LMFDB - Embedded newform 140.2.s.b.19.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [140,2,Mod(19,140)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(140, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 3, 5]))

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

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

chi := DirichletCharacter("140.19");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$N$	$=$	$140 = 2^{2} \cdot 5 \cdot 7$
Weight:	$k$	$=$	$2$
Character orbit:	$[\chi]$	$=$	140.s (of order $6$ , 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:	$1.11790562830$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$16$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			19.6
Character	$\chi$	$=$	140.19
Dual form			140.2.s.b.59.6

$q$ -expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.674125 - 1.24320i) q^{2} +(-0.634715 + 0.366453i) q^{3} +(-1.09111 + 1.67615i) q^{4} +(-0.661137 + 2.13609i) q^{5} +(0.883452 + 0.542044i) q^{6} +(-2.56107 + 0.664037i) q^{7} +(2.81934 + 0.226536i) q^{8} +(-1.23142 + 2.13289i) q^{9} +(3.10129 - 0.618067i) q^{10} +(-2.33007 + 1.34527i) q^{11} +(0.0783137 - 1.46372i) q^{12} +3.95118 q^{13} +(2.55201 + 2.73628i) q^{14} +(-0.363144 - 1.59809i) q^{15} +(-1.61896 - 3.65773i) q^{16} +(0.709509 + 1.22891i) q^{17} +(3.48175 + 0.0930760i) q^{18} +(1.61265 - 2.79319i) q^{19} +(-2.85904 - 3.43888i) q^{20} +(1.38221 - 1.35998i) q^{21} +(3.24320 + 1.98987i) q^{22} +(-2.45620 + 4.25426i) q^{23} +(-1.87249 + 0.889369i) q^{24} +(-4.12580 - 2.82450i) q^{25} +(-2.66359 - 4.91212i) q^{26} -4.00375i q^{27} +(1.68138 - 5.01727i) q^{28} -5.17926 q^{29} +(-1.74194 + 1.52877i) q^{30} +(3.81745 + 6.61201i) q^{31} +(-3.45592 + 4.47846i) q^{32} +(0.985953 - 1.70772i) q^{33} +(1.04948 - 1.71050i) q^{34} +(0.274770 - 5.90970i) q^{35} +(-2.23142 - 4.39127i) q^{36} +(-3.87963 - 2.23990i) q^{37} +(-4.55962 - 0.121890i) q^{38} +(-2.50787 + 1.44792i) q^{39} +(-2.34787 + 5.87261i) q^{40} +0.325509i q^{41} +(-2.62252 - 0.801566i) q^{42} +9.28165 q^{43} +(0.287494 - 5.37338i) q^{44} +(-3.74191 - 4.04057i) q^{45} +(6.94469 + 0.185649i) q^{46} +(5.68610 + 3.28287i) q^{47} +(2.36796 + 1.72834i) q^{48} +(6.11811 - 3.40128i) q^{49} +(-0.730128 + 7.03327i) q^{50} +(-0.900672 - 0.520003i) q^{51} +(-4.31117 + 6.62277i) q^{52} +(1.39942 - 0.807955i) q^{53} +(-4.97748 + 2.69903i) q^{54} +(-1.33312 - 5.86665i) q^{55} +(-7.37094 + 1.29197i) q^{56} +2.36383i q^{57} +(3.49147 + 6.43888i) q^{58} +(-3.81745 - 6.61201i) q^{59} +(3.07486 + 1.13500i) q^{60} +(12.3842 + 7.15003i) q^{61} +(5.64664 - 9.20319i) q^{62} +(1.73744 - 6.28018i) q^{63} +(7.89736 + 1.27737i) q^{64} +(-2.61227 + 8.44009i) q^{65} +(-2.78770 - 0.0745223i) q^{66} +(-1.51329 - 2.62109i) q^{67} +(-2.83398 - 0.151627i) q^{68} -3.60032i q^{69} +(-7.53218 + 3.64228i) q^{70} +15.4089i q^{71} +(-3.95498 + 5.73438i) q^{72} +(-0.709509 - 1.22891i) q^{73} +(-0.169301 + 6.33314i) q^{74} +(3.65375 + 0.280844i) q^{75} +(2.92222 + 5.75071i) q^{76} +(5.07415 - 4.99257i) q^{77} +(3.49068 + 2.14171i) q^{78} +(10.5765 + 6.10637i) q^{79} +(8.88360 - 1.03999i) q^{80} +(-2.22709 - 3.85743i) q^{81} +(0.404674 - 0.219434i) q^{82} +5.26172i q^{83} +(0.771396 + 3.80068i) q^{84} +(-3.09414 + 0.703103i) q^{85} +(-6.25699 - 11.5390i) q^{86} +(3.28735 - 1.89795i) q^{87} +(-6.87401 + 3.26492i) q^{88} +(4.10930 + 2.37250i) q^{89} +(-2.50073 + 7.37581i) q^{90} +(-10.1192 + 2.62373i) q^{91} +(-4.45079 - 8.75882i) q^{92} +(-4.84598 - 2.79783i) q^{93} +(0.248133 - 9.28205i) q^{94} +(4.90033 + 5.29144i) q^{95} +(0.552378 - 4.10898i) q^{96} -8.35134 q^{97} +(-8.35286 - 5.31316i) q^{98} -6.62638i q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$32 q + 6 q^{4} - 6 q^{5} + 4 q^{9} - 12 q^{10} + 22 q^{14} + 18 q^{16} - 52 q^{21} - 48 q^{24} - 26 q^{25} - 18 q^{26} - 26 q^{30} - 28 q^{36} + 42 q^{40} - 26 q^{44} + 36 q^{45} - 22 q^{46} + 36 q^{50}+ \cdots + 60 q^{96}+O(q^{100})$ 32 * q + 6 * q^4 - 6 * q^5 + 4 * q^9 - 12 * q^10 + 22 * q^14 + 18 * q^16 - 52 * q^21 - 48 * q^24 - 26 * q^25 - 18 * q^26 - 26 * q^30 - 28 * q^36 + 42 * q^40 - 26 * q^44 + 36 * q^45 - 22 * q^46 + 36 * q^50 + 48 * q^54 - 16 * q^56 + 4 * q^60 + 36 * q^61 + 36 * q^64 - 4 * q^65 - 24 * q^66 + 26 * q^70 + 14 * q^74 + 72 * q^80 + 72 * q^81 + 56 * q^84 + 20 * q^85 + 8 * q^86 - 108 * q^89 + 30 * q^94 + 60 * q^96

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/140\mathbb{Z}\right)^\times$ .

$n$	$57$	$71$	$101$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{5}{6}\right)$

Coefficient data

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

Display

a_p

with

p

up to: 50 250 1000 (See

a_n

instead) (See

a_n

instead) (See

a_n

instead) Display

a_n

with

n

up to: 50 250 1000 (See only

a_p

) (See only

a_p

) (See only

a_p

)

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

$2$	−0.674125	−	1.24320i	−0.476679	−	0.879078i
$2$	−0.674125	−	1.24320i	−0.476679	−	0.879078i
$3$	−0.634715	+	0.366453i	−0.366453	+	0.211572i	−0.671908	−	0.740635i	$-0.734525\pi$
$3$	−0.634715	+	0.366453i	−0.366453	+	0.211572i	0.305455	+	0.952207i	$0.401191\pi$
$4$	−1.09111	+	1.67615i	−0.545555	+	0.838075i
$5$	−0.661137	+	2.13609i	−0.295670	+	0.955290i
$5$	−0.661137	+	2.13609i	−0.295670	+	0.955290i
$6$	0.883452	+	0.542044i	0.360668	+	0.221289i
$7$	−2.56107	+	0.664037i	−0.967992	+	0.250982i
$7$	−2.56107	+	0.664037i	−0.967992	+	0.250982i
$8$	2.81934	+	0.226536i	0.996787	+	0.0800926i
$9$	−1.23142	+	2.13289i	−0.410475	+	0.710964i
$10$	3.10129	−	0.618067i	0.980714	−	0.195450i
$11$	−2.33007	+	1.34527i	−0.702542	+	0.405613i	−0.808294	−	0.588780i	$-0.799609\pi$
$11$	−2.33007	+	1.34527i	−0.702542	+	0.405613i	0.105751	+	0.994393i	$0.466275\pi$
$12$	0.0783137	−	1.46372i	0.0226072	−	0.422539i
$13$	3.95118			1.09586			0.547930	−	0.836524i	$-0.315416\pi$
$13$	3.95118			1.09586			0.547930	+	0.836524i	$0.315416\pi$
$14$	2.55201	+	2.73628i	0.682054	+	0.731302i
$15$	−0.363144	−	1.59809i	−0.0937633	−	0.412624i
$16$	−1.61896	−	3.65773i	−0.404740	−	0.914432i
$17$	0.709509	+	1.22891i	0.172081	+	0.298053i	0.939147	−	0.343515i	$-0.111618\pi$
$17$	0.709509	+	1.22891i	0.172081	+	0.298053i	−0.767066	+	0.641568i	$0.778284\pi$
$18$	3.48175	+	0.0930760i	0.820657	+	0.0219382i
$19$	1.61265	−	2.79319i	0.369966	−	0.640801i	−0.619593	−	0.784923i	$-0.712703\pi$
$19$	1.61265	−	2.79319i	0.369966	−	0.640801i	0.989560	+	0.144122i	$0.0460358\pi$
$20$	−2.85904	−	3.43888i	−0.639301	−	0.768957i
$21$	1.38221	−	1.35998i	0.301622	−	0.296773i
$22$	3.24320	+	1.98987i	0.691452	+	0.424242i
$23$	−2.45620	+	4.25426i	−0.512152	+	0.887074i	0.487748	+	0.872984i	$0.337818\pi$
$23$	−2.45620	+	4.25426i	−0.512152	+	0.887074i	−0.999901	+	0.0140897i	$0.995515\pi$
$24$	−1.87249	+	0.889369i	−0.382221	+	0.181542i
$25$	−4.12580	−	2.82450i	−0.825159	−	0.564900i
$26$	−2.66359	−	4.91212i	−0.522373	−	0.963345i
$27$		−	4.00375i		−	0.770522i
$28$	1.68138	−	5.01727i	0.317751	−	0.948174i
$29$	−5.17926			−0.961765			−0.480882	−	0.876785i	$-0.659684\pi$
$29$	−5.17926			−0.961765			−0.480882	+	0.876785i	$0.659684\pi$
$30$	−1.74194	+	1.52877i	−0.318033	+	0.279114i
$31$	3.81745	+	6.61201i	0.685634	+	1.18755i	0.973237	+	0.229803i	$0.0738082\pi$
$31$	3.81745	+	6.61201i	0.685634	+	1.18755i	−0.287603	+	0.957750i	$0.592858\pi$
$32$	−3.45592	+	4.47846i	−0.610926	+	0.791688i
$33$	0.985953	−	1.70772i	0.171632	−	0.297276i
$34$	1.04948	−	1.71050i	0.179985	−	0.293349i
$35$	0.274770	−	5.90970i	0.0464446	−	0.998921i
$36$	−2.23142	−	4.39127i	−0.371904	−	0.731878i
$37$	−3.87963	−	2.23990i	−0.637806	−	0.368238i	0.145963	−	0.989290i	$-0.453372\pi$
$37$	−3.87963	−	2.23990i	−0.637806	−	0.368238i	−0.783769	+	0.621052i	$0.786705\pi$
$38$	−4.55962	−	0.121890i	−0.739669	−	0.0197732i
$39$	−2.50787	+	1.44792i	−0.401581	+	0.231853i
$40$	−2.34787	+	5.87261i	−0.371231	+	0.928540i
$41$			0.325509i			0.0508359i	0.999677	+	0.0254180i	$0.00809166\pi$
$41$			0.325509i			0.0508359i	−0.999677	+	0.0254180i	$0.991908\pi$
$42$	−2.62252	−	0.801566i	−0.404663	−	0.123684i
$43$	9.28165			1.41544			0.707719	−	0.706494i	$-0.249724\pi$
$43$	9.28165			1.41544			0.707719	+	0.706494i	$0.249724\pi$
$44$	0.287494	−	5.37338i	0.0433413	−	0.810067i
$45$	−3.74191	−	4.04057i	−0.557812	−	0.602333i
$46$	6.94469	+	0.185649i	1.02394	+	0.0273725i
$47$	5.68610	+	3.28287i	0.829403	+	0.478856i	0.853648	−	0.520850i	$-0.174385\pi$
$47$	5.68610	+	3.28287i	0.829403	+	0.478856i	−0.0242453	+	0.999706i	$0.507718\pi$
$48$	2.36796	+	1.72834i	0.341786	+	0.249465i
$49$	6.11811	−	3.40128i	0.874016	−	0.485898i
$50$	−0.730128	+	7.03327i	−0.103256	+	0.994655i
$51$	−0.900672	−	0.520003i	−0.126119	−	0.0728150i
$52$	−4.31117	+	6.62277i	−0.597851	+	0.918412i
$53$	1.39942	−	0.807955i	0.192225	−	0.110981i	−0.400799	−	0.916166i	$-0.631267\pi$
$53$	1.39942	−	0.807955i	0.192225	−	0.110981i	0.593024	+	0.805185i	$0.297934\pi$
$54$	−4.97748	+	2.69903i	−0.677349	+	0.367292i
$55$	−1.33312	−	5.86665i	−0.179758	−	0.791059i
$56$	−7.37094	+	1.29197i	−0.984984	+	0.172647i
$57$			2.36383i			0.313097i
$58$	3.49147	+	6.43888i	0.458453	+	0.845466i
$59$	−3.81745	−	6.61201i	−0.496989	−	0.860811i	0.503005	−	0.864284i	$-0.332228\pi$
$59$	−3.81745	−	6.61201i	−0.496989	−	0.860811i	−0.999994	+	0.00347297i	$0.998895\pi$
$60$	3.07486	+	1.13500i	0.396963	+	0.146528i
$61$	12.3842	+	7.15003i	1.58564	+	0.915467i	0.994014	+	0.109252i	$0.0348455\pi$
$61$	12.3842	+	7.15003i	1.58564	+	0.915467i	0.591622	+	0.806215i	$0.298488\pi$
$62$	5.64664	−	9.20319i	0.717124	−	1.16881i
$63$	1.73744	−	6.28018i	0.218897	−	0.791229i
$64$	7.89736	+	1.27737i	0.987170	+	0.159671i
$65$	−2.61227	+	8.44009i	−0.324012	+	1.04686i
$66$	−2.78770	−	0.0745223i	−0.343142	−	0.00917306i
$67$	−1.51329	−	2.62109i	−0.184878	−	0.320218i	0.758658	−	0.651490i	$-0.225856\pi$
$67$	−1.51329	−	2.62109i	−0.184878	−	0.320218i	−0.943535	+	0.331272i	$0.892522\pi$
$68$	−2.83398	−	0.151627i	−0.343671	−	0.0183875i
$69$		−	3.60032i		−	0.433427i
$70$	−7.53218	+	3.64228i	−0.900268	+	0.435336i
$71$			15.4089i			1.82870i	0.404922	+	0.914351i	$0.367299\pi$
$71$			15.4089i			1.82870i	−0.404922	+	0.914351i	$0.632701\pi$
$72$	−3.95498	+	5.73438i	−0.466099	+	0.675803i
$73$	−0.709509	−	1.22891i	−0.0830418	−	0.143833i	0.821513	−	0.570189i	$-0.193130\pi$
$73$	−0.709509	−	1.22891i	−0.0830418	−	0.143833i	−0.904555	+	0.426357i	$0.859797\pi$
$74$	−0.169301	+	6.33314i	−0.0196808	+	0.736212i
$75$	3.65375	+	0.280844i	0.421899	+	0.0324291i
$76$	2.92222	+	5.75071i	0.335202	+	0.659652i
$77$	5.07415	−	4.99257i	0.578253	−	0.568956i
$78$	3.49068	+	2.14171i	0.395241	+	0.242501i
$79$	10.5765	+	6.10637i	1.18995	+	0.687021i	0.958296	−	0.285776i	$-0.0922515\pi$
$79$	10.5765	+	6.10637i	1.18995	+	0.687021i	0.231659	+	0.972797i	$0.425585\pi$
$80$	8.88360	−	1.03999i	0.993217	−	0.116274i
$81$	−2.22709	−	3.85743i	−0.247454	−	0.428604i
$82$	0.404674	−	0.219434i	0.0446887	−	0.0242324i
$83$			5.26172i			0.577549i	0.957397	+	0.288774i	$0.0932477\pi$
$83$			5.26172i			0.577549i	−0.957397	+	0.288774i	$0.906752\pi$
$84$	0.771396	+	3.80068i	0.0841662	+	0.414688i
$85$	−3.09414	+	0.703103i	−0.335607	+	0.0762622i
$86$	−6.25699	−	11.5390i	−0.674709	−	1.24428i
$87$	3.28735	−	1.89795i	0.352441	−	0.203482i
$88$	−6.87401	+	3.26492i	−0.732772	+	0.348041i
$89$	4.10930	+	2.37250i	0.435585	+	0.251485i	0.701723	−	0.712450i	$-0.252414\pi$
$89$	4.10930	+	2.37250i	0.435585	+	0.251485i	−0.266138	+	0.963935i	$0.585748\pi$
$90$	−2.50073	+	7.37581i	−0.263601	+	0.777479i
$91$	−10.1192	+	2.62373i	−1.06078	+	0.275041i
$92$	−4.45079	−	8.75882i	−0.464027	−	0.913170i
$93$	−4.84598	−	2.79783i	−0.502505	−	0.290121i
$94$	0.248133	−	9.28205i	0.0255929	−	0.957370i
$95$	4.90033	+	5.29144i	0.502763	+	0.542891i
$96$	0.552378	−	4.10898i	0.0563768	−	0.419371i
$97$	−8.35134			−0.847950			−0.423975	−	0.905674i	$-0.639366\pi$
$97$	−8.35134			−0.847950			−0.423975	+	0.905674i	$0.639366\pi$
$98$	−8.35286	−	5.31316i	−0.843766	−	0.536711i
$99$		−	6.62638i		−	0.665976i
$100$	9.23599	−	3.83361i	0.923599	−	0.383361i
$101$	−0.241927	+	0.139677i	−0.0240727	+	0.0138984i	−0.511988	−	0.858993i	$-0.671091\pi$
$101$	−0.241927	+	0.139677i	−0.0240727	+	0.0138984i	0.487915	+	0.872891i	$0.337757\pi$
$102$	−0.0393039	+	1.47027i	−0.00389167	+	0.145578i
$103$	−11.6053	−	6.70030i	−1.14350	−	0.660200i	−0.196206	−	0.980563i	$-0.562862\pi$
$103$	−11.6053	−	6.70030i	−1.14350	−	0.660200i	−0.947295	+	0.320362i	$0.896195\pi$
$104$	11.1397	+	0.895084i	1.09234	+	0.0877703i
$105$	1.99122	+	3.85166i	0.194323	+	0.375884i
$106$	−1.94784	−	1.19510i	−0.189191	−	0.116078i
$107$	−2.71447	+	4.70160i	−0.262418	+	0.454521i	−0.966884	−	0.255217i	$-0.917853\pi$
$107$	−2.71447	+	4.70160i	−0.262418	+	0.454521i	0.704466	+	0.709738i	$0.251187\pi$
$108$	6.71089	+	4.36853i	0.645756	+	0.420362i
$109$	−4.45851	−	7.72237i	−0.427048	−	0.739669i	0.569561	−	0.821949i	$-0.307113\pi$
$109$	−4.45851	−	7.72237i	−0.427048	−	0.739669i	−0.996609	+	0.0822798i	$0.973780\pi$
$110$	−6.39475	+	5.61220i	−0.609716	+	0.535102i
$111$	3.28327			0.311634
$112$	6.57512	+	8.29263i	0.621291	+	0.783580i
$113$			1.05161i			0.0989268i	0.998776	+	0.0494634i	$0.0157511\pi$
$113$			1.05161i			0.0989268i	−0.998776	+	0.0494634i	$0.984249\pi$
$114$	2.93873	−	1.59352i	0.275237	−	0.149247i
$115$	−7.46361	−	8.05931i	−0.695985	−	0.751535i
$116$	5.65114	−	8.68122i	0.524695	−	0.806031i
$117$	−4.86558	+	8.42743i	−0.449823	+	0.779116i
$118$	−5.64664	+	9.20319i	−0.519815	+	0.847222i
$119$	−2.63314	−	2.67617i	−0.241379	−	0.245324i
$120$	−0.661802	−	4.58781i	−0.0604140	−	0.418808i
$121$	−1.88052	+	3.25715i	−0.170956	+	0.296105i
$122$	0.540428	−	20.2161i	0.0489280	−	1.83028i
$123$	−0.119284	−	0.206605i	−0.0107554	−	0.0186290i
$124$	−15.2480	−	0.815817i	−1.36931	−	0.0732626i
$125$	8.76112	−	6.94570i	0.783618	−	0.621243i
$126$	−8.97880	+	2.07364i	−0.799895	+	0.184734i
$127$	−1.71773			−0.152424			−0.0762121	−	0.997092i	$-0.524283\pi$
$127$	−1.71773			−0.152424			−0.0762121	+	0.997092i	$0.524283\pi$
$128$	−3.73579	−	10.6791i	−0.330200	−	0.943911i
$129$	−5.89120	+	3.40128i	−0.518691	+	0.299466i
$130$	12.2537	−	2.44209i	1.07472	−	0.214186i
$131$	7.07173	−	12.2486i	0.617860	−	1.07016i	−0.372016	−	0.928226i	$-0.621333\pi$
$131$	7.07173	−	12.2486i	0.617860	−	1.07016i	0.989876	−	0.141938i	$-0.0453335\pi$
$132$	1.78661	+	3.51591i	0.155505	+	0.306021i
$133$	−2.27531	+	8.22439i	−0.197295	+	0.713145i
$134$	−2.23841	+	3.64827i	−0.193369	+	0.315163i
$135$	8.55239	+	2.64703i	0.736073	+	0.227820i
$136$	1.72196	+	3.62543i	0.147657	+	0.310878i
$137$	12.8787	−	7.43551i	1.10030	−	0.635259i	0.164000	−	0.986460i	$-0.447560\pi$
$137$	12.8787	−	7.43551i	1.10030	−	0.635259i	0.936300	+	0.351202i	$0.114227\pi$
$138$	−4.47593	+	2.42707i	−0.381016	+	0.206606i
$139$	−7.06762			−0.599468			−0.299734	−	0.954023i	$-0.596898\pi$
$139$	−7.06762			−0.599468			−0.299734	+	0.954023i	$0.596898\pi$
$140$	9.60573	+	6.90868i	0.811833	+	0.583890i
$141$	−4.81207			−0.405249
$142$	19.1564	−	10.3875i	1.60757	−	0.871703i
$143$	−9.20652	+	5.31538i	−0.769888	+	0.444495i
$144$	9.79516	+	1.05116i	0.816263	+	0.0875963i
$145$	3.42420	−	11.0634i	0.284365	−	0.918765i
$146$	−1.04948	+	1.71050i	−0.0868557	+	0.141562i
$147$	−2.63684	+	4.40084i	−0.217483	+	0.362975i
$148$	7.98751	−	4.05885i	0.656569	−	0.333636i
$149$	−4.39289	+	7.60870i	−0.359879	+	0.623329i	−0.987940	−	0.154835i	$-0.950515\pi$
$149$	−4.39289	+	7.60870i	−0.359879	+	0.623329i	0.628061	+	0.778164i	$0.283849\pi$
$150$	−2.11394	−	4.73168i	−0.172602	−	0.386340i
$151$	0.260095	−	0.150166i	0.0211663	−	0.0122204i	−0.489380	−	0.872071i	$-0.662777\pi$
$151$	0.260095	−	0.150166i	0.0211663	−	0.0122204i	0.510546	+	0.859851i	$0.329443\pi$
$152$	5.17936	−	7.50962i	0.420101	−	0.609110i
$153$	−3.49483			−0.282540
$154$	−9.62739	−	2.94259i	−0.775797	−	0.237121i
$155$	−16.6477	+	3.78298i	−1.33718	+	0.303856i
$156$	0.309431	−	5.78341i	0.0247743	−	0.463043i
$157$	9.61742	+	16.6579i	0.767553	+	1.32944i	0.938886	+	0.344228i	$0.111859\pi$
$157$	9.61742	+	16.6579i	0.767553	+	1.32944i	−0.171333	+	0.985213i	$0.554807\pi$
$158$	0.461544	−	17.2653i	0.0367185	−	1.37355i
$159$	−0.592155	+	1.02564i	−0.0469609	+	0.0813387i
$160$	−7.28158	−	10.3430i	−0.575659	−	0.817690i
$161$	3.46550	−	12.5264i	0.273119	−	0.987221i
$162$	−3.29424	+	5.36912i	−0.258820	+	0.421838i
$163$	5.35958	−	9.28306i	0.419795	−	0.727105i	−0.576124	−	0.817362i	$-0.695435\pi$
$163$	5.35958	−	9.28306i	0.419795	−	0.727105i	0.995919	+	0.0902569i	$0.0287688\pi$
$164$	−0.545602	−	0.355166i	−0.0426043	−	0.0277338i
$165$	2.99600	+	3.23512i	0.233238	+	0.251854i
$166$	6.54139	−	3.54706i	0.507710	−	0.275305i
$167$			13.2256i			1.02343i	0.859155	+	0.511715i	$0.170990\pi$
$167$			13.2256i			1.02343i	−0.859155	+	0.511715i	$0.829010\pi$
$168$	4.20500	−	3.52114i	0.324423	−	0.271661i
$169$	2.61180			0.200908
$170$	2.95994	+	3.37267i	0.227017	+	0.258672i
$171$	3.97171	+	6.87920i	0.303724	+	0.526065i
$172$	−10.1273	+	15.5574i	−0.772199	+	1.18624i
$173$	−5.62704	+	9.74632i	−0.427816	+	0.740999i	−0.996679	−	0.0814335i	$-0.974050\pi$
$173$	−5.62704	+	9.74632i	−0.427816	+	0.740999i	0.568863	+	0.822432i	$0.307384\pi$
$174$	−4.57563	−	2.80739i	−0.346878	−	0.212828i
$175$	12.4420	+	4.49405i	0.940527	+	0.339719i
$176$	8.69290	+	6.34483i	0.655252	+	0.478259i
$177$	4.84598	+	2.79783i	0.364246	+	0.210298i
$178$	0.179323	−	6.70806i	0.0134409	−	0.502790i
$179$	−0.697992	+	0.402986i	−0.0521703	+	0.0301206i	−0.525858	−	0.850572i	$-0.676256\pi$
$179$	−0.697992	+	0.402986i	−0.0521703	+	0.0301206i	0.473688	+	0.880693i	$0.342922\pi$
$180$	10.8554	−	1.86330i	0.809117	−	0.138882i
$181$		−	0.0667108i		−	0.00495857i	−0.999997	−	0.00247929i	$-0.999211\pi$
$181$		−	0.0667108i		−	0.00495857i	0.999997	−	0.00247929i	$-0.000789182\pi$
$182$	10.0835	+	10.8115i	0.747435	+	0.801404i
$183$	−10.4806			−0.774747
$184$	−7.88860	+	11.4378i	−0.581555	+	0.843205i
$185$	7.34961	−	6.80636i	0.540354	−	0.500414i
$186$	−0.211471	+	7.91062i	−0.0155058	+	0.580035i
$187$	−3.30641	−	1.90896i	−0.241789	−	0.139597i
$188$	−11.7067	+	5.94878i	−0.853802	+	0.433860i
$189$	2.65864	+	10.2539i	0.193388	+	0.745859i
$190$	3.27491	−	9.65920i	0.237587	−	0.700752i
$191$	−15.1210	−	8.73010i	−1.09412	−	0.631688i	−0.159446	−	0.987207i	$-0.550971\pi$
$191$	−15.1210	−	8.73010i	−1.09412	−	0.631688i	−0.934669	+	0.355519i	$0.884304\pi$
$192$	−5.48067	+	2.08325i	−0.395533	+	0.150345i
$193$	−14.8928	+	8.59835i	−1.07201	+	0.618923i	−0.928729	−	0.370760i	$-0.879097\pi$
$193$	−14.8928	+	8.59835i	−1.07201	+	0.618923i	−0.143277	+	0.989683i	$0.545764\pi$
$194$	5.62985	+	10.3824i	0.404200	+	0.745414i
$195$	−1.43485	−	6.31432i	−0.102751	−	0.452178i
$196$	−0.974468	+	13.9660i	−0.0696049	+	0.997575i
$197$		−	11.9392i		−	0.850635i	−0.905044	−	0.425318i	$-0.860162\pi$
$197$		−	11.9392i		−	0.850635i	0.905044	−	0.425318i	$-0.139838\pi$
$198$	−8.23793	+	4.46701i	−0.585445	+	0.317457i
$199$	7.76016	+	13.4410i	0.550103	+	0.952807i	0.998267	+	0.0588552i	$0.0187450\pi$
$199$	7.76016	+	13.4410i	0.550103	+	0.952807i	−0.448163	+	0.893952i	$0.647922\pi$
$200$	−10.9922	−	8.89788i	−0.777264	−	0.629175i
$201$	1.92101	+	1.10910i	0.135498	+	0.0782297i
$202$	0.336736	+	0.206605i	0.0236927	+	0.0145367i
$203$	13.2644	−	3.43922i	0.930980	−	0.241386i
$204$	1.85433	−	0.942281i	0.129829	−	0.0659728i
$205$	−0.695318	−	0.215206i	−0.0485631	−	0.0150306i
$206$	−0.506436	+	18.9445i	−0.0352850	+	1.31993i
$207$	−6.04924	−	10.4776i	−0.420452	−	0.728243i
$208$	−6.39679	−	14.4523i	−0.443538	−	1.00209i
$209$			8.67775i			0.600253i
$210$	3.44606	−	5.07200i	0.237801	−	0.350001i
$211$		−	14.1636i		−	0.975063i	−0.873105	−	0.487531i	$-0.837897\pi$
$211$		−	14.1636i		−	0.975063i	0.873105	−	0.487531i	$-0.162103\pi$
$212$	−0.172666	+	3.22720i	−0.0118588	+	0.221645i
$213$	−5.64664	−	9.78027i	−0.386901	−	0.670133i
$214$	7.67494	+	0.205171i	0.524648	+	0.0140252i
$215$	−6.13644	+	19.8265i	−0.418502	+	1.35215i
$216$	0.906994	−	11.2879i	0.0617132	−	0.768047i
$217$	−14.1674	−	14.3989i	−0.961742	−	0.977459i
$218$	−6.59488	+	10.7487i	−0.446662	+	0.727993i
$219$	0.900672	+	0.520003i	0.0608618	+	0.0351385i
$220$	11.2880	+	4.16665i	0.761035	+	0.280916i
$221$	2.80340	+	4.85563i	0.188577	+	0.326625i
$222$	−2.21334	−	4.08178i	−0.148550	−	0.273951i
$223$			3.03443i			0.203201i	0.994825	+	0.101600i	$0.0323963\pi$
$223$			3.03443i			0.203201i	−0.994825	+	0.101600i	$0.967604\pi$
$224$	5.87697	−	13.7645i	0.392672	−	0.919679i
$225$	11.1050	−	5.32171i	0.740331	−	0.354780i
$226$	1.30736	−	0.708914i	0.0869643	−	0.0471563i
$227$	12.7971	−	7.38839i	0.849371	−	0.490385i	−0.0110676	−	0.999939i	$-0.503523\pi$
$227$	12.7971	−	7.38839i	0.849371	−	0.490385i	0.860439	+	0.509554i	$0.170190\pi$
$228$	−3.96214	−	2.57920i	−0.262399	−	0.170812i
$229$	−5.56933	−	3.21545i	−0.368031	−	0.212483i	0.304567	−	0.952491i	$-0.401488\pi$
$229$	−5.56933	−	3.21545i	−0.368031	−	0.212483i	−0.672598	+	0.740008i	$0.734822\pi$
$230$	−4.98796	+	14.7118i	−0.328896	+	0.970066i
$231$	−1.39110	+	5.02829i	−0.0915277	+	0.330837i
$232$	−14.6021	−	1.17329i	−0.958675	−	0.0770303i
$233$	15.1300	+	8.73532i	0.991201	+	0.572270i	0.905633	−	0.424062i	$-0.139396\pi$
$233$	15.1300	+	8.73532i	0.991201	+	0.572270i	0.0855677	+	0.996332i	$0.472730\pi$
$234$	13.7570	+	0.367760i	0.899324	+	0.0240412i
$235$	−10.7718	+	9.97562i	−0.702676	+	0.650737i
$236$	15.2480	+	0.815817i	0.992559	+	0.0531052i
$237$	−8.95079			−0.581416
$238$	−1.55196	+	5.07760i	−0.100598	+	0.329132i
$239$		−	3.22490i		−	0.208601i	−0.994546	−	0.104301i	$-0.966740\pi$
$239$		−	3.22490i		−	0.208601i	0.994546	−	0.104301i	$-0.0332604\pi$
$240$	−5.25745	+	3.91552i	−0.339367	+	0.252745i
$241$	−17.7424	+	10.2436i	−1.14289	+	0.659848i	−0.947145	−	0.320807i	$-0.896046\pi$
$241$	−17.7424	+	10.2436i	−1.14289	+	0.659848i	−0.195745	+	0.980655i	$0.562713\pi$
$242$	5.31701	+	0.142137i	0.341790	+	0.00913692i
$243$	13.2292	+	7.63787i	0.848653	+	0.489970i
$244$	−25.4971	+	12.9563i	−1.63228	+	0.829444i
$245$	3.22055	+	15.3176i	0.205753	+	0.978604i
$246$	−0.176440	+	0.287572i	−0.0112494	+	0.0183349i
$247$	6.37185	−	11.0364i	0.405431	−	0.702227i
$248$	9.26482	+	19.5063i	0.588317	+	1.23865i
$249$	−1.92817	−	3.33969i	−0.122193	−	0.211644i
$250$	−14.5410	−	6.20958i	−0.919655	−	0.392728i
$251$	15.1647			0.957189			0.478594	−	0.878036i	$-0.341146\pi$
$251$	15.1647			0.957189			0.478594	+	0.878036i	$0.341146\pi$
$252$	8.63079	+	9.76458i	0.543689	+	0.615111i
$253$		−	13.2170i		−	0.830943i
$254$	1.15797	+	2.13549i	0.0726574	+	0.133993i
$255$	1.70624	−	1.58013i	0.106849	−	0.0989513i
$256$	−10.7579	+	11.8434i	−0.672372	+	0.740214i
$257$	2.36577	−	4.09764i	0.147573	−	0.255604i	−0.782757	−	0.622327i	$-0.786187\pi$
$257$	2.36577	−	4.09764i	0.147573	−	0.255604i	0.930330	+	0.366724i	$0.119521\pi$
$258$	8.19989	+	5.03106i	0.510503	+	0.313220i
$259$	11.4234	+	3.16032i	0.709813	+	0.196373i
$260$	−11.2966	−	13.5876i	−0.700584	−	0.842668i
$261$	6.37787	−	11.0468i	0.394780	−	0.683780i
$262$	−19.9947	−	0.534510i	−1.23528	−	0.0330221i
$263$	−2.35021	−	4.07068i	−0.144920	−	0.251009i	0.784423	−	0.620226i	$-0.212959\pi$
$263$	−2.35021	−	4.07068i	−0.144920	−	0.251009i	−0.929343	+	0.369217i	$0.879626\pi$
$264$	3.16660	−	4.59129i	0.194891	−	0.282574i
$265$	0.800660	+	3.52346i	0.0491842	+	0.216444i
$266$	11.7584	−	2.71559i	0.720956	−	0.166503i
$267$	−3.47764			−0.212828
$268$	6.04451	+	0.323401i	0.369227	+	0.0197549i
$269$	21.2532	−	12.2706i	1.29583	−	0.748149i	0.316151	−	0.948709i	$-0.397609\pi$
$269$	21.2532	−	12.2706i	1.29583	−	0.748149i	0.979682	+	0.200559i	$0.0642759\pi$
$270$	−2.47459	−	12.4168i	−0.150599	−	0.755662i
$271$	13.1957	−	22.8556i	0.801582	−	1.38838i	−0.116993	−	0.993133i	$-0.537325\pi$
$271$	13.1957	−	22.8556i	0.801582	−	1.38838i	0.918574	−	0.395248i	$-0.129341\pi$
$272$	3.34634	−	4.58474i	0.202902	−	0.277991i
$273$	5.46135	−	5.37353i	0.330536	−	0.325221i
$274$	−17.9257	−	10.9984i	−1.08293	−	0.664435i
$275$	13.4131	+	1.03099i	0.808840	+	0.0621712i
$276$	6.03468	+	3.92834i	0.363245	+	0.236458i
$277$	20.8453	−	12.0350i	1.25247	−	0.723115i	0.280872	−	0.959745i	$-0.409376\pi$
$277$	20.8453	−	12.0350i	1.25247	−	0.723115i	0.971600	+	0.236630i	$0.0760429\pi$
$278$	4.76446	+	8.78649i	0.285753	+	0.526979i
$279$	−18.8036			−1.12574
$280$	2.11343	−	16.5992i	0.126302	−	0.991992i
$281$	−7.78577			−0.464460			−0.232230	−	0.972661i	$-0.574602\pi$
$281$	−7.78577			−0.464460			−0.232230	+	0.972661i	$0.574602\pi$
$282$	3.24394	+	5.98238i	0.193174	+	0.356245i
$283$	6.88540	−	3.97529i	0.409294	−	0.236306i	−0.281192	−	0.959651i	$-0.590730\pi$
$283$	6.88540	−	3.97529i	0.409294	−	0.236306i	0.690487	+	0.723345i	$0.257396\pi$
$284$	−25.8277	−	16.8128i	−1.53259	−	0.997657i
$285$	−5.04937	−	1.56282i	−0.299099	−	0.0925734i
$286$	12.8145	+	7.86234i	0.757734	+	0.464910i
$287$	−0.216150	−	0.833649i	−0.0127589	−	0.0492088i
$288$	−5.29637	−	12.8860i	−0.312091	−	0.759314i
$289$	7.49319	−	12.9786i	0.440776	−	0.763447i
$290$	−16.0624	+	3.20113i	−0.943216	+	0.187977i
$291$	5.30071	−	3.06037i	0.310733	−	0.179402i
$292$	2.83398	+	0.151627i	0.165846	+	0.00887333i
$293$	2.11501			0.123560			0.0617801	−	0.998090i	$-0.480322\pi$
$293$	2.11501			0.123560			0.0617801	+	0.998090i	$0.480322\pi$
$294$	7.24871	+	0.311415i	0.422753	+	0.0181621i
$295$	16.6477	−	3.78298i	0.969269	−	0.220254i
$296$	−10.4306	−	7.19392i	−0.606264	−	0.418138i
$297$	5.38611	+	9.32902i	0.312534	+	0.541325i
$298$	12.4205	+	0.332032i	0.719501	+	0.0192341i
$299$	−9.70487	+	16.8093i	−0.561247	+	0.972108i
$300$	−4.45738	+	5.81780i	−0.257347	+	0.335891i
$301$	−23.7709	+	6.16335i	−1.37013	+	0.355250i
$302$	−0.362024	−	0.222121i	−0.0208321	−	0.0127816i
$303$	0.102370	−	0.177310i	0.00588100	−	0.0101862i
$304$	−12.8275	−	1.37657i	−0.735709	−	0.0789517i
$305$	−23.4608	+	21.7267i	−1.34336	+	1.24407i
$306$	2.35595	+	4.34478i	0.134681	+	0.248375i
$307$			18.6560i			1.06475i	0.846508	+	0.532376i	$0.178701\pi$
$307$			18.6560i			1.06475i	−0.846508	+	0.532376i	$0.821299\pi$
$308$	2.83183	+	13.9525i	0.161359	+	0.795016i
$309$	9.82137			0.558718
$310$	15.9257	+	18.1463i	0.904518	+	1.03064i
$311$	−4.09153	−	7.08673i	−0.232009	−	0.401852i	0.726390	−	0.687283i	$-0.241197\pi$
$311$	−4.09153	−	7.08673i	−0.232009	−	0.401852i	−0.958399	+	0.285431i	$0.907863\pi$
$312$	−7.39855	+	3.51405i	−0.418860	+	0.198944i
$313$	11.6871	−	20.2427i	0.660597	−	1.14419i	−0.319863	−	0.947464i	$-0.603637\pi$
$313$	11.6871	−	20.2427i	0.660597	−	1.14419i	0.980459	−	0.196723i	$-0.0630299\pi$
$314$	14.2258	−	23.1859i	0.802806	−	1.30846i
$315$	12.2664	+	7.86340i	0.691132	+	0.443052i
$316$	−21.7754	+	11.0652i	−1.22496	+	0.622464i
$317$	−22.6966	−	13.1039i	−1.27477	−	0.735988i	−0.298887	−	0.954288i	$-0.596615\pi$
$317$	−22.6966	−	13.1039i	−1.27477	−	0.735988i	−0.975882	+	0.218300i	$0.929949\pi$
$318$	1.67427	+	0.0447574i	0.0938883	+	0.00250987i
$319$	12.0680	−	6.96749i	0.675680	−	0.390104i
$320$	−7.94981	+	16.0250i	−0.444408	+	0.895824i
$321$		−	3.97890i		−	0.222081i
$322$	−17.9091	+	4.13607i	−0.998034	+	0.230494i
$323$	4.57675			0.254657
$324$	8.89563	+	0.475946i	0.494202	+	0.0264414i
$325$	−16.3017	−	11.1601i	−0.904258	−	0.619051i
$326$	−15.1538	−	0.405098i	−0.839289	−	0.0224363i
$327$	5.65977	+	3.26767i	0.312986	+	0.180702i
$328$	−0.0737395	+	0.917720i	−0.00407158	+	0.0506726i
$329$	−16.7424	−	4.63187i	−0.923039	−	0.255363i
$330$	2.00224	−	5.90552i	0.110220	−	0.325088i
$331$	−16.9060	−	9.76067i	−0.929237	−	0.536495i	−0.0426665	−	0.999089i	$-0.513585\pi$
$331$	−16.9060	−	9.76067i	−0.929237	−	0.536495i	−0.886570	+	0.462594i	$0.846919\pi$
$332$	−8.81943	−	5.74111i	−0.484029	−	0.315085i
$333$	9.55493	−	5.51654i	0.523607	−	0.302305i
$334$	16.4422	−	8.91574i	0.899675	−	0.487848i
$335$	6.59940	−	1.49963i	0.360564	−	0.0819333i
$336$	−7.21218	−	2.85398i	−0.393457	−	0.155697i
$337$			31.7520i			1.72964i	0.502082	+	0.864820i	$0.332567\pi$
$337$			31.7520i			1.72964i	−0.502082	+	0.864820i	$0.667433\pi$
$338$	−1.76068	−	3.24700i	−0.0957684	−	0.176614i
$339$	−0.385364	−	0.667470i	−0.0209301	−	0.0362520i
$340$	2.19754	−	5.95341i	0.119178	−	0.322869i
$341$	−17.7898	−	10.2710i	−0.963373	−	0.556204i
$342$	5.87481	−	9.57508i	0.317674	−	0.517761i
$343$	−13.4103	+	12.7736i	−0.724088	+	0.689707i
$344$	26.1681	+	2.10263i	1.41089	+	0.113366i
$345$	7.69062	+	2.38030i	0.414049	+	0.128151i
$346$	15.9100	+	0.425314i	0.855326	+	0.0228650i
$347$	−9.19210	−	15.9212i	−0.493458	−	0.854694i	0.506514	−	0.862232i	$-0.330934\pi$
$347$	−9.19210	−	15.9212i	−0.493458	−	0.854694i	−0.999972	+	0.00753782i	$0.997601\pi$
$348$	−0.405607	+	7.58097i	−0.0217428	+	0.406383i
$349$		−	2.37390i		−	0.127072i	−0.997980	−	0.0635360i	$-0.979762\pi$
$349$		−	2.37390i		−	0.127072i	0.997980	−	0.0635360i	$-0.0202378\pi$
$350$	−2.80045	−	18.4975i	−0.149690	−	0.988733i
$351$		−	15.8195i		−	0.844384i
$352$	2.02781	−	15.0843i	0.108082	−	0.803994i
$353$	−1.07710	−	1.86560i	−0.0573284	−	0.0992958i	0.835937	−	0.548826i	$-0.184925\pi$
$353$	−1.07710	−	1.86560i	−0.0573284	−	0.0992958i	−0.893265	+	0.449530i	$0.851592\pi$
$354$	0.211471	−	7.91062i	0.0112396	−	0.420445i
$355$	−32.9149	−	10.1874i	−1.74694	−	0.540692i
$356$	−8.46037	+	4.29914i	−0.448399	+	0.227854i
$357$	2.65198	+	0.733682i	0.140358	+	0.0388306i
$358$	0.971527	+	0.596083i	0.0513468	+	0.0315039i
$359$	−4.40004	−	2.54037i	−0.232225	−	0.134075i	0.379373	−	0.925244i	$-0.376140\pi$
$359$	−4.40004	−	2.54037i	−0.232225	−	0.134075i	−0.611598	+	0.791168i	$0.709473\pi$
$360$	−9.63439	−	12.2394i	−0.507777	−	0.645075i
$361$	4.29874	+	7.44564i	0.226250	+	0.391876i
$362$	−0.0829350	+	0.0449714i	−0.00435897	+	0.00236364i
$363$		−	2.75648i		−	0.144678i
$364$	6.64342	−	19.8241i	0.348210	−	1.03907i
$365$	3.09414	−	0.703103i	0.161955	−	0.0368021i
$366$	7.06523	+	13.0295i	0.369306	+	0.681063i
$367$	11.7306	−	6.77267i	0.612333	−	0.353530i	−0.161545	−	0.986865i	$-0.551648\pi$
$367$	11.7306	−	6.77267i	0.612333	−	0.353530i	0.773878	+	0.633335i	$0.218314\pi$
$368$	19.5374	+	2.09663i	1.01846	+	0.109295i
$369$	−0.694275	−	0.400840i	−0.0361425	−	0.0208669i
$370$	−13.4162	−	4.54872i	−0.697478	−	0.236476i
$371$	−3.04749	+	2.99849i	−0.158218	+	0.155674i
$372$	9.97707	−	5.06985i	0.517287	−	0.262860i
$373$	6.17822	+	3.56700i	0.319896	+	0.184692i	0.651346	−	0.758781i	$-0.274205\pi$
$373$	6.17822	+	3.56700i	0.319896	+	0.184692i	−0.331450	+	0.943473i	$0.607538\pi$
$374$	−0.144287	+	5.39742i	−0.00746089	+	0.279094i
$375$	−3.01554	+	7.61907i	−0.155722	+	0.393447i
$376$	15.2874	+	10.5436i	0.788386	+	0.543747i
$377$	−20.4642			−1.05396
$378$	10.9554	−	10.2176i	0.563484	−	0.525538i
$379$			16.2436i			0.834379i	0.908820	+	0.417189i	$0.136985\pi$
$379$			16.2436i			0.834379i	−0.908820	+	0.417189i	$0.863015\pi$
$380$	−14.2160	+	2.44014i	−0.729268	+	0.125176i
$381$	1.09027	−	0.629468i	0.0558562	−	0.0322486i
$382$	−0.659856	+	24.6836i	−0.0337612	+	1.26292i
$383$	−8.56254	−	4.94358i	−0.437525	−	0.252605i	0.265022	−	0.964242i	$-0.414621\pi$
$383$	−8.56254	−	4.94358i	−0.437525	−	0.252605i	−0.702547	+	0.711637i	$0.747954\pi$
$384$	6.28456	+	5.40921i	0.320707	+	0.276038i
$385$	7.30988	+	14.1396i	0.372546	+	0.720623i
$386$	20.7291	+	12.7184i	1.05508	+	0.647349i
$387$	−11.4296	+	19.7967i	−0.581002	+	1.00632i
$388$	9.11222	−	13.9981i	0.462603	−	0.710645i
$389$	15.9811	+	27.6802i	0.810276	+	1.40344i	0.912671	+	0.408696i	$0.134016\pi$
$389$	15.9811	+	27.6802i	0.810276	+	1.40344i	−0.102395	+	0.994744i	$0.532650\pi$
$390$	−6.88272	+	6.04045i	−0.348520	+	0.305870i
$391$	−6.97078			−0.352527
$392$	18.0195	−	8.20340i	0.910125	−	0.414334i
$393$			10.3658i			0.522886i
$394$	−14.8429	+	8.04854i	−0.747774	+	0.405480i
$395$	−20.0363	+	18.5554i	−1.00814	+	0.933621i
$396$	11.1068	+	7.23011i	0.558138	+	0.363326i
$397$	−8.73784	+	15.1344i	−0.438539	+	0.759573i	−0.997577	−	0.0695697i	$-0.977837\pi$
$397$	−8.73784	+	15.1344i	−0.438539	+	0.759573i	0.559038	+	0.829142i	$0.311171\pi$
$398$	11.4786	−	18.7084i	0.575369	−	0.937766i
$399$	−1.56967	−	6.05393i	−0.0785819	−	0.303076i
$400$	−3.65177	+	19.6638i	−0.182588	+	0.983189i
$401$	8.67926	−	15.0329i	0.433422	−	0.750708i	−0.563744	−	0.825950i	$-0.690639\pi$
$401$	8.67926	−	15.0329i	0.433422	−	0.750708i	0.997165	+	0.0752415i	$0.0239728\pi$
$402$	0.0838301	−	3.13588i	0.00418106	−	0.156404i
$403$	15.0834	+	26.1252i	0.751358	+	1.30139i
$404$	0.0298500	−	0.557909i	0.00148509	−	0.0277570i
$405$	9.71225	−	2.20698i	0.482606	−	0.109666i
$406$	−13.2175	−	14.1719i	−0.655975	−	0.703340i
$407$	12.0531			0.597448
$408$	−2.42150	−	1.67010i	−0.119882	−	0.0826823i
$409$	6.32187	−	3.64993i	0.312596	−	0.180478i	−0.335491	−	0.942043i	$-0.608902\pi$
$409$	6.32187	−	3.64993i	0.312596	−	0.180478i	0.648088	+	0.761566i	$0.275569\pi$
$410$	0.201186	+	1.00950i	0.00993589	+	0.0498555i
$411$	−5.44952	+	9.43885i	−0.268805	+	0.465584i
$412$	23.8933	−	12.1414i	1.17714	−	0.598164i
$413$	14.1674	+	14.3989i	0.697130	+	0.708522i
$414$	−8.94784	+	14.5837i	−0.439762	+	0.716748i
$415$	−11.2395	−	3.47872i	−0.551727	−	0.170764i
$416$	−13.6549	+	17.6952i	−0.669489	+	0.867578i
$417$	4.48592	−	2.58995i	0.219677	−	0.126830i
$418$	10.7882	−	5.84989i	0.527669	−	0.286128i
$419$	17.9278			0.875831			0.437915	−	0.899016i	$-0.355717\pi$
$419$	17.9278			0.875831			0.437915	+	0.899016i	$0.355717\pi$
$420$	−8.62860	−	0.864996i	−0.421033	−	0.0422075i
$421$	12.6334			0.615716			0.307858	−	0.951432i	$-0.400388\pi$
$421$	12.6334			0.615716			0.307858	+	0.951432i	$0.400388\pi$
$422$	−17.6082	+	9.54805i	−0.857156	+	0.464792i
$423$	−14.0040	+	8.08522i	−0.680898	+	0.393117i
$424$	4.12847	−	1.96088i	0.200496	−	0.0952288i
$425$	0.543758	−	7.07422i	0.0263761	−	0.343150i
$426$	−8.35232	+	13.6130i	−0.404671	+	0.659554i
$427$	−36.4647	−	10.0881i	−1.76465	−	0.488198i
$428$	−4.91881	−	9.67983i	−0.237759	−	0.467892i
$429$	3.89567	−	6.74750i	0.188085	−	0.325773i
$430$	28.7851	−	5.73668i	1.38814	−	0.276647i
$431$	28.2962	−	16.3368i	1.36298	−	0.786918i	0.372962	−	0.927847i	$-0.378342\pi$
$431$	28.2962	−	16.3368i	1.36298	−	0.786918i	0.990020	+	0.140929i	$0.0450090\pi$
$432$	−14.6446	+	6.48191i	−0.704590	+	0.311861i
$433$	23.5884			1.13359			0.566794	−	0.823860i	$-0.308184\pi$
$433$	23.5884			1.13359			0.566794	+	0.823860i	$0.308184\pi$
$434$	−8.35015	+	27.3195i	−0.400820	+	1.31138i
$435$	1.88082	+	8.27690i	0.0901783	+	0.396847i
$436$	17.8086	+	0.952818i	0.852877	+	0.0456317i
$437$	7.92195	+	13.7212i	0.378958	+	0.656375i
$438$	0.0393039	−	1.47027i	0.00187801	−	0.0702520i
$439$	−9.19501	+	15.9262i	−0.438854	+	0.760117i	−0.997601	−	0.0692207i	$-0.977949\pi$
$439$	−9.19501	+	15.9262i	−0.438854	+	0.760117i	0.558748	+	0.829338i	$0.311282\pi$
$440$	−2.42951	−	16.8421i	−0.115822	−	0.802915i
$441$	−0.279428	+	17.2377i	−0.0133061	+	0.820842i
$442$	4.14669	−	6.75849i	0.197238	−	0.321469i
$443$	−1.69217	+	2.93092i	−0.0803973	+	0.139252i	−0.903421	−	0.428755i	$-0.858952\pi$
$443$	−1.69217	+	2.93092i	−0.0803973	+	0.139252i	0.823023	+	0.568008i	$0.192286\pi$
$444$	−3.58241	+	5.50326i	−0.170014	+	0.261173i
$445$	−7.78470	+	7.20929i	−0.369030	+	0.341753i
$446$	3.77242	−	2.04559i	0.178629	−	0.0968614i
$447$		−	6.43914i		−	0.304561i
$448$	−21.0739	+	1.97272i	−0.995647	+	0.0932025i
$449$	−11.9013			−0.561658			−0.280829	−	0.959758i	$-0.590609\pi$
$449$	−11.9013			−0.561658			−0.280829	+	0.959758i	$0.590609\pi$
$450$	−14.1021	−	10.2182i	−0.664779	−	0.481692i
$451$	−0.437896	−	0.758458i	−0.0206197	−	0.0357144i
$452$	−1.76265	−	1.14742i	−0.0829081	−	0.0539700i
$453$	−0.110058	+	0.190625i	−0.00517096	+	0.00895636i
$454$	−17.8121	−	10.9287i	−0.835963	−	0.512907i
$455$	1.08567	−	23.3503i	0.0508968	−	1.09468i
$456$	−0.535494	+	6.66445i	−0.0250768	+	0.312092i
$457$	18.2475	+	10.5352i	0.853582	+	0.492816i	0.861858	−	0.507150i	$-0.169301\pi$
$457$	18.2475	+	10.5352i	0.853582	+	0.492816i	−0.00827601	+	0.999966i	$0.502634\pi$
$458$	−0.243037	+	9.09142i	−0.0113564	+	0.424814i
$459$	4.92023	−	2.84070i	0.229657	−	0.132592i
$460$	21.6522	−	3.71653i	1.00954	−	0.173284i
$461$			29.6708i			1.38191i	0.722899	+	0.690954i	$0.242809\pi$
$461$			29.6708i			1.38191i	−0.722899	+	0.690954i	$0.757191\pi$
$462$	7.18897	−	1.66028i	0.334461	−	0.0772432i
$463$	−15.0481			−0.699342			−0.349671	−	0.936873i	$-0.613707\pi$
$463$	−15.0481			−0.699342			−0.349671	+	0.936873i	$0.613707\pi$
$464$	8.38501	+	18.9443i	0.389264	+	0.879468i
$465$	9.18028	−	8.50172i	0.425725	−	0.394258i
$466$	0.660251	−	24.6984i	0.0305855	−	1.14413i
$467$	4.45656	+	2.57299i	0.206225	+	0.119064i	0.599556	−	0.800333i	$-0.295344\pi$
$467$	4.45656	+	2.57299i	0.206225	+	0.119064i	−0.393331	+	0.919397i	$0.628677\pi$
$468$	−8.81676	−	17.3507i	−0.407555	−	0.802036i
$469$	5.61614	+	5.70791i	0.259329	+	0.263567i
$470$	19.6633	+	6.66674i	0.906999	+	0.307514i
$471$	−12.2086	−	7.04865i	−0.562544	−	0.324785i
$472$	−9.26482	−	19.5063i	−0.426448	−	0.897850i
$473$	−21.6269	+	12.4863i	−0.994405	+	0.574120i
$474$	6.03395	+	11.1277i	0.277149	+	0.511110i
$475$	−14.5428	+	6.96919i	−0.667270	+	0.319768i
$476$	7.35870	−	1.49354i	0.337286	−	0.0684564i
$477$			3.97974i			0.182220i
$478$	−4.00921	+	2.17399i	−0.183377	+	0.0994358i
$479$	−19.9783	−	34.6035i	−0.912834	−	1.58107i	−0.810042	−	0.586372i	$-0.800556\pi$
$479$	−19.9783	−	34.6035i	−0.912834	−	1.58107i	−0.102792	−	0.994703i	$-0.532778\pi$
$480$	8.41196	+	3.89653i	0.383952	+	0.177851i
$481$	−15.3291	−	8.85025i	−0.698946	−	0.403537i
$482$	24.6955	+	15.1520i	1.12485	+	0.690153i
$483$	2.39074	+	9.22065i	0.108783	+	0.419554i
$484$	−3.40763	−	6.70594i	−0.154892	−	0.304816i
$485$	5.52138	−	17.8392i	0.250713	−	0.810038i
$486$	0.577301	−	21.5955i	0.0261869	−	0.979590i
$487$	6.11246	+	10.5871i	0.276982	+	0.479747i	0.970633	−	0.240564i	$-0.0773325\pi$
$487$	6.11246	+	10.5871i	0.276982	+	0.479747i	−0.693651	+	0.720311i	$0.743999\pi$
$488$	33.2956	+	22.9638i	1.50722	+	1.03952i
$489$			7.85613i			0.355266i
$490$	16.8718	−	14.3298i	0.762190	−	0.647353i
$491$			22.9515i			1.03579i	0.855445	+	0.517894i	$0.173284\pi$
$491$			22.9515i			1.03579i	−0.855445	+	0.517894i	$0.826716\pi$
$492$	0.476453	+	0.0254918i	0.0214802	+	0.00114926i
$493$	−3.67473	−	6.36483i	−0.165502	−	0.286657i
$494$	−18.0159	−	0.481610i	−0.810573	−	0.0216687i
$495$	14.1546	+	4.38094i	0.636200	+	0.196909i
$496$	18.0047	−	24.6678i	0.808433	−	1.10762i
$497$	−10.2321	−	39.4632i	−0.458972	−	1.77017i
$498$	−2.85209	+	4.64848i	−0.127805	+	0.208303i
$499$	3.64376	+	2.10372i	0.163117	+	0.0941756i	0.579336	−	0.815089i	$-0.303312\pi$
$499$	3.64376	+	2.10372i	0.163117	+	0.0941756i	−0.416219	+	0.909264i	$0.636645\pi$
$500$	2.08270	+	22.2635i	0.0931411	+	0.995653i
$501$	−4.84657	−	8.39451i	−0.216529	−	0.375039i
$502$	−10.2229	−	18.8528i	−0.456272	−	0.841443i
$503$		−	43.1904i		−	1.92576i	−0.269924	−	0.962882i	$-0.586999\pi$
$503$		−	43.1904i		−	1.92576i	0.269924	−	0.962882i	$-0.413001\pi$
$504$	6.32113	−	17.3124i	0.281565	−	0.771155i
$505$	−0.138416	−	0.609125i	−0.00615942	−	0.0271057i
$506$	−16.4314	+	8.90988i	−0.730463	+	0.396093i
$507$	−1.65775	+	0.957101i	−0.0736232	+	0.0425064i
$508$	1.87424	−	2.87918i	0.0831558	−	0.127743i
$509$	−32.3532	−	18.6791i	−1.43403	−	0.827937i	−0.436604	−	0.899654i	$-0.643819\pi$
$509$	−32.3532	−	18.6791i	−1.43403	−	0.827937i	−0.997425	+	0.0717169i	$0.977152\pi$
$510$	−3.11464	−	1.05600i	−0.137919	−	0.0467606i
$511$	2.63314	+	2.67617i	0.116483	+	0.118387i
$512$	21.9760	+	5.39037i	0.971211	+	0.238223i
$513$	−11.1832	−	6.45664i	−0.493751	−	0.285067i
$514$	−6.68903	−	0.178815i	−0.295040	−	0.00788717i
$515$	21.9851	−	20.3601i	0.968781	−	0.897174i
$516$	0.726880	−	13.5857i	0.0319991	−	0.598077i
$517$	−17.6653			−0.776921
$518$	−3.77185	−	16.3320i	−0.165725	−	0.717587i
$519$		−	8.24817i		−	0.362055i
$520$	−9.27686	+	23.2037i	−0.406817	+	1.01755i
$521$	13.9610	−	8.06040i	0.611643	−	0.353132i	−0.161965	−	0.986796i	$-0.551783\pi$
$521$	13.9610	−	8.06040i	0.611643	−	0.353132i	0.773608	+	0.633664i	$0.218450\pi$
$522$	−18.0329	−	0.482065i	−0.789279	−	0.0210994i
$523$	13.8279	+	7.98356i	0.604653	+	0.349097i	0.770870	−	0.636993i	$-0.219822\pi$
$523$	13.8279	+	7.98356i	0.604653	+	0.349097i	−0.166217	+	0.986089i	$0.553155\pi$
$524$	12.8145	+	25.2178i	0.559802	+	1.10165i
$525$	−9.54398	+	1.70696i	−0.416533	+	0.0744980i
$526$	−3.47635	+	5.66594i	−0.151576	+	0.247047i
$527$	−5.41703	+	9.38257i	−0.235969	+	0.408711i
$528$	−7.84259	−	0.841618i	−0.341305	−	0.0366267i
$529$	−0.565805	−	0.980002i	−0.0246002	−	0.0426088i
$530$	3.84063	−	3.37064i	0.166826	−	0.146411i
$531$	18.8036			0.816007
$532$	−11.3027	−	12.7875i	−0.490034	−	0.554407i
$533$			1.28614i			0.0557090i
$534$	2.34437	+	4.32342i	0.101451	+	0.187092i
$535$	−8.24843	−	8.90677i	−0.356611	−	0.385073i
$536$	−3.67271	−	7.73257i	−0.158637	−	0.333996i
$537$	0.295350	−	0.511562i	0.0127453	−	0.0220755i
$538$	−29.5822	−	18.1502i	−1.27538	−	0.782511i
$539$	−9.67999	+	16.1557i	−0.416947	+	0.695876i
$540$	−13.7684	+	11.4469i	−0.592498	+	0.492596i
$541$	7.31686	−	12.6732i	0.314576	−	0.544862i	−0.664771	−	0.747047i	$-0.731471\pi$
$541$	7.31686	−	12.6732i	0.314576	−	0.544862i	0.979347	+	0.202185i	$0.0648042\pi$
$542$	−37.3098	−	0.997384i	−1.60259	−	0.0428413i
$543$	0.0244463	+	0.0423423i	0.00104909	+	0.00181708i
$544$	−7.95562	−	1.06949i	−0.341094	−	0.0458540i
$545$	19.4434	−	4.41826i	0.832864	−	0.189257i
$546$	−10.3620	−	3.16713i	−0.443454	−	0.135541i
$547$	16.5936			0.709493			0.354747	−	0.934963i	$-0.384567\pi$
$547$	16.5936			0.709493			0.354747	+	0.934963i	$0.384567\pi$
$548$	−1.58902	+	29.6996i	−0.0678798	+	1.26870i
$549$	−30.5005	+	17.6094i	−1.30173	+	0.751553i
$550$	−7.76037	−	17.3702i	−0.330903	−	0.740669i
$551$	−8.35232	+	14.4666i	−0.355821	+	0.616300i
$552$	0.815602	−	10.1505i	0.0347143	−	0.432035i
$553$	−31.1421	−	8.61560i	−1.32430	−	0.366373i
$554$	−29.0143	−	17.8018i	−1.23270	−	0.756327i
$555$	−2.17069	+	7.01338i	−0.0921408	+	0.297701i
$556$	7.71155	−	11.8464i	0.327043	−	0.502399i
$557$	21.4562	−	12.3878i	0.909129	−	0.524886i	0.0289782	−	0.999580i	$-0.490775\pi$
$557$	21.4562	−	12.3878i	0.909129	−	0.524886i	0.880151	+	0.474694i	$0.157441\pi$
$558$	12.6760	+	23.3767i	0.536617	+	0.989615i
$559$	36.6734			1.55112
$560$	−22.0609	+	8.56252i	−0.932243	+	0.361832i
$561$	2.79817			0.118139
$562$	5.24859	+	9.67930i	0.221398	+	0.408296i
$563$	20.7434	−	11.9762i	0.874230	−	0.504737i	0.00547814	−	0.999985i	$-0.498256\pi$
$563$	20.7434	−	11.9762i	0.874230	−	0.504737i	0.868751	+	0.495248i	$0.164923\pi$
$564$	5.25049	−	8.06575i	0.221086	−	0.339629i
$565$	−2.24633	−	0.695256i	−0.0945038	−	0.0292496i
$566$	−9.58371	−	5.88011i	−0.402833	−	0.247159i
$567$	8.26520	+	8.40027i	0.347106	+	0.352778i
$568$	−3.49068	+	43.4430i	−0.146466	+	1.82283i
$569$	−4.58078	+	7.93415i	−0.192036	+	0.332617i	−0.945925	−	0.324385i	$-0.894843\pi$
$569$	−4.58078	+	7.93415i	−0.192036	+	0.332617i	0.753889	+	0.657002i	$0.228176\pi$
$570$	1.46101	+	7.33093i	0.0611949	+	0.307059i
$571$	−21.4132	+	12.3629i	−0.896114	+	0.517372i	−0.875938	−	0.482425i	$-0.839756\pi$
$571$	−21.4132	+	12.3629i	−0.896114	+	0.517372i	−0.0201768	+	0.999796i	$0.506423\pi$
$572$	1.13594	−	21.2312i	0.0474959	−	0.887720i
$573$	12.7967			0.534589
$574$	−0.890684	+	0.830703i	−0.0371764	+	0.0346729i
$575$	22.1499	−	10.6147i	0.923716	−	0.442662i
$576$	−12.4495	+	15.2712i	−0.518729	+	0.636301i
$577$	4.75184	+	8.23042i	0.197822	+	0.342637i	0.947822	−	0.318801i	$-0.103280\pi$
$577$	4.75184	+	8.23042i	0.197822	+	0.342637i	−0.750000	+	0.661438i	$0.769947\pi$
$578$	−21.1864	−	0.566366i	−0.881237	−	0.0235577i
$579$	6.30178	−	10.9150i	0.261893	−	0.453612i
$580$	14.8077	+	17.8109i	0.614857	+	0.739555i
$581$	−3.49398	−	13.4756i	−0.144955	−	0.559062i
$582$	−7.37801	−	4.52679i	−0.305828	−	0.187642i
$583$	−2.17383	+	3.76518i	−0.0900308	+	0.155938i
$584$	−1.72196	−	3.62543i	−0.0712551	−	0.150022i
$585$	−14.7850	−	15.9650i	−0.611283	−	0.660072i
$586$	−1.42578	−	2.62939i	−0.0588985	−	0.108619i
$587$		−	14.2100i		−	0.586508i	−0.956035	−	0.293254i	$-0.905262\pi$
$587$		−	14.2100i		−	0.586508i	0.956035	−	0.293254i	$-0.0947382\pi$
$588$	−4.49938	−	9.22155i	−0.185552	−	0.380290i
$589$	24.6248			1.01465
$590$	−15.9257	−	18.1463i	−0.655650	−	0.747072i
$591$	4.37516	+	7.57801i	0.179970	+	0.311717i
$592$	−1.91200	+	17.8169i	−0.0785828	+	0.732271i
$593$	8.87854	−	15.3781i	0.364598	−	0.631502i	−0.624114	−	0.781334i	$-0.714540\pi$
$593$	8.87854	−	15.3781i	0.364598	−	0.631502i	0.988712	+	0.149831i	$0.0478731\pi$
$594$	7.96695	−	12.9850i	0.326888	−	0.532779i
$595$	7.45741	−	3.85532i	0.305724	−	0.158053i
$596$	−7.96020	−	15.6651i	−0.326063	−	0.641666i
$597$	−9.85098	−	5.68746i	−0.403174	−	0.232772i
$598$	27.4397	+	0.733533i	1.12209	+	0.0299964i
$599$	−18.1537	+	10.4811i	−0.741741	+	0.428244i	−0.822702	−	0.568473i	$-0.807534\pi$
$599$	−18.1537	+	10.4811i	−0.741741	+	0.428244i	0.0809612	+	0.996717i	$0.474201\pi$
$600$	10.2375	+	1.61950i	0.417946	+	0.0661159i
$601$		−	20.7196i		−	0.845169i	−0.906324	−	0.422585i	$-0.861123\pi$
$601$		−	20.7196i		−	0.845169i	0.906324	−	0.422585i	$-0.138877\pi$
$602$	23.6869	+	25.3972i	0.965405	+	1.03511i
$603$	7.45401			0.303551
$604$	−0.0320917	+	0.599807i	−0.00130579	+	0.0244058i
$605$	−5.71430	−	6.17039i	−0.232320	−	0.250862i
$606$	−0.289442	−	0.00773753i	−0.0117578	−	0.000314316i
$607$	2.77584	+	1.60263i	0.112668	+	0.0650487i	0.555275	−	0.831667i	$-0.312613\pi$
$607$	2.77584	+	1.60263i	0.112668	+	0.0650487i	−0.442607	+	0.896716i	$0.645946\pi$
$608$	6.93600	+	16.8752i	0.281292	+	0.684380i
$609$	−7.15881	+	7.04371i	−0.290090	+	0.285425i
$610$	42.8262	+	14.5200i	1.73398	+	0.587899i
$611$	22.4668	+	12.9712i	0.908909	+	0.524759i
$612$	3.81324	−	5.85786i	0.154141	−	0.236790i
$613$	−4.15308	+	2.39778i	−0.167741	+	0.0968454i	−0.581520	−	0.813532i	$-0.697542\pi$
$613$	−4.15308	+	2.39778i	−0.167741	+	0.0968454i	0.413779	+	0.910377i	$0.364209\pi$
$614$	23.1932	−	12.5765i	0.936000	−	0.507545i
$615$	0.520191	−	0.118207i	0.0209761	−	0.00476655i
$616$	15.4368	−	12.9263i	0.621965	−	0.520814i
$617$		−	8.95961i		−	0.360700i	−0.983602	−	0.180350i	$-0.942277\pi$
$617$		−	8.95961i		−	0.360700i	0.983602	−	0.180350i	$-0.0577231\pi$
$618$	−6.62084	−	12.2100i	−0.266329	−	0.491157i
$619$	12.8347	+	22.2303i	0.515868	+	0.893510i	0.999830	+	0.0184212i	$0.00586397\pi$
$619$	12.8347	+	22.2303i	0.515868	+	0.893510i	−0.483962	+	0.875089i	$0.660803\pi$
$620$	11.8237	−	32.0318i	0.474850	−	1.28643i
$621$	17.0330	+	9.83400i	0.683510	+	0.394625i
$622$	−6.05205	+	9.86394i	−0.242665	+	0.395508i
$623$	−12.0996	−	3.34741i	−0.484761	−	0.134111i
$624$	9.35623	+	6.82898i	0.374549	+	0.273378i
$625$	9.04437	+	23.3066i	0.361775	+	0.932265i
$626$	−33.0444	−	0.883361i	−1.32072	−	0.0353062i
$627$	−3.17999	−	5.50790i	−0.126996	−	0.219964i
$628$	−38.4147	−	2.05531i	−1.53291	−	0.0820160i
$629$		−	6.35693i		−	0.253467i
$630$	1.50673	−	20.5505i	0.0600297	−	0.818752i
$631$		−	1.75095i		−	0.0697043i	−0.999392	−	0.0348521i	$-0.988904\pi$
$631$		−	1.75095i		−	0.0697043i	0.999392	−	0.0348521i	$-0.0110960\pi$
$632$	28.4356	+	19.6119i	1.13111	+	0.780120i
$633$	5.19029	+	8.98985i	0.206296	+	0.357314i
$634$	−0.990445	+	37.0502i	−0.0393356	+	1.47145i
$635$	1.13566	−	3.66924i	0.0450672	−	0.145609i
$636$	−1.07302	−	2.11163i	−0.0425482	−	0.0837315i
$637$	24.1737	−	13.4391i	0.957798	−	0.532475i
$638$	−16.7974	−	10.3061i	−0.665014	−	0.408021i
$639$	−32.8655	−	18.9749i	−1.30014	−	0.750636i
$640$	25.2815	−	0.919623i	0.999339	−	0.0363513i
$641$	20.3887	+	35.3143i	0.805306	+	1.39483i	0.916084	+	0.400986i	$0.131332\pi$
$641$	20.3887	+	35.3143i	0.805306	+	1.39483i	−0.110778	+	0.993845i	$0.535334\pi$
$642$	−4.94658	+	2.68228i	−0.195226	+	0.105861i
$643$		−	35.0077i		−	1.38057i	−0.723538	−	0.690285i	$-0.757485\pi$
$643$		−	35.0077i		−	1.38057i	0.723538	−	0.690285i	$-0.242515\pi$
$644$	17.2150	+	19.4764i	0.678364	+	0.767478i
$645$	−3.37057	−	14.8329i	−0.132716	−	0.584043i
$646$	−3.08530	−	5.68983i	−0.121390	−	0.223863i
$647$	20.9951	−	12.1215i	0.825404	−	0.476547i	−0.0268724	−	0.999639i	$-0.508555\pi$
$647$	20.9951	−	12.1215i	0.825404	−	0.476547i	0.852276	+	0.523092i	$0.175221\pi$
$648$	−5.40508	−	11.3799i	−0.212331	−	0.447046i
$649$	17.7898	+	10.2710i	0.698312	+	0.403171i
$650$	−2.88486	+	27.7897i	−0.113154	+	1.09000i
$651$	14.2687	+	3.94751i	0.559236	+	0.154715i
$652$	9.71192	+	19.1123i	0.380348	+	0.748495i
$653$	−37.4046	−	21.5956i	−1.46376	−	0.845100i	−0.464574	−	0.885534i	$-0.653792\pi$
$653$	−37.4046	−	21.5956i	−1.46376	−	0.845100i	−0.999182	+	0.0404346i	$0.987126\pi$
$654$	0.246984	−	9.23906i	0.00965782	−	0.361276i
$655$	21.4888	+	23.2039i	0.839636	+	0.906651i
$656$	1.19062	−	0.526985i	0.0464860	−	0.0205753i
$657$	3.49483			0.136346
$658$	5.52814	+	23.9367i	0.215509	+	0.933150i
$659$		−	11.6398i		−	0.453422i	−0.973962	−	0.226711i	$-0.927203\pi$
$659$		−	11.6398i		−	0.453422i	0.973962	−	0.226711i	$-0.0727973\pi$
$660$	−8.69152	+	1.49187i	−0.338317	+	0.0580710i
$661$	14.8021	−	8.54599i	0.575735	−	0.332400i	−0.183702	−	0.982982i	$-0.558808\pi$
$661$	14.8021	−	8.54599i	0.575735	−	0.332400i	0.759436	+	0.650582i	$0.225475\pi$
$662$	−0.737751	+	27.5975i	−0.0286735	+	1.07261i
$663$	−3.55871	−	2.05462i	−0.138209	−	0.0797950i
$664$	−1.19197	+	14.8346i	−0.0462574	+	0.575693i
$665$	−16.0638	−	10.2977i	−0.622926	−	0.399329i
$666$	−13.2994	−	8.15989i	−0.515342	−	0.316189i
$667$	12.7213	−	22.0339i	0.492570	−	0.853157i
$668$	−22.1682	−	14.4306i	−0.857712	−	0.558338i
$669$	−1.11198	−	1.92600i	−0.0429915	−	0.0744634i
$670$	−6.31316	−	7.19346i	−0.243899	−	0.277907i
$671$	−38.4748			−1.48530
$672$	1.31384	+	10.8902i	0.0506823	+	0.420097i
$673$			3.77972i			0.145697i	0.997343	+	0.0728487i	$0.0232090\pi$
$673$			3.77972i			0.145697i	−0.997343	+	0.0728487i	$0.976791\pi$
$674$	39.4742	−	21.4048i	1.52049	−	0.824482i
$675$	−11.3086	+	16.5187i	−0.435268	+	0.635803i
$676$	−2.84976	+	4.37777i	−0.109606	+	0.168376i
$677$	−13.8872	+	24.0534i	−0.533729	+	0.924446i	0.465494	+	0.885051i	$0.345877\pi$
$677$	−13.8872	+	24.0534i	−0.533729	+	0.924446i	−0.999224	+	0.0393956i	$0.987457\pi$
$678$	−0.570017	+	0.929044i	−0.0218914	+	0.0356797i
$679$	21.3883	−	5.54559i	0.820808	−	0.212820i
$680$	−8.88272	+	1.28135i	−0.340637	+	0.0491376i
$681$	−5.41499	+	9.37904i	−0.207503	+	0.359405i
$682$	−0.776321	+	29.0403i	−0.0297269	+	1.11201i
$683$	5.58652	+	9.67614i	0.213762	+	0.370247i	0.952889	−	0.303319i	$-0.0980948\pi$
$683$	5.58652	+	9.67614i	0.213762	+	0.370247i	−0.739127	+	0.673567i	$0.764761\pi$
$684$	−15.8641	−	0.848783i	−0.606580	−	0.0324540i
$685$	7.36837	+	32.4260i	0.281531	+	1.23893i
$686$	24.9204	+	8.06075i	0.951464	+	0.307761i
$687$	4.71324			0.179821
$688$	−15.0266	−	33.9497i	−0.572884	−	1.29432i
$689$	5.52935	−	3.19237i	0.210652	−	0.121620i
$690$	−2.22524	−	11.1656i	−0.0847134	−	0.425068i
$691$	−17.7057	+	30.6672i	−0.673556	+	1.16663i	0.303332	+	0.952885i	$0.401901\pi$
$691$	−17.7057	+	30.6672i	−0.673556	+	1.16663i	−0.976889	+	0.213749i	$0.931433\pi$
$692$	−10.1966	−	20.0661i	−0.387616	−	0.762797i
$693$	4.40016	+	16.9706i	0.167148	+	0.644659i
$694$	−13.5966	+	22.1605i	−0.516122	+	0.841202i
$695$	4.67267	−	15.0971i	0.177244	−	0.572666i
$696$	9.69812	−	4.60627i	0.367606	−	0.174600i
$697$	−0.400020	+	0.230952i	−0.0151518	+	0.00874791i
$698$	−2.95124	+	1.60031i	−0.111706	+	0.0605725i
$699$	−12.8043			−0.484304
$700$	−21.1083	+	15.9512i	−0.797819	+	0.602897i
$701$	2.24955			0.0849643			0.0424821	−	0.999097i	$-0.486473\pi$
$701$	2.24955			0.0849643			0.0424821	+	0.999097i	$0.486473\pi$
$702$	−19.6669	+	10.6643i	−0.742279	+	0.402500i
$703$	−12.5129	+	7.22434i	−0.471934	+	0.272471i
$704$	−20.1198	+	7.64771i	−0.758293	+	0.288234i
$705$	3.18144	−	10.2790i	0.119820	−	0.387131i
$706$	−1.59321	+	2.59671i	−0.0599614	+	0.0977283i
$707$	0.526841	−	0.518370i	0.0198139	−	0.0194953i
$708$	−9.97707	+	5.06985i	−0.374961	+	0.190537i
$709$	7.94601	−	13.7629i	0.298418	−	0.516876i	−0.677356	−	0.735656i	$-0.736874\pi$
$709$	7.94601	−	13.7629i	0.298418	−	0.516876i	0.975774	+	0.218780i	$0.0702076\pi$
$710$	9.52375	+	47.7875i	0.357420	+	1.79343i
$711$	−26.0485	+	15.0391i	−0.976893	+	0.564010i
$712$	11.0480	+	7.61980i	0.414043	+	0.285564i
$713$	−37.5056			−1.40460
$714$	−0.875651	−	3.79154i	−0.0327704	−	0.141895i
$715$	−5.26739	−	23.1802i	−0.196989	−	0.866890i
$716$	0.0861211	−	1.60964i	0.00321850	−	0.0601551i
$717$	1.18177	+	2.04689i	0.0441341	+	0.0764425i
$718$	−0.192011	+	7.18267i	−0.00716579	+	0.268055i
$719$	18.0142	−	31.2015i	0.671817	−	1.16362i	−0.305572	−	0.952169i	$-0.598848\pi$
$719$	18.0142	−	31.2015i	0.671817	−	1.16362i	0.977388	−	0.211452i	$-0.0678191\pi$
$720$	−8.72131	+	20.2284i	−0.325024	+	0.753869i
$721$	34.1711	+	9.45359i	1.27260	+	0.352070i
$722$	6.35856	−	10.3635i	0.236641	−	0.385690i
$723$	7.50758	−	13.0035i	0.279210	−	0.483606i
$724$	0.111817	+	0.0727888i	0.00415565	+	0.00270517i
$725$	21.3686	+	14.6288i	0.793609	+	0.543301i
$726$	−3.42687	+	1.85822i	−0.127183	+	0.0689648i
$727$			51.4779i			1.90921i	0.297878	+	0.954604i	$0.403721\pi$
$727$			51.4779i			1.90921i	−0.297878	+	0.954604i	$0.596279\pi$
$728$	−29.1239	+	5.10481i	−1.07940	+	0.189197i
$729$	2.16686			0.0802541
$730$	−2.95994	−	3.37267i	−0.109552	−	0.124828i
$731$	6.58541	+	11.4063i	0.243570	+	0.421876i
$732$	11.4355	−	17.5670i	0.422667	−	0.649296i
$733$	−17.9717	+	31.1280i	−0.663801	+	1.14974i	0.315807	+	0.948823i	$0.397725\pi$
$733$	−17.9717	+	31.1280i	−0.663801	+	1.14974i	−0.979609	+	0.200914i	$0.935609\pi$
$734$	−16.3277	−	10.0179i	−0.602667	−	0.369768i
$735$	−7.65730	−	8.54211i	−0.282444	−	0.315080i
$736$	−10.5641	−	25.7024i	−0.389398	−	0.947401i
$737$	7.05214	+	4.07155i	0.259769	+	0.149978i
$738$	−0.0302971	+	1.13334i	−0.00111525	+	0.0417189i
$739$	−15.7903	+	9.11653i	−0.580855	+	0.335357i	−0.761473	−	0.648196i	$-0.775524\pi$
$739$	−15.7903	+	9.11653i	−0.580855	+	0.335357i	0.180618	+	0.983553i	$0.442190\pi$
$740$	3.38925	+	19.7455i	0.124591	+	0.725860i
$741$			9.33993i			0.343111i
$742$	5.78213	+	1.76729i	0.212269	+	0.0648794i
$743$	−29.1171			−1.06820			−0.534102	−	0.845420i	$-0.679350\pi$
$743$	−29.1171			−1.06820			−0.534102	+	0.845420i	$0.679350\pi$
$744$	−13.0287	−	8.98582i	−0.477654	−	0.329436i
$745$	−13.3486	−	14.4140i	−0.489055	−	0.528088i
$746$	0.269608	−	10.0854i	0.00987105	−	0.369252i
$747$	−11.2227	−	6.47941i	−0.410616	−	0.237069i
$748$	6.80736	−	3.45916i	0.248902	−	0.126479i
$749$	3.82990	−	13.8436i	0.139942	−	0.505835i
$750$	11.5049	−	1.38728i	0.420100	−	0.0506564i
$751$	37.2703	+	21.5180i	1.36001	+	0.785203i	0.989625	−	0.143675i	$-0.0458921\pi$
$751$	37.2703	+	21.5180i	1.36001	+	0.785203i	0.370386	+	0.928878i	$0.379225\pi$
$752$	2.80229	−	26.1130i	0.102189	−	0.952245i
$753$	−9.62527	+	5.55715i	−0.350764	+	0.202514i
$754$	13.7954	+	25.4411i	0.502400	+	0.926512i
$755$	0.148810	+	0.654869i	0.00541576	+	0.0238331i
$756$	−20.0879	−	6.73182i	−0.730590	−	0.244834i
$757$		−	10.6531i		−	0.387193i	−0.981081	−	0.193597i	$-0.937985\pi$
$757$		−	10.6531i		−	0.387193i	0.981081	−	0.193597i	$-0.0620153\pi$
$758$	20.1941	−	10.9502i	0.733484	−	0.397730i
$759$	4.84339	+	8.38899i	0.175804	+	0.304501i
$760$	12.6170	+	16.0285i	0.457666	+	0.581414i
$761$	12.3298	+	7.11864i	0.446956	+	0.258050i	0.706544	−	0.707669i	$-0.250253\pi$
$761$	12.3298	+	7.11864i	0.446956	+	0.258050i	−0.259588	+	0.965720i	$0.583587\pi$
$762$	−1.51754	−	0.931088i	−0.0549745	−	0.0337297i
$763$	16.5465	+	16.8169i	0.599023	+	0.608812i
$764$	31.1316	−	15.8195i	1.12630	−	0.572331i
$765$	2.31056	−	7.46528i	0.0835385	−	0.269908i
$766$	−0.373656	+	13.9776i	−0.0135007	+	0.505030i
$767$	−15.0834	−	26.1252i	−0.544630	−	0.943327i
$768$	2.48817	−	11.4595i	0.0897842	−	0.413508i
$769$		−	35.5770i		−	1.28294i	−0.767149	−	0.641469i	$-0.778325\pi$
$769$		−	35.5770i		−	1.28294i	0.767149	−	0.641469i	$-0.221675\pi$
$770$	12.6507	−	18.6196i	0.455899	−	0.671002i
$771$			3.46777i			0.124889i
$772$	1.83753	−	34.3443i	0.0661342	−	1.23608i
$773$	−5.94268	−	10.2930i	−0.213743	−	0.370214i	0.739140	−	0.673552i	$-0.235232\pi$
$773$	−5.94268	−	10.2930i	−0.213743	−	0.370214i	−0.952883	+	0.303338i	$0.901899\pi$
$774$	32.3164	+	0.863899i	1.16159	+	0.0310522i
$775$	2.92564	−	38.0622i	0.105092	−	1.36723i
$776$	−23.5453	−	1.89188i	−0.845226	−	0.0679145i
$777$	−8.40868	+	2.18021i	−0.301660	+	0.0782148i
$778$	23.6388	−	38.5277i	0.847491	−	1.38129i
$779$	0.909207	+	0.524931i	0.0325757	+	0.0188076i
$780$	12.1493	+	4.48460i	0.435015	+	0.160574i
$781$	−20.7291	−	35.9038i	−0.741745	−	1.28474i
$782$	4.69918	+	8.66609i	0.168042	+	0.309899i
$783$			20.7365i			0.741061i
$784$	−22.3459	−	16.8718i	−0.798069	−	0.602566i
$785$	−41.9412	+	9.53058i	−1.49694	+	0.340161i
$786$	12.8868	−	6.98786i	0.459658	−	0.249249i
$787$	−40.1645	+	23.1890i	−1.43171	+	0.826597i	−0.997251	−	0.0740951i	$-0.976393\pi$
$787$	−40.1645	+	23.1890i	−1.43171	+	0.826597i	−0.434457	+	0.900692i	$0.643060\pi$
$788$	20.0119	+	13.0270i	0.712896	+	0.464068i
$789$	2.98342	+	1.72248i	0.106213	+	0.0613219i
$790$	36.5751	+	12.4006i	1.30128	+	0.441194i
$791$	−0.698305	−	2.69323i	−0.0248289	−	0.0957603i
$792$	1.50111	−	18.6820i	0.0533398	−	0.663836i
$793$	48.9322	+	28.2510i	1.73763	+	1.00322i
$794$	24.7055	+	0.660441i	0.876766	+	0.0234382i
$795$	−1.79937	−	1.94299i	−0.0638171	−	0.0689107i
$796$	−30.9963	−	1.65841i	−1.09864	−	0.0587806i
$797$	9.09251			0.322073			0.161037	−	0.986948i	$-0.448516\pi$
$797$	9.09251			0.322073			0.161037	+	0.986948i	$0.448516\pi$
$798$	−6.46811	+	6.03253i	−0.228969	+	0.213549i
$799$			9.31691i			0.329609i
$800$	26.9078	−	8.71597i	0.951336	−	0.308156i
$801$	−10.1206	+	5.84312i	−0.357593	+	0.206457i
$802$	−24.5399	−	0.656013i	−0.866534	−	0.0231646i
$803$	3.30641	+	1.90896i	0.116681	+	0.0673656i
$804$	−3.95505	+	2.00976i	−0.139484	+	0.0708788i
$805$	24.4665	+	15.6843i	0.862330	+	0.552800i
$806$	22.3109	−	36.3634i	0.785867	−	1.28085i
$807$	−8.99316	+	15.5766i	−0.316574	+	0.548323i
$808$	−0.713717	+	0.338991i	−0.0251085	+	0.0119257i
$809$	−8.66128	−	15.0018i	−0.304515	−	0.527435i	0.672639	−	0.739971i	$-0.265161\pi$
$809$	−8.66128	−	15.0018i	−0.304515	−	0.527435i	−0.977153	+	0.212536i	$0.931828\pi$
$810$	−9.29100	−	10.5865i	−0.326452	−	0.371972i
$811$	−16.4459			−0.577493			−0.288746	−	0.957406i	$-0.593238\pi$
$811$	−16.4459			−0.577493			−0.288746	+	0.957406i	$0.593238\pi$
$812$	−8.70830	+	25.9857i	−0.305601	+	0.911921i
$813$			19.3424i			0.678368i
$814$	−8.12527	−	14.9844i	−0.284791	−	0.525203i
$815$	16.2861	+	17.5859i	0.570476	+	0.616009i
$816$	−0.443879	+	4.13628i	−0.0155389	+	0.144799i
$817$	14.9680	−	25.9254i	0.523664	−	0.907013i
$818$	−8.79934	−	5.39886i	−0.307662	−	0.188767i
$819$	6.86494	−	24.8141i	0.239880	−	0.867075i
$820$	1.11939	−	0.930643i	0.0390906	−	0.0324995i
$821$	−22.4527	+	38.8892i	−0.783603	+	1.35724i	0.146226	+	0.989251i	$0.453287\pi$
$821$	−22.4527	+	38.8892i	−0.783603	+	1.35724i	−0.929830	+	0.367990i	$0.880046\pi$
$822$	15.4081	+	0.411897i	0.537418	+	0.0143666i
$823$	−11.8546	−	20.5328i	−0.413226	−	0.715729i	0.582014	−	0.813179i	$-0.302265\pi$
$823$	−11.8546	−	20.5328i	−0.413226	−	0.715729i	−0.995240	+	0.0974497i	$0.968931\pi$
$824$	−31.2013	−	21.5194i	−1.08695	−	0.749665i
$825$	−8.89130	+	4.26088i	−0.309555	+	0.148345i
$826$	8.35015	−	27.3195i	0.290539	−	0.950569i
$827$	−8.20536			−0.285328			−0.142664	−	0.989771i	$-0.545567\pi$
$827$	−8.20536			−0.285328			−0.142664	+	0.989771i	$0.545567\pi$
$828$	24.1624	+	1.29277i	0.839702	+	0.0449268i
$829$	−19.1548	+	11.0590i	−0.665272	+	0.384095i	−0.794283	−	0.607548i	$-0.792153\pi$
$829$	−19.1548	+	11.0590i	−0.665272	+	0.384095i	0.129011	+	0.991643i	$0.458820\pi$
$830$	3.25210	+	16.3181i	0.112882	+	0.566410i
$831$	−8.82054	+	15.2776i	−0.305981	+	0.529975i
$832$	31.2039	+	5.04710i	1.08180	+	0.174977i
$833$	8.52071	+	5.10534i	0.295225	+	0.176890i
$834$	−6.24391	−	3.83096i	−0.216209	−	0.132655i
$835$	−28.2512	−	8.74396i	−0.977674	−	0.302597i
$836$	−14.5452	−	9.46838i	−0.503057	−	0.327471i
$837$	26.4729	−	15.2841i	0.915036	−	0.528296i
$838$	−12.0856	−	22.2879i	−0.417490	−	0.769923i
$839$	3.64977			0.126004			0.0630020	−	0.998013i	$-0.479933\pi$
$839$	3.64977			0.126004			0.0630020	+	0.998013i	$0.479933\pi$
$840$	4.74140	+	11.3102i	0.163594	+	0.390240i
$841$	−2.17525			−0.0750086
$842$	−8.51652	−	15.7059i	−0.293499	−	0.541262i
$843$	4.94174	−	2.85312i	0.170203	−	0.0982665i
$844$	23.7403	+	15.4541i	0.817176	+	0.531950i
$845$	−1.72676	+	5.57905i	−0.0594023	+	0.191925i
$846$	19.4920	+	11.9594i	0.670150	+	0.411172i
$847$	2.65326	−	9.59051i	0.0911671	−	0.329534i
$848$	−5.22088	−	3.81065i	−0.179286	−	0.130858i
$849$	−2.91351	+	5.04634i	−0.0999913	+	0.173190i
$850$	−9.16126	+	4.09291i	−0.314229	+	0.140386i
$851$	19.0582	−	11.0033i	0.653308	−	0.377188i
$852$	22.5543	+	1.20673i	0.772697	+	0.0413419i
$853$	−1.03474			−0.0354290			−0.0177145	−	0.999843i	$-0.505639\pi$
$853$	−1.03474			−0.0354290			−0.0177145	+	0.999843i	$0.505639\pi$
$854$	12.0402	+	52.1337i	0.412006	+	1.78398i
$855$	−17.3205	+	3.93584i	−0.592347	+	0.134603i
$856$	−8.71810	+	12.6405i	−0.297979	+	0.432043i
$857$	24.2563	+	42.0132i	0.828581	+	1.43514i	0.899152	+	0.437637i	$0.144185\pi$
$857$	24.2563	+	42.0132i	0.828581	+	1.43514i	−0.0705709	+	0.997507i	$0.522482\pi$
$858$	−11.0147	−	0.294451i	−0.376035	−	0.0100524i
$859$	12.4674	−	21.5941i	0.425382	−	0.736783i	−0.571074	−	0.820898i	$-0.693473\pi$
$859$	12.4674	−	21.5941i	0.425382	−	0.736783i	0.996456	+	0.0841157i	$0.0268065\pi$
$860$	−26.5366	−	31.9184i	−0.904891	−	1.08841i
$861$	0.442687	+	0.449921i	0.0150867	+	0.0153333i
$862$	−39.3852	−	24.1649i	−1.34147	−	0.823060i
$863$	−2.98354	+	5.16765i	−0.101561	+	0.175909i	−0.912328	−	0.409460i	$-0.865717\pi$
$863$	−2.98354	+	5.16765i	−0.101561	+	0.175909i	0.810767	+	0.585369i	$0.199050\pi$
$864$	17.9307	+	13.8366i	0.610013	+	0.470732i
$865$	−17.0988	−	18.4635i	−0.581377	−	0.627779i
$866$	−15.9016	−	29.3252i	−0.540357	−	0.996511i
$867$			10.9836i			0.373023i
$868$	39.5928	−	8.03586i	1.34387	−	0.272755i
$869$	−32.8588			−1.11466
$870$	9.02197	−	7.91791i	0.305873	−	0.268442i
$871$	−5.97927	−	10.3564i	−0.202600	−	0.350913i
$872$	−10.8207	−	22.7820i	−0.366434	−	0.771496i
$873$	10.2840	−	17.8125i	0.348062	−	0.602861i
$874$	11.7179	−	19.0984i	0.396363	−	0.646014i
$875$	−17.8256	+	23.6061i	−0.602615	+	0.798032i
$876$	−1.85433	+	0.942281i	−0.0626522	+	0.0318367i
$877$	−29.2974	−	16.9149i	−0.989304	−	0.571175i	−0.0842381	−	0.996446i	$-0.526846\pi$
$877$	−29.2974	−	16.9149i	−0.989304	−	0.571175i	−0.905066	+	0.425270i	$0.860179\pi$
$878$	25.9981	+	0.694996i	0.877394	+	0.0234550i
$879$	−1.34243	+	0.775051i	−0.0452789	+	0.0261418i
$880$	−19.3004	+	14.3741i	−0.650615	+	0.484549i
$881$		−	20.9239i		−	0.704944i	−0.935822	−	0.352472i	$-0.885341\pi$
$881$		−	20.9239i		−	0.704944i	0.935822	−	0.352472i	$-0.114659\pi$
$882$	21.6183	−	11.2730i	0.727927	−	0.379581i
$883$	−14.7876			−0.497642			−0.248821	−	0.968549i	$-0.580043\pi$
$883$	−14.7876			−0.497642			−0.248821	+	0.968549i	$0.580043\pi$
$884$	−11.1976	−	0.599107i	−0.376615	−	0.0201501i
$885$	−9.18028	+	8.50172i	−0.308592	+	0.285782i
$886$	4.78446	+	0.127901i	0.160737	+	0.00429691i
$887$	−6.40786	−	3.69958i	−0.215155	−	0.124220i	0.388550	−	0.921428i	$-0.372976\pi$
$887$	−6.40786	−	3.69958i	−0.215155	−	0.124220i	−0.603705	+	0.797208i	$0.706309\pi$
$888$	9.25667	+	0.743780i	0.310633	+	0.0249596i
$889$	4.39923	−	1.14064i	0.147545	−	0.0382558i
$890$	14.2105	+	4.81800i	0.476336	+	0.161500i
$891$	10.3785	+	5.99206i	0.347694	+	0.200741i
$892$	−5.08617	−	3.31090i	−0.170297	−	0.110857i
$893$	18.3393	−	10.5882i	0.613702	−	0.354321i
$894$	−8.00516	+	4.34079i	−0.267733	+	0.145178i
$895$	−0.399347	−	1.75740i	−0.0133487	−	0.0587435i
$896$	16.6589	+	24.8693i	0.556536	+	0.830824i
$897$		−	14.2255i		−	0.474976i
$898$	8.02298	+	14.7958i	0.267730	+	0.493741i
$899$	−19.7716	−	34.2453i	−0.659418	−	1.14215i
$900$	−3.19675	+	24.4201i	−0.106558	+	0.814005i
$901$	1.98580	+	1.14650i	0.0661566	+	0.0381956i
$902$	−0.647721	+	1.05569i	−0.0215668	+	0.0351506i
$903$	12.8292	−	12.6229i	0.426928	−	0.420063i
$904$	−0.238227	+	2.96484i	−0.00792331	+	0.0986090i
$905$	0.142500	+	0.0441050i	0.00473687	+	0.00146610i
$906$	0.311179	+	0.00831860i	0.0103382	+	0.000276367i
$907$	−9.25608	−	16.0320i	−0.307343	−	0.532334i	0.670437	−	0.741966i	$-0.266107\pi$
$907$	−9.25608	−	16.0320i	−0.307343	−	0.532334i	−0.977780	+	0.209632i	$0.932773\pi$
$908$	−1.57895	+	29.5113i	−0.0523994	+	0.979368i
$909$		−	0.688006i		−	0.0228197i
$910$	−29.7610	+	14.3913i	−0.986567	+	0.477067i
$911$			10.8437i			0.359267i	0.983734	+	0.179634i	$0.0574912\pi$
$911$			10.8437i			0.359267i	−0.983734	+	0.179634i	$0.942509\pi$
$912$	8.64626	−	3.82695i	0.286306	−	0.126723i
$913$	−7.07841	−	12.2602i	−0.234261	−	0.405752i
$914$	0.796292	−	29.7874i	0.0263390	−	0.985279i
$915$	6.92911	−	22.3875i	0.229069	−	0.740109i
$916$	11.4663	−	5.82661i	0.378858	−	0.192517i
$917$	−9.97764	+	36.0653i	−0.329491	+	1.19098i
$918$	−6.84842	−	4.20187i	−0.226032	−	0.138682i
$919$	13.9555	+	8.05723i	0.460351	+	0.265784i	0.712192	−	0.701985i	$-0.247703\pi$
$919$	13.9555	+	8.05723i	0.460351	+	0.265784i	−0.251841	+	0.967769i	$0.581036\pi$
$920$	−19.2167	−	24.4127i	−0.633557	−	0.804864i
$921$	−6.83653	−	11.8412i	−0.225271	−	0.390181i
$922$	36.8869	−	20.0019i	1.21480	−	0.658726i
$923$			60.8834i			2.00400i
$924$	−6.91033	−	7.81811i	−0.227333	−	0.257197i
$925$	9.67993	+	20.1994i	0.318274	+	0.664152i
$926$	10.1443	+	18.7078i	0.333362	+	0.614776i
$927$	28.5820	−	16.5018i	0.938757	−	0.541991i
$928$	17.8991	−	23.1951i	0.587567	−	0.761417i
$929$	42.7419	+	24.6770i	1.40232	+	0.809627i	0.994630	−	0.103495i	$-0.0330025\pi$
$929$	42.7419	+	24.6770i	1.40232	+	0.809627i	0.407686	+	0.913122i	$0.366336\pi$
$930$	−16.7580	−	5.68173i	−0.549517	−	0.186311i
$931$	0.365932	−	22.5741i	0.0119930	−	0.739836i
$932$	−31.1502	+	15.8290i	−1.02036	+	0.518496i
$933$	5.19390	+	2.99870i	0.170041	+	0.0981731i
$934$	0.194477	−	7.27493i	0.00636349	−	0.238043i
$935$	6.26370	−	5.80072i	0.204845	−	0.189704i
$936$	−15.6268	+	22.6576i	−0.510779	+	0.740586i
$937$	−31.3085			−1.02280			−0.511402	−	0.859342i	$-0.670874\pi$
$937$	−31.3085			−1.02280			−0.511402	+	0.859342i	$0.670874\pi$
$938$	3.31012	−	10.8298i	0.108079	−	0.353607i
$939$			17.1311i			0.559054i
$940$	−4.96740	−	28.9397i	−0.162019	−	0.943908i
$941$	37.9492	−	21.9100i	1.23711	−	0.714245i	0.268606	−	0.963250i	$-0.413437\pi$
$941$	37.9492	−	21.9100i	1.23711	−	0.714245i	0.968502	+	0.249005i	$0.0801035\pi$
$942$	−0.532766	+	19.9295i	−0.0173584	+	0.649338i
$943$	−1.38480	−	0.799514i	−0.0450952	−	0.0260358i
$944$	−18.0047	+	24.6678i	−0.586002	+	0.802867i
$945$	−23.6610	−	1.10011i	−0.769691	−	0.0357866i
$946$	30.1022	+	18.4693i	0.978708	+	0.600488i
$947$	−7.31729	+	12.6739i	−0.237780	+	0.411847i	−0.960077	−	0.279736i	$-0.909753\pi$
$947$	−7.31729	+	12.6739i	−0.237780	+	0.411847i	0.722297	+	0.691583i	$0.243086\pi$
$948$	9.76629	−	15.0029i	0.317194	−	0.487270i
$949$	−2.80340	−	4.85563i	−0.0910021	−	0.157620i
$950$	18.4678	+	13.3816i	0.599174	+	0.434155i
$951$	19.2078			0.622857
$952$	−6.81746	−	8.14153i	−0.220955	−	0.263869i
$953$		−	28.2044i		−	0.913630i	−0.889562	−	0.456815i	$-0.848990\pi$
$953$		−	28.2044i		−	0.913630i	0.889562	−	0.456815i	$-0.151010\pi$
$954$	4.94763	−	2.68285i	0.160186	−	0.0868604i
$955$	28.6454	−	26.5280i	0.926942	−	0.858427i
$956$	5.40542	+	3.51872i	0.174824	+	0.113804i
$957$	−5.10651	+	8.84473i	−0.165070	+	0.285909i
$958$	−29.5513	+	48.1643i	−0.954759	+	1.55612i
$959$	−28.0457	+	27.5947i	−0.905643	+	0.891081i
$960$	−0.826540	−	13.0845i	−0.0266765	−	0.422301i
$961$	−13.6458	+	23.6352i	−0.440187	+	0.762427i
$962$	−0.668938	+	25.0234i	−0.0215674	+	0.806785i
$963$	−6.68534	−	11.5793i	−0.215432	−	0.373139i
$964$	2.18913	−	40.9158i	0.0705072	−	1.31781i
$965$	−8.52071	−	37.4971i	−0.274291	−	1.20707i
$966$	9.85149	−	9.18806i	0.316966	−	0.295621i
$967$	−8.88824			−0.285827			−0.142913	−	0.989735i	$-0.545647\pi$
$967$	−8.88824			−0.285827			−0.142913	+	0.989735i	$0.545647\pi$
$968$	−6.03968	+	8.75702i	−0.194123	+	0.281461i
$969$	−2.90493	+	1.67716i	−0.0933198	+	0.0538782i
$970$	−25.8999	+	5.16169i	−0.831596	+	0.165732i
$971$	4.37105	−	7.57089i	0.140274	−	0.242961i	−0.787326	−	0.616537i	$-0.788535\pi$
$971$	4.37105	−	7.57089i	0.140274	−	0.242961i	0.927600	+	0.373576i	$0.121868\pi$
$972$	−27.2367	+	13.8403i	−0.873618	+	0.443929i
$973$	18.1006	−	4.69316i	0.580280	−	0.150456i
$974$	9.04134	−	14.7360i	0.289703	−	0.472173i
$975$	14.4366	+	1.10967i	0.462342	+	0.0355377i
$976$	6.10333	−	56.8737i	0.195363	−	1.82048i
$977$	−36.3569	+	20.9907i	−1.16316	+	0.671551i	−0.952059	−	0.305914i	$-0.901038\pi$
$977$	−36.3569	+	20.9907i	−1.16316	+	0.671551i	−0.211100	+	0.977464i	$0.567705\pi$
$978$	9.76676	−	5.29601i	0.312307	−	0.169348i
$979$	−12.7666			−0.408022
$980$	−29.1885	−	11.3150i	−0.932393	−	0.361445i
$981$	21.9613			0.701170
$982$	28.5334	−	15.4722i	0.910539	−	0.493738i
$983$	−9.53036	+	5.50236i	−0.303971	+	0.175498i	−0.644226	−	0.764836i	$-0.722820\pi$
$983$	−9.53036	+	5.50236i	−0.303971	+	0.175498i	0.340254	+	0.940333i	$0.389487\pi$
$984$	−0.289497	−	0.609513i	−0.00922884	−	0.0194306i
$985$	25.5033	+	7.89347i	0.812603	+	0.251507i
$986$	−5.43554	+	8.85913i	−0.173103	+	0.282132i
$987$	12.3240	−	3.19539i	0.392278	−	0.101710i
$988$	11.5462	+	22.7221i	0.367334	+	0.722885i
$989$	−22.7975	+	39.4865i	−0.724920	+	1.25560i
$990$	−4.09555	−	20.5503i	−0.130165	−	0.653132i
$991$	−31.6799	+	18.2904i	−1.00634	+	0.581013i	−0.910119	−	0.414346i	$-0.864010\pi$
$991$	−31.6799	+	18.2904i	−1.00634	+	0.581013i	−0.0962255	+	0.995360i	$0.530677\pi$
$992$	−42.8044	−	5.75429i	−1.35904	−	0.182699i
$993$	14.3073			0.454028
$994$	−42.1631	+	39.3237i	−1.33733	+	1.24727i
$995$	−33.8418	+	7.69010i	−1.07286	+	0.243792i
$996$	7.70167	+	0.412065i	0.244037	+	0.0130568i
$997$	−7.23204	−	12.5263i	−0.229041	−	0.396711i	0.728483	−	0.685064i	$-0.240226\pi$
$997$	−7.23204	−	12.5263i	−0.229041	−	0.396711i	−0.957524	+	0.288353i	$0.906892\pi$
$998$	0.159008	−	5.94811i	0.00503331	−	0.188284i
$999$	−8.96801	+	15.5331i	−0.283735	+	0.491444i

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

)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	140.2.s.b.19.6	yes	32
4.3	odd	2	inner	140.2.s.b.19.1	✓	32
5.2	odd	4		700.2.p.e.551.14		32
5.3	odd	4		700.2.p.e.551.3		32
5.4	even	2	inner	140.2.s.b.19.11	yes	32
7.2	even	3		980.2.c.d.979.11		32
7.3	odd	6	inner	140.2.s.b.59.16	yes	32
7.4	even	3		980.2.s.e.619.16		32
7.5	odd	6		980.2.c.d.979.12		32
7.6	odd	2		980.2.s.e.19.6		32
20.3	even	4		700.2.p.e.551.9		32
20.7	even	4		700.2.p.e.551.8		32
20.19	odd	2	inner	140.2.s.b.19.16	yes	32
28.3	even	6	inner	140.2.s.b.59.11	yes	32
28.11	odd	6		980.2.s.e.619.11		32
28.19	even	6		980.2.c.d.979.23		32
28.23	odd	6		980.2.c.d.979.24		32
28.27	even	2		980.2.s.e.19.1		32
35.3	even	12		700.2.p.e.451.9		32
35.4	even	6		980.2.s.e.619.1		32
35.9	even	6		980.2.c.d.979.22		32
35.17	even	12		700.2.p.e.451.8		32
35.19	odd	6		980.2.c.d.979.21		32
35.24	odd	6	inner	140.2.s.b.59.1	yes	32
35.34	odd	2		980.2.s.e.19.11		32
140.3	odd	12		700.2.p.e.451.3		32
140.19	even	6		980.2.c.d.979.10		32
140.39	odd	6		980.2.s.e.619.6		32
140.59	even	6	inner	140.2.s.b.59.6	yes	32
140.79	odd	6		980.2.c.d.979.9		32
140.87	odd	12		700.2.p.e.451.14		32
140.139	even	2		980.2.s.e.19.16		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
140.2.s.b.19.1	✓	32	4.3	odd	2	inner
140.2.s.b.19.6	yes	32	1.1	even	1	trivial
140.2.s.b.19.11	yes	32	5.4	even	2	inner
140.2.s.b.19.16	yes	32	20.19	odd	2	inner
140.2.s.b.59.1	yes	32	35.24	odd	6	inner
140.2.s.b.59.6	yes	32	140.59	even	6	inner
140.2.s.b.59.11	yes	32	28.3	even	6	inner
140.2.s.b.59.16	yes	32	7.3	odd	6	inner
700.2.p.e.451.3		32	140.3	odd	12
700.2.p.e.451.8		32	35.17	even	12
700.2.p.e.451.9		32	35.3	even	12
700.2.p.e.451.14		32	140.87	odd	12
700.2.p.e.551.3		32	5.3	odd	4
700.2.p.e.551.8		32	20.7	even	4
700.2.p.e.551.9		32	20.3	even	4
700.2.p.e.551.14		32	5.2	odd	4
980.2.c.d.979.9		32	140.79	odd	6
980.2.c.d.979.10		32	140.19	even	6
980.2.c.d.979.11		32	7.2	even	3
980.2.c.d.979.12		32	7.5	odd	6
980.2.c.d.979.21		32	35.19	odd	6
980.2.c.d.979.22		32	35.9	even	6
980.2.c.d.979.23		32	28.19	even	6
980.2.c.d.979.24		32	28.23	odd	6
980.2.s.e.19.1		32	28.27	even	2
980.2.s.e.19.6		32	7.6	odd	2
980.2.s.e.19.11		32	35.34	odd	2
980.2.s.e.19.16		32	140.139	even	2
980.2.s.e.619.1		32	35.4	even	6
980.2.s.e.619.6		32	140.39	odd	6
980.2.s.e.619.11		32	28.11	odd	6
980.2.s.e.619.16		32	7.4	even	3

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 $\F_{q}$

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

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Newspace parameters

Newform invariants

Embedding invariants

$q$ -expansion

Character values

Coefficient data

Twists

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.

Label	140.2.s.b.19.6

Level	$140$
Weight	$2$
Character	140.19
Analytic conductor	$1.118$
Analytic rank	$0$
Dimension	$32$
Inner twists	$8$