LMFDB - Embedded newform 336.2.s.c.155.3

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			155.3
Character	$\chi$	$=$	336.155
Dual form			336.2.s.c.323.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.37293 + 0.339195i) q^{2} +(-1.63649 + 0.567369i) q^{3} +(1.76989 - 0.931385i) q^{4} +(0.132854 - 0.132854i) q^{5} +(2.05434 - 1.33405i) q^{6} -1.00000 q^{7} +(-2.11403 + 1.87907i) q^{8} +(2.35619 - 1.85698i) q^{9} +O(q^{10})$	\(q+(-1.37293 + 0.339195i) q^{2} +(-1.63649 + 0.567369i) q^{3} +(1.76989 - 0.931385i) q^{4} +(0.132854 - 0.132854i) q^{5} +(2.05434 - 1.33405i) 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} +(-2.36797 + 2.52838i) 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} +(-2.60501 + 3.34872i) q^{18} +(5.87341 + 5.87341i) q^{19} +(0.111399 - 0.358874i) q^{20} +(1.63649 - 0.567369i) q^{21} +(-1.22477 - 0.739484i) q^{22} +6.42354i q^{23} +(2.39345 - 4.27450i) q^{24} +4.96470i q^{25} +(-0.213312 + 0.353298i) q^{26} +(-2.80227 + 4.37576i) q^{27} +(-1.76989 + 0.931385i) q^{28} +(5.00314 + 5.00314i) q^{29} +(0.0956934 - 0.450160i) 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} +(2.44063 - 5.48118i) 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} +(-2.05434 + 1.33405i) q^{42} +(1.36769 - 1.36769i) q^{43} +(1.93236 + 0.599827i) q^{44} +(0.0663207 - 0.559735i) q^{45} +(-2.17883 - 8.81910i) q^{46} -0.603632 q^{47} +(-1.83616 + 6.68046i) q^{48} +1.00000 q^{49} +(-1.68400 - 6.81620i) q^{50} +(3.92619 + 11.3245i) q^{51} +(0.173027 - 0.557409i) q^{52} +(6.19471 - 6.19471i) q^{53} +(2.36310 - 6.95814i) 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} +(0.0213111 + 0.650498i) 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} +(2.42388 + 0.515261i) q^{66} +(2.55815 + 2.55815i) q^{67} +(-6.44517 - 12.2476i) q^{68} +(-3.64452 - 10.5120i) q^{69} +(0.137336 - 0.227462i) q^{70} +0.808658i q^{71} +(-1.49164 + 8.35314i) q^{72} -11.5367i q^{73} +(-10.5344 - 6.36037i) q^{74} +(-2.81682 - 8.12467i) q^{75} +(15.8657 + 4.92491i) q^{76} +(-0.715349 - 0.715349i) q^{77} +(0.148633 - 0.699195i) 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} +(2.36797 - 2.52838i) 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} +(0.0988052 + 0.790974i) q^{90} +(-0.206350 + 0.206350i) q^{91} +(5.98279 + 11.3690i) q^{92} +(1.43504 + 4.13916i) q^{93} +(0.828746 - 0.204749i) q^{94} +1.56061 q^{95} +(0.254949 - 9.79464i) q^{96} -5.56394 q^{97} +(-1.37293 + 0.339195i) q^{98} +(3.01389 + 0.357104i) 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
$3$	−1.63649	+	0.567369i	−0.944827	+	0.327570i
$3$	−1.63649	+	0.567369i	−0.944827	+	0.327570i
$4$	1.76989	−	0.931385i	0.884947	−	0.465692i
$5$	0.132854	−	0.132854i	0.0594139	−	0.0594139i	−0.676776	−	0.736189i	$-0.736623\pi$
$5$	0.132854	−	0.132854i	0.0594139	−	0.0594139i	0.736189	+	0.676776i	$0.236623\pi$
$6$	2.05434	−	1.33405i	0.838681	−	0.544623i
$7$	−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	0.806678	−	0.590992i	$-0.201263\pi$
$11$	0.715349	+	0.715349i	0.215686	+	0.215686i	−0.590992	+	0.806678i	$0.701263\pi$
$12$	−2.36797	+	2.52838i	−0.683574	+	0.729881i
$13$	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	$-0.683040\pi$
$17$		−	6.91999i		−	1.67834i	0.543866	−	0.839172i	$-0.316960\pi$
$18$	−2.60501	+	3.34872i	−0.614006	+	0.789301i
$19$	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
$21$	1.63649	−	0.567369i	0.357111	−	0.123810i
$22$	−1.22477	−	0.739484i	−0.261122	−	0.157659i
$23$			6.42354i			1.33940i	0.742631	+	0.669701i	$0.233578\pi$
$23$			6.42354i			1.33940i	−0.742631	+	0.669701i	$0.766422\pi$
$24$	2.39345	−	4.27450i	0.488561	−	0.872529i
$25$			4.96470i			0.992940i
$26$	−0.213312	+	0.353298i	−0.0418340	+	0.0692875i
$27$	−2.80227	+	4.37576i	−0.539298	+	0.842115i
$28$	−1.76989	+	0.931385i	−0.334478	+	0.176015i
$29$	5.00314	+	5.00314i	0.929059	+	0.929059i	0.997645	−	0.0685860i	$-0.0218488\pi$
$29$	5.00314	+	5.00314i	0.929059	+	0.929059i	−0.0685860	+	0.997645i	$0.521849\pi$
$30$	0.0956934	−	0.450160i	0.0174712	−	0.0821875i
$31$		−	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
$36$	2.44063	−	5.48118i	0.406772	−	0.913530i
$37$	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	$-0.367159\pi$
$41$	5.19068			0.810647			0.405324	+	0.914173i	$0.367159\pi$
$42$	−2.05434	+	1.33405i	−0.316992	+	0.205848i
$43$	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
$45$	0.0663207	−	0.559735i	0.00988651	−	0.0834403i
$46$	−2.17883	−	8.81910i	−0.321252	−	1.30030i
$47$	−0.603632			−0.0880487			−0.0440244	−	0.999030i	$-0.514018\pi$
$47$	−0.603632			−0.0880487			−0.0440244	+	0.999030i	$0.514018\pi$
$48$	−1.83616	+	6.68046i	−0.265027	+	0.964241i
$49$	1.00000			0.142857
$50$	−1.68400	−	6.81620i	−0.238154	−	0.963957i
$51$	3.92619	+	11.3245i	0.549776	+	1.58574i
$52$	0.173027	−	0.557409i	0.0239945	−	0.0772988i
$53$	6.19471	−	6.19471i	0.850909	−	0.850909i	−0.139336	−	0.990245i	$-0.544497\pi$
$53$	6.19471	−	6.19471i	0.850909	−	0.850909i	0.990245	+	0.139336i	$0.0444969\pi$
$54$	2.36310	−	6.95814i	0.321577	−	0.946883i
$55$	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	0.302226	−	0.953236i	$-0.402270\pi$
$59$	−5.00050	−	5.00050i	−0.651010	−	0.651010i	−0.953236	+	0.302226i	$0.902270\pi$
$60$	0.0213111	+	0.650498i	0.00275125	+	0.0839789i
$61$	−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
$66$	2.42388	+	0.515261i	0.298359	+	0.0634242i
$67$	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
$69$	−3.64452	−	10.5120i	−0.438748	−	1.26550i
$70$	0.137336	−	0.227462i	0.0164148	−	0.0271870i
$71$			0.808658i			0.0959700i	0.998848	+	0.0479850i	$0.0152800\pi$
$71$			0.808658i			0.0959700i	−0.998848	+	0.0479850i	$0.984720\pi$
$72$	−1.49164	+	8.35314i	−0.175791	+	0.984428i
$73$		−	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
$75$	−2.81682	−	8.12467i	−0.325258	−	0.938156i
$76$	15.8657	+	4.92491i	1.81992	+	0.564926i
$77$	−0.715349	−	0.715349i	−0.0815216	−	0.0815216i
$78$	0.148633	−	0.699195i	0.0168293	−	0.0791682i
$79$		−	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	−0.671015	−	0.741444i	$-0.734141\pi$
$83$	0.641645	−	0.641645i	0.0704297	−	0.0704297i	0.741444	+	0.671015i	$0.234141\pi$
$84$	2.36797	−	2.52838i	0.258367	−	0.275869i
$85$	−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	$-0.301760\pi$
$89$	11.0057			1.16661			0.583303	+	0.812254i	$0.301760\pi$
$90$	0.0988052	+	0.790974i	0.0104150	+	0.0833760i
$91$	−0.206350	+	0.206350i	−0.0216314	+	0.0216314i
$92$	5.98279	+	11.3690i	0.623749	+	1.18530i
$93$	1.43504	+	4.13916i	0.148807	+	0.429211i
$94$	0.828746	−	0.204749i	0.0854786	−	0.0211182i
$95$	1.56061			0.160115
$96$	0.254949	−	9.79464i	0.0260206	−	0.999661i
$97$	−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
$99$	3.01389	+	0.357104i	0.302907	+	0.0358903i
$100$	4.62404	+	8.78699i	0.462404	+	0.878699i
$101$	−7.49292	+	7.49292i	−0.745574	+	0.745574i	−0.973645	−	0.228071i	$-0.926758\pi$
$101$	−7.49292	+	7.49292i	−0.745574	+	0.745574i	0.228071	+	0.973645i	$0.426758\pi$
$102$	−9.23160	−	14.2160i	−0.914064	−	1.40760i
$103$	−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	0.929252	−	0.369447i	$-0.120453\pi$
$107$	5.79066	+	5.79066i	0.559804	+	0.559804i	−0.369447	+	0.929252i	$0.620453\pi$
$108$	−0.884215	+	10.3546i	−0.0850836	+	0.996374i
$109$	−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	$0.0882530\pi$
$113$			5.81929i			0.547433i	−0.961810	+	0.273716i	$0.911747\pi$
$114$	19.9014	+	4.23057i	1.86394	+	0.396230i
$115$	0.853390	+	0.853390i	0.0795791	+	0.0795791i
$116$	13.5149	+	4.19517i	1.25482	+	0.389512i
$117$	0.103010	−	0.869389i	0.00952332	−	0.0803750i
$118$	8.56150	+	5.16921i	0.788150	+	0.475864i
$119$			6.91999i			0.634354i
$120$	−0.249904	−	0.885862i	−0.0228130	−	0.0808677i
$121$		−	9.97655i		−	0.906959i
$122$	6.45724	−	10.6948i	0.584611	−	0.968261i
$123$	−8.49448	+	2.94503i	−0.765921	+	0.265544i
$124$	−2.35574	−	4.47658i	−0.211552	−	0.402009i
$125$	1.32385	+	1.32385i	0.118408	+	0.118408i
$126$	2.60501	−	3.34872i	0.232072	−	0.298328i
$127$		−	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	−0.314799	−	0.949158i	$-0.601937\pi$
$131$	7.26058	−	7.26058i	0.634359	−	0.634359i	0.949158	+	0.314799i	$0.101937\pi$
$132$	−3.50260	+	0.114750i	−0.304862	+	0.00998767i
$133$	−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	$-0.546139\pi$
$137$	−3.38132			−0.288886			−0.144443	+	0.989513i	$0.546139\pi$
$138$	8.56931	+	13.1961i	0.729468	+	1.12333i
$139$	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
$141$	0.987836	−	0.342482i	0.0831908	−	0.0288422i
$142$	−0.274293	−	1.11023i	−0.0230181	−	0.0931687i
$143$	0.295225			0.0246880
$144$	−0.785427	−	11.9743i	−0.0654523	−	0.997856i
$145$	1.32937			0.110398
$146$	3.91319	+	15.8391i	0.323858	+	1.31085i
$147$	−1.63649	+	0.567369i	−0.134975	+	0.0467958i
$148$	16.6204	+	5.15917i	1.36619	+	0.424081i
$149$	3.57067	−	3.57067i	0.292520	−	0.292520i	−0.545555	−	0.838075i	$-0.683681\pi$
$149$	3.57067	−	3.57067i	0.292520	−	0.292520i	0.838075	+	0.545555i	$0.183681\pi$
$150$	6.62315	+	10.1992i	0.540778	+	0.832760i
$151$	−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
$156$	0.0331008	+	1.01036i	0.00265018	+	0.0808938i
$157$	−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
$162$	0.0806435	+	12.7277i	0.00633595	+	0.999980i
$163$	−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
$165$	−0.311053	+	0.107842i	−0.0242154	+	0.00839546i
$166$	−0.663293	+	1.09858i	−0.0514815	+	0.0852662i
$167$			20.3703i			1.57630i	0.615484	+	0.788149i	$0.288961\pi$
$167$			20.3703i			1.57630i	−0.615484	+	0.788149i	$0.711039\pi$
$168$	−2.39345	+	4.27450i	−0.184659	+	0.329785i
$169$			12.9148i			0.993449i
$170$	1.57404	+	0.950363i	0.120723	+	0.0728895i
$171$	24.7457	+	2.93202i	1.89235	+	0.224217i
$172$	1.14682	−	3.69452i	0.0874445	−	0.281705i
$173$	2.77906	+	2.77906i	0.211288	+	0.211288i	0.804814	−	0.593527i	$-0.202265\pi$
$173$	2.77906	+	2.77906i	0.211288	+	0.211288i	−0.593527	+	0.804814i	$0.702265\pi$
$174$	16.9526	+	3.60372i	1.28517	+	0.273198i
$175$		−	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	−0.328969	−	0.944341i	$-0.606701\pi$
$179$	8.23312	−	8.23312i	0.615372	−	0.615372i	0.944341	+	0.328969i	$0.106701\pi$
$180$	−0.403947	−	1.05244i	−0.0301085	−	0.0784443i
$181$	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
$186$	−3.37420	−	5.19603i	−0.247408	−	0.380991i
$187$	4.95021	−	4.95021i	0.361995	−	0.361995i
$188$	−1.06836	+	0.562213i	−0.0779184	+	0.0410036i
$189$	2.80227	−	4.37576i	0.203836	−	0.318290i
$190$	−2.14261	+	0.529350i	−0.155441	+	0.0384031i
$191$	−18.9768			−1.37312			−0.686558	−	0.727075i	$-0.740879\pi$
$191$	−18.9768			−1.37312			−0.686558	+	0.727075i	$0.740879\pi$
$192$	2.97227	+	13.5339i	0.214505	+	0.976723i
$193$	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
$195$	0.0311081	+	0.0897266i	0.00222770	+	0.00642545i
$196$	1.76989	−	0.931385i	0.126421	−	0.0665275i
$197$	−16.3956	+	16.3956i	−1.16814	+	1.16814i	−0.185494	+	0.982645i	$0.559389\pi$
$197$	−16.3956	+	16.3956i	−1.16814	+	1.16814i	−0.982645	+	0.185494i	$0.940611\pi$
$198$	−4.25900	+	0.532016i	−0.302674	+	0.0378087i
$199$	−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
$204$	17.4964	+	16.3863i	1.22499	+	1.14727i
$205$	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
$210$	−0.0956934	+	0.450160i	−0.00660347	+	0.0310640i
$211$	−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
$213$	−0.458807	−	1.32336i	−0.0314369	−	0.0906750i
$214$	−9.91435	−	5.98603i	−0.677731	−	0.409196i
$215$		−	0.363406i		−	0.0247841i
$216$	−2.29827	−	14.5161i	−0.156377	−	0.987697i
$217$			2.52929i			0.171700i
$218$	5.89837	−	9.76918i	0.399488	−	0.661652i
$219$	6.54556	+	18.8797i	0.442308	+	1.27577i
$220$	0.336410	−	0.177031i	0.0226807	−	0.0119355i
$221$	−1.42794	−	1.42794i	−0.0960537	−	0.0960537i
$222$	20.8480	+	4.43181i	1.39923	+	0.297443i
$223$		−	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	−0.700069	−	0.714075i	$-0.746848\pi$
$227$	0.211018	−	0.211018i	0.0140058	−	0.0140058i	0.714075	+	0.700069i	$0.246848\pi$
$228$	−28.7583	+	0.942158i	−1.90456	+	0.0623959i
$229$	−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	$-0.434421\pi$
$233$	6.24518			0.409135			0.204568	+	0.978852i	$0.434421\pi$
$234$	0.153466	+	1.22855i	0.0100324	+	0.0803131i
$235$	−0.0801946	+	0.0801946i	−0.00523132	+	0.00523132i
$236$	−13.5077	−	4.19297i	−0.879279	−	0.272939i
$237$	1.97703	+	5.70245i	0.128422	+	0.370414i
$238$	−2.34723	−	9.50069i	−0.152148	−	0.615838i
$239$	25.8455			1.67180			0.835902	−	0.548878i	$-0.184945\pi$
$239$	25.8455			1.67180			0.835902	+	0.548878i	$0.184945\pi$
$240$	0.643582	+	1.13146i	0.0415430	+	0.0730356i
$241$	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
$243$	1.52303	+	15.5139i	0.0977025	+	0.995216i
$244$	−5.23774	+	16.8735i	−0.335312	+	1.08022i
$245$	0.132854	−	0.132854i	0.00848770	−	0.00848770i
$246$	10.6634	−	6.92461i	0.679875	−	0.441497i
$247$	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	0.289708	−	0.957115i	$-0.406442\pi$
$251$	−10.5737	−	10.5737i	−0.667407	−	0.667407i	−0.957115	+	0.289708i	$0.906442\pi$
$252$	−2.44063	+	5.48118i	−0.153745	+	0.345282i
$253$	−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	$-0.956986\pi$
$257$		−	4.31950i		−	0.269443i	0.990884	−	0.134722i	$-0.0430140\pi$
$258$	0.985140	−	4.63428i	0.0613322	−	0.288518i
$259$	−6.15279	−	6.15279i	−0.382316	−	0.382316i
$260$	−0.0510666	−	0.0970410i	−0.00316702	−	0.00601823i
$261$	21.0791	+	2.49757i	1.30476	+	0.154596i
$262$	−7.50554	+	12.4310i	−0.463694	+	0.767992i
$263$			11.9657i			0.737837i	0.929462	+	0.368918i	$0.120272\pi$
$263$			11.9657i			0.737837i	−0.929462	+	0.368918i	$0.879728\pi$
$264$	4.76992	−	1.34561i	0.293568	−	0.0828165i
$265$		−	1.64598i		−	0.101112i
$266$	10.0560	+	6.07157i	0.616575	+	0.372272i
$267$	−18.0108	+	6.24431i	−1.10224	+	0.382146i
$268$	6.91026	+	2.14503i	0.422112	+	0.131028i
$269$	−19.4957	−	19.4957i	−1.18867	−	1.18867i	−0.977435	−	0.211236i	$-0.932251\pi$
$269$	−19.4957	−	19.4957i	−1.18867	−	1.18867i	−0.211236	−	0.977435i	$-0.567749\pi$
$270$	−0.610467	−	1.23836i	−0.0371519	−	0.0753642i
$271$			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
$276$	−16.2412	−	15.2108i	−0.977603	−	0.915580i
$277$	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	$-0.661831\pi$
$281$	−16.3201			−0.973575			−0.486787	+	0.873520i	$0.661831\pi$
$282$	−1.24006	+	0.805274i	−0.0738448	+	0.0479533i
$283$	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
$285$	−2.55391	+	0.885439i	−0.151281	+	0.0524489i
$286$	−0.405324	+	0.100139i	−0.0239673	+	0.00592133i
$287$	−5.19068			−0.306396
$288$	5.13995	+	16.1735i	0.302875	+	0.953030i
$289$	−30.8863			−1.81684
$290$	−1.82514	+	0.450915i	−0.107176	+	0.0264787i
$291$	9.10533	−	3.15681i	0.533764	−	0.185055i
$292$	−10.7451	−	20.4187i	−0.628809	−	1.19492i
$293$	4.80343	−	4.80343i	0.280620	−	0.280620i	−0.552736	−	0.833356i	$-0.686416\pi$
$293$	4.80343	−	4.80343i	0.280620	−	0.280620i	0.833356	+	0.552736i	$0.186416\pi$
$294$	2.05434	−	1.33405i	0.119812	−	0.0778033i
$295$	−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
$300$	−12.5527	−	11.7563i	−0.724728	−	0.678748i
$301$	−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
$306$	23.1731	+	18.0266i	1.32472	+	1.03051i
$307$	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
$309$	0.931105	−	0.322813i	0.0529687	−	0.0183642i
$310$	0.575319	+	0.347363i	0.0326759	+	0.0197289i
$311$		−	16.8194i		−	0.953741i	−0.878973	−	0.476871i	$-0.841771\pi$
$311$		−	16.8194i		−	0.953741i	0.878973	−	0.476871i	$-0.158229\pi$
$312$	−0.388155	−	1.37593i	−0.0219750	−	0.0778970i
$313$			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
$315$	−0.0663207	+	0.559735i	−0.00373675	+	0.0315375i
$316$	−3.24547	−	6.16731i	−0.182572	−	0.346938i
$317$	−11.7725	−	11.7725i	−0.661211	−	0.661211i	0.294455	−	0.955665i	$-0.404862\pi$
$317$	−11.7725	−	11.7725i	−0.661211	−	0.661211i	−0.955665	+	0.294455i	$0.904862\pi$
$318$	4.46200	−	20.9901i	0.250217	−	1.17707i
$319$			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
$324$	−4.42788	−	17.4469i	−0.245993	−	0.969272i
$325$	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
$330$	0.390475	−	0.253567i	0.0214950	−	0.0139584i
$331$	−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
$333$	25.9227	+	3.07148i	1.42056	+	0.168316i
$334$	−6.90949	−	27.9670i	−0.378071	−	1.53029i
$335$	0.679718			0.0371369
$336$	1.83616	−	6.68046i	0.100171	−	0.364449i
$337$	−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
$339$	−3.30168	−	9.52320i	−0.179323	−	0.517229i
$340$	−2.48341	−	0.770879i	−0.134682	−	0.0418068i
$341$	1.80933	−	1.80933i	0.0979806	−	0.0979806i
$342$	−34.9687	+	4.36814i	−1.89089	+	0.236202i
$343$	−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	0.222670	−	0.974894i	$-0.428523\pi$
$347$	−14.0124	−	14.0124i	−0.752224	−	0.752224i	−0.974894	+	0.222670i	$0.928523\pi$
$348$	−24.4971	+	0.802556i	−1.31318	+	0.0430215i
$349$	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	$0.120700\pi$
$353$			13.9096i			0.740334i	−0.928965	+	0.370167i	$0.879300\pi$
$354$	−16.9436	−	3.60182i	−0.900544	−	0.191435i
$355$	0.107433	+	0.107433i	0.00570195	+	0.00570195i
$356$	19.4790	−	10.2506i	1.03238	−	0.543280i
$357$	−3.92619	−	11.3245i	−0.207796	−	0.599355i
$358$	−8.51089	+	14.0962i	−0.449815	+	0.745005i
$359$		−	20.7206i		−	1.09359i	−0.837266	−	0.546796i	$-0.815847\pi$
$359$		−	20.7206i		−	1.09359i	0.837266	−	0.546796i	$-0.184153\pi$
$360$	0.911576	+	1.30791i	0.0480443	+	0.0689331i
$361$			49.9939i			2.63126i
$362$	−8.41990	−	5.08372i	−0.442540	−	0.267194i
$363$	5.66038	+	16.3265i	0.297093	+	0.856919i
$364$	−0.173027	+	0.557409i	−0.00906905	+	0.0292162i
$365$	−1.53269	−	1.53269i	−0.0802247	−	0.0802247i
$366$	−4.49930	+	21.1655i	−0.235182	+	1.10634i
$367$			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
$372$	6.39502	+	5.98929i	0.331566	+	0.310530i
$373$	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
$378$	−2.36310	+	6.95814i	−0.121545	+	0.357888i
$379$	−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
$381$	8.62701	+	24.8833i	0.441975	+	1.27481i
$382$	26.0539	−	6.43685i	1.33304	−	0.329338i
$383$	10.0142			0.511702			0.255851	−	0.966716i	$-0.417644\pi$
$383$	10.0142			0.511702			0.255851	+	0.966716i	$0.417644\pi$
$384$	−8.67135	−	17.5729i	−0.442508	−	0.896765i
$385$	−0.190073			−0.00968704
$386$	−35.2192	+	8.70120i	−1.79261	+	0.442879i
$387$	0.682756	−	5.76233i	0.0347064	−	0.292916i
$388$	−9.84759	+	5.18217i	−0.499936	+	0.263085i
$389$	−18.2249	+	18.2249i	−0.924041	+	0.924041i	−0.997312	−	0.0732708i	$-0.976656\pi$
$389$	−18.2249	+	18.2249i	−0.924041	+	0.924041i	0.0732708	+	0.997312i	$0.476656\pi$
$390$	−0.0731442	−	0.112637i	−0.00370380	−	0.00570359i
$391$	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
$396$	5.66686	−	2.17505i	0.284770	−	0.109301i
$397$	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	$-0.834771\pi$
$401$		−	19.8682i		−	0.992169i	0.868274	−	0.496084i	$-0.165229\pi$
$402$	8.66799	+	1.84261i	0.432320	+	0.0919012i
$403$	−0.521920	−	0.521920i	−0.0259987	−	0.0259987i
$404$	−6.28288	+	20.2405i	−0.312585	+	1.00700i
$405$	−0.883154	−	1.44200i	−0.0438843	−	0.0716533i
$406$	8.56601	+	5.17194i	0.425124	+	0.256679i
$407$			8.80278i			0.436338i
$408$	−29.5795	−	16.5627i	−1.46440	−	0.819974i
$409$			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
$411$	5.53349	−	1.91845i	0.272947	−	0.0946304i
$412$	−1.00701	+	0.529926i	−0.0496118	+	0.0261076i
$413$	5.00050	+	5.00050i	0.246059	+	0.246059i
$414$	−21.5107	−	16.7334i	−1.05719	−	0.822400i
$415$		−	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	$0.524763\pi$
$419$	−21.9984	+	21.9984i	−1.07469	+	1.07469i	−0.996976	+	0.0777158i	$0.975237\pi$
$420$	−0.0213111	−	0.650498i	−0.00103988	−	0.0317410i
$421$	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
$426$	1.07879	+	1.66126i	0.0522675	+	0.0804882i
$427$	6.24649	−	6.24649i	0.302289	−	0.302289i
$428$	15.6422	+	4.85552i	0.756093	+	0.234700i
$429$	−0.483132	+	0.167501i	−0.0233258	+	0.00808704i
$430$	0.123266	+	0.498933i	0.00594439	+	0.0240607i
$431$	14.4548			0.696262			0.348131	−	0.937446i	$-0.386816\pi$
$431$	14.4548			0.696262			0.348131	+	0.937446i	$0.386816\pi$
$432$	8.07917	+	19.1501i	0.388709	+	0.921361i
$433$	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
$435$	−2.17550	+	0.754242i	−0.104307	+	0.0361632i
$436$	−4.78442	+	15.4131i	−0.229132	+	0.738155i
$437$	−37.7281	+	37.7281i	−1.80478	+	1.80478i
$438$	−15.3905	−	23.7003i	−0.735387	−	1.13244i
$439$	−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	0.292978	−	0.956119i	$-0.405354\pi$
$443$	−13.9575	−	13.9575i	−0.663141	−	0.663141i	−0.956119	+	0.292978i	$0.905354\pi$
$444$	−30.1262	+	0.986972i	−1.42973	+	0.0468396i
$445$	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	$0.108606\pi$
$449$			14.1807i			0.669228i	−0.942355	+	0.334614i	$0.891394\pi$
$450$	−16.6254	−	12.9331i	−0.783729	−	0.609671i
$451$	3.71315	+	3.71315i	0.174845	+	0.174845i
$452$	5.42000	+	10.2995i	0.254935	+	0.484449i
$453$	3.77200	−	1.30775i	0.177224	−	0.0614433i
$454$	−0.218137	+	0.361290i	−0.0102377	+	0.0169562i
$455$			0.0548287i			0.00257041i
$456$	39.1636	−	11.0482i	1.83401	−	0.517379i
$457$		−	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
$459$	30.2802	+	19.3917i	1.41336	+	0.905128i
$460$	2.30524	+	0.715576i	0.107483	+	0.0333639i
$461$	−10.5304	−	10.5304i	−0.490449	−	0.490449i	0.417999	−	0.908448i	$-0.362732\pi$
$461$	−10.5304	−	10.5304i	−0.490449	−	0.490449i	−0.908448	+	0.417999i	$0.862732\pi$
$462$	−2.42388	−	0.515261i	−0.112769	−	0.0239721i
$463$		−	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	−0.999127	−	0.0417774i	$-0.986698\pi$
$467$	−20.6885	+	20.6885i	−0.957349	+	0.957349i	0.0417774	+	0.999127i	$0.486698\pi$
$468$	−0.627418	−	1.63467i	−0.0290024	−	0.0755625i
$469$	−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
$474$	−4.64857	−	7.15848i	−0.213516	−	0.328800i
$475$	−29.1597	+	29.1597i	−1.33794	+	1.33794i
$476$	6.44517	+	12.2476i	0.295414	+	0.561370i
$477$	3.09241	−	26.0994i	0.141592	−	1.19501i
$478$	−35.4841	+	8.76666i	−1.62301	+	0.400978i
$479$	18.5260			0.846476			0.423238	−	0.906018i	$-0.360893\pi$
$479$	18.5260			0.846476			0.423238	+	0.906018i	$0.360893\pi$
$480$	−1.26738	−	1.33512i	−0.0578478	−	0.0609398i
$481$	2.53926			0.115780
$482$	−26.0661	+	6.43985i	−1.18728	+	0.293327i
$483$	3.64452	+	10.5120i	0.165831	+	0.478315i
$484$	−9.29201	−	17.6574i	−0.422364	−	0.802611i
$485$	−0.739190	+	0.739190i	−0.0335649	+	0.0335649i
$486$	−7.35325	−	20.7829i	−0.333550	−	0.942732i
$487$	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	0.764321	−	0.644836i	$-0.223074\pi$
$491$	2.64760	+	2.64760i	0.119485	+	0.119485i	−0.644836	+	0.764321i	$0.723074\pi$
$492$	−12.2914	+	13.1240i	−0.554138	+	0.591676i
$493$	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
$498$	0.462172	−	2.17414i	0.0207104	−	0.0974256i
$499$	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
$501$	−11.5575	−	33.3357i	−0.516349	−	1.48933i
$502$	18.1036	+	10.9305i	0.808002	+	0.487850i
$503$		−	19.8445i		−	0.884824i	−0.896812	−	0.442412i	$-0.854123\pi$
$503$		−	19.8445i		−	0.884824i	0.896812	−	0.442412i	$-0.145877\pi$
$504$	1.49164	−	8.35314i	0.0664428	−	0.372079i
$505$			1.99092i			0.0885949i
$506$	4.75011	−	7.86736i	0.211168	−	0.349747i
$507$	−7.32747	−	21.1350i	−0.325425	−	0.938637i
$508$	−14.1620	−	26.9118i	−0.628336	−	1.19402i
$509$	18.7709	+	18.7709i	0.832006	+	0.832006i	0.987791	−	0.155785i	$-0.0497908\pi$
$509$	18.7709	+	18.7709i	0.832006	+	0.832006i	−0.155785	+	0.987791i	$0.549791\pi$
$510$	−3.11510	−	0.662198i	−0.137939	−	0.0293226i
$511$			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
$516$	0.219393	+	6.69672i	0.00965823	+	0.294806i
$517$	−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	$-0.380906\pi$
$521$	16.6843			0.730951			0.365476	+	0.930821i	$0.380906\pi$
$522$	−29.7873	+	3.72091i	−1.30376	+	0.162860i
$523$	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
$525$	2.81682	+	8.12467i	0.122936	+	0.354590i
$526$	−4.05871	−	16.4281i	−0.176968	−	0.716300i
$527$	−17.5027			−0.762429
$528$	−6.09236	+	3.46536i	−0.265136	+	0.150811i
$529$	−18.2619			−0.793996
$530$	0.558308	+	2.25982i	0.0242513	+	0.0981603i
$531$	−21.0680	−	2.49626i	−0.914272	−	0.108328i
$532$	−15.8657	−	4.92491i	−0.687866	−	0.213522i
$533$	1.07110	−	1.07110i	0.0463944	−	0.0463944i
$534$	22.6095	−	14.6822i	0.978411	−	0.635361i
$535$	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
$540$	1.25818	+	1.49312i	0.0541433	+	0.0642536i
$541$	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
$546$	−0.148633	+	0.699195i	−0.00636089	+	0.0299228i
$547$	−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
$549$	−3.11826	+	26.3175i	−0.133084	+	1.12320i
$550$	3.67132	−	6.08061i	0.156545	−	0.259278i
$551$			58.7709i			2.50373i
$552$	27.4575	+	15.3744i	1.16867	+	0.654380i
$553$			3.48456i			0.148179i
$554$	−27.7322	−	16.7440i	−1.17823	−	0.711384i
$555$	−2.67539	+	0.927556i	−0.113564	+	0.0393726i
$556$	5.16351	−	16.6344i	0.218982	−	0.705455i
$557$	−20.6256	−	20.6256i	−0.873935	−	0.873935i	0.118964	−	0.992899i	$-0.462043\pi$
$557$	−20.6256	−	20.6256i	−0.873935	−	0.873935i	−0.992899	+	0.118964i	$0.962043\pi$
$558$	8.46990	+	6.58883i	0.358560	+	0.278927i
$559$		−	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	−0.766454	−	0.642299i	$-0.777981\pi$
$563$	−2.94590	+	2.94590i	−0.124155	+	0.124155i	0.642299	+	0.766454i	$0.277981\pi$
$564$	1.42938	−	1.52621i	0.0601878	−	0.0642651i
$565$	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	$-0.567319\pi$
$569$	−10.0145			−0.419832			−0.209916	+	0.977719i	$0.567319\pi$
$570$	3.20602	−	2.08192i	0.134285	−	0.0872022i
$571$	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
$573$	31.0554	−	10.7669i	1.29736	−	0.449792i
$574$	7.12645	−	1.76065i	0.297452	−	0.0734882i
$575$	−31.8910			−1.32995
$576$	−12.5428	−	20.4616i	−0.522615	−	0.852569i
$577$	−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
$579$	−41.9800	+	14.5544i	−1.74463	+	0.604861i
$580$	2.35284	−	1.23815i	0.0976964	−	0.0514115i
$581$	−0.641645	+	0.641645i	−0.0266199	+	0.0266199i
$582$	−11.4302	+	7.42257i	−0.473799	+	0.307675i
$583$	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	0.872797	−	0.488084i	$-0.162304\pi$
$587$	9.32085	+	9.32085i	0.384713	+	0.384713i	−0.488084	+	0.872797i	$0.662304\pi$
$588$	−2.36797	+	2.52838i	−0.0976535	+	0.104269i
$589$	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	$-0.718283\pi$
$593$		−	37.6934i		−	1.54788i	0.633257	−	0.773941i	$-0.281717\pi$
$594$	6.66795	−	3.28706i	0.273589	−	0.134870i
$595$	0.919345	+	0.919345i	0.0376895	+	0.0376895i
$596$	2.99404	−	9.64536i	0.122640	−	0.395090i
$597$	42.5373	−	14.7476i	1.74093	−	0.603580i
$598$	−2.26943	−	1.37022i	−0.0928037	−	0.0560325i
$599$		−	10.6528i		−	0.435260i	−0.976031	−	0.217630i	$-0.930167\pi$
$599$		−	10.6528i		−	0.435260i	0.976031	−	0.217630i	$-0.0698326\pi$
$600$	21.2216	+	11.8828i	0.866369	+	0.485112i
$601$			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
$603$	10.7779	+	1.27703i	0.438910	+	0.0520047i
$604$	−4.07949	+	2.14678i	−0.165992	+	0.0873512i
$605$	−1.32542	−	1.32542i	−0.0538860	−	0.0538860i
$606$	−5.39710	+	25.3889i	−0.219242	+	1.03136i
$607$			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
$612$	−37.9297	−	16.8891i	−1.53322	−	0.682703i
$613$	−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	$-0.538242\pi$
$617$	−5.95415			−0.239705			−0.119852	+	0.992792i	$0.538242\pi$
$618$	−1.16885	+	0.759028i	−0.0470180	+	0.0305326i
$619$	−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
$621$	−28.1079	−	18.0005i	−1.12793	−	0.722336i
$622$	5.70506	+	23.0919i	0.228752	+	0.925902i
$623$	−11.0057			−0.440936
$624$	0.999622	+	1.75741i	0.0400169	+	0.0703526i
$625$	−24.4717			−0.978870
$626$	−1.04967	−	4.24866i	−0.0419531	−	0.169811i
$627$	−4.76764	−	13.7515i	−0.190401	−	0.549183i
$628$	−10.1393	+	32.6641i	−0.404603	+	1.30344i
$629$	42.5772	−	42.5772i	1.69766	−	1.69766i
$630$	−0.0988052	−	0.790974i	−0.00393649	−	0.0315132i
$631$	−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
$636$	0.993697	+	30.3315i	0.0394027	+	1.20272i
$637$	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	$-0.997924\pi$
$641$		−	0.330226i		−	0.0130431i	0.999979	−	0.00652156i	$-0.00207589\pi$
$642$	19.6210	+	4.17097i	0.774379	+	0.164615i
$643$	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
$645$	0.206185	+	0.594710i	0.00811854	+	0.0234167i
$646$	−42.0152	+	69.5876i	−1.65307	+	2.73789i
$647$			37.5372i			1.47574i	0.674942	+	0.737871i	$0.264169\pi$
$647$			37.5372i			1.47574i	−0.674942	+	0.737871i	$0.735831\pi$
$648$	11.9971	+	22.4515i	0.471290	+	0.881978i
$649$		−	7.15421i		−	0.280827i
$650$	−1.75402	−	1.05903i	−0.0687983	−	0.0415386i
$651$	−1.43504	−	4.13916i	−0.0562437	−	0.162226i
$652$	−2.93732	−	0.911780i	−0.115034	−	0.0357081i
$653$	3.90230	+	3.90230i	0.152709	+	0.152709i	0.779327	−	0.626618i	$-0.215561\pi$
$653$	3.90230	+	3.90230i	0.152709	+	0.152709i	−0.626618	+	0.779327i	$0.715561\pi$
$654$	−4.10989	+	19.3337i	−0.160710	+	0.756007i
$655$		−	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	−0.885349	−	0.464928i	$-0.846080\pi$
$659$	−10.7926	+	10.7926i	−0.420421	+	0.420421i	0.464928	+	0.885349i	$0.346080\pi$
$660$	−0.450088	+	0.480578i	−0.0175197	+	0.0187065i
$661$	−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
$666$	−36.6320	+	4.57592i	−1.41946	+	0.177313i
$667$	−32.1379	+	32.1379i	−1.24438	+	1.24438i
$668$	18.9726	+	36.0532i	0.734070	+	1.39494i
$669$	6.61101	+	19.0685i	0.255597	+	0.737229i
$670$	−0.933207	+	0.230557i	−0.0360529	+	0.00890719i
$671$	−8.93684			−0.345003
$672$	−0.254949	+	9.79464i	−0.00983487	+	0.377836i
$673$	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
$675$	−21.7243	−	13.9125i	−0.836170	−	0.535491i
$676$	12.0287	+	22.8579i	0.462642	+	0.879150i
$677$	9.46846	−	9.46846i	0.363902	−	0.363902i	−0.501345	−	0.865247i	$-0.667161\pi$
$677$	9.46846	−	9.46846i	0.363902	−	0.363902i	0.865247	+	0.501345i	$0.167161\pi$
$678$	7.76322	+	11.9548i	0.298145	+	0.459122i
$679$	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	$-0.927253\pi$
$683$	−31.3757	−	31.3757i	−1.20056	−	1.20056i	−0.226558	−	0.973998i	$-0.572747\pi$
$684$	46.5280	−	17.8584i	1.77904	−	0.682832i
$685$	−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
$690$	2.89162	+	0.614691i	0.110082	+	0.0234009i
$691$	−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
$693$	−3.01389	−	0.357104i	−0.114488	−	0.0135652i
$694$	23.9910	+	14.4851i	0.910686	+	0.549848i
$695$		−	1.63622i		−	0.0620652i
$696$	33.3607	−	9.41116i	1.26453	−	0.356729i
$697$		−	35.9194i		−	1.36055i
$698$	−5.98359	+	9.91032i	−0.226482	+	0.375111i
$699$	−10.2202	+	3.54332i	−0.386562	+	0.134021i
$700$	−4.62404	−	8.78699i	−0.174772	−	0.332117i
$701$	−15.8683	−	15.8683i	−0.599338	−	0.599338i	0.340798	−	0.940136i	$-0.389303\pi$
$701$	−15.8683	−	15.8683i	−0.599338	−	0.599338i	−0.940136	+	0.340798i	$0.889303\pi$
$702$	−0.948188	−	1.92344i	−0.0357870	−	0.0725956i
$703$			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
$708$	24.4842	−	0.802134i	0.920173	−	0.0301460i
$709$	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
$714$	9.23160	+	14.2160i	0.345484	+	0.532021i
$715$	0.0392217	−	0.0392217i	0.00146681	−	0.00146681i
$716$	6.90354	−	22.2399i	0.257998	−	0.831146i
$717$	−42.2958	+	14.6639i	−1.57957	+	0.547634i
$718$	7.02832	+	28.4480i	0.262295	+	1.06167i
$719$	11.0849			0.413398			0.206699	−	0.978405i	$-0.433728\pi$
$719$	11.0849			0.413398			0.206699	+	0.978405i	$0.433728\pi$
$720$	−1.69517	−	1.48648i	−0.0631753	−	0.0553977i
$721$	0.568966			0.0211894
$722$	−16.9577	−	68.6383i	−0.631099	−	2.55445i
$723$	−31.0698	+	10.7719i	−1.15550	+	0.400611i
$724$	13.2843	+	4.12362i	0.493709	+	0.153253i
$725$	−24.8391	+	24.8391i	−0.922500	+	0.922500i
$726$	−13.3092	−	20.4952i	−0.493951	−	0.760650i
$727$	−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
$732$	−1.00200	−	30.5850i	−0.0370351	−	1.13045i
$733$	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
$738$	−13.5217	+	17.3821i	−0.497742	+	0.639845i
$739$	−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
$741$	−3.96678	+	1.37528i	−0.145723	+	0.0505221i
$742$	6.40371	−	10.6061i	0.235088	−	0.389364i
$743$		−	27.2593i		−	1.00005i	−0.866012	−	0.500023i	$-0.833325\pi$
$743$		−	27.2593i		−	1.00005i	0.866012	−	0.500023i	$-0.166675\pi$
$744$	−10.8115	−	6.05374i	−0.396368	−	0.221941i
$745$		−	0.948752i		−	0.0347596i
$746$	−18.2509	−	11.0194i	−0.668213	−	0.403450i
$747$	0.320310	−	2.70336i	0.0117195	−	0.0989107i
$748$	4.15079	−	13.3719i	0.151768	−	0.488925i
$749$	−5.79066	−	5.79066i	−0.211586	−	0.211586i
$750$	4.48570	+	0.953556i	0.163795	+	0.0348190i
$751$		−	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
$756$	0.884215	−	10.3546i	0.0321586	−	0.376594i
$757$	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	$-0.330913\pi$
$761$	27.9488			1.01314			0.506572	+	0.862198i	$0.330913\pi$
$762$	−20.2846	−	31.2369i	−0.734833	−	1.13159i
$763$	5.70587	−	5.70587i	0.206566	−	0.206566i
$764$	−33.5870	+	17.6747i	−1.21513	+	0.639449i
$765$	−3.87336	−	0.458939i	−0.140042	−	0.0165930i
$766$	−13.7488	+	3.39677i	−0.496766	+	0.122730i
$767$	−2.06371			−0.0745162
$768$	17.8658	+	21.1852i	0.644678	+	0.764455i
$769$	−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
$771$	2.45075	+	7.06881i	0.0882616	+	0.254577i
$772$	45.4022	−	23.8923i	1.63406	−	0.859904i
$773$	25.5398	−	25.5398i	0.918603	−	0.918603i	−0.0783250	−	0.996928i	$-0.524957\pi$
$773$	25.5398	−	25.5398i	0.918603	−	0.918603i	0.996928	+	0.0783250i	$0.0249572\pi$
$774$	1.01718	+	8.14288i	0.0365616	+	0.292690i
$775$	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
$780$	0.138628	+	0.129833i	0.00496368	+	0.00464876i
$781$	−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
$786$	5.22974	−	24.6017i	0.186539	−	0.877512i
$787$	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
$789$	−6.78896	−	19.5817i	−0.241693	−	0.697128i
$790$	0.792607	+	0.478555i	0.0281997	+	0.0170262i
$791$		−	5.81929i		−	0.206910i
$792$	−7.04246	+	4.90837i	−0.250243	+	0.174411i
$793$			2.57793i			0.0915450i
$794$	−3.20372	+	5.30615i	−0.113696	+	0.188308i
$795$	0.933877	+	2.69362i	0.0331212	+	0.0955330i
$796$	−46.0049	+	24.2095i	−1.63060	+	0.858083i
$797$	−22.0934	−	22.0934i	−0.782588	−	0.782588i	0.197679	−	0.980267i	$-0.436660\pi$
$797$	−22.0934	−	22.0934i	−0.782588	−	0.782588i	−0.980267	+	0.197679i	$0.936660\pi$
$798$	−19.9014	−	4.23057i	−0.704502	−	0.149761i
$799$			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
$804$	−12.5256	+	0.410354i	−0.441743	+	0.0144721i
$805$	−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	$-0.495592\pi$
$809$	0.787723			0.0276949			0.0138474	+	0.999904i	$0.495592\pi$
$810$	1.70163	+	1.68020i	0.0597892	+	0.0590363i
$811$	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
$813$	−2.72341	−	7.85527i	−0.0955142	−	0.275496i
$814$	−2.98586	−	12.0856i	−0.104654	−	0.423601i
$815$	−0.288925			−0.0101206
$816$	46.2287	+	12.7062i	1.61833	+	0.444806i
$817$	16.0661			0.562080
$818$	−1.52636	−	6.17814i	−0.0533680	−	0.216014i
$819$	−0.103010	+	0.869389i	−0.00359947	+	0.0303789i
$820$	0.578236	−	1.86280i	0.0201929	−	0.0650518i
$821$	2.46211	−	2.46211i	0.0859283	−	0.0859283i	−0.662836	−	0.748764i	$-0.730647\pi$
$821$	2.46211	−	2.46211i	0.0859283	−	0.0859283i	0.748764	+	0.662836i	$0.230647\pi$
$822$	−6.94638	+	4.51084i	−0.242283	+	0.157334i
$823$	−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	0.894043	−	0.447982i	$-0.147857\pi$
$827$	12.8277	+	12.8277i	0.446061	+	0.446061i	−0.447982	+	0.894043i	$0.647857\pi$
$828$	35.2086	+	15.6775i	1.22358	+	0.544831i
$829$	−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
$834$	4.43554	−	20.8656i	0.153590	−	0.722516i
$835$	2.70626	+	2.70626i	0.0936541	+	0.0936541i
$836$	7.82650	+	14.8726i	0.270685	+	0.514378i
$837$	11.0676	+	7.08778i	0.382551	+	0.244989i
$838$	22.7406	−	37.6641i	0.785560	−	1.30108i
$839$			4.28148i			0.147813i	0.997265	+	0.0739065i	$0.0235466\pi$
$839$			4.28148i			0.147813i	−0.997265	+	0.0739065i	$0.976453\pi$
$840$	0.249904	+	0.885862i	0.00862252	+	0.0305651i
$841$			21.0628i			0.726302i
$842$	−18.8136	−	11.3591i	−0.648358	−	0.391462i
$843$	26.7076	−	9.25951i	0.919859	−	0.318914i
$844$	−36.9899	−	11.4821i	−1.27325	−	0.395231i
$845$	1.71578	+	1.71578i	0.0590247	+	0.0590247i
$846$	1.57246	−	2.02139i	0.0540624	−	0.0694970i
$847$			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
$852$	−2.04460	−	1.91488i	−0.0700467	−	0.0656026i
$853$	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	$-0.540798\pi$
$857$	−7.48369			−0.255638			−0.127819	+	0.991798i	$0.540798\pi$
$858$	0.606493	−	0.393844i	0.0207053	−	0.0134456i
$859$	−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
$861$	8.49448	−	2.94503i	0.289491	−	0.100366i
$862$	−19.8454	+	4.90299i	−0.675938	+	0.166996i
$863$	−44.3294			−1.50899			−0.754495	−	0.656306i	$-0.772118\pi$
$863$	−44.3294			−1.50899			−0.754495	+	0.656306i	$0.772118\pi$
$864$	−17.5878	−	23.5514i	−0.598349	−	0.801236i
$865$	0.738415			0.0251069
$866$	−8.76507	+	2.16549i	−0.297849	+	0.0735862i
$867$	50.5450	−	17.5239i	1.71660	−	0.595143i
$868$	2.35574	+	4.47658i	0.0799592	+	0.151945i
$869$	2.49268	−	2.49268i	0.0845584	−	0.0845584i
$870$	2.73098	−	1.77344i	0.0925888	−	0.0601253i
$871$	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
$876$	29.1692	+	27.3186i	0.985535	+	0.923009i
$877$	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	$0.138249\pi$
$881$			24.9798i			0.841590i	−0.907156	+	0.420795i	$0.861751\pi$
$882$	−2.60501	+	3.34872i	−0.0877151	+	0.112757i
$883$	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
$885$	2.17435	−	0.753845i	0.0730900	−	0.0253402i
$886$	23.8970	+	14.4284i	0.802837	+	0.484732i
$887$			6.33001i			0.212541i	0.994337	+	0.106270i	$0.0338909\pi$
$887$			6.33001i			0.212541i	−0.994337	+	0.106270i	$0.966109\pi$
$888$	41.0265	−	11.5737i	1.37676	−	0.388388i
$889$			15.2053i			0.509969i
$890$	−1.51148	+	2.50339i	−0.0506650	+	0.0839139i
$891$	7.76441	−	4.75534i	0.260118	−	0.159310i
$892$	−10.8525	−	20.6229i	−0.363370	−	0.690506i
$893$	−3.54538	−	3.54538i	−0.118641	−	0.118641i
$894$	2.57193	−	12.0988i	0.0860180	−	0.404645i
$895$		−	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
$900$	27.2124	+	12.1170i	0.907080	+	0.403900i
$901$	−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
$906$	−4.73512	+	3.07489i	−0.157314	+	0.102156i
$907$	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
$909$	−3.74048	+	31.5690i	−0.124064	+	1.04708i
$910$	−0.0185976	−	0.0752762i	−0.000616506	−	0.00249538i
$911$	14.6002			0.483727			0.241864	−	0.970310i	$-0.422241\pi$
$911$	14.6002			0.483727			0.241864	+	0.970310i	$0.422241\pi$
$912$	−50.0216	+	28.4525i	−1.65638	+	0.942158i
$913$	0.918000			0.0303814
$914$	12.6697	+	51.2820i	0.419075	+	1.69626i
$915$	−0.941683	−	2.71614i	−0.0311311	−	0.0897928i
$916$	−31.7936	−	9.86910i	−1.05049	−	0.326084i
$917$	−7.26058	+	7.26058i	−0.239765	+	0.239765i
$918$	−48.1503	−	16.3526i	−1.58920	−	0.539718i
$919$	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
$924$	3.50260	−	0.114750i	0.115227	−	0.00377499i
$925$	−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	$0.0433463\pi$
$929$			8.27555i			0.271512i	−0.990742	+	0.135756i	$0.956654\pi$
$930$	−1.13859	−	0.242037i	−0.0373357	−	0.00793670i
$931$	5.87341	+	5.87341i	0.192493	+	0.192493i
$932$	11.0533	−	5.81666i	0.362063	−	0.190531i
$933$	9.54281	+	27.5248i	0.312417	+	0.901120i
$934$	21.3865	−	35.4214i	0.699788	−	1.15902i
$935$		−	1.31531i		−	0.0430151i
$936$	1.41587	+	2.03147i	0.0462793	+	0.0664008i
$937$		−	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
$939$	−1.75577	−	5.06425i	−0.0572974	−	0.165266i
$940$	−0.0672439	+	0.216628i	−0.00219325	+	0.00706562i
$941$	39.8696	+	39.8696i	1.29971	+	1.29971i	0.928579	+	0.371134i	$0.121031\pi$
$941$	39.8696	+	39.8696i	1.29971	+	1.29971i	0.371134	+	0.928579i	$0.378969\pi$
$942$	−8.70984	+	40.9727i	−0.283782	+	1.33496i
$943$			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	−0.170285	−	0.985395i	$-0.554469\pi$
$947$	25.0837	−	25.0837i	0.815110	−	0.815110i	0.985395	+	0.170285i	$0.0544689\pi$
$948$	8.81030	+	8.25134i	0.286145	+	0.267991i
$949$	−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	$-0.255283\pi$
$953$	42.9272			1.39055			0.695274	+	0.718745i	$0.255283\pi$
$954$	4.60710	+	36.8816i	0.149160	+	1.19409i
$955$	−2.52114	+	2.52114i	−0.0815822	+	0.0815822i
$956$	45.7437	−	24.0721i	1.47946	−	0.778547i
$957$	−4.06121	−	11.7139i	−0.131280	−	0.378658i
$958$	−25.4350	+	6.28394i	−0.821768	+	0.203025i
$959$	3.38132			0.109188
$960$	2.19290	+	1.40315i	0.0707755	+	0.0452864i
$961$	24.6027			0.793635
$962$	−3.48623	+	0.861304i	−0.112401	+	0.0277695i
$963$	24.3970	+	2.89071i	0.786183	+	0.0931517i
$964$	33.6026	−	17.6830i	1.08227	−	0.569530i
$965$	3.40803	−	3.40803i	0.109708	−	0.109708i
$966$	−8.56931	−	13.1961i	−0.275713	−	0.424579i
$967$	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	0.999830	−	0.0184358i	$-0.00586862\pi$
$971$	30.5811	+	30.5811i	0.981394	+	0.981394i	−0.0184358	+	0.999830i	$0.505869\pi$
$972$	17.1450	+	26.0394i	0.549926	+	0.835214i
$973$	−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	$0.0155007\pi$
$977$			3.04304i			0.0973554i	−0.998815	+	0.0486777i	$0.984499\pi$
$978$	−3.68448	−	0.783234i	−0.117817	−	0.0250451i
$979$	7.87295	+	7.87295i	0.251621	+	0.251621i
$980$	0.111399	−	0.358874i	0.00355851	−	0.0114638i
$981$	−2.84838	+	24.0398i	−0.0909417	+	0.767531i
$982$	−4.53304	−	2.73693i	−0.144655	−	0.0873389i
$983$		−	50.6697i		−	1.61611i	−0.589106	−	0.808056i	$-0.700520\pi$
$983$		−	50.6697i		−	1.61611i	0.589106	−	0.808056i	$-0.299480\pi$
$984$	12.4236	−	22.1876i	0.396051	−	0.707314i
$985$			4.35643i			0.138808i
$986$	−35.7897	+	59.2767i	−1.13978	+	1.88776i
$987$	−0.987836	+	0.342482i	−0.0314432	+	0.0109013i
$988$	4.29015	−	2.25764i	0.136488	−	0.0718250i
$989$	8.78544	+	8.78544i	0.279361	+	0.279361i
$990$	−0.495142	+	0.636503i	−0.0157367	+	0.0202294i
$991$		−	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
$996$	0.102927	+	3.14172i	0.00326136	+	0.0995492i
$997$	−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.155.3	✓	40
3.2	odd	2	inner	336.2.s.c.155.18	yes	40
4.3	odd	2		1344.2.s.c.911.18		40
12.11	even	2		1344.2.s.c.911.9		40
16.3	odd	4	inner	336.2.s.c.323.18	yes	40
16.13	even	4		1344.2.s.c.239.9		40
48.29	odd	4		1344.2.s.c.239.18		40
48.35	even	4	inner	336.2.s.c.323.3	yes	40

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

\(f(q)\)	\(=\)	\(q+(-1.37293 + 0.339195i) q^{2} +(-1.63649 + 0.567369i) q^{3} +(1.76989 - 0.931385i) q^{4} +(0.132854 - 0.132854i) q^{5} +(2.05434 - 1.33405i) q^{6} -1.00000 q^{7} +(-2.11403 + 1.87907i) q^{8} +(2.35619 - 1.85698i) q^{9} +O(q^{10})\)	\(q+(-1.37293 + 0.339195i) q^{2} +(-1.63649 + 0.567369i) q^{3} +(1.76989 - 0.931385i) q^{4} +(0.132854 - 0.132854i) q^{5} +(2.05434 - 1.33405i) 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} +(-2.36797 + 2.52838i) 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} +(-2.60501 + 3.34872i) q^{18} +(5.87341 + 5.87341i) q^{19} +(0.111399 - 0.358874i) q^{20} +(1.63649 - 0.567369i) q^{21} +(-1.22477 - 0.739484i) q^{22} +6.42354i q^{23} +(2.39345 - 4.27450i) q^{24} +4.96470i q^{25} +(-0.213312 + 0.353298i) q^{26} +(-2.80227 + 4.37576i) q^{27} +(-1.76989 + 0.931385i) q^{28} +(5.00314 + 5.00314i) q^{29} +(0.0956934 - 0.450160i) 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} +(2.44063 - 5.48118i) 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} +(-2.05434 + 1.33405i) q^{42} +(1.36769 - 1.36769i) q^{43} +(1.93236 + 0.599827i) q^{44} +(0.0663207 - 0.559735i) q^{45} +(-2.17883 - 8.81910i) q^{46} -0.603632 q^{47} +(-1.83616 + 6.68046i) q^{48} +1.00000 q^{49} +(-1.68400 - 6.81620i) q^{50} +(3.92619 + 11.3245i) q^{51} +(0.173027 - 0.557409i) q^{52} +(6.19471 - 6.19471i) q^{53} +(2.36310 - 6.95814i) 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} +(0.0213111 + 0.650498i) 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} +(2.42388 + 0.515261i) q^{66} +(2.55815 + 2.55815i) q^{67} +(-6.44517 - 12.2476i) q^{68} +(-3.64452 - 10.5120i) q^{69} +(0.137336 - 0.227462i) q^{70} +0.808658i q^{71} +(-1.49164 + 8.35314i) q^{72} -11.5367i q^{73} +(-10.5344 - 6.36037i) q^{74} +(-2.81682 - 8.12467i) q^{75} +(15.8657 + 4.92491i) q^{76} +(-0.715349 - 0.715349i) q^{77} +(0.148633 - 0.699195i) 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} +(2.36797 - 2.52838i) 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} +(0.0988052 + 0.790974i) q^{90} +(-0.206350 + 0.206350i) q^{91} +(5.98279 + 11.3690i) q^{92} +(1.43504 + 4.13916i) q^{93} +(0.828746 - 0.204749i) q^{94} +1.56061 q^{95} +(0.254949 - 9.79464i) q^{96} -5.56394 q^{97} +(-1.37293 + 0.339195i) q^{98} +(3.01389 + 0.357104i) 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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