LMFDB - Embedded newform 336.2.s.c.155.18

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [336,2,Mod(155,336)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(336, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 1, 2, 0]))

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

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

chi := DirichletCharacter("336.155");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 336 = 2^{4} \cdot 3 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	336.s (of order $4$, degree $2$, 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:	$2.68297350792$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$20$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			155.18
Character	$\chi$	$=$	336.155
Dual form			336.2.s.c.323.18

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.37293 - 0.339195i) q^{2} +(0.567369 - 1.63649i) q^{3} +(1.76989 - 0.931385i) q^{4} +(-0.132854 + 0.132854i) q^{5} +(0.223871 - 2.43924i) q^{6} -1.00000 q^{7} +(2.11403 - 1.87907i) q^{8} +(-2.35619 - 1.85698i) q^{9} +O(q^{10})$	\(q+(1.37293 - 0.339195i) q^{2} +(0.567369 - 1.63649i) q^{3} +(1.76989 - 0.931385i) q^{4} +(-0.132854 + 0.132854i) q^{5} +(0.223871 - 2.43924i) q^{6} -1.00000 q^{7} +(2.11403 - 1.87907i) q^{8} +(-2.35619 - 1.85698i) q^{9} +(-0.137336 + 0.227462i) q^{10} +(-0.715349 - 0.715349i) q^{11} +(-0.520017 - 3.42485i) q^{12} +(0.206350 - 0.206350i) q^{13} +(-1.37293 + 0.339195i) q^{14} +(0.142036 + 0.292790i) q^{15} +(2.26505 - 3.29690i) q^{16} +6.91999i q^{17} +(-3.86477 - 1.75031i) q^{18} +(5.87341 + 5.87341i) q^{19} +(-0.111399 + 0.358874i) q^{20} +(-0.567369 + 1.63649i) q^{21} +(-1.22477 - 0.739484i) q^{22} -6.42354i q^{23} +(-1.87564 - 4.52570i) q^{24} +4.96470i q^{25} +(0.213312 - 0.353298i) q^{26} +(-4.37576 + 2.80227i) q^{27} +(-1.76989 + 0.931385i) q^{28} +(-5.00314 - 5.00314i) q^{29} +(0.294319 + 0.353803i) q^{30} -2.52929i q^{31} +(1.99146 - 5.29472i) q^{32} +(-1.57653 + 0.764794i) q^{33} +(2.34723 + 9.50069i) q^{34} +(0.132854 - 0.132854i) q^{35} +(-5.89976 - 1.09215i) q^{36} +(6.15279 + 6.15279i) q^{37} +(10.0560 + 6.07157i) q^{38} +(-0.220613 - 0.454766i) q^{39} +(-0.0312149 + 0.530497i) q^{40} -5.19068 q^{41} +(-0.223871 + 2.43924i) q^{42} +(1.36769 - 1.36769i) q^{43} +(-1.93236 - 0.599827i) q^{44} +(0.559735 - 0.0663207i) q^{45} +(-2.17883 - 8.81910i) q^{46} +0.603632 q^{47} +(-4.11023 - 5.57728i) q^{48} +1.00000 q^{49} +(1.68400 + 6.81620i) q^{50} +(11.3245 + 3.92619i) q^{51} +(0.173027 - 0.557409i) q^{52} +(-6.19471 + 6.19471i) q^{53} +(-5.05711 + 5.33157i) q^{54} +0.190073 q^{55} +(-2.11403 + 1.87907i) q^{56} +(12.9442 - 6.27938i) q^{57} +(-8.56601 - 5.17194i) q^{58} +(5.00050 + 5.00050i) q^{59} +(0.524089 + 0.385917i) q^{60} +(-6.24649 + 6.24649i) q^{61} +(-0.857924 - 3.47255i) q^{62} +(2.35619 + 1.85698i) q^{63} +(0.938205 - 7.94480i) q^{64} +0.0548287i q^{65} +(-1.90505 + 1.58476i) q^{66} +(2.55815 + 2.55815i) q^{67} +(6.44517 + 12.2476i) q^{68} +(-10.5120 - 3.64452i) q^{69} +(0.137336 - 0.227462i) q^{70} -0.808658i q^{71} +(-8.47044 + 0.501723i) q^{72} -11.5367i q^{73} +(10.5344 + 6.36037i) q^{74} +(8.12467 + 2.81682i) q^{75} +(15.8657 + 4.92491i) q^{76} +(0.715349 + 0.715349i) q^{77} +(-0.457142 - 0.549533i) q^{78} -3.48456i q^{79} +(0.137086 + 0.738925i) q^{80} +(2.10322 + 8.75080i) q^{81} +(-7.12645 + 1.76065i) q^{82} +(-0.641645 + 0.641645i) q^{83} +(0.520017 + 3.42485i) q^{84} +(-0.919345 - 0.919345i) q^{85} +(1.41384 - 2.34167i) q^{86} +(-11.0262 + 5.34895i) q^{87} +(-2.85646 - 0.168076i) q^{88} -11.0057 q^{89} +(0.745983 - 0.280913i) q^{90} +(-0.206350 + 0.206350i) q^{91} +(-5.98279 - 11.3690i) q^{92} +(-4.13916 - 1.43504i) q^{93} +(0.828746 - 0.204749i) q^{94} -1.56061 q^{95} +(-7.53485 - 6.26307i) q^{96} -5.56394 q^{97} +(1.37293 - 0.339195i) q^{98} +(0.357104 + 3.01389i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q + 4 q^{3} - 2 q^{6} - 40 q^{7}+O(q^{10}) $ 40 * q + 4 * q^3 - 2 * q^6 - 40 * q^7	$ 40 q + 4 q^{3} - 2 q^{6} - 40 q^{7} - 8 q^{10} - 2 q^{12} + 24 q^{13} + 36 q^{16} + 12 q^{18} + 16 q^{19} - 4 q^{21} - 8 q^{22} + 6 q^{24} - 32 q^{27} - 32 q^{30} + 24 q^{33} + 12 q^{34} - 4 q^{36} - 8 q^{37} - 64 q^{39} - 60 q^{40} + 2 q^{42} + 24 q^{43} - 28 q^{45} + 20 q^{46} - 26 q^{48} + 40 q^{49} - 32 q^{51} + 84 q^{52} - 14 q^{54} + 16 q^{55} + 12 q^{58} - 24 q^{60} - 48 q^{61} - 12 q^{64} - 36 q^{66} + 40 q^{67} + 4 q^{69} + 8 q^{70} + 8 q^{72} + 40 q^{75} - 44 q^{76} + 24 q^{78} + 56 q^{81} - 84 q^{82} + 2 q^{84} - 48 q^{85} + 32 q^{87} + 52 q^{88} - 76 q^{90} - 24 q^{91} + 56 q^{93} - 62 q^{96} + 16 q^{97} + 24 q^{99}+O(q^{100}) $ 40 * q + 4 * q^3 - 2 * q^6 - 40 * q^7 - 8 * q^10 - 2 * q^12 + 24 * q^13 + 36 * q^16 + 12 * q^18 + 16 * q^19 - 4 * q^21 - 8 * q^22 + 6 * q^24 - 32 * q^27 - 32 * q^30 + 24 * q^33 + 12 * q^34 - 4 * q^36 - 8 * q^37 - 64 * q^39 - 60 * q^40 + 2 * q^42 + 24 * q^43 - 28 * q^45 + 20 * q^46 - 26 * q^48 + 40 * q^49 - 32 * q^51 + 84 * q^52 - 14 * q^54 + 16 * q^55 + 12 * q^58 - 24 * q^60 - 48 * q^61 - 12 * q^64 - 36 * q^66 + 40 * q^67 + 4 * q^69 + 8 * q^70 + 8 * q^72 + 40 * q^75 - 44 * q^76 + 24 * q^78 + 56 * q^81 - 84 * q^82 + 2 * q^84 - 48 * q^85 + 32 * q^87 + 52 * q^88 - 76 * q^90 - 24 * q^91 + 56 * q^93 - 62 * q^96 + 16 * q^97 + 24 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/336\mathbb{Z}\right)^\times$.

$n$	$85$	$113$	$127$	$241$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$-1$	$-1$	$1$

Coefficient data

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

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

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

$2$	1.37293	−	0.339195i	0.970811	−	0.239847i
$2$	1.37293	−	0.339195i	0.970811	−	0.239847i
$3$	0.567369	−	1.63649i	0.327570	−	0.944827i
$3$	0.567369	−	1.63649i	0.327570	−	0.944827i
$4$	1.76989	−	0.931385i	0.884947	−	0.465692i
$5$	−0.132854	+	0.132854i	−0.0594139	+	0.0594139i	−0.736189	−	0.676776i	$-0.763377\pi$
$5$	−0.132854	+	0.132854i	−0.0594139	+	0.0594139i	0.676776	+	0.736189i	$0.263377\pi$
$6$	0.223871	−	2.43924i	0.0913949	−	0.995815i
$7$	−1.00000			−0.377964
$7$	−1.00000			−0.377964
$8$	2.11403	−	1.87907i	0.747421	−	0.664351i
$9$	−2.35619	−	1.85698i	−0.785395	−	0.618995i
$10$	−0.137336	+	0.227462i	−0.0434294	+	0.0719299i
$11$	−0.715349	−	0.715349i	−0.215686	−	0.215686i	0.590992	−	0.806678i	$-0.298737\pi$
$11$	−0.715349	−	0.715349i	−0.215686	−	0.215686i	−0.806678	+	0.590992i	$0.798737\pi$
$12$	−0.520017	−	3.42485i	−0.150116	−	0.988668i
$13$	0.206350	−	0.206350i	0.0572313	−	0.0572313i	−0.677912	−	0.735143i	$-0.737115\pi$
$13$	0.206350	−	0.206350i	0.0572313	−	0.0572313i	0.735143	+	0.677912i	$0.237115\pi$
$14$	−1.37293	+	0.339195i	−0.366932	+	0.0906537i
$15$	0.142036	+	0.292790i	0.0366736	+	0.0755981i
$16$	2.26505	−	3.29690i	0.566261	−	0.824226i
$17$			6.91999i			1.67834i	0.543866	+	0.839172i	$0.316960\pi$
$17$			6.91999i			1.67834i	−0.543866	+	0.839172i	$0.683040\pi$
$18$	−3.86477	−	1.75031i	−0.910934	−	0.412552i
$19$	5.87341	+	5.87341i	1.34745	+	1.34745i	0.888419	+	0.459034i	$0.151804\pi$
$19$	5.87341	+	5.87341i	1.34745	+	1.34745i	0.459034	+	0.888419i	$0.348196\pi$
$20$	−0.111399	+	0.358874i	−0.0249096	+	0.0802468i
$21$	−0.567369	+	1.63649i	−0.123810	+	0.357111i
$22$	−1.22477	−	0.739484i	−0.261122	−	0.157659i
$23$		−	6.42354i		−	1.33940i	−0.742631	−	0.669701i	$-0.766422\pi$
$23$		−	6.42354i		−	1.33940i	0.742631	−	0.669701i	$-0.233578\pi$
$24$	−1.87564	−	4.52570i	−0.382864	−	0.923805i
$25$			4.96470i			0.992940i
$26$	0.213312	−	0.353298i	0.0418340	−	0.0692875i
$27$	−4.37576	+	2.80227i	−0.842115	+	0.539298i
$28$	−1.76989	+	0.931385i	−0.334478	+	0.176015i
$29$	−5.00314	−	5.00314i	−0.929059	−	0.929059i	0.0685860	−	0.997645i	$-0.478151\pi$
$29$	−5.00314	−	5.00314i	−0.929059	−	0.929059i	−0.997645	+	0.0685860i	$0.978151\pi$
$30$	0.294319	+	0.353803i	0.0537351	+	0.0645954i
$31$		−	2.52929i		−	0.454275i	−0.973863	−	0.227137i	$-0.927063\pi$
$31$		−	2.52929i		−	0.454275i	0.973863	−	0.227137i	$-0.0729366\pi$
$32$	1.99146	−	5.29472i	0.352044	−	0.935983i
$33$	−1.57653	+	0.764794i	−0.274438	+	0.133133i
$34$	2.34723	+	9.50069i	0.402546	+	1.62935i
$35$	0.132854	−	0.132854i	0.0224563	−	0.0224563i
$36$	−5.89976	−	1.09215i	−0.983294	−	0.182025i
$37$	6.15279	+	6.15279i	1.01151	+	1.01151i	0.999933	+	0.0115789i	$0.00368575\pi$
$37$	6.15279	+	6.15279i	1.01151	+	1.01151i	0.0115789	+	0.999933i	$0.496314\pi$
$38$	10.0560	+	6.07157i	1.63130	+	0.984939i
$39$	−0.220613	−	0.454766i	−0.0353264	−	0.0728209i
$40$	−0.0312149	+	0.530497i	−0.00493551	+	0.0838789i
$41$	−5.19068			−0.810647			−0.405324	−	0.914173i	$-0.632841\pi$
$41$	−5.19068			−0.810647			−0.405324	+	0.914173i	$0.632841\pi$
$42$	−0.223871	+	2.43924i	−0.0345440	+	0.376383i
$43$	1.36769	−	1.36769i	0.208571	−	0.208571i	−0.595089	−	0.803660i	$-0.702883\pi$
$43$	1.36769	−	1.36769i	0.208571	−	0.208571i	0.803660	+	0.595089i	$0.202883\pi$
$44$	−1.93236	−	0.599827i	−0.291314	−	0.0904273i
$45$	0.559735	−	0.0663207i	0.0834403	−	0.00988651i
$46$	−2.17883	−	8.81910i	−0.321252	−	1.30030i
$47$	0.603632			0.0880487			0.0440244	−	0.999030i	$-0.485982\pi$
$47$	0.603632			0.0880487			0.0440244	+	0.999030i	$0.485982\pi$
$48$	−4.11023	−	5.57728i	−0.593260	−	0.805011i
$49$	1.00000			0.142857
$50$	1.68400	+	6.81620i	0.238154	+	0.963957i
$51$	11.3245	+	3.92619i	1.58574	+	0.549776i
$52$	0.173027	−	0.557409i	0.0239945	−	0.0772988i
$53$	−6.19471	+	6.19471i	−0.850909	+	0.850909i	−0.990245	−	0.139336i	$-0.955503\pi$
$53$	−6.19471	+	6.19471i	−0.850909	+	0.850909i	0.139336	+	0.990245i	$0.455503\pi$
$54$	−5.05711	+	5.33157i	−0.688185	+	0.725535i
$55$	0.190073			0.0256295
$56$	−2.11403	+	1.87907i	−0.282499	+	0.251101i
$57$	12.9442	−	6.27938i	1.71449	−	0.831724i
$58$	−8.56601	−	5.17194i	−1.12477	−	0.679108i
$59$	5.00050	+	5.00050i	0.651010	+	0.651010i	0.953236	−	0.302226i	$-0.0977298\pi$
$59$	5.00050	+	5.00050i	0.651010	+	0.651010i	−0.302226	+	0.953236i	$0.597730\pi$
$60$	0.524089	+	0.385917i	0.0676596	+	0.0498217i
$61$	−6.24649	+	6.24649i	−0.799781	+	0.799781i	−0.983061	−	0.183280i	$-0.941329\pi$
$61$	−6.24649	+	6.24649i	−0.799781	+	0.799781i	0.183280	+	0.983061i	$0.441329\pi$
$62$	−0.857924	−	3.47255i	−0.108956	−	0.441015i
$63$	2.35619	+	1.85698i	0.296851	+	0.233958i
$64$	0.938205	−	7.94480i	0.117276	−	0.993099i
$65$			0.0548287i			0.00680067i
$66$	−1.90505	+	1.58476i	−0.234496	+	0.195071i
$67$	2.55815	+	2.55815i	0.312527	+	0.312527i	0.845888	−	0.533361i	$-0.179071\pi$
$67$	2.55815	+	2.55815i	0.312527	+	0.312527i	−0.533361	+	0.845888i	$0.679071\pi$
$68$	6.44517	+	12.2476i	0.781592	+	1.48525i
$69$	−10.5120	−	3.64452i	−1.26550	−	0.438748i
$70$	0.137336	−	0.227462i	0.0164148	−	0.0271870i
$71$		−	0.808658i		−	0.0959700i	−0.998848	−	0.0479850i	$-0.984720\pi$
$71$		−	0.808658i		−	0.0959700i	0.998848	−	0.0479850i	$-0.0152800\pi$
$72$	−8.47044	+	0.501723i	−0.998250	+	0.0591286i
$73$		−	11.5367i		−	1.35027i	−0.737695	−	0.675134i	$-0.764086\pi$
$73$		−	11.5367i		−	1.35027i	0.737695	−	0.675134i	$-0.235914\pi$
$74$	10.5344	+	6.36037i	1.22459	+	0.739378i
$75$	8.12467	+	2.81682i	0.938156	+	0.325258i
$76$	15.8657	+	4.92491i	1.81992	+	0.564926i
$77$	0.715349	+	0.715349i	0.0815216	+	0.0815216i
$78$	−0.457142	−	0.549533i	−0.0517611	−	0.0622224i
$79$		−	3.48456i		−	0.392044i	−0.980600	−	0.196022i	$-0.937198\pi$
$79$		−	3.48456i		−	0.392044i	0.980600	−	0.196022i	$-0.0628024\pi$
$80$	0.137086	+	0.738925i	0.0153267	+	0.0826143i
$81$	2.10322	+	8.75080i	0.233691	+	0.972311i
$82$	−7.12645	+	1.76065i	−0.786985	+	0.194431i
$83$	−0.641645	+	0.641645i	−0.0704297	+	0.0704297i	−0.741444	−	0.671015i	$-0.765859\pi$
$83$	−0.641645	+	0.641645i	−0.0704297	+	0.0704297i	0.671015	+	0.741444i	$0.265859\pi$
$84$	0.520017	+	3.42485i	0.0567386	+	0.373682i
$85$	−0.919345	−	0.919345i	−0.0997170	−	0.0997170i
$86$	1.41384	−	2.34167i	0.152458	−	0.252509i
$87$	−11.0262	+	5.34895i	−1.18213	+	0.573468i
$88$	−2.85646	−	0.168076i	−0.304499	−	0.0179170i
$89$	−11.0057			−1.16661			−0.583303	−	0.812254i	$-0.698240\pi$
$89$	−11.0057			−1.16661			−0.583303	+	0.812254i	$0.698240\pi$
$90$	0.745983	−	0.280913i	0.0786335	−	0.0296108i
$91$	−0.206350	+	0.206350i	−0.0216314	+	0.0216314i
$92$	−5.98279	−	11.3690i	−0.623749	−	1.18530i
$93$	−4.13916	−	1.43504i	−0.429211	−	0.148807i
$94$	0.828746	−	0.204749i	0.0854786	−	0.0211182i
$95$	−1.56061			−0.160115
$96$	−7.53485	−	6.26307i	−0.769023	−	0.639222i
$97$	−5.56394			−0.564933			−0.282466	−	0.959277i	$-0.591153\pi$
$97$	−5.56394			−0.564933			−0.282466	+	0.959277i	$0.591153\pi$
$98$	1.37293	−	0.339195i	0.138687	−	0.0342639i
$99$	0.357104	+	3.01389i	0.0358903	+	0.302907i
$100$	4.62404	+	8.78699i	0.462404	+	0.878699i
$101$	7.49292	−	7.49292i	0.745574	−	0.745574i	−0.228071	−	0.973645i	$-0.573242\pi$
$101$	7.49292	−	7.49292i	0.745574	−	0.745574i	0.973645	+	0.228071i	$0.0732418\pi$
$102$	16.8795	+	1.54918i	1.67132	+	0.153392i
$103$	−0.568966			−0.0560619			−0.0280309	−	0.999607i	$-0.508924\pi$
$103$	−0.568966			−0.0560619			−0.0280309	+	0.999607i	$0.508924\pi$
$104$	0.0484834	−	0.823976i	0.00475419	−	0.0807975i
$105$	−0.142036	−	0.292790i	−0.0138613	−	0.0285734i
$106$	−6.40371	+	10.6061i	−0.621983	+	1.03016i
$107$	−5.79066	−	5.79066i	−0.559804	−	0.559804i	0.369447	−	0.929252i	$-0.379547\pi$
$107$	−5.79066	−	5.79066i	−0.559804	−	0.559804i	−0.929252	+	0.369447i	$0.879547\pi$
$108$	−5.13463	+	9.03524i	−0.494080	+	0.869416i
$109$	−5.70587	+	5.70587i	−0.546523	+	0.546523i	−0.925433	−	0.378910i	$-0.876299\pi$
$109$	−5.70587	+	5.70587i	−0.546523	+	0.546523i	0.378910	+	0.925433i	$0.376299\pi$
$110$	0.260958	−	0.0644719i	0.0248814	−	0.00614716i
$111$	13.5599	−	6.57806i	1.28704	−	0.624362i
$112$	−2.26505	+	3.29690i	−0.214027	+	0.311528i
$113$		−	5.81929i		−	0.547433i	−0.961810	−	0.273716i	$-0.911747\pi$
$113$		−	5.81929i		−	0.547433i	0.961810	−	0.273716i	$-0.0882530\pi$
$114$	15.6415	−	13.0118i	1.46496	−	1.21866i
$115$	0.853390	+	0.853390i	0.0795791	+	0.0795791i
$116$	−13.5149	−	4.19517i	−1.25482	−	0.389512i
$117$	−0.869389	+	0.103010i	−0.0803750	+	0.00952332i
$118$	8.56150	+	5.16921i	0.788150	+	0.475864i
$119$		−	6.91999i		−	0.634354i
$120$	0.850441	+	0.352070i	0.0776343	+	0.0321394i
$121$		−	9.97655i		−	0.906959i
$122$	−6.45724	+	10.6948i	−0.584611	+	0.968261i
$123$	−2.94503	+	8.49448i	−0.265544	+	0.765921i
$124$	−2.35574	−	4.47658i	−0.211552	−	0.402009i
$125$	−1.32385	−	1.32385i	−0.118408	−	0.118408i
$126$	3.86477	+	1.75031i	0.344301	+	0.155930i
$127$		−	15.2053i		−	1.34925i	−0.738160	−	0.674626i	$-0.764305\pi$
$127$		−	15.2053i		−	1.34925i	0.738160	−	0.674626i	$-0.235695\pi$
$128$	−1.40674	−	11.2259i	−0.124340	−	0.992240i
$129$	−1.46223	−	3.01420i	−0.128742	−	0.265386i
$130$	0.0185976	+	0.0752762i	0.00163112	+	0.00660216i
$131$	−7.26058	+	7.26058i	−0.634359	+	0.634359i	−0.949158	−	0.314799i	$-0.898063\pi$
$131$	−7.26058	+	7.26058i	−0.634359	+	0.634359i	0.314799	+	0.949158i	$0.398063\pi$
$132$	−2.07797	+	2.82196i	−0.180864	+	0.245620i
$133$	−5.87341	−	5.87341i	−0.509289	−	0.509289i
$134$	4.37988	+	2.64445i	0.378364	+	0.228446i
$135$	0.209043	−	0.953627i	0.0179915	−	0.0820752i
$136$	13.0031	+	14.6290i	1.11501	+	1.25443i
$137$	3.38132			0.288886			0.144443	−	0.989513i	$-0.453861\pi$
$137$	3.38132			0.288886			0.144443	+	0.989513i	$0.453861\pi$
$138$	−15.6685	−	1.43804i	−1.33380	−	0.122414i
$139$	6.15797	−	6.15797i	0.522312	−	0.522312i	−0.395957	−	0.918269i	$-0.629587\pi$
$139$	6.15797	−	6.15797i	0.522312	−	0.522312i	0.918269	+	0.395957i	$0.129587\pi$
$140$	0.111399	−	0.358874i	0.00941493	−	0.0303304i
$141$	0.342482	−	0.987836i	0.0288422	−	0.0831908i
$142$	−0.274293	−	1.11023i	−0.0230181	−	0.0931687i
$143$	−0.295225			−0.0246880
$144$	−11.4592	+	3.56196i	−0.954930	+	0.296830i
$145$	1.32937			0.110398
$146$	−3.91319	−	15.8391i	−0.323858	−	1.31085i
$147$	0.567369	−	1.63649i	0.0467958	−	0.134975i
$148$	16.6204	+	5.15917i	1.36619	+	0.424081i
$149$	−3.57067	+	3.57067i	−0.292520	+	0.292520i	−0.838075	−	0.545555i	$-0.816319\pi$
$149$	−3.57067	+	3.57067i	−0.292520	+	0.292520i	0.545555	+	0.838075i	$0.316319\pi$
$150$	12.1101	+	1.11145i	0.988784	+	0.0907497i
$151$	−2.30493			−0.187573			−0.0937864	−	0.995592i	$-0.529897\pi$
$151$	−2.30493			−0.187573			−0.0937864	+	0.995592i	$0.529897\pi$
$152$	23.4531	+	1.38000i	1.90230	+	0.111933i
$153$	12.8503	−	16.3048i	1.03889	−	1.31816i
$154$	1.22477	+	0.739484i	0.0986948	+	0.0595893i
$155$	0.336026	+	0.336026i	0.0269902	+	0.0269902i
$156$	−0.814024	−	0.599412i	−0.0651741	−	0.0479914i
$157$	−12.0921	+	12.0921i	−0.965054	+	0.965054i	−0.999410	−	0.0343560i	$-0.989062\pi$
$157$	−12.0921	+	12.0921i	−0.965054	+	0.965054i	0.0343560	+	0.999410i	$0.489062\pi$
$158$	−1.18195	−	4.78407i	−0.0940306	−	0.380600i
$159$	6.62288	+	13.6523i	0.525229	+	1.08269i
$160$	0.438849	+	0.967996i	0.0346941	+	0.0765268i
$161$			6.42354i			0.506246i
$162$	5.85581	+	11.3009i	0.460076	+	0.887880i
$163$	−1.08738	−	1.08738i	−0.0851704	−	0.0851704i	0.663238	−	0.748408i	$-0.269182\pi$
$163$	−1.08738	−	1.08738i	−0.0851704	−	0.0851704i	−0.748408	+	0.663238i	$0.769182\pi$
$164$	−9.18694	+	4.83452i	−0.717380	+	0.377512i
$165$	0.107842	−	0.311053i	0.00839546	−	0.0242154i
$166$	−0.663293	+	1.09858i	−0.0514815	+	0.0852662i
$167$		−	20.3703i		−	1.57630i	−0.615484	−	0.788149i	$-0.711039\pi$
$167$		−	20.3703i		−	1.57630i	0.615484	−	0.788149i	$-0.288961\pi$
$168$	1.87564	+	4.52570i	0.144709	+	0.349165i
$169$			12.9148i			0.993449i
$170$	−1.57404	−	0.950363i	−0.120723	−	0.0728895i
$171$	−2.93202	−	24.7457i	−0.224217	−	1.89235i
$172$	1.14682	−	3.69452i	0.0874445	−	0.281705i
$173$	−2.77906	−	2.77906i	−0.211288	−	0.211288i	0.593527	−	0.804814i	$-0.297735\pi$
$173$	−2.77906	−	2.77906i	−0.211288	−	0.211288i	−0.804814	+	0.593527i	$0.797735\pi$
$174$	−13.3239	+	11.0838i	−1.01008	+	0.840260i
$175$		−	4.96470i		−	0.375296i
$176$	−3.97874	+	0.738138i	−0.299908	+	0.0556393i
$177$	11.0204	−	5.34613i	0.828343	−	0.401840i
$178$	−15.1102	+	3.73309i	−1.13255	+	0.279807i
$179$	−8.23312	+	8.23312i	−0.615372	+	0.615372i	−0.944341	−	0.328969i	$-0.893299\pi$
$179$	−8.23312	+	8.23312i	−0.615372	+	0.615372i	0.328969	+	0.944341i	$0.393299\pi$
$180$	0.928900	−	0.638709i	0.0692362	−	0.0476065i
$181$	4.91780	+	4.91780i	0.365537	+	0.365537i	0.865847	−	0.500310i	$-0.166780\pi$
$181$	4.91780	+	4.91780i	0.365537	+	0.365537i	−0.500310	+	0.865847i	$0.666780\pi$
$182$	−0.213312	+	0.353298i	−0.0158118	+	0.0261882i
$183$	6.67824	+	13.7664i	0.493670	+	1.01764i
$184$	−12.0703	−	13.5795i	−0.889832	−	1.00110i
$185$	−1.63484			−0.120196
$186$	−6.16955	−	0.566235i	−0.452373	−	0.0415184i
$187$	4.95021	−	4.95021i	0.361995	−	0.361995i
$188$	1.06836	−	0.562213i	0.0779184	−	0.0410036i
$189$	4.37576	−	2.80227i	0.318290	−	0.203836i
$190$	−2.14261	+	0.529350i	−0.155441	+	0.0384031i
$191$	18.9768			1.37312			0.686558	−	0.727075i	$-0.259121\pi$
$191$	18.9768			1.37312			0.686558	+	0.727075i	$0.259121\pi$
$192$	−12.4693	−	6.04299i	−0.899891	−	0.436115i
$193$	25.6525			1.84651			0.923254	−	0.384191i	$-0.125519\pi$
$193$	25.6525			1.84651			0.923254	+	0.384191i	$0.125519\pi$
$194$	−7.63893	+	1.88726i	−0.548443	+	0.135498i
$195$	0.0897266	+	0.0311081i	0.00642545	+	0.00222770i
$196$	1.76989	−	0.931385i	0.126421	−	0.0665275i
$197$	16.3956	−	16.3956i	1.16814	−	1.16814i	0.185494	−	0.982645i	$-0.440611\pi$
$197$	16.3956	−	16.3956i	1.16814	−	1.16814i	0.982645	−	0.185494i	$-0.0593886\pi$
$198$	1.51258	+	4.01674i	0.107494	+	0.285457i
$199$	−25.9930			−1.84260			−0.921298	−	0.388857i	$-0.872870\pi$
$199$	−25.9930			−1.84260			−0.921298	+	0.388857i	$0.872870\pi$
$200$	9.32901	+	10.4955i	0.659661	+	0.742144i
$201$	5.63779	−	2.73496i	0.397659	−	0.192909i
$202$	7.74572	−	12.8288i	0.544987	−	0.902635i
$203$	5.00314	+	5.00314i	0.351151	+	0.351151i
$204$	23.6999	−	3.59852i	1.65933	−	0.251946i
$205$	0.689600	−	0.689600i	0.0481637	−	0.0481637i
$206$	−0.781152	+	0.192990i	−0.0544254	+	0.0134463i
$207$	−11.9284	+	15.1351i	−0.829082	+	1.05196i
$208$	−0.212924	−	1.14771i	−0.0147636	−	0.0795793i
$209$		−	8.40308i		−	0.581253i
$210$	−0.294319	−	0.353803i	−0.0203100	−	0.0244148i
$211$	−13.6935	−	13.6935i	−0.942699	−	0.942699i	0.0557463	−	0.998445i	$-0.482246\pi$
$211$	−13.6935	−	13.6935i	−0.942699	−	0.942699i	−0.998445	+	0.0557463i	$0.982246\pi$
$212$	−5.19432	+	16.7336i	−0.356747	+	1.14927i
$213$	−1.32336	−	0.458807i	−0.0906750	−	0.0314369i
$214$	−9.91435	−	5.98603i	−0.677731	−	0.409196i
$215$			0.363406i			0.0247841i
$216$	−3.98480	+	14.1464i	−0.271131	+	0.962542i
$217$			2.52929i			0.171700i
$218$	−5.89837	+	9.76918i	−0.399488	+	0.661652i
$219$	−18.8797	−	6.54556i	−1.27577	−	0.442308i
$220$	0.336410	−	0.177031i	0.0226807	−	0.0119355i
$221$	1.42794	+	1.42794i	0.0960537	+	0.0960537i
$222$	16.3855	−	13.6307i	1.09973	−	0.914831i
$223$		−	11.6521i		−	0.780280i	−0.920756	−	0.390140i	$-0.872427\pi$
$223$		−	11.6521i		−	0.780280i	0.920756	−	0.390140i	$-0.127573\pi$
$224$	−1.99146	+	5.29472i	−0.133060	+	0.353768i
$225$	9.21937	−	11.6978i	0.614625	−	0.779850i
$226$	−1.97388	−	7.98950i	−0.131300	−	0.531454i
$227$	−0.211018	+	0.211018i	−0.0140058	+	0.0140058i	−0.714075	−	0.700069i	$-0.753152\pi$
$227$	−0.211018	+	0.211018i	−0.0140058	+	0.0140058i	0.700069	+	0.714075i	$0.253152\pi$
$228$	17.0613	−	23.1698i	1.12991	−	1.53446i
$229$	−11.7698	−	11.7698i	−0.777772	−	0.777772i	0.201680	−	0.979452i	$-0.435360\pi$
$229$	−11.7698	−	11.7698i	−0.777772	−	0.777772i	−0.979452	+	0.201680i	$0.935360\pi$
$230$	1.46111	+	0.882183i	0.0963430	+	0.0581694i
$231$	1.57653	−	0.764794i	0.103728	−	0.0503197i
$232$	−19.9780	−	1.17552i	−1.31162	−	0.0771768i
$233$	−6.24518			−0.409135			−0.204568	−	0.978852i	$-0.565579\pi$
$233$	−6.24518			−0.409135			−0.204568	+	0.978852i	$0.565579\pi$
$234$	−1.15867	+	0.436319i	−0.0757448	+	0.0285230i
$235$	−0.0801946	+	0.0801946i	−0.00523132	+	0.00523132i
$236$	13.5077	+	4.19297i	0.879279	+	0.272939i
$237$	−5.70245	−	1.97703i	−0.370414	−	0.128422i
$238$	−2.34723	−	9.50069i	−0.152148	−	0.615838i
$239$	−25.8455			−1.67180			−0.835902	−	0.548878i	$-0.815055\pi$
$239$	−25.8455			−1.67180			−0.835902	+	0.548878i	$0.815055\pi$
$240$	1.28702	+	0.194903i	0.0830768	+	0.0125810i
$241$	18.9857			1.22298			0.611488	−	0.791254i	$-0.290571\pi$
$241$	18.9857			1.22298			0.611488	+	0.791254i	$0.290571\pi$
$242$	−3.38400	−	13.6971i	−0.217532	−	0.880486i
$243$	15.5139	+	1.52303i	0.995216	+	0.0977025i
$244$	−5.23774	+	16.8735i	−0.335312	+	1.08022i
$245$	−0.132854	+	0.132854i	−0.00848770	+	0.00848770i
$246$	−1.16204	+	12.6613i	−0.0740891	+	0.807255i
$247$	2.42396			0.154233
$248$	−4.75272	−	5.34699i	−0.301798	−	0.339534i
$249$	0.685995	+	1.41409i	0.0434732	+	0.0896145i
$250$	−2.26659	−	1.36851i	−0.143352	−	0.0865522i
$251$	10.5737	+	10.5737i	0.667407	+	0.667407i	0.957115	−	0.289708i	$-0.0935582\pi$
$251$	10.5737	+	10.5737i	0.667407	+	0.667407i	−0.289708	+	0.957115i	$0.593558\pi$
$252$	5.89976	+	1.09215i	0.371650	+	0.0687989i
$253$	−4.59508	+	4.59508i	−0.288890	+	0.288890i
$254$	−5.15756	−	20.8759i	−0.323614	−	1.30987i
$255$	−2.02611	+	0.982890i	−0.126880	+	0.0615509i
$256$	−5.73914	−	14.9353i	−0.358696	−	0.933454i
$257$			4.31950i			0.269443i	0.990884	+	0.134722i	$0.0430140\pi$
$257$			4.31950i			0.269443i	−0.990884	+	0.134722i	$0.956986\pi$
$258$	−3.02995	−	3.64232i	−0.188636	−	0.226761i
$259$	−6.15279	−	6.15279i	−0.382316	−	0.382316i
$260$	0.0510666	+	0.0970410i	0.00316702	+	0.00601823i
$261$	2.49757	+	21.0791i	0.154596	+	1.30476i
$262$	−7.50554	+	12.4310i	−0.463694	+	0.767992i
$263$		−	11.9657i		−	0.737837i	−0.929462	−	0.368918i	$-0.879728\pi$
$263$		−	11.9657i		−	0.737837i	0.929462	−	0.368918i	$-0.120272\pi$
$264$	−1.89572	+	4.57919i	−0.116673	+	0.281830i
$265$		−	1.64598i		−	0.101112i
$266$	−10.0560	−	6.07157i	−0.616575	−	0.372272i
$267$	−6.24431	+	18.0108i	−0.382146	+	1.10224i
$268$	6.91026	+	2.14503i	0.422112	+	0.131028i
$269$	19.4957	+	19.4957i	1.18867	+	1.18867i	0.977435	+	0.211236i	$0.0677488\pi$
$269$	19.4957	+	19.4957i	1.18867	+	1.18867i	0.211236	+	0.977435i	$0.432251\pi$
$270$	−0.0364637	−	1.38017i	−0.00221911	−	0.0839947i
$271$			4.80008i			0.291584i	0.989315	+	0.145792i	$0.0465730\pi$
$271$			4.80008i			0.291584i	−0.989315	+	0.145792i	$0.953427\pi$
$272$	22.8145	+	15.6741i	1.38333	+	0.950381i
$273$	0.220613	+	0.454766i	0.0133521	+	0.0275237i
$274$	4.64233	−	1.14693i	0.280453	−	0.0692884i
$275$	3.55149	−	3.55149i	0.214163	−	0.214163i
$276$	−21.9997	+	3.34035i	−1.32422	+	0.201066i
$277$	16.1975	+	16.1975i	0.973214	+	0.973214i	0.999650	−	0.0264369i	$-0.00841612\pi$
$277$	16.1975	+	16.1975i	0.973214	+	0.973214i	−0.0264369	+	0.999650i	$0.508416\pi$
$278$	6.36573	−	10.5432i	0.381791	−	0.632341i
$279$	−4.69686	+	5.95949i	−0.281194	+	0.356785i
$280$	0.0312149	−	0.530497i	0.00186545	−	0.0317032i
$281$	16.3201			0.973575			0.486787	−	0.873520i	$-0.338169\pi$
$281$	16.3201			0.973575			0.486787	+	0.873520i	$0.338169\pi$
$282$	0.135136	−	1.47240i	0.00804720	−	0.0876802i
$283$	16.3557	−	16.3557i	0.972244	−	0.972244i	−0.0273808	−	0.999625i	$-0.508717\pi$
$283$	16.3557	−	16.3557i	0.972244	−	0.972244i	0.999625	+	0.0273808i	$0.00871666\pi$
$284$	−0.753171	−	1.43124i	−0.0446925	−	0.0849283i
$285$	−0.885439	+	2.55391i	−0.0524489	+	0.151281i
$286$	−0.405324	+	0.100139i	−0.0239673	+	0.00592133i
$287$	5.19068			0.306396
$288$	−14.5245	+	8.77723i	−0.855863	+	0.517203i
$289$	−30.8863			−1.81684
$290$	1.82514	−	0.450915i	0.107176	−	0.0264787i
$291$	−3.15681	+	9.10533i	−0.185055	+	0.533764i
$292$	−10.7451	−	20.4187i	−0.628809	−	1.19492i
$293$	−4.80343	+	4.80343i	−0.280620	+	0.280620i	−0.833356	−	0.552736i	$-0.813584\pi$
$293$	−4.80343	+	4.80343i	−0.280620	+	0.280620i	0.552736	+	0.833356i	$0.313584\pi$
$294$	0.223871	−	2.43924i	0.0130564	−	0.142259i
$295$	−1.32867			−0.0773581
$296$	24.5687	+	1.44564i	1.42802	+	0.0840261i
$297$	5.13480	+	1.12559i	0.297951	+	0.0653133i
$298$	−3.69114	+	6.11344i	−0.213822	+	0.354142i
$299$	−1.32550	−	1.32550i	−0.0766556	−	0.0766556i
$300$	17.0033	−	2.58173i	0.981688	−	0.149056i
$301$	−1.36769	+	1.36769i	−0.0788326	+	0.0788326i
$302$	−3.16452	+	0.781822i	−0.182098	+	0.0449888i
$303$	−8.01083	−	16.5133i	−0.460210	−	0.948666i
$304$	32.6676	−	6.06052i	1.87362	−	0.347595i
$305$		−	1.65974i		−	0.0950362i
$306$	12.1121	−	26.7441i	0.692404	−	1.52886i
$307$	2.57337	+	2.57337i	0.146870	+	0.146870i	0.776718	−	0.629848i	$-0.216883\pi$
$307$	2.57337	+	2.57337i	0.146870	+	0.146870i	−0.629848	+	0.776718i	$0.716883\pi$
$308$	1.93236	+	0.599827i	0.110106	+	0.0341783i
$309$	−0.322813	+	0.931105i	−0.0183642	+	0.0529687i
$310$	0.575319	+	0.347363i	0.0326759	+	0.0197289i
$311$			16.8194i			0.953741i	0.878973	+	0.476871i	$0.158229\pi$
$311$			16.8194i			0.953741i	−0.878973	+	0.476871i	$0.841771\pi$
$312$	−1.32092	−	0.546841i	−0.0747823	−	0.0309588i
$313$			3.09458i			0.174916i	0.996168	+	0.0874581i	$0.0278744\pi$
$313$			3.09458i			0.174916i	−0.996168	+	0.0874581i	$0.972126\pi$
$314$	−12.5001	+	20.7032i	−0.705419	+	1.16835i
$315$	−0.559735	+	0.0663207i	−0.0315375	+	0.00373675i
$316$	−3.24547	−	6.16731i	−0.182572	−	0.346938i
$317$	11.7725	+	11.7725i	0.661211	+	0.661211i	0.955665	−	0.294455i	$-0.0951380\pi$
$317$	11.7725	+	11.7725i	0.661211	+	0.661211i	−0.294455	+	0.955665i	$0.595138\pi$
$318$	13.7236	+	16.4972i	0.769579	+	0.925116i
$319$			7.15798i			0.400770i
$320$	0.930850	+	1.18014i	0.0520361	+	0.0659717i
$321$	−12.7618	+	6.19091i	−0.712293	+	0.345543i
$322$	2.17883	+	8.81910i	0.121422	+	0.491469i
$323$	−40.6439	+	40.6439i	−2.26149	+	2.26149i
$324$	11.8728	+	13.5291i	0.659602	+	0.751615i
$325$	1.02447	+	1.02447i	0.0568272	+	0.0568272i
$326$	−1.86174	−	1.12407i	−0.103112	−	0.0622565i
$327$	6.10025	+	12.5749i	0.337345	+	0.695394i
$328$	−10.9732	+	9.75363i	−0.605895	+	0.538554i
$329$	−0.603632			−0.0332793
$330$	0.0425519	−	0.463634i	0.00234240	−	0.0255222i
$331$	−14.8912	+	14.8912i	−0.818493	+	0.818493i	−0.985890	−	0.167397i	$-0.946464\pi$
$331$	−14.8912	+	14.8912i	−0.818493	+	0.818493i	0.167397	+	0.985890i	$0.446464\pi$
$332$	−0.538025	+	1.73326i	−0.0295279	+	0.0951250i
$333$	−3.07148	−	25.9227i	−0.168316	−	1.42056i
$334$	−6.90949	−	27.9670i	−0.378071	−	1.53029i
$335$	−0.679718			−0.0371369
$336$	4.11023	+	5.57728i	0.224231	+	0.304266i
$337$	−18.3243			−0.998187			−0.499093	−	0.866548i	$-0.666334\pi$
$337$	−18.3243			−0.998187			−0.499093	+	0.866548i	$0.666334\pi$
$338$	4.38065	+	17.7312i	0.238276	+	0.964451i
$339$	−9.52320	−	3.30168i	−0.517229	−	0.179323i
$340$	−2.48341	−	0.770879i	−0.134682	−	0.0418068i
$341$	−1.80933	+	1.80933i	−0.0979806	+	0.0979806i
$342$	−12.4191	−	32.9796i	−0.671547	−	1.78333i
$343$	−1.00000			−0.0539949
$344$	0.321349	−	5.46133i	0.0173260	−	0.294455i
$345$	1.88075	−	0.912376i	0.101256	−	0.0491207i
$346$	−4.75810	−	2.87282i	−0.255797	−	0.154444i
$347$	14.0124	+	14.0124i	0.752224	+	0.752224i	0.974894	−	0.222670i	$-0.0714773\pi$
$347$	14.0124	+	14.0124i	0.752224	+	0.752224i	−0.222670	+	0.974894i	$0.571477\pi$
$348$	−14.5333	+	19.7367i	−0.779065	+	1.05800i
$349$	5.78830	−	5.78830i	0.309841	−	0.309841i	−0.535007	−	0.844848i	$-0.679691\pi$
$349$	5.78830	−	5.78830i	0.309841	−	0.309841i	0.844848	+	0.535007i	$0.179691\pi$
$350$	−1.68400	−	6.81620i	−0.0900137	−	0.364341i
$351$	−0.324689	+	1.48119i	−0.0173306	+	0.0790600i
$352$	−5.21217	+	2.36298i	−0.277809	+	0.125947i
$353$		−	13.9096i		−	0.740334i	−0.928965	−	0.370167i	$-0.879300\pi$
$353$		−	13.9096i		−	0.740334i	0.928965	−	0.370167i	$-0.120700\pi$
$354$	13.3169	−	11.0779i	0.707784	−	0.588786i
$355$	0.107433	+	0.107433i	0.00570195	+	0.00570195i
$356$	−19.4790	+	10.2506i	−1.03238	+	0.543280i
$357$	−11.3245	−	3.92619i	−0.599355	−	0.207796i
$358$	−8.51089	+	14.0962i	−0.449815	+	0.745005i
$359$			20.7206i			1.09359i	0.837266	+	0.546796i	$0.184153\pi$
$359$			20.7206i			1.09359i	−0.837266	+	0.546796i	$0.815847\pi$
$360$	1.05867	−	1.19198i	0.0557969	−	0.0628230i
$361$			49.9939i			2.63126i
$362$	8.41990	+	5.08372i	0.442540	+	0.267194i
$363$	−16.3265	−	5.66038i	−0.856919	−	0.297093i
$364$	−0.173027	+	0.557409i	−0.00906905	+	0.0292162i
$365$	1.53269	+	1.53269i	0.0802247	+	0.0802247i
$366$	13.8383	+	16.6351i	0.723338	+	0.869530i
$367$			14.8824i			0.776856i	0.921479	+	0.388428i	$0.126982\pi$
$367$			14.8824i			0.776856i	−0.921479	+	0.388428i	$0.873018\pi$
$368$	−21.1778	−	14.5496i	−1.10397	−	0.758451i
$369$	12.2302	+	9.63900i	0.636679	+	0.501786i
$370$	−2.24453	+	0.554529i	−0.116687	+	0.0288286i
$371$	6.19471	−	6.19471i	0.321613	−	0.321613i
$372$	−8.66245	+	1.31528i	−0.449127	+	0.0681939i
$373$	10.6598	+	10.6598i	0.551942	+	0.551942i	0.927001	−	0.375059i	$-0.122377\pi$
$373$	10.6598	+	10.6598i	0.551942	+	0.551942i	−0.375059	+	0.927001i	$0.622377\pi$
$374$	5.11722	−	8.47539i	0.264605	−	0.438252i
$375$	−2.91757	+	1.41535i	−0.150662	+	0.0730883i
$376$	1.27609	−	1.13426i	0.0658094	−	0.0584952i
$377$	−2.06480			−0.106342
$378$	5.05711	−	5.33157i	0.260110	−	0.274227i
$379$	−5.54417	+	5.54417i	−0.284785	+	0.284785i	−0.835014	−	0.550229i	$-0.814540\pi$
$379$	−5.54417	+	5.54417i	−0.284785	+	0.284785i	0.550229	+	0.835014i	$0.314540\pi$
$380$	−2.76211	+	1.45353i	−0.141693	+	0.0745643i
$381$	−24.8833	−	8.62701i	−1.27481	−	0.441975i
$382$	26.0539	−	6.43685i	1.33304	−	0.329338i
$383$	−10.0142			−0.511702			−0.255851	−	0.966716i	$-0.582356\pi$
$383$	−10.0142			−0.511702			−0.255851	+	0.966716i	$0.582356\pi$
$384$	−19.1692	−	4.06711i	−0.978225	−	0.207549i
$385$	−0.190073			−0.00968704
$386$	35.2192	−	8.70120i	1.79261	−	0.442879i
$387$	−5.76233	+	0.682756i	−0.292916	+	0.0347064i
$388$	−9.84759	+	5.18217i	−0.499936	+	0.263085i
$389$	18.2249	−	18.2249i	0.924041	−	0.924041i	−0.0732708	−	0.997312i	$-0.523344\pi$
$389$	18.2249	−	18.2249i	0.924041	−	0.924041i	0.997312	+	0.0732708i	$0.0233438\pi$
$390$	0.133740	+	0.0122746i	0.00677220	+	0.000621546i
$391$	44.4508			2.24798
$392$	2.11403	−	1.87907i	0.106774	−	0.0949073i
$393$	7.76242	+	16.0013i	0.391562	+	0.807157i
$394$	16.9488	−	28.0714i	0.853868	−	1.41422i
$395$	0.462937	+	0.462937i	0.0232929	+	0.0232929i
$396$	3.43912	+	5.00166i	0.172822	+	0.251343i
$397$	3.09916	−	3.09916i	0.155542	−	0.155542i	−0.625046	−	0.780588i	$-0.714920\pi$
$397$	3.09916	−	3.09916i	0.155542	−	0.155542i	0.780588	+	0.625046i	$0.214920\pi$
$398$	−35.6867	+	8.81670i	−1.78881	+	0.441941i
$399$	−12.9442	+	6.27938i	−0.648018	+	0.314362i
$400$	16.3681	+	11.2453i	0.818407	+	0.562264i
$401$			19.8682i			0.992169i	0.868274	+	0.496084i	$0.165229\pi$
$401$			19.8682i			0.992169i	−0.868274	+	0.496084i	$0.834771\pi$
$402$	6.81262	−	5.66723i	0.339783	−	0.282656i
$403$	−0.521920	−	0.521920i	−0.0259987	−	0.0259987i
$404$	6.28288	−	20.2405i	0.312585	−	1.00700i
$405$	−1.44200	−	0.883154i	−0.0716533	−	0.0438843i
$406$	8.56601	+	5.17194i	0.425124	+	0.256679i
$407$		−	8.80278i		−	0.436338i
$408$	31.3178	−	12.9794i	1.55046	−	0.642577i
$409$			4.49996i			0.222509i	0.993792	+	0.111254i	$0.0354868\pi$
$409$			4.49996i			0.222509i	−0.993792	+	0.111254i	$0.964513\pi$
$410$	0.712866	−	1.18068i	0.0352059	−	0.0583098i
$411$	1.91845	−	5.53349i	0.0946304	−	0.272947i
$412$	−1.00701	+	0.529926i	−0.0496118	+	0.0261076i
$413$	−5.00050	−	5.00050i	−0.246059	−	0.246059i
$414$	−11.2432	+	24.8255i	−0.552572	+	1.22011i
$415$		−	0.170490i		−	0.00836900i
$416$	−0.681628	−	1.50351i	−0.0334196	−	0.0737155i
$417$	−6.58360	−	13.5713i	−0.322400	−	0.664588i
$418$	−2.85028	−	11.5369i	−0.139412	−	0.564287i
$419$	21.9984	−	21.9984i	1.07469	−	1.07469i	0.0777158	−	0.996976i	$-0.475237\pi$
$419$	21.9984	−	21.9984i	1.07469	−	1.07469i	0.996976	−	0.0777158i	$-0.0247627\pi$
$420$	−0.524089	−	0.385917i	−0.0255729	−	0.0188308i
$421$	10.9884	+	10.9884i	0.535542	+	0.535542i	0.922216	−	0.386674i	$-0.126376\pi$
$421$	10.9884	+	10.9884i	0.535542	+	0.535542i	−0.386674	+	0.922216i	$0.626376\pi$
$422$	−23.4450	−	14.1555i	−1.14129	−	0.689078i
$423$	−1.42227	−	1.12093i	−0.0691530	−	0.0545017i
$424$	−1.45549	+	24.7361i	−0.0706849	+	1.20129i
$425$	−34.3557			−1.66649
$426$	−1.97251	−	0.181035i	−0.0955683	−	0.00877117i
$427$	6.24649	−	6.24649i	0.302289	−	0.302289i
$428$	−15.6422	−	4.85552i	−0.756093	−	0.234700i
$429$	−0.167501	+	0.483132i	−0.00808704	+	0.0233258i
$430$	0.123266	+	0.498933i	0.00594439	+	0.0240607i
$431$	−14.4548			−0.696262			−0.348131	−	0.937446i	$-0.613184\pi$
$431$	−14.4548			−0.696262			−0.348131	+	0.937446i	$0.613184\pi$
$432$	−0.672463	+	20.7737i	−0.0323539	+	0.999476i
$433$	6.38419			0.306805			0.153402	−	0.988164i	$-0.450977\pi$
$433$	6.38419			0.306805			0.153402	+	0.988164i	$0.450977\pi$
$434$	0.857924	+	3.47255i	0.0411817	+	0.166688i
$435$	0.754242	−	2.17550i	0.0361632	−	0.104307i
$436$	−4.78442	+	15.4131i	−0.229132	+	0.738155i
$437$	37.7281	−	37.7281i	1.80478	−	1.80478i
$438$	−28.1407	−	2.58273i	−1.34462	−	0.123408i
$439$	−21.1960			−1.01163			−0.505816	−	0.862642i	$-0.668808\pi$
$439$	−21.1960			−1.01163			−0.505816	+	0.862642i	$0.668808\pi$
$440$	0.401820	−	0.357161i	0.0191560	−	0.0170270i
$441$	−2.35619	−	1.85698i	−0.112199	−	0.0884278i
$442$	2.44482	+	1.47612i	0.116288	+	0.0702118i
$443$	13.9575	+	13.9575i	0.663141	+	0.663141i	0.956119	−	0.292978i	$-0.0946463\pi$
$443$	13.9575	+	13.9575i	0.663141	+	0.663141i	−0.292978	+	0.956119i	$0.594646\pi$
$444$	17.8728	−	24.2719i	0.848206	−	1.15189i
$445$	1.46215	−	1.46215i	0.0693127	−	0.0693127i
$446$	−3.95232	−	15.9975i	−0.187148	−	0.757504i
$447$	3.81747	+	7.86924i	0.180560	+	0.372202i
$448$	−0.938205	+	7.94480i	−0.0443260	+	0.375356i
$449$		−	14.1807i		−	0.669228i	−0.942355	−	0.334614i	$-0.891394\pi$
$449$		−	14.1807i		−	0.669228i	0.942355	−	0.334614i	$-0.108606\pi$
$450$	8.68976	−	19.1874i	0.409639	−	0.904503i
$451$	3.71315	+	3.71315i	0.174845	+	0.174845i
$452$	−5.42000	−	10.2995i	−0.254935	−	0.484449i
$453$	−1.30775	+	3.77200i	−0.0614433	+	0.177224i
$454$	−0.218137	+	0.361290i	−0.0102377	+	0.0169562i
$455$		−	0.0548287i		−	0.00257041i
$456$	15.5649	−	37.5977i	0.728893	−	1.76067i
$457$		−	37.3522i		−	1.74726i	−0.486590	−	0.873630i	$-0.661759\pi$
$457$		−	37.3522i		−	1.74726i	0.486590	−	0.873630i	$-0.338241\pi$
$458$	−20.1515	−	12.1669i	−0.941615	−	0.568523i
$459$	−19.3917	−	30.2802i	−0.905128	−	1.41336i
$460$	2.30524	+	0.715576i	0.107483	+	0.0333639i
$461$	10.5304	+	10.5304i	0.490449	+	0.490449i	0.908448	−	0.417999i	$-0.137268\pi$
$461$	10.5304	+	10.5304i	0.490449	+	0.490449i	−0.417999	+	0.908448i	$0.637268\pi$
$462$	1.90505	−	1.58476i	0.0886311	−	0.0737298i
$463$		−	26.2737i		−	1.22104i	−0.792000	−	0.610521i	$-0.790960\pi$
$463$		−	26.2737i		−	1.22104i	0.792000	−	0.610521i	$-0.209040\pi$
$464$	−27.8272	+	5.16252i	−1.29184	+	0.239664i
$465$	0.740552	−	0.359252i	0.0343423	−	0.0166599i
$466$	−8.57422	+	2.11833i	−0.397193	+	0.0981299i
$467$	20.6885	−	20.6885i	0.957349	−	0.957349i	−0.0417774	−	0.999127i	$-0.513302\pi$
$467$	20.6885	−	20.6885i	0.957349	−	0.957349i	0.999127	+	0.0417774i	$0.0133020\pi$
$468$	−1.44278	+	0.992053i	−0.0666927	+	0.0458576i
$469$	−2.55815	−	2.55815i	−0.118124	−	0.118124i
$470$	−0.0829003	+	0.137303i	−0.00382390	+	0.00633334i
$471$	12.9279	+	26.6492i	0.595685	+	1.22793i
$472$	19.9675	+	1.17490i	0.919077	+	0.0540793i
$473$	−1.95676			−0.0899719
$474$	−8.49968	−	0.780092i	−0.390403	−	0.0358308i
$475$	−29.1597	+	29.1597i	−1.33794	+	1.33794i
$476$	−6.44517	−	12.2476i	−0.295414	−	0.561370i
$477$	26.0994	−	3.09241i	1.19501	−	0.141592i
$478$	−35.4841	+	8.76666i	−1.62301	+	0.400978i
$479$	−18.5260			−0.846476			−0.423238	−	0.906018i	$-0.639107\pi$
$479$	−18.5260			−0.846476			−0.423238	+	0.906018i	$0.639107\pi$
$480$	1.83310	−	0.168961i	0.0836693	−	0.00771199i
$481$	2.53926			0.115780
$482$	26.0661	−	6.43985i	1.18728	−	0.293327i
$483$	10.5120	+	3.64452i	0.478315	+	0.165831i
$484$	−9.29201	−	17.6574i	−0.422364	−	0.802611i
$485$	0.739190	−	0.739190i	0.0335649	−	0.0335649i
$486$	21.8161	−	3.17121i	0.989600	−	0.143849i
$487$	36.6140			1.65914			0.829570	−	0.558403i	$-0.188586\pi$
$487$	36.6140			1.65914			0.829570	+	0.558403i	$0.188586\pi$
$488$	−1.46766	+	24.9428i	−0.0664377	+	1.12911i
$489$	−2.39644	+	1.16254i	−0.108371	+	0.0525720i
$490$	−0.137336	+	0.227462i	−0.00620420	+	0.0102757i
$491$	−2.64760	−	2.64760i	−0.119485	−	0.119485i	0.644836	−	0.764321i	$-0.276926\pi$
$491$	−2.64760	−	2.64760i	−0.119485	−	0.119485i	−0.764321	+	0.644836i	$0.776926\pi$
$492$	2.69924	+	17.7773i	0.121691	+	0.801461i
$493$	34.6217	−	34.6217i	1.55928	−	1.55928i
$494$	3.32794	−	0.822195i	0.149731	−	0.0369923i
$495$	−0.447848	−	0.352963i	−0.0201293	−	0.0158645i
$496$	−8.33884	−	5.72897i	−0.374425	−	0.257238i
$497$			0.808658i			0.0362733i
$498$	1.42148	+	1.70877i	0.0636980	+	0.0765718i
$499$	15.3614	+	15.3614i	0.687671	+	0.687671i	0.961717	−	0.274045i	$-0.0883619\pi$
$499$	15.3614	+	15.3614i	0.687671	+	0.687671i	−0.274045	+	0.961717i	$0.588362\pi$
$500$	−3.57608	−	1.11006i	−0.159927	−	0.0496432i
$501$	−33.3357	−	11.5575i	−1.48933	−	0.516349i
$502$	18.1036	+	10.9305i	0.808002	+	0.487850i
$503$			19.8445i			0.884824i	0.896812	+	0.442412i	$0.145877\pi$
$503$			19.8445i			0.884824i	−0.896812	+	0.442412i	$0.854123\pi$
$504$	8.47044	−	0.501723i	0.377303	−	0.0223485i
$505$			1.99092i			0.0885949i
$506$	−4.75011	+	7.86736i	−0.211168	+	0.349747i
$507$	21.1350	+	7.32747i	0.938637	+	0.325425i
$508$	−14.1620	−	26.9118i	−0.628336	−	1.19402i
$509$	−18.7709	−	18.7709i	−0.832006	−	0.832006i	0.155785	−	0.987791i	$-0.450209\pi$
$509$	−18.7709	−	18.7709i	−0.832006	−	0.832006i	−0.987791	+	0.155785i	$0.950209\pi$
$510$	−2.44832	+	2.03669i	−0.108413	+	0.0901860i
$511$			11.5367i			0.510353i
$512$	−12.9454	−	18.5584i	−0.572112	−	0.820175i
$513$	−42.1595	−	9.24171i	−1.86139	−	0.408031i
$514$	1.46515	+	5.93039i	0.0646251	+	0.261578i
$515$	0.0755891	−	0.0755891i	0.00333085	−	0.00333085i
$516$	−5.39537	−	3.97292i	−0.237518	−	0.174898i
$517$	−0.431807	−	0.431807i	−0.0189909	−	0.0189909i
$518$	−10.5344	−	6.36037i	−0.462853	−	0.279459i
$519$	−6.12464	+	2.97114i	−0.268842	+	0.130419i
$520$	0.103027	+	0.115909i	0.00451803	+	0.00508296i
$521$	−16.6843			−0.730951			−0.365476	−	0.930821i	$-0.619094\pi$
$521$	−16.6843			−0.730951			−0.365476	+	0.930821i	$0.619094\pi$
$522$	10.5789	+	28.0930i	0.463027	+	1.22960i
$523$	13.3843	−	13.3843i	0.585255	−	0.585255i	−0.351087	−	0.936343i	$-0.614188\pi$
$523$	13.3843	−	13.3843i	0.585255	−	0.585255i	0.936343	+	0.351087i	$0.114188\pi$
$524$	−6.08806	+	19.6128i	−0.265958	+	0.856791i
$525$	−8.12467	−	2.81682i	−0.354590	−	0.122936i
$526$	−4.05871	−	16.4281i	−0.176968	−	0.716300i
$527$	17.5027			0.762429
$528$	−1.04946	+	6.92995i	−0.0456717	+	0.301587i
$529$	−18.2619			−0.793996
$530$	−0.558308	−	2.25982i	−0.0242513	−	0.0981603i
$531$	−2.49626	−	21.0680i	−0.108328	−	0.914272i
$532$	−15.8657	−	4.92491i	−0.687866	−	0.213522i
$533$	−1.07110	+	1.07110i	−0.0463944	+	0.0463944i
$534$	−2.46387	+	26.8456i	−0.106622	+	1.16172i
$535$	1.53862			0.0665203
$536$	10.2149	+	0.601055i	0.441217	+	0.0259616i
$537$	8.80219	+	18.1446i	0.379842	+	0.782998i
$538$	33.3791	+	20.1534i	1.43907	+	0.868875i
$539$	−0.715349	−	0.715349i	−0.0308123	−	0.0308123i
$540$	−0.518210	−	1.88252i	−0.0223002	−	0.0810107i
$541$	0.0442246	−	0.0442246i	0.00190136	−	0.00190136i	−0.706155	−	0.708057i	$-0.749572\pi$
$541$	0.0442246	−	0.0442246i	0.00190136	−	0.00190136i	0.708057	+	0.706155i	$0.249572\pi$
$542$	1.62816	+	6.59018i	0.0699355	+	0.283073i
$543$	10.8381	−	5.25771i	0.465108	−	0.225630i
$544$	36.6394	+	13.7809i	1.57090	+	0.590852i
$545$		−	1.51609i		−	0.0649421i
$546$	0.457142	+	0.549533i	0.0195639	+	0.0235179i
$547$	−22.5929	−	22.5929i	−0.966004	−	0.966004i	0.0334367	−	0.999441i	$-0.489355\pi$
$547$	−22.5929	−	22.5929i	−0.966004	−	0.966004i	−0.999441	+	0.0334367i	$0.989355\pi$
$548$	5.98457	−	3.14931i	0.255648	−	0.134532i
$549$	26.3175	−	3.11826i	1.12320	−	0.133084i
$550$	3.67132	−	6.08061i	0.156545	−	0.259278i
$551$		−	58.7709i		−	2.50373i
$552$	−29.0710	+	12.0483i	−1.23735	+	0.512808i
$553$			3.48456i			0.148179i
$554$	27.7322	+	16.7440i	1.17823	+	0.711384i
$555$	−0.927556	+	2.67539i	−0.0393726	+	0.113564i
$556$	5.16351	−	16.6344i	0.218982	−	0.705455i
$557$	20.6256	+	20.6256i	0.873935	+	0.873935i	0.992899	−	0.118964i	$-0.0379573\pi$
$557$	20.6256	+	20.6256i	0.873935	+	0.873935i	−0.118964	+	0.992899i	$0.537957\pi$
$558$	−4.42705	+	9.77513i	−0.187412	+	0.413814i
$559$		−	0.564448i		−	0.0238736i
$560$	−0.137086	−	0.738925i	−0.00579294	−	0.0312253i
$561$	−5.29236	−	10.9096i	−0.223444	−	0.460602i
$562$	22.4064	−	5.53569i	0.945157	−	0.233509i
$563$	2.94590	−	2.94590i	0.124155	−	0.124155i	−0.642299	−	0.766454i	$-0.722019\pi$
$563$	2.94590	−	2.94590i	0.124155	−	0.124155i	0.766454	+	0.642299i	$0.222019\pi$
$564$	−0.313899	−	2.06735i	−0.0132175	−	0.0870510i
$565$	0.773114	+	0.773114i	0.0325251	+	0.0325251i
$566$	16.9075	−	28.0030i	0.710675	−	1.17706i
$567$	−2.10322	−	8.75080i	−0.0883270	−	0.367499i
$568$	−1.51952	−	1.70952i	−0.0637578	−	0.0717300i
$569$	10.0145			0.419832			0.209916	−	0.977719i	$-0.432681\pi$
$569$	10.0145			0.419832			0.209916	+	0.977719i	$0.432681\pi$
$570$	−0.349374	+	3.80669i	−0.0146337	+	0.159445i
$571$	14.6624	−	14.6624i	0.613601	−	0.613601i	−0.330282	−	0.943882i	$-0.607144\pi$
$571$	14.6624	−	14.6624i	0.613601	−	0.613601i	0.943882	+	0.330282i	$0.107144\pi$
$572$	−0.522517	+	0.274968i	−0.0218475	+	0.0114970i
$573$	10.7669	−	31.0554i	0.449792	−	1.29736i
$574$	7.12645	−	1.76065i	0.297452	−	0.0734882i
$575$	31.8910			1.32995
$576$	−16.9639	+	16.9772i	−0.706831	+	0.707382i
$577$	−1.05507			−0.0439231			−0.0219615	−	0.999759i	$-0.506991\pi$
$577$	−1.05507			−0.0439231			−0.0219615	+	0.999759i	$0.506991\pi$
$578$	−42.4048	+	10.4765i	−1.76381	+	0.435763i
$579$	14.5544	−	41.9800i	0.604861	−	1.74463i
$580$	2.35284	−	1.23815i	0.0976964	−	0.0514115i
$581$	0.641645	−	0.641645i	0.0266199	−	0.0266199i
$582$	−1.24561	+	13.5718i	−0.0516320	+	0.562569i
$583$	8.86276			0.367058
$584$	−21.6782	−	24.3889i	−0.897052	−	1.00922i
$585$	0.101816	−	0.129187i	0.00420958	−	0.00534121i
$586$	−4.96549	+	8.22410i	−0.205123	+	0.339734i
$587$	−9.32085	−	9.32085i	−0.384713	−	0.384713i	0.488084	−	0.872797i	$-0.337696\pi$
$587$	−9.32085	−	9.32085i	−0.384713	−	0.384713i	−0.872797	+	0.488084i	$0.837696\pi$
$588$	−0.520017	−	3.42485i	−0.0214452	−	0.141238i
$589$	14.8556	−	14.8556i	0.612113	−	0.612113i
$590$	−1.82417	+	0.450678i	−0.0751001	+	0.0185541i
$591$	−17.5289	−	36.1336i	−0.721042	−	1.48634i
$592$	34.2215	−	6.34880i	1.40649	−	0.260934i
$593$			37.6934i			1.54788i	0.633257	+	0.773941i	$0.281717\pi$
$593$			37.6934i			1.54788i	−0.633257	+	0.773941i	$0.718283\pi$
$594$	7.43153	−	0.196339i	0.304920	−	0.00805588i
$595$	0.919345	+	0.919345i	0.0376895	+	0.0376895i
$596$	−2.99404	+	9.64536i	−0.122640	+	0.395090i
$597$	−14.7476	+	42.5373i	−0.603580	+	1.74093i
$598$	−2.26943	−	1.37022i	−0.0928037	−	0.0560325i
$599$			10.6528i			0.435260i	0.976031	+	0.217630i	$0.0698326\pi$
$599$			10.6528i			0.435260i	−0.976031	+	0.217630i	$0.930167\pi$
$600$	22.4687	−	9.31199i	0.917283	−	0.380161i
$601$			23.0989i			0.942224i	0.882073	+	0.471112i	$0.156147\pi$
$601$			23.0989i			0.942224i	−0.882073	+	0.471112i	$0.843853\pi$
$602$	−1.41384	+	2.34167i	−0.0576238	+	0.0954393i
$603$	−1.27703	−	10.7779i	−0.0520047	−	0.438910i
$604$	−4.07949	+	2.14678i	−0.165992	+	0.0873512i
$605$	1.32542	+	1.32542i	0.0538860	+	0.0538860i
$606$	−16.5996	−	19.9545i	−0.674312	−	0.810595i
$607$			41.9284i			1.70182i	0.525310	+	0.850911i	$0.323949\pi$
$607$			41.9284i			1.70182i	−0.525310	+	0.850911i	$0.676051\pi$
$608$	42.7948	−	19.4014i	1.73556	−	0.786830i
$609$	11.0262	−	5.34895i	0.446804	−	0.216750i
$610$	−0.562974	−	2.27871i	−0.0227942	−	0.0922622i
$611$	0.124560	−	0.124560i	0.00503914	−	0.00503914i
$612$	7.55766	−	40.8263i	0.305500	−	1.65031i
$613$	−31.9233	−	31.9233i	−1.28937	−	1.28937i	−0.935169	−	0.354202i	$-0.884753\pi$
$613$	−31.9233	−	31.9233i	−1.28937	−	1.28937i	−0.354202	−	0.935169i	$-0.615247\pi$
$614$	4.40593	+	2.66019i	0.177809	+	0.107356i
$615$	−0.737264	−	1.51978i	−0.0297294	−	0.0612834i
$616$	2.85646	+	0.168076i	0.115090	+	0.00677199i
$617$	5.95415			0.239705			0.119852	−	0.992792i	$-0.461758\pi$
$617$	5.95415			0.239705			0.119852	+	0.992792i	$0.461758\pi$
$618$	−0.127375	+	1.38784i	−0.00512377	+	0.0558272i
$619$	−1.32977	+	1.32977i	−0.0534480	+	0.0534480i	−0.733326	−	0.679878i	$-0.762033\pi$
$619$	−1.32977	+	1.32977i	−0.0534480	+	0.0534480i	0.679878	+	0.733326i	$0.262033\pi$
$620$	0.907699	+	0.281761i	0.0364541	+	0.0113158i
$621$	18.0005	+	28.1079i	0.722336	+	1.12793i
$622$	5.70506	+	23.0919i	0.228752	+	0.925902i
$623$	11.0057			0.440936
$624$	−1.99902	−	0.302727i	−0.0800248	−	0.0121188i
$625$	−24.4717			−0.978870
$626$	1.04967	+	4.24866i	0.0419531	+	0.169811i
$627$	−13.7515	−	4.76764i	−0.549183	−	0.190401i
$628$	−10.1393	+	32.6641i	−0.404603	+	1.30344i
$629$	−42.5772	+	42.5772i	−1.69766	+	1.69766i
$630$	−0.745983	+	0.280913i	−0.0297207	+	0.0111918i
$631$	−3.61315			−0.143837			−0.0719185	−	0.997411i	$-0.522912\pi$
$631$	−3.61315			−0.143837			−0.0719185	+	0.997411i	$0.522912\pi$
$632$	−6.54773	−	7.36645i	−0.260455	−	0.293022i
$633$	−30.1785	+	14.6400i	−1.19949	+	0.581887i
$634$	20.1561	+	12.1697i	0.800500	+	0.483321i
$635$	2.02008	+	2.02008i	0.0801643	+	0.0801643i
$636$	24.4373	+	17.9946i	0.969002	+	0.713531i
$637$	0.206350	−	0.206350i	0.00817590	−	0.00817590i
$638$	2.42795	+	9.82743i	0.0961235	+	0.389072i
$639$	−1.50166	+	1.90535i	−0.0594049	+	0.0753744i
$640$	1.67829	+	1.30451i	0.0663403	+	0.0515654i
$641$			0.330226i			0.0130431i	0.999979	+	0.00652156i	$0.00207589\pi$
$641$			0.330226i			0.0130431i	−0.999979	+	0.00652156i	$0.997924\pi$
$642$	−15.4212	+	12.8284i	−0.608624	+	0.506298i
$643$	1.15297	+	1.15297i	0.0454689	+	0.0454689i	0.729476	−	0.684007i	$-0.239764\pi$
$643$	1.15297	+	1.15297i	0.0454689	+	0.0454689i	−0.684007	+	0.729476i	$0.739764\pi$
$644$	5.98279	+	11.3690i	0.235755	+	0.448001i
$645$	0.594710	+	0.206185i	0.0234167	+	0.00811854i
$646$	−42.0152	+	69.5876i	−1.65307	+	2.73789i
$647$		−	37.5372i		−	1.47574i	−0.674942	−	0.737871i	$-0.735831\pi$
$647$		−	37.5372i		−	1.47574i	0.674942	−	0.737871i	$-0.264169\pi$
$648$	20.8896	+	14.5473i	0.820621	+	0.571472i
$649$		−	7.15421i		−	0.280827i
$650$	1.75402	+	1.05903i	0.0687983	+	0.0415386i
$651$	4.13916	+	1.43504i	0.162226	+	0.0562437i
$652$	−2.93732	−	0.911780i	−0.115034	−	0.0357081i
$653$	−3.90230	−	3.90230i	−0.152709	−	0.152709i	0.626618	−	0.779327i	$-0.284439\pi$
$653$	−3.90230	−	3.90230i	−0.152709	−	0.152709i	−0.779327	+	0.626618i	$0.784439\pi$
$654$	12.6406	+	15.1953i	0.494286	+	0.594185i
$655$		−	1.92919i		−	0.0753796i
$656$	−11.7571	+	17.1132i	−0.459038	+	0.668156i
$657$	−21.4235	+	27.1826i	−0.835809	+	1.06049i
$658$	−0.828746	+	0.204749i	−0.0323079	+	0.00798194i
$659$	10.7926	−	10.7926i	0.420421	−	0.420421i	−0.464928	−	0.885349i	$-0.653920\pi$
$659$	10.7926	−	10.7926i	0.420421	−	0.420421i	0.885349	+	0.464928i	$0.153920\pi$
$660$	−0.0988415	−	0.650972i	−0.00384740	−	0.0253391i
$661$	−35.6420	−	35.6420i	−1.38631	−	1.38631i	−0.832922	−	0.553390i	$-0.813334\pi$
$661$	−35.6420	−	35.6420i	−1.38631	−	1.38631i	−0.553390	−	0.832922i	$-0.686666\pi$
$662$	−15.3936	+	25.4956i	−0.598288	+	0.990915i
$663$	3.14698	−	1.52664i	0.122219	−	0.0592898i
$664$	−0.150759	+	2.56215i	−0.00585058	+	0.0994306i
$665$	1.56061			0.0605177
$666$	−13.0098	−	34.5484i	−0.504120	−	1.33872i
$667$	−32.1379	+	32.1379i	−1.24438	+	1.24438i
$668$	−18.9726	−	36.0532i	−0.734070	−	1.39494i
$669$	−19.0685	−	6.61101i	−0.737229	−	0.255597i
$670$	−0.933207	+	0.230557i	−0.0360529	+	0.00890719i
$671$	8.93684			0.345003
$672$	7.53485	+	6.26307i	0.290663	+	0.241603i
$673$	24.1133			0.929500			0.464750	−	0.885442i	$-0.346144\pi$
$673$	24.1133			0.929500			0.464750	+	0.885442i	$0.346144\pi$
$674$	−25.1580	+	6.21550i	−0.969050	+	0.239412i
$675$	−13.9125	−	21.7243i	−0.535491	−	0.836170i
$676$	12.0287	+	22.8579i	0.462642	+	0.879150i
$677$	−9.46846	+	9.46846i	−0.363902	+	0.363902i	−0.865247	−	0.501345i	$-0.832839\pi$
$677$	−9.46846	+	9.46846i	−0.363902	+	0.363902i	0.501345	+	0.865247i	$0.332839\pi$
$678$	−14.1946	−	1.30277i	−0.545142	−	0.0500326i
$679$	5.56394			0.213525
$680$	−3.67103	−	0.216007i	−0.140778	−	0.00828348i
$681$	0.225603	+	0.465053i	0.00864514	+	0.0178209i
$682$	−1.87037	+	3.09780i	−0.0716203	+	0.118621i
$683$	31.3757	+	31.3757i	1.20056	+	1.20056i	0.973998	+	0.226558i	$0.0727474\pi$
$683$	31.3757	+	31.3757i	1.20056	+	1.20056i	0.226558	+	0.973998i	$0.427253\pi$
$684$	−28.2371	−	41.0664i	−1.07967	−	1.57021i
$685$	−0.449220	+	0.449220i	−0.0171638	+	0.0171638i
$686$	−1.37293	+	0.339195i	−0.0524188	+	0.0129505i
$687$	−25.9390	+	12.5833i	−0.989635	+	0.480085i
$688$	−1.41127	−	7.60705i	−0.0538040	−	0.290016i
$689$			2.55656i			0.0973972i
$690$	2.27267	−	1.89057i	0.0865191	−	0.0719729i
$691$	−8.64022	−	8.64022i	−0.328689	−	0.328689i	0.523399	−	0.852088i	$-0.324664\pi$
$691$	−8.64022	−	8.64022i	−0.328689	−	0.328689i	−0.852088	+	0.523399i	$0.824664\pi$
$692$	−7.50701	−	2.33026i	−0.285374	−	0.0885833i
$693$	−0.357104	−	3.01389i	−0.0135652	−	0.114488i
$694$	23.9910	+	14.4851i	0.910686	+	0.549848i
$695$			1.63622i			0.0620652i
$696$	−13.2586	+	32.0268i	−0.502566	+	1.21397i
$697$		−	35.9194i		−	1.36055i
$698$	5.98359	−	9.91032i	0.226482	−	0.375111i
$699$	−3.54332	+	10.2202i	−0.134021	+	0.386562i
$700$	−4.62404	−	8.78699i	−0.174772	−	0.332117i
$701$	15.8683	+	15.8683i	0.599338	+	0.599338i	0.940136	−	0.340798i	$-0.110697\pi$
$701$	15.8683	+	15.8683i	0.599338	+	0.599338i	−0.340798	+	0.940136i	$0.610697\pi$
$702$	0.0566361	+	2.14371i	0.00213759	+	0.0809090i
$703$			72.2757i			2.72593i
$704$	−6.35445	+	5.01216i	−0.239492	+	0.188903i
$705$	0.0857376	+	0.176737i	0.00322906	+	0.00665632i
$706$	−4.71807	−	19.0970i	−0.177567	−	0.718725i
$707$	−7.49292	+	7.49292i	−0.281800	+	0.281800i
$708$	14.5256	−	19.7263i	0.545906	−	0.741360i
$709$	0.181876	+	0.181876i	0.00683048	+	0.00683048i	0.710514	−	0.703683i	$-0.248463\pi$
$709$	0.181876	+	0.181876i	0.00683048	+	0.00683048i	−0.703683	+	0.710514i	$0.748463\pi$
$710$	0.183939	+	0.111058i	0.00690311	+	0.00416792i
$711$	−6.47078	+	8.21028i	−0.242673	+	0.307909i
$712$	−23.2664	+	20.6805i	−0.871946	+	0.775036i
$713$	−16.2470			−0.608456
$714$	−16.8795	−	1.54918i	−0.631699	−	0.0579768i
$715$	0.0392217	−	0.0392217i	0.00146681	−	0.00146681i
$716$	−6.90354	+	22.2399i	−0.257998	+	0.831146i
$717$	−14.6639	+	42.2958i	−0.547634	+	1.57957i
$718$	7.02832	+	28.4480i	0.262295	+	1.06167i
$719$	−11.0849			−0.413398			−0.206699	−	0.978405i	$-0.566272\pi$
$719$	−11.0849			−0.413398			−0.206699	+	0.978405i	$0.566272\pi$
$720$	1.04917	−	1.99561i	0.0391003	−	0.0743720i
$721$	0.568966			0.0211894
$722$	16.9577	+	68.6383i	0.631099	+	2.55445i
$723$	10.7719	−	31.0698i	0.400611	−	1.15550i
$724$	13.2843	+	4.12362i	0.493709	+	0.153253i
$725$	24.8391	−	24.8391i	0.922500	−	0.922500i
$726$	−24.3352	−	2.23346i	−0.903163	−	0.0828915i
$727$	−15.6079			−0.578864			−0.289432	−	0.957199i	$-0.593466\pi$
$727$	−15.6079			−0.578864			−0.289432	+	0.957199i	$0.593466\pi$
$728$	−0.0484834	+	0.823976i	−0.00179692	+	0.0305386i
$729$	11.2945	−	24.5242i	0.418315	−	0.908302i
$730$	2.62416	+	1.58440i	0.0971247	+	0.0586413i
$731$	9.46443	+	9.46443i	0.350055	+	0.350055i
$732$	24.6416	+	18.1450i	0.910778	+	0.670658i
$733$	28.2446	−	28.2446i	1.04324	−	1.04324i	0.0442178	−	0.999022i	$-0.485920\pi$
$733$	28.2446	−	28.2446i	1.04324	−	1.04324i	0.999022	−	0.0442178i	$-0.0140796\pi$
$734$	5.04804	+	20.4326i	0.186327	+	0.754180i
$735$	0.142036	+	0.292790i	0.00523909	+	0.0107997i
$736$	−34.0109	−	12.7923i	−1.25366	−	0.471529i
$737$		−	3.65994i		−	0.134815i
$738$	20.0607	+	9.08529i	0.738446	+	0.334434i
$739$	−29.2990	−	29.2990i	−1.07778	−	1.07778i	−0.996708	−	0.0810730i	$-0.974165\pi$
$739$	−29.2990	−	29.2990i	−1.07778	−	1.07778i	−0.0810730	−	0.996708i	$-0.525835\pi$
$740$	−2.89349	+	1.52266i	−0.106367	+	0.0559742i
$741$	1.37528	−	3.96678i	0.0505221	−	0.145723i
$742$	6.40371	−	10.6061i	0.235088	−	0.389364i
$743$			27.2593i			1.00005i	0.866012	+	0.500023i	$0.166675\pi$
$743$			27.2593i			1.00005i	−0.866012	+	0.500023i	$0.833325\pi$
$744$	−11.4468	+	4.74405i	−0.419661	+	0.173925i
$745$		−	0.948752i		−	0.0347596i
$746$	18.2509	+	11.0194i	0.668213	+	0.403450i
$747$	2.70336	−	0.320310i	0.0989107	−	0.0117195i
$748$	4.15079	−	13.3719i	0.151768	−	0.488925i
$749$	5.79066	+	5.79066i	0.211586	+	0.211586i
$750$	−3.52555	+	2.93280i	−0.128735	+	0.107091i
$751$		−	40.8770i		−	1.49162i	−0.666157	−	0.745811i	$-0.732062\pi$
$751$		−	40.8770i		−	1.49162i	0.666157	−	0.745811i	$-0.267938\pi$
$752$	1.36725	−	1.99011i	0.0498586	−	0.0725720i
$753$	23.3030	−	11.3046i	0.849207	−	0.411961i
$754$	−2.83483	+	0.700369i	−0.103238	+	0.0255059i
$755$	0.306219	−	0.306219i	0.0111444	−	0.0111444i
$756$	5.13463	−	9.03524i	0.186745	−	0.328609i
$757$	11.5259	+	11.5259i	0.418914	+	0.418914i	0.884829	−	0.465915i	$-0.154275\pi$
$757$	11.5259	+	11.5259i	0.418914	+	0.418914i	−0.465915	+	0.884829i	$0.654275\pi$
$758$	−5.73122	+	9.49233i	−0.208167	+	0.344777i
$759$	4.91268	+	10.1269i	0.178319	+	0.367583i
$760$	−3.29916	+	2.93249i	−0.119673	+	0.106372i
$761$	−27.9488			−1.01314			−0.506572	−	0.862198i	$-0.669087\pi$
$761$	−27.9488			−1.01314			−0.506572	+	0.862198i	$0.669087\pi$
$762$	−37.0893	−	3.40402i	−1.34360	−	0.123315i
$763$	5.70587	−	5.70587i	0.206566	−	0.206566i
$764$	33.5870	−	17.6747i	1.21513	−	0.639449i
$765$	0.458939	+	3.87336i	0.0165930	+	0.140042i
$766$	−13.7488	+	3.39677i	−0.496766	+	0.122730i
$767$	2.06371			0.0745162
$768$	−27.6976	+	0.918222i	−0.999451	+	0.0331335i
$769$	−33.1252			−1.19453			−0.597263	−	0.802046i	$-0.703745\pi$
$769$	−33.1252			−1.19453			−0.597263	+	0.802046i	$0.703745\pi$
$770$	−0.260958	+	0.0644719i	−0.00940428	+	0.00232341i
$771$	7.06881	+	2.45075i	0.254577	+	0.0882616i
$772$	45.4022	−	23.8923i	1.63406	−	0.859904i
$773$	−25.5398	+	25.5398i	−0.918603	+	0.918603i	−0.996928	−	0.0783250i	$-0.975043\pi$
$773$	−25.5398	+	25.5398i	−0.918603	+	0.918603i	0.0783250	+	0.996928i	$0.475043\pi$
$774$	−7.67971	+	2.89193i	−0.276041	+	0.103948i
$775$	12.5572			0.451067
$776$	−11.7623	+	10.4550i	−0.422243	+	0.375314i
$777$	−13.5599	+	6.57806i	−0.486457	+	0.235987i
$778$	18.8398	−	31.2034i	0.675440	−	1.11870i
$779$	−30.4870	−	30.4870i	−1.09231	−	1.09231i
$780$	0.187780	−	0.0285119i	0.00672360	−	0.00102089i
$781$	−0.578473	+	0.578473i	−0.0206994	+	0.0206994i
$782$	61.0281	−	15.0775i	2.18236	−	0.539171i
$783$	35.9127	+	7.87235i	1.28341	+	0.281335i
$784$	2.26505	−	3.29690i	0.0808945	−	0.117747i
$785$		−	3.21295i		−	0.114675i
$786$	16.0848	+	19.3357i	0.573727	+	0.689682i
$787$	15.0726	+	15.0726i	0.537282	+	0.537282i	0.922730	−	0.385448i	$-0.125953\pi$
$787$	15.0726	+	15.0726i	0.537282	+	0.537282i	−0.385448	+	0.922730i	$0.625953\pi$
$788$	13.7479	−	44.2891i	0.489748	−	1.57773i
$789$	−19.5817	−	6.78896i	−0.697128	−	0.241693i
$790$	0.792607	+	0.478555i	0.0281997	+	0.0170262i
$791$			5.81929i			0.206910i
$792$	6.41823	+	5.70041i	0.228062	+	0.202555i
$793$			2.57793i			0.0915450i
$794$	3.20372	−	5.30615i	0.113696	−	0.188308i
$795$	−2.69362	−	0.933877i	−0.0955330	−	0.0331212i
$796$	−46.0049	+	24.2095i	−1.63060	+	0.858083i
$797$	22.0934	+	22.0934i	0.782588	+	0.782588i	0.980267	−	0.197679i	$-0.0633402\pi$
$797$	22.0934	+	22.0934i	0.782588	+	0.782588i	−0.197679	+	0.980267i	$0.563340\pi$
$798$	−15.6415	+	13.0118i	−0.553704	+	0.460611i
$799$			4.17712i			0.147776i
$800$	26.2867	+	9.88702i	0.929375	+	0.349559i
$801$	25.9316	+	20.4375i	0.916247	+	0.722123i
$802$	6.73918	+	27.2777i	0.237969	+	0.963208i
$803$	−8.25277	+	8.25277i	−0.291234	+	0.291234i
$804$	7.43098	−	10.0915i	0.262070	−	0.355901i
$805$	−0.853390	−	0.853390i	−0.0300781	−	0.0300781i
$806$	−0.893595	−	0.539529i	−0.0314755	−	0.0190041i
$807$	42.9656	−	20.8432i	1.51246	−	0.733715i
$808$	1.76052	−	29.9199i	0.0619347	−	1.05258i
$809$	−0.787723			−0.0276949			−0.0138474	−	0.999904i	$-0.504408\pi$
$809$	−0.787723			−0.0276949			−0.0138474	+	0.999904i	$0.504408\pi$
$810$	−2.27932	−	0.723394i	−0.0800873	−	0.0254175i
$811$	2.79456	−	2.79456i	0.0981301	−	0.0981301i	−0.656337	−	0.754468i	$-0.727895\pi$
$811$	2.79456	−	2.79456i	0.0981301	−	0.0981301i	0.754468	+	0.656337i	$0.227895\pi$
$812$	13.5149	+	4.19517i	0.474279	+	0.147222i
$813$	7.85527	+	2.72341i	0.275496	+	0.0955142i
$814$	−2.98586	−	12.0856i	−0.104654	−	0.423601i
$815$	0.288925			0.0101206
$816$	38.5947	−	28.4427i	1.35109	−	0.995694i
$817$	16.0661			0.562080
$818$	1.52636	+	6.17814i	0.0533680	+	0.216014i
$819$	0.869389	−	0.103010i	0.0303789	−	0.00359947i
$820$	0.578236	−	1.86280i	0.0201929	−	0.0650518i
$821$	−2.46211	+	2.46211i	−0.0859283	+	0.0859283i	−0.748764	−	0.662836i	$-0.769353\pi$
$821$	−2.46211	+	2.46211i	−0.0859283	+	0.0859283i	0.662836	+	0.748764i	$0.269353\pi$
$822$	0.756979	−	8.24784i	0.0264027	−	0.287676i
$823$	−40.9038			−1.42582			−0.712908	−	0.701258i	$-0.752622\pi$
$823$	−40.9038			−1.42582			−0.712908	+	0.701258i	$0.752622\pi$
$824$	−1.20281	+	1.06913i	−0.0419018	+	0.0372447i
$825$	−3.79697	−	7.82698i	−0.132194	−	0.272501i
$826$	−8.56150	−	5.16921i	−0.297893	−	0.179860i
$827$	−12.8277	−	12.8277i	−0.446061	−	0.446061i	0.447982	−	0.894043i	$-0.352143\pi$
$827$	−12.8277	−	12.8277i	−0.446061	−	0.446061i	−0.894043	+	0.447982i	$0.852143\pi$
$828$	−7.01546	+	37.8974i	−0.243804	+	1.31703i
$829$	−0.182463	+	0.182463i	−0.00633720	+	0.00633720i	−0.710268	−	0.703931i	$-0.751426\pi$
$829$	−0.182463	+	0.182463i	−0.00633720	+	0.00633720i	0.703931	+	0.710268i	$0.251426\pi$
$830$	−0.0578292	−	0.234071i	−0.00200728	−	0.00812472i
$831$	35.6970	−	17.3171i	1.23831	−	0.600722i
$832$	−1.44581	−	1.83301i	−0.0501245	−	0.0635482i
$833$			6.91999i			0.239763i
$834$	−13.6422	−	16.3993i	−0.472389	−	0.567863i
$835$	2.70626	+	2.70626i	0.0936541	+	0.0936541i
$836$	−7.82650	−	14.8726i	−0.270685	−	0.514378i
$837$	7.08778	+	11.0676i	0.244989	+	0.382551i
$838$	22.7406	−	37.6641i	0.785560	−	1.30108i
$839$		−	4.28148i		−	0.147813i	−0.997265	−	0.0739065i	$-0.976453\pi$
$839$		−	4.28148i		−	0.147813i	0.997265	−	0.0739065i	$-0.0235466\pi$
$840$	−0.850441	−	0.352070i	−0.0293430	−	0.0121476i
$841$			21.0628i			0.726302i
$842$	18.8136	+	11.3591i	0.648358	+	0.391462i
$843$	9.25951	−	26.7076i	0.318914	−	0.919859i
$844$	−36.9899	−	11.4821i	−1.27325	−	0.395231i
$845$	−1.71578	−	1.71578i	−0.0590247	−	0.0590247i
$846$	−2.33289	−	1.05654i	−0.0802066	−	0.0363247i
$847$			9.97655i			0.342798i
$848$	6.39205	+	34.4547i	0.219504	+	1.18318i
$849$	−17.4862	−	36.0456i	−0.600124	−	1.23708i
$850$	−47.1681	+	11.6533i	−1.61785	+	0.399704i
$851$	39.5227	−	39.5227i	1.35482	−	1.35482i
$852$	−2.76953	+	0.420516i	−0.0948825	+	0.0144066i
$853$	28.0775	+	28.0775i	0.961357	+	0.961357i	0.999281	−	0.0379241i	$-0.0120745\pi$
$853$	28.0775	+	28.0775i	0.961357	+	0.961357i	−0.0379241	+	0.999281i	$0.512075\pi$
$854$	6.45724	−	10.6948i	0.220962	−	0.365968i
$855$	3.67708	+	2.89802i	0.125753	+	0.0991103i
$856$	−23.1226	−	1.36056i	−0.790316	−	0.0465029i
$857$	7.48369			0.255638			0.127819	−	0.991798i	$-0.459202\pi$
$857$	7.48369			0.255638			0.127819	+	0.991798i	$0.459202\pi$
$858$	−0.0660923	+	0.720124i	−0.00225635	+	0.0245846i
$859$	−8.72002	+	8.72002i	−0.297523	+	0.297523i	−0.840043	−	0.542520i	$-0.817470\pi$
$859$	−8.72002	+	8.72002i	−0.297523	+	0.297523i	0.542520	+	0.840043i	$0.317470\pi$
$860$	0.338471	+	0.643190i	0.0115418	+	0.0219326i
$861$	2.94503	−	8.49448i	0.100366	−	0.289491i
$862$	−19.8454	+	4.90299i	−0.675938	+	0.166996i
$863$	44.3294			1.50899			0.754495	−	0.656306i	$-0.227882\pi$
$863$	44.3294			1.50899			0.754495	+	0.656306i	$0.227882\pi$
$864$	6.12310	+	28.7490i	0.208312	+	0.978062i
$865$	0.738415			0.0251069
$866$	8.76507	−	2.16549i	0.297849	−	0.0735862i
$867$	−17.5239	+	50.5450i	−0.595143	+	1.71660i
$868$	2.35574	+	4.47658i	0.0799592	+	0.151945i
$869$	−2.49268	+	2.49268i	−0.0845584	+	0.0845584i
$870$	0.297607	−	3.24265i	0.0100898	−	0.109936i
$871$	1.05575			0.0357727
$872$	−1.34063	+	22.7841i	−0.0453996	+	0.771566i
$873$	13.1097	+	10.3322i	0.443696	+	0.349690i
$874$	39.0010	−	64.5954i	1.31923	−	2.18497i
$875$	1.32385	+	1.32385i	0.0447542	+	0.0447542i
$876$	−39.5114	+	5.99928i	−1.33497	+	0.202697i
$877$	16.9604	−	16.9604i	0.572712	−	0.572712i	−0.360173	−	0.932885i	$-0.617282\pi$
$877$	16.9604	−	16.9604i	0.572712	−	0.572712i	0.932885	+	0.360173i	$0.117282\pi$
$878$	−29.1007	+	7.18959i	−0.982102	+	0.242637i
$879$	5.13544	+	10.5861i	0.173214	+	0.357060i
$880$	0.430525	−	0.626653i	0.0145130	−	0.0211245i
$881$		−	24.9798i		−	0.841590i	−0.907156	−	0.420795i	$-0.861751\pi$
$881$		−	24.9798i		−	0.841590i	0.907156	−	0.420795i	$-0.138249\pi$
$882$	−3.86477	−	1.75031i	−0.130133	−	0.0589360i
$883$	12.8228	+	12.8228i	0.431520	+	0.431520i	0.889145	−	0.457625i	$-0.151300\pi$
$883$	12.8228	+	12.8228i	0.431520	+	0.431520i	−0.457625	+	0.889145i	$0.651300\pi$
$884$	3.85727	+	1.19734i	0.129734	+	0.0402710i
$885$	−0.753845	+	2.17435i	−0.0253402	+	0.0730900i
$886$	23.8970	+	14.4284i	0.802837	+	0.484732i
$887$		−	6.33001i		−	0.212541i	−0.994337	−	0.106270i	$-0.966109\pi$
$887$		−	6.33001i		−	0.212541i	0.994337	−	0.106270i	$-0.0338909\pi$
$888$	16.3053	−	39.3861i	0.547169	−	1.32171i
$889$			15.2053i			0.509969i
$890$	1.51148	−	2.50339i	0.0506650	−	0.0839139i
$891$	4.75534	−	7.76441i	0.159310	−	0.260118i
$892$	−10.8525	−	20.6229i	−0.363370	−	0.690506i
$893$	3.54538	+	3.54538i	0.118641	+	0.118641i
$894$	7.91034	+	9.50907i	0.264561	+	0.318031i
$895$		−	2.18760i		−	0.0731233i
$896$	1.40674	+	11.2259i	0.0469959	+	0.375031i
$897$	−2.92121	+	1.41712i	−0.0975364	+	0.0473162i
$898$	−4.81002	−	19.4692i	−0.160512	−	0.649694i
$899$	−12.6544	+	12.6544i	−0.422048	+	0.422048i
$900$	5.42219	−	29.2906i	0.180740	−	0.976352i
$901$	−42.8673	−	42.8673i	−1.42812	−	1.42812i
$902$	6.35738	+	3.83842i	0.211678	+	0.127805i
$903$	1.46223	+	3.01420i	0.0486599	+	0.100306i
$904$	−10.9348	−	12.3021i	−0.363688	−	0.409163i
$905$	−1.30669			−0.0434360
$906$	−0.516007	+	5.62228i	−0.0171432	+	0.186788i
$907$	26.3398	−	26.3398i	0.874598	−	0.874598i	−0.118371	−	0.992969i	$-0.537767\pi$
$907$	26.3398	−	26.3398i	0.874598	−	0.874598i	0.992969	+	0.118371i	$0.0377673\pi$
$908$	−0.176940	+	0.570018i	−0.00587197	+	0.0189167i
$909$	−31.5690	+	3.74048i	−1.04708	+	0.124064i
$910$	−0.0185976	−	0.0752762i	−0.000616506	−	0.00249538i
$911$	−14.6002			−0.483727			−0.241864	−	0.970310i	$-0.577759\pi$
$911$	−14.6002			−0.483727			−0.241864	+	0.970310i	$0.577759\pi$
$912$	8.61661	−	56.8987i	0.285324	−	1.88410i
$913$	0.918000			0.0303814
$914$	−12.6697	−	51.2820i	−0.419075	−	1.69626i
$915$	−2.71614	−	0.941683i	−0.0897928	−	0.0311311i
$916$	−31.7936	−	9.86910i	−1.05049	−	0.326084i
$917$	7.26058	−	7.26058i	0.239765	−	0.239765i
$918$	−36.8944	−	34.9951i	−1.21770	−	1.15501i
$919$	48.0819			1.58608			0.793039	−	0.609171i	$-0.208498\pi$
$919$	48.0819			1.58608			0.793039	+	0.609171i	$0.208498\pi$
$920$	3.40767	+	0.200510i	0.112347	+	0.00661062i
$921$	5.67133	−	2.75124i	0.186877	−	0.0906563i
$922$	18.0294	+	10.8857i	0.593766	+	0.358500i
$923$	−0.166867	−	0.166867i	−0.00549248	−	0.00549248i
$924$	2.07797	−	2.82196i	0.0683601	−	0.0928355i
$925$	−30.5467	+	30.5467i	−1.00437	+	1.00437i
$926$	−8.91190	−	36.0720i	−0.292863	−	1.18540i
$927$	1.34059	+	1.05656i	0.0440307	+	0.0347020i
$928$	−36.4538	+	16.5266i	−1.19665	+	0.542514i
$929$		−	8.27555i		−	0.271512i	−0.990742	−	0.135756i	$-0.956654\pi$
$929$		−	8.27555i		−	0.271512i	0.990742	−	0.135756i	$-0.0433463\pi$
$930$	0.894873	−	0.744420i	0.0293440	−	0.0244105i
$931$	5.87341	+	5.87341i	0.192493	+	0.192493i
$932$	−11.0533	+	5.81666i	−0.362063	+	0.190531i
$933$	27.5248	+	9.54281i	0.901120	+	0.312417i
$934$	21.3865	−	35.4214i	0.699788	−	1.15902i
$935$			1.31531i			0.0430151i
$936$	−1.64435	+	1.85141i	−0.0537471	+	0.0605151i
$937$		−	55.6179i		−	1.81696i	−0.417933	−	0.908478i	$-0.637245\pi$
$937$		−	55.6179i		−	1.81696i	0.417933	−	0.908478i	$-0.362755\pi$
$938$	−4.37988	−	2.64445i	−0.143008	−	0.0863445i
$939$	5.06425	+	1.75577i	0.165266	+	0.0572974i
$940$	−0.0672439	+	0.216628i	−0.00219325	+	0.00706562i
$941$	−39.8696	−	39.8696i	−1.29971	−	1.29971i	−0.928579	−	0.371134i	$-0.878969\pi$
$941$	−39.8696	−	39.8696i	−1.29971	−	1.29971i	−0.371134	−	0.928579i	$-0.621031\pi$
$942$	26.7884	+	32.2025i	0.872814	+	1.04922i
$943$			33.3425i			1.08578i
$944$	27.8125	−	5.15980i	0.905221	−	0.167937i
$945$	−0.209043	+	0.953627i	−0.00680016	+	0.0310215i
$946$	−2.68650	+	0.663723i	−0.0873456	+	0.0215795i
$947$	−25.0837	+	25.0837i	−0.815110	+	0.815110i	−0.985395	−	0.170285i	$-0.945531\pi$
$947$	−25.0837	+	25.0837i	−0.815110	+	0.815110i	0.170285	+	0.985395i	$0.445531\pi$
$948$	−11.9341	+	1.81203i	−0.387601	+	0.0588521i
$949$	−2.38060	−	2.38060i	−0.0772776	−	0.0772776i
$950$	−30.1435	+	49.9252i	−0.977985	+	1.61979i
$951$	25.9450	−	12.5862i	0.841323	−	0.408137i
$952$	−13.0031	−	14.6290i	−0.421434	−	0.474130i
$953$	−42.9272			−1.39055			−0.695274	−	0.718745i	$-0.744717\pi$
$953$	−42.9272			−1.39055			−0.695274	+	0.718745i	$0.744717\pi$
$954$	34.7838	−	13.0984i	1.12617	−	0.424078i
$955$	−2.52114	+	2.52114i	−0.0815822	+	0.0815822i
$956$	−45.7437	+	24.0721i	−1.47946	+	0.778547i
$957$	11.7139	+	4.06121i	0.378658	+	0.131280i
$958$	−25.4350	+	6.28394i	−0.821768	+	0.203025i
$959$	−3.38132			−0.109188
$960$	2.45942	−	0.853752i	0.0793774	−	0.0275547i
$961$	24.6027			0.793635
$962$	3.48623	−	0.861304i	0.112401	−	0.0277695i
$963$	2.89071	+	24.3970i	0.0931517	+	0.786183i
$964$	33.6026	−	17.6830i	1.08227	−	0.569530i
$965$	−3.40803	+	3.40803i	−0.109708	+	0.109708i
$966$	15.6685	+	1.43804i	0.504127	+	0.0462683i
$967$	40.4433			1.30057			0.650285	−	0.759690i	$-0.274650\pi$
$967$	40.4433			1.30057			0.650285	+	0.759690i	$0.274650\pi$
$968$	−18.7466	−	21.0907i	−0.602539	−	0.677880i
$969$	43.4532	+	89.5734i	1.39592	+	2.87751i
$970$	0.764129	−	1.26559i	0.0245347	−	0.0406356i
$971$	−30.5811	−	30.5811i	−0.981394	−	0.981394i	0.0184358	−	0.999830i	$-0.494131\pi$
$971$	−30.5811	−	30.5811i	−0.981394	−	0.981394i	−0.999830	+	0.0184358i	$0.994131\pi$
$972$	28.8764	−	11.7538i	0.926212	−	0.377003i
$973$	−6.15797	+	6.15797i	−0.197415	+	0.197415i
$974$	50.2686	−	12.4193i	1.61071	−	0.397940i
$975$	2.25778	−	1.09528i	0.0723068	−	0.0350770i
$976$	6.44548	+	34.7427i	0.206315	+	1.11209i
$977$		−	3.04304i		−	0.0973554i	−0.998815	−	0.0486777i	$-0.984499\pi$
$977$		−	3.04304i		−	0.0973554i	0.998815	−	0.0486777i	$-0.0155007\pi$
$978$	−2.89582	+	2.40895i	−0.0925981	+	0.0770298i
$979$	7.87295	+	7.87295i	0.251621	+	0.251621i
$980$	−0.111399	+	0.358874i	−0.00355851	+	0.0114638i
$981$	24.0398	−	2.84838i	0.767531	−	0.0909417i
$982$	−4.53304	−	2.73693i	−0.144655	−	0.0873389i
$983$			50.6697i			1.61611i	0.589106	+	0.808056i	$0.299480\pi$
$983$			50.6697i			1.61611i	−0.589106	+	0.808056i	$0.700520\pi$
$984$	9.73584	+	23.4914i	0.310367	+	0.748880i
$985$			4.35643i			0.138808i
$986$	35.7897	−	59.2767i	1.13978	−	1.88776i
$987$	−0.342482	+	0.987836i	−0.0109013	+	0.0314432i
$988$	4.29015	−	2.25764i	0.136488	−	0.0718250i
$989$	−8.78544	−	8.78544i	−0.279361	−	0.279361i
$990$	−0.734589	−	0.332687i	−0.0233468	−	0.0105735i
$991$		−	12.2969i		−	0.390623i	−0.980741	−	0.195311i	$-0.937428\pi$
$991$		−	12.2969i		−	0.390623i	0.980741	−	0.195311i	$-0.0625717\pi$
$992$	−13.3919	−	5.03700i	−0.425193	−	0.159925i
$993$	15.9204	+	32.8180i	0.505220	+	1.04145i
$994$	0.274293	+	1.11023i	0.00870003	+	0.0352145i
$995$	3.45326	−	3.45326i	0.109476	−	0.109476i
$996$	2.53120	+	1.86387i	0.0802042	+	0.0590589i
$997$	−17.3109	−	17.3109i	−0.548242	−	0.548242i	0.377690	−	0.925932i	$-0.376719\pi$
$997$	−17.3109	−	17.3109i	−0.548242	−	0.548242i	−0.925932	+	0.377690i	$0.876719\pi$
$998$	26.3007	+	15.8797i	0.832535	+	0.502663i
$999$	−44.1649	−	9.68130i	−1.39732	−	0.306303i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	336.2.s.c.155.18	yes	40
3.2	odd	2	inner	336.2.s.c.155.3	✓	40
4.3	odd	2		1344.2.s.c.911.9		40
12.11	even	2		1344.2.s.c.911.18		40
16.3	odd	4	inner	336.2.s.c.323.3	yes	40
16.13	even	4		1344.2.s.c.239.18		40
48.29	odd	4		1344.2.s.c.239.9		40
48.35	even	4	inner	336.2.s.c.323.18	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
336.2.s.c.155.3	✓	40	3.2	odd	2	inner
336.2.s.c.155.18	yes	40	1.1	even	1	trivial
336.2.s.c.323.3	yes	40	16.3	odd	4	inner
336.2.s.c.323.18	yes	40	48.35	even	4	inner
1344.2.s.c.239.9		40	48.29	odd	4
1344.2.s.c.239.18		40	16.13	even	4
1344.2.s.c.911.9		40	4.3	odd	2
1344.2.s.c.911.18		40	12.11	even	2

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:	\( N \)	\(=\)	\( 336 = 2^{4} \cdot 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	336.s (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.37293 - 0.339195i) q^{2} +(0.567369 - 1.63649i) q^{3} +(1.76989 - 0.931385i) q^{4} +(-0.132854 + 0.132854i) q^{5} +(0.223871 - 2.43924i) q^{6} -1.00000 q^{7} +(2.11403 - 1.87907i) q^{8} +(-2.35619 - 1.85698i) q^{9} +O(q^{10})\)	\(q+(1.37293 - 0.339195i) q^{2} +(0.567369 - 1.63649i) q^{3} +(1.76989 - 0.931385i) q^{4} +(-0.132854 + 0.132854i) q^{5} +(0.223871 - 2.43924i) q^{6} -1.00000 q^{7} +(2.11403 - 1.87907i) q^{8} +(-2.35619 - 1.85698i) q^{9} +(-0.137336 + 0.227462i) q^{10} +(-0.715349 - 0.715349i) q^{11} +(-0.520017 - 3.42485i) q^{12} +(0.206350 - 0.206350i) q^{13} +(-1.37293 + 0.339195i) q^{14} +(0.142036 + 0.292790i) q^{15} +(2.26505 - 3.29690i) q^{16} +6.91999i q^{17} +(-3.86477 - 1.75031i) q^{18} +(5.87341 + 5.87341i) q^{19} +(-0.111399 + 0.358874i) q^{20} +(-0.567369 + 1.63649i) q^{21} +(-1.22477 - 0.739484i) q^{22} -6.42354i q^{23} +(-1.87564 - 4.52570i) q^{24} +4.96470i q^{25} +(0.213312 - 0.353298i) q^{26} +(-4.37576 + 2.80227i) q^{27} +(-1.76989 + 0.931385i) q^{28} +(-5.00314 - 5.00314i) q^{29} +(0.294319 + 0.353803i) q^{30} -2.52929i q^{31} +(1.99146 - 5.29472i) q^{32} +(-1.57653 + 0.764794i) q^{33} +(2.34723 + 9.50069i) q^{34} +(0.132854 - 0.132854i) q^{35} +(-5.89976 - 1.09215i) q^{36} +(6.15279 + 6.15279i) q^{37} +(10.0560 + 6.07157i) q^{38} +(-0.220613 - 0.454766i) q^{39} +(-0.0312149 + 0.530497i) q^{40} -5.19068 q^{41} +(-0.223871 + 2.43924i) q^{42} +(1.36769 - 1.36769i) q^{43} +(-1.93236 - 0.599827i) q^{44} +(0.559735 - 0.0663207i) q^{45} +(-2.17883 - 8.81910i) q^{46} +0.603632 q^{47} +(-4.11023 - 5.57728i) q^{48} +1.00000 q^{49} +(1.68400 + 6.81620i) q^{50} +(11.3245 + 3.92619i) q^{51} +(0.173027 - 0.557409i) q^{52} +(-6.19471 + 6.19471i) q^{53} +(-5.05711 + 5.33157i) q^{54} +0.190073 q^{55} +(-2.11403 + 1.87907i) q^{56} +(12.9442 - 6.27938i) q^{57} +(-8.56601 - 5.17194i) q^{58} +(5.00050 + 5.00050i) q^{59} +(0.524089 + 0.385917i) q^{60} +(-6.24649 + 6.24649i) q^{61} +(-0.857924 - 3.47255i) q^{62} +(2.35619 + 1.85698i) q^{63} +(0.938205 - 7.94480i) q^{64} +0.0548287i q^{65} +(-1.90505 + 1.58476i) q^{66} +(2.55815 + 2.55815i) q^{67} +(6.44517 + 12.2476i) q^{68} +(-10.5120 - 3.64452i) q^{69} +(0.137336 - 0.227462i) q^{70} -0.808658i q^{71} +(-8.47044 + 0.501723i) q^{72} -11.5367i q^{73} +(10.5344 + 6.36037i) q^{74} +(8.12467 + 2.81682i) q^{75} +(15.8657 + 4.92491i) q^{76} +(0.715349 + 0.715349i) q^{77} +(-0.457142 - 0.549533i) q^{78} -3.48456i q^{79} +(0.137086 + 0.738925i) q^{80} +(2.10322 + 8.75080i) q^{81} +(-7.12645 + 1.76065i) q^{82} +(-0.641645 + 0.641645i) q^{83} +(0.520017 + 3.42485i) q^{84} +(-0.919345 - 0.919345i) q^{85} +(1.41384 - 2.34167i) q^{86} +(-11.0262 + 5.34895i) q^{87} +(-2.85646 - 0.168076i) q^{88} -11.0057 q^{89} +(0.745983 - 0.280913i) q^{90} +(-0.206350 + 0.206350i) q^{91} +(-5.98279 - 11.3690i) q^{92} +(-4.13916 - 1.43504i) q^{93} +(0.828746 - 0.204749i) q^{94} -1.56061 q^{95} +(-7.53485 - 6.26307i) q^{96} -5.56394 q^{97} +(1.37293 - 0.339195i) q^{98} +(0.357104 + 3.01389i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q + 4 q^{3} - 2 q^{6} - 40 q^{7}+O(q^{10}) \) 40 * q + 4 * q^3 - 2 * q^6 - 40 * q^7	\( 40 q + 4 q^{3} - 2 q^{6} - 40 q^{7} - 8 q^{10} - 2 q^{12} + 24 q^{13} + 36 q^{16} + 12 q^{18} + 16 q^{19} - 4 q^{21} - 8 q^{22} + 6 q^{24} - 32 q^{27} - 32 q^{30} + 24 q^{33} + 12 q^{34} - 4 q^{36} - 8 q^{37} - 64 q^{39} - 60 q^{40} + 2 q^{42} + 24 q^{43} - 28 q^{45} + 20 q^{46} - 26 q^{48} + 40 q^{49} - 32 q^{51} + 84 q^{52} - 14 q^{54} + 16 q^{55} + 12 q^{58} - 24 q^{60} - 48 q^{61} - 12 q^{64} - 36 q^{66} + 40 q^{67} + 4 q^{69} + 8 q^{70} + 8 q^{72} + 40 q^{75} - 44 q^{76} + 24 q^{78} + 56 q^{81} - 84 q^{82} + 2 q^{84} - 48 q^{85} + 32 q^{87} + 52 q^{88} - 76 q^{90} - 24 q^{91} + 56 q^{93} - 62 q^{96} + 16 q^{97} + 24 q^{99}+O(q^{100}) \) 40 * q + 4 * q^3 - 2 * q^6 - 40 * q^7 - 8 * q^10 - 2 * q^12 + 24 * q^13 + 36 * q^16 + 12 * q^18 + 16 * q^19 - 4 * q^21 - 8 * q^22 + 6 * q^24 - 32 * q^27 - 32 * q^30 + 24 * q^33 + 12 * q^34 - 4 * q^36 - 8 * q^37 - 64 * q^39 - 60 * q^40 + 2 * q^42 + 24 * q^43 - 28 * q^45 + 20 * q^46 - 26 * q^48 + 40 * q^49 - 32 * q^51 + 84 * q^52 - 14 * q^54 + 16 * q^55 + 12 * q^58 - 24 * q^60 - 48 * q^61 - 12 * q^64 - 36 * q^66 + 40 * q^67 + 4 * q^69 + 8 * q^70 + 8 * q^72 + 40 * q^75 - 44 * q^76 + 24 * q^78 + 56 * q^81 - 84 * q^82 + 2 * q^84 - 48 * q^85 + 32 * q^87 + 52 * q^88 - 76 * q^90 - 24 * q^91 + 56 * q^93 - 62 * q^96 + 16 * q^97 + 24 * q^99

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