LMFDB - Embedded newform 54.3.f.a.29.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [54,3,Mod(5,54)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(54, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([5]))

N = Newforms(chi, 3, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("54.5");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 54 = 2 \cdot 3^{3} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	54.f (of order $18$, degree $6$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$1.47139342755$
Analytic rank:	$0$
Dimension:	$36$
Relative dimension:	$6$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			29.5
Character	$\chi$	$=$	54.29
Dual form			54.3.f.a.41.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.39273 + 0.245576i) q^{2} +(-0.101242 - 2.99829i) q^{3} +(1.87939 + 0.684040i) q^{4} +(0.379008 + 0.451684i) q^{5} +(0.595305 - 4.20067i) q^{6} +(2.96297 - 1.07843i) q^{7} +(2.44949 + 1.41421i) q^{8} +(-8.97950 + 0.607104i) q^{9} +(0.416932 + 0.722148i) q^{10} +(-6.03341 + 7.19034i) q^{11} +(1.86068 - 5.70420i) q^{12} +(2.11998 + 12.0230i) q^{13} +(4.39145 - 0.774332i) q^{14} +(1.31591 - 1.18210i) q^{15} +(3.06418 + 2.57115i) q^{16} +(-24.5140 + 14.1532i) q^{17} +(-12.6551 - 1.35961i) q^{18} +(11.2011 - 19.4008i) q^{19} +(0.403332 + 1.10814i) q^{20} +(-3.53344 - 8.77467i) q^{21} +(-10.1687 + 8.53254i) q^{22} +(3.44380 - 9.46175i) q^{23} +(3.99223 - 7.48746i) q^{24} +(4.28083 - 24.2778i) q^{25} +17.2654i q^{26} +(2.72938 + 26.8617i) q^{27} +6.30626 q^{28} +(-23.6767 - 4.17484i) q^{29} +(2.12300 - 1.32320i) q^{30} +(42.7251 + 15.5506i) q^{31} +(3.63616 + 4.33340i) q^{32} +(22.1696 + 17.3620i) q^{33} +(-37.6170 + 13.6915i) q^{34} +(1.61010 + 0.929592i) q^{35} +(-17.2912 - 5.00136i) q^{36} +(-15.7500 - 27.2799i) q^{37} +(20.3644 - 24.2694i) q^{38} +(35.8339 - 7.57355i) q^{39} +(0.289598 + 1.64239i) q^{40} +(69.7771 - 12.3036i) q^{41} +(-2.76627 - 13.0885i) q^{42} +(-11.1607 - 9.36490i) q^{43} +(-16.2576 + 9.38633i) q^{44} +(-3.67752 - 3.82580i) q^{45} +(7.11985 - 12.3319i) q^{46} +(-18.9216 - 51.9868i) q^{47} +(7.39884 - 9.44761i) q^{48} +(-29.9200 + 25.1059i) q^{49} +(11.9241 - 32.7611i) q^{50} +(44.9172 + 72.0672i) q^{51} +(-4.23996 + 24.0460i) q^{52} -25.4089i q^{53} +(-2.79530 + 38.0813i) q^{54} -5.53447 q^{55} +(8.78291 + 1.54866i) q^{56} +(-59.3034 - 31.6199i) q^{57} +(-31.9499 - 11.6288i) q^{58} +(18.4282 + 21.9619i) q^{59} +(3.28171 - 1.32150i) q^{60} +(-106.265 + 38.6772i) q^{61} +(55.6855 + 32.1501i) q^{62} +(-25.9513 + 11.4826i) q^{63} +(4.00000 + 6.92820i) q^{64} +(-4.62711 + 5.51438i) q^{65} +(26.6125 + 29.6248i) q^{66} +(8.68700 + 49.2664i) q^{67} +(-55.7526 + 9.83069i) q^{68} +(-28.7178 - 9.36758i) q^{69} +(2.01415 + 1.69007i) q^{70} +(-7.59817 + 4.38680i) q^{71} +(-22.8538 - 11.2118i) q^{72} +(-11.7358 + 20.3271i) q^{73} +(-15.2363 - 41.8613i) q^{74} +(-73.2253 - 10.3773i) q^{75} +(34.3221 - 28.7997i) q^{76} +(-10.1225 + 27.8114i) q^{77} +(51.7667 - 1.74798i) q^{78} +(23.0535 - 130.743i) q^{79} +2.35853i q^{80} +(80.2628 - 10.9030i) q^{81} +100.202 q^{82} +(-66.1377 - 11.6619i) q^{83} +(-0.638457 - 18.9080i) q^{84} +(-15.6838 - 5.70842i) q^{85} +(-13.2440 - 15.7835i) q^{86} +(-10.1203 + 71.4122i) q^{87} +(-24.9475 + 9.08013i) q^{88} +(62.9935 + 36.3693i) q^{89} +(-4.18226 - 6.23141i) q^{90} +(19.2475 + 33.3376i) q^{91} +(12.9444 - 15.4266i) q^{92} +(42.2998 - 129.677i) q^{93} +(-13.5860 - 77.0502i) q^{94} +(13.0083 - 2.29372i) q^{95} +(12.6247 - 11.3410i) q^{96} +(120.419 + 101.043i) q^{97} +(-47.8358 + 27.6180i) q^{98} +(49.8117 - 68.2286i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q + 18 q^{5} + 12 q^{6} - 12 q^{9} - 18 q^{11} - 12 q^{12} - 36 q^{14} - 18 q^{15} - 48 q^{18} - 72 q^{20} - 228 q^{21} + 36 q^{22} - 180 q^{23} + 18 q^{25} + 54 q^{27} + 144 q^{29} + 144 q^{30} - 90 q^{31}+ \cdots + 126 q^{99}+O(q^{100}) $ 36 * q + 18 * q^5 + 12 * q^6 - 12 * q^9 - 18 * q^11 - 12 * q^12 - 36 * q^14 - 18 * q^15 - 48 * q^18 - 72 * q^20 - 228 * q^21 + 36 * q^22 - 180 * q^23 + 18 * q^25 + 54 * q^27 + 144 * q^29 + 144 * q^30 - 90 * q^31 + 324 * q^33 - 72 * q^34 + 486 * q^35 + 168 * q^36 + 180 * q^38 + 102 * q^39 - 90 * q^41 + 48 * q^42 + 90 * q^43 - 378 * q^45 - 378 * q^47 - 24 * q^48 + 72 * q^49 - 54 * q^51 - 36 * q^54 - 72 * q^56 + 72 * q^57 + 252 * q^59 + 36 * q^60 - 144 * q^61 + 318 * q^63 + 144 * q^64 + 18 * q^65 - 432 * q^66 - 594 * q^67 - 180 * q^68 - 522 * q^69 - 360 * q^70 - 648 * q^71 - 192 * q^72 + 126 * q^73 - 504 * q^74 - 438 * q^75 - 72 * q^76 - 342 * q^77 - 288 * q^78 - 72 * q^79 + 324 * q^81 + 594 * q^83 + 216 * q^84 + 360 * q^85 + 540 * q^86 + 1062 * q^87 + 144 * q^88 + 648 * q^89 + 720 * q^90 - 198 * q^91 + 396 * q^92 + 462 * q^93 + 504 * q^94 + 252 * q^95 + 96 * q^96 + 702 * q^97 + 648 * q^98 + 126 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/54\mathbb{Z}\right)^\times$.

$n$	$29$
$\chi(n)$	$e\left(\frac{1}{18}\right)$

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 $

$2$	1.39273	+	0.245576i	0.696364	+	0.122788i
$2$	1.39273	+	0.245576i	0.696364	+	0.122788i
$3$	−0.101242	−	2.99829i	−0.0337472	−	0.999430i
$3$	−0.101242	−	2.99829i	−0.0337472	−	0.999430i
$4$	1.87939	+	0.684040i	0.469846	+	0.171010i
$5$	0.379008	+	0.451684i	0.0758015	+	0.0903368i	0.802612	−	0.596501i	$-0.203443\pi$
$5$	0.379008	+	0.451684i	0.0758015	+	0.0903368i	−0.726811	+	0.686838i	$0.758998\pi$
$6$	0.595305	−	4.20067i	0.0992175	−	0.700111i
$7$	2.96297	−	1.07843i	0.423282	−	0.154062i	−0.121592	−	0.992580i	$-0.538800\pi$
$7$	2.96297	−	1.07843i	0.423282	−	0.154062i	0.544874	+	0.838518i	$0.316578\pi$
$8$	2.44949	+	1.41421i	0.306186	+	0.176777i
$9$	−8.97950	+	0.607104i	−0.997722	+	0.0674561i
$10$	0.416932	+	0.722148i	0.0416932	+	0.0722148i
$11$	−6.03341	+	7.19034i	−0.548492	+	0.653667i	−0.967069	−	0.254514i	$-0.918085\pi$
$11$	−6.03341	+	7.19034i	−0.548492	+	0.653667i	0.418577	+	0.908181i	$0.362529\pi$
$12$	1.86068	−	5.70420i	0.155057	−	0.475350i
$13$	2.11998	+	12.0230i	0.163076	+	0.924847i	0.951027	+	0.309109i	$0.100031\pi$
$13$	2.11998	+	12.0230i	0.163076	+	0.924847i	−0.787951	+	0.615738i	$0.788858\pi$
$14$	4.39145	−	0.774332i	0.313675	−	0.0553094i
$15$	1.31591	−	1.18210i	0.0877272	−	0.0788070i
$16$	3.06418	+	2.57115i	0.191511	+	0.160697i
$17$	−24.5140	+	14.1532i	−1.44200	+	0.832539i	−0.997983	−	0.0634789i	$-0.979780\pi$
$17$	−24.5140	+	14.1532i	−1.44200	+	0.832539i	−0.444017	+	0.896018i	$0.646447\pi$
$18$	−12.6551	−	1.35961i	−0.703061	−	0.0755341i
$19$	11.2011	−	19.4008i	0.589530	−	1.02110i	−0.404764	−	0.914421i	$-0.632646\pi$
$19$	11.2011	−	19.4008i	0.589530	−	1.02110i	0.994294	−	0.106675i	$-0.0340205\pi$
$20$	0.403332	+	1.10814i	0.0201666	+	0.0554072i
$21$	−3.53344	−	8.77467i	−0.168259	−	0.417842i
$22$	−10.1687	+	8.53254i	−0.462213	+	0.387843i
$23$	3.44380	−	9.46175i	0.149730	−	0.411381i	−0.842039	−	0.539416i	$-0.818645\pi$
$23$	3.44380	−	9.46175i	0.149730	−	0.411381i	0.991770	+	0.128036i	$0.0408672\pi$
$24$	3.99223	−	7.48746i	0.166343	−	0.311978i
$25$	4.28083	−	24.2778i	0.171233	−	0.971112i
$26$			17.2654i			0.664054i
$27$	2.72938	+	26.8617i	0.101088	+	0.994877i
$28$	6.30626			0.225224
$29$	−23.6767	−	4.17484i	−0.816437	−	0.143960i	−0.250191	−	0.968196i	$-0.580494\pi$
$29$	−23.6767	−	4.17484i	−0.816437	−	0.143960i	−0.566246	+	0.824237i	$0.691605\pi$
$30$	2.12300	−	1.32320i	0.0707666	−	0.0441065i
$31$	42.7251	+	15.5506i	1.37823	+	0.501634i	0.921640	−	0.388045i	$-0.126849\pi$
$31$	42.7251	+	15.5506i	1.37823	+	0.501634i	0.456587	+	0.889679i	$0.349072\pi$
$32$	3.63616	+	4.33340i	0.113630	+	0.135419i
$33$	22.1696	+	17.3620i	0.671805	+	0.526120i
$34$	−37.6170	+	13.6915i	−1.10638	+	0.402691i
$35$	1.61010	+	0.929592i	0.0460029	+	0.0265598i
$36$	−17.2912	−	5.00136i	−0.480312	−	0.138927i
$37$	−15.7500	−	27.2799i	−0.425677	−	0.737293i	0.570807	−	0.821084i	$-0.306631\pi$
$37$	−15.7500	−	27.2799i	−0.425677	−	0.737293i	−0.996483	+	0.0837909i	$0.973297\pi$
$38$	20.3644	−	24.2694i	0.535906	−	0.638668i
$39$	35.8339	−	7.57355i	0.918817	−	0.194194i
$40$	0.289598	+	1.64239i	0.00723995	+	0.0410598i
$41$	69.7771	−	12.3036i	1.70188	−	0.300087i	0.763530	−	0.645773i	$-0.223465\pi$
$41$	69.7771	−	12.3036i	1.70188	−	0.300087i	0.938351	+	0.345685i	$0.112354\pi$
$42$	−2.76627	−	13.0885i	−0.0658636	−	0.311630i
$43$	−11.1607	−	9.36490i	−0.259550	−	0.217788i	0.503722	−	0.863866i	$-0.331964\pi$
$43$	−11.1607	−	9.36490i	−0.259550	−	0.217788i	−0.763272	+	0.646078i	$0.776408\pi$
$44$	−16.2576	+	9.38633i	−0.369491	+	0.213326i
$45$	−3.67752	−	3.82580i	−0.0817226	−	0.0850177i
$46$	7.11985	−	12.3319i	0.154779	−	0.268086i
$47$	−18.9216	−	51.9868i	−0.402588	−	1.10610i	−0.961002	−	0.276540i	$-0.910812\pi$
$47$	−18.9216	−	51.9868i	−0.402588	−	1.10610i	0.558414	−	0.829562i	$-0.311410\pi$
$48$	7.39884	−	9.44761i	0.154142	−	0.196825i
$49$	−29.9200	+	25.1059i	−0.610612	+	0.512364i
$50$	11.9241	−	32.7611i	0.238482	−	0.655223i
$51$	44.9172	+	72.0672i	0.880729	+	1.41308i
$52$	−4.23996	+	24.0460i	−0.0815378	+	0.462424i
$53$		−	25.4089i		−	0.479412i	−0.970845	−	0.239706i	$-0.922949\pi$
$53$		−	25.4089i		−	0.479412i	0.970845	−	0.239706i	$-0.0770511\pi$
$54$	−2.79530	+	38.0813i	−0.0517647	+	0.705209i
$55$	−5.53447			−0.100627
$56$	8.78291	+	1.54866i	0.156838	+	0.0276547i
$57$	−59.3034	−	31.6199i	−1.04041	−	0.554735i
$58$	−31.9499	−	11.6288i	−0.550861	−	0.200497i
$59$	18.4282	+	21.9619i	0.312343	+	0.372236i	0.899263	−	0.437409i	$-0.144104\pi$
$59$	18.4282	+	21.9619i	0.312343	+	0.372236i	−0.586919	+	0.809645i	$0.699659\pi$
$60$	3.28171	−	1.32150i	0.0546951	−	0.0220249i
$61$	−106.265	+	38.6772i	−1.74205	+	0.634053i	−0.999366	−	0.0355933i	$-0.988668\pi$
$61$	−106.265	+	38.6772i	−1.74205	+	0.634053i	−0.742680	+	0.669646i	$0.766446\pi$
$62$	55.6855	+	32.1501i	0.898154	+	0.518549i
$63$	−25.9513	+	11.4826i	−0.411925	+	0.182264i
$64$	4.00000	+	6.92820i	0.0625000	+	0.108253i
$65$	−4.62711	+	5.51438i	−0.0711863	+	0.0848365i
$66$	26.6125	+	29.6248i	0.403220	+	0.448861i
$67$	8.68700	+	49.2664i	0.129657	+	0.735320i	0.978432	+	0.206567i	$0.0662291\pi$
$67$	8.68700	+	49.2664i	0.129657	+	0.735320i	−0.848776	+	0.528753i	$0.822660\pi$
$68$	−55.7526	+	9.83069i	−0.819891	+	0.144569i
$69$	−28.7178	−	9.36758i	−0.416199	−	0.135762i
$70$	2.01415	+	1.69007i	0.0287735	+	0.0241439i
$71$	−7.59817	+	4.38680i	−0.107016	+	0.0617860i	−0.552553	−	0.833478i	$-0.686346\pi$
$71$	−7.59817	+	4.38680i	−0.107016	+	0.0617860i	0.445536	+	0.895264i	$0.353013\pi$
$72$	−22.8538	−	11.2118i	−0.317413	−	0.155720i
$73$	−11.7358	+	20.3271i	−0.160765	+	0.278453i	−0.935143	−	0.354270i	$-0.884729\pi$
$73$	−11.7358	+	20.3271i	−0.160765	+	0.278453i	0.774378	+	0.632723i	$0.218063\pi$
$74$	−15.2363	−	41.8613i	−0.205895	−	0.565693i
$75$	−73.2253	−	10.3773i	−0.976338	−	0.138363i
$76$	34.3221	−	28.7997i	0.451606	−	0.378943i
$77$	−10.1225	+	27.8114i	−0.131461	+	0.361187i
$78$	51.7667	−	1.74798i	0.663676	−	0.0224100i
$79$	23.0535	−	130.743i	0.291816	−	1.65497i	−0.388053	−	0.921637i	$-0.626852\pi$
$79$	23.0535	−	130.743i	0.291816	−	1.65497i	0.679869	−	0.733334i	$-0.262037\pi$
$80$			2.35853i			0.0294816i
$81$	80.2628	−	10.9030i	0.990899	−	0.134605i
$82$	100.202			1.22198
$83$	−66.1377	−	11.6619i	−0.796839	−	0.140504i	−0.239617	−	0.970868i	$-0.577022\pi$
$83$	−66.1377	−	11.6619i	−0.796839	−	0.140504i	−0.557223	+	0.830363i	$0.688133\pi$
$84$	−0.638457	−	18.9080i	−0.00760068	−	0.225095i
$85$	−15.6838	−	5.70842i	−0.184515	−	0.0671579i
$86$	−13.2440	−	15.7835i	−0.154000	−	0.183530i
$87$	−10.1203	+	71.4122i	−0.116325	+	0.820830i
$88$	−24.9475	+	9.08013i	−0.283494	+	0.103183i
$89$	62.9935	+	36.3693i	0.707792	+	0.408644i	0.810243	−	0.586094i	$-0.199335\pi$
$89$	62.9935	+	36.3693i	0.707792	+	0.408644i	−0.102451	+	0.994738i	$0.532668\pi$
$90$	−4.18226	−	6.23141i	−0.0464696	−	0.0692378i
$91$	19.2475	+	33.3376i	0.211511	+	0.366347i
$92$	12.9444	−	15.4266i	0.140700	−	0.167680i
$93$	42.2998	−	129.677i	0.454837	−	1.39437i
$94$	−13.5860	−	77.0502i	−0.144532	−	0.819683i
$95$	13.0083	−	2.29372i	0.136930	−	0.0241444i
$96$	12.6247	−	11.3410i	0.131507	−	0.118135i
$97$	120.419	+	101.043i	1.24143	+	1.04168i	0.997411	+	0.0719147i	$0.0229109\pi$
$97$	120.419	+	101.043i	1.24143	+	1.04168i	0.244021	+	0.969770i	$0.421534\pi$
$98$	−47.8358	+	27.6180i	−0.488120	+	0.281816i
$99$	49.8117	−	68.2286i	0.503149	−	0.689178i
$100$	24.6523	−	42.6991i	0.246523	−	0.426991i
$101$	42.9450	+	117.991i	0.425198	+	1.16822i	0.948694	+	0.316195i	$0.102405\pi$
$101$	42.9450	+	117.991i	0.425198	+	1.16822i	−0.523496	+	0.852028i	$0.675372\pi$
$102$	44.8595	+	111.401i	0.439799	+	1.09216i
$103$	72.1665	−	60.5548i	0.700645	−	0.587911i	−0.221312	−	0.975203i	$-0.571034\pi$
$103$	72.1665	−	60.5548i	0.700645	−	0.587911i	0.921957	+	0.387292i	$0.126589\pi$
$104$	−11.8102	+	32.4484i	−0.113560	+	0.312003i
$105$	2.62418	−	4.92166i	0.0249922	−	0.0468730i
$106$	6.23979	−	35.3876i	0.0588660	−	0.333846i
$107$		−	107.896i		−	1.00838i	−0.863594	−	0.504188i	$-0.831792\pi$
$107$		−	107.896i		−	1.00838i	0.863594	−	0.504188i	$-0.168208\pi$
$108$	−13.2449	+	52.3505i	−0.122638	+	0.484727i
$109$	−42.9667			−0.394190			−0.197095	−	0.980384i	$-0.563151\pi$
$109$	−42.9667			−0.394190			−0.197095	+	0.980384i	$0.563151\pi$
$110$	−7.70802	−	1.35913i	−0.0700729	−	0.0123557i
$111$	−80.1984	+	49.9850i	−0.722508	+	0.450316i
$112$	11.8519	+	4.31374i	0.105820	+	0.0385155i
$113$	6.89768	+	8.22034i	0.0610414	+	0.0727463i	0.795701	−	0.605689i	$-0.207103\pi$
$113$	6.89768	+	8.22034i	0.0610414	+	0.0727463i	−0.734660	+	0.678436i	$0.762658\pi$
$114$	−74.8284	−	58.6014i	−0.656390	−	0.514048i
$115$	5.57895	−	2.03057i	0.0485126	−	0.0176571i
$116$	−41.6418	−	24.0419i	−0.358981	−	0.207258i
$117$	−26.3356	−	106.674i	−0.225091	−	0.911740i
$118$	20.2722	+	35.1125i	0.171799	+	0.297564i
$119$	−57.3711	+	68.3722i	−0.482110	+	0.574556i
$120$	4.89505	−	1.03458i	0.0407921	−	0.00862148i
$121$	5.71249	+	32.3971i	0.0472106	+	0.267745i
$122$	−157.496	+	27.7708i	−1.29095	+	0.227630i
$123$	−43.9541	−	207.966i	−0.357350	−	1.69078i
$124$	69.6596	+	58.4513i	0.561771	+	0.471382i
$125$	25.3543	−	14.6383i	0.202834	−	0.117106i
$126$	−38.9630	+	9.61918i	−0.309230	+	0.0763427i
$127$	−49.1507	+	85.1315i	−0.387013	+	0.670327i	−0.992046	−	0.125874i	$-0.959827\pi$
$127$	−49.1507	+	85.1315i	−0.387013	+	0.670327i	0.605033	+	0.796200i	$0.293160\pi$
$128$	3.86952	+	10.6314i	0.0302306	+	0.0830579i
$129$	−26.9488	+	34.4110i	−0.208905	+	0.266752i
$130$	−7.79850	+	6.54372i	−0.0599885	+	0.0503363i
$131$	−46.8665	+	128.765i	−0.357760	+	0.982937i	0.622045	+	0.782981i	$0.286302\pi$
$131$	−46.8665	+	128.765i	−0.357760	+	0.982937i	−0.979805	+	0.199956i	$0.935920\pi$
$132$	29.7889	+	47.7947i	0.225673	+	0.362081i
$133$	12.2660	−	69.5638i	0.0922253	−	0.523036i
$134$			70.7481i			0.527971i
$135$	−11.0985	+	11.4136i	−0.0822114	+	0.0845452i
$136$	−80.0624			−0.588694
$137$	197.146	+	34.7622i	1.43902	+	0.253739i	0.838078	−	0.545550i	$-0.183679\pi$
$137$	197.146	+	34.7622i	1.43902	+	0.253739i	0.600947	+	0.799289i	$0.294790\pi$
$138$	−37.6956	−	20.0989i	−0.273156	−	0.145644i
$139$	−6.69802	−	2.43788i	−0.0481872	−	0.0175387i	0.317814	−	0.948153i	$-0.397051\pi$
$139$	−6.69802	−	2.43788i	−0.0481872	−	0.0175387i	−0.366001	+	0.930614i	$0.619273\pi$
$140$	2.39012	+	2.84844i	0.0170723	+	0.0203460i
$141$	−153.956	+	61.9958i	−1.09189	+	0.439687i
$142$	−11.6595	+	4.24370i	−0.0821090	+	0.0298852i
$143$	−99.2403	−	57.2964i	−0.693988	−	0.400674i
$144$	−29.0757	−	21.2274i	−0.201915	−	0.147412i
$145$	−7.08794	−	12.2767i	−0.0488823	−	0.0846666i
$146$	−21.3367	+	25.4281i	−0.146142	+	0.174165i
$147$	78.3038	+	87.1671i	0.532679	+	0.592973i
$148$	−10.9399	−	62.0430i	−0.0739180	−	0.419210i
$149$	92.3284	−	16.2800i	0.619654	−	0.109262i	0.144996	−	0.989432i	$-0.453683\pi$
$149$	92.3284	−	16.2800i	0.619654	−	0.109262i	0.474658	+	0.880171i	$0.342572\pi$
$150$	−99.4346	−	32.4351i	−0.662897	−	0.216234i
$151$	154.567	+	129.697i	1.02362	+	0.858921i	0.990078	−	0.140516i	$-0.0448762\pi$
$151$	154.567	+	129.697i	1.02362	+	0.858921i	0.0335439	+	0.999437i	$0.489321\pi$
$152$	54.8738	−	31.6814i	0.361012	−	0.208430i
$153$	211.531	−	141.971i	1.38256	−	0.927915i
$154$	−20.9277	+	36.2479i	−0.135894	+	0.235376i
$155$	9.16915	+	25.1920i	0.0591558	+	0.162529i
$156$	72.5263	+	10.2782i	0.464912	+	0.0658858i
$157$	−56.2262	+	47.1794i	−0.358128	+	0.300505i	−0.804044	−	0.594569i	$-0.797323\pi$
$157$	−56.2262	+	47.1794i	−0.358128	+	0.300505i	0.445916	+	0.895075i	$0.352878\pi$
$158$	64.2144	−	176.428i	0.406420	−	1.11663i
$159$	−76.1831	+	2.57244i	−0.479139	+	0.0161788i
$160$	−0.579196	+	3.28479i	−0.00361998	+	0.0205299i
$161$		−	31.7488i		−	0.197198i
$162$	114.462	+	4.52569i	0.706555	+	0.0279364i
$163$	−217.128			−1.33208			−0.666038	−	0.745918i	$-0.732011\pi$
$163$	−217.128			−1.33208			−0.666038	+	0.745918i	$0.732011\pi$
$164$	139.554	+	24.6072i	0.850940	+	0.150044i
$165$	0.560319	+	16.5940i	0.00339588	+	0.100569i
$166$	−89.2480	−	32.4836i	−0.537638	−	0.195684i
$167$	−138.533	−	165.098i	−0.829541	−	0.988609i	−0.999995	−	0.00324290i	$-0.998968\pi$
$167$	−138.533	−	165.098i	−0.829541	−	0.988609i	0.170454	−	0.985366i	$-0.445477\pi$
$168$	3.75415	−	26.4905i	0.0223461	−	0.157682i
$169$	18.7495	−	6.82427i	0.110944	−	0.0403803i
$170$	−20.4414	−	11.8018i	−0.120243	−	0.0694225i
$171$	−88.8017	+	181.010i	−0.519308	+	1.05854i
$172$	−14.5692	−	25.2346i	−0.0847046	−	0.146713i
$173$	40.5261	−	48.2971i	0.234255	−	0.279174i	−0.636092	−	0.771613i	$-0.719450\pi$
$173$	40.5261	−	48.2971i	0.234255	−	0.279174i	0.870347	+	0.492439i	$0.163895\pi$
$174$	−31.6319	+	96.9725i	−0.181793	+	0.557313i
$175$	−13.4980	−	76.5511i	−0.0771316	−	0.437435i
$176$	−36.9749	+	6.51967i	−0.210085	+	0.0370436i
$177$	63.9825	−	57.4767i	0.361483	−	0.324727i
$178$	78.8015	+	66.1223i	0.442705	+	0.371473i
$179$	172.225	−	99.4340i	0.962150	−	0.555497i	0.0653157	−	0.997865i	$-0.479195\pi$
$179$	172.225	−	99.4340i	0.962150	−	0.555497i	0.896834	+	0.442367i	$0.145861\pi$
$180$	−4.29448	−	9.70572i	−0.0238582	−	0.0539207i
$181$	−35.6490	+	61.7458i	−0.196956	+	0.341137i	−0.947540	−	0.319638i	$-0.896439\pi$
$181$	−35.6490	+	61.7458i	−0.196956	+	0.341137i	0.750584	+	0.660775i	$0.229772\pi$
$182$	18.6196	+	51.1569i	0.102306	+	0.281082i
$183$	126.724	+	314.697i	0.692481	+	1.71966i
$184$	21.8165	−	18.3062i	0.118568	−	0.0994902i
$185$	6.35249	−	17.4533i	0.0343378	−	0.0943422i
$186$	90.7575	−	170.216i	0.487944	−	0.915142i
$187$	46.1370	−	261.656i	0.246722	−	1.39923i
$188$		−	110.646i		−	0.588545i
$189$	37.0556	+	76.6470i	0.196062	+	0.405540i
$190$	18.6804			0.0983177
$191$	−98.1741	−	17.3107i	−0.514000	−	0.0906322i	−0.0893693	−	0.995999i	$-0.528485\pi$
$191$	−98.1741	−	17.3107i	−0.514000	−	0.0906322i	−0.424631	+	0.905366i	$0.639596\pi$
$192$	20.3678	−	12.6946i	0.106082	−	0.0661176i
$193$	−178.750	−	65.0595i	−0.926164	−	0.337096i	−0.165476	−	0.986214i	$-0.552916\pi$
$193$	−178.750	−	65.0595i	−0.926164	−	0.337096i	−0.760688	+	0.649118i	$0.775138\pi$
$194$	142.897	+	170.298i	0.736582	+	0.877825i
$195$	17.0022	+	13.3151i	0.0871906	+	0.0682828i
$196$	−73.4046	+	26.7171i	−0.374513	+	0.136312i
$197$	−159.929	−	92.3348i	−0.811820	−	0.468705i	0.0357675	−	0.999360i	$-0.488612\pi$
$197$	−159.929	−	92.3348i	−0.811820	−	0.468705i	−0.847588	+	0.530656i	$0.821946\pi$
$198$	86.1295	−	82.7914i	0.434998	−	0.418138i
$199$	−31.0944	−	53.8571i	−0.156253	−	0.270639i	0.777261	−	0.629178i	$-0.216608\pi$
$199$	−31.0944	−	53.8571i	−0.156253	−	0.270639i	−0.933515	+	0.358539i	$0.883275\pi$
$200$	44.8199	−	53.4142i	0.224099	−	0.267071i
$201$	146.836	−	31.0340i	0.730525	−	0.154398i
$202$	30.8352	+	174.875i	0.152649	+	0.865718i
$203$	−74.6556	+	13.1638i	−0.367762	+	0.0648463i
$204$	35.1198	+	166.167i	0.172156	+	0.814545i
$205$	32.0034	+	26.8540i	0.156114	+	0.130995i
$206$	115.379	−	66.6141i	0.560093	−	0.323370i
$207$	−25.1793	+	87.0526i	−0.121639	+	0.420544i
$208$	−24.4170	+	42.2914i	−0.117389	+	0.203324i
$209$	71.9179	+	197.593i	0.344105	+	0.945420i
$210$	4.86341	−	6.21011i	0.0231591	−	0.0295719i
$211$	5.60018	−	4.69911i	0.0265411	−	0.0222706i	−0.629421	−	0.777065i	$-0.716708\pi$
$211$	5.60018	−	4.69911i	0.0265411	−	0.0222706i	0.655962	+	0.754794i	$0.272263\pi$
$212$	17.3807	−	47.7530i	0.0819843	−	0.225250i
$213$	13.9222	+	22.3374i	0.0653623	+	0.104870i
$214$	26.4967	−	150.270i	0.123816	−	0.702197i
$215$		−	8.59045i		−	0.0399556i
$216$	−31.3026	+	69.6574i	−0.144919	+	0.322488i
$217$	143.364			0.660661
$218$	−59.8410	−	10.5516i	−0.274500	−	0.0484017i
$219$	62.1346	+	33.1295i	0.283720	+	0.151276i
$220$	−10.4014	−	3.78580i	−0.0472791	−	0.0172082i
$221$	−222.133	−	264.728i	−1.00513	−	1.19786i
$222$	−123.970	+	49.9208i	−0.558422	+	0.224869i
$223$	−80.8775	+	29.4370i	−0.362679	+	0.132004i	−0.516931	−	0.856027i	$-0.672926\pi$
$223$	−80.8775	+	29.4370i	−0.362679	+	0.132004i	0.154252	+	0.988032i	$0.450703\pi$
$224$	15.4471	+	8.91840i	0.0689604	+	0.0398143i
$225$	−23.7006	+	220.602i	−0.105336	+	0.980451i
$226$	7.58788	+	13.1426i	0.0335747	+	0.0581531i
$227$	42.0709	−	50.1382i	0.185335	−	0.220873i	−0.665375	−	0.746509i	$-0.731728\pi$
$227$	42.0709	−	50.1382i	0.185335	−	0.220873i	0.850709	+	0.525636i	$0.176173\pi$
$228$	−89.8246	−	99.9919i	−0.393967	−	0.438561i
$229$	−57.3799	−	325.418i	−0.250567	−	1.42104i	−0.807199	−	0.590279i	$-0.799018\pi$
$229$	−57.3799	−	325.418i	−0.250567	−	1.42104i	0.556632	−	0.830759i	$-0.312093\pi$
$230$	8.26862	−	1.45798i	0.0359505	−	0.00633904i
$231$	84.4116	+	27.5346i	0.365418	+	0.119197i
$232$	−52.0917	−	43.7101i	−0.224533	−	0.188406i
$233$	−123.820	+	71.4877i	−0.531418	+	0.306814i	−0.741594	−	0.670849i	$-0.765930\pi$
$233$	−123.820	+	71.4877i	−0.531418	+	0.306814i	0.210176	+	0.977664i	$0.432596\pi$
$234$	−10.4819	−	155.035i	−0.0447945	−	0.662542i
$235$	16.3101	−	28.2500i	0.0694049	−	0.120213i
$236$	19.6109	+	53.8806i	0.0830971	+	0.228308i
$237$	−394.339	−	55.8844i	−1.66388	−	0.235799i
$238$	−96.6929	+	81.1350i	−0.406273	+	0.340903i
$239$	−103.746	+	285.040i	−0.434084	+	1.19264i	0.509200	+	0.860649i	$0.329942\pi$
$239$	−103.746	+	285.040i	−0.434084	+	1.19264i	−0.943284	+	0.331988i	$0.892281\pi$
$240$	7.07154	−	0.238781i	0.0294648	−	0.000994922i
$241$	−54.3108	+	308.012i	−0.225356	+	1.27806i	0.636647	+	0.771155i	$0.280321\pi$
$241$	−54.3108	+	308.012i	−0.225356	+	1.27806i	−0.862003	+	0.506903i	$0.830790\pi$
$242$			46.5232i			0.192245i
$243$	−40.8163	−	239.548i	−0.167968	−	0.985792i
$244$	−226.169			−0.926924
$245$	−22.6798	−	3.99906i	−0.0925707	−	0.0163227i
$246$	−10.1446	−	300.435i	−0.0412383	−	1.22128i
$247$	257.003	+	93.5413i	1.04050	+	0.378710i
$248$	82.6626	+	98.5135i	0.333317	+	0.397232i
$249$	−28.2697	+	199.481i	−0.113533	+	0.801127i
$250$	38.9064	−	14.1608i	0.155626	−	0.0566431i
$251$	116.446	+	67.2298i	0.463926	+	0.267848i	0.713694	−	0.700458i	$-0.247021\pi$
$251$	116.446	+	67.2298i	0.463926	+	0.267848i	−0.249767	+	0.968306i	$0.580354\pi$
$252$	−56.6271	+	3.82856i	−0.224711	+	0.0151927i
$253$	47.2554	+	81.8488i	0.186780	+	0.323513i
$254$	−89.3598	+	106.495i	−0.351810	+	0.419271i
$255$	−15.5277	+	47.6024i	−0.0608928	+	0.186676i
$256$	2.77837	+	15.7569i	0.0108530	+	0.0615505i
$257$	46.8542	−	8.26166i	0.182312	−	0.0321465i	−0.0817466	−	0.996653i	$-0.526050\pi$
$257$	46.8542	−	8.26166i	0.182312	−	0.0321465i	0.264059	+	0.964507i	$0.414939\pi$
$258$	−45.9828	+	41.3072i	−0.178228	+	0.160106i
$259$	−76.0865	−	63.8441i	−0.293770	−	0.246502i
$260$	−12.4682	+	7.19851i	−0.0479545	+	0.0276866i
$261$	215.139	+	23.1137i	0.824288	+	0.0885584i
$262$	−96.8939	+	167.825i	−0.369824	+	0.640554i
$263$	−162.251	−	445.781i	−0.616924	−	1.69498i	−0.714392	−	0.699745i	$-0.753297\pi$
$263$	−162.251	−	445.781i	−0.616924	−	1.69498i	0.0974685	−	0.995239i	$-0.468925\pi$
$264$	29.7506	+	73.8805i	0.112692	+	0.279850i
$265$	11.4768	−	9.63015i	0.0433085	−	0.0363402i
$266$	34.1663	−	93.8712i	0.128445	−	0.352899i
$267$	102.668	−	192.555i	0.384525	−	0.721180i
$268$	−17.3740	+	98.5329i	−0.0648284	+	0.367660i
$269$			455.081i			1.69175i	0.533380	+	0.845876i	$0.320922\pi$
$269$			455.081i			1.69175i	−0.533380	+	0.845876i	$0.679078\pi$
$270$	−18.2601	+	13.1705i	−0.0676302	+	0.0487797i
$271$	440.939			1.62708			0.813541	−	0.581508i	$-0.197537\pi$
$271$	440.939			1.62708			0.813541	+	0.581508i	$0.197537\pi$
$272$	−111.505	−	19.6614i	−0.409946	−	0.0722845i
$273$	98.0072	−	61.0847i	0.359001	−	0.223753i
$274$	266.035	+	96.8287i	0.970929	+	0.353389i
$275$	148.738	+	177.259i	0.540864	+	0.644577i
$276$	−47.5639	−	37.2494i	−0.172333	−	0.134962i
$277$	−70.8393	+	25.7834i	−0.255738	+	0.0930808i	−0.466708	−	0.884412i	$-0.654560\pi$
$277$	−70.8393	+	25.7834i	−0.255738	+	0.0930808i	0.210970	+	0.977493i	$0.432338\pi$
$278$	−8.72984	−	5.04017i	−0.0314023	−	0.0181301i
$279$	−393.091	−	113.698i	−1.40893	−	0.407521i
$280$	2.62928	+	4.55405i	0.00939030	+	0.0162645i
$281$	4.98848	−	5.94504i	0.0177526	−	0.0211567i	−0.757095	−	0.653305i	$-0.773382\pi$
$281$	4.98848	−	5.94504i	0.0177526	−	0.0211567i	0.774848	+	0.632148i	$0.217827\pi$
$282$	−229.643	+	48.5356i	−0.814339	+	0.172112i
$283$	28.3852	+	160.981i	0.100301	+	0.568836i	0.992993	+	0.118169i	$0.0377026\pi$
$283$	28.3852	+	160.981i	0.100301	+	0.568836i	−0.892692	+	0.450667i	$0.851186\pi$
$284$	−17.2806	+	3.04704i	−0.0608473	+	0.0107290i
$285$	−8.19423	−	38.7706i	−0.0287517	−	0.136037i
$286$	−124.144	−	104.169i	−0.434071	−	0.364229i
$287$	193.479	−	111.705i	0.674143	−	0.389217i
$288$	−35.2817	−	36.7043i	−0.122506	−	0.127445i
$289$	256.124	−	443.620i	0.886244	−	1.53502i
$290$	−6.85672	−	18.8387i	−0.0236439	−	0.0649610i
$291$	290.766	−	371.281i	0.999196	−	1.27588i
$292$	−35.9607	+	30.1746i	−0.123153	+	0.103338i
$293$	18.4986	−	50.8246i	0.0631353	−	0.173463i	−0.904114	−	0.427292i	$-0.859468\pi$
$293$	18.4986	−	50.8246i	0.0631353	−	0.173463i	0.967249	+	0.253829i	$0.0816900\pi$
$294$	87.6498	+	140.630i	0.298129	+	0.478332i
$295$	−2.93540	+	16.6475i	−0.00995051	+	0.0564321i
$296$		−	89.0956i		−	0.300999i
$297$	−209.612	−	142.443i	−0.705765	−	0.479605i
$298$	132.586			0.444921
$299$	121.060	+	21.3461i	0.404882	+	0.0713915i
$300$	−130.520	−	69.5919i	−0.435067	−	0.231973i
$301$	−43.1681	−	15.7119i	−0.143416	−	0.0521991i
$302$	183.419	+	218.591i	0.607349	+	0.723810i
$303$	349.422	−	140.707i	1.15321	−	0.464381i
$304$	84.2046	−	30.6480i	0.276989	−	0.100816i
$305$	−57.7451	−	33.3391i	−0.189328	−	0.109309i
$306$	329.470	−	145.780i	1.07670	−	0.476406i
$307$	73.1993	+	126.785i	0.238434	+	0.412980i	0.960265	−	0.279089i	$-0.0900325\pi$
$307$	73.1993	+	126.785i	0.238434	+	0.412980i	−0.721831	+	0.692069i	$0.756699\pi$
$308$	−38.0483	+	45.3442i	−0.123533	+	0.147221i
$309$	−188.867	−	210.245i	−0.611221	−	0.680406i
$310$	6.58359	+	37.3374i	0.0212374	+	0.120443i
$311$	272.335	−	48.0200i	0.875676	−	0.154405i	0.282295	−	0.959328i	$-0.408904\pi$
$311$	272.335	−	48.0200i	0.875676	−	0.154405i	0.593380	+	0.804922i	$0.297793\pi$
$312$	98.4853	+	32.1254i	0.315658	+	0.102966i
$313$	−22.9780	−	19.2809i	−0.0734123	−	0.0616002i	0.605343	−	0.795965i	$-0.293036\pi$
$313$	−22.9780	−	19.2809i	−0.0734123	−	0.0616002i	−0.678755	+	0.734364i	$0.737480\pi$
$314$	−89.8939	+	51.9003i	−0.286286	+	0.165287i
$315$	−15.0223	−	7.36977i	−0.0476897	−	0.0233961i
$316$	132.760	−	229.946i	0.420125	−	0.727678i
$317$	−91.5339	−	251.487i	−0.288750	−	0.793335i	−0.996242	−	0.0866133i	$-0.972396\pi$
$317$	−91.5339	−	251.487i	−0.288750	−	0.793335i	0.707492	−	0.706722i	$-0.249827\pi$
$318$	−106.734	−	15.1260i	−0.335642	−	0.0475661i
$319$	172.870	−	145.055i	0.541911	−	0.454717i
$320$	−1.61333	+	4.43258i	−0.00504164	+	0.0138518i
$321$	−323.504	+	10.9236i	−1.00780	+	0.0340299i
$322$	7.79674	−	44.2175i	0.0242135	−	0.137321i
$323$			634.123i			1.96323i
$324$	158.303	+	34.4121i	0.488589	+	0.106210i
$325$	300.968			0.926055
$326$	−302.401	−	53.3214i	−0.927610	−	0.163563i
$327$	4.35002	+	128.827i	0.0133028	+	0.393965i
$328$	188.318	+	68.5422i	0.574141	+	0.208970i
$329$	−112.129	−	133.630i	−0.340817	−	0.406169i
$330$	−3.29470	+	23.2485i	−0.00998393	+	0.0704499i
$331$	−358.351	+	130.429i	−1.08263	+	0.394045i	−0.820886	−	0.571092i	$-0.806520\pi$
$331$	−358.351	+	130.429i	−1.08263	+	0.394045i	−0.261744	+	0.965137i	$0.584298\pi$
$332$	−116.321	−	67.1580i	−0.350364	−	0.202283i
$333$	157.989	+	235.398i	0.474442	+	0.706900i
$334$	−152.395	−	263.957i	−0.456274	−	0.790289i
$335$	−18.9604	+	22.5961i	−0.0565982	+	0.0674511i
$336$	11.7339	−	35.9722i	0.0349224	−	0.107060i
$337$	20.7953	+	117.936i	0.0617071	+	0.349958i	0.999992	+	0.00409401i	$0.00130317\pi$
$337$	20.7953	+	117.936i	0.0617071	+	0.349958i	−0.938285	+	0.345864i	$0.887586\pi$
$338$	27.7889	−	4.89993i	0.0822156	−	0.0144968i
$339$	23.9486	−	21.5135i	0.0706449	−	0.0634616i
$340$	−25.5710	−	21.4566i	−0.0752089	−	0.0631078i
$341$	−369.592	+	213.384i	−1.08385	+	0.625760i
$342$	−168.128	+	230.290i	−0.491603	+	0.673363i
$343$	−138.829	+	240.459i	−0.404749	+	0.701045i
$344$	−14.0939	−	38.7228i	−0.0409707	−	0.112566i
$345$	−6.65306	−	16.5217i	−0.0192842	−	0.0478891i
$346$	68.3024	−	57.3125i	0.197406	−	0.165643i
$347$	−85.0851	+	233.769i	−0.245202	+	0.673687i	0.754644	+	0.656135i	$0.227810\pi$
$347$	−85.0851	+	233.769i	−0.245202	+	0.673687i	−0.999846	+	0.0175526i	$0.994413\pi$
$348$	−67.8688	+	127.288i	−0.195025	+	0.365771i
$349$	−55.5583	+	315.087i	−0.159193	+	0.902827i	0.795659	+	0.605745i	$0.207125\pi$
$349$	−55.5583	+	315.087i	−0.159193	+	0.902827i	−0.954852	+	0.297082i	$0.903986\pi$
$350$		−	109.930i		−	0.314085i
$351$	−317.172	+	89.7616i	−0.903625	+	0.255731i
$352$	−53.0971			−0.150844
$353$	−326.236	−	57.5243i	−0.924182	−	0.162958i	−0.308746	−	0.951145i	$-0.599909\pi$
$353$	−326.236	−	57.5243i	−0.924182	−	0.162958i	−0.615437	+	0.788186i	$0.711020\pi$
$354$	103.225	−	64.3369i	0.291597	−	0.181743i
$355$	−4.86121	−	1.76934i	−0.0136936	−	0.00498405i
$356$	93.5110	+	111.442i	0.262671	+	0.313040i
$357$	210.808	+	165.093i	0.590499	+	0.462446i
$358$	264.281	−	96.1904i	0.738215	−	0.268688i
$359$	277.930	+	160.463i	0.774178	+	0.446972i	0.834363	−	0.551216i	$-0.185836\pi$
$359$	277.930	+	160.463i	0.774178	+	0.446972i	−0.0601853	+	0.998187i	$0.519169\pi$
$360$	−3.59755	−	14.5720i	−0.00999319	−	0.0404779i
$361$	−70.4283	−	121.985i	−0.195092	−	0.337910i
$362$	−64.8126	+	77.2407i	−0.179040	+	0.213372i
$363$	96.5577	−	20.4076i	0.265999	−	0.0562194i
$364$	13.3692	+	75.8202i	0.0367284	+	0.208297i
$365$	−13.6294	+	2.40323i	−0.0373408	+	0.00658419i
$366$	99.2103	+	469.408i	0.271066	+	1.28254i
$367$	−558.217	−	468.400i	−1.52103	−	1.27629i	−0.837617	−	0.546258i	$-0.816052\pi$
$367$	−558.217	−	468.400i	−1.52103	−	1.27629i	−0.683410	−	0.730035i	$-0.739504\pi$
$368$	34.8800	−	20.1380i	0.0947826	−	0.0547228i
$369$	−619.094	+	152.842i	−1.67776	+	0.414206i
$370$	13.1334	−	22.7477i	0.0354957	−	0.0614803i
$371$	−27.4018	−	75.2857i	−0.0738592	−	0.202927i
$372$	168.202	−	214.777i	0.452155	−	0.577359i
$373$	−262.562	+	220.316i	−0.703920	+	0.590659i	−0.922886	−	0.385073i	$-0.874176\pi$
$373$	−262.562	+	220.316i	−0.703920	+	0.590659i	0.218966	+	0.975733i	$0.429732\pi$
$374$	128.513	−	353.086i	0.343617	−	0.944079i
$375$	−46.4567	−	74.5374i	−0.123885	−	0.198766i
$376$	27.1721	−	154.100i	0.0722661	−	0.409841i
$377$		−	293.516i		−	0.778556i
$378$	32.7858	+	115.848i	0.0867349	+	0.306477i
$379$	−607.166			−1.60202			−0.801011	−	0.598650i	$-0.795704\pi$
$379$	−607.166			−1.60202			−0.801011	+	0.598650i	$0.795704\pi$
$380$	26.0167	+	4.58744i	0.0684649	+	0.0120722i
$381$	260.225	+	138.749i	0.683006	+	0.364171i
$382$	−132.479	−	48.2183i	−0.346803	−	0.126226i
$383$	−97.3839	−	116.058i	−0.254266	−	0.303023i	0.623779	−	0.781601i	$-0.285597\pi$
$383$	−97.3839	−	116.058i	−0.254266	−	0.303023i	−0.878045	+	0.478578i	$0.841152\pi$
$384$	31.4843	−	12.6783i	0.0819904	−	0.0330164i
$385$	−16.3985	+	5.96856i	−0.0425935	+	0.0155028i
$386$	−232.973	−	134.507i	−0.603556	−	0.348463i
$387$	105.903	+	77.3164i	0.273650	+	0.199784i
$388$	157.196	+	272.271i	0.405143	+	0.701729i
$389$	389.211	−	463.844i	1.00054	−	1.19240i	0.0192633	−	0.999814i	$-0.493868\pi$
$389$	389.211	−	463.844i	1.00054	−	1.19240i	0.981280	−	0.192587i	$-0.0616876\pi$
$390$	20.4095	+	22.7197i	0.0523321	+	0.0582556i
$391$	49.4925	+	280.686i	0.126579	+	0.717867i
$392$	−108.794	+	19.1833i	−0.277535	+	0.0489369i
$393$	390.819	+	127.483i	0.994451	+	0.324385i
$394$	−200.062	−	167.872i	−0.507771	−	0.426071i
$395$	67.7918	−	39.1396i	0.171625	−	0.0990876i
$396$	140.287	−	94.1546i	0.354259	−	0.237764i
$397$	301.433	−	522.097i	0.759277	−	1.31511i	−0.183942	−	0.982937i	$-0.558886\pi$
$397$	301.433	−	522.097i	0.759277	−	1.31511i	0.943220	−	0.332170i	$-0.107781\pi$
$398$	−30.0801	−	82.6444i	−0.0755782	−	0.207649i
$399$	−209.814	−	29.7342i	−0.525850	−	0.0745218i
$400$	75.5391	−	63.3849i	0.188848	−	0.158462i
$401$	151.840	−	417.177i	0.378653	−	1.04034i	−0.593262	−	0.805010i	$-0.702160\pi$
$401$	151.840	−	417.177i	0.378653	−	1.04034i	0.971915	−	0.235332i	$-0.0756177\pi$
$402$	212.123	−	7.16266i	0.527670	−	0.0178176i
$403$	−96.3893	+	546.651i	−0.239179	+	1.35645i
$404$			251.126i			0.621599i
$405$	35.3449	+	32.1211i	0.0872715	+	0.0793114i
$406$	−107.208			−0.264058
$407$	291.178	+	51.3425i	0.715425	+	0.126149i
$408$	8.10566	+	240.050i	0.0198668	+	0.588359i
$409$	−388.673	−	141.465i	−0.950300	−	0.345881i	−0.180075	−	0.983653i	$-0.557634\pi$
$409$	−388.673	−	141.465i	−0.950300	−	0.345881i	−0.770225	+	0.637772i	$0.779856\pi$
$410$	37.9773	+	45.2596i	0.0926276	+	0.110389i
$411$	84.2678	−	594.622i	0.205031	−	1.44677i
$412$	177.051	−	64.4411i	0.429734	−	0.156410i
$413$	78.2869	+	45.1989i	0.189557	+	0.109441i
$414$	−56.4459	+	115.057i	−0.136343	+	0.277916i
$415$	−19.7992	−	34.2932i	−0.0477090	−	0.0826343i
$416$	−44.3920	+	52.9043i	−0.106711	+	0.127174i
$417$	−6.63135	+	20.3294i	−0.0159025	+	0.0487516i
$418$	51.6381	+	292.854i	0.123536	+	0.700609i
$419$	606.886	−	107.010i	1.44842	−	0.255395i	0.606534	−	0.795057i	$-0.292559\pi$
$419$	606.886	−	107.010i	1.44842	−	0.255395i	0.841881	+	0.539662i	$0.181448\pi$
$420$	8.29846	−	7.45466i	0.0197582	−	0.0177492i
$421$	2.88941	+	2.42451i	0.00686322	+	0.00575892i	0.646213	−	0.763157i	$-0.276352\pi$
$421$	2.88941	+	2.42451i	0.00686322	+	0.00575892i	−0.639350	+	0.768916i	$0.720796\pi$
$422$	8.95351	−	5.16931i	0.0212169	−	0.0122496i
$423$	201.468	+	455.328i	0.476285	+	1.07643i
$424$	35.9335	−	62.2387i	0.0847489	−	0.146789i
$425$	238.668	+	655.734i	0.561571	+	1.54290i
$426$	13.9043	+	34.5289i	0.0326392	+	0.0810537i
$427$	−273.149	+	229.199i	−0.639693	+	0.536766i
$428$	73.8054	−	202.779i	0.172442	−	0.473782i
$429$	−161.744	+	303.352i	−0.377026	+	0.707115i
$430$	2.10961	−	11.9642i	0.00490606	−	0.0278237i
$431$		−	658.872i		−	1.52871i	−0.644798	−	0.764353i	$-0.723059\pi$
$431$		−	658.872i		−	1.52871i	0.644798	−	0.764353i	$-0.276941\pi$
$432$	−60.7022	+	89.3266i	−0.140514	+	0.206775i
$433$	170.484			0.393728			0.196864	−	0.980431i	$-0.436924\pi$
$433$	170.484			0.393728			0.196864	+	0.980431i	$0.436924\pi$
$434$	199.666	+	35.2066i	0.460061	+	0.0811212i
$435$	−36.0914	+	22.4946i	−0.0829688	+	0.0517117i
$436$	−80.7510	−	29.3910i	−0.185209	−	0.0674105i
$437$	−144.992	−	172.794i	−0.331789	−	0.395410i
$438$	78.4009	+	61.3992i	0.178997	+	0.140181i
$439$	805.882	−	293.317i	1.83572	−	0.668148i	0.844566	−	0.535452i	$-0.179859\pi$
$439$	805.882	−	293.317i	1.83572	−	0.668148i	0.991157	−	0.132697i	$-0.0423636\pi$
$440$	−13.5566	−	7.82692i	−0.0308105	−	0.0177885i
$441$	253.425	−	243.603i	0.574659	−	0.552387i
$442$	−244.360	−	423.244i	−0.552851	−	0.957566i
$443$	−160.598	+	191.394i	−0.362524	+	0.432040i	−0.916218	−	0.400681i	$-0.868774\pi$
$443$	−160.598	+	191.394i	−0.362524	+	0.432040i	0.553693	+	0.832721i	$0.313218\pi$
$444$	−184.915	+	39.0822i	−0.416476	+	0.0880230i
$445$	7.44759	+	42.2374i	0.0167362	+	0.0949155i
$446$	−119.869	+	21.1362i	−0.268765	+	0.0473906i
$447$	−58.1596	−	275.179i	−0.130111	−	0.615614i
$448$	19.3235	+	16.2143i	0.0431328	+	0.0361927i
$449$	−208.642	+	120.460i	−0.464682	+	0.268284i	−0.714011	−	0.700135i	$-0.753123\pi$
$449$	−208.642	+	120.460i	−0.464682	+	0.268284i	0.249329	+	0.968419i	$0.419790\pi$
$450$	−87.1828	+	301.418i	−0.193740	+	0.669817i
$451$	−332.527	+	575.954i	−0.737311	+	1.27706i
$452$	7.34036	+	20.1675i	0.0162397	+	0.0446183i
$453$	373.221	−	476.568i	0.823887	−	1.05203i
$454$	70.9061	−	59.4973i	0.156181	−	0.131051i
$455$	−7.76311	+	21.3290i	−0.0170618	+	0.0468769i
$456$	−100.546	−	161.320i	−0.220495	−	0.353773i
$457$	−33.0420	+	187.391i	−0.0723020	+	0.410045i	0.927079	+	0.374866i	$0.122311\pi$
$457$	−33.0420	+	187.391i	−0.0723020	+	0.410045i	−0.999381	+	0.0351791i	$0.988800\pi$
$458$		−	467.310i		−	1.02033i
$459$	−447.086	−	619.858i	−0.974044	−	1.35045i
$460$	11.8740			0.0258130
$461$	282.999	+	49.9003i	0.613880	+	0.108244i	0.471938	−	0.881632i	$-0.343554\pi$
$461$	282.999	+	49.9003i	0.613880	+	0.108244i	0.141941	+	0.989875i	$0.454666\pi$
$462$	110.801	+	59.0777i	0.239828	+	0.127874i
$463$	15.8899	+	5.78346i	0.0343195	+	0.0124913i	0.359123	−	0.933290i	$-0.383076\pi$
$463$	15.8899	+	5.78346i	0.0343195	+	0.0124913i	−0.324803	+	0.945782i	$0.605298\pi$
$464$	−61.8154	−	73.6687i	−0.133223	−	0.158769i
$465$	74.6047	−	30.0423i	0.160440	−	0.0646070i
$466$	−190.004	+	69.1557i	−0.407734	+	0.148403i
$467$	590.760	+	341.075i	1.26501	+	0.730354i	0.974040	−	0.226378i	$-0.0726883\pi$
$467$	590.760	+	341.075i	1.26501	+	0.730354i	0.290971	+	0.956732i	$0.406022\pi$
$468$	23.4743	−	218.495i	0.0501588	−	0.466871i
$469$	78.8699	+	136.607i	0.168166	+	0.291272i
$470$	29.6531	−	35.3392i	0.0630917	−	0.0751898i
$471$	147.150	+	163.806i	0.312420	+	0.347783i
$472$	14.0809	+	79.8570i	0.0298325	+	0.169189i
$473$	134.674	−	23.7466i	0.284722	−	0.0502042i
$474$	−535.483	−	174.672i	−1.12971	−	0.368506i
$475$	−423.060	−	354.989i	−0.890652	−	0.747346i
$476$	−154.592	+	89.2536i	−0.324772	+	0.187507i
$477$	15.4258	+	228.159i	0.0323393	+	0.478320i
$478$	−214.489	+	371.506i	−0.448722	+	0.777209i
$479$	−191.036	−	524.867i	−0.398822	−	1.09576i	−0.962859	−	0.270005i	$-0.912975\pi$
$479$	−191.036	−	524.867i	−0.398822	−	1.09576i	0.564037	−	0.825750i	$-0.309248\pi$
$480$	9.90738	+	1.40404i	0.0206404	+	0.00292509i
$481$	294.596	−	247.196i	0.612466	−	0.513920i
$482$	−151.280	+	415.640i	−0.313860	+	0.862323i
$483$	−95.1922	+	3.21431i	−0.197085	+	0.00665488i
$484$	−11.4250	+	64.7942i	−0.0236053	+	0.133872i
$485$			92.6875i			0.191108i
$486$	1.98103	−	343.648i	0.00407619	−	0.707095i
$487$	−115.842			−0.237869			−0.118935	−	0.992902i	$-0.537948\pi$
$487$	−115.842			−0.237869			−0.118935	+	0.992902i	$0.537948\pi$
$488$	−314.992	−	55.5417i	−0.645476	−	0.113815i
$489$	21.9825	+	651.014i	0.0449539	+	1.33132i
$490$	−30.6047	−	11.1392i	−0.0624587	−	0.0227331i
$491$	79.5701	+	94.8280i	0.162057	+	0.193132i	0.840962	−	0.541094i	$-0.181990\pi$
$491$	79.5701	+	94.8280i	0.162057	+	0.193132i	−0.678905	+	0.734226i	$0.737545\pi$
$492$	59.6507	−	420.915i	0.121241	−	0.855519i
$493$	639.497	−	232.758i	1.29715	−	0.472126i
$494$	334.963	+	193.391i	0.678063	+	0.391480i
$495$	49.6968	−	3.36000i	0.100398	−	0.00678788i
$496$	90.9341	+	157.502i	0.183335	+	0.317545i
$497$	−17.7823	+	21.1921i	−0.0357793	+	0.0426401i
$498$	−88.3597	+	270.880i	−0.177429	+	0.543936i
$499$	−65.4282	−	371.062i	−0.131119	−	0.743610i	−0.977484	−	0.211008i	$-0.932325\pi$
$499$	−65.4282	−	371.062i	−0.131119	−	0.743610i	0.846366	−	0.532602i	$-0.178786\pi$
$500$	57.6636	−	10.1676i	0.115327	−	0.0203353i
$501$	−480.985	+	432.078i	−0.960051	+	0.862431i
$502$	145.667	+	122.229i	0.290173	+	0.243484i
$503$	−363.520	+	209.878i	−0.722704	+	0.417253i	−0.815747	−	0.578409i	$-0.803674\pi$
$503$	−363.520	+	209.878i	−0.722704	+	0.417253i	0.0930432	+	0.995662i	$0.470341\pi$
$504$	−79.8063	−	8.57408i	−0.158346	−	0.0170121i
$505$	−37.0179	+	64.1169i	−0.0733028	+	0.126964i
$506$	45.7139	+	125.598i	0.0903436	+	0.248217i
$507$	−22.3594	−	55.5256i	−0.0441013	−	0.109518i
$508$	−150.606	+	126.374i	−0.296469	+	0.248767i
$509$	−41.8155	+	114.887i	−0.0821523	+	0.225712i	−0.973967	−	0.226689i	$-0.927210\pi$
$509$	−41.8155	+	114.887i	−0.0821523	+	0.225712i	0.891815	+	0.452400i	$0.149432\pi$
$510$	−33.3158	+	62.4840i	−0.0653251	+	0.122518i
$511$	−12.8516	+	72.8849i	−0.0251498	+	0.142632i
$512$			22.6274i			0.0441942i
$513$	551.711	+	247.928i	1.07546	+	0.483290i
$514$	67.2841			0.130903
$515$	54.7033	+	9.64566i	0.106220	+	0.0187294i
$516$	−74.1856	+	46.2375i	−0.143771	+	0.0896075i
$517$	487.965	+	177.605i	0.943840	+	0.343530i
$518$	−90.2892	−	107.602i	−0.174303	−	0.207727i
$519$	−148.912	−	116.619i	−0.286920	−	0.224700i
$520$	−19.1326	+	6.96368i	−0.0367934	+	0.0133917i
$521$	−891.453	−	514.680i	−1.71104	−	0.987870i	−0.933161	−	0.359458i	$-0.882962\pi$
$521$	−891.453	−	514.680i	−1.71104	−	0.987870i	−0.777880	−	0.628412i	$-0.783705\pi$
$522$	293.954	+	85.0241i	0.563131	+	0.162881i
$523$	−131.269	−	227.364i	−0.250992	−	0.434731i	0.712807	−	0.701360i	$-0.247423\pi$
$523$	−131.269	−	227.364i	−0.250992	−	0.434731i	−0.963799	+	0.266629i	$0.914090\pi$
$524$	−176.161	+	209.940i	−0.336184	+	0.400649i
$525$	−228.156	+	48.2212i	−0.434583	+	0.0918498i
$526$	−116.499	−	660.697i	−0.221480	−	1.25608i
$527$	−1267.45	+	223.486i	−2.40503	+	0.424072i
$528$	23.2913	+	110.201i	0.0441123	+	0.208715i
$529$	327.572	+	274.866i	0.619230	+	0.519595i
$530$	18.3489	−	10.5938i	0.0346207	−	0.0199882i
$531$	−178.810	−	186.019i	−0.336741	−	0.350319i
$532$	70.6369	−	122.347i	0.132776	−	0.229975i
$533$	295.852	+	812.848i	0.555070	+	1.52504i
$534$	190.276	−	242.964i	0.356322	−	0.454989i
$535$	48.7350	−	40.8935i	0.0910934	−	0.0764364i
$536$	−48.3945	+	132.963i	−0.0902883	+	0.248065i
$537$	−315.569	−	506.313i	−0.587651	−	0.942855i
$538$	−111.757	+	633.804i	−0.207726	+	1.17808i
$539$		−	366.609i		−	0.680165i
$540$	−28.6658	+	13.8587i	−0.0530848	+	0.0256643i
$541$	14.7044			0.0271800			0.0135900	−	0.999908i	$-0.495674\pi$
$541$	14.7044			0.0271800			0.0135900	+	0.999908i	$0.495674\pi$
$542$	614.109	+	108.284i	1.13304	+	0.199786i
$543$	188.741	+	100.635i	0.347590	+	0.185331i
$544$	−150.468	−	54.7659i	−0.276596	−	0.100673i
$545$	−16.2847	−	19.4074i	−0.0298802	−	0.0356098i
$546$	151.498	−	61.0062i	0.277469	−	0.111733i
$547$	353.812	−	128.777i	0.646823	−	0.235424i	0.00228579	−	0.999997i	$-0.499272\pi$
$547$	353.812	−	128.777i	0.646823	−	0.235424i	0.644537	+	0.764573i	$0.277050\pi$
$548$	346.735	+	200.188i	0.632729	+	0.365306i
$549$	930.724	−	411.816i	1.69531	−	0.750120i
$550$	163.621	+	283.400i	0.297492	+	0.515272i
$551$	−346.200	+	412.585i	−0.628311	+	0.748792i
$552$	−57.0961	−	63.5588i	−0.103435	−	0.115143i
$553$	−72.6906	−	412.249i	−0.131448	−	0.745477i
$554$	−104.992	+	18.5129i	−0.189516	+	0.0334167i
$555$	−52.9732	−	17.2796i	−0.0954473	−	0.0311344i
$556$	−10.9205	−	9.16343i	−0.0196413	−	0.0164810i
$557$	339.531	−	196.028i	0.609571	−	0.351936i	−0.163226	−	0.986589i	$-0.552190\pi$
$557$	339.531	−	196.028i	0.609571	−	0.351936i	0.772798	+	0.634653i	$0.218857\pi$
$558$	−519.547	−	254.885i	−0.931087	−	0.456782i
$559$	88.9339	−	154.038i	0.159095	−	0.275560i
$560$	2.54351	+	6.98825i	0.00454199	+	0.0124790i
$561$	−789.192	−	111.842i	−1.40676	−	0.199361i
$562$	8.40755	−	7.05477i	0.0149601	−	0.0125530i
$563$	−282.488	+	776.129i	−0.501754	+	1.37856i	0.387806	+	0.921741i	$0.373233\pi$
$563$	−282.488	+	776.129i	−0.501754	+	1.37856i	−0.889560	+	0.456818i	$0.848989\pi$
$564$	−331.750	+	11.2020i	−0.588209	+	0.0198618i
$565$	−1.09872	+	6.23114i	−0.00194463	+	0.0110286i
$566$			231.173i			0.408433i
$567$	226.058	−	118.863i	0.398692	−	0.209636i
$568$	−24.8155			−0.0436893
$569$	−820.292	−	144.640i	−1.44164	−	0.254200i	−0.602501	−	0.798118i	$-0.705829\pi$
$569$	−820.292	−	144.640i	−1.44164	−	0.254200i	−0.839138	+	0.543919i	$0.816940\pi$
$570$	−1.89123	−	56.0092i	−0.00331795	−	0.0982617i
$571$	−171.024	−	62.2478i	−0.299517	−	0.109015i	0.187890	−	0.982190i	$-0.439835\pi$
$571$	−171.024	−	62.2478i	−0.299517	−	0.109015i	−0.487407	+	0.873175i	$0.662057\pi$
$572$	−147.318	−	175.566i	−0.257548	−	0.306934i
$573$	−41.9633	+	296.107i	−0.0732344	+	0.516766i
$574$	296.896	−	108.061i	0.517240	−	0.188260i
$575$	−214.968	−	124.112i	−0.373858	−	0.215847i
$576$	−40.1241	−	59.7834i	−0.0696600	−	0.103791i
$577$	−25.3860	−	43.9699i	−0.0439966	−	0.0762043i	0.843189	−	0.537618i	$-0.180676\pi$
$577$	−25.3860	−	43.9699i	−0.0439966	−	0.0762043i	−0.887185	+	0.461414i	$0.847342\pi$
$578$	465.654	−	554.945i	0.805630	−	0.960112i
$579$	−176.971	+	542.530i	−0.305649	+	0.937012i
$580$	−4.92323	−	27.9210i	−0.00848832	−	0.0481397i
$581$	−208.541	+	36.7713i	−0.358934	+	0.0632898i
$582$	496.136	−	445.688i	0.852467	−	0.765787i
$583$	182.698	+	153.302i	0.313376	+	0.262954i
$584$	−57.4936	+	33.1940i	−0.0984480	+	0.0568390i
$585$	38.2013	−	52.3255i	0.0653014	−	0.0894453i
$586$	38.2449	−	66.2421i	0.0652643	−	0.113041i
$587$	29.4058	+	80.7919i	0.0500951	+	0.137635i	0.962217	−	0.272284i	$-0.0877791\pi$
$587$	29.4058	+	80.7919i	0.0500951	+	0.137635i	−0.912122	+	0.409919i	$0.865557\pi$
$588$	87.5372	+	217.383i	0.148873	+	0.369700i
$589$	780.262	−	654.718i	1.32472	−	1.11158i
$590$	−8.17643	+	22.4646i	−0.0138584	+	0.0380755i
$591$	−260.655	+	488.860i	−0.441041	+	0.827175i
$592$	21.8797	−	124.086i	0.0369590	−	0.209605i
$593$		−	333.051i		−	0.561638i	−0.959761	−	0.280819i	$-0.909394\pi$
$593$		−	333.051i		−	0.561638i	0.959761	−	0.280819i	$-0.0906060\pi$
$594$	−256.952	−	249.859i	−0.432580	−	0.420639i
$595$	−52.6267			−0.0884482
$596$	184.657	+	32.5600i	0.309827	+	0.0546308i
$597$	−158.331	+	98.6828i	−0.265212	+	0.165298i
$598$	163.361	+	59.4586i	0.273179	+	0.0994290i
$599$	376.276	+	448.428i	0.628173	+	0.748628i	0.982453	−	0.186512i	$-0.0597182\pi$
$599$	376.276	+	448.428i	0.628173	+	0.748628i	−0.354279	+	0.935140i	$0.615274\pi$
$600$	−164.689	−	128.975i	−0.274482	−	0.214959i
$601$	684.489	−	249.134i	1.13892	−	0.414532i	0.297395	−	0.954755i	$-0.403882\pi$
$601$	684.489	−	249.134i	1.13892	−	0.414532i	0.841522	+	0.540223i	$0.181660\pi$
$602$	−56.2630	−	32.4835i	−0.0934602	−	0.0539593i
$603$	−107.915	−	437.114i	−0.178963	−	0.724899i
$604$	201.773	+	349.481i	0.334061	+	0.578611i
$605$	−12.4682	+	14.8590i	−0.0206086	+	0.0245603i
$606$	521.205	−	110.158i	0.860073	−	0.181778i
$607$	50.2841	+	285.175i	0.0828404	+	0.469811i	0.997802	+	0.0662697i	$0.0211098\pi$
$607$	50.2841	+	285.175i	0.0828404	+	0.469811i	−0.914961	+	0.403541i	$0.867779\pi$
$608$	124.800	−	22.0057i	0.205264	−	0.0361936i
$609$	47.0272	+	222.507i	0.0772203	+	0.365364i
$610$	−72.2359	−	60.6131i	−0.118420	−	0.0993658i
$611$	584.925	−	337.706i	0.957323	−	0.552711i
$612$	494.662	−	122.122i	0.808272	−	0.199546i
$613$	−431.468	+	747.325i	−0.703864	+	1.21913i	0.263236	+	0.964731i	$0.415210\pi$
$613$	−431.468	+	747.325i	−0.703864	+	1.21913i	−0.967100	+	0.254396i	$0.918123\pi$
$614$	70.8115	+	194.553i	0.115328	+	0.316862i
$615$	77.2761	−	98.6742i	0.125652	−	0.160446i
$616$	−64.1263	+	53.8084i	−0.104101	+	0.0873513i
$617$	−37.3588	+	102.642i	−0.0605491	+	0.166357i	−0.966279	−	0.257499i	$-0.917102\pi$
$617$	−37.3588	+	102.642i	−0.0605491	+	0.166357i	0.905729	+	0.423856i	$0.139324\pi$
$618$	−211.410	−	339.196i	−0.342087	−	0.548861i
$619$	16.5748	−	94.0001i	0.0267767	−	0.151858i	−0.968488	−	0.249060i	$-0.919878\pi$
$619$	16.5748	−	94.0001i	0.0267767	−	0.151858i	0.995265	+	0.0972023i	$0.0309894\pi$
$620$			53.6176i			0.0864800i
$621$	263.558	+	66.6815i	0.424409	+	0.107378i
$622$	391.081			0.628748
$623$	225.870	+	39.8270i	0.362552	+	0.0639277i
$624$	129.274	+	68.9275i	0.207170	+	0.110461i
$625$	−562.919	−	204.886i	−0.900671	−	0.327817i
$626$	−27.2673	−	32.4959i	−0.0435579	−	0.0519103i
$627$	585.160	−	235.635i	0.933269	−	0.375814i
$628$	−137.943	+	50.2072i	−0.219655	+	0.0799478i
$629$	772.193	+	445.826i	1.22765	+	0.708785i
$630$	−19.1121	−	13.9532i	−0.0303367	−	0.0221479i
$631$	264.888	+	458.800i	0.419791	+	0.727100i	0.995918	−	0.0902603i	$-0.0287699\pi$
$631$	264.888	+	458.800i	0.419791	+	0.727100i	−0.576127	+	0.817360i	$0.695437\pi$
$632$	241.367	−	287.650i	0.381910	−	0.455143i
$633$	−14.6563	−	16.3152i	−0.0231537	−	0.0257744i
$634$	−65.7227	−	372.732i	−0.103664	−	0.587905i
$635$	−57.0810	+	10.0649i	−0.0898914	+	0.0158503i
$636$	−144.937	−	47.2777i	−0.227889	−	0.0743361i
$637$	−365.278	−	306.504i	−0.573435	−	0.481169i
$638$	276.382	−	159.569i	0.433201	−	0.250109i
$639$	65.5645	−	44.0042i	0.102605	−	0.0688642i
$640$	−3.33546	+	5.77718i	−0.00521165	+	0.00902685i
$641$	−90.7979	−	249.465i	−0.141650	−	0.389181i	0.848499	−	0.529197i	$-0.177507\pi$
$641$	−90.7979	−	249.465i	−0.141650	−	0.389181i	−0.990149	+	0.140016i	$0.955285\pi$
$642$	−453.236	−	64.2311i	−0.705975	−	0.100049i
$643$	111.106	−	93.2293i	0.172794	−	0.144991i	−0.552290	−	0.833652i	$-0.686246\pi$
$643$	111.106	−	93.2293i	0.172794	−	0.144991i	0.725083	+	0.688661i	$0.241801\pi$
$644$	21.7175	−	59.6683i	0.0337228	−	0.0926526i
$645$	−25.7567	+	0.869713i	−0.0399328	+	0.00134839i
$646$	−155.725	+	883.161i	−0.241061	+	1.36712i
$647$		−	578.671i		−	0.894391i	−0.894436	−	0.447196i	$-0.852423\pi$
$647$		−	578.671i		−	0.894391i	0.894436	−	0.447196i	$-0.147577\pi$
$648$	212.022	+	86.8020i	0.327195	+	0.133954i
$649$	−269.099			−0.414636
$650$	419.166	+	73.9103i	0.644871	+	0.113708i
$651$	−14.5144	−	429.846i	−0.0222955	−	0.660285i
$652$	−408.068	−	148.525i	−0.625871	−	0.227798i
$653$	−417.061	−	497.034i	−0.638684	−	0.761154i	0.345477	−	0.938427i	$-0.387717\pi$
$653$	−417.061	−	497.034i	−0.638684	−	0.761154i	−0.984162	+	0.177273i	$0.943273\pi$
$654$	−25.5783	+	180.489i	−0.0391105	+	0.275977i
$655$	−75.9237	+	27.6340i	−0.115914	+	0.0421893i
$656$	245.444	+	141.707i	0.374152	+	0.216017i
$657$	93.0413	−	189.652i	0.141615	−	0.288663i
$658$	−123.349	−	213.646i	−0.187460	−	0.324690i
$659$	−346.075	+	412.436i	−0.525151	+	0.625851i	−0.961791	−	0.273785i	$-0.911724\pi$
$659$	−346.075	+	412.436i	−0.525151	+	0.625851i	0.436639	+	0.899637i	$0.356169\pi$
$660$	−10.2979	+	31.5697i	−0.0156028	+	0.0478329i
$661$	−66.4965	−	377.120i	−0.100600	−	0.570530i	−0.992887	−	0.119061i	$-0.962011\pi$
$661$	−66.4965	−	377.120i	−0.100600	−	0.570530i	0.892287	−	0.451468i	$-0.149100\pi$
$662$	−531.115	+	93.6500i	−0.802289	+	0.141465i
$663$	−771.242	+	692.821i	−1.16326	+	1.04498i
$664$	−145.511	−	122.098i	−0.219143	−	0.183883i
$665$	36.0697	−	20.8249i	0.0542402	−	0.0313156i
$666$	162.228	+	366.643i	0.243586	+	0.550515i
$667$	−121.039	+	209.646i	−0.181468	+	0.314311i
$668$	−147.424	−	405.044i	−0.220695	−	0.606354i
$669$	96.4488	+	239.514i	0.144169	+	0.358018i
$670$	−31.9558	+	26.8141i	−0.0476952	+	0.0400210i
$671$	363.037	−	997.436i	0.541039	−	1.48649i
$672$	25.1761	−	47.2179i	0.0374644	−	0.0702647i
$673$	28.0045	−	158.821i	0.0416114	−	0.235990i	−0.956908	−	0.290392i	$-0.906214\pi$
$673$	28.0045	−	158.821i	0.0416114	−	0.235990i	0.998519	+	0.0544023i	$0.0173253\pi$
$674$			169.360i			0.251275i
$675$	663.827	+	48.7271i	0.983448	+	0.0721884i
$676$	39.9056			0.0590320
$677$	126.078	+	22.2310i	0.186231	+	0.0328375i	0.265986	−	0.963977i	$-0.414303\pi$
$677$	126.078	+	22.2310i	0.186231	+	0.0328375i	−0.0797548	+	0.996815i	$0.525414\pi$
$678$	38.6371	−	24.0813i	0.0569869	−	0.0355181i
$679$	465.766	+	169.525i	0.685959	+	0.249669i
$680$	−30.3443	−	36.1629i	−0.0446239	−	0.0531807i
$681$	−154.588	−	121.065i	−0.227002	−	0.177775i
$682$	−567.144	+	206.423i	−0.831589	+	0.302674i
$683$	−410.786	−	237.168i	−0.601444	−	0.347244i	0.168165	−	0.985759i	$-0.446216\pi$
$683$	−410.786	−	237.168i	−0.601444	−	0.347244i	−0.769609	+	0.638515i	$0.779549\pi$
$684$	−290.711	+	279.444i	−0.425016	+	0.408543i
$685$	59.0185	+	102.223i	0.0861583	+	0.149231i
$686$	−252.402	+	300.800i	−0.367932	+	0.438485i
$687$	−969.888	+	204.988i	−1.41177	+	0.298381i
$688$	−10.1197	−	57.3914i	−0.0147088	−	0.0834178i
$689$	305.491	−	53.8663i	0.443383	−	0.0781804i
$690$	−5.20858	−	24.6441i	−0.00754866	−	0.0357161i
$691$	−218.877	−	183.660i	−0.316754	−	0.265788i	0.470523	−	0.882388i	$-0.344065\pi$
$691$	−218.877	−	183.660i	−0.316754	−	0.265788i	−0.787277	+	0.616600i	$0.788510\pi$
$692$	109.201	−	63.0474i	0.157805	−	0.0911089i
$693$	74.0108	−	255.878i	0.106798	−	0.369233i
$694$	−175.909	+	304.683i	−0.253471	+	0.439024i
$695$	−1.43745	−	3.94936i	−0.00206827	−	0.00568253i
$696$	−125.782	+	160.611i	−0.180721	+	0.230763i
$697$	−1536.38	+	1289.18i	−2.20428	+	1.84961i
$698$	−154.755	+	425.186i	−0.221712	+	0.609149i
$699$	226.877	+	364.012i	0.324573	+	0.520761i
$700$	26.9960	−	153.102i	0.0385658	−	0.218717i
$701$		−	320.086i		−	0.456613i	−0.973589	−	0.228307i	$-0.926681\pi$
$701$		−	320.086i		−	0.456613i	0.973589	−	0.228307i	$-0.0733189\pi$
$702$	−463.778	+	47.1238i	−0.660653	+	0.0671279i
$703$	−705.669			−1.00380
$704$	−73.9498	−	13.0393i	−0.105042	−	0.0185218i
$705$	−86.3530	−	46.0425i	−0.122487	−	0.0653085i
$706$	−440.232	−	160.231i	−0.623558	−	0.226957i
$707$	254.490	+	303.289i	0.359958	+	0.428981i
$708$	159.564	−	64.2542i	0.225373	−	0.0907546i
$709$	−796.794	+	290.009i	−1.12383	+	0.409040i	−0.836048	−	0.548657i	$-0.815139\pi$
$709$	−796.794	+	290.009i	−1.12383	+	0.409040i	−0.287780	+	0.957697i	$0.592917\pi$
$710$	−6.33584	−	3.65800i	−0.00892372	−	0.00515211i
$711$	−127.634	+	1188.00i	−0.179514	+	1.67089i
$712$	102.868	+	178.173i	0.144478	+	0.250242i
$713$	294.273	−	350.701i	0.412725	−	0.491866i
$714$	253.056	+	281.699i	0.354420	+	0.394537i
$715$	−11.7330	−	66.5410i	−0.0164098	−	0.0930644i
$716$	391.694	−	69.0662i	0.547058	−	0.0964611i
$717$	865.137	+	282.203i	1.20661	+	0.393589i
$718$	347.675	+	291.734i	0.484227	+	0.406315i
$719$	143.869	−	83.0628i	0.200096	−	0.115525i	−0.396604	−	0.917990i	$-0.629811\pi$
$719$	143.869	−	83.0628i	0.200096	−	0.115525i	0.596700	+	0.802464i	$0.296478\pi$
$720$	−1.43187	−	21.1784i	−0.00198871	−	0.0294144i
$721$	148.523	−	257.249i	0.205996	−	0.356795i
$722$	−68.1308	−	187.188i	−0.0943640	−	0.259263i
$723$	929.008	+	131.656i	1.28494	+	0.182097i
$724$	−109.235	+	91.6589i	−0.150877	+	0.126601i
$725$	−202.712	+	556.946i	−0.279602	+	0.768201i
$726$	139.490	−	4.71009i	0.192135	−	0.00648773i
$727$	136.863	−	776.190i	0.188258	−	1.06766i	−0.733440	−	0.679754i	$-0.762087\pi$
$727$	136.863	−	776.190i	0.188258	−	1.06766i	0.921698	−	0.387908i	$-0.126802\pi$
$728$			108.880i			0.149561i
$729$	−714.101	+	146.631i	−0.979562	+	0.201140i
$730$	−19.5722			−0.0268112
$731$	406.135	+	71.6126i	0.555589	+	0.0979653i
$732$	22.8978	+	678.122i	0.0312811	+	0.926396i
$733$	650.225	+	236.663i	0.887074	+	0.322869i	0.745061	−	0.666996i	$-0.232420\pi$
$733$	650.225	+	236.663i	0.887074	+	0.322869i	0.142013	+	0.989865i	$0.454643\pi$
$734$	−662.417	−	789.438i	−0.902475	−	1.07553i
$735$	−9.69421	+	68.4055i	−0.0131894	+	0.0930688i
$736$	53.5238	−	19.4811i	0.0727225	−	0.0264688i
$737$	−406.655	−	234.782i	−0.551770	−	0.318565i
$738$	−899.764	+	60.8331i	−1.21919	+	0.0824297i
$739$	−117.695	−	203.854i	−0.159262	−	0.275851i	0.775340	−	0.631543i	$-0.217578\pi$
$739$	−117.695	−	203.854i	−0.159262	−	0.275851i	−0.934603	+	0.355693i	$0.884245\pi$
$740$	23.8775	−	28.4561i	0.0322669	−	0.0384542i
$741$	254.445	−	780.039i	0.343380	−	1.05268i
$742$	−19.6749	−	111.582i	−0.0265160	−	0.150380i
$743$	600.536	−	105.891i	0.808259	−	0.142518i	0.245776	−	0.969327i	$-0.420957\pi$
$743$	600.536	−	105.891i	0.808259	−	0.142518i	0.562483	+	0.826809i	$0.309846\pi$
$744$	287.003	−	257.820i	0.385757	−	0.346533i
$745$	42.3466	+	35.5330i	0.0568411	+	0.0476953i
$746$	−419.782	+	242.361i	−0.562711	+	0.324881i
$747$	600.963	+	64.5652i	0.804502	+	0.0864326i
$748$	265.692	−	460.193i	0.355204	−	0.615231i
$749$	−116.359	−	319.694i	−0.155352	−	0.426827i
$750$	−46.3971	−	115.219i	−0.0618628	−	0.153625i
$751$	163.414	−	137.121i	0.217596	−	0.182585i	−0.527474	−	0.849571i	$-0.676861\pi$
$751$	163.414	−	137.121i	0.217596	−	0.182585i	0.745070	+	0.666987i	$0.232416\pi$
$752$	75.6866	−	207.947i	0.100647	−	0.276526i
$753$	189.786	−	355.944i	0.252039	−	0.472701i
$754$	72.0803	−	408.787i	0.0955972	−	0.542158i
$755$			118.972i			0.157578i
$756$	17.2122	+	169.397i	0.0227674	+	0.224070i
$757$	−212.260			−0.280397			−0.140198	−	0.990123i	$-0.544774\pi$
$757$	−212.260			−0.280397			−0.140198	+	0.990123i	$0.544774\pi$
$758$	−845.618	−	149.105i	−1.11559	−	0.196709i
$759$	240.622	−	149.972i	0.317025	−	0.197592i
$760$	35.1076	+	12.7781i	0.0461942	+	0.0168133i
$761$	934.612	+	1113.83i	1.22814	+	1.46364i	0.840488	+	0.541830i	$0.182268\pi$
$761$	934.612	+	1113.83i	1.22814	+	1.46364i	0.387649	+	0.921807i	$0.373287\pi$
$762$	328.350	+	257.145i	0.430905	+	0.337461i
$763$	−127.309	+	46.3368i	−0.166853	+	0.0607297i
$764$	−172.666	−	99.6886i	−0.226002	−	0.130482i
$765$	144.298	+	41.7371i	0.188625	+	0.0545583i
$766$	−107.128	−	185.552i	−0.139854	−	0.242235i
$767$	−224.981	+	268.122i	−0.293326	+	0.349572i
$768$	46.9626	−	9.92562i	0.0611492	−	0.0129240i
$769$	150.826	+	855.378i	0.196133	+	1.11233i	0.910796	+	0.412856i	$0.135469\pi$
$769$	150.826	+	855.378i	0.196133	+	1.11233i	−0.714663	+	0.699469i	$0.753420\pi$
$770$	−24.3044	+	4.28552i	−0.0315641	+	0.00556561i
$771$	−29.5145	−	139.646i	−0.0382808	−	0.181123i
$772$	−291.436	−	244.544i	−0.377508	−	0.316767i
$773$	−14.6924	+	8.48268i	−0.0190070	+	0.0109737i	−0.509473	−	0.860486i	$-0.670160\pi$
$773$	−14.6924	+	8.48268i	−0.0190070	+	0.0109737i	0.490466	+	0.871460i	$0.336826\pi$
$774$	128.506	+	133.688i	0.166029	+	0.172723i
$775$	560.435	−	970.701i	0.723141	−	1.25252i
$776$	152.068	+	417.803i	0.195964	+	0.538406i
$777$	−183.720	+	234.593i	−0.236448	+	0.301922i
$778$	655.974	−	550.428i	0.843155	−	0.707491i
$779$	542.879	−	1491.55i	0.696892	−	1.91469i
$780$	22.8455	+	36.6544i	0.0292891	+	0.0469929i
$781$	14.3003	−	81.1008i	0.0183102	−	0.103842i
$782$			403.074i			0.515440i
$783$	47.5206	−	647.390i	0.0606904	−	0.826807i
$784$	−156.231			−0.199274
$785$	−42.6203	−	7.51511i	−0.0542934	−	0.00957339i
$786$	512.998	+	273.525i	0.652669	+	0.347996i
$787$	382.780	+	139.321i	0.486379	+	0.177027i	0.573557	−	0.819165i	$-0.305563\pi$
$787$	382.780	+	139.321i	0.486379	+	0.177027i	−0.0871788	+	0.996193i	$0.527785\pi$
$788$	−237.407	−	282.930i	−0.301277	−	0.359048i
$789$	−1320.15	+	531.607i	−1.67320	+	0.673773i
$790$	104.027	−	37.8628i	0.131680	−	0.0479276i
$791$	29.3027	+	16.9179i	0.0370452	+	0.0213880i
$792$	218.503	−	96.6808i	0.275888	−	0.122072i
$793$	−690.296	−	1195.63i	−0.870487	−	1.50773i
$794$	548.029	−	653.115i	0.690213	−	0.822563i
$795$	−30.0359	−	33.4357i	−0.0377810	−	0.0420575i
$796$	−21.5980	−	122.488i	−0.0271331	−	0.153880i
$797$	114.221	−	20.1403i	0.143314	−	0.0252702i	−0.101531	−	0.994832i	$-0.532374\pi$
$797$	114.221	−	20.1403i	0.143314	−	0.0252702i	0.244845	+	0.969562i	$0.421263\pi$
$798$	−284.912	−	92.9369i	−0.357033	−	0.116462i
$799$	1199.62	+	1006.60i	1.50141	+	1.25983i
$800$	120.771	−	69.7273i	0.150964	−	0.0871592i
$801$	−587.730	−	288.335i	−0.733746	−	0.359968i
$802$	313.920	−	543.726i	0.391422	−	0.677963i
$803$	−75.3514	−	207.026i	−0.0938374	−	0.257816i
$804$	297.189	+	42.1167i	0.369638	+	0.0523839i
$805$	14.3404	−	12.0331i	0.0178142	−	0.0149479i
$806$	−268.488	+	737.666i	−0.333112	+	0.915218i
$807$	1364.47	−	46.0732i	1.69079	−	0.0570919i
$808$	−61.6704	+	349.750i	−0.0763247	+	0.432859i
$809$			1246.51i			1.54080i	0.637560	+	0.770401i	$0.279944\pi$
$809$			1246.51i			1.54080i	−0.637560	+	0.770401i	$0.720056\pi$
$810$	41.3377	+	53.4158i	0.0510342	+	0.0659455i
$811$	593.707			0.732067			0.366034	−	0.930602i	$-0.380715\pi$
$811$	593.707			0.732067			0.366034	+	0.930602i	$0.380715\pi$
$812$	−149.311	−	26.3276i	−0.183881	−	0.0324232i
$813$	−44.6415	−	1322.06i	−0.0549095	−	1.62616i
$814$	392.923	+	143.012i	0.482707	+	0.175691i
$815$	−82.2933	−	98.0734i	−0.100973	−	0.120335i
$816$	−47.6615	+	336.316i	−0.0584088	+	0.412152i
$817$	−306.698	+	111.629i	−0.375396	+	0.136633i
$818$	−506.575	−	292.471i	−0.619285	−	0.357544i
$819$	−193.072	−	287.670i	−0.235741	−	0.351245i
$820$	41.7774	+	72.3607i	0.0509481	+	0.0882447i
$821$	291.743	−	347.685i	0.355350	−	0.423490i	−0.558523	−	0.829489i	$-0.688632\pi$
$821$	291.743	−	347.685i	0.355350	−	0.423490i	0.913874	+	0.405999i	$0.133076\pi$
$822$	263.387	−	807.453i	0.320422	−	0.982302i
$823$	25.9808	+	147.345i	0.0315685	+	0.179034i	0.996515	−	0.0834125i	$-0.0265819\pi$
$823$	25.9808	+	147.345i	0.0315685	+	0.179034i	−0.964947	+	0.262446i	$0.915471\pi$
$824$	262.408	−	46.2697i	0.318457	−	0.0561525i
$825$	516.415	−	463.905i	0.625957	−	0.562309i
$826$	97.9326	+	82.1752i	0.118562	+	0.0994857i
$827$	−858.941	+	495.910i	−1.03862	+	0.599649i	−0.919443	−	0.393223i	$-0.871360\pi$
$827$	−858.941	+	495.910i	−1.03862	+	0.599649i	−0.119180	+	0.992873i	$0.538027\pi$
$828$	−106.869	+	146.382i	−0.129069	+	0.176789i
$829$	−554.523	+	960.463i	−0.668906	+	1.15858i	0.309304	+	0.950963i	$0.399904\pi$
$829$	−554.523	+	960.463i	−0.668906	+	1.15858i	−0.978210	+	0.207617i	$0.933429\pi$
$830$	−19.1533	−	52.6234i	−0.0230763	−	0.0634017i
$831$	84.4780	+	209.786i	0.101658	+	0.252451i
$832$	−74.8180	+	62.7797i	−0.0899254	+	0.0754564i
$833$	378.131	−	1038.91i	0.453939	−	1.24719i
$834$	−14.2281	+	26.6849i	−0.0170601	+	0.0319962i
$835$	22.0667	−	125.147i	0.0264272	−	0.149876i
$836$			420.548i			0.503048i
$837$	−301.104	+	1190.11i	−0.359742	+	1.42188i
$838$	871.507			1.03998
$839$	−717.074	−	126.440i	−0.854677	−	0.150703i	−0.270891	−	0.962610i	$-0.587318\pi$
$839$	−717.074	−	126.440i	−0.854677	−	0.150703i	−0.583786	+	0.811907i	$0.698429\pi$
$840$	13.3882	−	8.34442i	0.0159383	−	0.00993383i
$841$	−247.126	−	89.9465i	−0.293848	−	0.106952i
$842$	3.42877	+	4.08625i	0.00407217	+	0.00485303i
$843$	−18.3300	−	14.3550i	−0.0217438	−	0.0170285i
$844$	13.7393	−	5.00069i	0.0162788	−	0.00592498i
$845$	10.1886	+	5.88240i	0.0120575	+	0.00696142i
$846$	168.773	+	683.624i	0.199496	+	0.808066i
$847$	51.8641	+	89.8313i	0.0612327	+	0.106058i
$848$	65.3300	−	77.8572i	0.0770401	−	0.0918128i
$849$	479.793	−	101.405i	0.565127	−	0.119441i
$850$	171.367	+	971.870i	0.201608	+	1.14338i
$851$	−312.355	+	55.0767i	−0.367045	+	0.0647199i
$852$	10.8854	+	51.5039i	0.0127763	+	0.0604506i
$853$	−1035.22	−	868.650i	−1.21362	−	1.01835i	−0.999134	−	0.0416200i	$-0.986748\pi$
$853$	−1035.22	−	868.650i	−1.21362	−	1.01835i	−0.214485	−	0.976727i	$-0.568807\pi$
$854$	−436.708	+	252.134i	−0.511368	+	0.295238i
$855$	−115.416	+	28.4939i	−0.134989	+	0.0333262i
$856$	152.588	−	264.291i	0.178257	−	0.308751i
$857$	469.442	+	1289.78i	0.547774	+	1.50500i	0.836709	+	0.547647i	$0.184476\pi$
$857$	469.442	+	1289.78i	0.547774	+	1.50500i	−0.288936	+	0.957348i	$0.593301\pi$
$858$	−299.761	+	382.767i	−0.349372	+	0.446115i
$859$	−49.4325	+	41.4788i	−0.0575466	+	0.0482873i	−0.671107	−	0.741360i	$-0.734181\pi$
$859$	−49.4325	+	41.4788i	−0.0575466	+	0.0482873i	0.613561	+	0.789648i	$0.289737\pi$
$860$	5.87622	−	16.1448i	0.00683281	−	0.0187730i
$861$	−354.513	−	568.797i	−0.411745	−	0.660624i
$862$	161.803	−	917.630i	0.187706	−	1.06454i
$863$			998.597i			1.15712i	0.815639	+	0.578561i	$0.196386\pi$
$863$			998.597i			1.15712i	−0.815639	+	0.578561i	$0.803614\pi$
$864$	−106.478	+	109.501i	−0.123239	+	0.126737i
$865$	37.1747			0.0429765
$866$	237.438	+	41.8667i	0.274178	+	0.0483449i
$867$	−1356.03	−	723.023i	−1.56405	−	0.833936i
$868$	269.435	+	98.0664i	0.310409	+	0.112980i
$869$	800.994	+	954.587i	0.921742	+	1.09849i
$870$	−55.7897	+	22.4657i	−0.0641261	+	0.0258226i
$871$	−573.915	+	208.888i	−0.658915	+	0.239825i
$872$	−105.247	−	60.7641i	−0.120696	−	0.0696836i
$873$	−1142.65	−	834.213i	−1.30887	−	0.955570i
$874$	−159.500	−	276.262i	−0.182494	−	0.316089i
$875$	59.3375	−	70.7157i	0.0678143	−	0.0808180i
$876$	94.1130	+	104.766i	0.107435	+	0.119596i
$877$	263.675	+	1495.37i	0.300656	+	1.70510i	0.643281	+	0.765630i	$0.277573\pi$
$877$	263.675	+	1495.37i	0.300656	+	1.70510i	−0.342625	+	0.939472i	$0.611316\pi$
$878$	1194.41	−	210.606i	1.36037	−	0.239870i
$879$	−154.260	−	50.3188i	−0.175495	−	0.0572455i
$880$	−16.9586	−	14.2300i	−0.0192711	−	0.0161704i
$881$	462.122	−	266.806i	0.524543	−	0.302845i	−0.214249	−	0.976779i	$-0.568730\pi$
$881$	462.122	−	266.806i	0.524543	−	0.302845i	0.738791	+	0.673934i	$0.235397\pi$
$882$	412.775	−	277.037i	0.467998	−	0.314101i
$883$	268.778	−	465.537i	0.304392	−	0.527222i	−0.672734	−	0.739885i	$-0.734880\pi$
$883$	268.778	−	465.537i	0.304392	−	0.527222i	0.977126	+	0.212662i	$0.0682134\pi$
$884$	−236.389	−	649.473i	−0.267408	−	0.734698i
$885$	50.2112	+	7.11576i	0.0567358	+	0.00804041i
$886$	−270.671	+	227.120i	−0.305498	+	0.256343i
$887$	−335.258	+	921.113i	−0.377968	+	1.03846i	0.594229	+	0.804296i	$0.297457\pi$
$887$	−335.258	+	921.113i	−0.377968	+	1.03846i	−0.972197	+	0.234163i	$0.924765\pi$
$888$	−267.135	+	9.02020i	−0.300827	+	0.0101579i
$889$	−53.8235	+	305.248i	−0.0605439	+	0.343361i
$890$			60.6542i			0.0681508i
$891$	−405.863	+	642.900i	−0.455514	+	0.721548i
$892$	−172.136			−0.192978
$893$	−1220.53	−	215.212i	−1.36678	−	0.240999i
$894$	−13.4233	−	397.533i	−0.0150149	−	0.444667i
$895$	110.187	+	40.1049i	0.123114	+	0.0448099i
$896$	22.9305	+	27.3276i	0.0255921	+	0.0304995i
$897$	51.7455	−	365.133i	0.0576872	−	0.407060i
$898$	−320.164	+	116.530i	−0.356530	+	0.129766i
$899$	−946.666	−	546.558i	−1.05302	−	0.607962i
$900$	−195.443	+	398.383i	−0.217159	+	0.442648i
$901$	359.616	+	622.873i	0.399130	+	0.691313i
$902$	−604.560	+	720.487i	−0.670244	+	0.798766i
$903$	−42.7385	+	131.021i	−0.0473294	+	0.145096i
$904$	5.27049	+	29.8904i	0.00583019	+	0.0330646i
$905$	−41.4008	+	7.30008i	−0.0457468	+	0.00806639i
$906$	636.829	−	572.075i	0.702902	−	0.631430i
$907$	261.282	+	219.241i	0.288072	+	0.241721i	0.775359	−	0.631521i	$-0.217569\pi$
$907$	261.282	+	219.241i	0.288072	+	0.241721i	−0.487287	+	0.873242i	$0.662013\pi$
$908$	113.364	−	65.4508i	0.124850	−	0.0720823i
$909$	−457.258	−	1033.42i	−0.503034	−	1.13688i
$910$	−16.0498	+	27.7990i	−0.0176371	+	0.0305484i
$911$	−468.039	−	1285.93i	−0.513764	−	1.41156i	−0.877285	−	0.479970i	$-0.840648\pi$
$911$	−468.039	−	1285.93i	−0.513764	−	1.41156i	0.363520	−	0.931586i	$-0.381575\pi$
$912$	−100.417	−	249.367i	−0.110106	−	0.273429i
$913$	482.889	−	405.192i	0.528903	−	0.443803i
$914$	−92.0371	+	252.870i	−0.100697	+	0.276663i
$915$	−94.1142	+	176.512i	−0.102857	+	0.192909i
$916$	114.760	−	650.835i	0.125284	−	0.710519i
$917$			432.069i			0.471177i
$918$	−470.447	−	973.088i	−0.512470	−	1.06001i
$919$	558.729			0.607975			0.303987	−	0.952676i	$-0.401682\pi$
$919$	558.729			0.607975			0.303987	+	0.952676i	$0.401682\pi$
$920$	16.5372	+	2.91596i	0.0179753	+	0.00316952i
$921$	372.727	−	232.309i	0.404699	−	0.252235i
$922$	381.886	+	138.995i	0.414193	+	0.150754i
$923$	−68.8506	−	82.0529i	−0.0745944	−	0.0888981i
$924$	139.807	+	109.489i	0.151306	+	0.118495i
$925$	−729.719	+	265.596i	−0.788885	+	0.287131i
$926$	20.7101	+	11.9570i	0.0223651	+	0.0129125i
$927$	−611.256	+	587.565i	−0.659391	+	0.633835i
$928$	−68.0008	−	117.781i	−0.0732768	−	0.126919i
$929$	−667.609	+	795.625i	−0.718632	+	0.856432i	−0.994497	−	0.104764i	$-0.966591\pi$
$929$	−667.609	+	795.625i	−0.718632	+	0.856432i	0.275865	+	0.961196i	$0.411036\pi$
$930$	111.282	−	23.5196i	0.119658	−	0.0252899i
$931$	151.938	+	861.685i	0.163199	+	0.925548i
$932$	−281.607	+	49.6549i	−0.302153	+	0.0532778i
$933$	−171.550	−	811.678i	−0.183869	−	0.869966i
$934$	739.008	+	620.102i	0.791230	+	0.663920i
$935$	135.672	−	78.3303i	0.145104	−	0.0837757i
$936$	86.3505	−	298.540i	0.0922548	−	0.318953i
$937$	323.576	−	560.450i	0.345332	−	0.598132i	−0.640082	−	0.768306i	$-0.721100\pi$
$937$	323.576	−	560.450i	0.345332	−	0.598132i	0.985414	+	0.170174i	$0.0544330\pi$
$938$	76.2971	+	209.625i	0.0813402	+	0.223480i
$939$	−55.4833	+	70.8469i	−0.0590877	+	0.0754493i
$940$	49.9772	−	41.9358i	0.0531672	−	0.0446126i
$941$	228.423	−	627.587i	0.242745	−	0.666936i	−0.757161	−	0.653228i	$-0.773414\pi$
$941$	228.423	−	627.587i	0.242745	−	0.666936i	0.999906	−	0.0137078i	$-0.00436346\pi$
$942$	164.713	+	264.274i	0.174855	+	0.280545i
$943$	123.885	−	702.585i	0.131373	−	0.745053i
$944$			114.677i			0.121480i
$945$	−20.5758	+	45.7872i	−0.0217734	+	0.0484521i
$946$	193.395			0.204435
$947$	1716.52	+	302.668i	1.81258	+	0.319607i	0.974237	−	0.225529i	$-0.0724110\pi$
$947$	1716.52	+	302.668i	1.81258	+	0.319607i	0.838347	+	0.545136i	$0.183522\pi$
$948$	−702.887	−	374.772i	−0.741442	−	0.395329i
$949$	−269.272	−	98.0071i	−0.283743	−	0.103274i
$950$	−502.031	−	598.297i	−0.528453	−	0.629786i
$951$	−744.765	+	299.906i	−0.783139	+	0.315359i
$952$	−237.223	+	86.3420i	−0.249184	+	0.0906954i
$953$	671.945	+	387.948i	0.705084	+	0.407080i	0.809238	−	0.587481i	$-0.199880\pi$
$953$	671.945	+	387.948i	0.705084	+	0.407080i	−0.104154	+	0.994561i	$0.533214\pi$
$954$	−34.5462	+	321.551i	−0.0362120	+	0.337056i
$955$	−29.3898	−	50.9045i	−0.0307746	−	0.0533032i
$956$	−389.958	+	464.734i	−0.407906	+	0.486123i
$957$	−452.418	−	503.628i	−0.472746	−	0.526257i
$958$	−137.167	−	777.911i	−0.143180	−	0.812015i
$959$	621.628	−	109.610i	0.648205	−	0.114296i
$960$	13.4535	+	4.38846i	0.0140141	+	0.00457131i
$961$	847.439	+	711.086i	0.881830	+	0.739943i
$962$	470.998	−	271.931i	0.489603	−	0.282672i
$963$	65.5043	+	968.854i	0.0680211	+	1.00608i
$964$	−312.764	+	541.722i	−0.324444	+	0.561953i
$965$	−38.3611	−	105.396i	−0.0397525	−	0.109219i
$966$	−133.366	−	18.9002i	−0.138060	−	0.0195655i
$967$	−149.339	+	125.310i	−0.154435	+	0.129586i	−0.716731	−	0.697350i	$-0.754363\pi$
$967$	−149.339	+	125.310i	−0.154435	+	0.129586i	0.562296	+	0.826936i	$0.309918\pi$
$968$	−31.8238	+	87.4351i	−0.0328758	+	0.0903255i
$969$	1901.29	−	64.1997i	1.96211	−	0.0662536i
$970$	−22.7618	+	129.088i	−0.0234658	+	0.133081i
$971$			1753.94i			1.80633i	0.429299	+	0.903163i	$0.358761\pi$
$971$			1753.94i			1.80633i	−0.429299	+	0.903163i	$0.641239\pi$
$972$	87.1506	−	478.122i	0.0896612	−	0.491895i
$973$	−22.4751			−0.0230988
$974$	−161.337	−	28.4481i	−0.165644	−	0.0292075i
$975$	−30.4705	−	902.389i	−0.0312518	−	0.925527i
$976$	−425.059	−	154.709i	−0.435512	−	0.158513i
$977$	88.8872	+	105.932i	0.0909797	+	0.108425i	0.809614	−	0.586963i	$-0.199677\pi$
$977$	88.8872	+	105.932i	0.0909797	+	0.108425i	−0.718634	+	0.695389i	$0.755232\pi$
$978$	−129.258	+	912.084i	−0.132165	+	0.932602i
$979$	−641.574	+	233.514i	−0.655336	+	0.238523i
$980$	−39.8886	−	23.0297i	−0.0407026	−	0.0234997i
$981$	385.820	−	26.0853i	0.393292	−	0.0265905i
$982$	87.5321	+	151.610i	0.0891366	+	0.154389i
$983$	−123.405	+	147.069i	−0.125540	+	0.149612i	−0.825153	−	0.564909i	$-0.808911\pi$
$983$	−123.405	+	147.069i	−0.125540	+	0.149612i	0.699613	+	0.714522i	$0.253356\pi$
$984$	186.444	−	571.572i	0.189475	−	0.580866i
$985$	−18.9080	−	107.233i	−0.0191960	−	0.108866i
$986$	947.806	−	167.124i	0.961264	−	0.169497i
$987$	−389.309	+	349.723i	−0.394436	+	0.354330i
$988$	419.021	+	351.600i	0.424110	+	0.355871i
$989$	−127.043	+	73.3485i	−0.128456	+	0.0741644i
$990$	70.0393	+	7.52475i	0.0707467	+	0.00760075i
$991$	193.368	−	334.923i	0.195124	−	0.337964i	−0.751817	−	0.659372i	$-0.770822\pi$
$991$	193.368	−	334.923i	0.195124	−	0.337964i	0.946941	+	0.321407i	$0.104156\pi$
$992$	87.9677	+	241.689i	0.0886772	+	0.243639i
$993$	427.344	+	1061.23i	0.430357	+	1.06872i
$994$	−29.9702	+	25.1480i	−0.0301511	+	0.0252998i
$995$	12.5414	−	34.4571i	0.0126044	−	0.0346303i
$996$	−189.583	+	355.563i	−0.190344	+	0.356991i
$997$	212.742	−	1206.52i	0.213382	−	1.21015i	−0.670310	−	0.742081i	$-0.733839\pi$
$997$	212.742	−	1206.52i	0.213382	−	1.21015i	0.883692	−	0.468069i	$-0.155050\pi$
$998$		−	532.856i		−	0.533923i
$999$	689.795	−	497.530i	0.690486	−	0.498028i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	54.3.f.a.29.5	✓	36
3.2	odd	2		162.3.f.a.89.2		36
4.3	odd	2		432.3.bc.c.353.3		36
27.11	odd	18		1458.3.b.c.1457.10		36
27.13	even	9		162.3.f.a.71.2		36
27.14	odd	18	inner	54.3.f.a.41.5	yes	36
27.16	even	9		1458.3.b.c.1457.27		36
108.95	even	18		432.3.bc.c.257.3		36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
54.3.f.a.29.5	✓	36	1.1	even	1	trivial
54.3.f.a.41.5	yes	36	27.14	odd	18	inner
162.3.f.a.71.2		36	27.13	even	9
162.3.f.a.89.2		36	3.2	odd	2
432.3.bc.c.257.3		36	108.95	even	18
432.3.bc.c.353.3		36	4.3	odd	2
1458.3.b.c.1457.10		36	27.11	odd	18
1458.3.b.c.1457.27		36	27.16	even	9

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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 54 = 2 \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	54.f (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(1.39273 + 0.245576i) q^{2} +(-0.101242 - 2.99829i) q^{3} +(1.87939 + 0.684040i) q^{4} +(0.379008 + 0.451684i) q^{5} +(0.595305 - 4.20067i) q^{6} +(2.96297 - 1.07843i) q^{7} +(2.44949 + 1.41421i) q^{8} +(-8.97950 + 0.607104i) q^{9} +(0.416932 + 0.722148i) q^{10} +(-6.03341 + 7.19034i) q^{11} +(1.86068 - 5.70420i) q^{12} +(2.11998 + 12.0230i) q^{13} +(4.39145 - 0.774332i) q^{14} +(1.31591 - 1.18210i) q^{15} +(3.06418 + 2.57115i) q^{16} +(-24.5140 + 14.1532i) q^{17} +(-12.6551 - 1.35961i) q^{18} +(11.2011 - 19.4008i) q^{19} +(0.403332 + 1.10814i) q^{20} +(-3.53344 - 8.77467i) q^{21} +(-10.1687 + 8.53254i) q^{22} +(3.44380 - 9.46175i) q^{23} +(3.99223 - 7.48746i) q^{24} +(4.28083 - 24.2778i) q^{25} +17.2654i q^{26} +(2.72938 + 26.8617i) q^{27} +6.30626 q^{28} +(-23.6767 - 4.17484i) q^{29} +(2.12300 - 1.32320i) q^{30} +(42.7251 + 15.5506i) q^{31} +(3.63616 + 4.33340i) q^{32} +(22.1696 + 17.3620i) q^{33} +(-37.6170 + 13.6915i) q^{34} +(1.61010 + 0.929592i) q^{35} +(-17.2912 - 5.00136i) q^{36} +(-15.7500 - 27.2799i) q^{37} +(20.3644 - 24.2694i) q^{38} +(35.8339 - 7.57355i) q^{39} +(0.289598 + 1.64239i) q^{40} +(69.7771 - 12.3036i) q^{41} +(-2.76627 - 13.0885i) q^{42} +(-11.1607 - 9.36490i) q^{43} +(-16.2576 + 9.38633i) q^{44} +(-3.67752 - 3.82580i) q^{45} +(7.11985 - 12.3319i) q^{46} +(-18.9216 - 51.9868i) q^{47} +(7.39884 - 9.44761i) q^{48} +(-29.9200 + 25.1059i) q^{49} +(11.9241 - 32.7611i) q^{50} +(44.9172 + 72.0672i) q^{51} +(-4.23996 + 24.0460i) q^{52} -25.4089i q^{53} +(-2.79530 + 38.0813i) q^{54} -5.53447 q^{55} +(8.78291 + 1.54866i) q^{56} +(-59.3034 - 31.6199i) q^{57} +(-31.9499 - 11.6288i) q^{58} +(18.4282 + 21.9619i) q^{59} +(3.28171 - 1.32150i) q^{60} +(-106.265 + 38.6772i) q^{61} +(55.6855 + 32.1501i) q^{62} +(-25.9513 + 11.4826i) q^{63} +(4.00000 + 6.92820i) q^{64} +(-4.62711 + 5.51438i) q^{65} +(26.6125 + 29.6248i) q^{66} +(8.68700 + 49.2664i) q^{67} +(-55.7526 + 9.83069i) q^{68} +(-28.7178 - 9.36758i) q^{69} +(2.01415 + 1.69007i) q^{70} +(-7.59817 + 4.38680i) q^{71} +(-22.8538 - 11.2118i) q^{72} +(-11.7358 + 20.3271i) q^{73} +(-15.2363 - 41.8613i) q^{74} +(-73.2253 - 10.3773i) q^{75} +(34.3221 - 28.7997i) q^{76} +(-10.1225 + 27.8114i) q^{77} +(51.7667 - 1.74798i) q^{78} +(23.0535 - 130.743i) q^{79} +2.35853i q^{80} +(80.2628 - 10.9030i) q^{81} +100.202 q^{82} +(-66.1377 - 11.6619i) q^{83} +(-0.638457 - 18.9080i) q^{84} +(-15.6838 - 5.70842i) q^{85} +(-13.2440 - 15.7835i) q^{86} +(-10.1203 + 71.4122i) q^{87} +(-24.9475 + 9.08013i) q^{88} +(62.9935 + 36.3693i) q^{89} +(-4.18226 - 6.23141i) q^{90} +(19.2475 + 33.3376i) q^{91} +(12.9444 - 15.4266i) q^{92} +(42.2998 - 129.677i) q^{93} +(-13.5860 - 77.0502i) q^{94} +(13.0083 - 2.29372i) q^{95} +(12.6247 - 11.3410i) q^{96} +(120.419 + 101.043i) q^{97} +(-47.8358 + 27.6180i) q^{98} +(49.8117 - 68.2286i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q + 18 q^{5} + 12 q^{6} - 12 q^{9} - 18 q^{11} - 12 q^{12} - 36 q^{14} - 18 q^{15} - 48 q^{18} - 72 q^{20} - 228 q^{21} + 36 q^{22} - 180 q^{23} + 18 q^{25} + 54 q^{27} + 144 q^{29} + 144 q^{30} - 90 q^{31}+ \cdots + 126 q^{99}+O(q^{100}) \) 36 * q + 18 * q^5 + 12 * q^6 - 12 * q^9 - 18 * q^11 - 12 * q^12 - 36 * q^14 - 18 * q^15 - 48 * q^18 - 72 * q^20 - 228 * q^21 + 36 * q^22 - 180 * q^23 + 18 * q^25 + 54 * q^27 + 144 * q^29 + 144 * q^30 - 90 * q^31 + 324 * q^33 - 72 * q^34 + 486 * q^35 + 168 * q^36 + 180 * q^38 + 102 * q^39 - 90 * q^41 + 48 * q^42 + 90 * q^43 - 378 * q^45 - 378 * q^47 - 24 * q^48 + 72 * q^49 - 54 * q^51 - 36 * q^54 - 72 * q^56 + 72 * q^57 + 252 * q^59 + 36 * q^60 - 144 * q^61 + 318 * q^63 + 144 * q^64 + 18 * q^65 - 432 * q^66 - 594 * q^67 - 180 * q^68 - 522 * q^69 - 360 * q^70 - 648 * q^71 - 192 * q^72 + 126 * q^73 - 504 * q^74 - 438 * q^75 - 72 * q^76 - 342 * q^77 - 288 * q^78 - 72 * q^79 + 324 * q^81 + 594 * q^83 + 216 * q^84 + 360 * q^85 + 540 * q^86 + 1062 * q^87 + 144 * q^88 + 648 * q^89 + 720 * q^90 - 198 * q^91 + 396 * q^92 + 462 * q^93 + 504 * q^94 + 252 * q^95 + 96 * q^96 + 702 * q^97 + 648 * q^98 + 126 * q^99

Introduction

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