812383	+	0.583125i	$0.198170\pi$
$200$	11.5253	+	21.6409i	0.814959	+	1.53024i
$201$	7.80574	−	11.6821i	0.550575	−	0.823993i
$202$	1.77932	+	1.36674i	0.125192	+	0.0961637i
$203$	−4.88436	+	9.13799i	−0.342815	+	0.641361i
$204$	−6.78359	−	10.9335i	−0.474946	−	0.765495i
$205$	−0.896555	−	9.10287i	−0.0626181	−	0.635772i
$206$	−0.407650	−	12.6473i	−0.0284023	−	0.881178i
$207$	−1.16586	+	2.81462i	−0.0810325	+	0.195630i
$208$	−0.512233	+	0.820047i	−0.0355170	+	0.0568600i
$209$	−10.3422	−	24.9684i	−0.715387	−	1.72710i
$210$	−9.33928	+	4.22590i	−0.644472	+	0.291615i
$211$	−2.90350	+	3.53793i	−0.199885	+	0.243561i	−0.863300	−	0.504691i	$-0.831607\pi$
$211$	−2.90350	+	3.53793i	−0.199885	+	0.243561i	0.663415	+	0.748252i	$0.269107\pi$
$212$	−0.825807	+	24.4716i	−0.0567166	+	1.68072i
$213$	−3.81865	−	12.5884i	−0.261650	−	0.862544i
$214$	8.02604	+	13.9177i	0.548649	+	0.951394i
$215$	10.7622	−	2.14073i	0.733975	−	0.145997i
$216$	2.77324	+	0.555991i	0.188695	+	0.0378304i
$217$	−0.442568	+	2.22494i	−0.0300435	+	0.151039i
$218$	−9.43797	+	19.1140i	−0.639220	+	1.29456i
$219$	−4.37829	−	5.33496i	−0.295857	−	0.360503i
$220$	−3.13803	+	23.6515i	−0.211566	+	1.59458i
$221$	1.37147	−	0.733068i	0.0922553	−	0.0493115i
$222$	5.12898	+	7.16511i	0.344235	+	0.480891i
$223$	10.2404	−	10.2404i	0.685745	−	0.685745i	−0.275544	−	0.961289i	$-0.588858\pi$
$223$	10.2404	−	10.2404i	0.685745	−	0.685745i	0.961289	+	0.275544i	$0.0888579\pi$
$224$	1.77905	+	10.9471i	0.118868	+	0.731432i
$225$	6.12964	+	6.12964i	0.408642	+	0.408642i
$226$	−0.863355	+	5.21292i	−0.0574295	+	0.346758i
$227$	−3.07541	−	5.75368i	−0.204122	−	0.381885i	0.758942	−	0.651158i	$-0.225717\pi$
$227$	−3.07541	−	5.75368i	−0.204122	−	0.381885i	−0.963064	+	0.269273i	$0.913217\pi$
$228$	−8.39027	+	14.4986i	−0.555659	+	0.960194i
$229$	1.04089	−	0.854237i	0.0687840	−	0.0564496i	−0.599373	−	0.800470i	$-0.704583\pi$
$229$	1.04089	−	0.854237i	0.0687840	−	0.0564496i	0.668157	+	0.744020i	$0.267083\pi$
$230$	5.11253	+	15.0860i	0.337110	+	0.994742i
$231$	−6.20459	−	1.23417i	−0.408232	−	0.0812025i
$232$	5.74121	−	13.8015i	0.376929	−	0.906111i
$233$	−1.35885	−	6.83142i	−0.0890215	−	0.447541i	−0.999428	−	0.0338258i	$-0.989231\pi$
$233$	−1.35885	−	6.83142i	−0.0890215	−	0.447541i	0.910406	−	0.413715i	$-0.135769\pi$
$234$	−0.0886421	+	0.330152i	−0.00579472	+	0.0215827i
$235$	−34.4643	+	10.4546i	−2.24820	+	0.681985i
$236$	−8.92352	+	3.34831i	−0.580872	+	0.217957i
$237$	−0.978769	−	0.803255i	−0.0635779	−	0.0521770i
$238$	6.29180	−	16.6914i	0.407837	−	1.08194i
$239$	7.79158	−	3.22738i	0.503995	−	0.208762i	−0.116175	−	0.993229i	$-0.537063\pi$
$239$	7.79158	−	3.22738i	0.503995	−	0.208762i	0.620170	+	0.784467i	$0.287063\pi$
$240$	12.8220	−	7.36839i	0.827659	−	0.475628i
$241$	13.9095	+	5.76149i	0.895987	+	0.371130i	0.782676	−	0.622429i	$-0.213854\pi$
$241$	13.9095	+	5.76149i	0.895987	+	0.371130i	0.113311	+	0.993560i	$0.463854\pi$
$242$	0.569274	−	0.607194i	0.0365943	−	0.0390319i
$243$	0.995185	−	0.0980171i	0.0638411	−	0.00628780i
$244$	8.95755	−	1.46963i	0.573448	−	0.0940832i
$245$	10.2908	+	5.50054i	0.657454	+	0.351417i
$246$	−3.46916	+	0.454946i	−0.221186	+	0.0290063i
$247$	−1.68337	−	1.12479i	−0.107110	−	0.0715686i
$248$	0.325703	−	3.25645i	0.0206822	−	0.206785i
$249$	4.32472	+	6.47241i	0.274068	+	0.410172i
$250$	19.1397	+	1.26417i	1.21050	+	0.0799528i
$251$	1.43818	−	14.6021i	0.0907770	−	0.921674i	−0.836667	−	0.547712i	$-0.815499\pi$
$251$	1.43818	−	14.6021i	0.0907770	−	0.921674i	0.927444	−	0.373962i	$-0.122001\pi$
$252$	1.73074	+	3.51852i	0.109026	+	0.221646i
$253$	−2.85355	+	9.40688i	−0.179401	+	0.591405i
$254$	−1.64065	−	7.05244i	−0.102944	−	0.442509i
$255$	−23.7852			−1.48949
$256$	−4.07877	−	15.4714i	−0.254923	−	0.966961i
$257$	−16.5637			−1.03321			−0.516607	−	0.856223i	$-0.672805\pi$
$257$	−16.5637			−1.03321			−0.516607	+	0.856223i	$0.672805\pi$
$258$	−0.951068	−	4.08822i	−0.0592109	−	0.254522i
$259$	−3.54609	+	11.6899i	−0.220344	+	0.726375i
$260$	0.788901	+	1.60381i	0.0489256	+	0.0994638i
$261$	0.518012	−	5.25946i	0.0320641	−	0.325552i
$262$	−8.75120	−	0.578013i	−0.540651	−	0.0357097i
$263$	−11.8501	−	17.7349i	−0.730709	−	1.09358i	−0.991741	−	0.128253i	$-0.959063\pi$
$263$	−11.8501	−	17.7349i	−0.730709	−	1.09358i	0.261032	−	0.965330i	$-0.415937\pi$
$264$	9.08112	+	0.908274i	0.558904	+	0.0559004i
$265$	37.6347	+	25.1467i	2.31188	+	1.54475i
$266$	−23.0258	+	3.01960i	−1.41180	+	0.185144i
$267$	13.4485	+	7.18838i	0.823036	+	0.439922i
$268$	−27.7292	+	4.54941i	−1.69383	+	0.277900i
$269$	32.3112	−	3.18238i	1.97005	−	0.194033i	0.971054	−	0.238859i	$-0.0767735\pi$
$269$	32.3112	−	3.18238i	1.97005	−	0.194033i	0.998995	+	0.0448264i	$0.0142735\pi$
$270$	3.57609	−	3.81429i	0.217634	−	0.232131i
$271$	13.9477	+	5.77734i	0.847264	+	0.350948i	0.763714	−	0.645555i	$-0.223374\pi$
$271$	13.9477	+	5.77734i	0.847264	+	0.350948i	0.0835508	+	0.996504i	$0.473374\pi$
$272$	−6.71049	+	24.8435i	−0.406883	+	1.50636i
$273$	−0.437837	+	0.181358i	−0.0264991	+	0.0109763i
$274$	5.82490	−	15.4528i	0.351895	−	0.933535i
$275$	21.6218	+	17.7445i	1.30384	+	1.07003i
$276$	5.70468	−	2.14053i	0.343382	−	0.128845i
$277$	−14.6835	+	4.45419i	−0.882245	+	0.267626i	−0.698725	−	0.715390i	$-0.746249\pi$
$277$	−14.6835	+	4.45419i	−0.882245	+	0.267626i	−0.183520	+	0.983016i	$0.558749\pi$
$278$	1.89283	−	7.04994i	0.113525	−	0.422827i
$279$	−0.225734	−	1.13484i	−0.0135143	−	0.0679411i
$280$	18.9293	+	7.87430i	1.13124	+	0.470580i
$281$	6.08927	+	1.21123i	0.363255	+	0.0722559i	0.373344	−	0.927693i	$-0.378211\pi$
$281$	6.08927	+	1.21123i	0.363255	+	0.0722559i	−0.0100884	+	0.999949i	$0.503211\pi$
$282$	4.42172	+	13.0476i	0.263309	+	0.776971i
$283$	−3.36042	+	2.75782i	−0.199756	+	0.163935i	−0.728954	−	0.684563i	$-0.759993\pi$
$283$	−3.36042	+	2.75782i	−0.199756	+	0.163935i	0.529198	+	0.848499i	$0.322493\pi$
$284$	−13.1778	+	22.7716i	−0.781959	+	1.35125i
$285$	14.5971	+	27.3093i	0.864660	+	1.61766i
$286$	−0.180226	+	1.08820i	−0.0106570	+	0.0643465i
$287$	−3.42990	−	3.42990i	−0.202460	−	0.202460i
$288$	−2.97509	−	4.81132i	−0.175309	−	0.283510i
$289$	17.2459	−	17.2459i	1.01447	−	1.01447i
$290$	−16.0838	−	22.4688i	−0.944473	−	1.31941i
$291$	−9.18507	+	4.90952i	−0.538439	+	0.287801i
$292$	−1.81545	+	13.6832i	−0.106241	+	0.800747i
$293$	19.1653	+	23.3530i	1.11965	+	1.36430i	0.923444	+	0.383734i	$0.125362\pi$
$293$	19.1653	+	23.3530i	1.11965	+	1.36430i	0.196206	+	0.980563i	$0.437138\pi$
$294$	1.97615	−	4.00216i	0.115252	−	0.233411i
$295$	−3.43722	+	17.2801i	−0.200123	+	1.00609i
$296$	3.46426	−	17.2795i	0.201356	−	1.00435i
$297$	3.16468	−	0.629494i	0.183633	−	0.0365269i
$298$	−4.81262	−	8.34540i	−0.278787	−	0.483436i
$299$	0.213768	+	0.704698i	0.0123625	+	0.0407537i
$300$	0.584720	−	17.3274i	0.0337588	−	1.00040i
$301$	3.69153	−	4.49815i	0.212776	−	0.259269i
$302$	12.6530	−	5.72533i	0.728100	−	0.329456i
$303$	−0.607127	−	1.46573i	−0.0348785	−	0.0842042i
$304$	32.6427	−	7.54187i	1.87219	−	0.432556i
$305$	6.42139	−	15.5026i	0.367688	−	0.887677i
$306$	0.293106	+	9.09356i	0.0167557	+	0.519844i
$307$	−2.67824	−	27.1926i	−0.152855	−	1.55196i	−0.699520	−	0.714613i	$-0.746603\pi$
$307$	−2.67824	−	27.1926i	−0.152855	−	1.55196i	0.546665	−	0.837351i	$-0.315897\pi$
$308$	6.67044	+	10.7511i	0.380084	+	0.612600i
$309$	−4.21788	+	7.89110i	−0.239947	+	0.448909i
$310$	−4.79774	−	3.68528i	−0.272493	−	0.209310i
$311$	−2.18643	+	3.27222i	−0.123981	+	0.185551i	−0.888268	−	0.459326i	$-0.848091\pi$
$311$	−2.18643	+	3.27222i	−0.123981	+	0.185551i	0.764287	+	0.644876i	$0.223091\pi$
$312$	0.603446	−	0.321377i	0.0341634	−	0.0181944i
$313$	−15.6076	+	10.4286i	−0.882192	+	0.589462i	−0.912044	−	0.410093i	$-0.865496\pi$
$313$	−15.6076	+	10.4286i	−0.882192	+	0.589462i	0.0298522	+	0.999554i	$0.490496\pi$
$314$	−1.91191	+	1.67499i	−0.107895	+	0.0945254i
$315$	7.21356	+	0.710474i	0.406438	+	0.0400307i
$316$	0.163078	+	2.52710i	0.00917383	+	0.142161i
$317$	12.3010	+	3.73147i	0.690893	+	0.209580i	0.616157	−	0.787623i	$-0.288689\pi$
$317$	12.3010	+	3.73147i	0.690893	+	0.209580i	0.0747357	+	0.997203i	$0.476189\pi$
$318$	9.15033	−	14.6984i	0.513125	−	0.824246i
$319$		−	17.0527i		−	0.954768i
$320$	−28.2772	−	8.67124i	−1.58074	−	0.484737i
$321$		−	11.3605i		−	0.634078i
$322$	7.17098	+	4.46421i	0.399623	+	0.248781i
$323$	−51.5642	−	15.6418i	−2.86911	−	0.870334i
$324$	−1.50235	−	1.32021i	−0.0834639	−	0.0733448i
$325$	2.08529	+	0.205383i	0.115671	+	0.0113926i
$326$	9.23387	+	10.5399i	0.511417	+	0.583752i
$327$	12.5332	−	8.37439i	0.693085	−	0.463105i
$328$	5.40260	+	4.44749i	0.298309	+	0.245571i
$329$	−10.6107	+	15.8801i	−0.584988	+	0.875496i
$330$	10.2770	−	13.3792i	0.565729	−	0.736503i
$331$	−11.9702	+	22.3946i	−0.657940	+	1.23092i	0.302690	+	0.953089i	$0.402115\pi$
$331$	−11.9702	+	22.3946i	−0.657940	+	1.23092i	−0.960630	+	0.277830i	$0.910385\pi$
$332$	3.55054	−	15.1583i	0.194861	−	0.831921i
$333$	−0.610723	−	6.20078i	−0.0334674	−	0.339800i
$334$	−19.6785	+	0.634281i	−1.07676	+	0.0347063i
$335$	−19.8782	+	47.9902i	−1.08606	+	2.62199i
$336$	2.77724	−	7.33408i	0.151511	−	0.400107i
$337$	−7.82627	−	18.8943i	−0.426324	−	1.02924i	−0.980444	−	0.196800i	$-0.936945\pi$
$337$	−7.82627	−	18.8943i	−0.426324	−	1.02924i	0.554120	−	0.832437i	$-0.313055\pi$
$338$	−7.54502	−	16.6746i	−0.410395	−	0.906977i
$339$	2.37029	−	2.88820i	0.128736	−	0.156866i
$340$	32.4838	+	34.7527i	1.76168	+	1.88473i
$341$	−1.08378	−	3.57274i	−0.0586899	−	0.193475i
$342$	10.2610	−	5.91731i	0.554853	−	0.319972i
$343$	19.5293	−	3.88462i	1.05448	−	0.209750i
$344$	−4.67444	+	6.97295i	−0.252029	+	0.375956i
$345$	2.19737	−	11.0469i	0.118302	−	0.594746i
$346$	10.9720	+	5.41765i	0.589856	+	0.291254i
$347$	−19.2145	−	23.4130i	−1.03149	−	1.25687i	−0.965869	−	0.259030i	$-0.916597\pi$
$347$	−19.2145	−	23.4130i	−1.03149	−	1.25687i	−0.0656210	−	0.997845i	$-0.520903\pi$
$348$	−8.39208	+	6.42604i	−0.449863	+	0.344472i
$349$	20.7670	−	11.1002i	1.11163	−	0.594180i	0.189821	−	0.981819i	$-0.439209\pi$
$349$	20.7670	−	11.1002i	1.11163	−	0.594180i	0.921811	+	0.387639i	$0.126709\pi$
$350$	19.5440	−	13.9901i	1.04467	−	0.747805i
$351$	0.170922	−	0.170922i	0.00912315	−	0.00912315i
$352$	−11.0751	−	14.5089i	−0.590306	−	0.773328i
$353$	−22.1356	−	22.1356i	−1.17816	−	1.17816i	−0.980212	−	0.197949i	$-0.936572\pi$
$353$	−22.1356	−	22.1356i	−1.17816	−	1.17816i	−0.197949	−	0.980212i	$-0.563428\pi$
$354$	6.64888	+	1.10118i	0.353384	+	0.0585269i
$355$	22.9264	+	42.8922i	1.21680	+	2.27648i
$356$	−7.86383	−	29.4670i	−0.416782	−	1.56175i
$357$	−9.75020	+	8.00178i	−0.516035	+	0.423499i
$358$	11.6441	−	3.94610i	0.615411	−	0.208558i
$359$	1.71653	+	0.341438i	0.0905947	+	0.0180204i	0.240180	−	0.970728i	$-0.422794\pi$
$359$	1.71653	+	0.341438i	0.0905947	+	0.0180204i	−0.149585	+	0.988749i	$0.547794\pi$
$360$	−10.4570	−	0.0158068i	−0.551132	−	0.000833094i
$361$	9.97918	+	50.1687i	0.525220	+	2.64046i
$362$	−29.4939	−	7.91881i	−1.55017	−	0.416203i
$363$	−0.563197	+	0.170844i	−0.0295602	+	0.00896699i
$364$	0.862942	+	0.392043i	0.0452305	+	0.0205486i
$365$	19.7239	+	16.1870i	1.03240	+	0.847267i
$366$	−6.00609	−	2.26399i	−0.313943	−	0.118341i
$367$	1.22937	−	0.509223i	0.0641728	−	0.0265812i	−0.350366	−	0.936613i	$-0.613943\pi$
$367$	1.22937	−	0.509223i	0.0641728	−	0.0265812i	0.414539	+	0.910032i	$0.363943\pi$
$368$	−10.9185	−	5.41179i	−0.569166	−	0.282109i
$369$	2.28575	+	0.946787i	0.118991	+	0.0492877i
$370$	−23.7660	−	22.2818i	−1.23554	−	1.15838i
$371$	23.8873	−	2.35270i	1.24017	−	0.122146i
$372$	−1.34983	+	1.87969i	−0.0699856	+	0.0974572i
$373$	−18.1530	−	9.70296i	−0.939925	−	0.502400i	−0.0710722	−	0.997471i	$-0.522642\pi$
$373$	−18.1530	−	9.70296i	−0.939925	−	0.502400i	−0.868853	+	0.495071i	$0.835142\pi$
$374$	3.81722	+	29.1080i	0.197384	+	1.50514i
$375$	−11.2775	−	7.53535i	−0.582365	−	0.389124i
$376$	13.0251	−	24.2798i	0.671716	−	1.25214i
$377$	−0.709724	−	1.06218i	−0.0365527	−	0.0547049i
$378$	0.182736	−	2.76664i	0.00939890	−	0.142301i
$379$	1.93027	−	19.5983i	0.0991512	−	1.00670i	−0.808930	−	0.587905i	$-0.799953\pi$
$379$	1.93027	−	19.5983i	0.0991512	−	1.00670i	0.908081	−	0.418794i	$-0.137547\pi$
$380$	19.9663	−	58.6246i	1.02425	−	3.00738i
$381$	−1.48625	+	4.89953i	−0.0761431	+	0.251010i
$382$	19.9617	−	4.64381i	1.02133	−	0.237598i
$383$	20.2716			1.03583			0.517915	−	0.855432i	$-0.326708\pi$
$383$	20.2716			1.03583			0.517915	+	0.855432i	$0.326708\pi$
$384$	−2.96673	+	10.9178i	−0.151395	+	0.557147i
$385$	23.3885			1.19199
$386$	−16.9639	+	3.94642i	−0.863440	+	0.200867i
$387$	−0.861566	+	2.84020i	−0.0437959	+	0.144376i
$388$	19.7175	+	6.71536i	1.00100	+	0.340921i
$389$	−3.09078	+	31.3813i	−0.156709	+	1.59109i	0.519557	+	0.854436i	$0.326097\pi$
$389$	−3.09078	+	31.3813i	−0.156709	+	1.59109i	−0.676266	+	0.736657i	$0.736403\pi$
$390$	0.0832942	−	1.26109i	0.00421777	−	0.0638576i
$391$	10.8890	+	16.2966i	0.550681	+	0.824152i
$392$	−8.54644	+	2.57843i	−0.431660	+	0.130230i
$393$	5.15637	+	3.44538i	0.260105	+	0.173796i
$394$	−2.32541	−	17.7323i	−0.117153	−	0.893340i
$395$	4.12845	+	2.20670i	0.207725	+	0.111031i
$396$	−5.24180	−	3.76422i	−0.263410	−	0.189159i
$397$	0.978932	−	0.0964164i	0.0491312	−	0.00483900i	−0.0734217	−	0.997301i	$-0.523392\pi$
$397$	0.978932	−	0.0964164i	0.0491312	−	0.00483900i	0.122553	+	0.992462i	$0.460892\pi$
$398$	10.2315	+	9.59254i	0.512859	+	0.480831i
$399$	15.1711	+	6.28408i	0.759506	+	0.314598i
$400$	−26.1157	+	22.8099i	−1.30578	+	1.14049i
$401$	14.7885	−	6.12561i	0.738503	−	0.305898i	0.0184624	−	0.999830i	$-0.494123\pi$
$401$	14.7885	−	6.12561i	0.738503	−	0.305898i	0.720041	+	0.693931i	$0.244123\pi$
$402$	18.5926	+	7.00846i	0.927315	+	0.349550i
$403$	−0.216202	−	0.177432i	−0.0107698	−	0.00883853i
$404$	−1.31243	+	2.88885i	−0.0652958	+	0.143726i
$405$	−3.53791	+	1.07321i	−0.175800	+	0.0533284i
$406$	−14.1521	−	3.79969i	−0.702357	−	0.188575i
$407$	−3.92224	−	19.7184i	−0.194418	−	0.977406i
$408$	12.8864	−	12.8475i	0.637970	−	0.636044i
$409$	−37.1861	−	7.39678i	−1.83874	−	0.365747i	−0.851416	−	0.524490i	$-0.824256\pi$
$409$	−37.1861	−	7.39678i	−1.83874	−	0.365747i	−0.987320	+	0.158743i	$0.949256\pi$
$410$	12.2513	−	4.15187i	0.605048	−	0.205046i
$411$	−9.02665	+	7.40798i	−0.445252	+	0.365409i
$412$	17.2901	−	4.61421i	0.851824	−	0.227326i
$413$	4.40433	+	8.23992i	0.216723	+	0.405460i
$414$	−4.25054	−	0.703967i	−0.208903	−	0.0345981i
$415$	−20.3501	−	20.3501i	−0.998947	−	0.998947i
$416$	−1.29370	−	0.442790i	−0.0634288	−	0.0217095i
$417$	−3.64981	+	3.64981i	−0.178732	+	0.178732i
$418$	31.0781	−	22.2466i	1.52008	−	1.08812i
$419$	11.5765	−	6.18777i	0.565550	−	0.302293i	−0.163733	−	0.986505i	$-0.552354\pi$
$419$	11.5765	−	6.18777i	0.565550	−	0.302293i	0.729283	+	0.684212i	$0.239854\pi$
$420$	−8.81357	−	11.5101i	−0.430058	−	0.561634i
$421$	9.15270	+	11.1526i	0.446075	+	0.543544i	0.946699	−	0.322121i	$-0.104396\pi$
$421$	9.15270	+	11.1526i	0.446075	+	0.543544i	−0.500623	+	0.865665i	$0.666896\pi$
$422$	−5.80366	−	2.86568i	−0.282518	−	0.139499i
$423$	1.90046	−	9.55424i	0.0924033	−	0.464543i
$424$	−33.9726	+	6.70421i	−1.64986	+	0.325585i
$425$	54.6976	−	10.8800i	2.65322	−	0.527759i
$426$	16.1160	−	9.29377i	0.780824	−	0.450285i
$427$	−2.58306	−	8.51522i	−0.125003	−	0.412080i
$428$	−16.5988	+	15.5151i	−0.802334	+	0.749951i
$429$	0.494798	−	0.602913i	0.0238891	−	0.0291089i
$430$	6.39735	+	14.1382i	0.308508	+	0.681805i
$431$	3.77841	+	9.12189i	0.182000	+	0.439386i	0.988378	−	0.152013i	$-0.0485757\pi$
$431$	3.77841	+	9.12189i	0.182000	+	0.439386i	−0.806379	+	0.591399i	$0.798576\pi$
$432$	0.122818	+	3.99811i	0.00590911	+	0.192359i
$433$	6.99247	−	16.8813i	0.336037	−	0.811265i	−0.662051	−	0.749458i	$-0.730314\pi$
$433$	6.99247	−	16.8813i	0.336037	−	0.811265i	0.998088	−	0.0618062i	$-0.0196861\pi$
$434$	−3.20652	+	0.103353i	−0.153918	+	0.00496111i
$435$	1.91515	+	19.4448i	0.0918242	+	0.932307i
$436$	−29.3526	−	6.87525i	−1.40573	−	0.329265i
$437$	12.0285	−	22.5037i	0.575399	−	1.07650i
$438$	5.94557	−	7.74033i	0.284090	−	0.369847i
$439$	7.72578	−	11.5625i	0.368732	−	0.551846i	−0.599986	−	0.800010i	$-0.704827\pi$
$439$	7.72578	−	11.5625i	0.368732	−	0.551846i	0.968718	+	0.248164i	$0.0798274\pi$
$440$	−33.5839	+	3.25647i	−1.60105	+	0.155246i
$441$	−2.62424	+	1.75346i	−0.124964	+	0.0834980i
$442$	1.44923	+	1.65421i	0.0689327	+	0.0786826i
$443$	−6.19798	−	0.610448i	−0.294475	−	0.0290032i	−0.0502990	−	0.998734i	$-0.516017\pi$
$443$	−6.19798	−	0.610448i	−0.294475	−	0.0290032i	−0.244176	+	0.969731i	$0.578517\pi$
$444$	−8.22591	+	9.36081i	−0.390385	+	0.444244i
$445$	−53.9500	−	16.3656i	−2.55748	−	0.775802i
$446$	17.3868	+	10.8240i	0.823289	+	0.512530i
$447$			6.81201i			0.322197i
$448$	−14.5088	+	5.95840i	−0.685475	+	0.281508i
$449$			40.8564i			1.92813i	0.265663	+	0.964066i	$0.414409\pi$
$449$			40.8564i			1.92813i	−0.265663	+	0.964066i	$0.585591\pi$
$450$	−6.47897	+	10.4073i	−0.305422	+	0.490607i
$451$	7.63929	+	2.31735i	0.359720	+	0.109120i
$452$	−7.45710	+	0.481217i	−0.350752	+	0.0226346i
$453$	−9.77306	−	0.962562i	−0.459178	−	0.0452251i
$454$	6.93982	−	6.07987i	0.325702	−	0.285343i
$455$	1.45682	−	0.973415i	0.0682967	−	0.0456344i
$456$	−22.6594	−	6.91108i	−1.06112	−	0.323641i
$457$	−8.71260	+	13.0393i	−0.407558	+	0.609954i	−0.977298	−	0.211871i	$-0.932044\pi$
$457$	−8.71260	+	13.0393i	−0.407558	+	0.609954i	0.569739	+	0.821826i	$0.307044\pi$
$458$	1.51020	+	1.16002i	0.0705669	+	0.0542044i
$459$	3.03271	−	5.67380i	0.141555	−	0.264831i
$460$	−19.1417	+	11.8763i	−0.892486	+	0.553737i
$461$	−0.495601	−	5.03192i	−0.0230824	−	0.234360i	−0.999803	−	0.0198446i	$-0.993683\pi$
$461$	−0.495601	−	5.03192i	−0.0230824	−	0.234360i	0.976721	−	0.214515i	$-0.0688172\pi$
$462$	−0.288217	−	8.94188i	−0.0134091	−	0.416014i
$463$	−0.357726	+	0.863627i	−0.0166249	+	0.0401362i	−0.931974	−	0.362525i	$-0.881915\pi$
$463$	−0.357726	+	0.863627i	−0.0166249	+	0.0401362i	0.915349	+	0.402661i	$0.131915\pi$
$464$	20.8503	+	3.48558i	0.967951	+	0.161814i
$465$	1.63705	+	3.95220i	0.0759165	+	0.183279i
$466$	8.97438	−	4.06079i	0.415730	−	0.188112i
$467$	8.27831	−	10.0872i	0.383075	−	0.466778i	−0.545399	−	0.838177i	$-0.683622\pi$
$467$	8.27831	−	10.0872i	0.383075	−	0.466778i	0.928473	+	0.371399i	$0.121122\pi$
$468$	−0.483166	−	0.0163046i	−0.0223343	−	0.000753683i
$469$	7.99619	+	26.3599i	0.369230	+	1.21719i
$470$	−25.4443	−	44.1221i	−1.17366	−	2.03520i
$471$	1.76282	−	0.350647i	0.0812266	−	0.0161570i
$472$	−7.47153	−	11.2186i	−0.343905	−	0.516378i
$473$	−1.86834	+	9.39278i	−0.0859064	+	0.431881i
$474$	0.792792	−	1.60558i	0.0364141	−	0.0737469i
$475$	−46.0603	−	56.1247i	−2.11339	−	2.57518i
$476$	25.0074	+	3.31793i	1.14621	+	0.152077i
$477$	−10.7972	+	5.77121i	−0.494369	+	0.264246i
$478$	6.94223	+	9.69818i	0.317530	+	0.443584i
$479$	3.01762	−	3.01762i	0.137879	−	0.137879i	−0.634799	−	0.772677i	$-0.718917\pi$
$479$	3.01762	−	3.01762i	0.137879	−	0.137879i	0.772677	+	0.634799i	$0.218917\pi$
$480$	14.2582	+	15.3004i	0.650793	+	0.698362i
$481$	−1.06498	−	1.06498i	−0.0485588	−	0.0485588i
$482$	−3.47890	+	21.0055i	−0.158460	+	0.956777i
$483$	−2.81563	−	5.26767i	−0.128115	−	0.239687i
$484$	1.01879	+	0.589567i	0.0463085	+	0.0267985i
$485$	29.7646	−	24.4272i	1.35154	−	1.10918i
$486$	0.453909	+	1.33939i	0.0205897	+	0.0607560i
$487$	0.431047	+	0.0857406i	0.0195326	+	0.00388528i	0.204847	−	0.978794i	$-0.434330\pi$
$487$	0.431047	+	0.0857406i	0.0195326	+	0.00388528i	−0.185314	+	0.982679i	$0.559330\pi$
$488$	4.89467	+	11.8675i	0.221571	+	0.537216i
$489$	−1.93304	−	9.71805i	−0.0874151	−	0.439465i
$490$	−4.27904	+	15.9375i	−0.193307	+	0.719981i
$491$	39.6454	−	12.0263i	1.78917	−	0.542740i	0.791517	−	0.611148i	$-0.209292\pi$
$491$	39.6454	−	12.0263i	1.78917	−	0.542740i	0.997657	+	0.0684078i	$0.0217919\pi$
$492$	−1.73832	−	4.63275i	−0.0783694	−	0.208861i
$493$	−26.2825	−	21.5695i	−1.18371	−	0.971442i
$494$	1.00990	−	2.67915i	0.0454376	−	0.120541i
$495$	−11.0213	+	4.56518i	−0.495371	+	0.205190i
$496$	4.58991	−	0.594864i	0.206093	−	0.0267102i
$497$	23.8279	+	9.86983i	1.06883	+	0.442722i
$498$	−7.52948	+	8.03103i	−0.337404	+	0.359879i
$499$	−1.94065	+	0.191137i	−0.0868754	+	0.00855648i	−0.141361	−	0.989958i	$-0.545148\pi$
$499$	−1.94065	+	0.191137i	−0.0868754	+	0.00855648i	0.0544860	+	0.998515i	$0.482648\pi$
$500$	4.39182	+	26.7687i	0.196408	+	1.19713i
$501$	12.2781	+	6.56280i	0.548546	+	0.293204i
$502$	20.5742	−	2.69810i	0.918271	−	0.120422i
$503$	17.0126	+	11.3674i	0.758552	+	0.506848i	0.873679	−	0.486502i	$-0.161728\pi$
$503$	17.0126	+	11.3674i	0.758552	+	0.506848i	−0.115127	+	0.993351i	$0.536728\pi$
$504$	−4.29192	+	3.51145i	−0.191177	+	0.156412i
$505$	3.25867	+	4.87695i	0.145009	+	0.217021i
$506$	−13.8717	−	0.916221i	−0.616673	−	0.0407310i
$507$	−1.26850	+	12.8793i	−0.0563359	+	0.571988i
$508$	9.18852	−	4.51977i	0.407675	−	0.200532i
$509$	−1.45915	+	4.81018i	−0.0646757	+	0.213207i	−0.983322	−	0.181874i	$-0.941784\pi$
$509$	−1.45915	+	4.81018i	−0.0646757	+	0.213207i	0.918646	+	0.395082i	$0.129284\pi$
$510$	−7.62174	−	32.7625i	−0.337496	−	1.45075i
$511$	13.5310			0.598576
$512$	20.0038	−	10.5759i	0.884050	−	0.467393i
$513$	−8.37565			−0.369794
$514$	−5.30767	−	22.8153i	−0.234111	−	1.00634i
$515$	9.60272	−	31.6559i	0.423146	−	1.39493i
$516$	5.32649	−	2.62006i	0.234486	−	0.115342i
$517$	3.08092	−	31.2811i	0.135499	−	1.37574i
$518$	−17.2384	−	1.13858i	−0.757410	−	0.0500265i
$519$	−4.80712	−	7.19437i	−0.211009	−	0.315798i
$520$	−1.95634	+	1.60058i	−0.0857911	+	0.0701902i
$521$	21.4444	+	14.3287i	0.939495	+	0.627750i	0.928158	−	0.372185i	$-0.121391\pi$
$521$	21.4444	+	14.3287i	0.939495	+	0.627750i	0.0113364	+	0.999936i	$0.496391\pi$
$522$	7.41054	−	0.971817i	0.324350	−	0.0425353i
$523$	21.8379	+	11.6726i	0.954905	+	0.510408i	0.873793	−	0.486297i	$-0.161653\pi$
$523$	21.8379	+	11.6726i	0.954905	+	0.510408i	0.0811120	+	0.996705i	$0.474153\pi$
$524$	−2.00806	−	12.2394i	−0.0877227	−	0.534681i
$525$	−16.9136	+	1.66585i	−0.738172	+	0.0727036i
$526$	20.6314	−	22.0057i	0.899572	−	0.959494i
$527$	−6.87734	−	2.84869i	−0.299582	−	0.124091i
$528$	1.65887	+	12.7997i	0.0721931	+	0.557034i
$529$	12.6744	−	5.24991i	0.551061	−	0.228257i
$530$	−22.5782	+	59.8973i	−0.980735	+	2.60177i
$531$	−3.68379	−	3.02321i	−0.159863	−	0.131196i
$532$	−11.5377	−	30.7489i	−0.500222	−	1.33313i
$533$	0.572283	−	0.173600i	0.0247883	−	0.00751945i
$534$	−5.59206	+	20.8279i	−0.241992	+	0.901310i
$535$	8.19395	+	41.1938i	0.354256	+	1.78096i
$536$	−15.1521	−	36.7373i	−0.654469	−	1.58681i
$537$	−8.52655	−	1.69604i	−0.367948	−	0.0731894i
$538$	14.7373	+	43.4867i	0.635371	+	1.87485i
$539$	−7.87223	+	6.46057i	−0.339081	+	0.278277i
$540$	6.39985	+	3.70356i	0.275406	+	0.159376i
$541$	−2.50330	−	4.68335i	−0.107625	−	0.201353i	0.822343	−	0.568992i	$-0.192666\pi$
$541$	−2.50330	−	4.68335i	−0.107625	−	0.201353i	−0.929969	+	0.367639i	$0.880166\pi$
$542$	−3.48848	+	21.0633i	−0.149843	+	0.904748i
$543$	15.2693	+	15.2693i	0.655266	+	0.655266i
$544$	−36.3705	−	1.28238i	−1.55937	−	0.0549818i
$545$	−39.4059	+	39.4059i	−1.68796	+	1.68796i
$546$	−0.390109	−	0.544976i	−0.0166951	−	0.0233228i
$547$	−33.7608	+	18.0455i	−1.44351	+	0.771570i	−0.992649	−	0.121026i	$-0.961381\pi$
$547$	−33.7608	+	18.0455i	−1.44351	+	0.771570i	−0.450857	+	0.892596i	$0.648881\pi$
$548$	23.1516	+	3.07171i	0.988989	+	0.131217i
$549$	2.87929	+	3.50843i	0.122885	+	0.149736i
$550$	−17.5134	+	35.4685i	−0.746773	+	1.51238i
$551$	−8.63559	+	43.4140i	−0.367888	+	1.84950i
$552$	4.77644	+	7.17190i	0.203299	+	0.305256i
$553$	2.43474	−	0.484300i	0.103536	−	0.0205945i
$554$	−10.8405	−	18.7982i	−0.460569	−	0.798659i
$555$	6.68696	+	22.0440i	0.283846	+	0.935714i
$556$	10.3173	+	0.348164i	0.437553	+	0.0147654i
$557$	−18.6629	+	22.7408i	−0.790772	+	0.963559i	−0.999897	−	0.0143302i	$-0.995438\pi$
$557$	−18.6629	+	22.7408i	−0.790772	+	0.963559i	0.209125	+	0.977889i	$0.432938\pi$
$558$	1.49083	−	0.674581i	0.0631119	−	0.0285573i
$559$	0.274547	+	0.662816i	0.0116121	+	0.0280341i
$560$	−4.78061	+	28.5970i	−0.202018	+	1.20844i
$561$	7.94401	−	19.1785i	0.335397	−	0.809719i
$562$	0.282859	+	8.77567i	0.0119317	+	0.370179i
$563$	−1.70965	−	17.3584i	−0.0720533	−	0.731570i	−0.961550	−	0.274629i	$-0.911445\pi$
$563$	−1.70965	−	17.3584i	−0.0720533	−	0.731570i	0.889497	−	0.456941i	$-0.151055\pi$
$564$	−16.5552	+	10.2716i	−0.697101	+	0.432511i
$565$	−6.51165	+	12.1824i	−0.273947	+	0.512519i
$566$	−4.87552	−	3.74503i	−0.204934	−	0.157415i
$567$	−1.08924	+	1.63016i	−0.0457437	+	0.0684603i
$568$	−35.5891	−	10.8546i	−1.49328	−	0.455449i
$569$	29.8709	−	19.9591i	1.25225	−	0.836728i	0.260571	−	0.965455i	$-0.416089\pi$
$569$	29.8709	−	19.9591i	1.25225	−	0.836728i	0.991680	+	0.128727i	$0.0410891\pi$
$570$	−32.9392	+	28.8576i	−1.37967	+	1.20871i
$571$	−18.4144	−	1.81366i	−0.770620	−	0.0758994i	−0.294937	−	0.955517i	$-0.595299\pi$
$571$	−18.4144	−	1.81366i	−0.770620	−	0.0758994i	−0.475682	+	0.879617i	$0.657799\pi$
$572$	−1.55667	+	0.100454i	−0.0650877	+	0.00420020i
$573$	−13.8680	−	4.20680i	−0.579342	−	0.175742i
$574$	3.62537	−	5.82353i	0.151320	−	0.243069i
$575$			26.4092i			1.10134i
$576$	5.67393	−	5.63973i	0.236414	−	0.234989i
$577$			7.10562i			0.295811i	0.989002	+	0.147905i	$0.0472531\pi$
$577$			7.10562i			0.295811i	−0.989002	+	0.147905i	$0.952747\pi$
$578$	29.2813	+	18.2288i	1.21794	+	0.758217i
$579$	11.7853	+	3.57503i	0.489780	+	0.148573i
$580$	25.7954	−	29.3542i	1.07109	−	1.21887i
$581$	−15.1882	−	1.49591i	−0.630113	−	0.0620608i
$582$	−9.70580	−	11.0786i	−0.402318	−	0.459223i
$583$	−32.8460	+	21.9470i	−1.36034	+	0.908952i
$584$	−19.4294	+	1.88398i	−0.803993	+	0.0779595i
$585$	−0.496494	+	0.743057i	−0.0205275	+	0.0307216i
$586$	−26.0258	+	33.8822i	−1.07512	+	1.39966i
$587$	−8.06732	+	15.0929i	−0.332974	+	0.622950i	−0.991574	−	0.129543i	$-0.958649\pi$
$587$	−8.06732	+	15.0929i	−0.332974	+	0.622950i	0.658600	+	0.752493i	$0.271149\pi$
$588$	6.14594	+	1.43956i	0.253454	+	0.0593666i
$589$	0.949908	+	9.64458i	0.0391403	+	0.397398i
$590$	−24.9036	+	0.802697i	−1.02526	+	0.0330465i
$591$	−4.83941	+	11.6834i	−0.199067	+	0.480590i
$592$	24.9114	−	0.765255i	1.02385	−	0.0314518i
$593$	−1.32336	−	3.19489i	−0.0543441	−	0.131198i	0.894376	−	0.447317i	$-0.147620\pi$
$593$	−1.32336	−	3.19489i	−0.0543441	−	0.131198i	−0.948720	+	0.316118i	$0.897620\pi$
$594$	1.88118	+	4.15741i	0.0771856	+	0.170581i
$595$	29.5835	−	36.0476i	1.21280	−	1.47781i
$596$	9.95307	−	9.30325i	0.407694	−	0.381076i
$597$	−2.87880	−	9.49014i	−0.117822	−	0.388406i
$598$	−0.902173	+	0.520264i	−0.0368926	+	0.0212752i
$599$	12.0226	−	2.39144i	0.491229	−	0.0977116i	0.0567408	−	0.998389i	$-0.481929\pi$
$599$	12.0226	−	2.39144i	0.491229	−	0.0977116i	0.434489	+	0.900677i	$0.356929\pi$
$600$	24.0546	−	4.74698i	0.982026	−	0.193794i
$601$	2.70132	−	13.5805i	0.110189	−	0.553958i	−0.885768	−	0.464128i	$-0.846368\pi$
$601$	2.70132	−	13.5805i	0.110189	−	0.553958i	0.995957	−	0.0898299i	$-0.0286323\pi$
$602$	7.37881	+	3.64345i	0.300738	+	0.148496i
$603$	−8.91321	−	10.8608i	−0.362974	−	0.442285i
$604$	11.9408	+	15.5940i	0.485864	+	0.634513i
$605$	1.91897	−	1.02571i	0.0780172	−	0.0417010i
$606$	1.82440	−	1.30596i	0.0741112	−	0.0530508i
$607$	−15.9816	+	15.9816i	−0.648673	+	0.648673i	−0.952672	−	0.303999i	$-0.901678\pi$
$607$	−15.9816	+	15.9816i	−0.648673	+	0.648673i	0.303999	+	0.952672i	$0.401678\pi$
$608$	20.8485	+	42.5464i	0.845516	+	1.72548i
$609$	7.32666	+	7.32666i	0.296891	+	0.296891i
$610$	23.4115	+	3.87737i	0.947902	+	0.156990i
$611$	−1.11000	−	2.07666i	−0.0449057	−	0.0840126i
$612$	−12.4318	+	3.31768i	−0.502527	+	0.134109i
$613$	17.2564	−	14.1620i	0.696980	−	0.571996i	−0.217779	−	0.975998i	$-0.569881\pi$
$613$	17.2564	−	14.1620i	0.696980	−	0.571996i	0.914758	+	0.404002i	$0.132381\pi$
$614$	36.5978	−	12.4027i	1.47697	−	0.500532i
$615$	−8.97116	−	1.78447i	−0.361752	−	0.0719570i
$616$	−12.6714	+	12.6332i	−0.510546	+	0.509005i
$617$	−7.36540	−	37.0284i	−0.296520	−	1.49071i	−0.785746	−	0.618549i	$-0.787721\pi$
$617$	−7.36540	−	37.0284i	−0.296520	−	1.49071i	0.489226	−	0.872157i	$-0.337279\pi$
$618$	−12.2210	−	3.28122i	−0.491602	−	0.131990i
$619$	−15.3638	+	4.66055i	−0.617522	+	0.187323i	−0.583520	−	0.812098i	$-0.698325\pi$
$619$	−15.3638	+	4.66055i	−0.617522	+	0.187323i	−0.0340018	+	0.999422i	$0.510825\pi$
$620$	3.53883	−	7.78947i	0.142123	−	0.312833i
$621$	2.35500	+	1.93270i	0.0945028	+	0.0775564i
$622$	−5.20788	−	1.96310i	−0.208817	−	0.0787133i
$623$	−27.6213	+	11.4411i	−1.10662	+	0.458378i
$624$	0.636043	+	0.728223i	0.0254621	+	0.0291523i
$625$	6.28407	+	2.60295i	0.251363	+	0.104118i
$626$	−19.3660	−	18.1566i	−0.774022	−	0.725684i
$627$	−26.8954	+	2.64897i	−1.07410	+	0.105790i
$628$	−2.91984	−	2.09679i	−0.116514	−	0.0836709i
$629$	−35.3522	−	18.8962i	−1.40959	−	0.753439i
$630$	1.33289	+	10.1639i	0.0531035	+	0.404937i
$631$	−15.0028	−	10.0246i	−0.597254	−	0.399072i	0.219874	−	0.975528i	$-0.429435\pi$
$631$	−15.0028	−	10.0246i	−0.597254	−	0.399072i	−0.817128	+	0.576456i	$0.804435\pi$
$632$	−3.42865	+	1.03441i	−0.136384	+	0.0411468i
$633$	2.54274	+	3.80549i	0.101065	+	0.151254i
$634$	−1.19810	+	18.1395i	−0.0475828	+	0.720411i
$635$	1.85538	−	18.8380i	0.0736286	−	0.747564i
$636$	23.1782	+	7.89399i	0.919075	+	0.313017i
$637$	−0.221459	+	0.730053i	−0.00877454	+	0.0289258i
$638$	23.4889	−	5.46437i	0.929936	−	0.216337i
$639$	−13.1549			−0.520398
$640$	2.88288	−	41.7285i	0.113956	−	1.64947i
$641$	13.3417			0.526967			0.263483	−	0.964664i	$-0.415129\pi$
$641$	13.3417			0.526967			0.263483	+	0.964664i	$0.415129\pi$
$642$	15.6482	−	3.64035i	0.617587	−	0.143673i
$643$	4.90830	−	16.1805i	0.193564	−	0.638096i	−0.805406	−	0.592724i	$-0.798053\pi$
$643$	4.90830	−	16.1805i	0.193564	−	0.638096i	0.998970	−	0.0453725i	$-0.0144475\pi$
$644$	−3.85128	+	11.3080i	−0.151762	+	0.445600i
$645$	1.07555	−	10.9202i	0.0423496	−	0.429982i
$646$	5.02230	−	76.0384i	0.197600	−	2.99169i
$647$	0.654688	+	0.979810i	0.0257385	+	0.0385203i	0.844116	−	0.536161i	$-0.180126\pi$
$647$	0.654688	+	0.979810i	0.0257385	+	0.0385203i	−0.818377	+	0.574681i	$0.805126\pi$
$648$	1.33708	−	2.49243i	0.0525255	−	0.0979120i
$649$	−12.7853	−	8.54288i	−0.501868	−	0.335337i
$650$	0.385310	+	2.93816i	0.0151131	+	0.115244i
$651$	2.00066	+	1.06938i	0.0784122	+	0.0419122i
$652$	−11.5591	+	16.0964i	−0.452690	+	0.630385i
$653$	−44.2463	+	4.35788i	−1.73149	+	0.170537i	−0.914085	−	0.405524i	$-0.867089\pi$
$653$	−44.2463	+	4.35788i	−1.73149	+	0.170537i	−0.817407	+	0.576061i	$0.804589\pi$
$654$	15.5513	+	14.5801i	0.608103	+	0.570126i
$655$	−21.1824	−	8.77404i	−0.827666	−	0.342830i
$656$	−4.39490	+	8.86687i	−0.171592	+	0.346193i
$657$	−6.37619	+	2.64111i	−0.248759	+	0.103039i
$658$	−25.2738	−	9.52692i	−0.985275	−	0.371398i
$659$	8.77222	+	7.19918i	0.341717	+	0.280440i	0.789561	−	0.613671i	$-0.210308\pi$
$659$	8.77222	+	7.19918i	0.341717	+	0.280440i	−0.447844	+	0.894112i	$0.647808\pi$
$660$	21.7222	+	9.86858i	0.845534	+	0.384134i
$661$	2.53055	−	0.767634i	0.0984270	−	0.0298575i	−0.240687	−	0.970603i	$-0.577373\pi$
$661$	2.53055	−	0.767634i	0.0984270	−	0.0298575i	0.339114	+	0.940745i	$0.389873\pi$
$662$	−34.6828	−	9.31195i	−1.34798	−	0.361919i
$663$	−0.303385	−	1.52522i	−0.0117825	−	0.0592345i
$664$	22.0173	+	0.0332815i	0.854437	+	0.00129157i
$665$	−59.5441	−	11.8441i	−2.30902	−	0.459293i
$666$	8.34545	−	2.82821i	0.323379	−	0.109591i
$667$	12.4459	−	10.2141i	0.481909	−	0.395492i
$668$	−7.17946	−	26.9025i	−0.277782	−	1.04089i
$669$	−6.82679	−	12.7720i	−0.263939	−	0.493795i
$670$	−72.4731	−	12.0029i	−2.79988	−	0.463711i
$671$	10.3554	+	10.3554i	0.399767	+	0.399767i
$672$	10.9921	+	1.47532i	0.424031	+	0.0569118i
$673$	9.72376	−	9.72376i	0.374823	−	0.374823i	−0.494407	−	0.869230i	$-0.664615\pi$
$673$	9.72376	−	9.72376i	0.374823	−	0.374823i	0.869230	+	0.494407i	$0.164615\pi$
$674$	23.5177	−	16.8346i	0.905869	−	0.648446i
$675$	7.64504	−	4.08636i	0.294258	−	0.157284i
$676$	20.5503	−	15.7360i	0.790398	−	0.605229i
$677$	5.24213	+	6.38755i	0.201471	+	0.245494i	0.863938	−	0.503597i	$-0.167991\pi$
$677$	5.24213	+	6.38755i	0.201471	+	0.245494i	−0.662467	+	0.749091i	$0.730491\pi$
$678$	4.73784	+	2.33941i	0.181955	+	0.0898445i
$679$	3.98357	−	20.0267i	0.152875	−	0.768556i
$680$	−37.4603	+	55.8803i	−1.43654	+	2.14291i
$681$	−6.39867	+	1.27278i	−0.245198	+	0.0487729i
$682$	4.57392	−	2.63768i	0.175144	−	0.101002i
$683$	−14.2301	−	46.9105i	−0.544501	−	1.79498i	−0.604286	−	0.796767i	$-0.706542\pi$
$683$	−14.2301	−	46.9105i	−0.544501	−	1.79498i	0.0597853	−	0.998211i	$-0.480958\pi$
$684$	11.4387	+	12.2377i	0.437371	+	0.467921i
$685$	27.3881	−	33.3725i	1.04645	−	1.27510i
$686$	11.6088	+	25.6555i	0.443225	+	0.979530i
$687$	−0.515299	−	1.24404i	−0.0196599	−	0.0474632i
$688$	−11.1026	−	4.20430i	−0.423284	−	0.160288i
$689$	−1.13249	+	2.73406i	−0.0431443	+	0.104160i
$690$	15.9205	−	0.513153i	0.606083	−	0.0195354i
$691$	2.58055	+	26.2008i	0.0981688	+	0.996725i	0.910495	+	0.413521i	$0.135701\pi$
$691$	2.58055	+	26.2008i	0.0981688	+	0.996725i	−0.812326	+	0.583204i	$0.801799\pi$
$692$	−3.94658	+	16.8492i	−0.150026	+	0.640509i
$693$	−2.98213	+	5.57917i	−0.113282	+	0.211935i
$694$	26.0927	−	33.9692i	0.990464	−	1.28945i
$695$	10.6020	−	15.8670i	0.402155	−	0.601868i
$696$	−11.5406	−	9.50035i	−0.437445	−	0.360110i
$697$	13.2344	−	8.84293i	0.501288	−	0.334950i
$698$	21.9444	+	25.0482i	0.830606	+	0.948088i
$699$	−6.93172	−	0.682714i	−0.262182	−	0.0258226i
$700$	25.5332	+	22.4375i	0.965063	+	0.848059i
$701$	43.3881	+	13.1616i	1.63875	+	0.497108i	0.969327	−	0.245776i	$-0.0790429\pi$
$701$	43.3881	+	13.1616i	1.63875	+	0.497108i	0.669420	+	0.742885i	$0.266543\pi$
$702$	0.290204	+	0.180663i	0.0109530	+	0.00681869i
$703$			52.1869i			1.96826i
$704$	16.4361	−	19.9045i	0.619460	−	0.750177i
$705$			36.0151i			1.35641i
$706$	23.3972	−	37.5835i	0.880564	−	1.41447i
$707$	2.97652	+	0.902916i	0.111943	+	0.0339577i
$708$	0.613774	+	9.51124i	0.0230671	+	0.357454i
$709$	−21.0103	−	2.06933i	−0.789058	−	0.0777154i	−0.304543	−	0.952499i	$-0.598504\pi$
$709$	−21.0103	−	2.06933i	−0.789058	−	0.0777154i	−0.484515	+	0.874783i	$0.661004\pi$
$710$	−51.7345	+	45.3239i	−1.94156	+	1.70098i
$711$	−1.05279	+	0.703451i	−0.0394827	+	0.0263815i
$712$	38.0688	−	20.2743i	1.42669	−	0.759811i
$713$	1.95841	−	2.93097i	0.0733432	−	0.109766i
$714$	−14.1463	−	10.8661i	−0.529411	−	0.406655i
$715$	−1.35931	+	2.54309i	−0.0508352	+	0.0951060i
$716$	9.16673	+	14.7745i	0.342577	+	0.552148i
$717$	−0.826632	−	8.39293i	−0.0308711	−	0.313440i
$718$	0.0797362	+	2.47381i	0.00297573	+	0.0923216i
$719$	1.93205	−	4.66439i	0.0720534	−	0.173952i	−0.883750	−	0.467960i	$-0.844989\pi$
$719$	1.93205	−	4.66439i	0.0720534	−	0.173952i	0.955803	+	0.294008i	$0.0949891\pi$
$720$	−3.32907	−	14.4089i	−0.124067	−	0.536986i
$721$	−6.71323	−	16.2072i	−0.250014	−	0.603586i
$722$	−65.9062	+	29.8217i	−2.45278	+	1.10985i
$723$	9.55111	−	11.6381i	0.355209	−	0.432824i
$724$	1.45657	−	43.1634i	0.0541329	−	1.60415i
$725$	−13.2988	−	43.8401i	−0.493904	−	1.62818i
$726$	−0.415797	−	0.721021i	−0.0154317	−	0.0267596i
$727$	44.9623	−	8.94356i	1.66756	−	0.331698i	0.731046	−	0.682328i	$-0.239032\pi$
$727$	44.9623	−	8.94356i	1.66756	−	0.331698i	0.936514	+	0.350630i	$0.114032\pi$
$728$	−0.263491	+	1.31427i	−0.00976561	+	0.0487101i
$729$	0.195090	−	0.980785i	0.00722557	−	0.0363254i
$730$	−15.9762	+	32.3554i	−0.591305	+	1.19753i
$731$	12.1134	+	14.7603i	0.448032	+	0.545929i
$732$	1.19390	−	8.99845i	0.0441276	−	0.332592i
$733$	−6.26977	+	3.35126i	−0.231579	+	0.123782i	−0.583106	−	0.812396i	$-0.698163\pi$
$733$	−6.26977	+	3.35126i	−0.231579	+	0.123782i	0.351526	+	0.936178i	$0.385663\pi$
$734$	1.09536	+	1.53020i	0.0404305	+	0.0564808i
$735$	8.25095	−	8.25095i	0.304341	−	0.304341i
$736$	3.95565	−	16.7736i	0.145807	−	0.618285i
$737$	−32.0565	−	32.0565i	−1.18082	−	1.18082i
$738$	−0.571689	+	3.45185i	−0.0210442	+	0.127064i
$739$	1.61953	+	3.02993i	0.0595753	+	0.111458i	0.909946	−	0.414726i	$-0.136123\pi$
$739$	1.61953	+	3.02993i	0.0595753	+	0.111458i	−0.850371	+	0.526183i	$0.823623\pi$
$740$	23.0761	−	39.8761i	0.848293	−	1.46587i
$741$	−1.56501	+	1.28437i	−0.0574921	+	0.0471825i
$742$	10.8951	+	32.1493i	0.399973	+	1.18024i
$743$	23.4966	+	4.67376i	0.862005	+	0.171463i	0.606246	−	0.795277i	$-0.292675\pi$
$743$	23.4966	+	4.67376i	0.862005	+	0.171463i	0.255759	+	0.966741i	$0.417675\pi$
$744$	−3.02168	−	1.25698i	−0.110780	−	0.0460830i
$745$	−4.91330	−	24.7008i	−0.180009	−	0.904969i
$746$	7.54822	−	28.1137i	0.276360	−	1.02932i
$747$	7.44911	−	2.25966i	0.272549	−	0.0826767i
$748$	−38.8711	+	14.5853i	−1.42127	+	0.533293i
$749$	17.2173	+	14.1299i	0.629106	+	0.516294i
$750$	6.76568	−	17.9485i	0.247048	−	0.655388i
$751$	42.8389	−	17.7444i	1.56321	−	0.647504i	0.577568	−	0.816342i	$-0.304002\pi$
$751$	42.8389	−	17.7444i	1.56321	−	0.647504i	0.985644	+	0.168839i	$0.0540017\pi$
$752$	37.6175	+	10.1609i	1.37177	+	0.370530i
$753$	−13.5558	−	5.61501i	−0.494002	−	0.204622i
$754$	1.23565	−	1.31796i	0.0449998	−	0.0479973i
$755$	36.1321	−	3.55870i	1.31498	−	0.129514i
$756$	3.86942	−	0.634839i	0.140729	−	0.0230889i
$757$	1.81648	+	0.970927i	0.0660210	+	0.0352889i	0.504077	−	0.863659i	$-0.331833\pi$
$757$	1.81648	+	0.970927i	0.0660210	+	0.0352889i	−0.438056	+	0.898948i	$0.644333\pi$
$758$	27.6139	−	3.62129i	1.00298	−	0.131531i
$759$	8.17348	+	5.46135i	0.296679	+	0.198234i
$760$	87.1494	+	8.71650i	3.16124	+	0.316181i
$761$	3.54202	+	5.30100i	0.128398	+	0.192161i	0.890099	−	0.455768i	$-0.150635\pi$
$761$	3.54202	+	5.30100i	0.128398	+	0.192161i	−0.761701	+	0.647929i	$0.775635\pi$
$762$	−7.22502	−	0.477209i	−0.261735	−	0.0172875i
$763$	−2.89667	+	29.4104i	−0.104867	+	1.06473i
$764$	12.7931	+	26.0078i	0.462837	+	0.940930i
$765$	−6.90448	+	22.7610i	−0.249632	+	0.822926i
$766$	6.49584	+	27.9227i	0.234704	+	1.00889i
$767$	−1.15192			−0.0415935
$768$	−15.9892	−	0.587961i	−0.576960	−	0.0212162i
$769$	18.9013			0.681600			0.340800	−	0.940136i	$-0.389302\pi$
$769$	18.9013			0.681600			0.340800	+	0.940136i	$0.389302\pi$
$770$	7.49461	+	32.2160i	0.270087	+	1.16098i
$771$	−4.80818	+	15.8504i	−0.173162	+	0.570840i
$772$	−10.8718	−	22.1020i	−0.391286	−	0.795469i
$773$	2.84391	−	28.8747i	0.102288	−	1.03855i	−0.797824	−	0.602891i	$-0.794015\pi$
$773$	2.84391	−	28.8747i	0.102288	−	1.03855i	0.900112	−	0.435659i	$-0.143485\pi$
$774$	−4.18827	−	0.276633i	−0.150544	−	0.00994337i
$775$	−5.57249	−	8.33983i	−0.200170	−	0.299575i
$776$	−2.93166	+	29.3114i	−0.105241	+	1.05222i
$777$	10.1572	+	6.78680i	0.364386	+	0.243475i
$778$	−44.2160	+	5.79848i	−1.58522	+	0.207885i
$779$	−18.2752	−	9.76827i	−0.654775	−	0.349985i
$780$	1.76375	−	0.289371i	0.0631525	−	0.0103612i
$781$	−42.2421	+	4.16049i	−1.51154	+	0.148874i
$782$	−18.9581	+	20.2209i	−0.677941	+	0.723099i
$783$	−4.88262	−	2.02245i	−0.174491	−	0.0722763i
$784$	−6.29024	−	10.9459i	−0.224651	−	0.390925i
$785$	−6.13921	+	2.54294i	−0.219118	+	0.0907616i
$786$	−3.09346	+	8.20659i	−0.110340	+	0.292719i
$787$	20.7212	+	17.0055i	0.738632	+	0.606179i	0.926623	−	0.375991i	$-0.122698\pi$
$787$	20.7212	+	17.0055i	0.738632	+	0.606179i	−0.187992	+	0.982171i	$0.560198\pi$
$788$	23.6799	−	8.88524i	0.843561	−	0.316524i
$789$	−20.4112	+	6.19167i	−0.726657	+	0.220429i
$790$	−1.71666	+	6.39378i	−0.0610760	+	0.227480i
$791$	1.42910	+	7.18455i	0.0508128	+	0.255453i
$792$	3.50527	−	8.42643i	0.124554	−	0.299420i
$793$	1.07600	+	0.214031i	0.0382101	+	0.00760045i
$794$	0.446496	+	1.31752i	0.0158456	+	0.0467569i
$795$	34.9887	−	28.7145i	1.24092	−	1.01840i
$796$	−9.93448	+	17.1670i	−0.352118	+	0.608470i
$797$	−12.4121	−	23.2214i	−0.439659	−	0.822545i	0.560324	−	0.828273i	$-0.310677\pi$
$797$	−12.4121	−	23.2214i	−0.439659	−	0.822545i	−0.999984	+	0.00572843i	$0.998177\pi$
$798$	−3.79446	+	22.9109i	−0.134322	+	0.811036i
$799$	−44.3151	−	44.3151i	−1.56776	−	1.56776i
$800$	−39.7876	−	28.6633i	−1.40670	−	1.01340i
$801$	10.7828	−	10.7828i	0.380990	−	0.380990i
$802$	13.1764	+	18.4073i	0.465276	+	0.649984i
$803$	−19.6396	+	10.4976i	−0.693065	+	0.370451i
$804$	−3.69585	+	27.8558i	−0.130343	+	0.982399i
$805$	14.0091	+	17.0701i	0.493755	+	0.601642i
$806$	0.175121	−	0.354660i	0.00616837	−	0.0124924i
$807$	6.33410	−	31.8437i	0.222971	−	1.12095i
$808$	−4.39975	−	0.882080i	−0.154783	−	0.0310315i
$809$	31.4091	−	6.24766i	1.10429	−	0.219656i	0.390904	−	0.920431i	$-0.372162\pi$
$809$	31.4091	−	6.24766i	1.10429	−	0.219656i	0.713382	+	0.700775i	$0.247162\pi$
$810$	−2.61197	−	4.52933i	−0.0917752	−	0.159145i
$811$	6.14750	+	20.2656i	0.215868	+	0.711621i	0.996266	+	0.0863378i	$0.0275164\pi$
$811$	6.14750	+	20.2656i	0.215868	+	0.711621i	−0.780398	+	0.625283i	$0.784984\pi$
$812$	0.698907	−	20.7111i	0.0245268	−	0.726818i
$813$	9.57738	−	11.6701i	0.335894	−	0.409287i
$814$	25.9039	−	11.7212i	0.907932	−	0.410828i
$815$	14.0187	+	33.8441i	0.491053	+	1.18551i
$816$	21.8258	+	13.6332i	0.764056	+	0.477258i
$817$	9.51312	−	22.9667i	0.332822	−	0.803503i
$818$	−1.72738	−	53.5916i	−0.0603963	−	1.87379i
$819$	0.0464514	+	0.471629i	0.00162314	+	0.0164801i
$820$	9.64472	+	15.5449i	0.336808	+	0.542851i
$821$	−5.76880	+	10.7927i	−0.201333	+	0.376667i	−0.962244	−	0.272189i	$-0.912252\pi$
$821$	−5.76880	+	10.7927i	−0.201333	+	0.376667i	0.760911	+	0.648856i	$0.224752\pi$
$822$	−13.0965	−	10.0598i	−0.456792	−	0.350875i
$823$	−17.2412	+	25.8033i	−0.600990	+	0.899445i	−0.999846	−	0.0175684i	$-0.994408\pi$
$823$	−17.2412	+	25.8033i	−0.600990	+	0.899445i	0.398855	+	0.917014i	$0.369408\pi$
$824$	11.8962	+	22.3374i	0.414425	+	0.778161i
$825$	23.2569	−	15.5398i	0.809702	−	0.541025i
$826$	−9.93861	+	8.70707i	−0.345808	+	0.302958i
$827$	−39.9042	−	3.93022i	−1.38760	−	0.136667i	−0.623532	−	0.781798i	$-0.714303\pi$
$827$	−39.9042	−	3.93022i	−1.38760	−	0.136667i	−0.764073	+	0.645130i	$0.776803\pi$
$828$	−0.392377	−	6.08040i	−0.0136361	−	0.211309i
$829$	−26.7092	−	8.10215i	−0.927649	−	0.281399i	−0.209917	−	0.977719i	$-0.567319\pi$
$829$	−26.7092	−	8.10215i	−0.927649	−	0.281399i	−0.717731	+	0.696320i	$0.754819\pi$
$830$	21.5099	−	34.5519i	0.746619	−	1.19931i
$831$			15.3442i			0.532284i
$832$	0.195359	−	1.92387i	0.00677286	−	0.0666982i
$833$			20.3049i			0.703523i
$834$	−6.19691	−	3.85782i	−0.214581	−	0.133585i
$835$	−49.2549	−	14.9413i	−1.70454	−	0.517065i
$836$	40.6018	+	35.6793i	1.40424	+	1.23399i
$837$	−1.15150	−	0.113413i	−0.0398017	−	0.00392013i
$838$	12.2328	+	13.9630i	0.422576	+	0.482345i
$839$	19.7338	−	13.1857i	0.681287	−	0.455221i	−0.166162	−	0.986098i	$-0.553137\pi$
$839$	19.7338	−	13.1857i	0.681287	−	0.455221i	0.847449	+	0.530877i	$0.178137\pi$
$840$	13.0301	−	15.8284i	0.449582	−	0.546131i
$841$	0.594323	−	0.889467i	0.0204939	−	0.0306713i
$842$	−12.4290	+	16.1810i	−0.428333	+	0.557633i
$843$	2.92670	−	5.47546i	0.100801	−	0.188585i
$844$	2.08756	−	8.91242i	0.0718567	−	0.306778i
$845$	−4.68977	−	47.6160i	−0.161333	−	1.63804i
$846$	13.7693	−	0.443815i	0.473398	−	0.0152587i
$847$	0.441570	−	1.06604i	0.0151725	−	0.0366297i
$848$	−20.1208	−	44.6467i	−0.690951	−	1.53317i
$849$	1.66359	+	4.01627i	0.0570944	+	0.137838i
$850$	32.5138	+	71.8558i	1.11521	+	2.46463i
$851$	12.0422	−	14.6735i	0.412801	−	0.503000i
$852$	17.9658	+	19.2206i	0.615497	+	0.658488i
$853$	13.6504	+	44.9993i	0.467380	+	1.54074i	0.801370	+	0.598169i	$0.204105\pi$
$853$	13.6504	+	44.9993i	0.467380	+	1.54074i	−0.333990	+	0.942576i	$0.608395\pi$
$854$	10.9014	−	6.28661i	0.373039	−	0.215123i
$855$	30.3707	−	6.04111i	1.03866	−	0.206602i
$856$	−26.6899	−	17.8921i	−0.912243	−	0.611538i
$857$	4.01786	−	20.1991i	0.137247	−	0.689990i	−0.849482	−	0.527617i	$-0.823085\pi$
$857$	4.01786	−	20.1991i	0.137247	−	0.689990i	0.986730	−	0.162372i	$-0.0519145\pi$
$858$	0.989024	+	0.488352i	0.0337647	+	0.0166721i
$859$	−10.4716	−	12.7597i	−0.357287	−	0.435355i	0.563086	−	0.826399i	$-0.309614\pi$
$859$	−10.4716	−	12.7597i	−0.357287	−	0.435355i	−0.920372	+	0.391044i	$0.872114\pi$
$860$	−17.4244	+	13.3424i	−0.594169	+	0.454971i
$861$	−4.27785	+	2.28656i	−0.145789	+	0.0779258i
$862$	−11.3540	+	8.12752i	−0.386720	+	0.276825i
$863$	27.0520	−	27.0520i	0.920861	−	0.920861i	−0.0762296	−	0.997090i	$-0.524288\pi$
$863$	27.0520	−	27.0520i	0.920861	−	0.920861i	0.997090	+	0.0762296i	$0.0242882\pi$
$864$	−5.46777	+	1.45033i	−0.186017	+	0.0493413i
$865$	22.6201	+	22.6201i	0.769105	+	0.769105i
$866$	25.4935	+	4.22220i	0.866306	+	0.143476i
$867$	−11.4971	−	21.5095i	−0.390461	−	0.730502i
$868$	−1.16986	−	4.38364i	−0.0397076	−	0.148791i
$869$	−3.15818	+	2.59185i	−0.107134	+	0.0879224i
$870$	−26.1702	+	8.86888i	−0.887252	+	0.300683i
$871$	−3.33091	−	0.662559i	−0.112863	−	0.0224499i
$872$	0.0644462	−	42.6342i	0.00218242	−	1.44378i
$873$	2.03184	+	10.2147i	0.0687672	+	0.345716i
$874$	34.8517	+	9.35730i	1.17888	+	0.316515i
$875$	25.4468	−	7.71920i	0.860259	−	0.260957i
$876$	12.5670	+	5.70930i	0.424599	+	0.192899i
$877$	23.3113	+	19.1311i	0.787168	+	0.646012i	0.939589	−	0.342304i	$-0.111207\pi$
$877$	23.3113	+	19.1311i	0.787168	+	0.646012i	−0.152422	+	0.988316i	$0.548707\pi$
$878$	18.4021	+	6.93666i	0.621042	+	0.234101i
$879$	27.9108	−	11.5610i	0.941409	−	0.389944i
$880$	−15.2472	−	45.2160i	−0.513983	−	1.52423i
$881$	15.6734	+	6.49212i	0.528049	+	0.218725i	0.630749	−	0.775987i	$-0.282748\pi$
$881$	15.6734	+	6.49212i	0.528049	+	0.218725i	−0.102699	+	0.994712i	$0.532748\pi$
$882$	−3.25618	−	3.05283i	−0.109641	−	0.102794i
$883$	−34.0859	+	3.35717i	−1.14708	+	0.112978i	−0.653643	−	0.756803i	$-0.726760\pi$
$883$	−34.0859	+	3.35717i	−1.14708	+	0.112978i	−0.493438	+	0.869781i	$0.664260\pi$
$884$	−1.81417	+	2.52629i	−0.0610170	+	0.0849682i
$885$	15.5382	+	8.30536i	0.522312	+	0.279182i
$886$	−1.14523	−	8.73290i	−0.0384748	−	0.293388i
$887$	12.0369	+	8.04283i	0.404161	+	0.270052i	0.740993	−	0.671513i	$-0.234355\pi$
$887$	12.0369	+	8.04283i	0.404161	+	0.270052i	−0.336832	+	0.941565i	$0.609355\pi$
$888$	−15.5298	−	8.33105i	−0.521146	−	0.279572i
$889$	−5.57689	−	8.34640i	−0.187043	−	0.279929i
$890$	5.25468	−	79.5567i	0.176137	−	2.66675i
$891$	0.316270	−	3.21114i	0.0105954	−	0.107577i
$892$	−9.33784	+	27.4176i	−0.312654	+	0.918008i
$893$	−23.6845	+	78.0775i	−0.792573	+	2.61276i
$894$	−9.38308	+	2.18284i	−0.313817	+	0.0730052i
$895$	32.1412			1.07436
$896$	−12.8565	−	18.0755i	−0.429505	−	0.603861i
$897$	0.736407			0.0245879
$898$	−56.2769	+	13.0920i	−1.87798	+	0.436887i
$899$	−1.77510	+	5.85171i	−0.0592028	+	0.195166i
$900$	−16.4115	−	5.58941i	−0.547051	−	0.186314i
$901$	−7.72017	+	78.3842i	−0.257196	+	2.61136i
$902$	−0.744059	+	11.2652i	−0.0247745	+	0.375089i
$903$	−3.23286	−	4.83832i	−0.107583	−	0.161009i
$904$	−3.05240	−	10.1174i	−0.101521	−	0.336501i
$905$	−66.3806	−	44.3541i	−2.20657	−	1.47438i
$906$	−1.80582	−	13.7702i	−0.0599943	−	0.457483i
$907$	24.2557	+	12.9649i	0.805396	+	0.430493i	0.822083	−	0.569368i	$-0.192812\pi$
$907$	24.2557	+	12.9649i	0.805396	+	0.430493i	−0.0166871	+	0.999861i	$0.505312\pi$
$908$	10.5984	+	7.61089i	0.351721	+	0.252576i
$909$	−1.57886	+	0.155504i	−0.0523675	+	0.00515774i
$910$	1.80764	+	1.69475i	0.0599226	+	0.0561803i
$911$	−23.1937	−	9.60716i	−0.768443	−	0.318299i	−0.0362014	−	0.999345i	$-0.511526\pi$
$911$	−23.1937	−	9.60716i	−0.768443	−	0.318299i	−0.732242	+	0.681045i	$0.761526\pi$
$912$	2.25855	−	33.4264i	0.0747881	−	1.10686i
$913$	23.2055	−	9.61202i	0.767989	−	0.318112i
$914$	−20.7527	−	7.82269i	−0.686437	−	0.258751i
$915$	−12.9710	−	10.6451i	−0.428809	−	0.351915i
$916$	−1.11393	+	2.45191i	−0.0368052	+	0.0810134i
$917$	−11.6350	+	3.52944i	−0.384222	+	0.116552i
$918$	8.78708	+	2.35924i	0.290017	+	0.0778664i
$919$	−0.0996109	−	0.500778i	−0.00328586	−	0.0165191i	0.979108	−	0.203343i	$-0.0651806\pi$
$919$	−0.0996109	−	0.500778i	−0.00328586	−	0.0165191i	−0.982393	+	0.186824i	$0.940181\pi$
$920$	−22.4926	−	22.5607i	−0.741559	−	0.743804i
$921$	−26.7992	−	5.33068i	−0.883062	−	0.175652i
$922$	6.77231	−	2.29509i	0.223034	−	0.0755846i
$923$	−2.45802	+	2.01724i	−0.0809066	+	0.0663983i
$924$	12.2245	−	3.26234i	0.402156	−	0.107323i
$925$	−25.4612	−	47.6345i	−0.837159	−	1.56621i
$926$	−1.30422	−	0.216002i	−0.0428592	−	0.00709827i
$927$	6.32693	+	6.32693i	0.207804	+	0.207804i
$928$	1.88013	+	29.8368i	0.0617182	+	0.979440i
$929$	−27.1763	+	27.1763i	−0.891626	+	0.891626i	−0.994676	−	0.103050i	$-0.967140\pi$
$929$	−27.1763	+	27.1763i	−0.891626	+	0.891626i	0.103050	+	0.994676i	$0.467140\pi$
$930$	−4.91930	+	3.52137i	−0.161310	+	0.115470i
$931$	23.3134	−	12.4613i	0.764065	−	0.408401i
$932$	8.46922	+	11.0604i	0.277418	+	0.362294i
$933$	2.49663	+	3.04216i	0.0817361	+	0.0995957i
$934$	16.5471	+	8.17048i	0.541437	+	0.267346i
$935$	−14.9726	+	75.2725i	−0.489658	+	2.46168i
$936$	−0.132367	−	0.670752i	−0.00432656	−	0.0219242i
$937$	6.82482	−	1.35754i	0.222957	−	0.0443490i	−0.0823474	−	0.996604i	$-0.526242\pi$
$937$	6.82482	−	1.35754i	0.222957	−	0.0443490i	0.305305	+	0.952255i	$0.401242\pi$
$938$	−33.7467	+	19.4610i	−1.10187	+	0.635424i
$939$	5.44895	+	17.9628i	0.177820	+	0.586193i
$940$	52.6218	−	49.1863i	1.71633	−	1.60428i
$941$	−9.25694	+	11.2796i	−0.301768	+	0.367705i	−0.901712	−	0.432337i	$-0.857689\pi$
$941$	−9.25694	+	11.2796i	−0.301768	+	0.367705i	0.599945	+	0.800041i	$0.295189\pi$
$942$	1.04787	+	2.31581i	0.0341415	+	0.0754531i
$943$	2.88441	+	6.96358i	0.0939293	+	0.226765i
$944$	13.0587	−	13.8864i	0.425024	−	0.451964i
$945$	2.77387	−	6.69671i	0.0902339	−	0.217844i
$946$	−13.5366	+	0.436315i	−0.440113	+	0.0141858i
$947$	2.71896	+	27.6061i	0.0883545	+	0.897078i	0.932550	+	0.361042i	$0.117579\pi$
$947$	2.71896	+	27.6061i	0.0883545	+	0.897078i	−0.844195	+	0.536036i	$0.819921\pi$
$948$	2.46562	+	0.577523i	0.0800797	+	0.0187571i
$949$	−0.786404	+	1.47126i	−0.0255278	+	0.0477591i
$950$	62.5483	−	81.4296i	2.02934	−	2.64192i
$951$	7.14158	−	10.6881i	0.231582	−	0.346586i
$952$	3.44316	+	35.5092i	0.111594	+	1.15086i
$953$	−11.5192	+	7.69689i	−0.373144	+	0.249327i	−0.727975	−	0.685604i	$-0.759538\pi$
$953$	−11.5192	+	7.69689i	−0.373144	+	0.249327i	0.354831	+	0.934930i	$0.384538\pi$
$954$	−11.4093	−	13.0230i	−0.369390	−	0.421636i
$955$	53.3204	+	5.25160i	1.72541	+	0.169938i
$956$	−11.1340	+	12.6701i	−0.360100	+	0.409781i
$957$	−16.3184	−	4.95014i	−0.527500	−	0.160015i
$958$	5.12353	+	3.18960i	0.165534	+	0.103051i
$959$		−	22.8942i		−	0.739291i
$960$	−16.5063	+	24.5425i	−0.532739	+	0.792105i
$961$		−	29.6612i		−	0.956812i
$962$	1.12567	−	1.80820i	0.0362931	−	0.0582986i
$963$	−10.8713	−	3.29776i	−0.350322	−	0.106269i
$964$	−30.0485	+	1.93907i	−0.967797	+	0.0624533i
$965$	−45.3129	−	4.46293i	−1.45867	−	0.143667i
$966$	6.35361	−	5.56631i	0.204424	−	0.179093i
$967$	−48.7039	+	32.5429i	−1.56621	+	1.04651i	−0.596388	+	0.802696i	$0.703398\pi$
$967$	−48.7039	+	32.5429i	−1.56621	+	1.04651i	−0.969823	+	0.243812i	$0.921602\pi$
$968$	−0.485627	+	1.59223i	−0.0156087	+	0.0511762i
$969$	−29.9366	+	44.8033i	−0.961702	+	1.43929i
$970$	43.1846	+	33.1713i	1.38657	+	1.06507i
$971$	16.1887	−	30.2869i	0.519519	−	0.971952i	−0.476183	−	0.879346i	$-0.657980\pi$
$971$	16.1887	−	30.2869i	0.519519	−	0.971952i	0.995703	−	0.0926064i	$-0.0295198\pi$
$972$	−1.69947	+	1.05442i	−0.0545105	+	0.0338207i
$973$	−0.991907	−	10.0710i	−0.0317991	−	0.322861i
$974$	0.0200231	+	0.621213i	0.000641580	+	0.0199049i
$975$	0.801868	−	1.93588i	0.0256803	−	0.0619978i
$976$	−14.7782	+	10.5449i	−0.473039	+	0.337534i
$977$	−5.16198	−	12.4621i	−0.165146	−	0.398699i	0.819543	−	0.573018i	$-0.194227\pi$
$977$	−5.16198	−	12.4621i	−0.165146	−	0.398699i	−0.984689	+	0.174319i	$0.944227\pi$
$978$	12.7665	−	5.77669i	0.408229	−	0.184718i
$979$	31.2147	−	38.0352i	0.997626	−	1.21561i
$980$	−23.3239	−	0.787077i	−0.745056	−	0.0251422i
$981$	−4.37561	−	14.4244i	−0.139702	−	0.460537i
$982$	29.2694	+	50.7552i	0.934025	+	1.61966i
$983$	−39.5438	+	7.86574i	−1.26125	+	0.250878i	−0.780042	−	0.625728i	$-0.784802\pi$
$983$	−39.5438	+	7.86574i	−1.26125	+	0.250878i	−0.481209	+	0.876606i	$0.659802\pi$
$984$	5.82427	−	3.87893i	0.185671	−	0.123656i
$985$	9.12118	−	45.8552i	0.290625	−	1.46107i
$986$	21.2886	−	43.1141i	0.677966	−	1.37303i
$987$	12.1161	+	14.7636i	0.385661	+	0.469929i
$988$	4.01396	+	0.532563i	0.127701	+	0.0169431i
$989$	−7.97442	+	4.26242i	−0.253572	+	0.135537i
$990$	−9.81990	−	13.7182i	−0.312097	−	0.435994i
$991$	24.1727	−	24.1727i	0.767870	−	0.767870i	−0.209861	−	0.977731i	$-0.567301\pi$
$991$	24.1727	−	24.1727i	0.767870	−	0.767870i	0.977731	+	0.209861i	$0.0673011\pi$
$992$	2.29017	+	6.13166i	0.0727131	+	0.194680i
$993$	17.9555	+	17.9555i	0.569802	+	0.569802i
$994$	−5.95960	+	35.9840i	−0.189027	+	1.14134i
$995$	17.2837	+	32.3355i	0.547930	+	1.02511i
$996$	−13.4749	−	7.79788i	−0.426970	−	0.247085i
$997$	−21.7650	+	17.8621i	−0.689305	+	0.565698i	−0.912500	−	0.409076i	$-0.865851\pi$
$997$	−21.7650	+	17.8621i	−0.689305	+	0.565698i	0.223196	+	0.974774i	$0.428351\pi$
$998$	−0.885141	−	2.61186i	−0.0280186	−	0.0826771i
$999$	−6.11106	−	1.21556i	−0.193345	−	0.0384588i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	384.2.v.a.325.20	yes	512
128.13	even	32	inner	384.2.v.a.13.20	✓	512

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
384.2.v.a.13.20	✓	512	128.13	even	32	inner
384.2.v.a.325.20	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)

\(f(q)\)	\(=\)	\(q+(0.320440 + 1.37743i) q^{2} +(0.290285 - 0.956940i) q^{3} +(-1.79464 + 0.882769i) q^{4} +(-0.362380 + 3.67931i) q^{5} +(1.41114 + 0.0932050i) q^{6} +(1.08924 + 1.63016i) q^{7} +(-1.79103 - 2.18911i) q^{8} +(-0.831470 - 0.555570i) q^{9} +O(q^{10})\)	\(q+(0.320440 + 1.37743i) q^{2} +(0.290285 - 0.956940i) q^{3} +(-1.79464 + 0.882769i) q^{4} +(-0.362380 + 3.67931i) q^{5} +(1.41114 + 0.0932050i) q^{6} +(1.08924 + 1.63016i) q^{7} +(-1.79103 - 2.18911i) q^{8} +(-0.831470 - 0.555570i) q^{9} +(-5.18411 + 0.679844i) q^{10} +(-2.84568 - 1.52105i) q^{11} +(0.323802 + 1.97361i) q^{12} +(-0.240556 + 0.0236927i) q^{13} +(-1.89640 + 2.02272i) q^{14} +(3.41568 + 1.41482i) q^{15} +(2.44144 - 3.16850i) q^{16} +(-5.94374 + 2.46198i) q^{17} +(0.498824 - 1.32332i) q^{18} +(6.47447 + 5.31346i) q^{19} +(-2.59764 - 6.92291i) q^{20} +(1.87615 - 0.569125i) q^{21} +(1.18327 - 4.40713i) q^{22} +(-0.594348 - 2.98799i) q^{23} +(-2.61476 + 1.07844i) q^{24} +(-8.50205 - 1.69116i) q^{25} +(-0.109719 - 0.323758i) q^{26} +(-0.773010 + 0.634393i) q^{27} +(-3.39384 - 1.96400i) q^{28} +(2.49129 + 4.66087i) q^{29} +(-0.854298 + 5.15824i) q^{30} +(0.818174 + 0.818174i) q^{31} +(5.14673 + 2.34760i) q^{32} +(-2.28161 + 2.28161i) q^{33} +(-5.29582 - 7.39818i) q^{34} +(-6.39257 + 3.41690i) q^{35} +(1.98263 + 0.263050i) q^{36} +(3.95276 + 4.81646i) q^{37} +(-5.24425 + 10.6208i) q^{38} +(-0.0471573 + 0.237076i) q^{39} +(8.70345 - 5.79645i) q^{40} +(-2.42653 + 0.482668i) q^{41} +(1.38513 + 2.40190i) q^{42} +(-0.861566 - 2.84020i) q^{43} +(6.44969 + 0.217648i) q^{44} +(2.34542 - 2.85790i) q^{45} +(3.92530 - 1.77615i) q^{46} +(3.72788 + 8.99989i) q^{47} +(-2.32335 - 3.25608i) q^{48} +(1.20780 - 2.91590i) q^{49} +(-0.394938 - 12.2529i) q^{50} +(0.630589 + 6.40248i) q^{51} +(0.410796 - 0.254876i) q^{52} +(5.77121 - 10.7972i) q^{53} +(-1.12154 - 0.861484i) q^{54} +(6.62761 - 9.91892i) q^{55} +(1.61775 - 5.30413i) q^{56} +(6.96410 - 4.65326i) q^{57} +(-5.62172 + 4.92511i) q^{58} +(4.74257 + 0.467102i) q^{59} +(-7.37887 + 0.476169i) q^{60} +(-4.34322 - 1.31750i) q^{61} +(-0.864803 + 1.38916i) q^{62} -1.96058i q^{63} +(-1.58444 + 7.84153i) q^{64} -0.893666i q^{65} +(-3.87388 - 2.41164i) q^{66} +(13.4450 + 4.07849i) q^{67} +(8.49349 - 9.66531i) q^{68} +(-3.03186 - 0.298612i) q^{69} +(-6.75499 - 7.71042i) q^{70} +(10.9379 - 7.30845i) q^{71} +(0.272979 + 2.81522i) q^{72} +(3.83429 - 5.73842i) q^{73} +(-5.36772 + 6.98805i) q^{74} +(-4.08636 + 7.64504i) q^{75} +(-16.3099 - 3.82026i) q^{76} +(-0.620071 - 6.29569i) q^{77} +(-0.341667 + 0.0110127i) q^{78} +(0.484546 - 1.16980i) q^{79} +(10.7732 + 10.1310i) q^{80} +(0.382683 + 0.923880i) q^{81} +(-1.44240 - 3.18772i) q^{82} +(-4.93831 + 6.01734i) q^{83} +(-2.86461 + 2.67758i) q^{84} +(-6.90448 - 22.7610i) q^{85} +(3.63611 - 2.09686i) q^{86} +(5.18336 - 1.03103i) q^{87} +(1.76695 + 8.95375i) q^{88} +(-2.97495 + 14.9561i) q^{89} +(4.68814 + 2.31487i) q^{90} +(-0.300646 - 0.366338i) q^{91} +(3.70434 + 4.83768i) q^{92} +(1.02045 - 0.545440i) q^{93} +(-11.2022 + 8.01883i) q^{94} +(-21.8961 + 21.8961i) q^{95} +(3.74053 - 4.24364i) q^{96} +(-7.36441 - 7.36441i) q^{97} +(4.40348 + 0.729296i) q^{98} +(1.52105 + 2.84568i) 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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