LMFDB - Embedded newform 132.2.c.d.23.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [132,2,Mod(23,132)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(132, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([1, 1, 0])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("132.23"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 132 = 2^{2} \cdot 3 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	132.c (of order $2$, degree $1$, minimal)

Newform invariants

comment:select newform

sage:traces = [8,0,2] 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:	$1.05402530668$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	8.0.386672896.3
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{6} - 2x^{5} + 2x^{4} - 4x^{3} - 4x^{2} + 16 $ x^8 - x^6 - 2x^5 + 2x^4 - 4x^3 - 4x^2 + 16
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			23.3
Root			$-0.835949 + 1.14070i$ of defining polynomial
Character	$\chi$	$=$	132.23
Dual form			132.2.c.d.23.4

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.835949 - 1.14070i) q^{2} +(1.10238 + 1.33595i) q^{3} +(-0.602380 + 1.90713i) q^{4} +0.671897i q^{5} +(0.602380 - 2.37427i) q^{6} +2.00000i q^{7} +(2.67901 - 0.907128i) q^{8} +(-0.569517 + 2.94545i) q^{9} +(0.766431 - 0.561672i) q^{10} -1.00000 q^{11} +(-3.21188 + 1.29763i) q^{12} +4.56279 q^{13} +(2.28139 - 1.67190i) q^{14} +(-0.897620 + 0.740686i) q^{15} +(-3.27428 - 2.29763i) q^{16} -4.40952i q^{17} +(3.83595 - 1.81259i) q^{18} -4.56279i q^{19} +(-1.28139 - 0.404737i) q^{20} +(-2.67190 + 2.20476i) q^{21} +(0.835949 + 1.14070i) q^{22} -3.42375 q^{23} +(4.16517 + 2.57903i) q^{24} +4.54855 q^{25} +(-3.81426 - 5.20476i) q^{26} +(-4.56279 + 2.48615i) q^{27} +(-3.81426 - 1.20476i) q^{28} +4.00000i q^{29} +(1.59526 + 0.404737i) q^{30} -1.32810i q^{31} +(0.116226 + 5.65566i) q^{32} +(-1.10238 - 1.33595i) q^{33} +(-5.02993 + 3.68613i) q^{34} -1.34379 q^{35} +(-5.27428 - 2.86042i) q^{36} -11.9865 q^{37} +(-5.20476 + 3.81426i) q^{38} +(5.02993 + 6.09565i) q^{39} +(0.609497 + 1.80002i) q^{40} -4.93428i q^{41} +(4.74853 + 1.20476i) q^{42} -8.97231i q^{43} +(0.602380 - 1.90713i) q^{44} +(-1.97904 - 0.382657i) q^{45} +(2.86208 + 3.90547i) q^{46} +5.21899 q^{47} +(-0.539980 - 6.90713i) q^{48} +3.00000 q^{49} +(-3.80236 - 5.18852i) q^{50} +(5.89089 - 4.86097i) q^{51} +(-2.74853 + 8.70182i) q^{52} +2.78101i q^{53} +(6.65021 + 3.12646i) q^{54} -0.671897i q^{55} +(1.81426 + 5.35803i) q^{56} +(6.09565 - 5.02993i) q^{57} +(4.56279 - 3.34379i) q^{58} +7.33034 q^{59} +(-0.871875 - 2.15805i) q^{60} -3.62851 q^{61} +(-1.51496 + 1.11023i) q^{62} +(-5.89089 - 1.13903i) q^{63} +(6.35424 - 4.86042i) q^{64} +3.06572i q^{65} +(-0.602380 + 2.37427i) q^{66} +0.803347i q^{67} +(8.40952 + 2.65621i) q^{68} +(-3.77428 - 4.57396i) q^{69} +(1.12334 + 1.53286i) q^{70} +9.70182 q^{71} +(1.14615 + 8.40752i) q^{72} +1.47524 q^{73} +(10.0201 + 13.6730i) q^{74} +(5.01423 + 6.07663i) q^{75} +(8.70182 + 2.74853i) q^{76} -2.00000i q^{77} +(2.74853 - 10.8333i) q^{78} -5.37226i q^{79} +(1.54377 - 2.19998i) q^{80} +(-8.35130 - 3.35496i) q^{81} +(-5.62851 + 4.12480i) q^{82} -12.7161 q^{83} +(-2.59526 - 6.42375i) q^{84} +2.96274 q^{85} +(-10.2347 + 7.50039i) q^{86} +(-5.34379 + 4.40952i) q^{87} +(-2.67901 + 0.907128i) q^{88} -15.2347i q^{89} +(1.21788 + 2.57736i) q^{90} +9.12558i q^{91} +(2.06240 - 6.52954i) q^{92} +(1.77428 - 1.46407i) q^{93} +(-4.36281 - 5.95329i) q^{94} +3.06572 q^{95} +(-7.42755 + 6.38996i) q^{96} +1.54855 q^{97} +(-2.50785 - 3.42209i) q^{98} +(0.569517 - 2.94545i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 2 q^{3} + 2 q^{4} - 2 q^{6} + 6 q^{8} + 2 q^{9} + 6 q^{10} - 8 q^{11} - 10 q^{12} - 8 q^{13} - 4 q^{14} - 14 q^{15} - 6 q^{16} + 24 q^{18} + 12 q^{20} - 8 q^{21} + 4 q^{23} - 18 q^{24} - 4 q^{25}+ \cdots - 2 q^{99}+O(q^{100}) $ 8 * q + 2 * q^3 + 2 * q^4 - 2 * q^6 + 6 * q^8 + 2 * q^9 + 6 * q^10 - 8 * q^11 - 10 * q^12 - 8 * q^13 - 4 * q^14 - 14 * q^15 - 6 * q^16 + 24 * q^18 + 12 * q^20 - 8 * q^21 + 4 * q^23 - 18 * q^24 - 4 * q^25 - 8 * q^26 + 8 * q^27 - 8 * q^28 + 8 * q^30 + 30 * q^32 - 2 * q^33 + 4 * q^34 + 16 * q^35 - 22 * q^36 - 20 * q^37 - 28 * q^38 - 4 * q^39 - 4 * q^40 + 16 * q^42 - 2 * q^44 + 18 * q^45 - 22 * q^46 + 24 * q^47 - 2 * q^48 + 24 * q^49 - 42 * q^50 + 16 * q^51 + 24 * q^54 - 8 * q^56 + 4 * q^57 - 8 * q^58 - 44 * q^59 - 12 * q^60 + 16 * q^61 + 10 * q^62 - 16 * q^63 + 26 * q^64 + 2 * q^66 + 40 * q^68 - 10 * q^69 + 36 * q^70 + 20 * q^71 - 6 * q^72 - 16 * q^73 - 14 * q^74 + 36 * q^75 + 12 * q^76 + 4 * q^80 + 2 * q^81 - 40 * q^83 - 16 * q^84 + 16 * q^85 - 24 * q^86 - 16 * q^87 - 6 * q^88 + 50 * q^90 + 12 * q^92 - 6 * q^93 + 28 * q^94 + 24 * q^95 - 22 * q^96 - 28 * q^97 - 2 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/132\mathbb{Z}\right)^\times$.

$n$	$13$	$67$	$89$
$\chi(n)$	$1$	$-1$	$-1$

Coefficient data

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

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

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

$2$	−0.835949	−	1.14070i	−0.591105	−	0.806595i
$2$	−0.835949	−	1.14070i	−0.591105	−	0.806595i
$3$	1.10238	+	1.33595i	0.636459	+	0.771310i
$3$	1.10238	+	1.33595i	0.636459	+	0.771310i
$4$	−0.602380	+	1.90713i	−0.301190	+	0.953564i
$5$			0.671897i			0.300482i	0.988649	+	0.150241i	$0.0480049\pi$
$5$			0.671897i			0.300482i	−0.988649	+	0.150241i	$0.951995\pi$
$6$	0.602380	−	2.37427i	0.245921	−	0.969290i
$7$			2.00000i			0.755929i	0.925820	+	0.377964i	$0.123376\pi$
$7$			2.00000i			0.755929i	−0.925820	+	0.377964i	$0.876624\pi$
$8$	2.67901	−	0.907128i	0.947175	−	0.320718i
$9$	−0.569517	+	2.94545i	−0.189839	+	0.981815i
$10$	0.766431	−	0.561672i	0.242367	−	0.177616i
$11$	−1.00000			−0.301511
$11$	−1.00000			−0.301511
$12$	−3.21188	+	1.29763i	−0.927189	+	0.374594i
$13$	4.56279			1.26549			0.632745	−	0.774360i	$-0.281928\pi$
$13$	4.56279			1.26549			0.632745	+	0.774360i	$0.281928\pi$
$14$	2.28139	−	1.67190i	0.609728	−	0.446833i
$15$	−0.897620	+	0.740686i	−0.231765	+	0.191244i
$16$	−3.27428	−	2.29763i	−0.818569	−	0.574408i
$17$		−	4.40952i		−	1.06947i	−0.845021	−	0.534733i	$-0.820412\pi$
$17$		−	4.40952i		−	1.06947i	0.845021	−	0.534733i	$-0.179588\pi$
$18$	3.83595	−	1.81259i	0.904142	−	0.427233i
$19$		−	4.56279i		−	1.04678i	−0.852095	−	0.523388i	$-0.824668\pi$
$19$		−	4.56279i		−	1.04678i	0.852095	−	0.523388i	$-0.175332\pi$
$20$	−1.28139	−	0.404737i	−0.286528	−	0.0905020i
$21$	−2.67190	+	2.20476i	−0.583056	+	0.481118i
$22$	0.835949	+	1.14070i	0.178225	+	0.243197i
$23$	−3.42375			−0.713902			−0.356951	−	0.934123i	$-0.616184\pi$
$23$	−3.42375			−0.713902			−0.356951	+	0.934123i	$0.616184\pi$
$24$	4.16517	+	2.57903i	0.850211	+	0.526441i
$25$	4.54855			0.909711
$26$	−3.81426	−	5.20476i	−0.748037	−	1.02074i
$27$	−4.56279	+	2.48615i	−0.878109	+	0.478461i
$28$	−3.81426	−	1.20476i	−0.720827	−	0.227678i
$29$			4.00000i			0.742781i	0.928477	+	0.371391i	$0.121119\pi$
$29$			4.00000i			0.742781i	−0.928477	+	0.371391i	$0.878881\pi$
$30$	1.59526	+	0.404737i	0.291254	+	0.0738946i
$31$		−	1.32810i		−	0.238534i	−0.992862	−	0.119267i	$-0.961946\pi$
$31$		−	1.32810i		−	0.238534i	0.992862	−	0.119267i	$-0.0380545\pi$
$32$	0.116226	+	5.65566i	0.0205460	+	0.999789i
$33$	−1.10238	−	1.33595i	−0.191900	−	0.232559i
$34$	−5.02993	+	3.68613i	−0.862625	+	0.632166i
$35$	−1.34379			−0.227143
$36$	−5.27428	−	2.86042i	−0.879046	−	0.476737i
$37$	−11.9865			−1.97058			−0.985288	−	0.170904i	$-0.945331\pi$
$37$	−11.9865			−1.97058			−0.985288	+	0.170904i	$0.945331\pi$
$38$	−5.20476	+	3.81426i	−0.844324	+	0.618754i
$39$	5.02993	+	6.09565i	0.805433	+	0.976085i
$40$	0.609497	+	1.80002i	0.0963699	+	0.284609i
$41$		−	4.93428i		−	0.770604i	−0.922790	−	0.385302i	$-0.874097\pi$
$41$		−	4.93428i		−	0.770604i	0.922790	−	0.385302i	$-0.125903\pi$
$42$	4.74853	+	1.20476i	0.732714	+	0.185898i
$43$		−	8.97231i		−	1.36826i	−0.729358	−	0.684132i	$-0.760181\pi$
$43$		−	8.97231i		−	1.36826i	0.729358	−	0.684132i	$-0.239819\pi$
$44$	0.602380	−	1.90713i	0.0908122	−	0.287510i
$45$	−1.97904	−	0.382657i	−0.295017	−	0.0570432i
$46$	2.86208	+	3.90547i	0.421991	+	0.575830i
$47$	5.21899			0.761269			0.380634	−	0.924726i	$-0.375706\pi$
$47$	5.21899			0.761269			0.380634	+	0.924726i	$0.375706\pi$
$48$	−0.539980	−	6.90713i	−0.0779393	−	0.996958i
$49$	3.00000			0.428571
$50$	−3.80236	−	5.18852i	−0.537735	−	0.733768i
$51$	5.89089	−	4.86097i	0.824890	−	0.680671i
$52$	−2.74853	+	8.70182i	−0.381153	+	1.20673i
$53$			2.78101i			0.382001i	0.981590	+	0.191000i	$0.0611731\pi$
$53$			2.78101i			0.382001i	−0.981590	+	0.191000i	$0.938827\pi$
$54$	6.65021	+	3.12646i	0.904978	+	0.425458i
$55$		−	0.671897i		−	0.0905986i
$56$	1.81426	+	5.35803i	0.242440	+	0.715997i
$57$	6.09565	−	5.02993i	0.807389	−	0.666230i
$58$	4.56279	−	3.34379i	0.599123	−	0.439062i
$59$	7.33034			0.954329			0.477164	−	0.878814i	$-0.341665\pi$
$59$	7.33034			0.954329			0.477164	+	0.878814i	$0.341665\pi$
$60$	−0.871875	−	2.15805i	−0.112559	−	0.278603i
$61$	−3.62851			−0.464584			−0.232292	−	0.972646i	$-0.574622\pi$
$61$	−3.62851			−0.464584			−0.232292	+	0.972646i	$0.574622\pi$
$62$	−1.51496	+	1.11023i	−0.192400	+	0.140999i
$63$	−5.89089	−	1.13903i	−0.742183	−	0.143505i
$64$	6.35424	−	4.86042i	0.794280	−	0.607552i
$65$			3.06572i			0.380256i
$66$	−0.602380	+	2.37427i	−0.0741478	+	0.292252i
$67$			0.803347i			0.0981445i	0.998795	+	0.0490722i	$0.0156265\pi$
$67$			0.803347i			0.0981445i	−0.998795	+	0.0490722i	$0.984374\pi$
$68$	8.40952	+	2.65621i	1.01980	+	0.322112i
$69$	−3.77428	−	4.57396i	−0.454370	−	0.550640i
$70$	1.12334	+	1.53286i	0.134265	+	0.183212i
$71$	9.70182			1.15139			0.575697	−	0.817663i	$-0.304731\pi$
$71$	9.70182			1.15139			0.575697	+	0.817663i	$0.304731\pi$
$72$	1.14615	+	8.40752i	0.135075	+	0.990835i
$73$	1.47524			0.172664			0.0863321	−	0.996266i	$-0.472485\pi$
$73$	1.47524			0.172664			0.0863321	+	0.996266i	$0.472485\pi$
$74$	10.0201	+	13.6730i	1.16482	+	1.58946i
$75$	5.01423	+	6.07663i	0.578994	+	0.701669i
$76$	8.70182	+	2.74853i	0.998168	+	0.315278i
$77$		−	2.00000i		−	0.227921i
$78$	2.74853	−	10.8333i	0.311210	−	1.22663i
$79$		−	5.37226i		−	0.604427i	−0.953240	−	0.302213i	$-0.902274\pi$
$79$		−	5.37226i		−	0.604427i	0.953240	−	0.302213i	$-0.0977255\pi$
$80$	1.54377	−	2.19998i	0.172599	−	0.245965i
$81$	−8.35130	−	3.35496i	−0.927922	−	0.372774i
$82$	−5.62851	+	4.12480i	−0.621565	+	0.455508i
$83$	−12.7161			−1.39577			−0.697884	−	0.716210i	$-0.745875\pi$
$83$	−12.7161			−1.39577			−0.697884	+	0.716210i	$0.745875\pi$
$84$	−2.59526	−	6.42375i	−0.283166	−	0.700889i
$85$	2.96274			0.321355
$86$	−10.2347	+	7.50039i	−1.10363	+	0.808788i
$87$	−5.34379	+	4.40952i	−0.572915	+	0.472750i
$88$	−2.67901	+	0.907128i	−0.285584	+	0.0967002i
$89$		−	15.2347i		−	1.61487i	−0.589954	−	0.807437i	$-0.700854\pi$
$89$		−	15.2347i		−	1.61487i	0.589954	−	0.807437i	$-0.299146\pi$
$90$	1.21788	+	2.57736i	0.128376	+	0.271678i
$91$			9.12558i			0.956620i
$92$	2.06240	−	6.52954i	0.215020	−	0.680751i
$93$	1.77428	−	1.46407i	0.183984	−	0.151817i
$94$	−4.36281	−	5.95329i	−0.449990	−	0.614035i
$95$	3.06572			0.314537
$96$	−7.42755	+	6.38996i	−0.758071	+	0.652172i
$97$	1.54855			0.157232			0.0786159	−	0.996905i	$-0.474950\pi$
$97$	1.54855			0.157232			0.0786159	+	0.996905i	$0.474950\pi$
$98$	−2.50785	−	3.42209i	−0.253331	−	0.345683i
$99$	0.569517	−	2.94545i	0.0572387	−	0.296028i
$100$	−2.73996	+	8.67468i	−0.273996	+	0.867468i
$101$			13.5351i			1.34679i	0.739282	+	0.673396i	$0.235165\pi$
$101$			13.5351i			1.34679i	−0.739282	+	0.673396i	$0.764835\pi$
$102$	−10.4694	−	2.65621i	−1.03662	−	0.263004i
$103$			13.2788i			1.30840i	0.756320	+	0.654202i	$0.226995\pi$
$103$			13.2788i			1.30840i	−0.756320	+	0.654202i	$0.773005\pi$
$104$	12.2238	−	4.13903i	1.19864	−	0.405866i
$105$	−1.48137	−	1.79524i	−0.144567	−	0.175198i
$106$	3.17229	−	2.32478i	0.308120	−	0.225802i
$107$	−16.6008			−1.60486			−0.802431	−	0.596745i	$-0.796460\pi$
$107$	−16.6008			−1.60486			−0.802431	+	0.596745i	$0.796460\pi$
$108$	−1.99288	−	10.1994i	−0.191765	−	0.981441i
$109$	3.21899			0.308324			0.154162	−	0.988046i	$-0.450732\pi$
$109$	3.21899			0.308324			0.154162	+	0.988046i	$0.450732\pi$
$110$	−0.766431	+	0.561672i	−0.0730764	+	0.0535533i
$111$	−13.2137	−	16.0134i	−1.25419	−	1.51993i
$112$	4.59526	−	6.54855i	0.434212	−	0.618780i
$113$			19.0165i			1.78892i	0.447149	+	0.894459i	$0.352439\pi$
$113$			19.0165i			1.78892i	−0.447149	+	0.894459i	$0.647561\pi$
$114$	−10.8333	−	2.74853i	−1.01463	−	0.257424i
$115$		−	2.30041i		−	0.214514i
$116$	−7.62851	−	2.40952i	−0.708290	−	0.223718i
$117$	−2.59859	+	13.4394i	−0.240239	+	1.24248i
$118$	−6.12778	−	8.36169i	−0.564108	−	0.769756i
$119$	8.81904			0.808440
$120$	−1.73284	+	2.79857i	−0.158186	+	0.255473i
$121$	1.00000			0.0909091
$122$	3.03325	+	4.13903i	0.274618	+	0.374731i
$123$	6.59194	−	5.43945i	0.594375	−	0.490458i
$124$	2.53286	+	0.800022i	0.227458	+	0.0718441i
$125$			6.41565i			0.573833i
$126$	3.62519	+	7.67190i	0.322957	+	0.683467i
$127$		−	5.47524i		−	0.485849i	−0.970045	−	0.242925i	$-0.921893\pi$
$127$		−	5.47524i		−	0.485849i	0.970045	−	0.242925i	$-0.0781068\pi$
$128$	−10.8561	−	3.18520i	−0.959551	−	0.281534i
$129$	11.9865	−	9.89089i	1.05536	−	0.870844i
$130$	3.49706	−	2.56279i	0.306713	−	0.224771i
$131$	5.34379			0.466889			0.233445	−	0.972370i	$-0.425000\pi$
$131$	5.34379			0.466889			0.233445	+	0.972370i	$0.425000\pi$
$132$	3.21188	−	1.29763i	0.279558	−	0.112944i
$133$	9.12558			0.791288
$134$	0.916376	−	0.671557i	0.0791628	−	0.0580137i
$135$	−1.67044	−	3.06572i	−0.143769	−	0.263856i
$136$	−4.00000	−	11.8132i	−0.342997	−	1.01297i
$137$		−	8.57848i		−	0.732909i	−0.930436	−	0.366455i	$-0.880572\pi$
$137$		−	8.57848i		−	0.732909i	0.930436	−	0.366455i	$-0.119428\pi$
$138$	−2.06240	+	8.12890i	−0.175563	+	0.691978i
$139$			20.3446i			1.72560i	0.505542	+	0.862802i	$0.331293\pi$
$139$			20.3446i			1.72560i	−0.505542	+	0.862802i	$0.668707\pi$
$140$	0.809475	−	2.56279i	0.0684131	−	0.216595i
$141$	5.75331	+	6.97231i	0.484516	+	0.587174i
$142$	−8.11023	−	11.0668i	−0.680595	−	0.928709i
$143$	−4.56279			−0.381560
$144$	8.63231	−	8.33566i	0.719359	−	0.694639i
$145$	−2.68759			−0.223192
$146$	−1.23323	−	1.68281i	−0.102063	−	0.139270i
$147$	3.30714	+	4.00785i	0.272768	+	0.330562i
$148$	7.22045	−	22.8599i	0.593517	−	1.87907i
$149$			11.0971i			0.909111i	0.890719	+	0.454555i	$0.150202\pi$
$149$			11.0971i			0.909111i	−0.890719	+	0.454555i	$0.849798\pi$
$150$	2.73996	−	10.7995i	0.223717	−	0.881774i
$151$		−	16.0599i		−	1.30693i	−0.756956	−	0.653466i	$-0.773314\pi$
$151$		−	16.0599i		−	1.30693i	0.756956	−	0.653466i	$-0.226686\pi$
$152$	−4.13903	−	12.2238i	−0.335720	−	0.991479i
$153$	12.9880	+	2.51130i	1.05002	+	0.203026i
$154$	−2.28139	+	1.67190i	−0.183840	+	0.134725i
$155$	0.892349			0.0716752
$156$	−14.6551	+	5.92082i	−1.17335	+	0.474045i
$157$	−16.5427			−1.32025			−0.660125	−	0.751156i	$-0.729497\pi$
$157$	−16.5427			−1.32025			−0.660125	+	0.751156i	$0.729497\pi$
$158$	−6.12813	+	4.49094i	−0.487527	+	0.357280i
$159$	−3.71528	+	3.06572i	−0.294641	+	0.243128i
$160$	−3.80002	+	0.0780919i	−0.300418	+	0.00617370i
$161$		−	6.84751i		−	0.539659i
$162$	3.15426	+	12.3309i	0.247822	+	0.968806i
$163$			6.84086i			0.535817i	0.963444	+	0.267909i	$0.0863325\pi$
$163$			6.84086i			0.535817i	−0.963444	+	0.267909i	$0.913667\pi$
$164$	9.41030	+	2.97231i	0.734821	+	0.232098i
$165$	0.897620	−	0.740686i	0.0698796	−	0.0576623i
$166$	10.6300	+	14.5052i	0.825046	+	1.12582i
$167$	−18.8789			−1.46089			−0.730446	−	0.682970i	$-0.760688\pi$
$167$	−18.8789			−1.46089			−0.730446	+	0.682970i	$0.760688\pi$
$168$	−5.15805	+	8.33034i	−0.397952	+	0.642699i
$169$	7.81904			0.601465
$170$	−2.47670	−	3.37959i	−0.189954	−	0.259203i
$171$	13.4394	+	2.59859i	1.02774	+	0.198719i
$172$	17.1113	+	5.40474i	1.30473	+	0.412107i
$173$		−	0.218217i		−	0.0165908i	−0.999966	−	0.00829538i	$-0.997359\pi$
$173$		−	0.218217i		−	0.0165908i	0.999966	−	0.00829538i	$-0.00264053\pi$
$174$	9.49706	+	2.40952i	0.719971	+	0.182665i
$175$			9.09711i			0.687677i
$176$	3.27428	+	2.29763i	0.246808	+	0.173190i
$177$	8.08082	+	9.79295i	0.607391	+	0.736083i
$178$	−17.3782	+	12.7354i	−1.30255	+	0.954560i
$179$	0.233228			0.0174323			0.00871615	−	0.999962i	$-0.497226\pi$
$179$	0.233228			0.0174323			0.00871615	+	0.999962i	$0.497226\pi$
$180$	1.92191	−	3.54377i	0.143251	−	0.264137i
$181$	−13.9581			−1.03750			−0.518748	−	0.854927i	$-0.673602\pi$
$181$	−13.9581			−1.03750			−0.518748	+	0.854927i	$0.673602\pi$
$182$	10.4095	−	7.62851i	0.771605	−	0.565463i
$183$	−4.00000	−	4.84751i	−0.295689	−	0.358338i
$184$	−9.17229	+	3.10578i	−0.676190	+	0.228961i
$185$		−	8.05372i		−	0.592122i
$186$	−3.15327	−	0.800022i	−0.231209	−	0.0586605i
$187$			4.40952i			0.322456i
$188$	−3.14382	+	9.95329i	−0.229286	+	0.725918i
$189$	−4.97231	−	9.12558i	−0.361682	−	0.663788i
$190$	−2.56279	−	3.49706i	−0.185924	−	0.253704i
$191$	15.0142			1.08639			0.543196	−	0.839606i	$-0.317214\pi$
$191$	15.0142			1.08639			0.543196	+	0.839606i	$0.317214\pi$
$192$	13.4981	+	3.13090i	0.974138	+	0.225954i
$193$	−13.0971			−0.942750			−0.471375	−	0.881933i	$-0.656242\pi$
$193$	−13.0971			−0.942750			−0.471375	+	0.881933i	$0.656242\pi$
$194$	−1.29451	−	1.76643i	−0.0929405	−	0.126822i
$195$	−4.09565	+	3.37959i	−0.293296	+	0.242018i
$196$	−1.80714	+	5.72139i	−0.129081	+	0.408670i
$197$		−	27.0388i		−	1.92644i	−0.268722	−	0.963218i	$-0.586601\pi$
$197$		−	27.0388i		−	1.92644i	0.268722	−	0.963218i	$-0.413399\pi$
$198$	−3.83595	+	1.81259i	−0.272609	+	0.128815i
$199$			14.2847i			1.01262i	0.862352	+	0.506308i	$0.168990\pi$
$199$			14.2847i			1.01262i	−0.862352	+	0.506308i	$0.831010\pi$
$200$	12.1856	−	4.12612i	0.861655	−	0.291761i
$201$	−1.07323	+	0.885594i	−0.0756998	+	0.0624650i
$202$	15.4394	−	11.3146i	1.08632	−	0.796096i
$203$	−8.00000			−0.561490
$204$	5.72193	+	14.1628i	0.400615	+	0.991597i
$205$	3.31533			0.231552
$206$	15.1471	−	11.1004i	1.05535	−	0.773404i
$207$	1.94989	−	10.0845i	0.135527	−	0.700920i
$208$	−14.9398	−	10.4836i	−1.03589	−	0.726907i
$209$			4.56279i			0.315615i
$210$	−0.809475	+	3.19053i	−0.0558591	+	0.220167i
$211$		−	2.75254i		−	0.189492i	−0.995501	−	0.0947462i	$-0.969796\pi$
$211$		−	2.75254i		−	0.189492i	0.995501	−	0.0947462i	$-0.0302040\pi$
$212$	−5.30374	−	1.67522i	−0.364262	−	0.115055i
$213$	10.6951	+	12.9611i	0.732816	+	0.888082i
$214$	13.8774	+	18.9365i	0.948642	+	1.29447i
$215$	6.02847			0.411138
$216$	−9.96852	+	10.7995i	−0.678272	+	0.734811i
$217$	2.65621			0.180315
$218$	−2.69091	−	3.67190i	−0.182252	−	0.248692i
$219$	1.62628	+	1.97085i	0.109894	+	0.133178i
$220$	1.28139	+	0.404737i	0.0863916	+	0.0272874i
$221$		−	20.1197i		−	1.35340i
$222$	−7.22045	+	28.4592i	−0.484605	+	1.91006i
$223$			5.32810i			0.356796i	0.983958	+	0.178398i	$0.0570915\pi$
$223$			5.32810i			0.356796i	−0.983958	+	0.178398i	$0.942909\pi$
$224$	−11.3113	+	0.232452i	−0.755769	+	0.0155313i
$225$	−2.59048	+	13.3975i	−0.172699	+	0.893168i
$226$	21.6920	−	15.8968i	1.44293	−	1.05744i
$227$	10.4694			0.694877			0.347438	−	0.937703i	$-0.387052\pi$
$227$	10.4694			0.694877			0.347438	+	0.937703i	$0.387052\pi$
$228$	5.92082	+	14.6551i	0.392116	+	0.970559i
$229$	−14.6741			−0.969694			−0.484847	−	0.874599i	$-0.661125\pi$
$229$	−14.6741			−0.969694			−0.484847	+	0.874599i	$0.661125\pi$
$230$	−2.62407	+	1.92303i	−0.173026	+	0.126801i
$231$	2.67190	−	2.20476i	0.175798	−	0.145063i
$232$	3.62851	+	10.7161i	0.238224	+	0.703544i
$233$		−	2.87442i		−	0.188310i	−0.995558	−	0.0941549i	$-0.969985\pi$
$233$		−	2.87442i		−	0.188310i	0.995558	−	0.0941549i	$-0.0300149\pi$
$234$	17.5026	−	8.27048i	1.14418	−	0.540658i
$235$			3.50663i			0.228747i
$236$	−4.41565	+	13.9799i	−0.287434	+	0.910014i
$237$	7.17707	−	5.92227i	0.466201	−	0.384693i
$238$	−7.37226	−	10.0599i	−0.477873	−	0.652083i
$239$	12.4095			0.802705			0.401353	−	0.915924i	$-0.368540\pi$
$239$	12.4095			0.802705			0.401353	+	0.915924i	$0.368540\pi$
$240$	4.64088	−	0.362811i	0.299568	−	0.0234193i
$241$	−0.540969			−0.0348469			−0.0174234	−	0.999848i	$-0.505546\pi$
$241$	−0.540969			−0.0348469			−0.0174234	+	0.999848i	$0.505546\pi$
$242$	−0.835949	−	1.14070i	−0.0537368	−	0.0733268i
$243$	−4.72424	−	14.8554i	−0.303060	−	0.952971i
$244$	2.18574	−	6.92004i	0.139928	−	0.443010i
$245$			2.01569i			0.128778i
$246$	−11.7153	−	2.97231i	−0.746939	−	0.189507i
$247$		−	20.8190i		−	1.32468i
$248$	−1.20476	−	3.55801i	−0.0765023	−	0.225934i
$249$	−14.0179	−	16.9880i	−0.888350	−	1.07657i
$250$	7.31831	−	5.36315i	0.462851	−	0.339195i
$251$	−8.33621			−0.526177			−0.263088	−	0.964772i	$-0.584741\pi$
$251$	−8.33621			−0.526177			−0.263088	+	0.964772i	$0.584741\pi$
$252$	5.72084	−	10.5486i	0.360379	−	0.664496i
$253$	3.42375			0.215250
$254$	−6.24560	+	4.57702i	−0.391884	+	0.287188i
$255$	3.26607	+	3.95807i	0.204529	+	0.247864i
$256$	5.44178	+	15.0462i	0.340111	+	0.940385i
$257$			6.38105i			0.398039i	0.979996	+	0.199020i	$0.0637757\pi$
$257$			6.38105i			0.398039i	−0.979996	+	0.199020i	$0.936224\pi$
$258$	−21.3026	−	5.40474i	−1.32624	−	0.336484i
$259$		−	23.9731i		−	1.48961i
$260$	−5.84673	−	1.84673i	−0.362599	−	0.114529i
$261$	−11.7818	−	2.27807i	−0.729274	−	0.141009i
$262$	−4.46714	−	6.09565i	−0.275981	−	0.376591i
$263$	3.21234			0.198082			0.0990408	−	0.995083i	$-0.468423\pi$
$263$	3.21234			0.198082			0.0990408	+	0.995083i	$0.468423\pi$
$264$	−4.16517	−	2.57903i	−0.256348	−	0.158728i
$265$	−1.86855			−0.114784
$266$	−7.62851	−	10.4095i	−0.467734	−	0.638249i
$267$	20.3528	−	16.7944i	1.24557	−	1.02780i
$268$	−1.53209	−	0.483920i	−0.0935870	−	0.0295601i
$269$			0.912456i			0.0556334i	0.999613	+	0.0278167i	$0.00885547\pi$
$269$			0.912456i			0.0556334i	−0.999613	+	0.0278167i	$0.991145\pi$
$270$	−2.10066	+	4.46825i	−0.127842	+	0.271929i
$271$		−	1.39918i		−	0.0849941i	−0.999097	−	0.0424970i	$-0.986469\pi$
$271$		−	1.39918i		−	0.0849941i	0.999097	−	0.0424970i	$-0.0135313\pi$
$272$	−10.1314	+	14.4380i	−0.614309	+	0.875432i
$273$	−12.1913	+	10.0599i	−0.737851	+	0.608850i
$274$	−9.78545	+	7.17117i	−0.591161	+	0.433226i
$275$	−4.54855			−0.274288
$276$	10.9967	−	4.44277i	0.661922	−	0.267423i
$277$	−5.35044			−0.321477			−0.160739	−	0.986997i	$-0.551388\pi$
$277$	−5.35044			−0.321477			−0.160739	+	0.986997i	$0.551388\pi$
$278$	23.2070	−	17.0070i	1.39186	−	1.02001i
$279$	3.91185	+	0.756378i	0.234197	+	0.0452831i
$280$	−3.60004	+	1.21899i	−0.215144	+	0.0728488i
$281$			9.09419i			0.542514i	0.962507	+	0.271257i	$0.0874393\pi$
$281$			9.09419i			0.542514i	−0.962507	+	0.271257i	$0.912561\pi$
$282$	3.14382	−	12.3913i	0.187212	−	0.737890i
$283$			3.05908i			0.181843i	0.995858	+	0.0909216i	$0.0289813\pi$
$283$			3.05908i			0.181843i	−0.995858	+	0.0909216i	$0.971019\pi$
$284$	−5.84418	+	18.5026i	−0.346788	+	1.09793i
$285$	3.37959	+	4.09565i	0.200190	+	0.242605i
$286$	3.81426	+	5.20476i	0.225542	+	0.307764i
$287$	9.86855			0.582522
$288$	−16.7246	−	2.87866i	−0.985508	−	0.169627i
$289$	−2.44386			−0.143757
$290$	2.24669	+	3.06572i	0.131930	+	0.180026i
$291$	1.70709	+	2.06879i	0.100072	+	0.121275i
$292$	−0.888657	+	2.81348i	−0.0520047	+	0.164646i
$293$			13.8103i			0.806803i	0.915023	+	0.403402i	$0.132172\pi$
$293$			13.8103i			0.806803i	−0.915023	+	0.403402i	$0.867828\pi$
$294$	1.80714	−	7.12280i	0.105395	−	0.415410i
$295$			4.92523i			0.286758i
$296$	−32.1121	+	10.8733i	−1.86648	+	0.632000i
$297$	4.56279	−	2.48615i	0.264760	−	0.144261i
$298$	12.6584	−	9.27661i	0.733284	−	0.537380i
$299$	−15.6219			−0.903436
$300$	−14.6094	+	5.90235i	−0.843474	+	0.340772i
$301$	17.9446			1.03431
$302$	−18.3194	+	13.4252i	−1.05416	+	0.772534i
$303$	−18.0822	+	14.9208i	−1.03879	+	0.857179i
$304$	−10.4836	+	14.9398i	−0.601276	+	0.856858i
$305$		−	2.43799i		−	0.139599i
$306$	−7.99267	−	16.9147i	−0.456911	−	0.966948i
$307$		−	2.12480i		−	0.121269i	−0.998160	−	0.0606344i	$-0.980688\pi$
$307$		−	2.12480i		−	0.121269i	0.998160	−	0.0606344i	$-0.0193124\pi$
$308$	3.81426	+	1.20476i	0.217337	+	0.0686476i
$309$	−17.7399	+	14.6383i	−1.00919	+	0.832746i
$310$	−0.745958	−	1.01790i	−0.0423675	−	0.0578128i
$311$	−9.77513			−0.554297			−0.277148	−	0.960827i	$-0.589389\pi$
$311$	−9.77513			−0.554297			−0.277148	+	0.960827i	$0.589389\pi$
$312$	19.0048	+	11.7675i	1.07593	+	0.666206i
$313$	5.13903			0.290475			0.145238	−	0.989397i	$-0.453605\pi$
$313$	5.13903			0.290475			0.145238	+	0.989397i	$0.453605\pi$
$314$	13.8288	+	18.8702i	0.780406	+	1.06491i
$315$	0.765314	−	3.95807i	0.0431206	−	0.223012i
$316$	10.2456	+	3.23614i	0.576360	+	0.182047i
$317$		−	21.7975i		−	1.22427i	−0.790754	−	0.612134i	$-0.790311\pi$
$317$		−	21.7975i		−	1.22427i	0.790754	−	0.612134i	$-0.209689\pi$
$318$	6.60285	+	1.67522i	0.370269	+	0.0939418i
$319$		−	4.00000i		−	0.223957i
$320$	3.26570	+	4.26939i	0.182558	+	0.238666i
$321$	−18.3004	−	22.1778i	−1.02143	−	1.23785i
$322$	−7.81093	+	5.72416i	−0.435286	+	0.318995i
$323$	−20.1197			−1.11949
$324$	11.4290	−	13.9060i	0.634945	−	0.772558i
$325$	20.7541			1.15123
$326$	7.80335	−	5.71861i	0.432187	−	0.316724i
$327$	3.54855	+	4.30041i	0.196235	+	0.237813i
$328$	−4.47602	−	13.2190i	−0.247147	−	0.729897i
$329$			10.4380i			0.575465i
$330$	−1.59526	−	0.404737i	−0.0878163	−	0.0222801i
$331$		−	19.7975i		−	1.08817i	−0.839031	−	0.544084i	$-0.816877\pi$
$331$		−	19.7975i		−	1.08817i	0.839031	−	0.544084i	$-0.183123\pi$
$332$	7.65990	−	24.2512i	0.420391	−	1.33095i
$333$	6.82654	−	35.3057i	0.374092	−	1.93474i
$334$	15.7818	+	21.5351i	0.863541	+	1.17835i
$335$	−0.539767			−0.0294906
$336$	13.8143	−	1.07996i	0.753629	−	0.0589166i
$337$	−11.7533			−0.640244			−0.320122	−	0.947376i	$-0.603724\pi$
$337$	−11.7533			−0.640244			−0.320122	+	0.947376i	$0.603724\pi$
$338$	−6.53631	−	8.91915i	−0.355529	−	0.485138i
$339$	−25.4050	+	20.9634i	−1.37981	+	1.13857i
$340$	−1.78470	+	5.65033i	−0.0967888	+	0.306432i
$341$			1.32810i			0.0719208i
$342$	−8.27048	−	17.5026i	−0.447217	−	0.946433i
$343$			20.0000i			1.07990i
$344$	−8.13903	−	24.0369i	−0.438827	−	1.29599i
$345$	3.07323	−	2.53593i	0.165457	−	0.136530i
$346$	−0.248920	+	0.182419i	−0.0133820	+	0.00980688i
$347$	14.6293			0.785341			0.392671	−	0.919679i	$-0.371551\pi$
$347$	14.6293			0.785341			0.392671	+	0.919679i	$0.371551\pi$
$348$	−5.19053	−	12.8475i	−0.278241	−	0.688699i
$349$	22.3475			1.19623			0.598117	−	0.801409i	$-0.295916\pi$
$349$	22.3475			1.19623			0.598117	+	0.801409i	$0.295916\pi$
$350$	10.3770	−	7.60472i	0.554676	−	0.406489i
$351$	−20.8190	+	11.3438i	−1.11124	+	0.605487i
$352$	−0.116226	−	5.65566i	−0.00619486	−	0.301448i
$353$			23.4843i			1.24994i	0.780648	+	0.624971i	$0.214889\pi$
$353$			23.4843i			1.24994i	−0.780648	+	0.624971i	$0.785111\pi$
$354$	4.41565	−	17.4042i	0.234689	−	0.925021i
$355$			6.51863i			0.345973i
$356$	29.0545	+	9.17707i	1.53989	+	0.486384i
$357$	9.72193	+	11.7818i	0.514539	+	0.623558i
$358$	−0.194967	−	0.266043i	−0.0103043	−	0.0140608i
$359$	−0.378136			−0.0199573			−0.00997863	−	0.999950i	$-0.503176\pi$
$359$	−0.378136			−0.0199573			−0.00997863	+	0.999950i	$0.503176\pi$
$360$	−5.64899	+	0.770096i	−0.297728	+	0.0405876i
$361$	−1.81904			−0.0957389
$362$	11.6682	+	15.9219i	0.613269	+	0.836838i
$363$	1.10238	+	1.33595i	0.0578599	+	0.0701191i
$364$	−17.4036	−	5.49706i	−0.912199	−	0.288124i
$365$			0.991213i			0.0518824i
$366$	−2.18574	+	8.61506i	−0.114251	+	0.450316i
$367$		−	13.7421i		−	0.717331i	−0.933466	−	0.358666i	$-0.883232\pi$
$367$		−	13.7421i		−	0.717331i	0.933466	−	0.358666i	$-0.116768\pi$
$368$	11.2103	+	7.86652i	0.584378	+	0.410071i
$369$	14.5336	+	2.81016i	0.756591	+	0.146291i
$370$	−9.18686	+	6.73250i	−0.477602	+	0.350006i
$371$	−5.56201			−0.288765
$372$	1.72339	+	4.26570i	0.0893535	+	0.221166i
$373$	−19.9664			−1.03382			−0.516911	−	0.856039i	$-0.672918\pi$
$373$	−19.9664			−1.03382			−0.516911	+	0.856039i	$0.672918\pi$
$374$	5.02993	−	3.68613i	0.260091	−	0.190605i
$375$	−8.57097	+	7.07248i	−0.442603	+	0.365221i
$376$	13.9818	−	4.73430i	0.721054	−	0.244153i
$377$			18.2512i			0.939982i
$378$	−6.25293	+	13.3004i	−0.321616	+	0.684099i
$379$			10.3967i			0.534045i	0.963690	+	0.267022i	$0.0860398\pi$
$379$			10.3967i			0.534045i	−0.963690	+	0.267022i	$0.913960\pi$
$380$	−1.84673	+	5.84673i	−0.0947353	+	0.299931i
$381$	7.31464	−	6.03580i	0.374741	−	0.309223i
$382$	−12.5511	−	17.1267i	−0.642172	−	0.876278i
$383$	31.8960			1.62981			0.814906	−	0.579593i	$-0.196789\pi$
$383$	31.8960			1.62981			0.814906	+	0.579593i	$0.196789\pi$
$384$	−7.71227	−	18.0145i	−0.393565	−	0.919297i
$385$	1.34379			0.0684861
$386$	10.9485	+	14.9398i	0.557264	+	0.760418i
$387$	26.4274	+	5.10989i	1.34338	+	0.259750i
$388$	−0.932818	+	2.95329i	−0.0473566	+	0.149931i
$389$			9.24134i			0.468554i	0.972170	+	0.234277i	$0.0752723\pi$
$389$			9.24134i			0.468554i	−0.972170	+	0.234277i	$0.924728\pi$
$390$	7.27885	+	1.84673i	0.368579	+	0.0935129i
$391$			15.0971i			0.763494i
$392$	8.03704	−	2.72139i	0.405932	−	0.137451i
$393$	5.89089	+	7.13903i	0.297156	+	0.360117i
$394$	−30.8431	+	22.6031i	−1.55385	+	1.13873i
$395$	3.60961			0.181619
$396$	5.27428	+	2.86042i	0.265042	+	0.143742i
$397$	12.9505			0.649966			0.324983	−	0.945720i	$-0.394641\pi$
$397$	12.9505			0.649966			0.324983	+	0.945720i	$0.394641\pi$
$398$	16.2945	−	11.9413i	0.816771	−	0.598563i
$399$	10.0599	+	12.1913i	0.503623	+	0.610328i
$400$	−14.8932	−	10.4509i	−0.744661	−	0.522545i
$401$		−	11.2570i		−	0.562149i	−0.959686	−	0.281075i	$-0.909309\pi$
$401$		−	11.2570i		−	0.562149i	0.959686	−	0.281075i	$-0.0906908\pi$
$402$	1.90736	+	0.483920i	0.0951304	+	0.0241357i
$403$		−	6.05985i		−	0.301863i
$404$	−25.8132	−	8.15327i	−1.28425	−	0.405640i
$405$	2.25419	−	5.61122i	0.112012	−	0.278824i
$406$	6.68759	+	9.12558i	0.331899	+	0.452895i
$407$	11.9865			0.594151
$408$	11.3723	−	18.3664i	0.563011	−	0.909272i
$409$	8.38105			0.414416			0.207208	−	0.978297i	$-0.433562\pi$
$409$	8.38105			0.414416			0.207208	+	0.978297i	$0.433562\pi$
$410$	−2.77144	−	3.78178i	−0.136872	−	0.186769i
$411$	11.4604	−	9.45674i	0.565300	−	0.466467i
$412$	−25.3245	−	7.99891i	−1.24765	−	0.394078i
$413$			14.6607i			0.721405i
$414$	−13.1333	+	6.20588i	−0.645469	+	0.305002i
$415$		−	8.54388i		−	0.419403i
$416$	0.530314	+	25.8056i	0.0260008	+	1.26522i
$417$	−27.1793	+	22.4274i	−1.33098	+	1.09828i
$418$	5.20476	−	3.81426i	0.254573	−	0.186561i
$419$	13.0686			0.638445			0.319222	−	0.947680i	$-0.396578\pi$
$419$	13.0686			0.638445			0.319222	+	0.947680i	$0.396578\pi$
$420$	4.31610	−	1.74375i	0.210604	−	0.0850863i
$421$	27.9446			1.36194			0.680969	−	0.732313i	$-0.261559\pi$
$421$	27.9446			1.36194			0.680969	+	0.732313i	$0.261559\pi$
$422$	−3.13981	+	2.30098i	−0.152844	+	0.112010i
$423$	−2.97231	+	15.3723i	−0.144519	+	0.747425i
$424$	2.52273	+	7.45036i	0.122515	+	0.361821i
$425$		−	20.0569i		−	0.972904i
$426$	5.84418	−	23.0347i	0.283152	−	1.11604i
$427$		−	7.25703i		−	0.351192i
$428$	10.0000	−	31.6599i	0.483368	−	1.53034i
$429$	−5.02993	−	6.09565i	−0.242847	−	0.294301i
$430$	−5.03949	−	6.87666i	−0.243026	−	0.331622i
$431$	3.53218			0.170139			0.0850696	−	0.996375i	$-0.472889\pi$
$431$	3.53218			0.170139			0.0850696	+	0.996375i	$0.472889\pi$
$432$	20.6521	+	2.34325i	0.993625	+	0.112740i
$433$	5.60549			0.269383			0.134691	−	0.990888i	$-0.456996\pi$
$433$	5.60549			0.269383			0.134691	+	0.990888i	$0.456996\pi$
$434$	−2.22045	−	3.02993i	−0.106585	−	0.145441i
$435$	−2.96274	−	3.59048i	−0.142053	−	0.172150i
$436$	−1.93906	+	6.13903i	−0.0928640	+	0.294006i
$437$			15.6219i			0.747295i
$438$	0.888657	−	3.50262i	0.0424617	−	0.167362i
$439$		−	24.1045i		−	1.15045i	−0.817996	−	0.575223i	$-0.804915\pi$
$439$		−	24.1045i		−	1.15045i	0.817996	−	0.575223i	$-0.195085\pi$
$440$	−0.609497	−	1.80002i	−0.0290566	−	0.0858127i
$441$	−1.70855	+	8.83634i	−0.0813596	+	0.420778i
$442$	−22.9505	+	16.8190i	−1.09164	+	0.800000i
$443$	−34.7340			−1.65026			−0.825131	−	0.564942i	$-0.808899\pi$
$443$	−34.7340			−1.65026			−0.825131	+	0.564942i	$0.808899\pi$
$444$	38.4993	−	15.5541i	1.82710	−	0.738166i
$445$	10.2361			0.485240
$446$	6.07775	−	4.45402i	0.287790	−	0.210904i
$447$	−14.8252	+	12.2332i	−0.701206	+	0.578612i
$448$	9.72084	+	12.7085i	0.459267	+	0.600419i
$449$			15.5290i			0.732857i	0.930446	+	0.366429i	$0.119420\pi$
$449$			15.5290i			0.732857i	−0.930446	+	0.366429i	$0.880580\pi$
$450$	17.4480	−	8.24468i	0.822508	−	0.388658i
$451$			4.93428i			0.232346i
$452$	−36.2668	−	11.4551i	−1.70585	−	0.538804i
$453$	21.4551	−	17.7041i	1.00805	−	0.831809i
$454$	−8.75186	−	11.9424i	−0.410745	−	0.560484i
$455$	−6.13145			−0.287447
$456$	11.7675	−	19.0048i	0.551066	−	0.889980i
$457$	16.0912			0.752716			0.376358	−	0.926474i	$-0.377176\pi$
$457$	16.0912			0.752716			0.376358	+	0.926474i	$0.377176\pi$
$458$	12.2668	+	16.7387i	0.573191	+	0.782150i
$459$	10.9627	+	20.1197i	0.511697	+	0.939107i
$460$	4.38718	+	1.38572i	0.204553	+	0.0646096i
$461$		−	10.9941i		−	0.512048i	−0.966670	−	0.256024i	$-0.917587\pi$
$461$		−	10.9941i		−	0.512048i	0.966670	−	0.256024i	$-0.0824125\pi$
$462$	−4.74853	−	1.20476i	−0.220922	−	0.0560505i
$463$			36.9544i			1.71742i	0.512463	+	0.858709i	$0.328733\pi$
$463$			36.9544i			1.71742i	−0.512463	+	0.858709i	$0.671267\pi$
$464$	9.19053	−	13.0971i	0.426659	−	0.608018i
$465$	0.983707	+	1.19213i	0.0456183	+	0.0552838i
$466$	−3.27885	+	2.40287i	−0.151890	+	0.111311i
$467$	19.0674			0.882336			0.441168	−	0.897425i	$-0.354564\pi$
$467$	19.0674			0.882336			0.441168	+	0.897425i	$0.354564\pi$
$468$	−24.0654	−	13.0515i	−1.11242	−	0.603305i
$469$	−1.60669			−0.0741902
$470$	4.00000	−	2.93136i	0.184506	−	0.135214i
$471$	−18.2363	−	22.1002i	−0.840285	−	1.01832i
$472$	19.6381	−	6.64956i	0.903916	−	0.306071i
$473$			8.97231i			0.412547i
$474$	−12.7552	−	3.23614i	−0.585865	−	0.148641i
$475$		−	20.7541i		−	0.952263i
$476$	−5.31241	+	16.8190i	−0.243494	+	0.770899i
$477$	−8.19130	−	1.58383i	−0.375054	−	0.0725187i
$478$	−10.3737	−	14.1555i	−0.474483	−	0.647458i
$479$	−16.8235			−0.768686			−0.384343	−	0.923190i	$-0.625572\pi$
$479$	−16.8235			−0.768686			−0.384343	+	0.923190i	$0.625572\pi$
$480$	−4.29339	−	4.99055i	−0.195966	−	0.227786i
$481$	−54.6921			−2.49374
$482$	0.452222	+	0.617082i	0.0205982	+	0.0281073i
$483$	9.14792	−	7.54855i	0.416245	−	0.343471i
$484$	−0.602380	+	1.90713i	−0.0273809	+	0.0866877i
$485$			1.04047i			0.0472453i
$486$	−12.9962	+	17.8072i	−0.589521	+	0.807753i
$487$		−	19.1967i		−	0.869883i	−0.900459	−	0.434942i	$-0.856769\pi$
$487$		−	19.1967i		−	0.869883i	0.900459	−	0.434942i	$-0.143231\pi$
$488$	−9.72084	+	3.29153i	−0.440042	+	0.149000i
$489$	−9.13903	+	7.54122i	−0.413281	+	0.341026i
$490$	2.29929	−	1.68501i	0.103872	−	0.0761212i
$491$	−33.7578			−1.52347			−0.761734	−	0.647890i	$-0.775652\pi$
$491$	−33.7578			−1.52347			−0.761734	+	0.647890i	$0.775652\pi$
$492$	6.40287	+	15.8483i	0.288664	+	0.714496i
$493$	17.6381			0.794379
$494$	−23.7482	+	17.4036i	−1.06848	+	0.783027i
$495$	1.97904	+	0.382657i	0.0889511	+	0.0171992i
$496$	−3.05149	+	4.34858i	−0.137016	+	0.195257i
$497$			19.4036i			0.870372i
$498$	−7.65990	+	30.1913i	−0.343248	+	1.35290i
$499$		−	27.4731i		−	1.22986i	−0.788580	−	0.614932i	$-0.789184\pi$
$499$		−	27.4731i		−	1.22986i	0.788580	−	0.614932i	$-0.210816\pi$
$500$	−12.2355	−	3.86466i	−0.547187	−	0.172833i
$501$	−20.8117	−	25.2212i	−0.929799	−	1.12680i
$502$	6.96864	+	9.50909i	0.311026	+	0.424411i
$503$	3.36001			0.149815			0.0749077	−	0.997190i	$-0.476134\pi$
$503$	3.36001			0.149815			0.0749077	+	0.997190i	$0.476134\pi$
$504$	−16.8150	+	2.29230i	−0.749001	+	0.102107i
$505$	−9.09419			−0.404686
$506$	−2.86208	−	3.90547i	−0.127235	−	0.173619i
$507$	8.61955	+	10.4458i	0.382808	+	0.463916i
$508$	10.4420	+	3.29818i	0.463289	+	0.146333i
$509$		−	30.6165i		−	1.35705i	−0.734576	−	0.678527i	$-0.762619\pi$
$509$		−	30.6165i		−	1.35705i	0.734576	−	0.678527i	$-0.237381\pi$
$510$	1.78470	−	7.03434i	0.0790277	−	0.311486i
$511$			2.95049i			0.130522i
$512$	12.6141	−	18.7852i	0.557468	−	0.830198i
$513$	11.3438	+	20.8190i	0.500841	+	0.919183i
$514$	7.27885	−	5.33423i	0.321056	−	0.235283i
$515$	−8.92202			−0.393151
$516$	11.6427	+	28.8179i	0.512543	+	1.26864i
$517$	−5.21899			−0.229531
$518$	−27.3460	+	20.0403i	−1.20152	+	0.880519i
$519$	0.291527	−	0.240559i	0.0127966	−	0.0105593i
$520$	2.78101	+	8.21312i	0.121955	+	0.360169i
$521$		−	24.0537i		−	1.05381i	−0.849923	−	0.526906i	$-0.823352\pi$
$521$		−	24.0537i		−	1.05381i	0.849923	−	0.526906i	$-0.176648\pi$
$522$	7.25038	+	15.3438i	0.317340	+	0.671580i
$523$			1.13223i			0.0495088i	0.999694	+	0.0247544i	$0.00788038\pi$
$523$			1.13223i			0.0495088i	−0.999694	+	0.0247544i	$0.992120\pi$
$524$	−3.21899	+	10.1913i	−0.140622	+	0.445209i
$525$	−12.1533	+	10.0285i	−0.530412	+	0.437678i
$526$	−2.68536	−	3.66431i	−0.117087	−	0.159772i
$527$	−5.85629			−0.255104
$528$	0.539980	+	6.90713i	0.0234996	+	0.300594i
$529$	−11.2779			−0.490344
$530$	1.56201	+	2.13145i	0.0678495	+	0.0925843i
$531$	−4.17475	+	21.5911i	−0.181169	+	0.936974i
$532$	−5.49706	+	17.4036i	−0.238328	+	0.754544i
$533$		−	22.5141i		−	0.975192i
$534$	−36.1712	−	9.17707i	−1.56528	−	0.397131i
$535$		−	11.1540i		−	0.482231i
$536$	0.728739	+	2.15218i	0.0314767	+	0.0929599i
$537$	0.257106	+	0.311581i	0.0110950	+	0.0134457i
$538$	1.04084	−	0.762766i	0.0448736	−	0.0328852i
$539$	−3.00000			−0.129219
$540$	6.85297	−	1.33901i	0.294905	−	0.0576219i
$541$	−18.4313			−0.792425			−0.396213	−	0.918159i	$-0.629676\pi$
$541$	−18.4313			−0.792425			−0.396213	+	0.918159i	$0.629676\pi$
$542$	−1.59604	+	1.16964i	−0.0685558	+	0.0502404i
$543$	−15.3871	−	18.6473i	−0.660324	−	0.800231i
$544$	24.9387	−	0.512500i	1.06924	−	0.0219733i
$545$			2.16283i			0.0926456i
$546$	21.6665	+	5.49706i	0.927243	+	0.235253i
$547$			44.0739i			1.88446i	0.334962	+	0.942232i	$0.391276\pi$
$547$			44.0739i			1.88446i	−0.334962	+	0.942232i	$0.608724\pi$
$548$	16.3603	+	5.16750i	0.698876	+	0.220745i
$549$	2.06650	−	10.6876i	0.0881961	−	0.456135i
$550$	3.80236	+	5.18852i	0.162133	+	0.221239i
$551$	18.2512			0.777525
$552$	−14.2605	−	8.82995i	−0.606968	−	0.375828i
$553$	10.7445			0.456904
$554$	4.47270	+	6.10324i	0.190027	+	0.259302i
$555$	10.7594	−	8.87826i	0.456709	−	0.376861i
$556$	−38.7997	−	12.2552i	−1.64547	−	0.519735i
$557$		−	19.9598i		−	0.845723i	−0.906194	−	0.422862i	$-0.861026\pi$
$557$		−	19.9598i		−	0.845723i	0.906194	−	0.422862i	$-0.138974\pi$
$558$	−2.40731	−	5.09453i	−0.101910	−	0.215669i
$559$		−	40.9387i		−	1.73152i
$560$	4.39996	+	3.08754i	0.185932	+	0.130473i
$561$	−5.89089	+	4.86097i	−0.248714	+	0.205230i
$562$	10.3737	−	7.60228i	0.437589	−	0.320683i
$563$	20.8190			0.877418			0.438709	−	0.898629i	$-0.355436\pi$
$563$	20.8190			0.877418			0.438709	+	0.898629i	$0.355436\pi$
$564$	−16.7628	+	6.77233i	−0.705840	+	0.285167i
$565$	−12.7771			−0.537537
$566$	3.48948	−	2.55723i	0.146674	−	0.107488i
$567$	6.70993	−	16.7026i	0.281791	−	0.701443i
$568$	25.9913	−	8.80080i	1.09057	−	0.369273i
$569$			4.49337i			0.188372i	0.995555	+	0.0941860i	$0.0300248\pi$
$569$			4.49337i			0.188372i	−0.995555	+	0.0941860i	$0.969975\pi$
$570$	1.84673	−	7.27885i	0.0773510	−	0.304877i
$571$		−	7.30868i		−	0.305859i	−0.988237	−	0.152929i	$-0.951129\pi$
$571$		−	7.30868i		−	0.305859i	0.988237	−	0.152929i	$-0.0488707\pi$
$572$	2.74853	−	8.70182i	0.114922	−	0.363842i
$573$	16.5514	+	20.0582i	0.691444	+	0.837945i
$574$	−8.24960	−	11.2570i	−0.344332	−	0.469859i
$575$	−15.5731			−0.649444
$576$	10.6973	+	21.4842i	0.445719	+	0.895173i
$577$	−0.236143			−0.00983076			−0.00491538	−	0.999988i	$-0.501565\pi$
$577$	−0.236143			−0.00983076			−0.00491538	+	0.999988i	$0.501565\pi$
$578$	2.04294	+	2.78771i	0.0849752	+	0.115953i
$579$	−14.4380	−	17.4971i	−0.600022	−	0.727153i
$580$	1.61895	−	5.12558i	0.0672232	−	0.212828i
$581$		−	25.4321i		−	1.05510i
$582$	0.932818	−	3.67668i	0.0386665	−	0.152403i
$583$		−	2.78101i		−	0.115177i
$584$	3.95220	−	1.33824i	0.163543	−	0.0553766i
$585$	−9.02993	−	1.74598i	−0.373341	−	0.0721875i
$586$	15.7533	−	11.5447i	0.650763	−	0.476906i
$587$	−18.1314			−0.748365			−0.374183	−	0.927355i	$-0.622077\pi$
$587$	−18.1314			−0.748365			−0.374183	+	0.927355i	$0.622077\pi$
$588$	−9.63563	+	3.89289i	−0.397367	+	0.160540i
$589$	−6.05985			−0.249692
$590$	5.61820	−	4.11724i	0.231298	−	0.169504i
$591$	36.1225	−	29.8070i	1.48588	−	1.22610i
$592$	39.2473	+	27.5407i	1.61305	+	1.13191i
$593$		−	11.0702i		−	0.454598i	−0.973825	−	0.227299i	$-0.927010\pi$
$593$		−	11.0702i		−	0.454598i	0.973825	−	0.227299i	$-0.0729895\pi$
$594$	−6.65021	−	3.12646i	−0.272861	−	0.128280i
$595$			5.92549i			0.242921i
$596$	−21.1636	−	6.68467i	−0.866895	−	0.273815i
$597$	−19.0837	+	15.7472i	−0.781042	+	0.644489i
$598$	13.0591	+	17.8198i	0.534025	+	0.728706i
$599$	3.35044			0.136895			0.0684477	−	0.997655i	$-0.478195\pi$
$599$	3.35044			0.136895			0.0684477	+	0.997655i	$0.478195\pi$
$600$	18.9455	+	11.7308i	0.773447	+	0.478909i
$601$	9.94170			0.405530			0.202765	−	0.979227i	$-0.435007\pi$
$601$	9.94170			0.405530			0.202765	+	0.979227i	$0.435007\pi$
$602$	−15.0008	−	20.4694i	−0.611386	−	0.834269i
$603$	−2.36622	−	0.457520i	−0.0963597	−	0.0186317i
$604$	30.6282	+	9.67413i	1.24624	+	0.393635i
$605$			0.671897i			0.0273165i
$606$	32.1359	+	8.15327i	1.30543	+	0.331204i
$607$			28.6921i			1.16457i	0.812983	+	0.582287i	$0.197842\pi$
$607$			28.6921i			1.16457i	−0.812983	+	0.582287i	$0.802158\pi$
$608$	25.8056	−	0.530314i	1.04655	−	0.0215071i
$609$	−8.81904	−	10.6876i	−0.357365	−	0.433083i
$610$	−2.78101	+	2.03803i	−0.112600	+	0.0825175i
$611$	23.8132			0.963378
$612$	−12.6131	+	23.2570i	−0.509853	+	0.940110i
$613$	−4.24159			−0.171316			−0.0856581	−	0.996325i	$-0.527299\pi$
$613$	−4.24159			−0.171316			−0.0856581	+	0.996325i	$0.527299\pi$
$614$	−2.42375	+	1.77622i	−0.0978147	+	0.0716826i
$615$	3.65475	+	4.42910i	0.147374	+	0.178599i
$616$	−1.81426	−	5.35803i	−0.0730985	−	0.215881i
$617$		−	35.6396i		−	1.43480i	−0.696663	−	0.717399i	$-0.745333\pi$
$617$		−	35.6396i		−	1.43480i	0.696663	−	0.717399i	$-0.254667\pi$
$618$	31.5275	+	7.99891i	1.26822	+	0.321763i
$619$		−	23.3041i		−	0.936671i	−0.883551	−	0.468335i	$-0.844854\pi$
$619$		−	23.3041i		−	0.936671i	0.883551	−	0.468335i	$-0.155146\pi$
$620$	−0.537533	+	1.70182i	−0.0215878	+	0.0683469i
$621$	15.6219	−	8.51198i	0.626884	−	0.341574i
$622$	8.17151	+	11.1505i	0.327648	+	0.447093i
$623$	30.4694			1.22073
$624$	−2.46381	−	31.5158i	−0.0986315	−	1.26164i
$625$	18.4321			0.737285
$626$	−4.29597	−	5.86208i	−0.171701	−	0.234296i
$627$	−6.09565	+	5.02993i	−0.243437	+	0.200876i
$628$	9.96498	−	31.5490i	0.397646	−	1.25894i
$629$			52.8549i			2.10746i
$630$	−5.15473	+	2.43575i	−0.205369	+	0.0970428i
$631$			8.30997i			0.330815i	0.986225	+	0.165407i	$0.0528939\pi$
$631$			8.30997i			0.330815i	−0.986225	+	0.165407i	$0.947106\pi$
$632$	−4.87333	−	14.3924i	−0.193851	−	0.572498i
$633$	3.67725	−	3.03434i	0.146157	−	0.120604i
$634$	−24.8643	+	18.2216i	−0.987488	+	0.723671i
$635$	3.67880			0.145989
$636$	−3.60872	−	8.93225i	−0.143095	−	0.354187i
$637$	13.6884			0.542353
$638$	−4.56279	+	3.34379i	−0.180643	+	0.132382i
$639$	−5.52536	+	28.5762i	−0.218580	+	1.13046i
$640$	2.14013	−	7.29417i	0.0845959	−	0.288327i
$641$			12.8850i			0.508928i	0.967082	+	0.254464i	$0.0818990\pi$
$641$			12.8850i			0.508928i	−0.967082	+	0.254464i	$0.918101\pi$
$642$	−10.0000	+	39.4148i	−0.394669	+	1.55558i
$643$			23.8858i			0.941964i	0.882143	+	0.470982i	$0.156100\pi$
$643$			23.8858i			0.941964i	−0.882143	+	0.470982i	$0.843900\pi$
$644$	13.0591	+	4.12480i	0.514600	+	0.162540i
$645$	6.64566	+	8.05372i	0.261673	+	0.317115i
$646$	16.8190	+	22.9505i	0.661736	+	0.902975i
$647$	5.24867			0.206346			0.103173	−	0.994663i	$-0.467100\pi$
$647$	5.24867			0.206346			0.103173	+	0.994663i	$0.467100\pi$
$648$	−25.4166	−	1.41230i	−0.998460	−	0.0554803i
$649$	−7.33034			−0.287741
$650$	−17.3494	−	23.6741i	−0.680498	−	0.928576i
$651$	2.92815	+	3.54855i	0.114763	+	0.139079i
$652$	−13.0464	−	4.12079i	−0.510936	−	0.161383i
$653$		−	28.9784i		−	1.13401i	−0.823713	−	0.567007i	$-0.808101\pi$
$653$		−	28.9784i		−	1.13401i	0.823713	−	0.567007i	$-0.191899\pi$
$654$	1.93906	−	7.64275i	0.0758231	−	0.298855i
$655$			3.59048i			0.140292i
$656$	−11.3371	+	16.1562i	−0.442641	+	0.630793i
$657$	−0.840177	+	4.34525i	−0.0327784	+	0.169524i
$658$	11.9066	−	8.72562i	0.464167	−	0.340160i
$659$	34.6607			1.35019			0.675094	−	0.737732i	$-0.264103\pi$
$659$	34.6607			1.35019			0.675094	+	0.737732i	$0.264103\pi$
$660$	0.871875	+	2.15805i	0.0339377	+	0.0840020i
$661$	−18.1180			−0.704708			−0.352354	−	0.935867i	$-0.614619\pi$
$661$	−18.1180			−0.704708			−0.352354	+	0.935867i	$0.614619\pi$
$662$	−22.5829	+	16.5497i	−0.877710	+	0.643221i
$663$	26.8789	−	22.1796i	1.04389	−	0.861383i
$664$	−34.0665	+	11.5351i	−1.32204	+	0.447649i
$665$			6.13145i			0.237767i
$666$	−45.9798	+	21.7267i	−1.78168	+	0.841894i
$667$		−	13.6950i		−	0.530273i
$668$	11.3723	−	36.0045i	0.440006	−	1.39305i
$669$	−7.11807	+	5.87359i	−0.275201	+	0.227086i
$670$	0.451217	+	0.615710i	0.0174320	+	0.0237870i
$671$	3.62851			0.140077
$672$	−12.7799	−	14.8551i	−0.492996	−	0.573048i
$673$	0.931360			0.0359013			0.0179507	−	0.999839i	$-0.494286\pi$
$673$	0.931360			0.0359013			0.0179507	+	0.999839i	$0.494286\pi$
$674$	9.82517	+	13.4070i	0.378451	+	0.516417i
$675$	−20.7541	+	11.3084i	−0.798825	+	0.435261i
$676$	−4.71003	+	14.9119i	−0.181155	+	0.573535i
$677$		−	30.3541i		−	1.16660i	−0.812255	−	0.583302i	$-0.801760\pi$
$677$		−	30.3541i		−	1.16660i	0.812255	−	0.583302i	$-0.198240\pi$
$678$	45.1502	+	11.4551i	1.73398	+	0.439932i
$679$			3.09711i			0.118856i
$680$	7.93723	−	2.68759i	0.304379	−	0.103064i
$681$	11.5412	+	13.9865i	0.442261	+	0.535965i
$682$	1.51496	−	1.11023i	0.0580109	−	0.0425127i
$683$	39.6396			1.51677			0.758384	−	0.651808i	$-0.225989\pi$
$683$	39.6396			1.51677			0.758384	+	0.651808i	$0.225989\pi$
$684$	−13.0515	+	24.0654i	−0.499036	+	0.920164i
$685$	5.76386			0.220226
$686$	22.8139	−	16.7190i	0.871040	−	0.638333i
$687$	−16.1765	−	19.6039i	−0.617171	−	0.747935i
$688$	−20.6151	+	29.3778i	−0.785942	+	1.12002i
$689$			12.6891i			0.483418i
$690$	−5.46179	−	1.38572i	−0.207927	−	0.0527535i
$691$			51.5984i			1.96290i	0.191731	+	0.981448i	$0.438590\pi$
$691$			51.5984i			1.96290i	−0.191731	+	0.981448i	$0.561410\pi$
$692$	0.416169	+	0.131450i	0.0158204	+	0.00499697i
$693$	5.89089	+	1.13903i	0.223776	+	0.0432684i
$694$	−12.2293	−	16.6876i	−0.464219	−	0.633452i
$695$	−13.6695			−0.518512
$696$	−10.3161	+	16.6607i	−0.391031	+	0.631521i
$697$	−21.7578			−0.824135
$698$	−18.6813	−	25.4917i	−0.707100	−	0.964876i
$699$	3.84008	−	3.16871i	0.145245	−	0.119851i
$700$	−17.3494	−	5.47991i	−0.655744	−	0.207121i
$701$			28.7161i			1.08459i	0.840188	+	0.542295i	$0.182445\pi$
$701$			28.7161i			1.08459i	−0.840188	+	0.542295i	$0.817555\pi$
$702$	30.3435	+	14.2654i	1.14524	+	0.538412i
$703$			54.6921i			2.06275i
$704$	−6.35424	+	4.86042i	−0.239484	+	0.183184i
$705$	−4.68467	+	3.86564i	−0.176435	+	0.145588i
$706$	26.7885	−	19.6317i	1.00820	−	0.738847i
$707$	−27.0702			−1.01808
$708$	−23.5441	+	9.51207i	−0.884843	+	0.357486i
$709$	−2.78490			−0.104589			−0.0522946	−	0.998632i	$-0.516653\pi$
$709$	−2.78490			−0.104589			−0.0522946	+	0.998632i	$0.516653\pi$
$710$	7.43578	−	5.44924i	0.279060	−	0.204506i
$711$	15.8237	+	3.05960i	0.593435	+	0.114744i
$712$	−13.8198	−	40.8139i	−0.517919	−	1.52957i
$713$			4.54710i			0.170290i
$714$	5.31241	−	20.9387i	0.198812	−	0.783613i
$715$		−	3.06572i		−	0.114652i
$716$	−0.140492	+	0.444796i	−0.00525044	+	0.0166228i
$717$	13.6800	+	16.5785i	0.510889	+	0.619135i
$718$	0.316102	+	0.431339i	0.0117968	+	0.0160974i
$719$	−45.5719			−1.69955			−0.849773	−	0.527149i	$-0.823261\pi$
$719$	−45.5719			−1.69955			−0.849773	+	0.527149i	$0.823261\pi$
$720$	5.60071	+	5.80002i	0.208726	+	0.216154i
$721$	−26.5577			−0.989060
$722$	1.52062	+	2.07497i	0.0565917	+	0.0772225i
$723$	−0.596354	−	0.722707i	−0.0221786	−	0.0268778i
$724$	8.40806	−	26.6198i	0.312483	−	0.989318i
$725$			18.1942i			0.675716i
$726$	0.602380	−	2.37427i	0.0223564	−	0.0881173i
$727$		−	17.6479i		−	0.654526i	−0.944933	−	0.327263i	$-0.893874\pi$
$727$		−	17.6479i		−	0.654526i	0.944933	−	0.327263i	$-0.106126\pi$
$728$	8.27807	+	24.4476i	0.306806	+	0.906087i
$729$	14.6381	−	22.6876i	0.542151	−	0.840281i
$730$	1.13067	−	0.828603i	0.0418481	−	0.0306680i
$731$	−39.5636			−1.46331
$732$	11.6543	−	4.70847i	0.430757	−	0.174030i
$733$	17.8169			0.658082			0.329041	−	0.944316i	$-0.393275\pi$
$733$	17.8169			0.658082			0.329041	+	0.944316i	$0.393275\pi$
$734$	−15.6756	+	11.4877i	−0.578596	+	0.424018i
$735$	−2.69286	+	2.22206i	−0.0993277	+	0.0819618i
$736$	−0.397929	−	19.3636i	−0.0146679	−	0.713751i
$737$		−	0.803347i		−	0.0295917i
$738$	−8.94384	−	18.9276i	−0.329227	−	0.696736i
$739$		−	5.71528i		−	0.210240i	−0.994460	−	0.105120i	$-0.966477\pi$
$739$		−	5.71528i		−	0.210240i	0.994460	−	0.105120i	$-0.0335227\pi$
$740$	15.3595	+	4.85140i	0.564626	+	0.178341i
$741$	27.8132	−	22.9505i	1.02174	−	0.843107i
$742$	4.64956	+	6.34457i	0.170691	+	0.232917i
$743$	−40.5694			−1.48835			−0.744174	−	0.667986i	$-0.767157\pi$
$743$	−40.5694			−1.48835			−0.744174	+	0.667986i	$0.767157\pi$
$744$	3.42521	−	5.53177i	0.125574	−	0.202805i
$745$	−7.45612			−0.273171
$746$	16.6909	+	22.7757i	0.611098	+	0.833876i
$747$	7.24202	−	37.4545i	0.264972	−	1.37039i
$748$	−8.40952	−	2.65621i	−0.307482	−	0.0971205i
$749$		−	33.2016i		−	1.21316i
$750$	15.2325	+	3.86466i	0.556210	+	0.141117i
$751$			8.54045i			0.311645i	0.987785	+	0.155823i	$0.0498028\pi$
$751$			8.54045i			0.311645i	−0.987785	+	0.155823i	$0.950197\pi$
$752$	−17.0884	−	11.9913i	−0.623151	−	0.437279i
$753$	−9.18967	−	11.1367i	−0.334890	−	0.405846i
$754$	20.8190	−	15.2570i	0.758185	−	0.555628i
$755$	10.7906			0.392709
$756$	20.3989	−	3.98577i	0.741900	−	0.144961i
$757$	1.87010			0.0679701			0.0339850	−	0.999422i	$-0.489180\pi$
$757$	1.87010			0.0679701			0.0339850	+	0.999422i	$0.489180\pi$
$758$	11.8595	−	8.69114i	0.430758	−	0.315677i
$759$	3.77428	+	4.57396i	0.136998	+	0.166024i
$760$	8.21312	−	2.78101i	0.297921	−	0.100878i
$761$			28.1344i			1.01987i	0.860213	+	0.509935i	$0.170331\pi$
$761$			28.1344i			1.01987i	−0.860213	+	0.509935i	$0.829669\pi$
$762$	−12.9997	−	3.29818i	−0.470929	−	0.119480i
$763$			6.43799i			0.233071i
$764$	−9.04427	+	28.6341i	−0.327210	+	1.03594i
$765$	−1.68733	+	8.72660i	−0.0610057	+	0.315511i
$766$	−26.6635	−	36.3837i	−0.963390	−	1.31460i
$767$	33.4468			1.20769
$768$	−14.1020	+	23.8565i	−0.508862	+	0.860848i
$769$	50.4901			1.82072			0.910359	−	0.413820i	$-0.135806\pi$
$769$	50.4901			1.82072			0.910359	+	0.413820i	$0.135806\pi$
$770$	−1.12334	−	1.53286i	−0.0404825	−	0.0552405i
$771$	−8.52476	+	7.03434i	−0.307012	+	0.253336i
$772$	7.88943	−	24.9779i	0.283947	−	0.898973i
$773$			15.4265i			0.554853i	0.960747	+	0.277426i	$0.0894815\pi$
$773$			15.4265i			0.554853i	−0.960747	+	0.277426i	$0.910519\pi$
$774$	−16.2632	−	34.4173i	−0.584567	−	1.23710i
$775$		−	6.04095i		−	0.216997i
$776$	4.14860	−	1.40474i	0.148926	−	0.0504271i
$777$	32.0268	−	26.4274i	1.14896	−	0.948079i
$778$	10.5416	−	7.72528i	0.377933	−	0.276965i
$779$	−22.5141			−0.806650
$780$	−3.97818	−	9.84673i	−0.142442	−	0.352570i
$781$	−9.70182			−0.347159
$782$	17.2212	−	12.6204i	0.615830	−	0.451305i
$783$	−9.94462	−	18.2512i	−0.355392	−	0.652243i
$784$	−9.82283	−	6.89289i	−0.350815	−	0.246175i
$785$		−	11.1150i		−	0.396711i
$786$	3.21899	−	12.6876i	0.114818	−	0.452551i
$787$			30.6359i			1.09205i	0.837768	+	0.546027i	$0.183860\pi$
$787$			30.6359i			1.09205i	−0.837768	+	0.546027i	$0.816140\pi$
$788$	51.5665	+	16.2876i	1.83698	+	0.580223i
$789$	3.54122	+	4.29153i	0.126071	+	0.152782i
$790$	−3.01745	−	4.11747i	−0.107356	−	0.146493i
$791$	−38.0329			−1.35230
$792$	−1.14615	−	8.40752i	−0.0407267	−	0.298748i
$793$	−16.5561			−0.587926
$794$	−10.8259	−	14.7726i	−0.384198	−	0.524259i
$795$	−2.05985	−	2.49629i	−0.0730554	−	0.0885342i
$796$	−27.2428	−	8.60483i	−0.965595	−	0.304990i
$797$			42.2115i			1.49521i	0.664146	+	0.747603i	$0.268796\pi$
$797$			42.2115i			1.49521i	−0.664146	+	0.747603i	$0.731204\pi$
$798$	5.49706	−	21.6665i	0.194594	−	0.766987i
$799$		−	23.0133i		−	0.814150i
$800$	0.528660	+	25.7251i	0.0186909	+	0.909519i
$801$	44.8729	+	8.67642i	1.58551	+	0.306566i
$802$	−12.8409	+	9.41030i	−0.453426	+	0.332289i
$803$	−1.47524			−0.0520602
$804$	−1.04245	−	2.58025i	−0.0367643	−	0.0909985i
$805$	4.60082			0.162158
$806$	−6.91246	+	5.06572i	−0.243481	+	0.178433i
$807$	−1.21899	+	1.00587i	−0.0429106	+	0.0354084i
$808$	12.2781	+	36.2607i	0.431941	+	1.27565i
$809$			22.0732i			0.776051i	0.921649	+	0.388025i	$0.126843\pi$
$809$			22.0732i			0.776051i	−0.921649	+	0.388025i	$0.873157\pi$
$810$	−8.28509	+	2.11934i	−0.291108	+	0.0744659i
$811$			34.3284i			1.20543i	0.797956	+	0.602716i	$0.205915\pi$
$811$			34.3284i			1.20543i	−0.797956	+	0.602716i	$0.794085\pi$
$812$	4.81904	−	15.2570i	0.169115	−	0.535417i
$813$	1.86923	−	1.54243i	0.0655568	−	0.0540953i
$814$	−10.0201	−	13.6730i	−0.351205	−	0.479239i
$815$	−4.59635			−0.161003
$816$	−30.4571	+	2.38105i	−1.06621	+	0.0833534i
$817$	−40.9387			−1.43227
$818$	−7.00613	−	9.56024i	−0.244964	−	0.334266i
$819$	−26.8789	−	5.19717i	−0.939224	−	0.181604i
$820$	−1.99709	+	6.32275i	−0.0697412	+	0.220800i
$821$			12.5248i			0.437117i	0.975824	+	0.218558i	$0.0701354\pi$
$821$			12.5248i			0.437117i	−0.975824	+	0.218558i	$0.929865\pi$
$822$	−20.3676	−	5.16750i	−0.710401	−	0.180237i
$823$		−	38.9976i		−	1.35937i	−0.733504	−	0.679685i	$-0.762117\pi$
$823$		−	38.9976i		−	1.35937i	0.733504	−	0.679685i	$-0.237883\pi$
$824$	12.0456	+	35.5742i	0.419629	+	1.23929i
$825$	−5.01423	−	6.07663i	−0.174573	−	0.211561i
$826$	16.7234	−	12.2556i	0.581881	−	0.426426i
$827$	−2.80283			−0.0974638			−0.0487319	−	0.998812i	$-0.515518\pi$
$827$	−2.80283			−0.0974638			−0.0487319	+	0.998812i	$0.515518\pi$
$828$	18.0578	+	9.79337i	0.627553	+	0.340343i
$829$	−6.71435			−0.233199			−0.116599	−	0.993179i	$-0.537199\pi$
$829$	−6.71435			−0.233199			−0.116599	+	0.993179i	$0.537199\pi$
$830$	−9.74598	+	7.14225i	−0.338288	+	0.247911i
$831$	−5.89822	−	7.14792i	−0.204607	−	0.247959i
$832$	28.9930	−	22.1771i	1.00515	−	0.768851i
$833$		−	13.2286i		−	0.458342i
$834$	48.3034	+	12.2552i	1.67261	+	0.424361i
$835$		−	12.6847i		−	0.438971i
$836$	−8.70182	−	2.74853i	−0.300959	−	0.0950600i
$837$	3.30187	+	6.05985i	0.114129	+	0.209459i
$838$	−10.9247	−	14.9074i	−0.377388	−	0.514966i
$839$	11.3399			0.391497			0.195748	−	0.980654i	$-0.437286\pi$
$839$	11.3399			0.391497			0.195748	+	0.980654i	$0.437286\pi$
$840$	−5.59713	−	3.46568i	−0.193119	−	0.119577i
$841$	13.0000			0.448276
$842$	−23.3603	−	31.8763i	−0.805048	−	1.09853i
$843$	−12.1494	+	10.0253i	−0.418447	+	0.345288i
$844$	5.24944	+	1.65807i	0.180693	+	0.0570732i
$845$			5.25359i			0.180729i
$846$	20.0198	−	9.45992i	0.688295	−	0.325239i
$847$			2.00000i			0.0687208i
$848$	6.38973	−	9.10578i	0.219424	−	0.312694i
$849$	−4.08677	+	3.37226i	−0.140258	+	0.115736i
$850$	−22.8789	+	16.7666i	−0.784739	+	0.575089i
$851$	41.0390			1.40680
$852$	−31.1611	+	12.5894i	−1.06756	+	0.431305i
$853$	−29.2264			−1.00069			−0.500346	−	0.865826i	$-0.666794\pi$
$853$	−29.2264			−1.00069			−0.500346	+	0.865826i	$0.666794\pi$
$854$	−8.27807	+	6.06650i	−0.283270	+	0.207591i
$855$	−1.74598	+	9.02993i	−0.0597114	+	0.308817i
$856$	−44.4738	+	15.0591i	−1.52008	+	0.514709i
$857$		−	5.56201i		−	0.189995i	−0.995478	−	0.0949974i	$-0.969716\pi$
$857$		−	5.56201i		−	0.189995i	0.995478	−	0.0949974i	$-0.0302843\pi$
$858$	−2.74853	+	10.8333i	−0.0938333	+	0.369842i
$859$		−	21.0529i		−	0.718317i	−0.933277	−	0.359159i	$-0.883064\pi$
$859$		−	21.0529i		−	0.718317i	0.933277	−	0.359159i	$-0.116936\pi$
$860$	−3.63143	+	11.4971i	−0.123831	+	0.392047i
$861$	10.8789	+	13.1839i	0.370752	+	0.449305i
$862$	−2.95272	−	4.02915i	−0.100570	−	0.137233i
$863$	53.2279			1.81190			0.905950	−	0.423385i	$-0.139158\pi$
$863$	53.2279			1.81190			0.905950	+	0.423385i	$0.139158\pi$
$864$	−14.5912	−	25.5166i	−0.496401	−	0.868093i
$865$	0.146620			0.00498522
$866$	−4.68590	−	6.39417i	−0.159233	−	0.217283i
$867$	−2.69406	−	3.26487i	−0.0914952	−	0.110881i
$868$	−1.60004	+	5.06572i	−0.0543091	+	0.171942i
$869$			5.37226i			0.182242i
$870$	−1.61895	+	6.38105i	−0.0548875	+	0.216338i
$871$			3.66550i			0.124201i
$872$	8.62373	−	2.92004i	0.292036	−	0.0988851i
$873$	−0.881928	+	4.56118i	−0.0298488	+	0.154373i
$874$	17.8198	−	13.0591i	0.602764	−	0.441730i
$875$	−12.8313			−0.433777
$876$	−4.73830	+	1.91432i	−0.160092	+	0.0646790i
$877$	17.3058			0.584374			0.292187	−	0.956361i	$-0.405617\pi$
$877$	17.3058			0.584374			0.292187	+	0.956361i	$0.405617\pi$
$878$	−27.4960	+	20.1502i	−0.927944	+	0.680035i
$879$	−18.4498	+	15.2241i	−0.622296	+	0.513498i
$880$	−1.54377	+	2.19998i	−0.0520405	+	0.0741612i
$881$			52.5124i			1.76919i	0.466362	+	0.884594i	$0.345564\pi$
$881$			52.5124i			1.76919i	−0.466362	+	0.884594i	$0.654436\pi$
$882$	11.5078	−	5.43778i	0.387489	−	0.183100i
$883$		−	23.4672i		−	0.789735i	−0.918738	−	0.394868i	$-0.870790\pi$
$883$		−	23.4672i		−	0.789735i	0.918738	−	0.394868i	$-0.129210\pi$
$884$	38.3709	+	12.1197i	1.29055	+	0.407630i
$885$	−6.57986	+	5.42948i	−0.221180	+	0.182510i
$886$	29.0358	+	39.6210i	0.975478	+	1.33109i
$887$	−50.4169			−1.69283			−0.846417	−	0.532521i	$-0.821245\pi$
$887$	−50.4169			−1.69283			−0.846417	+	0.532521i	$0.821245\pi$
$888$	−49.9260	−	30.9136i	−1.67541	−	1.03739i
$889$	10.9505			0.367268
$890$	−8.55689	−	11.6763i	−0.286828	−	0.391392i
$891$	8.35130	+	3.35496i	0.279779	+	0.112396i
$892$	−10.1614	−	3.20954i	−0.340228	−	0.107463i
$893$		−	23.8132i		−	0.796877i
$894$	26.3475	+	6.68467i	0.881192	+	0.223569i
$895$			0.156706i			0.00523809i
$896$	6.37040	−	21.7122i	0.212820	−	0.725352i
$897$	−17.2212	−	20.8700i	−0.575000	−	0.696829i
$898$	17.7138	−	12.9814i	0.591119	−	0.433196i
$899$	5.31241			0.177179
$900$	−23.9903	−	13.0108i	−0.799678	−	0.433692i
$901$	12.2629			0.408536
$902$	5.62851	−	4.12480i	0.187409	−	0.137341i
$903$	19.7818	+	23.9731i	0.658297	+	0.797774i
$904$	17.2504	+	50.9454i	0.573739	+	1.69442i
$905$		−	9.37839i		−	0.311748i
$906$	−38.1304	−	9.67413i	−1.26680	−	0.321401i
$907$			35.1038i			1.16560i	0.812615	+	0.582801i	$0.198043\pi$
$907$			35.1038i			1.16560i	−0.812615	+	0.582801i	$0.801957\pi$
$908$	−6.30654	+	19.9664i	−0.209290	+	0.662609i
$909$	−39.8669	−	7.70847i	−1.32230	−	0.255674i
$910$	5.12558	+	6.99413i	0.169911	+	0.231853i
$911$	3.78688			0.125465			0.0627324	−	0.998030i	$-0.480019\pi$
$911$	3.78688			0.125465			0.0627324	+	0.998030i	$0.480019\pi$
$912$	−31.5158	+	2.46381i	−1.04359	+	0.0815850i
$913$	12.7161			0.420840
$914$	−13.4514	−	18.3552i	−0.444934	−	0.607137i
$915$	3.25703	−	2.68759i	0.107674	−	0.0888489i
$916$	8.83940	−	27.9855i	0.292062	−	0.924665i
$917$			10.6876i			0.352935i
$918$	13.7862	−	29.3242i	0.455012	−	0.967843i
$919$			25.3914i			0.837585i	0.908082	+	0.418792i	$0.137546\pi$
$919$			25.3914i			0.837585i	−0.908082	+	0.418792i	$0.862454\pi$
$920$	−2.08677	−	6.16283i	−0.0687987	−	0.203183i
$921$	2.83862	−	2.34234i	0.0935358	−	0.0771826i
$922$	−12.5410	+	9.19053i	−0.413015	+	0.302674i
$923$	44.2674			1.45708
$924$	2.59526	+	6.42375i	0.0853779	+	0.211326i
$925$	−54.5214			−1.79265
$926$	42.1538	−	30.8920i	1.38526	−	1.01517i
$927$	−39.1121	−	7.56253i	−1.28461	−	0.248386i
$928$	−22.6226	+	0.464904i	−0.742625	+	0.0152612i
$929$		−	22.8073i		−	0.748283i	−0.927372	−	0.374142i	$-0.877937\pi$
$929$		−	22.8073i		−	0.748283i	0.927372	−	0.374142i	$-0.122063\pi$
$930$	0.537533	−	2.11867i	0.0176264	−	0.0694740i
$931$		−	13.6884i		−	0.448618i
$932$	5.48189	+	1.73149i	0.179565	+	0.0567170i
$933$	−10.7759	−	13.0591i	−0.352787	−	0.427535i
$934$	−15.9394	−	21.7502i	−0.521553	−	0.711687i
$935$	−2.96274			−0.0968921
$936$	5.22965	+	38.3617i	0.170936	+	1.25389i
$937$	35.9760			1.17528			0.587642	−	0.809121i	$-0.300056\pi$
$937$	35.9760			1.17528			0.587642	+	0.809121i	$0.300056\pi$
$938$	1.34311	+	1.83275i	0.0438542	+	0.0598415i
$939$	5.66517	+	6.86549i	0.184876	+	0.224047i
$940$	−6.68759	−	2.11232i	−0.218125	−	0.0688963i
$941$		−	7.73814i		−	0.252256i	−0.992014	−	0.126128i	$-0.959745\pi$
$941$		−	7.73814i		−	0.252256i	0.992014	−	0.126128i	$-0.0402551\pi$
$942$	−9.96498	+	39.2767i	−0.324677	+	1.27970i
$943$			16.8937i			0.550136i
$944$	−24.0016	−	16.8424i	−0.781184	−	0.548174i
$945$	6.13145	−	3.34088i	0.199456	−	0.108679i
$946$	10.2347	−	7.50039i	0.332758	−	0.243859i
$947$	−11.6369			−0.378148			−0.189074	−	0.981963i	$-0.560549\pi$
$947$	−11.6369			−0.378148			−0.189074	+	0.981963i	$0.560549\pi$
$948$	6.97122	+	17.2550i	0.226415	+	0.560418i
$949$	6.73123			0.218505
$950$	−23.6741	+	17.3494i	−0.768090	+	0.562887i
$951$	29.1203	−	24.0291i	0.944291	−	0.779197i
$952$	23.6263	−	8.00000i	0.765734	−	0.259281i
$953$		−	5.59203i		−	0.181144i	−0.995890	−	0.0905719i	$-0.971131\pi$
$953$		−	5.59203i		−	0.181144i	0.995890	−	0.0905719i	$-0.0288695\pi$
$954$	5.04084	+	10.6678i	0.163203	+	0.345383i
$955$			10.0880i			0.326441i
$956$	−7.47524	+	23.6665i	−0.241767	+	0.765431i
$957$	5.34379	−	4.40952i	0.172740	−	0.142540i
$958$	14.0636	+	19.1905i	0.454374	+	0.620018i
$959$	17.1570			0.554027
$960$	−2.10365	+	9.06930i	−0.0678949	+	0.292711i
$961$	29.2361			0.943101
$962$	45.7197	+	62.3871i	1.47406	+	2.01144i
$963$	9.45446	−	48.8968i	0.304666	−	1.57568i
$964$	0.325869	−	1.03170i	0.0104955	−	0.0332287i
$965$		−	8.79991i		−	0.283279i
$966$	−16.2578	−	4.12480i	−0.523086	−	0.132713i
$967$			58.0491i			1.86673i	0.358922	+	0.933367i	$0.383144\pi$
$967$			58.0491i			1.86673i	−0.358922	+	0.933367i	$0.616856\pi$
$968$	2.67901	−	0.907128i	0.0861068	−	0.0291562i
$969$	−22.1796	−	26.8789i	−0.712510	−	0.863474i
$970$	1.18686	−	0.869779i	0.0381078	−	0.0279269i
$971$	56.4290			1.81089			0.905446	−	0.424461i	$-0.139536\pi$
$971$	56.4290			1.81089			0.905446	+	0.424461i	$0.139536\pi$
$972$	31.1769	−	0.0611740i	0.999998	−	0.00196216i
$973$	−40.6891			−1.30443
$974$	−21.8976	+	16.0474i	−0.701643	+	0.514192i
$975$	22.8789	+	27.7264i	0.732711	+	0.887955i
$976$	11.8808	+	8.33699i	0.380294	+	0.266860i
$977$		−	31.9552i		−	1.02234i	−0.859480	−	0.511169i	$-0.829213\pi$
$977$		−	31.9552i		−	1.02234i	0.859480	−	0.511169i	$-0.170787\pi$
$978$	16.2420	+	4.12079i	0.519362	+	0.131768i
$979$			15.2347i			0.486903i
$980$	−3.84418	−	1.21421i	−0.122798	−	0.0387866i
$981$	−1.83327	+	9.48137i	−0.0585319	+	0.302717i
$982$	28.2198	+	38.5074i	0.900529	+	1.22882i
$983$	5.75876			0.183676			0.0918380	−	0.995774i	$-0.470726\pi$
$983$	5.75876			0.183676			0.0918380	+	0.995774i	$0.470726\pi$
$984$	12.7256	−	20.5521i	0.405678	−	0.655177i
$985$	18.1673			0.578858
$986$	−14.7445	−	20.1197i	−0.469561	−	0.640742i
$987$	−13.9446	+	11.5066i	−0.443862	+	0.366260i
$988$	39.7046	+	12.5410i	1.26317	+	0.398981i
$989$			30.7190i			0.976806i
$990$	−1.21788	−	2.57736i	−0.0387067	−	0.0819140i
$991$		−	26.4805i		−	0.841180i	−0.907251	−	0.420590i	$-0.861823\pi$
$991$		−	26.4805i		−	0.841180i	0.907251	−	0.420590i	$-0.138177\pi$
$992$	7.51130	−	0.154360i	0.238484	−	0.00490093i
$993$	26.4484	−	21.8243i	0.839315	−	0.692574i
$994$	22.1337	−	16.2205i	0.702038	−	0.514481i
$995$	−9.59786			−0.304273
$996$	40.8424	−	16.5008i	1.29414	−	0.522846i
$997$	16.1533			0.511579			0.255790	−	0.966732i	$-0.417665\pi$
$997$	16.1533			0.511579			0.255790	+	0.966732i	$0.417665\pi$
$998$	−31.3384	+	22.9661i	−0.992001	+	0.726978i
$999$	54.6921	−	29.8004i	1.73038	−	0.942843i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	132.2.c.d.23.3	yes	8
3.2	odd	2		132.2.c.c.23.6	yes	8
4.3	odd	2		132.2.c.c.23.5	✓	8
8.3	odd	2		2112.2.d.l.1343.6		8
8.5	even	2		2112.2.d.k.1343.3		8
12.11	even	2	inner	132.2.c.d.23.4	yes	8
24.5	odd	2		2112.2.d.l.1343.5		8
24.11	even	2		2112.2.d.k.1343.4		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
132.2.c.c.23.5	✓	8	4.3	odd	2
132.2.c.c.23.6	yes	8	3.2	odd	2
132.2.c.d.23.3	yes	8	1.1	even	1	trivial
132.2.c.d.23.4	yes	8	12.11	even	2	inner
2112.2.d.k.1343.3		8	8.5	even	2
2112.2.d.k.1343.4		8	24.11	even	2
2112.2.d.l.1343.5		8	24.5	odd	2
2112.2.d.l.1343.6		8	8.3	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 132 = 2^{2} \cdot 3 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	132.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.835949 - 1.14070i) q^{2} +(1.10238 + 1.33595i) q^{3} +(-0.602380 + 1.90713i) q^{4} +0.671897i q^{5} +(0.602380 - 2.37427i) q^{6} +2.00000i q^{7} +(2.67901 - 0.907128i) q^{8} +(-0.569517 + 2.94545i) q^{9} +(0.766431 - 0.561672i) q^{10} -1.00000 q^{11} +(-3.21188 + 1.29763i) q^{12} +4.56279 q^{13} +(2.28139 - 1.67190i) q^{14} +(-0.897620 + 0.740686i) q^{15} +(-3.27428 - 2.29763i) q^{16} -4.40952i q^{17} +(3.83595 - 1.81259i) q^{18} -4.56279i q^{19} +(-1.28139 - 0.404737i) q^{20} +(-2.67190 + 2.20476i) q^{21} +(0.835949 + 1.14070i) q^{22} -3.42375 q^{23} +(4.16517 + 2.57903i) q^{24} +4.54855 q^{25} +(-3.81426 - 5.20476i) q^{26} +(-4.56279 + 2.48615i) q^{27} +(-3.81426 - 1.20476i) q^{28} +4.00000i q^{29} +(1.59526 + 0.404737i) q^{30} -1.32810i q^{31} +(0.116226 + 5.65566i) q^{32} +(-1.10238 - 1.33595i) q^{33} +(-5.02993 + 3.68613i) q^{34} -1.34379 q^{35} +(-5.27428 - 2.86042i) q^{36} -11.9865 q^{37} +(-5.20476 + 3.81426i) q^{38} +(5.02993 + 6.09565i) q^{39} +(0.609497 + 1.80002i) q^{40} -4.93428i q^{41} +(4.74853 + 1.20476i) q^{42} -8.97231i q^{43} +(0.602380 - 1.90713i) q^{44} +(-1.97904 - 0.382657i) q^{45} +(2.86208 + 3.90547i) q^{46} +5.21899 q^{47} +(-0.539980 - 6.90713i) q^{48} +3.00000 q^{49} +(-3.80236 - 5.18852i) q^{50} +(5.89089 - 4.86097i) q^{51} +(-2.74853 + 8.70182i) q^{52} +2.78101i q^{53} +(6.65021 + 3.12646i) q^{54} -0.671897i q^{55} +(1.81426 + 5.35803i) q^{56} +(6.09565 - 5.02993i) q^{57} +(4.56279 - 3.34379i) q^{58} +7.33034 q^{59} +(-0.871875 - 2.15805i) q^{60} -3.62851 q^{61} +(-1.51496 + 1.11023i) q^{62} +(-5.89089 - 1.13903i) q^{63} +(6.35424 - 4.86042i) q^{64} +3.06572i q^{65} +(-0.602380 + 2.37427i) q^{66} +0.803347i q^{67} +(8.40952 + 2.65621i) q^{68} +(-3.77428 - 4.57396i) q^{69} +(1.12334 + 1.53286i) q^{70} +9.70182 q^{71} +(1.14615 + 8.40752i) q^{72} +1.47524 q^{73} +(10.0201 + 13.6730i) q^{74} +(5.01423 + 6.07663i) q^{75} +(8.70182 + 2.74853i) q^{76} -2.00000i q^{77} +(2.74853 - 10.8333i) q^{78} -5.37226i q^{79} +(1.54377 - 2.19998i) q^{80} +(-8.35130 - 3.35496i) q^{81} +(-5.62851 + 4.12480i) q^{82} -12.7161 q^{83} +(-2.59526 - 6.42375i) q^{84} +2.96274 q^{85} +(-10.2347 + 7.50039i) q^{86} +(-5.34379 + 4.40952i) q^{87} +(-2.67901 + 0.907128i) q^{88} -15.2347i q^{89} +(1.21788 + 2.57736i) q^{90} +9.12558i q^{91} +(2.06240 - 6.52954i) q^{92} +(1.77428 - 1.46407i) q^{93} +(-4.36281 - 5.95329i) q^{94} +3.06572 q^{95} +(-7.42755 + 6.38996i) q^{96} +1.54855 q^{97} +(-2.50785 - 3.42209i) q^{98} +(0.569517 - 2.94545i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 2 q^{3} + 2 q^{4} - 2 q^{6} + 6 q^{8} + 2 q^{9} + 6 q^{10} - 8 q^{11} - 10 q^{12} - 8 q^{13} - 4 q^{14} - 14 q^{15} - 6 q^{16} + 24 q^{18} + 12 q^{20} - 8 q^{21} + 4 q^{23} - 18 q^{24} - 4 q^{25}+ \cdots - 2 q^{99}+O(q^{100}) \) 8 * q + 2 * q^3 + 2 * q^4 - 2 * q^6 + 6 * q^8 + 2 * q^9 + 6 * q^10 - 8 * q^11 - 10 * q^12 - 8 * q^13 - 4 * q^14 - 14 * q^15 - 6 * q^16 + 24 * q^18 + 12 * q^20 - 8 * q^21 + 4 * q^23 - 18 * q^24 - 4 * q^25 - 8 * q^26 + 8 * q^27 - 8 * q^28 + 8 * q^30 + 30 * q^32 - 2 * q^33 + 4 * q^34 + 16 * q^35 - 22 * q^36 - 20 * q^37 - 28 * q^38 - 4 * q^39 - 4 * q^40 + 16 * q^42 - 2 * q^44 + 18 * q^45 - 22 * q^46 + 24 * q^47 - 2 * q^48 + 24 * q^49 - 42 * q^50 + 16 * q^51 + 24 * q^54 - 8 * q^56 + 4 * q^57 - 8 * q^58 - 44 * q^59 - 12 * q^60 + 16 * q^61 + 10 * q^62 - 16 * q^63 + 26 * q^64 + 2 * q^66 + 40 * q^68 - 10 * q^69 + 36 * q^70 + 20 * q^71 - 6 * q^72 - 16 * q^73 - 14 * q^74 + 36 * q^75 + 12 * q^76 + 4 * q^80 + 2 * q^81 - 40 * q^83 - 16 * q^84 + 16 * q^85 - 24 * q^86 - 16 * q^87 - 6 * q^88 + 50 * q^90 + 12 * q^92 - 6 * q^93 + 28 * q^94 + 24 * q^95 - 22 * q^96 - 28 * q^97 - 2 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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