LMFDB - Embedded newform 234.2.y.a.119.10

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [234,2,Mod(11,234)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("234.11"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(234, base_ring=CyclotomicField(12)) chi = DirichletCharacter(H, H._module([2, 7])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 234 = 2 \cdot 3^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	234.y (of order $12$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$1.86849940730$
Analytic rank:	$0$
Dimension:	$56$
Relative dimension:	$14$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			119.10
Character	$\chi$	$=$	234.119
Dual form			234.2.y.a.59.10

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.707107 + 0.707107i) q^{2} +(-0.613909 - 1.61960i) q^{3} +1.00000i q^{4} +(-0.964970 + 3.60132i) q^{5} +(0.711134 - 1.57933i) q^{6} +(-0.861011 + 3.21334i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(-2.24623 + 1.98858i) q^{9} +(-3.22885 + 1.86418i) q^{10} +(4.48313 - 4.48313i) q^{11} +(1.61960 - 0.613909i) q^{12} +(-0.905106 + 3.49010i) q^{13} +(-2.88100 + 1.66335i) q^{14} +(6.42511 - 0.648011i) q^{15} -1.00000 q^{16} +(1.38308 - 2.39556i) q^{17} +(-2.99446 - 0.182189i) q^{18} +(0.703205 + 2.62440i) q^{19} +(-3.60132 - 0.964970i) q^{20} +(5.73292 - 0.578199i) q^{21} +6.34010 q^{22} +(0.0915043 - 0.158490i) q^{23} +(1.57933 + 0.711134i) q^{24} +(-7.70819 - 4.45033i) q^{25} +(-3.10788 + 1.82787i) q^{26} +(4.59969 + 2.41720i) q^{27} +(-3.21334 - 0.861011i) q^{28} -0.948565i q^{29} +(5.00145 + 4.08503i) q^{30} +(2.14063 + 0.573581i) q^{31} +(-0.707107 - 0.707107i) q^{32} +(-10.0131 - 4.50866i) q^{33} +(2.67190 - 0.715935i) q^{34} +(-10.7414 - 6.20155i) q^{35} +(-1.98858 - 2.24623i) q^{36} +(1.96458 - 7.33191i) q^{37} +(-1.35849 + 2.35297i) q^{38} +(6.20823 - 0.676690i) q^{39} +(-1.86418 - 3.22885i) q^{40} +(2.27956 - 0.610806i) q^{41} +(4.46263 + 3.64493i) q^{42} +(-3.17570 + 1.83349i) q^{43} +(4.48313 + 4.48313i) q^{44} +(-4.99395 - 10.0083i) q^{45} +(0.176773 - 0.0473661i) q^{46} +(-1.38011 - 5.15065i) q^{47} +(0.613909 + 1.61960i) q^{48} +(-3.52202 - 2.03344i) q^{49} +(-2.30366 - 8.59737i) q^{50} +(-4.72895 - 0.769383i) q^{51} +(-3.49010 - 0.905106i) q^{52} +3.43327i q^{53} +(1.54325 + 4.96169i) q^{54} +(11.8191 + 20.4712i) q^{55} +(-1.66335 - 2.88100i) q^{56} +(3.81878 - 2.75005i) q^{57} +(0.670737 - 0.670737i) q^{58} +(3.31440 - 3.31440i) q^{59} +(0.648011 + 6.42511i) q^{60} +(4.13990 + 7.17052i) q^{61} +(1.10807 + 1.91924i) q^{62} +(-4.45594 - 8.93009i) q^{63} -1.00000i q^{64} +(-11.6955 - 6.62741i) q^{65} +(-3.89224 - 10.2684i) q^{66} +(1.93297 + 7.21395i) q^{67} +(2.39556 + 1.38308i) q^{68} +(-0.312866 - 0.0509022i) q^{69} +(-3.21016 - 11.9805i) q^{70} +(11.7943 - 3.16027i) q^{71} +(0.182189 - 2.99446i) q^{72} +(2.16027 + 2.16027i) q^{73} +(6.57361 - 3.79528i) q^{74} +(-2.47564 + 15.2163i) q^{75} +(-2.62440 + 0.703205i) q^{76} +(10.5458 + 18.2658i) q^{77} +(4.86837 + 3.91139i) q^{78} +(6.31331 - 10.9350i) q^{79} +(0.964970 - 3.60132i) q^{80} +(1.09112 - 8.93361i) q^{81} +(2.04380 + 1.17999i) q^{82} +(6.52658 - 1.74879i) q^{83} +(0.578199 + 5.73292i) q^{84} +(7.29255 + 7.29255i) q^{85} +(-3.54203 - 0.949085i) q^{86} +(-1.53630 + 0.582332i) q^{87} +6.34010i q^{88} +(0.643808 + 0.172508i) q^{89} +(3.54569 - 10.6082i) q^{90} +(-10.4356 - 5.91342i) q^{91} +(0.158490 + 0.0915043i) q^{92} +(-0.385180 - 3.81910i) q^{93} +(2.66617 - 4.61795i) q^{94} -10.1298 q^{95} +(-0.711134 + 1.57933i) q^{96} +(-5.65566 - 1.51543i) q^{97} +(-1.05259 - 3.92830i) q^{98} +(-1.15510 + 18.9852i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q + 4 q^{7} + 24 q^{15} - 56 q^{16} - 8 q^{19} + 36 q^{27} - 4 q^{28} + 8 q^{31} - 36 q^{33} + 24 q^{35} - 24 q^{36} - 4 q^{37} - 36 q^{38} - 24 q^{39} - 48 q^{41} + 36 q^{42} + 12 q^{43} - 36 q^{45}+ \cdots - 24 q^{99}+O(q^{100}) $ 56 * q + 4 * q^7 + 24 * q^15 - 56 * q^16 - 8 * q^19 + 36 * q^27 - 4 * q^28 + 8 * q^31 - 36 * q^33 + 24 * q^35 - 24 * q^36 - 4 * q^37 - 36 * q^38 - 24 * q^39 - 48 * q^41 + 36 * q^42 + 12 * q^43 - 36 * q^45 + 60 * q^47 - 24 * q^50 - 4 * q^52 + 24 * q^57 - 60 * q^63 - 120 * q^65 - 56 * q^67 - 36 * q^69 + 24 * q^71 + 28 * q^73 + 48 * q^74 + 4 * q^76 - 24 * q^77 + 36 * q^78 - 24 * q^79 - 120 * q^81 - 60 * q^83 + 24 * q^84 + 48 * q^86 + 48 * q^87 + 4 * q^91 - 24 * q^92 + 20 * q^97 - 48 * q^98 - 24 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/234\mathbb{Z}\right)^\times$.

$n$	$145$	$209$
$\chi(n)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{1}{6}\right)$

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 $

$2$	0.707107	+	0.707107i	0.500000	+	0.500000i
$2$	0.707107	+	0.707107i	0.500000	+	0.500000i
$3$	−0.613909	−	1.61960i	−0.354440	−	0.935079i
$3$	−0.613909	−	1.61960i	−0.354440	−	0.935079i
$4$			1.00000i			0.500000i
$5$	−0.964970	+	3.60132i	−0.431548	+	1.61056i	0.317648	+	0.948209i	$0.397107\pi$
$5$	−0.964970	+	3.60132i	−0.431548	+	1.61056i	−0.749195	+	0.662349i	$0.769560\pi$
$6$	0.711134	−	1.57933i	0.290319	−	0.644760i
$7$	−0.861011	+	3.21334i	−0.325432	+	1.21453i	0.588446	+	0.808537i	$0.299740\pi$
$7$	−0.861011	+	3.21334i	−0.325432	+	1.21453i	−0.913877	+	0.405991i	$0.866927\pi$
$8$	−0.707107	+	0.707107i	−0.250000	+	0.250000i
$9$	−2.24623	+	1.98858i	−0.748744	+	0.662859i
$10$	−3.22885	+	1.86418i	−1.02105	+	0.589505i
$11$	4.48313	−	4.48313i	1.35171	−	1.35171i	0.467968	−	0.883745i	$-0.344986\pi$
$11$	4.48313	−	4.48313i	1.35171	−	1.35171i	0.883745	−	0.467968i	$-0.155014\pi$
$12$	1.61960	−	0.613909i	0.467539	−	0.177220i
$13$	−0.905106	+	3.49010i	−0.251031	+	0.967979i
$13$	−0.905106	+	3.49010i	−0.251031	+	0.967979i
$14$	−2.88100	+	1.66335i	−0.769980	+	0.444548i
$15$	6.42511	−	0.648011i	1.65896	−	0.167316i
$16$	−1.00000			−0.250000
$17$	1.38308	−	2.39556i	0.335446	−	0.581010i	−0.648124	−	0.761534i	$-0.724446\pi$
$17$	1.38308	−	2.39556i	0.335446	−	0.581010i	0.983570	+	0.180525i	$0.0577797\pi$
$18$	−2.99446	−	0.182189i	−0.705802	−	0.0429424i
$19$	0.703205	+	2.62440i	0.161326	+	0.602078i	0.998480	+	0.0551104i	$0.0175511\pi$
$19$	0.703205	+	2.62440i	0.161326	+	0.602078i	−0.837154	+	0.546967i	$0.815782\pi$
$20$	−3.60132	−	0.964970i	−0.805279	−	0.215774i
$21$	5.73292	−	0.578199i	1.25102	−	0.126173i
$22$	6.34010			1.35171
$23$	0.0915043	−	0.158490i	0.0190800	−	0.0330475i	−0.856328	−	0.516433i	$-0.827260\pi$
$23$	0.0915043	−	0.158490i	0.0190800	−	0.0330475i	0.875408	+	0.483385i	$0.160593\pi$
$24$	1.57933	+	0.711134i	0.322380	+	0.145160i
$25$	−7.70819	−	4.45033i	−1.54164	−	0.890065i
$26$	−3.10788	+	1.82787i	−0.609505	+	0.358474i
$27$	4.59969	+	2.41720i	0.885211	+	0.465190i
$28$	−3.21334	−	0.861011i	−0.607264	−	0.162716i
$29$		−	0.948565i		−	0.176144i	−0.996114	−	0.0880720i	$-0.971929\pi$
$29$		−	0.948565i		−	0.176144i	0.996114	−	0.0880720i	$-0.0280706\pi$
$30$	5.00145	+	4.08503i	0.913136	+	0.745820i
$31$	2.14063	+	0.573581i	0.384469	+	0.103018i	0.445876	−	0.895095i	$-0.352892\pi$
$31$	2.14063	+	0.573581i	0.384469	+	0.103018i	−0.0614072	+	0.998113i	$0.519559\pi$
$32$	−0.707107	−	0.707107i	−0.125000	−	0.125000i
$33$	−10.0131	−	4.50866i	−1.74306	−	0.784857i
$34$	2.67190	−	0.715935i	0.458228	−	0.122782i
$35$	−10.7414	−	6.20155i	−1.81563	−	1.04825i
$36$	−1.98858	−	2.24623i	−0.331430	−	0.374372i
$37$	1.96458	−	7.33191i	0.322975	−	1.20536i	−0.593357	−	0.804939i	$-0.702198\pi$
$37$	1.96458	−	7.33191i	0.322975	−	1.20536i	0.916332	−	0.400419i	$-0.131136\pi$
$38$	−1.35849	+	2.35297i	−0.220376	+	0.381702i
$39$	6.20823	−	0.676690i	0.994112	−	0.108357i
$40$	−1.86418	−	3.22885i	−0.294753	−	0.510526i
$41$	2.27956	−	0.610806i	0.356007	−	0.0953919i	−0.0763827	−	0.997079i	$-0.524337\pi$
$41$	2.27956	−	0.610806i	0.356007	−	0.0953919i	0.432390	+	0.901687i	$0.357670\pi$
$42$	4.46263	+	3.64493i	0.688599	+	0.562426i
$43$	−3.17570	+	1.83349i	−0.484290	+	0.279605i	−0.722202	−	0.691682i	$-0.756870\pi$
$43$	−3.17570	+	1.83349i	−0.484290	+	0.279605i	0.237913	+	0.971287i	$0.423537\pi$
$44$	4.48313	+	4.48313i	0.675857	+	0.675857i
$45$	−4.99395	−	10.0083i	−0.744455	−	1.49195i
$46$	0.176773	−	0.0473661i	0.0260637	−	0.00698375i
$47$	−1.38011	−	5.15065i	−0.201310	−	0.751300i	−0.990543	−	0.137205i	$-0.956188\pi$
$47$	−1.38011	−	5.15065i	−0.201310	−	0.751300i	0.789232	−	0.614095i	$-0.210479\pi$
$48$	0.613909	+	1.61960i	0.0886101	+	0.233770i
$49$	−3.52202	−	2.03344i	−0.503146	−	0.290491i
$50$	−2.30366	−	8.59737i	−0.325786	−	1.21585i
$51$	−4.72895	−	0.769383i	−0.662185	−	0.107735i
$52$	−3.49010	−	0.905106i	−0.483990	−	0.125516i
$53$			3.43327i			0.471596i	0.971802	+	0.235798i	$0.0757704\pi$
$53$			3.43327i			0.471596i	−0.971802	+	0.235798i	$0.924230\pi$
$54$	1.54325	+	4.96169i	0.210010	+	0.675201i
$55$	11.8191	+	20.4712i	1.59368	+	2.76034i
$56$	−1.66335	−	2.88100i	−0.222274	−	0.384990i
$57$	3.81878	−	2.75005i	0.505809	−	0.364253i
$58$	0.670737	−	0.670737i	0.0880720	−	0.0880720i
$59$	3.31440	−	3.31440i	0.431498	−	0.431498i	−0.457640	−	0.889138i	$-0.651305\pi$
$59$	3.31440	−	3.31440i	0.431498	−	0.431498i	0.889138	+	0.457640i	$0.151305\pi$
$60$	0.648011	+	6.42511i	0.0836579	+	0.829478i
$61$	4.13990	+	7.17052i	0.530060	+	0.918090i	0.999385	+	0.0350651i	$0.0111639\pi$
$61$	4.13990	+	7.17052i	0.530060	+	0.918090i	−0.469325	+	0.883025i	$0.655503\pi$
$62$	1.10807	+	1.91924i	0.140725	+	0.243744i
$63$	−4.45594	−	8.93009i	−0.561396	−	1.12509i
$64$		−	1.00000i		−	0.125000i
$65$	−11.6955	−	6.62741i	−1.45065	−	0.822029i
$66$	−3.89224	−	10.2684i	−0.479102	−	1.26396i
$67$	1.93297	+	7.21395i	0.236150	+	0.881324i	0.977627	+	0.210346i	$0.0674589\pi$
$67$	1.93297	+	7.21395i	0.236150	+	0.881324i	−0.741477	+	0.670978i	$0.765874\pi$
$68$	2.39556	+	1.38308i	0.290505	+	0.167723i
$69$	−0.312866	−	0.0509022i	−0.0376647	−	0.00612791i
$70$	−3.21016	−	11.9805i	−0.383687	−	1.43194i
$71$	11.7943	−	3.16027i	1.39972	−	0.375055i	0.521478	−	0.853265i	$-0.325381\pi$
$71$	11.7943	−	3.16027i	1.39972	−	0.375055i	0.878245	+	0.478210i	$0.158714\pi$
$72$	0.182189	−	2.99446i	0.0214712	−	0.352901i
$73$	2.16027	+	2.16027i	0.252841	+	0.252841i	0.822134	−	0.569294i	$-0.192783\pi$
$73$	2.16027	+	2.16027i	0.252841	+	0.252841i	−0.569294	+	0.822134i	$0.692783\pi$
$74$	6.57361	−	3.79528i	0.764167	−	0.441192i
$75$	−2.47564	+	15.2163i	−0.285862	+	1.75703i
$76$	−2.62440	+	0.703205i	−0.301039	+	0.0806631i
$77$	10.5458	+	18.2658i	1.20180	+	2.08158i
$78$	4.86837	+	3.91139i	0.551235	+	0.442877i
$79$	6.31331	−	10.9350i	0.710302	−	1.23028i	−0.254441	−	0.967088i	$-0.581892\pi$
$79$	6.31331	−	10.9350i	0.710302	−	1.23028i	0.964744	−	0.263191i	$-0.0847751\pi$
$80$	0.964970	−	3.60132i	0.107887	−	0.402639i
$81$	1.09112	−	8.93361i	0.121235	−	0.992624i
$82$	2.04380	+	1.17999i	0.225700	+	0.130308i
$83$	6.52658	−	1.74879i	0.716385	−	0.191955i	0.117827	−	0.993034i	$-0.462407\pi$
$83$	6.52658	−	1.74879i	0.716385	−	0.191955i	0.598558	+	0.801079i	$0.295741\pi$
$84$	0.578199	+	5.73292i	0.0630867	+	0.625512i
$85$	7.29255	+	7.29255i	0.790989	+	0.790989i
$86$	−3.54203	−	0.949085i	−0.381947	−	0.102342i
$87$	−1.53630	+	0.582332i	−0.164709	+	0.0624326i
$88$			6.34010i			0.675857i
$89$	0.643808	+	0.172508i	0.0682435	+	0.0182858i	0.292779	−	0.956180i	$-0.405420\pi$
$89$	0.643808	+	0.172508i	0.0682435	+	0.0182858i	−0.224536	+	0.974466i	$0.572087\pi$
$90$	3.54569	−	10.6082i	0.373748	−	1.11820i
$91$	−10.4356	−	5.91342i	−1.09394	−	0.619895i
$92$	0.158490	+	0.0915043i	0.0165237	+	0.00953998i
$93$	−0.385180	−	3.81910i	−0.0399413	−	0.396022i
$94$	2.66617	−	4.61795i	0.274995	−	0.476305i
$95$	−10.1298			−1.03930
$96$	−0.711134	+	1.57933i	−0.0725798	+	0.161190i
$97$	−5.65566	−	1.51543i	−0.574246	−	0.153869i	−0.0400026	−	0.999200i	$-0.512737\pi$
$97$	−5.65566	−	1.51543i	−0.574246	−	0.153869i	−0.534243	+	0.845331i	$0.679403\pi$
$98$	−1.05259	−	3.92830i	−0.106327	−	0.396819i
$99$	−1.15510	+	18.9852i	−0.116092	+	1.90808i
$100$	4.45033	−	7.70819i	0.445033	−	0.770819i
$101$	−9.35186			−0.930545			−0.465272	−	0.885168i	$-0.654044\pi$
$101$	−9.35186			−0.930545			−0.465272	+	0.885168i	$0.654044\pi$
$102$	−2.79984	−	3.88791i	−0.277225	−	0.384960i
$103$	0.256212	−	0.147924i	0.0252453	−	0.0145754i	−0.487324	−	0.873221i	$-0.662027\pi$
$103$	0.256212	−	0.147924i	0.0252453	−	0.0145754i	0.512570	+	0.858646i	$0.328694\pi$
$104$	−1.82787	−	3.10788i	−0.179237	−	0.304753i
$105$	−3.44981	+	21.2040i	−0.336667	+	2.06930i
$106$	−2.42769	+	2.42769i	−0.235798	+	0.235798i
$107$	−16.2026	+	9.35458i	−1.56636	+	0.904341i	−0.569777	+	0.821799i	$0.692970\pi$
$107$	−16.2026	+	9.35458i	−1.56636	+	0.904341i	−0.996588	+	0.0825417i	$0.973696\pi$
$108$	−2.41720	+	4.59969i	−0.232595	+	0.442605i
$109$	−7.95895	+	7.95895i	−0.762329	+	0.762329i	−0.976743	−	0.214414i	$-0.931216\pi$
$109$	−7.95895	+	7.95895i	−0.762329	+	0.762329i	0.214414	+	0.976743i	$0.431216\pi$
$110$	−6.11801	+	22.8327i	−0.583329	+	2.17701i
$111$	−13.0809	+	1.31928i	−1.24158	+	0.125221i
$112$	0.861011	−	3.21334i	0.0813579	−	0.303632i
$113$		−	6.98898i		−	0.657468i	−0.944423	−	0.328734i	$-0.893378\pi$
$113$		−	6.98898i		−	0.657468i	0.944423	−	0.328734i	$-0.106622\pi$
$114$	4.64486	+	0.755702i	0.435031	+	0.0707780i
$115$	0.482474	+	0.482474i	0.0449910	+	0.0449910i
$116$	0.948565			0.0880720
$117$	−4.90725	−	9.63944i	−0.453676	−	0.891167i
$118$	4.68727			0.431498
$119$	6.50691	+	6.50691i	0.596487	+	0.596487i
$120$	−4.08503	+	5.00145i	−0.372910	+	0.456568i
$121$		−	29.1969i		−	2.65426i
$122$	−2.14297	+	7.99767i	−0.194015	+	0.724075i
$123$	−2.38870	−	3.31700i	−0.215382	−	0.299084i
$124$	−0.573581	+	2.14063i	−0.0515091	+	0.192234i
$125$	10.2835	−	10.2835i	0.919782	−	0.919782i
$126$	3.16370	−	9.46535i	0.281845	−	0.843241i
$127$	−1.39357	+	0.804578i	−0.123659	+	0.0713947i	−0.560554	−	0.828118i	$-0.689412\pi$
$127$	−1.39357	+	0.804578i	−0.123659	+	0.0713947i	0.436894	+	0.899513i	$0.356078\pi$
$128$	0.707107	−	0.707107i	0.0625000	−	0.0625000i
$129$	4.91912	+	4.01778i	0.433104	+	0.353746i
$130$	−3.58371	−	12.9563i	−0.314313	−	1.13634i
$131$	8.16562	−	4.71442i	0.713434	−	0.411901i	−0.0988974	−	0.995098i	$-0.531532\pi$
$131$	8.16562	−	4.71442i	0.713434	−	0.411901i	0.812331	+	0.583197i	$0.198198\pi$
$132$	4.50866	−	10.0131i	0.392428	−	0.871530i
$133$	−9.03853			−0.783740
$134$	−3.73421	+	6.46785i	−0.322587	+	0.558737i
$135$	−13.1437	+	14.2324i	−1.13123	+	1.22493i
$136$	0.715935	+	2.67190i	0.0613909	+	0.229114i
$137$	15.6755	+	4.20024i	1.33925	+	0.358851i	0.856155	−	0.516718i	$-0.172847\pi$
$137$	15.6755	+	4.20024i	1.33925	+	0.358851i	0.483093	+	0.875569i	$0.339513\pi$
$138$	−0.185237	−	0.257223i	−0.0157684	−	0.0218963i
$139$	8.89419			0.754396			0.377198	−	0.926133i	$-0.376888\pi$
$139$	8.89419			0.754396			0.377198	+	0.926133i	$0.376888\pi$
$140$	6.20155	−	10.7414i	0.524127	−	0.907814i
$141$	−7.49475	+	5.39727i	−0.631172	+	0.454532i
$142$	10.5745	+	6.10517i	0.887389	+	0.512334i
$143$	11.5888	+	19.7043i	0.969108	+	1.64775i
$144$	2.24623	−	1.98858i	0.187186	−	0.165715i
$145$	3.41608	+	0.915337i	0.283690	+	0.0760146i
$146$			3.05508i			0.252841i
$147$	−1.13117	+	6.95262i	−0.0932971	+	0.573443i
$148$	7.33191	+	1.96458i	0.602679	+	0.161487i
$149$	−16.7277	−	16.7277i	−1.37039	−	1.37039i	−0.859862	−	0.510527i	$-0.829450\pi$
$149$	−16.7277	−	16.7277i	−1.37039	−	1.37039i	−0.510527	−	0.859862i	$-0.670550\pi$
$150$	−12.5101	+	9.00901i	−1.02144	+	0.735583i
$151$	0.145209	−	0.0389086i	0.0118169	−	0.00316634i	−0.252906	−	0.967491i	$-0.581386\pi$
$151$	0.145209	−	0.0389086i	0.0118169	−	0.00316634i	0.264723	+	0.964325i	$0.414720\pi$
$152$	−2.35297	−	1.35849i	−0.190851	−	0.110188i
$153$	1.65705	+	8.13135i	0.133964	+	0.657381i
$154$	−5.45890	+	20.3729i	−0.439890	+	1.64169i
$155$	−4.13129	+	7.15561i	−0.331833	+	0.574752i
$156$	0.676690	+	6.20823i	0.0541785	+	0.497056i
$157$	0.888484	+	1.53890i	0.0709087	+	0.122818i	0.899300	−	0.437333i	$-0.144077\pi$
$157$	0.888484	+	1.53890i	0.0709087	+	0.122818i	−0.828391	+	0.560150i	$0.810743\pi$
$158$	12.1964	−	3.26801i	0.970291	−	0.259989i
$159$	5.56054	−	2.10772i	0.440980	−	0.167153i
$160$	3.22885	−	1.86418i	0.255263	−	0.147376i
$161$	0.430496	+	0.430496i	0.0339278	+	0.0339278i
$162$	7.08856	−	5.54548i	0.556929	−	0.435694i
$163$	−5.77944	+	1.54860i	−0.452681	+	0.121295i	−0.477953	−	0.878385i	$-0.658621\pi$
$163$	−5.77944	+	1.54860i	−0.452681	+	0.121295i	0.0252727	+	0.999681i	$0.491955\pi$
$164$	0.610806	+	2.27956i	0.0476959	+	0.178004i
$165$	25.8995	−	31.7097i	2.01627	−	2.46860i
$166$	5.85157	+	3.37840i	0.454170	+	0.262215i
$167$	4.60758	+	17.1957i	0.356545	+	1.33064i	0.878529	+	0.477689i	$0.158525\pi$
$167$	4.60758	+	17.1957i	0.356545	+	1.33064i	−0.521984	+	0.852955i	$0.674808\pi$
$168$	−3.64493	+	4.46263i	−0.281213	+	0.344300i
$169$	−11.3616	−	6.31781i	−0.873967	−	0.485986i
$170$			10.3132i			0.790989i
$171$	−6.79837	−	4.49662i	−0.519885	−	0.343865i
$172$	−1.83349	−	3.17570i	−0.139802	−	0.242145i
$173$	7.21223	+	12.4919i	0.548335	+	0.949745i	0.998389	+	0.0567432i	$0.0180716\pi$
$173$	7.21223	+	12.4919i	0.548335	+	0.949745i	−0.450053	+	0.893002i	$0.648595\pi$
$174$	−1.49810	−	0.674556i	−0.113571	−	0.0511380i
$175$	20.9372	−	20.9372i	1.58271	−	1.58271i
$176$	−4.48313	+	4.48313i	−0.337928	+	0.337928i
$177$	−7.40276	−	3.33328i	−0.556425	−	0.250544i
$178$	0.333259	+	0.577222i	0.0249788	+	0.0432646i
$179$	−7.51417	−	13.0149i	−0.561636	−	0.972782i	−0.997354	−	0.0726986i	$-0.976839\pi$
$179$	−7.51417	−	13.0149i	−0.561636	−	0.972782i	0.435718	−	0.900083i	$-0.356494\pi$
$180$	10.0083	−	4.99395i	0.745975	−	0.372227i
$181$			7.25012i			0.538897i	0.963015	+	0.269449i	$0.0868414\pi$
$181$			7.25012i			0.538897i	−0.963015	+	0.269449i	$0.913159\pi$
$182$	−3.19763	−	11.5605i	−0.237024	−	0.856919i
$183$	9.07187	−	11.1070i	0.670612	−	0.821056i
$184$	0.0473661	+	0.176773i	0.00349188	+	0.0130319i
$185$	24.5088	+	14.1501i	1.80192	+	1.04034i
$186$	2.42815	−	2.97288i	0.178041	−	0.217982i
$187$	−4.53910	−	16.9401i	−0.331932	−	1.23879i
$188$	5.15065	−	1.38011i	0.375650	−	0.100655i
$189$	−11.7277	+	12.6991i	−0.853062	+	0.923725i
$190$	−7.16289	−	7.16289i	−0.519650	−	0.519650i
$191$	−2.75813	+	1.59241i	−0.199571	+	0.115222i	−0.596455	−	0.802646i	$-0.703425\pi$
$191$	−2.75813	+	1.59241i	−0.199571	+	0.115222i	0.396884	+	0.917869i	$0.370091\pi$
$192$	−1.61960	+	0.613909i	−0.116885	+	0.0443051i
$193$	−13.6996	+	3.67080i	−0.986119	+	0.264230i	−0.715620	−	0.698490i	$-0.753856\pi$
$193$	−13.6996	+	3.67080i	−0.986119	+	0.264230i	−0.270500	+	0.962720i	$0.587189\pi$
$194$	−2.92759	−	5.07073i	−0.210189	−	0.364057i
$195$	−3.55378	+	23.0108i	−0.254491	+	1.64784i
$196$	2.03344	−	3.52202i	0.145246	−	0.251573i
$197$	−0.0907674	+	0.338748i	−0.00646691	+	0.0241348i	−0.969084	−	0.246731i	$-0.920643\pi$
$197$	−0.0907674	+	0.338748i	−0.00646691	+	0.0241348i	0.962617	+	0.270866i	$0.0873101\pi$
$198$	−14.2413	+	12.6078i	−1.01209	+	0.895996i
$199$	−17.1252	−	9.88723i	−1.21397	−	0.700887i	−0.250350	−	0.968155i	$-0.580546\pi$
$199$	−17.1252	−	9.88723i	−1.21397	−	0.700887i	−0.963622	+	0.267268i	$0.913879\pi$
$200$	8.59737	−	2.30366i	0.607926	−	0.162893i
$201$	10.4971	−	7.55935i	0.740406	−	0.533196i
$202$	−6.61276	−	6.61276i	−0.465272	−	0.465272i
$203$	3.04806	+	0.816725i	0.213932	+	0.0573229i
$204$	0.769383	−	4.72895i	0.0538676	−	0.331093i
$205$			8.79882i			0.614536i
$206$	0.285767	+	0.0765711i	0.0199103	+	0.00533496i
$207$	0.109630	+	0.537969i	0.00761981	+	0.0373914i
$208$	0.905106	−	3.49010i	0.0627578	−	0.241995i
$209$	14.9181	+	8.61294i	1.03190	+	0.595770i
$210$	−17.4329	+	12.5541i	−1.20298	+	0.866315i
$211$	4.63875	−	8.03456i	0.319345	−	0.553122i	−0.661007	−	0.750380i	$-0.729870\pi$
$211$	4.63875	−	8.03456i	0.319345	−	0.553122i	0.980352	+	0.197258i	$0.0632038\pi$
$212$	−3.43327			−0.235798
$213$	−12.3590	−	17.1619i	−0.846824	−	1.17592i
$214$	−18.0717	−	4.84229i	−1.23535	−	0.331012i
$215$	−3.53853	−	13.2060i	−0.241326	−	0.900639i
$216$	−4.96169	+	1.54325i	−0.337600	+	0.105005i
$217$	−3.68622	+	6.38472i	−0.250237	+	0.433423i
$218$	−11.2557			−0.762329
$219$	2.17257	−	4.82499i	0.146809	−	0.326043i
$220$	−20.4712	+	11.8191i	−1.38017	+	0.796842i
$221$	7.10892	+	6.99532i	0.478198	+	0.470556i
$222$	−10.1824	−	8.31669i	−0.683401	−	0.558180i
$223$	10.9424	−	10.9424i	0.732760	−	0.732760i	−0.238406	−	0.971166i	$-0.576625\pi$
$223$	10.9424	−	10.9424i	0.732760	−	0.732760i	0.971166	+	0.238406i	$0.0766248\pi$
$224$	2.88100	−	1.66335i	0.192495	−	0.111137i
$225$	26.1642	−	5.33187i	1.74428	−	0.355458i
$226$	4.94195	−	4.94195i	0.328734	−	0.328734i
$227$	1.90344	−	7.10373i	0.126336	−	0.471491i	−0.873548	−	0.486738i	$-0.838187\pi$
$227$	1.90344	−	7.10373i	0.126336	−	0.471491i	0.999884	+	0.0152467i	$0.00485335\pi$
$228$	2.75005	+	3.81878i	0.182127	+	0.252905i
$229$	−6.40571	+	23.9064i	−0.423301	+	1.57978i	0.344304	+	0.938858i	$0.388115\pi$
$229$	−6.40571	+	23.9064i	−0.423301	+	1.57978i	−0.767605	+	0.640923i	$0.778552\pi$
$230$			0.682322i			0.0449910i
$231$	23.1092	−	28.2935i	1.52048	−	1.86158i
$232$	0.670737	+	0.670737i	0.0440360	+	0.0440360i
$233$	−18.0279			−1.18105			−0.590525	−	0.807019i	$-0.701079\pi$
$233$	−18.0279			−1.18105			−0.590525	+	0.807019i	$0.701079\pi$
$234$	3.34616	−	10.2861i	0.218745	−	0.672421i
$235$	19.8809			1.29689
$236$	3.31440	+	3.31440i	0.215749	+	0.215749i
$237$	−21.5861	−	3.51198i	−1.40217	−	0.228128i
$238$			9.20216i			0.596487i
$239$	7.37545	−	27.5256i	0.477078	−	1.78048i	−0.136275	−	0.990671i	$-0.543513\pi$
$239$	7.37545	−	27.5256i	0.477078	−	1.78048i	0.613353	−	0.789809i	$-0.289820\pi$
$240$	−6.42511	+	0.648011i	−0.414739	+	0.0418289i
$241$	2.07549	−	7.74584i	0.133694	−	0.498954i	−0.866306	−	0.499514i	$-0.833512\pi$
$241$	2.07549	−	7.74584i	0.133694	−	0.498954i	1.00000		0.000560714i	$0.000178481\pi$
$242$	20.6453	−	20.6453i	1.32713	−	1.32713i
$243$	−15.1388	+	3.71725i	−0.971152	+	0.238462i
$244$	−7.17052	+	4.13990i	−0.459045	+	0.265030i
$245$	10.7217	−	10.7217i	0.684985	−	0.684985i
$246$	0.656406	−	4.03454i	0.0418509	−	0.257233i
$247$	−9.79587	+	0.0788981i	−0.623296	+	0.00502017i
$248$	−1.91924	+	1.10807i	−0.121872	+	0.0703627i
$249$	−6.83907	−	9.49687i	−0.433409	−	0.601840i
$250$	14.5430			0.919782
$251$	−3.03917	+	5.26399i	−0.191830	+	0.332260i	−0.945857	−	0.324584i	$-0.894776\pi$
$251$	−3.03917	+	5.26399i	−0.191830	+	0.332260i	0.754026	+	0.656844i	$0.228109\pi$
$252$	8.93009	−	4.45594i	0.562543	−	0.280698i
$253$	−0.300306	−	1.12076i	−0.0188801	−	0.0704614i
$254$	−1.55433	−	0.416480i	−0.0975270	−	0.0261323i
$255$	7.33408	−	16.2880i	0.459278	−	1.01999i
$256$	1.00000			0.0625000
$257$	−0.319391	+	0.553201i	−0.0199230	+	0.0345077i	−0.875815	−	0.482647i	$-0.839675\pi$
$257$	−0.319391	+	0.553201i	−0.0199230	+	0.0345077i	0.855892	+	0.517155i	$0.173009\pi$
$258$	0.637344	+	6.31934i	0.0396793	+	0.393425i
$259$	21.8684	+	12.6257i	1.35883	+	0.784524i
$260$	6.62741	−	11.6955i	0.411015	−	0.725327i
$261$	1.88630	+	2.13070i	0.116759	+	0.131887i
$262$	9.10757	+	2.44037i	0.562667	+	0.150766i
$263$		−	5.63477i		−	0.347455i	−0.984794	−	0.173727i	$-0.944419\pi$
$263$		−	5.63477i		−	0.347455i	0.984794	−	0.173727i	$-0.0555811\pi$
$264$	10.2684	−	3.89224i	0.631979	−	0.239551i
$265$	−12.3643	−	3.31300i	−0.759533	−	0.203516i
$266$	−6.39121	−	6.39121i	−0.391870	−	0.391870i
$267$	−0.115845	−	1.14862i	−0.00708960	−	0.0702942i
$268$	−7.21395	+	1.93297i	−0.440662	+	0.118075i
$269$	−17.6754	−	10.2049i	−1.07769	−	0.622202i	−0.147415	−	0.989075i	$-0.547095\pi$
$269$	−17.6754	−	10.2049i	−1.07769	−	0.622202i	−0.930271	+	0.366873i	$0.880428\pi$
$270$	−19.3578	+	0.769861i	−1.17808	+	0.0468522i
$271$	5.54365	−	20.6892i	0.336753	−	1.25678i	−0.565204	−	0.824951i	$-0.691202\pi$
$271$	5.54365	−	20.6892i	0.336753	−	1.25678i	0.901956	−	0.431827i	$-0.142131\pi$
$272$	−1.38308	+	2.39556i	−0.0838615	+	0.145252i
$273$	−3.17092	+	20.5318i	−0.191913	+	1.24264i
$274$	8.11424	+	14.0543i	0.490199	+	0.849049i
$275$	−54.5082	+	14.6054i	−3.28697	+	0.880740i
$276$	0.0509022	−	0.312866i	0.00306396	−	0.0188323i
$277$	−4.17616	+	2.41111i	−0.250921	+	0.144869i	−0.620186	−	0.784455i	$-0.712943\pi$
$277$	−4.17616	+	2.41111i	−0.250921	+	0.144869i	0.369265	+	0.929324i	$0.379610\pi$
$278$	6.28914	+	6.28914i	0.377198	+	0.377198i
$279$	−5.94897	+	2.96842i	−0.356155	+	0.177715i
$280$	11.9805	−	3.21016i	0.715970	−	0.191844i
$281$	−0.975427	−	3.64034i	−0.0581891	−	0.217165i	0.930709	−	0.365761i	$-0.119191\pi$
$281$	−0.975427	−	3.64034i	−0.0581891	−	0.217165i	−0.988898	+	0.148596i	$0.952525\pi$
$282$	−9.11604	−	1.48315i	−0.542852	−	0.0883201i
$283$	10.9117	+	6.29987i	0.648633	+	0.374489i	0.787932	−	0.615762i	$-0.211152\pi$
$283$	10.9117	+	6.29987i	0.648633	+	0.374489i	−0.139299	+	0.990250i	$0.544485\pi$
$284$	3.16027	+	11.7943i	0.187527	+	0.699861i
$285$	6.21880	+	16.4063i	0.368370	+	0.971828i
$286$	−5.73846	+	22.1276i	−0.339322	+	1.30843i
$287$			7.85090i			0.463424i
$288$	2.99446	+	0.182189i	0.176450	+	0.0107356i
$289$	4.67418	+	8.09592i	0.274952	+	0.476231i
$290$	1.76829	+	3.06278i	0.103838	+	0.179852i
$291$	1.01766	+	10.0903i	0.0596566	+	0.591502i
$292$	−2.16027	+	2.16027i	−0.126420	+	0.126420i
$293$	−21.0170	+	21.0170i	−1.22783	+	1.22783i	−0.263045	+	0.964784i	$0.584727\pi$
$293$	−21.0170	+	21.0170i	−1.22783	+	1.22783i	−0.964784	+	0.263045i	$0.915273\pi$
$294$	−5.71610	+	4.11639i	−0.333370	+	0.240073i
$295$	8.73791	+	15.1345i	0.508741	+	0.881165i
$296$	3.79528	+	6.57361i	0.220596	+	0.382083i
$297$	31.4576	−	9.78438i	1.82536	−	0.567747i
$298$		−	23.6566i		−	1.37039i
$299$	0.470325	+	0.462809i	0.0271996	+	0.0267650i
$300$	−15.2163	−	2.47564i	−0.878514	−	0.142931i
$301$	−3.15731	−	11.7832i	−0.181984	−	0.679175i
$302$	0.130191	+	0.0751656i	0.00749163	+	0.00432530i
$303$	5.74119	+	15.1463i	0.329823	+	0.870132i
$304$	−0.703205	−	2.62440i	−0.0403315	−	0.150519i
$305$	−29.8182	+	7.98976i	−1.70738	+	0.457492i
$306$	−4.57803	+	6.92144i	−0.261708	+	0.395673i
$307$	−22.9539	−	22.9539i	−1.31005	−	1.31005i	−0.921376	−	0.388674i	$-0.872933\pi$
$307$	−22.9539	−	22.9539i	−1.31005	−	1.31005i	−0.388674	−	0.921376i	$-0.627067\pi$
$308$	−18.2658	+	10.5458i	−1.04079	+	0.600901i
$309$	−0.396869	−	0.324150i	−0.0225771	−	0.0184402i
$310$	−7.98104	+	2.13851i	−0.453293	+	0.121459i
$311$	−11.8059	−	20.4483i	−0.669449	−	1.15952i	−0.978058	−	0.208331i	$-0.933197\pi$
$311$	−11.8059	−	20.4483i	−0.669449	−	1.15952i	0.308610	−	0.951189i	$-0.400136\pi$
$312$	−3.91139	+	4.86837i	−0.221439	+	0.275617i
$313$	8.71521	−	15.0952i	0.492613	−	0.853230i	−0.507351	−	0.861739i	$-0.669375\pi$
$313$	8.71521	−	15.0952i	0.492613	−	0.853230i	0.999964	+	0.00850920i	$0.00270860\pi$
$314$	−0.459913	+	1.71642i	−0.0259544	+	0.0968631i
$315$	36.4599	−	7.42999i	2.05428	−	0.418632i
$316$	10.9350	+	6.31331i	0.615140	+	0.355151i
$317$	0.604929	−	0.162090i	0.0339762	−	0.00910389i	−0.241791	−	0.970328i	$-0.577735\pi$
$317$	0.604929	−	0.162090i	0.0339762	−	0.00910389i	0.275767	+	0.961224i	$0.411068\pi$
$318$	5.42228	+	2.44152i	0.304066	+	0.136913i
$319$	−4.25254	−	4.25254i	−0.238096	−	0.238096i
$320$	3.60132	+	0.964970i	0.201320	+	0.0539435i
$321$	25.0976	+	20.4989i	1.40081	+	1.14414i
$322$			0.608813i			0.0339278i
$323$	7.25949	+	1.94518i	0.403929	+	0.108232i
$324$	8.93361	+	1.09112i	0.496312	+	0.0606176i
$325$	22.5088	−	22.8743i	1.24856	−	1.26884i
$326$	−5.18170	−	2.99166i	−0.286988	−	0.165693i
$327$	17.7764	+	8.00428i	0.983038	+	0.442637i
$328$	−1.17999	+	2.04380i	−0.0651539	+	0.112850i
$329$	17.7391			0.977987
$330$	40.7358	−	4.10846i	2.24243	−	0.226163i
$331$	29.8637	+	8.00195i	1.64146	+	0.439827i	0.957203	−	0.289418i	$-0.0934616\pi$
$331$	29.8637	+	8.00195i	1.64146	+	0.439827i	0.684253	+	0.729244i	$0.260128\pi$
$332$	1.74879	+	6.52658i	0.0959774	+	0.358192i
$333$	10.1672	+	20.3759i	0.557158	+	1.11659i
$334$	−8.90116	+	15.4173i	−0.487050	+	0.843595i
$335$	−27.8450			−1.52133
$336$	−5.73292	+	0.578199i	−0.312756	+	0.0315434i
$337$	7.79004	−	4.49758i	0.424350	−	0.244999i	−0.272586	−	0.962131i	$-0.587879\pi$
$337$	7.79004	−	4.49758i	0.424350	−	0.244999i	0.696937	+	0.717132i	$0.254546\pi$
$338$	−3.56647	−	12.5012i	−0.193991	−	0.679976i
$339$	−11.3194	+	4.29059i	−0.614784	+	0.233033i
$340$	−7.29255	+	7.29255i	−0.395494	+	0.395494i
$341$	12.1682	−	7.02529i	0.658943	−	0.380441i
$342$	−1.62758	−	7.98677i	−0.0880097	−	0.431875i
$343$	−6.89966	+	6.89966i	−0.372547	+	0.372547i
$344$	0.949085	−	3.54203i	0.0511712	−	0.190974i
$345$	0.485222	−	1.07761i	0.0261235	−	0.0580167i
$346$	−3.73332	+	13.9330i	−0.200705	+	0.749040i
$347$		−	7.42847i		−	0.398781i	−0.979920	−	0.199390i	$-0.936104\pi$
$347$		−	7.42847i		−	0.398781i	0.979920	−	0.199390i	$-0.0638962\pi$
$348$	−0.582332	−	1.53630i	−0.0312163	−	0.0823543i
$349$	25.5197	+	25.5197i	1.36604	+	1.36604i	0.866011	+	0.500024i	$0.166676\pi$
$349$	25.5197	+	25.5197i	1.36604	+	1.36604i	0.500024	+	0.866011i	$0.333324\pi$
$350$	29.6097			1.58271
$351$	−12.5995	+	13.8655i	−0.672510	+	0.740088i
$352$	−6.34010			−0.337928
$353$	−2.17346	−	2.17346i	−0.115682	−	0.115682i	0.646896	−	0.762578i	$-0.276067\pi$
$353$	−2.17346	−	2.17346i	−0.115682	−	0.115682i	−0.762578	+	0.646896i	$0.776067\pi$
$354$	−2.87756	−	7.59152i	−0.152940	−	0.403485i
$355$			45.5245i			2.41619i
$356$	−0.172508	+	0.643808i	−0.00914289	+	0.0341217i
$357$	6.54396	−	14.5333i	0.346343	−	0.769182i
$358$	3.88962	−	14.5163i	0.205573	−	0.767209i
$359$	9.73682	−	9.73682i	0.513890	−	0.513890i	−0.401826	−	0.915716i	$-0.631624\pi$
$359$	9.73682	−	9.73682i	0.513890	−	0.513890i	0.915716	+	0.401826i	$0.131624\pi$
$360$	10.6082	+	3.54569i	0.559101	+	0.186874i
$361$	10.0615	−	5.80903i	0.529554	−	0.305738i
$362$	−5.12661	+	5.12661i	−0.269449	+	0.269449i
$363$	−47.2873	+	17.9242i	−2.48194	+	0.940777i
$364$	5.91342	−	10.4356i	0.309948	−	0.546972i
$365$	−9.86442	+	5.69522i	−0.516327	+	0.298102i
$366$	14.2686	−	1.43908i	0.745834	−	0.0752219i
$367$	−15.8770			−0.828771			−0.414385	−	0.910102i	$-0.636003\pi$
$367$	−15.8770			−0.828771			−0.414385	+	0.910102i	$0.636003\pi$
$368$	−0.0915043	+	0.158490i	−0.00476999	+	0.00826187i
$369$	−3.90578	+	5.90509i	−0.203327	+	0.307407i
$370$	7.32466	+	27.3360i	0.380791	+	1.42113i
$371$	−11.0323	−	2.95609i	−0.572767	−	0.153472i
$372$	3.81910	−	0.385180i	0.198011	−	0.0199706i
$373$	−0.725285			−0.0375538			−0.0187769	−	0.999824i	$-0.505977\pi$
$373$	−0.725285			−0.0375538			−0.0187769	+	0.999824i	$0.505977\pi$
$374$	8.76886	−	15.1881i	0.453427	−	0.785359i
$375$	−22.9683	−	10.3420i	−1.18608	−	0.534060i
$376$	4.61795	+	2.66617i	0.238153	+	0.137497i
$377$	3.31058	+	0.858551i	0.170504	+	0.0442176i
$378$	−17.2723	+	0.686922i	−0.888394	+	0.0353314i
$379$	−2.92733	−	0.784375i	−0.150367	−	0.0402906i	0.182850	−	0.983141i	$-0.441468\pi$
$379$	−2.92733	−	0.784375i	−0.150367	−	0.0402906i	−0.333217	+	0.942850i	$0.608134\pi$
$380$		−	10.1298i		−	0.519650i
$381$	2.15862	+	1.76309i	0.110590	+	0.0903260i
$382$	−3.07629	−	0.824290i	−0.157397	−	0.0421744i
$383$	1.38928	+	1.38928i	0.0709889	+	0.0709889i	0.741710	−	0.670721i	$-0.234015\pi$
$383$	1.38928	+	1.38928i	0.0709889	+	0.0709889i	−0.670721	+	0.741710i	$0.734015\pi$
$384$	−1.57933	−	0.711134i	−0.0805949	−	0.0362899i
$385$	−75.9574	+	20.3527i	−3.87115	+	1.03727i
$386$	−12.2827	−	7.09144i	−0.625175	−	0.360945i
$387$	3.48732	−	10.4336i	0.177270	−	0.530368i
$388$	1.51543	−	5.65566i	0.0769343	−	0.287123i
$389$	11.5891	−	20.0729i	0.587591	−	1.01774i	−0.406956	−	0.913448i	$-0.633410\pi$
$389$	11.5891	−	20.0729i	0.587591	−	1.01774i	0.994547	−	0.104289i	$-0.0332568\pi$
$390$	−18.7840	+	13.7582i	−0.951164	+	0.696672i
$391$	−0.253115	−	0.438409i	−0.0128006	−	0.0221713i
$392$	3.92830	−	1.05259i	0.198409	−	0.0531636i
$393$	−12.6484	−	10.3308i	−0.638030	−	0.521122i
$394$	−0.303713	+	0.175349i	−0.0153009	+	0.00883396i
$395$	33.2881	+	33.2881i	1.67491	+	1.67491i
$396$	−18.9852	−	1.15510i	−0.954042	−	0.0580458i
$397$	−3.81012	+	1.02092i	−0.191224	+	0.0512384i	−0.353160	−	0.935563i	$-0.614893\pi$
$397$	−3.81012	+	1.02092i	−0.191224	+	0.0512384i	0.161936	+	0.986801i	$0.448226\pi$
$398$	−5.11801	−	19.1007i	−0.256543	−	0.957430i
$399$	5.54884	+	14.6388i	0.277789	+	0.732859i
$400$	7.70819	+	4.45033i	0.385409	+	0.222516i
$401$	5.75855	+	21.4912i	0.287568	+	1.07322i	0.946942	+	0.321404i	$0.104155\pi$
$401$	5.75855	+	21.4912i	0.287568	+	1.07322i	−0.659374	+	0.751815i	$0.729179\pi$
$402$	12.7678	+	2.07728i	0.636801	+	0.103605i
$403$	−3.93935	+	6.95187i	−0.196233	+	0.346297i
$404$		−	9.35186i		−	0.465272i
$405$	31.1199	+	12.5501i	1.54636	+	0.623621i
$406$	1.57779	+	2.73282i	0.0783045	+	0.135627i
$407$	−24.0624	−	41.6773i	−1.19273	−	2.06587i
$408$	3.88791	−	2.79984i	0.192480	−	0.138613i
$409$	−19.9999	+	19.9999i	−0.988934	+	0.988934i	−0.999939	−	0.0110057i	$-0.996497\pi$
$409$	−19.9999	+	19.9999i	−0.988934	+	0.988934i	0.0110057	+	0.999939i	$0.496497\pi$
$410$	−6.22171	+	6.22171i	−0.307268	+	0.307268i
$411$	−2.82061	−	27.9667i	−0.139130	−	1.37949i
$412$	0.147924	+	0.256212i	0.00728769	+	0.0126227i
$413$	7.79655	+	13.5040i	0.383643	+	0.664490i
$414$	−0.302881	+	0.457922i	−0.0148858	+	0.0225056i
$415$			25.1918i			1.23662i
$416$	3.10788	−	1.82787i	0.152376	−	0.0896185i
$417$	−5.46022	−	14.4051i	−0.267388	−	0.705419i
$418$	4.45839	+	16.6389i	0.218067	+	0.813836i
$419$	−9.72023	−	5.61198i	−0.474864	−	0.274163i	0.243409	−	0.969924i	$-0.421734\pi$
$419$	−9.72023	−	5.61198i	−0.474864	−	0.274163i	−0.718274	+	0.695761i	$0.755067\pi$
$420$	−21.2040	−	3.44981i	−1.03465	−	0.168334i
$421$	−0.256866	−	0.958636i	−0.0125189	−	0.0467211i	0.959384	−	0.282104i	$-0.0910323\pi$
$421$	−0.256866	−	0.958636i	−0.0125189	−	0.0467211i	−0.971903	+	0.235383i	$0.924366\pi$
$422$	8.96138	−	2.40120i	0.436233	−	0.116888i
$423$	13.3425	+	8.82510i	0.648736	+	0.429091i
$424$	−2.42769	−	2.42769i	−0.117899	−	0.117899i
$425$	−21.3221	+	12.3103i	−1.03427	+	0.597138i
$426$	3.39620	−	20.8744i	0.164546	−	1.01137i
$427$	−26.6058	+	7.12900i	−1.28754	+	0.344996i
$428$	−9.35458	−	16.2026i	−0.452171	−	0.783182i
$429$	24.7986	−	30.8660i	1.19729	−	1.49022i
$430$	6.83591	−	11.8401i	0.329657	−	0.570982i
$431$	−1.41740	+	5.28983i	−0.0682740	+	0.254802i	−0.991624	−	0.129157i	$-0.958773\pi$
$431$	−1.41740	+	5.28983i	−0.0682740	+	0.254802i	0.923350	+	0.383959i	$0.125440\pi$
$432$	−4.59969	−	2.41720i	−0.221303	−	0.116298i
$433$	−14.9131	−	8.61010i	−0.716680	−	0.413775i	0.0968497	−	0.995299i	$-0.469123\pi$
$433$	−14.9131	−	8.61010i	−0.716680	−	0.413775i	−0.813529	+	0.581524i	$0.802457\pi$
$434$	−7.12122	+	1.90813i	−0.341830	+	0.0915930i
$435$	−0.614681	−	6.09463i	−0.0294717	−	0.292215i
$436$	−7.95895	−	7.95895i	−0.381165	−	0.381165i
$437$	0.480287	+	0.128693i	0.0229752	+	0.00615620i
$438$	4.94803	−	1.87554i	0.236426	−	0.0896169i
$439$			5.14800i			0.245701i	0.992425	+	0.122850i	$0.0392035\pi$
$439$			5.14800i			0.245701i	−0.992425	+	0.122850i	$0.960796\pi$
$440$	−22.8327	−	6.11801i	−1.08851	−	0.291664i
$441$	11.9549	−	2.43624i	0.569282	−	0.116011i
$442$	0.0803264	+	9.97320i	0.00382074	+	0.474377i
$443$	19.9015	+	11.4901i	0.945547	+	0.545912i	0.891695	−	0.452637i	$-0.149517\pi$
$443$	19.9015	+	11.4901i	0.945547	+	0.545912i	0.0538522	+	0.998549i	$0.482850\pi$
$444$	−1.31928	−	13.0809i	−0.0626105	−	0.620790i
$445$	−1.24251	+	2.15209i	−0.0589006	+	0.102019i
$446$	15.4749			0.732760
$447$	−16.8230	+	37.3616i	−0.795700	+	1.76714i
$448$	3.21334	+	0.861011i	0.151816	+	0.0406790i
$449$	−4.11231	−	15.3473i	−0.194072	−	0.724286i	−0.992505	−	0.122203i	$-0.961004\pi$
$449$	−4.11231	−	15.3473i	−0.194072	−	0.724286i	0.798433	−	0.602083i	$-0.205662\pi$
$450$	22.2711	+	14.7307i	1.04987	+	0.694411i
$451$	7.48123	−	12.9579i	0.352277	−	0.610162i
$452$	6.98898			0.328734
$453$	−0.152161	−	0.211294i	−0.00714917	−	0.00992748i
$454$	6.36903	−	3.67716i	0.298913	−	0.172578i
$455$	31.3661	−	31.8755i	1.47047	−	1.49435i
$456$	−0.755702	+	4.64486i	−0.0353890	+	0.217516i
$457$	18.3372	−	18.3372i	0.857780	−	0.857780i	−0.133296	−	0.991076i	$-0.542556\pi$
$457$	18.3372	−	18.3372i	0.857780	−	0.857780i	0.991076	+	0.133296i	$0.0425562\pi$
$458$	−21.4339	+	12.3749i	−1.00154	+	0.578240i
$459$	12.1523	−	7.67567i	0.567220	−	0.358270i
$460$	−0.482474	+	0.482474i	−0.0224955	+	0.0224955i
$461$	0.435138	−	1.62396i	0.0202664	−	0.0756352i	−0.955052	−	0.296438i	$-0.904201\pi$
$461$	0.435138	−	1.62396i	0.0202664	−	0.0756352i	0.975318	+	0.220803i	$0.0708678\pi$
$462$	36.3473	−	3.66584i	1.69103	−	0.170550i
$463$	4.49747	−	16.7848i	0.209015	−	0.780055i	−0.779173	−	0.626809i	$-0.784361\pi$
$463$	4.49747	−	16.7848i	0.209015	−	0.780055i	0.988188	−	0.153246i	$-0.0489727\pi$
$464$			0.948565i			0.0440360i
$465$	14.1255	+	2.29817i	0.655054	+	0.106575i
$466$	−12.7477	−	12.7477i	−0.590525	−	0.590525i
$467$	−0.582570			−0.0269581			−0.0134791	−	0.999909i	$-0.504291\pi$
$467$	−0.582570			−0.0269581			−0.0134791	+	0.999909i	$0.504291\pi$
$468$	9.63944	−	4.90725i	0.445583	−	0.226838i
$469$	−24.8452			−1.14724
$470$	14.0579	+	14.0579i	0.648444	+	0.648444i
$471$	1.94696	−	2.38374i	0.0897111	−	0.109837i
$472$			4.68727i			0.215749i
$473$	−6.01729	+	22.4568i	−0.276675	+	1.03257i
$474$	−12.7803	−	17.7470i	−0.587020	−	0.815148i
$475$	6.25898	−	23.3588i	0.287182	−	1.07178i
$476$	−6.50691	+	6.50691i	−0.298244	+	0.298244i
$477$	−6.82733	−	7.71193i	−0.312602	−	0.353105i
$478$	24.6787	−	14.2483i	1.12878	−	0.651701i
$479$	5.53126	−	5.53126i	0.252730	−	0.252730i	−0.569359	−	0.822089i	$-0.692809\pi$
$479$	5.53126	−	5.53126i	0.252730	−	0.252730i	0.822089	+	0.569359i	$0.192809\pi$
$480$	−5.00145	−	4.08503i	−0.228284	−	0.186455i
$481$	23.8109	+	13.4927i	1.08569	+	0.615215i
$482$	6.94473	−	4.00954i	0.316324	−	0.182630i
$483$	0.432948	−	0.961518i	0.0196998	−	0.0437506i
$484$	29.1969			1.32713
$485$	10.9151	−	18.9055i	0.495629	−	0.858454i
$486$	−13.3332	−	8.07623i	−0.604807	−	0.366345i
$487$	1.40502	+	5.24359i	0.0636674	+	0.237610i	0.990425	−	0.138049i	$-0.0440831\pi$
$487$	1.40502	+	5.24359i	0.0636674	+	0.237610i	−0.926758	+	0.375659i	$0.877416\pi$
$488$	−7.99767	−	2.14297i	−0.362038	−	0.0970077i
$489$	6.05616	+	8.40971i	0.273869	+	0.380300i
$490$	15.1628			0.684985
$491$	1.20154	−	2.08113i	0.0542247	−	0.0939199i	−0.837639	−	0.546224i	$-0.816065\pi$
$491$	1.20154	−	2.08113i	0.0542247	−	0.0939199i	0.891864	+	0.452304i	$0.149398\pi$
$492$	3.31700	−	2.38870i	0.149542	−	0.107691i
$493$	−2.27235	−	1.31194i	−0.102341	−	0.0590868i
$494$	−6.98252	−	6.87094i	−0.314158	−	0.309138i
$495$	−67.2571	−	22.4800i	−3.02298	−	1.01040i
$496$	−2.14063	−	0.573581i	−0.0961172	−	0.0257545i
$497$			40.6200i			1.82206i
$498$	1.87935	−	11.5513i	0.0842156	−	0.517624i
$499$	−6.02143	−	1.61344i	−0.269556	−	0.0722273i	0.121509	−	0.992590i	$-0.461227\pi$
$499$	−6.02143	−	1.61344i	−0.269556	−	0.0722273i	−0.391065	+	0.920363i	$0.627893\pi$
$500$	10.2835	+	10.2835i	0.459891	+	0.459891i
$501$	25.0216	−	18.0191i	1.11788	−	0.805032i
$502$	−5.87122	+	1.57319i	−0.262045	+	0.0702148i
$503$	−11.8442	−	6.83823i	−0.528105	−	0.304901i	0.212140	−	0.977239i	$-0.431957\pi$
$503$	−11.8442	−	6.83823i	−0.528105	−	0.304901i	−0.740244	+	0.672338i	$0.765290\pi$
$504$	9.46535	+	3.16370i	0.421620	+	0.140922i
$505$	9.02426	−	33.6790i	0.401574	−	1.49870i
$506$	0.580146	−	1.00484i	0.0257907	−	0.0446707i
$507$	−3.25739	+	22.2798i	−0.144666	+	0.989481i
$508$	−0.804578	−	1.39357i	−0.0356974	−	0.0618297i
$509$	7.67175	−	2.05564i	0.340044	−	0.0911146i	−0.0847559	−	0.996402i	$-0.527011\pi$
$509$	7.67175	−	2.05564i	0.340044	−	0.0911146i	0.424800	+	0.905287i	$0.360344\pi$
$510$	16.7033	−	6.33138i	0.739636	−	0.280358i
$511$	−8.80170	+	5.08166i	−0.389364	+	0.224799i
$512$	0.707107	+	0.707107i	0.0312500	+	0.0312500i
$513$	−3.10917	+	13.7712i	−0.137273	+	0.608013i
$514$	−0.617015	+	0.165329i	−0.0272154	+	0.00729234i
$515$	0.285484	+	1.06544i	0.0125799	+	0.0469490i
$516$	−4.01778	+	4.91912i	−0.176873	+	0.216552i
$517$	−29.2783	−	16.9038i	−1.28766	−	0.743429i
$518$	6.53555	+	24.3910i	0.287156	+	1.07168i
$519$	15.8043	−	19.3499i	0.693734	−	0.849365i
$520$	12.9563	−	3.58371i	0.568171	−	0.157156i
$521$			40.0151i			1.75309i	0.481316	+	0.876547i	$0.340159\pi$
$521$			40.0151i			1.75309i	−0.481316	+	0.876547i	$0.659841\pi$
$522$	−0.172818	+	2.84044i	−0.00756404	+	0.124323i
$523$	5.07493	+	8.79004i	0.221911	+	0.384362i	0.955388	−	0.295353i	$-0.0954371\pi$
$523$	5.07493	+	8.79004i	0.221911	+	0.384362i	−0.733477	+	0.679714i	$0.762104\pi$
$524$	4.71442	+	8.16562i	0.205951	+	0.356717i
$525$	−46.7636	−	21.0565i	−2.04093	−	0.918980i
$526$	3.98438	−	3.98438i	0.173727	−	0.173727i
$527$	4.33471	−	4.33471i	0.188823	−	0.188823i
$528$	10.0131	+	4.50866i	0.435765	+	0.196214i
$529$	11.4833	+	19.8896i	0.499272	+	0.864764i
$530$	−6.40023	−	11.0855i	−0.278008	−	0.481525i
$531$	−0.853969	+	14.0359i	−0.0370591	+	0.609104i
$532$		−	9.03853i		−	0.391870i
$533$	0.0685312	+	8.50873i	0.00296842	+	0.368554i
$534$	0.730280	−	0.894110i	0.0316023	−	0.0386919i
$535$	−18.0538	−	67.3776i	−0.780533	−	2.91299i
$536$	−6.46785	−	3.73421i	−0.279368	−	0.161293i
$537$	−16.4660	+	20.1600i	−0.710561	+	0.869967i
$538$	−5.28243	−	19.7143i	−0.227742	−	0.849944i
$539$	−24.9058	+	6.67350i	−1.07277	+	0.287448i
$540$	−14.2324	−	13.1437i	−0.612466	−	0.565613i
$541$	24.3541	+	24.3541i	1.04706	+	1.04706i	0.998836	+	0.0482280i	$0.0153574\pi$
$541$	24.3541	+	24.3541i	1.04706	+	1.04706i	0.0482280	+	0.998836i	$0.484643\pi$
$542$	18.5494	−	10.7095i	0.796766	−	0.460013i
$543$	11.7423	−	4.45091i	0.503911	−	0.191007i
$544$	−2.67190	+	0.715935i	−0.114557	+	0.0306954i
$545$	−20.9826	−	36.3429i	−0.898794	−	1.55676i
$546$	−16.7603	+	12.2760i	−0.717276	+	0.525363i
$547$	−3.38921	+	5.87029i	−0.144912	+	0.250996i	−0.929340	−	0.369224i	$-0.879623\pi$
$547$	−3.38921	+	5.87029i	−0.144912	+	0.250996i	0.784428	+	0.620220i	$0.212957\pi$
$548$	−4.20024	+	15.6755i	−0.179425	+	0.669624i
$549$	−23.5583	−	7.87413i	−1.00544	−	0.336060i
$550$	−48.8707	−	28.2155i	−2.08385	−	1.20311i
$551$	2.48941	−	0.667035i	0.106052	−	0.0284167i
$552$	0.257223	−	0.185237i	0.0109482	−	0.00788420i
$553$	29.7019	+	29.7019i	1.26305	+	1.26305i
$554$	−4.65790	−	1.24808i	−0.197895	−	0.0530259i
$555$	7.87148	−	48.3814i	0.334126	−	2.05368i
$556$			8.89419i			0.377198i
$557$	−41.9906	−	11.2513i	−1.77920	−	0.476734i	−0.788760	−	0.614701i	$-0.789277\pi$
$557$	−41.9906	−	11.2513i	−1.77920	−	0.476734i	−0.990437	+	0.137967i	$0.955943\pi$
$558$	−6.30554	−	2.10757i	−0.266935	−	0.0892204i
$559$	−3.52472	−	12.7430i	−0.149080	−	0.538972i
$560$	10.7414	+	6.20155i	0.453907	+	0.262063i
$561$	−24.6497	+	17.7512i	−1.04071	+	0.749458i
$562$	1.88438	−	3.26384i	0.0794878	−	0.137677i
$563$	1.63879			0.0690668			0.0345334	−	0.999404i	$-0.489005\pi$
$563$	1.63879			0.0690668			0.0345334	+	0.999404i	$0.489005\pi$
$564$	−5.39727	−	7.49475i	−0.227266	−	0.315586i
$565$	25.1695	+	6.74415i	1.05889	+	0.283729i
$566$	3.26105	+	12.1704i	0.137072	+	0.511561i
$567$	27.7673	+	11.1981i	1.16612	+	0.470275i
$568$	−6.10517	+	10.5745i	−0.256167	+	0.443694i
$569$	3.08870			0.129485			0.0647424	−	0.997902i	$-0.479377\pi$
$569$	3.08870			0.129485			0.0647424	+	0.997902i	$0.479377\pi$
$570$	−7.20368	+	15.9984i	−0.301729	+	0.670099i
$571$	5.59791	−	3.23195i	0.234265	−	0.135253i	−0.378273	−	0.925694i	$-0.623482\pi$
$571$	5.59791	−	3.23195i	0.234265	−	0.135253i	0.612538	+	0.790441i	$0.290149\pi$
$572$	−19.7043	+	11.5888i	−0.823876	+	0.484554i
$573$	4.27231	+	3.48948i	0.178478	+	0.145775i
$574$	−5.55143	+	5.55143i	−0.231712	+	0.231712i
$575$	−1.41067	+	0.814448i	−0.0588288	+	0.0339648i
$576$	1.98858	+	2.24623i	0.0828574	+	0.0935930i
$577$	32.0507	−	32.0507i	1.33429	−	1.33429i	0.432795	−	0.901492i	$-0.357527\pi$
$577$	32.0507	−	32.0507i	1.33429	−	1.33429i	0.901492	−	0.432795i	$-0.142473\pi$
$578$	−2.41954	+	9.02983i	−0.100639	+	0.375591i
$579$	14.3555	+	19.9344i	0.596596	+	0.828445i
$580$	−0.915337	+	3.41608i	−0.0380073	+	0.141845i
$581$			22.4778i			0.932537i
$582$	−6.41530	+	7.85450i	−0.265923	+	0.325579i
$583$	15.3918	+	15.3918i	0.637463	+	0.637463i
$584$	−3.05508			−0.126420
$585$	39.4500	−	8.37081i	1.63106	−	0.346090i
$586$	−29.7226			−1.22783
$587$	−16.0190	−	16.0190i	−0.661174	−	0.661174i	0.294483	−	0.955657i	$-0.404853\pi$
$587$	−16.0190	−	16.0190i	−0.661174	−	0.661174i	−0.955657	+	0.294483i	$0.904853\pi$
$588$	−6.95262	−	1.13117i	−0.286721	−	0.0466485i
$589$			6.02121i			0.248100i
$590$	−4.52308	+	16.8803i	−0.186212	+	0.694953i
$591$	0.604361	−	0.0609535i	0.0248601	−	0.00250729i
$592$	−1.96458	+	7.33191i	−0.0807437	+	0.301340i
$593$	14.2009	−	14.2009i	0.583160	−	0.583160i	−0.352610	−	0.935770i	$-0.614706\pi$
$593$	14.2009	−	14.2009i	0.583160	−	0.583160i	0.935770	+	0.352610i	$0.114706\pi$
$594$	29.1625	+	15.3253i	1.19655	+	0.628804i
$595$	−29.7124	+	17.1545i	−1.21809	+	0.703265i
$596$	16.7277	−	16.7277i	0.685194	−	0.685194i
$597$	−5.50009	+	33.8059i	−0.225104	+	1.38358i
$598$	0.00531438	+	0.659826i	0.000217321	+	0.0269823i
$599$	−8.75479	+	5.05458i	−0.357711	+	0.206525i	−0.668076	−	0.744093i	$-0.732882\pi$
$599$	−8.75479	+	5.05458i	−0.357711	+	0.206525i	0.310365	+	0.950617i	$0.399549\pi$
$600$	−9.00901	−	12.5101i	−0.367791	−	0.510722i
$601$	−15.4541			−0.630387			−0.315194	−	0.949027i	$-0.602069\pi$
$601$	−15.4541			−0.630387			−0.315194	+	0.949027i	$0.602069\pi$
$602$	6.09946	−	10.5646i	0.248595	−	0.430580i
$603$	−18.6874	−	12.3603i	−0.761009	−	0.503352i
$604$	0.0389086	+	0.145209i	0.00158317	+	0.00590846i
$605$	105.147	+	28.1741i	4.27484	+	1.14544i
$606$	−6.65042	+	14.7697i	−0.270155	+	0.599977i
$607$	−28.3126			−1.14917			−0.574586	−	0.818444i	$-0.694837\pi$
$607$	−28.3126			−1.14917			−0.574586	+	0.818444i	$0.694837\pi$
$608$	1.35849	−	2.35297i	0.0550939	−	0.0954255i
$609$	−0.548460	−	5.43804i	−0.0222247	−	0.220361i
$610$	−26.7342	−	15.4350i	−1.08244	−	0.624946i
$611$	19.2254	−	0.154846i	0.777778	−	0.00626440i
$612$	−8.13135	+	1.65705i	−0.328690	+	0.0669822i
$613$	−10.9069	−	2.92249i	−0.440524	−	0.118038i	0.0317379	−	0.999496i	$-0.489896\pi$
$613$	−10.9069	−	2.92249i	−0.440524	−	0.118038i	−0.472262	+	0.881458i	$0.656562\pi$
$614$		−	32.4617i		−	1.31005i
$615$	14.2506	−	5.40167i	0.574640	−	0.217817i
$616$	−20.3729	−	5.45890i	−0.820847	−	0.219945i
$617$	27.0649	+	27.0649i	1.08959	+	1.08959i	0.995570	+	0.0940202i	$0.0299718\pi$
$617$	27.0649	+	27.0649i	1.08959	+	1.08959i	0.0940202	+	0.995570i	$0.470028\pi$
$618$	−0.0514202	−	0.509837i	−0.00206842	−	0.0205087i
$619$	25.4606	−	6.82214i	1.02335	−	0.274205i	0.292150	−	0.956372i	$-0.405629\pi$
$619$	25.4606	−	6.82214i	1.02335	−	0.274205i	0.731196	+	0.682168i	$0.238963\pi$
$620$	−7.15561	−	4.13129i	−0.287376	−	0.165917i
$621$	0.803994	−	0.507821i	0.0322632	−	0.0203782i
$622$	6.11116	−	22.8072i	0.245035	−	0.914484i
$623$	−1.10865	+	1.92024i	−0.0444172	+	0.0769328i
$624$	−6.20823	+	0.676690i	−0.248528	+	0.0270893i
$625$	4.85917	+	8.41632i	0.194367	+	0.336653i
$626$	16.8365	−	4.51132i	0.672921	−	0.180309i
$627$	4.79123	−	29.4489i	0.191343	−	1.17608i
$628$	−1.53890	+	0.888484i	−0.0614088	+	0.0354544i
$629$	−14.8469	−	14.8469i	−0.591984	−	0.591984i
$630$	31.0349	+	20.5273i	1.23646	+	0.817826i
$631$	38.1709	−	10.2279i	1.51956	−	0.407165i	0.599963	−	0.800028i	$-0.295182\pi$
$631$	38.1709	−	10.2279i	1.51956	−	0.407165i	0.919597	+	0.392863i	$0.128515\pi$
$632$	3.26801	+	12.1964i	0.129994	+	0.485146i
$633$	−15.8606	−	2.58046i	−0.630401	−	0.102564i
$634$	0.542364	+	0.313134i	0.0215400	+	0.0124361i
$635$	−1.55279	−	5.79508i	−0.0616205	−	0.229971i
$636$	2.10772	+	5.56054i	0.0835764	+	0.220490i
$637$	10.2847	−	10.4517i	0.407495	−	0.414112i
$638$		−	6.01399i		−	0.238096i
$639$	−20.2082	+	30.5525i	−0.799426	+	1.20864i
$640$	1.86418	+	3.22885i	0.0736881	+	0.127632i
$641$	−16.8449	−	29.1763i	−0.665335	−	1.15239i	−0.979194	−	0.202925i	$-0.934955\pi$
$641$	−16.8449	−	29.1763i	−0.665335	−	1.15239i	0.313859	−	0.949470i	$-0.398378\pi$
$642$	3.25176	+	32.2416i	0.128337	+	1.27248i
$643$	16.2755	−	16.2755i	0.641844	−	0.641844i	−0.309165	−	0.951009i	$-0.600049\pi$
$643$	16.2755	−	16.2755i	0.641844	−	0.641844i	0.951009	+	0.309165i	$0.100049\pi$
$644$	−0.430496	+	0.430496i	−0.0169639	+	0.0169639i
$645$	−19.2161	+	13.8383i	−0.756633	+	0.544881i
$646$	3.75779	+	6.50868i	0.147848	+	0.256081i
$647$	−3.32926	−	5.76644i	−0.130887	−	0.226702i	0.793132	−	0.609050i	$-0.208449\pi$
$647$	−3.32926	−	5.76644i	−0.130887	−	0.226702i	−0.924019	+	0.382348i	$0.875116\pi$
$648$	5.54548	+	7.08856i	0.217847	+	0.278465i
$649$		−	29.7178i		−	1.16652i
$650$	32.0907	−	0.258466i	1.25870	−	0.0101379i
$651$	12.6037	+	2.05058i	0.493978	+	0.0803685i
$652$	−1.54860	−	5.77944i	−0.0606477	−	0.226340i
$653$	18.3358	+	10.5862i	0.717536	+	0.414270i	0.813845	−	0.581082i	$-0.197370\pi$
$653$	18.3358	+	10.5862i	0.717536	+	0.414270i	−0.0963092	+	0.995351i	$0.530704\pi$
$654$	6.90995	+	18.2297i	0.270200	+	0.712838i
$655$	9.09855	+	33.9563i	0.355510	+	1.32678i
$656$	−2.27956	+	0.610806i	−0.0890018	+	0.0238480i
$657$	−9.14833	−	0.556603i	−0.356911	−	0.0217151i
$658$	12.5434	+	12.5434i	0.488994	+	0.488994i
$659$	−34.2945	+	19.7999i	−1.33592	+	0.771296i	−0.986200	−	0.165557i	$-0.947058\pi$
$659$	−34.2945	+	19.7999i	−1.33592	+	0.771296i	−0.349723	+	0.936853i	$0.613724\pi$
$660$	31.7097	+	25.8995i	1.23430	+	1.00814i
$661$	−24.0112	+	6.43378i	−0.933927	+	0.250245i	−0.693529	−	0.720429i	$-0.743945\pi$
$661$	−24.0112	+	6.43378i	−0.933927	+	0.250245i	−0.240399	+	0.970674i	$0.577278\pi$
$662$	15.4586	+	26.7750i	0.600815	+	1.04064i
$663$	6.96542	−	15.8081i	0.270514	−	0.613937i
$664$	−3.37840	+	5.85157i	−0.131108	+	0.227085i
$665$	8.72191	−	32.5506i	0.338221	−	1.26226i
$666$	−7.21865	+	21.5972i	−0.279717	+	0.836875i
$667$	−0.150338	−	0.0867978i	−0.00582112	−	0.00336082i
$668$	−17.1957	+	4.60758i	−0.665322	+	0.178273i
$669$	−24.4401	−	11.0048i	−0.944908	−	0.425468i
$670$	−19.6894	−	19.6894i	−0.760666	−	0.760666i
$671$	50.7060	+	13.5866i	1.95748	+	0.524506i
$672$	−4.46263	−	3.64493i	−0.172150	−	0.140606i
$673$			8.10263i			0.312334i	0.987731	+	0.156167i	$0.0499137\pi$
$673$			8.10263i			0.312334i	−0.987731	+	0.156167i	$0.950086\pi$
$674$	8.68866	+	2.32812i	0.334675	+	0.0896758i
$675$	−24.6980	−	39.1024i	−0.950625	−	1.50505i
$676$	6.31781	−	11.3616i	0.242993	−	0.436983i
$677$	−1.64864	−	0.951842i	−0.0633623	−	0.0365822i	0.467984	−	0.883737i	$-0.344980\pi$
$677$	−1.64864	−	0.951842i	−0.0633623	−	0.0365822i	−0.531346	+	0.847155i	$0.678314\pi$
$678$	−11.0379	−	4.97010i	−0.423909	−	0.190875i
$679$	9.73918	−	16.8688i	0.373755	−	0.647363i
$680$	−10.3132			−0.395494
$681$	−12.6738	+	1.27823i	−0.485660	+	0.0489817i
$682$	13.5718	+	3.63656i	0.519692	+	0.139251i
$683$	−1.49884	−	5.59375i	−0.0573515	−	0.214039i	0.931303	−	0.364245i	$-0.118673\pi$
$683$	−1.49884	−	5.59375i	−0.0573515	−	0.214039i	−0.988655	+	0.150206i	$0.952006\pi$
$684$	4.49662	−	6.79837i	0.171933	−	0.259942i
$685$	−30.2528	+	52.3993i	−1.15590	+	2.00208i
$686$	−9.75759			−0.372547
$687$	42.6515	−	4.30166i	1.62726	−	0.164119i
$688$	3.17570	−	1.83349i	0.121072	−	0.0699012i
$689$	−11.9825	−	3.10747i	−0.456495	−	0.118385i
$690$	1.10509	−	0.418883i	0.0420701	−	0.0159466i
$691$	−33.4689	+	33.4689i	−1.27322	+	1.27322i	−0.328828	+	0.944390i	$0.606654\pi$
$691$	−33.4689	+	33.4689i	−1.27322	+	1.27322i	−0.944390	+	0.328828i	$0.893346\pi$
$692$	−12.4919	+	7.21223i	−0.474872	+	0.274168i
$693$	−60.0113	−	20.0582i	−2.27964	−	0.761947i
$694$	5.25272	−	5.25272i	0.199390	−	0.199390i
$695$	−8.58263	+	32.0308i	−0.325558	+	1.21500i
$696$	0.674556	−	1.49810i	0.0255690	−	0.0567853i
$697$	1.68959	−	6.30562i	0.0639976	−	0.238842i
$698$			36.0902i			1.36604i
$699$	11.0675	+	29.1981i	0.418612	+	1.10437i
$700$	20.9372	+	20.9372i	0.791353	+	0.791353i
$701$	28.7797			1.08700			0.543498	−	0.839411i	$-0.317100\pi$
$701$	28.7797			1.08700			0.543498	+	0.839411i	$0.317100\pi$
$702$	−18.7136	+	0.895251i	−0.706299	+	0.0337891i
$703$	20.6233			0.777824
$704$	−4.48313	−	4.48313i	−0.168964	−	0.168964i
$705$	−12.2051	−	32.1992i	−0.459669	−	1.21269i
$706$		−	3.07374i		−	0.115682i
$707$	8.05205	−	30.0507i	0.302829	−	1.13017i
$708$	3.33328	−	7.40276i	0.125272	−	0.278213i
$709$	8.40582	−	31.3709i	0.315687	−	1.17816i	−0.607661	−	0.794197i	$-0.707892\pi$
$709$	8.40582	−	31.3709i	0.315687	−	1.17816i	0.923348	−	0.383964i	$-0.125441\pi$
$710$	−32.1907	+	32.1907i	−1.20809	+	1.20809i
$711$	7.56388	+	37.1170i	0.283668	+	1.39200i
$712$	−0.577222	+	0.333259i	−0.0216323	+	0.0124894i
$713$	0.286784	−	0.286784i	0.0107401	−	0.0107401i
$714$	14.9038	−	5.64929i	0.557763	−	0.211419i
$715$	−82.1442	+	22.7211i	−3.07202	+	0.849721i
$716$	13.0149	−	7.51417i	0.486391	−	0.280818i
$717$	−49.1083	+	4.95287i	−1.83398	+	0.184968i
$718$	13.7699			0.513890
$719$	−13.4021	+	23.2131i	−0.499813	+	0.865701i	−1.00000		0.000215949i	$-0.999931\pi$
$719$	−13.4021	+	23.2131i	−0.499813	+	0.865701i	0.500187	+	0.865917i	$0.333265\pi$
$720$	4.99395	+	10.0083i	0.186114	+	0.372988i
$721$	0.254728	+	0.950659i	0.00948658	+	0.0354044i
$722$	11.2222	+	3.00697i	0.417646	+	0.111908i
$723$	−13.8194	+	1.39377i	−0.513947	+	0.0518347i
$724$	−7.25012			−0.269449
$725$	−4.22142	+	7.31172i	−0.156780	+	0.271550i
$726$	−46.1115	−	20.7629i	−1.71136	−	0.770582i
$727$	−2.56179	−	1.47905i	−0.0950116	−	0.0548550i	0.451741	−	0.892149i	$-0.350803\pi$
$727$	−2.56179	−	1.47905i	−0.0950116	−	0.0548550i	−0.546753	+	0.837294i	$0.684136\pi$
$728$	11.5605	−	3.19763i	0.428460	−	0.118512i
$729$	15.3143	+	22.2367i	0.567196	+	0.823583i
$730$	−11.0023	−	2.94806i	−0.407214	−	0.109113i
$731$			10.1435i			0.375169i
$732$	11.1070	+	9.07187i	0.410528	+	0.335306i
$733$	46.8751	+	12.5601i	1.73137	+	0.463920i	0.980498	−	0.196527i	$-0.0629663\pi$
$733$	46.8751	+	12.5601i	1.73137	+	0.463920i	0.750873	+	0.660447i	$0.229633\pi$
$734$	−11.2267	−	11.2267i	−0.414385	−	0.414385i
$735$	−23.9471	−	10.7828i	−0.883301	−	0.397728i
$736$	−0.176773	+	0.0473661i	−0.00651593	+	0.00174594i
$737$	41.0068	+	23.6753i	1.51050	+	0.872090i
$738$	−6.93734	+	1.41373i	−0.255367	+	0.0520399i
$739$	−10.8543	+	40.5087i	−0.399281	+	1.49014i	0.415084	+	0.909783i	$0.363752\pi$
$739$	−10.8543	+	40.5087i	−0.399281	+	1.49014i	−0.814365	+	0.580354i	$0.802914\pi$
$740$	−14.1501	+	24.5088i	−0.520170	+	0.900960i
$741$	6.14155	+	15.8170i	0.225616	+	0.581052i
$742$	−5.71072	−	9.89126i	−0.209647	−	0.363119i
$743$	39.4848	−	10.5799i	1.44856	−	0.388140i	0.553035	−	0.833158i	$-0.313470\pi$
$743$	39.4848	−	10.5799i	1.44856	−	0.388140i	0.895521	+	0.445018i	$0.146803\pi$
$744$	2.97288	+	2.42815i	0.108991	+	0.0890203i
$745$	76.3836	−	44.1001i	2.79848	−	1.61570i
$746$	−0.512854	−	0.512854i	−0.0187769	−	0.0187769i
$747$	−11.1826	+	16.9068i	−0.409150	+	0.618587i
$748$	16.9401	−	4.53910i	0.619393	−	0.165966i
$749$	−16.1088	−	60.1188i	−0.588602	−	2.19669i
$750$	−8.92809	−	23.5539i	−0.326008	−	0.860068i
$751$	22.8343	+	13.1834i	0.833234	+	0.481068i	0.854959	−	0.518696i	$-0.173582\pi$
$751$	22.8343	+	13.1834i	0.833234	+	0.481068i	−0.0217248	+	0.999764i	$0.506916\pi$
$752$	1.38011	+	5.15065i	0.0503276	+	0.187825i
$753$	10.3913	+	1.69063i	0.378682	+	0.0616102i
$754$	1.73385	+	2.94802i	0.0631431	+	0.107361i
$755$			0.560489i			0.0203983i
$756$	−12.6991	−	11.7277i	−0.461862	−	0.426531i
$757$	−5.99038	−	10.3756i	−0.217724	−	0.377109i	0.736388	−	0.676560i	$-0.236530\pi$
$757$	−5.99038	−	10.3756i	−0.217724	−	0.377109i	−0.954112	+	0.299451i	$0.903197\pi$
$758$	−1.51530	−	2.62457i	−0.0550380	−	0.0953287i
$759$	−1.63082	+	1.17442i	−0.0591951	+	0.0426287i
$760$	7.16289	−	7.16289i	0.259825	−	0.259825i
$761$	−8.76263	+	8.76263i	−0.317645	+	0.317645i	−0.847862	−	0.530217i	$-0.822110\pi$
$761$	−8.76263	+	8.76263i	−0.317645	+	0.317645i	0.530217	+	0.847862i	$0.322110\pi$
$762$	0.279681	+	2.77307i	0.0101318	+	0.100458i
$763$	−18.7220	−	32.4275i	−0.677784	−	1.17396i
$764$	−1.59241	−	2.75813i	−0.0576112	−	0.0997856i
$765$	−30.8826	−	1.87896i	−1.11656	−	0.0679338i
$766$			1.96474i			0.0709889i
$767$	8.56770	+	14.5675i	0.309362	+	0.526001i
$768$	−0.613909	−	1.61960i	−0.0221525	−	0.0584424i
$769$	1.22527	+	4.57277i	0.0441843	+	0.164898i	0.984493	−	0.175425i	$-0.0561301\pi$
$769$	1.22527	+	4.57277i	0.0441843	+	0.164898i	−0.940308	+	0.340324i	$0.889463\pi$
$770$	−68.1015	−	39.3184i	−2.45421	−	1.41694i
$771$	1.09204	+	0.177671i	0.0393289	+	0.00639868i
$772$	−3.67080	−	13.6996i	−0.132115	−	0.493060i
$773$	26.0869	−	6.98997i	0.938281	−	0.251412i	0.242899	−	0.970052i	$-0.421902\pi$
$773$	26.0869	−	6.98997i	0.938281	−	0.251412i	0.695382	+	0.718640i	$0.255235\pi$
$774$	9.84355	−	4.91174i	0.353819	−	0.176549i
$775$	−13.9478	−	13.9478i	−0.501019	−	0.501019i
$776$	5.07073	−	2.92759i	0.182029	−	0.105094i
$777$	7.02346	−	43.1691i	0.251965	−	1.54868i
$778$	22.3884	−	5.99896i	0.802664	−	0.215073i
$779$	3.20599	+	5.55294i	0.114867	+	0.198955i
$780$	−23.0108	−	3.55378i	−0.823918	−	0.127246i
$781$	38.7074	−	67.0431i	1.38506	−	2.39899i
$782$	0.131022	−	0.488982i	0.00468534	−	0.0174859i
$783$	2.29287	−	4.36310i	0.0819405	−	0.155925i
$784$	3.52202	+	2.03344i	0.125786	+	0.0726228i
$785$	−6.39942	+	1.71472i	−0.228405	+	0.0612010i
$786$	−1.63879	−	16.2488i	−0.0584537	−	0.579576i
$787$	25.3004	+	25.3004i	0.901862	+	0.901862i	0.995597	−	0.0937351i	$-0.0298807\pi$
$787$	25.3004	+	25.3004i	0.901862	+	0.901862i	−0.0937351	+	0.995597i	$0.529881\pi$
$788$	−0.338748	−	0.0907674i	−0.0120674	−	0.00323345i
$789$	−9.12609	+	3.45923i	−0.324897	+	0.123152i
$790$			47.0765i			1.67491i
$791$	22.4579	+	6.01759i	0.798513	+	0.213961i
$792$	−12.6078	−	14.2413i	−0.447998	−	0.506044i
$793$	−28.7728	+	7.95858i	−1.02175	+	0.282617i
$794$	−3.41606	−	1.97226i	−0.121231	−	0.0699930i
$795$	2.22480	+	22.0591i	0.0789055	+	0.782357i
$796$	9.88723	−	17.1252i	0.350444	−	0.606986i
$797$	5.72377			0.202746			0.101373	−	0.994848i	$-0.467676\pi$
$797$	5.72377			0.202746			0.101373	+	0.994848i	$0.467676\pi$
$798$	−6.42761	+	14.2748i	−0.227535	+	0.505324i
$799$	−14.2475	−	3.81761i	−0.504041	−	0.135057i
$800$	2.30366	+	8.59737i	0.0814466	+	0.303963i
$801$	−1.78919	+	0.892769i	−0.0632178	+	0.0315445i
$802$	−11.1247	+	19.2685i	−0.392825	+	0.680393i
$803$	19.3695			0.683536
$804$	7.55935	+	10.4971i	0.266598	+	0.370203i
$805$	−1.96577	+	1.13494i	−0.0692842	+	0.0400013i
$806$	−7.70125	+	2.13017i	−0.271265	+	0.0750320i
$807$	−5.67679	+	34.8919i	−0.199833	+	1.22825i
$808$	6.61276	−	6.61276i	0.232636	−	0.232636i
$809$	−31.6723	+	18.2860i	−1.11354	+	0.642903i	−0.939744	−	0.341879i	$-0.888937\pi$
$809$	−31.6723	+	18.2860i	−1.11354	+	0.642903i	−0.173796	+	0.984782i	$0.555603\pi$
$810$	13.1308	+	30.8794i	0.461369	+	1.08499i
$811$	13.4164	−	13.4164i	0.471115	−	0.471115i	−0.431160	−	0.902275i	$-0.641896\pi$
$811$	13.4164	−	13.4164i	0.471115	−	0.471115i	0.902275	+	0.431160i	$0.141896\pi$
$812$	−0.816725	+	3.04806i	−0.0286614	+	0.106966i
$813$	−36.9116	+	3.72276i	−1.29455	+	0.130563i
$814$	12.4556	−	46.4850i	0.436570	−	1.62930i
$815$		−	22.3079i		−	0.781413i
$816$	4.72895	+	0.769383i	0.165546	+	0.0269338i
$817$	−7.04497	−	7.04497i	−0.246472	−	0.246472i
$818$	−28.2842			−0.988934
$819$	35.2000	−	7.46900i	1.22999	−	0.260988i
$820$	−8.79882			−0.307268
$821$	2.17233	+	2.17233i	0.0758148	+	0.0758148i	0.743997	−	0.668183i	$-0.232928\pi$
$821$	2.17233	+	2.17233i	0.0758148	+	0.0758148i	−0.668183	+	0.743997i	$0.732928\pi$
$822$	17.7809	−	21.7699i	0.620182	−	0.759312i
$823$			45.1543i			1.57398i	0.616965	+	0.786990i	$0.288362\pi$
$823$			45.1543i			1.57398i	−0.616965	+	0.786990i	$0.711638\pi$
$824$	−0.0765711	+	0.285767i	−0.00266748	+	0.00995517i
$825$	57.1180	+	79.3152i	1.98859	+	2.76140i
$826$	−4.03579	+	15.0618i	−0.140423	+	0.524066i
$827$	9.71124	−	9.71124i	0.337693	−	0.337693i	−0.517806	−	0.855498i	$-0.673251\pi$
$827$	9.71124	−	9.71124i	0.337693	−	0.337693i	0.855498	+	0.517806i	$0.173251\pi$
$828$	−0.537969	+	0.109630i	−0.0186957	+	0.00380991i
$829$	−11.7657	+	6.79293i	−0.408639	+	0.235928i	−0.690205	−	0.723614i	$-0.742480\pi$
$829$	−11.7657	+	6.79293i	−0.408639	+	0.235928i	0.281566	+	0.959542i	$0.409146\pi$
$830$	−17.8133	+	17.8133i	−0.618309	+	0.618309i
$831$	6.46882	+	5.28353i	0.224401	+	0.183283i
$832$	3.49010	+	0.905106i	0.120997	+	0.0313789i
$833$	−9.74247	+	5.62482i	−0.337557	+	0.194888i
$834$	6.32496	−	14.0469i	0.219015	−	0.486404i
$835$	−66.3734			−2.29695
$836$	−8.61294	+	14.9181i	−0.297885	+	0.515952i
$837$	8.45979	+	7.81263i	0.292413	+	0.270044i
$838$	−2.90497	−	10.8415i	−0.100351	−	0.374514i
$839$	−42.9336	−	11.5040i	−1.48223	−	0.397163i	−0.575127	−	0.818064i	$-0.695047\pi$
$839$	−42.9336	−	11.5040i	−1.48223	−	0.397163i	−0.907106	+	0.420901i	$0.861714\pi$
$840$	−12.5541	−	17.4329i	−0.433158	−	0.601491i
$841$	28.1002			0.968973
$842$	0.496227	−	0.859490i	0.0171011	−	0.0296200i
$843$	−5.29709	+	3.81464i	−0.182441	+	0.131383i
$844$	8.03456	+	4.63875i	0.276561	+	0.159672i
$845$	33.7160	−	34.8201i	1.15987	−	1.19785i
$846$	3.19431	+	15.6749i	0.109823	+	0.538914i
$847$	93.8193	+	25.1388i	3.22367	+	0.863780i
$848$		−	3.43327i		−	0.117899i
$849$	3.50451	−	21.5402i	0.120274	−	0.739257i
$850$	−23.7817	−	6.37228i	−0.815705	−	0.218568i
$851$	−0.982268	−	0.982268i	−0.0336717	−	0.0336717i
$852$	17.1619	−	12.3590i	0.587958	−	0.423412i
$853$	−15.3450	+	4.11168i	−0.525403	+	0.140781i	−0.511765	−	0.859126i	$-0.671008\pi$
$853$	−15.3450	+	4.11168i	−0.525403	+	0.140781i	−0.0136383	+	0.999907i	$0.504341\pi$
$854$	−23.8541	−	13.7722i	−0.816270	−	0.471274i
$855$	22.7540	−	20.1440i	0.778170	−	0.688910i
$856$	4.84229	−	18.0717i	0.165506	−	0.617676i
$857$	−11.7570	+	20.3638i	−0.401613	+	0.695614i	−0.993921	−	0.110098i	$-0.964884\pi$
$857$	−11.7570	+	20.3638i	−0.401613	+	0.695614i	0.592308	+	0.805712i	$0.298217\pi$
$858$	39.3608	−	4.29028i	1.34375	−	0.146468i
$859$	−4.23525	−	7.33567i	−0.144505	−	0.250290i	0.784683	−	0.619897i	$-0.212826\pi$
$859$	−4.23525	−	7.33567i	−0.144505	−	0.250290i	−0.929188	+	0.369607i	$0.879492\pi$
$860$	13.2060	−	3.53853i	0.450320	−	0.120663i
$861$	12.7154	−	4.81974i	0.433338	−	0.164256i
$862$	−4.74273	+	2.73822i	−0.161538	+	0.0932640i
$863$	4.48332	+	4.48332i	0.152614	+	0.152614i	0.779284	−	0.626670i	$-0.215583\pi$
$863$	4.48332	+	4.48332i	0.152614	+	0.152614i	−0.626670	+	0.779284i	$0.715583\pi$
$864$	−1.54325	−	4.96169i	−0.0525025	−	0.168800i
$865$	−51.9470	+	13.9192i	−1.76625	+	0.473266i
$866$	−4.45692	−	16.6334i	−0.151452	−	0.565227i
$867$	10.2427	−	12.5405i	0.347859	−	0.425897i
$868$	−6.38472	−	3.68622i	−0.216711	−	0.125118i
$869$	−20.7195	−	77.3262i	−0.702861	−	2.62311i
$870$	3.87491	−	4.74420i	0.131372	−	0.160843i
$871$	−26.9269	+	0.216875i	−0.912384	+	0.00734854i
$872$		−	11.2557i		−	0.381165i
$873$	15.7175	−	7.84272i	0.531956	−	0.265436i
$874$	0.248615	+	0.430614i	0.00840952	+	0.0145657i
$875$	24.1901	+	41.8984i	0.817774	+	1.41643i
$876$	4.82499	+	2.17257i	0.163021	+	0.0734044i
$877$	−9.00681	+	9.00681i	−0.304138	+	0.304138i	−0.842630	−	0.538492i	$-0.818994\pi$
$877$	−9.00681	+	9.00681i	−0.304138	+	0.304138i	0.538492	+	0.842630i	$0.318994\pi$
$878$	−3.64019	+	3.64019i	−0.122850	+	0.122850i
$879$	46.9418	+	21.1367i	1.58331	+	0.712924i
$880$	−11.8191	−	20.4712i	−0.398421	−	0.690085i
$881$	−28.5401	−	49.4329i	−0.961541	−	1.66544i	−0.718634	−	0.695389i	$-0.755232\pi$
$881$	−28.5401	−	49.4329i	−0.961541	−	1.66544i	−0.242907	−	0.970050i	$-0.578101\pi$
$882$	10.1761	+	6.73073i	0.342647	+	0.226636i
$883$		−	35.3145i		−	1.18843i	−0.804307	−	0.594214i	$-0.797463\pi$
$883$		−	35.3145i		−	1.18843i	0.804307	−	0.594214i	$-0.202537\pi$
$884$	−6.99532	+	7.10892i	−0.235278	+	0.239099i
$885$	19.1476	−	23.4432i	0.643640	−	0.788033i
$886$	5.94772	+	22.1972i	0.199818	+	0.745729i
$887$	−33.3408	−	19.2493i	−1.11947	−	0.646328i	−0.178207	−	0.983993i	$-0.557030\pi$
$887$	−33.3408	−	19.2493i	−1.11947	−	0.646328i	−0.941267	+	0.337665i	$0.890363\pi$
$888$	8.31669	−	10.1824i	0.279090	−	0.341700i
$889$	−1.38550	−	5.17076i	−0.0464682	−	0.173422i
$890$	−2.40035	+	0.643171i	−0.0804598	+	0.0215591i
$891$	−35.1589	−	44.9421i	−1.17787	−	1.50562i
$892$	10.9424	+	10.9424i	0.366380	+	0.366380i
$893$	12.5468	−	7.24393i	0.419864	−	0.242409i
$894$	−38.3143	+	14.5230i	−1.28142	+	0.485721i
$895$	54.1219	−	14.5019i	1.80909	−	0.484745i
$896$	1.66335	+	2.88100i	0.0555685	+	0.0962474i
$897$	0.460831	−	1.04586i	0.0153867	−	0.0349203i
$898$	7.94437	−	13.7601i	0.265107	−	0.459179i
$899$	0.544079	−	2.03053i	0.0181460	−	0.0677219i
$900$	5.33187	+	26.1642i	0.177729	+	0.872140i
$901$	8.22462	+	4.74849i	0.274002	+	0.158195i
$902$	14.4526	−	3.87257i	0.481220	−	0.128942i
$903$	−17.1459	+	12.3474i	−0.570580	+	0.410897i
$904$	4.94195	+	4.94195i	0.164367	+	0.164367i
$905$	−26.1100	−	6.99615i	−0.867925	−	0.232560i
$906$	0.0418133	−	0.257002i	0.00138915	−	0.00853832i
$907$		−	37.9356i		−	1.25963i	−0.776745	−	0.629815i	$-0.783131\pi$
$907$		−	37.9356i		−	1.25963i	0.776745	−	0.629815i	$-0.216869\pi$
$908$	7.10373	+	1.90344i	0.235746	+	0.0631678i
$909$	21.0064	−	18.5969i	0.696740	−	0.616820i
$910$	44.7186	−	0.360173i	1.48241	−	0.0119396i
$911$	−36.1297	−	20.8595i	−1.19703	−	0.691107i	−0.237140	−	0.971476i	$-0.576210\pi$
$911$	−36.1297	−	20.8595i	−1.19703	−	0.691107i	−0.959892	+	0.280369i	$0.909543\pi$
$912$	−3.81878	+	2.75005i	−0.126452	+	0.0910633i
$913$	21.4194	−	37.0995i	0.708879	−	1.22782i
$914$	25.9328			0.857780
$915$	31.2459	+	43.3887i	1.03296	+	1.43438i
$916$	−23.9064	−	6.40571i	−0.789891	−	0.211651i
$917$	8.11834	+	30.2981i	0.268091	+	1.00053i
$918$	14.0205	+	3.16545i	0.462745	+	0.104475i
$919$	−16.7214	+	28.9624i	−0.551590	+	0.955381i	0.446570	+	0.894748i	$0.352645\pi$
$919$	−16.7214	+	28.9624i	−0.551590	+	0.955381i	−0.998160	+	0.0606329i	$0.980688\pi$
$920$	−0.682322			−0.0224955
$921$	−23.0846	+	51.2679i	−0.760665	+	1.68933i
$922$	1.45600	−	0.840621i	0.0479508	−	0.0276844i
$923$	0.354576	+	44.0236i	0.0116710	+	1.44905i
$924$	28.2935	+	23.1092i	0.930789	+	0.760238i
$925$	−47.7727	+	47.7727i	−1.57076	+	1.57076i
$926$	15.0488	−	8.68844i	0.494535	−	0.285520i
$927$	−0.281353	+	0.841769i	−0.00924084	+	0.0276473i
$928$	−0.670737	+	0.670737i	−0.0220180	+	0.0220180i
$929$	2.86847	−	10.7053i	0.0941115	−	0.351229i	−0.902772	−	0.430120i	$-0.858471\pi$
$929$	2.86847	−	10.7053i	0.0941115	−	0.351229i	0.996883	+	0.0788911i	$0.0251379\pi$
$930$	8.36318	+	11.6133i	0.274239	+	0.380814i
$931$	2.85985	−	10.6731i	0.0937277	−	0.349797i
$932$		−	18.0279i		−	0.590525i
$933$	−25.8705	+	31.6742i	−0.846962	+	1.03697i
$934$	−0.411940	−	0.411940i	−0.0134791	−	0.0134791i
$935$	65.3869			2.13838
$936$	10.2861	+	3.34616i	0.336211	+	0.109373i
$937$	−10.8175			−0.353392			−0.176696	−	0.984265i	$-0.556541\pi$
$937$	−10.8175			−0.353392			−0.176696	+	0.984265i	$0.556541\pi$
$938$	−17.5682	−	17.5682i	−0.573621	−	0.573621i
$939$	−29.7986	−	4.84812i	−0.972439	−	0.158212i
$940$			19.8809i			0.648444i
$941$	3.40767	−	12.7176i	0.111087	−	0.414582i	−0.887877	−	0.460080i	$-0.847821\pi$
$941$	3.40767	−	12.7176i	0.111087	−	0.414582i	0.998964	+	0.0454978i	$0.0144874\pi$
$942$	3.06226	−	0.308848i	0.0997739	−	0.0100628i
$943$	0.111783	−	0.417179i	0.00364015	−	0.0135852i
$944$	−3.31440	+	3.31440i	−0.107875	+	0.107875i
$945$	−34.4167	−	54.4893i	−1.11958	−	1.77254i
$946$	−20.1342	+	11.6245i	−0.654621	+	0.377945i
$947$	−35.8279	+	35.8279i	−1.16425	+	1.16425i	−0.180716	+	0.983535i	$0.557841\pi$
$947$	−35.8279	+	35.8279i	−1.16425	+	1.16425i	−0.983535	+	0.180716i	$0.942159\pi$
$948$	3.51198	−	21.5861i	0.114064	−	0.701084i
$949$	−9.49483	+	5.58428i	−0.308215	+	0.181273i
$950$	20.9429	−	12.0914i	0.679479	−	0.392297i
$951$	−0.633893	−	0.880236i	−0.0205554	−	0.0285436i
$952$	−9.20216			−0.298244
$953$	−12.0254	+	20.8285i	−0.389540	+	0.674702i	−0.992388	−	0.123154i	$-0.960699\pi$
$953$	−12.0254	+	20.8285i	−0.389540	+	0.674702i	0.602848	+	0.797856i	$0.294033\pi$
$954$	0.625504	−	10.2808i	0.0202515	−	0.332853i
$955$	−3.07325	−	11.4695i	−0.0994480	−	0.371145i
$956$	27.5256	+	7.37545i	0.890240	+	0.238539i
$957$	−4.27675	+	9.49809i	−0.138248	+	0.307030i
$958$	7.82238			0.252730
$959$	−26.9936	+	46.7542i	−0.871668	+	1.50977i
$960$	−0.648011	−	6.42511i	−0.0209145	−	0.207370i
$961$	−22.5935	−	13.0443i	−0.728822	−	0.420785i
$962$	7.29607	+	26.3777i	0.235235	+	0.850450i
$963$	17.7925	−	53.2327i	0.573355	−	1.71540i
$964$	7.74584	+	2.07549i	0.249477	+	0.0668471i
$965$		−	52.8788i		−	1.70223i
$966$	0.986036	−	0.373756i	0.0317252	−	0.0120254i
$967$	31.8750	+	8.54089i	1.02503	+	0.274656i	0.731897	−	0.681415i	$-0.238635\pi$
$967$	31.8750	+	8.54089i	1.02503	+	0.274656i	0.293134	+	0.956071i	$0.405302\pi$
$968$	20.6453	+	20.6453i	0.663565	+	0.663565i
$969$	−1.30625	−	12.9517i	−0.0419629	−	0.416067i
$970$	21.0863	−	5.65007i	0.677042	−	0.181413i
$971$	−1.82907	−	1.05601i	−0.0586976	−	0.0338891i	0.470364	−	0.882472i	$-0.344123\pi$
$971$	−1.82907	−	1.05601i	−0.0586976	−	0.0338891i	−0.529062	+	0.848583i	$0.677456\pi$
$972$	−3.71725	−	15.1388i	−0.119231	−	0.485576i
$973$	−7.65800	+	28.5800i	−0.245504	+	0.916234i
$974$	−2.71428	+	4.70128i	−0.0869712	+	0.150639i
$975$	−50.8657	−	22.4126i	−1.62901	−	0.717777i
$976$	−4.13990	−	7.17052i	−0.132515	−	0.229523i
$977$	−39.4958	+	10.5829i	−1.26358	+	0.338576i	−0.827569	−	0.561364i	$-0.810277\pi$
$977$	−39.4958	+	10.5829i	−1.26358	+	0.338576i	−0.436014	+	0.899940i	$0.643610\pi$
$978$	−1.66421	+	10.2289i	−0.0532155	+	0.327085i
$979$	3.65965	−	2.11290i	0.116963	−	0.0675285i
$980$	10.7217	+	10.7217i	0.342492	+	0.342492i
$981$	2.05066	−	33.7046i	0.0654724	−	1.07611i
$982$	2.32119	−	0.621962i	0.0740723	−	0.0198476i
$983$	5.34955	+	19.9648i	0.170624	+	0.636777i	0.997256	+	0.0740342i	$0.0235874\pi$
$983$	5.34955	+	19.9648i	0.170624	+	0.636777i	−0.826632	+	0.562743i	$0.809746\pi$
$984$	4.03454	+	0.656406i	0.128617	+	0.0209255i
$985$	−1.13235	−	0.653764i	−0.0360798	−	0.0208307i
$986$	−0.679110	−	2.53447i	−0.0216273	−	0.0807141i
$987$	−10.8902	−	28.7303i	−0.346638	−	0.914495i
$988$	−0.0788981	−	9.79587i	−0.00251008	−	0.311648i
$989$			0.671089i			0.0213394i
$990$	−31.6622	−	63.4537i	−1.00629	−	2.01669i
$991$	−13.1411	−	22.7610i	−0.417439	−	0.723026i	0.578242	−	0.815866i	$-0.303739\pi$
$991$	−13.1411	−	22.7610i	−0.417439	−	0.723026i	−0.995681	+	0.0928392i	$0.970406\pi$
$992$	−1.10807	−	1.91924i	−0.0351814	−	0.0609359i
$993$	−5.37359	−	53.2798i	−0.170526	−	1.69078i
$994$	−28.7227	+	28.7227i	−0.911028	+	0.911028i
$995$	52.1324	−	52.1324i	1.65271	−	1.65271i
$996$	9.49687	−	6.83907i	0.300920	−	0.216704i
$997$	28.7034	+	49.7157i	0.909045	+	1.57451i	0.815393	+	0.578908i	$0.196521\pi$
$997$	28.7034	+	49.7157i	0.909045	+	1.57451i	0.0936524	+	0.995605i	$0.470146\pi$
$998$	−3.11692	−	5.39866i	−0.0986644	−	0.170892i
$999$	26.7592	−	28.9757i	0.846622	−	0.916752i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	234.2.y.a.119.10	yes	56
3.2	odd	2		702.2.bb.a.197.7		56
9.4	even	3		702.2.bc.a.665.7		56
9.5	odd	6		234.2.z.a.41.9	yes	56
13.7	odd	12		234.2.z.a.137.9	yes	56
39.20	even	12		702.2.bc.a.683.7		56
117.59	even	12	inner	234.2.y.a.59.10	✓	56
117.85	odd	12		702.2.bb.a.449.7		56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
234.2.y.a.59.10	✓	56	117.59	even	12	inner
234.2.y.a.119.10	yes	56	1.1	even	1	trivial
234.2.z.a.41.9	yes	56	9.5	odd	6
234.2.z.a.137.9	yes	56	13.7	odd	12
702.2.bb.a.197.7		56	3.2	odd	2
702.2.bb.a.449.7		56	117.85	odd	12
702.2.bc.a.665.7		56	9.4	even	3
702.2.bc.a.683.7		56	39.20	even	12

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:	\( N \)	\(=\)	\( 234 = 2 \cdot 3^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	234.y (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.707107 + 0.707107i) q^{2} +(-0.613909 - 1.61960i) q^{3} +1.00000i q^{4} +(-0.964970 + 3.60132i) q^{5} +(0.711134 - 1.57933i) q^{6} +(-0.861011 + 3.21334i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(-2.24623 + 1.98858i) q^{9} +(-3.22885 + 1.86418i) q^{10} +(4.48313 - 4.48313i) q^{11} +(1.61960 - 0.613909i) q^{12} +(-0.905106 + 3.49010i) q^{13} +(-2.88100 + 1.66335i) q^{14} +(6.42511 - 0.648011i) q^{15} -1.00000 q^{16} +(1.38308 - 2.39556i) q^{17} +(-2.99446 - 0.182189i) q^{18} +(0.703205 + 2.62440i) q^{19} +(-3.60132 - 0.964970i) q^{20} +(5.73292 - 0.578199i) q^{21} +6.34010 q^{22} +(0.0915043 - 0.158490i) q^{23} +(1.57933 + 0.711134i) q^{24} +(-7.70819 - 4.45033i) q^{25} +(-3.10788 + 1.82787i) q^{26} +(4.59969 + 2.41720i) q^{27} +(-3.21334 - 0.861011i) q^{28} -0.948565i q^{29} +(5.00145 + 4.08503i) q^{30} +(2.14063 + 0.573581i) q^{31} +(-0.707107 - 0.707107i) q^{32} +(-10.0131 - 4.50866i) q^{33} +(2.67190 - 0.715935i) q^{34} +(-10.7414 - 6.20155i) q^{35} +(-1.98858 - 2.24623i) q^{36} +(1.96458 - 7.33191i) q^{37} +(-1.35849 + 2.35297i) q^{38} +(6.20823 - 0.676690i) q^{39} +(-1.86418 - 3.22885i) q^{40} +(2.27956 - 0.610806i) q^{41} +(4.46263 + 3.64493i) q^{42} +(-3.17570 + 1.83349i) q^{43} +(4.48313 + 4.48313i) q^{44} +(-4.99395 - 10.0083i) q^{45} +(0.176773 - 0.0473661i) q^{46} +(-1.38011 - 5.15065i) q^{47} +(0.613909 + 1.61960i) q^{48} +(-3.52202 - 2.03344i) q^{49} +(-2.30366 - 8.59737i) q^{50} +(-4.72895 - 0.769383i) q^{51} +(-3.49010 - 0.905106i) q^{52} +3.43327i q^{53} +(1.54325 + 4.96169i) q^{54} +(11.8191 + 20.4712i) q^{55} +(-1.66335 - 2.88100i) q^{56} +(3.81878 - 2.75005i) q^{57} +(0.670737 - 0.670737i) q^{58} +(3.31440 - 3.31440i) q^{59} +(0.648011 + 6.42511i) q^{60} +(4.13990 + 7.17052i) q^{61} +(1.10807 + 1.91924i) q^{62} +(-4.45594 - 8.93009i) q^{63} -1.00000i q^{64} +(-11.6955 - 6.62741i) q^{65} +(-3.89224 - 10.2684i) q^{66} +(1.93297 + 7.21395i) q^{67} +(2.39556 + 1.38308i) q^{68} +(-0.312866 - 0.0509022i) q^{69} +(-3.21016 - 11.9805i) q^{70} +(11.7943 - 3.16027i) q^{71} +(0.182189 - 2.99446i) q^{72} +(2.16027 + 2.16027i) q^{73} +(6.57361 - 3.79528i) q^{74} +(-2.47564 + 15.2163i) q^{75} +(-2.62440 + 0.703205i) q^{76} +(10.5458 + 18.2658i) q^{77} +(4.86837 + 3.91139i) q^{78} +(6.31331 - 10.9350i) q^{79} +(0.964970 - 3.60132i) q^{80} +(1.09112 - 8.93361i) q^{81} +(2.04380 + 1.17999i) q^{82} +(6.52658 - 1.74879i) q^{83} +(0.578199 + 5.73292i) q^{84} +(7.29255 + 7.29255i) q^{85} +(-3.54203 - 0.949085i) q^{86} +(-1.53630 + 0.582332i) q^{87} +6.34010i q^{88} +(0.643808 + 0.172508i) q^{89} +(3.54569 - 10.6082i) q^{90} +(-10.4356 - 5.91342i) q^{91} +(0.158490 + 0.0915043i) q^{92} +(-0.385180 - 3.81910i) q^{93} +(2.66617 - 4.61795i) q^{94} -10.1298 q^{95} +(-0.711134 + 1.57933i) q^{96} +(-5.65566 - 1.51543i) q^{97} +(-1.05259 - 3.92830i) q^{98} +(-1.15510 + 18.9852i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q + 4 q^{7} + 24 q^{15} - 56 q^{16} - 8 q^{19} + 36 q^{27} - 4 q^{28} + 8 q^{31} - 36 q^{33} + 24 q^{35} - 24 q^{36} - 4 q^{37} - 36 q^{38} - 24 q^{39} - 48 q^{41} + 36 q^{42} + 12 q^{43} - 36 q^{45}+ \cdots - 24 q^{99}+O(q^{100}) \) 56 * q + 4 * q^7 + 24 * q^15 - 56 * q^16 - 8 * q^19 + 36 * q^27 - 4 * q^28 + 8 * q^31 - 36 * q^33 + 24 * q^35 - 24 * q^36 - 4 * q^37 - 36 * q^38 - 24 * q^39 - 48 * q^41 + 36 * q^42 + 12 * q^43 - 36 * q^45 + 60 * q^47 - 24 * q^50 - 4 * q^52 + 24 * q^57 - 60 * q^63 - 120 * q^65 - 56 * q^67 - 36 * q^69 + 24 * q^71 + 28 * q^73 + 48 * q^74 + 4 * q^76 - 24 * q^77 + 36 * q^78 - 24 * q^79 - 120 * q^81 - 60 * q^83 + 24 * q^84 + 48 * q^86 + 48 * q^87 + 4 * q^91 - 24 * q^92 + 20 * q^97 - 48 * q^98 - 24 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more