LMFDB - Embedded newform 357.2.u.a.127.6

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [357,2,Mod(43,357)] 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("357.43"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(357, base_ring=CyclotomicField(8)) chi = DirichletCharacter(H, H._module([0, 0, 1])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 357 = 3 \cdot 7 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	357.u (of order $8$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [32] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$2.85065935216$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$8$ over $\Q(\zeta_{8})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			127.6
Character	$\chi$	$=$	357.127
Dual form			357.2.u.a.253.6

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.904145 - 0.904145i) q^{2} +(0.382683 - 0.923880i) q^{3} +0.365044i q^{4} +(2.54273 + 1.05323i) q^{5} +(-0.489320 - 1.18132i) q^{6} +(-0.923880 + 0.382683i) q^{7} +(2.13834 + 2.13834i) q^{8} +(-0.707107 - 0.707107i) q^{9} +(3.25127 - 1.34672i) q^{10} +(1.22618 + 2.96026i) q^{11} +(0.337256 + 0.139696i) q^{12} -2.42357i q^{13} +(-0.489320 + 1.18132i) q^{14} +(1.94612 - 1.94612i) q^{15} +3.13666 q^{16} +(-3.37157 - 2.37329i) q^{17} -1.27865 q^{18} +(-0.00206932 + 0.00206932i) q^{19} +(-0.384476 + 0.928207i) q^{20} +1.00000i q^{21} +(3.78515 + 1.56786i) q^{22} +(-2.49092 - 6.01360i) q^{23} +(2.79388 - 1.15726i) q^{24} +(1.82064 + 1.82064i) q^{25} +(-2.19126 - 2.19126i) q^{26} +(-0.923880 + 0.382683i) q^{27} +(-0.139696 - 0.337256i) q^{28} +(-5.30880 - 2.19898i) q^{29} -3.51915i q^{30} +(-1.22777 + 2.96409i) q^{31} +(-1.44069 + 1.44069i) q^{32} +3.20417 q^{33} +(-5.19419 + 0.902586i) q^{34} -2.75223 q^{35} +(0.258125 - 0.258125i) q^{36} +(-0.127308 + 0.307348i) q^{37} +0.00374192i q^{38} +(-2.23909 - 0.927462i) q^{39} +(3.18505 + 7.68940i) q^{40} +(8.02642 - 3.32465i) q^{41} +(0.904145 + 0.904145i) q^{42} +(0.0148539 + 0.0148539i) q^{43} +(-1.08063 + 0.447610i) q^{44} +(-1.05323 - 2.54273i) q^{45} +(-7.68932 - 3.18502i) q^{46} -8.74318i q^{47} +(1.20035 - 2.89789i) q^{48} +(0.707107 - 0.707107i) q^{49} +3.29225 q^{50} +(-3.48288 + 2.20670i) q^{51} +0.884710 q^{52} +(-4.78094 + 4.78094i) q^{53} +(-0.489320 + 1.18132i) q^{54} +8.81860i q^{55} +(-2.79388 - 1.15726i) q^{56} +(0.00111991 + 0.00270369i) q^{57} +(-6.78812 + 2.81173i) q^{58} +(-1.47901 - 1.47901i) q^{59} +(0.710419 + 0.710419i) q^{60} +(3.83089 - 1.58680i) q^{61} +(1.56989 + 3.79005i) q^{62} +(0.923880 + 0.382683i) q^{63} +8.87850i q^{64} +(2.55259 - 6.16249i) q^{65} +(2.89703 - 2.89703i) q^{66} -6.49880 q^{67} +(0.866355 - 1.23077i) q^{68} -6.50907 q^{69} +(-2.48842 + 2.48842i) q^{70} +(-6.31029 + 15.2344i) q^{71} -3.02407i q^{72} +(5.99007 + 2.48117i) q^{73} +(0.162782 + 0.392992i) q^{74} +(2.37878 - 0.985323i) q^{75} +(-0.000755390 - 0.000755390i) q^{76} +(-2.26569 - 2.26569i) q^{77} +(-2.86302 + 1.18590i) q^{78} +(5.72729 + 13.8269i) q^{79} +(7.97567 + 3.30363i) q^{80} +1.00000i q^{81} +(4.25108 - 10.2630i) q^{82} +(-8.35386 + 8.35386i) q^{83} -0.365044 q^{84} +(-6.07336 - 9.58569i) q^{85} +0.0268601 q^{86} +(-4.06318 + 4.06318i) q^{87} +(-3.70806 + 8.95205i) q^{88} -8.16088i q^{89} +(-3.25127 - 1.34672i) q^{90} +(0.927462 + 2.23909i) q^{91} +(2.19523 - 0.909293i) q^{92} +(2.26862 + 2.26862i) q^{93} +(-7.90510 - 7.90510i) q^{94} +(-0.00744118 + 0.00308224i) q^{95} +(0.779697 + 1.88236i) q^{96} +(4.77433 + 1.97759i) q^{97} -1.27865i q^{98} +(1.22618 - 2.96026i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 8 q^{6} - 32 q^{10} + 8 q^{14} - 8 q^{16} - 8 q^{17} - 8 q^{18} + 8 q^{19} - 16 q^{20} - 8 q^{23} - 8 q^{24} + 24 q^{25} - 32 q^{26} + 24 q^{29} + 8 q^{31} - 40 q^{32} + 8 q^{33} - 8 q^{34} - 8 q^{35}+ \cdots + 96 q^{97}+O(q^{100}) $ 32 * q + 8 * q^6 - 32 * q^10 + 8 * q^14 - 8 * q^16 - 8 * q^17 - 8 * q^18 + 8 * q^19 - 16 * q^20 - 8 * q^23 - 8 * q^24 + 24 * q^25 - 32 * q^26 + 24 * q^29 + 8 * q^31 - 40 * q^32 + 8 * q^33 - 8 * q^34 - 8 * q^35 - 8 * q^36 + 72 * q^37 - 16 * q^39 + 40 * q^40 + 8 * q^41 - 32 * q^43 - 48 * q^44 + 8 * q^45 + 40 * q^46 + 32 * q^48 + 56 * q^50 - 16 * q^51 - 56 * q^53 + 8 * q^54 + 8 * q^56 + 16 * q^57 - 32 * q^58 - 48 * q^59 - 48 * q^60 + 8 * q^61 - 24 * q^62 + 16 * q^66 + 96 * q^67 - 16 * q^68 + 8 * q^69 - 16 * q^70 + 24 * q^71 - 24 * q^73 - 32 * q^74 - 16 * q^75 - 48 * q^76 - 24 * q^77 - 72 * q^78 - 48 * q^79 + 72 * q^80 + 96 * q^82 - 24 * q^83 + 24 * q^84 - 136 * q^85 - 32 * q^87 + 16 * q^88 + 32 * q^90 + 8 * q^91 + 136 * q^92 + 8 * q^93 - 32 * q^94 - 32 * q^95 - 32 * q^96 + 96 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/357\mathbb{Z}\right)^\times$.

$n$	$52$	$190$	$239$
$\chi(n)$	$1$	$e\left(\frac{5}{8}\right)$	$1$

Coefficient data

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

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

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

$2$	0.904145	−	0.904145i	0.639327	−	0.639327i	−0.311062	−	0.950389i	$-0.600685\pi$
$2$	0.904145	−	0.904145i	0.639327	−	0.639327i	0.950389	+	0.311062i	$0.100685\pi$
$3$	0.382683	−	0.923880i	0.220942	−	0.533402i
$3$	0.382683	−	0.923880i	0.220942	−	0.533402i
$4$			0.365044i			0.182522i
$5$	2.54273	+	1.05323i	1.13714	+	0.471020i	0.870203	−	0.492693i	$-0.163987\pi$
$5$	2.54273	+	1.05323i	1.13714	+	0.471020i	0.266940	+	0.963713i	$0.413987\pi$
$6$	−0.489320	−	1.18132i	−0.199764	−	0.482273i
$7$	−0.923880	+	0.382683i	−0.349194	+	0.144641i
$7$	−0.923880	+	0.382683i	−0.349194	+	0.144641i
$8$	2.13834	+	2.13834i	0.756018	+	0.756018i
$9$	−0.707107	−	0.707107i	−0.235702	−	0.235702i
$10$	3.25127	−	1.34672i	1.02814	−	0.425871i
$11$	1.22618	+	2.96026i	0.369708	+	0.892553i	0.993798	+	0.111201i	$0.0354697\pi$
$11$	1.22618	+	2.96026i	0.369708	+	0.892553i	−0.624090	+	0.781352i	$0.714530\pi$
$12$	0.337256	+	0.139696i	0.0973575	+	0.0403268i
$13$		−	2.42357i		−	0.672179i	−0.941830	−	0.336089i	$-0.890896\pi$
$13$		−	2.42357i		−	0.672179i	0.941830	−	0.336089i	$-0.109104\pi$
$14$	−0.489320	+	1.18132i	−0.130776	+	0.315722i
$15$	1.94612	−	1.94612i	0.502486	−	0.502486i
$16$	3.13666			0.784164
$17$	−3.37157	−	2.37329i	−0.817726	−	0.575608i
$17$	−3.37157	−	2.37329i	−0.817726	−	0.575608i
$18$	−1.27865			−0.301382
$19$	−0.00206932	+	0.00206932i	−0.000474734	+	0.000474734i	−0.707344	−	0.706869i	$-0.750107\pi$
$19$	−0.00206932	+	0.00206932i	−0.000474734	+	0.000474734i	0.706869	+	0.707344i	$0.250107\pi$
$20$	−0.384476	+	0.928207i	−0.0859714	+	0.207553i
$21$			1.00000i			0.218218i
$22$	3.78515	+	1.56786i	0.806997	+	0.334269i
$23$	−2.49092	−	6.01360i	−0.519392	−	1.25392i	−0.938277	−	0.345884i	$-0.887579\pi$
$23$	−2.49092	−	6.01360i	−0.519392	−	1.25392i	0.418886	−	0.908039i	$-0.362421\pi$
$24$	2.79388	−	1.15726i	0.570298	−	0.236225i
$25$	1.82064	+	1.82064i	0.364128	+	0.364128i
$26$	−2.19126	−	2.19126i	−0.429742	−	0.429742i
$27$	−0.923880	+	0.382683i	−0.177801	+	0.0736475i
$28$	−0.139696	−	0.337256i	−0.0264001	−	0.0637354i
$29$	−5.30880	−	2.19898i	−0.985819	−	0.408340i	−0.169241	−	0.985575i	$-0.554132\pi$
$29$	−5.30880	−	2.19898i	−0.985819	−	0.408340i	−0.816578	+	0.577235i	$0.804132\pi$
$30$		−	3.51915i		−	0.642506i
$31$	−1.22777	+	2.96409i	−0.220513	+	0.532366i	−0.994960	−	0.100273i	$-0.968028\pi$
$31$	−1.22777	+	2.96409i	−0.220513	+	0.532366i	0.774447	+	0.632639i	$0.218028\pi$
$32$	−1.44069	+	1.44069i	−0.254681	+	0.254681i
$33$	3.20417			0.557774
$34$	−5.19419	+	0.902586i	−0.890796	+	0.154792i
$35$	−2.75223			−0.465212
$36$	0.258125	−	0.258125i	0.0430208	−	0.0430208i
$37$	−0.127308	+	0.307348i	−0.0209292	+	0.0505277i	−0.933999	−	0.357276i	$-0.883705\pi$
$37$	−0.127308	+	0.307348i	−0.0209292	+	0.0505277i	0.913069	+	0.407804i	$0.133705\pi$
$38$			0.00374192i			0.000607020i
$39$	−2.23909	−	0.927462i	−0.358541	−	0.148513i
$40$	3.18505	+	7.68940i	0.503601	+	1.21580i
$41$	8.02642	−	3.32465i	1.25352	−	0.519224i	0.345603	−	0.938381i	$-0.387674\pi$
$41$	8.02642	−	3.32465i	1.25352	−	0.519224i	0.907914	+	0.419157i	$0.137674\pi$
$42$	0.904145	+	0.904145i	0.139513	+	0.139513i
$43$	0.0148539	+	0.0148539i	0.00226520	+	0.00226520i	0.708238	−	0.705973i	$-0.249490\pi$
$43$	0.0148539	+	0.0148539i	0.00226520	+	0.00226520i	−0.705973	+	0.708238i	$0.749490\pi$
$44$	−1.08063	+	0.447610i	−0.162910	+	0.0674797i
$45$	−1.05323	−	2.54273i	−0.157007	−	0.379048i
$46$	−7.68932	−	3.18502i	−1.13373	−	0.469605i
$47$		−	8.74318i		−	1.27532i	−0.770316	−	0.637662i	$-0.779902\pi$
$47$		−	8.74318i		−	1.27532i	0.770316	−	0.637662i	$-0.220098\pi$
$48$	1.20035	−	2.89789i	0.173255	−	0.418275i
$49$	0.707107	−	0.707107i	0.101015	−	0.101015i
$50$	3.29225			0.465594
$51$	−3.48288	+	2.20670i	−0.487701	+	0.309000i
$52$	0.884710			0.122687
$53$	−4.78094	+	4.78094i	−0.656713	+	0.656713i	−0.954601	−	0.297888i	$-0.903718\pi$
$53$	−4.78094	+	4.78094i	−0.656713	+	0.656713i	0.297888	+	0.954601i	$0.403718\pi$
$54$	−0.489320	+	1.18132i	−0.0665880	+	0.160758i
$55$			8.81860i			1.18910i
$56$	−2.79388	−	1.15726i	−0.373348	−	0.154646i
$57$	0.00111991	+	0.00270369i	0.000148335	+	0.000358113i
$58$	−6.78812	+	2.81173i	−0.891324	+	0.369198i
$59$	−1.47901	−	1.47901i	−0.192551	−	0.192551i	0.604246	−	0.796798i	$-0.293474\pi$
$59$	−1.47901	−	1.47901i	−0.192551	−	0.192551i	−0.796798	+	0.604246i	$0.793474\pi$
$60$	0.710419	+	0.710419i	0.0917147	+	0.0917147i
$61$	3.83089	−	1.58680i	0.490495	−	0.203170i	−0.123707	−	0.992319i	$-0.539478\pi$
$61$	3.83089	−	1.58680i	0.490495	−	0.203170i	0.614201	+	0.789149i	$0.289478\pi$
$62$	1.56989	+	3.79005i	0.199376	+	0.481336i
$63$	0.923880	+	0.382683i	0.116398	+	0.0482136i
$64$			8.87850i			1.10981i
$65$	2.55259	−	6.16249i	0.316610	−	0.764363i
$66$	2.89703	−	2.89703i	0.356600	−	0.356600i
$67$	−6.49880			−0.793954			−0.396977	−	0.917828i	$-0.629941\pi$
$67$	−6.49880			−0.793954			−0.396977	+	0.917828i	$0.629941\pi$
$68$	0.866355	−	1.23077i	0.105061	−	0.149253i
$69$	−6.50907			−0.783601
$70$	−2.48842	+	2.48842i	−0.297423	+	0.297423i
$71$	−6.31029	+	15.2344i	−0.748894	+	1.80799i	−0.183801	+	0.982964i	$0.558840\pi$
$71$	−6.31029	+	15.2344i	−0.748894	+	1.80799i	−0.565094	+	0.825027i	$0.691160\pi$
$72$		−	3.02407i		−	0.356390i
$73$	5.99007	+	2.48117i	0.701085	+	0.290399i	0.704610	−	0.709595i	$-0.251122\pi$
$73$	5.99007	+	2.48117i	0.701085	+	0.290399i	−0.00352484	+	0.999994i	$0.501122\pi$
$74$	0.162782	+	0.392992i	0.0189231	+	0.0456843i
$75$	2.37878	−	0.985323i	0.274678	−	0.113775i
$76$	−0.000755390	0	0.000755390i	−8.66492e−5	0	8.66492e-5i
$77$	−2.26569	−	2.26569i	−0.258199	−	0.258199i
$78$	−2.86302	+	1.18590i	−0.324173	+	0.134277i
$79$	5.72729	+	13.8269i	0.644371	+	1.55565i	0.820726	+	0.571322i	$0.193569\pi$
$79$	5.72729	+	13.8269i	0.644371	+	1.55565i	−0.176355	+	0.984327i	$0.556431\pi$
$80$	7.97567	+	3.30363i	0.891707	+	0.369357i
$81$			1.00000i			0.111111i
$82$	4.25108	−	10.2630i	0.469453	−	1.13336i
$83$	−8.35386	+	8.35386i	−0.916956	+	0.916956i	−0.996807	−	0.0798510i	$-0.974556\pi$
$83$	−8.35386	+	8.35386i	−0.916956	+	0.916956i	0.0798510	+	0.996807i	$0.474556\pi$
$84$	−0.365044			−0.0398295
$85$	−6.07336	−	9.58569i	−0.658748	−	1.03971i
$86$	0.0268601			0.00289640
$87$	−4.06318	+	4.06318i	−0.435619	+	0.435619i
$88$	−3.70806	+	8.95205i	−0.395281	+	0.954292i
$89$		−	8.16088i		−	0.865052i	−0.901621	−	0.432526i	$-0.857622\pi$
$89$		−	8.16088i		−	0.865052i	0.901621	−	0.432526i	$-0.142378\pi$
$90$	−3.25127	−	1.34672i	−0.342714	−	0.141957i
$91$	0.927462	+	2.23909i	0.0972244	+	0.234720i
$92$	2.19523	−	0.909293i	0.228868	−	0.0948003i
$93$	2.26862	+	2.26862i	0.235245	+	0.235245i
$94$	−7.90510	−	7.90510i	−0.815349	−	0.815349i
$95$	−0.00744118	+	0.00308224i	−0.000763449	+	0.000316231i
$96$	0.779697	+	1.88236i	0.0795775	+	0.192117i
$97$	4.77433	+	1.97759i	0.484760	+	0.200794i	0.611659	−	0.791122i	$-0.290502\pi$
$97$	4.77433	+	1.97759i	0.484760	+	0.200794i	−0.126899	+	0.991916i	$0.540502\pi$
$98$		−	1.27865i		−	0.129164i
$99$	1.22618	−	2.96026i	0.123236	−	0.297518i
$100$	−0.664613	+	0.664613i	−0.0664613	+	0.0664613i
$101$	13.0301			1.29654			0.648271	−	0.761410i	$-0.275493\pi$
$101$	13.0301			1.29654			0.648271	+	0.761410i	$0.275493\pi$
$102$	−1.15385	+	5.14421i	−0.114248	+	0.509353i
$103$	1.93260			0.190425			0.0952125	−	0.995457i	$-0.469647\pi$
$103$	1.93260			0.190425			0.0952125	+	0.995457i	$0.469647\pi$
$104$	5.18243	−	5.18243i	0.508179	−	0.508179i
$105$	−1.05323	+	2.54273i	−0.102785	+	0.248145i
$106$			8.64533i			0.839709i
$107$	−8.26516	−	3.42354i	−0.799023	−	0.330966i	−0.0544580	−	0.998516i	$-0.517343\pi$
$107$	−8.26516	−	3.42354i	−0.799023	−	0.330966i	−0.744565	+	0.667550i	$0.767343\pi$
$108$	−0.139696	−	0.337256i	−0.0134423	−	0.0324525i
$109$	7.81710	−	3.23795i	0.748742	−	0.310139i	0.0245138	−	0.999699i	$-0.492196\pi$
$109$	7.81710	−	3.23795i	0.748742	−	0.310139i	0.724228	+	0.689560i	$0.242196\pi$
$110$	7.97330	+	7.97330i	0.760224	+	0.760224i
$111$	0.235234	+	0.235234i	0.0223274	+	0.0223274i
$112$	−2.89789	+	1.20035i	−0.273825	+	0.113422i
$113$	−2.08550	−	5.03485i	−0.196187	−	0.473638i	0.794918	−	0.606717i	$-0.207514\pi$
$113$	−2.08550	−	5.03485i	−0.196187	−	0.473638i	−0.991106	+	0.133078i	$0.957514\pi$
$114$	0.00345709	+	0.00143197i	0.000323786	+	0.000134116i
$115$		−	17.9145i		−	1.67053i
$116$	0.802722	−	1.93794i	0.0745309	−	0.179934i
$117$	−1.71373	+	1.71373i	−0.158434	+	0.158434i
$118$	−2.67449			−0.246207
$119$	4.02314	+	0.902393i	0.368801	+	0.0827223i
$120$	8.32295			0.759778
$121$	0.518535	−	0.518535i	0.0471396	−	0.0471396i
$122$	2.02897	−	4.89838i	0.183695	−	0.443478i
$123$		−	8.68774i		−	0.783347i
$124$	−1.08202	−	0.448188i	−0.0971685	−	0.0402485i
$125$	−2.55433	−	6.16669i	−0.228466	−	0.551566i
$126$	1.18132	−	0.489320i	0.105241	−	0.0435921i
$127$	2.38866	+	2.38866i	0.211959	+	0.211959i	0.805099	−	0.593140i	$-0.202112\pi$
$127$	2.38866	+	2.38866i	0.211959	+	0.211959i	−0.593140	+	0.805099i	$0.702112\pi$
$128$	5.14607	+	5.14607i	0.454852	+	0.454852i
$129$	0.0194075	−	0.00803886i	0.00170874	−	0.000707783i
$130$	−3.26388	−	7.87970i	−0.286261	−	0.691095i
$131$	0.706073	+	0.292465i	0.0616899	+	0.0255528i	0.413315	−	0.910588i	$-0.364371\pi$
$131$	0.706073	+	0.292465i	0.0616899	+	0.0255528i	−0.351625	+	0.936141i	$0.614371\pi$
$132$			1.16966i			0.101806i
$133$	0.00111991	−	0.00270369i	9.71081e−5	−	0.000234440i
$134$	−5.87585	+	5.87585i	−0.507597	+	0.507597i
$135$	−2.75223			−0.236874
$136$	−2.13466	−	12.2845i	−0.183045	−	1.05339i
$137$	−20.0849			−1.71597			−0.857983	−	0.513679i	$-0.828282\pi$
$137$	−20.0849			−1.71597			−0.857983	+	0.513679i	$0.828282\pi$
$138$	−5.88515	+	5.88515i	−0.500977	+	0.500977i
$139$	−8.51498	+	20.5570i	−0.722232	+	1.74362i	−0.0553387	+	0.998468i	$0.517624\pi$
$139$	−8.51498	+	20.5570i	−0.722232	+	1.74362i	−0.666893	+	0.745154i	$0.732376\pi$
$140$		−	1.00468i		−	0.0849113i
$141$	−8.07764	−	3.34587i	−0.680260	−	0.281773i
$142$	8.06868	+	19.4795i	0.677109	+	1.63469i
$143$	7.17442	−	2.97174i	0.599955	−	0.248510i
$144$	−2.21795	−	2.21795i	−0.184829	−	0.184829i
$145$	−11.1828	−	11.1828i	−0.928682	−	0.928682i
$146$	7.65923	−	3.17256i	0.633883	−	0.262563i
$147$	−0.382683	−	0.923880i	−0.0315632	−	0.0762003i
$148$	−0.112195	−	0.0464728i	−0.00922240	−	0.00382004i
$149$		−	15.8783i		−	1.30080i	−0.759591	−	0.650400i	$-0.774601\pi$
$149$		−	15.8783i		−	1.30080i	0.759591	−	0.650400i	$-0.225399\pi$
$150$	1.25989	−	3.04164i	0.102869	−	0.248349i
$151$	1.14368	−	1.14368i	0.0930717	−	0.0930717i	−0.659038	−	0.752110i	$-0.729036\pi$
$151$	1.14368	−	1.14368i	0.0930717	−	0.0930717i	0.752110	+	0.659038i	$0.229036\pi$
$152$	−0.00884981			−0.000717814
$153$	0.705888	+	4.06223i	0.0570676	+	0.328412i
$154$	−4.09702			−0.330147
$155$	−6.24376	+	6.24376i	−0.501511	+	0.501511i
$156$	0.338564	−	0.817366i	0.0271068	−	0.0654416i
$157$		−	24.8562i		−	1.98374i	−0.127258	−	0.991870i	$-0.540618\pi$
$157$		−	24.8562i		−	1.98374i	0.127258	−	0.991870i	$-0.459382\pi$
$158$	17.6798	+	7.32323i	1.40653	+	0.582605i
$159$	2.58743	+	6.24660i	0.205196	+	0.495388i
$160$	−5.18068	+	2.14591i	−0.409569	+	0.169649i
$161$	4.60261	+	4.60261i	0.362737	+	0.362737i
$162$	0.904145	+	0.904145i	0.0710363	+	0.0710363i
$163$	7.79330	−	3.22809i	0.610419	−	0.252844i	−0.0559889	−	0.998431i	$-0.517831\pi$
$163$	7.79330	−	3.22809i	0.610419	−	0.252844i	0.666407	+	0.745588i	$0.267831\pi$
$164$	1.21364	+	2.92999i	0.0947696	+	0.228794i
$165$	8.14733	+	3.37473i	0.634269	+	0.262723i
$166$			15.1062i			1.17247i
$167$	1.50407	−	3.63114i	0.116388	−	0.280986i	−0.854941	−	0.518726i	$-0.826407\pi$
$167$	1.50407	−	3.63114i	0.116388	−	0.280986i	0.971329	+	0.237740i	$0.0764066\pi$
$168$	−2.13834	+	2.13834i	−0.164977	+	0.164977i
$169$	7.12629			0.548176
$170$	−14.1581	−	3.17566i	−1.08587	−	0.243562i
$171$	0.00292645			0.000223792
$172$	−0.00542232	+	0.00542232i	−0.000413448	+	0.000413448i
$173$	2.66666	−	6.43789i	0.202743	−	0.489464i	−0.789505	−	0.613745i	$-0.789662\pi$
$173$	2.66666	−	6.43789i	0.202743	−	0.489464i	0.992247	+	0.124281i	$0.0396624\pi$
$174$			7.34741i			0.557005i
$175$	−2.37878	−	0.985323i	−0.179819	−	0.0744834i
$176$	3.84611	+	9.28533i	0.289911	+	0.699908i
$177$	−1.93243	+	0.800437i	−0.145250	+	0.0601645i
$178$	−7.37862	−	7.37862i	−0.553051	−	0.553051i
$179$	3.43882	+	3.43882i	0.257029	+	0.257029i	0.823845	−	0.566816i	$-0.191825\pi$
$179$	3.43882	+	3.43882i	0.257029	+	0.257029i	−0.566816	+	0.823845i	$0.691825\pi$
$180$	0.928207	−	0.384476i	0.0691845	−	0.0286571i
$181$	7.41727	+	17.9069i	0.551322	+	1.33101i	0.916487	+	0.400065i	$0.131013\pi$
$181$	7.41727	+	17.9069i	0.551322	+	1.33101i	−0.365165	+	0.930943i	$0.618987\pi$
$182$	2.86302	+	1.18590i	0.212221	+	0.0879050i
$183$		−	4.14652i		−	0.306520i
$184$	7.53271	−	18.1856i	0.555319	−	1.34066i
$185$	−0.647418	+	0.647418i	−0.0475991	+	0.0475991i
$186$	4.10232			0.300796
$187$	2.89142	−	12.8908i	0.211441	−	0.942670i
$188$	3.19164			0.232774
$189$	0.707107	−	0.707107i	0.0514344	−	0.0514344i
$190$	−0.00394112	+	0.00951470i	−0.000285919	+	0.000690269i
$191$		−	19.1237i		−	1.38374i	−0.722020	−	0.691872i	$-0.756786\pi$
$191$		−	19.1237i		−	1.38374i	0.722020	−	0.691872i	$-0.243214\pi$
$192$	8.20267	+	3.39766i	0.591976	+	0.245205i
$193$	3.01861	+	7.28758i	0.217285	+	0.524571i	0.994509	−	0.104652i	$-0.0333730\pi$
$193$	3.01861	+	7.28758i	0.217285	+	0.524571i	−0.777224	+	0.629224i	$0.783373\pi$
$194$	6.10472	−	2.52866i	0.438293	−	0.181547i
$195$	−4.71657	−	4.71657i	−0.337761	−	0.337761i
$196$	0.258125	+	0.258125i	0.0184375	+	0.0184375i
$197$	−19.7338	+	8.17402i	−1.40598	+	0.582375i	−0.951296	−	0.308280i	$-0.900247\pi$
$197$	−19.7338	+	8.17402i	−1.40598	+	0.582375i	−0.454681	+	0.890654i	$0.650247\pi$
$198$	−1.56786	−	3.78515i	−0.111423	−	0.268999i
$199$	5.33429	+	2.20953i	0.378137	+	0.156630i	0.563653	−	0.826012i	$-0.309396\pi$
$199$	5.33429	+	2.20953i	0.378137	+	0.156630i	−0.185516	+	0.982641i	$0.559396\pi$
$200$			7.78630i			0.550575i
$201$	−2.48698	+	6.00411i	−0.175418	+	0.423497i
$202$	11.7811	−	11.7811i	0.828914	−	0.828914i
$203$	5.74620			0.403304
$204$	−0.805543	−	1.27140i	−0.0563993	−	0.0890160i
$205$	23.9107			1.66999
$206$	1.74735	−	1.74735i	0.121744	−	0.121744i
$207$	−2.49092	+	6.01360i	−0.173131	+	0.417974i
$208$		−	7.60192i		−	0.527098i
$209$	−0.00866308	−	0.00358836i	−0.000599237	−	0.000248212i
$210$	1.34672	+	3.25127i	0.0929326	+	0.224359i
$211$	−14.8254	+	6.14089i	−1.02062	+	0.422757i	−0.829320	−	0.558774i	$-0.811272\pi$
$211$	−14.8254	+	6.14089i	−1.02062	+	0.422757i	−0.191305	+	0.981531i	$0.561272\pi$
$212$	−1.74525	−	1.74525i	−0.119864	−	0.119864i
$213$	11.6599	+	11.6599i	0.798923	+	0.798923i
$214$	−10.5683	+	4.37752i	−0.722433	+	0.299241i
$215$	0.0221248	+	0.0534140i	0.00150890	+	0.00364281i
$216$	−2.79388	−	1.15726i	−0.190099	−	0.0787417i
$217$		−	3.20831i		−	0.217794i
$218$	4.14021	−	9.99536i	0.280411	−	0.676971i
$219$	4.58460	−	4.58460i	0.309799	−	0.309799i
$220$	−3.21917			−0.217037
$221$	−5.75185	+	8.17125i	−0.386912	+	0.549658i
$222$	0.425371			0.0285490
$223$	19.6432	−	19.6432i	1.31541	−	1.31541i	0.398036	−	0.917370i	$-0.369692\pi$
$223$	19.6432	−	19.6432i	1.31541	−	1.31541i	0.917370	−	0.398036i	$-0.130308\pi$
$224$	0.779697	−	1.88236i	0.0520957	−	0.125770i
$225$		−	2.57477i		−	0.171652i
$226$	−6.43783	−	2.66663i	−0.428238	−	0.177382i
$227$	5.33452	+	12.8787i	0.354064	+	0.854787i	0.996110	+	0.0881205i	$0.0280860\pi$
$227$	5.33452	+	12.8787i	0.354064	+	0.854787i	−0.642045	+	0.766667i	$0.721914\pi$
$228$	−0.000986965	0	0.000408814i	−6.53634e−5	0	2.70744e-5i
$229$	−10.4310	−	10.4310i	−0.689302	−	0.689302i	0.272775	−	0.962078i	$-0.412058\pi$
$229$	−10.4310	−	10.4310i	−0.689302	−	0.689302i	−0.962078	+	0.272775i	$0.912058\pi$
$230$	−16.1973	−	16.1973i	−1.06802	−	1.06802i
$231$	−2.96026	+	1.22618i	−0.194771	+	0.0806768i
$232$	−6.64987	−	16.0542i	−0.436585	−	1.05401i
$233$	22.9154	+	9.49188i	1.50124	+	0.621834i	0.973728	−	0.227715i	$-0.0731253\pi$
$233$	22.9154	+	9.49188i	1.50124	+	0.621834i	0.527511	+	0.849548i	$0.323125\pi$
$234$			3.09891i			0.202582i
$235$	9.20861	−	22.2315i	0.600703	−	1.45023i
$236$	0.539905	−	0.539905i	0.0351448	−	0.0351448i
$237$	14.9661			0.972155
$238$	4.45340	−	2.82161i	0.288671	−	0.182898i
$239$	−13.0277			−0.842692			−0.421346	−	0.906900i	$-0.638442\pi$
$239$	−13.0277			−0.842692			−0.421346	+	0.906900i	$0.638442\pi$
$240$	6.10431	−	6.10431i	0.394032	−	0.394032i
$241$	1.95441	−	4.71836i	0.125895	−	0.303937i	−0.848348	−	0.529439i	$-0.822402\pi$
$241$	1.95441	−	4.71836i	0.125895	−	0.303937i	0.974243	+	0.225503i	$0.0724024\pi$
$242$		−	0.937662i		−	0.0602752i
$243$	0.923880	+	0.382683i	0.0592669	+	0.0245492i
$244$	0.579253	+	1.39844i	0.0370829	+	0.0895260i
$245$	2.54273	−	1.05323i	0.162449	−	0.0672886i
$246$	−7.85497	−	7.85497i	−0.500815	−	0.500815i
$247$	0.00501514	+	0.00501514i	0.000319106	+	0.000319106i
$248$	−8.96363	+	3.71286i	−0.569191	+	0.235767i
$249$	4.52108	+	10.9149i	0.286512	+	0.691701i
$250$	−7.88507	−	3.26610i	−0.498696	−	0.206566i
$251$			7.24657i			0.457399i	0.973497	+	0.228700i	$0.0734474\pi$
$251$			7.24657i			0.457399i	−0.973497	+	0.228700i	$0.926553\pi$
$252$	−0.139696	+	0.337256i	−0.00880003	+	0.0212451i
$253$	14.7475	−	14.7475i	0.927169	−	0.927169i
$254$	4.31939			0.271023
$255$	−11.1802	+	1.94277i	−0.700131	+	0.121661i
$256$	−8.45142			−0.528214
$257$	−0.723023	+	0.723023i	−0.0451009	+	0.0451009i	−0.729298	−	0.684197i	$-0.760153\pi$
$257$	−0.723023	+	0.723023i	−0.0451009	+	0.0451009i	0.684197	+	0.729298i	$0.260153\pi$
$258$	0.0102789	−	0.0248155i	0.000639938	−	0.00154495i
$259$		−	0.332671i		−	0.0206712i
$260$	2.24958	+	0.931806i	0.139513	+	0.0577882i
$261$	2.19898	+	5.30880i	0.136113	+	0.328606i
$262$	0.902823	−	0.373962i	0.0557766	−	0.0231034i
$263$	11.8633	+	11.8633i	0.731520	+	0.731520i	0.970921	−	0.239401i	$-0.0769509\pi$
$263$	11.8633	+	11.8633i	0.731520	+	0.731520i	−0.239401	+	0.970921i	$0.576951\pi$
$264$	6.85160	+	6.85160i	0.421687	+	0.421687i
$265$	−17.1921	+	7.12120i	−1.05610	+	0.437452i
$266$	−0.00143197	−	0.00345709i	−8.77998e−5	−	0.000211968i
$267$	−7.53967	−	3.12303i	−0.461421	−	0.191127i
$268$		−	2.37234i		−	0.144914i
$269$	−7.85847	+	18.9720i	−0.479139	+	1.15675i	0.480874	+	0.876790i	$0.340320\pi$
$269$	−7.85847	+	18.9720i	−0.479139	+	1.15675i	−0.960013	+	0.279955i	$0.909680\pi$
$270$	−2.48842	+	2.48842i	−0.151440	+	0.151440i
$271$	−9.35234			−0.568114			−0.284057	−	0.958807i	$-0.591680\pi$
$271$	−9.35234			−0.568114			−0.284057	+	0.958807i	$0.591680\pi$
$272$	−10.5755	−	7.44420i	−0.641231	−	0.451371i
$273$	2.42357			0.146681
$274$	−18.1596	+	18.1596i	−1.09706	+	1.09706i
$275$	−3.15714	+	7.62201i	−0.190383	+	0.459624i
$276$		−	2.37610i		−	0.143024i
$277$	25.0290	+	10.3674i	1.50385	+	0.622915i	0.974278	−	0.225351i	$-0.0723528\pi$
$277$	25.0290	+	10.3674i	1.50385	+	0.622915i	0.529571	+	0.848265i	$0.322353\pi$
$278$	10.8877	+	26.2853i	0.653002	+	1.57649i
$279$	2.96409	−	1.22777i	0.177455	−	0.0735045i
$280$	−5.88521	−	5.88521i	−0.351709	−	0.351709i
$281$	15.8335	+	15.8335i	0.944546	+	0.944546i	0.998541	−	0.0539951i	$-0.0171955\pi$
$281$	15.8335	+	15.8335i	0.944546	+	0.944546i	−0.0539951	+	0.998541i	$0.517196\pi$
$282$	−10.3285	+	4.27821i	−0.615054	+	0.254764i
$283$	9.39361	+	22.6782i	0.558392	+	1.34808i	0.911038	+	0.412321i	$0.135282\pi$
$283$	9.39361	+	22.6782i	0.558392	+	1.34808i	−0.352646	+	0.935757i	$0.614718\pi$
$284$	−5.56122	−	2.30353i	−0.329998	−	0.136689i
$285$			0.00805428i			0.000477094i
$286$	3.79983	−	9.17360i	0.224689	−	0.542446i
$287$	−6.14316	+	6.14316i	−0.362619	+	0.362619i
$288$	2.03745			0.120058
$289$	5.73496	+	16.0034i	0.337350	+	0.941379i
$290$	−20.2218			−1.18746
$291$	3.65411	−	3.65411i	0.214208	−	0.214208i
$292$	−0.905735	+	2.18664i	−0.0530041	+	0.127963i
$293$			8.87511i			0.518490i	0.965812	+	0.259245i	$0.0834736\pi$
$293$			8.87511i			0.518490i	−0.965812	+	0.259245i	$0.916526\pi$
$294$	−1.18132	−	0.489320i	−0.0688961	−	0.0285377i
$295$	−2.20299	−	5.31848i	−0.128263	−	0.309654i
$296$	−0.929442	+	0.384988i	−0.0540227	+	0.0223769i
$297$	−2.26569	−	2.26569i	−0.131469	−	0.131469i
$298$	−14.3563	−	14.3563i	−0.831637	−	0.831637i
$299$	−14.5744	+	6.03692i	−0.842860	+	0.349124i
$300$	0.359686	+	0.868359i	0.0207665	+	0.0501347i
$301$	−0.0194075	−	0.00803886i	−0.00111863	−	0.000463352i
$302$		−	2.06811i		−	0.119006i
$303$	4.98639	−	12.0382i	0.286461	−	0.691578i
$304$	−0.00649073	+	0.00649073i	−0.000372269	+	0.000372269i
$305$	11.4122			0.653460
$306$	4.31107	+	3.03462i	0.246448	+	0.173478i
$307$	−8.17761			−0.466721			−0.233361	−	0.972390i	$-0.574972\pi$
$307$	−8.17761			−0.466721			−0.233361	+	0.972390i	$0.574972\pi$
$308$	0.827075	−	0.827075i	0.0471270	−	0.0471270i
$309$	0.739575	−	1.78549i	0.0420730	−	0.101573i
$310$			11.2905i			0.641259i
$311$	22.5859	+	9.35537i	1.28073	+	0.530495i	0.916209	−	0.400701i	$-0.131234\pi$
$311$	22.5859	+	9.35537i	1.28073	+	0.530495i	0.364519	+	0.931196i	$0.381234\pi$
$312$	−2.80471	−	6.77117i	−0.158786	−	0.383342i
$313$	−22.5289	+	9.33178i	−1.27341	+	0.527463i	−0.913999	−	0.405716i	$-0.867022\pi$
$313$	−22.5289	+	9.33178i	−1.27341	+	0.527463i	−0.359410	+	0.933180i	$0.617022\pi$
$314$	−22.4736	−	22.4736i	−1.26826	−	1.26826i
$315$	1.94612	+	1.94612i	0.109651	+	0.109651i
$316$	−5.04742	+	2.09071i	−0.283940	+	0.117612i
$317$	−5.83722	−	14.0923i	−0.327851	−	0.791502i	−0.998751	−	0.0499546i	$-0.984092\pi$
$317$	−5.83722	−	14.0923i	−0.327851	−	0.791502i	0.670901	−	0.741547i	$-0.265908\pi$
$318$	7.98724	+	3.30842i	0.447902	+	0.185527i
$319$		−	18.4118i		−	1.03086i
$320$	−9.35113	+	22.5756i	−0.522744	+	1.26202i
$321$	−6.32588	+	6.32588i	−0.353076	+	0.353076i
$322$	8.32286			0.463815
$323$	0.0118879	−	0.00206575i	0.000661462	−	0.000114941i
$324$	−0.365044			−0.0202802
$325$	4.41246	−	4.41246i	0.244759	−	0.244759i
$326$	4.12761	−	9.96494i	0.228607	−	0.551907i
$327$		−	8.46116i		−	0.467903i
$328$	24.2725	+	10.0540i	1.34022	+	0.555139i
$329$	3.34587	+	8.07764i	0.184464	+	0.445335i
$330$	10.4176	−	4.31512i	0.573471	−	0.237539i
$331$	6.16883	+	6.16883i	0.339069	+	0.339069i	0.856017	−	0.516948i	$-0.172932\pi$
$331$	6.16883	+	6.16883i	0.339069	+	0.339069i	−0.516948	+	0.856017i	$0.672932\pi$
$332$	−3.04952	−	3.04952i	−0.167364	−	0.167364i
$333$	0.307348	−	0.127308i	0.0168426	−	0.00697641i
$334$	−1.92318	−	4.64297i	−0.105232	−	0.254052i
$335$	−16.5247	−	6.84475i	−0.902840	−	0.373969i
$336$			3.13666i			0.171119i
$337$	9.48472	−	22.8981i	0.516665	−	1.24734i	−0.423275	−	0.906001i	$-0.639119\pi$
$337$	9.48472	−	22.8981i	0.516665	−	1.24734i	0.939940	−	0.341339i	$-0.110881\pi$
$338$	6.44320	−	6.44320i	0.350464	−	0.350464i
$339$	−5.44968			−0.295986
$340$	3.49920	−	2.21704i	0.189770	−	0.120236i
$341$	−10.2800			−0.556691
$342$	0.00264594	−	0.00264594i	0.000143076	−	0.000143076i
$343$	−0.382683	+	0.923880i	−0.0206630	+	0.0498848i
$344$			0.0635254i			0.00342506i
$345$	−16.5508	−	6.85557i	−0.891066	−	0.369092i
$346$	−3.40974	−	8.23184i	−0.183309	−	0.442546i
$347$	11.5833	−	4.79795i	0.621822	−	0.257567i	−0.0494517	−	0.998777i	$-0.515747\pi$
$347$	11.5833	−	4.79795i	0.621822	−	0.257567i	0.671274	+	0.741209i	$0.265747\pi$
$348$	−1.48324	−	1.48324i	−0.0795099	−	0.0795099i
$349$	−10.6974	−	10.6974i	−0.572619	−	0.572619i	0.360240	−	0.932860i	$-0.382695\pi$
$349$	−10.6974	−	10.6974i	−0.572619	−	0.572619i	−0.932860	+	0.360240i	$0.882695\pi$
$350$	−3.04164	+	1.25989i	−0.162582	+	0.0673438i
$351$	0.927462	+	2.23909i	0.0495042	+	0.119514i
$352$	−6.03138	−	2.49828i	−0.321474	−	0.133159i
$353$		−	3.26611i		−	0.173838i	−0.996215	−	0.0869188i	$-0.972298\pi$
$353$		−	3.26611i		−	0.173838i	0.996215	−	0.0869188i	$-0.0277021\pi$
$354$	−1.02348	+	2.47090i	−0.0543975	+	0.131327i
$355$	−32.0907	+	32.0907i	−1.70320	+	1.70320i
$356$	2.97908			0.157891
$357$	2.37329	−	3.37157i	0.125608	−	0.178442i
$358$	6.21838			0.328651
$359$	−21.5050	+	21.5050i	−1.13499	+	1.13499i	−0.145656	+	0.989335i	$0.546529\pi$
$359$	−21.5050	+	21.5050i	−1.13499	+	1.13499i	−0.989335	+	0.145656i	$0.953471\pi$
$360$	3.18505	−	7.68940i	0.167867	−	0.405267i
$361$			19.0000i			1.00000i
$362$	22.8967	+	9.48413i	1.20342	+	0.498475i
$363$	−0.280629	−	0.677499i	−0.0147292	−	0.0355595i
$364$	−0.817366	+	0.338564i	−0.0428416	+	0.0177456i
$365$	12.6179	+	12.6179i	0.660450	+	0.660450i
$366$	−3.74906	−	3.74906i	−0.195966	−	0.195966i
$367$	−11.1070	+	4.60068i	−0.579781	+	0.240153i	−0.653248	−	0.757144i	$-0.726594\pi$
$367$	−11.1070	+	4.60068i	−0.579781	+	0.240153i	0.0734662	+	0.997298i	$0.476594\pi$
$368$	−7.81314	−	18.8626i	−0.407288	−	0.983281i
$369$	−8.02642	−	3.32465i	−0.417839	−	0.173075i
$370$			1.17072i			0.0608628i
$371$	2.58743	−	6.24660i	0.134333	−	0.324307i
$372$	−0.828144	+	0.828144i	−0.0429373	+	0.0429373i
$373$	20.6521			1.06932			0.534662	−	0.845066i	$-0.320439\pi$
$373$	20.6521			1.06932			0.534662	+	0.845066i	$0.320439\pi$
$374$	−9.04091	−	14.2694i	−0.467494	−	0.737855i
$375$	−6.67478			−0.344684
$376$	18.6959	−	18.6959i	0.964168	−	0.964168i
$377$	−5.32938	+	12.8663i	−0.274477	+	0.662647i
$378$		−	1.27865i		−	0.0657669i
$379$	11.6589	+	4.82928i	0.598878	+	0.248063i	0.661465	−	0.749976i	$-0.269935\pi$
$379$	11.6589	+	4.82928i	0.598878	+	0.248063i	−0.0625871	+	0.998040i	$0.519935\pi$
$380$	−0.00112515	−	0.00271636i	−5.77190e−5	−	0.000139346i
$381$	3.12093	−	1.29273i	0.159890	−	0.0662287i
$382$	−17.2906	−	17.2906i	−0.884665	−	0.884665i
$383$	−21.8161	−	21.8161i	−1.11475	−	1.11475i	−0.992499	−	0.122253i	$-0.960988\pi$
$383$	−21.8161	−	21.8161i	−1.11475	−	1.11475i	−0.122253	−	0.992499i	$-0.539012\pi$
$384$	6.72366	−	2.78503i	0.343115	−	0.142123i
$385$	−3.37473	−	8.14733i	−0.171992	−	0.415226i
$386$	9.31829	+	3.85976i	0.474289	+	0.196457i
$387$		−	0.0210066i		−	0.00106782i
$388$	−0.721907	+	1.74284i	−0.0366493	+	0.0884792i
$389$	−21.8115	+	21.8115i	−1.10589	+	1.10589i	−0.112201	+	0.993686i	$0.535790\pi$
$389$	−21.8115	+	21.8115i	−1.10589	+	1.10589i	−0.993686	+	0.112201i	$0.964210\pi$
$390$	−8.52892			−0.431879
$391$	−5.87375	+	26.1869i	−0.297048	+	1.32433i
$392$	3.02407			0.152739
$393$	0.540405	−	0.540405i	0.0272598	−	0.0272598i
$394$	−10.4517	+	25.2327i	−0.526551	+	1.27121i
$395$			41.1903i			2.07251i
$396$	1.08063	+	0.447610i	0.0543035	+	0.0224932i
$397$	−4.65656	−	11.2419i	−0.233706	−	0.564216i	0.762902	−	0.646514i	$-0.223774\pi$
$397$	−4.65656	−	11.2419i	−0.233706	−	0.564216i	−0.996608	+	0.0822985i	$0.973774\pi$
$398$	6.82071	−	2.82523i	0.341891	−	0.141616i
$399$	−0.00206932	−	0.00206932i	−0.000103595	−	0.000103595i
$400$	5.71072	+	5.71072i	0.285536	+	0.285536i
$401$	20.3614	−	8.43397i	1.01680	−	0.421172i	0.188869	−	0.982002i	$-0.439518\pi$
$401$	20.3614	−	8.43397i	1.01680	−	0.421172i	0.827931	+	0.560830i	$0.189518\pi$
$402$	3.17999	+	7.67717i	0.158603	+	0.382903i
$403$	7.18369	+	2.97558i	0.357845	+	0.148224i
$404$			4.75655i			0.236647i
$405$	−1.05323	+	2.54273i	−0.0523356	+	0.126349i
$406$	5.19540	−	5.19540i	0.257843	−	0.257843i
$407$	−1.06593			−0.0528363
$408$	−12.1663	−	2.72890i	−0.602321	−	0.135101i
$409$	−33.2786			−1.64552			−0.822761	−	0.568387i	$-0.807568\pi$
$409$	−33.2786			−1.64552			−0.822761	+	0.568387i	$0.807568\pi$
$410$	21.6187	−	21.6187i	1.06767	−	1.06767i
$411$	−7.68614	+	18.5560i	−0.379129	+	0.915299i
$412$			0.705484i			0.0347567i
$413$	1.93243	+	0.800437i	0.0950885	+	0.0393869i
$414$	3.18502	+	7.68932i	0.156535	+	0.377909i
$415$	−30.0402	+	12.4431i	−1.47461	+	0.610805i
$416$	3.49163	+	3.49163i	0.171191	+	0.171191i
$417$	15.7336	+	15.7336i	0.770480	+	0.770480i
$418$	−0.0110771	+	0.00458828i	−0.000541798	+	0.000224420i
$419$	−8.12432	−	19.6138i	−0.396899	−	0.958199i	−0.988397	−	0.151893i	$-0.951463\pi$
$419$	−8.12432	−	19.6138i	−0.396899	−	0.958199i	0.591498	−	0.806306i	$-0.298537\pi$
$420$	−0.928207	−	0.384476i	−0.0452919	−	0.0187605i
$421$		−	31.6618i		−	1.54310i	−0.636167	−	0.771551i	$-0.719481\pi$
$421$		−	31.6618i		−	1.54310i	0.636167	−	0.771551i	$-0.280519\pi$
$422$	−7.85208	+	18.9566i	−0.382233	+	0.922793i
$423$	−6.18236	+	6.18236i	−0.300597	+	0.300597i
$424$	−20.4466			−0.992974
$425$	−1.81750	−	10.4593i	−0.0881618	−	0.507352i
$426$	21.0845			1.02155
$427$	−2.93203	+	2.93203i	−0.141891	+	0.141891i
$428$	1.24974	−	3.01714i	0.0604085	−	0.145839i
$429$		−	7.76553i		−	0.374924i
$430$	0.0682981	+	0.0282900i	0.00329362	+	0.00136426i
$431$	−5.92511	−	14.3045i	−0.285402	−	0.689022i	0.714542	−	0.699593i	$-0.246635\pi$
$431$	−5.92511	−	14.3045i	−0.285402	−	0.689022i	−0.999944	+	0.0105704i	$0.996635\pi$
$432$	−2.89789	+	1.20035i	−0.139425	+	0.0577517i
$433$	3.93227	+	3.93227i	0.188973	+	0.188973i	0.795252	−	0.606279i	$-0.207339\pi$
$433$	3.93227	+	3.93227i	0.188973	+	0.188973i	−0.606279	+	0.795252i	$0.707339\pi$
$434$	−2.90078	−	2.90078i	−0.139242	−	0.139242i
$435$	−14.6110	+	6.05209i	−0.700546	+	0.290176i
$436$	1.18199	+	2.85358i	0.0566071	+	0.136662i
$437$	0.0175985	+	0.00728955i	0.000841852	+	0.000348706i
$438$		−	8.29029i		−	0.396126i
$439$	5.35908	−	12.9380i	0.255775	−	0.617495i	−0.742876	−	0.669430i	$-0.766539\pi$
$439$	5.35908	−	12.9380i	0.255775	−	0.617495i	0.998651	+	0.0519341i	$0.0165386\pi$
$440$	−18.8572	+	18.8572i	−0.898982	+	0.898982i
$441$	−1.00000			−0.0476190
$442$	2.18748	+	12.5885i	0.104048	+	0.598774i
$443$	11.3060			0.537167			0.268583	−	0.963256i	$-0.413445\pi$
$443$	11.3060			0.537167			0.268583	+	0.963256i	$0.413445\pi$
$444$	−0.0858706	+	0.0858706i	−0.00407524	+	0.00407524i
$445$	8.59531	−	20.7509i	0.407457	−	0.983688i
$446$		−	35.5206i		−	1.68195i
$447$	−14.6696	−	6.07636i	−0.693850	−	0.287402i
$448$	−3.39766	−	8.20267i	−0.160524	−	0.387540i
$449$	11.6109	−	4.80940i	0.547953	−	0.226970i	−0.0914926	−	0.995806i	$-0.529164\pi$
$449$	11.6109	−	4.80940i	0.547953	−	0.226970i	0.639446	+	0.768836i	$0.279164\pi$
$450$	−2.32797	−	2.32797i	−0.109742	−	0.109742i
$451$	19.6837	+	19.6837i	0.926869	+	0.926869i
$452$	1.83794	−	0.761299i	0.0864493	−	0.0358085i
$453$	−0.618957	−	1.49429i	−0.0290811	−	0.0702081i
$454$	16.4674	+	6.82100i	0.772851	+	0.320126i
$455$			6.67024i			0.312705i
$456$	−0.00338668	+	0.00817616i	−0.000158596	+	0.000382884i
$457$	−10.4801	+	10.4801i	−0.490237	+	0.490237i	−0.908381	−	0.418144i	$-0.862681\pi$
$457$	−10.4801	+	10.4801i	−0.490237	+	0.490237i	0.418144	+	0.908381i	$0.362681\pi$
$458$	−18.8623			−0.881379
$459$	4.02314	+	0.902393i	0.187784	+	0.0421201i
$460$	6.53956			0.304909
$461$	4.92461	−	4.92461i	0.229362	−	0.229362i	−0.583064	−	0.812426i	$-0.698146\pi$
$461$	4.92461	−	4.92461i	0.229362	−	0.229362i	0.812426	+	0.583064i	$0.198146\pi$
$462$	−1.56786	+	3.78515i	−0.0729435	+	0.176101i
$463$			27.4504i			1.27573i	0.770149	+	0.637865i	$0.220182\pi$
$463$			27.4504i			1.27573i	−0.770149	+	0.637865i	$0.779818\pi$
$464$	−16.6519	−	6.89743i	−0.773044	−	0.320205i
$465$	3.37910	+	8.15786i	0.156702	+	0.378312i
$466$	29.3009	−	12.1368i	1.35734	−	0.562228i
$467$	−8.95834	−	8.95834i	−0.414542	−	0.414542i	0.468775	−	0.883318i	$-0.344695\pi$
$467$	−8.95834	−	8.95834i	−0.414542	−	0.414542i	−0.883318	+	0.468775i	$0.844695\pi$
$468$	−0.625585	−	0.625585i	−0.0289177	−	0.0289177i
$469$	6.00411	−	2.48698i	0.277244	−	0.114838i
$470$	−11.7746	−	28.4265i	−0.543123	−	1.31121i
$471$	−22.9641	−	9.51205i	−1.05813	−	0.438292i
$472$		−	6.32528i		−	0.291145i
$473$	−0.0257579	+	0.0621850i	−0.00118435	+	0.00285927i
$474$	13.5316	−	13.5316i	0.621525	−	0.621525i
$475$	−0.00753496			−0.000345728
$476$	−0.329413	+	1.46862i	−0.0150986	+	0.0673142i
$477$	6.76127			0.309577
$478$	−11.7789	+	11.7789i	−0.538756	+	0.538756i
$479$	12.8853	−	31.1078i	0.588742	−	1.42135i	−0.295963	−	0.955199i	$-0.595641\pi$
$479$	12.8853	−	31.1078i	0.588742	−	1.42135i	0.884706	−	0.466150i	$-0.154359\pi$
$480$			5.60752i			0.255947i
$481$	0.744880	+	0.308539i	0.0339636	+	0.0140682i
$482$	−2.49902	−	6.03316i	−0.113827	−	0.274803i
$483$	6.01360	−	2.49092i	0.273628	−	0.113341i
$484$	0.189288	+	0.189288i	0.00860400	+	0.00860400i
$485$	10.0570	+	10.0570i	0.456663	+	0.456663i
$486$	1.18132	−	0.489320i	0.0535859	−	0.0221960i
$487$	4.39198	+	10.6032i	0.199020	+	0.480476i	0.991608	−	0.129281i	$-0.0412670\pi$
$487$	4.39198	+	10.6032i	0.199020	+	0.480476i	−0.792588	+	0.609757i	$0.791267\pi$
$488$	11.5849	+	4.79861i	0.524423	+	0.217223i
$489$		−	8.43541i		−	0.381462i
$490$	1.34672	−	3.25127i	0.0608386	−	0.146877i
$491$	18.6919	−	18.6919i	0.843553	−	0.843553i	−0.145766	−	0.989319i	$-0.546565\pi$
$491$	18.6919	−	18.6919i	0.843553	−	0.843553i	0.989319	+	0.145766i	$0.0465648\pi$
$492$	3.17140			0.142978
$493$	12.6802	+	20.0133i	0.571086	+	0.901356i
$494$	0.00906883			0.000408026
$495$	6.23569	−	6.23569i	0.280274	−	0.280274i
$496$	−3.85108	+	9.29733i	−0.172919	+	0.417463i
$497$		−	16.4896i		−	0.739659i
$498$	13.9563	+	5.78090i	0.625398	+	0.259048i
$499$	8.76718	+	21.1659i	0.392473	+	0.947514i	0.989400	+	0.145218i	$0.0463883\pi$
$499$	8.76718	+	21.1659i	0.392473	+	0.947514i	−0.596927	+	0.802296i	$0.703612\pi$
$500$	2.25111	−	0.932441i	0.100673	−	0.0417000i
$501$	−2.77915	−	2.77915i	−0.124163	−	0.124163i
$502$	6.55195	+	6.55195i	0.292428	+	0.292428i
$503$	37.2612	−	15.4341i	1.66139	−	0.688172i	0.663211	−	0.748432i	$-0.269193\pi$
$503$	37.2612	−	15.4341i	1.66139	−	0.688172i	0.998183	+	0.0602606i	$0.0191932\pi$
$504$	1.15726	+	2.79388i	0.0515486	+	0.124449i
$505$	33.1320	+	13.7237i	1.47435	+	0.610697i
$506$		−	26.6678i		−	1.18553i
$507$	2.72711	−	6.58383i	0.121115	−	0.292398i
$508$	−0.871965	+	0.871965i	−0.0386872	+	0.0386872i
$509$	43.6773			1.93596			0.967981	−	0.251025i	$-0.0807676\pi$
$509$	43.6773			1.93596			0.967981	+	0.251025i	$0.0807676\pi$
$510$	−8.35198	+	11.8651i	−0.369832	+	0.525394i
$511$	−6.48361			−0.286818
$512$	−17.9334	+	17.9334i	−0.792554	+	0.792554i
$513$	0.00111991	−	0.00270369i	4.94450e−5	−	0.000119371i
$514$			1.30743i			0.0576685i
$515$	4.91409	+	2.03548i	0.216541	+	0.0896940i
$516$	0.00293454	+	0.00708460i	0.000129186	+	0.000311882i
$517$	25.8821	−	10.7207i	1.13829	−	0.471497i
$518$	−0.300783	−	0.300783i	−0.0132156	−	0.0132156i
$519$	−4.92735	−	4.92735i	−0.216287	−	0.216287i
$520$	18.6358	−	7.71921i	0.817235	−	0.338510i
$521$	−14.1515	−	34.1648i	−0.619990	−	1.49679i	−0.851714	−	0.524007i	$-0.824436\pi$
$521$	−14.1515	−	34.1648i	−0.619990	−	1.49679i	0.231724	−	0.972782i	$-0.425564\pi$
$522$	6.78812	+	2.81173i	0.297108	+	0.123066i
$523$		−	1.99829i		−	0.0873790i	−0.999045	−	0.0436895i	$-0.986089\pi$
$523$		−	1.99829i		−	0.0873790i	0.999045	−	0.0436895i	$-0.0139112\pi$
$524$	−0.106762	+	0.257747i	−0.00466394	+	0.0112597i
$525$	−1.82064	+	1.82064i	−0.0794592	+	0.0794592i
$526$	21.4522			0.935361
$527$	11.1742	−	7.07979i	0.486754	−	0.308400i
$528$	10.0504			0.437386
$529$	−13.6953	+	13.6953i	−0.595447	+	0.595447i
$530$	−9.10555	+	21.9827i	−0.395520	+	0.954869i
$531$			2.09164i			0.0907696i
$532$	0.000986965	0	0.000408814i	4.27904e−5	0	1.77243e-5i
$533$	−8.05754	−	19.4526i	−0.349011	−	0.842587i
$534$	−9.64063	+	3.99328i	−0.417191	+	0.172806i
$535$	−17.4103	−	17.4103i	−0.752712	−	0.752712i
$536$	−13.8967	−	13.8967i	−0.600244	−	0.600244i
$537$	4.49303	−	1.86107i	0.193889	−	0.0803113i
$538$	10.0483	+	24.2587i	0.433212	+	1.04587i
$539$	2.96026	+	1.22618i	0.127508	+	0.0528154i
$540$		−	1.00468i		−	0.0432347i
$541$	−17.7837	+	42.9336i	−0.764581	+	1.84586i	−0.340425	+	0.940272i	$0.610571\pi$
$541$	−17.7837	+	42.9336i	−0.764581	+	1.84586i	−0.424155	+	0.905589i	$0.639429\pi$
$542$	−8.45587	+	8.45587i	−0.363211	+	0.363211i
$543$	19.3823			0.831773
$544$	8.27658	−	1.43821i	0.354856	−	0.0616627i
$545$	23.2871			0.997509
$546$	2.19126	−	2.19126i	0.0937774	−	0.0937774i
$547$	5.46285	−	13.1885i	0.233574	−	0.563899i	−0.763018	−	0.646377i	$-0.776283\pi$
$547$	5.46285	−	13.1885i	0.233574	−	0.563899i	0.996593	+	0.0824781i	$0.0262834\pi$
$548$		−	7.33185i		−	0.313201i
$549$	−3.83089	−	1.58680i	−0.163498	−	0.0677232i
$550$	4.03689	+	9.74591i	0.172134	+	0.415567i
$551$	0.0155360	−	0.00643521i	0.000661854	−	0.000274149i
$552$	−13.9186	−	13.9186i	−0.592416	−	0.592416i
$553$	−10.5827	−	10.5827i	−0.450020	−	0.450020i
$554$	32.0035	−	13.2563i	1.35970	−	0.563205i
$555$	0.350380	+	0.845892i	0.0148728	+	0.0359061i
$556$	−7.50420	−	3.10834i	−0.318249	−	0.131823i
$557$		−	0.809691i		−	0.0343077i	−0.999853	−	0.0171538i	$-0.994539\pi$
$557$		−	0.809691i		−	0.0343077i	0.999853	−	0.0171538i	$-0.00546051\pi$
$558$	1.56989	−	3.79005i	0.0664587	−	0.160445i
$559$	0.0359995	−	0.0359995i	0.00152262	−	0.00152262i
$560$	−8.63280			−0.364802
$561$	−10.8031	−	7.60443i	−0.456106	−	0.321059i
$562$	28.6315			1.20775
$563$	1.92827	−	1.92827i	0.0812667	−	0.0812667i	−0.665305	−	0.746572i	$-0.731698\pi$
$563$	1.92827	−	1.92827i	0.0812667	−	0.0812667i	0.746572	+	0.665305i	$0.231698\pi$
$564$	1.22139	−	2.94869i	0.0514297	−	0.124162i
$565$		−	14.9988i		−	0.631003i
$566$	28.9976	+	12.0112i	1.21886	+	0.504868i
$567$	−0.382683	−	0.923880i	−0.0160712	−	0.0387993i
$568$	−46.0699	+	19.0828i	−1.93305	+	0.800696i
$569$	11.8353	+	11.8353i	0.496162	+	0.496162i	0.910241	−	0.414079i	$-0.135896\pi$
$569$	11.8353	+	11.8353i	0.496162	+	0.496162i	−0.414079	+	0.910241i	$0.635896\pi$
$570$	0.00728223	+	0.00728223i	0.000305019	+	0.000305019i
$571$	−6.32499	+	2.61990i	−0.264693	+	0.109639i	−0.511083	−	0.859531i	$-0.670755\pi$
$571$	−6.32499	+	2.61990i	−0.264693	+	0.109639i	0.246390	+	0.969171i	$0.420755\pi$
$572$	1.08482	+	2.61898i	0.0453584	+	0.109505i
$573$	−17.6680	−	7.31833i	−0.738092	−	0.305728i
$574$			11.1086i			0.463664i
$575$	6.41354	−	15.4837i	0.267463	−	0.645713i
$576$	6.27805	−	6.27805i	0.261585	−	0.261585i
$577$	−5.28827			−0.220154			−0.110077	−	0.993923i	$-0.535110\pi$
$577$	−5.28827			−0.220154			−0.110077	+	0.993923i	$0.535110\pi$
$578$	19.6547	+	9.28420i	0.817526	+	0.386172i
$579$	7.88802			0.327815
$580$	4.08221	−	4.08221i	0.169505	−	0.169505i
$581$	4.52108	−	10.9149i	0.187566	−	0.452824i
$582$		−	6.60770i		−	0.273898i
$583$	−20.0151	−	8.29055i	−0.828943	−	0.343359i
$584$	7.50324	+	18.1144i	0.310486	+	0.749580i
$585$	−6.16249	+	2.55259i	−0.254788	+	0.105537i
$586$	8.02439	+	8.02439i	0.331484	+	0.331484i
$587$	0.718111	+	0.718111i	0.0296396	+	0.0296396i	0.721771	−	0.692132i	$-0.243328\pi$
$587$	0.718111	+	0.718111i	0.0296396	+	0.0296396i	−0.692132	+	0.721771i	$0.743328\pi$
$588$	0.337256	−	0.139696i	0.0139082	−	0.00576097i
$589$	−0.00359300	−	0.00867428i	−0.000148047	−	0.000357417i
$590$	−6.80050	−	2.81686i	−0.279972	−	0.115968i
$591$			21.3597i			0.878622i
$592$	−0.399320	+	0.964044i	−0.0164120	+	0.0396220i
$593$	−11.1024	+	11.1024i	−0.455923	+	0.455923i	−0.897315	−	0.441392i	$-0.854485\pi$
$593$	−11.1024	+	11.1024i	−0.455923	+	0.455923i	0.441392	+	0.897315i	$0.354485\pi$
$594$	−4.09702			−0.168103
$595$	9.27934	+	6.53185i	0.380416	+	0.267780i
$596$	5.79627			0.237425
$597$	4.08269	−	4.08269i	0.167093	−	0.167093i
$598$	−7.71913	+	18.6356i	−0.315659	+	0.762068i
$599$		−	12.0085i		−	0.490652i	−0.969441	−	0.245326i	$-0.921105\pi$
$599$		−	12.0085i		−	0.490652i	0.969441	−	0.245326i	$-0.0788950\pi$
$600$	7.19361	+	2.97969i	0.293678	+	0.121645i
$601$	−8.42470	−	20.3390i	−0.343651	−	0.829647i	−0.997340	−	0.0728838i	$-0.976780\pi$
$601$	−8.42470	−	20.3390i	−0.343651	−	0.829647i	0.653690	−	0.756763i	$-0.273220\pi$
$602$	−0.0248155	+	0.0102789i	−0.00101141	+	0.000418938i
$603$	4.59534	+	4.59534i	0.187137	+	0.187137i
$604$	0.417494	+	0.417494i	0.0169876	+	0.0169876i
$605$	1.86463	−	0.772357i	0.0758081	−	0.0314008i
$606$	−6.37587	−	15.3927i	−0.259002	−	0.625287i
$607$	33.7590	+	13.9834i	1.37024	+	0.567571i	0.941853	−	0.336026i	$-0.109083\pi$
$607$	33.7590	+	13.9834i	1.37024	+	0.567571i	0.428384	+	0.903597i	$0.359083\pi$
$608$		−	0.00596250i		−	0.000241811i
$609$	2.19898	−	5.30880i	0.0891070	−	0.215123i
$610$	10.3183	−	10.3183i	0.417774	−	0.417774i
$611$	−21.1897			−0.857245
$612$	−1.48289	+	0.257680i	−0.0599423	+	0.0104161i
$613$	35.5715			1.43672			0.718360	−	0.695671i	$-0.244893\pi$
$613$	35.5715			1.43672			0.718360	+	0.695671i	$0.244893\pi$
$614$	−7.39375	+	7.39375i	−0.298387	+	0.298387i
$615$	9.15021	−	22.0906i	0.368972	−	0.890778i
$616$		−	9.68963i		−	0.390406i
$617$	21.7594	+	9.01303i	0.876000	+	0.362851i	0.774944	−	0.632030i	$-0.217778\pi$
$617$	21.7594	+	9.01303i	0.876000	+	0.362851i	0.101056	+	0.994881i	$0.467778\pi$
$618$	−0.945661	−	2.28303i	−0.0380401	−	0.0918368i
$619$	−38.4826	+	15.9400i	−1.54675	+	0.640683i	−0.982724	−	0.185077i	$-0.940746\pi$
$619$	−38.4826	+	15.9400i	−1.54675	+	0.640683i	−0.564021	+	0.825760i	$0.690746\pi$
$620$	−2.27924	−	2.27924i	−0.0915366	−	0.0915366i
$621$	4.60261	+	4.60261i	0.184696	+	0.184696i
$622$	28.8795	−	11.9623i	1.15796	−	0.479644i
$623$	3.12303	+	7.53967i	0.125122	+	0.302071i
$624$	−7.02326	−	2.90913i	−0.281155	−	0.116458i
$625$		−	31.2444i		−	1.24978i
$626$	−11.9321	+	28.8067i	−0.476903	+	1.15135i
$627$	−0.00663043	+	0.00663043i	−0.000264794	+	0.000264794i
$628$	9.07359			0.362076
$629$	1.15865	−	0.734106i	0.0461985	−	0.0292707i
$630$	3.51915			0.140206
$631$	1.24134	−	1.24134i	0.0494168	−	0.0494168i	−0.681967	−	0.731383i	$-0.738875\pi$
$631$	1.24134	−	1.24134i	0.0494168	−	0.0494168i	0.731383	+	0.681967i	$0.238875\pi$
$632$	−17.3198	+	41.8136i	−0.688943	+	1.66325i
$633$			16.0469i			0.637808i
$634$	−18.0192	−	7.46378i	−0.715632	−	0.296425i
$635$	3.55790	+	8.58953i	0.141191	+	0.340865i
$636$	−2.28028	+	0.944524i	−0.0904190	+	0.0374528i
$637$	−1.71373	−	1.71373i	−0.0679003	−	0.0679003i
$638$	−16.6469	−	16.6469i	−0.659058	−	0.659058i
$639$	15.2344	−	6.31029i	0.602663	−	0.249631i
$640$	7.66505	+	18.5051i	0.302988	+	0.731477i
$641$	7.57661	+	3.13833i	0.299258	+	0.123957i	0.527260	−	0.849704i	$-0.323219\pi$
$641$	7.57661	+	3.13833i	0.299258	+	0.123957i	−0.228002	+	0.973661i	$0.573219\pi$
$642$			11.4390i			0.451462i
$643$	−1.36320	+	3.29107i	−0.0537595	+	0.129787i	−0.948477	−	0.316845i	$-0.897377\pi$
$643$	−1.36320	+	3.29107i	−0.0537595	+	0.129787i	0.894718	+	0.446632i	$0.147377\pi$
$644$	−1.68015	+	1.68015i	−0.0662073	+	0.0662073i
$645$	0.0578149			0.00227646
$646$	0.00888068	−	0.0126162i	0.000349406	−	0.000496376i
$647$	−28.2664			−1.11127			−0.555634	−	0.831427i	$-0.687524\pi$
$647$	−28.2664			−1.11127			−0.555634	+	0.831427i	$0.687524\pi$
$648$	−2.13834	+	2.13834i	−0.0840020	+	0.0840020i
$649$	2.56473	−	6.19181i	0.100675	−	0.243050i
$650$		−	7.97900i		−	0.312962i
$651$	−2.96409	−	1.22777i	−0.116172	−	0.0481200i
$652$	1.17839	+	2.84490i	0.0461495	+	0.111415i
$653$	−7.43248	+	3.07864i	−0.290856	+	0.120476i	−0.523340	−	0.852124i	$-0.675314\pi$
$653$	−7.43248	+	3.07864i	−0.290856	+	0.120476i	0.232485	+	0.972600i	$0.425314\pi$
$654$	−7.65012	−	7.65012i	−0.299143	−	0.299143i
$655$	1.48732	+	1.48732i	0.0581143	+	0.0581143i
$656$	25.1761	−	10.4283i	0.982963	−	0.407156i
$657$	−2.48117	−	5.99007i	−0.0967997	−	0.233695i
$658$	10.3285	+	4.27821i	0.402647	+	0.166782i
$659$		−	40.3508i		−	1.57184i	−0.618325	−	0.785922i	$-0.712189\pi$
$659$		−	40.3508i		−	1.57184i	0.618325	−	0.785922i	$-0.287811\pi$
$660$	−1.23192	+	2.97413i	−0.0479526	+	0.115768i
$661$	−5.70033	+	5.70033i	−0.221717	+	0.221717i	−0.809221	−	0.587504i	$-0.800111\pi$
$661$	−5.70033	+	5.70033i	−0.221717	+	0.221717i	0.587504	+	0.809221i	$0.300111\pi$
$662$	11.1550			0.433552
$663$	5.34811	+	8.44102i	0.207703	+	0.327822i
$664$	−35.7268			−1.38647
$665$	0.00569523	−	0.00569523i	0.000220852	−	0.000220852i
$666$	0.162782	−	0.392992i	0.00630769	−	0.0152281i
$667$			37.4025i			1.44823i
$668$	1.32552	+	0.549050i	0.0512861	+	0.0212434i
$669$	−10.6308	−	25.6651i	−0.411011	−	0.992269i
$670$	−21.1294	+	8.75206i	−0.816298	+	0.338122i
$671$	9.39472	+	9.39472i	0.362679	+	0.362679i
$672$	−1.44069	−	1.44069i	−0.0555759	−	0.0555759i
$673$	−8.28104	+	3.43012i	−0.319211	+	0.132221i	−0.536535	−	0.843878i	$-0.680267\pi$
$673$	−8.28104	+	3.43012i	−0.319211	+	0.132221i	0.217324	+	0.976099i	$0.430267\pi$
$674$	−12.1277	−	29.2788i	−0.467141	−	1.12778i
$675$	−2.37878	−	0.985323i	−0.0915593	−	0.0379251i
$676$			2.60141i			0.100054i
$677$	−10.9344	+	26.3979i	−0.420242	+	1.01456i	0.562033	+	0.827115i	$0.310019\pi$
$677$	−10.9344	+	26.3979i	−0.420242	+	1.01456i	−0.982276	+	0.187441i	$0.939981\pi$
$678$	−4.92730	+	4.92730i	−0.189232	+	0.189232i
$679$	−5.16770			−0.198318
$680$	7.51057	−	33.4844i	0.288017	−	1.28407i
$681$	13.9398			0.534173
$682$	−9.29457	+	9.29457i	−0.355907	+	0.355907i
$683$	−2.35476	+	5.68490i	−0.0901025	+	0.217527i	−0.962506	−	0.271259i	$-0.912560\pi$
$683$	−2.35476	+	5.68490i	−0.0901025	+	0.217527i	0.872404	+	0.488786i	$0.162560\pi$
$684$			0.00106828i			4.08468e-5i
$685$	−51.0704	−	21.1540i	−1.95130	−	0.808254i
$686$	0.489320	+	1.18132i	0.0186823	+	0.0451031i
$687$	−13.6288	+	5.64524i	−0.519971	+	0.215379i
$688$	0.0465915	+	0.0465915i	0.00177629	+	0.00177629i
$689$	11.5870	+	11.5870i	0.441428	+	0.441428i
$690$	−21.1628	+	8.76591i	−0.805653	+	0.333712i
$691$	−5.29450	−	12.7820i	−0.201412	−	0.486252i	0.790609	−	0.612321i	$-0.209764\pi$
$691$	−5.29450	−	12.7820i	−0.201412	−	0.486252i	−0.992021	+	0.126069i	$0.959764\pi$
$692$	2.35011	+	0.973448i	0.0893378	+	0.0370049i
$693$			3.20417i			0.121716i
$694$	6.13491	−	14.8110i	0.232878	−	0.562218i
$695$	−43.3026	+	43.3026i	−1.64256	+	1.64256i
$696$	−17.3769			−0.658671
$697$	−34.9520	−	7.83976i	−1.32390	−	0.296952i
$698$	−19.3440			−0.732182
$699$	17.5387	−	17.5387i	0.663375	−	0.663375i
$700$	0.359686	−	0.868359i	0.0135949	−	0.0328209i
$701$			14.6979i			0.555130i	0.960707	+	0.277565i	$0.0895274\pi$
$701$			14.6979i			0.555130i	−0.960707	+	0.277565i	$0.910473\pi$
$702$	2.86302	+	1.18590i	0.108058	+	0.0447590i
$703$	−0.000372560	0	0.000899439i	−1.40514e−5	0	3.39230e-5i
$704$	−26.2827	+	10.8867i	−0.990567	+	0.410306i
$705$	−17.0153	−	17.0153i	−0.640833	−	0.640833i
$706$	−2.95304	−	2.95304i	−0.111139	−	0.111139i
$707$	−12.0382	+	4.98639i	−0.452744	+	0.187533i
$708$	−0.292194	−	0.705420i	−0.0109813	−	0.0265113i
$709$	−23.9288	−	9.91164i	−0.898666	−	0.372240i	−0.114959	−	0.993370i	$-0.536674\pi$
$709$	−23.9288	−	9.91164i	−0.898666	−	0.372240i	−0.783707	+	0.621131i	$0.786674\pi$
$710$			58.0294i			2.17780i
$711$	5.72729	−	13.8269i	0.214790	−	0.518550i
$712$	17.4508	−	17.4508i	0.653995	−	0.653995i
$713$	20.8831			0.782079
$714$	−0.902586	−	5.19419i	−0.0337784	−	0.194388i
$715$	21.3725			0.799288
$716$	−1.25532	+	1.25532i	−0.0469134	+	0.0469134i
$717$	−4.98549	+	12.0360i	−0.186186	+	0.449494i
$718$			38.8873i			1.45126i
$719$	−42.9393	−	17.7860i	−1.60136	−	0.663307i	−0.609756	−	0.792589i	$-0.708733\pi$
$719$	−42.9393	−	17.7860i	−1.60136	−	0.663307i	−0.991608	+	0.129282i	$0.958733\pi$
$720$	−3.30363	−	7.97567i	−0.123119	−	0.297236i
$721$	−1.78549	+	0.739575i	−0.0664952	+	0.0275432i
$722$	17.1787	+	17.1787i	0.639327	+	0.639327i
$723$	−3.61128	−	3.61128i	−0.134305	−	0.134305i
$724$	−6.53679	+	2.70763i	−0.242938	+	0.100628i
$725$	−5.66187	−	13.6690i	−0.210277	−	0.507652i
$726$	−0.866287	−	0.358828i	−0.0321509	−	0.0133173i
$727$		−	31.9356i		−	1.18443i	−0.805782	−	0.592213i	$-0.798254\pi$
$727$		−	31.9356i		−	1.18443i	0.805782	−	0.592213i	$-0.201746\pi$
$728$	−2.80471	+	6.77117i	−0.103950	+	0.250956i
$729$	0.707107	−	0.707107i	0.0261891	−	0.0261891i
$730$	22.8168			0.844488
$731$	−0.0148283	−	0.0853335i	−0.000548444	−	0.00315617i
$732$	1.51366			0.0559465
$733$	3.84410	−	3.84410i	0.141985	−	0.141985i	−0.632541	−	0.774527i	$-0.717988\pi$
$733$	3.84410	−	3.84410i	0.141985	−	0.141985i	0.774527	+	0.632541i	$0.217988\pi$
$734$	−5.88267	+	14.2020i	−0.217133	+	0.524206i
$735$		−	2.75223i		−	0.101518i
$736$	12.2524	+	5.07511i	0.451629	+	0.187071i
$737$	−7.96870	−	19.2381i	−0.293531	−	0.708646i
$738$	−10.2630	+	4.25108i	−0.377787	+	0.156484i
$739$	−5.10833	−	5.10833i	−0.187913	−	0.187913i	0.606880	−	0.794793i	$-0.292421\pi$
$739$	−5.10833	−	5.10833i	−0.187913	−	0.187913i	−0.794793	+	0.606880i	$0.792421\pi$
$740$	−0.236336	−	0.236336i	−0.00868787	−	0.00868787i
$741$	0.00655260	−	0.00271417i	0.000240716	−	9.97077e-5i
$742$	−3.30842	−	7.98724i	−0.121456	−	0.293221i
$743$	−46.6704	−	19.3315i	−1.71217	−	0.709205i	−0.999974	−	0.00722520i	$-0.997700\pi$
$743$	−46.6704	−	19.3315i	−1.71217	−	0.709205i	−0.712197	−	0.701979i	$-0.752300\pi$
$744$			9.70216i			0.355698i
$745$	16.7236	−	40.3742i	0.612703	−	1.47920i
$746$	18.6725	−	18.6725i	0.683648	−	0.683648i
$747$	11.8141			0.432257
$748$	4.70571	+	1.05549i	0.172058	+	0.0385927i
$749$	8.94614			0.326885
$750$	−6.03497	+	6.03497i	−0.220366	+	0.220366i
$751$	14.1262	−	34.1038i	0.515474	−	1.24446i	−0.425184	−	0.905107i	$-0.639790\pi$
$751$	14.1262	−	34.1038i	0.515474	−	1.24446i	0.940658	−	0.339357i	$-0.110210\pi$
$752$		−	27.4243i		−	1.00006i
$753$	6.69495	+	2.77314i	0.243978	+	0.101059i
$754$	6.81444	+	16.4515i	0.248167	+	0.599129i
$755$	4.11264	−	1.70351i	0.149674	−	0.0619972i
$756$	0.258125	+	0.258125i	0.00938791	+	0.00938791i
$757$	0.108743	+	0.108743i	0.00395232	+	0.00395232i	0.709080	−	0.705128i	$-0.249110\pi$
$757$	0.108743	+	0.108743i	0.00395232	+	0.00395232i	−0.705128	+	0.709080i	$0.749110\pi$
$758$	14.9077	−	6.17497i	0.541472	−	0.224285i
$759$	−7.98131	−	19.2686i	−0.289703	−	0.699405i
$760$	−0.0225027	−	0.00932091i	−0.000816258	−	0.000338105i
$761$			18.2742i			0.662439i	0.943554	+	0.331219i	$0.107460\pi$
$761$			18.2742i			0.662439i	−0.943554	+	0.331219i	$0.892540\pi$
$762$	1.65296	−	3.99060i	0.0598804	−	0.144564i
$763$	−5.98295	+	5.98295i	−0.216597	+	0.216597i
$764$	6.98099			0.252563
$765$	−2.48359	+	11.0726i	−0.0897946	+	0.400331i
$766$	−39.4499			−1.42538
$767$	−3.58450	+	3.58450i	−0.129429	+	0.129429i
$768$	−3.23422	+	7.80810i	−0.116705	+	0.281750i
$769$		−	30.0491i		−	1.08360i	−0.840508	−	0.541799i	$-0.817743\pi$
$769$		−	30.0491i		−	1.08360i	0.840508	−	0.541799i	$-0.182257\pi$
$770$	−10.4176	−	4.31512i	−0.375425	−	0.155506i
$771$	0.391297	+	0.944675i	0.0140922	+	0.0340216i
$772$	−2.66028	+	1.10193i	−0.0957457	+	0.0396592i
$773$	5.49243	+	5.49243i	0.197549	+	0.197549i	0.798949	−	0.601399i	$-0.205390\pi$
$773$	5.49243	+	5.49243i	0.197549	+	0.197549i	−0.601399	+	0.798949i	$0.705390\pi$
$774$	−0.0189930	−	0.0189930i	−0.000682689	−	0.000682689i
$775$	−7.63186	+	3.16122i	−0.274145	+	0.113554i
$776$	5.98038	+	14.4379i	0.214683	+	0.518291i
$777$	−0.307348	−	0.127308i	−0.0110260	−	0.00456714i
$778$			39.4415i			1.41405i
$779$	−0.00972944	+	0.0234890i	−0.000348594	+	0.000841579i
$780$	1.72175	−	1.72175i	0.0616487	−	0.0616487i
$781$	−52.8354			−1.89060
$782$	18.3661	+	28.9875i	0.656770	+	1.03659i
$783$	5.74620			0.205353
$784$	2.21795	−	2.21795i	0.0792125	−	0.0792125i
$785$	26.1794	−	63.2026i	0.934381	−	2.25580i
$786$		−	0.977209i		−	0.0348559i
$787$	16.9958	+	7.03989i	0.605835	+	0.250945i	0.664446	−	0.747336i	$-0.268667\pi$
$787$	16.9958	+	7.03989i	0.605835	+	0.250945i	−0.0586118	+	0.998281i	$0.518667\pi$
$788$	−2.98387	−	7.20370i	−0.106296	−	0.256621i
$789$	15.5001	−	6.42035i	0.551818	−	0.228571i
$790$	37.2420	+	37.2420i	1.32501	+	1.32501i
$791$	3.85350	+	3.85350i	0.137015	+	0.137015i
$792$	8.95205	−	3.70806i	0.318097	−	0.131760i
$793$	−3.84574	−	9.28444i	−0.136566	−	0.329700i
$794$	−14.3745	−	5.95412i	−0.510133	−	0.211304i
$795$			18.6086i			0.659978i
$796$	−0.806576	+	1.94725i	−0.0285883	+	0.0690183i
$797$	−20.9031	+	20.9031i	−0.740427	+	0.740427i	−0.972660	−	0.232233i	$-0.925397\pi$
$797$	−20.9031	+	20.9031i	−0.740427	+	0.740427i	0.232233	+	0.972660i	$0.425397\pi$
$798$	−0.00374192			−0.000132463
$799$	−20.7501	+	29.4782i	−0.734087	+	1.04287i
$800$	−5.24597			−0.185473
$801$	−5.77062	+	5.77062i	−0.203895	+	0.203895i
$802$	10.7841	−	26.0352i	0.380801	−	0.919334i
$803$			20.7746i			0.733118i
$804$	−2.19176	−	0.907857i	−0.0772974	−	0.0320176i
$805$	6.85557	+	16.5508i	0.241627	+	0.583340i
$806$	9.18546	−	3.80474i	0.323544	−	0.134016i
$807$	14.5206	+	14.5206i	0.511148	+	0.511148i
$808$	27.8628	+	27.8628i	0.980209	+	0.980209i
$809$	−33.4547	+	13.8574i	−1.17620	+	0.487200i	−0.883239	−	0.468923i	$-0.844642\pi$
$809$	−33.4547	+	13.8574i	−1.17620	+	0.487200i	−0.292966	+	0.956123i	$0.594642\pi$
$810$	1.34672	+	3.25127i	0.0473189	+	0.114238i
$811$	3.27245	+	1.35549i	0.114911	+	0.0475978i	0.439398	−	0.898292i	$-0.355192\pi$
$811$	3.27245	+	1.35549i	0.114911	+	0.0475978i	−0.324487	+	0.945890i	$0.605192\pi$
$812$			2.09761i			0.0736118i
$813$	−3.57898	+	8.64043i	−0.125520	+	0.303033i
$814$	−0.963758	+	0.963758i	−0.0337797	+	0.0337797i
$815$	23.2162			0.813228
$816$	−10.9246	+	6.92167i	−0.382437	+	0.242307i
$817$	−6.14748e−5	0		−2.15073e−6	0
$818$	−30.0887	+	30.0887i	−1.05203	+	1.05203i
$819$	0.927462	−	2.23909i	0.0324081	−	0.0782402i
$820$			8.72843i			0.304810i
$821$	−25.3033	−	10.4810i	−0.883092	−	0.365789i	−0.105397	−	0.994430i	$-0.533611\pi$
$821$	−25.3033	−	10.4810i	−0.883092	−	0.365789i	−0.777695	+	0.628642i	$0.783611\pi$
$822$	9.82792	+	23.7267i	0.342788	+	0.827563i
$823$	23.8640	−	9.88481i	0.831848	−	0.344563i	0.0742140	−	0.997242i	$-0.476355\pi$
$823$	23.8640	−	9.88481i	0.831848	−	0.344563i	0.757634	+	0.652680i	$0.226355\pi$
$824$	4.13257	+	4.13257i	0.143965	+	0.143965i
$825$	5.83363	+	5.83363i	0.203101	+	0.203101i
$826$	2.47090	−	1.02348i	0.0859737	−	0.0356115i
$827$	−3.50413	−	8.45972i	−0.121851	−	0.294173i	0.851171	−	0.524889i	$-0.175893\pi$
$827$	−3.50413	−	8.45972i	−0.121851	−	0.294173i	−0.973021	+	0.230716i	$0.925893\pi$
$828$	−2.19523	−	0.909293i	−0.0762894	−	0.0316001i
$829$		−	16.6214i		−	0.577285i	−0.957437	−	0.288642i	$-0.906796\pi$
$829$		−	16.6214i		−	0.577285i	0.957437	−	0.288642i	$-0.0932039\pi$
$830$	−15.9104	+	38.4110i	−0.552257	+	1.33327i
$831$	19.1564	−	19.1564i	0.664528	−	0.664528i
$832$	21.5177			0.745992
$833$	−4.06223	+	0.705888i	−0.140748	+	0.0244576i
$834$	28.4510			0.985177
$835$	7.64887	−	7.64887i	0.264700	−	0.264700i
$836$	0.00130991	−	0.00316240i	4.53042e−5	−	0.000109374i
$837$		−	3.20831i		−	0.110895i
$838$	−25.0793	−	10.3882i	−0.866351	−	0.358854i
$839$	−17.5650	−	42.4057i	−0.606411	−	1.46401i	−0.866876	−	0.498523i	$-0.833876\pi$
$839$	−17.5650	−	42.4057i	−0.606411	−	1.46401i	0.260465	−	0.965483i	$-0.416124\pi$
$840$	−7.68940	+	3.18505i	−0.265309	+	0.109895i
$841$	2.84176	+	2.84176i	0.0979917	+	0.0979917i
$842$	−28.6269	−	28.6269i	−0.986547	−	0.986547i
$843$	20.6874	−	8.56902i	0.712513	−	0.295133i
$844$	−2.24169	−	5.41193i	−0.0771623	−	0.186286i
$845$	18.1202	+	7.50564i	0.623355	+	0.258202i
$846$			11.1795i			0.384359i
$847$	−0.280629	+	0.677499i	−0.00964254	+	0.0232791i
$848$	−14.9962	+	14.9962i	−0.514971	+	0.514971i
$849$	24.5467			0.842440
$850$	−11.1000	−	7.81346i	−0.380728	−	0.268000i
$851$	2.16538			0.0742283
$852$	−4.25637	+	4.25637i	−0.145821	+	0.145821i
$853$	−9.66185	+	23.3258i	−0.330816	+	0.798659i	0.667712	+	0.744419i	$0.267274\pi$
$853$	−9.66185	+	23.3258i	−0.330816	+	0.798659i	−0.998528	+	0.0542400i	$0.982726\pi$
$854$			5.30197i			0.181430i
$855$	0.00744118	+	0.00308224i	0.000254483	+	0.000105410i
$856$	−10.3530	−	24.9944i	−0.353860	−	0.854292i
$857$	−26.7744	+	11.0903i	−0.914596	+	0.378838i	−0.789814	−	0.613346i	$-0.789823\pi$
$857$	−26.7744	+	11.0903i	−0.914596	+	0.378838i	−0.124782	+	0.992184i	$0.539823\pi$
$858$	−7.02117	−	7.02117i	−0.239699	−	0.239699i
$859$	25.3428	+	25.3428i	0.864686	+	0.864686i	0.991878	−	0.127192i	$-0.0405965\pi$
$859$	25.3428	+	25.3428i	0.864686	+	0.864686i	−0.127192	+	0.991878i	$0.540596\pi$
$860$	−0.0194984	+	0.00807652i	−0.000664891	+	0.000275407i
$861$	3.32465	+	8.02642i	0.113304	+	0.273540i
$862$	−18.2905	−	7.57616i	−0.622976	−	0.258045i
$863$		−	28.8989i		−	0.983730i	−0.870671	−	0.491865i	$-0.836315\pi$
$863$		−	28.8989i		−	0.983730i	0.870671	−	0.491865i	$-0.163685\pi$
$864$	0.779697	−	1.88236i	0.0265258	−	0.0640390i
$865$	13.5612	−	13.5612i	0.461095	−	0.461095i
$866$	7.11068			0.241631
$867$	16.9799	+	0.825843i	0.576669	+	0.0280471i
$868$	1.17117			0.0397522
$869$	−33.9086	+	33.9086i	−1.15027	+	1.15027i
$870$	−7.73853	+	18.6825i	−0.262361	+	0.633395i
$871$			15.7503i			0.533679i
$872$	23.6395	+	9.79179i	0.800533	+	0.331592i
$873$	−1.97759	−	4.77433i	−0.0669314	−	0.161587i
$874$	0.0225024	−	0.00932081i	0.000761156	−	0.000315281i
$875$	4.71978	+	4.71978i	0.159558	+	0.159558i
$876$	1.67358	+	1.67358i	0.0565450	+	0.0565450i
$877$	30.5868	−	12.6695i	1.03284	−	0.427818i	0.199106	−	0.979978i	$-0.436196\pi$
$877$	30.5868	−	12.6695i	1.03284	−	0.427818i	0.833738	+	0.552160i	$0.186196\pi$
$878$	−6.85241	−	16.5432i	−0.231258	−	0.558305i
$879$	8.19953	+	3.39636i	0.276563	+	0.114556i
$880$			27.6609i			0.932450i
$881$	−20.2898	+	48.9840i	−0.683582	+	1.65031i	0.0737450	+	0.997277i	$0.476505\pi$
$881$	−20.2898	+	48.9840i	−0.683582	+	1.65031i	−0.757327	+	0.653036i	$0.773495\pi$
$882$	−0.904145	+	0.904145i	−0.0304441	+	0.0304441i
$883$	−28.3693			−0.954704			−0.477352	−	0.878712i	$-0.658403\pi$
$883$	−28.3693			−0.954704			−0.477352	+	0.878712i	$0.658403\pi$
$884$	−2.98286	−	2.09968i	−0.100325	−	0.0706198i
$885$	−5.75668			−0.193509
$886$	10.2223	−	10.2223i	0.343425	−	0.343425i
$887$	11.2545	−	27.1709i	0.377890	−	0.912308i	−0.614471	−	0.788940i	$-0.710630\pi$
$887$	11.2545	−	27.1709i	0.377890	−	0.912308i	0.992361	−	0.123368i	$-0.0393696\pi$
$888$			1.00602i			0.0337598i
$889$	−3.12093	−	1.29273i	−0.104673	−	0.0433569i
$890$	−10.9904	−	26.5333i	−0.368400	−	0.889397i
$891$	−2.96026	+	1.22618i	−0.0991726	+	0.0410786i
$892$	7.17062	+	7.17062i	0.240090	+	0.240090i
$893$	0.0180924	+	0.0180924i	0.000605439	+	0.000605439i
$894$	−18.7574	+	7.76957i	−0.627341	+	0.259853i
$895$	5.12210	+	12.3659i	0.171213	+	0.413345i
$896$	−6.72366	−	2.78503i	−0.224622	−	0.0930414i
$897$			15.7752i			0.526720i
$898$	6.14956	−	14.8464i	0.205214	−	0.495429i
$899$	13.0359	−	13.0359i	0.434773	−	0.434773i
$900$	0.939905			0.0313302
$901$	27.4659	−	4.77270i	0.915020	−	0.159002i
$902$	35.5938			1.18514
$903$	−0.0148539	+	0.0148539i	−0.000494306	+	0.000494306i
$904$	6.30671	−	15.2257i	0.209758	−	0.506401i
$905$			53.3445i			1.77323i
$906$	−1.91069	−	0.791432i	−0.0634783	−	0.0262936i
$907$	18.9189	+	45.6742i	0.628191	+	1.51659i	0.841868	+	0.539683i	$0.181456\pi$
$907$	18.9189	+	45.6742i	0.628191	+	1.51659i	−0.213678	+	0.976904i	$0.568544\pi$
$908$	−4.70127	+	1.94733i	−0.156017	+	0.0646245i
$909$	−9.21366	−	9.21366i	−0.305598	−	0.305598i
$910$	6.03086	+	6.03086i	0.199921	+	0.199921i
$911$	−41.1178	+	17.0316i	−1.36229	+	0.564281i	−0.939688	−	0.342033i	$-0.888885\pi$
$911$	−41.1178	+	17.0316i	−1.36229	+	0.564281i	−0.422606	+	0.906313i	$0.638885\pi$
$912$	0.00351276	+	0.00848055i	0.000116319	+	0.000280819i
$913$	−34.9730	−	14.4863i	−1.15744	−	0.479426i
$914$			18.9510i			0.626843i
$915$	4.36725	−	10.5435i	0.144377	−	0.348557i
$916$	3.80778	−	3.80778i	0.125813	−	0.125813i
$917$	−0.764248			−0.0252377
$918$	4.45340	−	2.82161i	0.146984	−	0.0931270i
$919$	−9.22122			−0.304180			−0.152090	−	0.988367i	$-0.548600\pi$
$919$	−9.22122			−0.304180			−0.152090	+	0.988367i	$0.548600\pi$
$920$	38.3073	−	38.3073i	1.26295	−	1.26295i
$921$	−3.12944	+	7.55513i	−0.103118	+	0.248950i
$922$		−	8.90513i		−	0.293275i
$923$	36.9217	+	15.2935i	1.21529	+	0.503391i
$924$	−0.447610	−	1.08063i	−0.0147253	−	0.0355500i
$925$	−0.791351	+	0.327788i	−0.0260195	+	0.0107776i
$926$	24.8192	+	24.8192i	0.815608	+	0.815608i
$927$	−1.36656	−	1.36656i	−0.0448836	−	0.0448836i
$928$	10.8164	−	4.48030i	0.355066	−	0.147073i
$929$	8.00202	+	19.3186i	0.262538	+	0.633822i	0.999094	−	0.0425538i	$-0.0135494\pi$
$929$	8.00202	+	19.3186i	0.262538	+	0.633822i	−0.736556	+	0.676376i	$0.763549\pi$
$930$	10.4311	+	4.32070i	0.342049	+	0.141681i
$931$			0.00292645i			9.59107e-5i
$932$	−3.46495	+	8.36513i	−0.113498	+	0.274009i
$933$	17.2865	−	17.2865i	0.565934	−	0.565934i
$934$	−16.1993			−0.530056
$935$	20.9291	−	29.7325i	0.684456	−	0.972358i
$936$	−7.32907			−0.239558
$937$	−18.1625	+	18.1625i	−0.593341	+	0.593341i	−0.938532	−	0.345191i	$-0.887814\pi$
$937$	−18.1625	+	18.1625i	−0.593341	+	0.593341i	0.345191	+	0.938532i	$0.387814\pi$
$938$	3.17999	−	7.67717i	0.103830	−	0.250669i
$939$			24.3851i			0.795778i
$940$	8.11548	+	3.36154i	0.264698	+	0.109641i
$941$	10.2891	+	24.8401i	0.335415	+	0.809763i	0.998144	+	0.0609038i	$0.0193983\pi$
$941$	10.2891	+	24.8401i	0.335415	+	0.809763i	−0.662729	+	0.748860i	$0.730602\pi$
$942$	−29.3632	+	12.1626i	−0.956704	+	0.396280i
$943$	−39.9863	−	39.9863i	−1.30213	−	1.30213i
$944$	−4.63916	−	4.63916i	−0.150992	−	0.150992i
$945$	2.54273	−	1.05323i	0.0827150	−	0.0342617i
$946$	0.0329354	+	0.0795131i	0.00107082	+	0.00258519i
$947$	12.3852	+	5.13013i	0.402466	+	0.166707i	0.574728	−	0.818344i	$-0.305108\pi$
$947$	12.3852	+	5.13013i	0.402466	+	0.166707i	−0.172262	+	0.985051i	$0.555108\pi$
$948$			5.46329i			0.177439i
$949$	6.01330	−	14.5174i	0.195200	−	0.471254i
$950$	−0.00681269	+	0.00681269i	−0.000221033	+	0.000221033i
$951$	−15.2534			−0.494625
$952$	6.67323	+	10.5325i	0.216281	+	0.341360i
$953$	−7.77398			−0.251824			−0.125912	−	0.992041i	$-0.540186\pi$
$953$	−7.77398			−0.251824			−0.125912	+	0.992041i	$0.540186\pi$
$954$	6.11317	−	6.11317i	0.197921	−	0.197921i
$955$	20.1417	−	48.6265i	0.651771	−	1.57352i
$956$		−	4.75568i		−	0.153810i
$957$	−17.0103	−	7.04589i	−0.549864	−	0.227761i
$958$	−16.4758	−	39.7761i	−0.532308	−	1.28511i
$959$	18.5560	−	7.68614i	0.599204	−	0.248198i
$960$	17.2786	+	17.2786i	0.557666	+	0.557666i
$961$	14.6419	+	14.6419i	0.472319	+	0.472319i
$962$	0.952444	−	0.394515i	0.0307080	−	0.0127197i
$963$	3.42354	+	8.26516i	0.110322	+	0.266341i
$964$	1.72241	+	0.713445i	0.0554750	+	0.0229785i
$965$			21.7096i			0.698858i
$966$	3.18502	−	7.68932i	0.102476	−	0.247400i
$967$	31.0516	−	31.0516i	0.998551	−	0.998551i	−0.00144826	−	0.999999i	$-0.500461\pi$
$967$	31.0516	−	31.0516i	0.998551	−	0.998551i	0.999999	+	0.00144826i	$0.000460996\pi$
$968$	2.21761			0.0712768
$969$	0.00264081	−	0.0117735i	8.48351e−5	−	0.000378221i
$970$	18.1859			0.583914
$971$	23.1851	−	23.1851i	0.744046	−	0.744046i	−0.229308	−	0.973354i	$-0.573646\pi$
$971$	23.1851	−	23.1851i	0.744046	−	0.744046i	0.973354	+	0.229308i	$0.0736464\pi$
$972$	−0.139696	+	0.337256i	−0.00448076	+	0.0108175i
$973$		−	22.2507i		−	0.713326i
$974$	13.5578	+	5.61582i	0.434420	+	0.179943i
$975$	−2.38800	−	5.76515i	−0.0764773	−	0.184633i
$976$	12.0162	−	4.97726i	0.384628	−	0.159318i
$977$	−17.0120	−	17.0120i	−0.544263	−	0.544263i	0.380513	−	0.924776i	$-0.375747\pi$
$977$	−17.0120	−	17.0120i	−0.544263	−	0.544263i	−0.924776	+	0.380513i	$0.875747\pi$
$978$	−7.62683	−	7.62683i	−0.243879	−	0.243879i
$979$	24.1584	−	10.0067i	0.772105	−	0.319816i
$980$	0.384476	+	0.928207i	0.0122816	+	0.0296505i
$981$	−7.81710	−	3.23795i	−0.249581	−	0.103380i
$982$		−	33.8003i		−	1.07861i
$983$	17.4227	−	42.0620i	0.555696	−	1.34157i	−0.357448	−	0.933933i	$-0.616353\pi$
$983$	17.4227	−	42.0620i	0.555696	−	1.34157i	0.913144	−	0.407636i	$-0.133647\pi$
$984$	18.5774	−	18.5774i	0.592224	−	0.592224i
$985$	−58.7869			−1.87311
$986$	29.5597	+	6.63025i	0.941372	+	0.211150i
$987$	8.74318			0.278298
$988$	−0.00183074	+	0.00183074i	−5.82438e−5	+	5.82438e-5i
$989$	0.0523256	−	0.126325i	0.00166386	−	0.00401690i
$990$		−	11.2759i		−	0.358373i
$991$	−39.3790	−	16.3113i	−1.25092	−	0.518146i	−0.343806	−	0.939041i	$-0.611716\pi$
$991$	−39.3790	−	16.3113i	−1.25092	−	0.518146i	−0.907110	+	0.420894i	$0.861716\pi$
$992$	−2.50151	−	6.03918i	−0.0794230	−	0.191744i
$993$	8.05996	−	3.33854i	0.255775	−	0.105946i
$994$	−14.9090	−	14.9090i	−0.472884	−	0.472884i
$995$	11.2365	+	11.2365i	0.356221	+	0.356221i
$996$	−3.98440	+	1.65039i	−0.126250	+	0.0522946i
$997$	5.15376	+	12.4423i	0.163221	+	0.394051i	0.984237	−	0.176854i	$-0.0565922\pi$
$997$	5.15376	+	12.4423i	0.163221	+	0.394051i	−0.821016	+	0.570906i	$0.806592\pi$
$998$	27.0638	+	11.2102i	0.856690	+	0.354853i
$999$		−	0.332671i		−	0.0105252i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	357.2.u.a.127.6	✓	32
17.7	odd	16		6069.2.a.bj.1.6		16
17.10	odd	16		6069.2.a.bk.1.6		16
17.15	even	8	inner	357.2.u.a.253.6	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
357.2.u.a.127.6	✓	32	1.1	even	1	trivial
357.2.u.a.253.6	yes	32	17.15	even	8	inner
6069.2.a.bj.1.6		16	17.7	odd	16
6069.2.a.bk.1.6		16	17.10	odd	16

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:	\( N \)	\(=\)	\( 357 = 3 \cdot 7 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	357.u (of order \(8\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.904145 - 0.904145i) q^{2} +(0.382683 - 0.923880i) q^{3} +0.365044i q^{4} +(2.54273 + 1.05323i) q^{5} +(-0.489320 - 1.18132i) q^{6} +(-0.923880 + 0.382683i) q^{7} +(2.13834 + 2.13834i) q^{8} +(-0.707107 - 0.707107i) q^{9} +(3.25127 - 1.34672i) q^{10} +(1.22618 + 2.96026i) q^{11} +(0.337256 + 0.139696i) q^{12} -2.42357i q^{13} +(-0.489320 + 1.18132i) q^{14} +(1.94612 - 1.94612i) q^{15} +3.13666 q^{16} +(-3.37157 - 2.37329i) q^{17} -1.27865 q^{18} +(-0.00206932 + 0.00206932i) q^{19} +(-0.384476 + 0.928207i) q^{20} +1.00000i q^{21} +(3.78515 + 1.56786i) q^{22} +(-2.49092 - 6.01360i) q^{23} +(2.79388 - 1.15726i) q^{24} +(1.82064 + 1.82064i) q^{25} +(-2.19126 - 2.19126i) q^{26} +(-0.923880 + 0.382683i) q^{27} +(-0.139696 - 0.337256i) q^{28} +(-5.30880 - 2.19898i) q^{29} -3.51915i q^{30} +(-1.22777 + 2.96409i) q^{31} +(-1.44069 + 1.44069i) q^{32} +3.20417 q^{33} +(-5.19419 + 0.902586i) q^{34} -2.75223 q^{35} +(0.258125 - 0.258125i) q^{36} +(-0.127308 + 0.307348i) q^{37} +0.00374192i q^{38} +(-2.23909 - 0.927462i) q^{39} +(3.18505 + 7.68940i) q^{40} +(8.02642 - 3.32465i) q^{41} +(0.904145 + 0.904145i) q^{42} +(0.0148539 + 0.0148539i) q^{43} +(-1.08063 + 0.447610i) q^{44} +(-1.05323 - 2.54273i) q^{45} +(-7.68932 - 3.18502i) q^{46} -8.74318i q^{47} +(1.20035 - 2.89789i) q^{48} +(0.707107 - 0.707107i) q^{49} +3.29225 q^{50} +(-3.48288 + 2.20670i) q^{51} +0.884710 q^{52} +(-4.78094 + 4.78094i) q^{53} +(-0.489320 + 1.18132i) q^{54} +8.81860i q^{55} +(-2.79388 - 1.15726i) q^{56} +(0.00111991 + 0.00270369i) q^{57} +(-6.78812 + 2.81173i) q^{58} +(-1.47901 - 1.47901i) q^{59} +(0.710419 + 0.710419i) q^{60} +(3.83089 - 1.58680i) q^{61} +(1.56989 + 3.79005i) q^{62} +(0.923880 + 0.382683i) q^{63} +8.87850i q^{64} +(2.55259 - 6.16249i) q^{65} +(2.89703 - 2.89703i) q^{66} -6.49880 q^{67} +(0.866355 - 1.23077i) q^{68} -6.50907 q^{69} +(-2.48842 + 2.48842i) q^{70} +(-6.31029 + 15.2344i) q^{71} -3.02407i q^{72} +(5.99007 + 2.48117i) q^{73} +(0.162782 + 0.392992i) q^{74} +(2.37878 - 0.985323i) q^{75} +(-0.000755390 - 0.000755390i) q^{76} +(-2.26569 - 2.26569i) q^{77} +(-2.86302 + 1.18590i) q^{78} +(5.72729 + 13.8269i) q^{79} +(7.97567 + 3.30363i) q^{80} +1.00000i q^{81} +(4.25108 - 10.2630i) q^{82} +(-8.35386 + 8.35386i) q^{83} -0.365044 q^{84} +(-6.07336 - 9.58569i) q^{85} +0.0268601 q^{86} +(-4.06318 + 4.06318i) q^{87} +(-3.70806 + 8.95205i) q^{88} -8.16088i q^{89} +(-3.25127 - 1.34672i) q^{90} +(0.927462 + 2.23909i) q^{91} +(2.19523 - 0.909293i) q^{92} +(2.26862 + 2.26862i) q^{93} +(-7.90510 - 7.90510i) q^{94} +(-0.00744118 + 0.00308224i) q^{95} +(0.779697 + 1.88236i) q^{96} +(4.77433 + 1.97759i) q^{97} -1.27865i q^{98} +(1.22618 - 2.96026i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 8 q^{6} - 32 q^{10} + 8 q^{14} - 8 q^{16} - 8 q^{17} - 8 q^{18} + 8 q^{19} - 16 q^{20} - 8 q^{23} - 8 q^{24} + 24 q^{25} - 32 q^{26} + 24 q^{29} + 8 q^{31} - 40 q^{32} + 8 q^{33} - 8 q^{34} - 8 q^{35}+ \cdots + 96 q^{97}+O(q^{100}) \) 32 * q + 8 * q^6 - 32 * q^10 + 8 * q^14 - 8 * q^16 - 8 * q^17 - 8 * q^18 + 8 * q^19 - 16 * q^20 - 8 * q^23 - 8 * q^24 + 24 * q^25 - 32 * q^26 + 24 * q^29 + 8 * q^31 - 40 * q^32 + 8 * q^33 - 8 * q^34 - 8 * q^35 - 8 * q^36 + 72 * q^37 - 16 * q^39 + 40 * q^40 + 8 * q^41 - 32 * q^43 - 48 * q^44 + 8 * q^45 + 40 * q^46 + 32 * q^48 + 56 * q^50 - 16 * q^51 - 56 * q^53 + 8 * q^54 + 8 * q^56 + 16 * q^57 - 32 * q^58 - 48 * q^59 - 48 * q^60 + 8 * q^61 - 24 * q^62 + 16 * q^66 + 96 * q^67 - 16 * q^68 + 8 * q^69 - 16 * q^70 + 24 * q^71 - 24 * q^73 - 32 * q^74 - 16 * q^75 - 48 * q^76 - 24 * q^77 - 72 * q^78 - 48 * q^79 + 72 * q^80 + 96 * q^82 - 24 * q^83 + 24 * q^84 - 136 * q^85 - 32 * q^87 + 16 * q^88 + 32 * q^90 + 8 * q^91 + 136 * q^92 + 8 * q^93 - 32 * q^94 - 32 * q^95 - 32 * q^96 + 96 * q^97

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