LMFDB - Embedded newform 208.2.n.a.157.19

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [208,2,Mod(53,208)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(208, base_ring=CyclotomicField(4))

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

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

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

chi := DirichletCharacter("208.53");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 208 = 2^{4} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	208.n (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:	$1.66088836204$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$24$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			157.19
Character	$\chi$	$=$	208.157
Dual form			208.2.n.a.53.19

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.986819 + 1.01301i) q^{2} +(0.718176 + 0.718176i) q^{3} +(-0.0523779 + 1.99931i) q^{4} +(2.02033 - 2.02033i) q^{5} +(-0.0188099 + 1.43623i) q^{6} +0.407753i q^{7} +(-2.07701 + 1.91990i) q^{8} -1.96845i q^{9} +O(q^{10})$	\(q+(0.986819 + 1.01301i) q^{2} +(0.718176 + 0.718176i) q^{3} +(-0.0523779 + 1.99931i) q^{4} +(2.02033 - 2.02033i) q^{5} +(-0.0188099 + 1.43623i) q^{6} +0.407753i q^{7} +(-2.07701 + 1.91990i) q^{8} -1.96845i q^{9} +(4.04031 + 0.0529148i) q^{10} +(-1.76038 + 1.76038i) q^{11} +(-1.47348 + 1.39824i) q^{12} +(-0.707107 - 0.707107i) q^{13} +(-0.413057 + 0.402378i) q^{14} +2.90190 q^{15} +(-3.99451 - 0.209440i) q^{16} -4.09008 q^{17} +(1.99405 - 1.94250i) q^{18} +(-2.13946 - 2.13946i) q^{19} +(3.93345 + 4.14509i) q^{20} +(-0.292838 + 0.292838i) q^{21} +(-3.52046 - 0.0461065i) q^{22} +2.42989i q^{23} +(-2.87049 - 0.112834i) q^{24} -3.16343i q^{25} +(0.0185200 - 1.41409i) q^{26} +(3.56822 - 3.56822i) q^{27} +(-0.815226 - 0.0213572i) q^{28} +(2.51051 + 2.51051i) q^{29} +(2.86365 + 2.93965i) q^{30} +0.736081 q^{31} +(-3.72970 - 4.25316i) q^{32} -2.52853 q^{33} +(-4.03617 - 4.14329i) q^{34} +(0.823793 + 0.823793i) q^{35} +(3.93554 + 0.103103i) q^{36} +(1.13402 - 1.13402i) q^{37} +(0.0560349 - 4.27854i) q^{38} -1.01565i q^{39} +(-0.317416 + 8.07507i) q^{40} -10.6971i q^{41} +(-0.585627 - 0.00766979i) q^{42} +(-0.341182 + 0.341182i) q^{43} +(-3.42735 - 3.61176i) q^{44} +(-3.97690 - 3.97690i) q^{45} +(-2.46150 + 2.39786i) q^{46} +11.4260 q^{47} +(-2.71835 - 3.01918i) q^{48} +6.83374 q^{49} +(3.20459 - 3.12173i) q^{50} +(-2.93740 - 2.93740i) q^{51} +(1.45077 - 1.37669i) q^{52} +(-6.62837 + 6.62837i) q^{53} +(7.13583 + 0.0934560i) q^{54} +7.11308i q^{55} +(-0.782845 - 0.846907i) q^{56} -3.07301i q^{57} +(-0.0657534 + 5.02059i) q^{58} +(-9.01032 + 9.01032i) q^{59} +(-0.151996 + 5.80181i) q^{60} +(-2.36316 - 2.36316i) q^{61} +(0.726379 + 0.745657i) q^{62} +0.802639 q^{63} +(0.627960 - 7.97532i) q^{64} -2.85717 q^{65} +(-2.49520 - 2.56142i) q^{66} +(0.526396 + 0.526396i) q^{67} +(0.214230 - 8.17736i) q^{68} +(-1.74509 + 1.74509i) q^{69} +(-0.0215761 + 1.64745i) q^{70} +7.15228i q^{71} +(3.77922 + 4.08848i) q^{72} +5.01437i q^{73} +(2.26784 + 0.0297013i) q^{74} +(2.27190 - 2.27190i) q^{75} +(4.38950 - 4.16538i) q^{76} +(-0.717799 - 0.717799i) q^{77} +(1.02887 - 1.00227i) q^{78} +9.29431 q^{79} +(-8.49335 + 7.64708i) q^{80} -0.780111 q^{81} +(10.8362 - 10.5561i) q^{82} +(-10.8412 - 10.8412i) q^{83} +(-0.570138 - 0.600814i) q^{84} +(-8.26330 + 8.26330i) q^{85} +(-0.682305 - 0.00893596i) q^{86} +3.60598i q^{87} +(0.276575 - 7.03608i) q^{88} -11.8643i q^{89} +(0.104160 - 7.95312i) q^{90} +(0.288325 - 0.288325i) q^{91} +(-4.85811 - 0.127272i) q^{92} +(0.528636 + 0.528636i) q^{93} +(11.2754 + 11.5747i) q^{94} -8.64480 q^{95} +(0.375940 - 5.73310i) q^{96} +18.7995 q^{97} +(6.74366 + 6.92264i) q^{98} +(3.46521 + 3.46521i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 4 q^{4} - 12 q^{8}+O(q^{10}) $ 48 * q - 4 * q^4 - 12 * q^8	$ 48 q - 4 q^{4} - 12 q^{8} - 4 q^{10} - 8 q^{11} + 8 q^{12} - 4 q^{14} - 16 q^{15} + 12 q^{16} - 16 q^{19} - 28 q^{20} + 12 q^{22} + 28 q^{24} - 16 q^{29} + 4 q^{30} + 24 q^{31} - 20 q^{32} - 40 q^{34} + 24 q^{35} + 8 q^{36} - 16 q^{37} + 32 q^{40} + 40 q^{42} - 8 q^{43} + 20 q^{44} - 32 q^{46} - 40 q^{47} - 52 q^{48} - 48 q^{49} - 16 q^{50} - 24 q^{51} - 8 q^{52} + 16 q^{53} + 20 q^{54} + 20 q^{56} - 16 q^{58} - 68 q^{60} + 32 q^{61} - 32 q^{62} + 40 q^{63} + 32 q^{64} - 32 q^{66} + 16 q^{67} + 40 q^{68} + 32 q^{69} - 60 q^{70} + 40 q^{72} + 72 q^{74} - 40 q^{75} - 28 q^{76} + 16 q^{77} + 32 q^{79} - 52 q^{80} - 48 q^{81} + 40 q^{82} + 40 q^{83} - 36 q^{84} - 32 q^{85} - 72 q^{86} - 8 q^{88} + 28 q^{90} + 36 q^{92} + 28 q^{94} - 48 q^{95} + 68 q^{96} + 64 q^{98} - 40 q^{99}+O(q^{100}) $ 48 * q - 4 * q^4 - 12 * q^8 - 4 * q^10 - 8 * q^11 + 8 * q^12 - 4 * q^14 - 16 * q^15 + 12 * q^16 - 16 * q^19 - 28 * q^20 + 12 * q^22 + 28 * q^24 - 16 * q^29 + 4 * q^30 + 24 * q^31 - 20 * q^32 - 40 * q^34 + 24 * q^35 + 8 * q^36 - 16 * q^37 + 32 * q^40 + 40 * q^42 - 8 * q^43 + 20 * q^44 - 32 * q^46 - 40 * q^47 - 52 * q^48 - 48 * q^49 - 16 * q^50 - 24 * q^51 - 8 * q^52 + 16 * q^53 + 20 * q^54 + 20 * q^56 - 16 * q^58 - 68 * q^60 + 32 * q^61 - 32 * q^62 + 40 * q^63 + 32 * q^64 - 32 * q^66 + 16 * q^67 + 40 * q^68 + 32 * q^69 - 60 * q^70 + 40 * q^72 + 72 * q^74 - 40 * q^75 - 28 * q^76 + 16 * q^77 + 32 * q^79 - 52 * q^80 - 48 * q^81 + 40 * q^82 + 40 * q^83 - 36 * q^84 - 32 * q^85 - 72 * q^86 - 8 * q^88 + 28 * q^90 + 36 * q^92 + 28 * q^94 - 48 * q^95 + 68 * q^96 + 64 * q^98 - 40 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/208\mathbb{Z}\right)^\times$.

$n$	$53$	$79$	$145$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$1$	$1$

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 $

$2$	0.986819	+	1.01301i	0.697786	+	0.716306i
$2$	0.986819	+	1.01301i	0.697786	+	0.716306i
$3$	0.718176	+	0.718176i	0.414639	+	0.414639i	0.883351	−	0.468712i	$-0.155282\pi$
$3$	0.718176	+	0.718176i	0.414639	+	0.414639i	−0.468712	+	0.883351i	$0.655282\pi$
$4$	−0.0523779	+	1.99931i	−0.0261890	+	0.999657i
$5$	2.02033	−	2.02033i	0.903517	−	0.903517i	−0.0922213	−	0.995739i	$-0.529397\pi$
$5$	2.02033	−	2.02033i	0.903517	−	0.903517i	0.995739	+	0.0922213i	$0.0293967\pi$
$6$	−0.0188099	+	1.43623i	−0.00767911	+	0.586338i
$7$			0.407753i			0.154116i	0.997027	+	0.0770580i	$0.0245527\pi$
$7$			0.407753i			0.154116i	−0.997027	+	0.0770580i	$0.975447\pi$
$8$	−2.07701	+	1.91990i	−0.734335	+	0.678788i
$9$		−	1.96845i		−	0.656148i
$10$	4.04031	+	0.0529148i	1.27766	+	0.0167331i
$11$	−1.76038	+	1.76038i	−0.530774	+	0.530774i	−0.920803	−	0.390029i	$-0.872465\pi$
$11$	−1.76038	+	1.76038i	−0.530774	+	0.530774i	0.390029	+	0.920803i	$0.372465\pi$
$12$	−1.47348	+	1.39824i	−0.425356	+	0.403638i
$13$	−0.707107	−	0.707107i	−0.196116	−	0.196116i
$13$	−0.707107	−	0.707107i	−0.196116	−	0.196116i
$14$	−0.413057	+	0.402378i	−0.110394	+	0.107540i
$15$	2.90190			0.749268
$16$	−3.99451	−	0.209440i	−0.998628	−	0.0523600i
$17$	−4.09008			−0.991991			−0.495995	−	0.868325i	$-0.665197\pi$
$17$	−4.09008			−0.991991			−0.495995	+	0.868325i	$0.665197\pi$
$18$	1.99405	−	1.94250i	0.470003	−	0.457851i
$19$	−2.13946	−	2.13946i	−0.490825	−	0.490825i	0.417741	−	0.908566i	$-0.362822\pi$
$19$	−2.13946	−	2.13946i	−0.490825	−	0.490825i	−0.908566	+	0.417741i	$0.862822\pi$
$20$	3.93345	+	4.14509i	0.879545	+	0.926869i
$21$	−0.292838	+	0.292838i	−0.0639026	+	0.0639026i
$22$	−3.52046	−	0.0461065i	−0.750564	−	0.00982993i
$23$			2.42989i			0.506666i	0.967379	+	0.253333i	$0.0815269\pi$
$23$			2.42989i			0.506666i	−0.967379	+	0.253333i	$0.918473\pi$
$24$	−2.87049	−	0.112834i	−0.585936	−	0.0230321i
$25$		−	3.16343i		−	0.632687i
$26$	0.0185200	−	1.41409i	0.00363207	−	0.277326i
$27$	3.56822	−	3.56822i	0.686704	−	0.686704i
$28$	−0.815226	−	0.0213572i	−0.154063	−	0.00403614i
$29$	2.51051	+	2.51051i	0.466190	+	0.466190i	0.900678	−	0.434487i	$-0.143070\pi$
$29$	2.51051	+	2.51051i	0.466190	+	0.466190i	−0.434487	+	0.900678i	$0.643070\pi$
$30$	2.86365	+	2.93965i	0.522829	+	0.536705i
$31$	0.736081			0.132204			0.0661020	−	0.997813i	$-0.478944\pi$
$31$	0.736081			0.132204			0.0661020	+	0.997813i	$0.478944\pi$
$32$	−3.72970	−	4.25316i	−0.659323	−	0.751860i
$33$	−2.52853			−0.440160
$34$	−4.03617	−	4.14329i	−0.692197	−	0.710569i
$35$	0.823793	+	0.823793i	0.139246	+	0.139246i
$36$	3.93554	+	0.103103i	0.655923	+	0.0171838i
$37$	1.13402	−	1.13402i	0.186431	−	0.186431i	−0.607720	−	0.794151i	$-0.707916\pi$
$37$	1.13402	−	1.13402i	0.186431	−	0.186431i	0.794151	+	0.607720i	$0.207916\pi$
$38$	0.0560349	−	4.27854i	0.00909007	−	0.694072i
$39$		−	1.01565i		−	0.162635i
$40$	−0.317416	+	8.07507i	−0.0501879	+	1.27678i
$41$		−	10.6971i		−	1.67060i	−0.549795	−	0.835300i	$-0.685294\pi$
$41$		−	10.6971i		−	1.67060i	0.549795	−	0.835300i	$-0.314706\pi$
$42$	−0.585627	−	0.00766979i	−0.0903641	−	0.00118347i
$43$	−0.341182	+	0.341182i	−0.0520297	+	0.0520297i	−0.732643	−	0.680613i	$-0.761713\pi$
$43$	−0.341182	+	0.341182i	−0.0520297	+	0.0520297i	0.680613	+	0.732643i	$0.261713\pi$
$44$	−3.42735	−	3.61176i	−0.516692	−	0.544493i
$45$	−3.97690	−	3.97690i	−0.592841	−	0.592841i
$46$	−2.46150	+	2.39786i	−0.362928	+	0.353545i
$47$	11.4260			1.66666			0.833329	−	0.552778i	$-0.186432\pi$
$47$	11.4260			1.66666			0.833329	+	0.552778i	$0.186432\pi$
$48$	−2.71835	−	3.01918i	−0.392360	−	0.435781i
$49$	6.83374			0.976248
$50$	3.20459	−	3.12173i	0.453197	−	0.441480i
$51$	−2.93740	−	2.93740i	−0.411318	−	0.411318i
$52$	1.45077	−	1.37669i	0.201185	−	0.190913i
$53$	−6.62837	+	6.62837i	−0.910477	+	0.910477i	−0.996310	−	0.0858325i	$-0.972645\pi$
$53$	−6.62837	+	6.62837i	−0.910477	+	0.910477i	0.0858325	+	0.996310i	$0.472645\pi$
$54$	7.13583	+	0.0934560i	0.971063	+	0.0127178i
$55$			7.11308i			0.959127i
$56$	−0.782845	−	0.846907i	−0.104612	−	0.113173i
$57$		−	3.07301i		−	0.407031i
$58$	−0.0657534	+	5.02059i	−0.00863384	+	0.659236i
$59$	−9.01032	+	9.01032i	−1.17304	+	1.17304i	−0.191563	+	0.981480i	$0.561356\pi$
$59$	−9.01032	+	9.01032i	−1.17304	+	1.17304i	−0.981480	+	0.191563i	$0.938644\pi$
$60$	−0.151996	+	5.80181i	−0.0196225	+	0.749011i
$61$	−2.36316	−	2.36316i	−0.302571	−	0.302571i	0.539448	−	0.842019i	$-0.318633\pi$
$61$	−2.36316	−	2.36316i	−0.302571	−	0.302571i	−0.842019	+	0.539448i	$0.818633\pi$
$62$	0.726379	+	0.745657i	0.0922502	+	0.0946986i
$63$	0.802639			0.101123
$64$	0.627960	−	7.97532i	0.0784950	−	0.996915i
$65$	−2.85717			−0.354389
$66$	−2.49520	−	2.56142i	−0.307137	−	0.315289i
$67$	0.526396	+	0.526396i	0.0643095	+	0.0643095i	0.738530	−	0.674221i	$-0.235520\pi$
$67$	0.526396	+	0.526396i	0.0643095	+	0.0643095i	−0.674221	+	0.738530i	$0.735520\pi$
$68$	0.214230	−	8.17736i	0.0259792	−	0.991651i
$69$	−1.74509	+	1.74509i	−0.210084	+	0.210084i
$70$	−0.0215761	+	1.64745i	−0.00257884	+	0.196907i
$71$			7.15228i			0.848820i	0.905470	+	0.424410i	$0.139518\pi$
$71$			7.15228i			0.848820i	−0.905470	+	0.424410i	$0.860482\pi$
$72$	3.77922	+	4.08848i	0.445385	+	0.481833i
$73$			5.01437i			0.586887i	0.955976	+	0.293444i	$0.0948013\pi$
$73$			5.01437i			0.586887i	−0.955976	+	0.293444i	$0.905199\pi$
$74$	2.26784	+	0.0297013i	0.263631	+	0.00345270i
$75$	2.27190	−	2.27190i	0.262337	−	0.262337i
$76$	4.38950	−	4.16538i	0.503511	−	0.477802i
$77$	−0.717799	−	0.717799i	−0.0818008	−	0.0818008i
$78$	1.02887	−	1.00227i	0.116496	−	0.113484i
$79$	9.29431			1.04569			0.522846	−	0.852427i	$-0.324870\pi$
$79$	9.29431			1.04569			0.522846	+	0.852427i	$0.324870\pi$
$80$	−8.49335	+	7.64708i	−0.949586	+	0.854970i
$81$	−0.780111			−0.0866791
$82$	10.8362	−	10.5561i	1.19666	−	1.16572i
$83$	−10.8412	−	10.8412i	−1.18998	−	1.18998i	−0.977074	−	0.212902i	$-0.931709\pi$
$83$	−10.8412	−	10.8412i	−1.18998	−	1.18998i	−0.212902	−	0.977074i	$-0.568291\pi$
$84$	−0.570138	−	0.600814i	−0.0622071	−	0.0655542i
$85$	−8.26330	+	8.26330i	−0.896281	+	0.896281i
$86$	−0.682305	−	0.00893596i	−0.0735748	−	0.000963590i
$87$			3.60598i			0.386602i
$88$	0.276575	−	7.03608i	0.0294830	−	0.750049i
$89$		−	11.8643i		−	1.25761i	−0.777564	−	0.628804i	$-0.783545\pi$
$89$		−	11.8643i		−	1.25761i	0.777564	−	0.628804i	$-0.216455\pi$
$90$	0.104160	−	7.95312i	0.0109794	−	0.838332i
$91$	0.288325	−	0.288325i	0.0302246	−	0.0302246i
$92$	−4.85811	−	0.127272i	−0.506493	−	0.0132691i
$93$	0.528636	+	0.528636i	0.0548170	+	0.0548170i
$94$	11.2754	+	11.5747i	1.16297	+	1.19384i
$95$	−8.64480			−0.886937
$96$	0.375940	−	5.73310i	0.0383692	−	0.585132i
$97$	18.7995			1.90880			0.954402	−	0.298525i	$-0.0964947\pi$
$97$	18.7995			1.90880			0.954402	+	0.298525i	$0.0964947\pi$
$98$	6.74366	+	6.92264i	0.681213	+	0.699293i
$99$	3.46521	+	3.46521i	0.348267	+	0.348267i
$100$	6.32470	+	0.165694i	0.632470	+	0.0165694i
$101$	−9.02227	+	9.02227i	−0.897750	+	0.897750i	−0.995237	−	0.0974870i	$-0.968920\pi$
$101$	−9.02227	+	9.02227i	−0.897750	+	0.897750i	0.0974870	+	0.995237i	$0.468920\pi$
$102$	0.0769341	−	5.87430i	0.00761761	−	0.581642i
$103$			14.2429i			1.40339i	0.712477	+	0.701695i	$0.247573\pi$
$103$			14.2429i			1.40339i	−0.712477	+	0.701695i	$0.752427\pi$
$104$	2.82624	+	0.111094i	0.277136	+	0.0108937i
$105$			1.18326i			0.115474i
$106$	−13.2556	−	0.173605i	−1.28750	−	0.0168620i
$107$	−13.1547	+	13.1547i	−1.27172	+	1.27172i	−0.326531	+	0.945187i	$0.605880\pi$
$107$	−13.1547	+	13.1547i	−1.27172	+	1.27172i	−0.945187	+	0.326531i	$0.894120\pi$
$108$	6.94710	+	7.32089i	0.668485	+	0.704453i
$109$	6.47771	+	6.47771i	0.620452	+	0.620452i	0.945647	−	0.325195i	$-0.105430\pi$
$109$	6.47771	+	6.47771i	0.620452	+	0.620452i	−0.325195	+	0.945647i	$0.605430\pi$
$110$	−7.20562	+	7.01932i	−0.687029	+	0.669266i
$111$	1.62885			0.154603
$112$	0.0853997	−	1.62877i	0.00806951	−	0.153905i
$113$	−3.14431			−0.295792			−0.147896	−	0.989003i	$-0.547250\pi$
$113$	−3.14431			−0.295792			−0.147896	+	0.989003i	$0.547250\pi$
$114$	3.11299	−	3.03251i	0.291558	−	0.284020i
$115$	4.90916	+	4.90916i	0.457782	+	0.457782i
$116$	−5.15080	+	4.88781i	−0.478240	+	0.453821i
$117$	−1.39190	+	1.39190i	−0.128681	+	0.128681i
$118$	−18.0191	−	0.235991i	−1.65879	−	0.0217247i
$119$		−	1.66774i		−	0.152882i
$120$	−6.02728	+	5.57136i	−0.550213	+	0.508593i
$121$			4.80213i			0.436557i
$122$	0.0618939	−	4.72590i	0.00560361	−	0.427863i
$123$	7.68237	−	7.68237i	0.692696	−	0.692696i
$124$	−0.0385544	+	1.47166i	−0.00346229	+	0.132159i
$125$	3.71046	+	3.71046i	0.331874	+	0.331874i
$126$	0.792059	+	0.813081i	0.0705622	+	0.0724350i
$127$	−3.12783			−0.277550			−0.138775	−	0.990324i	$-0.544316\pi$
$127$	−3.12783			−0.277550			−0.138775	+	0.990324i	$0.544316\pi$
$128$	8.69876	−	7.23406i	0.768869	−	0.639407i
$129$	−0.490057			−0.0431471
$130$	−2.81951	−	2.89434i	−0.247287	−	0.253851i
$131$	−3.03332	−	3.03332i	−0.265022	−	0.265022i	0.562068	−	0.827091i	$-0.310006\pi$
$131$	−3.03332	−	3.03332i	−0.265022	−	0.265022i	−0.827091	+	0.562068i	$0.810006\pi$
$132$	0.132439	−	5.05532i	0.0115273	−	0.440009i
$133$	0.872369	−	0.872369i	0.0756440	−	0.0756440i
$134$	−0.0137870	+	1.05270i	−0.00119101	+	0.0909396i
$135$		−	14.4179i		−	1.24090i
$136$	8.49515	−	7.85255i	0.728453	−	0.673351i
$137$			9.98519i			0.853093i	0.904466	+	0.426546i	$0.140270\pi$
$137$			9.98519i			0.853093i	−0.904466	+	0.426546i	$0.859730\pi$
$138$	−3.48988	−	0.0457059i	−0.297078	−	0.00389075i
$139$	3.79802	−	3.79802i	0.322144	−	0.322144i	−0.527445	−	0.849589i	$-0.676850\pi$
$139$	3.79802	−	3.79802i	0.322144	−	0.322144i	0.849589	+	0.527445i	$0.176850\pi$
$140$	−1.69017	+	1.60387i	−0.142845	+	0.135552i
$141$	8.20590	+	8.20590i	0.691062	+	0.691062i
$142$	−7.24533	+	7.05801i	−0.608015	+	0.592295i
$143$	2.48955			0.208187
$144$	−0.412271	+	7.86298i	−0.0343559	+	0.655248i
$145$	10.1441			0.842422
$146$	−5.07960	+	4.94827i	−0.420391	+	0.409522i
$147$	4.90783	+	4.90783i	0.404791	+	0.404791i
$148$	2.20786	+	2.32665i	0.181485	+	0.191250i
$149$	7.99807	−	7.99807i	0.655228	−	0.655228i	−0.299019	−	0.954247i	$-0.596660\pi$
$149$	7.99807	−	7.99807i	0.655228	−	0.655228i	0.954247	+	0.299019i	$0.0966595\pi$
$150$	4.54342	+	0.0595039i	0.370968	+	0.00485847i
$151$		−	22.4410i		−	1.82622i	−0.407712	−	0.913111i	$-0.633673\pi$
$151$		−	22.4410i		−	1.82622i	0.407712	−	0.913111i	$-0.366327\pi$
$152$	8.55122	+	0.336133i	0.693595	+	0.0272640i
$153$			8.05110i			0.650893i
$154$	0.0188000	−	1.43548i	0.00151495	−	0.115674i
$155$	1.48712	−	1.48712i	0.119449	−	0.119449i
$156$	2.03061	+	0.0531979i	0.162579	+	0.00425924i
$157$	6.34627	+	6.34627i	0.506488	+	0.506488i	0.913447	−	0.406959i	$-0.133411\pi$
$157$	6.34627	+	6.34627i	0.506488	+	0.506488i	−0.406959	+	0.913447i	$0.633411\pi$
$158$	9.17180	+	9.41523i	0.729669	+	0.749035i
$159$	−9.52068			−0.755039
$160$	−16.1280	−	1.05757i	−1.27503	−	0.0836082i
$161$	−0.990793			−0.0780854
$162$	−0.769829	−	0.790261i	−0.0604834	−	0.0620887i
$163$	0.103215	+	0.103215i	0.00808440	+	0.00808440i	0.711137	−	0.703053i	$-0.248180\pi$
$163$	0.103215	+	0.103215i	0.00808440	+	0.00808440i	−0.703053	+	0.711137i	$0.748180\pi$
$164$	21.3868	+	0.560289i	1.67003	+	0.0437513i
$165$	−5.10845	+	5.10845i	−0.397692	+	0.397692i
$166$	0.283944	−	21.6805i	0.0220383	−	1.68274i
$167$		−	21.3956i		−	1.65564i	−0.560994	−	0.827820i	$-0.689581\pi$
$167$		−	21.3956i		−	1.65564i	0.560994	−	0.827820i	$-0.310419\pi$
$168$	0.0460082	−	1.17045i	0.00354961	−	0.0903022i
$169$			1.00000i			0.0769231i
$170$	−16.5252	−	0.216426i	−1.26742	−	0.0165991i
$171$	−4.21140	+	4.21140i	−0.322054	+	0.322054i
$172$	−0.664259	−	0.700000i	−0.0506493	−	0.0533745i
$173$	3.42646	+	3.42646i	0.260509	+	0.260509i	0.825261	−	0.564752i	$-0.191028\pi$
$173$	3.42646	+	3.42646i	0.260509	+	0.260509i	−0.564752	+	0.825261i	$0.691028\pi$
$174$	−3.65289	+	3.55845i	−0.276925	+	0.269765i
$175$	1.28990			0.0975072
$176$	7.40055	−	6.66316i	0.557837	−	0.502255i
$177$	−12.9420			−0.972780
$178$	12.0186	−	11.7079i	0.900833	−	0.877542i
$179$	−15.4432	−	15.4432i	−1.15428	−	1.15428i	−0.985686	−	0.168592i	$-0.946078\pi$
$179$	−15.4432	−	15.4432i	−1.15428	−	1.15428i	−0.168592	−	0.985686i	$-0.553922\pi$
$180$	8.15937	−	7.74277i	0.608164	−	0.577112i
$181$	−1.92082	+	1.92082i	−0.142773	+	0.142773i	−0.774881	−	0.632107i	$-0.782190\pi$
$181$	−1.92082	+	1.92082i	−0.142773	+	0.142773i	0.632107	+	0.774881i	$0.282190\pi$
$182$	0.576600	+	0.00755157i	0.0427404	+	0.000559760i
$183$		−	3.39432i		−	0.250916i
$184$	−4.66514	−	5.04690i	−0.343919	−	0.372063i
$185$		−	4.58216i		−	0.336887i
$186$	−0.0138456	+	1.05718i	−0.00101521	+	0.0775163i
$187$	7.20010	−	7.20010i	0.526523	−	0.526523i
$188$	−0.598472	+	22.8442i	−0.0436480	+	1.66609i
$189$	1.45495	+	1.45495i	0.105832	+	0.105832i
$190$	−8.53085	−	8.75726i	−0.618893	−	0.635319i
$191$	−15.7216			−1.13757			−0.568787	−	0.822485i	$-0.692587\pi$
$191$	−15.7216			−1.13757			−0.568787	+	0.822485i	$0.692587\pi$
$192$	6.17867	−	5.27670i	0.445907	−	0.380813i
$193$	−12.5269			−0.901703			−0.450852	−	0.892599i	$-0.648880\pi$
$193$	−12.5269			−0.901703			−0.450852	+	0.892599i	$0.648880\pi$
$194$	18.5517	+	19.0441i	1.33194	+	1.36729i
$195$	−2.05195	−	2.05195i	−0.146943	−	0.146943i
$196$	−0.357937	+	13.6628i	−0.0255669	+	0.975913i
$197$	17.3653	−	17.3653i	1.23723	−	1.23723i	0.276099	−	0.961129i	$-0.410958\pi$
$197$	17.3653	−	17.3653i	1.23723	−	1.23723i	0.961129	−	0.276099i	$-0.0890416\pi$
$198$	−0.0907580	+	6.92982i	−0.00644989	+	0.492481i
$199$		−	4.45169i		−	0.315572i	−0.987473	−	0.157786i	$-0.949564\pi$
$199$		−	4.45169i		−	0.315572i	0.987473	−	0.157786i	$-0.0504357\pi$
$200$	6.07348	+	6.57049i	0.429460	+	0.464604i
$201$			0.756091i			0.0533305i
$202$	−18.0430	−	0.236304i	−1.26950	−	0.0166263i
$203$	−1.02367	+	1.02367i	−0.0718474	+	0.0718474i
$204$	6.02664	−	5.71893i	0.421949	−	0.400405i
$205$	−21.6115	−	21.6115i	−1.50941	−	1.50941i
$206$	−14.4282	+	14.0551i	−1.00526	+	0.979266i
$207$	4.78310			0.332448
$208$	2.67645	+	2.97264i	0.185578	+	0.206116i
$209$	7.53251			0.521034
$210$	−1.19865	+	1.16766i	−0.0827148	+	0.0805763i
$211$	−3.71868	−	3.71868i	−0.256005	−	0.256005i	0.567422	−	0.823427i	$-0.307941\pi$
$211$	−3.71868	−	3.71868i	−0.256005	−	0.256005i	−0.823427	+	0.567422i	$0.807941\pi$
$212$	−12.9050	−	13.5994i	−0.886320	−	0.934009i
$213$	−5.13660	+	5.13660i	−0.351954	+	0.351954i
$214$	−26.3072	−	0.344539i	−1.79833	−	0.0235522i
$215$			1.37860i			0.0940195i
$216$	−0.560608	+	14.2619i	−0.0381445	+	0.970397i
$217$			0.300139i			0.0203748i
$218$	−0.169659	+	12.9543i	−0.0114908	+	0.877377i
$219$	−3.60120	+	3.60120i	−0.243347	+	0.243347i
$220$	−14.2213	−	0.372568i	−0.958798	−	0.0251186i
$221$	2.89213	+	2.89213i	0.194545	+	0.194545i
$222$	1.60738	+	1.65004i	0.107880	+	0.110743i
$223$	16.5325			1.10710			0.553550	−	0.832816i	$-0.313273\pi$
$223$	16.5325			1.10710			0.553550	+	0.832816i	$0.313273\pi$
$224$	1.73424	−	1.52079i	0.115874	−	0.101612i
$225$	−6.22704			−0.415136
$226$	−3.10287	−	3.18522i	−0.206400	−	0.211878i
$227$	10.9404	+	10.9404i	0.726138	+	0.726138i	0.969848	−	0.243710i	$-0.0783645\pi$
$227$	10.9404	+	10.9404i	0.726138	+	0.726138i	−0.243710	+	0.969848i	$0.578364\pi$
$228$	6.14392	+	0.160958i	0.406891	+	0.0106597i
$229$	6.11125	−	6.11125i	0.403843	−	0.403843i	−0.475742	−	0.879585i	$-0.657820\pi$
$229$	6.11125	−	6.11125i	0.403843	−	0.403843i	0.879585	+	0.475742i	$0.157820\pi$
$230$	−0.128577	+	9.81748i	−0.00847811	+	0.647346i
$231$		−	1.03101i		−	0.0678357i
$232$	−10.0343	−	0.394430i	−0.658784	−	0.0258956i
$233$		−	5.76935i		−	0.377963i	−0.981981	−	0.188981i	$-0.939481\pi$
$233$		−	5.76935i		−	0.377963i	0.981981	−	0.188981i	$-0.0605186\pi$
$234$	−2.78356	−	0.0364556i	−0.181967	−	0.00238318i
$235$	23.0843	−	23.0843i	1.50585	−	1.50585i
$236$	−17.5425	−	18.4864i	−1.14192	−	1.20336i
$237$	6.67496	+	6.67496i	0.433585	+	0.433585i
$238$	1.68944	−	1.64576i	0.109510	−	0.106679i
$239$	−5.22939			−0.338261			−0.169130	−	0.985594i	$-0.554096\pi$
$239$	−5.22939			−0.338261			−0.169130	+	0.985594i	$0.554096\pi$
$240$	−11.5917	−	0.607774i	−0.748240	−	0.0392316i
$241$	−6.63299			−0.427269			−0.213634	−	0.976914i	$-0.568530\pi$
$241$	−6.63299			−0.427269			−0.213634	+	0.976914i	$0.568530\pi$
$242$	−4.86461	+	4.73883i	−0.312709	+	0.304624i
$243$	−11.2649	−	11.2649i	−0.722645	−	0.722645i
$244$	4.84847	−	4.60091i	0.310391	−	0.294543i
$245$	13.8064	−	13.8064i	0.882057	−	0.882057i
$246$	15.3634	+	0.201211i	0.979536	+	0.0128287i
$247$			3.02565i			0.192517i
$248$	−1.52885	+	1.41320i	−0.0970820	+	0.0897385i
$249$		−	15.5718i		−	0.986821i
$250$	−0.0971815	+	7.42029i	−0.00614630	+	0.469300i
$251$	−16.7662	+	16.7662i	−1.05827	+	1.05827i	−0.0600813	+	0.998193i	$0.519136\pi$
$251$	−16.7662	+	16.7662i	−1.05827	+	1.05827i	−0.998193	+	0.0600813i	$0.980864\pi$
$252$	−0.0420406	+	1.60473i	−0.00264831	+	0.101088i
$253$	−4.27752	−	4.27752i	−0.268925	−	0.268925i
$254$	−3.08660	−	3.16852i	−0.193671	−	0.198811i
$255$	−11.8690			−0.743267
$256$	15.9123	+	1.67322i	0.994517	+	0.104576i
$257$	24.2947			1.51546			0.757730	−	0.652568i	$-0.226308\pi$
$257$	24.2947			1.51546			0.757730	+	0.652568i	$0.226308\pi$
$258$	−0.483598	−	0.496433i	−0.0301075	−	0.0309066i
$259$	0.462398	+	0.462398i	0.0287320	+	0.0287320i
$260$	0.149653	−	5.71238i	0.00928107	−	0.354267i
$261$	4.94181	−	4.94181i	0.305890	−	0.305890i
$262$	0.0794463	−	6.06612i	0.00490821	−	0.374766i
$263$		−	5.38766i		−	0.332217i	−0.986107	−	0.166109i	$-0.946880\pi$
$263$		−	5.38766i		−	0.332217i	0.986107	−	0.166109i	$-0.0531202\pi$
$264$	5.25178	−	4.85452i	0.323225	−	0.298775i
$265$			26.7829i			1.64526i
$266$	1.74459	+	0.0228484i	0.106968	+	0.00140092i
$267$	8.52063	−	8.52063i	0.521454	−	0.521454i
$268$	−1.08000	+	1.02486i	−0.0659717	+	0.0626033i
$269$	−8.84602	−	8.84602i	−0.539351	−	0.539351i	0.383987	−	0.923338i	$-0.374551\pi$
$269$	−8.84602	−	8.84602i	−0.539351	−	0.539351i	−0.923338	+	0.383987i	$0.874551\pi$
$270$	14.6055	−	14.2279i	0.888863	−	0.865882i
$271$	0.874013			0.0530925			0.0265463	−	0.999648i	$-0.491549\pi$
$271$	0.874013			0.0530925			0.0265463	+	0.999648i	$0.491549\pi$
$272$	16.3379	+	0.856626i	0.990630	+	0.0519406i
$273$	0.414136			0.0250647
$274$	−10.1151	+	9.85358i	−0.611076	+	0.595276i
$275$	5.56884	+	5.56884i	0.335814	+	0.335814i
$276$	−3.39757	−	3.58038i	−0.204510	−	0.215514i
$277$	14.8670	−	14.8670i	0.893272	−	0.893272i	−0.101557	−	0.994830i	$-0.532382\pi$
$277$	14.8670	−	14.8670i	0.893272	−	0.893272i	0.994830	+	0.101557i	$0.0323825\pi$
$278$	7.59538	+	0.0994747i	0.455541	+	0.00596609i
$279$		−	1.44894i		−	0.0867455i
$280$	−3.29263	−	0.129427i	−0.196772	−	0.00773476i
$281$			4.58756i			0.273671i	0.990594	+	0.136835i	$0.0436932\pi$
$281$			4.58756i			0.273671i	−0.990594	+	0.136835i	$0.956307\pi$
$282$	−0.214923	+	16.4104i	−0.0127984	+	0.977225i
$283$	5.75650	−	5.75650i	0.342188	−	0.342188i	−0.515001	−	0.857189i	$-0.672209\pi$
$283$	5.75650	−	5.75650i	0.342188	−	0.342188i	0.857189	+	0.515001i	$0.172209\pi$
$284$	−14.2997	−	0.374622i	−0.848529	−	0.0222297i
$285$	−6.20849	−	6.20849i	−0.367759	−	0.367759i
$286$	2.45674	+	2.52194i	0.145270	+	0.149125i
$287$	4.36175			0.257466
$288$	−8.37211	+	7.34170i	−0.493331	+	0.432614i
$289$	−0.271224			−0.0159543
$290$	10.0104	+	10.2761i	0.587830	+	0.603432i
$291$	13.5014	+	13.5014i	0.791465	+	0.791465i
$292$	−10.0253	−	0.262642i	−0.586686	−	0.0153700i
$293$	−16.5873	+	16.5873i	−0.969042	+	0.969042i	−0.999535	−	0.0304930i	$-0.990292\pi$
$293$	−16.5873	+	16.5873i	−0.969042	+	0.969042i	0.0304930	+	0.999535i	$0.490292\pi$
$294$	−0.128542	+	9.81482i	−0.00749672	+	0.572412i
$295$			36.4076i			2.11973i
$296$	−0.178167	+	4.53256i	−0.0103557	+	0.263450i
$297$			12.5628i			0.728970i
$298$	15.9948	+	0.209479i	0.926552	+	0.0121348i
$299$	1.71819	−	1.71819i	0.0993654	−	0.0993654i
$300$	4.42325	+	4.66125i	0.255376	+	0.269117i
$301$	−0.139118	−	0.139118i	−0.00801861	−	0.00801861i
$302$	22.7329	−	22.1452i	1.30813	−	1.27431i
$303$	−12.9592			−0.744485
$304$	8.09800	+	8.99417i	0.464452	+	0.515851i
$305$	−9.54869			−0.546756
$306$	−8.15585	+	7.94498i	−0.466239	+	0.454184i
$307$	1.80120	+	1.80120i	0.102800	+	0.102800i	0.756636	−	0.653836i	$-0.226841\pi$
$307$	1.80120	+	1.80120i	0.102800	+	0.102800i	−0.653836	+	0.756636i	$0.726841\pi$
$308$	1.47270	−	1.39751i	0.0839150	−	0.0796305i
$309$	−10.2289	+	10.2289i	−0.581901	+	0.581901i
$310$	2.97399	+	0.0389496i	0.168911	+	0.00221219i
$311$			26.6226i			1.50963i	0.655939	+	0.754814i	$0.272273\pi$
$311$			26.6226i			1.50963i	−0.655939	+	0.754814i	$0.727727\pi$
$312$	1.94996	+	2.10953i	0.110395	+	0.119428i
$313$			16.3652i			0.925013i	0.886616	+	0.462507i	$0.153050\pi$
$313$			16.3652i			0.925013i	−0.886616	+	0.462507i	$0.846950\pi$
$314$	−0.166217	+	12.6915i	−0.00938014	+	0.716220i
$315$	1.62159	−	1.62159i	0.0913664	−	0.0913664i
$316$	−0.486817	+	18.5822i	−0.0273856	+	1.04533i
$317$	12.3087	+	12.3087i	0.691328	+	0.691328i	0.962524	−	0.271196i	$-0.0874192\pi$
$317$	12.3087	+	12.3087i	0.691328	+	0.691328i	−0.271196	+	0.962524i	$0.587419\pi$
$318$	−9.39519	−	9.64455i	−0.526856	−	0.540839i
$319$	−8.83891			−0.494884
$320$	−14.8441	−	17.3814i	−0.829808	−	0.971651i
$321$	−18.8949			−1.05461
$322$	−0.977733	−	1.00368i	−0.0544869	−	0.0559331i
$323$	8.75055	+	8.75055i	0.486894	+	0.486894i
$324$	0.0408606	−	1.55969i	0.00227003	−	0.0866493i
$325$	−2.23689	+	2.23689i	−0.124080	+	0.124080i
$326$	−0.00270332	+	0.206412i	−0.000149723	+	0.0114321i
$327$			9.30428i			0.514528i
$328$	20.5373	+	22.2179i	1.13398	+	1.22678i
$329$			4.65899i			0.256859i
$330$	−10.2160	−	0.133796i	−0.562373	−	0.00736525i
$331$	18.0176	−	18.0176i	0.990335	−	0.990335i	−0.00961893	−	0.999954i	$-0.503062\pi$
$331$	18.0176	−	18.0176i	0.990335	−	0.990335i	0.999954	+	0.00961893i	$0.00306185\pi$
$332$	22.2428	−	21.1071i	1.22073	−	1.15840i
$333$	−2.23225	−	2.23225i	−0.122326	−	0.122326i
$334$	21.6739	−	21.1136i	1.18594	−	1.15528i
$335$	2.12698			0.116210
$336$	1.23108	−	1.10841i	0.0671609	−	0.0604690i
$337$	9.98836			0.544100			0.272050	−	0.962283i	$-0.412298\pi$
$337$	9.98836			0.544100			0.272050	+	0.962283i	$0.412298\pi$
$338$	−1.01301	+	0.986819i	−0.0551005	+	0.0536759i
$339$	−2.25817	−	2.25817i	−0.122647	−	0.122647i
$340$	−16.0881	−	16.9537i	−0.872501	−	0.919446i
$341$	−1.29578	+	1.29578i	−0.0701705	+	0.0701705i
$342$	−8.42208	−	0.110302i	−0.455414	−	0.00596443i
$343$			5.64074i			0.304572i
$344$	0.0536035	−	1.36367i	0.00289011	−	0.0735244i
$345$			7.05129i			0.379629i
$346$	−0.0897433	+	6.85234i	−0.00482463	+	0.368384i
$347$	−13.5959	+	13.5959i	−0.729869	+	0.729869i	−0.970593	−	0.240725i	$-0.922615\pi$
$347$	−13.5959	+	13.5959i	−0.729869	+	0.729869i	0.240725	+	0.970593i	$0.422615\pi$
$348$	−7.20949	−	0.188874i	−0.386469	−	0.0101247i
$349$	−4.10831	−	4.10831i	−0.219913	−	0.219913i	0.588549	−	0.808462i	$-0.299699\pi$
$349$	−4.10831	−	4.10831i	−0.219913	−	0.219913i	−0.808462	+	0.588549i	$0.799699\pi$
$350$	1.27290	+	1.30668i	0.0680391	+	0.0698450i
$351$	−5.04623			−0.269348
$352$	14.0529	+	0.921497i	0.749020	+	0.0491159i
$353$	19.5525			1.04068			0.520338	−	0.853960i	$-0.325806\pi$
$353$	19.5525			1.04068			0.520338	+	0.853960i	$0.325806\pi$
$354$	−12.7714	−	13.1104i	−0.678793	−	0.696808i
$355$	14.4499	+	14.4499i	0.766923	+	0.766923i
$356$	23.7204	+	0.621425i	1.25718	+	0.0329355i
$357$	1.19773	−	1.19773i	0.0633908	−	0.0633908i
$358$	0.404476	−	30.8837i	0.0213772	−	1.63226i
$359$		−	31.0034i		−	1.63630i	−0.575007	−	0.818148i	$-0.695001\pi$
$359$		−	31.0034i		−	1.63630i	0.575007	−	0.818148i	$-0.304999\pi$
$360$	15.8953	+	0.624816i	0.837757	+	0.0329307i
$361$		−	9.84546i		−	0.518182i
$362$	−3.84131	−	0.0503086i	−0.201895	−	0.00264416i
$363$	−3.44878	+	3.44878i	−0.181014	+	0.181014i
$364$	0.561350	+	0.591553i	0.0294227	+	0.0310058i
$365$	10.1307	+	10.1307i	0.530263	+	0.530263i
$366$	3.43848	−	3.34958i	0.179732	−	0.175086i
$367$	20.7682			1.08409			0.542046	−	0.840349i	$-0.317650\pi$
$367$	20.7682			1.08409			0.542046	+	0.840349i	$0.317650\pi$
$368$	0.508915	−	9.70621i	0.0265290	−	0.505971i
$369$	−21.0566			−1.09616
$370$	4.64178	−	4.52177i	0.241315	−	0.235075i
$371$	−2.70274	−	2.70274i	−0.140319	−	0.140319i
$372$	−1.08460	+	1.02922i	−0.0562338	+	0.0533626i
$373$	−1.05140	+	1.05140i	−0.0544395	+	0.0544395i	−0.733802	−	0.679363i	$-0.762256\pi$
$373$	−1.05140	+	1.05140i	−0.0544395	+	0.0544395i	0.679363	+	0.733802i	$0.262256\pi$
$374$	14.3990	+	0.188579i	0.744552	+	0.00975120i
$375$			5.32954i			0.275216i
$376$	−23.7320	+	21.9368i	−1.22388	+	1.13131i
$377$		−	3.55040i		−	0.182855i
$378$	−0.0381069	+	2.90965i	−0.00196001	+	0.149656i
$379$	−24.8039	+	24.8039i	−1.27409	+	1.27409i	−0.330166	+	0.943923i	$0.607105\pi$
$379$	−24.8039	+	24.8039i	−1.27409	+	1.27409i	−0.943923	+	0.330166i	$0.892895\pi$
$380$	0.452796	−	17.2837i	0.0232280	−	0.886633i
$381$	−2.24633	−	2.24633i	−0.115083	−	0.115083i
$382$	−15.5143	−	15.9261i	−0.793783	−	0.814851i
$383$	1.97075			0.100700			0.0503502	−	0.998732i	$-0.483966\pi$
$383$	1.97075			0.100700			0.0503502	+	0.998732i	$0.483966\pi$
$384$	11.4426	+	1.05191i	0.583926	+	0.0536801i
$385$	−2.90038			−0.147817
$386$	−12.3617	−	12.6898i	−0.629196	−	0.645896i
$387$	0.671598	+	0.671598i	0.0341392	+	0.0341392i
$388$	−0.984681	+	37.5862i	−0.0499896	+	1.90815i
$389$	25.6021	−	25.6021i	1.29808	−	1.29808i	0.368421	−	0.929659i	$-0.379898\pi$
$389$	25.6021	−	25.6021i	1.29808	−	1.29808i	0.929659	−	0.368421i	$-0.120102\pi$
$390$	0.0537432	−	4.10356i	0.00272139	−	0.207792i
$391$		−	9.93844i		−	0.502608i
$392$	−14.1938	+	13.1201i	−0.716893	+	0.662665i
$393$		−	4.35692i		−	0.219777i
$394$	34.7277	+	0.454819i	1.74955	+	0.0229134i
$395$	18.7775	−	18.7775i	0.944801	−	0.944801i
$396$	−7.10954	+	6.74654i	−0.357268	+	0.339026i
$397$	−17.0435	−	17.0435i	−0.855391	−	0.855391i	0.135400	−	0.990791i	$-0.456768\pi$
$397$	−17.0435	−	17.0435i	−0.855391	−	0.855391i	−0.990791	+	0.135400i	$0.956768\pi$
$398$	4.50961	−	4.39302i	0.226046	−	0.220202i
$399$	1.25303			0.0627299
$400$	−0.662549	+	12.6364i	−0.0331274	+	0.631819i
$401$	−26.8730			−1.34197			−0.670987	−	0.741469i	$-0.734130\pi$
$401$	−26.8730			−1.34197			−0.670987	+	0.741469i	$0.734130\pi$
$402$	−0.765928	+	0.746125i	−0.0382010	+	0.0372133i
$403$	−0.520488	−	0.520488i	−0.0259274	−	0.0259274i
$404$	−17.5658	−	18.5109i	−0.873931	−	0.920953i
$405$	−1.57608	+	1.57608i	−0.0783160	+	0.0783160i
$406$	−2.04716	−	0.0268111i	−0.101599	−	0.00133061i
$407$			3.99260i			0.197906i
$408$	11.7405	+	0.461499i	0.581243	+	0.0228476i
$409$			8.25499i			0.408183i	0.978952	+	0.204091i	$0.0654240\pi$
$409$			8.25499i			0.408183i	−0.978952	+	0.204091i	$0.934576\pi$
$410$	0.566032	−	43.2194i	0.0279543	−	2.13445i
$411$	−7.17113	+	7.17113i	−0.353726	+	0.353726i
$412$	−28.4759	−	0.746011i	−1.40291	−	0.0367533i
$413$	−3.67398	−	3.67398i	−0.180785	−	0.180785i
$414$	4.72005	+	4.84533i	0.231978	+	0.238135i
$415$	−43.8055			−2.15033
$416$	−0.370146	+	5.64473i	−0.0181479	+	0.276756i
$417$	5.45529			0.267147
$418$	7.43322	+	7.63050i	0.363571	+	0.373220i
$419$	0.0302615	+	0.0302615i	0.00147837	+	0.00147837i	0.707846	−	0.706367i	$-0.249667\pi$
$419$	0.0302615	+	0.0302615i	0.00147837	+	0.00147837i	−0.706367	+	0.707846i	$0.749667\pi$
$420$	−2.36570	−	0.0619766i	−0.115435	−	0.00302415i
$421$	−16.5765	+	16.5765i	−0.807888	+	0.807888i	−0.984314	−	0.176426i	$-0.943547\pi$
$421$	−16.5765	+	16.5765i	−0.807888	+	0.807888i	0.176426	+	0.984314i	$0.443547\pi$
$422$	0.0973969	−	7.43673i	0.00474120	−	0.362014i
$423$		−	22.4915i		−	1.09357i
$424$	1.04139	−	26.4930i	0.0505745	−	1.28662i
$425$			12.9387i			0.627619i
$426$	−10.2723	−	0.134534i	−0.497696	−	0.00651818i
$427$	0.963583	−	0.963583i	0.0466310	−	0.0466310i
$428$	−25.6115	−	26.9895i	−1.23798	−	1.30459i
$429$	1.78794	+	1.78794i	0.0863224	+	0.0863224i
$430$	−1.39653	+	1.36042i	−0.0673467	+	0.0656055i
$431$	−23.5443			−1.13409			−0.567044	−	0.823688i	$-0.691913\pi$
$431$	−23.5443			−1.13409			−0.567044	+	0.823688i	$0.691913\pi$
$432$	−15.0006	+	13.5060i	−0.721718	+	0.649807i
$433$	−14.4237			−0.693160			−0.346580	−	0.938020i	$-0.612657\pi$
$433$	−14.4237			−0.693160			−0.346580	+	0.938020i	$0.612657\pi$
$434$	−0.304044	+	0.296183i	−0.0145946	+	0.0142172i
$435$	7.28526	+	7.28526i	0.349301	+	0.349301i
$436$	−13.2903	+	12.6117i	−0.636488	+	0.603990i
$437$	5.19863	−	5.19863i	0.248684	−	0.248684i
$438$	−7.20178	−	0.0943198i	−0.344114	−	0.00450677i
$439$			28.7513i			1.37223i	0.727495	+	0.686113i	$0.240685\pi$
$439$			28.7513i			1.37223i	−0.727495	+	0.686113i	$0.759315\pi$
$440$	−13.6564	−	14.7740i	−0.651044	−	0.704321i
$441$		−	13.4518i		−	0.640564i
$442$	−0.0757483	+	5.78375i	−0.00360298	+	0.275105i
$443$	4.93518	−	4.93518i	0.234477	−	0.234477i	−0.580081	−	0.814559i	$-0.696979\pi$
$443$	4.93518	−	4.93518i	0.234477	−	0.234477i	0.814559	+	0.580081i	$0.196979\pi$
$444$	−0.0853157	+	3.25658i	−0.00404890	+	0.154550i
$445$	−23.9697	−	23.9697i	−1.13627	−	1.13627i
$446$	16.3146	+	16.7476i	0.772519	+	0.793023i
$447$	11.4881			0.543366
$448$	3.25196	+	0.256053i	0.153641	+	0.0120973i
$449$	0.938044			0.0442690			0.0221345	−	0.999755i	$-0.492954\pi$
$449$	0.938044			0.0442690			0.0221345	+	0.999755i	$0.492954\pi$
$450$	−6.14496	−	6.30806i	−0.289676	−	0.297365i
$451$	18.8309	+	18.8309i	0.886711	+	0.886711i
$452$	0.164693	−	6.28647i	0.00774649	−	0.295691i
$453$	16.1166	−	16.1166i	0.757223	−	0.757223i
$454$	−0.286542	+	21.8789i	−0.0134481	+	1.02683i
$455$		−	1.16502i		−	0.0546170i
$456$	5.89988	+	6.38269i	0.276287	+	0.298897i
$457$		−	13.2158i		−	0.618208i	−0.951028	−	0.309104i	$-0.899971\pi$
$457$		−	13.2158i		−	0.618208i	0.951028	−	0.309104i	$-0.100029\pi$
$458$	12.2215	+	0.160061i	0.571071	+	0.00747917i
$459$	−14.5943	+	14.5943i	−0.681204	+	0.681204i
$460$	−10.0721	+	9.55782i	−0.469614	+	0.445636i
$461$	5.25676	+	5.25676i	0.244832	+	0.244832i	0.818846	−	0.574014i	$-0.194614\pi$
$461$	5.25676	+	5.25676i	0.244832	+	0.244832i	−0.574014	+	0.818846i	$0.694614\pi$
$462$	1.04443	−	1.01742i	0.0485911	−	0.0473348i
$463$	−2.95710			−0.137428			−0.0687141	−	0.997636i	$-0.521890\pi$
$463$	−2.95710			−0.137428			−0.0687141	+	0.997636i	$0.521890\pi$
$464$	−9.50247	−	10.5541i	−0.441141	−	0.489961i
$465$	2.13603			0.0990562
$466$	5.84441	−	5.69330i	0.270737	−	0.263737i
$467$	14.9063	+	14.9063i	0.689782	+	0.689782i	0.962184	−	0.272401i	$-0.0878179\pi$
$467$	14.9063	+	14.9063i	0.689782	+	0.689782i	−0.272401	+	0.962184i	$0.587818\pi$
$468$	−2.70994	−	2.85575i	−0.125267	−	0.132007i
$469$	−0.214640	+	0.214640i	−0.00991113	+	0.00991113i
$470$	46.1646	+	0.604606i	2.12942	+	0.0278884i
$471$			9.11549i			0.420019i
$472$	1.41562	−	36.0135i	0.0651593	−	1.65765i
$473$		−	1.20122i		−	0.0552321i
$474$	−0.174825	+	13.3488i	−0.00802999	+	0.613129i
$475$	−6.76803	+	6.76803i	−0.310538	+	0.310538i
$476$	3.33434	+	0.0873529i	0.152829	+	0.00400381i
$477$	13.0476	+	13.0476i	0.597408	+	0.597408i
$478$	−5.16046	−	5.29742i	−0.236034	−	0.242298i
$479$	−12.6839			−0.579541			−0.289771	−	0.957096i	$-0.593579\pi$
$479$	−12.6839			−0.579541			−0.289771	+	0.957096i	$0.593579\pi$
$480$	−10.8232	−	12.3423i	−0.494010	−	0.563344i
$481$	−1.60374			−0.0731243
$482$	−6.54556	−	6.71929i	−0.298142	−	0.306055i
$483$	−0.711564	−	0.711564i	−0.0323773	−	0.0323773i
$484$	−9.60097	−	0.251526i	−0.436408	−	0.0114330i
$485$	37.9812	−	37.9812i	1.72464	−	1.72464i
$486$	0.295042	−	22.5279i	0.0133834	−	1.02189i
$487$		−	33.6458i		−	1.52464i	−0.647201	−	0.762319i	$-0.724061\pi$
$487$		−	33.6458i		−	1.52464i	0.647201	−	0.762319i	$-0.275939\pi$
$488$	9.44533	+	0.371278i	0.427570	+	0.0168070i
$489$			0.148253i			0.00670422i
$490$	27.6104	+	0.361606i	1.24731	+	0.0163357i
$491$	−16.3931	+	16.3931i	−0.739812	+	0.739812i	−0.972542	−	0.232729i	$-0.925234\pi$
$491$	−16.3931	+	16.3931i	−0.739812	+	0.739812i	0.232729	+	0.972542i	$0.425234\pi$
$492$	14.9571	+	15.7619i	0.674318	+	0.710600i
$493$	−10.2682	−	10.2682i	−0.462457	−	0.462457i
$494$	−3.06501	+	2.98577i	−0.137901	+	0.134336i
$495$	14.0017			0.629330
$496$	−2.94029	−	0.154165i	−0.132023	−	0.00692220i
$497$	−2.91636			−0.130817
$498$	15.7744	−	15.3665i	0.706866	−	0.688590i
$499$	−6.00409	−	6.00409i	−0.268780	−	0.268780i	0.559829	−	0.828608i	$-0.310867\pi$
$499$	−6.00409	−	6.00409i	−0.268780	−	0.268780i	−0.828608	+	0.559829i	$0.810867\pi$
$500$	−7.61273	+	7.22404i	−0.340452	+	0.323069i
$501$	15.3658	−	15.3658i	0.686493	−	0.686493i
$502$	−33.5296	−	0.439128i	−1.49650	−	0.0195992i
$503$		−	24.8163i		−	1.10650i	−0.833014	−	0.553252i	$-0.813387\pi$
$503$		−	24.8163i		−	1.10650i	0.833014	−	0.553252i	$-0.186613\pi$
$504$	−1.66709	+	1.54099i	−0.0742581	+	0.0686410i
$505$			36.4559i			1.62226i
$506$	0.112033	−	8.55431i	0.00498049	−	0.380285i
$507$	−0.718176	+	0.718176i	−0.0318953	+	0.0318953i
$508$	0.163829	−	6.25351i	0.00726875	−	0.277455i
$509$	−23.0515	−	23.0515i	−1.02174	−	1.02174i	−0.999758	−	0.0219805i	$-0.993003\pi$
$509$	−23.0515	−	23.0515i	−1.02174	−	1.02174i	−0.0219805	−	0.999758i	$-0.506997\pi$
$510$	−11.7126	−	12.0234i	−0.518641	−	0.532406i
$511$	−2.04462			−0.0904487
$512$	14.0075	+	17.7705i	0.619051	+	0.785350i
$513$	−15.2681			−0.674103
$514$	23.9744	+	24.6107i	1.05747	+	1.08553i
$515$	28.7752	+	28.7752i	1.26799	+	1.26799i
$516$	0.0256682	−	0.979779i	0.00112998	−	0.0431323i
$517$	−20.1141	+	20.1141i	−0.884619	+	0.884619i
$518$	−0.0121108	+	0.924717i	−0.000532117	+	0.0406297i
$519$			4.92161i			0.216035i
$520$	5.93438	−	5.48549i	0.260240	−	0.240555i
$521$		−	19.3809i		−	0.849095i	−0.905406	−	0.424547i	$-0.860433\pi$
$521$		−	19.3809i		−	0.849095i	0.905406	−	0.424547i	$-0.139567\pi$
$522$	9.88276	+	0.129432i	0.432557	+	0.00566508i
$523$	25.0909	−	25.0909i	1.09715	−	1.09715i	0.102404	−	0.994743i	$-0.467347\pi$
$523$	25.0909	−	25.0909i	1.09715	−	1.09715i	0.994743	−	0.102404i	$-0.0326533\pi$
$524$	6.22344	−	5.90568i	0.271872	−	0.257991i
$525$	0.926375	+	0.926375i	0.0404303	+	0.0404303i
$526$	5.45775	−	5.31664i	0.237969	−	0.231817i
$527$	−3.01063			−0.131145
$528$	10.1002	+	0.529574i	0.439556	+	0.0230468i
$529$	17.0957			0.743289
$530$	−27.1314	+	26.4299i	−1.17851	+	1.14804i
$531$	17.7363	+	17.7363i	0.769691	+	0.769691i
$532$	1.69845	+	1.78983i	0.0736370	+	0.0775991i
$533$	−7.56396	+	7.56396i	−0.327631	+	0.327631i
$534$	17.0398	+	0.223166i	0.737384	+	0.00965732i
$535$			53.1537i			2.29804i
$536$	−2.10396	−	0.0827028i	−0.0908773	−	0.00357222i
$537$		−	22.1819i		−	0.957218i
$538$	0.231688	−	17.6905i	0.00998878	−	0.762693i
$539$	−12.0300	+	12.0300i	−0.518167	+	0.518167i
$540$	28.8260	+	0.755182i	1.24047	+	0.0324978i
$541$	16.7987	+	16.7987i	0.722235	+	0.722235i	0.969060	−	0.246825i	$-0.0793874\pi$
$541$	16.7987	+	16.7987i	0.722235	+	0.722235i	−0.246825	+	0.969060i	$0.579387\pi$
$542$	0.862492	+	0.885384i	0.0370472	+	0.0380305i
$543$	−2.75898			−0.118399
$544$	15.2548	+	17.3958i	0.654043	+	0.745838i
$545$	26.1742			1.12118
$546$	0.408677	+	0.419524i	0.0174898	+	0.0179540i
$547$	−17.0203	−	17.0203i	−0.727736	−	0.727736i	0.242432	−	0.970168i	$-0.422055\pi$
$547$	−17.0203	−	17.0203i	−0.727736	−	0.727736i	−0.970168	+	0.242432i	$0.922055\pi$
$548$	−19.9635	−	0.523004i	−0.852800	−	0.0223416i
$549$	−4.65174	+	4.65174i	−0.198531	+	0.198531i
$550$	−0.145855	+	11.1367i	−0.00621927	+	0.474872i
$551$		−	10.7423i		−	0.457636i
$552$	0.274173	−	6.97496i	0.0116696	−	0.296874i
$553$			3.78978i			0.161158i
$554$	29.7315	+	0.389385i	1.26317	+	0.0165434i
$555$	3.29080	−	3.29080i	0.139687	−	0.139687i
$556$	7.39450	+	7.79236i	0.313597	+	0.330470i
$557$	0.258550	+	0.258550i	0.0109551	+	0.0109551i	0.712563	−	0.701608i	$-0.247534\pi$
$557$	0.258550	+	0.258550i	0.0109551	+	0.0109551i	−0.701608	+	0.712563i	$0.747534\pi$
$558$	1.46779	−	1.42984i	0.0621363	−	0.0605298i
$559$	0.482504			0.0204077
$560$	−3.11812	−	3.46319i	−0.131765	−	0.146346i
$561$	10.3419			0.436634
$562$	−4.64724	+	4.52709i	−0.196032	+	0.190964i
$563$	10.8497	+	10.8497i	0.457262	+	0.457262i	0.897756	−	0.440494i	$-0.145197\pi$
$563$	10.8497	+	10.8497i	0.457262	+	0.457262i	−0.440494	+	0.897756i	$0.645197\pi$
$564$	−16.8360	+	15.9764i	−0.708923	+	0.672726i
$565$	−6.35254	+	6.35254i	−0.267253	+	0.267253i
$566$	11.5120	+	0.150770i	0.483886	+	0.00633732i
$567$		−	0.318093i		−	0.0133586i
$568$	−13.7317	−	14.8554i	−0.576168	−	0.623318i
$569$			16.1403i			0.676637i	0.941032	+	0.338319i	$0.109858\pi$
$569$			16.1403i			0.676637i	−0.941032	+	0.338319i	$0.890142\pi$
$570$	0.162608	−	12.4159i	0.00681089	−	0.520045i
$571$	0.0741674	−	0.0741674i	0.00310381	−	0.00310381i	−0.705553	−	0.708657i	$-0.749301\pi$
$571$	0.0741674	−	0.0741674i	0.00310381	−	0.00310381i	0.708657	+	0.705553i	$0.249301\pi$
$572$	−0.130398	+	4.97740i	−0.00545220	+	0.208115i
$573$	−11.2909	−	11.2909i	−0.471683	−	0.471683i
$574$	4.30426	+	4.41850i	0.179656	+	0.184425i
$575$	7.68678			0.320561
$576$	−15.6990	−	1.23611i	−0.654124	−	0.0515044i
$577$	−35.3774			−1.47278			−0.736391	−	0.676556i	$-0.763472\pi$
$577$	−35.3774			−1.47278			−0.736391	+	0.676556i	$0.763472\pi$
$578$	−0.267649	−	0.274752i	−0.0111327	−	0.0114282i
$579$	−8.99650	−	8.99650i	−0.373882	−	0.373882i
$580$	−0.531327	+	20.2813i	−0.0220622	+	0.842133i
$581$	4.42053	−	4.42053i	0.183394	−	0.183394i
$582$	−0.353618	+	27.0005i	−0.0146579	+	1.11920i
$583$		−	23.3369i		−	0.966516i
$584$	−9.62709	−	10.4149i	−0.398372	−	0.430972i
$585$			5.62419i			0.232532i
$586$	−33.1718	−	0.434442i	−1.37031	−	0.0179466i
$587$	22.0590	−	22.0590i	0.910472	−	0.910472i	−0.0858369	−	0.996309i	$-0.527356\pi$
$587$	22.0590	−	22.0590i	0.910472	−	0.910472i	0.996309	+	0.0858369i	$0.0273564\pi$
$588$	−10.0694	+	9.55523i	−0.415253	+	0.394051i
$589$	−1.57481	−	1.57481i	−0.0648890	−	0.0648890i
$590$	−36.8812	+	35.9277i	−1.51838	+	1.47912i
$591$	24.9427			1.02601
$592$	−4.76735	+	4.29233i	−0.195937	+	0.176414i
$593$	22.5734			0.926979			0.463489	−	0.886102i	$-0.346597\pi$
$593$	22.5734			0.926979			0.463489	+	0.886102i	$0.346597\pi$
$594$	−12.7263	+	12.3972i	−0.522166	+	0.508665i
$595$	−3.36938	−	3.36938i	−0.138131	−	0.138131i
$596$	15.5717	+	16.4096i	0.637843	+	0.672163i
$597$	3.19710	−	3.19710i	0.130849	−	0.130849i
$598$	3.43608	+	0.0450015i	0.140512	+	0.00184025i
$599$			25.5423i			1.04363i	0.853059	+	0.521815i	$0.174745\pi$
$599$			25.5423i			1.04363i	−0.853059	+	0.521815i	$0.825255\pi$
$600$	−0.356942	+	9.08060i	−0.0145721	+	0.370714i
$601$		−	36.1215i		−	1.47343i	−0.676204	−	0.736714i	$-0.736376\pi$
$601$		−	36.1215i		−	1.47343i	0.676204	−	0.736714i	$-0.263624\pi$
$602$	0.00364366	−	0.278212i	0.000148505	−	0.0113391i
$603$	1.03618	−	1.03618i	0.0421966	−	0.0421966i
$604$	44.8666	+	1.17541i	1.82559	+	0.0478268i
$605$	9.70187	+	9.70187i	0.394437	+	0.394437i
$606$	−12.7883	−	13.1278i	−0.519491	−	0.533279i
$607$	11.9620			0.485522			0.242761	−	0.970086i	$-0.421947\pi$
$607$	11.9620			0.485522			0.242761	+	0.970086i	$0.421947\pi$
$608$	−1.11993	+	17.0790i	−0.0454192	+	0.692644i
$609$	−1.47035			−0.0595815
$610$	−9.42282	−	9.67291i	−0.381519	−	0.391645i
$611$	−8.07942	−	8.07942i	−0.326858	−	0.326858i
$612$	−16.0967	−	0.421700i	−0.650670	−	0.0170462i
$613$	−22.4398	+	22.4398i	−0.906333	+	0.906333i	−0.995974	−	0.0896411i	$-0.971428\pi$
$613$	−22.4398	+	22.4398i	−0.906333	+	0.906333i	0.0896411	+	0.995974i	$0.471428\pi$
$614$	−0.0471756	+	3.60209i	−0.00190385	+	0.145369i
$615$		−	31.0418i		−	1.25173i
$616$	2.86898	+	0.112774i	0.115595	+	0.00454381i
$617$		−	5.08975i		−	0.204906i	−0.994738	−	0.102453i	$-0.967331\pi$
$617$		−	5.08975i		−	0.204906i	0.994738	−	0.102453i	$-0.0326691\pi$
$618$	−20.4560	−	0.267907i	−0.822862	−	0.0107768i
$619$	4.34219	−	4.34219i	0.174527	−	0.174527i	−0.614438	−	0.788965i	$-0.710617\pi$
$619$	4.34219	−	4.34219i	0.174527	−	0.174527i	0.788965	+	0.614438i	$0.210617\pi$
$620$	2.89533	+	3.05112i	0.116279	+	0.122536i
$621$	8.67037	+	8.67037i	0.347930	+	0.347930i
$622$	−26.9689	+	26.2717i	−1.08136	+	1.05340i
$623$	4.83768			0.193818
$624$	−0.212719	+	4.05705i	−0.00851556	+	0.162412i
$625$	30.8099			1.23239
$626$	−16.5781	+	16.1494i	−0.662593	+	0.645461i
$627$	5.40967	+	5.40967i	0.216041	+	0.216041i
$628$	−13.0206	+	12.3558i	−0.519578	+	0.493050i
$629$	−4.63822	+	4.63822i	−0.184938	+	0.184938i
$630$	3.24291	+	0.0424715i	0.129200	+	0.00169210i
$631$		−	15.6244i		−	0.621997i	−0.950410	−	0.310998i	$-0.899337\pi$
$631$		−	15.6244i		−	0.621997i	0.950410	−	0.310998i	$-0.100663\pi$
$632$	−19.3044	+	17.8442i	−0.767888	+	0.709803i
$633$		−	5.34134i		−	0.212299i
$634$	−0.322381	+	24.6154i	−0.0128034	+	0.977602i
$635$	−6.31924	+	6.31924i	−0.250771	+	0.250771i
$636$	0.498674	−	19.0348i	0.0197737	−	0.754780i
$637$	−4.83218	−	4.83218i	−0.191458	−	0.191458i
$638$	−8.72240	−	8.95390i	−0.345323	−	0.354488i
$639$	14.0789			0.556952
$640$	2.95916	−	32.1895i	0.116971	−	1.27240i
$641$	−43.5489			−1.72008			−0.860039	−	0.510229i	$-0.829561\pi$
$641$	−43.5489			−1.72008			−0.860039	+	0.510229i	$0.829561\pi$
$642$	−18.6458	−	19.1407i	−0.735891	−	0.755422i
$643$	−14.5607	−	14.5607i	−0.574219	−	0.574219i	0.359086	−	0.933305i	$-0.383089\pi$
$643$	−14.5607	−	14.5607i	−0.574219	−	0.574219i	−0.933305	+	0.359086i	$0.883089\pi$
$644$	0.0518957	−	1.98091i	0.00204498	−	0.0780586i
$645$	−0.990076	+	0.990076i	−0.0389842	+	0.0389842i
$646$	−0.229188	+	17.4996i	−0.00901726	+	0.688513i
$647$		−	4.21827i		−	0.165837i	−0.996556	−	0.0829186i	$-0.973576\pi$
$647$		−	4.21827i		−	0.165837i	0.996556	−	0.0829186i	$-0.0264242\pi$
$648$	1.62030	−	1.49774i	0.0636514	−	0.0588367i
$649$		−	31.7232i		−	1.24524i
$650$	−4.47339	−	0.0585867i	−0.175461	−	0.00229796i
$651$	−0.215553	+	0.215553i	−0.00844818	+	0.00844818i
$652$	−0.211765	+	0.200952i	−0.00829335	+	0.00786990i
$653$	0.510765	+	0.510765i	0.0199878	+	0.0199878i	0.717030	−	0.697042i	$-0.245501\pi$
$653$	0.510765	+	0.510765i	0.0199878	+	0.0199878i	−0.697042	+	0.717030i	$0.745501\pi$
$654$	−9.42533	+	9.18164i	−0.368559	+	0.359030i
$655$	−12.2566			−0.478905
$656$	−2.24039	+	42.7295i	−0.0874725	+	1.66831i
$657$	9.87051			0.385085
$658$	−4.71961	+	4.59758i	−0.183989	+	0.179232i
$659$	−19.7169	−	19.7169i	−0.768060	−	0.768060i	0.209705	−	0.977765i	$-0.432750\pi$
$659$	−19.7169	−	19.7169i	−0.768060	−	0.768060i	−0.977765	+	0.209705i	$0.932750\pi$
$660$	−9.94582	−	10.4810i	−0.387140	−	0.407971i
$661$	−6.77903	+	6.77903i	−0.263674	+	0.263674i	−0.826545	−	0.562871i	$-0.809697\pi$
$661$	−6.77903	+	6.77903i	−0.263674	+	0.263674i	0.562871	+	0.826545i	$0.309697\pi$
$662$	36.0320	+	0.471902i	1.40042	+	0.0183410i
$663$			4.15411i			0.161332i
$664$	43.3313	+	1.70327i	1.68158	+	0.0660999i
$665$		−	3.52494i		−	0.136691i
$666$	0.0584653	−	4.46411i	0.00226548	−	0.172981i
$667$	−6.10026	+	6.10026i	−0.236203	+	0.236203i
$668$	42.7765	+	1.12066i	1.65507	+	0.0433595i
$669$	11.8733	+	11.8733i	0.459048	+	0.459048i
$670$	2.09895	+	2.15466i	0.0810894	+	0.0832416i
$671$	8.32010			0.321194
$672$	2.33769	+	0.153291i	0.0901782	+	0.00591331i
$673$	5.87422			0.226434			0.113217	−	0.993570i	$-0.463884\pi$
$673$	5.87422			0.226434			0.113217	+	0.993570i	$0.463884\pi$
$674$	9.85670	+	10.1183i	0.379666	+	0.389742i
$675$	−11.2878	−	11.2878i	−0.434469	−	0.434469i
$676$	−1.99931	−	0.0523779i	−0.0768967	−	0.00201454i
$677$	−19.9344	+	19.9344i	−0.766141	+	0.766141i	−0.977425	−	0.211284i	$-0.932236\pi$
$677$	−19.9344	+	19.9344i	−0.766141	+	0.766141i	0.211284	+	0.977425i	$0.432236\pi$
$678$	0.0591443	−	4.51596i	0.00227142	−	0.173434i
$679$			7.66556i			0.294177i
$680$	1.29826	−	33.0277i	0.0497859	−	1.26655i
$681$			15.7142i			0.602171i
$682$	−2.59134	−	0.0339381i	−0.0992276	−	0.00129956i
$683$	34.0613	−	34.0613i	1.30332	−	1.30332i	0.377181	−	0.926139i	$-0.376893\pi$
$683$	34.0613	−	34.0613i	1.30332	−	1.30332i	0.926139	−	0.377181i	$-0.123107\pi$
$684$	−8.19933	−	8.64050i	−0.313509	−	0.330378i
$685$	20.1733	+	20.1733i	0.770784	+	0.770784i
$686$	−5.71413	+	5.56639i	−0.218166	+	0.212526i
$687$	8.77792			0.334898
$688$	1.43431	−	1.29140i	0.0546826	−	0.0492341i
$689$	9.37394			0.357118
$690$	−7.14303	+	6.95834i	−0.271930	+	0.264900i
$691$	−28.8537	−	28.8537i	−1.09765	−	1.09765i	−0.994685	−	0.102962i	$-0.967168\pi$
$691$	−28.8537	−	28.8537i	−1.09765	−	1.09765i	−0.102962	−	0.994685i	$-0.532832\pi$
$692$	−7.03005	+	6.67111i	−0.267242	+	0.253597i
$693$	−1.41295	+	1.41295i	−0.0536735	+	0.0536735i
$694$	−27.1896	−	0.356094i	−1.03210	−	0.0135172i
$695$		−	15.3465i		−	0.582125i
$696$	−6.92313	−	7.48967i	−0.262420	−	0.283895i
$697$			43.7518i			1.65722i
$698$	0.107602	−	8.21592i	0.00407278	−	0.310977i
$699$	4.14341	−	4.14341i	0.156718	−	0.156718i
$700$	−0.0675622	+	2.57891i	−0.00255361	+	0.0974737i
$701$	17.9649	+	17.9649i	0.678524	+	0.678524i	0.959666	−	0.281142i	$-0.0907132\pi$
$701$	17.9649	+	17.9649i	0.678524	+	0.678524i	−0.281142	+	0.959666i	$0.590713\pi$
$702$	−4.97971	−	5.11188i	−0.187947	−	0.192935i
$703$	−4.85235			−0.183010
$704$	12.9341	+	15.1450i	0.487473	+	0.570800i
$705$	33.1572			1.24877
$706$	19.2948	+	19.8069i	0.726170	+	0.745443i
$707$	−3.67886	−	3.67886i	−0.138358	−	0.138358i
$708$	0.677875	−	25.8751i	0.0254761	−	0.972447i
$709$	−7.03632	+	7.03632i	−0.264254	+	0.264254i	−0.826780	−	0.562525i	$-0.809830\pi$
$709$	−7.03632	+	7.03632i	−0.264254	+	0.264254i	0.562525	+	0.826780i	$0.309830\pi$
$710$	−0.378461	+	28.8974i	−0.0142034	+	1.08450i
$711$		−	18.2953i		−	0.686129i
$712$	22.7782	+	24.6422i	0.853649	+	0.923506i
$713$			1.78859i			0.0669834i
$714$	2.39526	+	0.0313701i	0.0896404	+	0.00117400i
$715$	5.02971	−	5.02971i	0.188100	−	0.188100i
$716$	31.6847	−	30.0669i	1.18411	−	1.12365i
$717$	−3.75562	−	3.75562i	−0.140256	−	0.140256i
$718$	31.4067	−	30.5947i	1.17209	−	1.14178i
$719$	−37.7482			−1.40777			−0.703886	−	0.710313i	$-0.748553\pi$
$719$	−37.7482			−1.40777			−0.703886	+	0.710313i	$0.748553\pi$
$720$	15.0529	+	16.7187i	0.560987	+	0.623069i
$721$	−5.80756			−0.216285
$722$	9.97355	−	9.71568i	0.371177	−	0.361580i
$723$	−4.76366	−	4.76366i	−0.177162	−	0.177162i
$724$	−3.73972	−	3.94093i	−0.138985	−	0.146464i
$725$	7.94184	−	7.94184i	0.294952	−	0.294952i
$726$	−6.89696	−	0.0903277i	−0.255970	−	0.00335237i
$727$			9.16380i			0.339866i	0.985456	+	0.169933i	$0.0543552\pi$
$727$			9.16380i			0.339866i	−0.985456	+	0.169933i	$0.945645\pi$
$728$	−0.0452991	+	1.15241i	−0.00167890	+	0.0427111i
$729$		−	13.8401i		−	0.512595i
$730$	−0.265334	+	20.2596i	−0.00982046	+	0.749840i
$731$	1.39546	−	1.39546i	0.0516130	−	0.0516130i
$732$	6.78632	+	0.177788i	0.250830	+	0.00657122i
$733$	−23.9173	−	23.9173i	−0.883407	−	0.883407i	0.110473	−	0.993879i	$-0.464764\pi$
$733$	−23.9173	−	23.9173i	−0.883407	−	0.883407i	−0.993879	+	0.110473i	$0.964764\pi$
$734$	20.4945	+	21.0384i	0.756464	+	0.776542i
$735$	19.8308			0.731471
$736$	10.3347	−	9.06274i	0.380942	−	0.334057i
$737$	−1.85331			−0.0682677
$738$	−20.7790	−	21.3305i	−0.764886	−	0.785187i
$739$	−6.73513	−	6.73513i	−0.247756	−	0.247756i	0.572293	−	0.820049i	$-0.306054\pi$
$739$	−6.73513	−	6.73513i	−0.247756	−	0.247756i	−0.820049	+	0.572293i	$0.806054\pi$
$740$	9.16119	+	0.240004i	0.336772	+	0.00882273i
$741$	−2.17295	+	2.17295i	−0.0798253	+	0.0798253i
$742$	0.0707880	−	5.40501i	0.00259871	−	0.198424i
$743$			51.0784i			1.87388i	0.349485	+	0.936942i	$0.386357\pi$
$743$			51.0784i			1.87388i	−0.349485	+	0.936942i	$0.613643\pi$
$744$	−2.11291	−	0.0830547i	−0.0774631	−	0.00304493i
$745$		−	32.3174i		−	1.18402i
$746$	−2.10262	−	0.0275374i	−0.0769824	−	0.00100822i
$747$	−21.3403	+	21.3403i	−0.780800	+	0.780800i
$748$	14.0181	+	14.7724i	0.512553	+	0.540132i
$749$	−5.36388	−	5.36388i	−0.195992	−	0.195992i
$750$	−5.39887	+	5.25928i	−0.197139	+	0.192042i
$751$	48.6129			1.77391			0.886954	−	0.461858i	$-0.152817\pi$
$751$	48.6129			1.77391			0.886954	+	0.461858i	$0.152817\pi$
$752$	−45.6414	−	2.39307i	−1.66437	−	0.0872661i
$753$	−24.0822			−0.877605
$754$	3.59659	−	3.50360i	0.130980	−	0.127594i
$755$	−45.3381	−	45.3381i	−1.65002	−	1.65002i
$756$	−2.98511	+	2.83270i	−0.108567	+	0.103024i
$757$	−4.05596	+	4.05596i	−0.147416	+	0.147416i	−0.776963	−	0.629546i	$-0.783241\pi$
$757$	−4.05596	+	4.05596i	−0.147416	+	0.147416i	0.629546	+	0.776963i	$0.283241\pi$
$758$	−49.6035	−	0.649643i	−1.80168	−	0.0235961i
$759$		−	6.14403i		−	0.223014i
$760$	17.9553	−	16.5972i	0.651309	−	0.602042i
$761$			8.81915i			0.319694i	0.987142	+	0.159847i	$0.0511001\pi$
$761$			8.81915i			0.319694i	−0.987142	+	0.159847i	$0.948900\pi$
$762$	0.0588342	−	4.49228i	0.00213134	−	0.162738i
$763$	−2.64130	+	2.64130i	−0.0956216	+	0.0956216i
$764$	0.823463	−	31.4324i	0.0297919	−	1.13718i
$765$	16.2659	+	16.2659i	0.588093	+	0.588093i
$766$	1.94477	+	1.99639i	0.0702674	+	0.0721323i
$767$	12.7425			0.460106
$768$	10.2262	+	12.6295i	0.369004	+	0.455727i
$769$	54.0534			1.94922			0.974608	−	0.223919i	$-0.0718851\pi$
$769$	54.0534			1.94922			0.974608	+	0.223919i	$0.0718851\pi$
$770$	−2.86215	−	2.93811i	−0.103145	−	0.105882i
$771$	17.4479	+	17.4479i	0.628369	+	0.628369i
$772$	0.656131	−	25.0451i	0.0236147	−	0.901394i
$773$	−2.97462	+	2.97462i	−0.106990	+	0.106990i	−0.758575	−	0.651586i	$-0.774104\pi$
$773$	−2.97462	+	2.97462i	−0.106990	+	0.106990i	0.651586	+	0.758575i	$0.274104\pi$
$774$	−0.0175900	+	1.34308i	−0.000632258	+	0.0482760i
$775$		−	2.32854i		−	0.0836438i
$776$	−39.0469	+	36.0932i	−1.40170	+	1.29567i
$777$			0.664167i			0.0238269i
$778$	51.1999	+	0.670551i	1.83561	+	0.0240404i
$779$	−22.8859	+	22.8859i	−0.819971	+	0.819971i
$780$	4.20998	−	3.99502i	0.150741	−	0.143045i
$781$	−12.5907	−	12.5907i	−0.450532	−	0.450532i
$782$	10.0677	−	9.80743i	0.360021	−	0.350713i
$783$	17.9161			0.640270
$784$	−27.2975	−	1.43126i	−0.974909	−	0.0511163i
$785$	25.6431			0.915241
$786$	4.41360	−	4.29949i	0.157428	−	0.153358i
$787$	3.06914	+	3.06914i	0.109403	+	0.109403i	0.759689	−	0.650286i	$-0.225351\pi$
$787$	3.06914	+	3.06914i	0.109403	+	0.109403i	−0.650286	+	0.759689i	$0.725351\pi$
$788$	33.8092	+	35.6283i	1.20440	+	1.26921i
$789$	3.86929	−	3.86929i	0.137750	−	0.137750i
$790$	37.5519	+	0.491806i	1.33604	+	0.0174977i
$791$		−	1.28210i		−	0.0455863i
$792$	−13.8501	−	0.544424i	−0.492143	−	0.0193453i
$793$			3.34201i			0.118678i
$794$	0.446391	−	34.0842i	0.0158418	−	1.20960i
$795$	−19.2349	+	19.2349i	−0.682191	+	0.682191i
$796$	8.90034	+	0.233171i	0.315464	+	0.00826451i
$797$	22.2590	+	22.2590i	0.788453	+	0.788453i	0.981241	−	0.192788i	$-0.0617528\pi$
$797$	22.2590	+	22.2590i	0.788453	+	0.788453i	−0.192788	+	0.981241i	$0.561753\pi$
$798$	1.23651	+	1.26933i	0.0437721	+	0.0449338i
$799$	−46.7334			−1.65331
$800$	−13.4546	+	11.7986i	−0.475692	+	0.417145i
$801$	−23.3541			−0.825178
$802$	−26.5188	−	27.2226i	−0.936412	−	0.961265i
$803$	−8.82719	−	8.82719i	−0.311505	−	0.311505i
$804$	−1.51166	−	0.0396025i	−0.0533122	−	0.00139667i
$805$	−2.00172	+	2.00172i	−0.0705515	+	0.0705515i
$806$	0.0136322	−	1.04089i	0.000480174	−	0.0366637i
$807$		−	12.7060i		−	0.447273i
$808$	1.41750	−	36.0612i	0.0498675	−	1.26863i
$809$			9.98940i			0.351209i	0.984461	+	0.175604i	$0.0561879\pi$
$809$			9.98940i			0.351209i	−0.984461	+	0.175604i	$0.943812\pi$
$810$	−3.15189	−	0.0412794i	−0.110746	−	0.00145041i
$811$	10.2290	−	10.2290i	0.359189	−	0.359189i	−0.504325	−	0.863514i	$-0.668259\pi$
$811$	10.2290	−	10.2290i	0.359189	−	0.359189i	0.863514	+	0.504325i	$0.168259\pi$
$812$	−1.99302	−	2.10025i	−0.0699412	−	0.0737044i
$813$	0.627696	+	0.627696i	0.0220142	+	0.0220142i
$814$	−4.04454	+	3.93997i	−0.141761	+	0.138096i
$815$	0.417055			0.0146088
$816$	11.1183	+	12.3487i	0.389218	+	0.432291i
$817$	1.45989			0.0510750
$818$	−8.36238	+	8.14618i	−0.292384	+	0.284824i
$819$	−0.567551	−	0.567551i	−0.0198318	−	0.0198318i
$820$	44.3402	−	42.0763i	1.54843	−	1.46937i
$821$	−9.92456	+	9.92456i	−0.346370	+	0.346370i	−0.858755	−	0.512386i	$-0.828762\pi$
$821$	−9.92456	+	9.92456i	−0.346370	+	0.346370i	0.512386	+	0.858755i	$0.328762\pi$
$822$	−14.3410	−	0.187821i	−0.500201	−	0.00655100i
$823$			14.1587i			0.493540i	0.969074	+	0.246770i	$0.0793692\pi$
$823$			14.1587i			0.493540i	−0.969074	+	0.246770i	$0.920631\pi$
$824$	−27.3449	−	29.5826i	−0.952604	−	1.03056i
$825$			7.99882i			0.278483i
$826$	0.0962260	−	7.34733i	0.00334813	−	0.255646i
$827$	−3.69344	+	3.69344i	−0.128433	+	0.128433i	−0.768401	−	0.639968i	$-0.778948\pi$
$827$	−3.69344	+	3.69344i	−0.128433	+	0.128433i	0.639968	+	0.768401i	$0.278948\pi$
$828$	−0.250529	+	9.56291i	−0.00870648	+	0.332334i
$829$	16.4806	+	16.4806i	0.572395	+	0.572395i	0.932797	−	0.360402i	$-0.117361\pi$
$829$	16.4806	+	16.4806i	0.572395	+	0.572395i	−0.360402	+	0.932797i	$0.617361\pi$
$830$	−43.2281	−	44.3754i	−1.50047	−	1.54029i
$831$	21.3543			0.740772
$832$	−6.08344	+	5.19537i	−0.210905	+	0.180117i
$833$	−27.9506			−0.968429
$834$	5.38339	+	5.52627i	0.186411	+	0.191359i
$835$	−43.2260	−	43.2260i	−1.49590	−	1.49590i
$836$	−0.394537	+	15.0598i	−0.0136453	+	0.520856i
$837$	2.62650	−	2.62650i	0.0907851	−	0.0907851i
$838$	−0.000792585		0.0605178i	−2.73794e−5		0.00209055i
$839$		−	6.39930i		−	0.220928i	−0.993880	−	0.110464i	$-0.964766\pi$
$839$		−	6.39930i		−	0.220928i	0.993880	−	0.110464i	$-0.0352337\pi$
$840$	−2.27174	−	2.45764i	−0.0783824	−	0.0847967i
$841$		−	16.3947i		−	0.565333i
$842$	−33.1501	−	0.434158i	−1.14243	−	0.0149621i
$843$	−3.29468	+	3.29468i	−0.113475	+	0.113475i
$844$	7.62960	−	7.24004i	0.262622	−	0.249213i
$845$	2.02033	+	2.02033i	0.0695013	+	0.0695013i
$846$	22.7841	−	22.1950i	0.783334	−	0.763081i
$847$	−1.95808			−0.0672805
$848$	27.8654	−	25.0889i	0.956901	−	0.861556i
$849$	8.26836			0.283769
$850$	−13.1070	+	12.7682i	−0.449568	+	0.437944i
$851$	2.75553	+	2.75553i	0.0944584	+	0.0944584i
$852$	−10.0006	−	10.5387i	−0.342616	−	0.361051i
$853$	−6.65107	+	6.65107i	−0.227728	+	0.227728i	−0.811743	−	0.584015i	$-0.801481\pi$
$853$	−6.65107	+	6.65107i	−0.227728	+	0.227728i	0.584015	+	0.811743i	$0.301481\pi$
$854$	1.92700	+	0.0252374i	0.0659406	+	0.000863606i
$855$			17.0168i			0.581962i
$856$	2.06676	−	52.5784i	0.0706404	−	1.79709i
$857$		−	3.22288i		−	0.110091i	−0.998484	−	0.0550457i	$-0.982470\pi$
$857$		−	3.22288i		−	0.110091i	0.998484	−	0.0550457i	$-0.0175305\pi$
$858$	−0.0468282	+	3.57557i	−0.00159869	+	0.122068i
$859$	19.4169	−	19.4169i	0.662498	−	0.662498i	−0.293470	−	0.955968i	$-0.594810\pi$
$859$	19.4169	−	19.4169i	0.662498	−	0.662498i	0.955968	+	0.293470i	$0.0948102\pi$
$860$	−2.75625	−	0.0722080i	−0.0939873	−	0.00246227i
$861$	3.13251	+	3.13251i	0.106756	+	0.106756i
$862$	−23.2339	−	23.8506i	−0.791350	−	0.812354i
$863$	31.9205			1.08659			0.543294	−	0.839543i	$-0.317177\pi$
$863$	31.9205			1.08659			0.543294	+	0.839543i	$0.317177\pi$
$864$	−28.4846	−	1.86784i	−0.969065	−	0.0635451i
$865$	13.8451			0.470749
$866$	−14.2336	−	14.6114i	−0.483677	−	0.496515i
$867$	−0.194787	−	0.194787i	−0.00661530	−	0.00661530i
$868$	−0.600072	−	0.0157207i	−0.0203678	−	0.000533594i
$869$	−16.3615	+	16.3615i	−0.555026	+	0.555026i
$870$	−0.190810	+	14.5693i	−0.00646906	+	0.493944i
$871$		−	0.744437i		−	0.0252243i
$872$	−25.8908	−	1.01772i	−0.876775	−	0.0344644i
$873$		−	37.0059i		−	1.25246i
$874$	10.3964	+	0.136159i	0.351663	+	0.00460563i
$875$	−1.51295	+	1.51295i	−0.0511471	+	0.0511471i
$876$	−7.01131	−	7.38855i	−0.236890	−	0.249636i
$877$	35.4043	+	35.4043i	1.19552	+	1.19552i	0.975494	+	0.220024i	$0.0706137\pi$
$877$	35.4043	+	35.4043i	1.19552	+	1.19552i	0.220024	+	0.975494i	$0.429386\pi$
$878$	−29.1254	+	28.3724i	−0.982934	+	0.957521i
$879$	−23.8253			−0.803606
$880$	1.48976	−	28.4133i	0.0502199	−	0.957812i
$881$	4.61905			0.155620			0.0778098	−	0.996968i	$-0.475207\pi$
$881$	4.61905			0.155620			0.0778098	+	0.996968i	$0.475207\pi$
$882$	13.6268	−	13.2745i	0.458840	−	0.446976i
$883$	−22.0615	−	22.0615i	−0.742430	−	0.742430i	0.230615	−	0.973045i	$-0.425926\pi$
$883$	−22.0615	−	22.0615i	−0.742430	−	0.742430i	−0.973045	+	0.230615i	$0.925926\pi$
$884$	−5.93375	+	5.63078i	−0.199574	+	0.189384i
$885$	−26.1471	+	26.1471i	−0.878924	+	0.878924i
$886$	9.86951	+	0.129258i	0.331573	+	0.00434252i
$887$			50.0664i			1.68106i	0.541762	+	0.840532i	$0.317757\pi$
$887$			50.0664i			1.68106i	−0.541762	+	0.840532i	$0.682243\pi$
$888$	−3.38314	+	3.12723i	−0.113531	+	0.104943i
$889$		−	1.27538i		−	0.0427749i
$890$	0.627795	−	47.9352i	0.0210437	−	1.60679i
$891$	1.37329	−	1.37329i	0.0460070	−	0.0460070i
$892$	−0.865940	+	33.0537i	−0.0289938	+	1.10672i
$893$	−24.4455	−	24.4455i	−0.818037	−	0.818037i
$894$	11.3366	+	11.6375i	0.379154	+	0.389217i
$895$	−62.4006			−2.08582
$896$	2.94971	+	3.54694i	0.0985428	+	0.118495i
$897$	2.46793			0.0824016
$898$	0.925680	+	0.950248i	0.0308903	+	0.0317102i
$899$	1.84794	+	1.84794i	0.0616323	+	0.0616323i
$900$	0.326160	−	12.4498i	0.0108720	−	0.414994i
$901$	27.1106	−	27.1106i	0.903185	−	0.903185i
$902$	−0.493203	+	37.6585i	−0.0164219	+	1.25389i
$903$		−	0.199822i		−	0.00664967i
$904$	6.53078	−	6.03677i	0.217210	−	0.200780i
$905$			7.76137i			0.257997i
$906$	32.2304	+	0.422113i	1.07078	+	0.0140238i
$907$	−19.3463	+	19.3463i	−0.642383	+	0.642383i	−0.951141	−	0.308758i	$-0.900087\pi$
$907$	−19.3463	+	19.3463i	−0.642383	+	0.642383i	0.308758	+	0.951141i	$0.400087\pi$
$908$	−22.4463	+	21.3002i	−0.744906	+	0.706872i
$909$	17.7599	+	17.7599i	0.589057	+	0.589057i
$910$	1.18018	−	1.14966i	0.0391225	−	0.0381110i
$911$	20.6963			0.685700			0.342850	−	0.939390i	$-0.388608\pi$
$911$	20.6963			0.685700			0.342850	+	0.939390i	$0.388608\pi$
$912$	−0.643611	+	12.2752i	−0.0213121	+	0.406472i
$913$	38.1692			1.26322
$914$	13.3877	−	13.0416i	0.442826	−	0.431377i
$915$	−6.85764	−	6.85764i	−0.226707	−	0.226707i
$916$	11.8982	+	12.5384i	0.393128	+	0.414281i
$917$	1.23684	−	1.23684i	0.0408442	−	0.0408442i
$918$	−29.1861	−	0.382243i	−0.963286	−	0.0126159i
$919$		−	22.3399i		−	0.736924i	−0.929643	−	0.368462i	$-0.879885\pi$
$919$		−	22.3399i		−	0.736924i	0.929643	−	0.368462i	$-0.120115\pi$
$920$	−19.6215	−	0.771285i	−0.646902	−	0.0254285i
$921$			2.58716i			0.0852499i
$922$	−0.137681	+	10.5126i	−0.00453428	+	0.346214i
$923$	5.05743	−	5.05743i	0.166467	−	0.166467i
$924$	2.06132	+	0.0540023i	0.0678124	+	0.00177655i
$925$	−3.58738	−	3.58738i	−0.117952	−	0.117952i
$926$	−2.91812	−	2.99558i	−0.0958955	−	0.0984407i
$927$	28.0363			0.920832
$928$	1.31417	−	20.0411i	0.0431396	−	0.657880i
$929$	−34.2378			−1.12331			−0.561653	−	0.827373i	$-0.689834\pi$
$929$	−34.2378			−1.12331			−0.561653	+	0.827373i	$0.689834\pi$
$930$	2.10788	+	2.16382i	0.0691201	+	0.0709546i
$931$	−14.6205	−	14.6205i	−0.479167	−	0.479167i
$932$	11.5347	+	0.302187i	0.377833	+	0.00989845i
$933$	−19.1197	+	19.1197i	−0.625951	+	0.625951i
$934$	−0.390415	+	29.8101i	−0.0127748	+	0.975416i
$935$		−	29.0931i		−	0.951445i
$936$	0.218683	−	5.56331i	0.00714789	−	0.181842i
$937$			39.2677i			1.28282i	0.767199	+	0.641409i	$0.221650\pi$
$937$			39.2677i			1.28282i	−0.767199	+	0.641409i	$0.778350\pi$
$938$	−0.429242	−	0.00562167i	−0.0140153	−	0.000183554i
$939$	−11.7531	+	11.7531i	−0.383547	+	0.383547i
$940$	44.9436	+	47.3619i	1.46590	+	1.54477i
$941$	12.9717	+	12.9717i	0.422866	+	0.422866i	0.886189	−	0.463323i	$-0.153343\pi$
$941$	12.9717	+	12.9717i	0.422866	+	0.422866i	−0.463323	+	0.886189i	$0.653343\pi$
$942$	−9.23408	+	8.99533i	−0.300863	+	0.293084i
$943$	25.9926			0.846436
$944$	37.8790	−	34.1047i	1.23286	−	1.11001i
$945$	5.87895			0.191242
$946$	1.21685	−	1.18538i	0.0395631	−	0.0385402i
$947$	18.3494	+	18.3494i	0.596276	+	0.596276i	0.939320	−	0.343043i	$-0.111458\pi$
$947$	18.3494	+	18.3494i	0.596276	+	0.596276i	−0.343043	+	0.939320i	$0.611458\pi$
$948$	−13.6950	+	12.9957i	−0.444791	+	0.422081i
$949$	3.54569	−	3.54569i	0.115098	−	0.115098i
$950$	−13.5349	−	0.177263i	−0.439130	−	0.00575116i
$951$			17.6797i			0.573304i
$952$	3.20190	+	3.46392i	0.103774	+	0.112266i
$953$			46.3591i			1.50172i	0.660462	+	0.750860i	$0.270361\pi$
$953$			46.3591i			1.50172i	−0.660462	+	0.750860i	$0.729639\pi$
$954$	−0.341732	+	26.0929i	−0.0110640	+	0.844790i
$955$	−31.7627	+	31.7627i	−1.02782	+	1.02782i
$956$	0.273905	−	10.4552i	0.00885870	−	0.338145i
$957$	−6.34789	−	6.34789i	−0.205198	−	0.205198i
$958$	−12.5167	−	12.8489i	−0.404396	−	0.415129i
$959$	−4.07149			−0.131475
$960$	1.82228	−	23.1436i	0.0588138	−	0.746956i
$961$	−30.4582			−0.982522
$962$	−1.58260	−	1.62461i	−0.0510251	−	0.0523794i
$963$	25.8944	+	25.8944i	0.834435	+	0.834435i
$964$	0.347422	−	13.2614i	0.0111897	−	0.427122i
$965$	−25.3083	+	25.3083i	−0.814705	+	0.814705i
$966$	0.0186367	−	1.42301i	0.000599627	−	0.0457845i
$967$			22.0005i			0.707490i	0.935342	+	0.353745i	$0.115092\pi$
$967$			22.0005i			0.707490i	−0.935342	+	0.353745i	$0.884908\pi$
$968$	−9.21962	−	9.97409i	−0.296330	−	0.320579i
$969$			12.5689i			0.403771i
$970$	75.9559	+	0.994773i	2.43880	+	0.0319402i
$971$	24.7240	−	24.7240i	0.793431	−	0.793431i	−0.188619	−	0.982050i	$-0.560401\pi$
$971$	24.7240	−	24.7240i	0.793431	−	0.793431i	0.982050	+	0.188619i	$0.0604012\pi$
$972$	23.1121	−	21.9321i	0.741322	−	0.703472i
$973$	1.54865	+	1.54865i	0.0496475	+	0.0496475i
$974$	34.0836	−	33.2023i	1.09211	−	1.06387i
$975$	−3.21296			−0.102897
$976$	8.94472	+	9.93459i	0.286313	+	0.317999i
$977$	−14.6857			−0.469836			−0.234918	−	0.972015i	$-0.575482\pi$
$977$	−14.6857			−0.469836			−0.234918	+	0.972015i	$0.575482\pi$
$978$	−0.150181	+	0.146299i	−0.00480227	+	0.00467811i
$979$	20.8856	+	20.8856i	0.667506	+	0.667506i
$980$	26.8801	+	28.3264i	0.858654	+	0.904855i
$981$	12.7510	−	12.7510i	0.407109	−	0.407109i
$982$	−32.7835	−	0.429356i	−1.04616	−	0.0137013i
$983$			1.97361i			0.0629483i	0.999505	+	0.0314741i	$0.0100202\pi$
$983$			1.97361i			0.0629483i	−0.999505	+	0.0314741i	$0.989980\pi$
$984$	−1.20699	+	30.7058i	−0.0384774	+	0.978864i
$985$		−	70.1672i		−	2.23571i
$986$	0.268937	−	20.5346i	0.00856469	−	0.653956i
$987$	−3.34598	+	3.34598i	−0.106504	+	0.106504i
$988$	−6.04922	−	0.158477i	−0.192451	−	0.00504183i
$989$	−0.829033	−	0.829033i	−0.0263617	−	0.0263617i
$990$	13.8171	+	14.1839i	0.439138	+	0.450793i
$991$	−46.5830			−1.47976			−0.739878	−	0.672741i	$-0.765117\pi$
$991$	−46.5830			−1.47976			−0.739878	+	0.672741i	$0.765117\pi$
$992$	−2.74536	−	3.13067i	−0.0871652	−	0.0993989i
$993$	25.8796			0.821264
$994$	−2.87792	−	2.95430i	−0.0912821	−	0.0937048i
$995$	−8.99387	−	8.99387i	−0.285125	−	0.285125i
$996$	31.1329	+	0.815618i	0.986483	+	0.0258438i
$997$	9.04043	−	9.04043i	0.286313	−	0.286313i	−0.549307	−	0.835621i	$-0.685108\pi$
$997$	9.04043	−	9.04043i	0.286313	−	0.286313i	0.835621	+	0.549307i	$0.185108\pi$
$998$	0.157254	−	12.0071i	0.00497780	−	0.380079i
$999$		−	8.09284i		−	0.256046i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	208.2.n.a.157.19	yes	48
4.3	odd	2		832.2.n.a.209.9		48
8.3	odd	2		1664.2.n.a.417.16		48
8.5	even	2		1664.2.n.b.417.9		48
16.3	odd	4		1664.2.n.a.1249.16		48
16.5	even	4	inner	208.2.n.a.53.19	✓	48
16.11	odd	4		832.2.n.a.625.9		48
16.13	even	4		1664.2.n.b.1249.9		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
208.2.n.a.53.19	✓	48	16.5	even	4	inner
208.2.n.a.157.19	yes	48	1.1	even	1	trivial
832.2.n.a.209.9		48	4.3	odd	2
832.2.n.a.625.9		48	16.11	odd	4
1664.2.n.a.417.16		48	8.3	odd	2
1664.2.n.a.1249.16		48	16.3	odd	4
1664.2.n.b.417.9		48	8.5	even	2
1664.2.n.b.1249.9		48	16.13	even	4

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:	\( N \)	\(=\)	\( 208 = 2^{4} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	208.n (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.986819 + 1.01301i) q^{2} +(0.718176 + 0.718176i) q^{3} +(-0.0523779 + 1.99931i) q^{4} +(2.02033 - 2.02033i) q^{5} +(-0.0188099 + 1.43623i) q^{6} +0.407753i q^{7} +(-2.07701 + 1.91990i) q^{8} -1.96845i q^{9} +O(q^{10})\)	\(q+(0.986819 + 1.01301i) q^{2} +(0.718176 + 0.718176i) q^{3} +(-0.0523779 + 1.99931i) q^{4} +(2.02033 - 2.02033i) q^{5} +(-0.0188099 + 1.43623i) q^{6} +0.407753i q^{7} +(-2.07701 + 1.91990i) q^{8} -1.96845i q^{9} +(4.04031 + 0.0529148i) q^{10} +(-1.76038 + 1.76038i) q^{11} +(-1.47348 + 1.39824i) q^{12} +(-0.707107 - 0.707107i) q^{13} +(-0.413057 + 0.402378i) q^{14} +2.90190 q^{15} +(-3.99451 - 0.209440i) q^{16} -4.09008 q^{17} +(1.99405 - 1.94250i) q^{18} +(-2.13946 - 2.13946i) q^{19} +(3.93345 + 4.14509i) q^{20} +(-0.292838 + 0.292838i) q^{21} +(-3.52046 - 0.0461065i) q^{22} +2.42989i q^{23} +(-2.87049 - 0.112834i) q^{24} -3.16343i q^{25} +(0.0185200 - 1.41409i) q^{26} +(3.56822 - 3.56822i) q^{27} +(-0.815226 - 0.0213572i) q^{28} +(2.51051 + 2.51051i) q^{29} +(2.86365 + 2.93965i) q^{30} +0.736081 q^{31} +(-3.72970 - 4.25316i) q^{32} -2.52853 q^{33} +(-4.03617 - 4.14329i) q^{34} +(0.823793 + 0.823793i) q^{35} +(3.93554 + 0.103103i) q^{36} +(1.13402 - 1.13402i) q^{37} +(0.0560349 - 4.27854i) q^{38} -1.01565i q^{39} +(-0.317416 + 8.07507i) q^{40} -10.6971i q^{41} +(-0.585627 - 0.00766979i) q^{42} +(-0.341182 + 0.341182i) q^{43} +(-3.42735 - 3.61176i) q^{44} +(-3.97690 - 3.97690i) q^{45} +(-2.46150 + 2.39786i) q^{46} +11.4260 q^{47} +(-2.71835 - 3.01918i) q^{48} +6.83374 q^{49} +(3.20459 - 3.12173i) q^{50} +(-2.93740 - 2.93740i) q^{51} +(1.45077 - 1.37669i) q^{52} +(-6.62837 + 6.62837i) q^{53} +(7.13583 + 0.0934560i) q^{54} +7.11308i q^{55} +(-0.782845 - 0.846907i) q^{56} -3.07301i q^{57} +(-0.0657534 + 5.02059i) q^{58} +(-9.01032 + 9.01032i) q^{59} +(-0.151996 + 5.80181i) q^{60} +(-2.36316 - 2.36316i) q^{61} +(0.726379 + 0.745657i) q^{62} +0.802639 q^{63} +(0.627960 - 7.97532i) q^{64} -2.85717 q^{65} +(-2.49520 - 2.56142i) q^{66} +(0.526396 + 0.526396i) q^{67} +(0.214230 - 8.17736i) q^{68} +(-1.74509 + 1.74509i) q^{69} +(-0.0215761 + 1.64745i) q^{70} +7.15228i q^{71} +(3.77922 + 4.08848i) q^{72} +5.01437i q^{73} +(2.26784 + 0.0297013i) q^{74} +(2.27190 - 2.27190i) q^{75} +(4.38950 - 4.16538i) q^{76} +(-0.717799 - 0.717799i) q^{77} +(1.02887 - 1.00227i) q^{78} +9.29431 q^{79} +(-8.49335 + 7.64708i) q^{80} -0.780111 q^{81} +(10.8362 - 10.5561i) q^{82} +(-10.8412 - 10.8412i) q^{83} +(-0.570138 - 0.600814i) q^{84} +(-8.26330 + 8.26330i) q^{85} +(-0.682305 - 0.00893596i) q^{86} +3.60598i q^{87} +(0.276575 - 7.03608i) q^{88} -11.8643i q^{89} +(0.104160 - 7.95312i) q^{90} +(0.288325 - 0.288325i) q^{91} +(-4.85811 - 0.127272i) q^{92} +(0.528636 + 0.528636i) q^{93} +(11.2754 + 11.5747i) q^{94} -8.64480 q^{95} +(0.375940 - 5.73310i) q^{96} +18.7995 q^{97} +(6.74366 + 6.92264i) q^{98} +(3.46521 + 3.46521i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 4 q^{4} - 12 q^{8}+O(q^{10}) \) 48 * q - 4 * q^4 - 12 * q^8	\( 48 q - 4 q^{4} - 12 q^{8} - 4 q^{10} - 8 q^{11} + 8 q^{12} - 4 q^{14} - 16 q^{15} + 12 q^{16} - 16 q^{19} - 28 q^{20} + 12 q^{22} + 28 q^{24} - 16 q^{29} + 4 q^{30} + 24 q^{31} - 20 q^{32} - 40 q^{34} + 24 q^{35} + 8 q^{36} - 16 q^{37} + 32 q^{40} + 40 q^{42} - 8 q^{43} + 20 q^{44} - 32 q^{46} - 40 q^{47} - 52 q^{48} - 48 q^{49} - 16 q^{50} - 24 q^{51} - 8 q^{52} + 16 q^{53} + 20 q^{54} + 20 q^{56} - 16 q^{58} - 68 q^{60} + 32 q^{61} - 32 q^{62} + 40 q^{63} + 32 q^{64} - 32 q^{66} + 16 q^{67} + 40 q^{68} + 32 q^{69} - 60 q^{70} + 40 q^{72} + 72 q^{74} - 40 q^{75} - 28 q^{76} + 16 q^{77} + 32 q^{79} - 52 q^{80} - 48 q^{81} + 40 q^{82} + 40 q^{83} - 36 q^{84} - 32 q^{85} - 72 q^{86} - 8 q^{88} + 28 q^{90} + 36 q^{92} + 28 q^{94} - 48 q^{95} + 68 q^{96} + 64 q^{98} - 40 q^{99}+O(q^{100}) \) 48 * q - 4 * q^4 - 12 * q^8 - 4 * q^10 - 8 * q^11 + 8 * q^12 - 4 * q^14 - 16 * q^15 + 12 * q^16 - 16 * q^19 - 28 * q^20 + 12 * q^22 + 28 * q^24 - 16 * q^29 + 4 * q^30 + 24 * q^31 - 20 * q^32 - 40 * q^34 + 24 * q^35 + 8 * q^36 - 16 * q^37 + 32 * q^40 + 40 * q^42 - 8 * q^43 + 20 * q^44 - 32 * q^46 - 40 * q^47 - 52 * q^48 - 48 * q^49 - 16 * q^50 - 24 * q^51 - 8 * q^52 + 16 * q^53 + 20 * q^54 + 20 * q^56 - 16 * q^58 - 68 * q^60 + 32 * q^61 - 32 * q^62 + 40 * q^63 + 32 * q^64 - 32 * q^66 + 16 * q^67 + 40 * q^68 + 32 * q^69 - 60 * q^70 + 40 * q^72 + 72 * q^74 - 40 * q^75 - 28 * q^76 + 16 * q^77 + 32 * q^79 - 52 * q^80 - 48 * q^81 + 40 * q^82 + 40 * q^83 - 36 * q^84 - 32 * q^85 - 72 * q^86 - 8 * q^88 + 28 * q^90 + 36 * q^92 + 28 * q^94 - 48 * q^95 + 68 * q^96 + 64 * q^98 - 40 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more