LMFDB - Embedded newform 152.2.o.c.27.5

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [152,2,Mod(27,152)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(152, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([3, 3, 1])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("152.27"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 152 = 2^{3} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	152.o (of order $6$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [28,-3,-6] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$1.21372611072$
Analytic rank:	$0$
Dimension:	$28$
Relative dimension:	$14$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			27.5
Character	$\chi$	$=$	152.27
Dual form			152.2.o.c.107.5

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.853480 - 1.12764i) q^{2} +(0.179130 + 0.103421i) q^{3} +(-0.543142 + 1.92484i) q^{4} +(-0.520463 - 0.300489i) q^{5} +(-0.0362625 - 0.290261i) q^{6} -4.27429i q^{7} +(2.63408 - 1.03034i) q^{8} +(-1.47861 - 2.56102i) q^{9} +(0.105361 + 0.843356i) q^{10} +5.11222 q^{11} +(-0.296361 + 0.288623i) q^{12} +(-1.55195 - 2.68806i) q^{13} +(-4.81986 + 3.64803i) q^{14} +(-0.0621536 - 0.107653i) q^{15} +(-3.40999 - 2.09092i) q^{16} +(-1.52982 + 2.64973i) q^{17} +(-1.62595 + 3.85312i) q^{18} +(3.31192 + 2.83393i) q^{19} +(0.861078 - 0.838597i) q^{20} +(0.442050 - 0.765653i) q^{21} +(-4.36318 - 5.76474i) q^{22} +(-4.65161 + 2.68561i) q^{23} +(0.578401 + 0.0878537i) q^{24} +(-2.31941 - 4.01734i) q^{25} +(-1.70660 + 4.04424i) q^{26} -1.23220i q^{27} +(8.22732 + 2.32155i) q^{28} +(3.77565 + 6.53961i) q^{29} +(-0.0683471 + 0.161967i) q^{30} +9.59602 q^{31} +(0.552556 + 5.62980i) q^{32} +(0.915751 + 0.528709i) q^{33} +(4.29361 - 0.536404i) q^{34} +(-1.28438 + 2.22461i) q^{35} +(5.73265 - 1.45508i) q^{36} -4.44082 q^{37} +(0.368996 - 6.15336i) q^{38} -0.642014i q^{39} +(-1.68055 - 0.255260i) q^{40} +(-0.253756 - 0.146506i) q^{41} +(-1.24066 + 0.154997i) q^{42} +(-0.892400 + 1.54568i) q^{43} +(-2.77666 + 9.84019i) q^{44} +1.77722i q^{45} +(6.99845 + 2.95322i) q^{46} +(5.79677 - 3.34677i) q^{47} +(-0.394587 - 0.727209i) q^{48} -11.2696 q^{49} +(-2.55054 + 6.04418i) q^{50} +(-0.548073 + 0.316430i) q^{51} +(6.01700 - 1.52725i) q^{52} +(5.16606 + 8.94788i) q^{53} +(-1.38947 + 1.05166i) q^{54} +(-2.66072 - 1.53617i) q^{55} +(-4.40398 - 11.2588i) q^{56} +(0.300176 + 0.850162i) q^{57} +(4.15189 - 9.83900i) q^{58} +(-0.849928 - 0.490706i) q^{59} +(0.240973 - 0.0611645i) q^{60} +(-5.08985 + 2.93862i) q^{61} +(-8.19002 - 10.8209i) q^{62} +(-10.9466 + 6.32001i) q^{63} +(5.87679 - 5.42801i) q^{64} +1.86538i q^{65} +(-0.185382 - 1.48388i) q^{66} +(5.98445 - 3.45512i) q^{67} +(-4.26938 - 4.38383i) q^{68} -1.11099 q^{69} +(3.60475 - 0.450344i) q^{70} +(-0.173380 + 0.300304i) q^{71} +(-6.53351 - 5.22248i) q^{72} +(4.61539 - 7.99410i) q^{73} +(3.79016 + 5.00765i) q^{74} -0.959500i q^{75} +(-7.25370 + 4.83568i) q^{76} -21.8511i q^{77} +(-0.723961 + 0.547947i) q^{78} +(-3.63621 + 6.29810i) q^{79} +(1.14647 + 2.11291i) q^{80} +(-4.30839 + 7.46235i) q^{81} +(0.0513697 + 0.411185i) q^{82} -7.38699 q^{83} +(1.23366 + 1.26673i) q^{84} +(1.59243 - 0.919390i) q^{85} +(2.50462 - 0.312904i) q^{86} +1.56192i q^{87} +(13.4660 - 5.26733i) q^{88} +(5.44821 - 3.14552i) q^{89} +(2.00407 - 1.51683i) q^{90} +(-11.4895 + 6.63349i) q^{91} +(-2.64287 - 10.4123i) q^{92} +(1.71893 + 0.992426i) q^{93} +(-8.72138 - 3.68027i) q^{94} +(-0.872165 - 2.47015i) q^{95} +(-0.483258 + 1.06561i) q^{96} +(7.87192 + 4.54486i) q^{97} +(9.61837 + 12.7080i) q^{98} +(-7.55897 - 13.0925i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q - 3 q^{2} - 6 q^{3} + q^{4} - 3 q^{6} + 8 q^{9} + 6 q^{10} - 16 q^{11} + 13 q^{16} - 22 q^{17} + 4 q^{19} - 40 q^{20} - 21 q^{22} - 11 q^{24} + 16 q^{25} + 36 q^{26} - 10 q^{28} + 4 q^{30} - 3 q^{32}+ \cdots - 28 q^{99}+O(q^{100}) $ 28 * q - 3 * q^2 - 6 * q^3 + q^4 - 3 * q^6 + 8 * q^9 + 6 * q^10 - 16 * q^11 + 13 * q^16 - 22 * q^17 + 4 * q^19 - 40 * q^20 - 21 * q^22 - 11 * q^24 + 16 * q^25 + 36 * q^26 - 10 * q^28 + 4 * q^30 - 3 * q^32 + 36 * q^33 - 12 * q^34 - 28 * q^35 - 8 * q^36 + 38 * q^38 - 48 * q^40 + 6 * q^41 + 14 * q^42 + 30 * q^43 + 5 * q^44 - 15 * q^48 - 68 * q^49 - 42 * q^51 + 36 * q^52 + 23 * q^54 - 26 * q^57 + 20 * q^58 - 18 * q^59 - 42 * q^60 + 22 * q^62 + 70 * q^64 - 27 * q^66 + 78 * q^67 + 4 * q^68 + 18 * q^70 - 24 * q^72 + 14 * q^73 + 4 * q^74 + 47 * q^76 - 30 * q^78 - 20 * q^80 + 6 * q^81 + 23 * q^82 - 32 * q^83 + 42 * q^86 - 18 * q^89 - 96 * q^90 - 12 * q^91 + 46 * q^92 + 50 * q^96 + 30 * q^97 + 15 * q^98 - 28 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/152\mathbb{Z}\right)^\times$.

$n$	$39$	$77$	$97$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{1}{6}\right)$

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 $

$2$	−0.853480	−	1.12764i	−0.603502	−	0.797362i
$2$	−0.853480	−	1.12764i	−0.603502	−	0.797362i
$3$	0.179130	+	0.103421i	0.103421	+	0.0597099i	0.550818	−	0.834625i	$-0.314316\pi$
$3$	0.179130	+	0.103421i	0.103421	+	0.0597099i	−0.447398	+	0.894335i	$0.647649\pi$
$4$	−0.543142	+	1.92484i	−0.271571	+	0.962418i
$5$	−0.520463	−	0.300489i	−0.232758	−	0.134383i	0.379086	−	0.925362i	$-0.376239\pi$
$5$	−0.520463	−	0.300489i	−0.232758	−	0.134383i	−0.611844	+	0.790979i	$0.709572\pi$
$6$	−0.0362625	−	0.290261i	−0.0148041	−	0.118499i
$7$		−	4.27429i		−	1.61553i	−0.589504	−	0.807766i	$-0.700677\pi$
$7$		−	4.27429i		−	1.61553i	0.589504	−	0.807766i	$-0.299323\pi$
$8$	2.63408	−	1.03034i	0.931289	−	0.364281i
$9$	−1.47861	−	2.56102i	−0.492869	−	0.853675i
$10$	0.105361	+	0.843356i	0.0333181	+	0.266693i
$11$	5.11222			1.54139			0.770696	−	0.637203i	$-0.219909\pi$
$11$	5.11222			1.54139			0.770696	+	0.637203i	$0.219909\pi$
$12$	−0.296361	+	0.288623i	−0.0855520	+	0.0833184i
$13$	−1.55195	−	2.68806i	−0.430434	−	0.745533i	0.566477	−	0.824078i	$-0.308306\pi$
$13$	−1.55195	−	2.68806i	−0.430434	−	0.745533i	−0.996911	+	0.0785447i	$0.974973\pi$
$14$	−4.81986	+	3.64803i	−1.28816	+	0.974976i
$15$	−0.0621536	−	0.107653i	−0.0160480	−	0.0277959i
$16$	−3.40999	−	2.09092i	−0.852498	−	0.522730i
$17$	−1.52982	+	2.64973i	−0.371036	+	0.642653i	−0.989725	−	0.142983i	$-0.954331\pi$
$17$	−1.52982	+	2.64973i	−0.371036	+	0.642653i	0.618689	+	0.785636i	$0.287664\pi$
$18$	−1.62595	+	3.85312i	−0.383240	+	0.908190i
$19$	3.31192	+	2.83393i	0.759807	+	0.650149i
$19$	3.31192	+	2.83393i	0.759807	+	0.650149i
$20$	0.861078	−	0.838597i	0.192543	−	0.187516i
$21$	0.442050	−	0.765653i	0.0964632	−	0.167079i
$22$	−4.36318	−	5.76474i	−0.930233	−	1.22905i
$23$	−4.65161	+	2.68561i	−0.969927	+	0.559988i	−0.899214	−	0.437509i	$-0.855861\pi$
$23$	−4.65161	+	2.68561i	−0.969927	+	0.559988i	−0.0707131	+	0.997497i	$0.522527\pi$
$24$	0.578401	+	0.0878537i	0.118066	+	0.0179331i
$25$	−2.31941	−	4.01734i	−0.463882	−	0.803468i
$26$	−1.70660	+	4.04424i	−0.334692	+	0.793142i
$27$		−	1.23220i		−	0.237137i
$28$	8.22732	+	2.32155i	1.55482	+	0.438732i
$29$	3.77565	+	6.53961i	0.701120	+	1.21438i	0.968074	+	0.250666i	$0.0806496\pi$
$29$	3.77565	+	6.53961i	0.701120	+	1.21438i	−0.266954	+	0.963709i	$0.586017\pi$
$30$	−0.0683471	+	0.161967i	−0.0124784	+	0.0295709i
$31$	9.59602			1.72350			0.861748	−	0.507336i	$-0.169370\pi$
$31$	9.59602			1.72350			0.861748	+	0.507336i	$0.169370\pi$
$32$	0.552556	+	5.62980i	0.0976791	+	0.995218i
$33$	0.915751	+	0.528709i	0.159412	+	0.0920364i
$34$	4.29361	−	0.536404i	0.736348	−	0.0919925i
$35$	−1.28438	+	2.22461i	−0.217100	+	0.376028i
$36$	5.73265	−	1.45508i	0.955442	−	0.242513i
$37$	−4.44082			−0.730067			−0.365034	−	0.930994i	$-0.618942\pi$
$37$	−4.44082			−0.730067			−0.365034	+	0.930994i	$0.618942\pi$
$38$	0.368996	−	6.15336i	0.0598591	−	0.998207i
$39$		−	0.642014i		−	0.102805i
$40$	−1.68055	−	0.255260i	−0.265718	−	0.0403601i
$41$	−0.253756	−	0.146506i	−0.0396300	−	0.0228804i	0.480054	−	0.877239i	$-0.340617\pi$
$41$	−0.253756	−	0.146506i	−0.0396300	−	0.0228804i	−0.519684	+	0.854358i	$0.673950\pi$
$42$	−1.24066	+	0.154997i	−0.191438	+	0.0239165i
$43$	−0.892400	+	1.54568i	−0.136090	+	0.235714i	−0.926013	−	0.377491i	$-0.876787\pi$
$43$	−0.892400	+	1.54568i	−0.136090	+	0.235714i	0.789923	+	0.613205i	$0.210120\pi$
$44$	−2.77666	+	9.84019i	−0.418598	+	1.48346i
$45$			1.77722i			0.264933i
$46$	6.99845	+	2.95322i	1.03187	+	0.435429i
$47$	5.79677	−	3.34677i	0.845546	−	0.488176i	−0.0135997	−	0.999908i	$-0.504329\pi$
$47$	5.79677	−	3.34677i	0.845546	−	0.488176i	0.859145	+	0.511731i	$0.170996\pi$
$48$	−0.394587	−	0.727209i	−0.0569537	−	0.104964i
$49$	−11.2696			−1.60994
$50$	−2.55054	+	6.04418i	−0.360701	+	0.854776i
$51$	−0.548073	+	0.316430i	−0.0767455	+	0.0443090i
$52$	6.01700	−	1.52725i	0.834408	−	0.211792i
$53$	5.16606	+	8.94788i	0.709613	+	1.22909i	0.965001	+	0.262247i	$0.0844636\pi$
$53$	5.16606	+	8.94788i	0.709613	+	1.22909i	−0.255387	+	0.966839i	$0.582203\pi$
$54$	−1.38947	+	1.05166i	−0.189084	+	0.143112i
$55$	−2.66072	−	1.53617i	−0.358772	−	0.207137i
$56$	−4.40398	−	11.2588i	−0.588507	−	1.50453i
$57$	0.300176	+	0.850162i	0.0397593	+	0.112607i
$58$	4.15189	−	9.83900i	0.545169	−	1.29192i
$59$	−0.849928	−	0.490706i	−0.110651	−	0.0638845i	0.443653	−	0.896199i	$-0.353682\pi$
$59$	−0.849928	−	0.490706i	−0.110651	−	0.0638845i	−0.554304	+	0.832314i	$0.687016\pi$
$60$	0.240973	−	0.0611645i	0.0311095	−	0.00789630i
$61$	−5.08985	+	2.93862i	−0.651688	+	0.376252i	−0.789103	−	0.614261i	$-0.789454\pi$
$61$	−5.08985	+	2.93862i	−0.651688	+	0.376252i	0.137415	+	0.990514i	$0.456121\pi$
$62$	−8.19002	−	10.8209i	−1.04013	−	1.37425i
$63$	−10.9466	+	6.32001i	−1.37914	+	0.796246i
$64$	5.87679	−	5.42801i	0.734599	−	0.678501i
$65$			1.86538i			0.231372i
$66$	−0.185382	−	1.48388i	−0.0228190	−	0.182653i
$67$	5.98445	−	3.45512i	0.731117	−	0.422110i	−0.0877139	−	0.996146i	$-0.527956\pi$
$67$	5.98445	−	3.45512i	0.731117	−	0.422110i	0.818831	+	0.574035i	$0.194623\pi$
$68$	−4.26938	−	4.38383i	−0.517738	−	0.531618i
$69$	−1.11099			−0.133747
$70$	3.60475	−	0.450344i	0.430850	−	0.0538264i
$71$	−0.173380	+	0.300304i	−0.0205765	+	0.0356395i	−0.876130	−	0.482074i	$-0.839883\pi$
$71$	−0.173380	+	0.300304i	−0.0205765	+	0.0356395i	0.855554	+	0.517714i	$0.173217\pi$
$72$	−6.53351	−	5.22248i	−0.769981	−	0.615475i
$73$	4.61539	−	7.99410i	0.540191	−	0.935638i	−0.458702	−	0.888590i	$-0.651685\pi$
$73$	4.61539	−	7.99410i	0.540191	−	0.935638i	0.998893	−	0.0470480i	$-0.0149814\pi$
$74$	3.79016	+	5.00765i	0.440597	+	0.582127i
$75$		−	0.959500i		−	0.110793i
$76$	−7.25370	+	4.83568i	−0.832057	+	0.554690i
$77$		−	21.8511i		−	2.49017i
$78$	−0.723961	+	0.547947i	−0.0819724	+	0.0620427i
$79$	−3.63621	+	6.29810i	−0.409106	+	0.708592i	−0.994790	−	0.101948i	$-0.967493\pi$
$79$	−3.63621	+	6.29810i	−0.409106	+	0.708592i	0.585684	+	0.810539i	$0.300826\pi$
$80$	1.14647	+	2.11291i	0.128180	+	0.236231i
$81$	−4.30839	+	7.46235i	−0.478710	+	0.829150i
$82$	0.0513697	+	0.411185i	0.00567283	+	0.0454078i
$83$	−7.38699			−0.810828			−0.405414	−	0.914133i	$-0.632873\pi$
$83$	−7.38699			−0.810828			−0.405414	+	0.914133i	$0.632873\pi$
$84$	1.23366	+	1.26673i	0.134603	+	0.138212i
$85$	1.59243	−	0.919390i	0.172723	−	0.0997218i
$86$	2.50462	−	0.312904i	0.270080	−	0.0337413i
$87$			1.56192i			0.167455i
$88$	13.4660	−	5.26733i	1.43548	−	0.561500i
$89$	5.44821	−	3.14552i	0.577509	−	0.333425i	−0.182634	−	0.983181i	$-0.558462\pi$
$89$	5.44821	−	3.14552i	0.577509	−	0.333425i	0.760143	+	0.649756i	$0.225129\pi$
$90$	2.00407	−	1.51683i	0.211247	−	0.159888i
$91$	−11.4895	+	6.63349i	−1.20443	+	0.695379i
$92$	−2.64287	−	10.4123i	−0.275538	−	1.08555i
$93$	1.71893	+	0.992426i	0.178245	+	0.102910i
$94$	−8.72138	−	3.68027i	−0.899541	−	0.379591i
$95$	−0.872165	−	2.47015i	−0.0894822	−	0.253432i
$96$	−0.483258	+	1.06561i	−0.0493223	+	0.108758i
$97$	7.87192	+	4.54486i	0.799273	+	0.461460i	0.843217	−	0.537574i	$-0.180659\pi$
$97$	7.87192	+	4.54486i	0.799273	+	0.461460i	−0.0439442	+	0.999034i	$0.513992\pi$
$98$	9.61837	+	12.7080i	0.971602	+	1.28371i
$99$	−7.55897	−	13.0925i	−0.759705	−	1.31585i
$100$	8.99249	−	2.28250i	0.899249	−	0.228250i
$101$	3.45861	−	1.99683i	0.344145	−	0.198692i	−0.317959	−	0.948105i	$-0.602997\pi$
$101$	3.45861	−	1.99683i	0.344145	−	0.198692i	0.662103	+	0.749413i	$0.269664\pi$
$102$	0.824588	+	0.347962i	0.0816464	+	0.0344533i
$103$	5.76259			0.567805			0.283902	−	0.958853i	$-0.408371\pi$
$103$	5.76259			0.567805			0.283902	+	0.958853i	$0.408371\pi$
$104$	−6.85758	−	5.48153i	−0.672441	−	0.537508i
$105$	−0.460141	+	0.265663i	−0.0449052	+	0.0259260i
$106$	5.68085	−	13.4623i	0.551773	−	1.30757i
$107$			5.65018i			0.546223i	0.961982	+	0.273112i	$0.0880528\pi$
$107$			5.65018i			0.546223i	−0.961982	+	0.273112i	$0.911947\pi$
$108$	2.37178	+	0.669259i	0.228225	+	0.0643995i
$109$	−3.72756	+	6.45632i	−0.357035	+	0.618403i	−0.987464	−	0.157844i	$-0.949546\pi$
$109$	−3.72756	+	6.45632i	−0.357035	+	0.618403i	0.630429	+	0.776247i	$0.282879\pi$
$110$	0.538629	+	4.31142i	0.0513563	+	0.411078i
$111$	−0.795484	−	0.459273i	−0.0755040	−	0.0435922i
$112$	−8.93721	+	14.5753i	−0.844487	+	1.37724i
$113$			5.20979i			0.490096i	0.969511	+	0.245048i	$0.0788037\pi$
$113$			5.20979i			0.490096i	−0.969511	+	0.245048i	$0.921196\pi$
$114$	0.702482	−	1.06409i	0.0657935	−	0.0996609i
$115$	3.22799			0.301011
$116$	−14.6384	+	3.71556i	−1.35914	+	0.344981i
$117$	−4.58945	+	7.94917i	−0.424295	+	0.734901i
$118$	0.172057	+	1.37722i	0.0158392	+	0.126783i
$119$	11.3257	+	6.53890i	1.03823	+	0.599420i
$120$	−0.274637	−	0.219528i	−0.0250708	−	0.0200401i
$121$	15.1348			1.37589
$122$	7.65779	+	3.23145i	0.693304	+	0.292562i
$123$	−0.0303035	−	0.0524872i	−0.00273237	−	0.00473261i
$124$	−5.21201	+	18.4708i	−0.468052	+	1.65872i
$125$			5.79273i			0.518117i
$126$	16.4694	+	6.94979i	1.46721	+	0.619136i
$127$	−1.32713	−	2.29866i	−0.117764	−	0.203973i	0.801117	−	0.598507i	$-0.204239\pi$
$127$	−1.32713	−	2.29866i	−0.117764	−	0.203973i	−0.918881	+	0.394534i	$0.870906\pi$
$128$	−11.1366	−	1.99420i	−0.984343	−	0.176264i
$129$	−0.319711	+	0.184585i	−0.0281490	+	0.0162518i
$130$	2.10347	−	1.59206i	0.184487	−	0.139633i
$131$	4.48347	−	7.76560i	0.391723	−	0.678484i	−0.600954	−	0.799284i	$-0.705213\pi$
$131$	4.48347	−	7.76560i	0.391723	−	0.678484i	0.992677	+	0.120800i	$0.0385459\pi$
$132$	−1.51506	+	1.47551i	−0.131869	+	0.128426i
$133$	12.1131	−	14.1561i	1.05034	−	1.22749i
$134$	−9.00374	−	3.79942i	−0.777805	−	0.328220i
$135$	−0.370262	+	0.641313i	−0.0318671	+	0.0551954i
$136$	−1.29955	+	8.55584i	−0.111436	+	0.733657i
$137$	0.386829	+	0.670007i	0.0330490	+	0.0572426i	0.882077	−	0.471106i	$-0.156145\pi$
$137$	0.386829	+	0.670007i	0.0330490	+	0.0572426i	−0.849028	+	0.528348i	$0.822812\pi$
$138$	0.948206	+	1.25279i	0.0807167	+	0.106645i
$139$	−0.239838	−	0.415411i	−0.0203428	−	0.0352347i	0.855675	−	0.517514i	$-0.173142\pi$
$139$	−0.239838	−	0.415411i	−0.0203428	−	0.0352347i	−0.876018	+	0.482279i	$0.839809\pi$
$140$	−3.58441	−	3.68050i	−0.302938	−	0.311059i
$141$	1.38450			0.116596
$142$	0.486611	−	0.0607927i	0.0408355	−	0.00510161i
$143$	−7.93391	−	13.7419i	−0.663467	−	1.14916i
$144$	−0.312857	+	11.8247i	−0.0260714	+	0.985394i
$145$		−	4.53817i		−	0.376874i
$146$	−12.9536	+	1.61830i	−1.07205	+	0.133932i
$147$	−2.01872	−	1.16551i	−0.166501	−	0.0961294i
$148$	2.41200	−	8.54786i	0.198265	−	0.702630i
$149$	−8.65748	−	4.99840i	−0.709248	−	0.409485i	0.101534	−	0.994832i	$-0.467625\pi$
$149$	−8.65748	−	4.99840i	−0.709248	−	0.409485i	−0.810783	+	0.585347i	$0.800958\pi$
$150$	−1.08197	+	0.818914i	−0.0883425	+	0.0668641i
$151$	3.12214			0.254077			0.127038	−	0.991898i	$-0.459453\pi$
$151$	3.12214			0.254077			0.127038	+	0.991898i	$0.459453\pi$
$152$	11.6438	+	4.05241i	0.944437	+	0.328694i
$153$	9.04802			0.731489
$154$	−24.6402	+	18.6495i	−1.98556	+	1.50282i
$155$	−4.99437	−	2.88350i	−0.401158	−	0.231609i
$156$	1.23577	+	0.348705i	0.0989410	+	0.0279188i
$157$	8.23002	+	4.75160i	0.656827	+	0.379219i	0.791067	−	0.611730i	$-0.209526\pi$
$157$	8.23002	+	4.75160i	0.656827	+	0.379219i	−0.134240	+	0.990949i	$0.542859\pi$
$158$	10.2054	−	1.27497i	0.811900	−	0.101431i
$159$			2.13711i			0.169484i
$160$	1.40411	−	3.09614i	0.111005	−	0.244771i
$161$	11.4791	+	19.8823i	0.904678	+	1.56695i
$162$	12.0920	−	1.51066i	0.950035	−	0.118689i
$163$	−7.58106			−0.593794			−0.296897	−	0.954909i	$-0.595952\pi$
$163$	−7.58106			−0.593794			−0.296897	+	0.954909i	$0.595952\pi$
$164$	0.419826	−	0.408865i	0.0327829	−	0.0319270i
$165$	−0.317743	−	0.550347i	−0.0247362	−	0.0428444i
$166$	6.30465	+	8.32987i	0.489336	+	0.646523i
$167$	3.12919	+	5.41991i	0.242144	+	0.419405i	0.961325	−	0.275418i	$-0.0888161\pi$
$167$	3.12919	+	5.41991i	0.242144	+	0.419405i	−0.719181	+	0.694823i	$0.755483\pi$
$168$	0.375513	−	2.47226i	0.0289714	−	0.190739i
$169$	1.68290	−	2.91487i	0.129454	−	0.224221i
$170$	−2.39585	−	1.01101i	−0.183753	−	0.0775406i
$171$	2.36074	−	12.6722i	0.180530	−	0.969067i
$172$	−2.49049	−	2.55725i	−0.189898	−	0.194988i
$173$	6.64288	−	11.5058i	0.505049	−	0.874771i	−0.494934	−	0.868931i	$-0.664808\pi$
$173$	6.64288	−	11.5058i	0.505049	−	0.874771i	0.999983	−	0.00584002i	$-0.00185895\pi$
$174$	1.76128	−	1.33307i	0.133522	−	0.101060i
$175$	−17.1713	+	9.91385i	−1.29803	+	0.749417i
$176$	−17.4326	−	10.6893i	−1.31403	−	0.805733i
$177$	−0.101498	−	0.175800i	−0.00762908	−	0.0132139i
$178$	−8.19696	−	3.45897i	−0.614388	−	0.259261i
$179$			12.0379i			0.899756i	0.893090	+	0.449878i	$0.148533\pi$
$179$			12.0379i			0.899756i	−0.893090	+	0.449878i	$0.851467\pi$
$180$	−3.42087	−	0.965286i	−0.254976	−	0.0719482i
$181$	−9.24601	−	16.0146i	−0.687251	−	1.19035i	−0.972724	−	0.231966i	$-0.925484\pi$
$181$	−9.24601	−	16.0146i	−0.687251	−	1.19035i	0.285473	−	0.958387i	$-0.407849\pi$
$182$	17.2863	+	7.29451i	1.28135	+	0.540705i
$183$	−1.21566			−0.0898639
$184$	−9.48563	+	11.8669i	−0.699290	+	0.874836i
$185$	2.31128	+	1.33442i	0.169929	+	0.0981086i
$186$	−0.347976	−	2.78535i	−0.0255149	−	0.204232i
$187$	−7.82078	+	13.5460i	−0.571912	+	0.990581i
$188$	3.29351	+	12.9756i	0.240204	+	0.946343i
$189$	−5.26677			−0.383101
$190$	−2.04107	+	3.09172i	−0.148075	+	0.224297i
$191$		−	18.4324i		−	1.33372i	−0.745182	−	0.666861i	$-0.767637\pi$
$191$		−	18.4324i		−	1.33372i	0.745182	−	0.666861i	$-0.232363\pi$
$192$	1.61408	−	0.364537i	0.116486	−	0.0263082i
$193$	−20.8605	−	12.0438i	−1.50157	−	0.866931i	−0.999998	−	0.00181422i	$-0.999423\pi$
$193$	−20.8605	−	12.0438i	−1.50157	−	0.866931i	−0.501570	−	0.865117i	$-0.667244\pi$
$194$	−1.59357	−	12.7556i	−0.114412	−	0.915801i
$195$	−0.192919	+	0.334145i	−0.0138152	+	0.0239286i
$196$	6.12099	−	21.6921i	0.437214	−	1.54944i
$197$		−	2.85326i		−	0.203286i	−0.994821	−	0.101643i	$-0.967590\pi$
$197$		−	2.85326i		−	0.203286i	0.994821	−	0.101643i	$-0.0324100\pi$
$198$	−8.31222	+	19.6980i	−0.590723	+	1.39988i
$199$	−10.2863	+	5.93882i	−0.729179	+	0.420992i	−0.818122	−	0.575045i	$-0.804985\pi$
$199$	−10.2863	+	5.93882i	−0.729179	+	0.420992i	0.0889428	+	0.996037i	$0.471651\pi$
$200$	−10.2488	−	8.19222i	−0.724697	−	0.579278i
$201$	1.42932			0.100817
$202$	−5.20356	−	2.19581i	−0.366121	−	0.154497i
$203$	27.9522	−	16.1382i	1.96186	−	1.13268i
$204$	−0.311394	−	1.22682i	−0.0218020	−	0.0858943i
$205$	0.0880470	+	0.152502i	0.00614947	+	0.0106512i
$206$	−4.91826	−	6.49813i	−0.342671	−	0.452746i
$207$	13.7558	+	7.94192i	0.956095	+	0.552002i
$208$	−0.328375	+	12.4113i	−0.0227687	+	0.860566i
$209$	16.9313	+	14.4877i	1.17116	+	1.00213i
$210$	0.692293	+	0.292136i	0.0477728	+	0.0201593i
$211$	8.88899	+	5.13206i	0.611944	+	0.353306i	0.773726	−	0.633521i	$-0.218391\pi$
$211$	8.88899	+	5.13206i	0.611944	+	0.353306i	−0.161782	+	0.986827i	$0.551724\pi$
$212$	−20.0291	+	5.08385i	−1.37561	+	0.349160i
$213$	−0.0621152	+	0.0358622i	−0.00425606	+	0.00245724i
$214$	6.37136	−	4.82232i	0.435537	−	0.329647i
$215$	0.928922	−	0.536313i	0.0633520	−	0.0365763i
$216$	−1.26958	−	3.24571i	−0.0863843	−	0.220843i
$217$		−	41.0162i		−	2.78436i
$218$	10.4618	−	1.30700i	0.708562	−	0.0885212i
$219$	1.65351	−	0.954654i	0.111734	−	0.0645095i
$220$	4.40202	−	4.28710i	0.296784	−	0.289036i
$221$	9.49682			0.638825
$222$	0.161036	+	1.28900i	0.0108080	+	0.0865120i
$223$	4.32443	−	7.49013i	0.289585	−	0.501576i	−0.684126	−	0.729364i	$-0.739816\pi$
$223$	4.32443	−	7.49013i	0.289585	−	0.501576i	0.973711	+	0.227788i	$0.0731494\pi$
$224$	24.0634	−	2.36179i	1.60781	−	0.157804i
$225$	−6.85900	+	11.8801i	−0.457267	+	0.792010i
$226$	5.87476	−	4.44645i	0.390783	−	0.295774i
$227$			10.7324i			0.712331i	0.934423	+	0.356166i	$0.115916\pi$
$227$			10.7324i			0.712331i	−0.934423	+	0.356166i	$0.884084\pi$
$228$	−1.79946	+	0.116031i	−0.119172	+	0.00768435i
$229$			22.2288i			1.46892i	0.678652	+	0.734460i	$0.262564\pi$
$229$			22.2288i			1.46892i	−0.678652	+	0.734460i	$0.737436\pi$
$230$	−2.75502	−	3.64000i	−0.181661	−	0.240015i
$231$	2.25986	−	3.91419i	0.148688	−	0.257535i
$232$	16.6834	+	13.3357i	1.09532	+	0.875530i
$233$	1.78649	−	3.09429i	0.117037	−	0.202713i	−0.801555	−	0.597920i	$-0.795994\pi$
$233$	1.78649	−	3.09429i	0.117037	−	0.202713i	0.918592	+	0.395207i	$0.129327\pi$
$234$	12.8808	−	1.60921i	0.842045	−	0.105197i
$235$	−4.02267			−0.262410
$236$	1.40616	−	1.36945i	0.0915333	−	0.0891436i
$237$	−1.30271	+	0.752118i	−0.0846199	+	0.0488553i
$238$	−2.29275	−	18.3521i	−0.148617	−	1.18959i
$239$			8.97537i			0.580569i	0.956940	+	0.290284i	$0.0937499\pi$
$239$			8.97537i			0.580569i	−0.956940	+	0.290284i	$0.906250\pi$
$240$	−0.0131510	+	0.497055i	−0.000848894	+	0.0320847i
$241$	−14.5288	+	8.38822i	−0.935884	+	0.540333i	−0.888668	−	0.458552i	$-0.848368\pi$
$241$	−14.5288	+	8.38822i	−0.935884	+	0.540333i	−0.0472164	+	0.998885i	$0.515035\pi$
$242$	−12.9173	−	17.0666i	−0.830353	−	1.09708i
$243$	−4.74486	+	2.73945i	−0.304383	+	0.175736i
$244$	−2.89186	−	11.3932i	−0.185132	−	0.729376i
$245$	5.86540	+	3.38639i	0.374727	+	0.216349i
$246$	−0.0333232	+	0.0789682i	−0.00212461	+	0.00503483i
$247$	2.47784	−	13.3008i	0.157661	−	0.846307i
$248$	25.2767	−	9.88718i	1.60507	−	0.627837i
$249$	−1.32323	−	0.763967i	−0.0838563	−	0.0484144i
$250$	6.53211	−	4.94398i	0.413127	−	0.312685i
$251$	−10.6790	−	18.4965i	−0.674051	−	1.16749i	−0.976745	−	0.214403i	$-0.931220\pi$
$251$	−10.6790	−	18.4965i	−0.674051	−	1.16749i	0.302694	−	0.953088i	$-0.402114\pi$
$252$	−6.21943	−	24.5030i	−0.391787	−	1.54355i
$253$	−23.7800	+	13.7294i	−1.49504	+	0.863161i
$254$	−1.45938	+	3.45839i	−0.0915696	+	0.216999i
$255$	0.380335			0.0238175
$256$	7.25610	+	14.2601i	0.453506	+	0.891253i
$257$	−16.3942	+	9.46517i	−1.02264	+	0.590421i	−0.914867	−	0.403755i	$-0.867705\pi$
$257$	−16.3942	+	9.46517i	−1.02264	+	0.590421i	−0.107772	+	0.994176i	$0.534372\pi$
$258$	0.481012	+	0.202979i	0.0299465	+	0.0126369i
$259$			18.9814i			1.17945i
$260$	−3.59055	−	1.01317i	−0.222676	−	0.0628339i
$261$	11.1654	−	19.3390i	0.691121	−	1.19706i
$262$	−12.5834	+	1.57205i	−0.777402	+	0.0971214i
$263$	10.3306	+	5.96438i	0.637013	+	0.367780i	0.783463	−	0.621438i	$-0.213451\pi$
$263$	10.3306	+	5.96438i	0.637013	+	0.367780i	−0.146450	+	0.989218i	$0.546785\pi$
$264$	2.95691	+	0.449128i	0.181985	+	0.0276419i
$265$		−	6.20939i		−	0.381440i
$266$	−26.3013	−	1.57720i	−1.61263	−	0.0967043i
$267$	1.30125			0.0796351
$268$	3.40014	+	13.3957i	0.207697	+	0.818273i
$269$	−2.92391	+	5.06435i	−0.178274	+	0.308779i	−0.941289	−	0.337601i	$-0.890385\pi$
$269$	−2.92391	+	5.06435i	−0.178274	+	0.308779i	0.763016	+	0.646380i	$0.223718\pi$
$270$	1.03918	−	0.129826i	0.0632426	−	0.00790094i
$271$	−1.58549	−	0.915381i	−0.0963114	−	0.0556054i	0.451071	−	0.892488i	$-0.351042\pi$
$271$	−1.58549	−	0.915381i	−0.0963114	−	0.0556054i	−0.547382	+	0.836883i	$0.684376\pi$
$272$	10.7570	−	5.83681i	0.652242	−	0.353909i
$273$	−2.74416			−0.166084
$274$	0.425376	−	1.00804i	0.0256979	−	0.0608980i
$275$	−11.8573	−	20.5375i	−0.715025	−	1.23846i
$276$	0.603425	−	2.13847i	0.0363219	−	0.128721i
$277$			21.0912i			1.26725i	0.773642	+	0.633623i	$0.218433\pi$
$277$			21.0912i			1.26725i	−0.773642	+	0.633623i	$0.781567\pi$
$278$	−0.263737	+	0.624996i	−0.0158179	+	0.0374848i
$279$	−14.1888	−	24.5757i	−0.849459	−	1.47131i
$280$	−1.09105	+	7.18316i	−0.0652030	+	0.429276i
$281$	−18.1546	+	10.4816i	−1.08301	+	0.625279i	−0.931708	−	0.363208i	$-0.881681\pi$
$281$	−18.1546	+	10.4816i	−1.08301	+	0.625279i	−0.151306	+	0.988487i	$0.548348\pi$
$282$	−1.18164	−	1.56121i	−0.0703658	−	0.0929690i
$283$	−0.549154	+	0.951163i	−0.0326438	+	0.0565408i	−0.881886	−	0.471463i	$-0.843726\pi$
$283$	−0.549154	+	0.951163i	−0.0326438	+	0.0565408i	0.849242	+	0.528004i	$0.177059\pi$
$284$	−0.483865	−	0.496837i	−0.0287121	−	0.0294818i
$285$	0.0992341	−	0.532678i	0.00587812	−	0.0315531i
$286$	−8.72452	+	20.6751i	−0.515892	+	1.22254i
$287$	−0.626210	+	1.08463i	−0.0369640	+	0.0640235i
$288$	13.6011	−	9.73938i	0.801450	−	0.573899i
$289$	3.81930	+	6.61522i	0.224665	+	0.389131i
$290$	−5.11742	+	3.87324i	−0.300505	+	0.227444i
$291$	0.940063	+	1.62824i	0.0551075	+	0.0954490i
$292$	12.8805	+	13.2258i	0.753775	+	0.773982i
$293$	−32.5588			−1.90211			−0.951054	−	0.309025i	$-0.899997\pi$
$293$	−32.5588			−1.90211			−0.951054	+	0.309025i	$0.899997\pi$
$294$	0.408664	+	3.27112i	0.0238338	+	0.190776i
$295$	0.294904	+	0.510789i	0.0171700	+	0.0297393i
$296$	−11.6975	+	4.57557i	−0.679904	+	0.265949i
$297$		−	6.29927i		−	0.365521i
$298$	1.75260	+	14.0285i	0.101525	+	0.812652i
$299$	14.4381	+	8.33586i	0.834978	+	0.482075i
$300$	1.84688	+	0.521145i	0.106630	+	0.0300883i
$301$	6.60670	+	3.81438i	0.380804	+	0.219857i
$302$	−2.66469	−	3.52065i	−0.153336	−	0.202591i
$303$	0.826053			0.0474555
$304$	−5.36809	−	16.5887i	−0.307881	−	0.951425i
$305$	3.53210			0.202248
$306$	−7.72231	−	10.2029i	−0.441455	−	0.583261i
$307$	24.9620	+	14.4118i	1.42466	+	0.822527i	0.996692	−	0.0812673i	$-0.0258967\pi$
$307$	24.9620	+	14.4118i	1.42466	+	0.822527i	0.427967	+	0.903795i	$0.359230\pi$
$308$	42.0599	+	11.8683i	2.39658	+	0.676258i
$309$	1.03225	+	0.595970i	0.0587227	+	0.0339036i
$310$	1.01105	+	8.09287i	0.0574237	+	0.459644i
$311$			18.1993i			1.03199i	0.856592	+	0.515995i	$0.172578\pi$
$311$			18.1993i			1.03199i	−0.856592	+	0.515995i	$0.827422\pi$
$312$	−0.661494	−	1.69112i	−0.0374497	−	0.0957408i
$313$	−10.0939	−	17.4831i	−0.570540	−	0.988205i	−0.996511	−	0.0834674i	$-0.973401\pi$
$313$	−10.0939	−	17.4831i	−0.570540	−	0.988205i	0.425970	−	0.904737i	$-0.359933\pi$
$314$	−1.66606	−	13.3359i	−0.0940214	−	0.752588i
$315$	7.59638			0.428007
$316$	−10.1478	−	10.4199i	−0.570860	−	0.586164i
$317$	5.63351	+	9.75752i	0.316409	+	0.548037i	0.979736	−	0.200293i	$-0.0641893\pi$
$317$	5.63351	+	9.75752i	0.316409	+	0.548037i	−0.663327	+	0.748330i	$0.730856\pi$
$318$	2.40989	−	1.82398i	0.135140	−	0.102284i
$319$	19.3019	+	33.4319i	1.08070	+	1.87183i
$320$	−4.68971	+	1.05916i	−0.262163	+	0.0592091i
$321$	−0.584345	+	1.01211i	−0.0326149	+	0.0564907i
$322$	12.6229	−	29.9134i	0.703449	−	1.66701i
$323$	−12.5758	+	4.44028i	−0.699736	+	0.247064i
$324$	−12.0237	−	12.3461i	−0.667985	−	0.685893i
$325$	−7.19923	+	12.4694i	−0.399341	+	0.691679i
$326$	6.47028	+	8.54870i	0.358356	+	0.473469i
$327$	−1.33543	+	0.771012i	−0.0738496	+	0.0426371i
$328$	−0.819365	−	0.124454i	−0.0452419	−	0.00687182i
$329$	−14.3051	−	24.7771i	−0.788664	−	1.36601i
$330$	−0.349405	+	0.828009i	−0.0192341	+	0.0455804i
$331$			7.09639i			0.390053i	0.980798	+	0.195026i	$0.0624793\pi$
$331$			7.09639i			0.390053i	−0.980798	+	0.195026i	$0.937521\pi$
$332$	4.01219	−	14.2188i	0.220198	−	0.780356i
$333$	6.56624	+	11.3731i	0.359828	+	0.623240i
$334$	3.44101	−	8.15438i	0.188284	−	0.446188i
$335$	−4.15291			−0.226898
$336$	−3.10831	+	1.68658i	−0.169572	+	0.0920104i
$337$	−5.17102	−	2.98549i	−0.281683	−	0.162630i	0.352502	−	0.935811i	$-0.385331\pi$
$337$	−5.17102	−	2.98549i	−0.281683	−	0.162630i	−0.634185	+	0.773181i	$0.718664\pi$
$338$	−4.72324	+	0.590078i	−0.256911	+	0.0320960i
$339$	−0.538799	+	0.933228i	−0.0292636	+	0.0506860i
$340$	0.904759	+	3.56453i	0.0490674	+	0.193314i
$341$	49.0570			2.65659
$342$	−16.3045	+	8.15340i	−0.881647	+	0.440885i
$343$			18.2495i			0.985379i
$344$	−0.758076	+	4.99093i	−0.0408727	+	0.269093i
$345$	0.578228	+	0.333840i	0.0311307	+	0.0179733i
$346$	−18.6440	+	2.32921i	−1.00231	+	0.125219i
$347$	−17.0632	+	29.5544i	−0.916003	+	1.58656i	−0.110576	+	0.993868i	$0.535269\pi$
$347$	−17.0632	+	29.5544i	−0.916003	+	1.58656i	−0.805427	+	0.592695i	$0.798064\pi$
$348$	−3.00644	−	0.848344i	−0.161162	−	0.0454760i
$349$		−	30.1709i		−	1.61501i	−0.589859	−	0.807506i	$-0.700817\pi$
$349$		−	30.1709i		−	1.61501i	0.589859	−	0.807506i	$-0.299183\pi$
$350$	25.8346	+	10.9018i	1.38092	+	0.582723i
$351$	−3.31222	+	1.91231i	−0.176793	+	0.102072i
$352$	2.82479	+	28.7808i	0.150562	+	1.53402i
$353$	−31.1749			−1.65927			−0.829637	−	0.558304i	$-0.811452\pi$
$353$	−31.1749			−1.65927			−0.829637	+	0.558304i	$0.811452\pi$
$354$	−0.111612	+	0.264495i	−0.00593213	+	0.0140578i
$355$	0.180476	−	0.104198i	0.00957868	−	0.00553025i
$356$	3.09547	+	12.1954i	0.164059	+	0.646354i
$357$	1.35251	+	2.34262i	0.0715826	+	0.123985i
$358$	13.5744	−	10.2741i	0.717431	−	0.543004i
$359$	−14.9265	−	8.61784i	−0.787793	−	0.454832i	0.0513922	−	0.998679i	$-0.483634\pi$
$359$	−14.9265	−	8.61784i	−0.787793	−	0.454832i	−0.839185	+	0.543846i	$0.816967\pi$
$360$	1.83115	+	4.68136i	0.0965100	+	0.246729i
$361$	2.93764	+	18.7715i	0.154613	+	0.987975i
$362$	−10.1674	+	24.0943i	−0.534385	+	1.26637i
$363$	2.71109	+	1.56525i	0.142295	+	0.0821543i
$364$	−6.52793	−	25.7184i	−0.342156	−	1.34801i
$365$	−4.80428	+	2.77375i	−0.251468	+	0.145185i
$366$	1.03754	+	1.37082i	0.0542330	+	0.0716540i
$367$	29.7504	−	17.1764i	1.55296	−	0.896601i	0.555060	−	0.831810i	$-0.312695\pi$
$367$	29.7504	−	17.1764i	1.55296	−	0.896601i	0.997899	−	0.0647906i	$-0.0206380\pi$
$368$	21.4773	+	0.568245i	1.11958	+	0.0296218i
$369$			0.866500i			0.0451082i
$370$	−0.467890	−	3.74520i	−0.0243245	−	0.194704i
$371$	38.2459	−	22.0813i	1.98563	−	1.14640i
$372$	−2.84388	+	2.76964i	−0.147449	+	0.143599i
$373$	−11.8593			−0.614052			−0.307026	−	0.951701i	$-0.599334\pi$
$373$	−11.8593			−0.614052			−0.307026	+	0.951701i	$0.599334\pi$
$374$	21.9499	−	2.74221i	1.13500	−	0.141796i
$375$	−0.599087	+	1.03765i	−0.0309367	+	0.0535840i
$376$	11.8209	−	14.7883i	0.609614	−	0.762649i
$377$	11.7192	−	20.2983i	0.603571	−	1.04542i
$378$	4.49509	+	5.93902i	0.231202	+	0.305470i
$379$		−	3.54229i		−	0.181955i	−0.995853	−	0.0909777i	$-0.971001\pi$
$379$		−	3.54229i		−	0.181955i	0.995853	−	0.0909777i	$-0.0289992\pi$
$380$	5.22835	−	0.337129i	0.268209	−	0.0172944i
$381$		−	0.549011i		−	0.0281267i
$382$	−20.7851	+	15.7317i	−1.06346	+	0.804904i
$383$	5.89926	−	10.2178i	0.301438	−	0.522106i	−0.675024	−	0.737796i	$-0.735867\pi$
$383$	5.89926	−	10.2178i	0.301438	−	0.522106i	0.976462	+	0.215690i	$0.0692001\pi$
$384$	−1.78865	−	1.50897i	−0.0912766	−	0.0770044i
$385$	−6.56603	+	11.3727i	−0.334636	+	0.579607i
$386$	4.22294	+	33.8022i	0.214942	+	1.72049i
$387$	5.27804			0.268298
$388$	−13.0237	+	12.6837i	−0.661177	+	0.643915i
$389$	2.20471	−	1.27289i	0.111783	−	0.0645382i	−0.443066	−	0.896489i	$-0.646109\pi$
$389$	2.20471	−	1.27289i	0.111783	−	0.0645382i	0.554849	+	0.831951i	$0.312776\pi$
$390$	0.541447	−	0.0676434i	0.0274172	−	0.00342525i
$391$		−	16.4340i		−	0.831102i
$392$	−29.6850	+	11.6115i	−1.49932	+	0.586470i
$393$	1.60625	−	0.927367i	0.0810244	−	0.0467795i
$394$	−3.21744	+	2.43520i	−0.162093	+	0.122684i
$395$	3.78502	−	2.18528i	0.190445	−	0.109954i
$396$	29.3066	−	7.43868i	1.47271	−	0.373808i
$397$	−12.5610	−	7.25209i	−0.630418	−	0.363972i	0.150496	−	0.988611i	$-0.451913\pi$
$397$	−12.5610	−	7.25209i	−0.630418	−	0.363972i	−0.780914	+	0.624639i	$0.785246\pi$
$398$	15.4760	+	6.53061i	0.775743	+	0.327350i
$399$	3.63384	−	1.28304i	0.181920	−	0.0642324i
$400$	−0.490762	+	18.5488i	−0.0245381	+	0.927440i
$401$	20.4810	+	11.8247i	1.02277	+	0.590499i	0.914906	−	0.403666i	$-0.132264\pi$
$401$	20.4810	+	11.8247i	1.02277	+	0.590499i	0.107868	+	0.994165i	$0.465598\pi$
$402$	−1.21990	−	1.61176i	−0.0608430	−	0.0803873i
$403$	−14.8926	−	25.7947i	−0.741851	−	1.28492i
$404$	1.96505	+	7.74182i	0.0977650	+	0.385170i
$405$	4.48471	−	2.58925i	0.222847	−	0.128661i
$406$	−42.0548	−	17.7464i	−2.08714	−	0.880738i
$407$	−22.7025			−1.12532
$408$	−1.11764	+	1.39820i	−0.0553313	+	0.0692214i
$409$	−9.31853	+	5.38006i	−0.460772	+	0.266027i	−0.712369	−	0.701805i	$-0.752378\pi$
$409$	−9.31853	+	5.38006i	−0.460772	+	0.266027i	0.251597	+	0.967832i	$0.419044\pi$
$410$	0.0968208	−	0.229443i	0.00478164	−	0.0113314i
$411$			0.160024i			0.00789341i
$412$	−3.12991	+	11.0920i	−0.154199	+	0.546466i
$413$	−2.09742	+	3.63284i	−0.103207	+	0.178761i
$414$	−2.78469	−	22.2899i	−0.136860	−	1.09549i
$415$	3.84466	+	2.21971i	0.188727	+	0.108961i
$416$	14.2757	−	10.2225i	0.699923	−	0.501198i
$417$		−	0.0992166i		−	0.00485866i
$418$	1.88639	−	31.4573i	0.0922664	−	1.53863i
$419$	−12.8085			−0.625734			−0.312867	−	0.949797i	$-0.601289\pi$
$419$	−12.8085			−0.625734			−0.312867	+	0.949797i	$0.601289\pi$
$420$	−0.261435	−	1.02999i	−0.0127567	−	0.0502583i
$421$	−5.75808	+	9.97328i	−0.280632	+	0.486068i	−0.971540	−	0.236874i	$-0.923877\pi$
$421$	−5.75808	+	9.97328i	−0.280632	+	0.486068i	0.690909	+	0.722942i	$0.257211\pi$
$422$	−1.79946	−	14.4037i	−0.0875966	−	0.701161i
$423$	−17.1423	−	9.89711i	−0.833487	−	0.481214i
$424$	22.8272	+	18.2467i	1.10859	+	0.886136i
$425$	14.1931			0.688468
$426$	0.0934537	+	0.0394358i	0.00452785	+	0.00191067i
$427$	12.5605	+	21.7555i	0.607847	+	1.05282i
$428$	−10.8757	−	3.06885i	−0.525695	−	0.148339i
$429$		−	3.28212i		−	0.158462i
$430$	−1.39759	−	0.589756i	−0.0673975	−	0.0284406i
$431$	−8.52972	−	14.7739i	−0.410862	−	0.711634i	0.584122	−	0.811666i	$-0.301439\pi$
$431$	−8.52972	−	14.7739i	−0.410862	−	0.711634i	−0.994984	+	0.100032i	$0.968106\pi$
$432$	−2.57643	+	4.20178i	−0.123958	+	0.202158i
$433$	20.6969	−	11.9493i	0.994628	−	0.574249i	0.0879734	−	0.996123i	$-0.471961\pi$
$433$	20.6969	−	11.9493i	0.994628	−	0.574249i	0.906654	+	0.421874i	$0.138628\pi$
$434$	−46.2515	+	35.0065i	−2.22014	+	1.68037i
$435$	0.469340	−	0.812920i	0.0225031	−	0.0389765i
$436$	−10.4028	−	10.6816i	−0.498202	−	0.511558i
$437$	−23.0166	−	4.28783i	−1.10103	−	0.205115i
$438$	−2.48774	−	1.04978i	−0.118869	−	0.0501606i
$439$	16.5886	−	28.7323i	0.791730	−	1.37132i	−0.133166	−	0.991094i	$-0.542514\pi$
$439$	16.5886	−	28.7323i	0.791730	−	1.37132i	0.924895	−	0.380222i	$-0.124152\pi$
$440$	−8.59134	−	1.30494i	−0.409576	−	0.0622108i
$441$	16.6633	+	28.8617i	0.793491	+	1.37437i
$442$	−8.10535	−	10.7090i	−0.385532	−	0.509375i
$443$	−5.18902	−	8.98764i	−0.246538	−	0.427016i	0.716025	−	0.698074i	$-0.245960\pi$
$443$	−5.18902	−	8.98764i	−0.246538	−	0.427016i	−0.962563	+	0.271059i	$0.912626\pi$
$444$	1.31609	−	1.28173i	0.0624587	−	0.0608280i
$445$	−3.78079			−0.179226
$446$	−12.1370	+	1.51628i	−0.574702	+	0.0717980i
$447$	−1.03387	−	1.79072i	−0.0489006	−	0.0846983i
$448$	−23.2009	−	25.1191i	−1.09614	−	1.18677i
$449$		−	32.9836i		−	1.55659i	−0.627898	−	0.778296i	$-0.716085\pi$
$449$		−	32.9836i		−	1.55659i	0.627898	−	0.778296i	$-0.283915\pi$
$450$	19.2505	−	2.40498i	0.907480	−	0.113372i
$451$	−1.29726	−	0.748971i	−0.0610854	−	0.0352677i
$452$	−10.0280	−	2.82966i	−0.471677	−	0.133096i
$453$	0.559269	+	0.322894i	0.0262767	+	0.0151709i
$454$	12.1022	−	9.15985i	0.567986	−	0.429893i
$455$	7.97318			0.373788
$456$	1.66665	+	1.93011i	0.0780479	+	0.0903859i
$457$	16.7790			0.784888			0.392444	−	0.919776i	$-0.371630\pi$
$457$	16.7790			0.784888			0.392444	+	0.919776i	$0.371630\pi$
$458$	25.0661	−	18.9718i	1.17126	−	0.886496i
$459$	3.26499	+	1.88504i	0.152397	+	0.0879862i
$460$	−1.75326	+	6.21334i	−0.0817460	+	0.289699i
$461$	14.4561	+	8.34622i	0.673287	+	0.388722i	0.797321	−	0.603556i	$-0.206250\pi$
$461$	14.4561	+	8.34622i	0.673287	+	0.388722i	−0.124034	+	0.992278i	$0.539583\pi$
$462$	−6.34254	+	0.792378i	−0.295081	+	0.0368647i
$463$			10.5735i			0.491391i	0.969347	+	0.245696i	$0.0790164\pi$
$463$			10.5735i			0.491391i	−0.969347	+	0.245696i	$0.920984\pi$
$464$	0.798885	−	30.1946i	0.0370873	−	1.40175i
$465$	−0.596427	−	1.03304i	−0.0276586	−	0.0479062i
$466$	−5.01397	+	0.626399i	−0.232268	+	0.0290174i
$467$	21.2681			0.984171			0.492086	−	0.870547i	$-0.336235\pi$
$467$	21.2681			0.984171			0.492086	+	0.870547i	$0.336235\pi$
$468$	−12.8081	−	13.1515i	−0.592056	−	0.607927i
$469$	−14.7682	−	25.5793i	−0.681932	−	1.18114i
$470$	3.43327	+	4.53612i	0.158365	+	0.209236i
$471$	0.982827	+	1.70231i	0.0452863	+	0.0784381i
$472$	−2.74438	−	0.416845i	−0.126320	−	0.0191869i
$473$	−4.56215	+	7.90187i	−0.209768	+	0.363328i
$474$	1.95995	+	0.827065i	0.0900236	+	0.0379884i
$475$	3.70316	−	19.8782i	0.169913	−	0.912073i
$476$	−18.7378	+	18.2486i	−0.858845	+	0.836423i
$477$	15.2772	−	26.4608i	0.699493	−	1.21156i
$478$	10.1210	−	7.66030i	0.462923	−	0.350374i
$479$	3.20389	−	1.84977i	0.146390	−	0.0845180i	−0.425016	−	0.905186i	$-0.639732\pi$
$479$	3.20389	−	1.84977i	0.146390	−	0.0845180i	0.571406	+	0.820668i	$0.306398\pi$
$480$	0.571723	−	0.409397i	0.0260954	−	0.0186863i
$481$	6.89194	+	11.9372i	0.314245	+	0.544289i
$482$	21.8590	+	9.22410i	0.995648	+	0.420146i
$483$			4.74869i			0.216073i
$484$	−8.22035	+	29.1320i	−0.373652	+	1.32418i
$485$	−2.73136	−	4.73086i	−0.124025	−	0.214817i
$486$	7.13876	+	3.01243i	0.323821	+	0.136647i
$487$	−7.43224			−0.336787			−0.168393	−	0.985720i	$-0.553858\pi$
$487$	−7.43224			−0.336787			−0.168393	+	0.985720i	$0.553858\pi$
$488$	−10.3793	+	12.9849i	−0.469849	+	0.587797i
$489$	−1.35799	−	0.784037i	−0.0614106	−	0.0354554i
$490$	−1.18738	−	9.50428i	−0.0536402	−	0.429359i
$491$	−3.93958	+	6.82356i	−0.177791	+	0.307943i	−0.941124	−	0.338063i	$-0.890228\pi$
$491$	−3.93958	+	6.82356i	−0.177791	+	0.307943i	0.763333	+	0.646006i	$0.223562\pi$
$492$	0.117488	−	0.0298212i	0.00529678	−	0.00134445i
$493$	−23.1042			−1.04056
$494$	−17.1132	+	8.55783i	−0.769961	+	0.385035i
$495$			9.08556i			0.408366i
$496$	−32.7224	−	20.0645i	−1.46928	−	0.900924i
$497$	1.28359	+	0.741079i	0.0575767	+	0.0332419i
$498$	0.267871	+	2.14416i	0.0120036	+	0.0960820i
$499$	2.48644	−	4.30664i	0.111308	−	0.192792i	−0.804990	−	0.593289i	$-0.797829\pi$
$499$	2.48644	−	4.30664i	0.111308	−	0.192792i	0.916298	+	0.400497i	$0.131163\pi$
$500$	−11.1501	−	3.14628i	−0.498646	−	0.140706i
$501$			1.29449i			0.0578335i
$502$	−11.7431	+	27.8285i	−0.524121	+	1.24204i
$503$	−0.624097	+	0.360323i	−0.0278271	+	0.0160660i	−0.513849	−	0.857881i	$-0.671781\pi$
$503$	−0.624097	+	0.360323i	−0.0278271	+	0.0160660i	0.486022	+	0.873947i	$0.338448\pi$
$504$	−22.3224	+	27.9261i	−0.994320	+	1.24393i
$505$	−2.40010			−0.106803
$506$	35.7776	+	15.0975i	1.59051	+	0.671167i
$507$	0.602915	−	0.348093i	0.0267764	−	0.0154594i
$508$	5.14537	−	1.30601i	0.228289	−	0.0579450i
$509$	−9.37290	−	16.2343i	−0.415446	−	0.719574i	0.580029	−	0.814596i	$-0.303041\pi$
$509$	−9.37290	−	16.2343i	−0.415446	−	0.719574i	−0.995475	+	0.0950218i	$0.969708\pi$
$510$	−0.324609	−	0.428881i	−0.0143739	−	0.0189912i
$511$	−34.1691	−	19.7276i	−1.51155	−	0.872696i
$512$	9.88726	−	20.3529i	0.436959	−	0.899481i
$513$	3.49197	−	4.08094i	0.154174	−	0.180178i
$514$	24.6654	+	10.4084i	1.08794	+	0.459093i
$515$	−2.99921	−	1.73160i	−0.132161	−	0.0763033i
$516$	−0.181648	−	0.715647i	−0.00799659	−	0.0315046i
$517$	29.6344	−	17.1094i	1.30332	−	0.752471i
$518$	21.4042	−	16.2002i	0.940445	−	0.711798i
$519$	2.37988	−	1.37402i	0.104465	−	0.0603129i
$520$	1.92198	+	4.91356i	0.0842843	+	0.215474i
$521$		−	9.60218i		−	0.420679i	−0.977628	−	0.210339i	$-0.932543\pi$
$521$		−	9.60218i		−	0.420679i	0.977628	−	0.210339i	$-0.0674569\pi$
$522$	−31.3369	+	3.91495i	−1.37158	+	0.171352i
$523$	14.8877	−	8.59542i	0.650994	−	0.375851i	−0.137843	−	0.990454i	$-0.544017\pi$
$523$	14.8877	−	8.59542i	0.650994	−	0.375851i	0.788837	+	0.614603i	$0.210684\pi$
$524$	12.5124	+	12.8478i	0.546605	+	0.561258i
$525$	−4.10118			−0.178990
$526$	−2.09130	−	16.7397i	−0.0911851	−	0.729885i
$527$	−14.6802	+	25.4268i	−0.639479	+	1.10761i
$528$	−2.01721	−	3.71766i	−0.0877880	−	0.161790i
$529$	2.92497	−	5.06619i	0.127172	−	0.220269i
$530$	−7.00195	+	5.29959i	−0.304145	+	0.230199i
$531$			2.90225i			0.125947i
$532$	20.6691	+	31.0045i	0.896119	+	1.34421i
$533$			0.909480i			0.0393940i
$534$	−1.11059	−	1.46734i	−0.0480599	−	0.0634980i
$535$	1.69782	−	2.94071i	0.0734031	−	0.127138i
$536$	12.2036	−	15.2671i	0.527114	−	0.659439i
$537$	−1.24497	+	2.15635i	−0.0537243	+	0.0930533i
$538$	8.20626	−	1.02521i	0.353797	−	0.0442001i
$539$	−57.6126			−2.48155
$540$	−1.03332	−	1.06102i	−0.0444669	−	0.0456590i
$541$	31.1057	−	17.9589i	1.33734	−	0.772113i	0.350926	−	0.936403i	$-0.385867\pi$
$541$	31.1057	−	17.9589i	1.33734	−	0.772113i	0.986412	+	0.164290i	$0.0525334\pi$
$542$	0.320962	+	2.56912i	0.0137865	+	0.110353i
$543$		−	3.82491i		−	0.164143i
$544$	−15.7628	−	7.14846i	−0.675822	−	0.306488i
$545$	3.88011	−	2.24018i	0.166206	−	0.0959589i
$546$	2.34209	+	3.09442i	0.100232	+	0.132429i
$547$	−29.0529	+	16.7737i	−1.24221	+	0.717191i	−0.969544	−	0.244918i	$-0.921239\pi$
$547$	−29.0529	+	16.7737i	−1.24221	+	0.717191i	−0.272667	+	0.962109i	$0.587906\pi$
$548$	−1.49976	+	0.380673i	−0.0640665	+	0.0162615i
$549$	15.0518	+	8.69015i	0.642394	+	0.370886i
$550$	−13.0389	+	30.8992i	−0.555981	+	1.31755i
$551$	−6.02818	+	32.3586i	−0.256809	+	1.37852i
$552$	−2.92644	+	1.14470i	−0.124557	+	0.0487215i
$553$	26.9199	+	15.5422i	1.14475	+	0.660923i
$554$	23.7832	−	18.0009i	1.01045	−	0.764785i
$555$	0.276013	+	0.478069i	0.0117161	+	0.0202929i
$556$	0.929865	−	0.236021i	0.0394350	−	0.0100095i
$557$	−20.0662	+	11.5852i	−0.850234	+	0.490883i	−0.860730	−	0.509062i	$-0.829992\pi$
$557$	−20.0662	+	11.5852i	−0.850234	+	0.490883i	0.0104960	+	0.999945i	$0.496659\pi$
$558$	−15.6027	+	36.9747i	−0.660513	+	1.56526i
$559$	5.53984			0.234310
$560$	9.03121	−	4.90037i	0.381638	−	0.207078i
$561$	−2.80187	+	1.61766i	−0.118295	+	0.0682976i
$562$	27.3141	+	11.5261i	1.15217	+	0.486197i
$563$			0.474626i			0.0200031i	0.999950	+	0.0100016i	$0.00318365\pi$
$563$			0.474626i			0.0200031i	−0.999950	+	0.0100016i	$0.996816\pi$
$564$	−0.751980	+	2.66493i	−0.0316641	+	0.112214i
$565$	1.56549	−	2.71150i	0.0658605	−	0.114074i
$566$	1.54126	−	0.192551i	0.0647840	−	0.00809352i
$567$	31.8963	+	18.4153i	1.33952	+	0.773371i
$568$	−0.147283	+	0.969666i	−0.00617987	+	0.0406863i
$569$			27.0578i			1.13432i	0.823608	+	0.567160i	$0.191958\pi$
$569$			27.0578i			1.13432i	−0.823608	+	0.567160i	$0.808042\pi$
$570$	−0.685363	+	0.342730i	−0.0287067	+	0.0143554i
$571$	−28.4018			−1.18858			−0.594290	−	0.804251i	$-0.702567\pi$
$571$	−28.4018			−1.18858			−0.594290	+	0.804251i	$0.702567\pi$
$572$	30.7602	−	7.80766i	1.28615	−	0.326454i
$573$	1.90629	−	3.30179i	0.0796364	−	0.137934i
$574$	1.75753	−	0.219569i	0.0733577	−	0.00916463i
$575$	21.5780	+	12.4581i	0.899864	+	0.519537i
$576$	−22.5907	−	7.02471i	−0.941281	−	0.292696i
$577$	−0.893031			−0.0371774			−0.0185887	−	0.999827i	$-0.505917\pi$
$577$	−0.893031			−0.0371774			−0.0185887	+	0.999827i	$0.505917\pi$
$578$	4.19989	−	9.95275i	0.174692	−	0.413980i
$579$	−2.49115	−	4.31480i	−0.103529	−	0.179317i
$580$	8.73523	+	2.46487i	0.362711	+	0.102348i
$581$			31.5742i			1.30992i
$582$	1.03374	−	2.44972i	0.0428499	−	0.101544i
$583$	26.4101	+	45.7436i	1.09379	+	1.89450i
$584$	3.92069	−	25.8126i	0.162239	−	1.06813i
$585$	4.77728	−	2.75816i	0.197516	−	0.114036i
$586$	27.7883	+	36.7146i	1.14793	+	1.51667i
$587$	17.1794	−	29.7556i	0.709070	−	1.22814i	−0.256133	−	0.966642i	$-0.582448\pi$
$587$	17.1794	−	29.7556i	0.709070	−	1.22814i	0.965203	−	0.261503i	$-0.0842182\pi$
$588$	3.33986	−	3.25267i	0.137734	−	0.134138i
$589$	31.7813	+	27.1945i	1.30952	+	1.12053i
$590$	0.324291	−	0.768494i	0.0133508	−	0.0316384i
$591$	0.295085	−	0.511103i	0.0121382	−	0.0210240i
$592$	15.1432	+	9.28541i	0.622381	+	0.381628i
$593$	4.40937	+	7.63726i	0.181071	+	0.313625i	0.942246	−	0.334923i	$-0.108710\pi$
$593$	4.40937	+	7.63726i	0.181071	+	0.313625i	−0.761174	+	0.648547i	$0.775377\pi$
$594$	−7.10330	+	5.37630i	−0.291452	+	0.220592i
$595$	−3.92974	−	6.80651i	−0.161104	−	0.279040i
$596$	14.3233	−	13.9494i	0.586707	−	0.571389i
$597$	−2.45678			−0.100549
$598$	−2.92282	−	23.3955i	−0.119523	−	0.956713i
$599$	−5.46239	−	9.46114i	−0.223187	−	0.386572i	0.732587	−	0.680674i	$-0.238313\pi$
$599$	−5.46239	−	9.46114i	−0.223187	−	0.386572i	−0.955774	+	0.294102i	$0.904979\pi$
$600$	−0.988612	−	2.52740i	−0.0403599	−	0.103181i
$601$		−	2.56902i		−	0.104793i	−0.998626	−	0.0523963i	$-0.983314\pi$
$601$		−	2.56902i		−	0.104793i	0.998626	−	0.0523963i	$-0.0166859\pi$
$602$	−1.33744	−	10.7055i	−0.0545101	−	0.436323i
$603$	−17.6973	−	10.2175i	−0.720690	−	0.416091i
$604$	−1.69577	+	6.00962i	−0.0689999	+	0.244528i
$605$	−7.87710	−	4.54785i	−0.320250	−	0.184896i
$606$	−0.705020	−	0.931490i	−0.0286395	−	0.0378392i
$607$	−12.3893			−0.502864			−0.251432	−	0.967875i	$-0.580902\pi$
$607$	−12.3893			−0.502864			−0.251432	+	0.967875i	$0.580902\pi$
$608$	−14.1245	+	20.2114i	−0.572823	+	0.819679i
$609$	6.67610			0.270529
$610$	−3.01458	−	3.98294i	−0.122057	−	0.161264i
$611$	−17.9926	−	10.3880i	−0.727903	−	0.420255i
$612$	−4.91436	+	17.4160i	−0.198651	+	0.703999i
$613$	3.70950	+	2.14168i	0.149825	+	0.0865016i	0.573038	−	0.819528i	$-0.305765\pi$
$613$	3.70950	+	2.14168i	0.149825	+	0.0865016i	−0.423213	+	0.906030i	$0.639098\pi$
$614$	−5.05325	−	40.4484i	−0.203933	−	1.63237i
$615$			0.0364235i			0.00146874i
$616$	−22.5141	−	57.5577i	−0.907120	−	2.31907i
$617$	0.0393000	+	0.0680697i	0.00158216	+	0.00274038i	0.866815	−	0.498629i	$-0.166163\pi$
$617$	0.0393000	+	0.0680697i	0.00158216	+	0.00274038i	−0.865233	+	0.501370i	$0.832830\pi$
$618$	−0.208966	−	1.67266i	−0.00840585	−	0.0672841i
$619$	40.5582			1.63017			0.815087	−	0.579339i	$-0.196689\pi$
$619$	40.5582			1.63017			0.815087	+	0.579339i	$0.196689\pi$
$620$	8.26293	−	8.04720i	0.331847	−	0.323183i
$621$	3.30920	+	5.73170i	0.132794	+	0.230005i
$622$	20.5223	−	15.5328i	0.822868	−	0.622807i
$623$	−13.4449	−	23.2872i	−0.538658	−	0.932984i
$624$	−1.34240	+	2.18926i	−0.0537391	+	0.0876407i
$625$	−9.85641	+	17.0718i	−0.394256	+	0.682872i
$626$	−11.0997	+	26.3038i	−0.443634	+	1.05131i
$627$	1.53457	+	4.34622i	0.0612847	+	0.173571i
$628$	−13.6161	+	13.2606i	−0.543343	+	0.529157i
$629$	6.79366	−	11.7670i	0.270881	−	0.469180i
$630$	−6.48336	−	8.56598i	−0.258303	−	0.341277i
$631$	−14.6226	+	8.44235i	−0.582116	+	0.336085i	−0.761974	−	0.647608i	$-0.775770\pi$
$631$	−14.6226	+	8.44235i	−0.582116	+	0.336085i	0.179858	+	0.983693i	$0.442436\pi$
$632$	−3.08889	+	20.3363i	−0.122869	+	0.808933i
$633$	1.06152	+	1.83861i	0.0421917	+	0.0730782i
$634$	6.19488	−	14.6804i	0.246030	−	0.583034i
$635$			1.59516i			0.0633019i
$636$	−4.11359	−	1.16075i	−0.163114	−	0.0460269i
$637$	17.4898	+	30.2933i	0.692973	+	1.20026i
$638$	21.2254	−	50.2991i	0.840320	−	1.99136i
$639$	1.02545			0.0405661
$640$	5.19693	+	4.38433i	0.205427	+	0.173306i
$641$	10.4202	+	6.01609i	0.411572	+	0.237621i	0.691465	−	0.722410i	$-0.256966\pi$
$641$	10.4202	+	6.01609i	0.411572	+	0.237621i	−0.279893	+	0.960031i	$0.590299\pi$
$642$	1.64003	−	0.204890i	0.0647267	−	0.00808635i
$643$	−24.7354	+	42.8430i	−0.975469	+	1.68956i	−0.297089	+	0.954850i	$0.596016\pi$
$643$	−24.7354	+	42.8430i	−0.975469	+	1.68956i	−0.678380	+	0.734711i	$0.737318\pi$
$644$	−44.5050	+	11.2964i	−1.75374	+	0.445140i
$645$	0.221863			0.00873586
$646$	15.7402	+	10.3913i	0.619291	+	0.408839i
$647$			1.69379i			0.0665899i	0.999446	+	0.0332950i	$0.0106001\pi$
$647$			1.69379i			0.0665899i	−0.999446	+	0.0332950i	$0.989400\pi$
$648$	−3.65989	+	24.0956i	−0.143774	+	0.946563i
$649$	−4.34502	−	2.50860i	−0.170557	−	0.0984711i
$650$	20.2054	−	2.52428i	0.792522	−	0.0990103i
$651$	4.24192	−	7.34722i	0.166254	−	0.287960i
$652$	4.11759	−	14.5923i	0.161257	−	0.571479i
$653$			27.4151i			1.07284i	0.843953	+	0.536418i	$0.180223\pi$
$653$			27.4151i			1.07284i	−0.843953	+	0.536418i	$0.819777\pi$
$654$	2.00919	+	0.847842i	0.0785655	+	0.0331533i
$655$	−4.66696	+	2.69447i	−0.182353	+	0.105282i
$656$	0.558973	+	1.03017i	0.0218242	+	0.0402213i
$657$	−27.2974			−1.06497
$658$	−15.7305	+	37.2777i	−0.613240	+	1.45324i
$659$	−23.4040	+	13.5123i	−0.911692	+	0.526366i	−0.880975	−	0.473163i	$-0.843112\pi$
$659$	−23.4040	+	13.5123i	−0.911692	+	0.526366i	−0.0307167	+	0.999528i	$0.509779\pi$
$660$	1.23191	−	0.312686i	0.0479519	−	0.0121713i
$661$	−9.56723	−	16.5709i	−0.372122	−	0.644535i	0.617770	−	0.786359i	$-0.288036\pi$
$661$	−9.56723	−	16.5709i	−0.372122	−	0.644535i	−0.989892	+	0.141824i	$0.954703\pi$
$662$	8.00217	−	6.05663i	0.311013	−	0.235398i
$663$	1.70116	+	0.982167i	0.0660677	+	0.0381442i
$664$	−19.4580	+	7.61113i	−0.755115	+	0.295369i
$665$	−10.5582	+	3.72789i	−0.409428	+	0.144561i
$666$	7.22056	−	17.1110i	0.279791	−	0.663039i
$667$	−35.1256	−	20.2798i	−1.36007	−	0.785237i
$668$	−12.1320	+	3.07939i	−0.469403	+	0.119145i
$669$	1.54927	−	0.894469i	0.0598981	−	0.0345822i
$670$	3.54443	+	4.68299i	0.136933	+	0.180920i
$671$	−26.0204	+	15.0229i	−1.00451	+	0.579952i
$672$	4.55473	+	2.06559i	0.175703	+	0.0796818i
$673$		−	8.98439i		−	0.346323i	−0.984893	−	0.173161i	$-0.944602\pi$
$673$		−	8.98439i		−	0.346323i	0.984893	−	0.173161i	$-0.0553982\pi$
$674$	1.04681	+	8.37910i	0.0403215	+	0.322751i
$675$	−4.95016	+	2.85797i	−0.190532	+	0.110003i
$676$	4.69659	+	4.82250i	0.180638	+	0.185481i
$677$	−35.1548			−1.35111			−0.675555	−	0.737310i	$-0.736096\pi$
$677$	−35.1548			−1.35111			−0.675555	+	0.737310i	$0.736096\pi$
$678$	1.51220	−	0.188920i	0.0580757	−	0.00725543i
$679$	19.4261	−	33.6469i	0.745503	−	1.29125i
$680$	3.24731	−	4.06250i	0.124529	−	0.155790i
$681$	−1.10995	+	1.92248i	−0.0425332	+	0.0736697i
$682$	−41.8692	−	55.3186i	−1.60325	−	2.11826i
$683$			9.65567i			0.369464i	0.982789	+	0.184732i	$0.0591417\pi$
$683$			9.65567i			0.369464i	−0.982789	+	0.184732i	$0.940858\pi$
$684$	23.1097	+	11.4268i	0.883621	+	0.436916i
$685$		−	0.464952i		−	0.0177649i
$686$	20.5788	−	15.5756i	0.785703	−	0.594678i
$687$	−2.29891	+	3.98184i	−0.0877090	+	0.151917i
$688$	6.27498	−	3.40483i	0.239231	−	0.129808i
$689$	16.0349	−	27.7733i	0.610883	−	1.05808i
$690$	−0.117055	−	0.936959i	−0.00445620	−	0.0356694i
$691$	16.0346			0.609985			0.304993	−	0.952355i	$-0.401346\pi$
$691$	16.0346			0.609985			0.304993	+	0.952355i	$0.401346\pi$
$692$	18.5388	+	19.0358i	0.704739	+	0.723631i
$693$	−55.9613	+	32.3093i	−2.12579	+	1.22733i
$694$	47.8898	−	5.98291i	1.81787	−	0.227108i
$695$			0.288275i			0.0109349i
$696$	1.60931	+	4.11422i	0.0610007	+	0.155949i
$697$	0.776402	−	0.448256i	0.0294083	−	0.0169789i
$698$	−34.0219	+	25.7503i	−1.28775	+	0.974663i
$699$	0.640026	−	0.369519i	0.0242080	−	0.0139765i
$700$	−9.75608	−	38.4366i	−0.368745	−	1.45277i
$701$	−34.0643	−	19.6670i	−1.28659	−	0.742813i	−0.308545	−	0.951210i	$-0.599842\pi$
$701$	−34.0643	−	19.6670i	−1.28659	−	0.742813i	−0.978044	+	0.208397i	$0.933175\pi$
$702$	4.98331	+	2.10287i	0.188083	+	0.0793677i
$703$	−14.7077	−	12.5850i	−0.554710	−	0.474652i
$704$	30.0435	−	27.7492i	1.13231	−	1.04584i
$705$	−0.720580	−	0.416027i	−0.0271386	−	0.0156685i
$706$	26.6072	+	35.1541i	1.00137	+	1.32304i
$707$	−8.53504	−	14.7831i	−0.320993	−	0.555976i
$708$	0.393515	−	0.0998831i	0.0147892	−	0.00375384i
$709$	24.6303	−	14.2203i	0.925009	−	0.534054i	0.0397794	−	0.999208i	$-0.487334\pi$
$709$	24.6303	−	14.2203i	0.925009	−	0.534054i	0.885230	+	0.465154i	$0.154001\pi$
$710$	−0.271531	−	0.114581i	−0.0101904	−	0.00430015i
$711$	21.5061			0.806543
$712$	11.1101	−	13.8991i	0.416368	−	0.520890i
$713$	−44.6369	+	25.7711i	−1.67167	+	0.965137i
$714$	1.48729	−	3.52453i	0.0556604	−	0.131902i
$715$			9.53623i			0.356635i
$716$	−23.1710	−	6.53830i	−0.865942	−	0.244348i
$717$	−0.928238	+	1.60776i	−0.0346657	+	0.0600427i
$718$	3.02169	+	24.1869i	0.112768	+	0.902648i
$719$	−12.8976	−	7.44643i	−0.480999	−	0.277705i	0.239834	−	0.970814i	$-0.422907\pi$
$719$	−12.8976	−	7.44643i	−0.480999	−	0.277705i	−0.720833	+	0.693109i	$0.756240\pi$
$720$	3.71604	−	6.06032i	0.138488	−	0.225855i
$721$		−	24.6310i		−	0.917306i
$722$	18.6603	−	19.3337i	0.694464	−	0.719527i
$723$	−3.47006			−0.129053
$724$	35.8473	−	9.09887i	1.33226	−	0.338157i
$725$	17.5146	−	30.3361i	0.650474	−	1.12665i
$726$	−0.548826	−	4.39305i	−0.0203689	−	0.163041i
$727$	30.7029	+	17.7263i	1.13871	+	0.657433i	0.946110	−	0.323844i	$-0.104975\pi$
$727$	30.7029	+	17.7263i	1.13871	+	0.657433i	0.192598	+	0.981278i	$0.438309\pi$
$728$	−23.4297	+	29.3113i	−0.868361	+	1.08635i
$729$	24.7171			0.915447
$730$	7.22816	+	3.05016i	0.267526	+	0.112891i
$731$	−2.73042	−	4.72923i	−0.100988	−	0.174917i
$732$	0.660275	−	2.33994i	0.0244045	−	0.0864867i
$733$		−	44.4378i		−	1.64135i	−0.571398	−	0.820673i	$-0.693599\pi$
$733$		−	44.4378i		−	1.64135i	0.571398	−	0.820673i	$-0.306401\pi$
$734$	−44.7602	−	18.8880i	−1.65213	−	0.697169i
$735$	0.700445	+	1.21321i	0.0258363	+	0.0447498i
$736$	−17.6897	−	24.7037i	−0.652051	−	0.910590i
$737$	30.5938	−	17.6633i	1.12694	−	0.650638i
$738$	0.977100	−	0.739541i	0.0359675	−	0.0272229i
$739$	20.4324	−	35.3899i	0.751617	−	1.30184i	−0.195421	−	0.980719i	$-0.562607\pi$
$739$	20.4324	−	35.3899i	0.751617	−	1.30184i	0.947039	−	0.321120i	$-0.104059\pi$
$740$	−3.82390	+	3.72406i	−0.140569	+	0.136899i
$741$	1.81943	−	2.12630i	0.0668383	−	0.0781116i
$742$	−57.5418	−	24.2816i	−2.11243	−	0.891407i
$743$	−11.9523	+	20.7019i	−0.438486	+	0.759481i	−0.997573	−	0.0696286i	$-0.977819\pi$
$743$	−11.9523	+	20.7019i	−0.438486	+	0.759481i	0.559087	+	0.829109i	$0.311152\pi$
$744$	5.55035	+	0.843046i	0.203486	+	0.0309076i
$745$	3.00393	+	5.20296i	0.110055	+	0.190622i
$746$	10.1217	+	13.3730i	0.370582	+	0.489622i
$747$	10.9225	+	18.9183i	0.399632	+	0.692183i
$748$	−21.8260	−	22.4111i	−0.798038	−	0.819432i
$749$	24.1505			0.882441
$750$	1.68140	−	0.210059i	0.0613962	−	0.00767027i
$751$	4.45193	+	7.71097i	0.162453	+	0.281377i	0.935748	−	0.352669i	$-0.114726\pi$
$751$	4.45193	+	7.71097i	0.162453	+	0.281377i	−0.773295	+	0.634047i	$0.781393\pi$
$752$	−26.7648	−	0.708139i	−0.976011	−	0.0258232i
$753$		−	4.41770i		−	0.160990i
$754$	−32.8913	+	4.10913i	−1.19783	+	0.149646i
$755$	−1.62496	−	0.938171i	−0.0591384	−	0.0341436i
$756$	2.86061	−	10.1377i	0.104039	−	0.368704i
$757$	37.6088	+	21.7135i	1.36692	+	0.789189i	0.990533	−	0.137276i	$-0.0438346\pi$
$757$	37.6088	+	21.7135i	1.36692	+	0.789189i	0.376382	+	0.926464i	$0.377168\pi$
$758$	−3.99443	+	3.02328i	−0.145084	+	0.109810i
$759$	−5.67962			−0.206157
$760$	−4.84246	−	5.60797i	−0.175654	−	0.203422i
$761$	−24.9068			−0.902871			−0.451435	−	0.892304i	$-0.649088\pi$
$761$	−24.9068			−0.902871			−0.451435	+	0.892304i	$0.649088\pi$
$762$	−0.619087	+	0.468570i	−0.0224272	+	0.0169745i
$763$	27.5962	+	15.9327i	0.999049	+	0.576801i
$764$	35.4794	+	10.0114i	1.28360	+	0.362201i
$765$	−4.70916	−	2.71883i	−0.170260	−	0.0982997i
$766$	−16.5569	+	2.06847i	−0.598225	+	0.0747367i
$767$			3.04621i			0.109992i
$768$	−0.175000	+	3.30483i	−0.00631477	+	0.119253i
$769$	12.2427	+	21.2050i	0.441483	+	0.764672i	0.997800	−	0.0662988i	$-0.0211190\pi$
$769$	12.2427	+	21.2050i	0.441483	+	0.764672i	−0.556316	+	0.830971i	$0.687786\pi$
$770$	18.4283	−	2.30226i	0.664110	−	0.0829677i
$771$	−3.91557			−0.141016
$772$	34.5125	−	33.6115i	1.24213	−	1.20970i
$773$	14.6599	+	25.3917i	0.527281	+	0.913277i	0.999494	+	0.0317928i	$0.0101217\pi$
$773$	14.6599	+	25.3917i	0.527281	+	0.913277i	−0.472214	+	0.881484i	$0.656545\pi$
$774$	−4.50470	−	5.95173i	−0.161918	−	0.213930i
$775$	−22.2571	−	38.5505i	−0.799500	−	1.38477i
$776$	25.4181	+	3.86076i	0.912455	+	0.138593i
$777$	−1.96307	+	3.40013i	−0.0704246	+	0.121979i
$778$	−3.31704	−	1.39973i	−0.118922	−	0.0501829i
$779$	−0.425231	−	1.20434i	−0.0152355	−	0.0431501i
$780$	−0.538392	−	0.552825i	−0.0192775	−	0.0197943i
$781$	−0.886359	+	1.53522i	−0.0317164	+	0.0549345i
$782$	−18.5316	+	14.0261i	−0.662689	+	0.501572i
$783$	8.05809	−	4.65234i	0.287973	−	0.166261i
$784$	38.4292	+	23.5638i	1.37247	+	0.841565i
$785$	−2.85561	−	4.94607i	−0.101921	−	0.176533i
$786$	−2.41663	−	1.01978i	−0.0861985	−	0.0363743i
$787$			32.5060i			1.15871i	0.815074	+	0.579357i	$0.196696\pi$
$787$			32.5060i			1.15871i	−0.815074	+	0.579357i	$0.803304\pi$
$788$	5.49205	+	1.54972i	0.195646	+	0.0552067i
$789$	1.23368	+	2.13680i	0.0439202	+	0.0760720i
$790$	−5.69466	−	2.40305i	−0.202607	−	0.0854965i
$791$	22.2682			0.791765
$792$	−33.4007	−	26.6985i	−1.18684	−	0.948689i
$793$	15.7984	+	9.12120i	0.561017	+	0.323903i
$794$	2.54281	+	20.3538i	0.0902410	+	0.722328i
$795$	0.642178	−	1.11229i	0.0227757	−	0.0394487i
$796$	−5.84431	−	23.0251i	−0.207146	−	0.816104i
$797$	−34.6025			−1.22568			−0.612841	−	0.790206i	$-0.709973\pi$
$797$	−34.6025			−1.22568			−0.612841	+	0.790206i	$0.709973\pi$
$798$	−4.54822	−	3.00262i	−0.161005	−	0.106291i
$799$			20.4798i			0.724523i
$800$	21.3352	−	15.2776i	0.754314	−	0.540146i
$801$	−16.1115	−	9.30200i	−0.569273	−	0.328670i
$802$	−4.14613	−	33.1874i	−0.146405	−	1.17189i
$803$	23.5949	−	40.8676i	0.832647	−	1.44219i
$804$	−0.776326	+	2.75121i	−0.0273789	+	0.0970278i
$805$		−	13.7974i		−	0.486293i
$806$	−16.3766	+	38.8087i	−0.576840	+	1.36698i
$807$	−1.04752	+	0.604784i	−0.0368743	+	0.0212894i
$808$	7.05285	−	8.82337i	0.248118	−	0.310405i
$809$	−34.4643			−1.21170			−0.605851	−	0.795578i	$-0.707167\pi$
$809$	−34.4643			−1.21170			−0.605851	+	0.795578i	$0.707167\pi$
$810$	−6.74736	−	2.84727i	−0.237078	−	0.100043i
$811$	38.5781	−	22.2731i	1.35466	−	0.782114i	0.365763	−	0.930708i	$-0.380808\pi$
$811$	38.5781	−	22.2731i	1.35466	−	0.782114i	0.988898	+	0.148594i	$0.0474748\pi$
$812$	15.8814	+	62.5688i	0.557328	+	2.19573i
$813$	−0.189338	−	0.327944i	−0.00664039	−	0.0115015i
$814$	19.3761	+	25.6002i	0.679133	+	0.897287i
$815$	3.94566	+	2.27803i	0.138210	+	0.0797958i
$816$	2.53055	+	0.0669530i	0.0885871	+	0.00234382i
$817$	−7.33592	+	2.59018i	−0.256651	+	0.0906188i
$818$	14.0199	+	5.91617i	0.490196	+	0.206854i
$819$	33.9771	+	19.6167i	1.18726	+	0.685462i
$820$	−0.341363	+	0.0866459i	−0.0119209	+	0.00302580i
$821$	12.6533	−	7.30537i	0.441602	−	0.254959i	−0.262675	−	0.964884i	$-0.584605\pi$
$821$	12.6533	−	7.30537i	0.441602	−	0.254959i	0.704277	+	0.709925i	$0.251271\pi$
$822$	0.180450	−	0.136578i	0.00629390	−	0.00476369i
$823$	−35.6012	+	20.5544i	−1.24098	+	0.716480i	−0.969294	−	0.245906i	$-0.920914\pi$
$823$	−35.6012	+	20.5544i	−1.24098	+	0.716480i	−0.271686	+	0.962386i	$0.587581\pi$
$824$	15.1791	−	5.93743i	0.528791	−	0.206840i
$825$		−	4.90518i		−	0.170776i
$826$	5.88665	−	0.735423i	0.204823	−	0.0255886i
$827$	−18.9725	+	10.9538i	−0.659740	+	0.380901i	−0.792178	−	0.610290i	$-0.791053\pi$
$827$	−18.9725	+	10.9538i	−0.659740	+	0.380901i	0.132438	+	0.991191i	$0.457719\pi$
$828$	−22.7583	+	22.1641i	−0.790904	+	0.770256i
$829$	−31.0884			−1.07975			−0.539873	−	0.841746i	$-0.681528\pi$
$829$	−31.0884			−1.07975			−0.539873	+	0.841746i	$0.681528\pi$
$830$	−0.778302	−	6.22987i	−0.0270153	−	0.216242i
$831$	−2.18126	+	3.77805i	−0.0756671	+	0.131059i
$832$	−23.7113	−	7.37315i	−0.822041	−	0.255618i
$833$	17.2404	−	29.8613i	0.597346	−	1.03463i
$834$	−0.111881	+	0.0846795i	−0.00387411	+	0.00293221i
$835$		−	3.76115i		−	0.130160i
$836$	−37.0825	+	24.7211i	−1.28253	+	0.854995i
$837$		−	11.8242i		−	0.408704i
$838$	10.9318	+	14.4433i	0.377631	+	0.498936i
$839$	13.8355	−	23.9639i	0.477656	−	0.827325i	−0.522016	−	0.852936i	$-0.674820\pi$
$839$	13.8355	−	23.9639i	0.477656	−	0.827325i	0.999672	+	0.0256110i	$0.00815314\pi$
$840$	−0.938327	+	1.17388i	−0.0323754	+	0.0405027i
$841$	−14.0110	+	24.2678i	−0.483138	+	0.836820i
$842$	16.1607	−	2.01896i	0.556934	−	0.0695781i
$843$	−4.33604			−0.149341
$844$	−14.7064	+	14.3224i	−0.506214	+	0.492998i
$845$	−1.75177	+	1.01139i	−0.0602629	+	0.0347928i
$846$	3.47024	+	27.7773i	0.119309	+	0.955004i
$847$		−	64.6906i		−	2.22280i
$848$	1.09308	−	41.3140i	0.0375366	−	1.41873i
$849$	−0.196740	+	0.113588i	−0.00675209	+	0.00389832i
$850$	−12.1136	−	16.0047i	−0.415492	−	0.548958i
$851$	20.6570	−	11.9263i	0.708112	−	0.408829i
$852$	−0.0352915	−	0.139040i	−0.00120907	−	0.00476343i
$853$	23.2511	+	13.4240i	0.796102	+	0.459630i	0.842106	−	0.539311i	$-0.181315\pi$
$853$	23.2511	+	13.4240i	0.796102	+	0.459630i	−0.0460042	+	0.998941i	$0.514649\pi$
$854$	13.8122	−	32.7317i	0.472643	−	1.12005i
$855$	−5.03654	+	5.88603i	−0.172246	+	0.201298i
$856$	5.82161	+	14.8830i	0.198979	+	0.508692i
$857$	−40.6414	−	23.4643i	−1.38828	−	0.801526i	−0.395161	−	0.918612i	$-0.629311\pi$
$857$	−40.6414	−	23.4643i	−1.38828	−	0.801526i	−0.993122	+	0.117086i	$0.962645\pi$
$858$	−3.70105	+	2.80122i	−0.126352	+	0.0956322i
$859$	14.9976	+	25.9766i	0.511711	+	0.886310i	0.999908	+	0.0135764i	$0.00432164\pi$
$859$	14.9976	+	25.9766i	0.511711	+	0.886310i	−0.488196	+	0.872734i	$0.662345\pi$
$860$	0.527779	+	2.07932i	0.0179971	+	0.0709042i
$861$	−0.224346	+	0.129526i	−0.00764568	+	0.00441423i
$862$	−9.37969	+	22.2277i	−0.319474	+	0.757078i
$863$	34.0860			1.16030			0.580150	−	0.814509i	$-0.302994\pi$
$863$	34.0860			1.16030			0.580150	+	0.814509i	$0.302994\pi$
$864$	6.93703	−	0.680859i	0.236003	−	0.0231633i
$865$	−6.91475	+	3.99223i	−0.235109	+	0.135740i
$866$	−31.1389	−	13.1401i	−1.05814	−	0.446518i
$867$			1.57998i			0.0536588i
$868$	78.9495	+	22.2777i	2.67972	+	0.756153i
$869$	−18.5891	+	32.1973i	−0.630592	+	1.09222i
$870$	−1.31725	+	0.164565i	−0.0446591	+	0.00557929i
$871$	−18.5751	−	10.7244i	−0.629394	−	0.363381i
$872$	−3.16648	+	20.8471i	−0.107231	+	0.705973i
$873$		−	26.8802i		−	0.909759i
$874$	14.8091	+	29.6140i	0.500925	+	1.00171i
$875$	24.7598			0.837035
$876$	0.939462	+	3.70125i	0.0317415	+	0.125054i
$877$	6.18072	−	10.7053i	0.208708	−	0.361493i	−0.742600	−	0.669735i	$-0.766407\pi$
$877$	6.18072	−	10.7053i	0.208708	−	0.361493i	0.951308	+	0.308243i	$0.0997408\pi$
$878$	−46.5577	+	5.81648i	−1.57124	+	0.196297i
$879$	−5.83225	−	3.36725i	−0.196717	−	0.113575i
$880$	5.86103	+	10.8017i	0.197575	+	0.364125i
$881$	28.9288			0.974637			0.487319	−	0.873224i	$-0.337975\pi$
$881$	28.9288			0.974637			0.487319	+	0.873224i	$0.337975\pi$
$882$	18.3238	−	43.4231i	0.616994	−	1.46213i
$883$	−9.68171	−	16.7692i	−0.325815	−	0.564329i	0.655862	−	0.754881i	$-0.272305\pi$
$883$	−9.68171	−	16.7692i	−0.325815	−	0.564329i	−0.981677	+	0.190552i	$0.938972\pi$
$884$	−5.15813	+	18.2798i	−0.173487	+	0.614817i
$885$			0.121997i			0.00410087i
$886$	−5.70609	+	13.5221i	−0.191700	+	0.454284i
$887$	−21.0731	−	36.4996i	−0.707565	−	1.22554i	−0.965758	−	0.259445i	$-0.916460\pi$
$887$	−21.0731	−	36.4996i	−0.707565	−	1.22554i	0.258193	−	0.966093i	$-0.416873\pi$
$888$	−2.56858	−	0.390143i	−0.0861958	−	0.0130923i
$889$	−9.82515	+	5.67255i	−0.329525	+	0.190251i
$890$	3.22683	+	4.26337i	0.108164	+	0.142908i
$891$	−22.0254	+	38.1492i	−0.737880	+	1.27805i
$892$	12.0685	+	12.3920i	0.404083	+	0.414916i
$893$	28.6830	+	5.34343i	0.959838	+	0.178811i
$894$	−1.13690	+	2.69418i	−0.0380236	+	0.0901070i
$895$	3.61727	−	6.26529i	0.120912	−	0.209426i
$896$	−8.52382	+	47.6010i	−0.284761	+	1.59024i
$897$	1.72420	+	2.98640i	0.0575693	+	0.0997130i
$898$	−37.1936	+	28.1508i	−1.24117	+	0.939405i
$899$	36.2312	+	62.7543i	1.20838	+	2.09297i
$900$	−19.1419	−	19.6551i	−0.638064	−	0.655169i
$901$	−31.6126			−1.05317
$902$	0.262613	+	2.10207i	0.00874406	+	0.0699913i
$903$	0.788971	+	1.36654i	0.0262553	+	0.0454755i
$904$	5.36786	+	13.7230i	0.178532	+	0.456421i
$905$			11.1133i			0.369419i
$906$	−0.113217	−	0.906237i	−0.00376138	−	0.0301077i
$907$	8.39646	+	4.84770i	0.278800	+	0.160965i	0.632880	−	0.774250i	$-0.281873\pi$
$907$	8.39646	+	4.84770i	0.278800	+	0.160965i	−0.354080	+	0.935215i	$0.615206\pi$
$908$	−20.6580	−	5.82920i	−0.685561	−	0.193449i
$909$	−10.2279	−	5.90506i	−0.339237	−	0.195858i
$910$	−6.80495	−	8.99087i	−0.225582	−	0.298044i
$911$	56.3184			1.86591			0.932956	−	0.359990i	$-0.117220\pi$
$911$	56.3184			1.86591			0.932956	+	0.359990i	$0.117220\pi$
$912$	0.754023	−	3.52669i	0.0249682	−	0.116780i
$913$	−37.7639			−1.24980
$914$	−14.3205	−	18.9206i	−0.473681	−	0.625839i
$915$	0.632704	+	0.365292i	0.0209166	+	0.0120762i
$916$	−42.7868	−	12.0734i	−1.41372	−	0.398916i
$917$	−33.1925	−	19.1637i	−1.09611	−	0.632840i
$918$	−0.660955	−	5.29057i	−0.0218148	−	0.174615i
$919$		−	5.00431i		−	0.165077i	−0.996588	−	0.0825384i	$-0.973697\pi$
$919$		−	5.00431i		−	0.165077i	0.996588	−	0.0825384i	$-0.0263027\pi$
$920$	8.50278	−	3.32593i	0.280328	−	0.109653i
$921$	2.98096	+	5.16318i	0.0982260	+	0.170132i
$922$	−2.92645	−	23.4246i	−0.0963775	−	0.771448i
$923$	1.07631			0.0354272
$924$	6.30675	+	6.47582i	0.207477	+	0.213039i
$925$	10.3001	+	17.8403i	0.338665	+	0.586586i
$926$	11.9231	−	9.02426i	0.391817	−	0.296556i
$927$	−8.52061	−	14.7581i	−0.279854	−	0.484721i
$928$	−34.7305	+	24.8696i	−1.14008	+	0.816386i
$929$	18.4097	−	31.8866i	0.604003	−	1.04616i	−0.388205	−	0.921573i	$-0.626905\pi$
$929$	18.4097	−	31.8866i	0.604003	−	1.04616i	0.992208	−	0.124592i	$-0.0397620\pi$
$930$	−0.655860	+	1.55424i	−0.0215065	+	0.0509654i
$931$	−37.3240	−	31.9373i	−1.22324	−	1.04670i
$932$	4.98568	+	5.11933i	0.163311	+	0.167689i
$933$	−1.88218	+	3.26004i	−0.0616200	+	0.106729i
$934$	−18.1519	−	23.9828i	−0.593949	−	0.784740i
$935$	8.14085	−	4.70012i	0.266234	−	0.153710i
$936$	−3.89865	+	25.6675i	−0.127431	+	0.838968i
$937$	7.13314	+	12.3550i	0.233030	+	0.403619i	0.958698	−	0.284425i	$-0.0918028\pi$
$937$	7.13314	+	12.3550i	0.233030	+	0.403619i	−0.725669	+	0.688044i	$0.758469\pi$
$938$	−16.2398	+	38.4846i	−0.530250	+	1.25657i
$939$		−	4.17566i		−	0.136268i
$940$	2.18488	−	7.74298i	0.0712630	−	0.252548i
$941$	19.3865	+	33.5784i	0.631982	+	1.09462i	0.987146	+	0.159821i	$0.0510916\pi$
$941$	19.3865	+	33.5784i	0.631982	+	1.09462i	−0.355164	+	0.934804i	$0.615575\pi$
$942$	1.08076	−	2.56116i	0.0352132	−	0.0834471i
$943$	1.57383			0.0512510
$944$	1.87222	+	3.45044i	0.0609356	+	0.112302i
$945$	2.74116	+	1.58261i	0.0891700	+	0.0514823i
$946$	12.8042	−	1.59963i	0.416299	−	0.0520086i
$947$	8.53862	−	14.7893i	0.277468	−	0.480589i	−0.693287	−	0.720662i	$-0.743838\pi$
$947$	8.53862	−	14.7893i	0.277468	−	0.480589i	0.970755	+	0.240073i	$0.0771714\pi$
$948$	−0.740149	−	2.91600i	−0.0240389	−	0.0947074i
$949$	−28.6515			−0.930066
$950$	−25.5760	+	12.7898i	−0.829795	+	0.414956i
$951$			2.33048i			0.0755711i
$952$	36.5702	+	5.55467i	1.18525	+	0.180028i
$953$	8.50788	+	4.91202i	0.275597	+	0.159116i	0.631429	−	0.775434i	$-0.282469\pi$
$953$	8.50788	+	4.91202i	0.275597	+	0.159116i	−0.355831	+	0.934550i	$0.615802\pi$
$954$	−42.8770	+	5.35666i	−1.38820	+	0.173428i
$955$	−5.53874	+	9.59339i	−0.179230	+	0.310435i
$956$	−17.2761	−	4.87491i	−0.558750	−	0.157666i
$957$			7.98487i			0.258114i
$958$	−4.82033	−	2.03409i	−0.155738	−	0.0657186i
$959$	2.86381	−	1.65342i	0.0924771	−	0.0533917i
$960$	−0.949606	−	0.295285i	−0.0306484	−	0.00953028i
$961$	61.0837			1.97044
$962$	7.57871	−	17.9598i	0.244348	−	0.579047i
$963$	14.4702	−	8.35440i	0.466297	−	0.269217i
$964$	−8.25474	−	32.5216i	−0.265867	−	1.04745i
$965$	7.23806	+	12.5367i	0.233001	+	0.403570i
$966$	5.35481	−	4.05291i	0.172288	−	0.130400i
$967$	27.7028	+	15.9942i	0.890862	+	0.514340i	0.874225	−	0.485522i	$-0.161370\pi$
$967$	27.7028	+	15.9942i	0.890862	+	0.514340i	0.0166380	+	0.999862i	$0.494704\pi$
$968$	39.8663	−	15.5940i	1.28135	−	0.501211i
$969$	−2.71191	−	0.505211i	−0.0871192	−	0.0162297i
$970$	−3.00354	+	7.11769i	−0.0964378	+	0.228535i
$971$	−5.22335	−	3.01570i	−0.167625	−	0.0967784i	0.413840	−	0.910349i	$-0.364187\pi$
$971$	−5.22335	−	3.01570i	−0.167625	−	0.0967784i	−0.581466	+	0.813571i	$0.697520\pi$
$972$	−2.69585	−	10.6210i	−0.0864696	−	0.340669i
$973$	−1.77559	+	1.02514i	−0.0569228	+	0.0328644i
$974$	6.34327	+	8.38088i	0.203251	+	0.268541i
$975$	−2.57919	+	1.48910i	−0.0826002	+	0.0476892i
$976$	23.5008	+	0.621780i	0.752241	+	0.0199027i
$977$		−	31.3826i		−	1.00402i	−0.864863	−	0.502009i	$-0.832595\pi$
$977$		−	31.3826i		−	1.00402i	0.864863	−	0.502009i	$-0.167405\pi$
$978$	0.274908	+	2.20049i	0.00879060	+	0.0703638i
$979$	27.8524	−	16.0806i	0.890168	−	0.513939i
$980$	−9.70400	+	9.45065i	−0.309983	+	0.301890i
$981$	22.0464			0.703887
$982$	11.0569	−	1.38134i	0.352839	−	0.0440804i
$983$	−4.00280	+	6.93306i	−0.127670	+	0.221130i	−0.922773	−	0.385343i	$-0.874083\pi$
$983$	−4.00280	+	6.93306i	−0.127670	+	0.221130i	0.795104	+	0.606474i	$0.207416\pi$
$984$	−0.133902	−	0.107033i	−0.00426863	−	0.00341208i
$985$	−0.857373	+	1.48501i	−0.0273182	+	0.0473165i
$986$	19.7190	+	26.0533i	0.627982	+	0.829705i
$987$		−	5.91775i		−	0.188364i
$988$	24.2560	+	11.9936i	0.771685	+	0.381568i
$989$		−	9.58654i		−	0.304834i
$990$	10.2452	−	7.75435i	0.325615	−	0.246449i
$991$	−2.19902	+	3.80882i	−0.0698542	+	0.120991i	−0.898837	−	0.438283i	$-0.855587\pi$
$991$	−2.19902	+	3.80882i	−0.0698542	+	0.120991i	0.828983	+	0.559274i	$0.188920\pi$
$992$	5.30234	+	54.0237i	0.168350	+	1.71525i
$993$	−0.733913	+	1.27117i	−0.0232900	+	0.0403395i
$994$	−0.259846	−	2.07992i	−0.00824181	−	0.0659710i
$995$	7.13821			0.226296
$996$	2.18921	−	2.13206i	0.0693679	−	0.0675569i
$997$	25.2342	−	14.5690i	0.799176	−	0.461404i	−0.0440071	−	0.999031i	$-0.514012\pi$
$997$	25.2342	−	14.5690i	0.799176	−	0.461404i	0.843183	+	0.537627i	$0.180679\pi$
$998$	−6.97847	+	0.871825i	−0.220900	+	0.0275971i
$999$			5.47197i			0.173126i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	152.2.o.c.27.5	yes	28
4.3	odd	2		608.2.s.c.559.7		28
8.3	odd	2	inner	152.2.o.c.27.2	✓	28
8.5	even	2		608.2.s.c.559.8		28
19.12	odd	6	inner	152.2.o.c.107.2	yes	28
76.31	even	6		608.2.s.c.335.8		28
152.69	odd	6		608.2.s.c.335.7		28
152.107	even	6	inner	152.2.o.c.107.5	yes	28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
152.2.o.c.27.2	✓	28	8.3	odd	2	inner
152.2.o.c.27.5	yes	28	1.1	even	1	trivial
152.2.o.c.107.2	yes	28	19.12	odd	6	inner
152.2.o.c.107.5	yes	28	152.107	even	6	inner
608.2.s.c.335.7		28	152.69	odd	6
608.2.s.c.335.8		28	76.31	even	6
608.2.s.c.559.7		28	4.3	odd	2
608.2.s.c.559.8		28	8.5	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 152 = 2^{3} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	152.o (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.853480 - 1.12764i) q^{2} +(0.179130 + 0.103421i) q^{3} +(-0.543142 + 1.92484i) q^{4} +(-0.520463 - 0.300489i) q^{5} +(-0.0362625 - 0.290261i) q^{6} -4.27429i q^{7} +(2.63408 - 1.03034i) q^{8} +(-1.47861 - 2.56102i) q^{9} +(0.105361 + 0.843356i) q^{10} +5.11222 q^{11} +(-0.296361 + 0.288623i) q^{12} +(-1.55195 - 2.68806i) q^{13} +(-4.81986 + 3.64803i) q^{14} +(-0.0621536 - 0.107653i) q^{15} +(-3.40999 - 2.09092i) q^{16} +(-1.52982 + 2.64973i) q^{17} +(-1.62595 + 3.85312i) q^{18} +(3.31192 + 2.83393i) q^{19} +(0.861078 - 0.838597i) q^{20} +(0.442050 - 0.765653i) q^{21} +(-4.36318 - 5.76474i) q^{22} +(-4.65161 + 2.68561i) q^{23} +(0.578401 + 0.0878537i) q^{24} +(-2.31941 - 4.01734i) q^{25} +(-1.70660 + 4.04424i) q^{26} -1.23220i q^{27} +(8.22732 + 2.32155i) q^{28} +(3.77565 + 6.53961i) q^{29} +(-0.0683471 + 0.161967i) q^{30} +9.59602 q^{31} +(0.552556 + 5.62980i) q^{32} +(0.915751 + 0.528709i) q^{33} +(4.29361 - 0.536404i) q^{34} +(-1.28438 + 2.22461i) q^{35} +(5.73265 - 1.45508i) q^{36} -4.44082 q^{37} +(0.368996 - 6.15336i) q^{38} -0.642014i q^{39} +(-1.68055 - 0.255260i) q^{40} +(-0.253756 - 0.146506i) q^{41} +(-1.24066 + 0.154997i) q^{42} +(-0.892400 + 1.54568i) q^{43} +(-2.77666 + 9.84019i) q^{44} +1.77722i q^{45} +(6.99845 + 2.95322i) q^{46} +(5.79677 - 3.34677i) q^{47} +(-0.394587 - 0.727209i) q^{48} -11.2696 q^{49} +(-2.55054 + 6.04418i) q^{50} +(-0.548073 + 0.316430i) q^{51} +(6.01700 - 1.52725i) q^{52} +(5.16606 + 8.94788i) q^{53} +(-1.38947 + 1.05166i) q^{54} +(-2.66072 - 1.53617i) q^{55} +(-4.40398 - 11.2588i) q^{56} +(0.300176 + 0.850162i) q^{57} +(4.15189 - 9.83900i) q^{58} +(-0.849928 - 0.490706i) q^{59} +(0.240973 - 0.0611645i) q^{60} +(-5.08985 + 2.93862i) q^{61} +(-8.19002 - 10.8209i) q^{62} +(-10.9466 + 6.32001i) q^{63} +(5.87679 - 5.42801i) q^{64} +1.86538i q^{65} +(-0.185382 - 1.48388i) q^{66} +(5.98445 - 3.45512i) q^{67} +(-4.26938 - 4.38383i) q^{68} -1.11099 q^{69} +(3.60475 - 0.450344i) q^{70} +(-0.173380 + 0.300304i) q^{71} +(-6.53351 - 5.22248i) q^{72} +(4.61539 - 7.99410i) q^{73} +(3.79016 + 5.00765i) q^{74} -0.959500i q^{75} +(-7.25370 + 4.83568i) q^{76} -21.8511i q^{77} +(-0.723961 + 0.547947i) q^{78} +(-3.63621 + 6.29810i) q^{79} +(1.14647 + 2.11291i) q^{80} +(-4.30839 + 7.46235i) q^{81} +(0.0513697 + 0.411185i) q^{82} -7.38699 q^{83} +(1.23366 + 1.26673i) q^{84} +(1.59243 - 0.919390i) q^{85} +(2.50462 - 0.312904i) q^{86} +1.56192i q^{87} +(13.4660 - 5.26733i) q^{88} +(5.44821 - 3.14552i) q^{89} +(2.00407 - 1.51683i) q^{90} +(-11.4895 + 6.63349i) q^{91} +(-2.64287 - 10.4123i) q^{92} +(1.71893 + 0.992426i) q^{93} +(-8.72138 - 3.68027i) q^{94} +(-0.872165 - 2.47015i) q^{95} +(-0.483258 + 1.06561i) q^{96} +(7.87192 + 4.54486i) q^{97} +(9.61837 + 12.7080i) q^{98} +(-7.55897 - 13.0925i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q - 3 q^{2} - 6 q^{3} + q^{4} - 3 q^{6} + 8 q^{9} + 6 q^{10} - 16 q^{11} + 13 q^{16} - 22 q^{17} + 4 q^{19} - 40 q^{20} - 21 q^{22} - 11 q^{24} + 16 q^{25} + 36 q^{26} - 10 q^{28} + 4 q^{30} - 3 q^{32}+ \cdots - 28 q^{99}+O(q^{100}) \) 28 * q - 3 * q^2 - 6 * q^3 + q^4 - 3 * q^6 + 8 * q^9 + 6 * q^10 - 16 * q^11 + 13 * q^16 - 22 * q^17 + 4 * q^19 - 40 * q^20 - 21 * q^22 - 11 * q^24 + 16 * q^25 + 36 * q^26 - 10 * q^28 + 4 * q^30 - 3 * q^32 + 36 * q^33 - 12 * q^34 - 28 * q^35 - 8 * q^36 + 38 * q^38 - 48 * q^40 + 6 * q^41 + 14 * q^42 + 30 * q^43 + 5 * q^44 - 15 * q^48 - 68 * q^49 - 42 * q^51 + 36 * q^52 + 23 * q^54 - 26 * q^57 + 20 * q^58 - 18 * q^59 - 42 * q^60 + 22 * q^62 + 70 * q^64 - 27 * q^66 + 78 * q^67 + 4 * q^68 + 18 * q^70 - 24 * q^72 + 14 * q^73 + 4 * q^74 + 47 * q^76 - 30 * q^78 - 20 * q^80 + 6 * q^81 + 23 * q^82 - 32 * q^83 + 42 * q^86 - 18 * q^89 - 96 * q^90 - 12 * q^91 + 46 * q^92 + 50 * q^96 + 30 * q^97 + 15 * q^98 - 28 * q^99

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