LMFDB - Embedded newform 384.2.v.a.13.20

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			13.20
Character	$\chi$	$=$	384.13
Dual form			384.2.v.a.325.20

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

$n$	$127$	$133$	$257$
$\chi(n)$	$1$	$e\left(\frac{15}{32}\right)$	$1$

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	−0.640966	−	0.767569i	$-0.721466\pi$
$5$	−0.362380	−	3.67931i	−0.162061	−	1.64544i	0.478905	−	0.877867i	$-0.341034\pi$
$6$	1.41114	−	0.0932050i	0.576095	−	0.0380508i
$7$	1.08924	−	1.63016i	0.411693	−	0.616142i	−0.566445	−	0.824100i	$-0.691682\pi$
$7$	1.08924	−	1.63016i	0.411693	−	0.616142i	0.978138	+	0.207957i	$0.0666815\pi$
$8$	−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	−0.840868	−	0.541240i	$-0.817955\pi$
$11$	−2.84568	+	1.52105i	−0.858004	+	0.458613i	−0.0171361	+	0.999853i	$0.505455\pi$
$12$	0.323802	−	1.97361i	0.0934737	−	0.569733i
$13$	−0.240556	−	0.0236927i	−0.0667183	−	0.00657118i	0.0646029	−	0.997911i	$-0.479422\pi$
$13$	−0.240556	−	0.0236927i	−0.0667183	−	0.00657118i	−0.131321	+	0.991340i	$0.541922\pi$
$14$	−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	−0.481391	−	0.876506i	$-0.659868\pi$
$17$	−5.94374	−	2.46198i	−1.44157	−	0.597117i	−0.960178	+	0.279389i	$0.909868\pi$
$18$	0.498824	+	1.32332i	0.117574	+	0.311909i
$19$	6.47447	−	5.31346i	1.48534	−	1.21899i	0.566689	−	0.823932i	$-0.308224\pi$
$19$	6.47447	−	5.31346i	1.48534	−	1.21899i	0.918656	−	0.395059i	$-0.129276\pi$
$20$	−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	0.868033	+	0.496507i	$0.165384\pi$
$23$	−0.594348	+	2.98799i	−0.123930	+	0.623039i	−0.991963	+	0.126531i	$0.959616\pi$
$24$	−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	−0.537137	−	0.843495i	$-0.680494\pi$
$29$	2.49129	−	4.66087i	0.462621	−	0.865502i	0.999758	−	0.0220074i	$-0.00700573\pi$
$30$	−0.854298	−	5.15824i	−0.155973	−	0.941761i
$31$	0.818174	−	0.818174i	0.146948	−	0.146948i	−0.629805	−	0.776753i	$-0.716865\pi$
$31$	0.818174	−	0.818174i	0.146948	−	0.146948i	0.776753	+	0.629805i	$0.216865\pi$
$32$	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	−0.339013	−	0.940782i	$-0.610093\pi$
$37$	3.95276	−	4.81646i	0.649831	−	0.791821i	0.988843	+	0.148961i	$0.0475929\pi$
$38$	−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	0.00193451	−	0.999998i	$-0.499384\pi$
$41$	−2.42653	−	0.482668i	−0.378961	−	0.0753800i	−0.380895	+	0.924618i	$0.624384\pi$
$42$	1.38513	−	2.40190i	0.213730	−	0.370622i
$43$	−0.861566	+	2.84020i	−0.131388	+	0.433127i	−0.997807	−	0.0661900i	$-0.978916\pi$
$43$	−0.861566	+	2.84020i	−0.131388	+	0.433127i	0.866419	+	0.499317i	$0.166416\pi$
$44$	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	−0.378280	−	0.925691i	$-0.623484\pi$
$47$	3.72788	−	8.99989i	0.543767	−	1.31277i	0.922047	−	0.387078i	$-0.126516\pi$
$48$	−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	0.873741	+	0.486392i	$0.161687\pi$
$53$	5.77121	+	10.7972i	0.792737	+	1.48311i	−0.0810041	+	0.996714i	$0.525813\pi$
$54$	−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	0.215533	−	0.976497i	$-0.430851\pi$
$59$	4.74257	−	0.467102i	0.617429	−	0.0608115i	0.401897	+	0.915685i	$0.368351\pi$
$60$	−7.37887	−	0.476169i	−0.952608	−	0.0614732i
$61$	−4.34322	+	1.31750i	−0.556093	+	0.168689i	−0.555807	−	0.831311i	$-0.687591\pi$
$61$	−4.34322	+	1.31750i	−0.556093	+	0.168689i	−0.000285186		1.00000i	$0.500091\pi$
$62$	−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	0.672294	−	0.740284i	$-0.265309\pi$
$67$	13.4450	−	4.07849i	1.64257	−	0.498267i	0.970272	+	0.242017i	$0.0778091\pi$
$68$	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	0.996293	−	0.0860202i	$-0.0274150\pi$
$71$	10.9379	+	7.30845i	1.29809	+	0.867353i	0.301793	+	0.953374i	$0.402415\pi$
$72$	0.272979	−	2.81522i	0.0321709	−	0.331777i
$73$	3.83429	+	5.73842i	0.448770	+	0.671631i	0.985022	−	0.172426i	$-0.0551606\pi$
$73$	3.83429	+	5.73842i	0.448770	+	0.671631i	−0.536253	+	0.844057i	$0.680161\pi$
$74$	−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	0.948791	−	0.315905i	$-0.102308\pi$
$79$	0.484546	+	1.16980i	0.0545156	+	0.131612i	−0.894275	+	0.447518i	$0.852308\pi$
$80$	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	0.427891	−	0.903830i	$-0.359257\pi$
$83$	−4.93831	−	6.01734i	−0.542049	−	0.660489i	−0.969941	+	0.243341i	$0.921757\pi$
$84$	−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	−0.735263	−	0.677782i	$-0.762941\pi$
$89$	−2.97495	−	14.9561i	−0.315345	−	1.58534i	0.419918	−	0.907562i	$-0.362059\pi$
$90$	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	−0.974055	−	0.226312i	$-0.927333\pi$
$97$	−7.36441	+	7.36441i	−0.747742	+	0.747742i	0.226312	+	0.974055i	$0.427333\pi$
$98$	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	0.693429	−	0.720525i	$-0.256099\pi$
$101$	1.22638	+	1.00646i	0.122029	+	0.100147i	−0.571399	+	0.820672i	$0.693599\pi$
$102$	−8.61691	−	2.92021i	−0.853201	−	0.289144i
$103$	−8.77570	+	1.74560i	−0.864696	+	0.171999i	−0.607460	−	0.794350i	$-0.707812\pi$
$103$	−8.77570	+	1.74560i	−0.864696	+	0.171999i	−0.257235	+	0.966349i	$0.582812\pi$
$104$	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	0.768085	−	0.640348i	$-0.221210\pi$
$107$	10.8713	+	3.29776i	1.05097	+	0.318807i	0.282881	+	0.959155i	$0.408710\pi$
$108$	0.827249	+	1.82089i	0.0796021	+	0.175216i
$109$	11.6520	−	9.56253i	1.11606	−	0.915924i	0.119023	−	0.992892i	$-0.462024\pi$
$109$	11.6520	−	9.56253i	1.11606	−	0.915924i	0.997034	+	0.0769676i	$0.0245238\pi$
$110$	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	−0.214364	−	0.976754i	$-0.568768\pi$
$113$	3.45189	−	1.42982i	0.324727	−	0.134506i	0.539091	+	0.842248i	$0.318768\pi$
$114$	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	0.842512	−	0.538678i	$-0.181076\pi$
$131$	−1.80021	−	5.93448i	−0.157285	−	0.518498i	−0.999796	+	0.0201800i	$0.993576\pi$
$132$	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	−0.896274	−	0.443501i	$-0.853736\pi$
$137$	−9.70929	+	6.48754i	−0.829521	+	0.554268i	0.0667529	+	0.997770i	$0.478736\pi$
$138$	−0.560212	+	4.27186i	−0.0476884	+	0.363645i
$139$	−4.55213	+	2.43317i	−0.386107	+	0.206378i	−0.653017	−	0.757343i	$-0.726497\pi$
$139$	−4.55213	+	2.43317i	−0.386107	+	0.206378i	0.266911	+	0.963721i	$0.413997\pi$
$140$	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	0.0117392	−	0.999931i	$-0.496263\pi$
$149$	−6.51869	−	1.97742i	−0.534032	−	0.161997i	−0.545771	+	0.837934i	$0.683763\pi$
$150$	−11.8399	+	3.17890i	−0.966728	+	0.259556i
$151$	−1.91585	+	9.63165i	−0.155910	+	0.783812i	0.821127	+	0.570745i	$0.193345\pi$
$151$	−1.91585	+	9.63165i	−0.155910	+	0.783812i	−0.977037	+	0.213068i	$0.931655\pi$
$152$	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	−0.845840	−	0.533436i	$-0.820900\pi$
$157$	0.847269	−	1.58513i	0.0676195	−	0.126507i	0.913460	+	0.406929i	$0.133400\pi$
$158$	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	0.776683	−	0.629892i	$-0.216901\pi$
$163$	8.73846	+	4.67081i	0.684449	+	0.365846i	−0.0922338	+	0.995737i	$0.529401\pi$
$164$	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	−0.931422	−	0.363941i	$-0.881431\pi$
$167$	−2.71605	−	13.6545i	−0.210174	−	1.05662i	0.721248	−	0.692677i	$-0.243569\pi$
$168$	−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	0.938664	−	0.344833i	$-0.112065\pi$
$173$	5.48915	+	6.68855i	0.417332	+	0.508521i	−0.521332	+	0.853354i	$0.674565\pi$
$174$	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	0.909351	+	0.416030i	$0.136579\pi$
$179$	−0.852121	+	8.65173i	−0.0636905	+	0.646661i	−0.973041	+	0.230631i	$0.925921\pi$
$180$	−1.68631	−	7.19936i	−0.125690	−	0.536609i
$181$	−10.1793	−	19.0442i	−0.756624	−	1.41554i	−0.904472	−	0.426534i	$-0.859735\pi$
$181$	−10.1793	−	19.0442i	−0.756624	−	1.41554i	0.147848	−	0.989010i	$-0.452765\pi$
$182$	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	$0.175673\pi$
$191$			14.4920i			1.04860i	−0.851533	+	0.524301i	$0.824327\pi$
$192$	7.04394	−	3.79249i	0.508352	−	0.273699i
$193$		−	12.3156i		−	0.886496i	−0.896399	−	0.443248i	$-0.853826\pi$
$193$		−	12.3156i		−	0.886496i	0.896399	−	0.443248i	$-0.146174\pi$
$194$	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	−0.535833	−	0.844324i	$-0.680002\pi$
$197$	−12.5851	+	1.23952i	−0.896651	+	0.0883124i	−0.360818	+	0.932636i	$0.617502\pi$
$198$	−3.43232	−	3.00701i	−0.243924	−	0.213699i
$199$	8.24583	+	5.50969i	0.584531	+	0.390571i	0.812383	−	0.583125i	$-0.198170\pi$
$199$	8.24583	+	5.50969i	0.584531	+	0.390571i	−0.227851	+	0.973696i	$0.573170\pi$
$200$	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	0.663415	−	0.748252i	$-0.269107\pi$
$211$	−2.90350	−	3.53793i	−0.199885	−	0.243561i	−0.863300	+	0.504691i	$0.831607\pi$
$212$	−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	0.961289	−	0.275544i	$-0.0888579\pi$
$223$	10.2404	+	10.2404i	0.685745	+	0.685745i	−0.275544	+	0.961289i	$0.588858\pi$
$224$	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	−0.963064	−	0.269273i	$-0.913217\pi$
$227$	−3.07541	+	5.75368i	−0.204122	+	0.381885i	0.758942	+	0.651158i	$0.225717\pi$
$228$	−8.39027	−	14.4986i	−0.555659	−	0.960194i
$229$	1.04089	+	0.854237i	0.0687840	+	0.0564496i	0.668157	−	0.744020i	$-0.267083\pi$
$229$	1.04089	+	0.854237i	0.0687840	+	0.0564496i	−0.599373	+	0.800470i	$0.704583\pi$
$230$	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	0.910406	+	0.413715i	$0.135769\pi$
$233$	−1.35885	+	6.83142i	−0.0890215	+	0.447541i	−0.999428	+	0.0338258i	$0.989231\pi$
$234$	−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	0.620170	−	0.784467i	$-0.287063\pi$
$239$	7.79158	+	3.22738i	0.503995	+	0.208762i	−0.116175	+	0.993229i	$0.537063\pi$
$240$	12.8220	+	7.36839i	0.827659	+	0.475628i
$241$	13.9095	−	5.76149i	0.895987	−	0.371130i	0.113311	−	0.993560i	$-0.463854\pi$
$241$	13.9095	−	5.76149i	0.895987	−	0.371130i	0.782676	+	0.622429i	$0.213854\pi$
$242$	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	0.927444	+	0.373962i	$0.122001\pi$
$251$	1.43818	+	14.6021i	0.0907770	+	0.921674i	−0.836667	+	0.547712i	$0.815499\pi$
$252$	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	0.261032	+	0.965330i	$0.415937\pi$
$263$	−11.8501	+	17.7349i	−0.730709	+	1.09358i	−0.991741	+	0.128253i	$0.959063\pi$
$264$	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	0.998995	−	0.0448264i	$-0.0142735\pi$
$269$	32.3112	+	3.18238i	1.97005	+	0.194033i	0.971054	+	0.238859i	$0.0767735\pi$
$270$	3.57609	+	3.81429i	0.217634	+	0.232131i
$271$	13.9477	−	5.77734i	0.847264	−	0.350948i	0.0835508	−	0.996504i	$-0.473374\pi$
$271$	13.9477	−	5.77734i	0.847264	−	0.350948i	0.763714	+	0.645555i	$0.223374\pi$
$272$	−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	−0.183520	−	0.983016i	$-0.558749\pi$
$277$	−14.6835	−	4.45419i	−0.882245	−	0.267626i	−0.698725	+	0.715390i	$0.746249\pi$
$278$	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	−0.0100884	−	0.999949i	$-0.503211\pi$
$281$	6.08927	−	1.21123i	0.363255	−	0.0722559i	0.373344	+	0.927693i	$0.378211\pi$
$282$	4.42172	−	13.0476i	0.263309	−	0.776971i
$283$	−3.36042	−	2.75782i	−0.199756	−	0.163935i	0.529198	−	0.848499i	$-0.322493\pi$
$283$	−3.36042	−	2.75782i	−0.199756	−	0.163935i	−0.728954	+	0.684563i	$0.759993\pi$
$284$	−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	0.196206	−	0.980563i	$-0.437138\pi$
$293$	19.1653	−	23.3530i	1.11965	−	1.36430i	0.923444	−	0.383734i	$-0.125362\pi$
$294$	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	0.546665	+	0.837351i	$0.315897\pi$
$307$	−2.67824	+	27.1926i	−0.152855	+	1.55196i	−0.699520	+	0.714613i	$0.746603\pi$
$308$	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	0.764287	−	0.644876i	$-0.223091\pi$
$311$	−2.18643	−	3.27222i	−0.123981	−	0.185551i	−0.888268	+	0.459326i	$0.848091\pi$
$312$	0.603446	+	0.321377i	0.0341634	+	0.0181944i
$313$	−15.6076	−	10.4286i	−0.882192	−	0.589462i	0.0298522	−	0.999554i	$-0.490496\pi$
$313$	−15.6076	−	10.4286i	−0.882192	−	0.589462i	−0.912044	+	0.410093i	$0.865496\pi$
$314$	−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	0.0747357	−	0.997203i	$-0.476189\pi$
$317$	12.3010	−	3.73147i	0.690893	−	0.209580i	0.616157	+	0.787623i	$0.288689\pi$
$318$	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	−0.960630	−	0.277830i	$-0.910385\pi$
$331$	−11.9702	−	22.3946i	−0.657940	−	1.23092i	0.302690	−	0.953089i	$-0.402115\pi$
$332$	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	0.554120	+	0.832437i	$0.313055\pi$
$337$	−7.82627	+	18.8943i	−0.426324	+	1.02924i	−0.980444	+	0.196800i	$0.936945\pi$
$338$	−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	−0.0656210	+	0.997845i	$0.520903\pi$
$347$	−19.2145	+	23.4130i	−1.03149	+	1.25687i	−0.965869	+	0.259030i	$0.916597\pi$
$348$	−8.39208	−	6.42604i	−0.449863	−	0.344472i
$349$	20.7670	+	11.1002i	1.11163	+	0.594180i	0.921811	−	0.387639i	$-0.126709\pi$
$349$	20.7670	+	11.1002i	1.11163	+	0.594180i	0.189821	+	0.981819i	$0.439209\pi$
$350$	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	−0.197949	+	0.980212i	$0.563428\pi$
$353$	−22.1356	+	22.1356i	−1.17816	+	1.17816i	−0.980212	+	0.197949i	$0.936572\pi$
$354$	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	−0.149585	−	0.988749i	$-0.547794\pi$
$359$	1.71653	−	0.341438i	0.0905947	−	0.0180204i	0.240180	+	0.970728i	$0.422794\pi$
$360$	−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	0.414539	−	0.910032i	$-0.363943\pi$
$367$	1.22937	+	0.509223i	0.0641728	+	0.0265812i	−0.350366	+	0.936613i	$0.613943\pi$
$368$	−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	−0.868853	−	0.495071i	$-0.835142\pi$
$373$	−18.1530	+	9.70296i	−0.939925	+	0.502400i	−0.0710722	+	0.997471i	$0.522642\pi$
$374$	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	0.908081	+	0.418794i	$0.137547\pi$
$379$	1.93027	+	19.5983i	0.0991512	+	1.00670i	−0.808930	+	0.587905i	$0.799953\pi$
$380$	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	−0.676266	−	0.736657i	$-0.736403\pi$
$389$	−3.09078	−	31.3813i	−0.156709	−	1.59109i	0.519557	−	0.854436i	$-0.326097\pi$
$390$	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	0.122553	−	0.992462i	$-0.460892\pi$
$397$	0.978932	+	0.0964164i	0.0491312	+	0.00483900i	−0.0734217	+	0.997301i	$0.523392\pi$
$398$	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	0.720041	−	0.693931i	$-0.244123\pi$
$401$	14.7885	+	6.12561i	0.738503	+	0.305898i	0.0184624	+	0.999830i	$0.494123\pi$
$402$	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	−0.987320	−	0.158743i	$-0.949256\pi$
$409$	−37.1861	+	7.39678i	−1.83874	+	0.365747i	−0.851416	+	0.524490i	$0.824256\pi$
$410$	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	0.729283	−	0.684212i	$-0.239854\pi$
$419$	11.5765	+	6.18777i	0.565550	+	0.302293i	−0.163733	+	0.986505i	$0.552354\pi$
$420$	−8.81357	+	11.5101i	−0.430058	+	0.561634i
$421$	9.15270	−	11.1526i	0.446075	−	0.543544i	−0.500623	−	0.865665i	$-0.666896\pi$
$421$	9.15270	−	11.1526i	0.446075	−	0.543544i	0.946699	+	0.322121i	$0.104396\pi$
$422$	−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	−0.806379	−	0.591399i	$-0.798576\pi$
$431$	3.77841	−	9.12189i	0.182000	−	0.439386i	0.988378	+	0.152013i	$0.0485757\pi$
$432$	0.122818	−	3.99811i	0.00590911	−	0.192359i
$433$	6.99247	+	16.8813i	0.336037	+	0.811265i	0.998088	+	0.0618062i	$0.0196861\pi$
$433$	6.99247	+	16.8813i	0.336037	+	0.811265i	−0.662051	+	0.749458i	$0.730314\pi$
$434$	−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	0.968718	−	0.248164i	$-0.0798274\pi$
$439$	7.72578	+	11.5625i	0.368732	+	0.551846i	−0.599986	+	0.800010i	$0.704827\pi$
$440$	−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	−0.244176	−	0.969731i	$-0.578517\pi$
$443$	−6.19798	+	0.610448i	−0.294475	+	0.0290032i	−0.0502990	+	0.998734i	$0.516017\pi$
$444$	−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	$-0.585591\pi$
$449$		−	40.8564i		−	1.92813i	0.265663	−	0.964066i	$-0.414409\pi$
$450$	−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	0.569739	−	0.821826i	$-0.307044\pi$
$457$	−8.71260	−	13.0393i	−0.407558	−	0.609954i	−0.977298	+	0.211871i	$0.932044\pi$
$458$	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	0.976721	+	0.214515i	$0.0688172\pi$
$461$	−0.495601	+	5.03192i	−0.0230824	+	0.234360i	−0.999803	+	0.0198446i	$0.993683\pi$
$462$	−0.288217	+	8.94188i	−0.0134091	+	0.416014i
$463$	−0.357726	−	0.863627i	−0.0166249	−	0.0401362i	0.915349	−	0.402661i	$-0.131915\pi$
$463$	−0.357726	−	0.863627i	−0.0166249	−	0.0401362i	−0.931974	+	0.362525i	$0.881915\pi$
$464$	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	0.928473	−	0.371399i	$-0.121122\pi$
$467$	8.27831	+	10.0872i	0.383075	+	0.466778i	−0.545399	+	0.838177i	$0.683622\pi$
$468$	−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	0.772677	−	0.634799i	$-0.218917\pi$
$479$	3.01762	+	3.01762i	0.137879	+	0.137879i	−0.634799	+	0.772677i	$0.718917\pi$
$480$	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	−0.185314	−	0.982679i	$-0.559330\pi$
$487$	0.431047	−	0.0857406i	0.0195326	−	0.00388528i	0.204847	+	0.978794i	$0.434330\pi$
$488$	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	0.997657	−	0.0684078i	$-0.0217919\pi$
$491$	39.6454	+	12.0263i	1.78917	+	0.542740i	0.791517	+	0.611148i	$0.209292\pi$
$492$	−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	0.0544860	−	0.998515i	$-0.482648\pi$
$499$	−1.94065	−	0.191137i	−0.0868754	−	0.00855648i	−0.141361	+	0.989958i	$0.545148\pi$
$500$	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	−0.115127	−	0.993351i	$-0.536728\pi$
$503$	17.0126	−	11.3674i	0.758552	−	0.506848i	0.873679	+	0.486502i	$0.161728\pi$
$504$	−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	0.918646	−	0.395082i	$-0.129284\pi$
$509$	−1.45915	−	4.81018i	−0.0646757	−	0.213207i	−0.983322	+	0.181874i	$0.941784\pi$
$510$	−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	0.0113364	−	0.999936i	$-0.496391\pi$
$521$	21.4444	−	14.3287i	0.939495	−	0.627750i	0.928158	+	0.372185i	$0.121391\pi$
$522$	7.41054	+	0.971817i	0.324350	+	0.0425353i
$523$	21.8379	−	11.6726i	0.954905	−	0.510408i	0.0811120	−	0.996705i	$-0.474153\pi$
$523$	21.8379	−	11.6726i	0.954905	−	0.510408i	0.873793	+	0.486297i	$0.161653\pi$
$524$	−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	−0.929969	−	0.367639i	$-0.880166\pi$
$541$	−2.50330	+	4.68335i	−0.107625	+	0.201353i	0.822343	+	0.568992i	$0.192666\pi$
$542$	−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	−0.450857	−	0.892596i	$-0.648881\pi$
$547$	−33.7608	−	18.0455i	−1.44351	−	0.771570i	−0.992649	+	0.121026i	$0.961381\pi$
$548$	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	0.209125	−	0.977889i	$-0.432938\pi$
$557$	−18.6629	−	22.7408i	−0.790772	−	0.963559i	−0.999897	+	0.0143302i	$0.995438\pi$
$558$	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	0.889497	+	0.456941i	$0.151055\pi$
$563$	−1.70965	+	17.3584i	−0.0720533	+	0.731570i	−0.961550	+	0.274629i	$0.911445\pi$
$564$	−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	0.991680	−	0.128727i	$-0.0410891\pi$
$569$	29.8709	+	19.9591i	1.25225	+	0.836728i	0.260571	+	0.965455i	$0.416089\pi$
$570$	−32.9392	−	28.8576i	−1.37967	−	1.20871i
$571$	−18.4144	+	1.81366i	−0.770620	+	0.0758994i	−0.475682	−	0.879617i	$-0.657799\pi$
$571$	−18.4144	+	1.81366i	−0.770620	+	0.0758994i	−0.294937	+	0.955517i	$0.595299\pi$
$572$	−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	$-0.952747\pi$
$577$		−	7.10562i		−	0.295811i	0.989002	−	0.147905i	$-0.0472531\pi$
$578$	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	0.658600	−	0.752493i	$-0.271149\pi$
$587$	−8.06732	−	15.0929i	−0.332974	−	0.622950i	−0.991574	+	0.129543i	$0.958649\pi$
$588$	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	−0.948720	−	0.316118i	$-0.897620\pi$
$593$	−1.32336	+	3.19489i	−0.0543441	+	0.131198i	0.894376	+	0.447317i	$0.147620\pi$
$594$	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	0.434489	−	0.900677i	$-0.356929\pi$
$599$	12.0226	+	2.39144i	0.491229	+	0.0977116i	0.0567408	+	0.998389i	$0.481929\pi$
$600$	24.0546	+	4.74698i	0.982026	+	0.193794i
$601$	2.70132	+	13.5805i	0.110189	+	0.553958i	0.995957	+	0.0898299i	$0.0286323\pi$
$601$	2.70132	+	13.5805i	0.110189	+	0.553958i	−0.885768	+	0.464128i	$0.846368\pi$
$602$	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	0.303999	−	0.952672i	$-0.401678\pi$
$607$	−15.9816	−	15.9816i	−0.648673	−	0.648673i	−0.952672	+	0.303999i	$0.901678\pi$
$608$	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	0.914758	−	0.404002i	$-0.132381\pi$
$613$	17.2564	+	14.1620i	0.696980	+	0.571996i	−0.217779	+	0.975998i	$0.569881\pi$
$614$	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	0.489226	+	0.872157i	$0.337279\pi$
$617$	−7.36540	+	37.0284i	−0.296520	+	1.49071i	−0.785746	+	0.618549i	$0.787721\pi$
$618$	−12.2210	+	3.28122i	−0.491602	+	0.131990i
$619$	−15.3638	−	4.66055i	−0.617522	−	0.187323i	−0.0340018	−	0.999422i	$-0.510825\pi$
$619$	−15.3638	−	4.66055i	−0.617522	−	0.187323i	−0.583520	+	0.812098i	$0.698325\pi$
$620$	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	−0.817128	−	0.576456i	$-0.804435\pi$
$631$	−15.0028	+	10.0246i	−0.597254	+	0.399072i	0.219874	+	0.975528i	$0.429435\pi$
$632$	−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	0.998970	+	0.0453725i	$0.0144475\pi$
$643$	4.90830	+	16.1805i	0.193564	+	0.638096i	−0.805406	+	0.592724i	$0.798053\pi$
$644$	−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	−0.818377	−	0.574681i	$-0.805126\pi$
$647$	0.654688	−	0.979810i	0.0257385	−	0.0385203i	0.844116	+	0.536161i	$0.180126\pi$
$648$	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	−0.817407	−	0.576061i	$-0.804589\pi$
$653$	−44.2463	−	4.35788i	−1.73149	−	0.170537i	−0.914085	+	0.405524i	$0.867089\pi$
$654$	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	−0.447844	−	0.894112i	$-0.647808\pi$
$659$	8.77222	−	7.19918i	0.341717	−	0.280440i	0.789561	+	0.613671i	$0.210308\pi$
$660$	21.7222	−	9.86858i	0.845534	−	0.384134i
$661$	2.53055	+	0.767634i	0.0984270	+	0.0298575i	0.339114	−	0.940745i	$-0.389873\pi$
$661$	2.53055	+	0.767634i	0.0984270	+	0.0298575i	−0.240687	+	0.970603i	$0.577373\pi$
$662$	−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	0.869230	−	0.494407i	$-0.164615\pi$
$673$	9.72376	+	9.72376i	0.374823	+	0.374823i	−0.494407	+	0.869230i	$0.664615\pi$
$674$	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	−0.662467	−	0.749091i	$-0.730491\pi$
$677$	5.24213	−	6.38755i	0.201471	−	0.245494i	0.863938	+	0.503597i	$0.167991\pi$
$678$	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	0.0597853	+	0.998211i	$0.480958\pi$
$683$	−14.2301	+	46.9105i	−0.544501	+	1.79498i	−0.604286	+	0.796767i	$0.706542\pi$
$684$	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	−0.812326	−	0.583204i	$-0.801799\pi$
$691$	2.58055	−	26.2008i	0.0981688	−	0.996725i	0.910495	−	0.413521i	$-0.135701\pi$
$692$	−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	0.669420	−	0.742885i	$-0.266543\pi$
$701$	43.3881	−	13.1616i	1.63875	−	0.497108i	0.969327	+	0.245776i	$0.0790429\pi$
$702$	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	−0.484515	−	0.874783i	$-0.661004\pi$
$709$	−21.0103	+	2.06933i	−0.789058	+	0.0777154i	−0.304543	+	0.952499i	$0.598504\pi$
$710$	−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	0.955803	−	0.294008i	$-0.0949891\pi$
$719$	1.93205	+	4.66439i	0.0720534	+	0.173952i	−0.883750	+	0.467960i	$0.844989\pi$
$720$	−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	0.936514	−	0.350630i	$-0.114032\pi$
$727$	44.9623	+	8.94356i	1.66756	+	0.331698i	0.731046	+	0.682328i	$0.239032\pi$
$728$	−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	0.351526	−	0.936178i	$-0.385663\pi$
$733$	−6.26977	−	3.35126i	−0.231579	−	0.123782i	−0.583106	+	0.812396i	$0.698163\pi$
$734$	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	−0.850371	−	0.526183i	$-0.823623\pi$
$739$	1.61953	−	3.02993i	0.0595753	−	0.111458i	0.909946	+	0.414726i	$0.136123\pi$
$740$	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	0.255759	−	0.966741i	$-0.417675\pi$
$743$	23.4966	−	4.67376i	0.862005	−	0.171463i	0.606246	+	0.795277i	$0.292675\pi$
$744$	−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	0.985644	−	0.168839i	$-0.0540017\pi$
$751$	42.8389	+	17.7444i	1.56321	+	0.647504i	0.577568	+	0.816342i	$0.304002\pi$
$752$	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	−0.438056	−	0.898948i	$-0.644333\pi$
$757$	1.81648	−	0.970927i	0.0660210	−	0.0352889i	0.504077	+	0.863659i	$0.331833\pi$
$758$	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	−0.761701	−	0.647929i	$-0.775635\pi$
$761$	3.54202	−	5.30100i	0.128398	−	0.192161i	0.890099	+	0.455768i	$0.150635\pi$
$762$	−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	0.900112	+	0.435659i	$0.143485\pi$
$773$	2.84391	+	28.8747i	0.102288	+	1.03855i	−0.797824	+	0.602891i	$0.794015\pi$
$774$	−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	−0.187992	−	0.982171i	$-0.560198\pi$
$787$	20.7212	−	17.0055i	0.738632	−	0.606179i	0.926623	+	0.375991i	$0.122698\pi$
$788$	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	−0.999984	−	0.00572843i	$-0.998177\pi$
$797$	−12.4121	+	23.2214i	−0.439659	+	0.822545i	0.560324	+	0.828273i	$0.310677\pi$
$798$	−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	0.713382	−	0.700775i	$-0.247162\pi$
$809$	31.4091	+	6.24766i	1.10429	+	0.219656i	0.390904	+	0.920431i	$0.372162\pi$
$810$	−2.61197	+	4.52933i	−0.0917752	+	0.159145i
$811$	6.14750	−	20.2656i	0.215868	−	0.711621i	−0.780398	−	0.625283i	$-0.784984\pi$
$811$	6.14750	−	20.2656i	0.215868	−	0.711621i	0.996266	−	0.0863378i	$-0.0275164\pi$
$812$	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	0.760911	−	0.648856i	$-0.224752\pi$
$821$	−5.76880	−	10.7927i	−0.201333	−	0.376667i	−0.962244	+	0.272189i	$0.912252\pi$
$822$	−13.0965	+	10.0598i	−0.456792	+	0.350875i
$823$	−17.2412	−	25.8033i	−0.600990	−	0.899445i	0.398855	−	0.917014i	$-0.369408\pi$
$823$	−17.2412	−	25.8033i	−0.600990	−	0.899445i	−0.999846	+	0.0175684i	$0.994408\pi$
$824$	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	−0.764073	−	0.645130i	$-0.776803\pi$
$827$	−39.9042	+	3.93022i	−1.38760	+	0.136667i	−0.623532	+	0.781798i	$0.714303\pi$
$828$	−0.392377	+	6.08040i	−0.0136361	+	0.211309i
$829$	−26.7092	+	8.10215i	−0.927649	+	0.281399i	−0.717731	−	0.696320i	$-0.754819\pi$
$829$	−26.7092	+	8.10215i	−0.927649	+	0.281399i	−0.209917	+	0.977719i	$0.567319\pi$
$830$	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	0.847449	−	0.530877i	$-0.178137\pi$
$839$	19.7338	+	13.1857i	0.681287	+	0.455221i	−0.166162	+	0.986098i	$0.553137\pi$
$840$	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	−0.333990	−	0.942576i	$-0.608395\pi$
$853$	13.6504	−	44.9993i	0.467380	−	1.54074i	0.801370	−	0.598169i	$-0.204105\pi$
$854$	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	0.986730	+	0.162372i	$0.0519145\pi$
$857$	4.01786	+	20.1991i	0.137247	+	0.689990i	−0.849482	+	0.527617i	$0.823085\pi$
$858$	0.989024	−	0.488352i	0.0337647	−	0.0166721i
$859$	−10.4716	+	12.7597i	−0.357287	+	0.435355i	−0.920372	−	0.391044i	$-0.872114\pi$
$859$	−10.4716	+	12.7597i	−0.357287	+	0.435355i	0.563086	+	0.826399i	$0.309614\pi$
$860$	−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	0.997090	−	0.0762296i	$-0.0242882\pi$
$863$	27.0520	+	27.0520i	0.920861	+	0.920861i	−0.0762296	+	0.997090i	$0.524288\pi$
$864$	−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	−0.152422	−	0.988316i	$-0.548707\pi$
$877$	23.3113	−	19.1311i	0.787168	−	0.646012i	0.939589	+	0.342304i	$0.111207\pi$
$878$	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	−0.102699	−	0.994712i	$-0.532748\pi$
$881$	15.6734	−	6.49212i	0.528049	−	0.218725i	0.630749	+	0.775987i	$0.282748\pi$
$882$	−3.25618	+	3.05283i	−0.109641	+	0.102794i
$883$	−34.0859	−	3.35717i	−1.14708	−	0.112978i	−0.493438	−	0.869781i	$-0.664260\pi$
$883$	−34.0859	−	3.35717i	−1.14708	−	0.112978i	−0.653643	+	0.756803i	$0.726760\pi$
$884$	−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	−0.336832	−	0.941565i	$-0.609355\pi$
$887$	12.0369	−	8.04283i	0.404161	−	0.270052i	0.740993	+	0.671513i	$0.234355\pi$
$888$	−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	−0.0166871	−	0.999861i	$-0.505312\pi$
$907$	24.2557	−	12.9649i	0.805396	−	0.430493i	0.822083	+	0.569368i	$0.192812\pi$
$908$	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	−0.732242	−	0.681045i	$-0.761526\pi$
$911$	−23.1937	+	9.60716i	−0.768443	+	0.318299i	−0.0362014	+	0.999345i	$0.511526\pi$
$912$	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	−0.982393	−	0.186824i	$-0.940181\pi$
$919$	−0.0996109	+	0.500778i	−0.00328586	+	0.0165191i	0.979108	+	0.203343i	$0.0651806\pi$
$920$	−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	0.103050	−	0.994676i	$-0.467140\pi$
$929$	−27.1763	−	27.1763i	−0.891626	−	0.891626i	−0.994676	+	0.103050i	$0.967140\pi$
$930$	−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	0.305305	−	0.952255i	$-0.401242\pi$
$937$	6.82482	+	1.35754i	0.222957	+	0.0443490i	−0.0823474	+	0.996604i	$0.526242\pi$
$938$	−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	0.599945	−	0.800041i	$-0.295189\pi$
$941$	−9.25694	−	11.2796i	−0.301768	−	0.367705i	−0.901712	+	0.432337i	$0.857689\pi$
$942$	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	−0.844195	−	0.536036i	$-0.819921\pi$
$947$	2.71896	−	27.6061i	0.0883545	−	0.897078i	0.932550	−	0.361042i	$-0.117579\pi$
$948$	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	0.354831	−	0.934930i	$-0.384538\pi$
$953$	−11.5192	−	7.69689i	−0.373144	−	0.249327i	−0.727975	+	0.685604i	$0.759538\pi$
$954$	−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	−0.969823	−	0.243812i	$-0.921602\pi$
$967$	−48.7039	−	32.5429i	−1.56621	−	1.04651i	−0.596388	−	0.802696i	$-0.703398\pi$
$968$	−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	0.995703	+	0.0926064i	$0.0295198\pi$
$971$	16.1887	+	30.2869i	0.519519	+	0.971952i	−0.476183	+	0.879346i	$0.657980\pi$
$972$	−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	−0.984689	−	0.174319i	$-0.944227\pi$
$977$	−5.16198	+	12.4621i	−0.165146	+	0.398699i	0.819543	+	0.573018i	$0.194227\pi$
$978$	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	−0.481209	−	0.876606i	$-0.659802\pi$
$983$	−39.5438	−	7.86574i	−1.26125	−	0.250878i	−0.780042	+	0.625728i	$0.784802\pi$
$984$	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	0.977731	−	0.209861i	$-0.0673011\pi$
$991$	24.1727	+	24.1727i	0.767870	+	0.767870i	−0.209861	+	0.977731i	$0.567301\pi$
$992$	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	0.223196	−	0.974774i	$-0.428351\pi$
$997$	−21.7650	−	17.8621i	−0.689305	−	0.565698i	−0.912500	+	0.409076i	$0.865851\pi$
$998$	−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.13.20	✓	512
128.69	even	32	inner	384.2.v.a.325.20	yes	512

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
384.2.v.a.13.20	✓	512	1.1	even	1	trivial
384.2.v.a.325.20	yes	512	128.69	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)

\(f(q)\)	\(=\)	\(q+(0.320440 - 1.37743i) q^{2} +(0.290285 + 0.956940i) q^{3} +(-1.79464 - 0.882769i) q^{4} +(-0.362380 - 3.67931i) q^{5} +(1.41114 - 0.0932050i) q^{6} +(1.08924 - 1.63016i) q^{7} +(-1.79103 + 2.18911i) q^{8} +(-0.831470 + 0.555570i) q^{9} +O(q^{10})\)	\(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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