LMFDB - Embedded newform 304.2.k.b.77.22

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [304,2,Mod(77,304)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(304, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 3, 0]))

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

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

chi := DirichletCharacter("304.77");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 304 = 2^{4} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	304.k (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:	$2.42745222145$
Analytic rank:	$0$
Dimension:	$68$
Relative dimension:	$34$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			77.22
Character	$\chi$	$=$	304.77
Dual form			304.2.k.b.229.22

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.581253 + 1.28924i) q^{2} +(-0.951991 - 0.951991i) q^{3} +(-1.32429 + 1.49875i) q^{4} +(1.77844 - 1.77844i) q^{5} +(0.673999 - 1.78069i) q^{6} -2.10998i q^{7} +(-2.70200 - 0.836178i) q^{8} -1.18743i q^{9} +O(q^{10})$	\(q+(0.581253 + 1.28924i) q^{2} +(-0.951991 - 0.951991i) q^{3} +(-1.32429 + 1.49875i) q^{4} +(1.77844 - 1.77844i) q^{5} +(0.673999 - 1.78069i) q^{6} -2.10998i q^{7} +(-2.70200 - 0.836178i) q^{8} -1.18743i q^{9} +(3.32656 + 1.25912i) q^{10} +(1.29822 - 1.29822i) q^{11} +(2.68751 - 0.166085i) q^{12} +(1.24075 + 1.24075i) q^{13} +(2.72027 - 1.22643i) q^{14} -3.38612 q^{15} +(-0.492510 - 3.96956i) q^{16} +3.50292 q^{17} +(1.53088 - 0.690195i) q^{18} +(-0.707107 - 0.707107i) q^{19} +(0.310268 + 5.02061i) q^{20} +(-2.00868 + 2.00868i) q^{21} +(2.42831 + 0.919123i) q^{22} -1.82092i q^{23} +(1.77625 + 3.36831i) q^{24} -1.32570i q^{25} +(-0.878441 + 2.32082i) q^{26} +(-3.98639 + 3.98639i) q^{27} +(3.16233 + 2.79422i) q^{28} +(4.78838 + 4.78838i) q^{29} +(-1.96819 - 4.36553i) q^{30} -2.23005 q^{31} +(4.83146 - 2.94228i) q^{32} -2.47178 q^{33} +(2.03608 + 4.51612i) q^{34} +(-3.75247 - 3.75247i) q^{35} +(1.77966 + 1.57250i) q^{36} +(0.917582 - 0.917582i) q^{37} +(0.500624 - 1.32264i) q^{38} -2.36237i q^{39} +(-6.29244 + 3.31826i) q^{40} -6.01970i q^{41} +(-3.75722 - 1.42212i) q^{42} +(-0.780183 + 0.780183i) q^{43} +(0.226488 + 3.66492i) q^{44} +(-2.11177 - 2.11177i) q^{45} +(2.34760 - 1.05841i) q^{46} -3.26374 q^{47} +(-3.31012 + 4.24785i) q^{48} +2.54800 q^{49} +(1.70915 - 0.770570i) q^{50} +(-3.33475 - 3.33475i) q^{51} +(-3.50270 + 0.216463i) q^{52} +(-7.27172 + 7.27172i) q^{53} +(-7.45653 - 2.82232i) q^{54} -4.61760i q^{55} +(-1.76432 + 5.70116i) q^{56} +1.34632i q^{57} +(-3.39012 + 8.95664i) q^{58} +(-10.3529 + 10.3529i) q^{59} +(4.48421 - 5.07495i) q^{60} +(-5.66369 - 5.66369i) q^{61} +(-1.29622 - 2.87507i) q^{62} -2.50544 q^{63} +(6.60161 + 4.51870i) q^{64} +4.41322 q^{65} +(-1.43673 - 3.18672i) q^{66} +(6.96851 + 6.96851i) q^{67} +(-4.63889 + 5.25001i) q^{68} +(-1.73350 + 1.73350i) q^{69} +(2.65671 - 7.01897i) q^{70} -13.5536i q^{71} +(-0.992900 + 3.20843i) q^{72} +0.342654i q^{73} +(1.71633 + 0.649638i) q^{74} +(-1.26206 + 1.26206i) q^{75} +(1.99619 - 0.123362i) q^{76} +(-2.73921 - 2.73921i) q^{77} +(3.04567 - 1.37314i) q^{78} +8.81085 q^{79} +(-7.93553 - 6.18373i) q^{80} +4.02774 q^{81} +(7.76085 - 3.49897i) q^{82} +(9.85832 + 9.85832i) q^{83} +(-0.350436 - 5.67058i) q^{84} +(6.22974 - 6.22974i) q^{85} +(-1.45933 - 0.552362i) q^{86} -9.11699i q^{87} +(-4.59332 + 2.42224i) q^{88} +9.30967i q^{89} +(1.49511 - 3.95005i) q^{90} +(2.61796 - 2.61796i) q^{91} +(2.72910 + 2.41142i) q^{92} +(2.12298 + 2.12298i) q^{93} +(-1.89706 - 4.20775i) q^{94} -2.51510 q^{95} +(-7.40053 - 1.79847i) q^{96} +1.31560 q^{97} +(1.48103 + 3.28499i) q^{98} +(-1.54154 - 1.54154i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 68 q + 4 q^{3} + 4 q^{4} + 8 q^{5} - 8 q^{6}+O(q^{10}) $ 68 * q + 4 * q^3 + 4 * q^4 + 8 * q^5 - 8 * q^6	$ 68 q + 4 q^{3} + 4 q^{4} + 8 q^{5} - 8 q^{6} + 4 q^{11} - 4 q^{12} + 20 q^{14} - 16 q^{15} + 4 q^{16} + 4 q^{17} - 16 q^{18} + 16 q^{21} + 4 q^{22} - 4 q^{24} - 36 q^{26} + 28 q^{27} - 24 q^{28} + 24 q^{30} + 32 q^{31} - 20 q^{32} - 16 q^{33} - 32 q^{34} - 24 q^{35} + 52 q^{36} - 24 q^{37} - 4 q^{38} - 8 q^{40} - 40 q^{42} - 16 q^{43} - 36 q^{44} - 8 q^{46} - 24 q^{47} + 36 q^{48} - 56 q^{49} + 24 q^{50} - 52 q^{51} - 28 q^{52} + 32 q^{53} - 52 q^{54} + 12 q^{56} + 52 q^{58} + 28 q^{59} - 64 q^{60} - 12 q^{62} + 24 q^{63} - 32 q^{64} - 16 q^{65} - 44 q^{66} + 28 q^{67} - 48 q^{68} - 8 q^{69} + 4 q^{70} + 108 q^{72} + 72 q^{74} + 44 q^{75} - 12 q^{77} + 100 q^{78} + 8 q^{79} - 56 q^{80} - 76 q^{81} + 28 q^{82} + 40 q^{83} + 52 q^{84} - 8 q^{85} - 20 q^{86} - 56 q^{88} - 24 q^{90} - 4 q^{91} + 72 q^{92} - 84 q^{93} - 24 q^{94} + 32 q^{95} + 72 q^{96} - 16 q^{97} - 80 q^{98} - 24 q^{99}+O(q^{100}) $ 68 * q + 4 * q^3 + 4 * q^4 + 8 * q^5 - 8 * q^6 + 4 * q^11 - 4 * q^12 + 20 * q^14 - 16 * q^15 + 4 * q^16 + 4 * q^17 - 16 * q^18 + 16 * q^21 + 4 * q^22 - 4 * q^24 - 36 * q^26 + 28 * q^27 - 24 * q^28 + 24 * q^30 + 32 * q^31 - 20 * q^32 - 16 * q^33 - 32 * q^34 - 24 * q^35 + 52 * q^36 - 24 * q^37 - 4 * q^38 - 8 * q^40 - 40 * q^42 - 16 * q^43 - 36 * q^44 - 8 * q^46 - 24 * q^47 + 36 * q^48 - 56 * q^49 + 24 * q^50 - 52 * q^51 - 28 * q^52 + 32 * q^53 - 52 * q^54 + 12 * q^56 + 52 * q^58 + 28 * q^59 - 64 * q^60 - 12 * q^62 + 24 * q^63 - 32 * q^64 - 16 * q^65 - 44 * q^66 + 28 * q^67 - 48 * q^68 - 8 * q^69 + 4 * q^70 + 108 * q^72 + 72 * q^74 + 44 * q^75 - 12 * q^77 + 100 * q^78 + 8 * q^79 - 56 * q^80 - 76 * q^81 + 28 * q^82 + 40 * q^83 + 52 * q^84 - 8 * q^85 - 20 * q^86 - 56 * q^88 - 24 * q^90 - 4 * q^91 + 72 * q^92 - 84 * q^93 - 24 * q^94 + 32 * q^95 + 72 * q^96 - 16 * q^97 - 80 * q^98 - 24 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/304\mathbb{Z}\right)^\times$.

$n$	$97$	$191$	$229$
$\chi(n)$	$1$	$1$	$e\left(\frac{3}{4}\right)$

Coefficient data

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

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

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

$2$	0.581253	+	1.28924i	0.411008	+	0.911632i
$2$	0.581253	+	1.28924i	0.411008	+	0.911632i
$3$	−0.951991	−	0.951991i	−0.549632	−	0.549632i	0.376702	−	0.926334i	$-0.377058\pi$
$3$	−0.951991	−	0.951991i	−0.549632	−	0.549632i	−0.926334	+	0.376702i	$0.877058\pi$
$4$	−1.32429	+	1.49875i	−0.662145	+	0.749376i
$5$	1.77844	−	1.77844i	0.795343	−	0.795343i	−0.187014	−	0.982357i	$-0.559881\pi$
$5$	1.77844	−	1.77844i	0.795343	−	0.795343i	0.982357	+	0.187014i	$0.0598810\pi$
$6$	0.673999	−	1.78069i	0.275159	−	0.726965i
$7$		−	2.10998i		−	0.797496i	−0.917061	−	0.398748i	$-0.869445\pi$
$7$		−	2.10998i		−	0.797496i	0.917061	−	0.398748i	$-0.130555\pi$
$8$	−2.70200	−	0.836178i	−0.955301	−	0.295633i
$9$		−	1.18743i		−	0.395809i
$10$	3.32656	+	1.25912i	1.05195	+	0.398168i
$11$	1.29822	−	1.29822i	0.391427	−	0.391427i	−0.483769	−	0.875196i	$-0.660732\pi$
$11$	1.29822	−	1.29822i	0.391427	−	0.391427i	0.875196	+	0.483769i	$0.160732\pi$
$12$	2.68751	−	0.166085i	0.775817	−	0.0479446i
$13$	1.24075	+	1.24075i	0.344123	+	0.344123i	0.857915	−	0.513792i	$-0.171760\pi$
$13$	1.24075	+	1.24075i	0.344123	+	0.344123i	−0.513792	+	0.857915i	$0.671760\pi$
$14$	2.72027	−	1.22643i	0.727023	−	0.327777i
$15$	−3.38612			−0.874292
$16$	−0.492510	−	3.96956i	−0.123128	−	0.992391i
$17$	3.50292			0.849584			0.424792	−	0.905291i	$-0.360347\pi$
$17$	3.50292			0.849584			0.424792	+	0.905291i	$0.360347\pi$
$18$	1.53088	−	0.690195i	0.360832	−	0.162681i
$19$	−0.707107	−	0.707107i	−0.162221	−	0.162221i
$19$	−0.707107	−	0.707107i	−0.162221	−	0.162221i
$20$	0.310268	+	5.02061i	0.0693781	+	1.12264i
$21$	−2.00868	+	2.00868i	−0.438330	+	0.438330i
$22$	2.42831	+	0.919123i	0.517717	+	0.195958i
$23$		−	1.82092i		−	0.379688i	−0.981814	−	0.189844i	$-0.939202\pi$
$23$		−	1.82092i		−	0.379688i	0.981814	−	0.189844i	$-0.0607982\pi$
$24$	1.77625	+	3.36831i	0.362575	+	0.687554i
$25$		−	1.32570i		−	0.265141i
$26$	−0.878441	+	2.32082i	−0.172276	+	0.455151i
$27$	−3.98639	+	3.98639i	−0.767182	+	0.767182i
$28$	3.16233	+	2.79422i	0.597624	+	0.528058i
$29$	4.78838	+	4.78838i	0.889180	+	0.889180i	0.994444	−	0.105264i	$-0.0335689\pi$
$29$	4.78838	+	4.78838i	0.889180	+	0.889180i	−0.105264	+	0.994444i	$0.533569\pi$
$30$	−1.96819	−	4.36553i	−0.359341	−	0.797033i
$31$	−2.23005			−0.400528			−0.200264	−	0.979742i	$-0.564180\pi$
$31$	−2.23005			−0.400528			−0.200264	+	0.979742i	$0.564180\pi$
$32$	4.83146	−	2.94228i	0.854089	−	0.520127i
$33$	−2.47178			−0.430282
$34$	2.03608	+	4.51612i	0.349185	+	0.774507i
$35$	−3.75247	−	3.75247i	−0.634283	−	0.634283i
$36$	1.77966	+	1.57250i	0.296610	+	0.262083i
$37$	0.917582	−	0.917582i	0.150849	−	0.150849i	−0.627648	−	0.778497i	$-0.715982\pi$
$37$	0.917582	−	0.917582i	0.150849	−	0.150849i	0.778497	+	0.627648i	$0.215982\pi$
$38$	0.500624	−	1.32264i	0.0812119	−	0.214560i
$39$		−	2.36237i		−	0.378283i
$40$	−6.29244	+	3.31826i	−0.994922	+	0.524662i
$41$		−	6.01970i		−	0.940119i	−0.882635	−	0.470060i	$-0.844232\pi$
$41$		−	6.01970i		−	0.940119i	0.882635	−	0.470060i	$-0.155768\pi$
$42$	−3.75722	−	1.42212i	−0.579752	−	0.219438i
$43$	−0.780183	+	0.780183i	−0.118977	+	0.118977i	−0.764088	−	0.645112i	$-0.776811\pi$
$43$	−0.780183	+	0.780183i	−0.118977	+	0.118977i	0.645112	+	0.764088i	$0.276811\pi$
$44$	0.226488	+	3.66492i	0.0341443	+	0.552507i
$45$	−2.11177	−	2.11177i	−0.314804	−	0.314804i
$46$	2.34760	−	1.05841i	0.346135	−	0.156055i
$47$	−3.26374			−0.476065			−0.238033	−	0.971257i	$-0.576503\pi$
$47$	−3.26374			−0.476065			−0.238033	+	0.971257i	$0.576503\pi$
$48$	−3.31012	+	4.24785i	−0.477775	+	0.613125i
$49$	2.54800			0.364000
$50$	1.70915	−	0.770570i	0.241711	−	0.108975i
$51$	−3.33475	−	3.33475i	−0.466958	−	0.466958i
$52$	−3.50270	+	0.216463i	−0.485737	+	0.0300180i
$53$	−7.27172	+	7.27172i	−0.998847	+	0.998847i	−0.999999	−	0.00115194i	$-0.999633\pi$
$53$	−7.27172	+	7.27172i	−0.998847	+	0.998847i	0.00115194	+	0.999999i	$0.499633\pi$
$54$	−7.45653	−	2.82232i	−1.01470	−	0.384070i
$55$		−	4.61760i		−	0.622637i
$56$	−1.76432	+	5.70116i	−0.235767	+	0.761849i
$57$			1.34632i			0.178324i
$58$	−3.39012	+	8.95664i	−0.445145	+	1.17606i
$59$	−10.3529	+	10.3529i	−1.34784	+	1.34784i	−0.459831	+	0.888007i	$0.652090\pi$
$59$	−10.3529	+	10.3529i	−1.34784	+	1.34784i	−0.888007	+	0.459831i	$0.847910\pi$
$60$	4.48421	−	5.07495i	0.578908	−	0.655173i
$61$	−5.66369	−	5.66369i	−0.725161	−	0.725161i	0.244490	−	0.969652i	$-0.421379\pi$
$61$	−5.66369	−	5.66369i	−0.725161	−	0.725161i	−0.969652	+	0.244490i	$0.921379\pi$
$62$	−1.29622	−	2.87507i	−0.164620	−	0.365134i
$63$	−2.50544			−0.315656
$64$	6.60161	+	4.51870i	0.825202	+	0.564838i
$65$	4.41322			0.547392
$66$	−1.43673	−	3.18672i	−0.176849	−	0.392259i
$67$	6.96851	+	6.96851i	0.851339	+	0.851339i	0.990298	−	0.138959i	$-0.0443755\pi$
$67$	6.96851	+	6.96851i	0.851339	+	0.851339i	−0.138959	+	0.990298i	$0.544376\pi$
$68$	−4.63889	+	5.25001i	−0.562548	+	0.636657i
$69$	−1.73350	+	1.73350i	−0.208689	+	0.208689i
$70$	2.65671	−	7.01897i	0.317537	−	0.838928i
$71$		−	13.5536i		−	1.60852i	−0.594277	−	0.804260i	$-0.702562\pi$
$71$		−	13.5536i		−	1.60852i	0.594277	−	0.804260i	$-0.297438\pi$
$72$	−0.992900	+	3.20843i	−0.117014	+	0.378117i
$73$			0.342654i			0.0401046i	0.999799	+	0.0200523i	$0.00638328\pi$
$73$			0.342654i			0.0401046i	−0.999799	+	0.0200523i	$0.993617\pi$
$74$	1.71633	+	0.649638i	0.199520	+	0.0755189i
$75$	−1.26206	+	1.26206i	−0.145730	+	0.145730i
$76$	1.99619	−	0.123362i	0.228979	−	0.0141506i
$77$	−2.73921	−	2.73921i	−0.312162	−	0.312162i
$78$	3.04567	−	1.37314i	0.344854	−	0.155477i
$79$	8.81085			0.991299			0.495649	−	0.868523i	$-0.334930\pi$
$79$	8.81085			0.991299			0.495649	+	0.868523i	$0.334930\pi$
$80$	−7.93553	−	6.18373i	−0.887220	−	0.691363i
$81$	4.02774			0.447526
$82$	7.76085	−	3.49897i	0.857043	−	0.386396i
$83$	9.85832	+	9.85832i	1.08209	+	1.08209i	0.996314	+	0.0857768i	$0.0273372\pi$
$83$	9.85832	+	9.85832i	1.08209	+	1.08209i	0.0857768	+	0.996314i	$0.472663\pi$
$84$	−0.350436	−	5.67058i	−0.0382357	−	0.618711i
$85$	6.22974	−	6.22974i	0.675710	−	0.675710i
$86$	−1.45933	−	0.552362i	−0.157364	−	0.0595627i
$87$		−	9.11699i		−	0.977444i
$88$	−4.59332	+	2.42224i	−0.489650	+	0.258212i
$89$			9.30967i			0.986823i	0.869796	+	0.493412i	$0.164250\pi$
$89$			9.30967i			0.986823i	−0.869796	+	0.493412i	$0.835750\pi$
$90$	1.49511	−	3.95005i	0.157598	−	0.416372i
$91$	2.61796	−	2.61796i	0.274437	−	0.274437i
$92$	2.72910	+	2.41142i	0.284529	+	0.251408i
$93$	2.12298	+	2.12298i	0.220143	+	0.220143i
$94$	−1.89706	−	4.20775i	−0.195666	−	0.433996i
$95$	−2.51510			−0.258043
$96$	−7.40053	−	1.79847i	−0.755313	−	0.183556i
$97$	1.31560			0.133579			0.0667894	−	0.997767i	$-0.478724\pi$
$97$	1.31560			0.133579			0.0667894	+	0.997767i	$0.478724\pi$
$98$	1.48103	+	3.28499i	0.149607	+	0.331834i
$99$	−1.54154	−	1.54154i	−0.154930	−	0.154930i
$100$	1.98690	+	1.75562i	0.198690	+	0.175562i
$101$	−2.89827	+	2.89827i	−0.288389	+	0.288389i	−0.836443	−	0.548054i	$-0.815369\pi$
$101$	−2.89827	+	2.89827i	−0.288389	+	0.288389i	0.548054	+	0.836443i	$0.315369\pi$
$102$	2.36097	−	6.23763i	0.233771	−	0.617618i
$103$			3.72878i			0.367408i	0.982982	+	0.183704i	$0.0588087\pi$
$103$			3.72878i			0.367408i	−0.982982	+	0.183704i	$0.941191\pi$
$104$	−2.31503	−	4.39001i	−0.227007	−	0.430476i
$105$			7.14463i			0.697245i
$106$	−13.6017	−	5.14830i	−1.32112	−	0.500047i
$107$	−4.18299	+	4.18299i	−0.404385	+	0.404385i	−0.879775	−	0.475390i	$-0.842307\pi$
$107$	−4.18299	+	4.18299i	−0.404385	+	0.404385i	0.475390	+	0.879775i	$0.342307\pi$
$108$	−0.695469	−	11.2538i	−0.0669215	−	1.08289i
$109$	−1.96163	−	1.96163i	−0.187890	−	0.187890i	0.606893	−	0.794783i	$-0.292416\pi$
$109$	−1.96163	−	1.96163i	−0.187890	−	0.187890i	−0.794783	+	0.606893i	$0.792416\pi$
$110$	5.95321	−	2.68399i	0.567616	−	0.255909i
$111$	−1.74706			−0.165823
$112$	−8.37569	+	1.03918i	−0.791428	+	0.0981937i
$113$	17.4300			1.63967			0.819837	−	0.572597i	$-0.194064\pi$
$113$	17.4300			1.63967			0.819837	+	0.572597i	$0.194064\pi$
$114$	−1.73573	+	0.782551i	−0.162566	+	0.0732926i
$115$	−3.23839	−	3.23839i	−0.301982	−	0.301982i
$116$	−13.5178	+	0.835384i	−1.25510	+	0.0775635i
$117$	1.47330	−	1.47330i	0.136207	−	0.136207i
$118$	−19.3651	−	7.32977i	−1.78270	−	0.674760i
$119$		−	7.39108i		−	0.677540i
$120$	9.14930	+	2.83140i	0.835213	+	0.258470i
$121$			7.62927i			0.693570i
$122$	4.00983	−	10.5939i	0.363033	−	0.959127i
$123$	−5.73070	+	5.73070i	−0.516720	+	0.516720i
$124$	2.95323	−	3.34229i	0.265208	−	0.300146i
$125$	6.53452	+	6.53452i	0.584465	+	0.584465i
$126$	−1.45630	−	3.23012i	−0.129737	−	0.287762i
$127$	8.54285			0.758055			0.379028	−	0.925385i	$-0.376259\pi$
$127$	8.54285			0.758055			0.379028	+	0.925385i	$0.376259\pi$
$128$	−1.98850	+	11.1376i	−0.175760	+	0.984433i
$129$	1.48546			0.130787
$130$	2.56519	+	5.68971i	0.224982	+	0.499020i
$131$	5.26617	+	5.26617i	0.460107	+	0.460107i	0.898691	−	0.438583i	$-0.144520\pi$
$131$	5.26617	+	5.26617i	0.460107	+	0.460107i	−0.438583	+	0.898691i	$0.644520\pi$
$132$	3.27336	−	3.70458i	0.284909	−	0.322443i
$133$	−1.49198	+	1.49198i	−0.129371	+	0.129371i
$134$	−4.93363	+	13.0346i	−0.426201	+	1.12602i
$135$			14.1791i			1.22034i
$136$	−9.46490	−	2.92907i	−0.811608	−	0.251165i
$137$			18.6570i			1.59397i	0.603997	+	0.796987i	$0.293574\pi$
$137$			18.6570i			1.59397i	−0.603997	+	0.796987i	$0.706426\pi$
$138$	−3.24250	−	1.22730i	−0.276020	−	0.104474i
$139$	9.93359	−	9.93359i	0.842556	−	0.842556i	−0.146634	−	0.989191i	$-0.546844\pi$
$139$	9.93359	−	9.93359i	0.842556	−	0.842556i	0.989191	+	0.146634i	$0.0468441\pi$
$140$	10.5934	−	0.654659i	0.895304	−	0.0553288i
$141$	3.10705	+	3.10705i	0.261661	+	0.261661i
$142$	17.4739	−	7.87809i	1.46638	−	0.661115i
$143$	3.22154			0.269398
$144$	−4.71357	+	0.584820i	−0.392797	+	0.0487350i
$145$	17.0317			1.41441
$146$	−0.441764	+	0.199169i	−0.0365606	+	0.0164833i
$147$	−2.42567	−	2.42567i	−0.200066	−	0.200066i
$148$	0.160082	+	2.59037i	0.0131587	+	0.212927i
$149$	−11.6811	+	11.6811i	−0.956949	+	0.956949i	−0.999111	−	0.0421617i	$-0.986576\pi$
$149$	−11.6811	+	11.6811i	−0.956949	+	0.956949i	0.0421617	+	0.999111i	$0.486576\pi$
$150$	−2.36067	−	0.893524i	−0.192748	−	0.0729559i
$151$		−	6.71720i		−	0.546638i	−0.961923	−	0.273319i	$-0.911879\pi$
$151$		−	6.71720i		−	0.546638i	0.961923	−	0.273319i	$-0.0881215\pi$
$152$	1.31934	+	2.50187i	0.107012	+	0.202928i
$153$		−	4.15946i		−	0.336273i
$154$	1.93933	−	5.12367i	0.156276	−	0.412877i
$155$	−3.96601	+	3.96601i	−0.318557	+	0.318557i
$156$	3.54061	+	3.12847i	0.283476	+	0.250478i
$157$	−14.5583	−	14.5583i	−1.16188	−	1.16188i	−0.984065	−	0.177811i	$-0.943098\pi$
$157$	−14.5583	−	14.5583i	−1.16188	−	1.16188i	−0.177811	−	0.984065i	$-0.556902\pi$
$158$	5.12133	+	11.3593i	0.407431	+	0.903699i
$159$	13.8452			1.09800
$160$	3.35978	−	13.8251i	0.265614	−	1.09297i
$161$	−3.84209			−0.302799
$162$	2.34113	+	5.19273i	0.183937	+	0.407979i
$163$	7.27607	+	7.27607i	0.569906	+	0.569906i	0.932102	−	0.362196i	$-0.117973\pi$
$163$	7.27607	+	7.27607i	0.569906	+	0.569906i	−0.362196	+	0.932102i	$0.617973\pi$
$164$	9.02203	+	7.97183i	0.704502	+	0.622495i
$165$	−4.39592	+	4.39592i	−0.342222	+	0.342222i
$166$	−6.97958	+	18.4399i	−0.541721	+	1.43122i
$167$			5.81379i			0.449884i	0.974372	+	0.224942i	$0.0722193\pi$
$167$			5.81379i			0.449884i	−0.974372	+	0.224942i	$0.927781\pi$
$168$	7.10706	−	3.74784i	0.548322	−	0.289152i
$169$		−	9.92106i		−	0.763158i
$170$	11.6527	+	4.41059i	0.893721	+	0.338277i
$171$	−0.839638	+	0.839638i	−0.0642087	+	0.0642087i
$172$	−0.136111	−	2.20249i	−0.0103784	−	0.167938i
$173$	−13.5425	−	13.5425i	−1.02962	−	1.02962i	−0.999548	−	0.0300732i	$-0.990426\pi$
$173$	−13.5425	−	13.5425i	−1.02962	−	1.02962i	−0.0300732	−	0.999548i	$-0.509574\pi$
$174$	11.7540	−	5.29927i	0.891069	−	0.401737i
$175$	−2.79721			−0.211449
$176$	−5.79274	−	4.51397i	−0.436644	−	0.340253i
$177$	19.7118			1.48163
$178$	−12.0024	+	5.41127i	−0.899620	+	0.405592i
$179$	13.9286	+	13.9286i	1.04107	+	1.04107i	0.999120	+	0.0419528i	$0.0133579\pi$
$179$	13.9286	+	13.9286i	1.04107	+	1.04107i	0.0419528	+	0.999120i	$0.486642\pi$
$180$	5.96161	−	0.368421i	0.444352	−	0.0274605i
$181$	14.4847	−	14.4847i	1.07664	−	1.07664i	0.0798294	−	0.996809i	$-0.474562\pi$
$181$	14.4847	−	14.4847i	1.07664	−	1.07664i	0.996809	−	0.0798294i	$-0.0254375\pi$
$182$	4.89689	+	1.85349i	0.362981	+	0.137390i
$183$			10.7836i			0.797144i
$184$	−1.52261	+	4.92012i	−0.112248	+	0.362716i
$185$		−	3.26373i		−	0.239954i
$186$	−1.50305	+	3.97103i	−0.110209	+	0.291170i
$187$	4.54755	−	4.54755i	0.332550	−	0.332550i
$188$	4.32214	−	4.89153i	0.315224	−	0.356752i
$189$	8.41119	+	8.41119i	0.611824	+	0.611824i
$190$	−1.46191	−	3.24257i	−0.106058	−	0.235241i
$191$	−9.32880			−0.675008			−0.337504	−	0.941324i	$-0.609583\pi$
$191$	−9.32880			−0.675008			−0.337504	+	0.941324i	$0.609583\pi$
$192$	−1.98291	−	10.5864i	−0.143104	−	0.764011i
$193$	−10.3044			−0.741728			−0.370864	−	0.928687i	$-0.620938\pi$
$193$	−10.3044			−0.741728			−0.370864	+	0.928687i	$0.620938\pi$
$194$	0.764696	+	1.69613i	0.0549020	+	0.121775i
$195$	−4.20134	−	4.20134i	−0.300864	−	0.300864i
$196$	−3.37429	+	3.81882i	−0.241021	+	0.272773i
$197$	−13.2328	+	13.2328i	−0.942800	+	0.942800i	−0.998450	−	0.0556500i	$-0.982277\pi$
$197$	−13.2328	+	13.2328i	−0.942800	+	0.942800i	0.0556500	+	0.998450i	$0.482277\pi$
$198$	1.09139	−	2.88344i	0.0775618	−	0.204917i
$199$		−	11.6835i		−	0.828225i	−0.910226	−	0.414112i	$-0.864092\pi$
$199$		−	11.6835i		−	0.828225i	0.910226	−	0.414112i	$-0.135908\pi$
$200$	−1.10852	+	3.58205i	−0.0783845	+	0.253290i
$201$		−	13.2679i		−	0.935847i
$202$	−5.42121	−	2.05195i	−0.381435	−	0.144375i
$203$	10.1034	−	10.1034i	0.709117	−	0.709117i
$204$	9.41414	−	0.581783i	0.659122	−	0.0407330i
$205$	−10.7057	−	10.7057i	−0.747717	−	0.747717i
$206$	−4.80730	+	2.16736i	−0.334941	+	0.151007i
$207$	−2.16221			−0.150284
$208$	4.31417	−	5.53634i	0.299134	−	0.383876i
$209$	−1.83596			−0.126996
$210$	−9.21116	+	4.15284i	−0.635630	+	0.286573i
$211$	−7.74894	−	7.74894i	−0.533459	−	0.533459i	0.388141	−	0.921600i	$-0.373117\pi$
$211$	−7.74894	−	7.74894i	−0.533459	−	0.533459i	−0.921600	+	0.388141i	$0.873117\pi$
$212$	−1.26863	−	20.5284i	−0.0871298	−	1.40989i
$213$	−12.9029	+	12.9029i	−0.884095	+	0.884095i
$214$	−7.82427	−	2.96151i	−0.534856	−	0.202445i
$215$			2.77502i			0.189255i
$216$	14.1046	−	7.43790i	0.959694	−	0.506085i
$217$			4.70535i			0.319420i
$218$	1.38881	−	3.66922i	0.0940624	−	0.248511i
$219$	0.326204	−	0.326204i	0.0220428	−	0.0220428i
$220$	6.92064	+	6.11505i	0.466589	+	0.412276i
$221$	4.34627	+	4.34627i	0.292362	+	0.292362i
$222$	−1.01548	−	2.25238i	−0.0681547	−	0.151170i
$223$	−6.73464			−0.450985			−0.225493	−	0.974245i	$-0.572399\pi$
$223$	−6.73464			−0.450985			−0.225493	+	0.974245i	$0.572399\pi$
$224$	−6.20815	−	10.1943i	−0.414800	−	0.681132i
$225$	−1.57418			−0.104945
$226$	10.1312	+	22.4715i	0.673919	+	1.49478i
$227$	0.602631	+	0.602631i	0.0399980	+	0.0399980i	0.726823	−	0.686825i	$-0.240996\pi$
$227$	0.602631	+	0.602631i	0.0399980	+	0.0399980i	−0.686825	+	0.726823i	$0.740996\pi$
$228$	−2.01780	−	1.78292i	−0.133632	−	0.118077i
$229$	18.9430	−	18.9430i	1.25179	−	1.25179i	0.296871	−	0.954918i	$-0.404057\pi$
$229$	18.9430	−	18.9430i	1.25179	−	1.25179i	0.954918	−	0.296871i	$-0.0959432\pi$
$230$	2.29275	−	6.05740i	0.151179	−	0.399413i
$231$			5.21540i			0.343148i
$232$	−8.93427	−	16.9421i	−0.586563	−	1.11231i
$233$		−	17.5537i		−	1.14998i	−0.818160	−	0.574990i	$-0.805006\pi$
$233$		−	17.5537i		−	1.14998i	0.818160	−	0.574990i	$-0.194994\pi$
$234$	2.75581	+	1.04308i	0.180153	+	0.0681885i
$235$	−5.80437	+	5.80437i	−0.378635	+	0.378635i
$236$	−1.80618	−	29.2268i	−0.117572	−	1.90250i
$237$	−8.38785	−	8.38785i	−0.544850	−	0.544850i
$238$	9.52890	−	4.29609i	0.617667	−	0.278474i
$239$	−7.08511			−0.458298			−0.229149	−	0.973391i	$-0.573594\pi$
$239$	−7.08511			−0.458298			−0.229149	+	0.973391i	$0.573594\pi$
$240$	1.66770	+	13.4414i	0.107649	+	0.867640i
$241$	−5.45509			−0.351393			−0.175697	−	0.984444i	$-0.556218\pi$
$241$	−5.45509			−0.351393			−0.175697	+	0.984444i	$0.556218\pi$
$242$	−9.83597	+	4.43453i	−0.632280	+	0.285063i
$243$	8.12481	+	8.12481i	0.521207	+	0.521207i
$244$	15.9888	−	0.988092i	1.02358	−	0.0632561i
$245$	4.53147	−	4.53147i	0.289505	−	0.289505i
$246$	−10.7192	−	4.05727i	−0.683434	−	0.258682i
$247$		−	1.75469i		−	0.111648i
$248$	6.02559	+	1.86472i	0.382625	+	0.118410i
$249$		−	18.7701i		−	1.18950i
$250$	−4.62637	+	12.2228i	−0.292597	+	0.773037i
$251$	5.91372	−	5.91372i	0.373271	−	0.373271i	−0.495396	−	0.868667i	$-0.664977\pi$
$251$	5.91372	−	5.91372i	0.373271	−	0.373271i	0.868667	+	0.495396i	$0.164977\pi$
$252$	3.31793	−	3.75503i	0.209010	−	0.236545i
$253$	−2.36395	−	2.36395i	−0.148620	−	0.148620i
$254$	4.96555	+	11.0138i	0.311567	+	0.691067i
$255$	−11.8613			−0.742784
$256$	−15.5149	+	3.91010i	−0.969679	+	0.244381i
$257$	−27.6936			−1.72748			−0.863741	−	0.503937i	$-0.831884\pi$
$257$	−27.6936			−1.72748			−0.863741	+	0.503937i	$0.831884\pi$
$258$	0.863425	+	1.91511i	0.0537545	+	0.119230i
$259$	−1.93608	−	1.93608i	−0.120302	−	0.120302i
$260$	−5.84438	+	6.61431i	−0.362453	+	0.410202i
$261$	5.68585	−	5.68585i	0.351945	−	0.351945i
$262$	−3.72839	+	9.85034i	−0.230341	+	0.608556i
$263$			24.4570i			1.50808i	0.656826	+	0.754042i	$0.271898\pi$
$263$			24.4570i			1.50808i	−0.656826	+	0.754042i	$0.728102\pi$
$264$	6.67875	+	2.06685i	0.411049	+	0.127206i
$265$			25.8646i			1.58885i
$266$	−2.79074	−	1.05630i	−0.171111	−	0.0647662i
$267$	8.86272	−	8.86272i	0.542390	−	0.542390i
$268$	−19.6724	+	1.21573i	−1.20168	+	0.0742627i
$269$	−7.72199	−	7.72199i	−0.470818	−	0.470818i	0.431361	−	0.902179i	$-0.358034\pi$
$269$	−7.72199	−	7.72199i	−0.470818	−	0.470818i	−0.902179	+	0.431361i	$0.858034\pi$
$270$	−18.2803	+	8.24166i	−1.11251	+	0.501571i
$271$	12.3933			0.752839			0.376419	−	0.926449i	$-0.377155\pi$
$271$	12.3933			0.752839			0.376419	+	0.926449i	$0.377155\pi$
$272$	−1.72522	−	13.9051i	−0.104607	−	0.843119i
$273$	−4.98455			−0.301679
$274$	−24.0534	+	10.8444i	−1.45312	+	0.655136i
$275$	−1.72105	−	1.72105i	−0.103783	−	0.103783i
$276$	−0.302427	−	4.89373i	−0.0182040	−	0.294568i
$277$	−3.81408	+	3.81408i	−0.229166	+	0.229166i	−0.812344	−	0.583178i	$-0.801809\pi$
$277$	−3.81408	+	3.81408i	−0.229166	+	0.229166i	0.583178	+	0.812344i	$0.301809\pi$
$278$	18.5807	+	7.03288i	1.11440	+	0.421804i
$279$			2.64802i			0.158533i
$280$	7.00144	+	13.2769i	0.418416	+	0.793447i
$281$		−	25.6527i		−	1.53031i	−0.643845	−	0.765156i	$-0.722662\pi$
$281$		−	25.6527i		−	1.53031i	0.643845	−	0.765156i	$-0.277338\pi$
$282$	−2.19976	+	5.81172i	−0.130994	+	0.346083i
$283$	−5.11099	+	5.11099i	−0.303817	+	0.303817i	−0.842505	−	0.538688i	$-0.818920\pi$
$283$	−5.11099	+	5.11099i	−0.303817	+	0.303817i	0.538688	+	0.842505i	$0.318920\pi$
$284$	20.3135	+	17.9490i	1.20539	+	1.06507i
$285$	2.39435	+	2.39435i	0.141829	+	0.141829i
$286$	1.87253	+	4.15334i	0.110725	+	0.245592i
$287$	−12.7014			−0.749742
$288$	−3.49375	−	5.73700i	−0.205871	−	0.338056i
$289$	−4.72953			−0.278208
$290$	9.89972	+	21.9580i	0.581332	+	1.28942i
$291$	−1.25244	−	1.25244i	−0.0734193	−	0.0734193i
$292$	−0.513553	−	0.453773i	−0.0300534	−	0.0265551i
$293$	−9.54704	+	9.54704i	−0.557744	+	0.557744i	−0.928665	−	0.370920i	$-0.879042\pi$
$293$	−9.54704	+	9.54704i	−0.557744	+	0.557744i	0.370920	+	0.928665i	$0.379042\pi$
$294$	1.71735	−	4.53721i	0.100158	−	0.264615i
$295$			36.8242i			2.14399i
$296$	−3.24657	+	1.71204i	−0.188703	+	0.0995106i
$297$			10.3504i			0.600591i
$298$	−21.8493	−	8.27006i	−1.26570	−	0.479072i
$299$	2.25931	−	2.25931i	0.130659	−	0.130659i
$300$	−0.220180	−	3.56284i	−0.0127121	−	0.205701i
$301$	1.64617	+	1.64617i	0.0948836	+	0.0948836i
$302$	8.66010	−	3.90439i	0.498333	−	0.224673i
$303$	5.51826			0.317016
$304$	−2.45865	+	3.15516i	−0.141013	+	0.180961i
$305$	−20.1451			−1.15350
$306$	5.36256	−	2.41770i	0.306557	−	0.138211i
$307$	21.2585	+	21.2585i	1.21329	+	1.21329i	0.969940	+	0.243346i	$0.0782450\pi$
$307$	21.2585	+	21.2585i	1.21329	+	1.21329i	0.243346	+	0.969940i	$0.421755\pi$
$308$	7.73289	−	0.477884i	0.440622	−	0.0272300i
$309$	3.54977	−	3.54977i	0.201939	−	0.201939i
$310$	−7.41840	−	2.80789i	−0.421337	−	0.159478i
$311$		−	25.2437i		−	1.43144i	−0.698389	−	0.715719i	$-0.746099\pi$
$311$		−	25.2437i		−	1.43144i	0.698389	−	0.715719i	$-0.253901\pi$
$312$	−1.97536	+	6.38314i	−0.111833	+	0.361374i
$313$		−	17.4074i		−	0.983927i	−0.870616	−	0.491964i	$-0.836279\pi$
$313$		−	17.4074i		−	0.983927i	0.870616	−	0.491964i	$-0.163721\pi$
$314$	10.3071	−	27.2312i	0.581663	−	1.53674i
$315$	−4.45578	+	4.45578i	−0.251055	+	0.251055i
$316$	−11.6681	+	13.2053i	−0.656384	+	0.742855i
$317$	17.0893	+	17.0893i	0.959831	+	0.959831i	0.999224	−	0.0393928i	$-0.0125423\pi$
$317$	17.0893	+	17.0893i	0.959831	+	0.959831i	−0.0393928	+	0.999224i	$0.512542\pi$
$318$	8.04757	+	17.8498i	0.451285	+	1.00097i
$319$	12.4327			0.696098
$320$	19.7768	−	3.70433i	1.10556	−	0.207078i
$321$	7.96434			0.444526
$322$	−2.23323	−	4.95339i	−0.124453	−	0.276042i
$323$	−2.47694	−	2.47694i	−0.137821	−	0.137821i
$324$	−5.33389	+	6.03658i	−0.296327	+	0.335365i
$325$	1.64487	−	1.64487i	0.0912412	−	0.0912412i
$326$	−5.15138	+	13.6098i	−0.285308	+	0.753780i
$327$			3.73491i			0.206541i
$328$	−5.03354	+	16.2652i	−0.277931	+	0.898097i
$329$			6.88641i			0.379660i
$330$	−8.22254	−	3.11226i	−0.452636	−	0.171324i
$331$	−13.1107	+	13.1107i	−0.720630	+	0.720630i	−0.968733	−	0.248104i	$-0.920193\pi$
$331$	−13.1107	+	13.1107i	−0.720630	+	0.720630i	0.248104	+	0.968733i	$0.420193\pi$
$332$	−27.8304	+	1.71989i	−1.52739	+	0.0943912i
$333$	−1.08956	−	1.08956i	−0.0597076	−	0.0597076i
$334$	−7.49538	+	3.37928i	−0.410129	+	0.184906i
$335$	24.7862			1.35421
$336$	8.96287	+	6.98428i	0.488965	+	0.381024i
$337$	−31.3766			−1.70919			−0.854596	−	0.519294i	$-0.826195\pi$
$337$	−31.3766			−1.70919			−0.854596	+	0.519294i	$0.826195\pi$
$338$	12.7906	−	5.76664i	0.695719	−	0.313664i
$339$	−16.5932	−	16.5932i	−0.901218	−	0.901218i
$340$	1.08685	+	17.5868i	0.0589425	+	0.953779i
$341$	−2.89508	+	2.89508i	−0.156778	+	0.156778i
$342$	−1.57054	−	0.594454i	−0.0849250	−	0.0321444i
$343$		−	20.1461i		−	1.08778i
$344$	2.76043	−	1.45568i	0.148832	−	0.0784852i
$345$			6.16584i			0.331958i
$346$	9.58798	−	25.3313i	0.515453	−	1.36182i
$347$	12.6134	−	12.6134i	0.677125	−	0.677125i	−0.282224	−	0.959349i	$-0.591072\pi$
$347$	12.6134	−	12.6134i	0.677125	−	0.677125i	0.959349	+	0.282224i	$0.0910721\pi$
$348$	13.6641	+	12.0735i	0.732472	+	0.647210i
$349$	4.56530	+	4.56530i	0.244375	+	0.244375i	0.818657	−	0.574282i	$-0.194719\pi$
$349$	4.56530	+	4.56530i	0.244375	+	0.244375i	−0.574282	+	0.818657i	$0.694719\pi$
$350$	−1.62588	−	3.60628i	−0.0869071	−	0.192764i
$351$	−9.89227			−0.528010
$352$	2.45255	−	10.0920i	0.130722	−	0.537905i
$353$	−24.8322			−1.32168			−0.660842	−	0.750525i	$-0.729801\pi$
$353$	−24.8322			−1.32168			−0.660842	+	0.750525i	$0.729801\pi$
$354$	11.4575	+	25.4133i	0.608961	+	1.35070i
$355$	−24.1043	−	24.1043i	−1.27933	−	1.27933i
$356$	−13.9529	−	12.3287i	−0.739501	−	0.653420i
$357$	−7.03624	+	7.03624i	−0.372398	+	0.372398i
$358$	−9.86130	+	26.0534i	−0.521186	+	1.37696i
$359$		−	33.6368i		−	1.77528i	−0.460536	−	0.887641i	$-0.652343\pi$
$359$		−	33.6368i		−	1.77528i	0.460536	−	0.887641i	$-0.347657\pi$
$360$	3.94019	+	7.47181i	0.207666	+	0.393799i
$361$			1.00000i			0.0526316i
$362$	27.0935	+	10.2550i	1.42400	+	0.538991i
$363$	7.26299	−	7.26299i	0.381208	−	0.381208i
$364$	0.456732	+	7.39062i	0.0239393	+	0.387374i
$365$	0.609390	+	0.609390i	0.0318969	+	0.0318969i
$366$	−13.9026	+	6.26798i	−0.726702	+	0.327632i
$367$	−10.5421			−0.550293			−0.275147	−	0.961402i	$-0.588726\pi$
$367$	−10.5421			−0.550293			−0.275147	+	0.961402i	$0.588726\pi$
$368$	−7.22825	+	0.896820i	−0.376799	+	0.0467500i
$369$	−7.14795			−0.372108
$370$	4.20774	−	1.89705i	0.218750	−	0.0986230i
$371$	15.3432	+	15.3432i	0.796577	+	0.796577i
$372$	−5.99327	+	0.370378i	−0.310737	+	0.0192032i
$373$	15.4212	−	15.4212i	0.798480	−	0.798480i	−0.184376	−	0.982856i	$-0.559026\pi$
$373$	15.4212	−	15.4212i	0.798480	−	0.798480i	0.982856	+	0.184376i	$0.0590264\pi$
$374$	8.50617	+	3.21962i	0.439844	+	0.166482i
$375$		−	12.4416i		−	0.642482i
$376$	8.81862	+	2.72906i	0.454786	+	0.140741i
$377$			11.8824i			0.611975i
$378$	−5.95504	+	15.7331i	−0.306294	+	0.809223i
$379$	−14.5717	+	14.5717i	−0.748498	+	0.748498i	−0.974197	−	0.225699i	$-0.927533\pi$
$379$	−14.5717	+	14.5717i	−0.748498	+	0.748498i	0.225699	+	0.974197i	$0.427533\pi$
$380$	3.33072	−	3.76950i	0.170862	−	0.193371i
$381$	−8.13271	−	8.13271i	−0.416651	−	0.416651i
$382$	−5.42239	−	12.0271i	−0.277434	−	0.615359i
$383$	−1.03355			−0.0528120			−0.0264060	−	0.999651i	$-0.508406\pi$
$383$	−1.03355			−0.0528120			−0.0264060	+	0.999651i	$0.508406\pi$
$384$	12.4959	−	8.70985i	0.637679	−	0.444473i
$385$	−9.74303			−0.496551
$386$	−5.98947	−	13.2849i	−0.304856	−	0.676183i
$387$	0.926411	+	0.926411i	0.0470921	+	0.0470921i
$388$	−1.74224	+	1.97176i	−0.0884486	+	0.100101i
$389$	−13.0340	+	13.0340i	−0.660849	+	0.660849i	−0.955580	−	0.294731i	$-0.904770\pi$
$389$	−13.0340	+	13.0340i	−0.660849	+	0.660849i	0.294731	+	0.955580i	$0.404770\pi$
$390$	2.97451	−	7.85859i	0.150620	−	0.397935i
$391$		−	6.37853i		−	0.322576i
$392$	−6.88470	−	2.13058i	−0.347730	−	0.107611i
$393$		−	10.0267i		−	0.505779i
$394$	−24.7519	−	9.36870i	−1.24699	−	0.471988i
$395$	15.6696	−	15.6696i	0.788422	−	0.788422i
$396$	4.35182	−	0.268938i	0.218687	−	0.0135146i
$397$	−9.48221	−	9.48221i	−0.475898	−	0.475898i	0.427919	−	0.903817i	$-0.359247\pi$
$397$	−9.48221	−	9.48221i	−0.475898	−	0.475898i	−0.903817	+	0.427919i	$0.859247\pi$
$398$	15.0629	−	6.79109i	0.755036	−	0.340407i
$399$	2.84070			0.142213
$400$	−5.26247	+	0.652923i	−0.263123	+	0.0326461i
$401$	8.58054			0.428492			0.214246	−	0.976780i	$-0.431271\pi$
$401$	8.58054			0.428492			0.214246	+	0.976780i	$0.431271\pi$
$402$	17.1056	−	7.71202i	0.853148	−	0.384640i
$403$	−2.76694	−	2.76694i	−0.137831	−	0.137831i
$404$	−0.505635	−	8.18195i	−0.0251563	−	0.407067i
$405$	7.16309	−	7.16309i	0.355937	−	0.355937i
$406$	18.8983	+	7.15308i	0.937907	+	0.355001i
$407$		−	2.38244i		−	0.118093i
$408$	6.22205	+	11.7989i	0.308038	+	0.584135i
$409$		−	4.46951i		−	0.221003i	−0.993876	−	0.110502i	$-0.964754\pi$
$409$		−	4.46951i		−	0.221003i	0.993876	−	0.110502i	$-0.0352457\pi$
$410$	7.57951	−	20.0249i	0.374325	−	0.988961i
$411$	17.7613	−	17.7613i	0.876099	−	0.876099i
$412$	−5.58851	−	4.93799i	−0.275326	−	0.243277i
$413$	21.8444	+	21.8444i	1.07490	+	1.07490i
$414$	−1.25679	−	2.78761i	−0.0617678	−	0.137003i
$415$	35.0649			1.72127
$416$	9.64530	+	2.34400i	0.472900	+	0.114924i
$417$	−18.9134			−0.926192
$418$	−1.06715	−	2.36699i	−0.0521962	−	0.115773i
$419$	−5.47971	−	5.47971i	−0.267701	−	0.267701i	0.560472	−	0.828173i	$-0.310620\pi$
$419$	−5.47971	−	5.47971i	−0.267701	−	0.267701i	−0.828173	+	0.560472i	$0.810620\pi$
$420$	−10.7080	−	9.46157i	−0.522498	−	0.461677i
$421$	10.5132	−	10.5132i	0.512383	−	0.512383i	−0.402873	−	0.915256i	$-0.631988\pi$
$421$	10.5132	−	10.5132i	0.512383	−	0.512383i	0.915256	+	0.402873i	$0.131988\pi$
$422$	5.48616	−	14.4943i	0.267062	−	0.705574i
$423$			3.87545i			0.188431i
$424$	25.7286	−	13.5677i	1.24949	−	0.658908i
$425$		−	4.64384i		−	0.225259i
$426$	−24.1349	−	9.13514i	−1.16934	−	0.442599i
$427$	−11.9503	+	11.9503i	−0.578313	+	0.578313i
$428$	−0.729768	−	11.8088i	−0.0352747	−	0.570798i
$429$	−3.06687	−	3.06687i	−0.148070	−	0.148070i
$430$	−3.57767	+	1.61299i	−0.172531	+	0.0777852i
$431$	2.10759			0.101519			0.0507596	−	0.998711i	$-0.483836\pi$
$431$	2.10759			0.101519			0.0507596	+	0.998711i	$0.483836\pi$
$432$	17.7876	+	13.8609i	0.855805	+	0.666883i
$433$	33.7771			1.62323			0.811613	−	0.584196i	$-0.198590\pi$
$433$	33.7771			1.62323			0.811613	+	0.584196i	$0.198590\pi$
$434$	−6.06633	+	2.73500i	−0.291193	+	0.131284i
$435$	−16.2140	−	16.2140i	−0.777403	−	0.777403i
$436$	5.53777	−	0.342228i	0.265211	−	0.0163897i
$437$	−1.28758	+	1.28758i	−0.0615935	+	0.0615935i
$438$	0.610162	+	0.230949i	0.0291547	+	0.0110352i
$439$			24.4300i			1.16598i	0.812478	+	0.582991i	$0.198118\pi$
$439$			24.4300i			1.16598i	−0.812478	+	0.582991i	$0.801882\pi$
$440$	−3.86114	+	12.4768i	−0.184072	+	0.594806i
$441$		−	3.02556i		−	0.144074i
$442$	−3.07711	+	8.12967i	−0.146363	+	0.386689i
$443$	−0.290973	+	0.290973i	−0.0138245	+	0.0138245i	−0.713985	−	0.700161i	$-0.753112\pi$
$443$	−0.290973	+	0.290973i	−0.0138245	+	0.0138245i	0.700161	+	0.713985i	$0.253112\pi$
$444$	2.31361	−	2.61841i	0.109799	−	0.124264i
$445$	16.5567	+	16.5567i	0.784863	+	0.784863i
$446$	−3.91453	−	8.68259i	−0.185358	−	0.411132i
$447$	22.2405			1.05194
$448$	9.53436	−	13.9293i	0.450456	−	0.658095i
$449$	22.8119			1.07656			0.538280	−	0.842766i	$-0.319074\pi$
$449$	22.8119			1.07656			0.538280	+	0.842766i	$0.319074\pi$
$450$	−0.914995	−	2.02950i	−0.0431333	−	0.0956713i
$451$	−7.81487	−	7.81487i	−0.367988	−	0.367988i
$452$	−23.0824	+	26.1232i	−1.08570	+	1.22873i
$453$	−6.39472	+	6.39472i	−0.300450	+	0.300450i
$454$	−0.426656	+	1.12722i	−0.0200240	+	0.0529030i
$455$		−	9.31178i		−	0.436543i
$456$	1.12576	−	3.63775i	0.0527186	−	0.170353i
$457$			25.0540i			1.17198i	0.810320	+	0.585988i	$0.199294\pi$
$457$			25.0540i			1.17198i	−0.810320	+	0.585988i	$0.800706\pi$
$458$	35.4328	+	13.4114i	1.65567	+	0.626675i
$459$	−13.9640	+	13.9640i	−0.651785	+	0.651785i
$460$	9.14212	−	0.564973i	0.426254	−	0.0263420i
$461$	−18.4193	−	18.4193i	−0.857872	−	0.857872i	0.133215	−	0.991087i	$-0.457470\pi$
$461$	−18.4193	−	18.4193i	−0.857872	−	0.857872i	−0.991087	+	0.133215i	$0.957470\pi$
$462$	−6.72391	+	3.03147i	−0.312825	+	0.141037i
$463$	12.4783			0.579918			0.289959	−	0.957039i	$-0.406358\pi$
$463$	12.4783			0.579918			0.289959	+	0.957039i	$0.406358\pi$
$464$	16.6495	−	21.3661i	0.772931	−	0.991896i
$465$	7.55121			0.350179
$466$	22.6310	−	10.2031i	1.04836	−	0.472651i
$467$	3.13723	+	3.13723i	0.145174	+	0.145174i	0.775958	−	0.630785i	$-0.217267\pi$
$467$	3.13723	+	3.13723i	0.145174	+	0.145174i	−0.630785	+	0.775958i	$0.717267\pi$
$468$	0.257034	+	4.15920i	0.0118814	+	0.192259i
$469$	14.7034	−	14.7034i	0.678940	−	0.678940i
$470$	−10.8570	−	4.10943i	−0.500798	−	0.189554i
$471$			27.7187i			1.27721i
$472$	36.6305	−	19.3167i	1.68606	−	0.889125i
$473$			2.02569i			0.0931415i
$474$	5.93851	−	15.6894i	0.272765	−	0.720640i
$475$	−0.937415	+	0.937415i	−0.0430115	+	0.0430115i
$476$	11.0774	+	9.78794i	0.507732	+	0.448630i
$477$	8.63463	+	8.63463i	0.395353	+	0.395353i
$478$	−4.11824	−	9.13442i	−0.188364	−	0.417799i
$479$	−19.7335			−0.901647			−0.450824	−	0.892613i	$-0.648870\pi$
$479$	−19.7335			−0.901647			−0.450824	+	0.892613i	$0.648870\pi$
$480$	−16.3599	+	9.96293i	−0.746723	+	0.454743i
$481$	2.27699			0.103822
$482$	−3.17079	−	7.03293i	−0.144425	−	0.320341i
$483$	3.65764	+	3.65764i	0.166428	+	0.166428i
$484$	−11.4344	−	10.1034i	−0.519744	−	0.459244i
$485$	2.33972	−	2.33972i	0.106241	−	0.106241i
$486$	−5.75228	+	15.1974i	−0.260929	+	0.689369i
$487$		−	9.92532i		−	0.449759i	−0.974387	−	0.224880i	$-0.927801\pi$
$487$		−	9.92532i		−	0.449759i	0.974387	−	0.224880i	$-0.0721989\pi$
$488$	10.5674	+	20.0391i	0.478366	+	0.907129i
$489$		−	13.8535i		−	0.626477i
$490$	8.47608	+	3.20823i	0.382910	+	0.144933i
$491$	20.1142	−	20.1142i	0.907742	−	0.907742i	−0.0883479	−	0.996090i	$-0.528159\pi$
$491$	20.1142	−	20.1142i	0.907742	−	0.907742i	0.996090	+	0.0883479i	$0.0281587\pi$
$492$	−0.999782	−	16.1780i	−0.0450737	−	0.729361i
$493$	16.7733	+	16.7733i	0.755432	+	0.755432i
$494$	2.26222	−	1.01992i	0.101782	−	0.0458883i
$495$	−5.48306			−0.246445
$496$	1.09832	+	8.85232i	0.0493161	+	0.397481i
$497$	−28.5979			−1.28279
$498$	24.1992	−	10.9102i	1.08439	−	0.488896i
$499$	1.58577	+	1.58577i	0.0709887	+	0.0709887i	0.741710	−	0.670721i	$-0.234015\pi$
$499$	1.58577	+	1.58577i	0.0709887	+	0.0709887i	−0.670721	+	0.741710i	$0.734015\pi$
$500$	−18.4472	+	1.14002i	−0.824984	+	0.0509831i
$501$	5.53467	−	5.53467i	0.247271	−	0.247271i
$502$	11.0616	+	4.18685i	0.493703	+	0.186868i
$503$			36.2040i			1.61426i	0.590376	+	0.807128i	$0.298979\pi$
$503$			36.2040i			1.61426i	−0.590376	+	0.807128i	$0.701021\pi$
$504$	6.76971	+	2.09499i	0.301547	+	0.0933185i
$505$			10.3088i			0.458737i
$506$	1.67365	−	4.42175i	0.0744027	−	0.196571i
$507$	−9.44476	+	9.44476i	−0.419456	+	0.419456i
$508$	−11.3132	+	12.8036i	−0.501942	+	0.568068i
$509$	−14.6387	−	14.6387i	−0.648851	−	0.648851i	0.303865	−	0.952715i	$-0.401723\pi$
$509$	−14.6387	−	14.6387i	−0.648851	−	0.648851i	−0.952715	+	0.303865i	$0.901723\pi$
$510$	−6.89442	−	15.2921i	−0.305290	−	0.677146i
$511$	0.722992			0.0319833
$512$	−14.0591	−	17.7297i	−0.621331	−	0.783548i
$513$	5.63761			0.248907
$514$	−16.0970	−	35.7038i	−0.710008	−	1.57483i
$515$	6.63142	+	6.63142i	0.292215	+	0.292215i
$516$	−1.96717	+	2.22633i	−0.0866000	+	0.0980086i
$517$	−4.23704	+	4.23704i	−0.186345	+	0.186345i
$518$	1.37072	−	3.62142i	0.0602260	−	0.159116i
$519$			25.7848i			1.13183i
$520$	−11.9245	−	3.69023i	−0.522925	−	0.161827i
$521$			19.5773i			0.857698i	0.903376	+	0.428849i	$0.141081\pi$
$521$			19.5773i			0.857698i	−0.903376	+	0.428849i	$0.858919\pi$
$522$	10.6354	+	4.02552i	0.465497	+	0.176192i
$523$	−17.8312	+	17.8312i	−0.779702	+	0.779702i	−0.979780	−	0.200078i	$-0.935881\pi$
$523$	−17.8312	+	17.8312i	−0.779702	+	0.779702i	0.200078	+	0.979780i	$0.435881\pi$
$524$	−14.8666	+	0.918740i	−0.649451	+	0.0401353i
$525$	2.66291	+	2.66291i	0.116219	+	0.116219i
$526$	−31.5310	+	14.2157i	−1.37482	+	0.619834i
$527$	−7.81168			−0.340282
$528$	1.21738	+	9.81189i	0.0529795	+	0.427008i
$529$	19.6843			0.855837
$530$	−33.3458	+	15.0339i	−1.44845	+	0.653031i
$531$	12.2934	+	12.2934i	0.533486	+	0.533486i
$532$	−0.260292	−	4.21192i	−0.0112851	−	0.182610i
$533$	7.46897	−	7.46897i	0.323517	−	0.323517i
$534$	16.5777	+	6.27471i	0.717386	+	0.271533i
$535$			14.8784i			0.643250i
$536$	−13.0020	−	24.6558i	−0.561601	−	1.06497i
$537$		−	26.5198i		−	1.14441i
$538$	5.46709	−	14.4440i	0.235703	−	0.622723i
$539$	3.30785	−	3.30785i	0.142479	−	0.142479i
$540$	−21.2510	−	18.7773i	−0.914497	−	0.808045i
$541$	9.20384	+	9.20384i	0.395704	+	0.395704i	0.876715	−	0.481011i	$-0.159730\pi$
$541$	9.20384	+	9.20384i	0.395704	+	0.395704i	−0.481011	+	0.876715i	$0.659730\pi$
$542$	7.20363	+	15.9779i	0.309423	+	0.686312i
$543$	−27.5786			−1.18351
$544$	16.9242	−	10.3066i	0.725620	−	0.441892i
$545$	−6.97729			−0.298874
$546$	−2.89729	−	6.42630i	−0.123992	−	0.275020i
$547$	−12.8682	−	12.8682i	−0.550205	−	0.550205i	0.376295	−	0.926500i	$-0.377198\pi$
$547$	−12.8682	−	12.8682i	−0.550205	−	0.550205i	−0.926500	+	0.376295i	$0.877198\pi$
$548$	−27.9622	−	24.7073i	−1.19449	−	1.05544i
$549$	−6.72522	+	6.72522i	−0.287025	+	0.287025i
$550$	1.21849	−	3.21922i	0.0519564	−	0.137268i
$551$		−	6.77179i		−	0.288488i
$552$	6.13342	−	3.23440i	0.261056	−	0.137665i
$553$		−	18.5907i		−	0.790557i
$554$	−7.13422	−	2.70033i	−0.303104	−	0.114726i
$555$	−3.10704	+	3.10704i	−0.131887	+	0.131887i
$556$	1.73302	+	28.0429i	0.0734965	+	1.18929i
$557$	23.7061	+	23.7061i	1.00446	+	1.00446i	0.999990	+	0.00447021i	$0.00142292\pi$
$557$	23.7061	+	23.7061i	1.00446	+	1.00446i	0.00447021	+	0.999990i	$0.498577\pi$
$558$	−3.41394	+	1.53917i	−0.144523	+	0.0651582i
$559$	−1.93603			−0.0818854
$560$	−13.0475	+	16.7438i	−0.551359	+	0.707554i
$561$	−8.65846			−0.365560
$562$	33.0725	−	14.9107i	1.39508	−	0.628970i
$563$	−20.5712	−	20.5712i	−0.866975	−	0.866975i	0.125162	−	0.992136i	$-0.460055\pi$
$563$	−20.5712	−	20.5712i	−0.866975	−	0.866975i	−0.992136	+	0.125162i	$0.960055\pi$
$564$	−8.77133	+	0.542058i	−0.369340	+	0.0228248i
$565$	30.9982	−	30.9982i	1.30410	−	1.30410i
$566$	−9.56008	−	3.61852i	−0.401840	−	0.152098i
$567$		−	8.49843i		−	0.356901i
$568$	−11.3332	+	36.6219i	−0.475533	+	1.53662i
$569$			29.6393i			1.24254i	0.783595	+	0.621272i	$0.213384\pi$
$569$			29.6393i			1.24254i	−0.783595	+	0.621272i	$0.786616\pi$
$570$	−1.69517	+	4.47862i	−0.0710030	+	0.187589i
$571$	4.64127	−	4.64127i	0.194231	−	0.194231i	−0.603291	−	0.797521i	$-0.706144\pi$
$571$	4.64127	−	4.64127i	0.194231	−	0.194231i	0.797521	+	0.603291i	$0.206144\pi$
$572$	−4.26625	+	4.82828i	−0.178381	+	0.201881i
$573$	8.88093	+	8.88093i	0.371006	+	0.371006i
$574$	−7.38274	−	16.3752i	−0.308150	−	0.683488i
$575$	−2.41400			−0.100671
$576$	5.36563	−	7.83893i	0.223568	−	0.326622i
$577$	6.43063			0.267711			0.133855	−	0.991001i	$-0.457264\pi$
$577$	6.43063			0.267711			0.133855	+	0.991001i	$0.457264\pi$
$578$	−2.74905	−	6.09751i	−0.114346	−	0.253623i
$579$	9.80971	+	9.80971i	0.407678	+	0.407678i
$580$	−22.5549	+	25.5263i	−0.936542	+	1.05992i
$581$	20.8008	−	20.8008i	0.862964	−	0.862964i
$582$	0.886713	−	2.34268i	0.0367554	−	0.0971072i
$583$			18.8805i			0.781952i
$584$	0.286520	−	0.925851i	0.0118563	−	0.0383120i
$585$		−	5.24037i		−	0.216663i
$586$	−17.8577	−	6.75920i	−0.737695	−	0.279220i
$587$	5.83699	−	5.83699i	0.240918	−	0.240918i	−0.576312	−	0.817230i	$-0.695509\pi$
$587$	5.83699	−	5.83699i	0.240918	−	0.240918i	0.817230	+	0.576312i	$0.195509\pi$
$588$	6.84777	−	0.423185i	0.282397	−	0.0174518i
$589$	1.57688	+	1.57688i	0.0649743	+	0.0649743i
$590$	−47.4753	+	21.4041i	−1.95453	+	0.881195i
$591$	25.1951			1.03639
$592$	−4.09432	−	3.19048i	−0.168275	−	0.131128i
$593$	24.9841			1.02597			0.512986	−	0.858397i	$-0.328539\pi$
$593$	24.9841			1.02597			0.512986	+	0.858397i	$0.328539\pi$
$594$	−13.3442	+	6.01620i	−0.547518	+	0.246848i
$595$	−13.1446	−	13.1446i	−0.538876	−	0.538876i
$596$	−2.03789	−	32.9761i	−0.0834750	−	1.35075i
$597$	−11.1226	+	11.1226i	−0.455219	+	0.455219i
$598$	4.22603	+	1.59957i	0.172815	+	0.0654112i
$599$			31.3529i			1.28104i	0.767940	+	0.640522i	$0.221282\pi$
$599$			31.3529i			1.28104i	−0.767940	+	0.640522i	$0.778718\pi$
$600$	4.46539	−	2.35478i	0.182299	−	0.0961334i
$601$		−	14.4439i		−	0.589179i	−0.955624	−	0.294590i	$-0.904817\pi$
$601$		−	14.4439i		−	0.589179i	0.955624	−	0.294590i	$-0.0951829\pi$
$602$	−1.16547	+	3.07915i	−0.0475010	+	0.125497i
$603$	8.27460	−	8.27460i	0.336968	−	0.336968i
$604$	10.0674	+	8.89553i	0.409637	+	0.361954i
$605$	13.5682	+	13.5682i	0.551626	+	0.551626i
$606$	3.20751	+	7.11438i	0.130296	+	0.289002i
$607$	−43.5496			−1.76762			−0.883812	−	0.467843i	$-0.845031\pi$
$607$	−43.5496			−1.76762			−0.883812	+	0.467843i	$0.845031\pi$
$608$	−5.49686	−	1.33585i	−0.222927	−	0.0541757i
$609$	−19.2366			−0.779508
$610$	−11.7094	−	25.9719i	−0.474099	−	1.05157i
$611$	−4.04950	−	4.04950i	−0.163825	−	0.163825i
$612$	6.23400	+	5.50834i	0.251995	+	0.222661i
$613$	−4.46303	+	4.46303i	−0.180260	+	0.180260i	−0.791469	−	0.611209i	$-0.790683\pi$
$613$	−4.46303	+	4.46303i	−0.180260	+	0.180260i	0.611209	+	0.791469i	$0.290683\pi$
$614$	−15.0508	+	39.7639i	−0.607400	+	1.60474i
$615$			20.3834i			0.821939i
$616$	5.11087	+	9.69180i	0.205923	+	0.390494i
$617$			23.5328i			0.947395i	0.880688	+	0.473697i	$0.157081\pi$
$617$			23.5328i			0.947395i	−0.880688	+	0.473697i	$0.842919\pi$
$618$	6.63982	+	2.51320i	0.267093	+	0.101096i
$619$	−9.32396	+	9.32396i	−0.374762	+	0.374762i	−0.869208	−	0.494446i	$-0.835371\pi$
$619$	−9.32396	+	9.32396i	−0.374762	+	0.374762i	0.494446	+	0.869208i	$0.335371\pi$
$620$	−0.691913	−	11.1962i	−0.0277879	−	0.449650i
$621$	7.25889	+	7.25889i	0.291289	+	0.291289i
$622$	32.5452	−	14.6730i	1.30494	−	0.588332i
$623$	19.6432			0.786988
$624$	−9.37759	+	1.16349i	−0.375404	+	0.0465770i
$625$	29.8710			1.19484
$626$	22.4424	−	10.1181i	0.896979	−	0.404402i
$627$	1.74781	+	1.74781i	0.0698009	+	0.0698009i
$628$	41.0986	−	2.53985i	1.64001	−	0.101351i
$629$	3.21422	−	3.21422i	0.128159	−	0.128159i
$630$	−8.33452	−	3.15465i	−0.332055	−	0.125684i
$631$			13.0502i			0.519521i	0.965673	+	0.259761i	$0.0836437\pi$
$631$			13.0502i			0.519521i	−0.965673	+	0.259761i	$0.916356\pi$
$632$	−23.8069	−	7.36744i	−0.946989	−	0.293061i
$633$			14.7538i			0.586412i
$634$	−12.0990	+	31.9655i	−0.480514	+	1.26951i
$635$	15.1929	−	15.1929i	0.602914	−	0.602914i
$636$	−18.3351	+	20.7505i	−0.727034	+	0.822812i
$637$	3.16144	+	3.16144i	0.125261	+	0.125261i
$638$	7.22655	+	16.0288i	0.286102	+	0.634585i
$639$	−16.0940			−0.636667
$640$	16.2711	+	23.3440i	0.643172	+	0.922751i
$641$	−11.9983			−0.473906			−0.236953	−	0.971521i	$-0.576149\pi$
$641$	−11.9983			−0.473906			−0.236953	+	0.971521i	$0.576149\pi$
$642$	4.62930	+	10.2680i	0.182704	+	0.405244i
$643$	−16.9888	−	16.9888i	−0.669974	−	0.669974i	0.287736	−	0.957710i	$-0.407098\pi$
$643$	−16.9888	−	16.9888i	−0.669974	−	0.669974i	−0.957710	+	0.287736i	$0.907098\pi$
$644$	5.08805	−	5.75834i	0.200497	−	0.226910i
$645$	2.64179	−	2.64179i	0.104021	−	0.104021i
$646$	1.75365	−	4.63310i	0.0689963	−	0.182287i
$647$		−	40.6423i		−	1.59781i	−0.601456	−	0.798906i	$-0.705412\pi$
$647$		−	40.6423i		−	1.59781i	0.601456	−	0.798906i	$-0.294588\pi$
$648$	−10.8829	−	3.36790i	−0.427523	−	0.132304i
$649$			26.8807i			1.05516i
$650$	3.07673	+	1.16455i	0.120679	+	0.0456775i
$651$	4.47945	−	4.47945i	0.175563	−	0.175563i
$652$	−20.5406	+	1.26939i	−0.804434	+	0.0497131i
$653$	−0.314080	−	0.314080i	−0.0122909	−	0.0122909i	0.700935	−	0.713226i	$-0.252766\pi$
$653$	−0.314080	−	0.314080i	−0.0122909	−	0.0122909i	−0.713226	+	0.700935i	$0.752766\pi$
$654$	−4.81521	+	2.17093i	−0.188289	+	0.0848900i
$655$	18.7311			0.731886
$656$	−23.8956	+	2.96476i	−0.932966	+	0.115755i
$657$	0.406877			0.0158738
$658$	−8.87825	+	4.00275i	−0.346110	+	0.156043i
$659$	−33.2921	−	33.2921i	−1.29688	−	1.29688i	−0.930446	−	0.366430i	$-0.880580\pi$
$659$	−33.2921	−	33.2921i	−1.29688	−	1.29688i	−0.366430	−	0.930446i	$-0.619420\pi$
$660$	−0.766915	−	12.4099i	−0.0298521	−	0.483053i
$661$	14.9077	−	14.9077i	0.579842	−	0.579842i	−0.355018	−	0.934860i	$-0.615525\pi$
$661$	14.9077	−	14.9077i	0.579842	−	0.579842i	0.934860	+	0.355018i	$0.115525\pi$
$662$	−24.5235	−	9.28224i	−0.953134	−	0.360765i
$663$		−	8.27521i		−	0.321383i
$664$	−18.3939	−	34.8805i	−0.713821	−	1.35363i
$665$			5.30679i			0.205789i
$666$	0.771398	−	2.03802i	0.0298910	−	0.0789716i
$667$	8.71925	−	8.71925i	0.337611	−	0.337611i
$668$	−8.71342	−	7.69914i	−0.337132	−	0.297889i
$669$	6.41132	+	6.41132i	0.247876	+	0.247876i
$670$	14.4070	+	31.9554i	0.556592	+	1.23454i
$671$	−14.7054			−0.567695
$672$	−3.79474	+	15.6149i	−0.146385	+	0.602360i
$673$	−16.3298			−0.629469			−0.314735	−	0.949180i	$-0.601916\pi$
$673$	−16.3298			−0.629469			−0.314735	+	0.949180i	$0.601916\pi$
$674$	−18.2377	−	40.4520i	−0.702491	−	1.55815i
$675$	5.28478	+	5.28478i	0.203411	+	0.203411i
$676$	14.8692	+	13.1384i	0.571892	+	0.505322i
$677$	−22.5345	+	22.5345i	−0.866070	+	0.866070i	−0.992035	−	0.125965i	$-0.959797\pi$
$677$	−22.5345	+	22.5345i	−0.866070	+	0.866070i	0.125965	+	0.992035i	$0.459797\pi$
$678$	11.7478	−	31.0375i	0.451171	−	1.19199i
$679$		−	2.77588i		−	0.106529i
$680$	−22.0419	+	11.6236i	−0.845270	+	0.445744i
$681$		−	1.14740i		−	0.0439684i
$682$	−5.41524	−	2.04969i	−0.207360	−	0.0784866i
$683$	10.4592	−	10.4592i	0.400210	−	0.400210i	−0.478097	−	0.878307i	$-0.658673\pi$
$683$	10.4592	−	10.4592i	0.400210	−	0.400210i	0.878307	+	0.478097i	$0.158673\pi$
$684$	−0.146484	−	2.37033i	−0.00560095	−	0.0906319i
$685$	33.1803	+	33.1803i	1.26776	+	1.26776i
$686$	25.9731	−	11.7100i	0.991659	−	0.447088i
$687$	−36.0671			−1.37605
$688$	3.48124	+	2.71274i	0.132721	+	0.103422i
$689$	−18.0448			−0.687453
$690$	−7.94927	+	3.58391i	−0.302623	+	0.136437i
$691$	33.7338	+	33.7338i	1.28330	+	1.28330i	0.938781	+	0.344515i	$0.111957\pi$
$691$	33.7338	+	33.7338i	1.28330	+	1.28330i	0.344515	+	0.938781i	$0.388043\pi$
$692$	38.2312	−	2.36264i	1.45333	−	0.0898142i
$693$	−3.25261	+	3.25261i	−0.123556	+	0.123556i
$694$	23.5934	+	8.93018i	0.895592	+	0.338985i
$695$		−	35.3326i		−	1.34024i
$696$	−7.62342	+	24.6341i	−0.288965	+	0.933753i
$697$		−	21.0865i		−	0.798710i
$698$	−3.23219	+	8.53938i	−0.122340	+	0.323220i
$699$	−16.7110	+	16.7110i	−0.632067	+	0.632067i
$700$	3.70431	−	4.19232i	0.140010	−	0.158455i
$701$	21.8750	+	21.8750i	0.826208	+	0.826208i	0.986990	−	0.160782i	$-0.0514015\pi$
$701$	21.8750	+	21.8750i	0.826208	+	0.826208i	−0.160782	+	0.986990i	$0.551401\pi$
$702$	−5.74991	−	12.7535i	−0.217016	−	0.481351i
$703$	−1.29766			−0.0489420
$704$	14.4366	−	2.70407i	0.544099	−	0.101913i
$705$	11.0514			0.416220
$706$	−14.4338	−	32.0147i	−0.543223	−	1.20489i
$707$	6.11529	+	6.11529i	0.229989	+	0.229989i
$708$	−26.1041	+	29.5431i	−0.981054	+	1.11030i
$709$	−15.8876	+	15.8876i	−0.596672	+	0.596672i	−0.939426	−	0.342753i	$-0.888641\pi$
$709$	−15.8876	+	15.8876i	−0.596672	+	0.596672i	0.342753	+	0.939426i	$0.388641\pi$
$710$	17.0656	−	45.0871i	0.640461	−	1.69209i
$711$		−	10.4622i		−	0.392365i
$712$	7.78454	−	25.1547i	0.291738	−	0.942714i
$713$			4.06073i			0.152076i
$714$	−13.1613	−	4.98159i	−0.492548	−	0.186431i
$715$	5.72931	−	5.72931i	0.214264	−	0.214264i
$716$	−39.3210	+	2.42999i	−1.46950	+	0.0908131i
$717$	6.74496	+	6.74496i	0.251895	+	0.251895i
$718$	43.3660	−	19.5515i	1.61840	−	0.729655i
$719$	−25.5391			−0.952447			−0.476223	−	0.879324i	$-0.657995\pi$
$719$	−25.5391			−0.952447			−0.476223	+	0.879324i	$0.657995\pi$
$720$	−7.34273	+	9.42287i	−0.273647	+	0.351169i
$721$	7.86764			0.293006
$722$	−1.28924	+	0.581253i	−0.0479806	+	0.0216320i
$723$	5.19320	+	5.19320i	0.193137	+	0.193137i
$724$	2.52701	+	40.8909i	0.0939155	+	1.51970i
$725$	6.34798	−	6.34798i	0.235758	−	0.235758i
$726$	13.5854	+	5.14212i	0.504201	+	0.190842i
$727$			8.49155i			0.314934i	0.987524	+	0.157467i	$0.0503328\pi$
$727$			8.49155i			0.314934i	−0.987524	+	0.157467i	$0.949667\pi$
$728$	−9.26282	+	4.88465i	−0.343303	+	0.181037i
$729$		−	27.5527i		−	1.02047i
$730$	−0.431442	+	1.13986i	−0.0159684	+	0.0421881i
$731$	−2.73292	+	2.73292i	−0.101081	+	0.101081i
$732$	−16.1619	−	14.2806i	−0.597360	−	0.527825i
$733$	−16.0856	−	16.0856i	−0.594136	−	0.594136i	0.344610	−	0.938746i	$-0.388011\pi$
$733$	−16.0856	−	16.0856i	−0.594136	−	0.594136i	−0.938746	+	0.344610i	$0.888011\pi$
$734$	−6.12763	−	13.5913i	−0.226175	−	0.501665i
$735$	−8.62783			−0.318242
$736$	−5.35766	−	8.79768i	−0.197486	−	0.324287i
$737$	18.0933			0.666474
$738$	−4.15477	−	9.21544i	−0.152939	−	0.339225i
$739$	−32.4603	−	32.4603i	−1.19407	−	1.19407i	−0.975914	−	0.218156i	$-0.929996\pi$
$739$	−32.4603	−	32.4603i	−1.19407	−	1.19407i	−0.218156	−	0.975914i	$-0.570004\pi$
$740$	4.89152	+	4.32213i	0.179816	+	0.158885i
$741$	−1.67045	+	1.67045i	−0.0613655	+	0.0613655i
$742$	−10.8628	+	28.6993i	−0.398786	+	1.05358i
$743$			47.2804i			1.73455i	0.497831	+	0.867274i	$0.334130\pi$
$743$			47.2804i			1.73455i	−0.497831	+	0.867274i	$0.665870\pi$
$744$	−3.96111	−	7.51150i	−0.145221	−	0.275385i
$745$			41.5481i			1.52221i
$746$	28.8453	+	10.9180i	1.05610	+	0.399738i
$747$	11.7060	−	11.7060i	0.428301	−	0.428301i
$748$	0.793369	+	12.8379i	0.0290085	+	0.469401i
$749$	8.82602	+	8.82602i	0.322496	+	0.322496i
$750$	16.0402	−	7.23172i	0.585707	−	0.264065i
$751$	−13.8386			−0.504977			−0.252489	−	0.967600i	$-0.581249\pi$
$751$	−13.8386			−0.504977			−0.252489	+	0.967600i	$0.581249\pi$
$752$	1.60742	+	12.9556i	0.0586167	+	0.472443i
$753$	−11.2596			−0.410323
$754$	−15.3193	+	6.90668i	−0.557896	+	0.251527i
$755$	−11.9461	−	11.9461i	−0.434765	−	0.434765i
$756$	−23.7451	+	1.46742i	−0.863603	+	0.0533697i
$757$	−7.96094	+	7.96094i	−0.289345	+	0.289345i	−0.836821	−	0.547476i	$-0.815589\pi$
$757$	−7.96094	+	7.96094i	−0.289345	+	0.289345i	0.547476	+	0.836821i	$0.315589\pi$
$758$	−27.2563	−	10.3166i	−0.989993	−	0.374716i
$759$			4.50091i			0.163373i
$760$	6.79579	+	2.10307i	0.246509	+	0.0762862i
$761$		−	12.3189i		−	0.446558i	−0.974755	−	0.223279i	$-0.928324\pi$
$761$		−	12.3189i		−	0.446558i	0.974755	−	0.223279i	$-0.0716761\pi$
$762$	5.75787	−	15.2122i	0.208586	−	0.551080i
$763$	−4.13900	+	4.13900i	−0.149842	+	0.149842i
$764$	12.3540	−	13.9815i	0.446953	−	0.505835i
$765$	−7.39736	−	7.39736i	−0.267452	−	0.267452i
$766$	−0.600754	−	1.33250i	−0.0217061	−	0.0481451i
$767$	−25.6909			−0.927645
$768$	18.4924	+	11.0476i	0.667287	+	0.398647i
$769$	−7.59318			−0.273817			−0.136909	−	0.990584i	$-0.543717\pi$
$769$	−7.59318			−0.273817			−0.136909	+	0.990584i	$0.543717\pi$
$770$	−5.66317	−	12.5611i	−0.204086	−	0.452672i
$771$	26.3641	+	26.3641i	0.949479	+	0.949479i
$772$	13.6460	−	15.4438i	0.491132	−	0.555833i
$773$	−10.2342	+	10.2342i	−0.368098	+	0.368098i	−0.866783	−	0.498685i	$-0.833816\pi$
$773$	−10.2342	+	10.2342i	−0.368098	+	0.368098i	0.498685	+	0.866783i	$0.333816\pi$
$774$	−0.655889	+	1.73285i	−0.0235754	+	0.0622859i
$775$			2.95638i			0.106196i
$776$	−3.55475	−	1.10007i	−0.127608	−	0.0394904i
$777$			3.68625i			0.132244i
$778$	−24.3800	−	9.22792i	−0.874065	−	0.330837i
$779$	−4.25657	+	4.25657i	−0.152507	+	0.152507i
$780$	11.8606	−	0.732969i	0.424676	−	0.0262445i
$781$	−17.5956	−	17.5956i	−0.629618	−	0.629618i
$782$	8.22348	−	3.70754i	0.294071	−	0.132581i
$783$	−38.1767			−1.36432
$784$	−1.25492	−	10.1144i	−0.0448184	−	0.361230i
$785$	−51.7820			−1.84818
$786$	12.9268	−	5.82804i	0.461085	−	0.207879i
$787$	−28.9126	−	28.9126i	−1.03062	−	1.03062i	−0.999516	−	0.0311050i	$-0.990097\pi$
$787$	−28.9126	−	28.9126i	−1.03062	−	1.03062i	−0.0311050	−	0.999516i	$-0.509903\pi$
$788$	−2.30861	−	37.3568i	−0.0822408	−	1.33078i
$789$	23.2828	−	23.2828i	0.828891	−	0.828891i
$790$	29.3099	+	11.0939i	1.04280	+	0.394703i
$791$		−	36.7768i		−	1.30763i
$792$	2.87624	+	5.45423i	0.102203	+	0.193808i
$793$		−	14.0545i		−	0.499090i
$794$	6.71330	−	17.7364i	0.238246	−	0.629442i
$795$	24.6229	−	24.6229i	0.873285	−	0.873285i
$796$	17.5107	+	15.4724i	0.620651	+	0.548405i
$797$	−15.4854	−	15.4854i	−0.548520	−	0.548520i	0.377493	−	0.926012i	$-0.376786\pi$
$797$	−15.4854	−	15.4854i	−0.548520	−	0.548520i	−0.926012	+	0.377493i	$0.876786\pi$
$798$	1.65116	+	3.66235i	0.0584506	+	0.129646i
$799$	−11.4326			−0.404457
$800$	−3.90060	−	6.40508i	−0.137907	−	0.226454i
$801$	11.0546			0.390593
$802$	4.98746	+	11.0624i	0.176113	+	0.390627i
$803$	0.444839	+	0.444839i	0.0156980	+	0.0156980i
$804$	19.8853	+	17.5706i	0.701301	+	0.619667i
$805$	−6.83294	+	6.83294i	−0.240829	+	0.240829i
$806$	1.95896	−	5.17555i	0.0690016	−	0.182301i
$807$			14.7025i			0.517554i
$808$	10.2546	−	5.40767i	0.360756	−	0.190241i
$809$			34.3308i			1.20701i	0.797361	+	0.603503i	$0.206229\pi$
$809$			34.3308i			1.20701i	−0.797361	+	0.603503i	$0.793771\pi$
$810$	13.3985	+	5.07139i	0.470776	+	0.178191i
$811$	22.2742	−	22.2742i	0.782154	−	0.782154i	−0.198040	−	0.980194i	$-0.563458\pi$
$811$	22.2742	−	22.2742i	0.782154	−	0.782154i	0.980194	+	0.198040i	$0.0634575\pi$
$812$	1.76264	+	28.5222i	0.0618566	+	1.00093i
$813$	−11.7983	−	11.7983i	−0.413784	−	0.413784i
$814$	3.07154	−	1.38480i	0.107657	−	0.0485372i
$815$	25.8801			0.906541
$816$	−11.5951	+	14.8799i	−0.405910	+	0.520901i
$817$	1.10335			0.0386012
$818$	5.76228	−	2.59792i	0.201473	−	0.0908340i
$819$	−3.10864	−	3.10864i	−0.108625	−	0.108625i
$820$	30.2226	−	1.86772i	1.05542	−	0.0652237i
$821$	29.8937	−	29.8937i	1.04330	−	1.04330i	0.0442763	−	0.999019i	$-0.485902\pi$
$821$	29.8937	−	29.8937i	1.04330	−	1.04330i	0.999019	−	0.0442763i	$-0.0140982\pi$
$822$	33.2224	+	12.5748i	1.15876	+	0.438596i
$823$		−	8.77504i		−	0.305879i	−0.988236	−	0.152939i	$-0.951126\pi$
$823$		−	8.77504i		−	0.305879i	0.988236	−	0.152939i	$-0.0488739\pi$
$824$	3.11792	−	10.0752i	0.108618	−	0.350985i
$825$			3.27685i			0.114085i
$826$	−15.4656	+	40.8599i	−0.538118	+	1.42170i
$827$	−0.855008	+	0.855008i	−0.0297315	+	0.0297315i	−0.721816	−	0.692085i	$-0.756692\pi$
$827$	−0.855008	+	0.855008i	−0.0297315	+	0.0297315i	0.692085	+	0.721816i	$0.256692\pi$
$828$	2.86339	−	3.24061i	0.0995097	−	0.112619i
$829$	−37.2132	−	37.2132i	−1.29247	−	1.29247i	−0.933257	−	0.359210i	$-0.883046\pi$
$829$	−37.2132	−	37.2132i	−1.29247	−	1.29247i	−0.359210	−	0.933257i	$-0.616954\pi$
$830$	20.3816	+	45.2071i	0.707454	+	1.56916i
$831$	7.26195			0.251914
$832$	2.58438	+	13.7976i	0.0895972	+	0.478345i
$833$	8.92544			0.309248
$834$	−10.9935	−	24.3839i	−0.380672	−	0.844346i
$835$	10.3395	+	10.3395i	0.357812	+	0.357812i
$836$	2.43134	−	2.75164i	0.0840896	−	0.0951675i
$837$	8.88984	−	8.88984i	0.307278	−	0.307278i
$838$	3.87958	−	10.2498i	0.134018	−	0.354073i
$839$		−	39.9116i		−	1.37790i	−0.724809	−	0.688950i	$-0.758072\pi$
$839$		−	39.9116i		−	1.37790i	0.724809	−	0.688950i	$-0.241928\pi$
$840$	5.97418	−	19.3048i	0.206129	−	0.666079i
$841$			16.8572i			0.581281i
$842$	19.6649	+	7.44325i	0.677698	+	0.256511i
$843$	−24.4211	+	24.4211i	−0.841109	+	0.841109i
$844$	21.8756	−	1.35189i	0.752988	−	0.0465338i
$845$	−17.6440	−	17.6440i	−0.606973	−	0.606973i
$846$	−4.99639	+	2.25262i	−0.171780	+	0.0774465i
$847$	16.0976			0.553119
$848$	32.4469	+	25.2842i	1.11423	+	0.868261i
$849$	9.73123			0.333975
$850$	5.98704	−	2.69925i	0.205354	−	0.0925834i
$851$	−1.67084	−	1.67084i	−0.0572757	−	0.0572757i
$852$	−2.25106	−	36.4255i	−0.0771199	−	1.24792i
$853$	−24.5220	+	24.5220i	−0.839617	+	0.839617i	−0.988808	−	0.149191i	$-0.952333\pi$
$853$	−24.5220	+	24.5220i	−0.839617	+	0.839617i	0.149191	+	0.988808i	$0.452333\pi$
$854$	−22.3529	−	8.46065i	−0.764900	−	0.289518i
$855$			2.98649i			0.102136i
$856$	14.8002	−	7.80473i	0.505860	−	0.266760i
$857$		−	19.1501i		−	0.654154i	−0.944998	−	0.327077i	$-0.893936\pi$
$857$		−	19.1501i		−	0.654154i	0.944998	−	0.327077i	$-0.106064\pi$
$858$	2.17131	−	5.73657i	0.0741274	−	0.195843i
$859$	−18.4442	+	18.4442i	−0.629306	+	0.629306i	−0.947894	−	0.318587i	$-0.896792\pi$
$859$	−18.4442	+	18.4442i	−0.629306	+	0.629306i	0.318587	+	0.947894i	$0.396792\pi$
$860$	−4.15907	−	3.67493i	−0.141823	−	0.125314i
$861$	12.0916	+	12.0916i	0.412082	+	0.412082i
$862$	1.22504	+	2.71720i	0.0417252	+	0.0925481i
$863$	30.1155			1.02514			0.512571	−	0.858645i	$-0.328693\pi$
$863$	30.1155			1.02514			0.512571	+	0.858645i	$0.328693\pi$
$864$	−7.53098	+	30.9892i	−0.256209	+	1.05427i
$865$	−48.1692			−1.63780
$866$	19.6331	+	43.5469i	0.667158	+	1.47978i
$867$	4.50247	+	4.50247i	0.152912	+	0.152912i
$868$	−7.05215	−	6.23125i	−0.239365	−	0.211502i
$869$	11.4384	−	11.4384i	0.388021	−	0.388021i
$870$	11.4794	−	30.3282i	0.389187	−	1.02822i
$871$			17.2924i			0.585932i
$872$	3.66006	+	6.94060i	0.123945	+	0.235039i
$873$		−	1.56218i		−	0.0528717i
$874$	−2.40842	−	0.911595i	−0.0814660	−	0.0308352i
$875$	13.7877	−	13.7877i	0.466109	−	0.466109i
$876$	0.0569097	+	0.920886i	0.00192280	+	0.0311139i
$877$	1.23472	+	1.23472i	0.0416936	+	0.0416936i	0.727646	−	0.685953i	$-0.240614\pi$
$877$	1.23472	+	1.23472i	0.0416936	+	0.0416936i	−0.685953	+	0.727646i	$0.740614\pi$
$878$	−31.4962	+	14.2000i	−1.06295	+	0.479228i
$879$	18.1774			0.613108
$880$	−18.3299	+	2.27422i	−0.617900	+	0.0766638i
$881$	26.8526			0.904687			0.452343	−	0.891844i	$-0.350588\pi$
$881$	26.8526			0.904687			0.452343	+	0.891844i	$0.350588\pi$
$882$	3.90068	−	1.75862i	0.131343	−	0.0592157i
$883$	17.6467	+	17.6467i	0.593857	+	0.593857i	0.938671	−	0.344814i	$-0.112058\pi$
$883$	17.6467	+	17.6467i	0.593857	+	0.593857i	−0.344814	+	0.938671i	$0.612058\pi$
$884$	−12.2697	+	0.758253i	−0.412674	+	0.0255028i
$885$	35.0563	−	35.0563i	1.17840	−	1.17840i
$886$	−0.544263	−	0.206006i	−0.0182849	−	0.00692089i
$887$			32.7273i			1.09888i	0.835534	+	0.549438i	$0.185158\pi$
$887$			32.7273i			1.09888i	−0.835534	+	0.549438i	$0.814842\pi$
$888$	4.72055	+	1.46085i	0.158411	+	0.0490230i
$889$		−	18.0252i		−	0.604546i
$890$	−11.7220	+	30.9692i	−0.392921	+	1.03809i
$891$	5.22888	−	5.22888i	0.175174	−	0.175174i
$892$	8.91863	−	10.0936i	0.298618	−	0.337957i
$893$	2.30781	+	2.30781i	0.0772280	+	0.0772280i
$894$	12.9274	+	28.6734i	0.432356	+	0.958982i
$895$	49.5424			1.65602
$896$	23.5000	+	4.19568i	0.785082	+	0.140168i
$897$	−4.30169			−0.143629
$898$	13.2595	+	29.4100i	0.442474	+	0.981425i
$899$	−10.6783	−	10.6783i	−0.356142	−	0.356142i
$900$	2.08467	−	2.35930i	0.0694889	−	0.0786433i
$901$	−25.4723	+	25.4723i	−0.848604	+	0.848604i
$902$	5.53285	−	14.6177i	0.184224	−	0.486716i
$903$		−	3.13428i		−	0.104302i
$904$	−47.0958	−	14.5746i	−1.56638	−	0.484743i
$905$		−	51.5203i		−	1.71259i
$906$	−11.9613	−	4.52739i	−0.397387	−	0.150412i
$907$	29.1701	−	29.1701i	0.968578	−	0.968578i	−0.0309427	−	0.999521i	$-0.509851\pi$
$907$	29.1701	−	29.1701i	0.968578	−	0.968578i	0.999521	+	0.0309427i	$0.00985093\pi$
$908$	−1.70125	+	0.105136i	−0.0564581	+	0.00348904i
$909$	3.44149	+	3.44149i	0.114147	+	0.114147i
$910$	12.0051	−	5.41250i	0.397967	−	0.179423i
$911$	−25.4781			−0.844126			−0.422063	−	0.906566i	$-0.638694\pi$
$911$	−25.4781			−0.844126			−0.422063	+	0.906566i	$0.638694\pi$
$912$	5.34430	−	0.663075i	0.176967	−	0.0219566i
$913$	25.5965			0.847119
$914$	−32.3007	+	14.5627i	−1.06841	+	0.481691i
$915$	19.1779	+	19.1779i	0.634003	+	0.634003i
$916$	3.30481	+	53.4769i	0.109194	+	1.76693i
$917$	11.1115	−	11.1115i	0.366934	−	0.366934i
$918$	−26.1196	−	9.88638i	−0.862076	−	0.326299i
$919$			44.9833i			1.48386i	0.670476	+	0.741932i	$0.266090\pi$
$919$			44.9833i			1.48386i	−0.670476	+	0.741932i	$0.733910\pi$
$920$	6.04227	+	11.4580i	0.199208	+	0.377760i
$921$		−	40.4758i		−	1.33372i
$922$	13.0407	−	34.4532i	0.429471	−	1.13466i
$923$	16.8167	−	16.8167i	0.553530	−	0.553530i
$924$	−7.81658	−	6.90670i	−0.257147	−	0.227214i
$925$	−1.21644	−	1.21644i	−0.0399964	−	0.0399964i
$926$	7.25307	+	16.0876i	0.238351	+	0.528671i
$927$	4.42765			0.145423
$928$	37.2236	+	9.04607i	1.22193	+	0.296952i
$929$	22.8636			0.750132			0.375066	−	0.926998i	$-0.377620\pi$
$929$	22.8636			0.750132			0.375066	+	0.926998i	$0.377620\pi$
$930$	4.38916	+	9.73533i	0.143926	+	0.319234i
$931$	−1.80171	−	1.80171i	−0.0590486	−	0.0590486i
$932$	26.3086	+	23.2462i	0.861768	+	0.761454i
$933$	−24.0317	+	24.0317i	−0.786764	+	0.786764i
$934$	−2.22112	+	5.86817i	−0.0726774	+	0.192012i
$935$		−	16.1751i		−	0.528982i
$936$	−5.21282	+	2.74893i	−0.170386	+	0.0898515i
$937$			22.3141i			0.728969i	0.931210	+	0.364484i	$0.118755\pi$
$937$			22.3141i			0.728969i	−0.931210	+	0.364484i	$0.881245\pi$
$938$	27.5026	+	10.4098i	0.897993	+	0.339894i
$939$	−16.5717	+	16.5717i	−0.540798	+	0.540798i
$940$	−1.01263	−	16.3860i	−0.0330285	−	0.534451i
$941$	−11.0737	−	11.0737i	−0.360991	−	0.360991i	0.503187	−	0.864178i	$-0.332161\pi$
$941$	−11.0737	−	11.0737i	−0.360991	−	0.360991i	−0.864178	+	0.503187i	$0.832161\pi$
$942$	−35.7361	+	16.1115i	−1.16434	+	0.524943i
$943$	−10.9614			−0.356952
$944$	46.1956	+	35.9977i	1.50354	+	1.17163i
$945$	29.9176			0.973220
$946$	−2.61161	+	1.17744i	−0.0849108	+	0.0382819i
$947$	−23.3872	−	23.3872i	−0.759981	−	0.759981i	0.216338	−	0.976319i	$-0.430589\pi$
$947$	−23.3872	−	23.3872i	−0.759981	−	0.759981i	−0.976319	+	0.216338i	$0.930589\pi$
$948$	23.6793	−	1.46335i	0.769066	−	0.0475274i
$949$	−0.425149	+	0.425149i	−0.0138009	+	0.0138009i
$950$	−1.75343	−	0.663680i	−0.0568888	−	0.0215326i
$951$		−	32.5377i		−	1.05511i
$952$	−6.18026	+	19.9707i	−0.200303	+	0.647255i
$953$		−	20.1657i		−	0.653232i	−0.945157	−	0.326616i	$-0.894092\pi$
$953$		−	20.1657i		−	0.653232i	0.945157	−	0.326616i	$-0.105908\pi$
$954$	−6.11323	+	16.1510i	−0.197923	+	0.522909i
$955$	−16.5907	+	16.5907i	−0.536863	+	0.536863i
$956$	9.38274	−	10.6188i	0.303460	−	0.343437i
$957$	−11.8358	−	11.8358i	−0.382598	−	0.382598i
$958$	−11.4702	−	25.4413i	−0.370584	−	0.821971i
$959$	39.3658			1.27119
$960$	−22.3539	−	15.3009i	−0.721467	−	0.493834i
$961$	−26.0269			−0.839577
$962$	1.32351	+	2.93559i	0.0426715	+	0.0946471i
$963$	4.96700	+	4.96700i	0.160059	+	0.160059i
$964$	7.22412	−	8.17582i	0.232673	−	0.263326i
$965$	−18.3258	+	18.3258i	−0.589928	+	0.589928i
$966$	−2.58957	+	6.84159i	−0.0833180	+	0.220125i
$967$		−	49.0167i		−	1.57627i	−0.615502	−	0.788136i	$-0.711047\pi$
$967$		−	49.0167i		−	1.57627i	0.615502	−	0.788136i	$-0.288953\pi$
$968$	6.37942	−	20.6143i	0.205042	−	0.662568i
$969$			4.71605i			0.151501i
$970$	4.37643	+	1.65649i	0.140519	+	0.0531868i
$971$	4.07402	−	4.07402i	0.130741	−	0.130741i	−0.638708	−	0.769449i	$-0.720531\pi$
$971$	4.07402	−	4.07402i	0.130741	−	0.130741i	0.769449	+	0.638708i	$0.220531\pi$
$972$	−22.9367	+	1.41746i	−0.735694	+	0.0454651i
$973$	−20.9596	−	20.9596i	−0.671935	−	0.671935i
$974$	12.7961	−	5.76912i	0.410015	−	0.184855i
$975$	−3.13181			−0.100298
$976$	−19.6930	+	25.2718i	−0.630356	+	0.808931i
$977$	4.44973			0.142360			0.0711798	−	0.997464i	$-0.477324\pi$
$977$	4.44973			0.142360			0.0711798	+	0.997464i	$0.477324\pi$
$978$	17.8605	−	8.05239i	0.571116	−	0.257487i
$979$	12.0860	+	12.0860i	0.386269	+	0.386269i
$980$	0.790563	+	12.7925i	0.0252536	+	0.408642i
$981$	−2.32929	+	2.32929i	−0.0743686	+	0.0743686i
$982$	37.6235	+	14.2406i	1.20062	+	0.454437i
$983$			20.4711i			0.652928i	0.945210	+	0.326464i	$0.105857\pi$
$983$			20.4711i			0.652928i	−0.945210	+	0.326464i	$0.894143\pi$
$984$	20.2762	−	10.6925i	0.646383	−	0.340864i
$985$			47.0676i			1.49970i
$986$	−11.8753	+	31.3744i	−0.378188	+	0.999165i
$987$	6.55580	−	6.55580i	0.208673	−	0.208673i
$988$	2.62985	+	2.32372i	0.0836666	+	0.0739274i
$989$	1.42065	+	1.42065i	0.0451740	+	0.0451740i
$990$	−3.18705	−	7.06900i	−0.101291	−	0.224668i
$991$	40.7409			1.29418			0.647089	−	0.762414i	$-0.275986\pi$
$991$	40.7409			1.29418			0.647089	+	0.762414i	$0.275986\pi$
$992$	−10.7744	+	6.56143i	−0.342087	+	0.208326i
$993$	24.9626			0.792163
$994$	−16.6226	−	36.8696i	−0.527236	−	1.16943i
$995$	−20.7785	−	20.7785i	−0.658723	−	0.658723i
$996$	28.1317	+	24.8570i	0.891385	+	0.787625i
$997$	5.26293	−	5.26293i	0.166679	−	0.166679i	−0.618839	−	0.785518i	$-0.712397\pi$
$997$	5.26293	−	5.26293i	0.166679	−	0.166679i	0.785518	+	0.618839i	$0.212397\pi$
$998$	−1.12271	+	2.96617i	−0.0355387	+	0.0938925i
$999$			7.31568i			0.231458i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	304.2.k.b.77.22	✓	68
4.3	odd	2		1216.2.k.b.913.24		68
16.5	even	4	inner	304.2.k.b.229.22	yes	68
16.11	odd	4		1216.2.k.b.305.24		68

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
304.2.k.b.77.22	✓	68	1.1	even	1	trivial
304.2.k.b.229.22	yes	68	16.5	even	4	inner
1216.2.k.b.305.24		68	16.11	odd	4
1216.2.k.b.913.24		68	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:	\( N \)	\(=\)	\( 304 = 2^{4} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	304.k (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.581253 + 1.28924i) q^{2} +(-0.951991 - 0.951991i) q^{3} +(-1.32429 + 1.49875i) q^{4} +(1.77844 - 1.77844i) q^{5} +(0.673999 - 1.78069i) q^{6} -2.10998i q^{7} +(-2.70200 - 0.836178i) q^{8} -1.18743i q^{9} +O(q^{10})\)	\(q+(0.581253 + 1.28924i) q^{2} +(-0.951991 - 0.951991i) q^{3} +(-1.32429 + 1.49875i) q^{4} +(1.77844 - 1.77844i) q^{5} +(0.673999 - 1.78069i) q^{6} -2.10998i q^{7} +(-2.70200 - 0.836178i) q^{8} -1.18743i q^{9} +(3.32656 + 1.25912i) q^{10} +(1.29822 - 1.29822i) q^{11} +(2.68751 - 0.166085i) q^{12} +(1.24075 + 1.24075i) q^{13} +(2.72027 - 1.22643i) q^{14} -3.38612 q^{15} +(-0.492510 - 3.96956i) q^{16} +3.50292 q^{17} +(1.53088 - 0.690195i) q^{18} +(-0.707107 - 0.707107i) q^{19} +(0.310268 + 5.02061i) q^{20} +(-2.00868 + 2.00868i) q^{21} +(2.42831 + 0.919123i) q^{22} -1.82092i q^{23} +(1.77625 + 3.36831i) q^{24} -1.32570i q^{25} +(-0.878441 + 2.32082i) q^{26} +(-3.98639 + 3.98639i) q^{27} +(3.16233 + 2.79422i) q^{28} +(4.78838 + 4.78838i) q^{29} +(-1.96819 - 4.36553i) q^{30} -2.23005 q^{31} +(4.83146 - 2.94228i) q^{32} -2.47178 q^{33} +(2.03608 + 4.51612i) q^{34} +(-3.75247 - 3.75247i) q^{35} +(1.77966 + 1.57250i) q^{36} +(0.917582 - 0.917582i) q^{37} +(0.500624 - 1.32264i) q^{38} -2.36237i q^{39} +(-6.29244 + 3.31826i) q^{40} -6.01970i q^{41} +(-3.75722 - 1.42212i) q^{42} +(-0.780183 + 0.780183i) q^{43} +(0.226488 + 3.66492i) q^{44} +(-2.11177 - 2.11177i) q^{45} +(2.34760 - 1.05841i) q^{46} -3.26374 q^{47} +(-3.31012 + 4.24785i) q^{48} +2.54800 q^{49} +(1.70915 - 0.770570i) q^{50} +(-3.33475 - 3.33475i) q^{51} +(-3.50270 + 0.216463i) q^{52} +(-7.27172 + 7.27172i) q^{53} +(-7.45653 - 2.82232i) q^{54} -4.61760i q^{55} +(-1.76432 + 5.70116i) q^{56} +1.34632i q^{57} +(-3.39012 + 8.95664i) q^{58} +(-10.3529 + 10.3529i) q^{59} +(4.48421 - 5.07495i) q^{60} +(-5.66369 - 5.66369i) q^{61} +(-1.29622 - 2.87507i) q^{62} -2.50544 q^{63} +(6.60161 + 4.51870i) q^{64} +4.41322 q^{65} +(-1.43673 - 3.18672i) q^{66} +(6.96851 + 6.96851i) q^{67} +(-4.63889 + 5.25001i) q^{68} +(-1.73350 + 1.73350i) q^{69} +(2.65671 - 7.01897i) q^{70} -13.5536i q^{71} +(-0.992900 + 3.20843i) q^{72} +0.342654i q^{73} +(1.71633 + 0.649638i) q^{74} +(-1.26206 + 1.26206i) q^{75} +(1.99619 - 0.123362i) q^{76} +(-2.73921 - 2.73921i) q^{77} +(3.04567 - 1.37314i) q^{78} +8.81085 q^{79} +(-7.93553 - 6.18373i) q^{80} +4.02774 q^{81} +(7.76085 - 3.49897i) q^{82} +(9.85832 + 9.85832i) q^{83} +(-0.350436 - 5.67058i) q^{84} +(6.22974 - 6.22974i) q^{85} +(-1.45933 - 0.552362i) q^{86} -9.11699i q^{87} +(-4.59332 + 2.42224i) q^{88} +9.30967i q^{89} +(1.49511 - 3.95005i) q^{90} +(2.61796 - 2.61796i) q^{91} +(2.72910 + 2.41142i) q^{92} +(2.12298 + 2.12298i) q^{93} +(-1.89706 - 4.20775i) q^{94} -2.51510 q^{95} +(-7.40053 - 1.79847i) q^{96} +1.31560 q^{97} +(1.48103 + 3.28499i) q^{98} +(-1.54154 - 1.54154i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 68 q + 4 q^{3} + 4 q^{4} + 8 q^{5} - 8 q^{6}+O(q^{10}) \) 68 * q + 4 * q^3 + 4 * q^4 + 8 * q^5 - 8 * q^6	\( 68 q + 4 q^{3} + 4 q^{4} + 8 q^{5} - 8 q^{6} + 4 q^{11} - 4 q^{12} + 20 q^{14} - 16 q^{15} + 4 q^{16} + 4 q^{17} - 16 q^{18} + 16 q^{21} + 4 q^{22} - 4 q^{24} - 36 q^{26} + 28 q^{27} - 24 q^{28} + 24 q^{30} + 32 q^{31} - 20 q^{32} - 16 q^{33} - 32 q^{34} - 24 q^{35} + 52 q^{36} - 24 q^{37} - 4 q^{38} - 8 q^{40} - 40 q^{42} - 16 q^{43} - 36 q^{44} - 8 q^{46} - 24 q^{47} + 36 q^{48} - 56 q^{49} + 24 q^{50} - 52 q^{51} - 28 q^{52} + 32 q^{53} - 52 q^{54} + 12 q^{56} + 52 q^{58} + 28 q^{59} - 64 q^{60} - 12 q^{62} + 24 q^{63} - 32 q^{64} - 16 q^{65} - 44 q^{66} + 28 q^{67} - 48 q^{68} - 8 q^{69} + 4 q^{70} + 108 q^{72} + 72 q^{74} + 44 q^{75} - 12 q^{77} + 100 q^{78} + 8 q^{79} - 56 q^{80} - 76 q^{81} + 28 q^{82} + 40 q^{83} + 52 q^{84} - 8 q^{85} - 20 q^{86} - 56 q^{88} - 24 q^{90} - 4 q^{91} + 72 q^{92} - 84 q^{93} - 24 q^{94} + 32 q^{95} + 72 q^{96} - 16 q^{97} - 80 q^{98} - 24 q^{99}+O(q^{100}) \) 68 * q + 4 * q^3 + 4 * q^4 + 8 * q^5 - 8 * q^6 + 4 * q^11 - 4 * q^12 + 20 * q^14 - 16 * q^15 + 4 * q^16 + 4 * q^17 - 16 * q^18 + 16 * q^21 + 4 * q^22 - 4 * q^24 - 36 * q^26 + 28 * q^27 - 24 * q^28 + 24 * q^30 + 32 * q^31 - 20 * q^32 - 16 * q^33 - 32 * q^34 - 24 * q^35 + 52 * q^36 - 24 * q^37 - 4 * q^38 - 8 * q^40 - 40 * q^42 - 16 * q^43 - 36 * q^44 - 8 * q^46 - 24 * q^47 + 36 * q^48 - 56 * q^49 + 24 * q^50 - 52 * q^51 - 28 * q^52 + 32 * q^53 - 52 * q^54 + 12 * q^56 + 52 * q^58 + 28 * q^59 - 64 * q^60 - 12 * q^62 + 24 * q^63 - 32 * q^64 - 16 * q^65 - 44 * q^66 + 28 * q^67 - 48 * q^68 - 8 * q^69 + 4 * q^70 + 108 * q^72 + 72 * q^74 + 44 * q^75 - 12 * q^77 + 100 * q^78 + 8 * q^79 - 56 * q^80 - 76 * q^81 + 28 * q^82 + 40 * q^83 + 52 * q^84 - 8 * q^85 - 20 * q^86 - 56 * q^88 - 24 * q^90 - 4 * q^91 + 72 * q^92 - 84 * q^93 - 24 * q^94 + 32 * q^95 + 72 * q^96 - 16 * q^97 - 80 * q^98 - 24 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more