LMFDB - Embedded newform 234.2.z.a.137.8

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [234,2,Mod(41,234)] 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("234.41"); 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([10, 1])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 234 = 2 \cdot 3^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	234.z (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			137.8
Character	$\chi$	$=$	234.137
Dual form			234.2.z.a.41.8

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.965926 + 0.258819i) q^{2} +(-1.70264 - 0.317829i) q^{3} +(0.866025 + 0.500000i) q^{4} +(1.48652 + 0.398313i) q^{5} +(-1.56236 - 0.747675i) q^{6} +(1.01155 - 1.01155i) q^{7} +(0.707107 + 0.707107i) q^{8} +(2.79797 + 1.08230i) q^{9} +(1.33278 + 0.769482i) q^{10} +(0.128439 - 0.479340i) q^{11} +(-1.31562 - 1.12657i) q^{12} +(3.02688 + 1.95909i) q^{13} +(1.23890 - 0.715277i) q^{14} +(-2.40442 - 1.15064i) q^{15} +(0.500000 + 0.866025i) q^{16} +(1.10510 + 1.91408i) q^{17} +(2.42251 + 1.76959i) q^{18} +(0.805124 - 3.00476i) q^{19} +(1.08821 + 1.08821i) q^{20} +(-2.04381 + 1.40081i) q^{21} +(0.248125 - 0.429765i) q^{22} -1.77557 q^{23} +(-0.979210 - 1.42869i) q^{24} +(-2.27902 - 1.31580i) q^{25} +(2.41669 + 2.67575i) q^{26} +(-4.41995 - 2.73204i) q^{27} +(1.38181 - 0.370254i) q^{28} +(-4.07958 + 2.35535i) q^{29} +(-2.02468 - 1.73375i) q^{30} +(-0.0814346 + 0.303918i) q^{31} +(0.258819 + 0.965926i) q^{32} +(-0.371033 + 0.775323i) q^{33} +(0.572040 + 2.13488i) q^{34} +(1.90661 - 1.10078i) q^{35} +(1.88197 + 2.33628i) q^{36} +(-2.95350 - 11.0226i) q^{37} +(1.55538 - 2.69400i) q^{38} +(-4.53103 - 4.29765i) q^{39} +(0.769482 + 1.33278i) q^{40} +(-5.69511 + 5.69511i) q^{41} +(-2.33673 + 0.824102i) q^{42} -1.62219i q^{43} +(0.350901 - 0.350901i) q^{44} +(3.72816 + 2.72333i) q^{45} +(-1.71507 - 0.459552i) q^{46} +(-11.8388 + 3.17219i) q^{47} +(-0.576073 - 1.63344i) q^{48} +4.95352i q^{49} +(-1.86082 - 1.86082i) q^{50} +(-1.27323 - 3.61023i) q^{51} +(1.64181 + 3.21006i) q^{52} -2.02719i q^{53} +(-3.56224 - 3.78291i) q^{54} +(0.381855 - 0.661392i) q^{55} +1.43055 q^{56} +(-2.32584 + 4.86014i) q^{57} +(-4.55018 + 1.21922i) q^{58} +(-2.70586 + 0.725033i) q^{59} +(-1.50697 - 2.19870i) q^{60} +6.79318 q^{61} +(-0.157320 + 0.272485i) q^{62} +(3.92510 - 1.73550i) q^{63} +1.00000i q^{64} +(3.71920 + 4.11787i) q^{65} +(-0.559059 + 0.652874i) q^{66} +(-5.60189 - 5.60189i) q^{67} +2.21019i q^{68} +(3.02316 + 0.564328i) q^{69} +(2.12655 - 0.569808i) q^{70} +(10.8566 + 2.90902i) q^{71} +(1.21316 + 2.74376i) q^{72} +(4.45270 - 4.45270i) q^{73} -11.4115i q^{74} +(3.46216 + 2.96467i) q^{75} +(2.19964 - 2.19964i) q^{76} +(-0.354956 - 0.614801i) q^{77} +(-3.26432 - 5.32393i) q^{78} +(4.77307 - 8.26720i) q^{79} +(0.398313 + 1.48652i) q^{80} +(6.65727 + 6.05646i) q^{81} +(-6.97505 + 4.02705i) q^{82} +(2.17883 + 8.13149i) q^{83} +(-2.47040 + 0.191232i) q^{84} +(0.880349 + 3.28551i) q^{85} +(0.419853 - 1.56691i) q^{86} +(7.69466 - 2.71370i) q^{87} +(0.429765 - 0.248125i) q^{88} +(3.41203 - 0.914251i) q^{89} +(2.89628 + 3.59545i) q^{90} +(5.04357 - 1.08013i) q^{91} +(-1.53769 - 0.887787i) q^{92} +(0.235248 - 0.491581i) q^{93} -12.2564 q^{94} +(2.39367 - 4.14596i) q^{95} +(-0.133677 - 1.72688i) q^{96} +(5.21001 + 5.21001i) q^{97} +(-1.28206 + 4.78473i) q^{98} +(0.878156 - 1.20217i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q - 8 q^{7} - 24 q^{11} + 28 q^{16} - 8 q^{19} - 24 q^{21} + 36 q^{27} - 4 q^{28} - 24 q^{30} - 4 q^{31} + 60 q^{33} - 24 q^{35} - 4 q^{37} + 36 q^{38} - 48 q^{41} - 36 q^{42} - 84 q^{45} - 36 q^{47}+ \cdots + 60 q^{99}+O(q^{100}) $ 56 * q - 8 * q^7 - 24 * q^11 + 28 * q^16 - 8 * q^19 - 24 * q^21 + 36 * q^27 - 4 * q^28 - 24 * q^30 - 4 * q^31 + 60 * q^33 - 24 * q^35 - 4 * q^37 + 36 * q^38 - 48 * q^41 - 36 * q^42 - 84 * q^45 - 36 * q^47 - 24 * q^50 + 8 * q^52 - 36 * q^54 + 36 * q^57 + 24 * q^60 - 48 * q^63 - 36 * q^65 + 28 * q^67 + 84 * q^69 - 24 * q^71 - 24 * q^72 + 28 * q^73 + 4 * q^76 + 24 * q^77 - 60 * q^78 - 24 * q^79 + 24 * q^81 - 96 * q^83 - 72 * q^85 + 4 * q^91 - 24 * q^92 - 36 * q^93 - 52 * q^97 + 48 * q^98 + 60 * q^99

Character values

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

$n$	$145$	$209$
$\chi(n)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{1}{6}\right)$

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 $

$2$	0.965926	+	0.258819i	0.683013	+	0.183013i
$2$	0.965926	+	0.258819i	0.683013	+	0.183013i
$3$	−1.70264	−	0.317829i	−0.983020	−	0.183498i
$3$	−1.70264	−	0.317829i	−0.983020	−	0.183498i
$4$	0.866025	+	0.500000i	0.433013	+	0.250000i
$5$	1.48652	+	0.398313i	0.664794	+	0.178131i	0.575409	−	0.817866i	$-0.304843\pi$
$5$	1.48652	+	0.398313i	0.664794	+	0.178131i	0.0893855	+	0.995997i	$0.471510\pi$
$6$	−1.56236	−	0.747675i	−0.637833	−	0.305237i
$7$	1.01155	−	1.01155i	0.382331	−	0.382331i	−0.489610	−	0.871941i	$-0.662861\pi$
$7$	1.01155	−	1.01155i	0.382331	−	0.382331i	0.871941	+	0.489610i	$0.162861\pi$
$8$	0.707107	+	0.707107i	0.250000	+	0.250000i
$9$	2.79797	+	1.08230i	0.932657	+	0.360765i
$10$	1.33278	+	0.769482i	0.421463	+	0.243332i
$11$	0.128439	−	0.479340i	0.0387258	−	0.144527i	−0.943856	−	0.330357i	$-0.892831\pi$
$11$	0.128439	−	0.479340i	0.0387258	−	0.144527i	0.982582	+	0.185830i	$0.0594975\pi$
$12$	−1.31562	−	1.12657i	−0.379786	−	0.325212i
$13$	3.02688	+	1.95909i	0.839504	+	0.543353i
$13$	3.02688	+	1.95909i	0.839504	+	0.543353i
$14$	1.23890	−	0.715277i	0.331109	−	0.191166i
$15$	−2.40442	−	1.15064i	−0.620819	−	0.297095i
$16$	0.500000	+	0.866025i	0.125000	+	0.216506i
$17$	1.10510	+	1.91408i	0.268025	+	0.464233i	0.968352	−	0.249589i	$-0.0802956\pi$
$17$	1.10510	+	1.91408i	0.268025	+	0.464233i	−0.700327	+	0.713823i	$0.746962\pi$
$18$	2.42251	+	1.76959i	0.570992	+	0.417095i
$19$	0.805124	−	3.00476i	0.184708	−	0.689340i	−0.809985	−	0.586451i	$-0.800525\pi$
$19$	0.805124	−	3.00476i	0.184708	−	0.689340i	0.994693	−	0.102889i	$-0.0328086\pi$
$20$	1.08821	+	1.08821i	0.243332	+	0.243332i
$21$	−2.04381	+	1.40081i	−0.445997	+	0.305682i
$22$	0.248125	−	0.429765i	0.0529004	−	0.0916262i
$23$	−1.77557			−0.370233			−0.185116	−	0.982717i	$-0.559266\pi$
$23$	−1.77557			−0.370233			−0.185116	+	0.982717i	$0.559266\pi$
$24$	−0.979210	−	1.42869i	−0.199880	−	0.291630i
$25$	−2.27902	−	1.31580i	−0.455805	−	0.263159i
$26$	2.41669	+	2.67575i	0.473952	+	0.524757i
$27$	−4.41995	−	2.73204i	−0.850620	−	0.525781i
$28$	1.38181	−	0.370254i	0.261137	−	0.0699715i
$29$	−4.07958	+	2.35535i	−0.757559	+	0.437377i	−0.828419	−	0.560109i	$-0.810759\pi$
$29$	−4.07958	+	2.35535i	−0.757559	+	0.437377i	0.0708596	+	0.997486i	$0.477426\pi$
$30$	−2.02468	−	1.73375i	−0.369655	−	0.316537i
$31$	−0.0814346	+	0.303918i	−0.0146261	+	0.0545853i	−0.972853	−	0.231423i	$-0.925662\pi$
$31$	−0.0814346	+	0.303918i	−0.0146261	+	0.0545853i	0.958227	+	0.286008i	$0.0923285\pi$
$32$	0.258819	+	0.965926i	0.0457532	+	0.170753i
$33$	−0.371033	+	0.775323i	−0.0645886	+	0.134966i
$34$	0.572040	+	2.13488i	0.0981040	+	0.366129i
$35$	1.90661	−	1.10078i	0.322277	−	0.186067i
$36$	1.88197	+	2.33628i	0.313661	+	0.389380i
$37$	−2.95350	−	11.0226i	−0.485553	−	1.81211i	−0.577559	−	0.816349i	$-0.695995\pi$
$37$	−2.95350	−	11.0226i	−0.485553	−	1.81211i	0.0920063	−	0.995758i	$-0.470672\pi$
$38$	1.55538	−	2.69400i	0.252316	−	0.437024i
$39$	−4.53103	−	4.29765i	−0.725545	−	0.688174i
$40$	0.769482	+	1.33278i	0.121666	+	0.210731i
$41$	−5.69511	+	5.69511i	−0.889426	+	0.889426i	−0.994468	−	0.105041i	$-0.966502\pi$
$41$	−5.69511	+	5.69511i	−0.889426	+	0.889426i	0.105041	+	0.994468i	$0.466502\pi$
$42$	−2.33673	+	0.824102i	−0.360565	+	0.127162i
$43$		−	1.62219i		−	0.247381i	−0.992321	−	0.123691i	$-0.960527\pi$
$43$		−	1.62219i		−	0.247381i	0.992321	−	0.123691i	$-0.0394731\pi$
$44$	0.350901	−	0.350901i	0.0529004	−	0.0529004i
$45$	3.72816	+	2.72333i	0.555761	+	0.405970i
$46$	−1.71507	−	0.459552i	−0.252874	−	0.0677573i
$47$	−11.8388	+	3.17219i	−1.72686	+	0.462711i	−0.979456	−	0.201656i	$-0.935368\pi$
$47$	−11.8388	+	3.17219i	−1.72686	+	0.462711i	−0.747406	+	0.664368i	$0.768701\pi$
$48$	−0.576073	−	1.63344i	−0.0831489	−	0.235767i
$49$			4.95352i			0.707645i
$50$	−1.86082	−	1.86082i	−0.263159	−	0.263159i
$51$	−1.27323	−	3.61023i	−0.178288	−	0.505533i
$52$	1.64181	+	3.21006i	0.227678	+	0.445155i
$53$		−	2.02719i		−	0.278456i	−0.990260	−	0.139228i	$-0.955538\pi$
$53$		−	2.02719i		−	0.278456i	0.990260	−	0.139228i	$-0.0444621\pi$
$54$	−3.56224	−	3.78291i	−0.484760	−	0.514789i
$55$	0.381855	−	0.661392i	0.0514893	−	0.0891821i
$56$	1.43055			0.191166
$57$	−2.32584	+	4.86014i	−0.308065	+	0.643741i
$58$	−4.55018	+	1.21922i	−0.597468	+	0.160091i
$59$	−2.70586	+	0.725033i	−0.352273	+	0.0943913i	−0.430616	−	0.902535i	$-0.641704\pi$
$59$	−2.70586	+	0.725033i	−0.352273	+	0.0943913i	0.0783431	+	0.996926i	$0.475037\pi$
$60$	−1.50697	−	2.19870i	−0.194549	−	0.283851i
$61$	6.79318			0.869777			0.434888	−	0.900484i	$-0.356788\pi$
$61$	6.79318			0.869777			0.434888	+	0.900484i	$0.356788\pi$
$62$	−0.157320	+	0.272485i	−0.0199796	+	0.0346057i
$63$	3.92510	−	1.73550i	0.494516	−	0.218652i
$64$			1.00000i			0.125000i
$65$	3.71920	+	4.11787i	0.461310	+	0.510760i
$66$	−0.559059	+	0.652874i	−0.0688154	+	0.0803632i
$67$	−5.60189	−	5.60189i	−0.684379	−	0.684379i	0.276604	−	0.960984i	$-0.410791\pi$
$67$	−5.60189	−	5.60189i	−0.684379	−	0.684379i	−0.960984	+	0.276604i	$0.910791\pi$
$68$			2.21019i			0.268025i
$69$	3.02316	+	0.564328i	0.363946	+	0.0679371i
$70$	2.12655	−	0.569808i	0.254172	−	0.0681051i
$71$	10.8566	+	2.90902i	1.28844	+	0.345237i	0.837069	−	0.547097i	$-0.184267\pi$
$71$	10.8566	+	2.90902i	1.28844	+	0.345237i	0.451374	+	0.892335i	$0.350934\pi$
$72$	1.21316	+	2.74376i	0.142973	+	0.323355i
$73$	4.45270	−	4.45270i	0.521149	−	0.521149i	−0.396769	−	0.917918i	$-0.629869\pi$
$73$	4.45270	−	4.45270i	0.521149	−	0.521149i	0.917918	+	0.396769i	$0.129869\pi$
$74$		−	11.4115i		−	1.32655i
$75$	3.46216	+	2.96467i	0.399776	+	0.342330i
$76$	2.19964	−	2.19964i	0.252316	−	0.252316i
$77$	−0.354956	−	0.614801i	−0.0404510	−	0.0700631i
$78$	−3.26432	−	5.32393i	−0.369612	−	0.602816i
$79$	4.77307	−	8.26720i	0.537012	−	0.930133i	−0.462051	−	0.886853i	$-0.652886\pi$
$79$	4.77307	−	8.26720i	0.537012	−	0.930133i	0.999063	−	0.0432790i	$-0.0137805\pi$
$80$	0.398313	+	1.48652i	0.0445328	+	0.166199i
$81$	6.65727	+	6.05646i	0.739697	+	0.672940i
$82$	−6.97505	+	4.02705i	−0.770266	+	0.444713i
$83$	2.17883	+	8.13149i	0.239157	+	0.892547i	0.976231	+	0.216734i	$0.0695405\pi$
$83$	2.17883	+	8.13149i	0.239157	+	0.892547i	−0.737073	+	0.675813i	$0.763793\pi$
$84$	−2.47040	+	0.191232i	−0.269543	+	0.0208651i
$85$	0.880349	+	3.28551i	0.0954872	+	0.356363i
$86$	0.419853	−	1.56691i	0.0452739	−	0.168965i
$87$	7.69466	−	2.71370i	0.824954	−	0.290939i
$88$	0.429765	−	0.248125i	0.0458131	−	0.0264502i
$89$	3.41203	−	0.914251i	0.361674	−	0.0969104i	−0.0734055	−	0.997302i	$-0.523387\pi$
$89$	3.41203	−	0.914251i	0.361674	−	0.0969104i	0.435080	+	0.900392i	$0.356720\pi$
$90$	2.89628	+	3.59545i	0.305294	+	0.378994i
$91$	5.04357	−	1.08013i	0.528710	−	0.113228i
$92$	−1.53769	−	0.887787i	−0.160315	−	0.0925582i
$93$	0.235248	−	0.491581i	0.0243941	−	0.0509746i
$94$	−12.2564			−1.26415
$95$	2.39367	−	4.14596i	0.245586	−	0.425367i
$96$	−0.133677	−	1.72688i	−0.0136433	−	0.176249i
$97$	5.21001	+	5.21001i	0.528996	+	0.528996i	0.920273	−	0.391277i	$-0.127967\pi$
$97$	5.21001	+	5.21001i	0.528996	+	0.528996i	−0.391277	+	0.920273i	$0.627967\pi$
$98$	−1.28206	+	4.78473i	−0.129508	+	0.483331i
$99$	0.878156	−	1.20217i	0.0882580	−	0.120823i
$100$	−1.31580	−	2.27902i	−0.131580	−	0.227902i
$101$	2.75939	+	4.77940i	0.274569	+	0.475568i	0.970026	−	0.243000i	$-0.0781314\pi$
$101$	2.75939	+	4.77940i	0.274569	+	0.475568i	−0.695457	+	0.718568i	$0.744798\pi$
$102$	−0.295452	−	3.81675i	−0.0292541	−	0.377914i
$103$	−13.0560	+	7.53787i	−1.28644	+	0.742729i	−0.978018	−	0.208520i	$-0.933135\pi$
$103$	−13.0560	+	7.53787i	−1.28644	+	0.742729i	−0.308426	+	0.951248i	$0.599802\pi$
$104$	0.755042	+	3.52561i	0.0740379	+	0.345714i
$105$	−3.59614	+	1.26826i	−0.350947	+	0.123770i
$106$	0.524676	−	1.95812i	0.0509610	−	0.190189i
$107$	−10.8647	−	6.27276i	−1.05033	−	0.606411i	−0.127591	−	0.991827i	$-0.540724\pi$
$107$	−10.8647	−	6.27276i	−1.05033	−	0.606411i	−0.922743	+	0.385416i	$0.874058\pi$
$108$	−2.46177	−	4.57599i	−0.236884	−	0.440325i
$109$	−6.92733	−	6.92733i	−0.663518	−	0.663518i	0.292690	−	0.956208i	$-0.405450\pi$
$109$	−6.92733	−	6.92733i	−0.663518	−	0.663518i	−0.956208	+	0.292690i	$0.905450\pi$
$110$	0.540025	−	0.540025i	0.0514893	−	0.0514893i
$111$	1.52545	+	19.7063i	0.144789	+	1.87044i
$112$	1.38181	+	0.370254i	0.130569	+	0.0349858i
$113$	−12.3898	−	7.15327i	−1.16554	−	0.672923i	−0.212912	−	0.977071i	$-0.568295\pi$
$113$	−12.3898	−	7.15327i	−1.16554	−	0.672923i	−0.952625	+	0.304149i	$0.901628\pi$
$114$	−3.50448	+	4.09256i	−0.328225	+	0.383304i
$115$	−2.63943	−	0.707234i	−0.246128	−	0.0659499i
$116$	−4.71069			−0.437377
$117$	6.34880	+	8.75744i	0.586947	+	0.809626i
$118$	−2.80131			−0.257882
$119$	3.05406	+	0.818333i	0.279965	+	0.0750165i
$120$	−0.886555	−	2.51381i	−0.0809310	−	0.229479i
$121$	9.31301	+	5.37687i	0.846637	+	0.488806i
$122$	6.56170	+	1.75820i	0.594069	+	0.159180i
$123$	11.5068	−	7.88665i	1.03753	−	0.711116i
$124$	−0.222483	+	0.222483i	−0.0199796	+	0.0199796i
$125$	−8.30479	−	8.30479i	−0.742803	−	0.742803i
$126$	4.24053	−	0.660471i	0.377777	−	0.0588394i
$127$	2.50743	+	1.44766i	0.222498	+	0.128459i	0.607106	−	0.794621i	$-0.292330\pi$
$127$	2.50743	+	1.44766i	0.222498	+	0.128459i	−0.384608	+	0.923080i	$0.625663\pi$
$128$	−0.258819	+	0.965926i	−0.0228766	+	0.0853766i
$129$	−0.515578	+	2.76200i	−0.0453941	+	0.243181i
$130$	2.52668	+	4.94016i	0.221605	+	0.433281i
$131$	11.3218	−	6.53662i	0.989186	−	0.571107i	0.0841553	−	0.996453i	$-0.473181\pi$
$131$	11.3218	−	6.53662i	0.989186	−	0.571107i	0.905031	+	0.425346i	$0.139847\pi$
$132$	−0.708986	+	0.485933i	−0.0617093	+	0.0422950i
$133$	−2.22505	−	3.85391i	−0.192937	−	0.334176i
$134$	−3.96113	−	6.86088i	−0.342190	−	0.592690i
$135$	−5.48216	−	5.82176i	−0.471829	−	0.501058i
$136$	−0.572040	+	2.13488i	−0.0490520	+	0.183065i
$137$	4.60469	+	4.60469i	0.393405	+	0.393405i	0.875899	−	0.482494i	$-0.160269\pi$
$137$	4.60469	+	4.60469i	0.393405	+	0.393405i	−0.482494	+	0.875899i	$0.660269\pi$
$138$	2.77409	+	1.32755i	0.236146	+	0.113009i
$139$	−8.34095	+	14.4469i	−0.707470	+	1.22537i	0.258322	+	0.966059i	$0.416830\pi$
$139$	−8.34095	+	14.4469i	−0.707470	+	1.22537i	−0.965793	+	0.259316i	$0.916503\pi$
$140$	2.20157			0.186067
$141$	21.1654	−	1.63840i	1.78245	−	0.137978i
$142$	9.73378	+	5.61980i	0.816840	+	0.471603i
$143$	1.32784	−	1.19928i	0.111039	−	0.100289i
$144$	0.461689	+	2.96426i	0.0384741	+	0.247022i
$145$	−7.00256	+	1.87633i	−0.581531	+	0.155821i
$146$	5.45342	−	3.14853i	0.451328	−	0.260575i
$147$	1.57437	−	8.43406i	0.129852	−	0.695630i
$148$	2.95350	−	11.0226i	0.242776	−	0.906054i
$149$	−2.72321	−	10.1632i	−0.223094	−	0.832599i	−0.983159	−	0.182752i	$-0.941500\pi$
$149$	−2.72321	−	10.1632i	−0.223094	−	0.832599i	0.760065	−	0.649847i	$-0.225167\pi$
$150$	2.57688	+	3.75972i	0.210401	+	0.306980i
$151$	4.44836	+	16.6015i	0.362002	+	1.35101i	0.871440	+	0.490503i	$0.163187\pi$
$151$	4.44836	+	16.6015i	0.362002	+	1.35101i	−0.509437	+	0.860508i	$0.670146\pi$
$152$	2.69400	−	1.55538i	0.218512	−	0.126158i
$153$	1.02042	+	6.55159i	0.0824962	+	0.529664i
$154$	−0.183739	−	0.685722i	−0.0148061	−	0.0552570i
$155$	−0.242109	+	0.419345i	−0.0194467	+	0.0336826i
$156$	−1.77516	−	5.98739i	−0.142127	−	0.479375i
$157$	−10.9518	−	18.9690i	−0.874046	−	1.51389i	−0.857775	−	0.514025i	$-0.828154\pi$
$157$	−10.9518	−	18.9690i	−0.874046	−	1.51389i	−0.0162709	−	0.999868i	$-0.505179\pi$
$158$	6.75014	−	6.75014i	0.537012	−	0.537012i
$159$	−0.644300	+	3.45158i	−0.0510963	+	0.273728i
$160$			1.53896i			0.121666i
$161$	−1.79609	+	1.79609i	−0.141552	+	0.141552i
$162$	4.86290	+	7.57312i	0.382066	+	0.595001i
$163$	5.13664	+	1.37636i	0.402333	+	0.107805i	0.454310	−	0.890844i	$-0.349886\pi$
$163$	5.13664	+	1.37636i	0.402333	+	0.107805i	−0.0519776	+	0.998648i	$0.516552\pi$
$164$	−7.77966	+	2.08455i	−0.607490	+	0.162776i
$165$	−0.860371	+	1.00475i	−0.0669798	+	0.0782196i
$166$			8.41834i			0.653390i
$167$	7.67161	+	7.67161i	0.593647	+	0.593647i	0.938615	−	0.344968i	$-0.112110\pi$
$167$	7.67161	+	7.67161i	0.593647	+	0.593647i	−0.344968	+	0.938615i	$0.612110\pi$
$168$	−2.43572	−	0.454671i	−0.187920	−	0.0350786i
$169$	5.32396	+	11.8598i	0.409536	+	0.912294i
$170$			3.40141i			0.260876i
$171$	5.50475	−	7.53585i	0.420959	−	0.576281i
$172$	0.811094	−	1.40486i	0.0618453	−	0.107119i
$173$	1.60584			0.122090			0.0610448	−	0.998135i	$-0.480557\pi$
$173$	1.60584			0.122090			0.0610448	+	0.998135i	$0.480557\pi$
$174$	8.13483	−	0.629711i	0.616700	−	0.0477383i
$175$	−3.63635	+	0.974358i	−0.274882	+	0.0736545i
$176$	0.479340	−	0.128439i	0.0361316	−	0.00968144i
$177$	4.83754	−	0.374471i	0.363612	−	0.0281470i
$178$	3.53239			0.264764
$179$	5.02903	−	8.71053i	0.375887	−	0.651056i	−0.614572	−	0.788861i	$-0.710671\pi$
$179$	5.02903	−	8.71053i	0.375887	−	0.651056i	0.990459	+	0.137805i	$0.0440047\pi$
$180$	1.86702	+	4.22255i	0.139159	+	0.314730i
$181$			11.9484i			0.888116i	0.895998	+	0.444058i	$0.146462\pi$
$181$			11.9484i			0.888116i	−0.895998	+	0.444058i	$0.853538\pi$
$182$	5.15127	+	0.262049i	0.381838	+	0.0194244i
$183$	−11.5663	−	2.15907i	−0.855008	−	0.159603i
$184$	−1.25552	−	1.25552i	−0.0925582	−	0.0925582i
$185$		−	17.5618i		−	1.29117i
$186$	0.354462	−	0.413944i	0.0259904	−	0.0303519i
$187$	1.05943	−	0.283875i	0.0774735	−	0.0207590i
$188$	−11.8388	−	3.17219i	−0.863431	−	0.231356i
$189$	−7.23462	+	1.70742i	−0.526241	+	0.124196i
$190$	3.38516	−	3.38516i	0.245586	−	0.245586i
$191$		−	21.8456i		−	1.58069i	−0.612659	−	0.790347i	$-0.709900\pi$
$191$		−	21.8456i		−	1.58069i	0.612659	−	0.790347i	$-0.290100\pi$
$192$	0.317829	−	1.70264i	0.0229373	−	0.122877i
$193$	9.25729	−	9.25729i	0.666354	−	0.666354i	−0.290516	−	0.956870i	$-0.593827\pi$
$193$	9.25729	−	9.25729i	0.666354	−	0.666354i	0.956870	+	0.290516i	$0.0938269\pi$
$194$	3.68403	+	6.38093i	0.264498	+	0.458124i
$195$	−5.02368	−	8.19333i	−0.359753	−	0.586736i
$196$	−2.47676	+	4.28987i	−0.176911	+	0.306419i
$197$	−0.638138	−	2.38157i	−0.0454655	−	0.169680i	0.939460	−	0.342659i	$-0.111327\pi$
$197$	−0.638138	−	2.38157i	−0.0454655	−	0.169680i	−0.984926	+	0.172979i	$0.944661\pi$
$198$	1.15938	−	0.933924i	0.0823934	−	0.0663711i
$199$	−18.1467	+	10.4770i	−1.28639	+	0.742697i	−0.978008	−	0.208567i	$-0.933120\pi$
$199$	−18.1467	+	10.4770i	−1.28639	+	0.742697i	−0.308380	+	0.951263i	$0.599787\pi$
$200$	−0.681106	−	2.54192i	−0.0481615	−	0.179741i
$201$	7.75756	+	11.3184i	0.547176	+	0.798341i
$202$	1.42836	+	5.33073i	0.100499	+	0.375069i
$203$	−1.74416	+	6.50928i	−0.122416	+	0.456862i
$204$	0.702462	−	3.76316i	0.0491822	−	0.263474i
$205$	−10.7344	+	6.19748i	−0.749720	+	0.432851i
$206$	−14.5621	+	3.90189i	−1.01459	+	0.271858i
$207$	−4.96800	−	1.92170i	−0.345300	−	0.133567i
$208$	−0.183180	+	3.60090i	−0.0127013	+	0.249677i
$209$	−1.33689	−	0.771857i	−0.0924750	−	0.0533904i
$210$	−3.80186	+	0.294299i	−0.262353	+	0.0203086i
$211$	−14.1278			−0.972599			−0.486299	−	0.873792i	$-0.661654\pi$
$211$	−14.1278			−0.972599			−0.486299	+	0.873792i	$0.661654\pi$
$212$	1.01360	−	1.75560i	0.0696140	−	0.120575i
$213$	−17.5603	−	8.40356i	−1.20322	−	0.575803i
$214$	−8.87102	−	8.87102i	−0.606411	−	0.606411i
$215$	0.646139	−	2.41142i	0.0440663	−	0.164458i
$216$	−1.19354	−	5.05722i	−0.0812099	−	0.344100i
$217$	0.225054	+	0.389805i	0.0152777	+	0.0264617i
$218$	−4.89836	−	8.48421i	−0.331759	−	0.574623i
$219$	−8.99654	+	6.16615i	−0.607930	+	0.416670i
$220$	0.661392	−	0.381855i	0.0445911	−	0.0257447i
$221$	−0.404863	+	7.95867i	−0.0272341	+	0.535358i
$222$	−3.62689	+	19.4296i	−0.243421	+	1.30403i
$223$	−2.37228	+	8.85346i	−0.158859	+	0.592872i	0.839884	+	0.542765i	$0.182623\pi$
$223$	−2.37228	+	8.85346i	−0.158859	+	0.592872i	−0.998744	+	0.0501063i	$0.984044\pi$
$224$	1.23890	+	0.715277i	0.0827772	+	0.0477914i
$225$	−4.95256	−	6.14813i	−0.330171	−	0.409876i
$226$	−10.1162	−	10.1162i	−0.672923	−	0.672923i
$227$	18.6738	−	18.6738i	1.23943	−	1.23943i	0.279190	−	0.960236i	$-0.409934\pi$
$227$	18.6738	−	18.6738i	1.23943	−	1.23943i	0.960236	−	0.279190i	$-0.0900659\pi$
$228$	−4.44430	+	3.04609i	−0.294331	+	0.201732i
$229$	13.7346	+	3.68017i	0.907607	+	0.243193i	0.682280	−	0.731091i	$-0.260988\pi$
$229$	13.7346	+	3.68017i	0.907607	+	0.243193i	0.225327	+	0.974283i	$0.427655\pi$
$230$	−2.36645	−	1.36627i	−0.156039	−	0.0900893i
$231$	0.408961	+	1.15960i	0.0269076	+	0.0762961i
$232$	−4.55018	−	1.21922i	−0.298734	−	0.0800455i
$233$	−21.4490			−1.40517			−0.702586	−	0.711599i	$-0.747971\pi$
$233$	−21.4490			−1.40517			−0.702586	+	0.711599i	$0.747971\pi$
$234$	3.86588	+	10.1022i	0.252720	+	0.660403i
$235$	−18.8622			−1.23043
$236$	−2.70586	−	0.725033i	−0.176137	−	0.0471956i
$237$	−10.7544	+	12.5590i	−0.698572	+	0.815798i
$238$	2.73820	+	1.58090i	0.177491	+	0.102474i
$239$	7.59513	+	2.03511i	0.491288	+	0.131640i	0.495954	−	0.868349i	$-0.334819\pi$
$239$	7.59513	+	2.03511i	0.491288	+	0.131640i	−0.00466587	+	0.999989i	$0.501485\pi$
$240$	−0.205724	−	2.65761i	−0.0132794	−	0.171548i
$241$	13.0877	−	13.0877i	0.843051	−	0.843051i	−0.146203	−	0.989255i	$-0.546705\pi$
$241$	13.0877	−	13.0877i	0.843051	−	0.843051i	0.989255	+	0.146203i	$0.0467054\pi$
$242$	7.60404	+	7.60404i	0.488806	+	0.488806i
$243$	−9.41002	−	12.4279i	−0.603653	−	0.797247i
$244$	5.88306	+	3.39659i	0.376624	+	0.217444i
$245$	−1.97305	+	7.36353i	−0.126054	+	0.470438i
$246$	13.1559	−	4.63975i	0.838791	−	0.295819i
$247$	8.32360	−	7.51774i	0.529618	−	0.478342i
$248$	−0.272485	+	0.157320i	−0.0173028	+	0.00998980i
$249$	−1.12534	−	14.5375i	−0.0713153	−	0.921276i
$250$	−5.87237	−	10.1712i	−0.371401	−	0.643286i
$251$	11.0446	+	19.1298i	0.697127	+	1.20746i	0.969458	+	0.245256i	$0.0788722\pi$
$251$	11.0446	+	19.1298i	0.697127	+	1.20746i	−0.272331	+	0.962204i	$0.587795\pi$
$252$	4.26698	+	0.459565i	0.268795	+	0.0289499i
$253$	−0.228053	+	0.851104i	−0.0143375	+	0.0535084i
$254$	2.04731	+	2.04731i	0.128459	+	0.128459i
$255$	−0.454689	−	5.87384i	−0.0284738	−	0.367834i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−30.2080			−1.88432			−0.942162	−	0.335158i	$-0.891210\pi$
$257$	−30.2080			−1.88432			−0.942162	+	0.335158i	$0.891210\pi$
$258$	−1.21287	+	2.53445i	−0.0755099	+	0.157788i
$259$	−14.1376	−	8.16235i	−0.878468	−	0.507183i
$260$	1.16198	+	5.42578i	0.0720631	+	0.336493i
$261$	−13.9637	+	2.17488i	−0.864333	+	0.134621i
$262$	12.6278	−	3.38360i	0.780147	−	0.209040i
$263$	−4.77357	+	2.75602i	−0.294351	+	0.169943i	−0.639902	−	0.768456i	$-0.721025\pi$
$263$	−4.77357	+	2.75602i	−0.294351	+	0.169943i	0.345552	+	0.938400i	$0.387692\pi$
$264$	−0.810596	+	0.285876i	−0.0498887	+	0.0175944i
$265$	0.807457	−	3.01347i	0.0496017	−	0.185116i
$266$	−1.15177	−	4.29847i	−0.0706197	−	0.263556i
$267$	−6.10004	+	0.472199i	−0.373316	+	0.0288981i
$268$	−2.05043	−	7.65232i	−0.125250	−	0.467440i
$269$	16.8180	−	9.70985i	1.02541	−	0.592020i	0.109743	−	0.993960i	$-0.464997\pi$
$269$	16.8180	−	9.70985i	1.02541	−	0.592020i	0.915666	+	0.401940i	$0.131664\pi$
$270$	−3.78858	−	7.04228i	−0.230566	−	0.428580i
$271$	5.79813	+	21.6389i	0.352212	+	1.31447i	0.883957	+	0.467567i	$0.154869\pi$
$271$	5.79813	+	21.6389i	0.352212	+	1.31447i	−0.531746	+	0.846904i	$0.678464\pi$
$272$	−1.10510	+	1.91408i	−0.0670063	+	0.116058i
$273$	−8.93068	+	0.236078i	−0.540509	+	0.0142881i
$274$	3.25601	+	5.63957i	0.196703	+	0.340699i
$275$	−0.923429	+	0.923429i	−0.0556849	+	0.0556849i
$276$	2.33597	+	2.00030i	0.140609	+	0.120404i
$277$			8.82351i			0.530153i	0.964227	+	0.265077i	$0.0853973\pi$
$277$			8.82351i			0.530153i	−0.964227	+	0.265077i	$0.914603\pi$
$278$	−11.7959	+	11.7959i	−0.707470	+	0.707470i
$279$	−0.556781	+	0.762217i	−0.0333336	+	0.0456328i
$280$	2.12655	+	0.569808i	0.127086	+	0.0340525i
$281$	−17.2960	+	4.63444i	−1.03179	+	0.276467i	−0.734707	−	0.678384i	$-0.762680\pi$
$281$	−17.2960	+	4.63444i	−1.03179	+	0.276467i	−0.297083	+	0.954852i	$0.596014\pi$
$282$	20.8682	+	3.89543i	1.24269	+	0.231970i
$283$		−	7.31258i		−	0.434688i	−0.976095	−	0.217344i	$-0.930261\pi$
$283$		−	7.31258i		−	0.434688i	0.976095	−	0.217344i	$-0.0697393\pi$
$284$	7.94760	+	7.94760i	0.471603	+	0.471603i
$285$	−5.39327	+	6.29831i	−0.319470	+	0.373080i
$286$	1.59299	−	0.814747i	0.0941954	−	0.0481770i
$287$			11.5218i			0.680111i
$288$	−0.321250	+	2.98275i	−0.0189298	+	0.175760i
$289$	6.05752	−	10.4919i	0.356325	−	0.617173i
$290$	−7.24959			−0.425710
$291$	−7.21488	−	10.5267i	−0.422944	−	0.617084i
$292$	6.08250	−	1.62980i	0.355952	−	0.0953769i
$293$	13.7781	−	3.69183i	0.804925	−	0.215679i	0.167180	−	0.985926i	$-0.446534\pi$
$293$	13.7781	−	3.69183i	0.804925	−	0.215679i	0.637745	+	0.770247i	$0.279867\pi$
$294$	3.70362	−	7.73920i	0.216000	−	0.451359i
$295$	−4.31112			−0.251003
$296$	5.70573	−	9.88261i	0.331639	−	0.574415i
$297$	−1.87727	+	1.76776i	−0.108930	+	0.102576i
$298$		−	10.5217i		−	0.609505i
$299$	−5.37444	−	3.47850i	−0.310812	−	0.201167i
$300$	1.51599	+	4.29856i	0.0875256	+	0.248177i
$301$	−1.64093	−	1.64093i	−0.0945817	−	0.0945817i
$302$			17.1871i			0.989008i
$303$	−3.17922	−	9.01461i	−0.182641	−	0.517876i
$304$	3.00476	−	0.805124i	0.172335	−	0.0461770i
$305$	10.0982	+	2.70581i	0.578223	+	0.154934i
$306$	−0.710024	+	6.59245i	−0.0405894	+	0.376865i
$307$	15.5883	−	15.5883i	0.889669	−	0.889669i	−0.104822	−	0.994491i	$-0.533427\pi$
$307$	15.5883	−	15.5883i	0.889669	−	0.889669i	0.994491	+	0.104822i	$0.0334273\pi$
$308$		−	0.709911i		−	0.0404510i
$309$	24.6254	−	8.68472i	1.40089	−	0.494057i
$310$	−0.342394	+	0.342394i	−0.0194467	+	0.0194467i
$311$	12.3786	+	21.4403i	0.701923	+	1.21577i	0.967790	+	0.251757i	$0.0810084\pi$
$311$	12.3786	+	21.4403i	0.701923	+	1.21577i	−0.265867	+	0.964010i	$0.585658\pi$
$312$	−0.165025	−	6.24282i	−0.00934273	−	0.353430i
$313$	16.0705	−	27.8349i	0.908359	−	1.57332i	0.0920148	−	0.995758i	$-0.470669\pi$
$313$	16.0705	−	27.8349i	0.908359	−	1.57332i	0.816344	−	0.577566i	$-0.195997\pi$
$314$	−5.66905	−	21.1572i	−0.319923	−	1.19397i
$315$	6.52603	−	1.01644i	0.367700	−	0.0572699i
$316$	8.26720	−	4.77307i	0.465066	−	0.268506i
$317$	7.74554	+	28.9067i	0.435033	+	1.62356i	0.740988	+	0.671518i	$0.234357\pi$
$317$	7.74554	+	28.9067i	0.435033	+	1.62356i	−0.305956	+	0.952046i	$0.598976\pi$
$318$	−1.51568	+	3.16721i	−0.0849951	+	0.177608i
$319$	0.605036	+	2.25803i	0.0338755	+	0.126425i
$320$	−0.398313	+	1.48652i	−0.0222664	+	0.0830993i
$321$	16.5051	+	14.1334i	0.921224	+	0.788848i
$322$	−2.19975	+	1.27003i	−0.122587	+	0.0707758i
$323$	6.64110	−	1.77948i	0.369521	−	0.0990128i
$324$	2.73713	+	8.57369i	0.152063	+	0.476316i
$325$	−4.32057	−	8.44756i	−0.239662	−	0.468586i
$326$	4.60538	+	2.65892i	0.255069	+	0.147264i
$327$	9.59305	+	13.9965i	0.530497	+	0.774006i
$328$	−8.05410			−0.444713
$329$	−8.76671	+	15.1844i	−0.483325	+	0.837143i
$330$	−1.09110	+	0.747833i	−0.0600633	+	0.0411668i
$331$	4.69098	+	4.69098i	0.257839	+	0.257839i	0.824175	−	0.566335i	$-0.191639\pi$
$331$	4.69098	+	4.69098i	0.257839	+	0.257839i	−0.566335	+	0.824175i	$0.691639\pi$
$332$	−2.17883	+	8.13149i	−0.119579	+	0.446273i
$333$	3.66593	−	34.0375i	0.200892	−	1.86524i
$334$	5.42465	+	9.39577i	0.296824	+	0.514113i
$335$	−6.09604	−	10.5586i	−0.333062	−	0.576881i
$336$	−2.23505	−	1.06959i	−0.121932	−	0.0583508i
$337$	20.1675	−	11.6437i	1.09859	−	0.634274i	0.162743	−	0.986669i	$-0.447966\pi$
$337$	20.1675	−	11.6437i	1.09859	−	0.634274i	0.935851	+	0.352395i	$0.114633\pi$
$338$	2.07300	+	12.8337i	0.112757	+	0.698059i
$339$	18.8219	+	16.1173i	1.02227	+	0.875371i
$340$	−0.880349	+	3.28551i	−0.0477436	+	0.178182i
$341$	0.135221	+	0.0780698i	0.00732262	+	0.00422772i
$342$	7.26761	−	5.85434i	0.392987	−	0.316566i
$343$	12.0916	+	12.0916i	0.652886	+	0.652886i
$344$	1.14706	−	1.14706i	0.0618453	−	0.0618453i
$345$	4.26923	+	2.04305i	0.229848	+	0.109994i
$346$	1.55112	+	0.415621i	0.0833887	+	0.0223439i
$347$	−17.4763	−	10.0899i	−0.938175	−	0.541655i	−0.0487871	−	0.998809i	$-0.515536\pi$
$347$	−17.4763	−	10.0899i	−0.938175	−	0.541655i	−0.889388	+	0.457154i	$0.848869\pi$
$348$	8.02062	+	1.49719i	0.429950	+	0.0802580i
$349$	−24.2443	−	6.49625i	−1.29777	−	0.347736i	−0.457163	−	0.889383i	$-0.651134\pi$
$349$	−24.2443	−	6.49625i	−1.29777	−	0.347736i	−0.840606	+	0.541647i	$0.817801\pi$
$350$	−3.76463			−0.201228
$351$	−8.02636	−	16.9286i	−0.428415	−	0.903582i
$352$	0.496250			0.0264502
$353$	25.2002	+	6.75238i	1.34127	+	0.359393i	0.856906	−	0.515472i	$-0.172384\pi$
$353$	25.2002	+	6.75238i	1.34127	+	0.359393i	0.484366	+	0.874865i	$0.339050\pi$
$354$	4.76963	+	0.890338i	0.253503	+	0.0473209i
$355$	14.9799	+	8.64867i	0.795052	+	0.459024i
$356$	3.41203	+	0.914251i	0.180837	+	0.0484552i
$357$	−4.93988	−	2.36400i	−0.261446	−	0.125116i
$358$	7.11212	−	7.11212i	0.375887	−	0.375887i
$359$	23.1726	+	23.1726i	1.22300	+	1.22300i	0.966559	+	0.256444i	$0.0825509\pi$
$359$	23.1726	+	23.1726i	1.22300	+	1.22300i	0.256444	+	0.966559i	$0.417449\pi$
$360$	0.710523	+	4.56189i	0.0374478	+	0.240433i
$361$	8.07411	+	4.66159i	0.424953	+	0.245347i
$362$	−3.09247	+	11.5412i	−0.162537	+	0.606594i
$363$	−14.1478	−	12.1148i	−0.742566	−	0.635863i
$364$	4.90792	+	1.58637i	0.257245	+	0.0831482i
$365$	8.39262	−	4.84548i	0.439290	−	0.253624i
$366$	−10.6134	−	5.07909i	−0.554772	−	0.265488i
$367$	−0.292660	−	0.506902i	−0.0152767	−	0.0264601i	0.858286	−	0.513172i	$-0.171530\pi$
$367$	−0.292660	−	0.506902i	−0.0152767	−	0.0264601i	−0.873563	+	0.486712i	$0.838196\pi$
$368$	−0.887787	−	1.53769i	−0.0462791	−	0.0801577i
$369$	−22.0985	+	9.77095i	−1.15040	+	0.508655i
$370$	4.54533	−	16.9634i	0.236301	−	0.881886i
$371$	−2.05061	−	2.05061i	−0.106463	−	0.106463i
$372$	0.449521	−	0.308098i	0.0233066	−	0.0159741i
$373$	−13.6890	+	23.7100i	−0.708790	+	1.22766i	0.256517	+	0.966540i	$0.417425\pi$
$373$	−13.6890	+	23.7100i	−0.708790	+	1.22766i	−0.965306	+	0.261120i	$0.915908\pi$
$374$	1.09681			0.0567145
$375$	11.5006	+	16.7796i	0.593887	+	0.866493i
$376$	−10.6144	−	6.12820i	−0.547393	−	0.316038i
$377$	−16.9627	−	0.862906i	−0.873624	−	0.0444419i
$378$	−7.43002	−	0.223218i	−0.382159	−	0.0114811i
$379$	3.11912	−	0.835766i	0.160219	−	0.0429304i	−0.177818	−	0.984063i	$-0.556904\pi$
$379$	3.11912	−	0.835766i	0.160219	−	0.0429304i	0.338037	+	0.941133i	$0.390237\pi$
$380$	4.14596	−	2.39367i	0.212683	−	0.122793i
$381$	−3.80914	−	3.26178i	−0.195148	−	0.167106i
$382$	5.65407	−	21.1013i	0.289287	−	1.07963i
$383$	3.64974	+	13.6210i	0.186493	+	0.696001i	0.994306	+	0.106562i	$0.0339843\pi$
$383$	3.64974	+	13.6210i	0.186493	+	0.696001i	−0.807813	+	0.589439i	$0.799349\pi$
$384$	0.747675	−	1.56236i	0.0381546	−	0.0797291i
$385$	−0.282767	−	1.05530i	−0.0144111	−	0.0537831i
$386$	11.3378	−	6.54589i	0.577080	−	0.333177i
$387$	1.75569	−	4.53883i	0.0892466	−	0.230722i
$388$	1.90700	+	7.11700i	0.0968130	+	0.361311i
$389$	9.97462	−	17.2765i	0.505733	−	0.875956i	−0.494245	−	0.869323i	$-0.664555\pi$
$389$	9.97462	−	17.2765i	0.505733	−	0.875956i	0.999978	−	0.00663286i	$-0.00211132\pi$
$390$	−2.73191	−	9.21437i	−0.138336	−	0.466588i
$391$	−1.96218	−	3.39859i	−0.0992317	−	0.171874i
$392$	−3.50267	+	3.50267i	−0.176911	+	0.176911i
$393$	−21.3544	+	7.53113i	−1.07719	+	0.379895i
$394$		−	2.46558i		−	0.124214i
$395$	10.3882	−	10.3882i	0.522688	−	0.522688i
$396$	1.36159	−	0.602033i	0.0684225	−	0.0302533i
$397$	17.9027	+	4.79700i	0.898509	+	0.240755i	0.678376	−	0.734715i	$-0.262684\pi$
$397$	17.9027	+	4.79700i	0.898509	+	0.240755i	0.220133	+	0.975470i	$0.429351\pi$
$398$	−20.2401	+	5.42331i	−1.01454	+	0.271846i
$399$	2.56358	+	7.26900i	0.128340	+	0.363905i
$400$		−	2.63159i		−	0.131580i
$401$	−11.1565	−	11.1565i	−0.557131	−	0.557131i	0.371359	−	0.928489i	$-0.378892\pi$
$401$	−11.1565	−	11.1565i	−0.557131	−	0.557131i	−0.928489	+	0.371359i	$0.878892\pi$
$402$	4.56380	+	12.9406i	0.227622	+	0.645417i
$403$	−0.841894	+	0.760385i	−0.0419377	+	0.0378775i
$404$			5.51878i			0.274569i
$405$	7.48383	+	11.6548i	0.371874	+	0.579130i
$406$	−3.36945	+	5.83606i	−0.167223	+	0.289639i
$407$	−5.66293			−0.280701
$408$	1.65250	−	3.45313i	0.0818112	−	0.170955i
$409$	−10.7473	+	2.87972i	−0.531418	+	0.142393i	−0.514543	−	0.857464i	$-0.672038\pi$
$409$	−10.7473	+	2.87972i	−0.531418	+	0.142393i	−0.0168752	+	0.999858i	$0.505372\pi$
$410$	−11.9726	+	3.20805i	−0.591285	+	0.158434i
$411$	−6.37663	−	9.30363i	−0.314536	−	0.458914i
$412$	−15.0757			−0.742729
$413$	−2.00371	+	3.47053i	−0.0985963	+	0.170774i
$414$	−4.30135	−	3.14203i	−0.211400	−	0.154422i
$415$			12.9555i			0.635961i
$416$	−1.10892	+	3.43079i	−0.0543692	+	0.168208i
$417$	18.7933	−	21.9470i	0.920312	−	1.07475i
$418$	−1.09157	−	1.09157i	−0.0533904	−	0.0533904i
$419$		−	0.458051i		−	0.0223772i	−0.999937	−	0.0111886i	$-0.996438\pi$
$419$		−	0.458051i		−	0.0223772i	0.999937	−	0.0111886i	$-0.00356152\pi$
$420$	−3.74848	−	0.699722i	−0.182907	−	0.0341429i
$421$	4.37413	−	1.17205i	0.213182	−	0.0571220i	−0.150647	−	0.988588i	$-0.548136\pi$
$421$	4.37413	−	1.17205i	0.213182	−	0.0571220i	0.363829	+	0.931466i	$0.381469\pi$
$422$	−13.6464	−	3.65655i	−0.664297	−	0.177998i
$423$	−36.5578	−	3.93736i	−1.77750	−	0.191441i
$424$	1.43344	−	1.43344i	0.0696140	−	0.0696140i
$425$		−	5.81632i		−	0.282133i
$426$	−14.7870	−	12.6622i	−0.716432	−	0.613484i
$427$	6.87166	−	6.87166i	0.332543	−	0.332543i
$428$	−6.27276	−	10.8647i	−0.303205	−	0.525167i
$429$	−2.64200	+	1.61992i	−0.127557	+	0.0782105i
$430$	1.24824	−	2.16202i	0.0601957	−	0.104262i
$431$	3.86478	+	14.4235i	0.186160	+	0.694758i	0.994379	+	0.105876i	$0.0337648\pi$
$431$	3.86478	+	14.4235i	0.186160	+	0.694758i	−0.808220	+	0.588881i	$0.799569\pi$
$432$	0.156036	−	5.19381i	0.00750730	−	0.249887i
$433$	−3.91621	+	2.26103i	−0.188201	+	0.108658i	−0.591140	−	0.806569i	$-0.701322\pi$
$433$	−3.91621	+	2.26103i	−0.188201	+	0.108658i	0.402939	+	0.915227i	$0.367989\pi$
$434$	0.116497	+	0.434771i	0.00559201	+	0.0208697i
$435$	12.5192	−	0.969102i	0.600250	−	0.0464649i
$436$	−2.53558	−	9.46291i	−0.121432	−	0.453191i
$437$	−1.42956	+	5.33518i	−0.0683850	+	0.255216i
$438$	−10.2859	+	3.62757i	−0.491480	+	0.173332i
$439$	−11.5668	+	6.67809i	−0.552053	+	0.318728i	−0.749949	−	0.661495i	$-0.769922\pi$
$439$	−11.5668	+	6.67809i	−0.552053	+	0.318728i	0.197897	+	0.980223i	$0.436589\pi$
$440$	0.737687	−	0.197663i	0.0351679	−	0.00942320i
$441$	−5.36117	+	13.8598i	−0.255294	+	0.659990i
$442$	−2.45092	+	7.58270i	−0.116579	+	0.360672i
$443$	26.7016	+	15.4162i	1.26863	+	0.732445i	0.974729	−	0.223390i	$-0.0717124\pi$
$443$	26.7016	+	15.4162i	1.26863	+	0.732445i	0.293903	+	0.955835i	$0.405046\pi$
$444$	−8.53206	+	17.8289i	−0.404913	+	0.846120i
$445$	5.43623			0.257702
$446$	−4.58289	+	7.93780i	−0.217006	+	0.375865i
$447$	1.40651	+	18.1697i	0.0665254	+	0.859399i
$448$	1.01155	+	1.01155i	0.0477914	+	0.0477914i
$449$	10.3894	−	38.7738i	0.490306	−	1.82985i	−0.0645682	−	0.997913i	$-0.520567\pi$
$449$	10.3894	−	38.7738i	0.490306	−	1.82985i	0.554874	−	0.831934i	$-0.312766\pi$
$450$	−3.19255	−	7.22046i	−0.150498	−	0.340376i
$451$	1.99842	+	3.46137i	0.0941020	+	0.162989i
$452$	−7.15327	−	12.3898i	−0.336461	−	0.582768i
$453$	−2.29752	−	29.6802i	−0.107947	−	1.39450i
$454$	22.8707	−	13.2044i	1.07337	−	0.619713i
$455$	7.92762	+	0.403284i	0.371653	+	0.0189062i
$456$	−5.08125	+	1.79202i	−0.237951	+	0.0839192i
$457$	−4.27321	+	15.9478i	−0.199892	+	0.746008i	0.791054	+	0.611747i	$0.209533\pi$
$457$	−4.27321	+	15.9478i	−0.199892	+	0.746008i	−0.990946	+	0.134261i	$0.957134\pi$
$458$	12.3141	+	7.10955i	0.575400	+	0.332207i
$459$	0.344870	−	11.4793i	0.0160972	−	0.535809i
$460$	−1.93220	−	1.93220i	−0.0900893	−	0.0900893i
$461$	−9.76161	+	9.76161i	−0.454643	+	0.454643i	−0.896892	−	0.442249i	$-0.854181\pi$
$461$	−9.76161	+	9.76161i	−0.454643	+	0.454643i	0.442249	+	0.896892i	$0.354181\pi$
$462$	0.0948988	+	1.22594i	0.00441509	+	0.0570357i
$463$	37.1831	+	9.96318i	1.72805	+	0.463028i	0.979731	−	0.200316i	$-0.0641970\pi$
$463$	37.1831	+	9.96318i	1.72805	+	0.463028i	0.748314	+	0.663345i	$0.230864\pi$
$464$	−4.07958	−	2.35535i	−0.189390	−	0.109344i
$465$	0.545505	−	0.637045i	0.0252972	−	0.0295423i
$466$	−20.7182	−	5.55141i	−0.959750	−	0.257164i
$467$	8.54433			0.395385			0.197692	−	0.980264i	$-0.436655\pi$
$467$	8.54433			0.395385			0.197692	+	0.980264i	$0.436655\pi$
$468$	1.11950	+	10.7586i	0.0517489	+	0.497315i
$469$	−11.3332			−0.523319
$470$	−18.2194	−	4.88188i	−0.840400	−	0.225185i
$471$	12.6180	+	35.7782i	0.581408	+	1.64857i
$472$	−2.42601	−	1.40066i	−0.111666	−	0.0644704i
$473$	−0.777580	−	0.208352i	−0.0357532	−	0.00958003i
$474$	−13.6384	+	9.34767i	−0.626435	+	0.429353i
$475$	−5.78855	+	5.78855i	−0.265597	+	0.265597i
$476$	2.23573	+	2.23573i	0.102474	+	0.102474i
$477$	2.19402	−	5.67202i	0.100457	−	0.259704i
$478$	6.80960	+	3.93153i	0.311464	+	0.179824i
$479$	2.29400	−	8.56132i	0.104816	−	0.391177i	−0.893509	−	0.449046i	$-0.851764\pi$
$479$	2.29400	−	8.56132i	0.104816	−	0.391177i	0.998324	+	0.0578691i	$0.0184306\pi$
$480$	0.489127	−	2.62030i	0.0223255	−	0.119600i
$481$	12.6544	−	39.1503i	0.576990	−	1.78510i
$482$	16.0291	−	9.25438i	0.730104	−	0.421526i
$483$	3.62894	−	2.48724i	0.165123	−	0.113174i
$484$	5.37687	+	9.31301i	0.244403	+	0.423319i
$485$	5.66959	+	9.82002i	0.257443	+	0.445904i
$486$	−5.87282	−	14.4399i	−0.266396	−	0.655006i
$487$	−2.81256	+	10.4966i	−0.127449	+	0.475648i	−0.999915	−	0.0130276i	$-0.995853\pi$
$487$	−2.81256	+	10.4966i	−0.127449	+	0.475648i	0.872466	+	0.488675i	$0.162520\pi$
$488$	4.80350	+	4.80350i	0.217444	+	0.217444i
$489$	−8.30840	−	3.97601i	−0.375719	−	0.179802i
$490$	−3.81164	+	6.60196i	−0.172192	+	0.298246i
$491$	−17.3462			−0.782822			−0.391411	−	0.920216i	$-0.628013\pi$
$491$	−17.3462			−0.782822			−0.391411	+	0.920216i	$0.628013\pi$
$492$	13.9085	−	1.07665i	0.627044	−	0.0485390i
$493$	−9.01666	−	5.20577i	−0.406090	−	0.234456i
$494$	9.98571	−	5.10727i	0.449279	−	0.229787i
$495$	1.78424	−	1.43728i	0.0801957	−	0.0646007i
$496$	−0.303918	+	0.0814346i	−0.0136463	+	0.00365652i
$497$	13.9247	−	8.03942i	0.624607	−	0.360617i
$498$	2.67559	−	14.3334i	0.119896	−	0.642295i
$499$	−3.05648	+	11.4069i	−0.136827	+	0.510644i	0.863157	+	0.504936i	$0.168484\pi$
$499$	−3.05648	+	11.4069i	−0.136827	+	0.510644i	−0.999984	+	0.00570844i	$0.998183\pi$
$500$	−3.03976	−	11.3445i	−0.135942	−	0.507344i
$501$	−10.6237	−	15.5003i	−0.474634	−	0.692500i
$502$	5.71709	+	21.3365i	0.255166	+	0.952294i
$503$	−20.1247	+	11.6190i	−0.897316	+	0.518066i	−0.876329	−	0.481714i	$-0.840014\pi$
$503$	−20.1247	+	11.6190i	−0.897316	+	0.518066i	−0.0209877	+	0.999780i	$0.506681\pi$
$504$	4.00264	+	1.54828i	0.178292	+	0.0689660i
$505$	2.19820	+	8.20380i	0.0978186	+	0.365064i
$506$	−0.440564	+	0.763079i	−0.0195855	+	0.0339230i
$507$	−5.29540	−	21.8851i	−0.235177	−	0.971953i
$508$	1.44766	+	2.50743i	0.0642297	+	0.111249i
$509$	−2.53125	+	2.53125i	−0.112195	+	0.112195i	−0.760976	−	0.648780i	$-0.775279\pi$
$509$	−2.53125	+	2.53125i	−0.112195	+	0.112195i	0.648780	+	0.760976i	$0.275279\pi$
$510$	1.08106	−	5.79137i	0.0478703	−	0.256446i
$511$		−	9.00829i		−	0.398503i
$512$	−0.707107	+	0.707107i	−0.0312500	+	0.0312500i
$513$	−11.7677	+	11.0813i	−0.519558	+	0.489251i
$514$	−29.1787	−	7.81841i	−1.28702	−	0.344855i
$515$	−22.4105	+	6.00487i	−0.987523	+	0.264606i
$516$	−1.82751	+	2.13418i	−0.0804514	+	0.0939519i
$517$			6.08223i			0.267496i
$518$	−11.5433	−	11.5433i	−0.507183	−	0.507183i
$519$	−2.73416	−	0.510381i	−0.120017	−	0.0224033i
$520$	−0.281908	+	5.54165i	−0.0123625	+	0.243017i
$521$			4.89726i			0.214553i	0.994229	+	0.107277i	$0.0342130\pi$
$521$			4.89726i			0.214553i	−0.994229	+	0.107277i	$0.965787\pi$
$522$	−14.0508	−	1.51331i	−0.614988	−	0.0662357i
$523$	0.745466	−	1.29119i	0.0325970	−	0.0564596i	−0.849267	−	0.527964i	$-0.822956\pi$
$523$	0.745466	−	1.29119i	0.0325970	−	0.0564596i	0.881864	+	0.471504i	$0.156289\pi$
$524$	13.0732			0.571107
$525$	6.50108	−	0.503244i	0.283730	−	0.0219634i
$526$	−5.32422	+	1.42662i	−0.232147	+	0.0622036i
$527$	−0.671717	+	0.179986i	−0.0292605	+	0.00784032i
$528$	−0.856966	+	0.0663371i	−0.0372947	+	0.00288695i
$529$	−19.8473			−0.862928
$530$	1.55989	−	2.70180i	0.0677572	−	0.117359i
$531$	−8.35562	−	0.899921i	−0.362603	−	0.0390532i
$532$		−	4.45011i		−	0.192937i
$533$	−28.3956	+	6.08118i	−1.22995	+	0.263405i
$534$	−6.01440	−	1.12270i	−0.260268	−	0.0485838i
$535$	−13.6522	−	13.6522i	−0.590235	−	0.590235i
$536$		−	7.92226i		−	0.342190i
$537$	−11.3311	+	13.2325i	−0.488972	+	0.571026i
$538$	18.7580	−	5.02619i	0.808714	−	0.216694i
$539$	2.37442	+	0.636224i	0.102274	+	0.0274041i
$540$	−1.83681	−	7.78288i	−0.0790437	−	0.334922i
$541$	−1.70268	+	1.70268i	−0.0732039	+	0.0732039i	−0.742761	−	0.669557i	$-0.766484\pi$
$541$	−1.70268	+	1.70268i	−0.0732039	+	0.0732039i	0.669557	+	0.742761i	$0.266484\pi$
$542$			22.4023i			0.962260i
$543$	3.79754	−	20.3438i	0.162968	−	0.873036i
$544$	−1.56284	+	1.56284i	−0.0670063	+	0.0670063i
$545$	−7.53840	−	13.0569i	−0.322910	−	0.559296i
$546$	−8.68748	−	2.08340i	−0.371790	−	0.0891612i
$547$	6.38104	−	11.0523i	0.272833	−	0.472561i	−0.696753	−	0.717311i	$-0.745373\pi$
$547$	6.38104	−	11.0523i	0.272833	−	0.472561i	0.969586	+	0.244750i	$0.0787059\pi$
$548$	1.68543	+	6.29012i	0.0719981	+	0.268701i
$549$	19.0071	+	7.35223i	0.811203	+	0.313785i
$550$	−1.13097	+	0.652963i	−0.0482245	+	0.0278424i
$551$	3.79269	+	14.1545i	0.161574	+	0.603003i
$552$	1.73866	+	2.53674i	0.0740022	+	0.107971i
$553$	−3.53450	−	13.1909i	−0.150302	−	0.560936i
$554$	−2.28369	+	8.52286i	−0.0970248	+	0.362102i
$555$	−5.58165	+	29.9015i	−0.236928	+	1.26925i
$556$	−14.4469	+	8.34095i	−0.612687	+	0.353735i
$557$	−11.2158	+	3.00527i	−0.475229	+	0.127337i	−0.488480	−	0.872575i	$-0.662449\pi$
$557$	−11.2158	+	3.00527i	−0.475229	+	0.127337i	0.0132513	+	0.999912i	$0.495782\pi$
$558$	−0.735085	+	0.592140i	−0.0311186	+	0.0250673i
$559$	3.17801	−	4.91016i	0.134415	−	0.207678i
$560$	1.90661	+	1.10078i	0.0805692	+	0.0465166i
$561$	−1.89406	+	0.146618i	−0.0799673	+	0.00619021i
$562$	−17.9061			−0.755323
$563$	20.4323	−	35.3898i	0.861119	−	1.49150i	−0.00973001	−	0.999953i	$-0.503097\pi$
$563$	20.4323	−	35.3898i	0.861119	−	1.49150i	0.870849	−	0.491550i	$-0.163569\pi$
$564$	19.1490	+	9.16380i	0.806317	+	0.385866i
$565$	−15.5685	−	15.5685i	−0.654973	−	0.654973i
$566$	1.89264	−	7.06341i	0.0795534	−	0.296897i
$567$	12.8606	−	0.607750i	0.540096	−	0.0255231i
$568$	5.61980	+	9.73378i	0.235802	+	0.408420i
$569$	−3.20683	−	5.55440i	−0.134437	−	0.232852i	0.790945	−	0.611887i	$-0.209589\pi$
$569$	−3.20683	−	5.55440i	−0.134437	−	0.232852i	−0.925382	+	0.379035i	$0.876256\pi$
$570$	−6.83962	+	4.68782i	−0.286480	+	0.196351i
$571$	11.8701	−	6.85319i	0.496747	−	0.286797i	−0.230622	−	0.973043i	$-0.574076\pi$
$571$	11.8701	−	6.85319i	0.496747	−	0.286797i	0.727369	+	0.686246i	$0.240743\pi$
$572$	1.74958	−	0.374689i	0.0731537	−	0.0156665i
$573$	−6.94317	+	37.1953i	−0.290055	+	1.55385i
$574$	−2.98207	+	11.1292i	−0.124469	+	0.464525i
$575$	4.04658	+	2.33629i	0.168754	+	0.0974301i
$576$	−1.08230	+	2.79797i	−0.0450957	+	0.116582i
$577$	−10.8626	−	10.8626i	−0.452214	−	0.452214i	0.443875	−	0.896089i	$-0.353604\pi$
$577$	−10.8626	−	10.8626i	−0.452214	−	0.452214i	−0.896089	+	0.443875i	$0.853604\pi$
$578$	8.56663	−	8.56663i	0.356325	−	0.356325i
$579$	−18.7041	+	12.8196i	−0.777315	+	0.532765i
$580$	−7.00256	−	1.87633i	−0.290766	−	0.0779104i
$581$	10.4294	+	6.02144i	0.432686	+	0.249811i
$582$	−4.24454	−	12.0353i	−0.175942	−	0.498880i
$583$	−0.971715	−	0.260370i	−0.0402443	−	0.0107834i
$584$	6.29707			0.260575
$585$	5.94944	+	15.5470i	0.245979	+	0.642788i
$586$	14.2641			0.589246
$587$	2.47016	+	0.661876i	0.101954	+	0.0273186i	0.309435	−	0.950920i	$-0.399860\pi$
$587$	2.47016	+	0.661876i	0.101954	+	0.0273186i	−0.207481	+	0.978239i	$0.566527\pi$
$588$	5.58047	−	6.51693i	0.230135	−	0.268753i
$589$	0.847637	+	0.489383i	0.0349263	+	0.0201647i
$590$	−4.16422	−	1.11580i	−0.171438	−	0.0459368i
$591$	0.329591	+	4.25777i	0.0135576	+	0.175141i
$592$	8.06912	−	8.06912i	0.331639	−	0.331639i
$593$	−15.9796	−	15.9796i	−0.656204	−	0.656204i	0.298276	−	0.954480i	$-0.403588\pi$
$593$	−15.9796	−	15.9796i	−0.656204	−	0.656204i	−0.954480	+	0.298276i	$0.903588\pi$
$594$	−2.27083	+	1.22165i	−0.0931734	+	0.0501251i
$595$	4.21399	+	2.43295i	0.172757	+	0.0997411i
$596$	2.72321	−	10.1632i	0.111547	−	0.416299i
$597$	34.2273	−	12.0711i	1.40083	−	0.494035i
$598$	−4.29101	−	4.75098i	−0.175472	−	0.194282i
$599$	20.6867	−	11.9435i	0.845237	−	0.487998i	−0.0138036	−	0.999905i	$-0.504394\pi$
$599$	20.6867	−	11.9435i	0.845237	−	0.487998i	0.859041	+	0.511907i	$0.171061\pi$
$600$	0.351783	+	4.54445i	0.0143615	+	0.185527i
$601$	12.7060	+	22.0074i	0.518287	+	0.897700i	0.999774	+	0.0212465i	$0.00676348\pi$
$601$	12.7060	+	22.0074i	0.518287	+	0.897700i	−0.481487	+	0.876453i	$0.659903\pi$
$602$	−1.16031	−	2.00972i	−0.0472908	−	0.0819101i
$603$	−9.61101	−	21.7368i	−0.391391	−	0.885191i
$604$	−4.44836	+	16.6015i	−0.181001	+	0.675505i
$605$	11.7023	+	11.7023i	0.475768	+	0.475768i
$606$	−0.737733	−	9.53029i	−0.0299683	−	0.387142i
$607$	−10.3003	+	17.8407i	−0.418078	+	0.724132i	−0.995746	−	0.0921396i	$-0.970629\pi$
$607$	−10.3003	+	17.8407i	−0.418078	+	0.724132i	0.577668	+	0.816272i	$0.303963\pi$
$608$	3.11076			0.126158
$609$	5.03850	−	10.5286i	0.204170	−	0.426641i
$610$	9.05382	+	5.22722i	0.366578	+	0.211644i
$611$	−42.0491	−	13.5913i	−1.70112	−	0.549847i
$612$	−2.39208	+	6.18405i	−0.0966942	+	0.249975i
$613$	−6.32348	+	1.69437i	−0.255403	+	0.0684350i	−0.384249	−	0.923230i	$-0.625539\pi$
$613$	−6.32348	+	1.69437i	−0.255403	+	0.0684350i	0.128846	+	0.991665i	$0.458873\pi$
$614$	19.0916	−	11.0226i	0.770476	−	0.444835i
$615$	20.2465	−	7.14040i	0.816417	−	0.287929i
$616$	0.183739	−	0.685722i	0.00740304	−	0.0276285i
$617$	−4.13493	−	15.4318i	−0.166466	−	0.621260i	−0.997849	−	0.0655593i	$-0.979117\pi$
$617$	−4.13493	−	15.4318i	−0.166466	−	0.621260i	0.831383	−	0.555700i	$-0.187550\pi$
$618$	26.0341	−	2.01528i	1.04724	−	0.0810664i
$619$	5.84160	+	21.8012i	0.234794	+	0.876263i	0.978242	+	0.207469i	$0.0665225\pi$
$619$	5.84160	+	21.8012i	0.234794	+	0.876263i	−0.743448	+	0.668794i	$0.766811\pi$
$620$	−0.419345	+	0.242109i	−0.0168413	+	0.00972334i
$621$	7.84795	+	4.85093i	0.314927	+	0.194661i
$622$	6.40761	+	23.9135i	0.256922	+	0.958845i
$623$	2.52664	−	4.37627i	0.101228	−	0.175331i
$624$	1.45636	−	6.07281i	0.0583010	−	0.243107i
$625$	−2.45839	−	4.25805i	−0.0983355	−	0.170322i
$626$	22.7271	−	22.7271i	0.908359	−	0.908359i
$627$	2.03093	+	1.73910i	0.0811077	+	0.0694529i
$628$		−	21.9035i		−	0.874046i
$629$	17.8343	−	17.8343i	0.711100	−	0.711100i
$630$	6.56673	+	0.707253i	0.261625	+	0.0281777i
$631$	−16.8737	−	4.52128i	−0.671730	−	0.179989i	−0.0931960	−	0.995648i	$-0.529708\pi$
$631$	−16.8737	−	4.52128i	−0.671730	−	0.179989i	−0.578534	+	0.815658i	$0.696375\pi$
$632$	9.22086	−	2.47072i	0.366786	−	0.0982801i
$633$	24.0546	+	4.49022i	0.956084	+	0.178470i
$634$			29.9265i			1.18853i
$635$	3.15073	+	3.15073i	0.125033	+	0.125033i
$636$	−2.28377	+	2.66700i	−0.0905573	+	0.105754i
$637$	−9.70437	+	14.9937i	−0.384501	+	0.594072i
$638$			2.33768i			0.0925496i
$639$	27.2281	+	19.8894i	1.07713	+	0.786814i
$640$	−0.769482	+	1.33278i	−0.0304164	+	0.0526828i
$641$	−36.5684			−1.44436			−0.722182	−	0.691703i	$-0.756861\pi$
$641$	−36.5684			−1.44436			−0.722182	+	0.691703i	$0.756861\pi$
$642$	12.2847	+	17.9236i	0.484838	+	0.707389i
$643$	−33.7924	+	9.05466i	−1.33264	+	0.357081i	−0.853700	−	0.520765i	$-0.825647\pi$
$643$	−33.7924	+	9.05466i	−1.33264	+	0.357081i	−0.478944	+	0.877846i	$0.658980\pi$
$644$	−2.45350	+	0.657414i	−0.0966815	+	0.0259057i
$645$	−1.86656	+	3.90042i	−0.0734958	+	0.153579i
$646$	6.87538			0.270508
$647$	−9.58684	+	16.6049i	−0.376897	+	0.652806i	−0.990609	−	0.136725i	$-0.956342\pi$
$647$	−9.58684	+	16.6049i	−0.376897	+	0.652806i	0.613712	+	0.789530i	$0.289676\pi$
$648$	0.424835	+	8.98997i	0.0166891	+	0.353159i
$649$			1.39015i			0.0545682i
$650$	−1.98696	−	9.27796i	−0.0779350	−	0.363911i
$651$	−0.259295	−	0.735226i	−0.0101626	−	0.0288158i
$652$	3.76028	+	3.76028i	0.147264	+	0.147264i
$653$		−	6.63054i		−	0.259473i	−0.991548	−	0.129737i	$-0.958587\pi$
$653$		−	6.63054i		−	0.259473i	0.991548	−	0.129737i	$-0.0414132\pi$
$654$	5.64363	+	16.0024i	0.220683	+	0.625744i
$655$	19.4337	−	5.20724i	0.759337	−	0.203464i
$656$	−7.77966	−	2.08455i	−0.303745	−	0.0813882i
$657$	17.2777	−	7.63938i	0.674066	−	0.298041i
$658$	−12.3980	+	12.3980i	−0.483325	+	0.483325i
$659$		−	21.6577i		−	0.843665i	−0.906674	−	0.421833i	$-0.861387\pi$
$659$		−	21.6577i		−	0.843665i	0.906674	−	0.421833i	$-0.138613\pi$
$660$	−1.24748	+	0.439952i	−0.0485580	+	0.0171251i
$661$	7.30997	−	7.30997i	0.284325	−	0.284325i	−0.550506	−	0.834831i	$-0.685565\pi$
$661$	7.30997	−	7.30997i	0.284325	−	0.284325i	0.834831	+	0.550506i	$0.185565\pi$
$662$	3.31702	+	5.74525i	0.128920	+	0.223295i
$663$	3.21883	−	13.4221i	0.125009	−	0.521270i
$664$	−4.20917	+	7.29049i	−0.163347	+	0.282926i
$665$	−1.77254	−	6.61519i	−0.0687360	−	0.256526i
$666$	12.3506	−	31.9289i	0.478575	−	1.23722i
$667$	7.24360	−	4.18209i	0.280473	−	0.161931i
$668$	2.80800	+	10.4796i	0.108645	+	0.405469i
$669$	6.85302	−	14.3203i	0.264953	−	0.553654i
$670$	−3.15554	−	11.7766i	−0.121909	−	0.454971i
$671$	0.872508	−	3.25624i	0.0336828	−	0.125706i
$672$	−1.88206	−	1.61162i	−0.0726020	−	0.0621694i
$673$	22.7770	−	13.1503i	0.877990	−	0.506908i	0.00799497	−	0.999968i	$-0.497455\pi$
$673$	22.7770	−	13.1503i	0.877990	−	0.506908i	0.869995	+	0.493060i	$0.164122\pi$
$674$	22.4939	−	6.02723i	0.866434	−	0.232160i
$675$	6.47838	+	12.0421i	0.249353	+	0.463502i
$676$	−1.31923	+	12.9329i	−0.0507394	+	0.497419i
$677$	−0.260338	−	0.150306i	−0.0100056	−	0.00577673i	0.494989	−	0.868899i	$-0.335172\pi$
$677$	−0.260338	−	0.150306i	−0.0100056	−	0.00577673i	−0.504994	+	0.863123i	$0.668505\pi$
$678$	14.0091	+	20.4396i	0.538016	+	0.784977i
$679$	10.5404			0.404504
$680$	−1.70070	+	2.94570i	−0.0652190	+	0.112963i
$681$	−37.7299	+	25.8597i	−1.44581	+	0.990948i
$682$	0.110407	+	0.110407i	0.00422772	+	0.00422772i
$683$	0.894421	−	3.33802i	0.0342241	−	0.127726i	−0.946700	−	0.322116i	$-0.895606\pi$
$683$	0.894421	−	3.33802i	0.0342241	−	0.127726i	0.980924	+	0.194390i	$0.0622727\pi$
$684$	8.53518	−	3.77386i	0.326351	−	0.144297i
$685$	5.01088	+	8.67909i	0.191456	+	0.331611i
$686$	8.55007	+	14.8092i	0.326443	+	0.565416i
$687$	−22.2154	−	10.6313i	−0.847571	−	0.405608i
$688$	1.40486	−	0.811094i	0.0535596	−	0.0309227i
$689$	3.97144	−	6.13606i	0.151300	−	0.233765i
$690$	3.59498	+	3.07840i	0.136858	+	0.117193i
$691$	8.65698	−	32.3083i	0.329327	−	1.22906i	−0.580563	−	0.814215i	$-0.697168\pi$
$691$	8.65698	−	32.3083i	0.329327	−	1.22906i	0.909890	−	0.414849i	$-0.136166\pi$
$692$	1.39070	+	0.802919i	0.0528663	+	0.0305224i
$693$	−0.327758	−	2.10436i	−0.0124505	−	0.0799381i
$694$	−14.2693	−	14.2693i	−0.541655	−	0.541655i
$695$	−18.1534	+	18.1534i	−0.688599	+	0.688599i
$696$	7.35982	+	3.52207i	0.278973	+	0.133504i
$697$	−17.1946	−	4.60727i	−0.651290	−	0.174513i
$698$	−21.7369	−	12.5498i	−0.822752	−	0.475016i
$699$	36.5200	+	6.81711i	1.38131	+	0.257847i
$700$	−3.63635	−	0.974358i	−0.137441	−	0.0368273i
$701$	14.8908			0.562418			0.281209	−	0.959647i	$-0.409265\pi$
$701$	14.8908			0.562418			0.281209	+	0.959647i	$0.409265\pi$
$702$	−3.37142	−	18.4291i	−0.127246	−	0.695563i
$703$	−35.4983			−1.33884
$704$	0.479340	+	0.128439i	0.0180658	+	0.00484072i
$705$	32.1155	+	5.99493i	1.20954	+	0.225782i
$706$	22.5939	+	13.0446i	0.850333	+	0.490940i
$707$	7.62589	+	2.04335i	0.286801	+	0.0768481i
$708$	4.37667	+	2.09447i	0.164485	+	0.0787150i
$709$	−17.4183	+	17.4183i	−0.654157	+	0.654157i	−0.953991	−	0.299834i	$-0.903069\pi$
$709$	−17.4183	+	17.4183i	−0.654157	+	0.654157i	0.299834	+	0.953991i	$0.403069\pi$
$710$	12.2311	+	12.2311i	0.459024	+	0.459024i
$711$	22.3025	−	17.9655i	0.836408	−	0.673759i
$712$	3.05914	+	1.76620i	0.114646	+	0.0661910i
$713$	0.144593	−	0.539629i	0.00541505	−	0.0202093i
$714$	−4.15971	−	3.56198i	−0.155673	−	0.133304i
$715$	2.45155	−	1.25387i	0.0916829	−	0.0468919i
$716$	8.71053	−	5.02903i	0.325528	−	0.187944i
$717$	−12.2850	−	5.87901i	−0.458790	−	0.219556i
$718$	16.3855	+	28.3805i	0.611502	+	1.05915i
$719$	−17.8371	−	30.8948i	−0.665213	−	1.15218i	−0.979227	−	0.202765i	$-0.935007\pi$
$719$	−17.8371	−	30.8948i	−0.665213	−	1.15218i	0.314014	−	0.949418i	$-0.398326\pi$
$720$	−0.494392	+	4.59034i	−0.0184249	+	0.171072i
$721$	−5.58186	+	20.8318i	−0.207879	+	0.775816i
$722$	6.59248	+	6.59248i	0.245347	+	0.245347i
$723$	−26.4432	+	18.1240i	−0.983435	+	0.674037i
$724$	−5.97419	+	10.3476i	−0.222029	+	0.384565i
$725$	12.3966			0.460399
$726$	−10.5302	−	15.3637i	−0.390811	−	0.570201i
$727$	−8.14708	−	4.70372i	−0.302159	−	0.174451i	0.341254	−	0.939971i	$-0.389149\pi$
$727$	−8.14708	−	4.70372i	−0.302159	−	0.174451i	−0.643412	+	0.765520i	$0.722482\pi$
$728$	4.33011	+	2.80258i	0.160484	+	0.103870i
$729$	12.0720	+	24.1509i	0.447110	+	0.894479i
$730$	9.36075	−	2.50821i	0.346457	−	0.0928328i
$731$	3.10500	−	1.79267i	0.114843	−	0.0663044i
$732$	−8.93721	−	7.65297i	−0.330329	−	0.282862i
$733$	−8.37893	+	31.2706i	−0.309483	+	1.15501i	0.619534	+	0.784970i	$0.287322\pi$
$733$	−8.37893	+	31.2706i	−0.309483	+	1.15501i	−0.929017	+	0.370037i	$0.879345\pi$
$734$	−0.151492	−	0.565376i	−0.00559167	−	0.0208684i
$735$	5.69974	−	11.9103i	0.210238	−	0.439320i
$736$	−0.459552	−	1.71507i	−0.0169393	−	0.0632184i
$737$	−3.40471	+	1.96571i	−0.125414	+	0.0724079i
$738$	−23.8745	+	3.71849i	−0.878831	+	0.136880i
$739$	7.68766	+	28.6907i	0.282795	+	1.05541i	0.950436	+	0.310922i	$0.100638\pi$
$739$	7.68766	+	28.6907i	0.282795	+	1.05541i	−0.667640	+	0.744484i	$0.732696\pi$
$740$	8.78091	−	15.2090i	0.322793	−	0.559093i
$741$	−16.5615	+	10.1545i	−0.608400	+	0.373036i
$742$	−1.45000	−	2.51148i	−0.0532313	−	0.0921993i
$743$	−17.4277	+	17.4277i	−0.639359	+	0.639359i	−0.950397	−	0.311038i	$-0.899323\pi$
$743$	−17.4277	+	17.4277i	−0.639359	+	0.639359i	0.311038	+	0.950397i	$0.399323\pi$
$744$	0.513946	−	0.181255i	0.0188422	−	0.00664513i
$745$		−	16.1925i		−	0.593247i
$746$	−19.3592	+	19.3592i	−0.708790	+	0.708790i
$747$	−2.70439	+	25.1098i	−0.0989484	+	0.918719i
$748$	1.05943	+	0.283875i	0.0387368	+	0.0103795i
$749$	−17.3355	+	4.64503i	−0.633425	+	0.169726i
$750$	6.76582	+	19.1844i	0.247053	+	0.700515i
$751$		−	22.1321i		−	0.807610i	−0.914845	−	0.403805i	$-0.867687\pi$
$751$		−	22.1321i		−	0.807610i	0.914845	−	0.403805i	$-0.132313\pi$
$752$	−8.66658	−	8.66658i	−0.316038	−	0.316038i
$753$	−12.7250	−	36.0814i	−0.463723	−	1.31488i
$754$	−16.1614	−	5.22378i	−0.588563	−	0.190239i
$755$			26.4504i			0.962628i
$756$	−7.11907	−	2.13864i	−0.258918	−	0.0777817i
$757$	25.1440	−	43.5507i	0.913875	−	1.58288i	0.105336	−	0.994437i	$-0.466408\pi$
$757$	25.1440	−	43.5507i	0.913875	−	1.58288i	0.808540	−	0.588442i	$-0.200258\pi$
$758$	3.22915			0.117288
$759$	0.658797	−	1.37664i	0.0239128	−	0.0499690i
$760$	4.62422	−	1.23906i	0.167738	−	0.0449453i
$761$	8.09766	−	2.16976i	0.293540	−	0.0786538i	−0.109044	−	0.994037i	$-0.534779\pi$
$761$	8.09766	−	2.16976i	0.293540	−	0.0786538i	0.402584	+	0.915383i	$0.368112\pi$
$762$	−2.83513	−	4.13652i	−0.102706	−	0.149850i
$763$	−14.0147			−0.507368
$764$	10.9228	−	18.9189i	0.395174	−	0.684461i
$765$	−1.09270	+	10.1455i	−0.0395067	+	0.366813i
$766$			14.1015i			0.509508i
$767$	−9.61071	−	3.10643i	−0.347023	−	0.112167i
$768$	1.12657	−	1.31562i	0.0406515	−	0.0474732i
$769$	−10.9600	−	10.9600i	−0.395229	−	0.395229i	0.481317	−	0.876547i	$-0.340159\pi$
$769$	−10.9600	−	10.9600i	−0.395229	−	0.395229i	−0.876547	+	0.481317i	$0.840159\pi$
$770$		−	1.09253i		−	0.0393720i
$771$	51.4334	+	9.60097i	1.85233	+	0.345770i
$772$	12.6457	−	3.38840i	0.455128	−	0.121951i
$773$	−6.28210	−	1.68328i	−0.225951	−	0.0605435i	0.144067	−	0.989568i	$-0.453982\pi$
$773$	−6.28210	−	1.68328i	−0.225951	−	0.0605435i	−0.370018	+	0.929024i	$0.620649\pi$
$774$	2.87060	−	3.92977i	0.103182	−	0.141253i
$775$	0.585485	−	0.585485i	0.0210313	−	0.0210313i
$776$			7.36806i			0.264498i
$777$	21.4770	+	18.3909i	0.770484	+	0.659769i
$778$	14.1062	−	14.1062i	0.505733	−	0.505733i
$779$	12.5272	+	21.6977i	0.448833	+	0.777401i
$780$	−0.253968	−	9.60747i	−0.00909352	−	0.344003i
$781$	2.78882	−	4.83038i	0.0997919	−	0.172845i
$782$	−1.01570	−	3.79064i	−0.0363213	−	0.135553i
$783$	24.4664	+	0.735040i	0.874359	+	0.0262682i
$784$	−4.28987	+	2.47676i	−0.153210	+	0.0884557i
$785$	−8.72447	−	32.5601i	−0.311390	−	1.16212i
$786$	−22.5760	+	1.74759i	−0.805258	+	0.0623345i
$787$	−13.8656	−	51.7471i	−0.494255	−	1.84458i	−0.534164	−	0.845381i	$-0.679373\pi$
$787$	−13.8656	−	51.7471i	−0.494255	−	1.84458i	0.0399086	−	0.999203i	$-0.487293\pi$
$788$	0.638138	−	2.38157i	0.0227327	−	0.0848398i
$789$	9.00361	−	3.17533i	0.320537	−	0.113045i
$790$	12.7229	−	7.34558i	0.452661	−	0.261344i
$791$	−19.7689	+	5.29706i	−0.702901	+	0.188342i
$792$	1.47101	−	0.229113i	0.0522702	−	0.00814118i
$793$	20.5621	+	13.3084i	0.730182	+	0.472596i
$794$	16.0511	+	9.26710i	0.569632	+	0.328877i
$795$	−2.33258	+	4.87422i	−0.0827280	+	0.172871i
$796$	−20.9541			−0.742697
$797$	−23.3358	+	40.4188i	−0.826597	+	1.43171i	0.0740951	+	0.997251i	$0.476393\pi$
$797$	−23.3358	+	40.4188i	−0.826597	+	1.43171i	−0.900692	+	0.434457i	$0.856940\pi$
$798$	0.594876	+	7.68482i	0.0210584	+	0.272040i
$799$	−19.1548	−	19.1548i	−0.677649	−	0.677649i
$800$	0.681106	−	2.54192i	0.0240807	−	0.0898705i
$801$	10.5362	+	1.13478i	0.372280	+	0.0400955i
$802$	−7.88886	−	13.6639i	−0.278565	−	0.482489i
$803$	−1.56246	−	2.70626i	−0.0551380	−	0.0955018i
$804$	1.05902	+	13.6808i	0.0373489	+	0.482486i
$805$	−3.38533	+	1.95452i	−0.119317	+	0.0688879i
$806$	−1.01001	+	0.516577i	−0.0355761	+	0.0181957i
$807$	−31.7210	+	11.1872i	−1.11663	+	0.393807i
$808$	−1.42836	+	5.33073i	−0.0502497	+	0.187534i
$809$	3.13155	+	1.80800i	0.110099	+	0.0635659i	0.554039	−	0.832491i	$-0.313086\pi$
$809$	3.13155	+	1.80800i	0.110099	+	0.0635659i	−0.443939	+	0.896057i	$0.646419\pi$
$810$	4.21235	+	13.1946i	0.148007	+	0.463611i
$811$	0.430194	+	0.430194i	0.0151062	+	0.0151062i	0.714620	−	0.699513i	$-0.246600\pi$
$811$	0.430194	+	0.430194i	0.0151062	+	0.0151062i	−0.699513	+	0.714620i	$0.746600\pi$
$812$	−4.76512	+	4.76512i	−0.167223	+	0.167223i
$813$	−2.99467	−	38.6861i	−0.105028	−	1.35678i
$814$	−5.46997	−	1.46567i	−0.191722	−	0.0513719i
$815$	7.08752	+	4.09198i	0.248265	+	0.143336i
$816$	2.48993	−	2.90776i	0.0871651	−	0.101792i
$817$	−4.87429	−	1.30606i	−0.170530	−	0.0456933i
$818$	−11.1264			−0.389025
$819$	15.2808	+	2.43647i	0.533953	+	0.0851372i
$820$	−12.3950			−0.432851
$821$	49.9310	+	13.3790i	1.74260	+	0.466929i	0.983022	−	0.183485i	$-0.0587379\pi$
$821$	49.9310	+	13.3790i	1.74260	+	0.466929i	0.759580	+	0.650414i	$0.225405\pi$
$822$	−3.75139	−	10.6370i	−0.130845	−	0.371008i
$823$	16.1344	+	9.31518i	0.562408	+	0.324707i	0.754112	−	0.656746i	$-0.228068\pi$
$823$	16.1344	+	9.31518i	0.562408	+	0.324707i	−0.191703	+	0.981453i	$0.561401\pi$
$824$	−14.5621	−	3.90189i	−0.507293	−	0.135929i
$825$	1.86576	−	1.27878i	0.0649574	−	0.0445213i
$826$	−2.83368	+	2.83368i	−0.0985963	+	0.0985963i
$827$	−23.9908	−	23.9908i	−0.834244	−	0.834244i	0.153851	−	0.988094i	$-0.450833\pi$
$827$	−23.9908	−	23.9908i	−0.834244	−	0.834244i	−0.988094	+	0.153851i	$0.950833\pi$
$828$	−3.34157	−	4.14824i	−0.116127	−	0.144161i
$829$	−11.0843	−	6.39953i	−0.384974	−	0.222265i	0.295006	−	0.955495i	$-0.404678\pi$
$829$	−11.0843	−	6.39953i	−0.384974	−	0.222265i	−0.679980	+	0.733230i	$0.738012\pi$
$830$	−3.35313	+	12.5141i	−0.116389	+	0.434370i
$831$	2.80436	−	15.0233i	0.0972823	−	0.521151i
$832$	−1.95909	+	3.02688i	−0.0679191	+	0.104938i
$833$	−9.48144	+	5.47411i	−0.328513	+	0.189667i
$834$	23.8332	−	16.3351i	0.825277	−	0.565638i
$835$	8.34834	+	14.4597i	0.288906	+	0.500400i
$836$	−0.771857	−	1.33689i	−0.0266952	−	0.0462375i
$837$	1.19025	−	1.12082i	0.0411411	−	0.0387412i
$838$	0.118552	−	0.442443i	0.00409532	−	0.0152839i
$839$	−14.9217	−	14.9217i	−0.515155	−	0.515155i	0.400946	−	0.916102i	$-0.368681\pi$
$839$	−14.9217	−	14.9217i	−0.515155	−	0.515155i	−0.916102	+	0.400946i	$0.868681\pi$
$840$	−3.43965	−	1.64606i	−0.118679	−	0.0567944i
$841$	−3.40468	+	5.89708i	−0.117403	+	0.203348i
$842$	4.52844			0.156060
$843$	30.9218	−	2.39363i	1.06500	−	0.0824410i
$844$	−12.2350	−	7.06391i	−0.421148	−	0.243150i
$845$	3.19028	+	19.7505i	0.109749	+	0.679439i
$846$	−34.2930	−	13.2650i	−1.17902	−	0.456062i
$847$	14.8596	−	3.98162i	0.510582	−	0.136810i
$848$	1.75560	−	1.01360i	0.0602875	−	0.0348070i
$849$	−2.32415	+	12.4507i	−0.0797646	+	0.427307i
$850$	1.50537	−	5.61814i	0.0516339	−	0.192700i
$851$	5.24416	+	19.5715i	0.179767	+	0.670901i
$852$	−11.0059	−	16.0579i	−0.377057	−	0.550134i
$853$	−2.43856	−	9.10083i	−0.0834947	−	0.311606i	0.911530	−	0.411233i	$-0.134902\pi$
$853$	−2.43856	−	9.10083i	−0.0834947	−	0.311606i	−0.995025	+	0.0996268i	$0.968235\pi$
$854$	8.41603	−	4.85900i	0.287991	−	0.166272i
$855$	11.1846	−	9.00962i	0.382505	−	0.308122i
$856$	−3.24702	−	12.1180i	−0.110981	−	0.414186i
$857$	7.45337	−	12.9096i	0.254602	−	0.440984i	−0.710185	−	0.704015i	$-0.751389\pi$
$857$	7.45337	−	12.9096i	0.254602	−	0.440984i	0.964787	+	0.263031i	$0.0847221\pi$
$858$	−2.97124	+	0.880924i	−0.101436	+	0.0300742i
$859$	17.7711	+	30.7804i	0.606341	+	1.05021i	0.991838	+	0.127504i	$0.0406967\pi$
$859$	17.7711	+	30.7804i	0.606341	+	1.05021i	−0.385497	+	0.922709i	$0.625970\pi$
$860$	1.76528	−	1.76528i	0.0601957	−	0.0601957i
$861$	3.66196	−	19.6175i	0.124799	−	0.668563i
$862$			14.9323i			0.508598i
$863$	−0.118264	+	0.118264i	−0.00402577	+	0.00402577i	−0.709117	−	0.705091i	$-0.750906\pi$
$863$	−0.118264	+	0.118264i	−0.00402577	+	0.00402577i	0.705091	+	0.709117i	$0.250906\pi$
$864$	1.49498	−	4.97645i	0.0508601	−	0.169302i
$865$	2.38712	+	0.639626i	0.0811644	+	0.0217479i
$866$	−4.36797	+	1.17039i	−0.148430	+	0.0397716i
$867$	−13.6484	+	15.9387i	−0.463525	+	0.541308i
$868$			0.450108i			0.0152777i
$869$	−3.34975	−	3.34975i	−0.113633	−	0.113633i
$870$	12.3434	+	2.30413i	0.418482	+	0.0781172i
$871$	−5.98164	−	27.9308i	−0.202680	−	0.946399i
$872$		−	9.79673i		−	0.331759i
$873$	8.93867	+	20.2162i	0.302528	+	0.684215i
$874$	−2.76169	+	4.78339i	−0.0934156	+	0.161801i
$875$	−16.8015			−0.567994
$876$	−10.8743	+	0.841773i	−0.367409	+	0.0284409i
$877$	−41.3195	+	11.0715i	−1.39526	+	0.373859i	−0.876640	−	0.481147i	$-0.840220\pi$
$877$	−41.3195	+	11.0715i	−1.39526	+	0.373859i	−0.518619	+	0.855005i	$0.673554\pi$
$878$	−12.9011	+	3.45683i	−0.435390	+	0.116662i
$879$	−24.6325	+	1.90679i	−0.830834	+	0.0643143i
$880$	0.763710			0.0257447
$881$	−13.3432	+	23.1111i	−0.449544	+	0.778633i	−0.998356	−	0.0573124i	$-0.981747\pi$
$881$	−13.3432	+	23.1111i	−0.449544	+	0.778633i	0.548812	+	0.835946i	$0.315080\pi$
$882$	−8.76567	+	12.0000i	−0.295156	+	0.404060i
$883$		−	11.8585i		−	0.399071i	−0.979891	−	0.199536i	$-0.936057\pi$
$883$		−	11.8585i		−	0.399071i	0.979891	−	0.199536i	$-0.0639433\pi$
$884$	−4.32996	+	6.68998i	−0.145632	+	0.225008i
$885$	7.34029	+	1.37020i	0.246741	+	0.0460587i
$886$	21.8018	+	21.8018i	0.732445	+	0.732445i
$887$		−	52.7911i		−	1.77255i	−0.463156	−	0.886277i	$-0.653283\pi$
$887$		−	52.7911i		−	1.77255i	0.463156	−	0.886277i	$-0.346717\pi$
$888$	−12.8558	+	15.0131i	−0.431412	+	0.503806i
$889$	4.00079	−	1.07201i	0.134182	−	0.0359540i
$890$	5.25099	+	1.40700i	0.176014	+	0.0471627i
$891$	3.75816	−	2.41321i	0.125903	−	0.0808457i
$892$	−6.48118	+	6.48118i	−0.217006	+	0.217006i
$893$			38.1267i			1.27586i
$894$	−3.34409	+	17.9146i	−0.111843	+	0.599155i
$895$	10.9453	−	10.9453i	0.365861	−	0.365861i
$896$	0.715277	+	1.23890i	0.0238957	+	0.0413886i
$897$	8.04517	+	7.63079i	0.268621	+	0.254785i
$898$	20.0708	−	34.7636i	0.669771	−	1.16008i
$899$	−0.383613	−	1.43167i	−0.0127942	−	0.0477487i
$900$	−1.21498	−	7.80072i	−0.0404992	−	0.260024i
$901$	3.88021	−	2.24024i	0.129269	−	0.0746333i
$902$	1.03446	+	3.86065i	0.0344437	+	0.128546i
$903$	2.27238	+	3.31545i	0.0756201	+	0.110331i
$904$	−3.70280	−	13.8190i	−0.123153	−	0.459615i
$905$	−4.75920	+	17.7616i	−0.158201	+	0.590414i
$906$	5.46256	−	29.2635i	0.181482	−	0.972215i
$907$	−15.9624	+	9.21592i	−0.530024	+	0.306009i	−0.741026	−	0.671476i	$-0.765661\pi$
$907$	−15.9624	+	9.21592i	−0.530024	+	0.306009i	0.211002	+	0.977486i	$0.432327\pi$
$908$	25.5089	−	6.83510i	0.846544	−	0.226831i
$909$	2.54796	+	16.3591i	0.0845105	+	0.542597i
$910$	7.55312	+	2.44136i	0.250383	+	0.0809303i
$911$	−37.3282	−	21.5514i	−1.23674	−	0.714030i	−0.268311	−	0.963332i	$-0.586466\pi$
$911$	−37.3282	−	21.5514i	−1.23674	−	0.714030i	−0.968426	+	0.249302i	$0.919799\pi$
$912$	−5.37192	+	0.415837i	−0.177882	+	0.0137697i
$913$	4.17760			0.138258
$914$	−8.25520	+	14.2984i	−0.273058	+	0.472950i
$915$	−16.3337	−	7.81653i	−0.539974	−	0.258406i
$916$	10.0544	+	10.0544i	0.332207	+	0.332207i
$917$	4.84042	−	18.0647i	0.159845	−	0.596549i
$918$	3.30419	−	10.9989i	0.109054	−	0.363018i
$919$	−25.3781	−	43.9562i	−0.837147	−	1.44998i	−0.892270	−	0.451502i	$-0.850888\pi$
$919$	−25.3781	−	43.9562i	−0.837147	−	1.44998i	0.0551224	−	0.998480i	$-0.482445\pi$
$920$	−1.36627	−	2.36645i	−0.0450446	−	0.0780196i
$921$	−31.4956	+	21.5868i	−1.03782	+	0.711310i
$922$	−11.9555	+	6.90250i	−0.393733	+	0.227322i
$923$	27.1626	+	30.0743i	0.894068	+	0.989908i
$924$	−0.225630	+	1.20872i	−0.00742269	+	0.0397641i
$925$	−7.77241	+	29.0070i	−0.255555	+	0.953745i
$926$	33.3375	+	19.2474i	1.09554	+	0.632508i
$927$	−44.6884	+	6.96031i	−1.46776	+	0.228607i
$928$	−3.33096	−	3.33096i	−0.109344	−	0.109344i
$929$	32.8640	−	32.8640i	1.07823	−	1.07823i	0.0815633	−	0.996668i	$-0.474009\pi$
$929$	32.8640	−	32.8640i	1.07823	−	1.07823i	0.996668	−	0.0815633i	$-0.0259913\pi$
$930$	0.691796	−	0.474151i	0.0226849	−	0.0155480i
$931$	14.8841	+	3.98820i	0.487808	+	0.130708i
$932$	−18.5754	−	10.7245i	−0.608457	−	0.351293i
$933$	−14.2619	−	40.4393i	−0.466913	−	1.32392i
$934$	8.25319	+	2.21144i	0.270053	+	0.0723604i
$935$	1.68795			0.0552018
$936$	−1.70317	+	10.6817i	−0.0556698	+	0.349143i
$937$	−13.9838			−0.456832			−0.228416	−	0.973564i	$-0.573355\pi$
$937$	−13.9838			−0.456832			−0.228416	+	0.973564i	$0.573355\pi$
$938$	−10.9471	−	2.93325i	−0.357434	−	0.0957741i
$939$	−36.2090	+	42.2852i	−1.18164	+	1.37993i
$940$	−16.3351	−	9.43108i	−0.532792	−	0.307608i
$941$	24.7787	+	6.63944i	0.807764	+	0.216440i	0.638990	−	0.769215i	$-0.279353\pi$
$941$	24.7787	+	6.63944i	0.807764	+	0.216440i	0.168774	+	0.985655i	$0.446019\pi$
$942$	2.92800	+	37.8249i	0.0953993	+	1.23240i
$943$	10.1121	−	10.1121i	0.329295	−	0.329295i
$944$	−1.98083	−	1.98083i	−0.0644704	−	0.0644704i
$945$	−11.4345	−	0.343525i	−0.371965	−	0.0111749i
$946$	−0.697159	−	0.402505i	−0.0226666	−	0.0130866i
$947$	0.714319	−	2.66588i	0.0232123	−	0.0866293i	−0.953348	−	0.301873i	$-0.902388\pi$
$947$	0.714319	−	2.66588i	0.0232123	−	0.0866293i	0.976560	+	0.215244i	$0.0690547\pi$
$948$	−15.5931	+	5.49927i	−0.506440	+	0.178608i
$949$	22.2010	−	4.75455i	0.720675	−	0.154339i
$950$	−7.08950	+	4.09312i	−0.230014	+	0.132798i
$951$	−4.00048	−	51.6795i	−0.129724	−	1.67582i
$952$	1.58090	+	2.73820i	0.0512372	+	0.0887455i
$953$	14.2452	+	24.6735i	0.461448	+	0.799252i	0.999033	−	0.0439575i	$-0.0139966\pi$
$953$	14.2452	+	24.6735i	0.461448	+	0.799252i	−0.537585	+	0.843210i	$0.680663\pi$
$954$	3.58729	−	4.91090i	0.116143	−	0.158996i
$955$	8.70140	−	32.4741i	0.281571	−	1.05084i
$956$	5.56002	+	5.56002i	0.179824	+	0.179824i
$957$	−0.312494	−	4.03690i	−0.0101015	−	0.130495i
$958$	4.43167	−	7.67587i	0.143181	−	0.247996i
$959$	9.31578			0.300822
$960$	1.15064	−	2.40442i	0.0371369	−	0.0776024i
$961$	26.7611	+	15.4505i	0.863260	+	0.498403i
$962$	22.3560	−	34.5411i	0.720787	−	1.11365i
$963$	−23.6102	−	29.3099i	−0.760829	−	0.944497i
$964$	17.8781	−	4.79042i	0.575815	−	0.154289i
$965$	17.4485	−	10.0739i	0.561687	−	0.324290i
$966$	4.14903	−	1.46325i	0.133493	−	0.0470794i
$967$	−2.73120	+	10.1930i	−0.0878293	+	0.327783i	−0.995835	−	0.0911745i	$-0.970938\pi$
$967$	−2.73120	+	10.1930i	−0.0878293	+	0.327783i	0.908006	+	0.418958i	$0.137605\pi$
$968$	2.78327	+	10.3873i	0.0894577	+	0.333861i
$969$	−11.8730	+	0.919079i	−0.381415	+	0.0295251i
$970$	2.93480	+	10.9528i	0.0942306	+	0.351674i
$971$	−36.5800	+	21.1195i	−1.17391	+	0.677756i	−0.954597	−	0.297899i	$-0.903714\pi$
$971$	−36.5800	+	21.1195i	−1.17391	+	0.677756i	−0.219310	+	0.975655i	$0.570381\pi$
$972$	−1.93539	−	15.4678i	−0.0620778	−	0.496131i
$973$	6.17655	+	23.0512i	0.198011	+	0.738987i
$974$	−5.43346	+	9.41102i	−0.174099	+	0.301549i
$975$	4.67150	+	15.7564i	0.149608	+	0.504607i
$976$	3.39659	+	5.88306i	0.108722	+	0.188312i
$977$	−37.3318	+	37.3318i	−1.19435	+	1.19435i	−0.218516	+	0.975833i	$0.570122\pi$
$977$	−37.3318	+	37.3318i	−1.19435	+	1.19435i	−0.975833	+	0.218516i	$0.929878\pi$
$978$	−6.99623	−	5.99091i	−0.223715	−	0.191568i
$979$		−	1.75295i		−	0.0560245i
$980$	−5.39048	+	5.39048i	−0.172192	+	0.172192i
$981$	−11.8850	−	26.8799i	−0.379460	−	0.858209i
$982$	−16.7551	−	4.48952i	−0.534678	−	0.143266i
$983$	32.7120	−	8.76515i	1.04335	−	0.279565i	0.303849	−	0.952720i	$-0.401728\pi$
$983$	32.7120	−	8.76515i	1.04335	−	0.279565i	0.739501	+	0.673155i	$0.235061\pi$
$984$	13.7132	+	2.55982i	0.437162	+	0.0816042i
$985$		−	3.79443i		−	0.120901i
$986$	−7.36207	−	7.36207i	−0.234456	−	0.234456i
$987$	19.7526	−	23.0673i	0.628732	−	0.734239i
$988$	10.9673	−	2.34875i	0.348917	−	0.0747238i
$989$			2.88031i			0.0915887i
$990$	2.09544	−	0.926506i	0.0665974	−	0.0294463i
$991$	20.3156	−	35.1877i	0.645347	−	1.11777i	−0.338874	−	0.940832i	$-0.610046\pi$
$991$	20.3156	−	35.1877i	0.645347	−	1.11777i	0.984221	−	0.176942i	$-0.0566205\pi$
$992$	−0.314639			−0.00998980
$993$	−6.49612	−	9.47797i	−0.206148	−	0.300774i
$994$	15.5310	−	4.16151i	0.492612	−	0.131995i
$995$	−31.1487	+	8.34627i	−0.987481	+	0.264595i
$996$	6.29418	−	13.1525i	0.199439	−	0.416753i
$997$	15.3421			0.485888			0.242944	−	0.970040i	$-0.421887\pi$
$997$	15.3421			0.485888			0.242944	+	0.970040i	$0.421887\pi$
$998$	−5.90466	+	10.2272i	−0.186909	+	0.323735i
$999$	−17.0599	+	56.7885i	−0.539750	+	1.79671i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	234.2.z.a.137.8	yes	56
3.2	odd	2		702.2.bc.a.683.2		56
9.4	even	3		702.2.bb.a.449.2		56
9.5	odd	6		234.2.y.a.59.12	✓	56
13.2	odd	12		234.2.y.a.119.12	yes	56
39.2	even	12		702.2.bb.a.197.2		56
117.41	even	12	inner	234.2.z.a.41.8	yes	56
117.67	odd	12		702.2.bc.a.665.2		56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
234.2.y.a.59.12	✓	56	9.5	odd	6
234.2.y.a.119.12	yes	56	13.2	odd	12
234.2.z.a.41.8	yes	56	117.41	even	12	inner
234.2.z.a.137.8	yes	56	1.1	even	1	trivial
702.2.bb.a.197.2		56	39.2	even	12
702.2.bb.a.449.2		56	9.4	even	3
702.2.bc.a.665.2		56	117.67	odd	12
702.2.bc.a.683.2		56	3.2	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:	\( N \)	\(=\)	\( 234 = 2 \cdot 3^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	234.z (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.965926 + 0.258819i) q^{2} +(-1.70264 - 0.317829i) q^{3} +(0.866025 + 0.500000i) q^{4} +(1.48652 + 0.398313i) q^{5} +(-1.56236 - 0.747675i) q^{6} +(1.01155 - 1.01155i) q^{7} +(0.707107 + 0.707107i) q^{8} +(2.79797 + 1.08230i) q^{9} +(1.33278 + 0.769482i) q^{10} +(0.128439 - 0.479340i) q^{11} +(-1.31562 - 1.12657i) q^{12} +(3.02688 + 1.95909i) q^{13} +(1.23890 - 0.715277i) q^{14} +(-2.40442 - 1.15064i) q^{15} +(0.500000 + 0.866025i) q^{16} +(1.10510 + 1.91408i) q^{17} +(2.42251 + 1.76959i) q^{18} +(0.805124 - 3.00476i) q^{19} +(1.08821 + 1.08821i) q^{20} +(-2.04381 + 1.40081i) q^{21} +(0.248125 - 0.429765i) q^{22} -1.77557 q^{23} +(-0.979210 - 1.42869i) q^{24} +(-2.27902 - 1.31580i) q^{25} +(2.41669 + 2.67575i) q^{26} +(-4.41995 - 2.73204i) q^{27} +(1.38181 - 0.370254i) q^{28} +(-4.07958 + 2.35535i) q^{29} +(-2.02468 - 1.73375i) q^{30} +(-0.0814346 + 0.303918i) q^{31} +(0.258819 + 0.965926i) q^{32} +(-0.371033 + 0.775323i) q^{33} +(0.572040 + 2.13488i) q^{34} +(1.90661 - 1.10078i) q^{35} +(1.88197 + 2.33628i) q^{36} +(-2.95350 - 11.0226i) q^{37} +(1.55538 - 2.69400i) q^{38} +(-4.53103 - 4.29765i) q^{39} +(0.769482 + 1.33278i) q^{40} +(-5.69511 + 5.69511i) q^{41} +(-2.33673 + 0.824102i) q^{42} -1.62219i q^{43} +(0.350901 - 0.350901i) q^{44} +(3.72816 + 2.72333i) q^{45} +(-1.71507 - 0.459552i) q^{46} +(-11.8388 + 3.17219i) q^{47} +(-0.576073 - 1.63344i) q^{48} +4.95352i q^{49} +(-1.86082 - 1.86082i) q^{50} +(-1.27323 - 3.61023i) q^{51} +(1.64181 + 3.21006i) q^{52} -2.02719i q^{53} +(-3.56224 - 3.78291i) q^{54} +(0.381855 - 0.661392i) q^{55} +1.43055 q^{56} +(-2.32584 + 4.86014i) q^{57} +(-4.55018 + 1.21922i) q^{58} +(-2.70586 + 0.725033i) q^{59} +(-1.50697 - 2.19870i) q^{60} +6.79318 q^{61} +(-0.157320 + 0.272485i) q^{62} +(3.92510 - 1.73550i) q^{63} +1.00000i q^{64} +(3.71920 + 4.11787i) q^{65} +(-0.559059 + 0.652874i) q^{66} +(-5.60189 - 5.60189i) q^{67} +2.21019i q^{68} +(3.02316 + 0.564328i) q^{69} +(2.12655 - 0.569808i) q^{70} +(10.8566 + 2.90902i) q^{71} +(1.21316 + 2.74376i) q^{72} +(4.45270 - 4.45270i) q^{73} -11.4115i q^{74} +(3.46216 + 2.96467i) q^{75} +(2.19964 - 2.19964i) q^{76} +(-0.354956 - 0.614801i) q^{77} +(-3.26432 - 5.32393i) q^{78} +(4.77307 - 8.26720i) q^{79} +(0.398313 + 1.48652i) q^{80} +(6.65727 + 6.05646i) q^{81} +(-6.97505 + 4.02705i) q^{82} +(2.17883 + 8.13149i) q^{83} +(-2.47040 + 0.191232i) q^{84} +(0.880349 + 3.28551i) q^{85} +(0.419853 - 1.56691i) q^{86} +(7.69466 - 2.71370i) q^{87} +(0.429765 - 0.248125i) q^{88} +(3.41203 - 0.914251i) q^{89} +(2.89628 + 3.59545i) q^{90} +(5.04357 - 1.08013i) q^{91} +(-1.53769 - 0.887787i) q^{92} +(0.235248 - 0.491581i) q^{93} -12.2564 q^{94} +(2.39367 - 4.14596i) q^{95} +(-0.133677 - 1.72688i) q^{96} +(5.21001 + 5.21001i) q^{97} +(-1.28206 + 4.78473i) q^{98} +(0.878156 - 1.20217i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q - 8 q^{7} - 24 q^{11} + 28 q^{16} - 8 q^{19} - 24 q^{21} + 36 q^{27} - 4 q^{28} - 24 q^{30} - 4 q^{31} + 60 q^{33} - 24 q^{35} - 4 q^{37} + 36 q^{38} - 48 q^{41} - 36 q^{42} - 84 q^{45} - 36 q^{47}+ \cdots + 60 q^{99}+O(q^{100}) \) 56 * q - 8 * q^7 - 24 * q^11 + 28 * q^16 - 8 * q^19 - 24 * q^21 + 36 * q^27 - 4 * q^28 - 24 * q^30 - 4 * q^31 + 60 * q^33 - 24 * q^35 - 4 * q^37 + 36 * q^38 - 48 * q^41 - 36 * q^42 - 84 * q^45 - 36 * q^47 - 24 * q^50 + 8 * q^52 - 36 * q^54 + 36 * q^57 + 24 * q^60 - 48 * q^63 - 36 * q^65 + 28 * q^67 + 84 * q^69 - 24 * q^71 - 24 * q^72 + 28 * q^73 + 4 * q^76 + 24 * q^77 - 60 * q^78 - 24 * q^79 + 24 * q^81 - 96 * q^83 - 72 * q^85 + 4 * q^91 - 24 * q^92 - 36 * q^93 - 52 * q^97 + 48 * q^98 + 60 * q^99

Introduction

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