LMFDB - Embedded newform 392.2.z.a.37.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [392,2,Mod(37,392)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(392, base_ring=CyclotomicField(42))

chi = DirichletCharacter(H, H._module([0, 21, 32]))

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("392.37");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 392 = 2^{3} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	392.z (of order $42$, degree $12$, 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:	$3.13013575923$
Analytic rank:	$0$
Dimension:	$648$
Relative dimension:	$54$ over $\Q(\zeta_{42})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{42}]$

Embedding invariants

Embedding label			37.14
Character	$\chi$	$=$	392.37
Dual form			392.2.z.a.53.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.05324 + 0.943763i) q^{2} +(-1.08411 - 1.16839i) q^{3} +(0.218622 - 1.98802i) q^{4} +(0.529378 - 1.71620i) q^{5} +(2.24451 + 0.207452i) q^{6} +(-2.34752 + 1.22032i) q^{7} +(1.64596 + 2.30018i) q^{8} +(0.0343439 - 0.458288i) q^{9} +O(q^{10})$	\(q+(-1.05324 + 0.943763i) q^{2} +(-1.08411 - 1.16839i) q^{3} +(0.218622 - 1.98802i) q^{4} +(0.529378 - 1.71620i) q^{5} +(2.24451 + 0.207452i) q^{6} +(-2.34752 + 1.22032i) q^{7} +(1.64596 + 2.30018i) q^{8} +(0.0343439 - 0.458288i) q^{9} +(1.06213 + 2.30718i) q^{10} +(4.71137 - 0.353068i) q^{11} +(-2.55979 + 1.89979i) q^{12} +(0.558298 - 1.15932i) q^{13} +(1.32080 - 3.50078i) q^{14} +(-2.57910 + 1.24203i) q^{15} +(-3.90441 - 0.869246i) q^{16} +(-3.60762 - 0.543762i) q^{17} +(0.396343 + 0.515099i) q^{18} +(-4.74129 - 2.73738i) q^{19} +(-3.29610 - 1.42761i) q^{20} +(3.97077 + 1.41986i) q^{21} +(-4.62898 + 4.81828i) q^{22} +(-7.55176 + 1.13824i) q^{23} +(0.903116 - 4.41676i) q^{24} +(1.46609 + 0.999561i) q^{25} +(0.506101 + 1.74794i) q^{26} +(-4.31111 + 3.43799i) q^{27} +(1.91279 + 4.93368i) q^{28} +(-6.72404 - 5.36224i) q^{29} +(1.54422 - 3.74221i) q^{30} +(-0.368485 - 0.638234i) q^{31} +(4.93264 - 2.76931i) q^{32} +(-5.52016 - 5.12196i) q^{33} +(4.31287 - 2.83203i) q^{34} +(0.851585 + 4.67482i) q^{35} +(-0.903575 - 0.168468i) q^{36} +(6.57534 - 2.58063i) q^{37} +(7.57715 - 1.59154i) q^{38} +(-1.95979 + 0.604515i) q^{39} +(4.81891 - 1.60713i) q^{40} +(-1.11229 - 4.87325i) q^{41} +(-5.52218 + 2.25201i) q^{42} +(0.167094 + 0.0381381i) q^{43} +(0.328102 - 9.44346i) q^{44} +(-0.768333 - 0.301549i) q^{45} +(6.87957 - 8.32592i) q^{46} +(-8.06065 + 5.49566i) q^{47} +(3.21718 + 5.50423i) q^{48} +(4.02166 - 5.72942i) q^{49} +(-2.48749 + 0.330863i) q^{50} +(3.27573 + 4.80461i) q^{51} +(-2.18268 - 1.36336i) q^{52} +(-1.16683 - 0.457945i) q^{53} +(1.29597 - 7.68969i) q^{54} +(1.88816 - 8.27257i) q^{55} +(-6.67085 - 3.39113i) q^{56} +(1.94174 + 8.50730i) q^{57} +(12.1427 - 0.698183i) q^{58} +(0.0541481 + 0.175544i) q^{59} +(1.90532 + 5.39882i) q^{60} +(-6.56223 + 2.57549i) q^{61} +(0.990444 + 0.324450i) q^{62} +(0.478633 + 1.11775i) q^{63} +(-2.58166 + 7.57199i) q^{64} +(-1.69407 - 1.57187i) q^{65} +(10.6480 + 0.184919i) q^{66} +(10.3484 - 5.97464i) q^{67} +(-1.86971 + 7.05313i) q^{68} +(9.51684 + 7.58943i) q^{69} +(-5.30884 - 4.12000i) q^{70} +(8.89597 + 11.1552i) q^{71} +(1.11067 - 0.675324i) q^{72} +(3.14522 + 2.14437i) q^{73} +(-4.48990 + 8.92359i) q^{74} +(-0.421519 - 2.79659i) q^{75} +(-6.47851 + 8.82730i) q^{76} +(-10.6292 + 6.57819i) q^{77} +(1.49361 - 2.48628i) q^{78} +(-0.347223 + 0.601408i) q^{79} +(-3.55871 + 6.24059i) q^{80} +(7.32731 + 1.10441i) q^{81} +(5.77070 + 4.08296i) q^{82} +(-5.85761 - 12.1635i) q^{83} +(3.69080 - 7.58353i) q^{84} +(-2.84300 + 5.90355i) q^{85} +(-0.211983 + 0.117529i) q^{86} +(1.02439 + 13.6696i) q^{87} +(8.56682 + 10.2559i) q^{88} +(0.439562 - 5.86555i) q^{89} +(1.09383 - 0.407522i) q^{90} +(0.104120 + 3.40282i) q^{91} +(0.611870 + 15.2619i) q^{92} +(-0.346229 + 1.12245i) q^{93} +(3.30318 - 13.3956i) q^{94} +(-7.20784 + 6.68790i) q^{95} +(-8.58315 - 2.76101i) q^{96} +14.1075 q^{97} +(1.17145 + 9.82994i) q^{98} -2.17129i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 648 q - 13 q^{2} - 13 q^{4} - 6 q^{6} - 24 q^{7} - 16 q^{8} - 76 q^{9}+O(q^{10}) $ 648 * q - 13 * q^2 - 13 * q^4 - 6 * q^6 - 24 * q^7 - 16 * q^8 - 76 * q^9	$ 648 q - 13 q^{2} - 13 q^{4} - 6 q^{6} - 24 q^{7} - 16 q^{8} - 76 q^{9} - 6 q^{10} - 47 q^{12} - 33 q^{14} - 8 q^{15} - 17 q^{16} - 26 q^{17} - 8 q^{18} - 22 q^{20} - 18 q^{22} - 26 q^{23} - 74 q^{24} - 72 q^{25} - 12 q^{26} + 2 q^{28} - 11 q^{30} + 60 q^{31} - 13 q^{32} - 14 q^{33} - 18 q^{34} + 8 q^{36} - 46 q^{38} - 32 q^{39} + 32 q^{40} - 20 q^{41} - 36 q^{42} + 38 q^{44} - 22 q^{46} - 58 q^{47} + 28 q^{48} - 16 q^{49} - 132 q^{50} + 18 q^{52} - 37 q^{54} - 32 q^{55} + 96 q^{56} - 66 q^{57} + 100 q^{60} + 28 q^{62} - 72 q^{63} - 28 q^{64} - 36 q^{65} - 4 q^{66} - 11 q^{68} - 36 q^{70} + 60 q^{71} - 130 q^{72} - 18 q^{73} - 12 q^{74} + 11 q^{76} - 132 q^{78} - 12 q^{79} - 64 q^{80} - 58 q^{81} + 152 q^{82} - 224 q^{84} + 55 q^{86} - 8 q^{87} - 169 q^{88} - 18 q^{89} + 144 q^{90} - 54 q^{92} + 154 q^{94} - 64 q^{95} - 142 q^{96} - 96 q^{97} + 151 q^{98}+O(q^{100}) $ 648 * q - 13 * q^2 - 13 * q^4 - 6 * q^6 - 24 * q^7 - 16 * q^8 - 76 * q^9 - 6 * q^10 - 47 * q^12 - 33 * q^14 - 8 * q^15 - 17 * q^16 - 26 * q^17 - 8 * q^18 - 22 * q^20 - 18 * q^22 - 26 * q^23 - 74 * q^24 - 72 * q^25 - 12 * q^26 + 2 * q^28 - 11 * q^30 + 60 * q^31 - 13 * q^32 - 14 * q^33 - 18 * q^34 + 8 * q^36 - 46 * q^38 - 32 * q^39 + 32 * q^40 - 20 * q^41 - 36 * q^42 + 38 * q^44 - 22 * q^46 - 58 * q^47 + 28 * q^48 - 16 * q^49 - 132 * q^50 + 18 * q^52 - 37 * q^54 - 32 * q^55 + 96 * q^56 - 66 * q^57 + 100 * q^60 + 28 * q^62 - 72 * q^63 - 28 * q^64 - 36 * q^65 - 4 * q^66 - 11 * q^68 - 36 * q^70 + 60 * q^71 - 130 * q^72 - 18 * q^73 - 12 * q^74 + 11 * q^76 - 132 * q^78 - 12 * q^79 - 64 * q^80 - 58 * q^81 + 152 * q^82 - 224 * q^84 + 55 * q^86 - 8 * q^87 - 169 * q^88 - 18 * q^89 + 144 * q^90 - 54 * q^92 + 154 * q^94 - 64 * q^95 - 142 * q^96 - 96 * q^97 + 151 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/392\mathbb{Z}\right)^\times$.

$n$	$197$	$295$	$297$
$\chi(n)$	$-1$	$1$	$e\left(\frac{16}{21}\right)$

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 $

$2$	−1.05324	+	0.943763i	−0.744752	+	0.667341i
$2$	−1.05324	+	0.943763i	−0.744752	+	0.667341i
$3$	−1.08411	−	1.16839i	−0.625910	−	0.674571i	0.337893	−	0.941184i	$-0.390286\pi$
$3$	−1.08411	−	1.16839i	−0.625910	−	0.674571i	−0.963803	+	0.266614i	$0.914095\pi$
$4$	0.218622	−	1.98802i	0.109311	−	0.994008i
$5$	0.529378	−	1.71620i	0.236745	−	0.767509i	−0.756757	−	0.653696i	$-0.773217\pi$
$5$	0.529378	−	1.71620i	0.236745	−	0.767509i	0.993502	−	0.113813i	$-0.0363063\pi$
$6$	2.24451	+	0.207452i	0.916317	+	0.0846920i
$7$	−2.34752	+	1.22032i	−0.887277	+	0.461236i
$7$	−2.34752	+	1.22032i	−0.887277	+	0.461236i
$8$	1.64596	+	2.30018i	0.581933	+	0.813237i
$9$	0.0343439	−	0.458288i	0.0114480	−	0.152763i
$10$	1.06213	+	2.30718i	0.335874	+	0.729593i
$11$	4.71137	−	0.353068i	1.42053	−	0.106454i	0.657811	−	0.753183i	$-0.271482\pi$
$11$	4.71137	−	0.353068i	1.42053	−	0.106454i	0.762720	+	0.646729i	$0.223863\pi$
$12$	−2.55979	+	1.89979i	−0.738947	+	0.548422i
$13$	0.558298	−	1.15932i	0.154844	−	0.321537i	−0.809087	−	0.587689i	$-0.800038\pi$
$13$	0.558298	−	1.15932i	0.154844	−	0.321537i	0.963931	+	0.266152i	$0.0857523\pi$
$14$	1.32080	−	3.50078i	0.353000	−	0.935623i
$15$	−2.57910	+	1.24203i	−0.665920	+	0.320690i
$16$	−3.90441	−	0.869246i	−0.976102	−	0.217312i
$17$	−3.60762	−	0.543762i	−0.874977	−	0.131882i	−0.303827	−	0.952727i	$-0.598265\pi$
$17$	−3.60762	−	0.543762i	−0.874977	−	0.131882i	−0.571150	+	0.820846i	$0.693503\pi$
$18$	0.396343	+	0.515099i	0.0934189	+	0.121410i
$19$	−4.74129	−	2.73738i	−1.08773	−	0.627999i	−0.154756	−	0.987953i	$-0.549459\pi$
$19$	−4.74129	−	2.73738i	−1.08773	−	0.627999i	−0.932970	+	0.359954i	$0.882793\pi$
$20$	−3.29610	−	1.42761i	−0.737031	−	0.319223i
$21$	3.97077	+	1.41986i	0.866492	+	0.309839i
$22$	−4.62898	+	4.81828i	−0.986902	+	1.02726i
$23$	−7.55176	+	1.13824i	−1.57465	+	0.237340i	−0.877497	−	0.479581i	$-0.840789\pi$
$23$	−7.55176	+	1.13824i	−1.57465	+	0.237340i	−0.697154	+	0.716922i	$0.745550\pi$
$24$	0.903116	−	4.41676i	0.184348	−	0.901568i
$25$	1.46609	+	0.999561i	0.293217	+	0.199912i
$26$	0.506101	+	1.74794i	0.0992545	+	0.342799i
$27$	−4.31111	+	3.43799i	−0.829673	+	0.661642i
$28$	1.91279	+	4.93368i	0.361483	+	0.932379i
$29$	−6.72404	−	5.36224i	−1.24862	−	0.995744i	−0.999629	−	0.0272387i	$-0.991329\pi$
$29$	−6.72404	−	5.36224i	−1.24862	−	0.995744i	−0.248994	−	0.968505i	$-0.580100\pi$
$30$	1.54422	−	3.74221i	0.281935	−	0.683231i
$31$	−0.368485	−	0.638234i	−0.0661818	−	0.114630i	0.831036	−	0.556219i	$-0.187748\pi$
$31$	−0.368485	−	0.638234i	−0.0661818	−	0.114630i	−0.897218	+	0.441589i	$0.854415\pi$
$32$	4.93264	−	2.76931i	0.871975	−	0.489550i
$33$	−5.52016	−	5.12196i	−0.960936	−	0.891618i
$34$	4.31287	−	2.83203i	0.739651	−	0.485690i
$35$	0.851585	+	4.67482i	0.143944	+	0.790189i
$36$	−0.903575	−	0.168468i	−0.150596	−	0.0280780i
$37$	6.57534	−	2.58063i	1.08098	−	0.424253i	0.243040	−	0.970016i	$-0.421855\pi$
$37$	6.57534	−	2.58063i	1.08098	−	0.424253i	0.837940	+	0.545763i	$0.183760\pi$
$38$	7.57715	−	1.59154i	1.22918	−	0.258181i
$39$	−1.95979	+	0.604515i	−0.313818	+	0.0967999i
$40$	4.81891	−	1.60713i	0.761936	−	0.254109i
$41$	−1.11229	−	4.87325i	−0.173710	−	0.761074i	−0.984450	−	0.175667i	$-0.943792\pi$
$41$	−1.11229	−	4.87325i	−0.173710	−	0.761074i	0.810740	−	0.585407i	$-0.199065\pi$
$42$	−5.52218	+	2.25201i	−0.852090	+	0.347493i
$43$	0.167094	+	0.0381381i	0.0254816	+	0.00581601i	0.235243	−	0.971937i	$-0.424411\pi$
$43$	0.167094	+	0.0381381i	0.0254816	+	0.00581601i	−0.209761	+	0.977753i	$0.567269\pi$
$44$	0.328102	−	9.44346i	0.0494632	−	1.42366i
$45$	−0.768333	−	0.301549i	−0.114536	−	0.0449522i
$46$	6.87957	−	8.32592i	1.01434	−	1.22759i
$47$	−8.06065	+	5.49566i	−1.17577	+	0.801624i	−0.983711	−	0.179760i	$-0.942468\pi$
$47$	−8.06065	+	5.49566i	−1.17577	+	0.801624i	−0.192056	+	0.981384i	$0.561516\pi$
$48$	3.21718	+	5.50423i	0.464360	+	0.794467i
$49$	4.02166	−	5.72942i	0.574523	−	0.818489i
$50$	−2.48749	+	0.330863i	−0.351784	+	0.0467911i
$51$	3.27573	+	4.80461i	0.458694	+	0.672780i
$52$	−2.18268	−	1.36336i	−0.302684	−	0.189064i
$53$	−1.16683	−	0.457945i	−0.160276	−	0.0629036i	0.283847	−	0.958870i	$-0.408389\pi$
$53$	−1.16683	−	0.457945i	−0.160276	−	0.0629036i	−0.444123	+	0.895966i	$0.646485\pi$
$54$	1.29597	−	7.68969i	0.176359	−	1.04643i
$55$	1.88816	−	8.27257i	0.254599	−	1.11547i
$56$	−6.67085	−	3.39113i	−0.891430	−	0.453158i
$57$	1.94174	+	8.50730i	0.257189	+	1.12682i
$58$	12.1427	−	0.698183i	1.59442	−	0.0916759i
$59$	0.0541481	+	0.175544i	0.00704949	+	0.0228539i	0.959029	−	0.283307i	$-0.0914316\pi$
$59$	0.0541481	+	0.175544i	0.00704949	+	0.0228539i	−0.951980	+	0.306161i	$0.900955\pi$
$60$	1.90532	+	5.39882i	0.245976	+	0.696984i
$61$	−6.56223	+	2.57549i	−0.840208	+	0.329757i	−0.746124	−	0.665807i	$-0.768087\pi$
$61$	−6.56223	+	2.57549i	−0.840208	+	0.329757i	−0.0940839	+	0.995564i	$0.529992\pi$
$62$	0.990444	+	0.324450i	0.125786	+	0.0412052i
$63$	0.478633	+	1.11775i	0.0603021	+	0.140823i
$64$	−2.58166	+	7.57199i	−0.322708	+	0.946499i
$65$	−1.69407	−	1.57187i	−0.210124	−	0.194966i
$66$	10.6480	+	0.184919i	1.31067	+	0.0227620i
$67$	10.3484	−	5.97464i	1.26426	−	0.729919i	0.290361	−	0.956917i	$-0.406224\pi$
$67$	10.3484	−	5.97464i	1.26426	−	0.729919i	0.973895	+	0.226998i	$0.0728911\pi$
$68$	−1.86971	+	7.05313i	−0.226736	+	0.855318i
$69$	9.51684	+	7.58943i	1.14569	+	0.913660i
$70$	−5.30884	−	4.12000i	−0.634528	−	0.492435i
$71$	8.89597	+	11.1552i	1.05576	+	1.32388i	0.943929	+	0.330150i	$0.107099\pi$
$71$	8.89597	+	11.1552i	1.05576	+	1.32388i	0.111828	+	0.993728i	$0.464329\pi$
$72$	1.11067	−	0.675324i	0.130894	−	0.0795877i
$73$	3.14522	+	2.14437i	0.368120	+	0.250980i	0.733225	−	0.679986i	$-0.238014\pi$
$73$	3.14522	+	2.14437i	0.368120	+	0.250980i	−0.365105	+	0.930967i	$0.618967\pi$
$74$	−4.48990	+	8.92359i	−0.521940	+	1.03735i
$75$	−0.421519	−	2.79659i	−0.0486728	−	0.322923i
$76$	−6.47851	+	8.82730i	−0.743136	+	1.01256i
$77$	−10.6292	+	6.57819i	−1.21130	+	0.749654i
$78$	1.49361	−	2.48628i	0.169118	−	0.281516i
$79$	−0.347223	+	0.601408i	−0.0390657	+	0.0676637i	−0.884897	−	0.465786i	$-0.845771\pi$
$79$	−0.347223	+	0.601408i	−0.0390657	+	0.0676637i	0.845831	+	0.533450i	$0.179105\pi$
$80$	−3.55871	+	6.24059i	−0.397876	+	0.697720i
$81$	7.32731	+	1.10441i	0.814146	+	0.122713i
$82$	5.77070	+	4.08296i	0.637267	+	0.450887i
$83$	−5.85761	−	12.1635i	−0.642956	−	1.33511i	−0.926551	−	0.376168i	$-0.877241\pi$
$83$	−5.85761	−	12.1635i	−0.642956	−	1.33511i	0.283595	−	0.958944i	$-0.408473\pi$
$84$	3.69080	−	7.58353i	0.402699	−	0.827431i
$85$	−2.84300	+	5.90355i	−0.308367	+	0.640330i
$86$	−0.211983	+	0.117529i	−0.0228587	+	0.0126735i
$87$	1.02439	+	13.6696i	0.109826	+	1.46553i
$88$	8.56682	+	10.2559i	0.913226	+	1.09328i
$89$	0.439562	−	5.86555i	0.0465935	−	0.621747i	−0.924212	−	0.381879i	$-0.875277\pi$
$89$	0.439562	−	5.86555i	0.0465935	−	0.621747i	0.970806	−	0.239867i	$-0.0771040\pi$
$90$	1.09383	−	0.407522i	0.115300	−	0.0429566i
$91$	0.104120	+	3.40282i	0.0109148	+	0.356712i
$92$	0.611870	+	15.2619i	0.0637919	+	1.59116i
$93$	−0.346229	+	1.12245i	−0.0359023	+	0.116392i
$94$	3.30318	−	13.3956i	0.340697	−	1.38165i
$95$	−7.20784	+	6.68790i	−0.739509	+	0.686164i
$96$	−8.58315	−	2.76101i	−0.876014	−	0.281794i
$97$	14.1075			1.43240			0.716200	−	0.697895i	$-0.245880\pi$
$97$	14.1075			1.43240			0.716200	+	0.697895i	$0.245880\pi$
$98$	1.17145	+	9.82994i	0.118334	+	0.992974i
$99$		−	2.17129i		−	0.218223i
$100$	2.30766	−	2.69608i	0.230766	−	0.269608i
$101$	−5.65948	−	6.09947i	−0.563139	−	0.606920i	0.385721	−	0.922615i	$-0.373953\pi$
$101$	−5.65948	−	6.09947i	−0.563139	−	0.606920i	−0.948861	+	0.315695i	$0.897762\pi$
$102$	−7.98454	−	1.96889i	−0.790587	−	0.194949i
$103$	−3.45678	−	1.06628i	−0.340607	−	0.105063i	0.119733	−	0.992806i	$-0.461796\pi$
$103$	−3.45678	−	1.06628i	−0.340607	−	0.105063i	−0.460340	+	0.887743i	$0.652272\pi$
$104$	3.58557	−	0.623999i	0.351594	−	0.0611881i
$105$	4.53880	−	6.06299i	0.442942	−	0.591687i
$106$	1.66114	−	0.618882i	0.161344	−	0.0601111i
$107$	−16.9460	−	1.26993i	−1.63824	−	0.122769i	−0.776497	−	0.630121i	$-0.783005\pi$
$107$	−16.9460	−	1.26993i	−1.63824	−	0.122769i	−0.861739	+	0.507352i	$0.830624\pi$
$108$	5.89228	+	9.32217i	0.566985	+	0.897026i
$109$	−5.34912	+	0.400861i	−0.512353	+	0.0383955i	−0.328399	−	0.944539i	$-0.606509\pi$
$109$	−5.34912	+	0.400861i	−0.512353	+	0.0383955i	−0.183954	+	0.982935i	$0.558890\pi$
$110$	5.81866	+	10.4950i	0.554788	+	1.00066i
$111$	−10.1436	−	4.88488i	−0.962785	−	0.463653i
$112$	10.2264	−	2.72404i	0.966306	−	0.257398i
$113$	0.136045	−	0.0655158i	0.0127980	−	0.00616320i	−0.427474	−	0.904028i	$-0.640596\pi$
$113$	0.136045	−	0.0655158i	0.0127980	−	0.00616320i	0.440272	+	0.897865i	$0.354882\pi$
$114$	−10.0740	−	7.12767i	−0.943515	−	0.667568i
$115$	−2.04428	+	13.5629i	−0.190630	+	1.26475i
$116$	−12.1302	+	12.1952i	−1.12626	+	1.13230i
$117$	−0.512127	−	0.295677i	−0.0473462	−	0.0273353i
$118$	−0.222703	−	0.133787i	−0.0205015	−	0.0123161i
$119$	9.13251	−	3.12595i	0.837176	−	0.286555i
$120$	−7.10197	−	3.88807i	−0.648318	−	0.354930i
$121$	11.1952	−	1.68741i	1.01775	−	0.153400i
$122$	4.48095	−	8.90580i	0.405686	−	0.806293i
$123$	−4.48802	+	6.58271i	−0.404671	+	0.593543i
$124$	−1.34938	+	0.593021i	−0.121178	+	0.0532549i
$125$	9.51238	−	7.58587i	0.850813	−	0.678501i
$126$	−1.55900	−	0.725539i	−0.138887	−	0.0646361i
$127$	7.58090	−	9.50614i	0.672696	−	0.843534i	−0.321963	−	0.946752i	$-0.604343\pi$
$127$	7.58090	−	9.50614i	0.672696	−	0.843534i	0.994659	+	0.103218i	$0.0329141\pi$
$128$	−4.42706	−	10.4116i	−0.391300	−	0.920263i
$129$	−0.136588	−	0.236577i	−0.0120259	−	0.0208295i
$130$	3.26773	+	0.0567496i	0.286599	+	0.00497727i
$131$	13.9506	−	15.0352i	1.21887	−	1.31363i	0.283925	−	0.958847i	$-0.408363\pi$
$131$	13.9506	−	15.0352i	1.21887	−	1.31363i	0.934948	−	0.354786i	$-0.115446\pi$
$132$	−11.3894	+	9.85438i	−0.991316	+	0.857714i
$133$	14.4707	+	0.640183i	1.25477	+	0.0555109i
$134$	−5.26067	+	16.0592i	−0.454452	+	1.38730i
$135$	3.61809	+	9.21873i	0.311395	+	0.793422i
$136$	−4.68724	−	9.19319i	−0.401927	−	0.788310i
$137$	−2.48412	+	0.766250i	−0.212233	+	0.0654651i	−0.399048	−	0.916930i	$-0.630659\pi$
$137$	−2.48412	+	0.766250i	−0.212233	+	0.0654651i	0.186816	+	0.982395i	$0.440183\pi$
$138$	−17.1861	+	0.988170i	−1.46298	+	0.0841186i
$139$	13.2218	−	3.01779i	1.12146	−	0.255965i	0.378695	−	0.925521i	$-0.376373\pi$
$139$	13.2218	−	3.01779i	1.12146	−	0.255965i	0.742761	+	0.669556i	$0.233516\pi$
$140$	9.47979	−	0.670947i	0.801188	−	0.0567053i
$141$	15.1597	+	3.46010i	1.27668	+	0.291393i
$142$	−19.8974	−	3.35338i	−1.66976	−	0.281410i
$143$	2.22103	−	5.65909i	0.185732	−	0.473237i
$144$	−0.532458	+	1.75949i	−0.0443715	+	0.146624i
$145$	−12.7623	+	8.70116i	−1.05985	+	0.722592i
$146$	−5.33645	+	0.709806i	−0.441648	+	0.0587439i
$147$	−11.0541	+	1.51244i	−0.911728	+	0.124744i
$148$	−3.69282	−	13.6361i	−0.303548	−	1.12088i
$149$	5.73660	+	8.41404i	0.469960	+	0.689305i	0.985903	−	0.167318i	$-0.0535106\pi$
$149$	5.73660	+	8.41404i	0.469960	+	0.689305i	−0.515943	+	0.856623i	$0.672558\pi$
$150$	3.08328	+	2.54767i	0.251749	+	0.208016i
$151$	−1.52307	+	3.88071i	−0.123945	+	0.315808i	−0.979356	−	0.202143i	$-0.935210\pi$
$151$	−1.52307	+	3.88071i	−0.123945	+	0.315808i	0.855411	+	0.517950i	$0.173305\pi$
$152$	−1.50747	−	15.4114i	−0.122272	−	1.25003i
$153$	−0.373099	+	1.63466i	−0.0301633	+	0.132154i
$154$	4.98678	−	16.9598i	0.401846	−	1.36666i
$155$	−1.29041	+	0.294527i	−0.103648	+	0.0236570i
$156$	0.773333	+	4.02825i	0.0619162	+	0.322518i
$157$	0.368243	+	1.19382i	0.0293890	+	0.0952768i	0.969079	−	0.246750i	$-0.0793627\pi$
$157$	0.368243	+	1.19382i	0.0293890	+	0.0952768i	−0.939690	+	0.342027i	$0.888887\pi$
$158$	−0.201878	−	0.961123i	−0.0160606	−	0.0764628i
$159$	0.729906	+	1.85977i	0.0578853	+	0.147489i
$160$	−2.14147	−	9.93141i	−0.169298	−	0.785147i
$161$	16.3389	−	11.8876i	1.28768	−	0.936873i
$162$	−8.75971	+	5.75203i	−0.688228	+	0.451923i
$163$	8.82868	−	9.51506i	0.691516	−	0.745277i	−0.285515	−	0.958374i	$-0.592165\pi$
$163$	8.82868	−	9.51506i	0.691516	−	0.745277i	0.977031	+	0.213097i	$0.0683551\pi$
$164$	−9.93126	+	1.14585i	−0.775501	+	0.0894756i
$165$	−11.7126	+	6.76225i	−0.911821	+	0.526440i
$166$	17.6489	+	7.28282i	1.36982	+	0.565256i
$167$	11.4133	−	14.3119i	0.883191	−	1.10749i	−0.110337	−	0.993894i	$-0.535193\pi$
$167$	11.4133	−	14.3119i	0.883191	−	1.10749i	0.993528	−	0.113592i	$-0.0362356\pi$
$168$	3.26977	+	11.4705i	0.252268	+	0.884969i
$169$	7.07305	+	8.86932i	0.544081	+	0.682255i
$170$	−2.57720	−	8.90097i	−0.197662	−	0.682673i
$171$	−1.41734	+	2.07886i	−0.108387	+	0.158975i
$172$	0.112350	−	0.323848i	0.00856658	−	0.0246932i
$173$	3.33164	+	22.1040i	0.253300	+	1.68054i	0.647932	+	0.761698i	$0.275634\pi$
$173$	3.33164	+	22.1040i	0.253300	+	1.68054i	−0.394632	+	0.918839i	$0.629128\pi$
$174$	−13.9798	−	13.4305i	−1.05980	−	1.01817i
$175$	−4.66144	−	0.557396i	−0.352372	−	0.0421352i
$176$	−18.7020	−	2.71682i	−1.40972	−	0.204788i
$177$	0.146401	−	0.253575i	0.0110042	−	0.0190598i
$178$	5.07272	+	6.59266i	0.380217	+	0.494141i
$179$	0.565149	−	3.74952i	0.0422412	−	0.280252i	−0.957731	−	0.287664i	$-0.907121\pi$
$179$	0.565149	−	3.74952i	0.0422412	−	0.280252i	0.999973	+	0.00741200i	$0.00235934\pi$
$180$	−0.767458	+	1.46153i	−0.0572029	+	0.108936i
$181$	−2.17360	−	4.51353i	−0.161563	−	0.335488i	0.804434	−	0.594041i	$-0.202468\pi$
$181$	−2.17360	−	4.51353i	−0.161563	−	0.335488i	−0.965997	+	0.258553i	$0.916754\pi$
$182$	−3.32112	−	3.48571i	−0.246178	−	0.258378i
$183$	10.1233	+	4.87515i	0.748339	+	0.360381i
$184$	−15.0480	−	15.4969i	−1.10936	−	1.14245i
$185$	−0.948042	−	12.6507i	−0.0697014	−	0.930101i
$186$	−0.694664	−	1.50896i	−0.0509352	−	0.110643i
$187$	−17.1888	−	1.28812i	−1.25697	−	0.0941970i
$188$	9.16322	+	17.2262i	0.668296	+	1.25635i
$189$	5.92496	−	13.3317i	0.430977	−	0.969736i
$190$	1.27978	−	13.8464i	0.0928450	−	1.00453i
$191$	−9.41485	−	2.90410i	−0.681234	−	0.210133i	−0.0652235	−	0.997871i	$-0.520776\pi$
$191$	−9.41485	−	2.90410i	−0.681234	−	0.210133i	−0.616011	+	0.787738i	$0.711252\pi$
$192$	11.6458	−	5.19246i	0.840466	−	0.374734i
$193$	0.106231	−	0.0985677i	0.00764665	−	0.00709506i	−0.676340	−	0.736589i	$-0.736435\pi$
$193$	0.106231	−	0.0985677i	0.00764665	−	0.00709506i	0.683987	+	0.729494i	$0.260245\pi$
$194$	−14.8586	+	13.3141i	−1.06678	+	0.955900i
$195$			3.68341i			0.263775i
$196$	−10.5110	−	9.24769i	−0.750782	−	0.660550i
$197$		−	4.71073i		−	0.335626i	−0.985819	−	0.167813i	$-0.946330\pi$
$197$		−	4.71073i		−	0.335626i	0.985819	−	0.167813i	$-0.0536705\pi$
$198$	2.04918	+	2.28688i	0.145629	+	0.162522i
$199$	4.52487	−	4.19846i	0.320759	−	0.297621i	−0.503315	−	0.864103i	$-0.667886\pi$
$199$	4.52487	−	4.19846i	0.320759	−	0.297621i	0.824074	+	0.566482i	$0.191696\pi$
$200$	0.113942	+	5.01750i	0.00805693	+	0.354791i
$201$	−18.1995	−	5.61380i	−1.28369	−	0.395967i
$202$	11.7172	+	1.08298i	0.824422	+	0.0761985i
$203$	22.3284	+	4.38250i	1.56715	+	0.307591i
$204$	10.2678	−	5.46181i	0.718889	−	0.382403i
$205$	−8.95230	−	0.670882i	−0.625256	−	0.0468564i
$206$	4.64713	−	2.13934i	0.323781	−	0.149055i
$207$	0.262287	+	3.49997i	0.0182302	+	0.243265i
$208$	−3.18756	+	4.04115i	−0.221017	+	0.280203i
$209$	−23.3044	−	11.2228i	−1.61200	−	0.776299i
$210$	0.941587	+	10.6693i	0.0649757	+	0.736254i
$211$	−3.58316	−	7.44050i	−0.246675	−	0.512225i	0.740463	−	0.672097i	$-0.234606\pi$
$211$	−3.58316	−	7.44050i	−0.246675	−	0.512225i	−0.987138	+	0.159872i	$0.948892\pi$
$212$	−1.16550	+	2.21955i	−0.0800466	+	0.152439i
$213$	3.38943	−	22.4874i	0.232240	−	1.54081i
$214$	19.0467	−	14.6555i	1.30201	−	1.00183i
$215$	0.153909	−	0.266578i	0.0104965	−	0.0181805i
$216$	−15.0039	−	4.25754i	−1.02089	−	0.289689i
$217$	1.64387	+	1.04860i	0.111593	+	0.0711834i
$218$	5.25558	−	5.47051i	0.355953	−	0.370510i
$219$	−0.904291	−	5.99958i	−0.0611063	−	0.405414i
$220$	−16.0332	−	5.56225i	−1.08096	−	0.375007i
$221$	−2.64452	+	3.87880i	−0.177890	+	0.260916i
$222$	15.2938	−	4.42818i	1.02645	−	0.297200i
$223$	−11.3319	−	14.2097i	−0.758838	−	0.951553i	0.240982	−	0.970530i	$-0.422530\pi$
$223$	−11.3319	−	14.2097i	−0.758838	−	0.951553i	−0.999820	+	0.0189770i	$0.993959\pi$
$224$	−8.20000	+	12.5204i	−0.547886	+	0.836553i
$225$	0.508438	−	0.637561i	0.0338959	−	0.0425041i
$226$	−0.0814563	+	0.197398i	−0.00541839	+	0.0131307i
$227$	−10.0579	+	5.80694i	−0.667567	+	0.385420i	−0.795154	−	0.606407i	$-0.792610\pi$
$227$	−10.0579	+	5.80694i	−0.667567	+	0.385420i	0.127587	+	0.991827i	$0.459277\pi$
$228$	17.3371	−	2.00032i	1.14818	−	0.132474i
$229$	3.23859	−	3.49037i	0.214012	−	0.230650i	−0.616918	−	0.787028i	$-0.711619\pi$
$229$	3.23859	−	3.49037i	0.214012	−	0.230650i	0.830929	+	0.556378i	$0.187809\pi$
$230$	−10.6471	−	16.2143i	−0.702046	−	1.06914i
$231$	19.2091	+	5.28754i	1.26386	+	0.347894i
$232$	1.26666	−	24.2925i	0.0831603	−	1.59488i
$233$	8.83993	+	22.5238i	0.579123	+	1.47558i	0.857180	+	0.515017i	$0.172214\pi$
$233$	8.83993	+	22.5238i	0.579123	+	1.47558i	−0.278057	+	0.960565i	$0.589690\pi$
$234$	0.818440	−	0.171909i	0.0535031	−	0.0112380i
$235$	5.16453	+	16.7430i	0.336897	+	1.09219i
$236$	0.360822	−	0.0692696i	0.0234875	−	0.00450907i
$237$	1.07911	−	0.246299i	0.0700956	−	0.0159989i
$238$	−6.66856	+	11.9113i	−0.432258	+	0.772095i
$239$	4.58150	−	20.0729i	0.296352	−	1.29841i	−0.579162	−	0.815213i	$-0.696620\pi$
$239$	4.58150	−	20.0729i	0.296352	−	1.29841i	0.875514	−	0.483192i	$-0.160523\pi$
$240$	11.1495	−	2.60751i	0.719696	−	0.168314i
$241$	−5.28494	+	13.4658i	−0.340433	+	0.867409i	0.653450	+	0.756970i	$0.273321\pi$
$241$	−5.28494	+	13.4658i	−0.340433	+	0.867409i	−0.993883	+	0.110439i	$0.964774\pi$
$242$	−10.1987	+	12.3429i	−0.655598	+	0.793429i
$243$	2.66543	+	3.90946i	0.170987	+	0.250792i
$244$	3.68546	+	13.6089i	0.235937	+	0.871219i
$245$	−7.70386	−	9.93501i	−0.492182	−	0.634724i
$246$	−1.48557	−	11.1688i	−0.0947166	−	0.712096i
$247$	−5.82055	+	3.96838i	−0.370353	+	0.252502i
$248$	0.861544	−	1.89809i	0.0547081	−	0.120529i
$249$	−7.86138	+	20.0305i	−0.498195	+	1.26938i
$250$	−2.85954	+	16.9672i	−0.180853	+	1.07310i
$251$	14.9926	+	3.42195i	0.946322	+	0.215992i	0.667718	−	0.744414i	$-0.267271\pi$
$251$	14.9926	+	3.42195i	0.946322	+	0.215992i	0.278604	+	0.960406i	$0.410128\pi$
$252$	2.32674	−	0.707166i	0.146571	−	0.0445472i
$253$	−35.1773	+	8.02898i	−2.21158	+	0.504778i
$254$	0.987059	+	17.1668i	0.0619336	+	1.07714i
$255$	9.97978	−	3.07835i	0.624958	−	0.192774i
$256$	14.4888	+	6.78779i	0.905551	+	0.424237i
$257$	−5.74227	−	14.6311i	−0.358193	−	0.912661i	−0.990446	−	0.137899i	$-0.955965\pi$
$257$	−5.74227	−	14.6311i	−0.358193	−	0.912661i	0.632253	−	0.774762i	$-0.282130\pi$
$258$	0.367132	+	0.120265i	0.0228567	+	0.00748740i
$259$	−12.2865	+	14.0821i	−0.763448	+	0.875017i
$260$	−3.49526	+	3.02420i	−0.216767	+	0.187553i
$261$	−2.68838	+	2.89739i	−0.166407	+	0.179344i
$262$	−0.503664	+	29.0018i	−0.0311165	+	1.79173i
$263$	−6.77977	−	11.7429i	−0.418059	−	0.724099i	0.577685	−	0.816259i	$-0.303956\pi$
$263$	−6.77977	−	11.7429i	−0.418059	−	0.724099i	−0.995744	+	0.0921605i	$0.970623\pi$
$264$	2.69550	−	21.1279i	0.165896	−	1.30033i
$265$	−1.40362	+	1.76008i	−0.0862236	+	0.108121i
$266$	−15.8453	+	12.9827i	−0.971538	+	0.796019i
$267$	−7.32978	+	5.84531i	−0.448575	+	0.357727i
$268$	−9.61530	−	21.8789i	−0.587348	−	1.33647i
$269$	−0.673944	+	0.988494i	−0.0410911	+	0.0602695i	−0.846235	−	0.532810i	$-0.821136\pi$
$269$	−0.673944	+	0.988494i	−0.0410911	+	0.0602695i	0.805144	+	0.593080i	$0.202088\pi$
$270$	−12.5110	−	6.29490i	−0.761396	−	0.383096i
$271$	12.5924	−	1.89801i	0.764936	−	0.115296i	0.245026	−	0.969516i	$-0.421203\pi$
$271$	12.5924	−	1.89801i	0.764936	−	0.115296i	0.519910	+	0.854221i	$0.325965\pi$
$272$	13.6130	+	5.25898i	0.825408	+	0.318873i
$273$	3.86294	−	3.81067i	0.233796	−	0.230632i
$274$	1.89321	−	3.15147i	0.114373	−	0.190387i
$275$	7.26019	+	4.19167i	0.437806	+	0.252767i
$276$	17.1685	−	17.2604i	1.03342	−	1.03895i
$277$	3.17141	−	21.0409i	0.190552	−	1.26423i	−0.665131	−	0.746726i	$-0.731624\pi$
$277$	3.17141	−	21.0409i	0.190552	−	1.26423i	0.855683	−	0.517501i	$-0.173137\pi$
$278$	−11.0776	+	15.6567i	−0.664391	+	0.939025i
$279$	−0.305150	+	0.146953i	−0.0182689	+	0.00879782i
$280$	−9.35126	+	9.65334i	−0.558845	+	0.576897i
$281$	−4.99644	−	2.40616i	−0.298063	−	0.143540i	0.278875	−	0.960327i	$-0.410038\pi$
$281$	−4.99644	−	2.40616i	−0.298063	−	0.143540i	−0.576938	+	0.816788i	$0.695753\pi$
$282$	−19.2323	+	10.6629i	−1.14527	+	0.634964i
$283$	17.5354	−	1.31410i	1.04237	−	0.0781149i	0.457474	−	0.889223i	$-0.348754\pi$
$283$	17.5354	−	1.31410i	1.04237	−	0.0781149i	0.584896	+	0.811108i	$0.301135\pi$
$284$	24.1215	−	15.2465i	1.43135	−	0.904716i
$285$	15.6282	+	1.17117i	0.925732	+	0.0693740i
$286$	3.00157	+	8.05650i	0.177486	+	0.476391i
$287$	8.55801	+	10.0827i	0.505164	+	0.595162i
$288$	−1.09974	−	2.35568i	−0.0648026	−	0.138810i
$289$	−3.52547	−	1.08746i	−0.207380	−	0.0639684i
$290$	5.22986	−	21.2089i	0.307108	−	1.24543i
$291$	−15.2941	−	16.4831i	−0.896554	−	0.966255i
$292$	4.95066	−	5.78394i	0.289716	−	0.338479i
$293$			3.23255i			0.188847i	0.995532	+	0.0944237i	$0.0301008\pi$
$293$			3.23255i			0.188847i	−0.995532	+	0.0944237i	$0.969899\pi$
$294$	10.2152	−	12.0254i	0.595764	−	0.701337i
$295$	0.329934			0.0192095
$296$	16.7586	+	10.8769i	0.974076	+	0.632205i
$297$	−19.0974	+	17.7198i	−1.10814	+	1.02821i
$298$	−13.9829	−	3.44800i	−0.810006	−	0.199737i
$299$	−2.89655	+	9.39037i	−0.167512	+	0.543059i
$300$	−5.65183	+	0.226590i	−0.326308	+	0.0130822i
$301$	−0.438797	+	0.114378i	−0.0252918	+	0.00659262i
$302$	−2.05832	−	5.52473i	−0.118443	−	0.317912i
$303$	−0.991074	+	13.2250i	−0.0569357	+	0.759755i
$304$	16.1325	+	14.8092i	0.925261	+	0.849367i
$305$	0.946152	+	12.6255i	0.0541765	+	0.722935i
$306$	−1.14976	−	2.07380i	−0.0657277	−	0.118551i
$307$	−13.2248	+	27.4615i	−0.754777	+	1.56731i	0.0671668	+	0.997742i	$0.478604\pi$
$307$	−13.2248	+	27.4615i	−0.754777	+	1.56731i	−0.821944	+	0.569569i	$0.807110\pi$
$308$	10.7538	+	22.5691i	0.612754	+	1.28599i
$309$	2.50170	+	5.19483i	0.142317	+	0.295524i
$310$	1.08114	−	1.52804i	0.0614047	−	0.0867871i
$311$	4.24097	+	0.639223i	0.240483	+	0.0362470i	0.268178	−	0.963369i	$-0.413578\pi$
$311$	4.24097	+	0.639223i	0.240483	+	0.0362470i	−0.0276946	+	0.999616i	$0.508817\pi$
$312$	−4.61622	−	3.51287i	−0.261342	−	0.198877i
$313$	10.8903	−	18.8625i	0.615556	−	1.06617i	−0.374731	−	0.927134i	$-0.622265\pi$
$313$	10.8903	−	18.8625i	0.615556	−	1.06617i	0.990287	−	0.139041i	$-0.0444019\pi$
$314$	−1.51453	−	0.909837i	−0.0854697	−	0.0513451i
$315$	2.17166	−	0.229719i	0.122359	−	0.0129432i
$316$	1.11970	+	0.821766i	0.0629880	+	0.0462280i
$317$	0.828649	+	5.49772i	0.0465415	+	0.308783i	0.999974	+	0.00717713i	$0.00228457\pi$
$317$	0.828649	+	5.49772i	0.0465415	+	0.308783i	−0.953433	+	0.301606i	$0.902477\pi$
$318$	−2.52395	−	1.26992i	−0.141536	−	0.0712137i
$319$	−33.5727	−	22.8895i	−1.87971	−	1.28156i
$320$	11.6284	+	8.43910i	0.650046	+	0.471760i
$321$	16.8876	+	21.1763i	0.942572	+	1.18195i
$322$	−5.98965	+	27.9405i	−0.333790	+	1.55706i
$323$	15.6163	+	12.4536i	0.868914	+	0.692936i
$324$	3.79750	−	14.3254i	0.210972	−	0.795853i
$325$	1.97732	−	1.14161i	0.109682	−	0.0633250i
$326$	−0.318745	+	18.3538i	−0.0176536	+	1.01652i
$327$	6.26739	+	5.81529i	0.346587	+	0.321586i
$328$	9.37858	−	10.5796i	0.517845	−	0.584161i
$329$	12.2161	−	22.7377i	0.673493	−	1.25357i
$330$	5.95415	−	18.1761i	0.327765	−	1.00056i
$331$	−9.19726	+	3.60966i	−0.505527	+	0.198405i	−0.604378	−	0.796697i	$-0.706578\pi$
$331$	−9.19726	+	3.60966i	−0.505527	+	0.198405i	0.0988511	+	0.995102i	$0.468483\pi$
$332$	−25.4617	+	8.98582i	−1.39739	+	0.493161i
$333$	−0.956849	−	3.10203i	−0.0524350	−	0.169990i
$334$	1.48606	+	25.8453i	0.0813134	+	1.41419i
$335$	−4.77548	−	20.9228i	−0.260913	−	1.14313i
$336$	−14.2693	−	8.99529i	−0.778453	−	0.490733i
$337$	−5.25632	+	23.0295i	−0.286330	+	1.25449i	0.603190	+	0.797598i	$0.293896\pi$
$337$	−5.25632	+	23.0295i	−0.286330	+	1.25449i	−0.889520	+	0.456897i	$0.848961\pi$
$338$	−15.8201	−	2.66623i	−0.860502	−	0.145024i
$339$	−0.224035	−	0.0879274i	−0.0121679	−	0.00477556i
$340$	11.1148	+	6.94258i	0.602785	+	0.376514i
$341$	−1.96141	−	2.87686i	−0.106216	−	0.155790i
$342$	−0.469153	−	3.52718i	−0.0253689	−	0.190728i
$343$	−2.44921	+	18.3576i	−0.132245	+	0.991217i
$344$	0.187305	+	0.447120i	0.0100988	+	0.0241071i
$345$	18.0630	−	12.3151i	0.972479	−	0.663025i
$346$	−24.3700	−	20.1365i	−1.31014	−	1.08255i
$347$	−13.5950	−	5.33566i	−0.729820	−	0.286433i	−0.0288100	−	0.999585i	$-0.509172\pi$
$347$	−13.5950	−	5.33566i	−0.729820	−	0.286433i	−0.701010	+	0.713152i	$0.747267\pi$
$348$	27.3992	+	0.951954i	1.46875	+	0.0510301i
$349$	−2.20321	−	0.502869i	−0.117935	−	0.0269179i	0.163146	−	0.986602i	$-0.447836\pi$
$349$	−2.20321	−	0.502869i	−0.117935	−	0.0269179i	−0.281081	+	0.959684i	$0.590693\pi$
$350$	5.43566	−	3.81223i	0.290548	−	0.203772i
$351$	1.57884	+	6.91737i	0.0842725	+	0.369222i
$352$	22.2617	−	14.7888i	1.18655	−	0.788247i
$353$	−12.6017	+	3.88711i	−0.670722	+	0.206890i	−0.611368	−	0.791347i	$-0.709380\pi$
$353$	−12.6017	+	3.88711i	−0.670722	+	0.206890i	−0.0593540	+	0.998237i	$0.518904\pi$
$354$	0.0851189	+	0.405243i	0.00452402	+	0.0215384i
$355$	23.8539	−	9.36196i	1.26603	−	0.496881i
$356$	−11.5647	−	2.15619i	−0.612928	−	0.114278i
$357$	−13.5530	−	7.28148i	−0.717299	−	0.385377i
$358$	2.94342	+	4.48251i	0.155565	+	0.236908i
$359$	16.4052	+	15.2218i	0.865834	+	0.803377i	0.981808	−	0.189875i	$-0.0608084\pi$
$359$	16.4052	+	15.2218i	0.865834	+	0.803377i	−0.115974	+	0.993252i	$0.536999\pi$
$360$	−0.571026	−	2.26364i	−0.0300957	−	0.119304i
$361$	5.48655	+	9.50298i	0.288766	+	0.500157i
$362$	6.54902	+	2.70246i	0.344209	+	0.142038i
$363$	−14.1084	−	11.2510i	−0.740497	−	0.590526i
$364$	6.78761	+	0.536936i	0.355768	+	0.0281431i
$365$	5.34519	−	4.26265i	0.279780	−	0.223117i
$366$	−15.2633	+	4.41935i	−0.797824	+	0.231003i
$367$	14.7949	+	10.0870i	0.772288	+	0.526537i	0.884159	−	0.467186i	$-0.154732\pi$
$367$	14.7949	+	10.0870i	0.772288	+	0.526537i	−0.111871	+	0.993723i	$0.535684\pi$
$368$	30.4746	+	2.12017i	1.58860	+	0.110521i
$369$	−2.27155	+	0.342381i	−0.118252	+	0.0178237i
$370$	12.9378	+	12.4295i	0.672605	+	0.646180i
$371$	3.29798	−	0.348862i	0.171223	−	0.0181120i
$372$	2.15575	+	0.933701i	0.111770	+	0.0484101i
$373$	−0.355138	−	0.205039i	−0.0183884	−	0.0106165i	0.490778	−	0.871285i	$-0.336713\pi$
$373$	−0.355138	−	0.205039i	−0.0183884	−	0.0106165i	−0.509166	+	0.860668i	$0.670046\pi$
$374$	19.3196	−	14.8655i	0.998994	−	0.768676i
$375$	−19.1757	−	2.89027i	−0.990229	−	0.149253i
$376$	−25.9085	−	9.49534i	−1.33613	−	0.489685i
$377$	−9.97056	+	4.80157i	−0.513510	+	0.247293i
$378$	6.34154	+	19.6332i	0.326174	+	1.00982i
$379$	7.45061	−	15.4714i	0.382712	−	0.794710i	−0.617256	−	0.786762i	$-0.711756\pi$
$379$	7.45061	−	15.4714i	0.382712	−	0.794710i	0.999968	−	0.00794794i	$-0.00252994\pi$
$380$	11.7199	+	15.7914i	0.601216	+	0.810082i
$381$	−19.3254	+	1.44824i	−0.990070	+	0.0741955i
$382$	12.6569	−	5.82668i	0.647581	−	0.298119i
$383$	0.169421	−	2.26077i	0.00865701	−	0.115520i	−0.991201	−	0.132364i	$-0.957743\pi$
$383$	0.169421	−	2.26077i	0.00865701	−	0.115520i	0.999858	+	0.0168448i	$0.00536211\pi$
$384$	−7.36539	+	16.4598i	−0.375863	+	0.839962i
$385$	5.66266	+	21.7241i	0.288596	+	1.10716i
$386$	−0.0188617	+	0.204072i	−0.000960034	+	0.0103870i
$387$	0.0232169	−	0.0752674i	0.00118018	−	0.00382606i
$388$	3.08420	−	28.0459i	0.156577	−	1.42382i
$389$	13.5528	+	14.6064i	0.687152	+	0.740574i	0.976231	−	0.216731i	$-0.0695396\pi$
$389$	13.5528	+	14.6064i	0.687152	+	0.740574i	−0.289079	+	0.957305i	$0.593349\pi$
$390$	−3.47627	−	3.87951i	−0.176028	−	0.196447i
$391$	27.8628			1.40908
$392$	19.7982	−	0.179827i	0.999959	−	0.00908263i
$393$	−32.6910			−1.64904
$394$	4.44582	+	4.96152i	0.223977	+	0.249958i
$395$	0.848326	+	0.914278i	0.0426839	+	0.0460023i
$396$	−4.31656	−	0.474691i	−0.216915	−	0.0238541i
$397$	7.69881	−	24.9589i	0.386392	−	1.25265i	−0.528492	−	0.848938i	$-0.677242\pi$
$397$	7.69881	−	24.9589i	0.386392	−	1.25265i	0.914885	−	0.403715i	$-0.132281\pi$
$398$	−0.803408	+	8.69239i	−0.0402712	+	0.435710i
$399$	−14.9398	−	17.6015i	−0.747928	−	0.881177i
$400$	−4.85534	−	5.17709i	−0.242767	−	0.258854i
$401$	−1.56320	+	20.8594i	−0.0780623	+	1.04167i	0.811349	+	0.584562i	$0.198734\pi$
$401$	−1.56320	+	20.8594i	−0.0780623	+	1.04167i	−0.889411	+	0.457108i	$0.848885\pi$
$402$	24.4665	−	11.2633i	1.22028	−	0.561764i
$403$	−0.945640	+	0.0708659i	−0.0471057	+	0.00353008i
$404$	−13.3631	+	9.91766i	−0.664840	+	0.493422i
$405$	5.77432	−	11.9905i	0.286928	−	0.595812i
$406$	−27.6532	+	16.4569i	−1.37240	+	0.816744i
$407$	30.0677	−	14.4799i	1.49040	−	0.717740i
$408$	−5.65977	+	15.4429i	−0.280200	+	0.764539i
$409$	−34.7495	−	5.23764i	−1.71825	−	0.258985i	−0.785333	−	0.619074i	$-0.787508\pi$
$409$	−34.7495	−	5.23764i	−1.71825	−	0.258985i	−0.932918	+	0.360089i	$0.882746\pi$
$410$	10.0621	−	7.74225i	0.496930	−	0.382363i
$411$	3.58833	+	2.07173i	0.176999	+	0.102191i
$412$	−2.87550	+	6.63903i	−0.141666	+	0.327081i
$413$	−0.341333	−	0.346014i	−0.0167959	−	0.0170263i
$414$	−3.57940	−	3.43877i	−0.175918	−	0.169006i
$415$	−23.9758	+	3.61377i	−1.17693	+	0.177393i
$416$	−0.456635	−	7.26459i	−0.0223884	−	0.356176i
$417$	−17.8598	−	12.1766i	−0.874598	−	0.596291i
$418$	35.1368	−	10.1736i	1.71860	−	0.497606i
$419$	11.1334	−	8.87857i	0.543901	−	0.433746i	−0.312605	−	0.949883i	$-0.601202\pi$
$419$	11.1334	−	8.87857i	0.543901	−	0.433746i	0.856506	+	0.516137i	$0.172630\pi$
$420$	−11.0610	−	10.3487i	−0.539724	−	0.504966i
$421$	21.1272	+	16.8484i	1.02968	+	0.821139i	0.984063	−	0.177820i	$-0.0569046\pi$
$421$	21.1272	+	16.8484i	1.02968	+	0.821139i	0.0456124	+	0.998959i	$0.485476\pi$
$422$	10.7960	+	4.45497i	0.525540	+	0.216864i
$423$	2.24176	+	3.88284i	0.108998	+	0.188790i
$424$	−0.867186	−	3.43767i	−0.0421143	−	0.166948i
$425$	−4.74557	−	4.40324i	−0.230194	−	0.213589i
$426$	17.6529	+	26.8834i	0.855286	+	1.30251i
$427$	12.2620	−	14.0540i	0.593402	−	0.680120i
$428$	−6.22941	+	33.4114i	−0.301110	+	1.61500i
$429$	−9.01986	+	3.54004i	−0.435483	+	0.170915i
$430$	0.0894837	+	0.426023i	0.00431529	+	0.0205447i
$431$	−5.66735	+	1.74814i	−0.272986	+	0.0842052i	−0.428226	−	0.903672i	$-0.640861\pi$
$431$	−5.66735	+	1.74814i	−0.272986	+	0.0842052i	0.155239	+	0.987877i	$0.450385\pi$
$432$	19.8208	−	9.67592i	0.953629	−	0.465533i
$433$	3.66833	+	16.0720i	0.176289	+	0.772371i	0.983323	+	0.181867i	$0.0582140\pi$
$433$	3.66833	+	16.0720i	0.176289	+	0.772371i	−0.807034	+	0.590504i	$0.798929\pi$
$434$	−2.72101	+	0.447002i	−0.130613	+	0.0214568i
$435$	24.0020	+	5.47830i	1.15081	+	0.262665i
$436$	−0.372515	+	10.7218i	−0.0178402	+	0.513480i
$437$	38.9209	+	15.2753i	1.86184	+	0.730718i
$438$	6.61462	+	5.46555i	0.316059	+	0.261154i
$439$	2.23769	−	1.52563i	0.106799	−	0.0728145i	−0.508743	−	0.860919i	$-0.669890\pi$
$439$	2.23769	−	1.52563i	0.106799	−	0.0728145i	0.615542	+	0.788104i	$0.288937\pi$
$440$	22.1362	−	9.27317i	1.05530	−	0.442081i
$441$	−2.48760	−	2.03985i	−0.118457	−	0.0971356i
$442$	−0.875359	−	6.58110i	−0.0416366	−	0.313031i
$443$	−22.9280	−	33.6292i	−1.08934	−	1.59777i	−0.755510	−	0.655137i	$-0.772611\pi$
$443$	−22.9280	−	33.6292i	−1.08934	−	1.59777i	−0.333831	−	0.942633i	$-0.608342\pi$
$444$	−11.9288	+	19.0976i	−0.566117	+	0.906333i
$445$	−9.83377	−	3.85947i	−0.466165	−	0.182956i
$446$	25.3458	+	4.27161i	1.20016	+	0.202267i
$447$	3.61180	−	15.8243i	0.170832	−	0.748464i
$448$	−3.17972	−	20.9258i	−0.150228	−	0.988651i
$449$	−0.333083	−	1.45933i	−0.0157192	−	0.0688702i	0.966460	−	0.256817i	$-0.0826738\pi$
$449$	−0.333083	−	1.45933i	−0.0157192	−	0.0688702i	−0.982179	+	0.187947i	$0.939817\pi$
$450$	0.0662004	+	1.15135i	0.00312072	+	0.0542751i
$451$	−6.96099	−	22.5670i	−0.327780	−	1.06264i
$452$	−0.100504	−	0.284782i	−0.00472731	−	0.0133950i
$453$	6.18536	−	2.42757i	0.290613	−	0.114057i
$454$	5.11300	−	15.6084i	0.239965	−	0.732538i
$455$	5.89504	+	1.62268i	0.276364	+	0.0760726i
$456$	−16.3723	+	18.4690i	−0.766704	+	0.864889i
$457$	−0.414336	−	0.384448i	−0.0193818	−	0.0179837i	0.670422	−	0.741980i	$-0.266113\pi$
$457$	−0.414336	−	0.384448i	−0.0193818	−	0.0179837i	−0.689804	+	0.723996i	$0.742303\pi$
$458$	−0.116924	+	6.73265i	−0.00546348	+	0.314596i
$459$	17.4223	−	10.0588i	0.813204	−	0.469503i
$460$	26.5163	+	7.02920i	1.23633	+	0.327738i
$461$	−14.0152	−	11.1768i	−0.652754	−	0.520554i	0.240187	−	0.970727i	$-0.422791\pi$
$461$	−14.0152	−	11.1768i	−0.652754	−	0.520554i	−0.892942	+	0.450172i	$0.851363\pi$
$462$	−25.2219	+	12.5598i	−1.17343	+	0.584333i
$463$	−6.61157	−	8.29064i	−0.307266	−	0.385299i	0.604092	−	0.796915i	$-0.293536\pi$
$463$	−6.61157	−	8.29064i	−0.307266	−	0.385299i	−0.911357	+	0.411616i	$0.864965\pi$
$464$	21.5923	+	26.7812i	1.00240	+	1.24329i
$465$	1.74306	+	1.18840i	0.0808325	+	0.0551107i
$466$	−30.5677	−	15.3801i	−1.41602	−	0.712469i
$467$	1.69306	+	11.2327i	0.0783454	+	0.519788i	0.993238	+	0.116092i	$0.0370366\pi$
$467$	1.69306	+	11.2327i	0.0783454	+	0.519788i	−0.914893	+	0.403696i	$0.867725\pi$
$468$	−0.699772	+	0.953475i	−0.0323470	+	0.0440744i
$469$	−17.0020	+	26.6539i	−0.785082	+	1.23076i
$470$	−21.2409	−	12.7603i	−0.979769	−	0.588587i
$471$	0.995627	−	1.72448i	0.0458761	−	0.0794597i
$472$	−0.314657	+	0.413488i	−0.0144833	+	0.0190323i
$473$	0.800707	+	0.120687i	0.0368166	+	0.00554920i
$474$	−0.904109	+	1.27783i	−0.0415271	+	0.0586929i
$475$	−4.21496	−	8.75245i	−0.193396	−	0.401590i
$476$	−4.21787	−	18.8390i	−0.193326	−	0.863483i
$477$	−0.249944	+	0.519014i	−0.0114442	+	0.0237640i
$478$	14.1186	+	25.4653i	0.645770	+	1.16476i
$479$	0.162667	+	2.17064i	0.00743244	+	0.0991790i	0.999686	−	0.0250481i	$-0.00797390\pi$
$479$	0.162667	+	2.17064i	0.00743244	+	0.0991790i	−0.992254	+	0.124227i	$0.960355\pi$
$480$	−9.28218	+	13.2688i	−0.423672	+	0.605635i
$481$	0.679228	−	9.06367i	0.0309701	−	0.413268i
$482$	−7.14223	−	19.1704i	−0.325320	−	0.873189i
$483$	−31.6024	−	6.20275i	−1.43796	−	0.282235i
$484$	−0.907074	−	22.6251i	−0.0412306	−	1.02842i
$485$	7.46820	−	24.2113i	0.339114	−	1.09938i
$486$	−6.49694	−	1.60206i	−0.294707	−	0.0726711i
$487$	13.8737	−	12.8729i	0.628678	−	0.583328i	−0.300126	−	0.953900i	$-0.597029\pi$
$487$	13.8737	−	12.8729i	0.628678	−	0.583328i	0.928804	+	0.370572i	$0.120838\pi$
$488$	−16.7252	−	10.8552i	−0.757116	−	0.491391i
$489$	−20.6886			−0.935569
$490$	17.4903	+	3.19331i	0.790131	+	0.144259i
$491$			27.3837i			1.23581i	0.786252	+	0.617905i	$0.212019\pi$
$491$			27.3837i			1.23581i	−0.786252	+	0.617905i	$0.787981\pi$
$492$	12.1054	+	10.3614i	0.545752	+	0.467127i
$493$	21.3420	+	23.0012i	0.961197	+	1.03592i
$494$	2.38521	−	9.67288i	0.107316	−	0.435203i
$495$	−3.72637	−	1.14943i	−0.167488	−	0.0516632i
$496$	0.883932	+	2.81223i	0.0396897	+	0.126273i
$497$	−34.4963	−	15.3311i	−1.54737	−	0.687693i
$498$	−10.6241	−	28.5161i	−0.476078	−	1.27784i
$499$	−15.9456	−	1.19496i	−0.713822	−	0.0534935i	−0.287131	−	0.957891i	$-0.592702\pi$
$499$	−15.9456	−	1.19496i	−0.713822	−	0.0534935i	−0.426690	+	0.904398i	$0.640321\pi$
$500$	−13.0012	−	20.5692i	−0.581432	−	0.919882i
$501$	−29.0952	+	2.18038i	−1.29988	+	0.0974122i
$502$	−19.0202	+	10.5453i	−0.848915	+	0.470659i
$503$	−36.6694	−	17.6590i	−1.63501	−	0.787378i	−0.999888	−	0.0149632i	$-0.995237\pi$
$503$	−36.6694	−	17.6590i	−1.63501	−	0.787378i	−0.635119	−	0.772415i	$-0.719049\pi$
$504$	−1.78321	+	2.94071i	−0.0794307	+	0.130989i
$505$	−13.4639	+	6.48389i	−0.599137	+	0.288529i
$506$	29.4726	−	41.6554i	1.31022	−	1.85181i
$507$	2.69488	−	17.8794i	0.119684	−	0.794051i
$508$	−17.2410	−	17.1492i	−0.764946	−	0.760872i
$509$	−16.0286	−	9.25412i	−0.710455	−	0.410182i	0.100774	−	0.994909i	$-0.467868\pi$
$509$	−16.0286	−	9.25412i	−0.710455	−	0.410182i	−0.811230	+	0.584728i	$0.801201\pi$
$510$	−7.60585	+	12.6608i	−0.336793	+	0.560629i
$511$	−10.0003	−	1.19579i	−0.442386	−	0.0528987i
$512$	−21.6662	+	6.52486i	−0.957522	+	0.288361i
$513$	29.8513	−	4.49936i	1.31797	−	0.198652i
$514$	19.8562	+	9.99065i	0.875821	+	0.440669i
$515$	−3.65989	+	5.36807i	−0.161274	+	0.236546i
$516$	−0.500180	+	0.219818i	−0.0220192	+	0.00967694i
$517$	−36.0364	+	28.7380i	−1.58488	+	1.26390i
$518$	−0.349491	−	26.4274i	−0.0153558	−	1.16115i
$519$	22.2143	−	27.8558i	0.975098	−	1.22273i
$520$	0.827216	−	6.48390i	0.0362758	−	0.284338i
$521$	−11.2513	−	19.4879i	−0.492930	−	0.853780i	0.507037	−	0.861924i	$-0.330741\pi$
$521$	−11.2513	−	19.4879i	−0.492930	−	0.853780i	−0.999967	+	0.00814475i	$0.997407\pi$
$522$	0.0970594	−	5.58883i	0.00424817	−	0.244617i
$523$	−19.5192	+	21.0367i	−0.853515	+	0.919871i	−0.997568	−	0.0696993i	$-0.977796\pi$
$523$	−19.5192	+	21.0367i	−0.853515	+	0.919871i	0.144053	+	0.989570i	$0.453986\pi$
$524$	−26.8403	−	31.0211i	−1.17252	−	1.35516i
$525$	4.40225	+	6.05066i	0.192130	+	0.264073i
$526$	18.2232	+	5.96958i	0.794571	+	0.260286i
$527$	0.982306	+	2.50288i	0.0427899	+	0.109027i
$528$	17.1007	+	24.7966i	0.744213	+	1.07913i
$529$	33.7553	−	10.4121i	1.46762	−	0.452702i
$530$	−0.182756	−	3.17847i	−0.00793842	−	0.138064i
$531$	0.0823093	−	0.0187866i	0.00357192	−	0.000815267i
$532$	4.43631	−	28.6281i	0.192338	−	1.24118i
$533$	−6.27063	−	1.43123i	−0.271611	−	0.0619935i
$534$	2.20342	−	13.0741i	0.0953514	−	0.565771i
$535$	−11.1503	+	28.4106i	−0.482070	+	1.22830i
$536$	30.7757	+	13.9692i	1.32931	+	0.603376i
$537$	−4.99359	+	3.40457i	−0.215489	+	0.146918i
$538$	−0.223081	−	1.67716i	−0.00961770	−	0.0723076i
$539$	16.9246	−	28.4133i	0.728996	−	1.22385i
$540$	19.1180	−	5.17740i	0.822706	−	0.222800i
$541$	8.26090	+	12.1165i	0.355164	+	0.520930i	0.961692	−	0.274132i	$-0.0883906\pi$
$541$	8.26090	+	12.1165i	0.355164	+	0.520930i	−0.606528	+	0.795062i	$0.707438\pi$
$542$	−11.4716	+	13.8833i	−0.492746	+	0.596340i
$543$	−2.91715	+	7.43277i	−0.125187	+	0.318971i
$544$	−19.3009	+	7.30847i	−0.827521	+	0.313348i
$545$	−2.14375	+	9.39238i	−0.0918281	+	0.402325i
$546$	−0.472223	+	7.65925i	−0.0202093	+	0.327786i
$547$	−7.67274	+	1.75125i	−0.328063	+	0.0748782i	−0.383380	−	0.923591i	$-0.625240\pi$
$547$	−7.67274	+	1.75125i	−0.328063	+	0.0748782i	0.0553174	+	0.998469i	$0.482383\pi$
$548$	0.980234	+	5.10599i	0.0418735	+	0.218117i
$549$	0.954941	+	3.09584i	0.0407559	+	0.132127i
$550$	−11.6027	+	2.43707i	−0.494739	+	0.103917i
$551$	17.2021	+	43.8302i	0.732834	+	1.86723i
$552$	−1.79276	+	34.3823i	−0.0763049	+	1.46341i
$553$	0.0812040	−	1.83554i	0.00345314	−	0.0780550i
$554$	16.5174	+	25.1542i	0.701757	+	1.06870i
$555$	−13.7532	+	14.8225i	−0.583792	+	0.629178i
$556$	−3.10884	−	26.9449i	−0.131844	−	1.14272i
$557$	27.7821	−	16.0400i	1.17717	−	0.679638i	0.221810	−	0.975090i	$-0.428804\pi$
$557$	27.7821	−	16.0400i	1.17717	−	0.679638i	0.955357	+	0.295452i	$0.0954703\pi$
$558$	0.182707	−	0.442765i	0.00773462	−	0.0187438i
$559$	0.137503	−	0.172423i	0.00581574	−	0.00729270i
$560$	0.738634	−	18.9926i	0.0312130	−	0.802586i
$561$	17.1295	+	21.4797i	0.723209	+	0.906875i
$562$	7.53329	−	2.18120i	0.317773	−	0.0920084i
$563$	−15.7932	+	23.1643i	−0.665603	+	0.976261i	0.333831	+	0.942633i	$0.391658\pi$
$563$	−15.7932	+	23.1643i	−0.665603	+	0.976261i	−0.999434	+	0.0336278i	$0.989294\pi$
$564$	10.1930	−	29.3812i	0.429201	−	1.23717i
$565$	−0.0404191	−	0.268163i	−0.00170044	−	0.0112817i
$566$	−17.2287	+	17.9333i	−0.724178	+	0.753793i
$567$	−18.5487	+	6.34900i	−0.778973	+	0.266633i
$568$	−11.0166	+	38.8233i	−0.462246	+	1.62899i
$569$	3.88734	−	6.73308i	0.162966	−	0.282265i	−0.772965	−	0.634448i	$-0.781227\pi$
$569$	3.88734	−	6.73308i	0.162966	−	0.282265i	0.935931	+	0.352183i	$0.114561\pi$
$570$	−17.5655	+	13.5158i	−0.735737	+	0.566113i
$571$	3.45416	−	22.9168i	0.144552	−	0.959039i	−0.792506	−	0.609865i	$-0.791224\pi$
$571$	3.45416	−	22.9168i	0.144552	−	0.959039i	0.937058	−	0.349175i	$-0.113538\pi$
$572$	−10.7648	−	5.65264i	−0.450099	−	0.236349i
$573$	6.81359	+	14.1486i	0.284642	+	0.591065i
$574$	−18.5293	−	2.54273i	−0.773398	−	0.106132i
$575$	−12.2093	−	5.87968i	−0.509162	−	0.245200i
$576$	3.38149	+	1.44320i	0.140895	+	0.0601332i
$577$	2.67577	+	35.7057i	0.111394	+	1.48645i	0.720554	+	0.693399i	$0.243888\pi$
$577$	2.67577	+	35.7057i	0.111394	+	1.48645i	−0.609160	+	0.793047i	$0.708493\pi$
$578$	4.73946	−	2.18185i	0.197136	−	0.0907529i
$579$	−0.230331	−	0.0172609i	−0.00957223	−	0.000717340i
$580$	14.5079	+	27.2738i	0.602409	+	1.13248i
$581$	28.5941	+	21.4058i	1.18628	+	0.888061i
$582$	31.6644	+	2.92663i	1.31253	+	0.121313i
$583$	−5.65903	−	1.74558i	−0.234373	−	0.0722945i
$584$	0.244442	+	10.7641i	0.0101151	+	0.445422i
$585$	−0.778550	+	0.722388i	−0.0321891	+	0.0298671i
$586$	−3.05076	−	3.40464i	−0.126026	−	0.140644i
$587$			45.6463i			1.88402i	0.335580	+	0.942012i	$0.391068\pi$
$587$			45.6463i			1.88402i	−0.335580	+	0.942012i	$0.608932\pi$
$588$	0.590090	+	22.3064i	0.0243349	+	0.919900i
$589$			4.03474i			0.166248i
$590$	−0.347499	+	0.311379i	−0.0143063	+	0.0128193i
$591$	−5.50398	+	5.10694i	−0.226403	+	0.210072i
$592$	−27.9160	+	4.36025i	−1.14734	+	0.179205i
$593$	−10.3440	−	3.19070i	−0.424777	−	0.131026i	0.0749937	−	0.997184i	$-0.476106\pi$
$593$	−10.3440	−	3.19070i	−0.424777	−	0.131026i	−0.499771	+	0.866158i	$0.666583\pi$
$594$	3.39081	−	36.6866i	0.139127	−	1.50527i
$595$	−0.530209	−	17.3280i	−0.0217364	−	0.710381i
$596$	17.9814	−	9.56495i	0.736546	−	0.391796i
$597$	−9.81089	−	0.735225i	−0.401533	−	0.0300907i
$598$	−5.81153	−	12.6239i	−0.237651	−	0.516232i
$599$	0.734468	+	9.80079i	0.0300095	+	0.400450i	0.991901	+	0.127017i	$0.0405401\pi$
$599$	0.734468	+	9.80079i	0.0300095	+	0.400450i	−0.961891	+	0.273433i	$0.911841\pi$
$600$	5.73887	−	5.57264i	0.234288	−	0.227502i
$601$	40.4470	+	19.4783i	1.64987	+	0.794535i	0.999387	+	0.0350143i	$0.0111477\pi$
$601$	40.4470	+	19.4783i	1.64987	+	0.794535i	0.650483	+	0.759521i	$0.274567\pi$
$602$	0.354212	−	0.534587i	0.0144366	−	0.0217881i
$603$	−2.38270	−	4.94773i	−0.0970311	−	0.201487i
$604$	7.38194	+	3.87629i	0.300367	+	0.157724i
$605$	3.03057	−	20.1065i	0.123210	−	0.817445i
$606$	−11.4374	−	14.8644i	−0.464613	−	0.603824i
$607$	10.5883	−	18.3395i	0.429767	−	0.744377i	−0.567086	−	0.823659i	$-0.691929\pi$
$607$	10.5883	−	18.3395i	0.429767	−	0.744377i	0.996852	+	0.0792813i	$0.0252625\pi$
$608$	−30.9677	−	0.372398i	−1.25591	−	0.0151027i
$609$	−19.0860	−	30.8394i	−0.773402	−	1.24968i
$610$	−12.9120	−	12.4047i	−0.522793	−	0.502253i
$611$	1.87097	+	12.4131i	0.0756913	+	0.502179i
$612$	3.16815	+	1.09910i	0.128065	+	0.0444284i
$613$	17.1860	−	25.2072i	0.694135	−	1.01811i	−0.303728	−	0.952759i	$-0.598231\pi$
$613$	17.1860	−	25.2072i	0.694135	−	1.01811i	0.997862	−	0.0653499i	$-0.0208164\pi$
$614$	−11.9883	−	41.4045i	−0.483810	−	1.67095i
$615$	8.92141	+	11.1871i	0.359746	+	0.451107i
$616$	−32.6261	−	13.6216i	−1.31454	−	0.548829i
$617$	19.8769	−	24.9248i	0.800212	−	1.00343i	−0.199511	−	0.979896i	$-0.563935\pi$
$617$	19.8769	−	24.9248i	0.800212	−	1.00343i	0.999723	−	0.0235387i	$-0.00749329\pi$
$618$	−7.53758	−	3.11038i	−0.303206	−	0.125118i
$619$	12.2316	−	7.06192i	0.491630	−	0.283842i	−0.233621	−	0.972328i	$-0.575057\pi$
$619$	12.2316	−	7.06192i	0.491630	−	0.283842i	0.725250	+	0.688485i	$0.241724\pi$
$620$	0.303413	+	2.62974i	0.0121854	+	0.105613i
$621$	28.6432	−	30.8700i	1.14941	−	1.23877i
$622$	−5.07003	+	3.32922i	−0.203290	+	0.133489i
$623$	6.12594	+	14.3059i	0.245431	+	0.573152i
$624$	8.17730	−	0.656735i	0.327354	−	0.0262904i
$625$	−4.74191	−	12.0822i	−0.189677	−	0.483288i
$626$	6.33170	+	30.1446i	0.253066	+	1.20482i
$627$	12.1519	+	39.3955i	0.485300	+	1.57330i
$628$	2.45383	−	0.471079i	0.0979184	−	0.0187981i
$629$	−25.1246	+	5.73453i	−1.00178	+	0.228651i
$630$	−2.07047	+	2.29148i	−0.0824897	+	0.0912948i
$631$	−3.70989	+	16.2541i	−0.147688	+	0.647065i	0.845836	+	0.533443i	$0.179102\pi$
$631$	−3.70989	+	16.2541i	−0.147688	+	0.647065i	−0.993524	+	0.113622i	$0.963755\pi$
$632$	−1.95486	+	0.191215i	−0.0777602	+	0.00760612i
$633$	−4.80888	+	12.2528i	−0.191136	+	0.487006i
$634$	−6.06132	−	5.00837i	−0.240726	−	0.198908i
$635$	−12.3013	−	18.0427i	−0.488162	−	0.716002i
$636$	3.85683	−	1.04448i	0.152933	−	0.0414163i
$637$	−4.39693	−	7.86110i	−0.174213	−	0.311468i
$638$	56.9623	−	7.57660i	2.25516	−	0.299961i
$639$	5.41781	−	3.69380i	0.214325	−	0.146124i
$640$	−20.2120	+	2.08606i	−0.798948	+	0.0824588i
$641$	4.76591	−	12.1433i	0.188242	−	0.479633i	−0.805331	−	0.592826i	$-0.798012\pi$
$641$	4.76591	−	12.1433i	0.188242	−	0.479633i	0.993573	+	0.113192i	$0.0361076\pi$
$642$	−37.7721	−	6.36586i	−1.49075	−	0.251241i
$643$	1.42816	+	0.325967i	0.0563210	+	0.0128549i	0.250589	−	0.968094i	$-0.419376\pi$
$643$	1.42816	+	0.325967i	0.0563210	+	0.0128549i	−0.194268	+	0.980949i	$0.562233\pi$
$644$	−20.0607	−	35.0808i	−0.790501	−	1.38238i
$645$	−0.478321	+	0.109174i	−0.0188339	+	0.00429870i
$646$	−28.2009	+	1.62150i	−1.10955	+	0.0637971i
$647$	37.1103	−	11.4470i	1.45896	−	0.450029i	0.539087	−	0.842250i	$-0.318769\pi$
$647$	37.1103	−	11.4470i	1.45896	−	0.450029i	0.919871	+	0.392221i	$0.128293\pi$
$648$	9.52007	+	18.6720i	0.373984	+	0.733504i
$649$	0.317091	+	0.807934i	0.0124469	+	0.0317142i
$650$	−1.00518	+	3.06851i	−0.0394266	+	0.120357i
$651$	−0.556962	−	3.05747i	−0.0218291	−	0.119832i
$652$	−16.9859	−	19.6318i	−0.665221	−	0.768839i
$653$	−14.6719	+	15.8125i	−0.574155	+	0.618791i	−0.951637	−	0.307225i	$-0.900599\pi$
$653$	−14.6719	+	15.8125i	−0.574155	+	0.618791i	0.377482	+	0.926017i	$0.376790\pi$
$654$	−12.0893	−	0.209951i	−0.472729	−	0.00820973i
$655$	−18.4183	−	31.9014i	−0.719662	−	1.24649i
$656$	0.106772	+	19.9940i	0.00416874	+	0.780635i
$657$	1.09076	−	1.36777i	0.0425546	−	0.0533618i
$658$	8.59256	+	35.4773i	0.334973	+	1.38305i
$659$	18.5432	−	14.7877i	0.722342	−	0.576048i	−0.191804	−	0.981433i	$-0.561434\pi$
$659$	18.5432	−	14.7877i	0.722342	−	0.576048i	0.914146	+	0.405385i	$0.132862\pi$
$660$	10.8828	+	24.7631i	0.423614	+	0.963903i
$661$	−5.12744	+	7.52057i	−0.199434	+	0.292516i	−0.912908	−	0.408166i	$-0.866168\pi$
$661$	−5.12744	+	7.52057i	−0.199434	+	0.292516i	0.713474	+	0.700682i	$0.247121\pi$
$662$	6.28024	−	12.4819i	0.244089	−	0.485122i
$663$	7.39890	−	1.11520i	0.287350	−	0.0433110i
$664$	18.3368	−	33.4941i	0.711605	−	1.29982i
$665$	8.75917	−	24.4958i	0.339666	−	0.949906i
$666$	3.93537	+	2.36414i	0.152493	+	0.0916084i
$667$	56.8819	+	32.8408i	2.20248	+	1.27160i
$668$	−25.9570	−	25.8188i	−1.00431	−	0.998958i
$669$	−4.31752	+	28.6449i	−0.166925	+	1.10748i
$670$	24.7759	+	17.5297i	0.957175	+	0.677232i
$671$	−30.0078	+	14.4510i	−1.15844	+	0.557874i
$672$	23.5184	−	3.99264i	0.907241	−	0.154020i
$673$	−12.6587	−	6.09609i	−0.487956	−	0.234987i	0.173695	−	0.984800i	$-0.444429\pi$
$673$	−12.6587	−	6.09609i	−0.487956	−	0.234987i	−0.661650	+	0.749812i	$0.730144\pi$
$674$	−16.1982	−	29.2162i	−0.623931	−	1.12537i
$675$	−9.75695	+	0.731182i	−0.375545	+	0.0281432i
$676$	19.1787	−	12.1223i	0.737641	−	0.466242i
$677$	−32.0367	−	2.40082i	−1.23127	−	0.0922709i	−0.556846	−	0.830616i	$-0.687989\pi$
$677$	−32.0367	−	2.40082i	−1.23127	−	0.0922709i	−0.674423	+	0.738345i	$0.735608\pi$
$678$	0.318945	−	0.118828i	0.0122490	−	0.00456356i
$679$	−33.1176	+	17.2156i	−1.27094	+	0.660674i
$680$	−18.2587	+	3.17757i	−0.700189	+	0.121854i
$681$	17.6886	+	5.45622i	0.677830	+	0.209083i
$682$	4.78090	+	1.17891i	0.183070	+	0.0451428i
$683$	−17.6103	−	18.9794i	−0.673840	−	0.726226i	0.299880	−	0.953977i	$-0.403053\pi$
$683$	−17.6103	−	18.9794i	−0.673840	−	0.726226i	−0.973719	+	0.227751i	$0.926863\pi$
$684$	3.82295	+	3.27219i	0.146174	+	0.125115i
$685$			4.66889i			0.178389i
$686$	−14.7456	−	21.6464i	−0.562991	−	0.826463i
$687$	−7.58909			−0.289542
$688$	−0.619252	−	0.294153i	−0.0236088	−	0.0112145i
$689$	−1.18234	+	1.09705i	−0.0450436	+	0.0417943i
$690$	−7.40206	+	30.0180i	−0.281792	+	1.14276i
$691$	−4.27088	+	13.8459i	−0.162472	+	0.526721i	−0.999800	−	0.0199791i	$-0.993640\pi$
$691$	−4.27088	+	13.8459i	−0.162472	+	0.526721i	0.837328	+	0.546700i	$0.184116\pi$
$692$	44.6715	−	1.79094i	1.69816	−	0.0680815i
$693$	2.64966	+	5.09713i	0.100652	+	0.193624i
$694$	19.3544	−	7.21078i	0.734683	−	0.273717i
$695$	1.82019	−	24.2888i	0.0690439	−	0.921326i
$696$	−29.7564	+	24.8558i	−1.12791	+	0.942156i
$697$	1.36283	+	18.1857i	0.0516208	+	0.688831i
$698$	2.79510	−	1.54967i	0.105796	−	0.0586559i
$699$	16.7331	−	34.7467i	0.632905	−	1.31424i
$700$	−2.12720	+	9.14516i	−0.0804008	+	0.345654i
$701$	−11.0585	−	22.9632i	−0.417674	−	0.867310i	−0.998577	−	0.0533364i	$-0.983014\pi$
$701$	−11.0585	−	22.9632i	−0.417674	−	0.867310i	0.580902	−	0.813973i	$-0.302700\pi$
$702$	−8.19126	−	5.79558i	−0.309159	−	0.218740i
$703$	−38.2398	−	5.76372i	−1.44224	−	0.217383i
$704$	−9.48974	+	36.5859i	−0.357658	+	1.37888i
$705$	13.9634	−	24.1854i	0.525894	−	0.910874i
$706$	9.60409	−	15.9871i	0.361455	−	0.601682i
$707$	20.7290	+	7.41225i	0.779594	+	0.278766i
$708$	−0.472104	−	0.346485i	−0.0177428	−	0.0130217i
$709$	0.238351	+	1.58136i	0.00895147	+	0.0593891i	0.992861	−	0.119280i	$-0.0380588\pi$
$709$	0.238351	+	1.58136i	0.00895147	+	0.0593891i	−0.983909	+	0.178670i	$0.942821\pi$
$710$	−16.2883	+	32.3728i	−0.611291	+	1.21493i
$711$	0.263693	+	0.179783i	0.00988926	+	0.00674239i
$712$	14.2153	−	8.64336i	0.532742	−	0.323923i
$713$	3.50917	+	4.40036i	0.131420	+	0.164795i
$714$	21.1465	−	5.12166i	0.791387	−	0.191673i
$715$	−8.53638	−	6.80753i	−0.319242	−	0.254587i
$716$	−7.33055	−	1.94325i	−0.273956	−	0.0726227i
$717$	−28.4198	+	16.4082i	−1.06136	+	0.612774i
$718$	−31.6444	−	0.549558i	−1.18096	−	0.0205093i
$719$	−8.43517	−	7.82670i	−0.314579	−	0.291886i	0.507041	−	0.861922i	$-0.330739\pi$
$719$	−8.43517	−	7.82670i	−0.314579	−	0.291886i	−0.821620	+	0.570035i	$0.806930\pi$
$720$	2.73777	+	1.84524i	0.102031	+	0.0687680i
$721$	9.41605	−	1.71527i	0.350672	−	0.0638799i
$722$	−14.7472	−	4.83090i	−0.548834	−	0.179788i
$723$	21.4628	−	8.42352i	0.798209	−	0.313274i
$724$	−9.44816	+	3.33440i	−0.351138	+	0.123922i
$725$	−4.49814	−	14.5826i	−0.167057	−	0.541584i
$726$	25.4778	−	1.46493i	0.945569	−	0.0543685i
$727$	10.7707	+	47.1893i	0.399462	+	1.75016i	0.629525	+	0.776980i	$0.283249\pi$
$727$	10.7707	+	47.1893i	0.399462	+	1.75016i	−0.230064	+	0.973176i	$0.573893\pi$
$728$	−7.65571	+	5.84038i	−0.283740	+	0.216459i
$729$	6.62486	−	29.0254i	0.245365	−	1.07501i
$730$	−1.60683	+	9.53418i	−0.0594714	+	0.352876i
$731$	−0.582075	−	0.228447i	−0.0215288	−	0.00844944i
$732$	11.9050	−	19.0596i	0.440023	−	0.704461i
$733$	−11.7048	−	17.1678i	−0.432328	−	0.634108i	0.546822	−	0.837249i	$-0.315837\pi$
$733$	−11.7048	−	17.1678i	−0.432328	−	0.634108i	−0.979150	+	0.203141i	$0.934885\pi$
$734$	−25.1023	+	3.33888i	−0.926543	+	0.123240i
$735$	−3.25615	+	19.7717i	−0.120105	+	0.729292i
$736$	−34.0979	+	26.5278i	−1.25687	+	0.977826i
$737$	46.6456	−	31.8024i	1.71821	−	1.17146i
$738$	2.06936	−	2.50442i	0.0761741	−	0.0921888i
$739$	4.00411	+	1.57150i	0.147294	+	0.0578085i	0.437843	−	0.899052i	$-0.355743\pi$
$739$	4.00411	+	1.57150i	0.147294	+	0.0578085i	−0.290549	+	0.956860i	$0.593838\pi$
$740$	−25.3571	−	0.881004i	−0.932147	−	0.0323863i
$741$	10.9467	+	2.49852i	0.402138	+	0.0917854i
$742$	−3.14431	+	3.47995i	−0.115431	+	0.127753i
$743$	−0.807993	−	3.54005i	−0.0296424	−	0.129872i	0.957942	−	0.286963i	$-0.0926456\pi$
$743$	−0.807993	−	3.54005i	−0.0296424	−	0.129872i	−0.987584	+	0.157091i	$0.949788\pi$
$744$	−3.15171	+	1.05111i	−0.115547	+	0.0385355i
$745$	17.4770	−	5.39095i	0.640309	−	0.197509i
$746$	0.567554	−	0.119211i	0.0207796	−	0.00436464i
$747$	−5.77553	+	2.26673i	−0.211316	+	0.0829353i
$748$	−6.31866	+	33.8900i	−0.231033	+	1.23914i
$749$	41.3308	−	17.6983i	1.51020	−	0.646683i
$750$	22.9243	−	15.0532i	0.837078	−	0.549665i
$751$	−11.7996	−	10.9484i	−0.430573	−	0.399513i	0.434892	−	0.900482i	$-0.356786\pi$
$751$	−11.7996	−	10.9484i	−0.430573	−	0.399513i	−0.865465	+	0.500969i	$0.832977\pi$
$752$	36.2492	−	14.4506i	1.32187	−	0.526959i
$753$	−12.2554	−	21.2269i	−0.446611	−	0.773552i
$754$	5.96983	−	14.4670i	0.217408	−	0.526859i
$755$	5.85381	+	4.66825i	0.213042	+	0.169895i
$756$	−25.2082	−	14.6935i	−0.916814	−	0.534397i
$757$	35.9029	−	28.6316i	1.30491	−	1.04063i	0.308931	−	0.951084i	$-0.400029\pi$
$757$	35.9029	−	28.6316i	1.30491	−	1.04063i	0.995982	−	0.0895496i	$-0.0285428\pi$
$758$	6.75403	+	23.3266i	0.245317	+	0.847262i
$759$	47.5169	+	32.3965i	1.72476	+	1.17592i
$760$	−27.2472	−	5.57135i	−0.988358	−	0.202094i
$761$	36.9682	−	5.57206i	1.34010	−	0.201987i	0.560440	−	0.828195i	$-0.310632\pi$
$761$	36.9682	−	5.57206i	1.34010	−	0.201987i	0.779656	+	0.626208i	$0.215394\pi$
$762$	18.9875	−	19.7639i	0.687843	−	0.715972i
$763$	12.0680	−	7.46865i	0.436890	−	0.270383i
$764$	−7.83167	+	18.0820i	−0.283340	+	0.654182i
$765$	2.60789	+	1.50566i	0.0942884	+	0.0544374i
$766$	1.95519	+	2.54102i	0.0706438	+	0.0918107i
$767$	0.233742	+	0.0352309i	0.00843993	+	0.00127212i
$768$	−7.77666	−	24.2873i	−0.280616	−	0.876392i
$769$	16.1737	−	7.78885i	0.583239	−	0.280873i	−0.118908	−	0.992905i	$-0.537939\pi$
$769$	16.1737	−	7.78885i	0.583239	−	0.280873i	0.702147	+	0.712032i	$0.252225\pi$
$770$	−26.4666	−	17.5365i	−0.953789	−	0.631971i
$771$	−10.8696	+	22.5709i	−0.391458	+	0.812870i
$772$	−0.172730	−	0.232737i	−0.00621668	−	0.00837640i
$773$	−43.9789	+	3.29576i	−1.58181	+	0.118540i	−0.836420	−	0.548089i	$-0.815356\pi$
$773$	−43.9789	+	3.29576i	−1.58181	+	0.118540i	−0.745390	+	0.666629i	$0.767737\pi$
$774$	0.0465817	+	0.101186i	0.00167434	+	0.00363705i
$775$	0.0977235	−	1.30403i	0.00351033	−	0.0468421i
$776$	23.2203	+	32.4498i	0.833561	+	1.16488i
$777$	29.7733	−	0.911012i	1.06811	−	0.0326824i
$778$	−28.0593	−	2.59342i	−1.00597	−	0.0929787i
$779$	−8.06628	+	26.1502i	−0.289005	+	0.936930i
$780$	7.32268	+	0.805274i	0.262194	+	0.0288334i
$781$	45.8507	+	49.4153i	1.64067	+	1.76822i
$782$	−29.3462	+	26.2959i	−1.04942	+	0.940341i
$783$	47.4234			1.69478
$784$	−20.6825	+	18.8742i	−0.738660	+	0.674078i
$785$	2.24377			0.0800835
$786$	34.4314	−	30.8526i	1.22813	−	1.10047i
$787$	−22.0371	−	23.7504i	−0.785539	−	0.846610i	0.205710	−	0.978613i	$-0.434050\pi$
$787$	−22.0371	−	23.7504i	−0.785539	−	0.846610i	−0.991249	+	0.132003i	$0.957859\pi$
$788$	−9.36501	−	1.02987i	−0.333615	−	0.0366875i
$789$	−6.37030	+	20.6520i	−0.226789	+	0.735231i
$790$	−1.75635	−	0.162334i	−0.0624882	−	0.00577557i
$791$	−0.239418	+	0.319817i	−0.00851271	+	0.0113714i
$792$	4.99436	−	3.57384i	0.177467	−	0.126991i
$793$	−0.677874	+	9.04560i	−0.0240720	+	0.321219i
$794$	15.4467	+	33.5536i	0.548181	+	1.19077i
$795$	3.57814	−	0.268144i	0.126903	−	0.00951010i
$796$	−7.35738	−	9.91338i	−0.260775	−	0.351370i
$797$	13.6151	−	28.2720i	0.482271	−	1.00145i	−0.507878	−	0.861429i	$-0.669570\pi$
$797$	13.6151	−	28.2720i	0.482271	−	1.00145i	0.990149	−	0.140018i	$-0.0447159\pi$
$798$	32.3469	+	4.43888i	1.14507	+	0.157135i
$799$	32.0681	−	15.4432i	1.13449	−	0.546341i
$800$	9.99977	+	0.870415i	0.353545	+	0.0307738i
$801$	−2.67301	−	0.402892i	−0.0944462	−	0.0142355i
$802$	−18.0399	−	23.4452i	−0.637012	−	0.827880i
$803$	15.5754	+	8.99246i	0.549644	+	0.317337i
$804$	−15.1391	+	34.9536i	−0.533916	+	1.23272i
$805$	−11.7521	−	34.3338i	−0.414205	−	1.21011i
$806$	0.929103	−	0.967099i	0.0327263	−	0.0340646i
$807$	1.88558	−	0.284205i	0.0663754	−	0.0100045i
$808$	4.71463	−	23.0573i	0.165860	−	0.811152i
$809$	8.86629	+	6.04493i	0.311722	+	0.212529i	0.709068	−	0.705141i	$-0.249116\pi$
$809$	8.86629	+	6.04493i	0.311722	+	0.212529i	−0.397345	+	0.917669i	$0.630069\pi$
$810$	5.23445	+	18.0784i	0.183920	+	0.635211i
$811$	−6.85918	+	5.47001i	−0.240858	+	0.192078i	−0.736478	−	0.676462i	$-0.763512\pi$
$811$	−6.85918	+	5.47001i	−0.240858	+	0.192078i	0.495620	+	0.868540i	$0.334941\pi$
$812$	13.5939	−	43.4311i	0.477054	−	1.52413i
$813$	−15.8692	−	12.6553i	−0.556557	−	0.443839i
$814$	−18.0029	+	43.6276i	−0.631002	+	1.52914i
$815$	−11.6560	−	20.1889i	−0.408294	−	0.707185i
$816$	−8.61339	−	21.6066i	−0.301529	−	0.756382i
$817$	−0.687843	−	0.638225i	−0.0240646	−	0.0223287i
$818$	41.5426	−	27.2788i	1.45250	−	0.953780i
$819$	1.56304	+	0.0691489i	0.0546172	+	0.00241626i
$820$	−3.29089	+	17.6506i	−0.114923	+	0.616387i
$821$	10.3418	−	4.05887i	0.360932	−	0.141656i	−0.177943	−	0.984041i	$-0.556944\pi$
$821$	10.3418	−	4.05887i	0.360932	−	0.141656i	0.538876	+	0.842385i	$0.318849\pi$
$822$	−5.73459	+	1.20452i	−0.200017	+	0.0420124i
$823$	19.8678	−	6.12839i	0.692546	−	0.213622i	0.0715515	−	0.997437i	$-0.477205\pi$
$823$	19.8678	−	6.12839i	0.692546	−	0.213622i	0.620995	+	0.783815i	$0.286729\pi$
$824$	−3.23708	−	9.70627i	−0.112769	−	0.338134i
$825$	−2.97332	−	13.0270i	−0.103518	−	0.453541i
$826$	0.686060	+	0.0422983i	0.0238711	+	0.00147175i
$827$	−42.8479	−	9.77976i	−1.48997	−	0.340076i	−0.601448	−	0.798912i	$-0.705409\pi$
$827$	−42.8479	−	9.77976i	−1.48997	−	0.340076i	−0.888521	+	0.458837i	$0.848266\pi$
$828$	7.01534	+	0.243740i	0.243800	+	0.00847054i
$829$	−29.2275	−	11.4709i	−1.01511	−	0.398402i	−0.201300	−	0.979530i	$-0.564517\pi$
$829$	−29.2275	−	11.4709i	−1.01511	−	0.398402i	−0.813813	+	0.581127i	$0.802612\pi$
$830$	21.8417	−	26.4337i	0.758137	−	0.917526i
$831$	−28.0222	+	19.1052i	−0.972079	+	0.662752i
$832$	7.33700	+	7.22039i	0.254365	+	0.250322i
$833$	−17.6241	+	18.4828i	−0.610638	+	0.640390i
$834$	30.3024	−	4.03056i	1.04929	−	0.139567i
$835$	−18.5201	−	27.1640i	−0.640914	−	0.940048i
$836$	−27.4060	+	43.8760i	−0.947857	+	1.51748i
$837$	3.78282	+	1.48465i	0.130753	+	0.0513169i
$838$	−3.34683	+	19.8585i	−0.115614	+	0.686001i
$839$	2.30824	−	10.1131i	0.0796892	−	0.349141i	−0.919327	−	0.393495i	$-0.871266\pi$
$839$	2.30824	−	10.1131i	0.0796892	−	0.349141i	0.999016	+	0.0443539i	$0.0141229\pi$
$840$	21.4166	+	0.460658i	0.738945	+	0.0158942i
$841$	10.0060	+	43.8390i	0.345033	+	1.51169i
$842$	−38.1528	+	2.19372i	−1.31483	+	0.0756004i
$843$	2.60535	+	8.44634i	0.0897330	+	0.290907i
$844$	−15.5752	+	5.49671i	−0.536120	+	0.189205i
$845$	18.9659	−	7.44355i	0.652445	−	0.256066i
$846$	−6.02559	−	1.97387i	−0.207164	−	0.0678629i
$847$	−24.2217	+	17.6229i	−0.832269	+	0.605530i
$848$	4.15770	+	2.80226i	0.142776	+	0.0962302i
$849$	−20.5456	−	19.0636i	−0.705124	−	0.654260i
$850$	9.15383	+	0.158972i	0.313974	+	0.00545268i
$851$	−46.7180	+	26.9727i	−1.60147	+	0.924611i
$852$	−43.9643	−	11.6545i	−1.50619	−	0.399275i
$853$	−1.22563	−	0.977405i	−0.0419647	−	0.0334657i	0.602283	−	0.798283i	$-0.294258\pi$
$853$	−1.22563	−	0.977405i	−0.0419647	−	0.0334657i	−0.644248	+	0.764817i	$0.722829\pi$
$854$	0.348795	+	26.3747i	0.0119355	+	0.902522i
$855$	2.81744	+	3.53295i	0.0963543	+	0.120824i
$856$	−24.9714	−	41.0692i	−0.853503	−	1.40372i
$857$	16.5895	+	11.3105i	0.566686	+	0.386360i	0.812504	−	0.582956i	$-0.198104\pi$
$857$	16.5895	+	11.3105i	0.566686	+	0.386360i	−0.245818	+	0.969316i	$0.579056\pi$
$858$	6.15911	−	12.2411i	0.210269	−	0.417905i
$859$	7.06673	+	46.8847i	0.241114	+	1.59969i	0.701967	+	0.712209i	$0.252305\pi$
$859$	7.06673	+	46.8847i	0.241114	+	1.59969i	−0.460853	+	0.887476i	$0.652457\pi$
$860$	−0.496313	−	0.364253i	−0.0169241	−	0.0124209i
$861$	2.50270	−	20.9298i	0.0852919	−	0.713287i
$862$	4.31923	−	7.18985i	0.147114	−	0.244887i
$863$	−19.1166	+	33.1110i	−0.650738	+	1.12711i	0.332206	+	0.943207i	$0.392207\pi$
$863$	−19.1166	+	33.1110i	−0.650738	+	1.12711i	−0.982944	+	0.183905i	$0.941126\pi$
$864$	−11.7442	+	28.8972i	−0.399547	+	0.983103i
$865$	39.6987	+	5.98361i	1.34979	+	0.203449i
$866$	−19.0318	−	13.4656i	−0.646727	−	0.457580i
$867$	2.55141	+	5.29805i	0.0866503	+	0.179931i
$868$	2.44401	−	3.03879i	0.0829552	−	0.103143i
$869$	−1.42356	+	2.95605i	−0.0482909	+	0.100277i
$870$	−30.4501	+	16.8823i	−1.03235	+	0.572362i
$871$	−1.14903	−	15.3327i	−0.0389333	−	0.519529i
$872$	−9.72647	−	11.6441i	−0.329380	−	0.394321i
$873$	0.484507	−	6.46530i	0.0163981	−	0.218817i
$874$	−55.4093	+	20.6436i	−1.87425	+	0.698279i
$875$	−13.0733	+	29.4161i	−0.441958	+	0.994444i
$876$	−12.1250	+	0.486107i	−0.409664	+	0.0164240i
$877$	2.46349	−	7.98642i	0.0831860	−	0.269682i	−0.904418	−	0.426647i	$-0.859695\pi$
$877$	2.46349	−	7.98642i	0.0831860	−	0.269682i	0.987604	+	0.156965i	$0.0501709\pi$
$878$	−0.916987	+	3.71871i	−0.0309468	+	0.125500i
$879$	3.77688	−	3.50443i	0.127391	−	0.118201i
$880$	−14.5630	+	30.6582i	−0.490920	+	1.03349i
$881$	25.1866			0.848558			0.424279	−	0.905532i	$-0.360528\pi$
$881$	25.1866			0.848558			0.424279	+	0.905532i	$0.360528\pi$
$882$	4.54517	−	0.199263i	0.153044	−	0.00670955i
$883$		−	6.03599i		−	0.203127i	−0.994829	−	0.101564i	$-0.967615\pi$
$883$		−	6.03599i		−	0.203127i	0.994829	−	0.101564i	$-0.0323846\pi$
$884$	7.13296	+	6.10534i	0.239908	+	0.205345i
$885$	−0.357684	−	0.385491i	−0.0120234	−	0.0129582i
$886$	55.8866	+	13.7809i	1.87755	+	0.462980i
$887$	51.6212	+	15.9230i	1.73327	+	0.534644i	0.990812	−	0.135247i	$-0.0431828\pi$
$887$	51.6212	+	15.9230i	1.73327	+	0.534644i	0.742460	+	0.669890i	$0.233659\pi$
$888$	−5.45974	−	31.3723i	−0.183217	−	1.05279i
$889$	−6.19578	+	31.5669i	−0.207800	+	1.05872i
$890$	13.9997	−	5.21581i	0.469272	−	0.174834i
$891$	34.9116	+	2.61626i	1.16958	+	0.0876481i
$892$	−30.7265	+	19.4214i	−1.02880	+	0.650276i
$893$	53.2616	−	3.99141i	1.78233	−	0.133567i
$894$	11.1303	+	20.0755i	0.372254	+	0.671424i
$895$	−6.13576	−	2.95482i	−0.205096	−	0.0987689i
$896$	23.0980	+	19.0390i	0.771651	+	0.636047i
$897$	14.1118	−	6.79588i	0.471179	−	0.226908i
$898$	1.72808	+	1.22267i	0.0576668	+	0.0408012i
$899$	−0.944661	+	6.26742i	−0.0315062	+	0.209030i
$900$	−1.15633	−	1.15017i	−0.0385442	−	0.0383389i
$901$	3.96045	+	2.28657i	0.131942	+	0.0761767i
$902$	28.6294	+	17.1989i	0.953256	+	0.572660i
$903$	0.609341	+	0.388688i	0.0202776	+	0.0129347i
$904$	0.374622	+	0.205092i	0.0124597	+	0.00682125i
$905$	−8.89678	+	1.34097i	−0.295739	+	0.0445755i
$906$	−4.22360	+	8.39433i	−0.140320	+	0.278883i
$907$	18.5598	−	27.2223i	0.616269	−	0.903901i	−0.383538	−	0.923525i	$-0.625295\pi$
$907$	18.5598	−	27.2223i	0.616269	−	0.903901i	0.999807	+	0.0196243i	$0.00624702\pi$
$908$	9.34541	+	21.2648i	0.310138	+	0.705697i
$909$	−2.98968	+	2.38419i	−0.0991615	+	0.0790786i
$910$	−7.74031	+	3.85445i	−0.256589	+	0.127774i
$911$	−5.82904	+	7.30938i	−0.193125	+	0.242171i	−0.868960	−	0.494882i	$-0.835211\pi$
$911$	−5.82904	+	7.30938i	−0.193125	+	0.242171i	0.675836	+	0.737052i	$0.263783\pi$
$912$	−0.186393	−	34.9038i	−0.00617209	−	1.15578i
$913$	−31.8919	−	55.2384i	−1.05547	−	1.82812i
$914$	0.799222	+	0.0138798i	0.0264359	+	0.000459104i
$915$	13.7258	−	14.7929i	0.453761	−	0.489038i
$916$	−6.23088	−	7.20143i	−0.205874	−	0.237942i
$917$	−14.4016	+	52.3196i	−0.475584	+	1.72774i
$918$	−8.85674	+	27.0368i	−0.292316	+	0.892348i
$919$	5.26005	+	13.4024i	0.173513	+	0.442104i	0.991003	−	0.133839i	$-0.0427304\pi$
$919$	5.26005	+	13.4024i	0.173513	+	0.442104i	−0.817490	+	0.575943i	$0.804635\pi$
$920$	−34.5619	+	17.6217i	−1.13947	+	0.580971i
$921$	46.4228	−	14.3195i	1.52968	−	0.471845i
$922$	25.3096	−	1.45526i	0.833527	−	0.0479263i
$923$	17.8990	−	4.08533i	0.589153	−	0.134470i
$924$	14.7112	−	37.0319i	0.483964	−	1.21826i
$925$	12.2195	+	2.78903i	0.401775	+	0.0917026i
$926$	14.7880	+	2.49227i	0.485962	+	0.0819010i
$927$	−0.607381	+	1.54758i	−0.0199490	+	0.0508292i
$928$	−48.0170	−	7.82901i	−1.57623	−	0.257000i
$929$	−31.8774	+	21.7336i	−1.04586	+	0.713057i	−0.959070	−	0.283170i	$-0.908614\pi$
$929$	−31.8774	+	21.7336i	−1.04586	+	0.713057i	−0.0867923	+	0.996226i	$0.527662\pi$
$930$	−2.95743	+	0.393370i	−0.0969778	+	0.0128991i
$931$	−34.7515	+	16.1560i	−1.13893	+	0.529492i
$932$	46.7102	−	12.6497i	1.53004	−	0.414356i
$933$	−3.85081	−	5.64810i	−0.126070	−	0.184910i
$934$	−12.3842	−	10.2329i	−0.405224	−	0.334830i
$935$	−11.3101	+	28.8176i	−0.369879	+	0.942436i
$936$	−0.162828	−	1.66466i	−0.00532221	−	0.0544110i
$937$	−12.1524	+	53.2433i	−0.397003	+	1.73938i	0.242090	+	0.970254i	$0.422167\pi$
$937$	−12.1524	+	53.2433i	−0.397003	+	1.73938i	−0.639093	+	0.769129i	$0.720690\pi$
$938$	−7.24774	−	44.1188i	−0.236647	−	1.44053i
$939$	−33.8451	+	7.72492i	−1.10449	+	0.252093i
$940$	34.4144	−	6.60678i	1.12247	−	0.215489i
$941$	3.80378	+	12.3315i	0.124000	+	0.401997i	0.996194	−	0.0871624i	$-0.0277799\pi$
$941$	3.80378	+	12.3315i	0.124000	+	0.401997i	−0.872195	+	0.489159i	$0.837304\pi$
$942$	0.578865	+	2.75592i	0.0188605	+	0.0897928i
$943$	13.9467	+	35.5356i	0.454166	+	1.15720i
$944$	−0.0588256	−	0.732463i	−0.00191461	−	0.0238397i
$945$	−19.7433	−	17.2259i	−0.642249	−	0.560359i
$946$	−0.957236	+	0.628566i	−0.0311224	+	0.0204364i
$947$	27.6775	−	29.8293i	0.899399	−	0.969322i	−0.100272	−	0.994960i	$-0.531971\pi$
$947$	27.6775	−	29.8293i	0.899399	−	0.969322i	0.999671	+	0.0256384i	$0.00816186\pi$
$948$	−0.253730	−	2.19913i	−0.00824078	−	0.0714244i
$949$	4.24198	−	2.44911i	0.137701	−	0.0795014i
$950$	12.6996	+	5.24049i	0.412029	+	0.170024i
$951$	5.52515	−	6.92831i	0.179165	−	0.224666i
$952$	22.2220	+	15.8613i	0.720218	+	0.514066i
$953$	−7.57510	−	9.49887i	−0.245382	−	0.307699i	0.643854	−	0.765148i	$-0.277334\pi$
$953$	−7.57510	−	9.49887i	−0.245382	−	0.307699i	−0.889236	+	0.457450i	$0.848763\pi$
$954$	−0.226576	−	0.782534i	−0.00733567	−	0.0253355i
$955$	−9.96803	+	14.6204i	−0.322558	+	0.473105i
$956$	−38.9035	−	13.4964i	−1.25823	−	0.436506i
$957$	9.65258	+	64.0407i	0.312023	+	2.07014i
$958$	−2.21990	−	2.13268i	−0.0717216	−	0.0689038i
$959$	4.89645	−	4.83019i	0.158114	−	0.155975i
$960$	−2.74626	−	22.7354i	−0.0886352	−	0.733782i
$961$	15.2284	−	26.3764i	0.491240	−	0.850853i
$962$	7.83857	+	10.1872i	0.252726	+	0.328450i
$963$	−1.16399	+	7.72255i	−0.0375090	+	0.248856i
$964$	25.6148	+	13.4505i	0.824998	+	0.433210i
$965$	−0.112926	−	0.234493i	−0.00363521	−	0.00754859i
$966$	39.1388	−	23.2922i	1.25927	−	0.749416i
$967$	−50.9355	−	24.5292i	−1.63797	−	0.788807i	−0.999821	−	0.0188975i	$-0.993984\pi$
$967$	−50.9355	−	24.5292i	−1.63797	−	0.788807i	−0.638153	−	0.769909i	$-0.720301\pi$
$968$	22.3081	+	22.9736i	0.717011	+	0.738399i
$969$	−2.37911	−	31.7470i	−0.0764279	−	1.01986i
$970$	14.9840	+	32.5485i	0.481106	+	1.04507i
$971$	−18.9618	−	1.42099i	−0.608515	−	0.0456019i	−0.233091	−	0.972455i	$-0.574884\pi$
$971$	−18.9618	−	1.42099i	−0.608515	−	0.0456019i	−0.375424	+	0.926853i	$0.622503\pi$
$972$	8.35479	−	4.44422i	0.267980	−	0.142548i
$973$	−27.3557	+	23.2190i	−0.876983	+	0.744368i
$974$	−2.46333	+	26.6518i	−0.0789302	+	0.853978i
$975$	−3.47747	−	1.07266i	−0.111368	−	0.0343526i
$976$	27.8604	−	4.35156i	0.891789	−	0.139290i
$977$	−2.01770	+	1.87215i	−0.0645518	+	0.0598953i	−0.711789	−	0.702393i	$-0.752115\pi$
$977$	−2.01770	+	1.87215i	−0.0645518	+	0.0598953i	0.647237	+	0.762289i	$0.275924\pi$
$978$	21.7900	−	19.5251i	0.696767	−	0.624344i
$979$		−	27.7900i		−	0.888171i
$980$	−21.4352	+	13.1434i	−0.684722	+	0.419850i
$981$			2.46520i			0.0787079i
$982$	−25.8438	−	28.8416i	−0.824708	−	0.920372i
$983$	32.8320	−	30.4636i	1.04718	−	0.971639i	0.0475488	−	0.998869i	$-0.484859\pi$
$983$	32.8320	−	30.4636i	1.04718	−	0.971639i	0.999629	+	0.0272298i	$0.00866857\pi$
$984$	−22.5285	+	0.511599i	−0.718183	+	0.0163092i
$985$	−8.08457	−	2.49376i	−0.257596	−	0.0794578i
$986$	−44.1860	−	4.08396i	−1.40717	−	0.130060i
$987$	−39.8100	+	10.3770i	−1.26717	+	0.330303i
$988$	6.61671	+	12.4389i	0.210506	+	0.395735i
$989$	−1.30527	−	0.0978161i	−0.0415050	−	0.00311037i
$990$	5.00955	−	2.30618i	0.159214	−	0.0732953i
$991$	−1.99837	−	26.6665i	−0.0634805	−	0.847088i	−0.934528	−	0.355889i	$-0.884178\pi$
$991$	−1.99837	−	26.6665i	−0.0634805	−	0.847088i	0.871048	−	0.491199i	$-0.163441\pi$
$992$	−3.58507	−	2.12773i	−0.113826	−	0.0675554i
$993$	14.1883	+	6.83273i	0.450253	+	0.216830i
$994$	50.8017	−	16.4090i	1.61133	−	0.520463i
$995$	−4.81004	−	9.98816i	−0.152489	−	0.316646i
$996$	38.1022	+	20.0076i	1.20731	+	0.633966i
$997$	3.78826	−	25.1335i	0.119975	−	0.795985i	−0.845213	−	0.534429i	$-0.820527\pi$
$997$	3.78826	−	25.1335i	0.119975	−	0.795985i	0.965189	−	0.261555i	$-0.0842354\pi$
$998$	17.9222	−	13.7903i	0.567318	−	0.436523i
$999$	−19.4748	+	33.7314i	−0.616156	+	1.06721i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	392.2.z.a.37.14	yes	648
8.5	even	2	inner	392.2.z.a.37.8	✓	648
49.4	even	21	inner	392.2.z.a.53.8	yes	648
392.53	even	42	inner	392.2.z.a.53.14	yes	648

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
392.2.z.a.37.8	✓	648	8.5	even	2	inner
392.2.z.a.37.14	yes	648	1.1	even	1	trivial
392.2.z.a.53.8	yes	648	49.4	even	21	inner
392.2.z.a.53.14	yes	648	392.53	even	42	inner

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:	\( N \)	\(=\)	\( 392 = 2^{3} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	392.z (of order \(42\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.05324 + 0.943763i) q^{2} +(-1.08411 - 1.16839i) q^{3} +(0.218622 - 1.98802i) q^{4} +(0.529378 - 1.71620i) q^{5} +(2.24451 + 0.207452i) q^{6} +(-2.34752 + 1.22032i) q^{7} +(1.64596 + 2.30018i) q^{8} +(0.0343439 - 0.458288i) q^{9} +O(q^{10})\)	\(q+(-1.05324 + 0.943763i) q^{2} +(-1.08411 - 1.16839i) q^{3} +(0.218622 - 1.98802i) q^{4} +(0.529378 - 1.71620i) q^{5} +(2.24451 + 0.207452i) q^{6} +(-2.34752 + 1.22032i) q^{7} +(1.64596 + 2.30018i) q^{8} +(0.0343439 - 0.458288i) q^{9} +(1.06213 + 2.30718i) q^{10} +(4.71137 - 0.353068i) q^{11} +(-2.55979 + 1.89979i) q^{12} +(0.558298 - 1.15932i) q^{13} +(1.32080 - 3.50078i) q^{14} +(-2.57910 + 1.24203i) q^{15} +(-3.90441 - 0.869246i) q^{16} +(-3.60762 - 0.543762i) q^{17} +(0.396343 + 0.515099i) q^{18} +(-4.74129 - 2.73738i) q^{19} +(-3.29610 - 1.42761i) q^{20} +(3.97077 + 1.41986i) q^{21} +(-4.62898 + 4.81828i) q^{22} +(-7.55176 + 1.13824i) q^{23} +(0.903116 - 4.41676i) q^{24} +(1.46609 + 0.999561i) q^{25} +(0.506101 + 1.74794i) q^{26} +(-4.31111 + 3.43799i) q^{27} +(1.91279 + 4.93368i) q^{28} +(-6.72404 - 5.36224i) q^{29} +(1.54422 - 3.74221i) q^{30} +(-0.368485 - 0.638234i) q^{31} +(4.93264 - 2.76931i) q^{32} +(-5.52016 - 5.12196i) q^{33} +(4.31287 - 2.83203i) q^{34} +(0.851585 + 4.67482i) q^{35} +(-0.903575 - 0.168468i) q^{36} +(6.57534 - 2.58063i) q^{37} +(7.57715 - 1.59154i) q^{38} +(-1.95979 + 0.604515i) q^{39} +(4.81891 - 1.60713i) q^{40} +(-1.11229 - 4.87325i) q^{41} +(-5.52218 + 2.25201i) q^{42} +(0.167094 + 0.0381381i) q^{43} +(0.328102 - 9.44346i) q^{44} +(-0.768333 - 0.301549i) q^{45} +(6.87957 - 8.32592i) q^{46} +(-8.06065 + 5.49566i) q^{47} +(3.21718 + 5.50423i) q^{48} +(4.02166 - 5.72942i) q^{49} +(-2.48749 + 0.330863i) q^{50} +(3.27573 + 4.80461i) q^{51} +(-2.18268 - 1.36336i) q^{52} +(-1.16683 - 0.457945i) q^{53} +(1.29597 - 7.68969i) q^{54} +(1.88816 - 8.27257i) q^{55} +(-6.67085 - 3.39113i) q^{56} +(1.94174 + 8.50730i) q^{57} +(12.1427 - 0.698183i) q^{58} +(0.0541481 + 0.175544i) q^{59} +(1.90532 + 5.39882i) q^{60} +(-6.56223 + 2.57549i) q^{61} +(0.990444 + 0.324450i) q^{62} +(0.478633 + 1.11775i) q^{63} +(-2.58166 + 7.57199i) q^{64} +(-1.69407 - 1.57187i) q^{65} +(10.6480 + 0.184919i) q^{66} +(10.3484 - 5.97464i) q^{67} +(-1.86971 + 7.05313i) q^{68} +(9.51684 + 7.58943i) q^{69} +(-5.30884 - 4.12000i) q^{70} +(8.89597 + 11.1552i) q^{71} +(1.11067 - 0.675324i) q^{72} +(3.14522 + 2.14437i) q^{73} +(-4.48990 + 8.92359i) q^{74} +(-0.421519 - 2.79659i) q^{75} +(-6.47851 + 8.82730i) q^{76} +(-10.6292 + 6.57819i) q^{77} +(1.49361 - 2.48628i) q^{78} +(-0.347223 + 0.601408i) q^{79} +(-3.55871 + 6.24059i) q^{80} +(7.32731 + 1.10441i) q^{81} +(5.77070 + 4.08296i) q^{82} +(-5.85761 - 12.1635i) q^{83} +(3.69080 - 7.58353i) q^{84} +(-2.84300 + 5.90355i) q^{85} +(-0.211983 + 0.117529i) q^{86} +(1.02439 + 13.6696i) q^{87} +(8.56682 + 10.2559i) q^{88} +(0.439562 - 5.86555i) q^{89} +(1.09383 - 0.407522i) q^{90} +(0.104120 + 3.40282i) q^{91} +(0.611870 + 15.2619i) q^{92} +(-0.346229 + 1.12245i) q^{93} +(3.30318 - 13.3956i) q^{94} +(-7.20784 + 6.68790i) q^{95} +(-8.58315 - 2.76101i) q^{96} +14.1075 q^{97} +(1.17145 + 9.82994i) q^{98} -2.17129i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 648 q - 13 q^{2} - 13 q^{4} - 6 q^{6} - 24 q^{7} - 16 q^{8} - 76 q^{9}+O(q^{10}) \) 648 * q - 13 * q^2 - 13 * q^4 - 6 * q^6 - 24 * q^7 - 16 * q^8 - 76 * q^9	\( 648 q - 13 q^{2} - 13 q^{4} - 6 q^{6} - 24 q^{7} - 16 q^{8} - 76 q^{9} - 6 q^{10} - 47 q^{12} - 33 q^{14} - 8 q^{15} - 17 q^{16} - 26 q^{17} - 8 q^{18} - 22 q^{20} - 18 q^{22} - 26 q^{23} - 74 q^{24} - 72 q^{25} - 12 q^{26} + 2 q^{28} - 11 q^{30} + 60 q^{31} - 13 q^{32} - 14 q^{33} - 18 q^{34} + 8 q^{36} - 46 q^{38} - 32 q^{39} + 32 q^{40} - 20 q^{41} - 36 q^{42} + 38 q^{44} - 22 q^{46} - 58 q^{47} + 28 q^{48} - 16 q^{49} - 132 q^{50} + 18 q^{52} - 37 q^{54} - 32 q^{55} + 96 q^{56} - 66 q^{57} + 100 q^{60} + 28 q^{62} - 72 q^{63} - 28 q^{64} - 36 q^{65} - 4 q^{66} - 11 q^{68} - 36 q^{70} + 60 q^{71} - 130 q^{72} - 18 q^{73} - 12 q^{74} + 11 q^{76} - 132 q^{78} - 12 q^{79} - 64 q^{80} - 58 q^{81} + 152 q^{82} - 224 q^{84} + 55 q^{86} - 8 q^{87} - 169 q^{88} - 18 q^{89} + 144 q^{90} - 54 q^{92} + 154 q^{94} - 64 q^{95} - 142 q^{96} - 96 q^{97} + 151 q^{98}+O(q^{100}) \) 648 * q - 13 * q^2 - 13 * q^4 - 6 * q^6 - 24 * q^7 - 16 * q^8 - 76 * q^9 - 6 * q^10 - 47 * q^12 - 33 * q^14 - 8 * q^15 - 17 * q^16 - 26 * q^17 - 8 * q^18 - 22 * q^20 - 18 * q^22 - 26 * q^23 - 74 * q^24 - 72 * q^25 - 12 * q^26 + 2 * q^28 - 11 * q^30 + 60 * q^31 - 13 * q^32 - 14 * q^33 - 18 * q^34 + 8 * q^36 - 46 * q^38 - 32 * q^39 + 32 * q^40 - 20 * q^41 - 36 * q^42 + 38 * q^44 - 22 * q^46 - 58 * q^47 + 28 * q^48 - 16 * q^49 - 132 * q^50 + 18 * q^52 - 37 * q^54 - 32 * q^55 + 96 * q^56 - 66 * q^57 + 100 * q^60 + 28 * q^62 - 72 * q^63 - 28 * q^64 - 36 * q^65 - 4 * q^66 - 11 * q^68 - 36 * q^70 + 60 * q^71 - 130 * q^72 - 18 * q^73 - 12 * q^74 + 11 * q^76 - 132 * q^78 - 12 * q^79 - 64 * q^80 - 58 * q^81 + 152 * q^82 - 224 * q^84 + 55 * q^86 - 8 * q^87 - 169 * q^88 - 18 * q^89 + 144 * q^90 - 54 * q^92 + 154 * q^94 - 64 * q^95 - 142 * q^96 - 96 * q^97 + 151 * q^98

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