LMFDB - Embedded newform 672.2.cf.a.187.54

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [672,2,Mod(19,672)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(672, base_ring=CyclotomicField(24))

chi = DirichletCharacter(H, H._module([12, 21, 0, 20]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("672.19");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 672 = 2^{5} \cdot 3 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	672.cf (of order $24$, degree $8$, 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:	$5.36594701583$
Analytic rank:	$0$
Dimension:	$512$
Relative dimension:	$64$ over $\Q(\zeta_{24})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{24}]$

Embedding invariants

Embedding label			187.54
Character	$\chi$	$=$	672.187
Dual form			672.2.cf.a.115.54

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.28368 + 0.593440i) q^{2} +(0.608761 - 0.793353i) q^{3} +(1.29566 + 1.52357i) q^{4} +(-2.51275 - 3.27468i) q^{5} +(1.25226 - 0.657147i) q^{6} +(2.57022 - 0.627676i) q^{7} +(0.759059 + 2.72467i) q^{8} +(-0.258819 - 0.965926i) q^{9} +O(q^{10})$	\(q+(1.28368 + 0.593440i) q^{2} +(0.608761 - 0.793353i) q^{3} +(1.29566 + 1.52357i) q^{4} +(-2.51275 - 3.27468i) q^{5} +(1.25226 - 0.657147i) q^{6} +(2.57022 - 0.627676i) q^{7} +(0.759059 + 2.72467i) q^{8} +(-0.258819 - 0.965926i) q^{9} +(-1.28224 - 5.69481i) q^{10} +(-0.235475 - 1.78861i) q^{11} +(1.99748 - 0.100423i) q^{12} +(-1.43468 - 3.46362i) q^{13} +(3.67182 + 0.719536i) q^{14} -4.12765 q^{15} +(-0.642540 + 3.94806i) q^{16} +(-2.80619 - 4.86047i) q^{17} +(0.240979 - 1.39353i) q^{18} +(-0.508184 + 3.86004i) q^{19} +(1.73355 - 8.07123i) q^{20} +(1.06668 - 2.42120i) q^{21} +(0.759159 - 2.43574i) q^{22} +(6.08447 - 1.63033i) q^{23} +(2.62371 + 1.05647i) q^{24} +(-3.11553 + 11.6273i) q^{25} +(0.213785 - 5.29757i) q^{26} +(-0.923880 - 0.382683i) q^{27} +(4.28643 + 3.10266i) q^{28} +(1.57052 + 3.79156i) q^{29} +(-5.29857 - 2.44951i) q^{30} +(2.96548 + 5.13636i) q^{31} +(-3.16775 + 4.68672i) q^{32} +(-1.56235 - 0.902022i) q^{33} +(-0.717852 - 7.90458i) q^{34} +(-8.51376 - 6.83946i) q^{35} +(1.13632 - 1.64584i) q^{36} +(7.36451 - 5.65099i) q^{37} +(-2.94305 + 4.65347i) q^{38} +(-3.62125 - 0.970311i) q^{39} +(7.01510 - 9.33210i) q^{40} +(-3.07356 - 3.07356i) q^{41} +(2.80611 - 2.47503i) q^{42} +(-0.205826 - 0.0852559i) q^{43} +(2.41998 - 2.67619i) q^{44} +(-2.51275 + 3.27468i) q^{45} +(8.77800 + 1.51795i) q^{46} +(9.51477 + 5.49335i) q^{47} +(2.74105 + 2.91319i) q^{48} +(6.21205 - 3.22653i) q^{49} +(-10.8994 + 13.0768i) q^{50} +(-5.56437 - 0.732563i) q^{51} +(3.41822 - 6.67350i) q^{52} +(1.25714 - 0.165506i) q^{53} +(-0.958864 - 1.03951i) q^{54} +(-5.26544 + 5.26544i) q^{55} +(3.66116 + 6.52655i) q^{56} +(2.75301 + 2.75301i) q^{57} +(-0.234027 + 5.79916i) q^{58} +(-1.27906 - 9.71546i) q^{59} +(-5.34802 - 6.28877i) q^{60} +(-1.07051 + 8.13137i) q^{61} +(0.758599 + 8.35327i) q^{62} +(-1.27151 - 2.32019i) q^{63} +(-6.84766 + 4.13637i) q^{64} +(-7.73726 + 13.4013i) q^{65} +(-1.47026 - 2.08507i) q^{66} +(-4.94622 - 3.79536i) q^{67} +(3.76941 - 10.5729i) q^{68} +(2.41056 - 5.81961i) q^{69} +(-6.87012 - 13.8321i) q^{70} +(-7.91899 + 7.91899i) q^{71} +(2.43537 - 1.43839i) q^{72} +(-2.65154 + 9.89569i) q^{73} +(12.8072 - 2.88365i) q^{74} +(7.32795 + 9.54997i) q^{75} +(-6.53948 + 4.22704i) q^{76} +(-1.72789 - 4.44932i) q^{77} +(-4.07270 - 3.39456i) q^{78} +(-3.50917 + 6.07805i) q^{79} +(14.5432 - 7.81637i) q^{80} +(-0.866025 + 0.500000i) q^{81} +(-2.12149 - 5.76944i) q^{82} +(1.72365 - 0.713960i) q^{83} +(5.07092 - 1.51188i) q^{84} +(-8.86523 + 21.4025i) q^{85} +(-0.213620 - 0.231586i) q^{86} +(3.96412 + 1.06218i) q^{87} +(4.69463 - 1.99925i) q^{88} +(4.53066 + 16.9087i) q^{89} +(-5.16889 + 2.71247i) q^{90} +(-5.86147 - 8.00174i) q^{91} +(10.3673 + 7.15777i) q^{92} +(5.88022 + 0.774146i) q^{93} +(8.95392 + 12.6981i) q^{94} +(13.9174 - 8.03519i) q^{95} +(1.78982 + 5.36624i) q^{96} -2.96515i q^{97} +(9.88902 - 0.455349i) q^{98} +(-1.66672 + 0.690378i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 512 q+O(q^{10}) $ 512 * q	$ 512 q + 64 q^{14} + 8 q^{16} - 8 q^{18} - 16 q^{22} - 16 q^{23} - 40 q^{28} + 48 q^{35} + 32 q^{43} + 8 q^{44} + 48 q^{50} - 72 q^{52} + 32 q^{53} + 32 q^{58} - 192 q^{59} - 48 q^{60} + 144 q^{64} - 144 q^{66} - 16 q^{67} - 72 q^{70} + 128 q^{71} + 32 q^{74} + 48 q^{78} - 72 q^{80} - 120 q^{82} + 88 q^{88} - 48 q^{91} + 128 q^{92} - 72 q^{94} - 120 q^{96} - 136 q^{98}+O(q^{100}) $ 512 * q + 64 * q^14 + 8 * q^16 - 8 * q^18 - 16 * q^22 - 16 * q^23 - 40 * q^28 + 48 * q^35 + 32 * q^43 + 8 * q^44 + 48 * q^50 - 72 * q^52 + 32 * q^53 + 32 * q^58 - 192 * q^59 - 48 * q^60 + 144 * q^64 - 144 * q^66 - 16 * q^67 - 72 * q^70 + 128 * q^71 + 32 * q^74 + 48 * q^78 - 72 * q^80 - 120 * q^82 + 88 * q^88 - 48 * q^91 + 128 * q^92 - 72 * q^94 - 120 * q^96 - 136 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/672\mathbb{Z}\right)^\times$.

$n$	$127$	$421$	$449$	$577$
$\chi(n)$	$-1$	$e\left(\frac{1}{8}\right)$	$1$	$e\left(\frac{5}{6}\right)$

Coefficient data

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

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

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

$2$	1.28368	+	0.593440i	0.907697	+	0.419625i
$2$	1.28368	+	0.593440i	0.907697	+	0.419625i
$3$	0.608761	−	0.793353i	0.351469	−	0.458043i
$3$	0.608761	−	0.793353i	0.351469	−	0.458043i
$4$	1.29566	+	1.52357i	0.647829	+	0.761786i
$5$	−2.51275	−	3.27468i	−1.12374	−	1.46448i	−0.867208	−	0.497946i	$-0.834088\pi$
$5$	−2.51275	−	3.27468i	−1.12374	−	1.46448i	−0.256529	−	0.966536i	$-0.582579\pi$
$6$	1.25226	−	0.657147i	0.511233	−	0.268279i
$7$	2.57022	−	0.627676i	0.971451	−	0.237239i
$7$	2.57022	−	0.627676i	0.971451	−	0.237239i
$8$	0.759059	+	2.72467i	0.268368	+	0.963316i
$9$	−0.258819	−	0.965926i	−0.0862730	−	0.321975i
$10$	−1.28224	−	5.69481i	−0.405479	−	1.80086i
$11$	−0.235475	−	1.78861i	−0.0709984	−	0.539286i	−0.989572	−	0.144037i	$-0.953992\pi$
$11$	−0.235475	−	1.78861i	−0.0709984	−	0.539286i	0.918574	−	0.395249i	$-0.129342\pi$
$12$	1.99748	−	0.100423i	0.576622	−	0.0289896i
$13$	−1.43468	−	3.46362i	−0.397908	−	0.960635i	−0.988162	−	0.153417i	$-0.950972\pi$
$13$	−1.43468	−	3.46362i	−0.397908	−	0.960635i	0.590254	−	0.807218i	$-0.299028\pi$
$14$	3.67182	+	0.719536i	0.981335	+	0.192304i
$15$	−4.12765			−1.06575
$16$	−0.642540	+	3.94806i	−0.160635	+	0.987014i
$17$	−2.80619	−	4.86047i	−0.680602	−	1.17884i	−0.974797	−	0.223092i	$-0.928385\pi$
$17$	−2.80619	−	4.86047i	−0.680602	−	1.17884i	0.294196	−	0.955745i	$-0.404948\pi$
$18$	0.240979	−	1.39353i	0.0567992	−	0.328458i
$19$	−0.508184	+	3.86004i	−0.116585	+	0.885554i	0.828787	+	0.559564i	$0.189031\pi$
$19$	−0.508184	+	3.86004i	−0.116585	+	0.885554i	−0.945373	+	0.325991i	$0.894302\pi$
$20$	1.73355	−	8.07123i	0.387633	−	1.80478i
$21$	1.06668	−	2.42120i	0.232769	−	0.528348i
$22$	0.759159	−	2.43574i	0.161853	−	0.519301i
$23$	6.08447	−	1.63033i	1.26870	−	0.339947i	0.439167	−	0.898406i	$-0.355274\pi$
$23$	6.08447	−	1.63033i	1.26870	−	0.339947i	0.829532	+	0.558459i	$0.188607\pi$
$24$	2.62371	+	1.05647i	0.535563	+	0.215651i
$25$	−3.11553	+	11.6273i	−0.623105	+	2.32546i
$26$	0.213785	−	5.29757i	0.0419268	−	1.03894i
$27$	−0.923880	−	0.382683i	−0.177801	−	0.0736475i
$28$	4.28643	+	3.10266i	0.810060	+	0.586347i
$29$	1.57052	+	3.79156i	0.291638	+	0.704076i	0.999998	−	0.00177484i	$-0.000564948\pi$
$29$	1.57052	+	3.79156i	0.291638	+	0.704076i	−0.708361	+	0.705851i	$0.750565\pi$
$30$	−5.29857	−	2.44951i	−0.967382	−	0.447217i
$31$	2.96548	+	5.13636i	0.532616	+	0.922518i	0.999275	+	0.0380808i	$0.0121244\pi$
$31$	2.96548	+	5.13636i	0.532616	+	0.922518i	−0.466658	+	0.884438i	$0.654542\pi$
$32$	−3.16775	+	4.68672i	−0.559984	+	0.828503i
$33$	−1.56235	−	0.902022i	−0.271970	−	0.157022i
$34$	−0.717852	−	7.90458i	−0.123111	−	1.35562i
$35$	−8.51376	−	6.83946i	−1.43909	−	1.15608i
$36$	1.13632	−	1.64584i	0.189386	−	0.274306i
$37$	7.36451	−	5.65099i	1.21072	−	0.929017i	0.211885	−	0.977295i	$-0.432040\pi$
$37$	7.36451	−	5.65099i	1.21072	−	0.929017i	0.998834	+	0.0482777i	$0.0153732\pi$
$38$	−2.94305	+	4.65347i	−0.477425	+	0.754893i
$39$	−3.62125	−	0.970311i	−0.579864	−	0.155374i
$40$	7.01510	−	9.33210i	1.10919	−	1.47553i
$41$	−3.07356	−	3.07356i	−0.480010	−	0.480010i	0.425125	−	0.905135i	$-0.360230\pi$
$41$	−3.07356	−	3.07356i	−0.480010	−	0.480010i	−0.905135	+	0.425125i	$0.860230\pi$
$42$	2.80611	−	2.47503i	0.432992	−	0.381905i
$43$	−0.205826	−	0.0852559i	−0.0313882	−	0.0130014i	0.366934	−	0.930247i	$-0.380407\pi$
$43$	−0.205826	−	0.0852559i	−0.0313882	−	0.0130014i	−0.398322	+	0.917246i	$0.630407\pi$
$44$	2.41998	−	2.67619i	0.364826	−	0.403451i
$45$	−2.51275	+	3.27468i	−0.374579	+	0.488161i
$46$	8.77800	+	1.51795i	1.29425	+	0.223809i
$47$	9.51477	+	5.49335i	1.38787	+	0.801288i	0.993075	−	0.117480i	$-0.0374817\pi$
$47$	9.51477	+	5.49335i	1.38787	+	0.801288i	0.394797	+	0.918769i	$0.370815\pi$
$48$	2.74105	+	2.91319i	0.395636	+	0.420482i
$49$	6.21205	−	3.22653i	0.887435	−	0.460933i
$50$	−10.8994	+	13.0768i	−1.54141	+	1.84934i
$51$	−5.56437	−	0.732563i	−0.779168	−	0.102579i
$52$	3.41822	−	6.67350i	0.474022	−	0.925448i
$53$	1.25714	−	0.165506i	0.172682	−	0.0227340i	−0.0436895	−	0.999045i	$-0.513911\pi$
$53$	1.25714	−	0.165506i	0.172682	−	0.0227340i	0.216371	+	0.976311i	$0.430578\pi$
$54$	−0.958864	−	1.03951i	−0.130485	−	0.141459i
$55$	−5.26544	+	5.26544i	−0.709992	+	0.709992i
$56$	3.66116	+	6.52655i	0.489243	+	0.872148i
$57$	2.75301	+	2.75301i	0.364646	+	0.364646i
$58$	−0.234027	+	5.79916i	−0.0307293	+	0.761466i
$59$	−1.27906	−	9.71546i	−0.166520	−	1.26484i	−0.846808	−	0.531899i	$-0.821478\pi$
$59$	−1.27906	−	9.71546i	−0.166520	−	1.26484i	0.680288	−	0.732945i	$-0.261855\pi$
$60$	−5.34802	−	6.28877i	−0.690426	−	0.811876i
$61$	−1.07051	+	8.13137i	−0.137065	+	1.04111i	0.775258	+	0.631645i	$0.217620\pi$
$61$	−1.07051	+	8.13137i	−0.137065	+	1.04111i	−0.912324	+	0.409470i	$0.865714\pi$
$62$	0.758599	+	8.35327i	0.0963422	+	1.06087i
$63$	−1.27151	−	2.32019i	−0.160195	−	0.292316i
$64$	−6.84766	+	4.13637i	−0.855957	+	0.517047i
$65$	−7.73726	+	13.4013i	−0.959689	+	1.66223i
$66$	−1.47026	−	2.08507i	−0.180976	−	0.256654i
$67$	−4.94622	−	3.79536i	−0.604276	−	0.463678i	0.260748	−	0.965407i	$-0.416031\pi$
$67$	−4.94622	−	3.79536i	−0.604276	−	0.463678i	−0.865025	+	0.501729i	$0.832697\pi$
$68$	3.76941	−	10.5729i	0.457108	−	1.28216i
$69$	2.41056	−	5.81961i	0.290198	−	0.700599i
$70$	−6.87012	−	13.8321i	−0.821137	−	1.65325i
$71$	−7.91899	+	7.91899i	−0.939811	+	0.939811i	−0.998289	−	0.0584781i	$-0.981375\pi$
$71$	−7.91899	+	7.91899i	−0.939811	+	0.939811i	0.0584781	+	0.998289i	$0.481375\pi$
$72$	2.43537	−	1.43839i	0.287011	−	0.169516i
$73$	−2.65154	+	9.89569i	−0.310339	+	1.15820i	0.617911	+	0.786248i	$0.287979\pi$
$73$	−2.65154	+	9.89569i	−0.310339	+	1.15820i	−0.928251	+	0.371955i	$0.878688\pi$
$74$	12.8072	−	2.88365i	1.48881	−	0.335218i
$75$	7.32795	+	9.54997i	0.846159	+	1.10274i
$76$	−6.53948	+	4.22704i	−0.750130	+	0.484875i
$77$	−1.72789	−	4.44932i	−0.196911	−	0.507047i
$78$	−4.07270	−	3.39456i	−0.461142	−	0.384358i
$79$	−3.50917	+	6.07805i	−0.394812	+	0.683834i	−0.993077	−	0.117464i	$-0.962524\pi$
$79$	−3.50917	+	6.07805i	−0.394812	+	0.683834i	0.598265	+	0.801298i	$0.295857\pi$
$80$	14.5432	−	7.81637i	1.62598	−	0.873897i
$81$	−0.866025	+	0.500000i	−0.0962250	+	0.0555556i
$82$	−2.12149	−	5.76944i	−0.234279	−	0.637128i
$83$	1.72365	−	0.713960i	0.189195	−	0.0783673i	−0.286074	−	0.958207i	$-0.592350\pi$
$83$	1.72365	−	0.713960i	0.189195	−	0.0783673i	0.475270	+	0.879840i	$0.342350\pi$
$84$	5.07092	−	1.51188i	0.553283	−	0.164959i
$85$	−8.86523	+	21.4025i	−0.961569	+	2.32143i
$86$	−0.213620	−	0.231586i	−0.0230352	−	0.0249726i
$87$	3.96412	+	1.06218i	0.424998	+	0.113878i
$88$	4.69463	−	1.99925i	0.500450	−	0.213121i
$89$	4.53066	+	16.9087i	0.480249	+	1.79231i	0.600562	+	0.799578i	$0.294944\pi$
$89$	4.53066	+	16.9087i	0.480249	+	1.79231i	−0.120313	+	0.992736i	$0.538390\pi$
$90$	−5.16889	+	2.71247i	−0.544849	+	0.285919i
$91$	−5.86147	−	8.00174i	−0.614449	−	0.838811i
$92$	10.3673	+	7.15777i	1.08087	+	0.746249i
$93$	5.88022	+	0.774146i	0.609751	+	0.0802752i
$94$	8.95392	+	12.6981i	0.923527	+	1.30971i
$95$	13.9174	−	8.03519i	1.42789	−	0.824393i
$96$	1.78982	+	5.36624i	0.182673	+	0.547690i
$97$		−	2.96515i		−	0.301065i	−0.988605	−	0.150533i	$-0.951901\pi$
$97$		−	2.96515i		−	0.301065i	0.988605	−	0.150533i	$-0.0480989\pi$
$98$	9.88902	−	0.455349i	0.998942	−	0.0459972i
$99$	−1.66672	+	0.690378i	−0.167512	+	0.0693856i
$100$	−21.7517	+	10.3183i	−2.17517	+	1.03183i
$101$	−13.4271	+	1.76771i	−1.33604	+	0.175894i	−0.764472	−	0.644657i	$-0.777000\pi$
$101$	−13.4271	+	1.76771i	−1.33604	+	0.175894i	−0.571573	+	0.820551i	$0.693667\pi$
$102$	−6.70813	−	4.24250i	−0.664204	−	0.420070i
$103$	3.11432	−	0.834479i	0.306863	−	0.0822237i	−0.102101	−	0.994774i	$-0.532557\pi$
$103$	3.11432	−	0.834479i	0.306863	−	0.0822237i	0.408965	+	0.912550i	$0.365890\pi$
$104$	8.34821	−	6.53812i	0.818610	−	0.641115i
$105$	−10.6090	+	2.59083i	−1.03533	+	0.252839i
$106$	1.71198	+	0.533582i	0.166282	+	0.0518260i
$107$	4.54313	−	3.48607i	0.439201	−	0.337011i	−0.365375	−	0.930860i	$-0.619059\pi$
$107$	4.54313	−	3.48607i	0.439201	−	0.337011i	0.804576	+	0.593850i	$0.202393\pi$
$108$	−0.613986	−	1.90342i	−0.0590809	−	0.183157i
$109$	1.79849	+	1.38003i	0.172265	+	0.132183i	0.691295	−	0.722572i	$-0.257040\pi$
$109$	1.79849	+	1.38003i	0.172265	+	0.132183i	−0.519031	+	0.854756i	$0.673707\pi$
$110$	−9.88385	+	3.63441i	−0.942388	+	0.346527i
$111$		−	9.28277i		−	0.881081i
$112$	0.826631	+	10.5507i	0.0781093	+	0.996945i
$113$			9.92749i			0.933900i	0.884284	+	0.466950i	$0.154647\pi$
$113$			9.92749i			0.933900i	−0.884284	+	0.466950i	$0.845353\pi$
$114$	1.90024	+	5.16773i	0.177973	+	0.484003i
$115$	−20.6276	−	15.8281i	−1.92353	−	1.47598i
$116$	−3.74187	+	7.30537i	−0.347424	+	0.678286i
$117$	−2.97428	+	2.28224i	−0.274972	+	0.210993i
$118$	4.12363	−	13.2306i	0.379611	−	1.21797i
$119$	−10.2633	−	10.7311i	−0.940838	−	0.983717i
$120$	−3.13313	−	11.2465i	−0.286014	−	1.02666i
$121$	7.48151	−	2.00466i	0.680137	−	0.182242i
$122$	−6.19967	+	9.80277i	−0.561292	+	0.887501i
$123$	−4.30949	+	0.567355i	−0.388574	+	0.0511567i
$124$	−3.98337	+	11.1731i	−0.357717	+	1.00337i
$125$	26.8370	−	11.1163i	2.40038	−	0.994269i
$126$	−0.255318	−	3.73294i	−0.0227456	−	0.332556i
$127$		−	18.4746i		−	1.63935i	−0.572827	−	0.819676i	$-0.694153\pi$
$127$		−	18.4746i		−	1.63935i	0.572827	−	0.819676i	$-0.305847\pi$
$128$	−11.2449	+	1.24610i	−0.993916	+	0.110141i
$129$	−0.192937	+	0.111392i	−0.0169871	+	0.00980753i
$130$	−17.8850	+	12.6114i	−1.56862	+	1.10609i
$131$	−0.770519	−	0.101441i	−0.0673205	−	0.00886292i	0.0967907	−	0.995305i	$-0.469142\pi$
$131$	−0.770519	−	0.101441i	−0.0673205	−	0.00886292i	−0.164111	+	0.986442i	$0.552476\pi$
$132$	−0.649974	−	3.54906i	−0.0565729	−	0.308906i
$133$	1.11671	+	10.2401i	0.0968312	+	0.887932i
$134$	−4.09703	−	7.80731i	−0.353929	−	0.674449i
$135$	1.06831	+	3.98700i	0.0919458	+	0.343146i
$136$	11.1131	−	11.3353i	0.952941	−	0.971997i
$137$	−5.72890	−	1.53505i	−0.489453	−	0.131149i	0.00564791	−	0.999984i	$-0.498202\pi$
$137$	−5.72890	−	1.53505i	−0.489453	−	0.131149i	−0.495101	+	0.868836i	$0.664869\pi$
$138$	6.54798	−	6.03998i	0.557401	−	0.514158i
$139$	−7.29682	+	17.6161i	−0.618908	+	1.49418i	0.234064	+	0.972221i	$0.424797\pi$
$139$	−7.29682	+	17.6161i	−0.618908	+	1.49418i	−0.852973	+	0.521956i	$0.825203\pi$
$140$	−0.610526	−	21.8329i	−0.0515989	−	1.84522i
$141$	10.1504	−	4.20443i	0.854818	−	0.354077i
$142$	−14.8649	+	5.46598i	−1.24743	+	0.458695i
$143$	−5.85723	+	3.38167i	−0.489806	+	0.282790i
$144$	3.97983	−	0.401186i	0.331653	−	0.0334321i
$145$	8.46985	−	14.6702i	0.703383	−	1.21829i
$146$	−9.27622	+	11.1293i	−0.767705	+	0.921071i
$147$	1.22188	−	6.89253i	0.100779	−	0.568487i
$148$	18.1516	+	3.89861i	1.49205	+	0.320464i
$149$	−4.78957	−	6.24188i	−0.392377	−	0.511355i	0.554837	−	0.831959i	$-0.312781\pi$
$149$	−4.78957	−	6.24188i	−0.392377	−	0.511355i	−0.947213	+	0.320604i	$0.896114\pi$
$150$	3.73939	+	16.6078i	0.305320	+	1.35602i
$151$	−0.629927	+	2.35092i	−0.0512627	+	0.191315i	−0.986809	−	0.161889i	$-0.948241\pi$
$151$	−0.629927	+	2.35092i	−0.0512627	+	0.191315i	0.935546	+	0.353204i	$0.114908\pi$
$152$	−10.9031	+	1.54537i	−0.884357	+	0.125346i
$153$	−3.96856	+	3.96856i	−0.320839	+	0.320839i
$154$	0.422348	−	6.73689i	0.0340338	−	0.542874i
$155$	9.36844	−	22.6174i	0.752492	−	1.81668i
$156$	−3.21356	−	6.77442i	−0.257291	−	0.542388i
$157$	8.51864	+	6.53658i	0.679861	+	0.521676i	0.889980	−	0.456000i	$-0.150718\pi$
$157$	8.51864	+	6.53658i	0.679861	+	0.521676i	−0.210119	+	0.977676i	$0.567385\pi$
$158$	−8.11160	+	5.71978i	−0.645324	+	0.455042i
$159$	0.633995	−	1.09811i	0.0502790	−	0.0870859i
$160$	23.3073	−	1.40320i	1.84260	−	0.110933i
$161$	14.6151	−	8.00937i	1.15183	−	0.631227i
$162$	−1.40842	+	0.127905i	−0.110656	+	0.0100492i
$163$	0.707625	−	5.37494i	0.0554255	−	0.420998i	−0.941128	−	0.338049i	$-0.890233\pi$
$163$	0.707625	−	5.37494i	0.0554255	−	0.420998i	0.996554	−	0.0829487i	$-0.0264338\pi$
$164$	0.700507	−	8.66508i	0.0547004	−	0.676629i
$165$	0.971958	+	7.38275i	0.0756668	+	0.574746i
$166$	2.63631	+	0.106389i	0.204617	+	0.00825740i
$167$	−1.65653	−	1.65653i	−0.128186	−	0.128186i	0.640103	−	0.768289i	$-0.278892\pi$
$167$	−1.65653	−	1.65653i	−0.128186	−	0.128186i	−0.768289	+	0.640103i	$0.778892\pi$
$168$	7.40664	+	1.06852i	0.571434	+	0.0824383i
$169$	−0.745965	+	0.745965i	−0.0573820	+	0.0573820i
$170$	−24.0812	+	22.2130i	−1.84695	+	1.70366i
$171$	3.86004	−	0.508184i	0.295185	−	0.0388618i
$172$	−0.136787	−	0.424053i	−0.0104299	−	0.0323337i
$173$	16.9465	+	2.23105i	1.28842	+	0.169624i	0.743428	−	0.668816i	$-0.233199\pi$
$173$	16.9465	+	2.23105i	1.28842	+	0.169624i	0.544993	+	0.838440i	$0.316532\pi$
$174$	4.45831	+	3.71597i	0.337984	+	0.281707i
$175$	−0.709404	+	31.8403i	−0.0536259	+	2.40690i
$176$	7.21283	+	0.219586i	0.543688	+	0.0165519i
$177$	−8.48643	−	4.89965i	−0.637879	−	0.368280i
$178$	−4.21836	+	24.3940i	−0.316180	+	1.82840i
$179$	4.85002	−	6.32067i	0.362508	−	0.472429i	−0.576118	−	0.817366i	$-0.695433\pi$
$179$	4.85002	−	6.32067i	0.362508	−	0.472429i	0.938626	+	0.344937i	$0.112100\pi$
$180$	−8.24488	+	0.414511i	−0.614537	+	0.0308958i
$181$	13.0440	+	5.40300i	0.969552	+	0.401602i	0.810545	−	0.585676i	$-0.199171\pi$
$181$	13.0440	+	5.40300i	0.969552	+	0.401602i	0.159007	+	0.987278i	$0.449171\pi$
$182$	−2.77568	−	13.7501i	−0.205747	−	1.01922i
$183$	5.79936	+	5.79936i	0.428701	+	0.428701i
$184$	9.06058	+	15.3407i	0.667955	+	1.13093i
$185$	−37.0104	−	9.91691i	−2.72106	−	0.729105i
$186$	7.08890	+	4.48331i	0.519784	+	0.328732i
$187$	−8.03270	+	6.16370i	−0.587409	+	0.450735i
$188$	3.95837	+	21.6139i	0.288694	+	1.57636i
$189$	−2.61477	−	0.403683i	−0.190197	−	0.0293636i
$190$	22.6338	−	2.05548i	1.64203	−	0.149120i
$191$	1.69877	+	0.980784i	0.122919	+	0.0709671i	0.560199	−	0.828358i	$-0.310725\pi$
$191$	1.69877	+	0.980784i	0.122919	+	0.0709671i	−0.437280	+	0.899325i	$0.644058\pi$
$192$	−0.886984	+	7.95068i	−0.0640125	+	0.573791i
$193$	−7.59828	−	13.1606i	−0.546936	−	0.947321i	−0.998482	−	0.0550735i	$-0.982461\pi$
$193$	−7.59828	−	13.1606i	−0.546936	−	0.947321i	0.451546	−	0.892248i	$-0.350873\pi$
$194$	1.75964	−	3.80630i	0.126335	−	0.273276i
$195$	5.92184	+	14.2966i	0.424072	+	1.02380i
$196$	12.9645	+	5.28402i	0.926038	+	0.377430i
$197$	−16.2638	−	6.73670i	−1.15875	−	0.479970i	−0.281291	−	0.959622i	$-0.590763\pi$
$197$	−16.2638	−	6.73670i	−1.15875	−	0.479970i	−0.877459	+	0.479652i	$0.840763\pi$
$198$	−2.54923	−	0.102875i	−0.181166	−	0.00731102i
$199$	4.65535	−	17.3740i	0.330009	−	1.23161i	−0.579171	−	0.815206i	$-0.696624\pi$
$199$	4.65535	−	17.3740i	0.330009	−	1.23161i	0.909180	−	0.416403i	$-0.136710\pi$
$200$	−34.0454	+	0.337032i	−2.40738	+	0.0238318i
$201$	−6.02213	+	1.61363i	−0.424768	+	0.113816i
$202$	−18.2851	−	5.69900i	−1.28653	−	0.400980i
$203$	6.41645	+	8.75937i	0.450346	+	0.614787i
$204$	−6.09341	−	9.42687i	−0.426624	−	0.660013i
$205$	−2.34184	+	17.7881i	−0.163561	+	1.24237i
$206$	4.49300	+	0.776959i	0.313042	+	0.0541333i
$207$	−3.14955	−	5.45518i	−0.218909	−	0.379161i
$208$	14.5964	−	3.43867i	1.01208	−	0.238429i
$209$	7.02377			0.485845
$210$	−15.1560	−	2.96999i	−1.04586	−	0.204949i
$211$	−0.784883	−	1.89488i	−0.0540336	−	0.130449i	0.894558	−	0.446953i	$-0.147491\pi$
$211$	−0.784883	−	1.89488i	−0.0540336	−	0.130449i	−0.948591	+	0.316504i	$0.897491\pi$
$212$	1.88099	+	1.70091i	0.129187	+	0.116819i
$213$	1.46178	+	11.1033i	0.100160	+	0.760787i
$214$	7.90069	−	1.77891i	0.540080	−	0.121604i
$215$	0.238004	+	0.888242i	0.0162317	+	0.0605776i
$216$	0.341407	−	2.80775i	0.0232298	−	0.191043i
$217$	10.8459	+	11.3402i	0.736268	+	0.769824i
$218$	1.48972	+	2.83882i	0.100897	+	0.192269i
$219$	6.23662	+	8.12772i	0.421432	+	0.549220i
$220$	−14.8445	−	1.20006i	−1.00081	−	0.0809083i
$221$	−12.8088	+	16.6928i	−0.861615	+	1.12288i
$222$	5.50876	−	11.9161i	0.369724	−	0.799755i
$223$	0.877266			0.0587461			0.0293730	−	0.999569i	$-0.490649\pi$
$223$	0.877266			0.0587461			0.0293730	+	0.999569i	$0.490649\pi$
$224$	−5.20006	+	14.0342i	−0.347444	+	0.937701i
$225$	12.0375			0.802498
$226$	−5.89137	+	12.7437i	−0.391888	+	0.847699i
$227$	−6.71711	+	8.75391i	−0.445831	+	0.581018i	−0.961166	−	0.275971i	$-0.911001\pi$
$227$	−6.71711	+	8.75391i	−0.445831	+	0.581018i	0.515335	+	0.856989i	$0.327667\pi$
$228$	−0.627449	+	7.76138i	−0.0415538	+	0.514010i
$229$	3.16943	+	4.13049i	0.209442	+	0.272950i	0.886248	−	0.463211i	$-0.153303\pi$
$229$	3.16943	+	4.13049i	0.209442	+	0.272950i	−0.676806	+	0.736162i	$0.736636\pi$
$230$	−17.0861	−	32.5594i	−1.12663	−	2.14690i
$231$	−4.58175	−	1.33774i	−0.301457	−	0.0880172i
$232$	−9.13865	+	7.15717i	−0.599982	+	0.469891i
$233$	−1.27228	−	4.74822i	−0.0833500	−	0.311066i	0.911647	−	0.410975i	$-0.134812\pi$
$233$	−1.27228	−	4.74822i	−0.0833500	−	0.311066i	−0.994997	+	0.0999086i	$0.968145\pi$
$234$	−5.17239	+	1.16461i	−0.338130	+	0.0761329i
$235$	−5.91927	−	44.9613i	−0.386130	−	2.93295i
$236$	13.1450	−	14.5367i	0.855664	−	0.946256i
$237$	2.68580	+	6.48409i	0.174461	+	0.421187i
$238$	−6.80655	−	19.8659i	−0.441203	−	1.28772i
$239$	17.6156			1.13946			0.569730	−	0.821832i	$-0.307048\pi$
$239$	17.6156			1.13946			0.569730	+	0.821832i	$0.307048\pi$
$240$	2.65218	−	16.2962i	0.171197	−	1.05191i
$241$	1.32127	+	2.28851i	0.0851106	+	0.147416i	0.905438	−	0.424478i	$-0.139542\pi$
$241$	1.32127	+	2.28851i	0.0851106	+	0.147416i	−0.820328	+	0.571894i	$0.806209\pi$
$242$	10.7935	+	1.86648i	0.693832	+	0.119982i
$243$	−0.130526	+	0.991445i	−0.00837326	+	0.0636012i
$244$	−13.7757	+	8.90446i	−0.881901	+	0.570050i
$245$	−26.1752	−	12.2350i	−1.67227	−	0.781666i
$246$	−5.86869	−	1.82912i	−0.374174	−	0.116621i
$247$	14.0988	−	3.77776i	0.897085	−	0.240373i
$248$	−11.7439	+	11.9788i	−0.745740	+	0.760652i
$249$	0.482870	−	1.80210i	0.0306006	−	0.114203i
$250$	41.0470	+	1.65647i	2.59604	+	0.104764i
$251$	−0.824127	−	0.341365i	−0.0520184	−	0.0215467i	0.356523	−	0.934287i	$-0.383962\pi$
$251$	−0.824127	−	0.341365i	−0.0520184	−	0.0215467i	−0.408541	+	0.912740i	$0.633962\pi$
$252$	1.88753	−	4.94340i	0.118903	−	0.311405i
$253$	−4.34876	−	10.4988i	−0.273404	−	0.660056i
$254$	10.9635	−	23.7154i	0.687914	−	1.48804i
$255$	11.5830	+	20.0623i	0.725354	+	1.25635i
$256$	−15.1743	−	5.07357i	−0.948393	−	0.317098i
$257$	−21.3134	−	12.3053i	−1.32949	−	0.767582i	−0.344271	−	0.938870i	$-0.611874\pi$
$257$	−21.3134	−	12.3053i	−1.32949	−	0.767582i	−0.985221	+	0.171288i	$0.945207\pi$
$258$	−0.313773	+	0.0284952i	−0.0195347	+	0.00177403i
$259$	15.3814	−	19.1468i	0.955755	−	1.18972i
$260$	−30.4427	+	5.57527i	−1.88798	+	0.345764i
$261$	3.25589	−	2.49833i	0.201535	−	0.154643i
$262$	−0.928899	−	0.587474i	−0.0573876	−	0.0362943i
$263$	7.10142	+	1.90282i	0.437892	+	0.117333i	0.471029	−	0.882118i	$-0.343883\pi$
$263$	7.10142	+	1.90282i	0.437892	+	0.117333i	−0.0331362	+	0.999451i	$0.510550\pi$
$264$	1.27180	−	4.94157i	0.0782737	−	0.304133i
$265$	−3.70086	−	3.70086i	−0.227342	−	0.227342i
$266$	−4.64340	+	13.8077i	−0.284705	+	0.846606i
$267$	16.1726	+	6.69892i	0.989749	+	0.409968i
$268$	−0.626095	−	12.4534i	−0.0382448	−	0.760713i
$269$	2.67485	−	3.48593i	0.163089	−	0.212541i	−0.704659	−	0.709546i	$-0.748900\pi$
$269$	2.67485	−	3.48593i	0.163089	−	0.212541i	0.867748	+	0.497005i	$0.165567\pi$
$270$	−0.994675	+	5.75201i	−0.0605340	+	0.350056i
$271$	0.202997	+	0.117200i	0.0123312	+	0.00711941i	0.506153	−	0.862444i	$-0.331067\pi$
$271$	0.202997	+	0.117200i	0.0123312	+	0.00711941i	−0.493822	+	0.869563i	$0.664400\pi$
$272$	20.9925	−	7.95596i	1.27286	−	0.482401i
$273$	−9.91644	−	0.220939i	−0.600171	−	0.0133718i
$274$	−6.44310	−	5.37027i	−0.389242	−	0.324430i
$275$	21.5303	+	2.83452i	1.29833	+	0.170928i
$276$	11.9899	−	3.86756i	0.721705	−	0.232800i
$277$	−13.3958	+	1.76360i	−0.804879	+	0.105964i	−0.521729	−	0.853111i	$-0.674713\pi$
$277$	−13.3958	+	1.76360i	−0.804879	+	0.105964i	−0.283150	+	0.959076i	$0.591379\pi$
$278$	−19.8209	+	18.2832i	−1.18878	+	1.09655i
$279$	4.19382	−	4.19382i	0.251078	−	0.251078i
$280$	12.1728	−	28.3888i	0.727464	−	1.69655i
$281$	1.01306	+	1.01306i	0.0604338	+	0.0604338i	0.736678	−	0.676244i	$-0.236393\pi$
$281$	1.01306	+	1.01306i	0.0604338	+	0.0604338i	−0.676244	+	0.736678i	$0.736393\pi$
$282$	15.5249	+	0.626514i	0.924495	+	0.0373084i
$283$	0.459663	+	3.49149i	0.0273242	+	0.207548i	0.999661	−	0.0260354i	$-0.00828827\pi$
$283$	0.459663	+	3.49149i	0.0273242	+	0.207548i	−0.972337	+	0.233583i	$0.924955\pi$
$284$	−22.3254	−	1.80484i	−1.32477	−	0.107098i
$285$	2.09761	−	15.9329i	0.124251	−	0.943783i
$286$	−9.52562	+	0.865065i	−0.563262	+	0.0511524i
$287$	−9.82893	−	5.97053i	−0.580184	−	0.352429i
$288$	5.34690	+	1.84680i	0.315069	+	0.108824i
$289$	−7.24944	+	12.5564i	−0.426438	+	0.738612i
$290$	19.5784	−	13.8055i	1.14969	−	0.810686i
$291$	−2.35241	−	1.80507i	−0.137901	−	0.105815i
$292$	−18.5123	+	8.78161i	−1.08335	+	0.513905i
$293$	9.89293	−	23.8837i	0.577951	−	1.39530i	−0.316697	−	0.948527i	$-0.602574\pi$
$293$	9.89293	−	23.8837i	0.577951	−	1.39530i	0.894648	−	0.446771i	$-0.147426\pi$
$294$	5.65880	−	8.12268i	0.330028	−	0.473725i
$295$	−28.6011	+	28.6011i	−1.66522	+	1.66522i
$296$	20.9872	+	15.7764i	1.21986	+	0.916987i
$297$	−0.466921	+	1.74257i	−0.0270935	+	0.101114i
$298$	−2.44408	−	10.8549i	−0.141582	−	0.628807i
$299$	−14.3761	−	18.7353i	−0.831390	−	1.08349i
$300$	−5.05554	+	23.5381i	−0.291882	+	1.35898i
$301$	−0.582531	−	0.0899342i	−0.0335765	−	0.00518372i
$302$	−2.20375	+	2.64400i	−0.126812	+	0.152145i
$303$	−6.77147	+	11.7285i	−0.389011	+	0.673787i
$304$	−14.9131	−	4.48657i	−0.855327	−	0.257323i
$305$	29.3176	−	16.9265i	1.67872	−	0.969209i
$306$	−7.44945	+	2.73925i	−0.425857	+	0.156592i
$307$	4.06442	−	1.68354i	0.231969	−	0.0960846i	−0.263672	−	0.964613i	$-0.584933\pi$
$307$	4.06442	−	1.68354i	0.231969	−	0.0960846i	0.495640	+	0.868528i	$0.334933\pi$
$308$	4.54010	−	8.39736i	0.258696	−	0.478484i
$309$	1.23384	−	2.97875i	0.0701907	−	0.169455i
$310$	25.4481	−	23.4739i	1.44536	−	1.33323i
$311$	−21.6530	−	5.80190i	−1.22783	−	0.328995i	−0.414094	−	0.910234i	$-0.635902\pi$
$311$	−21.6530	−	5.80190i	−1.22783	−	0.328995i	−0.813733	+	0.581239i	$0.802568\pi$
$312$	−0.104966	−	10.6032i	−0.00594256	−	0.600290i
$313$	2.70304	+	10.0879i	0.152785	+	0.570200i	0.999285	+	0.0378119i	$0.0120388\pi$
$313$	2.70304	+	10.0879i	0.152785	+	0.570200i	−0.846500	+	0.532388i	$0.821295\pi$
$314$	7.05612	+	13.4462i	0.398200	+	0.758811i
$315$	−4.40288	+	9.99384i	−0.248074	+	0.563089i
$316$	−13.8070	+	2.52861i	−0.776706	+	0.142246i
$317$	9.98317	+	1.31431i	0.560711	+	0.0738190i	0.405554	−	0.914071i	$-0.367079\pi$
$317$	9.98317	+	1.31431i	0.560711	+	0.0738190i	0.155156	+	0.987890i	$0.450412\pi$
$318$	1.46551	−	1.03338i	0.0821816	−	0.0579492i
$319$	6.41181	−	3.70186i	0.358993	−	0.207264i
$320$	30.7518	+	12.0302i	1.71908	+	0.672510i
$321$		−	5.72649i		−	0.319622i
$322$	23.5142	−	1.60828i	1.31039	−	0.0896258i
$323$	20.1877	−	8.36201i	1.12327	−	0.465275i
$324$	−1.88386	−	0.671623i	−0.104659	−	0.0373124i
$325$	44.7423	−	5.89044i	2.48186	−	0.326743i
$326$	4.09807	−	6.47976i	0.226971	−	0.358881i
$327$	2.18971	−	0.586730i	0.121091	−	0.0324463i
$328$	6.04143	−	10.7075i	0.333582	−	0.591221i
$329$	27.9031	+	8.14693i	1.53835	+	0.449155i
$330$	−3.13354	+	10.0539i	−0.172496	+	0.553448i
$331$	−9.87833	+	7.57991i	−0.542962	+	0.416630i	−0.843491	−	0.537143i	$-0.819504\pi$
$331$	−9.87833	+	7.57991i	−0.542962	+	0.416630i	0.300529	+	0.953773i	$0.402837\pi$
$332$	3.32103	+	1.70106i	0.182265	+	0.0933577i
$333$	−7.36451	−	5.65099i	−0.403573	−	0.309672i
$334$	−1.14340	−	3.10950i	−0.0625641	−	0.170145i
$335$			25.7341i			1.40600i
$336$	8.87363	+	5.76703i	0.484096	+	0.314617i
$337$			16.2770i			0.886664i	0.896358	+	0.443332i	$0.146204\pi$
$337$			16.2770i			0.886664i	−0.896358	+	0.443332i	$0.853796\pi$
$338$	−1.40027	+	0.514894i	−0.0761644	+	0.0280065i
$339$	7.87601	+	6.04347i	0.427766	+	0.328236i
$340$	−44.0946	+	14.2236i	−2.39137	+	0.771382i
$341$	8.48866	−	6.51358i	0.459687	−	0.352730i
$342$	5.25663	+	1.63836i	0.284246	+	0.0885923i
$343$	13.9411	−	12.1920i	0.752749	−	0.658308i
$344$	0.0760601	−	0.625522i	0.00410088	−	0.0337259i
$345$	−25.1145	+	6.72942i	−1.35212	+	0.362300i
$346$	20.4299	+	12.9207i	1.09832	+	0.694621i
$347$	−31.4342	+	4.13839i	−1.68748	+	0.222161i	−0.912282	−	0.409562i	$-0.865681\pi$
$347$	−31.4342	+	4.13839i	−1.68748	+	0.222161i	−0.775194	+	0.631723i	$0.782348\pi$
$348$	3.51783	+	7.41585i	0.188576	+	0.397531i
$349$	5.59124	−	2.31597i	0.299292	−	0.123971i	−0.227984	−	0.973665i	$-0.573213\pi$
$349$	5.59124	−	2.31597i	0.299292	−	0.123971i	0.527276	+	0.849694i	$0.323213\pi$
$350$	−19.8059	+	40.4516i	−1.05867	+	2.16223i
$351$			3.74899i			0.200106i
$352$	9.12864	+	4.56226i	0.486558	+	0.243169i
$353$	−12.6819	+	7.32192i	−0.674991	+	0.389706i	−0.797965	−	0.602704i	$-0.794090\pi$
$353$	−12.6819	+	7.32192i	−0.674991	+	0.389706i	0.122974	+	0.992410i	$0.460757\pi$
$354$	−7.98620	−	11.3258i	−0.424462	−	0.601957i
$355$	45.8306	+	6.03371i	2.43244	+	0.320236i
$356$	−19.8914	+	28.8106i	−1.05424	+	1.52696i
$357$	−14.7615	+	1.60978i	−0.781259	+	0.0851983i
$358$	9.97680	−	5.23551i	0.527290	−	0.276705i
$359$	2.10142	+	7.84262i	0.110909	+	0.413918i	0.998948	−	0.0458497i	$-0.0145995\pi$
$359$	2.10142	+	7.84262i	0.110909	+	0.413918i	−0.888039	+	0.459767i	$0.847933\pi$
$360$	−10.8298	−	4.36074i	−0.570778	−	0.229831i
$361$	3.71092	+	0.994337i	0.195311	+	0.0523335i
$362$	13.5379	+	14.6765i	0.711537	+	0.771381i
$363$	2.96405	−	7.15584i	0.155572	−	0.375584i
$364$	4.59677	−	19.2979i	0.240936	−	1.01148i
$365$	39.0679	−	16.1825i	2.04491	−	0.847028i
$366$	4.00294	+	10.8861i	0.209237	+	0.569024i
$367$	23.7199	−	13.6947i	1.23817	−	0.714857i	0.269449	−	0.963015i	$-0.413158\pi$
$367$	23.7199	−	13.6947i	1.23817	−	0.714857i	0.968720	+	0.248158i	$0.0798251\pi$
$368$	2.52711	+	25.0694i	0.131735	+	1.30683i
$369$	−2.17334	+	3.76433i	−0.113139	+	0.195963i
$370$	−41.6243	−	34.6936i	−2.16395	−	1.80363i
$371$	3.12724	−	1.21446i	0.162358	−	0.0630518i
$372$	6.43929	+	9.96197i	0.333862	+	0.516504i
$373$	2.91287	+	3.79613i	0.150823	+	0.196556i	0.862654	−	0.505794i	$-0.168801\pi$
$373$	2.91287	+	3.79613i	0.150823	+	0.196556i	−0.711831	+	0.702351i	$0.752134\pi$
$374$	−13.9692	+	3.14529i	−0.722329	+	0.162639i
$375$	7.51823	−	28.0584i	0.388240	−	1.44893i
$376$	−7.74530	+	30.0944i	−0.399434	+	1.55200i
$377$	10.8793	−	10.8793i	0.560315	−	0.560315i
$378$	−3.11697	−	2.06991i	−0.160319	−	0.106465i
$379$	−5.38926	+	13.0108i	−0.276828	+	0.668322i	−0.999744	−	0.0226138i	$-0.992801\pi$
$379$	−5.38926	+	13.0108i	−0.276828	+	0.668322i	0.722916	+	0.690936i	$0.242801\pi$
$380$	30.2743	+	10.7932i	1.55304	+	0.553681i
$381$	−14.6569	−	11.2466i	−0.750894	−	0.576181i
$382$	1.59863	+	2.26713i	0.0817933	+	0.115996i
$383$	−3.57175	+	6.18646i	−0.182508	+	0.316113i	−0.942734	−	0.333546i	$-0.891755\pi$
$383$	−3.57175	+	6.18646i	−0.182508	+	0.316113i	0.760226	+	0.649659i	$0.225088\pi$
$384$	−5.85685	+	9.67974i	−0.298881	+	0.493967i
$385$	−10.2283	+	16.8383i	−0.521284	+	0.858160i
$386$	−1.94371	−	21.4031i	−0.0989325	−	1.08939i
$387$	−0.0290792	+	0.220878i	−0.00147818	+	0.0112279i
$388$	4.51762	−	3.84182i	0.229347	−	0.195039i
$389$	−1.22007	−	9.26737i	−0.0618601	−	0.469874i	−0.994137	−	0.108129i	$-0.965514\pi$
$389$	−1.22007	−	9.26737i	−0.0618601	−	0.469874i	0.932277	−	0.361746i	$-0.117819\pi$
$390$	−0.882431	+	21.8665i	−0.0446836	+	1.10725i
$391$	−24.9983	−	24.9983i	−1.26422	−	1.26422i
$392$	13.5065	+	14.4766i	0.682183	+	0.731181i
$393$	−0.549540	+	0.549540i	−0.0277207	+	0.0277207i
$394$	−16.8797	−	18.2994i	−0.850387	−	0.921908i
$395$	28.7214	−	3.78124i	1.44513	−	0.190255i
$396$	−3.21134	−	1.64487i	−0.161376	−	0.0826579i
$397$	−18.6013	−	2.44891i	−0.933573	−	0.122907i	−0.351632	−	0.936138i	$-0.614373\pi$
$397$	−18.6013	−	2.44891i	−0.933573	−	0.122907i	−0.581941	+	0.813231i	$0.697707\pi$
$398$	16.2864	−	19.5399i	0.816363	−	0.979449i
$399$	8.80385	+	5.34785i	0.440744	+	0.267727i
$400$	−43.9034	−	19.7713i	−2.19517	−	0.988564i
$401$	7.36964	+	4.25486i	0.368022	+	0.212478i	0.672594	−	0.740012i	$-0.265180\pi$
$401$	7.36964	+	4.25486i	0.368022	+	0.212478i	−0.304572	+	0.952489i	$0.598513\pi$
$402$	−8.68807	−	1.50240i	−0.433321	−	0.0749328i
$403$	13.5359	−	17.6403i	0.674271	−	0.878727i
$404$	−20.0901	−	18.1668i	−0.999522	−	0.903831i
$405$	3.81345	+	1.57958i	0.189492	+	0.0784901i
$406$	3.03849	+	15.0520i	0.150798	+	0.747018i
$407$	−11.8416	−	11.8416i	−0.586965	−	0.586965i
$408$	−2.22770	−	15.7171i	−0.110287	−	0.778114i
$409$	−30.4721	−	8.16498i	−1.50675	−	0.403732i	−0.591395	−	0.806382i	$-0.701422\pi$
$409$	−30.4721	−	8.16498i	−1.50675	−	0.403732i	−0.915354	+	0.402650i	$0.868089\pi$
$410$	−13.5623	+	21.4444i	−0.669795	+	1.05906i
$411$	−4.70537	+	3.61056i	−0.232099	+	0.178096i
$412$	5.30648	+	3.66369i	0.261432	+	0.180497i
$413$	−9.38563	−	24.1680i	−0.461837	−	1.18923i
$414$	−0.805686	−	8.87177i	−0.0395973	−	0.436024i
$415$	−6.66910	−	3.85041i	−0.327373	−	0.189009i
$416$	20.7777	+	4.24794i	1.01871	+	0.208272i
$417$	9.53376	+	16.5130i	0.466870	+	0.808643i
$418$	9.01626	+	4.16819i	0.441000	+	0.203873i
$419$	2.08507	+	5.03381i	0.101863	+	0.245918i	0.966592	−	0.256320i	$-0.0825101\pi$
$419$	2.08507	+	5.03381i	0.101863	+	0.245918i	−0.864729	+	0.502238i	$0.832510\pi$
$420$	−17.6929	−	12.8067i	−0.863324	−	0.624902i
$421$	17.8636	+	7.39936i	0.870620	+	0.360623i	0.772852	−	0.634587i	$-0.218830\pi$
$421$	17.8636	+	7.39936i	0.870620	+	0.360623i	0.0977683	+	0.995209i	$0.468830\pi$
$422$	0.116958	−	2.89819i	0.00569341	−	0.141082i
$423$	2.84357	−	10.6123i	0.138259	−	0.515990i
$424$	1.40519	+	3.29967i	0.0682422	+	0.160246i
$425$	65.2569	−	17.4855i	3.16543	−	0.848173i
$426$	−4.71270	+	15.1206i	−0.228331	+	0.732594i
$427$	2.35241	+	21.5713i	0.113841	+	1.04391i
$428$	11.1976	+	2.40503i	0.541257	+	0.116252i
$429$	−0.882794	+	6.70549i	−0.0426217	+	0.323744i
$430$	−0.221598	+	1.28146i	−0.0106864	+	0.0617973i
$431$	15.2845	+	26.4735i	0.736228	+	1.27518i	0.954182	+	0.299225i	$0.0967283\pi$
$431$	15.2845	+	26.4735i	0.736228	+	1.27518i	−0.217954	+	0.975959i	$0.569938\pi$
$432$	2.10449	−	3.40164i	0.101252	−	0.163661i
$433$	−4.94614			−0.237696			−0.118848	−	0.992912i	$-0.537920\pi$
$433$	−4.94614			−0.237696			−0.118848	+	0.992912i	$0.537920\pi$
$434$	7.19292	+	20.9936i	0.345271	+	1.00772i
$435$	−6.48254	−	15.6502i	−0.310814	−	0.750372i
$436$	0.227654	+	4.52819i	0.0109027	+	0.216861i
$437$	3.20110	+	24.3148i	0.153130	+	1.16313i
$438$	3.18250	+	14.1344i	0.152066	+	0.675369i
$439$	−2.72404	−	10.1663i	−0.130011	−	0.485209i	0.869957	−	0.493127i	$-0.164146\pi$
$439$	−2.72404	−	10.1663i	−0.130011	−	0.485209i	−0.999969	+	0.00791781i	$0.997480\pi$
$440$	−18.3434	−	10.3498i	−0.874486	−	0.493408i
$441$	−4.72438	−	5.16529i	−0.224971	−	0.245966i
$442$	−26.3486	+	13.8269i	−1.25327	+	0.657678i
$443$	17.1096	+	22.2977i	0.812904	+	1.05940i	0.997069	+	0.0765013i	$0.0243749\pi$
$443$	17.1096	+	22.2977i	0.812904	+	1.05940i	−0.184166	+	0.982895i	$0.558958\pi$
$444$	14.1430	−	12.0273i	0.671195	−	0.570790i
$445$	43.9861	−	57.3238i	2.08514	−	2.71741i
$446$	1.12613	+	0.520605i	0.0533237	+	0.0246513i
$447$	−7.86772			−0.372130
$448$	−15.0037	+	14.9295i	−0.708857	+	0.705352i
$449$	−14.3328			−0.676409			−0.338204	−	0.941073i	$-0.609820\pi$
$449$	−14.3328			−0.676409			−0.338204	+	0.941073i	$0.609820\pi$
$450$	15.4522	+	7.14352i	0.728425	+	0.336749i
$451$	−4.77366	+	6.22115i	−0.224783	+	0.292943i
$452$	−15.1252	+	12.8626i	−0.711432	+	0.605007i
$453$	1.48163	+	1.93090i	0.0696132	+	0.0907217i
$454$	−13.8175	+	7.25100i	−0.648489	+	0.340306i
$455$	−11.4748	+	39.3008i	−0.537945	+	1.84245i
$456$	−5.41136	+	9.59076i	−0.253410	+	0.449128i
$457$	−8.49904	−	31.7188i	−0.397568	−	1.48375i	−0.817361	−	0.576125i	$-0.804564\pi$
$457$	−8.49904	−	31.7188i	−0.397568	−	1.48375i	0.419793	−	0.907620i	$-0.362103\pi$
$458$	1.61734	+	7.18308i	0.0755732	+	0.335643i
$459$	0.732563	+	5.56437i	0.0341931	+	0.259723i
$460$	−2.61105	−	51.9354i	−0.121741	−	2.42150i
$461$	−0.414359	−	1.00035i	−0.0192986	−	0.0465910i	0.913936	−	0.405857i	$-0.133027\pi$
$461$	−0.414359	−	1.00035i	−0.0192986	−	0.0465910i	−0.933235	+	0.359266i	$0.883027\pi$
$462$	−5.08762	−	4.43623i	−0.236698	−	0.206392i
$463$	−26.0713			−1.21164			−0.605819	−	0.795603i	$-0.707154\pi$
$463$	−26.0713			−1.21164			−0.605819	+	0.795603i	$0.707154\pi$
$464$	−15.9784	+	3.76426i	−0.741780	+	0.174751i
$465$	−12.2405	−	21.2011i	−0.567638	−	0.983178i
$466$	1.18458	−	6.85021i	0.0548748	−	0.317330i
$467$	2.61779	−	19.8841i	0.121137	−	0.920126i	−0.817671	−	0.575685i	$-0.804735\pi$
$467$	2.61779	−	19.8841i	0.121137	−	0.920126i	0.938808	−	0.344441i	$-0.111931\pi$
$468$	−7.33081	−	1.57452i	−0.338867	−	0.0727821i
$469$	−15.0951	−	6.65030i	−0.697028	−	0.307082i
$470$	19.0834	−	61.2285i	0.880251	−	2.82426i
$471$	10.3716	−	2.77907i	0.477900	−	0.128053i
$472$	25.5005	−	10.8596i	1.17376	−	0.499855i
$473$	−0.104023	+	0.388218i	−0.00478297	+	0.0178503i
$474$	−0.400219	+	9.91735i	−0.0183826	+	0.455519i
$475$	−43.2986	−	17.9349i	−1.98668	−	0.822909i
$476$	3.05181	−	29.5407i	0.139880	−	1.35400i
$477$	−0.485238	−	1.17147i	−0.0222175	−	0.0536379i
$478$	22.6128	+	10.4538i	1.03429	+	0.478147i
$479$	−5.05164	−	8.74969i	−0.230815	−	0.399783i	0.727233	−	0.686391i	$-0.240806\pi$
$479$	−5.05164	−	8.74969i	−0.230815	−	0.399783i	−0.958048	+	0.286607i	$0.907473\pi$
$480$	13.0753	−	19.3451i	0.596805	−	0.882981i
$481$	−30.1386	−	17.4005i	−1.37420	−	0.793395i
$482$	0.337994	+	3.72181i	0.0153952	+	0.169524i
$483$	2.54284	−	16.4707i	0.115703	−	0.749444i
$484$	12.7477	+	8.80125i	0.579442	+	0.400057i
$485$	−9.70993	+	7.45069i	−0.440905	+	0.338318i
$486$	−0.755917	+	1.19524i	−0.0342891	+	0.0542170i
$487$	18.8823	+	5.05951i	0.855640	+	0.229268i	0.659868	−	0.751381i	$-0.270612\pi$
$487$	18.8823	+	5.05951i	0.855640	+	0.229268i	0.195772	+	0.980649i	$0.437279\pi$
$488$	−22.9679	+	3.25539i	−1.03971	+	0.147365i
$489$	−3.83346	−	3.83346i	−0.173355	−	0.173355i
$490$	−26.3398	−	31.2392i	−1.18991	−	1.41124i
$491$	−19.8003	−	8.20154i	−0.893573	−	0.370130i	−0.111828	−	0.993728i	$-0.535670\pi$
$491$	−19.8003	−	8.20154i	−0.893573	−	0.370130i	−0.781746	+	0.623598i	$0.785670\pi$
$492$	−6.44803	−	5.83072i	−0.290700	−	0.262869i
$493$	14.0216	−	18.2733i	0.631501	−	0.822989i
$494$	20.3402	+	3.51736i	0.915148	+	0.158254i
$495$	6.44882	+	3.72323i	0.289853	+	0.167347i
$496$	−22.1841	+	8.40756i	−0.996095	+	0.377511i
$497$	−15.3830	+	25.3241i	−0.690020	+	1.13594i
$498$	1.68928	−	2.02676i	0.0756987	−	0.0908211i
$499$	5.45888	+	0.718675i	0.244373	+	0.0321723i	0.251718	−	0.967801i	$-0.419005\pi$
$499$	5.45888	+	0.718675i	0.244373	+	0.0321723i	−0.00734475	+	0.999973i	$0.502338\pi$
$500$	51.7081	+	26.4853i	2.31245	+	1.18446i
$501$	−2.32265	+	0.305782i	−0.103768	+	0.0136613i
$502$	−0.855334	−	0.927272i	−0.0381754	−	0.0413862i
$503$	−21.3499	+	21.3499i	−0.951945	+	0.951945i	−0.998897	−	0.0469521i	$-0.985049\pi$
$503$	−21.3499	+	21.3499i	−0.951945	+	0.951945i	0.0469521	+	0.998897i	$0.485049\pi$
$504$	5.35659	−	5.22560i	0.238601	−	0.232767i
$505$	39.5276	+	39.5276i	1.75896	+	1.75896i
$506$	0.648021	−	16.0579i	0.0288080	−	0.713859i
$507$	0.137699	+	1.04593i	0.00611544	+	0.0464513i
$508$	28.1473	−	23.9367i	1.24884	−	1.06202i
$509$	−4.95390	+	37.6286i	−0.219578	+	1.66786i	0.426425	+	0.904523i	$0.359773\pi$
$509$	−4.95390	+	37.6286i	−0.219578	+	1.66786i	−0.646003	+	0.763335i	$0.723561\pi$
$510$	2.96304	+	32.6273i	0.131206	+	1.44476i
$511$	−0.603754	+	27.0984i	−0.0267085	+	1.19876i
$512$	−16.4680	−	15.5179i	−0.727791	−	0.685799i
$513$	1.94668	−	3.37174i	0.0859478	−	0.148866i
$514$	−20.0571	−	28.4442i	−0.884679	−	1.25462i
$515$	−10.5582	−	8.10157i	−0.465249	−	0.356998i
$516$	−0.419694	−	0.149627i	−0.0184760	−	0.00658696i
$517$	7.58498	−	18.3118i	0.333587	−	0.805350i
$518$	31.1073	−	15.4504i	1.36677	−	0.678851i
$519$	12.0864	−	12.0864i	0.530534	−	0.530534i
$520$	−42.3873	−	10.9091i	−1.85880	−	0.478395i
$521$	2.59231	−	9.67463i	0.113571	−	0.423853i	−0.885605	−	0.464439i	$-0.846256\pi$
$521$	2.59231	−	9.67463i	0.113571	−	0.423853i	0.999176	+	0.0405862i	$0.0129225\pi$
$522$	5.66212	−	1.27488i	0.247824	−	0.0557999i
$523$	0.562221	+	0.732701i	0.0245842	+	0.0320388i	0.805484	−	0.592618i	$-0.201906\pi$
$523$	0.562221	+	0.732701i	0.0245842	+	0.0320388i	−0.780899	+	0.624657i	$0.785239\pi$
$524$	−0.843777	−	1.30537i	−0.0368606	−	0.0570255i
$525$	24.8287	+	19.9459i	1.08361	+	0.870512i
$526$	7.98673	+	6.65688i	0.348238	+	0.290254i
$527$	16.6434	−	28.8273i	0.724999	−	1.25574i
$528$	4.56510	−	5.58865i	0.198671	−	0.243215i
$529$	14.4442	−	8.33935i	0.628008	−	0.362580i
$530$	−2.55448	−	6.94696i	−0.110959	−	0.301757i
$531$	−9.05336	+	3.75003i	−0.392883	+	0.162737i
$532$	−14.1547	+	14.9691i	−0.613684	+	0.648993i
$533$	−6.23608	+	15.0552i	−0.270115	+	0.652114i
$534$	16.7850	+	18.1967i	0.726360	+	0.787450i
$535$	−22.8315	−	6.11769i	−0.987093	−	0.264491i
$536$	6.58665	−	16.3577i	0.284500	−	0.706546i
$537$	−2.06202	−	7.69556i	−0.0889827	−	0.332088i
$538$	5.50234	−	2.88745i	0.237223	−	0.124487i
$539$	−7.23378	−	10.3512i	−0.311581	−	0.445856i
$540$	−4.69031	+	6.79344i	−0.201839	+	0.292343i
$541$	22.3093	+	2.93707i	0.959151	+	0.126275i	0.593816	−	0.804601i	$-0.297621\pi$
$541$	22.3093	+	2.93707i	0.959151	+	0.126275i	0.365336	+	0.930876i	$0.380954\pi$
$542$	0.191031	+	0.270914i	0.00820549	+	0.0116367i
$543$	12.2272	−	7.05935i	0.524718	−	0.302946i
$544$	31.6690	+	2.24490i	1.35780	+	0.0962491i
$545$		−	9.35718i		−	0.400818i
$546$	−12.5984	−	6.16843i	−0.539162	−	0.263984i
$547$	−19.7147	+	8.16610i	−0.842940	+	0.349157i	−0.762012	−	0.647563i	$-0.775788\pi$
$547$	−19.7147	+	8.16610i	−0.842940	+	0.349157i	−0.0809282	+	0.996720i	$0.525788\pi$
$548$	−5.08393	−	10.7173i	−0.217175	−	0.457820i
$549$	8.13137	−	1.07051i	0.347038	−	0.0456884i
$550$	25.9559	+	16.4156i	1.10676	+	0.699963i
$551$	−15.4337	+	4.13545i	−0.657498	+	0.176176i
$552$	17.6863	+	2.15056i	0.752778	+	0.0915337i
$553$	−5.20427	+	17.8245i	−0.221308	+	0.757977i
$554$	−18.2425	−	5.68574i	−0.775051	−	0.241564i
$555$	−30.3981	+	23.3253i	−1.29033	+	0.990104i
$556$	−36.2936	+	11.7072i	−1.53919	+	0.496496i
$557$	−31.9510	−	24.5169i	−1.35381	−	1.03881i	−0.994406	−	0.105629i	$-0.966314\pi$
$557$	−31.9510	−	24.5169i	−1.35381	−	1.03881i	−0.359401	−	0.933183i	$-0.617019\pi$
$558$	7.87230	−	2.89474i	0.333261	−	0.122544i
$559$			0.835217i			0.0353259i
$560$	32.4730	−	29.2182i	1.37223	−	1.23469i
$561$			10.1250i			0.427477i
$562$	0.699250	+	1.90163i	0.0294961	+	0.0802152i
$563$	14.8326	+	11.3814i	0.625117	+	0.479670i	0.872085	−	0.489354i	$-0.162767\pi$
$563$	14.8326	+	11.3814i	0.625117	+	0.479670i	−0.246968	+	0.969024i	$0.579434\pi$
$564$	19.5572	+	10.0173i	0.823506	+	0.421806i
$565$	32.5094	−	24.9453i	1.36768	−	1.04946i
$566$	−1.48193	+	4.75473i	−0.0622902	+	0.199856i
$567$	−1.91204	+	1.82869i	−0.0802980	+	0.0767979i
$568$	−27.5876	−	15.5656i	−1.15755	−	0.653120i
$569$	−27.6442	+	7.40724i	−1.15890	+	0.310528i	−0.786528	−	0.617554i	$-0.788124\pi$
$569$	−27.6442	+	7.40724i	−1.15890	+	0.310528i	−0.372376	+	0.928082i	$0.621457\pi$
$570$	12.1479	−	19.2079i	0.508818	−	0.804530i
$571$	−31.8373	+	4.19147i	−1.33235	+	0.175407i	−0.762846	−	0.646580i	$-0.776199\pi$
$571$	−31.8373	+	4.19147i	−1.33235	+	0.175407i	−0.569505	+	0.821988i	$0.692865\pi$
$572$	−12.7412	−	4.54242i	−0.532736	−	0.189928i
$573$	1.81225	−	0.750660i	0.0757080	−	0.0313593i
$574$	−9.07403	−	13.4971i	−0.378743	−	0.563359i
$575$			75.8253i			3.16213i
$576$	5.76773	+	5.54376i	0.240322	+	0.230990i
$577$	24.7805	−	14.3070i	1.03163	−	0.595609i	0.114176	−	0.993461i	$-0.463577\pi$
$577$	24.7805	−	14.3070i	1.03163	−	0.595609i	0.917450	+	0.397851i	$0.130244\pi$
$578$	−16.7574	+	11.8163i	−0.697017	+	0.491492i
$579$	−15.0666	−	1.98355i	−0.626145	−	0.0824335i
$580$	33.3251	−	6.10315i	1.38375	−	0.253420i
$581$	3.98202	−	2.91693i	0.165202	−	0.121015i
$582$	−1.94854	−	3.71314i	−0.0807695	−	0.153915i
$583$	−0.592051	−	2.20956i	−0.0245202	−	0.0915108i
$584$	−28.9752	+	0.286839i	−1.19900	+	0.0118695i
$585$	14.9472	+	4.00510i	0.617992	+	0.165591i
$586$	26.8729	−	24.7881i	1.11011	−	1.02399i
$587$	−7.54874	+	18.2243i	−0.311570	+	0.752197i	0.688077	+	0.725637i	$0.258455\pi$
$587$	−7.54874	+	18.2243i	−0.311570	+	0.752197i	−0.999647	+	0.0265591i	$0.991545\pi$
$588$	12.0844	−	7.06875i	0.498352	−	0.291510i
$589$	−21.3336	+	8.83667i	−0.879036	+	0.364108i
$590$	−53.6876	+	19.7415i	−2.21028	+	0.812746i
$591$	−15.2454	+	8.80192i	−0.627111	+	0.362063i
$592$	17.5784	+	32.7065i	0.722469	+	1.34423i
$593$	−9.13076	+	15.8149i	−0.374955	+	0.649442i	−0.990320	−	0.138801i	$-0.955675\pi$
$593$	−9.13076	+	15.8149i	−0.374955	+	0.649442i	0.615365	+	0.788242i	$0.289009\pi$
$594$	−1.63349	+	1.95981i	−0.0670228	+	0.0804121i
$595$	−9.35170	+	60.5737i	−0.383382	+	2.48328i
$596$	3.30432	−	15.3846i	0.135350	−	0.630177i
$597$	−10.9497	−	14.2699i	−0.448142	−	0.584030i
$598$	−7.33600	−	32.5814i	−0.299991	−	1.33235i
$599$	−1.14715	+	4.28123i	−0.0468714	+	0.174926i	−0.985394	−	0.170293i	$-0.945529\pi$
$599$	−1.14715	+	4.28123i	−0.0468714	+	0.174926i	0.938522	+	0.345219i	$0.112195\pi$
$600$	−20.4582	+	27.2152i	−0.835201	+	1.11106i
$601$	−32.5922	+	32.5922i	−1.32946	+	1.32946i	−0.423629	+	0.905836i	$0.639244\pi$
$601$	−32.5922	+	32.5922i	−1.32946	+	1.32946i	−0.905836	+	0.423629i	$0.860756\pi$
$602$	−0.694411	−	0.461144i	−0.0283021	−	0.0187948i
$603$	−2.38587	+	5.75999i	−0.0971600	+	0.234565i
$604$	−4.39796	+	2.08625i	−0.178951	+	0.0848882i
$605$	−25.3638	−	19.4623i	−1.03119	−	0.791257i
$606$	−15.6526	+	11.0372i	−0.635842	+	0.448356i
$607$	21.9983	−	38.1021i	0.892882	−	1.54652i	0.0564780	−	0.998404i	$-0.482013\pi$
$607$	21.9983	−	38.1021i	0.892882	−	1.54652i	0.836404	−	0.548113i	$-0.184654\pi$
$608$	−16.4811	−	14.6094i	−0.668399	−	0.592488i
$609$	10.8554	+	0.241858i	0.439882	+	0.00980060i
$610$	47.6792	−	4.32997i	1.93047	−	0.175315i
$611$	5.37626	−	40.8367i	0.217500	−	1.65208i
$612$	−11.1883	−	0.904487i	−0.452259	−	0.0365617i
$613$	0.584464	+	4.43944i	0.0236063	+	0.179307i	0.999186	−	0.0403377i	$-0.0128434\pi$
$613$	0.584464	+	4.43944i	0.0236063	+	0.179307i	−0.975580	+	0.219645i	$0.929510\pi$
$614$	6.21648	+	0.250869i	0.250877	+	0.0101242i
$615$	12.6866	+	12.6866i	0.511573	+	0.511573i
$616$	10.8113	−	8.08523i	0.435602	−	0.325763i
$617$	−17.2445	+	17.2445i	−0.694238	+	0.694238i	−0.963162	−	0.268923i	$-0.913332\pi$
$617$	−17.2445	+	17.2445i	−0.694238	+	0.694238i	0.268923	+	0.963162i	$0.413332\pi$
$618$	3.35157	−	3.09155i	0.134820	−	0.124360i
$619$	−34.9978	+	4.60754i	−1.40668	+	0.185193i	−0.795334	−	0.606172i	$-0.792704\pi$
$619$	−34.9978	+	4.60754i	−1.40668	+	0.185193i	−0.611345	+	0.791364i	$0.709371\pi$
$620$	46.5976	−	15.0310i	1.87140	−	0.603658i
$621$	−6.24521	−	0.822198i	−0.250612	−	0.0329937i
$622$	−24.3524	−	20.2975i	−0.976441	−	0.813856i
$623$	22.2580	+	40.6152i	0.891746	+	1.62721i
$624$	6.15764	−	13.6734i	0.246503	−	0.547375i
$625$	−51.7133	−	29.8567i	−2.06853	−	1.19427i
$626$	−2.51672	+	14.5537i	−0.100588	+	0.581682i
$627$	4.27580	−	5.57234i	0.170759	−	0.222538i
$628$	1.07829	+	21.4479i	0.0430286	+	0.855865i
$629$	−48.1327	−	19.9372i	−1.91918	−	0.794949i
$630$	−11.5826	+	10.2160i	−0.461463	+	0.407016i
$631$	−21.6103	−	21.6103i	−0.860291	−	0.860291i	0.131081	−	0.991372i	$-0.458155\pi$
$631$	−21.6103	−	21.6103i	−0.860291	−	0.860291i	−0.991372	+	0.131081i	$0.958155\pi$
$632$	−19.2244	−	4.94772i	−0.764704	−	0.196810i
$633$	−1.98111	−	0.530837i	−0.0787421	−	0.0210989i
$634$	12.0352	+	7.61156i	0.477979	+	0.302294i
$635$	−60.4983	+	46.4220i	−2.40080	+	1.84220i
$636$	2.49449	−	0.456840i	0.0989130	−	0.0181149i
$637$	−20.0878	−	16.8871i	−0.795906	−	0.669092i
$638$	10.4275	−	0.946972i	0.412830	−	0.0374910i
$639$	9.69874	+	5.59957i	0.383676	+	0.221515i
$640$	32.3362	+	33.6923i	1.27820	+	1.33180i
$641$	16.6894	+	28.9070i	0.659193	+	1.14176i	0.980825	+	0.194891i	$0.0624354\pi$
$641$	16.6894	+	28.9070i	0.659193	+	1.14176i	−0.321632	+	0.946865i	$0.604231\pi$
$642$	3.39833	−	7.35097i	0.134121	−	0.290120i
$643$	7.35226	+	17.7499i	0.289945	+	0.699989i	0.999991	−	0.00416585i	$-0.00132603\pi$
$643$	7.35226	+	17.7499i	0.289945	+	0.699989i	−0.710046	+	0.704155i	$0.751326\pi$
$644$	31.1390	+	11.8897i	1.22705	+	0.468521i
$645$	0.849577	+	0.351906i	0.0334521	+	0.0138563i
$646$	30.8768	+	1.24605i	1.21483	+	0.0490251i
$647$	−4.39380	+	16.3979i	−0.172738	+	0.644667i	0.824188	+	0.566316i	$0.191632\pi$
$647$	−4.39380	+	16.3979i	−0.172738	+	0.644667i	−0.996926	+	0.0783504i	$0.975035\pi$
$648$	−2.01970	−	1.98010i	−0.0793413	−	0.0777858i
$649$	−17.0760	+	4.57549i	−0.670291	+	0.179604i
$650$	60.9304	+	18.9905i	2.38989	+	0.744867i
$651$	15.5994	−	1.70115i	0.611388	−	0.0666734i
$652$	9.10595	−	5.88597i	0.356617	−	0.230512i
$653$	−5.15114	+	39.1268i	−0.201580	+	1.53115i	0.529176	+	0.848512i	$0.322501\pi$
$653$	−5.15114	+	39.1268i	−0.201580	+	1.53115i	−0.730756	+	0.682639i	$0.760832\pi$
$654$	3.15907	+	0.546287i	0.123529	+	0.0213615i
$655$	1.60394	+	2.77810i	0.0626710	+	0.108549i
$656$	14.1095	−	10.1597i	0.550883	−	0.396670i
$657$	10.2448			0.399686
$658$	30.9839	+	27.0168i	1.20788	+	1.05323i
$659$	−1.33294	−	3.21799i	−0.0519238	−	0.125355i	0.895789	−	0.444479i	$-0.146611\pi$
$659$	−1.33294	−	3.21799i	−0.0519238	−	0.125355i	−0.947713	+	0.319124i	$0.896611\pi$
$660$	−9.98882	+	11.0464i	−0.388814	+	0.429979i
$661$	−2.93243	−	22.2740i	−0.114058	−	0.866359i	−0.948835	−	0.315771i	$-0.897737\pi$
$661$	−2.93243	−	22.2740i	−0.114058	−	0.866359i	0.834777	−	0.550588i	$-0.185596\pi$
$662$	−17.1788	+	3.86797i	−0.667674	+	0.150333i
$663$	5.44576	+	20.3239i	0.211496	+	0.789313i
$664$	3.25366	+	4.15444i	0.126266	+	0.161224i
$665$	30.7271	−	29.3878i	1.19155	−	1.13961i
$666$	−6.10014	−	11.6244i	−0.236376	−	0.450438i
$667$	15.7373	+	20.5092i	0.609349	+	0.794119i
$668$	0.377546	−	4.67014i	0.0146077	−	0.180693i
$669$	0.534046	−	0.695982i	0.0206474	−	0.0269082i
$670$	−15.2716	+	33.0343i	−0.589995	+	1.27623i
$671$	14.7959			0.571190
$672$	7.96850	+	12.6690i	0.307392	+	0.488716i
$673$	25.6539			0.988884			0.494442	−	0.869211i	$-0.335373\pi$
$673$	25.6539			0.988884			0.494442	+	0.869211i	$0.335373\pi$
$674$	−9.65941	+	20.8944i	−0.372067	+	0.804823i
$675$	7.32795	−	9.54997i	0.282053	−	0.367578i
$676$	−2.10305	−	0.170016i	−0.0808865	−	0.00653906i
$677$	16.0039	+	20.8567i	0.615080	+	0.801587i	0.992210	−	0.124573i	$-0.0397560\pi$
$677$	16.0039	+	20.8567i	0.615080	+	0.801587i	−0.377131	+	0.926160i	$0.623089\pi$
$678$	6.52382	+	12.4318i	0.250546	+	0.477441i
$679$	−1.86115	−	7.62108i	−0.0714245	−	0.292470i
$680$	−65.0441	−	7.90901i	−2.49433	−	0.303297i
$681$	2.85583	+	10.6581i	0.109436	+	0.408419i
$682$	14.7621	−	3.32383i	0.565271	−	0.127276i
$683$	2.22175	+	16.8759i	0.0850131	+	0.645738i	0.979906	+	0.199458i	$0.0639182\pi$
$683$	2.22175	+	16.8759i	0.0850131	+	0.645738i	−0.894893	+	0.446280i	$0.852748\pi$
$684$	5.77555	+	5.22262i	0.220834	+	0.199692i
$685$	9.36849	+	22.6175i	0.357952	+	0.864172i
$686$	25.1311	−	7.37744i	0.959511	−	0.281672i
$687$	5.20636			0.198635
$688$	0.468846	−	0.757832i	0.0178746	−	0.0288921i
$689$	−2.37684	−	4.11681i	−0.0905505	−	0.156838i
$690$	−36.2325	−	6.26556i	−1.37935	−	0.238526i
$691$	0.999081	−	7.58877i	0.0380068	−	0.288691i	−0.961877	−	0.273481i	$-0.911825\pi$
$691$	0.999081	−	7.58877i	0.0380068	−	0.288691i	0.999884	−	0.0152099i	$-0.00484164\pi$
$692$	18.5577	+	28.7099i	0.705459	+	1.09139i
$693$	−3.85050	+	2.82058i	−0.146268	+	0.107145i
$694$	−42.8073	−	13.3420i	−1.62494	−	0.506454i
$695$	76.0222	−	20.3701i	2.88369	−	0.772682i
$696$	0.114905	+	11.6072i	0.00435546	+	0.439969i
$697$	−6.31395	+	23.5640i	−0.239158	+	0.892549i
$698$	8.55174	+	0.345109i	0.323688	+	0.0130626i
$699$	−4.54153	−	1.88116i	−0.171777	−	0.0711522i
$700$	−49.4301	+	40.1733i	−1.86828	+	1.51841i
$701$	1.72108	+	4.15506i	0.0650044	+	0.156935i	0.953044	−	0.302833i	$-0.0979326\pi$
$701$	1.72108	+	4.15506i	0.0650044	+	0.156935i	−0.888039	+	0.459768i	$0.847933\pi$
$702$	−2.22480	+	4.81250i	−0.0839698	+	0.181636i
$703$	18.0705	+	31.2991i	0.681543	+	1.18047i
$704$	9.01081	+	11.2738i	0.339608	+	0.424896i
$705$	−39.2736	−	22.6746i	−1.47913	−	0.853976i
$706$	−20.6246	+	1.87302i	−0.776218	+	0.0704920i
$707$	−33.4010	+	12.9713i	−1.25617	+	0.487834i
$708$	−3.53056	−	19.2780i	−0.132686	−	0.724510i
$709$	−24.3507	+	18.6850i	−0.914511	+	0.701729i	−0.954734	−	0.297461i	$-0.903860\pi$
$709$	−24.3507	+	18.6850i	−0.914511	+	0.701729i	0.0402224	+	0.999191i	$0.487193\pi$
$710$	55.2511	+	34.9431i	2.07354	+	1.31139i
$711$	6.77919	+	1.81648i	0.254239	+	0.0681232i
$712$	−42.6315	+	25.1792i	−1.59768	+	0.943632i
$713$	26.4173	+	26.4173i	0.989337	+	0.989337i
$714$	−19.9043	−	6.69361i	−0.744899	−	0.250502i
$715$	25.7917	+	10.6833i	0.964554	+	0.399531i
$716$	15.9140	−	0.800074i	0.594733	−	0.0299002i
$717$	10.7237	−	13.9754i	0.400485	−	0.521922i
$718$	−1.95657	+	11.3145i	−0.0730186	+	0.422252i
$719$	−10.8484	−	6.26334i	−0.404578	−	0.233583i	0.283879	−	0.958860i	$-0.408378\pi$
$719$	−10.8484	−	6.26334i	−0.404578	−	0.233583i	−0.688457	+	0.725277i	$0.741712\pi$
$720$	−11.3141	−	12.0246i	−0.421651	−	0.448130i
$721$	7.48070	−	4.09958i	0.278596	−	0.152676i
$722$	4.17354	+	3.47861i	0.155323	+	0.129461i
$723$	2.61994	+	0.344921i	0.0974365	+	0.0128278i
$724$	8.66869	+	26.8739i	0.322170	+	0.998760i
$725$	−48.9787	+	6.44816i	−1.81902	+	0.239479i
$726$	8.05144	−	7.42681i	0.298817	−	0.275635i
$727$	5.53687	−	5.53687i	0.205351	−	0.205351i	−0.596937	−	0.802288i	$-0.703616\pi$
$727$	5.53687	−	5.53687i	0.205351	−	0.205351i	0.802288	+	0.596937i	$0.203616\pi$
$728$	17.3529	−	22.0444i	0.643142	−	0.817018i
$729$	0.707107	+	0.707107i	0.0261891	+	0.0261891i
$730$	59.7539	+	2.41139i	2.21159	+	0.0892497i
$731$	0.163204	+	1.23965i	0.00603631	+	0.0458503i
$732$	−1.32175	+	16.3497i	−0.0488533	+	0.604303i
$733$	0.533620	−	4.05324i	0.0197097	−	0.149710i	−0.978760	−	0.205009i	$-0.934278\pi$
$733$	0.533620	−	4.05324i	0.0197097	−	0.149710i	0.998470	+	0.0552987i	$0.0176111\pi$
$734$	38.5757	−	3.50324i	1.42385	−	0.129307i
$735$	−25.6411	+	13.3180i	−0.945787	+	0.491241i
$736$	−11.6332	+	33.6807i	−0.428804	+	1.24149i
$737$	−5.62372	+	9.74056i	−0.207152	+	0.358798i
$738$	−5.02377	+	3.54244i	−0.184928	+	0.130399i
$739$	27.1008	+	20.7952i	0.996920	+	0.764963i	0.972061	−	0.234728i	$-0.0754198\pi$
$739$	27.1008	+	20.7952i	0.996920	+	0.764963i	0.0248584	+	0.999691i	$0.492086\pi$
$740$	−32.8437	−	69.2369i	−1.20736	−	2.54520i
$741$	5.58570	−	13.4851i	0.205196	−	0.495387i
$742$	4.73509	+	0.296851i	0.173830	+	0.0108978i
$743$	35.1019	−	35.1019i	1.28776	−	1.28776i	0.351620	−	0.936143i	$-0.385631\pi$
$743$	35.1019	−	35.1019i	1.28776	−	1.28776i	0.936143	−	0.351620i	$-0.114369\pi$
$744$	2.35415	+	16.6093i	0.0863072	+	0.608926i
$745$	−8.40520	+	31.3686i	−0.307943	+	1.14926i
$746$	1.48642	+	6.60163i	0.0544216	+	0.241703i
$747$	−1.13575	−	1.48013i	−0.0415548	−	0.0541552i
$748$	−19.7985	−	4.25233i	−0.723904	−	0.155481i
$749$	9.48872	−	11.8116i	0.346710	−	0.431585i
$750$	26.3020	−	31.5563i	0.960412	−	1.15227i
$751$	20.0398	−	34.7099i	0.731262	−	1.26658i	−0.225083	−	0.974340i	$-0.572265\pi$
$751$	20.0398	−	34.7099i	0.731262	−	1.26658i	0.956344	−	0.292243i	$-0.0944015\pi$
$752$	−27.8017	+	34.0351i	−1.01382	+	1.24113i
$753$	−0.772520	+	0.446014i	−0.0281522	+	0.0162537i
$754$	20.4218	−	7.50934i	0.743719	−	0.273474i
$755$	9.28136	−	3.84447i	0.337783	−	0.139914i
$756$	−2.77281	−	4.50683i	−0.100846	−	0.163912i
$757$	0.721560	−	1.74200i	0.0262255	−	0.0633141i	−0.910224	−	0.414116i	$-0.864091\pi$
$757$	0.721560	−	1.74200i	0.0262255	−	0.0633141i	0.936450	+	0.350802i	$0.114091\pi$
$758$	−14.6392	+	13.5035i	−0.531721	+	0.490470i
$759$	−10.9766	−	2.94118i	−0.398427	−	0.106758i
$760$	32.4573	+	31.8210i	1.17735	+	1.15427i
$761$	4.37058	+	16.3112i	0.158434	+	0.591282i	0.998787	+	0.0492430i	$0.0156809\pi$
$761$	4.37058	+	16.3112i	0.158434	+	0.591282i	−0.840353	+	0.542039i	$0.817652\pi$
$762$	−12.1405	−	23.1350i	−0.439804	−	0.838092i
$763$	5.48874	+	2.41811i	0.198706	+	0.0875416i
$764$	0.706728	+	3.85896i	0.0255685	+	0.139612i
$765$	22.9678	+	3.02376i	0.830401	+	0.109324i
$766$	−8.25627	+	5.82180i	−0.298311	+	0.210350i
$767$	−31.8156	+	18.3687i	−1.14879	+	0.663257i
$768$	−13.2627	+	8.94998i	−0.478575	+	0.322954i
$769$		−	29.7691i		−	1.07350i	−0.843741	−	0.536751i	$-0.819652\pi$
$769$		−	29.7691i		−	1.07350i	0.843741	−	0.536751i	$-0.180348\pi$
$770$	−23.1224	+	15.5451i	−0.833274	+	0.560206i
$771$	−22.7372	+	9.41805i	−0.818860	+	0.339183i
$772$	10.2064	−	28.6282i	0.367335	−	1.03035i
$773$	−23.8570	+	3.14084i	−0.858078	+	0.112968i	−0.546711	−	0.837321i	$-0.684120\pi$
$773$	−23.8570	+	3.14084i	−0.858078	+	0.112968i	−0.311367	+	0.950290i	$0.600787\pi$
$774$	−0.168406	+	0.266280i	−0.00605324	+	0.00957124i
$775$	−68.9611	+	18.4781i	−2.47716	+	0.663752i
$776$	8.07906	−	2.25073i	0.290021	−	0.0807963i
$777$	−5.82657	−	23.8587i	−0.209027	−	0.855927i
$778$	3.93345	−	12.6204i	0.141021	−	0.452462i
$779$	13.4260	−	10.3022i	0.481037	−	0.369113i
$780$	−14.1092	+	27.5459i	−0.505190	+	0.986300i
$781$	16.0287	+	12.2993i	0.573552	+	0.440102i
$782$	−17.2548	−	46.9248i	−0.617031	−	1.67803i
$783$		−	4.10396i		−	0.146664i
$784$	8.74703	+	26.5987i	0.312394	+	0.949953i
$785$		−	44.3206i		−	1.58187i
$786$	−1.03155	+	0.379314i	−0.0367943	+	0.0135297i
$787$	−39.6473	−	30.4224i	−1.41327	−	1.08444i	−0.983379	−	0.181562i	$-0.941885\pi$
$787$	−39.6473	−	30.4224i	−1.41327	−	1.08444i	−0.429893	−	0.902880i	$-0.641449\pi$
$788$	−10.8085	−	33.5076i	−0.385038	−	1.19366i
$789$	5.83268	−	4.47557i	0.207649	−	0.159335i
$790$	39.1129	+	12.1905i	1.39158	+	0.433719i
$791$	6.23125	+	25.5158i	0.221558	+	0.907238i
$792$	−3.14619	−	4.01722i	−0.111795	−	0.142746i
$793$	29.6998	−	7.95804i	1.05467	−	0.282598i
$794$	−22.4248	−	14.1824i	−0.795827	−	0.503314i
$795$	−5.18904	+	0.683150i	−0.184036	+	0.0242288i
$796$	32.5023	−	15.4180i	1.15201	−	0.546476i
$797$	−43.2338	+	17.9080i	−1.53142	+	0.634335i	−0.979839	−	0.199787i	$-0.935975\pi$
$797$	−43.2338	+	17.9080i	−1.53142	+	0.634335i	−0.551581	+	0.834122i	$0.685975\pi$
$798$	8.12768	+	12.0895i	0.287717	+	0.427963i
$799$		−	61.6617i		−	2.18143i
$800$	−44.6247	−	51.4340i	−1.57772	−	1.81847i
$801$	15.1599	−	8.75257i	0.535648	−	0.309257i
$802$	6.93524	+	9.83531i	0.244892	+	0.347297i
$803$	18.3239	+	2.41239i	0.646636	+	0.0851313i
$804$	−10.2611	−	7.08444i	−0.361881	−	0.249849i
$805$	−62.9523	−	27.7342i	−2.21878	−	0.977503i
$806$	27.8442	−	14.6118i	0.980770	−	0.514677i
$807$	−1.13723	−	4.24421i	−0.0400324	−	0.149403i
$808$	−15.0084	−	35.2426i	−0.527993	−	1.23983i
$809$	9.51910	+	2.55064i	0.334674	+	0.0896756i	0.422243	−	0.906483i	$-0.361243\pi$
$809$	9.51910	+	2.55064i	0.334674	+	0.0896756i	−0.0875687	+	0.996158i	$0.527910\pi$
$810$	3.95785	+	4.29073i	0.139065	+	0.150761i
$811$	8.04623	−	19.4253i	0.282541	−	0.682115i	−0.717352	−	0.696711i	$-0.754646\pi$
$811$	8.04623	−	19.4253i	0.282541	−	0.682115i	0.999893	+	0.0145957i	$0.00464613\pi$
$812$	−5.03201	+	21.1251i	−0.176589	+	0.741345i
$813$	0.216558	−	0.0897012i	0.00759501	−	0.00314596i
$814$	−8.17350	−	22.2280i	−0.286481	−	0.779092i
$815$	−19.3793	+	11.1887i	−0.678828	+	0.391922i
$816$	6.46753	−	21.4977i	0.226409	−	0.752572i
$817$	0.433689	−	0.751171i	0.0151729	−	0.0262801i
$818$	−34.2709	−	28.5646i	−1.19826	−	0.998736i
$819$	−6.21203	+	7.73274i	−0.217066	+	0.270204i
$820$	−30.1356	+	19.4793i	−1.05238	+	0.680246i
$821$	−9.88911	−	12.8877i	−0.345132	−	0.449785i	0.588245	−	0.808683i	$-0.299819\pi$
$821$	−9.88911	−	12.8877i	−0.345132	−	0.449785i	−0.933377	+	0.358898i	$0.883153\pi$
$822$	−8.18283	+	1.84244i	−0.285409	+	0.0642625i
$823$	−11.2971	+	42.1615i	−0.393793	+	1.46966i	0.430032	+	0.902814i	$0.358502\pi$
$823$	−11.2971	+	42.1615i	−0.393793	+	1.46966i	−0.823826	+	0.566843i	$0.808164\pi$
$824$	4.63763	+	7.85207i	0.161560	+	0.273540i
$825$	15.3556	−	15.3556i	0.534614	−	0.534614i
$826$	2.29413	−	36.5937i	0.0798230	−	1.27326i
$827$	9.24861	−	22.3281i	0.321606	−	0.776425i	−0.677555	−	0.735472i	$-0.736961\pi$
$827$	9.24861	−	22.3281i	0.321606	−	0.776425i	0.999161	−	0.0409529i	$-0.0130394\pi$
$828$	4.23062	−	11.8666i	0.147024	−	0.412394i
$829$	−32.5014	−	24.9392i	−1.12882	−	0.866175i	−0.136595	−	0.990627i	$-0.543616\pi$
$829$	−32.5014	−	24.9392i	−1.12882	−	0.866175i	−0.992226	+	0.124452i	$0.960283\pi$
$830$	−6.27599	−	8.90039i	−0.217843	−	0.308937i
$831$	−6.75572	+	11.7013i	−0.234353	+	0.405912i
$832$	24.1510	+	17.7833i	0.837285	+	0.616525i
$833$	−33.1146	−	21.1392i	−1.14735	−	0.732430i
$834$	2.43883	+	26.8550i	0.0844497	+	0.929913i
$835$	−1.26216	+	9.58707i	−0.0436789	+	0.331774i
$836$	9.10041	+	10.7012i	0.314744	+	0.370110i
$837$	−0.774146	−	5.88022i	−0.0267584	−	0.203250i
$838$	−0.310703	+	7.69916i	−0.0107331	+	0.265963i
$839$	−21.7907	−	21.7907i	−0.752300	−	0.752300i	0.222608	−	0.974908i	$-0.428543\pi$
$839$	−21.7907	−	21.7907i	−0.752300	−	0.752300i	−0.974908	+	0.222608i	$0.928543\pi$
$840$	−15.1120	−	26.9393i	−0.521413	−	0.929495i
$841$	8.59666	−	8.59666i	0.296437	−	0.296437i
$842$	18.5401	+	20.0994i	0.638933	+	0.692671i
$843$	1.42042	−	0.187002i	0.0489219	−	0.00644069i
$844$	1.87004	−	3.65094i	0.0643694	−	0.125670i
$845$	4.31723	+	0.568374i	0.148517	+	0.0195526i
$846$	9.94802	−	11.9353i	0.342020	−	0.410346i
$847$	17.9708	−	9.84839i	0.617485	−	0.338395i
$848$	−0.154338	+	5.06961i	−0.00529999	+	0.174091i
$849$	3.04981	+	1.76081i	0.104669	+	0.0604308i
$850$	94.1455	+	16.2803i	3.22916	+	0.558408i
$851$	35.5962	−	46.3898i	1.22022	−	1.59022i
$852$	−15.0227	+	16.6132i	−0.514671	+	0.569160i
$853$	42.0630	+	17.4231i	1.44021	+	0.596554i	0.959849	−	0.280517i	$-0.0905058\pi$
$853$	42.0630	+	17.4231i	1.44021	+	0.596554i	0.480361	+	0.877071i	$0.340506\pi$
$854$	−9.78155	+	29.0866i	−0.334718	+	0.995324i
$855$	−11.3635	−	11.3635i	−0.388623	−	0.388623i
$856$	12.9469	+	9.73240i	0.442516	+	0.332647i
$857$	−6.70093	−	1.79551i	−0.228899	−	0.0613334i	0.142546	−	0.989788i	$-0.454471\pi$
$857$	−6.70093	−	1.79551i	−0.228899	−	0.0613334i	−0.371445	+	0.928455i	$0.621138\pi$
$858$	−5.11253	+	8.08380i	−0.174539	+	0.275976i
$859$	32.4856	−	24.9271i	1.10839	−	0.850501i	0.118592	−	0.992943i	$-0.462162\pi$
$859$	32.4856	−	24.9271i	1.10839	−	0.850501i	0.989803	+	0.142442i	$0.0454954\pi$
$860$	−1.04493	+	1.51347i	−0.0356318	+	0.0516090i
$861$	−10.7202	+	4.16319i	−0.365344	+	0.141881i
$862$	3.90992	+	43.0539i	0.133172	+	1.46642i
$863$	−24.8466	−	14.3452i	−0.845788	−	0.488316i	0.0134394	−	0.999910i	$-0.495722\pi$
$863$	−24.8466	−	14.3452i	−0.845788	−	0.488316i	−0.859227	+	0.511594i	$0.829055\pi$
$864$	4.72015	−	3.11772i	0.160583	−	0.106067i
$865$	−35.2764	−	61.1006i	−1.19944	−	2.07748i
$866$	−6.34925	−	2.93524i	−0.215756	−	0.0997434i
$867$	5.54848	+	13.3952i	0.188436	+	0.454925i
$868$	−3.22504	+	31.2176i	−0.109465	+	1.05959i
$869$	11.6976	+	4.84530i	0.396813	+	0.164366i
$870$	0.965982	−	23.9369i	0.0327499	−	0.811536i
$871$	−6.04947	+	22.5769i	−0.204978	+	0.764990i
$872$	−2.39497	+	5.94783i	−0.0811040	+	0.201419i
$873$	−2.86412	+	0.767437i	−0.0969356	+	0.0259738i
$874$	−10.3202	+	33.1120i	−0.349086	+	1.12003i
$875$	61.9996	−	45.4162i	2.09597	−	1.53535i
$876$	−4.30264	+	20.0327i	−0.145373	+	0.676842i
$877$	1.23962	−	9.41583i	0.0418589	−	0.317950i	−0.957687	−	0.287812i	$-0.907072\pi$
$877$	1.23962	−	9.41583i	0.0418589	−	0.317950i	0.999546	−	0.0301377i	$-0.00959458\pi$
$878$	2.53628	−	14.6668i	0.0855951	−	0.494980i
$879$	−12.9257	−	22.3880i	−0.435974	−	0.755130i
$880$	−17.4050	−	24.1715i	−0.586722	−	0.814821i
$881$	17.8084			0.599980			0.299990	−	0.953942i	$-0.403017\pi$
$881$	17.8084			0.599980			0.299990	+	0.953942i	$0.403017\pi$
$882$	−2.99930	−	9.43420i	−0.100992	−	0.317666i
$883$	3.58595	+	8.65726i	0.120677	+	0.291340i	0.972662	−	0.232227i	$-0.0746011\pi$
$883$	3.58595	+	8.65726i	0.120677	+	0.291340i	−0.851985	+	0.523567i	$0.824601\pi$
$884$	−42.0285	+	2.11298i	−1.41357	+	0.0710673i
$885$	5.27953	+	40.1020i	0.177469	+	1.34801i
$886$	8.73091	+	38.7766i	0.293321	+	1.30273i
$887$	−2.12744	−	7.93972i	−0.0714325	−	0.266590i	0.920968	−	0.389638i	$-0.127400\pi$
$887$	−2.12744	−	7.93972i	−0.0714325	−	0.266590i	−0.992401	+	0.123048i	$0.960733\pi$
$888$	25.2925	−	7.04617i	0.848760	−	0.236454i
$889$	−11.5960	−	47.4837i	−0.388919	−	1.59255i
$890$	90.4822	−	47.4822i	3.03297	−	1.59161i
$891$	1.09823	+	1.43124i	0.0367922	+	0.0479485i
$892$	1.13664	+	1.33658i	0.0380574	+	0.0447519i
$893$	−26.0398	+	33.9358i	−0.871390	+	1.13562i
$894$	−10.0996	−	4.66902i	−0.337782	−	0.156155i
$895$	−32.8851			−1.09923
$896$	−28.1196	+	10.2609i	−0.939411	+	0.342792i
$897$	−23.6153			−0.788492
$898$	−18.3988	−	8.50568i	−0.613975	−	0.283838i
$899$	−14.8175	+	19.3106i	−0.494192	+	0.644043i
$900$	15.5964	+	18.3400i	0.519882	+	0.611332i
$901$	−4.33222	−	5.64586i	−0.144327	−	0.188091i
$902$	−9.81972	+	5.15308i	−0.326961	+	0.171579i
$903$	−0.425972	+	0.407404i	−0.0141755	+	0.0135576i
$904$	−27.0491	+	7.53556i	−0.899641	+	0.250629i
$905$	−15.0832	−	56.2913i	−0.501383	−	1.87119i
$906$	0.756066	+	3.35792i	0.0251186	+	0.111559i
$907$	6.91648	+	52.5359i	0.229658	+	1.74443i	0.586217	+	0.810154i	$0.300616\pi$
$907$	6.91648	+	52.5359i	0.229658	+	1.74443i	−0.356559	+	0.934273i	$0.616050\pi$
$908$	−22.0403	+	1.10808i	−0.731433	+	0.0367728i
$909$	5.18266	+	12.5121i	0.171898	+	0.414999i
$910$	−38.0526	+	43.6400i	−1.26143	+	1.44665i
$911$	11.9841			0.397052			0.198526	−	0.980096i	$-0.436384\pi$
$911$	11.9841			0.397052			0.198526	+	0.980096i	$0.436384\pi$
$912$	−12.6380	+	9.10013i	−0.418485	+	0.301335i
$913$	−1.68287	−	2.91482i	−0.0556949	−	0.0964665i
$914$	7.91320	−	45.7605i	0.261745	−	1.51362i
$915$	4.41871	−	33.5634i	0.146078	−	1.10957i
$916$	−2.18659	+	10.1806i	−0.0722469	+	0.336375i
$917$	−2.04407	+	0.222911i	−0.0675013	+	0.00736118i
$918$	−2.36174	+	7.57759i	−0.0779492	+	0.250098i
$919$	23.6143	−	6.32745i	0.778965	−	0.208723i	0.152637	−	0.988282i	$-0.451224\pi$
$919$	23.6143	−	6.32745i	0.778965	−	0.208723i	0.626329	+	0.779559i	$0.284557\pi$
$920$	27.4688	−	68.2178i	0.905619	−	2.24907i
$921$	1.13862	−	4.24939i	0.0375189	−	0.140022i
$922$	0.0617449	−	1.53003i	0.00203346	−	0.0503888i
$923$	38.7895	+	16.0672i	1.27677	+	0.528857i
$924$	−3.89823	−	8.71389i	−0.128243	−	0.286666i
$925$	42.7614	+	103.235i	1.40599	+	3.39435i
$926$	−33.4672	−	15.4718i	−1.09980	−	0.508434i
$927$	−1.61209	−	2.79222i	−0.0529480	−	0.0917086i
$928$	−22.7450	−	4.65014i	−0.746642	−	0.152648i
$929$	16.9248	+	9.77156i	0.555286	+	0.320594i	0.751251	−	0.660016i	$-0.229451\pi$
$929$	16.9248	+	9.77156i	0.555286	+	0.320594i	−0.195965	+	0.980611i	$0.562784\pi$
$930$	−3.13123	−	34.4794i	−0.102677	−	1.13062i
$931$	9.29768	+	25.6184i	0.304719	+	0.839610i
$932$	5.58581	−	8.09048i	0.182969	−	0.265013i
$933$	−17.7844	+	13.6465i	−0.582237	+	0.446766i
$934$	15.1604	−	23.9713i	0.496064	−	0.784364i
$935$	40.3683	+	10.8167i	1.32019	+	0.353743i
$936$	−8.47601	−	6.37157i	−0.277047	−	0.208261i
$937$	−21.0554	−	21.0554i	−0.687851	−	0.687851i	0.273906	−	0.961757i	$-0.411684\pi$
$937$	−21.0554	−	21.0554i	−0.687851	−	0.687851i	−0.961757	+	0.273906i	$0.911684\pi$
$938$	−15.4307	−	17.4949i	−0.503831	−	0.571228i
$939$	9.64875	+	3.99664i	0.314875	+	0.130426i
$940$	60.8324	−	67.2729i	1.98413	−	2.19420i
$941$	−18.8484	+	24.5637i	−0.614439	+	0.800753i	−0.992134	−	0.125177i	$-0.960050\pi$
$941$	−18.8484	+	24.5637i	−0.614439	+	0.800753i	0.377695	+	0.925930i	$0.376717\pi$
$942$	14.9631	+	2.58751i	0.487523	+	0.0843056i
$943$	−23.7119	−	13.6901i	−0.772166	−	0.445810i
$944$	39.1790	+	1.19276i	1.27517	+	0.0388209i
$945$	5.24835	+	9.57691i	0.170729	+	0.311537i
$946$	−0.363916	+	0.436616i	−0.0118319	+	0.0141956i
$947$	33.3845	+	4.39515i	1.08485	+	0.142823i	0.651684	−	0.758491i	$-0.274063\pi$
$947$	33.3845	+	4.39515i	1.08485	+	0.142823i	0.433166	+	0.901314i	$0.357396\pi$
$948$	−6.39910	+	12.4932i	−0.207833	+	0.405759i
$949$	38.0790	−	5.01319i	1.23610	−	0.162735i
$950$	−44.9382	−	48.7177i	−1.45799	−	1.58061i
$951$	7.12008	−	7.12008i	0.230884	−	0.230884i
$952$	21.4482	−	36.1097i	0.695140	−	1.17032i
$953$	14.0386	+	14.0386i	0.454755	+	0.454755i	0.896929	−	0.442174i	$-0.145793\pi$
$953$	14.0386	+	14.0386i	0.454755	+	0.454755i	−0.442174	+	0.896929i	$0.645793\pi$
$954$	0.0723068	−	1.79175i	0.00234102	−	0.0580100i
$955$	−1.05683	−	8.02740i	−0.0341981	−	0.259760i
$956$	22.8238	+	26.8387i	0.738176	+	0.868025i
$957$	0.966380	−	7.34038i	0.0312386	−	0.237281i
$958$	−1.29226	−	14.2296i	−0.0417510	−	0.459738i
$959$	−15.6880	−	0.349531i	−0.506593	−	0.0112869i
$960$	28.2647	−	17.0735i	0.912240	−	0.551045i
$961$	−2.08816	+	3.61681i	−0.0673601	+	0.116671i
$962$	−28.3621	−	40.2221i	−0.914430	−	1.29681i
$963$	−4.54313	−	3.48607i	−0.146400	−	0.112337i
$964$	−1.77479	+	4.97818i	−0.0571622	+	0.160336i
$965$	−24.0042	+	57.9513i	−0.772723	+	1.86552i
$966$	13.0386	−	19.6341i	0.419509	−	0.631716i
$967$	−10.6416	+	10.6416i	−0.342210	+	0.342210i	−0.857198	−	0.514988i	$-0.827797\pi$
$967$	−10.6416	+	10.6416i	−0.342210	+	0.342210i	0.514988	+	0.857198i	$0.327797\pi$
$968$	11.1410	+	18.8630i	0.358084	+	0.606279i
$969$	5.65545	−	21.1064i	0.181679	−	0.678036i
$970$	−16.8860	+	3.80203i	−0.542175	+	0.122076i
$971$	33.9150	+	44.1989i	1.08838	+	1.41841i	0.899774	+	0.436357i	$0.143731\pi$
$971$	33.9150	+	44.1989i	1.08838	+	1.41841i	0.188609	+	0.982052i	$0.439602\pi$
$972$	−1.67965	+	1.08571i	−0.0538749	+	0.0348241i
$973$	−7.69723	+	49.8572i	−0.246762	+	1.59835i
$974$	21.2363	+	17.7003i	0.680456	+	0.567155i
$975$	22.5642	−	39.0824i	0.722633	−	1.25164i
$976$	−31.4152	−	9.45118i	−1.00558	−	0.302525i
$977$	35.9043	−	20.7294i	1.14868	−	0.663191i	0.200115	−	0.979772i	$-0.435868\pi$
$977$	35.9043	−	20.7294i	1.14868	−	0.663191i	0.948565	+	0.316581i	$0.102535\pi$
$978$	−2.64600	−	7.19585i	−0.0846096	−	0.230098i
$979$	29.1761	−	12.0852i	0.932474	−	0.386243i
$980$	−15.2732	−	55.7322i	−0.487884	−	1.78030i
$981$	0.867525	−	2.09439i	0.0276979	−	0.0668688i
$982$	−20.5500	−	22.2784i	−0.655778	−	0.710932i
$983$	14.9665	+	4.01025i	0.477356	+	0.127907i	0.489471	−	0.872019i	$-0.337190\pi$
$983$	14.9665	+	4.01025i	0.477356	+	0.127907i	−0.0121152	+	0.999927i	$0.503856\pi$
$984$	−4.81701	−	11.3113i	−0.153561	−	0.360590i
$985$	18.8064	+	70.1865i	0.599223	+	2.23633i
$986$	28.8433	−	15.1361i	0.918559	−	0.482031i
$987$	23.4497	−	17.1775i	0.746413	−	0.546765i
$988$	24.0229	+	16.5858i	0.764270	+	0.527666i
$989$	−1.39134	−	0.183173i	−0.0442419	−	0.00582456i
$990$	6.06870	+	8.60641i	0.192876	+	0.273530i
$991$	31.4859	−	18.1784i	1.00018	−	0.577455i	0.0918800	−	0.995770i	$-0.470712\pi$
$991$	31.4859	−	18.1784i	1.00018	−	0.577455i	0.908302	+	0.418315i	$0.137379\pi$
$992$	−33.4666	−	2.37232i	−1.06257	−	0.0753213i
$993$			12.4514i			0.395132i
$994$	−34.7751	+	23.3791i	−1.10300	+	0.741540i
$995$	−68.5920	+	28.4118i	−2.17451	+	0.900713i
$996$	3.37126	−	1.59921i	0.106822	−	0.0506730i
$997$	20.9501	−	2.75814i	0.663497	−	0.0873511i	0.208747	−	0.977970i	$-0.433062\pi$
$997$	20.9501	−	2.75814i	0.663497	−	0.0873511i	0.454751	+	0.890619i	$0.349728\pi$
$998$	6.58095	+	4.16206i	0.208316	+	0.131748i
$999$	−8.96646	+	2.40256i	−0.283686	+	0.0760135i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	672.2.cf.a.187.54	yes	512
7.3	odd	6	inner	672.2.cf.a.283.13	yes	512
32.19	odd	8	inner	672.2.cf.a.19.13	✓	512
224.115	even	24	inner	672.2.cf.a.115.54	yes	512

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
672.2.cf.a.19.13	✓	512	32.19	odd	8	inner
672.2.cf.a.115.54	yes	512	224.115	even	24	inner
672.2.cf.a.187.54	yes	512	1.1	even	1	trivial
672.2.cf.a.283.13	yes	512	7.3	odd	6	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:	\( N \)	\(=\)	\( 672 = 2^{5} \cdot 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	672.cf (of order \(24\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(1.28368 + 0.593440i) q^{2} +(0.608761 - 0.793353i) q^{3} +(1.29566 + 1.52357i) q^{4} +(-2.51275 - 3.27468i) q^{5} +(1.25226 - 0.657147i) q^{6} +(2.57022 - 0.627676i) q^{7} +(0.759059 + 2.72467i) q^{8} +(-0.258819 - 0.965926i) q^{9} +O(q^{10})\)	\(q+(1.28368 + 0.593440i) q^{2} +(0.608761 - 0.793353i) q^{3} +(1.29566 + 1.52357i) q^{4} +(-2.51275 - 3.27468i) q^{5} +(1.25226 - 0.657147i) q^{6} +(2.57022 - 0.627676i) q^{7} +(0.759059 + 2.72467i) q^{8} +(-0.258819 - 0.965926i) q^{9} +(-1.28224 - 5.69481i) q^{10} +(-0.235475 - 1.78861i) q^{11} +(1.99748 - 0.100423i) q^{12} +(-1.43468 - 3.46362i) q^{13} +(3.67182 + 0.719536i) q^{14} -4.12765 q^{15} +(-0.642540 + 3.94806i) q^{16} +(-2.80619 - 4.86047i) q^{17} +(0.240979 - 1.39353i) q^{18} +(-0.508184 + 3.86004i) q^{19} +(1.73355 - 8.07123i) q^{20} +(1.06668 - 2.42120i) q^{21} +(0.759159 - 2.43574i) q^{22} +(6.08447 - 1.63033i) q^{23} +(2.62371 + 1.05647i) q^{24} +(-3.11553 + 11.6273i) q^{25} +(0.213785 - 5.29757i) q^{26} +(-0.923880 - 0.382683i) q^{27} +(4.28643 + 3.10266i) q^{28} +(1.57052 + 3.79156i) q^{29} +(-5.29857 - 2.44951i) q^{30} +(2.96548 + 5.13636i) q^{31} +(-3.16775 + 4.68672i) q^{32} +(-1.56235 - 0.902022i) q^{33} +(-0.717852 - 7.90458i) q^{34} +(-8.51376 - 6.83946i) q^{35} +(1.13632 - 1.64584i) q^{36} +(7.36451 - 5.65099i) q^{37} +(-2.94305 + 4.65347i) q^{38} +(-3.62125 - 0.970311i) q^{39} +(7.01510 - 9.33210i) q^{40} +(-3.07356 - 3.07356i) q^{41} +(2.80611 - 2.47503i) q^{42} +(-0.205826 - 0.0852559i) q^{43} +(2.41998 - 2.67619i) q^{44} +(-2.51275 + 3.27468i) q^{45} +(8.77800 + 1.51795i) q^{46} +(9.51477 + 5.49335i) q^{47} +(2.74105 + 2.91319i) q^{48} +(6.21205 - 3.22653i) q^{49} +(-10.8994 + 13.0768i) q^{50} +(-5.56437 - 0.732563i) q^{51} +(3.41822 - 6.67350i) q^{52} +(1.25714 - 0.165506i) q^{53} +(-0.958864 - 1.03951i) q^{54} +(-5.26544 + 5.26544i) q^{55} +(3.66116 + 6.52655i) q^{56} +(2.75301 + 2.75301i) q^{57} +(-0.234027 + 5.79916i) q^{58} +(-1.27906 - 9.71546i) q^{59} +(-5.34802 - 6.28877i) q^{60} +(-1.07051 + 8.13137i) q^{61} +(0.758599 + 8.35327i) q^{62} +(-1.27151 - 2.32019i) q^{63} +(-6.84766 + 4.13637i) q^{64} +(-7.73726 + 13.4013i) q^{65} +(-1.47026 - 2.08507i) q^{66} +(-4.94622 - 3.79536i) q^{67} +(3.76941 - 10.5729i) q^{68} +(2.41056 - 5.81961i) q^{69} +(-6.87012 - 13.8321i) q^{70} +(-7.91899 + 7.91899i) q^{71} +(2.43537 - 1.43839i) q^{72} +(-2.65154 + 9.89569i) q^{73} +(12.8072 - 2.88365i) q^{74} +(7.32795 + 9.54997i) q^{75} +(-6.53948 + 4.22704i) q^{76} +(-1.72789 - 4.44932i) q^{77} +(-4.07270 - 3.39456i) q^{78} +(-3.50917 + 6.07805i) q^{79} +(14.5432 - 7.81637i) q^{80} +(-0.866025 + 0.500000i) q^{81} +(-2.12149 - 5.76944i) q^{82} +(1.72365 - 0.713960i) q^{83} +(5.07092 - 1.51188i) q^{84} +(-8.86523 + 21.4025i) q^{85} +(-0.213620 - 0.231586i) q^{86} +(3.96412 + 1.06218i) q^{87} +(4.69463 - 1.99925i) q^{88} +(4.53066 + 16.9087i) q^{89} +(-5.16889 + 2.71247i) q^{90} +(-5.86147 - 8.00174i) q^{91} +(10.3673 + 7.15777i) q^{92} +(5.88022 + 0.774146i) q^{93} +(8.95392 + 12.6981i) q^{94} +(13.9174 - 8.03519i) q^{95} +(1.78982 + 5.36624i) q^{96} -2.96515i q^{97} +(9.88902 - 0.455349i) q^{98} +(-1.66672 + 0.690378i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 512 q+O(q^{10}) \) 512 * q	\( 512 q + 64 q^{14} + 8 q^{16} - 8 q^{18} - 16 q^{22} - 16 q^{23} - 40 q^{28} + 48 q^{35} + 32 q^{43} + 8 q^{44} + 48 q^{50} - 72 q^{52} + 32 q^{53} + 32 q^{58} - 192 q^{59} - 48 q^{60} + 144 q^{64} - 144 q^{66} - 16 q^{67} - 72 q^{70} + 128 q^{71} + 32 q^{74} + 48 q^{78} - 72 q^{80} - 120 q^{82} + 88 q^{88} - 48 q^{91} + 128 q^{92} - 72 q^{94} - 120 q^{96} - 136 q^{98}+O(q^{100}) \) 512 * q + 64 * q^14 + 8 * q^16 - 8 * q^18 - 16 * q^22 - 16 * q^23 - 40 * q^28 + 48 * q^35 + 32 * q^43 + 8 * q^44 + 48 * q^50 - 72 * q^52 + 32 * q^53 + 32 * q^58 - 192 * q^59 - 48 * q^60 + 144 * q^64 - 144 * q^66 - 16 * q^67 - 72 * q^70 + 128 * q^71 + 32 * q^74 + 48 * q^78 - 72 * q^80 - 120 * q^82 + 88 * q^88 - 48 * q^91 + 128 * q^92 - 72 * q^94 - 120 * q^96 - 136 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more