LMFDB - Embedded newform 189.2.bd.a.173.22

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [189,2,Mod(47,189)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(189, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([7, 15]))

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

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

chi := DirichletCharacter("189.47");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 189 = 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	189.bd (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:	$1.50917259820$
Analytic rank:	$0$
Dimension:	$132$
Relative dimension:	$22$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			173.22
Character	$\chi$	$=$	189.173
Dual form			189.2.bd.a.59.22

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.873917 + 2.40107i) q^{2} +(-1.61037 + 0.637747i) q^{3} +(-3.46930 + 2.91109i) q^{4} +(0.802125 - 0.673063i) q^{5} +(-2.93860 - 3.30926i) q^{6} +(-2.47251 + 0.941638i) q^{7} +(-5.59594 - 3.23082i) q^{8} +(2.18656 - 2.05401i) q^{9} +O(q^{10})$	\(q+(0.873917 + 2.40107i) q^{2} +(-1.61037 + 0.637747i) q^{3} +(-3.46930 + 2.91109i) q^{4} +(0.802125 - 0.673063i) q^{5} +(-2.93860 - 3.30926i) q^{6} +(-2.47251 + 0.941638i) q^{7} +(-5.59594 - 3.23082i) q^{8} +(2.18656 - 2.05401i) q^{9} +(2.31706 + 1.33776i) q^{10} +(-2.64358 + 3.15050i) q^{11} +(3.73031 - 6.90046i) q^{12} +(2.92808 + 3.48955i) q^{13} +(-4.42171 - 5.11375i) q^{14} +(-0.862472 + 1.59543i) q^{15} +(1.29417 - 7.33959i) q^{16} +(1.74141 - 3.01622i) q^{17} +(6.84269 + 3.45504i) q^{18} +(4.80366 - 2.77339i) q^{19} +(-0.823468 + 4.67012i) q^{20} +(3.38112 - 3.09322i) q^{21} +(-9.87483 - 3.59414i) q^{22} +(-2.07660 + 5.70542i) q^{23} +(11.0720 + 1.63401i) q^{24} +(-0.677850 + 3.84428i) q^{25} +(-5.81974 + 10.0801i) q^{26} +(-2.21122 + 4.70218i) q^{27} +(5.83670 - 10.4645i) q^{28} +(-1.57154 + 1.87289i) q^{29} +(-4.58447 - 0.676579i) q^{30} +(-0.681381 - 0.812039i) q^{31} +(6.02691 - 1.06271i) q^{32} +(2.24792 - 6.75939i) q^{33} +(8.76399 + 1.54533i) q^{34} +(-1.34948 + 2.41947i) q^{35} +(-1.60642 + 13.4913i) q^{36} +3.28433 q^{37} +(10.8571 + 9.11019i) q^{38} +(-6.94073 - 3.75208i) q^{39} +(-6.66319 + 1.17490i) q^{40} +(0.164894 - 0.138363i) q^{41} +(10.3818 + 5.41509i) q^{42} +(9.06382 - 3.29896i) q^{43} -18.6257i q^{44} +(0.371415 - 3.11927i) q^{45} -15.5139 q^{46} +(-0.674442 - 0.565924i) q^{47} +(2.59671 + 12.6448i) q^{48} +(5.22663 - 4.65642i) q^{49} +(-9.82275 + 1.73202i) q^{50} +(-0.880732 + 5.96779i) q^{51} +(-20.3168 - 3.58240i) q^{52} +(0.554487 - 0.320133i) q^{53} +(-13.2227 - 1.19998i) q^{54} +4.30639i q^{55} +(16.8783 + 2.71888i) q^{56} +(-5.96692 + 7.52969i) q^{57} +(-5.87034 - 2.13663i) q^{58} +(-1.85273 - 10.5073i) q^{59} +(-1.65227 - 8.04577i) q^{60} +(1.30597 - 1.55639i) q^{61} +(1.35429 - 2.34570i) q^{62} +(-3.47216 + 7.13752i) q^{63} +(0.365832 + 0.633640i) q^{64} +(4.69737 + 0.828274i) q^{65} +(18.1942 - 0.509751i) q^{66} +(10.6115 + 3.86227i) q^{67} +(2.73899 + 15.5336i) q^{68} +(-0.294521 - 10.5122i) q^{69} +(-6.98864 - 1.12578i) q^{70} +(9.48338 - 5.47523i) q^{71} +(-18.8720 + 4.42975i) q^{72} +11.4939i q^{73} +(2.87023 + 7.88590i) q^{74} +(-1.36009 - 6.62299i) q^{75} +(-8.59174 + 23.6056i) q^{76} +(3.56966 - 10.2789i) q^{77} +(2.94337 - 19.9442i) q^{78} +(5.09203 - 1.85335i) q^{79} +(-3.90192 - 6.75833i) q^{80} +(0.562076 - 8.98243i) q^{81} +(0.476322 + 0.275005i) q^{82} +(-7.87254 - 6.60584i) q^{83} +(-2.72550 + 20.5741i) q^{84} +(-0.633272 - 3.59147i) q^{85} +(15.8420 + 18.8798i) q^{86} +(1.33633 - 4.01829i) q^{87} +(24.9720 - 9.08907i) q^{88} +(2.18525 + 3.78496i) q^{89} +(7.81415 - 1.83419i) q^{90} +(-10.5256 - 5.87076i) q^{91} +(-9.40464 - 25.8390i) q^{92} +(1.61515 + 0.873131i) q^{93} +(0.769415 - 2.11395i) q^{94} +(1.98647 - 5.45777i) q^{95} +(-9.02779 + 5.55499i) q^{96} +(-3.53959 - 9.72494i) q^{97} +(15.7480 + 8.48017i) q^{98} +(0.690812 + 12.3187i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 132 q - 3 q^{2} - 9 q^{3} - 3 q^{4} - 9 q^{5} + 18 q^{6} - 6 q^{7} - 18 q^{8} - 15 q^{9}+O(q^{10}) $ 132 * q - 3 * q^2 - 9 * q^3 - 3 * q^4 - 9 * q^5 + 18 * q^6 - 6 * q^7 - 18 * q^8 - 15 * q^9	\( 132 q - 3 q^{2} - 9 q^{3} - 3 q^{4} - 9 q^{5} + 18 q^{6} - 6 q^{7} - 18 q^{8} - 15 q^{9} - 9 q^{10} + 9 q^{11} - 9 q^{12} - 42 q^{14} - 24 q^{15} - 15 q^{16} - 9 q^{17} - 3 q^{18} - 9 q^{19} - 18 q^{20} + 15 q^{21} - 12 q^{22} + 30 q^{23} - 36 q^{24} - 3 q^{25} - 12 q^{28} + 6 q^{29} - 3 q^{30} - 9 q^{31} - 51 q^{32} - 9 q^{33} + 18 q^{34} - 9 q^{35} - 6 q^{37} - 9 q^{38} - 9 q^{39} - 9 q^{40} + 27 q^{42} - 12 q^{43} - 63 q^{45} - 6 q^{46} + 45 q^{47} + 30 q^{49} - 9 q^{50} + 33 q^{51} - 9 q^{52} + 45 q^{53} + 117 q^{54} - 51 q^{56} - 3 q^{58} - 9 q^{59} - 15 q^{60} - 63 q^{61} + 99 q^{62} - 33 q^{63} + 18 q^{64} - 102 q^{65} + 63 q^{66} - 3 q^{67} + 144 q^{68} - 108 q^{69} - 15 q^{70} + 18 q^{71} + 15 q^{72} - 33 q^{74} - 9 q^{75} - 36 q^{76} - 57 q^{77} + 66 q^{78} - 21 q^{79} - 72 q^{80} + 57 q^{81} - 18 q^{82} + 90 q^{83} + 51 q^{84} + 9 q^{85} - 33 q^{86} - 9 q^{87} + 45 q^{88} - 9 q^{89} - 81 q^{90} - 21 q^{91} + 150 q^{92} - 87 q^{93} - 9 q^{94} + 27 q^{95} - 9 q^{96} - 180 q^{98} + 96 q^{99}+O(q^{100}) \) 132 * q - 3 * q^2 - 9 * q^3 - 3 * q^4 - 9 * q^5 + 18 * q^6 - 6 * q^7 - 18 * q^8 - 15 * q^9 - 9 * q^10 + 9 * q^11 - 9 * q^12 - 42 * q^14 - 24 * q^15 - 15 * q^16 - 9 * q^17 - 3 * q^18 - 9 * q^19 - 18 * q^20 + 15 * q^21 - 12 * q^22 + 30 * q^23 - 36 * q^24 - 3 * q^25 - 12 * q^28 + 6 * q^29 - 3 * q^30 - 9 * q^31 - 51 * q^32 - 9 * q^33 + 18 * q^34 - 9 * q^35 - 6 * q^37 - 9 * q^38 - 9 * q^39 - 9 * q^40 + 27 * q^42 - 12 * q^43 - 63 * q^45 - 6 * q^46 + 45 * q^47 + 30 * q^49 - 9 * q^50 + 33 * q^51 - 9 * q^52 + 45 * q^53 + 117 * q^54 - 51 * q^56 - 3 * q^58 - 9 * q^59 - 15 * q^60 - 63 * q^61 + 99 * q^62 - 33 * q^63 + 18 * q^64 - 102 * q^65 + 63 * q^66 - 3 * q^67 + 144 * q^68 - 108 * q^69 - 15 * q^70 + 18 * q^71 + 15 * q^72 - 33 * q^74 - 9 * q^75 - 36 * q^76 - 57 * q^77 + 66 * q^78 - 21 * q^79 - 72 * q^80 + 57 * q^81 - 18 * q^82 + 90 * q^83 + 51 * q^84 + 9 * q^85 - 33 * q^86 - 9 * q^87 + 45 * q^88 - 9 * q^89 - 81 * q^90 - 21 * q^91 + 150 * q^92 - 87 * q^93 - 9 * q^94 + 27 * q^95 - 9 * q^96 - 180 * q^98 + 96 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/189\mathbb{Z}\right)^\times$.

$n$	$29$	$136$
$\chi(n)$	$e\left(\frac{13}{18}\right)$	$e\left(\frac{5}{6}\right)$

Coefficient data

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

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

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

$2$	0.873917	+	2.40107i	0.617953	+	1.69781i	0.711943	+	0.702238i	$0.247816\pi$
$2$	0.873917	+	2.40107i	0.617953	+	1.69781i	−0.0939899	+	0.995573i	$0.529962\pi$
$3$	−1.61037	+	0.637747i	−0.929745	+	0.368203i
$3$	−1.61037	+	0.637747i	−0.929745	+	0.368203i
$4$	−3.46930	+	2.91109i	−1.73465	+	1.45555i
$5$	0.802125	−	0.673063i	0.358721	−	0.301003i	−0.445559	−	0.895252i	$-0.646995\pi$
$5$	0.802125	−	0.673063i	0.358721	−	0.301003i	0.804281	+	0.594249i	$0.202551\pi$
$6$	−2.93860	−	3.30926i	−1.19968	−	1.35100i
$7$	−2.47251	+	0.941638i	−0.934522	+	0.355906i
$7$	−2.47251	+	0.941638i	−0.934522	+	0.355906i
$8$	−5.59594	−	3.23082i	−1.97846	−	1.14227i
$9$	2.18656	−	2.05401i	0.728853	−	0.684670i
$10$	2.31706	+	1.33776i	0.732719	+	0.423036i
$11$	−2.64358	+	3.15050i	−0.797070	+	0.949911i	−0.999569	−	0.0293714i	$-0.990649\pi$
$11$	−2.64358	+	3.15050i	−0.797070	+	0.949911i	0.202498	+	0.979283i	$0.435094\pi$
$12$	3.73031	−	6.90046i	1.07685	−	1.99199i
$13$	2.92808	+	3.48955i	0.812103	+	0.967827i	0.999897	−	0.0143818i	$-0.00457802\pi$
$13$	2.92808	+	3.48955i	0.812103	+	0.967827i	−0.187793	+	0.982209i	$0.560134\pi$
$14$	−4.42171	−	5.11375i	−1.18175	−	1.36671i
$15$	−0.862472	+	1.59543i	−0.222689	+	0.411938i
$16$	1.29417	−	7.33959i	0.323542	−	1.83490i
$17$	1.74141	−	3.01622i	0.422355	−	0.731540i	−0.573814	−	0.818985i	$-0.694537\pi$
$17$	1.74141	−	3.01622i	0.422355	−	0.731540i	0.996169	+	0.0874452i	$0.0278703\pi$
$18$	6.84269	+	3.45504i	1.61284	+	0.814360i
$19$	4.80366	−	2.77339i	1.10203	−	0.636260i	0.165280	−	0.986247i	$-0.447147\pi$
$19$	4.80366	−	2.77339i	1.10203	−	0.636260i	0.936755	+	0.349987i	$0.113814\pi$
$20$	−0.823468	+	4.67012i	−0.184133	+	1.04427i
$21$	3.38112	−	3.09322i	0.737822	−	0.674996i
$22$	−9.87483	−	3.59414i	−2.10532	−	0.766274i
$23$	−2.07660	+	5.70542i	−0.433002	+	1.18966i	0.510959	+	0.859605i	$0.329290\pi$
$23$	−2.07660	+	5.70542i	−0.433002	+	1.18966i	−0.943961	+	0.330058i	$0.892932\pi$
$24$	11.0720	+	1.63401i	2.26005	+	0.333540i
$25$	−0.677850	+	3.84428i	−0.135570	+	0.768855i
$26$	−5.81974	+	10.0801i	−1.14135	+	1.97687i
$27$	−2.21122	+	4.70218i	−0.425550	+	0.904935i
$28$	5.83670	−	10.4645i	1.10303	−	1.97761i
$29$	−1.57154	+	1.87289i	−0.291828	+	0.347787i	−0.891960	−	0.452114i	$-0.850670\pi$
$29$	−1.57154	+	1.87289i	−0.291828	+	0.347787i	0.600132	+	0.799901i	$0.295115\pi$
$30$	−4.58447	−	0.676579i	−0.837005	−	0.123526i
$31$	−0.681381	−	0.812039i	−0.122380	−	0.145846i	0.701376	−	0.712792i	$-0.252570\pi$
$31$	−0.681381	−	0.812039i	−0.122380	−	0.145846i	−0.823755	+	0.566945i	$0.808125\pi$
$32$	6.02691	−	1.06271i	1.06542	−	0.187862i
$33$	2.24792	−	6.75939i	0.391312	−	1.17666i
$34$	8.76399	+	1.54533i	1.50301	+	0.265022i
$35$	−1.34948	+	2.41947i	−0.228104	+	0.408965i
$36$	−1.60642	+	13.4913i	−0.267737	+	2.24854i
$37$	3.28433			0.539941			0.269970	−	0.962869i	$-0.412986\pi$
$37$	3.28433			0.539941			0.269970	+	0.962869i	$0.412986\pi$
$38$	10.8571	+	9.11019i	1.76125	+	1.47787i
$39$	−6.94073	−	3.75208i	−1.11141	−	0.600813i
$40$	−6.66319	+	1.17490i	−1.05354	+	0.185768i
$41$	0.164894	−	0.138363i	0.0257522	−	0.0216086i	−0.629821	−	0.776741i	$-0.716872\pi$
$41$	0.164894	−	0.138363i	0.0257522	−	0.0216086i	0.655573	+	0.755132i	$0.272427\pi$
$42$	10.3818	+	5.41509i	1.60195	+	0.835566i
$43$	9.06382	−	3.29896i	1.38222	−	0.503087i	0.459369	−	0.888246i	$-0.348076\pi$
$43$	9.06382	−	3.29896i	1.38222	−	0.503087i	0.922850	+	0.385159i	$0.125853\pi$
$44$		−	18.6257i		−	2.80794i
$45$	0.371415	−	3.11927i	0.0553673	−	0.464993i
$46$	−15.5139			−2.28740
$47$	−0.674442	−	0.565924i	−0.0983774	−	0.0825485i	0.592272	−	0.805738i	$-0.298231\pi$
$47$	−0.674442	−	0.565924i	−0.0983774	−	0.0825485i	−0.690650	+	0.723189i	$0.742675\pi$
$48$	2.59671	+	12.6448i	0.374803	+	1.82512i
$49$	5.22663	−	4.65642i	0.746662	−	0.665203i
$50$	−9.82275	+	1.73202i	−1.38915	+	0.244944i
$51$	−0.880732	+	5.96779i	−0.123327	+	0.835658i
$52$	−20.3168	−	3.58240i	−2.81743	−	0.496789i
$53$	0.554487	−	0.320133i	0.0761647	−	0.0439737i	−0.461434	−	0.887175i	$-0.652665\pi$
$53$	0.554487	−	0.320133i	0.0761647	−	0.0439737i	0.537599	+	0.843201i	$0.319332\pi$
$54$	−13.2227	−	1.19998i	−1.79938	−	0.163296i
$55$			4.30639i			0.580674i
$56$	16.8783	+	2.71888i	2.25546	+	0.363326i
$57$	−5.96692	+	7.52969i	−0.790338	+	0.997332i
$58$	−5.87034	−	2.13663i	−0.770813	−	0.280553i
$59$	−1.85273	−	10.5073i	−0.241205	−	1.36794i	−0.829144	−	0.559035i	$-0.811172\pi$
$59$	−1.85273	−	10.5073i	−0.241205	−	1.36794i	0.587939	−	0.808905i	$-0.299939\pi$
$60$	−1.65227	−	8.04577i	−0.213307	−	1.03870i
$61$	1.30597	−	1.55639i	0.167212	−	0.199275i	−0.675931	−	0.736965i	$-0.736258\pi$
$61$	1.30597	−	1.55639i	0.167212	−	0.199275i	0.843143	+	0.537690i	$0.180703\pi$
$62$	1.35429	−	2.34570i	0.171995	−	0.297904i
$63$	−3.47216	+	7.13752i	−0.437451	+	0.899242i
$64$	0.365832	+	0.633640i	0.0457290	+	0.0792050i
$65$	4.69737	+	0.828274i	0.582638	+	0.102735i
$66$	18.1942	−	0.509751i	2.23956	−	0.0627461i
$67$	10.6115	+	3.86227i	1.29640	+	0.471851i	0.895822	−	0.444412i	$-0.146587\pi$
$67$	10.6115	+	3.86227i	1.29640	+	0.471851i	0.400577	+	0.916263i	$0.368810\pi$
$68$	2.73899	+	15.5336i	0.332151	+	1.88372i
$69$	−0.294521	−	10.5122i	−0.0354562	−	1.26552i
$70$	−6.98864	−	1.12578i	−0.835303	−	0.134557i
$71$	9.48338	−	5.47523i	1.12547	−	0.649791i	0.182679	−	0.983173i	$-0.441523\pi$
$71$	9.48338	−	5.47523i	1.12547	−	0.649791i	0.942792	+	0.333382i	$0.108190\pi$
$72$	−18.8720	+	4.42975i	−2.22408	+	0.522051i
$73$			11.4939i			1.34526i	0.739980	+	0.672628i	$0.234835\pi$
$73$			11.4939i			1.34526i	−0.739980	+	0.672628i	$0.765165\pi$
$74$	2.87023	+	7.88590i	0.333658	+	0.916717i
$75$	−1.36009	−	6.62299i	−0.157049	−	0.764757i
$76$	−8.59174	+	23.6056i	−0.985541	+	2.70775i
$77$	3.56966	−	10.2789i	0.406801	−	1.17139i
$78$	2.94337	−	19.9442i	0.333271	−	2.25823i
$79$	5.09203	−	1.85335i	0.572899	−	0.208518i	−0.0392926	−	0.999228i	$-0.512510\pi$
$79$	5.09203	−	1.85335i	0.572899	−	0.208518i	0.612191	+	0.790710i	$0.290288\pi$
$80$	−3.90192	−	6.75833i	−0.436248	−	0.755604i
$81$	0.562076	−	8.98243i	0.0624529	−	0.998048i
$82$	0.476322	+	0.275005i	0.0526010	+	0.0303692i
$83$	−7.87254	−	6.60584i	−0.864123	−	0.725085i	0.0987291	−	0.995114i	$-0.468522\pi$
$83$	−7.87254	−	6.60584i	−0.864123	−	0.725085i	−0.962852	+	0.270029i	$0.912967\pi$
$84$	−2.72550	+	20.5741i	−0.297377	+	2.24482i
$85$	−0.633272	−	3.59147i	−0.0686880	−	0.389549i
$86$	15.8420	+	18.8798i	1.70829	+	2.03586i
$87$	1.33633	−	4.01829i	0.143270	−	0.430806i
$88$	24.9720	−	9.08907i	2.66203	−	0.968898i
$89$	2.18525	+	3.78496i	0.231636	+	0.401205i	0.958290	−	0.285799i	$-0.0922589\pi$
$89$	2.18525	+	3.78496i	0.231636	+	0.401205i	−0.726654	+	0.687004i	$0.758926\pi$
$90$	7.81415	−	1.83419i	0.823684	−	0.193340i
$91$	−10.5256	−	5.87076i	−1.10338	−	0.615423i
$92$	−9.40464	−	25.8390i	−0.980501	−	2.69390i
$93$	1.61515	+	0.873131i	0.167483	+	0.0905394i
$94$	0.769415	−	2.11395i	0.0793591	−	0.218037i
$95$	1.98647	−	5.45777i	0.203807	−	0.559956i
$96$	−9.02779	+	5.55499i	−0.921395	+	0.566953i
$97$	−3.53959	−	9.72494i	−0.359391	−	0.987418i	−0.979241	−	0.202698i	$-0.935029\pi$
$97$	−3.53959	−	9.72494i	−0.359391	−	0.987418i	0.619851	−	0.784720i	$-0.287193\pi$
$98$	15.7480	+	8.48017i	1.59079	+	0.856627i
$99$	0.690812	+	12.3187i	0.0694293	+	1.23808i
$100$	−8.83937	−	15.3102i	−0.883937	−	1.53102i
$101$	−10.3142	+	3.75407i	−1.02630	+	0.373544i	−0.799673	−	0.600436i	$-0.794994\pi$
$101$	−10.3142	+	3.75407i	−1.02630	+	0.373544i	−0.226632	+	0.973980i	$0.572771\pi$
$102$	−15.0988	+	3.10066i	−1.49500	+	0.307011i
$103$	7.17676	+	8.55293i	0.707148	+	0.842746i	0.993315	−	0.115434i	$-0.0368259\pi$
$103$	7.17676	+	8.55293i	0.707148	+	0.842746i	−0.286168	+	0.958180i	$0.592381\pi$
$104$	−5.11126	−	28.9874i	−0.501200	−	2.84245i
$105$	0.630154	−	4.75686i	0.0614967	−	0.464222i
$106$	1.25324	+	1.05159i	0.121725	+	0.102140i
$107$	−1.14302	−	0.659921i	−0.110500	−	0.0637970i	0.443732	−	0.896160i	$-0.353654\pi$
$107$	−1.14302	−	0.659921i	−0.110500	−	0.0637970i	−0.554231	+	0.832363i	$0.686988\pi$
$108$	−6.01708	−	22.7504i	−0.578994	−	2.18915i
$109$	−6.88550	−	11.9260i	−0.659511	−	1.14231i	−0.980742	−	0.195306i	$-0.937430\pi$
$109$	−6.88550	−	11.9260i	−0.659511	−	1.14231i	0.321231	−	0.947001i	$-0.395903\pi$
$110$	−10.3399	+	3.76343i	−0.985875	+	0.358829i
$111$	−5.28898	+	2.09457i	−0.502007	+	0.198808i
$112$	3.71139	+	19.3659i	0.350694	+	1.82990i
$113$	−2.09848	+	5.76552i	−0.197408	+	0.542374i	−0.998415	−	0.0562808i	$-0.982076\pi$
$113$	−2.09848	+	5.76552i	−0.197408	+	0.542374i	0.801007	+	0.598655i	$0.204298\pi$
$114$	−23.2939	−	7.74666i	−2.18167	−	0.725541i
$115$	2.17441	+	5.97415i	0.202765	+	0.557092i
$116$		−	11.0725i		−	1.02806i
$117$	13.5700	+	1.61580i	1.25455	+	0.149380i
$118$	23.6097	−	13.6311i	2.17345	−	1.25484i
$119$	−1.46548	+	9.09742i	−0.134340	+	0.833959i
$120$	9.98089	−	6.14145i	0.911126	−	0.560635i
$121$	−1.02699	−	5.82432i	−0.0933623	−	0.529484i
$122$	4.87830	+	1.77556i	0.441660	+	0.160751i
$123$	−0.177300	+	0.327975i	−0.0159866	+	0.0295725i
$124$	4.72784	+	0.833645i	0.424572	+	0.0748636i
$125$	4.66147	+	8.07391i	0.416935	+	0.722152i
$126$	−20.1720	−	2.09929i	−1.79707	−	0.187019i
$127$	−9.17375	+	15.8894i	−0.814039	+	1.40996i	0.0959776	+	0.995383i	$0.469402\pi$
$127$	−9.17375	+	15.8894i	−0.814039	+	1.40996i	−0.910016	+	0.414573i	$0.863931\pi$
$128$	6.66586	−	7.94407i	0.589185	−	0.702163i
$129$	−12.4922	+	11.0930i	−1.09987	+	0.976680i
$130$	2.11637	+	12.0026i	0.185618	+	1.05269i
$131$	−11.6575	−	4.24298i	−1.01852	−	0.370711i	−0.221821	−	0.975087i	$-0.571200\pi$
$131$	−11.6575	−	4.24298i	−1.01852	−	0.370711i	−0.796699	+	0.604377i	$0.793422\pi$
$132$	11.8785	+	29.9943i	1.03389	+	2.61067i
$133$	−9.26557	+	11.3806i	−0.803427	+	0.986819i
$134$			28.8542i			2.49262i
$135$	1.39119	+	5.26003i	0.119734	+	0.452711i
$136$	−19.4897	+	11.2524i	−1.67123	+	0.964883i
$137$	−3.16758	−	0.558531i	−0.270625	−	0.0477185i	0.0366888	−	0.999327i	$-0.488319\pi$
$137$	−3.16758	−	0.558531i	−0.270625	−	0.0477185i	−0.307314	+	0.951608i	$0.599430\pi$
$138$	24.9830	−	9.89392i	2.12670	−	0.842227i
$139$	7.01041	−	1.23613i	0.594616	−	0.104847i	0.131762	−	0.991281i	$-0.457937\pi$
$139$	7.01041	−	1.23613i	0.594616	−	0.104847i	0.462854	+	0.886435i	$0.346825\pi$
$140$	−2.36153	−	12.3223i	−0.199586	−	1.04143i
$141$	1.44701	+	0.481222i	0.121861	+	0.0405262i
$142$	21.4341	+	17.9853i	1.79871	+	1.50930i
$143$	−18.7344			−1.56665
$144$	−12.2458	−	18.7067i	−1.02049	−	1.55889i
$145$			2.56004i			0.212600i
$146$	−27.5976	+	10.0447i	−2.28399	+	0.831305i
$147$	−5.44718	+	10.8318i	−0.449276	+	0.893393i
$148$	−11.3943	+	9.56099i	−0.936609	+	0.785908i
$149$	−2.74559	+	0.484122i	−0.224928	+	0.0396608i	−0.284976	−	0.958535i	$-0.591986\pi$
$149$	−2.74559	+	0.484122i	−0.224928	+	0.0396608i	0.0600483	+	0.998195i	$0.480875\pi$
$150$	14.7136	−	9.05361i	1.20136	−	0.739224i
$151$	−2.08446	−	1.74907i	−0.169631	−	0.142337i	0.554020	−	0.832503i	$-0.313093\pi$
$151$	−2.08446	−	1.74907i	−0.169631	−	0.142337i	−0.723651	+	0.690166i	$0.757537\pi$
$152$	−35.8413			−2.90711
$153$	−2.38764	−	10.1720i	−0.193029	−	0.822359i
$154$	27.8000	−	0.411951i	2.24019	−	0.0331960i
$155$	−1.09311	−	0.192744i	−0.0878004	−	0.0154816i
$156$	35.0021	−	7.18799i	2.80241	−	0.575500i
$157$	15.1880	−	2.67806i	1.21214	−	0.213732i	0.469198	−	0.883093i	$-0.344543\pi$
$157$	15.1880	−	2.67806i	1.21214	−	0.213732i	0.742938	+	0.669360i	$0.233432\pi$
$158$	8.90003	+	10.6066i	0.708048	+	0.843819i
$159$	−0.688763	+	0.869154i	−0.0546225	+	0.0689284i
$160$	4.11907	−	4.90891i	0.325641	−	0.388084i
$161$	−0.238015	−	16.0621i	−0.0187582	−	1.26587i
$162$	22.0586	−	6.50032i	1.73309	−	0.510713i
$163$	−0.0485493	+	0.0840899i	−0.00380267	+	0.00658643i	−0.867920	−	0.496703i	$-0.834544\pi$
$163$	−0.0485493	+	0.0840899i	−0.00380267	+	0.00658643i	0.864118	+	0.503290i	$0.167877\pi$
$164$	−0.169282	+	0.960044i	−0.0132187	+	0.0749669i
$165$	−2.74639	−	6.93487i	−0.213806	−	0.539879i
$166$	8.98113	−	24.6754i	0.697071	−	1.91519i
$167$	7.08005	+	2.57693i	0.547871	+	0.199409i	0.601100	−	0.799174i	$-0.294729\pi$
$167$	7.08005	+	2.57693i	0.547871	+	0.199409i	−0.0532293	+	0.998582i	$0.516951\pi$
$168$	−28.9142	+	6.38567i	−2.23078	+	0.492665i
$169$	−1.34588	+	7.63285i	−0.103529	+	0.587142i
$170$	8.06992	−	4.65917i	0.618935	−	0.357342i
$171$	4.80690	−	15.9309i	0.367593	−	1.21827i
$172$	−21.8416	+	37.8307i	−1.66540	+	2.88456i
$173$	2.45923	−	13.9470i	0.186972	−	1.06037i	−0.736424	−	0.676520i	$-0.763487\pi$
$173$	2.45923	−	13.9470i	0.186972	−	1.06037i	0.923396	−	0.383849i	$-0.125402\pi$
$174$	10.8160	−	0.303034i	0.819960	−	0.0229730i
$175$	−1.94393	−	10.1433i	−0.146947	−	0.766762i
$176$	19.7021	+	23.4801i	1.48510	+	1.76988i
$177$	9.68460	+	15.7391i	0.727939	+	1.18302i
$178$	−7.17822	+	8.55467i	−0.538030	+	0.641199i
$179$	−12.8430	−	7.41494i	−0.959934	−	0.554218i	−0.0637814	−	0.997964i	$-0.520316\pi$
$179$	−12.8430	−	7.41494i	−0.959934	−	0.554218i	−0.896153	+	0.443746i	$0.853649\pi$
$180$	7.79192	+	11.9029i	0.580775	+	0.887190i
$181$	−7.99205	−	4.61421i	−0.594045	−	0.342972i	0.172651	−	0.984983i	$-0.444767\pi$
$181$	−7.99205	−	4.61421i	−0.594045	−	0.342972i	−0.766695	+	0.642011i	$0.778100\pi$
$182$	4.89759	−	30.4032i	0.363033	−	2.25364i
$183$	−1.11050	+	3.33923i	−0.0820906	+	0.246843i
$184$	30.0537	−	25.2181i	2.21559	−	1.85910i
$185$	2.63445	−	2.21056i	0.193688	−	0.162524i
$186$	−0.684940	+	4.64112i	−0.0502223	+	0.340304i
$187$	4.89902	+	13.4599i	0.358252	+	0.984288i
$188$	3.98730			0.290804
$189$	1.03952	−	13.7084i	0.0756139	−	0.997137i
$190$	14.8405			1.07664
$191$	7.05227	+	19.3759i	0.510284	+	1.40199i	0.880942	+	0.473225i	$0.156910\pi$
$191$	7.05227	+	19.3759i	0.510284	+	1.40199i	−0.370658	+	0.928770i	$0.620868\pi$
$192$	−0.993225	−	0.787084i	−0.0716799	−	0.0568029i
$193$	−6.15262	+	5.16266i	−0.442875	+	0.371616i	−0.836784	−	0.547533i	$-0.815567\pi$
$193$	−6.15262	+	5.16266i	−0.442875	+	0.371616i	0.393909	+	0.919150i	$0.371123\pi$
$194$	20.2569	−	16.9976i	1.45436	−	1.22036i
$195$	−8.09272	+	1.66191i	−0.579532	+	0.119012i
$196$	−4.57751	+	31.3698i	−0.326965	+	2.24070i
$197$	18.9779	+	10.9569i	1.35212	+	0.780646i	0.988546	−	0.150920i	$-0.0482237\pi$
$197$	18.9779	+	10.9569i	1.35212	+	0.780646i	0.363572	+	0.931566i	$0.381557\pi$
$198$	−28.9743	+	12.4242i	−2.05911	+	0.882950i
$199$	−14.8877	−	8.59540i	−1.05536	−	0.609312i	−0.131214	−	0.991354i	$-0.541888\pi$
$199$	−14.8877	−	8.59540i	−1.05536	−	0.609312i	−0.924145	+	0.382042i	$0.875221\pi$
$200$	16.2134	−	19.3223i	1.14646	−	1.36629i
$201$	−19.5515	+	0.547779i	−1.37906	+	0.0386373i
$202$	−18.0276	−	21.4844i	−1.26842	−	1.51164i
$203$	2.12207	−	6.11057i	0.148940	−	0.428878i
$204$	−14.3173	−	23.2680i	−1.00241	−	1.62908i
$205$	0.0391390	−	0.221968i	0.00273359	−	0.0155030i
$206$	−14.2643	+	24.7064i	−0.993839	+	1.72138i
$207$	7.17838	+	16.7406i	0.498932	+	1.16355i
$208$	29.4013	−	16.9748i	2.03861	−	1.17699i
$209$	−3.96129	+	22.4656i	−0.274008	+	1.55398i
$210$	11.9722	−	2.64406i	0.826163	−	0.182457i
$211$	−14.7618	−	5.37287i	−1.01625	−	0.369884i	−0.220418	−	0.975405i	$-0.570742\pi$
$211$	−14.7618	−	5.37287i	−1.01625	−	0.369884i	−0.795829	+	0.605522i	$0.792964\pi$
$212$	−0.991747	+	2.72480i	−0.0681135	+	0.187140i
$213$	−11.7799	+	14.8651i	−0.807146	+	1.01854i
$214$	0.585613	−	3.32118i	0.0400317	−	0.227031i
$215$	5.04991	−	8.74670i	0.344401	−	0.596520i
$216$	27.5657	−	19.1691i	1.87561	−	1.30429i
$217$	2.44937	+	1.36616i	0.166274	+	0.0927410i
$218$	22.6179	−	26.9549i	1.53187	−	1.82562i
$219$	−7.33018	−	18.5094i	−0.495328	−	1.25075i
$220$	−12.5363	−	14.9402i	−0.845198	−	1.00727i
$221$	15.6242	−	2.75497i	1.05100	−	0.185320i
$222$	−9.65133	−	10.8687i	−0.647755	−	0.729460i
$223$	1.32691	+	0.233969i	0.0888562	+	0.0156678i	0.217900	−	0.975971i	$-0.430079\pi$
$223$	1.32691	+	0.233969i	0.0888562	+	0.0156678i	−0.129043	+	0.991639i	$0.541191\pi$
$224$	−13.9009	+	8.30272i	−0.928794	+	0.554749i
$225$	6.41403	+	9.79805i	0.427602	+	0.653203i
$226$	−15.6773			−1.04284
$227$	15.1925	+	12.7480i	1.00836	+	0.846117i	0.988121	−	0.153678i	$-0.0491120\pi$
$227$	15.1925	+	12.7480i	1.00836	+	0.846117i	0.0202416	+	0.999795i	$0.493556\pi$
$228$	−1.21855	−	43.4930i	−0.0807006	−	2.88040i
$229$	0.817942	−	0.144225i	0.0540511	−	0.00953067i	−0.146557	−	0.989202i	$-0.546819\pi$
$229$	0.817942	−	0.144225i	0.0540511	−	0.00953067i	0.200608	+	0.979672i	$0.435708\pi$
$230$	−12.4441	+	10.4418i	−0.820538	+	0.688513i
$231$	0.806903	+	18.8294i	0.0530903	+	1.23888i
$232$	14.8452	−	5.40322i	0.974637	−	0.354739i
$233$			3.95980i			0.259415i	0.991552	+	0.129707i	$0.0414038\pi$
$233$			3.95980i			0.259415i	−0.991552	+	0.129707i	$0.958596\pi$
$234$	7.97941	+	33.9945i	0.521630	+	2.22229i
$235$	−0.921889			−0.0601374
$236$	37.0155	+	31.0597i	2.40951	+	2.02182i
$237$	−7.01807	+	6.23200i	−0.455873	+	0.404812i
$238$	−23.1242	+	4.43167i	−1.49892	+	0.287262i
$239$	23.0139	−	4.05798i	1.48865	−	0.262489i	0.630620	−	0.776092i	$-0.282801\pi$
$239$	23.0139	−	4.05798i	1.48865	−	0.262489i	0.858028	+	0.513603i	$0.171690\pi$
$240$	10.5936	+	8.39494i	0.683815	+	0.541891i
$241$	4.03917	+	0.712215i	0.260186	+	0.0458778i	0.302219	−	0.953238i	$-0.402272\pi$
$241$	4.03917	+	0.712215i	0.260186	+	0.0458778i	−0.0420335	+	0.999116i	$0.513384\pi$
$242$	13.0871	−	7.55584i	0.841270	−	0.485708i
$243$	4.82337	+	14.8235i	0.309419	+	0.950926i
$244$			9.20137i			0.589057i
$245$	1.05835	−	7.25289i	0.0676155	−	0.463370i
$246$	−0.942436	−	0.139085i	−0.0600875	−	0.00886776i
$247$	23.7434	+	8.64188i	1.51075	+	0.549870i
$248$	1.18942	+	6.74554i	0.0755282	+	0.428342i
$249$	16.8905	+	5.61714i	1.07039	+	0.355972i
$250$	−15.3123	+	18.2484i	−0.968432	+	1.15413i
$251$	−2.57441	+	4.45900i	−0.162495	+	0.281450i	−0.935763	−	0.352630i	$-0.885288\pi$
$251$	−2.57441	+	4.45900i	−0.162495	+	0.281450i	0.773268	+	0.634080i	$0.218621\pi$
$252$	−8.73199	−	34.8700i	−0.550064	−	2.19660i
$253$	−12.4853	−	21.6251i	−0.784941	−	1.35956i
$254$	−46.1686	−	8.14077i	−2.89688	−	0.510797i
$255$	3.31025	+	5.37971i	0.207296	+	0.336890i
$256$	26.2747	+	9.56322i	1.64217	+	0.597701i
$257$	−4.14398	−	23.5017i	−0.258495	−	1.46600i	−0.786941	−	0.617029i	$-0.788336\pi$
$257$	−4.14398	−	23.5017i	−0.258495	−	1.46600i	0.528446	−	0.848967i	$-0.322775\pi$
$258$	−37.5520	−	20.3002i	−2.33789	−	1.26384i
$259$	−8.12055	+	3.09265i	−0.504586	+	0.192168i
$260$	−18.7078	+	10.8010i	−1.16021	+	0.669847i
$261$	0.410670	+	7.32315i	0.0254199	+	0.453292i
$262$		−	31.6984i		−	1.95834i
$263$	−5.83611	−	16.0346i	−0.359870	−	0.988734i	−0.979074	−	0.203504i	$-0.934767\pi$
$263$	−5.83611	−	16.0346i	−0.359870	−	0.988734i	0.619204	−	0.785230i	$-0.287455\pi$
$264$	−34.4176	+	30.5625i	−2.11825	+	1.88099i
$265$	0.229298	−	0.629992i	0.0140857	−	0.0387001i
$266$	−35.4228	−	12.3016i	−2.17191	−	0.754259i
$267$	−5.93289	−	4.70154i	−0.363087	−	0.287729i
$268$	−48.0579	+	17.4916i	−2.93560	+	1.06847i
$269$	0.632582	+	1.09566i	0.0385692	+	0.0668038i	0.884666	−	0.466226i	$-0.154387\pi$
$269$	0.632582	+	1.09566i	0.0385692	+	0.0668038i	−0.846096	+	0.533030i	$0.821053\pi$
$270$	−11.4139	+	7.93716i	−0.694628	+	0.483040i
$271$	0.441176	+	0.254713i	0.0267995	+	0.0154727i	0.513340	−	0.858185i	$-0.328408\pi$
$271$	0.441176	+	0.254713i	0.0267995	+	0.0154727i	−0.486540	+	0.873658i	$0.661741\pi$
$272$	−19.8841	−	16.6848i	−1.20565	−	1.01166i
$273$	20.6941	+	2.74141i	1.25247	+	0.165918i
$274$	−1.42714	−	8.09369i	−0.0862164	−	0.488958i
$275$	−10.3194	−	12.2982i	−0.622286	−	0.741611i
$276$	31.6237	+	35.6125i	1.90352	+	2.14362i
$277$	−6.66781	+	2.42689i	−0.400630	+	0.145817i	−0.534474	−	0.845185i	$-0.679490\pi$
$277$	−6.66781	+	2.42689i	−0.400630	+	0.145817i	0.133844	+	0.991002i	$0.457268\pi$
$278$	9.09454	+	15.7522i	0.545454	+	0.944755i
$279$	−3.15782	−	0.376005i	−0.189054	−	0.0225108i
$280$	15.3685	−	9.17927i	0.918443	−	0.548566i
$281$	4.02711	+	11.0644i	0.240237	+	0.660046i	0.999952	+	0.00978955i	$0.00311616\pi$
$281$	4.02711	+	11.0644i	0.240237	+	0.660046i	−0.759715	+	0.650256i	$0.774662\pi$
$282$	0.109125	+	3.89493i	0.00649829	+	0.231939i
$283$	2.64326	−	7.26230i	0.157126	−	0.431699i	−0.836003	−	0.548724i	$-0.815114\pi$
$283$	2.64326	−	7.26230i	0.157126	−	0.431699i	0.993129	+	0.117025i	$0.0373359\pi$
$284$	−16.9618	+	46.6022i	−1.00650	+	2.76533i
$285$	0.281737	+	10.0559i	0.0166887	+	0.595659i
$286$	−16.3723	−	44.9826i	−0.968117	−	2.65988i
$287$	−0.277415	+	0.497374i	−0.0163753	+	0.0293591i
$288$	10.9954	−	14.7030i	0.647909	−	0.866383i
$289$	2.43496	+	4.21747i	0.143233	+	0.248086i
$290$	−6.14683	+	2.23726i	−0.360954	+	0.131377i
$291$	11.9021	+	13.4034i	0.697712	+	0.785718i
$292$	−33.4597	−	39.8758i	−1.95808	−	2.33355i
$293$	−1.74277	−	9.88373i	−0.101814	−	0.577414i	−0.992445	−	0.122688i	$-0.960848\pi$
$293$	−1.74277	−	9.88373i	−0.101814	−	0.577414i	0.890632	−	0.454725i	$-0.150263\pi$
$294$	−30.7683	−	3.61293i	−1.79444	−	0.210710i
$295$	−8.55823	−	7.18121i	−0.498279	−	0.418106i
$296$	−18.3789	−	10.6111i	−1.06825	−	0.616756i
$297$	−8.96867	−	19.3971i	−0.520415	−	1.12553i
$298$	−3.56183	−	6.16927i	−0.206331	−	0.357376i
$299$	−25.9898	+	9.45952i	−1.50303	+	0.547058i
$300$	23.9987	+	19.0178i	1.38556	+	1.09799i
$301$	−19.3040	+	16.6916i	−1.11266	+	0.962085i
$302$	2.37799	−	6.53347i	0.136838	−	0.375959i
$303$	14.2155	−	12.6233i	0.816662	−	0.725190i
$304$	−14.1388	−	38.8461i	−0.810917	−	2.22798i
$305$		−	2.12742i		−	0.121815i
$306$	22.3371	−	14.6224i	1.27693	−	0.835906i
$307$	20.1755	−	11.6483i	1.15148	−	0.664805i	0.202229	−	0.979338i	$-0.435181\pi$
$307$	20.1755	−	11.6483i	1.15148	−	0.664805i	0.949246	+	0.314534i	$0.101848\pi$
$308$	17.5387	+	46.0524i	0.999361	+	2.62408i
$309$	−17.0118	−	9.19640i	−0.967769	−	0.523165i
$310$	−0.492493	−	2.79306i	−0.0279717	−	0.158635i
$311$	8.98780	+	3.27129i	0.509651	+	0.185498i	0.584030	−	0.811732i	$-0.301475\pi$
$311$	8.98780	+	3.27129i	0.509651	+	0.185498i	−0.0743787	+	0.997230i	$0.523697\pi$
$312$	26.7176	+	43.4206i	1.51259	+	2.45821i
$313$	6.58420	+	1.16097i	0.372161	+	0.0656220i	0.356601	−	0.934257i	$-0.383936\pi$
$313$	6.58420	+	1.16097i	0.372161	+	0.0656220i	0.0155604	+	0.999879i	$0.495047\pi$
$314$	19.7033	+	34.1271i	1.11192	+	1.92590i
$315$	2.01889	+	8.06216i	0.113752	+	0.454251i
$316$	−12.2705	+	21.2532i	−0.690272	+	1.19559i
$317$	−1.60211	+	1.90932i	−0.0899834	+	0.107238i	−0.809157	−	0.587592i	$-0.800076\pi$
$317$	−1.60211	+	1.90932i	−0.0899834	+	0.107238i	0.719174	+	0.694830i	$0.244520\pi$
$318$	−2.68882	−	0.894199i	−0.150782	−	0.0501442i
$319$	−1.74604	−	9.90229i	−0.0977595	−	0.554422i
$320$	0.719923	+	0.262030i	0.0402449	+	0.0146479i
$321$	2.26154	+	0.333760i	0.126227	+	0.0186286i
$322$	38.3583	−	14.6085i	2.13762	−	0.814098i
$323$		−	19.3185i		−	1.07491i
$324$	24.1987	+	32.7990i	1.34437	+	1.82217i
$325$	−15.3996	+	8.89096i	−0.854216	+	0.493182i
$326$	−0.244333	−	0.0430826i	−0.0135324	−	0.00238612i
$327$	18.6940	+	14.8141i	1.03378	+	0.819221i
$328$	−1.36976	+	0.241526i	−0.0756325	+	0.0133360i
$329$	2.20046	+	0.764173i	0.121315	+	0.0421302i
$330$	14.2510	−	12.6548i	0.784490	−	0.696622i
$331$	−23.4806	−	19.7025i	−1.29061	−	1.08295i	−0.991687	−	0.128671i	$-0.958929\pi$
$331$	−23.4806	−	19.7025i	−1.29061	−	1.08295i	−0.298921	−	0.954278i	$-0.596627\pi$
$332$	46.5424			2.55435
$333$	7.18138	−	6.74605i	0.393537	−	0.369681i
$334$			19.2517i			1.05341i
$335$	11.1113	−	4.04418i	0.607075	−	0.220957i
$336$	−18.3272	−	28.8192i	−0.999831	−	1.57222i
$337$	−9.52767	+	7.99467i	−0.519005	+	0.435497i	−0.864285	−	0.503003i	$-0.832229\pi$
$337$	−9.52767	+	7.99467i	−0.519005	+	0.435497i	0.345279	+	0.938500i	$0.387784\pi$
$338$	−19.5032	+	3.43894i	−1.06083	+	0.187053i
$339$	−0.297623	−	10.6229i	−0.0161647	−	0.576956i
$340$	12.6521	+	10.6164i	0.686156	+	0.575754i
$341$	4.35961			0.236086
$342$	42.4521	−	2.38064i	2.29555	−	0.128730i
$343$	−8.53825	+	16.4347i	−0.461022	+	0.887389i
$344$	−61.3789	−	10.8228i	−3.30933	−	0.583524i
$345$	−7.31159	−	8.23384i	−0.393643	−	0.443295i
$346$	35.6368	−	6.28372i	1.91584	−	0.337815i
$347$	4.69084	+	5.59032i	0.251817	+	0.300104i	0.877113	−	0.480284i	$-0.159466\pi$
$347$	4.69084	+	5.59032i	0.251817	+	0.300104i	−0.625296	+	0.780388i	$0.715022\pi$
$348$	7.06147	+	17.8308i	0.378535	+	0.955833i
$349$	11.2139	−	13.3642i	0.600265	−	0.715368i	−0.377279	−	0.926100i	$-0.623140\pi$
$349$	11.2139	−	13.3642i	0.600265	−	0.715368i	0.977544	+	0.210732i	$0.0675846\pi$
$350$	22.6559	−	13.5319i	1.21101	−	0.723311i
$351$	−22.8831	+	6.05219i	−1.22141	+	0.323042i
$352$	−12.5846	+	21.7971i	−0.670760	+	1.16179i
$353$	3.77759	−	21.4238i	0.201061	−	1.14027i	−0.702459	−	0.711725i	$-0.747914\pi$
$353$	3.77759	−	21.4238i	0.201061	−	1.14027i	0.903519	−	0.428547i	$-0.140974\pi$
$354$	−29.3271	+	37.0080i	−1.55872	+	1.96696i
$355$	3.92168	−	10.7747i	0.208141	−	0.571864i
$356$	−18.5997	−	6.76972i	−0.985780	−	0.358794i
$357$	−3.44188	−	15.5848i	−0.182164	−	0.824834i
$358$	6.58000	−	37.3171i	0.347764	−	1.97227i
$359$	11.2506	−	6.49553i	0.593783	−	0.342821i	−0.172809	−	0.984955i	$-0.555284\pi$
$359$	11.2506	−	6.49553i	0.593783	−	0.342821i	0.766592	+	0.642135i	$0.221951\pi$
$360$	−12.1562	+	16.2553i	−0.640688	+	0.856727i
$361$	5.88341	−	10.1904i	0.309653	−	0.536335i
$362$	4.09465	−	23.2219i	0.215210	−	1.22052i
$363$	5.36826	+	8.72434i	0.281761	+	0.457909i
$364$	53.6068	−	10.2735i	2.80976	−	0.538480i
$365$	7.73611	+	9.21953i	0.404926	+	0.482572i
$366$	−8.98820	+	0.251824i	−0.469821	+	0.0131631i
$367$	1.88358	−	2.24476i	0.0983218	−	0.117175i	−0.714640	−	0.699493i	$-0.753409\pi$
$367$	1.88358	−	2.24476i	0.0983218	−	0.117175i	0.812962	+	0.582317i	$0.197854\pi$
$368$	39.1880	+	22.6252i	2.04281	+	1.17942i
$369$	0.0763524	−	0.641233i	0.00397475	−	0.0333812i
$370$	7.60999	+	4.39363i	0.395625	+	0.228414i
$371$	−1.06953	+	1.31366i	−0.0555270	+	0.0682018i
$372$	−8.14520	+	1.67269i	−0.422309	+	0.0867248i
$373$	−2.83985	+	2.38292i	−0.147042	+	0.123383i	−0.713341	−	0.700817i	$-0.752819\pi$
$373$	−2.83985	+	2.38292i	−0.147042	+	0.123383i	0.566299	+	0.824200i	$0.308375\pi$
$374$	−28.0369	+	23.5257i	−1.44975	+	1.21649i
$375$	−12.6558	−	10.0291i	−0.653542	−	0.517901i
$376$	1.94574	+	5.34587i	0.100344	+	0.275692i
$377$	−11.1371			−0.573592
$378$	33.8232	−	9.48402i	1.73968	−	0.487805i
$379$	33.6065			1.72625			0.863125	−	0.504990i	$-0.168504\pi$
$379$	33.6065			1.72625			0.863125	+	0.504990i	$0.168504\pi$
$380$	8.99642	+	24.7175i	0.461507	+	1.26798i
$381$	4.63968	−	31.4383i	0.237698	−	1.61063i
$382$	−40.3598	+	33.8659i	−2.06499	+	1.73273i
$383$	−20.7078	+	17.3759i	−1.05812	+	0.887869i	−0.993924	−	0.110069i	$-0.964893\pi$
$383$	−20.7078	+	17.3759i	−1.05812	+	0.887869i	−0.0641967	+	0.997937i	$0.520449\pi$
$384$	−5.66818	+	17.0440i	−0.289253	+	0.869772i
$385$	−4.05506	−	10.6476i	−0.206665	−	0.542653i
$386$	−17.7728	−	10.2611i	−0.904610	−	0.522277i
$387$	13.0425	−	25.8305i	0.662986	−	1.31304i
$388$	40.5901	+	23.4347i	2.06065	+	1.18972i
$389$	24.1340	−	28.7618i	1.22364	−	1.45828i	0.376917	−	0.926247i	$-0.376984\pi$
$389$	24.1340	−	28.7618i	1.22364	−	1.45828i	0.846724	−	0.532032i	$-0.178572\pi$
$390$	−11.0627	−	17.9788i	−0.560183	−	0.910392i
$391$	13.5926	+	16.1990i	0.687405	+	0.819218i
$392$	−44.2920	+	9.17077i	−2.23708	+	0.463194i
$393$	21.4788	−	0.601774i	1.08346	−	0.0303555i
$394$	−9.72312	+	55.1426i	−0.489844	+	2.77804i
$395$	2.83703	−	4.91388i	0.142746	−	0.247244i
$396$	−38.2575	−	40.7263i	−1.92251	−	2.04657i
$397$	−27.2081	+	15.7086i	−1.36554	+	0.788392i	−0.990354	−	0.138559i	$-0.955753\pi$
$397$	−27.2081	+	15.7086i	−1.36554	+	0.788392i	−0.375181	+	0.926951i	$0.622420\pi$
$398$	7.62755	−	43.2580i	0.382334	−	2.16833i
$399$	7.66305	−	24.2359i	0.383632	−	1.21331i
$400$	27.3382	+	9.95028i	1.36691	+	0.497514i
$401$	−8.37342	+	23.0058i	−0.418148	+	1.14885i	0.534603	+	0.845103i	$0.320461\pi$
$401$	−8.37342	+	23.0058i	−0.418148	+	1.14885i	−0.952752	+	0.303750i	$0.901761\pi$
$402$	−18.4017	−	46.4658i	−0.917792	−	2.31750i
$403$	0.838510	−	4.75543i	0.0417692	−	0.236885i
$404$	24.8548	−	43.0497i	1.23657	−	2.14180i
$405$	−5.59489	−	7.58335i	−0.278012	−	0.376820i
$406$	16.5264	−	0.244895i	0.820192	−	0.0121539i
$407$	−8.68240	+	10.3473i	−0.430371	+	0.512896i
$408$	24.2094	−	30.5499i	1.19854	−	1.51245i
$409$	8.91121	+	10.6200i	0.440631	+	0.525124i	0.939958	−	0.341290i	$-0.110864\pi$
$409$	8.91121	+	10.6200i	0.440631	+	0.525124i	−0.499327	+	0.866414i	$0.666419\pi$
$410$	0.567165	−	0.100007i	0.0280103	−	0.00493897i
$411$	5.45717	−	1.12068i	0.269182	−	0.0552789i
$412$	−49.7967	−	8.78051i	−2.45331	−	0.432585i
$413$	14.4750	+	24.2350i	0.712269	+	1.19252i
$414$	−33.9220	+	31.8657i	−1.66718	+	1.56611i
$415$	−10.7609			−0.528232
$416$	21.3556	+	17.9195i	1.04705	+	0.878576i
$417$	−10.5010	+	6.46148i	−0.514236	+	0.316420i
$418$	−57.4033	+	10.1217i	−2.80769	+	0.495071i
$419$	17.2126	−	14.4431i	0.840893	−	0.705593i	−0.116872	−	0.993147i	$-0.537287\pi$
$419$	17.2126	−	14.4431i	0.840893	−	0.705593i	0.957764	+	0.287554i	$0.0928422\pi$
$420$	11.6615	+	18.3374i	0.569021	+	0.894775i
$421$	9.17695	−	3.34014i	0.447257	−	0.162788i	−0.108565	−	0.994089i	$-0.534626\pi$
$421$	9.17695	−	3.34014i	0.447257	−	0.162788i	0.555822	+	0.831301i	$0.312403\pi$
$422$		−	40.1396i		−	1.95397i
$423$	−2.63712	+	0.147885i	−0.128221	+	0.00719043i
$424$	−4.13717			−0.200919
$425$	10.4148	+	8.73902i	0.505190	+	0.423905i
$426$	−45.9868	−	15.2935i	−2.22807	−	0.740971i
$427$	−1.76346	+	5.07794i	−0.0853398	+	0.245739i
$428$	5.88657	−	1.03796i	0.284538	−	0.0501717i
$429$	30.1693	−	11.9478i	1.45659	−	0.576846i
$430$	25.4146	+	4.48128i	1.22560	+	0.216107i
$431$	−14.5924	+	8.42491i	−0.702890	+	0.405814i	−0.808423	−	0.588602i	$-0.799679\pi$
$431$	−14.5924	+	8.42491i	−0.702890	+	0.405814i	0.105533	+	0.994416i	$0.466345\pi$
$432$	31.6504	+	22.3149i	1.52278	+	1.07362i
$433$		−	18.8726i		−	0.906959i	−0.891267	−	0.453480i	$-0.850183\pi$
$433$		−	18.8726i		−	0.906959i	0.891267	−	0.453480i	$-0.149817\pi$
$434$	−1.13970	+	7.07501i	−0.0547072	+	0.339612i
$435$	−1.63266	−	4.12260i	−0.0782800	−	0.197664i
$436$	58.6057	+	21.3307i	2.80670	+	1.02156i
$437$	5.84808	+	33.1661i	0.279752	+	1.58655i
$438$	38.0362	−	33.7759i	1.81744	−	1.61387i
$439$	10.1083	−	12.0465i	0.482441	−	0.574950i	−0.468838	−	0.883284i	$-0.655327\pi$
$439$	10.1083	−	12.0465i	0.482441	−	0.574950i	0.951278	+	0.308334i	$0.0997715\pi$
$440$	13.9132	−	24.0983i	0.663284	−	1.14884i
$441$	1.86400	−	20.9171i	0.0887617	−	0.996053i
$442$	20.2692	+	35.1072i	0.964106	+	1.66988i
$443$	−14.4942	−	2.55572i	−0.688640	−	0.121426i	−0.181631	−	0.983367i	$-0.558138\pi$
$443$	−14.4942	−	2.55572i	−0.688640	−	0.121426i	−0.507009	+	0.861941i	$0.669249\pi$
$444$	12.2516	−	22.6634i	0.581434	−	1.07556i
$445$	4.30036	+	1.56520i	0.203857	+	0.0741977i
$446$	0.597830	+	3.39046i	0.0283081	+	0.160543i
$447$	4.11266	−	2.53061i	0.194522	−	0.119694i
$448$	−1.50118	−	1.22220i	−0.0709243	−	0.0577436i
$449$	3.11418	−	1.79797i	0.146967	−	0.0848516i	−0.424713	−	0.905328i	$-0.639625\pi$
$449$	3.11418	−	1.79797i	0.146967	−	0.0848516i	0.571680	+	0.820476i	$0.306292\pi$
$450$	−17.9204	+	23.9632i	−0.844778	+	1.12964i
$451$			0.885272i			0.0416858i
$452$	−9.50370	−	26.1112i	−0.447016	−	1.22817i
$453$	4.47221	+	1.48728i	0.210123	+	0.0698787i
$454$	−17.3319	+	47.6190i	−0.813426	+	2.23487i
$455$	−12.3942	+	2.37531i	−0.581051	+	0.111356i
$456$	57.7176	−	22.8577i	2.70287	−	1.07041i
$457$	−0.424178	+	0.154388i	−0.0198422	+	0.00722197i	−0.351922	−	0.936029i	$-0.614472\pi$
$457$	−0.424178	+	0.154388i	−0.0198422	+	0.00722197i	0.332080	+	0.943251i	$0.392250\pi$
$458$	1.06111	+	1.83789i	0.0495823	+	0.0858790i
$459$	10.3321	+	14.8580i	0.482263	+	0.693510i
$460$	−24.9350	−	14.3962i	−1.16260	−	0.671227i
$461$	18.3882	+	15.4295i	0.856422	+	0.718623i	0.961194	−	0.275873i	$-0.0889669\pi$
$461$	18.3882	+	15.4295i	0.856422	+	0.718623i	−0.104772	+	0.994496i	$0.533411\pi$
$462$	−44.5055	+	18.3928i	−2.07058	+	0.855709i
$463$	−4.16621	−	23.6278i	−0.193620	−	1.09808i	−0.914370	−	0.404880i	$-0.867313\pi$
$463$	−4.16621	−	23.6278i	−0.193620	−	1.09808i	0.720750	−	0.693195i	$-0.243798\pi$
$464$	11.7124	+	13.9583i	0.543735	+	0.647998i
$465$	1.88322	−	0.386736i	0.0873324	−	0.0179345i
$466$	−9.50774	+	3.46053i	−0.440437	+	0.160306i
$467$	−19.8132	−	34.3175i	−0.916847	−	1.58803i	−0.804174	−	0.594394i	$-0.797392\pi$
$467$	−19.8132	−	34.3175i	−0.916847	−	1.58803i	−0.112673	−	0.993632i	$-0.535941\pi$
$468$	−51.7821	+	33.8978i	−2.39363	+	1.56693i
$469$	−29.8739	+	0.442683i	−1.37945	+	0.0204412i
$470$	−0.805655	−	2.21352i	−0.0371621	−	0.102102i
$471$	−22.7504	+	13.9988i	−1.04828	+	0.645029i
$472$	−23.5796	+	64.7843i	−1.08534	+	2.98194i
$473$	−13.5676	+	37.2766i	−0.623838	+	1.71398i
$474$	−21.0967	−	11.4046i	−0.969002	−	0.523831i
$475$	7.40553	+	20.3465i	0.339789	+	0.933563i
$476$	−21.3992	−	35.8279i	−0.980831	−	1.64217i
$477$	0.554861	−	1.83891i	0.0254053	−	0.0841980i
$478$	29.8557	+	51.7117i	1.36557	+	2.36524i
$479$	−11.2982	+	4.11220i	−0.516227	+	0.187891i	−0.586978	−	0.809603i	$-0.699683\pi$
$479$	−11.2982	+	4.11220i	−0.516227	+	0.187891i	0.0707512	+	0.997494i	$0.477460\pi$
$480$	−3.50256	+	10.5321i	−0.159869	+	0.480721i
$481$	9.61678	+	11.4608i	0.438487	+	0.522569i
$482$	1.81982	+	10.3207i	0.0828907	+	0.470097i
$483$	10.6269	+	25.7141i	0.483539	+	1.17003i
$484$	20.5181	+	17.2167i	0.932639	+	0.782577i
$485$	−9.38469	−	5.41825i	−0.426137	−	0.246030i
$486$	−31.3769	+	24.5357i	−1.42329	+	1.11296i
$487$	19.9583	+	34.5688i	0.904397	+	1.56646i	0.821724	+	0.569885i	$0.193012\pi$
$487$	19.9583	+	34.5688i	0.904397	+	1.56646i	0.0826731	+	0.996577i	$0.473654\pi$
$488$	−12.3365	+	4.49012i	−0.558448	+	0.203258i
$489$	0.0245541	−	0.166378i	0.00111038	−	0.00752386i
$490$	18.3396	−	3.79726i	0.828498	−	0.171543i
$491$	6.49001	−	17.8311i	0.292890	−	0.804708i	−0.702751	−	0.711436i	$-0.748045\pi$
$491$	6.49001	−	17.8311i	0.292890	−	0.804708i	0.995641	−	0.0932723i	$-0.0297327\pi$
$492$	−0.339660	−	1.65398i	−0.0153130	−	0.0745673i
$493$	2.91234	+	8.00159i	0.131165	+	0.360374i
$494$			64.5617i			2.90477i
$495$	8.84538	+	9.41618i	0.397570	+	0.423226i
$496$	−6.84185	+	3.95014i	−0.307208	+	0.177367i
$497$	−18.2921	+	22.4675i	−0.820512	+	1.00780i
$498$	1.27378	+	45.4642i	0.0570794	+	2.03730i
$499$	−2.67810	−	15.1882i	−0.119888	−	0.679919i	−0.984213	−	0.176986i	$-0.943365\pi$
$499$	−2.67810	−	15.1882i	−0.119888	−	0.679919i	0.864325	−	0.502933i	$-0.167746\pi$
$500$	−39.6759	−	14.4409i	−1.77436	−	0.645815i
$501$	−13.0449	+	0.365481i	−0.582803	+	0.0163285i
$502$	−12.9562	−	2.28453i	−0.578263	−	0.101963i
$503$	1.41541	+	2.45156i	0.0631098	+	0.109309i	0.895854	−	0.444349i	$-0.146565\pi$
$503$	1.41541	+	2.45156i	0.0631098	+	0.109309i	−0.832744	+	0.553658i	$0.813231\pi$
$504$	42.4900	−	28.7232i	1.89265	−	1.27943i
$505$	−5.74658	+	9.95337i	−0.255719	+	0.442919i
$506$	41.0122	−	48.8765i	1.82322	−	2.17282i
$507$	−2.70047	−	13.1500i	−0.119932	−	0.584013i
$508$	−14.4290	−	81.8308i	−0.640182	−	3.63065i
$509$	13.6310	+	4.96127i	0.604183	+	0.219904i	0.625956	−	0.779858i	$-0.284709\pi$
$509$	13.6310	+	4.96127i	0.604183	+	0.219904i	−0.0217733	+	0.999763i	$0.506931\pi$
$510$	−10.0242	+	12.6495i	−0.443877	+	0.560131i
$511$	−10.8231	−	28.4188i	−0.478785	−	1.25717i
$512$			50.7044i			2.24084i
$513$	2.41904	+	28.7202i	0.106803	+	1.26803i
$514$	52.8077	−	30.4885i	2.32925	−	1.34479i
$515$	11.5133	+	2.03011i	0.507338	+	0.0894574i
$516$	11.0465	−	74.8506i	0.486296	−	3.29512i
$517$	3.56588	−	0.628762i	0.156827	−	0.0276529i
$518$	−14.5223	−	16.7953i	−0.638075	−	0.737941i
$519$	4.93438	+	24.0281i	0.216595	+	1.05472i
$520$	−23.6102	−	19.8113i	−1.03538	−	0.868784i
$521$	−13.0627			−0.572288			−0.286144	−	0.958187i	$-0.592374\pi$
$521$	−13.0627			−0.572288			−0.286144	+	0.958187i	$0.592374\pi$
$522$	−17.2245	+	7.38588i	−0.753896	+	0.323271i
$523$		−	3.97179i		−	0.173674i	−0.996223	−	0.0868370i	$-0.972324\pi$
$523$		−	3.97179i		−	0.173674i	0.996223	−	0.0868370i	$-0.0276759\pi$
$524$	52.7951	−	19.2158i	2.30636	−	0.839448i
$525$	9.59929	+	15.0947i	0.418948	+	0.658787i
$526$	33.3998	−	28.0258i	1.45630	−	1.22198i
$527$	−3.63585	+	0.641099i	−0.158380	+	0.0279267i
$528$	−46.7020	−	25.2466i	−2.03244	−	1.09872i
$529$	−10.6205	−	8.91168i	−0.461762	−	0.387464i
$530$	1.71304			0.0744097
$531$	−25.6333	−	19.1694i	−1.11239	−	0.831881i
$532$	−0.984763	−	66.4555i	−0.0426949	−	2.88121i
$533$	0.965647	+	0.170270i	0.0418268	+	0.00737519i
$534$	6.10385	−	18.3540i	0.264139	−	0.794257i
$535$	−1.36101	+	0.239983i	−0.0588417	+	0.0103754i
$536$	−46.9030	−	55.8968i	−2.02590	−	2.41437i
$537$	25.4109	+	3.75015i	1.09656	+	0.161831i
$538$	−2.07794	+	2.47639i	−0.0895863	+	0.106765i
$539$	0.853019	+	28.7762i	0.0367421	+	1.23948i
$540$	−20.1389	−	14.1988i	−0.866639	−	0.611018i
$541$	−2.33907	+	4.05139i	−0.100564	+	0.174183i	−0.911917	−	0.410374i	$-0.865398\pi$
$541$	−2.33907	+	4.05139i	−0.100564	+	0.174183i	0.811353	+	0.584557i	$0.198732\pi$
$542$	−0.226032	+	1.28189i	−0.00970890	+	0.0550619i
$543$	15.8128	+	2.33367i	0.678594	+	0.100147i
$544$	7.28999	−	20.0291i	0.312556	−	0.858739i
$545$	−13.5500	−	4.93180i	−0.580419	−	0.211255i
$546$	11.5027	+	52.0838i	0.492268	+	2.22898i
$547$	5.54303	−	31.4361i	0.237003	−	1.34411i	−0.601352	−	0.798985i	$-0.705371\pi$
$547$	5.54303	−	31.4361i	0.237003	−	1.34411i	0.838354	−	0.545126i	$-0.183518\pi$
$548$	12.6152	−	7.28341i	0.538897	−	0.311132i
$549$	−0.341271	−	6.08560i	−0.0145651	−	0.259727i
$550$	20.5105	−	35.5253i	0.874572	−	1.51480i
$551$	−2.35489	+	13.3552i	−0.100322	+	0.568952i
$552$	−32.3148	+	59.7770i	−1.37541	+	2.54428i
$553$	−10.8449	+	9.37728i	−0.461174	+	0.398763i
$554$	−11.6542	−	13.8890i	−0.495141	−	0.590086i
$555$	−2.83264	+	5.23992i	−0.120239	+	0.222422i
$556$	−20.7228	+	24.6965i	−0.878842	+	1.04736i
$557$	−5.76159	−	3.32646i	−0.244127	−	0.140947i	0.372945	−	0.927853i	$-0.378348\pi$
$557$	−5.76159	−	3.32646i	−0.244127	−	0.140947i	−0.617072	+	0.786907i	$0.711681\pi$
$558$	−1.85686	−	7.91073i	−0.0786070	−	0.334888i
$559$	38.0515	+	21.9690i	1.60940	+	0.929190i
$560$	16.0115	+	13.0358i	0.676607	+	0.550865i
$561$	−16.4732	−	18.5511i	−0.695501	−	0.783228i
$562$	−23.0470	+	19.3387i	−0.972178	+	0.815754i
$563$	22.8963	−	19.2123i	0.964963	−	0.809700i	−0.0167900	−	0.999859i	$-0.505345\pi$
$563$	22.8963	−	19.2123i	0.964963	−	0.809700i	0.981753	+	0.190159i	$0.0609002\pi$
$564$	−6.42101	+	2.54289i	−0.270373	+	0.107075i
$565$	2.19732	+	6.03708i	0.0924418	+	0.253982i
$566$	19.7473			0.830039
$567$	7.06846	+	22.7384i	0.296847	+	0.954925i
$568$	−70.7579			−2.96894
$569$	−3.17529	−	8.72404i	−0.133115	−	0.365731i	0.855170	−	0.518347i	$-0.173452\pi$
$569$	−3.17529	−	8.72404i	−0.133115	−	0.365731i	−0.988286	+	0.152616i	$0.951230\pi$
$570$	−23.8986	+	9.46447i	−1.00100	+	0.396423i
$571$	13.5798	−	11.3948i	0.568296	−	0.476857i	−0.312784	−	0.949824i	$-0.601262\pi$
$571$	13.5798	−	11.3948i	0.568296	−	0.476857i	0.881080	+	0.472968i	$0.156817\pi$
$572$	64.9955	−	54.5377i	2.71760	−	2.28033i
$573$	−23.7137	−	26.7048i	−0.990653	−	1.11561i
$574$	−1.43667	−	0.231429i	−0.0599653	−	0.00965968i
$575$	−20.5256	−	11.8505i	−0.855976	−	0.494198i
$576$	2.10142	+	0.634067i	0.0875590	+	0.0264195i
$577$	−30.7652	−	17.7623i	−1.28077	−	0.739454i	−0.303783	−	0.952741i	$-0.598250\pi$
$577$	−30.7652	−	17.7623i	−1.28077	−	0.739454i	−0.976990	+	0.213287i	$0.931583\pi$
$578$	−7.99847	+	9.53221i	−0.332693	+	0.396488i
$579$	6.61550	−	12.2376i	0.274931	−	0.508577i
$580$	−7.45252	−	8.88156i	−0.309449	−	0.368787i
$581$	25.6853	+	8.91995i	1.06560	+	0.370062i
$582$	−21.7809	+	40.2911i	−0.902848	+	1.67012i
$583$	−0.457253	+	2.59321i	−0.0189375	+	0.107400i
$584$	37.1346	−	64.3190i	1.53664	−	2.66154i
$585$	11.9724	−	7.83739i	0.494996	−	0.324036i
$586$	22.2085	−	12.8221i	0.917423	−	0.529675i
$587$	−4.89817	+	27.7789i	−0.202169	+	1.14656i	0.699664	+	0.714472i	$0.253333\pi$
$587$	−4.89817	+	27.7789i	−0.202169	+	1.14656i	−0.901833	+	0.432085i	$0.857778\pi$
$588$	−12.6345	−	53.4361i	−0.521038	−	2.20367i
$589$	−5.52522	−	2.01102i	−0.227663	−	0.0828625i
$590$	9.76338	−	26.8247i	0.401952	−	1.10435i
$591$	−37.5491	−	5.54152i	−1.54456	−	0.227948i
$592$	4.25047	−	24.1056i	0.174693	−	0.990736i
$593$	−13.6717	+	23.6801i	−0.561429	+	0.972424i	0.435943	+	0.899974i	$0.356415\pi$
$593$	−13.6717	+	23.6801i	−0.561429	+	0.972424i	−0.997372	+	0.0724497i	$0.976918\pi$
$594$	38.7358	−	38.4858i	1.58935	−	1.57909i
$595$	4.94764	+	8.28363i	0.202833	+	0.339596i
$596$	8.11597	−	9.67224i	0.332443	−	0.396190i
$597$	29.4563	+	4.34718i	1.20557	+	0.177918i
$598$	−45.4259	−	54.1364i	−1.85760	−	2.21380i
$599$	−24.7808	+	4.36953i	−1.01252	+	0.178534i	−0.655205	−	0.755451i	$-0.727418\pi$
$599$	−24.7808	+	4.36953i	−1.01252	+	0.178534i	−0.357312	+	0.933985i	$0.616307\pi$
$600$	−13.7867	+	41.4560i	−0.562839	+	1.69244i
$601$	13.1380	+	2.31659i	0.535912	+	0.0944957i	0.435053	−	0.900405i	$-0.356730\pi$
$601$	13.1380	+	2.31659i	0.535912	+	0.0944957i	0.100859	+	0.994901i	$0.467841\pi$
$602$	−56.9476	−	31.7631i	−2.32101	−	1.29457i
$603$	31.1358	−	13.3510i	1.26795	−	0.543697i
$604$	12.3233			0.501429
$605$	−4.74391	−	3.98061i	−0.192867	−	0.161835i
$606$	42.7326	+	23.1008i	1.73589	+	0.938404i
$607$	−23.9188	+	4.21753i	−0.970835	+	0.171184i	−0.636506	−	0.771272i	$-0.719621\pi$
$607$	−23.9188	+	4.21753i	−0.970835	+	0.171184i	−0.334329	+	0.942456i	$0.608510\pi$
$608$	26.0039	−	21.8199i	1.05460	−	0.884912i
$609$	0.479683	+	11.1936i	0.0194377	+	0.453588i
$610$	5.10807	−	1.85919i	0.206820	−	0.0752762i
$611$		−	4.01057i		−	0.162250i
$612$	37.8951	+	28.3392i	1.53182	+	1.14554i
$613$	22.4413			0.906395			0.453197	−	0.891410i	$-0.350283\pi$
$613$	22.4413			0.906395			0.453197	+	0.891410i	$0.350283\pi$
$614$	45.6001	+	38.2630i	1.84027	+	1.54417i
$615$	0.0785315	+	0.382411i	0.00316669	+	0.0154203i
$616$	−53.1850	+	45.9874i	−2.14288	+	1.85289i
$617$	−3.16928	+	0.558829i	−0.127590	+	0.0224976i	−0.237079	−	0.971490i	$-0.576190\pi$
$617$	−3.16928	+	0.558829i	−0.127590	+	0.0224976i	0.109488	+	0.993988i	$0.465079\pi$
$618$	7.21425	−	48.8834i	0.290200	−	1.96638i
$619$	4.74774	+	0.837155i	0.190828	+	0.0336481i	0.268245	−	0.963351i	$-0.413556\pi$
$619$	4.74774	+	0.837155i	0.190828	+	0.0336481i	−0.0774173	+	0.996999i	$0.524667\pi$
$620$	4.35341	−	2.51344i	0.174837	−	0.100942i
$621$	−22.2361	−	22.3805i	−0.892304	−	0.898099i
$622$			24.4391i			0.979920i
$623$	−8.96711	−	7.30065i	−0.359260	−	0.292494i
$624$	−36.5212	+	46.0863i	−1.46202	+	1.84493i
$625$	−9.16750	−	3.33670i	−0.366700	−	0.133468i
$626$	2.96647	+	16.8237i	0.118564	+	0.672410i
$627$	−7.94823	−	38.7041i	−0.317422	−	1.54569i
$628$	−44.8958	+	53.5047i	−1.79154	+	2.13507i
$629$	5.71938	−	9.90625i	0.228047	−	0.394988i
$630$	−17.5935	+	11.8932i	−0.700940	+	0.473835i
$631$	12.8825	+	22.3131i	0.512843	+	0.888271i	0.999889	+	0.0148943i	$0.00474119\pi$
$631$	12.8825	+	22.3131i	0.512843	+	0.888271i	−0.487046	+	0.873377i	$0.661925\pi$
$632$	−34.4825	−	6.08020i	−1.37164	−	0.241857i
$633$	27.1985	−	0.762025i	1.08104	−	0.0302878i
$634$	−5.98451	−	2.17819i	−0.237675	−	0.0865068i
$635$	3.33607	+	18.9198i	0.132388	+	0.750810i
$636$	−0.140658	−	5.02041i	−0.00557744	−	0.199072i
$637$	31.5528	+	4.60422i	1.25017	+	0.182426i
$638$	22.2502	−	12.8461i	0.880892	−	0.508584i
$639$	9.48978	−	31.4509i	0.375410	−	1.24418i
$640$		−	10.8587i		−	0.429227i
$641$	5.98065	+	16.4317i	0.236222	+	0.649014i	0.999994	+	0.00352769i	$0.00112290\pi$
$641$	5.98065	+	16.4317i	0.236222	+	0.649014i	−0.763772	+	0.645486i	$0.776655\pi$
$642$	1.17502	+	5.72179i	0.0463743	+	0.225821i
$643$	−1.98614	+	5.45689i	−0.0783259	+	0.215199i	−0.972675	−	0.232171i	$-0.925417\pi$
$643$	−1.98614	+	5.45689i	−0.0783259	+	0.215199i	0.894349	+	0.447370i	$0.147639\pi$
$644$	47.5841	+	55.0315i	1.87508	+	2.16855i
$645$	−2.55403	+	17.3060i	−0.100565	+	0.681421i
$646$	46.3850	−	16.8828i	1.82499	−	0.664243i
$647$	19.8634	+	34.4044i	0.780910	+	1.35258i	0.931412	+	0.363966i	$0.118577\pi$
$647$	19.8634	+	34.4044i	0.780910	+	1.35258i	−0.150503	+	0.988610i	$0.548089\pi$
$648$	−32.1659	+	48.4492i	−1.26360	+	1.90326i
$649$	38.0012	+	21.9400i	1.49168	+	0.861221i
$650$	−34.8057	−	29.2055i	−1.36519	−	1.14553i
$651$	−4.81565	−	0.637942i	−0.188740	−	0.0250029i
$652$	−0.0763610	−	0.433065i	−0.00299053	−	0.0169601i
$653$	−2.86765	−	3.41754i	−0.112220	−	0.133739i	0.707010	−	0.707203i	$-0.250043\pi$
$653$	−2.86765	−	3.41754i	−0.112220	−	0.133739i	−0.819230	+	0.573465i	$0.805599\pi$
$654$	−19.2326	+	57.8317i	−0.752055	+	2.26140i
$655$	−12.2066	+	4.44282i	−0.476950	+	0.173596i
$656$	−0.802125	−	1.38932i	−0.0313177	−	0.0542438i
$657$	23.6086	+	25.1320i	0.921058	+	0.980494i
$658$	0.0881883	+	5.95128i	0.00343794	+	0.232005i
$659$	12.2037	+	33.5295i	0.475390	+	1.30612i	0.913367	+	0.407136i	$0.133473\pi$
$659$	12.2037	+	33.5295i	0.475390	+	1.30612i	−0.437978	+	0.898986i	$0.644305\pi$
$660$	29.7161	+	16.0642i	1.15670	+	0.625298i
$661$	−8.52482	+	23.4218i	−0.331577	+	0.911001i	0.656125	+	0.754652i	$0.272194\pi$
$661$	−8.52482	+	23.4218i	−0.331577	+	0.911001i	−0.987702	+	0.156348i	$0.950028\pi$
$662$	26.7870	−	73.5968i	1.04111	−	2.86042i
$663$	−23.4038	+	14.4008i	−0.908927	+	0.559282i
$664$	22.7120	+	62.4006i	0.881395	+	2.42161i
$665$	0.227683	+	15.3649i	0.00882919	+	0.595827i
$666$	22.4737	+	11.3475i	0.870836	+	0.439706i
$667$	−7.42217	−	12.8556i	−0.287387	−	0.497770i
$668$	−32.0645	+	11.6705i	−1.24061	+	0.451547i
$669$	−2.28602	+	0.469454i	−0.0883826	+	0.0181501i
$670$	19.4207	+	23.1447i	0.750287	+	0.894157i
$671$	1.45097	+	8.22888i	0.0560142	+	0.317673i
$672$	17.0905	−	22.2357i	0.659282	−	0.857760i
$673$	−26.8068	−	22.4936i	−1.03333	−	0.867064i	−0.0420841	−	0.999114i	$-0.513400\pi$
$673$	−26.8068	−	22.4936i	−1.03333	−	0.867064i	−0.991243	+	0.132050i	$0.957844\pi$
$674$	−27.5221	−	15.8899i	−1.06011	−	0.612056i
$675$	−16.5776	−	11.6879i	−0.638072	−	0.449868i
$676$	−17.5507	−	30.3987i	−0.675026	−	1.16918i
$677$	−5.78121	+	2.10419i	−0.222190	+	0.0808706i	−0.450717	−	0.892667i	$-0.648831\pi$
$677$	−5.78121	+	2.10419i	−0.222190	+	0.0808706i	0.228526	+	0.973538i	$0.426609\pi$
$678$	25.2462	−	9.99814i	0.969574	−	0.383976i
$679$	17.9091	+	20.7120i	0.687286	+	0.794854i
$680$	−8.05962	+	22.1436i	−0.309072	+	0.849169i
$681$	−32.5955	−	10.8400i	−1.24906	−	0.415391i
$682$	3.80994	+	10.4677i	0.145890	+	0.400830i
$683$		−	31.8592i		−	1.21906i	−0.792764	−	0.609529i	$-0.791358\pi$
$683$		−	31.8592i		−	1.21906i	0.792764	−	0.609529i	$-0.208642\pi$
$684$	29.6999	+	69.2626i	1.13560	+	2.64832i
$685$	−2.91673	+	1.68397i	−0.111442	+	0.0643413i
$686$	−46.9225	−	6.13838i	−1.79151	−	0.234365i
$687$	−1.22521	+	0.753895i	−0.0467445	+	0.0287629i
$688$	−12.4829	−	70.7941i	−0.475906	−	2.69900i
$689$	2.74070	+	0.997534i	0.104412	+	0.0380030i
$690$	13.3803	−	24.7513i	0.509379	−	0.942267i
$691$	−42.6451	−	7.51949i	−1.62230	−	0.286055i	−0.712676	−	0.701493i	$-0.752517\pi$
$691$	−42.6451	−	7.51949i	−1.62230	−	0.286055i	−0.909621	+	0.415438i	$0.863628\pi$
$692$	32.0691	+	55.5453i	1.21908	+	2.11152i
$693$	−13.3078	−	29.8076i	−0.505521	−	1.13230i
$694$	−9.32333	+	16.1485i	−0.353909	+	0.612988i
$695$	4.79124	−	5.70998i	0.181742	−	0.216592i
$696$	−20.4604	+	18.1687i	−0.775548	+	0.688681i
$697$	−0.130183	−	0.738303i	−0.00493103	−	0.0279652i
$698$	41.8883	+	15.2461i	1.58550	+	0.577073i
$699$	−2.52535	−	6.37672i	−0.0955174	−	0.241190i
$700$	36.2722	+	29.5313i	1.37096	+	1.11618i
$701$		−	3.02278i		−	0.114169i	−0.998369	−	0.0570845i	$-0.981820\pi$
$701$		−	3.02278i		−	0.114169i	0.998369	−	0.0570845i	$-0.0181804\pi$
$702$	−34.5297	−	49.6548i	−1.30324	−	1.87410i
$703$	15.7768	−	9.10874i	0.595033	−	0.343543i
$704$	−2.96339	−	0.522525i	−0.111687	−	0.0196934i
$705$	1.48458	−	0.587932i	0.0559125	−	0.0221428i
$706$	54.7412	−	9.65235i	2.06021	−	0.363271i
$707$	21.9671	−	18.9943i	0.826158	−	0.714353i
$708$	−79.4168	−	26.4110i	−2.98467	−	0.992586i
$709$	−25.5968	−	21.4783i	−0.961309	−	0.806634i	0.0198565	−	0.999803i	$-0.493679\pi$
$709$	−25.5968	−	21.4783i	−0.961309	−	0.806634i	−0.981166	+	0.193169i	$0.938123\pi$
$710$	29.2981			1.09954
$711$	7.32723	−	14.5116i	0.274793	−	0.544226i
$712$		−	28.2405i		−	1.05836i
$713$	6.04798	−	2.20128i	0.226499	−	0.0824388i
$714$	34.4122	−	21.8840i	1.28784	−	0.818988i
$715$	−15.0274	+	12.6095i	−0.561992	+	0.471567i
$716$	66.1420	−	11.6626i	2.47184	−	0.435852i
$717$	−34.4729	+	21.2119i	−1.28741	+	0.792172i
$718$	25.4283	+	21.3368i	0.948974	+	0.796284i
$719$	−31.0029			−1.15621			−0.578106	−	0.815961i	$-0.696208\pi$
$719$	−31.0029			−1.15621			−0.578106	+	0.815961i	$0.696208\pi$
$720$	−22.4135	−	6.76289i	−0.835300	−	0.252038i
$721$	−25.7984	−	14.3893i	−0.960783	−	0.535886i
$722$	29.6093	+	5.22093i	1.10195	+	0.194303i
$723$	−6.95876	+	1.42904i	−0.258799	+	0.0531466i
$724$	41.1593	−	7.25749i	1.52967	−	0.269722i
$725$	−6.13464	−	7.31098i	−0.227835	−	0.271523i
$726$	−16.2563	+	20.5139i	−0.603328	+	0.761343i
$727$	−1.31648	+	1.56892i	−0.0488256	+	0.0581881i	−0.789905	−	0.613230i	$-0.789870\pi$
$727$	−1.31648	+	1.56892i	−0.0488256	+	0.0581881i	0.741079	+	0.671418i	$0.234314\pi$
$728$	39.9333	+	66.8587i	1.48003	+	2.47795i
$729$	−17.2210	−	20.7951i	−0.637815	−	0.770190i
$730$	−15.3760	+	26.6320i	−0.569091	+	0.985695i
$731$	5.83348	−	33.0833i	0.215759	−	1.22363i
$732$	−5.86814	−	14.8176i	−0.216893	−	0.547673i
$733$	−7.29080	+	20.0313i	−0.269292	+	0.739874i	0.729165	+	0.684338i	$0.239909\pi$
$733$	−7.29080	+	20.0313i	−0.269292	+	0.739874i	−0.998457	+	0.0555354i	$0.982313\pi$
$734$	7.03590	+	2.56086i	0.259700	+	0.0945230i
$735$	2.92118	+	12.3548i	0.107749	+	0.455713i
$736$	−6.45231	+	36.5929i	−0.237835	+	1.34883i
$737$	−40.2204	+	23.2213i	−1.48154	+	0.855366i
$738$	1.60637	−	0.377057i	0.0591312	−	0.0138797i
$739$	9.85260	−	17.0652i	0.362434	−	0.627754i	−0.625927	−	0.779882i	$-0.715279\pi$
$739$	9.85260	−	17.0652i	0.362434	−	0.627754i	0.988361	+	0.152128i	$0.0486126\pi$
$740$	−2.70454	+	15.3382i	−0.0994210	+	0.563844i
$741$	−43.7469	+	1.22566i	−1.60708	+	0.0450259i
$742$	−4.08886	−	1.41998i	−0.150107	−	0.0521289i
$743$	6.53488	+	7.78797i	0.239741	+	0.285713i	0.872477	−	0.488655i	$-0.162512\pi$
$743$	6.53488	+	7.78797i	0.239741	+	0.285713i	−0.632735	+	0.774368i	$0.718068\pi$
$744$	−6.21734	−	10.1042i	−0.227939	−	0.370439i
$745$	−1.87646	+	2.23628i	−0.0687484	+	0.0819311i
$746$	−8.20333	−	4.73619i	−0.300345	−	0.173404i
$747$	−30.7822	+	1.72622i	−1.12626	+	0.0631590i
$748$	−56.1793	−	32.4351i	−2.05412	−	1.18595i
$749$	3.44753	+	0.555355i	0.125970	+	0.0202922i
$750$	13.0205	−	39.1520i	0.475440	−	1.42963i
$751$	14.0359	−	11.7775i	0.512177	−	0.429768i	−0.349717	−	0.936855i	$-0.613722\pi$
$751$	14.0359	−	11.7775i	0.512177	−	0.429768i	0.861895	+	0.507087i	$0.169278\pi$
$752$	−5.02649	+	4.21772i	−0.183297	+	0.153805i
$753$	1.30202	−	8.82245i	0.0474484	−	0.321508i
$754$	−9.73294	−	26.7410i	−0.354453	−	0.973851i
$755$	−2.84923			−0.103694
$756$	36.2999	+	50.5846i	1.32022	+	1.83975i
$757$	−11.2021			−0.407149			−0.203574	−	0.979059i	$-0.565256\pi$
$757$	−11.2021			−0.407149			−0.203574	+	0.979059i	$0.565256\pi$
$758$	29.3693	+	80.6915i	1.06674	+	2.93085i
$759$	33.8972	+	26.8619i	1.23039	+	0.975025i
$760$	−28.7492	+	24.1234i	−1.04284	+	0.875049i
$761$	−7.89879	+	6.62787i	−0.286331	+	0.240260i	−0.774628	−	0.632417i	$-0.782063\pi$
$761$	−7.89879	+	6.62787i	−0.286331	+	0.240260i	0.488297	+	0.872678i	$0.337618\pi$
$762$	79.5401	−	16.3343i	2.88143	−	0.591728i
$763$	28.2545	+	23.0036i	1.02288	+	0.832787i
$764$	−80.8716	−	46.6912i	−2.92583	−	1.68923i
$765$	−8.76160	−	6.55220i	−0.316776	−	0.236895i
$766$	−59.8177	−	34.5358i	−2.16130	−	1.24783i
$767$	31.2410	−	37.2315i	1.12805	−	1.34435i
$768$	−48.4108	+	1.35633i	−1.74688	+	0.0489425i
$769$	−27.7396	−	33.0588i	−1.00032	−	1.19213i	−0.981334	−	0.192312i	$-0.938402\pi$
$769$	−27.7396	−	33.0588i	−1.00032	−	1.19213i	−0.0189831	−	0.999820i	$-0.506043\pi$
$770$	22.0218	−	19.0416i	0.793612	−	0.686212i
$771$	21.6615	+	35.2035i	0.780119	+	1.26782i
$772$	6.31633	−	35.8217i	0.227330	−	1.28925i
$773$	−5.50170	+	9.52923i	−0.197882	+	0.342743i	−0.947842	−	0.318742i	$-0.896740\pi$
$773$	−5.50170	+	9.52923i	−0.197882	+	0.342743i	0.749959	+	0.661484i	$0.230073\pi$
$774$	73.4189	+	8.74208i	2.63899	+	0.314228i
$775$	3.58357	−	2.06898i	0.128726	−	0.0743199i
$776$	−11.6122	+	65.8559i	−0.416853	+	2.36409i
$777$	11.1047	−	10.1592i	0.398380	−	0.364458i
$778$	90.1500	+	32.8119i	3.23203	+	1.17636i
$779$	0.408361	−	1.12196i	0.0146311	−	0.0401985i
$780$	23.2381	−	29.3243i	0.832059	−	1.04998i
$781$	−7.82039	+	44.3516i	−0.279835	+	1.58703i
$782$	−27.0161	+	46.7932i	−0.966093	+	1.67332i
$783$	−5.33165	−	11.5311i	−0.190538	−	0.412086i
$784$	−27.4121	−	44.3875i	−0.979004	−	1.58527i
$785$	10.3802	−	12.3706i	0.370485	−	0.441527i
$786$	20.2156	+	51.0461i	0.721065	+	1.82075i
$787$	−12.1770	−	14.5120i	−0.434064	−	0.517298i	0.504026	−	0.863688i	$-0.331852\pi$
$787$	−12.1770	−	14.5120i	−0.434064	−	0.517298i	−0.938090	+	0.346391i	$0.887407\pi$
$788$	−97.7365	+	17.2336i	−3.48172	+	0.613921i
$789$	19.6243	+	22.0996i	0.698643	+	0.786766i
$790$	14.2779	+	2.51758i	0.507984	+	0.0895713i
$791$	−0.240522	−	16.2313i	−0.00855197	−	0.577119i
$792$	35.9337	−	71.1666i	1.27685	−	2.52879i
$793$	9.25506			0.328657
$794$	−61.4950	−	51.6005i	−2.18238	−	1.83123i
$795$	0.0325210	+	1.16075i	0.00115340	+	0.0411676i
$796$	76.6719	−	13.5193i	2.71756	−	0.479180i
$797$	−26.1233	+	21.9201i	−0.925336	+	0.776449i	−0.974974	−	0.222318i	$-0.928638\pi$
$797$	−26.1233	+	21.9201i	−0.925336	+	0.776449i	0.0496383	+	0.998767i	$0.484193\pi$
$798$	64.8890	−	2.78071i	2.29705	−	0.0984361i
$799$	−2.88143	+	1.04876i	−0.101938	+	0.0371023i
$800$			23.8895i			0.844620i
$801$	12.5525	+	3.78751i	0.443522	+	0.133825i
$802$	−62.5561			−2.20893
$803$	−36.2115	−	30.3850i	−1.27787	−	1.07226i
$804$	66.2356	−	58.8167i	2.33595	−	2.07431i
$805$	−11.0017	−	12.7236i	−0.387761	−	0.448450i
$806$	12.1509	−	2.14253i	0.427997	−	0.0754674i
$807$	−1.71745	−	1.36099i	−0.0604569	−	0.0479093i
$808$	69.8466	+	12.3158i	2.45719	+	0.433269i
$809$	0.963498	−	0.556276i	0.0338748	−	0.0195576i	−0.482967	−	0.875639i	$-0.660441\pi$
$809$	0.963498	−	0.556276i	0.0338748	−	0.0195576i	0.516842	+	0.856081i	$0.327108\pi$
$810$	13.3187	−	20.0609i	0.467970	−	0.704869i
$811$		−	29.7633i		−	1.04513i	−0.852599	−	0.522566i	$-0.824975\pi$
$811$		−	29.7633i		−	1.04513i	0.852599	−	0.522566i	$-0.175025\pi$
$812$	10.4263	+	27.3770i	0.365892	+	0.960744i
$813$	−0.872897	−	0.128823i	−0.0306138	−	0.00451801i
$814$	−32.4322	−	11.8044i	−1.13675	−	0.413743i
$815$	0.0176552	+	0.100127i	0.000618433	+	0.00350731i
$816$	42.6613	+	14.1875i	1.49345	+	0.496663i
$817$	34.3901	−	40.9846i	1.20316	−	1.43387i
$818$	−17.7116	+	30.6774i	−0.619271	+	1.07261i
$819$	−35.0735	+	8.78295i	−1.22557	+	0.306901i
$820$	0.510385	+	0.884013i	0.0178234	+	0.0308711i
$821$	33.9602	+	5.98811i	1.18522	+	0.208986i	0.731300	−	0.682056i	$-0.238914\pi$
$821$	33.9602	+	5.98811i	1.18522	+	0.208986i	0.453921	+	0.891042i	$0.350025\pi$
$822$	7.45994	+	12.1237i	0.260195	+	0.422861i
$823$	33.0036	+	12.0123i	1.15043	+	0.418723i	0.845670	−	0.533706i	$-0.179201\pi$
$823$	33.0036	+	12.0123i	1.15043	+	0.418723i	0.304762	+	0.952429i	$0.401423\pi$
$824$	−12.5278	−	71.0485i	−0.436425	−	2.47509i
$825$	24.4612	+	13.2235i	0.851631	+	0.460382i
$826$	−45.5398	+	55.9348i	−1.58453	+	1.94622i
$827$	12.1233	−	6.99937i	0.421567	−	0.243392i	−0.274180	−	0.961678i	$-0.588407\pi$
$827$	12.1233	−	6.99937i	0.421567	−	0.243392i	0.695748	+	0.718286i	$0.255073\pi$
$828$	−73.6374	−	37.1813i	−2.55908	−	1.29214i
$829$			35.3511i			1.22780i	0.789386	+	0.613898i	$0.210399\pi$
$829$			35.3511i			1.22780i	−0.789386	+	0.613898i	$0.789601\pi$
$830$	−9.40414	−	25.8377i	−0.326423	−	0.896839i
$831$	9.18988	−	8.16055i	0.318794	−	0.283086i
$832$	−1.13993	+	3.13194i	−0.0395200	+	0.108580i
$833$	−4.94305	−	23.8734i	−0.171267	−	0.827165i
$834$	−24.6915	−	19.5668i	−0.854995	−	0.677543i
$835$	7.41353	−	2.69830i	0.256556	−	0.0933786i
$836$	−51.6565	−	89.4717i	−1.78658	−	3.09444i
$837$	5.32504	−	1.40838i	0.184060	−	0.0486808i
$838$	49.7213	+	28.7066i	1.71759	+	0.991654i
$839$	−16.5214	−	13.8631i	−0.570381	−	0.478607i	0.311391	−	0.950282i	$-0.399205\pi$
$839$	−16.5214	−	13.8631i	−0.570381	−	0.478607i	−0.881772	+	0.471675i	$0.843650\pi$
$840$	−18.8948	+	24.5832i	−0.651934	+	0.848200i
$841$	3.99782	+	22.6728i	0.137856	+	0.781819i
$842$	16.0398	+	19.1155i	0.552767	+	0.658762i
$843$	−13.5414	−	15.2494i	−0.466390	−	0.525218i
$844$	66.8542	−	24.3329i	2.30122	−	0.837574i
$845$	4.05783	+	7.02837i	0.139594	+	0.241783i
$846$	−2.65971	−	6.20266i	−0.0914426	−	0.213252i
$847$	8.02364	+	13.4337i	0.275696	+	0.461586i
$848$	−1.63205	−	4.48401i	−0.0560447	−	0.153982i
$849$	0.374889	+	13.3807i	0.0128662	+	0.459224i
$850$	−11.8813	+	32.6437i	−0.407526	+	1.11967i
$851$	−6.82025	+	18.7385i	−0.233795	+	0.642347i
$852$	−2.40567	−	85.8640i	−0.0824168	−	2.94165i
$853$	9.78005	+	26.8705i	0.334863	+	0.920028i	0.986827	+	0.161778i	$0.0517229\pi$
$853$	9.78005	+	26.8705i	0.334863	+	0.920028i	−0.651964	+	0.758249i	$0.726055\pi$
$854$	−13.7336	+	0.203509i	−0.469954	+	0.00696395i
$855$	−6.86680	−	16.0140i	−0.234840	−	0.547666i
$856$	4.26417	+	7.38576i	0.145746	+	0.252440i
$857$	−8.21388	+	2.98961i	−0.280581	+	0.102123i	−0.478477	−	0.878100i	$-0.658811\pi$
$857$	−8.21388	+	2.98961i	−0.280581	+	0.102123i	0.197897	+	0.980223i	$0.436589\pi$
$858$	55.0530	+	61.9971i	1.87948	+	2.11655i
$859$	−18.8402	−	22.4529i	−0.642819	−	0.766082i	0.341994	−	0.939702i	$-0.388898\pi$
$859$	−18.8402	−	22.4529i	−0.642819	−	0.766082i	−0.984813	+	0.173620i	$0.944453\pi$
$860$	7.94277	+	45.0457i	0.270846	+	1.53605i
$861$	0.129542	−	0.977875i	0.00441477	−	0.0333259i
$862$	−32.9813	−	27.6746i	−1.12335	−	0.942601i
$863$	−11.0734	−	6.39323i	−0.376943	−	0.217628i	0.299544	−	0.954082i	$-0.403165\pi$
$863$	−11.0734	−	6.39323i	−0.376943	−	0.217628i	−0.676487	+	0.736454i	$0.736499\pi$
$864$	−8.32979	+	30.6895i	−0.283385	+	1.04408i
$865$	−7.41458	−	12.8424i	−0.252103	−	0.436656i
$866$	45.3144	−	16.4931i	1.53985	−	0.560458i
$867$	−6.61085	−	5.23878i	−0.224516	−	0.177918i
$868$	−12.4746	+	2.39071i	−0.423416	+	0.0811461i
$869$	−7.62224	+	20.9419i	−0.258567	+	0.710406i
$870$	8.47184	−	7.52294i	0.287222	−	0.255051i
$871$	17.5937	+	48.3383i	0.596140	+	1.63788i
$872$			88.9832i			3.01335i
$873$	−27.7147	−	13.9938i	−0.937999	−	0.473618i
$874$	−74.5233	+	43.0261i	−2.52079	+	1.45538i
$875$	−19.1282	−	15.5734i	−0.646653	−	0.526477i
$876$	79.3131	+	42.8757i	2.67974	+	1.44864i
$877$	1.33790	+	7.58764i	0.0451778	+	0.256216i	0.999029	−	0.0440646i	$-0.0140307\pi$
$877$	1.33790	+	7.58764i	0.0451778	+	0.256216i	−0.953851	+	0.300281i	$0.902920\pi$
$878$	37.7583	+	13.7429i	1.27428	+	0.463801i
$879$	9.10981	+	14.8050i	0.307266	+	0.499360i
$880$	31.6072	+	5.57319i	1.06548	+	0.187872i
$881$	−21.4033	−	37.0716i	−0.721095	−	1.24897i	−0.960561	−	0.278068i	$-0.910306\pi$
$881$	−21.4033	−	37.0716i	−0.721095	−	1.24897i	0.239466	−	0.970905i	$-0.423027\pi$
$882$	51.8524	−	13.8042i	1.74596	−	0.464813i
$883$	16.7356	−	28.9869i	0.563197	−	0.975486i	−0.434018	−	0.900904i	$-0.642905\pi$
$883$	16.7356	−	28.9869i	0.563197	−	0.975486i	0.997215	−	0.0745816i	$-0.0237621\pi$
$884$	−46.1852	+	55.0414i	−1.55338	+	1.85124i
$885$	18.3617	+	6.10639i	0.617221	+	0.205264i
$886$	−6.53027	−	37.0350i	−0.219389	−	1.24422i
$887$	−2.06145	−	0.750308i	−0.0692169	−	0.0251929i	0.307180	−	0.951652i	$-0.400615\pi$
$887$	−2.06145	−	0.750308i	−0.0692169	−	0.0251929i	−0.376397	+	0.926459i	$0.622837\pi$
$888$	36.3640	+	5.36662i	1.22029	+	0.180092i
$889$	7.72014	−	47.9251i	0.258925	−	1.60736i
$890$			11.6933i			0.391961i
$891$	26.8132	+	25.5166i	0.898278	+	0.854839i
$892$	−5.28455	+	3.05104i	−0.176940	+	0.102156i
$893$	−4.80931	−	0.848012i	−0.160938	−	0.0283776i
$894$	9.67028	+	7.66324i	0.323423	+	0.256297i
$895$	−15.2925	+	2.69647i	−0.511170	+	0.0901331i
$896$	−9.00099	+	25.9186i	−0.300702	+	0.865881i
$897$	35.8203	−	31.8082i	1.19601	−	1.06204i
$898$	7.03859	+	5.90608i	0.234881	+	0.197088i
$899$	2.59168			0.0864374
$900$	−50.7752	−	15.3206i	−1.69251	−	0.510686i
$901$		−	2.22994i		−	0.0742900i
$902$	−2.12560	+	0.773655i	−0.0707747	+	0.0257599i
$903$	20.4415	−	39.1906i	0.680250	−	1.30418i
$904$	30.3703	−	25.4837i	1.01010	−	0.847575i
$905$	−9.51629	+	1.67798i	−0.316332	+	0.0557779i
$906$	0.337266	+	12.0378i	0.0112049	+	0.399930i
$907$	−18.7127	−	15.7018i	−0.621344	−	0.521370i	0.276881	−	0.960904i	$-0.410699\pi$
$907$	−18.7127	−	15.7018i	−0.621344	−	0.521370i	−0.898226	+	0.439534i	$0.855144\pi$
$908$	−89.8181			−2.98072
$909$	−14.8418	+	29.3941i	−0.492270	+	0.974939i
$910$	−16.5348	−	27.6836i	−0.548124	−	0.917702i
$911$	−8.92434	−	1.57360i	−0.295676	−	0.0521357i	0.0238421	−	0.999716i	$-0.492410\pi$
$911$	−8.92434	−	1.57360i	−0.295676	−	0.0521357i	−0.319519	+	0.947580i	$0.603521\pi$
$912$	47.5426	+	53.5394i	1.57429	+	1.77287i
$913$	41.6234	−	7.33933i	1.37753	−	0.242896i
$914$	−0.741392	−	0.883557i	−0.0245231	−	0.0292255i
$915$	1.35675	+	3.42592i	0.0448529	+	0.113257i
$916$	−2.41784	+	2.88146i	−0.0798875	+	0.0952062i
$917$	32.8186	−	0.486319i	1.08377	−	0.0160597i
$918$	−26.6455	+	37.7928i	−0.879434	+	1.24735i
$919$	10.1125	−	17.5154i	0.333582	−	0.577781i	−0.649629	−	0.760251i	$-0.725076\pi$
$919$	10.1125	−	17.5154i	0.333582	−	0.577781i	0.983211	+	0.182470i	$0.0584092\pi$
$920$	7.13350	−	40.4561i	0.235185	−	1.33380i
$921$	−25.0612	+	31.6249i	−0.825796	+	1.04208i
$922$	−20.9775	+	57.6353i	−0.690858	+	1.89812i
$923$	46.8742	+	17.0608i	1.54288	+	0.561563i
$924$	−57.6135	−	62.9760i	−1.89535	−	2.07176i
$925$	−2.22628	+	12.6259i	−0.0731997	+	0.415136i
$926$	53.0909	−	30.6521i	1.74468	−	1.00729i
$927$	33.2602	+	3.96034i	1.09241	+	0.130075i
$928$	−7.48121	+	12.9578i	−0.245583	+	0.425362i
$929$	9.34095	−	52.9752i	0.306467	−	1.73806i	−0.310053	−	0.950719i	$-0.600347\pi$
$929$	9.34095	−	52.9752i	0.306467	−	1.73806i	0.616520	−	0.787339i	$-0.288542\pi$
$930$	2.57436	+	4.18377i	0.0844166	+	0.137191i
$931$	12.1929	−	36.8634i	0.399605	−	1.20815i
$932$	−11.5273	−	13.7377i	−0.377590	−	0.449994i
$933$	−16.5599	+	0.463961i	−0.542147	+	0.0151894i
$934$	65.0836	−	77.5636i	2.12960	−	2.53796i
$935$	12.9890	+	7.49921i	0.424786	+	0.245250i
$936$	−70.7165	−	52.8840i	−2.31144	−	1.72857i
$937$	−15.9506	−	9.20909i	−0.521084	−	0.300848i	0.216294	−	0.976328i	$-0.430603\pi$
$937$	−15.9506	−	9.20909i	−0.521084	−	0.300848i	−0.737378	+	0.675480i	$0.763936\pi$
$938$	−27.1702	−	71.3424i	−0.887139	−	2.32941i
$939$	−11.3434	+	2.32946i	−0.370177	+	0.0760191i
$940$	3.19831	−	2.68370i	0.104318	−	0.0875328i
$941$	1.53310	−	1.28643i	0.0499778	−	0.0419363i	−0.617457	−	0.786605i	$-0.711837\pi$
$941$	1.53310	−	1.28643i	0.0499778	−	0.0419363i	0.667434	+	0.744669i	$0.267392\pi$
$942$	−53.4939	−	42.3914i	−1.74293	−	1.38119i
$943$	0.446997	+	1.22812i	0.0145562	+	0.0399929i
$944$	−79.5174			−2.58807
$945$	−8.39277	−	11.6955i	−0.273017	−	0.380454i
$946$	−101.361			−3.29552
$947$	−9.63302	−	26.4665i	−0.313031	−	0.860046i	−0.992041	−	0.125916i	$-0.959813\pi$
$947$	−9.63302	−	26.4665i	−0.313031	−	0.860046i	0.679010	−	0.734129i	$-0.262409\pi$
$948$	6.20591	−	42.0509i	0.201559	−	1.36575i
$949$	−40.1085	+	33.6550i	−1.30198	+	1.09249i
$950$	−42.3816	+	35.5623i	−1.37504	+	1.15379i
$951$	1.36232	−	4.09644i	0.0441763	−	0.132836i
$952$	37.5928	−	46.1739i	1.21839	−	1.49650i
$953$	39.6503	+	22.8921i	1.28440	+	0.741548i	0.977649	−	0.210242i	$-0.0674253\pi$
$953$	39.6503	+	22.8921i	1.28440	+	0.741548i	0.306749	+	0.951790i	$0.400759\pi$
$954$	4.90026	−	0.274798i	0.158652	−	0.00889692i
$955$	18.6980	+	10.7953i	0.605054	+	0.349328i
$956$	−68.0292	+	81.0740i	−2.20022	+	2.62212i
$957$	9.12692	+	14.8328i	0.295031	+	0.479476i
$958$	−19.7473	−	23.5340i	−0.638008	−	0.760348i
$959$	8.35782	−	1.60174i	0.269888	−	0.0517230i
$960$	−1.32645	+	0.0371633i	−0.0428109	+	0.00119944i
$961$	5.18797	−	29.4224i	0.167354	−	0.949110i
$962$	−19.1140	+	33.1064i	−0.616259	+	1.06739i
$963$	−3.85476	+	0.904814i	−0.124218	+	0.0291572i
$964$	−16.0864	+	9.28751i	−0.518109	+	0.299130i
$965$	−1.46038	+	8.28220i	−0.0470112	+	0.266614i
$966$	−52.4543	+	47.9878i	−1.68769	+	1.54398i
$967$	−28.8765	−	10.5102i	−0.928605	−	0.337985i	−0.166949	−	0.985966i	$-0.553391\pi$
$967$	−28.8765	−	10.5102i	−0.928605	−	0.337985i	−0.761657	+	0.647981i	$0.775614\pi$
$968$	−13.0704	+	35.9106i	−0.420098	+	1.15421i
$969$	12.3203	+	31.1098i	0.395785	+	0.999392i
$970$	4.80815	−	27.2684i	0.154380	−	0.875535i
$971$	16.2356	−	28.1209i	0.521026	−	0.902444i	−0.478675	−	0.877992i	$-0.658883\pi$
$971$	16.2356	−	28.1209i	0.521026	−	0.902444i	0.999701	−	0.0244515i	$-0.00778393\pi$
$972$	−59.8862	−	37.3858i	−1.92085	−	1.19915i
$973$	−16.1694	+	9.65761i	−0.518366	+	0.309609i
$974$	−65.5601	+	78.1315i	−2.10068	+	2.50349i
$975$	19.1288	−	24.1387i	0.612612	−	0.773058i
$976$	−9.73312	−	11.5995i	−0.311549	−	0.371290i
$977$	−5.12538	+	0.903742i	−0.163975	+	0.0289133i	−0.255033	−	0.966932i	$-0.582086\pi$
$977$	−5.12538	+	0.903742i	−0.163975	+	0.0289133i	0.0910577	+	0.995846i	$0.470975\pi$
$978$	0.420942	−	0.0864441i	0.0134602	−	0.00276418i
$979$	−17.7014	−	3.12123i	−0.565739	−	0.0997550i
$980$	17.4421	+	28.2434i	0.557167	+	0.902203i
$981$	−39.5518	−	11.9341i	−1.26279	−	0.381026i
$982$	48.4855			1.54723
$983$	−25.3404	−	21.2631i	−0.808232	−	0.678187i	0.141953	−	0.989873i	$-0.454662\pi$
$983$	−25.3404	−	21.2631i	−0.808232	−	0.678187i	−0.950185	+	0.311686i	$0.899106\pi$
$984$	2.05179	−	1.26251i	0.0654086	−	0.0402473i
$985$	22.5973	−	3.98452i	0.720010	−	0.126957i
$986$	−16.6672	+	13.9855i	−0.530792	+	0.445388i
$987$	−4.03090	+	0.172737i	−0.128305	+	0.00549829i
$988$	−107.530	+	39.1378i	−3.42099	+	1.24514i
$989$			58.5635i			1.86221i
$990$	−14.8788	+	29.4673i	−0.472878	+	0.936533i
$991$	20.1146			0.638961			0.319480	−	0.947593i	$-0.396492\pi$
$991$	20.1146			0.638961			0.319480	+	0.947593i	$0.396492\pi$
$992$	−4.96958	−	4.16997i	−0.157784	−	0.132397i
$993$	50.3775	+	16.7536i	1.59868	+	0.531661i
$994$	−69.9317	−	24.2858i	−2.21810	−	0.770299i
$995$	−17.7270	+	3.12575i	−0.561985	+	0.0990931i
$996$	−74.9504	+	29.6823i	−2.37489	+	0.940519i
$997$	−13.0420	−	2.29965i	−0.413043	−	0.0728307i	−0.0367347	−	0.999325i	$-0.511696\pi$
$997$	−13.0420	−	2.29965i	−0.413043	−	0.0728307i	−0.376309	+	0.926494i	$0.622807\pi$
$998$	34.1276	−	19.7036i	1.08029	−	0.623705i
$999$	−7.26238	+	15.4435i	−0.229772	+	0.488611i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	189.2.bd.a.173.22	yes	132
3.2	odd	2		567.2.bd.a.278.1		132
7.3	odd	6		189.2.ba.a.38.1	yes	132
21.17	even	6		567.2.ba.a.521.22		132
27.5	odd	18		189.2.ba.a.5.1	✓	132
27.22	even	9		567.2.ba.a.530.22		132
189.59	even	18	inner	189.2.bd.a.59.22	yes	132
189.157	odd	18		567.2.bd.a.206.1		132

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
189.2.ba.a.5.1	✓	132	27.5	odd	18
189.2.ba.a.38.1	yes	132	7.3	odd	6
189.2.bd.a.59.22	yes	132	189.59	even	18	inner
189.2.bd.a.173.22	yes	132	1.1	even	1	trivial
567.2.ba.a.521.22		132	21.17	even	6
567.2.ba.a.530.22		132	27.22	even	9
567.2.bd.a.206.1		132	189.157	odd	18
567.2.bd.a.278.1		132	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 189 = 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	189.bd (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(0.873917 + 2.40107i) q^{2} +(-1.61037 + 0.637747i) q^{3} +(-3.46930 + 2.91109i) q^{4} +(0.802125 - 0.673063i) q^{5} +(-2.93860 - 3.30926i) q^{6} +(-2.47251 + 0.941638i) q^{7} +(-5.59594 - 3.23082i) q^{8} +(2.18656 - 2.05401i) q^{9} +O(q^{10})\)	\(q+(0.873917 + 2.40107i) q^{2} +(-1.61037 + 0.637747i) q^{3} +(-3.46930 + 2.91109i) q^{4} +(0.802125 - 0.673063i) q^{5} +(-2.93860 - 3.30926i) q^{6} +(-2.47251 + 0.941638i) q^{7} +(-5.59594 - 3.23082i) q^{8} +(2.18656 - 2.05401i) q^{9} +(2.31706 + 1.33776i) q^{10} +(-2.64358 + 3.15050i) q^{11} +(3.73031 - 6.90046i) q^{12} +(2.92808 + 3.48955i) q^{13} +(-4.42171 - 5.11375i) q^{14} +(-0.862472 + 1.59543i) q^{15} +(1.29417 - 7.33959i) q^{16} +(1.74141 - 3.01622i) q^{17} +(6.84269 + 3.45504i) q^{18} +(4.80366 - 2.77339i) q^{19} +(-0.823468 + 4.67012i) q^{20} +(3.38112 - 3.09322i) q^{21} +(-9.87483 - 3.59414i) q^{22} +(-2.07660 + 5.70542i) q^{23} +(11.0720 + 1.63401i) q^{24} +(-0.677850 + 3.84428i) q^{25} +(-5.81974 + 10.0801i) q^{26} +(-2.21122 + 4.70218i) q^{27} +(5.83670 - 10.4645i) q^{28} +(-1.57154 + 1.87289i) q^{29} +(-4.58447 - 0.676579i) q^{30} +(-0.681381 - 0.812039i) q^{31} +(6.02691 - 1.06271i) q^{32} +(2.24792 - 6.75939i) q^{33} +(8.76399 + 1.54533i) q^{34} +(-1.34948 + 2.41947i) q^{35} +(-1.60642 + 13.4913i) q^{36} +3.28433 q^{37} +(10.8571 + 9.11019i) q^{38} +(-6.94073 - 3.75208i) q^{39} +(-6.66319 + 1.17490i) q^{40} +(0.164894 - 0.138363i) q^{41} +(10.3818 + 5.41509i) q^{42} +(9.06382 - 3.29896i) q^{43} -18.6257i q^{44} +(0.371415 - 3.11927i) q^{45} -15.5139 q^{46} +(-0.674442 - 0.565924i) q^{47} +(2.59671 + 12.6448i) q^{48} +(5.22663 - 4.65642i) q^{49} +(-9.82275 + 1.73202i) q^{50} +(-0.880732 + 5.96779i) q^{51} +(-20.3168 - 3.58240i) q^{52} +(0.554487 - 0.320133i) q^{53} +(-13.2227 - 1.19998i) q^{54} +4.30639i q^{55} +(16.8783 + 2.71888i) q^{56} +(-5.96692 + 7.52969i) q^{57} +(-5.87034 - 2.13663i) q^{58} +(-1.85273 - 10.5073i) q^{59} +(-1.65227 - 8.04577i) q^{60} +(1.30597 - 1.55639i) q^{61} +(1.35429 - 2.34570i) q^{62} +(-3.47216 + 7.13752i) q^{63} +(0.365832 + 0.633640i) q^{64} +(4.69737 + 0.828274i) q^{65} +(18.1942 - 0.509751i) q^{66} +(10.6115 + 3.86227i) q^{67} +(2.73899 + 15.5336i) q^{68} +(-0.294521 - 10.5122i) q^{69} +(-6.98864 - 1.12578i) q^{70} +(9.48338 - 5.47523i) q^{71} +(-18.8720 + 4.42975i) q^{72} +11.4939i q^{73} +(2.87023 + 7.88590i) q^{74} +(-1.36009 - 6.62299i) q^{75} +(-8.59174 + 23.6056i) q^{76} +(3.56966 - 10.2789i) q^{77} +(2.94337 - 19.9442i) q^{78} +(5.09203 - 1.85335i) q^{79} +(-3.90192 - 6.75833i) q^{80} +(0.562076 - 8.98243i) q^{81} +(0.476322 + 0.275005i) q^{82} +(-7.87254 - 6.60584i) q^{83} +(-2.72550 + 20.5741i) q^{84} +(-0.633272 - 3.59147i) q^{85} +(15.8420 + 18.8798i) q^{86} +(1.33633 - 4.01829i) q^{87} +(24.9720 - 9.08907i) q^{88} +(2.18525 + 3.78496i) q^{89} +(7.81415 - 1.83419i) q^{90} +(-10.5256 - 5.87076i) q^{91} +(-9.40464 - 25.8390i) q^{92} +(1.61515 + 0.873131i) q^{93} +(0.769415 - 2.11395i) q^{94} +(1.98647 - 5.45777i) q^{95} +(-9.02779 + 5.55499i) q^{96} +(-3.53959 - 9.72494i) q^{97} +(15.7480 + 8.48017i) q^{98} +(0.690812 + 12.3187i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 132 q - 3 q^{2} - 9 q^{3} - 3 q^{4} - 9 q^{5} + 18 q^{6} - 6 q^{7} - 18 q^{8} - 15 q^{9}+O(q^{10}) \) 132 * q - 3 * q^2 - 9 * q^3 - 3 * q^4 - 9 * q^5 + 18 * q^6 - 6 * q^7 - 18 * q^8 - 15 * q^9	\( 132 q - 3 q^{2} - 9 q^{3} - 3 q^{4} - 9 q^{5} + 18 q^{6} - 6 q^{7} - 18 q^{8} - 15 q^{9} - 9 q^{10} + 9 q^{11} - 9 q^{12} - 42 q^{14} - 24 q^{15} - 15 q^{16} - 9 q^{17} - 3 q^{18} - 9 q^{19} - 18 q^{20} + 15 q^{21} - 12 q^{22} + 30 q^{23} - 36 q^{24} - 3 q^{25} - 12 q^{28} + 6 q^{29} - 3 q^{30} - 9 q^{31} - 51 q^{32} - 9 q^{33} + 18 q^{34} - 9 q^{35} - 6 q^{37} - 9 q^{38} - 9 q^{39} - 9 q^{40} + 27 q^{42} - 12 q^{43} - 63 q^{45} - 6 q^{46} + 45 q^{47} + 30 q^{49} - 9 q^{50} + 33 q^{51} - 9 q^{52} + 45 q^{53} + 117 q^{54} - 51 q^{56} - 3 q^{58} - 9 q^{59} - 15 q^{60} - 63 q^{61} + 99 q^{62} - 33 q^{63} + 18 q^{64} - 102 q^{65} + 63 q^{66} - 3 q^{67} + 144 q^{68} - 108 q^{69} - 15 q^{70} + 18 q^{71} + 15 q^{72} - 33 q^{74} - 9 q^{75} - 36 q^{76} - 57 q^{77} + 66 q^{78} - 21 q^{79} - 72 q^{80} + 57 q^{81} - 18 q^{82} + 90 q^{83} + 51 q^{84} + 9 q^{85} - 33 q^{86} - 9 q^{87} + 45 q^{88} - 9 q^{89} - 81 q^{90} - 21 q^{91} + 150 q^{92} - 87 q^{93} - 9 q^{94} + 27 q^{95} - 9 q^{96} - 180 q^{98} + 96 q^{99}+O(q^{100}) \) 132 * q - 3 * q^2 - 9 * q^3 - 3 * q^4 - 9 * q^5 + 18 * q^6 - 6 * q^7 - 18 * q^8 - 15 * q^9 - 9 * q^10 + 9 * q^11 - 9 * q^12 - 42 * q^14 - 24 * q^15 - 15 * q^16 - 9 * q^17 - 3 * q^18 - 9 * q^19 - 18 * q^20 + 15 * q^21 - 12 * q^22 + 30 * q^23 - 36 * q^24 - 3 * q^25 - 12 * q^28 + 6 * q^29 - 3 * q^30 - 9 * q^31 - 51 * q^32 - 9 * q^33 + 18 * q^34 - 9 * q^35 - 6 * q^37 - 9 * q^38 - 9 * q^39 - 9 * q^40 + 27 * q^42 - 12 * q^43 - 63 * q^45 - 6 * q^46 + 45 * q^47 + 30 * q^49 - 9 * q^50 + 33 * q^51 - 9 * q^52 + 45 * q^53 + 117 * q^54 - 51 * q^56 - 3 * q^58 - 9 * q^59 - 15 * q^60 - 63 * q^61 + 99 * q^62 - 33 * q^63 + 18 * q^64 - 102 * q^65 + 63 * q^66 - 3 * q^67 + 144 * q^68 - 108 * q^69 - 15 * q^70 + 18 * q^71 + 15 * q^72 - 33 * q^74 - 9 * q^75 - 36 * q^76 - 57 * q^77 + 66 * q^78 - 21 * q^79 - 72 * q^80 + 57 * q^81 - 18 * q^82 + 90 * q^83 + 51 * q^84 + 9 * q^85 - 33 * q^86 - 9 * q^87 + 45 * q^88 - 9 * q^89 - 81 * q^90 - 21 * q^91 + 150 * q^92 - 87 * q^93 - 9 * q^94 + 27 * q^95 - 9 * q^96 - 180 * q^98 + 96 * q^99

Introduction

L-functions

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